LMFDB - Embedded newform 62.8.g.b.7.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(7,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,144] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	62.7
Dual form			62.8.g.b.9.3

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.47214 - 7.60845i) q^{2} +(-34.2192 + 7.27353i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(141.827 - 245.651i) q^{5} +(139.935 + 242.374i) q^{6} +(360.576 + 160.539i) q^{7} +(414.217 + 300.946i) q^{8} +(-879.871 + 391.744i) q^{9} +(-2219.64 - 471.799i) q^{10} +(746.464 + 7102.13i) q^{11} +(1498.16 - 1663.87i) q^{12} +(2944.45 + 3270.14i) q^{13} +(330.059 - 3140.30i) q^{14} +(-3066.45 + 9437.57i) q^{15} +(1265.73 - 3895.53i) q^{16} +(3036.67 - 28892.0i) q^{17} +(5155.73 + 5726.01i) q^{18} +(30867.2 - 34281.5i) q^{19} +(1897.59 + 18054.4i) q^{20} +(-13506.3 - 2870.86i) q^{21} +(52190.8 - 23236.9i) q^{22} +(7550.37 + 5485.66i) q^{23} +(-16363.1 - 7285.33i) q^{24} +(-1167.11 - 2021.50i) q^{25} +(17601.6 - 30486.9i) q^{26} +(89156.6 - 64776.0i) q^{27} +(-24708.8 + 5252.01i) q^{28} +(-76473.5 - 235361. i) q^{29} +79386.0 q^{30} +(-137850. + 92249.9i) q^{31} -32768.0 q^{32} +(-77200.9 - 237600. i) q^{33} +(-227330. + 48320.6i) q^{34} +(90575.8 - 65807.2i) q^{35} +(30820.5 - 53382.6i) q^{36} +(74583.0 + 129181. i) q^{37} +(-337137. - 150103. i) q^{38} +(-124542. - 90485.1i) q^{39} +(132675. - 59070.6i) q^{40} +(710337. + 150987. i) q^{41} +(11546.7 + 109859. i) q^{42} +(590213. - 655498. i) q^{43} +(-305819. - 339647. i) q^{44} +(-28556.9 + 271701. i) q^{45} +(23071.9 - 71007.9i) q^{46} +(2581.56 - 7945.22i) q^{47} +(-14978.2 + 142508. i) q^{48} +(-446815. - 496239. i) q^{49} +(-12495.2 + 13877.3i) q^{50} +(106234. + 1.01075e6i) q^{51} +(-275472. - 58553.3i) q^{52} +(943954. - 420275. i) q^{53} +(-713253. - 518208. i) q^{54} +(1.85051e6 + 823902. i) q^{55} +(101043. + 175012. i) q^{56} +(-806905. + 1.39760e6i) q^{57} +(-1.60168e6 + 1.16369e6i) q^{58} +(1.97409e6 - 419606. i) q^{59} +(-196253. - 604005. i) q^{60} -2.98026e6 q^{61} +(1.04266e6 + 820770. i) q^{62} -380151. q^{63} +(81007.0 + 249314. i) q^{64} +(1.22091e6 - 259513. i) q^{65} +(-1.61692e6 + 1.17476e6i) q^{66} +(-231103. + 400282. i) q^{67} +(929636. + 1.61018e6i) q^{68} +(-298268. - 132797. i) q^{69} +(-724606. - 526457. i) q^{70} +(2.36560e6 - 1.05323e6i) q^{71} +(-482351. - 102527. i) q^{72} +(495953. + 4.71868e6i) q^{73} +(798492. - 886815. i) q^{74} +(54641.1 + 60685.1i) q^{75} +(-308604. + 2.93617e6i) q^{76} +(-871010. + 2.68069e6i) q^{77} +(-380567. + 1.17126e6i) q^{78} +(35589.9 - 338615. i) q^{79} +(-777425. - 863418. i) q^{80} +(-1.17027e6 + 1.29972e6i) q^{81} +(-607274. - 5.77782e6i) q^{82} +(-2.80589e6 - 596411. i) q^{83} +(807315. - 359440. i) q^{84} +(-6.66667e6 - 4.84362e6i) q^{85} +(-6.44641e6 - 2.87013e6i) q^{86} +(4.32877e6 + 7.49765e6i) q^{87} +(-1.82816e6 + 3.16647e6i) q^{88} +(-2.36090e6 + 1.71530e6i) q^{89} +(2.13782e6 - 454408. i) q^{90} +(536712. + 1.65183e6i) q^{91} -597297. q^{92} +(4.04614e6 - 4.15938e6i) q^{93} -66832.8 q^{94} +(-4.04349e6 - 1.24446e7i) q^{95} +(1.12130e6 - 238339. i) q^{96} +(9.62154e6 - 6.99046e6i) q^{97} +(-2.67102e6 + 4.62634e6i) q^{98} +(-3.43901e6 - 5.95654e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) $ 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.47214	−	7.60845i	−0.218508	−	0.672499i
$2$	−2.47214	−	7.60845i	−0.218508	−	0.672499i
$3$	−34.2192	+	7.27353i	−0.731722	+	0.155532i	−0.558681	−	0.829382i	$-0.688693\pi$
$3$	−34.2192	+	7.27353i	−0.731722	+	0.155532i	−0.173041	+	0.984915i	$0.555359\pi$
$4$	−51.7771	+	37.6183i	−0.404508	+	0.293893i
$5$	141.827	−	245.651i	0.507415	−	0.878868i	−0.492549	−	0.870285i	$-0.663935\pi$
$5$	141.827	−	245.651i	0.507415	−	0.878868i	0.999963	−	0.00858284i	$-0.00273204\pi$
$6$	139.935	+	242.374i	0.264482	+	0.458097i
$7$	360.576	+	160.539i	0.397332	+	0.176904i	0.595669	−	0.803230i	$-0.296887\pi$
$7$	360.576	+	160.539i	0.397332	+	0.176904i	−0.198336	+	0.980134i	$0.563554\pi$
$8$	414.217	+	300.946i	0.286031	+	0.207813i
$9$	−879.871	+	391.744i	−0.402319	+	0.179124i
$10$	−2219.64	−	471.799i	−0.701911	−	0.149196i
$11$	746.464	+	7102.13i	0.169096	+	1.60884i	0.669337	+	0.742959i	$0.266578\pi$
$11$	746.464	+	7102.13i	0.169096	+	1.60884i	−0.500241	+	0.865886i	$0.666755\pi$
$12$	1498.16	−	1663.87i	0.250278	−	0.277962i
$13$	2944.45	+	3270.14i	0.371708	+	0.412823i	0.899758	−	0.436390i	$-0.143743\pi$
$13$	2944.45	+	3270.14i	0.371708	+	0.412823i	−0.528050	+	0.849213i	$0.677077\pi$
$14$	330.059	−	3140.30i	0.0321472	−	0.305860i
$15$	−3066.45	+	9437.57i	−0.234594	+	0.722006i
$16$	1265.73	−	3895.53i	0.0772542	−	0.237764i
$17$	3036.67	−	28892.0i	0.149909	−	1.42628i	−0.618228	−	0.785999i	$-0.712149\pi$
$17$	3036.67	−	28892.0i	0.149909	−	1.42628i	0.768137	−	0.640286i	$-0.221184\pi$
$18$	5155.73	+	5726.01i	0.208370	+	0.231419i
$19$	30867.2	−	34281.5i	1.03243	−	1.14663i	0.0433758	−	0.999059i	$-0.486189\pi$
$19$	30867.2	−	34281.5i	1.03243	−	1.14663i	0.989052	−	0.147568i	$-0.0471446\pi$
$20$	1897.59	+	18054.4i	0.0530393	+	0.504635i
$21$	−13506.3	−	2870.86i	−0.318251	−	0.0676463i
$22$	52190.8	−	23236.9i	1.04500	−	0.465263i
$23$	7550.37	+	5485.66i	0.129396	+	0.0940117i	0.650601	−	0.759420i	$-0.274517\pi$
$23$	7550.37	+	5485.66i	0.129396	+	0.0940117i	−0.521205	+	0.853432i	$0.674517\pi$
$24$	−16363.1	−	7285.33i	−0.241617	−	0.107575i
$25$	−1167.11	−	2021.50i	−0.0149390	−	0.0258752i
$26$	17601.6	−	30486.9i	0.196402	−	0.340178i
$27$	89156.6	−	64776.0i	0.871726	−	0.633346i
$28$	−24708.8	+	5252.01i	−0.212715	+	0.0452139i
$29$	−76473.5	−	235361.i	−0.582262	−	1.79202i	−0.610000	−	0.792401i	$-0.708831\pi$
$29$	−76473.5	−	235361.i	−0.582262	−	1.79202i	0.0277384	−	0.999615i	$-0.491169\pi$
$30$	79386.0			0.536809
$31$	−137850.	+	92249.9i	−0.831075	+	0.556160i
$31$	−137850.	+	92249.9i	−0.831075	+	0.556160i
$32$	−32768.0			−0.176777
$33$	−77200.9	−	237600.i	−0.373959	−	1.15093i
$34$	−227330.	+	48320.6i	−0.991931	+	0.210841i
$35$	90575.8	−	65807.2i	0.357087	−	0.259439i
$36$	30820.5	−	53382.6i	0.110098	−	0.190696i
$37$	74583.0	+	129181.i	0.242066	+	0.419270i	0.961303	−	0.275495i	$-0.0888416\pi$
$37$	74583.0	+	129181.i	0.242066	+	0.419270i	−0.719237	+	0.694765i	$0.755508\pi$
$38$	−337137.	−	150103.i	−0.996699	−	0.443759i
$39$	−124542.	−	90485.1i	−0.336194	−	0.244259i
$40$	132675.	−	59070.6i	0.327777	−	0.145936i
$41$	710337.	+	150987.i	1.60961	+	0.342133i	0.922972	−	0.384866i	$-0.125752\pi$
$41$	710337.	+	150987.i	1.60961	+	0.342133i	0.686638	+	0.726999i	$0.259086\pi$
$42$	11546.7	+	109859.i	0.0240483	+	0.228804i
$43$	590213.	−	655498.i	1.13206	−	1.25728i	0.169701	−	0.985496i	$-0.445720\pi$
$43$	590213.	−	655498.i	1.13206	−	1.25728i	0.962358	−	0.271784i	$-0.0876135\pi$
$44$	−305819.	−	339647.i	−0.541229	−	0.601095i
$45$	−28556.9	+	271701.i	−0.0467162	+	0.444475i
$46$	23071.9	−	71007.9i	0.0349487	−	0.107561i
$47$	2581.56	−	7945.22i	0.00362693	−	0.0111625i	−0.949227	−	0.314593i	$-0.898132\pi$
$47$	2581.56	−	7945.22i	0.00362693	−	0.0111625i	0.952854	+	0.303430i	$0.0981320\pi$
$48$	−14978.2	+	142508.i	−0.0195486	+	0.185993i
$49$	−446815.	−	496239.i	−0.542553	−	0.602566i
$50$	−12495.2	+	13877.3i	−0.0141367	+	0.0157004i
$51$	106234.	+	1.01075e6i	0.112142	+	1.06696i
$52$	−275472.	−	58553.3i	−0.271685	−	0.0577484i
$53$	943954.	−	420275.i	0.870934	−	0.387765i	0.0779138	−	0.996960i	$-0.475174\pi$
$53$	943954.	−	420275.i	0.870934	−	0.387765i	0.793020	+	0.609195i	$0.208507\pi$
$54$	−713253.	−	518208.i	−0.616404	−	0.447843i
$55$	1.85051e6	+	823902.i	1.49976	+	0.667738i
$56$	101043.	+	175012.i	0.0768862	+	0.133171i
$57$	−806905.	+	1.39760e6i	−0.577112	+	0.999588i
$58$	−1.60168e6	+	1.16369e6i	−1.07790	+	0.783140i
$59$	1.97409e6	−	419606.i	1.25137	−	0.265986i	0.465871	−	0.884853i	$-0.345741\pi$
$59$	1.97409e6	−	419606.i	1.25137	−	0.265986i	0.785496	+	0.618867i	$0.212408\pi$
$60$	−196253.	−	604005.i	−0.117297	−	0.361003i
$61$	−2.98026e6			−1.68113			−0.840563	−	0.541715i	$-0.817775\pi$
$61$	−2.98026e6			−1.68113			−0.840563	+	0.541715i	$0.817775\pi$
$62$	1.04266e6	+	820770.i	0.555613	+	0.437371i
$63$	−380151.			−0.191542
$64$	81007.0	+	249314.i	0.0386271	+	0.118882i
$65$	1.22091e6	−	259513.i	0.551427	−	0.117209i
$66$	−1.61692e6	+	1.17476e6i	−0.692284	+	0.502974i
$67$	−231103.	+	400282.i	−0.0938736	+	0.162594i	−0.909138	−	0.416495i	$-0.863258\pi$
$67$	−231103.	+	400282.i	−0.0938736	+	0.162594i	0.815264	+	0.579089i	$0.196592\pi$
$68$	929636.	+	1.61018e6i	0.358535	+	0.621001i
$69$	−298268.	−	132797.i	−0.109304	−	0.0486651i
$70$	−724606.	−	526457.i	−0.252499	−	0.183451i
$71$	2.36560e6	−	1.05323e6i	0.784400	−	0.349237i	0.0248538	−	0.999691i	$-0.492088\pi$
$71$	2.36560e6	−	1.05323e6i	0.784400	−	0.349237i	0.759546	+	0.650454i	$0.225421\pi$
$72$	−482351.	−	102527.i	−0.152300	−	0.0323723i
$73$	495953.	+	4.71868e6i	0.149214	+	1.41968i	0.771171	+	0.636628i	$0.219671\pi$
$73$	495953.	+	4.71868e6i	0.149214	+	1.41968i	−0.621957	+	0.783052i	$0.713662\pi$
$74$	798492.	−	886815.i	0.229065	−	0.254403i
$75$	54641.1	+	60685.1i	0.0149556	+	0.0166099i
$76$	−308604.	+	2.93617e6i	−0.0806405	+	0.767243i
$77$	−871010.	+	2.68069e6i	−0.217423	+	0.669159i
$78$	−380567.	+	1.17126e6i	−0.0908029	+	0.279463i
$79$	35589.9	−	338615.i	0.00812142	−	0.0772702i	−0.989710	−	0.143085i	$-0.954298\pi$
$79$	35589.9	−	338615.i	0.00812142	−	0.0772702i	0.997832	+	0.0658145i	$0.0209646\pi$
$80$	−777425.	−	863418.i	−0.169763	−	0.188541i
$81$	−1.17027e6	+	1.29972e6i	−0.244675	+	0.271739i
$82$	−607274.	−	5.77782e6i	−0.121629	−	1.15722i
$83$	−2.80589e6	−	596411.i	−0.538639	−	0.114491i	−0.0694440	−	0.997586i	$-0.522123\pi$
$83$	−2.80589e6	−	596411.i	−0.538639	−	0.114491i	−0.469195	+	0.883095i	$0.655456\pi$
$84$	807315.	−	359440.i	0.148616	−	0.0661681i
$85$	−6.66667e6	−	4.84362e6i	−1.17745	−	0.855467i
$86$	−6.44641e6	−	2.87013e6i	−1.09288	−	0.486583i
$87$	4.32877e6	+	7.49765e6i	0.704770	+	1.22070i
$88$	−1.82816e6	+	3.16647e6i	−0.285973	+	0.495320i
$89$	−2.36090e6	+	1.71530e6i	−0.354987	+	0.257913i	−0.750958	−	0.660350i	$-0.770408\pi$
$89$	−2.36090e6	+	1.71530e6i	−0.354987	+	0.257913i	0.395971	+	0.918263i	$0.370408\pi$
$90$	2.13782e6	−	454408.i	0.309117	−	0.0657048i
$91$	536712.	+	1.65183e6i	0.0746615	+	0.229784i
$92$	−597297.			−0.0799711
$93$	4.04614e6	−	4.15938e6i	0.521615	−	0.536214i
$94$	−66832.8			−0.00829931
$95$	−4.04349e6	−	1.24446e7i	−0.483865	−	1.48918i
$96$	1.12130e6	−	238339.i	0.129351	−	0.0274945i
$97$	9.62154e6	−	6.99046e6i	1.07039	−	0.777686i	0.0944104	−	0.995533i	$-0.469903\pi$
$97$	9.62154e6	−	6.99046e6i	1.07039	−	0.777686i	0.975983	+	0.217847i	$0.0699034\pi$
$98$	−2.67102e6	+	4.62634e6i	−0.286673	+	0.496531i
$99$	−3.43901e6	−	5.95654e6i	−0.356213	−	0.616979i
$100$	136475.	+	60762.5i	0.0136475	+	0.00607625i
$101$	1.00360e7	+	7.29158e6i	0.969251	+	0.704202i	0.955281	−	0.295701i	$-0.0955531\pi$
$101$	1.00360e7	+	7.29158e6i	0.969251	+	0.704202i	0.0139699	+	0.999902i	$0.495553\pi$
$102$	7.42761e6	−	3.30699e6i	0.693025	−	0.308554i
$103$	1.97273e7	+	4.19317e6i	1.77884	+	0.378105i	0.975946	−	0.218011i	$-0.0699570\pi$
$103$	1.97273e7	+	4.19317e6i	1.77884	+	0.378105i	0.802898	+	0.596116i	$0.203290\pi$
$104$	235503.	+	2.24066e6i	0.0205296	+	0.195326i
$105$	−2.62079e6	+	2.91068e6i	−0.220937	+	0.245376i
$106$	−5.53123e6	−	6.14305e6i	−0.451077	−	0.500972i
$107$	728582.	−	6.93199e6i	0.0574957	−	0.547035i	−0.927423	−	0.374015i	$-0.877981\pi$
$107$	728582.	−	6.93199e6i	0.0574957	−	0.547035i	0.984918	−	0.173020i	$-0.0553525\pi$
$108$	−2.17951e6	+	6.70783e6i	−0.166485	+	0.512388i
$109$	1.32586e6	−	4.08058e6i	0.0980630	−	0.301807i	−0.889977	−	0.456006i	$-0.849280\pi$
$109$	1.32586e6	−	4.08058e6i	0.0980630	−	0.301807i	0.988040	+	0.154199i	$0.0492796\pi$
$110$	1.69390e6	−	1.61163e7i	0.121342	−	1.15449i
$111$	−3.49178e6	−	3.87801e6i	−0.242335	−	0.269140i
$112$	1.08178e6	−	1.20143e6i	0.0727569	−	0.0808048i
$113$	−191862.	−	1.82545e6i	−0.0125088	−	0.119013i	0.986486	−	0.163848i	$-0.0523906\pi$
$113$	−191862.	−	1.82545e6i	−0.0125088	−	0.119013i	−0.998994	+	0.0448346i	$0.985724\pi$
$114$	1.26284e7	+	2.68424e6i	0.798325	+	0.169689i
$115$	2.41840e6	−	1.07674e6i	0.148281	−	0.0660190i
$116$	1.28135e7	+	9.30952e6i	0.762190	+	0.553764i
$117$	−3.87179e6	−	1.72383e6i	−0.223492	−	0.0995049i
$118$	−8.07276e6	−	1.39824e7i	−0.452309	−	0.783422i
$119$	5.73323e6	−	9.93025e6i	0.311878	−	0.540189i
$120$	−4.11038e6	+	2.98636e6i	−0.217144	+	0.157764i
$121$	−3.08217e7	+	6.55135e6i	−1.58164	+	0.336188i
$122$	7.36761e6	+	2.26752e7i	0.367339	+	1.13055i
$123$	−2.54054e7			−1.23100
$124$	3.66718e6	−	9.96210e6i	0.172726	−	0.469218i
$125$	2.14983e7			0.984508
$126$	939784.	+	2.89236e6i	0.0418534	+	0.128812i
$127$	1.75051e6	−	372081.i	0.0758316	−	0.0161185i	−0.169840	−	0.985472i	$-0.554325\pi$
$127$	1.75051e6	−	372081.i	0.0758316	−	0.0161185i	0.245671	+	0.969353i	$0.420992\pi$
$128$	1.69663e6	−	1.23268e6i	0.0715077	−	0.0519534i
$129$	−1.54289e7	+	2.67236e7i	−0.632805	+	1.09605i
$130$	−4.99276e6	−	8.64771e6i	−0.199314	−	0.345223i
$131$	−1.88697e7	−	8.40132e6i	−0.733356	−	0.326511i	0.00585673	−	0.999983i	$-0.498136\pi$
$131$	−1.88697e7	−	8.40132e6i	−0.733356	−	0.326511i	−0.739213	+	0.673472i	$0.764802\pi$
$132$	1.29353e7	+	9.39807e6i	0.489518	+	0.355656i
$133$	1.66335e7	−	7.40570e6i	0.613059	−	0.272952i
$134$	3.61684e6	+	768784.i	0.129856	+	0.0276018i
$135$	−3.26752e6	−	3.10884e7i	−0.114301	−	1.08750i
$136$	9.95277e6	−	1.10537e7i	0.339280	−	0.376808i
$137$	−1.05957e7	−	1.17677e7i	−0.352053	−	0.390994i	0.540943	−	0.841059i	$-0.318067\pi$
$137$	−1.05957e7	−	1.17677e7i	−0.352053	−	0.390994i	−0.892996	+	0.450065i	$0.851401\pi$
$138$	−273024.	+	2.59765e6i	−0.00884350	+	0.0841403i
$139$	−3.15928e6	+	9.72326e6i	−0.0997783	+	0.307086i	−0.988469	−	0.151420i	$-0.951615\pi$
$139$	−3.15928e6	+	9.72326e6i	−0.0997783	+	0.307086i	0.888691	+	0.458506i	$0.151615\pi$
$140$	−2.21420e6	+	6.81461e6i	−0.0681975	+	0.209890i
$141$	−30549.2	+	290656.i	−0.000917768	+	0.00873198i
$142$	−1.38616e7	−	1.53948e7i	−0.406259	−	0.451196i
$143$	−2.10270e7	+	2.33529e7i	−0.601314	+	0.667827i
$144$	412367.	+	3.92341e6i	0.0115084	+	0.109495i
$145$	−6.86627e7	−	1.45947e7i	−1.87039	−	0.397564i
$146$	3.46758e7	−	1.54386e7i	0.922128	−	0.410558i
$147$	1.88991e7	+	1.37310e7i	0.490716	+	0.356526i
$148$	−8.72127e6	−	3.88296e6i	−0.221138	−	0.0984571i
$149$	1.99650e7	+	3.45803e7i	0.494443	+	0.856401i	0.999979	−	0.00640433i	$-0.00203858\pi$
$149$	1.99650e7	+	3.45803e7i	0.494443	+	0.856401i	−0.505536	+	0.862805i	$0.668705\pi$
$150$	326639.	−	565756.i	0.00790222	−	0.0136870i
$151$	5.55992e7	−	4.03952e7i	1.31416	−	0.954796i	0.314179	−	0.949364i	$-0.398271\pi$
$151$	5.55992e7	−	4.03952e7i	1.31416	−	0.954796i	0.999985	−	0.00543195i	$-0.00172905\pi$
$152$	2.31026e7	−	4.91061e6i	0.533591	−	0.113418i
$153$	8.64638e6	+	2.66108e7i	0.195171	+	0.600673i
$154$	2.25492e7			0.497517
$155$	3.11049e6	+	4.69464e7i	0.0670916	+	1.01261i
$156$	9.85232e6			0.207779
$157$	−3.57118e6	−	1.09910e7i	−0.0736483	−	0.226666i	0.907455	−	0.420148i	$-0.138022\pi$
$157$	−3.57118e6	−	1.09910e7i	−0.0736483	−	0.226666i	−0.981104	+	0.193482i	$0.938022\pi$
$158$	−2.66432e6	+	566319.i	−0.0537387	+	0.0114225i
$159$	−2.92445e7	+	2.12474e7i	−0.576972	+	0.419194i
$160$	−4.64738e6	+	8.04949e6i	−0.0896991	+	0.155363i
$161$	1.84182e6	+	3.19013e6i	0.0347822	+	0.0602445i
$162$	1.27819e7	+	5.69089e6i	0.236208	+	0.105166i
$163$	−4.36609e7	−	3.17215e7i	−0.789652	−	0.573716i	0.118208	−	0.992989i	$-0.462285\pi$
$163$	−4.36609e7	−	3.17215e7i	−0.789652	−	0.573716i	−0.907860	+	0.419273i	$0.862285\pi$
$164$	−4.24590e7	+	1.89040e7i	−0.751652	+	0.334657i
$165$	−6.93158e7	−	1.47335e7i	−1.20126	−	0.255337i
$166$	2.39878e6	+	2.28229e7i	0.0407017	+	0.387251i
$167$	−5.23764e7	+	5.81698e7i	−0.870217	+	0.966474i	−0.999685	−	0.0251096i	$-0.992007\pi$
$167$	−5.23764e7	+	5.81698e7i	−0.870217	+	0.966474i	0.129468	+	0.991584i	$0.458673\pi$
$168$	−4.73057e6	−	5.25383e6i	−0.0769717	−	0.0854857i
$169$	4.53496e6	−	4.31473e7i	0.0722720	−	0.687623i
$170$	−2.03715e7	+	6.26971e7i	−0.318018	+	0.978760i
$171$	−1.37296e7	+	4.22553e7i	−0.209977	+	0.646242i
$172$	−5.90082e6	+	5.61426e7i	−0.0884225	+	0.841284i
$173$	1.23589e7	+	1.37260e7i	0.181476	+	0.201549i	0.827018	−	0.562175i	$-0.190035\pi$
$173$	1.23589e7	+	1.37260e7i	0.181476	+	0.201549i	−0.645542	+	0.763724i	$0.723369\pi$
$174$	4.63442e7	−	5.14705e7i	0.666919	−	0.740689i
$175$	−96303.8	−	916270.i	−0.00135835	−	0.0129238i
$176$	2.86114e7	+	6.08153e6i	0.395589	+	0.0840850i
$177$	−6.44998e7	+	2.87172e7i	−0.874283	+	0.389256i
$178$	1.88872e7	+	1.37224e7i	0.251014	+	0.182372i
$179$	1.10319e8	+	4.91174e7i	1.43769	+	0.640102i	0.969849	−	0.243709i	$-0.0783640\pi$
$179$	1.10319e8	+	4.91174e7i	1.43769	+	0.640102i	0.467845	+	0.883811i	$0.345031\pi$
$180$	−8.74232e6	−	1.51421e7i	−0.111731	−	0.193524i
$181$	−6.83492e7	+	1.18384e8i	−0.856759	+	1.48395i	0.0182454	+	0.999834i	$0.494192\pi$
$181$	−6.83492e7	+	1.18384e8i	−0.856759	+	1.48395i	−0.875004	+	0.484116i	$0.839141\pi$
$182$	1.12410e7	−	8.16710e6i	0.138216	−	0.100419i
$183$	1.01982e8	−	2.16770e7i	1.23012	−	0.261469i
$184$	1.47660e6	+	4.54451e6i	0.0174743	+	0.0537804i
$185$	4.23114e7			0.491311
$186$	−4.16490e7	−	2.05023e7i	−0.474580	−	0.233618i
$187$	2.07461e8			2.32002
$188$	165220.	+	508494.i	0.00181347	+	0.00558127i
$189$	4.25468e7	−	9.04360e6i	0.458406	−	0.0974372i
$190$	−8.46880e7	+	6.15294e7i	−0.895745	+	0.650797i
$191$	1.74838e7	−	3.02828e7i	0.181559	−	0.314470i	−0.760852	−	0.648925i	$-0.775219\pi$
$191$	1.74838e7	−	3.02828e7i	0.181559	−	0.314470i	0.942412	+	0.334455i	$0.108552\pi$
$192$	−4.58539e6	−	7.94212e6i	−0.0467543	−	0.0809808i
$193$	−1.03163e8	−	4.59313e7i	−1.03294	−	0.459894i	−0.180971	−	0.983488i	$-0.557924\pi$
$193$	−1.03163e8	−	4.59313e7i	−1.03294	−	0.459894i	−0.851968	+	0.523594i	$0.824591\pi$
$194$	−7.69723e7	−	5.59236e7i	−0.756882	−	0.549907i
$195$	−3.98912e7	+	1.77607e7i	−0.385261	+	0.171529i
$196$	4.18024e7	+	8.88538e6i	0.396557	+	0.0842908i
$197$	−1.30928e6	−	1.24570e7i	−0.0122011	−	0.116086i	0.986726	−	0.162393i	$-0.0519214\pi$
$197$	−1.30928e6	−	1.24570e7i	−0.0122011	−	0.116086i	−0.998927	+	0.0463072i	$0.985255\pi$
$198$	−3.68183e7	+	4.08909e7i	−0.337082	+	0.374368i
$199$	−7.96551e7	−	8.84660e7i	−0.716520	−	0.795776i	0.269394	−	0.963030i	$-0.413177\pi$
$199$	−7.96551e7	−	8.84660e7i	−0.716520	−	0.795776i	−0.985914	+	0.167254i	$0.946510\pi$
$200$	124924.	−	1.18858e6i	0.00110418	−	0.0105056i
$201$	4.99670e6	−	1.53783e7i	0.0434008	−	0.133574i
$202$	3.06673e7	−	9.43843e7i	0.261786	−	0.805693i
$203$	1.02101e7	−	9.71426e7i	0.0856631	−	0.815030i
$204$	−4.35231e7	−	4.83373e7i	−0.358934	−	0.398636i
$205$	1.37835e8	−	1.53081e8i	1.11743	−	1.24103i
$206$	−1.68651e7	−	1.60460e8i	−0.134417	−	1.27889i
$207$	−8.79233e6	−	1.86887e6i	−0.0688982	−	0.0146448i
$208$	1.64658e7	−	7.33104e6i	0.126871	−	0.0564864i
$209$	2.66513e8	+	1.93633e8i	2.01932	+	1.46713i
$210$	2.86247e7	+	1.27445e7i	0.213291	+	0.0949634i
$211$	8.79540e6	+	1.52341e7i	0.0644565	+	0.111642i	0.896453	−	0.443139i	$-0.146135\pi$
$211$	8.79540e6	+	1.52341e7i	0.0644565	+	0.111642i	−0.831996	+	0.554781i	$0.812802\pi$
$212$	−3.30652e7	+	5.72705e7i	−0.238339	+	0.412815i
$213$	−7.32884e7	+	5.32471e7i	−0.519645	+	0.377544i
$214$	−5.45429e7	+	1.15935e7i	−0.380443	+	0.0808657i
$215$	−7.73158e7	−	2.37954e8i	−0.530559	−	1.63289i
$216$	5.64242e7			0.380958
$217$	−6.45150e7	+	1.11328e7i	−0.428600	+	0.0739601i
$218$	−3.43246e7			−0.224392
$219$	−5.12926e7	−	1.57862e8i	−0.329989	−	1.01560i
$220$	−1.26808e8	+	2.69539e7i	−0.802910	+	0.170664i
$221$	1.03422e8	−	7.51405e7i	0.644526	−	0.468275i
$222$	−2.08735e7	+	3.61540e7i	−0.128044	+	0.221779i
$223$	−3.80731e7	−	6.59446e7i	−0.229907	−	0.398210i	0.727874	−	0.685711i	$-0.240509\pi$
$223$	−3.80731e7	−	6.59446e7i	−0.229907	−	0.398210i	−0.957780	+	0.287501i	$0.907175\pi$
$224$	−1.18154e7	−	5.26053e6i	−0.0702391	−	0.0312724i
$225$	1.81882e6	+	1.32145e6i	0.0106451	+	0.00773412i
$226$	−1.34145e7	+	5.97253e6i	−0.0773029	+	0.0344175i
$227$	1.38569e8	+	2.94537e7i	0.786275	+	0.167128i	0.583517	−	0.812101i	$-0.301676\pi$
$227$	1.38569e8	+	2.94537e7i	0.786275	+	0.167128i	0.202758	+	0.979229i	$0.435009\pi$
$228$	−1.07961e7	−	1.02718e8i	−0.0603247	−	0.573951i
$229$	2.55226e7	−	2.83457e7i	0.140443	−	0.155978i	−0.668820	−	0.743425i	$-0.733200\pi$
$229$	2.55226e7	−	2.83457e7i	0.140443	−	0.155978i	0.809263	+	0.587447i	$0.199867\pi$
$230$	−1.41710e7	−	1.57384e7i	−0.0767983	−	0.0852932i
$231$	1.03072e7	−	9.80666e7i	0.0550173	−	0.523455i
$232$	3.91544e7	−	1.20505e8i	0.205861	−	0.633574i
$233$	−4.77039e7	+	1.46818e8i	−0.247063	+	0.760383i	0.748227	+	0.663443i	$0.230905\pi$
$233$	−4.77039e7	+	1.46818e8i	−0.247063	+	0.760383i	−0.995290	+	0.0969399i	$0.969095\pi$
$234$	−3.54410e6	+	3.37199e7i	−0.0180822	+	0.172040i
$235$	−1.58562e6	−	1.76101e6i	−0.00797004	−	0.00885163i
$236$	−8.64277e7	+	9.59877e7i	−0.428017	+	0.475361i
$237$	1.24507e6	+	1.18460e7i	0.00607538	+	0.0578034i
$238$	−8.97272e7	−	1.90721e7i	−0.431424	−	0.0917021i
$239$	7.23511e7	−	3.22128e7i	0.342809	−	0.152629i	−0.228109	−	0.973636i	$-0.573254\pi$
$239$	7.23511e7	−	3.22128e7i	0.342809	−	0.152629i	0.570918	+	0.821007i	$0.306587\pi$
$240$	3.28830e7	+	2.38909e7i	0.153544	+	0.111556i
$241$	−2.90965e8	−	1.29546e8i	−1.33900	−	0.596161i	−0.392765	−	0.919639i	$-0.628481\pi$
$241$	−2.90965e8	−	1.29546e8i	−1.33900	−	0.596161i	−0.946236	+	0.323478i	$0.895148\pi$
$242$	1.26041e8	+	2.18310e8i	0.571687	+	0.990191i
$243$	−8.99153e7	+	1.55738e8i	−0.401987	+	0.696261i
$244$	1.54309e8	−	1.12112e8i	0.680029	−	0.494070i
$245$	−1.85272e8	+	3.93808e7i	−0.804875	+	0.171081i
$246$	6.28056e7	+	1.93296e8i	0.268983	+	0.827846i
$247$	2.02992e8			0.857116
$248$	−8.48619e7	−	3.27392e6i	−0.353291	−	0.0136297i
$249$	1.00354e8			0.411941
$250$	−5.31467e7	−	1.63569e8i	−0.215123	−	0.662080i
$251$	3.24540e8	−	6.89831e7i	1.29542	−	0.275350i	0.491912	−	0.870645i	$-0.336298\pi$
$251$	3.24540e8	−	6.89831e7i	1.29542	−	0.275350i	0.803507	+	0.595295i	$0.202965\pi$
$252$	1.96831e7	−	1.43006e7i	0.0774803	−	0.0562927i
$253$	−3.33238e7	+	5.77185e7i	−0.129370	+	0.224075i
$254$	−7.15845e6	−	1.23988e7i	−0.0274095	−	0.0474746i
$255$	2.63358e8	+	1.17255e8i	0.994619	+	0.442833i
$256$	−1.35731e7	−	9.86140e6i	−0.0505636	−	0.0367366i
$257$	−3.00687e8	+	1.33874e8i	−1.10497	+	0.491962i	−0.876409	−	0.481568i	$-0.840067\pi$
$257$	−3.00687e8	+	1.33874e8i	−1.10497	+	0.491962i	−0.228557	+	0.973531i	$0.573401\pi$
$258$	2.41467e8	+	5.13255e7i	0.875365	+	0.186065i
$259$	6.15419e6	+	5.85532e7i	0.0220101	+	0.209412i
$260$	−5.34529e7	+	5.93655e7i	−0.188610	+	0.209473i
$261$	1.59488e8	+	1.77130e8i	0.555248	+	0.616665i
$262$	−1.72727e7	+	1.64338e8i	−0.0593341	+	0.564526i
$263$	−8.85195e7	+	2.72435e8i	−0.300050	+	0.923459i	0.681428	+	0.731885i	$0.261359\pi$
$263$	−8.85195e7	+	2.72435e8i	−0.300050	+	0.923459i	−0.981478	+	0.191574i	$0.938641\pi$
$264$	3.95269e7	−	1.21651e8i	0.132214	−	0.406914i
$265$	3.06368e7	−	2.91490e8i	0.101131	−	0.962193i
$266$	−9.74662e7	−	1.08247e8i	−0.317518	−	0.352639i
$267$	6.83120e7	−	7.58682e7i	0.219638	−	0.243933i
$268$	−3.09207e6	−	2.94191e7i	−0.00981246	−	0.0933593i
$269$	−2.74394e8	−	5.83241e7i	−0.859490	−	0.182690i	−0.242974	−	0.970033i	$-0.578123\pi$
$269$	−2.74394e8	−	5.83241e7i	−0.859490	−	0.182690i	−0.616516	+	0.787342i	$0.711456\pi$
$270$	−2.28457e8	+	1.01715e8i	−0.706367	+	0.314495i
$271$	−6.18243e7	−	4.49180e7i	−0.188698	−	0.137097i	0.489426	−	0.872045i	$-0.337206\pi$
$271$	−6.18243e7	−	4.49180e7i	−0.188698	−	0.137097i	−0.678123	+	0.734948i	$0.737206\pi$
$272$	−1.08706e8	−	4.83990e7i	−0.327538	−	0.145829i
$273$	−3.03805e7	−	5.26206e7i	−0.0903703	−	0.156526i
$274$	−6.33401e7	+	1.09708e8i	−0.186017	+	0.322190i
$275$	1.34857e7	−	9.79795e6i	0.0391030	−	0.0284100i
$276$	2.04391e7	−	4.34446e6i	0.0585166	−	0.0124381i
$277$	9.42630e7	+	2.90112e8i	0.266478	+	0.820136i	0.991349	+	0.131251i	$0.0418995\pi$
$277$	9.42630e7	+	2.90112e8i	0.266478	+	0.820136i	−0.724871	+	0.688885i	$0.758101\pi$
$278$	8.17891e7			0.228317
$279$	8.51518e7	−	1.35170e8i	0.234736	−	0.372619i
$280$	5.73224e7			0.156053
$281$	−3.24225e7	−	9.97863e7i	−0.0871715	−	0.268286i	0.897963	−	0.440071i	$-0.145047\pi$
$281$	−3.24225e7	−	9.97863e7i	−0.0871715	−	0.268286i	−0.985135	+	0.171785i	$0.945047\pi$
$282$	2.28697e6	−	486110.i	0.00607278	−	0.00129081i
$283$	1.33540e8	−	9.70223e7i	0.350234	−	0.254460i	−0.398733	−	0.917067i	$-0.630550\pi$
$283$	1.33540e8	−	9.70223e7i	0.350234	−	0.254460i	0.748967	+	0.662607i	$0.230550\pi$
$284$	−8.28631e7	+	1.43523e8i	−0.214658	+	0.371799i
$285$	2.28881e8	+	3.96434e8i	0.585670	+	1.01441i
$286$	2.29661e8	+	1.02252e8i	0.580505	+	0.258457i
$287$	2.31891e8	+	1.68479e8i	0.579025	+	0.420687i
$288$	2.88316e7	−	1.28367e7i	0.0711206	−	0.0316649i
$289$	−4.24154e8	−	9.01567e7i	−1.03367	−	0.219713i
$290$	5.87004e7	+	5.58497e8i	0.141335	+	1.34471i
$291$	−2.78396e8	+	3.09191e8i	−0.662275	+	0.735531i
$292$	−2.03187e8	−	2.25662e8i	−0.477592	−	0.530419i
$293$	−3.86636e7	+	3.67860e8i	−0.0897978	+	0.854369i	0.853203	+	0.521579i	$0.174657\pi$
$293$	−3.86636e7	+	3.67860e8i	−0.0897978	+	0.854369i	−0.943001	+	0.332790i	$0.892010\pi$
$294$	5.77505e7	−	1.77738e8i	0.132538	−	0.407910i
$295$	1.76902e8	−	5.44448e8i	0.401195	−	1.23475i
$296$	−7.98315e6	+	7.59546e7i	−0.0178918	+	0.170229i
$297$	5.26600e8	+	5.84849e8i	1.16636	+	1.29538i
$298$	2.13747e8	−	2.37390e8i	0.467889	−	0.519643i
$299$	4.29277e6	+	4.08430e7i	0.00928728	+	0.0883626i
$300$	−5.11202e6	−	1.08659e6i	−0.0109312	−	0.00232350i
$301$	3.18049e8	−	1.41605e8i	0.672221	−	0.299292i
$302$	−4.44794e8	−	3.23162e8i	−0.929254	−	0.675143i
$303$	−3.96460e8	−	1.76515e8i	−0.818748	−	0.364530i
$304$	−9.44749e7	−	1.63635e8i	−0.192867	−	0.334056i
$305$	−4.22681e8	+	7.32104e8i	−0.853027	+	1.47749i
$306$	1.81092e8	−	1.31571e8i	0.361306	−	0.262504i
$307$	−7.16469e8	+	1.52290e8i	−1.41323	+	0.300392i	−0.850381	−	0.526167i	$-0.823629\pi$
$307$	−7.16469e8	+	1.52290e8i	−1.41323	+	0.300392i	−0.562850	+	0.826559i	$0.690295\pi$
$308$	−5.57446e7	−	1.71564e8i	−0.108712	−	0.334580i
$309$	−7.05553e8			−1.36043
$310$	3.49500e8	−	1.39724e8i	0.666318	−	0.266382i
$311$	2.77389e8			0.522910			0.261455	−	0.965216i	$-0.415798\pi$
$311$	2.77389e8			0.522910			0.261455	+	0.965216i	$0.415798\pi$
$312$	−2.43563e7	−	7.49609e7i	−0.0454015	−	0.139731i
$313$	−8.18467e8	+	1.73971e8i	−1.50868	+	0.320679i	−0.886696	−	0.462354i	$-0.847005\pi$
$313$	−8.18467e8	+	1.73971e8i	−1.50868	+	0.320679i	−0.621980	+	0.783033i	$0.713672\pi$
$314$	−7.47958e7	+	5.43423e7i	−0.136340	+	0.0990568i
$315$	−5.39155e7	+	9.33844e7i	−0.0971911	+	0.168340i
$316$	1.08954e7	+	1.88713e7i	0.0194239	+	0.0336433i
$317$	−3.16997e8	−	1.41136e8i	−0.558917	−	0.248846i	0.107780	−	0.994175i	$-0.465626\pi$
$317$	−3.16997e8	−	1.41136e8i	−0.558917	−	0.248846i	−0.666697	+	0.745329i	$0.732293\pi$
$318$	2.33956e8	+	1.69979e8i	0.407981	+	0.296415i
$319$	1.61448e9	−	7.18813e8i	2.78462	−	1.23979i
$320$	7.27331e7	+	1.54599e7i	0.124082	+	0.0263744i
$321$	2.54885e7	+	2.42507e8i	0.0430107	+	0.409220i
$322$	1.97187e7	−	2.18998e7i	0.0329141	−	0.0365549i
$323$	−8.96727e8	−	9.95916e8i	−1.48065	−	1.64443i
$324$	1.17001e7	−	1.11319e8i	0.0191110	−	0.181829i
$325$	3.17408e6	−	9.76880e6i	0.00512891	−	0.0157852i
$326$	−1.33416e8	+	4.10611e8i	−0.213278	+	0.656401i
$327$	−1.56898e7	+	1.49278e8i	−0.0248141	+	0.236091i
$328$	2.48795e8	+	2.76314e8i	0.389298	+	0.432359i
$329$	2.20636e6	−	2.45041e6i	0.00341579	−	0.00379362i
$330$	5.92588e7	+	5.63810e8i	0.0907724	+	0.863642i
$331$	−3.86377e8	−	8.21270e7i	−0.585617	−	0.124477i	−0.0944307	−	0.995531i	$-0.530103\pi$
$331$	−3.86377e8	−	8.21270e7i	−0.585617	−	0.124477i	−0.491186	+	0.871055i	$0.663436\pi$
$332$	1.67717e8	−	7.46724e7i	0.251532	−	0.111989i
$333$	−1.16229e8	−	8.44457e7i	−0.172489	−	0.125321i
$334$	5.72064e8	+	2.54699e8i	0.840102	+	0.374037i
$335$	6.55531e7	+	1.13541e8i	0.0952656	+	0.165005i
$336$	−2.82789e7	+	4.89805e7i	−0.0406701	+	0.0704427i
$337$	−5.79114e7	+	4.20751e7i	−0.0824250	+	0.0598853i	−0.628235	−	0.778024i	$-0.716222\pi$
$337$	−5.79114e7	+	4.20751e7i	−0.0824250	+	0.0598853i	0.545810	+	0.837909i	$0.316222\pi$
$338$	−3.39495e8	+	7.21619e7i	−0.478217	+	0.101648i
$339$	1.98428e7	+	6.10699e7i	0.0276633	+	0.0851390i
$340$	5.27389e8			0.727704
$341$	−7.58070e8	−	9.10166e8i	−1.03531	−	1.24303i
$342$	3.55439e8			0.480479
$343$	−1.81892e8	−	5.59806e8i	−0.243380	−	0.749045i
$344$	4.41746e8	−	9.38959e7i	0.585083	−	0.124363i
$345$	−7.49242e7	+	5.44356e7i	−0.0982325	+	0.0713701i
$346$	7.38804e7	−	1.27965e8i	0.0958876	−	0.166082i
$347$	3.85144e8	+	6.67089e8i	0.494846	+	0.857098i	0.999982	−	0.00594155i	$-0.00189127\pi$
$347$	3.85144e8	+	6.67089e8i	0.494846	+	0.857098i	−0.505137	+	0.863039i	$0.668558\pi$
$348$	−5.06180e8	−	2.25366e8i	−0.643839	−	0.286656i
$349$	−3.91116e8	−	2.84163e8i	−0.492512	−	0.357831i	0.313638	−	0.949543i	$-0.398452\pi$
$349$	−3.91116e8	−	2.84163e8i	−0.492512	−	0.357831i	−0.806149	+	0.591712i	$0.798452\pi$
$350$	−6.73332e6	+	2.99787e6i	−0.00839442	+	0.00373744i
$351$	4.74343e8	+	1.00825e8i	0.585488	+	0.124449i
$352$	−2.44601e7	−	2.32723e8i	−0.0298923	−	0.284406i
$353$	5.38406e8	−	5.97960e8i	0.651476	−	0.723537i	−0.323406	−	0.946260i	$-0.604828\pi$
$353$	5.38406e8	−	5.97960e8i	0.651476	−	0.723537i	0.974882	+	0.222723i	$0.0714946\pi$
$354$	3.77946e8	+	4.19751e8i	0.452812	+	0.502899i
$355$	7.67775e7	−	7.30489e8i	0.0910824	−	0.866591i
$356$	5.77142e7	−	1.77626e8i	0.0677965	−	0.208656i
$357$	−1.23959e8	+	3.81507e8i	−0.144191	+	0.443776i
$358$	1.00983e8	−	9.60784e8i	0.116320	−	1.10671i
$359$	5.70008e8	+	6.33058e8i	0.650205	+	0.722126i	0.974639	−	0.223782i	$-0.0718404\pi$
$359$	5.70008e8	+	6.33058e8i	0.650205	+	0.722126i	−0.324434	+	0.945908i	$0.605174\pi$
$360$	−9.35961e7	+	1.03949e8i	−0.105730	+	0.117425i
$361$	−1.29002e8	−	1.22737e9i	−0.144318	−	1.37310i
$362$	1.06969e9	+	2.27370e8i	1.18516	+	0.251914i
$363$	1.00704e9	−	4.48365e8i	1.10503	−	0.491992i
$364$	−8.99284e7	−	6.53368e7i	−0.0977332	−	0.0710073i
$365$	1.22949e9	+	5.47403e8i	1.32342	+	0.589226i
$366$	−4.17043e8	−	7.22339e8i	−0.444628	−	0.770118i
$367$	1.77167e8	−	3.06862e8i	0.187091	−	0.324050i	−0.757188	−	0.653196i	$-0.773428\pi$
$367$	1.77167e8	−	3.06862e8i	0.187091	−	0.324050i	0.944279	+	0.329146i	$0.106761\pi$
$368$	3.09263e7	−	2.24693e7i	0.0323490	−	0.0235029i
$369$	−6.84153e8	+	1.45421e8i	−0.708861	+	0.150673i
$370$	−1.04600e8	−	3.21924e8i	−0.107355	−	0.330406i
$371$	4.07838e8			0.414647
$372$	−5.30287e7	+	3.67569e8i	−0.0534085	+	0.370202i
$373$	−1.51465e9			−1.51123			−0.755616	−	0.655015i	$-0.772662\pi$
$373$	−1.51465e9			−1.51123			−0.755616	+	0.655015i	$0.772662\pi$
$374$	−5.12873e8	−	1.57846e9i	−0.506943	−	1.56021i
$375$	−7.35656e8	+	1.56368e8i	−0.720386	+	0.153123i
$376$	3.46041e6	−	2.51413e6i	0.00335714	−	0.00243911i
$377$	5.44492e8	−	9.43087e8i	0.523355	−	0.906478i
$378$	−1.73989e8	−	3.01358e8i	−0.165692	−	0.286987i
$379$	7.82664e8	+	3.48464e8i	0.738479	+	0.328792i	0.741273	−	0.671204i	$-0.234223\pi$
$379$	7.82664e8	+	3.48464e8i	0.738479	+	0.328792i	−0.00279369	+	0.999996i	$0.500889\pi$
$380$	6.77504e8	+	4.92236e8i	0.633387	+	0.460183i
$381$	−5.71946e7	+	2.54647e7i	−0.0529807	+	0.0235885i
$382$	−2.73628e8	−	5.81613e7i	−0.251153	−	0.0533842i
$383$	9.50480e6	+	9.04321e7i	0.00864464	+	0.0822483i	0.997994	−	0.0633149i	$-0.0201673\pi$
$383$	9.50480e6	+	9.04321e7i	0.00864464	+	0.0822483i	−0.989349	+	0.145563i	$0.953501\pi$
$384$	−4.90916e7	+	5.45217e7i	−0.0442433	+	0.0491372i
$385$	5.34983e8	+	5.94158e8i	0.477779	+	0.530627i
$386$	−9.44321e7	+	8.98461e8i	−0.0835726	+	0.795140i
$387$	−2.62524e8	+	8.07966e8i	−0.230240	+	0.708606i
$388$	−2.35206e8	+	7.23891e8i	−0.204427	+	0.629161i
$389$	−4.58117e7	+	4.35869e8i	−0.0394596	+	0.375433i	0.956916	+	0.290366i	$0.0937771\pi$
$389$	−4.58117e7	+	4.35869e8i	−0.0394596	+	0.375433i	−0.996375	+	0.0850669i	$0.972890\pi$
$390$	2.33748e8	+	2.59603e8i	0.199536	+	0.221607i
$391$	1.81420e8	−	2.01487e8i	0.153485	−	0.170462i
$392$	−3.57373e7	−	3.40018e8i	−0.0299654	−	0.285102i
$393$	7.06814e8	+	1.50238e8i	0.587396	+	0.124855i
$394$	−9.15415e7	+	4.07569e7i	−0.0754017	+	0.0335710i
$395$	−7.81336e7	−	5.67674e7i	−0.0637893	−	0.0463457i
$396$	4.02136e8	+	1.79043e8i	0.325417	+	0.144885i
$397$	7.02536e7	+	1.21683e8i	0.0563511	+	0.0976029i	0.892825	−	0.450404i	$-0.148720\pi$
$397$	7.02536e7	+	1.21683e8i	0.0563511	+	0.0976029i	−0.836474	+	0.548007i	$0.815387\pi$
$398$	−4.76171e8	+	8.24752e8i	−0.378593	+	0.655742i
$399$	−5.15320e8	+	3.74402e8i	−0.406136	+	0.295075i
$400$	−9.35205e6	+	1.98784e6i	−0.00730629	+	0.00155300i
$401$	−4.93202e8	−	1.51792e9i	−0.381961	−	1.17556i	−0.938661	−	0.344842i	$-0.887932\pi$
$401$	−4.93202e8	−	1.51792e9i	−0.381961	−	1.17556i	0.556699	−	0.830714i	$-0.312068\pi$
$402$	−1.29357e8			−0.0993116
$403$	−7.07561e8	−	1.79163e8i	−0.538513	−	0.136358i
$404$	−7.93932e8			−0.599030
$405$	1.53302e8	+	4.71814e8i	0.114671	+	0.352922i
$406$	−7.64346e8	+	1.62467e8i	−0.566824	+	0.120482i
$407$	−8.61790e8	+	6.26127e8i	−0.633609	+	0.460344i
$408$	−2.60177e8	+	4.50640e8i	−0.189652	+	0.328488i
$409$	1.96721e8	+	3.40730e8i	0.142173	+	0.246251i	0.928315	−	0.371795i	$-0.121258\pi$
$409$	1.96721e8	+	3.40730e8i	0.142173	+	0.246251i	−0.786141	+	0.618047i	$0.787924\pi$
$410$	−1.50546e9	−	6.70272e8i	−1.07876	−	0.480295i
$411$	4.48169e8	+	3.25614e8i	0.318417	+	0.231343i
$412$	−1.17916e9	+	5.24997e8i	−0.830680	+	0.369843i
$413$	7.79172e8	+	1.65618e8i	0.544262	+	0.115686i
$414$	7.51665e6	+	7.15161e7i	0.00520622	+	0.0495339i
$415$	−5.44459e8	+	6.04684e8i	−0.373936	+	0.415298i
$416$	−9.64836e7	−	1.07156e8i	−0.0657093	−	0.0729776i
$417$	3.73858e7	−	3.55702e8i	0.0252482	−	0.240220i
$418$	8.14391e8	−	2.50644e9i	0.545401	−	1.67857i
$419$	−1.41951e8	+	4.36881e8i	−0.0942736	+	0.290144i	−0.987064	−	0.160329i	$-0.948745\pi$
$419$	−1.41951e8	+	4.36881e8i	−0.0942736	+	0.290144i	0.892790	+	0.450473i	$0.148745\pi$
$420$	2.62020e7	−	2.49296e8i	0.0172569	−	0.164188i
$421$	8.36590e8	+	9.29127e8i	0.546418	+	0.606859i	0.951586	−	0.307383i	$-0.0994534\pi$
$421$	8.36590e8	+	9.29127e8i	0.546418	+	0.606859i	−0.405167	+	0.914243i	$0.632787\pi$
$422$	9.41643e7	−	1.04580e8i	0.0609948	−	0.0677416i
$423$	841052.	+	8.00208e6i	0.000540296	+	0.00514057i
$424$	5.17482e8	+	1.09994e8i	0.329697	+	0.0700792i
$425$	−6.19492e7	+	2.75816e7i	−0.0391448	+	0.0174284i
$426$	5.86307e8	+	4.25977e8i	0.367444	+	0.266964i
$427$	−1.07461e9	−	4.78448e8i	−0.667965	−	0.297397i
$428$	2.23046e8	+	3.86326e8i	0.137512	+	0.238178i
$429$	5.49671e8	−	9.52058e8i	0.336126	−	0.582188i
$430$	−1.61932e9	+	1.17651e9i	−0.982186	+	0.713600i
$431$	−1.48290e9	+	3.15200e8i	−0.892156	+	0.189634i	−0.631111	−	0.775693i	$-0.717401\pi$
$431$	−1.48290e9	+	3.15200e8i	−0.892156	+	0.189634i	−0.261046	+	0.965326i	$0.584067\pi$
$432$	−1.39488e8	−	4.29301e8i	−0.0832425	−	0.256194i
$433$	1.85507e9			1.09812			0.549062	−	0.835782i	$-0.314985\pi$
$433$	1.85507e9			1.09812			0.549062	+	0.835782i	$0.314985\pi$
$434$	2.44194e8	+	4.63338e8i	0.143390	+	0.272072i
$435$	2.45574e9			1.43044
$436$	8.48551e7	+	2.61157e8i	0.0490315	+	0.150903i
$437$	4.21116e8	−	8.95109e7i	0.241388	−	0.0513087i
$438$	−1.07429e9	+	7.80514e8i	−0.610886	+	0.443835i
$439$	1.43378e9	−	2.48337e9i	0.808826	−	1.40093i	−0.104851	−	0.994488i	$-0.533437\pi$
$439$	1.43378e9	−	2.48337e9i	0.808826	−	1.40093i	0.913677	−	0.406440i	$-0.133230\pi$
$440$	5.18564e8	+	8.98179e8i	0.290214	+	0.502665i
$441$	5.87539e8	+	2.61589e8i	0.326213	+	0.145239i
$442$	−8.27377e8	−	6.01124e8i	−0.455749	−	0.331121i
$443$	−2.27720e9	+	1.01387e9i	−1.24448	+	0.554078i	−0.920039	−	0.391827i	$-0.871843\pi$
$443$	−2.27720e9	+	1.01387e9i	−1.24448	+	0.554078i	−0.324442	+	0.945906i	$0.605176\pi$
$444$	3.26678e8	+	6.94376e7i	0.177125	+	0.0376491i
$445$	8.65252e7	+	8.23232e8i	0.0465460	+	0.442856i
$446$	−4.07614e8	+	4.52701e8i	−0.217559	+	0.241624i
$447$	−9.34707e8	−	1.03810e9i	−0.494993	−	0.549746i
$448$	−1.08154e7	+	1.02901e8i	−0.00568287	+	0.0540689i
$449$	1.06010e8	−	3.26265e8i	0.0552694	−	0.170102i	−0.919611	−	0.392830i	$-0.871496\pi$
$449$	1.06010e8	−	3.26265e8i	0.0552694	−	0.170102i	0.974881	+	0.222728i	$0.0714962\pi$
$450$	5.55781e6	−	1.71052e7i	0.00287515	−	0.00884879i
$451$	−5.42087e8	+	5.15761e9i	−0.278260	+	2.64747i
$452$	7.86042e7	+	8.72988e7i	0.0400370	+	0.0444656i
$453$	−1.60875e9	+	1.78670e9i	−0.813101	+	0.903040i
$454$	−1.18464e8	−	1.12711e9i	−0.0594141	−	0.565288i
$455$	4.81894e8	+	1.02430e8i	0.239834	+	0.0509784i
$456$	−7.54836e8	+	3.36075e8i	−0.372800	+	0.165981i
$457$	1.29878e9	+	9.43616e8i	0.636543	+	0.462475i	0.858661	−	0.512544i	$-0.171297\pi$
$457$	1.29878e9	+	9.43616e8i	0.636543	+	0.462475i	−0.222118	+	0.975020i	$0.571297\pi$
$458$	−2.78762e8	−	1.24113e8i	−0.135583	−	0.0603654i
$459$	−1.60077e9	−	2.77261e9i	−0.772653	−	1.33827i
$460$	−8.47127e7	+	1.46727e8i	−0.0405785	+	0.0702840i
$461$	2.55221e9	−	1.85429e9i	1.21329	−	0.881505i	0.217762	−	0.976002i	$-0.430124\pi$
$461$	2.55221e9	−	1.85429e9i	1.21329	−	0.881505i	0.995525	+	0.0944973i	$0.0301244\pi$
$462$	−7.71616e8	+	1.64012e8i	−0.364044	+	0.0773800i
$463$	−1.58898e8	−	4.89038e8i	−0.0744022	−	0.228986i	0.906939	−	0.421263i	$-0.138413\pi$
$463$	−1.58898e8	−	4.89038e8i	−0.0744022	−	0.228986i	−0.981341	+	0.192276i	$0.938413\pi$
$464$	−1.01365e9			−0.471059
$465$	−4.47905e8	−	1.58385e9i	−0.206586	−	0.730513i
$466$	1.23499e9			0.565342
$467$	6.97375e8	+	2.14630e9i	0.316853	+	0.975172i	0.974985	+	0.222270i	$0.0713466\pi$
$467$	6.97375e8	+	2.14630e9i	0.316853	+	0.975172i	−0.658133	+	0.752902i	$0.728653\pi$
$468$	2.65318e8	−	5.63950e7i	0.119648	−	0.0254320i
$469$	−1.47591e8	+	1.07231e8i	−0.0660624	+	0.0479972i
$470$	−9.47867e6	+	1.64175e7i	−0.00421119	+	0.00729399i
$471$	2.02146e8	+	3.50127e8i	0.0891440	+	0.154402i
$472$	9.43979e8	+	4.20287e8i	0.413205	+	0.183971i
$473$	5.09600e9	+	3.70246e9i	2.21419	+	1.60871i
$474$	8.70520e7	−	3.87580e7i	0.0375452	−	0.0167162i
$475$	−1.05325e8	−	2.23876e7i	−0.0450926	−	0.00958473i
$476$	7.67086e7	+	7.29834e8i	0.0326002	+	0.310170i
$477$	−6.65918e8	+	7.39577e8i	−0.280935	+	0.312010i
$478$	−4.23951e8	−	4.70846e8i	−0.177549	−	0.197188i
$479$	3.65665e8	−	3.47907e9i	0.152023	−	1.44640i	−0.606669	−	0.794954i	$-0.707495\pi$
$479$	3.65665e8	−	3.47907e9i	0.152023	−	1.44640i	0.758692	−	0.651449i	$-0.225839\pi$
$480$	1.00482e8	−	3.09250e8i	0.0414708	−	0.127634i
$481$	−2.02836e8	+	6.24264e8i	−0.0831068	+	0.255777i
$482$	−2.66339e8	+	2.53405e9i	−0.108335	+	1.03074i
$483$	−8.62291e7	−	9.57672e7i	−0.0348208	−	0.0386724i
$484$	1.34941e9	−	1.49867e9i	0.540984	−	0.600823i
$485$	−3.52622e8	−	3.35497e9i	−0.140350	−	1.33534i
$486$	1.40721e9	+	2.99111e8i	0.556072	+	0.118197i
$487$	−3.03060e9	+	1.34931e9i	−1.18899	+	0.529372i	−0.903324	−	0.428958i	$-0.858881\pi$
$487$	−3.03060e9	+	1.34931e9i	−1.18899	+	0.529372i	−0.285664	+	0.958330i	$0.592214\pi$
$488$	−1.23447e9	−	8.96898e8i	−0.480853	−	0.349360i
$489$	1.72477e9	+	7.67916e8i	0.667037	+	0.296984i
$490$	7.57644e8	+	1.31228e9i	0.290924	+	0.503894i
$491$	−6.17552e8	+	1.06963e9i	−0.235444	+	0.407802i	−0.959402	−	0.282043i	$-0.908988\pi$
$491$	−6.17552e8	+	1.06963e9i	−0.235444	+	0.407802i	0.723957	+	0.689845i	$0.242321\pi$
$492$	1.31542e9	−	9.55707e8i	0.497950	−	0.361782i
$493$	−7.03228e9	+	1.49476e9i	−2.64321	+	0.561832i
$494$	−5.01824e8	−	1.54445e9i	−0.187287	−	0.576409i
$495$	−1.95097e9			−0.722991
$496$	1.84881e8	+	6.53762e8i	0.0680308	+	0.240566i
$497$	1.02206e9			0.373448
$498$	−2.48088e8	−	7.63535e8i	−0.0900124	−	0.277030i
$499$	−7.67795e8	+	1.63200e8i	−0.276626	+	0.0587987i	−0.344136	−	0.938920i	$-0.611828\pi$
$499$	−7.67795e8	+	1.63200e8i	−0.276626	+	0.0587987i	0.0675096	+	0.997719i	$0.478495\pi$
$500$	−1.11312e9	+	8.08729e8i	−0.398242	+	0.289340i
$501$	1.36918e9	−	2.37149e9i	0.486439	−	0.842537i
$502$	−1.32716e9	−	2.29871e9i	−0.468232	−	0.811001i
$503$	2.01630e9	+	8.97714e8i	0.706426	+	0.314521i	0.728318	−	0.685239i	$-0.240302\pi$
$503$	2.01630e9	+	8.97714e8i	0.706426	+	0.314521i	−0.0218920	+	0.999760i	$0.506969\pi$
$504$	−1.57465e8	−	1.14405e8i	−0.0547869	−	0.0398050i
$505$	3.21456e9	−	1.43121e9i	1.11071	−	0.494521i
$506$	5.21530e8	+	1.10855e8i	0.178958	+	0.0380388i
$507$	1.58650e8	+	1.50945e9i	0.0540645	+	0.514389i
$508$	−7.66390e7	+	8.51163e7i	−0.0259374	+	0.0288064i
$509$	1.73526e9	+	1.92721e9i	0.583248	+	0.647763i	0.960478	−	0.278357i	$-0.0897898\pi$
$509$	1.73526e9	+	1.92721e9i	0.583248	+	0.647763i	−0.377229	+	0.926120i	$0.623123\pi$
$510$	2.41069e8	−	2.29362e9i	0.0804722	−	0.765642i
$511$	−5.78702e8	+	1.78106e9i	−0.191859	+	0.590481i
$512$	−4.14756e7	+	1.27649e8i	−0.0136568	+	0.0420312i
$513$	5.31394e8	−	5.05588e9i	0.173782	−	1.65343i
$514$	1.76192e9	+	1.95681e9i	0.572288	+	0.635590i
$515$	3.82792e9	−	4.25133e9i	1.23492	−	1.37151i
$516$	−2.06433e8	−	1.96408e9i	−0.0661461	−	0.629339i
$517$	5.83550e7	+	1.24037e7i	0.0185721	+	0.00394762i
$518$	4.30285e8	−	1.91575e8i	0.136020	−	0.0605599i
$519$	−5.22748e8	−	3.79799e8i	−0.164137	−	0.119253i
$520$	5.83822e8	+	2.59934e8i	0.182083	+	0.0810685i
$521$	−1.65357e9	−	2.86407e9i	−0.512260	−	0.887261i	−0.999899	−	0.0142155i	$-0.995475\pi$
$521$	−1.65357e9	−	2.86407e9i	−0.512260	−	0.887261i	0.487638	−	0.873046i	$-0.337858\pi$
$522$	9.53406e8	−	1.65135e9i	0.293380	−	0.508150i
$523$	−1.60445e9	+	1.16570e9i	−0.490424	+	0.356314i	−0.805347	−	0.592803i	$-0.798021\pi$
$523$	−1.60445e9	+	1.16570e9i	−0.490424	+	0.356314i	0.314924	+	0.949117i	$0.398021\pi$
$524$	1.29306e9	−	2.74848e8i	0.392608	−	0.0834514i
$525$	9.95995e6	+	3.06536e7i	0.00300400	+	0.00924536i
$526$	2.29164e9			0.686588
$527$	2.24668e9	+	4.26289e9i	0.668657	+	1.26872i
$528$	−1.02329e9			−0.302539
$529$	−1.02523e9	−	3.15534e9i	−0.301112	−	0.926727i
$530$	−2.29352e9	+	4.87503e8i	−0.669172	+	0.142237i
$531$	−1.57257e9	+	1.14254e9i	−0.455804	+	0.331161i
$532$	−5.82644e8	+	1.00917e9i	−0.167769	+	0.290585i
$533$	1.59780e9	+	2.76747e9i	0.457064	+	0.791659i
$534$	−7.46116e8	−	3.32192e8i	−0.212037	−	0.0944050i
$535$	−1.59952e9	−	1.16212e9i	−0.451597	−	0.328105i
$536$	−2.16190e8	+	9.62539e7i	−0.0606399	+	0.0269986i
$537$	−4.13230e9	−	8.78348e8i	−1.15155	−	0.244769i
$538$	2.34582e8	+	2.23190e9i	0.0649465	+	0.617925i
$539$	3.19082e9	−	3.54377e9i	0.877691	−	0.974775i
$540$	1.33867e9	+	1.48675e9i	0.365844	+	0.406311i
$541$	4.55864e8	−	4.33725e9i	0.123778	−	1.17767i	−0.739576	−	0.673073i	$-0.764974\pi$
$541$	4.55864e8	−	4.33725e9i	0.123778	−	1.17767i	0.863354	−	0.504599i	$-0.168360\pi$
$542$	−1.88918e8	+	5.81430e8i	−0.0509655	+	0.156856i
$543$	1.47779e9	−	4.54816e9i	0.396107	−	1.21909i
$544$	−9.95056e7	+	9.46733e8i	−0.0265003	+	0.252134i
$545$	−8.14356e8	−	9.04434e8i	−0.215490	−	0.239326i
$546$	−3.25257e8	+	3.61234e8i	−0.0855169	+	0.0949761i
$547$	3.14962e8	+	2.99666e9i	0.0822815	+	0.782856i	0.955393	+	0.295336i	$0.0954316\pi$
$547$	3.14962e8	+	2.99666e9i	0.0822815	+	0.782856i	−0.873112	+	0.487520i	$0.837902\pi$
$548$	9.91295e8	+	2.10706e8i	0.257318	+	0.0546947i
$549$	2.62225e9	−	1.16750e9i	0.676348	−	0.301130i
$550$	−1.07886e8	−	7.83836e7i	−0.0276500	−	0.0200889i
$551$	−1.04291e10	−	4.64332e9i	−2.65592	−	1.18249i
$552$	−8.35827e7	−	1.44770e8i	−0.0211509	−	0.0366345i
$553$	6.71938e7	−	1.16383e8i	0.0168963	−	0.0292652i
$554$	1.97427e9	−	1.43439e9i	0.493313	−	0.358413i
$555$	−1.44786e9	+	3.07753e8i	−0.359503	+	0.0764147i
$556$	−2.02194e8	−	6.22289e8i	−0.0498892	−	0.153543i
$557$	−1.11114e9			−0.272442			−0.136221	−	0.990678i	$-0.543496\pi$
$557$	−1.11114e9			−0.272442			−0.136221	+	0.990678i	$0.543496\pi$
$558$	−1.23894e9	−	3.13715e8i	−0.301877	−	0.0764391i
$559$	3.88142e9			0.939830
$560$	−1.41709e8	−	4.36135e8i	−0.0340988	−	0.104945i
$561$	−7.09917e9	+	1.50898e9i	−1.69761	+	0.360838i
$562$	−6.79066e8	+	4.93370e8i	−0.161375	+	0.117245i
$563$	−1.65523e9	+	2.86694e9i	−0.390912	+	0.677079i	−0.992570	−	0.121675i	$-0.961173\pi$
$563$	−1.65523e9	+	2.86694e9i	−0.390912	+	0.677079i	0.601659	+	0.798753i	$0.294507\pi$
$564$	−9.35223e6	−	1.61985e7i	−0.00219502	−	0.00380189i
$565$	−4.75634e8	−	2.11766e8i	−0.110944	−	0.0493954i
$566$	−1.06832e9	−	7.76179e8i	−0.247653	−	0.179930i
$567$	−6.30628e8	+	2.80774e8i	−0.145289	+	0.0646868i
$568$	1.29684e9	+	2.75651e8i	0.296939	+	0.0631162i
$569$	−6.17429e8	−	5.87444e9i	−0.140506	−	1.33682i	−0.806663	−	0.591011i	$-0.798729\pi$
$569$	−6.17429e8	−	5.87444e9i	−0.140506	−	1.33682i	0.666158	−	0.745811i	$-0.267938\pi$
$570$	2.45042e9	−	2.72147e9i	0.554216	−	0.615519i
$571$	3.79669e8	+	4.21666e8i	0.0853452	+	0.0947855i	0.784305	−	0.620376i	$-0.213020\pi$
$571$	3.79669e8	+	4.21666e8i	0.0853452	+	0.0947855i	−0.698959	+	0.715161i	$0.746353\pi$
$572$	2.10224e8	−	2.00014e9i	0.0469673	−	0.446864i
$573$	−3.78019e8	+	1.16342e9i	−0.0839407	+	0.258343i
$574$	7.08596e8	−	2.18084e9i	0.156389	−	0.481317i
$575$	2.27713e6	−	2.16654e7i	0.000499517	−	0.00475258i
$576$	−1.68943e8	−	1.87630e8i	−0.0368350	−	0.0409095i
$577$	−7.80507e8	+	8.66841e8i	−0.169146	+	0.187856i	−0.821758	−	0.569837i	$-0.807006\pi$
$577$	−7.80507e8	+	8.66841e8i	−0.169146	+	0.187856i	0.652612	+	0.757692i	$0.273673\pi$
$578$	3.62613e8	+	3.45003e9i	0.0781081	+	0.743149i
$579$	3.86425e9	+	8.21372e8i	0.827352	+	0.175859i
$580$	4.10418e9	−	1.82730e9i	0.873431	−	0.388877i
$581$	−9.15991e8	−	6.65506e8i	−0.193765	−	0.140778i
$582$	3.04070e9	+	1.35381e9i	0.639356	+	0.284660i
$583$	3.68948e9	+	6.39036e9i	0.771125	+	1.33563i
$584$	−1.21464e9	+	2.10381e9i	−0.252349	+	0.437081i
$585$	−9.72584e8	+	7.06624e8i	−0.200855	+	0.145929i
$586$	2.89442e9	−	6.15229e8i	0.594183	−	0.126298i
$587$	2.03005e8	+	6.24786e8i	0.0414261	+	0.127496i	0.969631	−	0.244574i	$-0.0786481\pi$
$587$	2.03005e8	+	6.24786e8i	0.0414261	+	0.127496i	−0.928205	+	0.372070i	$0.878648\pi$
$588$	−1.49508e9			−0.303279
$589$	−1.09257e9	+	7.57319e9i	−0.220317	+	1.52713i
$590$	−4.57973e9			−0.918033
$591$	1.35409e8	+	4.16745e8i	0.0269830	+	0.0830451i
$592$	5.97632e8	−	1.27031e8i	0.118388	−	0.0251642i
$593$	6.66412e9	−	4.84176e9i	1.31235	−	0.953481i	0.312360	−	0.949964i	$-0.398880\pi$
$593$	6.66412e9	−	4.84176e9i	1.31235	−	0.953481i	0.999994	−	0.00351753i	$-0.00111967\pi$
$594$	3.14797e9	−	5.45244e9i	0.616279	−	1.06743i
$595$	−1.62625e9	−	2.81675e9i	−0.316503	−	0.548200i
$596$	−2.33458e9	−	1.03942e9i	−0.451697	−	0.201108i
$597$	3.36920e9	+	2.44787e9i	0.648062	+	0.470845i
$598$	3.00140e8	−	1.33631e8i	0.0573943	−	0.0255536i
$599$	3.68707e9	+	7.83712e8i	0.700951	+	0.148992i	0.544583	−	0.838707i	$-0.316688\pi$
$599$	3.68707e9	+	7.83712e8i	0.700951	+	0.148992i	0.156368	+	0.987699i	$0.450021\pi$
$600$	4.37032e6	+	4.15808e7i	0.000826007	+	0.00785893i
$601$	−2.41644e9	+	2.68372e9i	−0.454061	+	0.504286i	−0.926093	−	0.377295i	$-0.876854\pi$
$601$	−2.41644e9	+	2.68372e9i	−0.454061	+	0.504286i	0.472032	+	0.881582i	$0.343521\pi$
$602$	−1.86365e9	−	2.06980e9i	−0.348159	−	0.386670i
$603$	4.65328e7	−	4.42730e8i	0.00864267	−	0.0822296i
$604$	−1.35917e9	+	4.18309e9i	−0.250983	+	0.772446i
$605$	−2.76199e9	+	8.50054e9i	−0.507082	+	1.56064i
$606$	−3.62906e8	+	3.45282e9i	−0.0662429	+	0.630260i
$607$	4.66070e9	+	5.17623e9i	0.845844	+	0.939405i	0.998807	−	0.0488266i	$-0.0155482\pi$
$607$	4.66070e9	+	5.17623e9i	0.845844	+	0.939405i	−0.152963	+	0.988232i	$0.548881\pi$
$608$	−1.01146e9	+	1.12334e9i	−0.182509	+	0.202697i
$609$	3.57187e8	+	3.39841e9i	0.0640819	+	0.609699i
$610$	6.61511e9	+	1.40608e9i	1.18000	+	0.250817i
$611$	3.35832e7	−	1.49522e7i	0.00595632	−	0.00265192i
$612$	−1.44874e9	−	1.05257e9i	−0.255482	−	0.185618i
$613$	−3.06677e9	−	1.36541e9i	−0.537736	−	0.239416i	0.119854	−	0.992792i	$-0.461757\pi$
$613$	−3.06677e9	−	1.36541e9i	−0.537736	−	0.239416i	−0.657590	+	0.753376i	$0.728424\pi$
$614$	2.92990e9	+	5.07474e9i	0.510815	+	0.884758i
$615$	−3.60316e9	+	6.24086e9i	−0.624627	+	1.08189i
$616$	−1.16753e9	+	8.48261e8i	−0.201250	+	0.146217i
$617$	1.82519e9	−	3.87956e8i	0.312831	−	0.0664944i	−0.0488205	−	0.998808i	$-0.515546\pi$
$617$	1.82519e9	−	3.87956e8i	0.312831	−	0.0664944i	0.361652	+	0.932313i	$0.382213\pi$
$618$	1.74422e9	+	5.36817e9i	0.297264	+	0.914885i
$619$	−7.55269e9			−1.27992			−0.639962	−	0.768406i	$-0.721050\pi$
$619$	−7.55269e9			−1.27992			−0.639962	+	0.768406i	$0.721050\pi$
$620$	−1.92710e9	−	2.31374e9i	−0.324737	−	0.389891i
$621$	1.02850e9			0.172340
$622$	−6.85742e8	−	2.11050e9i	−0.114260	−	0.351656i
$623$	−1.12666e9	+	2.39478e8i	−0.186674	+	0.0396787i
$624$	−5.10125e8	+	3.70627e8i	−0.0840485	+	0.0610648i
$625$	3.14021e9	−	5.43901e9i	0.514493	−	0.891127i
$626$	3.34701e9	+	5.79719e9i	0.545314	+	0.944511i
$627$	−1.05283e10	−	4.68748e9i	−1.70577	−	0.759458i
$628$	5.98366e8	+	4.34738e8i	0.0964069	+	0.0700437i
$629$	3.95879e9	−	1.76257e9i	0.634287	−	0.282403i
$630$	8.43797e8	+	1.79355e8i	0.134445	+	0.0285773i
$631$	7.66312e8	+	7.29097e9i	0.121424	+	1.15527i	0.870288	+	0.492544i	$0.163933\pi$
$631$	7.66312e8	+	7.29097e9i	0.121424	+	1.15527i	−0.748864	+	0.662724i	$0.769400\pi$
$632$	1.16647e8	−	1.29550e8i	0.0183808	−	0.0204139i
$633$	−4.11777e8	−	4.57325e8i	−0.0645282	−	0.0716658i
$634$	−2.90168e8	+	2.76076e9i	−0.0452207	+	0.430246i
$635$	1.56866e8	−	4.82785e8i	0.0243120	−	0.0748248i
$636$	7.14906e8	−	2.20026e9i	0.110192	−	0.339135i
$637$	3.07146e8	−	2.92230e9i	0.0470822	−	0.447957i
$638$	−9.46028e9	−	1.05067e10i	−1.44222	−	1.60175i
$639$	−1.66883e9	+	1.85342e9i	−0.253022	+	0.281009i
$640$	−6.21802e7	−	5.91605e8i	−0.00937611	−	0.0892077i
$641$	2.76789e9	+	5.88333e8i	0.415093	+	0.0882307i	0.410724	−	0.911760i	$-0.365276\pi$
$641$	2.76789e9	+	5.88333e8i	0.415093	+	0.0882307i	0.00436894	+	0.999990i	$0.498609\pi$
$642$	1.78209e9	−	7.93438e8i	0.265802	−	0.118342i
$643$	−8.08426e9	−	5.87356e9i	−1.19923	−	0.871291i	−0.205020	−	0.978758i	$-0.565726\pi$
$643$	−8.08426e9	−	5.87356e9i	−1.19923	−	0.871291i	−0.994209	+	0.107467i	$0.965726\pi$
$644$	−2.15371e8	−	9.58894e7i	−0.0317751	−	0.0141472i
$645$	4.37645e9	+	7.58023e9i	0.642189	+	1.11230i
$646$	−5.36055e9	+	9.28475e9i	−0.782340	+	1.35505i
$647$	−2.63125e9	+	1.91172e9i	−0.381942	+	0.277497i	−0.762146	−	0.647406i	$-0.775854\pi$
$647$	−2.63125e9	+	1.91172e9i	−0.381942	+	0.277497i	0.380203	+	0.924903i	$0.375854\pi$
$648$	−8.75893e8	+	1.86177e8i	−0.126456	+	0.0268790i
$649$	4.45368e9	+	1.37070e10i	0.639532	+	1.96828i
$650$	−8.21722e7			−0.0117362
$651$	2.12668e9	−	8.50209e8i	0.302113	−	0.120779i
$652$	3.45394e9			0.488032
$653$	−1.87977e9	−	5.78533e9i	−0.264185	−	0.813078i	−0.991880	−	0.127177i	$-0.959408\pi$
$653$	−1.87977e9	−	5.78533e9i	−0.264185	−	0.813078i	0.727695	−	0.685901i	$-0.240592\pi$
$654$	1.17456e9	−	2.49661e8i	0.164193	−	0.0349002i
$655$	−4.74002e9	+	3.44383e9i	−0.659076	+	0.478847i
$656$	1.48727e9	−	2.57603e9i	0.205696	−	0.356276i
$657$	−2.28489e9	−	3.95754e9i	−0.314330	−	0.544436i
$658$	−2.40983e7	−	1.07292e7i	−0.00329758	−	0.00146818i
$659$	5.75814e9	+	4.18353e9i	0.783760	+	0.569435i	0.906105	−	0.423053i	$-0.139042\pi$
$659$	5.75814e9	+	4.18353e9i	0.783760	+	0.569435i	−0.122345	+	0.992488i	$0.539042\pi$
$660$	4.14322e9	−	1.84468e9i	0.560963	−	0.249757i
$661$	−6.73989e9	−	1.43261e9i	−0.907712	−	0.192940i	−0.269680	−	0.962950i	$-0.586918\pi$
$661$	−6.73989e9	−	1.43261e9i	−0.907712	−	0.192940i	−0.638032	+	0.770010i	$0.720251\pi$
$662$	3.30317e8	+	3.14276e9i	0.0442516	+	0.421025i
$663$	−2.99249e9	+	3.32350e9i	−0.398782	+	0.442892i
$664$	−9.82760e8	−	1.09147e9i	−0.130274	−	0.144684i
$665$	5.39853e8	−	5.13636e9i	0.0711868	−	0.677298i
$666$	−3.55166e8	+	1.09309e9i	−0.0465877	+	0.143382i
$667$	7.13710e8	−	2.19657e9i	0.0931282	−	0.286619i
$668$	5.23647e8	−	4.98217e9i	0.0679706	−	0.646697i
$669$	1.78248e9	+	1.97965e9i	0.230162	+	0.255621i
$670$	7.01817e8	−	7.79447e8i	0.0901493	−	0.100121i
$671$	−2.22466e9	−	2.11662e10i	−0.284272	−	2.70467i
$672$	4.42575e8	+	9.40722e7i	0.0562593	+	0.0119583i
$673$	−1.12778e9	+	5.02120e8i	−0.142617	+	0.0634972i	−0.476804	−	0.879010i	$-0.658205\pi$
$673$	−1.12778e9	+	5.02120e8i	−0.142617	+	0.0634972i	0.334187	+	0.942507i	$0.391538\pi$
$674$	4.63291e8	+	3.36601e8i	0.0582833	+	0.0423453i
$675$	−2.35000e8	−	1.04629e8i	−0.0294107	−	0.0130945i
$676$	1.38832e9	+	2.40464e9i	0.172853	+	0.299389i
$677$	2.14775e9	−	3.72002e9i	0.266026	−	0.460771i	−0.701806	−	0.712368i	$-0.747623\pi$
$677$	2.14775e9	−	3.72002e9i	0.266026	−	0.460771i	0.967832	+	0.251597i	$0.0809559\pi$
$678$	4.15593e8	−	3.01946e8i	0.0512112	−	0.0372071i
$679$	4.59153e9	−	9.75961e8i	0.562877	−	0.119643i
$680$	−1.30378e9	−	4.01261e9i	−0.159009	−	0.489380i
$681$	−4.95595e9			−0.601328
$682$	−5.05090e9	+	8.01780e9i	−0.609710	+	0.967854i
$683$	1.00631e10			1.20854			0.604270	−	0.796779i	$-0.293465\pi$
$683$	1.00631e10			1.20854			0.604270	+	0.796779i	$0.293465\pi$
$684$	−8.78694e8	−	2.70434e9i	−0.104988	−	0.323121i
$685$	−4.39350e9	+	9.33868e8i	−0.522269	+	0.111012i
$686$	−3.80959e9	+	2.76783e9i	−0.450551	+	0.327345i
$687$	−6.67191e8	+	1.15561e9i	−0.0785057	+	0.135976i
$688$	−1.80646e9	−	3.12888e9i	−0.211480	−	0.366293i
$689$	4.15378e9	+	1.84938e9i	0.483811	+	0.215407i
$690$	5.99394e8	+	4.35485e8i	0.0694609	+	0.0504663i
$691$	−1.12124e9	+	4.99207e8i	−0.129278	+	0.0575583i	−0.470356	−	0.882477i	$-0.655875\pi$
$691$	−1.12124e9	+	4.99207e8i	−0.129278	+	0.0575583i	0.341078	+	0.940035i	$0.389208\pi$
$692$	−1.15625e9	−	2.45769e8i	−0.132642	−	0.0281940i
$693$	−2.83769e8	−	2.69988e9i	−0.0323890	−	0.308161i
$694$	4.12338e9	−	4.57948e9i	0.468269	−	0.520066i
$695$	1.94046e9	+	2.15510e9i	0.219259	+	0.243512i
$696$	−4.63339e8	+	4.40838e9i	−0.0520915	+	0.495618i
$697$	6.51937e9	−	2.00645e10i	0.729274	−	2.24447i
$698$	−1.19514e9	+	3.67828e9i	−0.133023	+	0.409402i
$699$	5.64511e8	−	5.37096e9i	0.0625176	−	0.594815i
$700$	3.94548e7	+	4.38190e7i	0.00434767	+	0.00482858i
$701$	4.26758e9	−	4.73963e9i	0.467917	−	0.519675i	−0.462280	−	0.886734i	$-0.652969\pi$
$701$	4.26758e9	−	4.73963e9i	0.467917	−	0.519675i	0.930198	+	0.367059i	$0.119635\pi$
$702$	−4.05521e8	−	3.85827e9i	−0.0442418	−	0.420933i
$703$	6.73070e9	+	1.43065e9i	0.730662	+	0.155307i
$704$	−1.71019e9	+	7.61426e8i	−0.184731	+	0.0822476i
$705$	6.70673e7	+	4.87273e7i	0.00720857	+	0.00523733i
$706$	−5.88056e9	−	2.61820e9i	−0.628930	−	0.280018i
$707$	2.44816e9	+	4.24034e9i	0.260539	+	0.451266i
$708$	2.25932e9	−	3.91326e9i	0.239255	−	0.414403i
$709$	9.13928e9	−	6.64008e9i	0.963053	−	0.699699i	0.00919533	−	0.999958i	$-0.497073\pi$
$709$	9.13928e9	−	6.64008e9i	0.963053	−	0.699699i	0.953858	+	0.300259i	$0.0970730\pi$
$710$	−5.74769e9	+	1.22171e9i	−0.602684	+	0.128104i
$711$	1.01336e8	+	3.11880e8i	0.0105735	+	0.0325420i
$712$	−1.49414e9			−0.155135
$713$	−1.54687e9	−	5.96772e7i	−0.159823	−	0.00616588i
$714$	3.20912e9			0.329945
$715$	2.75446e9	+	8.47737e9i	0.281816	+	0.867341i
$716$	−7.55972e9	+	1.60687e9i	−0.769680	+	0.163601i
$717$	−2.24150e9	+	1.62855e9i	−0.227102	+	0.165000i
$718$	3.40746e9	−	5.90189e9i	0.343554	−	0.595053i
$719$	8.11111e9	+	1.40489e10i	0.813822	+	1.40958i	0.910171	+	0.414233i	$0.135950\pi$
$719$	8.11111e9	+	1.40489e10i	0.813822	+	1.40958i	−0.0963492	+	0.995348i	$0.530717\pi$
$720$	1.02227e9	+	4.55145e8i	0.102071	+	0.0454450i
$721$	6.44003e9	+	4.67896e9i	0.639904	+	0.464917i
$722$	−9.01950e9	+	4.01574e9i	−0.891871	+	0.397087i
$723$	1.08988e10	+	2.31662e9i	1.07250	+	0.227967i
$724$	−9.14488e8	−	8.70077e9i	−0.0895557	−	0.852065i
$725$	−3.86529e8	+	4.29284e8i	−0.0376703	+	0.0418371i
$726$	−5.90091e9	−	6.55363e9i	−0.572323	−	0.635629i
$727$	7.99042e8	−	7.60238e9i	0.0771257	−	0.733802i	−0.885806	−	0.464056i	$-0.846394\pi$
$727$	7.99042e8	−	7.60238e9i	0.0771257	−	0.733802i	0.962932	−	0.269746i	$-0.0869397\pi$
$728$	−2.74797e8	+	8.45737e8i	−0.0263968	+	0.0812411i
$729$	3.12604e9	−	9.62097e9i	0.298847	−	0.919756i
$730$	1.12543e9	−	1.07077e10i	0.107075	−	1.01875i
$731$	−1.71464e10	−	1.90430e10i	−1.62353	−	1.80312i
$732$	−4.46490e9	+	4.95877e9i	−0.420748	+	0.467289i
$733$	1.14161e9	+	1.08617e10i	0.107067	+	1.01867i	0.907730	+	0.419556i	$0.137814\pi$
$733$	1.14161e9	+	1.08617e10i	0.107067	+	1.01867i	−0.800663	+	0.599115i	$0.795519\pi$
$734$	−2.77273e9	−	5.89362e8i	−0.258804	−	0.0550105i
$735$	6.05343e9	−	2.69516e9i	0.562336	−	0.250368i
$736$	−2.47410e8	−	1.79754e8i	−0.0228742	−	0.0166191i
$737$	−3.01536e9	−	1.34253e9i	−0.277462	−	0.123534i
$738$	2.79775e9	+	4.84585e9i	0.256219	+	0.443785i
$739$	−7.34224e9	+	1.27171e10i	−0.669227	+	1.15913i	0.308894	+	0.951096i	$0.400041\pi$
$739$	−7.34224e9	+	1.27171e10i	−0.669227	+	1.15913i	−0.978121	+	0.208038i	$0.933292\pi$
$740$	−2.19076e9	+	1.59168e9i	−0.198739	+	0.144393i
$741$	−6.94623e9	+	1.47647e9i	−0.627170	+	0.133309i
$742$	−1.00823e9	−	3.10301e9i	−0.0906037	−	0.278850i
$743$	−2.02592e10			−1.81202			−0.906008	−	0.423261i	$-0.860885\pi$
$743$	−2.02592e10			−1.81202			−0.906008	+	0.423261i	$0.860885\pi$
$744$	2.92772e9	−	5.05214e8i	0.260630	−	0.0449749i
$745$	1.13263e10			1.00355
$746$	3.74442e9	+	1.15241e10i	0.330216	+	1.01630i
$747$	2.70247e9	−	5.74427e8i	0.237213	−	0.0504211i
$748$	−1.07417e10	+	7.80434e9i	−0.938468	+	0.681837i
$749$	1.37556e9	−	2.38254e9i	0.119617	−	0.207183i
$750$	3.00836e9	+	5.21064e9i	0.260385	+	0.451000i
$751$	7.02305e9	+	3.12686e9i	0.605043	+	0.269382i	0.686309	−	0.727310i	$-0.259230\pi$
$751$	7.02305e9	+	3.12686e9i	0.605043	+	0.269382i	−0.0812664	+	0.996692i	$0.525896\pi$
$752$	−2.76832e7	−	2.01131e7i	−0.00237386	−	0.00172471i
$753$	−1.06038e10	+	4.72110e9i	−0.905060	+	0.402959i
$754$	−8.52149e9	−	1.81130e9i	−0.723962	−	0.153883i
$755$	−2.03767e9	−	1.93871e10i	−0.172314	−	1.63945i
$756$	−1.86274e9	+	2.06879e9i	−0.156793	+	0.174136i
$757$	1.55051e10	+	1.72201e10i	1.29909	+	1.44278i	0.828034	+	0.560678i	$0.189460\pi$
$757$	1.55051e10	+	1.72201e10i	1.29909	+	1.44278i	0.471054	+	0.882104i	$0.343874\pi$
$758$	7.16423e8	−	6.81631e9i	0.0597486	−	0.568470i
$759$	7.20499e8	−	2.21747e9i	0.0598118	−	0.184082i
$760$	2.07027e9	−	6.37163e9i	0.171072	−	0.526506i
$761$	−4.36826e8	+	4.15612e9i	−0.0359304	+	0.341855i	0.961758	+	0.273900i	$0.0883139\pi$
$761$	−4.36826e8	+	4.15612e9i	−0.0359304	+	0.341855i	−0.997688	+	0.0679544i	$0.978353\pi$
$762$	3.35140e8	+	3.72210e8i	0.0274400	+	0.0304752i
$763$	1.13317e9	−	1.25851e9i	0.0923543	−	0.102570i
$764$	2.33927e8	+	2.22567e9i	0.0189781	+	0.180565i
$765$	7.76327e9	+	1.65013e9i	0.626945	+	0.133261i
$766$	6.64551e8	−	2.95877e8i	0.0534229	−	0.0237854i
$767$	7.18476e9	+	5.22004e9i	0.574948	+	0.417724i
$768$	5.36187e8	+	2.38726e8i	0.0427122	+	0.0190167i
$769$	−2.92656e8	−	5.06895e8i	−0.0232068	−	0.0401953i	0.854189	−	0.519963i	$-0.174054\pi$
$769$	−2.92656e8	−	5.06895e8i	−0.0232068	−	0.0401953i	−0.877396	+	0.479768i	$0.840721\pi$
$770$	3.19808e9	−	5.53923e9i	0.252448	−	0.437252i
$771$	9.31554e9	−	6.76814e9i	0.732011	−	0.531837i
$772$	7.06935e9	−	1.50264e9i	0.552992	−	0.117542i
$773$	4.80822e9	+	1.47982e10i	0.374418	+	1.15234i	0.943871	+	0.330315i	$0.107155\pi$
$773$	4.80822e9	+	1.47982e10i	0.374418	+	1.15234i	−0.569453	+	0.822024i	$0.692845\pi$
$774$	6.79637e9			0.526846
$775$	3.47369e8	+	1.70997e8i	0.0268062	+	0.0131957i
$776$	6.08915e9			0.467779
$777$	−6.36480e8	−	1.95888e9i	−0.0486756	−	0.149808i
$778$	3.42954e9	−	7.28971e8i	0.261100	−	0.0554986i
$779$	2.71022e10	−	1.96909e10i	2.05411	−	1.49240i
$780$	1.39732e9	−	2.42023e9i	0.105430	−	0.182611i
$781$	9.24604e9	+	1.60146e10i	0.694508	+	1.20292i
$782$	−1.98150e9	−	8.82220e8i	−0.148173	−	0.0659710i
$783$	−2.20639e10	−	1.60304e10i	−1.64254	−	1.19338i
$784$	−2.49866e9	+	1.11248e9i	−0.185183	+	0.0824488i
$785$	−3.20643e9	−	6.81548e8i	−0.236580	−	0.0502866i
$786$	−6.04262e8	−	5.74917e9i	−0.0443860	−	0.422305i
$787$	−2.96088e9	+	3.28839e9i	−0.216525	+	0.240476i	−0.841616	−	0.540076i	$-0.818395\pi$
$787$	−2.96088e9	+	3.28839e9i	−0.216525	+	0.240476i	0.625091	+	0.780552i	$0.285062\pi$
$788$	5.36400e8	+	5.95733e8i	0.0390523	+	0.0433720i
$789$	1.04751e9	−	9.96637e9i	0.0759255	−	0.722383i
$790$	−2.38755e8	+	7.34813e8i	−0.0172289	+	0.0530251i
$791$	2.23874e8	−	6.89014e8i	0.0160837	−	0.0495006i
$792$	3.68102e8	−	3.50225e9i	0.0263287	−	0.250501i
$793$	−8.77522e9	−	9.74587e9i	−0.624887	−	0.694008i
$794$	7.52142e8	−	8.35338e8i	0.0533246	−	0.0592230i
$795$	1.07179e9	+	1.01974e10i	0.0756527	+	0.719787i
$796$	7.45225e9	+	1.58402e9i	0.523711	+	0.111318i
$797$	2.37891e8	−	1.05916e8i	0.0166446	−	0.00741066i	−0.398397	−	0.917213i	$-0.630434\pi$
$797$	2.37891e8	−	1.05916e8i	0.0166446	−	0.00741066i	0.415042	+	0.909802i	$0.363767\pi$
$798$	4.12256e9	+	2.99521e9i	0.287182	+	0.208650i
$799$	−2.21714e8	−	9.87133e7i	−0.0153773	−	0.00684640i
$800$	3.82439e7	+	6.62404e7i	0.00264087	+	0.00457412i
$801$	1.40533e9	−	2.43411e9i	0.0966196	−	0.167350i
$802$	−1.03298e10	+	7.50501e9i	−0.707098	+	0.513737i
$803$	−3.31424e10	+	7.04464e9i	−2.25881	+	0.480125i
$804$	3.19789e8	+	9.84209e8i	0.0217004	+	0.0667869i
$805$	1.04488e9			0.0705959
$806$	3.86032e8	+	5.82636e9i	0.0259688	+	0.391945i
$807$	9.81376e9			0.657322
$808$	1.96271e9	+	6.04059e9i	0.130893	+	0.402847i
$809$	−1.26067e10	+	2.67963e9i	−0.837106	+	0.177932i	−0.606469	−	0.795107i	$-0.707414\pi$
$809$	−1.26067e10	+	2.67963e9i	−0.837106	+	0.177932i	−0.230637	+	0.973040i	$0.574081\pi$
$810$	3.21079e9	−	2.33278e9i	0.212283	−	0.154232i
$811$	2.06175e9	−	3.57106e9i	0.135726	−	0.235085i	−0.790148	−	0.612916i	$-0.789997\pi$
$811$	2.06175e9	−	3.57106e9i	0.135726	−	0.235085i	0.925875	+	0.377831i	$0.123330\pi$
$812$	3.12569e9	+	5.41385e9i	0.204880	+	0.354862i
$813$	2.44229e9	+	1.08738e9i	0.159397	+	0.0709682i
$814$	6.89432e9	+	5.00902e9i	0.448029	+	0.325512i
$815$	−1.39847e10	+	6.22638e9i	−0.904901	+	0.402888i
$816$	4.07187e9	+	8.65502e8i	0.262348	+	0.0557638i
$817$	−4.25323e9	−	4.04668e10i	−0.272861	−	2.59610i
$818$	2.10611e9	−	2.33907e9i	0.134538	−	0.149419i
$819$	−1.11933e9	−	1.24314e9i	−0.0711976	−	0.0790730i
$820$	−1.37804e9	+	1.31112e10i	−0.0872798	+	0.830412i
$821$	−2.68283e9	+	8.25689e9i	−0.169196	+	0.520733i	−0.999321	−	0.0368448i	$-0.988269\pi$
$821$	−2.68283e9	+	8.25689e9i	−0.169196	+	0.520733i	0.830125	+	0.557578i	$0.188269\pi$
$822$	1.36948e9	−	4.21484e9i	0.0860014	−	0.264685i
$823$	−1.68826e9	+	1.60627e10i	−0.105570	+	1.00443i	0.805617	+	0.592436i	$0.201834\pi$
$823$	−1.68826e9	+	1.60627e10i	−0.105570	+	1.00443i	−0.911187	+	0.411993i	$0.864833\pi$
$824$	6.90947e9	+	7.67374e9i	0.430229	+	0.477817i
$825$	−3.90206e8	+	4.33367e8i	−0.0241938	+	0.0268700i
$826$	−6.66122e8	−	6.33772e9i	−0.0411266	−	0.391294i
$827$	1.63649e10	+	3.47846e9i	1.00610	+	0.213854i	0.681361	−	0.731948i	$-0.261389\pi$
$827$	1.63649e10	+	3.47846e9i	1.00610	+	0.213854i	0.324744	+	0.945802i	$0.394722\pi$
$828$	5.25545e8	−	2.33988e8i	0.0321739	−	0.0143247i
$829$	−1.70721e10	−	1.24036e10i	−1.04075	−	0.756150i	−0.0703193	−	0.997525i	$-0.522402\pi$
$829$	−1.70721e10	−	1.24036e10i	−1.04075	−	0.756150i	−0.970432	+	0.241374i	$0.922402\pi$
$830$	5.94668e9	+	2.64763e9i	0.360995	+	0.160725i
$831$	−5.33574e9	−	9.24178e9i	−0.322546	−	0.558666i
$832$	−5.76770e8	+	9.98995e8i	−0.0347193	+	0.0601356i
$833$	−1.56942e10	+	1.14025e10i	−0.940764	+	0.683505i
$834$	−2.79876e9	+	5.94895e8i	−0.167065	+	0.0355107i
$835$	6.86111e9	+	2.11163e10i	0.407842	+	1.25521i
$836$	−2.10834e10			−1.24801
$837$	−6.31464e9	+	1.71541e10i	−0.372228	+	1.01118i
$838$	3.67491e9			0.215721
$839$	2.31733e9	+	7.13202e9i	0.135463	+	0.416913i	0.995662	−	0.0930463i	$-0.0296605\pi$
$839$	2.31733e9	+	7.13202e9i	0.135463	+	0.416913i	−0.860199	+	0.509959i	$0.829660\pi$
$840$	−1.96153e9	+	4.16936e8i	−0.114187	+	0.0242712i
$841$	−3.55913e10	+	2.58586e10i	−2.06328	+	1.49906i
$842$	5.00106e9	−	8.66208e9i	0.288715	−	0.500069i
$843$	1.83527e9	+	3.17878e9i	0.105513	+	0.182753i
$844$	−1.02848e9	−	4.57909e8i	−0.0588840	−	0.0262168i
$845$	−9.95600e9	−	7.23346e9i	−0.567657	−	0.412427i
$846$	5.88042e7	−	2.61813e7i	0.00333897	−	0.00148660i
$847$	−1.21653e10	−	2.58582e9i	−0.687909	−	0.146220i
$848$	−4.42400e8	−	4.20916e9i	−0.0249132	−	0.237033i
$849$	−3.86394e9	+	4.29134e9i	−0.216697	+	0.240666i
$850$	3.63000e8	+	4.03152e8i	0.0202740	+	0.0225166i
$851$	−1.45517e8	+	1.38450e9i	−0.00809396	+	0.0770089i
$852$	1.79159e9	−	5.51396e9i	0.0992433	−	0.305439i
$853$	−7.40387e9	+	2.27868e10i	−0.408449	+	1.25708i	0.509533	+	0.860451i	$0.329818\pi$
$853$	−7.40387e9	+	2.27868e10i	−0.408449	+	1.25708i	−0.917981	+	0.396624i	$0.870182\pi$
$854$	−9.83661e8	+	9.35891e9i	−0.0540435	+	0.514189i
$855$	8.43285e9	+	9.36562e9i	0.461416	+	0.512455i
$856$	2.38795e9	−	2.65208e9i	0.130127	−	0.144520i
$857$	−3.19495e9	−	3.03979e10i	−0.173393	−	1.64972i	−0.642286	−	0.766465i	$-0.722014\pi$
$857$	−3.19495e9	−	3.03979e10i	−0.173393	−	1.64972i	0.468893	−	0.883255i	$-0.344653\pi$
$858$	−8.60255e9	−	1.82853e9i	−0.464966	−	0.0988317i
$859$	3.17319e10	−	1.41280e10i	1.70813	−	0.760507i	0.709696	−	0.704508i	$-0.248832\pi$
$859$	3.17319e10	−	1.41280e10i	1.70813	−	0.760507i	0.998431	−	0.0559993i	$-0.0178345\pi$
$860$	1.29546e10	+	9.41206e9i	0.694511	+	0.504591i
$861$	−9.16058e9	−	4.07855e9i	−0.489116	−	0.217768i
$862$	6.06411e9	+	1.05033e10i	0.322472	+	0.558537i
$863$	−1.48057e10	+	2.56442e10i	−0.784135	+	1.35816i	0.145379	+	0.989376i	$0.453560\pi$
$863$	−1.48057e10	+	2.56442e10i	−0.784135	+	1.35816i	−0.929514	+	0.368786i	$0.879773\pi$
$864$	−2.92148e9	+	2.12258e9i	−0.154101	+	0.111961i
$865$	5.12462e9	−	1.08927e9i	0.269219	−	0.0572242i
$866$	−4.58597e9	−	1.41142e10i	−0.239949	−	0.738487i
$867$	1.51700e10			0.790530
$868$	2.92160e9	−	3.00337e9i	0.151636	−	0.155880i
$869$	2.43146e9			0.125689
$870$	−6.07093e9	−	1.86844e10i	−0.312563	−	0.961970i
$871$	−1.98945e9	+	4.22870e8i	−0.102016	+	0.0216842i
$872$	1.77723e9	−	1.29123e9i	0.0907686	−	0.0659472i
$873$	−5.72725e9	+	9.91988e9i	−0.291337	+	0.504611i
$874$	−1.72209e9	−	2.98275e9i	−0.0872503	−	0.151122i
$875$	7.75177e9	+	3.45131e9i	0.391177	+	0.174163i
$876$	8.59428e9	+	6.24411e9i	0.431962	+	0.313839i
$877$	−1.43383e10	+	6.38381e9i	−0.717791	+	0.319581i	−0.732930	−	0.680304i	$-0.761848\pi$
$877$	−1.43383e10	+	6.38381e9i	−0.717791	+	0.319581i	0.0151387	+	0.999885i	$0.495181\pi$
$878$	−2.24391e10	−	4.76958e9i	−1.11886	−	0.237820i
$879$	−1.35260e9	−	1.28691e10i	−0.0671749	−	0.639127i
$880$	5.55179e9	−	6.16589e9i	0.274627	−	0.305004i
$881$	1.28384e10	+	1.42585e10i	0.632551	+	0.702519i	0.971166	−	0.238406i	$-0.0766249\pi$
$881$	1.28384e10	+	1.42585e10i	0.632551	+	0.702519i	−0.338615	+	0.940925i	$0.609958\pi$
$882$	5.37812e8	−	5.11694e9i	0.0263931	−	0.251114i
$883$	−6.57168e7	+	2.02256e8i	−0.00321228	+	0.00988640i	−0.952650	−	0.304070i	$-0.901654\pi$
$883$	−6.57168e7	+	2.02256e8i	−0.00321228	+	0.00988640i	0.949438	+	0.313956i	$0.101654\pi$
$884$	−2.52824e9	+	7.78112e9i	−0.123093	+	0.378843i
$885$	−2.09339e9	+	1.99173e10i	−0.101519	+	0.965893i
$886$	1.33436e10	+	1.48195e10i	0.644546	+	0.715841i
$887$	−9.70000e9	+	1.07729e10i	−0.466701	+	0.518324i	−0.929841	−	0.367961i	$-0.880056\pi$
$887$	−9.70000e9	+	1.07729e10i	−0.466701	+	0.518324i	0.463140	+	0.886285i	$0.346723\pi$
$888$	−2.79280e8	−	2.65717e9i	−0.0133843	−	0.127343i
$889$	6.90924e8	+	1.46860e8i	0.0329818	+	0.00701049i
$890$	6.04962e9	−	2.69347e9i	0.287649	−	0.128070i
$891$	−1.01044e10	−	7.34124e9i	−0.478560	−	0.347694i
$892$	4.45203e9	+	1.98217e9i	0.210030	+	0.0935114i
$893$	−1.92688e8	−	3.33746e8i	−0.00905473	−	0.0156833i
$894$	−5.58759e9	+	9.67799e9i	−0.261543	+	0.453006i
$895$	2.77120e10	−	2.01339e10i	1.29207	−	0.938745i
$896$	8.09657e8	−	1.72098e8i	0.0376030	−	0.00799277i
$897$	−4.43968e8	−	1.36639e9i	−0.0205389	−	0.0632123i
$898$	−2.74445e9			−0.126470
$899$	3.22539e10	+	2.53898e10i	1.48055	+	1.16547i
$900$	−1.43884e8			−0.00657904
$901$	−9.27612e9	−	2.85489e10i	−0.422503	−	1.30033i
$902$	4.05815e10	−	8.62587e9i	1.84122	−	0.391363i
$903$	−9.85345e9	+	7.15895e9i	−0.445329	+	0.323551i
$904$	4.69889e8	−	8.13871e8i	0.0211546	−	0.0366409i
$905$	1.93875e10	+	3.35801e10i	0.869463	+	1.50595i
$906$	1.75710e10	+	7.82313e9i	0.784962	+	0.349488i
$907$	−2.61643e10	−	1.90094e10i	−1.16435	−	0.845949i	−0.174027	−	0.984741i	$-0.555678\pi$
$907$	−2.61643e10	−	1.90094e10i	−1.16435	−	0.845949i	−0.990322	+	0.138792i	$0.955678\pi$
$908$	−8.28268e9	+	3.68769e9i	−0.367173	+	0.163476i
$909$	−1.16868e10	−	2.48411e9i	−0.516087	−	0.109698i
$910$	−4.11976e8	−	3.91969e9i	−0.0181229	−	0.172428i
$911$	1.27421e10	−	1.41515e10i	0.558375	−	0.620138i	−0.396180	−	0.918173i	$-0.629664\pi$
$911$	1.27421e10	−	1.41515e10i	0.558375	−	0.620138i	0.954555	+	0.298035i	$0.0963311\pi$
$912$	4.42306e9	+	4.91231e9i	0.193082	+	0.214439i
$913$	2.14129e9	−	2.03730e10i	0.0931167	−	0.885947i
$914$	3.96871e9	−	1.22144e10i	0.171924	−	0.529129i
$915$	9.13883e9	−	2.81264e10i	0.394382	−	1.21378i
$916$	−2.55169e8	+	2.42777e9i	−0.0109697	+	0.104370i
$917$	−5.45522e9	−	6.05863e9i	−0.233625	−	0.259467i
$918$	−1.71380e10	+	1.90337e10i	−0.731157	+	0.812032i
$919$	−7.82255e8	−	7.44266e9i	−0.0332464	−	0.316318i	−0.998489	−	0.0549609i	$-0.982497\pi$
$919$	−7.82255e8	−	7.44266e9i	−0.0332464	−	0.316318i	0.965242	−	0.261357i	$-0.0841701\pi$
$920$	1.32578e9	+	2.81804e8i	0.0561326	+	0.0119314i
$921$	2.34094e10	−	1.04225e10i	0.987372	−	0.439606i
$922$	−2.04177e10	−	1.48343e10i	−0.857923	−	0.623318i
$923$	1.04096e10	+	4.63465e9i	0.435741	+	0.194004i
$924$	3.15542e9	+	5.46534e9i	0.131585	+	0.227911i
$925$	1.74093e8	−	3.01538e8i	0.00723246	−	0.0125270i
$926$	−3.32801e9	+	2.41794e9i	−0.137735	+	0.100071i
$927$	−1.90002e10	+	4.03861e9i	−0.783390	+	0.166515i
$928$	2.50588e9	+	7.71232e9i	0.102930	+	0.316787i
$929$	3.64918e10			1.49328			0.746639	−	0.665230i	$-0.231666\pi$
$929$	3.64918e10			1.49328			0.746639	+	0.665230i	$0.231666\pi$
$930$	−1.09433e10	+	7.32335e9i	−0.446128	+	0.298552i
$931$	−3.08038e10			−1.25106
$932$	−3.05305e9	−	9.39633e9i	−0.123532	−	0.380191i
$933$	−9.49203e9	+	2.01759e9i	−0.382625	+	0.0813294i
$934$	1.46060e10	−	1.06119e10i	0.586567	−	0.426166i
$935$	2.94236e10	−	5.09631e10i	1.17721	−	2.03899i
$936$	−1.08498e9	−	1.87924e9i	−0.0432470	−	0.0749060i
$937$	−1.91880e10	−	8.54303e9i	−0.761974	−	0.339253i	−0.0113092	−	0.999936i	$-0.503600\pi$
$937$	−1.91880e10	−	8.54303e9i	−0.761974	−	0.339253i	−0.750665	+	0.660683i	$0.770267\pi$
$938$	1.18073e9	+	8.57848e8i	0.0467132	+	0.0339391i
$939$	2.67419e10	−	1.19063e10i	1.05406	−	0.469296i
$940$	1.48345e8	+	3.15316e7i	0.00582538	+	0.00123822i
$941$	4.19617e9	+	3.99239e10i	0.164168	+	1.56196i	0.697832	+	0.716261i	$0.254148\pi$
$941$	4.19617e9	+	3.99239e10i	0.164168	+	1.56196i	−0.533664	+	0.845697i	$0.679185\pi$
$942$	2.16419e9	−	2.40358e9i	0.0843564	−	0.0936873i
$943$	4.53504e9	+	5.03667e9i	0.176113	+	0.195593i
$944$	8.64086e8	−	8.22123e9i	0.0334314	−	0.318079i
$945$	3.81270e9	−	1.17343e10i	0.146968	−	0.452319i
$946$	1.55720e10	−	4.79257e10i	0.598033	−	1.84056i
$947$	1.93485e9	−	1.84089e10i	0.0740325	−	0.704372i	−0.893058	−	0.449941i	$-0.851445\pi$
$947$	1.93485e9	−	1.84089e10i	0.0740325	−	0.704372i	0.967091	−	0.254431i	$-0.0818883\pi$
$948$	−5.10093e8	−	5.66516e8i	−0.0194455	−	0.0215965i
$949$	−1.39704e10	+	1.55157e10i	−0.530613	+	0.589305i
$950$	9.00437e7	+	8.56708e8i	0.00340738	+	0.0324191i
$951$	1.18740e10	+	2.52389e9i	0.447676	+	0.0951564i
$952$	5.36327e9	−	2.38788e9i	0.201465	−	0.0896982i
$953$	−2.99960e10	−	2.17934e10i	−1.12263	−	0.815641i	−0.138027	−	0.990428i	$-0.544076\pi$
$953$	−2.99960e10	−	2.17934e10i	−1.12263	−	0.815641i	−0.984606	+	0.174788i	$0.944076\pi$
$954$	7.27327e9	+	3.23827e9i	0.271213	+	0.120752i
$955$	−4.95933e9	−	8.58982e9i	−0.184252	−	0.319133i
$956$	−2.53434e9	+	4.38961e9i	−0.0938129	+	0.162489i
$957$	−5.00180e10	+	3.63402e10i	−1.84474	+	1.34028i
$958$	−2.73743e10	+	5.81860e9i	−1.00592	+	0.213815i
$959$	−1.93138e9	−	5.94417e9i	−0.0707135	−	0.217634i
$960$	−2.60132e9			−0.0948953
$961$	1.04925e10	−	2.54333e10i	0.381372	−	0.924422i
$962$	5.25112e9			0.190169
$963$	2.07451e9	+	6.38468e9i	0.0748554	+	0.230381i
$964$	1.99386e10	−	4.23808e9i	0.716844	−	0.152370i
$965$	−2.59144e10	+	1.88279e10i	−0.928314	+	0.674460i
$966$	−5.15470e8	+	8.92820e8i	−0.0183985	+	0.0318672i
$967$	−9.81881e8	−	1.70067e9i	−0.0349193	−	0.0604821i	0.848038	−	0.529936i	$-0.177784\pi$
$967$	−9.81881e8	−	1.70067e9i	−0.0349193	−	0.0604821i	−0.882957	+	0.469454i	$0.844451\pi$
$968$	−1.47385e10	−	6.56199e9i	−0.522262	−	0.232526i
$969$	3.79292e10	+	2.75571e10i	1.33918	+	0.972973i
$970$	−2.46544e10	+	1.09769e10i	−0.867349	+	0.386169i
$971$	1.44187e10	+	3.06478e9i	0.505427	+	0.107432i	0.453566	−	0.891223i	$-0.350152\pi$
$971$	1.44187e10	+	3.06478e9i	0.505427	+	0.107432i	0.0518605	+	0.998654i	$0.483485\pi$
$972$	−1.20303e9	−	1.14461e10i	−0.0420190	−	0.399785i
$973$	−2.70012e9	+	2.99879e9i	−0.0939698	+	0.104364i
$974$	1.77582e10	+	1.97225e10i	0.615805	+	0.683921i
$975$	−3.75609e7	+	3.57368e8i	−0.00129783	+	0.0123481i
$976$	−3.77222e9	+	1.16097e10i	−0.129874	+	0.399711i
$977$	1.28884e10	−	3.96665e10i	0.442149	−	1.36079i	−0.443432	−	0.896308i	$-0.646239\pi$
$977$	1.28884e10	−	3.96665e10i	0.442149	−	1.36079i	0.885580	−	0.464486i	$-0.153761\pi$
$978$	1.57879e9	−	1.50212e10i	0.0539684	−	0.513475i
$979$	−1.39446e10	−	1.54870e10i	−0.474970	−	0.527507i
$980$	8.11141e9	−	9.00863e9i	0.275299	−	0.305751i
$981$	4.31956e8	+	4.10978e9i	0.0146082	+	0.138988i
$982$	9.66492e9	+	2.05434e9i	0.325693	+	0.0692281i
$983$	1.50110e10	−	6.68335e9i	0.504050	−	0.224418i	−0.138927	−	0.990303i	$-0.544365\pi$
$983$	1.50110e10	−	6.68335e9i	0.504050	−	0.224418i	0.642978	+	0.765885i	$0.277699\pi$
$984$	−1.05233e10	−	7.64565e9i	−0.352104	−	0.255818i
$985$	−3.24576e9	−	1.44510e9i	−0.108215	−	0.0481806i
$986$	2.87575e10	+	4.98095e10i	0.955394	+	1.65479i
$987$	−5.76769e7	+	9.98993e7i	−0.00190938	+	0.00330714i
$988$	−1.05103e10	+	7.63620e9i	−0.346711	+	0.251900i
$989$	8.05217e9	−	1.71154e9i	0.264683	−	0.0562601i
$990$	4.82307e9	+	1.48439e10i	0.157979	+	0.486210i
$991$	2.71709e10			0.886841			0.443421	−	0.896314i	$-0.353765\pi$
$991$	2.71709e10			0.886841			0.443421	+	0.896314i	$0.353765\pi$
$992$	4.51706e9	−	3.02284e9i	0.146915	−	0.0983162i
$993$	1.38189e10			0.447869
$994$	−2.52668e9	−	7.77632e9i	−0.0816015	−	0.251144i
$995$	−3.30290e10	+	7.02053e9i	−1.06295	+	0.225938i
$996$	−5.19602e9	+	3.77513e9i	−0.166634	+	0.121066i
$997$	5.98991e8	−	1.03748e9i	0.0191420	−	0.0331549i	−0.856296	−	0.516486i	$-0.827240\pi$
$997$	5.98991e8	−	1.03748e9i	0.0191420	−	0.0331549i	0.875438	+	0.483331i	$0.160573\pi$
$998$	3.13979e9	+	5.43828e9i	0.0999871	+	0.173183i
$999$	1.50174e10	+	6.68619e9i	0.476559	+	0.212178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.g.b.7.3	✓	72
31.9	even	15	inner	62.8.g.b.9.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.g.b.7.3	✓	72	1.1	even	1	trivial
62.8.g.b.9.3	yes	72	31.9	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.47214 - 7.60845i) q^{2} +(-34.2192 + 7.27353i) q^{3} +(-51.7771 + 37.6183i) q^{4} +(141.827 - 245.651i) q^{5} +(139.935 + 242.374i) q^{6} +(360.576 + 160.539i) q^{7} +(414.217 + 300.946i) q^{8} +(-879.871 + 391.744i) q^{9} +(-2219.64 - 471.799i) q^{10} +(746.464 + 7102.13i) q^{11} +(1498.16 - 1663.87i) q^{12} +(2944.45 + 3270.14i) q^{13} +(330.059 - 3140.30i) q^{14} +(-3066.45 + 9437.57i) q^{15} +(1265.73 - 3895.53i) q^{16} +(3036.67 - 28892.0i) q^{17} +(5155.73 + 5726.01i) q^{18} +(30867.2 - 34281.5i) q^{19} +(1897.59 + 18054.4i) q^{20} +(-13506.3 - 2870.86i) q^{21} +(52190.8 - 23236.9i) q^{22} +(7550.37 + 5485.66i) q^{23} +(-16363.1 - 7285.33i) q^{24} +(-1167.11 - 2021.50i) q^{25} +(17601.6 - 30486.9i) q^{26} +(89156.6 - 64776.0i) q^{27} +(-24708.8 + 5252.01i) q^{28} +(-76473.5 - 235361. i) q^{29} +79386.0 q^{30} +(-137850. + 92249.9i) q^{31} -32768.0 q^{32} +(-77200.9 - 237600. i) q^{33} +(-227330. + 48320.6i) q^{34} +(90575.8 - 65807.2i) q^{35} +(30820.5 - 53382.6i) q^{36} +(74583.0 + 129181. i) q^{37} +(-337137. - 150103. i) q^{38} +(-124542. - 90485.1i) q^{39} +(132675. - 59070.6i) q^{40} +(710337. + 150987. i) q^{41} +(11546.7 + 109859. i) q^{42} +(590213. - 655498. i) q^{43} +(-305819. - 339647. i) q^{44} +(-28556.9 + 271701. i) q^{45} +(23071.9 - 71007.9i) q^{46} +(2581.56 - 7945.22i) q^{47} +(-14978.2 + 142508. i) q^{48} +(-446815. - 496239. i) q^{49} +(-12495.2 + 13877.3i) q^{50} +(106234. + 1.01075e6i) q^{51} +(-275472. - 58553.3i) q^{52} +(943954. - 420275. i) q^{53} +(-713253. - 518208. i) q^{54} +(1.85051e6 + 823902. i) q^{55} +(101043. + 175012. i) q^{56} +(-806905. + 1.39760e6i) q^{57} +(-1.60168e6 + 1.16369e6i) q^{58} +(1.97409e6 - 419606. i) q^{59} +(-196253. - 604005. i) q^{60} -2.98026e6 q^{61} +(1.04266e6 + 820770. i) q^{62} -380151. q^{63} +(81007.0 + 249314. i) q^{64} +(1.22091e6 - 259513. i) q^{65} +(-1.61692e6 + 1.17476e6i) q^{66} +(-231103. + 400282. i) q^{67} +(929636. + 1.61018e6i) q^{68} +(-298268. - 132797. i) q^{69} +(-724606. - 526457. i) q^{70} +(2.36560e6 - 1.05323e6i) q^{71} +(-482351. - 102527. i) q^{72} +(495953. + 4.71868e6i) q^{73} +(798492. - 886815. i) q^{74} +(54641.1 + 60685.1i) q^{75} +(-308604. + 2.93617e6i) q^{76} +(-871010. + 2.68069e6i) q^{77} +(-380567. + 1.17126e6i) q^{78} +(35589.9 - 338615. i) q^{79} +(-777425. - 863418. i) q^{80} +(-1.17027e6 + 1.29972e6i) q^{81} +(-607274. - 5.77782e6i) q^{82} +(-2.80589e6 - 596411. i) q^{83} +(807315. - 359440. i) q^{84} +(-6.66667e6 - 4.84362e6i) q^{85} +(-6.44641e6 - 2.87013e6i) q^{86} +(4.32877e6 + 7.49765e6i) q^{87} +(-1.82816e6 + 3.16647e6i) q^{88} +(-2.36090e6 + 1.71530e6i) q^{89} +(2.13782e6 - 454408. i) q^{90} +(536712. + 1.65183e6i) q^{91} -597297. q^{92} +(4.04614e6 - 4.15938e6i) q^{93} -66832.8 q^{94} +(-4.04349e6 - 1.24446e7i) q^{95} +(1.12130e6 - 238339. i) q^{96} +(9.62154e6 - 6.99046e6i) q^{97} +(-2.67102e6 + 4.62634e6i) q^{98} +(-3.43901e6 - 5.95654e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 144 q^{2} + 53 q^{3} - 1152 q^{4} + 97 q^{5} + 656 q^{6} - 3516 q^{7} + 9216 q^{8} + 4100 q^{9} - 3616 q^{10} - 6385 q^{11} + 3392 q^{12} - 7108 q^{13} - 25872 q^{14} - 37456 q^{15} - 73728 q^{16}+ \cdots + 20676441 q^{99}+O(q^{100}) \) 72 * q + 144 * q^2 + 53 * q^3 - 1152 * q^4 + 97 * q^5 + 656 * q^6 - 3516 * q^7 + 9216 * q^8 + 4100 * q^9 - 3616 * q^10 - 6385 * q^11 + 3392 * q^12 - 7108 * q^13 - 25872 * q^14 - 37456 * q^15 - 73728 * q^16 - 8376 * q^17 - 70280 * q^18 - 49913 * q^19 + 2048 * q^20 + 323383 * q^21 - 67960 * q^22 - 345829 * q^23 + 6144 * q^24 - 372591 * q^25 + 227584 * q^26 - 71038 * q^27 - 142784 * q^28 - 324657 * q^29 - 926672 * q^30 - 1450215 * q^31 - 2359296 * q^32 + 83140 * q^33 + 542768 * q^34 + 220312 * q^35 - 1649280 * q^36 - 1077276 * q^37 + 242544 * q^38 - 2082538 * q^39 - 16384 * q^40 - 561831 * q^41 + 2046856 * q^42 + 541504 * q^43 + 69440 * q^44 - 3560198 * q^45 - 1210168 * q^46 + 701593 * q^47 - 49152 * q^48 + 2939863 * q^49 - 2047672 * q^50 + 2343644 * q^51 - 454912 * q^52 + 5870237 * q^53 + 568304 * q^54 + 4095901 * q^55 + 358912 * q^56 - 2524936 * q^57 - 4505944 * q^58 + 3564614 * q^59 - 2397184 * q^60 + 6621588 * q^61 - 6588440 * q^62 + 37503466 * q^63 - 4718592 * q^64 + 2623034 * q^65 - 1265000 * q^66 + 6997086 * q^67 + 1117376 * q^68 + 18122809 * q^69 - 1762496 * q^70 + 17340555 * q^71 - 4497920 * q^72 + 893895 * q^73 - 7099272 * q^74 - 4691620 * q^75 + 11121408 * q^76 - 12966527 * q^77 - 31068816 * q^78 + 16057037 * q^79 - 2510848 * q^80 + 17531660 * q^81 + 31965608 * q^82 + 35981510 * q^83 + 13155712 * q^84 + 8693293 * q^85 - 8631272 * q^86 - 7183623 * q^87 + 263680 * q^88 - 23416374 * q^89 - 76756056 * q^90 + 13467668 * q^91 + 24903424 * q^92 - 88528776 * q^93 - 19578704 * q^94 - 9538258 * q^95 - 1736704 * q^96 - 11254011 * q^97 + 30592696 * q^98 + 20676441 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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