LMFDB - Embedded newform 91.8.h.a.16.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(16,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.18
Character	$\chi$	$=$	91.16
Dual form			91.8.h.a.74.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.4816 q^{2} +(28.8130 - 49.9056i) q^{3} +3.82665 q^{4} +(-60.6077 + 104.976i) q^{5} +(-330.819 + 572.995i) q^{6} +(720.487 + 551.762i) q^{7} +1425.71 q^{8} +(-566.877 - 981.860i) q^{9} +O(q^{10})$	\(q-11.4816 q^{2} +(28.8130 - 49.9056i) q^{3} +3.82665 q^{4} +(-60.6077 + 104.976i) q^{5} +(-330.819 + 572.995i) q^{6} +(720.487 + 551.762i) q^{7} +1425.71 q^{8} +(-566.877 - 981.860i) q^{9} +(695.873 - 1205.29i) q^{10} +(2272.19 - 3935.55i) q^{11} +(110.257 - 190.971i) q^{12} +(-7093.76 + 3525.21i) q^{13} +(-8272.33 - 6335.10i) q^{14} +(3492.58 + 6049.33i) q^{15} -16859.2 q^{16} -35880.0 q^{17} +(6508.65 + 11273.3i) q^{18} +(-6796.26 - 11771.5i) q^{19} +(-231.925 + 401.705i) q^{20} +(48295.4 - 20058.4i) q^{21} +(-26088.3 + 45186.3i) q^{22} -54443.7 q^{23} +(41078.9 - 71150.7i) q^{24} +(31715.9 + 54933.6i) q^{25} +(81447.6 - 40474.9i) q^{26} +60694.3 q^{27} +(2757.05 + 2111.40i) q^{28} +(2178.76 + 3773.73i) q^{29} +(-40100.3 - 69455.8i) q^{30} +(21833.7 + 37817.1i) q^{31} +11079.5 q^{32} +(-130937. - 226790. i) q^{33} +411960. q^{34} +(-101589. + 42192.6i) q^{35} +(-2169.24 - 3757.23i) q^{36} -139256. q^{37} +(78031.7 + 135155. i) q^{38} +(-28465.0 + 455590. i) q^{39} +(-86408.8 + 149664. i) q^{40} +(270441. + 468418. i) q^{41} +(-554507. + 230302. i) q^{42} +(-173280. + 300130. i) q^{43} +(8694.87 - 15059.9i) q^{44} +137429. q^{45} +625099. q^{46} +(-123457. + 213834. i) q^{47} +(-485763. + 841366. i) q^{48} +(214660. + 795075. i) q^{49} +(-364149. - 630724. i) q^{50} +(-1.03381e6 + 1.79061e6i) q^{51} +(-27145.3 + 13489.7i) q^{52} +(82979.0 + 143724. i) q^{53} -696866. q^{54} +(275424. + 477049. i) q^{55} +(1.02720e6 + 786651. i) q^{56} -783282. q^{57} +(-25015.6 - 43328.4i) q^{58} -569138. q^{59} +(13364.9 + 23148.7i) q^{60} +(-767660. - 1.32963e6i) q^{61} +(-250686. - 434200. i) q^{62} +(133326. - 1.02020e6i) q^{63} +2.03076e6 q^{64} +(59875.8 - 958327. i) q^{65} +(1.50336e6 + 2.60390e6i) q^{66} +(-2.18573e6 + 3.78580e6i) q^{67} -137300. q^{68} +(-1.56869e6 + 2.71704e6i) q^{69} +(1.16640e6 - 484437. i) q^{70} +(-1.65719e6 + 2.87034e6i) q^{71} +(-808200. - 1.39984e6i) q^{72} +(-2.44581e6 - 4.23626e6i) q^{73} +1.59887e6 q^{74} +3.65532e6 q^{75} +(-26006.9 - 45045.2i) q^{76} +(3.80857e6 - 1.58180e6i) q^{77} +(326824. - 5.23089e6i) q^{78} +(-1.28561e6 + 2.22674e6i) q^{79} +(1.02180e6 - 1.76980e6i) q^{80} +(2.98855e6 - 5.17631e6i) q^{81} +(-3.10509e6 - 5.37818e6i) q^{82} +6.19637e6 q^{83} +(184810. - 76756.4i) q^{84} +(2.17461e6 - 3.76653e6i) q^{85} +(1.98953e6 - 3.44597e6i) q^{86} +251107. q^{87} +(3.23947e6 - 5.61093e6i) q^{88} -480670. q^{89} -1.57790e6 q^{90} +(-7.05604e6 - 1.37420e6i) q^{91} -208337. q^{92} +2.51638e6 q^{93} +(1.41748e6 - 2.45515e6i) q^{94} +1.64762e6 q^{95} +(319233. - 552928. i) q^{96} +(-8.79753e6 + 1.52378e7i) q^{97} +(-2.46464e6 - 9.12872e6i) q^{98} -5.15221e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) $ 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−11.4816			−1.01484			−0.507419	−	0.861700i	$-0.669400\pi$
$2$	−11.4816			−1.01484			−0.507419	+	0.861700i	$0.669400\pi$
$3$	28.8130	−	49.9056i	0.616118	−	1.06715i	−0.374069	−	0.927401i	$-0.622038\pi$
$3$	28.8130	−	49.9056i	0.616118	−	1.06715i	0.990187	−	0.139747i	$-0.0446290\pi$
$4$	3.82665			0.0298957
$5$	−60.6077	+	104.976i	−0.216837	+	0.375572i	−0.953839	−	0.300318i	$-0.902907\pi$
$5$	−60.6077	+	104.976i	−0.216837	+	0.375572i	0.737002	+	0.675890i	$0.236241\pi$
$6$	−330.819	+	572.995i	−0.625260	+	1.08298i
$7$	720.487	+	551.762i	0.793931	+	0.608007i
$7$	720.487	+	551.762i	0.793931	+	0.608007i
$8$	1425.71			0.984498
$9$	−566.877	−	981.860i	−0.259203	−	0.448953i
$10$	695.873	−	1205.29i	0.220054	−	0.381145i
$11$	2272.19	−	3935.55i	0.514719	−	0.891519i	−0.485136	−	0.874439i	$-0.661230\pi$
$11$	2272.19	−	3935.55i	0.514719	−	0.891519i	0.999854	−	0.0170798i	$-0.00543694\pi$
$12$	110.257	−	190.971i	0.0184193	−	0.0319031i
$13$	−7093.76	+	3525.21i	−0.895519	+	0.445023i
$13$	−7093.76	+	3525.21i	−0.895519	+	0.445023i
$14$	−8272.33	−	6335.10i	−0.805712	−	0.617029i
$15$	3492.58	+	6049.33i	0.267194	+	0.462794i
$16$	−16859.2			−1.02900
$17$	−35880.0			−1.77126			−0.885629	−	0.464394i	$-0.846272\pi$
$17$	−35880.0			−1.77126			−0.885629	+	0.464394i	$0.846272\pi$
$18$	6508.65	+	11273.3i	0.263049	+	0.455614i
$19$	−6796.26	−	11771.5i	−0.227317	−	0.393725i	0.729695	−	0.683773i	$-0.239662\pi$
$19$	−6796.26	−	11771.5i	−0.227317	−	0.393725i	−0.957012	+	0.290048i	$0.906329\pi$
$20$	−231.925	+	401.705i	−0.00648249	+	0.0112280i
$21$	48295.4	−	20058.4i	1.13799	−	0.472638i
$22$	−26088.3	+	45186.3i	−0.522356	+	0.904747i
$23$	−54443.7			−0.933039			−0.466520	−	0.884511i	$-0.654492\pi$
$23$	−54443.7			−0.933039			−0.466520	+	0.884511i	$0.654492\pi$
$24$	41078.9	−	71150.7i	0.606567	−	1.05061i
$25$	31715.9	+	54933.6i	0.405964	+	0.703150i
$26$	81447.6	−	40474.9i	0.908806	−	0.451627i
$27$	60694.3			0.593437
$28$	2757.05	+	2111.40i	0.0237351	+	0.0181768i
$29$	2178.76	+	3773.73i	0.0165889	+	0.0287328i	0.874201	−	0.485565i	$-0.161386\pi$
$29$	2178.76	+	3773.73i	0.0165889	+	0.0287328i	−0.857612	+	0.514298i	$0.828053\pi$
$30$	−40100.3	−	69455.8i	−0.271159	−	0.469661i
$31$	21833.7	+	37817.1i	0.131632	+	0.227994i	0.924306	−	0.381653i	$-0.124645\pi$
$31$	21833.7	+	37817.1i	0.131632	+	0.227994i	−0.792674	+	0.609646i	$0.791312\pi$
$32$	11079.5			0.0597715
$33$	−130937.	−	226790.i	−0.634255	−	1.09856i
$34$	411960.			1.79754
$35$	−101589.	+	42192.6i	−0.400504	+	0.166340i
$36$	−2169.24	−	3757.23i	−0.00774906	−	0.0134218i
$37$	−139256.			−0.451967			−0.225983	−	0.974131i	$-0.572560\pi$
$37$	−139256.			−0.451967			−0.225983	+	0.974131i	$0.572560\pi$
$38$	78031.7	+	135155.i	0.230690	+	0.399567i
$39$	−28465.0	+	455590.i	−0.0768397	+	1.22984i
$40$	−86408.8	+	149664.i	−0.213476	+	0.369751i
$41$	270441.	+	468418.i	0.612815	+	1.06143i	0.990764	+	0.135600i	$0.0432962\pi$
$41$	270441.	+	468418.i	0.612815	+	1.06143i	−0.377949	+	0.925826i	$0.623370\pi$
$42$	−554507.	+	230302.i	−1.15487	+	0.479651i
$43$	−173280.	+	300130.i	−0.332361	+	0.575666i	−0.982974	−	0.183743i	$-0.941178\pi$
$43$	−173280.	+	300130.i	−0.332361	+	0.575666i	0.650613	+	0.759409i	$0.274512\pi$
$44$	8694.87	−	15059.9i	0.0153879	−	0.0266526i
$45$	137429.			0.224819
$46$	625099.			0.946884
$47$	−123457.	+	213834.i	−0.173449	+	0.300423i	−0.939624	−	0.342210i	$-0.888825\pi$
$47$	−123457.	+	213834.i	−0.173449	+	0.300423i	0.766174	+	0.642633i	$0.222158\pi$
$48$	−485763.	+	841366.i	−0.633987	+	1.09810i
$49$	214660.	+	795075.i	0.260654	+	0.965432i
$50$	−364149.	−	630724.i	−0.411987	−	0.713583i
$51$	−1.03381e6	+	1.79061e6i	−1.09130	+	1.89019i
$52$	−27145.3	+	13489.7i	−0.0267722	+	0.0133043i
$53$	82979.0	+	143724.i	0.0765601	+	0.132606i	0.901764	−	0.432229i	$-0.142273\pi$
$53$	82979.0	+	143724.i	0.0765601	+	0.132606i	−0.825204	+	0.564835i	$0.808940\pi$
$54$	−696866.			−0.602243
$55$	275424.	+	477049.i	0.223220	+	0.386628i
$56$	1.02720e6	+	786651.i	0.781624	+	0.598582i
$57$	−783282.			−0.560217
$58$	−25015.6	−	43328.4i	−0.0168350	−	0.0291591i
$59$	−569138.			−0.360774			−0.180387	−	0.983596i	$-0.557735\pi$
$59$	−569138.			−0.360774			−0.180387	+	0.983596i	$0.557735\pi$
$60$	13364.9	+	23148.7i	0.00798796	+	0.0138355i
$61$	−767660.	−	1.32963e6i	−0.433027	−	0.750024i	0.564106	−	0.825703i	$-0.309221\pi$
$61$	−767660.	−	1.32963e6i	−0.433027	−	0.750024i	−0.997132	+	0.0756786i	$0.975888\pi$
$62$	−250686.	−	434200.i	−0.133585	−	0.231376i
$63$	133326.	−	1.02020e6i	0.0671772	−	0.514035i
$64$	2.03076e6			0.968344
$65$	59875.8	−	958327.i	0.0270430	−	0.432830i
$66$	1.50336e6	+	2.60390e6i	0.643666	+	1.11486i
$67$	−2.18573e6	+	3.78580e6i	−0.887841	+	1.53779i	−0.0454181	+	0.998968i	$0.514462\pi$
$67$	−2.18573e6	+	3.78580e6i	−0.887841	+	1.53779i	−0.842423	+	0.538817i	$0.818871\pi$
$68$	−137300.			−0.0529530
$69$	−1.56869e6	+	2.71704e6i	−0.574862	+	0.995691i
$70$	1.16640e6	−	484437.i	0.406447	−	0.168809i
$71$	−1.65719e6	+	2.87034e6i	−0.549501	+	0.951763i	0.448808	+	0.893628i	$0.351849\pi$
$71$	−1.65719e6	+	2.87034e6i	−0.549501	+	0.951763i	−0.998309	+	0.0581348i	$0.981485\pi$
$72$	−808200.	−	1.39984e6i	−0.255185	−	0.441994i
$73$	−2.44581e6	−	4.23626e6i	−0.735855	−	1.27454i	−0.954347	−	0.298699i	$-0.903447\pi$
$73$	−2.44581e6	−	4.23626e6i	−0.735855	−	1.27454i	0.218493	−	0.975839i	$-0.429886\pi$
$74$	1.59887e6			0.458673
$75$	3.65532e6			1.00049
$76$	−26006.9	−	45045.2i	−0.00679580	−	0.0117707i
$77$	3.80857e6	−	1.58180e6i	0.950701	−	0.394852i
$78$	326824.	−	5.23089e6i	0.0779798	−	1.24809i
$79$	−1.28561e6	+	2.22674e6i	−0.293368	+	0.508129i	−0.974604	−	0.223935i	$-0.928110\pi$
$79$	−1.28561e6	+	2.22674e6i	−0.293368	+	0.508129i	0.681236	+	0.732064i	$0.261443\pi$
$80$	1.02180e6	−	1.76980e6i	0.223126	−	0.386465i
$81$	2.98855e6	−	5.17631e6i	0.624831	−	1.08224i
$82$	−3.10509e6	−	5.37818e6i	−0.621908	−	1.07718i
$83$	6.19637e6			1.18950			0.594750	−	0.803911i	$-0.297251\pi$
$83$	6.19637e6			1.18950			0.594750	+	0.803911i	$0.297251\pi$
$84$	184810.	−	76756.4i	0.0340210	−	0.0141298i
$85$	2.17461e6	−	3.76653e6i	0.384074	−	0.665236i
$86$	1.98953e6	−	3.44597e6i	0.337292	−	0.584207i
$87$	251107.			0.0408828
$88$	3.23947e6	−	5.61093e6i	0.506740	−	0.877699i
$89$	−480670.			−0.0722739			−0.0361370	−	0.999347i	$-0.511505\pi$
$89$	−480670.			−0.0722739			−0.0361370	+	0.999347i	$0.511505\pi$
$90$	−1.57790e6			−0.228155
$91$	−7.05604e6	−	1.37420e6i	−0.981558	−	0.191164i
$92$	−208337.			−0.0278939
$93$	2.51638e6			0.324404
$94$	1.41748e6	−	2.45515e6i	0.176023	−	0.304881i
$95$	1.64762e6			0.197163
$96$	319233.	−	552928.i	0.0368263	−	0.0637851i
$97$	−8.79753e6	+	1.52378e7i	−0.978722	+	1.69520i	−0.311663	+	0.950193i	$0.600886\pi$
$97$	−8.79753e6	+	1.52378e7i	−0.978722	+	1.69520i	−0.667060	+	0.745004i	$0.732447\pi$
$98$	−2.46464e6	−	9.12872e6i	−0.264522	−	0.979757i
$99$	−5.15221e6			−0.533667
$100$	121366.	+	210211.i	0.0121366	+	0.0210211i
$101$	1.02867e6	−	1.78172e6i	0.0993466	−	0.172073i	−0.812068	−	0.583563i	$-0.801658\pi$
$101$	1.02867e6	−	1.78172e6i	0.0993466	−	0.172073i	0.911414	+	0.411490i	$0.134991\pi$
$102$	1.18698e7	−	2.05591e7i	1.10750	−	1.91824i
$103$	−5.57832e6	+	9.66193e6i	−0.503006	+	0.871231i	0.496988	+	0.867757i	$0.334439\pi$
$103$	−5.57832e6	+	9.66193e6i	−0.503006	+	0.871231i	−0.999994	+	0.00347413i	$0.998894\pi$
$104$	−1.01136e7	+	5.02591e6i	−0.881637	+	0.438125i
$105$	−821431.	+	6.28554e6i	−0.0692482	+	0.529883i
$106$	−952730.	−	1.65018e6i	−0.0776961	−	0.134574i
$107$	7.40674e6			0.584499			0.292250	−	0.956342i	$-0.405596\pi$
$107$	7.40674e6			0.584499			0.292250	+	0.956342i	$0.405596\pi$
$108$	232256.			0.0177412
$109$	−601953.	−	1.04261e6i	−0.0445215	−	0.0771135i	0.842906	−	0.538061i	$-0.180843\pi$
$109$	−601953.	−	1.04261e6i	−0.0445215	−	0.0771135i	−0.887427	+	0.460947i	$0.847510\pi$
$110$	−3.16231e6	−	5.47728e6i	−0.226532	−	0.392365i
$111$	−4.01237e6	+	6.94963e6i	−0.278465	+	0.482316i
$112$	−1.21468e7	−	9.30225e6i	−0.816957	−	0.625641i
$113$	−8.05543e6	+	1.39524e7i	−0.525187	+	0.909651i	0.474383	+	0.880319i	$0.342671\pi$
$113$	−8.05543e6	+	1.39524e7i	−0.525187	+	0.909651i	−0.999570	+	0.0293318i	$0.990662\pi$
$114$	8.99331e6			0.568529
$115$	3.29971e6	−	5.71526e6i	0.202317	−	0.350424i
$116$	8337.36	+	14440.7i	0.000495936	+	0.000858987i
$117$	7.48255e6	+	4.96672e6i	0.431916	+	0.286694i
$118$	6.53461e6			0.366128
$119$	−2.58511e7	−	1.97972e7i	−1.40626	−	1.07694i
$120$	4.97939e6	+	8.62456e6i	0.263052	+	0.455620i
$121$	−582092.	−	1.00821e6i	−0.0298705	−	0.0517372i
$122$	8.81395e6	+	1.52662e7i	0.439452	+	0.761153i
$123$	3.11689e7			1.51027
$124$	83550.0	+	144713.i	0.00393523	+	0.00681603i
$125$	−1.71589e7			−0.785785
$126$	−1.53079e6	+	1.17135e7i	−0.0681739	+	0.521662i
$127$	278160.	+	481787.i	0.0120499	+	0.0208710i	0.871987	−	0.489528i	$-0.162831\pi$
$127$	278160.	+	481787.i	0.0120499	+	0.0208710i	−0.859938	+	0.510399i	$0.829498\pi$
$128$	−2.47345e7			−1.04248
$129$	9.98545e6	+	1.72953e7i	0.409547	+	0.709356i
$130$	−687469.	+	1.10031e7i	−0.0274442	+	0.439252i
$131$	5.21123e6	−	9.02612e6i	0.202531	−	0.350793i	−0.746812	−	0.665035i	$-0.768417\pi$
$131$	5.21123e6	−	9.02612e6i	0.202531	−	0.350793i	0.949343	+	0.314241i	$0.101750\pi$
$132$	−501050.	−	867844.i	−0.0189615	−	0.0328423i
$133$	1.59843e6	−	1.22311e7i	0.0589133	−	0.450801i
$134$	2.50957e7	−	4.34669e7i	0.901014	−	1.56060i
$135$	−3.67855e6	+	6.37143e6i	−0.128679	+	0.222879i
$136$	−5.11544e7			−1.74380
$137$	4.76750e7			1.58405			0.792025	−	0.610489i	$-0.209027\pi$
$137$	4.76750e7			1.58405			0.792025	+	0.610489i	$0.209027\pi$
$138$	1.80110e7	−	3.11959e7i	0.583392	−	1.01046i
$139$	−1.18392e7	+	2.05061e7i	−0.373913	+	0.647637i	−0.990164	−	0.139913i	$-0.955318\pi$
$139$	−1.18392e7	+	2.05061e7i	−0.373913	+	0.647637i	0.616250	+	0.787550i	$0.288651\pi$
$140$	−388744.	+	161456.i	−0.0119734	+	0.00497286i
$141$	7.11432e6	+	1.23224e7i	0.213731	+	0.370192i
$142$	1.90272e7	−	3.29560e7i	0.557654	−	0.965885i
$143$	−2.24475e6	+	3.59277e7i	−0.0641936	+	1.02743i
$144$	9.55708e6	+	1.65533e7i	0.266721	+	0.461974i
$145$	−528200.			−0.0143883
$146$	2.80817e7	+	4.86390e7i	0.746773	+	1.29345i
$147$	4.58637e7	+	1.21958e7i	1.19085	+	0.316664i
$148$	−532882.			−0.0135119
$149$	−2.45439e7	−	4.25112e7i	−0.607843	−	1.05281i	−0.991595	−	0.129378i	$-0.958702\pi$
$149$	−2.45439e7	−	4.25112e7i	−0.607843	−	1.05281i	0.383753	−	0.923436i	$-0.374632\pi$
$150$	−4.19688e7			−1.01533
$151$	2.13301e7	+	3.69449e7i	0.504167	+	0.873243i	0.999988	+	0.00481821i	$0.00153369\pi$
$151$	2.13301e7	+	3.69449e7i	0.504167	+	0.873243i	−0.495822	+	0.868424i	$0.665133\pi$
$152$	−9.68946e6	−	1.67826e7i	−0.223793	−	0.387621i
$153$	2.03396e7	+	3.52292e7i	0.459116	+	0.795211i
$154$	−4.37284e7	+	1.81616e7i	−0.964807	+	0.400711i
$155$	−5.29317e6			−0.114171
$156$	−108926.	+	1.74338e6i	−0.00229718	+	0.0367669i
$157$	−2.58548e7	−	4.47819e7i	−0.533203	−	0.923535i	−0.999248	−	0.0387741i	$-0.987655\pi$
$157$	−2.58548e7	−	4.47819e7i	−0.533203	−	0.923535i	0.466045	−	0.884761i	$-0.345679\pi$
$158$	1.47608e7	−	2.55664e7i	0.297721	−	0.515668i
$159$	9.56349e6			0.188680
$160$	−671502.	+	1.16308e6i	−0.0129607	+	0.0224485i
$161$	−3.92260e7	−	3.00400e7i	−0.740769	−	0.567295i
$162$	−3.43132e7	+	5.94322e7i	−0.634102	+	1.09830i
$163$	−3.11802e7	−	5.40057e7i	−0.563926	−	0.976749i	−0.997149	−	0.0754619i	$-0.975957\pi$
$163$	−3.11802e7	−	5.40057e7i	−0.563926	−	0.976749i	0.433222	−	0.901287i	$-0.357376\pi$
$164$	1.03488e6	+	1.79247e6i	0.0183205	+	0.0317321i
$165$	3.17432e7			0.550119
$166$	−7.11442e7			−1.20715
$167$	1.80153e7	+	3.12035e7i	0.299319	+	0.518436i	0.975980	−	0.217858i	$-0.0699071\pi$
$167$	1.80153e7	+	3.12035e7i	0.299319	+	0.518436i	−0.676661	+	0.736295i	$0.736574\pi$
$168$	6.88550e7	−	2.85974e7i	1.12035	−	0.465311i
$169$	3.78944e7	−	5.00139e7i	0.603908	−	0.797054i
$170$	−2.49679e7	+	4.32457e7i	−0.389773	+	0.675106i
$171$	−7.70529e6	+	1.33459e7i	−0.117843	+	0.204109i
$172$	−663083.	+	1.14849e6i	−0.00993616	+	0.0172099i
$173$	2.87877e6	+	4.98617e6i	0.0422713	+	0.0732160i	0.886387	−	0.462945i	$-0.153207\pi$
$173$	2.87877e6	+	4.98617e6i	0.0422713	+	0.0732160i	−0.844116	+	0.536161i	$0.819874\pi$
$174$	−2.88310e6			−0.0414895
$175$	−7.45936e6	+	5.70785e7i	−0.105213	+	0.805081i
$176$	−3.83072e7	+	6.63500e7i	−0.529646	+	0.917375i
$177$	−1.63986e7	+	2.84032e7i	−0.222280	+	0.385000i
$178$	5.51885e6			0.0733463
$179$	−1.88048e7	+	3.25708e7i	−0.245065	+	0.424466i	−0.962150	−	0.272520i	$-0.912143\pi$
$179$	−1.88048e7	+	3.25708e7i	−0.245065	+	0.424466i	0.717085	+	0.696986i	$0.245476\pi$
$180$	525891.			0.00672113
$181$	1.13532e8			1.42313			0.711565	−	0.702620i	$-0.247987\pi$
$181$	1.13532e8			1.42313			0.711565	+	0.702620i	$0.247987\pi$
$182$	8.10145e7	+	1.57780e7i	0.996122	+	0.194000i
$183$	−8.84743e7			−1.06718
$184$	−7.76207e7			−0.918576
$185$	8.43997e6	−	1.46185e7i	0.0980031	−	0.169746i
$186$	−2.88920e7			−0.329217
$187$	−8.15262e7	+	1.41208e8i	−0.911699	+	1.57911i
$188$	−472426.	+	818266.i	−0.00518539	+	0.00898136i
$189$	4.37295e7	+	3.34888e7i	0.471148	+	0.360814i
$190$	−1.89173e7			−0.200088
$191$	−3.72652e7	−	6.45452e7i	−0.386978	−	0.670266i	0.605063	−	0.796177i	$-0.293148\pi$
$191$	−3.72652e7	−	6.45452e7i	−0.386978	−	0.670266i	−0.992041	+	0.125912i	$0.959814\pi$
$192$	5.85124e7	−	1.01346e8i	0.596614	−	1.03337i
$193$	−5.07143e7	+	8.78397e7i	−0.507785	+	0.879509i	0.492175	+	0.870496i	$0.336202\pi$
$193$	−5.07143e7	+	8.78397e7i	−0.507785	+	0.879509i	−0.999959	+	0.00901227i	$0.997131\pi$
$194$	1.01009e8	−	1.74954e8i	0.993244	−	1.72035i
$195$	−4.61007e7	−	3.06004e7i	−0.445232	−	0.295533i
$196$	821429.	+	3.04247e6i	0.00779244	+	0.0288623i
$197$	−5.13429e7	−	8.89286e7i	−0.478464	−	0.828723i	0.521232	−	0.853415i	$-0.325473\pi$
$197$	−5.13429e7	−	8.89286e7i	−0.478464	−	0.828723i	−0.999695	+	0.0246922i	$0.992139\pi$
$198$	5.91555e7			0.541585
$199$	−1.84881e8			−1.66305			−0.831526	−	0.555486i	$-0.812532\pi$
$199$	−1.84881e8			−1.66305			−0.831526	+	0.555486i	$0.812532\pi$
$200$	4.52176e7	+	7.83191e7i	0.399671	+	0.692250i
$201$	1.25955e8	+	2.18160e8i	1.09403	+	1.89491i
$202$	−1.18108e7	+	2.04569e7i	−0.100821	+	0.174626i
$203$	−512430.	+	3.92108e6i	−0.00429931	+	0.0328980i
$204$	−3.95603e6	+	6.85205e6i	−0.0326253	+	0.0565087i
$205$	−6.55633e7			−0.531523
$206$	6.40479e7	−	1.10934e8i	0.510469	−	0.884159i
$207$	3.08629e7	+	5.34561e7i	0.241847	+	0.418891i
$208$	1.19595e8	−	5.94320e7i	0.921491	−	0.457930i
$209$	−6.17695e7			−0.468017
$210$	9.43132e6	−	7.21679e7i	0.0702757	−	0.537745i
$211$	1.21108e8	+	2.09766e8i	0.887535	+	1.53726i	0.842780	+	0.538258i	$0.180917\pi$
$211$	1.21108e8	+	2.09766e8i	0.887535	+	1.53726i	0.0447545	+	0.998998i	$0.485749\pi$
$212$	317531.	+	549981.i	0.00228882	+	0.00396435i
$213$	9.54972e7	+	1.65406e8i	0.677115	+	1.17280i
$214$	−8.50411e7			−0.593172
$215$	−2.10043e7	−	3.63805e7i	−0.144136	−	0.249651i
$216$	8.65322e7			0.584238
$217$	−5.13514e6	+	3.92938e7i	−0.0341148	+	0.261045i
$218$	6.91137e6	+	1.19709e7i	0.0451821	+	0.0782577i
$219$	−2.81884e8			−1.81349
$220$	1.05395e6	+	1.82550e6i	0.00667332	+	0.0115585i
$221$	2.54524e8	−	1.26485e8i	1.58619	−	0.788251i
$222$	4.60684e7	−	7.97927e7i	0.282597	−	0.489472i
$223$	−1.34754e8	−	2.33400e8i	−0.813718	−	1.40940i	−0.910245	−	0.414070i	$-0.864107\pi$
$223$	−1.34754e8	−	2.33400e8i	−0.813718	−	1.40940i	0.0965269	−	0.995330i	$-0.469227\pi$
$224$	7.98262e6	+	6.11324e6i	0.0474545	+	0.0363415i
$225$	3.59581e7	−	6.22812e7i	0.210454	−	0.364517i
$226$	9.24890e7	−	1.60196e8i	0.532980	−	0.923148i
$227$	2.16837e8			1.23039			0.615195	−	0.788375i	$-0.289077\pi$
$227$	2.16837e8			1.23039			0.615195	+	0.788375i	$0.289077\pi$
$228$	−2.99734e6			−0.0167481
$229$	1.04814e7	−	1.81544e7i	0.0576762	−	0.0998981i	−0.835746	−	0.549117i	$-0.814964\pi$
$229$	1.04814e7	−	1.81544e7i	0.0576762	−	0.0998981i	0.893422	+	0.449219i	$0.148298\pi$
$230$	−3.78859e7	+	6.56202e7i	−0.205319	+	0.355623i
$231$	3.07955e7	−	2.35645e8i	0.164379	−	1.25781i
$232$	3.10628e6	+	5.38023e6i	0.0163317	+	0.0282874i
$233$	6.27434e7	−	1.08675e8i	0.324954	−	0.562837i	−0.656549	−	0.754284i	$-0.727984\pi$
$233$	6.27434e7	−	1.08675e8i	0.324954	−	0.562837i	0.981503	+	0.191446i	$0.0613178\pi$
$234$	−8.59115e7	−	5.70258e7i	−0.438325	−	0.290948i
$235$	−1.49649e7	−	2.59199e7i	−0.0752204	−	0.130286i
$236$	−2.17789e6			−0.0107856
$237$	7.40843e7	+	1.28318e8i	0.361499	+	0.626135i
$238$	2.96812e8	+	2.27304e8i	1.42712	+	1.09292i
$239$	−2.21315e8			−1.04862			−0.524310	−	0.851527i	$-0.675677\pi$
$239$	−2.21315e8			−1.04862			−0.524310	+	0.851527i	$0.675677\pi$
$240$	−5.88820e7	−	1.01987e8i	−0.274943	−	0.476216i
$241$	−3.32788e8			−1.53147			−0.765733	−	0.643159i	$-0.777624\pi$
$241$	−3.32788e8			−1.53147			−0.765733	+	0.643159i	$0.777624\pi$
$242$	6.68333e6	+	1.15759e7i	0.0303137	+	0.0525049i
$243$	−1.05849e8	−	1.83335e8i	−0.473220	−	0.819642i
$244$	−2.93757e6	−	5.08801e6i	−0.0129456	−	0.0224225i
$245$	−9.64736e7	−	2.56536e7i	−0.419109	−	0.111447i
$246$	−3.57868e8			−1.53267
$247$	8.97078e7	+	5.95457e7i	0.378784	+	0.251427i
$248$	3.11285e7	+	5.39161e7i	0.129592	+	0.224459i
$249$	1.78536e8	−	3.09234e8i	0.732872	−	1.26937i
$250$	1.97011e8			0.797444
$251$	1.52469e8	−	2.64084e8i	0.608589	−	1.05411i	−0.382884	−	0.923796i	$-0.625069\pi$
$251$	1.52469e8	−	2.64084e8i	0.608589	−	1.05411i	0.991473	−	0.130311i	$-0.0415974\pi$
$252$	510190.	−	3.90394e6i	0.00200831	−	0.0153674i
$253$	−1.23706e8	+	2.14266e8i	−0.480253	+	0.831822i
$254$	−3.19372e6	−	5.53168e6i	−0.0122286	−	0.0211806i
$255$	−1.25314e8	−	2.17050e8i	−0.473270	−	0.819727i
$256$	2.40539e7			0.0896077
$257$	4.66131e8			1.71294			0.856470	−	0.516196i	$-0.172652\pi$
$257$	4.66131e8			1.71294			0.856470	+	0.516196i	$0.172652\pi$
$258$	−1.14649e8	−	1.98577e8i	−0.415624	−	0.719882i
$259$	−1.00332e8	−	7.68360e7i	−0.358831	−	0.274799i
$260$	229124.	−	3.66718e6i	0.000808469	−	0.0129397i
$261$	2.47018e6	−	4.27848e6i	0.00859978	−	0.0148953i
$262$	−5.98332e7	+	1.03634e8i	−0.205536	+	0.355998i
$263$	−1.66060e8	+	2.87625e8i	−0.562887	+	0.974949i	0.434356	+	0.900741i	$0.356976\pi$
$263$	−1.66060e8	+	2.87625e8i	−0.562887	+	0.974949i	−0.997243	+	0.0742073i	$0.976357\pi$
$264$	−1.86678e8	−	3.23335e8i	−0.624423	−	1.08153i
$265$	−2.01167e7			−0.0664042
$266$	−1.83525e7	+	1.40432e8i	−0.0597875	+	0.457490i
$267$	−1.38495e7	+	2.39881e7i	−0.0445293	+	0.0771270i
$268$	−8.36403e6	+	1.44869e7i	−0.0265426	+	0.0459732i
$269$	−2.72984e8			−0.855074			−0.427537	−	0.903998i	$-0.640619\pi$
$269$	−2.72984e8			−0.855074			−0.427537	+	0.903998i	$0.640619\pi$
$270$	4.22355e7	−	7.31540e7i	0.130588	−	0.226186i
$271$	−3.30000e8			−1.00721			−0.503607	−	0.863933i	$-0.667994\pi$
$271$	−3.30000e8			−1.00721			−0.503607	+	0.863933i	$0.667994\pi$
$272$	6.04908e8			1.82263
$273$	−2.71886e8	+	3.12541e8i	−0.808756	+	0.929688i
$274$	−5.47384e8			−1.60755
$275$	2.88258e8			0.835828
$276$	−6.00281e6	+	1.03972e7i	−0.0171859	+	0.0297669i
$277$	−4.49965e8			−1.27204			−0.636018	−	0.771674i	$-0.719420\pi$
$277$	−4.49965e8			−1.27204			−0.636018	+	0.771674i	$0.719420\pi$
$278$	1.35933e8	−	2.35443e8i	0.379462	−	0.657247i
$279$	2.47541e7	−	4.28753e7i	0.0682389	−	0.118193i
$280$	−1.44836e8	+	6.01542e7i	−0.394296	+	0.163762i
$281$	6.72068e8			1.80693			0.903464	−	0.428664i	$-0.141015\pi$
$281$	6.72068e8			1.80693			0.903464	+	0.428664i	$0.141015\pi$
$282$	−8.16837e7	−	1.41480e8i	−0.216902	−	0.375685i
$283$	−4.49004e6	+	7.77698e6i	−0.0117760	+	0.0203966i	−0.871853	−	0.489767i	$-0.837082\pi$
$283$	−4.49004e6	+	7.77698e6i	−0.0117760	+	0.0203966i	0.860077	+	0.510164i	$0.170415\pi$
$284$	−6.34149e6	+	1.09838e7i	−0.0164277	+	0.0284536i
$285$	4.74730e7	−	8.22256e7i	0.121476	−	0.210402i
$286$	2.57733e7	−	4.12507e8i	0.0651460	−	1.04268i
$287$	−6.36059e7	+	4.86708e8i	−0.158822	+	1.21530i
$288$	−6.28071e6	−	1.08785e7i	−0.0154930	−	0.0268346i
$289$	8.77039e8			2.13735
$290$	6.06457e6			0.0146018
$291$	5.06966e8	+	8.78091e8i	1.20602	+	2.08888i
$292$	−9.35924e6	−	1.62107e7i	−0.0219989	−	0.0381032i
$293$	3.18049e8	−	5.50877e8i	0.738682	−	1.27943i	−0.214407	−	0.976744i	$-0.568782\pi$
$293$	3.18049e8	−	5.50877e8i	0.738682	−	1.27943i	0.953089	−	0.302690i	$-0.0978848\pi$
$294$	−5.26587e8	−	1.40027e8i	−1.20852	−	0.321362i
$295$	3.44942e7	−	5.97457e7i	0.0782292	−	0.135497i
$296$	−1.98538e8			−0.444961
$297$	1.37909e8	−	2.38865e8i	0.305453	−	0.529060i
$298$	2.81802e8	+	4.88096e8i	0.616862	+	1.06844i
$299$	3.86210e8	−	1.91925e8i	0.835554	−	0.415224i
$300$	1.39876e7			0.0299102
$301$	−2.90447e8	+	1.20631e8i	−0.613881	+	0.254961i
$302$	−2.44904e8	−	4.24186e8i	−0.511648	−	0.886200i
$303$	−5.92783e7	−	1.02673e8i	−0.122418	−	0.212035i
$304$	1.14579e8	+	1.98457e8i	0.233910	+	0.405144i
$305$	1.86105e8			0.375584
$306$	−2.33531e8	−	4.04487e8i	−0.465928	−	0.807011i
$307$	−6.56734e8			−1.29540			−0.647702	−	0.761894i	$-0.724270\pi$
$307$	−6.56734e8			−1.29540			−0.647702	+	0.761894i	$0.724270\pi$
$308$	1.45740e7	−	6.05300e6i	0.0284219	−	0.0118044i
$309$	3.21456e8	+	5.56778e8i	0.619822	+	1.07356i
$310$	6.07740e7			0.115865
$311$	1.11671e8	+	1.93420e8i	0.210514	+	0.364620i	0.951875	−	0.306485i	$-0.0991530\pi$
$311$	1.11671e8	+	1.93420e8i	0.210514	+	0.364620i	−0.741362	+	0.671106i	$0.765820\pi$
$312$	−4.05828e7	+	6.49537e8i	−0.0756486	+	1.21077i
$313$	−7.11363e7	+	1.23212e8i	−0.131125	+	0.227115i	−0.924111	−	0.382125i	$-0.875192\pi$
$313$	−7.11363e7	+	1.23212e8i	−0.131125	+	0.227115i	0.792985	+	0.609241i	$0.208526\pi$
$314$	2.96854e8	+	5.14167e8i	0.541115	+	0.937238i
$315$	9.90155e7	+	7.58279e7i	0.178491	+	0.136692i
$316$	−4.91956e6	+	8.52093e6i	−0.00877045	+	0.0151909i
$317$	−3.97983e8	+	6.89327e8i	−0.701709	+	1.21540i	0.266157	+	0.963930i	$0.414246\pi$
$317$	−3.97983e8	+	6.89327e8i	−0.701709	+	1.21540i	−0.967866	+	0.251466i	$0.919087\pi$
$318$	−1.09804e8			−0.191480
$319$	1.98022e7			0.0341544
$320$	−1.23080e8	+	2.13181e8i	−0.209973	+	0.363683i
$321$	2.13410e8	−	3.69638e8i	0.360121	−	0.623747i
$322$	4.50376e8	+	3.44906e8i	0.751761	+	0.575712i
$323$	2.43850e8	+	4.22361e8i	0.402637	+	0.697388i
$324$	1.14361e7	−	1.98079e7i	0.0186797	−	0.0323543i
$325$	−4.18637e8	−	2.77880e8i	−0.676466	−	0.449020i
$326$	3.57998e8	+	6.20071e8i	0.572294	+	0.991242i
$327$	−6.93763e7			−0.109722
$328$	3.85570e8	+	6.67826e8i	0.603315	+	1.04497i
$329$	−2.06934e8	+	8.59455e7i	−0.320366	+	0.133057i
$330$	−3.64462e8			−0.558282
$331$	1.37477e8	+	2.38117e8i	0.208368	+	0.360904i	0.951201	−	0.308573i	$-0.0998515\pi$
$331$	1.37477e8	+	2.38117e8i	0.208368	+	0.360904i	−0.742833	+	0.669477i	$0.766518\pi$
$332$	2.37113e7			0.0355609
$333$	7.89408e7	+	1.36730e8i	0.117151	+	0.202912i
$334$	−2.06844e8	−	3.58265e8i	−0.303760	−	0.526128i
$335$	−2.64945e8	−	4.58897e8i	−0.385033	−	0.666897i
$336$	−8.14220e8	+	3.38168e8i	−1.17099	+	0.486345i
$337$	−8.39575e8			−1.19496			−0.597482	−	0.801882i	$-0.703832\pi$
$337$	−8.39575e8			−1.19496			−0.597482	+	0.801882i	$0.703832\pi$
$338$	−4.35087e8	+	5.74239e8i	−0.612869	+	0.808880i
$339$	4.64202e8	+	8.04021e8i	0.647154	+	1.12090i
$340$	8.32146e6	−	1.44132e7i	0.0114822	−	0.0198877i
$341$	1.98441e8			0.271014
$342$	8.84688e7	−	1.53233e8i	0.119591	−	0.207138i
$343$	−2.84032e8	+	6.91282e8i	−0.380048	+	0.924967i
$344$	−2.47047e8	+	4.27898e8i	−0.327209	+	0.566742i
$345$	−1.90149e8	−	3.29348e8i	−0.249303	−	0.431805i
$346$	−3.30528e7	−	5.72491e7i	−0.0428985	−	0.0743023i
$347$	3.49002e7			0.0448410			0.0224205	−	0.999749i	$-0.492863\pi$
$347$	3.49002e7			0.0448410			0.0224205	+	0.999749i	$0.492863\pi$
$348$	960898.			0.00122222
$349$	7.95453e7	+	1.37776e8i	0.100167	+	0.173495i	0.911753	−	0.410738i	$-0.134729\pi$
$349$	7.95453e7	+	1.37776e8i	0.100167	+	0.173495i	−0.811586	+	0.584233i	$0.801396\pi$
$350$	8.56452e7	−	6.55352e8i	0.106774	−	0.817027i
$351$	−4.30551e8	+	2.13960e8i	−0.531434	+	0.264093i
$352$	2.51747e7	−	4.36038e7i	0.0307655	−	0.0532875i
$353$	−2.40277e8	+	4.16172e8i	−0.290737	+	0.503572i	−0.973984	−	0.226615i	$-0.927234\pi$
$353$	−2.40277e8	+	4.16172e8i	−0.290737	+	0.503572i	0.683247	+	0.730187i	$0.260567\pi$
$354$	1.88282e8	−	3.26113e8i	0.225578	−	0.390712i
$355$	−2.00877e8	−	3.47929e8i	−0.238304	−	0.412755i
$356$	−1.83935e6			−0.00216068
$357$	−1.73284e9	+	7.19696e8i	−2.01567	+	0.837164i
$358$	2.15908e8	−	3.73964e8i	0.248702	−	0.430764i
$359$	6.68716e8	−	1.15825e9i	0.762800	−	1.32121i	−0.178601	−	0.983922i	$-0.557157\pi$
$359$	6.68716e8	−	1.15825e9i	0.762800	−	1.32121i	0.941402	−	0.337287i	$-0.109509\pi$
$360$	1.95933e8			0.221334
$361$	3.54558e8	−	6.14112e8i	0.396654	−	0.687025i
$362$	−1.30353e9			−1.44425
$363$	−6.70872e7			−0.0736150
$364$	−2.70010e7	−	5.25859e6i	−0.0293444	−	0.00571498i
$365$	5.92939e8			0.638242
$366$	1.01583e9			1.08302
$367$	7.84418e8	−	1.35865e9i	0.828355	−	1.43475i	−0.0709732	−	0.997478i	$-0.522610\pi$
$367$	7.84418e8	−	1.35865e9i	0.828355	−	1.43475i	0.899328	−	0.437275i	$-0.144056\pi$
$368$	9.17875e8			0.960099
$369$	3.06614e8	−	5.31071e8i	0.317687	−	0.550250i
$370$	−9.69042e7	+	1.67843e8i	−0.0994572	+	0.172265i
$371$	−1.95161e7	+	1.49336e8i	−0.0198419	+	0.151829i
$372$	9.62930e6			0.00969828
$373$	4.45462e8	+	7.71562e8i	0.444457	+	0.769822i	0.998014	−	0.0629894i	$-0.0200634\pi$
$373$	4.45462e8	+	7.71562e8i	0.444457	+	0.769822i	−0.553557	+	0.832811i	$0.686730\pi$
$374$	9.36050e8	−	1.62129e9i	0.925227	−	1.60254i
$375$	−4.94399e8	+	8.56324e8i	−0.484137	+	0.838549i
$376$	−1.76013e8	+	3.04864e8i	−0.170761	+	0.295766i
$377$	−2.87588e7	−	1.90893e7i	−0.0276424	−	0.0183483i
$378$	−5.02083e8	−	3.84505e8i	−0.478139	−	0.366168i
$379$	−6.64272e8	−	1.15055e9i	−0.626770	−	1.08560i	−0.988196	−	0.153197i	$-0.951043\pi$
$379$	−6.64272e8	−	1.15055e9i	−0.626770	−	1.08560i	0.361425	−	0.932401i	$-0.382290\pi$
$380$	6.30487e6			0.00589432
$381$	3.20585e7			0.0296965
$382$	4.27863e8	+	7.41081e8i	0.392720	+	0.680211i
$383$	−6.08158e8	−	1.05336e9i	−0.553121	−	0.958034i	−0.998047	−	0.0624669i	$-0.980103\pi$
$383$	−6.08158e8	−	1.05336e9i	−0.553121	−	0.958034i	0.444926	−	0.895568i	$-0.353230\pi$
$384$	−7.12676e8	+	1.23439e9i	−0.642293	+	1.11248i
$385$	−6.47779e7	+	4.95676e8i	−0.0578515	+	0.442676i
$386$	5.82280e8	−	1.00854e9i	0.515319	−	0.892559i
$387$	3.92915e8			0.344596
$388$	−3.36650e7	+	5.83096e7i	−0.0292596	+	0.0506791i
$389$	−6.23676e8	−	1.08024e9i	−0.537199	−	0.930456i	−0.999053	−	0.0435003i	$-0.986149\pi$
$389$	−6.23676e8	−	1.08024e9i	−0.537199	−	0.930456i	0.461854	−	0.886956i	$-0.347184\pi$
$390$	5.29308e8	+	3.51341e8i	0.451838	+	0.299918i
$391$	1.95344e9			1.65265
$392$	3.06042e8	+	1.13354e9i	0.256614	+	0.950467i
$393$	−3.00302e8	−	5.20139e8i	−0.249566	−	0.432260i
$394$	5.89498e8	+	1.02104e9i	0.485563	+	0.841020i
$395$	−1.55835e8	−	2.69915e8i	−0.127226	−	0.220362i
$396$	−1.97157e7			−0.0159543
$397$	−1.12302e9	−	1.94514e9i	−0.900788	−	1.56021i	−0.826473	−	0.562976i	$-0.809656\pi$
$397$	−1.12302e9	−	1.94514e9i	−0.900788	−	1.56021i	−0.0743148	−	0.997235i	$-0.523677\pi$
$398$	2.12272e9			1.68773
$399$	−5.64344e8	−	4.32185e8i	−0.444774	−	0.340616i
$400$	−5.34704e8	−	9.26134e8i	−0.417737	−	0.723542i
$401$	1.14733e9			0.888550			0.444275	−	0.895891i	$-0.353461\pi$
$401$	1.14733e9			0.888550			0.444275	+	0.895891i	$0.353461\pi$
$402$	−1.44616e9	−	2.50483e9i	−1.11026	−	1.92303i
$403$	−2.88196e8	−	1.91297e8i	−0.219342	−	0.145593i
$404$	3.93637e6	−	6.81800e6i	0.00297003	−	0.00514425i
$405$	3.62258e8	+	6.27449e8i	0.270973	+	0.469338i
$406$	5.88351e6	−	4.50202e7i	0.00436310	−	0.0333862i
$407$	−3.16415e8	+	5.48047e8i	−0.232636	+	0.402937i
$408$	−1.47391e9	+	2.55289e9i	−1.07439	+	1.86089i
$409$	−8.90063e8			−0.643264			−0.321632	−	0.946865i	$-0.604231\pi$
$409$	−8.90063e8			−0.643264			−0.321632	+	0.946865i	$0.604231\pi$
$410$	7.52770e8			0.539410
$411$	1.37366e9	−	2.37925e9i	0.975962	−	1.69042i
$412$	−2.13463e7	+	3.69728e7i	−0.0150377	+	0.0260461i
$413$	−4.10057e8	−	3.14029e8i	−0.286430	−	0.219353i
$414$	−3.54355e8	−	6.13760e8i	−0.245435	−	0.425106i
$415$	−3.75548e8	+	6.50469e8i	−0.257927	+	0.446743i
$416$	−7.85952e7	+	3.90575e7i	−0.0535266	+	0.0265997i
$417$	6.82246e8	+	1.18169e9i	0.460750	+	0.798042i
$418$	7.09211e8			0.474962
$419$	−3.50522e7	−	6.07123e7i	−0.0232791	−	0.0403206i	0.854151	−	0.520025i	$-0.174077\pi$
$419$	−3.50522e7	−	6.07123e7i	−0.0232791	−	0.0403206i	−0.877430	+	0.479704i	$0.840744\pi$
$420$	−3.14333e6	+	2.40525e7i	−0.00207022	+	0.0158412i
$421$	6.95778e8			0.454447			0.227224	−	0.973843i	$-0.427035\pi$
$421$	6.95778e8			0.454447			0.227224	+	0.973843i	$0.427035\pi$
$422$	−1.39051e9	−	2.40844e9i	−0.900704	−	1.56006i
$423$	2.79940e8			0.179835
$424$	1.18304e8	+	2.04908e8i	0.0753733	+	0.130550i
$425$	−1.13797e9	−	1.97102e9i	−0.719066	−	1.24546i
$426$	−1.09646e9	−	1.89912e9i	−0.687161	−	1.19020i
$427$	1.80548e8	−	1.38154e9i	0.112227	−	0.858751i
$428$	2.83430e7			0.0174740
$429$	1.72832e9	+	1.14721e9i	1.05687	+	0.701525i
$430$	2.41162e8	+	4.17705e8i	0.146275	+	0.253355i
$431$	5.89667e8	−	1.02133e9i	0.354761	−	0.614464i	−0.632316	−	0.774711i	$-0.717896\pi$
$431$	5.89667e8	−	1.02133e9i	0.354761	−	0.614464i	0.987077	+	0.160246i	$0.0512288\pi$
$432$	−1.02326e9			−0.610648
$433$	2.11852e8	−	3.66938e8i	0.125408	−	0.217213i	−0.796484	−	0.604659i	$-0.793309\pi$
$433$	2.11852e8	−	3.66938e8i	0.125408	−	0.217213i	0.921892	+	0.387446i	$0.126643\pi$
$434$	5.89595e7	−	4.51155e8i	0.0346210	−	0.264918i
$435$	−1.52190e7	+	2.63601e7i	−0.00886491	+	0.0153545i
$436$	−2.30346e6	−	3.98972e6i	−0.00133100	−	0.00230536i
$437$	3.70013e8	+	6.40881e8i	0.212096	+	0.367361i
$438$	3.23647e9			1.84040
$439$	9.95513e8			0.561592			0.280796	−	0.959767i	$-0.409402\pi$
$439$	9.95513e8			0.561592			0.280796	+	0.959767i	$0.409402\pi$
$440$	3.92674e8	+	6.80132e8i	0.219760	+	0.380635i
$441$	6.58967e8	−	6.61476e8i	0.365871	−	0.367265i
$442$	−2.92234e9	+	1.45224e9i	−1.60973	+	0.799947i
$443$	1.15433e9	−	1.99936e9i	0.630838	−	1.09264i	−0.356543	−	0.934279i	$-0.616045\pi$
$443$	1.15433e9	−	1.99936e9i	0.630838	−	1.09264i	0.987381	−	0.158364i	$-0.0506220\pi$
$444$	−1.53539e7	+	2.65938e7i	−0.00832491	+	0.0144192i
$445$	2.91323e7	−	5.04586e7i	0.0156717	−	0.0271441i
$446$	1.54719e9	+	2.67980e9i	0.825792	+	1.43031i
$447$	−2.82873e9			−1.49801
$448$	1.46314e9	+	1.12050e9i	0.768798	+	0.588760i
$449$	−5.61164e8	+	9.71964e8i	−0.292568	+	0.506743i	−0.974416	−	0.224751i	$-0.927843\pi$
$449$	−5.61164e8	+	9.71964e8i	−0.292568	+	0.506743i	0.681848	+	0.731494i	$0.261177\pi$
$450$	−4.12855e8	+	7.15086e8i	−0.213577	+	0.369926i
$451$	2.45797e9			1.26171
$452$	−3.08253e7	+	5.33910e7i	−0.0157008	+	0.0271946i
$453$	2.45834e9			1.24251
$454$	−2.48963e9			−1.24865
$455$	5.71908e8	−	6.57425e8i	0.284634	−	0.327195i
$456$	−1.11673e9			−0.551533
$457$	4.26397e8			0.208981			0.104491	−	0.994526i	$-0.466679\pi$
$457$	4.26397e8			0.208981			0.104491	+	0.994526i	$0.466679\pi$
$458$	−1.20343e8	+	2.08441e8i	−0.0585320	+	0.101380i
$459$	−2.17771e9			−1.05113
$460$	1.26268e7	−	2.18703e7i	0.00604842	−	0.0104762i
$461$	4.75964e8	−	8.24395e8i	0.226267	−	0.391906i	−0.730432	−	0.682986i	$-0.760681\pi$
$461$	4.75964e8	−	8.24395e8i	0.226267	−	0.391906i	0.956699	+	0.291080i	$0.0940145\pi$
$462$	−3.53581e8	+	2.70558e9i	−0.166818	+	1.27648i
$463$	−1.48646e8			−0.0696018			−0.0348009	−	0.999394i	$-0.511080\pi$
$463$	−1.48646e8			−0.0696018			−0.0348009	+	0.999394i	$0.511080\pi$
$464$	−3.67321e7	−	6.36219e7i	−0.0170700	−	0.0295661i
$465$	−1.52512e8	+	2.64159e8i	−0.0703427	+	0.121837i
$466$	−7.20393e8	+	1.24776e9i	−0.329776	+	0.571189i
$467$	−1.07439e9	+	1.86089e9i	−0.488148	+	0.845497i	−0.999907	−	0.0136318i	$-0.995661\pi$
$467$	−1.07439e9	+	1.86089e9i	−0.488148	+	0.845497i	0.511759	+	0.859129i	$0.328994\pi$
$468$	2.86331e7	+	1.90059e7i	0.0129124	+	0.00857093i
$469$	−3.66365e9	+	1.52161e9i	−1.63987	+	0.681083i
$470$	1.71821e8	+	2.97602e8i	0.0763365	+	0.132219i
$471$	−2.97982e9			−1.31407
$472$	−8.11424e8			−0.355182
$473$	7.87451e8	+	1.36391e9i	0.342145	+	0.592612i
$474$	−8.50605e8	−	1.47329e9i	−0.366863	−	0.635425i
$475$	4.31099e8	−	7.46685e8i	0.184565	−	0.319676i
$476$	−9.89231e7	−	7.57571e7i	−0.0420410	−	0.0321958i
$477$	9.40778e7	−	1.62948e8i	0.0396892	−	0.0687438i
$478$	2.54105e9			1.06418
$479$	−1.94539e9	+	3.36951e9i	−0.808783	+	1.40085i	0.104924	+	0.994480i	$0.466540\pi$
$479$	−1.94539e9	+	3.36951e9i	−0.808783	+	1.40085i	−0.913707	+	0.406373i	$0.866793\pi$
$480$	3.86960e7	+	6.70234e7i	0.0159706	+	0.0276619i
$481$	9.87846e8	−	4.90905e8i	0.404745	−	0.201136i
$482$	3.82093e9			1.55419
$483$	−2.62938e9	+	1.09205e9i	−1.06179	+	0.440990i
$484$	−2.22746e6	−	3.85807e6i	−0.000892999	−	0.00154672i
$485$	−1.06640e9	−	1.84705e9i	−0.424446	−	0.735162i
$486$	1.21531e9	+	2.10498e9i	0.480242	+	0.831803i
$487$	9.24173e8			0.362578			0.181289	−	0.983430i	$-0.441973\pi$
$487$	9.24173e8			0.362578			0.181289	+	0.983430i	$0.441973\pi$
$488$	−1.09446e9	−	1.89566e9i	−0.426314	−	0.738397i
$489$	−3.59358e9			−1.38978
$490$	1.10767e9	+	2.94544e8i	0.425328	+	0.113100i
$491$	1.63574e9	+	2.83319e9i	0.623633	+	1.08016i	0.988803	+	0.149223i	$0.0476774\pi$
$491$	1.63574e9	+	2.83319e9i	0.623633	+	1.08016i	−0.365170	+	0.930941i	$0.618989\pi$
$492$	1.19272e8			0.0451504
$493$	−7.81741e7	−	1.35402e8i	−0.0293832	−	0.0508932i
$494$	−1.02999e9	−	6.83679e8i	−0.384404	−	0.255157i
$495$	3.12264e8	−	5.40857e8i	0.115719	−	0.200431i
$496$	−3.68098e8	−	6.37565e8i	−0.135450	−	0.234606i
$497$	−2.77773e9	+	1.15367e9i	−1.01494	+	0.421534i
$498$	−2.04988e9	+	3.55049e9i	−0.743746	+	1.28821i
$499$	−7.80698e7	+	1.35221e8i	−0.0281275	+	0.0487183i	−0.879747	−	0.475443i	$-0.842288\pi$
$499$	−7.80698e7	+	1.35221e8i	−0.0281275	+	0.0487183i	0.851619	+	0.524161i	$0.175621\pi$
$500$	−6.56610e7			−0.0234916
$501$	2.07630e9			0.737664
$502$	−1.75059e9	+	3.03211e9i	−0.617619	+	1.06975i
$503$	1.67090e9	−	2.89409e9i	0.585414	−	1.01397i	−0.409409	−	0.912351i	$-0.634265\pi$
$503$	1.67090e9	−	2.89409e9i	0.585414	−	1.01397i	0.994824	−	0.101617i	$-0.0324015\pi$
$504$	1.90083e8	−	1.45450e9i	0.0661358	−	0.506067i
$505$	1.24691e8	+	2.15971e8i	0.0430840	+	0.0746237i
$506$	1.42034e9	−	2.46011e9i	0.487379	−	0.844164i
$507$	−1.40412e9	−	3.33219e9i	−0.478495	−	1.13554i
$508$	1.06442e6	+	1.84363e6i	0.000360239	+	0.000623952i
$509$	3.33031e8			0.111937			0.0559684	−	0.998433i	$-0.482175\pi$
$509$	3.33031e8			0.111937			0.0559684	+	0.998433i	$0.482175\pi$
$510$	1.43880e9	+	2.49208e9i	0.480292	+	0.831890i
$511$	5.75236e8	−	4.40167e9i	0.190710	−	1.45930i
$512$	2.88985e9			0.951546
$513$	−4.12494e8	−	7.14461e8i	−0.134898	−	0.233651i
$514$	−5.35192e9			−1.73836
$515$	−6.76178e8	−	1.17118e9i	−0.218140	−	0.377830i
$516$	3.82108e7	+	6.61831e7i	0.0122437	+	0.0212067i
$517$	5.61034e8	+	9.71740e8i	0.178555	+	0.309267i
$518$	1.15197e9	+	8.82198e8i	0.364155	+	0.278877i
$519$	3.31784e8			0.104176
$520$	8.53653e7	−	1.36629e9i	0.0266238	−	0.426120i
$521$	9.40187e8	+	1.62845e9i	0.291261	+	0.504478i	0.974108	−	0.226083i	$-0.0725919\pi$
$521$	9.40187e8	+	1.62845e9i	0.291261	+	0.504478i	−0.682847	+	0.730561i	$0.739259\pi$
$522$	−2.83616e7	+	4.91237e7i	−0.00872738	+	0.0151163i
$523$	2.41701e9			0.738791			0.369396	−	0.929272i	$-0.379565\pi$
$523$	2.41701e9			0.738791			0.369396	+	0.929272i	$0.379565\pi$
$524$	1.99416e7	−	3.45398e7i	0.00605480	−	0.0104872i
$525$	2.63361e9	+	2.01687e9i	0.794317	+	0.608303i
$526$	1.90664e9	−	3.30239e9i	0.571239	−	0.989415i
$527$	−7.83395e8	−	1.35688e9i	−0.233154	−	0.403835i
$528$	2.20749e9	+	3.82349e9i	0.652650	+	1.13042i
$529$	−4.40713e8			−0.129438
$530$	2.30971e8			0.0673895
$531$	3.22632e8	+	5.58814e8i	0.0935139	+	0.161971i
$532$	6.11664e6	−	4.68041e7i	0.00176125	−	0.0134770i
$533$	−3.56971e9	−	2.36948e9i	−1.02115	−	0.677811i
$534$	1.59015e8	−	2.75421e8i	0.0451900	−	0.0782714i
$535$	−4.48906e8	+	7.77528e8i	−0.126741	+	0.219522i
$536$	−3.11621e9	+	5.39744e9i	−0.874078	+	1.51395i
$537$	1.08364e9	+	1.87692e9i	0.301979	+	0.523042i
$538$	3.13429e9			0.867762
$539$	3.61680e9	+	9.61755e8i	0.994865	+	0.264548i
$540$	−1.40765e7	+	2.43812e7i	−0.00384695	+	0.00666311i
$541$	1.61889e7	−	2.80400e7i	0.00439568	−	0.00761355i	−0.863819	−	0.503802i	$-0.831934\pi$
$541$	1.61889e7	−	2.80400e7i	0.00439568	−	0.00761355i	0.868215	+	0.496188i	$0.165267\pi$
$542$	3.78892e9			1.02216
$543$	3.27121e9	−	5.66590e9i	0.876816	−	1.51869i
$544$	−3.97532e8			−0.105871
$545$	1.45932e8			0.0386156
$546$	3.12168e9	−	3.58846e9i	0.820756	−	0.943483i
$547$	5.32187e9			1.39030			0.695150	−	0.718864i	$-0.255338\pi$
$547$	5.32187e9			1.39030			0.695150	+	0.718864i	$0.255338\pi$
$548$	1.82436e8			0.0473563
$549$	−8.70338e8	+	1.50747e9i	−0.224484	+	0.388817i
$550$	−3.30966e9			−0.848230
$551$	2.96149e7	−	5.12945e7i	0.00754187	−	0.0130629i
$552$	−2.23648e9	+	3.87370e9i	−0.565951	+	0.980256i
$553$	−2.15489e9	+	8.94985e8i	−0.541860	+	0.225049i
$554$	5.16631e9			1.29091
$555$	−4.86362e8	−	8.42403e8i	−0.120763	−	0.209168i
$556$	−4.53045e7	+	7.84697e7i	−0.0111784	+	0.0193616i
$557$	−1.35138e9	+	2.34066e9i	−0.331349	+	0.573913i	−0.982777	−	0.184798i	$-0.940837\pi$
$557$	−1.35138e9	+	2.34066e9i	−0.331349	+	0.573913i	0.651428	+	0.758711i	$0.274170\pi$
$558$	−2.84216e8	+	4.92277e8i	−0.0692515	+	0.119947i
$559$	1.71188e8	−	2.73990e9i	0.0414507	−	0.663428i
$560$	1.71270e9	−	7.11332e8i	0.412120	−	0.171165i
$561$	4.69803e9	+	8.13722e9i	1.12343	+	1.94584i
$562$	−7.71640e9			−1.83374
$563$	9.28207e8			0.219213			0.109606	−	0.993975i	$-0.465041\pi$
$563$	9.28207e8			0.219213			0.109606	+	0.993975i	$0.465041\pi$
$564$	2.72240e7	+	4.71534e7i	0.00638963	+	0.0110672i
$565$	−9.76442e8	−	1.69125e9i	−0.227760	−	0.394492i
$566$	5.15528e7	−	8.92920e7i	0.0119507	−	0.0206993i
$567$	5.00930e9	−	2.08050e9i	1.15408	−	0.479322i
$568$	−2.36267e9	+	4.09226e9i	−0.540982	+	0.937009i
$569$	−4.01097e9			−0.912759			−0.456380	−	0.889785i	$-0.650854\pi$
$569$	−4.01097e9			−0.912759			−0.456380	+	0.889785i	$0.650854\pi$
$570$	−5.45064e8	+	9.44079e8i	−0.123278	+	0.213524i
$571$	−3.62026e8	−	6.27047e8i	−0.0813792	−	0.140953i	0.822463	−	0.568818i	$-0.192599\pi$
$571$	−3.62026e8	−	6.27047e8i	−0.0813792	−	0.140953i	−0.903843	+	0.427865i	$0.859266\pi$
$572$	−8.58986e6	+	1.37483e8i	−0.00191911	+	0.0307158i
$573$	−4.29489e9			−0.953697
$574$	7.30296e8	−	5.58818e9i	0.161179	−	1.23333i
$575$	−1.72673e9	−	2.99078e9i	−0.378780	−	0.656066i
$576$	−1.15119e9	−	1.99393e9i	−0.250998	−	0.434741i
$577$	−1.44166e9	−	2.49702e9i	−0.312425	−	0.541137i	0.666462	−	0.745539i	$-0.267808\pi$
$577$	−1.44166e9	−	2.49702e9i	−0.312425	−	0.541137i	−0.978887	+	0.204403i	$0.934475\pi$
$578$	−1.00698e10			−2.16907
$579$	2.92246e9	+	5.06185e9i	0.625711	+	1.08376i
$580$	−2.02124e6			−0.000430149
$581$	4.46441e9	+	3.41892e9i	0.944381	+	0.723224i
$582$	−5.82077e9	−	1.00819e10i	−1.22391	−	2.11988i
$583$	7.54175e8			0.157628
$584$	−3.48700e9	−	6.03966e9i	−0.724448	−	1.25478i
$585$	−9.74886e8	+	4.84464e8i	−0.201330	+	0.100050i
$586$	−3.65171e9	+	6.32494e9i	−0.749642	+	1.29842i
$587$	−2.94118e9	−	5.09427e9i	−0.600189	−	1.03956i	−0.992792	−	0.119850i	$-0.961759\pi$
$587$	−2.94118e9	−	5.09427e9i	−0.600189	−	1.03956i	0.392603	−	0.919708i	$-0.371575\pi$
$588$	1.75504e8	+	4.66689e7i	0.0356014	+	0.00946688i
$589$	2.96775e8	−	5.14030e8i	0.0598445	−	0.103654i
$590$	−3.96048e8	+	6.85975e8i	−0.0793899	+	0.137507i
$591$	−5.91737e9			−1.17916
$592$	2.34773e9			0.465075
$593$	−3.91345e9	+	6.77830e9i	−0.770671	+	1.33484i	0.166525	+	0.986037i	$0.446745\pi$
$593$	−3.91345e9	+	6.77830e9i	−0.770671	+	1.33484i	−0.937196	+	0.348804i	$0.886588\pi$
$594$	−1.58341e9	+	2.74255e9i	−0.309985	+	0.536911i
$595$	3.64501e9	−	1.51387e9i	0.709396	−	0.294632i
$596$	−9.39208e7	−	1.62676e8i	−0.0181719	−	0.0314746i
$597$	−5.32697e9	+	9.22658e9i	−1.02464	+	1.77472i
$598$	−4.43430e9	+	2.20360e9i	−0.847952	+	0.421385i
$599$	−7.61826e8	−	1.31952e9i	−0.144831	−	0.250855i	0.784479	−	0.620156i	$-0.212931\pi$
$599$	−7.61826e8	−	1.31952e9i	−0.144831	−	0.250855i	−0.929310	+	0.369301i	$0.879597\pi$
$600$	5.21141e9			0.984977
$601$	2.10187e9	+	3.64055e9i	0.394954	+	0.684080i	0.993095	−	0.117311i	$-0.0374274\pi$
$601$	2.10187e9	+	3.64055e9i	0.394954	+	0.684080i	−0.598142	+	0.801390i	$0.704094\pi$
$602$	3.33479e9	−	1.38503e9i	0.622989	−	0.258744i
$603$	4.95617e9			0.920525
$604$	8.16229e7	+	1.41375e8i	0.0150724	+	0.0261062i
$605$	1.41117e8			0.0259081
$606$	6.80609e8	+	1.17885e9i	0.124235	+	0.215181i
$607$	4.88463e9	+	8.46043e9i	0.886485	+	1.53544i	0.844002	+	0.536339i	$0.180193\pi$
$607$	4.88463e9	+	8.46043e9i	0.886485	+	1.53544i	0.0424822	+	0.999097i	$0.486473\pi$
$608$	−7.52990e7	−	1.30422e8i	−0.0135871	−	0.0235335i
$609$	1.80919e8	+	1.38551e8i	0.0324582	+	0.0248571i
$610$	−2.13677e9			−0.381157
$611$	1.21966e8	−	1.95210e9i	0.0216319	−	0.346224i
$612$	7.78324e7	+	1.34810e8i	0.0137256	+	0.0237734i
$613$	3.82222e9	−	6.62028e9i	0.670199	−	1.16082i	−0.307648	−	0.951500i	$-0.599542\pi$
$613$	3.82222e9	−	6.62028e9i	0.670199	−	1.16082i	0.977847	−	0.209319i	$-0.0671246\pi$
$614$	7.54034e9			1.31462
$615$	−1.88908e9	+	3.27197e9i	−0.327481	+	0.567214i
$616$	5.42990e9	−	2.25518e9i	0.935964	−	0.388731i
$617$	−4.36451e9	+	7.55956e9i	−0.748062	+	1.29568i	0.200688	+	0.979655i	$0.435682\pi$
$617$	−4.36451e9	+	7.55956e9i	−0.748062	+	1.29568i	−0.948750	+	0.316027i	$0.897651\pi$
$618$	−3.69082e9	−	6.39269e9i	−0.629019	−	1.08949i
$619$	−6.65409e8	−	1.15252e9i	−0.112764	−	0.195313i	0.804120	−	0.594468i	$-0.202637\pi$
$619$	−6.65409e8	−	1.15252e9i	−0.112764	−	0.195313i	−0.916884	+	0.399154i	$0.869304\pi$
$620$	−2.02551e7			−0.00341322
$621$	−3.30442e9			−0.553700
$622$	−1.28216e9	−	2.22077e9i	−0.213637	−	0.370031i
$623$	−3.46316e8	−	2.65215e8i	−0.0573806	−	0.0439431i
$624$	4.79897e8	−	7.68087e9i	0.0790682	−	1.26551i
$625$	−1.43784e9	+	2.49042e9i	−0.235576	+	0.408030i
$626$	8.16757e8	−	1.41466e9i	0.133071	−	0.230485i
$627$	−1.77976e9	+	3.08264e9i	−0.288354	+	0.499444i
$628$	−9.89373e7	−	1.71365e8i	−0.0159405	−	0.0276097i
$629$	4.99650e9			0.800550
$630$	−1.13685e9	−	8.70624e8i	−0.181139	−	0.138720i
$631$	−3.67771e8	+	6.36998e8i	−0.0582740	+	0.100933i	−0.893691	−	0.448684i	$-0.851893\pi$
$631$	−3.67771e8	+	6.36998e8i	−0.0582740	+	0.100933i	0.835417	+	0.549617i	$0.185226\pi$
$632$	−1.83290e9	+	3.17467e9i	−0.288821	+	0.500252i
$633$	1.39580e10			2.18731
$634$	4.56947e9	−	7.91456e9i	0.712121	−	1.23343i
$635$	−6.74346e7			−0.0104514
$636$	3.65961e7			0.00564073
$637$	−4.32555e9	−	4.88335e9i	−0.663061	−	0.748566i
$638$	−2.27361e8			−0.0346612
$639$	3.75769e9			0.569729
$640$	1.49910e9	−	2.59653e9i	0.226049	−	0.391528i
$641$	2.23310e9			0.334892			0.167446	−	0.985881i	$-0.446448\pi$
$641$	2.23310e9			0.334892			0.167446	+	0.985881i	$0.446448\pi$
$642$	−2.45029e9	+	4.24403e9i	−0.365464	+	0.633002i
$643$	−3.35688e9	+	5.81429e9i	−0.497964	+	0.862499i	−0.999997	−	0.00234949i	$-0.999252\pi$
$643$	−3.35688e9	+	5.81429e9i	−0.497964	+	0.862499i	0.502033	+	0.864848i	$0.332585\pi$
$644$	−1.50104e8	−	1.14952e8i	−0.0221458	−	0.0169597i
$645$	−2.42078e9			−0.355220
$646$	−2.79978e9	−	4.84937e9i	−0.408611	−	0.707736i
$647$	3.85074e9	−	6.66967e9i	0.558958	−	0.968143i	−0.438626	−	0.898670i	$-0.644535\pi$
$647$	3.85074e9	−	6.66967e9i	0.558958	−	0.968143i	0.997584	−	0.0694735i	$-0.0221319\pi$
$648$	4.26079e9	−	7.37990e9i	0.615145	−	1.06546i
$649$	−1.29319e9	+	2.23987e9i	−0.185697	+	0.321637i
$650$	4.80662e9	+	3.19051e9i	0.686503	+	0.455683i
$651$	1.81302e9	+	1.38844e9i	0.257554	+	0.197240i
$652$	−1.19316e8	−	2.06661e8i	−0.0168590	−	0.0292006i
$653$	−1.21399e9			−0.170615			−0.0853075	−	0.996355i	$-0.527187\pi$
$653$	−1.21399e9			−0.170615			−0.0853075	+	0.996355i	$0.527187\pi$
$654$	7.96550e8			0.111350
$655$	6.31682e8	+	1.09411e9i	0.0878322	+	0.152130i
$656$	−4.55941e9	−	7.89713e9i	−0.630588	−	1.09221i
$657$	−2.77294e9	+	4.80288e9i	−0.381472	+	0.660728i
$658$	2.37593e9	−	9.86790e8i	0.325120	−	0.135031i
$659$	2.77363e9	−	4.80408e9i	0.377529	−	0.653899i	−0.613173	−	0.789949i	$-0.710107\pi$
$659$	2.77363e9	−	4.80408e9i	0.377529	−	0.653899i	0.990702	+	0.136049i	$0.0434405\pi$
$660$	1.21470e8			0.0164462
$661$	−5.59456e8	+	9.69006e8i	−0.0753461	+	0.130503i	−0.901237	−	0.433327i	$-0.857339\pi$
$661$	−5.59456e8	+	9.69006e8i	−0.0753461	+	0.130503i	0.825891	+	0.563830i	$0.190673\pi$
$662$	−1.57845e9	−	2.73396e9i	−0.211460	−	0.366259i
$663$	1.02133e9	−	1.63466e10i	0.136103	−	2.17836i
$664$	8.83421e9			1.17106
$665$	1.18709e9	+	9.09096e8i	0.156534	+	0.119876i
$666$	−9.06366e8	−	1.56987e9i	−0.118890	−	0.205923i
$667$	−1.18620e8	−	2.05456e8i	−0.0154781	−	0.0268088i
$668$	6.89383e7	+	1.19405e8i	0.00894836	+	0.0154990i
$669$	−1.55306e10			−2.00539
$670$	3.04198e9	+	5.26887e9i	0.390746	+	0.676792i
$671$	−6.97707e9			−0.891547
$672$	5.35088e8	−	2.22237e8i	0.0680194	−	0.0282503i
$673$	7.27354e9	+	1.25981e10i	0.919800	+	1.59314i	0.799718	+	0.600376i	$0.204982\pi$
$673$	7.27354e9	+	1.25981e10i	0.919800	+	1.59314i	0.120082	+	0.992764i	$0.461684\pi$
$674$	9.63965e9			1.21270
$675$	1.92497e9	+	3.33415e9i	0.240914	+	0.417275i
$676$	1.45008e8	−	1.91386e8i	0.0180543	−	0.0238285i
$677$	−1.57980e9	+	2.73629e9i	−0.195678	+	0.338924i	−0.947122	−	0.320872i	$-0.896024\pi$
$677$	−1.57980e9	+	2.73629e9i	−0.195678	+	0.338924i	0.751445	+	0.659796i	$0.229357\pi$
$678$	−5.32977e9	−	9.23143e9i	−0.656757	−	1.13754i
$679$	−1.47461e10	+	6.12447e9i	−1.80773	+	0.750800i
$680$	3.10035e9	−	5.36997e9i	0.378120	−	0.654923i
$681$	6.24772e9	−	1.08214e10i	0.758065	−	1.31301i
$682$	−2.27842e9			−0.275035
$683$	9.88014e9			1.18656			0.593281	−	0.804995i	$-0.297832\pi$
$683$	9.88014e9			1.18656			0.593281	+	0.804995i	$0.297832\pi$
$684$	−2.94854e7	+	5.10703e7i	−0.00352299	+	0.00610199i
$685$	−2.88947e9	+	5.00472e9i	−0.343480	+	0.594925i
$686$	3.26114e9	−	7.93701e9i	0.385687	−	0.938691i
$687$	−6.04003e8	−	1.04616e9i	−0.0710707	−	0.123098i
$688$	2.92136e9	−	5.05995e9i	0.342000	−	0.592361i
$689$	−1.09529e9	−	7.27024e8i	−0.127574	−	0.0846802i
$690$	2.18321e9	+	3.78143e9i	0.253002	+	0.438212i
$691$	−8.14758e9			−0.939411			−0.469705	−	0.882823i	$-0.655640\pi$
$691$	−8.14758e9			−0.939411			−0.469705	+	0.882823i	$0.655640\pi$
$692$	1.10160e7	+	1.90803e7i	0.00126373	+	0.00218884i
$693$	−3.71210e9	−	2.84279e9i	−0.423695	−	0.324473i
$694$	−4.00709e8			−0.0455063
$695$	−1.43510e9	−	2.48566e9i	−0.162156	−	0.280863i
$696$	3.58005e8			0.0402491
$697$	−9.70344e9	−	1.68069e10i	−1.08545	−	1.88006i
$698$	−9.13305e8	−	1.58189e9i	−0.101653	−	0.176069i
$699$	−3.61565e9	−	6.26249e9i	−0.400420	−	0.693549i
$700$	−2.85443e7	+	2.18420e8i	−0.00314541	+	0.0240685i
$701$	1.34586e10			1.47567			0.737833	−	0.674983i	$-0.235849\pi$
$701$	1.34586e10			1.47567			0.737833	+	0.674983i	$0.235849\pi$
$702$	4.94340e9	−	2.45660e9i	0.539320	−	0.268012i
$703$	9.46417e8	+	1.63924e9i	0.102740	+	0.177951i
$704$	4.61428e9	−	7.99216e9i	0.498424	−	0.863296i
$705$	−1.72473e9			−0.185379
$706$	2.75876e9	−	4.77831e9i	0.295051	−	0.511044i
$707$	1.72423e9	−	7.16119e8i	0.183496	−	0.0762110i
$708$	−6.27516e7	+	1.08689e8i	−0.00664521	+	0.0115098i
$709$	3.34209e9	+	5.78866e9i	0.352173	+	0.609981i	0.986630	−	0.162977i	$-0.0521096\pi$
$709$	3.34209e9	+	5.78866e9i	0.352173	+	0.609981i	−0.634457	+	0.772958i	$0.718776\pi$
$710$	2.30639e9	+	3.99478e9i	0.241840	+	0.418879i
$711$	2.91512e9			0.304168
$712$	−6.85294e8			−0.0711536
$713$	−1.18871e9	−	2.05890e9i	−0.122818	−	0.212727i
$714$	1.98957e10	−	8.26325e9i	2.04558	−	0.849585i
$715$	−3.63549e9	−	2.41314e9i	−0.371956	−	0.246895i
$716$	−7.19592e7	+	1.24637e8i	−0.00732640	+	0.0126897i
$717$	−6.37675e9	+	1.10449e10i	−0.646074	+	1.11903i
$718$	−7.67791e9	+	1.32985e10i	−0.774119	+	1.34081i
$719$	7.85077e9	+	1.35979e10i	0.787701	+	1.36434i	0.927372	+	0.374140i	$0.122062\pi$
$719$	7.85077e9	+	1.35979e10i	0.787701	+	1.36434i	−0.139671	+	0.990198i	$0.544605\pi$
$720$	−2.31693e9			−0.231339
$721$	−9.35019e9	+	3.88339e9i	−0.929067	+	0.385867i
$722$	−4.07088e9	+	7.05097e9i	−0.402539	+	0.697219i
$723$	−9.58860e9	+	1.66080e10i	−0.943564	+	1.63430i
$724$	4.34448e8			0.0425455
$725$	−1.38203e8	+	2.39374e8i	−0.0134690	+	0.0233289i
$726$	7.70267e8			0.0747073
$727$	−5.02488e9			−0.485016			−0.242508	−	0.970149i	$-0.577970\pi$
$727$	−5.02488e9			−0.485016			−0.242508	+	0.970149i	$0.577970\pi$
$728$	−1.00598e10	−	1.95921e9i	−0.966342	−	0.188201i
$729$	8.72630e8			0.0834227
$730$	−6.80788e9			−0.647712
$731$	6.21731e9	−	1.07687e10i	0.588697	−	1.01965i
$732$	−3.38560e8			−0.0319041
$733$	−3.64707e7	+	6.31690e7i	−0.00342042	+	0.00592435i	−0.867731	−	0.497035i	$-0.834422\pi$
$733$	−3.64707e7	+	6.31690e7i	−0.00342042	+	0.00592435i	0.864310	+	0.502959i	$0.167755\pi$
$734$	−9.00636e9	+	1.55995e10i	−0.840646	+	1.45604i
$735$	−4.05995e9	+	4.07541e9i	−0.377151	+	0.378587i
$736$	−6.03208e8			−0.0557692
$737$	9.93279e9	+	1.72041e10i	0.913976	+	1.58305i
$738$	−3.52041e9	+	6.09753e9i	−0.322401	+	0.558415i
$739$	−7.36520e9	+	1.27569e10i	−0.671319	+	1.16276i	0.306211	+	0.951964i	$0.400939\pi$
$739$	−7.36520e9	+	1.27569e10i	−0.671319	+	1.16276i	−0.977530	+	0.210795i	$0.932395\pi$
$740$	3.22968e7	−	5.59397e7i	0.00292987	−	0.00507468i
$741$	5.55641e9	−	2.76123e9i	0.501685	−	0.249310i
$742$	2.24075e8	−	1.71461e9i	0.0201363	−	0.154082i
$743$	−5.51633e9	−	9.55457e9i	−0.493389	−	0.854575i	0.506582	−	0.862192i	$-0.330909\pi$
$743$	−5.51633e9	−	9.55457e9i	−0.493389	−	0.854575i	−0.999971	+	0.00761691i	$0.997575\pi$
$744$	3.58762e9			0.319375
$745$	5.95019e9			0.527211
$746$	−5.11460e9	−	8.85875e9i	−0.451051	−	0.781244i
$747$	−3.51258e9	−	6.08397e9i	−0.308322	−	0.534029i
$748$	−3.11972e8	+	5.40352e8i	−0.0272559	+	0.0472086i
$749$	5.33646e9	+	4.08676e9i	0.464053	+	0.355380i
$750$	5.67648e9	−	9.83195e9i	0.491320	−	0.850991i
$751$	4.28198e9			0.368897			0.184449	−	0.982842i	$-0.440950\pi$
$751$	4.28198e9			0.368897			0.184449	+	0.982842i	$0.440950\pi$
$752$	2.08138e9	−	3.60506e9i	0.178480	−	0.309136i
$753$	−8.78619e9	−	1.52181e10i	−0.749925	−	1.29891i
$754$	3.30196e8	+	2.19176e8i	0.0280526	+	0.0186206i
$755$	−5.17109e9			−0.437288
$756$	1.67337e8	+	1.28150e8i	0.0140853	+	0.0107868i
$757$	4.28875e9	+	7.42833e9i	0.359331	+	0.622380i	0.987849	−	0.155415i	$-0.0496715\pi$
$757$	4.28875e9	+	7.42833e9i	0.359331	+	0.622380i	−0.628518	+	0.777795i	$0.716338\pi$
$758$	7.62689e9	+	1.32102e10i	0.636070	+	1.10171i
$759$	7.12869e9	+	1.23473e10i	0.591785	+	1.02500i
$760$	2.34903e9			0.194107
$761$	−3.70821e9	−	6.42281e9i	−0.305013	−	0.528298i	0.672251	−	0.740323i	$-0.265327\pi$
$761$	−3.70821e9	−	6.42281e9i	−0.305013	−	0.528298i	−0.977264	+	0.212025i	$0.931994\pi$
$762$	−3.68082e8			−0.0301372
$763$	1.41575e8	−	1.08332e9i	0.0115386	−	0.0882923i
$764$	−1.42601e8	−	2.46992e8i	−0.0115690	−	0.0200381i
$765$	−4.93094e9			−0.398213
$766$	6.98261e9	+	1.20942e10i	0.561329	+	0.972249i
$767$	4.03733e9	−	2.00633e9i	0.323080	−	0.160553i
$768$	6.93065e8	−	1.20042e9i	0.0552089	−	0.0956247i
$769$	−3.71480e9	−	6.43423e9i	−0.294573	−	0.510216i	0.680312	−	0.732923i	$-0.261844\pi$
$769$	−3.71480e9	−	6.43423e9i	−0.294573	−	0.510216i	−0.974886	+	0.222706i	$0.928511\pi$
$770$	7.43753e8	−	5.69115e9i	0.0587098	−	0.449244i
$771$	1.34306e10	−	2.32626e10i	1.05537	−	1.82796i
$772$	−1.94066e8	+	3.36132e8i	−0.0151806	+	0.0262935i
$773$	−1.92957e10			−1.50256			−0.751281	−	0.659982i	$-0.770564\pi$
$773$	−1.92957e10			−1.50256			−0.751281	+	0.659982i	$0.770564\pi$
$774$	−4.51128e9			−0.349709
$775$	−1.38495e9	+	2.39881e9i	−0.106876	+	0.185114i
$776$	−1.25427e10	+	2.17246e10i	−0.963551	+	1.66892i
$777$	−6.72540e9	+	2.79324e9i	−0.514334	+	0.213617i
$778$	7.16078e9	+	1.24028e10i	0.545170	+	0.944262i
$779$	3.67597e9	−	6.36697e9i	0.278607	−	0.482561i
$780$	−1.76411e8	−	1.17097e8i	−0.0133105	−	0.00883517i
$781$	7.53090e9	+	1.30439e10i	0.565676	+	0.979780i
$782$	−2.24286e10			−1.67717
$783$	1.32239e8	+	2.29044e8i	0.00984446	+	0.0170511i
$784$	−3.61899e9	−	1.34043e10i	−0.268214	−	0.993432i
$785$	6.26801e9			0.462473
$786$	3.44795e9	+	5.97202e9i	0.253269	+	0.438674i
$787$	−1.01300e9			−0.0740795			−0.0370397	−	0.999314i	$-0.511793\pi$
$787$	−1.01300e9			−0.0740795			−0.0370397	+	0.999314i	$0.511793\pi$
$788$	−1.96471e8	−	3.40298e8i	−0.0143040	−	0.0247753i
$789$	9.56940e9	+	1.65747e10i	0.693610	+	1.20137i
$790$	1.78924e9	+	3.09905e9i	0.129114	+	0.223632i
$791$	−1.35022e10	+	5.60785e9i	−0.970037	+	0.402883i
$792$	−7.34553e9			−0.525394
$793$	1.01328e10	+	6.72589e9i	0.721562	+	0.478954i
$794$	1.28941e10	+	2.23332e10i	0.914154	+	1.58336i
$795$	−5.79622e8	+	1.00393e9i	−0.0409128	+	0.0708631i
$796$	−7.07474e8			−0.0497181
$797$	−1.24278e10	+	2.15255e10i	−0.869538	+	1.50608i	−0.00706934	+	0.999975i	$0.502250\pi$
$797$	−1.24278e10	+	2.15255e10i	−0.869538	+	1.50608i	−0.862469	+	0.506110i	$0.831083\pi$
$798$	6.47957e9	+	4.96217e9i	0.451373	+	0.345670i
$799$	4.42964e9	−	7.67236e9i	0.307224	−	0.532127i
$800$	3.51396e8	+	6.08635e8i	0.0242651	+	0.0420283i
$801$	2.72481e8	+	4.71951e8i	0.0187336	+	0.0324476i
$802$	−1.31731e10			−0.901734
$803$	−2.22293e10			−1.51503
$804$	4.81985e8	+	8.34823e8i	0.0327068	+	0.0566498i
$805$	5.53086e9	−	2.29712e9i	0.373686	−	0.155202i
$806$	3.30895e9	+	2.19639e9i	0.222596	+	0.147753i
$807$	−7.86548e9	+	1.36234e10i	−0.526827	+	0.912491i
$808$	1.46659e9	−	2.54020e9i	0.0978065	−	0.169406i
$809$	−8.42521e9	+	1.45929e10i	−0.559449	+	0.968995i	0.438093	+	0.898930i	$0.355654\pi$
$809$	−8.42521e9	+	1.45929e10i	−0.559449	+	0.968995i	−0.997542	+	0.0700652i	$0.977679\pi$
$810$	−4.15929e9	−	7.20411e9i	−0.274993	−	0.476302i
$811$	2.71148e10			1.78498			0.892489	−	0.451070i	$-0.148958\pi$
$811$	2.71148e10			1.78498			0.892489	+	0.451070i	$0.148958\pi$
$812$	−1.96089e6	+	1.50046e7i	−0.000128531	+	0.000983509i
$813$	−9.50829e9	+	1.64688e10i	−0.620563	+	1.07485i
$814$	3.63294e9	−	6.29244e9i	0.236088	−	0.408916i
$815$	7.55905e9			0.489120
$816$	1.74292e10	−	3.01883e10i	1.12295	−	1.94501i
$817$	4.71063e9			0.302205
$818$	1.02193e10			0.652809
$819$	2.65063e9	+	7.70705e9i	0.168599	+	0.490224i
$820$	−2.50888e8			−0.0158903
$821$	1.54912e10			0.976978			0.488489	−	0.872570i	$-0.337548\pi$
$821$	1.54912e10			0.976978			0.488489	+	0.872570i	$0.337548\pi$
$822$	−1.57718e10	+	2.73175e10i	−0.990443	+	1.71550i
$823$	−1.43412e10			−0.896783			−0.448391	−	0.893837i	$-0.648003\pi$
$823$	−1.43412e10			−0.896783			−0.448391	+	0.893837i	$0.648003\pi$
$824$	−7.95304e9	+	1.37751e10i	−0.495208	+	0.857726i
$825$	8.30558e9	−	1.43857e10i	0.514969	−	0.891952i
$826$	4.70810e9	+	3.60555e9i	0.290680	+	0.222608i
$827$	2.55775e10			1.57249			0.786247	−	0.617913i	$-0.212022\pi$
$827$	2.55775e10			1.57249			0.786247	+	0.617913i	$0.212022\pi$
$828$	1.18101e8	+	2.04558e8i	0.00723018	+	0.0125230i
$829$	1.04686e10	−	1.81321e10i	0.638184	−	1.10537i	−0.347646	−	0.937626i	$-0.613019\pi$
$829$	1.04686e10	−	1.81321e10i	0.638184	−	1.10537i	0.985831	−	0.167742i	$-0.0536476\pi$
$830$	4.31189e9	−	7.46841e9i	0.261754	−	0.453372i
$831$	−1.29648e10	+	2.24558e10i	−0.783724	+	1.35745i
$832$	−1.44057e10	+	7.15886e9i	−0.867170	+	0.430936i
$833$	−7.70201e9	−	2.85273e10i	−0.461686	−	1.71003i
$834$	−7.83327e9	−	1.35676e10i	−0.467586	−	0.809883i
$835$	−4.36747e9			−0.259614
$836$	−2.36370e8			−0.0139917
$837$	1.32518e9	+	2.29528e9i	0.0781154	+	0.135300i
$838$	4.02455e8	+	6.97073e8i	0.0236245	+	0.0409189i
$839$	8.30400e9	−	1.43829e10i	0.485423	−	0.840777i	−0.514437	−	0.857528i	$-0.671999\pi$
$839$	8.30400e9	−	1.43829e10i	0.485423	−	0.840777i	0.999860	+	0.0167510i	$0.00533226\pi$
$840$	−1.17112e9	+	8.96133e9i	−0.0681747	+	0.521669i
$841$	8.61544e9	−	1.49224e10i	0.499450	−	0.865072i
$842$	−7.98863e9			−0.461190
$843$	1.93643e10	−	3.35399e10i	1.11328	−	1.92826i
$844$	4.63439e8	+	8.02700e8i	0.0265335	+	0.0459573i
$845$	2.95356e9	+	7.00922e9i	0.168402	+	0.399642i
$846$	−3.21415e9			−0.182503
$847$	1.36904e8	−	1.04758e9i	0.00774148	−	0.0592373i
$848$	−1.39896e9	−	2.42306e9i	−0.0787805	−	0.136452i
$849$	2.58743e8	+	4.48156e8i	0.0145108	+	0.0251335i
$850$	1.30657e10	+	2.26304e10i	0.729735	+	1.26394i
$851$	7.58159e9			0.421703
$852$	3.65434e8	+	6.32951e8i	0.0202428	+	0.0350616i
$853$	−4.12703e9			−0.227676			−0.113838	−	0.993499i	$-0.536314\pi$
$853$	−4.12703e9			−0.227676			−0.113838	+	0.993499i	$0.536314\pi$
$854$	−2.07298e9	+	1.58623e10i	−0.113892	+	0.871493i
$855$	−9.34000e8	−	1.61774e9i	−0.0511052	−	0.0885169i
$856$	1.05598e10			0.575439
$857$	−2.89528e9	−	5.01477e9i	−0.157129	−	0.272156i	0.776703	−	0.629867i	$-0.216891\pi$
$857$	−2.89528e9	−	5.01477e9i	−0.157129	−	0.272156i	−0.933832	+	0.357711i	$0.883557\pi$
$858$	−1.98438e10	−	1.31718e10i	−1.07255	−	0.711934i
$859$	1.76227e10	−	3.05235e10i	0.948631	−	1.64308i	0.200318	−	0.979731i	$-0.435802\pi$
$859$	1.76227e10	−	3.05235e10i	0.948631	−	1.64308i	0.748313	−	0.663346i	$-0.230864\pi$
$860$	−8.03759e7	−	1.39215e8i	−0.00430905	−	0.00746349i
$861$	2.24568e10	+	1.71978e10i	1.19905	+	0.918252i
$862$	−6.77030e9	+	1.17265e10i	−0.360025	+	0.623582i
$863$	−7.68969e9	+	1.33189e10i	−0.407260	+	0.705394i	−0.994582	−	0.103959i	$-0.966849\pi$
$863$	−7.68969e9	+	1.33189e10i	−0.407260	+	0.705394i	0.587322	+	0.809353i	$0.300182\pi$
$864$	6.72461e8			0.0354707
$865$	−6.97902e8			−0.0366639
$866$	−2.43239e9	+	4.21303e9i	−0.127269	+	0.220436i
$867$	2.52701e10	−	4.37691e10i	1.31686	−	2.28087i
$868$	−1.96504e7	+	1.50363e8i	−0.00101989	+	0.00780411i
$869$	5.84228e9	+	1.01191e10i	0.302004	+	0.523087i
$870$	1.74738e8	−	3.02656e8i	0.00899644	−	0.0155823i
$871$	2.15934e9	−	3.45607e10i	0.110728	−	1.77223i
$872$	−8.58208e8	−	1.48646e9i	−0.0438314	−	0.0759182i
$873$	1.99485e10			1.01475
$874$	−4.24833e9	−	7.35833e9i	−0.215243	−	0.372811i
$875$	−1.23627e10	−	9.46762e9i	−0.623860	−	0.477763i
$876$	−1.07867e9			−0.0542156
$877$	−3.36908e9	−	5.83542e9i	−0.168660	−	0.292128i	0.769289	−	0.638901i	$-0.220611\pi$
$877$	−3.36908e9	−	5.83542e9i	−0.168660	−	0.292128i	−0.937949	+	0.346773i	$0.887277\pi$
$878$	−1.14301e10			−0.569925
$879$	−1.83279e10	−	3.17448e10i	−0.910231	−	1.57657i
$880$	−4.64343e9	−	8.04265e9i	−0.229694	−	0.397841i
$881$	−1.00106e10	−	1.73389e10i	−0.493224	−	0.854290i	0.506745	−	0.862096i	$-0.330849\pi$
$881$	−1.00106e10	−	1.73389e10i	−0.493224	−	0.854290i	−0.999970	+	0.00780611i	$0.997515\pi$
$882$	−7.56598e9	+	7.59479e9i	−0.371300	+	0.372714i
$883$	5.01100e9			0.244941			0.122471	−	0.992472i	$-0.460918\pi$
$883$	5.01100e9			0.244941			0.122471	+	0.992472i	$0.460918\pi$
$884$	9.73976e8	−	4.84012e8i	0.0474204	−	0.0235653i
$885$	−1.98776e9	−	3.44290e9i	−0.0963969	−	0.166964i
$886$	−1.32536e10	+	2.29558e10i	−0.640198	+	1.10886i
$887$	−9.36791e9			−0.450723			−0.225362	−	0.974275i	$-0.572356\pi$
$887$	−9.36791e9			−0.450723			−0.225362	+	0.974275i	$0.572356\pi$
$888$	−5.72046e9	+	9.90813e9i	−0.274148	+	0.474839i
$889$	−6.54213e7	+	5.00600e8i	−0.00312294	+	0.0238965i
$890$	−3.34485e8	+	5.79345e8i	−0.0159042	+	0.0275469i
$891$	−1.35811e10	−	2.35231e10i	−0.643224	−	1.11410i
$892$	−5.15655e8	−	8.93141e8i	−0.0243267	−	0.0421350i
$893$	3.35618e9			0.157712
$894$	3.24783e10			1.52024
$895$	−2.27943e9	−	3.94808e9i	−0.106278	−	0.184080i
$896$	−1.78209e10	−	1.36476e10i	−0.827660	−	0.633837i
$897$	1.54974e9	−	2.48040e10i	0.0716944	−	1.14749i
$898$	6.44304e9	−	1.11597e10i	0.296909	−	0.514262i
$899$	−9.51411e7	+	1.64789e8i	−0.00436726	+	0.00756432i
$900$	1.37599e8	−	2.38328e8i	0.00629167	−	0.0108975i
$901$	−2.97729e9	−	5.15682e9i	−0.135608	−	0.234879i
$902$	−2.82214e10			−1.28043
$903$	−2.34851e9	+	1.79706e10i	−0.106141	+	0.812188i
$904$	−1.14847e10	+	1.98920e10i	−0.517046	+	0.895550i
$905$	−6.88094e9	+	1.19181e10i	−0.308587	+	0.534488i
$906$	−2.82256e10			−1.26094
$907$	−1.42116e10	+	2.46152e10i	−0.632437	+	1.09541i	0.354615	+	0.935012i	$0.384612\pi$
$907$	−1.42116e10	+	2.46152e10i	−0.632437	+	1.09541i	−0.987052	+	0.160400i	$0.948721\pi$
$908$	8.29758e8			0.0367833
$909$	−2.33253e9			−0.103004
$910$	−6.56641e9	+	7.54828e9i	−0.288857	+	0.332050i
$911$	−4.41472e10			−1.93459			−0.967294	−	0.253656i	$-0.918367\pi$
$911$	−4.41472e10			−1.93459			−0.967294	+	0.253656i	$0.918367\pi$
$912$	1.32055e10			0.576464
$913$	1.40793e10	−	2.43861e10i	0.612258	−	1.06046i
$914$	−4.89571e9			−0.212082
$915$	5.36223e9	−	9.28766e9i	0.231404	−	0.400804i
$916$	4.01088e7	−	6.94704e7i	0.00172427	−	0.00298652i
$917$	8.73489e9	−	3.62784e9i	0.374080	−	0.155366i
$918$	2.50036e10			1.06673
$919$	1.40109e10	+	2.42676e10i	0.595474	+	1.03139i	0.993480	+	0.114008i	$0.0363689\pi$
$919$	1.40109e10	+	2.42676e10i	0.595474	+	1.03139i	−0.398006	+	0.917383i	$0.630298\pi$
$920$	4.70441e9	−	8.14828e9i	0.199181	−	0.344992i
$921$	−1.89225e10	+	3.27747e10i	−0.798122	+	1.38239i
$922$	−5.46482e9	+	9.46535e9i	−0.229624	+	0.397721i
$923$	1.63718e9	−	2.62034e10i	0.0685314	−	1.09686i
$924$	1.17844e8	−	9.01731e8i	0.00491421	−	0.0376032i
$925$	−4.41662e9	−	7.64981e9i	−0.183482	−	0.317800i
$926$	1.70669e9			0.0706346
$927$	1.26489e10			0.521523
$928$	2.41396e7	+	4.18110e7i	0.000991543	+	0.00171740i
$929$	5.76499e9	+	9.98526e9i	0.235909	+	0.408606i	0.959536	−	0.281585i	$-0.0908601\pi$
$929$	5.76499e9	+	9.98526e9i	0.235909	+	0.408606i	−0.723628	+	0.690190i	$0.757527\pi$
$930$	1.75108e9	−	3.03296e9i	0.0713864	−	0.123645i
$931$	7.90031e9	−	7.93040e9i	0.320863	−	0.322085i
$932$	2.40097e8	−	4.15860e8i	0.00971473	−	0.0168264i
$933$	1.28703e10			0.518805
$934$	1.23357e10	−	2.13660e10i	0.495391	−	0.858043i
$935$	−9.88224e9	−	1.71165e10i	−0.395380	−	0.684818i
$936$	1.06679e10	+	7.08109e9i	0.425221	+	0.282250i
$937$	1.70108e10			0.675517			0.337759	−	0.941233i	$-0.390331\pi$
$937$	1.70108e10			0.675517			0.337759	+	0.941233i	$0.390331\pi$
$938$	4.20645e10	−	1.74705e10i	1.66420	−	0.691188i
$939$	4.09930e9	+	7.10019e9i	0.161577	+	0.279860i
$940$	−5.72654e7	−	9.91865e7i	−0.00224877	−	0.00389498i
$941$	−2.34635e10	−	4.06400e10i	−0.917971	−	1.58997i	−0.802492	−	0.596663i	$-0.796493\pi$
$941$	−2.34635e10	−	4.06400e10i	−0.917971	−	1.58997i	−0.115479	−	0.993310i	$-0.536840\pi$
$942$	3.42130e10			1.33356
$943$	−1.47238e10	−	2.55024e10i	−0.571780	−	0.990353i
$944$	9.59520e9			0.371238
$945$	−6.16586e9	+	2.56085e9i	−0.237674	+	0.0987126i
$946$	−9.04118e9	−	1.56598e10i	−0.347221	−	0.601405i
$947$	−4.05168e10			−1.55028			−0.775140	−	0.631790i	$-0.782321\pi$
$947$	−4.05168e10			−1.55028			−0.775140	+	0.631790i	$0.782321\pi$
$948$	2.83495e8	+	4.91027e8i	0.0108073	+	0.0187187i
$949$	3.22837e10	+	2.14290e10i	1.22617	+	0.813900i
$950$	−4.94969e9	+	8.57312e9i	−0.187303	+	0.324419i
$951$	2.29342e10	+	3.97231e10i	0.864671	+	1.49765i
$952$	−3.68561e10	−	2.82251e10i	−1.38446	−	1.06024i
$953$	−1.04310e10	+	1.80670e10i	−0.390391	+	0.676177i	−0.992501	−	0.122236i	$-0.960993\pi$
$953$	−1.04310e10	+	1.80670e10i	−0.390391	+	0.676177i	0.602110	+	0.798413i	$0.294327\pi$
$954$	−1.08016e9	+	1.87090e9i	−0.0402781	+	0.0697638i
$955$	9.03423e9			0.335644
$956$	−8.46895e8			−0.0313492
$957$	5.70562e8	−	9.88242e8i	0.0210432	−	0.0364478i
$958$	2.23361e10	−	3.86873e10i	0.820784	−	1.42164i
$959$	3.43492e10	+	2.63053e10i	1.25763	+	0.963114i
$960$	7.09261e9	+	1.22848e10i	0.258736	+	0.448144i
$961$	1.28029e10	−	2.21752e10i	0.465346	−	0.806003i
$962$	−1.13420e10	+	5.63636e9i	−0.410750	+	0.204120i
$963$	−4.19872e9	−	7.27239e9i	−0.151504	−	0.262413i
$964$	−1.27346e9			−0.0457842
$965$	−6.14735e9	−	1.06475e10i	−0.220213	−	0.381420i
$966$	3.01894e10	−	1.25385e10i	1.07754	−	0.447533i
$967$	−4.16282e10			−1.48046			−0.740228	−	0.672356i	$-0.765282\pi$
$967$	−4.16282e10			−1.48046			−0.740228	+	0.672356i	$0.765282\pi$
$968$	−8.29892e8	−	1.43741e9i	−0.0294075	−	0.0509352i
$969$	2.81042e10			0.992288
$970$	1.22439e10	+	2.12071e10i	0.430744	+	0.746071i
$971$	−4.11103e9	−	7.12051e9i	−0.144106	−	0.249599i	0.784933	−	0.619581i	$-0.212697\pi$
$971$	−4.11103e9	−	7.12051e9i	−0.144106	−	0.249599i	−0.929039	+	0.369981i	$0.879364\pi$
$972$	−4.05046e8	−	7.01560e8i	−0.0141473	−	0.0245038i
$973$	−1.98445e10	+	8.24196e9i	−0.690630	+	0.286837i
$974$	−1.06110e10			−0.367958
$975$	−2.59300e10	+	1.28858e10i	−0.895954	+	0.445240i
$976$	1.29421e10	+	2.24164e10i	0.445585	+	0.771776i
$977$	−8.02348e9	+	1.38971e10i	−0.275253	+	0.476752i	−0.970199	−	0.242310i	$-0.922095\pi$
$977$	−8.02348e9	+	1.38971e10i	−0.275253	+	0.476752i	0.694946	+	0.719062i	$0.255428\pi$
$978$	4.12600e10			1.41040
$979$	−1.09217e9	+	1.89170e9i	−0.0372007	+	0.0644336i
$980$	−3.69171e8	−	9.81673e7i	−0.0125296	−	0.00333178i
$981$	−6.82467e8	+	1.18207e9i	−0.0230802	+	0.0399761i
$982$	−1.87809e10	−	3.25294e10i	−0.632886	−	1.09619i
$983$	−4.85724e9	−	8.41299e9i	−0.163099	−	0.282496i	0.772879	−	0.634553i	$-0.218816\pi$
$983$	−4.85724e9	−	8.41299e9i	−0.163099	−	0.282496i	−0.935979	+	0.352057i	$0.885482\pi$
$984$	4.44377e10			1.48685
$985$	1.24471e10			0.414994
$986$	8.97562e8	+	1.55462e9i	0.0298192	+	0.0516483i
$987$	−1.67324e9	+	1.28035e10i	−0.0553921	+	0.423857i
$988$	3.43280e8	+	2.27861e8i	0.0113240	+	0.00751657i
$989$	9.43402e9	−	1.63402e10i	0.310106	−	0.537119i
$990$	−3.58528e9	+	6.20989e9i	−0.117436	+	0.203404i
$991$	3.44777e9	−	5.97172e9i	0.112533	−	0.194913i	−0.804258	−	0.594281i	$-0.797437\pi$
$991$	3.44777e9	−	5.97172e9i	0.112533	−	0.194913i	0.916791	+	0.399367i	$0.130770\pi$
$992$	2.41906e8	+	4.18994e8i	0.00786786	+	0.0136275i
$993$	1.58445e10			0.513517
$994$	3.18927e10	−	1.32459e10i	1.03000	−	0.427789i
$995$	1.12052e10	−	1.94080e10i	0.360611	−	0.624597i
$996$	6.83195e8	−	1.18333e9i	0.0219097	−	0.0379488i
$997$	−5.25743e10			−1.68012			−0.840060	−	0.542493i	$-0.817481\pi$
$997$	−5.25743e10			−1.68012			−0.840060	+	0.542493i	$0.817481\pi$
$998$	8.96365e8	−	1.55255e9i	0.0285449	−	0.0494412i
$999$	−8.45202e9			−0.268214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.h.a.16.18	yes	126
7.4	even	3		91.8.g.a.81.46	yes	126
13.9	even	3		91.8.g.a.9.46	✓	126
91.74	even	3	inner	91.8.h.a.74.18	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.g.a.9.46	✓	126	13.9	even	3
91.8.g.a.81.46	yes	126	7.4	even	3
91.8.h.a.16.18	yes	126	1.1	even	1	trivial
91.8.h.a.74.18	yes	126	91.74	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-11.4816 q^{2} +(28.8130 - 49.9056i) q^{3} +3.82665 q^{4} +(-60.6077 + 104.976i) q^{5} +(-330.819 + 572.995i) q^{6} +(720.487 + 551.762i) q^{7} +1425.71 q^{8} +(-566.877 - 981.860i) q^{9} +O(q^{10})\)	\(q-11.4816 q^{2} +(28.8130 - 49.9056i) q^{3} +3.82665 q^{4} +(-60.6077 + 104.976i) q^{5} +(-330.819 + 572.995i) q^{6} +(720.487 + 551.762i) q^{7} +1425.71 q^{8} +(-566.877 - 981.860i) q^{9} +(695.873 - 1205.29i) q^{10} +(2272.19 - 3935.55i) q^{11} +(110.257 - 190.971i) q^{12} +(-7093.76 + 3525.21i) q^{13} +(-8272.33 - 6335.10i) q^{14} +(3492.58 + 6049.33i) q^{15} -16859.2 q^{16} -35880.0 q^{17} +(6508.65 + 11273.3i) q^{18} +(-6796.26 - 11771.5i) q^{19} +(-231.925 + 401.705i) q^{20} +(48295.4 - 20058.4i) q^{21} +(-26088.3 + 45186.3i) q^{22} -54443.7 q^{23} +(41078.9 - 71150.7i) q^{24} +(31715.9 + 54933.6i) q^{25} +(81447.6 - 40474.9i) q^{26} +60694.3 q^{27} +(2757.05 + 2111.40i) q^{28} +(2178.76 + 3773.73i) q^{29} +(-40100.3 - 69455.8i) q^{30} +(21833.7 + 37817.1i) q^{31} +11079.5 q^{32} +(-130937. - 226790. i) q^{33} +411960. q^{34} +(-101589. + 42192.6i) q^{35} +(-2169.24 - 3757.23i) q^{36} -139256. q^{37} +(78031.7 + 135155. i) q^{38} +(-28465.0 + 455590. i) q^{39} +(-86408.8 + 149664. i) q^{40} +(270441. + 468418. i) q^{41} +(-554507. + 230302. i) q^{42} +(-173280. + 300130. i) q^{43} +(8694.87 - 15059.9i) q^{44} +137429. q^{45} +625099. q^{46} +(-123457. + 213834. i) q^{47} +(-485763. + 841366. i) q^{48} +(214660. + 795075. i) q^{49} +(-364149. - 630724. i) q^{50} +(-1.03381e6 + 1.79061e6i) q^{51} +(-27145.3 + 13489.7i) q^{52} +(82979.0 + 143724. i) q^{53} -696866. q^{54} +(275424. + 477049. i) q^{55} +(1.02720e6 + 786651. i) q^{56} -783282. q^{57} +(-25015.6 - 43328.4i) q^{58} -569138. q^{59} +(13364.9 + 23148.7i) q^{60} +(-767660. - 1.32963e6i) q^{61} +(-250686. - 434200. i) q^{62} +(133326. - 1.02020e6i) q^{63} +2.03076e6 q^{64} +(59875.8 - 958327. i) q^{65} +(1.50336e6 + 2.60390e6i) q^{66} +(-2.18573e6 + 3.78580e6i) q^{67} -137300. q^{68} +(-1.56869e6 + 2.71704e6i) q^{69} +(1.16640e6 - 484437. i) q^{70} +(-1.65719e6 + 2.87034e6i) q^{71} +(-808200. - 1.39984e6i) q^{72} +(-2.44581e6 - 4.23626e6i) q^{73} +1.59887e6 q^{74} +3.65532e6 q^{75} +(-26006.9 - 45045.2i) q^{76} +(3.80857e6 - 1.58180e6i) q^{77} +(326824. - 5.23089e6i) q^{78} +(-1.28561e6 + 2.22674e6i) q^{79} +(1.02180e6 - 1.76980e6i) q^{80} +(2.98855e6 - 5.17631e6i) q^{81} +(-3.10509e6 - 5.37818e6i) q^{82} +6.19637e6 q^{83} +(184810. - 76756.4i) q^{84} +(2.17461e6 - 3.76653e6i) q^{85} +(1.98953e6 - 3.44597e6i) q^{86} +251107. q^{87} +(3.23947e6 - 5.61093e6i) q^{88} -480670. q^{89} -1.57790e6 q^{90} +(-7.05604e6 - 1.37420e6i) q^{91} -208337. q^{92} +2.51638e6 q^{93} +(1.41748e6 - 2.45515e6i) q^{94} +1.64762e6 q^{95} +(319233. - 552928. i) q^{96} +(-8.79753e6 + 1.52378e7i) q^{97} +(-2.46464e6 - 9.12872e6i) q^{98} -5.15221e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9	\( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q - 2 * q^2 - 80 * q^3 + 7678 * q^4 - 2 * q^5 - 258 * q^6 + 953 * q^7 - 264 * q^8 - 41707 * q^9 - 4255 * q^10 + 7423 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 + 410294 * q^16 + 99274 * q^17 - 21111 * q^18 - 4844 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 + 34130 * q^23 - 130304 * q^24 - 810669 * q^25 + 390708 * q^26 + 416614 * q^27 + 69267 * q^28 + 191096 * q^29 + 70666 * q^30 + 183609 * q^31 + 695346 * q^32 + 178591 * q^33 - 742000 * q^34 + 579437 * q^35 - 1732409 * q^36 - 1362898 * q^37 - 877438 * q^38 + 459227 * q^39 - 1502882 * q^40 + 593701 * q^41 + 1442877 * q^42 - 592188 * q^43 + 1254066 * q^44 + 1954226 * q^45 - 1385452 * q^46 + 98278 * q^47 - 374916 * q^48 - 1497637 * q^49 + 289562 * q^50 - 281250 * q^51 - 8455 * q^52 - 1256681 * q^53 - 293814 * q^54 - 3015554 * q^55 - 1646151 * q^56 + 2743072 * q^57 + 1851469 * q^58 - 2279458 * q^59 + 1031485 * q^60 - 1127636 * q^61 - 7724680 * q^62 + 5142530 * q^63 + 11827496 * q^64 - 2789048 * q^65 + 435059 * q^66 + 4373348 * q^67 + 8737122 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 - 11660951 * q^72 - 5060877 * q^73 + 1184002 * q^74 + 22637254 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 - 123568 * q^80 - 30756895 * q^81 + 8626952 * q^82 - 18679806 * q^83 + 11302461 * q^84 + 5330093 * q^85 - 8512356 * q^86 - 16508762 * q^87 - 6438219 * q^88 - 6176684 * q^89 + 53481084 * q^90 + 29236777 * q^91 + 2460546 * q^92 + 27682404 * q^93 - 17421794 * q^94 + 39553398 * q^95 + 26667066 * q^96 + 7705262 * q^97 + 14093080 * q^98 - 60531432 * q^99

Introduction

L-functions

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