LMFDB - Embedded newform 62.7.f.a.15.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	62.15
Dual form			62.7.f.a.29.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.57649 + 3.32502i) q^{2} +(-25.5799 + 35.2077i) q^{3} +(9.88854 - 30.4338i) q^{4} -242.487 q^{5} -246.181i q^{6} +(114.010 - 350.886i) q^{7} +(55.9381 + 172.160i) q^{8} +(-359.977 - 1107.90i) q^{9} +(1109.74 - 806.272i) q^{10} +(-92.0678 - 29.9146i) q^{11} +(818.556 + 1126.65i) q^{12} +(-1937.90 + 2667.29i) q^{13} +(644.937 + 1984.91i) q^{14} +(6202.78 - 8537.40i) q^{15} +(-828.433 - 601.892i) q^{16} +(-6475.21 + 2103.92i) q^{17} +(5331.21 + 3873.35i) q^{18} +(-3396.25 + 2467.52i) q^{19} +(-2397.84 + 7379.80i) q^{20} +(9437.53 + 12989.6i) q^{21} +(520.814 - 169.223i) q^{22} +(-2109.06 + 685.275i) q^{23} +(-7492.23 - 2434.37i) q^{24} +43174.9 q^{25} -18650.4i q^{26} +(18042.0 + 5862.20i) q^{27} +(-9551.41 - 6939.50i) q^{28} +(11816.2 + 16263.6i) q^{29} +59695.7i q^{30} +(22017.3 - 20068.4i) q^{31} +5792.62 q^{32} +(3408.31 - 2476.28i) q^{33} +(22638.2 - 31158.8i) q^{34} +(-27645.9 + 85085.2i) q^{35} -37277.2 q^{36} -77698.9i q^{37} +(7338.36 - 22585.1i) q^{38} +(-44337.9 - 136458. i) q^{39} +(-13564.2 - 41746.4i) q^{40} +(5559.12 - 4038.94i) q^{41} +(-86381.5 - 28067.1i) q^{42} +(53616.3 + 73796.5i) q^{43} +(-1820.83 + 2506.16i) q^{44} +(87289.8 + 268650. i) q^{45} +(7373.55 - 10148.8i) q^{46} +(16098.4 + 11696.2i) q^{47} +(42382.5 - 13770.9i) q^{48} +(-14942.8 - 10856.6i) q^{49} +(-197589. + 143557. i) q^{50} +(91560.8 - 281795. i) q^{51} +(62012.9 + 85353.4i) q^{52} +(-231467. + 75208.3i) q^{53} +(-102061. + 33161.6i) q^{54} +(22325.2 + 7253.90i) q^{55} +66785.9 q^{56} -182693. i q^{57} +(-108154. - 35141.2i) q^{58} +(138919. + 100930. i) q^{59} +(-198489. - 273197. i) q^{60} -233403. i q^{61} +(-34034.4 + 165051. i) q^{62} -429787. q^{63} +(-26509.9 + 19260.5i) q^{64} +(469916. - 646783. i) q^{65} +(-7364.42 + 22665.4i) q^{66} -311746. q^{67} +217870. i q^{68} +(29822.6 - 91784.4i) q^{69} +(-156389. - 481315. i) q^{70} +(-115712. - 356126. i) q^{71} +(170599. - 123947. i) q^{72} +(387864. + 126024. i) q^{73} +(258350. + 355588. i) q^{74} +(-1.10441e6 + 1.52009e6i) q^{75} +(41512.0 + 127761. i) q^{76} +(-20993.3 + 28894.7i) q^{77} +(656637. + 477075. i) q^{78} +(248693. - 80805.4i) q^{79} +(200884. + 145951. i) q^{80} +(19127.1 - 13896.7i) q^{81} +(-12011.7 + 36968.3i) q^{82} +(356485. + 490660. i) q^{83} +(488648. - 158771. i) q^{84} +(1.57015e6 - 510174. i) q^{85} +(-490749. - 159454. i) q^{86} -874862. q^{87} -17523.7i q^{88} +(162301. + 52734.7i) q^{89} +(-1.29275e6 - 939236. i) q^{90} +(714976. + 984080. i) q^{91} +70963.1i q^{92} +(143361. + 1.28853e6i) q^{93} -112564. q^{94} +(823545. - 598341. i) q^{95} +(-148175. + 203945. i) q^{96} +(50557.4 - 155600. i) q^{97} +104484. q^{98} +112770. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−4.57649	+	3.32502i	−0.572061	+	0.415627i
$2$	−4.57649	+	3.32502i	−0.572061	+	0.415627i
$3$	−25.5799	+	35.2077i	−0.947403	+	1.30399i	0.00526824	+	0.999986i	$0.498323\pi$
$3$	−25.5799	+	35.2077i	−0.947403	+	1.30399i	−0.952671	+	0.304002i	$0.901677\pi$
$4$	9.88854	−	30.4338i	0.154508	−	0.475528i
$5$	−242.487			−1.93989			−0.969947	−	0.243315i	$-0.921765\pi$
$5$	−242.487			−1.93989			−0.969947	+	0.243315i	$0.921765\pi$
$6$		−	246.181i		−	1.13973i
$7$	114.010	−	350.886i	0.332390	−	1.02299i	−0.635603	−	0.772016i	$-0.719249\pi$
$7$	114.010	−	350.886i	0.332390	−	1.02299i	0.967993	−	0.250976i	$-0.0807514\pi$
$8$	55.9381	+	172.160i	0.109254	+	0.336249i
$9$	−359.977	−	1107.90i	−0.493796	−	1.51975i
$10$	1109.74	−	806.272i	1.10974	−	0.806272i
$11$	−92.0678	−	29.9146i	−0.0691719	−	0.0224753i	0.274227	−	0.961665i	$-0.411578\pi$
$11$	−92.0678	−	29.9146i	−0.0691719	−	0.0224753i	−0.343399	+	0.939190i	$0.611578\pi$
$12$	818.556	+	1126.65i	0.473702	+	0.651994i
$13$	−1937.90	+	2667.29i	−0.882067	+	1.21406i	0.0937766	+	0.995593i	$0.470106\pi$
$13$	−1937.90	+	2667.29i	−0.882067	+	1.21406i	−0.975844	+	0.218468i	$0.929894\pi$
$14$	644.937	+	1984.91i	0.235035	+	0.723364i
$15$	6202.78	−	8537.40i	1.83786	−	2.52960i
$16$	−828.433	−	601.892i	−0.202254	−	0.146946i
$17$	−6475.21	+	2103.92i	−1.31797	+	0.428236i	−0.881799	−	0.471625i	$-0.843667\pi$
$17$	−6475.21	+	2103.92i	−1.31797	+	0.428236i	−0.436176	+	0.899861i	$0.643667\pi$
$18$	5331.21	+	3873.35i	0.914130	+	0.664155i
$19$	−3396.25	+	2467.52i	−0.495152	+	0.359749i	−0.807162	−	0.590330i	$-0.798998\pi$
$19$	−3396.25	+	2467.52i	−0.495152	+	0.359749i	0.312010	+	0.950079i	$0.398998\pi$
$20$	−2397.84	+	7379.80i	−0.299730	+	0.922475i
$21$	9437.53	+	12989.6i	1.01906	+	1.40262i
$22$	520.814	−	169.223i	0.0489119	−	0.0158924i
$23$	−2109.06	+	685.275i	−0.173343	+	0.0563225i	−0.394402	−	0.918938i	$-0.629048\pi$
$23$	−2109.06	+	685.275i	−0.173343	+	0.0563225i	0.221060	+	0.975260i	$0.429048\pi$
$24$	−7492.23	−	2434.37i	−0.541973	−	0.176098i
$25$	43174.9			2.76319
$26$		−	18650.4i		−	1.06113i
$27$	18042.0	+	5862.20i	0.916629	+	0.297831i
$28$	−9551.41	−	6939.50i	−0.435104	−	0.316122i
$29$	11816.2	+	16263.6i	0.484489	+	0.666843i	0.979360	−	0.202124i	$-0.0647845\pi$
$29$	11816.2	+	16263.6i	0.484489	+	0.666843i	−0.494870	+	0.868967i	$0.664784\pi$
$30$			59695.7i			2.21095i
$31$	22017.3	−	20068.4i	0.739060	−	0.673640i
$31$	22017.3	−	20068.4i	0.739060	−	0.673640i
$32$	5792.62			0.176777
$33$	3408.31	−	2476.28i	0.0948412	−	0.0689062i
$34$	22638.2	−	31158.8i	0.575976	−	0.792763i
$35$	−27645.9	+	85085.2i	−0.644802	+	1.98450i
$36$	−37277.2			−0.798979
$37$		−	77698.9i		−	1.53395i	−0.641680	−	0.766973i	$-0.721762\pi$
$37$		−	77698.9i		−	1.53395i	0.641680	−	0.766973i	$-0.278238\pi$
$38$	7338.36	−	22585.1i	0.133736	−	0.411597i
$39$	−44337.9	−	136458.i	−0.747449	−	2.30041i
$40$	−13564.2	−	41746.4i	−0.211941	−	0.652288i
$41$	5559.12	−	4038.94i	0.0806593	−	0.0586024i	−0.546725	−	0.837312i	$-0.684126\pi$
$41$	5559.12	−	4038.94i	0.0806593	−	0.0586024i	0.627384	+	0.778710i	$0.284126\pi$
$42$	−86381.5	−	28067.1i	−1.16593	−	0.378834i
$43$	53616.3	+	73796.5i	0.674360	+	0.928176i	0.999849	−	0.0173693i	$-0.00552909\pi$
$43$	53616.3	+	73796.5i	0.674360	+	0.928176i	−0.325490	+	0.945546i	$0.605529\pi$
$44$	−1820.83	+	2506.16i	−0.0213753	+	0.0294206i
$45$	87289.8	+	268650.i	0.957913	+	2.94815i
$46$	7373.55	−	10148.8i	0.0757535	−	0.104266i
$47$	16098.4	+	11696.2i	0.155056	+	0.112655i	0.662608	−	0.748966i	$-0.269450\pi$
$47$	16098.4	+	11696.2i	0.155056	+	0.112655i	−0.507552	+	0.861621i	$0.669450\pi$
$48$	42382.5	−	13770.9i	0.383233	−	0.124520i
$49$	−14942.8	−	10856.6i	−0.127011	−	0.0922792i
$50$	−197589.	+	143557.i	−1.58071	+	1.14846i
$51$	91560.8	−	281795.i	0.690239	−	2.12434i
$52$	62012.9	+	85353.4i	0.441034	+	0.607031i
$53$	−231467.	+	75208.3i	−1.55476	+	0.505171i	−0.955401	−	0.295312i	$-0.904576\pi$
$53$	−231467.	+	75208.3i	−1.55476	+	0.505171i	−0.599356	+	0.800483i	$0.704576\pi$
$54$	−102061.	+	33161.6i	−0.648154	+	0.210598i
$55$	22325.2	+	7253.90i	0.134186	+	0.0435997i
$56$	66785.9			0.380295
$57$		−	182693.i		−	0.986500i
$58$	−108154.	−	35141.2i	−0.554315	−	0.180108i
$59$	138919.	+	100930.i	0.676401	+	0.491434i	0.872162	−	0.489218i	$-0.162718\pi$
$59$	138919.	+	100930.i	0.676401	+	0.491434i	−0.195761	+	0.980652i	$0.562718\pi$
$60$	−198489.	−	273197.i	−0.918931	−	1.26480i
$61$		−	233403.i		−	1.02830i	−0.857702	−	0.514148i	$-0.828108\pi$
$61$		−	233403.i		−	1.02830i	0.857702	−	0.514148i	$-0.171892\pi$
$62$	−34034.4	+	165051.i	−0.142805	+	0.692536i
$63$	−429787.			−1.71882
$64$	−26509.9	+	19260.5i	−0.101127	+	0.0734732i
$65$	469916.	−	646783.i	1.71112	−	2.35515i
$66$	−7364.42	+	22665.4i	−0.0256157	+	0.0788371i
$67$	−311746.			−1.03652			−0.518258	−	0.855224i	$-0.673419\pi$
$67$	−311746.			−1.03652			−0.518258	+	0.855224i	$0.673419\pi$
$68$			217870.i			0.692900i
$69$	29822.6	−	91784.4i	0.0907816	−	0.279397i
$70$	−156389.	−	481315.i	−0.455944	−	1.40325i
$71$	−115712.	−	356126.i	−0.323299	−	0.995013i	−0.972202	−	0.234142i	$-0.924772\pi$
$71$	−115712.	−	356126.i	−0.323299	−	0.995013i	0.648903	−	0.760871i	$-0.275228\pi$
$72$	170599.	−	123947.i	0.457065	−	0.332077i
$73$	387864.	+	126024.i	0.997035	+	0.323956i	0.761680	−	0.647953i	$-0.224375\pi$
$73$	387864.	+	126024.i	0.997035	+	0.323956i	0.235355	+	0.971910i	$0.424375\pi$
$74$	258350.	+	355588.i	0.637549	+	0.877511i
$75$	−1.10441e6	+	1.52009e6i	−2.61786	+	3.60317i
$76$	41512.0	+	127761.i	0.0945656	+	0.291043i
$77$	−20993.3	+	28894.7i	−0.0459841	+	0.0632917i
$78$	656637.	+	477075.i	1.38370	+	1.00532i
$79$	248693.	−	80805.4i	0.504409	−	0.163892i	−0.0457490	−	0.998953i	$-0.514567\pi$
$79$	248693.	−	80805.4i	0.504409	−	0.163892i	0.550158	+	0.835060i	$0.314567\pi$
$80$	200884.	+	145951.i	0.392352	+	0.285060i
$81$	19127.1	−	13896.7i	0.0359911	−	0.0261490i
$82$	−12011.7	+	36968.3i	−0.0217853	+	0.0670484i
$83$	356485.	+	490660.i	0.623458	+	0.858116i	0.997599	−	0.0692554i	$-0.0220623\pi$
$83$	356485.	+	490660.i	0.623458	+	0.858116i	−0.374141	+	0.927372i	$0.622062\pi$
$84$	488648.	−	158771.i	0.824438	−	0.267876i
$85$	1.57015e6	−	510174.i	2.55673	−	0.830733i
$86$	−490749.	−	159454.i	−0.771550	−	0.250692i
$87$	−874862.			−1.32856
$88$		−	17523.7i		−	0.0257145i
$89$	162301.	+	52734.7i	0.230224	+	0.0748043i	0.421857	−	0.906662i	$-0.361378\pi$
$89$	162301.	+	52734.7i	0.230224	+	0.0748043i	−0.191633	+	0.981467i	$0.561378\pi$
$90$	−1.29275e6	−	939236.i	−1.77332	−	1.28839i
$91$	714976.	+	984080.i	0.948784	+	1.30589i
$92$			70963.1i			0.0911316i
$93$	143361.	+	1.28853e6i	0.178231	+	1.60193i
$94$	−112564.			−0.135524
$95$	823545.	−	598341.i	0.960542	−	0.697875i
$96$	−148175.	+	203945.i	−0.167479	+	0.230515i
$97$	50557.4	−	155600.i	0.0553949	−	0.170488i	−0.919531	−	0.393017i	$-0.871431\pi$
$97$	50557.4	−	155600.i	0.0553949	−	0.170488i	0.974926	+	0.222529i	$0.0714313\pi$
$98$	104484.			0.111012
$99$			112770.i			0.116222i
$100$	426936.	−	1.31398e6i	0.426936	−	1.31398i
$101$	−89800.6	−	276378.i	−0.0871596	−	0.268250i	0.897972	−	0.440053i	$-0.145040\pi$
$101$	−89800.6	−	276378.i	−0.0871596	−	0.268250i	−0.985131	+	0.171804i	$0.945040\pi$
$102$	517946.	+	1.59408e6i	0.488072	+	1.50213i
$103$	−806109.	+	585673.i	−0.737704	+	0.535973i	−0.891991	−	0.452053i	$-0.850692\pi$
$103$	−806109.	+	585673.i	−0.737704	+	0.535973i	0.154287	+	0.988026i	$0.450692\pi$
$104$	−567603.	−	184425.i	−0.504597	−	0.163953i
$105$	−2.28848e6	−	3.14982e6i	−1.97687	−	2.72093i
$106$	809240.	−	1.11382e6i	0.679453	−	0.935187i
$107$	−705833.	−	2.17233e6i	−0.576170	−	1.77327i	−0.632160	−	0.774838i	$-0.717832\pi$
$107$	−705833.	−	2.17233e6i	−0.576170	−	1.77327i	0.0559904	−	0.998431i	$-0.482168\pi$
$108$	356818.	−	491118.i	0.283254	−	0.389865i
$109$	−103612.	−	75278.9i	−0.0800079	−	0.0581291i	0.547062	−	0.837092i	$-0.315746\pi$
$109$	−103612.	−	75278.9i	−0.0800079	−	0.0581291i	−0.627070	+	0.778963i	$0.715746\pi$
$110$	−126291.	+	41034.3i	−0.0948839	+	0.0308297i
$111$	2.73560e6	+	1.98753e6i	2.00025	+	1.45326i
$112$	−305645.	+	222064.i	−0.217552	+	0.158061i
$113$	−197161.	+	606798.i	−0.136642	+	0.420542i	−0.995842	−	0.0910990i	$-0.970962\pi$
$113$	−197161.	+	606798.i	−0.136642	+	0.420542i	0.859200	+	0.511641i	$0.170962\pi$
$114$	607456.	+	836092.i	0.410016	+	0.564338i
$115$	511419.	−	166170.i	0.336267	−	0.109260i
$116$	611809.	−	198789.i	0.391960	−	0.127356i
$117$	3.65269e6	+	1.18683e6i	2.28063	+	0.741022i
$118$	−971354.			−0.591196
$119$			2.51193e6i			1.49062i
$120$	1.81677e6	+	590303.i	1.05137	+	0.341611i
$121$	−1.42564e6	−	1.03579e6i	−0.804737	−	0.584676i
$122$	776070.	+	1.06817e6i	0.427387	+	0.588248i
$123$			299039.i			0.160699i
$124$	−393039.	−	868519.i	−0.206144	−	0.455527i
$125$	−6.68048e6			−3.42040
$126$	1.96691e6	−	1.42905e6i	0.983272	−	0.714389i
$127$	495436.	−	681909.i	0.241867	−	0.332901i	−0.670775	−	0.741661i	$-0.734038\pi$
$127$	495436.	−	681909.i	0.241867	−	0.332901i	0.912642	+	0.408759i	$0.134038\pi$
$128$	57280.6	−	176291.i	0.0273135	−	0.0840623i
$129$	−3.96970e6			−1.84922
$130$			4.52248e6i			2.05848i
$131$	95878.0	−	295082.i	0.0426486	−	0.131259i	−0.927465	−	0.373910i	$-0.878017\pi$
$131$	95878.0	−	295082.i	0.0426486	−	0.131259i	0.970114	+	0.242651i	$0.0780169\pi$
$132$	−41659.5	−	128215.i	−0.0181131	−	0.0557463i
$133$	478612.	+	1.47302e6i	0.203436	+	0.626113i
$134$	1.42670e6	−	1.03656e6i	0.592951	−	0.430804i
$135$	−4.37495e6	−	1.42151e6i	−1.77816	−	0.577760i
$136$	−724421.	−	997080.i	−0.287988	−	0.396382i
$137$	534802.	−	736091.i	0.207985	−	0.286266i	−0.692262	−	0.721646i	$-0.743386\pi$
$137$	534802.	−	736091.i	0.207985	−	0.286266i	0.900247	+	0.435380i	$0.143386\pi$
$138$	168702.	+	519211.i	0.0641923	+	0.197563i
$139$	16894.0	−	23252.5i	0.00629053	−	0.00865817i	−0.805860	−	0.592106i	$-0.798297\pi$
$139$	16894.0	−	23252.5i	0.00629053	−	0.00865817i	0.812151	+	0.583448i	$0.198297\pi$
$140$	2.31609e6	+	1.68274e6i	0.844056	+	0.613243i
$141$	−823590.	+	267600.i	−0.293801	+	0.0954618i
$142$	1.71368e6	+	1.24506e6i	0.598501	+	0.434836i
$143$	258209.	−	187600.i	0.0883007	−	0.0641542i
$144$	−368617.	+	1.13449e6i	−0.123449	+	0.379937i
$145$	−2.86528e6	−	3.94371e6i	−0.939858	−	1.29360i
$146$	−2.19409e6	+	712902.i	−0.705010	+	0.229072i
$147$	764468.	−	248391.i	0.240662	−	0.0781958i
$148$	−2.36467e6	−	768329.i	−0.729434	−	0.237008i
$149$	3.65093e6			1.10368			0.551841	−	0.833949i	$-0.313925\pi$
$149$	3.65093e6			1.10368			0.551841	+	0.833949i	$0.313925\pi$
$150$		−	1.06288e7i		−	3.14928i
$151$	−1.20424e6	−	391280.i	−0.349769	−	0.113647i	0.128863	−	0.991662i	$-0.458867\pi$
$151$	−1.20424e6	−	391280.i	−0.349769	−	0.113647i	−0.478632	+	0.878016i	$0.658867\pi$
$152$	−614786.	−	446668.i	−0.175063	−	0.127190i
$153$	4.66186e6	+	6.41650e6i	1.30162	+	1.79153i
$154$		−	202039.i		−	0.0553190i
$155$	−5.33891e6	+	4.86632e6i	−1.43370	+	1.30679i
$156$	−4.59138e6			−1.20940
$157$	3.48612e6	−	2.53282e6i	0.900832	−	0.654492i	−0.0378479	−	0.999284i	$-0.512050\pi$
$157$	3.48612e6	−	2.53282e6i	0.900832	−	0.654492i	0.938679	+	0.344791i	$0.112050\pi$
$158$	−869464.	+	1.19671e6i	−0.220435	+	0.303403i
$159$	3.27300e6	−	1.00733e7i	0.814244	−	2.50598i
$160$	−1.40463e6			−0.342928
$161$			818168.i			0.196049i
$162$	−41328.5	+	127196.i	−0.00972086	+	0.0299177i
$163$	111016.	+	341674.i	0.0256345	+	0.0788948i	0.963055	−	0.269304i	$-0.0867935\pi$
$163$	111016.	+	341674.i	0.0256345	+	0.0788948i	−0.937421	+	0.348198i	$0.886794\pi$
$164$	−67948.6	−	209124.i	−0.0154046	−	0.0474103i
$165$	−826470.	+	600465.i	−0.183982	+	0.133671i
$166$	−3.26290e6	−	1.06018e6i	−0.713313	−	0.231769i
$167$	1.45135e6	+	1.99761e6i	0.311618	+	0.428906i	0.935885	−	0.352306i	$-0.114602\pi$
$167$	1.45135e6	+	1.99761e6i	0.311618	+	0.428906i	−0.624267	+	0.781211i	$0.714602\pi$
$168$	−1.70838e6	+	2.35138e6i	−0.360293	+	0.495900i
$169$	−1.86742e6	−	5.74734e6i	−0.386886	−	1.19071i
$170$	−5.48946e6	+	7.55559e6i	−1.11733	+	1.53788i
$171$	3.95633e6	+	2.87444e6i	0.791232	+	0.574864i
$172$	2.77610e6	−	902008.i	0.545568	−	0.177266i
$173$	1.23422e6	+	896710.i	0.238371	+	0.173186i	0.700557	−	0.713596i	$-0.252935\pi$
$173$	1.23422e6	+	896710.i	0.238371	+	0.173186i	−0.462186	+	0.886783i	$0.652935\pi$
$174$	4.00380e6	−	2.90893e6i	0.760019	−	0.552186i
$175$	4.92236e6	−	1.51495e7i	0.918457	−	2.82672i
$176$	58266.6	+	80197.2i	0.0106876	+	0.0147103i
$177$	−7.10704e6	+	2.30922e6i	−1.28165	+	0.416433i
$178$	−918111.	+	298312.i	−0.162793	+	0.0528946i
$179$	2.93513e6	+	953680.i	0.511762	+	0.166281i	0.553503	−	0.832847i	$-0.313291\pi$
$179$	2.93513e6	+	953680.i	0.511762	+	0.166281i	−0.0417416	+	0.999128i	$0.513291\pi$
$180$	9.03922e6			1.54994
$181$		−	8.74285e6i		−	1.47441i	−0.675671	−	0.737203i	$-0.736146\pi$
$181$		−	8.74285e6i		−	1.47441i	0.675671	−	0.737203i	$-0.263854\pi$
$182$	−6.54417e6	−	2.12633e6i	−1.08553	−	0.352709i
$183$	8.21760e6	+	5.97043e6i	1.34088	+	0.974210i
$184$	−235953.	−	324762.i	−0.0378768	−	0.0521329i
$185$			1.88410e7i			2.97569i
$186$	−4.94046e6	−	5.42025e6i	−0.767766	−	0.842327i
$187$	659096.			0.100792
$188$	515148.	−	374277.i	0.0775280	−	0.0563274i
$189$	4.11393e6	−	5.66234e6i	0.609356	−	0.838707i
$190$	−1.77946e6	+	5.47660e6i	−0.259434	+	0.798455i
$191$	−1.16280e7			−1.66880			−0.834400	−	0.551160i	$-0.814185\pi$
$191$	−1.16280e7			−1.66880			−0.834400	+	0.551160i	$0.814185\pi$
$192$		−	1.42603e6i		−	0.201477i
$193$	−578449.	+	1.78028e6i	−0.0804624	+	0.247638i	−0.983193	−	0.182568i	$-0.941559\pi$
$193$	−578449.	+	1.78028e6i	−0.0804624	+	0.247638i	0.902731	+	0.430206i	$0.141559\pi$
$194$	285996.	+	880204.i	0.0391701	+	0.120553i
$195$	1.07514e7	+	3.30893e7i	1.44997	+	4.46256i
$196$	−478168.	+	347410.i	−0.0635057	+	0.0461396i
$197$	9.13458e6	+	2.96800e6i	1.19479	+	0.388209i	0.837840	−	0.545916i	$-0.183818\pi$
$197$	9.13458e6	+	2.96800e6i	1.19479	+	0.388209i	0.356945	+	0.934125i	$0.383818\pi$
$198$	−374963.	−	516092.i	−0.0483050	−	0.0664862i
$199$	−6.13412e6	+	8.44290e6i	−0.778383	+	1.07135i	0.217075	+	0.976155i	$0.430348\pi$
$199$	−6.13412e6	+	8.44290e6i	−0.778383	+	1.07135i	−0.995458	+	0.0951975i	$0.969652\pi$
$200$	2.41512e6	+	7.43297e6i	0.301890	+	0.929121i
$201$	7.97442e6	−	1.09758e7i	0.981999	−	1.35161i
$202$	1.32993e6	+	966252.i	0.161352	+	0.117229i
$203$	7.05384e6	−	2.29193e6i	0.843214	−	0.273977i
$204$	−7.67070e6	−	5.57309e6i	−0.903534	−	0.656456i
$205$	−1.34801e6	+	979389.i	−0.156471	+	0.113682i
$206$	1.74178e6	−	5.36065e6i	0.199247	−	0.613219i
$207$	1.51843e6	+	2.08994e6i	0.171192	+	0.235626i
$208$	3.21085e6	−	1.04327e6i	0.356804	−	0.115933i
$209$	386500.	−	125581.i	0.0423361	−	0.0137558i
$210$	2.09464e7	+	6.80589e6i	2.26178	+	0.734898i
$211$	9.45028e6			1.00600			0.502999	−	0.864287i	$-0.332230\pi$
$211$	9.45028e6			1.00600			0.502999	+	0.864287i	$0.332230\pi$
$212$			7.78814e6i			0.817384i
$213$	1.54983e7	+	5.03570e6i	1.60378	+	0.521100i
$214$	1.04533e7	+	7.59475e6i	1.06662	+	0.774947i
$215$	−1.30012e7	−	1.78947e7i	−1.30819	−	1.80056i
$216$			3.43402e6i			0.340755i
$217$	−4.53153e6	−	1.00136e7i	−0.443472	−	0.979963i
$218$	724485.			0.0699294
$219$	−1.43585e7	+	1.04321e7i	−1.36703	+	0.993205i
$220$	441528.	−	607711.i	0.0414658	−	0.0570728i
$221$	6.93654e6	−	2.13485e7i	0.642638	−	1.97784i
$222$	−1.91280e7			−1.74828
$223$			1.16548e7i			1.05097i	0.850802	+	0.525486i	$0.176116\pi$
$223$			1.16548e7i			1.05097i	−0.850802	+	0.525486i	$0.823884\pi$
$224$	660415.	−	2.03255e6i	0.0587588	−	0.180841i
$225$	−1.55420e7	−	4.78333e7i	−1.36445	−	4.19936i
$226$	−1.11531e6	−	3.43257e6i	−0.0966207	−	0.297368i
$227$	−4.80201e6	+	3.48886e6i	−0.410530	+	0.298268i	−0.773816	−	0.633410i	$-0.781655\pi$
$227$	−4.80201e6	+	3.48886e6i	−0.410530	+	0.298268i	0.363286	+	0.931678i	$0.381655\pi$
$228$	−5.56004e6	−	1.80657e6i	−0.469108	−	0.152423i
$229$	−639871.	−	880707.i	−0.0532826	−	0.0733373i	0.781544	−	0.623850i	$-0.214432\pi$
$229$	−639871.	−	880707.i	−0.0532826	−	0.0733373i	−0.834827	+	0.550513i	$0.814432\pi$
$230$	−1.78799e6	+	2.46095e6i	−0.146954	+	0.202265i
$231$	−480312.	−	1.47825e6i	−0.0389661	−	0.119925i
$232$	−2.13896e6	+	2.94403e6i	−0.171293	+	0.235764i
$233$	−5.51152e6	−	4.00435e6i	−0.435716	−	0.316566i	0.348214	−	0.937415i	$-0.386788\pi$
$233$	−5.51152e6	−	4.00435e6i	−0.435716	−	0.316566i	−0.783930	+	0.620849i	$0.786788\pi$
$234$	−2.06627e7	+	6.71372e6i	−1.61265	+	0.523981i
$235$	−3.90365e6	−	2.83616e6i	−0.300792	−	0.218538i
$236$	4.44539e6	−	3.22977e6i	0.338200	−	0.245717i
$237$	−3.51658e6	+	1.08229e7i	−0.264165	+	0.813016i
$238$	−8.35220e6	−	1.14958e7i	−0.619541	−	0.852725i
$239$	2.12841e7	−	6.91562e6i	1.55905	−	0.506567i	0.602499	−	0.798119i	$-0.294172\pi$
$239$	2.12841e7	−	6.91562e6i	1.55905	−	0.506567i	0.956555	+	0.291552i	$0.0941716\pi$
$240$	−1.02772e7	+	3.33926e6i	−0.743431	+	0.241555i
$241$	−3.47286e6	−	1.12840e6i	−0.248105	−	0.0806143i	0.182324	−	0.983238i	$-0.441638\pi$
$241$	−3.47286e6	−	1.12840e6i	−0.248105	−	0.0806143i	−0.430430	+	0.902624i	$0.641638\pi$
$242$	9.96845e6			0.703366
$243$			1.48584e7i			1.03551i
$244$	−7.10336e6	−	2.30802e6i	−0.488983	−	0.158880i
$245$	3.62342e6	+	2.63257e6i	0.246389	+	0.179012i
$246$	−994310.	−	1.36855e6i	−0.0667908	−	0.0919296i
$247$		−	1.38406e7i		−	0.918468i
$248$	4.68658e6	+	2.66791e6i	0.307256	+	0.174910i
$249$	−2.63938e7			−1.70964
$250$	3.05731e7	−	2.22127e7i	1.95668	−	1.42161i
$251$	−1.49105e6	+	2.05225e6i	−0.0942910	+	0.129780i	−0.853556	−	0.521001i	$-0.825559\pi$
$251$	−1.49105e6	+	2.05225e6i	−0.0942910	+	0.129780i	0.759265	+	0.650782i	$0.225559\pi$
$252$	−4.24996e6	+	1.30800e7i	−0.265573	+	0.817349i
$253$	214676.			0.0132563
$254$			4.76808e6i			0.290966i
$255$	−2.22023e7	+	6.83316e7i	−1.33899	+	4.12099i
$256$	324028.	+	997255.i	0.0193136	+	0.0594410i
$257$	5.67137e6	+	1.74547e7i	0.334109	+	1.02828i	0.967159	+	0.254172i	$0.0818028\pi$
$257$	5.67137e6	+	1.74547e7i	0.334109	+	1.02828i	−0.633050	+	0.774111i	$0.718197\pi$
$258$	1.81673e7	−	1.31993e7i	1.05787	−	0.768586i
$259$	−2.72635e7	−	8.85844e6i	−1.56921	−	0.509868i
$260$	−1.50373e7	−	2.06971e7i	−0.855559	−	1.17758i
$261$	1.37648e7	−	1.89457e7i	0.774194	−	1.06559i
$262$	542368.	+	1.66924e6i	0.0301571	+	0.0928141i
$263$	9.65523e6	−	1.32893e7i	0.530757	−	0.730524i	−0.456489	−	0.889729i	$-0.650893\pi$
$263$	9.65523e6	−	1.32893e7i	0.530757	−	0.730524i	0.987245	+	0.159205i	$0.0508932\pi$
$264$	616970.	+	448255.i	0.0335314	+	0.0243620i
$265$	5.61278e7	−	1.82370e7i	3.01606	−	0.979978i
$266$	−7.08817e6	−	5.14986e6i	−0.376608	−	0.273621i
$267$	−6.00830e6	+	4.36529e6i	−0.315659	+	0.229339i
$268$	−3.08271e6	+	9.48761e6i	−0.160151	+	0.492893i
$269$	−3.30435e6	−	4.54804e6i	−0.169757	−	0.233651i	0.715659	−	0.698450i	$-0.246127\pi$
$269$	−3.30435e6	−	4.54804e6i	−0.169757	−	0.233651i	−0.885416	+	0.464799i	$0.846127\pi$
$270$	2.47484e7	−	8.04125e6i	1.25735	−	0.408538i
$271$	505527.	−	164256.i	0.0254002	−	0.00825302i	−0.296289	−	0.955098i	$-0.595749\pi$
$271$	505527.	−	164256.i	0.0254002	−	0.00825302i	0.321690	+	0.946845i	$0.395749\pi$
$272$	6.63062e6	+	2.15442e6i	0.329494	+	0.107059i
$273$	−5.29362e7			−2.60175
$274$			5.14694e6i			0.250206i
$275$	−3.97501e6	−	1.29156e6i	−0.191135	−	0.0621036i
$276$	−2.49845e6	−	1.81523e6i	−0.118835	−	0.0863384i
$277$	1.43231e7	+	1.97141e7i	0.673905	+	0.927551i	0.999841	−	0.0178413i	$-0.00567936\pi$
$277$	1.43231e7	+	1.97141e7i	0.673905	+	0.927551i	−0.325936	+	0.945392i	$0.605679\pi$
$278$			162588.i			0.00756752i
$279$	−3.01595e7	−	1.71688e7i	−1.38871	−	0.790544i
$280$	−1.61947e7			−0.737732
$281$	−6.99172e6	+	5.07978e6i	−0.315112	+	0.228942i	−0.734087	−	0.679055i	$-0.762390\pi$
$281$	−6.99172e6	+	5.07978e6i	−0.315112	+	0.228942i	0.418975	+	0.907998i	$0.362390\pi$
$282$	2.87937e6	−	3.96312e6i	0.128396	−	0.176722i
$283$	−1.14580e7	+	3.52642e7i	−0.505534	+	1.55587i	0.294336	+	0.955702i	$0.404902\pi$
$283$	−1.14580e7	+	3.52642e7i	−0.505534	+	1.55587i	−0.799870	+	0.600173i	$0.795098\pi$
$284$	−1.19825e7			−0.523109
$285$			4.43006e7i			1.91371i
$286$	−557920.	+	1.71710e6i	−0.0238492	+	0.0734003i
$287$	−783413.	−	2.41110e6i	−0.0331394	−	0.101993i
$288$	−2.08521e6	−	6.41762e6i	−0.0872917	−	0.268656i
$289$	1.79742e7	−	1.30590e7i	0.744655	−	0.541023i
$290$	2.62258e7	+	8.52129e6i	1.07531	+	0.349391i
$291$	4.18505e6	+	5.76023e6i	0.169833	+	0.233755i
$292$	7.67081e6	−	1.05580e7i	0.308101	−	0.424064i
$293$	−1.18108e7	−	3.63499e7i	−0.469545	−	1.44511i	−0.853176	−	0.521624i	$-0.825327\pi$
$293$	−1.18108e7	−	3.63499e7i	−0.469545	−	1.44511i	0.383631	−	0.923486i	$-0.374673\pi$
$294$	−2.67268e6	+	3.67863e6i	−0.105173	+	0.144758i
$295$	−3.36859e7	−	2.44742e7i	−1.31215	−	0.953330i
$296$	1.33766e7	−	4.34633e6i	0.515788	−	0.167590i
$297$	−1.48572e6	−	1.07944e6i	−0.0567111	−	0.0412030i
$298$	−1.67084e7	+	1.21394e7i	−0.631374	+	0.458720i
$299$	2.25932e6	−	6.95348e6i	0.0845210	−	0.260129i
$300$	3.53410e7	+	4.86428e7i	1.30893	+	1.80158i
$301$	3.20070e7	−	1.03997e7i	1.17367	−	0.381348i
$302$	6.81219e6	−	2.21341e6i	0.247324	−	0.0803604i
$303$	1.20277e7	+	3.90804e6i	0.432370	+	0.140485i
$304$	4.29874e6			0.153010
$305$			5.65973e7i			1.99478i
$306$	−4.26699e7	−	1.38643e7i	−1.48922	−	0.483876i
$307$	−3.51148e7	−	2.55124e7i	−1.21360	−	0.881732i	−0.218047	−	0.975938i	$-0.569969\pi$
$307$	−3.51148e7	−	2.55124e7i	−1.21360	−	0.881732i	−0.995553	+	0.0942065i	$0.969969\pi$
$308$	671784.	+	924632.i	0.0229920	+	0.0316458i
$309$		−	4.33627e7i		−	1.46974i
$310$	8.25289e6	−	4.00227e7i	0.277026	−	1.34345i
$311$	−4.09339e7			−1.36082			−0.680412	−	0.732830i	$-0.738199\pi$
$311$	−4.09339e7			−1.36082			−0.680412	+	0.732830i	$0.738199\pi$
$312$	2.10124e7	−	1.52664e7i	0.691850	−	0.502658i
$313$	2.81831e7	−	3.87906e7i	0.919084	−	1.26501i	−0.0448846	−	0.998992i	$-0.514292\pi$
$313$	2.81831e7	−	3.87906e7i	0.919084	−	1.26501i	0.963968	−	0.266018i	$-0.0857080\pi$
$314$	−7.53255e6	+	2.31828e7i	−0.243306	+	0.748820i
$315$	1.04218e8			3.33434
$316$		−	8.36773e6i		−	0.265184i
$317$	3.06362e6	−	9.42885e6i	0.0961739	−	0.295993i	−0.891384	−	0.453249i	$-0.850265\pi$
$317$	3.06362e6	−	9.42885e6i	0.0961739	−	0.295993i	0.987558	+	0.157256i	$0.0502648\pi$
$318$	1.85149e7	+	5.69829e7i	0.575757	+	1.77200i
$319$	−601372.	−	1.85083e6i	−0.0185256	−	0.0570158i
$320$	6.42829e6	−	4.67043e6i	0.196176	−	0.142530i
$321$	9.45379e7	+	3.07172e7i	2.85819	+	0.928681i
$322$	−2.72042e6	−	3.74434e6i	−0.0814833	−	0.112152i
$323$	1.67999e7	−	2.31231e7i	0.498540	−	0.686182i
$324$	−233789.	−	719529.i	−0.00687368	−	0.0211550i
$325$	−8.36686e7	+	1.15160e8i	−2.43732	+	3.35468i
$326$	−1.64414e6	−	1.19453e6i	−0.0474553	−	0.0344783i
$327$	5.30079e6	−	1.72233e6i	0.151599	−	0.0492576i
$328$	1.00631e6	+	731126.i	0.0285174	+	0.0207191i
$329$	5.93939e6	−	4.31522e6i	0.166784	−	0.121176i
$330$	1.78577e6	−	5.49605e6i	0.0496918	−	0.152936i
$331$	−2.69787e7	−	3.71331e7i	−0.743940	−	1.02395i	−0.998382	−	0.0568572i	$-0.981892\pi$
$331$	−2.69787e7	−	3.71331e7i	−0.743940	−	1.02395i	0.254443	−	0.967088i	$-0.418108\pi$
$332$	1.84578e7	−	5.99729e6i	0.504388	−	0.163886i
$333$	−8.60824e7	+	2.79699e7i	−2.33121	+	0.757456i
$334$	−1.32842e7	−	4.31629e6i	−0.356529	−	0.115843i
$335$	7.55942e7			2.01073
$336$		−	1.64414e7i		−	0.433433i
$337$	5.26221e7	+	1.70979e7i	1.37492	+	0.446739i	0.900997	−	0.433826i	$-0.142837\pi$
$337$	5.26221e7	+	1.70979e7i	1.37492	+	0.446739i	0.473925	+	0.880565i	$0.342837\pi$
$338$	2.76562e7	+	2.00934e7i	0.716214	+	0.520360i
$339$	−1.63206e7	−	2.24634e7i	−0.418926	−	0.576602i
$340$		−	5.28306e7i		−	1.34415i
$341$	−2.62743e6	+	1.18901e6i	−0.0662624	+	0.0299863i
$342$	−2.76637e7			−0.691562
$343$	2.96030e7	−	2.15079e7i	0.733590	−	0.532985i
$344$	−9.70559e6	+	1.33586e7i	−0.238422	+	0.328160i
$345$	−7.23158e6	+	2.22565e7i	−0.176107	+	0.542001i
$346$	−8.62995e6			−0.208344
$347$		−	1.54906e7i		−	0.370748i	−0.982668	−	0.185374i	$-0.940650\pi$
$347$		−	1.54906e7i		−	0.370748i	0.982668	−	0.185374i	$-0.0593497\pi$
$348$	−8.65111e6	+	2.66254e7i	−0.205274	+	0.631769i
$349$	−1.06842e7	−	3.28825e7i	−0.251342	−	0.773550i	−0.994528	−	0.104466i	$-0.966687\pi$
$349$	−1.06842e7	−	3.28825e7i	−0.251342	−	0.773550i	0.743187	−	0.669084i	$-0.233313\pi$
$350$	2.78451e7	+	8.56983e7i	0.649447	+	1.99879i
$351$	−5.05998e7	+	3.67629e7i	−1.17011	+	0.850137i
$352$	−533314.	−	173284.i	−0.0122280	−	0.00397311i
$353$	−3.38592e6	−	4.66032e6i	−0.0769756	−	0.105948i	0.768793	−	0.639498i	$-0.220858\pi$
$353$	−3.38592e6	−	4.66032e6i	−0.0769756	−	0.105948i	−0.845769	+	0.533550i	$0.820858\pi$
$354$	2.48471e7	−	3.41991e7i	0.560101	−	0.770913i
$355$	2.80587e7	+	8.63559e7i	0.627166	+	1.93022i
$356$	3.20984e6	−	4.41796e6i	0.0711431	−	0.0979201i
$357$	−8.84392e7	−	6.42549e7i	−1.94375	−	1.41222i
$358$	−1.66036e7	+	5.39483e6i	−0.361870	+	0.117579i
$359$	−1.04219e7	−	7.57194e6i	−0.225249	−	0.163653i	0.469437	−	0.882966i	$-0.344457\pi$
$359$	−1.04219e7	−	7.57194e6i	−0.225249	−	0.163653i	−0.694686	+	0.719313i	$0.744457\pi$
$360$	−4.13679e7	+	3.00556e7i	−0.886658	+	0.644195i
$361$	−9.09213e6	+	2.79827e7i	−0.193261	+	0.594796i
$362$	2.90701e7	+	4.00116e7i	0.612803	+	0.843451i
$363$	7.29355e7	−	2.36982e7i	1.52482	−	0.495444i
$364$	3.70194e7	−	1.20283e7i	0.767583	−	0.249403i
$365$	−9.40518e7	−	3.05593e7i	−1.93414	−	0.628441i
$366$	−5.74595e7			−1.17198
$367$			3.93980e7i			0.797032i	0.917161	+	0.398516i	$0.130475\pi$
$367$			3.93980e7i			0.797032i	−0.917161	+	0.398516i	$0.869525\pi$
$368$	2.15968e6	+	701722.i	0.0433357	+	0.0140806i
$369$	−6.47588e6	−	4.70500e6i	−0.128890	−	0.0936442i
$370$	−6.26465e7	−	8.62255e7i	−1.23678	−	1.70228i
$371$			8.97932e7i			1.75842i
$372$	4.06324e7	+	8.37862e6i	0.789303	+	0.162759i
$373$	3.58085e7			0.690017			0.345008	−	0.938600i	$-0.387876\pi$
$373$	3.58085e7			0.690017			0.345008	+	0.938600i	$0.387876\pi$
$374$	−3.01635e6	+	2.19151e6i	−0.0576590	+	0.0418917i
$375$	1.70886e8	−	2.35204e8i	3.24050	−	4.46017i
$376$	−1.11309e6	+	3.42575e6i	−0.0209396	+	0.0644455i
$377$	−6.62785e7			−1.23694
$378$			3.95925e7i			0.733057i
$379$	−2.68703e7	+	8.26983e7i	−0.493577	+	1.51907i	0.325585	+	0.945513i	$0.394439\pi$
$379$	−2.68703e7	+	8.26983e7i	−0.493577	+	1.51907i	−0.819162	+	0.573562i	$0.805561\pi$
$380$	−1.00661e7	−	3.09803e7i	−0.183447	−	0.564593i
$381$	1.13353e7	+	3.48863e7i	0.204954	+	0.630783i
$382$	5.32153e7	−	3.86632e7i	0.954656	−	0.693598i
$383$	8.22229e6	+	2.67158e6i	0.146351	+	0.0475524i	0.381277	−	0.924461i	$-0.375485\pi$
$383$	8.22229e6	+	2.67158e6i	0.146351	+	0.0475524i	−0.234925	+	0.972013i	$0.575485\pi$
$384$	4.74158e6	+	6.52623e6i	0.0837394	+	0.115257i
$385$	5.09059e6	−	7.00659e6i	0.0892043	−	0.122779i
$386$	−3.27220e6	−	1.00708e7i	−0.0568955	−	0.175106i
$387$	6.24583e7	−	8.59664e7i	1.07760	−	1.48319i
$388$	−4.23555e6	−	3.07731e6i	−0.0725128	−	0.0526836i
$389$	1.36947e7	−	4.44968e6i	0.232650	−	0.0755927i	−0.190372	−	0.981712i	$-0.560969\pi$
$389$	1.36947e7	−	4.44968e6i	0.232650	−	0.0755927i	0.423022	+	0.906119i	$0.360969\pi$
$390$	−1.59226e8	−	1.15684e8i	−2.68423	−	1.95021i
$391$	1.22148e7	−	8.87460e6i	0.204342	−	0.148463i
$392$	1.03319e6	−	3.17984e6i	0.0171523	−	0.0527894i
$393$	7.93661e6	+	1.09238e7i	0.130755	+	0.179969i
$394$	−5.16730e7	+	1.67896e7i	−0.844841	+	0.274505i
$395$	−6.03049e7	+	1.95942e7i	−0.978501	+	0.317934i
$396$	3.43203e6	+	1.11513e6i	0.0552669	+	0.0179573i
$397$	1.15446e8			1.84504			0.922522	−	0.385945i	$-0.126125\pi$
$397$	1.15446e8			1.84504			0.922522	+	0.385945i	$0.126125\pi$
$398$		−	5.90349e7i		−	0.936396i
$399$	−6.41044e7	−	2.08288e7i	−1.00918	−	0.327903i
$400$	−3.57675e7	−	2.59866e7i	−0.558867	−	0.406041i
$401$	6.24108e7	+	8.59011e7i	0.967892	+	1.33219i	0.943105	+	0.332496i	$0.107891\pi$
$401$	6.24108e7	+	8.59011e7i	0.967892	+	1.33219i	0.0247874	+	0.999693i	$0.492109\pi$
$402$			7.67459e7i			1.18135i
$403$	1.08609e7	+	9.76173e7i	0.165940	+	1.49146i
$404$	−9.29923e6			−0.141027
$405$	−4.63808e6	+	3.36976e6i	−0.0698189	+	0.0507264i
$406$	−2.46611e7	+	3.39431e7i	−0.368498	+	0.507194i
$407$	−2.32433e6	+	7.15357e6i	−0.0344759	+	0.106106i
$408$	5.36355e7			0.789718
$409$		−	8.71297e7i		−	1.27349i	−0.771073	−	0.636746i	$-0.780280\pi$
$409$		−	8.71297e7i		−	1.27349i	0.771073	−	0.636746i	$-0.219720\pi$
$410$	2.91269e6	−	8.96433e6i	0.0422612	−	0.130067i
$411$	1.22359e7	+	3.76583e7i	0.176243	+	0.542419i
$412$	9.85300e6	+	3.03244e7i	0.140889	+	0.433612i
$413$	5.12531e7	−	3.72375e7i	0.727562	−	0.528605i
$414$	−1.38982e7	−	4.51578e6i	−0.195865	−	0.0636403i
$415$	−8.64430e7	−	1.18979e8i	−1.20944	−	1.66466i
$416$	−1.12255e7	+	1.54506e7i	−0.155929	+	0.214618i
$417$	386523.	+	1.18959e6i	0.00533049	+	0.0164055i
$418$	−1.35125e6	+	1.85984e6i	−0.0185015	+	0.0254652i
$419$	−9.02750e7	−	6.55886e7i	−1.22723	−	0.891634i	−0.230549	−	0.973061i	$-0.574052\pi$
$419$	−9.02750e7	−	6.55886e7i	−1.22723	−	0.891634i	−0.996679	+	0.0814269i	$0.974052\pi$
$420$	−1.18491e8	+	3.84999e7i	−1.59932	+	0.519652i
$421$	4.72755e7	+	3.43476e7i	0.633563	+	0.460310i	0.857633	−	0.514263i	$-0.171934\pi$
$421$	4.72755e7	+	3.43476e7i	0.633563	+	0.460310i	−0.224070	+	0.974573i	$0.571934\pi$
$422$	−4.32491e7	+	3.14223e7i	−0.575493	+	0.418120i
$423$	7.16308e6	−	2.20457e7i	0.0946409	−	0.291275i
$424$	−2.58957e7	−	3.56423e7i	−0.339727	−	0.467594i
$425$	−2.79566e8	+	9.08366e7i	−3.64182	+	1.18330i
$426$	−8.76715e7	+	2.84862e7i	−1.13404	+	0.368473i
$427$	−8.18980e7	−	2.66103e7i	−1.05194	−	0.341795i
$428$	−7.30920e7			−0.932263
$429$			1.38897e7i			0.175923i
$430$	1.19000e8	+	3.86655e7i	1.49673	+	0.486316i
$431$	9.07396e7	+	6.59262e7i	1.13335	+	0.823429i	0.986179	−	0.165682i	$-0.0529824\pi$
$431$	9.07396e7	+	6.59262e7i	1.13335	+	0.823429i	0.147174	+	0.989111i	$0.452982\pi$
$432$	−1.14182e7	−	1.57158e7i	−0.141627	−	0.194933i
$433$			1.08368e8i			1.33486i	0.744672	+	0.667431i	$0.232606\pi$
$433$			1.08368e8i			1.33486i	−0.744672	+	0.667431i	$0.767394\pi$
$434$	5.40338e7	+	3.07596e7i	0.660992	+	0.376280i
$435$	2.12142e8			2.57727
$436$	−3.31560e6	+	2.40892e6i	−0.0400039	+	0.0290646i
$437$	5.47196e6	−	7.53151e6i	0.0655690	−	0.0902480i
$438$	3.10249e7	−	9.54847e7i	0.369222	−	1.13635i
$439$	1.19256e8			1.40957			0.704785	−	0.709421i	$-0.251044\pi$
$439$	1.19256e8			1.40957			0.704785	+	0.709421i	$0.251044\pi$
$440$			4.24927e6i			0.0498834i
$441$	−6.64888e6	+	2.04632e7i	−0.0775234	+	0.238593i
$442$	3.92390e7	+	1.20765e8i	0.454414	+	1.39854i
$443$	−1.68245e7	−	5.17804e7i	−0.193522	−	0.595599i	−0.999991	−	0.00432242i	$-0.998624\pi$
$443$	−1.68245e7	−	5.17804e7i	−0.193522	−	0.595599i	0.806469	−	0.591277i	$-0.201376\pi$
$444$	8.75392e7	−	6.36009e7i	1.00012	−	0.726632i
$445$	−3.93558e7	−	1.27875e7i	−0.446610	−	0.145112i
$446$	−3.87525e7	−	5.33382e7i	−0.436812	−	0.601220i
$447$	−9.33903e7	+	1.28541e8i	−1.04563	+	1.43919i
$448$	3.73587e6	+	1.14978e7i	0.0415488	+	0.127874i
$449$	8.72218e7	−	1.20051e8i	0.963576	−	1.32625i	0.0183502	−	0.999832i	$-0.494159\pi$
$449$	8.72218e7	−	1.20051e8i	0.963576	−	1.32625i	0.945226	−	0.326417i	$-0.105841\pi$
$450$	2.30174e8	+	1.67231e8i	2.52592	+	1.83519i
$451$	−632639.	+	205557.i	−0.00689646	+	0.00224080i
$452$	1.65175e7	+	1.20007e7i	0.178867	+	0.129954i
$453$	4.45803e7	−	3.23895e7i	0.479566	−	0.348425i
$454$	1.03758e7	−	3.19335e7i	0.110880	−	0.341255i
$455$	−1.73372e8	−	2.38627e8i	−1.84054	−	2.53329i
$456$	3.14523e7	−	1.02195e7i	0.331710	−	0.107779i
$457$	−1.31043e7	+	4.25784e6i	−0.137298	+	0.0446109i	−0.376860	−	0.926270i	$-0.622996\pi$
$457$	−1.31043e7	+	4.25784e6i	−0.137298	+	0.0446109i	0.239562	+	0.970881i	$0.422996\pi$
$458$	5.85673e6	+	1.90297e6i	0.0609619	+	0.0198077i
$459$	−1.29159e8			−1.33564
$460$		−	1.72076e7i		−	0.176786i
$461$	6.52216e7	+	2.11918e7i	0.665715	+	0.216304i	0.622331	−	0.782754i	$-0.286186\pi$
$461$	6.52216e7	+	2.11918e7i	0.665715	+	0.216304i	0.0433846	+	0.999058i	$0.486186\pi$
$462$	7.11334e6	+	5.16815e6i	0.0721353	+	0.0524093i
$463$	−6.43681e7	−	8.85951e7i	−0.648526	−	0.892620i	0.350508	−	0.936560i	$-0.386009\pi$
$463$	−6.43681e7	−	8.85951e7i	−0.648526	−	0.892620i	−0.999034	+	0.0439398i	$0.986009\pi$
$464$		−	2.05854e7i		−	0.206066i
$465$	−3.47632e7	−	3.12451e8i	−0.345749	−	3.10758i
$466$	3.85379e7			0.380830
$467$	6.60621e7	−	4.79969e7i	0.648637	−	0.471262i	−0.214170	−	0.976796i	$-0.568705\pi$
$467$	6.60621e7	−	4.79969e7i	0.648637	−	0.471262i	0.862807	+	0.505534i	$0.168705\pi$
$468$	7.22395e7	−	9.94292e7i	0.704753	−	0.970010i
$469$	−3.55421e7	+	1.09387e8i	−0.344528	+	1.06035i
$470$	2.72953e7			0.262902
$471$			1.87527e8i			1.79474i
$472$	−9.60528e6	+	2.95620e7i	−0.0913448	+	0.281130i
$473$	−2.72874e6	−	8.39819e6i	−0.0257857	−	0.0793602i
$474$	−1.98928e7	−	6.12236e7i	−0.186793	−	0.574889i
$475$	−1.46632e8	+	1.06535e8i	−1.36820	+	0.994055i
$476$	7.64476e7	+	2.48393e7i	0.708831	+	0.230313i
$477$	1.66646e8	+	2.29369e8i	1.53547	+	2.11339i
$478$	−7.44119e7	+	1.02419e8i	−0.681332	+	0.937773i
$479$	1.66532e6	+	5.12532e6i	0.0151527	+	0.0466353i	0.958347	−	0.285606i	$-0.0921950\pi$
$479$	1.66532e6	+	5.12532e6i	0.0151527	+	0.0466353i	−0.943194	+	0.332242i	$0.892195\pi$
$480$	3.59304e7	−	4.94539e7i	0.324891	−	0.447174i
$481$	2.07246e8	+	1.50573e8i	1.86230	+	1.35304i
$482$	1.96455e7	−	6.38319e6i	0.175437	−	0.0570029i
$483$	−2.88058e7	−	2.09286e7i	−0.255646	−	0.185738i
$484$	−4.56205e7	+	3.31453e7i	−0.402369	+	0.292338i
$485$	−1.22595e7	+	3.77309e7i	−0.107460	+	0.330728i
$486$	−4.94043e7	−	6.79992e7i	−0.430384	−	0.592373i
$487$	1.98591e7	−	6.45261e6i	0.171938	−	0.0558662i	−0.221783	−	0.975096i	$-0.571188\pi$
$487$	1.98591e7	−	6.45261e6i	0.171938	−	0.0558662i	0.393721	+	0.919230i	$0.371188\pi$
$488$	4.01826e7	−	1.30561e7i	0.345763	−	0.112345i
$489$	−1.48693e7	−	4.83134e6i	−0.127164	−	0.0413181i
$490$	−2.53359e7			−0.215352
$491$		−	2.94191e7i		−	0.248533i	−0.992249	−	0.124267i	$-0.960342\pi$
$491$		−	2.94191e7i		−	0.248533i	0.992249	−	0.124267i	$-0.0396578\pi$
$492$	9.10090e6	+	2.95706e6i	0.0764169	+	0.0248293i
$493$	−1.10730e8	−	8.04500e7i	−0.924111	−	0.671406i
$494$	4.60202e7	+	6.33414e7i	0.381740	+	0.525420i
$495$		−	2.73453e7i		−	0.225459i
$496$	−3.03189e7	+	3.37328e6i	−0.248467	+	0.0276444i
$497$	−1.38152e8			−1.12535
$498$	1.20791e8	−	8.77600e7i	0.978019	−	0.710572i
$499$	−1.54707e7	+	2.12936e7i	−0.124511	+	0.171375i	−0.866722	−	0.498792i	$-0.833777\pi$
$499$	−1.54707e7	+	2.12936e7i	−0.124511	+	0.171375i	0.742211	+	0.670166i	$0.233777\pi$
$500$	−6.60602e7	+	2.03312e8i	−0.528481	+	1.62650i
$501$	−1.07457e8			−0.854516
$502$		−	1.43499e7i		−	0.113432i
$503$	5.68044e7	−	1.74826e8i	0.446352	−	1.37373i	−0.434641	−	0.900604i	$-0.643125\pi$
$503$	5.68044e7	−	1.74826e8i	0.446352	−	1.37373i	0.880994	−	0.473128i	$-0.156875\pi$
$504$	−2.40414e7	−	7.39919e7i	−0.187788	−	0.577953i
$505$	2.17755e7	+	6.70180e7i	0.169080	+	0.520376i
$506$	−982464.	+	713802.i	−0.00758342	+	0.00550968i
$507$	2.50119e8	+	8.12686e7i	1.91921	+	0.623590i
$508$	−1.58540e7	−	2.18211e7i	−0.120933	−	0.166451i
$509$	8.12840e7	−	1.11878e8i	0.616384	−	0.848380i	−0.380699	−	0.924699i	$-0.624317\pi$
$509$	8.12840e7	−	1.11878e8i	0.616384	−	0.848380i	0.997083	+	0.0763188i	$0.0243167\pi$
$510$	−1.25595e8	−	3.86542e8i	−0.946809	−	2.91398i
$511$	8.84405e7	−	1.21728e8i	0.662809	−	0.912278i
$512$	−4.79880e6	−	3.48653e6i	−0.0357538	−	0.0259767i
$513$	−7.57402e7	+	2.46095e7i	−0.561015	+	0.182285i
$514$	−8.39921e7	−	6.10238e7i	−0.618513	−	0.449376i
$515$	1.95471e8	−	1.42018e8i	1.43107	−	1.03973i
$516$	−3.92546e7	+	1.20813e8i	−0.285720	+	0.879357i
$517$	−1.13226e6	−	1.55842e6i	−0.00819357	−	0.0112775i
$518$	1.54225e8	−	5.01109e7i	1.10960	−	0.360531i
$519$	−6.31422e7	+	2.05161e7i	−0.451666	+	0.146755i
$520$	1.37636e8	+	4.47207e7i	0.978864	+	0.318052i
$521$	1.27944e8			0.904705			0.452352	−	0.891839i	$-0.350585\pi$
$521$	1.27944e8			0.904705			0.452352	+	0.891839i	$0.350585\pi$
$522$			1.32473e8i			0.931357i
$523$	−2.33395e8	−	7.58347e7i	−1.63150	−	0.530106i	−0.656884	−	0.753992i	$-0.728126\pi$
$523$	−2.33395e8	−	7.58347e7i	−1.63150	−	0.530106i	−0.974615	+	0.223886i	$0.928126\pi$
$524$	−8.03238e6	−	5.83587e6i	−0.0558278	−	0.0405613i
$525$	4.07464e8	+	5.60826e8i	2.81586	+	3.87570i
$526$			9.29221e7i			0.638501i
$527$	−1.00344e8	+	1.76270e8i	−0.685586	+	1.20433i
$528$	−4.31401e6			−0.0293075
$529$	−1.15785e8	+	8.41227e7i	−0.782142	+	0.568259i
$530$	−1.96230e8	+	2.70087e8i	−1.31807	+	1.81416i
$531$	6.18127e7	−	1.90240e8i	0.412852	−	1.27063i
$532$	4.95623e7			0.329167
$533$			2.26549e7i			0.149617i
$534$	1.29823e7	−	3.99554e7i	0.0852565	−	0.262393i
$535$	1.71155e8	+	5.26762e8i	1.11771	+	3.43995i
$536$	−1.74384e7	−	5.36700e7i	−0.113244	−	0.348528i
$537$	−1.08657e8	+	7.89440e7i	−0.701674	+	0.509796i
$538$	3.02446e7	+	9.82708e6i	0.194223	+	0.0631070i
$539$	1.05098e6	+	1.44655e6i	0.00671162	+	0.00923775i
$540$	−8.65237e7	+	1.19090e8i	−0.549482	+	0.756298i
$541$	3.24577e7	+	9.98945e7i	0.204987	+	0.630884i	0.999714	+	0.0239174i	$0.00761387\pi$
$541$	3.24577e7	+	9.98945e7i	0.204987	+	0.630884i	−0.794727	+	0.606967i	$0.792386\pi$
$542$	−1.76739e6	+	2.43260e6i	−0.0111003	+	0.0152782i
$543$	3.07816e8	+	2.23641e8i	1.92261	+	1.39686i
$544$	−3.75084e7	+	1.21872e7i	−0.232987	+	0.0757021i
$545$	2.51247e7	+	1.82541e7i	0.155207	+	0.112764i
$546$	2.42262e8	−	1.76014e8i	1.48836	−	1.08136i
$547$	1.79547e7	−	5.52589e7i	0.109702	−	0.337629i	−0.881103	−	0.472925i	$-0.843198\pi$
$547$	1.79547e7	−	5.52589e7i	0.109702	−	0.337629i	0.990805	+	0.135295i	$0.0431983\pi$
$548$	−1.71137e7	−	2.35549e7i	−0.103992	−	0.143133i
$549$	−2.58587e8	+	8.40200e7i	−1.56275	+	0.507768i
$550$	2.24861e7	−	7.30617e6i	0.135153	−	0.0439138i
$551$	−8.02616e7	−	2.60786e7i	−0.479792	−	0.155894i
$552$	1.74698e7			0.103865
$553$		−	9.64757e7i		−	0.570483i
$554$	−1.31099e8	−	4.25968e7i	−0.771030	−	0.250523i
$555$	−6.63347e8	−	4.81950e8i	−3.88027	−	2.81918i
$556$	−540607.	−	744081.i	−0.00314526	−	0.00432908i
$557$		−	1.89370e8i		−	1.09584i	−0.836532	−	0.547919i	$-0.815420\pi$
$557$		−	1.89370e8i		−	1.09584i	0.836532	−	0.547919i	$-0.184580\pi$
$558$	1.95111e8	−	2.17080e7i	1.12300	−	0.124945i
$559$	−3.00740e8			−1.72169
$560$	7.41149e7	−	5.38476e7i	0.422028	−	0.306621i
$561$	−1.68596e7	+	2.32053e7i	−0.0954902	+	0.131431i
$562$	1.51072e7	−	4.64952e7i	0.0851089	−	0.261938i
$563$	8.00337e7			0.448485			0.224242	−	0.974533i	$-0.428009\pi$
$563$	8.00337e7			0.448485			0.224242	+	0.974533i	$0.428009\pi$
$564$			2.77111e7i			0.154460i
$565$	4.78089e7	−	1.47141e8i	0.265072	−	0.815806i
$566$	−6.48164e7	−	1.99484e8i	−0.357467	−	1.10017i
$567$	−2.69547e6	−	8.29580e6i	−0.0147872	−	0.0455102i
$568$	5.48378e7	−	3.98420e7i	0.299251	−	0.217418i
$569$	−2.13408e8	−	6.93404e7i	−1.15844	−	0.376400i	−0.334123	−	0.942529i	$-0.608440\pi$
$569$	−2.13408e8	−	6.93404e7i	−1.15844	−	0.376400i	−0.824316	+	0.566129i	$0.808440\pi$
$570$	−1.47300e8	−	2.02741e8i	−0.795387	−	1.09476i
$571$	8.92511e7	−	1.22844e8i	0.479408	−	0.659848i	−0.498983	−	0.866612i	$-0.666293\pi$
$571$	8.92511e7	−	1.22844e8i	0.479408	−	0.659848i	0.978391	+	0.206764i	$0.0662931\pi$
$572$	−3.15607e6	−	9.71339e6i	−0.0168639	−	0.0519018i
$573$	2.97442e8	−	4.09394e8i	1.58103	−	2.17609i
$574$	1.16022e7	+	8.42950e6i	0.0613487	+	0.0445724i
$575$	−9.10584e7	+	2.95867e7i	−0.478979	+	0.155630i
$576$	3.08817e7	+	2.24368e7i	0.161597	+	0.117407i
$577$	−1.43021e8	+	1.03911e8i	−0.744513	+	0.540921i	−0.894121	−	0.447825i	$-0.852199\pi$
$577$	−1.43021e8	+	1.03911e8i	−0.744513	+	0.540921i	0.149608	+	0.988745i	$0.452199\pi$
$578$	−3.88372e7	+	1.19529e8i	−0.201124	+	0.618997i
$579$	−4.78830e7	−	6.59053e7i	−0.246687	−	0.339535i
$580$	−1.48356e8	+	4.82037e7i	−0.760361	+	0.247056i
$581$	2.12809e8	−	6.91457e7i	1.08508	−	0.352563i
$582$	−3.83057e7	−	1.24463e7i	−0.194310	−	0.0631350i
$583$	2.35605e7			0.118899
$584$			7.38240e7i			0.370646i
$585$	−8.85728e8	−	2.87791e8i	−4.42418	−	1.43750i
$586$	1.74916e8	+	1.27084e8i	0.869235	+	0.631536i
$587$	−4.39249e7	−	6.04574e7i	−0.217168	−	0.298907i	0.686508	−	0.727122i	$-0.259142\pi$
$587$	−4.39249e7	−	6.04574e7i	−0.217168	−	0.298907i	−0.903677	+	0.428215i	$0.859142\pi$
$588$		−	2.57219e7i		−	0.126523i
$589$	−2.52572e7	+	1.22485e8i	−0.123606	+	0.599430i
$590$	2.35541e8			1.14686
$591$	−3.38158e8	+	2.45686e8i	−1.63816	+	1.19020i
$592$	−4.67664e7	+	6.43684e7i	−0.225408	+	0.310247i
$593$	3.03672e7	−	9.34606e7i	0.145627	−	0.448192i	−0.851465	−	0.524412i	$-0.824285\pi$
$593$	3.03672e7	−	9.34606e7i	0.145627	−	0.448192i	0.997091	+	0.0762199i	$0.0242851\pi$
$594$	1.03885e7			0.0495673
$595$		−	6.09110e8i		−	2.89164i
$596$	3.61023e7	−	1.11112e8i	0.170528	−	0.524832i
$597$	−1.40345e8	−	4.31937e8i	−0.659589	−	2.03001i
$598$	1.27807e7	+	3.93348e7i	0.0597654	+	0.183939i
$599$	2.77962e8	−	2.01951e8i	1.29331	−	0.939648i	0.293448	−	0.955975i	$-0.405197\pi$
$599$	2.77962e8	−	2.01951e8i	1.29331	−	0.939648i	0.999867	+	0.0163267i	$0.00519717\pi$
$600$	−3.23476e8	−	1.05104e8i	−1.49757	−	0.486591i
$601$	−7.64662e7	−	1.05247e8i	−0.352246	−	0.484825i	0.595722	−	0.803191i	$-0.296866\pi$
$601$	−7.64662e7	−	1.05247e8i	−0.352246	−	0.484825i	−0.947968	+	0.318366i	$0.896866\pi$
$602$	−1.11900e8	+	1.54018e8i	−0.512911	+	0.705962i
$603$	1.12221e8	+	3.45382e8i	0.511828	+	1.57524i
$604$	−2.38163e7	+	3.27803e7i	−0.108084	+	0.148765i
$605$	3.45699e8	+	2.51165e8i	1.56111	+	1.13421i
$606$	−6.80390e7	+	2.21072e7i	−0.305732	+	0.0993382i
$607$	9.47955e7	+	6.88730e7i	0.423859	+	0.307952i	0.779189	−	0.626789i	$-0.215631\pi$
$607$	9.47955e7	+	6.88730e7i	0.423859	+	0.307952i	−0.355329	+	0.934741i	$0.615631\pi$
$608$	−1.96732e7	+	1.42934e7i	−0.0875313	+	0.0635952i
$609$	−9.97428e7	+	3.06977e8i	−0.441601	+	1.35911i
$610$	−1.88187e8	−	2.59017e8i	−0.829086	−	1.14114i
$611$	−6.23942e7	+	2.02731e7i	−0.273540	+	0.0888785i
$612$	2.41378e8	−	7.84283e7i	1.05303	−	0.342152i
$613$	1.69128e8	+	5.49531e7i	0.734234	+	0.238567i	0.652184	−	0.758061i	$-0.273853\pi$
$613$	1.69128e8	+	5.49531e7i	0.734234	+	0.238567i	0.0820507	+	0.996628i	$0.473853\pi$
$614$	2.45532e8			1.06073
$615$		−	7.25131e7i		−	0.311739i
$616$	−6.14883e6	−	1.99788e6i	−0.0263057	−	0.00854725i
$617$	−1.88859e8	−	1.37214e8i	−0.804050	−	0.584176i	0.108050	−	0.994145i	$-0.465539\pi$
$617$	−1.88859e8	−	1.37214e8i	−0.804050	−	0.584176i	−0.912099	+	0.409969i	$0.865539\pi$
$618$	1.44182e8	+	1.98449e8i	0.610864	+	0.840782i
$619$			1.15611e8i			0.487446i	0.969845	+	0.243723i	$0.0783688\pi$
$619$			1.15611e8i			0.487446i	−0.969845	+	0.243723i	$0.921631\pi$
$620$	9.53067e7	+	2.10604e8i	0.399897	+	0.883674i
$621$	−4.20689e7			−0.175665
$622$	1.87334e8	−	1.36106e8i	0.778475	−	0.565595i
$623$	3.70077e7	−	5.09368e7i	0.153048	−	0.210653i
$624$	−4.54020e7	+	1.39733e8i	−0.186862	+	0.575103i
$625$	9.45320e8			3.87203
$626$			2.71234e8i			1.10566i
$627$	−5.46519e6	+	1.68201e7i	−0.0221719	+	0.0682380i
$628$	−4.26106e7	−	1.31142e8i	−0.172044	−	0.529496i
$629$	1.63473e8	+	5.03117e8i	0.656890	+	2.02170i
$630$	−4.76951e8	+	3.46525e8i	−1.90744	+	1.38584i
$631$	2.16826e8	+	7.04511e7i	0.863025	+	0.280414i	0.706891	−	0.707322i	$-0.250097\pi$
$631$	2.16826e8	+	7.04511e7i	0.863025	+	0.280414i	0.156134	+	0.987736i	$0.450097\pi$
$632$	2.78228e7	+	3.82949e7i	0.110217	+	0.151701i
$633$	−2.41737e8	+	3.32723e8i	−0.953086	+	1.31181i
$634$	1.73305e7	+	5.33377e7i	0.0680052	+	0.209299i
$635$	−1.20137e8	+	1.65354e8i	−0.469196	+	0.645793i
$636$	−2.74202e8	−	1.99220e8i	−1.06586	−	0.774392i
$637$	5.79152e7	−	1.88178e7i	0.224065	−	0.0728032i
$638$	8.90622e6	+	6.47075e6i	0.0342951	+	0.0249168i
$639$	−3.52897e8	+	2.56395e8i	−1.35253	+	0.982667i
$640$	−1.38898e7	+	4.27484e7i	−0.0529853	+	0.163072i
$641$	−2.54521e7	−	3.50318e7i	−0.0966383	−	0.133011i	0.757960	−	0.652301i	$-0.226196\pi$
$641$	−2.54521e7	−	3.50318e7i	−0.0966383	−	0.133011i	−0.854598	+	0.519290i	$0.826196\pi$
$642$	−5.34787e8	+	1.73763e8i	−2.02104	+	0.656677i
$643$	−6.85904e7	+	2.22864e7i	−0.258006	+	0.0838313i	−0.435164	−	0.900351i	$-0.643310\pi$
$643$	−6.85904e7	+	2.22864e7i	−0.258006	+	0.0838313i	0.177158	+	0.984182i	$0.443310\pi$
$644$	2.49000e7	+	8.09049e6i	0.0932269	+	0.0302913i
$645$	9.62601e8			3.58729
$646$			1.61683e8i			0.599745i
$647$	1.29752e8	+	4.21591e7i	0.479074	+	0.155660i	0.538592	−	0.842567i	$-0.318956\pi$
$647$	1.29752e8	+	4.21591e7i	0.479074	+	0.155660i	−0.0595183	+	0.998227i	$0.518956\pi$
$648$	3.46238e6	+	2.51557e6i	0.0127248	+	0.00924508i
$649$	−9.77063e6	−	1.34481e7i	−0.0357428	−	0.0491957i
$650$		−	8.05228e8i		−	2.93210i
$651$	4.68471e8	+	9.66012e7i	1.69801	+	0.350138i
$652$	1.14962e7			0.0414775
$653$	−1.79007e8	+	1.30056e8i	−0.642880	+	0.467080i	−0.860839	−	0.508878i	$-0.830060\pi$
$653$	−1.79007e8	+	1.30056e8i	−0.642880	+	0.467080i	0.217958	+	0.975958i	$0.430060\pi$
$654$	−1.85322e7	+	2.55074e7i	−0.0662514	+	0.0911872i
$655$	−2.32492e7	+	7.15535e7i	−0.0827339	+	0.254629i
$656$	−7.03636e6			−0.0249251
$657$		−	4.75079e8i		−	1.67521i
$658$	−1.28334e7	+	3.94972e7i	−0.0450468	+	0.138640i
$659$	−6.91720e7	−	2.12890e8i	−0.241699	−	0.743872i	−0.996162	−	0.0875297i	$-0.972103\pi$
$659$	−6.91720e7	−	2.12890e8i	−0.241699	−	0.743872i	0.754463	−	0.656342i	$-0.227897\pi$
$660$	1.01019e7	+	3.10904e7i	0.0351374	+	0.108142i
$661$	−2.73318e7	+	1.98577e7i	−0.0946377	+	0.0687583i	−0.634098	−	0.773253i	$-0.718628\pi$
$661$	−2.73318e7	+	1.98577e7i	−0.0946377	+	0.0687583i	0.539460	+	0.842011i	$0.318628\pi$
$662$	2.46936e8	+	8.02344e7i	0.851158	+	0.276558i
$663$	5.74195e8	+	7.90311e8i	1.97024	+	2.71180i
$664$	−6.45307e7	+	8.88189e7i	−0.220426	+	0.303390i
$665$	−1.16057e8	−	3.57187e8i	−0.394645	−	1.21459i
$666$	3.00955e8	−	4.14229e8i	1.01878	−	1.40223i
$667$	−3.60662e7	−	2.62036e7i	−0.121541	−	0.0883046i
$668$	7.51467e7	−	2.44166e7i	0.252104	−	0.0819137i
$669$	−4.10339e8	−	2.98129e8i	−1.37045	−	0.995694i
$670$	−3.45956e8	+	2.51352e8i	−1.15026	+	0.835714i
$671$	−6.98218e6	+	2.14889e7i	−0.0231112	+	0.0711291i
$672$	5.46680e7	+	7.52441e7i	0.180146	+	0.247950i
$673$	−4.72445e8	+	1.53507e8i	−1.54991	+	0.503596i	−0.954089	−	0.299522i	$-0.903173\pi$
$673$	−4.72445e8	+	1.53507e8i	−1.54991	+	0.503596i	−0.595820	+	0.803118i	$0.703173\pi$
$674$	−2.97675e8	+	9.67206e7i	−0.972217	+	0.315892i
$675$	7.78961e8	+	2.53100e8i	2.53282	+	0.822963i
$676$	−1.93379e8			−0.625994
$677$		−	2.76844e8i		−	0.892216i	−0.894979	−	0.446108i	$-0.852810\pi$
$677$		−	2.76844e8i		−	0.892216i	0.894979	−	0.446108i	$-0.147190\pi$
$678$	1.49382e8	+	4.85372e7i	0.479303	+	0.155735i
$679$	−4.88337e7	−	3.54798e7i	−0.155995	−	0.113337i
$680$	1.75663e8	+	2.41779e8i	0.558666	+	0.768938i
$681$		−	2.58312e8i		−	0.817906i
$682$	8.07091e6	−	1.41777e7i	0.0254430	−	0.0446945i
$683$	−1.42617e8			−0.447621			−0.223810	−	0.974633i	$-0.571850\pi$
$683$	−1.42617e8			−0.447621			−0.223810	+	0.974633i	$0.571850\pi$
$684$	1.26602e8	−	9.19821e7i	0.395616	−	0.287432i
$685$	−1.29682e8	+	1.78492e8i	−0.403468	+	0.555326i
$686$	−6.39640e7	+	1.96861e8i	−0.198136	+	0.609800i
$687$	4.73755e7			0.146111
$688$		−	9.34067e7i		−	0.286822i
$689$	2.47959e8	−	7.63138e8i	0.758091	−	2.33316i
$690$	−4.09080e7	−	1.25902e8i	−0.124526	−	0.383252i
$691$	8.94628e7	+	2.75338e8i	0.271149	+	0.834511i	0.990213	+	0.139567i	$0.0445710\pi$
$691$	8.94628e7	+	2.75338e8i	0.271149	+	0.834511i	−0.719064	+	0.694944i	$0.755429\pi$
$692$	3.94949e7	−	2.86947e7i	0.119185	−	0.0865932i
$693$	3.95695e7	+	1.28569e7i	0.118894	+	0.0386311i
$694$	5.15064e7	+	7.08925e7i	0.154093	+	0.212091i
$695$	−4.09656e6	+	5.63843e6i	−0.0122030	+	0.0167959i
$696$	−4.89381e7	−	1.50616e8i	−0.145151	−	0.446728i
$697$	−2.74989e7	+	3.78489e7i	−0.0812113	+	0.111778i
$698$	1.58231e8	+	1.14961e8i	0.465291	+	0.338054i
$699$	2.81968e8	−	9.16170e7i	0.825597	−	0.268253i
$700$	−4.12381e8	−	2.99612e8i	−1.20228	−	0.873505i
$701$	2.25219e8	−	1.63631e8i	0.653810	−	0.475021i	−0.210757	−	0.977539i	$-0.567593\pi$
$701$	2.25219e8	−	1.63631e8i	0.653810	−	0.475021i	0.864567	+	0.502518i	$0.167593\pi$
$702$	1.09332e8	−	3.36490e8i	0.316037	−	0.972661i
$703$	1.91723e8	+	2.63885e8i	0.551835	+	0.759536i
$704$	3.01688e6	−	980243.i	0.00864649	−	0.00280941i
$705$	1.99710e8	−	6.48896e7i	0.569943	−	0.185186i
$706$	3.09913e7	+	1.00697e7i	0.0880695	+	0.0286155i
$707$	−1.07215e8			−0.303388
$708$			2.39129e8i			0.673803i
$709$	1.06726e8	+	3.46775e7i	0.299456	+	0.0972991i	0.454891	−	0.890547i	$-0.349678\pi$
$709$	1.06726e8	+	3.46775e7i	0.299456	+	0.0972991i	−0.155435	+	0.987846i	$0.549678\pi$
$710$	−4.15545e8	−	3.01911e8i	−1.16103	−	0.843537i
$711$	−1.79048e8	−	2.46439e8i	−0.498151	−	0.685646i
$712$			3.08915e7i			0.0855853i
$713$	−3.26835e7	+	5.74134e7i	−0.0901696	+	0.158396i
$714$	6.18390e8			1.69890
$715$	−6.26124e7	+	4.54906e7i	−0.171294	+	0.124452i
$716$	5.80483e7	−	7.98966e7i	0.158143	−	0.217665i
$717$	−3.00961e8	+	9.26264e8i	−0.816495	+	2.51291i
$718$	7.28724e7			0.196875
$719$		−	3.55128e8i		−	0.955430i	−0.878515	−	0.477715i	$-0.841465\pi$
$719$		−	3.55128e8i		−	0.955430i	0.878515	−	0.477715i	$-0.158535\pi$
$720$	8.93847e7	−	2.75098e8i	0.239478	−	0.737038i
$721$	1.13600e8	+	3.49625e8i	0.303091	+	0.932817i
$722$	−5.14328e7	−	1.58294e8i	−0.136656	−	0.420584i
$723$	1.28564e8	−	9.34070e7i	0.340176	−	0.247152i
$724$	−2.66078e8	−	8.64541e7i	−0.701122	−	0.227808i
$725$	5.10163e8	+	7.02180e8i	1.33874	+	1.84261i
$726$	−2.54992e8	+	3.50966e8i	−0.666371	+	0.917181i
$727$	−5.29659e7	−	1.63012e8i	−0.137846	−	0.424246i	0.858176	−	0.513356i	$-0.171598\pi$
$727$	−5.29659e7	−	1.63012e8i	−0.137846	−	0.424246i	−0.996022	+	0.0891099i	$0.971598\pi$
$728$	−1.29425e8	+	1.78138e8i	−0.335446	+	0.461702i
$729$	−5.09185e8	−	3.69945e8i	−1.31430	−	0.954892i
$730$	5.32037e8	−	1.72869e8i	1.36765	−	0.444375i
$731$	−5.02439e8	−	3.65043e8i	−1.28627	−	0.934528i
$732$	2.62963e8	−	1.91054e8i	0.670442	−	0.487105i
$733$	2.49027e7	−	7.66426e7i	0.0632316	−	0.194607i	−0.914450	−	0.404699i	$-0.867376\pi$
$733$	2.49027e7	−	7.66426e7i	0.0632316	−	0.194607i	0.977682	+	0.210092i	$0.0673764\pi$
$734$	−1.30999e8	−	1.80305e8i	−0.331268	−	0.455951i
$735$	−1.85373e8	+	6.02315e7i	−0.466859	+	0.151692i
$736$	−1.22170e7	+	3.96954e6i	−0.0306429	+	0.00995650i
$737$	2.87017e7	+	9.32576e6i	0.0716978	+	0.0232960i
$738$	4.52810e7			0.112654
$739$			1.87557e8i			0.464730i	0.972629	+	0.232365i	$0.0746464\pi$
$739$			1.87557e8i			0.464730i	−0.972629	+	0.232365i	$0.925354\pi$
$740$	5.73402e8	+	1.86310e8i	1.41503	+	0.459770i
$741$	4.87295e8	+	3.54041e8i	1.19767	+	0.870159i
$742$	−2.98564e8	−	4.10938e8i	−0.730845	−	1.00592i
$743$			3.09583e8i			0.754764i	0.926058	+	0.377382i	$0.123176\pi$
$743$			3.09583e8i			0.754764i	−0.926058	+	0.377382i	$0.876824\pi$
$744$	−2.13813e8	+	9.67587e7i	−0.519177	+	0.234948i
$745$	−8.85301e8			−2.14103
$746$	−1.63877e8	+	1.19064e8i	−0.394732	+	0.286790i
$747$	4.15274e8	−	5.71575e8i	0.996260	−	1.37123i
$748$	6.51750e6	−	2.00588e7i	0.0155732	−	0.0479292i
$749$	−8.42712e8			−2.00555
$750$			1.64461e9i			3.89833i
$751$	5.04488e7	−	1.55265e8i	0.119105	−	0.366568i	−0.873676	−	0.486508i	$-0.838270\pi$
$751$	5.04488e7	−	1.55265e8i	0.119105	−	0.366568i	0.992781	+	0.119940i	$0.0382703\pi$
$752$	−6.29661e6	−	1.93790e7i	−0.0148065	−	0.0455698i
$753$	−3.41142e7	−	1.04993e8i	−0.0799006	−	0.245909i
$754$	3.03323e8	−	2.20377e8i	0.707606	−	0.514106i
$755$	2.92011e8	+	9.48803e7i	0.678514	+	0.220463i
$756$	−1.31646e8	−	1.81195e8i	−0.304678	−	0.419354i
$757$	−6.71225e7	+	9.23862e7i	−0.154732	+	0.212971i	−0.879344	−	0.476186i	$-0.842019\pi$
$757$	−6.71225e7	+	9.23862e7i	−0.154732	+	0.212971i	0.724612	+	0.689157i	$0.242019\pi$
$758$	−1.52001e8	−	4.67812e8i	−0.349012	−	1.07415i
$759$	−5.49139e6	+	7.55826e6i	−0.0125591	+	0.0172861i
$760$	1.49078e8	+	1.08311e8i	0.339603	+	0.246736i
$761$	2.46718e8	−	8.01634e7i	0.559817	−	0.181896i	−0.0154219	−	0.999881i	$-0.504909\pi$
$761$	2.46718e8	−	8.01634e7i	0.559817	−	0.181896i	0.575239	+	0.817986i	$0.304909\pi$
$762$	−1.67873e8	−	1.21967e8i	−0.379417	−	0.275662i
$763$	−3.82272e7	+	2.77737e7i	−0.0860594	+	0.0625258i
$764$	−1.14984e8	+	3.53884e8i	−0.257844	+	0.793561i
$765$	−1.13044e9	−	1.55592e9i	−2.52501	−	3.47538i
$766$	−4.65123e7	+	1.51128e7i	−0.103486	+	0.0336246i
$767$	−5.38421e8	+	1.74944e8i	−1.19326	+	0.387714i
$768$	−4.33996e7	−	1.41014e7i	−0.0958081	−	0.0311300i
$769$	−5.37370e8			−1.18167			−0.590833	−	0.806794i	$-0.701201\pi$
$769$	−5.37370e8			−1.18167			−0.590833	+	0.806794i	$0.701201\pi$
$770$			4.89919e7i			0.107313i
$771$	−7.59612e8	−	2.46813e8i	−1.65740	−	0.538524i
$772$	4.84608e7	+	3.52088e7i	0.105327	+	0.0765243i
$773$	1.21415e7	+	1.67114e7i	0.0262866	+	0.0361805i	0.821958	−	0.569548i	$-0.192882\pi$
$773$	1.21415e7	+	1.67114e7i	0.0262866	+	0.0361805i	−0.795671	+	0.605729i	$0.792882\pi$
$774$			6.01099e8i			1.29635i
$775$	9.50595e8	−	8.66450e8i	2.04216	−	1.86140i
$776$	2.96161e7			0.0633785
$777$	1.00928e9	−	7.33286e8i	2.15154	−	1.56318i
$778$	−4.78784e7	+	6.58990e7i	−0.101672	+	0.139939i
$779$	−8.91399e6	+	2.74345e7i	−0.0188565	+	0.0580342i
$780$	1.11335e9			2.34610
$781$			3.62492e7i			0.0760932i
$782$	−2.63929e7	+	8.12291e7i	−0.0551909	+	0.169860i
$783$	1.17847e8	+	3.62697e8i	0.245491	+	0.755543i
$784$	5.84461e6	+	1.79879e7i	0.0121285	+	0.0373277i
$785$	−8.45339e8	+	6.14174e8i	−1.74752	+	1.26965i
$786$	−7.26437e7	−	2.36034e7i	−0.149600	−	0.0486078i
$787$	−3.36196e8	−	4.62735e8i	−0.689714	−	0.949309i	0.310285	−	0.950643i	$-0.399575\pi$
$787$	−3.36196e8	−	4.62735e8i	−0.689714	−	0.949309i	−0.999999	+	0.00133399i	$0.999575\pi$
$788$	1.80655e8	−	2.48651e8i	0.369209	−	0.508172i
$789$	2.20905e8	+	6.79877e8i	0.449754	+	1.38420i
$790$	2.10834e8	−	2.90187e8i	0.427620	−	0.588569i
$791$	1.90439e8	+	1.38362e8i	0.384792	+	0.279568i
$792$	−1.94145e7	+	6.30815e6i	−0.0390796	+	0.0126977i
$793$	6.22555e8	+	4.52313e8i	1.24841	+	0.907026i
$794$	−5.28337e8	+	3.83859e8i	−1.05548	+	0.766850i
$795$	−7.93659e8	+	2.44263e9i	−1.57955	+	4.86135i
$796$	1.96292e8	+	2.70173e8i	0.389192	+	0.535676i
$797$	5.71637e7	−	1.85736e7i	0.112913	−	0.0366878i	−0.252015	−	0.967723i	$-0.581093\pi$
$797$	5.71637e7	−	1.85736e7i	0.112913	−	0.0366878i	0.364929	+	0.931035i	$0.381093\pi$
$798$	3.62629e8	−	1.17825e8i	0.713598	−	0.231862i
$799$	−1.28848e8	−	4.18653e7i	−0.252603	−	0.0820756i
$800$	2.50095e8			0.488468
$801$		−	1.98796e8i		−	0.386821i
$802$	−5.71245e8	−	1.85609e8i	−1.10739	−	0.359812i
$803$	−3.19398e7	−	2.32056e7i	−0.0616858	−	0.0448173i
$804$	−2.55181e8	−	3.51227e8i	−0.490999	−	0.675803i
$805$		−	1.98395e8i		−	0.380315i
$806$	−3.74284e8	−	4.10632e8i	−0.714819	−	0.784238i
$807$	2.44651e8			0.465507
$808$	4.25578e7	−	3.09201e7i	0.0806762	−	0.0586147i
$809$	1.54040e8	−	2.12019e8i	0.290931	−	0.400431i	−0.638386	−	0.769717i	$-0.720397\pi$
$809$	1.54040e8	−	2.12019e8i	0.290931	−	0.400431i	0.929316	+	0.369285i	$0.120397\pi$
$810$	1.00216e7	−	3.08434e7i	0.0188574	−	0.0580372i
$811$	−3.47858e8			−0.652138			−0.326069	−	0.945346i	$-0.605724\pi$
$811$	−3.47858e8			−0.652138			−0.326069	+	0.945346i	$0.605724\pi$
$812$		−	2.37339e8i		−	0.443304i
$813$	−7.14826e6	+	2.20001e7i	−0.0133024	+	0.0409405i
$814$	−1.31484e7	−	4.04667e7i	−0.0243781	−	0.0750282i
$815$	−2.69200e7	−	8.28513e7i	−0.0497282	−	0.153048i
$816$	−2.45462e8	+	1.78339e8i	−0.451767	+	0.328228i
$817$	−3.64188e8	−	1.18332e8i	−0.667821	−	0.216988i
$818$	2.89708e8	+	3.98748e8i	0.529298	+	0.728516i
$819$	8.32884e8	−	1.14637e9i	1.51612	−	2.08676i
$820$	1.64766e7	+	5.07099e7i	0.0298832	+	0.0919711i
$821$	1.34104e8	−	1.84578e8i	0.242333	−	0.333543i	−0.670475	−	0.741932i	$-0.733910\pi$
$821$	1.34104e8	−	1.84578e8i	0.242333	−	0.333543i	0.912808	+	0.408390i	$0.133910\pi$
$822$	−1.81212e8	−	1.31658e8i	−0.326265	−	0.237046i
$823$	−6.14313e8	+	1.99602e8i	−1.10202	+	0.358069i	−0.802881	−	0.596140i	$-0.796700\pi$
$823$	−6.14313e8	+	1.99602e8i	−1.10202	+	0.358069i	−0.299142	+	0.954209i	$0.596700\pi$
$824$	−1.45921e8	−	1.06018e8i	−0.260818	−	0.189495i
$825$	1.47153e8	−	1.06913e8i	0.262064	−	0.190401i
$826$	−1.10744e8	+	3.40835e8i	−0.196508	+	0.604789i
$827$	−1.77272e8	−	2.43994e8i	−0.313418	−	0.431383i	0.623025	−	0.782202i	$-0.285903\pi$
$827$	−1.77272e8	−	2.43994e8i	−0.313418	−	0.431383i	−0.936443	+	0.350819i	$0.885903\pi$
$828$	7.86198e7	−	2.55451e7i	0.138497	−	0.0450005i
$829$	4.36548e8	−	1.41843e8i	0.766246	−	0.248969i	0.100289	−	0.994958i	$-0.468023\pi$
$829$	4.36548e8	−	1.41843e8i	0.766246	−	0.248969i	0.665957	+	0.745990i	$0.268023\pi$
$830$	7.91211e8	+	2.57080e8i	1.38375	+	0.449608i
$831$	−1.06047e9			−1.84797
$832$		−	1.08035e8i		−	0.187583i
$833$	1.19599e8	+	3.88600e7i	0.206915	+	0.0672308i
$834$	−5.72434e6	−	4.15897e6i	−0.00986795	−	0.00716949i
$835$	−3.51933e8	−	4.84395e8i	−0.604506	−	0.832032i
$836$		−	1.30045e7i		−	0.0222574i
$837$	5.14882e8	−	2.33004e8i	0.878074	−	0.397363i
$838$	6.31226e8			1.07264
$839$	−7.06731e8	+	5.13470e8i	−1.19665	+	0.869419i	−0.993951	−	0.109822i	$-0.964972\pi$
$839$	−7.06731e8	+	5.13470e8i	−1.19665	+	0.869419i	−0.202701	+	0.979241i	$0.564972\pi$
$840$	4.14259e8	−	5.70178e8i	0.698930	−	0.961994i
$841$	5.89280e7	−	1.81362e8i	0.0990680	−	0.304900i
$842$	−3.30562e8			−0.553754
$843$		−	3.76103e8i		−	0.627804i
$844$	9.34495e7	−	2.87608e8i	0.155435	−	0.478381i
$845$	4.52826e8	+	1.39365e9i	0.750517	+	2.30986i
$846$	4.05205e7	+	1.24709e8i	0.0669212	+	0.205962i
$847$	−5.25981e8	+	3.82148e8i	−0.865605	+	0.628899i
$848$	2.37023e8	+	7.70133e7i	0.388689	+	0.126293i
$849$	−9.48476e8	−	1.30546e9i	−1.54990	−	2.13325i
$850$	9.77399e8	−	1.34527e9i	1.59153	−	2.19056i
$851$	5.32451e7	+	1.63872e8i	0.0863955	+	0.265898i
$852$	3.06511e8	−	4.21876e8i	0.495595	−	0.682128i
$853$	6.22475e8	+	4.52255e8i	1.00294	+	0.728678i	0.962717	−	0.270512i	$-0.0871931\pi$
$853$	6.22475e8	+	4.52255e8i	1.00294	+	0.728678i	0.0402233	+	0.999191i	$0.487193\pi$
$854$	4.63285e8	−	1.50530e8i	0.743832	−	0.241686i
$855$	−9.59357e8	−	6.97014e8i	−1.53491	−	1.11518i
$856$	3.34505e8	−	2.43032e8i	0.533311	−	0.387473i
$857$	−6.90834e6	+	2.12617e7i	−0.0109757	+	0.0337796i	−0.956394	−	0.292078i	$-0.905653\pi$
$857$	−6.90834e6	+	2.12617e7i	−0.0109757	+	0.0337796i	0.945419	+	0.325858i	$0.105653\pi$
$858$	−4.61836e7	−	6.35663e7i	−0.0731183	−	0.100639i
$859$	2.17176e8	−	7.05648e7i	0.342636	−	0.111329i	−0.132644	−	0.991164i	$-0.542347\pi$
$859$	2.17176e8	−	7.05648e7i	0.342636	−	0.111329i	0.475280	+	0.879835i	$0.342347\pi$
$860$	−6.73167e8	+	2.18725e8i	−1.05835	+	0.343877i
$861$	1.04929e8	+	3.40934e7i	0.164394	+	0.0534147i
$862$	−6.34475e8			−0.990587
$863$			9.13870e8i			1.42184i	0.703271	+	0.710922i	$0.251722\pi$
$863$			9.13870e8i			1.42184i	−0.703271	+	0.710922i	$0.748278\pi$
$864$	1.04510e8	+	3.39575e7i	0.162039	+	0.0526495i
$865$	−2.99281e8	−	2.17440e8i	−0.462414	−	0.335963i
$866$	−3.60324e8	−	4.95944e8i	−0.554804	−	0.763623i
$867$			9.66876e8i			1.48359i
$868$	−3.49561e8	+	3.88921e7i	−0.534520	+	0.0594706i
$869$	−2.53139e7			−0.0385745
$870$	−9.70868e8	+	7.05377e8i	−1.47436	+	1.07118i
$871$	6.04133e8	−	8.31517e8i	0.914277	−	1.25839i
$872$	7.16410e6	−	2.20488e7i	0.0108047	−	0.0332534i
$873$	−1.90588e8			−0.286452
$874$			5.26622e7i			0.0788797i
$875$	−7.61640e8	+	2.34409e9i	−1.13691	+	3.49904i
$876$	1.75503e8	+	5.40143e8i	0.261079	+	0.803520i
$877$	−3.80918e7	−	1.17234e8i	−0.0564719	−	0.173803i	0.918842	−	0.394626i	$-0.129126\pi$
$877$	−3.80918e7	−	1.17234e8i	−0.0564719	−	0.173803i	−0.975314	+	0.220823i	$0.929126\pi$
$878$	−5.45774e8	+	3.96528e8i	−0.806360	+	0.585855i
$879$	1.58192e9	+	5.13996e8i	2.32925	+	0.756821i
$880$	−1.41289e7	−	1.94468e7i	−0.0207329	−	0.0285364i
$881$	2.83516e8	−	3.90226e8i	0.414619	−	0.570674i	−0.549718	−	0.835350i	$-0.685265\pi$
$881$	2.83516e8	−	3.90226e8i	0.414619	−	0.570674i	0.964337	+	0.264676i	$0.0852650\pi$
$882$	−3.76118e7	−	1.15757e8i	−0.0548173	−	0.168710i
$883$	1.86839e8	−	2.57161e8i	0.271384	−	0.373528i	−0.651472	−	0.758672i	$-0.725848\pi$
$883$	1.86839e8	−	2.57161e8i	0.271384	−	0.373528i	0.922856	+	0.385144i	$0.125848\pi$
$884$	−5.81123e8	−	4.22211e8i	−0.841224	−	0.611185i
$885$	1.72336e9	−	5.59955e8i	2.48626	−	0.807836i
$886$	2.49168e8	+	1.81031e8i	0.358253	+	0.260286i
$887$	8.16461e8	−	5.93194e8i	1.16994	−	0.850013i	0.178941	−	0.983860i	$-0.442733\pi$
$887$	8.16461e8	−	5.93194e8i	1.16994	−	0.850013i	0.991002	+	0.133847i	$0.0427329\pi$
$888$	−1.89148e8	+	5.82138e8i	−0.270124	+	0.831356i
$889$	−1.82788e8	−	2.51586e8i	−0.260161	−	0.358081i
$890$	2.22630e8	−	7.23368e7i	0.315801	−	0.102610i
$891$	−2.17671e6	+	707255.i	−0.00307728	+	0.000999868i
$892$	3.54701e8	+	1.15249e8i	0.499767	+	0.162384i
$893$	−8.35346e7			−0.117304
$894$		−	8.98789e8i		−	1.25790i
$895$	−7.11729e8	−	2.31255e8i	−0.992764	−	0.322568i
$896$	−5.53277e7	−	4.01979e7i	−0.0769163	−	0.0558830i
$897$	1.87023e8	+	2.57415e8i	0.259130	+	0.356661i
$898$			8.39424e8i			1.15918i
$899$	5.86546e8	+	1.20949e8i	0.807278	+	0.166465i
$900$	−1.60944e9			−2.20773
$901$	1.34057e9	−	9.73980e8i	1.83280	−	1.33161i
$902$	2.21179e6	−	3.04426e6i	0.00301386	−	0.00414823i
$903$	−4.52585e8	+	1.39291e9i	−0.614663	+	1.89174i
$904$	−1.15495e8			−0.156336
$905$			2.12003e9i			2.86019i
$906$	−9.63258e7	+	2.96460e8i	−0.129526	+	0.398641i
$907$	7.28519e7	+	2.24215e8i	0.0976380	+	0.300499i	0.987932	−	0.154887i	$-0.0495013\pi$
$907$	7.28519e7	+	2.24215e8i	0.0976380	+	0.300499i	−0.890294	+	0.455386i	$0.849501\pi$
$908$	5.86945e7	+	1.80643e8i	0.0784043	+	0.241304i
$909$	−2.73872e8	+	1.98980e8i	−0.364633	+	0.264921i
$910$	1.58687e9	+	5.15607e8i	2.10581	+	0.684218i
$911$	7.17199e8	+	9.87140e8i	0.948604	+	1.30564i	0.952145	+	0.305647i	$0.0988728\pi$
$911$	7.17199e8	+	9.87140e8i	0.948604	+	1.30564i	−0.00354127	+	0.999994i	$0.501127\pi$
$912$	−1.09961e8	+	1.51349e8i	−0.144962	+	0.199524i
$913$	−1.81429e7	−	5.58381e7i	−0.0238393	−	0.0733699i
$914$	4.58142e7	−	6.30579e7i	0.0600015	−	0.0825849i
$915$	−1.99266e9	−	1.44775e9i	−2.60118	−	1.88986i
$916$	−3.31306e7	+	1.07648e7i	−0.0431066	+	0.0140062i
$917$	−9.26092e7	−	6.72845e7i	−0.120101	−	0.0872584i
$918$	5.91097e8	−	4.29457e8i	0.764065	−	0.555126i
$919$	2.44342e8	−	7.52007e8i	0.314812	−	0.968892i	−0.661020	−	0.750369i	$-0.729876\pi$
$919$	2.44342e8	−	7.52007e8i	0.314812	−	0.968892i	0.975832	−	0.218523i	$-0.0701240\pi$
$920$	5.72156e7	+	7.87505e7i	0.0734769	+	0.101132i
$921$	1.79647e9	−	5.83707e8i	2.29954	−	0.747165i
$922$	−3.68949e8	+	1.19879e8i	−0.470732	+	0.152950i
$923$	1.17413e9	+	3.81499e8i	1.49318	+	0.485163i
$924$	−4.97383e7			−0.0630485
$925$		−	3.35464e9i		−	4.23858i
$926$	5.89160e8	+	1.91430e8i	0.741994	+	0.241088i
$927$	9.39046e8	+	6.82257e8i	1.17882	+	0.856463i
$928$	6.84468e7	+	9.42090e7i	0.0856464	+	0.117882i
$929$		−	5.96414e8i		−	0.743877i	−0.928257	−	0.371938i	$-0.878693\pi$
$929$		−	5.96414e8i		−	0.743877i	0.928257	−	0.371938i	$-0.121307\pi$
$930$	1.19800e9	+	1.31434e9i	1.48938	+	1.63403i
$931$	7.75381e7			0.0960873
$932$	−1.76369e8	+	1.28139e8i	−0.217858	+	0.158283i
$933$	1.04708e9	−	1.44119e9i	1.28925	−	1.77450i
$934$	−1.42742e8	+	4.39315e8i	−0.175191	+	0.539182i
$935$	−1.59822e8			−0.195525
$936$			6.95234e8i			0.847820i
$937$	−3.84078e8	+	1.18207e9i	−0.466875	+	1.43689i	0.389735	+	0.920927i	$0.372567\pi$
$937$	−3.84078e8	+	1.18207e9i	−0.466875	+	1.43689i	−0.856609	+	0.515965i	$0.827433\pi$
$938$	−2.01056e8	−	6.18788e8i	−0.243618	−	0.749779i
$939$	6.44810e8	+	1.98452e9i	0.778816	+	2.39695i
$940$	−1.24917e8	+	9.07573e7i	−0.150396	+	0.109269i
$941$	−1.56378e9	−	5.08104e8i	−1.87676	−	0.609795i	−0.988668	−	0.150122i	$-0.952033\pi$
$941$	−1.56378e9	−	5.08104e8i	−1.87676	−	0.609795i	−0.888088	−	0.459673i	$-0.847967\pi$
$942$	−6.23532e8	−	8.58218e8i	−0.745943	−	1.02670i
$943$	−8.95673e6	+	1.23279e7i	−0.0106811	+	0.0147012i
$944$	−5.43357e7	−	1.67228e8i	−0.0645905	−	0.198789i
$945$	−9.97574e8	+	1.37304e9i	−1.18209	+	1.62700i
$946$	4.04122e7	+	2.93612e7i	0.0477352	+	0.0346817i
$947$	6.85188e8	−	2.22631e8i	0.806789	−	0.262142i	0.123552	−	0.992338i	$-0.460571\pi$
$947$	6.85188e8	−	2.22631e8i	0.806789	−	0.262142i	0.683237	+	0.730196i	$0.260571\pi$
$948$	2.94609e8	+	2.14046e8i	0.345796	+	0.251236i
$949$	−1.08779e9	+	7.90323e8i	−1.27275	+	0.924711i
$950$	3.16833e8	−	9.75110e8i	0.369538	−	1.13732i
$951$	2.53601e8	+	3.49052e8i	0.294856	+	0.405834i
$952$	−4.32453e8	+	1.40512e8i	−0.501219	+	0.162856i
$953$	−8.36046e8	+	2.71648e8i	−0.965943	+	0.313854i	−0.749177	−	0.662369i	$-0.769551\pi$
$953$	−8.36046e8	+	2.71648e8i	−0.965943	+	0.313854i	−0.216766	+	0.976224i	$0.569551\pi$
$954$	−1.52531e9	−	4.95603e8i	−1.75676	−	0.570806i
$955$	2.81963e9			3.23729
$956$		−	7.16141e8i		−	0.819643i
$957$	8.05466e7	+	2.61712e7i	0.0918991	+	0.0298598i
$958$	−2.46631e7	−	1.79188e7i	−0.0280512	−	0.0203804i
$959$	−1.97312e8	−	2.71576e8i	−0.223716	−	0.307918i
$960$			3.45794e8i			0.390845i
$961$	8.20221e7	−	8.83705e8i	0.0924189	−	0.995720i
$962$	−1.44912e9			−1.62771
$963$	−2.15263e9	+	1.56398e9i	−2.41041	+	1.75127i
$964$	−6.86830e7	+	9.45341e7i	−0.0766687	+	0.105525i
$965$	1.40266e8	−	4.31695e8i	0.156089	−	0.480391i
$966$	2.01418e8			0.223443
$967$			5.76971e8i			0.638079i	0.947741	+	0.319040i	$0.103360\pi$
$967$			5.76971e8i			0.638079i	−0.947741	+	0.319040i	$0.896640\pi$
$968$	9.85735e7	−	3.03378e8i	0.108676	−	0.334471i
$969$	3.84372e8	+	1.18297e9i	0.422455	+	1.30018i
$970$	−6.93502e7	−	2.13438e8i	−0.0759858	−	0.233860i
$971$	−4.85935e8	+	3.53052e8i	−0.530787	+	0.385639i	−0.820652	−	0.571428i	$-0.806390\pi$
$971$	−4.85935e8	+	3.53052e8i	−0.530787	+	0.385639i	0.289865	+	0.957067i	$0.406390\pi$
$972$	4.52197e8	+	1.46928e8i	0.492412	+	0.159994i
$973$	−6.23292e6	−	8.57887e6i	−0.00676632	−	0.00931304i
$974$	−6.94300e7	+	9.55622e7i	−0.0751398	+	0.103421i
$975$	−1.91428e9	−	5.89156e9i	−2.06534	−	6.35647i
$976$	−1.40484e8	+	1.93359e8i	−0.151104	+	0.207977i
$977$	1.00032e9	+	7.26778e8i	1.07265	+	0.779324i	0.976386	−	0.216033i	$-0.0693117\pi$
$977$	1.00032e9	+	7.26778e8i	1.07265	+	0.779324i	0.0962607	+	0.995356i	$0.469312\pi$
$978$	8.41136e7	−	2.73302e7i	0.0899186	−	0.0292163i
$979$	−1.33651e7	−	9.71033e6i	−0.0142438	−	0.0103487i
$980$	1.15950e8	−	8.42423e7i	0.123194	−	0.0895059i
$981$	−4.61031e7	+	1.41891e8i	−0.0488341	+	0.150296i
$982$	9.78188e7	+	1.34636e8i	0.103297	+	0.142176i
$983$	−3.27232e8	+	1.06324e8i	−0.344505	+	0.111937i	−0.476159	−	0.879359i	$-0.657971\pi$
$983$	−3.27232e8	+	1.06324e8i	−0.344505	+	0.111937i	0.131654	+	0.991296i	$0.457971\pi$
$984$	−5.14825e7	+	1.67277e7i	−0.0540349	+	0.0175570i
$985$	−2.21501e9	−	7.19702e8i	−2.31776	−	0.753085i
$986$	7.74252e8			0.807703
$987$			3.19495e8i			0.332287i
$988$	−4.21222e8	−	1.36863e8i	−0.436757	−	0.141911i
$989$	−1.63651e8	−	1.18899e8i	−0.169172	−	0.122911i
$990$	9.09235e7	+	1.25145e8i	0.0937067	+	0.128976i
$991$		−	8.57756e7i		−	0.0881339i	−0.999029	−	0.0440669i	$-0.985969\pi$
$991$		−	8.57756e7i		−	0.0881339i	0.999029	−	0.0440669i	$-0.0140315\pi$
$992$	1.27538e8	−	1.16249e8i	0.130649	−	0.119084i
$993$	1.99748e9			2.04002
$994$	6.32251e8	−	4.59358e8i	0.643770	−	0.467726i
$995$	1.48744e9	−	2.04729e9i	1.50998	−	2.07831i
$996$	−2.60997e8	+	8.03265e8i	−0.264154	+	0.812982i
$997$	−2.94678e8			−0.297346			−0.148673	−	0.988886i	$-0.547500\pi$
$997$	−2.94678e8			−0.297346			−0.148673	+	0.988886i	$0.547500\pi$
$998$		−	1.48890e8i		−	0.149787i
$999$	4.55487e8	−	1.40184e9i	0.456856	−	1.40606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.15.1	✓	64
31.29	odd	10	inner	62.7.f.a.29.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.1	✓	64	1.1	even	1	trivial
62.7.f.a.29.1	yes	64	31.29	odd	10	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.57649 + 3.32502i) q^{2} +(-25.5799 + 35.2077i) q^{3} +(9.88854 - 30.4338i) q^{4} -242.487 q^{5} -246.181i q^{6} +(114.010 - 350.886i) q^{7} +(55.9381 + 172.160i) q^{8} +(-359.977 - 1107.90i) q^{9} +(1109.74 - 806.272i) q^{10} +(-92.0678 - 29.9146i) q^{11} +(818.556 + 1126.65i) q^{12} +(-1937.90 + 2667.29i) q^{13} +(644.937 + 1984.91i) q^{14} +(6202.78 - 8537.40i) q^{15} +(-828.433 - 601.892i) q^{16} +(-6475.21 + 2103.92i) q^{17} +(5331.21 + 3873.35i) q^{18} +(-3396.25 + 2467.52i) q^{19} +(-2397.84 + 7379.80i) q^{20} +(9437.53 + 12989.6i) q^{21} +(520.814 - 169.223i) q^{22} +(-2109.06 + 685.275i) q^{23} +(-7492.23 - 2434.37i) q^{24} +43174.9 q^{25} -18650.4i q^{26} +(18042.0 + 5862.20i) q^{27} +(-9551.41 - 6939.50i) q^{28} +(11816.2 + 16263.6i) q^{29} +59695.7i q^{30} +(22017.3 - 20068.4i) q^{31} +5792.62 q^{32} +(3408.31 - 2476.28i) q^{33} +(22638.2 - 31158.8i) q^{34} +(-27645.9 + 85085.2i) q^{35} -37277.2 q^{36} -77698.9i q^{37} +(7338.36 - 22585.1i) q^{38} +(-44337.9 - 136458. i) q^{39} +(-13564.2 - 41746.4i) q^{40} +(5559.12 - 4038.94i) q^{41} +(-86381.5 - 28067.1i) q^{42} +(53616.3 + 73796.5i) q^{43} +(-1820.83 + 2506.16i) q^{44} +(87289.8 + 268650. i) q^{45} +(7373.55 - 10148.8i) q^{46} +(16098.4 + 11696.2i) q^{47} +(42382.5 - 13770.9i) q^{48} +(-14942.8 - 10856.6i) q^{49} +(-197589. + 143557. i) q^{50} +(91560.8 - 281795. i) q^{51} +(62012.9 + 85353.4i) q^{52} +(-231467. + 75208.3i) q^{53} +(-102061. + 33161.6i) q^{54} +(22325.2 + 7253.90i) q^{55} +66785.9 q^{56} -182693. i q^{57} +(-108154. - 35141.2i) q^{58} +(138919. + 100930. i) q^{59} +(-198489. - 273197. i) q^{60} -233403. i q^{61} +(-34034.4 + 165051. i) q^{62} -429787. q^{63} +(-26509.9 + 19260.5i) q^{64} +(469916. - 646783. i) q^{65} +(-7364.42 + 22665.4i) q^{66} -311746. q^{67} +217870. i q^{68} +(29822.6 - 91784.4i) q^{69} +(-156389. - 481315. i) q^{70} +(-115712. - 356126. i) q^{71} +(170599. - 123947. i) q^{72} +(387864. + 126024. i) q^{73} +(258350. + 355588. i) q^{74} +(-1.10441e6 + 1.52009e6i) q^{75} +(41512.0 + 127761. i) q^{76} +(-20993.3 + 28894.7i) q^{77} +(656637. + 477075. i) q^{78} +(248693. - 80805.4i) q^{79} +(200884. + 145951. i) q^{80} +(19127.1 - 13896.7i) q^{81} +(-12011.7 + 36968.3i) q^{82} +(356485. + 490660. i) q^{83} +(488648. - 158771. i) q^{84} +(1.57015e6 - 510174. i) q^{85} +(-490749. - 159454. i) q^{86} -874862. q^{87} -17523.7i q^{88} +(162301. + 52734.7i) q^{89} +(-1.29275e6 - 939236. i) q^{90} +(714976. + 984080. i) q^{91} +70963.1i q^{92} +(143361. + 1.28853e6i) q^{93} -112564. q^{94} +(823545. - 598341. i) q^{95} +(-148175. + 203945. i) q^{96} +(50557.4 - 155600. i) q^{97} +104484. q^{98} +112770. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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