LMFDB - Embedded newform 76.7.g.a.7.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(7,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	76.7
Dual form			76.7.g.a.11.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.43934 - 6.65524i) q^{2} +(-40.1020 + 23.1529i) q^{3} +(-24.5845 + 59.0898i) q^{4} +(19.2234 + 33.2960i) q^{5} +(332.115 + 164.105i) q^{6} -622.494i q^{7} +(502.396 - 98.7039i) q^{8} +(707.614 - 1225.62i) q^{9} +O(q^{10})$	\(q+(-4.43934 - 6.65524i) q^{2} +(-40.1020 + 23.1529i) q^{3} +(-24.5845 + 59.0898i) q^{4} +(19.2234 + 33.2960i) q^{5} +(332.115 + 164.105i) q^{6} -622.494i q^{7} +(502.396 - 98.7039i) q^{8} +(707.614 - 1225.62i) q^{9} +(136.253 - 275.749i) q^{10} +2041.42i q^{11} +(-382.212 - 2938.82i) q^{12} +(1561.55 - 2704.68i) q^{13} +(-4142.85 + 2763.46i) q^{14} +(-1541.80 - 890.157i) q^{15} +(-2887.20 - 2905.39i) q^{16} +(1377.30 + 2385.54i) q^{17} +(-11298.2 + 731.618i) q^{18} +(-4625.25 + 5064.88i) q^{19} +(-2440.05 + 317.344i) q^{20} +(14412.6 + 24963.3i) q^{21} +(13586.2 - 9062.58i) q^{22} +(-7179.53 - 4145.10i) q^{23} +(-17861.8 + 15590.1i) q^{24} +(7073.42 - 12251.5i) q^{25} +(-24932.6 + 1614.52i) q^{26} +31776.4i q^{27} +(36783.1 + 15303.7i) q^{28} +(-5257.45 + 9106.16i) q^{29} +(920.353 + 14212.7i) q^{30} -2120.77i q^{31} +(-6518.76 + 32113.0i) q^{32} +(-47264.9 - 81865.2i) q^{33} +(9762.10 - 19756.5i) q^{34} +(20726.6 - 11966.5i) q^{35} +(55025.5 + 71944.1i) q^{36} -5854.48 q^{37} +(54241.0 + 8297.42i) q^{38} +144618. i q^{39} +(12944.2 + 14830.3i) q^{40} +(36928.6 + 63962.3i) q^{41} +(102154. - 206740. i) q^{42} +(-85760.4 + 49513.8i) q^{43} +(-120627. - 50187.4i) q^{44} +54411.1 q^{45} +(4285.71 + 66183.0i) q^{46} +(-59854.6 - 34557.1i) q^{47} +(183051. + 49664.6i) q^{48} -269850. q^{49} +(-112938. + 7313.36i) q^{50} +(-110465. - 63776.8i) q^{51} +(121429. + 158765. i) q^{52} +(-52787.9 + 91431.3i) q^{53} +(211480. - 141066. i) q^{54} +(-67971.2 + 39243.2i) q^{55} +(-61442.6 - 312739. i) q^{56} +(68215.1 - 310200. i) q^{57} +(83943.3 - 5435.79i) q^{58} +(83908.5 - 48444.6i) q^{59} +(90503.5 - 69220.4i) q^{60} +(-204077. + 353472. i) q^{61} +(-14114.2 + 9414.80i) q^{62} +(-762944. - 440486. i) q^{63} +(242659. - 99176.8i) q^{64} +120073. q^{65} +(-335008. + 677987. i) q^{66} +(230256. + 132938. i) q^{67} +(-174821. + 22736.6i) q^{68} +383885. q^{69} +(-171652. - 84817.0i) q^{70} +(168474. - 97268.7i) q^{71} +(234529. - 685593. i) q^{72} +(-203411. - 352318. i) q^{73} +(25990.0 + 38963.0i) q^{74} +655081. i q^{75} +(-185573. - 397822. i) q^{76} +1.27078e6 q^{77} +(962466. - 642007. i) q^{78} +(16986.8 - 9807.34i) q^{79} +(41235.6 - 151984. i) q^{80} +(-219865. - 380817. i) q^{81} +(261746. - 529720. i) q^{82} +221516. i q^{83} +(-1.82940e6 + 237925. i) q^{84} +(-52952.7 + 91716.8i) q^{85} +(710246. + 350948. i) q^{86} -486901. i q^{87} +(201497. + 1.02560e6i) q^{88} +(-119079. + 206251. i) q^{89} +(-241550. - 362119. i) q^{90} +(-1.68365e6 - 972056. i) q^{91} +(421438. - 322332. i) q^{92} +(49101.9 + 85047.0i) q^{93} +(35729.3 + 551758. i) q^{94} +(-257553. - 56637.7i) q^{95} +(-482095. - 1.43873e6i) q^{96} +(360293. + 624046. i) q^{97} +(1.19796e6 + 1.79592e6i) q^{98} +(2.50202e6 + 1.44454e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) $ 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−4.43934	−	6.65524i	−0.554918	−	0.831905i
$2$	−4.43934	−	6.65524i	−0.554918	−	0.831905i
$3$	−40.1020	+	23.1529i	−1.48526	+	0.857515i	−0.999859	−	0.0167767i	$-0.994660\pi$
$3$	−40.1020	+	23.1529i	−1.48526	+	0.857515i	−0.485401	+	0.874292i	$0.661326\pi$
$4$	−24.5845	+	59.0898i	−0.384133	+	0.923278i
$5$	19.2234	+	33.2960i	0.153788	+	0.266368i	0.932617	−	0.360868i	$-0.117520\pi$
$5$	19.2234	+	33.2960i	0.153788	+	0.266368i	−0.778829	+	0.627236i	$0.784186\pi$
$6$	332.115	+	164.105i	1.53757	+	0.759745i
$7$		−	622.494i		−	1.81485i	−0.420212	−	0.907426i	$-0.638044\pi$
$7$		−	622.494i		−	1.81485i	0.420212	−	0.907426i	$-0.361956\pi$
$8$	502.396	−	98.7039i	0.981242	−	0.192781i
$9$	707.614	−	1225.62i	0.970665	−	1.68124i
$10$	136.253	−	275.749i	0.136253	−	0.275749i
$11$			2041.42i			1.53375i	0.641795	+	0.766876i	$0.278190\pi$
$11$			2041.42i			1.53375i	−0.641795	+	0.766876i	$0.721810\pi$
$12$	−382.212	−	2938.82i	−0.221188	−	1.70071i
$13$	1561.55	−	2704.68i	0.710765	−	1.23108i	−0.253806	−	0.967255i	$-0.581682\pi$
$13$	1561.55	−	2704.68i	0.710765	−	1.23108i	0.964571	−	0.263825i	$-0.0849842\pi$
$14$	−4142.85	+	2763.46i	−1.50979	+	1.00709i
$15$	−1541.80	−	890.157i	−0.456829	−	0.263750i
$16$	−2887.20	−	2905.39i	−0.704884	−	0.709323i
$17$	1377.30	+	2385.54i	0.280337	+	0.485558i	0.971468	−	0.237172i	$-0.0762205\pi$
$17$	1377.30	+	2385.54i	0.280337	+	0.485558i	−0.691131	+	0.722730i	$0.742887\pi$
$18$	−11298.2	+	731.618i	−1.93727	+	0.125449i
$19$	−4625.25	+	5064.88i	−0.674332	+	0.738428i
$19$	−4625.25	+	5064.88i	−0.674332	+	0.738428i
$20$	−2440.05	+	317.344i	−0.305006	+	0.0396680i
$21$	14412.6	+	24963.3i	1.55626	+	2.69553i
$22$	13586.2	−	9062.58i	1.27594	−	0.851106i
$23$	−7179.53	−	4145.10i	−0.590082	−	0.340684i	0.175048	−	0.984560i	$-0.443992\pi$
$23$	−7179.53	−	4145.10i	−0.590082	−	0.340684i	−0.765130	+	0.643876i	$0.777325\pi$
$24$	−17861.8	+	15590.1i	−1.29209	+	1.12776i
$25$	7073.42	−	12251.5i	0.452699	−	0.784097i
$26$	−24932.6	+	1614.52i	−1.41856	+	0.0918594i
$27$			31776.4i			1.61441i
$28$	36783.1	+	15303.7i	1.67561	+	0.697144i
$29$	−5257.45	+	9106.16i	−0.215566	+	0.373372i	−0.953448	−	0.301559i	$-0.902493\pi$
$29$	−5257.45	+	9106.16i	−0.215566	+	0.373372i	0.737881	+	0.674930i	$0.235826\pi$
$30$	920.353	+	14212.7i	0.0340872	+	0.526398i
$31$		−	2120.77i		−	0.0711881i	−0.999366	−	0.0355941i	$-0.988668\pi$
$31$		−	2120.77i		−	0.0711881i	0.999366	−	0.0355941i	$-0.0113323\pi$
$32$	−6518.76	+	32113.0i	−0.198937	+	0.980012i
$33$	−47264.9	−	81865.2i	−1.31522	−	2.27802i
$34$	9762.10	−	19756.5i	0.248374	−	0.502658i
$35$	20726.6	−	11966.5i	0.483418	−	0.279102i
$36$	55025.5	+	71944.1i	1.17939	+	1.54201i
$37$	−5854.48			−0.115580			−0.0577901	−	0.998329i	$-0.518405\pi$
$37$	−5854.48			−0.115580			−0.0577901	+	0.998329i	$0.518405\pi$
$38$	54241.0	+	8297.42i	0.988501	+	0.151214i
$39$			144618.i			2.43797i
$40$	12944.2	+	14830.3i	0.202253	+	0.231724i
$41$	36928.6	+	63962.3i	0.535811	+	0.928052i	0.999124	+	0.0418573i	$0.0133275\pi$
$41$	36928.6	+	63962.3i	0.535811	+	0.928052i	−0.463312	+	0.886195i	$0.653339\pi$
$42$	102154.	−	206740.i	1.37883	−	2.79046i
$43$	−85760.4	+	49513.8i	−1.07865	+	0.622760i	−0.930532	−	0.366210i	$-0.880655\pi$
$43$	−85760.4	+	49513.8i	−1.07865	+	0.622760i	−0.148119	+	0.988969i	$0.547322\pi$
$44$	−120627.	−	50187.4i	−1.41608	−	0.589165i
$45$	54411.1			0.597104
$46$	4285.71	+	66183.0i	0.0440301	+	0.679944i
$47$	−59854.6	−	34557.1i	−0.576506	−	0.332846i	0.183237	−	0.983069i	$-0.441342\pi$
$47$	−59854.6	−	34557.1i	−0.576506	−	0.332846i	−0.759744	+	0.650223i	$0.774676\pi$
$48$	183051.	+	49664.6i	1.65519	+	0.449080i
$49$	−269850.			−2.29369
$50$	−112938.	+	7313.36i	−0.903505	+	0.0585069i
$51$	−110465.	−	63776.8i	−0.832746	−	0.480786i
$52$	121429.	+	158765.i	0.863601	+	1.12913i
$53$	−52787.9	+	91431.3i	−0.354574	+	0.614140i	−0.987045	−	0.160444i	$-0.948707\pi$
$53$	−52787.9	+	91431.3i	−0.354574	+	0.614140i	0.632471	+	0.774584i	$0.282041\pi$
$54$	211480.	−	141066.i	1.34303	−	0.895863i
$55$	−67971.2	+	39243.2i	−0.408542	+	0.235872i
$56$	−61442.6	−	312739.i	−0.349869	−	1.78081i
$57$	68215.1	−	310200.i	0.368346	−	1.67501i
$58$	83943.3	−	5435.79i	0.430231	−	0.0278598i
$59$	83908.5	−	48444.6i	0.408554	−	0.235879i	−0.281614	−	0.959528i	$-0.590870\pi$
$59$	83908.5	−	48444.6i	0.408554	−	0.235879i	0.690168	+	0.723649i	$0.257536\pi$
$60$	90503.5	−	69220.4i	0.418998	−	0.320465i
$61$	−204077.	+	353472.i	−0.899093	+	1.55727i	−0.0704367	+	0.997516i	$0.522439\pi$
$61$	−204077.	+	353472.i	−0.899093	+	1.55727i	−0.828656	+	0.559758i	$0.810894\pi$
$62$	−14114.2	+	9414.80i	−0.0592218	+	0.0395036i
$63$	−762944.	−	440486.i	−3.05120	−	1.76161i
$64$	242659.	−	99176.8i	0.925671	−	0.378330i
$65$	120073.			0.437227
$66$	−335008.	+	677987.i	−1.16526	+	2.35825i
$67$	230256.	+	132938.i	0.765572	+	0.442003i	0.831293	−	0.555835i	$-0.187601\pi$
$67$	230256.	+	132938.i	0.765572	+	0.442003i	−0.0657205	+	0.997838i	$0.520935\pi$
$68$	−174821.	+	22736.6i	−0.555991	+	0.0723102i
$69$	383885.			1.16857
$70$	−171652.	−	84817.0i	−0.500443	−	0.247280i
$71$	168474.	−	97268.7i	0.470716	−	0.271768i	−0.245824	−	0.969315i	$-0.579058\pi$
$71$	168474.	−	97268.7i	0.470716	−	0.271768i	0.716539	+	0.697547i	$0.245725\pi$
$72$	234529.	−	685593.i	0.628345	−	1.83683i
$73$	−203411.	−	352318.i	−0.522885	−	0.905663i	−0.999645	−	0.0266295i	$-0.991523\pi$
$73$	−203411.	−	352318.i	−0.522885	−	0.905663i	0.476761	−	0.879033i	$-0.341811\pi$
$74$	25990.0	+	38963.0i	0.0641375	+	0.0961518i
$75$			655081.i			1.55278i
$76$	−185573.	−	397822.i	−0.422741	−	0.906251i
$77$	1.27078e6			2.78353
$78$	962466.	−	642007.i	2.02816	−	1.35287i
$79$	16986.8	−	9807.34i	0.0344533	−	0.0198916i	−0.482674	−	0.875800i	$-0.660335\pi$
$79$	16986.8	−	9807.34i	0.0344533	−	0.0198916i	0.517128	+	0.855908i	$0.327001\pi$
$80$	41235.6	−	151984.i	0.0805384	−	0.296843i
$81$	−219865.	−	380817.i	−0.413715	−	0.716575i
$82$	261746.	−	529720.i	0.474721	−	0.960737i
$83$			221516.i			0.387411i	0.981060	+	0.193705i	$0.0620506\pi$
$83$			221516.i			0.387411i	−0.981060	+	0.193705i	$0.937949\pi$
$84$	−1.82940e6	+	237925.i	−3.08653	+	0.401423i
$85$	−52952.7	+	91716.8i	−0.0862246	+	0.149345i
$86$	710246.	+	350948.i	1.11664	+	0.551756i
$87$		−	486901.i		−	0.739405i
$88$	201497.	+	1.02560e6i	0.295678	+	1.50498i
$89$	−119079.	+	206251.i	−0.168914	+	0.292568i	−0.938038	−	0.346531i	$-0.887359\pi$
$89$	−119079.	+	206251.i	−0.168914	+	0.292568i	0.769124	+	0.639099i	$0.220693\pi$
$90$	−241550.	−	362119.i	−0.331344	−	0.496734i
$91$	−1.68365e6	−	972056.i	−2.23423	−	1.28993i
$92$	421438.	−	322332.i	0.541216	−	0.413942i
$93$	49101.9	+	85047.0i	0.0610449	+	0.105733i
$94$	35729.3	+	551758.i	0.0430171	+	0.664301i
$95$	−257553.	−	56637.7i	−0.300397	−	0.0660595i
$96$	−482095.	−	1.43873e6i	−0.544903	−	1.62616i
$97$	360293.	+	624046.i	0.394767	+	0.683757i	0.993071	−	0.117512i	$-0.0374919\pi$
$97$	360293.	+	624046.i	0.394767	+	0.683757i	−0.598304	+	0.801269i	$0.704159\pi$
$98$	1.19796e6	+	1.79592e6i	1.27281	+	1.90813i
$99$	2.50202e6	+	1.44454e6i	2.57861	+	1.48876i
$100$	550043.	+	719164.i	0.550043	+	0.719164i
$101$	−257731.	+	446402.i	−0.250151	+	0.433274i	−0.963567	−	0.267467i	$-0.913814\pi$
$101$	−257731.	+	446402.i	−0.250151	+	0.433274i	0.713416	+	0.700740i	$0.247147\pi$
$102$	65940.2	+	1.01830e6i	0.0621369	+	0.959563i
$103$			1.34405e6i			1.23000i	0.788527	+	0.615000i	$0.210844\pi$
$103$			1.34405e6i			1.23000i	−0.788527	+	0.615000i	$0.789156\pi$
$104$	517553.	−	1.51295e6i	0.460103	−	1.34501i
$105$	−554118.	+	959760.i	−0.478668	+	0.829077i
$106$	842841.	−	54578.6i	0.707666	−	0.0458252i
$107$			108437.i			0.0885171i	0.999020	+	0.0442585i	$0.0140925\pi$
$107$			108437.i			0.0885171i	−0.999020	+	0.0442585i	$0.985907\pi$
$108$	−1.87766e6	−	781207.i	−1.49055	−	0.620147i
$109$	101185.	+	175258.i	0.0781334	+	0.135331i	0.902445	−	0.430806i	$-0.141771\pi$
$109$	101185.	+	175258.i	0.0781334	+	0.135331i	−0.824311	+	0.566137i	$0.808437\pi$
$110$	562920.	+	278151.i	0.422930	+	0.208979i
$111$	234777.	−	135548.i	0.171667	−	0.0991118i
$112$	−1.80859e6	+	1.79727e6i	−1.28732	+	1.27926i
$113$	−2.35254e6			−1.63043			−0.815213	−	0.579162i	$-0.803380\pi$
$113$	−2.35254e6			−1.63043			−0.815213	+	0.579162i	$0.803380\pi$
$114$	−2.36728e6	+	923095.i	−1.59785	+	0.623062i
$115$		−	318733.i		−	0.209572i
$116$	−408829.	−	534532.i	−0.261920	−	0.342452i
$117$	−2.20995e6	−	3.82775e6i	−1.37983	−	2.38993i
$118$	−694909.	−	343369.i	−0.422943	−	0.208985i
$119$	1.48499e6	−	857358.i	0.881215	−	0.508770i
$120$	−862455.	−	295030.i	−0.499106	−	0.170735i
$121$	−2.39585e6			−1.35240
$122$	3.25841e6	−	211000.i	1.79443	−	0.116199i
$123$	−2.96183e6	−	1.71001e6i	−1.59164	−	0.918933i
$124$	125316.	+	52138.0i	0.0657264	+	0.0273457i
$125$	1.14463e6			0.586053
$126$	455428.	+	7.03305e6i	0.227671	+	3.51586i
$127$	2.03652e6	+	1.17579e6i	0.994209	+	0.574007i	0.906530	−	0.422142i	$-0.138722\pi$
$127$	2.03652e6	+	1.17579e6i	0.994209	+	0.574007i	0.0876795	+	0.996149i	$0.472055\pi$
$128$	−1.73729e6	−	1.17468e6i	−0.828406	−	0.560129i
$129$	2.29278e6	−	3.97120e6i	1.06805	−	1.84992i
$130$	−533047.	−	799118.i	−0.242625	−	0.363731i
$131$	−737718.	+	425922.i	−0.328153	+	0.189459i	−0.655021	−	0.755611i	$-0.727340\pi$
$131$	−737718.	+	425922.i	−0.328153	+	0.189459i	0.326868	+	0.945070i	$0.394007\pi$
$132$	5.99938e6	−	780258.i	2.60846	−	0.339247i
$133$	3.15286e6	+	2.87919e6i	1.34014	+	1.22381i
$134$	−137448.	−	2.12257e6i	−0.0571246	−	0.882159i
$135$	−1.05803e6	+	610852.i	−0.430026	+	0.248276i
$136$	927410.	+	1.06254e6i	0.368685	+	0.422406i
$137$	−2.11956e6	+	3.67119e6i	−0.824298	+	1.42773i	0.0781559	+	0.996941i	$0.475097\pi$
$137$	−2.11956e6	+	3.67119e6i	−0.824298	+	1.42773i	−0.902454	+	0.430786i	$0.858237\pi$
$138$	−1.70420e6	−	2.55485e6i	−0.648458	−	0.972137i
$139$	−3.79151e6	−	2.18903e6i	−1.41178	−	0.815093i	−0.416226	−	0.909261i	$-0.636648\pi$
$139$	−3.79151e6	−	2.18903e6i	−1.41178	−	0.815093i	−0.995556	+	0.0941679i	$0.969981\pi$
$140$	197545.	+	1.51892e6i	0.0719916	+	0.553541i
$141$	3.20039e6			1.14168
$142$	−1.39526e6	−	689428.i	−0.487293	−	0.240782i
$143$	5.52141e6	+	3.18779e6i	1.88817	+	1.09014i
$144$	−5.60394e6	+	1.48273e6i	−1.87675	+	0.496565i
$145$	−404265.			−0.132606
$146$	−1.44175e6	+	2.91781e6i	−0.463268	+	0.937559i
$147$	1.08215e7	−	6.24782e6i	3.40672	−	1.96687i
$148$	143930.	−	345940.i	0.0443981	−	0.106713i
$149$	992528.	+	1.71911e6i	0.300043	+	0.519690i	0.976145	−	0.217118i	$-0.0696656\pi$
$149$	992528.	+	1.71911e6i	0.300043	+	0.519690i	−0.676102	+	0.736808i	$0.736332\pi$
$150$	4.35972e6	−	2.90813e6i	1.29177	−	0.861667i
$151$			3.85427e6i			1.11947i	0.828673	+	0.559733i	$0.189096\pi$
$151$			3.85427e6i			1.11947i	−0.828673	+	0.559733i	$0.810904\pi$
$152$	−1.82378e6	+	3.00110e6i	−0.519328	+	0.854575i
$153$	3.89838e6			1.08845
$154$	−5.64140e6	−	8.45732e6i	−1.54463	−	2.31564i
$155$	70613.0	−	40768.4i	0.0189622	−	0.0109478i
$156$	−8.54543e6	−	3.55535e6i	−2.25092	−	0.936503i
$157$	565252.	+	979045.i	0.146064	+	0.252990i	0.929769	−	0.368142i	$-0.120006\pi$
$157$	565252.	+	979045.i	0.146064	+	0.252990i	−0.783705	+	0.621133i	$0.786673\pi$
$158$	−140681.	−	69513.2i	−0.0356667	−	0.0176237i
$159$		−	4.88877e6i		−	1.21621i
$160$	−1.19455e6	+	400275.i	−0.291638	+	0.0977233i
$161$	−2.58030e6	+	4.46922e6i	−0.618291	+	1.07091i
$162$	−1.55838e6	+	3.15383e6i	−0.366545	+	0.741812i
$163$			226081.i			0.0522037i	0.999659	+	0.0261019i	$0.00830942\pi$
$163$			226081.i			0.0522037i	−0.999659	+	0.0261019i	$0.991691\pi$
$164$	−4.68739e6	+	609625.i	−1.06267	+	0.138207i
$165$	1.81719e6	−	3.14746e6i	0.404528	−	0.700662i
$166$	1.47425e6	−	983387.i	0.322289	−	0.214981i
$167$	2.81687e6	+	1.62632e6i	0.604807	+	0.349185i	0.770930	−	0.636919i	$-0.219792\pi$
$167$	2.81687e6	+	1.62632e6i	0.604807	+	0.349185i	−0.166123	+	0.986105i	$0.553125\pi$
$168$	9.70478e6	+	1.11189e7i	2.04672	+	2.34495i
$169$	−2.46347e6	−	4.26686e6i	−0.510372	−	0.883991i
$170$	845472.	−	54749.0i	0.172089	−	0.0111437i
$171$	2.93474e6	+	9.25279e6i	0.586924	+	1.85048i
$172$	−817382.	−	6.28483e6i	−0.160635	−	1.23512i
$173$	−2.46296e6	−	4.26597e6i	−0.475685	−	0.823910i	0.523927	−	0.851763i	$-0.324466\pi$
$173$	−2.46296e6	−	4.26597e6i	−0.475685	−	0.823910i	−0.999612	+	0.0278529i	$0.991133\pi$
$174$	−3.24044e6	+	2.16152e6i	−0.615115	+	0.410309i
$175$	−7.62650e6	−	4.40316e6i	−1.42302	−	0.821581i
$176$	5.93112e6	−	5.89401e6i	1.08793	−	1.08112i
$177$	−2.24327e6	+	3.88545e6i	−0.404539	+	0.700683i
$178$	1.90129e6	−	123119.i	0.337123	−	0.0218305i
$179$		−	5.39551e6i		−	0.940748i	−0.882467	−	0.470374i	$-0.844119\pi$
$179$		−	5.39551e6i		−	0.940748i	0.882467	−	0.470374i	$-0.155881\pi$
$180$	−1.33767e6	+	3.21514e6i	−0.229367	+	0.551293i
$181$	774472.	−	1.34142e6i	0.130608	−	0.226220i	−0.793303	−	0.608827i	$-0.791640\pi$
$181$	774472.	−	1.34142e6i	0.130608	−	0.226220i	0.923911	+	0.382607i	$0.124974\pi$
$182$	1.00503e6	+	1.55204e7i	0.166711	+	2.57447i
$183$		−	1.88999e7i		−	3.08394i
$184$	−4.01610e6	−	1.37384e6i	−0.644691	−	0.220537i
$185$	−112543.	−	194931.i	−0.0177748	−	0.0307868i
$186$	348028.	−	704338.i	0.0540848	−	0.109457i
$187$	−4.86991e6	+	2.81164e6i	−0.744725	+	0.429967i
$188$	3.51347e6	−	2.68723e6i	0.528765	−	0.404419i
$189$	1.97806e7			2.92991
$190$	766429.	+	1.96551e6i	0.111741	+	0.286560i
$191$			2.76307e6i			0.396544i	0.980147	+	0.198272i	$0.0635329\pi$
$191$			2.76307e6i			0.396544i	−0.980147	+	0.198272i	$0.936467\pi$
$192$	−7.43489e6	+	9.59545e6i	−1.05044	+	1.35569i
$193$	1.39004e6	+	2.40762e6i	0.193355	+	0.334901i	0.946360	−	0.323114i	$-0.104730\pi$
$193$	1.39004e6	+	2.40762e6i	0.193355	+	0.334901i	−0.753005	+	0.658015i	$0.771396\pi$
$194$	2.55371e6	−	5.16819e6i	0.349758	−	0.707838i
$195$	−4.81519e6	+	2.78005e6i	−0.649396	+	0.374929i
$196$	6.63413e6	−	1.59454e7i	0.881081	−	2.11771i
$197$	−6.16417e6			−0.806261			−0.403131	−	0.915142i	$-0.632078\pi$
$197$	−6.16417e6			−0.806261			−0.403131	+	0.915142i	$0.632078\pi$
$198$	−1.49354e6	−	2.30644e7i	−0.192408	−	2.97129i
$199$	−3.02115e6	−	1.74426e6i	−0.383366	−	0.221336i	0.295916	−	0.955214i	$-0.404375\pi$
$199$	−3.02115e6	−	1.74426e6i	−0.383366	−	0.221336i	−0.679282	+	0.733878i	$0.737709\pi$
$200$	2.34438e6	−	6.85329e6i	0.293048	−	0.856661i
$201$	−1.23116e7			−1.51610
$202$	4.11507e6	−	266473.i	0.499256	−	0.0323295i
$203$	5.66853e6	+	3.27273e6i	0.677614	+	0.391221i
$204$	6.48427e6	−	4.95941e6i	0.763784	−	0.584170i
$205$	−1.41979e6	+	2.45915e6i	−0.164802	+	0.285446i
$206$	8.94501e6	−	5.96672e6i	1.02324	−	0.682549i
$207$	−1.01607e7	+	5.86627e6i	−1.14554	+	0.661380i
$208$	−1.23667e7	+	3.27207e6i	−1.37424	+	0.363607i
$209$	−1.03396e7	−	9.44209e6i	−1.13257	−	1.03426i
$210$	8.84735e6	−	572915.i	0.955335	−	0.0618631i
$211$	1.91651e6	−	1.10650e6i	0.204016	−	0.117789i	−0.394511	−	0.918891i	$-0.629086\pi$
$211$	1.91651e6	−	1.10650e6i	0.204016	−	0.117789i	0.598527	+	0.801102i	$0.295753\pi$
$212$	−4.10489e6	−	5.36702e6i	−0.430818	−	0.563282i
$213$	−4.50411e6	+	7.80134e6i	−0.466090	+	0.807291i
$214$	721676.	−	481390.i	0.0736378	−	0.0491197i
$215$	−3.29722e6	−	1.90365e6i	−0.331766	−	0.191545i
$216$	3.13645e6	+	1.59643e7i	0.311227	+	1.58412i
$217$	−1.32016e6			−0.129196
$218$	717187.	−	1.45144e6i	0.0692250	−	0.140097i
$219$	1.63144e7	+	9.41911e6i	1.55324	+	0.896763i
$220$	−647834.	−	4.98118e6i	−0.0608409	−	0.467804i
$221$	8.60286e6			0.797014
$222$	−1.94436e6	−	960750.i	−0.177712	−	0.0878115i
$223$	8.52291e6	−	4.92070e6i	0.768552	−	0.443724i	−0.0638060	−	0.997962i	$-0.520324\pi$
$223$	8.52291e6	−	4.92070e6i	0.768552	−	0.443724i	0.832358	+	0.554239i	$0.186991\pi$
$224$	1.99902e7	+	4.05789e6i	1.77858	+	0.361041i
$225$	−1.00105e7	−	1.73387e7i	−0.878837	−	1.52219i
$226$	1.04437e7	+	1.56567e7i	0.904752	+	1.35636i
$227$		−	7.28260e6i		−	0.622600i	−0.950312	−	0.311300i	$-0.899236\pi$
$227$		−	7.28260e6i		−	0.622600i	0.950312	−	0.311300i	$-0.100764\pi$
$228$	1.66526e7	+	1.16569e7i	1.40500	+	0.983511i
$229$	−2.58143e6			−0.214958			−0.107479	−	0.994207i	$-0.534278\pi$
$229$	−2.58143e6			−0.214958			−0.107479	+	0.994207i	$0.534278\pi$
$230$	−2.12124e6	+	1.41496e6i	−0.174344	+	0.116295i
$231$	−5.09606e7	+	2.94221e7i	−4.13427	+	2.38692i
$232$	−1.74250e6	+	5.09383e6i	−0.139544	+	0.407925i
$233$	8.38743e6	+	1.45274e7i	0.663072	+	1.14848i	0.979804	+	0.199960i	$0.0640812\pi$
$233$	8.38743e6	+	1.45274e7i	0.663072	+	1.14848i	−0.316732	+	0.948515i	$0.602585\pi$
$234$	−1.56639e7	+	3.17004e7i	−1.22251	+	2.47410i
$235$		−	2.65722e6i		−	0.204750i
$236$	799732.	+	6.14912e6i	0.0608427	+	0.467818i
$237$	−454137.	+	786589.i	−0.0341147	+	0.0590884i
$238$	−1.22983e7	−	6.07685e6i	−0.912250	−	0.450762i
$239$			2.00374e7i			1.46773i	0.679293	+	0.733867i	$0.262287\pi$
$239$			2.00374e7i			1.46773i	−0.679293	+	0.733867i	$0.737713\pi$
$240$	1.86524e6	+	7.04958e6i	0.134927	+	0.509952i
$241$	−8.17083e6	+	1.41523e7i	−0.583734	+	1.01106i	0.411298	+	0.911501i	$0.365076\pi$
$241$	−8.17083e6	+	1.41523e7i	−0.583734	+	1.01106i	−0.995032	+	0.0995564i	$0.968258\pi$
$242$	1.06360e7	+	1.59450e7i	0.750468	+	1.12507i
$243$	−2.42741e6	−	1.40147e6i	−0.169170	−	0.0976706i
$244$	−1.58694e7	−	2.07488e7i	−1.09243	−	1.42831i
$245$	−5.18745e6	−	8.98493e6i	−0.352741	−	0.610965i
$246$	1.76802e6	+	2.73030e7i	0.118763	+	1.83402i
$247$	6.47634e6	+	2.04189e7i	0.429772	+	1.35501i
$248$	−209328.	−	1.06546e6i	−0.0137237	−	0.0698528i
$249$	−5.12875e6	−	8.88325e6i	−0.332211	−	0.575406i
$250$	−5.08142e6	−	7.61782e6i	−0.325211	−	0.487540i
$251$	−9.45112e6	−	5.45661e6i	−0.597671	−	0.345066i	0.170454	−	0.985366i	$-0.445477\pi$
$251$	−9.45112e6	−	5.45661e6i	−0.597671	−	0.345066i	−0.768125	+	0.640300i	$0.778810\pi$
$252$	4.47848e7	−	3.42531e7i	2.79853	−	2.14041i
$253$	8.46191e6	−	1.46565e7i	0.522525	−	0.905040i
$254$	−1.21567e6	−	1.87733e7i	−0.0741848	−	1.14561i
$255$		−	4.90404e6i		−	0.295756i
$256$	−105315.	+	1.67769e7i	−0.00627727	+	0.999980i
$257$	−3.70212e6	+	6.41225e6i	−0.218097	+	0.377756i	−0.954226	−	0.299086i	$-0.903318\pi$
$257$	−3.70212e6	+	6.41225e6i	−0.218097	+	0.377756i	0.736129	+	0.676841i	$0.236652\pi$
$258$	−3.66077e7	+	2.37055e6i	−2.13164	+	0.138035i
$259$			3.64438e6i			0.209761i
$260$	−2.95195e6	+	7.09511e6i	−0.167953	+	0.403682i
$261$	7.44049e6	+	1.28873e7i	0.418485	+	0.724837i
$262$	6.10959e6	+	3.01888e6i	0.339710	+	0.167858i
$263$	97961.0	−	56557.8i	0.00538501	−	0.00310903i	−0.497305	−	0.867576i	$-0.665677\pi$
$263$	97961.0	−	56557.8i	0.00538501	−	0.00310903i	0.502690	+	0.864467i	$0.332344\pi$
$264$	−3.18261e7	−	3.64635e7i	−1.72970	−	1.98174i
$265$	−4.05906e6			−0.218116
$266$	5.16509e6	−	3.37647e7i	0.274431	−	1.79398i
$267$		−	1.10281e7i		−	0.579386i
$268$	−1.35160e7	+	1.03375e7i	−0.702173	+	0.537048i
$269$	1.36448e7	+	2.36335e7i	0.700989	+	1.21415i	0.968120	+	0.250489i	$0.0805912\pi$
$269$	1.36448e7	+	2.36335e7i	0.700989	+	1.21415i	−0.267130	+	0.963660i	$0.586075\pi$
$270$	8.76230e6	+	4.32964e6i	0.445171	+	0.219969i
$271$	−877593.	+	506679.i	−0.0440946	+	0.0254580i	−0.521885	−	0.853016i	$-0.674771\pi$
$271$	−877593.	+	506679.i	−0.0440946	+	0.0254580i	0.477791	+	0.878474i	$0.341438\pi$
$272$	2.95440e6	−	1.08891e7i	0.146812	−	0.541111i
$273$	9.00237e7			4.42455
$274$	3.38421e7	−	2.19146e6i	1.64515	−	0.106533i
$275$	2.50106e7	+	1.44398e7i	1.20261	+	0.694328i
$276$	−9.43762e6	+	2.26837e7i	−0.448885	+	1.07891i
$277$	−2.69854e7			−1.26967			−0.634834	−	0.772648i	$-0.718932\pi$
$277$	−2.69854e7			−1.26967			−0.634834	+	0.772648i	$0.718932\pi$
$278$	2.26329e6	+	3.49513e7i	0.105343	+	1.62678i
$279$	−2.59926e6	−	1.50068e6i	−0.119684	−	0.0690998i
$280$	9.23180e6	−	8.05770e6i	0.420545	−	0.367060i
$281$	1.79936e7	−	3.11658e7i	0.810958	−	1.40462i	−0.101237	−	0.994862i	$-0.532280\pi$
$281$	1.79936e7	−	3.11658e7i	0.810958	−	1.40462i	0.912195	−	0.409757i	$-0.134387\pi$
$282$	−1.42076e7	−	2.12994e7i	−0.633540	−	0.949772i
$283$	−2.05397e7	+	1.18586e7i	−0.906224	+	0.523209i	−0.879214	−	0.476427i	$-0.841932\pi$
$283$	−2.05397e7	+	1.18586e7i	−0.906224	+	0.523209i	−0.0270096	+	0.999635i	$0.508598\pi$
$284$	1.60573e6	+	1.23464e7i	0.0700998	+	0.538996i
$285$	1.16397e7	−	3.69182e6i	0.502815	−	0.159480i
$286$	−3.29592e6	−	5.08980e7i	−0.140890	−	2.17572i
$287$	3.98162e7	−	2.29879e7i	1.68428	−	0.972418i
$288$	3.47458e7	+	3.07132e7i	1.45454	+	1.28572i
$289$	8.27490e6	−	1.43325e7i	0.342822	−	0.593786i
$290$	1.79467e6	+	2.69048e6i	0.0735852	+	0.110315i
$291$	−2.88970e7	−	1.66837e7i	−1.17266	−	0.677038i
$292$	2.58192e7	−	3.35794e6i	1.03704	−	0.134873i
$293$	−1.61290e7			−0.641215			−0.320607	−	0.947212i	$-0.603887\pi$
$293$	−1.61290e7			−0.641215			−0.320607	+	0.947212i	$0.603887\pi$
$294$	−8.96212e7	−	4.42838e7i	−3.52670	−	1.74262i
$295$	3.22602e6	+	1.86254e6i	0.125661	+	0.0725505i
$296$	−2.94127e6	+	577860.i	−0.113412	+	0.0222817i
$297$	−6.48691e7			−2.47610
$298$	7.03491e6	−	1.42372e7i	0.265834	−	0.537993i
$299$	−2.24224e7	+	1.29456e7i	−0.838819	+	0.484292i
$300$	−3.87086e7	−	1.61048e7i	−1.43365	−	0.596475i
$301$	3.08220e7	+	5.33853e7i	1.13022	+	1.95759i
$302$	2.56511e7	−	1.71104e7i	0.931290	−	0.621211i
$303$		−	2.38688e7i		−	0.858032i
$304$	2.80695e7	−	1.18521e6i	0.999110	−	0.0421867i
$305$	−1.56922e7			−0.553077
$306$	−1.73062e7	−	2.59446e7i	−0.604001	−	0.905489i
$307$	3.63804e7	−	2.10042e7i	1.25734	−	0.725924i	0.284782	−	0.958592i	$-0.408079\pi$
$307$	3.63804e7	−	2.10042e7i	1.25734	−	0.725924i	0.972556	+	0.232668i	$0.0747456\pi$
$308$	−3.12414e7	+	7.50898e7i	−1.06925	+	2.56998i
$309$	−3.11188e7	−	5.38993e7i	−1.05474	−	1.82687i
$310$	−584799.	−	288962.i	−0.0196300	−	0.00969962i
$311$		−	2.30838e7i		−	0.767406i	−0.923456	−	0.383703i	$-0.874649\pi$
$311$		−	2.30838e7i		−	0.767406i	0.923456	−	0.383703i	$-0.125351\pi$
$312$	1.42743e7	+	7.26553e7i	0.469993	+	2.39223i
$313$	−5.56461e6	+	9.63818e6i	−0.181469	+	0.314313i	−0.942381	−	0.334542i	$-0.891418\pi$
$313$	−5.56461e6	+	9.63818e6i	−0.181469	+	0.314313i	0.760912	+	0.648855i	$0.224752\pi$
$314$	4.00644e6	−	8.10821e6i	0.129410	−	0.261900i
$315$		−	3.38706e7i		−	1.08366i
$316$	161901.	+	1.24486e6i	0.00513085	+	0.0394510i
$317$	−1.02704e7	+	1.77889e7i	−0.322411	+	0.558432i	−0.980985	−	0.194084i	$-0.937827\pi$
$317$	−1.02704e7	+	1.77889e7i	−0.322411	+	0.558432i	0.658574	+	0.752516i	$0.271160\pi$
$318$	−3.25360e7	+	2.17029e7i	−1.01177	+	0.674896i
$319$	−1.85895e7	−	1.07327e7i	−0.572660	−	0.330625i
$320$	7.96693e6	+	6.17305e6i	0.243131	+	0.188387i
$321$	−2.51064e6	−	4.34855e6i	−0.0759047	−	0.131471i
$322$	4.11986e7	−	2.66783e6i	1.23400	−	0.0799081i
$323$	−1.84528e7	−	4.05790e6i	−0.547590	−	0.120419i
$324$	2.79077e7	−	3.62957e6i	0.820519	−	0.106714i
$325$	−2.20910e7	−	3.82627e7i	−0.643524	−	1.11462i
$326$	1.50462e6	−	1.00365e6i	0.0434286	−	0.0289688i
$327$	−8.11544e6	−	4.68545e6i	−0.232097	−	0.134001i
$328$	2.48661e7	+	2.84894e7i	0.704671	+	0.807350i
$329$	−2.15116e7	+	3.72592e7i	−0.604067	+	1.04627i
$330$	−2.90143e7	+	1.87883e6i	−0.807364	+	0.0522813i
$331$		−	1.99145e7i		−	0.549142i	−0.961567	−	0.274571i	$-0.911464\pi$
$331$		−	1.99145e7i		−	0.549142i	0.961567	−	0.274571i	$-0.0885359\pi$
$332$	−1.30894e7	−	5.44587e6i	−0.357688	−	0.148817i
$333$	−4.14272e6	+	7.17540e6i	−0.112190	+	0.194318i
$334$	−1.68149e6	−	2.59667e7i	−0.0451288	−	0.696911i
$335$			1.02221e7i			0.271898i
$336$	3.09160e7	−	1.13948e8i	0.815013	−	3.00393i
$337$	−6.96662e6	−	1.20665e7i	−0.182026	−	0.315278i	0.760545	−	0.649286i	$-0.224932\pi$
$337$	−6.96662e6	−	1.20665e7i	−0.182026	−	0.315278i	−0.942570	+	0.334008i	$0.891599\pi$
$338$	−1.74608e7	+	3.53370e7i	−0.452182	+	0.915124i
$339$	9.43414e7	−	5.44681e7i	2.42161	−	1.39811i
$340$	−4.11771e6	−	5.38377e6i	−0.104766	−	0.136978i
$341$	4.32938e6			0.109185
$342$	4.85513e7	−	6.06077e7i	1.21373	−	1.51513i
$343$			9.47444e7i			2.34785i
$344$	−3.81984e7	+	3.33404e7i	−0.938362	+	0.819022i
$345$	7.37959e6	+	1.27818e7i	0.179711	+	0.311269i
$346$	−1.74572e7	+	3.53297e7i	−0.421449	+	0.852927i
$347$	−1.44528e7	+	8.34432e6i	−0.345910	+	0.199711i	−0.662882	−	0.748723i	$-0.730667\pi$
$347$	−1.44528e7	+	8.34432e6i	−0.345910	+	0.199711i	0.316972	+	0.948435i	$0.397334\pi$
$348$	2.87709e7	+	1.19702e7i	0.682677	+	0.284030i
$349$	−3.69599e7			−0.869470			−0.434735	−	0.900558i	$-0.643158\pi$
$349$	−3.69599e7			−0.869470			−0.434735	+	0.900558i	$0.643158\pi$
$350$	4.55253e6	+	7.03034e7i	0.106181	+	1.63973i
$351$	8.59451e7	+	4.96204e7i	1.98747	+	1.14746i
$352$	−6.55563e7	−	1.33076e7i	−1.50310	−	0.305120i
$353$	4.93330e7			1.12154			0.560768	−	0.827973i	$-0.310506\pi$
$353$	4.93330e7			1.12154			0.560768	+	0.827973i	$0.310506\pi$
$354$	3.58172e7	−	2.31936e6i	0.807388	−	0.0522828i
$355$	6.47731e6	+	3.73968e6i	0.144780	+	0.0835890i
$356$	−9.25985e6	−	1.21070e7i	−0.205236	−	0.268340i
$357$	−3.97007e7	+	6.87636e7i	−0.872556	+	1.51131i
$358$	−3.59084e7	+	2.39525e7i	−0.782613	+	0.522038i
$359$	6.15167e7	−	3.55167e7i	1.32956	−	0.767625i	0.344333	−	0.938848i	$-0.388105\pi$
$359$	6.15167e7	−	3.55167e7i	1.32956	−	0.767625i	0.985232	+	0.171223i	$0.0547719\pi$
$360$	2.73359e7	−	5.37059e6i	0.585904	−	0.115110i
$361$	−4.26008e6	−	4.68526e7i	−0.0905516	−	0.995892i
$362$	−1.23656e7	+	800743.i	−0.260670	+	0.0168798i
$363$	9.60785e7	−	5.54710e7i	2.00866	−	1.15970i
$364$	9.88303e7	−	7.55890e7i	2.04921	−	1.56731i
$365$	7.82052e6	−	1.35455e7i	0.160826	−	0.278559i
$366$	−1.25783e8	+	8.39031e7i	−2.56555	+	1.71133i
$367$	−6.87663e7	−	3.97023e7i	−1.39116	−	0.803188i	−0.397718	−	0.917508i	$-0.630198\pi$
$367$	−6.87663e7	−	3.97023e7i	−1.39116	−	0.803188i	−0.993444	+	0.114320i	$0.963531\pi$
$368$	8.68565e6	+	3.28271e7i	0.174284	+	0.658701i
$369$	1.04525e8			2.08037
$370$	−797693.	+	1.61437e6i	−0.0157482	+	0.0318711i
$371$	5.69155e7	+	3.28602e7i	1.11457	+	0.643499i
$372$	−6.23255e6	+	810583.i	−0.121070	+	0.0157459i
$373$	7.03230e7			1.35510			0.677550	−	0.735477i	$-0.263042\pi$
$373$	7.03230e7			1.35510			0.677550	+	0.735477i	$0.263042\pi$
$374$	4.03314e7	+	1.99286e7i	0.770953	+	0.380944i
$375$	−4.59021e7	+	2.65016e7i	−0.870441	+	0.502549i
$376$	−3.34816e7	−	1.14535e7i	−0.629859	−	0.215463i
$377$	1.64195e7	+	2.84394e7i	0.306434	+	0.530759i
$378$	−8.78129e7	−	1.31645e8i	−1.62586	−	2.43741i
$379$		−	1.54386e7i		−	0.283590i	−0.989896	−	0.141795i	$-0.954713\pi$
$379$		−	1.54386e7i		−	0.283590i	0.989896	−	0.141795i	$-0.0452874\pi$
$380$	9.67853e6	−	1.38264e7i	0.176384	−	0.251975i
$381$	−1.08892e8			−1.96888
$382$	1.83889e7	−	1.22662e7i	0.329887	−	0.220049i
$383$	−4.15272e7	+	2.39757e7i	−0.739156	+	0.426752i	−0.821762	−	0.569831i	$-0.807009\pi$
$383$	−4.15272e7	+	2.39757e7i	−0.739156	+	0.426752i	0.0826066	+	0.996582i	$0.473676\pi$
$384$	9.68661e7	+	6.88347e6i	1.71072	+	0.121567i
$385$	2.44287e7	+	4.23117e7i	0.428073	+	0.741444i
$386$	9.85245e6	−	1.99393e7i	0.171310	−	0.346696i
$387$			1.40147e8i			2.41796i
$388$	−4.57324e7	+	5.94779e6i	−0.782940	+	0.101826i
$389$	4.52780e7	−	7.84237e7i	0.769198	−	1.33229i	−0.168800	−	0.985650i	$-0.553989\pi$
$389$	4.52780e7	−	7.84237e7i	0.769198	−	1.33229i	0.937998	−	0.346640i	$-0.112677\pi$
$390$	3.98782e7	+	1.97046e7i	0.672266	+	0.332181i
$391$		−	2.28361e7i		−	0.382025i
$392$	−1.35572e8	+	2.66353e7i	−2.25066	+	0.442180i
$393$	1.97226e7	−	3.41606e7i	0.324928	−	0.562792i
$394$	2.73648e7	+	4.10240e7i	0.447409	+	0.670733i
$395$	653090.	+	377062.i	0.0105970	+	0.00611817i
$396$	−1.46869e8	+	1.12330e8i	−2.36507	+	1.80889i
$397$	−2.06669e7	−	3.57961e7i	−0.330296	−	0.572090i	0.652273	−	0.757984i	$-0.273815\pi$
$397$	−2.06669e7	−	3.57961e7i	−0.330296	−	0.572090i	−0.982570	+	0.185894i	$0.940482\pi$
$398$	1.80343e6	+	2.78499e7i	0.0286056	+	0.441747i
$399$	−1.93098e8	−	4.24635e7i	−3.03989	−	0.668493i
$400$	−5.60178e7	+	1.48216e7i	−0.875278	+	0.231588i
$401$	1.34853e6	+	2.33572e6i	0.0209135	+	0.0362233i	0.876293	−	0.481779i	$-0.160009\pi$
$401$	1.34853e6	+	2.33572e6i	0.0209135	+	0.0362233i	−0.855379	+	0.518002i	$0.826676\pi$
$402$	5.46555e7	+	8.19369e7i	0.841310	+	1.26125i
$403$	−5.73600e6	−	3.31168e6i	−0.0876383	−	0.0505980i
$404$	−2.00416e7	−	2.62038e7i	−0.303941	−	0.397393i
$405$	8.45312e6	−	1.46412e7i	0.127248	−	0.220401i
$406$	−3.38375e6	−	5.22542e7i	−0.0505615	−	0.780806i
$407$		−	1.19515e7i		−	0.177271i
$408$	−6.17920e7	−	2.11379e7i	−0.909812	−	0.311230i
$409$	−3.66685e7	+	6.35118e7i	−0.535949	+	0.928291i	0.463168	+	0.886271i	$0.346713\pi$
$409$	−3.66685e7	+	6.35118e7i	−0.535949	+	0.928291i	−0.999117	+	0.0420204i	$0.986621\pi$
$410$	2.26692e7	−	1.46795e6i	0.328915	−	0.0212991i
$411$		−	1.96296e8i		−	2.82739i
$412$	−7.94199e7	−	3.30429e7i	−1.13563	−	0.472484i
$413$	−3.01565e7	−	5.22325e7i	−0.428085	−	0.741466i
$414$	8.41482e7	+	4.15794e7i	1.18589	+	0.585972i
$415$	−7.37561e6	+	4.25831e6i	−0.103194	+	0.0595789i
$416$	7.66763e7	+	6.77773e7i	1.06508	+	0.941465i
$417$	2.02730e8			2.79582
$418$	−1.69385e7	+	1.10729e8i	−0.231925	+	1.51612i
$419$			1.29643e8i			1.76242i	0.472729	+	0.881208i	$0.343269\pi$
$419$			1.29643e8i			1.76242i	−0.472729	+	0.881208i	$0.656731\pi$
$420$	−4.30893e7	−	5.63379e7i	−0.581596	−	0.760419i
$421$	4.21130e7	+	7.29418e7i	0.564378	+	0.977531i	0.997107	+	0.0760069i	$0.0242171\pi$
$421$	4.21130e7	+	7.29418e7i	0.564378	+	0.977531i	−0.432730	+	0.901524i	$0.642450\pi$
$422$	−1.58721e7	−	7.84272e6i	−0.211201	−	0.104359i
$423$	−8.47080e7	+	4.89062e7i	−1.11919	+	0.646164i
$424$	−1.74958e7	+	5.11451e7i	−0.229528	+	0.670975i
$425$	3.89687e7			0.507633
$426$	7.19151e7	−	4.65689e6i	0.930232	−	0.0602376i
$427$	2.20034e8	+	1.27037e8i	2.82622	+	1.63172i
$428$	−6.40753e6	−	2.66588e6i	−0.0817259	−	0.0340023i
$429$	−2.95226e8			−3.73924
$430$	1.96823e6	+	3.03947e7i	0.0247554	+	0.382290i
$431$	3.98828e7	+	2.30263e7i	0.498143	+	0.287603i	0.727946	−	0.685634i	$-0.240475\pi$
$431$	3.98828e7	+	2.30263e7i	0.498143	+	0.287603i	−0.229804	+	0.973237i	$0.573808\pi$
$432$	9.23227e7	−	9.17449e7i	1.14514	−	1.13797i
$433$	5.12176e7	−	8.87115e7i	0.630893	−	1.09274i	−0.356477	−	0.934304i	$-0.616022\pi$
$433$	5.12176e7	−	8.87115e7i	0.630893	−	1.09274i	0.987370	−	0.158434i	$-0.0506446\pi$
$434$	5.86066e6	+	8.78602e6i	0.0716931	+	0.107479i
$435$	1.62118e7	−	9.35991e6i	0.196954	−	0.113711i
$436$	−1.28435e7	+	1.67038e6i	−0.154962	+	0.0201537i
$437$	5.42015e7	−	1.71913e7i	0.649482	−	0.205999i
$438$	−9.73863e6	−	1.50391e8i	−0.115898	−	1.78978i
$439$	−3.13936e6	+	1.81251e6i	−0.0371063	+	0.0214233i	−0.518438	−	0.855115i	$-0.673486\pi$
$439$	−3.13936e6	+	1.81251e6i	−0.0371063	+	0.0214233i	0.481332	+	0.876538i	$0.340153\pi$
$440$	−3.02750e7	+	2.64246e7i	−0.355407	+	0.310207i
$441$	−1.90950e8	+	3.30735e8i	−2.22640	+	3.85624i
$442$	−3.81910e7	−	5.72541e7i	−0.442277	−	0.663040i
$443$	1.46083e7	+	8.43409e6i	0.168030	+	0.0970124i	0.581657	−	0.813434i	$-0.302405\pi$
$443$	1.46083e7	+	8.43409e6i	0.168030	+	0.0970124i	−0.413626	+	0.910447i	$0.635738\pi$
$444$	2.23766e6	+	1.72053e7i	0.0255649	+	0.196568i
$445$	−9.15646e6			−0.103908
$446$	−7.05845e7	−	3.48773e7i	−0.795619	−	0.393132i
$447$	−7.96047e7	−	4.59598e7i	−0.891284	−	0.514583i
$448$	−6.17370e7	−	1.51054e8i	−0.686612	−	1.67996i
$449$	2.01598e7			0.222714			0.111357	−	0.993780i	$-0.464480\pi$
$449$	2.01598e7			0.222714			0.111357	+	0.993780i	$0.464480\pi$
$450$	−7.09532e7	+	1.43595e8i	−0.778636	+	1.57580i
$451$	−1.30574e8	+	7.53870e7i	−1.42340	+	0.821802i
$452$	5.78359e7	−	1.39011e8i	0.626300	−	1.50534i
$453$	−8.92375e7	−	1.54564e8i	−0.959959	−	1.66270i
$454$	−4.84675e7	+	3.23299e7i	−0.517944	+	0.345492i
$455$		−	7.47450e7i		−	0.793502i
$456$	3.65304e6	−	1.62576e8i	0.0385266	−	1.71460i
$457$	1.46945e8			1.53959			0.769795	−	0.638291i	$-0.220358\pi$
$457$	1.46945e8			1.53959			0.769795	+	0.638291i	$0.220358\pi$
$458$	1.14598e7	+	1.71800e7i	0.119284	+	0.178824i
$459$	−7.58040e7	+	4.37655e7i	−0.783888	+	0.452578i
$460$	1.88338e7	+	7.83588e6i	0.193493	+	0.0805034i
$461$	1.54642e7	+	2.67848e7i	0.157843	+	0.273392i	0.934091	−	0.357036i	$-0.116213\pi$
$461$	1.54642e7	+	2.67848e7i	0.157843	+	0.273392i	−0.776248	+	0.630428i	$0.782879\pi$
$462$	4.22043e8	+	2.08540e8i	4.27987	+	2.11478i
$463$			1.25607e8i			1.26552i	0.774347	+	0.632761i	$0.218078\pi$
$463$			1.25607e8i			1.26552i	−0.774347	+	0.632761i	$0.781922\pi$
$464$	4.16362e7	−	1.10164e7i	0.416790	−	0.110278i
$465$	−1.88782e6	+	3.26979e6i	−0.0187759	+	0.0325208i
$466$	5.94490e7	−	1.20313e8i	0.587472	−	1.18892i
$467$		−	1.85437e8i		−	1.82073i	−0.413805	−	0.910365i	$-0.635801\pi$
$467$		−	1.85437e8i		−	1.82073i	0.413805	−	0.910365i	$-0.364199\pi$
$468$	2.80511e8	−	3.64822e7i	2.73661	−	0.355913i
$469$	8.27533e7	−	1.43333e8i	0.802171	−	1.38940i
$470$	−1.76845e7	+	1.17963e7i	−0.170333	+	0.113620i
$471$	−4.53355e7	−	2.61745e7i	−0.433886	−	0.250504i
$472$	3.73736e7	−	3.26204e7i	0.355418	−	0.310216i
$473$	−1.01079e8	−	1.75073e8i	−0.955159	−	1.65438i
$474$	7.25101e6	−	469542.i	0.0680869	−	0.00440900i
$475$	2.93361e7	+	9.24923e7i	0.273730	+	0.863028i
$476$	1.41534e7	+	1.08825e8i	0.131232	+	1.00904i
$477$	7.47070e7	+	1.29396e8i	0.688345	+	1.19225i
$478$	1.33354e8	−	8.89528e7i	1.22102	−	0.814472i
$479$	−1.15679e8	−	6.67870e7i	−1.05256	−	0.607695i	−0.129194	−	0.991619i	$-0.541239\pi$
$479$	−1.15679e8	−	6.67870e7i	−1.05256	−	0.607695i	−0.923365	+	0.383924i	$0.874572\pi$
$480$	3.86363e7	−	4.37091e7i	0.349359	−	0.395228i
$481$	−9.14207e6	+	1.58345e7i	−0.0821503	+	0.142288i
$482$	1.30460e8	−	8.44800e6i	1.16503	−	0.0754420i
$483$		−	2.38966e8i		−	2.12078i
$484$	5.89008e7	−	1.41570e8i	0.519500	−	1.24864i
$485$	−1.38522e7	+	2.39926e7i	−0.121421	+	0.210307i
$486$	1.44901e6	+	2.23766e7i	0.0126230	+	0.194933i
$487$		−	4.95536e7i		−	0.429031i	−0.976721	−	0.214516i	$-0.931183\pi$
$487$		−	4.95536e7i		−	0.429031i	0.976721	−	0.214516i	$-0.0688173\pi$
$488$	−6.76384e7	+	1.97726e8i	−0.582014	+	1.70139i
$489$	−5.23444e6	−	9.06631e6i	−0.0447655	−	0.0775361i
$490$	−3.67680e7	+	7.44109e7i	−0.312523	+	0.632482i
$491$	1.97343e7	−	1.13936e7i	0.166716	−	0.0962533i	−0.414321	−	0.910131i	$-0.635981\pi$
$491$	1.97343e7	−	1.13936e7i	0.166716	−	0.0962533i	0.581036	+	0.813878i	$0.302647\pi$
$492$	1.73859e8	−	1.32974e8i	1.45983	−	1.11653i
$493$	−2.89642e7			−0.241725
$494$	1.07142e8	−	1.33748e8i	0.888748	−	1.10945i
$495$			1.11076e8i			0.915810i
$496$	−6.16164e6	+	6.12308e6i	−0.0504954	+	0.0501794i
$497$	−6.05492e7	−	1.04874e8i	−0.493218	−	0.854279i
$498$	−3.63519e7	+	7.35689e7i	−0.294333	+	0.595670i
$499$	−5.58972e7	+	3.22723e7i	−0.449872	+	0.259733i	−0.707776	−	0.706437i	$-0.750301\pi$
$499$	−5.58972e7	+	3.22723e7i	−0.449872	+	0.259733i	0.257904	+	0.966170i	$0.416968\pi$
$500$	−2.81403e7	+	6.76362e7i	−0.225122	+	0.541090i
$501$	−1.50616e8			−1.19773
$502$	5.64171e6	+	8.71232e7i	0.0445964	+	0.688689i
$503$	4.06378e6	+	2.34623e6i	0.0319320	+	0.0184360i	0.515881	−	0.856660i	$-0.327465\pi$
$503$	4.06378e6	+	2.34623e6i	0.0319320	+	0.0184360i	−0.483949	+	0.875096i	$0.660798\pi$
$504$	−4.26778e8	−	1.45993e8i	−3.33357	−	1.14035i
$505$	−1.98179e7			−0.153880
$506$	−1.35108e8	+	8.74896e6i	−1.04287	+	0.0675313i
$507$	1.97580e8	+	1.14073e8i	1.51607	+	0.875304i
$508$	−1.19544e8	+	9.14315e7i	−0.911877	+	0.697437i
$509$	−1.25427e8	+	2.17246e8i	−0.951125	+	1.64740i	−0.208128	+	0.978102i	$0.566737\pi$
$509$	−1.25427e8	+	2.17246e8i	−0.951125	+	1.64740i	−0.742997	+	0.669295i	$0.766596\pi$
$510$	−3.26376e7	+	2.17707e7i	−0.246041	+	0.164120i
$511$	−2.19316e8	+	1.26622e8i	−1.64364	+	0.948958i
$512$	1.12122e8	−	7.37774e7i	0.835372	−	0.549685i
$513$	−1.60944e8	−	1.46974e8i	−1.19212	−	1.08865i
$514$	5.91100e7	−	3.82770e6i	0.435283	−	0.0281870i
$515$	−4.47516e7	+	2.58374e7i	−0.327633	+	0.189159i
$516$	1.78291e8	+	2.33110e8i	1.29772	+	1.69672i
$517$	7.05457e7	−	1.22189e8i	0.510504	−	0.884218i
$518$	2.42542e7	−	1.61787e7i	0.174501	−	0.116400i
$519$	1.97539e8	+	1.14049e8i	1.41303	+	0.815814i
$520$	6.03244e7	−	1.18517e7i	0.429025	−	0.0842891i
$521$	−2.22686e8			−1.57464			−0.787319	−	0.616546i	$-0.788531\pi$
$521$	−2.22686e8			−1.57464			−0.787319	+	0.616546i	$0.788531\pi$
$522$	5.27373e7	−	1.06729e8i	0.370771	−	0.750365i
$523$	−1.10734e8	−	6.39322e7i	−0.774061	−	0.446904i	0.0602602	−	0.998183i	$-0.480807\pi$
$523$	−1.10734e8	−	6.39322e7i	−0.774061	−	0.446904i	−0.834321	+	0.551278i	$0.814140\pi$
$524$	−7.03119e6	−	5.40626e7i	−0.0488692	−	0.375754i
$525$	4.07784e8			2.81807
$526$	−811289.	−	400875.i	−0.00557466	−	0.00275456i
$527$	5.05918e6	−	2.92092e6i	0.0345659	−	0.0199567i
$528$	−1.01387e8	+	3.73684e8i	−0.688777	+	2.53865i
$529$	−3.96542e7	−	6.86831e7i	−0.267869	−	0.463962i
$530$	1.80196e7	+	2.70140e7i	0.121037	+	0.181452i
$531$		−	1.37120e8i		−	0.915837i
$532$	−2.47642e8	+	1.15518e8i	−1.64471	+	0.767212i
$533$	2.30664e8			1.52334
$534$	−7.33949e7	+	4.89576e7i	−0.481995	+	0.321512i
$535$	−3.61052e6	+	2.08454e6i	−0.0235781	+	0.0136128i
$536$	1.28801e8	+	4.40605e7i	0.836421	+	0.286124i
$537$	1.24922e8	+	2.16371e8i	0.806706	+	1.39726i
$538$	9.67129e7	−	1.95727e8i	0.621066	−	1.25691i
$539$		−	5.50879e8i		−	3.51795i
$540$	−1.00840e7	−	7.75360e7i	−0.0640403	−	0.492405i
$541$	−2.85928e7	+	4.95241e7i	−0.180578	+	0.312770i	−0.942077	−	0.335395i	$-0.891130\pi$
$541$	−2.85928e7	+	4.95241e7i	−0.180578	+	0.312770i	0.761500	+	0.648165i	$0.224463\pi$
$542$	7.26801e6	+	3.59128e6i	0.0456475	+	0.0225554i
$543$			7.17251e7i			0.447993i
$544$	−8.55854e7	+	2.86783e7i	−0.531622	+	0.178138i
$545$	−3.89025e6	+	6.73811e6i	−0.0240319	+	0.0416244i
$546$	−3.99646e8	−	5.99129e8i	−2.45526	−	3.68080i
$547$	9.14088e7	+	5.27749e7i	0.558503	+	0.322452i	0.752545	−	0.658541i	$-0.228826\pi$
$547$	9.14088e7	+	5.27749e7i	0.558503	+	0.322452i	−0.194041	+	0.980993i	$0.562160\pi$
$548$	−1.64821e8	−	2.15499e8i	−1.00155	−	1.30949i
$549$	2.88816e8	+	5.00243e8i	1.74543	+	3.02318i
$550$	−1.49297e7	−	2.30555e8i	−0.0897351	−	1.38575i
$551$	−2.18046e7	−	6.87466e7i	−0.130345	−	0.410957i
$552$	1.92862e8	−	3.78909e7i	1.14665	−	0.225278i
$553$	−6.10502e6	−	1.05742e7i	−0.0361003	−	0.0625276i
$554$	1.19798e8	+	1.79595e8i	0.704561	+	1.05624i
$555$	9.02643e6	+	5.21141e6i	0.0528004	+	0.0304843i
$556$	2.22562e8	−	1.70223e8i	1.29487	−	0.990364i
$557$	−1.85044e7	+	3.20506e7i	−0.107080	+	0.185468i	−0.914586	−	0.404391i	$-0.867484\pi$
$557$	−1.85044e7	+	3.20506e7i	−0.107080	+	0.185468i	0.807506	+	0.589859i	$0.200817\pi$
$558$	1.55159e6	+	2.39608e7i	0.00893048	+	0.137911i
$559$			3.09273e8i			1.77054i
$560$	−9.46091e7	−	2.56690e7i	−0.538727	−	0.146165i
$561$	1.30195e8	−	2.25505e8i	0.737407	−	1.27723i
$562$	−2.87295e8	+	1.86039e7i	−1.61853	+	0.104808i
$563$		−	2.64704e7i		−	0.148332i	−0.997246	−	0.0741661i	$-0.976371\pi$
$563$		−	2.64704e7i		−	0.148332i	0.997246	−	0.0741661i	$-0.0236295\pi$
$564$	−7.86800e7	+	1.89110e8i	−0.438558	+	1.05409i
$565$	−4.52238e7	−	7.83300e7i	−0.250739	−	0.434293i
$566$	1.70105e8	+	8.40524e7i	0.938140	+	0.463555i
$567$	−2.37057e8	+	1.36865e8i	−1.30048	+	0.750831i
$568$	7.50400e7	−	6.54964e7i	0.409494	−	0.357415i
$569$	1.69662e8			0.920973			0.460486	−	0.887667i	$-0.347675\pi$
$569$	1.69662e8			0.920973			0.460486	+	0.887667i	$0.347675\pi$
$570$	−7.62427e7	−	6.10760e7i	−0.411693	−	0.329796i
$571$			2.64069e8i			1.41843i	0.704991	+	0.709216i	$0.250951\pi$
$571$			2.64069e8i			1.41843i	−0.704991	+	0.709216i	$0.749049\pi$
$572$	−3.24107e8	+	2.47889e8i	−1.73181	+	1.32455i
$573$	−6.39730e7	−	1.10805e8i	−0.340042	−	0.588971i
$574$	−3.29747e8	−	1.62935e8i	−1.74360	−	0.861548i
$575$	−1.01568e8	+	5.86401e7i	−0.534259	+	0.308455i
$576$	5.01556e7	−	3.67588e8i	0.262453	−	1.92351i
$577$	−2.01488e8			−1.04887			−0.524436	−	0.851450i	$-0.675724\pi$
$577$	−2.01488e8			−1.04887			−0.524436	+	0.851450i	$0.675724\pi$
$578$	−1.32122e8	+	8.55560e6i	−0.684212	+	0.0443065i
$579$	−1.11487e8	−	6.43671e7i	−0.574366	−	0.331610i
$580$	9.93865e6	−	2.38879e7i	0.0509382	−	0.122432i
$581$	1.37893e8			0.703093
$582$	1.72496e7	+	2.66381e8i	0.0875005	+	1.35125i
$583$	−1.86650e8	−	1.07762e8i	−0.941939	−	0.543829i
$584$	−1.36968e8	−	1.56926e8i	−0.687671	−	0.787872i
$585$	8.49657e7	−	1.47165e8i	0.424401	−	0.735084i
$586$	7.16019e7	+	1.07342e8i	0.355821	+	0.533430i
$587$	1.41924e8	−	8.19401e7i	0.701686	−	0.405118i	−0.106289	−	0.994335i	$-0.533897\pi$
$587$	1.41924e8	−	8.19401e7i	0.701686	−	0.405118i	0.807975	+	0.589217i	$0.200564\pi$
$588$	1.03140e8	+	7.93042e8i	0.507336	+	3.90089i
$589$	1.07414e7	+	9.80906e6i	0.0525673	+	0.0480045i
$590$	−1.92572e6	−	2.97384e7i	−0.00937644	−	0.144798i
$591$	2.47196e8	−	1.42718e8i	1.19751	−	0.691381i
$592$	1.69031e7	+	1.70095e7i	0.0814706	+	0.0819836i
$593$	−1.25756e7	+	2.17815e7i	−0.0603063	+	0.104454i	−0.894602	−	0.446863i	$-0.852541\pi$
$593$	−1.25756e7	+	2.17815e7i	−0.0603063	+	0.104454i	0.834296	+	0.551317i	$0.185874\pi$
$594$	2.87976e8	+	4.31720e8i	1.37403	+	2.05988i
$595$	5.70932e7	+	3.29628e7i	0.271040	+	0.156485i
$596$	−1.25983e8	+	1.63848e7i	−0.595075	+	0.0773932i
$597$	1.61539e8			0.759197
$598$	1.85697e8	+	9.17566e7i	0.868361	+	0.429076i
$599$	2.22235e8	+	1.28307e8i	1.03403	+	0.596996i	0.918136	−	0.396266i	$-0.129694\pi$
$599$	2.22235e8	+	1.28307e8i	1.03403	+	0.596996i	0.115891	+	0.993262i	$0.463028\pi$
$600$	6.46590e7	+	3.29110e8i	0.299347	+	1.52366i
$601$	−2.08962e8			−0.962595			−0.481298	−	0.876557i	$-0.659834\pi$
$601$	−2.08962e8			−0.962595			−0.481298	+	0.876557i	$0.659834\pi$
$602$	2.18463e8	−	4.42124e8i	1.00136	−	2.02654i
$603$	3.25865e8	−	1.88138e8i	1.48623	−	0.858074i
$604$	−2.27748e8	−	9.47552e7i	−1.03358	−	0.430024i
$605$	−4.60565e7	−	7.97722e7i	−0.207982	−	0.360235i
$606$	−1.58853e8	+	1.05962e8i	−0.713802	+	0.476137i
$607$			2.54709e8i			1.13888i	0.822033	+	0.569440i	$0.192840\pi$
$607$			2.54709e8i			1.13888i	−0.822033	+	0.569440i	$0.807160\pi$
$608$	−1.32498e8	−	1.81547e8i	−0.589519	−	0.807755i
$609$	−3.03093e8			−1.34191
$610$	6.96632e7	+	1.04436e8i	0.306912	+	0.460108i
$611$	−1.86932e8	+	1.07925e8i	−0.819521	+	0.473151i
$612$	−9.58396e7	+	2.30354e8i	−0.418110	+	1.00494i
$613$	−9.14996e7	−	1.58482e8i	−0.397226	−	0.688016i	0.596157	−	0.802868i	$-0.296694\pi$
$613$	−9.14996e7	−	1.58482e8i	−0.397226	−	0.688016i	−0.993383	+	0.114853i	$0.963360\pi$
$614$	−3.01293e8	−	1.48875e8i	−1.30162	−	0.643158i
$615$		−	1.31489e8i		−	0.565282i
$616$	6.38432e8	−	1.25430e8i	2.73132	−	0.536612i
$617$	2.17497e7	−	3.76716e7i	0.0925972	−	0.160383i	−0.816006	−	0.578043i	$-0.803816\pi$
$617$	2.17497e7	−	3.76716e7i	0.0925972	−	0.160383i	0.908603	+	0.417660i	$0.137150\pi$
$618$	−2.20566e8	+	4.46380e8i	−0.934487	+	1.89121i
$619$			2.41335e8i			1.01753i	0.860905	+	0.508766i	$0.169898\pi$
$619$			2.41335e8i			1.01753i	−0.860905	+	0.508766i	$0.830102\pi$
$620$	673012.	+	5.17478e6i	0.00282389	+	0.0217128i
$621$	1.31716e8	−	2.28140e8i	0.550003	−	0.952633i
$622$	−1.53628e8	+	1.02477e8i	−0.638409	+	0.425847i
$623$	1.28390e8	+	7.41262e7i	0.530968	+	0.306554i
$624$	4.20170e8	−	4.17541e8i	1.72930	−	1.71848i
$625$	−8.85184e7	−	1.53318e8i	−0.362571	−	0.627992i
$626$	8.88476e7	−	5.75337e6i	0.362179	−	0.0234530i
$627$	6.33249e8	+	1.39256e8i	2.56905	+	0.564951i
$628$	−7.17480e7	+	9.33128e6i	−0.289688	+	0.0376758i
$629$	−8.06335e6	−	1.39661e7i	−0.0324014	−	0.0561208i
$630$	−2.25417e8	+	1.50363e8i	−0.901499	+	0.601340i
$631$	1.66321e8	+	9.60255e7i	0.662002	+	0.382207i	0.793039	−	0.609171i	$-0.208498\pi$
$631$	1.66321e8	+	9.60255e7i	0.662002	+	0.382207i	−0.131038	+	0.991377i	$0.541831\pi$
$632$	7.56608e6	−	6.60383e6i	0.0299723	−	0.0261604i
$633$	−5.12373e7	+	8.87456e7i	−0.202011	+	0.349894i
$634$	1.63983e8	−	1.06188e7i	0.643474	−	0.0416685i
$635$			9.04106e7i			0.353101i
$636$	2.88877e8	+	1.20188e8i	1.12290	+	0.467186i
$637$	−4.21384e8	+	7.29859e8i	−1.63027	+	2.82371i
$638$	1.10968e7	+	1.71364e8i	0.0427301	+	0.659868i
$639$		−	2.75315e8i		−	1.05518i
$640$	5.71522e6	−	8.04262e7i	0.0218018	−	0.306801i
$641$	−2.16446e8	−	3.74895e8i	−0.821817	−	1.42343i	−0.904328	−	0.426838i	$-0.859627\pi$
$641$	−2.16446e8	−	3.74895e8i	−0.821817	−	1.42343i	0.0825114	−	0.996590i	$-0.473706\pi$
$642$	−1.77951e7	+	3.60136e7i	−0.0672504	+	0.136101i
$643$	2.83163e8	−	1.63484e8i	1.06513	−	0.614954i	0.138285	−	0.990393i	$-0.455841\pi$
$643$	2.83163e8	−	1.63484e8i	1.06513	−	0.614954i	0.926847	+	0.375438i	$0.122508\pi$
$644$	−2.00650e8	−	2.62343e8i	−0.751243	−	0.982227i
$645$	1.76300e8			0.657012
$646$	5.49120e7	+	1.40822e8i	0.203690	+	0.522365i
$647$		−	4.29794e8i		−	1.58689i	−0.608641	−	0.793446i	$-0.708285\pi$
$647$		−	4.29794e8i		−	1.58689i	0.608641	−	0.793446i	$-0.291715\pi$
$648$	−1.48047e8	−	1.69620e8i	−0.544096	−	0.623377i
$649$	9.88959e7	+	1.71293e8i	0.361780	+	0.626621i
$650$	−1.56578e8	+	3.16882e8i	−0.570153	+	1.15387i
$651$	5.29413e7	−	3.05657e7i	0.191890	−	0.110787i
$652$	−1.33591e7	−	5.55809e6i	−0.0481985	−	0.0200532i
$653$	2.87689e8			1.03320			0.516600	−	0.856227i	$-0.327198\pi$
$653$	2.87689e8			1.03320			0.516600	+	0.856227i	$0.327198\pi$
$654$	4.84439e6	+	7.48106e7i	0.0173183	+	0.267442i
$655$	−2.83629e7	−	1.63754e7i	−0.100932	−	0.0582729i
$656$	7.92146e7	−	2.91964e8i	0.280604	−	1.03423i
$657$	−5.75746e8			−2.03018
$658$	3.43466e8	−	2.22413e7i	1.20561	−	0.0780697i
$659$	−1.32942e8	−	7.67542e7i	−0.464522	−	0.268192i	0.249422	−	0.968395i	$-0.419759\pi$
$659$	−1.32942e8	−	7.67542e7i	−0.464522	−	0.268192i	−0.713944	+	0.700203i	$0.753093\pi$
$660$	1.41308e8	+	1.84756e8i	0.491514	+	0.642639i
$661$	−1.80220e8	+	3.12150e8i	−0.624020	+	1.08083i	0.364709	+	0.931121i	$0.381168\pi$
$661$	−1.80220e8	+	3.12150e8i	−0.624020	+	1.08083i	−0.988729	+	0.149713i	$0.952165\pi$
$662$	−1.32536e8	+	8.84072e7i	−0.456834	+	0.304729i
$663$	−3.44992e8	+	1.99181e8i	−1.18377	+	0.683452i
$664$	2.18645e7	+	1.11289e8i	0.0746854	+	0.380144i
$665$	−3.52567e7	+	1.60325e8i	−0.119888	+	0.545177i
$666$	6.61449e7	−	4.28325e6i	0.223910	−	0.0144994i
$667$	7.54920e7	−	4.35853e7i	0.254404	−	0.146880i
$668$	−1.65350e8	+	1.26466e8i	−0.554721	+	0.424271i
$669$	−2.27857e8	+	3.94660e8i	−0.760999	+	1.31809i
$670$	6.80307e7	−	4.53795e7i	0.226194	−	0.150881i
$671$	−7.21586e8	−	4.16608e8i	−2.38847	−	1.37899i
$672$	−8.95599e8	+	3.00101e8i	−2.95125	+	0.988918i
$673$	−2.59844e8			−0.852447			−0.426223	−	0.904618i	$-0.640156\pi$
$673$	−2.59844e8			−0.852447			−0.426223	+	0.904618i	$0.640156\pi$
$674$	−4.93785e7	+	9.99320e7i	−0.161272	+	0.326381i
$675$	3.89309e8	+	2.24768e8i	1.26585	+	0.730841i
$676$	3.12691e8	−	4.06674e7i	1.01222	−	0.131646i
$677$	1.67734e8			0.540573			0.270287	−	0.962780i	$-0.412882\pi$
$677$	1.67734e8			0.540573			0.270287	+	0.962780i	$0.412882\pi$
$678$	−7.81312e8	−	3.86063e8i	−2.50689	−	1.23871i
$679$	3.88465e8	−	2.24281e8i	1.24092	−	0.716444i
$680$	−1.75504e7	+	5.13048e7i	−0.0558162	+	0.163166i
$681$	1.68613e8	+	2.92047e8i	0.533889	+	0.924722i
$682$	−1.92196e7	−	2.88131e7i	−0.0605887	−	0.0908316i
$683$		−	1.22331e8i		−	0.383951i	−0.981400	−	0.191975i	$-0.938511\pi$
$683$		−	1.22331e8i		−	0.383951i	0.981400	−	0.191975i	$-0.0614893\pi$
$684$	−6.18895e8	−	5.40619e7i	−1.93396	−	0.168936i
$685$	−1.62981e8			−0.507067
$686$	6.30547e8	−	4.20602e8i	1.95319	−	1.30287i
$687$	1.03520e8	−	5.97675e7i	0.319268	−	0.184330i
$688$	3.91464e8	+	1.06211e8i	1.20206	+	0.326139i
$689$	1.64862e8	+	2.85549e8i	0.504037	+	0.873018i
$690$	5.23056e7	−	1.05856e8i	0.159221	−	0.322231i
$691$			2.91951e8i			0.884864i	0.896802	+	0.442432i	$0.145884\pi$
$691$			2.91951e8i			0.884864i	−0.896802	+	0.442432i	$0.854116\pi$
$692$	3.12626e8	−	4.06590e7i	0.943424	−	0.122698i
$693$	8.99219e8	−	1.55749e9i	2.70188	−	4.67979i
$694$	1.19694e8	+	5.91435e7i	0.358093	+	0.176941i
$695$		−	1.68323e8i		−	0.501405i
$696$	−4.80590e7	−	2.44617e8i	−0.142543	−	0.725535i
$697$	−1.01723e8	+	1.76190e8i	−0.300415	+	0.520335i
$698$	1.64078e8	+	2.45977e8i	0.482484	+	0.723317i
$699$	−6.72705e8	−	3.88387e8i	−1.96967	−	1.13719i
$700$	4.47676e8	−	3.42399e8i	1.30518	−	0.998247i
$701$	2.42619e8	+	4.20229e8i	0.704322	+	1.21992i	0.966936	+	0.255020i	$0.0820821\pi$
$701$	2.42619e8	+	4.20229e8i	0.704322	+	1.21992i	−0.262614	+	0.964901i	$0.584585\pi$
$702$	−5.13036e7	−	7.92267e8i	−0.148299	−	2.29013i
$703$	2.70784e7	−	2.96522e7i	0.0779395	−	0.0853476i
$704$	2.02462e8	+	4.95370e8i	0.580264	+	1.41975i
$705$	6.15225e7	+	1.06560e8i	0.175577	+	0.304108i
$706$	−2.19006e8	−	3.28323e8i	−0.622360	−	0.933011i
$707$	2.77883e8	+	1.60436e8i	0.786328	+	0.453987i
$708$	−1.74441e8	−	2.28076e8i	−0.491528	−	0.642658i
$709$	3.00333e8	−	5.20191e8i	0.842682	−	1.45957i	−0.0449368	−	0.998990i	$-0.514309\pi$
$709$	3.00333e8	−	5.20191e8i	0.842682	−	1.45957i	0.887619	−	0.460578i	$-0.152358\pi$
$710$	−3.86653e6	−	5.97098e7i	−0.0108031	−	0.166829i
$711$		−	2.77593e7i		−	0.0772324i
$712$	−3.94671e7	+	1.15373e8i	−0.109344	+	0.319644i
$713$	−8.79079e6	+	1.52261e7i	−0.0242527	+	0.0420068i
$714$	6.33883e8	−	4.10474e7i	1.74146	−	0.112769i
$715$			2.45121e8i			0.670598i
$716$	3.18819e8	+	1.32646e8i	0.868572	+	0.361372i
$717$	−4.63924e8	−	8.03540e8i	−1.25860	−	2.17997i
$718$	−5.09466e8	−	2.51738e8i	−1.37639	−	0.680104i
$719$	−5.26147e8	+	3.03771e8i	−1.41553	+	0.817258i	−0.995902	−	0.0904364i	$-0.971174\pi$
$719$	−5.26147e8	+	3.03771e8i	−1.41553	+	0.817258i	−0.419631	+	0.907695i	$0.637840\pi$
$720$	−1.57096e8	−	1.58085e8i	−0.420889	−	0.423540i
$721$	8.36667e8			2.23227
$722$	−2.92904e8	+	2.36347e8i	−0.778239	+	0.627968i
$723$		−	7.56714e8i		−	2.00224i
$724$	6.02245e7	+	7.87416e7i	0.158693	+	0.207486i
$725$	7.43762e7	+	1.28823e8i	0.195173	+	0.338050i
$726$	−7.95698e8	−	3.93171e8i	−2.07940	−	1.02748i
$727$	−3.12588e7	+	1.80473e7i	−0.0813522	+	0.0469687i	−0.540124	−	0.841585i	$-0.681623\pi$
$727$	−3.12588e7	+	1.80473e7i	−0.0813522	+	0.0469687i	0.458772	+	0.888554i	$0.348289\pi$
$728$	−9.41804e8	−	3.22174e8i	−2.44099	−	0.835019i
$729$	4.50355e8			1.16245
$730$	−1.24867e8	+	8.08581e6i	−0.320980	+	0.0207852i
$731$	−2.36235e8	−	1.36390e8i	−0.604772	−	0.349165i
$732$	1.11679e9	+	4.64645e8i	2.84734	+	1.18464i
$733$	1.43038e7			0.0363194			0.0181597	−	0.999835i	$-0.494219\pi$
$733$	1.43038e7			0.0363194			0.0181597	+	0.999835i	$0.494219\pi$
$734$	4.10490e7	+	6.33908e8i	0.103804	+	1.60302i
$735$	4.16054e8	+	2.40209e8i	1.04782	+	0.604961i
$736$	1.79914e8	−	2.03536e8i	0.451264	−	0.510513i
$737$	−2.71383e8	+	4.70050e8i	−0.677924	+	1.17420i
$738$	−4.64022e8	−	6.95639e8i	−1.15444	−	1.73067i
$739$	2.22374e8	−	1.28388e8i	0.550999	−	0.318119i	−0.198526	−	0.980096i	$-0.563615\pi$
$739$	2.22374e8	−	1.28388e8i	0.550999	−	0.318119i	0.749525	+	0.661976i	$0.230282\pi$
$740$	1.42852e7	−	1.85788e6i	0.0352527	−	0.00458483i
$741$	−7.32471e8	−	6.68892e8i	−1.80026	−	1.64400i
$742$	−3.39748e7	−	5.24664e8i	−0.0831660	−	1.28431i
$743$	−1.26247e8	+	7.28885e7i	−0.307789	+	0.177702i	−0.645937	−	0.763391i	$-0.723533\pi$
$743$	−1.26247e8	+	7.28885e7i	−0.307789	+	0.177702i	0.338148	+	0.941093i	$0.390200\pi$
$744$	3.30631e7	+	3.78807e7i	0.0802831	+	0.0919812i
$745$	−3.81596e7	+	6.60944e7i	−0.0922858	+	0.159844i
$746$	−3.12188e8	−	4.68017e8i	−0.751969	−	1.12731i
$747$	2.71496e8	+	1.56748e8i	0.651331	+	0.376046i
$748$	−4.64151e7	−	3.56885e8i	−0.110906	−	0.852753i
$749$	6.75016e7			0.160645
$750$	3.80150e8	+	1.87840e8i	0.901096	+	0.445251i
$751$	−2.11526e8	−	1.22124e8i	−0.499394	−	0.288325i	0.229069	−	0.973410i	$-0.426432\pi$
$751$	−2.11526e8	−	1.22124e8i	−0.499394	−	0.288325i	−0.728463	+	0.685085i	$0.759765\pi$
$752$	7.24109e7	+	2.73674e8i	0.170275	+	0.643547i
$753$	5.05345e8			1.18360
$754$	1.16380e8	−	2.35528e8i	0.271496	−	0.549451i
$755$	−1.28332e8	+	7.40923e7i	−0.298190	+	0.172160i
$756$	−4.86297e8	+	1.16883e9i	−1.12548	+	2.70512i
$757$	2.88983e8	+	5.00534e8i	0.666170	+	1.15384i	0.978967	+	0.204020i	$0.0654007\pi$
$757$	2.88983e8	+	5.00534e8i	0.666170	+	1.15384i	−0.312797	+	0.949820i	$0.601266\pi$
$758$	−1.02748e8	+	6.85373e7i	−0.235920	+	0.157369i
$759$			7.83672e8i			1.79229i
$760$	−1.34984e8	−	3.03306e6i	−0.307497	−	0.00690939i
$761$	−4.74094e8			−1.07575			−0.537874	−	0.843025i	$-0.680773\pi$
$761$	−4.74094e8			−1.07575			−0.537874	+	0.843025i	$0.680773\pi$
$762$	4.83407e8	+	7.24699e8i	1.09257	+	1.63792i
$763$	1.09097e8	−	6.29871e7i	0.245606	−	0.141801i
$764$	−1.63269e8	−	6.79286e7i	−0.366120	−	0.152326i
$765$	7.49402e7	+	1.29800e8i	0.167390	+	0.289929i
$766$	3.43917e8	+	1.69937e8i	0.765188	+	0.378095i
$767$		−	3.02594e8i		−	0.670617i
$768$	−3.84210e8	−	6.75225e8i	−0.848175	−	1.49061i
$769$	2.78332e8	−	4.82085e8i	0.612046	−	1.06009i	−0.378849	−	0.925458i	$-0.623680\pi$
$769$	2.78332e8	−	4.82085e8i	0.612046	−	1.06009i	0.990895	−	0.134636i	$-0.0429866\pi$
$770$	1.73147e8	−	3.50415e8i	0.379266	−	0.767556i
$771$		−	3.42859e8i		−	0.748088i
$772$	−1.76439e8	+	2.29471e7i	−0.383481	+	0.0498741i
$773$	−3.12751e8	+	5.41701e8i	−0.677111	+	1.17279i	0.298735	+	0.954336i	$0.403435\pi$
$773$	−3.12751e8	+	5.41701e8i	−0.677111	+	1.17279i	−0.975847	+	0.218455i	$0.929898\pi$
$774$	9.32710e8	−	6.22159e8i	2.01152	−	1.34177i
$775$	−2.59826e7	−	1.50011e7i	−0.0558184	−	0.0322268i
$776$	2.42606e8	+	2.77956e8i	0.519177	+	0.594827i
$777$	−8.43780e7	−	1.46147e8i	−0.179873	−	0.311549i
$778$	−7.22933e8	+	4.68139e7i	−1.53518	+	0.0994113i
$779$	−4.94765e8	−	1.08802e8i	−1.04661	−	0.230158i
$780$	−4.58935e7	−	3.52874e8i	−0.0967092	−	0.743595i
$781$	1.98567e8	+	3.43927e8i	0.416824	+	0.721961i
$782$	−1.51980e8	+	1.01377e8i	−0.317809	+	0.211993i
$783$	−2.89361e8	−	1.67063e8i	−0.602774	−	0.348012i
$784$	7.79113e8	+	7.84019e8i	1.61678	+	1.62697i
$785$	−2.17322e7	+	3.76412e7i	−0.0449256	+	0.0778135i
$786$	−3.14903e8	+	2.03917e7i	−0.648498	+	0.0419938i
$787$			5.75878e8i			1.18142i	0.806882	+	0.590712i	$0.201153\pi$
$787$			5.75878e8i			1.18142i	−0.806882	+	0.590712i	$0.798847\pi$
$788$	1.51543e8	−	3.64239e8i	0.309711	−	0.744403i
$789$	−2.61896e6	+	4.53617e6i	−0.00533209	+	0.00923545i
$790$	−389853.	−	6.02038e6i	−0.000790713	−	0.0122108i
$791$			1.46444e9i			2.95898i
$792$	1.39959e9	+	4.78773e8i	2.81724	+	0.963726i
$793$	6.37353e8	+	1.10393e9i	1.27809	+	2.21371i
$794$	−1.46484e8	+	2.96454e8i	−0.292638	+	0.592238i
$795$	1.62777e8	−	9.39791e7i	0.323959	−	0.187038i
$796$	1.77342e8	−	1.35637e8i	0.351618	−	0.268930i
$797$	−4.81370e8			−0.950832			−0.475416	−	0.879761i	$-0.657702\pi$
$797$	−4.81370e8			−0.950832			−0.475416	+	0.879761i	$0.657702\pi$
$798$	5.74621e8	+	1.47362e9i	1.13077	+	2.89986i
$799$		−	1.90381e8i		−	0.373236i
$800$	3.47324e8	+	3.07014e8i	0.678367	+	0.599636i
$801$	1.68525e8	+	2.91893e8i	0.327918	+	0.567971i
$802$	9.55822e6	−	1.93439e7i	0.0185291	−	0.0374990i
$803$	7.19231e8	−	4.15248e8i	1.38906	−	0.801975i
$804$	3.02675e8	−	7.27492e8i	0.582383	−	1.39978i
$805$	−1.98409e8			−0.380342
$806$	3.42402e6	+	5.28762e7i	0.00653930	+	0.100984i
$807$	−1.09437e9	−	6.31835e8i	−2.08230	−	1.20222i
$808$	−8.54211e7	+	2.49710e8i	−0.161931	+	0.473371i
$809$	−7.67030e8			−1.44866			−0.724331	−	0.689453i	$-0.757851\pi$
$809$	−7.67030e8			−1.44866			−0.724331	+	0.689453i	$0.757851\pi$
$810$	−1.34967e8	+	8.73987e6i	−0.253965	+	0.0164456i
$811$	−4.37682e8	−	2.52696e8i	−0.820532	−	0.473735i	0.0300676	−	0.999548i	$-0.490428\pi$
$811$	−4.37682e8	−	2.52696e8i	−0.820532	−	0.473735i	−0.850600	+	0.525813i	$0.823761\pi$
$812$	−3.32743e8	+	2.54494e8i	−0.621500	+	0.475346i
$813$	2.34622e7	−	4.06377e7i	0.0436613	−	0.0756236i
$814$	−7.95400e7	+	5.30567e7i	−0.147473	+	0.0983710i
$815$	−7.52759e6	+	4.34606e6i	−0.0139054	+	0.00802828i
$816$	1.33638e8	+	5.05079e8i	0.245957	+	0.929584i
$817$	1.45882e8	−	6.63379e8i	0.267507	−	1.21645i
$818$	5.85470e8	−	3.79124e7i	1.06966	−	0.0692662i
$819$	−2.38275e9	+	1.37568e9i	−4.33737	+	2.50418i
$820$	−1.10406e8	−	1.44352e8i	−0.200240	−	0.261807i
$821$	3.41643e8	−	5.91743e8i	0.617367	−	1.06931i	−0.372597	−	0.927993i	$-0.621533\pi$
$821$	3.41643e8	−	5.91743e8i	0.617367	−	1.06931i	0.989964	−	0.141318i	$-0.0451339\pi$
$822$	−1.30640e9	+	8.71425e8i	−2.35212	+	1.56897i
$823$	1.89975e8	+	1.09682e8i	0.340799	+	0.196760i	0.660625	−	0.750716i	$-0.270291\pi$
$823$	1.89975e8	+	1.09682e8i	0.340799	+	0.196760i	−0.319826	+	0.947476i	$0.603625\pi$
$824$	1.32663e8	+	6.75248e8i	0.237121	+	1.20693i
$825$	−1.33730e9			−2.38159
$826$	−2.13745e8	+	4.32577e8i	−0.379277	+	0.767579i
$827$	4.82751e8	+	2.78716e8i	0.853506	+	0.492772i	0.861832	−	0.507193i	$-0.169317\pi$
$827$	4.82751e8	+	2.78716e8i	0.853506	+	0.492772i	−0.00832608	+	0.999965i	$0.502650\pi$
$828$	−9.68414e7	−	7.44612e8i	−0.170597	−	1.31171i
$829$	−8.18117e8			−1.43599			−0.717995	−	0.696048i	$-0.754940\pi$
$829$	−8.18117e8			−1.43599			−0.717995	+	0.696048i	$0.754940\pi$
$830$	6.10829e7	+	3.01824e7i	0.106828	+	0.0527860i
$831$	1.08217e9	−	6.24791e8i	1.88579	−	1.08876i
$832$	1.10682e8	−	8.11186e8i	0.192180	−	1.40848i
$833$	−3.71663e8	−	6.43740e8i	−0.643005	−	1.11372i
$834$	−8.99986e8	−	1.34921e9i	−1.55145	−	2.32586i
$835$			1.25054e8i			0.214802i
$836$	8.12124e8	−	3.78833e8i	1.38996	−	0.648380i
$837$	6.73903e7			0.114927
$838$	8.62808e8	−	5.75531e8i	1.46616	−	0.977995i
$839$	6.08942e8	−	3.51573e8i	1.03107	−	0.595291i	0.113782	−	0.993506i	$-0.463704\pi$
$839$	6.08942e8	−	3.51573e8i	1.03107	−	0.595291i	0.917292	+	0.398215i	$0.130370\pi$
$840$	−1.83654e8	+	5.36873e8i	−0.309859	+	0.905803i
$841$	2.42130e8	+	4.19382e8i	0.407062	+	0.705053i
$842$	2.98492e8	−	6.04086e8i	0.500030	−	1.01196i
$843$			1.66641e9i			2.78163i
$844$	1.82663e7	+	1.40449e8i	0.0303824	+	0.233610i
$845$	9.47128e7	−	1.64047e8i	0.156978	−	0.271894i
$846$	7.01530e8	+	3.46641e8i	1.15860	+	0.572491i
$847$			1.49140e9i			2.45440i
$848$	4.18053e8	−	1.10612e8i	0.685557	−	0.181390i
$849$	5.49123e8	−	9.51109e8i	0.897319	−	1.55420i
$850$	−1.72996e8	−	2.59346e8i	−0.281694	−	0.422302i
$851$	4.20324e7	+	2.42674e7i	0.0682018	+	0.0393763i
$852$	−3.50248e8	−	4.57939e8i	−0.566314	−	0.740438i
$853$	1.16462e8	+	2.01717e8i	0.187644	+	0.325010i	0.944464	−	0.328614i	$-0.106581\pi$
$853$	1.16462e8	+	2.01717e8i	0.187644	+	0.325010i	−0.756820	+	0.653623i	$0.773248\pi$
$854$	−1.31346e8	−	2.02834e9i	−0.210884	−	3.25662i
$855$	−2.51665e8	+	2.75586e8i	−0.402647	+	0.440919i
$856$	1.07032e7	+	5.44784e7i	0.0170644	+	0.0868567i
$857$	−2.50240e8	−	4.33428e8i	−0.397570	−	0.688612i	0.595855	−	0.803092i	$-0.296813\pi$
$857$	−2.50240e8	−	4.33428e8i	−0.397570	−	0.688612i	−0.993426	+	0.114480i	$0.963480\pi$
$858$	1.31061e9	+	1.96480e9i	2.07497	+	3.11069i
$859$	−1.17101e8	−	6.76083e7i	−0.184749	−	0.106665i	0.404773	−	0.914417i	$-0.367350\pi$
$859$	−1.17101e8	−	6.76083e7i	−0.184749	−	0.106665i	−0.589522	+	0.807752i	$0.700684\pi$
$860$	1.93547e8	−	1.48032e8i	0.304292	−	0.232734i
$861$	−1.06447e9	+	1.84372e9i	−1.66773	+	2.88859i
$862$	−2.38074e7	−	3.67651e8i	−0.0371698	−	0.574003i
$863$		−	9.71249e8i		−	1.51112i	−0.655081	−	0.755559i	$-0.727366\pi$
$863$		−	9.71249e8i		−	1.51112i	0.655081	−	0.755559i	$-0.272634\pi$
$864$	−1.02044e9	−	2.07143e8i	−1.58214	−	0.321165i
$865$	9.46932e7	−	1.64013e8i	0.146309	−	0.253414i
$866$	−8.17769e8	+	5.29550e7i	−1.25915	+	0.0815368i
$867$			7.66352e8i			1.17590i
$868$	3.24556e7	−	7.80082e7i	0.0496284	−	0.119284i
$869$	2.00210e7	+	3.46773e7i	0.0305088	+	0.0528428i
$870$	−1.34262e8	−	6.63419e7i	−0.203890	−	0.100746i
$871$	7.19112e8	−	4.15179e8i	1.08828	−	0.628321i
$872$	6.81335e7	+	7.80613e7i	0.102757	+	0.117730i
$873$	1.01980e9			1.53275
$874$	−3.55031e8	−	2.84406e8i	−0.531781	−	0.425995i
$875$		−	7.12528e8i		−	1.06360i
$876$	−9.57654e8	+	7.32449e8i	−1.42461	+	1.08959i
$877$	−4.69953e8	−	8.13982e8i	−0.696716	−	1.20675i	−0.969599	−	0.244700i	$-0.921311\pi$
$877$	−4.69953e8	−	8.13982e8i	−0.696716	−	1.20675i	0.272883	−	0.962047i	$-0.412023\pi$
$878$	2.59994e7	+	1.28469e7i	0.0384131	+	0.0189807i
$879$	6.46804e8	−	3.73432e8i	0.952370	−	0.549851i
$880$	3.10263e8	+	8.41795e7i	0.455284	+	0.123526i
$881$	−1.04799e8			−0.153260			−0.0766300	−	0.997060i	$-0.524416\pi$
$881$	−1.04799e8			−0.153260			−0.0766300	+	0.997060i	$0.524416\pi$
$882$	3.04881e9	−	1.97427e8i	4.44350	−	0.287741i
$883$	−1.00052e9	−	5.77648e8i	−1.45326	−	0.839038i	−0.454591	−	0.890700i	$-0.650215\pi$
$883$	−1.00052e9	−	5.77648e8i	−1.45326	−	0.839038i	−0.998665	+	0.0516628i	$0.983548\pi$
$884$	−2.11497e8	+	5.08341e8i	−0.306159	+	0.735865i
$885$	−1.72493e8			−0.248853
$886$	−8.72019e6	−	1.34663e8i	−0.0125379	−	0.193619i
$887$	−3.88491e8	−	2.24295e8i	−0.556686	−	0.321403i	0.195128	−	0.980778i	$-0.437488\pi$
$887$	−3.88491e8	−	2.24295e8i	−0.556686	−	0.321403i	−0.751814	+	0.659375i	$0.770821\pi$
$888$	1.04572e8	−	9.12723e7i	0.149340	−	0.130347i
$889$	7.31920e8	−	1.26772e9i	1.04174	−	1.80434i
$890$	4.06486e7	+	6.09385e7i	0.0576602	+	0.0864413i
$891$	7.77410e8	−	4.48838e8i	1.09905	−	0.634536i
$892$	8.12318e7	+	6.24590e8i	0.114454	+	0.880035i
$893$	4.51870e8	−	1.43321e8i	0.634540	−	0.201260i
$894$	4.75189e7	+	7.33820e8i	0.0665049	+	1.02702i
$895$	1.79649e8	−	1.03720e8i	0.250585	−	0.144675i
$896$	−7.31229e8	+	1.08145e9i	−1.01655	+	1.50343i
$897$	5.99455e8	−	1.03829e9i	0.830576	−	1.43860i
$898$	−8.94963e7	−	1.34168e8i	−0.123588	−	0.185277i
$899$	1.93120e7	+	1.11498e7i	0.0265796	+	0.0153458i
$900$	1.27064e9	−	1.65255e8i	1.74300	−	0.226688i
$901$	−2.90818e8			−0.397601
$902$	1.08138e9	+	5.34334e8i	1.47353	+	0.728104i
$903$	−2.47205e9	−	1.42724e9i	−3.35733	−	1.93836i
$904$	−1.18190e9	+	2.32204e8i	−1.59984	+	0.314315i
$905$	5.95521e7			0.0803436
$906$	−6.32504e8	+	1.28006e9i	−0.850509	+	1.72126i
$907$	−1.16810e9	+	6.74402e8i	−1.56552	+	0.903852i	−0.568836	+	0.822451i	$0.692606\pi$
$907$	−1.16810e9	+	6.74402e8i	−1.56552	+	0.903852i	−0.996681	+	0.0814008i	$0.974061\pi$
$908$	4.30327e8	+	1.79039e8i	0.574833	+	0.239161i
$909$	3.64748e8	+	6.31762e8i	0.485625	+	0.841127i
$910$	−4.97446e8	+	3.31819e8i	−0.660119	+	0.440328i
$911$			1.27283e9i			1.68350i	0.539864	+	0.841752i	$0.318476\pi$
$911$			1.27283e9i			1.68350i	−0.539864	+	0.841752i	$0.681524\pi$
$912$	−1.09820e9	+	6.97419e8i	−1.44776	+	0.919410i
$913$	−4.52209e8			−0.594192
$914$	−6.52337e8	−	9.77952e8i	−0.854346	−	1.28079i
$915$	6.29291e8	−	3.63321e8i	0.821463	−	0.474272i
$916$	6.34630e7	−	1.52536e8i	0.0825723	−	0.198466i
$917$	2.65134e8	+	4.59225e8i	0.343840	+	0.595549i
$918$	6.27790e8	+	3.10204e8i	0.811496	+	0.400977i
$919$			1.03595e8i			0.133473i	0.997771	+	0.0667365i	$0.0212587\pi$
$919$			1.03595e8i			0.133473i	−0.997771	+	0.0667365i	$0.978741\pi$
$920$	−3.14601e7	−	1.60130e8i	−0.0404015	−	0.205641i
$921$	−9.72617e8	+	1.68462e9i	−1.24498	+	2.15637i
$922$	1.09608e8	−	2.21825e8i	0.139846	−	0.283020i
$923$		−	6.07559e8i		−	0.772651i
$924$	−4.85706e8	−	3.73458e9i	−0.615683	−	4.73398i
$925$	−4.14112e7	+	7.17263e7i	−0.0523230	+	0.0906261i
$926$	8.35942e8	−	5.57610e8i	1.05279	−	0.702260i
$927$	1.64731e9	+	9.51073e8i	2.06793	+	1.19392i
$928$	−2.58155e8	−	2.28193e8i	−0.323025	−	0.285535i
$929$	6.13703e8	+	1.06296e9i	0.765440	+	1.32578i	0.940014	+	0.341137i	$0.110812\pi$
$929$	6.13703e8	+	1.06296e9i	0.765440	+	1.32578i	−0.174574	+	0.984644i	$0.555855\pi$
$930$	3.01419e7	−	1.95185e6i	0.0374733	−	0.00242660i
$931$	1.24812e9	−	1.36676e9i	1.54671	−	1.69372i
$932$	−1.06462e9	+	1.38461e8i	−1.31507	+	0.171033i
$933$	5.34456e8	+	9.25705e8i	0.658063	+	1.13980i
$934$	−1.23413e9	+	8.23218e8i	−1.51468	+	1.01036i
$935$	−1.87233e8	−	1.08099e8i	−0.229059	−	0.132247i
$936$	−1.48808e9	−	1.70491e9i	−1.81468	−	2.07910i
$937$	1.24363e8	−	2.15403e8i	0.151172	−	0.261838i	−0.780486	−	0.625173i	$-0.785029\pi$
$937$	1.24363e8	−	2.15403e8i	0.151172	−	0.261838i	0.931659	+	0.363335i	$0.118362\pi$
$938$	−1.32129e9	+	8.55605e7i	−1.60099	+	0.103673i
$939$		−	5.15347e8i		−	0.622448i
$940$	1.57015e8	+	6.53265e7i	0.189041	+	0.0786513i
$941$	6.96064e8	−	1.20562e9i	0.835373	−	1.44691i	−0.0583529	−	0.998296i	$-0.518585\pi$
$941$	6.96064e8	−	1.20562e9i	0.835373	−	1.44691i	0.893726	−	0.448613i	$-0.148082\pi$
$942$	2.70623e7	+	4.17916e8i	0.0323752	+	0.499961i
$943$		−	6.12292e8i		−	0.730170i
$944$	−3.83011e8	−	1.03917e8i	−0.455298	−	0.123530i
$945$	3.80252e8	+	6.58615e8i	0.450584	+	0.780434i
$946$	−7.16433e8	+	1.44991e9i	−0.846257	+	1.71265i
$947$	−5.66738e8	+	3.27207e8i	−0.667318	+	0.385276i	−0.795060	−	0.606531i	$-0.792560\pi$
$947$	−5.66738e8	+	3.27207e8i	−0.667318	+	0.385276i	0.127742	+	0.991807i	$0.459227\pi$
$948$	−3.53146e7	−	4.61727e7i	−0.0414505	−	0.0541952i
$949$	−1.27055e9			−1.48659
$950$	4.85325e8	−	6.05844e8i	0.566060	−	0.706627i
$951$		−	9.51159e8i		−	1.10589i
$952$	6.61427e8	−	5.77307e8i	0.766604	−	0.669108i
$953$	−9.68770e7	−	1.67796e8i	−0.111929	−	0.193866i	0.804619	−	0.593791i	$-0.202370\pi$
$953$	−9.68770e7	−	1.67796e8i	−0.111929	−	0.193866i	−0.916548	+	0.399925i	$0.869036\pi$
$954$	5.29514e8	−	1.07163e9i	0.609863	−	1.23424i
$955$	−9.19990e7	+	5.31157e7i	−0.105627	+	0.0609835i
$956$	−1.18401e9	−	4.92609e8i	−1.35513	−	0.563805i
$957$	9.93971e8			1.13406
$958$	6.90526e7	+	1.06636e9i	0.0785386	+	1.21285i
$959$	2.28529e9	+	1.31942e9i	2.59111	+	1.49598i
$960$	−4.62414e8	−	6.30941e7i	−0.522658	−	0.0713141i
$961$	8.83006e8			0.994932
$962$	1.45967e8	−	9.45218e6i	0.163957	−	0.0106171i
$963$	1.32903e8	+	7.67318e7i	0.148818	+	0.0859204i
$964$	−6.35380e8	−	8.30740e8i	−0.709255	−	0.927329i
$965$	−5.34428e7	+	9.25657e7i	−0.0594713	+	0.103007i
$966$	−1.59038e9	+	1.06085e9i	−1.76429	+	1.17686i
$967$	7.99925e8	−	4.61837e8i	0.884647	−	0.510751i	0.0124592	−	0.999922i	$-0.496034\pi$
$967$	7.99925e8	−	4.61837e8i	0.884647	−	0.510751i	0.872188	+	0.489171i	$0.162701\pi$
$968$	−1.20367e9	+	2.36480e8i	−1.32703	+	0.260716i
$969$	8.33948e8	−	2.64506e8i	0.916574	−	0.290713i
$970$	2.21171e8	−	1.43220e7i	0.242334	−	0.0156924i
$971$	2.98996e8	−	1.72625e8i	0.326594	−	0.188559i	−0.327734	−	0.944770i	$-0.606285\pi$
$971$	2.98996e8	−	1.72625e8i	0.326594	−	0.188559i	0.654328	+	0.756211i	$0.272952\pi$
$972$	1.42489e8	−	1.08981e8i	0.155161	−	0.118673i
$973$	−1.36266e9	+	2.36019e9i	−1.47927	+	2.56218i
$974$	−3.29792e8	+	2.19986e8i	−0.356913	+	0.238077i
$975$	1.77179e9	+	1.02294e9i	1.91160	+	1.10366i
$976$	1.61618e9	−	4.27623e8i	1.73837	−	0.459951i
$977$	−3.52314e8			−0.377786			−0.188893	−	0.981998i	$-0.560490\pi$
$977$	−3.52314e8			−0.377786			−0.188893	+	0.981998i	$0.560490\pi$
$978$	−3.71010e7	+	7.50849e7i	−0.0396615	+	0.0802668i
$979$	−4.21047e8	−	2.43091e8i	−0.448727	−	0.259073i
$980$	6.58448e8	−	8.56353e7i	0.699590	−	0.0909860i
$981$	2.86400e8			0.303365
$982$	−1.63434e8	−	8.07563e7i	−0.172587	−	0.0852789i
$983$	−1.01634e9	+	5.86784e8i	−1.06999	+	0.617757i	−0.928178	−	0.372137i	$-0.878625\pi$
$983$	−1.01634e9	+	5.86784e8i	−1.06999	+	0.617757i	−0.141809	+	0.989894i	$0.545292\pi$
$984$	−1.65679e9	−	5.66759e8i	−1.73893	−	0.594857i
$985$	−1.18497e8	−	2.05242e8i	−0.123993	−	0.214762i
$986$	1.28582e8	+	1.92764e8i	0.134137	+	0.201092i
$987$		−	1.99222e9i		−	2.07199i
$988$	−1.36576e9	−	1.19303e8i	−1.41614	−	0.123703i
$989$	8.20959e8			0.848658
$990$	7.39239e8	−	4.93105e8i	0.761867	−	0.508199i
$991$	5.83274e8	−	3.36753e8i	0.599310	−	0.346012i	−0.169460	−	0.985537i	$-0.554202\pi$
$991$	5.83274e8	−	3.36753e8i	0.599310	−	0.346012i	0.768770	+	0.639525i	$0.220869\pi$
$992$	6.81042e7	+	1.38248e7i	0.0697653	+	0.0141619i
$993$	4.61078e8	+	7.98611e8i	0.470898	+	0.815619i
$994$	−4.29165e8	+	8.68542e8i	−0.436984	+	0.884365i
$995$		−	1.34123e8i		−	0.136155i
$996$	6.50997e8	−	8.46663e7i	0.658872	−	0.0856905i
$997$	7.52736e8	−	1.30378e9i	0.759551	−	1.31558i	−0.183528	−	0.983014i	$-0.558752\pi$
$997$	7.52736e8	−	1.30378e9i	0.759551	−	1.31558i	0.943080	−	0.332567i	$-0.107915\pi$
$998$	4.62927e8	+	2.28742e8i	0.465715	+	0.230120i
$999$		−	1.86034e8i		−	0.186594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.g.a.7.18	✓	116
4.3	odd	2	inner	76.7.g.a.7.20	yes	116
19.11	even	3	inner	76.7.g.a.11.20	yes	116
76.11	odd	6	inner	76.7.g.a.11.18	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.g.a.7.18	✓	116	1.1	even	1	trivial
76.7.g.a.7.20	yes	116	4.3	odd	2	inner
76.7.g.a.11.18	yes	116	76.11	odd	6	inner
76.7.g.a.11.20	yes	116	19.11	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.43934 - 6.65524i) q^{2} +(-40.1020 + 23.1529i) q^{3} +(-24.5845 + 59.0898i) q^{4} +(19.2234 + 33.2960i) q^{5} +(332.115 + 164.105i) q^{6} -622.494i q^{7} +(502.396 - 98.7039i) q^{8} +(707.614 - 1225.62i) q^{9} +O(q^{10})\)	\(q+(-4.43934 - 6.65524i) q^{2} +(-40.1020 + 23.1529i) q^{3} +(-24.5845 + 59.0898i) q^{4} +(19.2234 + 33.2960i) q^{5} +(332.115 + 164.105i) q^{6} -622.494i q^{7} +(502.396 - 98.7039i) q^{8} +(707.614 - 1225.62i) q^{9} +(136.253 - 275.749i) q^{10} +2041.42i q^{11} +(-382.212 - 2938.82i) q^{12} +(1561.55 - 2704.68i) q^{13} +(-4142.85 + 2763.46i) q^{14} +(-1541.80 - 890.157i) q^{15} +(-2887.20 - 2905.39i) q^{16} +(1377.30 + 2385.54i) q^{17} +(-11298.2 + 731.618i) q^{18} +(-4625.25 + 5064.88i) q^{19} +(-2440.05 + 317.344i) q^{20} +(14412.6 + 24963.3i) q^{21} +(13586.2 - 9062.58i) q^{22} +(-7179.53 - 4145.10i) q^{23} +(-17861.8 + 15590.1i) q^{24} +(7073.42 - 12251.5i) q^{25} +(-24932.6 + 1614.52i) q^{26} +31776.4i q^{27} +(36783.1 + 15303.7i) q^{28} +(-5257.45 + 9106.16i) q^{29} +(920.353 + 14212.7i) q^{30} -2120.77i q^{31} +(-6518.76 + 32113.0i) q^{32} +(-47264.9 - 81865.2i) q^{33} +(9762.10 - 19756.5i) q^{34} +(20726.6 - 11966.5i) q^{35} +(55025.5 + 71944.1i) q^{36} -5854.48 q^{37} +(54241.0 + 8297.42i) q^{38} +144618. i q^{39} +(12944.2 + 14830.3i) q^{40} +(36928.6 + 63962.3i) q^{41} +(102154. - 206740. i) q^{42} +(-85760.4 + 49513.8i) q^{43} +(-120627. - 50187.4i) q^{44} +54411.1 q^{45} +(4285.71 + 66183.0i) q^{46} +(-59854.6 - 34557.1i) q^{47} +(183051. + 49664.6i) q^{48} -269850. q^{49} +(-112938. + 7313.36i) q^{50} +(-110465. - 63776.8i) q^{51} +(121429. + 158765. i) q^{52} +(-52787.9 + 91431.3i) q^{53} +(211480. - 141066. i) q^{54} +(-67971.2 + 39243.2i) q^{55} +(-61442.6 - 312739. i) q^{56} +(68215.1 - 310200. i) q^{57} +(83943.3 - 5435.79i) q^{58} +(83908.5 - 48444.6i) q^{59} +(90503.5 - 69220.4i) q^{60} +(-204077. + 353472. i) q^{61} +(-14114.2 + 9414.80i) q^{62} +(-762944. - 440486. i) q^{63} +(242659. - 99176.8i) q^{64} +120073. q^{65} +(-335008. + 677987. i) q^{66} +(230256. + 132938. i) q^{67} +(-174821. + 22736.6i) q^{68} +383885. q^{69} +(-171652. - 84817.0i) q^{70} +(168474. - 97268.7i) q^{71} +(234529. - 685593. i) q^{72} +(-203411. - 352318. i) q^{73} +(25990.0 + 38963.0i) q^{74} +655081. i q^{75} +(-185573. - 397822. i) q^{76} +1.27078e6 q^{77} +(962466. - 642007. i) q^{78} +(16986.8 - 9807.34i) q^{79} +(41235.6 - 151984. i) q^{80} +(-219865. - 380817. i) q^{81} +(261746. - 529720. i) q^{82} +221516. i q^{83} +(-1.82940e6 + 237925. i) q^{84} +(-52952.7 + 91716.8i) q^{85} +(710246. + 350948. i) q^{86} -486901. i q^{87} +(201497. + 1.02560e6i) q^{88} +(-119079. + 206251. i) q^{89} +(-241550. - 362119. i) q^{90} +(-1.68365e6 - 972056. i) q^{91} +(421438. - 322332. i) q^{92} +(49101.9 + 85047.0i) q^{93} +(35729.3 + 551758. i) q^{94} +(-257553. - 56637.7i) q^{95} +(-482095. - 1.43873e6i) q^{96} +(360293. + 624046. i) q^{97} +(1.19796e6 + 1.79592e6i) q^{98} +(2.50202e6 + 1.44454e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Introduction

L-functions

Modular forms

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Database

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