LMFDB - Embedded newform 21.30.c.a.20.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.c (of order $2$, degree $1$, 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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.9
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1978.96i q^{2} +(6.63697e6 + 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 - 1.31343e10i) q^{6} +(1.76916e12 - 2.99987e11i) q^{7} -2.11714e12i q^{8} +(1.94684e13 + 6.58112e13i) q^{9} +O(q^{10})$	\(q-1978.96i q^{2} +(6.63697e6 + 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 - 1.31343e10i) q^{6} +(1.76916e12 - 2.99987e11i) q^{7} -2.11714e12i q^{8} +(1.94684e13 + 6.58112e13i) q^{9} +4.15753e13i q^{10} +1.97233e15i q^{11} +(3.53721e15 + 2.64235e15i) q^{12} +2.35122e16i q^{13} +(-5.93662e14 - 3.50109e15i) q^{14} +(-1.39434e17 - 1.04159e17i) q^{15} +2.81938e17 q^{16} -4.82044e17 q^{17} +(1.30238e17 - 3.85272e16i) q^{18} +5.67589e17i q^{19} -1.11967e19 q^{20} +(1.32292e19 + 6.78033e18i) q^{21} +3.90316e18 q^{22} -7.46696e19i q^{23} +(1.04966e19 - 1.40514e19i) q^{24} +2.55100e20 q^{25} +4.65296e19 q^{26} +(-1.97075e20 + 5.33310e20i) q^{27} +(9.42880e20 - 1.59879e20i) q^{28} -1.34770e21i q^{29} +(-2.06127e20 + 2.75934e20i) q^{30} -7.84435e20i q^{31} -1.69458e21i q^{32} +(-9.77865e21 + 1.30903e22i) q^{33} +9.53945e20i q^{34} +(-3.71676e22 + 6.30233e21i) q^{35} +(1.03758e22 + 3.50744e22i) q^{36} -8.59247e22 q^{37} +1.12324e21 q^{38} +(-1.16571e23 + 1.56050e23i) q^{39} +4.44783e22i q^{40} +1.02991e23 q^{41} +(1.34180e22 - 2.61800e22i) q^{42} +2.29840e23 q^{43} +1.05116e24i q^{44} +(-4.09006e23 - 1.38261e24i) q^{45} -1.47768e23 q^{46} +1.10078e21 q^{47} +(1.87122e24 + 1.39783e24i) q^{48} +(3.03992e24 - 1.06145e24i) q^{49} -5.04833e23i q^{50} +(-3.19931e24 - 2.38993e24i) q^{51} +1.25309e25i q^{52} +1.34593e25i q^{53} +(1.05540e24 + 3.90003e23i) q^{54} -4.14360e25i q^{55} +(-6.35114e23 - 3.74555e24i) q^{56} +(-2.81406e24 + 3.76707e24i) q^{57} -2.66705e24 q^{58} -4.98939e25 q^{59} +(-7.43120e25 - 5.55122e25i) q^{60} +1.41438e26i q^{61} -1.55236e24 q^{62} +(5.41852e25 + 1.10590e26i) q^{63} +1.48011e26 q^{64} -4.93960e26i q^{65} +(2.59052e25 + 1.93516e25i) q^{66} +2.07066e26 q^{67} -2.56907e26 q^{68} +(3.70206e26 - 4.95580e26i) q^{69} +(1.24720e25 + 7.35532e25i) q^{70} +4.38368e24i q^{71} +(1.39332e26 - 4.12174e25i) q^{72} -1.18319e27i q^{73} +1.70041e26i q^{74} +(1.69309e27 + 1.26477e27i) q^{75} +3.02499e26i q^{76} +(5.91673e26 + 3.48936e27i) q^{77} +(3.08816e26 + 2.30690e26i) q^{78} -4.92576e27 q^{79} -5.92315e27 q^{80} +(-3.95209e27 + 2.56248e27i) q^{81} -2.03815e26i q^{82} -1.26288e28 q^{83} +(7.05054e27 + 3.61361e27i) q^{84} +1.01271e28 q^{85} -4.54844e26i q^{86} +(6.68179e27 - 8.94465e27i) q^{87} +4.17570e27 q^{88} +3.53689e27 q^{89} +(-2.73612e27 + 8.09407e26i) q^{90} +(7.05334e27 + 4.15967e28i) q^{91} -3.97955e28i q^{92} +(3.88916e27 - 5.20627e27i) q^{93} -2.17840e24i q^{94} -1.19243e28i q^{95} +(8.40157e27 - 1.12469e28i) q^{96} -6.07788e28i q^{97} +(-2.10056e27 - 6.01588e27i) q^{98} +(-1.29801e29 + 3.83982e28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1978.96i		−	0.0854087i	−0.999088	−	0.0427043i	$-0.986403\pi$
$2$		−	1978.96i		−	0.0854087i	0.999088	−	0.0427043i	$-0.0135973\pi$
$3$	6.63697e6	+	4.95792e6i	0.801146	+	0.598469i
$3$	6.63697e6	+	4.95792e6i	0.801146	+	0.598469i
$4$	5.32955e8			0.992705
$5$	−2.10087e10			−1.53934			−0.769669	−	0.638444i	$-0.779579\pi$
$5$	−2.10087e10			−1.53934			−0.769669	+	0.638444i	$0.779579\pi$
$6$	9.81152e9	−	1.31343e10i	0.0511144	−	0.0684248i
$7$	1.76916e12	−	2.99987e11i	0.985927	−	0.167179i
$7$	1.76916e12	−	2.99987e11i	0.985927	−	0.167179i
$8$		−	2.11714e12i		−	0.170194i
$9$	1.94684e13	+	6.58112e13i	0.283671	+	0.958922i
$10$			4.15753e13i			0.131473i
$11$			1.97233e15i			1.56598i	0.622036	+	0.782989i	$0.286306\pi$
$11$			1.97233e15i			1.56598i	−0.622036	+	0.782989i	$0.713694\pi$
$12$	3.53721e15	+	2.64235e15i	0.795302	+	0.594103i
$13$			2.35122e16i			1.65621i	0.560577	+	0.828103i	$0.310580\pi$
$13$			2.35122e16i			1.65621i	−0.560577	+	0.828103i	$0.689420\pi$
$14$	−5.93662e14	−	3.50109e15i	−0.0142785	−	0.0842067i
$15$	−1.39434e17	−	1.04159e17i	−1.23323	−	0.921245i
$16$	2.81938e17			0.978169
$17$	−4.82044e17			−0.694348			−0.347174	−	0.937801i	$-0.612859\pi$
$17$	−4.82044e17			−0.694348			−0.347174	+	0.937801i	$0.612859\pi$
$18$	1.30238e17	−	3.85272e16i	0.0819002	−	0.0242279i
$19$			5.67589e17i			0.162970i	0.996675	+	0.0814848i	$0.0259662\pi$
$19$			5.67589e17i			0.162970i	−0.996675	+	0.0814848i	$0.974034\pi$
$20$	−1.11967e19			−1.52811
$21$	1.32292e19	+	6.78033e18i	0.889923	+	0.456112i
$22$	3.90316e18			0.133748
$23$		−	7.46696e19i		−	1.34304i	−0.740985	−	0.671522i	$-0.765641\pi$
$23$		−	7.46696e19i		−	1.34304i	0.740985	−	0.671522i	$-0.234359\pi$
$24$	1.04966e19	−	1.40514e19i	0.101856	−	0.136351i
$25$	2.55100e20			1.36956
$26$	4.65296e19			0.141454
$27$	−1.97075e20	+	5.33310e20i	−0.346623	+	0.938005i
$28$	9.42880e20	−	1.59879e20i	0.978735	−	0.165959i
$29$		−	1.34770e21i		−	0.841051i	−0.907281	−	0.420526i	$-0.861846\pi$
$29$		−	1.34770e21i		−	0.841051i	0.907281	−	0.420526i	$-0.138154\pi$
$30$	−2.06127e20	+	2.75934e20i	−0.0786823	+	0.105329i
$31$		−	7.84435e20i		−	0.186128i	−0.995660	−	0.0930641i	$-0.970334\pi$
$31$		−	7.84435e20i		−	0.186128i	0.995660	−	0.0930641i	$-0.0296662\pi$
$32$		−	1.69458e21i		−	0.253738i
$33$	−9.77865e21	+	1.30903e22i	−0.937188	+	1.25458i
$34$			9.53945e20i			0.0593033i
$35$	−3.71676e22	+	6.30233e21i	−1.51767	+	0.257344i
$36$	1.03758e22	+	3.50744e22i	0.281602	+	0.951927i
$37$	−8.59247e22			−1.56745			−0.783723	−	0.621110i	$-0.786682\pi$
$37$	−8.59247e22			−1.56745			−0.783723	+	0.621110i	$0.786682\pi$
$38$	1.12324e21			0.0139190
$39$	−1.16571e23	+	1.56050e23i	−0.991187	+	1.32686i
$40$			4.44783e22i			0.261986i
$41$	1.02991e23			0.424066			0.212033	−	0.977263i	$-0.431992\pi$
$41$	1.02991e23			0.424066			0.212033	+	0.977263i	$0.431992\pi$
$42$	1.34180e22	−	2.61800e22i	0.0389559	−	0.0760071i
$43$	2.29840e23			0.474387			0.237194	−	0.971462i	$-0.423772\pi$
$43$	2.29840e23			0.474387			0.237194	+	0.971462i	$0.423772\pi$
$44$			1.05116e24i			1.55455i
$45$	−4.09006e23	−	1.38261e24i	−0.436665	−	1.47610i
$46$	−1.47768e23			−0.114708
$47$	1.10078e21			0.000625579			0.000312789	−	1.00000i	$-0.499900\pi$
$47$	1.10078e21			0.000625579			0.000312789		1.00000i	$0.499900\pi$
$48$	1.87122e24	+	1.39783e24i	0.783657	+	0.585404i
$49$	3.03992e24	−	1.06145e24i	0.944103	−	0.329652i
$50$		−	5.04833e23i		−	0.116972i
$51$	−3.19931e24	−	2.38993e24i	−0.556274	−	0.415545i
$52$			1.25309e25i			1.64412i
$53$			1.34593e25i			1.33975i	0.742474	+	0.669875i	$0.233652\pi$
$53$			1.34593e25i			1.33975i	−0.742474	+	0.669875i	$0.766348\pi$
$54$	1.05540e24	+	3.90003e23i	0.0801137	+	0.0296046i
$55$		−	4.14360e25i		−	2.41057i
$56$	−6.35114e23	−	3.74555e24i	−0.0284528	−	0.167799i
$57$	−2.81406e24	+	3.76707e24i	−0.0975322	+	0.130563i
$58$	−2.66705e24			−0.0718331
$59$	−4.98939e25			−1.04880			−0.524401	−	0.851471i	$-0.675711\pi$
$59$	−4.98939e25			−1.04880			−0.524401	+	0.851471i	$0.675711\pi$
$60$	−7.43120e25	−	5.55122e25i	−1.22424	−	0.914525i
$61$			1.41438e26i			1.83351i	0.399447	+	0.916756i	$0.369202\pi$
$61$			1.41438e26i			1.83351i	−0.399447	+	0.916756i	$0.630798\pi$
$62$	−1.55236e24			−0.0158970
$63$	5.41852e25	+	1.10590e26i	0.439990	+	0.898003i
$64$	1.48011e26			0.956498
$65$		−	4.93960e26i		−	2.54946i
$66$	2.59052e25	+	1.93516e25i	0.107152	+	0.0800440i
$67$	2.07066e26			0.688692			0.344346	−	0.938843i	$-0.388101\pi$
$67$	2.07066e26			0.688692			0.344346	+	0.938843i	$0.388101\pi$
$68$	−2.56907e26			−0.689283
$69$	3.70206e26	−	4.95580e26i	0.803770	−	1.07597i
$70$	1.24720e25	+	7.35532e25i	0.0219794	+	0.129622i
$71$			4.38368e24i			0.00628916i	0.999995	+	0.00314458i	$0.00100095\pi$
$71$			4.38368e24i			0.00628916i	−0.999995	+	0.00314458i	$0.998999\pi$
$72$	1.39332e26	−	4.12174e25i	0.163203	−	0.0482792i
$73$		−	1.18319e27i		−	1.13468i	−0.823483	−	0.567342i	$-0.807972\pi$
$73$		−	1.18319e27i		−	1.13468i	0.823483	−	0.567342i	$-0.192028\pi$
$74$			1.70041e26i			0.133874i
$75$	1.69309e27	+	1.26477e27i	1.09722	+	0.819638i
$76$			3.02499e26i			0.161781i
$77$	5.91673e26	+	3.48936e27i	0.261798	+	1.54394i
$78$	3.08816e26	+	2.30690e26i	0.113326	+	0.0846559i
$79$	−4.92576e27			−1.50273			−0.751364	−	0.659888i	$-0.770604\pi$
$79$	−4.92576e27			−1.50273			−0.751364	+	0.659888i	$0.770604\pi$
$80$	−5.92315e27			−1.50573
$81$	−3.95209e27	+	2.56248e27i	−0.839062	+	0.544036i
$82$		−	2.03815e26i		−	0.0362189i
$83$	−1.26288e28			−1.88248			−0.941241	−	0.337736i	$-0.890339\pi$
$83$	−1.26288e28			−1.88248			−0.941241	+	0.337736i	$0.890339\pi$
$84$	7.05054e27	+	3.61361e27i	0.883431	+	0.452784i
$85$	1.01271e28			1.06884
$86$		−	4.54844e26i		−	0.0405168i
$87$	6.68179e27	−	8.94465e27i	0.503343	−	0.673805i
$88$	4.17570e27			0.266520
$89$	3.53689e27			0.191631			0.0958157	−	0.995399i	$-0.469454\pi$
$89$	3.53689e27			0.191631			0.0958157	+	0.995399i	$0.469454\pi$
$90$	−2.73612e27	+	8.09407e26i	−0.126072	+	0.0372950i
$91$	7.05334e27	+	4.15967e28i	0.276882	+	1.63290i
$92$		−	3.97955e28i		−	1.33325i
$93$	3.88916e27	−	5.20627e27i	0.111392	−	0.149116i
$94$		−	2.17840e24i		−	5.34299e-5i
$95$		−	1.19243e28i		−	0.250865i
$96$	8.40157e27	−	1.12469e28i	0.151854	−	0.203282i
$97$		−	6.07788e28i		−	0.945283i	−0.881255	−	0.472642i	$-0.843300\pi$
$97$		−	6.07788e28i		−	0.945283i	0.881255	−	0.472642i	$-0.156700\pi$
$98$	−2.10056e27	−	6.01588e27i	−0.0281551	−	0.0806345i
$99$	−1.29801e29	+	3.83982e28i	−1.50165	+	0.444222i
$100$	1.35957e29			1.35957
$101$	−7.18680e28			−0.622123			−0.311061	−	0.950390i	$-0.600684\pi$
$101$	−7.18680e28			−0.622123			−0.311061	+	0.950390i	$0.600684\pi$
$102$	−4.72958e27	+	6.33131e27i	−0.0354912	+	0.0475106i
$103$			1.31814e29i			0.858660i	0.903148	+	0.429330i	$0.141250\pi$
$103$			1.31814e29i			0.858660i	−0.903148	+	0.429330i	$0.858750\pi$
$104$	4.97786e28			0.281877
$105$	−2.77927e29	−	1.42446e29i	−1.36989	−	0.702109i
$106$	2.66355e28			0.114426
$107$			2.73974e29i			1.02717i	0.858037	+	0.513587i	$0.171684\pi$
$107$			2.73974e29i			1.02717i	−0.858037	+	0.513587i	$0.828316\pi$
$108$	−1.05032e29	+	2.84230e29i	−0.344094	+	0.931162i
$109$	2.85051e28			0.0817030			0.0408515	−	0.999165i	$-0.486993\pi$
$109$	2.85051e28			0.0817030			0.0408515	+	0.999165i	$0.486993\pi$
$110$	−8.20002e28			−0.205883
$111$	−5.70280e29	−	4.26008e29i	−1.25575	−	0.938068i
$112$	4.98793e29	−	8.45777e28i	0.964403	−	0.163529i
$113$			2.49842e29i			0.424647i	0.977199	+	0.212324i	$0.0681031\pi$
$113$			2.49842e29i			0.424647i	−0.977199	+	0.212324i	$0.931897\pi$
$114$	7.45488e27	+	5.56891e27i	0.0111512	+	0.00833009i
$115$			1.56871e30i			2.06740i
$116$		−	7.18263e29i		−	0.834916i
$117$	−1.54736e30	+	4.57745e29i	−1.58817	+	0.469817i
$118$			9.87381e28i			0.0895768i
$119$	−8.52811e29	+	1.44607e29i	−0.684576	+	0.116080i
$120$	−2.20520e29	+	2.95202e29i	−0.156791	+	0.209889i
$121$	−2.30378e30			−1.45229
$122$	2.79900e29			0.156598
$123$	6.83548e29	+	5.10621e29i	0.339739	+	0.253790i
$124$		−	4.18068e29i		−	0.184770i
$125$	−1.44615e30			−0.568875
$126$	2.18853e29	−	1.07230e29i	0.0766972	−	0.0375789i
$127$	1.61971e29			0.0506155			0.0253078	−	0.999680i	$-0.491943\pi$
$127$	1.61971e29			0.0506155			0.0253078	+	0.999680i	$0.491943\pi$
$128$		−	1.20268e30i		−	0.335432i
$129$	1.52544e30	+	1.13953e30i	0.380053	+	0.283906i
$130$	−9.77526e29			−0.217746
$131$	−4.01899e30			−0.801093			−0.400546	−	0.916276i	$-0.631180\pi$
$131$	−4.01899e30			−0.801093			−0.400546	+	0.916276i	$0.631180\pi$
$132$	−5.21158e30	+	6.97654e30i	−0.930352	+	1.24543i
$133$	1.70269e29	+	1.00415e30i	0.0272450	+	0.160676i
$134$		−	4.09776e29i		−	0.0588203i
$135$	4.14028e30	−	1.12041e31i	0.533569	−	1.44391i
$136$			1.02055e30i			0.118174i
$137$		−	9.93083e30i		−	1.03404i	−0.855973	−	0.517020i	$-0.827041\pi$
$137$		−	9.93083e30i		−	1.03404i	0.855973	−	0.517020i	$-0.172959\pi$
$138$	−9.80733e29	−	7.32623e29i	−0.0918976	−	0.0686489i
$139$			1.76006e31i			1.48530i	0.669681	+	0.742649i	$0.266431\pi$
$139$			1.76006e31i			1.48530i	−0.669681	+	0.742649i	$0.733569\pi$
$140$	−1.98087e31	+	3.35885e30i	−1.50660	+	0.255467i
$141$	7.30586e27	+	5.45759e27i	0.000501180	+	0.000374389i
$142$	8.67512e27			0.000537149
$143$	−4.63738e31			−2.59358
$144$	5.48889e30	+	1.85547e31i	0.277478	+	0.937988i
$145$			2.83134e31i			1.29466i
$146$	−2.34149e30			−0.0969118
$147$	2.54384e31	+	8.02689e30i	0.953650	+	0.300917i
$148$	−4.57939e31			−1.55601
$149$			2.16357e31i			0.666759i	0.942793	+	0.333380i	$0.108189\pi$
$149$			2.16357e31i			0.666759i	−0.942793	+	0.333380i	$0.891811\pi$
$150$	2.50292e30	−	3.35056e30i	0.0700042	−	0.0937118i
$151$	−1.76044e28			−0.000447151			−0.000223576	−	1.00000i	$-0.500071\pi$
$151$	−1.76044e28			−0.000447151			−0.000223576		1.00000i	$0.500071\pi$
$152$	1.20167e30			0.0277365
$153$	−9.38464e30	−	3.17239e31i	−0.196966	−	0.665825i
$154$	6.90530e30	−	1.17090e30i	0.131866	−	0.0223598i
$155$			1.64799e31i			0.286514i
$156$	−6.21273e31	+	8.31674e31i	−0.983956	+	1.31718i
$157$		−	6.76929e31i		−	0.977233i	−0.872499	−	0.488617i	$-0.837502\pi$
$157$		−	6.76929e31i		−	0.977233i	0.872499	−	0.488617i	$-0.162498\pi$
$158$			9.74788e30i			0.128346i
$159$	−6.67303e31	+	8.93293e31i	−0.801798	+	1.07334i
$160$			3.56008e31i			0.390589i
$161$	−2.23999e31	−	1.32102e32i	−0.224528	−	1.32414i
$162$	5.07105e30	+	7.82102e30i	0.0464654	+	0.0716631i
$163$	1.32662e32			1.11180			0.555900	−	0.831249i	$-0.312374\pi$
$163$	1.32662e32			1.11180			0.555900	+	0.831249i	$0.312374\pi$
$164$	5.48895e31			0.420972
$165$	2.05437e32	−	2.75010e32i	1.44265	−	1.93122i
$166$			2.49919e31i			0.160780i
$167$	6.46226e31			0.381062			0.190531	−	0.981681i	$-0.438979\pi$
$167$	6.46226e31			0.381062			0.190531	+	0.981681i	$0.438979\pi$
$168$	1.43549e31	−	2.80080e31i	0.0776276	−	0.151460i
$169$	−3.51284e32			−1.74302
$170$		−	2.00411e31i		−	0.0912878i
$171$	−3.73537e31	+	1.10501e31i	−0.156275	+	0.0462297i
$172$	1.22494e32			0.470927
$173$	1.74835e32			0.617959			0.308980	−	0.951069i	$-0.400012\pi$
$173$	1.74835e32			0.617959			0.308980	+	0.951069i	$0.400012\pi$
$174$	−1.77011e31	−	1.32230e31i	−0.0575488	−	0.0429898i
$175$	4.51312e32	−	7.65267e31i	1.35028	−	0.228961i
$176$			5.56075e32i			1.53179i
$177$	−3.31145e32	−	2.47370e32i	−0.840244	−	0.627675i
$178$		−	6.99936e30i		−	0.0163670i
$179$		−	1.94233e32i		−	0.418749i	−0.977836	−	0.209375i	$-0.932857\pi$
$179$		−	1.94233e32i		−	0.418749i	0.977836	−	0.209375i	$-0.0671428\pi$
$180$	−2.17982e32	−	7.36866e32i	−0.433480	−	1.46534i
$181$		−	2.90896e31i		−	0.0533824i	−0.999644	−	0.0266912i	$-0.991503\pi$
$181$		−	2.90896e31i		−	0.0533824i	0.999644	−	0.0266912i	$-0.00849707\pi$
$182$	8.23182e31	−	1.39583e31i	0.139464	−	0.0236481i
$183$	−7.01239e32	+	9.38721e32i	−1.09730	+	1.46891i
$184$	−1.58086e32			−0.228578
$185$	1.80516e33			2.41283
$186$	−1.03030e31	−	7.69650e30i	−0.0127358	−	0.00951383i
$187$		−	9.50749e32i		−	1.08733i
$188$	5.86666e29			0.000621016
$189$	−1.88670e32	+	1.00263e33i	−0.184930	+	0.982752i
$190$	−2.35977e31			−0.0214261
$191$			7.24655e32i			0.609744i	0.952393	+	0.304872i	$0.0986136\pi$
$191$			7.24655e32i			0.609744i	−0.952393	+	0.304872i	$0.901386\pi$
$192$	9.82344e32	+	7.33826e32i	0.766295	+	0.572434i
$193$	1.23473e33			0.893285			0.446642	−	0.894713i	$-0.352620\pi$
$193$	1.23473e33			0.893285			0.446642	+	0.894713i	$0.352620\pi$
$194$	−1.20279e32			−0.0807354
$195$	2.44901e33	−	3.27840e33i	1.52577	−	2.04249i
$196$	1.62014e33	−	5.65703e32i	0.937216	−	0.327247i
$197$			3.28498e32i			0.176511i	0.996098	+	0.0882556i	$0.0281292\pi$
$197$			3.28498e32i			0.176511i	−0.996098	+	0.0882556i	$0.971871\pi$
$198$	7.59884e31	+	2.56871e32i	0.0379404	+	0.128254i
$199$		−	2.51190e33i		−	1.16582i	−0.812536	−	0.582911i	$-0.801914\pi$
$199$		−	2.51190e33i		−	1.16582i	0.812536	−	0.582911i	$-0.198086\pi$
$200$		−	5.40083e32i		−	0.233091i
$201$	1.37429e33	+	1.02662e33i	0.551743	+	0.412160i
$202$			1.42224e32i			0.0531347i
$203$	−4.04292e32	−	2.38429e33i	−0.140606	−	0.829215i
$204$	−1.70509e33	−	1.27373e33i	−0.552216	−	0.412514i
$205$	−2.16370e33			−0.652780
$206$	2.60854e32			0.0733370
$207$	4.91409e33	−	1.45370e33i	1.28787	−	0.380982i
$208$			6.62898e33i			1.62005i
$209$	−1.11947e33			−0.255207
$210$	−2.81894e32	+	5.50006e32i	−0.0599662	+	0.117001i
$211$	−7.51239e33			−1.49170			−0.745852	−	0.666112i	$-0.767957\pi$
$211$	−7.51239e33			−1.49170			−0.745852	+	0.666112i	$0.767957\pi$
$212$			7.17322e33i			1.32998i
$213$	−2.17339e31	+	2.90944e31i	−0.00376386	+	0.00503854i
$214$	5.42183e32			0.0877296
$215$	−4.82863e33			−0.730242
$216$	1.12909e33	+	4.17235e32i	0.159643	+	0.0589932i
$217$	−2.35320e32	−	1.38779e33i	−0.0311166	−	0.183509i
$218$		−	5.64104e31i		−	0.00697814i
$219$	5.86618e33	−	7.85283e33i	0.679072	−	0.909047i
$220$		−	2.20835e34i		−	2.39298i
$221$		−	1.13339e34i		−	1.14998i
$222$	−8.43052e32	+	1.12856e33i	−0.0801191	+	0.107252i
$223$			1.18591e34i			1.05592i	0.849268	+	0.527962i	$0.177044\pi$
$223$			1.18591e34i			1.05592i	−0.849268	+	0.527962i	$0.822956\pi$
$224$	−5.08350e32	−	2.99797e33i	−0.0424196	−	0.250167i
$225$	4.96640e33	+	1.67884e34i	0.388504	+	1.31330i
$226$	4.94427e32			0.0362685
$227$	1.14437e34			0.787392			0.393696	−	0.919241i	$-0.371196\pi$
$227$	1.14437e34			0.787392			0.393696	+	0.919241i	$0.371196\pi$
$228$	−1.49977e33	+	2.00768e33i	−0.0968207	+	0.129610i
$229$			1.47875e34i			0.895941i	0.894048	+	0.447971i	$0.147853\pi$
$229$			1.47875e34i			0.895941i	−0.894048	+	0.447971i	$0.852147\pi$
$230$	3.10441e33			0.176574
$231$	−1.33730e34	+	2.60923e34i	−0.714261	+	1.39360i
$232$	−2.85327e33			−0.143142
$233$			2.51857e34i			1.18712i	0.804791	+	0.593558i	$0.202277\pi$
$233$			2.51857e34i			1.18712i	−0.804791	+	0.593558i	$0.797723\pi$
$234$	9.05859e32	+	3.06217e33i	0.0401265	+	0.135644i
$235$	−2.31260e31			−0.000962977
$236$	−2.65912e34			−1.04115
$237$	−3.26921e34	−	2.44215e34i	−1.20391	−	0.899336i
$238$	2.86171e32	+	1.68768e33i	0.00991424	+	0.0584687i
$239$		−	1.71355e34i		−	0.558635i	−0.960199	−	0.279318i	$-0.909892\pi$
$239$		−	1.71355e34i		−	0.558635i	0.960199	−	0.279318i	$-0.0901082\pi$
$240$	−3.93118e34	−	2.93665e34i	−1.20631	−	0.901133i
$241$			1.04237e34i			0.301145i	0.988599	+	0.150573i	$0.0481118\pi$
$241$			1.04237e34i			0.301145i	−0.988599	+	0.150573i	$0.951888\pi$
$242$			4.55908e33i			0.124038i
$243$	−3.89345e34	−	2.58702e33i	−0.997800	−	0.0662993i
$244$			7.53801e34i			1.82014i
$245$	−6.38647e34	+	2.22996e34i	−1.45329	+	0.507445i
$246$	1.01050e33	−	1.35271e33i	0.0216759	−	0.0290166i
$247$	−1.33452e34			−0.269911
$248$	−1.66076e33			−0.0316780
$249$	−8.38172e34	−	6.26127e34i	−1.50814	−	1.12661i
$250$			2.86186e33i			0.0485869i
$251$	6.64584e34			1.06483			0.532416	−	0.846483i	$-0.321284\pi$
$251$	6.64584e34			1.06483			0.532416	+	0.846483i	$0.321284\pi$
$252$	2.88782e34	+	5.89394e34i	0.436780	+	0.891452i
$253$	1.47273e35			2.10318
$254$		−	3.20534e32i		−	0.00432300i
$255$	6.72133e34	+	5.02094e34i	0.856293	+	0.639664i
$256$	7.70827e34			0.927849
$257$	−9.04327e34			−1.02871			−0.514357	−	0.857576i	$-0.671970\pi$
$257$	−9.04327e34			−1.02871			−0.514357	+	0.857576i	$0.671970\pi$
$258$	2.25508e33	−	3.01879e33i	0.0242480	−	0.0324599i
$259$	−1.52014e35	+	2.57763e34i	−1.54539	+	0.262043i
$260$		−	2.63258e35i		−	2.53086i
$261$	8.86938e34	−	2.62376e34i	0.806503	−	0.238582i
$262$			7.95341e33i			0.0684203i
$263$			6.75085e34i			0.549541i	0.961510	+	0.274770i	$0.0886018\pi$
$263$			6.75085e34i			0.549541i	−0.961510	+	0.274770i	$0.911398\pi$
$264$	2.77140e34	+	2.07028e34i	0.213522	+	0.159504i
$265$		−	2.82763e35i		−	2.06233i
$266$	1.98718e33	−	3.36956e32i	0.0137231	−	0.00232696i
$267$	2.34742e34	+	1.75356e34i	0.153525	+	0.114685i
$268$	1.10357e35			0.683668
$269$	1.02148e35			0.599546			0.299773	−	0.954011i	$-0.403089\pi$
$269$	1.02148e35			0.599546			0.299773	+	0.954011i	$0.403089\pi$
$270$	−2.21725e34	−	8.19345e33i	−0.123322	−	0.0455714i
$271$			1.68808e35i			0.889896i	0.895556	+	0.444948i	$0.146778\pi$
$271$			1.68808e35i			0.889896i	−0.895556	+	0.444948i	$0.853222\pi$
$272$	−1.35906e35			−0.679190
$273$	−1.59420e35	+	3.11046e35i	−0.755414	+	1.47389i
$274$	−1.96527e34			−0.0883160
$275$			5.03142e35i			2.14470i
$276$	1.97303e35	−	2.64122e35i	0.797906	−	1.06813i
$277$	−2.12651e35			−0.816039			−0.408019	−	0.912973i	$-0.633780\pi$
$277$	−2.12651e35			−0.816039			−0.408019	+	0.912973i	$0.633780\pi$
$278$	3.48309e34			0.126857
$279$	5.16246e34	−	1.52717e34i	0.178482	−	0.0527992i
$280$	1.33429e34	+	7.86891e34i	0.0437985	+	0.258299i
$281$		−	1.60703e35i		−	0.500937i	−0.968125	−	0.250469i	$-0.919415\pi$
$281$		−	1.60703e35i		−	0.500937i	0.968125	−	0.250469i	$-0.0805847\pi$
$282$	1.08003e31	−	1.44580e31i	3.19761e−5	−	4.28051e-5i
$283$		−	2.55313e35i		−	0.718075i	−0.933323	−	0.359038i	$-0.883105\pi$
$283$		−	2.55313e35i		−	0.718075i	0.933323	−	0.359038i	$-0.116895\pi$
$284$			2.33630e33i			0.00624328i
$285$	5.91197e34	−	7.91412e34i	0.150135	−	0.200980i
$286$			9.17718e34i			0.221514i
$287$	1.82207e35	−	3.08959e34i	0.418098	−	0.0708947i
$288$	1.11522e35	−	3.29907e34i	0.243315	−	0.0719782i
$289$	−2.49602e35			−0.517881
$290$	5.60311e34			0.110575
$291$	3.01336e35	−	4.03387e35i	0.565722	−	0.757310i
$292$		−	6.30589e35i		−	1.12641i
$293$	2.44043e35			0.414845			0.207422	−	0.978251i	$-0.433493\pi$
$293$	2.44043e35			0.414845			0.207422	+	0.978251i	$0.433493\pi$
$294$	1.58849e34	−	5.03416e34i	0.0257009	−	0.0814500i
$295$	1.04821e36			1.61446
$296$			1.81915e35i			0.266771i
$297$	−1.05186e36	−	3.88697e35i	−1.46889	−	0.542803i
$298$	4.28161e34			0.0569470
$299$	1.75564e36			2.22436
$300$	9.02342e35	+	6.74063e35i	1.08921	+	0.813659i
$301$	4.06623e35	−	6.89489e34i	0.467711	−	0.0793073i
$302$			3.48383e31i			3.81906e-5i
$303$	−4.76986e35	−	3.56316e35i	−0.498411	−	0.372321i
$304$			1.60025e35i			0.159412i
$305$		−	2.97143e36i		−	2.82239i
$306$	−6.27802e34	+	1.85718e34i	−0.0568672	+	0.0168226i
$307$		−	8.70461e35i		−	0.752043i	−0.926611	−	0.376022i	$-0.877292\pi$
$307$		−	8.70461e35i		−	0.752043i	0.926611	−	0.376022i	$-0.122708\pi$
$308$	3.15335e35	+	1.85967e36i	0.259888	+	1.53268i
$309$	−6.53522e35	+	8.74844e35i	−0.513881	+	0.687912i
$310$	3.26131e34			0.0244708
$311$	1.19319e36			0.854446			0.427223	−	0.904146i	$-0.359492\pi$
$311$	1.19319e36			0.854446			0.427223	+	0.904146i	$0.359492\pi$
$312$	3.30379e35	+	2.46798e35i	0.225824	+	0.168694i
$313$			1.55805e35i			0.101669i	0.998707	+	0.0508345i	$0.0161881\pi$
$313$			1.55805e35i			0.101669i	−0.998707	+	0.0508345i	$0.983812\pi$
$314$	−1.33961e35			−0.0834642
$315$	−1.13836e36	−	2.32335e36i	−0.677293	−	1.38233i
$316$	−2.62521e36			−1.49177
$317$			2.35251e36i			1.27694i	0.769645	+	0.638472i	$0.220433\pi$
$317$			2.35251e36i			1.27694i	−0.769645	+	0.638472i	$0.779567\pi$
$318$	1.76779e35	+	1.32057e35i	0.0916722	+	0.0684805i
$319$	2.65811e36			1.31707
$320$	−3.10951e36			−1.47237
$321$	−1.35834e36	+	1.81836e36i	−0.614731	+	0.822917i
$322$	−2.61425e35	+	4.43285e34i	−0.113093	+	0.0191766i
$323$		−	2.73603e35i		−	0.113158i
$324$	−2.10628e36	+	1.36569e36i	−0.832941	+	0.540068i
$325$			5.99796e36i			2.26827i
$326$		−	2.62533e35i		−	0.0949573i
$327$	1.89187e35	+	1.41326e35i	0.0654560	+	0.0488967i
$328$		−	2.18046e35i		−	0.0721736i
$329$	1.94745e33	−	3.30220e32i	0.000616775	−	0.000104583i
$330$	−5.44233e35	−	4.06551e35i	−0.164943	−	0.123215i
$331$	2.47394e36			0.717600			0.358800	−	0.933414i	$-0.383186\pi$
$331$	2.47394e36			0.717600			0.358800	+	0.933414i	$0.383186\pi$
$332$	−6.73059e36			−1.86875
$333$	−1.67282e36	−	5.65480e36i	−0.444639	−	1.50306i
$334$		−	1.27886e35i		−	0.0325460i
$335$	−4.35019e36			−1.06013
$336$	3.72980e36	+	1.91163e36i	0.870495	+	0.446154i
$337$	8.95109e35			0.200098			0.100049	−	0.994983i	$-0.468100\pi$
$337$	8.95109e35			0.200098			0.100049	+	0.994983i	$0.468100\pi$
$338$			6.95177e35i			0.148869i
$339$	−1.23870e36	+	1.65820e36i	−0.254138	+	0.340205i
$340$	5.39729e36			1.06104
$341$	1.54716e36			0.291473
$342$	2.18676e34	+	7.39214e34i	0.00394842	+	0.0133472i
$343$	5.05968e36	−	2.78980e36i	0.875705	−	0.482846i
$344$		−	4.86604e35i		−	0.0807380i
$345$	−7.77754e36	+	1.04115e37i	−1.23727	+	1.65629i
$346$		−	3.45991e35i		−	0.0527791i
$347$		−	7.30251e36i		−	1.06830i	−0.845388	−	0.534152i	$-0.820631\pi$
$347$		−	7.30251e36i		−	1.06830i	0.845388	−	0.534152i	$-0.179369\pi$
$348$	3.56109e36	−	4.76710e36i	0.499671	−	0.668890i
$349$			6.48377e36i			0.872688i	0.899780	+	0.436344i	$0.143727\pi$
$349$			6.48377e36i			0.872688i	−0.899780	+	0.436344i	$0.856273\pi$
$350$	−1.51443e35	−	8.93128e35i	−0.0195552	−	0.115326i
$351$	−1.25393e37	−	4.63366e36i	−1.55353	−	0.574078i
$352$	3.34226e36			0.397349
$353$	−7.12394e36			−0.812806			−0.406403	−	0.913694i	$-0.633217\pi$
$353$	−7.12394e36			−0.812806			−0.406403	+	0.913694i	$0.633217\pi$
$354$	−4.89535e35	+	6.55322e35i	−0.0536089	+	0.0717641i
$355$		−	9.20953e34i		−	0.00968114i
$356$	1.88500e36			0.190233
$357$	−6.37703e36	−	3.26842e36i	−0.617916	−	0.316700i
$358$	−3.84379e35			−0.0357648
$359$		−	9.29988e36i		−	0.831013i	−0.909590	−	0.415507i	$-0.863604\pi$
$359$		−	9.29988e36i		−	0.831013i	0.909590	−	0.415507i	$-0.136396\pi$
$360$	−2.92717e36	+	8.65924e35i	−0.251224	+	0.0743179i
$361$	1.18077e37			0.973441
$362$	−5.75670e34			−0.00455932
$363$	−1.52901e37	−	1.14219e37i	−1.16349	−	0.869148i
$364$	3.75911e36	+	2.21692e37i	0.274862	+	1.62099i
$365$			2.48574e37i			1.74666i
$366$	1.85769e36	+	1.38772e36i	0.125458	+	0.0937189i
$367$		−	1.60683e36i		−	0.104306i	−0.998639	−	0.0521532i	$-0.983392\pi$
$367$		−	1.60683e36i		−	0.104306i	0.998639	−	0.0521532i	$-0.0166084\pi$
$368$		−	2.10522e37i		−	1.31372i
$369$	2.00507e36	+	6.77796e36i	0.120295	+	0.406646i
$370$		−	3.57235e36i		−	0.206076i
$371$	4.03763e36	+	2.38117e37i	0.223977	+	1.32090i
$372$	2.07275e36	−	2.77471e36i	0.110579	−	0.148028i
$373$	−1.00669e37			−0.516554			−0.258277	−	0.966071i	$-0.583155\pi$
$373$	−1.00669e37			−0.516554			−0.258277	+	0.966071i	$0.583155\pi$
$374$	−1.88149e36			−0.0928677
$375$	−9.59803e36	−	7.16988e36i	−0.455752	−	0.340454i
$376$		−	2.33051e33i		−	0.000106470i
$377$	3.16874e37			1.39295
$378$	1.98416e36	+	3.73371e35i	0.0839355	+	0.0157946i
$379$	3.58578e37			1.45987			0.729937	−	0.683515i	$-0.239550\pi$
$379$	3.58578e37			1.45987			0.729937	+	0.683515i	$0.239550\pi$
$380$		−	6.35511e36i		−	0.249035i
$381$	1.07500e36	+	8.03040e35i	0.0405504	+	0.0302918i
$382$	1.43406e36			0.0520774
$383$	1.48831e37			0.520369			0.260184	−	0.965559i	$-0.416217\pi$
$383$	1.48831e37			0.520369			0.260184	+	0.965559i	$0.416217\pi$
$384$	5.96277e36	−	7.98213e36i	0.200745	−	0.268730i
$385$	−1.24303e37	−	7.33068e37i	−0.402995	−	2.37664i
$386$		−	2.44347e36i		−	0.0762943i
$387$	4.47462e36	+	1.51260e37i	0.134570	+	0.454900i
$388$		−	3.23923e37i		−	0.938388i
$389$			6.86856e37i			1.91689i	0.285281	+	0.958444i	$0.407913\pi$
$389$			6.86856e37i			1.91689i	−0.285281	+	0.958444i	$0.592087\pi$
$390$	−6.48781e36	−	4.84650e36i	−0.174446	−	0.130314i
$391$			3.59940e37i			0.932540i
$392$	−2.24723e36	−	6.43594e36i	−0.0561048	−	0.160681i
$393$	−2.66739e37	−	1.99258e37i	−0.641793	−	0.479429i
$394$	6.50084e35			0.0150756
$395$	1.03484e38			2.31321
$396$	−6.91782e37	+	2.04645e37i	−1.49070	+	0.440982i
$397$			2.07347e37i			0.430761i	0.976530	+	0.215380i	$0.0690992\pi$
$397$			2.07347e37i			0.430761i	−0.976530	+	0.215380i	$0.930901\pi$
$398$	−4.97094e36			−0.0995712
$399$	−3.84844e36	+	7.50872e36i	−0.0743323	+	0.145030i
$400$	7.19225e37			1.33966
$401$		−	2.55625e37i		−	0.459209i	−0.973284	−	0.229605i	$-0.926257\pi$
$401$		−	2.55625e37i		−	0.459209i	0.973284	−	0.229605i	$-0.0737433\pi$
$402$	2.03164e36	−	2.71967e36i	0.0352021	−	0.0471236i
$403$	1.84438e37			0.308267
$404$	−3.83024e37			−0.617584
$405$	8.30282e37	−	5.38343e37i	1.29160	−	0.837455i
$406$	−4.71842e36	+	8.00078e35i	−0.0708221	+	0.0120089i
$407$		−	1.69472e38i		−	2.45459i
$408$	−5.05983e36	+	6.77339e36i	−0.0707234	+	0.0946747i
$409$		−	5.28502e37i		−	0.712950i	−0.934305	−	0.356475i	$-0.883979\pi$
$409$		−	5.28502e37i		−	0.712950i	0.934305	−	0.356475i	$-0.116021\pi$
$410$			4.28188e36i			0.0557531i
$411$	4.92363e37	−	6.59107e37i	0.618841	−	0.828418i
$412$			7.02508e37i			0.852396i
$413$	−8.82702e37	+	1.49675e37i	−1.03404	+	0.175337i
$414$	−2.87681e36	−	9.72479e36i	−0.0325392	−	0.109996i
$415$	2.65315e38			2.89777
$416$	3.98432e37			0.420243
$417$	−8.72625e37	+	1.16815e38i	−0.888904	+	1.18994i
$418$			2.21539e36i			0.0217969i
$419$	−5.82158e37			−0.553271			−0.276635	−	0.960975i	$-0.589219\pi$
$419$	−5.82158e37			−0.553271			−0.276635	+	0.960975i	$0.589219\pi$
$420$	−1.48122e38	−	7.59172e37i	−1.35990	−	0.696988i
$421$	8.94985e37			0.793826			0.396913	−	0.917856i	$-0.370081\pi$
$421$	8.94985e37			0.793826			0.396913	+	0.917856i	$0.370081\pi$
$422$			1.48667e37i			0.127404i
$423$	2.14305e34	+	7.24437e34i	0.000177459	+	0.000599881i
$424$	2.84953e37			0.228018
$425$	−1.22969e38			−0.950950
$426$	5.75766e34	+	4.30106e34i	0.000430335	+	0.000321467i
$427$	4.24296e37	+	2.50226e38i	0.306524	+	1.80771i
$428$			1.46016e38i			1.01968i
$429$	−3.07781e38	−	2.29917e38i	−2.07784	−	1.55218i
$430$			9.55567e36i			0.0623690i
$431$			1.43236e38i			0.903922i	0.892038	+	0.451961i	$0.149275\pi$
$431$			1.43236e38i			0.903922i	−0.892038	+	0.451961i	$0.850725\pi$
$432$	−5.55629e37	+	1.50360e38i	−0.339056	+	0.917527i
$433$		−	1.76466e38i		−	1.04132i	−0.853763	−	0.520662i	$-0.825685\pi$
$433$		−	1.76466e38i		−	1.04132i	0.853763	−	0.520662i	$-0.174315\pi$
$434$	−2.74637e36	+	4.65689e35i	−0.0156732	+	0.00265763i
$435$	−1.40376e38	+	1.87915e38i	−0.774814	+	1.03721i
$436$	1.51919e37			0.0811070
$437$	4.23816e37			0.218875
$438$	−1.55404e37	−	1.16089e37i	−0.0776405	−	0.0579986i
$439$			4.44385e36i			0.0214795i	0.999942	+	0.0107397i	$0.00341863\pi$
$439$			4.44385e36i			0.0214795i	−0.999942	+	0.0107397i	$0.996581\pi$
$440$	−8.77260e37			−0.410265
$441$	1.29038e38	+	1.79396e38i	0.583924	+	0.811808i
$442$	−2.24293e37			−0.0982185
$443$		−	5.30865e37i		−	0.224973i	−0.993653	−	0.112486i	$-0.964119\pi$
$443$		−	5.30865e37i		−	0.224973i	0.993653	−	0.112486i	$-0.0358815\pi$
$444$	−3.03933e38	−	2.27043e38i	−1.24659	−	0.931225i
$445$	−7.43054e37			−0.294985
$446$	2.34687e37			0.0901850
$447$	−1.07268e38	+	1.43595e38i	−0.399034	+	0.534172i
$448$	2.61854e38	−	4.44013e37i	0.943037	−	0.159906i
$449$			1.24111e38i			0.432750i	0.976310	+	0.216375i	$0.0694234\pi$
$449$			1.24111e38i			0.432750i	−0.976310	+	0.216375i	$0.930577\pi$
$450$	3.32236e37	−	9.82831e36i	0.112167	−	0.0331816i
$451$			2.03132e38i			0.664078i
$452$			1.33155e38i			0.421550i
$453$	−1.16840e35	−	8.72810e34i	−0.000358234	−	0.000267606i
$454$		−	2.26466e37i		−	0.0672501i
$455$	−1.48181e38	−	8.73892e38i	−0.426215	−	2.51358i
$456$	7.97542e36	+	5.95776e36i	0.0222210	+	0.0165994i
$457$	−1.68118e38			−0.453762			−0.226881	−	0.973922i	$-0.572853\pi$
$457$	−1.68118e38			−0.453762			−0.226881	+	0.973922i	$0.572853\pi$
$458$	2.92638e37			0.0765212
$459$	9.49987e37	−	2.57079e38i	0.240677	−	0.651302i
$460$			8.36051e38i			2.05232i
$461$	4.79870e38			1.14146			0.570729	−	0.821138i	$-0.306661\pi$
$461$	4.79870e38			1.14146			0.570729	+	0.821138i	$0.306661\pi$
$462$	5.16355e37	+	2.64647e37i	0.119025	+	0.0610040i
$463$	9.50054e37			0.212238			0.106119	−	0.994353i	$-0.466158\pi$
$463$	9.50054e37			0.212238			0.106119	+	0.994353i	$0.466158\pi$
$464$		−	3.79968e38i		−	0.822691i
$465$	−8.17062e37	+	1.09377e38i	−0.171470	+	0.229540i
$466$	4.98415e37			0.101390
$467$	−5.35352e38			−1.05571			−0.527856	−	0.849334i	$-0.677004\pi$
$467$	−5.35352e38			−1.05571			−0.527856	+	0.849334i	$0.677004\pi$
$468$	−8.24674e38	+	2.43957e38i	−1.57659	+	0.466390i
$469$	3.66333e38	−	6.21172e37i	0.679000	−	0.115135i
$470$			4.57653e34i			8.22466e-5i
$471$	3.35616e38	−	4.49276e38i	0.584843	−	0.782907i
$472$			1.05633e38i			0.178500i
$473$			4.53320e38i			0.742880i
$474$	−4.83292e37	+	6.46964e37i	−0.0768111	+	0.102824i
$475$			1.44792e38i			0.223196i
$476$	−4.54509e38	+	7.70688e37i	−0.679582	+	0.115233i
$477$	−8.85775e38	+	2.62032e38i	−1.28472	+	0.380048i
$478$	−3.39105e37			−0.0477123
$479$	4.79011e38			0.653854			0.326927	−	0.945050i	$-0.393987\pi$
$479$	4.79011e38			0.653854			0.326927	+	0.945050i	$0.393987\pi$
$480$	−1.76506e38	+	2.36282e38i	−0.233755	+	0.312919i
$481$		−	2.02028e39i		−	2.59601i
$482$	2.06281e37			0.0257204
$483$	5.06285e38	−	9.87816e38i	0.612578	−	1.19521i
$484$	−1.22781e39			−1.44169
$485$			1.27688e39i			1.45511i
$486$	−5.11961e36	+	7.70497e37i	−0.00566253	+	0.0852207i
$487$	8.62466e38			0.925917			0.462959	−	0.886380i	$-0.346788\pi$
$487$	8.62466e38			0.925917			0.462959	+	0.886380i	$0.346788\pi$
$488$	2.99444e38			0.312053
$489$	8.80474e38	+	6.57728e38i	0.890714	+	0.665377i
$490$	4.41300e37	+	1.26386e38i	0.0433402	+	0.124124i
$491$			3.03296e38i			0.289191i	0.989491	+	0.144596i	$0.0461881\pi$
$491$			3.03296e38i			0.289191i	−0.989491	+	0.144596i	$0.953812\pi$
$492$	3.64300e38	+	2.72138e38i	0.337260	+	0.251939i
$493$			6.49651e38i			0.583982i
$494$			2.64097e37i			0.0230528i
$495$	2.72695e39	−	8.06695e38i	2.31155	−	0.683808i
$496$		−	2.21162e38i		−	0.182065i
$497$	1.31505e36	+	7.75541e36i	0.00105141	+	0.00620065i
$498$	−1.23908e38	+	1.65871e38i	−0.0962219	+	0.128809i
$499$	−6.83045e36			−0.00515219			−0.00257609	−	0.999997i	$-0.500820\pi$
$499$	−6.83045e36			−0.00515219			−0.00257609	+	0.999997i	$0.500820\pi$
$500$	−7.70730e38			−0.564725
$501$	4.28898e38	+	3.20394e38i	0.305286	+	0.228054i
$502$		−	1.31519e38i		−	0.0909459i
$503$	1.47544e39			0.991257			0.495628	−	0.868535i	$-0.334938\pi$
$503$	1.47544e39			0.991257			0.495628	+	0.868535i	$0.334938\pi$
$504$	2.34135e38	−	1.14718e38i	0.152835	−	0.0748838i
$505$	1.50985e39			0.957656
$506$		−	2.91447e38i		−	0.179630i
$507$	−2.33146e39	−	1.74164e39i	−1.39641	−	1.04314i
$508$	8.63233e37			0.0502463
$509$	−1.76025e38			−0.0995790			−0.0497895	−	0.998760i	$-0.515855\pi$
$509$	−1.76025e38			−0.0995790			−0.0497895	+	0.998760i	$0.515855\pi$
$510$	9.93623e37	−	1.33012e38i	0.0546329	−	0.0731349i
$511$	−3.54943e38	−	2.09326e39i	−0.189695	−	1.11871i
$512$		−	7.98225e38i		−	0.414678i
$513$	−3.02701e38	−	1.11858e38i	−0.152866	−	0.0564890i
$514$			1.78963e38i			0.0878612i
$515$		−	2.76923e39i		−	1.32177i
$516$	8.12991e38	+	6.07317e38i	0.377281	+	0.281835i
$517$			2.17110e36i			0.000979643i
$518$	5.10102e37	+	3.00830e38i	0.0223808	+	0.131989i
$519$	1.16038e39	+	8.66818e38i	0.495076	+	0.369829i
$520$	−1.04578e39			−0.433903
$521$	4.59666e39			1.85479			0.927397	−	0.374079i	$-0.122041\pi$
$521$	4.59666e39			1.85479			0.927397	+	0.374079i	$0.122041\pi$
$522$	−5.19232e37	−	1.75521e38i	−0.0203770	−	0.0688823i
$523$			1.84113e39i			0.702766i	0.936232	+	0.351383i	$0.114288\pi$
$523$			1.84113e39i			0.702766i	−0.936232	+	0.351383i	$0.885712\pi$
$524$	−2.14194e39			−0.795249
$525$	3.37476e39	+	1.72966e39i	1.21880	+	0.624672i
$526$	1.33597e38			0.0469355
$527$			3.78132e38i			0.129238i
$528$	−2.75697e39	+	3.69065e39i	−0.916729	+	1.22719i
$529$	−2.48449e39			−0.803768
$530$	−5.59577e38			−0.176141
$531$	−9.71357e38	−	3.28358e39i	−0.297515	−	1.00572i
$532$	9.07457e37	+	5.35168e38i	0.0270463	+	0.159504i
$533$			2.42154e39i			0.702340i
$534$	3.47023e37	−	4.64546e37i	0.00979512	−	0.0131123i
$535$		−	5.75583e39i		−	1.58117i
$536$		−	4.38389e38i		−	0.117211i
$537$	9.62991e38	−	1.28912e39i	0.250608	−	0.335479i
$538$		−	2.02147e38i		−	0.0512064i
$539$	2.09352e39	+	5.99573e39i	0.516227	+	1.47844i
$540$	2.20658e39	−	5.97130e39i	0.529677	−	1.43337i
$541$	−3.87248e39			−0.904959			−0.452479	−	0.891775i	$-0.649460\pi$
$541$	−3.87248e39			−0.904959			−0.452479	+	0.891775i	$0.649460\pi$
$542$	3.34065e38			0.0760049
$543$	1.44224e38	−	1.93067e38i	0.0319477	−	0.0427671i
$544$			8.16860e38i			0.176183i
$545$	−5.98854e38			−0.125768
$546$	6.15548e38	+	3.15486e38i	0.125883	+	0.0645189i
$547$	1.53871e39			0.306436			0.153218	−	0.988192i	$-0.451036\pi$
$547$	1.53871e39			0.306436			0.153218	+	0.988192i	$0.451036\pi$
$548$		−	5.29268e39i		−	1.02650i
$549$	−9.30821e39	+	2.75358e39i	−1.75819	+	0.520114i
$550$	9.95697e38			0.183176
$551$	7.64940e38			0.137066
$552$	−1.04921e39	−	7.83778e38i	−0.183125	−	0.136797i
$553$	−8.71444e39	+	1.47766e39i	−1.48158	+	0.251224i
$554$			4.20828e38i			0.0696968i
$555$	1.19808e40	+	8.94986e39i	1.93303	+	1.44400i
$556$			9.38033e39i			1.47446i
$557$		−	1.96926e39i		−	0.301580i	−0.988566	−	0.150790i	$-0.951818\pi$
$557$		−	1.96926e39i		−	0.301580i	0.988566	−	0.150790i	$-0.0481817\pi$
$558$	−3.02221e37	−	1.02163e38i	−0.00450951	−	0.0152439i
$559$			5.40404e39i			0.785682i
$560$	−1.04790e40	+	1.77687e39i	−1.48454	+	0.251726i
$561$	4.71374e39	−	6.31010e39i	0.650735	−	0.871113i
$562$	−3.18025e38			−0.0427844
$563$	1.17023e40			1.53426			0.767130	−	0.641491i	$-0.221684\pi$
$563$	1.17023e40			1.53426			0.767130	+	0.641491i	$0.221684\pi$
$564$	3.89369e36	+	2.90865e36i	0.000497524	+	0.000371658i
$565$		−	5.24885e39i		−	0.653675i
$566$	−5.05255e38			−0.0613299
$567$	−6.22315e39	+	5.71900e39i	−0.736302	+	0.676653i
$568$	9.28087e36			0.00107038
$569$			7.01848e39i			0.789069i	0.918881	+	0.394534i	$0.129094\pi$
$569$			7.01848e39i			0.789069i	−0.918881	+	0.394534i	$0.870906\pi$
$570$	−1.56617e38	−	1.16995e38i	−0.0171654	−	0.0128228i
$571$	−1.23568e40			−1.32033			−0.660165	−	0.751121i	$-0.729514\pi$
$571$	−1.23568e40			−1.32033			−0.660165	+	0.751121i	$0.729514\pi$
$572$	−2.47151e40			−2.57466
$573$	−3.59278e39	+	4.80951e39i	−0.364912	+	0.488494i
$574$	−6.11418e37	−	3.60580e38i	−0.00605502	−	0.0357092i
$575$		−	1.90482e40i		−	1.83938i
$576$	2.88154e39	+	9.74077e39i	0.271331	+	0.917207i
$577$		−	1.25657e40i		−	1.15381i	−0.816810	−	0.576907i	$-0.804259\pi$
$577$		−	1.25657e40i		−	1.15381i	0.816810	−	0.576907i	$-0.195741\pi$
$578$			4.93953e38i			0.0442315i
$579$	8.19485e39	+	6.12168e39i	0.715652	+	0.534603i
$580$			1.50898e40i			1.28522i
$581$	−2.23424e40	+	3.78848e39i	−1.85599	+	0.314711i
$582$	−7.98287e38	−	5.96333e38i	−0.0646809	−	0.0483176i
$583$	−2.65463e40			−2.09802
$584$	−2.50499e39			−0.193117
$585$	3.25081e40	−	9.61662e39i	2.44473	−	0.723207i
$586$		−	4.82951e38i		−	0.0354313i
$587$	1.00668e40			0.720507			0.360254	−	0.932854i	$-0.382690\pi$
$587$	1.00668e40			0.720507			0.360254	+	0.932854i	$0.382690\pi$
$588$	1.35575e40	+	4.27797e39i	0.946694	+	0.298722i
$589$	4.45236e38			0.0303332
$590$		−	2.07436e39i		−	0.137889i
$591$	−1.62867e39	+	2.18023e39i	−0.105636	+	0.141411i
$592$	−2.42254e40			−1.53323
$593$	1.55472e38			0.00960197			0.00480098	−	0.999988i	$-0.498472\pi$
$593$	1.55472e38			0.00960197			0.00480098	+	0.999988i	$0.498472\pi$
$594$	−7.69215e38	+	2.08159e39i	−0.0463601	+	0.125456i
$595$	1.79164e40	−	3.03800e39i	1.05379	−	0.178686i
$596$			1.15308e40i			0.661896i
$597$	1.24538e40	−	1.66714e40i	0.697707	−	0.933994i
$598$		−	3.47435e39i		−	0.189979i
$599$		−	2.22330e40i		−	1.18661i	−0.804976	−	0.593307i	$-0.797822\pi$
$599$		−	2.22330e40i		−	1.18661i	0.804976	−	0.593307i	$-0.202178\pi$
$600$	2.67769e39	−	3.58452e39i	0.139498	−	0.186740i
$601$		−	2.95704e40i		−	1.50376i	−0.659302	−	0.751879i	$-0.729148\pi$
$601$		−	2.95704e40i		−	1.50376i	0.659302	−	0.751879i	$-0.270852\pi$
$602$	−1.36447e38	−	8.04690e38i	−0.00677353	−	0.0399466i
$603$	4.03126e39	+	1.36273e40i	0.195362	+	0.660402i
$604$	−9.38233e36			−0.000443890
$605$	4.83993e40			2.23556
$606$	−7.05135e38	+	9.43936e38i	−0.0317994	+	0.0425686i
$607$			3.19733e40i			1.40783i	0.710282	+	0.703917i	$0.248567\pi$
$607$			3.19733e40i			1.40783i	−0.710282	+	0.703917i	$0.751433\pi$
$608$	9.61822e38			0.0413517
$609$	9.13786e39	−	1.78289e40i	0.383613	−	0.748471i
$610$	−5.88034e39			−0.241057
$611$			2.58818e37i			0.00103609i
$612$	−5.00159e39	−	1.69074e40i	−0.195529	−	0.660968i
$613$	3.18991e40			1.21787			0.608936	−	0.793220i	$-0.291597\pi$
$613$	3.18991e40			1.21787			0.608936	+	0.793220i	$0.291597\pi$
$614$	−1.72261e39			−0.0642310
$615$	−1.43604e40	−	1.07275e40i	−0.522972	−	0.390668i
$616$	7.38747e39	−	1.25265e39i	0.262770	−	0.0445565i
$617$			3.69563e40i			1.28397i	0.766719	+	0.641983i	$0.221888\pi$
$617$			3.69563e40i			1.28397i	−0.766719	+	0.641983i	$0.778112\pi$
$618$	1.73128e39	+	1.29329e39i	0.0587536	+	0.0438899i
$619$		−	2.50412e40i		−	0.830118i	−0.909794	−	0.415059i	$-0.863761\pi$
$619$		−	2.50412e40i		−	0.830118i	0.909794	−	0.415059i	$-0.136239\pi$
$620$			8.78306e39i			0.284424i
$621$	3.98220e40	+	1.47155e40i	1.25978	+	0.465529i
$622$		−	2.36128e39i		−	0.0729771i
$623$	6.25731e39	−	1.06102e39i	0.188934	−	0.0320366i
$624$	−3.28659e40	+	4.39963e40i	−0.969548	+	1.29790i
$625$	−1.71345e40			−0.493868
$626$	3.08332e38			0.00868342
$627$	−7.42991e39	−	5.55025e39i	−0.204458	−	0.152733i
$628$		−	3.60772e40i		−	0.970104i
$629$	4.14194e40			1.08835
$630$	−4.59781e39	+	2.25277e39i	−0.118063	+	0.0578467i
$631$	−4.78919e40			−1.20181			−0.600906	−	0.799320i	$-0.705194\pi$
$631$	−4.78919e40			−1.20181			−0.600906	+	0.799320i	$0.705194\pi$
$632$			1.04285e40i			0.255756i
$633$	−4.98595e40	−	3.72458e40i	−1.19507	−	0.892737i
$634$	4.65552e39			0.109062
$635$	−3.40280e39			−0.0779143
$636$	−3.55642e40	+	4.76085e40i	−0.795949	+	1.06551i
$637$	2.49569e40	+	7.14752e40i	0.545971	+	1.56363i
$638$		−	5.26029e39i		−	0.112489i
$639$	−2.88495e38	+	8.53434e37i	−0.00603081	+	0.00178405i
$640$			2.52666e40i			0.516342i
$641$			2.95196e40i			0.589751i	0.955536	+	0.294876i	$0.0952783\pi$
$641$			2.95196e40i			0.589751i	−0.955536	+	0.294876i	$0.904722\pi$
$642$	3.59845e39	+	2.68810e39i	0.0702842	+	0.0525034i
$643$		−	7.38431e40i		−	1.41010i	−0.709156	−	0.705052i	$-0.750924\pi$
$643$		−	7.38431e40i		−	1.41010i	0.709156	−	0.705052i	$-0.249076\pi$
$644$	−1.19381e40	−	7.04045e40i	−0.222890	−	1.31448i
$645$	−3.20475e40	−	2.39400e40i	−0.585030	−	0.437027i
$646$	−5.41449e38			−0.00966464
$647$	8.34491e40			1.45650			0.728248	−	0.685314i	$-0.240335\pi$
$647$	8.34491e40			1.45650			0.728248	+	0.685314i	$0.240335\pi$
$648$	5.42513e39	+	8.36713e39i	0.0925919	+	0.142804i
$649$		−	9.84073e40i		−	1.64240i
$650$	1.18697e40			0.193730
$651$	5.31873e39	−	1.03774e40i	0.0848952	−	0.165640i
$652$	7.07028e40			1.10369
$653$			7.49523e40i			1.14431i	0.820145	+	0.572155i	$0.193893\pi$
$653$			7.49523e40i			1.14431i	−0.820145	+	0.572155i	$0.806107\pi$
$654$	2.79678e38	−	3.74394e38i	0.00417620	−	0.00559051i
$655$	8.44336e40			1.23315
$656$	2.90371e40			0.414808
$657$	7.78674e40	−	2.30349e40i	1.08807	−	0.321877i
$658$	−6.53492e35	−	3.85393e36i	−8.93233e−6	−	5.26779e-5i
$659$		−	8.48295e40i		−	1.13425i	−0.823632	−	0.567125i	$-0.808056\pi$
$659$		−	8.48295e40i		−	1.13425i	0.823632	−	0.567125i	$-0.191944\pi$
$660$	1.09488e41	−	1.46568e41i	1.43213	−	1.91713i
$661$			1.12075e41i			1.43413i	0.697007	+	0.717065i	$0.254515\pi$
$661$			1.12075e41i			1.43413i	−0.697007	+	0.717065i	$0.745485\pi$
$662$		−	4.89582e39i		−	0.0612893i
$663$	5.61925e40	−	7.52228e40i	0.688228	−	0.921304i
$664$			2.67370e40i			0.320388i
$665$	−3.57713e39	−	2.10959e40i	−0.0419393	−	0.247335i
$666$	−1.11906e40	+	3.31044e39i	−0.128374	+	0.0379760i
$667$	−1.00632e41			−1.12957
$668$	3.44409e40			0.378282
$669$	−5.87966e40	+	7.87087e40i	−0.631937	+	0.845949i
$670$			8.60885e39i			0.0905442i
$671$	−2.78963e41			−2.87124
$672$	1.14898e40	−	2.24178e40i	0.115733	−	0.225808i
$673$	5.52796e40			0.544937			0.272469	−	0.962165i	$-0.412160\pi$
$673$	5.52796e40			0.544937			0.272469	+	0.962165i	$0.412160\pi$
$674$		−	1.77139e39i		−	0.0170901i
$675$	−5.02738e40	+	1.36047e41i	−0.474720	+	1.28465i
$676$	−1.87219e41			−1.73030
$677$	−4.74373e40			−0.429125			−0.214563	−	0.976710i	$-0.568833\pi$
$677$	−4.74373e40			−0.429125			−0.214563	+	0.976710i	$0.568833\pi$
$678$	3.28150e39	+	2.45133e39i	0.0290564	+	0.0217056i
$679$	−1.82328e40	−	1.07527e41i	−0.158031	−	0.931980i
$680$		−	2.14405e40i		−	0.181910i
$681$	7.59514e40	+	5.67369e40i	0.630816	+	0.471229i
$682$		−	3.06177e39i		−	0.0248943i
$683$			1.82712e41i			1.45434i	0.686456	+	0.727171i	$0.259165\pi$
$683$			1.82712e41i			1.45434i	−0.686456	+	0.727171i	$0.740835\pi$
$684$	−1.99078e40	+	5.88919e39i	−0.155135	+	0.0458925i
$685$			2.08634e41i			1.59174i
$686$	−5.52090e39	−	1.00129e40i	−0.0412392	−	0.0747928i
$687$	−7.33151e40	+	9.81441e40i	−0.536193	+	0.717780i
$688$	6.48006e40			0.464031
$689$	−3.16458e41			−2.21890
$690$	2.06039e40	+	1.53914e40i	0.141461	+	0.105674i
$691$			1.17641e41i			0.790909i	0.918486	+	0.395455i	$0.129413\pi$
$691$			1.17641e41i			0.790909i	−0.918486	+	0.395455i	$0.870587\pi$
$692$	9.31791e40			0.613452
$693$	−2.18120e41	+	1.06871e41i	−1.40625	+	0.689014i
$694$	−1.44514e40			−0.0912424
$695$		−	3.69766e41i		−	2.28637i
$696$	−1.89371e40	−	1.41463e40i	−0.114678	−	0.0856661i
$697$	−4.96462e40			−0.294449
$698$	1.28311e40			0.0745351
$699$	−1.24869e41	+	1.67157e41i	−0.710452	+	0.951054i
$700$	2.40529e41	−	4.07852e40i	1.34043	−	0.227291i
$701$			1.32146e41i			0.721343i	0.932693	+	0.360672i	$0.117452\pi$
$701$			1.32146e41i			0.721343i	−0.932693	+	0.360672i	$0.882548\pi$
$702$	−9.16982e39	+	2.48147e40i	−0.0490312	+	0.132685i
$703$		−	4.87699e40i		−	0.255446i
$704$			2.91926e41i			1.49785i
$705$	−1.53486e38	−	1.14657e38i	−0.000771485	−	0.000576311i
$706$			1.40980e40i			0.0694207i
$707$	−1.27146e41	+	2.15595e40i	−0.613367	+	0.104006i
$708$	−1.76485e41	−	1.31837e41i	−0.834115	−	0.623097i
$709$	−1.20297e41			−0.557036			−0.278518	−	0.960431i	$-0.589843\pi$
$709$	−1.20297e41			−0.557036			−0.278518	+	0.960431i	$0.589843\pi$
$710$	−1.82253e38			−0.000826853
$711$	−9.58969e40	−	3.24170e41i	−0.426280	−	1.44100i
$712$		−	7.48810e39i		−	0.0326146i
$713$	−5.85734e40			−0.249978
$714$	−6.46806e39	+	1.26199e40i	−0.0270489	+	0.0527754i
$715$	9.74251e41			3.99239
$716$		−	1.03517e41i		−	0.415694i
$717$	8.49566e40	−	1.13728e41i	0.334326	−	0.447549i
$718$	−1.84041e40			−0.0709757
$719$	4.09014e41			1.54586			0.772929	−	0.634492i	$-0.218791\pi$
$719$	4.09014e41			1.54586			0.772929	+	0.634492i	$0.218791\pi$
$720$	−1.15314e41	−	3.89809e41i	−0.427132	−	1.44388i
$721$	3.95424e40	+	2.33199e41i	0.143549	+	0.846575i
$722$		−	2.33669e40i		−	0.0831403i
$723$	−5.16800e40	+	6.91820e40i	−0.180226	+	0.241262i
$724$		−	1.55034e40i		−	0.0529929i
$725$		−	3.43799e41i		−	1.15187i
$726$	−2.26035e40	+	3.02585e40i	−0.0742327	+	0.0993725i
$727$			4.68908e41i			1.50952i	0.656001	+	0.754760i	$0.272247\pi$
$727$			4.68908e41i			1.50952i	−0.656001	+	0.754760i	$0.727753\pi$
$728$	8.80661e40	−	1.49329e40i	0.277910	−	0.0471237i
$729$	−2.45581e41	−	2.10204e41i	−0.759706	−	0.650267i
$730$	4.91917e40			0.149180
$731$	−1.10793e41			−0.329390
$732$	−3.73728e41	+	5.00296e41i	−1.08930	+	1.45820i
$733$		−	2.91963e41i		−	0.834297i	−0.908838	−	0.417149i	$-0.863029\pi$
$733$		−	2.91963e41i		−	0.834297i	0.908838	−	0.417149i	$-0.136971\pi$
$734$	−3.17984e39			−0.00890867
$735$	−5.34428e41	−	1.68634e41i	−1.46799	−	0.463212i
$736$	−1.26533e41			−0.340782
$737$			4.08403e41i			1.07848i
$738$	1.34133e40	−	3.96796e39i	0.0347311	−	0.0102742i
$739$	3.80301e41			0.965568			0.482784	−	0.875740i	$-0.339626\pi$
$739$	3.80301e41			0.965568			0.482784	+	0.875740i	$0.339626\pi$
$740$	9.62070e41			2.39523
$741$	−8.85720e40	−	6.61647e40i	−0.216238	−	0.161533i
$742$	4.71223e40	−	7.99030e39i	0.112816	−	0.0191296i
$743$		−	3.20943e41i		−	0.753512i	−0.926313	−	0.376756i	$-0.877040\pi$
$743$		−	3.20943e41i		−	0.753512i	0.926313	−	0.376756i	$-0.122960\pi$
$744$	−1.10224e40	−	8.23391e39i	−0.0253787	−	0.0189583i
$745$		−	4.54536e41i		−	1.02637i
$746$			1.99219e40i			0.0441182i
$747$	−2.45864e41	−	8.31118e41i	−0.534005	−	1.80515i
$748$		−	5.06706e41i		−	1.07940i
$749$	8.21885e40	+	4.84702e41i	0.171721	+	1.01272i
$750$	−1.41889e40	+	1.89941e40i	−0.0290777	+	0.0389252i
$751$	1.32199e41			0.265736			0.132868	−	0.991134i	$-0.457581\pi$
$751$	1.32199e41			0.265736			0.132868	+	0.991134i	$0.457581\pi$
$752$	3.10352e38			0.000611922
$753$	4.41083e41	+	3.29496e41i	0.853086	+	0.637269i
$754$		−	6.27080e40i		−	0.118970i
$755$	3.69844e38			0.000688317
$756$	−1.00553e41	+	5.34355e41i	−0.183581	+	0.975583i
$757$	−3.52532e41			−0.631405			−0.315703	−	0.948858i	$-0.602240\pi$
$757$	−3.52532e41			−0.631405			−0.315703	+	0.948858i	$0.602240\pi$
$758$		−	7.09611e40i		−	0.124686i
$759$	9.77448e41	+	7.30168e41i	1.68495	+	1.25869i
$760$	−2.52454e40			−0.0426958
$761$	−6.34527e41			−1.05287			−0.526433	−	0.850217i	$-0.676471\pi$
$761$	−6.34527e41			−1.05287			−0.526433	+	0.850217i	$0.676471\pi$
$762$	1.58918e39	−	2.12738e39i	0.00258718	−	0.00346336i
$763$	5.04299e40	−	8.55114e39i	0.0805531	−	0.0136590i
$764$			3.86208e41i			0.605296i
$765$	1.97159e41	+	6.66476e41i	0.303197	+	1.02493i
$766$		−	2.94531e40i		−	0.0444440i
$767$		−	1.17311e42i		−	1.73703i
$768$	5.11596e41	+	3.82170e41i	0.743343	+	0.555288i
$769$			3.10503e41i			0.442725i	0.975192	+	0.221363i	$0.0710505\pi$
$769$			3.10503e41i			0.442725i	−0.975192	+	0.221363i	$0.928950\pi$
$770$	−1.45071e41	+	2.45990e40i	−0.202986	+	0.0344193i
$771$	−6.00199e41	−	4.48358e41i	−0.824151	−	0.615653i
$772$	6.58053e41			0.886769
$773$	7.51883e41			0.994370			0.497185	−	0.867645i	$-0.334367\pi$
$773$	7.51883e41			0.994370			0.497185	+	0.867645i	$0.334367\pi$
$774$	2.99338e40	−	8.85510e39i	0.0388524	−	0.0114934i
$775$		−	2.00109e41i		−	0.254913i
$776$	−1.28677e41			−0.160882
$777$	−1.13671e42	−	5.82598e41i	−1.39491	−	0.714931i
$778$	1.35926e41			0.163719
$779$			5.84565e40i			0.0691099i
$780$	1.30521e42	−	1.74724e42i	1.51464	−	2.02759i
$781$	−8.64606e39			−0.00984869
$782$	7.12307e40			0.0796470
$783$	7.18742e41	+	2.65598e41i	0.788910	+	0.291527i
$784$	8.57070e41	−	2.99262e41i	0.923492	−	0.322455i
$785$			1.42214e42i			1.50429i
$786$	−3.94324e40	+	5.27866e40i	−0.0409474	+	0.0548146i
$787$			3.78389e41i			0.385749i	0.981223	+	0.192874i	$0.0617810\pi$
$787$			3.78389e41i			0.385749i	−0.981223	+	0.192874i	$0.938219\pi$
$788$			1.75075e41i			0.175224i
$789$	−3.34702e41	+	4.48052e41i	−0.328883	+	0.440263i
$790$		−	2.04790e41i		−	0.197568i
$791$	7.49493e40	+	4.42010e41i	0.0709919	+	0.418671i
$792$	8.12944e40	+	2.74808e41i	0.0756041	+	0.255572i
$793$	−3.32552e42			−3.03667
$794$	4.10332e40			0.0367907
$795$	1.40192e42	−	1.87669e42i	1.23424	−	1.65223i
$796$		−	1.33873e42i		−	1.15732i
$797$	−2.04749e42			−1.73811			−0.869053	−	0.494719i	$-0.835271\pi$
$797$	−2.04749e42			−1.73811			−0.869053	+	0.494719i	$0.835271\pi$
$798$	1.48595e40	+	7.61591e39i	0.0123868	+	0.00634863i
$799$	−5.30625e38			−0.000434369
$800$		−	4.32286e41i		−	0.347510i
$801$	6.88577e40	+	2.32767e41i	0.0543602	+	0.183759i
$802$	−5.05872e40			−0.0392204
$803$	2.33365e42			1.77689
$804$	7.32436e41	+	5.47141e41i	0.547718	+	0.409154i
$805$	4.70592e41	+	2.77529e42i	0.345624	+	2.03830i
$806$		−	3.64995e40i		−	0.0263286i
$807$	6.77955e41	+	5.06443e41i	0.480324	+	0.358810i
$808$			1.52155e41i			0.105882i
$809$		−	2.19323e42i		−	1.49910i	−0.661948	−	0.749550i	$-0.730270\pi$
$809$		−	2.19323e42i		−	1.49910i	0.661948	−	0.749550i	$-0.269730\pi$
$810$	−1.06536e41	−	1.64309e41i	−0.0715259	−	0.110314i
$811$		−	3.40425e39i		−	0.00224502i	−0.999999	−	0.00112251i	$-0.999643\pi$
$811$		−	3.40425e39i		−	0.00224502i	0.999999	−	0.00112251i	$-0.000357306\pi$
$812$	−2.15470e41	−	1.27072e42i	−0.139580	−	0.823166i
$813$	−8.36939e41	+	1.12038e42i	−0.532575	+	0.712937i
$814$	−3.35378e41			−0.209643
$815$	−2.78705e42			−1.71143
$816$	−9.02008e41	−	6.73814e41i	−0.544130	−	0.406474i
$817$			1.30455e41i			0.0773107i
$818$	−1.04588e41			−0.0608921
$819$	−2.60021e42	+	1.27401e42i	−1.48728	+	0.728713i
$820$	−1.15316e42			−0.648018
$821$			2.78680e42i			1.53862i	0.638877	+	0.769309i	$0.279399\pi$
$821$			2.78680e42i			1.53862i	−0.638877	+	0.769309i	$0.720601\pi$
$822$	−1.30435e41	−	9.74366e40i	−0.0707540	−	0.0528543i
$823$	3.16453e42			1.68660			0.843300	−	0.537444i	$-0.180610\pi$
$823$	3.16453e42			1.68660			0.843300	+	0.537444i	$0.180610\pi$
$824$	2.79068e41			0.146139
$825$	−2.49454e42	+	3.33934e42i	−1.28353	+	1.71822i
$826$	2.96201e40	+	1.74683e41i	0.0149753	+	0.0883162i
$827$		−	3.51481e42i		−	1.74611i	−0.487619	−	0.873056i	$-0.662135\pi$
$827$		−	3.51481e42i		−	1.74611i	0.487619	−	0.873056i	$-0.337865\pi$
$828$	2.61899e42	−	7.74757e41i	1.27848	−	0.378203i
$829$		−	2.77766e42i		−	1.33241i	−0.745769	−	0.666205i	$-0.767918\pi$
$829$		−	2.77766e42i		−	1.33241i	0.745769	−	0.666205i	$-0.232082\pi$
$830$		−	5.25048e41i		−	0.247495i
$831$	−1.41136e42	−	1.05431e42i	−0.653766	−	0.488374i
$832$			3.48006e42i			1.58416i
$833$	−1.46538e42	+	5.11664e41i	−0.655536	+	0.228893i
$834$	2.31172e41	+	1.72689e41i	0.101631	+	0.0759201i
$835$	−1.35764e42			−0.586583
$836$	−5.96628e41			−0.253345
$837$	4.18347e41	+	1.54592e41i	0.174589	+	0.0645162i
$838$			1.15207e41i			0.0472541i
$839$	−2.07644e42			−0.837087			−0.418543	−	0.908197i	$-0.637459\pi$
$839$	−2.07644e42			−0.837087			−0.418543	+	0.908197i	$0.637459\pi$
$840$	−3.01578e41	+	5.88411e41i	−0.119495	+	0.233148i
$841$	7.51388e41			0.292632
$842$		−	1.77114e41i		−	0.0677996i
$843$	7.96754e41	−	1.06658e42i	0.299795	−	0.401324i
$844$	−4.00376e42			−1.48082
$845$	7.38002e42			2.68309
$846$	1.43363e38	−	4.24101e37i	5.12350e−5	−	1.51565e-5i
$847$	−4.07574e42	+	6.91102e41i	−1.43185	+	0.242791i
$848$			3.79470e42i			1.31050i
$849$	1.26582e42	−	1.69451e42i	0.429746	−	0.575283i
$850$			2.43351e41i			0.0812194i
$851$			6.41596e42i			2.10515i
$852$	−1.15832e40	+	1.55060e40i	−0.00373641	+	0.00500178i
$853$		−	9.65721e41i		−	0.306260i	−0.988206	−	0.153130i	$-0.951065\pi$
$853$		−	9.65721e41i		−	0.306260i	0.988206	−	0.153130i	$-0.0489354\pi$
$854$	4.95187e41	−	8.39664e40i	0.154394	−	0.0261798i
$855$	7.84752e41	−	2.32147e41i	0.240560	−	0.0711631i
$856$	5.80041e41			0.174819
$857$	−1.47188e42			−0.436165			−0.218082	−	0.975930i	$-0.569980\pi$
$857$	−1.47188e42			−0.436165			−0.218082	+	0.975930i	$0.569980\pi$
$858$	−4.54997e41	+	6.09087e41i	−0.132569	+	0.177465i
$859$		−	1.39111e42i		−	0.398530i	−0.979946	−	0.199265i	$-0.936145\pi$
$859$		−	1.39111e42i		−	0.398530i	0.979946	−	0.199265i	$-0.0638554\pi$
$860$	−2.57344e42			−0.724915
$861$	1.36248e42	+	6.98313e41i	0.377386	+	0.193421i
$862$	2.83458e41			0.0772028
$863$			2.63894e42i			0.706762i	0.935480	+	0.353381i	$0.114968\pi$
$863$			2.63894e42i			0.706762i	−0.935480	+	0.353381i	$0.885032\pi$
$864$	9.03734e41	+	3.33958e41i	0.238008	+	0.0879515i
$865$	−3.67305e42			−0.951248
$866$	−3.49219e41			−0.0889382
$867$	−1.65660e42	−	1.23751e42i	−0.414899	−	0.309936i
$868$	−1.25415e41	−	7.39628e41i	−0.0308897	−	0.182170i
$869$		−	9.71523e42i		−	2.35324i
$870$	3.71877e41	+	2.77798e41i	0.0885870	+	0.0661758i
$871$			4.86858e42i			1.14062i
$872$		−	6.03493e40i		−	0.0139054i
$873$	3.99992e42	−	1.18327e42i	0.906453	−	0.268149i
$874$		−	8.38715e40i		−	0.0186939i
$875$	−2.55846e42	+	4.33825e41i	−0.560869	+	0.0951037i
$876$	3.12641e42	−	4.18520e42i	0.674119	−	0.902416i
$877$	2.16209e42			0.458543			0.229271	−	0.973363i	$-0.426366\pi$
$877$	2.16209e42			0.458543			0.229271	+	0.973363i	$0.426366\pi$
$878$	8.79420e39			0.00183453
$879$	1.61971e42	+	1.20994e42i	0.332351	+	0.248272i
$880$		−	1.16824e43i		−	2.35794i
$881$	−3.60234e42			−0.715210			−0.357605	−	0.933873i	$-0.616407\pi$
$881$	−3.60234e42			−0.715210			−0.357605	+	0.933873i	$0.616407\pi$
$882$	3.55017e41	−	2.55360e41i	0.0693354	−	0.0498722i
$883$	2.30854e42			0.443514			0.221757	−	0.975102i	$-0.428821\pi$
$883$	2.30854e42			0.443514			0.221757	+	0.975102i	$0.428821\pi$
$884$		−	6.04045e42i		−	1.14159i
$885$	6.95691e42	+	5.19692e42i	1.29342	+	0.966204i
$886$	−1.05056e41			−0.0192146
$887$	1.03993e43			1.87116			0.935580	−	0.353116i	$-0.114878\pi$
$887$	1.03993e43			1.87116			0.935580	+	0.353116i	$0.114878\pi$
$888$	−9.01918e41	+	1.20736e42i	−0.159654	+	0.213722i
$889$	2.86552e41	−	4.85892e40i	0.0499032	−	0.00846183i
$890$			1.47047e41i			0.0251943i
$891$	−5.05406e42	−	7.79482e42i	−0.851949	−	1.31395i
$892$			6.32038e42i			1.04822i
$893$			6.24791e38i			0.000101950i
$894$	2.84169e41	+	2.12279e41i	0.0456229	+	0.0340810i
$895$			4.08058e42i			0.644596i
$896$	−3.60787e41	−	2.12772e42i	−0.0560770	−	0.330711i
$897$	1.16522e43	+	8.70435e42i	1.78204	+	1.33121i
$898$	2.45610e41			0.0369606
$899$	−1.05718e42			−0.156543
$900$	2.64687e42	+	8.94748e42i	0.385670	+	1.30372i
$901$		−	6.48799e42i		−	0.930253i
$902$	4.01990e41			0.0567180
$903$	3.04059e42	+	1.55839e42i	0.422168	+	0.216373i
$904$	5.28951e41			0.0722725
$905$			6.11133e41i			0.0821734i
$906$	−1.72726e38	+	2.31221e38i	−2.28559e−5	+	3.05963e-5i
$907$	−1.35793e43			−1.76836			−0.884180	−	0.467146i	$-0.845282\pi$
$907$	−1.35793e43			−1.76836			−0.884180	+	0.467146i	$0.845282\pi$
$908$	6.09896e42			0.781648
$909$	−1.39916e42	−	4.72972e42i	−0.176478	−	0.596567i
$910$	−1.72940e42	+	2.93245e41i	−0.214681	+	0.0364024i
$911$			6.61361e42i			0.808020i	0.914754	+	0.404010i	$0.132384\pi$
$911$			6.61361e42i			0.808020i	−0.914754	+	0.404010i	$0.867616\pi$
$912$	−7.93391e41	+	1.06208e42i	−0.0954030	+	0.127712i
$913$		−	2.49082e43i		−	2.94792i
$914$			3.32698e41i			0.0387552i
$915$	1.47321e43	−	1.97213e43i	1.68911	−	2.26115i
$916$			7.88106e42i			0.889406i
$917$	−7.11022e42	+	1.20564e42i	−0.789819	+	0.133926i
$918$	−5.08748e41	−	1.87999e41i	−0.0556268	−	0.0205559i
$919$	1.80097e42			0.193835			0.0969176	−	0.995292i	$-0.469102\pi$
$919$	1.80097e42			0.193835			0.0969176	+	0.995292i	$0.469102\pi$
$920$	3.32118e42			0.351859
$921$	4.31568e42	−	5.77723e42i	0.450074	−	0.602497i
$922$		−	9.49643e41i		−	0.0974904i
$923$	−1.03070e41			−0.0104161
$924$	−7.12723e42	+	1.39060e43i	−0.709050	+	1.38343i
$925$	−2.19194e43			−2.14671
$926$		−	1.88012e41i		−	0.0181270i
$927$	−8.67482e42	+	2.56621e42i	−0.823387	+	0.243577i
$928$	−2.28378e42			−0.213407
$929$	1.40405e43			1.29168			0.645841	−	0.763472i	$-0.276507\pi$
$929$	1.40405e43			1.29168			0.645841	+	0.763472i	$0.276507\pi$
$930$	2.16452e41	+	1.61693e41i	0.0196047	+	0.0146450i
$931$	6.02465e41	+	1.72543e42i	0.0537232	+	0.153860i
$932$			1.34228e43i			1.17846i
$933$	7.91918e42	+	5.91575e42i	0.684536	+	0.511359i
$934$			1.05944e42i			0.0901669i
$935$			1.99740e43i			1.67377i
$936$	9.69111e41	+	3.27599e42i	0.0799602	+	0.270298i
$937$			1.69093e43i			1.37373i	0.726784	+	0.686866i	$0.241014\pi$
$937$			1.69093e43i			1.37373i	−0.726784	+	0.686866i	$0.758986\pi$
$938$	−1.22927e41	−	7.24958e41i	−0.00983348	−	0.0579925i
$939$	−7.72469e41	+	1.03407e42i	−0.0608457	+	0.0814518i
$940$	−1.23251e40			−0.000955952
$941$	2.13448e43			1.63020			0.815101	−	0.579318i	$-0.196681\pi$
$941$	2.13448e43			1.63020			0.815101	+	0.579318i	$0.196681\pi$
$942$	−8.89099e41	−	6.64170e41i	−0.0668670	−	0.0499507i
$943$		−	7.69030e42i		−	0.569539i
$944$	−1.40670e43			−1.02591
$945$	3.96372e42	−	2.10639e43i	0.284670	−	1.51279i
$946$	8.97102e41			0.0634484
$947$		−	2.02683e43i		−	1.41170i	−0.708362	−	0.705849i	$-0.750566\pi$
$947$		−	2.02683e43i		−	1.41170i	0.708362	−	0.705849i	$-0.249434\pi$
$948$	−1.74234e43	−	1.30156e43i	−1.19512	−	0.892775i
$949$	2.78195e43			1.87927
$950$	2.86538e41			0.0190629
$951$	−1.16636e43	+	1.56135e43i	−0.764211	+	1.02302i
$952$	3.06153e41	+	1.80552e42i	0.0197562	+	0.116511i
$953$		−	1.04751e43i		−	0.665748i	−0.942971	−	0.332874i	$-0.891982\pi$
$953$		−	1.04751e43i		−	0.665748i	0.942971	−	0.332874i	$-0.108018\pi$
$954$	5.18551e41	+	1.75291e42i	0.0324594	+	0.109726i
$955$		−	1.52240e43i		−	0.938601i
$956$		−	9.13247e42i		−	0.554560i
$957$	1.76418e43	+	1.31787e43i	1.05516	+	0.788224i
$958$		−	9.47944e41i		−	0.0558448i
$959$	−2.97912e42	−	1.75692e43i	−0.172869	−	1.01949i
$960$	−2.06378e43	−	1.54167e43i	−1.17959	−	0.881169i
$961$	1.71465e43			0.965356
$962$	−3.99804e42			−0.221722
$963$	−1.80305e43	+	5.33384e42i	−0.984980	+	0.291379i
$964$			5.55538e42i			0.298949i
$965$	−2.59400e43			−1.37507
$966$	−1.95485e42	−	1.00192e42i	−0.102081	−	0.0523195i
$967$	3.96273e42			0.203850			0.101925	−	0.994792i	$-0.467500\pi$
$967$	3.96273e42			0.203850			0.101925	+	0.994792i	$0.467500\pi$
$968$			4.87742e42i			0.247171i
$969$	1.35650e42	−	1.81589e42i	0.0677213	−	0.0906558i
$970$	2.52690e42			0.124279
$971$	−1.43815e43			−0.696826			−0.348413	−	0.937341i	$-0.613279\pi$
$971$	−1.43815e43			−0.696826			−0.348413	+	0.937341i	$0.613279\pi$
$972$	−2.07503e43	−	1.37876e42i	−0.990521	−	0.0658157i
$973$	5.27995e42	+	3.11383e43i	0.248310	+	1.46439i
$974$		−	1.70679e42i		−	0.0790813i
$975$	−2.97374e43	+	3.98083e43i	−1.35749	+	1.81722i
$976$			3.98768e43i			1.79349i
$977$		−	1.83738e43i		−	0.814195i	−0.913385	−	0.407097i	$-0.866541\pi$
$977$		−	1.83738e43i		−	0.814195i	0.913385	−	0.407097i	$-0.133459\pi$
$978$	1.30162e42	−	1.74242e42i	0.0568289	−	0.0760747i
$979$			6.97592e42i			0.300090i
$980$	−3.40370e43	+	1.18847e43i	−1.44269	+	0.503743i
$981$	5.54949e41	+	1.87595e42i	0.0231768	+	0.0783468i
$982$	6.00211e41			0.0246994
$983$	3.71565e43			1.50664			0.753318	−	0.657656i	$-0.228452\pi$
$983$	3.71565e43			1.50664			0.753318	+	0.657656i	$0.228452\pi$
$984$	1.08106e42	−	1.44717e42i	0.0431936	−	0.0578216i
$985$		−	6.90131e42i		−	0.271710i
$986$	1.28563e42			0.0498771
$987$	1.45624e40	+	7.46366e39i	0.000556717	+	0.000285334i
$988$	−7.11241e42			−0.267942
$989$		−	1.71621e43i		−	0.637123i
$990$	−1.59642e42	−	5.39653e42i	−0.0584031	−	0.197426i
$991$	1.40666e43			0.507132			0.253566	−	0.967318i	$-0.418397\pi$
$991$	1.40666e43			0.507132			0.253566	+	0.967318i	$0.418397\pi$
$992$	−1.32928e42			−0.0472279
$993$	1.64194e43	+	1.22656e43i	0.574903	+	0.429461i
$994$	1.53476e40	−	2.60242e39i	0.000529589	−	8.97998e-5i
$995$			5.27716e43i			1.79459i
$996$	−4.46708e43	−	3.33697e43i	−1.49714	−	1.11839i
$997$		−	2.23345e43i		−	0.737730i	−0.929483	−	0.368865i	$-0.879747\pi$
$997$		−	2.23345e43i		−	0.737730i	0.929483	−	0.368865i	$-0.120253\pi$
$998$			1.35172e40i			0.000440041i
$999$	1.69336e43	−	4.58245e43i	0.543312	−	1.47027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.9	✓	76
3.2	odd	2	inner	21.30.c.a.20.68	yes	76
7.6	odd	2	inner	21.30.c.a.20.67	yes	76
21.20	even	2	inner	21.30.c.a.20.10	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.9	✓	76	1.1	even	1	trivial
21.30.c.a.20.10	yes	76	21.20	even	2	inner
21.30.c.a.20.67	yes	76	7.6	odd	2	inner
21.30.c.a.20.68	yes	76	3.2	odd	2	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1978.96i q^{2} +(6.63697e6 + 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 - 1.31343e10i) q^{6} +(1.76916e12 - 2.99987e11i) q^{7} -2.11714e12i q^{8} +(1.94684e13 + 6.58112e13i) q^{9} +O(q^{10})\)	\(q-1978.96i q^{2} +(6.63697e6 + 4.95792e6i) q^{3} +5.32955e8 q^{4} -2.10087e10 q^{5} +(9.81152e9 - 1.31343e10i) q^{6} +(1.76916e12 - 2.99987e11i) q^{7} -2.11714e12i q^{8} +(1.94684e13 + 6.58112e13i) q^{9} +4.15753e13i q^{10} +1.97233e15i q^{11} +(3.53721e15 + 2.64235e15i) q^{12} +2.35122e16i q^{13} +(-5.93662e14 - 3.50109e15i) q^{14} +(-1.39434e17 - 1.04159e17i) q^{15} +2.81938e17 q^{16} -4.82044e17 q^{17} +(1.30238e17 - 3.85272e16i) q^{18} +5.67589e17i q^{19} -1.11967e19 q^{20} +(1.32292e19 + 6.78033e18i) q^{21} +3.90316e18 q^{22} -7.46696e19i q^{23} +(1.04966e19 - 1.40514e19i) q^{24} +2.55100e20 q^{25} +4.65296e19 q^{26} +(-1.97075e20 + 5.33310e20i) q^{27} +(9.42880e20 - 1.59879e20i) q^{28} -1.34770e21i q^{29} +(-2.06127e20 + 2.75934e20i) q^{30} -7.84435e20i q^{31} -1.69458e21i q^{32} +(-9.77865e21 + 1.30903e22i) q^{33} +9.53945e20i q^{34} +(-3.71676e22 + 6.30233e21i) q^{35} +(1.03758e22 + 3.50744e22i) q^{36} -8.59247e22 q^{37} +1.12324e21 q^{38} +(-1.16571e23 + 1.56050e23i) q^{39} +4.44783e22i q^{40} +1.02991e23 q^{41} +(1.34180e22 - 2.61800e22i) q^{42} +2.29840e23 q^{43} +1.05116e24i q^{44} +(-4.09006e23 - 1.38261e24i) q^{45} -1.47768e23 q^{46} +1.10078e21 q^{47} +(1.87122e24 + 1.39783e24i) q^{48} +(3.03992e24 - 1.06145e24i) q^{49} -5.04833e23i q^{50} +(-3.19931e24 - 2.38993e24i) q^{51} +1.25309e25i q^{52} +1.34593e25i q^{53} +(1.05540e24 + 3.90003e23i) q^{54} -4.14360e25i q^{55} +(-6.35114e23 - 3.74555e24i) q^{56} +(-2.81406e24 + 3.76707e24i) q^{57} -2.66705e24 q^{58} -4.98939e25 q^{59} +(-7.43120e25 - 5.55122e25i) q^{60} +1.41438e26i q^{61} -1.55236e24 q^{62} +(5.41852e25 + 1.10590e26i) q^{63} +1.48011e26 q^{64} -4.93960e26i q^{65} +(2.59052e25 + 1.93516e25i) q^{66} +2.07066e26 q^{67} -2.56907e26 q^{68} +(3.70206e26 - 4.95580e26i) q^{69} +(1.24720e25 + 7.35532e25i) q^{70} +4.38368e24i q^{71} +(1.39332e26 - 4.12174e25i) q^{72} -1.18319e27i q^{73} +1.70041e26i q^{74} +(1.69309e27 + 1.26477e27i) q^{75} +3.02499e26i q^{76} +(5.91673e26 + 3.48936e27i) q^{77} +(3.08816e26 + 2.30690e26i) q^{78} -4.92576e27 q^{79} -5.92315e27 q^{80} +(-3.95209e27 + 2.56248e27i) q^{81} -2.03815e26i q^{82} -1.26288e28 q^{83} +(7.05054e27 + 3.61361e27i) q^{84} +1.01271e28 q^{85} -4.54844e26i q^{86} +(6.68179e27 - 8.94465e27i) q^{87} +4.17570e27 q^{88} +3.53689e27 q^{89} +(-2.73612e27 + 8.09407e26i) q^{90} +(7.05334e27 + 4.15967e28i) q^{91} -3.97955e28i q^{92} +(3.88916e27 - 5.20627e27i) q^{93} -2.17840e24i q^{94} -1.19243e28i q^{95} +(8.40157e27 - 1.12469e28i) q^{96} -6.07788e28i q^{97} +(-2.10056e27 - 6.01588e27i) q^{98} +(-1.29801e29 + 3.83982e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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