LMFDB - Embedded newform 50.26.b.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not 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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 74193735x^{2} + 1376177615409424 $ x^4 - 74193735*x^2 + 1376177615409424
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$6090.72 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.c.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00i q^{2} +701909. i q^{3} -1.67772e7 q^{4} +2.87502e9 q^{6} -7.10199e8i q^{7} +6.87195e10i q^{8} +3.54612e11 q^{9} +6.69047e12 q^{11} -1.17761e13i q^{12} +4.06505e12i q^{13} -2.90898e12 q^{14} +2.81475e14 q^{16} +2.05623e15i q^{17} -1.45249e15i q^{18} -1.32410e16 q^{19} +4.98495e14 q^{21} -2.74041e16i q^{22} +2.83334e16i q^{23} -4.82348e16 q^{24} +1.66504e16 q^{26} +8.43625e17i q^{27} +1.19152e16i q^{28} -8.79820e17 q^{29} -3.20276e17 q^{31} -1.15292e18i q^{32} +4.69610e18i q^{33} +8.42232e18 q^{34} -5.94940e18 q^{36} -4.64680e19i q^{37} +5.42350e19i q^{38} -2.85329e18 q^{39} -1.18387e20 q^{41} -2.04184e18i q^{42} +1.34535e20i q^{43} -1.12247e20 q^{44} +1.16053e20 q^{46} -7.78716e20i q^{47} +1.97570e20i q^{48} +1.34056e21 q^{49} -1.44329e21 q^{51} -6.82002e19i q^{52} +3.18129e21i q^{53} +3.45549e21 q^{54} +4.88045e19 q^{56} -9.29396e21i q^{57} +3.60374e21i q^{58} +2.03629e21 q^{59} +3.16043e22 q^{61} +1.31185e21i q^{62} -2.51845e20i q^{63} -4.72237e21 q^{64} +1.92352e22 q^{66} +4.98952e22i q^{67} -3.44978e22i q^{68} -1.98875e22 q^{69} +1.16862e23 q^{71} +2.43688e22i q^{72} +1.07622e23i q^{73} -1.90333e23 q^{74} +2.22147e23 q^{76} -4.75156e21i q^{77} +1.16871e22i q^{78} -2.51396e23 q^{79} -2.91689e23 q^{81} +4.84913e23i q^{82} +1.47962e24i q^{83} -8.36336e21 q^{84} +5.51054e23 q^{86} -6.17554e23i q^{87} +4.59765e23i q^{88} +1.69758e24 q^{89} +2.88699e21 q^{91} -4.75355e23i q^{92} -2.24804e23i q^{93} -3.18962e24 q^{94} +8.09246e23 q^{96} -4.56953e24i q^{97} -5.49095e24i q^{98} +2.37252e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 67108864 q^{4} - 4466376704 q^{6} - 706820944772 q^{9} - 16758339752832 q^{11} + 315947884249088 q^{14} + 11\!\cdots\!24 q^{16} - 69\!\cdots\!40 q^{19} + 98\!\cdots\!68 q^{21} + 74\!\cdots\!64 q^{24}+ \cdots + 26\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 67108864 * q^4 - 4466376704 * q^6 - 706820944772 * q^9 - 16758339752832 * q^11 + 315947884249088 * q^14 + 1125899906842624 * q^16 - 6978922831721840 * q^19 + 98965981439235568 * q^21 + 74933366700376064 * q^24 + 1224243095117725696 * q^26 + 1074887575919712360 * q^29 - 7248055568882624272 * q^31 + 27519011219504529408 * q^34 + 11858487663763914752 * q^36 + 356903093544598090256 * q^39 - 425179161247761543912 * q^41 + 281158285834649075712 * q^44 - 592856694194362220544 * q^46 + 2277734314701483659532 * q^49 + 363481383446781200688 * q^51 + 5488177642216870707200 * q^54 - 5300725898789947179008 * q^56 + 26295013412413600195920 * q^59 + 228823556614751495048 * q^61 - 18889465931478580854784 * q^64 + 192428119729102082015232 * q^66 - 290954022626555501624784 * q^69 + 167498518990330675485648 * q^71 + 155963987267122346098688 * q^74 + 117086895795128961597440 * q^76 - 211743190052114441384480 * q^79 - 2216381757932045545655596 * q^81 - 1660373647258045999218688 * q^84 + 111971687855373081542656 * q^86 + 3754707904362558847478040 * q^89 - 11414610679497993001794032 * q^91 - 13645264040406039381245952 * q^94 - 1257173278739416506957824 * q^96 + 26084325647996078762722176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	− 4096.00i	− 0.707107i
$2$	− 4096.00i	− 0.707107i
$3$	701909.i	0.762545i	0.924463	+	0.381272i	$0.124514\pi$
$3$	701909.i	0.762545i	−0.924463	+	0.381272i	$0.875486\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	2.87502e9	0.539200
$7$	− 7.10199e8i	− 0.0193934i	−0.999953	−	0.00969672i	$-0.996913\pi$
$7$	− 7.10199e8i	− 0.0193934i	0.999953	−	0.00969672i	$-0.00308661\pi$
$8$	6.87195e10i	0.353553i
$9$	3.54612e11	0.418526
$10$	0	0
$11$	6.69047e12	0.642758	0.321379	−	0.946951i	$-0.395854\pi$
$11$	6.69047e12	0.642758	0.321379	+	0.946951i	$0.395854\pi$
$12$	− 1.17761e13i	− 0.381272i
$13$	4.06505e12i	0.0483920i	0.999707	+	0.0241960i	$0.00770258\pi$
$13$	4.06505e12i	0.0483920i	−0.999707	+	0.0241960i	$0.992297\pi$
$14$	−2.90898e12	−0.0137132
$15$	0	0
$16$	2.81475e14	0.250000
$17$	2.05623e15i	0.855974i	0.903785	+	0.427987i	$0.140777\pi$
$17$	2.05623e15i	0.855974i	−0.903785	+	0.427987i	$0.859223\pi$
$18$	− 1.45249e15i	− 0.295942i
$19$	−1.32410e16	−1.37246	−0.686230	−	0.727384i	$-0.740736\pi$
$19$	−1.32410e16	−1.37246	−0.686230	+	0.727384i	$0.740736\pi$
$20$	0	0
$21$	4.98495e14	0.0147884
$22$	− 2.74041e16i	− 0.454499i
$23$	2.83334e16i	0.269588i	0.990874	+	0.134794i	$0.0430372\pi$
$23$	2.83334e16i	0.269588i	−0.990874	+	0.134794i	$0.956963\pi$
$24$	−4.82348e16	−0.269600
$25$	0	0
$26$	1.66504e16	0.0342183
$27$	8.43625e17i	1.08169i
$28$	1.19152e16i	0.00969672i
$29$	−8.79820e17	−0.461763	−0.230881	−	0.972982i	$-0.574161\pi$
$29$	−8.79820e17	−0.461763	−0.230881	+	0.972982i	$0.574161\pi$
$30$	0	0
$31$	−3.20276e17	−0.0730302	−0.0365151	−	0.999333i	$-0.511626\pi$
$31$	−3.20276e17	−0.0730302	−0.0365151	+	0.999333i	$0.511626\pi$
$32$	− 1.15292e18i	− 0.176777i
$33$	4.69610e18i	0.490132i
$34$	8.42232e18	0.605265
$35$	0	0
$36$	−5.94940e18	−0.209263
$37$	− 4.64680e19i	− 1.16047i	−0.814450	−	0.580233i	$-0.802961\pi$
$37$	− 4.64680e19i	− 1.16047i	0.814450	−	0.580233i	$-0.197039\pi$
$38$	5.42350e19i	0.970476i
$39$	−2.85329e18	−0.0369011
$40$	0	0
$41$	−1.18387e20	−0.819418	−0.409709	−	0.912216i	$-0.634370\pi$
$41$	−1.18387e20	−0.819418	−0.409709	+	0.912216i	$0.634370\pi$
$42$	− 2.04184e18i	− 0.0104569i
$43$	1.34535e20i	0.513426i	0.966488	+	0.256713i	$0.0826396\pi$
$43$	1.34535e20i	0.513426i	−0.966488	+	0.256713i	$0.917360\pi$
$44$	−1.12247e20	−0.321379
$45$	0	0
$46$	1.16053e20	0.190627
$47$	− 7.78716e20i	− 0.977587i	−0.872399	−	0.488794i	$-0.837437\pi$
$47$	− 7.78716e20i	− 0.977587i	0.872399	−	0.488794i	$-0.162563\pi$
$48$	1.97570e20i	0.190636i
$49$	1.34056e21	0.999624
$50$	0	0
$51$	−1.44329e21	−0.652718
$52$	− 6.82002e19i	− 0.0241960i
$53$	3.18129e21i	0.889517i	0.895651	+	0.444759i	$0.146711\pi$
$53$	3.18129e21i	0.889517i	−0.895651	+	0.444759i	$0.853289\pi$
$54$	3.45549e21	0.764870
$55$	0	0
$56$	4.88045e19	0.00685661
$57$	− 9.29396e21i	− 1.04656i
$58$	3.60374e21i	0.326516i
$59$	2.03629e21	0.149001	0.0745005	−	0.997221i	$-0.476264\pi$
$59$	2.03629e21	0.149001	0.0745005	+	0.997221i	$0.476264\pi$
$60$	0	0
$61$	3.16043e22	1.52448	0.762242	−	0.647292i	$-0.224099\pi$
$61$	3.16043e22	1.52448	0.762242	+	0.647292i	$0.224099\pi$
$62$	1.31185e21i	0.0516402i
$63$	− 2.51845e20i	− 0.00811665i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	1.92352e22	0.346576
$67$	4.98952e22i	0.744945i	0.928043	+	0.372472i	$0.121490\pi$
$67$	4.98952e22i	0.744945i	−0.928043	+	0.372472i	$0.878510\pi$
$68$	− 3.44978e22i	− 0.427987i
$69$	−1.98875e22	−0.205573
$70$	0	0
$71$	1.16862e23	0.845169	0.422585	−	0.906324i	$-0.361123\pi$
$71$	1.16862e23	0.845169	0.422585	+	0.906324i	$0.361123\pi$
$72$	2.43688e22i	0.147971i
$73$	1.07622e23i	0.550001i	0.961444	+	0.275001i	$0.0886780\pi$
$73$	1.07622e23i	0.550001i	−0.961444	+	0.275001i	$0.911322\pi$
$74$	−1.90333e23	−0.820574
$75$	0	0
$76$	2.22147e23	0.686230
$77$	− 4.75156e21i	− 0.0124653i
$78$	1.16871e22i	0.0260930i
$79$	−2.51396e23	−0.478651	−0.239326	−	0.970939i	$-0.576926\pi$
$79$	−2.51396e23	−0.478651	−0.239326	+	0.970939i	$0.576926\pi$
$80$	0	0
$81$	−2.91689e23	−0.406310
$82$	4.84913e23i	0.579416i
$83$	1.47962e24i	1.51941i	0.650270	+	0.759703i	$0.274656\pi$
$83$	1.47962e24i	1.51941i	−0.650270	+	0.759703i	$0.725344\pi$
$84$	−8.36336e21	−0.00739418
$85$	0	0
$86$	5.51054e23	0.363047
$87$	− 6.17554e23i	− 0.352115i
$88$	4.59765e23i	0.227249i
$89$	1.69758e24	0.728544	0.364272	−	0.931293i	$-0.381318\pi$
$89$	1.69758e24	0.728544	0.364272	+	0.931293i	$0.381318\pi$
$90$	0	0
$91$	2.88699e21	0.000938487 0
$92$	− 4.75355e23i	− 0.134794i
$93$	− 2.24804e23i	− 0.0556888i
$94$	−3.18962e24	−0.691259
$95$	0	0
$96$	8.09246e23	0.134800
$97$	− 4.56953e24i	− 0.668689i	−0.942451	−	0.334345i	$-0.891485\pi$
$97$	− 4.56953e24i	− 0.668689i	0.942451	−	0.334345i	$-0.108515\pi$
$98$	− 5.49095e24i	− 0.706841i
$99$	2.37252e24	0.269011
$100$	0	0
$101$	−1.34474e25	−1.18747	−0.593735	−	0.804661i	$-0.702347\pi$
$101$	−1.34474e25	−1.18747	−0.593735	+	0.804661i	$0.702347\pi$
$102$	5.91170e24i	0.461541i
$103$	1.45443e25i	1.00514i	0.864536	+	0.502571i	$0.167612\pi$
$103$	1.45443e25i	1.00514i	−0.864536	+	0.502571i	$0.832388\pi$
$104$	−2.79348e23	−0.0171092
$105$	0	0
$106$	1.30305e25	0.628984
$107$	− 3.33812e25i	− 1.43286i	−0.697657	−	0.716432i	$-0.745774\pi$
$107$	− 3.33812e25i	− 1.43286i	0.697657	−	0.716432i	$-0.254226\pi$
$108$	− 1.41537e25i	− 0.540845i
$109$	−4.20504e25	−1.43199	−0.715993	−	0.698107i	$-0.754026\pi$
$109$	−4.20504e25	−1.43199	−0.715993	+	0.698107i	$0.754026\pi$
$110$	0	0
$111$	3.26163e25	0.884908
$112$	− 1.99903e23i	− 0.00484836i
$113$	− 7.61141e25i	− 1.65190i	−0.563741	−	0.825952i	$-0.690638\pi$
$113$	− 7.61141e25i	− 1.65190i	0.563741	−	0.825952i	$-0.309362\pi$
$114$	−3.80681e25	−0.740031
$115$	0	0
$116$	1.47609e25	0.230881
$117$	1.44152e24i	0.0202533i
$118$	− 8.34063e24i	− 0.105360i
$119$	1.46033e24	0.0166003
$120$	0	0
$121$	−6.35847e25	−0.586862
$122$	− 1.29451e26i	− 1.07797i
$123$	− 8.30968e25i	− 0.624843i
$124$	5.37333e24	0.0365151
$125$	0	0
$126$	−1.03156e24	−0.00573934
$127$	− 2.50269e26i	− 1.26142i	−0.776018	−	0.630710i	$-0.782764\pi$
$127$	− 2.50269e26i	− 1.26142i	0.776018	−	0.630710i	$-0.217236\pi$
$128$	1.93428e25i	0.0883883i
$129$	−9.44310e25	−0.391510
$130$	0	0
$131$	−3.42885e26	−1.17289	−0.586445	−	0.809989i	$-0.699473\pi$
$131$	−3.42885e26	−1.17289	−0.586445	+	0.809989i	$0.699473\pi$
$132$	− 7.87875e25i	− 0.245066i
$133$	9.40373e24i	0.0266167i
$134$	2.04371e26	0.526755
$135$	0	0
$136$	−1.41303e26	−0.302632
$137$	1.44437e26i	0.282274i	0.989990	+	0.141137i	$0.0450757\pi$
$137$	1.44437e26i	0.282274i	−0.989990	+	0.141137i	$0.954924\pi$
$138$	8.14590e25i	0.145362i
$139$	−4.93300e26	−0.804314	−0.402157	−	0.915571i	$-0.631739\pi$
$139$	−4.93300e26	−0.804314	−0.402157	+	0.915571i	$0.631739\pi$
$140$	0	0
$141$	5.46588e26	0.745454
$142$	− 4.78666e26i	− 0.597625i
$143$	2.71971e25i	0.0311044i
$144$	9.98144e25	0.104631
$145$	0	0
$146$	4.40818e26	0.388910
$147$	9.40954e26i	0.762258i
$148$	7.79604e26i	0.580233i
$149$	−1.50844e27	−1.03205	−0.516023	−	0.856575i	$-0.672588\pi$
$149$	−1.50844e27	−1.03205	−0.516023	+	0.856575i	$0.672588\pi$
$150$	0	0
$151$	1.70083e26	0.0985027	0.0492513	−	0.998786i	$-0.484316\pi$
$151$	1.70083e26	0.0985027	0.0492513	+	0.998786i	$0.484316\pi$
$152$	− 9.09913e26i	− 0.485238i
$153$	7.29164e26i	0.358247i
$154$	−1.94624e25	−0.00881429
$155$	0	0
$156$	4.78703e25	0.0184505
$157$	3.29198e27i	1.17142i	0.810522	+	0.585708i	$0.199184\pi$
$157$	3.29198e27i	1.17142i	−0.810522	+	0.585708i	$0.800816\pi$
$158$	1.02972e27i	0.338458i
$159$	−2.23297e27	−0.678296
$160$	0	0
$161$	2.01223e25	0.00522823
$162$	1.19476e27i	0.287305i
$163$	− 5.07392e26i	− 0.112979i	−0.998403	−	0.0564896i	$-0.982009\pi$
$163$	− 5.07392e26i	− 0.112979i	0.998403	−	0.0564896i	$-0.0179908\pi$
$164$	1.98620e27	0.409709
$165$	0	0
$166$	6.06052e27	1.07438
$167$	− 8.44897e26i	− 0.138947i	−0.997584	−	0.0694733i	$-0.977868\pi$
$167$	− 8.44897e26i	− 0.138947i	0.997584	−	0.0694733i	$-0.0221319\pi$
$168$	3.42563e25i	0.00522847i
$169$	7.03989e27	0.997658
$170$	0	0
$171$	−4.69541e27	−0.574410
$172$	− 2.25712e27i	− 0.256713i
$173$	7.54461e27i	0.798106i	0.916928	+	0.399053i	$0.130661\pi$
$173$	7.54461e27i	0.798106i	−0.916928	+	0.399053i	$0.869339\pi$
$174$	−2.52950e27	−0.248983
$175$	0	0
$176$	1.88320e27	0.160690
$177$	1.42929e27i	0.113620i
$178$	− 6.95330e27i	− 0.515159i
$179$	5.46396e27	0.377437	0.188718	−	0.982031i	$-0.439567\pi$
$179$	5.46396e27	0.377437	0.188718	+	0.982031i	$0.439567\pi$
$180$	0	0
$181$	−2.74350e28	−1.64939	−0.824693	−	0.565581i	$-0.808652\pi$
$181$	−2.74350e28	−1.64939	−0.824693	+	0.565581i	$0.808652\pi$
$182$	− 1.18251e25i	0 0.000663611i
$183$	2.21833e28i	1.16249i
$184$	−1.94705e27	−0.0953137
$185$	0	0
$186$	−9.20799e26	−0.0393779
$187$	1.37571e28i	0.550184i
$188$	1.30647e28i	0.488794i
$189$	5.99142e26	0.0209777
$190$	0	0
$191$	−2.53537e28	−0.778258	−0.389129	−	0.921183i	$-0.627224\pi$
$191$	−2.53537e28	−0.778258	−0.389129	+	0.921183i	$0.627224\pi$
$192$	− 3.31467e27i	− 0.0953181i
$193$	− 4.66476e27i	− 0.125708i	−0.998023	−	0.0628540i	$-0.979980\pi$
$193$	− 4.66476e27i	− 0.125708i	0.998023	−	0.0628540i	$-0.0200202\pi$
$194$	−1.87168e28	−0.472835
$195$	0	0
$196$	−2.24909e28	−0.499812
$197$	− 1.14775e28i	− 0.239343i	−0.992814	−	0.119672i	$-0.961816\pi$
$197$	− 1.14775e28i	− 0.239343i	0.992814	−	0.119672i	$-0.0381842\pi$
$198$	− 9.71784e27i	− 0.190219i
$199$	−1.02205e29	−1.87849	−0.939243	−	0.343254i	$-0.888471\pi$
$199$	−1.02205e29	−1.87849	−0.939243	+	0.343254i	$0.888471\pi$
$200$	0	0
$201$	−3.50219e28	−0.568053
$202$	5.50807e28i	0.839668i
$203$	6.24848e26i	0.00895517i
$204$	2.42143e28	0.326359
$205$	0	0
$206$	5.95734e28	0.710742
$207$	1.00474e28i	0.112829i
$208$	1.14421e27i	0.0120980i
$209$	−8.85883e28	−0.882161
$210$	0	0
$211$	1.45021e29	1.28204	0.641020	−	0.767524i	$-0.278512\pi$
$211$	1.45021e29	1.28204	0.641020	+	0.767524i	$0.278512\pi$
$212$	− 5.33731e28i	− 0.444759i
$213$	8.20264e28i	0.644479i
$214$	−1.36729e29	−1.01319
$215$	0	0
$216$	−5.79735e28	−0.382435
$217$	2.27460e26i	0.00141631i
$218$	1.72238e29i	1.01257i
$219$	−7.55406e28	−0.419400
$220$	0	0
$221$	−8.35868e27	−0.0414223
$222$	− 1.33597e29i	− 0.625724i
$223$	3.26058e29i	1.44372i	0.692038	+	0.721861i	$0.256713\pi$
$223$	3.26058e29i	1.44372i	−0.692038	+	0.721861i	$0.743287\pi$
$224$	−8.18804e26	−0.00342831
$225$	0	0
$226$	−3.11763e29	−1.16807
$227$	− 4.25210e29i	− 1.50758i	−0.657115	−	0.753791i	$-0.728223\pi$
$227$	− 4.25210e29i	− 1.50758i	0.657115	−	0.753791i	$-0.271777\pi$
$228$	1.55927e29i	0.523281i
$229$	−5.46098e29	−1.73511	−0.867555	−	0.497342i	$-0.834310\pi$
$229$	−5.46098e29	−1.73511	−0.867555	+	0.497342i	$0.834310\pi$
$230$	0	0
$231$	3.33517e27	0.00950534
$232$	− 6.04608e28i	− 0.163258i
$233$	2.50604e29i	0.641268i	0.947203	+	0.320634i	$0.103896\pi$
$233$	2.50604e29i	0.641268i	−0.947203	+	0.320634i	$0.896104\pi$
$234$	5.90445e27	0.0143213
$235$	0	0
$236$	−3.41632e28	−0.0745005
$237$	− 1.76457e29i	− 0.364993i
$238$	− 5.98153e27i	− 0.0117382i
$239$	−6.64864e29	−1.23811	−0.619055	−	0.785348i	$-0.712484\pi$
$239$	−6.64864e29	−1.23811	−0.619055	+	0.785348i	$0.712484\pi$
$240$	0	0
$241$	2.77555e29	0.465731	0.232866	−	0.972509i	$-0.425190\pi$
$241$	2.77555e29	0.465731	0.232866	+	0.972509i	$0.425190\pi$
$242$	2.60443e29i	0.414974i
$243$	5.10055e29i	0.771859i
$244$	−5.30232e29	−0.762242
$245$	0	0
$246$	−3.40365e29	−0.441830
$247$	− 5.38252e28i	− 0.0664161i
$248$	− 2.20092e28i	− 0.0258201i
$249$	−1.03856e30	−1.15862
$250$	0	0
$251$	−1.49015e30	−1.50421	−0.752105	−	0.659043i	$-0.770962\pi$
$251$	−1.49015e30	−1.50421	−0.752105	+	0.659043i	$0.770962\pi$
$252$	4.22526e27i	0.00405833i
$253$	1.89563e29i	0.173280i
$254$	−1.02510e30	−0.891959
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	− 7.29296e29i	− 0.547948i	−0.961737	−	0.273974i	$-0.911662\pi$
$257$	− 7.29296e29i	− 0.547948i	0.961737	−	0.273974i	$-0.0883383\pi$
$258$	3.86790e29i	0.276840i
$259$	−3.30016e28	−0.0225054
$260$	0	0
$261$	−3.11995e29	−0.193260
$262$	1.40446e30i	0.829358i
$263$	5.88360e29i	0.331281i	0.986186	+	0.165640i	$0.0529691\pi$
$263$	5.88360e29i	0.331281i	−0.986186	+	0.165640i	$0.947031\pi$
$264$	−3.22713e29	−0.173288
$265$	0	0
$266$	3.85177e28	0.0188209
$267$	1.19155e30i	0.555548i
$268$	− 8.37103e29i	− 0.372472i
$269$	−1.22413e30	−0.519904	−0.259952	−	0.965622i	$-0.583707\pi$
$269$	−1.22413e30	−0.519904	−0.259952	+	0.965622i	$0.583707\pi$
$270$	0	0
$271$	−1.53605e30	−0.594688	−0.297344	−	0.954770i	$-0.596101\pi$
$271$	−1.53605e30	−0.594688	−0.297344	+	0.954770i	$0.596101\pi$
$272$	5.78778e29i	0.213993i
$273$	2.02641e27i	0 0.000715638i
$274$	5.91613e29	0.199598
$275$	0	0
$276$	3.33656e29	0.102786
$277$	− 4.32632e29i	− 0.127386i	−0.997970	−	0.0636929i	$-0.979712\pi$
$277$	− 4.32632e29i	− 0.127386i	0.997970	−	0.0636929i	$-0.0202878\pi$
$278$	2.02056e30i	0.568736i
$279$	−1.13574e29	−0.0305650
$280$	0	0
$281$	−3.63667e30	−0.895107	−0.447554	−	0.894257i	$-0.647705\pi$
$281$	−3.63667e30	−0.895107	−0.447554	+	0.894257i	$0.647705\pi$
$282$	− 2.23882e30i	− 0.527116i
$283$	8.38888e30i	1.88962i	0.327624	+	0.944808i	$0.393752\pi$
$283$	8.38888e30i	1.88962i	−0.327624	+	0.944808i	$0.606248\pi$
$284$	−1.96062e30	−0.422585
$285$	0	0
$286$	1.11399e29	0.0219941
$287$	8.40783e28i	0.0158913i
$288$	− 4.08840e29i	− 0.0739856i
$289$	1.54254e30	0.267309
$290$	0	0
$291$	3.20739e30	0.509906
$292$	− 1.80559e30i	− 0.275001i
$293$	8.70672e30i	1.27060i	0.772265	+	0.635301i	$0.219124\pi$
$293$	8.70672e30i	1.27060i	−0.772265	+	0.635301i	$0.780876\pi$
$294$	3.85415e30	0.538998
$295$	0	0
$296$	3.19326e30	0.410287
$297$	5.64425e30i	0.695265i
$298$	6.17856e30i	0.729767i
$299$	−1.15177e29	−0.0130459
$300$	0	0
$301$	9.55463e28	0.00995710
$302$	− 6.96658e29i	− 0.0696519i
$303$	− 9.43888e30i	− 0.905498i
$304$	−3.72700e30	−0.343115
$305$	0	0
$306$	2.98666e30	0.253319
$307$	3.24336e30i	0.264098i	0.991243	+	0.132049i	$0.0421557\pi$
$307$	3.24336e30i	0.264098i	−0.991243	+	0.132049i	$0.957844\pi$
$308$	7.97180e28i	0.00623265i
$309$	−1.02088e31	−0.766465
$310$	0	0
$311$	−1.24495e30	−0.0862281	−0.0431140	−	0.999070i	$-0.513728\pi$
$311$	−1.24495e30	−0.0862281	−0.0431140	+	0.999070i	$0.513728\pi$
$312$	− 1.96077e29i	− 0.0130465i
$313$	− 2.33420e31i	− 1.49222i	−0.665820	−	0.746112i	$-0.731918\pi$
$313$	− 2.33420e31i	− 1.49222i	0.665820	−	0.746112i	$-0.268082\pi$
$314$	1.34839e31	0.828316
$315$	0	0
$316$	4.21772e30	0.239326
$317$	2.11447e31i	1.15335i	0.816974	+	0.576674i	$0.195650\pi$
$317$	2.11447e31i	1.15335i	−0.816974	+	0.576674i	$0.804350\pi$
$318$	9.14626e30i	0.479628i
$319$	−5.88641e30	−0.296802
$320$	0	0
$321$	2.34306e31	1.09262
$322$	− 8.24211e28i	− 0.00369692i
$323$	− 2.72265e31i	− 1.17479i
$324$	4.89374e30	0.203155
$325$	0	0
$326$	−2.07828e30	−0.0798883
$327$	− 2.95156e31i	− 1.09195i
$328$	− 8.13549e30i	− 0.289708i
$329$	−5.53043e29	−0.0189588
$330$	0	0
$331$	−4.35367e31	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$331$	−4.35367e31	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$332$	− 2.48239e31i	− 0.759703i
$333$	− 1.64781e31i	− 0.485685i
$334$	−3.46070e30	−0.0982501
$335$	0	0
$336$	1.40314e29	0.00369709
$337$	− 5.97252e30i	− 0.151630i	−0.997122	−	0.0758148i	$-0.975844\pi$
$337$	− 5.97252e30i	− 0.151630i	0.997122	−	0.0758148i	$-0.0241558\pi$
$338$	− 2.88354e31i	− 0.705451i
$339$	5.34252e31	1.25965
$340$	0	0
$341$	−2.14279e30	−0.0469408
$342$	1.92324e31i	0.406169i
$343$	− 1.90449e30i	− 0.0387796i
$344$	−9.24514e30	−0.181524
$345$	0	0
$346$	3.09027e31	0.564346
$347$	− 9.71425e31i	− 1.71116i	−0.517670	−	0.855580i	$-0.673201\pi$
$347$	− 9.71425e31i	− 1.71116i	0.517670	−	0.855580i	$-0.326799\pi$
$348$	1.03608e31i	0.176057i
$349$	7.20784e31	1.18165	0.590823	−	0.806801i	$-0.298803\pi$
$349$	7.20784e31	1.18165	0.590823	+	0.806801i	$0.298803\pi$
$350$	0	0
$351$	−3.42938e30	−0.0523451
$352$	− 7.71358e30i	− 0.113625i
$353$	− 6.98207e31i	− 0.992660i	−0.868134	−	0.496330i	$-0.834681\pi$
$353$	− 6.98207e31i	− 0.992660i	0.868134	−	0.496330i	$-0.165319\pi$
$354$	5.85437e30	0.0803414
$355$	0	0
$356$	−2.84807e31	−0.364272
$357$	1.02502e30i	0.0126584i
$358$	− 2.23804e31i	− 0.266888i
$359$	1.33870e32	1.54171	0.770857	−	0.637009i	$-0.219829\pi$
$359$	1.33870e32	1.54171	0.770857	+	0.637009i	$0.219829\pi$
$360$	0	0
$361$	8.22469e31	0.883649
$362$	1.12374e32i	1.16629i
$363$	− 4.46307e31i	− 0.447508i
$364$	−4.84357e28	−0.000469244 0
$365$	0	0
$366$	9.08629e31	0.822003
$367$	6.63971e31i	0.580528i	0.956947	+	0.290264i	$0.0937431\pi$
$367$	6.63971e31i	0.580528i	−0.956947	+	0.290264i	$0.906257\pi$
$368$	7.97514e30i	0.0673970i
$369$	−4.19814e31	−0.342947
$370$	0	0
$371$	2.25935e30	0.0172508
$372$	3.77159e30i	0.0278444i
$373$	− 2.18553e32i	− 1.56026i	−0.625619	−	0.780129i	$-0.715154\pi$
$373$	− 2.18553e32i	− 1.56026i	0.625619	−	0.780129i	$-0.284846\pi$
$374$	5.63493e31	0.389039
$375$	0	0
$376$	5.35129e31	0.345629
$377$	− 3.57651e30i	− 0.0223456i
$378$	− 2.45409e30i	− 0.0148334i
$379$	1.48811e32	0.870253	0.435126	−	0.900369i	$-0.356704\pi$
$379$	1.48811e32	0.870253	0.435126	+	0.900369i	$0.356704\pi$
$380$	0	0
$381$	1.75666e32	0.961889
$382$	1.03849e32i	0.550311i
$383$	2.09320e32i	1.07356i	0.843723	+	0.536779i	$0.180359\pi$
$383$	2.09320e32i	1.07356i	−0.843723	+	0.536779i	$0.819641\pi$
$384$	−1.35769e31	−0.0674001
$385$	0	0
$386$	−1.91068e31	−0.0888889
$387$	4.77076e31i	0.214882i
$388$	7.66639e31i	0.334345i
$389$	2.78926e32	1.17793	0.588965	−	0.808158i	$-0.299535\pi$
$389$	2.78926e32	1.17793	0.588965	+	0.808158i	$0.299535\pi$
$390$	0	0
$391$	−5.82600e31	−0.230760
$392$	9.21229e31i	0.353420i
$393$	− 2.40674e32i	− 0.894381i
$394$	−4.70120e31	−0.169241
$395$	0	0
$396$	−3.98043e31	−0.134505
$397$	4.22963e32i	1.38491i	0.721461	+	0.692455i	$0.243471\pi$
$397$	4.22963e32i	1.38491i	−0.721461	+	0.692455i	$0.756529\pi$
$398$	4.18631e32i	1.32829i
$399$	−6.60056e30	−0.0202964
$400$	0	0
$401$	−2.59389e32	−0.749284	−0.374642	−	0.927169i	$-0.622234\pi$
$401$	−2.59389e32	−0.749284	−0.374642	+	0.927169i	$0.622234\pi$
$402$	1.43450e32i	0.401674i
$403$	− 1.30194e30i	− 0.00353408i
$404$	2.25611e32	0.593735
$405$	0	0
$406$	2.55938e30	0.00633226
$407$	− 3.10893e32i	− 0.745900i
$408$	− 9.91820e31i	− 0.230771i
$409$	−7.31347e32	−1.65037	−0.825186	−	0.564861i	$-0.808930\pi$
$409$	−7.31347e32	−1.65037	−0.825186	+	0.564861i	$0.808930\pi$
$410$	0	0
$411$	−1.01381e32	−0.215246
$412$	− 2.44013e32i	− 0.502571i
$413$	− 1.44617e30i	− 0.00288964i
$414$	4.11540e31	0.0797825
$415$	0	0
$416$	4.68668e30	0.00855458
$417$	− 3.46252e32i	− 0.613325i
$418$	3.62858e32i	0.623782i
$419$	6.24972e32	1.04276	0.521381	−	0.853324i	$-0.325417\pi$
$419$	6.24972e32	1.04276	0.521381	+	0.853324i	$0.325417\pi$
$420$	0	0
$421$	−2.51168e32	−0.394855	−0.197427	−	0.980318i	$-0.563259\pi$
$421$	−2.51168e32	−0.394855	−0.197427	+	0.980318i	$0.563259\pi$
$422$	− 5.94008e32i	− 0.906539i
$423$	− 2.76142e32i	− 0.409146i
$424$	−2.18616e32	−0.314492
$425$	0	0
$426$	3.35980e32	0.455716
$427$	− 2.24453e31i	− 0.0295650i
$428$	5.60044e32i	0.716432i
$429$	−1.90899e31	−0.0237185
$430$	0	0
$431$	−1.55381e33	−1.82151	−0.910754	−	0.412948i	$-0.864499\pi$
$431$	−1.55381e33	−1.82151	−0.910754	+	0.412948i	$0.864499\pi$
$432$	2.37459e32i	0.270422i
$433$	− 1.08349e33i	− 1.19874i	−0.800472	−	0.599370i	$-0.795418\pi$
$433$	− 1.08349e33i	− 1.19874i	0.800472	−	0.599370i	$-0.204582\pi$
$434$	9.31674e29	0.00100148
$435$	0	0
$436$	7.05489e32	0.715993
$437$	− 3.75161e32i	− 0.369999i
$438$	3.09414e32i	0.296561i
$439$	−1.66407e33	−1.55012	−0.775058	−	0.631890i	$-0.782279\pi$
$439$	−1.66407e33	−1.55012	−0.775058	+	0.631890i	$0.782279\pi$
$440$	0	0
$441$	4.75380e32	0.418368
$442$	3.42371e31i	0.0292900i
$443$	− 3.77416e32i	− 0.313887i	−0.987608	−	0.156944i	$-0.949836\pi$
$443$	− 3.77416e32i	− 0.313887i	0.987608	−	0.156944i	$-0.0501641\pi$
$444$	−5.47211e32	−0.442454
$445$	0	0
$446$	1.33553e33	1.02087
$447$	− 1.05879e33i	− 0.786981i
$448$	3.35382e30i	0.00242418i
$449$	−2.15921e33	−1.51781	−0.758903	−	0.651204i	$-0.774264\pi$
$449$	−2.15921e33	−1.51781	−0.758903	+	0.651204i	$0.774264\pi$
$450$	0	0
$451$	−7.92063e32	−0.526688
$452$	1.27698e33i	0.825952i
$453$	1.19383e32i	0.0751127i
$454$	−1.74166e33	−1.06602
$455$	0	0
$456$	6.38676e32	0.370016
$457$	8.65127e30i	0.00487671i	0.999997	+	0.00243836i	$0.000776154\pi$
$457$	8.65127e30i	0.00487671i	−0.999997	+	0.00243836i	$0.999224\pi$
$458$	2.23682e33i	1.22691i
$459$	−1.73469e33	−0.925897
$460$	0	0
$461$	−3.15151e33	−1.59315	−0.796575	−	0.604539i	$-0.793357\pi$
$461$	−3.15151e33	−1.59315	−0.796575	+	0.604539i	$0.793357\pi$
$462$	− 1.36608e31i	− 0.00672129i
$463$	2.93719e33i	1.40660i	0.710895	+	0.703298i	$0.248290\pi$
$463$	2.93719e33i	1.40660i	−0.710895	+	0.703298i	$0.751710\pi$
$464$	−2.47647e32	−0.115441
$465$	0	0
$466$	1.02648e33	0.453445
$467$	− 2.28078e33i	− 0.980895i	−0.871471	−	0.490448i	$-0.836833\pi$
$467$	− 2.28078e33i	− 0.980895i	0.871471	−	0.490448i	$-0.163167\pi$
$468$	− 2.41846e31i	− 0.0101267i
$469$	3.54356e31	0.0144470
$470$	0	0
$471$	−2.31067e33	−0.893257
$472$	1.39933e32i	0.0526798i
$473$	9.00099e32i	0.330009i
$474$	−7.22768e32	−0.258089
$475$	0	0
$476$	−2.45003e31	−0.00830013
$477$	1.12812e33i	0.372286i
$478$	2.72328e33i	0.875476i
$479$	7.97173e32	0.249666	0.124833	−	0.992178i	$-0.460161\pi$
$479$	7.97173e32	0.249666	0.124833	+	0.992178i	$0.460161\pi$
$480$	0	0
$481$	1.88895e32	0.0561573
$482$	− 1.13686e33i	− 0.329322i
$483$	1.41241e31i	0.00398676i
$484$	1.06677e33	0.293431
$485$	0	0
$486$	2.08918e33	0.545787
$487$	− 7.32515e32i	− 0.186511i	−0.995642	−	0.0932555i	$-0.970273\pi$
$487$	− 7.32515e32i	− 0.186511i	0.995642	−	0.0932555i	$-0.0297273\pi$
$488$	2.17183e33i	0.538987i
$489$	3.56143e32	0.0861516
$490$	0	0
$491$	−2.35651e33	−0.541690	−0.270845	−	0.962623i	$-0.587303\pi$
$491$	−2.35651e33	−0.541690	−0.270845	+	0.962623i	$0.587303\pi$
$492$	1.39413e33i	0.312421i
$493$	− 1.80911e33i	− 0.395257i
$494$	−2.20468e32	−0.0469633
$495$	0	0
$496$	−9.01496e31	−0.0182576
$497$	− 8.29952e31i	− 0.0163907i
$498$	4.25394e33i	0.819265i
$499$	−1.11697e33	−0.209789	−0.104895	−	0.994483i	$-0.533451\pi$
$499$	−1.11697e33	−0.209789	−0.104895	+	0.994483i	$0.533451\pi$
$500$	0	0
$501$	5.93041e32	0.105953
$502$	6.10366e33i	1.06364i
$503$	− 3.79303e33i	− 0.644743i	−0.946613	−	0.322372i	$-0.895520\pi$
$503$	− 3.79303e33i	− 0.644743i	0.946613	−	0.322372i	$-0.104480\pi$
$504$	1.73067e31	0.00286967
$505$	0	0
$506$	7.76452e32	0.122527
$507$	4.94136e33i	0.760759i
$508$	4.19881e33i	0.630710i
$509$	7.62370e33	1.11736	0.558681	−	0.829383i	$-0.311308\pi$
$509$	7.62370e33	1.11736	0.558681	+	0.829383i	$0.311308\pi$
$510$	0	0
$511$	7.64328e31	0.0106664
$512$	− 3.24519e32i	− 0.0441942i
$513$	− 1.11704e34i	− 1.48458i
$514$	−2.98720e33	−0.387458
$515$	0	0
$516$	1.58429e33	0.195755
$517$	− 5.20997e33i	− 0.628353i
$518$	1.35174e32i	0.0159137i
$519$	−5.29563e33	−0.608592
$520$	0	0
$521$	5.33662e33	0.584514	0.292257	−	0.956340i	$-0.405594\pi$
$521$	5.33662e33	0.584514	0.292257	+	0.956340i	$0.405594\pi$
$522$	1.27793e33i	0.136655i
$523$	− 1.14894e34i	− 1.19957i	−0.800160	−	0.599786i	$-0.795252\pi$
$523$	− 1.14894e34i	− 1.19957i	0.800160	−	0.599786i	$-0.204748\pi$
$524$	5.75265e33	0.586445
$525$	0	0
$526$	2.40992e33	0.234251
$527$	− 6.58561e32i	− 0.0625120i
$528$	1.32183e33i	0.122533i
$529$	1.02430e34	0.927322
$530$	0	0
$531$	7.22092e32	0.0623607
$532$	− 1.57768e32i	− 0.0133084i
$533$	− 4.81248e32i	− 0.0396533i
$534$	4.88059e33	0.392831
$535$	0	0
$536$	−3.42877e33	−0.263378
$537$	3.83520e33i	0.287812i
$538$	5.01403e33i	0.367628i
$539$	8.96900e33	0.642517
$540$	0	0
$541$	−2.08461e34	−1.42580	−0.712901	−	0.701265i	$-0.752619\pi$
$541$	−2.08461e34	−1.42580	−0.712901	+	0.701265i	$0.752619\pi$
$542$	6.29167e33i	0.420508i
$543$	− 1.92569e34i	− 1.25773i
$544$	2.37067e33	0.151316
$545$	0	0
$546$	8.30016e30	0.000506033 0
$547$	− 5.82664e33i	− 0.347197i	−0.984816	−	0.173599i	$-0.944460\pi$
$547$	− 5.82664e33i	− 0.347197i	0.984816	−	0.173599i	$-0.0555395\pi$
$548$	− 2.42324e33i	− 0.141137i
$549$	1.12073e34	0.638036
$550$	0	0
$551$	1.16497e34	0.633751
$552$	− 1.36666e33i	− 0.0726809i
$553$	1.78541e32i	0.00928270i
$554$	−1.77206e33	−0.0900754
$555$	0	0
$556$	8.27619e33	0.402157
$557$	− 2.41168e34i	− 1.14586i	−0.819606	−	0.572928i	$-0.805807\pi$
$557$	− 2.41168e34i	− 1.14586i	0.819606	−	0.572928i	$-0.194193\pi$
$558$	4.65198e32i	0.0216127i
$559$	−5.46889e32	−0.0248457
$560$	0	0
$561$	−9.65626e33	−0.419540
$562$	1.48958e34i	0.632937i
$563$	− 1.42755e34i	− 0.593248i	−0.954994	−	0.296624i	$-0.904139\pi$
$563$	− 1.42755e34i	− 0.593248i	0.954994	−	0.296624i	$-0.0958608\pi$
$564$	−9.17022e33	−0.372727
$565$	0	0
$566$	3.43609e34	1.33616
$567$	2.07158e32i	0.00787975i
$568$	8.03069e33i	0.298812i
$569$	4.47698e34	1.62960	0.814802	−	0.579739i	$-0.196846\pi$
$569$	4.47698e34	1.62960	0.814802	+	0.579739i	$0.196846\pi$
$570$	0	0
$571$	−1.37949e33	−0.0480581	−0.0240291	−	0.999711i	$-0.507649\pi$
$571$	−1.37949e33	−0.0480581	−0.0240291	+	0.999711i	$0.507649\pi$
$572$	− 4.56291e32i	− 0.0155522i
$573$	− 1.77960e34i	− 0.593456i
$574$	3.44385e32	0.0112369
$575$	0	0
$576$	−1.67461e33	−0.0523157
$577$	− 2.32241e33i	− 0.0709973i	−0.999370	−	0.0354986i	$-0.988698\pi$
$577$	− 2.32241e33i	− 0.0709973i	0.999370	−	0.0354986i	$-0.0113019\pi$
$578$	− 6.31825e33i	− 0.189016i
$579$	3.27424e33	0.0958579
$580$	0	0
$581$	1.05082e33	0.0294665
$582$	− 1.31375e34i	− 0.360558i
$583$	2.12843e34i	0.571745i
$584$	−7.39570e33	−0.194455
$585$	0	0
$586$	3.56627e34	0.898451
$587$	4.35047e34i	1.07290i	0.843931	+	0.536451i	$0.180235\pi$
$587$	4.35047e34i	1.07290i	−0.843931	+	0.536451i	$0.819765\pi$
$588$	− 1.57866e34i	− 0.381129i
$589$	4.24076e33	0.100231
$590$	0	0
$591$	8.05619e33	0.182510
$592$	− 1.30796e34i	− 0.290117i
$593$	− 5.31713e34i	− 1.15476i	−0.816474	−	0.577382i	$-0.804074\pi$
$593$	− 5.31713e34i	− 1.15476i	0.816474	−	0.577382i	$-0.195926\pi$
$594$	2.31188e34	0.491626
$595$	0	0
$596$	2.53074e34	0.516023
$597$	− 7.17385e34i	− 1.43243i
$598$	4.71763e32i	0.00922484i
$599$	−7.13123e34	−1.36562	−0.682809	−	0.730597i	$-0.739242\pi$
$599$	−7.13123e34	−1.36562	−0.682809	+	0.730597i	$0.739242\pi$
$600$	0	0
$601$	3.07608e34	0.565023	0.282512	−	0.959264i	$-0.408832\pi$
$601$	3.07608e34	0.565023	0.282512	+	0.959264i	$0.408832\pi$
$602$	− 3.91358e32i	− 0.00704073i
$603$	1.76935e34i	0.311779i
$604$	−2.85351e33	−0.0492513
$605$	0	0
$606$	−3.86617e34	−0.640284
$607$	2.76184e34i	0.448064i	0.974582	+	0.224032i	$0.0719221\pi$
$607$	2.76184e34i	0.448064i	−0.974582	+	0.224032i	$0.928078\pi$
$608$	1.52658e34i	0.242619i
$609$	−4.38586e32	−0.00682871
$610$	0	0
$611$	3.16552e33	0.0473074
$612$	− 1.22333e34i	− 0.179124i
$613$	− 4.94974e34i	− 0.710112i	−0.934845	−	0.355056i	$-0.884462\pi$
$613$	− 4.94974e34i	− 0.710112i	0.934845	−	0.355056i	$-0.115538\pi$
$614$	1.32848e34	0.186746
$615$	0	0
$616$	3.26525e32	0.00440715
$617$	1.12825e35i	1.49225i	0.665805	+	0.746126i	$0.268088\pi$
$617$	1.12825e35i	1.49225i	−0.665805	+	0.746126i	$0.731912\pi$
$618$	4.18151e34i	0.541973i
$619$	−5.35184e34	−0.679782	−0.339891	−	0.940465i	$-0.610390\pi$
$619$	−5.35184e34	−0.679782	−0.339891	+	0.940465i	$0.610390\pi$
$620$	0	0
$621$	−2.39027e34	−0.291610
$622$	5.09934e33i	0.0609725i
$623$	− 1.20562e33i	− 0.0141290i
$624$	−8.03131e32	−0.00922527
$625$	0	0
$626$	−9.56089e34	−1.05516
$627$	− 6.21809e34i	− 0.672687i
$628$	− 5.52302e34i	− 0.585708i
$629$	9.55490e34	0.993329
$630$	0	0
$631$	−9.73214e34	−0.972392	−0.486196	−	0.873850i	$-0.661616\pi$
$631$	−9.73214e34	−0.972392	−0.486196	+	0.873850i	$0.661616\pi$
$632$	− 1.72758e34i	− 0.169229i
$633$	1.01792e35i	0.977612i
$634$	8.66087e34	0.815541
$635$	0	0
$636$	3.74631e34	0.339148
$637$	5.44946e33i	0.0483738i
$638$	2.41107e34i	0.209871i
$639$	4.14406e34	0.353725
$640$	0	0
$641$	−2.79912e34	−0.229772	−0.114886	−	0.993379i	$-0.536650\pi$
$641$	−2.79912e34	−0.229772	−0.114886	+	0.993379i	$0.536650\pi$
$642$	− 9.59717e34i	− 0.772601i
$643$	1.80728e35i	1.42688i	0.700714	+	0.713442i	$0.252865\pi$
$643$	1.80728e35i	1.42688i	−0.700714	+	0.713442i	$0.747135\pi$
$644$	−3.37597e32	−0.00261412
$645$	0	0
$646$	−1.11520e35	−0.830702
$647$	7.31933e34i	0.534771i	0.963590	+	0.267385i	$0.0861597\pi$
$647$	7.31933e34i	0.534771i	−0.963590	+	0.267385i	$0.913840\pi$
$648$	− 2.00447e34i	− 0.143652i
$649$	1.36237e34	0.0957716
$650$	0	0
$651$	−1.59656e32	−0.00108000
$652$	8.51262e33i	0.0564896i
$653$	7.32271e32i	0.00476713i	0.999997	+	0.00238357i	$0.000758713\pi$
$653$	7.32271e32i	0.00476713i	−0.999997	+	0.00238357i	$0.999241\pi$
$654$	−1.20896e35	−0.772128
$655$	0	0
$656$	−3.33229e34	−0.204854
$657$	3.81639e34i	0.230190i
$658$	2.26526e33i	0.0134059i
$659$	−3.37009e35	−1.95692	−0.978460	−	0.206434i	$-0.933814\pi$
$659$	−3.37009e35	−1.95692	−0.978460	+	0.206434i	$0.933814\pi$
$660$	0	0
$661$	1.22749e34	0.0686275	0.0343138	−	0.999411i	$-0.489075\pi$
$661$	1.22749e34	0.0686275	0.0343138	+	0.999411i	$0.489075\pi$
$662$	1.78326e35i	0.978343i
$663$	− 5.86703e33i	− 0.0315863i
$664$	−1.01679e35	−0.537191
$665$	0	0
$666$	−6.74944e34	−0.343431
$667$	− 2.49283e34i	− 0.124486i
$668$	1.41750e34i	0.0694733i
$669$	−2.28863e35	−1.10090
$670$	0	0
$671$	2.11447e35	0.979875
$672$	− 5.74726e32i	− 0.00261424i
$673$	4.17789e35i	1.86538i	0.360673	+	0.932692i	$0.382547\pi$
$673$	4.17789e35i	1.86538i	−0.360673	+	0.932692i	$0.617453\pi$
$674$	−2.44634e34	−0.107218
$675$	0	0
$676$	−1.18110e35	−0.498829
$677$	2.87478e35i	1.19192i	0.803014	+	0.595959i	$0.203228\pi$
$677$	2.87478e35i	1.19192i	−0.803014	+	0.595959i	$0.796772\pi$
$678$	− 2.18830e35i	− 0.890707i
$679$	−3.24527e33	−0.0129682
$680$	0	0
$681$	2.98459e35	1.14960
$682$	8.77688e33i	0.0331922i
$683$	3.52227e35i	1.30787i	0.756551	+	0.653935i	$0.226883\pi$
$683$	3.52227e35i	1.30787i	−0.756551	+	0.653935i	$0.773117\pi$
$684$	7.87759e34	0.287205
$685$	0	0
$686$	−7.80081e33	−0.0274213
$687$	− 3.83311e35i	− 1.32310i
$688$	3.78681e34i	0.128357i
$689$	−1.29321e34	−0.0430455
$690$	0	0
$691$	−1.41869e35	−0.455421	−0.227711	−	0.973729i	$-0.573124\pi$
$691$	−1.41869e35	−0.455421	−0.227711	+	0.973729i	$0.573124\pi$
$692$	− 1.26578e35i	− 0.399053i
$693$	− 1.68496e33i	− 0.00521705i
$694$	−3.97896e35	−1.20997
$695$	0	0
$696$	4.24380e34	0.124491
$697$	− 2.43431e35i	− 0.701400i
$698$	− 2.95233e35i	− 0.835550i
$699$	−1.75901e35	−0.488995
$700$	0	0
$701$	4.11949e35	1.10502	0.552508	−	0.833508i	$-0.313671\pi$
$701$	4.11949e35	1.10502	0.552508	+	0.833508i	$0.313671\pi$
$702$	1.40467e34i	0.0370136i
$703$	6.15282e35i	1.59270i
$704$	−3.15948e34	−0.0803448
$705$	0	0
$706$	−2.85986e35	−0.701917
$707$	9.55036e33i	0.0230291i
$708$	− 2.39795e34i	− 0.0568099i
$709$	3.69515e35	0.860110	0.430055	−	0.902803i	$-0.358494\pi$
$709$	3.69515e35	0.860110	0.430055	+	0.902803i	$0.358494\pi$
$710$	0	0
$711$	−8.91480e34	−0.200328
$712$	1.16657e35i	0.257579i
$713$	− 9.07449e33i	− 0.0196881i
$714$	4.19849e33	0.00895087
$715$	0	0
$716$	−9.16700e34	−0.188718
$717$	− 4.66674e35i	− 0.944114i
$718$	− 5.48333e35i	− 1.09016i
$719$	−2.40654e35	−0.470200	−0.235100	−	0.971971i	$-0.575542\pi$
$719$	−2.40654e35	−0.470200	−0.235100	+	0.971971i	$0.575542\pi$
$720$	0	0
$721$	1.03293e34	0.0194931
$722$	− 3.36883e35i	− 0.624834i
$723$	1.94818e35i	0.355141i
$724$	4.60282e35	0.824693
$725$	0	0
$726$	−1.82807e35	−0.316436
$727$	− 2.82511e34i	− 0.0480680i	−0.999711	−	0.0240340i	$-0.992349\pi$
$727$	− 2.82511e34i	− 0.0480680i	0.999711	−	0.0240340i	$-0.00765099\pi$
$728$	1.98393e32i	0 0.000331805i
$729$	−6.05157e35	−0.994888
$730$	0	0
$731$	−2.76634e35	−0.439479
$732$	− 3.72175e35i	− 0.581244i
$733$	− 1.13647e36i	− 1.74486i	−0.488743	−	0.872428i	$-0.662544\pi$
$733$	− 1.13647e36i	− 1.74486i	0.488743	−	0.872428i	$-0.337456\pi$
$734$	2.71963e35	0.410495
$735$	0	0
$736$	3.26662e34	0.0476568
$737$	3.33822e35i	0.478819i
$738$	1.71956e35i	0.242500i
$739$	7.59548e35	1.05317	0.526587	−	0.850121i	$-0.323472\pi$
$739$	7.59548e35	1.05317	0.526587	+	0.850121i	$0.323472\pi$
$740$	0	0
$741$	3.77804e34	0.0506453
$742$	− 9.25428e33i	− 0.0121982i
$743$	2.06273e35i	0.267352i	0.991025	+	0.133676i	$0.0426781\pi$
$743$	2.06273e35i	0.267352i	−0.991025	+	0.133676i	$0.957322\pi$
$744$	1.54484e34	0.0196890
$745$	0	0
$746$	−8.95193e35	−1.10327
$747$	5.24691e35i	0.635911i
$748$	− 2.30807e35i	− 0.275092i
$749$	−2.37073e34	−0.0277881
$750$	0	0
$751$	−7.61805e34	−0.0863664	−0.0431832	−	0.999067i	$-0.513750\pi$
$751$	−7.61805e34	−0.0863664	−0.0431832	+	0.999067i	$0.513750\pi$
$752$	− 2.19189e35i	− 0.244397i
$753$	− 1.04595e36i	− 1.14703i
$754$	−1.46494e34	−0.0158008
$755$	0	0
$756$	−1.00519e34	−0.0104888
$757$	1.93605e36i	1.98709i	0.113428	+	0.993546i	$0.463817\pi$
$757$	1.93605e36i	1.98709i	−0.113428	+	0.993546i	$0.536183\pi$
$758$	− 6.09530e35i	− 0.615362i
$759$	−1.33056e35	−0.132134
$760$	0	0
$761$	1.19339e36	1.14677	0.573383	−	0.819288i	$-0.305631\pi$
$761$	1.19339e36	1.14677	0.573383	+	0.819288i	$0.305631\pi$
$762$	− 7.19527e35i	− 0.680158i
$763$	2.98642e34i	0.0277711i
$764$	4.25364e35	0.389129
$765$	0	0
$766$	8.57374e35	0.759121
$767$	8.27761e33i	0.00721046i
$768$	5.56110e34i	0.0476590i
$769$	9.68810e35	0.816882	0.408441	−	0.912785i	$-0.366073\pi$
$769$	9.68810e35	0.816882	0.408441	+	0.912785i	$0.366073\pi$
$770$	0	0
$771$	5.11899e35	0.417835
$772$	7.82616e34i	0.0628540i
$773$	8.25175e35i	0.652082i	0.945356	+	0.326041i	$0.105715\pi$
$773$	8.25175e35i	0.652082i	−0.945356	+	0.326041i	$0.894285\pi$
$774$	1.95410e35	0.151945
$775$	0	0
$776$	3.14015e35	0.236417
$777$	− 2.31641e34i	− 0.0171614i
$778$	− 1.14248e36i	− 0.832923i
$779$	1.56756e36	1.12462
$780$	0	0
$781$	7.81861e35	0.543240
$782$	2.38633e35i	0.163172i
$783$	− 7.42239e35i	− 0.499484i
$784$	3.77335e35	0.249906
$785$	0	0
$786$	−9.85801e35	−0.632423
$787$	8.02076e35i	0.506444i	0.967408	+	0.253222i	$0.0814903\pi$
$787$	8.02076e35i	0.506444i	−0.967408	+	0.253222i	$0.918510\pi$
$788$	1.92561e35i	0.119672i
$789$	−4.12975e35	−0.252616
$790$	0	0
$791$	−5.40562e34	−0.0320361
$792$	1.63038e35i	0.0951097i
$793$	1.28473e35i	0.0737729i
$794$	1.73246e36	0.979279
$795$	0	0
$796$	1.71471e36	0.939243
$797$	8.65699e35i	0.466807i	0.972380	+	0.233404i	$0.0749864\pi$
$797$	8.65699e35i	0.466807i	−0.972380	+	0.233404i	$0.925014\pi$
$798$	2.70359e34i	0.0143518i
$799$	1.60122e36	0.836789
$800$	0	0
$801$	6.01984e35	0.304915
$802$	1.06246e36i	0.529824i
$803$	7.20038e35i	0.353518i
$804$	5.87570e35	0.284027
$805$	0	0
$806$	−5.33273e33	−0.00249897
$807$	− 8.59226e35i	− 0.396450i
$808$	− 9.24101e35i	− 0.419834i
$809$	3.72457e36	1.66617	0.833086	−	0.553144i	$-0.186572\pi$
$809$	3.72457e36	1.66617	0.833086	+	0.553144i	$0.186572\pi$
$810$	0	0
$811$	6.42225e35	0.278565	0.139282	−	0.990253i	$-0.455520\pi$
$811$	6.42225e35	0.278565	0.139282	+	0.990253i	$0.455520\pi$
$812$	− 1.04832e34i	− 0.00447758i
$813$	− 1.07817e36i	− 0.453476i
$814$	−1.27342e36	−0.527431
$815$	0	0
$816$	−4.06249e35	−0.163180
$817$	− 1.78137e36i	− 0.704657i
$818$	2.99560e36i	1.16699i
$819$	1.02376e33	0.000392781 0
$820$	0	0
$821$	−2.68244e36	−0.998254	−0.499127	−	0.866529i	$-0.666346\pi$
$821$	−2.68244e36	−0.998254	−0.499127	+	0.866529i	$0.666346\pi$
$822$	4.15258e35i	0.152202i
$823$	8.11664e35i	0.293007i	0.989210	+	0.146504i	$0.0468020\pi$
$823$	8.11664e35i	0.293007i	−0.989210	+	0.146504i	$0.953198\pi$
$824$	−9.99476e35	−0.355371
$825$	0	0
$826$	−5.92351e33	−0.00204328
$827$	− 1.42939e36i	− 0.485661i	−0.970069	−	0.242830i	$-0.921924\pi$
$827$	− 1.42939e36i	− 0.485661i	0.970069	−	0.242830i	$-0.0780758\pi$
$828$	− 1.68567e35i	− 0.0564147i
$829$	1.47702e36	0.486915	0.243458	−	0.969912i	$-0.421718\pi$
$829$	1.47702e36	0.486915	0.243458	+	0.969912i	$0.421718\pi$
$830$	0	0
$831$	3.03668e35	0.0971374
$832$	− 1.91966e34i	− 0.00604900i
$833$	2.75651e36i	0.855652i
$834$	−1.41825e36	−0.433687
$835$	0	0
$836$	1.48626e36	0.441080
$837$	− 2.70193e35i	− 0.0789960i
$838$	− 2.55989e36i	− 0.737344i
$839$	−3.59874e36	−1.02124	−0.510618	−	0.859808i	$-0.670583\pi$
$839$	−3.59874e36	−1.02124	−0.510618	+	0.859808i	$0.670583\pi$
$840$	0	0
$841$	−2.85628e36	−0.786775
$842$	1.02878e36i	0.279204i
$843$	− 2.55261e36i	− 0.682559i
$844$	−2.43306e36	−0.641020
$845$	0	0
$846$	−1.13108e36	−0.289310
$847$	4.51578e34i	0.0113813i
$848$	8.95452e35i	0.222379i
$849$	−5.88823e36	−1.44092
$850$	0	0
$851$	1.31660e36	0.312848
$852$	− 1.37618e36i	− 0.322240i
$853$	− 2.51059e36i	− 0.579312i	−0.957131	−	0.289656i	$-0.906459\pi$
$853$	− 2.51059e36i	− 0.579312i	0.957131	−	0.289656i	$-0.0935409\pi$
$854$	−9.19361e34	−0.0209056
$855$	0	0
$856$	2.29394e36	0.506594
$857$	− 1.62785e36i	− 0.354286i	−0.984185	−	0.177143i	$-0.943314\pi$
$857$	− 1.62785e36i	− 0.354286i	0.984185	−	0.177143i	$-0.0566855\pi$
$858$	7.81921e34i	0.0167715i
$859$	−1.44920e36	−0.306348	−0.153174	−	0.988199i	$-0.548949\pi$
$859$	−1.44920e36	−0.306348	−0.153174	+	0.988199i	$0.548949\pi$
$860$	0	0
$861$	−5.90153e34	−0.0121178
$862$	6.36440e36i	1.28800i
$863$	− 5.15478e36i	− 1.02819i	−0.857732	−	0.514097i	$-0.828127\pi$
$863$	− 5.15478e36i	− 1.02819i	0.857732	−	0.514097i	$-0.171873\pi$
$864$	9.72634e35	0.191217
$865$	0	0
$866$	−4.43796e36	−0.847637
$867$	1.08272e36i	0.203835i
$868$	− 3.81614e33i	0 0.000708154i
$869$	−1.68196e36	−0.307657
$870$	0	0
$871$	−2.02826e35	−0.0360494
$872$	− 2.88968e36i	− 0.506284i
$873$	− 1.62041e36i	− 0.279864i
$874$	−1.53666e36	−0.261629
$875$	0	0
$876$	1.26736e36	0.209700
$877$	− 1.01431e37i	− 1.65453i	−0.561810	−	0.827266i	$-0.689895\pi$
$877$	− 1.01431e37i	− 1.65453i	0.561810	−	0.827266i	$-0.310105\pi$
$878$	6.81602e36i	1.09610i
$879$	−6.11132e36	−0.968890
$880$	0	0
$881$	−3.63479e36	−0.560120	−0.280060	−	0.959983i	$-0.590354\pi$
$881$	−3.63479e36	−0.560120	−0.280060	+	0.959983i	$0.590354\pi$
$882$	− 1.94716e36i	− 0.295831i
$883$	− 4.65240e36i	− 0.696896i	−0.937328	−	0.348448i	$-0.886709\pi$
$883$	− 4.65240e36i	− 0.696896i	0.937328	−	0.348448i	$-0.113291\pi$
$884$	1.40235e35	0.0207111
$885$	0	0
$886$	−1.54589e36	−0.221952
$887$	9.05035e35i	0.128121i	0.997946	+	0.0640604i	$0.0204050\pi$
$887$	9.05035e35i	0.128121i	−0.997946	+	0.0640604i	$0.979595\pi$
$888$	2.24138e36i	0.312862i
$889$	−1.77741e35	−0.0244633
$890$	0	0
$891$	−1.95154e36	−0.261159
$892$	− 5.47034e36i	− 0.721861i
$893$	1.03110e37i	1.34170i
$894$	−4.33679e36	−0.556480
$895$	0	0
$896$	1.37373e34	0.00171415
$897$	− 8.08434e34i	− 0.00994808i
$898$	8.84413e36i	1.07325i
$899$	2.81785e35	0.0337227
$900$	0	0
$901$	−6.54146e36	−0.761403
$902$	3.24429e36i	0.372424i
$903$	6.70648e34i	0.00759273i
$904$	5.23052e36	0.584036
$905$	0	0
$906$	4.88991e35	0.0531127
$907$	− 3.58423e36i	− 0.383977i	−0.981397	−	0.191988i	$-0.938506\pi$
$907$	− 3.58423e36i	− 0.383977i	0.981397	−	0.191988i	$-0.0614936\pi$
$908$	7.13385e36i	0.753791i
$909$	−4.76862e36	−0.496986
$910$	0	0
$911$	5.15388e36	0.522582	0.261291	−	0.965260i	$-0.415852\pi$
$911$	5.15388e36	0.522582	0.261291	+	0.965260i	$0.415852\pi$
$912$	− 2.61602e36i	− 0.261641i
$913$	9.89934e36i	0.976611i
$914$	3.54356e34	0.00344836
$915$	0	0
$916$	9.16200e36	0.867555
$917$	2.43517e35i	0.0227464i
$918$	7.10528e36i	0.654708i
$919$	−1.45442e36	−0.132205	−0.0661023	−	0.997813i	$-0.521056\pi$
$919$	−1.45442e36	−0.132205	−0.0661023	+	0.997813i	$0.521056\pi$
$920$	0	0
$921$	−2.27655e36	−0.201387
$922$	1.29086e37i	1.12653i
$923$	4.75049e35i	0.0408994i
$924$	−5.59548e34	−0.00475267
$925$	0	0
$926$	1.20307e37	0.994614
$927$	5.15758e36i	0.420678i
$928$	1.01436e36i	0.0816289i
$929$	−1.48492e37	−1.17898	−0.589491	−	0.807775i	$-0.700672\pi$
$929$	−1.48492e37	−1.17898	−0.589491	+	0.807775i	$0.700672\pi$
$930$	0	0
$931$	−1.77504e37	−1.37194
$932$	− 4.20444e36i	− 0.320634i
$933$	− 8.73845e35i	− 0.0657528i
$934$	−9.34208e36	−0.693598
$935$	0	0
$936$	−9.90602e34	−0.00716063
$937$	4.13990e36i	0.295288i	0.989041	+	0.147644i	$0.0471689\pi$
$937$	4.13990e36i	0.295288i	−0.989041	+	0.147644i	$0.952831\pi$
$938$	− 1.45144e35i	− 0.0102156i
$939$	1.63840e37	1.13789
$940$	0	0
$941$	3.04574e36	0.205979	0.102989	−	0.994682i	$-0.467159\pi$
$941$	3.04574e36	0.205979	0.102989	+	0.994682i	$0.467159\pi$
$942$	9.46450e36i	0.631628i
$943$	− 3.35430e36i	− 0.220905i
$944$	5.73164e35	0.0372502
$945$	0	0
$946$	3.68680e36	0.233352
$947$	1.93836e37i	1.21076i	0.795935	+	0.605382i	$0.206980\pi$
$947$	1.93836e37i	1.21076i	−0.795935	+	0.605382i	$0.793020\pi$
$948$	2.96046e36i	0.182497i
$949$	−4.37487e35	−0.0266157
$950$	0	0
$951$	−1.48417e37	−0.879480
$952$	1.00353e35i	0.00586908i
$953$	7.72509e35i	0.0445905i	0.999751	+	0.0222952i	$0.00709738\pi$
$953$	7.72509e35i	0.0445905i	−0.999751	+	0.0222952i	$0.992903\pi$
$954$	4.62079e36	0.263246
$955$	0	0
$956$	1.11546e37	0.619055
$957$	− 4.13172e36i	− 0.226325i
$958$	− 3.26522e36i	− 0.176540i
$959$	1.02579e35	0.00547425
$960$	0	0
$961$	−1.91302e37	−0.994667
$962$	− 7.73713e35i	− 0.0397092i
$963$	− 1.18374e37i	− 0.599690i
$964$	−4.65659e36	−0.232866
$965$	0	0
$966$	5.78521e34	0.00281907
$967$	− 6.95372e36i	− 0.334492i	−0.985915	−	0.167246i	$-0.946513\pi$
$967$	− 6.95372e36i	− 0.334492i	0.985915	−	0.167246i	$-0.0534874\pi$
$968$	− 4.36951e36i	− 0.207487i
$969$	1.91105e37	0.895830
$970$	0	0
$971$	2.67539e37	1.22221	0.611106	−	0.791549i	$-0.290725\pi$
$971$	2.67539e37	1.22221	0.611106	+	0.791549i	$0.290725\pi$
$972$	− 8.55729e36i	− 0.385930i
$973$	3.50341e35i	0.0155984i
$974$	−3.00038e36	−0.131883
$975$	0	0
$976$	8.89581e36	0.381121
$977$	2.82491e37i	1.19488i	0.801915	+	0.597438i	$0.203815\pi$
$977$	2.82491e37i	1.19488i	−0.801915	+	0.597438i	$0.796185\pi$
$978$	− 1.45876e36i	− 0.0609184i
$979$	1.13576e37	0.468278
$980$	0	0
$981$	−1.49116e37	−0.599323
$982$	9.65226e36i	0.383032i
$983$	− 3.52532e37i	− 1.38127i	−0.723203	−	0.690636i	$-0.757331\pi$
$983$	− 3.52532e37i	− 1.38127i	0.723203	−	0.690636i	$-0.242669\pi$
$984$	5.71037e36	0.220915
$985$	0	0
$986$	−7.41013e36	−0.279489
$987$	− 3.88186e35i	− 0.0144569i
$988$	9.03037e35i	0.0332081i
$989$	−3.81182e36	−0.138413
$990$	0	0
$991$	−1.01549e36	−0.0359547	−0.0179774	−	0.999838i	$-0.505723\pi$
$991$	−1.01549e36	−0.0359547	−0.0179774	+	0.999838i	$0.505723\pi$
$992$	3.69253e35i	0.0129100i
$993$	− 3.05588e37i	− 1.05505i
$994$	−3.39948e35	−0.0115900
$995$	0	0
$996$	1.74241e37	0.579308
$997$	− 5.04007e37i	− 1.65481i	−0.561608	−	0.827403i	$-0.689817\pi$
$997$	− 5.04007e37i	− 1.65481i	0.561608	−	0.827403i	$-0.310183\pi$
$998$	4.57509e36i	0.148343i
$999$	3.92016e37	1.25526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.c.49.2		4
5.2	odd	4		50.26.a.e.1.2		2
5.3	odd	4		10.26.a.c.1.1	✓	2
5.4	even	2	inner	50.26.b.c.49.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.c.1.1	✓	2	5.3	odd	4
50.26.a.e.1.2		2	5.2	odd	4
50.26.b.c.49.2		4	1.1	even	1	trivial
50.26.b.c.49.3		4	5.4	even	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4096.00i q^{2} +701909. i q^{3} -1.67772e7 q^{4} +2.87502e9 q^{6} -7.10199e8i q^{7} +6.87195e10i q^{8} +3.54612e11 q^{9} +6.69047e12 q^{11} -1.17761e13i q^{12} +4.06505e12i q^{13} -2.90898e12 q^{14} +2.81475e14 q^{16} +2.05623e15i q^{17} -1.45249e15i q^{18} -1.32410e16 q^{19} +4.98495e14 q^{21} -2.74041e16i q^{22} +2.83334e16i q^{23} -4.82348e16 q^{24} +1.66504e16 q^{26} +8.43625e17i q^{27} +1.19152e16i q^{28} -8.79820e17 q^{29} -3.20276e17 q^{31} -1.15292e18i q^{32} +4.69610e18i q^{33} +8.42232e18 q^{34} -5.94940e18 q^{36} -4.64680e19i q^{37} +5.42350e19i q^{38} -2.85329e18 q^{39} -1.18387e20 q^{41} -2.04184e18i q^{42} +1.34535e20i q^{43} -1.12247e20 q^{44} +1.16053e20 q^{46} -7.78716e20i q^{47} +1.97570e20i q^{48} +1.34056e21 q^{49} -1.44329e21 q^{51} -6.82002e19i q^{52} +3.18129e21i q^{53} +3.45549e21 q^{54} +4.88045e19 q^{56} -9.29396e21i q^{57} +3.60374e21i q^{58} +2.03629e21 q^{59} +3.16043e22 q^{61} +1.31185e21i q^{62} -2.51845e20i q^{63} -4.72237e21 q^{64} +1.92352e22 q^{66} +4.98952e22i q^{67} -3.44978e22i q^{68} -1.98875e22 q^{69} +1.16862e23 q^{71} +2.43688e22i q^{72} +1.07622e23i q^{73} -1.90333e23 q^{74} +2.22147e23 q^{76} -4.75156e21i q^{77} +1.16871e22i q^{78} -2.51396e23 q^{79} -2.91689e23 q^{81} +4.84913e23i q^{82} +1.47962e24i q^{83} -8.36336e21 q^{84} +5.51054e23 q^{86} -6.17554e23i q^{87} +4.59765e23i q^{88} +1.69758e24 q^{89} +2.88699e21 q^{91} -4.75355e23i q^{92} -2.24804e23i q^{93} -3.18962e24 q^{94} +8.09246e23 q^{96} -4.56953e24i q^{97} -5.49095e24i q^{98} +2.37252e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 67108864 q^{4} - 4466376704 q^{6} - 706820944772 q^{9} - 16758339752832 q^{11} + 315947884249088 q^{14} + 11\!\cdots\!24 q^{16} - 69\!\cdots\!40 q^{19} + 98\!\cdots\!68 q^{21} + 74\!\cdots\!64 q^{24}+ \cdots + 26\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 67108864 * q^4 - 4466376704 * q^6 - 706820944772 * q^9 - 16758339752832 * q^11 + 315947884249088 * q^14 + 1125899906842624 * q^16 - 6978922831721840 * q^19 + 98965981439235568 * q^21 + 74933366700376064 * q^24 + 1224243095117725696 * q^26 + 1074887575919712360 * q^29 - 7248055568882624272 * q^31 + 27519011219504529408 * q^34 + 11858487663763914752 * q^36 + 356903093544598090256 * q^39 - 425179161247761543912 * q^41 + 281158285834649075712 * q^44 - 592856694194362220544 * q^46 + 2277734314701483659532 * q^49 + 363481383446781200688 * q^51 + 5488177642216870707200 * q^54 - 5300725898789947179008 * q^56 + 26295013412413600195920 * q^59 + 228823556614751495048 * q^61 - 18889465931478580854784 * q^64 + 192428119729102082015232 * q^66 - 290954022626555501624784 * q^69 + 167498518990330675485648 * q^71 + 155963987267122346098688 * q^74 + 117086895795128961597440 * q^76 - 211743190052114441384480 * q^79 - 2216381757932045545655596 * q^81 - 1660373647258045999218688 * q^84 + 111971687855373081542656 * q^86 + 3754707904362558847478040 * q^89 - 11414610679497993001794032 * q^91 - 13645264040406039381245952 * q^94 - 1257173278739416506957824 * q^96 + 26084325647996078762722176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more