LMFDB - Embedded newform 950.2.b.h.799.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.63107136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 42x^{2} + 9 $ x^6 + 13x^4 + 42x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.4
Root			$-2.25342i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.h.799.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.25342i q^{3} -1.00000 q^{4} +3.25342 q^{6} -0.0778929i q^{7} -1.00000i q^{8} -7.58473 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.25342i q^{3} -1.00000 q^{4} +3.25342 q^{6} -0.0778929i q^{7} -1.00000i q^{8} -7.58473 q^{9} -4.50684 q^{11} +3.25342i q^{12} +5.33131i q^{13} +0.0778929 q^{14} +1.00000 q^{16} +7.33131i q^{17} -7.58473i q^{18} -1.00000 q^{19} -0.253418 q^{21} -4.50684i q^{22} -3.40920i q^{23} -3.25342 q^{24} -5.33131 q^{26} +14.9160i q^{27} +0.0778929i q^{28} +1.33131 q^{29} -2.50684 q^{31} +1.00000i q^{32} +14.6626i q^{33} -7.33131 q^{34} +7.58473 q^{36} -5.50684i q^{37} -1.00000i q^{38} +17.3450 q^{39} -0.253418i q^{42} -0.506836i q^{43} +4.50684 q^{44} +3.40920 q^{46} -5.66262i q^{47} -3.25342i q^{48} +6.99393 q^{49} +23.8518 q^{51} -5.33131i q^{52} +12.9358i q^{53} -14.9160 q^{54} -0.0778929 q^{56} +3.25342i q^{57} +1.33131i q^{58} -7.56499 q^{59} -2.15579 q^{61} -2.50684i q^{62} +0.590796i q^{63} -1.00000 q^{64} -14.6626 q^{66} -4.58473i q^{67} -7.33131i q^{68} -11.0916 q^{69} -10.8579 q^{71} +7.58473i q^{72} +5.09763i q^{73} +5.50684 q^{74} +1.00000 q^{76} +0.351050i q^{77} +17.3450i q^{78} -17.0137 q^{79} +25.7739 q^{81} +13.1695i q^{83} +0.253418 q^{84} +0.506836 q^{86} -4.33131i q^{87} +4.50684i q^{88} -15.0137 q^{89} +0.415271 q^{91} +3.40920i q^{92} +8.15579i q^{93} +5.66262 q^{94} +3.25342 q^{96} +7.67629i q^{97} +6.99393i q^{98} +34.1831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{6} - 10 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 4 * q^6 - 10 * q^9	$ 6 q - 6 q^{4} + 4 q^{6} - 10 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} - 6 q^{19} + 14 q^{21} - 4 q^{24} - 12 q^{26} - 12 q^{29} + 16 q^{31} - 24 q^{34} + 10 q^{36} + 22 q^{39} - 4 q^{44} - 4 q^{46} - 18 q^{49} + 30 q^{51} - 34 q^{54} + 4 q^{56} - 12 q^{59} - 4 q^{61} - 6 q^{64} - 48 q^{66} - 12 q^{71} + 2 q^{74} + 6 q^{76} - 40 q^{79} + 46 q^{81} - 14 q^{84} - 28 q^{86} - 28 q^{89} + 38 q^{91} - 6 q^{94} + 4 q^{96} + 72 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^6 - 10 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 - 6 * q^19 + 14 * q^21 - 4 * q^24 - 12 * q^26 - 12 * q^29 + 16 * q^31 - 24 * q^34 + 10 * q^36 + 22 * q^39 - 4 * q^44 - 4 * q^46 - 18 * q^49 + 30 * q^51 - 34 * q^54 + 4 * q^56 - 12 * q^59 - 4 * q^61 - 6 * q^64 - 48 * q^66 - 12 * q^71 + 2 * q^74 + 6 * q^76 - 40 * q^79 + 46 * q^81 - 14 * q^84 - 28 * q^86 - 28 * q^89 + 38 * q^91 - 6 * q^94 + 4 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 3.25342i	− 1.87836i	−0.343423	−	0.939181i	$-0.611586\pi$
$3$	− 3.25342i	− 1.87836i	0.343423	−	0.939181i	$-0.388414\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	3.25342	1.32820
$7$	− 0.0778929i	− 0.0294407i	−0.999892	−	0.0147204i	$-0.995314\pi$
$7$	− 0.0778929i	− 0.0294407i	0.999892	−	0.0147204i	$-0.00468581\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−7.58473	−2.52824
$10$	0	0
$11$	−4.50684	−1.35886	−0.679431	−	0.733739i	$-0.737773\pi$
$11$	−4.50684	−1.35886	−0.679431	+	0.733739i	$0.737773\pi$
$12$	3.25342i	0.939181i
$13$	5.33131i	1.47864i	0.673354	+	0.739320i	$0.264853\pi$
$13$	5.33131i	1.47864i	−0.673354	+	0.739320i	$0.735147\pi$
$14$	0.0778929	0.0208177
$15$	0	0
$16$	1.00000	0.250000
$17$	7.33131i	1.77810i	0.457806	+	0.889052i	$0.348635\pi$
$17$	7.33131i	1.77810i	−0.457806	+	0.889052i	$0.651365\pi$
$18$	− 7.58473i	− 1.78774i
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	−0.253418	−0.0553003
$22$	− 4.50684i	− 0.960861i
$23$	− 3.40920i	− 0.710868i	−0.934701	−	0.355434i	$-0.884333\pi$
$23$	− 3.40920i	− 0.710868i	0.934701	−	0.355434i	$-0.115667\pi$
$24$	−3.25342	−0.664101
$25$	0	0
$26$	−5.33131	−1.04556
$27$	14.9160i	2.87059i
$28$	0.0778929i	0.0147204i
$29$	1.33131	0.247218	0.123609	−	0.992331i	$-0.460553\pi$
$29$	1.33131	0.247218	0.123609	+	0.992331i	$0.460553\pi$
$30$	0	0
$31$	−2.50684	−0.450241	−0.225121	−	0.974331i	$-0.572278\pi$
$31$	−2.50684	−0.450241	−0.225121	+	0.974331i	$0.572278\pi$
$32$	1.00000i	0.176777i
$33$	14.6626i	2.55243i
$34$	−7.33131	−1.25731
$35$	0	0
$36$	7.58473	1.26412
$37$	− 5.50684i	− 0.905318i	−0.891684	−	0.452659i	$-0.850475\pi$
$37$	− 5.50684i	− 0.905318i	0.891684	−	0.452659i	$-0.149525\pi$
$38$	− 1.00000i	− 0.162221i
$39$	17.3450	2.77742
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	− 0.253418i	− 0.0391033i
$43$	− 0.506836i	− 0.0772918i	−0.999253	−	0.0386459i	$-0.987696\pi$
$43$	− 0.506836i	− 0.0772918i	0.999253	−	0.0386459i	$-0.0123044\pi$
$44$	4.50684	0.679431
$45$	0	0
$46$	3.40920	0.502660
$47$	− 5.66262i	− 0.825978i	−0.910736	−	0.412989i	$-0.864485\pi$
$47$	− 5.66262i	− 0.825978i	0.910736	−	0.412989i	$-0.135515\pi$
$48$	− 3.25342i	− 0.469590i
$49$	6.99393	0.999133
$50$	0	0
$51$	23.8518	3.33992
$52$	− 5.33131i	− 0.739320i
$53$	12.9358i	1.77687i	0.459006	+	0.888433i	$0.348206\pi$
$53$	12.9358i	1.77687i	−0.459006	+	0.888433i	$0.651794\pi$
$54$	−14.9160	−2.02982
$55$	0	0
$56$	−0.0778929	−0.0104089
$57$	3.25342i	0.430926i
$58$	1.33131i	0.174810i
$59$	−7.56499	−0.984878	−0.492439	−	0.870347i	$-0.663894\pi$
$59$	−7.56499	−0.984878	−0.492439	+	0.870347i	$0.663894\pi$
$60$	0	0
$61$	−2.15579	−0.276020	−0.138010	−	0.990431i	$-0.544071\pi$
$61$	−2.15579	−0.276020	−0.138010	+	0.990431i	$0.544071\pi$
$62$	− 2.50684i	− 0.318369i
$63$	0.590796i	0.0744333i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−14.6626	−1.80484
$67$	− 4.58473i	− 0.560114i	−0.959983	−	0.280057i	$-0.909647\pi$
$67$	− 4.58473i	− 0.560114i	0.959983	−	0.280057i	$-0.0903533\pi$
$68$	− 7.33131i	− 0.889052i
$69$	−11.0916	−1.33527
$70$	0	0
$71$	−10.8579	−1.28859	−0.644297	−	0.764775i	$-0.722850\pi$
$71$	−10.8579	−1.28859	−0.644297	+	0.764775i	$0.722850\pi$
$72$	7.58473i	0.893869i
$73$	5.09763i	0.596633i	0.954467	+	0.298316i	$0.0964250\pi$
$73$	5.09763i	0.596633i	−0.954467	+	0.298316i	$0.903575\pi$
$74$	5.50684	0.640157
$75$	0	0
$76$	1.00000	0.114708
$77$	0.351050i	0.0400059i
$78$	17.3450i	1.96393i
$79$	−17.0137	−1.91419	−0.957094	−	0.289778i	$-0.906418\pi$
$79$	−17.0137	−1.91419	−0.957094	+	0.289778i	$0.906418\pi$
$80$	0	0
$81$	25.7739	2.86377
$82$	0	0
$83$	13.1695i	1.44554i	0.691091	+	0.722768i	$0.257130\pi$
$83$	13.1695i	1.44554i	−0.691091	+	0.722768i	$0.742870\pi$
$84$	0.253418	0.0276502
$85$	0	0
$86$	0.506836	0.0546535
$87$	− 4.33131i	− 0.464365i
$88$	4.50684i	0.480430i
$89$	−15.0137	−1.59145	−0.795723	−	0.605661i	$-0.792909\pi$
$89$	−15.0137	−1.59145	−0.795723	+	0.605661i	$0.792909\pi$
$90$	0	0
$91$	0.415271	0.0435322
$92$	3.40920i	0.355434i
$93$	8.15579i	0.845716i
$94$	5.66262	0.584055
$95$	0	0
$96$	3.25342	0.332051
$97$	7.67629i	0.779410i	0.920940	+	0.389705i	$0.127423\pi$
$97$	7.67629i	0.779410i	−0.920940	+	0.389705i	$0.872577\pi$
$98$	6.99393i	0.706494i
$99$	34.1831	3.43553
$100$	0	0
$101$	−4.15579	−0.413516	−0.206758	−	0.978392i	$-0.566291\pi$
$101$	−4.15579	−0.413516	−0.206758	+	0.978392i	$0.566291\pi$
$102$	23.8518i	2.36168i
$103$	− 2.35105i	− 0.231656i	−0.993269	−	0.115828i	$-0.963048\pi$
$103$	− 2.35105i	− 0.231656i	0.993269	−	0.115828i	$-0.0369521\pi$
$104$	5.33131	0.522778
$105$	0	0
$106$	−12.9358	−1.25643
$107$	− 14.0334i	− 1.35666i	−0.734757	−	0.678331i	$-0.762704\pi$
$107$	− 14.0334i	− 1.35666i	0.734757	−	0.678331i	$-0.237296\pi$
$108$	− 14.9160i	− 1.43530i
$109$	0.0778929	0.00746078	0.00373039	−	0.999993i	$-0.498813\pi$
$109$	0.0778929	0.00746078	0.00373039	+	0.999993i	$0.498813\pi$
$110$	0	0
$111$	−17.9160	−1.70052
$112$	− 0.0778929i	− 0.00736018i
$113$	6.00000i	0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$	6.00000i	0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$	−3.25342	−0.304711
$115$	0	0
$116$	−1.33131	−0.123609
$117$	− 40.4365i	− 3.73836i
$118$	− 7.56499i	− 0.696414i
$119$	0.571057	0.0523487
$120$	0	0
$121$	9.31157	0.846506
$122$	− 2.15579i	− 0.195176i
$123$	0	0
$124$	2.50684	0.225121
$125$	0	0
$126$	−0.590796	−0.0526323
$127$	17.8321i	1.58234i	0.611596	+	0.791171i	$0.290528\pi$
$127$	17.8321i	1.58234i	−0.611596	+	0.791171i	$0.709472\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.64895	−0.145182
$130$	0	0
$131$	−1.49316	−0.130458	−0.0652292	−	0.997870i	$-0.520778\pi$
$131$	−1.49316	−0.130458	−0.0652292	+	0.997870i	$0.520778\pi$
$132$	− 14.6626i	− 1.27622i
$133$	0.0778929i	0.00675417i
$134$	4.58473	0.396060
$135$	0	0
$136$	7.33131	0.628655
$137$	− 8.42894i	− 0.720133i	−0.932927	−	0.360067i	$-0.882754\pi$
$137$	− 8.42894i	− 0.720133i	0.932927	−	0.360067i	$-0.117246\pi$
$138$	− 11.0916i	− 0.944177i
$139$	−8.81841	−0.747968	−0.373984	−	0.927435i	$-0.622008\pi$
$139$	−8.81841	−0.747968	−0.373984	+	0.927435i	$0.622008\pi$
$140$	0	0
$141$	−18.4229	−1.55149
$142$	− 10.8579i	− 0.911174i
$143$	− 24.0273i	− 2.00927i
$144$	−7.58473	−0.632061
$145$	0	0
$146$	−5.09763	−0.421883
$147$	− 22.7542i	− 1.87673i
$148$	5.50684i	0.452659i
$149$	−17.6763	−1.44810	−0.724049	−	0.689748i	$-0.757721\pi$
$149$	−17.6763	−1.44810	−0.724049	+	0.689748i	$0.757721\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	1.00000i	0.0811107i
$153$	− 55.6060i	− 4.49548i
$154$	−0.351050	−0.0282884
$155$	0	0
$156$	−17.3450	−1.38871
$157$	0.506836i	0.0404499i	0.999795	+	0.0202250i	$0.00643824\pi$
$157$	0.506836i	0.0404499i	−0.999795	+	0.0202250i	$0.993562\pi$
$158$	− 17.0137i	− 1.35354i
$159$	42.0855	3.33760
$160$	0	0
$161$	−0.265553	−0.0209285
$162$	25.7739i	2.02499i
$163$	− 0.830542i	− 0.0650531i	−0.999471	−	0.0325265i	$-0.989645\pi$
$163$	− 0.830542i	− 0.0650531i	0.999471	−	0.0325265i	$-0.0103553\pi$
$164$	0	0
$165$	0	0
$166$	−13.1695	−1.02215
$167$	16.5068i	1.27734i	0.769482	+	0.638669i	$0.220515\pi$
$167$	16.5068i	1.27734i	−0.769482	+	0.638669i	$0.779485\pi$
$168$	0.253418i	0.0195516i
$169$	−15.4229	−1.18638
$170$	0	0
$171$	7.58473	0.580019
$172$	0.506836i	0.0386459i
$173$	− 18.8321i	− 1.43178i	−0.698215	−	0.715888i	$-0.746022\pi$
$173$	− 18.8321i	− 1.43178i	0.698215	−	0.715888i	$-0.253978\pi$
$174$	4.33131	0.328356
$175$	0	0
$176$	−4.50684	−0.339716
$177$	24.6121i	1.84996i
$178$	− 15.0137i	− 1.12532i
$179$	7.15579	0.534849	0.267424	−	0.963579i	$-0.413827\pi$
$179$	7.15579	0.534849	0.267424	+	0.963579i	$0.413827\pi$
$180$	0	0
$181$	12.5205	0.930642	0.465321	−	0.885142i	$-0.345939\pi$
$181$	12.5205	0.930642	0.465321	+	0.885142i	$0.345939\pi$
$182$	0.415271i	0.0307819i
$183$	7.01367i	0.518466i
$184$	−3.40920	−0.251330
$185$	0	0
$186$	−8.15579	−0.598011
$187$	− 33.0410i	− 2.41620i
$188$	5.66262i	0.412989i
$189$	1.16185	0.0845124
$190$	0	0
$191$	−4.90237	−0.354723	−0.177361	−	0.984146i	$-0.556756\pi$
$191$	−4.90237	−0.354723	−0.177361	+	0.984146i	$0.556756\pi$
$192$	3.25342i	0.234795i
$193$	− 18.1558i	− 1.30688i	−0.756977	−	0.653441i	$-0.773325\pi$
$193$	− 18.1558i	− 1.30688i	0.756977	−	0.653441i	$-0.226675\pi$
$194$	−7.67629	−0.551126
$195$	0	0
$196$	−6.99393	−0.499567
$197$	− 2.98633i	− 0.212767i	−0.994325	−	0.106384i	$-0.966073\pi$
$197$	− 2.98633i	− 0.212767i	0.994325	−	0.106384i	$-0.0339271\pi$
$198$	34.1831i	2.42929i
$199$	3.06422	0.217217	0.108608	−	0.994085i	$-0.465361\pi$
$199$	3.06422	0.217217	0.108608	+	0.994085i	$0.465361\pi$
$200$	0	0
$201$	−14.9160	−1.05210
$202$	− 4.15579i	− 0.292400i
$203$	− 0.103700i	− 0.00727829i
$204$	−23.8518	−1.66996
$205$	0	0
$206$	2.35105	0.163805
$207$	25.8579i	1.79725i
$208$	5.33131i	0.369660i
$209$	4.50684	0.311744
$210$	0	0
$211$	19.2534	1.32546	0.662730	−	0.748858i	$-0.269398\pi$
$211$	19.2534	1.32546	0.662730	+	0.748858i	$0.269398\pi$
$212$	− 12.9358i	− 0.888433i
$213$	35.3252i	2.42045i
$214$	14.0334	0.959304
$215$	0	0
$216$	14.9160	1.01491
$217$	0.195265i	0.0132554i
$218$	0.0778929i	0.00527557i
$219$	16.5847	1.12069
$220$	0	0
$221$	−39.0855	−2.62918
$222$	− 17.9160i	− 1.20245i
$223$	14.5068i	0.971450i	0.874112	+	0.485725i	$0.161444\pi$
$223$	14.5068i	0.971450i	−0.874112	+	0.485725i	$0.838556\pi$
$224$	0.0778929	0.00520444
$225$	0	0
$226$	−6.00000	−0.399114
$227$	− 21.5984i	− 1.43354i	−0.697312	−	0.716768i	$-0.745621\pi$
$227$	− 21.5984i	− 1.43354i	0.697312	−	0.716768i	$-0.254379\pi$
$228$	− 3.25342i	− 0.215463i
$229$	19.0137	1.25646	0.628229	−	0.778028i	$-0.283780\pi$
$229$	19.0137	1.25646	0.628229	+	0.778028i	$0.283780\pi$
$230$	0	0
$231$	1.14211	0.0751456
$232$	− 1.33131i	− 0.0874048i
$233$	6.01367i	0.393969i	0.980407	+	0.196984i	$0.0631148\pi$
$233$	6.01367i	0.393969i	−0.980407	+	0.196984i	$0.936885\pi$
$234$	40.4365	2.64342
$235$	0	0
$236$	7.56499	0.492439
$237$	55.3526i	3.59554i
$238$	0.571057i	0.0370161i
$239$	−15.4092	−0.996739	−0.498369	−	0.866965i	$-0.666068\pi$
$239$	−15.4092	−0.996739	−0.498369	+	0.866965i	$0.666068\pi$
$240$	0	0
$241$	−4.81841	−0.310381	−0.155190	−	0.987885i	$-0.549599\pi$
$241$	−4.81841	−0.310381	−0.155190	+	0.987885i	$0.549599\pi$
$242$	9.31157i	0.598570i
$243$	− 39.1052i	− 2.50860i
$244$	2.15579	0.138010
$245$	0	0
$246$	0	0
$247$	− 5.33131i	− 0.339223i
$248$	2.50684i	0.159184i
$249$	42.8458	2.71524
$250$	0	0
$251$	1.52051	0.0959736	0.0479868	−	0.998848i	$-0.484719\pi$
$251$	1.52051	0.0959736	0.0479868	+	0.998848i	$0.484719\pi$
$252$	− 0.590796i	− 0.0372167i
$253$	15.3647i	0.965972i
$254$	−17.8321	−1.11888
$255$	0	0
$256$	1.00000	0.0625000
$257$	16.5068i	1.02967i	0.857290	+	0.514834i	$0.172146\pi$
$257$	16.5068i	1.02967i	−0.857290	+	0.514834i	$0.827854\pi$
$258$	− 1.64895i	− 0.102659i
$259$	−0.428943	−0.0266532
$260$	0	0
$261$	−10.0976	−0.625028
$262$	− 1.49316i	− 0.0922480i
$263$	18.0273i	1.11161i	0.831311	+	0.555807i	$0.187591\pi$
$263$	18.0273i	1.11161i	−0.831311	+	0.555807i	$0.812409\pi$
$264$	14.6626	0.902422
$265$	0	0
$266$	−0.0778929	−0.00477592
$267$	48.8458i	2.98931i
$268$	4.58473i	0.280057i
$269$	−20.2089	−1.23216	−0.616080	−	0.787683i	$-0.711280\pi$
$269$	−20.2089	−1.23216	−0.616080	+	0.787683i	$0.711280\pi$
$270$	0	0
$271$	6.08396	0.369574	0.184787	−	0.982779i	$-0.440840\pi$
$271$	6.08396	0.369574	0.184787	+	0.982779i	$0.440840\pi$
$272$	7.33131i	0.444526i
$273$	− 1.35105i	− 0.0817693i
$274$	8.42894	0.509211
$275$	0	0
$276$	11.0916	0.667634
$277$	− 31.3647i	− 1.88452i	−0.334877	−	0.942262i	$-0.608695\pi$
$277$	− 31.3647i	− 1.88452i	0.334877	−	0.942262i	$-0.391305\pi$
$278$	− 8.81841i	− 0.528893i
$279$	19.0137	1.13832
$280$	0	0
$281$	11.3252	0.675607	0.337804	−	0.941217i	$-0.390316\pi$
$281$	11.3252	0.675607	0.337804	+	0.941217i	$0.390316\pi$
$282$	− 18.4229i	− 1.09707i
$283$	− 26.1437i	− 1.55408i	−0.629452	−	0.777039i	$-0.716721\pi$
$283$	− 26.1437i	− 1.55408i	0.629452	−	0.777039i	$-0.283279\pi$
$284$	10.8579	0.644297
$285$	0	0
$286$	24.0273	1.42077
$287$	0	0
$288$	− 7.58473i	− 0.446934i
$289$	−36.7481	−2.16165
$290$	0	0
$291$	24.9742	1.46401
$292$	− 5.09763i	− 0.298316i
$293$	− 1.33131i	− 0.0777760i	−0.999244	−	0.0388880i	$-0.987618\pi$
$293$	− 1.33131i	− 0.0777760i	0.999244	−	0.0388880i	$-0.0123816\pi$
$294$	22.7542	1.32705
$295$	0	0
$296$	−5.50684	−0.320078
$297$	− 67.2241i	− 3.90074i
$298$	− 17.6763i	− 1.02396i
$299$	18.1755	1.05112
$300$	0	0
$301$	−0.0394789	−0.00227553
$302$	20.0000i	1.15087i
$303$	13.5205i	0.776733i
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	55.6060	3.17878
$307$	− 2.84421i	− 0.162328i	−0.996701	−	0.0811639i	$-0.974136\pi$
$307$	− 2.84421i	− 0.162328i	0.996701	−	0.0811639i	$-0.0258637\pi$
$308$	− 0.351050i	− 0.0200030i
$309$	−7.64895	−0.435134
$310$	0	0
$311$	−16.3895	−0.929361	−0.464681	−	0.885478i	$-0.653831\pi$
$311$	−16.3895	−0.929361	−0.464681	+	0.885478i	$0.653831\pi$
$312$	− 17.3450i	− 0.981966i
$313$	21.0471i	1.18965i	0.803855	+	0.594826i	$0.202779\pi$
$313$	21.0471i	1.18965i	−0.803855	+	0.594826i	$0.797221\pi$
$314$	−0.506836	−0.0286024
$315$	0	0
$316$	17.0137	0.957094
$317$	− 30.8902i	− 1.73497i	−0.497465	−	0.867484i	$-0.665736\pi$
$317$	− 30.8902i	− 1.73497i	0.497465	−	0.867484i	$-0.334264\pi$
$318$	42.0855i	2.36004i
$319$	−6.00000	−0.335936
$320$	0	0
$321$	−45.6566	−2.54830
$322$	− 0.265553i	− 0.0147987i
$323$	− 7.33131i	− 0.407925i
$324$	−25.7739	−1.43188
$325$	0	0
$326$	0.830542	0.0459995
$327$	− 0.253418i	− 0.0140140i
$328$	0	0
$329$	−0.441078	−0.0243174
$330$	0	0
$331$	28.3845	1.56015	0.780076	−	0.625685i	$-0.215181\pi$
$331$	28.3845	1.56015	0.780076	+	0.625685i	$0.215181\pi$
$332$	− 13.1695i	− 0.722768i
$333$	41.7679i	2.28886i
$334$	−16.5068	−0.903214
$335$	0	0
$336$	−0.253418	−0.0138251
$337$	− 17.8716i	− 0.973526i	−0.873534	−	0.486763i	$-0.838178\pi$
$337$	− 17.8716i	− 0.973526i	0.873534	−	0.486763i	$-0.161822\pi$
$338$	− 15.4229i	− 0.838894i
$339$	19.5205	1.06021
$340$	0	0
$341$	11.2979	0.611816
$342$	7.58473i	0.410135i
$343$	− 1.09003i	− 0.0588560i
$344$	−0.506836	−0.0273268
$345$	0	0
$346$	18.8321	1.01242
$347$	33.0410i	1.77373i	0.462024	+	0.886867i	$0.347123\pi$
$347$	33.0410i	1.77373i	−0.462024	+	0.886867i	$0.652877\pi$
$348$	4.33131i	0.232183i
$349$	19.7158	1.05536	0.527681	−	0.849443i	$-0.323062\pi$
$349$	19.7158	1.05536	0.527681	+	0.849443i	$0.323062\pi$
$350$	0	0
$351$	−79.5220	−4.24457
$352$	− 4.50684i	− 0.240215i
$353$	5.90997i	0.314556i	0.987554	+	0.157278i	$0.0502719\pi$
$353$	5.90997i	0.314556i	−0.987554	+	0.157278i	$0.949728\pi$
$354$	−24.6121	−1.30812
$355$	0	0
$356$	15.0137	0.795723
$357$	− 1.85789i	− 0.0983298i
$358$	7.15579i	0.378195i
$359$	7.00760	0.369847	0.184924	−	0.982753i	$-0.440796\pi$
$359$	7.00760	0.369847	0.184924	+	0.982753i	$0.440796\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	12.5205i	0.658063i
$363$	− 30.2944i	− 1.59005i
$364$	−0.415271	−0.0217661
$365$	0	0
$366$	−7.01367	−0.366611
$367$	17.7158i	0.924756i	0.886683	+	0.462378i	$0.153004\pi$
$367$	17.7158i	0.924756i	−0.886683	+	0.462378i	$0.846996\pi$
$368$	− 3.40920i	− 0.177717i
$369$	0	0
$370$	0	0
$371$	1.00760	0.0523122
$372$	− 8.15579i	− 0.422858i
$373$	− 15.4487i	− 0.799902i	−0.916536	−	0.399951i	$-0.869027\pi$
$373$	− 15.4487i	− 0.799902i	0.916536	−	0.399951i	$-0.130973\pi$
$374$	33.0410	1.70851
$375$	0	0
$376$	−5.66262	−0.292027
$377$	7.09763i	0.365547i
$378$	1.16185i	0.0597593i
$379$	−34.4563	−1.76990	−0.884950	−	0.465685i	$-0.845808\pi$
$379$	−34.4563	−1.76990	−0.884950	+	0.465685i	$0.845808\pi$
$380$	0	0
$381$	58.0152	2.97221
$382$	− 4.90237i	− 0.250827i
$383$	12.0273i	0.614569i	0.951618	+	0.307284i	$0.0994203\pi$
$383$	12.0273i	0.614569i	−0.951618	+	0.307284i	$0.900580\pi$
$384$	−3.25342	−0.166025
$385$	0	0
$386$	18.1558	0.924105
$387$	3.84421i	0.195412i
$388$	− 7.67629i	− 0.389705i
$389$	15.3647	0.779022	0.389511	−	0.921022i	$-0.372644\pi$
$389$	15.3647	0.779022	0.389511	+	0.921022i	$0.372644\pi$
$390$	0	0
$391$	24.9939	1.26400
$392$	− 6.99393i	− 0.353247i
$393$	4.85789i	0.245048i
$394$	2.98633	0.150449
$395$	0	0
$396$	−34.1831	−1.71777
$397$	1.32524i	0.0665121i	0.999447	+	0.0332560i	$0.0105877\pi$
$397$	1.32524i	0.0665121i	−0.999447	+	0.0332560i	$0.989412\pi$
$398$	3.06422i	0.153596i
$399$	0.253418	0.0126868
$400$	0	0
$401$	−6.46736	−0.322964	−0.161482	−	0.986876i	$-0.551627\pi$
$401$	−6.46736	−0.322964	−0.161482	+	0.986876i	$0.551627\pi$
$402$	− 14.9160i	− 0.743944i
$403$	− 13.3647i	− 0.665744i
$404$	4.15579	0.206758
$405$	0	0
$406$	0.103700	0.00514653
$407$	24.8184i	1.23020i
$408$	− 23.8518i	− 1.18084i
$409$	1.36472	0.0674812	0.0337406	−	0.999431i	$-0.489258\pi$
$409$	1.36472	0.0674812	0.0337406	+	0.999431i	$0.489258\pi$
$410$	0	0
$411$	−27.4229	−1.35267
$412$	2.35105i	0.115828i
$413$	0.589259i	0.0289955i
$414$	−25.8579	−1.27085
$415$	0	0
$416$	−5.33131	−0.261389
$417$	28.6900i	1.40495i
$418$	4.50684i	0.220437i
$419$	−16.6231	−0.812094	−0.406047	−	0.913852i	$-0.633093\pi$
$419$	−16.6231	−0.812094	−0.406047	+	0.913852i	$0.633093\pi$
$420$	0	0
$421$	−31.1128	−1.51635	−0.758174	−	0.652053i	$-0.773908\pi$
$421$	−31.1128	−1.51635	−0.758174	+	0.652053i	$0.773908\pi$
$422$	19.2534i	0.937242i
$423$	42.9495i	2.08827i
$424$	12.9358	0.628217
$425$	0	0
$426$	−35.3252	−1.71151
$427$	0.167920i	0.00812623i
$428$	14.0334i	0.678331i
$429$	−78.1710	−3.77413
$430$	0	0
$431$	−10.1831	−0.490504	−0.245252	−	0.969459i	$-0.578871\pi$
$431$	−10.1831	−0.490504	−0.245252	+	0.969459i	$0.578871\pi$
$432$	14.9160i	0.717648i
$433$	− 22.1953i	− 1.06664i	−0.845915	−	0.533318i	$-0.820945\pi$
$433$	− 22.1953i	− 1.06664i	0.845915	−	0.533318i	$-0.179055\pi$
$434$	−0.195265	−0.00937300
$435$	0	0
$436$	−0.0778929	−0.00373039
$437$	3.40920i	0.163084i
$438$	16.5847i	0.792449i
$439$	9.32524	0.445070	0.222535	−	0.974925i	$-0.428567\pi$
$439$	9.32524	0.445070	0.222535	+	0.974925i	$0.428567\pi$
$440$	0	0
$441$	−53.0471	−2.52605
$442$	− 39.0855i	− 1.85911i
$443$	13.9879i	0.664584i	0.943177	+	0.332292i	$0.107822\pi$
$443$	13.9879i	0.664584i	−0.943177	+	0.332292i	$0.892178\pi$
$444$	17.9160	0.850258
$445$	0	0
$446$	−14.5068	−0.686919
$447$	57.5084i	2.72005i
$448$	0.0778929i	0.00368009i
$449$	−13.4932	−0.636782	−0.318391	−	0.947960i	$-0.603142\pi$
$449$	−13.4932	−0.636782	−0.318391	+	0.947960i	$0.603142\pi$
$450$	0	0
$451$	0	0
$452$	− 6.00000i	− 0.282216i
$453$	− 65.0684i	− 3.05718i
$454$	21.5984	1.01366
$455$	0	0
$456$	3.25342	0.152355
$457$	9.68236i	0.452922i	0.974020	+	0.226461i	$0.0727155\pi$
$457$	9.68236i	0.452922i	−0.974020	+	0.226461i	$0.927284\pi$
$458$	19.0137i	0.888451i
$459$	−109.354	−5.10421
$460$	0	0
$461$	8.66262	0.403459	0.201729	−	0.979441i	$-0.435344\pi$
$461$	8.66262	0.403459	0.201729	+	0.979441i	$0.435344\pi$
$462$	1.14211i	0.0531359i
$463$	− 28.0015i	− 1.30134i	−0.759360	−	0.650671i	$-0.774488\pi$
$463$	− 28.0015i	− 1.30134i	0.759360	−	0.650671i	$-0.225512\pi$
$464$	1.33131	0.0618046
$465$	0	0
$466$	−6.01367	−0.278578
$467$	16.9742i	0.785472i	0.919651	+	0.392736i	$0.128471\pi$
$467$	16.9742i	0.785472i	−0.919651	+	0.392736i	$0.871529\pi$
$468$	40.4365i	1.86918i
$469$	−0.357118	−0.0164902
$470$	0	0
$471$	1.64895	0.0759796
$472$	7.56499i	0.348207i
$473$	2.28423i	0.105029i
$474$	−55.3526	−2.54243
$475$	0	0
$476$	−0.571057	−0.0261743
$477$	− 98.1144i	− 4.49235i
$478$	− 15.4092i	− 0.704801i
$479$	−10.0532	−0.459340	−0.229670	−	0.973269i	$-0.573765\pi$
$479$	−10.0532	−0.459340	−0.229670	+	0.973269i	$0.573765\pi$
$480$	0	0
$481$	29.3587	1.33864
$482$	− 4.81841i	− 0.219472i
$483$	0.863954i	0.0393113i
$484$	−9.31157	−0.423253
$485$	0	0
$486$	39.1052	1.77385
$487$	19.2089i	0.870440i	0.900324	+	0.435220i	$0.143329\pi$
$487$	19.2089i	0.870440i	−0.900324	+	0.435220i	$0.856671\pi$
$488$	2.15579i	0.0975878i
$489$	−2.70210	−0.122193
$490$	0	0
$491$	5.32524	0.240325	0.120162	−	0.992754i	$-0.461658\pi$
$491$	5.32524	0.240325	0.120162	+	0.992754i	$0.461658\pi$
$492$	0	0
$493$	9.76025i	0.439580i
$494$	5.33131	0.239867
$495$	0	0
$496$	−2.50684	−0.112560
$497$	0.845752i	0.0379372i
$498$	42.8458i	1.91996i
$499$	11.9605	0.535426	0.267713	−	0.963499i	$-0.413732\pi$
$499$	11.9605	0.535426	0.267713	+	0.963499i	$0.413732\pi$
$500$	0	0
$501$	53.7036	2.39930
$502$	1.52051i	0.0678636i
$503$	19.3313i	0.861941i	0.902366	+	0.430970i	$0.141829\pi$
$503$	19.3313i	0.861941i	−0.902366	+	0.430970i	$0.858171\pi$
$504$	0.590796	0.0263162
$505$	0	0
$506$	−15.3647	−0.683045
$507$	50.1771i	2.22844i
$508$	− 17.8321i	− 0.791171i
$509$	36.1573	1.60265	0.801323	−	0.598232i	$-0.204130\pi$
$509$	36.1573	1.60265	0.801323	+	0.598232i	$0.204130\pi$
$510$	0	0
$511$	0.397069	0.0175653
$512$	1.00000i	0.0441942i
$513$	− 14.9160i	− 0.658559i
$514$	−16.5068	−0.728085
$515$	0	0
$516$	1.64895	0.0725910
$517$	25.5205i	1.12239i
$518$	− 0.428943i	− 0.0188467i
$519$	−61.2686	−2.68939
$520$	0	0
$521$	−31.5205	−1.38094	−0.690469	−	0.723362i	$-0.742596\pi$
$521$	−31.5205	−1.38094	−0.690469	+	0.723362i	$0.742596\pi$
$522$	− 10.0976i	− 0.441961i
$523$	− 5.59840i	− 0.244801i	−0.992481	−	0.122400i	$-0.960941\pi$
$523$	− 5.59840i	− 0.244801i	0.992481	−	0.122400i	$-0.0390592\pi$
$524$	1.49316	0.0652292
$525$	0	0
$526$	−18.0273	−0.786030
$527$	− 18.3784i	− 0.800575i
$528$	14.6626i	0.638109i
$529$	11.3773	0.494667
$530$	0	0
$531$	57.3784	2.49001
$532$	− 0.0778929i	− 0.00337708i
$533$	0	0
$534$	−48.8458	−2.11376
$535$	0	0
$536$	−4.58473	−0.198030
$537$	− 23.2808i	− 1.00464i
$538$	− 20.2089i	− 0.871269i
$539$	−31.5205	−1.35768
$540$	0	0
$541$	15.1968	0.653362	0.326681	−	0.945135i	$-0.394070\pi$
$541$	15.1968	0.653362	0.326681	+	0.945135i	$0.394070\pi$
$542$	6.08396i	0.261328i
$543$	− 40.7344i	− 1.74808i
$544$	−7.33131	−0.314327
$545$	0	0
$546$	1.35105	0.0578196
$547$	− 26.6505i	− 1.13949i	−0.821821	−	0.569746i	$-0.807041\pi$
$547$	− 26.6505i	− 1.13949i	0.821821	−	0.569746i	$-0.192959\pi$
$548$	8.42894i	0.360067i
$549$	16.3511	0.697846
$550$	0	0
$551$	−1.33131	−0.0567158
$552$	11.0916i	0.472088i
$553$	1.32524i	0.0563551i
$554$	31.3647	1.33256
$555$	0	0
$556$	8.81841	0.373984
$557$	12.8458i	0.544292i	0.962256	+	0.272146i	$0.0877334\pi$
$557$	12.8458i	0.544292i	−0.962256	+	0.272146i	$0.912267\pi$
$558$	19.0137i	0.804913i
$559$	2.70210	0.114287
$560$	0	0
$561$	−107.496	−4.53849
$562$	11.3252i	0.477727i
$563$	− 10.1968i	− 0.429744i	−0.976642	−	0.214872i	$-0.931067\pi$
$563$	− 10.1968i	− 0.429744i	0.976642	−	0.214872i	$-0.0689334\pi$
$564$	18.4229	0.775743
$565$	0	0
$566$	26.1437	1.09890
$567$	− 2.00760i	− 0.0843115i
$568$	10.8579i	0.455587i
$569$	24.3784	1.02200	0.510998	−	0.859582i	$-0.329276\pi$
$569$	24.3784	1.02200	0.510998	+	0.859582i	$0.329276\pi$
$570$	0	0
$571$	8.32371	0.348336	0.174168	−	0.984716i	$-0.444276\pi$
$571$	8.32371	0.348336	0.174168	+	0.984716i	$0.444276\pi$
$572$	24.0273i	1.00463i
$573$	15.9495i	0.666298i
$574$	0	0
$575$	0	0
$576$	7.58473	0.316030
$577$	− 7.29290i	− 0.303607i	−0.988411	−	0.151804i	$-0.951492\pi$
$577$	− 7.29290i	− 0.303607i	0.988411	−	0.151804i	$-0.0485081\pi$
$578$	− 36.7481i	− 1.52852i
$579$	−59.0684	−2.45480
$580$	0	0
$581$	1.02581	0.0425576
$582$	24.9742i	1.03521i
$583$	− 58.2994i	− 2.41452i
$584$	5.09763	0.210942
$585$	0	0
$586$	1.33131	0.0549959
$587$	5.53264i	0.228357i	0.993460	+	0.114178i	$0.0364235\pi$
$587$	5.53264i	0.228357i	−0.993460	+	0.114178i	$0.963576\pi$
$588$	22.7542i	0.938367i
$589$	2.50684	0.103292
$590$	0	0
$591$	−9.71577	−0.399653
$592$	− 5.50684i	− 0.226330i
$593$	26.3252i	1.08105i	0.841329	+	0.540524i	$0.181774\pi$
$593$	26.3252i	1.08105i	−0.841329	+	0.540524i	$0.818226\pi$
$594$	67.2241	2.75824
$595$	0	0
$596$	17.6763	0.724049
$597$	− 9.96919i	− 0.408012i
$598$	18.1755i	0.743252i
$599$	−22.2994	−0.911130	−0.455565	−	0.890202i	$-0.650563\pi$
$599$	−22.2994	−0.911130	−0.455565	+	0.890202i	$0.650563\pi$
$600$	0	0
$601$	32.4947	1.32549	0.662743	−	0.748847i	$-0.269392\pi$
$601$	32.4947	1.32549	0.662743	+	0.748847i	$0.269392\pi$
$602$	− 0.0394789i	− 0.00160904i
$603$	34.7739i	1.41610i
$604$	−20.0000	−0.813788
$605$	0	0
$606$	−13.5205	−0.549233
$607$	8.35105i	0.338959i	0.985534	+	0.169479i	$0.0542086\pi$
$607$	8.35105i	0.338959i	−0.985534	+	0.169479i	$0.945791\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	−0.337378	−0.0136713
$610$	0	0
$611$	30.1892	1.22132
$612$	55.6060i	2.24774i
$613$	38.2994i	1.54690i	0.633858	+	0.773450i	$0.281471\pi$
$613$	38.2994i	1.54690i	−0.633858	+	0.773450i	$0.718529\pi$
$614$	2.84421	0.114783
$615$	0	0
$616$	0.351050	0.0141442
$617$	− 14.3526i	− 0.577813i	−0.957357	−	0.288907i	$-0.906708\pi$
$617$	− 14.3526i	− 0.577813i	0.957357	−	0.288907i	$-0.0932917\pi$
$618$	− 7.64895i	− 0.307686i
$619$	8.62314	0.346593	0.173297	−	0.984870i	$-0.444558\pi$
$619$	8.62314	0.346593	0.173297	+	0.984870i	$0.444558\pi$
$620$	0	0
$621$	50.8518	2.04061
$622$	− 16.3895i	− 0.657158i
$623$	1.16946i	0.0468533i
$624$	17.3450	0.694355
$625$	0	0
$626$	−21.0471	−0.841211
$627$	− 14.6626i	− 0.585569i
$628$	− 0.506836i	− 0.0202250i
$629$	40.3723	1.60975
$630$	0	0
$631$	−10.3374	−0.411525	−0.205762	−	0.978602i	$-0.565967\pi$
$631$	−10.3374	−0.411525	−0.205762	+	0.978602i	$0.565967\pi$
$632$	17.0137i	0.676768i
$633$	− 62.6394i	− 2.48969i
$634$	30.8902	1.22681
$635$	0	0
$636$	−42.0855	−1.66880
$637$	37.2868i	1.47736i
$638$	− 6.00000i	− 0.237542i
$639$	82.3541	3.25788
$640$	0	0
$641$	5.88369	0.232392	0.116196	−	0.993226i	$-0.462930\pi$
$641$	5.88369	0.232392	0.116196	+	0.993226i	$0.462930\pi$
$642$	− 45.6566i	− 1.80192i
$643$	25.5084i	1.00595i	0.864300	+	0.502976i	$0.167762\pi$
$643$	25.5084i	1.00595i	−0.864300	+	0.502976i	$0.832238\pi$
$644$	0.265553	0.0104642
$645$	0	0
$646$	7.33131	0.288447
$647$	− 5.09157i	− 0.200170i	−0.994979	−	0.100085i	$-0.968089\pi$
$647$	− 5.09157i	− 0.200170i	0.994979	−	0.100085i	$-0.0319115\pi$
$648$	− 25.7739i	− 1.01250i
$649$	34.0942	1.33831
$650$	0	0
$651$	0.635277	0.0248985
$652$	0.830542i	0.0325265i
$653$	11.1816i	0.437570i	0.975773	+	0.218785i	$0.0702093\pi$
$653$	11.1816i	0.437570i	−0.975773	+	0.218785i	$0.929791\pi$
$654$	0.253418	0.00990943
$655$	0	0
$656$	0	0
$657$	− 38.6642i	− 1.50843i
$658$	− 0.441078i	− 0.0171950i
$659$	13.7542	0.535787	0.267894	−	0.963449i	$-0.413672\pi$
$659$	13.7542	0.535787	0.267894	+	0.963449i	$0.413672\pi$
$660$	0	0
$661$	−12.6171	−0.490747	−0.245374	−	0.969429i	$-0.578911\pi$
$661$	−12.6171	−0.490747	−0.245374	+	0.969429i	$0.578911\pi$
$662$	28.3845i	1.10319i
$663$	127.161i	4.93854i
$664$	13.1695	0.511074
$665$	0	0
$666$	−41.7679	−1.61847
$667$	− 4.53871i	− 0.175740i
$668$	− 16.5068i	− 0.638669i
$669$	47.1968	1.82473
$670$	0	0
$671$	9.71577	0.375073
$672$	− 0.253418i	− 0.00977581i
$673$	− 2.35105i	− 0.0906263i	−0.998973	−	0.0453132i	$-0.985571\pi$
$673$	− 2.35105i	− 0.0906263i	0.998973	−	0.0453132i	$-0.0144286\pi$
$674$	17.8716	0.688387
$675$	0	0
$676$	15.4229	0.593188
$677$	− 23.7663i	− 0.913414i	−0.889617	−	0.456707i	$-0.849029\pi$
$677$	− 23.7663i	− 0.913414i	0.889617	−	0.456707i	$-0.150971\pi$
$678$	19.5205i	0.749681i
$679$	0.597928	0.0229464
$680$	0	0
$681$	−70.2686	−2.69270
$682$	11.2979i	0.432619i
$683$	− 28.1695i	− 1.07787i	−0.842346	−	0.538937i	$-0.818826\pi$
$683$	− 28.1695i	− 1.07787i	0.842346	−	0.538937i	$-0.181174\pi$
$684$	−7.58473	−0.290009
$685$	0	0
$686$	1.09003	0.0416174
$687$	− 61.8594i	− 2.36008i
$688$	− 0.506836i	− 0.0193229i
$689$	−68.9647	−2.62734
$690$	0	0
$691$	2.32371	0.0883979	0.0441990	−	0.999023i	$-0.485926\pi$
$691$	2.32371	0.0883979	0.0441990	+	0.999023i	$0.485926\pi$
$692$	18.8321i	0.715888i
$693$	− 2.66262i	− 0.101145i
$694$	−33.0410	−1.25422
$695$	0	0
$696$	−4.33131	−0.164178
$697$	0	0
$698$	19.7158i	0.746253i
$699$	19.5650	0.740016
$700$	0	0
$701$	23.7036	0.895274	0.447637	−	0.894215i	$-0.352266\pi$
$701$	23.7036	0.895274	0.447637	+	0.894215i	$0.352266\pi$
$702$	− 79.5220i	− 3.00137i
$703$	5.50684i	0.207694i
$704$	4.50684	0.169858
$705$	0	0
$706$	−5.90997	−0.222425
$707$	0.323706i	0.0121742i
$708$	− 24.6121i	− 0.924978i
$709$	−9.05315	−0.339998	−0.169999	−	0.985444i	$-0.554376\pi$
$709$	−9.05315	−0.339998	−0.169999	+	0.985444i	$0.554376\pi$
$710$	0	0
$711$	129.044	4.83953
$712$	15.0137i	0.562661i
$713$	8.54631i	0.320062i
$714$	1.85789	0.0695297
$715$	0	0
$716$	−7.15579	−0.267424
$717$	50.1326i	1.87224i
$718$	7.00760i	0.261521i
$719$	−35.0734	−1.30802	−0.654008	−	0.756488i	$-0.726914\pi$
$719$	−35.0734	−1.30802	−0.654008	+	0.756488i	$0.726914\pi$
$720$	0	0
$721$	−0.183130	−0.00682012
$722$	1.00000i	0.0372161i
$723$	15.6763i	0.583008i
$724$	−12.5205	−0.465321
$725$	0	0
$726$	30.2944	1.12433
$727$	30.1386i	1.11778i	0.829242	+	0.558890i	$0.188773\pi$
$727$	30.1386i	1.11778i	−0.829242	+	0.558890i	$0.811227\pi$
$728$	− 0.415271i	− 0.0153910i
$729$	−49.9039	−1.84829
$730$	0	0
$731$	3.71577	0.137433
$732$	− 7.01367i	− 0.259233i
$733$	− 47.8321i	− 1.76672i	−0.468697	−	0.883359i	$-0.655276\pi$
$733$	− 47.8321i	− 1.76672i	0.468697	−	0.883359i	$-0.344724\pi$
$734$	−17.7158	−0.653901
$735$	0	0
$736$	3.40920	0.125665
$737$	20.6626i	0.761117i
$738$	0	0
$739$	22.4674	0.826475	0.413238	−	0.910623i	$-0.364398\pi$
$739$	22.4674	0.826475	0.413238	+	0.910623i	$0.364398\pi$
$740$	0	0
$741$	−17.3450	−0.637184
$742$	1.00760i	0.0369903i
$743$	11.7926i	0.432629i	0.976324	+	0.216314i	$0.0694036\pi$
$743$	11.7926i	0.432629i	−0.976324	+	0.216314i	$0.930596\pi$
$744$	8.15579	0.299006
$745$	0	0
$746$	15.4487	0.565616
$747$	− 99.8868i	− 3.65467i
$748$	33.0410i	1.20810i
$749$	−1.09310	−0.0399411
$750$	0	0
$751$	−2.03948	−0.0744216	−0.0372108	−	0.999307i	$-0.511847\pi$
$751$	−2.03948	−0.0744216	−0.0372108	+	0.999307i	$0.511847\pi$
$752$	− 5.66262i	− 0.206495i
$753$	− 4.94685i	− 0.180273i
$754$	−7.09763	−0.258481
$755$	0	0
$756$	−1.16185	−0.0422562
$757$	43.3526i	1.57568i	0.615882	+	0.787838i	$0.288800\pi$
$757$	43.3526i	1.57568i	−0.615882	+	0.787838i	$0.711200\pi$
$758$	− 34.4563i	− 1.25151i
$759$	49.9879	1.81444
$760$	0	0
$761$	6.62921	0.240309	0.120154	−	0.992755i	$-0.461661\pi$
$761$	6.62921	0.240309	0.120154	+	0.992755i	$0.461661\pi$
$762$	58.0152i	2.10167i
$763$	− 0.00606730i	0 0.000219651i
$764$	4.90237	0.177361
$765$	0	0
$766$	−12.0273	−0.434566
$767$	− 40.3313i	− 1.45628i
$768$	− 3.25342i	− 0.117398i
$769$	19.6429	0.708340	0.354170	−	0.935181i	$-0.384763\pi$
$769$	19.6429	0.708340	0.354170	+	0.935181i	$0.384763\pi$
$770$	0	0
$771$	53.7036	1.93409
$772$	18.1558i	0.653441i
$773$	− 14.4107i	− 0.518318i	−0.965835	−	0.259159i	$-0.916555\pi$
$773$	− 14.4107i	− 0.518318i	0.965835	−	0.259159i	$-0.0834454\pi$
$774$	−3.84421	−0.138177
$775$	0	0
$776$	7.67629	0.275563
$777$	1.39553i	0.0500644i
$778$	15.3647i	0.550852i
$779$	0	0
$780$	0	0
$781$	48.9347	1.75102
$782$	24.9939i	0.893781i
$783$	19.8579i	0.709663i
$784$	6.99393	0.249783
$785$	0	0
$786$	−4.85789	−0.173275
$787$	24.3176i	0.866830i	0.901194	+	0.433415i	$0.142692\pi$
$787$	24.3176i	0.866830i	−0.901194	+	0.433415i	$0.857308\pi$
$788$	2.98633i	0.106384i
$789$	58.6505	2.08801
$790$	0	0
$791$	0.467357	0.0166173
$792$	− 34.1831i	− 1.21464i
$793$	− 11.4932i	− 0.408134i
$794$	−1.32524	−0.0470311
$795$	0	0
$796$	−3.06422	−0.108608
$797$	− 7.30397i	− 0.258720i	−0.991598	−	0.129360i	$-0.958708\pi$
$797$	− 7.30397i	− 0.258720i	0.991598	−	0.129360i	$-0.0412922\pi$
$798$	0.253418i	0.00897090i
$799$	41.5144	1.46868
$800$	0	0
$801$	113.875	4.02356
$802$	− 6.46736i	− 0.228370i
$803$	− 22.9742i	− 0.810742i
$804$	14.9160	0.526048
$805$	0	0
$806$	13.3647	0.470752
$807$	65.7481i	2.31444i
$808$	4.15579i	0.146200i
$809$	0.584729	0.0205580	0.0102790	−	0.999947i	$-0.496728\pi$
$809$	0.584729	0.0205580	0.0102790	+	0.999947i	$0.496728\pi$
$810$	0	0
$811$	1.90997	0.0670682	0.0335341	−	0.999438i	$-0.489324\pi$
$811$	1.90997	0.0670682	0.0335341	+	0.999438i	$0.489324\pi$
$812$	0.103700i	0.00363914i
$813$	− 19.7937i	− 0.694194i
$814$	−24.8184	−0.869885
$815$	0	0
$816$	23.8518	0.834981
$817$	0.506836i	0.0177319i
$818$	1.36472i	0.0477164i
$819$	−3.14972	−0.110060
$820$	0	0
$821$	−38.2226	−1.33398	−0.666989	−	0.745067i	$-0.732417\pi$
$821$	−38.2226	−1.33398	−0.666989	+	0.745067i	$0.732417\pi$
$822$	− 27.4229i	− 0.956483i
$823$	45.7481i	1.59468i	0.603531	+	0.797340i	$0.293760\pi$
$823$	45.7481i	1.59468i	−0.603531	+	0.797340i	$0.706240\pi$
$824$	−2.35105	−0.0819027
$825$	0	0
$826$	−0.589259	−0.0205029
$827$	− 22.6687i	− 0.788268i	−0.919053	−	0.394134i	$-0.871045\pi$
$827$	− 22.6687i	− 0.788268i	0.919053	−	0.394134i	$-0.128955\pi$
$828$	− 25.8579i	− 0.898624i
$829$	4.63028	0.160816	0.0804081	−	0.996762i	$-0.474378\pi$
$829$	4.63028	0.160816	0.0804081	+	0.996762i	$0.474378\pi$
$830$	0	0
$831$	−102.043	−3.53982
$832$	− 5.33131i	− 0.184830i
$833$	51.2747i	1.77656i
$834$	−28.6900	−0.993452
$835$	0	0
$836$	−4.50684	−0.155872
$837$	− 37.3921i	− 1.29246i
$838$	− 16.6231i	− 0.574237i
$839$	50.4826	1.74285	0.871426	−	0.490527i	$-0.163196\pi$
$839$	50.4826	1.74285	0.871426	+	0.490527i	$0.163196\pi$
$840$	0	0
$841$	−27.2276	−0.938883
$842$	− 31.1128i	− 1.07222i
$843$	− 36.8458i	− 1.26904i
$844$	−19.2534	−0.662730
$845$	0	0
$846$	−42.9495	−1.47663
$847$	− 0.725305i	− 0.0249218i
$848$	12.9358i	0.444216i
$849$	−85.0562	−2.91912
$850$	0	0
$851$	−18.7739	−0.643562
$852$	− 35.3252i	− 1.21022i
$853$	− 36.2105i	− 1.23982i	−0.784672	−	0.619912i	$-0.787168\pi$
$853$	− 36.2105i	− 1.23982i	0.784672	−	0.619912i	$-0.212832\pi$
$854$	−0.167920	−0.00574611
$855$	0	0
$856$	−14.0334	−0.479652
$857$	25.1968i	0.860706i	0.902661	+	0.430353i	$0.141611\pi$
$857$	25.1968i	0.860706i	−0.902661	+	0.430353i	$0.858389\pi$
$858$	− 78.1710i	− 2.66871i
$859$	−18.8579	−0.643423	−0.321711	−	0.946838i	$-0.604258\pi$
$859$	−18.8579	−0.643423	−0.321711	+	0.946838i	$0.604258\pi$
$860$	0	0
$861$	0	0
$862$	− 10.1831i	− 0.346839i
$863$	− 15.0137i	− 0.511071i	−0.966800	−	0.255536i	$-0.917748\pi$
$863$	− 15.0137i	− 0.511071i	0.966800	−	0.255536i	$-0.0822518\pi$
$864$	−14.9160	−0.507454
$865$	0	0
$866$	22.1953	0.754226
$867$	119.557i	4.06037i
$868$	− 0.195265i	− 0.00662771i
$869$	76.6778	2.60112
$870$	0	0
$871$	24.4426	0.828206
$872$	− 0.0778929i	− 0.00263779i
$873$	− 58.2226i	− 1.97054i
$874$	−3.40920	−0.115318
$875$	0	0
$876$	−16.5847	−0.560346
$877$	35.1128i	1.18568i	0.805322	+	0.592838i	$0.201993\pi$
$877$	35.1128i	1.18568i	−0.805322	+	0.592838i	$0.798007\pi$
$878$	9.32524i	0.314712i
$879$	−4.33131	−0.146091
$880$	0	0
$881$	−41.3389	−1.39274	−0.696372	−	0.717681i	$-0.745203\pi$
$881$	−41.3389	−1.39274	−0.696372	+	0.717681i	$0.745203\pi$
$882$	− 53.0471i	− 1.78619i
$883$	12.6353i	0.425211i	0.977138	+	0.212605i	$0.0681949\pi$
$883$	12.6353i	0.425211i	−0.977138	+	0.212605i	$0.931805\pi$
$884$	39.0855	1.31459
$885$	0	0
$886$	−13.9879	−0.469932
$887$	4.15579i	0.139538i	0.997563	+	0.0697688i	$0.0222262\pi$
$887$	4.15579i	0.139538i	−0.997563	+	0.0697688i	$0.977774\pi$
$888$	17.9160i	0.601223i
$889$	1.38899	0.0465853
$890$	0	0
$891$	−116.159	−3.89147
$892$	− 14.5068i	− 0.485725i
$893$	5.66262i	0.189492i
$894$	−57.5084	−1.92337
$895$	0	0
$896$	−0.0778929	−0.00260222
$897$	− 59.1326i	− 1.97438i
$898$	− 13.4932i	− 0.450273i
$899$	−3.33738	−0.111308
$900$	0	0
$901$	−94.8362	−3.15945
$902$	0	0
$903$	0.128441i	0.00427426i
$904$	6.00000	0.199557
$905$	0	0
$906$	65.0684	2.16175
$907$	− 41.7542i	− 1.38643i	−0.720733	−	0.693213i	$-0.756195\pi$
$907$	− 41.7542i	− 1.38643i	0.720733	−	0.693213i	$-0.243805\pi$
$908$	21.5984i	0.716768i
$909$	31.5205	1.04547
$910$	0	0
$911$	−9.12998	−0.302490	−0.151245	−	0.988496i	$-0.548328\pi$
$911$	−9.12998	−0.302490	−0.151245	+	0.988496i	$0.548328\pi$
$912$	3.25342i	0.107731i
$913$	− 59.3526i	− 1.96428i
$914$	−9.68236	−0.320264
$915$	0	0
$916$	−19.0137	−0.628229
$917$	0.116307i	0.00384079i
$918$	− 109.354i	− 3.60922i
$919$	−19.0197	−0.627403	−0.313702	−	0.949522i	$-0.601569\pi$
$919$	−19.0197	−0.627403	−0.313702	+	0.949522i	$0.601569\pi$
$920$	0	0
$921$	−9.25342	−0.304910
$922$	8.66262i	0.285288i
$923$	− 57.8868i	− 1.90537i
$924$	−1.14211	−0.0375728
$925$	0	0
$926$	28.0015	0.920188
$927$	17.8321i	0.585682i
$928$	1.33131i	0.0437024i
$929$	7.77239	0.255004	0.127502	−	0.991838i	$-0.459304\pi$
$929$	7.77239	0.255004	0.127502	+	0.991838i	$0.459304\pi$
$930$	0	0
$931$	−6.99393	−0.229217
$932$	− 6.01367i	− 0.196984i
$933$	53.3218i	1.74568i
$934$	−16.9742	−0.555413
$935$	0	0
$936$	−40.4365	−1.32171
$937$	− 45.9818i	− 1.50216i	−0.660211	−	0.751080i	$-0.729533\pi$
$937$	− 45.9818i	− 1.50216i	0.660211	−	0.751080i	$-0.270467\pi$
$938$	− 0.357118i	− 0.0116603i
$939$	68.4750	2.23460
$940$	0	0
$941$	−40.6242	−1.32431	−0.662156	−	0.749366i	$-0.730358\pi$
$941$	−40.6242	−1.32431	−0.662156	+	0.749366i	$0.730358\pi$
$942$	1.64895i	0.0537257i
$943$	0	0
$944$	−7.56499	−0.246219
$945$	0	0
$946$	−2.28423	−0.0742666
$947$	− 2.28423i	− 0.0742274i	−0.999311	−	0.0371137i	$-0.988184\pi$
$947$	− 2.28423i	− 0.0742274i	0.999311	−	0.0371137i	$-0.0118164\pi$
$948$	− 55.3526i	− 1.79777i
$949$	−27.1771	−0.882205
$950$	0	0
$951$	−100.499	−3.25890
$952$	− 0.571057i	− 0.0185081i
$953$	57.5084i	1.86288i	0.363896	+	0.931439i	$0.381446\pi$
$953$	57.5084i	1.86288i	−0.363896	+	0.931439i	$0.618554\pi$
$954$	98.1144	3.17657
$955$	0	0
$956$	15.4092	0.498369
$957$	19.5205i	0.631008i
$958$	− 10.0532i	− 0.324803i
$959$	−0.656555	−0.0212013
$960$	0	0
$961$	−24.7158	−0.797283
$962$	29.3587i	0.946561i
$963$	106.440i	3.42997i
$964$	4.81841	0.155190
$965$	0	0
$966$	−0.863954	−0.0277973
$967$	− 4.70210i	− 0.151209i	−0.997138	−	0.0756047i	$-0.975911\pi$
$967$	− 4.70210i	− 0.151209i	0.997138	−	0.0756047i	$-0.0240887\pi$
$968$	− 9.31157i	− 0.299285i
$969$	−23.8518	−0.766231
$970$	0	0
$971$	14.9863	0.480934	0.240467	−	0.970657i	$-0.422699\pi$
$971$	14.9863	0.480934	0.240467	+	0.970657i	$0.422699\pi$
$972$	39.1052i	1.25430i
$973$	0.686891i	0.0220207i
$974$	−19.2089	−0.615494
$975$	0	0
$976$	−2.15579	−0.0690050
$977$	8.89737i	0.284652i	0.989820	+	0.142326i	$0.0454581\pi$
$977$	8.89737i	0.284652i	−0.989820	+	0.142326i	$0.954542\pi$
$978$	− 2.70210i	− 0.0864037i
$979$	67.6642	2.16256
$980$	0	0
$981$	−0.590796	−0.0188627
$982$	5.32524i	0.169935i
$983$	1.60947i	0.0513341i	0.999671	+	0.0256671i	$0.00817098\pi$
$983$	1.60947i	0.0513341i	−0.999671	+	0.0256671i	$0.991829\pi$
$984$	0	0
$985$	0	0
$986$	−9.76025	−0.310830
$987$	1.43501i	0.0456769i
$988$	5.33131i	0.169612i
$989$	−1.72791	−0.0549443
$990$	0	0
$991$	16.8974	0.536763	0.268381	−	0.963313i	$-0.413511\pi$
$991$	16.8974	0.536763	0.268381	+	0.963313i	$0.413511\pi$
$992$	− 2.50684i	− 0.0795921i
$993$	− 92.3465i	− 2.93053i
$994$	−0.845752	−0.0268256
$995$	0	0
$996$	−42.8458	−1.35762
$997$	24.1558i	0.765021i	0.923951	+	0.382511i	$0.124940\pi$
$997$	24.1558i	0.765021i	−0.923951	+	0.382511i	$0.875060\pi$
$998$	11.9605i	0.378604i
$999$	82.1402	2.59880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.h.799.4		6
5.2	odd	4		950.2.a.j.1.1	✓	3
5.3	odd	4		950.2.a.l.1.3	yes	3
5.4	even	2	inner	950.2.b.h.799.3		6
15.2	even	4		8550.2.a.cp.1.2		3
15.8	even	4		8550.2.a.ci.1.2		3
20.3	even	4		7600.2.a.bk.1.1		3
20.7	even	4		7600.2.a.bz.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.j.1.1	✓	3	5.2	odd	4
950.2.a.l.1.3	yes	3	5.3	odd	4
950.2.b.h.799.3		6	5.4	even	2	inner
950.2.b.h.799.4		6	1.1	even	1	trivial
7600.2.a.bk.1.1		3	20.3	even	4
7600.2.a.bz.1.3		3	20.7	even	4
8550.2.a.ci.1.2		3	15.8	even	4
8550.2.a.cp.1.2		3	15.2	even	4

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.25342i q^{3} -1.00000 q^{4} +3.25342 q^{6} -0.0778929i q^{7} -1.00000i q^{8} -7.58473 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.25342i q^{3} -1.00000 q^{4} +3.25342 q^{6} -0.0778929i q^{7} -1.00000i q^{8} -7.58473 q^{9} -4.50684 q^{11} +3.25342i q^{12} +5.33131i q^{13} +0.0778929 q^{14} +1.00000 q^{16} +7.33131i q^{17} -7.58473i q^{18} -1.00000 q^{19} -0.253418 q^{21} -4.50684i q^{22} -3.40920i q^{23} -3.25342 q^{24} -5.33131 q^{26} +14.9160i q^{27} +0.0778929i q^{28} +1.33131 q^{29} -2.50684 q^{31} +1.00000i q^{32} +14.6626i q^{33} -7.33131 q^{34} +7.58473 q^{36} -5.50684i q^{37} -1.00000i q^{38} +17.3450 q^{39} -0.253418i q^{42} -0.506836i q^{43} +4.50684 q^{44} +3.40920 q^{46} -5.66262i q^{47} -3.25342i q^{48} +6.99393 q^{49} +23.8518 q^{51} -5.33131i q^{52} +12.9358i q^{53} -14.9160 q^{54} -0.0778929 q^{56} +3.25342i q^{57} +1.33131i q^{58} -7.56499 q^{59} -2.15579 q^{61} -2.50684i q^{62} +0.590796i q^{63} -1.00000 q^{64} -14.6626 q^{66} -4.58473i q^{67} -7.33131i q^{68} -11.0916 q^{69} -10.8579 q^{71} +7.58473i q^{72} +5.09763i q^{73} +5.50684 q^{74} +1.00000 q^{76} +0.351050i q^{77} +17.3450i q^{78} -17.0137 q^{79} +25.7739 q^{81} +13.1695i q^{83} +0.253418 q^{84} +0.506836 q^{86} -4.33131i q^{87} +4.50684i q^{88} -15.0137 q^{89} +0.415271 q^{91} +3.40920i q^{92} +8.15579i q^{93} +5.66262 q^{94} +3.25342 q^{96} +7.67629i q^{97} +6.99393i q^{98} +34.1831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 10 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 4 * q^6 - 10 * q^9	\( 6 q - 6 q^{4} + 4 q^{6} - 10 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} - 6 q^{19} + 14 q^{21} - 4 q^{24} - 12 q^{26} - 12 q^{29} + 16 q^{31} - 24 q^{34} + 10 q^{36} + 22 q^{39} - 4 q^{44} - 4 q^{46} - 18 q^{49} + 30 q^{51} - 34 q^{54} + 4 q^{56} - 12 q^{59} - 4 q^{61} - 6 q^{64} - 48 q^{66} - 12 q^{71} + 2 q^{74} + 6 q^{76} - 40 q^{79} + 46 q^{81} - 14 q^{84} - 28 q^{86} - 28 q^{89} + 38 q^{91} - 6 q^{94} + 4 q^{96} + 72 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^6 - 10 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 - 6 * q^19 + 14 * q^21 - 4 * q^24 - 12 * q^26 - 12 * q^29 + 16 * q^31 - 24 * q^34 + 10 * q^36 + 22 * q^39 - 4 * q^44 - 4 * q^46 - 18 * q^49 + 30 * q^51 - 34 * q^54 + 4 * q^56 - 12 * q^59 - 4 * q^61 - 6 * q^64 - 48 * q^66 - 12 * q^71 + 2 * q^74 + 6 * q^76 - 40 * q^79 + 46 * q^81 - 14 * q^84 - 28 * q^86 - 28 * q^89 + 38 * q^91 - 6 * q^94 + 4 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more