LMFDB - Embedded newform 950.2.b.h.799.2

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			799.2
Root			$-0.480031i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.h.799.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +0.960061 q^{11} -0.519969i q^{12} +2.24960i q^{13} -4.76957 q^{14} +1.00000 q^{16} +0.249601i q^{17} -2.72963i q^{18} -1.00000 q^{19} +2.48003 q^{21} -0.960061i q^{22} -9.01917i q^{23} -0.519969 q^{24} +2.24960 q^{26} +2.97923i q^{27} +4.76957i q^{28} -6.24960 q^{29} +2.96006 q^{31} -1.00000i q^{32} +0.499202i q^{33} +0.249601 q^{34} -2.72963 q^{36} +0.0399387i q^{37} +1.00000i q^{38} -1.16972 q^{39} -2.48003i q^{42} -4.96006i q^{43} -0.960061 q^{44} -9.01917 q^{46} -9.49920i q^{47} +0.519969i q^{48} -15.7488 q^{49} -0.129785 q^{51} -2.24960i q^{52} -6.84945i q^{53} +2.97923 q^{54} +4.76957 q^{56} -0.519969i q^{57} +6.24960i q^{58} +14.5583 q^{59} +7.53914 q^{61} -2.96006i q^{62} -13.0192i q^{63} -1.00000 q^{64} +0.499202 q^{66} -5.72963i q^{67} -0.249601i q^{68} +4.68969 q^{69} -9.61902 q^{71} +2.72963i q^{72} -12.0591i q^{73} +0.0399387 q^{74} +1.00000 q^{76} -4.57908i q^{77} +1.16972i q^{78} -6.07988 q^{79} +6.63979 q^{81} +7.45926i q^{83} -2.48003 q^{84} -4.96006 q^{86} -3.24960i q^{87} +0.960061i q^{88} -4.07988 q^{89} +10.7296 q^{91} +9.01917i q^{92} +1.53914i q^{93} -9.49920 q^{94} +0.519969 q^{96} +18.4193i q^{97} +15.7488i q^{98} +2.62061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.519969i	0.300204i	0.988670	+	0.150102i	$0.0479603\pi$
$3$	0.519969i	0.300204i	−0.988670	+	0.150102i	$0.952040\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.519969	0.212277
$7$	− 4.76957i	− 1.80273i	−0.433062	−	0.901364i	$-0.642567\pi$
$7$	− 4.76957i	− 1.80273i	0.433062	−	0.901364i	$-0.357433\pi$
$8$	1.00000i	0.353553i
$9$	2.72963	0.909877
$10$	0	0
$11$	0.960061	0.289469	0.144735	−	0.989471i	$-0.453767\pi$
$11$	0.960061	0.289469	0.144735	+	0.989471i	$0.453767\pi$
$12$	− 0.519969i	− 0.150102i
$13$	2.24960i	0.623927i	0.950094	+	0.311964i	$0.100987\pi$
$13$	2.24960i	0.623927i	−0.950094	+	0.311964i	$0.899013\pi$
$14$	−4.76957	−1.27472
$15$	0	0
$16$	1.00000	0.250000
$17$	0.249601i	0.0605372i	0.999542	+	0.0302686i	$0.00963626\pi$
$17$	0.249601i	0.0605372i	−0.999542	+	0.0302686i	$0.990364\pi$
$18$	− 2.72963i	− 0.643380i
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	2.48003	0.541187
$22$	− 0.960061i	− 0.204686i
$23$	− 9.01917i	− 1.88063i	−0.340309	−	0.940314i	$-0.610532\pi$
$23$	− 9.01917i	− 1.88063i	0.340309	−	0.940314i	$-0.389468\pi$
$24$	−0.519969	−0.106138
$25$	0	0
$26$	2.24960	0.441183
$27$	2.97923i	0.573354i
$28$	4.76957i	0.901364i
$29$	−6.24960	−1.16052	−0.580261	−	0.814431i	$-0.697049\pi$
$29$	−6.24960	−1.16052	−0.580261	+	0.814431i	$0.697049\pi$
$30$	0	0
$31$	2.96006	0.531643	0.265821	−	0.964022i	$-0.414357\pi$
$31$	2.96006	0.531643	0.265821	+	0.964022i	$0.414357\pi$
$32$	− 1.00000i	− 0.176777i
$33$	0.499202i	0.0869000i
$34$	0.249601	0.0428063
$35$	0	0
$36$	−2.72963	−0.454939
$37$	0.0399387i	0.00656589i	0.999995	+	0.00328294i	$0.00104500\pi$
$37$	0.0399387i	0.00656589i	−0.999995	+	0.00328294i	$0.998955\pi$
$38$	1.00000i	0.162221i
$39$	−1.16972	−0.187306
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	− 2.48003i	− 0.382677i
$43$	− 4.96006i	− 0.756402i	−0.925723	−	0.378201i	$-0.876543\pi$
$43$	− 4.96006i	− 0.756402i	0.925723	−	0.378201i	$-0.123457\pi$
$44$	−0.960061	−0.144735
$45$	0	0
$46$	−9.01917	−1.32980
$47$	− 9.49920i	− 1.38560i	−0.721129	−	0.692801i	$-0.756377\pi$
$47$	− 9.49920i	− 1.38560i	0.721129	−	0.692801i	$-0.243623\pi$
$48$	0.519969i	0.0750511i
$49$	−15.7488	−2.24983
$50$	0	0
$51$	−0.129785	−0.0181735
$52$	− 2.24960i	− 0.311964i
$53$	− 6.84945i	− 0.940844i	−0.882442	−	0.470422i	$-0.844102\pi$
$53$	− 6.84945i	− 0.940844i	0.882442	−	0.470422i	$-0.155898\pi$
$54$	2.97923	0.405422
$55$	0	0
$56$	4.76957	0.637361
$57$	− 0.519969i	− 0.0688716i
$58$	6.24960i	0.820613i
$59$	14.5583	1.89533	0.947665	−	0.319265i	$-0.103436\pi$
$59$	14.5583	1.89533	0.947665	+	0.319265i	$0.103436\pi$
$60$	0	0
$61$	7.53914	0.965288	0.482644	−	0.875817i	$-0.339676\pi$
$61$	7.53914	0.965288	0.482644	+	0.875817i	$0.339676\pi$
$62$	− 2.96006i	− 0.375928i
$63$	− 13.0192i	− 1.64026i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.499202	0.0614476
$67$	− 5.72963i	− 0.699986i	−0.936752	−	0.349993i	$-0.886184\pi$
$67$	− 5.72963i	− 0.699986i	0.936752	−	0.349993i	$-0.113816\pi$
$68$	− 0.249601i	− 0.0302686i
$69$	4.68969	0.564573
$70$	0	0
$71$	−9.61902	−1.14157	−0.570784	−	0.821100i	$-0.693361\pi$
$71$	−9.61902	−1.14157	−0.570784	+	0.821100i	$0.693361\pi$
$72$	2.72963i	0.321690i
$73$	− 12.0591i	− 1.41141i	−0.708505	−	0.705706i	$-0.750630\pi$
$73$	− 12.0591i	− 1.41141i	0.708505	−	0.705706i	$-0.249370\pi$
$74$	0.0399387	0.00464278
$75$	0	0
$76$	1.00000	0.114708
$77$	− 4.57908i	− 0.521835i
$78$	1.16972i	0.132445i
$79$	−6.07988	−0.684040	−0.342020	−	0.939693i	$-0.611111\pi$
$79$	−6.07988	−0.684040	−0.342020	+	0.939693i	$0.611111\pi$
$80$	0	0
$81$	6.63979	0.737754
$82$	0	0
$83$	7.45926i	0.818761i	0.912364	+	0.409380i	$0.134255\pi$
$83$	7.45926i	0.818761i	−0.912364	+	0.409380i	$0.865745\pi$
$84$	−2.48003	−0.270594
$85$	0	0
$86$	−4.96006	−0.534857
$87$	− 3.24960i	− 0.348394i
$88$	0.960061i	0.102343i
$89$	−4.07988	−0.432466	−0.216233	−	0.976342i	$-0.569377\pi$
$89$	−4.07988	−0.432466	−0.216233	+	0.976342i	$0.569377\pi$
$90$	0	0
$91$	10.7296	1.12477
$92$	9.01917i	0.940314i
$93$	1.53914i	0.159602i
$94$	−9.49920	−0.979768
$95$	0	0
$96$	0.519969	0.0530692
$97$	18.4193i	1.87020i	0.354385	+	0.935100i	$0.384690\pi$
$97$	18.4193i	1.87020i	−0.354385	+	0.935100i	$0.615310\pi$
$98$	15.7488i	1.59087i
$99$	2.62061	0.263382
$100$	0	0
$101$	5.53914	0.551165	0.275583	−	0.961277i	$-0.411129\pi$
$101$	5.53914	0.551165	0.275583	+	0.961277i	$0.411129\pi$
$102$	0.129785i	0.0128506i
$103$	6.57908i	0.648256i	0.946013	+	0.324128i	$0.105071\pi$
$103$	6.57908i	0.648256i	−0.946013	+	0.324128i	$0.894929\pi$
$104$	−2.24960	−0.220592
$105$	0	0
$106$	−6.84945	−0.665277
$107$	14.9086i	1.44126i	0.693317	+	0.720632i	$0.256148\pi$
$107$	14.9086i	1.44126i	−0.693317	+	0.720632i	$0.743852\pi$
$108$	− 2.97923i	− 0.286677i
$109$	−4.76957	−0.456842	−0.228421	−	0.973562i	$-0.573356\pi$
$109$	−4.76957	−0.456842	−0.228421	+	0.973562i	$0.573356\pi$
$110$	0	0
$111$	−0.0207669	−0.00197111
$112$	− 4.76957i	− 0.450682i
$113$	− 6.00000i	− 0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$	− 6.00000i	− 0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−0.519969	−0.0486996
$115$	0	0
$116$	6.24960	0.580261
$117$	6.14058i	0.567697i
$118$	− 14.5583i	− 1.34020i
$119$	1.19049	0.109132
$120$	0	0
$121$	−10.0783	−0.916207
$122$	− 7.53914i	− 0.682562i
$123$	0	0
$124$	−2.96006	−0.265821
$125$	0	0
$126$	−13.0192	−1.15984
$127$	17.9585i	1.59356i	0.604272	+	0.796778i	$0.293464\pi$
$127$	17.9585i	1.59356i	−0.604272	+	0.796778i	$0.706536\pi$
$128$	1.00000i	0.0883883i
$129$	2.57908	0.227075
$130$	0	0
$131$	−6.96006	−0.608103	−0.304052	−	0.952656i	$-0.598340\pi$
$131$	−6.96006	−0.608103	−0.304052	+	0.952656i	$0.598340\pi$
$132$	− 0.499202i	− 0.0434500i
$133$	4.76957i	0.413574i
$134$	−5.72963	−0.494965
$135$	0	0
$136$	−0.249601	−0.0214031
$137$	7.80951i	0.667211i	0.942713	+	0.333606i	$0.108265\pi$
$137$	7.80951i	0.667211i	−0.942713	+	0.333606i	$0.891735\pi$
$138$	− 4.68969i	− 0.399213i
$139$	16.0383	1.36035	0.680177	−	0.733048i	$-0.261903\pi$
$139$	16.0383	1.36035	0.680177	+	0.733048i	$0.261903\pi$
$140$	0	0
$141$	4.93929	0.415964
$142$	9.61902i	0.807210i
$143$	2.15975i	0.180608i
$144$	2.72963	0.227469
$145$	0	0
$146$	−12.0591	−0.998019
$147$	− 8.18890i	− 0.675409i
$148$	− 0.0399387i	− 0.00328294i
$149$	8.41932	0.689738	0.344869	−	0.938651i	$-0.387923\pi$
$149$	8.41932	0.689738	0.344869	+	0.938651i	$0.387923\pi$
$150$	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
$153$	0.681319i	0.0550814i
$154$	−4.57908	−0.368993
$155$	0	0
$156$	1.16972	0.0936529
$157$	4.96006i	0.395856i	0.980217	+	0.197928i	$0.0634212\pi$
$157$	4.96006i	0.395856i	−0.980217	+	0.197928i	$0.936579\pi$
$158$	6.07988i	0.483689i
$159$	3.56150	0.282446
$160$	0	0
$161$	−43.0176	−3.39026
$162$	− 6.63979i	− 0.521671i
$163$	21.4593i	1.68082i	0.541952	+	0.840410i	$0.317686\pi$
$163$	21.4593i	1.68082i	−0.541952	+	0.840410i	$0.682314\pi$
$164$	0	0
$165$	0	0
$166$	7.45926	0.578951
$167$	− 11.0399i	− 0.854296i	−0.904182	−	0.427148i	$-0.859518\pi$
$167$	− 11.0399i	− 0.854296i	0.904182	−	0.427148i	$-0.140482\pi$
$168$	2.48003i	0.191339i
$169$	7.93929	0.610715
$170$	0	0
$171$	−2.72963	−0.208740
$172$	4.96006i	0.378201i
$173$	− 16.9585i	− 1.28933i	−0.764466	−	0.644664i	$-0.776997\pi$
$173$	− 16.9585i	− 1.28933i	0.764466	−	0.644664i	$-0.223003\pi$
$174$	−3.24960	−0.246352
$175$	0	0
$176$	0.960061	0.0723673
$177$	7.56988i	0.568987i
$178$	4.07988i	0.305800i
$179$	−2.53914	−0.189784	−0.0948922	−	0.995488i	$-0.530251\pi$
$179$	−2.53914	−0.189784	−0.0948922	+	0.995488i	$0.530251\pi$
$180$	0	0
$181$	−3.88018	−0.288412	−0.144206	−	0.989548i	$-0.546063\pi$
$181$	−3.88018	−0.288412	−0.144206	+	0.989548i	$0.546063\pi$
$182$	− 10.7296i	− 0.795333i
$183$	3.92012i	0.289784i
$184$	9.01917	0.664902
$185$	0	0
$186$	1.53914	0.112855
$187$	0.239632i	0.0175237i
$188$	9.49920i	0.692801i
$189$	14.2097	1.03360
$190$	0	0
$191$	2.05911	0.148992	0.0744960	−	0.997221i	$-0.476265\pi$
$191$	2.05911	0.148992	0.0744960	+	0.997221i	$0.476265\pi$
$192$	− 0.519969i	− 0.0375256i
$193$	8.46086i	0.609026i	0.952508	+	0.304513i	$0.0984937\pi$
$193$	8.46086i	0.609026i	−0.952508	+	0.304513i	$0.901506\pi$
$194$	18.4193	1.32243
$195$	0	0
$196$	15.7488	1.12491
$197$	13.9201i	0.991768i	0.868389	+	0.495884i	$0.165156\pi$
$197$	13.9201i	0.991768i	−0.868389	+	0.495884i	$0.834844\pi$
$198$	− 2.62061i	− 0.186239i
$199$	9.15055	0.648665	0.324333	−	0.945943i	$-0.394860\pi$
$199$	9.15055	0.648665	0.324333	+	0.945943i	$0.394860\pi$
$200$	0	0
$201$	2.97923	0.210139
$202$	− 5.53914i	− 0.389733i
$203$	29.8079i	2.09211i
$204$	0.129785	0.00908677
$205$	0	0
$206$	6.57908	0.458386
$207$	− 24.6190i	− 1.71114i
$208$	2.24960i	0.155982i
$209$	−0.960061	−0.0664088
$210$	0	0
$211$	16.5200	1.13728	0.568641	−	0.822586i	$-0.307469\pi$
$211$	16.5200	1.13728	0.568641	+	0.822586i	$0.307469\pi$
$212$	6.84945i	0.470422i
$213$	− 5.00160i	− 0.342704i
$214$	14.9086	1.01913
$215$	0	0
$216$	−2.97923	−0.202711
$217$	− 14.1182i	− 0.958407i
$218$	4.76957i	0.323036i
$219$	6.27037	0.423712
$220$	0	0
$221$	−0.561503	−0.0377708
$222$	0.0207669i	0.00139378i
$223$	− 9.03994i	− 0.605359i	−0.953092	−	0.302680i	$-0.902119\pi$
$223$	− 9.03994i	− 0.605359i	0.953092	−	0.302680i	$-0.0978812\pi$
$224$	−4.76957	−0.318680
$225$	0	0
$226$	−6.00000	−0.399114
$227$	0.350246i	0.0232466i	0.999932	+	0.0116233i	$0.00369990\pi$
$227$	0.350246i	0.0232466i	−0.999932	+	0.0116233i	$0.996300\pi$
$228$	0.519969i	0.0344358i
$229$	8.07988	0.533933	0.266967	−	0.963706i	$-0.413979\pi$
$229$	8.07988	0.533933	0.266967	+	0.963706i	$0.413979\pi$
$230$	0	0
$231$	2.38098	0.156657
$232$	− 6.24960i	− 0.410306i
$233$	4.92012i	0.322328i	0.986928	+	0.161164i	$0.0515248\pi$
$233$	4.92012i	0.322328i	−0.986928	+	0.161164i	$0.948475\pi$
$234$	6.14058	0.401422
$235$	0	0
$236$	−14.5583	−0.947665
$237$	− 3.16135i	− 0.205352i
$238$	− 1.19049i	− 0.0771680i
$239$	−2.98083	−0.192814	−0.0964069	−	0.995342i	$-0.530735\pi$
$239$	−2.98083	−0.192814	−0.0964069	+	0.995342i	$0.530735\pi$
$240$	0	0
$241$	20.0383	1.29078	0.645392	−	0.763852i	$-0.276694\pi$
$241$	20.0383	1.29078	0.645392	+	0.763852i	$0.276694\pi$
$242$	10.0783i	0.647857i
$243$	12.3902i	0.794831i
$244$	−7.53914	−0.482644
$245$	0	0
$246$	0	0
$247$	− 2.24960i	− 0.143139i
$248$	2.96006i	0.187964i
$249$	−3.87859	−0.245796
$250$	0	0
$251$	−14.8802	−0.939229	−0.469614	−	0.882872i	$-0.655607\pi$
$251$	−14.8802	−0.939229	−0.469614	+	0.882872i	$0.655607\pi$
$252$	13.0192i	0.820131i
$253$	− 8.65896i	− 0.544384i
$254$	17.9585	1.12681
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 11.0399i	− 0.688652i	−0.938850	−	0.344326i	$-0.888107\pi$
$257$	− 11.0399i	− 0.688652i	0.938850	−	0.344326i	$-0.111893\pi$
$258$	− 2.57908i	− 0.160567i
$259$	0.190491	0.0118365
$260$	0	0
$261$	−17.0591	−1.05593
$262$	6.96006i	0.429994i
$263$	3.84025i	0.236800i	0.992966	+	0.118400i	$0.0377764\pi$
$263$	3.84025i	0.236800i	−0.992966	+	0.118400i	$0.962224\pi$
$264$	−0.499202	−0.0307238
$265$	0	0
$266$	4.76957	0.292441
$267$	− 2.12141i	− 0.129828i
$268$	5.72963i	0.349993i
$269$	−23.1981	−1.41441	−0.707207	−	0.707007i	$-0.750045\pi$
$269$	−23.1981	−1.41441	−0.707207	+	0.707007i	$0.750045\pi$
$270$	0	0
$271$	23.9792	1.45663	0.728317	−	0.685240i	$-0.240303\pi$
$271$	23.9792	1.45663	0.728317	+	0.685240i	$0.240303\pi$
$272$	0.249601i	0.0151343i
$273$	5.57908i	0.337661i
$274$	7.80951	0.471790
$275$	0	0
$276$	−4.68969	−0.282286
$277$	24.6590i	1.48161i	0.671718	+	0.740807i	$0.265556\pi$
$277$	24.6590i	1.48161i	−0.671718	+	0.740807i	$0.734444\pi$
$278$	− 16.0383i	− 0.961916i
$279$	8.07988	0.483730
$280$	0	0
$281$	−18.9984	−1.13335	−0.566675	−	0.823941i	$-0.691770\pi$
$281$	−18.9984	−1.13335	−0.566675	+	0.823941i	$0.691770\pi$
$282$	− 4.93929i	− 0.294131i
$283$	− 29.0367i	− 1.72606i	−0.505156	−	0.863028i	$-0.668565\pi$
$283$	− 29.0367i	− 1.72606i	0.505156	−	0.863028i	$-0.331435\pi$
$284$	9.61902	0.570784
$285$	0	0
$286$	2.15975	0.127709
$287$	0	0
$288$	− 2.72963i	− 0.160845i
$289$	16.9377	0.996335
$290$	0	0
$291$	−9.57748	−0.561442
$292$	12.0591i	0.705706i
$293$	− 6.24960i	− 0.365106i	−0.983196	−	0.182553i	$-0.941564\pi$
$293$	− 6.24960i	− 0.365106i	0.983196	−	0.182553i	$-0.0584360\pi$
$294$	−8.18890	−0.477586
$295$	0	0
$296$	−0.0399387	−0.00232139
$297$	2.86025i	0.165968i
$298$	− 8.41932i	− 0.487718i
$299$	20.2895	1.17337
$300$	0	0
$301$	−23.6574	−1.36359
$302$	− 20.0000i	− 1.15087i
$303$	2.88018i	0.165462i
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	0.681319	0.0389484
$307$	12.5391i	0.715647i	0.933789	+	0.357823i	$0.116481\pi$
$307$	12.5391i	0.715647i	−0.933789	+	0.357823i	$0.883519\pi$
$308$	4.57908i	0.260917i
$309$	−3.42092	−0.194609
$310$	0	0
$311$	7.84785	0.445011	0.222505	−	0.974931i	$-0.428576\pi$
$311$	7.84785	0.445011	0.222505	+	0.974931i	$0.428576\pi$
$312$	− 1.16972i	− 0.0662226i
$313$	− 10.9884i	− 0.621103i	−0.950557	−	0.310552i	$-0.899486\pi$
$313$	− 10.9884i	− 0.621103i	0.950557	−	0.310552i	$-0.100514\pi$
$314$	4.96006	0.279912
$315$	0	0
$316$	6.07988	0.342020
$317$	− 21.5567i	− 1.21075i	−0.795942	−	0.605373i	$-0.793024\pi$
$317$	− 21.5567i	− 1.21075i	0.795942	−	0.605373i	$-0.206976\pi$
$318$	− 3.56150i	− 0.199719i
$319$	−6.00000	−0.335936
$320$	0	0
$321$	−7.75199	−0.432674
$322$	43.0176i	2.39728i
$323$	− 0.249601i	− 0.0138882i
$324$	−6.63979	−0.368877
$325$	0	0
$326$	21.4593	1.18852
$327$	− 2.48003i	− 0.137146i
$328$	0	0
$329$	−45.3071	−2.49786
$330$	0	0
$331$	33.4876	1.84065	0.920324	−	0.391158i	$-0.127925\pi$
$331$	33.4876	1.84065	0.920324	+	0.391158i	$0.127925\pi$
$332$	− 7.45926i	− 0.409380i
$333$	0.109018i	0.00597415i
$334$	−11.0399	−0.604079
$335$	0	0
$336$	2.48003	0.135297
$337$	5.69890i	0.310439i	0.987880	+	0.155219i	$0.0496084\pi$
$337$	5.69890i	0.310439i	−0.987880	+	0.155219i	$0.950392\pi$
$338$	− 7.93929i	− 0.431841i
$339$	3.11982	0.169445
$340$	0	0
$341$	2.84184	0.153894
$342$	2.72963i	0.147602i
$343$	41.7280i	2.25310i
$344$	4.96006	0.267429
$345$	0	0
$346$	−16.9585	−0.911693
$347$	− 0.239632i	− 0.0128641i	−0.999979	−	0.00643207i	$-0.997953\pi$
$347$	− 0.239632i	− 0.0128641i	0.999979	−	0.00643207i	$-0.00204741\pi$
$348$	3.24960i	0.174197i
$349$	17.2380	0.922731	0.461365	−	0.887210i	$-0.347360\pi$
$349$	17.2380	0.922731	0.461365	+	0.887210i	$0.347360\pi$
$350$	0	0
$351$	−6.70209	−0.357731
$352$	− 0.960061i	− 0.0511714i
$353$	34.7280i	1.84839i	0.381925	+	0.924193i	$0.375261\pi$
$353$	34.7280i	1.84839i	−0.381925	+	0.924193i	$0.624739\pi$
$354$	7.56988	0.402334
$355$	0	0
$356$	4.07988	0.216233
$357$	0.619019i	0.0327619i
$358$	2.53914i	0.134198i
$359$	−26.6689	−1.40753	−0.703766	−	0.710432i	$-0.748500\pi$
$359$	−26.6689	−1.40753	−0.703766	+	0.710432i	$0.748500\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	3.88018i	0.203938i
$363$	− 5.24040i	− 0.275050i
$364$	−10.7296	−0.562386
$365$	0	0
$366$	3.92012	0.204908
$367$	− 15.2380i	− 0.795419i	−0.917511	−	0.397710i	$-0.869805\pi$
$367$	− 15.2380i	− 0.795419i	0.917511	−	0.397710i	$-0.130195\pi$
$368$	− 9.01917i	− 0.470157i
$369$	0	0
$370$	0	0
$371$	−32.6689	−1.69609
$372$	− 1.53914i	− 0.0798008i
$373$	26.6382i	1.37927i	0.724156	+	0.689637i	$0.242230\pi$
$373$	26.6382i	1.37927i	−0.724156	+	0.689637i	$0.757770\pi$
$374$	0.239632	0.0123911
$375$	0	0
$376$	9.49920	0.489884
$377$	− 14.0591i	− 0.724081i
$378$	− 14.2097i	− 0.730866i
$379$	−11.9693	−0.614820	−0.307410	−	0.951577i	$-0.599462\pi$
$379$	−11.9693	−0.614820	−0.307410	+	0.951577i	$0.599462\pi$
$380$	0	0
$381$	−9.33785	−0.478393
$382$	− 2.05911i	− 0.105353i
$383$	9.84025i	0.502813i	0.967882	+	0.251407i	$0.0808931\pi$
$383$	9.84025i	0.502813i	−0.967882	+	0.251407i	$0.919107\pi$
$384$	−0.519969	−0.0265346
$385$	0	0
$386$	8.46086	0.430646
$387$	− 13.5391i	− 0.688233i
$388$	− 18.4193i	− 0.935100i
$389$	8.65896	0.439027	0.219513	−	0.975610i	$-0.429553\pi$
$389$	8.65896	0.439027	0.219513	+	0.975610i	$0.429553\pi$
$390$	0	0
$391$	2.25120	0.113848
$392$	− 15.7488i	− 0.795435i
$393$	− 3.61902i	− 0.182555i
$394$	13.9201	0.701286
$395$	0	0
$396$	−2.62061	−0.131691
$397$	28.9984i	1.45539i	0.685902	+	0.727694i	$0.259408\pi$
$397$	28.9984i	1.45539i	−0.685902	+	0.727694i	$0.740592\pi$
$398$	− 9.15055i	− 0.458676i
$399$	−2.48003	−0.124157
$400$	0	0
$401$	22.6174	1.12946	0.564730	−	0.825276i	$-0.308980\pi$
$401$	22.6174	1.12946	0.564730	+	0.825276i	$0.308980\pi$
$402$	− 2.97923i	− 0.148591i
$403$	6.65896i	0.331706i
$404$	−5.53914	−0.275583
$405$	0	0
$406$	29.8079	1.47934
$407$	0.0383436i	0.00190062i
$408$	− 0.129785i	− 0.00642531i
$409$	−5.34104	−0.264098	−0.132049	−	0.991243i	$-0.542156\pi$
$409$	−5.34104	−0.264098	−0.132049	+	0.991243i	$0.542156\pi$
$410$	0	0
$411$	−4.06071	−0.200300
$412$	− 6.57908i	− 0.324128i
$413$	− 69.4369i	− 3.41677i
$414$	−24.6190	−1.20996
$415$	0	0
$416$	2.24960	0.110296
$417$	8.33945i	0.408384i
$418$	0.960061i	0.0469581i
$419$	22.1566	1.08242	0.541210	−	0.840888i	$-0.317967\pi$
$419$	22.1566	1.08242	0.541210	+	0.840888i	$0.317967\pi$
$420$	0	0
$421$	29.2787	1.42696	0.713479	−	0.700676i	$-0.247118\pi$
$421$	29.2787	1.42696	0.713479	+	0.700676i	$0.247118\pi$
$422$	− 16.5200i	− 0.804180i
$423$	− 25.9293i	− 1.26073i
$424$	6.84945	0.332639
$425$	0	0
$426$	−5.00160	−0.242328
$427$	− 35.9585i	− 1.74015i
$428$	− 14.9086i	− 0.720632i
$429$	−1.12301	−0.0542193
$430$	0	0
$431$	21.3794	1.02981	0.514904	−	0.857248i	$-0.327827\pi$
$431$	21.3794	1.02981	0.514904	+	0.857248i	$0.327827\pi$
$432$	2.97923i	0.143338i
$433$	36.1182i	1.73573i	0.496799	+	0.867865i	$0.334509\pi$
$433$	36.1182i	1.73573i	−0.496799	+	0.867865i	$0.665491\pi$
$434$	−14.1182	−0.677696
$435$	0	0
$436$	4.76957	0.228421
$437$	9.01917i	0.431445i
$438$	− 6.27037i	− 0.299610i
$439$	−20.9984	−1.00220	−0.501100	−	0.865390i	$-0.667071\pi$
$439$	−20.9984	−1.00220	−0.501100	+	0.865390i	$0.667071\pi$
$440$	0	0
$441$	−42.9884	−2.04707
$442$	0.561503i	0.0267080i
$443$	31.4976i	1.49650i	0.663419	+	0.748248i	$0.269105\pi$
$443$	31.4976i	1.49650i	−0.663419	+	0.748248i	$0.730895\pi$
$444$	0.0207669	0.000985555 0
$445$	0	0
$446$	−9.03994	−0.428054
$447$	4.37779i	0.207062i
$448$	4.76957i	0.225341i
$449$	−18.9601	−0.894781	−0.447390	−	0.894339i	$-0.647647\pi$
$449$	−18.9601	−0.894781	−0.447390	+	0.894339i	$0.647647\pi$
$450$	0	0
$451$	0	0
$452$	6.00000i	0.282216i
$453$	10.3994i	0.488606i
$454$	0.350246	0.0164378
$455$	0	0
$456$	0.519969	0.0243498
$457$	− 6.32948i	− 0.296081i	−0.988981	−	0.148040i	$-0.952703\pi$
$457$	− 6.32948i	− 0.296081i	0.988981	−	0.148040i	$-0.0472965\pi$
$458$	− 8.07988i	− 0.377548i
$459$	−0.743620	−0.0347092
$460$	0	0
$461$	−6.49920	−0.302698	−0.151349	−	0.988480i	$-0.548362\pi$
$461$	−6.49920	−0.302698	−0.151349	+	0.988480i	$0.548362\pi$
$462$	− 2.38098i	− 0.110773i
$463$	− 28.4177i	− 1.32068i	−0.750965	−	0.660342i	$-0.770411\pi$
$463$	− 28.4177i	− 1.32068i	0.750965	−	0.660342i	$-0.229589\pi$
$464$	−6.24960	−0.290130
$465$	0	0
$466$	4.92012	0.227920
$467$	17.5775i	0.813389i	0.913564	+	0.406694i	$0.133319\pi$
$467$	17.5775i	0.813389i	−0.913564	+	0.406694i	$0.866681\pi$
$468$	− 6.14058i	− 0.283849i
$469$	−27.3279	−1.26188
$470$	0	0
$471$	−2.57908	−0.118838
$472$	14.5583i	0.670101i
$473$	− 4.76196i	− 0.218955i
$474$	−3.16135	−0.145206
$475$	0	0
$476$	−1.19049	−0.0545660
$477$	− 18.6965i	− 0.856053i
$478$	2.98083i	0.136340i
$479$	−22.7372	−1.03889	−0.519446	−	0.854504i	$-0.673861\pi$
$479$	−22.7372	−1.03889	−0.519446	+	0.854504i	$0.673861\pi$
$480$	0	0
$481$	−0.0898462	−0.00409664
$482$	− 20.0383i	− 0.912722i
$483$	− 22.3678i	− 1.01777i
$484$	10.0783	0.458104
$485$	0	0
$486$	12.3902	0.562030
$487$	− 22.1981i	− 1.00589i	−0.864318	−	0.502946i	$-0.832249\pi$
$487$	− 22.1981i	− 1.00589i	0.864318	−	0.502946i	$-0.167751\pi$
$488$	7.53914i	0.341281i
$489$	−11.1582	−0.504589
$490$	0	0
$491$	−24.9984	−1.12816	−0.564081	−	0.825719i	$-0.690769\pi$
$491$	−24.9984	−1.12816	−0.564081	+	0.825719i	$0.690769\pi$
$492$	0	0
$493$	− 1.55991i	− 0.0702547i
$494$	−2.24960	−0.101214
$495$	0	0
$496$	2.96006	0.132911
$497$	45.8786i	2.05794i
$498$	3.87859i	0.173804i
$499$	−11.6574	−0.521855	−0.260928	−	0.965358i	$-0.584028\pi$
$499$	−11.6574	−0.521855	−0.260928	+	0.965358i	$0.584028\pi$
$500$	0	0
$501$	5.74043	0.256463
$502$	14.8802i	0.664135i
$503$	− 11.7504i	− 0.523924i	−0.965078	−	0.261962i	$-0.915630\pi$
$503$	− 11.7504i	− 0.523924i	0.965078	−	0.261962i	$-0.0843696\pi$
$504$	13.0192	0.579920
$505$	0	0
$506$	−8.65896	−0.384938
$507$	4.12819i	0.183339i
$508$	− 17.9585i	− 0.796778i
$509$	−29.9569	−1.32781	−0.663907	−	0.747815i	$-0.731103\pi$
$509$	−29.9569	−1.32781	−0.663907	+	0.747815i	$0.731103\pi$
$510$	0	0
$511$	−57.5168	−2.54439
$512$	− 1.00000i	− 0.0441942i
$513$	− 2.97923i	− 0.131536i
$514$	−11.0399	−0.486951
$515$	0	0
$516$	−2.57908	−0.113538
$517$	− 9.11982i	− 0.401089i
$518$	− 0.190491i	− 0.00836968i
$519$	8.81788	0.387062
$520$	0	0
$521$	−15.1198	−0.662411	−0.331206	−	0.943559i	$-0.607455\pi$
$521$	−15.1198	−0.662411	−0.331206	+	0.943559i	$0.607455\pi$
$522$	17.0591i	0.746657i
$523$	− 15.6498i	− 0.684316i	−0.939642	−	0.342158i	$-0.888842\pi$
$523$	− 15.6498i	− 0.684316i	0.939642	−	0.342158i	$-0.111158\pi$
$524$	6.96006	0.304052
$525$	0	0
$526$	3.84025	0.167443
$527$	0.738835i	0.0321842i
$528$	0.499202i	0.0217250i
$529$	−58.3455	−2.53676
$530$	0	0
$531$	39.7388	1.72452
$532$	− 4.76957i	− 0.206787i
$533$	0	0
$534$	−2.12141	−0.0918024
$535$	0	0
$536$	5.72963	0.247482
$537$	− 1.32028i	− 0.0569741i
$538$	23.1981i	1.00014i
$539$	−15.1198	−0.651257
$540$	0	0
$541$	−27.2995	−1.17370	−0.586849	−	0.809697i	$-0.699632\pi$
$541$	−27.2995	−1.17370	−0.586849	+	0.809697i	$0.699632\pi$
$542$	− 23.9792i	− 1.03000i
$543$	− 2.01758i	− 0.0865825i
$544$	0.249601	0.0107016
$545$	0	0
$546$	5.57908	0.238763
$547$	− 33.9968i	− 1.45360i	−0.686850	−	0.726799i	$-0.741007\pi$
$547$	− 33.9968i	− 1.45360i	0.686850	−	0.726799i	$-0.258993\pi$
$548$	− 7.80951i	− 0.333606i
$549$	20.5791	0.878294
$550$	0	0
$551$	6.24960	0.266242
$552$	4.68969i	0.199607i
$553$	28.9984i	1.23314i
$554$	24.6590	1.04766
$555$	0	0
$556$	−16.0383	−0.680177
$557$	33.8786i	1.43548i	0.696310	+	0.717741i	$0.254824\pi$
$557$	33.8786i	1.43548i	−0.696310	+	0.717741i	$0.745176\pi$
$558$	− 8.07988i	− 0.342048i
$559$	11.1582	0.471940
$560$	0	0
$561$	−0.124602	−0.00526068
$562$	18.9984i	0.801399i
$563$	− 32.2995i	− 1.36126i	−0.732626	−	0.680631i	$-0.761706\pi$
$563$	− 32.2995i	− 1.36126i	0.732626	−	0.680631i	$-0.238294\pi$
$564$	−4.93929	−0.207982
$565$	0	0
$566$	−29.0367	−1.22051
$567$	− 31.6689i	− 1.32997i
$568$	− 9.61902i	− 0.403605i
$569$	6.73883	0.282507	0.141253	−	0.989973i	$-0.454887\pi$
$569$	6.73883	0.282507	0.141253	+	0.989973i	$0.454887\pi$
$570$	0	0
$571$	34.4193	1.44040	0.720202	−	0.693764i	$-0.244049\pi$
$571$	34.4193	1.44040	0.720202	+	0.693764i	$0.244049\pi$
$572$	− 2.15975i	− 0.0903039i
$573$	1.07067i	0.0447281i
$574$	0	0
$575$	0	0
$576$	−2.72963	−0.113735
$577$	28.1773i	1.17304i	0.809936	+	0.586519i	$0.199502\pi$
$577$	28.1773i	1.17304i	−0.809936	+	0.586519i	$0.800498\pi$
$578$	− 16.9377i	− 0.704515i
$579$	−4.39939	−0.182832
$580$	0	0
$581$	35.5775	1.47600
$582$	9.57748i	0.397000i
$583$	− 6.57589i	− 0.272346i
$584$	12.0591	0.499010
$585$	0	0
$586$	−6.24960	−0.258169
$587$	− 34.6174i	− 1.42881i	−0.699730	−	0.714407i	$-0.746697\pi$
$587$	− 34.6174i	− 1.42881i	0.699730	−	0.714407i	$-0.253303\pi$
$588$	8.18890i	0.337704i
$589$	−2.96006	−0.121967
$590$	0	0
$591$	−7.23804	−0.297733
$592$	0.0399387i	0.00164147i
$593$	3.99840i	0.164195i	0.996624	+	0.0820974i	$0.0261619\pi$
$593$	3.99840i	0.164195i	−0.996624	+	0.0820974i	$0.973838\pi$
$594$	2.86025	0.117357
$595$	0	0
$596$	−8.41932	−0.344869
$597$	4.75801i	0.194732i
$598$	− 20.2895i	− 0.829701i
$599$	42.5759	1.73960	0.869802	−	0.493401i	$-0.164247\pi$
$599$	42.5759	1.73960	0.869802	+	0.493401i	$0.164247\pi$
$600$	0	0
$601$	−18.4577	−0.752904	−0.376452	−	0.926436i	$-0.622856\pi$
$601$	−18.4577	−0.752904	−0.376452	+	0.926436i	$0.622856\pi$
$602$	23.6574i	0.964202i
$603$	− 15.6398i	− 0.636901i
$604$	−20.0000	−0.813788
$605$	0	0
$606$	2.88018	0.116999
$607$	− 12.5791i	− 0.510569i	−0.966866	−	0.255285i	$-0.917831\pi$
$607$	− 12.5791i	− 0.510569i	0.966866	−	0.255285i	$-0.0821691\pi$
$608$	1.00000i	0.0405554i
$609$	−15.4992	−0.628059
$610$	0	0
$611$	21.3694	0.864514
$612$	− 0.681319i	− 0.0275407i
$613$	26.5759i	1.07339i	0.843776	+	0.536695i	$0.180327\pi$
$613$	26.5759i	1.07339i	−0.843776	+	0.536695i	$0.819673\pi$
$614$	12.5391	0.506039
$615$	0	0
$616$	4.57908	0.184496
$617$	− 37.8386i	− 1.52333i	−0.647973	−	0.761663i	$-0.724383\pi$
$617$	− 37.8386i	− 1.52333i	0.647973	−	0.761663i	$-0.275617\pi$
$618$	3.42092i	0.137610i
$619$	−30.1566	−1.21209	−0.606047	−	0.795429i	$-0.707246\pi$
$619$	−30.1566	−1.21209	−0.606047	+	0.795429i	$0.707246\pi$
$620$	0	0
$621$	26.8702	1.07826
$622$	− 7.84785i	− 0.314670i
$623$	19.4593i	0.779619i
$624$	−1.16972	−0.0468264
$625$	0	0
$626$	−10.9884	−0.439186
$627$	− 0.499202i	− 0.0199362i
$628$	− 4.96006i	− 0.197928i
$629$	−0.00996876	−0.000397480 0
$630$	0	0
$631$	−25.4992	−1.01511	−0.507554	−	0.861620i	$-0.669450\pi$
$631$	−25.4992	−1.01511	−0.507554	+	0.861620i	$0.669450\pi$
$632$	− 6.07988i	− 0.241845i
$633$	8.58988i	0.341417i
$634$	−21.5567	−0.856127
$635$	0	0
$636$	−3.56150	−0.141223
$637$	− 35.4285i	− 1.40373i
$638$	6.00000i	0.237542i
$639$	−26.2564	−1.03869
$640$	0	0
$641$	39.1965	1.54817	0.774084	−	0.633082i	$-0.218211\pi$
$641$	39.1965	1.54817	0.774084	+	0.633082i	$0.218211\pi$
$642$	7.75199i	0.305947i
$643$	36.3778i	1.43460i	0.696764	+	0.717300i	$0.254622\pi$
$643$	36.3778i	1.43460i	−0.696764	+	0.717300i	$0.745378\pi$
$644$	43.0176	1.69513
$645$	0	0
$646$	−0.249601	−0.00982043
$647$	− 10.6897i	− 0.420255i	−0.977674	−	0.210128i	$-0.932612\pi$
$647$	− 10.6897i	− 0.420255i	0.977674	−	0.210128i	$-0.0673879\pi$
$648$	6.63979i	0.260835i
$649$	13.9769	0.548640
$650$	0	0
$651$	7.34104	0.287718
$652$	− 21.4593i	− 0.840410i
$653$	− 36.0383i	− 1.41029i	−0.709063	−	0.705145i	$-0.750882\pi$
$653$	− 36.0383i	− 1.41029i	0.709063	−	0.705145i	$-0.249118\pi$
$654$	−2.48003	−0.0969769
$655$	0	0
$656$	0	0
$657$	− 32.9169i	− 1.28421i
$658$	45.3071i	1.76626i
$659$	−17.1889	−0.669584	−0.334792	−	0.942292i	$-0.608666\pi$
$659$	−17.1889	−0.669584	−0.334792	+	0.942292i	$0.608666\pi$
$660$	0	0
$661$	48.9054	1.90220	0.951099	−	0.308886i	$-0.0999560\pi$
$661$	48.9054	1.90220	0.951099	+	0.308886i	$0.0999560\pi$
$662$	− 33.4876i	− 1.30153i
$663$	− 0.291964i	− 0.0113390i
$664$	−7.45926	−0.289476
$665$	0	0
$666$	0.109018	0.00422436
$667$	56.3662i	2.18251i
$668$	11.0399i	0.427148i
$669$	4.70049	0.181731
$670$	0	0
$671$	7.23804	0.279421
$672$	− 2.48003i	− 0.0956693i
$673$	6.57908i	0.253605i	0.991928	+	0.126802i	$0.0404714\pi$
$673$	6.57908i	0.253605i	−0.991928	+	0.126802i	$0.959529\pi$
$674$	5.69890	0.219513
$675$	0	0
$676$	−7.93929	−0.305357
$677$	38.3087i	1.47232i	0.676806	+	0.736162i	$0.263364\pi$
$677$	38.3087i	1.47232i	−0.676806	+	0.736162i	$0.736636\pi$
$678$	− 3.11982i	− 0.119816i
$679$	87.8523	3.37146
$680$	0	0
$681$	−0.182117	−0.00697874
$682$	− 2.84184i	− 0.108820i
$683$	7.54074i	0.288538i	0.989538	+	0.144269i	$0.0460831\pi$
$683$	7.54074i	0.288538i	−0.989538	+	0.144269i	$0.953917\pi$
$684$	2.72963	0.104370
$685$	0	0
$686$	41.7280	1.59318
$687$	4.20129i	0.160289i
$688$	− 4.96006i	− 0.189101i
$689$	15.4085	0.587018
$690$	0	0
$691$	28.4193	1.08112	0.540561	−	0.841305i	$-0.318212\pi$
$691$	28.4193	1.08112	0.540561	+	0.841305i	$0.318212\pi$
$692$	16.9585i	0.644664i
$693$	− 12.4992i	− 0.474805i
$694$	−0.239632	−0.00909632
$695$	0	0
$696$	3.24960	0.123176
$697$	0	0
$698$	− 17.2380i	− 0.652469i
$699$	−2.55831	−0.0967643
$700$	0	0
$701$	−24.2596	−0.916271	−0.458136	−	0.888882i	$-0.651483\pi$
$701$	−24.2596	−0.916271	−0.458136	+	0.888882i	$0.651483\pi$
$702$	6.70209i	0.252954i
$703$	− 0.0399387i	− 0.00150632i
$704$	−0.960061	−0.0361837
$705$	0	0
$706$	34.7280	1.30701
$707$	− 26.4193i	− 0.993601i
$708$	− 7.56988i	− 0.284493i
$709$	−21.7372	−0.816359	−0.408180	−	0.912902i	$-0.633836\pi$
$709$	−21.7372	−0.816359	−0.408180	+	0.912902i	$0.633836\pi$
$710$	0	0
$711$	−16.5958	−0.622392
$712$	− 4.07988i	− 0.152900i
$713$	− 26.6973i	− 0.999822i
$714$	0.619019	0.0231662
$715$	0	0
$716$	2.53914	0.0948922
$717$	− 1.54994i	− 0.0578835i
$718$	26.6689i	0.995275i
$719$	48.9361	1.82501	0.912504	−	0.409067i	$-0.134146\pi$
$719$	48.9361	1.82501	0.912504	+	0.409067i	$0.134146\pi$
$720$	0	0
$721$	31.3794	1.16863
$722$	− 1.00000i	− 0.0372161i
$723$	10.4193i	0.387499i
$724$	3.88018	0.144206
$725$	0	0
$726$	−5.24040	−0.194489
$727$	− 4.29874i	− 0.159432i	−0.996818	−	0.0797158i	$-0.974599\pi$
$727$	− 4.29874i	− 0.159432i	0.996818	−	0.0797158i	$-0.0254013\pi$
$728$	10.7296i	0.397667i
$729$	13.4768	0.499142
$730$	0	0
$731$	1.23804	0.0457905
$732$	− 3.92012i	− 0.144892i
$733$	12.0415i	0.444764i	0.974960	+	0.222382i	$0.0713832\pi$
$733$	12.0415i	0.444764i	−0.974960	+	0.222382i	$0.928617\pi$
$734$	−15.2380	−0.562446
$735$	0	0
$736$	−9.01917	−0.332451
$737$	− 5.50080i	− 0.202624i
$738$	0	0
$739$	−6.61742	−0.243426	−0.121713	−	0.992565i	$-0.538839\pi$
$739$	−6.61742	−0.243426	−0.121713	+	0.992565i	$0.538839\pi$
$740$	0	0
$741$	1.16972	0.0429709
$742$	32.6689i	1.19931i
$743$	47.6158i	1.74686i	0.486954	+	0.873428i	$0.338108\pi$
$743$	47.6158i	1.74686i	−0.486954	+	0.873428i	$0.661892\pi$
$744$	−1.53914	−0.0564277
$745$	0	0
$746$	26.6382	0.975293
$747$	20.3610i	0.744972i
$748$	− 0.239632i	− 0.00876183i
$749$	71.1074	2.59821
$750$	0	0
$751$	−25.6574	−0.936250	−0.468125	−	0.883662i	$-0.655070\pi$
$751$	−25.6574	−0.936250	−0.468125	+	0.883662i	$0.655070\pi$
$752$	− 9.49920i	− 0.346400i
$753$	− 7.73724i	− 0.281961i
$754$	−14.0591	−0.512003
$755$	0	0
$756$	−14.2097	−0.516800
$757$	8.83865i	0.321246i	0.987016	+	0.160623i	$0.0513504\pi$
$757$	8.83865i	0.321246i	−0.987016	+	0.160623i	$0.948650\pi$
$758$	11.9693i	0.434743i
$759$	4.50239	0.163426
$760$	0	0
$761$	−9.40776	−0.341031	−0.170516	−	0.985355i	$-0.554543\pi$
$761$	−9.40776	−0.341031	−0.170516	+	0.985355i	$0.554543\pi$
$762$	9.33785i	0.338275i
$763$	22.7488i	0.823562i
$764$	−2.05911	−0.0744960
$765$	0	0
$766$	9.84025	0.355543
$767$	32.7504i	1.18255i
$768$	0.519969i	0.0187628i
$769$	−7.32788	−0.264250	−0.132125	−	0.991233i	$-0.542180\pi$
$769$	−7.32788	−0.264250	−0.132125	+	0.991233i	$0.542180\pi$
$770$	0	0
$771$	5.74043	0.206737
$772$	− 8.46086i	− 0.304513i
$773$	− 54.4369i	− 1.95796i	−0.203958	−	0.978980i	$-0.565381\pi$
$773$	− 54.4369i	− 1.95796i	0.203958	−	0.978980i	$-0.434619\pi$
$774$	−13.5391	−0.486654
$775$	0	0
$776$	−18.4193	−0.661215
$777$	0.0990493i	0.00355337i
$778$	− 8.65896i	− 0.310439i
$779$	0	0
$780$	0	0
$781$	−9.23485	−0.330449
$782$	− 2.25120i	− 0.0805026i
$783$	− 18.6190i	− 0.665389i
$784$	−15.7488	−0.562457
$785$	0	0
$786$	−3.61902	−0.129086
$787$	− 27.6705i	− 0.986348i	−0.869931	−	0.493174i	$-0.835837\pi$
$787$	− 27.6705i	− 0.986348i	0.869931	−	0.493174i	$-0.164163\pi$
$788$	− 13.9201i	− 0.495884i
$789$	−1.99681	−0.0710883
$790$	0	0
$791$	−28.6174	−1.01752
$792$	2.62061i	0.0931195i
$793$	16.9601i	0.602269i
$794$	28.9984	1.02911
$795$	0	0
$796$	−9.15055	−0.324333
$797$	21.5906i	0.764780i	0.924001	+	0.382390i	$0.124899\pi$
$797$	21.5906i	0.764780i	−0.924001	+	0.382390i	$0.875101\pi$
$798$	2.48003i	0.0877921i
$799$	2.37101	0.0838804
$800$	0	0
$801$	−11.1366	−0.393491
$802$	− 22.6174i	− 0.798649i
$803$	− 11.5775i	− 0.408561i
$804$	−2.97923	−0.105069
$805$	0	0
$806$	6.65896	0.234552
$807$	− 12.0623i	− 0.424613i
$808$	5.53914i	0.194866i
$809$	−9.72963	−0.342076	−0.171038	−	0.985264i	$-0.554712\pi$
$809$	−9.72963	−0.342076	−0.171038	+	0.985264i	$0.554712\pi$
$810$	0	0
$811$	−38.7280	−1.35993	−0.679963	−	0.733247i	$-0.738004\pi$
$811$	−38.7280	−1.35993	−0.679963	+	0.733247i	$0.738004\pi$
$812$	− 29.8079i	− 1.04605i
$813$	12.4685i	0.437288i
$814$	0.0383436	0.00134394
$815$	0	0
$816$	−0.129785	−0.00454338
$817$	4.96006i	0.173531i
$818$	5.34104i	0.186745i
$819$	29.2879	1.02340
$820$	0	0
$821$	−30.2780	−1.05671	−0.528354	−	0.849024i	$-0.677191\pi$
$821$	−30.2780	−1.05671	−0.528354	+	0.849024i	$0.677191\pi$
$822$	4.06071i	0.141633i
$823$	7.93770i	0.276691i	0.990384	+	0.138345i	$0.0441784\pi$
$823$	7.93770i	0.276691i	−0.990384	+	0.138345i	$0.955822\pi$
$824$	−6.57908	−0.229193
$825$	0	0
$826$	−69.4369	−2.41602
$827$	30.2496i	1.05188i	0.850521	+	0.525941i	$0.176287\pi$
$827$	30.2496i	1.05188i	−0.850521	+	0.525941i	$0.823713\pi$
$828$	24.6190i	0.855570i
$829$	40.6765	1.41275	0.706377	−	0.707836i	$-0.250328\pi$
$829$	40.6765	1.41275	0.706377	+	0.707836i	$0.250328\pi$
$830$	0	0
$831$	−12.8219	−0.444787
$832$	− 2.24960i	− 0.0779909i
$833$	− 3.93092i	− 0.136198i
$834$	8.33945	0.288771
$835$	0	0
$836$	0.960061	0.0332044
$837$	8.81871i	0.304819i
$838$	− 22.1566i	− 0.765386i
$839$	−45.9553	−1.58655	−0.793276	−	0.608862i	$-0.791626\pi$
$839$	−45.9553	−1.58655	−0.793276	+	0.608862i	$0.791626\pi$
$840$	0	0
$841$	10.0575	0.346811
$842$	− 29.2787i	− 1.00901i
$843$	− 9.87859i	− 0.340237i
$844$	−16.5200	−0.568641
$845$	0	0
$846$	−25.9293	−0.891469
$847$	48.0691i	1.65167i
$848$	− 6.84945i	− 0.235211i
$849$	15.0982	0.518170
$850$	0	0
$851$	0.360214	0.0123480
$852$	5.00160i	0.171352i
$853$	− 17.2196i	− 0.589589i	−0.955561	−	0.294794i	$-0.904749\pi$
$853$	− 17.2196i	− 0.589589i	0.955561	−	0.294794i	$-0.0952512\pi$
$854$	−35.9585	−1.23047
$855$	0	0
$856$	−14.9086	−0.509564
$857$	17.2995i	0.590940i	0.955352	+	0.295470i	$0.0954762\pi$
$857$	17.2995i	0.590940i	−0.955352	+	0.295470i	$0.904524\pi$
$858$	1.12301i	0.0383388i
$859$	−17.6190	−0.601153	−0.300577	−	0.953758i	$-0.597179\pi$
$859$	−17.6190	−0.601153	−0.300577	+	0.953758i	$0.597179\pi$
$860$	0	0
$861$	0	0
$862$	− 21.3794i	− 0.728185i
$863$	4.07988i	0.138881i	0.997586	+	0.0694403i	$0.0221213\pi$
$863$	4.07988i	0.138881i	−0.997586	+	0.0694403i	$0.977879\pi$
$864$	2.97923	0.101356
$865$	0	0
$866$	36.1182	1.22735
$867$	8.80708i	0.299104i
$868$	14.1182i	0.479204i
$869$	−5.83705	−0.198009
$870$	0	0
$871$	12.8894	0.436740
$872$	− 4.76957i	− 0.161518i
$873$	50.2780i	1.70165i
$874$	9.01917	0.305078
$875$	0	0
$876$	−6.27037	−0.211856
$877$	25.2787i	0.853602i	0.904345	+	0.426801i	$0.140360\pi$
$877$	25.2787i	0.853602i	−0.904345	+	0.426801i	$0.859640\pi$
$878$	20.9984i	0.708662i
$879$	3.24960	0.109606
$880$	0	0
$881$	−0.0814726	−0.00274488	−0.00137244	−	0.999999i	$-0.500437\pi$
$881$	−0.0814726	−0.00274488	−0.00137244	+	0.999999i	$0.500437\pi$
$882$	42.9884i	1.44750i
$883$	− 19.3410i	− 0.650878i	−0.945563	−	0.325439i	$-0.894488\pi$
$883$	− 19.3410i	− 0.650878i	0.945563	−	0.325439i	$-0.105512\pi$
$884$	0.561503	0.0188854
$885$	0	0
$886$	31.4976	1.05818
$887$	5.53914i	0.185986i	0.995667	+	0.0929931i	$0.0296434\pi$
$887$	5.53914i	0.185986i	−0.995667	+	0.0929931i	$0.970357\pi$
$888$	− 0.0207669i	0 0.000696892i
$889$	85.6542	2.87275
$890$	0	0
$891$	6.37460	0.213557
$892$	9.03994i	0.302680i
$893$	9.49920i	0.317879i
$894$	4.37779	0.146415
$895$	0	0
$896$	4.76957	0.159340
$897$	10.5499i	0.352252i
$898$	18.9601i	0.632705i
$899$	−18.4992	−0.616983
$900$	0	0
$901$	1.70963	0.0569561
$902$	0	0
$903$	− 12.3011i	− 0.409355i
$904$	6.00000	0.199557
$905$	0	0
$906$	10.3994	0.345497
$907$	10.8111i	0.358977i	0.983760	+	0.179488i	$0.0574442\pi$
$907$	10.8111i	0.358977i	−0.983760	+	0.179488i	$0.942556\pi$
$908$	− 0.350246i	− 0.0116233i
$909$	15.1198	0.501493
$910$	0	0
$911$	35.1166	1.16347	0.581733	−	0.813380i	$-0.302375\pi$
$911$	35.1166	1.16347	0.581733	+	0.813380i	$0.302375\pi$
$912$	− 0.519969i	− 0.0172179i
$913$	7.16135i	0.237006i
$914$	−6.32948	−0.209361
$915$	0	0
$916$	−8.07988	−0.266967
$917$	33.1965i	1.09625i
$918$	0.743620i	0.0245431i
$919$	−30.8287	−1.01694	−0.508472	−	0.861078i	$-0.669790\pi$
$919$	−30.8287	−1.01694	−0.508472	+	0.861078i	$0.669790\pi$
$920$	0	0
$921$	−6.51997	−0.214840
$922$	6.49920i	0.214040i
$923$	− 21.6390i	− 0.712255i
$924$	−2.38098	−0.0783285
$925$	0	0
$926$	−28.4177	−0.933865
$927$	17.9585i	0.589833i
$928$	6.24960i	0.205153i
$929$	45.0575	1.47829	0.739145	−	0.673547i	$-0.235230\pi$
$929$	45.0575	1.47829	0.739145	+	0.673547i	$0.235230\pi$
$930$	0	0
$931$	15.7488	0.516146
$932$	− 4.92012i	− 0.161164i
$933$	4.08064i	0.133594i
$934$	17.5775	0.575153
$935$	0	0
$936$	−6.14058	−0.200711
$937$	− 22.2464i	− 0.726759i	−0.931641	−	0.363379i	$-0.881623\pi$
$937$	− 22.2464i	− 0.726759i	0.931641	−	0.363379i	$-0.118377\pi$
$938$	27.3279i	0.892287i
$939$	5.71365	0.186458
$940$	0	0
$941$	−53.9277	−1.75799	−0.878997	−	0.476828i	$-0.841787\pi$
$941$	−53.9277	−1.75799	−0.878997	+	0.476828i	$0.841787\pi$
$942$	2.57908i	0.0840310i
$943$	0	0
$944$	14.5583	0.473833
$945$	0	0
$946$	−4.76196	−0.154825
$947$	4.76196i	0.154743i	0.997002	+	0.0773715i	$0.0246528\pi$
$947$	4.76196i	0.154743i	−0.997002	+	0.0773715i	$0.975347\pi$
$948$	3.16135i	0.102676i
$949$	27.1282	0.880618
$950$	0	0
$951$	11.2088	0.363471
$952$	1.19049i	0.0385840i
$953$	4.37779i	0.141811i	0.997483	+	0.0709053i	$0.0225888\pi$
$953$	4.37779i	0.141811i	−0.997483	+	0.0709053i	$0.977411\pi$
$954$	−18.6965	−0.605321
$955$	0	0
$956$	2.98083	0.0964069
$957$	− 3.11982i	− 0.100849i
$958$	22.7372i	0.734607i
$959$	37.2480	1.20280
$960$	0	0
$961$	−22.2380	−0.717356
$962$	0.0898462i	0.00289676i
$963$	40.6949i	1.31137i
$964$	−20.0383	−0.645392
$965$	0	0
$966$	−22.3678	−0.719673
$967$	13.1582i	0.423138i	0.977363	+	0.211569i	$0.0678573\pi$
$967$	13.1582i	0.423138i	−0.977363	+	0.211569i	$0.932143\pi$
$968$	− 10.0783i	− 0.323928i
$969$	0.129785	0.00416929
$970$	0	0
$971$	25.9201	0.831816	0.415908	−	0.909407i	$-0.363464\pi$
$971$	25.9201	0.831816	0.415908	+	0.909407i	$0.363464\pi$
$972$	− 12.3902i	− 0.397415i
$973$	− 76.4960i	− 2.45235i
$974$	−22.1981	−0.711273
$975$	0	0
$976$	7.53914	0.241322
$977$	− 31.2764i	− 1.00062i	−0.865846	−	0.500310i	$-0.833219\pi$
$977$	− 31.2764i	− 1.00062i	0.865846	−	0.500310i	$-0.166781\pi$
$978$	11.1582i	0.356799i
$979$	−3.91693	−0.125186
$980$	0	0
$981$	−13.0192	−0.415670
$982$	24.9984i	0.797731i
$983$	26.2364i	0.836813i	0.908260	+	0.418406i	$0.137411\pi$
$983$	26.2364i	0.836813i	−0.908260	+	0.418406i	$0.862589\pi$
$984$	0	0
$985$	0	0
$986$	−1.55991	−0.0496776
$987$	− 23.5583i	− 0.749869i
$988$	2.24960i	0.0715693i
$989$	−44.7356	−1.42251
$990$	0	0
$991$	39.2764	1.24766	0.623828	−	0.781562i	$-0.285577\pi$
$991$	39.2764	1.24766	0.623828	+	0.781562i	$0.285577\pi$
$992$	− 2.96006i	− 0.0939820i
$993$	17.4125i	0.552570i
$994$	45.8786	1.45518
$995$	0	0
$996$	3.87859	0.122898
$997$	− 14.4609i	− 0.457980i	−0.973429	−	0.228990i	$-0.926458\pi$
$997$	− 14.4609i	− 0.457980i	0.973429	−	0.228990i	$-0.0735423\pi$
$998$	11.6574i	0.369007i
$999$	−0.118987	−0.00376458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.h.799.2		6
5.2	odd	4		950.2.a.l.1.2	yes	3
5.3	odd	4		950.2.a.j.1.2	✓	3
5.4	even	2	inner	950.2.b.h.799.5		6
15.2	even	4		8550.2.a.ci.1.3		3
15.8	even	4		8550.2.a.cp.1.1		3
20.3	even	4		7600.2.a.bz.1.2		3
20.7	even	4		7600.2.a.bk.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.j.1.2	✓	3	5.3	odd	4
950.2.a.l.1.2	yes	3	5.2	odd	4
950.2.b.h.799.2		6	1.1	even	1	trivial
950.2.b.h.799.5		6	5.4	even	2	inner
7600.2.a.bk.1.2		3	20.7	even	4
7600.2.a.bz.1.2		3	20.3	even	4
8550.2.a.ci.1.3		3	15.2	even	4
8550.2.a.cp.1.1		3	15.8	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.519969i q^{3} -1.00000 q^{4} +0.519969 q^{6} -4.76957i q^{7} +1.00000i q^{8} +2.72963 q^{9} +0.960061 q^{11} -0.519969i q^{12} +2.24960i q^{13} -4.76957 q^{14} +1.00000 q^{16} +0.249601i q^{17} -2.72963i q^{18} -1.00000 q^{19} +2.48003 q^{21} -0.960061i q^{22} -9.01917i q^{23} -0.519969 q^{24} +2.24960 q^{26} +2.97923i q^{27} +4.76957i q^{28} -6.24960 q^{29} +2.96006 q^{31} -1.00000i q^{32} +0.499202i q^{33} +0.249601 q^{34} -2.72963 q^{36} +0.0399387i q^{37} +1.00000i q^{38} -1.16972 q^{39} -2.48003i q^{42} -4.96006i q^{43} -0.960061 q^{44} -9.01917 q^{46} -9.49920i q^{47} +0.519969i q^{48} -15.7488 q^{49} -0.129785 q^{51} -2.24960i q^{52} -6.84945i q^{53} +2.97923 q^{54} +4.76957 q^{56} -0.519969i q^{57} +6.24960i q^{58} +14.5583 q^{59} +7.53914 q^{61} -2.96006i q^{62} -13.0192i q^{63} -1.00000 q^{64} +0.499202 q^{66} -5.72963i q^{67} -0.249601i q^{68} +4.68969 q^{69} -9.61902 q^{71} +2.72963i q^{72} -12.0591i q^{73} +0.0399387 q^{74} +1.00000 q^{76} -4.57908i q^{77} +1.16972i q^{78} -6.07988 q^{79} +6.63979 q^{81} +7.45926i q^{83} -2.48003 q^{84} -4.96006 q^{86} -3.24960i q^{87} +0.960061i q^{88} -4.07988 q^{89} +10.7296 q^{91} +9.01917i q^{92} +1.53914i q^{93} -9.49920 q^{94} +0.519969 q^{96} +18.4193i q^{97} +15.7488i q^{98} +2.62061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 10 q^{9}+O(q^{10}) \) 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

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