LMFDB - Embedded newform 7935.2.a.bi.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,0,8,8,8,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.635899$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.635899 q^{2} +1.00000 q^{3} -1.59563 q^{4} +1.00000 q^{5} +0.635899 q^{6} +4.78252 q^{7} -2.28646 q^{8} +1.00000 q^{9} +0.635899 q^{10} +0.276255 q^{11} -1.59563 q^{12} +4.93303 q^{13} +3.04120 q^{14} +1.00000 q^{15} +1.73731 q^{16} +2.88784 q^{17} +0.635899 q^{18} -4.56893 q^{19} -1.59563 q^{20} +4.78252 q^{21} +0.175670 q^{22} -2.28646 q^{24} +1.00000 q^{25} +3.13691 q^{26} +1.00000 q^{27} -7.63115 q^{28} +3.42186 q^{29} +0.635899 q^{30} +3.30888 q^{31} +5.67767 q^{32} +0.276255 q^{33} +1.83637 q^{34} +4.78252 q^{35} -1.59563 q^{36} +4.64027 q^{37} -2.90538 q^{38} +4.93303 q^{39} -2.28646 q^{40} +1.66260 q^{41} +3.04120 q^{42} -0.886572 q^{43} -0.440801 q^{44} +1.00000 q^{45} -13.5078 q^{47} +1.73731 q^{48} +15.8725 q^{49} +0.635899 q^{50} +2.88784 q^{51} -7.87130 q^{52} +10.8054 q^{53} +0.635899 q^{54} +0.276255 q^{55} -10.9350 q^{56} -4.56893 q^{57} +2.17596 q^{58} +6.78102 q^{59} -1.59563 q^{60} -11.7346 q^{61} +2.10411 q^{62} +4.78252 q^{63} +0.135808 q^{64} +4.93303 q^{65} +0.175670 q^{66} +3.25200 q^{67} -4.60793 q^{68} +3.04120 q^{70} -10.0627 q^{71} -2.28646 q^{72} -6.87641 q^{73} +2.95075 q^{74} +1.00000 q^{75} +7.29033 q^{76} +1.32119 q^{77} +3.13691 q^{78} -13.4336 q^{79} +1.73731 q^{80} +1.00000 q^{81} +1.05725 q^{82} -13.0860 q^{83} -7.63115 q^{84} +2.88784 q^{85} -0.563770 q^{86} +3.42186 q^{87} -0.631645 q^{88} +9.69588 q^{89} +0.635899 q^{90} +23.5923 q^{91} +3.30888 q^{93} -8.58958 q^{94} -4.56893 q^{95} +5.67767 q^{96} -0.0430940 q^{97} +10.0933 q^{98} +0.276255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

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 $

$2$	0.635899	0.449648	0.224824	−	0.974399i	$-0.427819\pi$
$2$	0.635899	0.449648	0.224824	+	0.974399i	$0.427819\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.59563	−0.797816
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.635899	0.259605
$7$	4.78252	1.80762	0.903812	−	0.427931i	$-0.140757\pi$
$7$	4.78252	1.80762	0.903812	+	0.427931i	$0.140757\pi$
$8$	−2.28646	−0.808385
$9$	1.00000	0.333333
$10$	0.635899	0.201089
$11$	0.276255	0.0832939	0.0416469	−	0.999132i	$-0.486740\pi$
$11$	0.276255	0.0832939	0.0416469	+	0.999132i	$0.486740\pi$
$12$	−1.59563	−0.460619
$13$	4.93303	1.36818	0.684088	−	0.729399i	$-0.260200\pi$
$13$	4.93303	1.36818	0.684088	+	0.729399i	$0.260200\pi$
$14$	3.04120	0.812795
$15$	1.00000	0.258199
$16$	1.73731	0.434327
$17$	2.88784	0.700404	0.350202	−	0.936674i	$-0.386113\pi$
$17$	2.88784	0.700404	0.350202	+	0.936674i	$0.386113\pi$
$18$	0.635899	0.149883
$19$	−4.56893	−1.04818	−0.524092	−	0.851662i	$-0.675595\pi$
$19$	−4.56893	−1.04818	−0.524092	+	0.851662i	$0.675595\pi$
$20$	−1.59563	−0.356794
$21$	4.78252	1.04363
$22$	0.175670	0.0374530
$23$	0	0
$23$	0	0
$24$	−2.28646	−0.466721
$25$	1.00000	0.200000
$26$	3.13691	0.615198
$27$	1.00000	0.192450
$28$	−7.63115	−1.44215
$29$	3.42186	0.635424	0.317712	−	0.948187i	$-0.397085\pi$
$29$	3.42186	0.635424	0.317712	+	0.948187i	$0.397085\pi$
$30$	0.635899	0.116099
$31$	3.30888	0.594292	0.297146	−	0.954832i	$-0.403965\pi$
$31$	3.30888	0.594292	0.297146	+	0.954832i	$0.403965\pi$
$32$	5.67767	1.00368
$33$	0.276255	0.0480897
$34$	1.83637	0.314936
$35$	4.78252	0.808394
$36$	−1.59563	−0.265939
$37$	4.64027	0.762857	0.381428	−	0.924398i	$-0.375432\pi$
$37$	4.64027	0.762857	0.381428	+	0.924398i	$0.375432\pi$
$38$	−2.90538	−0.471314
$39$	4.93303	0.789917
$40$	−2.28646	−0.361521
$41$	1.66260	0.259655	0.129827	−	0.991537i	$-0.458558\pi$
$41$	1.66260	0.259655	0.129827	+	0.991537i	$0.458558\pi$
$42$	3.04120	0.469267
$43$	−0.886572	−0.135201	−0.0676005	−	0.997712i	$-0.521534\pi$
$43$	−0.886572	−0.135201	−0.0676005	+	0.997712i	$0.521534\pi$
$44$	−0.440801	−0.0664532
$45$	1.00000	0.149071
$46$	0	0
$47$	−13.5078	−1.97031	−0.985155	−	0.171665i	$-0.945085\pi$
$47$	−13.5078	−1.97031	−0.985155	+	0.171665i	$0.945085\pi$
$48$	1.73731	0.250759
$49$	15.8725	2.26750
$50$	0.635899	0.0899297
$51$	2.88784	0.404379
$52$	−7.87130	−1.09155
$53$	10.8054	1.48424	0.742121	−	0.670266i	$-0.233820\pi$
$53$	10.8054	1.48424	0.742121	+	0.670266i	$0.233820\pi$
$54$	0.635899	0.0865349
$55$	0.276255	0.0372502
$56$	−10.9350	−1.46126
$57$	−4.56893	−0.605169
$58$	2.17596	0.285717
$59$	6.78102	0.882813	0.441407	−	0.897307i	$-0.354480\pi$
$59$	6.78102	0.882813	0.441407	+	0.897307i	$0.354480\pi$
$60$	−1.59563	−0.205995
$61$	−11.7346	−1.50246	−0.751232	−	0.660039i	$-0.770540\pi$
$61$	−11.7346	−1.50246	−0.751232	+	0.660039i	$0.770540\pi$
$62$	2.10411	0.267223
$63$	4.78252	0.602541
$64$	0.135808	0.0169760
$65$	4.93303	0.611867
$66$	0.175670	0.0216235
$67$	3.25200	0.397295	0.198647	−	0.980071i	$-0.436345\pi$
$67$	3.25200	0.397295	0.198647	+	0.980071i	$0.436345\pi$
$68$	−4.60793	−0.558794
$69$	0	0
$70$	3.04120	0.363493
$71$	−10.0627	−1.19423	−0.597114	−	0.802157i	$-0.703686\pi$
$71$	−10.0627	−1.19423	−0.597114	+	0.802157i	$0.703686\pi$
$72$	−2.28646	−0.269462
$73$	−6.87641	−0.804822	−0.402411	−	0.915459i	$-0.631828\pi$
$73$	−6.87641	−0.804822	−0.402411	+	0.915459i	$0.631828\pi$
$74$	2.95075	0.343017
$75$	1.00000	0.115470
$76$	7.29033	0.836258
$77$	1.32119	0.150564
$78$	3.13691	0.355185
$79$	−13.4336	−1.51140	−0.755701	−	0.654917i	$-0.772704\pi$
$79$	−13.4336	−1.51140	−0.755701	+	0.654917i	$0.772704\pi$
$80$	1.73731	0.194237
$81$	1.00000	0.111111
$82$	1.05725	0.116753
$83$	−13.0860	−1.43637	−0.718186	−	0.695851i	$-0.755028\pi$
$83$	−13.0860	−1.43637	−0.718186	+	0.695851i	$0.755028\pi$
$84$	−7.63115	−0.832626
$85$	2.88784	0.313230
$86$	−0.563770	−0.0607929
$87$	3.42186	0.366862
$88$	−0.631645	−0.0673336
$89$	9.69588	1.02776	0.513881	−	0.857862i	$-0.328207\pi$
$89$	9.69588	1.02776	0.513881	+	0.857862i	$0.328207\pi$
$90$	0.635899	0.0670296
$91$	23.5923	2.47315
$92$	0	0
$93$	3.30888	0.343115
$94$	−8.58958	−0.885947
$95$	−4.56893	−0.468762
$96$	5.67767	0.579475
$97$	−0.0430940	−0.00437553	−0.00218777	−	0.999998i	$-0.500696\pi$
$97$	−0.0430940	−0.00437553	−0.00218777	+	0.999998i	$0.500696\pi$
$98$	10.0933	1.01958
$99$	0.276255	0.0277646
$100$	−1.59563	−0.159563
$101$	8.98133	0.893676	0.446838	−	0.894615i	$-0.352550\pi$
$101$	8.98133	0.893676	0.446838	+	0.894615i	$0.352550\pi$
$102$	1.83637	0.181828
$103$	−9.20908	−0.907398	−0.453699	−	0.891155i	$-0.649896\pi$
$103$	−9.20908	−0.907398	−0.453699	+	0.891155i	$0.649896\pi$
$104$	−11.2792	−1.10601
$105$	4.78252	0.466726
$106$	6.87117	0.667387
$107$	13.5129	1.30634	0.653169	−	0.757212i	$-0.273439\pi$
$107$	13.5129	1.30634	0.653169	+	0.757212i	$0.273439\pi$
$108$	−1.59563	−0.153540
$109$	−0.408532	−0.0391303	−0.0195651	−	0.999809i	$-0.506228\pi$
$109$	−0.408532	−0.0391303	−0.0195651	+	0.999809i	$0.506228\pi$
$110$	0.175670	0.0167495
$111$	4.64027	0.440435
$112$	8.30871	0.785100
$113$	16.3292	1.53612	0.768060	−	0.640378i	$-0.221222\pi$
$113$	16.3292	1.53612	0.768060	+	0.640378i	$0.221222\pi$
$114$	−2.90538	−0.272113
$115$	0	0
$116$	−5.46004	−0.506952
$117$	4.93303	0.456059
$118$	4.31204	0.396956
$119$	13.8112	1.26607
$120$	−2.28646	−0.208724
$121$	−10.9237	−0.993062
$122$	−7.46203	−0.675580
$123$	1.66260	0.149912
$124$	−5.27975	−0.474136
$125$	1.00000	0.0894427
$126$	3.04120	0.270932
$127$	20.5073	1.81973	0.909866	−	0.414902i	$-0.136184\pi$
$127$	20.5073	1.81973	0.909866	+	0.414902i	$0.136184\pi$
$128$	−11.2690	−0.996047
$129$	−0.886572	−0.0780583
$130$	3.13691	0.275125
$131$	3.68291	0.321777	0.160889	−	0.986973i	$-0.448564\pi$
$131$	3.68291	0.321777	0.160889	+	0.986973i	$0.448564\pi$
$132$	−0.440801	−0.0383668
$133$	−21.8510	−1.89472
$134$	2.06794	0.178643
$135$	1.00000	0.0860663
$136$	−6.60293	−0.566196
$137$	15.6536	1.33738	0.668690	−	0.743541i	$-0.266855\pi$
$137$	15.6536	1.33738	0.668690	+	0.743541i	$0.266855\pi$
$138$	0	0
$139$	3.88597	0.329604	0.164802	−	0.986327i	$-0.447302\pi$
$139$	3.88597	0.329604	0.164802	+	0.986327i	$0.447302\pi$
$140$	−7.63115	−0.644950
$141$	−13.5078	−1.13756
$142$	−6.39889	−0.536983
$143$	1.36277	0.113961
$144$	1.73731	0.144776
$145$	3.42186	0.284170
$146$	−4.37270	−0.361887
$147$	15.8725	1.30914
$148$	−7.40417	−0.608619
$149$	−2.36121	−0.193438	−0.0967190	−	0.995312i	$-0.530835\pi$
$149$	−2.36121	−0.193438	−0.0967190	+	0.995312i	$0.530835\pi$
$150$	0.635899	0.0519209
$151$	−23.8788	−1.94323	−0.971615	−	0.236567i	$-0.923978\pi$
$151$	−23.8788	−1.94323	−0.971615	+	0.236567i	$0.923978\pi$
$152$	10.4467	0.847337
$153$	2.88784	0.233468
$154$	0.840146	0.0677009
$155$	3.30888	0.265776
$156$	−7.87130	−0.630209
$157$	10.0588	0.802776	0.401388	−	0.915908i	$-0.368528\pi$
$157$	10.0588	0.802776	0.401388	+	0.915908i	$0.368528\pi$
$158$	−8.54243	−0.679600
$159$	10.8054	0.856928
$160$	5.67767	0.448859
$161$	0	0
$162$	0.635899	0.0499609
$163$	−12.2640	−0.960592	−0.480296	−	0.877107i	$-0.659471\pi$
$163$	−12.2640	−0.960592	−0.480296	+	0.877107i	$0.659471\pi$
$164$	−2.65290	−0.207157
$165$	0.276255	0.0215064
$166$	−8.32136	−0.645863
$167$	−19.3110	−1.49433	−0.747164	−	0.664640i	$-0.768585\pi$
$167$	−19.3110	−1.49433	−0.747164	+	0.664640i	$0.768585\pi$
$168$	−10.9350	−0.843657
$169$	11.3348	0.871907
$170$	1.83637	0.140844
$171$	−4.56893	−0.349395
$172$	1.41464	0.107866
$173$	4.41269	0.335491	0.167745	−	0.985830i	$-0.446351\pi$
$173$	4.41269	0.335491	0.167745	+	0.985830i	$0.446351\pi$
$174$	2.17596	0.164959
$175$	4.78252	0.361525
$176$	0.479939	0.0361768
$177$	6.78102	0.509693
$178$	6.16560	0.462131
$179$	−23.0942	−1.72614	−0.863069	−	0.505086i	$-0.831461\pi$
$179$	−23.0942	−1.72614	−0.863069	+	0.505086i	$0.831461\pi$
$180$	−1.59563	−0.118931
$181$	−0.243579	−0.0181051	−0.00905254	−	0.999959i	$-0.502882\pi$
$181$	−0.243579	−0.0181051	−0.00905254	+	0.999959i	$0.502882\pi$
$182$	15.0023	1.11205
$183$	−11.7346	−0.867448
$184$	0	0
$185$	4.64027	0.341160
$186$	2.10411	0.154281
$187$	0.797779	0.0583394
$188$	21.5534	1.57195
$189$	4.78252	0.347877
$190$	−2.90538	−0.210778
$191$	−6.05875	−0.438396	−0.219198	−	0.975680i	$-0.570344\pi$
$191$	−6.05875	−0.438396	−0.219198	+	0.975680i	$0.570344\pi$
$192$	0.135808	0.00980111
$193$	−22.7498	−1.63757	−0.818785	−	0.574101i	$-0.805352\pi$
$193$	−22.7498	−1.63757	−0.818785	+	0.574101i	$0.805352\pi$
$194$	−0.0274034	−0.00196745
$195$	4.93303	0.353262
$196$	−25.3267	−1.80905
$197$	18.4262	1.31281	0.656405	−	0.754409i	$-0.272076\pi$
$197$	18.4262	1.31281	0.656405	+	0.754409i	$0.272076\pi$
$198$	0.175670	0.0124843
$199$	−2.95464	−0.209449	−0.104724	−	0.994501i	$-0.533396\pi$
$199$	−2.95464	−0.209449	−0.104724	+	0.994501i	$0.533396\pi$
$200$	−2.28646	−0.161677
$201$	3.25200	0.229378
$202$	5.71122	0.401840
$203$	16.3651	1.14861
$204$	−4.60793	−0.322620
$205$	1.66260	0.116121
$206$	−5.85604	−0.408010
$207$	0	0
$208$	8.57019	0.594236
$209$	−1.26219	−0.0873073
$210$	3.04120	0.209863
$211$	0.206723	0.0142314	0.00711568	−	0.999975i	$-0.497735\pi$
$211$	0.206723	0.0142314	0.00711568	+	0.999975i	$0.497735\pi$
$212$	−17.2415	−1.18415
$213$	−10.0627	−0.689488
$214$	8.59282	0.587393
$215$	−0.886572	−0.0604637
$216$	−2.28646	−0.155574
$217$	15.8248	1.07426
$218$	−0.259785	−0.0175949
$219$	−6.87641	−0.464664
$220$	−0.440801	−0.0297188
$221$	14.2458	0.958276
$222$	2.95075	0.198041
$223$	−10.4059	−0.696830	−0.348415	−	0.937340i	$-0.613280\pi$
$223$	−10.4059	−0.696830	−0.348415	+	0.937340i	$0.613280\pi$
$224$	27.1536	1.81427
$225$	1.00000	0.0666667
$226$	10.3837	0.690714
$227$	27.3102	1.81264	0.906321	−	0.422589i	$-0.138879\pi$
$227$	27.3102	1.81264	0.906321	+	0.422589i	$0.138879\pi$
$228$	7.29033	0.482814
$229$	−5.12017	−0.338350	−0.169175	−	0.985586i	$-0.554110\pi$
$229$	−5.12017	−0.338350	−0.169175	+	0.985586i	$0.554110\pi$
$230$	0	0
$231$	1.32119	0.0869281
$232$	−7.82395	−0.513667
$233$	14.8351	0.971879	0.485939	−	0.873993i	$-0.338478\pi$
$233$	14.8351	0.971879	0.485939	+	0.873993i	$0.338478\pi$
$234$	3.13691	0.205066
$235$	−13.5078	−0.881150
$236$	−10.8200	−0.704323
$237$	−13.4336	−0.872608
$238$	8.78250	0.569285
$239$	−3.28108	−0.212236	−0.106118	−	0.994354i	$-0.533842\pi$
$239$	−3.28108	−0.212236	−0.106118	+	0.994354i	$0.533842\pi$
$240$	1.73731	0.112143
$241$	6.29954	0.405789	0.202895	−	0.979201i	$-0.434965\pi$
$241$	6.29954	0.405789	0.202895	+	0.979201i	$0.434965\pi$
$242$	−6.94636	−0.446529
$243$	1.00000	0.0641500
$244$	18.7241	1.19869
$245$	15.8725	1.01406
$246$	1.05725	0.0674076
$247$	−22.5387	−1.43410
$248$	−7.56561	−0.480417
$249$	−13.0860	−0.829290
$250$	0.635899	0.0402178
$251$	−16.3129	−1.02966	−0.514830	−	0.857292i	$-0.672145\pi$
$251$	−16.3129	−1.02966	−0.514830	+	0.857292i	$0.672145\pi$
$252$	−7.63115	−0.480717
$253$	0	0
$254$	13.0406	0.818240
$255$	2.88784	0.180844
$256$	−7.43755	−0.464847
$257$	15.0080	0.936173	0.468087	−	0.883683i	$-0.344944\pi$
$257$	15.0080	0.936173	0.468087	+	0.883683i	$0.344944\pi$
$258$	−0.563770	−0.0350988
$259$	22.1922	1.37896
$260$	−7.87130	−0.488157
$261$	3.42186	0.211808
$262$	2.34196	0.144687
$263$	−23.6251	−1.45679	−0.728394	−	0.685158i	$-0.759733\pi$
$263$	−23.6251	−1.45679	−0.728394	+	0.685158i	$0.759733\pi$
$264$	−0.631645	−0.0388750
$265$	10.8054	0.663773
$266$	−13.8950	−0.851959
$267$	9.69588	0.593378
$268$	−5.18899	−0.316968
$269$	0.484312	0.0295290	0.0147645	−	0.999891i	$-0.495300\pi$
$269$	0.484312	0.0295290	0.0147645	+	0.999891i	$0.495300\pi$
$270$	0.635899	0.0386996
$271$	0.957311	0.0581525	0.0290762	−	0.999577i	$-0.490743\pi$
$271$	0.957311	0.0581525	0.0290762	+	0.999577i	$0.490743\pi$
$272$	5.01707	0.304205
$273$	23.5923	1.42787
$274$	9.95413	0.601351
$275$	0.276255	0.0166588
$276$	0	0
$277$	−20.1251	−1.20920	−0.604601	−	0.796529i	$-0.706667\pi$
$277$	−20.1251	−1.20920	−0.604601	+	0.796529i	$0.706667\pi$
$278$	2.47108	0.148206
$279$	3.30888	0.198097
$280$	−10.9350	−0.653494
$281$	16.5116	0.985002	0.492501	−	0.870312i	$-0.336083\pi$
$281$	16.5116	0.985002	0.492501	+	0.870312i	$0.336083\pi$
$282$	−8.58958	−0.511502
$283$	4.25932	0.253191	0.126595	−	0.991954i	$-0.459595\pi$
$283$	4.25932	0.253191	0.126595	+	0.991954i	$0.459595\pi$
$284$	16.0564	0.952774
$285$	−4.56893	−0.270640
$286$	0.866585	0.0512423
$287$	7.95143	0.469358
$288$	5.67767	0.334560
$289$	−8.66038	−0.509434
$290$	2.17596	0.127777
$291$	−0.0430940	−0.00252621
$292$	10.9722	0.642100
$293$	23.7671	1.38849	0.694243	−	0.719741i	$-0.255739\pi$
$293$	23.7671	1.38849	0.694243	+	0.719741i	$0.255739\pi$
$294$	10.0933	0.588654
$295$	6.78102	0.394806
$296$	−10.6098	−0.616682
$297$	0.276255	0.0160299
$298$	−1.50149	−0.0869791
$299$	0	0
$300$	−1.59563	−0.0921239
$301$	−4.24005	−0.244392
$302$	−15.1845	−0.873771
$303$	8.98133	0.515964
$304$	−7.93764	−0.455255
$305$	−11.7346	−0.671922
$306$	1.83637	0.104979
$307$	13.4702	0.768785	0.384393	−	0.923170i	$-0.374411\pi$
$307$	13.4702	0.768785	0.384393	+	0.923170i	$0.374411\pi$
$308$	−2.10814	−0.120122
$309$	−9.20908	−0.523886
$310$	2.10411	0.119506
$311$	4.85030	0.275035	0.137518	−	0.990499i	$-0.456088\pi$
$311$	4.85030	0.275035	0.137518	+	0.990499i	$0.456088\pi$
$312$	−11.2792	−0.638557
$313$	13.2171	0.747074	0.373537	−	0.927615i	$-0.378145\pi$
$313$	13.2171	0.747074	0.373537	+	0.927615i	$0.378145\pi$
$314$	6.39635	0.360967
$315$	4.78252	0.269465
$316$	21.4351	1.20582
$317$	−4.43910	−0.249325	−0.124662	−	0.992199i	$-0.539785\pi$
$317$	−4.43910	−0.249325	−0.124662	+	0.992199i	$0.539785\pi$
$318$	6.87117	0.385316
$319$	0.945305	0.0529269
$320$	0.135808	0.00759191
$321$	13.5129	0.754215
$322$	0	0
$323$	−13.1943	−0.734153
$324$	−1.59563	−0.0886463
$325$	4.93303	0.273635
$326$	−7.79867	−0.431929
$327$	−0.408532	−0.0225919
$328$	−3.80147	−0.209901
$329$	−64.6012	−3.56158
$330$	0.175670	0.00967031
$331$	−35.2457	−1.93728	−0.968641	−	0.248466i	$-0.920073\pi$
$331$	−35.2457	−1.93728	−0.968641	+	0.248466i	$0.920073\pi$
$332$	20.8804	1.14596
$333$	4.64027	0.254286
$334$	−12.2798	−0.671922
$335$	3.25200	0.177676
$336$	8.30871	0.453278
$337$	26.1549	1.42475	0.712375	−	0.701799i	$-0.247619\pi$
$337$	26.1549	1.42475	0.712375	+	0.701799i	$0.247619\pi$
$338$	7.20778	0.392051
$339$	16.3292	0.886879
$340$	−4.60793	−0.249900
$341$	0.914093	0.0495009
$342$	−2.90538	−0.157105
$343$	42.4330	2.29117
$344$	2.02711	0.109294
$345$	0	0
$346$	2.80603	0.150853
$347$	1.91484	0.102794	0.0513971	−	0.998678i	$-0.483633\pi$
$347$	1.91484	0.102794	0.0513971	+	0.998678i	$0.483633\pi$
$348$	−5.46004	−0.292689
$349$	−7.71255	−0.412843	−0.206422	−	0.978463i	$-0.566182\pi$
$349$	−7.71255	−0.412843	−0.206422	+	0.978463i	$0.566182\pi$
$350$	3.04120	0.162559
$351$	4.93303	0.263306
$352$	1.56848	0.0836004
$353$	19.6911	1.04805	0.524025	−	0.851703i	$-0.324430\pi$
$353$	19.6911	1.04805	0.524025	+	0.851703i	$0.324430\pi$
$354$	4.31204	0.229182
$355$	−10.0627	−0.534075
$356$	−15.4711	−0.819965
$357$	13.8112	0.730964
$358$	−14.6856	−0.776156
$359$	11.6997	0.617488	0.308744	−	0.951145i	$-0.400091\pi$
$359$	11.6997	0.617488	0.308744	+	0.951145i	$0.400091\pi$
$360$	−2.28646	−0.120507
$361$	1.87511	0.0986901
$362$	−0.154892	−0.00814092
$363$	−10.9237	−0.573345
$364$	−37.6447	−1.97312
$365$	−6.87641	−0.359928
$366$	−7.46203	−0.390047
$367$	7.62881	0.398221	0.199110	−	0.979977i	$-0.436195\pi$
$367$	7.62881	0.398221	0.199110	+	0.979977i	$0.436195\pi$
$368$	0	0
$369$	1.66260	0.0865516
$370$	2.95075	0.153402
$371$	51.6773	2.68295
$372$	−5.27975	−0.273742
$373$	32.3600	1.67554	0.837769	−	0.546026i	$-0.183860\pi$
$373$	32.3600	1.67554	0.837769	+	0.546026i	$0.183860\pi$
$374$	0.507307	0.0262322
$375$	1.00000	0.0516398
$376$	30.8850	1.59277
$377$	16.8802	0.869372
$378$	3.04120	0.156422
$379$	25.0429	1.28637	0.643185	−	0.765711i	$-0.277613\pi$
$379$	25.0429	1.28637	0.643185	+	0.765711i	$0.277613\pi$
$380$	7.29033	0.373986
$381$	20.5073	1.05062
$382$	−3.85275	−0.197124
$383$	16.0017	0.817649	0.408824	−	0.912613i	$-0.365939\pi$
$383$	16.0017	0.817649	0.408824	+	0.912613i	$0.365939\pi$
$384$	−11.2690	−0.575068
$385$	1.32119	0.0673343
$386$	−14.4666	−0.736330
$387$	−0.886572	−0.0450670
$388$	0.0687622	0.00349087
$389$	5.29456	0.268445	0.134223	−	0.990951i	$-0.457146\pi$
$389$	5.29456	0.268445	0.134223	+	0.990951i	$0.457146\pi$
$390$	3.13691	0.158844
$391$	0	0
$392$	−36.2918	−1.83302
$393$	3.68291	0.185778
$394$	11.7172	0.590303
$395$	−13.4336	−0.675920
$396$	−0.440801	−0.0221511
$397$	−12.7457	−0.639687	−0.319843	−	0.947470i	$-0.603630\pi$
$397$	−12.7457	−0.639687	−0.319843	+	0.947470i	$0.603630\pi$
$398$	−1.87885	−0.0941783
$399$	−21.8510	−1.09392
$400$	1.73731	0.0868654
$401$	−2.33281	−0.116495	−0.0582474	−	0.998302i	$-0.518551\pi$
$401$	−2.33281	−0.116495	−0.0582474	+	0.998302i	$0.518551\pi$
$402$	2.06794	0.103140
$403$	16.3228	0.813096
$404$	−14.3309	−0.712989
$405$	1.00000	0.0496904
$406$	10.4066	0.516469
$407$	1.28190	0.0635413
$408$	−6.60293	−0.326894
$409$	3.07590	0.152093	0.0760466	−	0.997104i	$-0.475770\pi$
$409$	3.07590	0.152093	0.0760466	+	0.997104i	$0.475770\pi$
$410$	1.05725	0.0522137
$411$	15.6536	0.772137
$412$	14.6943	0.723937
$413$	32.4304	1.59579
$414$	0	0
$415$	−13.0860	−0.642366
$416$	28.0081	1.37321
$417$	3.88597	0.190297
$418$	−0.802624	−0.0392576
$419$	−27.6788	−1.35220	−0.676098	−	0.736811i	$-0.736331\pi$
$419$	−27.6788	−1.35220	−0.676098	+	0.736811i	$0.736331\pi$
$420$	−7.63115	−0.372362
$421$	23.1877	1.13010	0.565051	−	0.825056i	$-0.308857\pi$
$421$	23.1877	1.13010	0.565051	+	0.825056i	$0.308857\pi$
$422$	0.131455	0.00639911
$423$	−13.5078	−0.656770
$424$	−24.7062	−1.19984
$425$	2.88784	0.140081
$426$	−6.39889	−0.310027
$427$	−56.1210	−2.71589
$428$	−21.5616	−1.04222
$429$	1.36277	0.0657953
$430$	−0.563770	−0.0271874
$431$	−20.5619	−0.990430	−0.495215	−	0.868771i	$-0.664911\pi$
$431$	−20.5619	−0.990430	−0.495215	+	0.868771i	$0.664911\pi$
$432$	1.73731	0.0835863
$433$	−2.82470	−0.135747	−0.0678733	−	0.997694i	$-0.521621\pi$
$433$	−2.82470	−0.135747	−0.0678733	+	0.997694i	$0.521621\pi$
$434$	10.0630	0.483038
$435$	3.42186	0.164066
$436$	0.651867	0.0312188
$437$	0	0
$438$	−4.37270	−0.208936
$439$	12.2548	0.584891	0.292445	−	0.956282i	$-0.405531\pi$
$439$	12.2548	0.584891	0.292445	+	0.956282i	$0.405531\pi$
$440$	−0.631645	−0.0301125
$441$	15.8725	0.755834
$442$	9.05889	0.430888
$443$	5.69816	0.270728	0.135364	−	0.990796i	$-0.456780\pi$
$443$	5.69816	0.270728	0.135364	+	0.990796i	$0.456780\pi$
$444$	−7.40417	−0.351387
$445$	9.69588	0.459629
$446$	−6.61710	−0.313329
$447$	−2.36121	−0.111682
$448$	0.649505	0.0306862
$449$	−28.0191	−1.32230	−0.661151	−	0.750253i	$-0.729932\pi$
$449$	−28.0191	−1.32230	−0.661151	+	0.750253i	$0.729932\pi$
$450$	0.635899	0.0299766
$451$	0.459302	0.0216277
$452$	−26.0554	−1.22554
$453$	−23.8788	−1.12192
$454$	17.3665	0.815052
$455$	23.5923	1.10603
$456$	10.4467	0.489210
$457$	−32.3063	−1.51123	−0.755613	−	0.655018i	$-0.772661\pi$
$457$	−32.3063	−1.51123	−0.755613	+	0.655018i	$0.772661\pi$
$458$	−3.25591	−0.152139
$459$	2.88784	0.134793
$460$	0	0
$461$	10.3298	0.481108	0.240554	−	0.970636i	$-0.422671\pi$
$461$	10.3298	0.481108	0.240554	+	0.970636i	$0.422671\pi$
$462$	0.840146	0.0390871
$463$	8.72911	0.405676	0.202838	−	0.979212i	$-0.434984\pi$
$463$	8.72911	0.405676	0.202838	+	0.979212i	$0.434984\pi$
$464$	5.94483	0.275982
$465$	3.30888	0.153446
$466$	9.43361	0.437004
$467$	40.8983	1.89255	0.946274	−	0.323367i	$-0.104815\pi$
$467$	40.8983	1.89255	0.946274	+	0.323367i	$0.104815\pi$
$468$	−7.87130	−0.363851
$469$	15.5527	0.718159
$470$	−8.58958	−0.396208
$471$	10.0588	0.463483
$472$	−15.5045	−0.713653
$473$	−0.244920	−0.0112614
$474$	−8.54243	−0.392367
$475$	−4.56893	−0.209637
$476$	−22.0375	−1.01009
$477$	10.8054	0.494747
$478$	−2.08644	−0.0954314
$479$	−6.34911	−0.290098	−0.145049	−	0.989424i	$-0.546334\pi$
$479$	−6.34911	−0.290098	−0.145049	+	0.989424i	$0.546334\pi$
$480$	5.67767	0.259149
$481$	22.8906	1.04372
$482$	4.00587	0.182462
$483$	0	0
$484$	17.4302	0.792281
$485$	−0.0430940	−0.00195680
$486$	0.635899	0.0288450
$487$	31.0880	1.40873	0.704365	−	0.709837i	$-0.251232\pi$
$487$	31.0880	1.40873	0.704365	+	0.709837i	$0.251232\pi$
$488$	26.8307	1.21457
$489$	−12.2640	−0.554598
$490$	10.0933	0.455969
$491$	−39.1888	−1.76857	−0.884283	−	0.466951i	$-0.845353\pi$
$491$	−39.1888	−1.76857	−0.884283	+	0.466951i	$0.845353\pi$
$492$	−2.65290	−0.119602
$493$	9.88179	0.445054
$494$	−14.3323	−0.644841
$495$	0.276255	0.0124167
$496$	5.74854	0.258117
$497$	−48.1253	−2.15871
$498$	−8.32136	−0.372889
$499$	36.0301	1.61293	0.806464	−	0.591284i	$-0.201379\pi$
$499$	36.0301	1.61293	0.806464	+	0.591284i	$0.201379\pi$
$500$	−1.59563	−0.0713589
$501$	−19.3110	−0.862750
$502$	−10.3733	−0.462985
$503$	−11.2088	−0.499774	−0.249887	−	0.968275i	$-0.580393\pi$
$503$	−11.2088	−0.499774	−0.249887	+	0.968275i	$0.580393\pi$
$504$	−10.9350	−0.487085
$505$	8.98133	0.399664
$506$	0	0
$507$	11.3348	0.503395
$508$	−32.7222	−1.45181
$509$	14.4226	0.639269	0.319635	−	0.947541i	$-0.396440\pi$
$509$	14.4226	0.639269	0.319635	+	0.947541i	$0.396440\pi$
$510$	1.83637	0.0813160
$511$	−32.8866	−1.45482
$512$	17.8084	0.787029
$513$	−4.56893	−0.201723
$514$	9.54357	0.420949
$515$	−9.20908	−0.405801
$516$	1.41464	0.0622762
$517$	−3.73158	−0.164115
$518$	14.1120	0.620046
$519$	4.41269	0.193696
$520$	−11.2792	−0.494624
$521$	−21.7210	−0.951613	−0.475806	−	0.879550i	$-0.657844\pi$
$521$	−21.7210	−0.951613	−0.475806	+	0.879550i	$0.657844\pi$
$522$	2.17596	0.0952391
$523$	−39.5934	−1.73130	−0.865650	−	0.500650i	$-0.833094\pi$
$523$	−39.5934	−1.73130	−0.865650	+	0.500650i	$0.833094\pi$
$524$	−5.87657	−0.256719
$525$	4.78252	0.208726
$526$	−15.0232	−0.655043
$527$	9.55551	0.416245
$528$	0.479939	0.0208867
$529$	0	0
$530$	6.87117	0.298465
$531$	6.78102	0.294271
$532$	34.8662	1.51164
$533$	8.20167	0.355254
$534$	6.16560	0.266812
$535$	13.5129	0.584213
$536$	−7.43555	−0.321167
$537$	−23.0942	−0.996587
$538$	0.307973	0.0132777
$539$	4.38485	0.188869
$540$	−1.59563	−0.0686651
$541$	27.4309	1.17935	0.589673	−	0.807642i	$-0.299257\pi$
$541$	27.4309	1.17935	0.589673	+	0.807642i	$0.299257\pi$
$542$	0.608753	0.0261482
$543$	−0.243579	−0.0104530
$544$	16.3962	0.702982
$545$	−0.408532	−0.0174996
$546$	15.0023	0.642041
$547$	40.7538	1.74251	0.871253	−	0.490834i	$-0.163308\pi$
$547$	40.7538	1.74251	0.871253	+	0.490834i	$0.163308\pi$
$548$	−24.9774	−1.06698
$549$	−11.7346	−0.500821
$550$	0.175670	0.00749059
$551$	−15.6342	−0.666041
$552$	0	0
$553$	−64.2466	−2.73205
$554$	−12.7975	−0.543716
$555$	4.64027	0.196969
$556$	−6.20058	−0.262963
$557$	−34.1084	−1.44522	−0.722610	−	0.691256i	$-0.757058\pi$
$557$	−34.1084	−1.44522	−0.722610	+	0.691256i	$0.757058\pi$
$558$	2.10411	0.0890742
$559$	−4.37349	−0.184979
$560$	8.30871	0.351107
$561$	0.797779	0.0336823
$562$	10.4997	0.442904
$563$	23.0379	0.970932	0.485466	−	0.874255i	$-0.338650\pi$
$563$	23.0379	0.970932	0.485466	+	0.874255i	$0.338650\pi$
$564$	21.5534	0.907563
$565$	16.3292	0.686973
$566$	2.70850	0.113847
$567$	4.78252	0.200847
$568$	23.0080	0.965396
$569$	10.3930	0.435699	0.217849	−	0.975982i	$-0.430096\pi$
$569$	10.3930	0.435699	0.217849	+	0.975982i	$0.430096\pi$
$570$	−2.90538	−0.121693
$571$	−22.4405	−0.939104	−0.469552	−	0.882905i	$-0.655585\pi$
$571$	−22.4405	−0.939104	−0.469552	+	0.882905i	$0.655585\pi$
$572$	−2.17448	−0.0909197
$573$	−6.05875	−0.253108
$574$	5.05631	0.211046
$575$	0	0
$576$	0.135808	0.00565867
$577$	−16.0318	−0.667411	−0.333706	−	0.942677i	$-0.608299\pi$
$577$	−16.0318	−0.667411	−0.333706	+	0.942677i	$0.608299\pi$
$578$	−5.50712	−0.229066
$579$	−22.7498	−0.945451
$580$	−5.46004	−0.226716
$581$	−62.5840	−2.59642
$582$	−0.0274034	−0.00113591
$583$	2.98505	0.123628
$584$	15.7226	0.650607
$585$	4.93303	0.203956
$586$	15.1134	0.624331
$587$	39.5757	1.63346	0.816731	−	0.577018i	$-0.195784\pi$
$587$	39.5757	1.63346	0.816731	+	0.577018i	$0.195784\pi$
$588$	−25.3267	−1.04446
$589$	−15.1180	−0.622928
$590$	4.31204	0.177524
$591$	18.4262	0.757951
$592$	8.06159	0.331329
$593$	3.04461	0.125027	0.0625137	−	0.998044i	$-0.480088\pi$
$593$	3.04461	0.125027	0.0625137	+	0.998044i	$0.480088\pi$
$594$	0.175670	0.00720783
$595$	13.8112	0.566202
$596$	3.76763	0.154328
$597$	−2.95464	−0.120925
$598$	0	0
$599$	−1.83121	−0.0748213	−0.0374107	−	0.999300i	$-0.511911\pi$
$599$	−1.83121	−0.0748213	−0.0374107	+	0.999300i	$0.511911\pi$
$600$	−2.28646	−0.0933443
$601$	9.28980	0.378939	0.189469	−	0.981887i	$-0.439323\pi$
$601$	9.28980	0.378939	0.189469	+	0.981887i	$0.439323\pi$
$602$	−2.69624	−0.109891
$603$	3.25200	0.132432
$604$	38.1018	1.55034
$605$	−10.9237	−0.444111
$606$	5.71122	0.232002
$607$	40.1078	1.62793	0.813963	−	0.580917i	$-0.197306\pi$
$607$	40.1078	1.62793	0.813963	+	0.580917i	$0.197306\pi$
$608$	−25.9409	−1.05204
$609$	16.3651	0.663149
$610$	−7.46203	−0.302129
$611$	−66.6342	−2.69573
$612$	−4.60793	−0.186265
$613$	−28.0144	−1.13149	−0.565745	−	0.824580i	$-0.691411\pi$
$613$	−28.0144	−1.13149	−0.565745	+	0.824580i	$0.691411\pi$
$614$	8.56569	0.345683
$615$	1.66260	0.0670426
$616$	−3.02085	−0.121714
$617$	20.4486	0.823231	0.411615	−	0.911358i	$-0.364965\pi$
$617$	20.4486	0.823231	0.411615	+	0.911358i	$0.364965\pi$
$618$	−5.85604	−0.235565
$619$	3.74645	0.150582	0.0752912	−	0.997162i	$-0.476011\pi$
$619$	3.74645	0.150582	0.0752912	+	0.997162i	$0.476011\pi$
$620$	−5.27975	−0.212040
$621$	0	0
$622$	3.08430	0.123669
$623$	46.3708	1.85781
$624$	8.57019	0.343082
$625$	1.00000	0.0400000
$626$	8.40474	0.335921
$627$	−1.26219	−0.0504069
$628$	−16.0501	−0.640468
$629$	13.4004	0.534308
$630$	3.04120	0.121164
$631$	12.2854	0.489074	0.244537	−	0.969640i	$-0.421364\pi$
$631$	12.2854	0.489074	0.244537	+	0.969640i	$0.421364\pi$
$632$	30.7155	1.22180
$633$	0.206723	0.00821649
$634$	−2.82282	−0.112108
$635$	20.5073	0.813809
$636$	−17.2415	−0.683671
$637$	78.2996	3.10234
$638$	0.601119	0.0237985
$639$	−10.0627	−0.398076
$640$	−11.2690	−0.445446
$641$	−45.8424	−1.81066	−0.905332	−	0.424704i	$-0.860378\pi$
$641$	−45.8424	−1.81066	−0.905332	+	0.424704i	$0.860378\pi$
$642$	8.59282	0.339132
$643$	−42.4023	−1.67219	−0.836093	−	0.548588i	$-0.815165\pi$
$643$	−42.4023	−1.67219	−0.836093	+	0.548588i	$0.815165\pi$
$644$	0	0
$645$	−0.886572	−0.0349087
$646$	−8.39027	−0.330111
$647$	−24.0474	−0.945400	−0.472700	−	0.881224i	$-0.656721\pi$
$647$	−24.0474	−0.945400	−0.472700	+	0.881224i	$0.656721\pi$
$648$	−2.28646	−0.0898206
$649$	1.87329	0.0735330
$650$	3.13691	0.123040
$651$	15.8248	0.620222
$652$	19.5689	0.766376
$653$	4.66651	0.182615	0.0913074	−	0.995823i	$-0.470895\pi$
$653$	4.66651	0.182615	0.0913074	+	0.995823i	$0.470895\pi$
$654$	−0.259785	−0.0101584
$655$	3.68291	0.143903
$656$	2.88845	0.112775
$657$	−6.87641	−0.268274
$658$	−41.0798	−1.60146
$659$	27.5539	1.07335	0.536674	−	0.843789i	$-0.319680\pi$
$659$	27.5539	1.07335	0.536674	+	0.843789i	$0.319680\pi$
$660$	−0.440801	−0.0171581
$661$	3.61245	0.140508	0.0702539	−	0.997529i	$-0.477619\pi$
$661$	3.61245	0.140508	0.0702539	+	0.997529i	$0.477619\pi$
$662$	−22.4127	−0.871095
$663$	14.2458	0.553261
$664$	29.9206	1.16114
$665$	−21.8510	−0.847345
$666$	2.95075	0.114339
$667$	0	0
$668$	30.8132	1.19220
$669$	−10.4059	−0.402315
$670$	2.06794	0.0798915
$671$	−3.24174	−0.125146
$672$	27.1536	1.04747
$673$	−1.85557	−0.0715269	−0.0357634	−	0.999360i	$-0.511386\pi$
$673$	−1.85557	−0.0715269	−0.0357634	+	0.999360i	$0.511386\pi$
$674$	16.6319	0.640637
$675$	1.00000	0.0384900
$676$	−18.0862	−0.695621
$677$	−34.6412	−1.33137	−0.665684	−	0.746233i	$-0.731860\pi$
$677$	−34.6412	−1.33137	−0.665684	+	0.746233i	$0.731860\pi$
$678$	10.3837	0.398784
$679$	−0.206098	−0.00790931
$680$	−6.60293	−0.253211
$681$	27.3102	1.04653
$682$	0.581271	0.0222580
$683$	−40.7572	−1.55953	−0.779765	−	0.626072i	$-0.784661\pi$
$683$	−40.7572	−1.55953	−0.779765	+	0.626072i	$0.784661\pi$
$684$	7.29033	0.278753
$685$	15.6536	0.598094
$686$	26.9831	1.03022
$687$	−5.12017	−0.195347
$688$	−1.54025	−0.0587214
$689$	53.3036	2.03071
$690$	0	0
$691$	−34.9175	−1.32832	−0.664162	−	0.747589i	$-0.731211\pi$
$691$	−34.9175	−1.32832	−0.664162	+	0.747589i	$0.731211\pi$
$692$	−7.04104	−0.267660
$693$	1.32119	0.0501880
$694$	1.21765	0.0462212
$695$	3.88597	0.147403
$696$	−7.82395	−0.296566
$697$	4.80133	0.181863
$698$	−4.90440	−0.185634
$699$	14.8351	0.561114
$700$	−7.63115	−0.288430
$701$	41.4901	1.56706	0.783529	−	0.621355i	$-0.213418\pi$
$701$	41.4901	1.56706	0.783529	+	0.621355i	$0.213418\pi$
$702$	3.13691	0.118395
$703$	−21.2011	−0.799614
$704$	0.0375176	0.00141400
$705$	−13.5078	−0.508732
$706$	12.5215	0.471254
$707$	42.9534	1.61543
$708$	−10.8200	−0.406641
$709$	−25.7260	−0.966159	−0.483079	−	0.875577i	$-0.660482\pi$
$709$	−25.7260	−0.966159	−0.483079	+	0.875577i	$0.660482\pi$
$710$	−6.39889	−0.240146
$711$	−13.4336	−0.503801
$712$	−22.1692	−0.830827
$713$	0	0
$714$	8.78250	0.328677
$715$	1.36277	0.0509648
$716$	36.8498	1.37714
$717$	−3.28108	−0.122534
$718$	7.43985	0.277653
$719$	−33.4004	−1.24563	−0.622813	−	0.782371i	$-0.714010\pi$
$719$	−33.4004	−1.24563	−0.622813	+	0.782371i	$0.714010\pi$
$720$	1.73731	0.0647457
$721$	−44.0426	−1.64023
$722$	1.19238	0.0443758
$723$	6.29954	0.234282
$724$	0.388662	0.0144445
$725$	3.42186	0.127085
$726$	−6.94636	−0.257804
$727$	7.11992	0.264063	0.132032	−	0.991246i	$-0.457850\pi$
$727$	7.11992	0.264063	0.132032	+	0.991246i	$0.457850\pi$
$728$	−53.9429	−1.99926
$729$	1.00000	0.0370370
$730$	−4.37270	−0.161841
$731$	−2.56028	−0.0946953
$732$	18.7241	0.692064
$733$	−13.2309	−0.488695	−0.244347	−	0.969688i	$-0.578574\pi$
$733$	−13.2309	−0.488695	−0.244347	+	0.969688i	$0.578574\pi$
$734$	4.85115	0.179059
$735$	15.8725	0.585466
$736$	0	0
$737$	0.898379	0.0330922
$738$	1.05725	0.0389178
$739$	8.50028	0.312688	0.156344	−	0.987703i	$-0.450029\pi$
$739$	8.50028	0.312688	0.156344	+	0.987703i	$0.450029\pi$
$740$	−7.40417	−0.272183
$741$	−22.5387	−0.827978
$742$	32.8615	1.20638
$743$	11.5939	0.425340	0.212670	−	0.977124i	$-0.431784\pi$
$743$	11.5939	0.425340	0.212670	+	0.977124i	$0.431784\pi$
$744$	−7.56561	−0.277369
$745$	−2.36121	−0.0865081
$746$	20.5777	0.753403
$747$	−13.0860	−0.478791
$748$	−1.27296	−0.0465441
$749$	64.6256	2.36137
$750$	0.635899	0.0232197
$751$	6.18707	0.225769	0.112885	−	0.993608i	$-0.463991\pi$
$751$	6.18707	0.225769	0.112885	+	0.993608i	$0.463991\pi$
$752$	−23.4672	−0.855759
$753$	−16.3129	−0.594474
$754$	10.7341	0.390912
$755$	−23.8788	−0.869039
$756$	−7.63115	−0.277542
$757$	−9.34373	−0.339604	−0.169802	−	0.985478i	$-0.554313\pi$
$757$	−9.34373	−0.339604	−0.169802	+	0.985478i	$0.554313\pi$
$758$	15.9248	0.578414
$759$	0	0
$760$	10.4467	0.378940
$761$	−28.3362	−1.02719	−0.513593	−	0.858034i	$-0.671686\pi$
$761$	−28.3362	−1.02719	−0.513593	+	0.858034i	$0.671686\pi$
$762$	13.0406	0.472411
$763$	−1.95381	−0.0707328
$764$	9.66754	0.349759
$765$	2.88784	0.104410
$766$	10.1755	0.367654
$767$	33.4510	1.20784
$768$	−7.43755	−0.268379
$769$	8.17561	0.294820	0.147410	−	0.989075i	$-0.452906\pi$
$769$	8.17561	0.294820	0.147410	+	0.989075i	$0.452906\pi$
$770$	0.840146	0.0302767
$771$	15.0080	0.540500
$772$	36.3004	1.30648
$773$	41.0583	1.47677	0.738383	−	0.674382i	$-0.235590\pi$
$773$	41.0583	1.47677	0.738383	+	0.674382i	$0.235590\pi$
$774$	−0.563770	−0.0202643
$775$	3.30888	0.118858
$776$	0.0985326	0.00353712
$777$	22.1922	0.796141
$778$	3.36681	0.120706
$779$	−7.59631	−0.272166
$780$	−7.87130	−0.281838
$781$	−2.77988	−0.0994719
$782$	0	0
$783$	3.42186	0.122287
$784$	27.5754	0.984837
$785$	10.0588	0.359012
$786$	2.34196	0.0835348
$787$	−2.26628	−0.0807842	−0.0403921	−	0.999184i	$-0.512861\pi$
$787$	−2.26628	−0.0807842	−0.0403921	+	0.999184i	$0.512861\pi$
$788$	−29.4014	−1.04738
$789$	−23.6251	−0.841077
$790$	−8.54243	−0.303926
$791$	78.0946	2.77672
$792$	−0.631645	−0.0224445
$793$	−57.8872	−2.05563
$794$	−8.10496	−0.287634
$795$	10.8054	0.383230
$796$	4.71452	0.167102
$797$	−1.52558	−0.0540389	−0.0270194	−	0.999635i	$-0.508602\pi$
$797$	−1.52558	−0.0540389	−0.0270194	+	0.999635i	$0.508602\pi$
$798$	−13.8950	−0.491879
$799$	−39.0083	−1.38001
$800$	5.67767	0.200736
$801$	9.69588	0.342587
$802$	−1.48343	−0.0523817
$803$	−1.89964	−0.0670368
$804$	−5.18899	−0.183002
$805$	0	0
$806$	10.3796	0.365608
$807$	0.484312	0.0170486
$808$	−20.5354	−0.722434
$809$	−45.6859	−1.60623	−0.803115	−	0.595823i	$-0.796826\pi$
$809$	−45.6859	−1.60623	−0.803115	+	0.595823i	$0.796826\pi$
$810$	0.635899	0.0223432
$811$	7.29703	0.256233	0.128117	−	0.991759i	$-0.459107\pi$
$811$	7.29703	0.256233	0.128117	+	0.991759i	$0.459107\pi$
$812$	−26.1127	−0.916377
$813$	0.957311	0.0335744
$814$	0.815157	0.0285712
$815$	−12.2640	−0.429590
$816$	5.01707	0.175633
$817$	4.05068	0.141716
$818$	1.95596	0.0683885
$819$	23.5923	0.824382
$820$	−2.65290	−0.0926434
$821$	−46.7060	−1.63005	−0.815025	−	0.579426i	$-0.803277\pi$
$821$	−46.7060	−1.63005	−0.815025	+	0.579426i	$0.803277\pi$
$822$	9.95413	0.347190
$823$	35.2111	1.22738	0.613691	−	0.789546i	$-0.289684\pi$
$823$	35.2111	1.22738	0.613691	+	0.789546i	$0.289684\pi$
$824$	21.0562	0.733527
$825$	0.276255	0.00961795
$826$	20.6224	0.717546
$827$	−14.0766	−0.489491	−0.244746	−	0.969587i	$-0.578704\pi$
$827$	−14.0766	−0.489491	−0.244746	+	0.969587i	$0.578704\pi$
$828$	0	0
$829$	−33.1502	−1.15135	−0.575677	−	0.817677i	$-0.695262\pi$
$829$	−33.1502	−1.15135	−0.575677	+	0.817677i	$0.695262\pi$
$830$	−8.32136	−0.288839
$831$	−20.1251	−0.698133
$832$	0.669946	0.0232262
$833$	45.8373	1.58817
$834$	2.47108	0.0855667
$835$	−19.3110	−0.668283
$836$	2.01399	0.0696552
$837$	3.30888	0.114372
$838$	−17.6009	−0.608013
$839$	3.44347	0.118882	0.0594408	−	0.998232i	$-0.481068\pi$
$839$	3.44347	0.118882	0.0594408	+	0.998232i	$0.481068\pi$
$840$	−10.9350	−0.377295
$841$	−17.2909	−0.596236
$842$	14.7451	0.508148
$843$	16.5116	0.568691
$844$	−0.329853	−0.0113540
$845$	11.3348	0.389928
$846$	−8.58958	−0.295316
$847$	−52.2428	−1.79508
$848$	18.7724	0.644647
$849$	4.25932	0.146180
$850$	1.83637	0.0629871
$851$	0	0
$852$	16.0564	0.550084
$853$	3.90205	0.133603	0.0668017	−	0.997766i	$-0.478720\pi$
$853$	3.90205	0.133603	0.0668017	+	0.997766i	$0.478720\pi$
$854$	−35.6873	−1.22119
$855$	−4.56893	−0.156254
$856$	−30.8966	−1.05603
$857$	15.8206	0.540423	0.270212	−	0.962801i	$-0.412906\pi$
$857$	15.8206	0.540423	0.270212	+	0.962801i	$0.412906\pi$
$858$	0.866585	0.0295847
$859$	−34.2881	−1.16990	−0.584948	−	0.811071i	$-0.698885\pi$
$859$	−34.2881	−1.16990	−0.584948	+	0.811071i	$0.698885\pi$
$860$	1.41464	0.0482389
$861$	7.95143	0.270984
$862$	−13.0753	−0.445345
$863$	8.05614	0.274234	0.137117	−	0.990555i	$-0.456216\pi$
$863$	8.05614	0.274234	0.137117	+	0.990555i	$0.456216\pi$
$864$	5.67767	0.193158
$865$	4.41269	0.150036
$866$	−1.79623	−0.0610382
$867$	−8.66038	−0.294122
$868$	−25.2505	−0.857059
$869$	−3.71110	−0.125891
$870$	2.17596	0.0737719
$871$	16.0422	0.543569
$872$	0.934092	0.0316323
$873$	−0.0430940	−0.00145851
$874$	0	0
$875$	4.78252	0.161679
$876$	10.9722	0.370717
$877$	13.2393	0.447060	0.223530	−	0.974697i	$-0.428242\pi$
$877$	13.2393	0.447060	0.223530	+	0.974697i	$0.428242\pi$
$878$	7.79283	0.262995
$879$	23.7671	0.801643
$880$	0.479939	0.0161788
$881$	−23.1953	−0.781469	−0.390734	−	0.920503i	$-0.627779\pi$
$881$	−23.1953	−0.781469	−0.390734	+	0.920503i	$0.627779\pi$
$882$	10.0933	0.339860
$883$	−23.7129	−0.798003	−0.399002	−	0.916950i	$-0.630643\pi$
$883$	−23.7129	−0.798003	−0.399002	+	0.916950i	$0.630643\pi$
$884$	−22.7311	−0.764529
$885$	6.78102	0.227941
$886$	3.62345	0.121732
$887$	29.5497	0.992182	0.496091	−	0.868271i	$-0.334768\pi$
$887$	29.5497	0.992182	0.496091	+	0.868271i	$0.334768\pi$
$888$	−10.6098	−0.356042
$889$	98.0768	3.28939
$890$	6.16560	0.206671
$891$	0.276255	0.00925488
$892$	16.6040	0.555943
$893$	61.7160	2.06525
$894$	−1.50149	−0.0502174
$895$	−23.0942	−0.771953
$896$	−53.8941	−1.80048
$897$	0	0
$898$	−17.8173	−0.594571
$899$	11.3225	0.377627
$900$	−1.59563	−0.0531878
$901$	31.2044	1.03957
$902$	0.292069	0.00972485
$903$	−4.24005	−0.141100
$904$	−37.3360	−1.24178
$905$	−0.243579	−0.00809684
$906$	−15.1845	−0.504472
$907$	2.44003	0.0810197	0.0405099	−	0.999179i	$-0.487102\pi$
$907$	2.44003	0.0810197	0.0405099	+	0.999179i	$0.487102\pi$
$908$	−43.5771	−1.44616
$909$	8.98133	0.297892
$910$	15.0023	0.497322
$911$	−8.56162	−0.283659	−0.141830	−	0.989891i	$-0.545298\pi$
$911$	−8.56162	−0.283659	−0.141830	+	0.989891i	$0.545298\pi$
$912$	−7.93764	−0.262841
$913$	−3.61506	−0.119641
$914$	−20.5436	−0.679520
$915$	−11.7346	−0.387934
$916$	8.16991	0.269941
$917$	17.6136	0.581652
$918$	1.83637	0.0606094
$919$	−47.2959	−1.56015	−0.780073	−	0.625688i	$-0.784818\pi$
$919$	−47.2959	−1.56015	−0.780073	+	0.625688i	$0.784818\pi$
$920$	0	0
$921$	13.4702	0.443858
$922$	6.56872	0.216329
$923$	−49.6398	−1.63391
$924$	−2.10814	−0.0693527
$925$	4.64027	0.152571
$926$	5.55083	0.182412
$927$	−9.20908	−0.302466
$928$	19.4282	0.637762
$929$	−42.6047	−1.39781	−0.698907	−	0.715213i	$-0.746330\pi$
$929$	−42.6047	−1.39781	−0.698907	+	0.715213i	$0.746330\pi$
$930$	2.10411	0.0689966
$931$	−72.5204	−2.37676
$932$	−23.6713	−0.775381
$933$	4.85030	0.158792
$934$	26.0072	0.850981
$935$	0.797779	0.0260902
$936$	−11.2792	−0.368671
$937$	8.97008	0.293040	0.146520	−	0.989208i	$-0.453193\pi$
$937$	8.97008	0.293040	0.146520	+	0.989208i	$0.453193\pi$
$938$	9.88997	0.322919
$939$	13.2171	0.431324
$940$	21.5534	0.702996
$941$	−6.68773	−0.218014	−0.109007	−	0.994041i	$-0.534767\pi$
$941$	−6.68773	−0.218014	−0.109007	+	0.994041i	$0.534767\pi$
$942$	6.39635	0.208404
$943$	0	0
$944$	11.7807	0.383430
$945$	4.78252	0.155575
$946$	−0.155744	−0.00506368
$947$	6.67892	0.217036	0.108518	−	0.994094i	$-0.465390\pi$
$947$	6.67892	0.217036	0.108518	+	0.994094i	$0.465390\pi$
$948$	21.4351	0.696181
$949$	−33.9215	−1.10114
$950$	−2.90538	−0.0942629
$951$	−4.43910	−0.143948
$952$	−31.5786	−1.02347
$953$	54.3566	1.76078	0.880391	−	0.474248i	$-0.157280\pi$
$953$	54.3566	1.76078	0.880391	+	0.474248i	$0.157280\pi$
$954$	6.87117	0.222462
$955$	−6.05875	−0.196057
$956$	5.23540	0.169325
$957$	0.945305	0.0305574
$958$	−4.03739	−0.130442
$959$	74.8638	2.41748
$960$	0.135808	0.00438319
$961$	−20.0513	−0.646817
$962$	14.5561	0.469308
$963$	13.5129	0.435446
$964$	−10.0518	−0.323745
$965$	−22.7498	−0.732343
$966$	0	0
$967$	17.7075	0.569436	0.284718	−	0.958611i	$-0.408100\pi$
$967$	17.7075	0.569436	0.284718	+	0.958611i	$0.408100\pi$
$968$	24.9766	0.802777
$969$	−13.1943	−0.423863
$970$	−0.0274034	−0.000879871 0
$971$	−22.6800	−0.727835	−0.363917	−	0.931431i	$-0.618561\pi$
$971$	−22.6800	−0.727835	−0.363917	+	0.931431i	$0.618561\pi$
$972$	−1.59563	−0.0511799
$973$	18.5847	0.595799
$974$	19.7688	0.633434
$975$	4.93303	0.157983
$976$	−20.3866	−0.652561
$977$	17.8693	0.571689	0.285844	−	0.958276i	$-0.407726\pi$
$977$	17.8693	0.571689	0.285844	+	0.958276i	$0.407726\pi$
$978$	−7.79867	−0.249374
$979$	2.67853	0.0856063
$980$	−25.3267	−0.809032
$981$	−0.408532	−0.0130434
$982$	−24.9201	−0.795233
$983$	−17.0482	−0.543754	−0.271877	−	0.962332i	$-0.587644\pi$
$983$	−17.0482	−0.543754	−0.271877	+	0.962332i	$0.587644\pi$
$984$	−3.80147	−0.121187
$985$	18.4262	0.587106
$986$	6.28382	0.200118
$987$	−64.6012	−2.05628
$988$	35.9634	1.14415
$989$	0	0
$990$	0.175670	0.00558316
$991$	−20.9252	−0.664711	−0.332355	−	0.943154i	$-0.607843\pi$
$991$	−20.9252	−0.664711	−0.332355	+	0.943154i	$0.607843\pi$
$992$	18.7867	0.596479
$993$	−35.2457	−1.11849
$994$	−30.6028	−0.970662
$995$	−2.95464	−0.0936684
$996$	20.8804	0.661621
$997$	1.58791	0.0502895	0.0251448	−	0.999684i	$-0.491995\pi$
$997$	1.58791	0.0502895	0.0251448	+	0.999684i	$0.491995\pi$
$998$	22.9115	0.725250
$999$	4.64027	0.146812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.5	yes	8
23.22	odd	2		7935.2.a.bh.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.5	✓	8	23.22	odd	2
7935.2.a.bi.1.5	yes	8	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.635899 q^{2} +1.00000 q^{3} -1.59563 q^{4} +1.00000 q^{5} +0.635899 q^{6} +4.78252 q^{7} -2.28646 q^{8} +1.00000 q^{9} +0.635899 q^{10} +0.276255 q^{11} -1.59563 q^{12} +4.93303 q^{13} +3.04120 q^{14} +1.00000 q^{15} +1.73731 q^{16} +2.88784 q^{17} +0.635899 q^{18} -4.56893 q^{19} -1.59563 q^{20} +4.78252 q^{21} +0.175670 q^{22} -2.28646 q^{24} +1.00000 q^{25} +3.13691 q^{26} +1.00000 q^{27} -7.63115 q^{28} +3.42186 q^{29} +0.635899 q^{30} +3.30888 q^{31} +5.67767 q^{32} +0.276255 q^{33} +1.83637 q^{34} +4.78252 q^{35} -1.59563 q^{36} +4.64027 q^{37} -2.90538 q^{38} +4.93303 q^{39} -2.28646 q^{40} +1.66260 q^{41} +3.04120 q^{42} -0.886572 q^{43} -0.440801 q^{44} +1.00000 q^{45} -13.5078 q^{47} +1.73731 q^{48} +15.8725 q^{49} +0.635899 q^{50} +2.88784 q^{51} -7.87130 q^{52} +10.8054 q^{53} +0.635899 q^{54} +0.276255 q^{55} -10.9350 q^{56} -4.56893 q^{57} +2.17596 q^{58} +6.78102 q^{59} -1.59563 q^{60} -11.7346 q^{61} +2.10411 q^{62} +4.78252 q^{63} +0.135808 q^{64} +4.93303 q^{65} +0.175670 q^{66} +3.25200 q^{67} -4.60793 q^{68} +3.04120 q^{70} -10.0627 q^{71} -2.28646 q^{72} -6.87641 q^{73} +2.95075 q^{74} +1.00000 q^{75} +7.29033 q^{76} +1.32119 q^{77} +3.13691 q^{78} -13.4336 q^{79} +1.73731 q^{80} +1.00000 q^{81} +1.05725 q^{82} -13.0860 q^{83} -7.63115 q^{84} +2.88784 q^{85} -0.563770 q^{86} +3.42186 q^{87} -0.631645 q^{88} +9.69588 q^{89} +0.635899 q^{90} +23.5923 q^{91} +3.30888 q^{93} -8.58958 q^{94} -4.56893 q^{95} +5.67767 q^{96} -0.0430940 q^{97} +10.0933 q^{98} +0.276255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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