LMFDB - Embedded newform 3467.2.a.c.1.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3467,2,Mod(1,3467)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3467.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3467, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3467.a (trivial)

Newform invariants

comment:select newform

sage:traces = [162] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$27.6841343808$
Analytic rank:	$0$
Dimension:	$162$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	3467.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.41030 q^{2} +2.99235 q^{3} +3.80954 q^{4} -2.37452 q^{5} -7.21245 q^{6} +3.58446 q^{7} -4.36154 q^{8} +5.95415 q^{9} +5.72329 q^{10} -5.47371 q^{11} +11.3995 q^{12} +2.68607 q^{13} -8.63962 q^{14} -7.10538 q^{15} +2.89353 q^{16} +4.30605 q^{17} -14.3513 q^{18} +3.21371 q^{19} -9.04582 q^{20} +10.7260 q^{21} +13.1933 q^{22} -2.38479 q^{23} -13.0512 q^{24} +0.638327 q^{25} -6.47424 q^{26} +8.83984 q^{27} +13.6552 q^{28} +1.63049 q^{29} +17.1261 q^{30} +0.794782 q^{31} +1.74881 q^{32} -16.3793 q^{33} -10.3789 q^{34} -8.51136 q^{35} +22.6826 q^{36} -5.49840 q^{37} -7.74600 q^{38} +8.03767 q^{39} +10.3565 q^{40} +2.65665 q^{41} -25.8528 q^{42} +7.32376 q^{43} -20.8523 q^{44} -14.1382 q^{45} +5.74805 q^{46} +6.93681 q^{47} +8.65844 q^{48} +5.84836 q^{49} -1.53856 q^{50} +12.8852 q^{51} +10.2327 q^{52} +0.702901 q^{53} -21.3067 q^{54} +12.9974 q^{55} -15.6338 q^{56} +9.61654 q^{57} -3.92998 q^{58} +9.07114 q^{59} -27.0682 q^{60} +6.59025 q^{61} -1.91566 q^{62} +21.3424 q^{63} -10.0022 q^{64} -6.37813 q^{65} +39.4789 q^{66} -12.9929 q^{67} +16.4041 q^{68} -7.13611 q^{69} +20.5149 q^{70} -6.48396 q^{71} -25.9692 q^{72} +6.51527 q^{73} +13.2528 q^{74} +1.91010 q^{75} +12.2428 q^{76} -19.6203 q^{77} -19.3732 q^{78} +1.24316 q^{79} -6.87072 q^{80} +8.58944 q^{81} -6.40331 q^{82} +0.923598 q^{83} +40.8610 q^{84} -10.2248 q^{85} -17.6524 q^{86} +4.87900 q^{87} +23.8738 q^{88} -13.4653 q^{89} +34.0773 q^{90} +9.62813 q^{91} -9.08494 q^{92} +2.37827 q^{93} -16.7198 q^{94} -7.63101 q^{95} +5.23306 q^{96} +8.34606 q^{97} -14.0963 q^{98} -32.5913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 9 q^{2} + 24 q^{3} + 189 q^{4} + 32 q^{5} + 9 q^{6} + 23 q^{7} + 27 q^{8} + 196 q^{9} + 50 q^{10} + 12 q^{11} + 69 q^{12} + 144 q^{13} + 11 q^{14} + 17 q^{15} + 223 q^{16} + 33 q^{17} + 39 q^{18}+ \cdots - 25 q^{99}+O(q^{100}) $ 162 * q + 9 * q^2 + 24 * q^3 + 189 * q^4 + 32 * q^5 + 9 * q^6 + 23 * q^7 + 27 * q^8 + 196 * q^9 + 50 * q^10 + 12 * q^11 + 69 * q^12 + 144 * q^13 + 11 * q^14 + 17 * q^15 + 223 * q^16 + 33 * q^17 + 39 * q^18 + 35 * q^19 + 52 * q^20 + 44 * q^21 + 53 * q^22 + 31 * q^23 + 21 * q^24 + 266 * q^25 + 22 * q^26 + 93 * q^27 + 65 * q^28 + 25 * q^29 + 11 * q^30 + 81 * q^31 + 38 * q^32 + 96 * q^33 + 47 * q^34 + 14 * q^35 + 234 * q^36 + 153 * q^37 + 57 * q^38 + 18 * q^39 + 124 * q^40 + 19 * q^41 + 22 * q^42 + 87 * q^43 - 22 * q^44 + 135 * q^45 - 5 * q^46 + 53 * q^47 + 133 * q^48 + 291 * q^49 + 14 * q^50 - q^51 + 280 * q^52 + 122 * q^53 - 6 * q^54 + 88 * q^55 + 8 * q^56 + 37 * q^57 + 62 * q^58 + 26 * q^59 - 22 * q^60 + 128 * q^61 + 9 * q^62 + 11 * q^63 + 281 * q^64 + 23 * q^65 - 34 * q^66 + 124 * q^67 + 32 * q^68 + 138 * q^69 + 39 * q^70 + 16 * q^71 + 53 * q^72 + 161 * q^73 - 32 * q^74 + 71 * q^75 + 96 * q^76 + 126 * q^77 + 31 * q^78 + 34 * q^79 + 73 * q^80 + 242 * q^81 + 173 * q^82 + 27 * q^83 - 11 * q^84 + 130 * q^85 - 51 * q^86 + 87 * q^87 + 121 * q^88 + 33 * q^89 + 62 * q^90 + 66 * q^91 + 50 * q^92 + 173 * q^93 + 85 * q^94 - 11 * q^95 - 15 * q^96 + 205 * q^97 + 40 * q^98 - 25 * 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 $

$2$	−2.41030	−1.70434	−0.852169	−	0.523266i	$-0.824713\pi$
$2$	−2.41030	−1.70434	−0.852169	+	0.523266i	$0.824713\pi$
$3$	2.99235	1.72763	0.863817	−	0.503806i	$-0.168068\pi$
$3$	2.99235	1.72763	0.863817	+	0.503806i	$0.168068\pi$
$4$	3.80954	1.90477
$5$	−2.37452	−1.06192	−0.530958	−	0.847398i	$-0.678168\pi$
$5$	−2.37452	−1.06192	−0.530958	+	0.847398i	$0.678168\pi$
$6$	−7.21245	−2.94447
$7$	3.58446	1.35480	0.677399	−	0.735615i	$-0.263107\pi$
$7$	3.58446	1.35480	0.677399	+	0.735615i	$0.263107\pi$
$8$	−4.36154	−1.54204
$9$	5.95415	1.98472
$10$	5.72329	1.80986
$11$	−5.47371	−1.65039	−0.825193	−	0.564851i	$-0.808934\pi$
$11$	−5.47371	−1.65039	−0.825193	+	0.564851i	$0.808934\pi$
$12$	11.3995	3.29075
$13$	2.68607	0.744983	0.372492	−	0.928036i	$-0.378504\pi$
$13$	2.68607	0.744983	0.372492	+	0.928036i	$0.378504\pi$
$14$	−8.63962	−2.30904
$15$	−7.10538	−1.83460
$16$	2.89353	0.723381
$17$	4.30605	1.04437	0.522185	−	0.852832i	$-0.325117\pi$
$17$	4.30605	1.04437	0.522185	+	0.852832i	$0.325117\pi$
$18$	−14.3513	−3.38263
$19$	3.21371	0.737276	0.368638	−	0.929573i	$-0.379824\pi$
$19$	3.21371	0.737276	0.368638	+	0.929573i	$0.379824\pi$
$20$	−9.04582	−2.02271
$21$	10.7260	2.34060
$22$	13.1933	2.81282
$23$	−2.38479	−0.497262	−0.248631	−	0.968598i	$-0.579981\pi$
$23$	−2.38479	−0.497262	−0.248631	+	0.968598i	$0.579981\pi$
$24$	−13.0512	−2.66407
$25$	0.638327	0.127665
$26$	−6.47424	−1.26970
$27$	8.83984	1.70123
$28$	13.6552	2.58058
$29$	1.63049	0.302775	0.151387	−	0.988474i	$-0.451626\pi$
$29$	1.63049	0.302775	0.151387	+	0.988474i	$0.451626\pi$
$30$	17.1261	3.12678
$31$	0.794782	0.142747	0.0713735	−	0.997450i	$-0.477262\pi$
$31$	0.794782	0.142747	0.0713735	+	0.997450i	$0.477262\pi$
$32$	1.74881	0.309149
$33$	−16.3793	−2.85126
$34$	−10.3789	−1.77996
$35$	−8.51136	−1.43868
$36$	22.6826	3.78043
$37$	−5.49840	−0.903932	−0.451966	−	0.892035i	$-0.649277\pi$
$37$	−5.49840	−0.903932	−0.451966	+	0.892035i	$0.649277\pi$
$38$	−7.74600	−1.25657
$39$	8.03767	1.28706
$40$	10.3565	1.63751
$41$	2.65665	0.414899	0.207449	−	0.978246i	$-0.433484\pi$
$41$	2.65665	0.414899	0.207449	+	0.978246i	$0.433484\pi$
$42$	−25.8528	−3.98917
$43$	7.32376	1.11686	0.558431	−	0.829551i	$-0.311403\pi$
$43$	7.32376	1.11686	0.558431	+	0.829551i	$0.311403\pi$
$44$	−20.8523	−3.14361
$45$	−14.1382	−2.10760
$46$	5.74805	0.847503
$47$	6.93681	1.01184	0.505919	−	0.862581i	$-0.331154\pi$
$47$	6.93681	1.01184	0.505919	+	0.862581i	$0.331154\pi$
$48$	8.65844	1.24974
$49$	5.84836	0.835480
$50$	−1.53856	−0.217585
$51$	12.8852	1.80429
$52$	10.2327	1.41902
$53$	0.702901	0.0965509	0.0482755	−	0.998834i	$-0.484627\pi$
$53$	0.702901	0.0965509	0.0482755	+	0.998834i	$0.484627\pi$
$54$	−21.3067	−2.89947
$55$	12.9974	1.75257
$56$	−15.6338	−2.08915
$57$	9.61654	1.27374
$58$	−3.92998	−0.516031
$59$	9.07114	1.18096	0.590481	−	0.807052i	$-0.298938\pi$
$59$	9.07114	1.18096	0.590481	+	0.807052i	$0.298938\pi$
$60$	−27.0682	−3.49449
$61$	6.59025	0.843795	0.421897	−	0.906644i	$-0.361364\pi$
$61$	6.59025	0.843795	0.421897	+	0.906644i	$0.361364\pi$
$62$	−1.91566	−0.243289
$63$	21.3424	2.68889
$64$	−10.0022	−1.25028
$65$	−6.37813	−0.791109
$66$	39.4789	4.85952
$67$	−12.9929	−1.58733	−0.793665	−	0.608355i	$-0.791830\pi$
$67$	−12.9929	−1.58733	−0.793665	+	0.608355i	$0.791830\pi$
$68$	16.4041	1.98929
$69$	−7.13611	−0.859087
$70$	20.5149	2.45200
$71$	−6.48396	−0.769505	−0.384753	−	0.923020i	$-0.625713\pi$
$71$	−6.48396	−0.769505	−0.384753	+	0.923020i	$0.625713\pi$
$72$	−25.9692	−3.06050
$73$	6.51527	0.762555	0.381277	−	0.924461i	$-0.375484\pi$
$73$	6.51527	0.762555	0.381277	+	0.924461i	$0.375484\pi$
$74$	13.2528	1.54061
$75$	1.91010	0.220559
$76$	12.2428	1.40434
$77$	−19.6203	−2.23594
$78$	−19.3732	−2.19358
$79$	1.24316	0.139866	0.0699330	−	0.997552i	$-0.477721\pi$
$79$	1.24316	0.139866	0.0699330	+	0.997552i	$0.477721\pi$
$80$	−6.87072	−0.768170
$81$	8.58944	0.954382
$82$	−6.40331	−0.707128
$83$	0.923598	0.101378	0.0506890	−	0.998714i	$-0.483858\pi$
$83$	0.923598	0.101378	0.0506890	+	0.998714i	$0.483858\pi$
$84$	40.8610	4.45830
$85$	−10.2248	−1.10903
$86$	−17.6524	−1.90351
$87$	4.87900	0.523084
$88$	23.8738	2.54496
$89$	−13.4653	−1.42732	−0.713658	−	0.700494i	$-0.752963\pi$
$89$	−13.4653	−1.42732	−0.713658	+	0.700494i	$0.752963\pi$
$90$	34.0773	3.59207
$91$	9.62813	1.00930
$92$	−9.08494	−0.947171
$93$	2.37827	0.246615
$94$	−16.7198	−1.72451
$95$	−7.63101	−0.782925
$96$	5.23306	0.534097
$97$	8.34606	0.847414	0.423707	−	0.905799i	$-0.360729\pi$
$97$	8.34606	0.847414	0.423707	+	0.905799i	$0.360729\pi$
$98$	−14.0963	−1.42394
$99$	−32.5913	−3.27555
$100$	2.43173	0.243173
$101$	11.4644	1.14075	0.570374	−	0.821385i	$-0.306798\pi$
$101$	11.4644	1.14075	0.570374	+	0.821385i	$0.306798\pi$
$102$	−31.0572	−3.07512
$103$	8.22340	0.810275	0.405138	−	0.914256i	$-0.367224\pi$
$103$	8.22340	0.810275	0.405138	+	0.914256i	$0.367224\pi$
$104$	−11.7154	−1.14879
$105$	−25.4690	−2.48552
$106$	−1.69420	−0.164556
$107$	−10.6095	−1.02566	−0.512829	−	0.858491i	$-0.671403\pi$
$107$	−10.6095	−1.02566	−0.512829	+	0.858491i	$0.671403\pi$
$108$	33.6757	3.24045
$109$	5.66573	0.542679	0.271339	−	0.962484i	$-0.412533\pi$
$109$	5.66573	0.542679	0.271339	+	0.962484i	$0.412533\pi$
$110$	−31.3277	−2.98698
$111$	−16.4531	−1.56166
$112$	10.3717	0.980036
$113$	12.9836	1.22139	0.610696	−	0.791865i	$-0.290890\pi$
$113$	12.9836	1.22139	0.610696	+	0.791865i	$0.290890\pi$
$114$	−23.1787	−2.17089
$115$	5.66271	0.528051
$116$	6.21143	0.576717
$117$	15.9933	1.47858
$118$	−21.8642	−2.01276
$119$	15.4349	1.41491
$120$	30.9904	2.82902
$121$	18.9615	1.72377
$122$	−15.8845	−1.43811
$123$	7.94961	0.716792
$124$	3.02776	0.271901
$125$	10.3569	0.926346
$126$	−51.4416	−4.58278
$127$	10.1043	0.896608	0.448304	−	0.893881i	$-0.352028\pi$
$127$	10.1043	0.896608	0.448304	+	0.893881i	$0.352028\pi$
$128$	20.6107	1.82175
$129$	21.9152	1.92953
$130$	15.3732	1.34832
$131$	3.60847	0.315274	0.157637	−	0.987497i	$-0.449612\pi$
$131$	3.60847	0.315274	0.157637	+	0.987497i	$0.449612\pi$
$132$	−62.3974	−5.43100
$133$	11.5194	0.998860
$134$	31.3167	2.70535
$135$	−20.9903	−1.80656
$136$	−18.7810	−1.61046
$137$	−2.89660	−0.247473	−0.123737	−	0.992315i	$-0.539488\pi$
$137$	−2.89660	−0.247473	−0.123737	+	0.992315i	$0.539488\pi$
$138$	17.2002	1.46417
$139$	10.3809	0.880500	0.440250	−	0.897875i	$-0.354890\pi$
$139$	10.3809	0.880500	0.440250	+	0.897875i	$0.354890\pi$
$140$	−32.4244	−2.74036
$141$	20.7573	1.74808
$142$	15.6283	1.31150
$143$	−14.7028	−1.22951
$144$	17.2285	1.43571
$145$	−3.87163	−0.321522
$146$	−15.7038	−1.29965
$147$	17.5003	1.44340
$148$	−20.9464	−1.72178
$149$	−5.21007	−0.426826	−0.213413	−	0.976962i	$-0.568458\pi$
$149$	−5.21007	−0.426826	−0.213413	+	0.976962i	$0.568458\pi$
$150$	−4.60391	−0.375907
$151$	−1.73870	−0.141493	−0.0707467	−	0.997494i	$-0.522538\pi$
$151$	−1.73870	−0.141493	−0.0707467	+	0.997494i	$0.522538\pi$
$152$	−14.0167	−1.13691
$153$	25.6389	2.07278
$154$	47.2908	3.81080
$155$	−1.88722	−0.151585
$156$	30.6198	2.45155
$157$	−12.6385	−1.00866	−0.504332	−	0.863510i	$-0.668261\pi$
$157$	−12.6385	−1.00866	−0.504332	+	0.863510i	$0.668261\pi$
$158$	−2.99638	−0.238379
$159$	2.10333	0.166805
$160$	−4.15258	−0.328291
$161$	−8.54817	−0.673690
$162$	−20.7031	−1.62659
$163$	7.18808	0.563014	0.281507	−	0.959559i	$-0.409166\pi$
$163$	7.18808	0.563014	0.281507	+	0.959559i	$0.409166\pi$
$164$	10.1206	0.790287
$165$	38.8928	3.02780
$166$	−2.22615	−0.172783
$167$	−21.6023	−1.67164	−0.835818	−	0.549006i	$-0.815006\pi$
$167$	−21.6023	−1.67164	−0.835818	+	0.549006i	$0.815006\pi$
$168$	−46.7817	−3.60928
$169$	−5.78500	−0.445000
$170$	24.6448	1.89017
$171$	19.1349	1.46328
$172$	27.9002	2.12737
$173$	21.8458	1.66091	0.830455	−	0.557086i	$-0.188081\pi$
$173$	21.8458	1.66091	0.830455	+	0.557086i	$0.188081\pi$
$174$	−11.7599	−0.891512
$175$	2.28806	0.172961
$176$	−15.8383	−1.19386
$177$	27.1440	2.04027
$178$	32.4553	2.43263
$179$	−2.84643	−0.212752	−0.106376	−	0.994326i	$-0.533925\pi$
$179$	−2.84643	−0.212752	−0.106376	+	0.994326i	$0.533925\pi$
$180$	−53.8602	−4.01450
$181$	16.0974	1.19651	0.598257	−	0.801305i	$-0.295860\pi$
$181$	16.0974	1.19651	0.598257	+	0.801305i	$0.295860\pi$
$182$	−23.2067	−1.72019
$183$	19.7203	1.45777
$184$	10.4013	0.766796
$185$	13.0560	0.959899
$186$	−5.73233	−0.420315
$187$	−23.5701	−1.72361
$188$	26.4261	1.92732
$189$	31.6861	2.30482
$190$	18.3930	1.33437
$191$	17.7808	1.28657	0.643285	−	0.765627i	$-0.277571\pi$
$191$	17.7808	1.28657	0.643285	+	0.765627i	$0.277571\pi$
$192$	−29.9301	−2.16002
$193$	−20.7767	−1.49554	−0.747769	−	0.663959i	$-0.768875\pi$
$193$	−20.7767	−1.49554	−0.747769	+	0.663959i	$0.768875\pi$
$194$	−20.1165	−1.44428
$195$	−19.0856	−1.36675
$196$	22.2796	1.59140
$197$	−2.25573	−0.160714	−0.0803569	−	0.996766i	$-0.525606\pi$
$197$	−2.25573	−0.160714	−0.0803569	+	0.996766i	$0.525606\pi$
$198$	78.5548	5.58264
$199$	−9.36237	−0.663681	−0.331840	−	0.943336i	$-0.607670\pi$
$199$	−9.36237	−0.663681	−0.331840	+	0.943336i	$0.607670\pi$
$200$	−2.78409	−0.196865
$201$	−38.8792	−2.74233
$202$	−27.6326	−1.94422
$203$	5.84444	0.410199
$204$	49.0867	3.43676
$205$	−6.30825	−0.440587
$206$	−19.8208	−1.38098
$207$	−14.1994	−0.986924
$208$	7.77223	0.538907
$209$	−17.5909	−1.21679
$210$	61.3878	4.23616
$211$	24.2441	1.66903	0.834516	−	0.550984i	$-0.185747\pi$
$211$	24.2441	1.66903	0.834516	+	0.550984i	$0.185747\pi$
$212$	2.67773	0.183907
$213$	−19.4023	−1.32942
$214$	25.5721	1.74807
$215$	−17.3904	−1.18601
$216$	−38.5553	−2.62336
$217$	2.84887	0.193394
$218$	−13.6561	−0.924909
$219$	19.4960	1.31741
$220$	49.5142	3.33825
$221$	11.5664	0.778038
$222$	39.6570	2.66160
$223$	−27.9252	−1.87001	−0.935006	−	0.354631i	$-0.884606\pi$
$223$	−27.9252	−1.87001	−0.935006	+	0.354631i	$0.884606\pi$
$224$	6.26855	0.418835
$225$	3.80070	0.253380
$226$	−31.2943	−2.08166
$227$	−3.96899	−0.263431	−0.131716	−	0.991288i	$-0.542049\pi$
$227$	−3.96899	−0.263431	−0.131716	+	0.991288i	$0.542049\pi$
$228$	36.6346	2.42619
$229$	24.2322	1.60131	0.800653	−	0.599128i	$-0.204486\pi$
$229$	24.2322	1.60131	0.800653	+	0.599128i	$0.204486\pi$
$230$	−13.6488	−0.899977
$231$	−58.7108	−3.86289
$232$	−7.11146	−0.466890
$233$	13.9551	0.914227	0.457113	−	0.889408i	$-0.348883\pi$
$233$	13.9551	0.914227	0.457113	+	0.889408i	$0.348883\pi$
$234$	−38.5486	−2.52000
$235$	−16.4716	−1.07449
$236$	34.5569	2.24946
$237$	3.71995	0.241637
$238$	−37.2026	−2.41149
$239$	5.53496	0.358027	0.179013	−	0.983847i	$-0.442709\pi$
$239$	5.53496	0.358027	0.179013	+	0.983847i	$0.442709\pi$
$240$	−20.5596	−1.32712
$241$	−29.0642	−1.87219	−0.936093	−	0.351752i	$-0.885586\pi$
$241$	−29.0642	−1.87219	−0.936093	+	0.351752i	$0.885586\pi$
$242$	−45.7029	−2.93790
$243$	−0.816925	−0.0524058
$244$	25.1058	1.60724
$245$	−13.8870	−0.887209
$246$	−19.1609	−1.22166
$247$	8.63226	0.549258
$248$	−3.46647	−0.220121
$249$	2.76373	0.175144
$250$	−24.9631	−1.57881
$251$	−19.4535	−1.22789	−0.613946	−	0.789348i	$-0.710419\pi$
$251$	−19.4535	−1.22789	−0.613946	+	0.789348i	$0.710419\pi$
$252$	81.3048	5.12172
$253$	13.0536	0.820675
$254$	−24.3543	−1.52812
$255$	−30.5961	−1.91600
$256$	−29.6735	−1.85460
$257$	−13.6034	−0.848555	−0.424277	−	0.905532i	$-0.639472\pi$
$257$	−13.6034	−0.848555	−0.424277	+	0.905532i	$0.639472\pi$
$258$	−52.8223	−3.28857
$259$	−19.7088	−1.22465
$260$	−24.2977	−1.50688
$261$	9.70820	0.600922
$262$	−8.69750	−0.537333
$263$	−28.1842	−1.73791	−0.868957	−	0.494887i	$-0.835209\pi$
$263$	−28.1842	−1.73791	−0.868957	+	0.494887i	$0.835209\pi$
$264$	71.4387	4.39675
$265$	−1.66905	−0.102529
$266$	−27.7652	−1.70240
$267$	−40.2928	−2.46588
$268$	−49.4969	−3.02350
$269$	27.7199	1.69011	0.845055	−	0.534680i	$-0.179568\pi$
$269$	27.7199	1.69011	0.845055	+	0.534680i	$0.179568\pi$
$270$	50.5930	3.07899
$271$	13.0678	0.793811	0.396906	−	0.917859i	$-0.370084\pi$
$271$	13.0678	0.793811	0.396906	+	0.917859i	$0.370084\pi$
$272$	12.4597	0.755478
$273$	28.8107	1.74370
$274$	6.98167	0.421778
$275$	−3.49402	−0.210697
$276$	−27.1853	−1.63636
$277$	−16.3227	−0.980736	−0.490368	−	0.871516i	$-0.663138\pi$
$277$	−16.3227	−0.980736	−0.490368	+	0.871516i	$0.663138\pi$
$278$	−25.0212	−1.50067
$279$	4.73225	0.283312
$280$	37.1226	2.21850
$281$	26.4348	1.57697	0.788484	−	0.615056i	$-0.210866\pi$
$281$	26.4348	1.57697	0.788484	+	0.615056i	$0.210866\pi$
$282$	−50.0314	−2.97933
$283$	−14.3471	−0.852845	−0.426423	−	0.904524i	$-0.640226\pi$
$283$	−14.3471	−0.852845	−0.426423	+	0.904524i	$0.640226\pi$
$284$	−24.7009	−1.46573
$285$	−22.8346	−1.35261
$286$	35.4381	2.09550
$287$	9.52265	0.562104
$288$	10.4127	0.613574
$289$	1.54206	0.0907092
$290$	9.33179	0.547982
$291$	24.9743	1.46402
$292$	24.8202	1.45249
$293$	31.2285	1.82439	0.912195	−	0.409756i	$-0.134386\pi$
$293$	31.2285	1.82439	0.912195	+	0.409756i	$0.134386\pi$
$294$	−42.1810	−2.46005
$295$	−21.5396	−1.25408
$296$	23.9815	1.39390
$297$	−48.3867	−2.80768
$298$	12.5578	0.727456
$299$	−6.40571	−0.370452
$300$	7.27660	0.420114
$301$	26.2517	1.51312
$302$	4.19079	0.241153
$303$	34.3054	1.97079
$304$	9.29895	0.533331
$305$	−15.6486	−0.896039
$306$	−61.7973	−3.53272
$307$	14.5301	0.829275	0.414638	−	0.909987i	$-0.363908\pi$
$307$	14.5301	0.829275	0.414638	+	0.909987i	$0.363908\pi$
$308$	−74.7444	−4.25896
$309$	24.6073	1.39986
$310$	4.54877	0.258353
$311$	−7.14700	−0.405269	−0.202634	−	0.979254i	$-0.564950\pi$
$311$	−7.14700	−0.405269	−0.202634	+	0.979254i	$0.564950\pi$
$312$	−35.0566	−1.98469
$313$	−17.1075	−0.966970	−0.483485	−	0.875353i	$-0.660629\pi$
$313$	−17.1075	−0.966970	−0.483485	+	0.875353i	$0.660629\pi$
$314$	30.4626	1.71910
$315$	−50.6779	−2.85538
$316$	4.73585	0.266413
$317$	−3.91600	−0.219945	−0.109972	−	0.993935i	$-0.535076\pi$
$317$	−3.91600	−0.219945	−0.109972	+	0.993935i	$0.535076\pi$
$318$	−5.06964	−0.284292
$319$	−8.92485	−0.499696
$320$	23.7504	1.32769
$321$	−31.7473	−1.77196
$322$	20.6037	1.14820
$323$	13.8384	0.769989
$324$	32.7218	1.81788
$325$	1.71459	0.0951086
$326$	−17.3254	−0.959567
$327$	16.9538	0.937550
$328$	−11.5871	−0.639789
$329$	24.8647	1.37084
$330$	−93.7433	−5.16040
$331$	11.7296	0.644717	0.322358	−	0.946618i	$-0.395524\pi$
$331$	11.7296	0.644717	0.322358	+	0.946618i	$0.395524\pi$
$332$	3.51849	0.193102
$333$	−32.7383	−1.79405
$334$	52.0680	2.84903
$335$	30.8518	1.68561
$336$	31.0358	1.69314
$337$	18.4279	1.00383	0.501915	−	0.864917i	$-0.332629\pi$
$337$	18.4279	1.00383	0.501915	+	0.864917i	$0.332629\pi$
$338$	13.9436	0.758431
$339$	38.8514	2.11012
$340$	−38.9517	−2.11245
$341$	−4.35041	−0.235588
$342$	−46.1208	−2.49393
$343$	−4.12802	−0.222892
$344$	−31.9428	−1.72224
$345$	16.9448	0.912278
$346$	−52.6550	−2.83075
$347$	−26.9522	−1.44687	−0.723436	−	0.690391i	$-0.757438\pi$
$347$	−26.9522	−1.44687	−0.723436	+	0.690391i	$0.757438\pi$
$348$	18.5868	0.996355
$349$	−19.0325	−1.01879	−0.509394	−	0.860533i	$-0.670130\pi$
$349$	−19.0325	−1.01879	−0.509394	+	0.860533i	$0.670130\pi$
$350$	−5.51491	−0.294784
$351$	23.7445	1.26739
$352$	−9.57249	−0.510216
$353$	24.5262	1.30540	0.652699	−	0.757617i	$-0.273637\pi$
$353$	24.5262	1.30540	0.652699	+	0.757617i	$0.273637\pi$
$354$	−65.4252	−3.47731
$355$	15.3963	0.817150
$356$	−51.2965	−2.71871
$357$	46.1865	2.44445
$358$	6.86076	0.362602
$359$	32.3445	1.70708	0.853538	−	0.521030i	$-0.174452\pi$
$359$	32.3445	1.70708	0.853538	+	0.521030i	$0.174452\pi$
$360$	61.6644	3.25000
$361$	−8.67207	−0.456425
$362$	−38.7996	−2.03926
$363$	56.7395	2.97805
$364$	36.6788	1.92249
$365$	−15.4706	−0.809769
$366$	−47.5319	−2.48453
$367$	−18.4750	−0.964390	−0.482195	−	0.876064i	$-0.660160\pi$
$367$	−18.4750	−0.964390	−0.482195	+	0.876064i	$0.660160\pi$
$368$	−6.90044	−0.359710
$369$	15.8181	0.823456
$370$	−31.4690	−1.63599
$371$	2.51952	0.130807
$372$	9.06010	0.469744
$373$	11.6829	0.604920	0.302460	−	0.953162i	$-0.402192\pi$
$373$	11.6829	0.604920	0.302460	+	0.953162i	$0.402192\pi$
$374$	56.8109	2.93762
$375$	30.9913	1.60039
$376$	−30.2551	−1.56029
$377$	4.37963	0.225562
$378$	−76.3729	−3.92820
$379$	−8.77391	−0.450686	−0.225343	−	0.974280i	$-0.572350\pi$
$379$	−8.77391	−0.450686	−0.225343	+	0.974280i	$0.572350\pi$
$380$	−29.0706	−1.49129
$381$	30.2355	1.54901
$382$	−42.8569	−2.19275
$383$	−23.9733	−1.22498	−0.612489	−	0.790479i	$-0.709831\pi$
$383$	−23.9733	−1.22498	−0.612489	+	0.790479i	$0.709831\pi$
$384$	61.6744	3.14731
$385$	46.5887	2.37438
$386$	50.0780	2.54890
$387$	43.6068	2.21666
$388$	31.7947	1.61413
$389$	−15.5334	−0.787574	−0.393787	−	0.919202i	$-0.628835\pi$
$389$	−15.5334	−0.787574	−0.393787	+	0.919202i	$0.628835\pi$
$390$	46.0020	2.32940
$391$	−10.2690	−0.519326
$392$	−25.5078	−1.28834
$393$	10.7978	0.544678
$394$	5.43697	0.273911
$395$	−2.95189	−0.148526
$396$	−124.158	−6.23917
$397$	12.5788	0.631311	0.315655	−	0.948874i	$-0.397776\pi$
$397$	12.5788	0.631311	0.315655	+	0.948874i	$0.397776\pi$
$398$	22.5661	1.13114
$399$	34.4701	1.72566
$400$	1.84702	0.0923508
$401$	6.72108	0.335635	0.167817	−	0.985818i	$-0.446328\pi$
$401$	6.72108	0.335635	0.167817	+	0.985818i	$0.446328\pi$
$402$	93.7104	4.67385
$403$	2.13484	0.106344
$404$	43.6740	2.17286
$405$	−20.3958	−1.01347
$406$	−14.0868	−0.699118
$407$	30.0967	1.49184
$408$	−56.1993	−2.78228
$409$	−0.438323	−0.0216737	−0.0108368	−	0.999941i	$-0.503450\pi$
$409$	−0.438323	−0.0216737	−0.0108368	+	0.999941i	$0.503450\pi$
$410$	15.2048	0.750910
$411$	−8.66764	−0.427543
$412$	31.3274	1.54339
$413$	32.5151	1.59997
$414$	34.2247	1.68205
$415$	−2.19310	−0.107655
$416$	4.69744	0.230311
$417$	31.0634	1.52118
$418$	42.3994	2.07382
$419$	24.9550	1.21913	0.609566	−	0.792735i	$-0.291344\pi$
$419$	24.9550	1.21913	0.609566	+	0.792735i	$0.291344\pi$
$420$	−97.0250	−4.73434
$421$	−10.3555	−0.504694	−0.252347	−	0.967637i	$-0.581202\pi$
$421$	−10.3555	−0.504694	−0.252347	+	0.967637i	$0.581202\pi$
$422$	−58.4355	−2.84460
$423$	41.3028	2.00821
$424$	−3.06573	−0.148885
$425$	2.74867	0.133330
$426$	46.7653	2.26579
$427$	23.6225	1.14317
$428$	−40.4173	−1.95365
$429$	−43.9959	−2.12414
$430$	41.9160	2.02137
$431$	25.0805	1.20809	0.604043	−	0.796952i	$-0.293555\pi$
$431$	25.0805	1.20809	0.604043	+	0.796952i	$0.293555\pi$
$432$	25.5783	1.23064
$433$	35.6851	1.71491	0.857457	−	0.514555i	$-0.172043\pi$
$433$	35.6851	1.71491	0.857457	+	0.514555i	$0.172043\pi$
$434$	−6.86662	−0.329608
$435$	−11.5853	−0.555471
$436$	21.5838	1.03368
$437$	−7.66401	−0.366619
$438$	−46.9911	−2.24532
$439$	24.6016	1.17417	0.587084	−	0.809526i	$-0.300276\pi$
$439$	24.6016	1.17417	0.587084	+	0.809526i	$0.300276\pi$
$440$	−56.6887	−2.70253
$441$	34.8220	1.65819
$442$	−27.8784	−1.32604
$443$	14.9974	0.712546	0.356273	−	0.934382i	$-0.384047\pi$
$443$	14.9974	0.712546	0.356273	+	0.934382i	$0.384047\pi$
$444$	−62.6789	−2.97461
$445$	31.9735	1.51569
$446$	67.3082	3.18713
$447$	−15.5904	−0.737398
$448$	−35.8525	−1.69387
$449$	−21.1084	−0.996166	−0.498083	−	0.867129i	$-0.665963\pi$
$449$	−21.1084	−0.996166	−0.498083	+	0.867129i	$0.665963\pi$
$450$	−9.16081	−0.431845
$451$	−14.5417	−0.684743
$452$	49.4614	2.32647
$453$	−5.20280	−0.244449
$454$	9.56646	0.448976
$455$	−22.8621	−1.07179
$456$	−41.9429	−1.96416
$457$	−39.3856	−1.84238	−0.921191	−	0.389110i	$-0.872783\pi$
$457$	−39.3856	−1.84238	−0.921191	+	0.389110i	$0.872783\pi$
$458$	−58.4068	−2.72917
$459$	38.0648	1.77671
$460$	21.5723	1.00582
$461$	−10.9460	−0.509805	−0.254903	−	0.966967i	$-0.582043\pi$
$461$	−10.9460	−0.509805	−0.254903	+	0.966967i	$0.582043\pi$
$462$	141.511	6.58367
$463$	11.0524	0.513651	0.256825	−	0.966458i	$-0.417324\pi$
$463$	11.0524	0.513651	0.256825	+	0.966458i	$0.417324\pi$
$464$	4.71787	0.219022
$465$	−5.64723	−0.261884
$466$	−33.6359	−1.55815
$467$	−11.6032	−0.536931	−0.268466	−	0.963289i	$-0.586517\pi$
$467$	−11.6032	−0.536931	−0.268466	+	0.963289i	$0.586517\pi$
$468$	60.9271	2.81636
$469$	−46.5724	−2.15051
$470$	39.7014	1.83129
$471$	−37.8188	−1.74260
$472$	−39.5641	−1.82109
$473$	−40.0881	−1.84325
$474$	−8.96620	−0.411831
$475$	2.05140	0.0941246
$476$	58.7998	2.69508
$477$	4.18518	0.191626
$478$	−13.3409	−0.610199
$479$	−31.1938	−1.42528	−0.712641	−	0.701528i	$-0.752501\pi$
$479$	−31.1938	−1.42528	−0.712641	+	0.701528i	$0.752501\pi$
$480$	−12.4260	−0.567166
$481$	−14.7691	−0.673414
$482$	70.0533	3.19084
$483$	−25.5791	−1.16389
$484$	72.2347	3.28340
$485$	−19.8179	−0.899883
$486$	1.96903	0.0893172
$487$	11.4483	0.518774	0.259387	−	0.965774i	$-0.416480\pi$
$487$	11.4483	0.518774	0.259387	+	0.965774i	$0.416480\pi$
$488$	−28.7436	−1.30116
$489$	21.5093	0.972682
$490$	33.4719	1.51211
$491$	27.0498	1.22074	0.610371	−	0.792116i	$-0.291020\pi$
$491$	27.0498	1.22074	0.610371	+	0.792116i	$0.291020\pi$
$492$	30.2844	1.36533
$493$	7.02098	0.316209
$494$	−20.8063	−0.936121
$495$	77.3886	3.47836
$496$	2.29972	0.103261
$497$	−23.2415	−1.04252
$498$	−6.66141	−0.298505
$499$	21.6714	0.970146	0.485073	−	0.874474i	$-0.338793\pi$
$499$	21.6714	0.970146	0.485073	+	0.874474i	$0.338793\pi$
$500$	39.4549	1.76448
$501$	−64.6416	−2.88797
$502$	46.8887	2.09275
$503$	−24.7566	−1.10384	−0.551921	−	0.833896i	$-0.686105\pi$
$503$	−24.7566	−1.10384	−0.551921	+	0.833896i	$0.686105\pi$
$504$	−93.0857	−4.14637
$505$	−27.2223	−1.21138
$506$	−31.4632	−1.39871
$507$	−17.3107	−0.768797
$508$	38.4926	1.70783
$509$	28.2808	1.25353	0.626763	−	0.779210i	$-0.284380\pi$
$509$	28.2808	1.25353	0.626763	+	0.779210i	$0.284380\pi$
$510$	73.7458	3.26552
$511$	23.3537	1.03311
$512$	30.3007	1.33911
$513$	28.4087	1.25427
$514$	32.7882	1.44622
$515$	−19.5266	−0.860444
$516$	83.4870	3.67531
$517$	−37.9701	−1.66992
$518$	47.5041	2.08721
$519$	65.3704	2.86944
$520$	27.8184	1.21992
$521$	−14.7141	−0.644636	−0.322318	−	0.946631i	$-0.604462\pi$
$521$	−14.7141	−0.644636	−0.322318	+	0.946631i	$0.604462\pi$
$522$	−23.3997	−1.02418
$523$	2.00236	0.0875570	0.0437785	−	0.999041i	$-0.486060\pi$
$523$	2.00236	0.0875570	0.0437785	+	0.999041i	$0.486060\pi$
$524$	13.7466	0.600524
$525$	6.84667	0.298813
$526$	67.9324	2.96200
$527$	3.42237	0.149081
$528$	−47.3938	−2.06255
$529$	−17.3128	−0.752730
$530$	4.02291	0.174744
$531$	54.0109	2.34387
$532$	43.8837	1.90260
$533$	7.13595	0.309092
$534$	97.1176	4.20269
$535$	25.1924	1.08916
$536$	56.6689	2.44772
$537$	−8.51752	−0.367558
$538$	−66.8131	−2.88052
$539$	−32.0122	−1.37886
$540$	−79.9636	−3.44109
$541$	7.37487	0.317070	0.158535	−	0.987353i	$-0.449323\pi$
$541$	7.37487	0.317070	0.158535	+	0.987353i	$0.449323\pi$
$542$	−31.4973	−1.35292
$543$	48.1691	2.06714
$544$	7.53047	0.322866
$545$	−13.4534	−0.576279
$546$	−69.4424	−2.97186
$547$	38.7908	1.65857	0.829287	−	0.558823i	$-0.188747\pi$
$547$	38.7908	1.65857	0.829287	+	0.558823i	$0.188747\pi$
$548$	−11.0347	−0.471380
$549$	39.2393	1.67469
$550$	8.42163	0.359100
$551$	5.23993	0.223229
$552$	31.1244	1.32474
$553$	4.45604	0.189490
$554$	39.3426	1.67151
$555$	39.0682	1.65835
$556$	39.5466	1.67715
$557$	−18.6669	−0.790943	−0.395471	−	0.918478i	$-0.629419\pi$
$557$	−18.6669	−0.790943	−0.395471	+	0.918478i	$0.629419\pi$
$558$	−11.4061	−0.482860
$559$	19.6722	0.832044
$560$	−24.6278	−1.04072
$561$	−70.5299	−2.97777
$562$	−63.7158	−2.68769
$563$	34.1575	1.43957	0.719784	−	0.694198i	$-0.244241\pi$
$563$	34.1575	1.43957	0.719784	+	0.694198i	$0.244241\pi$
$564$	79.0760	3.32970
$565$	−30.8297	−1.29701
$566$	34.5807	1.45354
$567$	30.7885	1.29300
$568$	28.2801	1.18660
$569$	−3.23760	−0.135727	−0.0678636	−	0.997695i	$-0.521618\pi$
$569$	−3.23760	−0.135727	−0.0678636	+	0.997695i	$0.521618\pi$
$570$	55.0383	2.30530
$571$	−14.4006	−0.602647	−0.301323	−	0.953522i	$-0.597428\pi$
$571$	−14.4006	−0.602647	−0.301323	+	0.953522i	$0.597428\pi$
$572$	−56.0109	−2.34193
$573$	53.2062	2.22272
$574$	−22.9524	−0.958016
$575$	−1.52227	−0.0634832
$576$	−59.5547	−2.48144
$577$	34.0788	1.41872	0.709360	−	0.704846i	$-0.248984\pi$
$577$	34.0788	1.41872	0.709360	+	0.704846i	$0.248984\pi$
$578$	−3.71682	−0.154599
$579$	−62.1710	−2.58374
$580$	−14.7491	−0.612425
$581$	3.31060	0.137347
$582$	−60.1956	−2.49519
$583$	−3.84748	−0.159346
$584$	−28.4166	−1.17589
$585$	−37.9763	−1.57013
$586$	−75.2701	−3.10938
$587$	0.490115	0.0202292	0.0101146	−	0.999949i	$-0.496780\pi$
$587$	0.490115	0.0202292	0.0101146	+	0.999949i	$0.496780\pi$
$588$	66.6682	2.74935
$589$	2.55420	0.105244
$590$	51.9168	2.13738
$591$	−6.74992	−0.277654
$592$	−15.9098	−0.653887
$593$	21.2146	0.871179	0.435589	−	0.900145i	$-0.356540\pi$
$593$	21.2146	0.871179	0.435589	+	0.900145i	$0.356540\pi$
$594$	116.627	4.78524
$595$	−36.6503	−1.50252
$596$	−19.8480	−0.813005
$597$	−28.0155	−1.14660
$598$	15.4397	0.631376
$599$	22.6521	0.925538	0.462769	−	0.886479i	$-0.346856\pi$
$599$	22.6521	0.925538	0.462769	+	0.886479i	$0.346856\pi$
$600$	−8.33096	−0.340110
$601$	−23.7438	−0.968530	−0.484265	−	0.874922i	$-0.660913\pi$
$601$	−23.7438	−0.968530	−0.484265	+	0.874922i	$0.660913\pi$
$602$	−63.2745	−2.57888
$603$	−77.3614	−3.15040
$604$	−6.62365	−0.269513
$605$	−45.0244	−1.83050
$606$	−82.6863	−3.35890
$607$	−25.7742	−1.04614	−0.523072	−	0.852289i	$-0.675214\pi$
$607$	−25.7742	−1.04614	−0.523072	+	0.852289i	$0.675214\pi$
$608$	5.62018	0.227928
$609$	17.4886	0.708674
$610$	37.7179	1.52715
$611$	18.6328	0.753802
$612$	97.6723	3.94817
$613$	−10.5489	−0.426067	−0.213034	−	0.977045i	$-0.568334\pi$
$613$	−10.5489	−0.426067	−0.213034	+	0.977045i	$0.568334\pi$
$614$	−35.0218	−1.41337
$615$	−18.8765	−0.761173
$616$	85.5747	3.44790
$617$	35.1490	1.41504	0.707522	−	0.706692i	$-0.249813\pi$
$617$	35.1490	1.41504	0.707522	+	0.706692i	$0.249813\pi$
$618$	−59.3109	−2.38583
$619$	−40.3930	−1.62353	−0.811766	−	0.583983i	$-0.801494\pi$
$619$	−40.3930	−1.62353	−0.811766	+	0.583983i	$0.801494\pi$
$620$	−7.18946	−0.288735
$621$	−21.0811	−0.845957
$622$	17.2264	0.690716
$623$	−48.2657	−1.93373
$624$	23.2572	0.931033
$625$	−27.7842	−1.11137
$626$	41.2341	1.64805
$627$	−52.6382	−2.10217
$628$	−48.1470	−1.92127
$629$	−23.6764	−0.944039
$630$	122.149	4.86653
$631$	15.8057	0.629216	0.314608	−	0.949222i	$-0.398127\pi$
$631$	15.8057	0.629216	0.314608	+	0.949222i	$0.398127\pi$
$632$	−5.42207	−0.215678
$633$	72.5468	2.88348
$634$	9.43874	0.374860
$635$	−23.9927	−0.952122
$636$	8.01271	0.317725
$637$	15.7091	0.622418
$638$	21.5116	0.851650
$639$	−38.6065	−1.52725
$640$	−48.9404	−1.93454
$641$	8.48744	0.335234	0.167617	−	0.985852i	$-0.446393\pi$
$641$	8.48744	0.335234	0.167617	+	0.985852i	$0.446393\pi$
$642$	76.5205	3.02002
$643$	−11.0349	−0.435175	−0.217587	−	0.976041i	$-0.569819\pi$
$643$	−11.0349	−0.435175	−0.217587	+	0.976041i	$0.569819\pi$
$644$	−32.5646	−1.28323
$645$	−52.0381	−2.04900
$646$	−33.3547	−1.31232
$647$	13.9546	0.548611	0.274305	−	0.961643i	$-0.411552\pi$
$647$	13.9546	0.548611	0.274305	+	0.961643i	$0.411552\pi$
$648$	−37.4632	−1.47169
$649$	−49.6528	−1.94904
$650$	−4.13269	−0.162097
$651$	8.52480	0.334113
$652$	27.3833	1.07241
$653$	18.3816	0.719326	0.359663	−	0.933082i	$-0.382892\pi$
$653$	18.3816	0.719326	0.359663	+	0.933082i	$0.382892\pi$
$654$	−40.8638	−1.59790
$655$	−8.56838	−0.334794
$656$	7.68708	0.300130
$657$	38.7929	1.51345
$658$	−59.9314	−2.33637
$659$	−14.5433	−0.566527	−0.283263	−	0.959042i	$-0.591417\pi$
$659$	−14.5433	−0.566527	−0.283263	+	0.959042i	$0.591417\pi$
$660$	148.164	5.76727
$661$	−37.7961	−1.47010	−0.735049	−	0.678014i	$-0.762841\pi$
$661$	−37.7961	−1.47010	−0.735049	+	0.678014i	$0.762841\pi$
$662$	−28.2718	−1.09882
$663$	34.6106	1.34416
$664$	−4.02831	−0.156329
$665$	−27.3530	−1.06071
$666$	78.9091	3.05767
$667$	−3.88838	−0.150559
$668$	−82.2949	−3.18408
$669$	−83.5620	−3.23070
$670$	−74.3620	−2.87285
$671$	−36.0731	−1.39259
$672$	18.7577	0.723593
$673$	−9.91444	−0.382174	−0.191087	−	0.981573i	$-0.561201\pi$
$673$	−9.91444	−0.382174	−0.191087	+	0.981573i	$0.561201\pi$
$674$	−44.4166	−1.71087
$675$	5.64271	0.217188
$676$	−22.0382	−0.847624
$677$	−12.6376	−0.485703	−0.242851	−	0.970064i	$-0.578083\pi$
$677$	−12.6376	−0.485703	−0.242851	+	0.970064i	$0.578083\pi$
$678$	−93.6434	−3.59635
$679$	29.9161	1.14808
$680$	44.5958	1.71017
$681$	−11.8766	−0.455113
$682$	10.4858	0.401521
$683$	−12.3352	−0.471994	−0.235997	−	0.971754i	$-0.575836\pi$
$683$	−12.3352	−0.471994	−0.235997	+	0.971754i	$0.575836\pi$
$684$	72.8952	2.78722
$685$	6.87802	0.262796
$686$	9.94975	0.379883
$687$	72.5111	2.76647
$688$	21.1915	0.807918
$689$	1.88805	0.0719288
$690$	−40.8421	−1.55483
$691$	32.1220	1.22198	0.610989	−	0.791639i	$-0.290772\pi$
$691$	32.1220	1.22198	0.610989	+	0.791639i	$0.290772\pi$
$692$	83.2227	3.16365
$693$	−116.822	−4.43771
$694$	64.9630	2.46596
$695$	−24.6497	−0.935016
$696$	−21.2800	−0.806614
$697$	11.4397	0.433308
$698$	45.8741	1.73636
$699$	41.7584	1.57945
$700$	8.71646	0.329451
$701$	30.6491	1.15760	0.578799	−	0.815470i	$-0.303521\pi$
$701$	30.6491	1.15760	0.578799	+	0.815470i	$0.303521\pi$
$702$	−57.2313	−2.16006
$703$	−17.6703	−0.666447
$704$	54.7492	2.06344
$705$	−49.2886	−1.85632
$706$	−59.1155	−2.22484
$707$	41.0936	1.54548
$708$	103.406	3.88624
$709$	17.8311	0.669663	0.334831	−	0.942278i	$-0.391321\pi$
$709$	17.8311	0.669663	0.334831	+	0.942278i	$0.391321\pi$
$710$	−37.1096	−1.39270
$711$	7.40193	0.277594
$712$	58.7293	2.20097
$713$	−1.89539	−0.0709827
$714$	−111.323	−4.16617
$715$	34.9120	1.30564
$716$	−10.8436	−0.405245
$717$	16.5625	0.618539
$718$	−77.9599	−2.90944
$719$	−1.29805	−0.0484090	−0.0242045	−	0.999707i	$-0.507705\pi$
$719$	−1.29805	−0.0484090	−0.0242045	+	0.999707i	$0.507705\pi$
$720$	−40.9093	−1.52460
$721$	29.4764	1.09776
$722$	20.9023	0.777902
$723$	−86.9701	−3.23445
$724$	61.3239	2.27908
$725$	1.04079	0.0386539
$726$	−136.759	−5.07561
$727$	−34.2361	−1.26975	−0.634873	−	0.772617i	$-0.718948\pi$
$727$	−34.2361	−1.26975	−0.634873	+	0.772617i	$0.718948\pi$
$728$	−41.9934	−1.55638
$729$	−28.2128	−1.04492
$730$	37.2888	1.38012
$731$	31.5365	1.16642
$732$	75.1254	2.77671
$733$	38.7202	1.43016	0.715082	−	0.699041i	$-0.246390\pi$
$733$	38.7202	1.43016	0.715082	+	0.699041i	$0.246390\pi$
$734$	44.5304	1.64365
$735$	−41.5548	−1.53277
$736$	−4.17054	−0.153728
$737$	71.1192	2.61971
$738$	−38.1263	−1.40345
$739$	−49.3220	−1.81434	−0.907169	−	0.420767i	$-0.861761\pi$
$739$	−49.3220	−1.81434	−0.907169	+	0.420767i	$0.861761\pi$
$740$	49.7375	1.82839
$741$	25.8307	0.948916
$742$	−6.07280	−0.222940
$743$	−4.32261	−0.158581	−0.0792906	−	0.996852i	$-0.525266\pi$
$743$	−4.32261	−0.158581	−0.0792906	+	0.996852i	$0.525266\pi$
$744$	−10.3729	−0.380289
$745$	12.3714	0.453253
$746$	−28.1594	−1.03099
$747$	5.49924	0.201207
$748$	−89.7912	−3.28309
$749$	−38.0293	−1.38956
$750$	−74.6984	−2.72760
$751$	−5.24001	−0.191211	−0.0956054	−	0.995419i	$-0.530479\pi$
$751$	−5.24001	−0.191211	−0.0956054	+	0.995419i	$0.530479\pi$
$752$	20.0718	0.731944
$753$	−58.2116	−2.12135
$754$	−10.5562	−0.384434
$755$	4.12857	0.150254
$756$	120.709	4.39016
$757$	17.0577	0.619971	0.309986	−	0.950741i	$-0.399676\pi$
$757$	17.0577	0.619971	0.309986	+	0.950741i	$0.399676\pi$
$758$	21.1478	0.768121
$759$	39.0610	1.41782
$760$	33.2829	1.20730
$761$	−51.5839	−1.86991	−0.934957	−	0.354761i	$-0.884562\pi$
$761$	−51.5839	−1.86991	−0.934957	+	0.354761i	$0.884562\pi$
$762$	−72.8765	−2.64004
$763$	20.3086	0.735221
$764$	67.7365	2.45062
$765$	−60.8799	−2.20112
$766$	57.7828	2.08778
$767$	24.3657	0.879796
$768$	−88.7935	−3.20406
$769$	−20.3063	−0.732263	−0.366131	−	0.930563i	$-0.619318\pi$
$769$	−20.3063	−0.732263	−0.366131	+	0.930563i	$0.619318\pi$
$770$	−112.293	−4.04675
$771$	−40.7060	−1.46599
$772$	−79.1496	−2.84866
$773$	−26.1670	−0.941163	−0.470581	−	0.882357i	$-0.655956\pi$
$773$	−26.1670	−0.941163	−0.470581	+	0.882357i	$0.655956\pi$
$774$	−105.105	−3.77793
$775$	0.507331	0.0182239
$776$	−36.4017	−1.30674
$777$	−58.9756	−2.11574
$778$	37.4401	1.34229
$779$	8.53769	0.305895
$780$	−72.7073	−2.60334
$781$	35.4914	1.26998
$782$	24.7514	0.885107
$783$	14.4133	0.515089
$784$	16.9224	0.604370
$785$	30.0104	1.07112
$786$	−26.0260	−0.928315
$787$	11.0240	0.392963	0.196481	−	0.980508i	$-0.437049\pi$
$787$	11.0240	0.392963	0.196481	+	0.980508i	$0.437049\pi$
$788$	−8.59328	−0.306123
$789$	−84.3371	−3.00248
$790$	7.11495	0.253138
$791$	46.5391	1.65474
$792$	142.148	5.05101
$793$	17.7019	0.628613
$794$	−30.3186	−1.07597
$795$	−4.99438	−0.177132
$796$	−35.6663	−1.26416
$797$	14.6481	0.518862	0.259431	−	0.965762i	$-0.416465\pi$
$797$	14.6481	0.518862	0.259431	+	0.965762i	$0.416465\pi$
$798$	−83.0833	−2.94112
$799$	29.8702	1.05673
$800$	1.11631	0.0394677
$801$	−80.1742	−2.83282
$802$	−16.1998	−0.572035
$803$	−35.6627	−1.25851
$804$	−148.112	−5.22350
$805$	20.2978	0.715402
$806$	−5.14561	−0.181246
$807$	82.9475	2.91989
$808$	−50.0023	−1.75907
$809$	−33.6797	−1.18411	−0.592057	−	0.805896i	$-0.701684\pi$
$809$	−33.6797	−1.18411	−0.592057	+	0.805896i	$0.701684\pi$
$810$	49.1599	1.72730
$811$	−18.4325	−0.647252	−0.323626	−	0.946185i	$-0.604902\pi$
$811$	−18.4325	−0.647252	−0.323626	+	0.946185i	$0.604902\pi$
$812$	22.2646	0.781335
$813$	39.1034	1.37141
$814$	−72.5420	−2.54259
$815$	−17.0682	−0.597874
$816$	37.2836	1.30519
$817$	23.5364	0.823436
$818$	1.05649	0.0369393
$819$	57.3273	2.00318
$820$	−24.0315	−0.839218
$821$	−29.1734	−1.01816	−0.509080	−	0.860719i	$-0.670014\pi$
$821$	−29.1734	−1.01816	−0.509080	+	0.860719i	$0.670014\pi$
$822$	20.8916	0.728678
$823$	35.2009	1.22703	0.613514	−	0.789684i	$-0.289755\pi$
$823$	35.2009	1.22703	0.613514	+	0.789684i	$0.289755\pi$
$824$	−35.8666	−1.24947
$825$	−10.4553	−0.364008
$826$	−78.3712	−2.72688
$827$	23.8691	0.830010	0.415005	−	0.909819i	$-0.363780\pi$
$827$	23.8691	0.830010	0.415005	+	0.909819i	$0.363780\pi$
$828$	−54.0931	−1.87987
$829$	2.02759	0.0704213	0.0352106	−	0.999380i	$-0.488790\pi$
$829$	2.02759	0.0704213	0.0352106	+	0.999380i	$0.488790\pi$
$830$	5.28602	0.183481
$831$	−48.8432	−1.69435
$832$	−26.8667	−0.931435
$833$	25.1833	0.872550
$834$	−74.8720	−2.59261
$835$	51.2950	1.77514
$836$	−67.0133	−2.31770
$837$	7.02575	0.242845
$838$	−60.1490	−2.07781
$839$	−47.5590	−1.64192	−0.820960	−	0.570986i	$-0.806561\pi$
$839$	−47.5590	−1.64192	−0.820960	+	0.570986i	$0.806561\pi$
$840$	111.084	3.83275
$841$	−26.3415	−0.908327
$842$	24.9598	0.860170
$843$	79.1021	2.72442
$844$	92.3589	3.17912
$845$	13.7366	0.472553
$846$	−99.5521	−3.42267
$847$	67.9668	2.33537
$848$	2.03386	0.0698432
$849$	−42.9314	−1.47340
$850$	−6.62511	−0.227239
$851$	13.1125	0.449491
$852$	−73.9138	−2.53225
$853$	−13.1715	−0.450983	−0.225491	−	0.974245i	$-0.572399\pi$
$853$	−13.1715	−0.450983	−0.225491	+	0.974245i	$0.572399\pi$
$854$	−56.9372	−1.94835
$855$	−45.4361	−1.55388
$856$	46.2737	1.58160
$857$	−28.1725	−0.962355	−0.481178	−	0.876623i	$-0.659791\pi$
$857$	−28.1725	−0.962355	−0.481178	+	0.876623i	$0.659791\pi$
$858$	106.043	3.62026
$859$	8.64906	0.295102	0.147551	−	0.989054i	$-0.452861\pi$
$859$	8.64906	0.295102	0.147551	+	0.989054i	$0.452861\pi$
$860$	−66.2494	−2.25909
$861$	28.4951	0.971110
$862$	−60.4516	−2.05899
$863$	33.6894	1.14680	0.573401	−	0.819275i	$-0.305624\pi$
$863$	33.6894	1.14680	0.573401	+	0.819275i	$0.305624\pi$
$864$	15.4592	0.525934
$865$	−51.8733	−1.76375
$866$	−86.0117	−2.92280
$867$	4.61437	0.156712
$868$	10.8529	0.368370
$869$	−6.80468	−0.230833
$870$	27.9240	0.946711
$871$	−34.8998	−1.18253
$872$	−24.7113	−0.836830
$873$	49.6937	1.68188
$874$	18.4726	0.624844
$875$	37.1238	1.25501
$876$	74.2707	2.50937
$877$	5.65402	0.190923	0.0954614	−	0.995433i	$-0.469567\pi$
$877$	5.65402	0.190923	0.0954614	+	0.995433i	$0.469567\pi$
$878$	−59.2971	−2.00118
$879$	93.4466	3.15188
$880$	37.6084	1.26778
$881$	32.3309	1.08926	0.544628	−	0.838678i	$-0.316671\pi$
$881$	32.3309	1.08926	0.544628	+	0.838678i	$0.316671\pi$
$882$	−83.9314	−2.82612
$883$	−28.3254	−0.953224	−0.476612	−	0.879114i	$-0.658135\pi$
$883$	−28.3254	−0.953224	−0.476612	+	0.879114i	$0.658135\pi$
$884$	44.0626	1.48198
$885$	−64.4539	−2.16659
$886$	−36.1481	−1.21442
$887$	31.0824	1.04365	0.521823	−	0.853054i	$-0.325252\pi$
$887$	31.0824	1.04365	0.521823	+	0.853054i	$0.325252\pi$
$888$	71.7610	2.40814
$889$	36.2183	1.21472
$890$	−77.0657	−2.58325
$891$	−47.0161	−1.57510
$892$	−106.382	−3.56195
$893$	22.2929	0.746003
$894$	37.5774	1.25678
$895$	6.75890	0.225925
$896$	73.8782	2.46810
$897$	−19.1681	−0.640005
$898$	50.8775	1.69780
$899$	1.29589	0.0432202
$900$	14.4789	0.482630
$901$	3.02673	0.100835
$902$	35.0499	1.16703
$903$	78.5543	2.61412
$904$	−56.6283	−1.88343
$905$	−38.2236	−1.27060
$906$	12.5403	0.416623
$907$	2.49770	0.0829346	0.0414673	−	0.999140i	$-0.486797\pi$
$907$	2.49770	0.0829346	0.0414673	+	0.999140i	$0.486797\pi$
$908$	−15.1200	−0.501776
$909$	68.2606	2.26406
$910$	55.1046	1.82670
$911$	−48.3836	−1.60302	−0.801509	−	0.597982i	$-0.795969\pi$
$911$	−48.3836	−1.60302	−0.801509	+	0.597982i	$0.795969\pi$
$912$	27.8257	0.921401
$913$	−5.05551	−0.167313
$914$	94.9312	3.14004
$915$	−46.8262	−1.54803
$916$	92.3135	3.05012
$917$	12.9344	0.427133
$918$	−91.7475	−3.02812
$919$	28.1069	0.927162	0.463581	−	0.886055i	$-0.346564\pi$
$919$	28.1069	0.927162	0.463581	+	0.886055i	$0.346564\pi$
$920$	−24.6981	−0.814273
$921$	43.4790	1.43268
$922$	26.3831	0.868881
$923$	−17.4164	−0.573268
$924$	−223.661	−7.35791
$925$	−3.50978	−0.115401
$926$	−26.6397	−0.875435
$927$	48.9633	1.60817
$928$	2.85143	0.0936026
$929$	−34.5665	−1.13409	−0.567045	−	0.823687i	$-0.691913\pi$
$929$	−34.5665	−1.13409	−0.567045	+	0.823687i	$0.691913\pi$
$930$	13.6115	0.446339
$931$	18.7949	0.615979
$932$	53.1624	1.74139
$933$	−21.3863	−0.700156
$934$	27.9671	0.915113
$935$	55.9675	1.83033
$936$	−69.7553	−2.28002
$937$	−2.77196	−0.0905561	−0.0452780	−	0.998974i	$-0.514417\pi$
$937$	−2.77196	−0.0905561	−0.0452780	+	0.998974i	$0.514417\pi$
$938$	112.253	3.66520
$939$	−51.1915	−1.67057
$940$	−62.7491	−2.04665
$941$	−2.36761	−0.0771819	−0.0385909	−	0.999255i	$-0.512287\pi$
$941$	−2.36761	−0.0771819	−0.0385909	+	0.999255i	$0.512287\pi$
$942$	91.1547	2.96998
$943$	−6.33553	−0.206313
$944$	26.2476	0.854285
$945$	−75.2391	−2.44753
$946$	96.6244	3.14153
$947$	−45.6424	−1.48318	−0.741590	−	0.670854i	$-0.765928\pi$
$947$	−45.6424	−1.48318	−0.741590	+	0.670854i	$0.765928\pi$
$948$	14.1713	0.460263
$949$	17.5005	0.568090
$950$	−4.94448	−0.160420
$951$	−11.7180	−0.379984
$952$	−67.3197	−2.18184
$953$	15.1144	0.489604	0.244802	−	0.969573i	$-0.421277\pi$
$953$	15.1144	0.489604	0.244802	+	0.969573i	$0.421277\pi$
$954$	−10.0875	−0.326596
$955$	−42.2207	−1.36623
$956$	21.0857	0.681959
$957$	−26.7063	−0.863291
$958$	75.1865	2.42916
$959$	−10.3828	−0.335276
$960$	71.0695	2.29376
$961$	−30.3683	−0.979623
$962$	35.5980	1.14773
$963$	−63.1705	−2.03564
$964$	−110.721	−3.56609
$965$	49.3345	1.58814
$966$	61.6533	1.98366
$967$	−55.3288	−1.77925	−0.889627	−	0.456687i	$-0.849036\pi$
$967$	−55.3288	−1.77925	−0.889627	+	0.456687i	$0.849036\pi$
$968$	−82.7014	−2.65812
$969$	41.4093	1.33026
$970$	47.7670	1.53370
$971$	−51.3472	−1.64781	−0.823905	−	0.566728i	$-0.808209\pi$
$971$	−51.3472	−1.64781	−0.823905	+	0.566728i	$0.808209\pi$
$972$	−3.11211	−0.0998210
$973$	37.2101	1.19290
$974$	−27.5939	−0.884166
$975$	5.13066	0.164313
$976$	19.0690	0.610385
$977$	−60.8298	−1.94612	−0.973059	−	0.230556i	$-0.925945\pi$
$977$	−60.8298	−1.94612	−0.973059	+	0.230556i	$0.925945\pi$
$978$	−51.8437	−1.65778
$979$	73.7050	2.35562
$980$	−52.9032	−1.68993
$981$	33.7346	1.07706
$982$	−65.1982	−2.08056
$983$	−52.9430	−1.68862	−0.844310	−	0.535854i	$-0.819990\pi$
$983$	−52.9430	−1.68862	−0.844310	+	0.535854i	$0.819990\pi$
$984$	−34.6725	−1.10532
$985$	5.35626	0.170665
$986$	−16.9227	−0.538927
$987$	74.4039	2.36830
$988$	32.8850	1.04621
$989$	−17.4656	−0.555374
$990$	−186.530	−5.92830
$991$	−15.9377	−0.506277	−0.253138	−	0.967430i	$-0.581463\pi$
$991$	−15.9377	−0.506277	−0.253138	+	0.967430i	$0.581463\pi$
$992$	1.38992	0.0441302
$993$	35.0990	1.11383
$994$	56.0190	1.77682
$995$	22.2311	0.704773
$996$	10.5285	0.333609
$997$	−38.5120	−1.21969	−0.609843	−	0.792522i	$-0.708767\pi$
$997$	−38.5120	−1.21969	−0.609843	+	0.792522i	$0.708767\pi$
$998$	−52.2346	−1.65346
$999$	−48.6050	−1.53779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.2.a.c.1.16	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.2.a.c.1.16	✓	162	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3467.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41030 q^{2} +2.99235 q^{3} +3.80954 q^{4} -2.37452 q^{5} -7.21245 q^{6} +3.58446 q^{7} -4.36154 q^{8} +5.95415 q^{9} +5.72329 q^{10} -5.47371 q^{11} +11.3995 q^{12} +2.68607 q^{13} -8.63962 q^{14} -7.10538 q^{15} +2.89353 q^{16} +4.30605 q^{17} -14.3513 q^{18} +3.21371 q^{19} -9.04582 q^{20} +10.7260 q^{21} +13.1933 q^{22} -2.38479 q^{23} -13.0512 q^{24} +0.638327 q^{25} -6.47424 q^{26} +8.83984 q^{27} +13.6552 q^{28} +1.63049 q^{29} +17.1261 q^{30} +0.794782 q^{31} +1.74881 q^{32} -16.3793 q^{33} -10.3789 q^{34} -8.51136 q^{35} +22.6826 q^{36} -5.49840 q^{37} -7.74600 q^{38} +8.03767 q^{39} +10.3565 q^{40} +2.65665 q^{41} -25.8528 q^{42} +7.32376 q^{43} -20.8523 q^{44} -14.1382 q^{45} +5.74805 q^{46} +6.93681 q^{47} +8.65844 q^{48} +5.84836 q^{49} -1.53856 q^{50} +12.8852 q^{51} +10.2327 q^{52} +0.702901 q^{53} -21.3067 q^{54} +12.9974 q^{55} -15.6338 q^{56} +9.61654 q^{57} -3.92998 q^{58} +9.07114 q^{59} -27.0682 q^{60} +6.59025 q^{61} -1.91566 q^{62} +21.3424 q^{63} -10.0022 q^{64} -6.37813 q^{65} +39.4789 q^{66} -12.9929 q^{67} +16.4041 q^{68} -7.13611 q^{69} +20.5149 q^{70} -6.48396 q^{71} -25.9692 q^{72} +6.51527 q^{73} +13.2528 q^{74} +1.91010 q^{75} +12.2428 q^{76} -19.6203 q^{77} -19.3732 q^{78} +1.24316 q^{79} -6.87072 q^{80} +8.58944 q^{81} -6.40331 q^{82} +0.923598 q^{83} +40.8610 q^{84} -10.2248 q^{85} -17.6524 q^{86} +4.87900 q^{87} +23.8738 q^{88} -13.4653 q^{89} +34.0773 q^{90} +9.62813 q^{91} -9.08494 q^{92} +2.37827 q^{93} -16.7198 q^{94} -7.63101 q^{95} +5.23306 q^{96} +8.34606 q^{97} -14.0963 q^{98} -32.5913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 9 q^{2} + 24 q^{3} + 189 q^{4} + 32 q^{5} + 9 q^{6} + 23 q^{7} + 27 q^{8} + 196 q^{9} + 50 q^{10} + 12 q^{11} + 69 q^{12} + 144 q^{13} + 11 q^{14} + 17 q^{15} + 223 q^{16} + 33 q^{17} + 39 q^{18}+ \cdots - 25 q^{99}+O(q^{100}) \) 162 * q + 9 * q^2 + 24 * q^3 + 189 * q^4 + 32 * q^5 + 9 * q^6 + 23 * q^7 + 27 * q^8 + 196 * q^9 + 50 * q^10 + 12 * q^11 + 69 * q^12 + 144 * q^13 + 11 * q^14 + 17 * q^15 + 223 * q^16 + 33 * q^17 + 39 * q^18 + 35 * q^19 + 52 * q^20 + 44 * q^21 + 53 * q^22 + 31 * q^23 + 21 * q^24 + 266 * q^25 + 22 * q^26 + 93 * q^27 + 65 * q^28 + 25 * q^29 + 11 * q^30 + 81 * q^31 + 38 * q^32 + 96 * q^33 + 47 * q^34 + 14 * q^35 + 234 * q^36 + 153 * q^37 + 57 * q^38 + 18 * q^39 + 124 * q^40 + 19 * q^41 + 22 * q^42 + 87 * q^43 - 22 * q^44 + 135 * q^45 - 5 * q^46 + 53 * q^47 + 133 * q^48 + 291 * q^49 + 14 * q^50 - q^51 + 280 * q^52 + 122 * q^53 - 6 * q^54 + 88 * q^55 + 8 * q^56 + 37 * q^57 + 62 * q^58 + 26 * q^59 - 22 * q^60 + 128 * q^61 + 9 * q^62 + 11 * q^63 + 281 * q^64 + 23 * q^65 - 34 * q^66 + 124 * q^67 + 32 * q^68 + 138 * q^69 + 39 * q^70 + 16 * q^71 + 53 * q^72 + 161 * q^73 - 32 * q^74 + 71 * q^75 + 96 * q^76 + 126 * q^77 + 31 * q^78 + 34 * q^79 + 73 * q^80 + 242 * q^81 + 173 * q^82 + 27 * q^83 - 11 * q^84 + 130 * q^85 - 51 * q^86 + 87 * q^87 + 121 * q^88 + 33 * q^89 + 62 * q^90 + 66 * q^91 + 50 * q^92 + 173 * q^93 + 85 * q^94 - 11 * q^95 - 15 * q^96 + 205 * q^97 + 40 * q^98 - 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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