LMFDB - Embedded newform 7381.2.a.n.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$58.9375817319$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.187299 q^{2} -1.41219 q^{3} -1.96492 q^{4} -3.44089 q^{5} +0.264503 q^{6} -2.09401 q^{7} +0.742627 q^{8} -1.00571 q^{9} +O(q^{10})$	\(q-0.187299 q^{2} -1.41219 q^{3} -1.96492 q^{4} -3.44089 q^{5} +0.264503 q^{6} -2.09401 q^{7} +0.742627 q^{8} -1.00571 q^{9} +0.644477 q^{10} +2.77484 q^{12} -2.81148 q^{13} +0.392207 q^{14} +4.85920 q^{15} +3.79074 q^{16} -4.39423 q^{17} +0.188369 q^{18} -2.77217 q^{19} +6.76108 q^{20} +2.95714 q^{21} -3.43080 q^{23} -1.04873 q^{24} +6.83975 q^{25} +0.526588 q^{26} +5.65684 q^{27} +4.11456 q^{28} -4.62012 q^{29} -0.910125 q^{30} -5.82178 q^{31} -2.19526 q^{32} +0.823036 q^{34} +7.20527 q^{35} +1.97614 q^{36} -4.54515 q^{37} +0.519226 q^{38} +3.97035 q^{39} -2.55530 q^{40} -0.0254235 q^{41} -0.553871 q^{42} +11.1595 q^{43} +3.46055 q^{45} +0.642587 q^{46} +12.4551 q^{47} -5.35326 q^{48} -2.61512 q^{49} -1.28108 q^{50} +6.20550 q^{51} +5.52433 q^{52} -10.6456 q^{53} -1.05952 q^{54} -1.55507 q^{56} +3.91484 q^{57} +0.865346 q^{58} +3.02616 q^{59} -9.54794 q^{60} +1.00000 q^{61} +1.09042 q^{62} +2.10597 q^{63} -7.17032 q^{64} +9.67400 q^{65} +12.8709 q^{67} +8.63431 q^{68} +4.84496 q^{69} -1.34954 q^{70} +0.0988925 q^{71} -0.746869 q^{72} -8.44306 q^{73} +0.851303 q^{74} -9.65904 q^{75} +5.44709 q^{76} -0.743644 q^{78} +14.6335 q^{79} -13.0435 q^{80} -4.97140 q^{81} +0.00476180 q^{82} +12.9379 q^{83} -5.81055 q^{84} +15.1201 q^{85} -2.09017 q^{86} +6.52450 q^{87} +14.9739 q^{89} -0.648159 q^{90} +5.88727 q^{91} +6.74125 q^{92} +8.22147 q^{93} -2.33283 q^{94} +9.53875 q^{95} +3.10013 q^{96} -3.17409 q^{97} +0.489811 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9}+O(q^{10}) $ 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9	$ 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9} - q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} - 10 q^{17} - 40 q^{18} - 17 q^{19} - 6 q^{20} - 15 q^{21} - 4 q^{23} + 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} + 29 q^{28} - 35 q^{29} + 6 q^{30} - 12 q^{31} - 47 q^{32} - 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} - 20 q^{39} - 69 q^{40} - 24 q^{41} - 32 q^{42} - 24 q^{43} - 16 q^{45} - 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} - 26 q^{50} - 76 q^{51} - q^{52} - 27 q^{53} - 13 q^{54} - 9 q^{56} - 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} + 25 q^{61} - 25 q^{62} - 4 q^{63} + 5 q^{64} - 20 q^{65} + 13 q^{67} + 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} - 54 q^{72} - 39 q^{73} - 56 q^{74} + 7 q^{75} - 42 q^{76} + 30 q^{78} - 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} - 51 q^{83} - 125 q^{84} - 5 q^{85} - 10 q^{86} - 3 q^{87} + 17 q^{89} + 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} + 29 q^{94} - 81 q^{95} + 48 q^{96} - 15 q^{97} - 25 q^{98}+O(q^{100}) $ 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9 - q^12 - 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 - 10 * q^17 - 40 * q^18 - 17 * q^19 - 6 * q^20 - 15 * q^21 - 4 * q^23 + 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 + 29 * q^28 - 35 * q^29 + 6 * q^30 - 12 * q^31 - 47 * q^32 - 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 - 20 * q^39 - 69 * q^40 - 24 * q^41 - 32 * q^42 - 24 * q^43 - 16 * q^45 - 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 - 26 * q^50 - 76 * q^51 - q^52 - 27 * q^53 - 13 * q^54 - 9 * q^56 - 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 + 25 * q^61 - 25 * q^62 - 4 * q^63 + 5 * q^64 - 20 * q^65 + 13 * q^67 + 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 - 54 * q^72 - 39 * q^73 - 56 * q^74 + 7 * q^75 - 42 * q^76 + 30 * q^78 - 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 - 51 * q^83 - 125 * q^84 - 5 * q^85 - 10 * q^86 - 3 * q^87 + 17 * q^89 + 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 + 29 * q^94 - 81 * q^95 + 48 * q^96 - 15 * q^97 - 25 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−0.187299	−0.132441	−0.0662203	−	0.997805i	$-0.521094\pi$
$2$	−0.187299	−0.132441	−0.0662203	+	0.997805i	$0.521094\pi$
$3$	−1.41219	−0.815330	−0.407665	−	0.913132i	$-0.633657\pi$
$3$	−1.41219	−0.815330	−0.407665	+	0.913132i	$0.633657\pi$
$4$	−1.96492	−0.982459
$5$	−3.44089	−1.53881	−0.769407	−	0.638759i	$-0.779448\pi$
$5$	−3.44089	−1.53881	−0.769407	+	0.638759i	$0.779448\pi$
$6$	0.264503	0.107983
$7$	−2.09401	−0.791461	−0.395731	−	0.918367i	$-0.629509\pi$
$7$	−2.09401	−0.791461	−0.395731	+	0.918367i	$0.629509\pi$
$8$	0.742627	0.262558
$9$	−1.00571	−0.335238
$10$	0.644477	0.203802
$11$	0	0
$11$	0	0
$12$	2.77484	0.801028
$13$	−2.81148	−0.779764	−0.389882	−	0.920865i	$-0.627484\pi$
$13$	−2.81148	−0.779764	−0.389882	+	0.920865i	$0.627484\pi$
$14$	0.392207	0.104822
$15$	4.85920	1.25464
$16$	3.79074	0.947686
$17$	−4.39423	−1.06576	−0.532879	−	0.846192i	$-0.678890\pi$
$17$	−4.39423	−1.06576	−0.532879	+	0.846192i	$0.678890\pi$
$18$	0.188369	0.0443991
$19$	−2.77217	−0.635980	−0.317990	−	0.948094i	$-0.603008\pi$
$19$	−2.77217	−0.635980	−0.317990	+	0.948094i	$0.603008\pi$
$20$	6.76108	1.51182
$21$	2.95714	0.645302
$22$	0	0
$23$	−3.43080	−0.715372	−0.357686	−	0.933842i	$-0.616434\pi$
$23$	−3.43080	−0.715372	−0.357686	+	0.933842i	$0.616434\pi$
$24$	−1.04873	−0.214071
$25$	6.83975	1.36795
$26$	0.526588	0.103272
$27$	5.65684	1.08866
$28$	4.11456	0.777579
$29$	−4.62012	−0.857935	−0.428968	−	0.903320i	$-0.641123\pi$
$29$	−4.62012	−0.857935	−0.428968	+	0.903320i	$0.641123\pi$
$30$	−0.910125	−0.166165
$31$	−5.82178	−1.04562	−0.522811	−	0.852448i	$-0.675117\pi$
$31$	−5.82178	−1.04562	−0.522811	+	0.852448i	$0.675117\pi$
$32$	−2.19526	−0.388070
$33$	0	0
$34$	0.823036	0.141150
$35$	7.20527	1.21791
$36$	1.97614	0.329357
$37$	−4.54515	−0.747218	−0.373609	−	0.927586i	$-0.621880\pi$
$37$	−4.54515	−0.747218	−0.373609	+	0.927586i	$0.621880\pi$
$38$	0.519226	0.0842295
$39$	3.97035	0.635765
$40$	−2.55530	−0.404028
$41$	−0.0254235	−0.00397048	−0.00198524	−	0.999998i	$-0.500632\pi$
$41$	−0.0254235	−0.00397048	−0.00198524	+	0.999998i	$0.500632\pi$
$42$	−0.553871	−0.0854642
$43$	11.1595	1.70181	0.850907	−	0.525316i	$-0.176053\pi$
$43$	11.1595	1.70181	0.850907	+	0.525316i	$0.176053\pi$
$44$	0	0
$45$	3.46055	0.515868
$46$	0.642587	0.0947443
$47$	12.4551	1.81677	0.908383	−	0.418140i	$-0.137318\pi$
$47$	12.4551	1.81677	0.908383	+	0.418140i	$0.137318\pi$
$48$	−5.35326	−0.772677
$49$	−2.61512	−0.373589
$50$	−1.28108	−0.181172
$51$	6.20550	0.868944
$52$	5.52433	0.766087
$53$	−10.6456	−1.46229	−0.731143	−	0.682224i	$-0.761013\pi$
$53$	−10.6456	−1.46229	−0.731143	+	0.682224i	$0.761013\pi$
$54$	−1.05952	−0.144183
$55$	0	0
$56$	−1.55507	−0.207805
$57$	3.91484	0.518533
$58$	0.865346	0.113625
$59$	3.02616	0.393973	0.196986	−	0.980406i	$-0.436884\pi$
$59$	3.02616	0.393973	0.196986	+	0.980406i	$0.436884\pi$
$60$	−9.54794	−1.23263
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	1.09042	0.138483
$63$	2.10597	0.265328
$64$	−7.17032	−0.896290
$65$	9.67400	1.19991
$66$	0	0
$67$	12.8709	1.57243	0.786213	−	0.617956i	$-0.212039\pi$
$67$	12.8709	1.57243	0.786213	+	0.617956i	$0.212039\pi$
$68$	8.63431	1.04706
$69$	4.84496	0.583264
$70$	−1.34954	−0.161301
$71$	0.0988925	0.0117364	0.00586819	−	0.999983i	$-0.498132\pi$
$71$	0.0988925	0.0117364	0.00586819	+	0.999983i	$0.498132\pi$
$72$	−0.746869	−0.0880193
$73$	−8.44306	−0.988186	−0.494093	−	0.869409i	$-0.664500\pi$
$73$	−8.44306	−0.988186	−0.494093	+	0.869409i	$0.664500\pi$
$74$	0.851303	0.0989620
$75$	−9.65904	−1.11533
$76$	5.44709	0.624824
$77$	0	0
$78$	−0.743644	−0.0842011
$79$	14.6335	1.64640	0.823200	−	0.567751i	$-0.192186\pi$
$79$	14.6335	1.64640	0.823200	+	0.567751i	$0.192186\pi$
$80$	−13.0435	−1.45831
$81$	−4.97140	−0.552378
$82$	0.00476180	0.000525853 0
$83$	12.9379	1.42012	0.710062	−	0.704140i	$-0.248667\pi$
$83$	12.9379	1.42012	0.710062	+	0.704140i	$0.248667\pi$
$84$	−5.81055	−0.633983
$85$	15.1201	1.64000
$86$	−2.09017	−0.225389
$87$	6.52450	0.699500
$88$	0	0
$89$	14.9739	1.58723	0.793614	−	0.608421i	$-0.208197\pi$
$89$	14.9739	1.58723	0.793614	+	0.608421i	$0.208197\pi$
$90$	−0.648159	−0.0683219
$91$	5.88727	0.617153
$92$	6.74125	0.702824
$93$	8.22147	0.852527
$94$	−2.33283	−0.240614
$95$	9.53875	0.978655
$96$	3.10013	0.316405
$97$	−3.17409	−0.322280	−0.161140	−	0.986932i	$-0.551517\pi$
$97$	−3.17409	−0.322280	−0.161140	+	0.986932i	$0.551517\pi$
$98$	0.489811	0.0494783
$99$	0	0
$100$	−13.4395	−1.34395
$101$	10.7954	1.07418	0.537091	−	0.843524i	$-0.319523\pi$
$101$	10.7954	1.07418	0.537091	+	0.843524i	$0.319523\pi$
$102$	−1.16229	−0.115083
$103$	0.366505	0.0361128	0.0180564	−	0.999837i	$-0.494252\pi$
$103$	0.366505	0.0361128	0.0180564	+	0.999837i	$0.494252\pi$
$104$	−2.08788	−0.204733
$105$	−10.1752	−0.993000
$106$	1.99391	0.193666
$107$	−9.52490	−0.920807	−0.460404	−	0.887710i	$-0.652295\pi$
$107$	−9.52490	−0.920807	−0.460404	+	0.887710i	$0.652295\pi$
$108$	−11.1152	−1.06956
$109$	1.75514	0.168112	0.0840558	−	0.996461i	$-0.473213\pi$
$109$	1.75514	0.168112	0.0840558	+	0.996461i	$0.473213\pi$
$110$	0	0
$111$	6.41862	0.609229
$112$	−7.93786	−0.750057
$113$	−14.1385	−1.33004	−0.665019	−	0.746826i	$-0.731577\pi$
$113$	−14.1385	−1.33004	−0.665019	+	0.746826i	$0.731577\pi$
$114$	−0.733247	−0.0686748
$115$	11.8050	1.10082
$116$	9.07816	0.842886
$117$	2.82754	0.261406
$118$	−0.566798	−0.0521780
$119$	9.20156	0.843506
$120$	3.60857	0.329416
$121$	0	0
$122$	−0.187299	−0.0169573
$123$	0.0359028	0.00323725
$124$	11.4393	1.02728
$125$	−6.33038	−0.566206
$126$	−0.394447	−0.0351401
$127$	12.5884	1.11704	0.558518	−	0.829492i	$-0.311370\pi$
$127$	12.5884	1.11704	0.558518	+	0.829492i	$0.311370\pi$
$128$	5.73351	0.506775
$129$	−15.7594	−1.38754
$130$	−1.81193	−0.158917
$131$	−1.62439	−0.141924	−0.0709618	−	0.997479i	$-0.522607\pi$
$131$	−1.62439	−0.141924	−0.0709618	+	0.997479i	$0.522607\pi$
$132$	0	0
$133$	5.80495	0.503353
$134$	−2.41070	−0.208253
$135$	−19.4646	−1.67524
$136$	−3.26327	−0.279823
$137$	−15.1655	−1.29568	−0.647838	−	0.761778i	$-0.724327\pi$
$137$	−15.1655	−1.29568	−0.647838	+	0.761778i	$0.724327\pi$
$138$	−0.907457	−0.0772478
$139$	−16.9513	−1.43779	−0.718894	−	0.695120i	$-0.755351\pi$
$139$	−16.9513	−1.43779	−0.718894	+	0.695120i	$0.755351\pi$
$140$	−14.1578	−1.19655
$141$	−17.5890	−1.48126
$142$	−0.0185225	−0.00155437
$143$	0	0
$144$	−3.81240	−0.317700
$145$	15.8973	1.32020
$146$	1.58138	0.130876
$147$	3.69306	0.304598
$148$	8.93085	0.734111
$149$	−8.85233	−0.725211	−0.362606	−	0.931943i	$-0.618113\pi$
$149$	−8.85233	−0.725211	−0.362606	+	0.931943i	$0.618113\pi$
$150$	1.80913	0.147715
$151$	9.26514	0.753987	0.376993	−	0.926216i	$-0.376958\pi$
$151$	9.26514	0.753987	0.376993	+	0.926216i	$0.376958\pi$
$152$	−2.05869	−0.166982
$153$	4.41933	0.357282
$154$	0	0
$155$	20.0321	1.60902
$156$	−7.80142	−0.624613
$157$	13.8967	1.10908	0.554540	−	0.832157i	$-0.312894\pi$
$157$	13.8967	1.10908	0.554540	+	0.832157i	$0.312894\pi$
$158$	−2.74085	−0.218050
$159$	15.0336	1.19225
$160$	7.55365	0.597168
$161$	7.18414	0.566189
$162$	0.931141	0.0731573
$163$	3.38340	0.265008	0.132504	−	0.991182i	$-0.457698\pi$
$163$	3.38340	0.265008	0.132504	+	0.991182i	$0.457698\pi$
$164$	0.0499551	0.00390084
$165$	0	0
$166$	−2.42327	−0.188082
$167$	−6.18827	−0.478863	−0.239431	−	0.970913i	$-0.576961\pi$
$167$	−6.18827	−0.478863	−0.239431	+	0.970913i	$0.576961\pi$
$168$	2.19605	0.169429
$169$	−5.09558	−0.391968
$170$	−2.83198	−0.217203
$171$	2.78801	0.213204
$172$	−21.9276	−1.67196
$173$	19.8990	1.51289	0.756445	−	0.654057i	$-0.226934\pi$
$173$	19.8990	1.51289	0.756445	+	0.654057i	$0.226934\pi$
$174$	−1.22203	−0.0926422
$175$	−14.3225	−1.08268
$176$	0	0
$177$	−4.27352	−0.321218
$178$	−2.80460	−0.210213
$179$	13.7230	1.02571	0.512853	−	0.858476i	$-0.328589\pi$
$179$	13.7230	1.02571	0.512853	+	0.858476i	$0.328589\pi$
$180$	−6.79970	−0.506820
$181$	14.9578	1.11180	0.555901	−	0.831249i	$-0.312373\pi$
$181$	14.9578	1.11180	0.555901	+	0.831249i	$0.312373\pi$
$182$	−1.10268	−0.0817361
$183$	−1.41219	−0.104392
$184$	−2.54781	−0.187827
$185$	15.6394	1.14983
$186$	−1.53988	−0.112909
$187$	0	0
$188$	−24.4733	−1.78490
$189$	−11.8455	−0.861631
$190$	−1.78660	−0.129614
$191$	5.80689	0.420172	0.210086	−	0.977683i	$-0.432626\pi$
$191$	5.80689	0.420172	0.210086	+	0.977683i	$0.432626\pi$
$192$	10.1259	0.730772
$193$	−11.8372	−0.852058	−0.426029	−	0.904710i	$-0.640088\pi$
$193$	−11.8372	−0.852058	−0.426029	+	0.904710i	$0.640088\pi$
$194$	0.594504	0.0426829
$195$	−13.6616	−0.978324
$196$	5.13850	0.367036
$197$	−13.3266	−0.949481	−0.474741	−	0.880126i	$-0.657458\pi$
$197$	−13.3266	−0.949481	−0.474741	+	0.880126i	$0.657458\pi$
$198$	0	0
$199$	−14.4164	−1.02195	−0.510974	−	0.859596i	$-0.670715\pi$
$199$	−14.4164	−1.02195	−0.510974	+	0.859596i	$0.670715\pi$
$200$	5.07938	0.359166
$201$	−18.1761	−1.28205
$202$	−2.02197	−0.142265
$203$	9.67458	0.679022
$204$	−12.1933	−0.853702
$205$	0.0874795	0.00610983
$206$	−0.0686461	−0.00478280
$207$	3.45040	0.239820
$208$	−10.6576	−0.738972
$209$	0	0
$210$	1.90581	0.131514
$211$	−0.164829	−0.0113473	−0.00567365	−	0.999984i	$-0.501806\pi$
$211$	−0.164829	−0.0113473	−0.00567365	+	0.999984i	$0.501806\pi$
$212$	20.9177	1.43664
$213$	−0.139655	−0.00956902
$214$	1.78401	0.121952
$215$	−38.3988	−2.61878
$216$	4.20092	0.285836
$217$	12.1909	0.827570
$218$	−0.328736	−0.0222648
$219$	11.9232	0.805697
$220$	0	0
$221$	12.3543	0.831040
$222$	−1.20220	−0.0806866
$223$	12.0350	0.805927	0.402963	−	0.915216i	$-0.367980\pi$
$223$	12.0350	0.805927	0.402963	+	0.915216i	$0.367980\pi$
$224$	4.59689	0.307143
$225$	−6.87882	−0.458588
$226$	2.64813	0.176151
$227$	−11.5415	−0.766033	−0.383017	−	0.923741i	$-0.625115\pi$
$227$	−11.5415	−0.766033	−0.383017	+	0.923741i	$0.625115\pi$
$228$	−7.69234	−0.509438
$229$	−19.8934	−1.31459	−0.657297	−	0.753632i	$-0.728300\pi$
$229$	−19.8934	−1.31459	−0.657297	+	0.753632i	$0.728300\pi$
$230$	−2.21107	−0.145794
$231$	0	0
$232$	−3.43102	−0.225258
$233$	−6.89256	−0.451546	−0.225773	−	0.974180i	$-0.572491\pi$
$233$	−6.89256	−0.451546	−0.225773	+	0.974180i	$0.572491\pi$
$234$	−0.529596	−0.0346208
$235$	−42.8567	−2.79566
$236$	−5.94617	−0.387062
$237$	−20.6654	−1.34236
$238$	−1.72345	−0.111714
$239$	−9.41049	−0.608714	−0.304357	−	0.952558i	$-0.598442\pi$
$239$	−9.41049	−0.608714	−0.304357	+	0.952558i	$0.598442\pi$
$240$	18.4200	1.18901
$241$	−17.2941	−1.11401	−0.557006	−	0.830509i	$-0.688050\pi$
$241$	−17.2941	−1.11401	−0.557006	+	0.830509i	$0.688050\pi$
$242$	0	0
$243$	−9.94993	−0.638288
$244$	−1.96492	−0.125791
$245$	8.99836	0.574884
$246$	−0.00672458	−0.000428743 0
$247$	7.79390	0.495914
$248$	−4.32341	−0.274537
$249$	−18.2709	−1.15787
$250$	1.18567	0.0749887
$251$	3.34823	0.211338	0.105669	−	0.994401i	$-0.466302\pi$
$251$	3.34823	0.211338	0.105669	+	0.994401i	$0.466302\pi$
$252$	−4.13806	−0.260674
$253$	0	0
$254$	−2.35779	−0.147941
$255$	−21.3525	−1.33714
$256$	13.2668	0.829172
$257$	−7.50372	−0.468069	−0.234035	−	0.972228i	$-0.575193\pi$
$257$	−7.50372	−0.468069	−0.234035	+	0.972228i	$0.575193\pi$
$258$	2.95173	0.183767
$259$	9.51759	0.591394
$260$	−19.0086	−1.17887
$261$	4.64651	0.287612
$262$	0.304247	0.0187964
$263$	−12.4792	−0.769501	−0.384751	−	0.923021i	$-0.625713\pi$
$263$	−12.4792	−0.769501	−0.384751	+	0.923021i	$0.625713\pi$
$264$	0	0
$265$	36.6304	2.25019
$266$	−1.08726	−0.0666644
$267$	−21.1460	−1.29411
$268$	−25.2902	−1.54484
$269$	−3.31809	−0.202307	−0.101154	−	0.994871i	$-0.532253\pi$
$269$	−3.31809	−0.202307	−0.101154	+	0.994871i	$0.532253\pi$
$270$	3.64570	0.221870
$271$	17.7597	1.07883	0.539413	−	0.842041i	$-0.318646\pi$
$271$	17.7597	1.07883	0.539413	+	0.842041i	$0.318646\pi$
$272$	−16.6574	−1.01000
$273$	−8.31395	−0.503183
$274$	2.84049	0.171600
$275$	0	0
$276$	−9.51994	−0.573033
$277$	26.6839	1.60328	0.801640	−	0.597808i	$-0.203961\pi$
$277$	26.6839	1.60328	0.801640	+	0.597808i	$0.203961\pi$
$278$	3.17496	0.190422
$279$	5.85504	0.350532
$280$	5.35082	0.319773
$281$	7.51821	0.448499	0.224250	−	0.974532i	$-0.428007\pi$
$281$	7.51821	0.448499	0.224250	+	0.974532i	$0.428007\pi$
$282$	3.29441	0.196179
$283$	−24.2522	−1.44165	−0.720823	−	0.693120i	$-0.756236\pi$
$283$	−24.2522	−1.44165	−0.720823	+	0.693120i	$0.756236\pi$
$284$	−0.194316	−0.0115305
$285$	−13.4705	−0.797926
$286$	0	0
$287$	0.0532370	0.00314248
$288$	2.20780	0.130096
$289$	2.30927	0.135839
$290$	−2.97756	−0.174848
$291$	4.48242	0.262764
$292$	16.5899	0.970852
$293$	−30.9468	−1.80793	−0.903965	−	0.427606i	$-0.859357\pi$
$293$	−30.9468	−1.80793	−0.903965	+	0.427606i	$0.859357\pi$
$294$	−0.691707	−0.0403412
$295$	−10.4127	−0.606251
$296$	−3.37535	−0.196188
$297$	0	0
$298$	1.65804	0.0960474
$299$	9.64563	0.557821
$300$	18.9792	1.09577
$301$	−23.3682	−1.34692
$302$	−1.73535	−0.0998585
$303$	−15.2452	−0.875813
$304$	−10.5086	−0.602709
$305$	−3.44089	−0.197025
$306$	−0.827738	−0.0473186
$307$	22.2459	1.26964	0.634821	−	0.772659i	$-0.281074\pi$
$307$	22.2459	1.26964	0.634821	+	0.772659i	$0.281074\pi$
$308$	0	0
$309$	−0.517576	−0.0294438
$310$	−3.75200	−0.213099
$311$	−14.3645	−0.814538	−0.407269	−	0.913308i	$-0.633519\pi$
$311$	−14.3645	−0.814538	−0.407269	+	0.913308i	$0.633519\pi$
$312$	2.94849	0.166925
$313$	13.7759	0.778662	0.389331	−	0.921098i	$-0.372706\pi$
$313$	13.7759	0.778662	0.389331	+	0.921098i	$0.372706\pi$
$314$	−2.60285	−0.146887
$315$	−7.24643	−0.408290
$316$	−28.7537	−1.61752
$317$	18.2850	1.02699	0.513493	−	0.858094i	$-0.328351\pi$
$317$	18.2850	1.02699	0.513493	+	0.858094i	$0.328351\pi$
$318$	−2.81579	−0.157902
$319$	0	0
$320$	24.6723	1.37922
$321$	13.4510	0.750761
$322$	−1.34558	−0.0749865
$323$	12.1816	0.677800
$324$	9.76841	0.542689
$325$	−19.2298	−1.06668
$326$	−0.633708	−0.0350978
$327$	−2.47859	−0.137066
$328$	−0.0188801	−0.00104248
$329$	−26.0811	−1.43790
$330$	0	0
$331$	14.1586	0.778224	0.389112	−	0.921190i	$-0.372782\pi$
$331$	14.1586	0.778224	0.389112	+	0.921190i	$0.372782\pi$
$332$	−25.4220	−1.39521
$333$	4.57111	0.250495
$334$	1.15906	0.0634209
$335$	−44.2872	−2.41967
$336$	11.2098	0.611544
$337$	1.89736	0.103356	0.0516778	−	0.998664i	$-0.483543\pi$
$337$	1.89736	0.103356	0.0516778	+	0.998664i	$0.483543\pi$
$338$	0.954399	0.0519125
$339$	19.9663	1.08442
$340$	−29.7097	−1.61124
$341$	0	0
$342$	−0.522192	−0.0282369
$343$	20.1342	1.08714
$344$	8.28737	0.446825
$345$	−16.6710	−0.897535
$346$	−3.72706	−0.200368
$347$	−9.95797	−0.534572	−0.267286	−	0.963617i	$-0.586127\pi$
$347$	−9.95797	−0.534572	−0.267286	+	0.963617i	$0.586127\pi$
$348$	−12.8201	−0.687230
$349$	−7.08199	−0.379090	−0.189545	−	0.981872i	$-0.560701\pi$
$349$	−7.08199	−0.379090	−0.189545	+	0.981872i	$0.560701\pi$
$350$	2.68259	0.143391
$351$	−15.9041	−0.848897
$352$	0	0
$353$	25.3320	1.34829	0.674143	−	0.738601i	$-0.264513\pi$
$353$	25.3320	1.34829	0.674143	+	0.738601i	$0.264513\pi$
$354$	0.800428	0.0425423
$355$	−0.340279	−0.0180601
$356$	−29.4225	−1.55939
$357$	−12.9944	−0.687735
$358$	−2.57031	−0.135845
$359$	27.7146	1.46272	0.731361	−	0.681990i	$-0.238885\pi$
$359$	27.7146	1.46272	0.731361	+	0.681990i	$0.238885\pi$
$360$	2.56990	0.135445
$361$	−11.3151	−0.595530
$362$	−2.80158	−0.147248
$363$	0	0
$364$	−11.5680	−0.606328
$365$	29.0517	1.52063
$366$	0.264503	0.0138258
$367$	−4.72721	−0.246758	−0.123379	−	0.992360i	$-0.539373\pi$
$367$	−4.72721	−0.246758	−0.123379	+	0.992360i	$0.539373\pi$
$368$	−13.0053	−0.677948
$369$	0.0255687	0.00133105
$370$	−2.92924	−0.152284
$371$	22.2920	1.15734
$372$	−16.1545	−0.837573
$373$	6.70862	0.347359	0.173680	−	0.984802i	$-0.444434\pi$
$373$	6.70862	0.347359	0.173680	+	0.984802i	$0.444434\pi$
$374$	0	0
$375$	8.93971	0.461645
$376$	9.24950	0.477007
$377$	12.9894	0.668987
$378$	2.21865	0.114115
$379$	−14.4103	−0.740210	−0.370105	−	0.928990i	$-0.620678\pi$
$379$	−14.4103	−0.740210	−0.370105	+	0.928990i	$0.620678\pi$
$380$	−18.7429	−0.961489
$381$	−17.7772	−0.910753
$382$	−1.08763	−0.0556478
$383$	11.0617	0.565226	0.282613	−	0.959234i	$-0.408799\pi$
$383$	11.0617	0.565226	0.282613	+	0.959234i	$0.408799\pi$
$384$	−8.09682	−0.413189
$385$	0	0
$386$	2.21709	0.112847
$387$	−11.2233	−0.570512
$388$	6.23682	0.316627
$389$	5.81223	0.294692	0.147346	−	0.989085i	$-0.452927\pi$
$389$	5.81223	0.294692	0.147346	+	0.989085i	$0.452927\pi$
$390$	2.55880	0.129570
$391$	15.0757	0.762413
$392$	−1.94206	−0.0980888
$393$	2.29395	0.115714
$394$	2.49606	0.125750
$395$	−50.3524	−2.53350
$396$	0	0
$397$	−5.90084	−0.296155	−0.148077	−	0.988976i	$-0.547308\pi$
$397$	−5.90084	−0.296155	−0.148077	+	0.988976i	$0.547308\pi$
$398$	2.70017	0.135348
$399$	−8.19771	−0.410399
$400$	25.9277	1.29639
$401$	15.0359	0.750856	0.375428	−	0.926852i	$-0.377496\pi$
$401$	15.0359	0.750856	0.375428	+	0.926852i	$0.377496\pi$
$402$	3.40438	0.169795
$403$	16.3678	0.815339
$404$	−21.2121	−1.05534
$405$	17.1061	0.850008
$406$	−1.81204	−0.0899301
$407$	0	0
$408$	4.60837	0.228148
$409$	−16.0645	−0.794339	−0.397170	−	0.917745i	$-0.630008\pi$
$409$	−16.0645	−0.794339	−0.397170	+	0.917745i	$0.630008\pi$
$410$	−0.0163848	−0.000809190 0
$411$	21.4166	1.05640
$412$	−0.720153	−0.0354794
$413$	−6.33682	−0.311814
$414$	−0.646258	−0.0317618
$415$	−44.5181	−2.18531
$416$	6.17192	0.302603
$417$	23.9385	1.17227
$418$	0	0
$419$	−17.9721	−0.877993	−0.438996	−	0.898489i	$-0.644666\pi$
$419$	−17.9721	−0.877993	−0.438996	+	0.898489i	$0.644666\pi$
$420$	19.9935	0.975582
$421$	−28.3176	−1.38011	−0.690057	−	0.723755i	$-0.742415\pi$
$421$	−28.3176	−1.38011	−0.690057	+	0.723755i	$0.742415\pi$
$422$	0.0308724	0.00150284
$423$	−12.5263	−0.609048
$424$	−7.90571	−0.383935
$425$	−30.0554	−1.45790
$426$	0.0261573	0.00126733
$427$	−2.09401	−0.101336
$428$	18.7157	0.904656
$429$	0	0
$430$	7.19207	0.346832
$431$	21.3201	1.02695	0.513477	−	0.858103i	$-0.328357\pi$
$431$	21.3201	1.02695	0.513477	+	0.858103i	$0.328357\pi$
$432$	21.4436	1.03171
$433$	21.7636	1.04589	0.522945	−	0.852366i	$-0.324833\pi$
$433$	21.7636	1.04589	0.522945	+	0.852366i	$0.324833\pi$
$434$	−2.28334	−0.109604
$435$	−22.4501	−1.07640
$436$	−3.44870	−0.165163
$437$	9.51078	0.454962
$438$	−2.23321	−0.106707
$439$	30.3601	1.44901	0.724505	−	0.689270i	$-0.242069\pi$
$439$	30.3601	1.44901	0.724505	+	0.689270i	$0.242069\pi$
$440$	0	0
$441$	2.63006	0.125241
$442$	−2.31395	−0.110063
$443$	−37.6210	−1.78743	−0.893715	−	0.448636i	$-0.851910\pi$
$443$	−37.6210	−1.78743	−0.893715	+	0.448636i	$0.851910\pi$
$444$	−12.6121	−0.598543
$445$	−51.5235	−2.44245
$446$	−2.25416	−0.106737
$447$	12.5012	0.591286
$448$	15.0147	0.709379
$449$	−4.88484	−0.230530	−0.115265	−	0.993335i	$-0.536772\pi$
$449$	−4.88484	−0.230530	−0.115265	+	0.993335i	$0.536772\pi$
$450$	1.28840	0.0607357
$451$	0	0
$452$	27.7810	1.30671
$453$	−13.0842	−0.614748
$454$	2.16171	0.101454
$455$	−20.2575	−0.949684
$456$	2.90726	0.136145
$457$	−14.3944	−0.673343	−0.336672	−	0.941622i	$-0.609301\pi$
$457$	−14.3944	−0.673343	−0.336672	+	0.941622i	$0.609301\pi$
$458$	3.72602	0.174106
$459$	−24.8574	−1.16025
$460$	−23.1959	−1.08152
$461$	7.82654	0.364518	0.182259	−	0.983251i	$-0.441659\pi$
$461$	7.82654	0.364518	0.182259	+	0.983251i	$0.441659\pi$
$462$	0	0
$463$	−6.90943	−0.321109	−0.160554	−	0.987027i	$-0.551328\pi$
$463$	−6.90943	−0.321109	−0.160554	+	0.987027i	$0.551328\pi$
$464$	−17.5137	−0.813053
$465$	−28.2892	−1.31188
$466$	1.29097	0.0598031
$467$	6.76465	0.313031	0.156515	−	0.987676i	$-0.449974\pi$
$467$	6.76465	0.313031	0.156515	+	0.987676i	$0.449974\pi$
$468$	−5.55589	−0.256821
$469$	−26.9517	−1.24451
$470$	8.02704	0.370260
$471$	−19.6248	−0.904265
$472$	2.24731	0.103441
$473$	0	0
$474$	3.87061	0.177783
$475$	−18.9610	−0.869988
$476$	−18.0803	−0.828710
$477$	10.7064	0.490213
$478$	1.76258	0.0806184
$479$	−5.59699	−0.255733	−0.127867	−	0.991791i	$-0.540813\pi$
$479$	−5.59699	−0.255733	−0.127867	+	0.991791i	$0.540813\pi$
$480$	−10.6672	−0.486889
$481$	12.7786	0.582654
$482$	3.23917	0.147540
$483$	−10.1454	−0.461631
$484$	0	0
$485$	10.9217	0.495928
$486$	1.86362	0.0845353
$487$	10.9938	0.498175	0.249088	−	0.968481i	$-0.419869\pi$
$487$	10.9938	0.498175	0.249088	+	0.968481i	$0.419869\pi$
$488$	0.742627	0.0336171
$489$	−4.77801	−0.216069
$490$	−1.68539	−0.0761380
$491$	−11.8561	−0.535060	−0.267530	−	0.963550i	$-0.586207\pi$
$491$	−11.8561	−0.535060	−0.267530	+	0.963550i	$0.586207\pi$
$492$	−0.0705462	−0.00318047
$493$	20.3019	0.914351
$494$	−1.45979	−0.0656792
$495$	0	0
$496$	−22.0689	−0.990922
$497$	−0.207082	−0.00928890
$498$	3.42212	0.153349
$499$	−15.0340	−0.673014	−0.336507	−	0.941681i	$-0.609246\pi$
$499$	−15.0340	−0.673014	−0.336507	+	0.941681i	$0.609246\pi$
$500$	12.4387	0.556274
$501$	8.73903	0.390431
$502$	−0.627121	−0.0279898
$503$	−23.5232	−1.04885	−0.524424	−	0.851457i	$-0.675719\pi$
$503$	−23.5232	−1.04885	−0.524424	+	0.851457i	$0.675719\pi$
$504$	1.56395	0.0696639
$505$	−37.1458	−1.65297
$506$	0	0
$507$	7.19595	0.319583
$508$	−24.7351	−1.09744
$509$	30.7656	1.36366	0.681830	−	0.731511i	$-0.261184\pi$
$509$	30.7656	1.36366	0.681830	+	0.731511i	$0.261184\pi$
$510$	3.99930	0.177092
$511$	17.6799	0.782111
$512$	−13.9519	−0.616592
$513$	−15.6817	−0.692365
$514$	1.40544	0.0619914
$515$	−1.26110	−0.0555709
$516$	30.9660	1.36320
$517$	0	0
$518$	−1.78264	−0.0783246
$519$	−28.1012	−1.23350
$520$	7.18417	0.315047
$521$	24.0270	1.05264	0.526321	−	0.850286i	$-0.323571\pi$
$521$	24.0270	1.05264	0.526321	+	0.850286i	$0.323571\pi$
$522$	−0.870289	−0.0380915
$523$	21.4927	0.939808	0.469904	−	0.882717i	$-0.344288\pi$
$523$	21.4927	0.939808	0.469904	+	0.882717i	$0.344288\pi$
$524$	3.19179	0.139434
$525$	20.2261	0.882740
$526$	2.33735	0.101913
$527$	25.5822	1.11438
$528$	0	0
$529$	−11.2296	−0.488243
$530$	−6.86085	−0.298016
$531$	−3.04345	−0.132075
$532$	−11.4063	−0.494524
$533$	0.0714776	0.00309604
$534$	3.96063	0.171393
$535$	32.7742	1.41695
$536$	9.55824	0.412853
$537$	−19.3795	−0.836289
$538$	0.621476	0.0267937
$539$	0	0
$540$	38.2463	1.64586
$541$	−24.5285	−1.05456	−0.527281	−	0.849691i	$-0.676789\pi$
$541$	−24.5285	−1.05456	−0.527281	+	0.849691i	$0.676789\pi$
$542$	−3.32638	−0.142880
$543$	−21.1232	−0.906485
$544$	9.64647	0.413589
$545$	−6.03924	−0.258692
$546$	1.55720	0.0666419
$547$	42.5218	1.81810	0.909051	−	0.416684i	$-0.136808\pi$
$547$	42.5218	1.81810	0.909051	+	0.416684i	$0.136808\pi$
$548$	29.7990	1.27295
$549$	−1.00571	−0.0429228
$550$	0	0
$551$	12.8078	0.545629
$552$	3.59799	0.153141
$553$	−30.6428	−1.30306
$554$	−4.99787	−0.212339
$555$	−22.0858	−0.937490
$556$	33.3079	1.41257
$557$	−36.3219	−1.53901	−0.769504	−	0.638642i	$-0.779497\pi$
$557$	−36.3219	−1.53901	−0.769504	+	0.638642i	$0.779497\pi$
$558$	−1.09664	−0.0464247
$559$	−31.3748	−1.32701
$560$	27.3133	1.15420
$561$	0	0
$562$	−1.40816	−0.0593995
$563$	−40.0034	−1.68594	−0.842970	−	0.537960i	$-0.819195\pi$
$563$	−40.0034	−1.68594	−0.842970	+	0.537960i	$0.819195\pi$
$564$	34.5610	1.45528
$565$	48.6491	2.04668
$566$	4.54243	0.190932
$567$	10.4102	0.437186
$568$	0.0734402	0.00308148
$569$	28.4375	1.19216	0.596082	−	0.802924i	$-0.296723\pi$
$569$	28.4375	1.19216	0.596082	+	0.802924i	$0.296723\pi$
$570$	2.52302	0.105678
$571$	−31.4888	−1.31776	−0.658882	−	0.752247i	$-0.728970\pi$
$571$	−31.4888	−1.31776	−0.658882	+	0.752247i	$0.728970\pi$
$572$	0	0
$573$	−8.20044	−0.342578
$574$	−0.00997125	−0.000416192 0
$575$	−23.4658	−0.978593
$576$	7.21128	0.300470
$577$	−11.3752	−0.473555	−0.236778	−	0.971564i	$-0.576091\pi$
$577$	−11.3752	−0.473555	−0.236778	+	0.971564i	$0.576091\pi$
$578$	−0.432524	−0.0179906
$579$	16.7164	0.694708
$580$	−31.2370	−1.29705
$581$	−27.0922	−1.12397
$582$	−0.839554	−0.0348006
$583$	0	0
$584$	−6.27004	−0.259456
$585$	−9.72926	−0.402256
$586$	5.79631	0.239443
$587$	36.1789	1.49326	0.746632	−	0.665238i	$-0.231670\pi$
$587$	36.1789	1.49326	0.746632	+	0.665238i	$0.231670\pi$
$588$	−7.25656	−0.299255
$589$	16.1390	0.664995
$590$	1.95029	0.0802923
$591$	18.8197	0.774140
$592$	−17.2295	−0.708128
$593$	7.08601	0.290988	0.145494	−	0.989359i	$-0.453523\pi$
$593$	7.08601	0.290988	0.145494	+	0.989359i	$0.453523\pi$
$594$	0	0
$595$	−31.6616	−1.29800
$596$	17.3941	0.712491
$597$	20.3587	0.833225
$598$	−1.80662	−0.0738782
$599$	27.2053	1.11158	0.555790	−	0.831323i	$-0.312416\pi$
$599$	27.2053	1.11158	0.555790	+	0.831323i	$0.312416\pi$
$600$	−7.17306	−0.292839
$601$	−21.8176	−0.889960	−0.444980	−	0.895540i	$-0.646789\pi$
$601$	−21.8176	−0.889960	−0.444980	+	0.895540i	$0.646789\pi$
$602$	4.37685	0.178387
$603$	−12.9444	−0.527136
$604$	−18.2053	−0.740761
$605$	0	0
$606$	2.85541	0.115993
$607$	35.7707	1.45189	0.725945	−	0.687753i	$-0.241403\pi$
$607$	35.7707	1.45189	0.725945	+	0.687753i	$0.241403\pi$
$608$	6.08563	0.246805
$609$	−13.6624	−0.553627
$610$	0.644477	0.0260941
$611$	−35.0173	−1.41665
$612$	−8.68363	−0.351015
$613$	−30.3921	−1.22753	−0.613763	−	0.789490i	$-0.710345\pi$
$613$	−30.3921	−1.22753	−0.613763	+	0.789490i	$0.710345\pi$
$614$	−4.16664	−0.168152
$615$	−0.123538	−0.00498153
$616$	0	0
$617$	39.6953	1.59807	0.799036	−	0.601283i	$-0.205344\pi$
$617$	39.6953	1.59807	0.799036	+	0.601283i	$0.205344\pi$
$618$	0.0969416	0.00389956
$619$	42.4727	1.70712	0.853561	−	0.520993i	$-0.174438\pi$
$619$	42.4727	1.70712	0.853561	+	0.520993i	$0.174438\pi$
$620$	−39.3615	−1.58080
$621$	−19.4075	−0.778796
$622$	2.69047	0.107878
$623$	−31.3555	−1.25623
$624$	15.0506	0.602505
$625$	−12.4166	−0.496664
$626$	−2.58022	−0.103126
$627$	0	0
$628$	−27.3059	−1.08963
$629$	19.9724	0.796353
$630$	1.35725	0.0540742
$631$	31.1675	1.24076	0.620379	−	0.784302i	$-0.286979\pi$
$631$	31.1675	1.24076	0.620379	+	0.784302i	$0.286979\pi$
$632$	10.8672	0.432276
$633$	0.232770	0.00925180
$634$	−3.42476	−0.136015
$635$	−43.3152	−1.71891
$636$	−29.5399	−1.17133
$637$	7.35236	0.291311
$638$	0	0
$639$	−0.0994575	−0.00393448
$640$	−19.7284	−0.779833
$641$	−6.61092	−0.261116	−0.130558	−	0.991441i	$-0.541677\pi$
$641$	−6.61092	−0.261116	−0.130558	+	0.991441i	$0.541677\pi$
$642$	−2.51936	−0.0994313
$643$	−10.2023	−0.402339	−0.201169	−	0.979556i	$-0.564474\pi$
$643$	−10.2023	−0.402339	−0.201169	+	0.979556i	$0.564474\pi$
$644$	−14.1162	−0.556258
$645$	54.2265	2.13517
$646$	−2.28160	−0.0897683
$647$	20.1403	0.791799	0.395899	−	0.918294i	$-0.370433\pi$
$647$	20.1403	0.791799	0.395899	+	0.918294i	$0.370433\pi$
$648$	−3.69190	−0.145031
$649$	0	0
$650$	3.60173	0.141271
$651$	−17.2158	−0.674742
$652$	−6.64810	−0.260360
$653$	−35.5774	−1.39225	−0.696126	−	0.717920i	$-0.745094\pi$
$653$	−35.5774	−1.39225	−0.696126	+	0.717920i	$0.745094\pi$
$654$	0.464238	0.0181532
$655$	5.58935	0.218394
$656$	−0.0963739	−0.00376277
$657$	8.49129	0.331277
$658$	4.88498	0.190436
$659$	−16.2759	−0.634018	−0.317009	−	0.948423i	$-0.602679\pi$
$659$	−16.2759	−0.634018	−0.317009	+	0.948423i	$0.602679\pi$
$660$	0	0
$661$	−14.5476	−0.565835	−0.282917	−	0.959144i	$-0.591302\pi$
$661$	−14.5476	−0.565835	−0.282917	+	0.959144i	$0.591302\pi$
$662$	−2.65189	−0.103069
$663$	−17.4466	−0.677571
$664$	9.60806	0.372865
$665$	−19.9742	−0.774567
$666$	−0.856166	−0.0331758
$667$	15.8507	0.613743
$668$	12.1595	0.470463
$669$	−16.9958	−0.657096
$670$	8.29497	0.320463
$671$	0	0
$672$	−6.49169	−0.250422
$673$	9.85134	0.379741	0.189871	−	0.981809i	$-0.439193\pi$
$673$	9.85134	0.379741	0.189871	+	0.981809i	$0.439193\pi$
$674$	−0.355374	−0.0136885
$675$	38.6913	1.48923
$676$	10.0124	0.385093
$677$	30.5500	1.17413	0.587066	−	0.809539i	$-0.300283\pi$
$677$	30.5500	1.17413	0.587066	+	0.809539i	$0.300283\pi$
$678$	−3.73967	−0.143621
$679$	6.64657	0.255072
$680$	11.2286	0.430596
$681$	16.2988	0.624570
$682$	0	0
$683$	9.25665	0.354196	0.177098	−	0.984193i	$-0.443329\pi$
$683$	9.25665	0.354196	0.177098	+	0.984193i	$0.443329\pi$
$684$	−5.47821	−0.209465
$685$	52.1829	1.99381
$686$	−3.77111	−0.143982
$687$	28.0933	1.07183
$688$	42.3030	1.61279
$689$	29.9299	1.14024
$690$	3.12246	0.118870
$691$	23.2631	0.884970	0.442485	−	0.896776i	$-0.354097\pi$
$691$	23.2631	0.884970	0.442485	+	0.896776i	$0.354097\pi$
$692$	−39.0999	−1.48635
$693$	0	0
$694$	1.86512	0.0707990
$695$	58.3275	2.21249
$696$	4.84527	0.183659
$697$	0.111717	0.00423157
$698$	1.32645	0.0502069
$699$	9.73362	0.368159
$700$	28.1426	1.06369
$701$	−15.9428	−0.602152	−0.301076	−	0.953600i	$-0.597346\pi$
$701$	−15.9428	−0.602152	−0.301076	+	0.953600i	$0.597346\pi$
$702$	2.97882	0.112428
$703$	12.5999	0.475215
$704$	0	0
$705$	60.5219	2.27939
$706$	−4.74466	−0.178568
$707$	−22.6057	−0.850174
$708$	8.39713	0.315583
$709$	10.2543	0.385109	0.192554	−	0.981286i	$-0.438323\pi$
$709$	10.2543	0.385109	0.192554	+	0.981286i	$0.438323\pi$
$710$	0.0637340	0.00239189
$711$	−14.7171	−0.551935
$712$	11.1200	0.416740
$713$	19.9734	0.748009
$714$	2.43384	0.0910841
$715$	0	0
$716$	−26.9646	−1.00771
$717$	13.2894	0.496302
$718$	−5.19093	−0.193724
$719$	9.61255	0.358488	0.179244	−	0.983805i	$-0.442635\pi$
$719$	9.61255	0.358488	0.179244	+	0.983805i	$0.442635\pi$
$720$	13.1181	0.488881
$721$	−0.767465	−0.0285819
$722$	2.11930	0.0788723
$723$	24.4226	0.908287
$724$	−29.3908	−1.09230
$725$	−31.6005	−1.17361
$726$	0	0
$727$	23.7893	0.882295	0.441148	−	0.897435i	$-0.354571\pi$
$727$	23.7893	0.882295	0.441148	+	0.897435i	$0.354571\pi$
$728$	4.37204	0.162039
$729$	28.9654	1.07279
$730$	−5.44136	−0.201394
$731$	−49.0376	−1.81372
$732$	2.77484	0.102561
$733$	25.9367	0.957995	0.478998	−	0.877816i	$-0.341000\pi$
$733$	25.9367	0.957995	0.478998	+	0.877816i	$0.341000\pi$
$734$	0.885403	0.0326808
$735$	−12.7074	−0.468720
$736$	7.53150	0.277615
$737$	0	0
$738$	−0.00478900	−0.000176286 0
$739$	−2.44197	−0.0898293	−0.0449146	−	0.998991i	$-0.514302\pi$
$739$	−2.44197	−0.0898293	−0.0449146	+	0.998991i	$0.514302\pi$
$740$	−30.7301	−1.12966
$741$	−11.0065	−0.404333
$742$	−4.17528	−0.153279
$743$	−0.267305	−0.00980648	−0.00490324	−	0.999988i	$-0.501561\pi$
$743$	−0.267305	−0.00980648	−0.00490324	+	0.999988i	$0.501561\pi$
$744$	6.10548	0.223838
$745$	30.4599	1.11597
$746$	−1.25652	−0.0460045
$747$	−13.0118	−0.476079
$748$	0	0
$749$	19.9452	0.728783
$750$	−1.67440	−0.0611405
$751$	39.5919	1.44473	0.722364	−	0.691513i	$-0.243055\pi$
$751$	39.5919	1.44473	0.722364	+	0.691513i	$0.243055\pi$
$752$	47.2142	1.72172
$753$	−4.72834	−0.172310
$754$	−2.43290	−0.0886010
$755$	−31.8804	−1.16025
$756$	23.2754	0.846518
$757$	54.0528	1.96458	0.982291	−	0.187364i	$-0.0599943\pi$
$757$	54.0528	1.96458	0.982291	+	0.187364i	$0.0599943\pi$
$758$	2.69905	0.0980339
$759$	0	0
$760$	7.08373	0.256954
$761$	7.22801	0.262015	0.131008	−	0.991381i	$-0.458179\pi$
$761$	7.22801	0.262015	0.131008	+	0.991381i	$0.458179\pi$
$762$	3.32966	0.120621
$763$	−3.67527	−0.133054
$764$	−11.4101	−0.412802
$765$	−15.2065	−0.549791
$766$	−2.07185	−0.0748589
$767$	−8.50800	−0.307206
$768$	−18.7352	−0.676049
$769$	−7.16899	−0.258520	−0.129260	−	0.991611i	$-0.541260\pi$
$769$	−7.16899	−0.258520	−0.129260	+	0.991611i	$0.541260\pi$
$770$	0	0
$771$	10.5967	0.381631
$772$	23.2591	0.837112
$773$	32.2001	1.15816	0.579079	−	0.815271i	$-0.303412\pi$
$773$	32.2001	1.15816	0.579079	+	0.815271i	$0.303412\pi$
$774$	2.10211	0.0755589
$775$	−39.8195	−1.43036
$776$	−2.35716	−0.0846171
$777$	−13.4407	−0.482181
$778$	−1.08863	−0.0390291
$779$	0.0704782	0.00252514
$780$	26.8438	0.961164
$781$	0	0
$782$	−2.82368	−0.100974
$783$	−26.1353	−0.933999
$784$	−9.91326	−0.354045
$785$	−47.8171	−1.70667
$786$	−0.429655	−0.0153253
$787$	−31.2368	−1.11347	−0.556736	−	0.830689i	$-0.687947\pi$
$787$	−31.2368	−1.11347	−0.556736	+	0.830689i	$0.687947\pi$
$788$	26.1857	0.932827
$789$	17.6231	0.627397
$790$	9.43097	0.335539
$791$	29.6062	1.05267
$792$	0	0
$793$	−2.81148	−0.0998386
$794$	1.10522	0.0392229
$795$	−51.7292	−1.83464
$796$	28.3270	1.00402
$797$	22.4559	0.795428	0.397714	−	0.917509i	$-0.369804\pi$
$797$	22.4559	0.795428	0.397714	+	0.917509i	$0.369804\pi$
$798$	1.53543	0.0543535
$799$	−54.7307	−1.93623
$800$	−15.0150	−0.530861
$801$	−15.0594	−0.532099
$802$	−2.81621	−0.0994438
$803$	0	0
$804$	35.7146	1.25956
$805$	−24.7199	−0.871260
$806$	−3.06568	−0.107984
$807$	4.68578	0.164947
$808$	8.01695	0.282035
$809$	−45.4320	−1.59730	−0.798651	−	0.601794i	$-0.794453\pi$
$809$	−45.4320	−1.59730	−0.798651	+	0.601794i	$0.794453\pi$
$810$	−3.20396	−0.112576
$811$	−14.1767	−0.497812	−0.248906	−	0.968528i	$-0.580071\pi$
$811$	−14.1767	−0.497812	−0.248906	+	0.968528i	$0.580071\pi$
$812$	−19.0098	−0.667112
$813$	−25.0801	−0.879599
$814$	0	0
$815$	−11.6419	−0.407798
$816$	23.5235	0.823486
$817$	−30.9362	−1.08232
$818$	3.00887	0.105203
$819$	−5.92090	−0.206893
$820$	−0.171890	−0.00600266
$821$	−39.0596	−1.36319	−0.681595	−	0.731729i	$-0.738714\pi$
$821$	−39.0596	−1.36319	−0.681595	+	0.731729i	$0.738714\pi$
$822$	−4.01132	−0.139911
$823$	23.4585	0.817711	0.408856	−	0.912599i	$-0.365928\pi$
$823$	23.4585	0.817711	0.408856	+	0.912599i	$0.365928\pi$
$824$	0.272176	0.00948171
$825$	0	0
$826$	1.18688	0.0412969
$827$	−37.9366	−1.31919	−0.659593	−	0.751623i	$-0.729271\pi$
$827$	−37.9366	−1.31919	−0.659593	+	0.751623i	$0.729271\pi$
$828$	−6.77976	−0.235613
$829$	41.5376	1.44266	0.721330	−	0.692592i	$-0.243531\pi$
$829$	41.5376	1.44266	0.721330	+	0.692592i	$0.243531\pi$
$830$	8.33820	0.289423
$831$	−37.6828	−1.30720
$832$	20.1592	0.698895
$833$	11.4915	0.398155
$834$	−4.48366	−0.155256
$835$	21.2932	0.736881
$836$	0	0
$837$	−32.9329	−1.13833
$838$	3.36615	0.116282
$839$	−7.01440	−0.242164	−0.121082	−	0.992643i	$-0.538636\pi$
$839$	−7.01440	−0.242164	−0.121082	+	0.992643i	$0.538636\pi$
$840$	−7.55639	−0.260720
$841$	−7.65448	−0.263947
$842$	5.30386	0.182783
$843$	−10.6172	−0.365675
$844$	0.323876	0.0111483
$845$	17.5334	0.603166
$846$	2.34616	0.0806627
$847$	0	0
$848$	−40.3548	−1.38579
$849$	34.2488	1.17542
$850$	5.62936	0.193086
$851$	15.5935	0.534539
$852$	0.274411	0.00940118
$853$	−33.8172	−1.15788	−0.578940	−	0.815370i	$-0.696533\pi$
$853$	−33.8172	−1.15788	−0.578940	+	0.815370i	$0.696533\pi$
$854$	0.392207	0.0134210
$855$	−9.59324	−0.328082
$856$	−7.07345	−0.241765
$857$	−1.84512	−0.0630282	−0.0315141	−	0.999503i	$-0.510033\pi$
$857$	−1.84512	−0.0630282	−0.0315141	+	0.999503i	$0.510033\pi$
$858$	0	0
$859$	−36.8076	−1.25586	−0.627930	−	0.778270i	$-0.716098\pi$
$859$	−36.8076	−1.25586	−0.627930	+	0.778270i	$0.716098\pi$
$860$	75.4505	2.57284
$861$	−0.0751809	−0.00256216
$862$	−3.99324	−0.136010
$863$	9.53957	0.324731	0.162365	−	0.986731i	$-0.448088\pi$
$863$	9.53957	0.324731	0.162365	+	0.986731i	$0.448088\pi$
$864$	−12.4182	−0.422476
$865$	−68.4702	−2.32806
$866$	−4.07630	−0.138518
$867$	−3.26113	−0.110754
$868$	−23.9541	−0.813054
$869$	0	0
$870$	4.20489	0.142559
$871$	−36.1861	−1.22612
$872$	1.30341	0.0441391
$873$	3.19222	0.108040
$874$	−1.78136	−0.0602555
$875$	13.2559	0.448130
$876$	−23.4282	−0.791565
$877$	1.06504	0.0359640	0.0179820	−	0.999838i	$-0.494276\pi$
$877$	1.06504	0.0359640	0.0179820	+	0.999838i	$0.494276\pi$
$878$	−5.68643	−0.191908
$879$	43.7028	1.47406
$880$	0	0
$881$	22.5051	0.758217	0.379109	−	0.925352i	$-0.376231\pi$
$881$	22.5051	0.758217	0.379109	+	0.925352i	$0.376231\pi$
$882$	−0.492609	−0.0165870
$883$	3.03920	0.102277	0.0511386	−	0.998692i	$-0.483715\pi$
$883$	3.03920	0.102277	0.0511386	+	0.998692i	$0.483715\pi$
$884$	−24.2752	−0.816463
$885$	14.7047	0.494295
$886$	7.04639	0.236728
$887$	31.6071	1.06126	0.530631	−	0.847603i	$-0.321955\pi$
$887$	31.6071	1.06126	0.530631	+	0.847603i	$0.321955\pi$
$888$	4.76664	0.159958
$889$	−26.3602	−0.884091
$890$	9.65032	0.323480
$891$	0	0
$892$	−23.6479	−0.791790
$893$	−34.5277	−1.15543
$894$	−2.34147	−0.0783103
$895$	−47.2194	−1.57837
$896$	−12.0060	−0.401093
$897$	−13.6215	−0.454808
$898$	0.914928	0.0305315
$899$	26.8973	0.897076
$900$	13.5163	0.450544
$901$	46.7792	1.55844
$902$	0	0
$903$	33.0004	1.09818
$904$	−10.4996	−0.349213
$905$	−51.4681	−1.71086
$906$	2.45066	0.0814176
$907$	−42.7431	−1.41926	−0.709630	−	0.704574i	$-0.751138\pi$
$907$	−42.7431	−1.41926	−0.709630	+	0.704574i	$0.751138\pi$
$908$	22.6780	0.752597
$909$	−10.8571	−0.360106
$910$	3.79421	0.125777
$911$	−56.1546	−1.86048	−0.930242	−	0.366947i	$-0.880403\pi$
$911$	−56.1546	−1.86048	−0.930242	+	0.366947i	$0.880403\pi$
$912$	14.8402	0.491407
$913$	0	0
$914$	2.69607	0.0891780
$915$	4.85920	0.160640
$916$	39.0890	1.29154
$917$	3.40149	0.112327
$918$	4.65578	0.153664
$919$	45.3610	1.49632	0.748161	−	0.663518i	$-0.230937\pi$
$919$	45.3610	1.49632	0.748161	+	0.663518i	$0.230937\pi$
$920$	8.76673	0.289031
$921$	−31.4155	−1.03518
$922$	−1.46591	−0.0482770
$923$	−0.278034	−0.00915161
$924$	0	0
$925$	−31.0877	−1.02216
$926$	1.29413	0.0425278
$927$	−0.368599	−0.0121064
$928$	10.1424	0.332939
$929$	−39.9925	−1.31211	−0.656055	−	0.754713i	$-0.727776\pi$
$929$	−39.9925	−1.31211	−0.656055	+	0.754713i	$0.727776\pi$
$930$	5.29855	0.173746
$931$	7.24957	0.237595
$932$	13.5433	0.443626
$933$	20.2855	0.664117
$934$	−1.26701	−0.0414580
$935$	0	0
$936$	2.09981	0.0686343
$937$	20.9795	0.685370	0.342685	−	0.939450i	$-0.388664\pi$
$937$	20.9795	0.685370	0.342685	+	0.939450i	$0.388664\pi$
$938$	5.04803	0.164824
$939$	−19.4543	−0.634866
$940$	84.2100	2.74663
$941$	17.2302	0.561689	0.280845	−	0.959753i	$-0.409385\pi$
$941$	17.2302	0.561689	0.280845	+	0.959753i	$0.409385\pi$
$942$	3.67572	0.119761
$943$	0.0872230	0.00284037
$944$	11.4714	0.373363
$945$	40.7590	1.32589
$946$	0	0
$947$	−8.24928	−0.268065	−0.134033	−	0.990977i	$-0.542793\pi$
$947$	−8.24928	−0.268065	−0.134033	+	0.990977i	$0.542793\pi$
$948$	40.6058	1.31881
$949$	23.7375	0.770552
$950$	3.55137	0.115222
$951$	−25.8219	−0.837332
$952$	6.83333	0.221469
$953$	30.0790	0.974353	0.487177	−	0.873303i	$-0.338027\pi$
$953$	30.0790	0.974353	0.487177	+	0.873303i	$0.338027\pi$
$954$	−2.00530	−0.0649241
$955$	−19.9809	−0.646566
$956$	18.4908	0.598037
$957$	0	0
$958$	1.04831	0.0338694
$959$	31.7567	1.02548
$960$	−34.8420	−1.12452
$961$	2.89312	0.0933263
$962$	−2.39342	−0.0771670
$963$	9.57931	0.308689
$964$	33.9815	1.09447
$965$	40.7304	1.31116
$966$	1.90022	0.0611387
$967$	43.9009	1.41176	0.705878	−	0.708333i	$-0.250553\pi$
$967$	43.9009	1.41176	0.705878	+	0.708333i	$0.250553\pi$
$968$	0	0
$969$	−17.2027	−0.552631
$970$	−2.04562	−0.0656811
$971$	31.6717	1.01639	0.508196	−	0.861241i	$-0.330312\pi$
$971$	31.6717	1.01639	0.508196	+	0.861241i	$0.330312\pi$
$972$	19.5508	0.627092
$973$	35.4961	1.13795
$974$	−2.05912	−0.0659786
$975$	27.1562	0.869694
$976$	3.79074	0.121339
$977$	−2.89469	−0.0926094	−0.0463047	−	0.998927i	$-0.514745\pi$
$977$	−2.89469	−0.0926094	−0.0463047	+	0.998927i	$0.514745\pi$
$978$	0.894918	0.0286163
$979$	0	0
$980$	−17.6810	−0.564800
$981$	−1.76516	−0.0563573
$982$	2.22065	0.0708636
$983$	55.8073	1.77998	0.889989	−	0.455983i	$-0.150712\pi$
$983$	55.8073	1.77998	0.889989	+	0.455983i	$0.150712\pi$
$984$	0.0266624	0.000849966 0
$985$	45.8554	1.46108
$986$	−3.80253	−0.121097
$987$	36.8316	1.17236
$988$	−15.3144	−0.487216
$989$	−38.2862	−1.21743
$990$	0	0
$991$	18.9409	0.601679	0.300839	−	0.953675i	$-0.402733\pi$
$991$	18.9409	0.601679	0.300839	+	0.953675i	$0.402733\pi$
$992$	12.7803	0.405775
$993$	−19.9946	−0.634510
$994$	0.0387863	0.00123023
$995$	49.6052	1.57259
$996$	35.9008	1.13756
$997$	57.0224	1.80592	0.902959	−	0.429727i	$-0.141390\pi$
$997$	57.0224	1.80592	0.902959	+	0.429727i	$0.141390\pi$
$998$	2.81585	0.0891343
$999$	−25.7112	−0.813465

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.n.1.12	✓	25
11.10	odd	2		7381.2.a.o.1.14	yes	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.n.1.12	✓	25	1.1	even	1	trivial
7381.2.a.o.1.14	yes	25	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.187299 q^{2} -1.41219 q^{3} -1.96492 q^{4} -3.44089 q^{5} +0.264503 q^{6} -2.09401 q^{7} +0.742627 q^{8} -1.00571 q^{9} +O(q^{10})\)	\(q-0.187299 q^{2} -1.41219 q^{3} -1.96492 q^{4} -3.44089 q^{5} +0.264503 q^{6} -2.09401 q^{7} +0.742627 q^{8} -1.00571 q^{9} +0.644477 q^{10} +2.77484 q^{12} -2.81148 q^{13} +0.392207 q^{14} +4.85920 q^{15} +3.79074 q^{16} -4.39423 q^{17} +0.188369 q^{18} -2.77217 q^{19} +6.76108 q^{20} +2.95714 q^{21} -3.43080 q^{23} -1.04873 q^{24} +6.83975 q^{25} +0.526588 q^{26} +5.65684 q^{27} +4.11456 q^{28} -4.62012 q^{29} -0.910125 q^{30} -5.82178 q^{31} -2.19526 q^{32} +0.823036 q^{34} +7.20527 q^{35} +1.97614 q^{36} -4.54515 q^{37} +0.519226 q^{38} +3.97035 q^{39} -2.55530 q^{40} -0.0254235 q^{41} -0.553871 q^{42} +11.1595 q^{43} +3.46055 q^{45} +0.642587 q^{46} +12.4551 q^{47} -5.35326 q^{48} -2.61512 q^{49} -1.28108 q^{50} +6.20550 q^{51} +5.52433 q^{52} -10.6456 q^{53} -1.05952 q^{54} -1.55507 q^{56} +3.91484 q^{57} +0.865346 q^{58} +3.02616 q^{59} -9.54794 q^{60} +1.00000 q^{61} +1.09042 q^{62} +2.10597 q^{63} -7.17032 q^{64} +9.67400 q^{65} +12.8709 q^{67} +8.63431 q^{68} +4.84496 q^{69} -1.34954 q^{70} +0.0988925 q^{71} -0.746869 q^{72} -8.44306 q^{73} +0.851303 q^{74} -9.65904 q^{75} +5.44709 q^{76} -0.743644 q^{78} +14.6335 q^{79} -13.0435 q^{80} -4.97140 q^{81} +0.00476180 q^{82} +12.9379 q^{83} -5.81055 q^{84} +15.1201 q^{85} -2.09017 q^{86} +6.52450 q^{87} +14.9739 q^{89} -0.648159 q^{90} +5.88727 q^{91} +6.74125 q^{92} +8.22147 q^{93} -2.33283 q^{94} +9.53875 q^{95} +3.10013 q^{96} -3.17409 q^{97} +0.489811 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9}+O(q^{10}) \) 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9	\( 25 q - 5 q^{2} - q^{3} + 25 q^{4} - q^{5} - 4 q^{7} - 21 q^{8} + 24 q^{9} - q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} - 10 q^{17} - 40 q^{18} - 17 q^{19} - 6 q^{20} - 15 q^{21} - 4 q^{23} + 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} + 29 q^{28} - 35 q^{29} + 6 q^{30} - 12 q^{31} - 47 q^{32} - 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} - 20 q^{39} - 69 q^{40} - 24 q^{41} - 32 q^{42} - 24 q^{43} - 16 q^{45} - 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} - 26 q^{50} - 76 q^{51} - q^{52} - 27 q^{53} - 13 q^{54} - 9 q^{56} - 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} + 25 q^{61} - 25 q^{62} - 4 q^{63} + 5 q^{64} - 20 q^{65} + 13 q^{67} + 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} - 54 q^{72} - 39 q^{73} - 56 q^{74} + 7 q^{75} - 42 q^{76} + 30 q^{78} - 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} - 51 q^{83} - 125 q^{84} - 5 q^{85} - 10 q^{86} - 3 q^{87} + 17 q^{89} + 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} + 29 q^{94} - 81 q^{95} + 48 q^{96} - 15 q^{97} - 25 q^{98}+O(q^{100}) \) 25 * q - 5 * q^2 - q^3 + 25 * q^4 - q^5 - 4 * q^7 - 21 * q^8 + 24 * q^9 - q^12 - 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 - 10 * q^17 - 40 * q^18 - 17 * q^19 - 6 * q^20 - 15 * q^21 - 4 * q^23 + 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 + 29 * q^28 - 35 * q^29 + 6 * q^30 - 12 * q^31 - 47 * q^32 - 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 - 20 * q^39 - 69 * q^40 - 24 * q^41 - 32 * q^42 - 24 * q^43 - 16 * q^45 - 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 - 26 * q^50 - 76 * q^51 - q^52 - 27 * q^53 - 13 * q^54 - 9 * q^56 - 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 + 25 * q^61 - 25 * q^62 - 4 * q^63 + 5 * q^64 - 20 * q^65 + 13 * q^67 + 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 - 54 * q^72 - 39 * q^73 - 56 * q^74 + 7 * q^75 - 42 * q^76 + 30 * q^78 - 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 - 51 * q^83 - 125 * q^84 - 5 * q^85 - 10 * q^86 - 3 * q^87 + 17 * q^89 + 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 + 29 * q^94 - 81 * q^95 + 48 * q^96 - 15 * q^97 - 25 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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