LMFDB - Embedded newform 1175.4.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,4,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1175.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:	$69.3272442567$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} - 100 x^{16} + 101 x^{15} + 4071 x^{14} - 4087 x^{13} - 87059 x^{12} + 85913 x^{11} + \cdots + 2210048 $ x^18 - x^17 - 100x^16 + 101x^15 + 4071x^14 - 4087x^13 - 87059x^12 + 85913x^11 + 1053776x^10 - 1018524x^9 - 7240869x^8 + 6905654x^7 + 26589812x^6 - 25700032x^5 - 43438288x^4 + 45003424x^3 + 15090240x^2 - 19699840x + 2210048
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.129263$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.129263 q^{2} -1.21829 q^{3} -7.98329 q^{4} -0.157480 q^{6} -6.32492 q^{7} -2.06605 q^{8} -25.5158 q^{9} +O(q^{10})$	\(q+0.129263 q^{2} -1.21829 q^{3} -7.98329 q^{4} -0.157480 q^{6} -6.32492 q^{7} -2.06605 q^{8} -25.5158 q^{9} -8.00264 q^{11} +9.72598 q^{12} -35.8750 q^{13} -0.817579 q^{14} +63.5993 q^{16} +113.308 q^{17} -3.29825 q^{18} +148.867 q^{19} +7.70559 q^{21} -1.03445 q^{22} -45.2379 q^{23} +2.51705 q^{24} -4.63731 q^{26} +63.9795 q^{27} +50.4936 q^{28} +217.417 q^{29} -81.3389 q^{31} +24.7494 q^{32} +9.74955 q^{33} +14.6465 q^{34} +203.700 q^{36} +39.1103 q^{37} +19.2430 q^{38} +43.7062 q^{39} -228.699 q^{41} +0.996049 q^{42} -86.3238 q^{43} +63.8874 q^{44} -5.84759 q^{46} -47.0000 q^{47} -77.4825 q^{48} -302.995 q^{49} -138.042 q^{51} +286.400 q^{52} -180.096 q^{53} +8.27020 q^{54} +13.0676 q^{56} -181.363 q^{57} +28.1040 q^{58} -182.051 q^{59} +48.8763 q^{61} -10.5141 q^{62} +161.385 q^{63} -505.595 q^{64} +1.26026 q^{66} +563.874 q^{67} -904.568 q^{68} +55.1129 q^{69} -3.84676 q^{71} +52.7169 q^{72} -279.922 q^{73} +5.05551 q^{74} -1188.45 q^{76} +50.6160 q^{77} +5.64960 q^{78} -489.581 q^{79} +610.980 q^{81} -29.5624 q^{82} +87.9572 q^{83} -61.5160 q^{84} -11.1585 q^{86} -264.877 q^{87} +16.5339 q^{88} +820.048 q^{89} +226.906 q^{91} +361.147 q^{92} +99.0945 q^{93} -6.07537 q^{94} -30.1520 q^{96} +1441.10 q^{97} -39.1662 q^{98} +204.194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} + 7 q^{3} + 57 q^{4} - 14 q^{6} + 6 q^{7} - 18 q^{8} + 57 q^{9}+O(q^{10}) $ 18 * q + q^2 + 7 * q^3 + 57 * q^4 - 14 * q^6 + 6 * q^7 - 18 * q^8 + 57 * q^9	\( 18 q + q^{2} + 7 q^{3} + 57 q^{4} - 14 q^{6} + 6 q^{7} - 18 q^{8} + 57 q^{9} - 31 q^{11} - 31 q^{12} - 16 q^{13} - 229 q^{14} + 41 q^{16} + 5 q^{17} + 109 q^{18} - 283 q^{19} - 338 q^{21} - 214 q^{22} + 160 q^{23} - 324 q^{24} - 197 q^{26} - 11 q^{27} + 264 q^{28} - 464 q^{29} - 390 q^{31} - 168 q^{32} - 237 q^{33} - 824 q^{34} - 621 q^{36} - 362 q^{37} + 19 q^{38} - 378 q^{39} - 591 q^{41} + 79 q^{42} - 54 q^{43} - 859 q^{44} - 1164 q^{46} - 846 q^{47} - 484 q^{48} - 662 q^{49} - 1796 q^{51} + 502 q^{52} - 260 q^{53} - 62 q^{54} - 1261 q^{56} + 759 q^{57} - 805 q^{58} - 44 q^{59} - 1754 q^{61} + 1168 q^{62} - 2133 q^{63} - 1304 q^{64} - 2051 q^{66} + 1593 q^{67} - 1418 q^{68} - 1536 q^{69} - 2214 q^{71} + 1890 q^{72} - 1831 q^{73} + 477 q^{74} - 4034 q^{76} + 1406 q^{77} - 2903 q^{78} - 2268 q^{79} - 2610 q^{81} + 2299 q^{82} - 1794 q^{83} - 611 q^{84} - 3005 q^{86} + 2296 q^{87} - 2793 q^{88} - 1505 q^{89} - 3626 q^{91} + 2379 q^{92} - 1770 q^{93} - 47 q^{94} - 5976 q^{96} + 2436 q^{97} - 3428 q^{98} - 1456 q^{99}+O(q^{100}) \) 18 * q + q^2 + 7 * q^3 + 57 * q^4 - 14 * q^6 + 6 * q^7 - 18 * q^8 + 57 * q^9 - 31 * q^11 - 31 * q^12 - 16 * q^13 - 229 * q^14 + 41 * q^16 + 5 * q^17 + 109 * q^18 - 283 * q^19 - 338 * q^21 - 214 * q^22 + 160 * q^23 - 324 * q^24 - 197 * q^26 - 11 * q^27 + 264 * q^28 - 464 * q^29 - 390 * q^31 - 168 * q^32 - 237 * q^33 - 824 * q^34 - 621 * q^36 - 362 * q^37 + 19 * q^38 - 378 * q^39 - 591 * q^41 + 79 * q^42 - 54 * q^43 - 859 * q^44 - 1164 * q^46 - 846 * q^47 - 484 * q^48 - 662 * q^49 - 1796 * q^51 + 502 * q^52 - 260 * q^53 - 62 * q^54 - 1261 * q^56 + 759 * q^57 - 805 * q^58 - 44 * q^59 - 1754 * q^61 + 1168 * q^62 - 2133 * q^63 - 1304 * q^64 - 2051 * q^66 + 1593 * q^67 - 1418 * q^68 - 1536 * q^69 - 2214 * q^71 + 1890 * q^72 - 1831 * q^73 + 477 * q^74 - 4034 * q^76 + 1406 * q^77 - 2903 * q^78 - 2268 * q^79 - 2610 * q^81 + 2299 * q^82 - 1794 * q^83 - 611 * q^84 - 3005 * q^86 + 2296 * q^87 - 2793 * q^88 - 1505 * q^89 - 3626 * q^91 + 2379 * q^92 - 1770 * q^93 - 47 * q^94 - 5976 * q^96 + 2436 * q^97 - 3428 * q^98 - 1456 * q^99

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 $

$2$	0.129263	0.0457014	0.0228507	−	0.999739i	$-0.492726\pi$
$2$	0.129263	0.0457014	0.0228507	+	0.999739i	$0.492726\pi$
$3$	−1.21829	−0.234460	−0.117230	−	0.993105i	$-0.537402\pi$
$3$	−1.21829	−0.234460	−0.117230	+	0.993105i	$0.537402\pi$
$4$	−7.98329	−0.997911
$5$	0	0
$5$	0	0
$6$	−0.157480	−0.0107152
$7$	−6.32492	−0.341513	−0.170757	−	0.985313i	$-0.554621\pi$
$7$	−6.32492	−0.341513	−0.170757	+	0.985313i	$0.554621\pi$
$8$	−2.06605	−0.0913074
$9$	−25.5158	−0.945028
$10$	0	0
$11$	−8.00264	−0.219353	−0.109677	−	0.993967i	$-0.534982\pi$
$11$	−8.00264	−0.219353	−0.109677	+	0.993967i	$0.534982\pi$
$12$	9.72598	0.233971
$13$	−35.8750	−0.765379	−0.382690	−	0.923877i	$-0.625002\pi$
$13$	−35.8750	−0.765379	−0.382690	+	0.923877i	$0.625002\pi$
$14$	−0.817579	−0.0156076
$15$	0	0
$16$	63.5993	0.993738
$17$	113.308	1.61654	0.808269	−	0.588814i	$-0.200405\pi$
$17$	113.308	1.61654	0.808269	+	0.588814i	$0.200405\pi$
$18$	−3.29825	−0.0431891
$19$	148.867	1.79749	0.898747	−	0.438467i	$-0.144478\pi$
$19$	148.867	1.79749	0.898747	+	0.438467i	$0.144478\pi$
$20$	0	0
$21$	7.70559	0.0800713
$22$	−1.03445	−0.0100248
$23$	−45.2379	−0.410120	−0.205060	−	0.978749i	$-0.565739\pi$
$23$	−45.2379	−0.410120	−0.205060	+	0.978749i	$0.565739\pi$
$24$	2.51705	0.0214080
$25$	0	0
$26$	−4.63731	−0.0349789
$27$	63.9795	0.456032
$28$	50.4936	0.340800
$29$	217.417	1.39218	0.696091	−	0.717954i	$-0.254921\pi$
$29$	217.417	1.39218	0.696091	+	0.717954i	$0.254921\pi$
$30$	0	0
$31$	−81.3389	−0.471255	−0.235627	−	0.971843i	$-0.575714\pi$
$31$	−81.3389	−0.471255	−0.235627	+	0.971843i	$0.575714\pi$
$32$	24.7494	0.136723
$33$	9.74955	0.0514297
$34$	14.6465	0.0738781
$35$	0	0
$36$	203.700	0.943055
$37$	39.1103	0.173775	0.0868876	−	0.996218i	$-0.472308\pi$
$37$	39.1103	0.173775	0.0868876	+	0.996218i	$0.472308\pi$
$38$	19.2430	0.0821481
$39$	43.7062	0.179451
$40$	0	0
$41$	−228.699	−0.871143	−0.435571	−	0.900154i	$-0.643454\pi$
$41$	−228.699	−0.871143	−0.435571	+	0.900154i	$0.643454\pi$
$42$	0.996049	0.00365937
$43$	−86.3238	−0.306146	−0.153073	−	0.988215i	$-0.548917\pi$
$43$	−86.3238	−0.306146	−0.153073	+	0.988215i	$0.548917\pi$
$44$	63.8874	0.218895
$45$	0	0
$46$	−5.84759	−0.0187431
$47$	−47.0000	−0.145865
$47$	−47.0000	−0.145865
$48$	−77.4825	−0.232992
$49$	−302.995	−0.883369
$50$	0	0
$51$	−138.042	−0.379014
$52$	286.400	0.763780
$53$	−180.096	−0.466758	−0.233379	−	0.972386i	$-0.574978\pi$
$53$	−180.096	−0.466758	−0.233379	+	0.972386i	$0.574978\pi$
$54$	8.27020	0.0208413
$55$	0	0
$56$	13.0676	0.0311827
$57$	−181.363	−0.421441
$58$	28.1040	0.0636247
$59$	−182.051	−0.401712	−0.200856	−	0.979621i	$-0.564372\pi$
$59$	−182.051	−0.401712	−0.200856	+	0.979621i	$0.564372\pi$
$60$	0	0
$61$	48.8763	0.102590	0.0512948	−	0.998684i	$-0.483665\pi$
$61$	48.8763	0.102590	0.0512948	+	0.998684i	$0.483665\pi$
$62$	−10.5141	−0.0215370
$63$	161.385	0.322740
$64$	−505.595	−0.987490
$65$	0	0
$66$	1.26026	0.00235041
$67$	563.874	1.02818	0.514091	−	0.857736i	$-0.328130\pi$
$67$	563.874	1.02818	0.514091	+	0.857736i	$0.328130\pi$
$68$	−904.568	−1.61316
$69$	55.1129	0.0961568
$70$	0	0
$71$	−3.84676	−0.00642994	−0.00321497	−	0.999995i	$-0.501023\pi$
$71$	−3.84676	−0.00642994	−0.00321497	+	0.999995i	$0.501023\pi$
$72$	52.7169	0.0862881
$73$	−279.922	−0.448799	−0.224400	−	0.974497i	$-0.572042\pi$
$73$	−279.922	−0.448799	−0.224400	+	0.974497i	$0.572042\pi$
$74$	5.05551	0.00794178
$75$	0	0
$76$	−1188.45	−1.79374
$77$	50.6160	0.0749121
$78$	5.64960	0.00820117
$79$	−489.581	−0.697243	−0.348621	−	0.937264i	$-0.613350\pi$
$79$	−489.581	−0.697243	−0.348621	+	0.937264i	$0.613350\pi$
$80$	0	0
$81$	610.980	0.838107
$82$	−29.5624	−0.0398125
$83$	87.9572	0.116320	0.0581600	−	0.998307i	$-0.481477\pi$
$83$	87.9572	0.116320	0.0581600	+	0.998307i	$0.481477\pi$
$84$	−61.5160	−0.0799041
$85$	0	0
$86$	−11.1585	−0.0139913
$87$	−264.877	−0.326411
$88$	16.5339	0.0200286
$89$	820.048	0.976684	0.488342	−	0.872652i	$-0.337602\pi$
$89$	820.048	0.976684	0.488342	+	0.872652i	$0.337602\pi$
$90$	0	0
$91$	226.906	0.261387
$92$	361.147	0.409263
$93$	99.0945	0.110491
$94$	−6.07537	−0.00666624
$95$	0	0
$96$	−30.1520	−0.0320560
$97$	1441.10	1.50847	0.754234	−	0.656605i	$-0.228008\pi$
$97$	1441.10	1.50847	0.754234	+	0.656605i	$0.228008\pi$
$98$	−39.1662	−0.0403712
$99$	204.194	0.207295
$100$	0	0
$101$	−58.5653	−0.0576977	−0.0288488	−	0.999584i	$-0.509184\pi$
$101$	−58.5653	−0.0576977	−0.0288488	+	0.999584i	$0.509184\pi$
$102$	−17.8437	−0.0173215
$103$	602.452	0.576324	0.288162	−	0.957582i	$-0.406956\pi$
$103$	602.452	0.576324	0.288162	+	0.957582i	$0.406956\pi$
$104$	74.1195	0.0698848
$105$	0	0
$106$	−23.2798	−0.0213315
$107$	−732.613	−0.661910	−0.330955	−	0.943647i	$-0.607371\pi$
$107$	−732.613	−0.661910	−0.330955	+	0.943647i	$0.607371\pi$
$108$	−510.767	−0.455080
$109$	−878.807	−0.772242	−0.386121	−	0.922448i	$-0.626185\pi$
$109$	−878.807	−0.772242	−0.386121	+	0.922448i	$0.626185\pi$
$110$	0	0
$111$	−47.6477	−0.0407434
$112$	−402.260	−0.339375
$113$	−267.112	−0.222369	−0.111185	−	0.993800i	$-0.535465\pi$
$113$	−267.112	−0.222369	−0.111185	+	0.993800i	$0.535465\pi$
$114$	−23.4436	−0.0192605
$115$	0	0
$116$	−1735.70	−1.38927
$117$	915.377	0.723305
$118$	−23.5325	−0.0183588
$119$	−716.661	−0.552069
$120$	0	0
$121$	−1266.96	−0.951884
$122$	6.31790	0.00468849
$123$	278.623	0.204248
$124$	649.352	0.470270
$125$	0	0
$126$	20.8611	0.0147497
$127$	434.984	0.303926	0.151963	−	0.988386i	$-0.451441\pi$
$127$	434.984	0.303926	0.151963	+	0.988386i	$0.451441\pi$
$128$	−263.350	−0.181852
$129$	105.168	0.0717790
$130$	0	0
$131$	−1822.66	−1.21562	−0.607811	−	0.794082i	$-0.707952\pi$
$131$	−1822.66	−1.21562	−0.607811	+	0.794082i	$0.707952\pi$
$132$	−77.8335	−0.0513223
$133$	−941.570	−0.613868
$134$	72.8881	0.0469894
$135$	0	0
$136$	−234.099	−0.147602
$137$	−1342.78	−0.837383	−0.418691	−	0.908129i	$-0.637511\pi$
$137$	−1342.78	−0.837383	−0.418691	+	0.908129i	$0.637511\pi$
$138$	7.12407	0.00439450
$139$	−2033.36	−1.24077	−0.620386	−	0.784297i	$-0.713024\pi$
$139$	−2033.36	−1.24077	−0.620386	+	0.784297i	$0.713024\pi$
$140$	0	0
$141$	57.2597	0.0341996
$142$	−0.497244	−0.000293858 0
$143$	287.095	0.167889
$144$	−1622.78	−0.939111
$145$	0	0
$146$	−36.1836	−0.0205108
$147$	369.137	0.207115
$148$	−312.229	−0.173412
$149$	−2630.89	−1.44652	−0.723259	−	0.690577i	$-0.757357\pi$
$149$	−2630.89	−1.44652	−0.723259	+	0.690577i	$0.757357\pi$
$150$	0	0
$151$	−2355.72	−1.26958	−0.634788	−	0.772686i	$-0.718913\pi$
$151$	−2355.72	−1.26958	−0.634788	+	0.772686i	$0.718913\pi$
$152$	−307.567	−0.164125
$153$	−2891.13	−1.52767
$154$	6.54279	0.00342359
$155$	0	0
$156$	−348.919	−0.179076
$157$	−699.472	−0.355567	−0.177783	−	0.984070i	$-0.556893\pi$
$157$	−699.472	−0.355567	−0.177783	+	0.984070i	$0.556893\pi$
$158$	−63.2848	−0.0318650
$159$	219.410	0.109436
$160$	0	0
$161$	286.126	0.140061
$162$	78.9772	0.0383027
$163$	2425.38	1.16546	0.582731	−	0.812665i	$-0.301984\pi$
$163$	2425.38	1.16546	0.582731	+	0.812665i	$0.301984\pi$
$164$	1825.77	0.869323
$165$	0	0
$166$	11.3696	0.00531599
$167$	2253.52	1.04421	0.522104	−	0.852882i	$-0.325147\pi$
$167$	2253.52	1.04421	0.522104	+	0.852882i	$0.325147\pi$
$168$	−15.9201	−0.00731111
$169$	−909.986	−0.414195
$170$	0	0
$171$	−3798.45	−1.69868
$172$	689.148	0.305506
$173$	−2266.77	−0.996179	−0.498090	−	0.867126i	$-0.665965\pi$
$173$	−2266.77	−0.996179	−0.498090	+	0.867126i	$0.665965\pi$
$174$	−34.2388	−0.0149175
$175$	0	0
$176$	−508.962	−0.217980
$177$	221.791	0.0941856
$178$	106.002	0.0446359
$179$	322.451	0.134643	0.0673216	−	0.997731i	$-0.478555\pi$
$179$	322.451	0.134643	0.0673216	+	0.997731i	$0.478555\pi$
$180$	0	0
$181$	−1419.93	−0.583110	−0.291555	−	0.956554i	$-0.594173\pi$
$181$	−1419.93	−0.583110	−0.291555	+	0.956554i	$0.594173\pi$
$182$	29.3306	0.0119458
$183$	−59.5456	−0.0240532
$184$	93.4638	0.0374470
$185$	0	0
$186$	12.8093	0.00504958
$187$	−906.760	−0.354593
$188$	375.215	0.145560
$189$	−404.665	−0.155741
$190$	0	0
$191$	566.346	0.214552	0.107276	−	0.994229i	$-0.465787\pi$
$191$	566.346	0.214552	0.107276	+	0.994229i	$0.465787\pi$
$192$	615.962	0.231527
$193$	645.518	0.240753	0.120377	−	0.992728i	$-0.461590\pi$
$193$	645.518	0.240753	0.120377	+	0.992728i	$0.461590\pi$
$194$	186.281	0.0689392
$195$	0	0
$196$	2418.90	0.881524
$197$	4153.99	1.50233	0.751166	−	0.660114i	$-0.229492\pi$
$197$	4153.99	1.50233	0.751166	+	0.660114i	$0.229492\pi$
$198$	26.3947	0.00947369
$199$	−658.432	−0.234548	−0.117274	−	0.993100i	$-0.537416\pi$
$199$	−658.432	−0.234548	−0.117274	+	0.993100i	$0.537416\pi$
$200$	0	0
$201$	−686.963	−0.241068
$202$	−7.57034	−0.00263687
$203$	−1375.14	−0.475449
$204$	1102.03	0.378222
$205$	0	0
$206$	77.8748	0.0263388
$207$	1154.28	0.387575
$208$	−2281.62	−0.760587
$209$	−1191.33	−0.394287
$210$	0	0
$211$	−2486.56	−0.811288	−0.405644	−	0.914031i	$-0.632953\pi$
$211$	−2486.56	−0.811288	−0.405644	+	0.914031i	$0.632953\pi$
$212$	1437.76	0.465783
$213$	4.68647	0.00150757
$214$	−94.6999	−0.0302502
$215$	0	0
$216$	−132.185	−0.0416391
$217$	514.462	0.160940
$218$	−113.597	−0.0352926
$219$	341.026	0.105226
$220$	0	0
$221$	−4064.91	−1.23726
$222$	−6.15909	−0.00186203
$223$	4152.35	1.24691	0.623457	−	0.781857i	$-0.285728\pi$
$223$	4152.35	1.24691	0.623457	+	0.781857i	$0.285728\pi$
$224$	−156.538	−0.0466926
$225$	0	0
$226$	−34.5277	−0.0101626
$227$	−3043.69	−0.889943	−0.444972	−	0.895545i	$-0.646786\pi$
$227$	−3043.69	−0.889943	−0.444972	+	0.895545i	$0.646786\pi$
$228$	1447.88	0.420561
$229$	3738.04	1.07868	0.539338	−	0.842089i	$-0.318674\pi$
$229$	3738.04	1.07868	0.539338	+	0.842089i	$0.318674\pi$
$230$	0	0
$231$	−61.6651	−0.0175639
$232$	−449.194	−0.127116
$233$	−5209.53	−1.46475	−0.732377	−	0.680900i	$-0.761589\pi$
$233$	−5209.53	−1.46475	−0.732377	+	0.680900i	$0.761589\pi$
$234$	118.325	0.0330561
$235$	0	0
$236$	1453.37	0.400873
$237$	596.452	0.163476
$238$	−92.6379	−0.0252303
$239$	−2700.22	−0.730807	−0.365404	−	0.930849i	$-0.619069\pi$
$239$	−2700.22	−0.730807	−0.365404	+	0.930849i	$0.619069\pi$
$240$	0	0
$241$	3987.31	1.06575	0.532874	−	0.846195i	$-0.321112\pi$
$241$	3987.31	1.06575	0.532874	+	0.846195i	$0.321112\pi$
$242$	−163.771	−0.0435025
$243$	−2471.80	−0.652535
$244$	−390.194	−0.102375
$245$	0	0
$246$	36.0157	0.00933445
$247$	−5340.60	−1.37577
$248$	168.050	0.0430290
$249$	−107.158	−0.0272724
$250$	0	0
$251$	−4330.98	−1.08912	−0.544560	−	0.838722i	$-0.683303\pi$
$251$	−4330.98	−1.08912	−0.544560	+	0.838722i	$0.683303\pi$
$252$	−1288.38	−0.322066
$253$	362.023	0.0899611
$254$	56.2274	0.0138898
$255$	0	0
$256$	4010.72	0.979179
$257$	2521.74	0.612070	0.306035	−	0.952020i	$-0.400998\pi$
$257$	2521.74	0.612070	0.306035	+	0.952020i	$0.400998\pi$
$258$	13.5943	0.00328040
$259$	−247.369	−0.0593466
$260$	0	0
$261$	−5547.55	−1.31565
$262$	−235.603	−0.0555557
$263$	−2913.19	−0.683022	−0.341511	−	0.939878i	$-0.610939\pi$
$263$	−2913.19	−0.683022	−0.341511	+	0.939878i	$0.610939\pi$
$264$	−20.1431	−0.00469591
$265$	0	0
$266$	−121.710	−0.0280547
$267$	−999.058	−0.228994
$268$	−4501.57	−1.02603
$269$	−1229.73	−0.278730	−0.139365	−	0.990241i	$-0.544506\pi$
$269$	−1229.73	−0.278730	−0.139365	+	0.990241i	$0.544506\pi$
$270$	0	0
$271$	2900.85	0.650237	0.325119	−	0.945673i	$-0.394596\pi$
$271$	2900.85	0.650237	0.325119	+	0.945673i	$0.394596\pi$
$272$	7206.28	1.60642
$273$	−276.438	−0.0612849
$274$	−173.572	−0.0382696
$275$	0	0
$276$	−439.983	−0.0959560
$277$	6015.21	1.30476	0.652381	−	0.757892i	$-0.273770\pi$
$277$	6015.21	1.30476	0.652381	+	0.757892i	$0.273770\pi$
$278$	−262.839	−0.0567051
$279$	2075.42	0.445349
$280$	0	0
$281$	138.906	0.0294892	0.0147446	−	0.999891i	$-0.495306\pi$
$281$	138.906	0.0294892	0.0147446	+	0.999891i	$0.495306\pi$
$282$	7.40157	0.00156297
$283$	−8256.67	−1.73430	−0.867152	−	0.498043i	$-0.834052\pi$
$283$	−8256.67	−1.73430	−0.867152	+	0.498043i	$0.834052\pi$
$284$	30.7098	0.00641651
$285$	0	0
$286$	37.1108	0.00767275
$287$	1446.50	0.297507
$288$	−631.501	−0.129207
$289$	7925.61	1.61319
$290$	0	0
$291$	−1755.68	−0.353676
$292$	2234.70	0.447862
$293$	−8348.59	−1.66461	−0.832303	−	0.554321i	$-0.812978\pi$
$293$	−8348.59	−1.66461	−0.832303	+	0.554321i	$0.812978\pi$
$294$	47.7158	0.00946545
$295$	0	0
$296$	−80.8038	−0.0158670
$297$	−512.005	−0.100032
$298$	−340.077	−0.0661079
$299$	1622.91	0.313897
$300$	0	0
$301$	545.991	0.104553
$302$	−304.508	−0.0580215
$303$	71.3496	0.0135278
$304$	9467.82	1.78624
$305$	0	0
$306$	−373.717	−0.0698169
$307$	4519.06	0.840119	0.420059	−	0.907497i	$-0.362009\pi$
$307$	4519.06	0.840119	0.420059	+	0.907497i	$0.362009\pi$
$308$	−404.083	−0.0747557
$309$	−733.962	−0.135125
$310$	0	0
$311$	−2734.46	−0.498575	−0.249288	−	0.968429i	$-0.580196\pi$
$311$	−2734.46	−0.498575	−0.249288	+	0.968429i	$0.580196\pi$
$312$	−90.2992	−0.0163852
$313$	8327.19	1.50377	0.751886	−	0.659293i	$-0.229144\pi$
$313$	8327.19	1.50377	0.751886	+	0.659293i	$0.229144\pi$
$314$	−90.4160	−0.0162499
$315$	0	0
$316$	3908.47	0.695786
$317$	7868.54	1.39414	0.697068	−	0.717005i	$-0.254488\pi$
$317$	7868.54	1.39414	0.697068	+	0.717005i	$0.254488\pi$
$318$	28.3616	0.00500139
$319$	−1739.91	−0.305380
$320$	0	0
$321$	892.536	0.155192
$322$	36.9855	0.00640100
$323$	16867.7	2.90572
$324$	−4877.63	−0.836356
$325$	0	0
$326$	313.512	0.0532632
$327$	1070.64	0.181060
$328$	472.505	0.0795418
$329$	297.271	0.0498148
$330$	0	0
$331$	585.628	0.0972479	0.0486239	−	0.998817i	$-0.484516\pi$
$331$	585.628	0.0972479	0.0486239	+	0.998817i	$0.484516\pi$
$332$	−702.188	−0.116077
$333$	−997.928	−0.164223
$334$	291.297	0.0477218
$335$	0	0
$336$	490.070	0.0795700
$337$	−8969.53	−1.44986	−0.724928	−	0.688825i	$-0.758127\pi$
$337$	−8969.53	−1.44986	−0.724928	+	0.688825i	$0.758127\pi$
$338$	−117.628	−0.0189293
$339$	325.420	0.0521368
$340$	0	0
$341$	650.926	0.103371
$342$	−491.000	−0.0776323
$343$	4085.87	0.643196
$344$	178.349	0.0279534
$345$	0	0
$346$	−293.009	−0.0455268
$347$	−1631.70	−0.252434	−0.126217	−	0.992003i	$-0.540284\pi$
$347$	−1631.70	−0.252434	−0.126217	+	0.992003i	$0.540284\pi$
$348$	2114.59	0.325730
$349$	−9431.83	−1.44663	−0.723315	−	0.690518i	$-0.757383\pi$
$349$	−9431.83	−1.44663	−0.723315	+	0.690518i	$0.757383\pi$
$350$	0	0
$351$	−2295.26	−0.349037
$352$	−198.061	−0.0299906
$353$	4250.22	0.640840	0.320420	−	0.947276i	$-0.396176\pi$
$353$	4250.22	0.640840	0.320420	+	0.947276i	$0.396176\pi$
$354$	28.6694	0.00430442
$355$	0	0
$356$	−6546.68	−0.974644
$357$	873.102	0.129438
$358$	41.6811	0.00615339
$359$	−6584.55	−0.968020	−0.484010	−	0.875062i	$-0.660820\pi$
$359$	−6584.55	−0.968020	−0.484010	+	0.875062i	$0.660820\pi$
$360$	0	0
$361$	15302.3	2.23099
$362$	−183.545	−0.0266490
$363$	1543.52	0.223179
$364$	−1811.46	−0.260841
$365$	0	0
$366$	−7.69705	−0.00109927
$367$	−9720.59	−1.38259	−0.691295	−	0.722573i	$-0.742959\pi$
$367$	−9720.59	−1.38259	−0.691295	+	0.722573i	$0.742959\pi$
$368$	−2877.10	−0.407552
$369$	5835.44	0.823255
$370$	0	0
$371$	1139.09	0.159404
$372$	−791.100	−0.110260
$373$	8823.15	1.22479	0.612394	−	0.790553i	$-0.290207\pi$
$373$	8823.15	1.22479	0.612394	+	0.790553i	$0.290207\pi$
$374$	−117.211	−0.0162054
$375$	0	0
$376$	97.1044	0.0133186
$377$	−7799.82	−1.06555
$378$	−52.3083	−0.00711759
$379$	−9838.82	−1.33347	−0.666737	−	0.745293i	$-0.732309\pi$
$379$	−9838.82	−1.33347	−0.666737	+	0.745293i	$0.732309\pi$
$380$	0	0
$381$	−529.937	−0.0712586
$382$	73.2077	0.00980531
$383$	8741.08	1.16618	0.583092	−	0.812406i	$-0.301843\pi$
$383$	8741.08	1.16618	0.583092	+	0.812406i	$0.301843\pi$
$384$	320.838	0.0426372
$385$	0	0
$386$	83.4417	0.0110028
$387$	2202.62	0.289316
$388$	−11504.7	−1.50532
$389$	−1610.00	−0.209846	−0.104923	−	0.994480i	$-0.533460\pi$
$389$	−1610.00	−0.209846	−0.104923	+	0.994480i	$0.533460\pi$
$390$	0	0
$391$	−5125.80	−0.662974
$392$	626.004	0.0806581
$393$	2220.53	0.285015
$394$	536.958	0.0686587
$395$	0	0
$396$	−1630.14	−0.206862
$397$	−9456.49	−1.19549	−0.597743	−	0.801688i	$-0.703936\pi$
$397$	−9456.49	−1.19549	−0.597743	+	0.801688i	$0.703936\pi$
$398$	−85.1110	−0.0107192
$399$	1147.11	0.143928
$400$	0	0
$401$	−3183.00	−0.396388	−0.198194	−	0.980163i	$-0.563508\pi$
$401$	−3183.00	−0.396388	−0.198194	+	0.980163i	$0.563508\pi$
$402$	−88.7990	−0.0110171
$403$	2918.03	0.360688
$404$	467.544	0.0575772
$405$	0	0
$406$	−177.755	−0.0217287
$407$	−312.985	−0.0381182
$408$	285.201	0.0346068
$409$	−7837.92	−0.947580	−0.473790	−	0.880638i	$-0.657114\pi$
$409$	−7837.92	−0.947580	−0.473790	+	0.880638i	$0.657114\pi$
$410$	0	0
$411$	1635.90	0.196333
$412$	−4809.55	−0.575120
$413$	1151.46	0.137190
$414$	149.206	0.0177127
$415$	0	0
$416$	−887.886	−0.104645
$417$	2477.23	0.290912
$418$	−153.995	−0.0180195
$419$	−5888.93	−0.686619	−0.343309	−	0.939222i	$-0.611548\pi$
$419$	−5888.93	−0.686619	−0.343309	+	0.939222i	$0.611548\pi$
$420$	0	0
$421$	−2.73792	−0.000316955 0	−0.000158477	−	1.00000i	$-0.500050\pi$
$421$	−2.73792	−0.000316955 0	−0.000158477		1.00000i	$0.500050\pi$
$422$	−321.420	−0.0370770
$423$	1199.24	0.137847
$424$	372.088	0.0426184
$425$	0	0
$426$	0.605788	6.88980e−5 0
$427$	−309.138	−0.0350357
$428$	5848.66	0.660527
$429$	−349.765	−0.0393632
$430$	0	0
$431$	17890.1	1.99939	0.999696	−	0.0246541i	$-0.00784843\pi$
$431$	17890.1	1.99939	0.999696	+	0.0246541i	$0.00784843\pi$
$432$	4069.05	0.453177
$433$	−11811.8	−1.31094	−0.655471	−	0.755221i	$-0.727530\pi$
$433$	−11811.8	−1.31094	−0.655471	+	0.755221i	$0.727530\pi$
$434$	66.5009	0.00735518
$435$	0	0
$436$	7015.77	0.770630
$437$	−6734.42	−0.737188
$438$	44.0821	0.00480896
$439$	6864.31	0.746277	0.373139	−	0.927776i	$-0.378282\pi$
$439$	6864.31	0.746277	0.373139	+	0.927776i	$0.378282\pi$
$440$	0	0
$441$	7731.16	0.834808
$442$	−525.443	−0.0565447
$443$	−13017.8	−1.39615	−0.698073	−	0.716027i	$-0.745959\pi$
$443$	−13017.8	−1.39615	−0.698073	+	0.716027i	$0.745959\pi$
$444$	380.385	0.0406583
$445$	0	0
$446$	536.746	0.0569858
$447$	3205.19	0.339151
$448$	3197.85	0.337241
$449$	495.308	0.0520602	0.0260301	−	0.999661i	$-0.491713\pi$
$449$	495.308	0.0520602	0.0260301	+	0.999661i	$0.491713\pi$
$450$	0	0
$451$	1830.20	0.191088
$452$	2132.43	0.221905
$453$	2869.96	0.297665
$454$	−393.438	−0.0406717
$455$	0	0
$456$	374.706	0.0384807
$457$	−8043.15	−0.823288	−0.411644	−	0.911345i	$-0.635045\pi$
$457$	−8043.15	−0.823288	−0.411644	+	0.911345i	$0.635045\pi$
$458$	483.191	0.0492970
$459$	7249.37	0.737193
$460$	0	0
$461$	−7994.16	−0.807647	−0.403824	−	0.914837i	$-0.632319\pi$
$461$	−7994.16	−0.807647	−0.403824	+	0.914837i	$0.632319\pi$
$462$	−7.97103	−0.000802696 0
$463$	19303.4	1.93759	0.968794	−	0.247867i	$-0.0797295\pi$
$463$	19303.4	1.93759	0.968794	+	0.247867i	$0.0797295\pi$
$464$	13827.5	1.38346
$465$	0	0
$466$	−673.400	−0.0669413
$467$	−17530.1	−1.73703	−0.868516	−	0.495661i	$-0.834926\pi$
$467$	−17530.1	−1.73703	−0.868516	+	0.495661i	$0.834926\pi$
$468$	−7307.72	−0.721794
$469$	−3566.45	−0.351138
$470$	0	0
$471$	852.161	0.0833662
$472$	376.127	0.0366793
$473$	690.819	0.0671541
$474$	77.0993	0.00747108
$475$	0	0
$476$	5721.31	0.550916
$477$	4595.30	0.441099
$478$	−349.039	−0.0333989
$479$	8032.49	0.766208	0.383104	−	0.923705i	$-0.374855\pi$
$479$	8032.49	0.766208	0.383104	+	0.923705i	$0.374855\pi$
$480$	0	0
$481$	−1403.08	−0.133004
$482$	515.412	0.0487062
$483$	−348.585	−0.0328388
$484$	10114.5	0.949896
$485$	0	0
$486$	−319.513	−0.0298218
$487$	3875.13	0.360573	0.180286	−	0.983614i	$-0.442298\pi$
$487$	3875.13	0.360573	0.180286	+	0.983614i	$0.442298\pi$
$488$	−100.981	−0.00936719
$489$	−2954.82	−0.273254
$490$	0	0
$491$	12215.0	1.12272	0.561358	−	0.827573i	$-0.310279\pi$
$491$	12215.0	1.12272	0.561358	+	0.827573i	$0.310279\pi$
$492$	−2224.33	−0.203822
$493$	24635.0	2.25051
$494$	−690.342	−0.0628744
$495$	0	0
$496$	−5173.09	−0.468304
$497$	24.3304	0.00219591
$498$	−13.8515	−0.00124639
$499$	−10016.6	−0.898611	−0.449305	−	0.893378i	$-0.648328\pi$
$499$	−10016.6	−0.898611	−0.449305	+	0.893378i	$0.648328\pi$
$500$	0	0
$501$	−2745.44	−0.244825
$502$	−559.836	−0.0497743
$503$	−15499.1	−1.37390	−0.686948	−	0.726707i	$-0.741050\pi$
$503$	−15499.1	−1.37390	−0.686948	+	0.726707i	$0.741050\pi$
$504$	−333.430	−0.0294685
$505$	0	0
$506$	46.7962	0.00411135
$507$	1108.63	0.0971123
$508$	−3472.60	−0.303291
$509$	−2221.82	−0.193478	−0.0967392	−	0.995310i	$-0.530841\pi$
$509$	−2221.82	−0.193478	−0.0967392	+	0.995310i	$0.530841\pi$
$510$	0	0
$511$	1770.48	0.153271
$512$	2625.24	0.226602
$513$	9524.43	0.819715
$514$	325.968	0.0279725
$515$	0	0
$516$	−839.584	−0.0716291
$517$	376.124	0.0319960
$518$	−31.9757	−0.00271222
$519$	2761.58	0.233565
$520$	0	0
$521$	−9655.51	−0.811930	−0.405965	−	0.913889i	$-0.633065\pi$
$521$	−9655.51	−0.811930	−0.405965	+	0.913889i	$0.633065\pi$
$522$	−717.094	−0.0601271
$523$	−8546.73	−0.714574	−0.357287	−	0.933995i	$-0.616298\pi$
$523$	−8546.73	−0.714574	−0.357287	+	0.933995i	$0.616298\pi$
$524$	14550.8	1.21308
$525$	0	0
$526$	−376.568	−0.0312151
$527$	−9216.31	−0.761801
$528$	620.064	0.0511077
$529$	−10120.5	−0.831802
$530$	0	0
$531$	4645.17	0.379629
$532$	7516.83	0.612586
$533$	8204.59	0.666755
$534$	−129.141	−0.0104653
$535$	0	0
$536$	−1164.99	−0.0938806
$537$	−392.840	−0.0315685
$538$	−158.959	−0.0127383
$539$	2424.76	0.193770
$540$	0	0
$541$	8854.58	0.703675	0.351837	−	0.936061i	$-0.385557\pi$
$541$	8854.58	0.703675	0.351837	+	0.936061i	$0.385557\pi$
$542$	374.974	0.0297168
$543$	1729.89	0.136716
$544$	2804.30	0.221017
$545$	0	0
$546$	−35.7332	−0.00280081
$547$	−1396.73	−0.109177	−0.0545884	−	0.998509i	$-0.517385\pi$
$547$	−1396.73	−0.109177	−0.0545884	+	0.998509i	$0.517385\pi$
$548$	10719.8	0.835634
$549$	−1247.12	−0.0969501
$550$	0	0
$551$	32366.1	2.50244
$552$	−113.866	−0.00877983
$553$	3096.56	0.238118
$554$	777.545	0.0596295
$555$	0	0
$556$	16232.9	1.23818
$557$	−14702.1	−1.11840	−0.559198	−	0.829034i	$-0.688891\pi$
$557$	−14702.1	−1.11840	−0.559198	+	0.829034i	$0.688891\pi$
$558$	268.276	0.0203531
$559$	3096.87	0.234317
$560$	0	0
$561$	1104.70	0.0831380
$562$	17.9555	0.00134770
$563$	3074.89	0.230180	0.115090	−	0.993355i	$-0.463284\pi$
$563$	3074.89	0.230180	0.115090	+	0.993355i	$0.463284\pi$
$564$	−457.121	−0.0341281
$565$	0	0
$566$	−1067.28	−0.0792602
$567$	−3864.40	−0.286225
$568$	7.94759	0.000587101 0
$569$	22066.2	1.62577	0.812884	−	0.582425i	$-0.197896\pi$
$569$	22066.2	1.62577	0.812884	+	0.582425i	$0.197896\pi$
$570$	0	0
$571$	940.599	0.0689366	0.0344683	−	0.999406i	$-0.489026\pi$
$571$	940.599	0.0689366	0.0344683	+	0.999406i	$0.489026\pi$
$572$	−2291.96	−0.167538
$573$	−689.975	−0.0503038
$574$	186.980	0.0135965
$575$	0	0
$576$	12900.6	0.933206
$577$	−24716.0	−1.78326	−0.891628	−	0.452768i	$-0.850436\pi$
$577$	−24716.0	−1.78326	−0.891628	+	0.452768i	$0.850436\pi$
$578$	1024.49	0.0737252
$579$	−786.429	−0.0564471
$580$	0	0
$581$	−556.322	−0.0397248
$582$	−226.945	−0.0161635
$583$	1441.25	0.102385
$584$	578.332	0.0409787
$585$	0	0
$586$	−1079.16	−0.0760749
$587$	25041.8	1.76080	0.880398	−	0.474235i	$-0.157275\pi$
$587$	25041.8	1.76080	0.880398	+	0.474235i	$0.157275\pi$
$588$	−2946.93	−0.206682
$589$	−12108.7	−0.847078
$590$	0	0
$591$	−5060.77	−0.352237
$592$	2487.38	0.172687
$593$	−13049.2	−0.903655	−0.451827	−	0.892105i	$-0.649228\pi$
$593$	−13049.2	−0.903655	−0.451827	+	0.892105i	$0.649228\pi$
$594$	−66.1834	−0.00457161
$595$	0	0
$596$	21003.2	1.44350
$597$	802.162	0.0549922
$598$	209.782	0.0143455
$599$	−4131.86	−0.281842	−0.140921	−	0.990021i	$-0.545006\pi$
$599$	−4131.86	−0.281842	−0.140921	+	0.990021i	$0.545006\pi$
$600$	0	0
$601$	−10984.7	−0.745551	−0.372775	−	0.927922i	$-0.621594\pi$
$601$	−10984.7	−0.745551	−0.372775	+	0.927922i	$0.621594\pi$
$602$	70.5765	0.00477821
$603$	−14387.7	−0.971660
$604$	18806.4	1.26693
$605$	0	0
$606$	9.22288	0.000618241 0
$607$	1875.13	0.125386	0.0626930	−	0.998033i	$-0.480031\pi$
$607$	1875.13	0.125386	0.0626930	+	0.998033i	$0.480031\pi$
$608$	3684.37	0.245758
$609$	1675.32	0.111474
$610$	0	0
$611$	1686.12	0.111642
$612$	23080.7	1.52448
$613$	9852.52	0.649167	0.324584	−	0.945857i	$-0.394776\pi$
$613$	9852.52	0.649167	0.324584	+	0.945857i	$0.394776\pi$
$614$	584.148	0.0383946
$615$	0	0
$616$	−104.575	−0.00684003
$617$	−23197.7	−1.51362	−0.756810	−	0.653635i	$-0.773243\pi$
$617$	−23197.7	−1.51362	−0.756810	+	0.653635i	$0.773243\pi$
$618$	−94.8743	−0.00617541
$619$	−6217.12	−0.403695	−0.201847	−	0.979417i	$-0.564695\pi$
$619$	−6217.12	−0.403695	−0.201847	+	0.979417i	$0.564695\pi$
$620$	0	0
$621$	−2894.30	−0.187028
$622$	−353.465	−0.0227856
$623$	−5186.73	−0.333551
$624$	2779.68	0.178327
$625$	0	0
$626$	1076.40	0.0687245
$627$	1451.39	0.0924446
$628$	5584.09	0.354824
$629$	4431.49	0.280914
$630$	0	0
$631$	13322.4	0.840501	0.420251	−	0.907408i	$-0.361942\pi$
$631$	13322.4	0.840501	0.420251	+	0.907408i	$0.361942\pi$
$632$	1011.50	0.0636634
$633$	3029.35	0.190215
$634$	1017.11	0.0637140
$635$	0	0
$636$	−1751.61	−0.109208
$637$	10870.0	0.676112
$638$	−224.906	−0.0139563
$639$	98.1529	0.00607648
$640$	0	0
$641$	−7097.75	−0.437355	−0.218677	−	0.975797i	$-0.570174\pi$
$641$	−7097.75	−0.437355	−0.218677	+	0.975797i	$0.570174\pi$
$642$	115.372	0.00709248
$643$	3592.65	0.220343	0.110171	−	0.993913i	$-0.464860\pi$
$643$	3592.65	0.220343	0.110171	+	0.993913i	$0.464860\pi$
$644$	−2284.23	−0.139769
$645$	0	0
$646$	2180.38	0.132795
$647$	−24757.8	−1.50437	−0.752187	−	0.658950i	$-0.771001\pi$
$647$	−24757.8	−1.50437	−0.752187	+	0.658950i	$0.771001\pi$
$648$	−1262.32	−0.0765254
$649$	1456.89	0.0881170
$650$	0	0
$651$	−626.764	−0.0377340
$652$	−19362.5	−1.16303
$653$	−26129.5	−1.56589	−0.782945	−	0.622091i	$-0.786283\pi$
$653$	−26129.5	−1.56589	−0.782945	+	0.622091i	$0.786283\pi$
$654$	138.395	0.00827471
$655$	0	0
$656$	−14545.1	−0.865688
$657$	7142.42	0.424128
$658$	38.4262	0.00227661
$659$	6934.27	0.409895	0.204947	−	0.978773i	$-0.434298\pi$
$659$	6934.27	0.409895	0.204947	+	0.978773i	$0.434298\pi$
$660$	0	0
$661$	−9453.53	−0.556278	−0.278139	−	0.960541i	$-0.589718\pi$
$661$	−9453.53	−0.556278	−0.278139	+	0.960541i	$0.589718\pi$
$662$	75.7002	0.00444437
$663$	4952.24	0.290089
$664$	−181.724	−0.0106209
$665$	0	0
$666$	−128.995	−0.00750521
$667$	−9835.47	−0.570961
$668$	−17990.5	−1.04203
$669$	−5058.77	−0.292352
$670$	0	0
$671$	−391.140	−0.0225034
$672$	190.709	0.0109476
$673$	18934.7	1.08452	0.542259	−	0.840211i	$-0.317569\pi$
$673$	18934.7	1.08452	0.542259	+	0.840211i	$0.317569\pi$
$674$	−1159.43	−0.0662605
$675$	0	0
$676$	7264.68	0.413330
$677$	34328.2	1.94880	0.974400	−	0.224820i	$-0.0721793\pi$
$677$	34328.2	1.94880	0.974400	+	0.224820i	$0.0721793\pi$
$678$	42.0648	0.00238273
$679$	−9114.83	−0.515162
$680$	0	0
$681$	3708.11	0.208656
$682$	84.1408	0.00472422
$683$	22407.3	1.25533	0.627665	−	0.778484i	$-0.284011\pi$
$683$	22407.3	1.25533	0.627665	+	0.778484i	$0.284011\pi$
$684$	30324.2	1.69514
$685$	0	0
$686$	528.152	0.0293950
$687$	−4554.03	−0.252907
$688$	−5490.13	−0.304229
$689$	6460.96	0.357246
$690$	0	0
$691$	−26355.2	−1.45094	−0.725468	−	0.688256i	$-0.758377\pi$
$691$	−26355.2	−1.45094	−0.725468	+	0.688256i	$0.758377\pi$
$692$	18096.2	0.994098
$693$	−1291.51	−0.0707941
$694$	−210.919	−0.0115366
$695$	0	0
$696$	547.249	0.0298038
$697$	−25913.4	−1.40823
$698$	−1219.19	−0.0661131
$699$	6346.72	0.343427
$700$	0	0
$701$	17651.3	0.951043	0.475521	−	0.879704i	$-0.342259\pi$
$701$	17651.3	0.951043	0.475521	+	0.879704i	$0.342259\pi$
$702$	−296.693	−0.0159515
$703$	5822.22	0.312360
$704$	4046.10	0.216609
$705$	0	0
$706$	549.397	0.0292873
$707$	370.421	0.0197045
$708$	−1770.62	−0.0939889
$709$	906.005	0.0479912	0.0239956	−	0.999712i	$-0.492361\pi$
$709$	906.005	0.0479912	0.0239956	+	0.999712i	$0.492361\pi$
$710$	0	0
$711$	12492.0	0.658914
$712$	−1694.26	−0.0891785
$713$	3679.60	0.193271
$714$	112.860	0.00591551
$715$	0	0
$716$	−2574.22	−0.134362
$717$	3289.66	0.171345
$718$	−851.140	−0.0442399
$719$	−602.629	−0.0312577	−0.0156288	−	0.999878i	$-0.504975\pi$
$719$	−602.629	−0.0312577	−0.0156288	+	0.999878i	$0.504975\pi$
$720$	0	0
$721$	−3810.46	−0.196822
$722$	1978.03	0.101959
$723$	−4857.71	−0.249876
$724$	11335.8	0.581892
$725$	0	0
$726$	199.521	0.0101996
$727$	−2968.50	−0.151438	−0.0757192	−	0.997129i	$-0.524125\pi$
$727$	−2968.50	−0.151438	−0.0757192	+	0.997129i	$0.524125\pi$
$728$	−468.800	−0.0238666
$729$	−13485.1	−0.685113
$730$	0	0
$731$	−9781.15	−0.494896
$732$	475.370	0.0240030
$733$	22429.8	1.13024	0.565119	−	0.825010i	$-0.308830\pi$
$733$	22429.8	1.13024	0.565119	+	0.825010i	$0.308830\pi$
$734$	−1256.51	−0.0631863
$735$	0	0
$736$	−1119.61	−0.0560727
$737$	−4512.48	−0.225535
$738$	754.308	0.0376239
$739$	−240.420	−0.0119675	−0.00598376	−	0.999982i	$-0.501905\pi$
$739$	−240.420	−0.0119675	−0.00598376	+	0.999982i	$0.501905\pi$
$740$	0	0
$741$	6506.40	0.322562
$742$	147.243	0.00728499
$743$	29874.9	1.47511	0.737554	−	0.675288i	$-0.235981\pi$
$743$	29874.9	1.47511	0.737554	+	0.675288i	$0.235981\pi$
$744$	−204.734	−0.0100886
$745$	0	0
$746$	1140.51	0.0559745
$747$	−2244.30	−0.109926
$748$	7238.93	0.353852
$749$	4633.71	0.226051
$750$	0	0
$751$	28100.3	1.36537	0.682686	−	0.730712i	$-0.260812\pi$
$751$	28100.3	1.36537	0.682686	+	0.730712i	$0.260812\pi$
$752$	−2989.17	−0.144952
$753$	5276.40	0.255355
$754$	−1008.23	−0.0486970
$755$	0	0
$756$	3230.56	0.155416
$757$	9885.75	0.474641	0.237321	−	0.971431i	$-0.423731\pi$
$757$	9885.75	0.474641	0.237321	+	0.971431i	$0.423731\pi$
$758$	−1271.80	−0.0609416
$759$	−441.049	−0.0210923
$760$	0	0
$761$	−19450.9	−0.926538	−0.463269	−	0.886218i	$-0.653324\pi$
$761$	−19450.9	−0.926538	−0.463269	+	0.886218i	$0.653324\pi$
$762$	−68.5014	−0.00325662
$763$	5558.38	0.263731
$764$	−4521.30	−0.214103
$765$	0	0
$766$	1129.90	0.0532963
$767$	6531.08	0.307462
$768$	−4886.22	−0.229579
$769$	3163.33	0.148339	0.0741693	−	0.997246i	$-0.476369\pi$
$769$	3163.33	0.148339	0.0741693	+	0.997246i	$0.476369\pi$
$770$	0	0
$771$	−3072.22	−0.143506
$772$	−5153.36	−0.240251
$773$	−19723.6	−0.917734	−0.458867	−	0.888505i	$-0.651745\pi$
$773$	−19723.6	−0.917734	−0.458867	+	0.888505i	$0.651745\pi$
$774$	284.717	0.0132222
$775$	0	0
$776$	−2977.38	−0.137734
$777$	301.368	0.0139144
$778$	−208.114	−0.00959028
$779$	−34045.8	−1.56588
$780$	0	0
$781$	30.7842	0.00141043
$782$	−662.577	−0.0302988
$783$	13910.2	0.634879
$784$	−19270.3	−0.877837
$785$	0	0
$786$	287.033	0.0130256
$787$	8787.41	0.398014	0.199007	−	0.979998i	$-0.436228\pi$
$787$	8787.41	0.398014	0.199007	+	0.979998i	$0.436228\pi$
$788$	−33162.5	−1.49919
$789$	3549.11	0.160142
$790$	0	0
$791$	1689.46	0.0759421
$792$	−421.874	−0.0189276
$793$	−1753.44	−0.0785200
$794$	−1222.38	−0.0546354
$795$	0	0
$796$	5256.45	0.234058
$797$	4142.26	0.184098	0.0920492	−	0.995754i	$-0.470658\pi$
$797$	4142.26	0.184098	0.0920492	+	0.995754i	$0.470658\pi$
$798$	148.279	0.00657771
$799$	−5325.46	−0.235796
$800$	0	0
$801$	−20924.2	−0.922994
$802$	−411.445	−0.0181155
$803$	2240.11	0.0984457
$804$	5484.22	0.240564
$805$	0	0
$806$	377.194	0.0164840
$807$	1498.18	0.0653510
$808$	120.999	0.00526822
$809$	−25911.5	−1.12608	−0.563041	−	0.826429i	$-0.690369\pi$
$809$	−25911.5	−1.12608	−0.563041	+	0.826429i	$0.690369\pi$
$810$	0	0
$811$	−3669.03	−0.158862	−0.0794309	−	0.996840i	$-0.525310\pi$
$811$	−3669.03	−0.158862	−0.0794309	+	0.996840i	$0.525310\pi$
$812$	10978.2	0.474456
$813$	−3534.09	−0.152455
$814$	−40.4575	−0.00174206
$815$	0	0
$816$	−8779.35	−0.376641
$817$	−12850.8	−0.550295
$818$	−1013.15	−0.0433058
$819$	−5789.69	−0.247018
$820$	0	0
$821$	1990.83	0.0846291	0.0423145	−	0.999104i	$-0.486527\pi$
$821$	1990.83	0.0846291	0.0423145	+	0.999104i	$0.486527\pi$
$822$	211.461	0.00897270
$823$	−8381.67	−0.355002	−0.177501	−	0.984121i	$-0.556801\pi$
$823$	−8381.67	−0.355002	−0.177501	+	0.984121i	$0.556801\pi$
$824$	−1244.70	−0.0526226
$825$	0	0
$826$	148.841	0.00626978
$827$	19405.7	0.815964	0.407982	−	0.912990i	$-0.366233\pi$
$827$	19405.7	0.815964	0.407982	+	0.912990i	$0.366233\pi$
$828$	−9214.95	−0.386765
$829$	−26704.0	−1.11878	−0.559389	−	0.828905i	$-0.688964\pi$
$829$	−26704.0	−1.11878	−0.559389	+	0.828905i	$0.688964\pi$
$830$	0	0
$831$	−7328.28	−0.305915
$832$	18138.2	0.755804
$833$	−34331.7	−1.42800
$834$	320.214	0.0132951
$835$	0	0
$836$	9510.72	0.393463
$837$	−5204.02	−0.214907
$838$	−761.222	−0.0313795
$839$	−22391.6	−0.921386	−0.460693	−	0.887560i	$-0.652399\pi$
$839$	−22391.6	−0.921386	−0.460693	+	0.887560i	$0.652399\pi$
$840$	0	0
$841$	22881.0	0.938169
$842$	−0.353912	−1.44853e−5 0
$843$	−169.229	−0.00691405
$844$	19850.9	0.809593
$845$	0	0
$846$	155.018	0.00629978
$847$	8013.40	0.325081
$848$	−11454.0	−0.463835
$849$	10059.0	0.406626
$850$	0	0
$851$	−1769.27	−0.0712687
$852$	−37.4135	−0.00150442
$853$	−764.822	−0.0306999	−0.0153499	−	0.999882i	$-0.504886\pi$
$853$	−764.822	−0.0306999	−0.0153499	+	0.999882i	$0.504886\pi$
$854$	−39.9602	−0.00160118
$855$	0	0
$856$	1513.62	0.0604373
$857$	−5188.48	−0.206809	−0.103404	−	0.994639i	$-0.532974\pi$
$857$	−5188.48	−0.206809	−0.103404	+	0.994639i	$0.532974\pi$
$858$	−45.2117	−0.00179895
$859$	−16688.7	−0.662878	−0.331439	−	0.943477i	$-0.607534\pi$
$859$	−16688.7	−0.662878	−0.331439	+	0.943477i	$0.607534\pi$
$860$	0	0
$861$	−1762.27	−0.0697536
$862$	2312.54	0.0913751
$863$	42559.5	1.67873	0.839364	−	0.543570i	$-0.182928\pi$
$863$	42559.5	1.67873	0.839364	+	0.543570i	$0.182928\pi$
$864$	1583.46	0.0623499
$865$	0	0
$866$	−1526.83	−0.0599119
$867$	−9655.71	−0.378230
$868$	−4107.10	−0.160604
$869$	3917.94	0.152943
$870$	0	0
$871$	−20229.0	−0.786948
$872$	1815.66	0.0705115
$873$	−36770.8	−1.42555
$874$	−870.513	−0.0336905
$875$	0	0
$876$	−2722.51	−0.105006
$877$	−1997.00	−0.0768917	−0.0384459	−	0.999261i	$-0.512241\pi$
$877$	−1997.00	−0.0768917	−0.0384459	+	0.999261i	$0.512241\pi$
$878$	887.303	0.0341059
$879$	10171.0	0.390284
$880$	0	0
$881$	−2016.92	−0.0771302	−0.0385651	−	0.999256i	$-0.512279\pi$
$881$	−2016.92	−0.0771302	−0.0385651	+	0.999256i	$0.512279\pi$
$882$	999.354	0.0381519
$883$	−27127.0	−1.03386	−0.516928	−	0.856029i	$-0.672925\pi$
$883$	−27127.0	−1.03386	−0.516928	+	0.856029i	$0.672925\pi$
$884$	32451.3	1.23468
$885$	0	0
$886$	−1682.72	−0.0638059
$887$	41848.3	1.58414	0.792068	−	0.610433i	$-0.209005\pi$
$887$	41848.3	1.58414	0.792068	+	0.610433i	$0.209005\pi$
$888$	98.4426	0.00372018
$889$	−2751.24	−0.103795
$890$	0	0
$891$	−4889.45	−0.183842
$892$	−33149.4	−1.24431
$893$	−6996.74	−0.262192
$894$	414.314	0.0154997
$895$	0	0
$896$	1665.67	0.0621050
$897$	−1977.18	−0.0735964
$898$	64.0251	0.00237923
$899$	−17684.4	−0.656072
$900$	0	0
$901$	−20406.3	−0.754531
$902$	236.578	0.00873300
$903$	−665.176	−0.0245135
$904$	551.866	0.0203040
$905$	0	0
$906$	370.980	0.0136037
$907$	635.189	0.0232537	0.0116268	−	0.999932i	$-0.496299\pi$
$907$	635.189	0.0232537	0.0116268	+	0.999932i	$0.496299\pi$
$908$	24298.7	0.888084
$909$	1494.34	0.0545259
$910$	0	0
$911$	−9050.59	−0.329154	−0.164577	−	0.986364i	$-0.552626\pi$
$911$	−9050.59	−0.329154	−0.164577	+	0.986364i	$0.552626\pi$
$912$	−11534.6	−0.418802
$913$	−703.890	−0.0255152
$914$	−1039.68	−0.0376254
$915$	0	0
$916$	−29841.9	−1.07642
$917$	11528.2	0.415151
$918$	937.076	0.0336908
$919$	−17359.9	−0.623123	−0.311561	−	0.950226i	$-0.600852\pi$
$919$	−17359.9	−0.623123	−0.311561	+	0.950226i	$0.600852\pi$
$920$	0	0
$921$	−5505.53	−0.196975
$922$	−1033.35	−0.0369106
$923$	138.002	0.00492134
$924$	492.290	0.0175272
$925$	0	0
$926$	2495.21	0.0885506
$927$	−15372.0	−0.544642
$928$	5380.94	0.190343
$929$	−35216.6	−1.24372	−0.621862	−	0.783127i	$-0.713623\pi$
$929$	−35216.6	−1.24372	−0.621862	+	0.783127i	$0.713623\pi$
$930$	0	0
$931$	−45106.0	−1.58785
$932$	41589.2	1.46169
$933$	3331.37	0.116896
$934$	−2265.99	−0.0793849
$935$	0	0
$936$	−1891.22	−0.0660431
$937$	−16036.6	−0.559119	−0.279559	−	0.960128i	$-0.590188\pi$
$937$	−16036.6	−0.559119	−0.279559	+	0.960128i	$0.590188\pi$
$938$	−461.011	−0.0160475
$939$	−10144.9	−0.352575
$940$	0	0
$941$	−53642.9	−1.85835	−0.929176	−	0.369637i	$-0.879482\pi$
$941$	−53642.9	−1.85835	−0.929176	+	0.369637i	$0.879482\pi$
$942$	110.153	0.00380996
$943$	10345.9	0.357273
$944$	−11578.3	−0.399197
$945$	0	0
$946$	89.2974	0.00306904
$947$	−13020.0	−0.446772	−0.223386	−	0.974730i	$-0.571711\pi$
$947$	−13020.0	−0.446772	−0.223386	+	0.974730i	$0.571711\pi$
$948$	−4761.65	−0.163134
$949$	10042.2	0.343502
$950$	0	0
$951$	−9586.18	−0.326870
$952$	1480.66	0.0504080
$953$	12519.5	0.425548	0.212774	−	0.977101i	$-0.431750\pi$
$953$	12519.5	0.425548	0.212774	+	0.977101i	$0.431750\pi$
$954$	594.003	0.0201589
$955$	0	0
$956$	21556.7	0.729281
$957$	2119.72	0.0715995
$958$	1038.31	0.0350168
$959$	8492.97	0.285977
$960$	0	0
$961$	−23175.0	−0.777919
$962$	−181.366	−0.00607847
$963$	18693.2	0.625524
$964$	−31831.9	−1.06352
$965$	0	0
$966$	−45.0592	−0.00150078
$967$	−29837.8	−0.992264	−0.496132	−	0.868247i	$-0.665247\pi$
$967$	−29837.8	−0.992264	−0.496132	+	0.868247i	$0.665247\pi$
$968$	2617.60	0.0869141
$969$	−20549.8	−0.681275
$970$	0	0
$971$	6450.28	0.213181	0.106591	−	0.994303i	$-0.466007\pi$
$971$	6450.28	0.213181	0.106591	+	0.994303i	$0.466007\pi$
$972$	19733.1	0.651172
$973$	12860.8	0.423740
$974$	500.912	0.0164787
$975$	0	0
$976$	3108.50	0.101947
$977$	14558.4	0.476730	0.238365	−	0.971176i	$-0.423389\pi$
$977$	14558.4	0.476730	0.238365	+	0.971176i	$0.423389\pi$
$978$	−381.949	−0.0124881
$979$	−6562.55	−0.214239
$980$	0	0
$981$	22423.4	0.729791
$982$	1578.95	0.0513098
$983$	3890.97	0.126249	0.0631244	−	0.998006i	$-0.479894\pi$
$983$	3890.97	0.126249	0.0631244	+	0.998006i	$0.479894\pi$
$984$	−575.649	−0.0186494
$985$	0	0
$986$	3184.39	0.102852
$987$	−362.163	−0.0116796
$988$	42635.5	1.37289
$989$	3905.11	0.125556
$990$	0	0
$991$	−30500.7	−0.977686	−0.488843	−	0.872372i	$-0.662581\pi$
$991$	−30500.7	−0.977686	−0.488843	+	0.872372i	$0.662581\pi$
$992$	−2013.09	−0.0644312
$993$	−713.466	−0.0228008
$994$	3.14503	0.000100356 0
$995$	0	0
$996$	855.470	0.0272155
$997$	15056.1	0.478266	0.239133	−	0.970987i	$-0.423137\pi$
$997$	15056.1	0.478266	0.239133	+	0.970987i	$0.423137\pi$
$998$	−1294.78	−0.0410678
$999$	2502.26	0.0792471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.4.a.h.1.9	yes	18
5.4	even	2		1175.4.a.g.1.10	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1175.4.a.g.1.10	✓	18	5.4	even	2
1175.4.a.h.1.9	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q+0.129263 q^{2} -1.21829 q^{3} -7.98329 q^{4} -0.157480 q^{6} -6.32492 q^{7} -2.06605 q^{8} -25.5158 q^{9} +O(q^{10})\)	\(q+0.129263 q^{2} -1.21829 q^{3} -7.98329 q^{4} -0.157480 q^{6} -6.32492 q^{7} -2.06605 q^{8} -25.5158 q^{9} -8.00264 q^{11} +9.72598 q^{12} -35.8750 q^{13} -0.817579 q^{14} +63.5993 q^{16} +113.308 q^{17} -3.29825 q^{18} +148.867 q^{19} +7.70559 q^{21} -1.03445 q^{22} -45.2379 q^{23} +2.51705 q^{24} -4.63731 q^{26} +63.9795 q^{27} +50.4936 q^{28} +217.417 q^{29} -81.3389 q^{31} +24.7494 q^{32} +9.74955 q^{33} +14.6465 q^{34} +203.700 q^{36} +39.1103 q^{37} +19.2430 q^{38} +43.7062 q^{39} -228.699 q^{41} +0.996049 q^{42} -86.3238 q^{43} +63.8874 q^{44} -5.84759 q^{46} -47.0000 q^{47} -77.4825 q^{48} -302.995 q^{49} -138.042 q^{51} +286.400 q^{52} -180.096 q^{53} +8.27020 q^{54} +13.0676 q^{56} -181.363 q^{57} +28.1040 q^{58} -182.051 q^{59} +48.8763 q^{61} -10.5141 q^{62} +161.385 q^{63} -505.595 q^{64} +1.26026 q^{66} +563.874 q^{67} -904.568 q^{68} +55.1129 q^{69} -3.84676 q^{71} +52.7169 q^{72} -279.922 q^{73} +5.05551 q^{74} -1188.45 q^{76} +50.6160 q^{77} +5.64960 q^{78} -489.581 q^{79} +610.980 q^{81} -29.5624 q^{82} +87.9572 q^{83} -61.5160 q^{84} -11.1585 q^{86} -264.877 q^{87} +16.5339 q^{88} +820.048 q^{89} +226.906 q^{91} +361.147 q^{92} +99.0945 q^{93} -6.07537 q^{94} -30.1520 q^{96} +1441.10 q^{97} -39.1662 q^{98} +204.194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} + 7 q^{3} + 57 q^{4} - 14 q^{6} + 6 q^{7} - 18 q^{8} + 57 q^{9}+O(q^{10}) \) 18 * q + q^2 + 7 * q^3 + 57 * q^4 - 14 * q^6 + 6 * q^7 - 18 * q^8 + 57 * q^9	\( 18 q + q^{2} + 7 q^{3} + 57 q^{4} - 14 q^{6} + 6 q^{7} - 18 q^{8} + 57 q^{9} - 31 q^{11} - 31 q^{12} - 16 q^{13} - 229 q^{14} + 41 q^{16} + 5 q^{17} + 109 q^{18} - 283 q^{19} - 338 q^{21} - 214 q^{22} + 160 q^{23} - 324 q^{24} - 197 q^{26} - 11 q^{27} + 264 q^{28} - 464 q^{29} - 390 q^{31} - 168 q^{32} - 237 q^{33} - 824 q^{34} - 621 q^{36} - 362 q^{37} + 19 q^{38} - 378 q^{39} - 591 q^{41} + 79 q^{42} - 54 q^{43} - 859 q^{44} - 1164 q^{46} - 846 q^{47} - 484 q^{48} - 662 q^{49} - 1796 q^{51} + 502 q^{52} - 260 q^{53} - 62 q^{54} - 1261 q^{56} + 759 q^{57} - 805 q^{58} - 44 q^{59} - 1754 q^{61} + 1168 q^{62} - 2133 q^{63} - 1304 q^{64} - 2051 q^{66} + 1593 q^{67} - 1418 q^{68} - 1536 q^{69} - 2214 q^{71} + 1890 q^{72} - 1831 q^{73} + 477 q^{74} - 4034 q^{76} + 1406 q^{77} - 2903 q^{78} - 2268 q^{79} - 2610 q^{81} + 2299 q^{82} - 1794 q^{83} - 611 q^{84} - 3005 q^{86} + 2296 q^{87} - 2793 q^{88} - 1505 q^{89} - 3626 q^{91} + 2379 q^{92} - 1770 q^{93} - 47 q^{94} - 5976 q^{96} + 2436 q^{97} - 3428 q^{98} - 1456 q^{99}+O(q^{100}) \) 18 * q + q^2 + 7 * q^3 + 57 * q^4 - 14 * q^6 + 6 * q^7 - 18 * q^8 + 57 * q^9 - 31 * q^11 - 31 * q^12 - 16 * q^13 - 229 * q^14 + 41 * q^16 + 5 * q^17 + 109 * q^18 - 283 * q^19 - 338 * q^21 - 214 * q^22 + 160 * q^23 - 324 * q^24 - 197 * q^26 - 11 * q^27 + 264 * q^28 - 464 * q^29 - 390 * q^31 - 168 * q^32 - 237 * q^33 - 824 * q^34 - 621 * q^36 - 362 * q^37 + 19 * q^38 - 378 * q^39 - 591 * q^41 + 79 * q^42 - 54 * q^43 - 859 * q^44 - 1164 * q^46 - 846 * q^47 - 484 * q^48 - 662 * q^49 - 1796 * q^51 + 502 * q^52 - 260 * q^53 - 62 * q^54 - 1261 * q^56 + 759 * q^57 - 805 * q^58 - 44 * q^59 - 1754 * q^61 + 1168 * q^62 - 2133 * q^63 - 1304 * q^64 - 2051 * q^66 + 1593 * q^67 - 1418 * q^68 - 1536 * q^69 - 2214 * q^71 + 1890 * q^72 - 1831 * q^73 + 477 * q^74 - 4034 * q^76 + 1406 * q^77 - 2903 * q^78 - 2268 * q^79 - 2610 * q^81 + 2299 * q^82 - 1794 * q^83 - 611 * q^84 - 3005 * q^86 + 2296 * q^87 - 2793 * q^88 - 1505 * q^89 - 3626 * q^91 + 2379 * q^92 - 1770 * q^93 - 47 * q^94 - 5976 * q^96 + 2436 * q^97 - 3428 * q^98 - 1456 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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