LMFDB - Embedded newform 7935.2.a.bp.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.523893$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.523893 q^{2} -1.00000 q^{3} -1.72554 q^{4} -1.00000 q^{5} -0.523893 q^{6} -3.44277 q^{7} -1.95178 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.523893 q^{2} -1.00000 q^{3} -1.72554 q^{4} -1.00000 q^{5} -0.523893 q^{6} -3.44277 q^{7} -1.95178 q^{8} +1.00000 q^{9} -0.523893 q^{10} +3.03893 q^{11} +1.72554 q^{12} -5.69114 q^{13} -1.80364 q^{14} +1.00000 q^{15} +2.42855 q^{16} +3.41423 q^{17} +0.523893 q^{18} -4.93298 q^{19} +1.72554 q^{20} +3.44277 q^{21} +1.59207 q^{22} +1.95178 q^{24} +1.00000 q^{25} -2.98155 q^{26} -1.00000 q^{27} +5.94063 q^{28} +5.89421 q^{29} +0.523893 q^{30} +4.05776 q^{31} +5.17586 q^{32} -3.03893 q^{33} +1.78869 q^{34} +3.44277 q^{35} -1.72554 q^{36} -3.08493 q^{37} -2.58436 q^{38} +5.69114 q^{39} +1.95178 q^{40} -8.27734 q^{41} +1.80364 q^{42} +3.73441 q^{43} -5.24378 q^{44} -1.00000 q^{45} +6.25801 q^{47} -2.42855 q^{48} +4.85268 q^{49} +0.523893 q^{50} -3.41423 q^{51} +9.82027 q^{52} -2.95432 q^{53} -0.523893 q^{54} -3.03893 q^{55} +6.71954 q^{56} +4.93298 q^{57} +3.08794 q^{58} +3.07863 q^{59} -1.72554 q^{60} +8.01885 q^{61} +2.12583 q^{62} -3.44277 q^{63} -2.14549 q^{64} +5.69114 q^{65} -1.59207 q^{66} +11.7456 q^{67} -5.89138 q^{68} +1.80364 q^{70} -11.5634 q^{71} -1.95178 q^{72} +12.9119 q^{73} -1.61617 q^{74} -1.00000 q^{75} +8.51204 q^{76} -10.4623 q^{77} +2.98155 q^{78} +15.5829 q^{79} -2.42855 q^{80} +1.00000 q^{81} -4.33644 q^{82} -13.2187 q^{83} -5.94063 q^{84} -3.41423 q^{85} +1.95643 q^{86} -5.89421 q^{87} -5.93133 q^{88} -7.14601 q^{89} -0.523893 q^{90} +19.5933 q^{91} -4.05776 q^{93} +3.27853 q^{94} +4.93298 q^{95} -5.17586 q^{96} +9.56262 q^{97} +2.54229 q^{98} +3.03893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9}+O(q^{10}) $ 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9	$ 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} + q^{28} - 3 q^{29} - 22 q^{31} - 13 q^{33} + q^{34} + 5 q^{35} + 12 q^{36} - 6 q^{37} - 17 q^{38} + 24 q^{39} - 20 q^{41} - 15 q^{42} - 4 q^{43} - 18 q^{44} - 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} - 2 q^{51} - 55 q^{52} + 4 q^{53} - 13 q^{55} + 25 q^{56} - 13 q^{57} + 2 q^{58} + 9 q^{59} + 12 q^{60} + 13 q^{61} - 7 q^{62} - 5 q^{63} - 26 q^{64} + 24 q^{65} + 9 q^{66} - 32 q^{67} + 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} - 11 q^{74} - 15 q^{75} + 88 q^{76} - 21 q^{77} + 9 q^{78} + 33 q^{79} - 2 q^{80} + 15 q^{81} - 35 q^{82} - 12 q^{83} - q^{84} - 2 q^{85} + 77 q^{86} + 3 q^{87} - 37 q^{88} + 29 q^{89} + 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} + 18 q^{97} - 19 q^{98} + 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * 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 $

$2$	0.523893	0.370448	0.185224	−	0.982696i	$-0.440699\pi$
$2$	0.523893	0.370448	0.185224	+	0.982696i	$0.440699\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.72554	−0.862768
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.523893	−0.213878
$7$	−3.44277	−1.30125	−0.650623	−	0.759401i	$-0.725492\pi$
$7$	−3.44277	−1.30125	−0.650623	+	0.759401i	$0.725492\pi$
$8$	−1.95178	−0.690059
$9$	1.00000	0.333333
$10$	−0.523893	−0.165670
$11$	3.03893	0.916272	0.458136	−	0.888882i	$-0.348517\pi$
$11$	3.03893	0.916272	0.458136	+	0.888882i	$0.348517\pi$
$12$	1.72554	0.498119
$13$	−5.69114	−1.57844	−0.789219	−	0.614112i	$-0.789514\pi$
$13$	−5.69114	−1.57844	−0.789219	+	0.614112i	$0.789514\pi$
$14$	−1.80364	−0.482044
$15$	1.00000	0.258199
$16$	2.42855	0.607137
$17$	3.41423	0.828073	0.414036	−	0.910260i	$-0.364119\pi$
$17$	3.41423	0.828073	0.414036	+	0.910260i	$0.364119\pi$
$18$	0.523893	0.123483
$19$	−4.93298	−1.13170	−0.565852	−	0.824507i	$-0.691453\pi$
$19$	−4.93298	−1.13170	−0.565852	+	0.824507i	$0.691453\pi$
$20$	1.72554	0.385842
$21$	3.44277	0.751275
$22$	1.59207	0.339432
$23$	0	0
$23$	0	0
$24$	1.95178	0.398406
$25$	1.00000	0.200000
$26$	−2.98155	−0.584730
$27$	−1.00000	−0.192450
$28$	5.94063	1.12267
$29$	5.89421	1.09453	0.547264	−	0.836960i	$-0.315669\pi$
$29$	5.89421	1.09453	0.547264	+	0.836960i	$0.315669\pi$
$30$	0.523893	0.0956494
$31$	4.05776	0.728795	0.364398	−	0.931243i	$-0.381275\pi$
$31$	4.05776	0.728795	0.364398	+	0.931243i	$0.381275\pi$
$32$	5.17586	0.914972
$33$	−3.03893	−0.529010
$34$	1.78869	0.306758
$35$	3.44277	0.581935
$36$	−1.72554	−0.287589
$37$	−3.08493	−0.507159	−0.253579	−	0.967315i	$-0.581608\pi$
$37$	−3.08493	−0.507159	−0.253579	+	0.967315i	$0.581608\pi$
$38$	−2.58436	−0.419238
$39$	5.69114	0.911312
$40$	1.95178	0.308604
$41$	−8.27734	−1.29270	−0.646352	−	0.763040i	$-0.723706\pi$
$41$	−8.27734	−1.29270	−0.646352	+	0.763040i	$0.723706\pi$
$42$	1.80364	0.278308
$43$	3.73441	0.569492	0.284746	−	0.958603i	$-0.408091\pi$
$43$	3.73441	0.569492	0.284746	+	0.958603i	$0.408091\pi$
$44$	−5.24378	−0.790530
$45$	−1.00000	−0.149071
$46$	0	0
$47$	6.25801	0.912824	0.456412	−	0.889769i	$-0.349134\pi$
$47$	6.25801	0.912824	0.456412	+	0.889769i	$0.349134\pi$
$48$	−2.42855	−0.350530
$49$	4.85268	0.693240
$50$	0.523893	0.0740897
$51$	−3.41423	−0.478088
$52$	9.82027	1.36183
$53$	−2.95432	−0.405807	−0.202903	−	0.979199i	$-0.565038\pi$
$53$	−2.95432	−0.405807	−0.202903	+	0.979199i	$0.565038\pi$
$54$	−0.523893	−0.0712928
$55$	−3.03893	−0.409769
$56$	6.71954	0.897937
$57$	4.93298	0.653390
$58$	3.08794	0.405466
$59$	3.07863	0.400804	0.200402	−	0.979714i	$-0.435775\pi$
$59$	3.07863	0.400804	0.200402	+	0.979714i	$0.435775\pi$
$60$	−1.72554	−0.222766
$61$	8.01885	1.02671	0.513354	−	0.858177i	$-0.328403\pi$
$61$	8.01885	1.02671	0.513354	+	0.858177i	$0.328403\pi$
$62$	2.12583	0.269981
$63$	−3.44277	−0.433749
$64$	−2.14549	−0.268187
$65$	5.69114	0.705899
$66$	−1.59207	−0.195971
$67$	11.7456	1.43496	0.717478	−	0.696581i	$-0.245296\pi$
$67$	11.7456	1.43496	0.717478	+	0.696581i	$0.245296\pi$
$68$	−5.89138	−0.714435
$69$	0	0
$70$	1.80364	0.215577
$71$	−11.5634	−1.37232	−0.686162	−	0.727449i	$-0.740706\pi$
$71$	−11.5634	−1.37232	−0.686162	+	0.727449i	$0.740706\pi$
$72$	−1.95178	−0.230020
$73$	12.9119	1.51122	0.755611	−	0.655021i	$-0.227340\pi$
$73$	12.9119	1.51122	0.755611	+	0.655021i	$0.227340\pi$
$74$	−1.61617	−0.187876
$75$	−1.00000	−0.115470
$76$	8.51204	0.976398
$77$	−10.4623	−1.19230
$78$	2.98155	0.337594
$79$	15.5829	1.75321	0.876604	−	0.481212i	$-0.159803\pi$
$79$	15.5829	1.75321	0.876604	+	0.481212i	$0.159803\pi$
$80$	−2.42855	−0.271520
$81$	1.00000	0.111111
$82$	−4.33644	−0.478880
$83$	−13.2187	−1.45094	−0.725469	−	0.688255i	$-0.758377\pi$
$83$	−13.2187	−1.45094	−0.725469	+	0.688255i	$0.758377\pi$
$84$	−5.94063	−0.648176
$85$	−3.41423	−0.370325
$86$	1.95643	0.210967
$87$	−5.89421	−0.631926
$88$	−5.93133	−0.632282
$89$	−7.14601	−0.757476	−0.378738	−	0.925504i	$-0.623642\pi$
$89$	−7.14601	−0.757476	−0.378738	+	0.925504i	$0.623642\pi$
$90$	−0.523893	−0.0552232
$91$	19.5933	2.05394
$92$	0	0
$93$	−4.05776	−0.420770
$94$	3.27853	0.338154
$95$	4.93298	0.506114
$96$	−5.17586	−0.528259
$97$	9.56262	0.970937	0.485469	−	0.874254i	$-0.338649\pi$
$97$	9.56262	0.970937	0.485469	+	0.874254i	$0.338649\pi$
$98$	2.54229	0.256810
$99$	3.03893	0.305424
$100$	−1.72554	−0.172554
$101$	8.02293	0.798312	0.399156	−	0.916883i	$-0.369303\pi$
$101$	8.02293	0.798312	0.399156	+	0.916883i	$0.369303\pi$
$102$	−1.78869	−0.177107
$103$	−5.60122	−0.551904	−0.275952	−	0.961171i	$-0.588993\pi$
$103$	−5.60122	−0.551904	−0.275952	+	0.961171i	$0.588993\pi$
$104$	11.1079	1.08922
$105$	−3.44277	−0.335980
$106$	−1.54775	−0.150330
$107$	13.7106	1.32545	0.662726	−	0.748862i	$-0.269399\pi$
$107$	13.7106	1.32545	0.662726	+	0.748862i	$0.269399\pi$
$108$	1.72554	0.166040
$109$	9.62984	0.922372	0.461186	−	0.887304i	$-0.347424\pi$
$109$	9.62984	0.922372	0.461186	+	0.887304i	$0.347424\pi$
$110$	−1.59207	−0.151798
$111$	3.08493	0.292808
$112$	−8.36093	−0.790034
$113$	−8.25997	−0.777032	−0.388516	−	0.921442i	$-0.627012\pi$
$113$	−8.25997	−0.777032	−0.388516	+	0.921442i	$0.627012\pi$
$114$	2.58436	0.242047
$115$	0	0
$116$	−10.1707	−0.944323
$117$	−5.69114	−0.526146
$118$	1.61287	0.148477
$119$	−11.7544	−1.07753
$120$	−1.95178	−0.178173
$121$	−1.76490	−0.160445
$122$	4.20102	0.380342
$123$	8.27734	0.746343
$124$	−7.00181	−0.628781
$125$	−1.00000	−0.0894427
$126$	−1.80364	−0.160681
$127$	−0.754529	−0.0669536	−0.0334768	−	0.999439i	$-0.510658\pi$
$127$	−0.754529	−0.0669536	−0.0334768	+	0.999439i	$0.510658\pi$
$128$	−11.4757	−1.01432
$129$	−3.73441	−0.328796
$130$	2.98155	0.261499
$131$	−2.25401	−0.196934	−0.0984670	−	0.995140i	$-0.531394\pi$
$131$	−2.25401	−0.196934	−0.0984670	+	0.995140i	$0.531394\pi$
$132$	5.24378	0.456413
$133$	16.9831	1.47263
$134$	6.15345	0.531577
$135$	1.00000	0.0860663
$136$	−6.66384	−0.571419
$137$	4.53680	0.387605	0.193803	−	0.981041i	$-0.437918\pi$
$137$	4.53680	0.387605	0.193803	+	0.981041i	$0.437918\pi$
$138$	0	0
$139$	−13.2060	−1.12012	−0.560061	−	0.828452i	$-0.689222\pi$
$139$	−13.2060	−1.12012	−0.560061	+	0.828452i	$0.689222\pi$
$140$	−5.94063	−0.502075
$141$	−6.25801	−0.527019
$142$	−6.05799	−0.508375
$143$	−17.2950	−1.44628
$144$	2.42855	0.202379
$145$	−5.89421	−0.489488
$146$	6.76445	0.559830
$147$	−4.85268	−0.400242
$148$	5.32315	0.437561
$149$	3.32273	0.272209	0.136104	−	0.990695i	$-0.456542\pi$
$149$	3.32273	0.272209	0.136104	+	0.990695i	$0.456542\pi$
$150$	−0.523893	−0.0427757
$151$	1.82016	0.148122	0.0740612	−	0.997254i	$-0.476404\pi$
$151$	1.82016	0.148122	0.0740612	+	0.997254i	$0.476404\pi$
$152$	9.62811	0.780943
$153$	3.41423	0.276024
$154$	−5.48115	−0.441684
$155$	−4.05776	−0.325927
$156$	−9.82027	−0.786251
$157$	−22.7622	−1.81662	−0.908310	−	0.418297i	$-0.862627\pi$
$157$	−22.7622	−1.81662	−0.908310	+	0.418297i	$0.862627\pi$
$158$	8.16375	0.649473
$159$	2.95432	0.234293
$160$	−5.17586	−0.409188
$161$	0	0
$162$	0.523893	0.0411609
$163$	−22.3686	−1.75205	−0.876023	−	0.482269i	$-0.839813\pi$
$163$	−22.3686	−1.75205	−0.876023	+	0.482269i	$0.839813\pi$
$164$	14.2828	1.11530
$165$	3.03893	0.236580
$166$	−6.92517	−0.537498
$167$	−5.03240	−0.389419	−0.194709	−	0.980861i	$-0.562376\pi$
$167$	−5.03240	−0.389419	−0.194709	+	0.980861i	$0.562376\pi$
$168$	−6.71954	−0.518424
$169$	19.3891	1.49147
$170$	−1.78869	−0.137186
$171$	−4.93298	−0.377235
$172$	−6.44386	−0.491339
$173$	11.3375	0.861976	0.430988	−	0.902358i	$-0.358165\pi$
$173$	11.3375	0.861976	0.430988	+	0.902358i	$0.358165\pi$
$174$	−3.08794	−0.234096
$175$	−3.44277	−0.260249
$176$	7.38018	0.556302
$177$	−3.07863	−0.231404
$178$	−3.74375	−0.280606
$179$	19.4815	1.45611	0.728057	−	0.685516i	$-0.240424\pi$
$179$	19.4815	1.45611	0.728057	+	0.685516i	$0.240424\pi$
$180$	1.72554	0.128614
$181$	−6.96629	−0.517800	−0.258900	−	0.965904i	$-0.583360\pi$
$181$	−6.96629	−0.517800	−0.258900	+	0.965904i	$0.583360\pi$
$182$	10.2648	0.760877
$183$	−8.01885	−0.592770
$184$	0	0
$185$	3.08493	0.226808
$186$	−2.12583	−0.155874
$187$	10.3756	0.758740
$188$	−10.7984	−0.787555
$189$	3.44277	0.250425
$190$	2.58436	0.187489
$191$	−8.16189	−0.590574	−0.295287	−	0.955409i	$-0.595415\pi$
$191$	−8.16189	−0.590574	−0.295287	+	0.955409i	$0.595415\pi$
$192$	2.14549	0.154838
$193$	−7.72194	−0.555838	−0.277919	−	0.960605i	$-0.589645\pi$
$193$	−7.72194	−0.555838	−0.277919	+	0.960605i	$0.589645\pi$
$194$	5.00979	0.359682
$195$	−5.69114	−0.407551
$196$	−8.37348	−0.598106
$197$	−12.4046	−0.883790	−0.441895	−	0.897067i	$-0.645694\pi$
$197$	−12.4046	−0.883790	−0.441895	+	0.897067i	$0.645694\pi$
$198$	1.59207	0.113144
$199$	6.06341	0.429824	0.214912	−	0.976633i	$-0.431054\pi$
$199$	6.06341	0.429824	0.214912	+	0.976633i	$0.431054\pi$
$200$	−1.95178	−0.138012
$201$	−11.7456	−0.828472
$202$	4.20316	0.295733
$203$	−20.2924	−1.42425
$204$	5.89138	0.412479
$205$	8.27734	0.578114
$206$	−2.93444	−0.204452
$207$	0	0
$208$	−13.8212	−0.958328
$209$	−14.9910	−1.03695
$210$	−1.80364	−0.124463
$211$	−15.2126	−1.04728	−0.523638	−	0.851941i	$-0.675426\pi$
$211$	−15.2126	−1.04728	−0.523638	+	0.851941i	$0.675426\pi$
$212$	5.09778	0.350117
$213$	11.5634	0.792312
$214$	7.18288	0.491012
$215$	−3.73441	−0.254685
$216$	1.95178	0.132802
$217$	−13.9699	−0.948342
$218$	5.04501	0.341691
$219$	−12.9119	−0.872504
$220$	5.24378	0.353536
$221$	−19.4309	−1.30706
$222$	1.61617	0.108470
$223$	−21.5896	−1.44575	−0.722874	−	0.690980i	$-0.757179\pi$
$223$	−21.5896	−1.44575	−0.722874	+	0.690980i	$0.757179\pi$
$224$	−17.8193	−1.19060
$225$	1.00000	0.0666667
$226$	−4.32734	−0.287850
$227$	−20.2665	−1.34514	−0.672568	−	0.740035i	$-0.734809\pi$
$227$	−20.2665	−1.34514	−0.672568	+	0.740035i	$0.734809\pi$
$228$	−8.51204	−0.563724
$229$	28.3627	1.87426	0.937128	−	0.348985i	$-0.113474\pi$
$229$	28.3627	1.87426	0.937128	+	0.348985i	$0.113474\pi$
$230$	0	0
$231$	10.4623	0.688372
$232$	−11.5042	−0.755289
$233$	−23.6760	−1.55106	−0.775532	−	0.631308i	$-0.782519\pi$
$233$	−23.6760	−1.55106	−0.775532	+	0.631308i	$0.782519\pi$
$234$	−2.98155	−0.194910
$235$	−6.25801	−0.408227
$236$	−5.31229	−0.345800
$237$	−15.5829	−1.01222
$238$	−6.15806	−0.399168
$239$	−13.9181	−0.900284	−0.450142	−	0.892957i	$-0.648627\pi$
$239$	−13.9181	−0.900284	−0.450142	+	0.892957i	$0.648627\pi$
$240$	2.42855	0.156762
$241$	21.7825	1.40313	0.701566	−	0.712605i	$-0.252485\pi$
$241$	21.7825	1.40313	0.701566	+	0.712605i	$0.252485\pi$
$242$	−0.924619	−0.0594367
$243$	−1.00000	−0.0641500
$244$	−13.8368	−0.885811
$245$	−4.85268	−0.310026
$246$	4.33644	0.276481
$247$	28.0743	1.78633
$248$	−7.91987	−0.502912
$249$	13.2187	0.837700
$250$	−0.523893	−0.0331339
$251$	0.366842	0.0231549	0.0115774	−	0.999933i	$-0.496315\pi$
$251$	0.366842	0.0231549	0.0115774	+	0.999933i	$0.496315\pi$
$252$	5.94063	0.374224
$253$	0	0
$254$	−0.395292	−0.0248028
$255$	3.41423	0.213807
$256$	−1.72107	−0.107567
$257$	−1.20206	−0.0749826	−0.0374913	−	0.999297i	$-0.511937\pi$
$257$	−1.20206	−0.0749826	−0.0374913	+	0.999297i	$0.511937\pi$
$258$	−1.95643	−0.121802
$259$	10.6207	0.659938
$260$	−9.82027	−0.609027
$261$	5.89421	0.364843
$262$	−1.18086	−0.0729539
$263$	12.7569	0.786625	0.393313	−	0.919405i	$-0.371329\pi$
$263$	12.7569	0.786625	0.393313	+	0.919405i	$0.371329\pi$
$264$	5.93133	0.365048
$265$	2.95432	0.181482
$266$	8.89735	0.545532
$267$	7.14601	0.437329
$268$	−20.2675	−1.23803
$269$	27.7412	1.69141	0.845704	−	0.533652i	$-0.179181\pi$
$269$	27.7412	1.69141	0.845704	+	0.533652i	$0.179181\pi$
$270$	0.523893	0.0318831
$271$	24.6744	1.49886	0.749432	−	0.662082i	$-0.230327\pi$
$271$	24.6744	1.49886	0.749432	+	0.662082i	$0.230327\pi$
$272$	8.29162	0.502753
$273$	−19.5933	−1.18584
$274$	2.37680	0.143588
$275$	3.03893	0.183254
$276$	0	0
$277$	7.57947	0.455406	0.227703	−	0.973731i	$-0.426878\pi$
$277$	7.57947	0.455406	0.227703	+	0.973731i	$0.426878\pi$
$278$	−6.91855	−0.414947
$279$	4.05776	0.242932
$280$	−6.71954	−0.401570
$281$	14.3719	0.857356	0.428678	−	0.903457i	$-0.358980\pi$
$281$	14.3719	0.857356	0.428678	+	0.903457i	$0.358980\pi$
$282$	−3.27853	−0.195233
$283$	2.54836	0.151484	0.0757422	−	0.997127i	$-0.475867\pi$
$283$	2.54836	0.151484	0.0757422	+	0.997127i	$0.475867\pi$
$284$	19.9531	1.18400
$285$	−4.93298	−0.292205
$286$	−9.06072	−0.535772
$287$	28.4970	1.68212
$288$	5.17586	0.304991
$289$	−5.34303	−0.314296
$290$	−3.08794	−0.181330
$291$	−9.56262	−0.560571
$292$	−22.2799	−1.30383
$293$	5.55942	0.324785	0.162392	−	0.986726i	$-0.448079\pi$
$293$	5.55942	0.324785	0.162392	+	0.986726i	$0.448079\pi$
$294$	−2.54229	−0.148269
$295$	−3.07863	−0.179245
$296$	6.02111	0.349970
$297$	−3.03893	−0.176337
$298$	1.74075	0.100839
$299$	0	0
$300$	1.72554	0.0996239
$301$	−12.8567	−0.741049
$302$	0.953568	0.0548717
$303$	−8.02293	−0.460906
$304$	−11.9800	−0.687099
$305$	−8.01885	−0.459158
$306$	1.78869	0.102253
$307$	−29.6268	−1.69089	−0.845445	−	0.534063i	$-0.820664\pi$
$307$	−29.6268	−1.69089	−0.845445	+	0.534063i	$0.820664\pi$
$308$	18.0532	1.02867
$309$	5.60122	0.318642
$310$	−2.12583	−0.120739
$311$	−25.7894	−1.46238	−0.731192	−	0.682172i	$-0.761036\pi$
$311$	−25.7894	−1.46238	−0.731192	+	0.682172i	$0.761036\pi$
$312$	−11.1079	−0.628859
$313$	−12.9716	−0.733201	−0.366600	−	0.930379i	$-0.619478\pi$
$313$	−12.9716	−0.733201	−0.366600	+	0.930379i	$0.619478\pi$
$314$	−11.9250	−0.672964
$315$	3.44277	0.193978
$316$	−26.8888	−1.51261
$317$	2.81124	0.157895	0.0789476	−	0.996879i	$-0.474844\pi$
$317$	2.81124	0.157895	0.0789476	+	0.996879i	$0.474844\pi$
$318$	1.54775	0.0867933
$319$	17.9121	1.00289
$320$	2.14549	0.119937
$321$	−13.7106	−0.765250
$322$	0	0
$323$	−16.8424	−0.937133
$324$	−1.72554	−0.0958631
$325$	−5.69114	−0.315688
$326$	−11.7188	−0.649043
$327$	−9.62984	−0.532531
$328$	16.1556	0.892042
$329$	−21.5449	−1.18781
$330$	1.59207	0.0876408
$331$	8.12602	0.446647	0.223323	−	0.974744i	$-0.428309\pi$
$331$	8.12602	0.446647	0.223323	+	0.974744i	$0.428309\pi$
$332$	22.8093	1.25182
$333$	−3.08493	−0.169053
$334$	−2.63644	−0.144260
$335$	−11.7456	−0.641732
$336$	8.36093	0.456126
$337$	−22.1592	−1.20709	−0.603545	−	0.797329i	$-0.706246\pi$
$337$	−22.1592	−1.20709	−0.603545	+	0.797329i	$0.706246\pi$
$338$	10.1578	0.552512
$339$	8.25997	0.448620
$340$	5.89138	0.319505
$341$	12.3313	0.667775
$342$	−2.58436	−0.139746
$343$	7.39273	0.399170
$344$	−7.28875	−0.392983
$345$	0	0
$346$	5.93965	0.319318
$347$	7.41356	0.397981	0.198990	−	0.980001i	$-0.436234\pi$
$347$	7.41356	0.397981	0.198990	+	0.980001i	$0.436234\pi$
$348$	10.1707	0.545205
$349$	−33.5300	−1.79482	−0.897410	−	0.441197i	$-0.854554\pi$
$349$	−33.5300	−1.79482	−0.897410	+	0.441197i	$0.854554\pi$
$350$	−1.80364	−0.0964089
$351$	5.69114	0.303771
$352$	15.7291	0.838363
$353$	−35.4463	−1.88662	−0.943308	−	0.331919i	$-0.892304\pi$
$353$	−35.4463	−1.88662	−0.943308	+	0.331919i	$0.892304\pi$
$354$	−1.61287	−0.0857233
$355$	11.5634	0.613722
$356$	12.3307	0.653526
$357$	11.7544	0.622110
$358$	10.2062	0.539415
$359$	20.2764	1.07015	0.535075	−	0.844805i	$-0.320283\pi$
$359$	20.2764	1.07015	0.535075	+	0.844805i	$0.320283\pi$
$360$	1.95178	0.102868
$361$	5.33434	0.280755
$362$	−3.64959	−0.191818
$363$	1.76490	0.0926332
$364$	−33.8089	−1.77207
$365$	−12.9119	−0.675839
$366$	−4.20102	−0.219591
$367$	10.2169	0.533320	0.266660	−	0.963791i	$-0.414080\pi$
$367$	10.2169	0.533320	0.266660	+	0.963791i	$0.414080\pi$
$368$	0	0
$369$	−8.27734	−0.430901
$370$	1.61617	0.0840208
$371$	10.1710	0.528054
$372$	7.00181	0.363027
$373$	−23.6870	−1.22647	−0.613233	−	0.789902i	$-0.710131\pi$
$373$	−23.6870	−1.22647	−0.613233	+	0.789902i	$0.710131\pi$
$374$	5.43571	0.281074
$375$	1.00000	0.0516398
$376$	−12.2143	−0.629903
$377$	−33.5448	−1.72764
$378$	1.80364	0.0927695
$379$	−9.67562	−0.497003	−0.248502	−	0.968632i	$-0.579938\pi$
$379$	−9.67562	−0.497003	−0.248502	+	0.968632i	$0.579938\pi$
$380$	−8.51204	−0.436659
$381$	0.754529	0.0386557
$382$	−4.27596	−0.218777
$383$	21.0688	1.07657	0.538284	−	0.842764i	$-0.319073\pi$
$383$	21.0688	1.07657	0.538284	+	0.842764i	$0.319073\pi$
$384$	11.4757	0.585619
$385$	10.4623	0.533211
$386$	−4.04547	−0.205909
$387$	3.73441	0.189831
$388$	−16.5007	−0.837694
$389$	−11.7714	−0.596834	−0.298417	−	0.954436i	$-0.596459\pi$
$389$	−11.7714	−0.596834	−0.298417	+	0.954436i	$0.596459\pi$
$390$	−2.98155	−0.150977
$391$	0	0
$392$	−9.47138	−0.478377
$393$	2.25401	0.113700
$394$	−6.49868	−0.327399
$395$	−15.5829	−0.784059
$396$	−5.24378	−0.263510
$397$	−12.6068	−0.632717	−0.316359	−	0.948640i	$-0.602460\pi$
$397$	−12.6068	−0.632717	−0.316359	+	0.948640i	$0.602460\pi$
$398$	3.17658	0.159227
$399$	−16.9831	−0.850221
$400$	2.42855	0.121427
$401$	−36.6809	−1.83176	−0.915879	−	0.401455i	$-0.868505\pi$
$401$	−36.6809	−1.83176	−0.915879	+	0.401455i	$0.868505\pi$
$402$	−6.15345	−0.306906
$403$	−23.0933	−1.15036
$404$	−13.8439	−0.688758
$405$	−1.00000	−0.0496904
$406$	−10.6311	−0.527611
$407$	−9.37488	−0.464696
$408$	6.66384	0.329909
$409$	−28.3730	−1.40296	−0.701478	−	0.712691i	$-0.747476\pi$
$409$	−28.3730	−1.40296	−0.701478	+	0.712691i	$0.747476\pi$
$410$	4.33644	0.214162
$411$	−4.53680	−0.223784
$412$	9.66510	0.476165
$413$	−10.5990	−0.521544
$414$	0	0
$415$	13.2187	0.648879
$416$	−29.4566	−1.44423
$417$	13.2060	0.646702
$418$	−7.85368	−0.384136
$419$	−0.0737623	−0.00360352	−0.00180176	−	0.999998i	$-0.500574\pi$
$419$	−0.0737623	−0.00360352	−0.00180176	+	0.999998i	$0.500574\pi$
$420$	5.94063	0.289873
$421$	11.9878	0.584248	0.292124	−	0.956380i	$-0.405638\pi$
$421$	11.9878	0.584248	0.292124	+	0.956380i	$0.405638\pi$
$422$	−7.96976	−0.387962
$423$	6.25801	0.304275
$424$	5.76618	0.280031
$425$	3.41423	0.165615
$426$	6.05799	0.293511
$427$	−27.6071	−1.33600
$428$	−23.6581	−1.14356
$429$	17.2950	0.835009
$430$	−1.95643	−0.0943475
$431$	35.4712	1.70859	0.854294	−	0.519790i	$-0.173990\pi$
$431$	35.4712	1.70859	0.854294	+	0.519790i	$0.173990\pi$
$432$	−2.42855	−0.116843
$433$	1.84187	0.0885145	0.0442573	−	0.999020i	$-0.485908\pi$
$433$	1.84187	0.0885145	0.0442573	+	0.999020i	$0.485908\pi$
$434$	−7.31876	−0.351312
$435$	5.89421	0.282606
$436$	−16.6166	−0.795793
$437$	0	0
$438$	−6.76445	−0.323218
$439$	24.8046	1.18386	0.591929	−	0.805990i	$-0.298366\pi$
$439$	24.8046	1.18386	0.591929	+	0.805990i	$0.298366\pi$
$440$	5.93133	0.282765
$441$	4.85268	0.231080
$442$	−10.1797	−0.484199
$443$	9.79711	0.465475	0.232737	−	0.972540i	$-0.425232\pi$
$443$	9.79711	0.465475	0.232737	+	0.972540i	$0.425232\pi$
$444$	−5.32315	−0.252626
$445$	7.14601	0.338754
$446$	−11.3107	−0.535575
$447$	−3.32273	−0.157160
$448$	7.38645	0.348977
$449$	4.66426	0.220120	0.110060	−	0.993925i	$-0.464896\pi$
$449$	4.66426	0.220120	0.110060	+	0.993925i	$0.464896\pi$
$450$	0.523893	0.0246966
$451$	−25.1543	−1.18447
$452$	14.2529	0.670399
$453$	−1.82016	−0.0855185
$454$	−10.6175	−0.498304
$455$	−19.5933	−0.918548
$456$	−9.62811	−0.450878
$457$	12.0635	0.564307	0.282153	−	0.959369i	$-0.408951\pi$
$457$	12.0635	0.564307	0.282153	+	0.959369i	$0.408951\pi$
$458$	14.8590	0.694315
$459$	−3.41423	−0.159363
$460$	0	0
$461$	−14.7023	−0.684755	−0.342378	−	0.939562i	$-0.611232\pi$
$461$	−14.7023	−0.684755	−0.342378	+	0.939562i	$0.611232\pi$
$462$	5.48115	0.255006
$463$	19.5280	0.907541	0.453770	−	0.891119i	$-0.350079\pi$
$463$	19.5280	0.907541	0.453770	+	0.891119i	$0.350079\pi$
$464$	14.3144	0.664528
$465$	4.05776	0.188174
$466$	−12.4037	−0.574589
$467$	10.7066	0.495441	0.247720	−	0.968832i	$-0.420319\pi$
$467$	10.7066	0.495441	0.247720	+	0.968832i	$0.420319\pi$
$468$	9.82027	0.453942
$469$	−40.4375	−1.86723
$470$	−3.27853	−0.151227
$471$	22.7622	1.04883
$472$	−6.00882	−0.276578
$473$	11.3486	0.521810
$474$	−8.16375	−0.374974
$475$	−4.93298	−0.226341
$476$	20.2827	0.929655
$477$	−2.95432	−0.135269
$478$	−7.29157	−0.333509
$479$	12.6795	0.579340	0.289670	−	0.957127i	$-0.406454\pi$
$479$	12.6795	0.579340	0.289670	+	0.957127i	$0.406454\pi$
$480$	5.17586	0.236245
$481$	17.5568	0.800519
$482$	11.4117	0.519788
$483$	0	0
$484$	3.04540	0.138427
$485$	−9.56262	−0.434216
$486$	−0.523893	−0.0237643
$487$	−20.1324	−0.912288	−0.456144	−	0.889906i	$-0.650770\pi$
$487$	−20.1324	−0.912288	−0.456144	+	0.889906i	$0.650770\pi$
$488$	−15.6510	−0.708490
$489$	22.3686	1.01154
$490$	−2.54229	−0.114849
$491$	13.7494	0.620503	0.310252	−	0.950654i	$-0.399587\pi$
$491$	13.7494	0.620503	0.310252	+	0.950654i	$0.399587\pi$
$492$	−14.2828	−0.643920
$493$	20.1242	0.906348
$494$	14.7079	0.661741
$495$	−3.03893	−0.136590
$496$	9.85446	0.442478
$497$	39.8102	1.78573
$498$	6.92517	0.310324
$499$	−8.56703	−0.383513	−0.191757	−	0.981443i	$-0.561418\pi$
$499$	−8.56703	−0.383513	−0.191757	+	0.981443i	$0.561418\pi$
$500$	1.72554	0.0771683
$501$	5.03240	0.224831
$502$	0.192186	0.00857768
$503$	−35.9186	−1.60153	−0.800766	−	0.598977i	$-0.795574\pi$
$503$	−35.9186	−1.60153	−0.800766	+	0.598977i	$0.795574\pi$
$504$	6.71954	0.299312
$505$	−8.02293	−0.357016
$506$	0	0
$507$	−19.3891	−0.861099
$508$	1.30197	0.0577654
$509$	−25.9928	−1.15211	−0.576055	−	0.817411i	$-0.695409\pi$
$509$	−25.9928	−1.15211	−0.576055	+	0.817411i	$0.695409\pi$
$510$	1.78869	0.0792046
$511$	−44.4527	−1.96647
$512$	22.0498	0.974473
$513$	4.93298	0.217797
$514$	−0.629752	−0.0277772
$515$	5.60122	0.246819
$516$	6.44386	0.283675
$517$	19.0176	0.836395
$518$	5.56411	0.244473
$519$	−11.3375	−0.497662
$520$	−11.1079	−0.487112
$521$	37.4494	1.64069	0.820343	−	0.571872i	$-0.193782\pi$
$521$	37.4494	1.64069	0.820343	+	0.571872i	$0.193782\pi$
$522$	3.08794	0.135155
$523$	−26.2026	−1.14576	−0.572880	−	0.819639i	$-0.694174\pi$
$523$	−26.2026	−1.14576	−0.572880	+	0.819639i	$0.694174\pi$
$524$	3.88938	0.169908
$525$	3.44277	0.150255
$526$	6.68326	0.291404
$527$	13.8541	0.603495
$528$	−7.38018	−0.321181
$529$	0	0
$530$	1.54775	0.0672298
$531$	3.07863	0.133601
$532$	−29.3050	−1.27053
$533$	47.1075	2.04045
$534$	3.74375	0.162008
$535$	−13.7106	−0.592760
$536$	−22.9249	−0.990205
$537$	−19.4815	−0.840688
$538$	14.5334	0.626580
$539$	14.7470	0.635197
$540$	−1.72554	−0.0742552
$541$	−6.83998	−0.294074	−0.147037	−	0.989131i	$-0.546974\pi$
$541$	−6.83998	−0.294074	−0.147037	+	0.989131i	$0.546974\pi$
$542$	12.9267	0.555251
$543$	6.96629	0.298952
$544$	17.6716	0.757663
$545$	−9.62984	−0.412497
$546$	−10.2648	−0.439293
$547$	18.4221	0.787670	0.393835	−	0.919181i	$-0.371148\pi$
$547$	18.4221	0.787670	0.393835	+	0.919181i	$0.371148\pi$
$548$	−7.82842	−0.334414
$549$	8.01885	0.342236
$550$	1.59207	0.0678863
$551$	−29.0761	−1.23868
$552$	0	0
$553$	−53.6482	−2.28136
$554$	3.97083	0.168704
$555$	−3.08493	−0.130948
$556$	22.7875	0.966405
$557$	8.63799	0.366003	0.183002	−	0.983113i	$-0.441419\pi$
$557$	8.63799	0.366003	0.183002	+	0.983113i	$0.441419\pi$
$558$	2.12583	0.0899937
$559$	−21.2530	−0.898908
$560$	8.36093	0.353314
$561$	−10.3756	−0.438059
$562$	7.52934	0.317606
$563$	9.94971	0.419330	0.209665	−	0.977773i	$-0.432763\pi$
$563$	9.94971	0.419330	0.209665	+	0.977773i	$0.432763\pi$
$564$	10.7984	0.454695
$565$	8.25997	0.347499
$566$	1.33507	0.0561172
$567$	−3.44277	−0.144583
$568$	22.5693	0.946985
$569$	−14.6993	−0.616225	−0.308112	−	0.951350i	$-0.599697\pi$
$569$	−14.6993	−0.616225	−0.308112	+	0.951350i	$0.599697\pi$
$570$	−2.58436	−0.108247
$571$	10.9224	0.457087	0.228543	−	0.973534i	$-0.426604\pi$
$571$	10.9224	0.457087	0.228543	+	0.973534i	$0.426604\pi$
$572$	29.8431	1.24780
$573$	8.16189	0.340968
$574$	14.9294	0.623140
$575$	0	0
$576$	−2.14549	−0.0893956
$577$	−13.9938	−0.582569	−0.291284	−	0.956637i	$-0.594083\pi$
$577$	−13.9938	−0.582569	−0.291284	+	0.956637i	$0.594083\pi$
$578$	−2.79917	−0.116430
$579$	7.72194	0.320913
$580$	10.1707	0.422314
$581$	45.5089	1.88803
$582$	−5.00979	−0.207663
$583$	−8.97797	−0.371829
$584$	−25.2012	−1.04283
$585$	5.69114	0.235300
$586$	2.91254	0.120316
$587$	11.7084	0.483257	0.241629	−	0.970369i	$-0.422318\pi$
$587$	11.7084	0.483257	0.241629	+	0.970369i	$0.422318\pi$
$588$	8.37348	0.345316
$589$	−20.0169	−0.824781
$590$	−1.61287	−0.0664009
$591$	12.4046	0.510257
$592$	−7.49189	−0.307915
$593$	−40.0959	−1.64654	−0.823270	−	0.567649i	$-0.807853\pi$
$593$	−40.0959	−1.64654	−0.823270	+	0.567649i	$0.807853\pi$
$594$	−1.59207	−0.0653236
$595$	11.7544	0.481884
$596$	−5.73349	−0.234853
$597$	−6.06341	−0.248159
$598$	0	0
$599$	11.5493	0.471890	0.235945	−	0.971766i	$-0.424182\pi$
$599$	11.5493	0.471890	0.235945	+	0.971766i	$0.424182\pi$
$600$	1.95178	0.0796812
$601$	−13.7569	−0.561154	−0.280577	−	0.959831i	$-0.590526\pi$
$601$	−13.7569	−0.561154	−0.280577	+	0.959831i	$0.590526\pi$
$602$	−6.73555	−0.274520
$603$	11.7456	0.478319
$604$	−3.14075	−0.127795
$605$	1.76490	0.0717534
$606$	−4.20316	−0.170742
$607$	−13.8897	−0.563767	−0.281884	−	0.959449i	$-0.590959\pi$
$607$	−13.8897	−0.563767	−0.281884	+	0.959449i	$0.590959\pi$
$608$	−25.5325	−1.03548
$609$	20.2924	0.822291
$610$	−4.20102	−0.170094
$611$	−35.6152	−1.44084
$612$	−5.89138	−0.238145
$613$	9.32960	0.376819	0.188409	−	0.982091i	$-0.439667\pi$
$613$	9.32960	0.376819	0.188409	+	0.982091i	$0.439667\pi$
$614$	−15.5213	−0.626387
$615$	−8.27734	−0.333775
$616$	20.4202	0.822754
$617$	−44.7373	−1.80106	−0.900528	−	0.434799i	$-0.856820\pi$
$617$	−44.7373	−1.80106	−0.900528	+	0.434799i	$0.856820\pi$
$618$	2.93444	0.118040
$619$	−26.0499	−1.04703	−0.523516	−	0.852016i	$-0.675380\pi$
$619$	−26.0499	−1.04703	−0.523516	+	0.852016i	$0.675380\pi$
$620$	7.00181	0.281200
$621$	0	0
$622$	−13.5109	−0.541738
$623$	24.6021	0.985662
$624$	13.8212	0.553291
$625$	1.00000	0.0400000
$626$	−6.79575	−0.271613
$627$	14.9910	0.598683
$628$	39.2770	1.56732
$629$	−10.5327	−0.419965
$630$	1.80364	0.0718589
$631$	43.1878	1.71928	0.859639	−	0.510901i	$-0.170688\pi$
$631$	43.1878	1.71928	0.859639	+	0.510901i	$0.170688\pi$
$632$	−30.4144	−1.20982
$633$	15.2126	0.604645
$634$	1.47279	0.0584920
$635$	0.754529	0.0299426
$636$	−5.09778	−0.202140
$637$	−27.6173	−1.09424
$638$	9.38403	0.371517
$639$	−11.5634	−0.457441
$640$	11.4757	0.453618
$641$	1.74644	0.0689803	0.0344901	−	0.999405i	$-0.489019\pi$
$641$	1.74644	0.0689803	0.0344901	+	0.999405i	$0.489019\pi$
$642$	−7.18288	−0.283486
$643$	12.8549	0.506946	0.253473	−	0.967342i	$-0.418427\pi$
$643$	12.8549	0.506946	0.253473	+	0.967342i	$0.418427\pi$
$644$	0	0
$645$	3.73441	0.147042
$646$	−8.82359	−0.347160
$647$	−49.6926	−1.95362	−0.976809	−	0.214113i	$-0.931314\pi$
$647$	−49.6926	−1.95362	−0.976809	+	0.214113i	$0.931314\pi$
$648$	−1.95178	−0.0766733
$649$	9.35575	0.367245
$650$	−2.98155	−0.116946
$651$	13.9699	0.547525
$652$	38.5979	1.51161
$653$	−0.328818	−0.0128676	−0.00643382	−	0.999979i	$-0.502048\pi$
$653$	−0.328818	−0.0128676	−0.00643382	+	0.999979i	$0.502048\pi$
$654$	−5.04501	−0.197275
$655$	2.25401	0.0880716
$656$	−20.1019	−0.784847
$657$	12.9119	0.503741
$658$	−11.2872	−0.440022
$659$	23.6429	0.920998	0.460499	−	0.887660i	$-0.347671\pi$
$659$	23.6429	0.920998	0.460499	+	0.887660i	$0.347671\pi$
$660$	−5.24378	−0.204114
$661$	26.5515	1.03273	0.516366	−	0.856368i	$-0.327284\pi$
$661$	26.5515	1.03273	0.516366	+	0.856368i	$0.327284\pi$
$662$	4.25717	0.165460
$663$	19.4309	0.754632
$664$	25.8000	1.00123
$665$	−16.9831	−0.658578
$666$	−1.61617	−0.0626254
$667$	0	0
$668$	8.68358	0.335978
$669$	21.5896	0.834703
$670$	−6.15345	−0.237729
$671$	24.3687	0.940744
$672$	17.8193	0.687395
$673$	−25.9589	−1.00064	−0.500321	−	0.865840i	$-0.666785\pi$
$673$	−25.9589	−1.00064	−0.500321	+	0.865840i	$0.666785\pi$
$674$	−11.6091	−0.447165
$675$	−1.00000	−0.0384900
$676$	−33.4565	−1.28679
$677$	2.43409	0.0935496	0.0467748	−	0.998905i	$-0.485106\pi$
$677$	2.43409	0.0935496	0.0467748	+	0.998905i	$0.485106\pi$
$678$	4.32734	0.166191
$679$	−32.9219	−1.26343
$680$	6.66384	0.255546
$681$	20.2665	0.776615
$682$	6.46026	0.247376
$683$	23.6749	0.905895	0.452947	−	0.891537i	$-0.350373\pi$
$683$	23.6749	0.905895	0.452947	+	0.891537i	$0.350373\pi$
$684$	8.51204	0.325466
$685$	−4.53680	−0.173342
$686$	3.87300	0.147872
$687$	−28.3627	−1.08210
$688$	9.06918	0.345759
$689$	16.8134	0.640541
$690$	0	0
$691$	44.7928	1.70400	0.851999	−	0.523543i	$-0.175390\pi$
$691$	44.7928	1.70400	0.851999	+	0.523543i	$0.175390\pi$
$692$	−19.5633	−0.743685
$693$	−10.4623	−0.397432
$694$	3.88391	0.147431
$695$	13.2060	0.500933
$696$	11.5042	0.436066
$697$	−28.2607	−1.07045
$698$	−17.5661	−0.664888
$699$	23.6760	0.895508
$700$	5.94063	0.224535
$701$	17.1487	0.647697	0.323849	−	0.946109i	$-0.395023\pi$
$701$	17.1487	0.647697	0.323849	+	0.946109i	$0.395023\pi$
$702$	2.98155	0.112531
$703$	15.2179	0.573954
$704$	−6.52001	−0.245732
$705$	6.25801	0.235690
$706$	−18.5701	−0.698894
$707$	−27.6211	−1.03880
$708$	5.31229	0.199648
$709$	21.2424	0.797774	0.398887	−	0.917000i	$-0.369397\pi$
$709$	21.2424	0.797774	0.398887	+	0.917000i	$0.369397\pi$
$710$	6.05799	0.227352
$711$	15.5829	0.584403
$712$	13.9475	0.522703
$713$	0	0
$714$	6.15806	0.230460
$715$	17.2950	0.646796
$716$	−33.6160	−1.25629
$717$	13.9181	0.519779
$718$	10.6227	0.396435
$719$	−10.8451	−0.404454	−0.202227	−	0.979339i	$-0.564818\pi$
$719$	−10.8451	−0.404454	−0.202227	+	0.979339i	$0.564818\pi$
$720$	−2.42855	−0.0905066
$721$	19.2837	0.718163
$722$	2.79462	0.104005
$723$	−21.7825	−0.810098
$724$	12.0206	0.446741
$725$	5.89421	0.218906
$726$	0.924619	0.0343158
$727$	−29.5832	−1.09718	−0.548590	−	0.836091i	$-0.684835\pi$
$727$	−29.5832	−1.09718	−0.548590	+	0.836091i	$0.684835\pi$
$728$	−38.2419	−1.41734
$729$	1.00000	0.0370370
$730$	−6.76445	−0.250363
$731$	12.7501	0.471581
$732$	13.8368	0.511423
$733$	−15.5723	−0.575178	−0.287589	−	0.957754i	$-0.592854\pi$
$733$	−15.5723	−0.575178	−0.287589	+	0.957754i	$0.592854\pi$
$734$	5.35259	0.197568
$735$	4.85268	0.178994
$736$	0	0
$737$	35.6941	1.31481
$738$	−4.33644	−0.159627
$739$	23.1710	0.852360	0.426180	−	0.904638i	$-0.359859\pi$
$739$	23.1710	0.852360	0.426180	+	0.904638i	$0.359859\pi$
$740$	−5.32315	−0.195683
$741$	−28.0743	−1.03134
$742$	5.32854	0.195617
$743$	40.3407	1.47996	0.739978	−	0.672631i	$-0.234836\pi$
$743$	40.3407	1.47996	0.739978	+	0.672631i	$0.234836\pi$
$744$	7.91987	0.290356
$745$	−3.32273	−0.121735
$746$	−12.4095	−0.454343
$747$	−13.2187	−0.483646
$748$	−17.9035	−0.654617
$749$	−47.2024	−1.72474
$750$	0.523893	0.0191299
$751$	−1.05344	−0.0384407	−0.0192203	−	0.999815i	$-0.506118\pi$
$751$	−1.05344	−0.0384407	−0.0192203	+	0.999815i	$0.506118\pi$
$752$	15.1979	0.554209
$753$	−0.366842	−0.0133685
$754$	−17.5739	−0.640003
$755$	−1.82016	−0.0662423
$756$	−5.94063	−0.216059
$757$	15.2233	0.553300	0.276650	−	0.960971i	$-0.410776\pi$
$757$	15.2233	0.553300	0.276650	+	0.960971i	$0.410776\pi$
$758$	−5.06899	−0.184114
$759$	0	0
$760$	−9.62811	−0.349248
$761$	−8.34704	−0.302580	−0.151290	−	0.988489i	$-0.548343\pi$
$761$	−8.34704	−0.302580	−0.151290	+	0.988489i	$0.548343\pi$
$762$	0.395292	0.0143199
$763$	−33.1534	−1.20023
$764$	14.0836	0.509528
$765$	−3.41423	−0.123442
$766$	11.0378	0.398813
$767$	−17.5209	−0.632644
$768$	1.72107	0.0621039
$769$	21.7972	0.786027	0.393014	−	0.919533i	$-0.371432\pi$
$769$	21.7972	0.786027	0.393014	+	0.919533i	$0.371432\pi$
$770$	5.48115	0.197527
$771$	1.20206	0.0432912
$772$	13.3245	0.479559
$773$	18.9456	0.681425	0.340712	−	0.940168i	$-0.389332\pi$
$773$	18.9456	0.681425	0.340712	+	0.940168i	$0.389332\pi$
$774$	1.95643	0.0703225
$775$	4.05776	0.145759
$776$	−18.6642	−0.670004
$777$	−10.6207	−0.381016
$778$	−6.16696	−0.221096
$779$	40.8320	1.46296
$780$	9.82027	0.351622
$781$	−35.1404	−1.25742
$782$	0	0
$783$	−5.89421	−0.210642
$784$	11.7850	0.420892
$785$	22.7622	0.812418
$786$	1.18086	0.0421199
$787$	25.6353	0.913800	0.456900	−	0.889518i	$-0.348960\pi$
$787$	25.6353	0.913800	0.456900	+	0.889518i	$0.348960\pi$
$788$	21.4046	0.762506
$789$	−12.7569	−0.454158
$790$	−8.16375	−0.290453
$791$	28.4372	1.01111
$792$	−5.93133	−0.210761
$793$	−45.6364	−1.62060
$794$	−6.60462	−0.234389
$795$	−2.95432	−0.104779
$796$	−10.4626	−0.370838
$797$	3.10723	0.110064	0.0550319	−	0.998485i	$-0.482474\pi$
$797$	3.10723	0.110064	0.0550319	+	0.998485i	$0.482474\pi$
$798$	−8.89735	−0.314963
$799$	21.3663	0.755885
$800$	5.17586	0.182994
$801$	−7.14601	−0.252492
$802$	−19.2169	−0.678572
$803$	39.2383	1.38469
$804$	20.2675	0.714779
$805$	0	0
$806$	−12.0984	−0.426148
$807$	−27.7412	−0.976535
$808$	−15.6590	−0.550883
$809$	−55.7451	−1.95989	−0.979947	−	0.199260i	$-0.936146\pi$
$809$	−55.7451	−1.95989	−0.979947	+	0.199260i	$0.936146\pi$
$810$	−0.523893	−0.0184077
$811$	−41.1046	−1.44338	−0.721689	−	0.692217i	$-0.756634\pi$
$811$	−41.1046	−1.44338	−0.721689	+	0.692217i	$0.756634\pi$
$812$	35.0153	1.22880
$813$	−24.6744	−0.865369
$814$	−4.91144	−0.172146
$815$	22.3686	0.783539
$816$	−8.29162	−0.290265
$817$	−18.4218	−0.644496
$818$	−14.8644	−0.519722
$819$	19.5933	0.684645
$820$	−14.2828	−0.498779
$821$	−37.7035	−1.31586	−0.657931	−	0.753078i	$-0.728568\pi$
$821$	−37.7035	−1.31586	−0.657931	+	0.753078i	$0.728568\pi$
$822$	−2.37680	−0.0829004
$823$	34.0194	1.18584	0.592922	−	0.805260i	$-0.297974\pi$
$823$	34.0194	1.18584	0.592922	+	0.805260i	$0.297974\pi$
$824$	10.9324	0.380847
$825$	−3.03893	−0.105802
$826$	−5.55276	−0.193205
$827$	−36.0431	−1.25334	−0.626670	−	0.779285i	$-0.715583\pi$
$827$	−36.0431	−1.25334	−0.626670	+	0.779285i	$0.715583\pi$
$828$	0	0
$829$	45.0473	1.56456	0.782279	−	0.622928i	$-0.214057\pi$
$829$	45.0473	1.56456	0.782279	+	0.622928i	$0.214057\pi$
$830$	6.92517	0.240376
$831$	−7.57947	−0.262929
$832$	12.2103	0.423316
$833$	16.5682	0.574053
$834$	6.91855	0.239570
$835$	5.03240	0.174153
$836$	25.8675	0.894647
$837$	−4.05776	−0.140257
$838$	−0.0386435	−0.00133492
$839$	−49.1881	−1.69816	−0.849081	−	0.528262i	$-0.822844\pi$
$839$	−49.1881	−1.69816	−0.849081	+	0.528262i	$0.822844\pi$
$840$	6.71954	0.231846
$841$	5.74173	0.197991
$842$	6.28031	0.216434
$843$	−14.3719	−0.494995
$844$	26.2498	0.903556
$845$	−19.3891	−0.667004
$846$	3.27853	0.112718
$847$	6.07615	0.208779
$848$	−7.17470	−0.246380
$849$	−2.54836	−0.0874596
$850$	1.78869	0.0613516
$851$	0	0
$852$	−19.9531	−0.683581
$853$	0.0722050	0.00247225	0.00123613	−	0.999999i	$-0.499607\pi$
$853$	0.0722050	0.00247225	0.00123613	+	0.999999i	$0.499607\pi$
$854$	−14.4632	−0.494919
$855$	4.93298	0.168705
$856$	−26.7601	−0.914641
$857$	39.4461	1.34745	0.673726	−	0.738981i	$-0.264693\pi$
$857$	39.4461	1.34745	0.673726	+	0.738981i	$0.264693\pi$
$858$	9.06072	0.309328
$859$	−19.7194	−0.672817	−0.336409	−	0.941716i	$-0.609212\pi$
$859$	−19.7194	−0.672817	−0.336409	+	0.941716i	$0.609212\pi$
$860$	6.44386	0.219734
$861$	−28.4970	−0.971175
$862$	18.5831	0.632944
$863$	11.6133	0.395322	0.197661	−	0.980270i	$-0.436665\pi$
$863$	11.6133	0.395322	0.197661	+	0.980270i	$0.436665\pi$
$864$	−5.17586	−0.176086
$865$	−11.3375	−0.385487
$866$	0.964942	0.0327901
$867$	5.34303	0.181459
$868$	24.1056	0.818199
$869$	47.3552	1.60642
$870$	3.08794	0.104691
$871$	−66.8460	−2.26499
$872$	−18.7954	−0.636491
$873$	9.56262	0.323646
$874$	0	0
$875$	3.44277	0.116387
$876$	22.2799	0.752769
$877$	2.37026	0.0800381	0.0400191	−	0.999199i	$-0.487258\pi$
$877$	2.37026	0.0800381	0.0400191	+	0.999199i	$0.487258\pi$
$878$	12.9950	0.438559
$879$	−5.55942	−0.187514
$880$	−7.38018	−0.248786
$881$	−21.0167	−0.708070	−0.354035	−	0.935232i	$-0.615191\pi$
$881$	−21.0167	−0.708070	−0.354035	+	0.935232i	$0.615191\pi$
$882$	2.54229	0.0856032
$883$	35.2759	1.18713	0.593564	−	0.804787i	$-0.297720\pi$
$883$	35.2759	1.18713	0.593564	+	0.804787i	$0.297720\pi$
$884$	33.5287	1.12769
$885$	3.07863	0.103487
$886$	5.13264	0.172434
$887$	44.0850	1.48023	0.740115	−	0.672480i	$-0.234771\pi$
$887$	44.0850	1.48023	0.740115	+	0.672480i	$0.234771\pi$
$888$	−6.02111	−0.202055
$889$	2.59767	0.0871231
$890$	3.74375	0.125491
$891$	3.03893	0.101808
$892$	37.2537	1.24734
$893$	−30.8706	−1.03305
$894$	−1.74075	−0.0582195
$895$	−19.4815	−0.651194
$896$	39.5084	1.31988
$897$	0	0
$898$	2.44358	0.0815432
$899$	23.9173	0.797687
$900$	−1.72554	−0.0575179
$901$	−10.0867	−0.336037
$902$	−13.1781	−0.438784
$903$	12.8567	0.427845
$904$	16.1217	0.536199
$905$	6.96629	0.231567
$906$	−0.953568	−0.0316802
$907$	36.3153	1.20583	0.602915	−	0.797806i	$-0.294006\pi$
$907$	36.3153	1.20583	0.602915	+	0.797806i	$0.294006\pi$
$908$	34.9706	1.16054
$909$	8.02293	0.266104
$910$	−10.2648	−0.340275
$911$	−45.2775	−1.50011	−0.750054	−	0.661376i	$-0.769973\pi$
$911$	−45.2775	−1.50011	−0.750054	+	0.661376i	$0.769973\pi$
$912$	11.9800	0.396697
$913$	−40.1706	−1.32945
$914$	6.31998	0.209046
$915$	8.01885	0.265095
$916$	−48.9408	−1.61705
$917$	7.76005	0.256260
$918$	−1.78869	−0.0590356
$919$	−12.3632	−0.407825	−0.203913	−	0.978989i	$-0.565366\pi$
$919$	−12.3632	−0.407825	−0.203913	+	0.978989i	$0.565366\pi$
$920$	0	0
$921$	29.6268	0.976235
$922$	−7.70245	−0.253667
$923$	65.8090	2.16613
$924$	−18.0532	−0.593905
$925$	−3.08493	−0.101432
$926$	10.2306	0.336197
$927$	−5.60122	−0.183968
$928$	30.5076	1.00146
$929$	35.9039	1.17797	0.588984	−	0.808145i	$-0.299528\pi$
$929$	35.9039	1.17797	0.588984	+	0.808145i	$0.299528\pi$
$930$	2.12583	0.0697088
$931$	−23.9382	−0.784543
$932$	40.8538	1.33821
$933$	25.7894	0.844308
$934$	5.60910	0.183535
$935$	−10.3756	−0.339319
$936$	11.1079	0.363072
$937$	13.7296	0.448526	0.224263	−	0.974529i	$-0.428002\pi$
$937$	13.7296	0.448526	0.224263	+	0.974529i	$0.428002\pi$
$938$	−21.1849	−0.691713
$939$	12.9716	0.423314
$940$	10.7984	0.352205
$941$	−11.6736	−0.380547	−0.190273	−	0.981731i	$-0.560937\pi$
$941$	−11.6736	−0.380547	−0.190273	+	0.981731i	$0.560937\pi$
$942$	11.9250	0.388536
$943$	0	0
$944$	7.47660	0.243343
$945$	−3.44277	−0.111993
$946$	5.94546	0.193304
$947$	−5.63001	−0.182951	−0.0914754	−	0.995807i	$-0.529158\pi$
$947$	−5.63001	−0.182951	−0.0914754	+	0.995807i	$0.529158\pi$
$948$	26.8888	0.873307
$949$	−73.4833	−2.38537
$950$	−2.58436	−0.0838476
$951$	−2.81124	−0.0911609
$952$	22.9421	0.743557
$953$	−37.3500	−1.20989	−0.604943	−	0.796268i	$-0.706804\pi$
$953$	−37.3500	−1.20989	−0.604943	+	0.796268i	$0.706804\pi$
$954$	−1.54775	−0.0501101
$955$	8.16189	0.264113
$956$	24.0161	0.776736
$957$	−17.9121	−0.579016
$958$	6.64269	0.214615
$959$	−15.6192	−0.504370
$960$	−2.14549	−0.0692455
$961$	−14.5346	−0.468857
$962$	9.19786	0.296551
$963$	13.7106	0.441817
$964$	−37.5864	−1.21058
$965$	7.72194	0.248578
$966$	0	0
$967$	16.7707	0.539308	0.269654	−	0.962957i	$-0.413091\pi$
$967$	16.7707	0.539308	0.269654	+	0.962957i	$0.413091\pi$
$968$	3.44470	0.110717
$969$	16.8424	0.541054
$970$	−5.00979	−0.160855
$971$	9.47876	0.304188	0.152094	−	0.988366i	$-0.451398\pi$
$971$	9.47876	0.304188	0.152094	+	0.988366i	$0.451398\pi$
$972$	1.72554	0.0553466
$973$	45.4654	1.45755
$974$	−10.5472	−0.337956
$975$	5.69114	0.182262
$976$	19.4741	0.623352
$977$	30.4419	0.973923	0.486962	−	0.873423i	$-0.338105\pi$
$977$	30.4419	0.973923	0.486962	+	0.873423i	$0.338105\pi$
$978$	11.7188	0.374725
$979$	−21.7162	−0.694054
$980$	8.37348	0.267481
$981$	9.62984	0.307457
$982$	7.20323	0.229864
$983$	−39.0808	−1.24648	−0.623241	−	0.782030i	$-0.714185\pi$
$983$	−39.0808	−1.24648	−0.623241	+	0.782030i	$0.714185\pi$
$984$	−16.1556	−0.515021
$985$	12.4046	0.395243
$986$	10.5429	0.335755
$987$	21.5449	0.685781
$988$	−48.4432	−1.54118
$989$	0	0
$990$	−1.59207	−0.0505995
$991$	−5.27456	−0.167552	−0.0837760	−	0.996485i	$-0.526698\pi$
$991$	−5.27456	−0.167552	−0.0837760	+	0.996485i	$0.526698\pi$
$992$	21.0024	0.666827
$993$	−8.12602	−0.257872
$994$	20.8563	0.661521
$995$	−6.06341	−0.192223
$996$	−22.8093	−0.722740
$997$	50.2281	1.59074	0.795370	−	0.606124i	$-0.207277\pi$
$997$	50.2281	1.59074	0.795370	+	0.606124i	$0.207277\pi$
$998$	−4.48821	−0.142072
$999$	3.08493	0.0976028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bp.1.9		15
23.3	even	11		345.2.m.a.331.1	yes	30
23.8	even	11		345.2.m.a.271.1	✓	30
23.22	odd	2		7935.2.a.bq.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.271.1	✓	30	23.8	even	11
345.2.m.a.331.1	yes	30	23.3	even	11
7935.2.a.bp.1.9		15	1.1	even	1	trivial
7935.2.a.bq.1.9		15	23.22	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.523893 q^{2} -1.00000 q^{3} -1.72554 q^{4} -1.00000 q^{5} -0.523893 q^{6} -3.44277 q^{7} -1.95178 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.523893 q^{2} -1.00000 q^{3} -1.72554 q^{4} -1.00000 q^{5} -0.523893 q^{6} -3.44277 q^{7} -1.95178 q^{8} +1.00000 q^{9} -0.523893 q^{10} +3.03893 q^{11} +1.72554 q^{12} -5.69114 q^{13} -1.80364 q^{14} +1.00000 q^{15} +2.42855 q^{16} +3.41423 q^{17} +0.523893 q^{18} -4.93298 q^{19} +1.72554 q^{20} +3.44277 q^{21} +1.59207 q^{22} +1.95178 q^{24} +1.00000 q^{25} -2.98155 q^{26} -1.00000 q^{27} +5.94063 q^{28} +5.89421 q^{29} +0.523893 q^{30} +4.05776 q^{31} +5.17586 q^{32} -3.03893 q^{33} +1.78869 q^{34} +3.44277 q^{35} -1.72554 q^{36} -3.08493 q^{37} -2.58436 q^{38} +5.69114 q^{39} +1.95178 q^{40} -8.27734 q^{41} +1.80364 q^{42} +3.73441 q^{43} -5.24378 q^{44} -1.00000 q^{45} +6.25801 q^{47} -2.42855 q^{48} +4.85268 q^{49} +0.523893 q^{50} -3.41423 q^{51} +9.82027 q^{52} -2.95432 q^{53} -0.523893 q^{54} -3.03893 q^{55} +6.71954 q^{56} +4.93298 q^{57} +3.08794 q^{58} +3.07863 q^{59} -1.72554 q^{60} +8.01885 q^{61} +2.12583 q^{62} -3.44277 q^{63} -2.14549 q^{64} +5.69114 q^{65} -1.59207 q^{66} +11.7456 q^{67} -5.89138 q^{68} +1.80364 q^{70} -11.5634 q^{71} -1.95178 q^{72} +12.9119 q^{73} -1.61617 q^{74} -1.00000 q^{75} +8.51204 q^{76} -10.4623 q^{77} +2.98155 q^{78} +15.5829 q^{79} -2.42855 q^{80} +1.00000 q^{81} -4.33644 q^{82} -13.2187 q^{83} -5.94063 q^{84} -3.41423 q^{85} +1.95643 q^{86} -5.89421 q^{87} -5.93133 q^{88} -7.14601 q^{89} -0.523893 q^{90} +19.5933 q^{91} -4.05776 q^{93} +3.27853 q^{94} +4.93298 q^{95} -5.17586 q^{96} +9.56262 q^{97} +2.54229 q^{98} +3.03893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9}+O(q^{10}) \) 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9	\( 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} + q^{28} - 3 q^{29} - 22 q^{31} - 13 q^{33} + q^{34} + 5 q^{35} + 12 q^{36} - 6 q^{37} - 17 q^{38} + 24 q^{39} - 20 q^{41} - 15 q^{42} - 4 q^{43} - 18 q^{44} - 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} - 2 q^{51} - 55 q^{52} + 4 q^{53} - 13 q^{55} + 25 q^{56} - 13 q^{57} + 2 q^{58} + 9 q^{59} + 12 q^{60} + 13 q^{61} - 7 q^{62} - 5 q^{63} - 26 q^{64} + 24 q^{65} + 9 q^{66} - 32 q^{67} + 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} - 11 q^{74} - 15 q^{75} + 88 q^{76} - 21 q^{77} + 9 q^{78} + 33 q^{79} - 2 q^{80} + 15 q^{81} - 35 q^{82} - 12 q^{83} - q^{84} - 2 q^{85} + 77 q^{86} + 3 q^{87} - 37 q^{88} + 29 q^{89} + 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} + 18 q^{97} - 19 q^{98} + 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

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Database

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