LMFDB - Embedded newform 7595.2.a.u.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 9x^{5} + 29x^{4} + 18x^{3} - 70x^{2} - 10x + 48 $ x^7 - 3x^6 - 9x^5 + 29x^4 + 18x^3 - 70x^2 - 10x + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.13413$ of defining polynomial
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13413 q^{2} +2.48623 q^{3} -0.713738 q^{4} +1.00000 q^{5} +2.81973 q^{6} -3.07775 q^{8} +3.18136 q^{9} +O(q^{10})$	\(q+1.13413 q^{2} +2.48623 q^{3} -0.713738 q^{4} +1.00000 q^{5} +2.81973 q^{6} -3.07775 q^{8} +3.18136 q^{9} +1.13413 q^{10} -3.49393 q^{11} -1.77452 q^{12} -0.596091 q^{13} +2.48623 q^{15} -2.06310 q^{16} +4.26076 q^{17} +3.60810 q^{18} -2.77745 q^{19} -0.713738 q^{20} -3.96259 q^{22} +4.86252 q^{23} -7.65200 q^{24} +1.00000 q^{25} -0.676047 q^{26} +0.450913 q^{27} +4.26643 q^{29} +2.81973 q^{30} +1.00000 q^{31} +3.81565 q^{32} -8.68673 q^{33} +4.83227 q^{34} -2.27066 q^{36} +3.54376 q^{37} -3.15001 q^{38} -1.48202 q^{39} -3.07775 q^{40} +6.20120 q^{41} +9.56691 q^{43} +2.49375 q^{44} +3.18136 q^{45} +5.51475 q^{46} +3.35025 q^{47} -5.12936 q^{48} +1.13413 q^{50} +10.5932 q^{51} +0.425453 q^{52} +7.47103 q^{53} +0.511396 q^{54} -3.49393 q^{55} -6.90540 q^{57} +4.83870 q^{58} -0.643687 q^{59} -1.77452 q^{60} -5.24422 q^{61} +1.13413 q^{62} +8.45367 q^{64} -0.596091 q^{65} -9.85192 q^{66} +3.34222 q^{67} -3.04106 q^{68} +12.0894 q^{69} +3.73730 q^{71} -9.79143 q^{72} -3.37458 q^{73} +4.01910 q^{74} +2.48623 q^{75} +1.98237 q^{76} -1.68081 q^{78} +12.1818 q^{79} -2.06310 q^{80} -8.42302 q^{81} +7.03300 q^{82} +6.87035 q^{83} +4.26076 q^{85} +10.8502 q^{86} +10.6073 q^{87} +10.7534 q^{88} +2.40648 q^{89} +3.60810 q^{90} -3.47056 q^{92} +2.48623 q^{93} +3.79964 q^{94} -2.77745 q^{95} +9.48661 q^{96} +0.815852 q^{97} -11.1155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9	$ 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9} + 3 q^{10} + 5 q^{11} - 4 q^{12} - 9 q^{13} - 2 q^{15} + 13 q^{16} + 2 q^{17} - 5 q^{18} - 13 q^{19} + 13 q^{20} + 20 q^{22} + 8 q^{23} + 8 q^{24} + 7 q^{25} - 4 q^{26} - 8 q^{27} - q^{29} + 12 q^{30} + 7 q^{31} + 11 q^{32} + 13 q^{33} - 20 q^{34} - 3 q^{36} + 37 q^{37} + 4 q^{38} + 21 q^{39} + 9 q^{40} - 9 q^{41} + 19 q^{43} + 16 q^{44} + 11 q^{45} + 8 q^{46} + q^{47} - 8 q^{48} + 3 q^{50} - 4 q^{51} - 26 q^{52} + 25 q^{53} + 32 q^{54} + 5 q^{55} + 33 q^{57} + 4 q^{58} - 7 q^{59} - 4 q^{60} + 34 q^{61} + 3 q^{62} + 49 q^{64} - 9 q^{65} - 32 q^{66} + 20 q^{68} - 4 q^{69} - 23 q^{71} - 17 q^{72} + 3 q^{73} - 18 q^{74} - 2 q^{75} - 10 q^{76} + 14 q^{78} + 13 q^{79} + 13 q^{80} - 5 q^{81} + 78 q^{82} + 13 q^{83} + 2 q^{85} + 10 q^{86} + 17 q^{87} + 52 q^{88} + 10 q^{89} - 5 q^{90} + 60 q^{92} - 2 q^{93} + 38 q^{94} - 13 q^{95} + 26 q^{96} - 3 q^{97} - 36 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9 + 3 * q^10 + 5 * q^11 - 4 * q^12 - 9 * q^13 - 2 * q^15 + 13 * q^16 + 2 * q^17 - 5 * q^18 - 13 * q^19 + 13 * q^20 + 20 * q^22 + 8 * q^23 + 8 * q^24 + 7 * q^25 - 4 * q^26 - 8 * q^27 - q^29 + 12 * q^30 + 7 * q^31 + 11 * q^32 + 13 * q^33 - 20 * q^34 - 3 * q^36 + 37 * q^37 + 4 * q^38 + 21 * q^39 + 9 * q^40 - 9 * q^41 + 19 * q^43 + 16 * q^44 + 11 * q^45 + 8 * q^46 + q^47 - 8 * q^48 + 3 * q^50 - 4 * q^51 - 26 * q^52 + 25 * q^53 + 32 * q^54 + 5 * q^55 + 33 * q^57 + 4 * q^58 - 7 * q^59 - 4 * q^60 + 34 * q^61 + 3 * q^62 + 49 * q^64 - 9 * q^65 - 32 * q^66 + 20 * q^68 - 4 * q^69 - 23 * q^71 - 17 * q^72 + 3 * q^73 - 18 * q^74 - 2 * q^75 - 10 * q^76 + 14 * q^78 + 13 * q^79 + 13 * q^80 - 5 * q^81 + 78 * q^82 + 13 * q^83 + 2 * q^85 + 10 * q^86 + 17 * q^87 + 52 * q^88 + 10 * q^89 - 5 * q^90 + 60 * q^92 - 2 * q^93 + 38 * q^94 - 13 * q^95 + 26 * q^96 - 3 * q^97 - 36 * 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 $

$2$	1.13413	0.801954	0.400977	−	0.916088i	$-0.368671\pi$
$2$	1.13413	0.801954	0.400977	+	0.916088i	$0.368671\pi$
$3$	2.48623	1.43543	0.717714	−	0.696338i	$-0.245188\pi$
$3$	2.48623	1.43543	0.717714	+	0.696338i	$0.245188\pi$
$4$	−0.713738	−0.356869
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.81973	1.15115
$7$	0	0
$7$	0	0
$8$	−3.07775	−1.08815
$9$	3.18136	1.06045
$10$	1.13413	0.358645
$11$	−3.49393	−1.05346	−0.526730	−	0.850033i	$-0.676582\pi$
$11$	−3.49393	−1.05346	−0.526730	+	0.850033i	$0.676582\pi$
$12$	−1.77452	−0.512260
$13$	−0.596091	−0.165326	−0.0826629	−	0.996578i	$-0.526342\pi$
$13$	−0.596091	−0.165326	−0.0826629	+	0.996578i	$0.526342\pi$
$14$	0	0
$15$	2.48623	0.641943
$16$	−2.06310	−0.515776
$17$	4.26076	1.03338	0.516692	−	0.856171i	$-0.327163\pi$
$17$	4.26076	1.03338	0.516692	+	0.856171i	$0.327163\pi$
$18$	3.60810	0.850436
$19$	−2.77745	−0.637192	−0.318596	−	0.947891i	$-0.603211\pi$
$19$	−2.77745	−0.637192	−0.318596	+	0.947891i	$0.603211\pi$
$20$	−0.713738	−0.159597
$21$	0	0
$22$	−3.96259	−0.844826
$23$	4.86252	1.01390	0.506952	−	0.861974i	$-0.330772\pi$
$23$	4.86252	1.01390	0.506952	+	0.861974i	$0.330772\pi$
$24$	−7.65200	−1.56196
$25$	1.00000	0.200000
$26$	−0.676047	−0.132584
$27$	0.450913	0.0867782
$28$	0	0
$29$	4.26643	0.792255	0.396128	−	0.918195i	$-0.370354\pi$
$29$	4.26643	0.792255	0.396128	+	0.918195i	$0.370354\pi$
$30$	2.81973	0.514809
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	3.81565	0.674519
$33$	−8.68673	−1.51217
$34$	4.83227	0.828728
$35$	0	0
$36$	−2.27066	−0.378443
$37$	3.54376	0.582591	0.291295	−	0.956633i	$-0.405914\pi$
$37$	3.54376	0.582591	0.291295	+	0.956633i	$0.405914\pi$
$38$	−3.15001	−0.510999
$39$	−1.48202	−0.237313
$40$	−3.07775	−0.486634
$41$	6.20120	0.968465	0.484233	−	0.874939i	$-0.339099\pi$
$41$	6.20120	0.968465	0.484233	+	0.874939i	$0.339099\pi$
$42$	0	0
$43$	9.56691	1.45894	0.729470	−	0.684012i	$-0.239767\pi$
$43$	9.56691	1.45894	0.729470	+	0.684012i	$0.239767\pi$
$44$	2.49375	0.375947
$45$	3.18136	0.474250
$46$	5.51475	0.813105
$47$	3.35025	0.488684	0.244342	−	0.969689i	$-0.421428\pi$
$47$	3.35025	0.488684	0.244342	+	0.969689i	$0.421428\pi$
$48$	−5.12936	−0.740359
$49$	0	0
$50$	1.13413	0.160391
$51$	10.5932	1.48335
$52$	0.425453	0.0589997
$53$	7.47103	1.02622	0.513112	−	0.858322i	$-0.328492\pi$
$53$	7.47103	1.02622	0.513112	+	0.858322i	$0.328492\pi$
$54$	0.511396	0.0695922
$55$	−3.49393	−0.471121
$56$	0	0
$57$	−6.90540	−0.914643
$58$	4.83870	0.635353
$59$	−0.643687	−0.0838008	−0.0419004	−	0.999122i	$-0.513341\pi$
$59$	−0.643687	−0.0838008	−0.0419004	+	0.999122i	$0.513341\pi$
$60$	−1.77452	−0.229090
$61$	−5.24422	−0.671454	−0.335727	−	0.941959i	$-0.608982\pi$
$61$	−5.24422	−0.671454	−0.335727	+	0.941959i	$0.608982\pi$
$62$	1.13413	0.144035
$63$	0	0
$64$	8.45367	1.05671
$65$	−0.596091	−0.0739359
$66$	−9.85192	−1.21269
$67$	3.34222	0.408317	0.204158	−	0.978938i	$-0.434554\pi$
$67$	3.34222	0.408317	0.204158	+	0.978938i	$0.434554\pi$
$68$	−3.04106	−0.368783
$69$	12.0894	1.45539
$70$	0	0
$71$	3.73730	0.443536	0.221768	−	0.975099i	$-0.428817\pi$
$71$	3.73730	0.443536	0.221768	+	0.975099i	$0.428817\pi$
$72$	−9.79143	−1.15393
$73$	−3.37458	−0.394964	−0.197482	−	0.980306i	$-0.563276\pi$
$73$	−3.37458	−0.394964	−0.197482	+	0.980306i	$0.563276\pi$
$74$	4.01910	0.467211
$75$	2.48623	0.287086
$76$	1.98237	0.227394
$77$	0	0
$78$	−1.68081	−0.190314
$79$	12.1818	1.37056	0.685279	−	0.728281i	$-0.259680\pi$
$79$	12.1818	1.37056	0.685279	+	0.728281i	$0.259680\pi$
$80$	−2.06310	−0.230662
$81$	−8.42302	−0.935891
$82$	7.03300	0.776665
$83$	6.87035	0.754119	0.377059	−	0.926189i	$-0.376935\pi$
$83$	6.87035	0.754119	0.377059	+	0.926189i	$0.376935\pi$
$84$	0	0
$85$	4.26076	0.462144
$86$	10.8502	1.17000
$87$	10.6073	1.13723
$88$	10.7534	1.14632
$89$	2.40648	0.255086	0.127543	−	0.991833i	$-0.459291\pi$
$89$	2.40648	0.255086	0.127543	+	0.991833i	$0.459291\pi$
$90$	3.60810	0.380327
$91$	0	0
$92$	−3.47056	−0.361831
$93$	2.48623	0.257811
$94$	3.79964	0.391902
$95$	−2.77745	−0.284961
$96$	9.48661	0.968223
$97$	0.815852	0.0828372	0.0414186	−	0.999142i	$-0.486812\pi$
$97$	0.815852	0.0828372	0.0414186	+	0.999142i	$0.486812\pi$
$98$	0	0
$99$	−11.1155	−1.11715
$100$	−0.713738	−0.0713738
$101$	7.53090	0.749352	0.374676	−	0.927156i	$-0.377754\pi$
$101$	7.53090	0.749352	0.374676	+	0.927156i	$0.377754\pi$
$102$	12.0142	1.18958
$103$	−8.51589	−0.839095	−0.419548	−	0.907733i	$-0.637811\pi$
$103$	−8.51589	−0.839095	−0.419548	+	0.907733i	$0.637811\pi$
$104$	1.83462	0.179899
$105$	0	0
$106$	8.47315	0.822985
$107$	12.7948	1.23692	0.618462	−	0.785815i	$-0.287756\pi$
$107$	12.7948	1.23692	0.618462	+	0.785815i	$0.287756\pi$
$108$	−0.321834	−0.0309685
$109$	−8.58259	−0.822063	−0.411031	−	0.911621i	$-0.634831\pi$
$109$	−8.58259	−0.822063	−0.411031	+	0.911621i	$0.634831\pi$
$110$	−3.96259	−0.377818
$111$	8.81063	0.836268
$112$	0	0
$113$	−1.90225	−0.178949	−0.0894743	−	0.995989i	$-0.528519\pi$
$113$	−1.90225	−0.178949	−0.0894743	+	0.995989i	$0.528519\pi$
$114$	−7.83166	−0.733502
$115$	4.86252	0.453432
$116$	−3.04511	−0.282731
$117$	−1.89638	−0.175321
$118$	−0.730027	−0.0672045
$119$	0	0
$120$	−7.65200	−0.698529
$121$	1.20754	0.109776
$122$	−5.94765	−0.538475
$123$	15.4177	1.39016
$124$	−0.713738	−0.0640956
$125$	1.00000	0.0894427
$126$	0	0
$127$	−1.10624	−0.0981627	−0.0490814	−	0.998795i	$-0.515629\pi$
$127$	−1.10624	−0.0981627	−0.0490814	+	0.998795i	$0.515629\pi$
$128$	1.95629	0.172914
$129$	23.7856	2.09420
$130$	−0.676047	−0.0592933
$131$	10.8124	0.944687	0.472343	−	0.881415i	$-0.343408\pi$
$131$	10.8124	0.944687	0.472343	+	0.881415i	$0.343408\pi$
$132$	6.20005	0.539645
$133$	0	0
$134$	3.79052	0.327451
$135$	0.450913	0.0388084
$136$	−13.1135	−1.12447
$137$	−10.6915	−0.913439	−0.456720	−	0.889611i	$-0.650976\pi$
$137$	−10.6915	−0.913439	−0.456720	+	0.889611i	$0.650976\pi$
$138$	13.7110	1.16715
$139$	1.24488	0.105590	0.0527948	−	0.998605i	$-0.483187\pi$
$139$	1.24488	0.105590	0.0527948	+	0.998605i	$0.483187\pi$
$140$	0	0
$141$	8.32951	0.701471
$142$	4.23861	0.355696
$143$	2.08270	0.174164
$144$	−6.56348	−0.546957
$145$	4.26643	0.354307
$146$	−3.82723	−0.316743
$147$	0	0
$148$	−2.52932	−0.207909
$149$	2.14072	0.175374	0.0876872	−	0.996148i	$-0.472052\pi$
$149$	2.14072	0.175374	0.0876872	+	0.996148i	$0.472052\pi$
$150$	2.81973	0.230230
$151$	−5.93846	−0.483265	−0.241632	−	0.970368i	$-0.577683\pi$
$151$	−5.93846	−0.483265	−0.241632	+	0.970368i	$0.577683\pi$
$152$	8.54830	0.693358
$153$	13.5550	1.09586
$154$	0	0
$155$	1.00000	0.0803219
$156$	1.05777	0.0846898
$157$	−6.96186	−0.555617	−0.277809	−	0.960636i	$-0.589608\pi$
$157$	−6.96186	−0.555617	−0.277809	+	0.960636i	$0.589608\pi$
$158$	13.8158	1.09912
$159$	18.5747	1.47307
$160$	3.81565	0.301654
$161$	0	0
$162$	−9.55284	−0.750542
$163$	−10.9084	−0.854409	−0.427205	−	0.904155i	$-0.640502\pi$
$163$	−10.9084	−0.854409	−0.427205	+	0.904155i	$0.640502\pi$
$164$	−4.42604	−0.345615
$165$	−8.68673	−0.676261
$166$	7.79190	0.604769
$167$	−22.4391	−1.73639	−0.868195	−	0.496224i	$-0.834720\pi$
$167$	−22.4391	−1.73639	−0.868195	+	0.496224i	$0.834720\pi$
$168$	0	0
$169$	−12.6447	−0.972667
$170$	4.83227	0.370618
$171$	−8.83609	−0.675713
$172$	−6.82827	−0.520651
$173$	−3.69732	−0.281102	−0.140551	−	0.990073i	$-0.544887\pi$
$173$	−3.69732	−0.281102	−0.140551	+	0.990073i	$0.544887\pi$
$174$	12.0301	0.912003
$175$	0	0
$176$	7.20833	0.543348
$177$	−1.60036	−0.120290
$178$	2.72927	0.204567
$179$	17.9483	1.34152	0.670760	−	0.741674i	$-0.265968\pi$
$179$	17.9483	1.34152	0.670760	+	0.741674i	$0.265968\pi$
$180$	−2.27066	−0.169245
$181$	11.6054	0.862620	0.431310	−	0.902204i	$-0.358052\pi$
$181$	11.6054	0.862620	0.431310	+	0.902204i	$0.358052\pi$
$182$	0	0
$183$	−13.0384	−0.963823
$184$	−14.9656	−1.10328
$185$	3.54376	0.260543
$186$	2.81973	0.206752
$187$	−14.8868	−1.08863
$188$	−2.39120	−0.174396
$189$	0	0
$190$	−3.15001	−0.228526
$191$	−2.87871	−0.208296	−0.104148	−	0.994562i	$-0.533212\pi$
$191$	−2.87871	−0.208296	−0.104148	+	0.994562i	$0.533212\pi$
$192$	21.0178	1.51683
$193$	10.6376	0.765711	0.382856	−	0.923808i	$-0.374941\pi$
$193$	10.6376	0.765711	0.382856	+	0.923808i	$0.374941\pi$
$194$	0.925286	0.0664317
$195$	−1.48202	−0.106130
$196$	0	0
$197$	−4.38153	−0.312171	−0.156086	−	0.987744i	$-0.549888\pi$
$197$	−4.38153	−0.312171	−0.156086	+	0.987744i	$0.549888\pi$
$198$	−12.6064	−0.895900
$199$	8.77515	0.622054	0.311027	−	0.950401i	$-0.399327\pi$
$199$	8.77515	0.622054	0.311027	+	0.950401i	$0.399327\pi$
$200$	−3.07775	−0.217629
$201$	8.30953	0.586109
$202$	8.54105	0.600946
$203$	0	0
$204$	−7.56080	−0.529362
$205$	6.20120	0.433111
$206$	−9.65816	−0.672916
$207$	15.4694	1.07520
$208$	1.22980	0.0852710
$209$	9.70423	0.671255
$210$	0	0
$211$	6.09472	0.419578	0.209789	−	0.977747i	$-0.432722\pi$
$211$	6.09472	0.419578	0.209789	+	0.977747i	$0.432722\pi$
$212$	−5.33236	−0.366228
$213$	9.29182	0.636665
$214$	14.5111	0.991956
$215$	9.56691	0.652458
$216$	−1.38780	−0.0944275
$217$	0	0
$218$	−9.73381	−0.659257
$219$	−8.38999	−0.566943
$220$	2.49375	0.168129
$221$	−2.53980	−0.170845
$222$	9.99244	0.670649
$223$	−16.8231	−1.12656	−0.563278	−	0.826268i	$-0.690460\pi$
$223$	−16.8231	−1.12656	−0.563278	+	0.826268i	$0.690460\pi$
$224$	0	0
$225$	3.18136	0.212091
$226$	−2.15741	−0.143509
$227$	−21.4000	−1.42037	−0.710185	−	0.704015i	$-0.751389\pi$
$227$	−21.4000	−1.42037	−0.710185	+	0.704015i	$0.751389\pi$
$228$	4.92865	0.326408
$229$	−15.6341	−1.03313	−0.516564	−	0.856249i	$-0.672789\pi$
$229$	−15.6341	−1.03313	−0.516564	+	0.856249i	$0.672789\pi$
$230$	5.51475	0.363632
$231$	0	0
$232$	−13.1310	−0.862090
$233$	16.1455	1.05773	0.528863	−	0.848707i	$-0.322619\pi$
$233$	16.1455	1.05773	0.528863	+	0.848707i	$0.322619\pi$
$234$	−2.15075	−0.140599
$235$	3.35025	0.218546
$236$	0.459424	0.0299059
$237$	30.2868	1.96734
$238$	0	0
$239$	6.15080	0.397862	0.198931	−	0.980013i	$-0.436253\pi$
$239$	6.15080	0.397862	0.198931	+	0.980013i	$0.436253\pi$
$240$	−5.12936	−0.331099
$241$	−8.51660	−0.548603	−0.274301	−	0.961644i	$-0.588447\pi$
$241$	−8.51660	−0.548603	−0.274301	+	0.961644i	$0.588447\pi$
$242$	1.36951	0.0880353
$243$	−22.2943	−1.43018
$244$	3.74300	0.239621
$245$	0	0
$246$	17.4857	1.11485
$247$	1.65561	0.105344
$248$	−3.07775	−0.195437
$249$	17.0813	1.08248
$250$	1.13413	0.0717290
$251$	11.0399	0.696833	0.348416	−	0.937340i	$-0.386720\pi$
$251$	11.0399	0.696833	0.348416	+	0.937340i	$0.386720\pi$
$252$	0	0
$253$	−16.9893	−1.06811
$254$	−1.25462	−0.0787220
$255$	10.5932	0.663374
$256$	−14.6886	−0.918040
$257$	30.7032	1.91521	0.957606	−	0.288080i	$-0.0930169\pi$
$257$	30.7032	1.91521	0.957606	+	0.288080i	$0.0930169\pi$
$258$	26.9761	1.67946
$259$	0	0
$260$	0.425453	0.0263854
$261$	13.5731	0.840151
$262$	12.2628	0.757596
$263$	30.6721	1.89132	0.945661	−	0.325153i	$-0.105416\pi$
$263$	30.6721	1.89132	0.945661	+	0.325153i	$0.105416\pi$
$264$	26.7355	1.64546
$265$	7.47103	0.458942
$266$	0	0
$267$	5.98307	0.366158
$268$	−2.38547	−0.145716
$269$	−15.9045	−0.969715	−0.484857	−	0.874593i	$-0.661128\pi$
$269$	−15.9045	−0.969715	−0.484857	+	0.874593i	$0.661128\pi$
$270$	0.511396	0.0311226
$271$	−2.27053	−0.137925	−0.0689625	−	0.997619i	$-0.521969\pi$
$271$	−2.27053	−0.137925	−0.0689625	+	0.997619i	$0.521969\pi$
$272$	−8.79037	−0.532995
$273$	0	0
$274$	−12.1256	−0.732537
$275$	−3.49393	−0.210692
$276$	−8.62863	−0.519383
$277$	19.6358	1.17980	0.589899	−	0.807477i	$-0.299167\pi$
$277$	19.6358	1.17980	0.589899	+	0.807477i	$0.299167\pi$
$278$	1.41186	0.0846780
$279$	3.18136	0.190463
$280$	0	0
$281$	−32.0043	−1.90921	−0.954607	−	0.297867i	$-0.903725\pi$
$281$	−32.0043	−1.90921	−0.954607	+	0.297867i	$0.903725\pi$
$282$	9.44679	0.562548
$283$	−6.56426	−0.390205	−0.195102	−	0.980783i	$-0.562504\pi$
$283$	−6.56426	−0.390205	−0.195102	+	0.980783i	$0.562504\pi$
$284$	−2.66746	−0.158284
$285$	−6.90540	−0.409041
$286$	2.36206	0.139672
$287$	0	0
$288$	12.1390	0.715296
$289$	1.15403	0.0678844
$290$	4.83870	0.284138
$291$	2.02840	0.118907
$292$	2.40856	0.140951
$293$	−19.0106	−1.11061	−0.555306	−	0.831646i	$-0.687399\pi$
$293$	−19.0106	−1.11061	−0.555306	+	0.831646i	$0.687399\pi$
$294$	0	0
$295$	−0.643687	−0.0374769
$296$	−10.9068	−0.633945
$297$	−1.57546	−0.0914173
$298$	2.42786	0.140642
$299$	−2.89850	−0.167625
$300$	−1.77452	−0.102452
$301$	0	0
$302$	−6.73501	−0.387556
$303$	18.7236	1.07564
$304$	5.73017	0.328648
$305$	−5.24422	−0.300283
$306$	15.3732	0.878828
$307$	−30.1274	−1.71946	−0.859730	−	0.510749i	$-0.829368\pi$
$307$	−30.1274	−1.71946	−0.859730	+	0.510749i	$0.829368\pi$
$308$	0	0
$309$	−21.1725	−1.20446
$310$	1.13413	0.0644145
$311$	−22.3862	−1.26940	−0.634702	−	0.772757i	$-0.718877\pi$
$311$	−22.3862	−1.26940	−0.634702	+	0.772757i	$0.718877\pi$
$312$	4.56128	0.258232
$313$	29.1901	1.64992	0.824962	−	0.565188i	$-0.191197\pi$
$313$	29.1901	1.64992	0.824962	+	0.565188i	$0.191197\pi$
$314$	−7.89569	−0.445580
$315$	0	0
$316$	−8.69460	−0.489110
$317$	26.0152	1.46116	0.730579	−	0.682828i	$-0.239250\pi$
$317$	26.0152	1.46116	0.730579	+	0.682828i	$0.239250\pi$
$318$	21.0662	1.18134
$319$	−14.9066	−0.834608
$320$	8.45367	0.472575
$321$	31.8110	1.77552
$322$	0	0
$323$	−11.8341	−0.658464
$324$	6.01183	0.333990
$325$	−0.596091	−0.0330652
$326$	−12.3716	−0.685198
$327$	−21.3383	−1.18001
$328$	−19.0857	−1.05383
$329$	0	0
$330$	−9.85192	−0.542330
$331$	27.8722	1.53199	0.765997	−	0.642844i	$-0.222246\pi$
$331$	27.8722	1.53199	0.765997	+	0.642844i	$0.222246\pi$
$332$	−4.90363	−0.269122
$333$	11.2740	0.617811
$334$	−25.4490	−1.39251
$335$	3.34222	0.182605
$336$	0	0
$337$	15.1221	0.823754	0.411877	−	0.911239i	$-0.364873\pi$
$337$	15.1221	0.823754	0.411877	+	0.911239i	$0.364873\pi$
$338$	−14.3408	−0.780035
$339$	−4.72944	−0.256868
$340$	−3.04106	−0.164925
$341$	−3.49393	−0.189207
$342$	−10.0213	−0.541891
$343$	0	0
$344$	−29.4445	−1.58754
$345$	12.0894	0.650869
$346$	−4.19326	−0.225431
$347$	−16.6554	−0.894107	−0.447053	−	0.894507i	$-0.647527\pi$
$347$	−16.6554	−0.894107	−0.447053	+	0.894507i	$0.647527\pi$
$348$	−7.57086	−0.405841
$349$	−35.7240	−1.91226	−0.956131	−	0.292939i	$-0.905367\pi$
$349$	−35.7240	−1.91226	−0.956131	+	0.292939i	$0.905367\pi$
$350$	0	0
$351$	−0.268785	−0.0143467
$352$	−13.3316	−0.710578
$353$	−7.41971	−0.394911	−0.197456	−	0.980312i	$-0.563268\pi$
$353$	−7.41971	−0.394911	−0.197456	+	0.980312i	$0.563268\pi$
$354$	−1.81502	−0.0964672
$355$	3.73730	0.198356
$356$	−1.71759	−0.0910323
$357$	0	0
$358$	20.3558	1.07584
$359$	−3.02740	−0.159780	−0.0798901	−	0.996804i	$-0.525457\pi$
$359$	−3.02740	−0.159780	−0.0798901	+	0.996804i	$0.525457\pi$
$360$	−9.79143	−0.516053
$361$	−11.2857	−0.593987
$362$	13.1620	0.691782
$363$	3.00222	0.157576
$364$	0	0
$365$	−3.37458	−0.176633
$366$	−14.7873	−0.772943
$367$	−32.4780	−1.69534	−0.847669	−	0.530525i	$-0.821995\pi$
$367$	−32.4780	−1.69534	−0.847669	+	0.530525i	$0.821995\pi$
$368$	−10.0319	−0.522947
$369$	19.7283	1.02701
$370$	4.01910	0.208943
$371$	0	0
$372$	−1.77452	−0.0920046
$373$	−8.32014	−0.430801	−0.215400	−	0.976526i	$-0.569106\pi$
$373$	−8.32014	−0.430801	−0.215400	+	0.976526i	$0.569106\pi$
$374$	−16.8836	−0.873031
$375$	2.48623	0.128389
$376$	−10.3112	−0.531760
$377$	−2.54318	−0.130980
$378$	0	0
$379$	10.3388	0.531069	0.265535	−	0.964101i	$-0.414452\pi$
$379$	10.3388	0.531069	0.265535	+	0.964101i	$0.414452\pi$
$380$	1.98237	0.101694
$381$	−2.75037	−0.140906
$382$	−3.26485	−0.167044
$383$	−5.46517	−0.279257	−0.139628	−	0.990204i	$-0.544591\pi$
$383$	−5.46517	−0.279257	−0.139628	+	0.990204i	$0.544591\pi$
$384$	4.86381	0.248205
$385$	0	0
$386$	12.0645	0.614066
$387$	30.4358	1.54714
$388$	−0.582305	−0.0295620
$389$	10.4631	0.530502	0.265251	−	0.964179i	$-0.414545\pi$
$389$	10.4631	0.530502	0.265251	+	0.964179i	$0.414545\pi$
$390$	−1.68081	−0.0851112
$391$	20.7180	1.04775
$392$	0	0
$393$	26.8823	1.35603
$394$	−4.96925	−0.250347
$395$	12.1818	0.612932
$396$	7.93352	0.398675
$397$	−17.4674	−0.876662	−0.438331	−	0.898814i	$-0.644430\pi$
$397$	−17.4674	−0.876662	−0.438331	+	0.898814i	$0.644430\pi$
$398$	9.95220	0.498859
$399$	0	0
$400$	−2.06310	−0.103155
$401$	25.8921	1.29299	0.646494	−	0.762919i	$-0.276234\pi$
$401$	25.8921	1.29299	0.646494	+	0.762919i	$0.276234\pi$
$402$	9.42413	0.470033
$403$	−0.596091	−0.0296934
$404$	−5.37509	−0.267421
$405$	−8.42302	−0.418543
$406$	0	0
$407$	−12.3817	−0.613736
$408$	−32.6033	−1.61410
$409$	8.14906	0.402945	0.201472	−	0.979494i	$-0.435427\pi$
$409$	8.14906	0.402945	0.201472	+	0.979494i	$0.435427\pi$
$410$	7.03300	0.347335
$411$	−26.5817	−1.31118
$412$	6.07811	0.299447
$413$	0	0
$414$	17.5444	0.862261
$415$	6.87035	0.337252
$416$	−2.27448	−0.111515
$417$	3.09507	0.151566
$418$	11.0059	0.538316
$419$	−2.10872	−0.103018	−0.0515088	−	0.998673i	$-0.516403\pi$
$419$	−2.10872	−0.103018	−0.0515088	+	0.998673i	$0.516403\pi$
$420$	0	0
$421$	7.45891	0.363525	0.181763	−	0.983342i	$-0.441820\pi$
$421$	7.45891	0.363525	0.181763	+	0.983342i	$0.441820\pi$
$422$	6.91223	0.336482
$423$	10.6584	0.518227
$424$	−22.9939	−1.11668
$425$	4.26076	0.206677
$426$	10.5382	0.510576
$427$	0	0
$428$	−9.13216	−0.441420
$429$	5.17808	0.250000
$430$	10.8502	0.523242
$431$	−32.8972	−1.58460	−0.792302	−	0.610130i	$-0.791117\pi$
$431$	−32.8972	−1.58460	−0.792302	+	0.610130i	$0.791117\pi$
$432$	−0.930280	−0.0447581
$433$	37.1810	1.78680	0.893402	−	0.449258i	$-0.148312\pi$
$433$	37.1810	1.78680	0.893402	+	0.449258i	$0.148312\pi$
$434$	0	0
$435$	10.6073	0.508583
$436$	6.12572	0.293369
$437$	−13.5054	−0.646052
$438$	−9.51538	−0.454663
$439$	35.1916	1.67960	0.839802	−	0.542893i	$-0.182671\pi$
$439$	35.1916	1.67960	0.839802	+	0.542893i	$0.182671\pi$
$440$	10.7534	0.512649
$441$	0	0
$442$	−2.88047	−0.137010
$443$	−7.35091	−0.349252	−0.174626	−	0.984635i	$-0.555872\pi$
$443$	−7.35091	−0.349252	−0.174626	+	0.984635i	$0.555872\pi$
$444$	−6.28848	−0.298438
$445$	2.40648	0.114078
$446$	−19.0796	−0.903446
$447$	5.32233	0.251737
$448$	0	0
$449$	19.1125	0.901975	0.450987	−	0.892530i	$-0.351072\pi$
$449$	19.1125	0.901975	0.450987	+	0.892530i	$0.351072\pi$
$450$	3.60810	0.170087
$451$	−21.6666	−1.02024
$452$	1.35771	0.0638612
$453$	−14.7644	−0.693692
$454$	−24.2705	−1.13907
$455$	0	0
$456$	21.2531	0.995266
$457$	−26.1029	−1.22104	−0.610521	−	0.792000i	$-0.709040\pi$
$457$	−26.1029	−1.22104	−0.610521	+	0.792000i	$0.709040\pi$
$458$	−17.7311	−0.828521
$459$	1.92123	0.0896753
$460$	−3.47056	−0.161816
$461$	−11.4660	−0.534025	−0.267012	−	0.963693i	$-0.586036\pi$
$461$	−11.4660	−0.534025	−0.267012	+	0.963693i	$0.586036\pi$
$462$	0	0
$463$	11.6256	0.540285	0.270143	−	0.962820i	$-0.412929\pi$
$463$	11.6256	0.540285	0.270143	+	0.962820i	$0.412929\pi$
$464$	−8.80207	−0.408626
$465$	2.48623	0.115296
$466$	18.3112	0.848248
$467$	−5.95875	−0.275738	−0.137869	−	0.990450i	$-0.544025\pi$
$467$	−5.95875	−0.275738	−0.137869	+	0.990450i	$0.544025\pi$
$468$	1.35352	0.0625665
$469$	0	0
$470$	3.79964	0.175264
$471$	−17.3088	−0.797549
$472$	1.98110	0.0911877
$473$	−33.4261	−1.53693
$474$	34.3493	1.57771
$475$	−2.77745	−0.127438
$476$	0	0
$477$	23.7681	1.08826
$478$	6.97584	0.319068
$479$	11.7509	0.536910	0.268455	−	0.963292i	$-0.413487\pi$
$479$	11.7509	0.536910	0.268455	+	0.963292i	$0.413487\pi$
$480$	9.48661	0.433003
$481$	−2.11240	−0.0963173
$482$	−9.65898	−0.439954
$483$	0	0
$484$	−0.861864	−0.0391756
$485$	0.815852	0.0370459
$486$	−25.2848	−1.14694
$487$	−35.7980	−1.62216	−0.811082	−	0.584933i	$-0.801121\pi$
$487$	−35.7980	−1.62216	−0.811082	+	0.584933i	$0.801121\pi$
$488$	16.1404	0.730640
$489$	−27.1208	−1.22644
$490$	0	0
$491$	−32.0853	−1.44799	−0.723994	−	0.689806i	$-0.757696\pi$
$491$	−32.0853	−1.44799	−0.723994	+	0.689806i	$0.757696\pi$
$492$	−11.0042	−0.496106
$493$	18.1782	0.818705
$494$	1.87769	0.0844813
$495$	−11.1155	−0.499603
$496$	−2.06310	−0.0926360
$497$	0	0
$498$	19.3725	0.868103
$499$	4.89732	0.219234	0.109617	−	0.993974i	$-0.465038\pi$
$499$	4.89732	0.219234	0.109617	+	0.993974i	$0.465038\pi$
$500$	−0.713738	−0.0319193
$501$	−55.7889	−2.49246
$502$	12.5207	0.558828
$503$	44.5087	1.98455	0.992273	−	0.124076i	$-0.0395966\pi$
$503$	44.5087	1.98455	0.992273	+	0.124076i	$0.0395966\pi$
$504$	0	0
$505$	7.53090	0.335121
$506$	−19.2681	−0.856573
$507$	−31.4376	−1.39619
$508$	0.789564	0.0350312
$509$	35.2704	1.56333	0.781667	−	0.623697i	$-0.214370\pi$
$509$	35.2704	1.56333	0.781667	+	0.623697i	$0.214370\pi$
$510$	12.0142	0.531996
$511$	0	0
$512$	−20.5715	−0.909140
$513$	−1.25239	−0.0552944
$514$	34.8216	1.53591
$515$	−8.51589	−0.375255
$516$	−16.9767	−0.747357
$517$	−11.7055	−0.514809
$518$	0	0
$519$	−9.19241	−0.403502
$520$	1.83462	0.0804532
$521$	11.7860	0.516352	0.258176	−	0.966098i	$-0.416879\pi$
$521$	11.7860	0.516352	0.258176	+	0.966098i	$0.416879\pi$
$522$	15.3937	0.673763
$523$	15.8664	0.693787	0.346894	−	0.937904i	$-0.387236\pi$
$523$	15.8664	0.693787	0.346894	+	0.937904i	$0.387236\pi$
$524$	−7.71725	−0.337129
$525$	0	0
$526$	34.7863	1.51675
$527$	4.26076	0.185601
$528$	17.9216	0.779938
$529$	0.644061	0.0280026
$530$	8.47315	0.368050
$531$	−2.04780	−0.0888670
$532$	0	0
$533$	−3.69648	−0.160112
$534$	6.78560	0.293642
$535$	12.7948	0.553169
$536$	−10.2865	−0.444309
$537$	44.6237	1.92566
$538$	−18.0379	−0.777667
$539$	0	0
$540$	−0.321834	−0.0138495
$541$	22.9807	0.988018	0.494009	−	0.869457i	$-0.335531\pi$
$541$	22.9807	0.988018	0.494009	+	0.869457i	$0.335531\pi$
$542$	−2.57509	−0.110610
$543$	28.8537	1.23823
$544$	16.2576	0.697037
$545$	−8.58259	−0.367638
$546$	0	0
$547$	−7.03469	−0.300781	−0.150391	−	0.988627i	$-0.548053\pi$
$547$	−7.03469	−0.300781	−0.150391	+	0.988627i	$0.548053\pi$
$548$	7.63095	0.325978
$549$	−16.6838	−0.712046
$550$	−3.96259	−0.168965
$551$	−11.8498	−0.504819
$552$	−37.2080	−1.58368
$553$	0	0
$554$	22.2696	0.946145
$555$	8.81063	0.373990
$556$	−0.888520	−0.0376816
$557$	−24.7119	−1.04708	−0.523539	−	0.852002i	$-0.675389\pi$
$557$	−24.7119	−1.04708	−0.523539	+	0.852002i	$0.675389\pi$
$558$	3.60810	0.152743
$559$	−5.70275	−0.241201
$560$	0	0
$561$	−37.0120	−1.56265
$562$	−36.2972	−1.53110
$563$	−5.12923	−0.216171	−0.108086	−	0.994142i	$-0.534472\pi$
$563$	−5.12923	−0.216171	−0.108086	+	0.994142i	$0.534472\pi$
$564$	−5.94509	−0.250333
$565$	−1.90225	−0.0800282
$566$	−7.44476	−0.312927
$567$	0	0
$568$	−11.5025	−0.482633
$569$	16.7687	0.702980	0.351490	−	0.936192i	$-0.385675\pi$
$569$	16.7687	0.702980	0.351490	+	0.936192i	$0.385675\pi$
$570$	−7.83166	−0.328032
$571$	−6.10363	−0.255429	−0.127715	−	0.991811i	$-0.540764\pi$
$571$	−6.10363	−0.255429	−0.127715	+	0.991811i	$0.540764\pi$
$572$	−1.48650	−0.0621537
$573$	−7.15715	−0.298994
$574$	0	0
$575$	4.86252	0.202781
$576$	26.8942	1.12059
$577$	4.77821	0.198919	0.0994597	−	0.995042i	$-0.468289\pi$
$577$	4.77821	0.198919	0.0994597	+	0.995042i	$0.468289\pi$
$578$	1.30883	0.0544402
$579$	26.4476	1.09912
$580$	−3.04511	−0.126441
$581$	0	0
$582$	2.30048	0.0953579
$583$	−26.1032	−1.08109
$584$	10.3861	0.429779
$585$	−1.89638	−0.0784057
$586$	−21.5606	−0.890660
$587$	−32.7344	−1.35109	−0.675547	−	0.737316i	$-0.736093\pi$
$587$	−32.7344	−1.35109	−0.675547	+	0.737316i	$0.736093\pi$
$588$	0	0
$589$	−2.77745	−0.114443
$590$	−0.730027	−0.0300548
$591$	−10.8935	−0.448099
$592$	−7.31114	−0.300486
$593$	11.8716	0.487506	0.243753	−	0.969837i	$-0.421621\pi$
$593$	11.8716	0.487506	0.243753	+	0.969837i	$0.421621\pi$
$594$	−1.78678	−0.0733125
$595$	0	0
$596$	−1.52791	−0.0625857
$597$	21.8171	0.892914
$598$	−3.28729	−0.134427
$599$	−10.0548	−0.410827	−0.205413	−	0.978675i	$-0.565854\pi$
$599$	−10.0548	−0.410827	−0.205413	+	0.978675i	$0.565854\pi$
$600$	−7.65200	−0.312391
$601$	−42.6341	−1.73908	−0.869540	−	0.493863i	$-0.835584\pi$
$601$	−42.6341	−1.73908	−0.869540	+	0.493863i	$0.835584\pi$
$602$	0	0
$603$	10.6328	0.433001
$604$	4.23850	0.172462
$605$	1.20754	0.0490933
$606$	21.2351	0.862615
$607$	−27.4583	−1.11450	−0.557249	−	0.830345i	$-0.688143\pi$
$607$	−27.4583	−1.11450	−0.557249	+	0.830345i	$0.688143\pi$
$608$	−10.5978	−0.429798
$609$	0	0
$610$	−5.94765	−0.240813
$611$	−1.99705	−0.0807921
$612$	−9.67473	−0.391078
$613$	13.7873	0.556865	0.278433	−	0.960456i	$-0.410185\pi$
$613$	13.7873	0.556865	0.278433	+	0.960456i	$0.410185\pi$
$614$	−34.1685	−1.37893
$615$	15.4177	0.621700
$616$	0	0
$617$	4.95032	0.199293	0.0996463	−	0.995023i	$-0.468229\pi$
$617$	4.95032	0.199293	0.0996463	+	0.995023i	$0.468229\pi$
$618$	−24.0125	−0.965923
$619$	10.3825	0.417308	0.208654	−	0.977990i	$-0.433092\pi$
$619$	10.3825	0.417308	0.208654	+	0.977990i	$0.433092\pi$
$620$	−0.713738	−0.0286644
$621$	2.19257	0.0879849
$622$	−25.3889	−1.01800
$623$	0	0
$624$	3.05756	0.122400
$625$	1.00000	0.0400000
$626$	33.1055	1.32316
$627$	24.1270	0.963539
$628$	4.96895	0.198283
$629$	15.0991	0.602041
$630$	0	0
$631$	33.3494	1.32762	0.663809	−	0.747902i	$-0.268939\pi$
$631$	33.3494	1.32762	0.663809	+	0.747902i	$0.268939\pi$
$632$	−37.4924	−1.49137
$633$	15.1529	0.602274
$634$	29.5047	1.17178
$635$	−1.10624	−0.0438997
$636$	−13.2575	−0.525694
$637$	0	0
$638$	−16.9061	−0.669318
$639$	11.8897	0.470350
$640$	1.95629	0.0773293
$641$	−34.1430	−1.34857	−0.674284	−	0.738473i	$-0.735547\pi$
$641$	−34.1430	−1.34857	−0.674284	+	0.738473i	$0.735547\pi$
$642$	36.0779	1.42388
$643$	5.14207	0.202784	0.101392	−	0.994847i	$-0.467670\pi$
$643$	5.14207	0.202784	0.101392	+	0.994847i	$0.467670\pi$
$644$	0	0
$645$	23.7856	0.936557
$646$	−13.4214	−0.528058
$647$	−20.1185	−0.790942	−0.395471	−	0.918479i	$-0.629419\pi$
$647$	−20.1185	−0.790942	−0.395471	+	0.918479i	$0.629419\pi$
$648$	25.9239	1.01839
$649$	2.24899	0.0882808
$650$	−0.676047	−0.0265168
$651$	0	0
$652$	7.78572	0.304912
$653$	44.8535	1.75525	0.877626	−	0.479345i	$-0.159126\pi$
$653$	44.8535	1.75525	0.877626	+	0.479345i	$0.159126\pi$
$654$	−24.2005	−0.946316
$655$	10.8124	0.422477
$656$	−12.7937	−0.499511
$657$	−10.7358	−0.418842
$658$	0	0
$659$	34.8327	1.35689	0.678445	−	0.734651i	$-0.262654\pi$
$659$	34.8327	1.35689	0.678445	+	0.734651i	$0.262654\pi$
$660$	6.20005	0.241336
$661$	44.7576	1.74087	0.870435	−	0.492283i	$-0.163837\pi$
$661$	44.7576	1.74087	0.870435	+	0.492283i	$0.163837\pi$
$662$	31.6108	1.22859
$663$	−6.31453	−0.245236
$664$	−21.1452	−0.820592
$665$	0	0
$666$	12.7862	0.495457
$667$	20.7456	0.803271
$668$	16.0156	0.619663
$669$	−41.8261	−1.61709
$670$	3.79052	0.146441
$671$	18.3229	0.707349
$672$	0	0
$673$	10.8749	0.419196	0.209598	−	0.977788i	$-0.432785\pi$
$673$	10.8749	0.419196	0.209598	+	0.977788i	$0.432785\pi$
$674$	17.1505	0.660614
$675$	0.450913	0.0173556
$676$	9.02499	0.347115
$677$	32.6761	1.25584	0.627922	−	0.778276i	$-0.283906\pi$
$677$	32.6761	1.25584	0.627922	+	0.778276i	$0.283906\pi$
$678$	−5.36382	−0.205996
$679$	0	0
$680$	−13.1135	−0.502880
$681$	−53.2055	−2.03884
$682$	−3.96259	−0.151735
$683$	−24.4646	−0.936111	−0.468056	−	0.883699i	$-0.655045\pi$
$683$	−24.4646	−0.936111	−0.468056	+	0.883699i	$0.655045\pi$
$684$	6.30666	0.241141
$685$	−10.6915	−0.408502
$686$	0	0
$687$	−38.8699	−1.48298
$688$	−19.7375	−0.752486
$689$	−4.45341	−0.169661
$690$	13.7110	0.521967
$691$	30.1141	1.14560	0.572798	−	0.819697i	$-0.305858\pi$
$691$	30.1141	1.14560	0.572798	+	0.819697i	$0.305858\pi$
$692$	2.63892	0.100317
$693$	0	0
$694$	−18.8894	−0.717033
$695$	1.24488	0.0472211
$696$	−32.6467	−1.23747
$697$	26.4218	1.00080
$698$	−40.5158	−1.53355
$699$	40.1415	1.51829
$700$	0	0
$701$	−30.3285	−1.14549	−0.572746	−	0.819733i	$-0.694122\pi$
$701$	−30.3285	−1.14549	−0.572746	+	0.819733i	$0.694122\pi$
$702$	−0.304838	−0.0115054
$703$	−9.84264	−0.371222
$704$	−29.5365	−1.11320
$705$	8.32951	0.313707
$706$	−8.41495	−0.316701
$707$	0	0
$708$	1.14223	0.0429278
$709$	43.7373	1.64259	0.821295	−	0.570504i	$-0.193252\pi$
$709$	43.7373	1.64259	0.821295	+	0.570504i	$0.193252\pi$
$710$	4.23861	0.159072
$711$	38.7547	1.45341
$712$	−7.40652	−0.277571
$713$	4.86252	0.182103
$714$	0	0
$715$	2.08270	0.0778885
$716$	−12.8104	−0.478747
$717$	15.2923	0.571103
$718$	−3.43348	−0.128136
$719$	2.01233	0.0750473	0.0375237	−	0.999296i	$-0.488053\pi$
$719$	2.01233	0.0750473	0.0375237	+	0.999296i	$0.488053\pi$
$720$	−6.56348	−0.244606
$721$	0	0
$722$	−12.7996	−0.476350
$723$	−21.1743	−0.787480
$724$	−8.28319	−0.307842
$725$	4.26643	0.158451
$726$	3.40492	0.126368
$727$	−38.0122	−1.40980	−0.704898	−	0.709309i	$-0.749007\pi$
$727$	−38.0122	−1.40980	−0.704898	+	0.709309i	$0.749007\pi$
$728$	0	0
$729$	−30.1599	−1.11703
$730$	−3.82723	−0.141652
$731$	40.7623	1.50765
$732$	9.30597	0.343959
$733$	26.3132	0.971901	0.485951	−	0.873986i	$-0.338473\pi$
$733$	26.3132	0.971901	0.485951	+	0.873986i	$0.338473\pi$
$734$	−36.8345	−1.35958
$735$	0	0
$736$	18.5537	0.683898
$737$	−11.6775	−0.430145
$738$	22.3745	0.823618
$739$	17.1248	0.629946	0.314973	−	0.949101i	$-0.398005\pi$
$739$	17.1248	0.629946	0.314973	+	0.949101i	$0.398005\pi$
$740$	−2.52932	−0.0929796
$741$	4.11625	0.151214
$742$	0	0
$743$	−39.5270	−1.45011	−0.725053	−	0.688693i	$-0.758185\pi$
$743$	−39.5270	−1.45011	−0.725053	+	0.688693i	$0.758185\pi$
$744$	−7.65200	−0.280536
$745$	2.14072	0.0784298
$746$	−9.43616	−0.345482
$747$	21.8571	0.799709
$748$	10.6253	0.388498
$749$	0	0
$750$	2.81973	0.102962
$751$	39.0342	1.42438	0.712189	−	0.701988i	$-0.247704\pi$
$751$	39.0342	1.42438	0.712189	+	0.701988i	$0.247704\pi$
$752$	−6.91191	−0.252051
$753$	27.4478	1.00025
$754$	−2.88430	−0.105040
$755$	−5.93846	−0.216123
$756$	0	0
$757$	−25.0099	−0.909000	−0.454500	−	0.890747i	$-0.650182\pi$
$757$	−25.0099	−0.909000	−0.454500	+	0.890747i	$0.650182\pi$
$758$	11.7256	0.425893
$759$	−42.2393	−1.53319
$760$	8.54830	0.310079
$761$	15.7099	0.569484	0.284742	−	0.958604i	$-0.408092\pi$
$761$	15.7099	0.569484	0.284742	+	0.958604i	$0.408092\pi$
$762$	−3.11929	−0.113000
$763$	0	0
$764$	2.05464	0.0743344
$765$	13.5550	0.490083
$766$	−6.19824	−0.223951
$767$	0.383696	0.0138544
$768$	−36.5194	−1.31778
$769$	−33.1653	−1.19597	−0.597985	−	0.801507i	$-0.704032\pi$
$769$	−33.1653	−1.19597	−0.597985	+	0.801507i	$0.704032\pi$
$770$	0	0
$771$	76.3354	2.74915
$772$	−7.59246	−0.273259
$773$	−38.8939	−1.39892	−0.699459	−	0.714673i	$-0.746576\pi$
$773$	−38.8939	−1.39892	−0.699459	+	0.714673i	$0.746576\pi$
$774$	34.5183	1.24074
$775$	1.00000	0.0359211
$776$	−2.51098	−0.0901391
$777$	0	0
$778$	11.8666	0.425439
$779$	−17.2236	−0.617098
$780$	1.05777	0.0378744
$781$	−13.0579	−0.467248
$782$	23.4970	0.840251
$783$	1.92379	0.0687505
$784$	0	0
$785$	−6.96186	−0.248480
$786$	30.4881	1.08747
$787$	−42.0531	−1.49903	−0.749516	−	0.661987i	$-0.769714\pi$
$787$	−42.0531	−1.49903	−0.749516	+	0.661987i	$0.769714\pi$
$788$	3.12727	0.111404
$789$	76.2580	2.71486
$790$	13.8158	0.491544
$791$	0	0
$792$	34.2105	1.21562
$793$	3.12603	0.111009
$794$	−19.8103	−0.703043
$795$	18.5747	0.658778
$796$	−6.26316	−0.221992
$797$	3.58387	0.126947	0.0634736	−	0.997984i	$-0.479782\pi$
$797$	3.58387	0.126947	0.0634736	+	0.997984i	$0.479782\pi$
$798$	0	0
$799$	14.2746	0.504999
$800$	3.81565	0.134904
$801$	7.65588	0.270507
$802$	29.3651	1.03692
$803$	11.7905	0.416079
$804$	−5.93083	−0.209164
$805$	0	0
$806$	−0.676047	−0.0238127
$807$	−39.5423	−1.39196
$808$	−23.1782	−0.815406
$809$	28.4328	0.999644	0.499822	−	0.866128i	$-0.333399\pi$
$809$	28.4328	0.999644	0.499822	+	0.866128i	$0.333399\pi$
$810$	−9.55284	−0.335652
$811$	−45.3632	−1.59292	−0.796459	−	0.604692i	$-0.793296\pi$
$811$	−45.3632	−1.59292	−0.796459	+	0.604692i	$0.793296\pi$
$812$	0	0
$813$	−5.64508	−0.197982
$814$	−14.0425	−0.492188
$815$	−10.9084	−0.382104
$816$	−21.8549	−0.765076
$817$	−26.5717	−0.929625
$818$	9.24213	0.323143
$819$	0	0
$820$	−4.42604	−0.154564
$821$	40.5498	1.41520	0.707598	−	0.706615i	$-0.249779\pi$
$821$	40.5498	1.41520	0.707598	+	0.706615i	$0.249779\pi$
$822$	−30.1472	−1.05150
$823$	49.1468	1.71315	0.856575	−	0.516022i	$-0.172588\pi$
$823$	49.1468	1.71315	0.856575	+	0.516022i	$0.172588\pi$
$824$	26.2097	0.913059
$825$	−8.68673	−0.302433
$826$	0	0
$827$	22.3575	0.777445	0.388723	−	0.921355i	$-0.372916\pi$
$827$	22.3575	0.777445	0.388723	+	0.921355i	$0.372916\pi$
$828$	−11.0411	−0.383706
$829$	37.5243	1.30327	0.651637	−	0.758531i	$-0.274082\pi$
$829$	37.5243	1.30327	0.651637	+	0.758531i	$0.274082\pi$
$830$	7.79190	0.270461
$831$	48.8191	1.69352
$832$	−5.03915	−0.174701
$833$	0	0
$834$	3.51023	0.121549
$835$	−22.4391	−0.776537
$836$	−6.92628	−0.239550
$837$	0.450913	0.0155858
$838$	−2.39157	−0.0826154
$839$	−43.8836	−1.51503	−0.757516	−	0.652817i	$-0.773587\pi$
$839$	−43.8836	−1.51503	−0.757516	+	0.652817i	$0.773587\pi$
$840$	0	0
$841$	−10.7976	−0.372332
$842$	8.45941	0.291531
$843$	−79.5701	−2.74054
$844$	−4.35003	−0.149734
$845$	−12.6447	−0.434990
$846$	12.0880	0.415595
$847$	0	0
$848$	−15.4135	−0.529301
$849$	−16.3203	−0.560111
$850$	4.83227	0.165746
$851$	17.2316	0.590692
$852$	−6.63192	−0.227206
$853$	−2.90857	−0.0995875	−0.0497937	−	0.998760i	$-0.515856\pi$
$853$	−2.90857	−0.0995875	−0.0497937	+	0.998760i	$0.515856\pi$
$854$	0	0
$855$	−8.83609	−0.302188
$856$	−39.3792	−1.34595
$857$	34.9585	1.19416	0.597080	−	0.802182i	$-0.296328\pi$
$857$	34.9585	1.19416	0.597080	+	0.802182i	$0.296328\pi$
$858$	5.87264	0.200489
$859$	−14.8052	−0.505147	−0.252574	−	0.967578i	$-0.581277\pi$
$859$	−14.8052	−0.505147	−0.252574	+	0.967578i	$0.581277\pi$
$860$	−6.82827	−0.232842
$861$	0	0
$862$	−37.3099	−1.27078
$863$	55.5840	1.89210	0.946050	−	0.324021i	$-0.105035\pi$
$863$	55.5840	1.89210	0.946050	+	0.324021i	$0.105035\pi$
$864$	1.72053	0.0585336
$865$	−3.69732	−0.125713
$866$	42.1682	1.43294
$867$	2.86920	0.0974432
$868$	0	0
$869$	−42.5623	−1.44383
$870$	12.0301	0.407860
$871$	−1.99226	−0.0675053
$872$	26.4150	0.894525
$873$	2.59552	0.0878451
$874$	−15.3170	−0.518104
$875$	0	0
$876$	5.98826	0.202324
$877$	−53.2429	−1.79789	−0.898943	−	0.438067i	$-0.855663\pi$
$877$	−53.2429	−1.79789	−0.898943	+	0.438067i	$0.855663\pi$
$878$	39.9120	1.34697
$879$	−47.2648	−1.59420
$880$	7.20833	0.242993
$881$	40.2395	1.35570	0.677851	−	0.735199i	$-0.262911\pi$
$881$	40.2395	1.35570	0.677851	+	0.735199i	$0.262911\pi$
$882$	0	0
$883$	−8.52699	−0.286956	−0.143478	−	0.989653i	$-0.545829\pi$
$883$	−8.52699	−0.286956	−0.143478	+	0.989653i	$0.545829\pi$
$884$	1.81275	0.0609694
$885$	−1.60036	−0.0537954
$886$	−8.33692	−0.280084
$887$	−26.1125	−0.876772	−0.438386	−	0.898787i	$-0.644450\pi$
$887$	−26.1125	−0.876772	−0.438386	+	0.898787i	$0.644450\pi$
$888$	−27.1169	−0.909982
$889$	0	0
$890$	2.72927	0.0914853
$891$	29.4294	0.985922
$892$	12.0073	0.402033
$893$	−9.30517	−0.311386
$894$	6.03624	0.201882
$895$	17.9483	0.599946
$896$	0	0
$897$	−7.20635	−0.240613
$898$	21.6762	0.723343
$899$	4.26643	0.142293
$900$	−2.27066	−0.0756887
$901$	31.8322	1.06048
$902$	−24.5728	−0.818185
$903$	0	0
$904$	5.85464	0.194722
$905$	11.6054	0.385775
$906$	−16.7448	−0.556309
$907$	−42.5686	−1.41347	−0.706734	−	0.707480i	$-0.749832\pi$
$907$	−42.5686	−1.41347	−0.706734	+	0.707480i	$0.749832\pi$
$908$	15.2740	0.506886
$909$	23.9585	0.794654
$910$	0	0
$911$	−46.1090	−1.52766	−0.763829	−	0.645419i	$-0.776683\pi$
$911$	−46.1090	−1.52766	−0.763829	+	0.645419i	$0.776683\pi$
$912$	14.2466	0.471751
$913$	−24.0045	−0.794433
$914$	−29.6042	−0.979221
$915$	−13.0384	−0.431035
$916$	11.1586	0.368691
$917$	0	0
$918$	2.17893	0.0719155
$919$	8.88694	0.293153	0.146577	−	0.989199i	$-0.453175\pi$
$919$	8.88694	0.293153	0.146577	+	0.989199i	$0.453175\pi$
$920$	−14.9656	−0.493401
$921$	−74.9037	−2.46816
$922$	−13.0040	−0.428263
$923$	−2.22777	−0.0733280
$924$	0	0
$925$	3.54376	0.116518
$926$	13.1849	0.433284
$927$	−27.0921	−0.889822
$928$	16.2792	0.534391
$929$	5.00252	0.164127	0.0820637	−	0.996627i	$-0.473849\pi$
$929$	5.00252	0.164127	0.0820637	+	0.996627i	$0.473849\pi$
$930$	2.81973	0.0924624
$931$	0	0
$932$	−11.5236	−0.377469
$933$	−55.6573	−1.82214
$934$	−6.75803	−0.221129
$935$	−14.8868	−0.486850
$936$	5.83658	0.190775
$937$	−13.1243	−0.428754	−0.214377	−	0.976751i	$-0.568772\pi$
$937$	−13.1243	−0.428754	−0.214377	+	0.976751i	$0.568772\pi$
$938$	0	0
$939$	72.5735	2.36835
$940$	−2.39120	−0.0779924
$941$	−6.53336	−0.212982	−0.106491	−	0.994314i	$-0.533961\pi$
$941$	−6.53336	−0.212982	−0.106491	+	0.994314i	$0.533961\pi$
$942$	−19.6305	−0.639598
$943$	30.1535	0.981932
$944$	1.32799	0.0432224
$945$	0	0
$946$	−37.9097	−1.23255
$947$	−42.6522	−1.38601	−0.693006	−	0.720932i	$-0.743714\pi$
$947$	−42.6522	−1.38601	−0.693006	+	0.720932i	$0.743714\pi$
$948$	−21.6168	−0.702082
$949$	2.01155	0.0652978
$950$	−3.15001	−0.102200
$951$	64.6799	2.09739
$952$	0	0
$953$	−29.6738	−0.961229	−0.480615	−	0.876932i	$-0.659586\pi$
$953$	−29.6738	−0.961229	−0.480615	+	0.876932i	$0.659586\pi$
$954$	26.9562	0.872739
$955$	−2.87871	−0.0931529
$956$	−4.39006	−0.141985
$957$	−37.0613	−1.19802
$958$	13.3271	0.430578
$959$	0	0
$960$	21.0178	0.678347
$961$	1.00000	0.0322581
$962$	−2.39575	−0.0772421
$963$	40.7050	1.31170
$964$	6.07862	0.195779
$965$	10.6376	0.342436
$966$	0	0
$967$	32.3021	1.03876	0.519382	−	0.854542i	$-0.326162\pi$
$967$	32.3021	1.03876	0.519382	+	0.854542i	$0.326162\pi$
$968$	−3.71649	−0.119452
$969$	−29.4222	−0.945178
$970$	0.925286	0.0297092
$971$	−33.3123	−1.06904	−0.534522	−	0.845155i	$-0.679508\pi$
$971$	−33.3123	−1.06904	−0.534522	+	0.845155i	$0.679508\pi$
$972$	15.9123	0.510388
$973$	0	0
$974$	−40.5998	−1.30090
$975$	−1.48202	−0.0474627
$976$	10.8194	0.346319
$977$	−7.77433	−0.248723	−0.124361	−	0.992237i	$-0.539688\pi$
$977$	−7.77433	−0.248723	−0.124361	+	0.992237i	$0.539688\pi$
$978$	−30.7586	−0.983552
$979$	−8.40806	−0.268723
$980$	0	0
$981$	−27.3043	−0.871760
$982$	−36.3890	−1.16122
$983$	−34.0463	−1.08591	−0.542954	−	0.839763i	$-0.682694\pi$
$983$	−34.0463	−1.08591	−0.542954	+	0.839763i	$0.682694\pi$
$984$	−47.4516	−1.51270
$985$	−4.38153	−0.139607
$986$	20.6165	0.656564
$987$	0	0
$988$	−1.18168	−0.0375941
$989$	46.5193	1.47923
$990$	−12.6064	−0.400659
$991$	−25.6677	−0.815360	−0.407680	−	0.913125i	$-0.633662\pi$
$991$	−25.6677	−0.815360	−0.407680	+	0.913125i	$0.633662\pi$
$992$	3.81565	0.121147
$993$	69.2968	2.19907
$994$	0	0
$995$	8.77515	0.278191
$996$	−12.1916	−0.386305
$997$	43.5257	1.37847	0.689237	−	0.724536i	$-0.257946\pi$
$997$	43.5257	1.37847	0.689237	+	0.724536i	$0.257946\pi$
$998$	5.55422	0.175816
$999$	1.59793	0.0505562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.u.1.4		7
7.6	odd	2		1085.2.a.p.1.4	✓	7
21.20	even	2		9765.2.a.bc.1.4		7
35.34	odd	2		5425.2.a.ba.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.a.p.1.4	✓	7	7.6	odd	2
5425.2.a.ba.1.4		7	35.34	odd	2
7595.2.a.u.1.4		7	1.1	even	1	trivial
9765.2.a.bc.1.4		7	21.20	even	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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q+1.13413 q^{2} +2.48623 q^{3} -0.713738 q^{4} +1.00000 q^{5} +2.81973 q^{6} -3.07775 q^{8} +3.18136 q^{9} +O(q^{10})\)	\(q+1.13413 q^{2} +2.48623 q^{3} -0.713738 q^{4} +1.00000 q^{5} +2.81973 q^{6} -3.07775 q^{8} +3.18136 q^{9} +1.13413 q^{10} -3.49393 q^{11} -1.77452 q^{12} -0.596091 q^{13} +2.48623 q^{15} -2.06310 q^{16} +4.26076 q^{17} +3.60810 q^{18} -2.77745 q^{19} -0.713738 q^{20} -3.96259 q^{22} +4.86252 q^{23} -7.65200 q^{24} +1.00000 q^{25} -0.676047 q^{26} +0.450913 q^{27} +4.26643 q^{29} +2.81973 q^{30} +1.00000 q^{31} +3.81565 q^{32} -8.68673 q^{33} +4.83227 q^{34} -2.27066 q^{36} +3.54376 q^{37} -3.15001 q^{38} -1.48202 q^{39} -3.07775 q^{40} +6.20120 q^{41} +9.56691 q^{43} +2.49375 q^{44} +3.18136 q^{45} +5.51475 q^{46} +3.35025 q^{47} -5.12936 q^{48} +1.13413 q^{50} +10.5932 q^{51} +0.425453 q^{52} +7.47103 q^{53} +0.511396 q^{54} -3.49393 q^{55} -6.90540 q^{57} +4.83870 q^{58} -0.643687 q^{59} -1.77452 q^{60} -5.24422 q^{61} +1.13413 q^{62} +8.45367 q^{64} -0.596091 q^{65} -9.85192 q^{66} +3.34222 q^{67} -3.04106 q^{68} +12.0894 q^{69} +3.73730 q^{71} -9.79143 q^{72} -3.37458 q^{73} +4.01910 q^{74} +2.48623 q^{75} +1.98237 q^{76} -1.68081 q^{78} +12.1818 q^{79} -2.06310 q^{80} -8.42302 q^{81} +7.03300 q^{82} +6.87035 q^{83} +4.26076 q^{85} +10.8502 q^{86} +10.6073 q^{87} +10.7534 q^{88} +2.40648 q^{89} +3.60810 q^{90} -3.47056 q^{92} +2.48623 q^{93} +3.79964 q^{94} -2.77745 q^{95} +9.48661 q^{96} +0.815852 q^{97} -11.1155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9	\( 7 q + 3 q^{2} - 2 q^{3} + 13 q^{4} + 7 q^{5} + 12 q^{6} + 9 q^{8} + 11 q^{9} + 3 q^{10} + 5 q^{11} - 4 q^{12} - 9 q^{13} - 2 q^{15} + 13 q^{16} + 2 q^{17} - 5 q^{18} - 13 q^{19} + 13 q^{20} + 20 q^{22} + 8 q^{23} + 8 q^{24} + 7 q^{25} - 4 q^{26} - 8 q^{27} - q^{29} + 12 q^{30} + 7 q^{31} + 11 q^{32} + 13 q^{33} - 20 q^{34} - 3 q^{36} + 37 q^{37} + 4 q^{38} + 21 q^{39} + 9 q^{40} - 9 q^{41} + 19 q^{43} + 16 q^{44} + 11 q^{45} + 8 q^{46} + q^{47} - 8 q^{48} + 3 q^{50} - 4 q^{51} - 26 q^{52} + 25 q^{53} + 32 q^{54} + 5 q^{55} + 33 q^{57} + 4 q^{58} - 7 q^{59} - 4 q^{60} + 34 q^{61} + 3 q^{62} + 49 q^{64} - 9 q^{65} - 32 q^{66} + 20 q^{68} - 4 q^{69} - 23 q^{71} - 17 q^{72} + 3 q^{73} - 18 q^{74} - 2 q^{75} - 10 q^{76} + 14 q^{78} + 13 q^{79} + 13 q^{80} - 5 q^{81} + 78 q^{82} + 13 q^{83} + 2 q^{85} + 10 q^{86} + 17 q^{87} + 52 q^{88} + 10 q^{89} - 5 q^{90} + 60 q^{92} - 2 q^{93} + 38 q^{94} - 13 q^{95} + 26 q^{96} - 3 q^{97} - 36 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 - 2 * q^3 + 13 * q^4 + 7 * q^5 + 12 * q^6 + 9 * q^8 + 11 * q^9 + 3 * q^10 + 5 * q^11 - 4 * q^12 - 9 * q^13 - 2 * q^15 + 13 * q^16 + 2 * q^17 - 5 * q^18 - 13 * q^19 + 13 * q^20 + 20 * q^22 + 8 * q^23 + 8 * q^24 + 7 * q^25 - 4 * q^26 - 8 * q^27 - q^29 + 12 * q^30 + 7 * q^31 + 11 * q^32 + 13 * q^33 - 20 * q^34 - 3 * q^36 + 37 * q^37 + 4 * q^38 + 21 * q^39 + 9 * q^40 - 9 * q^41 + 19 * q^43 + 16 * q^44 + 11 * q^45 + 8 * q^46 + q^47 - 8 * q^48 + 3 * q^50 - 4 * q^51 - 26 * q^52 + 25 * q^53 + 32 * q^54 + 5 * q^55 + 33 * q^57 + 4 * q^58 - 7 * q^59 - 4 * q^60 + 34 * q^61 + 3 * q^62 + 49 * q^64 - 9 * q^65 - 32 * q^66 + 20 * q^68 - 4 * q^69 - 23 * q^71 - 17 * q^72 + 3 * q^73 - 18 * q^74 - 2 * q^75 - 10 * q^76 + 14 * q^78 + 13 * q^79 + 13 * q^80 - 5 * q^81 + 78 * q^82 + 13 * q^83 + 2 * q^85 + 10 * q^86 + 17 * q^87 + 52 * q^88 + 10 * q^89 - 5 * q^90 + 60 * q^92 - 2 * q^93 + 38 * q^94 - 13 * q^95 + 26 * q^96 - 3 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

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