LMFDB - Embedded newform 1445.2.a.q.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(1,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-4,8,12,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 $ x^12 - 4x^11 - 10x^10 + 52x^9 + 21x^8 - 232x^7 + 44x^6 + 424x^5 - 137x^4 - 316x^3 + 46x^2 + 92*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.301687$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.301687 q^{2} -1.06101 q^{3} -1.90899 q^{4} -1.00000 q^{5} -0.320094 q^{6} -2.50984 q^{7} -1.17929 q^{8} -1.87425 q^{9} -0.301687 q^{10} +2.44557 q^{11} +2.02546 q^{12} -5.61335 q^{13} -0.757185 q^{14} +1.06101 q^{15} +3.46219 q^{16} -0.565436 q^{18} -7.13107 q^{19} +1.90899 q^{20} +2.66297 q^{21} +0.737797 q^{22} -0.860805 q^{23} +1.25124 q^{24} +1.00000 q^{25} -1.69348 q^{26} +5.17165 q^{27} +4.79124 q^{28} +3.75143 q^{29} +0.320094 q^{30} -2.24733 q^{31} +3.40308 q^{32} -2.59479 q^{33} +2.50984 q^{35} +3.57791 q^{36} -5.10557 q^{37} -2.15135 q^{38} +5.95585 q^{39} +1.17929 q^{40} +12.3496 q^{41} +0.803384 q^{42} -2.62014 q^{43} -4.66856 q^{44} +1.87425 q^{45} -0.259694 q^{46} -2.30114 q^{47} -3.67344 q^{48} -0.700712 q^{49} +0.301687 q^{50} +10.7158 q^{52} +2.77475 q^{53} +1.56022 q^{54} -2.44557 q^{55} +2.95983 q^{56} +7.56616 q^{57} +1.13176 q^{58} +7.44167 q^{59} -2.02546 q^{60} +0.906291 q^{61} -0.677989 q^{62} +4.70406 q^{63} -5.89773 q^{64} +5.61335 q^{65} -0.782813 q^{66} +6.69889 q^{67} +0.913326 q^{69} +0.757185 q^{70} -0.240766 q^{71} +2.21028 q^{72} -6.45746 q^{73} -1.54028 q^{74} -1.06101 q^{75} +13.6131 q^{76} -6.13799 q^{77} +1.79680 q^{78} +14.7096 q^{79} -3.46219 q^{80} +0.135560 q^{81} +3.72571 q^{82} +13.8984 q^{83} -5.08358 q^{84} -0.790460 q^{86} -3.98032 q^{87} -2.88404 q^{88} -0.395163 q^{89} +0.565436 q^{90} +14.0886 q^{91} +1.64326 q^{92} +2.38445 q^{93} -0.694222 q^{94} +7.13107 q^{95} -3.61071 q^{96} -8.95923 q^{97} -0.211396 q^{98} -4.58361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 8 q^{3} + 12 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} - 12 q^{8} + 12 q^{9} + 4 q^{10} + 16 q^{11} + 16 q^{12} - 8 q^{13} - 16 q^{14} - 8 q^{15} + 12 q^{16} + 4 q^{18} - 12 q^{20} + 16 q^{21}+ \cdots + 56 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 8 * q^3 + 12 * q^4 - 12 * q^5 + 8 * q^6 + 16 * q^7 - 12 * q^8 + 12 * q^9 + 4 * q^10 + 16 * q^11 + 16 * q^12 - 8 * q^13 - 16 * q^14 - 8 * q^15 + 12 * q^16 + 4 * q^18 - 12 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 12 * q^25 + 16 * q^26 + 32 * q^27 + 40 * q^28 + 16 * q^29 - 8 * q^30 + 24 * q^31 - 28 * q^32 - 16 * q^35 + 12 * q^36 + 24 * q^37 - 24 * q^38 + 8 * q^39 + 12 * q^40 + 8 * q^41 - 16 * q^43 + 8 * q^44 - 12 * q^45 + 40 * q^46 - 32 * q^47 - 24 * q^48 + 20 * q^49 - 4 * q^50 - 24 * q^52 + 8 * q^54 - 16 * q^55 - 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 16 * q^60 + 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 8 * q^65 + 40 * q^66 - 8 * q^67 + 48 * q^69 + 16 * q^70 - 16 * q^71 + 12 * q^72 + 16 * q^73 + 8 * q^75 + 16 * q^76 + 24 * q^77 - 24 * q^78 + 40 * q^79 - 12 * q^80 + 36 * q^81 - 16 * q^82 - 40 * q^83 + 32 * q^84 - 8 * q^86 - 32 * q^87 + 48 * q^88 + 8 * q^89 - 4 * q^90 + 72 * q^91 - 8 * q^92 + 24 * q^93 - 16 * q^94 + 8 * q^96 + 32 * q^97 - 60 * q^98 + 56 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.301687	0.213325	0.106662	−	0.994295i	$-0.465984\pi$
$2$	0.301687	0.213325	0.106662	+	0.994295i	$0.465984\pi$
$3$	−1.06101	−0.612577	−0.306288	−	0.951939i	$-0.599087\pi$
$3$	−1.06101	−0.612577	−0.306288	+	0.951939i	$0.599087\pi$
$4$	−1.90899	−0.954493
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.320094	−0.130678
$7$	−2.50984	−0.948630	−0.474315	−	0.880355i	$-0.657304\pi$
$7$	−2.50984	−0.948630	−0.474315	+	0.880355i	$0.657304\pi$
$8$	−1.17929	−0.416942
$9$	−1.87425	−0.624750
$10$	−0.301687	−0.0954017
$11$	2.44557	0.737368	0.368684	−	0.929555i	$-0.379808\pi$
$11$	2.44557	0.737368	0.368684	+	0.929555i	$0.379808\pi$
$12$	2.02546	0.584700
$13$	−5.61335	−1.55686	−0.778432	−	0.627729i	$-0.783985\pi$
$13$	−5.61335	−1.55686	−0.778432	+	0.627729i	$0.783985\pi$
$14$	−0.757185	−0.202366
$15$	1.06101	0.273953
$16$	3.46219	0.865549
$17$	0	0
$17$	0	0
$18$	−0.565436	−0.133275
$19$	−7.13107	−1.63598	−0.817990	−	0.575233i	$-0.804911\pi$
$19$	−7.13107	−1.63598	−0.817990	+	0.575233i	$0.804911\pi$
$20$	1.90899	0.426862
$21$	2.66297	0.581108
$22$	0.737797	0.157299
$23$	−0.860805	−0.179490	−0.0897451	−	0.995965i	$-0.528605\pi$
$23$	−0.860805	−0.179490	−0.0897451	+	0.995965i	$0.528605\pi$
$24$	1.25124	0.255409
$25$	1.00000	0.200000
$26$	−1.69348	−0.332118
$27$	5.17165	0.995284
$28$	4.79124	0.905460
$29$	3.75143	0.696624	0.348312	−	0.937379i	$-0.386755\pi$
$29$	3.75143	0.696624	0.348312	+	0.937379i	$0.386755\pi$
$30$	0.320094	0.0584409
$31$	−2.24733	−0.403632	−0.201816	−	0.979423i	$-0.564684\pi$
$31$	−2.24733	−0.403632	−0.201816	+	0.979423i	$0.564684\pi$
$32$	3.40308	0.601585
$33$	−2.59479	−0.451694
$34$	0	0
$35$	2.50984	0.424240
$36$	3.57791	0.596319
$37$	−5.10557	−0.839351	−0.419675	−	0.907674i	$-0.637856\pi$
$37$	−5.10557	−0.839351	−0.419675	+	0.907674i	$0.637856\pi$
$38$	−2.15135	−0.348995
$39$	5.95585	0.953699
$40$	1.17929	0.186462
$41$	12.3496	1.92868	0.964340	−	0.264666i	$-0.0852617\pi$
$41$	12.3496	1.92868	0.964340	+	0.264666i	$0.0852617\pi$
$42$	0.803384	0.123965
$43$	−2.62014	−0.399567	−0.199783	−	0.979840i	$-0.564024\pi$
$43$	−2.62014	−0.399567	−0.199783	+	0.979840i	$0.564024\pi$
$44$	−4.66856	−0.703812
$45$	1.87425	0.279397
$46$	−0.259694	−0.0382897
$47$	−2.30114	−0.335655	−0.167828	−	0.985816i	$-0.553675\pi$
$47$	−2.30114	−0.335655	−0.167828	+	0.985816i	$0.553675\pi$
$48$	−3.67344	−0.530215
$49$	−0.700712	−0.100102
$50$	0.301687	0.0426650
$51$	0	0
$52$	10.7158	1.48602
$53$	2.77475	0.381141	0.190571	−	0.981674i	$-0.438966\pi$
$53$	2.77475	0.381141	0.190571	+	0.981674i	$0.438966\pi$
$54$	1.56022	0.212319
$55$	−2.44557	−0.329761
$56$	2.95983	0.395523
$57$	7.56616	1.00216
$58$	1.13176	0.148607
$59$	7.44167	0.968823	0.484412	−	0.874840i	$-0.339034\pi$
$59$	7.44167	0.968823	0.484412	+	0.874840i	$0.339034\pi$
$60$	−2.02546	−0.261486
$61$	0.906291	0.116039	0.0580193	−	0.998315i	$-0.481522\pi$
$61$	0.906291	0.116039	0.0580193	+	0.998315i	$0.481522\pi$
$62$	−0.677989	−0.0861047
$63$	4.70406	0.592656
$64$	−5.89773	−0.737216
$65$	5.61335	0.696251
$66$	−0.782813	−0.0963576
$67$	6.69889	0.818399	0.409200	−	0.912445i	$-0.365808\pi$
$67$	6.69889	0.818399	0.409200	+	0.912445i	$0.365808\pi$
$68$	0	0
$69$	0.913326	0.109952
$70$	0.757185	0.0905009
$71$	−0.240766	−0.0285737	−0.0142868	−	0.999898i	$-0.504548\pi$
$71$	−0.240766	−0.0285737	−0.0142868	+	0.999898i	$0.504548\pi$
$72$	2.21028	0.260484
$73$	−6.45746	−0.755788	−0.377894	−	0.925849i	$-0.623352\pi$
$73$	−6.45746	−0.755788	−0.377894	+	0.925849i	$0.623352\pi$
$74$	−1.54028	−0.179054
$75$	−1.06101	−0.122515
$76$	13.6131	1.56153
$77$	−6.13799	−0.699489
$78$	1.79680	0.203448
$79$	14.7096	1.65496	0.827479	−	0.561497i	$-0.189774\pi$
$79$	14.7096	1.65496	0.827479	+	0.561497i	$0.189774\pi$
$80$	−3.46219	−0.387085
$81$	0.135560	0.0150623
$82$	3.72571	0.411435
$83$	13.8984	1.52555	0.762775	−	0.646664i	$-0.223836\pi$
$83$	13.8984	1.52555	0.762775	+	0.646664i	$0.223836\pi$
$84$	−5.08358	−0.554664
$85$	0	0
$86$	−0.790460	−0.0852375
$87$	−3.98032	−0.426736
$88$	−2.88404	−0.307439
$89$	−0.395163	−0.0418872	−0.0209436	−	0.999781i	$-0.506667\pi$
$89$	−0.395163	−0.0418872	−0.0209436	+	0.999781i	$0.506667\pi$
$90$	0.565436	0.0596022
$91$	14.0886	1.47689
$92$	1.64326	0.171322
$93$	2.38445	0.247255
$94$	−0.694222	−0.0716036
$95$	7.13107	0.731632
$96$	−3.61071	−0.368517
$97$	−8.95923	−0.909672	−0.454836	−	0.890575i	$-0.650302\pi$
$97$	−8.95923	−0.909672	−0.454836	+	0.890575i	$0.650302\pi$
$98$	−0.211396	−0.0213542
$99$	−4.58361	−0.460671
$100$	−1.90899	−0.190899
$101$	−15.2882	−1.52124	−0.760619	−	0.649199i	$-0.775104\pi$
$101$	−15.2882	−1.52124	−0.760619	+	0.649199i	$0.775104\pi$
$102$	0	0
$103$	−14.7746	−1.45579	−0.727894	−	0.685690i	$-0.759501\pi$
$103$	−14.7746	−1.45579	−0.727894	+	0.685690i	$0.759501\pi$
$104$	6.61977	0.649122
$105$	−2.66297	−0.259880
$106$	0.837105	0.0813068
$107$	1.47078	0.142185	0.0710926	−	0.997470i	$-0.477351\pi$
$107$	1.47078	0.142185	0.0710926	+	0.997470i	$0.477351\pi$
$108$	−9.87260	−0.949991
$109$	9.43771	0.903969	0.451984	−	0.892026i	$-0.350716\pi$
$109$	9.43771	0.903969	0.451984	+	0.892026i	$0.350716\pi$
$110$	−0.737797	−0.0703462
$111$	5.41708	0.514167
$112$	−8.68955	−0.821085
$113$	14.9610	1.40742	0.703708	−	0.710489i	$-0.251526\pi$
$113$	14.9610	1.40742	0.703708	+	0.710489i	$0.251526\pi$
$114$	2.28261	0.213786
$115$	0.860805	0.0802705
$116$	−7.16143	−0.664922
$117$	10.5208	0.972651
$118$	2.24505	0.206674
$119$	0	0
$120$	−1.25124	−0.114222
$121$	−5.01917	−0.456288
$122$	0.273416	0.0247539
$123$	−13.1031	−1.18146
$124$	4.29011	0.385264
$125$	−1.00000	−0.0894427
$126$	1.41915	0.126428
$127$	−5.95484	−0.528406	−0.264203	−	0.964467i	$-0.585109\pi$
$127$	−5.95484	−0.528406	−0.264203	+	0.964467i	$0.585109\pi$
$128$	−8.58542	−0.758851
$129$	2.78000	0.244765
$130$	1.69348	0.148528
$131$	4.18730	0.365846	0.182923	−	0.983127i	$-0.441444\pi$
$131$	4.18730	0.365846	0.182923	+	0.983127i	$0.441444\pi$
$132$	4.95341	0.431139
$133$	17.8978	1.55194
$134$	2.02097	0.174585
$135$	−5.17165	−0.445104
$136$	0	0
$137$	7.25998	0.620262	0.310131	−	0.950694i	$-0.399627\pi$
$137$	7.25998	0.620262	0.310131	+	0.950694i	$0.399627\pi$
$138$	0.275538	0.0234554
$139$	−10.3932	−0.881540	−0.440770	−	0.897620i	$-0.645295\pi$
$139$	−10.3932	−0.881540	−0.440770	+	0.897620i	$0.645295\pi$
$140$	−4.79124	−0.404934
$141$	2.44154	0.205615
$142$	−0.0726360	−0.00609548
$143$	−13.7279	−1.14798
$144$	−6.48902	−0.540751
$145$	−3.75143	−0.311540
$146$	−1.94813	−0.161228
$147$	0.743466	0.0613200
$148$	9.74646	0.801154
$149$	−6.01765	−0.492985	−0.246492	−	0.969145i	$-0.579278\pi$
$149$	−6.01765	−0.492985	−0.246492	+	0.969145i	$0.579278\pi$
$150$	−0.320094	−0.0261356
$151$	−10.4183	−0.847828	−0.423914	−	0.905702i	$-0.639344\pi$
$151$	−10.4183	−0.847828	−0.423914	+	0.905702i	$0.639344\pi$
$152$	8.40959	0.682108
$153$	0	0
$154$	−1.85175	−0.149218
$155$	2.24733	0.180510
$156$	−11.3696	−0.910298
$157$	13.4073	1.07002	0.535008	−	0.844847i	$-0.320309\pi$
$157$	13.4073	1.07002	0.535008	+	0.844847i	$0.320309\pi$
$158$	4.43769	0.353044
$159$	−2.94405	−0.233478
$160$	−3.40308	−0.269037
$161$	2.16048	0.170270
$162$	0.0408968	0.00321315
$163$	−1.57513	−0.123374	−0.0616870	−	0.998096i	$-0.519648\pi$
$163$	−1.57513	−0.123374	−0.0616870	+	0.998096i	$0.519648\pi$
$164$	−23.5752	−1.84091
$165$	2.59479	0.202004
$166$	4.19297	0.325438
$167$	−17.6049	−1.36231	−0.681154	−	0.732140i	$-0.738522\pi$
$167$	−17.6049	−1.36231	−0.681154	+	0.732140i	$0.738522\pi$
$168$	−3.14042	−0.242288
$169$	18.5098	1.42383
$170$	0	0
$171$	13.3654	1.02208
$172$	5.00180	0.381384
$173$	18.8429	1.43260	0.716300	−	0.697793i	$-0.245834\pi$
$173$	18.8429	1.43260	0.716300	+	0.697793i	$0.245834\pi$
$174$	−1.20081	−0.0910333
$175$	−2.50984	−0.189726
$176$	8.46705	0.638228
$177$	−7.89572	−0.593479
$178$	−0.119215	−0.00893557
$179$	3.31384	0.247688	0.123844	−	0.992302i	$-0.460478\pi$
$179$	3.31384	0.247688	0.123844	+	0.992302i	$0.460478\pi$
$180$	−3.57791	−0.266682
$181$	−15.8652	−1.17925	−0.589624	−	0.807678i	$-0.700724\pi$
$181$	−15.8652	−1.17925	−0.589624	+	0.807678i	$0.700724\pi$
$182$	4.25035	0.315057
$183$	−0.961587	−0.0710826
$184$	1.01514	0.0748370
$185$	5.10557	0.375369
$186$	0.719356	0.0527457
$187$	0	0
$188$	4.39284	0.320380
$189$	−12.9800	−0.944156
$190$	2.15135	0.156075
$191$	27.4943	1.98941	0.994707	−	0.102748i	$-0.0327636\pi$
$191$	27.4943	1.98941	0.994707	+	0.102748i	$0.0327636\pi$
$192$	6.25757	0.451601
$193$	−14.7613	−1.06254	−0.531270	−	0.847203i	$-0.678285\pi$
$193$	−14.7613	−1.06254	−0.531270	+	0.847203i	$0.678285\pi$
$194$	−2.70288	−0.194056
$195$	−5.95585	−0.426507
$196$	1.33765	0.0955464
$197$	0.376406	0.0268178	0.0134089	−	0.999910i	$-0.495732\pi$
$197$	0.376406	0.0268178	0.0134089	+	0.999910i	$0.495732\pi$
$198$	−1.38282	−0.0982724
$199$	−7.53004	−0.533791	−0.266895	−	0.963726i	$-0.585998\pi$
$199$	−7.53004	−0.533791	−0.266895	+	0.963726i	$0.585998\pi$
$200$	−1.17929	−0.0833883
$201$	−7.10761	−0.501332
$202$	−4.61226	−0.324518
$203$	−9.41549	−0.660838
$204$	0	0
$205$	−12.3496	−0.862532
$206$	−4.45731	−0.310556
$207$	1.61336	0.112137
$208$	−19.4345	−1.34754
$209$	−17.4395	−1.20632
$210$	−0.803384	−0.0554388
$211$	8.69248	0.598415	0.299207	−	0.954188i	$-0.403278\pi$
$211$	8.69248	0.598415	0.299207	+	0.954188i	$0.403278\pi$
$212$	−5.29695	−0.363796
$213$	0.255456	0.0175036
$214$	0.443714	0.0303316
$215$	2.62014	0.178692
$216$	−6.09887	−0.414975
$217$	5.64043	0.382897
$218$	2.84723	0.192839
$219$	6.85145	0.462978
$220$	4.66856	0.314754
$221$	0	0
$222$	1.63426	0.109684
$223$	6.46310	0.432801	0.216401	−	0.976305i	$-0.430568\pi$
$223$	6.46310	0.432801	0.216401	+	0.976305i	$0.430568\pi$
$224$	−8.54117	−0.570681
$225$	−1.87425	−0.124950
$226$	4.51355	0.300237
$227$	−3.06060	−0.203139	−0.101570	−	0.994828i	$-0.532386\pi$
$227$	−3.06060	−0.203139	−0.101570	+	0.994828i	$0.532386\pi$
$228$	−14.4437	−0.956557
$229$	−7.55923	−0.499528	−0.249764	−	0.968307i	$-0.580353\pi$
$229$	−7.55923	−0.499528	−0.249764	+	0.968307i	$0.580353\pi$
$230$	0.259694	0.0171237
$231$	6.51250	0.428491
$232$	−4.42403	−0.290452
$233$	−22.3478	−1.46406	−0.732028	−	0.681275i	$-0.761426\pi$
$233$	−22.3478	−1.46406	−0.732028	+	0.681275i	$0.761426\pi$
$234$	3.17400	0.207491
$235$	2.30114	0.150110
$236$	−14.2060	−0.924735
$237$	−15.6071	−1.01379
$238$	0	0
$239$	−3.45981	−0.223797	−0.111898	−	0.993720i	$-0.535693\pi$
$239$	−3.45981	−0.223797	−0.111898	+	0.993720i	$0.535693\pi$
$240$	3.67344	0.237119
$241$	18.0262	1.16117	0.580585	−	0.814199i	$-0.302824\pi$
$241$	18.0262	1.16117	0.580585	+	0.814199i	$0.302824\pi$
$242$	−1.51422	−0.0973376
$243$	−15.6588	−1.00451
$244$	−1.73010	−0.110758
$245$	0.700712	0.0447669
$246$	−3.95302	−0.252036
$247$	40.0292	2.54700
$248$	2.65025	0.168291
$249$	−14.7464	−0.934516
$250$	−0.301687	−0.0190803
$251$	24.0478	1.51788	0.758941	−	0.651159i	$-0.225717\pi$
$251$	24.0478	1.51788	0.758941	+	0.651159i	$0.225717\pi$
$252$	−8.97999	−0.565686
$253$	−2.10516	−0.132350
$254$	−1.79650	−0.112722
$255$	0	0
$256$	9.20534	0.575334
$257$	−14.8017	−0.923302	−0.461651	−	0.887062i	$-0.652743\pi$
$257$	−14.8017	−0.923302	−0.461651	+	0.887062i	$0.652743\pi$
$258$	0.838689	0.0522145
$259$	12.8142	0.796233
$260$	−10.7158	−0.664566
$261$	−7.03113	−0.435216
$262$	1.26325	0.0780440
$263$	−24.5163	−1.51174	−0.755871	−	0.654720i	$-0.772786\pi$
$263$	−24.5163	−1.51174	−0.755871	+	0.654720i	$0.772786\pi$
$264$	3.06000	0.188330
$265$	−2.77475	−0.170451
$266$	5.39954	0.331067
$267$	0.419273	0.0256591
$268$	−12.7881	−0.781156
$269$	6.59468	0.402085	0.201042	−	0.979583i	$-0.435567\pi$
$269$	6.59468	0.402085	0.201042	+	0.979583i	$0.435567\pi$
$270$	−1.56022	−0.0949518
$271$	26.1956	1.59127	0.795634	−	0.605778i	$-0.207138\pi$
$271$	26.1956	1.59127	0.795634	+	0.605778i	$0.207138\pi$
$272$	0	0
$273$	−14.9482	−0.904707
$274$	2.19024	0.132317
$275$	2.44557	0.147474
$276$	−1.74353	−0.104948
$277$	9.56504	0.574708	0.287354	−	0.957825i	$-0.407224\pi$
$277$	9.56504	0.574708	0.287354	+	0.957825i	$0.407224\pi$
$278$	−3.13549	−0.188054
$279$	4.21205	0.252169
$280$	−2.95983	−0.176883
$281$	12.4173	0.740755	0.370377	−	0.928881i	$-0.379228\pi$
$281$	12.4173	0.740755	0.370377	+	0.928881i	$0.379228\pi$
$282$	0.736580	0.0438627
$283$	16.8433	1.00123	0.500616	−	0.865670i	$-0.333107\pi$
$283$	16.8433	1.00123	0.500616	+	0.865670i	$0.333107\pi$
$284$	0.459619	0.0272734
$285$	−7.56616	−0.448181
$286$	−4.14152	−0.244893
$287$	−30.9954	−1.82960
$288$	−6.37822	−0.375840
$289$	0	0
$290$	−1.13176	−0.0664591
$291$	9.50586	0.557244
$292$	12.3272	0.721394
$293$	−20.8806	−1.21986	−0.609930	−	0.792456i	$-0.708802\pi$
$293$	−20.8806	−1.21986	−0.609930	+	0.792456i	$0.708802\pi$
$294$	0.224294	0.0130811
$295$	−7.44167	−0.433271
$296$	6.02095	0.349960
$297$	12.6476	0.733890
$298$	−1.81544	−0.105166
$299$	4.83200	0.279442
$300$	2.02546	0.116940
$301$	6.57612	0.379041
$302$	−3.14306	−0.180863
$303$	16.2210	0.931875
$304$	−24.6891	−1.41602
$305$	−0.906291	−0.0518941
$306$	0	0
$307$	−29.9529	−1.70950	−0.854751	−	0.519038i	$-0.826290\pi$
$307$	−29.9529	−1.70950	−0.854751	+	0.519038i	$0.826290\pi$
$308$	11.7173	0.667657
$309$	15.6761	0.891782
$310$	0.677989	0.0385072
$311$	0.210323	0.0119264	0.00596318	−	0.999982i	$-0.498102\pi$
$311$	0.210323	0.0119264	0.00596318	+	0.999982i	$0.498102\pi$
$312$	−7.02367	−0.397637
$313$	−32.4242	−1.83273	−0.916363	−	0.400349i	$-0.868889\pi$
$313$	−32.4242	−1.83273	−0.916363	+	0.400349i	$0.868889\pi$
$314$	4.04479	0.228261
$315$	−4.70406	−0.265044
$316$	−28.0804	−1.57965
$317$	−33.4391	−1.87813	−0.939063	−	0.343746i	$-0.888304\pi$
$317$	−33.4391	−1.87813	−0.939063	+	0.343746i	$0.888304\pi$
$318$	−0.888180	−0.0498067
$319$	9.17441	0.513668
$320$	5.89773	0.329693
$321$	−1.56051	−0.0870994
$322$	0.651789	0.0363228
$323$	0	0
$324$	−0.258783	−0.0143768
$325$	−5.61335	−0.311373
$326$	−0.475197	−0.0263187
$327$	−10.0135	−0.553750
$328$	−14.5637	−0.804147
$329$	5.77548	0.318413
$330$	0.782813	0.0430924
$331$	−0.885340	−0.0486627	−0.0243313	−	0.999704i	$-0.507746\pi$
$331$	−0.885340	−0.0486627	−0.0243313	+	0.999704i	$0.507746\pi$
$332$	−26.5319	−1.45613
$333$	9.56912	0.524384
$334$	−5.31117	−0.290614
$335$	−6.69889	−0.365999
$336$	9.21973	0.502977
$337$	17.1565	0.934575	0.467287	−	0.884105i	$-0.345231\pi$
$337$	17.1565	0.934575	0.467287	+	0.884105i	$0.345231\pi$
$338$	5.58415	0.303738
$339$	−15.8739	−0.862150
$340$	0	0
$341$	−5.49600	−0.297625
$342$	4.03216	0.218034
$343$	19.3275	1.04359
$344$	3.08990	0.166596
$345$	−0.913326	−0.0491718
$346$	5.68466	0.305609
$347$	30.9101	1.65934	0.829671	−	0.558253i	$-0.188528\pi$
$347$	30.9101	1.65934	0.829671	+	0.558253i	$0.188528\pi$
$348$	7.59838	0.407316
$349$	3.37170	0.180483	0.0902414	−	0.995920i	$-0.471236\pi$
$349$	3.37170	0.180483	0.0902414	+	0.995920i	$0.471236\pi$
$350$	−0.757185	−0.0404732
$351$	−29.0303	−1.54952
$352$	8.32247	0.443589
$353$	23.7918	1.26631	0.633155	−	0.774025i	$-0.281760\pi$
$353$	23.7918	1.26631	0.633155	+	0.774025i	$0.281760\pi$
$354$	−2.38203	−0.126604
$355$	0.240766	0.0127785
$356$	0.754360	0.0399810
$357$	0	0
$358$	0.999743	0.0528381
$359$	31.7129	1.67374	0.836871	−	0.547399i	$-0.184382\pi$
$359$	31.7129	1.67374	0.836871	+	0.547399i	$0.184382\pi$
$360$	−2.21028	−0.116492
$361$	31.8521	1.67643
$362$	−4.78631	−0.251563
$363$	5.32541	0.279512
$364$	−26.8950	−1.40968
$365$	6.45746	0.337999
$366$	−0.290098	−0.0151637
$367$	4.51687	0.235779	0.117889	−	0.993027i	$-0.462387\pi$
$367$	4.51687	0.235779	0.117889	+	0.993027i	$0.462387\pi$
$368$	−2.98027	−0.155358
$369$	−23.1462	−1.20494
$370$	1.54028	0.0800755
$371$	−6.96417	−0.361562
$372$	−4.55187	−0.236003
$373$	5.12748	0.265491	0.132745	−	0.991150i	$-0.457621\pi$
$373$	5.12748	0.265491	0.132745	+	0.991150i	$0.457621\pi$
$374$	0	0
$375$	1.06101	0.0547905
$376$	2.71371	0.139949
$377$	−21.0581	−1.08455
$378$	−3.91589	−0.201412
$379$	5.53013	0.284064	0.142032	−	0.989862i	$-0.454636\pi$
$379$	5.53013	0.284064	0.142032	+	0.989862i	$0.454636\pi$
$380$	−13.6131	−0.698337
$381$	6.31816	0.323689
$382$	8.29466	0.424391
$383$	20.4344	1.04415	0.522075	−	0.852899i	$-0.325158\pi$
$383$	20.4344	1.04415	0.522075	+	0.852899i	$0.325158\pi$
$384$	9.10925	0.464854
$385$	6.13799	0.312821
$386$	−4.45328	−0.226666
$387$	4.91079	0.249629
$388$	17.1030	0.868275
$389$	5.18629	0.262955	0.131478	−	0.991319i	$-0.458028\pi$
$389$	5.18629	0.262955	0.131478	+	0.991319i	$0.458028\pi$
$390$	−1.79680	−0.0909845
$391$	0	0
$392$	0.826343	0.0417366
$393$	−4.44278	−0.224109
$394$	0.113557	0.00572091
$395$	−14.7096	−0.740120
$396$	8.75005	0.439707
$397$	6.17353	0.309841	0.154920	−	0.987927i	$-0.450488\pi$
$397$	6.17353	0.309841	0.154920	+	0.987927i	$0.450488\pi$
$398$	−2.27171	−0.113871
$399$	−18.9898	−0.950681
$400$	3.46219	0.173110
$401$	9.49644	0.474229	0.237115	−	0.971482i	$-0.423798\pi$
$401$	9.49644	0.474229	0.237115	+	0.971482i	$0.423798\pi$
$402$	−2.14427	−0.106947
$403$	12.6150	0.628400
$404$	29.1850	1.45201
$405$	−0.135560	−0.00673605
$406$	−2.84053	−0.140973
$407$	−12.4860	−0.618910
$408$	0	0
$409$	14.3886	0.711469	0.355734	−	0.934587i	$-0.384231\pi$
$409$	14.3886	0.711469	0.355734	+	0.934587i	$0.384231\pi$
$410$	−3.72571	−0.183999
$411$	−7.70294	−0.379958
$412$	28.2046	1.38954
$413$	−18.6774	−0.919055
$414$	0.486730	0.0239215
$415$	−13.8984	−0.682247
$416$	−19.1027	−0.936586
$417$	11.0273	0.540011
$418$	−5.26128	−0.257338
$419$	21.2233	1.03683	0.518413	−	0.855130i	$-0.326523\pi$
$419$	21.2233	1.03683	0.518413	+	0.855130i	$0.326523\pi$
$420$	5.08358	0.248053
$421$	−20.1672	−0.982887	−0.491444	−	0.870909i	$-0.663531\pi$
$421$	−20.1672	−0.982887	−0.491444	+	0.870909i	$0.663531\pi$
$422$	2.62241	0.127657
$423$	4.31290	0.209701
$424$	−3.27223	−0.158914
$425$	0	0
$426$	0.0770678	0.00373395
$427$	−2.27464	−0.110078
$428$	−2.80769	−0.135715
$429$	14.5655	0.703227
$430$	0.790460	0.0381194
$431$	19.9686	0.961851	0.480926	−	0.876761i	$-0.340301\pi$
$431$	19.9686	0.961851	0.480926	+	0.876761i	$0.340301\pi$
$432$	17.9052	0.861466
$433$	−18.2236	−0.875770	−0.437885	−	0.899031i	$-0.644272\pi$
$433$	−18.2236	−0.875770	−0.437885	+	0.899031i	$0.644272\pi$
$434$	1.70164	0.0816815
$435$	3.98032	0.190842
$436$	−18.0165	−0.862832
$437$	6.13846	0.293642
$438$	2.06699	0.0987648
$439$	14.7332	0.703178	0.351589	−	0.936155i	$-0.385642\pi$
$439$	14.7332	0.703178	0.351589	+	0.936155i	$0.385642\pi$
$440$	2.88404	0.137491
$441$	1.31331	0.0625386
$442$	0	0
$443$	−23.3335	−1.10861	−0.554305	−	0.832314i	$-0.687016\pi$
$443$	−23.3335	−1.10861	−0.554305	+	0.832314i	$0.687016\pi$
$444$	−10.3411	−0.490768
$445$	0.395163	0.0187325
$446$	1.94983	0.0923272
$447$	6.38481	0.301991
$448$	14.8023	0.699345
$449$	−1.71162	−0.0807764	−0.0403882	−	0.999184i	$-0.512859\pi$
$449$	−1.71162	−0.0807764	−0.0403882	+	0.999184i	$0.512859\pi$
$450$	−0.565436	−0.0266549
$451$	30.2018	1.42215
$452$	−28.5604	−1.34337
$453$	11.0539	0.519359
$454$	−0.923344	−0.0433347
$455$	−14.0886	−0.660484
$456$	−8.92269	−0.417843
$457$	−13.2168	−0.618258	−0.309129	−	0.951020i	$-0.600037\pi$
$457$	−13.2168	−0.618258	−0.309129	+	0.951020i	$0.600037\pi$
$458$	−2.28052	−0.106562
$459$	0	0
$460$	−1.64326	−0.0766176
$461$	−29.2906	−1.36420	−0.682099	−	0.731260i	$-0.738933\pi$
$461$	−29.2906	−1.36420	−0.682099	+	0.731260i	$0.738933\pi$
$462$	1.96473	0.0914077
$463$	9.80371	0.455617	0.227808	−	0.973706i	$-0.426844\pi$
$463$	9.80371	0.455617	0.227808	+	0.973706i	$0.426844\pi$
$464$	12.9882	0.602962
$465$	−2.38445	−0.110576
$466$	−6.74205	−0.312319
$467$	13.6819	0.633125	0.316562	−	0.948572i	$-0.397471\pi$
$467$	13.6819	0.633125	0.316562	+	0.948572i	$0.397471\pi$
$468$	−20.0841	−0.928388
$469$	−16.8131	−0.776358
$470$	0.694222	0.0320221
$471$	−14.2253	−0.655466
$472$	−8.77589	−0.403943
$473$	−6.40773	−0.294628
$474$	−4.70845	−0.216266
$475$	−7.13107	−0.327196
$476$	0	0
$477$	−5.20057	−0.238118
$478$	−1.04378	−0.0477414
$479$	11.0100	0.503060	0.251530	−	0.967850i	$-0.419066\pi$
$479$	11.0100	0.503060	0.251530	+	0.967850i	$0.419066\pi$
$480$	3.61071	0.164806
$481$	28.6594	1.30676
$482$	5.43827	0.247707
$483$	−2.29230	−0.104303
$484$	9.58153	0.435524
$485$	8.95923	0.406818
$486$	−4.72404	−0.214287
$487$	10.0942	0.457413	0.228707	−	0.973495i	$-0.426550\pi$
$487$	10.0942	0.457413	0.228707	+	0.973495i	$0.426550\pi$
$488$	−1.06878	−0.0483813
$489$	1.67124	0.0755760
$490$	0.211396	0.00954988
$491$	17.0827	0.770933	0.385466	−	0.922722i	$-0.374041\pi$
$491$	17.0827	0.770933	0.385466	+	0.922722i	$0.374041\pi$
$492$	25.0136	1.12770
$493$	0	0
$494$	12.0763	0.543338
$495$	4.58361	0.206018
$496$	−7.78068	−0.349363
$497$	0.604284	0.0271059
$498$	−4.44880	−0.199356
$499$	31.3595	1.40384	0.701921	−	0.712254i	$-0.252326\pi$
$499$	31.3595	1.40384	0.701921	+	0.712254i	$0.252326\pi$
$500$	1.90899	0.0853724
$501$	18.6791	0.834519
$502$	7.25490	0.323802
$503$	8.67535	0.386815	0.193407	−	0.981119i	$-0.438046\pi$
$503$	8.67535	0.386815	0.193407	+	0.981119i	$0.438046\pi$
$504$	−5.54745	−0.247103
$505$	15.2882	0.680318
$506$	−0.635099	−0.0282336
$507$	−19.6391	−0.872203
$508$	11.3677	0.504360
$509$	14.1196	0.625840	0.312920	−	0.949780i	$-0.398693\pi$
$509$	14.1196	0.625840	0.312920	+	0.949780i	$0.398693\pi$
$510$	0	0
$511$	16.2072	0.716963
$512$	19.9480	0.881584
$513$	−36.8794	−1.62826
$514$	−4.46546	−0.196963
$515$	14.7746	0.651048
$516$	−5.30698	−0.233627
$517$	−5.62760	−0.247501
$518$	3.86586	0.169856
$519$	−19.9926	−0.877577
$520$	−6.61977	−0.290296
$521$	−17.6222	−0.772044	−0.386022	−	0.922490i	$-0.626151\pi$
$521$	−17.6222	−0.772044	−0.386022	+	0.922490i	$0.626151\pi$
$522$	−2.12120	−0.0928423
$523$	−26.3853	−1.15375	−0.576875	−	0.816833i	$-0.695728\pi$
$523$	−26.3853	−1.15375	−0.576875	+	0.816833i	$0.695728\pi$
$524$	−7.99349	−0.349197
$525$	2.66297	0.116222
$526$	−7.39626	−0.322492
$527$	0	0
$528$	−8.98366	−0.390963
$529$	−22.2590	−0.967783
$530$	−0.837105	−0.0363615
$531$	−13.9476	−0.605272
$532$	−34.1667	−1.48131
$533$	−69.3226	−3.00269
$534$	0.126489	0.00547372
$535$	−1.47078	−0.0635872
$536$	−7.89992	−0.341225
$537$	−3.51603	−0.151728
$538$	1.98953	0.0857746
$539$	−1.71364	−0.0738118
$540$	9.87260	0.424849
$541$	−4.40821	−0.189524	−0.0947620	−	0.995500i	$-0.530209\pi$
$541$	−4.40821	−0.189524	−0.0947620	+	0.995500i	$0.530209\pi$
$542$	7.90286	0.339457
$543$	16.8331	0.722379
$544$	0	0
$545$	−9.43771	−0.404267
$546$	−4.50968	−0.192996
$547$	22.6638	0.969034	0.484517	−	0.874782i	$-0.338995\pi$
$547$	22.6638	0.969034	0.484517	+	0.874782i	$0.338995\pi$
$548$	−13.8592	−0.592035
$549$	−1.69861	−0.0724951
$550$	0.737797	0.0314598
$551$	−26.7517	−1.13966
$552$	−1.07708	−0.0458434
$553$	−36.9187	−1.56994
$554$	2.88565	0.122599
$555$	−5.41708	−0.229942
$556$	19.8405	0.841423
$557$	11.4954	0.487076	0.243538	−	0.969891i	$-0.421692\pi$
$557$	11.4954	0.487076	0.243538	+	0.969891i	$0.421692\pi$
$558$	1.27072	0.0537939
$559$	14.7078	0.622072
$560$	8.68955	0.367200
$561$	0	0
$562$	3.74614	0.158021
$563$	13.5441	0.570817	0.285409	−	0.958406i	$-0.407871\pi$
$563$	13.5441	0.570817	0.285409	+	0.958406i	$0.407871\pi$
$564$	−4.66086	−0.196258
$565$	−14.9610	−0.629415
$566$	5.08141	0.213587
$567$	−0.340234	−0.0142885
$568$	0.283933	0.0119136
$569$	15.8764	0.665574	0.332787	−	0.943002i	$-0.392011\pi$
$569$	15.8764	0.665574	0.332787	+	0.943002i	$0.392011\pi$
$570$	−2.28261	−0.0956081
$571$	−3.54043	−0.148162	−0.0740812	−	0.997252i	$-0.523602\pi$
$571$	−3.54043	−0.148162	−0.0740812	+	0.997252i	$0.523602\pi$
$572$	26.2063	1.09574
$573$	−29.1718	−1.21867
$574$	−9.35092	−0.390300
$575$	−0.860805	−0.0358981
$576$	11.0538	0.460575
$577$	−18.5078	−0.770492	−0.385246	−	0.922814i	$-0.625883\pi$
$577$	−18.5078	−0.770492	−0.385246	+	0.922814i	$0.625883\pi$
$578$	0	0
$579$	15.6619	0.650887
$580$	7.16143	0.297362
$581$	−34.8828	−1.44718
$582$	2.86779	0.118874
$583$	6.78585	0.281041
$584$	7.61521	0.315120
$585$	−10.5208	−0.434983
$586$	−6.29941	−0.260226
$587$	−13.7261	−0.566535	−0.283268	−	0.959041i	$-0.591418\pi$
$587$	−13.7261	−0.566535	−0.283268	+	0.959041i	$0.591418\pi$
$588$	−1.41926	−0.0585295
$589$	16.0258	0.660333
$590$	−2.24505	−0.0924274
$591$	−0.399372	−0.0164280
$592$	−17.6765	−0.726499
$593$	20.3238	0.834598	0.417299	−	0.908769i	$-0.362977\pi$
$593$	20.3238	0.834598	0.417299	+	0.908769i	$0.362977\pi$
$594$	3.81563	0.156557
$595$	0	0
$596$	11.4876	0.470550
$597$	7.98948	0.326988
$598$	1.45775	0.0596119
$599$	−26.7277	−1.09206	−0.546032	−	0.837764i	$-0.683862\pi$
$599$	−26.7277	−1.09206	−0.546032	+	0.837764i	$0.683862\pi$
$600$	1.25124	0.0510817
$601$	−27.6591	−1.12824	−0.564119	−	0.825693i	$-0.690784\pi$
$601$	−27.6591	−1.12824	−0.564119	+	0.825693i	$0.690784\pi$
$602$	1.98393	0.0808588
$603$	−12.5554	−0.511295
$604$	19.8883	0.809245
$605$	5.01917	0.204058
$606$	4.89367	0.198792
$607$	23.6186	0.958649	0.479325	−	0.877638i	$-0.340882\pi$
$607$	23.6186	0.958649	0.479325	+	0.877638i	$0.340882\pi$
$608$	−24.2676	−0.984180
$609$	9.98997	0.404814
$610$	−0.273416	−0.0110703
$611$	12.9171	0.522570
$612$	0	0
$613$	12.0396	0.486275	0.243137	−	0.969992i	$-0.421823\pi$
$613$	12.0396	0.486275	0.243137	+	0.969992i	$0.421823\pi$
$614$	−9.03639	−0.364679
$615$	13.1031	0.528367
$616$	7.23847	0.291646
$617$	15.5478	0.625931	0.312966	−	0.949764i	$-0.398678\pi$
$617$	15.5478	0.625931	0.312966	+	0.949764i	$0.398678\pi$
$618$	4.72927	0.190239
$619$	33.4929	1.34619	0.673097	−	0.739554i	$-0.264964\pi$
$619$	33.4929	1.34619	0.673097	+	0.739554i	$0.264964\pi$
$620$	−4.29011	−0.172295
$621$	−4.45178	−0.178644
$622$	0.0634518	0.00254419
$623$	0.991795	0.0397354
$624$	20.6203	0.825473
$625$	1.00000	0.0400000
$626$	−9.78196	−0.390966
$627$	18.5036	0.738963
$628$	−25.5942	−1.02132
$629$	0	0
$630$	−1.41915	−0.0565404
$631$	−0.544614	−0.0216807	−0.0108404	−	0.999941i	$-0.503451\pi$
$631$	−0.544614	−0.0216807	−0.0108404	+	0.999941i	$0.503451\pi$
$632$	−17.3469	−0.690021
$633$	−9.22284	−0.366575
$634$	−10.0881	−0.400651
$635$	5.95484	0.236310
$636$	5.62014	0.222853
$637$	3.93335	0.155845
$638$	2.76780	0.109578
$639$	0.451256	0.0178514
$640$	8.58542	0.339368
$641$	−12.4241	−0.490723	−0.245361	−	0.969432i	$-0.578907\pi$
$641$	−12.4241	−0.490723	−0.245361	+	0.969432i	$0.578907\pi$
$642$	−0.470786	−0.0185805
$643$	38.3641	1.51293	0.756467	−	0.654032i	$-0.226924\pi$
$643$	38.3641	1.51293	0.756467	+	0.654032i	$0.226924\pi$
$644$	−4.12433	−0.162521
$645$	−2.78000	−0.109462
$646$	0	0
$647$	19.6602	0.772923	0.386462	−	0.922305i	$-0.373697\pi$
$647$	19.6602	0.772923	0.386462	+	0.922305i	$0.373697\pi$
$648$	−0.159865	−0.00628008
$649$	18.1992	0.714379
$650$	−1.69348	−0.0664236
$651$	−5.98457	−0.234554
$652$	3.00691	0.117760
$653$	31.1272	1.21810	0.609051	−	0.793131i	$-0.291551\pi$
$653$	31.1272	1.21810	0.609051	+	0.793131i	$0.291551\pi$
$654$	−3.02095	−0.118129
$655$	−4.18730	−0.163611
$656$	42.7566	1.66937
$657$	12.1029	0.472179
$658$	1.74239	0.0679253
$659$	−4.15956	−0.162033	−0.0810167	−	0.996713i	$-0.525817\pi$
$659$	−4.15956	−0.162033	−0.0810167	+	0.996713i	$0.525817\pi$
$660$	−4.95341	−0.192811
$661$	−6.86044	−0.266840	−0.133420	−	0.991060i	$-0.542596\pi$
$661$	−6.86044	−0.266840	−0.133420	+	0.991060i	$0.542596\pi$
$662$	−0.267095	−0.0103810
$663$	0	0
$664$	−16.3903	−0.636066
$665$	−17.8978	−0.694048
$666$	2.88688	0.111864
$667$	−3.22925	−0.125037
$668$	33.6075	1.30031
$669$	−6.85744	−0.265124
$670$	−2.02097	−0.0780767
$671$	2.21640	0.0855632
$672$	9.06230	0.349586
$673$	17.2806	0.666116	0.333058	−	0.942906i	$-0.391919\pi$
$673$	17.2806	0.666116	0.333058	+	0.942906i	$0.391919\pi$
$674$	5.17589	0.199368
$675$	5.17165	0.199057
$676$	−35.3348	−1.35903
$677$	8.13384	0.312609	0.156304	−	0.987709i	$-0.450042\pi$
$677$	8.13384	0.312609	0.156304	+	0.987709i	$0.450042\pi$
$678$	−4.78894	−0.183918
$679$	22.4862	0.862942
$680$	0	0
$681$	3.24734	0.124438
$682$	−1.65807	−0.0634908
$683$	29.1370	1.11489	0.557447	−	0.830212i	$-0.311781\pi$
$683$	29.1370	1.11489	0.557447	+	0.830212i	$0.311781\pi$
$684$	−25.5143	−0.975566
$685$	−7.25998	−0.277390
$686$	5.83086	0.222623
$687$	8.02044	0.305999
$688$	−9.07142	−0.345845
$689$	−15.5756	−0.593385
$690$	−0.275538	−0.0104896
$691$	37.3851	1.42219	0.711097	−	0.703093i	$-0.248198\pi$
$691$	37.3851	1.42219	0.711097	+	0.703093i	$0.248198\pi$
$692$	−35.9708	−1.36741
$693$	11.5041	0.437006
$694$	9.32517	0.353979
$695$	10.3932	0.394237
$696$	4.69395	0.177924
$697$	0	0
$698$	1.01720	0.0385015
$699$	23.7114	0.896846
$700$	4.79124	0.181092
$701$	14.6423	0.553031	0.276515	−	0.961009i	$-0.410820\pi$
$701$	14.6423	0.553031	0.276515	+	0.961009i	$0.410820\pi$
$702$	−8.75805	−0.330551
$703$	36.4082	1.37316
$704$	−14.4233	−0.543599
$705$	−2.44154	−0.0919536
$706$	7.17767	0.270135
$707$	38.3710	1.44309
$708$	15.0728	0.566471
$709$	28.3593	1.06506	0.532528	−	0.846413i	$-0.321242\pi$
$709$	28.3593	1.06506	0.532528	+	0.846413i	$0.321242\pi$
$710$	0.0726360	0.00272598
$711$	−27.5694	−1.03393
$712$	0.466011	0.0174645
$713$	1.93451	0.0724480
$714$	0	0
$715$	13.7279	0.513393
$716$	−6.32608	−0.236417
$717$	3.67091	0.137093
$718$	9.56736	0.357051
$719$	−12.6354	−0.471222	−0.235611	−	0.971848i	$-0.575709\pi$
$719$	−12.6354	−0.471222	−0.235611	+	0.971848i	$0.575709\pi$
$720$	6.48902	0.241831
$721$	37.0819	1.38100
$722$	9.60936	0.357624
$723$	−19.1261	−0.711306
$724$	30.2863	1.12558
$725$	3.75143	0.139325
$726$	1.60661	0.0596268
$727$	−15.0242	−0.557218	−0.278609	−	0.960405i	$-0.589873\pi$
$727$	−15.0242	−0.557218	−0.278609	+	0.960405i	$0.589873\pi$
$728$	−16.6145	−0.615776
$729$	16.2075	0.600277
$730$	1.94813	0.0721035
$731$	0	0
$732$	1.83566	0.0678478
$733$	−1.76679	−0.0652578	−0.0326289	−	0.999468i	$-0.510388\pi$
$733$	−1.76679	−0.0652578	−0.0326289	+	0.999468i	$0.510388\pi$
$734$	1.36268	0.0502974
$735$	−0.743466	−0.0274231
$736$	−2.92939	−0.107979
$737$	16.3826	0.603461
$738$	−6.98290	−0.257044
$739$	19.7149	0.725225	0.362613	−	0.931940i	$-0.381885\pi$
$739$	19.7149	0.725225	0.362613	+	0.931940i	$0.381885\pi$
$740$	−9.74646	−0.358287
$741$	−42.4715	−1.56023
$742$	−2.10100	−0.0771301
$743$	28.3615	1.04048	0.520242	−	0.854019i	$-0.325842\pi$
$743$	28.3615	1.04048	0.520242	+	0.854019i	$0.325842\pi$
$744$	−2.81195	−0.103091
$745$	6.01765	0.220470
$746$	1.54689	0.0566357
$747$	−26.0491	−0.953087
$748$	0	0
$749$	−3.69141	−0.134881
$750$	0.320094	0.0116882
$751$	−17.9518	−0.655072	−0.327536	−	0.944839i	$-0.606218\pi$
$751$	−17.9518	−0.655072	−0.327536	+	0.944839i	$0.606218\pi$
$752$	−7.96698	−0.290526
$753$	−25.5150	−0.929819
$754$	−6.35296	−0.231361
$755$	10.4183	0.379160
$756$	24.7786	0.901190
$757$	−43.9323	−1.59675	−0.798374	−	0.602162i	$-0.794306\pi$
$757$	−43.9323	−1.59675	−0.798374	+	0.602162i	$0.794306\pi$
$758$	1.66837	0.0605978
$759$	2.23361	0.0810748
$760$	−8.40959	−0.305048
$761$	13.2781	0.481331	0.240666	−	0.970608i	$-0.422634\pi$
$761$	13.2781	0.481331	0.240666	+	0.970608i	$0.422634\pi$
$762$	1.90611	0.0690510
$763$	−23.6871	−0.857532
$764$	−52.4861	−1.89888
$765$	0	0
$766$	6.16480	0.222743
$767$	−41.7728	−1.50833
$768$	−9.76700	−0.352436
$769$	24.8906	0.897578	0.448789	−	0.893638i	$-0.351856\pi$
$769$	24.8906	0.897578	0.448789	+	0.893638i	$0.351856\pi$
$770$	1.85175	0.0667325
$771$	15.7048	0.565593
$772$	28.1790	1.01419
$773$	53.7048	1.93163	0.965813	−	0.259238i	$-0.0834715\pi$
$773$	53.7048	1.93163	0.965813	+	0.259238i	$0.0834715\pi$
$774$	1.48152	0.0532521
$775$	−2.24733	−0.0807264
$776$	10.5655	0.379280
$777$	−13.5960	−0.487754
$778$	1.56463	0.0560949
$779$	−88.0657	−3.15528
$780$	11.3696	0.407098
$781$	−0.588811	−0.0210693
$782$	0	0
$783$	19.4011	0.693339
$784$	−2.42600	−0.0866429
$785$	−13.4073	−0.478525
$786$	−1.34033	−0.0478079
$787$	51.4777	1.83498	0.917491	−	0.397757i	$-0.130211\pi$
$787$	51.4777	1.83498	0.917491	+	0.397757i	$0.130211\pi$
$788$	−0.718554	−0.0255974
$789$	26.0122	0.926058
$790$	−4.43769	−0.157886
$791$	−37.5498	−1.33512
$792$	5.40541	0.192073
$793$	−5.08733	−0.180656
$794$	1.86247	0.0660967
$795$	2.94405	0.104415
$796$	14.3747	0.509499
$797$	−18.9183	−0.670119	−0.335059	−	0.942197i	$-0.608756\pi$
$797$	−18.9183	−0.670119	−0.335059	+	0.942197i	$0.608756\pi$
$798$	−5.72898	−0.202804
$799$	0	0
$800$	3.40308	0.120317
$801$	0.740634	0.0261690
$802$	2.86495	0.101165
$803$	−15.7922	−0.557294
$804$	13.5683	0.478518
$805$	−2.16048	−0.0761470
$806$	3.80579	0.134053
$807$	−6.99705	−0.246308
$808$	18.0293	0.634267
$809$	−30.2347	−1.06300	−0.531498	−	0.847059i	$-0.678371\pi$
$809$	−30.2347	−1.06300	−0.531498	+	0.847059i	$0.678371\pi$
$810$	−0.0408968	−0.00143697
$811$	17.1714	0.602969	0.301484	−	0.953471i	$-0.402518\pi$
$811$	17.1714	0.602969	0.301484	+	0.953471i	$0.402518\pi$
$812$	17.9740	0.630765
$813$	−27.7939	−0.974773
$814$	−3.76688	−0.132029
$815$	1.57513	0.0551745
$816$	0	0
$817$	18.6844	0.653683
$818$	4.34084	0.151774
$819$	−26.4056	−0.922686
$820$	23.5752	0.823280
$821$	−43.7843	−1.52808	−0.764041	−	0.645168i	$-0.776787\pi$
$821$	−43.7843	−1.52808	−0.764041	+	0.645168i	$0.776787\pi$
$822$	−2.32388	−0.0810545
$823$	25.2696	0.880842	0.440421	−	0.897791i	$-0.354829\pi$
$823$	25.2696	0.880842	0.440421	+	0.897791i	$0.354829\pi$
$824$	17.4236	0.606979
$825$	−2.59479	−0.0903389
$826$	−5.63472	−0.196057
$827$	−22.0678	−0.767371	−0.383686	−	0.923464i	$-0.625345\pi$
$827$	−22.0678	−0.767371	−0.383686	+	0.923464i	$0.625345\pi$
$828$	−3.07989	−0.107033
$829$	−20.9555	−0.727816	−0.363908	−	0.931435i	$-0.618558\pi$
$829$	−20.9555	−0.727816	−0.363908	+	0.931435i	$0.618558\pi$
$830$	−4.19297	−0.145540
$831$	−10.1486	−0.352052
$832$	33.1060	1.14774
$833$	0	0
$834$	3.32680	0.115198
$835$	17.6049	0.609243
$836$	33.2918	1.15142
$837$	−11.6224	−0.401728
$838$	6.40279	0.221181
$839$	−20.2251	−0.698247	−0.349123	−	0.937077i	$-0.613521\pi$
$839$	−20.2251	−0.698247	−0.349123	+	0.937077i	$0.613521\pi$
$840$	3.14042	0.108355
$841$	−14.9267	−0.514715
$842$	−6.08417	−0.209674
$843$	−13.1749	−0.453769
$844$	−16.5938	−0.571182
$845$	−18.5098	−0.636755
$846$	1.30115	0.0447343
$847$	12.5973	0.432849
$848$	9.60672	0.329896
$849$	−17.8710	−0.613331
$850$	0	0
$851$	4.39490	0.150655
$852$	−0.487662	−0.0167070
$853$	−11.4942	−0.393553	−0.196776	−	0.980448i	$-0.563047\pi$
$853$	−11.4942	−0.393553	−0.196776	+	0.980448i	$0.563047\pi$
$854$	−0.686230	−0.0234823
$855$	−13.3654	−0.457087
$856$	−1.73447	−0.0592830
$857$	−28.0863	−0.959411	−0.479705	−	0.877430i	$-0.659256\pi$
$857$	−28.0863	−0.959411	−0.479705	+	0.877430i	$0.659256\pi$
$858$	4.39421	0.150016
$859$	−3.15015	−0.107482	−0.0537409	−	0.998555i	$-0.517115\pi$
$859$	−3.15015	−0.107482	−0.0537409	+	0.998555i	$0.517115\pi$
$860$	−5.00180	−0.170560
$861$	32.8866	1.12077
$862$	6.02425	0.205187
$863$	−34.5368	−1.17565	−0.587823	−	0.808989i	$-0.700015\pi$
$863$	−34.5368	−1.17565	−0.587823	+	0.808989i	$0.700015\pi$
$864$	17.5995	0.598747
$865$	−18.8429	−0.640678
$866$	−5.49781	−0.186823
$867$	0	0
$868$	−10.7675	−0.365473
$869$	35.9734	1.22031
$870$	1.20081	0.0407113
$871$	−37.6032	−1.27414
$872$	−11.1298	−0.376902
$873$	16.7918	0.568317
$874$	1.85189	0.0626412
$875$	2.50984	0.0848480
$876$	−13.0793	−0.441909
$877$	15.8248	0.534367	0.267184	−	0.963646i	$-0.413907\pi$
$877$	15.8248	0.534367	0.267184	+	0.963646i	$0.413907\pi$
$878$	4.44481	0.150005
$879$	22.1546	0.747257
$880$	−8.46705	−0.285424
$881$	31.5651	1.06346	0.531728	−	0.846915i	$-0.321543\pi$
$881$	31.5651	1.06346	0.531728	+	0.846915i	$0.321543\pi$
$882$	0.396208	0.0133410
$883$	20.2779	0.682406	0.341203	−	0.939990i	$-0.389166\pi$
$883$	20.2779	0.682406	0.341203	+	0.939990i	$0.389166\pi$
$884$	0	0
$885$	7.89572	0.265412
$886$	−7.03942	−0.236494
$887$	−48.8392	−1.63986	−0.819930	−	0.572465i	$-0.805987\pi$
$887$	−48.8392	−1.63986	−0.819930	+	0.572465i	$0.805987\pi$
$888$	−6.38831	−0.214378
$889$	14.9457	0.501262
$890$	0.119215	0.00399611
$891$	0.331523	0.0111064
$892$	−12.3380	−0.413106
$893$	16.4096	0.549125
$894$	1.92621	0.0644222
$895$	−3.31384	−0.110770
$896$	21.5480	0.719869
$897$	−5.12682	−0.171180
$898$	−0.516374	−0.0172316
$899$	−8.43070	−0.281180
$900$	3.57791	0.119264
$901$	0	0
$902$	9.11148	0.303379
$903$	−6.97735	−0.232192
$904$	−17.6434	−0.586810
$905$	15.8652	0.527375
$906$	3.33483	0.110792
$907$	41.7064	1.38484	0.692419	−	0.721495i	$-0.256545\pi$
$907$	41.7064	1.38484	0.692419	+	0.721495i	$0.256545\pi$
$908$	5.84265	0.193895
$909$	28.6540	0.950393
$910$	−4.25035	−0.140898
$911$	−6.40146	−0.212090	−0.106045	−	0.994361i	$-0.533819\pi$
$911$	−6.40146	−0.212090	−0.106045	+	0.994361i	$0.533819\pi$
$912$	26.1955	0.867420
$913$	33.9896	1.12489
$914$	−3.98735	−0.131890
$915$	0.961587	0.0317891
$916$	14.4305	0.476796
$917$	−10.5094	−0.347052
$918$	0	0
$919$	−23.6812	−0.781170	−0.390585	−	0.920567i	$-0.627727\pi$
$919$	−23.6812	−0.781170	−0.390585	+	0.920567i	$0.627727\pi$
$920$	−1.01514	−0.0334681
$921$	31.7804	1.04720
$922$	−8.83658	−0.291017
$923$	1.35151	0.0444854
$924$	−12.4323	−0.408991
$925$	−5.10557	−0.167870
$926$	2.95765	0.0971944
$927$	27.6914	0.909503
$928$	12.7664	0.419078
$929$	54.8951	1.80105	0.900524	−	0.434805i	$-0.143183\pi$
$929$	54.8951	1.80105	0.900524	+	0.434805i	$0.143183\pi$
$930$	−0.719356	−0.0235886
$931$	4.99683	0.163764
$932$	42.6617	1.39743
$933$	−0.223156	−0.00730580
$934$	4.12766	0.135061
$935$	0	0
$936$	−12.4071	−0.405539
$937$	6.77360	0.221284	0.110642	−	0.993860i	$-0.464709\pi$
$937$	6.77360	0.221284	0.110642	+	0.993860i	$0.464709\pi$
$938$	−5.07230	−0.165616
$939$	34.4025	1.12268
$940$	−4.39284	−0.143278
$941$	25.2189	0.822111	0.411056	−	0.911610i	$-0.365160\pi$
$941$	25.2189	0.822111	0.411056	+	0.911610i	$0.365160\pi$
$942$	−4.29158	−0.139827
$943$	−10.6306	−0.346179
$944$	25.7645	0.838564
$945$	12.9800	0.422239
$946$	−1.93313	−0.0628514
$947$	−24.5012	−0.796183	−0.398091	−	0.917346i	$-0.630327\pi$
$947$	−24.5012	−0.796183	−0.398091	+	0.917346i	$0.630327\pi$
$948$	29.7937	0.967654
$949$	36.2480	1.17666
$950$	−2.15135	−0.0697990
$951$	35.4793	1.15050
$952$	0	0
$953$	30.3936	0.984545	0.492272	−	0.870441i	$-0.336166\pi$
$953$	30.3936	0.984545	0.492272	+	0.870441i	$0.336166\pi$
$954$	−1.56894	−0.0507964
$955$	−27.4943	−0.889693
$956$	6.60473	0.213612
$957$	−9.73417	−0.314661
$958$	3.32157	0.107315
$959$	−18.2214	−0.588399
$960$	−6.25757	−0.201962
$961$	−25.9495	−0.837081
$962$	8.64616	0.278763
$963$	−2.75660	−0.0888302
$964$	−34.4118	−1.10833
$965$	14.7613	0.475182
$966$	−0.691557	−0.0222505
$967$	43.9516	1.41339	0.706694	−	0.707520i	$-0.250186\pi$
$967$	43.9516	1.41339	0.706694	+	0.707520i	$0.250186\pi$
$968$	5.91906	0.190246
$969$	0	0
$970$	2.70288	0.0867843
$971$	42.3938	1.36048	0.680241	−	0.732989i	$-0.261875\pi$
$971$	42.3938	1.36048	0.680241	+	0.732989i	$0.261875\pi$
$972$	29.8924	0.958798
$973$	26.0853	0.836255
$974$	3.04530	0.0975776
$975$	5.95585	0.190740
$976$	3.13775	0.100437
$977$	−23.7293	−0.759168	−0.379584	−	0.925157i	$-0.623933\pi$
$977$	−23.7293	−0.759168	−0.379584	+	0.925157i	$0.623933\pi$
$978$	0.504191	0.0161222
$979$	−0.966400	−0.0308863
$980$	−1.33765	−0.0427296
$981$	−17.6886	−0.564754
$982$	5.15363	0.164459
$983$	−28.0626	−0.895057	−0.447529	−	0.894270i	$-0.647696\pi$
$983$	−28.0626	−0.895057	−0.447529	+	0.894270i	$0.647696\pi$
$984$	15.4523	0.492602
$985$	−0.376406	−0.0119933
$986$	0	0
$987$	−6.12786	−0.195052
$988$	−76.4152	−2.43109
$989$	2.25543	0.0717184
$990$	1.38282	0.0439488
$991$	44.5466	1.41507	0.707535	−	0.706679i	$-0.249807\pi$
$991$	44.5466	1.41507	0.707535	+	0.706679i	$0.249807\pi$
$992$	−7.64783	−0.242819
$993$	0.939358	0.0298096
$994$	0.182305	0.00578235
$995$	7.53004	0.238718
$996$	28.1507	0.891989
$997$	−20.5479	−0.650757	−0.325379	−	0.945584i	$-0.605492\pi$
$997$	−20.5479	−0.650757	−0.325379	+	0.945584i	$0.605492\pi$
$998$	9.46074	0.299474
$999$	−26.4042	−0.835392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.q.1.7		12
5.4	even	2		7225.2.a.bq.1.6		12
17.4	even	4		1445.2.d.j.866.12		24
17.11	odd	16		85.2.l.a.36.4	yes	24
17.13	even	4		1445.2.d.j.866.11		24
17.14	odd	16		85.2.l.a.26.4	✓	24
17.16	even	2		1445.2.a.p.1.7		12
51.11	even	16		765.2.be.b.631.3		24
51.14	even	16		765.2.be.b.451.3		24
85.14	odd	16		425.2.m.b.26.3		24
85.28	even	16		425.2.n.f.274.4		24
85.48	even	16		425.2.n.c.349.3		24
85.62	even	16		425.2.n.c.274.3		24
85.79	odd	16		425.2.m.b.376.3		24
85.82	even	16		425.2.n.f.349.4		24
85.84	even	2		7225.2.a.bs.1.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.4	✓	24	17.14	odd	16
85.2.l.a.36.4	yes	24	17.11	odd	16
425.2.m.b.26.3		24	85.14	odd	16
425.2.m.b.376.3		24	85.79	odd	16
425.2.n.c.274.3		24	85.62	even	16
425.2.n.c.349.3		24	85.48	even	16
425.2.n.f.274.4		24	85.28	even	16
425.2.n.f.349.4		24	85.82	even	16
765.2.be.b.451.3		24	51.14	even	16
765.2.be.b.631.3		24	51.11	even	16
1445.2.a.p.1.7		12	17.16	even	2
1445.2.a.q.1.7		12	1.1	even	1	trivial
1445.2.d.j.866.11		24	17.13	even	4
1445.2.d.j.866.12		24	17.4	even	4
7225.2.a.bq.1.6		12	5.4	even	2
7225.2.a.bs.1.6		12	85.84	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q+0.301687 q^{2} -1.06101 q^{3} -1.90899 q^{4} -1.00000 q^{5} -0.320094 q^{6} -2.50984 q^{7} -1.17929 q^{8} -1.87425 q^{9} -0.301687 q^{10} +2.44557 q^{11} +2.02546 q^{12} -5.61335 q^{13} -0.757185 q^{14} +1.06101 q^{15} +3.46219 q^{16} -0.565436 q^{18} -7.13107 q^{19} +1.90899 q^{20} +2.66297 q^{21} +0.737797 q^{22} -0.860805 q^{23} +1.25124 q^{24} +1.00000 q^{25} -1.69348 q^{26} +5.17165 q^{27} +4.79124 q^{28} +3.75143 q^{29} +0.320094 q^{30} -2.24733 q^{31} +3.40308 q^{32} -2.59479 q^{33} +2.50984 q^{35} +3.57791 q^{36} -5.10557 q^{37} -2.15135 q^{38} +5.95585 q^{39} +1.17929 q^{40} +12.3496 q^{41} +0.803384 q^{42} -2.62014 q^{43} -4.66856 q^{44} +1.87425 q^{45} -0.259694 q^{46} -2.30114 q^{47} -3.67344 q^{48} -0.700712 q^{49} +0.301687 q^{50} +10.7158 q^{52} +2.77475 q^{53} +1.56022 q^{54} -2.44557 q^{55} +2.95983 q^{56} +7.56616 q^{57} +1.13176 q^{58} +7.44167 q^{59} -2.02546 q^{60} +0.906291 q^{61} -0.677989 q^{62} +4.70406 q^{63} -5.89773 q^{64} +5.61335 q^{65} -0.782813 q^{66} +6.69889 q^{67} +0.913326 q^{69} +0.757185 q^{70} -0.240766 q^{71} +2.21028 q^{72} -6.45746 q^{73} -1.54028 q^{74} -1.06101 q^{75} +13.6131 q^{76} -6.13799 q^{77} +1.79680 q^{78} +14.7096 q^{79} -3.46219 q^{80} +0.135560 q^{81} +3.72571 q^{82} +13.8984 q^{83} -5.08358 q^{84} -0.790460 q^{86} -3.98032 q^{87} -2.88404 q^{88} -0.395163 q^{89} +0.565436 q^{90} +14.0886 q^{91} +1.64326 q^{92} +2.38445 q^{93} -0.694222 q^{94} +7.13107 q^{95} -3.61071 q^{96} -8.95923 q^{97} -0.211396 q^{98} -4.58361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 8 q^{3} + 12 q^{4} - 12 q^{5} + 8 q^{6} + 16 q^{7} - 12 q^{8} + 12 q^{9} + 4 q^{10} + 16 q^{11} + 16 q^{12} - 8 q^{13} - 16 q^{14} - 8 q^{15} + 12 q^{16} + 4 q^{18} - 12 q^{20} + 16 q^{21}+ \cdots + 56 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 8 * q^3 + 12 * q^4 - 12 * q^5 + 8 * q^6 + 16 * q^7 - 12 * q^8 + 12 * q^9 + 4 * q^10 + 16 * q^11 + 16 * q^12 - 8 * q^13 - 16 * q^14 - 8 * q^15 + 12 * q^16 + 4 * q^18 - 12 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^23 + 12 * q^25 + 16 * q^26 + 32 * q^27 + 40 * q^28 + 16 * q^29 - 8 * q^30 + 24 * q^31 - 28 * q^32 - 16 * q^35 + 12 * q^36 + 24 * q^37 - 24 * q^38 + 8 * q^39 + 12 * q^40 + 8 * q^41 - 16 * q^43 + 8 * q^44 - 12 * q^45 + 40 * q^46 - 32 * q^47 - 24 * q^48 + 20 * q^49 - 4 * q^50 - 24 * q^52 + 8 * q^54 - 16 * q^55 - 24 * q^56 + 32 * q^57 - 16 * q^58 + 8 * q^59 - 16 * q^60 + 24 * q^61 + 8 * q^62 + 48 * q^63 + 36 * q^64 + 8 * q^65 + 40 * q^66 - 8 * q^67 + 48 * q^69 + 16 * q^70 - 16 * q^71 + 12 * q^72 + 16 * q^73 + 8 * q^75 + 16 * q^76 + 24 * q^77 - 24 * q^78 + 40 * q^79 - 12 * q^80 + 36 * q^81 - 16 * q^82 - 40 * q^83 + 32 * q^84 - 8 * q^86 - 32 * q^87 + 48 * q^88 + 8 * q^89 - 4 * q^90 + 72 * q^91 - 8 * q^92 + 24 * q^93 - 16 * q^94 + 8 * q^96 + 32 * q^97 - 60 * q^98 + 56 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

Properties

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