LMFDB - Embedded newform 1150.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +0.302776 q^{6} -3.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +0.302776 q^{6} -3.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} -1.69722 q^{11} +0.302776 q^{12} -3.30278 q^{13} -3.30278 q^{14} +1.00000 q^{16} -6.90833 q^{17} -2.90833 q^{18} +5.90833 q^{19} -1.00000 q^{21} -1.69722 q^{22} +1.00000 q^{23} +0.302776 q^{24} -3.30278 q^{26} -1.78890 q^{27} -3.30278 q^{28} -2.60555 q^{29} -7.90833 q^{31} +1.00000 q^{32} -0.513878 q^{33} -6.90833 q^{34} -2.90833 q^{36} -8.00000 q^{37} +5.90833 q^{38} -1.00000 q^{39} +0.908327 q^{41} -1.00000 q^{42} +9.21110 q^{43} -1.69722 q^{44} +1.00000 q^{46} +2.60555 q^{47} +0.302776 q^{48} +3.90833 q^{49} -2.09167 q^{51} -3.30278 q^{52} +11.2111 q^{53} -1.78890 q^{54} -3.30278 q^{56} +1.78890 q^{57} -2.60555 q^{58} -3.39445 q^{59} +11.5139 q^{61} -7.90833 q^{62} +9.60555 q^{63} +1.00000 q^{64} -0.513878 q^{66} +4.00000 q^{67} -6.90833 q^{68} +0.302776 q^{69} -16.3028 q^{71} -2.90833 q^{72} +5.81665 q^{73} -8.00000 q^{74} +5.90833 q^{76} +5.60555 q^{77} -1.00000 q^{78} -14.4222 q^{79} +8.18335 q^{81} +0.908327 q^{82} -11.2111 q^{83} -1.00000 q^{84} +9.21110 q^{86} -0.788897 q^{87} -1.69722 q^{88} +10.9083 q^{91} +1.00000 q^{92} -2.39445 q^{93} +2.60555 q^{94} +0.302776 q^{96} -6.30278 q^{97} +3.90833 q^{98} +4.93608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + 5 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + 5 q^{9} - 7 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} - 2 q^{21} - 7 q^{22} + 2 q^{23} - 3 q^{24} - 3 q^{26} - 18 q^{27} - 3 q^{28} + 2 q^{29} - 5 q^{31} + 2 q^{32} + 17 q^{33} - 3 q^{34} + 5 q^{36} - 16 q^{37} + q^{38} - 2 q^{39} - 9 q^{41} - 2 q^{42} + 4 q^{43} - 7 q^{44} + 2 q^{46} - 2 q^{47} - 3 q^{48} - 3 q^{49} - 15 q^{51} - 3 q^{52} + 8 q^{53} - 18 q^{54} - 3 q^{56} + 18 q^{57} + 2 q^{58} - 14 q^{59} + 5 q^{61} - 5 q^{62} + 12 q^{63} + 2 q^{64} + 17 q^{66} + 8 q^{67} - 3 q^{68} - 3 q^{69} - 29 q^{71} + 5 q^{72} - 10 q^{73} - 16 q^{74} + q^{76} + 4 q^{77} - 2 q^{78} + 38 q^{81} - 9 q^{82} - 8 q^{83} - 2 q^{84} + 4 q^{86} - 16 q^{87} - 7 q^{88} + 11 q^{91} + 2 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{96} - 9 q^{97} - 3 q^{98} - 37 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + 5 * q^9 - 7 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 - 2 * q^21 - 7 * q^22 + 2 * q^23 - 3 * q^24 - 3 * q^26 - 18 * q^27 - 3 * q^28 + 2 * q^29 - 5 * q^31 + 2 * q^32 + 17 * q^33 - 3 * q^34 + 5 * q^36 - 16 * q^37 + q^38 - 2 * q^39 - 9 * q^41 - 2 * q^42 + 4 * q^43 - 7 * q^44 + 2 * q^46 - 2 * q^47 - 3 * q^48 - 3 * q^49 - 15 * q^51 - 3 * q^52 + 8 * q^53 - 18 * q^54 - 3 * q^56 + 18 * q^57 + 2 * q^58 - 14 * q^59 + 5 * q^61 - 5 * q^62 + 12 * q^63 + 2 * q^64 + 17 * q^66 + 8 * q^67 - 3 * q^68 - 3 * q^69 - 29 * q^71 + 5 * q^72 - 10 * q^73 - 16 * q^74 + q^76 + 4 * q^77 - 2 * q^78 + 38 * q^81 - 9 * q^82 - 8 * q^83 - 2 * q^84 + 4 * q^86 - 16 * q^87 - 7 * q^88 + 11 * q^91 + 2 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^96 - 9 * q^97 - 3 * q^98 - 37 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.302776	0.174808	0.0874038	−	0.996173i	$-0.472143\pi$
$3$	0.302776	0.174808	0.0874038	+	0.996173i	$0.472143\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.302776	0.123608
$7$	−3.30278	−1.24833	−0.624166	−	0.781292i	$-0.714561\pi$
$7$	−3.30278	−1.24833	−0.624166	+	0.781292i	$0.714561\pi$
$8$	1.00000	0.353553
$9$	−2.90833	−0.969442
$10$	0	0
$11$	−1.69722	−0.511732	−0.255866	−	0.966712i	$-0.582361\pi$
$11$	−1.69722	−0.511732	−0.255866	+	0.966712i	$0.582361\pi$
$12$	0.302776	0.0874038
$13$	−3.30278	−0.916025	−0.458013	−	0.888946i	$-0.651439\pi$
$13$	−3.30278	−0.916025	−0.458013	+	0.888946i	$0.651439\pi$
$14$	−3.30278	−0.882704
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.90833	−1.67552	−0.837758	−	0.546042i	$-0.816134\pi$
$17$	−6.90833	−1.67552	−0.837758	+	0.546042i	$0.816134\pi$
$18$	−2.90833	−0.685499
$19$	5.90833	1.35546	0.677732	−	0.735309i	$-0.262963\pi$
$19$	5.90833	1.35546	0.677732	+	0.735309i	$0.262963\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−1.69722	−0.361849
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.302776	0.0618038
$25$	0	0
$26$	−3.30278	−0.647728
$27$	−1.78890	−0.344273
$28$	−3.30278	−0.624166
$29$	−2.60555	−0.483839	−0.241919	−	0.970296i	$-0.577777\pi$
$29$	−2.60555	−0.483839	−0.241919	+	0.970296i	$0.577777\pi$
$30$	0	0
$31$	−7.90833	−1.42038	−0.710189	−	0.704011i	$-0.751390\pi$
$31$	−7.90833	−1.42038	−0.710189	+	0.704011i	$0.751390\pi$
$32$	1.00000	0.176777
$33$	−0.513878	−0.0894547
$34$	−6.90833	−1.18477
$35$	0	0
$36$	−2.90833	−0.484721
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	5.90833	0.958457
$39$	−1.00000	−0.160128
$40$	0	0
$41$	0.908327	0.141857	0.0709284	−	0.997481i	$-0.477404\pi$
$41$	0.908327	0.141857	0.0709284	+	0.997481i	$0.477404\pi$
$42$	−1.00000	−0.154303
$43$	9.21110	1.40468	0.702340	−	0.711842i	$-0.252139\pi$
$43$	9.21110	1.40468	0.702340	+	0.711842i	$0.252139\pi$
$44$	−1.69722	−0.255866
$45$	0	0
$46$	1.00000	0.147442
$47$	2.60555	0.380059	0.190029	−	0.981778i	$-0.439142\pi$
$47$	2.60555	0.380059	0.190029	+	0.981778i	$0.439142\pi$
$48$	0.302776	0.0437019
$49$	3.90833	0.558332
$50$	0	0
$51$	−2.09167	−0.292893
$52$	−3.30278	−0.458013
$53$	11.2111	1.53996	0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111	1.53996	0.769982	+	0.638066i	$0.220265\pi$
$54$	−1.78890	−0.243438
$55$	0	0
$56$	−3.30278	−0.441352
$57$	1.78890	0.236945
$58$	−2.60555	−0.342126
$59$	−3.39445	−0.441920	−0.220960	−	0.975283i	$-0.570919\pi$
$59$	−3.39445	−0.441920	−0.220960	+	0.975283i	$0.570919\pi$
$60$	0	0
$61$	11.5139	1.47420	0.737101	−	0.675783i	$-0.236194\pi$
$61$	11.5139	1.47420	0.737101	+	0.675783i	$0.236194\pi$
$62$	−7.90833	−1.00436
$63$	9.60555	1.21019
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.513878	−0.0632540
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	−6.90833	−0.837758
$69$	0.302776	0.0364499
$70$	0	0
$71$	−16.3028	−1.93478	−0.967392	−	0.253285i	$-0.918489\pi$
$71$	−16.3028	−1.93478	−0.967392	+	0.253285i	$0.918489\pi$
$72$	−2.90833	−0.342750
$73$	5.81665	0.680788	0.340394	−	0.940283i	$-0.389440\pi$
$73$	5.81665	0.680788	0.340394	+	0.940283i	$0.389440\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	5.90833	0.677732
$77$	5.60555	0.638812
$78$	−1.00000	−0.113228
$79$	−14.4222	−1.62262	−0.811312	−	0.584613i	$-0.801246\pi$
$79$	−14.4222	−1.62262	−0.811312	+	0.584613i	$0.801246\pi$
$80$	0	0
$81$	8.18335	0.909261
$82$	0.908327	0.100308
$83$	−11.2111	−1.23058	−0.615289	−	0.788301i	$-0.710961\pi$
$83$	−11.2111	−1.23058	−0.615289	+	0.788301i	$0.710961\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	9.21110	0.993259
$87$	−0.788897	−0.0845787
$88$	−1.69722	−0.180925
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	10.9083	1.14350
$92$	1.00000	0.104257
$93$	−2.39445	−0.248293
$94$	2.60555	0.268742
$95$	0	0
$96$	0.302776	0.0309019
$97$	−6.30278	−0.639950	−0.319975	−	0.947426i	$-0.603675\pi$
$97$	−6.30278	−0.639950	−0.319975	+	0.947426i	$0.603675\pi$
$98$	3.90833	0.394801
$99$	4.93608	0.496095
$100$	0	0
$101$	2.60555	0.259262	0.129631	−	0.991562i	$-0.458621\pi$
$101$	2.60555	0.259262	0.129631	+	0.991562i	$0.458621\pi$
$102$	−2.09167	−0.207106
$103$	−8.11943	−0.800031	−0.400016	−	0.916508i	$-0.630995\pi$
$103$	−8.11943	−0.800031	−0.400016	+	0.916508i	$0.630995\pi$
$104$	−3.30278	−0.323864
$105$	0	0
$106$	11.2111	1.08892
$107$	2.60555	0.251888	0.125944	−	0.992037i	$-0.459804\pi$
$107$	2.60555	0.251888	0.125944	+	0.992037i	$0.459804\pi$
$108$	−1.78890	−0.172137
$109$	1.48612	0.142345	0.0711723	−	0.997464i	$-0.477326\pi$
$109$	1.48612	0.142345	0.0711723	+	0.997464i	$0.477326\pi$
$110$	0	0
$111$	−2.42221	−0.229906
$112$	−3.30278	−0.312083
$113$	16.4222	1.54487	0.772436	−	0.635093i	$-0.219038\pi$
$113$	16.4222	1.54487	0.772436	+	0.635093i	$0.219038\pi$
$114$	1.78890	0.167546
$115$	0	0
$116$	−2.60555	−0.241919
$117$	9.60555	0.888034
$118$	−3.39445	−0.312484
$119$	22.8167	2.09160
$120$	0	0
$121$	−8.11943	−0.738130
$122$	11.5139	1.04242
$123$	0.275019	0.0247977
$124$	−7.90833	−0.710189
$125$	0	0
$126$	9.60555	0.855731
$127$	−9.81665	−0.871087	−0.435544	−	0.900168i	$-0.643444\pi$
$127$	−9.81665	−0.871087	−0.435544	+	0.900168i	$0.643444\pi$
$128$	1.00000	0.0883883
$129$	2.78890	0.245549
$130$	0	0
$131$	−11.2111	−0.979519	−0.489759	−	0.871858i	$-0.662915\pi$
$131$	−11.2111	−0.979519	−0.489759	+	0.871858i	$0.662915\pi$
$132$	−0.513878	−0.0447274
$133$	−19.5139	−1.69207
$134$	4.00000	0.345547
$135$	0	0
$136$	−6.90833	−0.592384
$137$	−3.90833	−0.333911	−0.166955	−	0.985964i	$-0.553394\pi$
$137$	−3.90833	−0.333911	−0.166955	+	0.985964i	$0.553394\pi$
$138$	0.302776	0.0257740
$139$	−12.6056	−1.06919	−0.534594	−	0.845109i	$-0.679536\pi$
$139$	−12.6056	−1.06919	−0.534594	+	0.845109i	$0.679536\pi$
$140$	0	0
$141$	0.788897	0.0664372
$142$	−16.3028	−1.36810
$143$	5.60555	0.468760
$144$	−2.90833	−0.242361
$145$	0	0
$146$	5.81665	0.481390
$147$	1.18335	0.0976007
$148$	−8.00000	−0.657596
$149$	13.3028	1.08981	0.544903	−	0.838499i	$-0.316567\pi$
$149$	13.3028	1.08981	0.544903	+	0.838499i	$0.316567\pi$
$150$	0	0
$151$	8.90833	0.724949	0.362475	−	0.931994i	$-0.381932\pi$
$151$	8.90833	0.724949	0.362475	+	0.931994i	$0.381932\pi$
$152$	5.90833	0.479229
$153$	20.0917	1.62432
$154$	5.60555	0.451708
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	18.6056	1.48488	0.742442	−	0.669910i	$-0.233667\pi$
$157$	18.6056	1.48488	0.742442	+	0.669910i	$0.233667\pi$
$158$	−14.4222	−1.14737
$159$	3.39445	0.269197
$160$	0	0
$161$	−3.30278	−0.260295
$162$	8.18335	0.642944
$163$	−9.30278	−0.728650	−0.364325	−	0.931272i	$-0.618700\pi$
$163$	−9.30278	−0.728650	−0.364325	+	0.931272i	$0.618700\pi$
$164$	0.908327	0.0709284
$165$	0	0
$166$	−11.2111	−0.870150
$167$	−6.78890	−0.525341	−0.262670	−	0.964886i	$-0.584603\pi$
$167$	−6.78890	−0.525341	−0.262670	+	0.964886i	$0.584603\pi$
$168$	−1.00000	−0.0771517
$169$	−2.09167	−0.160898
$170$	0	0
$171$	−17.1833	−1.31404
$172$	9.21110	0.702340
$173$	−19.6972	−1.49755	−0.748776	−	0.662823i	$-0.769358\pi$
$173$	−19.6972	−1.49755	−0.748776	+	0.662823i	$0.769358\pi$
$174$	−0.788897	−0.0598062
$175$	0	0
$176$	−1.69722	−0.127933
$177$	−1.02776	−0.0772509
$178$	0	0
$179$	9.39445	0.702174	0.351087	−	0.936343i	$-0.385812\pi$
$179$	9.39445	0.702174	0.351087	+	0.936343i	$0.385812\pi$
$180$	0	0
$181$	17.1194	1.27248	0.636239	−	0.771492i	$-0.280489\pi$
$181$	17.1194	1.27248	0.636239	+	0.771492i	$0.280489\pi$
$182$	10.9083	0.808579
$183$	3.48612	0.257702
$184$	1.00000	0.0737210
$185$	0	0
$186$	−2.39445	−0.175569
$187$	11.7250	0.857416
$188$	2.60555	0.190029
$189$	5.90833	0.429768
$190$	0	0
$191$	−8.60555	−0.622676	−0.311338	−	0.950299i	$-0.600777\pi$
$191$	−8.60555	−0.622676	−0.311338	+	0.950299i	$0.600777\pi$
$192$	0.302776	0.0218509
$193$	17.8167	1.28247	0.641235	−	0.767344i	$-0.278422\pi$
$193$	17.8167	1.28247	0.641235	+	0.767344i	$0.278422\pi$
$194$	−6.30278	−0.452513
$195$	0	0
$196$	3.90833	0.279166
$197$	−4.30278	−0.306560	−0.153280	−	0.988183i	$-0.548984\pi$
$197$	−4.30278	−0.306560	−0.153280	+	0.988183i	$0.548984\pi$
$198$	4.93608	0.350792
$199$	−20.4222	−1.44769	−0.723846	−	0.689962i	$-0.757627\pi$
$199$	−20.4222	−1.44769	−0.723846	+	0.689962i	$0.757627\pi$
$200$	0	0
$201$	1.21110	0.0854246
$202$	2.60555	0.183326
$203$	8.60555	0.603991
$204$	−2.09167	−0.146446
$205$	0	0
$206$	−8.11943	−0.565707
$207$	−2.90833	−0.202143
$208$	−3.30278	−0.229006
$209$	−10.0278	−0.693634
$210$	0	0
$211$	7.21110	0.496433	0.248216	−	0.968705i	$-0.420156\pi$
$211$	7.21110	0.496433	0.248216	+	0.968705i	$0.420156\pi$
$212$	11.2111	0.769982
$213$	−4.93608	−0.338215
$214$	2.60555	0.178112
$215$	0	0
$216$	−1.78890	−0.121719
$217$	26.1194	1.77310
$218$	1.48612	0.100653
$219$	1.76114	0.119007
$220$	0	0
$221$	22.8167	1.53481
$222$	−2.42221	−0.162568
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−3.30278	−0.220676
$225$	0	0
$226$	16.4222	1.09239
$227$	14.6056	0.969404	0.484702	−	0.874679i	$-0.338928\pi$
$227$	14.6056	0.969404	0.484702	+	0.874679i	$0.338928\pi$
$228$	1.78890	0.118473
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	1.69722	0.111669
$232$	−2.60555	−0.171063
$233$	−25.8167	−1.69131	−0.845653	−	0.533734i	$-0.820788\pi$
$233$	−25.8167	−1.69131	−0.845653	+	0.533734i	$0.820788\pi$
$234$	9.60555	0.627935
$235$	0	0
$236$	−3.39445	−0.220960
$237$	−4.36669	−0.283647
$238$	22.8167	1.47898
$239$	5.21110	0.337078	0.168539	−	0.985695i	$-0.446095\pi$
$239$	5.21110	0.337078	0.168539	+	0.985695i	$0.446095\pi$
$240$	0	0
$241$	−14.4222	−0.929016	−0.464508	−	0.885569i	$-0.653769\pi$
$241$	−14.4222	−0.929016	−0.464508	+	0.885569i	$0.653769\pi$
$242$	−8.11943	−0.521937
$243$	7.84441	0.503219
$244$	11.5139	0.737101
$245$	0	0
$246$	0.275019	0.0175346
$247$	−19.5139	−1.24164
$248$	−7.90833	−0.502179
$249$	−3.39445	−0.215114
$250$	0	0
$251$	12.5139	0.789869	0.394934	−	0.918709i	$-0.370767\pi$
$251$	12.5139	0.789869	0.394934	+	0.918709i	$0.370767\pi$
$252$	9.60555	0.605093
$253$	−1.69722	−0.106704
$254$	−9.81665	−0.615952
$255$	0	0
$256$	1.00000	0.0625000
$257$	1.81665	0.113320	0.0566599	−	0.998394i	$-0.481955\pi$
$257$	1.81665	0.113320	0.0566599	+	0.998394i	$0.481955\pi$
$258$	2.78890	0.173629
$259$	26.4222	1.64180
$260$	0	0
$261$	7.57779	0.469054
$262$	−11.2111	−0.692624
$263$	−3.51388	−0.216675	−0.108338	−	0.994114i	$-0.534553\pi$
$263$	−3.51388	−0.216675	−0.108338	+	0.994114i	$0.534553\pi$
$264$	−0.513878	−0.0316270
$265$	0	0
$266$	−19.5139	−1.19647
$267$	0	0
$268$	4.00000	0.244339
$269$	4.18335	0.255063	0.127532	−	0.991835i	$-0.459295\pi$
$269$	4.18335	0.255063	0.127532	+	0.991835i	$0.459295\pi$
$270$	0	0
$271$	−2.69722	−0.163845	−0.0819224	−	0.996639i	$-0.526106\pi$
$271$	−2.69722	−0.163845	−0.0819224	+	0.996639i	$0.526106\pi$
$272$	−6.90833	−0.418879
$273$	3.30278	0.199893
$274$	−3.90833	−0.236111
$275$	0	0
$276$	0.302776	0.0182250
$277$	27.2111	1.63496	0.817478	−	0.575959i	$-0.195371\pi$
$277$	27.2111	1.63496	0.817478	+	0.575959i	$0.195371\pi$
$278$	−12.6056	−0.756031
$279$	23.0000	1.37697
$280$	0	0
$281$	−26.6056	−1.58715	−0.793577	−	0.608470i	$-0.791784\pi$
$281$	−26.6056	−1.58715	−0.793577	+	0.608470i	$0.791784\pi$
$282$	0.788897	0.0469782
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	−16.3028	−0.967392
$285$	0	0
$286$	5.60555	0.331463
$287$	−3.00000	−0.177084
$288$	−2.90833	−0.171375
$289$	30.7250	1.80735
$290$	0	0
$291$	−1.90833	−0.111868
$292$	5.81665	0.340394
$293$	−23.2111	−1.35601	−0.678004	−	0.735059i	$-0.737155\pi$
$293$	−23.2111	−1.35601	−0.678004	+	0.735059i	$0.737155\pi$
$294$	1.18335	0.0690142
$295$	0	0
$296$	−8.00000	−0.464991
$297$	3.03616	0.176176
$298$	13.3028	0.770609
$299$	−3.30278	−0.191004
$300$	0	0
$301$	−30.4222	−1.75351
$302$	8.90833	0.512617
$303$	0.788897	0.0453210
$304$	5.90833	0.338866
$305$	0	0
$306$	20.0917	1.14856
$307$	11.6972	0.667596	0.333798	−	0.942645i	$-0.391670\pi$
$307$	11.6972	0.667596	0.333798	+	0.942645i	$0.391670\pi$
$308$	5.60555	0.319406
$309$	−2.45837	−0.139852
$310$	0	0
$311$	22.4222	1.27145	0.635723	−	0.771917i	$-0.280702\pi$
$311$	22.4222	1.27145	0.635723	+	0.771917i	$0.280702\pi$
$312$	−1.00000	−0.0566139
$313$	−19.7250	−1.11492	−0.557461	−	0.830203i	$-0.688224\pi$
$313$	−19.7250	−1.11492	−0.557461	+	0.830203i	$0.688224\pi$
$314$	18.6056	1.04997
$315$	0	0
$316$	−14.4222	−0.811312
$317$	−17.7250	−0.995534	−0.497767	−	0.867311i	$-0.665847\pi$
$317$	−17.7250	−0.995534	−0.497767	+	0.867311i	$0.665847\pi$
$318$	3.39445	0.190351
$319$	4.42221	0.247596
$320$	0	0
$321$	0.788897	0.0440320
$322$	−3.30278	−0.184056
$323$	−40.8167	−2.27110
$324$	8.18335	0.454630
$325$	0	0
$326$	−9.30278	−0.515233
$327$	0.449961	0.0248829
$328$	0.908327	0.0501540
$329$	−8.60555	−0.474439
$330$	0	0
$331$	16.6056	0.912724	0.456362	−	0.889794i	$-0.349152\pi$
$331$	16.6056	0.912724	0.456362	+	0.889794i	$0.349152\pi$
$332$	−11.2111	−0.615289
$333$	23.2666	1.27500
$334$	−6.78890	−0.371472
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	22.5139	1.22641	0.613205	−	0.789924i	$-0.289880\pi$
$337$	22.5139	1.22641	0.613205	+	0.789924i	$0.289880\pi$
$338$	−2.09167	−0.113772
$339$	4.97224	0.270055
$340$	0	0
$341$	13.4222	0.726853
$342$	−17.1833	−0.929169
$343$	10.2111	0.551348
$344$	9.21110	0.496629
$345$	0	0
$346$	−19.6972	−1.05893
$347$	−28.5416	−1.53220	−0.766098	−	0.642724i	$-0.777804\pi$
$347$	−28.5416	−1.53220	−0.766098	+	0.642724i	$0.777804\pi$
$348$	−0.788897	−0.0422893
$349$	−27.2111	−1.45658	−0.728288	−	0.685271i	$-0.759684\pi$
$349$	−27.2111	−1.45658	−0.728288	+	0.685271i	$0.759684\pi$
$350$	0	0
$351$	5.90833	0.315363
$352$	−1.69722	−0.0904624
$353$	10.4222	0.554718	0.277359	−	0.960766i	$-0.410541\pi$
$353$	10.4222	0.554718	0.277359	+	0.960766i	$0.410541\pi$
$354$	−1.02776	−0.0546246
$355$	0	0
$356$	0	0
$357$	6.90833	0.365627
$358$	9.39445	0.496512
$359$	11.2111	0.591699	0.295850	−	0.955235i	$-0.404397\pi$
$359$	11.2111	0.591699	0.295850	+	0.955235i	$0.404397\pi$
$360$	0	0
$361$	15.9083	0.837280
$362$	17.1194	0.899777
$363$	−2.45837	−0.129031
$364$	10.9083	0.571752
$365$	0	0
$366$	3.48612	0.182223
$367$	−14.7889	−0.771974	−0.385987	−	0.922504i	$-0.626139\pi$
$367$	−14.7889	−0.771974	−0.385987	+	0.922504i	$0.626139\pi$
$368$	1.00000	0.0521286
$369$	−2.64171	−0.137522
$370$	0	0
$371$	−37.0278	−1.92239
$372$	−2.39445	−0.124146
$373$	−4.60555	−0.238466	−0.119233	−	0.992866i	$-0.538044\pi$
$373$	−4.60555	−0.238466	−0.119233	+	0.992866i	$0.538044\pi$
$374$	11.7250	0.606284
$375$	0	0
$376$	2.60555	0.134371
$377$	8.60555	0.443208
$378$	5.90833	0.303892
$379$	14.9083	0.765789	0.382895	−	0.923792i	$-0.374927\pi$
$379$	14.9083	0.765789	0.382895	+	0.923792i	$0.374927\pi$
$380$	0	0
$381$	−2.97224	−0.152273
$382$	−8.60555	−0.440298
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0.302776	0.0154510
$385$	0	0
$386$	17.8167	0.906844
$387$	−26.7889	−1.36176
$388$	−6.30278	−0.319975
$389$	−25.9361	−1.31501	−0.657506	−	0.753449i	$-0.728388\pi$
$389$	−25.9361	−1.31501	−0.657506	+	0.753449i	$0.728388\pi$
$390$	0	0
$391$	−6.90833	−0.349369
$392$	3.90833	0.197400
$393$	−3.39445	−0.171227
$394$	−4.30278	−0.216771
$395$	0	0
$396$	4.93608	0.248048
$397$	−10.7250	−0.538271	−0.269136	−	0.963102i	$-0.586738\pi$
$397$	−10.7250	−0.538271	−0.269136	+	0.963102i	$0.586738\pi$
$398$	−20.4222	−1.02367
$399$	−5.90833	−0.295786
$400$	0	0
$401$	−8.60555	−0.429741	−0.214870	−	0.976643i	$-0.568933\pi$
$401$	−8.60555	−0.429741	−0.214870	+	0.976643i	$0.568933\pi$
$402$	1.21110	0.0604043
$403$	26.1194	1.30110
$404$	2.60555	0.129631
$405$	0	0
$406$	8.60555	0.427086
$407$	13.5778	0.673026
$408$	−2.09167	−0.103553
$409$	−25.9083	−1.28108	−0.640542	−	0.767923i	$-0.721290\pi$
$409$	−25.9083	−1.28108	−0.640542	+	0.767923i	$0.721290\pi$
$410$	0	0
$411$	−1.18335	−0.0583702
$412$	−8.11943	−0.400016
$413$	11.2111	0.551662
$414$	−2.90833	−0.142936
$415$	0	0
$416$	−3.30278	−0.161932
$417$	−3.81665	−0.186902
$418$	−10.0278	−0.490474
$419$	3.63331	0.177499	0.0887493	−	0.996054i	$-0.471713\pi$
$419$	3.63331	0.177499	0.0887493	+	0.996054i	$0.471713\pi$
$420$	0	0
$421$	30.6972	1.49609	0.748046	−	0.663647i	$-0.230992\pi$
$421$	30.6972	1.49609	0.748046	+	0.663647i	$0.230992\pi$
$422$	7.21110	0.351031
$423$	−7.57779	−0.368445
$424$	11.2111	0.544459
$425$	0	0
$426$	−4.93608	−0.239154
$427$	−38.0278	−1.84029
$428$	2.60555	0.125944
$429$	1.69722	0.0819428
$430$	0	0
$431$	−30.2389	−1.45655	−0.728277	−	0.685283i	$-0.759679\pi$
$431$	−30.2389	−1.45655	−0.728277	+	0.685283i	$0.759679\pi$
$432$	−1.78890	−0.0860684
$433$	24.0917	1.15777	0.578886	−	0.815409i	$-0.303488\pi$
$433$	24.0917	1.15777	0.578886	+	0.815409i	$0.303488\pi$
$434$	26.1194	1.25377
$435$	0	0
$436$	1.48612	0.0711723
$437$	5.90833	0.282634
$438$	1.76114	0.0841506
$439$	−14.6972	−0.701460	−0.350730	−	0.936477i	$-0.614067\pi$
$439$	−14.6972	−0.701460	−0.350730	+	0.936477i	$0.614067\pi$
$440$	0	0
$441$	−11.3667	−0.541271
$442$	22.8167	1.08528
$443$	−17.4861	−0.830791	−0.415395	−	0.909641i	$-0.636357\pi$
$443$	−17.4861	−0.830791	−0.415395	+	0.909641i	$0.636357\pi$
$444$	−2.42221	−0.114953
$445$	0	0
$446$	4.00000	0.189405
$447$	4.02776	0.190506
$448$	−3.30278	−0.156041
$449$	−2.09167	−0.0987122	−0.0493561	−	0.998781i	$-0.515717\pi$
$449$	−2.09167	−0.0987122	−0.0493561	+	0.998781i	$0.515717\pi$
$450$	0	0
$451$	−1.54163	−0.0725927
$452$	16.4222	0.772436
$453$	2.69722	0.126727
$454$	14.6056	0.685472
$455$	0	0
$456$	1.78890	0.0837728
$457$	32.4222	1.51665	0.758323	−	0.651879i	$-0.226019\pi$
$457$	32.4222	1.51665	0.758323	+	0.651879i	$0.226019\pi$
$458$	2.00000	0.0934539
$459$	12.3583	0.576836
$460$	0	0
$461$	10.1833	0.474286	0.237143	−	0.971475i	$-0.423789\pi$
$461$	10.1833	0.474286	0.237143	+	0.971475i	$0.423789\pi$
$462$	1.69722	0.0789620
$463$	−17.6333	−0.819489	−0.409745	−	0.912200i	$-0.634382\pi$
$463$	−17.6333	−0.819489	−0.409745	+	0.912200i	$0.634382\pi$
$464$	−2.60555	−0.120960
$465$	0	0
$466$	−25.8167	−1.19593
$467$	1.81665	0.0840647	0.0420324	−	0.999116i	$-0.486617\pi$
$467$	1.81665	0.0840647	0.0420324	+	0.999116i	$0.486617\pi$
$468$	9.60555	0.444017
$469$	−13.2111	−0.610032
$470$	0	0
$471$	5.63331	0.259569
$472$	−3.39445	−0.156242
$473$	−15.6333	−0.718820
$474$	−4.36669	−0.200569
$475$	0	0
$476$	22.8167	1.04580
$477$	−32.6056	−1.49291
$478$	5.21110	0.238350
$479$	−30.0000	−1.37073	−0.685367	−	0.728197i	$-0.740358\pi$
$479$	−30.0000	−1.37073	−0.685367	+	0.728197i	$0.740358\pi$
$480$	0	0
$481$	26.4222	1.20475
$482$	−14.4222	−0.656913
$483$	−1.00000	−0.0455016
$484$	−8.11943	−0.369065
$485$	0	0
$486$	7.84441	0.355830
$487$	−9.81665	−0.444835	−0.222418	−	0.974952i	$-0.571395\pi$
$487$	−9.81665	−0.444835	−0.222418	+	0.974952i	$0.571395\pi$
$488$	11.5139	0.521209
$489$	−2.81665	−0.127373
$490$	0	0
$491$	−4.18335	−0.188792	−0.0943959	−	0.995535i	$-0.530092\pi$
$491$	−4.18335	−0.188792	−0.0943959	+	0.995535i	$0.530092\pi$
$492$	0.275019	0.0123988
$493$	18.0000	0.810679
$494$	−19.5139	−0.877971
$495$	0	0
$496$	−7.90833	−0.355094
$497$	53.8444	2.41525
$498$	−3.39445	−0.152109
$499$	−31.6333	−1.41610	−0.708051	−	0.706162i	$-0.750425\pi$
$499$	−31.6333	−1.41610	−0.708051	+	0.706162i	$0.750425\pi$
$500$	0	0
$501$	−2.05551	−0.0918335
$502$	12.5139	0.558522
$503$	−29.7250	−1.32537	−0.662686	−	0.748898i	$-0.730583\pi$
$503$	−29.7250	−1.32537	−0.662686	+	0.748898i	$0.730583\pi$
$504$	9.60555	0.427865
$505$	0	0
$506$	−1.69722	−0.0754508
$507$	−0.633308	−0.0281262
$508$	−9.81665	−0.435544
$509$	−35.4500	−1.57129	−0.785646	−	0.618676i	$-0.787669\pi$
$509$	−35.4500	−1.57129	−0.785646	+	0.618676i	$0.787669\pi$
$510$	0	0
$511$	−19.2111	−0.849849
$512$	1.00000	0.0441942
$513$	−10.5694	−0.466650
$514$	1.81665	0.0801292
$515$	0	0
$516$	2.78890	0.122774
$517$	−4.42221	−0.194488
$518$	26.4222	1.16093
$519$	−5.96384	−0.261784
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	7.57779	0.331671
$523$	20.4222	0.893001	0.446500	−	0.894783i	$-0.352670\pi$
$523$	20.4222	0.893001	0.446500	+	0.894783i	$0.352670\pi$
$524$	−11.2111	−0.489759
$525$	0	0
$526$	−3.51388	−0.153212
$527$	54.6333	2.37986
$528$	−0.513878	−0.0223637
$529$	1.00000	0.0434783
$530$	0	0
$531$	9.87217	0.428416
$532$	−19.5139	−0.846034
$533$	−3.00000	−0.129944
$534$	0	0
$535$	0	0
$536$	4.00000	0.172774
$537$	2.84441	0.122745
$538$	4.18335	0.180357
$539$	−6.63331	−0.285717
$540$	0	0
$541$	28.8444	1.24012	0.620059	−	0.784555i	$-0.287109\pi$
$541$	28.8444	1.24012	0.620059	+	0.784555i	$0.287109\pi$
$542$	−2.69722	−0.115856
$543$	5.18335	0.222439
$544$	−6.90833	−0.296192
$545$	0	0
$546$	3.30278	0.141346
$547$	10.5139	0.449541	0.224770	−	0.974412i	$-0.427837\pi$
$547$	10.5139	0.449541	0.224770	+	0.974412i	$0.427837\pi$
$548$	−3.90833	−0.166955
$549$	−33.4861	−1.42915
$550$	0	0
$551$	−15.3944	−0.655826
$552$	0.302776	0.0128870
$553$	47.6333	2.02557
$554$	27.2111	1.15609
$555$	0	0
$556$	−12.6056	−0.534594
$557$	−22.4222	−0.950059	−0.475030	−	0.879970i	$-0.657563\pi$
$557$	−22.4222	−0.950059	−0.475030	+	0.879970i	$0.657563\pi$
$558$	23.0000	0.973668
$559$	−30.4222	−1.28672
$560$	0	0
$561$	3.55004	0.149883
$562$	−26.6056	−1.12229
$563$	3.63331	0.153126	0.0765628	−	0.997065i	$-0.475605\pi$
$563$	3.63331	0.153126	0.0765628	+	0.997065i	$0.475605\pi$
$564$	0.788897	0.0332186
$565$	0	0
$566$	−2.00000	−0.0840663
$567$	−27.0278	−1.13506
$568$	−16.3028	−0.684049
$569$	28.4222	1.19152	0.595760	−	0.803162i	$-0.296851\pi$
$569$	28.4222	1.19152	0.595760	+	0.803162i	$0.296851\pi$
$570$	0	0
$571$	−16.1194	−0.674577	−0.337289	−	0.941401i	$-0.609510\pi$
$571$	−16.1194	−0.674577	−0.337289	+	0.941401i	$0.609510\pi$
$572$	5.60555	0.234380
$573$	−2.60555	−0.108848
$574$	−3.00000	−0.125218
$575$	0	0
$576$	−2.90833	−0.121180
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	30.7250	1.27799
$579$	5.39445	0.224186
$580$	0	0
$581$	37.0278	1.53617
$582$	−1.90833	−0.0791027
$583$	−19.0278	−0.788049
$584$	5.81665	0.240695
$585$	0	0
$586$	−23.2111	−0.958842
$587$	−16.5416	−0.682746	−0.341373	−	0.939928i	$-0.610892\pi$
$587$	−16.5416	−0.682746	−0.341373	+	0.939928i	$0.610892\pi$
$588$	1.18335	0.0488004
$589$	−46.7250	−1.92527
$590$	0	0
$591$	−1.30278	−0.0535890
$592$	−8.00000	−0.328798
$593$	1.81665	0.0746010	0.0373005	−	0.999304i	$-0.488124\pi$
$593$	1.81665	0.0746010	0.0373005	+	0.999304i	$0.488124\pi$
$594$	3.03616	0.124575
$595$	0	0
$596$	13.3028	0.544903
$597$	−6.18335	−0.253068
$598$	−3.30278	−0.135061
$599$	−35.3305	−1.44357	−0.721783	−	0.692119i	$-0.756677\pi$
$599$	−35.3305	−1.44357	−0.721783	+	0.692119i	$0.756677\pi$
$600$	0	0
$601$	42.9361	1.75140	0.875700	−	0.482856i	$-0.160401\pi$
$601$	42.9361	1.75140	0.875700	+	0.482856i	$0.160401\pi$
$602$	−30.4222	−1.23992
$603$	−11.6333	−0.473745
$604$	8.90833	0.362475
$605$	0	0
$606$	0.788897	0.0320468
$607$	−46.0555	−1.86934	−0.934668	−	0.355522i	$-0.884303\pi$
$607$	−46.0555	−1.86934	−0.934668	+	0.355522i	$0.884303\pi$
$608$	5.90833	0.239614
$609$	2.60555	0.105582
$610$	0	0
$611$	−8.60555	−0.348143
$612$	20.0917	0.812158
$613$	−3.57779	−0.144506	−0.0722529	−	0.997386i	$-0.523019\pi$
$613$	−3.57779	−0.144506	−0.0722529	+	0.997386i	$0.523019\pi$
$614$	11.6972	0.472062
$615$	0	0
$616$	5.60555	0.225854
$617$	−18.9083	−0.761221	−0.380610	−	0.924736i	$-0.624286\pi$
$617$	−18.9083	−0.761221	−0.380610	+	0.924736i	$0.624286\pi$
$618$	−2.45837	−0.0988900
$619$	−12.3305	−0.495606	−0.247803	−	0.968810i	$-0.579709\pi$
$619$	−12.3305	−0.495606	−0.247803	+	0.968810i	$0.579709\pi$
$620$	0	0
$621$	−1.78890	−0.0717860
$622$	22.4222	0.899049
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	0	0
$626$	−19.7250	−0.788369
$627$	−3.03616	−0.121253
$628$	18.6056	0.742442
$629$	55.2666	2.20362
$630$	0	0
$631$	23.3944	0.931318	0.465659	−	0.884964i	$-0.345817\pi$
$631$	23.3944	0.931318	0.465659	+	0.884964i	$0.345817\pi$
$632$	−14.4222	−0.573685
$633$	2.18335	0.0867802
$634$	−17.7250	−0.703949
$635$	0	0
$636$	3.39445	0.134599
$637$	−12.9083	−0.511447
$638$	4.42221	0.175077
$639$	47.4138	1.87566
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	0.788897	0.0311353
$643$	34.2389	1.35025	0.675124	−	0.737704i	$-0.264090\pi$
$643$	34.2389	1.35025	0.675124	+	0.737704i	$0.264090\pi$
$644$	−3.30278	−0.130148
$645$	0	0
$646$	−40.8167	−1.60591
$647$	−26.8444	−1.05536	−0.527681	−	0.849442i	$-0.676938\pi$
$647$	−26.8444	−1.05536	−0.527681	+	0.849442i	$0.676938\pi$
$648$	8.18335	0.321472
$649$	5.76114	0.226145
$650$	0	0
$651$	7.90833	0.309952
$652$	−9.30278	−0.364325
$653$	−41.7250	−1.63282	−0.816412	−	0.577469i	$-0.804040\pi$
$653$	−41.7250	−1.63282	−0.816412	+	0.577469i	$0.804040\pi$
$654$	0.449961	0.0175949
$655$	0	0
$656$	0.908327	0.0354642
$657$	−16.9167	−0.659985
$658$	−8.60555	−0.335479
$659$	15.6333	0.608987	0.304494	−	0.952514i	$-0.401513\pi$
$659$	15.6333	0.608987	0.304494	+	0.952514i	$0.401513\pi$
$660$	0	0
$661$	−34.9083	−1.35778	−0.678888	−	0.734242i	$-0.737538\pi$
$661$	−34.9083	−1.35778	−0.678888	+	0.734242i	$0.737538\pi$
$662$	16.6056	0.645393
$663$	6.90833	0.268297
$664$	−11.2111	−0.435075
$665$	0	0
$666$	23.2666	0.901563
$667$	−2.60555	−0.100887
$668$	−6.78890	−0.262670
$669$	1.21110	0.0468239
$670$	0	0
$671$	−19.5416	−0.754396
$672$	−1.00000	−0.0385758
$673$	37.6333	1.45066	0.725329	−	0.688403i	$-0.241688\pi$
$673$	37.6333	1.45066	0.725329	+	0.688403i	$0.241688\pi$
$674$	22.5139	0.867202
$675$	0	0
$676$	−2.09167	−0.0804490
$677$	−16.4222	−0.631157	−0.315578	−	0.948900i	$-0.602198\pi$
$677$	−16.4222	−0.631157	−0.315578	+	0.948900i	$0.602198\pi$
$678$	4.97224	0.190958
$679$	20.8167	0.798870
$680$	0	0
$681$	4.42221	0.169459
$682$	13.4222	0.513963
$683$	0.275019	0.0105233	0.00526166	−	0.999986i	$-0.498325\pi$
$683$	0.275019	0.0105233	0.00526166	+	0.999986i	$0.498325\pi$
$684$	−17.1833	−0.657022
$685$	0	0
$686$	10.2111	0.389862
$687$	0.605551	0.0231032
$688$	9.21110	0.351170
$689$	−37.0278	−1.41065
$690$	0	0
$691$	51.8167	1.97120	0.985599	−	0.169098i	$-0.0540855\pi$
$691$	51.8167	1.97120	0.985599	+	0.169098i	$0.0540855\pi$
$692$	−19.6972	−0.748776
$693$	−16.3028	−0.619291
$694$	−28.5416	−1.08343
$695$	0	0
$696$	−0.788897	−0.0299031
$697$	−6.27502	−0.237683
$698$	−27.2111	−1.02996
$699$	−7.81665	−0.295653
$700$	0	0
$701$	32.0917	1.21209	0.606043	−	0.795432i	$-0.292756\pi$
$701$	32.0917	1.21209	0.606043	+	0.795432i	$0.292756\pi$
$702$	5.90833	0.222995
$703$	−47.2666	−1.78269
$704$	−1.69722	−0.0639665
$705$	0	0
$706$	10.4222	0.392245
$707$	−8.60555	−0.323645
$708$	−1.02776	−0.0386254
$709$	−15.8806	−0.596407	−0.298204	−	0.954502i	$-0.596387\pi$
$709$	−15.8806	−0.596407	−0.298204	+	0.954502i	$0.596387\pi$
$710$	0	0
$711$	41.9445	1.57304
$712$	0	0
$713$	−7.90833	−0.296169
$714$	6.90833	0.258538
$715$	0	0
$716$	9.39445	0.351087
$717$	1.57779	0.0589238
$718$	11.2111	0.418395
$719$	10.6972	0.398939	0.199470	−	0.979904i	$-0.436078\pi$
$719$	10.6972	0.398939	0.199470	+	0.979904i	$0.436078\pi$
$720$	0	0
$721$	26.8167	0.998704
$722$	15.9083	0.592047
$723$	−4.36669	−0.162399
$724$	17.1194	0.636239
$725$	0	0
$726$	−2.45837	−0.0912385
$727$	−2.90833	−0.107864	−0.0539319	−	0.998545i	$-0.517175\pi$
$727$	−2.90833	−0.107864	−0.0539319	+	0.998545i	$0.517175\pi$
$728$	10.9083	0.404289
$729$	−22.1749	−0.821294
$730$	0	0
$731$	−63.6333	−2.35356
$732$	3.48612	0.128851
$733$	−29.6333	−1.09453	−0.547266	−	0.836959i	$-0.684331\pi$
$733$	−29.6333	−1.09453	−0.547266	+	0.836959i	$0.684331\pi$
$734$	−14.7889	−0.545868
$735$	0	0
$736$	1.00000	0.0368605
$737$	−6.78890	−0.250072
$738$	−2.64171	−0.0972427
$739$	35.6333	1.31079	0.655396	−	0.755285i	$-0.272502\pi$
$739$	35.6333	1.31079	0.655396	+	0.755285i	$0.272502\pi$
$740$	0	0
$741$	−5.90833	−0.217048
$742$	−37.0278	−1.35933
$743$	32.3305	1.18609	0.593046	−	0.805169i	$-0.297925\pi$
$743$	32.3305	1.18609	0.593046	+	0.805169i	$0.297925\pi$
$744$	−2.39445	−0.0877847
$745$	0	0
$746$	−4.60555	−0.168621
$747$	32.6056	1.19297
$748$	11.7250	0.428708
$749$	−8.60555	−0.314440
$750$	0	0
$751$	21.8167	0.796101	0.398051	−	0.917364i	$-0.369687\pi$
$751$	21.8167	0.796101	0.398051	+	0.917364i	$0.369687\pi$
$752$	2.60555	0.0950147
$753$	3.78890	0.138075
$754$	8.60555	0.313396
$755$	0	0
$756$	5.90833	0.214884
$757$	−13.2111	−0.480166	−0.240083	−	0.970752i	$-0.577175\pi$
$757$	−13.2111	−0.480166	−0.240083	+	0.970752i	$0.577175\pi$
$758$	14.9083	0.541495
$759$	−0.513878	−0.0186526
$760$	0	0
$761$	−49.5416	−1.79588	−0.897941	−	0.440115i	$-0.854938\pi$
$761$	−49.5416	−1.79588	−0.897941	+	0.440115i	$0.854938\pi$
$762$	−2.97224	−0.107673
$763$	−4.90833	−0.177693
$764$	−8.60555	−0.311338
$765$	0	0
$766$	0	0
$767$	11.2111	0.404809
$768$	0.302776	0.0109255
$769$	45.2666	1.63236	0.816178	−	0.577801i	$-0.196089\pi$
$769$	45.2666	1.63236	0.816178	+	0.577801i	$0.196089\pi$
$770$	0	0
$771$	0.550039	0.0198092
$772$	17.8167	0.641235
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	−26.7889	−0.962907
$775$	0	0
$776$	−6.30278	−0.226256
$777$	8.00000	0.286998
$778$	−25.9361	−0.929854
$779$	5.36669	0.192282
$780$	0	0
$781$	27.6695	0.990091
$782$	−6.90833	−0.247041
$783$	4.66106	0.166573
$784$	3.90833	0.139583
$785$	0	0
$786$	−3.39445	−0.121076
$787$	−37.4500	−1.33495	−0.667473	−	0.744634i	$-0.732624\pi$
$787$	−37.4500	−1.33495	−0.667473	+	0.744634i	$0.732624\pi$
$788$	−4.30278	−0.153280
$789$	−1.06392	−0.0378764
$790$	0	0
$791$	−54.2389	−1.92851
$792$	4.93608	0.175396
$793$	−38.0278	−1.35041
$794$	−10.7250	−0.380615
$795$	0	0
$796$	−20.4222	−0.723846
$797$	−1.81665	−0.0643492	−0.0321746	−	0.999482i	$-0.510243\pi$
$797$	−1.81665	−0.0643492	−0.0321746	+	0.999482i	$0.510243\pi$
$798$	−5.90833	−0.209153
$799$	−18.0000	−0.636794
$800$	0	0
$801$	0	0
$802$	−8.60555	−0.303873
$803$	−9.87217	−0.348381
$804$	1.21110	0.0427123
$805$	0	0
$806$	26.1194	0.920018
$807$	1.26662	0.0445870
$808$	2.60555	0.0916630
$809$	50.7250	1.78340	0.891698	−	0.452631i	$-0.149515\pi$
$809$	50.7250	1.78340	0.891698	+	0.452631i	$0.149515\pi$
$810$	0	0
$811$	−41.0278	−1.44068	−0.720340	−	0.693621i	$-0.756014\pi$
$811$	−41.0278	−1.44068	−0.720340	+	0.693621i	$0.756014\pi$
$812$	8.60555	0.301996
$813$	−0.816654	−0.0286413
$814$	13.5778	0.475901
$815$	0	0
$816$	−2.09167	−0.0732232
$817$	54.4222	1.90399
$818$	−25.9083	−0.905863
$819$	−31.7250	−1.10856
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	−1.18335	−0.0412739
$823$	15.2111	0.530226	0.265113	−	0.964217i	$-0.414591\pi$
$823$	15.2111	0.530226	0.265113	+	0.964217i	$0.414591\pi$
$824$	−8.11943	−0.282854
$825$	0	0
$826$	11.2111	0.390084
$827$	29.4500	1.02408	0.512038	−	0.858963i	$-0.328891\pi$
$827$	29.4500	1.02408	0.512038	+	0.858963i	$0.328891\pi$
$828$	−2.90833	−0.101071
$829$	31.2111	1.08401	0.542003	−	0.840376i	$-0.317666\pi$
$829$	31.2111	1.08401	0.542003	+	0.840376i	$0.317666\pi$
$830$	0	0
$831$	8.23886	0.285803
$832$	−3.30278	−0.114503
$833$	−27.0000	−0.935495
$834$	−3.81665	−0.132160
$835$	0	0
$836$	−10.0278	−0.346817
$837$	14.1472	0.488998
$838$	3.63331	0.125511
$839$	−43.8167	−1.51272	−0.756359	−	0.654156i	$-0.773024\pi$
$839$	−43.8167	−1.51272	−0.756359	+	0.654156i	$0.773024\pi$
$840$	0	0
$841$	−22.2111	−0.765900
$842$	30.6972	1.05790
$843$	−8.05551	−0.277447
$844$	7.21110	0.248216
$845$	0	0
$846$	−7.57779	−0.260530
$847$	26.8167	0.921431
$848$	11.2111	0.384991
$849$	−0.605551	−0.0207825
$850$	0	0
$851$	−8.00000	−0.274236
$852$	−4.93608	−0.169107
$853$	21.7250	0.743849	0.371925	−	0.928263i	$-0.378698\pi$
$853$	21.7250	0.743849	0.371925	+	0.928263i	$0.378698\pi$
$854$	−38.0278	−1.30128
$855$	0	0
$856$	2.60555	0.0890559
$857$	−9.63331	−0.329068	−0.164534	−	0.986371i	$-0.552612\pi$
$857$	−9.63331	−0.329068	−0.164534	+	0.986371i	$0.552612\pi$
$858$	1.69722	0.0579423
$859$	−35.8167	−1.22205	−0.611024	−	0.791612i	$-0.709242\pi$
$859$	−35.8167	−1.22205	−0.611024	+	0.791612i	$0.709242\pi$
$860$	0	0
$861$	−0.908327	−0.0309557
$862$	−30.2389	−1.02994
$863$	41.4500	1.41097	0.705487	−	0.708723i	$-0.250729\pi$
$863$	41.4500	1.41097	0.705487	+	0.708723i	$0.250729\pi$
$864$	−1.78890	−0.0608595
$865$	0	0
$866$	24.0917	0.818668
$867$	9.30278	0.315939
$868$	26.1194	0.886551
$869$	24.4777	0.830350
$870$	0	0
$871$	−13.2111	−0.447641
$872$	1.48612	0.0503264
$873$	18.3305	0.620395
$874$	5.90833	0.199852
$875$	0	0
$876$	1.76114	0.0595034
$877$	48.1749	1.62675	0.813376	−	0.581738i	$-0.197627\pi$
$877$	48.1749	1.62675	0.813376	+	0.581738i	$0.197627\pi$
$878$	−14.6972	−0.496007
$879$	−7.02776	−0.237040
$880$	0	0
$881$	55.2666	1.86198	0.930990	−	0.365045i	$-0.118946\pi$
$881$	55.2666	1.86198	0.930990	+	0.365045i	$0.118946\pi$
$882$	−11.3667	−0.382736
$883$	−8.27502	−0.278477	−0.139238	−	0.990259i	$-0.544465\pi$
$883$	−8.27502	−0.278477	−0.139238	+	0.990259i	$0.544465\pi$
$884$	22.8167	0.767407
$885$	0	0
$886$	−17.4861	−0.587458
$887$	−27.6333	−0.927836	−0.463918	−	0.885878i	$-0.653557\pi$
$887$	−27.6333	−0.927836	−0.463918	+	0.885878i	$0.653557\pi$
$888$	−2.42221	−0.0812839
$889$	32.4222	1.08741
$890$	0	0
$891$	−13.8890	−0.465298
$892$	4.00000	0.133930
$893$	15.3944	0.515156
$894$	4.02776	0.134708
$895$	0	0
$896$	−3.30278	−0.110338
$897$	−1.00000	−0.0333890
$898$	−2.09167	−0.0698000
$899$	20.6056	0.687234
$900$	0	0
$901$	−77.4500	−2.58023
$902$	−1.54163	−0.0513308
$903$	−9.21110	−0.306526
$904$	16.4222	0.546194
$905$	0	0
$906$	2.69722	0.0896093
$907$	−48.6611	−1.61576	−0.807882	−	0.589344i	$-0.799386\pi$
$907$	−48.6611	−1.61576	−0.807882	+	0.589344i	$0.799386\pi$
$908$	14.6056	0.484702
$909$	−7.57779	−0.251340
$910$	0	0
$911$	−4.18335	−0.138600	−0.0693002	−	0.997596i	$-0.522077\pi$
$911$	−4.18335	−0.138600	−0.0693002	+	0.997596i	$0.522077\pi$
$912$	1.78890	0.0592363
$913$	19.0278	0.629727
$914$	32.4222	1.07243
$915$	0	0
$916$	2.00000	0.0660819
$917$	37.0278	1.22276
$918$	12.3583	0.407884
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	0	0
$921$	3.54163	0.116701
$922$	10.1833	0.335371
$923$	53.8444	1.77231
$924$	1.69722	0.0558346
$925$	0	0
$926$	−17.6333	−0.579466
$927$	23.6140	0.775584
$928$	−2.60555	−0.0855314
$929$	−14.3667	−0.471356	−0.235678	−	0.971831i	$-0.575731\pi$
$929$	−14.3667	−0.471356	−0.235678	+	0.971831i	$0.575731\pi$
$930$	0	0
$931$	23.0917	0.756799
$932$	−25.8167	−0.845653
$933$	6.78890	0.222259
$934$	1.81665	0.0594427
$935$	0	0
$936$	9.60555	0.313967
$937$	−37.9638	−1.24022	−0.620112	−	0.784513i	$-0.712913\pi$
$937$	−37.9638	−1.24022	−0.620112	+	0.784513i	$0.712913\pi$
$938$	−13.2111	−0.431358
$939$	−5.97224	−0.194897
$940$	0	0
$941$	25.9361	0.845492	0.422746	−	0.906248i	$-0.361066\pi$
$941$	25.9361	0.845492	0.422746	+	0.906248i	$0.361066\pi$
$942$	5.63331	0.183543
$943$	0.908327	0.0295792
$944$	−3.39445	−0.110480
$945$	0	0
$946$	−15.6333	−0.508283
$947$	4.93608	0.160401	0.0802006	−	0.996779i	$-0.474444\pi$
$947$	4.93608	0.160401	0.0802006	+	0.996779i	$0.474444\pi$
$948$	−4.36669	−0.141824
$949$	−19.2111	−0.623619
$950$	0	0
$951$	−5.36669	−0.174027
$952$	22.8167	0.739492
$953$	41.3305	1.33883	0.669414	−	0.742890i	$-0.266545\pi$
$953$	41.3305	1.33883	0.669414	+	0.742890i	$0.266545\pi$
$954$	−32.6056	−1.05564
$955$	0	0
$956$	5.21110	0.168539
$957$	1.33894	0.0432817
$958$	−30.0000	−0.969256
$959$	12.9083	0.416832
$960$	0	0
$961$	31.5416	1.01747
$962$	26.4222	0.851886
$963$	−7.57779	−0.244191
$964$	−14.4222	−0.464508
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	12.6056	0.405367	0.202684	−	0.979244i	$-0.435034\pi$
$967$	12.6056	0.405367	0.202684	+	0.979244i	$0.435034\pi$
$968$	−8.11943	−0.260968
$969$	−12.3583	−0.397005
$970$	0	0
$971$	−17.0917	−0.548498	−0.274249	−	0.961659i	$-0.588429\pi$
$971$	−17.0917	−0.548498	−0.274249	+	0.961659i	$0.588429\pi$
$972$	7.84441	0.251610
$973$	41.6333	1.33470
$974$	−9.81665	−0.314546
$975$	0	0
$976$	11.5139	0.368550
$977$	−6.51388	−0.208397	−0.104199	−	0.994556i	$-0.533228\pi$
$977$	−6.51388	−0.208397	−0.104199	+	0.994556i	$0.533228\pi$
$978$	−2.81665	−0.0900667
$979$	0	0
$980$	0	0
$981$	−4.32213	−0.137995
$982$	−4.18335	−0.133496
$983$	−34.5416	−1.10171	−0.550854	−	0.834602i	$-0.685698\pi$
$983$	−34.5416	−1.10171	−0.550854	+	0.834602i	$0.685698\pi$
$984$	0.275019	0.00876729
$985$	0	0
$986$	18.0000	0.573237
$987$	−2.60555	−0.0829356
$988$	−19.5139	−0.620819
$989$	9.21110	0.292896
$990$	0	0
$991$	−15.3305	−0.486990	−0.243495	−	0.969902i	$-0.578294\pi$
$991$	−15.3305	−0.486990	−0.243495	+	0.969902i	$0.578294\pi$
$992$	−7.90833	−0.251090
$993$	5.02776	0.159551
$994$	53.8444	1.70784
$995$	0	0
$996$	−3.39445	−0.107557
$997$	16.7889	0.531710	0.265855	−	0.964013i	$-0.414346\pi$
$997$	16.7889	0.531710	0.265855	+	0.964013i	$0.414346\pi$
$998$	−31.6333	−1.00133
$999$	14.3112	0.452786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.m.1.2		2
4.3	odd	2		9200.2.a.ca.1.1		2
5.2	odd	4		1150.2.b.f.599.3		4
5.3	odd	4		1150.2.b.f.599.2		4
5.4	even	2		230.2.a.b.1.1	✓	2
15.14	odd	2		2070.2.a.w.1.2		2
20.19	odd	2		1840.2.a.j.1.2		2
40.19	odd	2		7360.2.a.bu.1.1		2
40.29	even	2		7360.2.a.bc.1.2		2
115.114	odd	2		5290.2.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.b.1.1	✓	2	5.4	even	2
1150.2.a.m.1.2		2	1.1	even	1	trivial
1150.2.b.f.599.2		4	5.3	odd	4
1150.2.b.f.599.3		4	5.2	odd	4
1840.2.a.j.1.2		2	20.19	odd	2
2070.2.a.w.1.2		2	15.14	odd	2
5290.2.a.j.1.1		2	115.114	odd	2
7360.2.a.bc.1.2		2	40.29	even	2
7360.2.a.bu.1.1		2	40.19	odd	2
9200.2.a.ca.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +0.302776 q^{6} -3.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.302776 q^{3} +1.00000 q^{4} +0.302776 q^{6} -3.30278 q^{7} +1.00000 q^{8} -2.90833 q^{9} -1.69722 q^{11} +0.302776 q^{12} -3.30278 q^{13} -3.30278 q^{14} +1.00000 q^{16} -6.90833 q^{17} -2.90833 q^{18} +5.90833 q^{19} -1.00000 q^{21} -1.69722 q^{22} +1.00000 q^{23} +0.302776 q^{24} -3.30278 q^{26} -1.78890 q^{27} -3.30278 q^{28} -2.60555 q^{29} -7.90833 q^{31} +1.00000 q^{32} -0.513878 q^{33} -6.90833 q^{34} -2.90833 q^{36} -8.00000 q^{37} +5.90833 q^{38} -1.00000 q^{39} +0.908327 q^{41} -1.00000 q^{42} +9.21110 q^{43} -1.69722 q^{44} +1.00000 q^{46} +2.60555 q^{47} +0.302776 q^{48} +3.90833 q^{49} -2.09167 q^{51} -3.30278 q^{52} +11.2111 q^{53} -1.78890 q^{54} -3.30278 q^{56} +1.78890 q^{57} -2.60555 q^{58} -3.39445 q^{59} +11.5139 q^{61} -7.90833 q^{62} +9.60555 q^{63} +1.00000 q^{64} -0.513878 q^{66} +4.00000 q^{67} -6.90833 q^{68} +0.302776 q^{69} -16.3028 q^{71} -2.90833 q^{72} +5.81665 q^{73} -8.00000 q^{74} +5.90833 q^{76} +5.60555 q^{77} -1.00000 q^{78} -14.4222 q^{79} +8.18335 q^{81} +0.908327 q^{82} -11.2111 q^{83} -1.00000 q^{84} +9.21110 q^{86} -0.788897 q^{87} -1.69722 q^{88} +10.9083 q^{91} +1.00000 q^{92} -2.39445 q^{93} +2.60555 q^{94} +0.302776 q^{96} -6.30278 q^{97} +3.90833 q^{98} +4.93608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + 5 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + 5 q^{9} - 7 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{16} - 3 q^{17} + 5 q^{18} + q^{19} - 2 q^{21} - 7 q^{22} + 2 q^{23} - 3 q^{24} - 3 q^{26} - 18 q^{27} - 3 q^{28} + 2 q^{29} - 5 q^{31} + 2 q^{32} + 17 q^{33} - 3 q^{34} + 5 q^{36} - 16 q^{37} + q^{38} - 2 q^{39} - 9 q^{41} - 2 q^{42} + 4 q^{43} - 7 q^{44} + 2 q^{46} - 2 q^{47} - 3 q^{48} - 3 q^{49} - 15 q^{51} - 3 q^{52} + 8 q^{53} - 18 q^{54} - 3 q^{56} + 18 q^{57} + 2 q^{58} - 14 q^{59} + 5 q^{61} - 5 q^{62} + 12 q^{63} + 2 q^{64} + 17 q^{66} + 8 q^{67} - 3 q^{68} - 3 q^{69} - 29 q^{71} + 5 q^{72} - 10 q^{73} - 16 q^{74} + q^{76} + 4 q^{77} - 2 q^{78} + 38 q^{81} - 9 q^{82} - 8 q^{83} - 2 q^{84} + 4 q^{86} - 16 q^{87} - 7 q^{88} + 11 q^{91} + 2 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{96} - 9 q^{97} - 3 q^{98} - 37 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 3 * q^6 - 3 * q^7 + 2 * q^8 + 5 * q^9 - 7 * q^11 - 3 * q^12 - 3 * q^13 - 3 * q^14 + 2 * q^16 - 3 * q^17 + 5 * q^18 + q^19 - 2 * q^21 - 7 * q^22 + 2 * q^23 - 3 * q^24 - 3 * q^26 - 18 * q^27 - 3 * q^28 + 2 * q^29 - 5 * q^31 + 2 * q^32 + 17 * q^33 - 3 * q^34 + 5 * q^36 - 16 * q^37 + q^38 - 2 * q^39 - 9 * q^41 - 2 * q^42 + 4 * q^43 - 7 * q^44 + 2 * q^46 - 2 * q^47 - 3 * q^48 - 3 * q^49 - 15 * q^51 - 3 * q^52 + 8 * q^53 - 18 * q^54 - 3 * q^56 + 18 * q^57 + 2 * q^58 - 14 * q^59 + 5 * q^61 - 5 * q^62 + 12 * q^63 + 2 * q^64 + 17 * q^66 + 8 * q^67 - 3 * q^68 - 3 * q^69 - 29 * q^71 + 5 * q^72 - 10 * q^73 - 16 * q^74 + q^76 + 4 * q^77 - 2 * q^78 + 38 * q^81 - 9 * q^82 - 8 * q^83 - 2 * q^84 + 4 * q^86 - 16 * q^87 - 7 * q^88 + 11 * q^91 + 2 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^96 - 9 * q^97 - 3 * q^98 - 37 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more