LMFDB - Embedded newform 5262.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5262,2,Mod(1,5262)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5262, 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("5262.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5262 = 2 \cdot 3 \cdot 877 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5262.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:	$42.0172815436$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} -2.38197 q^{11} -1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +0.763932 q^{17} +1.00000 q^{18} -4.61803 q^{19} -3.23607 q^{20} -2.38197 q^{22} +8.47214 q^{23} -1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} -1.00000 q^{27} -8.61803 q^{29} +3.23607 q^{30} +1.23607 q^{31} +1.00000 q^{32} +2.38197 q^{33} +0.763932 q^{34} +1.00000 q^{36} +7.85410 q^{37} -4.61803 q^{38} -3.23607 q^{39} -3.23607 q^{40} +10.0902 q^{41} -10.1803 q^{43} -2.38197 q^{44} -3.23607 q^{45} +8.47214 q^{46} +7.09017 q^{47} -1.00000 q^{48} -7.00000 q^{49} +5.47214 q^{50} -0.763932 q^{51} +3.23607 q^{52} +4.85410 q^{53} -1.00000 q^{54} +7.70820 q^{55} +4.61803 q^{57} -8.61803 q^{58} +12.4721 q^{59} +3.23607 q^{60} -12.0000 q^{61} +1.23607 q^{62} +1.00000 q^{64} -10.4721 q^{65} +2.38197 q^{66} -12.4721 q^{67} +0.763932 q^{68} -8.47214 q^{69} -13.2361 q^{71} +1.00000 q^{72} -6.56231 q^{73} +7.85410 q^{74} -5.47214 q^{75} -4.61803 q^{76} -3.23607 q^{78} -2.29180 q^{79} -3.23607 q^{80} +1.00000 q^{81} +10.0902 q^{82} -9.61803 q^{83} -2.47214 q^{85} -10.1803 q^{86} +8.61803 q^{87} -2.38197 q^{88} -10.4721 q^{89} -3.23607 q^{90} +8.47214 q^{92} -1.23607 q^{93} +7.09017 q^{94} +14.9443 q^{95} -1.00000 q^{96} +11.0902 q^{97} -7.00000 q^{98} -2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 7 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{15} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 7 q^{22} + 8 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} - 2 q^{27} - 15 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} + 7 q^{33} + 6 q^{34} + 2 q^{36} + 9 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 9 q^{41} + 2 q^{43} - 7 q^{44} - 2 q^{45} + 8 q^{46} + 3 q^{47} - 2 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 2 q^{52} + 3 q^{53} - 2 q^{54} + 2 q^{55} + 7 q^{57} - 15 q^{58} + 16 q^{59} + 2 q^{60} - 24 q^{61} - 2 q^{62} + 2 q^{64} - 12 q^{65} + 7 q^{66} - 16 q^{67} + 6 q^{68} - 8 q^{69} - 22 q^{71} + 2 q^{72} + 7 q^{73} + 9 q^{74} - 2 q^{75} - 7 q^{76} - 2 q^{78} - 18 q^{79} - 2 q^{80} + 2 q^{81} + 9 q^{82} - 17 q^{83} + 4 q^{85} + 2 q^{86} + 15 q^{87} - 7 q^{88} - 12 q^{89} - 2 q^{90} + 8 q^{92} + 2 q^{93} + 3 q^{94} + 12 q^{95} - 2 q^{96} + 11 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 7 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^15 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 7 * q^22 + 8 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 - 2 * q^27 - 15 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 + 7 * q^33 + 6 * q^34 + 2 * q^36 + 9 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 9 * q^41 + 2 * q^43 - 7 * q^44 - 2 * q^45 + 8 * q^46 + 3 * q^47 - 2 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 2 * q^52 + 3 * q^53 - 2 * q^54 + 2 * q^55 + 7 * q^57 - 15 * q^58 + 16 * q^59 + 2 * q^60 - 24 * q^61 - 2 * q^62 + 2 * q^64 - 12 * q^65 + 7 * q^66 - 16 * q^67 + 6 * q^68 - 8 * q^69 - 22 * q^71 + 2 * q^72 + 7 * q^73 + 9 * q^74 - 2 * q^75 - 7 * q^76 - 2 * q^78 - 18 * q^79 - 2 * q^80 + 2 * q^81 + 9 * q^82 - 17 * q^83 + 4 * q^85 + 2 * q^86 + 15 * q^87 - 7 * q^88 - 12 * q^89 - 2 * q^90 + 8 * q^92 + 2 * q^93 + 3 * q^94 + 12 * q^95 - 2 * q^96 + 11 * q^97 - 14 * q^98 - 7 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.23607	−1.44721	−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.23607	−1.02333
$11$	−2.38197	−0.718190	−0.359095	−	0.933301i	$-0.616915\pi$
$11$	−2.38197	−0.718190	−0.359095	+	0.933301i	$0.616915\pi$
$12$	−1.00000	−0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	0	0
$15$	3.23607	0.835549
$16$	1.00000	0.250000
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	1.00000	0.235702
$19$	−4.61803	−1.05945	−0.529725	−	0.848170i	$-0.677705\pi$
$19$	−4.61803	−1.05945	−0.529725	+	0.848170i	$0.677705\pi$
$20$	−3.23607	−0.723607
$21$	0	0
$22$	−2.38197	−0.507837
$23$	8.47214	1.76656	0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214	1.76656	0.883281	+	0.468844i	$0.155329\pi$
$24$	−1.00000	−0.204124
$25$	5.47214	1.09443
$26$	3.23607	0.634645
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.61803	−1.60033	−0.800164	−	0.599781i	$-0.795254\pi$
$29$	−8.61803	−1.60033	−0.800164	+	0.599781i	$0.795254\pi$
$30$	3.23607	0.590822
$31$	1.23607	0.222004	0.111002	−	0.993820i	$-0.464594\pi$
$31$	1.23607	0.222004	0.111002	+	0.993820i	$0.464594\pi$
$32$	1.00000	0.176777
$33$	2.38197	0.414647
$34$	0.763932	0.131013
$35$	0	0
$36$	1.00000	0.166667
$37$	7.85410	1.29121	0.645603	−	0.763673i	$-0.276606\pi$
$37$	7.85410	1.29121	0.645603	+	0.763673i	$0.276606\pi$
$38$	−4.61803	−0.749144
$39$	−3.23607	−0.518186
$40$	−3.23607	−0.511667
$41$	10.0902	1.57582	0.787910	−	0.615791i	$-0.211163\pi$
$41$	10.0902	1.57582	0.787910	+	0.615791i	$0.211163\pi$
$42$	0	0
$43$	−10.1803	−1.55249	−0.776244	−	0.630433i	$-0.782877\pi$
$43$	−10.1803	−1.55249	−0.776244	+	0.630433i	$0.782877\pi$
$44$	−2.38197	−0.359095
$45$	−3.23607	−0.482405
$46$	8.47214	1.24915
$47$	7.09017	1.03421	0.517104	−	0.855923i	$-0.327010\pi$
$47$	7.09017	1.03421	0.517104	+	0.855923i	$0.327010\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	5.47214	0.773877
$51$	−0.763932	−0.106972
$52$	3.23607	0.448762
$53$	4.85410	0.666762	0.333381	−	0.942792i	$-0.391810\pi$
$53$	4.85410	0.666762	0.333381	+	0.942792i	$0.391810\pi$
$54$	−1.00000	−0.136083
$55$	7.70820	1.03937
$56$	0	0
$57$	4.61803	0.611674
$58$	−8.61803	−1.13160
$59$	12.4721	1.62373	0.811867	−	0.583843i	$-0.198451\pi$
$59$	12.4721	1.62373	0.811867	+	0.583843i	$0.198451\pi$
$60$	3.23607	0.417775
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	1.23607	0.156981
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.4721	−1.29891
$66$	2.38197	0.293200
$67$	−12.4721	−1.52371	−0.761857	−	0.647745i	$-0.775712\pi$
$67$	−12.4721	−1.52371	−0.761857	+	0.647745i	$0.775712\pi$
$68$	0.763932	0.0926404
$69$	−8.47214	−1.01993
$70$	0	0
$71$	−13.2361	−1.57083	−0.785416	−	0.618968i	$-0.787551\pi$
$71$	−13.2361	−1.57083	−0.785416	+	0.618968i	$0.787551\pi$
$72$	1.00000	0.117851
$73$	−6.56231	−0.768060	−0.384030	−	0.923321i	$-0.625464\pi$
$73$	−6.56231	−0.768060	−0.384030	+	0.923321i	$0.625464\pi$
$74$	7.85410	0.913021
$75$	−5.47214	−0.631868
$76$	−4.61803	−0.529725
$77$	0	0
$78$	−3.23607	−0.366413
$79$	−2.29180	−0.257847	−0.128924	−	0.991655i	$-0.541152\pi$
$79$	−2.29180	−0.257847	−0.128924	+	0.991655i	$0.541152\pi$
$80$	−3.23607	−0.361803
$81$	1.00000	0.111111
$82$	10.0902	1.11427
$83$	−9.61803	−1.05572	−0.527858	−	0.849333i	$-0.677005\pi$
$83$	−9.61803	−1.05572	−0.527858	+	0.849333i	$0.677005\pi$
$84$	0	0
$85$	−2.47214	−0.268141
$86$	−10.1803	−1.09777
$87$	8.61803	0.923950
$88$	−2.38197	−0.253918
$89$	−10.4721	−1.11004	−0.555022	−	0.831836i	$-0.687290\pi$
$89$	−10.4721	−1.11004	−0.555022	+	0.831836i	$0.687290\pi$
$90$	−3.23607	−0.341112
$91$	0	0
$92$	8.47214	0.883281
$93$	−1.23607	−0.128174
$94$	7.09017	0.731295
$95$	14.9443	1.53325
$96$	−1.00000	−0.102062
$97$	11.0902	1.12604	0.563018	−	0.826445i	$-0.309640\pi$
$97$	11.0902	1.12604	0.563018	+	0.826445i	$0.309640\pi$
$98$	−7.00000	−0.707107
$99$	−2.38197	−0.239397
$100$	5.47214	0.547214
$101$	4.94427	0.491973	0.245987	−	0.969273i	$-0.420888\pi$
$101$	4.94427	0.491973	0.245987	+	0.969273i	$0.420888\pi$
$102$	−0.763932	−0.0756405
$103$	−7.14590	−0.704106	−0.352053	−	0.935980i	$-0.614516\pi$
$103$	−7.14590	−0.704106	−0.352053	+	0.935980i	$0.614516\pi$
$104$	3.23607	0.317323
$105$	0	0
$106$	4.85410	0.471472
$107$	16.7984	1.62396	0.811980	−	0.583685i	$-0.198390\pi$
$107$	16.7984	1.62396	0.811980	+	0.583685i	$0.198390\pi$
$108$	−1.00000	−0.0962250
$109$	−12.5623	−1.20325	−0.601625	−	0.798778i	$-0.705480\pi$
$109$	−12.5623	−1.20325	−0.601625	+	0.798778i	$0.705480\pi$
$110$	7.70820	0.734948
$111$	−7.85410	−0.745478
$112$	0	0
$113$	13.2361	1.24514	0.622572	−	0.782562i	$-0.286088\pi$
$113$	13.2361	1.24514	0.622572	+	0.782562i	$0.286088\pi$
$114$	4.61803	0.432519
$115$	−27.4164	−2.55659
$116$	−8.61803	−0.800164
$117$	3.23607	0.299175
$118$	12.4721	1.14815
$119$	0	0
$120$	3.23607	0.295411
$121$	−5.32624	−0.484203
$122$	−12.0000	−1.08643
$123$	−10.0902	−0.909800
$124$	1.23607	0.111002
$125$	−1.52786	−0.136656
$126$	0	0
$127$	9.52786	0.845461	0.422731	−	0.906255i	$-0.361072\pi$
$127$	9.52786	0.845461	0.422731	+	0.906255i	$0.361072\pi$
$128$	1.00000	0.0883883
$129$	10.1803	0.896329
$130$	−10.4721	−0.918467
$131$	−8.18034	−0.714720	−0.357360	−	0.933967i	$-0.616323\pi$
$131$	−8.18034	−0.714720	−0.357360	+	0.933967i	$0.616323\pi$
$132$	2.38197	0.207324
$133$	0	0
$134$	−12.4721	−1.07743
$135$	3.23607	0.278516
$136$	0.763932	0.0655066
$137$	−13.4164	−1.14624	−0.573121	−	0.819471i	$-0.694267\pi$
$137$	−13.4164	−1.14624	−0.573121	+	0.819471i	$0.694267\pi$
$138$	−8.47214	−0.721196
$139$	−21.2705	−1.80414	−0.902071	−	0.431589i	$-0.857953\pi$
$139$	−21.2705	−1.80414	−0.902071	+	0.431589i	$0.857953\pi$
$140$	0	0
$141$	−7.09017	−0.597100
$142$	−13.2361	−1.11075
$143$	−7.70820	−0.644592
$144$	1.00000	0.0833333
$145$	27.8885	2.31602
$146$	−6.56231	−0.543100
$147$	7.00000	0.577350
$148$	7.85410	0.645603
$149$	−2.56231	−0.209912	−0.104956	−	0.994477i	$-0.533470\pi$
$149$	−2.56231	−0.209912	−0.104956	+	0.994477i	$0.533470\pi$
$150$	−5.47214	−0.446798
$151$	−11.1459	−0.907040	−0.453520	−	0.891246i	$-0.649832\pi$
$151$	−11.1459	−0.907040	−0.453520	+	0.891246i	$0.649832\pi$
$152$	−4.61803	−0.374572
$153$	0.763932	0.0617602
$154$	0	0
$155$	−4.00000	−0.321288
$156$	−3.23607	−0.259093
$157$	2.47214	0.197298	0.0986490	−	0.995122i	$-0.468548\pi$
$157$	2.47214	0.197298	0.0986490	+	0.995122i	$0.468548\pi$
$158$	−2.29180	−0.182326
$159$	−4.85410	−0.384955
$160$	−3.23607	−0.255834
$161$	0	0
$162$	1.00000	0.0785674
$163$	−22.9443	−1.79713	−0.898567	−	0.438836i	$-0.855391\pi$
$163$	−22.9443	−1.79713	−0.898567	+	0.438836i	$0.855391\pi$
$164$	10.0902	0.787910
$165$	−7.70820	−0.600083
$166$	−9.61803	−0.746504
$167$	2.94427	0.227835	0.113917	−	0.993490i	$-0.463660\pi$
$167$	2.94427	0.227835	0.113917	+	0.993490i	$0.463660\pi$
$168$	0	0
$169$	−2.52786	−0.194451
$170$	−2.47214	−0.189604
$171$	−4.61803	−0.353150
$172$	−10.1803	−0.776244
$173$	9.52786	0.724390	0.362195	−	0.932102i	$-0.382027\pi$
$173$	9.52786	0.724390	0.362195	+	0.932102i	$0.382027\pi$
$174$	8.61803	0.653331
$175$	0	0
$176$	−2.38197	−0.179547
$177$	−12.4721	−0.937463
$178$	−10.4721	−0.784920
$179$	−3.81966	−0.285495	−0.142747	−	0.989759i	$-0.545594\pi$
$179$	−3.81966	−0.285495	−0.142747	+	0.989759i	$0.545594\pi$
$180$	−3.23607	−0.241202
$181$	−8.29180	−0.616324	−0.308162	−	0.951334i	$-0.599714\pi$
$181$	−8.29180	−0.616324	−0.308162	+	0.951334i	$0.599714\pi$
$182$	0	0
$183$	12.0000	0.887066
$184$	8.47214	0.624574
$185$	−25.4164	−1.86865
$186$	−1.23607	−0.0906329
$187$	−1.81966	−0.133067
$188$	7.09017	0.517104
$189$	0	0
$190$	14.9443	1.08417
$191$	−24.3262	−1.76018	−0.880092	−	0.474802i	$-0.842520\pi$
$191$	−24.3262	−1.76018	−0.880092	+	0.474802i	$0.842520\pi$
$192$	−1.00000	−0.0721688
$193$	15.4164	1.10970	0.554849	−	0.831951i	$-0.312776\pi$
$193$	15.4164	1.10970	0.554849	+	0.831951i	$0.312776\pi$
$194$	11.0902	0.796228
$195$	10.4721	0.749925
$196$	−7.00000	−0.500000
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	−2.38197	−0.169279
$199$	3.41641	0.242183	0.121091	−	0.992641i	$-0.461361\pi$
$199$	3.41641	0.242183	0.121091	+	0.992641i	$0.461361\pi$
$200$	5.47214	0.386938
$201$	12.4721	0.879717
$202$	4.94427	0.347878
$203$	0	0
$204$	−0.763932	−0.0534859
$205$	−32.6525	−2.28055
$206$	−7.14590	−0.497878
$207$	8.47214	0.588854
$208$	3.23607	0.224381
$209$	11.0000	0.760886
$210$	0	0
$211$	−8.56231	−0.589453	−0.294727	−	0.955582i	$-0.595229\pi$
$211$	−8.56231	−0.589453	−0.294727	+	0.955582i	$0.595229\pi$
$212$	4.85410	0.333381
$213$	13.2361	0.906920
$214$	16.7984	1.14831
$215$	32.9443	2.24678
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.5623	−0.850827
$219$	6.56231	0.443440
$220$	7.70820	0.519687
$221$	2.47214	0.166294
$222$	−7.85410	−0.527133
$223$	−4.14590	−0.277630	−0.138815	−	0.990318i	$-0.544329\pi$
$223$	−4.14590	−0.277630	−0.138815	+	0.990318i	$0.544329\pi$
$224$	0	0
$225$	5.47214	0.364809
$226$	13.2361	0.880450
$227$	−25.4164	−1.68695	−0.843473	−	0.537171i	$-0.819493\pi$
$227$	−25.4164	−1.68695	−0.843473	+	0.537171i	$0.819493\pi$
$228$	4.61803	0.305837
$229$	−9.70820	−0.641536	−0.320768	−	0.947158i	$-0.603941\pi$
$229$	−9.70820	−0.641536	−0.320768	+	0.947158i	$0.603941\pi$
$230$	−27.4164	−1.80778
$231$	0	0
$232$	−8.61803	−0.565802
$233$	−20.5066	−1.34343	−0.671715	−	0.740809i	$-0.734442\pi$
$233$	−20.5066	−1.34343	−0.671715	+	0.740809i	$0.734442\pi$
$234$	3.23607	0.211548
$235$	−22.9443	−1.49672
$236$	12.4721	0.811867
$237$	2.29180	0.148868
$238$	0	0
$239$	12.1803	0.787881	0.393940	−	0.919136i	$-0.371112\pi$
$239$	12.1803	0.787881	0.393940	+	0.919136i	$0.371112\pi$
$240$	3.23607	0.208887
$241$	−9.27051	−0.597166	−0.298583	−	0.954384i	$-0.596514\pi$
$241$	−9.27051	−0.597166	−0.298583	+	0.954384i	$0.596514\pi$
$242$	−5.32624	−0.342384
$243$	−1.00000	−0.0641500
$244$	−12.0000	−0.768221
$245$	22.6525	1.44721
$246$	−10.0902	−0.643326
$247$	−14.9443	−0.950881
$248$	1.23607	0.0784904
$249$	9.61803	0.609518
$250$	−1.52786	−0.0966306
$251$	28.3607	1.79011	0.895055	−	0.445956i	$-0.147136\pi$
$251$	28.3607	1.79011	0.895055	+	0.445956i	$0.147136\pi$
$252$	0	0
$253$	−20.1803	−1.26873
$254$	9.52786	0.597831
$255$	2.47214	0.154811
$256$	1.00000	0.0625000
$257$	−6.65248	−0.414970	−0.207485	−	0.978238i	$-0.566528\pi$
$257$	−6.65248	−0.414970	−0.207485	+	0.978238i	$0.566528\pi$
$258$	10.1803	0.633800
$259$	0	0
$260$	−10.4721	−0.649454
$261$	−8.61803	−0.533443
$262$	−8.18034	−0.505383
$263$	−8.47214	−0.522414	−0.261207	−	0.965283i	$-0.584121\pi$
$263$	−8.47214	−0.522414	−0.261207	+	0.965283i	$0.584121\pi$
$264$	2.38197	0.146600
$265$	−15.7082	−0.964947
$266$	0	0
$267$	10.4721	0.640884
$268$	−12.4721	−0.761857
$269$	−7.90983	−0.482271	−0.241135	−	0.970491i	$-0.577520\pi$
$269$	−7.90983	−0.482271	−0.241135	+	0.970491i	$0.577520\pi$
$270$	3.23607	0.196941
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0.763932	0.0463202
$273$	0	0
$274$	−13.4164	−0.810515
$275$	−13.0344	−0.786006
$276$	−8.47214	−0.509963
$277$	9.23607	0.554942	0.277471	−	0.960734i	$-0.410504\pi$
$277$	9.23607	0.554942	0.277471	+	0.960734i	$0.410504\pi$
$278$	−21.2705	−1.27572
$279$	1.23607	0.0740015
$280$	0	0
$281$	−6.03444	−0.359985	−0.179992	−	0.983668i	$-0.557607\pi$
$281$	−6.03444	−0.359985	−0.179992	+	0.983668i	$0.557607\pi$
$282$	−7.09017	−0.422213
$283$	18.1803	1.08071	0.540355	−	0.841437i	$-0.318290\pi$
$283$	18.1803	1.08071	0.540355	+	0.841437i	$0.318290\pi$
$284$	−13.2361	−0.785416
$285$	−14.9443	−0.885222
$286$	−7.70820	−0.455796
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.4164	−0.965671
$290$	27.8885	1.63767
$291$	−11.0902	−0.650117
$292$	−6.56231	−0.384030
$293$	−20.9443	−1.22358	−0.611789	−	0.791021i	$-0.709550\pi$
$293$	−20.9443	−1.22358	−0.611789	+	0.791021i	$0.709550\pi$
$294$	7.00000	0.408248
$295$	−40.3607	−2.34989
$296$	7.85410	0.456510
$297$	2.38197	0.138216
$298$	−2.56231	−0.148430
$299$	27.4164	1.58553
$300$	−5.47214	−0.315934
$301$	0	0
$302$	−11.1459	−0.641374
$303$	−4.94427	−0.284041
$304$	−4.61803	−0.264862
$305$	38.8328	2.22356
$306$	0.763932	0.0436711
$307$	16.5623	0.945261	0.472630	−	0.881261i	$-0.343305\pi$
$307$	16.5623	0.945261	0.472630	+	0.881261i	$0.343305\pi$
$308$	0	0
$309$	7.14590	0.406516
$310$	−4.00000	−0.227185
$311$	2.79837	0.158681	0.0793406	−	0.996848i	$-0.474719\pi$
$311$	2.79837	0.158681	0.0793406	+	0.996848i	$0.474719\pi$
$312$	−3.23607	−0.183206
$313$	31.8885	1.80245	0.901224	−	0.433355i	$-0.142670\pi$
$313$	31.8885	1.80245	0.901224	+	0.433355i	$0.142670\pi$
$314$	2.47214	0.139511
$315$	0	0
$316$	−2.29180	−0.128924
$317$	4.18034	0.234791	0.117396	−	0.993085i	$-0.462545\pi$
$317$	4.18034	0.234791	0.117396	+	0.993085i	$0.462545\pi$
$318$	−4.85410	−0.272205
$319$	20.5279	1.14934
$320$	−3.23607	−0.180902
$321$	−16.7984	−0.937594
$322$	0	0
$323$	−3.52786	−0.196296
$324$	1.00000	0.0555556
$325$	17.7082	0.982274
$326$	−22.9443	−1.27077
$327$	12.5623	0.694697
$328$	10.0902	0.557136
$329$	0	0
$330$	−7.70820	−0.424323
$331$	−18.0000	−0.989369	−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000	−0.989369	−0.494685	+	0.869072i	$0.664716\pi$
$332$	−9.61803	−0.527858
$333$	7.85410	0.430402
$334$	2.94427	0.161103
$335$	40.3607	2.20514
$336$	0	0
$337$	−21.8885	−1.19234	−0.596172	−	0.802856i	$-0.703313\pi$
$337$	−21.8885	−1.19234	−0.596172	+	0.802856i	$0.703313\pi$
$338$	−2.52786	−0.137498
$339$	−13.2361	−0.718885
$340$	−2.47214	−0.134070
$341$	−2.94427	−0.159441
$342$	−4.61803	−0.249715
$343$	0	0
$344$	−10.1803	−0.548887
$345$	27.4164	1.47605
$346$	9.52786	0.512221
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	8.61803	0.461975
$349$	−25.4164	−1.36051	−0.680255	−	0.732976i	$-0.738131\pi$
$349$	−25.4164	−1.36051	−0.680255	+	0.732976i	$0.738131\pi$
$350$	0	0
$351$	−3.23607	−0.172729
$352$	−2.38197	−0.126959
$353$	−12.7426	−0.678223	−0.339111	−	0.940746i	$-0.610126\pi$
$353$	−12.7426	−0.678223	−0.339111	+	0.940746i	$0.610126\pi$
$354$	−12.4721	−0.662887
$355$	42.8328	2.27333
$356$	−10.4721	−0.555022
$357$	0	0
$358$	−3.81966	−0.201875
$359$	25.6869	1.35570	0.677852	−	0.735199i	$-0.262911\pi$
$359$	25.6869	1.35570	0.677852	+	0.735199i	$0.262911\pi$
$360$	−3.23607	−0.170556
$361$	2.32624	0.122434
$362$	−8.29180	−0.435807
$363$	5.32624	0.279555
$364$	0	0
$365$	21.2361	1.11155
$366$	12.0000	0.627250
$367$	−8.27051	−0.431717	−0.215859	−	0.976425i	$-0.569255\pi$
$367$	−8.27051	−0.431717	−0.215859	+	0.976425i	$0.569255\pi$
$368$	8.47214	0.441641
$369$	10.0902	0.525273
$370$	−25.4164	−1.32134
$371$	0	0
$372$	−1.23607	−0.0640871
$373$	20.2918	1.05067	0.525335	−	0.850896i	$-0.323940\pi$
$373$	20.2918	1.05067	0.525335	+	0.850896i	$0.323940\pi$
$374$	−1.81966	−0.0940924
$375$	1.52786	0.0788986
$376$	7.09017	0.365648
$377$	−27.8885	−1.43633
$378$	0	0
$379$	−16.6525	−0.855380	−0.427690	−	0.903925i	$-0.640673\pi$
$379$	−16.6525	−0.855380	−0.427690	+	0.903925i	$0.640673\pi$
$380$	14.9443	0.766625
$381$	−9.52786	−0.488127
$382$	−24.3262	−1.24464
$383$	15.3820	0.785982	0.392991	−	0.919542i	$-0.371440\pi$
$383$	15.3820	0.785982	0.392991	+	0.919542i	$0.371440\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	15.4164	0.784675
$387$	−10.1803	−0.517496
$388$	11.0902	0.563018
$389$	6.50658	0.329897	0.164948	−	0.986302i	$-0.447254\pi$
$389$	6.50658	0.329897	0.164948	+	0.986302i	$0.447254\pi$
$390$	10.4721	0.530277
$391$	6.47214	0.327310
$392$	−7.00000	−0.353553
$393$	8.18034	0.412644
$394$	0	0
$395$	7.41641	0.373160
$396$	−2.38197	−0.119698
$397$	1.50658	0.0756130	0.0378065	−	0.999285i	$-0.487963\pi$
$397$	1.50658	0.0756130	0.0378065	+	0.999285i	$0.487963\pi$
$398$	3.41641	0.171249
$399$	0	0
$400$	5.47214	0.273607
$401$	−33.7771	−1.68675	−0.843374	−	0.537328i	$-0.819434\pi$
$401$	−33.7771	−1.68675	−0.843374	+	0.537328i	$0.819434\pi$
$402$	12.4721	0.622054
$403$	4.00000	0.199254
$404$	4.94427	0.245987
$405$	−3.23607	−0.160802
$406$	0	0
$407$	−18.7082	−0.927331
$408$	−0.763932	−0.0378203
$409$	32.8328	1.62348	0.811739	−	0.584020i	$-0.198521\pi$
$409$	32.8328	1.62348	0.811739	+	0.584020i	$0.198521\pi$
$410$	−32.6525	−1.61259
$411$	13.4164	0.661783
$412$	−7.14590	−0.352053
$413$	0	0
$414$	8.47214	0.416383
$415$	31.1246	1.52785
$416$	3.23607	0.158661
$417$	21.2705	1.04162
$418$	11.0000	0.538028
$419$	−38.1803	−1.86523	−0.932616	−	0.360871i	$-0.882480\pi$
$419$	−38.1803	−1.86523	−0.932616	+	0.360871i	$0.882480\pi$
$420$	0	0
$421$	14.2705	0.695502	0.347751	−	0.937587i	$-0.386945\pi$
$421$	14.2705	0.695502	0.347751	+	0.937587i	$0.386945\pi$
$422$	−8.56231	−0.416807
$423$	7.09017	0.344736
$424$	4.85410	0.235736
$425$	4.18034	0.202776
$426$	13.2361	0.641290
$427$	0	0
$428$	16.7984	0.811980
$429$	7.70820	0.372156
$430$	32.9443	1.58871
$431$	1.34752	0.0649080	0.0324540	−	0.999473i	$-0.489668\pi$
$431$	1.34752	0.0649080	0.0324540	+	0.999473i	$0.489668\pi$
$432$	−1.00000	−0.0481125
$433$	29.9787	1.44069	0.720343	−	0.693619i	$-0.243985\pi$
$433$	29.9787	1.44069	0.720343	+	0.693619i	$0.243985\pi$
$434$	0	0
$435$	−27.8885	−1.33715
$436$	−12.5623	−0.601625
$437$	−39.1246	−1.87158
$438$	6.56231	0.313559
$439$	−26.8328	−1.28066	−0.640330	−	0.768100i	$-0.721202\pi$
$439$	−26.8328	−1.28066	−0.640330	+	0.768100i	$0.721202\pi$
$440$	7.70820	0.367474
$441$	−7.00000	−0.333333
$442$	2.47214	0.117588
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	−7.85410	−0.372739
$445$	33.8885	1.60647
$446$	−4.14590	−0.196314
$447$	2.56231	0.121193
$448$	0	0
$449$	−9.70820	−0.458158	−0.229079	−	0.973408i	$-0.573571\pi$
$449$	−9.70820	−0.458158	−0.229079	+	0.973408i	$0.573571\pi$
$450$	5.47214	0.257959
$451$	−24.0344	−1.13174
$452$	13.2361	0.622572
$453$	11.1459	0.523680
$454$	−25.4164	−1.19285
$455$	0	0
$456$	4.61803	0.216259
$457$	−1.05573	−0.0493849	−0.0246924	−	0.999695i	$-0.507861\pi$
$457$	−1.05573	−0.0493849	−0.0246924	+	0.999695i	$0.507861\pi$
$458$	−9.70820	−0.453635
$459$	−0.763932	−0.0356573
$460$	−27.4164	−1.27830
$461$	−26.5066	−1.23453	−0.617267	−	0.786754i	$-0.711760\pi$
$461$	−26.5066	−1.23453	−0.617267	+	0.786754i	$0.711760\pi$
$462$	0	0
$463$	−24.0000	−1.11537	−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000	−1.11537	−0.557687	+	0.830051i	$0.688311\pi$
$464$	−8.61803	−0.400082
$465$	4.00000	0.185496
$466$	−20.5066	−0.949949
$467$	12.1803	0.563639	0.281819	−	0.959467i	$-0.409062\pi$
$467$	12.1803	0.563639	0.281819	+	0.959467i	$0.409062\pi$
$468$	3.23607	0.149587
$469$	0	0
$470$	−22.9443	−1.05834
$471$	−2.47214	−0.113910
$472$	12.4721	0.574077
$473$	24.2492	1.11498
$474$	2.29180	0.105266
$475$	−25.2705	−1.15949
$476$	0	0
$477$	4.85410	0.222254
$478$	12.1803	0.557116
$479$	11.0557	0.505149	0.252575	−	0.967577i	$-0.418723\pi$
$479$	11.0557	0.505149	0.252575	+	0.967577i	$0.418723\pi$
$480$	3.23607	0.147706
$481$	25.4164	1.15889
$482$	−9.27051	−0.422260
$483$	0	0
$484$	−5.32624	−0.242102
$485$	−35.8885	−1.62961
$486$	−1.00000	−0.0453609
$487$	27.1459	1.23010	0.615049	−	0.788489i	$-0.289136\pi$
$487$	27.1459	1.23010	0.615049	+	0.788489i	$0.289136\pi$
$488$	−12.0000	−0.543214
$489$	22.9443	1.03758
$490$	22.6525	1.02333
$491$	−20.1803	−0.910726	−0.455363	−	0.890306i	$-0.650491\pi$
$491$	−20.1803	−0.910726	−0.455363	+	0.890306i	$0.650491\pi$
$492$	−10.0902	−0.454900
$493$	−6.58359	−0.296510
$494$	−14.9443	−0.672375
$495$	7.70820	0.346458
$496$	1.23607	0.0555011
$497$	0	0
$498$	9.61803	0.430994
$499$	12.0000	0.537194	0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000	0.537194	0.268597	+	0.963253i	$0.413440\pi$
$500$	−1.52786	−0.0683282
$501$	−2.94427	−0.131540
$502$	28.3607	1.26580
$503$	31.0344	1.38376	0.691879	−	0.722014i	$-0.256783\pi$
$503$	31.0344	1.38376	0.691879	+	0.722014i	$0.256783\pi$
$504$	0	0
$505$	−16.0000	−0.711991
$506$	−20.1803	−0.897126
$507$	2.52786	0.112266
$508$	9.52786	0.422731
$509$	13.8541	0.614072	0.307036	−	0.951698i	$-0.400663\pi$
$509$	13.8541	0.614072	0.307036	+	0.951698i	$0.400663\pi$
$510$	2.47214	0.109468
$511$	0	0
$512$	1.00000	0.0441942
$513$	4.61803	0.203891
$514$	−6.65248	−0.293428
$515$	23.1246	1.01899
$516$	10.1803	0.448164
$517$	−16.8885	−0.742757
$518$	0	0
$519$	−9.52786	−0.418227
$520$	−10.4721	−0.459234
$521$	9.52786	0.417423	0.208712	−	0.977977i	$-0.433073\pi$
$521$	9.52786	0.417423	0.208712	+	0.977977i	$0.433073\pi$
$522$	−8.61803	−0.377201
$523$	−21.8885	−0.957119	−0.478560	−	0.878055i	$-0.658841\pi$
$523$	−21.8885	−0.957119	−0.478560	+	0.878055i	$0.658841\pi$
$524$	−8.18034	−0.357360
$525$	0	0
$526$	−8.47214	−0.369403
$527$	0.944272	0.0411331
$528$	2.38197	0.103662
$529$	48.7771	2.12074
$530$	−15.7082	−0.682321
$531$	12.4721	0.541245
$532$	0	0
$533$	32.6525	1.41434
$534$	10.4721	0.453174
$535$	−54.3607	−2.35022
$536$	−12.4721	−0.538714
$537$	3.81966	0.164831
$538$	−7.90983	−0.341017
$539$	16.6738	0.718190
$540$	3.23607	0.139258
$541$	−3.43769	−0.147798	−0.0738990	−	0.997266i	$-0.523544\pi$
$541$	−3.43769	−0.147798	−0.0738990	+	0.997266i	$0.523544\pi$
$542$	0	0
$543$	8.29180	0.355835
$544$	0.763932	0.0327533
$545$	40.6525	1.74136
$546$	0	0
$547$	24.9787	1.06801	0.534006	−	0.845480i	$-0.320686\pi$
$547$	24.9787	1.06801	0.534006	+	0.845480i	$0.320686\pi$
$548$	−13.4164	−0.573121
$549$	−12.0000	−0.512148
$550$	−13.0344	−0.555790
$551$	39.7984	1.69547
$552$	−8.47214	−0.360598
$553$	0	0
$554$	9.23607	0.392403
$555$	25.4164	1.07887
$556$	−21.2705	−0.902071
$557$	26.9443	1.14167	0.570833	−	0.821066i	$-0.306620\pi$
$557$	26.9443	1.14167	0.570833	+	0.821066i	$0.306620\pi$
$558$	1.23607	0.0523269
$559$	−32.9443	−1.39339
$560$	0	0
$561$	1.81966	0.0768261
$562$	−6.03444	−0.254548
$563$	−30.3607	−1.27955	−0.639775	−	0.768562i	$-0.720972\pi$
$563$	−30.3607	−1.27955	−0.639775	+	0.768562i	$0.720972\pi$
$564$	−7.09017	−0.298550
$565$	−42.8328	−1.80199
$566$	18.1803	0.764177
$567$	0	0
$568$	−13.2361	−0.555373
$569$	−14.2918	−0.599143	−0.299572	−	0.954074i	$-0.596844\pi$
$569$	−14.2918	−0.599143	−0.299572	+	0.954074i	$0.596844\pi$
$570$	−14.9443	−0.625947
$571$	−6.58359	−0.275515	−0.137757	−	0.990466i	$-0.543989\pi$
$571$	−6.58359	−0.275515	−0.137757	+	0.990466i	$0.543989\pi$
$572$	−7.70820	−0.322296
$573$	24.3262	1.01624
$574$	0	0
$575$	46.3607	1.93337
$576$	1.00000	0.0416667
$577$	−29.9230	−1.24571	−0.622855	−	0.782337i	$-0.714027\pi$
$577$	−29.9230	−1.24571	−0.622855	+	0.782337i	$0.714027\pi$
$578$	−16.4164	−0.682833
$579$	−15.4164	−0.640684
$580$	27.8885	1.15801
$581$	0	0
$582$	−11.0902	−0.459702
$583$	−11.5623	−0.478862
$584$	−6.56231	−0.271550
$585$	−10.4721	−0.432970
$586$	−20.9443	−0.865200
$587$	27.5967	1.13904	0.569520	−	0.821978i	$-0.307129\pi$
$587$	27.5967	1.13904	0.569520	+	0.821978i	$0.307129\pi$
$588$	7.00000	0.288675
$589$	−5.70820	−0.235202
$590$	−40.3607	−1.66162
$591$	0	0
$592$	7.85410	0.322802
$593$	43.6312	1.79172	0.895859	−	0.444338i	$-0.146561\pi$
$593$	43.6312	1.79172	0.895859	+	0.444338i	$0.146561\pi$
$594$	2.38197	0.0977332
$595$	0	0
$596$	−2.56231	−0.104956
$597$	−3.41641	−0.139824
$598$	27.4164	1.12114
$599$	−3.59675	−0.146959	−0.0734796	−	0.997297i	$-0.523410\pi$
$599$	−3.59675	−0.146959	−0.0734796	+	0.997297i	$0.523410\pi$
$600$	−5.47214	−0.223399
$601$	25.9787	1.05969	0.529847	−	0.848093i	$-0.322249\pi$
$601$	25.9787	1.05969	0.529847	+	0.848093i	$0.322249\pi$
$602$	0	0
$603$	−12.4721	−0.507905
$604$	−11.1459	−0.453520
$605$	17.2361	0.700746
$606$	−4.94427	−0.200847
$607$	49.0132	1.98938	0.994691	−	0.102904i	$-0.0328134\pi$
$607$	49.0132	1.98938	0.994691	+	0.102904i	$0.0328134\pi$
$608$	−4.61803	−0.187286
$609$	0	0
$610$	38.8328	1.57229
$611$	22.9443	0.928226
$612$	0.763932	0.0308801
$613$	30.9098	1.24844	0.624218	−	0.781250i	$-0.285418\pi$
$613$	30.9098	1.24844	0.624218	+	0.781250i	$0.285418\pi$
$614$	16.5623	0.668400
$615$	32.6525	1.31667
$616$	0	0
$617$	31.8541	1.28240	0.641199	−	0.767375i	$-0.278437\pi$
$617$	31.8541	1.28240	0.641199	+	0.767375i	$0.278437\pi$
$618$	7.14590	0.287450
$619$	21.8885	0.879775	0.439887	−	0.898053i	$-0.355018\pi$
$619$	21.8885	0.879775	0.439887	+	0.898053i	$0.355018\pi$
$620$	−4.00000	−0.160644
$621$	−8.47214	−0.339975
$622$	2.79837	0.112205
$623$	0	0
$624$	−3.23607	−0.129546
$625$	−22.4164	−0.896656
$626$	31.8885	1.27452
$627$	−11.0000	−0.439298
$628$	2.47214	0.0986490
$629$	6.00000	0.239236
$630$	0	0
$631$	17.0902	0.680349	0.340174	−	0.940362i	$-0.389514\pi$
$631$	17.0902	0.680349	0.340174	+	0.940362i	$0.389514\pi$
$632$	−2.29180	−0.0911628
$633$	8.56231	0.340321
$634$	4.18034	0.166023
$635$	−30.8328	−1.22356
$636$	−4.85410	−0.192478
$637$	−22.6525	−0.897524
$638$	20.5279	0.812706
$639$	−13.2361	−0.523611
$640$	−3.23607	−0.127917
$641$	−48.3394	−1.90929	−0.954646	−	0.297744i	$-0.903766\pi$
$641$	−48.3394	−1.90929	−0.954646	+	0.297744i	$0.903766\pi$
$642$	−16.7984	−0.662979
$643$	8.36068	0.329713	0.164857	−	0.986318i	$-0.447284\pi$
$643$	8.36068	0.329713	0.164857	+	0.986318i	$0.447284\pi$
$644$	0	0
$645$	−32.9443	−1.29718
$646$	−3.52786	−0.138802
$647$	−30.3607	−1.19360	−0.596801	−	0.802389i	$-0.703562\pi$
$647$	−30.3607	−1.19360	−0.596801	+	0.802389i	$0.703562\pi$
$648$	1.00000	0.0392837
$649$	−29.7082	−1.16615
$650$	17.7082	0.694573
$651$	0	0
$652$	−22.9443	−0.898567
$653$	34.6525	1.35606	0.678028	−	0.735036i	$-0.262835\pi$
$653$	34.6525	1.35606	0.678028	+	0.735036i	$0.262835\pi$
$654$	12.5623	0.491225
$655$	26.4721	1.03435
$656$	10.0902	0.393955
$657$	−6.56231	−0.256020
$658$	0	0
$659$	−22.4721	−0.875390	−0.437695	−	0.899123i	$-0.644205\pi$
$659$	−22.4721	−0.875390	−0.437695	+	0.899123i	$0.644205\pi$
$660$	−7.70820	−0.300041
$661$	20.8328	0.810303	0.405151	−	0.914250i	$-0.367219\pi$
$661$	20.8328	0.810303	0.405151	+	0.914250i	$0.367219\pi$
$662$	−18.0000	−0.699590
$663$	−2.47214	−0.0960098
$664$	−9.61803	−0.373252
$665$	0	0
$666$	7.85410	0.304340
$667$	−73.0132	−2.82708
$668$	2.94427	0.113917
$669$	4.14590	0.160290
$670$	40.3607	1.55927
$671$	28.5836	1.10346
$672$	0	0
$673$	2.58359	0.0995902	0.0497951	−	0.998759i	$-0.484143\pi$
$673$	2.58359	0.0995902	0.0497951	+	0.998759i	$0.484143\pi$
$674$	−21.8885	−0.843115
$675$	−5.47214	−0.210623
$676$	−2.52786	−0.0972255
$677$	36.0689	1.38624	0.693120	−	0.720822i	$-0.256236\pi$
$677$	36.0689	1.38624	0.693120	+	0.720822i	$0.256236\pi$
$678$	−13.2361	−0.508328
$679$	0	0
$680$	−2.47214	−0.0948021
$681$	25.4164	0.973959
$682$	−2.94427	−0.112742
$683$	−49.1591	−1.88102	−0.940509	−	0.339768i	$-0.889652\pi$
$683$	−49.1591	−1.88102	−0.940509	+	0.339768i	$0.889652\pi$
$684$	−4.61803	−0.176575
$685$	43.4164	1.65886
$686$	0	0
$687$	9.70820	0.370391
$688$	−10.1803	−0.388122
$689$	15.7082	0.598435
$690$	27.4164	1.04372
$691$	15.6180	0.594138	0.297069	−	0.954856i	$-0.403991\pi$
$691$	15.6180	0.594138	0.297069	+	0.954856i	$0.403991\pi$
$692$	9.52786	0.362195
$693$	0	0
$694$	0	0
$695$	68.8328	2.61098
$696$	8.61803	0.326666
$697$	7.70820	0.291969
$698$	−25.4164	−0.962025
$699$	20.5066	0.775630
$700$	0	0
$701$	−51.0132	−1.92674	−0.963370	−	0.268175i	$-0.913579\pi$
$701$	−51.0132	−1.92674	−0.963370	+	0.268175i	$0.913579\pi$
$702$	−3.23607	−0.122138
$703$	−36.2705	−1.36797
$704$	−2.38197	−0.0897737
$705$	22.9443	0.864131
$706$	−12.7426	−0.479576
$707$	0	0
$708$	−12.4721	−0.468732
$709$	−0.583592	−0.0219173	−0.0109586	−	0.999940i	$-0.503488\pi$
$709$	−0.583592	−0.0219173	−0.0109586	+	0.999940i	$0.503488\pi$
$710$	42.8328	1.60749
$711$	−2.29180	−0.0859491
$712$	−10.4721	−0.392460
$713$	10.4721	0.392185
$714$	0	0
$715$	24.9443	0.932863
$716$	−3.81966	−0.142747
$717$	−12.1803	−0.454883
$718$	25.6869	0.958627
$719$	−45.1033	−1.68207	−0.841035	−	0.540981i	$-0.818053\pi$
$719$	−45.1033	−1.68207	−0.841035	+	0.540981i	$0.818053\pi$
$720$	−3.23607	−0.120601
$721$	0	0
$722$	2.32624	0.0865736
$723$	9.27051	0.344774
$724$	−8.29180	−0.308162
$725$	−47.1591	−1.75144
$726$	5.32624	0.197675
$727$	16.6738	0.618396	0.309198	−	0.950998i	$-0.399939\pi$
$727$	16.6738	0.618396	0.309198	+	0.950998i	$0.399939\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	21.2361	0.785982
$731$	−7.77709	−0.287646
$732$	12.0000	0.443533
$733$	−36.5066	−1.34840	−0.674201	−	0.738548i	$-0.735512\pi$
$733$	−36.5066	−1.34840	−0.674201	+	0.738548i	$0.735512\pi$
$734$	−8.27051	−0.305270
$735$	−22.6525	−0.835549
$736$	8.47214	0.312287
$737$	29.7082	1.09432
$738$	10.0902	0.371424
$739$	24.3951	0.897389	0.448695	−	0.893685i	$-0.351889\pi$
$739$	24.3951	0.897389	0.448695	+	0.893685i	$0.351889\pi$
$740$	−25.4164	−0.934326
$741$	14.9443	0.548992
$742$	0	0
$743$	−24.3262	−0.892443	−0.446222	−	0.894923i	$-0.647231\pi$
$743$	−24.3262	−0.892443	−0.446222	+	0.894923i	$0.647231\pi$
$744$	−1.23607	−0.0453165
$745$	8.29180	0.303788
$746$	20.2918	0.742935
$747$	−9.61803	−0.351905
$748$	−1.81966	−0.0665334
$749$	0	0
$750$	1.52786	0.0557897
$751$	−28.9443	−1.05619	−0.528096	−	0.849185i	$-0.677094\pi$
$751$	−28.9443	−1.05619	−0.528096	+	0.849185i	$0.677094\pi$
$752$	7.09017	0.258552
$753$	−28.3607	−1.03352
$754$	−27.8885	−1.01564
$755$	36.0689	1.31268
$756$	0	0
$757$	51.5623	1.87406	0.937032	−	0.349244i	$-0.113561\pi$
$757$	51.5623	1.87406	0.937032	+	0.349244i	$0.113561\pi$
$758$	−16.6525	−0.604845
$759$	20.1803	0.732500
$760$	14.9443	0.542086
$761$	5.02129	0.182021	0.0910107	−	0.995850i	$-0.470990\pi$
$761$	5.02129	0.182021	0.0910107	+	0.995850i	$0.470990\pi$
$762$	−9.52786	−0.345158
$763$	0	0
$764$	−24.3262	−0.880092
$765$	−2.47214	−0.0893803
$766$	15.3820	0.555773
$767$	40.3607	1.45734
$768$	−1.00000	−0.0360844
$769$	−1.97871	−0.0713542	−0.0356771	−	0.999363i	$-0.511359\pi$
$769$	−1.97871	−0.0713542	−0.0356771	+	0.999363i	$0.511359\pi$
$770$	0	0
$771$	6.65248	0.239583
$772$	15.4164	0.554849
$773$	13.7984	0.496293	0.248147	−	0.968723i	$-0.420179\pi$
$773$	13.7984	0.496293	0.248147	+	0.968723i	$0.420179\pi$
$774$	−10.1803	−0.365925
$775$	6.76393	0.242968
$776$	11.0902	0.398114
$777$	0	0
$778$	6.50658	0.233272
$779$	−46.5967	−1.66950
$780$	10.4721	0.374963
$781$	31.5279	1.12816
$782$	6.47214	0.231443
$783$	8.61803	0.307983
$784$	−7.00000	−0.250000
$785$	−8.00000	−0.285532
$786$	8.18034	0.291783
$787$	41.4164	1.47634	0.738168	−	0.674617i	$-0.235691\pi$
$787$	41.4164	1.47634	0.738168	+	0.674617i	$0.235691\pi$
$788$	0	0
$789$	8.47214	0.301616
$790$	7.41641	0.263864
$791$	0	0
$792$	−2.38197	−0.0846395
$793$	−38.8328	−1.37899
$794$	1.50658	0.0534664
$795$	15.7082	0.557113
$796$	3.41641	0.121091
$797$	−32.4721	−1.15022	−0.575111	−	0.818075i	$-0.695041\pi$
$797$	−32.4721	−1.15022	−0.575111	+	0.818075i	$0.695041\pi$
$798$	0	0
$799$	5.41641	0.191619
$800$	5.47214	0.193469
$801$	−10.4721	−0.370015
$802$	−33.7771	−1.19271
$803$	15.6312	0.551613
$804$	12.4721	0.439858
$805$	0	0
$806$	4.00000	0.140894
$807$	7.90983	0.278439
$808$	4.94427	0.173939
$809$	−4.47214	−0.157232	−0.0786160	−	0.996905i	$-0.525050\pi$
$809$	−4.47214	−0.157232	−0.0786160	+	0.996905i	$0.525050\pi$
$810$	−3.23607	−0.113704
$811$	−6.36068	−0.223354	−0.111677	−	0.993745i	$-0.535622\pi$
$811$	−6.36068	−0.223354	−0.111677	+	0.993745i	$0.535622\pi$
$812$	0	0
$813$	0	0
$814$	−18.7082	−0.655722
$815$	74.2492	2.60084
$816$	−0.763932	−0.0267430
$817$	47.0132	1.64478
$818$	32.8328	1.14797
$819$	0	0
$820$	−32.6525	−1.14027
$821$	29.7771	1.03923	0.519614	−	0.854401i	$-0.326076\pi$
$821$	29.7771	1.03923	0.519614	+	0.854401i	$0.326076\pi$
$822$	13.4164	0.467951
$823$	−34.6869	−1.20911	−0.604555	−	0.796563i	$-0.706649\pi$
$823$	−34.6869	−1.20911	−0.604555	+	0.796563i	$0.706649\pi$
$824$	−7.14590	−0.248939
$825$	13.0344	0.453801
$826$	0	0
$827$	−34.6869	−1.20618	−0.603091	−	0.797672i	$-0.706064\pi$
$827$	−34.6869	−1.20618	−0.603091	+	0.797672i	$0.706064\pi$
$828$	8.47214	0.294427
$829$	−18.9787	−0.659158	−0.329579	−	0.944128i	$-0.606907\pi$
$829$	−18.9787	−0.659158	−0.329579	+	0.944128i	$0.606907\pi$
$830$	31.1246	1.08035
$831$	−9.23607	−0.320396
$832$	3.23607	0.112190
$833$	−5.34752	−0.185281
$834$	21.2705	0.736538
$835$	−9.52786	−0.329725
$836$	11.0000	0.380443
$837$	−1.23607	−0.0427248
$838$	−38.1803	−1.31892
$839$	−7.63932	−0.263739	−0.131869	−	0.991267i	$-0.542098\pi$
$839$	−7.63932	−0.263739	−0.131869	+	0.991267i	$0.542098\pi$
$840$	0	0
$841$	45.2705	1.56105
$842$	14.2705	0.491794
$843$	6.03444	0.207837
$844$	−8.56231	−0.294727
$845$	8.18034	0.281412
$846$	7.09017	0.243765
$847$	0	0
$848$	4.85410	0.166691
$849$	−18.1803	−0.623948
$850$	4.18034	0.143384
$851$	66.5410	2.28100
$852$	13.2361	0.453460
$853$	7.59675	0.260108	0.130054	−	0.991507i	$-0.458485\pi$
$853$	7.59675	0.260108	0.130054	+	0.991507i	$0.458485\pi$
$854$	0	0
$855$	14.9443	0.511083
$856$	16.7984	0.574157
$857$	46.4721	1.58746	0.793729	−	0.608272i	$-0.208137\pi$
$857$	46.4721	1.58746	0.793729	+	0.608272i	$0.208137\pi$
$858$	7.70820	0.263154
$859$	50.4721	1.72209	0.861044	−	0.508531i	$-0.169811\pi$
$859$	50.4721	1.72209	0.861044	+	0.508531i	$0.169811\pi$
$860$	32.9443	1.12339
$861$	0	0
$862$	1.34752	0.0458969
$863$	8.20163	0.279187	0.139593	−	0.990209i	$-0.455420\pi$
$863$	8.20163	0.279187	0.139593	+	0.990209i	$0.455420\pi$
$864$	−1.00000	−0.0340207
$865$	−30.8328	−1.04835
$866$	29.9787	1.01872
$867$	16.4164	0.557530
$868$	0	0
$869$	5.45898	0.185183
$870$	−27.8885	−0.945510
$871$	−40.3607	−1.36757
$872$	−12.5623	−0.425413
$873$	11.0902	0.375345
$874$	−39.1246	−1.32341
$875$	0	0
$876$	6.56231	0.221720
$877$	1.00000	0.0337676
$877$	1.00000	0.0337676
$878$	−26.8328	−0.905564
$879$	20.9443	0.706433
$880$	7.70820	0.259844
$881$	56.8328	1.91475	0.957373	−	0.288854i	$-0.0932743\pi$
$881$	56.8328	1.91475	0.957373	+	0.288854i	$0.0932743\pi$
$882$	−7.00000	−0.235702
$883$	23.2148	0.781240	0.390620	−	0.920552i	$-0.372261\pi$
$883$	23.2148	0.781240	0.390620	+	0.920552i	$0.372261\pi$
$884$	2.47214	0.0831469
$885$	40.3607	1.35671
$886$	−12.0000	−0.403148
$887$	−55.1935	−1.85322	−0.926608	−	0.376028i	$-0.877289\pi$
$887$	−55.1935	−1.85322	−0.926608	+	0.376028i	$0.877289\pi$
$888$	−7.85410	−0.263566
$889$	0	0
$890$	33.8885	1.13595
$891$	−2.38197	−0.0797989
$892$	−4.14590	−0.138815
$893$	−32.7426	−1.09569
$894$	2.56231	0.0856963
$895$	12.3607	0.413172
$896$	0	0
$897$	−27.4164	−0.915407
$898$	−9.70820	−0.323967
$899$	−10.6525	−0.355280
$900$	5.47214	0.182405
$901$	3.70820	0.123538
$902$	−24.0344	−0.800259
$903$	0	0
$904$	13.2361	0.440225
$905$	26.8328	0.891953
$906$	11.1459	0.370298
$907$	4.87539	0.161885	0.0809423	−	0.996719i	$-0.474207\pi$
$907$	4.87539	0.161885	0.0809423	+	0.996719i	$0.474207\pi$
$908$	−25.4164	−0.843473
$909$	4.94427	0.163991
$910$	0	0
$911$	18.8754	0.625370	0.312685	−	0.949857i	$-0.398772\pi$
$911$	18.8754	0.625370	0.312685	+	0.949857i	$0.398772\pi$
$912$	4.61803	0.152918
$913$	22.9098	0.758205
$914$	−1.05573	−0.0349204
$915$	−38.8328	−1.28377
$916$	−9.70820	−0.320768
$917$	0	0
$918$	−0.763932	−0.0252135
$919$	−42.4721	−1.40103	−0.700513	−	0.713639i	$-0.747046\pi$
$919$	−42.4721	−1.40103	−0.700513	+	0.713639i	$0.747046\pi$
$920$	−27.4164	−0.903892
$921$	−16.5623	−0.545747
$922$	−26.5066	−0.872948
$923$	−42.8328	−1.40986
$924$	0	0
$925$	42.9787	1.41313
$926$	−24.0000	−0.788689
$927$	−7.14590	−0.234702
$928$	−8.61803	−0.282901
$929$	−3.59675	−0.118005	−0.0590027	−	0.998258i	$-0.518792\pi$
$929$	−3.59675	−0.118005	−0.0590027	+	0.998258i	$0.518792\pi$
$930$	4.00000	0.131165
$931$	32.3262	1.05945
$932$	−20.5066	−0.671715
$933$	−2.79837	−0.0916146
$934$	12.1803	0.398553
$935$	5.88854	0.192576
$936$	3.23607	0.105774
$937$	−36.8328	−1.20328	−0.601638	−	0.798769i	$-0.705485\pi$
$937$	−36.8328	−1.20328	−0.601638	+	0.798769i	$0.705485\pi$
$938$	0	0
$939$	−31.8885	−1.04064
$940$	−22.9443	−0.748360
$941$	12.1115	0.394822	0.197411	−	0.980321i	$-0.436747\pi$
$941$	12.1115	0.394822	0.197411	+	0.980321i	$0.436747\pi$
$942$	−2.47214	−0.0805465
$943$	85.4853	2.78378
$944$	12.4721	0.405933
$945$	0	0
$946$	24.2492	0.788410
$947$	−30.0000	−0.974869	−0.487435	−	0.873160i	$-0.662067\pi$
$947$	−30.0000	−0.974869	−0.487435	+	0.873160i	$0.662067\pi$
$948$	2.29180	0.0744341
$949$	−21.2361	−0.689352
$950$	−25.2705	−0.819884
$951$	−4.18034	−0.135557
$952$	0	0
$953$	−37.7771	−1.22372	−0.611860	−	0.790966i	$-0.709578\pi$
$953$	−37.7771	−1.22372	−0.611860	+	0.790966i	$0.709578\pi$
$954$	4.85410	0.157157
$955$	78.7214	2.54736
$956$	12.1803	0.393940
$957$	−20.5279	−0.663572
$958$	11.0557	0.357194
$959$	0	0
$960$	3.23607	0.104444
$961$	−29.4721	−0.950714
$962$	25.4164	0.819458
$963$	16.7984	0.541320
$964$	−9.27051	−0.298583
$965$	−49.8885	−1.60597
$966$	0	0
$967$	−30.0000	−0.964735	−0.482367	−	0.875969i	$-0.660223\pi$
$967$	−30.0000	−0.964735	−0.482367	+	0.875969i	$0.660223\pi$
$968$	−5.32624	−0.171192
$969$	3.52786	0.113331
$970$	−35.8885	−1.15231
$971$	−46.3607	−1.48779	−0.743893	−	0.668299i	$-0.767023\pi$
$971$	−46.3607	−1.48779	−0.743893	+	0.668299i	$0.767023\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	27.1459	0.869811
$975$	−17.7082	−0.567116
$976$	−12.0000	−0.384111
$977$	−9.05573	−0.289718	−0.144859	−	0.989452i	$-0.546273\pi$
$977$	−9.05573	−0.289718	−0.144859	+	0.989452i	$0.546273\pi$
$978$	22.9443	0.733677
$979$	24.9443	0.797222
$980$	22.6525	0.723607
$981$	−12.5623	−0.401084
$982$	−20.1803	−0.643981
$983$	−24.9443	−0.795599	−0.397799	−	0.917472i	$-0.630226\pi$
$983$	−24.9443	−0.795599	−0.397799	+	0.917472i	$0.630226\pi$
$984$	−10.0902	−0.321663
$985$	0	0
$986$	−6.58359	−0.209664
$987$	0	0
$988$	−14.9443	−0.475441
$989$	−86.2492	−2.74257
$990$	7.70820	0.244983
$991$	−34.0689	−1.08223	−0.541117	−	0.840947i	$-0.681998\pi$
$991$	−34.0689	−1.08223	−0.541117	+	0.840947i	$0.681998\pi$
$992$	1.23607	0.0392452
$993$	18.0000	0.571213
$994$	0	0
$995$	−11.0557	−0.350490
$996$	9.61803	0.304759
$997$	−17.7295	−0.561499	−0.280749	−	0.959781i	$-0.590583\pi$
$997$	−17.7295	−0.561499	−0.280749	+	0.959781i	$0.590583\pi$
$998$	12.0000	0.379853
$999$	−7.85410	−0.248493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5262.2.a.g.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5262.2.a.g.1.1	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5262 = 2 \cdot 3 \cdot 877 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5262.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.23607 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.23607 q^{10} -2.38197 q^{11} -1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +0.763932 q^{17} +1.00000 q^{18} -4.61803 q^{19} -3.23607 q^{20} -2.38197 q^{22} +8.47214 q^{23} -1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} -1.00000 q^{27} -8.61803 q^{29} +3.23607 q^{30} +1.23607 q^{31} +1.00000 q^{32} +2.38197 q^{33} +0.763932 q^{34} +1.00000 q^{36} +7.85410 q^{37} -4.61803 q^{38} -3.23607 q^{39} -3.23607 q^{40} +10.0902 q^{41} -10.1803 q^{43} -2.38197 q^{44} -3.23607 q^{45} +8.47214 q^{46} +7.09017 q^{47} -1.00000 q^{48} -7.00000 q^{49} +5.47214 q^{50} -0.763932 q^{51} +3.23607 q^{52} +4.85410 q^{53} -1.00000 q^{54} +7.70820 q^{55} +4.61803 q^{57} -8.61803 q^{58} +12.4721 q^{59} +3.23607 q^{60} -12.0000 q^{61} +1.23607 q^{62} +1.00000 q^{64} -10.4721 q^{65} +2.38197 q^{66} -12.4721 q^{67} +0.763932 q^{68} -8.47214 q^{69} -13.2361 q^{71} +1.00000 q^{72} -6.56231 q^{73} +7.85410 q^{74} -5.47214 q^{75} -4.61803 q^{76} -3.23607 q^{78} -2.29180 q^{79} -3.23607 q^{80} +1.00000 q^{81} +10.0902 q^{82} -9.61803 q^{83} -2.47214 q^{85} -10.1803 q^{86} +8.61803 q^{87} -2.38197 q^{88} -10.4721 q^{89} -3.23607 q^{90} +8.47214 q^{92} -1.23607 q^{93} +7.09017 q^{94} +14.9443 q^{95} -1.00000 q^{96} +11.0902 q^{97} -7.00000 q^{98} -2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 7 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{15} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 7 q^{22} + 8 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} - 2 q^{27} - 15 q^{29} + 2 q^{30} - 2 q^{31} + 2 q^{32} + 7 q^{33} + 6 q^{34} + 2 q^{36} + 9 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 9 q^{41} + 2 q^{43} - 7 q^{44} - 2 q^{45} + 8 q^{46} + 3 q^{47} - 2 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} + 2 q^{52} + 3 q^{53} - 2 q^{54} + 2 q^{55} + 7 q^{57} - 15 q^{58} + 16 q^{59} + 2 q^{60} - 24 q^{61} - 2 q^{62} + 2 q^{64} - 12 q^{65} + 7 q^{66} - 16 q^{67} + 6 q^{68} - 8 q^{69} - 22 q^{71} + 2 q^{72} + 7 q^{73} + 9 q^{74} - 2 q^{75} - 7 q^{76} - 2 q^{78} - 18 q^{79} - 2 q^{80} + 2 q^{81} + 9 q^{82} - 17 q^{83} + 4 q^{85} + 2 q^{86} + 15 q^{87} - 7 q^{88} - 12 q^{89} - 2 q^{90} + 8 q^{92} + 2 q^{93} + 3 q^{94} + 12 q^{95} - 2 q^{96} + 11 q^{97} - 14 q^{98} - 7 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 7 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^15 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 7 * q^22 + 8 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 - 2 * q^27 - 15 * q^29 + 2 * q^30 - 2 * q^31 + 2 * q^32 + 7 * q^33 + 6 * q^34 + 2 * q^36 + 9 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 9 * q^41 + 2 * q^43 - 7 * q^44 - 2 * q^45 + 8 * q^46 + 3 * q^47 - 2 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 + 2 * q^52 + 3 * q^53 - 2 * q^54 + 2 * q^55 + 7 * q^57 - 15 * q^58 + 16 * q^59 + 2 * q^60 - 24 * q^61 - 2 * q^62 + 2 * q^64 - 12 * q^65 + 7 * q^66 - 16 * q^67 + 6 * q^68 - 8 * q^69 - 22 * q^71 + 2 * q^72 + 7 * q^73 + 9 * q^74 - 2 * q^75 - 7 * q^76 - 2 * q^78 - 18 * q^79 - 2 * q^80 + 2 * q^81 + 9 * q^82 - 17 * q^83 + 4 * q^85 + 2 * q^86 + 15 * q^87 - 7 * q^88 - 12 * q^89 - 2 * q^90 + 8 * q^92 + 2 * q^93 + 3 * q^94 + 12 * q^95 - 2 * q^96 + 11 * q^97 - 14 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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