LMFDB - Embedded newform 33.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.37228 q^{2} +3.00000 q^{3} -2.37228 q^{4} +19.4891 q^{5} -7.11684 q^{6} +6.74456 q^{7} +24.6060 q^{8} +9.00000 q^{9} -46.2337 q^{10} +11.0000 q^{11} -7.11684 q^{12} -60.9783 q^{13} -16.0000 q^{14} +58.4674 q^{15} -39.3940 q^{16} -99.1684 q^{17} -21.3505 q^{18} +24.7011 q^{19} -46.2337 q^{20} +20.2337 q^{21} -26.0951 q^{22} +112.000 q^{23} +73.8179 q^{24} +254.826 q^{25} +144.658 q^{26} +27.0000 q^{27} -16.0000 q^{28} -21.1249 q^{29} -138.701 q^{30} -318.717 q^{31} -103.394 q^{32} +33.0000 q^{33} +235.255 q^{34} +131.446 q^{35} -21.3505 q^{36} -150.380 q^{37} -58.5979 q^{38} -182.935 q^{39} +479.549 q^{40} -252.745 q^{41} -48.0000 q^{42} +214.016 q^{43} -26.0951 q^{44} +175.402 q^{45} -265.696 q^{46} +105.870 q^{47} -118.182 q^{48} -297.511 q^{49} -604.519 q^{50} -297.505 q^{51} +144.658 q^{52} +325.652 q^{53} -64.0516 q^{54} +214.380 q^{55} +165.957 q^{56} +74.1032 q^{57} +50.1143 q^{58} +196.000 q^{59} -138.701 q^{60} -402.641 q^{61} +756.087 q^{62} +60.7011 q^{63} +560.432 q^{64} -1188.41 q^{65} -78.2853 q^{66} +27.4132 q^{67} +235.255 q^{68} +336.000 q^{69} -311.826 q^{70} -300.500 q^{71} +221.454 q^{72} +427.815 q^{73} +356.745 q^{74} +764.478 q^{75} -58.5979 q^{76} +74.1902 q^{77} +433.973 q^{78} +97.5488 q^{79} -767.755 q^{80} +81.0000 q^{81} +599.581 q^{82} +1104.62 q^{83} -48.0000 q^{84} -1932.71 q^{85} -507.707 q^{86} -63.3748 q^{87} +270.666 q^{88} +463.022 q^{89} -416.103 q^{90} -411.272 q^{91} -265.696 q^{92} -956.152 q^{93} -251.152 q^{94} +481.402 q^{95} -310.182 q^{96} -1798.36 q^{97} +705.779 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 6 q^{3} + q^{4} + 16 q^{5} + 3 q^{6} + 2 q^{7} + 9 q^{8} + 18 q^{9} - 58 q^{10} + 22 q^{11} + 3 q^{12} - 76 q^{13} - 32 q^{14} + 48 q^{15} - 119 q^{16} - 26 q^{17} + 9 q^{18} - 54 q^{19}+ \cdots + 198 q^{99}+O(q^{100}) $ 2 * q + q^2 + 6 * q^3 + q^4 + 16 * q^5 + 3 * q^6 + 2 * q^7 + 9 * q^8 + 18 * q^9 - 58 * q^10 + 22 * q^11 + 3 * q^12 - 76 * q^13 - 32 * q^14 + 48 * q^15 - 119 * q^16 - 26 * q^17 + 9 * q^18 - 54 * q^19 - 58 * q^20 + 6 * q^21 + 11 * q^22 + 224 * q^23 + 27 * q^24 + 142 * q^25 + 94 * q^26 + 54 * q^27 - 32 * q^28 + 222 * q^29 - 174 * q^30 - 40 * q^31 - 247 * q^32 + 66 * q^33 + 482 * q^34 + 148 * q^35 + 9 * q^36 - 48 * q^37 - 324 * q^38 - 228 * q^39 + 534 * q^40 - 494 * q^41 - 96 * q^42 - 66 * q^43 + 11 * q^44 + 144 * q^45 + 112 * q^46 - 64 * q^47 - 357 * q^48 - 618 * q^49 - 985 * q^50 - 78 * q^51 + 94 * q^52 - 84 * q^53 + 27 * q^54 + 176 * q^55 + 240 * q^56 - 162 * q^57 + 870 * q^58 + 392 * q^59 - 174 * q^60 - 1104 * q^61 + 1696 * q^62 + 18 * q^63 + 713 * q^64 - 1136 * q^65 + 33 * q^66 + 928 * q^67 + 482 * q^68 + 672 * q^69 - 256 * q^70 + 456 * q^71 + 81 * q^72 - 592 * q^73 + 702 * q^74 + 426 * q^75 - 324 * q^76 + 22 * q^77 + 282 * q^78 - 230 * q^79 - 490 * q^80 + 162 * q^81 - 214 * q^82 + 348 * q^83 - 96 * q^84 - 2188 * q^85 - 1452 * q^86 + 666 * q^87 + 99 * q^88 + 972 * q^89 - 522 * q^90 - 340 * q^91 + 112 * q^92 - 120 * q^93 - 824 * q^94 + 756 * q^95 - 741 * q^96 - 1184 * q^97 - 375 * q^98 + 198 * q^99

Coefficient data

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

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

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

$2$	−2.37228	−0.838728	−0.419364	−	0.907818i	$-0.637747\pi$
$2$	−2.37228	−0.838728	−0.419364	+	0.907818i	$0.637747\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.37228	−0.296535
$5$	19.4891	1.74316	0.871580	−	0.490253i	$-0.163096\pi$
$5$	19.4891	1.74316	0.871580	+	0.490253i	$0.163096\pi$
$6$	−7.11684	−0.484240
$7$	6.74456	0.364172	0.182086	−	0.983283i	$-0.441715\pi$
$7$	6.74456	0.364172	0.182086	+	0.983283i	$0.441715\pi$
$8$	24.6060	1.08744
$9$	9.00000	0.333333
$10$	−46.2337	−1.46204
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−7.11684	−0.171205
$13$	−60.9783	−1.30095	−0.650474	−	0.759529i	$-0.725430\pi$
$13$	−60.9783	−1.30095	−0.650474	+	0.759529i	$0.725430\pi$
$14$	−16.0000	−0.305441
$15$	58.4674	1.00641
$16$	−39.3940	−0.615532
$17$	−99.1684	−1.41482	−0.707408	−	0.706805i	$-0.750136\pi$
$17$	−99.1684	−1.41482	−0.707408	+	0.706805i	$0.750136\pi$
$18$	−21.3505	−0.279576
$19$	24.7011	0.298253	0.149127	−	0.988818i	$-0.452354\pi$
$19$	24.7011	0.298253	0.149127	+	0.988818i	$0.452354\pi$
$20$	−46.2337	−0.516908
$21$	20.2337	0.210255
$22$	−26.0951	−0.252886
$23$	112.000	1.01537	0.507687	−	0.861541i	$-0.330501\pi$
$23$	112.000	1.01537	0.507687	+	0.861541i	$0.330501\pi$
$24$	73.8179	0.627834
$25$	254.826	2.03861
$26$	144.658	1.09114
$27$	27.0000	0.192450
$28$	−16.0000	−0.107990
$29$	−21.1249	−0.135269	−0.0676345	−	0.997710i	$-0.521545\pi$
$29$	−21.1249	−0.135269	−0.0676345	+	0.997710i	$0.521545\pi$
$30$	−138.701	−0.844108
$31$	−318.717	−1.84656	−0.923279	−	0.384130i	$-0.874502\pi$
$31$	−318.717	−1.84656	−0.923279	+	0.384130i	$0.874502\pi$
$32$	−103.394	−0.571177
$33$	33.0000	0.174078
$34$	235.255	1.18665
$35$	131.446	0.634810
$36$	−21.3505	−0.0988451
$37$	−150.380	−0.668172	−0.334086	−	0.942543i	$-0.608428\pi$
$37$	−150.380	−0.668172	−0.334086	+	0.942543i	$0.608428\pi$
$38$	−58.5979	−0.250153
$39$	−182.935	−0.751103
$40$	479.549	1.89558
$41$	−252.745	−0.962733	−0.481367	−	0.876519i	$-0.659859\pi$
$41$	−252.745	−0.962733	−0.481367	+	0.876519i	$0.659859\pi$
$42$	−48.0000	−0.176347
$43$	214.016	0.759004	0.379502	−	0.925191i	$-0.376095\pi$
$43$	214.016	0.759004	0.379502	+	0.925191i	$0.376095\pi$
$44$	−26.0951	−0.0894087
$45$	175.402	0.581053
$46$	−265.696	−0.851623
$47$	105.870	0.328567	0.164284	−	0.986413i	$-0.447469\pi$
$47$	105.870	0.328567	0.164284	+	0.986413i	$0.447469\pi$
$48$	−118.182	−0.355377
$49$	−297.511	−0.867379
$50$	−604.519	−1.70984
$51$	−297.505	−0.816845
$52$	144.658	0.385777
$53$	325.652	0.843995	0.421998	−	0.906597i	$-0.361329\pi$
$53$	325.652	0.843995	0.421998	+	0.906597i	$0.361329\pi$
$54$	−64.0516	−0.161413
$55$	214.380	0.525583
$56$	165.957	0.396016
$57$	74.1032	0.172197
$58$	50.1143	0.113454
$59$	196.000	0.432492	0.216246	−	0.976339i	$-0.430619\pi$
$59$	196.000	0.432492	0.216246	+	0.976339i	$0.430619\pi$
$60$	−138.701	−0.298437
$61$	−402.641	−0.845130	−0.422565	−	0.906333i	$-0.638870\pi$
$61$	−402.641	−0.845130	−0.422565	+	0.906333i	$0.638870\pi$
$62$	756.087	1.54876
$63$	60.7011	0.121391
$64$	560.432	1.09459
$65$	−1188.41	−2.26776
$66$	−78.2853	−0.146004
$67$	27.4132	0.0499860	0.0249930	−	0.999688i	$-0.492044\pi$
$67$	27.4132	0.0499860	0.0249930	+	0.999688i	$0.492044\pi$
$68$	235.255	0.419543
$69$	336.000	0.586227
$70$	−311.826	−0.532433
$71$	−300.500	−0.502292	−0.251146	−	0.967949i	$-0.580807\pi$
$71$	−300.500	−0.502292	−0.251146	+	0.967949i	$0.580807\pi$
$72$	221.454	0.362480
$73$	427.815	0.685917	0.342959	−	0.939351i	$-0.388571\pi$
$73$	427.815	0.685917	0.342959	+	0.939351i	$0.388571\pi$
$74$	356.745	0.560415
$75$	764.478	1.17699
$76$	−58.5979	−0.0884426
$77$	74.1902	0.109802
$78$	433.973	0.629971
$79$	97.5488	0.138925	0.0694627	−	0.997585i	$-0.477872\pi$
$79$	97.5488	0.138925	0.0694627	+	0.997585i	$0.477872\pi$
$80$	−767.755	−1.07297
$81$	81.0000	0.111111
$82$	599.581	0.807472
$83$	1104.62	1.46082	0.730408	−	0.683011i	$-0.239330\pi$
$83$	1104.62	1.46082	0.730408	+	0.683011i	$0.239330\pi$
$84$	−48.0000	−0.0623480
$85$	−1932.71	−2.46625
$86$	−507.707	−0.636598
$87$	−63.3748	−0.0780976
$88$	270.666	0.327876
$89$	463.022	0.551463	0.275732	−	0.961235i	$-0.411080\pi$
$89$	463.022	0.551463	0.275732	+	0.961235i	$0.411080\pi$
$90$	−416.103	−0.487346
$91$	−411.272	−0.473769
$92$	−265.696	−0.301094
$93$	−956.152	−1.06611
$94$	−251.152	−0.275578
$95$	481.402	0.519903
$96$	−310.182	−0.329769
$97$	−1798.36	−1.88243	−0.941214	−	0.337810i	$-0.890314\pi$
$97$	−1798.36	−1.88243	−0.941214	+	0.337810i	$0.890314\pi$
$98$	705.779	0.727495
$99$	99.0000	0.100504
$100$	−604.519	−0.604519
$101$	741.918	0.730927	0.365463	−	0.930826i	$-0.380911\pi$
$101$	741.918	0.730927	0.365463	+	0.930826i	$0.380911\pi$
$102$	705.766	0.685111
$103$	389.837	0.372930	0.186465	−	0.982462i	$-0.440297\pi$
$103$	389.837	0.372930	0.186465	+	0.982462i	$0.440297\pi$
$104$	−1500.43	−1.41470
$105$	394.337	0.366508
$106$	−772.538	−0.707882
$107$	1538.42	1.38995	0.694977	−	0.719032i	$-0.255415\pi$
$107$	1538.42	1.38995	0.694977	+	0.719032i	$0.255415\pi$
$108$	−64.0516	−0.0570682
$109$	779.783	0.685226	0.342613	−	0.939477i	$-0.388688\pi$
$109$	779.783	0.685226	0.342613	+	0.939477i	$0.388688\pi$
$110$	−508.571	−0.440821
$111$	−451.141	−0.385770
$112$	−265.696	−0.224160
$113$	−1514.55	−1.26086	−0.630430	−	0.776246i	$-0.717122\pi$
$113$	−1514.55	−1.26086	−0.630430	+	0.776246i	$0.717122\pi$
$114$	−175.794	−0.144426
$115$	2182.78	1.76996
$116$	50.1143	0.0401120
$117$	−548.804	−0.433649
$118$	−464.967	−0.362743
$119$	−668.848	−0.515237
$120$	1438.65	1.09442
$121$	121.000	0.0909091
$122$	955.179	0.708834
$123$	−758.234	−0.555834
$124$	756.087	0.547569
$125$	2530.20	1.81046
$126$	−144.000	−0.101814
$127$	2302.74	1.60894	0.804471	−	0.593992i	$-0.202449\pi$
$127$	2302.74	1.60894	0.804471	+	0.593992i	$0.202449\pi$
$128$	−502.350	−0.346890
$129$	642.049	0.438211
$130$	2819.25	1.90203
$131$	−2020.59	−1.34763	−0.673815	−	0.738900i	$-0.735345\pi$
$131$	−2020.59	−1.34763	−0.673815	+	0.738900i	$0.735345\pi$
$132$	−78.2853	−0.0516201
$133$	166.598	0.108616
$134$	−65.0319	−0.0419246
$135$	526.206	0.335471
$136$	−2440.14	−1.53853
$137$	1475.40	0.920088	0.460044	−	0.887896i	$-0.347834\pi$
$137$	1475.40	0.920088	0.460044	+	0.887896i	$0.347834\pi$
$138$	−797.087	−0.491685
$139$	−1623.71	−0.990802	−0.495401	−	0.868665i	$-0.664979\pi$
$139$	−1623.71	−0.990802	−0.495401	+	0.868665i	$0.664979\pi$
$140$	−311.826	−0.188244
$141$	317.609	0.189698
$142$	712.870	0.421287
$143$	−670.761	−0.392251
$144$	−354.546	−0.205177
$145$	−411.707	−0.235796
$146$	−1014.90	−0.575298
$147$	−892.533	−0.500781
$148$	356.745	0.198137
$149$	−1104.11	−0.607064	−0.303532	−	0.952821i	$-0.598166\pi$
$149$	−1104.11	−0.607064	−0.303532	+	0.952821i	$0.598166\pi$
$150$	−1813.56	−0.987175
$151$	2980.07	1.60606	0.803029	−	0.595940i	$-0.203221\pi$
$151$	2980.07	1.60606	0.803029	+	0.595940i	$0.203221\pi$
$152$	607.794	0.324333
$153$	−892.516	−0.471605
$154$	−176.000	−0.0920941
$155$	−6211.52	−3.21885
$156$	433.973	0.222728
$157$	2844.67	1.44605	0.723024	−	0.690823i	$-0.242751\pi$
$157$	2844.67	1.44605	0.723024	+	0.690823i	$0.242751\pi$
$158$	−231.413	−0.116521
$159$	976.956	0.487281
$160$	−2015.06	−0.995653
$161$	755.391	0.369771
$162$	−192.155	−0.0931920
$163$	−1528.51	−0.734492	−0.367246	−	0.930124i	$-0.619699\pi$
$163$	−1528.51	−0.734492	−0.367246	+	0.930124i	$0.619699\pi$
$164$	599.581	0.285484
$165$	643.141	0.303445
$166$	−2620.47	−1.22523
$167$	−383.881	−0.177878	−0.0889388	−	0.996037i	$-0.528348\pi$
$167$	−383.881	−0.177878	−0.0889388	+	0.996037i	$0.528348\pi$
$168$	497.870	0.228640
$169$	1521.35	0.692466
$170$	4584.92	2.06851
$171$	222.310	0.0994178
$172$	−507.707	−0.225071
$173$	2702.85	1.18783	0.593914	−	0.804529i	$-0.297582\pi$
$173$	2702.85	1.18783	0.593914	+	0.804529i	$0.297582\pi$
$174$	150.343	0.0655027
$175$	1718.69	0.742404
$176$	−433.334	−0.185590
$177$	588.000	0.249699
$178$	−1098.42	−0.462528
$179$	−2777.61	−1.15982	−0.579911	−	0.814680i	$-0.696913\pi$
$179$	−2777.61	−1.15982	−0.579911	+	0.814680i	$0.696913\pi$
$180$	−416.103	−0.172303
$181$	−3993.61	−1.64001	−0.820007	−	0.572354i	$-0.806030\pi$
$181$	−3993.61	−1.64001	−0.820007	+	0.572354i	$0.806030\pi$
$182$	975.652	0.397363
$183$	−1207.92	−0.487936
$184$	2755.87	1.10416
$185$	−2930.78	−1.16473
$186$	2268.26	0.894177
$187$	−1090.85	−0.426583
$188$	−251.152	−0.0974317
$189$	182.103	0.0700850
$190$	−1142.02	−0.436058
$191$	895.587	0.339280	0.169640	−	0.985506i	$-0.445740\pi$
$191$	895.587	0.339280	0.169640	+	0.985506i	$0.445740\pi$
$192$	1681.30	0.631964
$193$	1328.24	0.495382	0.247691	−	0.968839i	$-0.420328\pi$
$193$	1328.24	0.495382	0.247691	+	0.968839i	$0.420328\pi$
$194$	4266.21	1.57885
$195$	−3565.24	−1.30929
$196$	705.779	0.257208
$197$	154.114	0.0557370	0.0278685	−	0.999612i	$-0.491128\pi$
$197$	154.114	0.0557370	0.0278685	+	0.999612i	$0.491128\pi$
$198$	−234.856	−0.0842953
$199$	1316.15	0.468842	0.234421	−	0.972135i	$-0.424681\pi$
$199$	1316.15	0.468842	0.234421	+	0.972135i	$0.424681\pi$
$200$	6270.24	2.21686
$201$	82.2397	0.0288594
$202$	−1760.04	−0.613049
$203$	−142.478	−0.0492612
$204$	705.766	0.242223
$205$	−4925.77	−1.67820
$206$	−924.803	−0.312787
$207$	1008.00	0.338458
$208$	2402.18	0.800775
$209$	271.712	0.0899268
$210$	−935.478	−0.307401
$211$	−1735.76	−0.566324	−0.283162	−	0.959072i	$-0.591383\pi$
$211$	−1735.76	−0.566324	−0.283162	+	0.959072i	$0.591383\pi$
$212$	−772.538	−0.250274
$213$	−901.499	−0.289999
$214$	−3649.57	−1.16579
$215$	4170.99	1.32307
$216$	664.361	0.209278
$217$	−2149.61	−0.672465
$218$	−1849.86	−0.574718
$219$	1283.44	0.396014
$220$	−508.571	−0.155854
$221$	6047.12	1.84060
$222$	1070.23	0.323556
$223$	1663.71	0.499597	0.249798	−	0.968298i	$-0.419636\pi$
$223$	1663.71	0.499597	0.249798	+	0.968298i	$0.419636\pi$
$224$	−697.348	−0.208007
$225$	2293.43	0.679536
$226$	3592.95	1.05752
$227$	−3658.84	−1.06980	−0.534902	−	0.844914i	$-0.679651\pi$
$227$	−3658.84	−1.06980	−0.534902	+	0.844914i	$0.679651\pi$
$228$	−175.794	−0.0510624
$229$	1927.07	0.556090	0.278045	−	0.960568i	$-0.410314\pi$
$229$	1927.07	0.556090	0.278045	+	0.960568i	$0.410314\pi$
$230$	−5178.17	−1.48452
$231$	222.571	0.0633942
$232$	−519.800	−0.147097
$233$	−2784.27	−0.782847	−0.391423	−	0.920211i	$-0.628017\pi$
$233$	−2784.27	−0.782847	−0.391423	+	0.920211i	$0.628017\pi$
$234$	1301.92	0.363714
$235$	2063.30	0.572745
$236$	−464.967	−0.128249
$237$	292.646	0.0802086
$238$	1586.70	0.432144
$239$	1222.60	0.330892	0.165446	−	0.986219i	$-0.447094\pi$
$239$	1222.60	0.330892	0.165446	+	0.986219i	$0.447094\pi$
$240$	−2303.27	−0.619480
$241$	−2013.01	−0.538047	−0.269024	−	0.963134i	$-0.586701\pi$
$241$	−2013.01	−0.538047	−0.269024	+	0.963134i	$0.586701\pi$
$242$	−287.046	−0.0762480
$243$	243.000	0.0641500
$244$	955.179	0.250611
$245$	−5798.23	−1.51198
$246$	1798.74	0.466194
$247$	−1506.23	−0.388012
$248$	−7842.35	−2.00802
$249$	3313.86	0.843402
$250$	−6002.33	−1.51848
$251$	2706.63	0.680641	0.340320	−	0.940310i	$-0.389464\pi$
$251$	2706.63	0.680641	0.340320	+	0.940310i	$0.389464\pi$
$252$	−144.000	−0.0359966
$253$	1232.00	0.306147
$254$	−5462.76	−1.34946
$255$	−5798.12	−1.42389
$256$	−3291.74	−0.803647
$257$	225.741	0.0547912	0.0273956	−	0.999625i	$-0.491279\pi$
$257$	225.741	0.0547912	0.0273956	+	0.999625i	$0.491279\pi$
$258$	−1523.12	−0.367540
$259$	−1014.25	−0.243330
$260$	2819.25	0.672471
$261$	−190.124	−0.0450897
$262$	4793.40	1.13029
$263$	1953.42	0.457997	0.228998	−	0.973427i	$-0.426455\pi$
$263$	1953.42	0.457997	0.228998	+	0.973427i	$0.426455\pi$
$264$	811.997	0.189299
$265$	6346.67	1.47122
$266$	−395.217	−0.0910989
$267$	1389.07	0.318387
$268$	−65.0319	−0.0148226
$269$	−350.848	−0.0795225	−0.0397613	−	0.999209i	$-0.512660\pi$
$269$	−350.848	−0.0795225	−0.0397613	+	0.999209i	$0.512660\pi$
$270$	−1248.31	−0.281369
$271$	254.779	0.0571096	0.0285548	−	0.999592i	$-0.490909\pi$
$271$	254.779	0.0571096	0.0285548	+	0.999592i	$0.490909\pi$
$272$	3906.64	0.870864
$273$	−1233.81	−0.273531
$274$	−3500.07	−0.771704
$275$	2803.09	0.614663
$276$	−797.087	−0.173837
$277$	116.478	0.0252654	0.0126327	−	0.999920i	$-0.495979\pi$
$277$	116.478	0.0252654	0.0126327	+	0.999920i	$0.495979\pi$
$278$	3851.90	0.831013
$279$	−2868.46	−0.615519
$280$	3234.35	0.690319
$281$	8226.47	1.74644	0.873221	−	0.487325i	$-0.162027\pi$
$281$	8226.47	1.74644	0.873221	+	0.487325i	$0.162027\pi$
$282$	−753.457	−0.159105
$283$	1561.52	0.327995	0.163997	−	0.986461i	$-0.447561\pi$
$283$	1561.52	0.327995	0.163997	+	0.986461i	$0.447561\pi$
$284$	712.870	0.148947
$285$	1444.21	0.300166
$286$	1591.23	0.328992
$287$	−1704.65	−0.350601
$288$	−930.546	−0.190392
$289$	4921.38	1.00171
$290$	976.684	0.197768
$291$	−5395.07	−1.08682
$292$	−1014.90	−0.203399
$293$	9486.19	1.89143	0.945715	−	0.324997i	$-0.105363\pi$
$293$	9486.19	1.89143	0.945715	+	0.324997i	$0.105363\pi$
$294$	2117.34	0.420019
$295$	3819.87	0.753903
$296$	−3700.25	−0.726598
$297$	297.000	0.0580259
$298$	2619.27	0.509161
$299$	−6829.56	−1.32095
$300$	−1813.56	−0.349019
$301$	1443.45	0.276408
$302$	−7069.56	−1.34705
$303$	2225.75	0.422001
$304$	−973.074	−0.183584
$305$	−7847.13	−1.47320
$306$	2117.30	0.395549
$307$	−8443.06	−1.56961	−0.784806	−	0.619742i	$-0.787237\pi$
$307$	−8443.06	−1.56961	−0.784806	+	0.619742i	$0.787237\pi$
$308$	−176.000	−0.0325602
$309$	1169.51	0.215311
$310$	14735.5	2.69974
$311$	4447.17	0.810856	0.405428	−	0.914127i	$-0.367123\pi$
$311$	4447.17	0.810856	0.405428	+	0.914127i	$0.367123\pi$
$312$	−4501.29	−0.816779
$313$	6480.75	1.17033	0.585165	−	0.810914i	$-0.301030\pi$
$313$	6480.75	1.17033	0.585165	+	0.810914i	$0.301030\pi$
$314$	−6748.36	−1.21284
$315$	1183.01	0.211603
$316$	−231.413	−0.0411962
$317$	−1252.75	−0.221960	−0.110980	−	0.993823i	$-0.535399\pi$
$317$	−1252.75	−0.221960	−0.110980	+	0.993823i	$0.535399\pi$
$318$	−2317.61	−0.408696
$319$	−232.374	−0.0407852
$320$	10922.3	1.90805
$321$	4615.27	0.802490
$322$	−1792.00	−0.310137
$323$	−2449.57	−0.421974
$324$	−192.155	−0.0329484
$325$	−15538.8	−2.65212
$326$	3626.06	0.616039
$327$	2339.35	0.395615
$328$	−6219.02	−1.04692
$329$	714.043	0.119655
$330$	−1525.71	−0.254508
$331$	3801.44	0.631258	0.315629	−	0.948883i	$-0.397785\pi$
$331$	3801.44	0.631258	0.315629	+	0.948883i	$0.397785\pi$
$332$	−2620.47	−0.433183
$333$	−1353.42	−0.222724
$334$	910.673	0.149191
$335$	534.260	0.0871336
$336$	−797.087	−0.129419
$337$	−5456.53	−0.882007	−0.441003	−	0.897506i	$-0.645377\pi$
$337$	−5456.53	−0.882007	−0.441003	+	0.897506i	$0.645377\pi$
$338$	−3609.06	−0.580790
$339$	−4543.66	−0.727958
$340$	4584.92	0.731330
$341$	−3505.89	−0.556758
$342$	−527.381	−0.0833845
$343$	−4319.97	−0.680047
$344$	5266.08	0.825371
$345$	6548.35	1.02189
$346$	−6411.93	−0.996264
$347$	−4240.53	−0.656033	−0.328017	−	0.944672i	$-0.606380\pi$
$347$	−4240.53	−0.656033	−0.328017	+	0.944672i	$0.606380\pi$
$348$	150.343	0.0231587
$349$	−8471.53	−1.29934	−0.649672	−	0.760215i	$-0.725094\pi$
$349$	−8471.53	−1.29934	−0.649672	+	0.760215i	$0.725094\pi$
$350$	−4077.22	−0.622675
$351$	−1646.41	−0.250368
$352$	−1137.33	−0.172216
$353$	981.282	0.147956	0.0739778	−	0.997260i	$-0.476431\pi$
$353$	981.282	0.147956	0.0739778	+	0.997260i	$0.476431\pi$
$354$	−1394.90	−0.209430
$355$	−5856.48	−0.875576
$356$	−1098.42	−0.163528
$357$	−2006.54	−0.297472
$358$	6589.27	0.972776
$359$	−3020.09	−0.443995	−0.221997	−	0.975047i	$-0.571258\pi$
$359$	−3020.09	−0.443995	−0.221997	+	0.975047i	$0.571258\pi$
$360$	4315.94	0.631861
$361$	−6248.86	−0.911045
$362$	9473.96	1.37553
$363$	363.000	0.0524864
$364$	975.652	0.140489
$365$	8337.74	1.19566
$366$	2865.54	0.409246
$367$	8689.40	1.23592	0.617960	−	0.786209i	$-0.287959\pi$
$367$	8689.40	1.23592	0.617960	+	0.786209i	$0.287959\pi$
$368$	−4412.13	−0.624995
$369$	−2274.70	−0.320911
$370$	6952.64	0.976893
$371$	2196.38	0.307360
$372$	2268.26	0.316139
$373$	5340.53	0.741346	0.370673	−	0.928763i	$-0.379127\pi$
$373$	5340.53	0.741346	0.370673	+	0.928763i	$0.379127\pi$
$374$	2587.81	0.357787
$375$	7590.59	1.04527
$376$	2605.02	0.357297
$377$	1288.16	0.175978
$378$	−432.000	−0.0587822
$379$	−1603.49	−0.217324	−0.108662	−	0.994079i	$-0.534657\pi$
$379$	−1603.49	−0.217324	−0.108662	+	0.994079i	$0.534657\pi$
$380$	−1142.02	−0.154170
$381$	6908.23	0.928923
$382$	−2124.58	−0.284563
$383$	−830.236	−0.110765	−0.0553826	−	0.998465i	$-0.517638\pi$
$383$	−830.236	−0.110765	−0.0553826	+	0.998465i	$0.517638\pi$
$384$	−1507.05	−0.200277
$385$	1445.90	0.191403
$386$	−3150.96	−0.415491
$387$	1926.15	0.253001
$388$	4266.21	0.558206
$389$	−1746.12	−0.227588	−0.113794	−	0.993504i	$-0.536300\pi$
$389$	−1746.12	−0.227588	−0.113794	+	0.993504i	$0.536300\pi$
$390$	8457.75	1.09814
$391$	−11106.9	−1.43657
$392$	−7320.54	−0.943223
$393$	−6061.76	−0.778054
$394$	−365.602	−0.0467482
$395$	1901.14	0.242169
$396$	−234.856	−0.0298029
$397$	−10016.2	−1.26624	−0.633119	−	0.774054i	$-0.718226\pi$
$397$	−10016.2	−1.26624	−0.633119	+	0.774054i	$0.718226\pi$
$398$	−3122.28	−0.393231
$399$	499.794	0.0627092
$400$	−10038.6	−1.25483
$401$	8228.38	1.02470	0.512351	−	0.858776i	$-0.328775\pi$
$401$	8228.38	1.02470	0.512351	+	0.858776i	$0.328775\pi$
$402$	−195.096	−0.0242052
$403$	19434.8	2.40228
$404$	−1760.04	−0.216746
$405$	1578.62	0.193684
$406$	337.999	0.0413168
$407$	−1654.18	−0.201462
$408$	−7320.41	−0.888270
$409$	−12311.5	−1.48843	−0.744213	−	0.667943i	$-0.767175\pi$
$409$	−12311.5	−1.48843	−0.744213	+	0.667943i	$0.767175\pi$
$410$	11685.3	1.40755
$411$	4426.21	0.531213
$412$	−924.803	−0.110587
$413$	1321.93	0.157502
$414$	−2391.26	−0.283874
$415$	21528.1	2.54644
$416$	6304.79	0.743071
$417$	−4871.14	−0.572040
$418$	−644.577	−0.0754241
$419$	13260.4	1.54610	0.773048	−	0.634347i	$-0.218731\pi$
$419$	13260.4	1.54610	0.773048	+	0.634347i	$0.218731\pi$
$420$	−935.478	−0.108683
$421$	−6177.74	−0.715165	−0.357583	−	0.933881i	$-0.616399\pi$
$421$	−6177.74	−0.715165	−0.357583	+	0.933881i	$0.616399\pi$
$422$	4117.70	0.474992
$423$	952.826	0.109522
$424$	8012.98	0.917795
$425$	−25270.7	−2.88426
$426$	2138.61	0.243230
$427$	−2715.64	−0.307773
$428$	−3649.57	−0.412170
$429$	−2012.28	−0.226466
$430$	−9894.76	−1.10969
$431$	1668.05	0.186421	0.0932103	−	0.995646i	$-0.470287\pi$
$431$	1668.05	0.186421	0.0932103	+	0.995646i	$0.470287\pi$
$432$	−1063.64	−0.118459
$433$	−731.748	−0.0812138	−0.0406069	−	0.999175i	$-0.512929\pi$
$433$	−731.748	−0.0812138	−0.0406069	+	0.999175i	$0.512929\pi$
$434$	5099.48	0.564015
$435$	−1235.12	−0.136137
$436$	−1849.86	−0.203194
$437$	2766.52	0.302839
$438$	−3044.69	−0.332148
$439$	−14248.0	−1.54902	−0.774508	−	0.632564i	$-0.782002\pi$
$439$	−14248.0	−1.54902	−0.774508	+	0.632564i	$0.782002\pi$
$440$	5275.04	0.571540
$441$	−2677.60	−0.289126
$442$	−14345.5	−1.54377
$443$	174.262	0.0186895	0.00934473	−	0.999956i	$-0.497025\pi$
$443$	174.262	0.0186895	0.00934473	+	0.999956i	$0.497025\pi$
$444$	1070.23	0.114394
$445$	9023.89	0.961288
$446$	−3946.78	−0.419026
$447$	−3312.34	−0.350488
$448$	3779.87	0.398621
$449$	7469.97	0.785144	0.392572	−	0.919721i	$-0.371585\pi$
$449$	7469.97	0.785144	0.392572	+	0.919721i	$0.371585\pi$
$450$	−5440.67	−0.569946
$451$	−2780.19	−0.290275
$452$	3592.95	0.373890
$453$	8940.21	0.927258
$454$	8679.79	0.897275
$455$	−8015.32	−0.825855
$456$	1823.38	0.187254
$457$	8762.68	0.896939	0.448469	−	0.893798i	$-0.351969\pi$
$457$	8762.68	0.896939	0.448469	+	0.893798i	$0.351969\pi$
$458$	−4571.56	−0.466409
$459$	−2677.55	−0.272282
$460$	−5178.17	−0.524856
$461$	4339.67	0.438435	0.219218	−	0.975676i	$-0.429650\pi$
$461$	4339.67	0.438435	0.219218	+	0.975676i	$0.429650\pi$
$462$	−528.000	−0.0531705
$463$	−3932.49	−0.394726	−0.197363	−	0.980330i	$-0.563238\pi$
$463$	−3932.49	−0.394726	−0.197363	+	0.980330i	$0.563238\pi$
$464$	832.197	0.0832624
$465$	−18634.6	−1.85840
$466$	6605.06	0.656596
$467$	−8383.97	−0.830758	−0.415379	−	0.909648i	$-0.636351\pi$
$467$	−8383.97	−0.830758	−0.415379	+	0.909648i	$0.636351\pi$
$468$	1301.92	0.128592
$469$	184.890	0.0182035
$470$	−4894.74	−0.480377
$471$	8534.02	0.834876
$472$	4822.77	0.470309
$473$	2354.18	0.228848
$474$	−694.240	−0.0672732
$475$	6294.47	0.608022
$476$	1586.70	0.152786
$477$	2930.87	0.281332
$478$	−2900.35	−0.277529
$479$	9534.10	0.909445	0.454722	−	0.890633i	$-0.349739\pi$
$479$	9534.10	0.909445	0.454722	+	0.890633i	$0.349739\pi$
$480$	−6045.18	−0.574840
$481$	9169.93	0.869258
$482$	4775.43	0.451275
$483$	2266.17	0.213487
$484$	−287.046	−0.0269577
$485$	−35048.4	−3.28138
$486$	−576.464	−0.0538044
$487$	4451.09	0.414164	0.207082	−	0.978324i	$-0.433603\pi$
$487$	4451.09	0.414164	0.207082	+	0.978324i	$0.433603\pi$
$488$	−9907.38	−0.919029
$489$	−4585.53	−0.424059
$490$	13755.0	1.26814
$491$	−9757.40	−0.896833	−0.448417	−	0.893825i	$-0.648012\pi$
$491$	−9757.40	−0.896833	−0.448417	+	0.893825i	$0.648012\pi$
$492$	1798.74	0.164824
$493$	2094.93	0.191381
$494$	3573.20	0.325437
$495$	1929.42	0.175194
$496$	12555.6	1.13662
$497$	−2026.74	−0.182921
$498$	−7861.40	−0.707385
$499$	−7173.69	−0.643564	−0.321782	−	0.946814i	$-0.604282\pi$
$499$	−7173.69	−0.643564	−0.321782	+	0.946814i	$0.604282\pi$
$500$	−6002.33	−0.536865
$501$	−1151.64	−0.102698
$502$	−6420.88	−0.570873
$503$	−15617.0	−1.38435	−0.692177	−	0.721728i	$-0.743348\pi$
$503$	−15617.0	−1.38435	−0.692177	+	0.721728i	$0.743348\pi$
$504$	1493.61	0.132005
$505$	14459.3	1.27412
$506$	−2922.65	−0.256774
$507$	4564.04	0.399795
$508$	−5462.76	−0.477108
$509$	−8789.23	−0.765375	−0.382688	−	0.923878i	$-0.625001\pi$
$509$	−8789.23	−0.765375	−0.382688	+	0.923878i	$0.625001\pi$
$510$	13754.8	1.19426
$511$	2885.42	0.249792
$512$	11827.7	1.02093
$513$	666.929	0.0573989
$514$	−535.521	−0.0459549
$515$	7597.58	0.650077
$516$	−1523.12	−0.129945
$517$	1164.56	0.0990667
$518$	2406.09	0.204088
$519$	8108.56	0.685792
$520$	−29242.0	−2.46606
$521$	13099.3	1.10152	0.550760	−	0.834664i	$-0.314338\pi$
$521$	13099.3	1.10152	0.550760	+	0.834664i	$0.314338\pi$
$522$	451.029	0.0378180
$523$	16824.2	1.40664	0.703318	−	0.710876i	$-0.251701\pi$
$523$	16824.2	1.40664	0.703318	+	0.710876i	$0.251701\pi$
$524$	4793.40	0.399620
$525$	5156.07	0.428627
$526$	−4634.07	−0.384135
$527$	31606.7	2.61254
$528$	−1300.00	−0.107150
$529$	377.000	0.0309855
$530$	−15056.1	−1.23395
$531$	1764.00	0.144164
$532$	−395.217	−0.0322083
$533$	15411.9	1.25247
$534$	−3295.25	−0.267040
$535$	29982.5	2.42291
$536$	674.529	0.0543568
$537$	−8332.83	−0.669624
$538$	832.310	0.0666978
$539$	−3272.62	−0.261525
$540$	−1248.31	−0.0994791
$541$	18863.1	1.49905	0.749527	−	0.661974i	$-0.230281\pi$
$541$	18863.1	1.49905	0.749527	+	0.661974i	$0.230281\pi$
$542$	−604.407	−0.0478995
$543$	−11980.8	−0.946862
$544$	10253.4	0.808110
$545$	15197.3	1.19446
$546$	2926.96	0.229418
$547$	−12283.0	−0.960119	−0.480059	−	0.877236i	$-0.659385\pi$
$547$	−12283.0	−0.960119	−0.480059	+	0.877236i	$0.659385\pi$
$548$	−3500.07	−0.272839
$549$	−3623.77	−0.281710
$550$	−6649.71	−0.515536
$551$	−521.809	−0.0403444
$552$	8267.61	0.637487
$553$	657.924	0.0505927
$554$	−276.320	−0.0211908
$555$	−8792.35	−0.672458
$556$	3851.90	0.293808
$557$	−9752.05	−0.741845	−0.370923	−	0.928664i	$-0.620958\pi$
$557$	−9752.05	−0.741845	−0.370923	+	0.928664i	$0.620958\pi$
$558$	6804.78	0.516253
$559$	−13050.3	−0.987424
$560$	−5178.17	−0.390746
$561$	−3272.56	−0.246288
$562$	−19515.5	−1.46479
$563$	−3447.50	−0.258072	−0.129036	−	0.991640i	$-0.541188\pi$
$563$	−3447.50	−0.258072	−0.129036	+	0.991640i	$0.541188\pi$
$564$	−753.457	−0.0562522
$565$	−29517.3	−2.19788
$566$	−3704.36	−0.275098
$567$	546.310	0.0404636
$568$	−7394.09	−0.546213
$569$	−3371.02	−0.248366	−0.124183	−	0.992259i	$-0.539631\pi$
$569$	−3371.02	−0.248366	−0.124183	+	0.992259i	$0.539631\pi$
$570$	−3426.06	−0.251758
$571$	−15852.5	−1.16183	−0.580916	−	0.813964i	$-0.697305\pi$
$571$	−15852.5	−1.16183	−0.580916	+	0.813964i	$0.697305\pi$
$572$	1591.23	0.116316
$573$	2686.76	0.195883
$574$	4043.91	0.294059
$575$	28540.5	2.06995
$576$	5043.89	0.364865
$577$	1376.35	0.0993036	0.0496518	−	0.998767i	$-0.484189\pi$
$577$	1376.35	0.0993036	0.0496518	+	0.998767i	$0.484189\pi$
$578$	−11674.9	−0.840159
$579$	3984.72	0.286009
$580$	976.684	0.0699217
$581$	7450.17	0.531988
$582$	12798.6	0.911547
$583$	3582.17	0.254474
$584$	10526.8	0.745894
$585$	−10695.7	−0.755920
$586$	−22503.9	−1.58640
$587$	−23021.4	−1.61873	−0.809366	−	0.587304i	$-0.800189\pi$
$587$	−23021.4	−1.61873	−0.809366	+	0.587304i	$0.800189\pi$
$588$	2117.34	0.148499
$589$	−7872.66	−0.550742
$590$	−9061.80	−0.632320
$591$	462.343	0.0321798
$592$	5924.09	0.411281
$593$	2818.69	0.195194	0.0975968	−	0.995226i	$-0.468884\pi$
$593$	2818.69	0.195194	0.0975968	+	0.995226i	$0.468884\pi$
$594$	−704.568	−0.0486679
$595$	−13035.3	−0.898140
$596$	2619.27	0.180016
$597$	3948.46	0.270686
$598$	16201.6	1.10792
$599$	−17691.4	−1.20676	−0.603380	−	0.797454i	$-0.706180\pi$
$599$	−17691.4	−1.20676	−0.603380	+	0.797454i	$0.706180\pi$
$600$	18810.7	1.27991
$601$	−24516.1	−1.66394	−0.831972	−	0.554817i	$-0.812788\pi$
$601$	−24516.1	−1.66394	−0.831972	+	0.554817i	$0.812788\pi$
$602$	−3424.26	−0.231831
$603$	246.719	0.0166620
$604$	−7069.56	−0.476252
$605$	2358.18	0.158469
$606$	−5280.12	−0.353944
$607$	4288.59	0.286768	0.143384	−	0.989667i	$-0.454202\pi$
$607$	4288.59	0.286768	0.143384	+	0.989667i	$0.454202\pi$
$608$	−2553.94	−0.170355
$609$	−427.435	−0.0284410
$610$	18615.6	1.23561
$611$	−6455.74	−0.427449
$612$	2117.30	0.139848
$613$	−8124.07	−0.535283	−0.267641	−	0.963519i	$-0.586244\pi$
$613$	−8124.07	−0.535283	−0.267641	+	0.963519i	$0.586244\pi$
$614$	20029.3	1.31648
$615$	−14777.3	−0.968908
$616$	1825.52	0.119403
$617$	−14923.1	−0.973714	−0.486857	−	0.873482i	$-0.661857\pi$
$617$	−14923.1	−0.973714	−0.486857	+	0.873482i	$0.661857\pi$
$618$	−2774.41	−0.180588
$619$	3627.68	0.235556	0.117778	−	0.993040i	$-0.462423\pi$
$619$	3627.68	0.235556	0.117778	+	0.993040i	$0.462423\pi$
$620$	14735.5	0.954501
$621$	3024.00	0.195409
$622$	−10549.9	−0.680087
$623$	3122.88	0.200827
$624$	7206.54	0.462328
$625$	17458.0	1.11731
$626$	−15374.2	−0.981589
$627$	815.135	0.0519192
$628$	−6748.36	−0.428804
$629$	14913.0	0.945341
$630$	−2806.43	−0.177478
$631$	12576.5	0.793445	0.396723	−	0.917939i	$-0.370147\pi$
$631$	12576.5	0.793445	0.396723	+	0.917939i	$0.370147\pi$
$632$	2400.28	0.151073
$633$	−5207.27	−0.326967
$634$	2971.87	0.186164
$635$	44878.5	2.80464
$636$	−2317.61	−0.144496
$637$	18141.7	1.12841
$638$	551.257	0.0342077
$639$	−2704.50	−0.167431
$640$	−9790.36	−0.604685
$641$	−7292.77	−0.449371	−0.224686	−	0.974431i	$-0.572136\pi$
$641$	−7292.77	−0.449371	−0.224686	+	0.974431i	$0.572136\pi$
$642$	−10948.7	−0.673071
$643$	−12946.3	−0.794016	−0.397008	−	0.917815i	$-0.629951\pi$
$643$	−12946.3	−0.794016	−0.397008	+	0.917815i	$0.629951\pi$
$644$	−1792.00	−0.109650
$645$	12513.0	0.763872
$646$	5811.06	0.353921
$647$	21973.3	1.33518	0.667589	−	0.744530i	$-0.267327\pi$
$647$	21973.3	1.33518	0.667589	+	0.744530i	$0.267327\pi$
$648$	1993.08	0.120827
$649$	2156.00	0.130401
$650$	36862.5	2.22441
$651$	−6448.83	−0.388248
$652$	3626.06	0.217803
$653$	−27495.6	−1.64776	−0.823880	−	0.566764i	$-0.808195\pi$
$653$	−27495.6	−1.64776	−0.823880	+	0.566764i	$0.808195\pi$
$654$	−5549.59	−0.331814
$655$	−39379.5	−2.34913
$656$	9956.63	0.592593
$657$	3850.33	0.228639
$658$	−1693.91	−0.100358
$659$	5156.28	0.304796	0.152398	−	0.988319i	$-0.451301\pi$
$659$	5156.28	0.304796	0.152398	+	0.988319i	$0.451301\pi$
$660$	−1525.71	−0.0899822
$661$	9328.59	0.548926	0.274463	−	0.961598i	$-0.411500\pi$
$661$	9328.59	0.548926	0.274463	+	0.961598i	$0.411500\pi$
$662$	−9018.10	−0.529454
$663$	18141.4	1.06267
$664$	27180.2	1.58855
$665$	3246.85	0.189334
$666$	3210.70	0.186805
$667$	−2365.99	−0.137349
$668$	910.673	0.0527470
$669$	4991.12	0.288442
$670$	−1267.42	−0.0730814
$671$	−4429.06	−0.254816
$672$	−2092.04	−0.120093
$673$	22182.4	1.27053	0.635267	−	0.772293i	$-0.280890\pi$
$673$	22182.4	1.27053	0.635267	+	0.772293i	$0.280890\pi$
$674$	12944.4	0.739764
$675$	6880.30	0.392330
$676$	−3609.06	−0.205340
$677$	−13507.1	−0.766797	−0.383399	−	0.923583i	$-0.625246\pi$
$677$	−13507.1	−0.766797	−0.383399	+	0.923583i	$0.625246\pi$
$678$	10778.8	0.610559
$679$	−12129.1	−0.685528
$680$	−47556.1	−2.68190
$681$	−10976.5	−0.617652
$682$	8316.96	0.466969
$683$	−19465.6	−1.09053	−0.545264	−	0.838264i	$-0.683571\pi$
$683$	−19465.6	−1.09053	−0.545264	+	0.838264i	$0.683571\pi$
$684$	−527.381	−0.0294809
$685$	28754.3	1.60386
$686$	10248.2	0.570375
$687$	5781.22	0.321059
$688$	−8430.96	−0.467191
$689$	−19857.7	−1.09799
$690$	−15534.5	−0.857086
$691$	−19971.8	−1.09951	−0.549757	−	0.835324i	$-0.685280\pi$
$691$	−19971.8	−1.09951	−0.549757	+	0.835324i	$0.685280\pi$
$692$	−6411.93	−0.352233
$693$	667.712	0.0366007
$694$	10059.7	0.550234
$695$	−31644.7	−1.72713
$696$	−1559.40	−0.0849265
$697$	25064.3	1.36209
$698$	20096.9	1.08980
$699$	−8352.80	−0.451977
$700$	−4077.22	−0.220149
$701$	−14180.1	−0.764018	−0.382009	−	0.924159i	$-0.624768\pi$
$701$	−14180.1	−0.764018	−0.382009	+	0.924159i	$0.624768\pi$
$702$	3905.75	0.209990
$703$	−3714.56	−0.199285
$704$	6164.75	0.330032
$705$	6189.91	0.330675
$706$	−2327.88	−0.124095
$707$	5003.91	0.266183
$708$	−1394.90	−0.0740446
$709$	15870.6	0.840667	0.420334	−	0.907370i	$-0.361913\pi$
$709$	15870.6	0.840667	0.420334	+	0.907370i	$0.361913\pi$
$710$	13893.2	0.734370
$711$	877.939	0.0463084
$712$	11393.1	0.599683
$713$	−35696.3	−1.87495
$714$	4760.09	0.249498
$715$	−13072.5	−0.683756
$716$	6589.27	0.343928
$717$	3667.79	0.191041
$718$	7164.50	0.372391
$719$	−6040.05	−0.313290	−0.156645	−	0.987655i	$-0.550068\pi$
$719$	−6040.05	−0.313290	−0.156645	+	0.987655i	$0.550068\pi$
$720$	−6909.80	−0.357657
$721$	2629.28	0.135811
$722$	14824.0	0.764119
$723$	−6039.03	−0.310642
$724$	9473.96	0.486322
$725$	−5383.18	−0.275761
$726$	−861.138	−0.0440218
$727$	37252.3	1.90043	0.950213	−	0.311601i	$-0.100865\pi$
$727$	37252.3	1.90043	0.950213	+	0.311601i	$0.100865\pi$
$728$	−10119.7	−0.515196
$729$	729.000	0.0370370
$730$	−19779.5	−1.00284
$731$	−21223.7	−1.07385
$732$	2865.54	0.144690
$733$	6125.52	0.308665	0.154332	−	0.988019i	$-0.450677\pi$
$733$	6125.52	0.308665	0.154332	+	0.988019i	$0.450677\pi$
$734$	−20613.7	−1.03660
$735$	−17394.7	−0.872942
$736$	−11580.1	−0.579958
$737$	301.546	0.0150713
$738$	5396.23	0.269157
$739$	−5225.97	−0.260136	−0.130068	−	0.991505i	$-0.541520\pi$
$739$	−5225.97	−0.260136	−0.130068	+	0.991505i	$0.541520\pi$
$740$	6952.64	0.345384
$741$	−4518.68	−0.224019
$742$	−5210.43	−0.257791
$743$	7062.96	0.348741	0.174371	−	0.984680i	$-0.444211\pi$
$743$	7062.96	0.348741	0.174371	+	0.984680i	$0.444211\pi$
$744$	−23527.0	−1.15933
$745$	−21518.2	−1.05821
$746$	−12669.2	−0.621788
$747$	9941.57	0.486939
$748$	2587.81	0.126497
$749$	10376.0	0.506182
$750$	−18007.0	−0.876697
$751$	−20755.4	−1.00849	−0.504244	−	0.863561i	$-0.668229\pi$
$751$	−20755.4	−1.00849	−0.504244	+	0.863561i	$0.668229\pi$
$752$	−4170.63	−0.202243
$753$	8119.89	0.392968
$754$	−3055.88	−0.147598
$755$	58079.0	2.79962
$756$	−432.000	−0.0207827
$757$	31182.9	1.49717	0.748587	−	0.663037i	$-0.230733\pi$
$757$	31182.9	1.49717	0.748587	+	0.663037i	$0.230733\pi$
$758$	3803.93	0.182276
$759$	3696.00	0.176754
$760$	11845.4	0.565364
$761$	32047.8	1.52659	0.763293	−	0.646052i	$-0.223581\pi$
$761$	32047.8	1.52659	0.763293	+	0.646052i	$0.223581\pi$
$762$	−16388.3	−0.779114
$763$	5259.29	0.249540
$764$	−2124.58	−0.100608
$765$	−17394.4	−0.822084
$766$	1969.55	0.0929019
$767$	−11951.7	−0.562650
$768$	−9875.22	−0.463986
$769$	2215.88	0.103910	0.0519548	−	0.998649i	$-0.483455\pi$
$769$	2215.88	0.103910	0.0519548	+	0.998649i	$0.483455\pi$
$770$	−3430.09	−0.160535
$771$	677.223	0.0316337
$772$	−3150.96	−0.146898
$773$	5300.56	0.246634	0.123317	−	0.992367i	$-0.460647\pi$
$773$	5300.56	0.246634	0.123317	+	0.992367i	$0.460647\pi$
$774$	−4569.36	−0.212199
$775$	−81217.4	−3.76441
$776$	−44250.3	−2.04703
$777$	−3042.75	−0.140487
$778$	4142.29	0.190885
$779$	−6243.06	−0.287138
$780$	8457.75	0.388251
$781$	−3305.50	−0.151447
$782$	26348.6	1.20489
$783$	−570.373	−0.0260325
$784$	11720.2	0.533899
$785$	55440.2	2.52069
$786$	14380.2	0.652576
$787$	34374.1	1.55693	0.778466	−	0.627687i	$-0.215998\pi$
$787$	34374.1	1.55693	0.778466	+	0.627687i	$0.215998\pi$
$788$	−365.602	−0.0165280
$789$	5860.27	0.264425
$790$	−4510.04	−0.203114
$791$	−10215.0	−0.459170
$792$	2435.99	0.109292
$793$	24552.4	1.09947
$794$	23761.2	1.06203
$795$	19040.0	0.849409
$796$	−3122.28	−0.139028
$797$	29867.1	1.32741	0.663707	−	0.747993i	$-0.268982\pi$
$797$	29867.1	1.32741	0.663707	+	0.747993i	$0.268982\pi$
$798$	−1185.65	−0.0525960
$799$	−10498.9	−0.464862
$800$	−26347.5	−1.16441
$801$	4167.20	0.183821
$802$	−19520.0	−0.859447
$803$	4705.96	0.206812
$804$	−195.096	−0.00855783
$805$	14721.9	0.644570
$806$	−46104.9	−2.01486
$807$	−1052.54	−0.0459124
$808$	18255.6	0.794839
$809$	−15857.2	−0.689133	−0.344566	−	0.938762i	$-0.611974\pi$
$809$	−15857.2	−0.689133	−0.344566	+	0.938762i	$0.611974\pi$
$810$	−3744.93	−0.162449
$811$	36122.6	1.56404	0.782020	−	0.623253i	$-0.214189\pi$
$811$	36122.6	1.56404	0.782020	+	0.623253i	$0.214189\pi$
$812$	337.999	0.0146077
$813$	764.337	0.0329723
$814$	3924.19	0.168971
$815$	−29789.3	−1.28034
$816$	11719.9	0.502794
$817$	5286.43	0.226375
$818$	29206.4	1.24838
$819$	−3701.44	−0.157923
$820$	11685.3	0.497645
$821$	25779.6	1.09588	0.547938	−	0.836519i	$-0.315413\pi$
$821$	25779.6	1.09588	0.547938	+	0.836519i	$0.315413\pi$
$822$	−10500.2	−0.445544
$823$	−22130.2	−0.937315	−0.468658	−	0.883380i	$-0.655262\pi$
$823$	−22130.2	−0.937315	−0.468658	+	0.883380i	$0.655262\pi$
$824$	9592.32	0.405539
$825$	8409.26	0.354876
$826$	−3136.00	−0.132101
$827$	18288.6	0.768994	0.384497	−	0.923126i	$-0.374375\pi$
$827$	18288.6	0.768994	0.384497	+	0.923126i	$0.374375\pi$
$828$	−2391.26	−0.100365
$829$	−34956.6	−1.46453	−0.732263	−	0.681022i	$-0.761536\pi$
$829$	−34956.6	−1.46453	−0.732263	+	0.681022i	$0.761536\pi$
$830$	−51070.6	−2.13577
$831$	349.435	0.0145870
$832$	−34174.2	−1.42401
$833$	29503.7	1.22718
$834$	11555.7	0.479786
$835$	−7481.50	−0.310069
$836$	−644.577	−0.0266664
$837$	−8605.37	−0.355370
$838$	−31457.5	−1.29675
$839$	−14507.5	−0.596965	−0.298482	−	0.954415i	$-0.596480\pi$
$839$	−14507.5	−0.596965	−0.298482	+	0.954415i	$0.596480\pi$
$840$	9703.04	0.398556
$841$	−23942.7	−0.981702
$842$	14655.3	0.599829
$843$	24679.4	1.00831
$844$	4117.70	0.167935
$845$	29649.7	1.20708
$846$	−2260.37	−0.0918595
$847$	816.092	0.0331066
$848$	−12828.7	−0.519506
$849$	4684.55	0.189368
$850$	59949.2	2.41911
$851$	−16842.6	−0.678445
$852$	2138.61	0.0859948
$853$	−44146.9	−1.77205	−0.886027	−	0.463634i	$-0.846545\pi$
$853$	−44146.9	−1.77205	−0.886027	+	0.463634i	$0.846545\pi$
$854$	6442.26	0.258138
$855$	4332.62	0.173301
$856$	37854.4	1.51149
$857$	−47679.3	−1.90046	−0.950230	−	0.311549i	$-0.899152\pi$
$857$	−47679.3	−1.90046	−0.950230	+	0.311549i	$0.899152\pi$
$858$	4773.70	0.189943
$859$	7525.09	0.298897	0.149449	−	0.988769i	$-0.452250\pi$
$859$	7525.09	0.298897	0.149449	+	0.988769i	$0.452250\pi$
$860$	−9894.76	−0.392335
$861$	−5113.95	−0.202419
$862$	−3957.09	−0.156356
$863$	45816.1	1.80718	0.903591	−	0.428396i	$-0.140921\pi$
$863$	45816.1	1.80718	0.903591	+	0.428396i	$0.140921\pi$
$864$	−2791.64	−0.109923
$865$	52676.2	2.07057
$866$	1735.91	0.0681163
$867$	14764.1	0.578335
$868$	5099.48	0.199410
$869$	1073.04	0.0418876
$870$	2930.05	0.114182
$871$	−1671.61	−0.0650292
$872$	19187.3	0.745142
$873$	−16185.2	−0.627476
$874$	−6562.96	−0.253999
$875$	17065.1	0.659319
$876$	−3044.69	−0.117432
$877$	−34168.3	−1.31560	−0.657801	−	0.753192i	$-0.728513\pi$
$877$	−34168.3	−1.31560	−0.657801	+	0.753192i	$0.728513\pi$
$878$	33800.2	1.29920
$879$	28458.6	1.09202
$880$	−8445.31	−0.323513
$881$	−100.796	−0.00385460	−0.00192730	−	0.999998i	$-0.500613\pi$
$881$	−100.796	−0.00385460	−0.00192730	+	0.999998i	$0.500613\pi$
$882$	6352.02	0.242498
$883$	−12346.1	−0.470531	−0.235266	−	0.971931i	$-0.575596\pi$
$883$	−12346.1	−0.470531	−0.235266	+	0.971931i	$0.575596\pi$
$884$	−14345.5	−0.545803
$885$	11459.6	0.435266
$886$	−413.398	−0.0156754
$887$	−37345.1	−1.41367	−0.706834	−	0.707379i	$-0.749877\pi$
$887$	−37345.1	−1.41367	−0.706834	+	0.707379i	$0.749877\pi$
$888$	−11100.8	−0.419501
$889$	15531.0	0.585932
$890$	−21407.2	−0.806260
$891$	891.000	0.0335013
$892$	−3946.78	−0.148148
$893$	2615.09	0.0979962
$894$	7857.80	0.293964
$895$	−54133.2	−2.02176
$896$	−3388.13	−0.126328
$897$	−20488.7	−0.762651
$898$	−17720.9	−0.658523
$899$	6732.88	0.249782
$900$	−5440.67	−0.201506
$901$	−32294.4	−1.19410
$902$	6595.39	0.243462
$903$	4330.34	0.159584
$904$	−37267.1	−1.37111
$905$	−77831.9	−2.85881
$906$	−21208.7	−0.777717
$907$	10308.6	0.377390	0.188695	−	0.982036i	$-0.439574\pi$
$907$	10308.6	0.377390	0.188695	+	0.982036i	$0.439574\pi$
$908$	8679.79	0.317235
$909$	6677.26	0.243642
$910$	19014.6	0.692668
$911$	−22590.8	−0.821589	−0.410795	−	0.911728i	$-0.634749\pi$
$911$	−22590.8	−0.821589	−0.410795	+	0.911728i	$0.634749\pi$
$912$	−2919.22	−0.105992
$913$	12150.8	0.440453
$914$	−20787.5	−0.752288
$915$	−23541.4	−0.850551
$916$	−4571.56	−0.164900
$917$	−13628.0	−0.490769
$918$	6351.90	0.228370
$919$	47712.1	1.71260	0.856299	−	0.516481i	$-0.172758\pi$
$919$	47712.1	1.71260	0.856299	+	0.516481i	$0.172758\pi$
$920$	53709.5	1.92473
$921$	−25329.2	−0.906216
$922$	−10294.9	−0.367728
$923$	18323.9	0.653456
$924$	−528.000	−0.0187986
$925$	−38320.8	−1.36214
$926$	9328.96	0.331068
$927$	3508.53	0.124310
$928$	2184.19	0.0772625
$929$	10714.3	0.378391	0.189196	−	0.981939i	$-0.439412\pi$
$929$	10714.3	0.378391	0.189196	+	0.981939i	$0.439412\pi$
$930$	44206.4	1.55869
$931$	−7348.84	−0.258699
$932$	6605.06	0.232142
$933$	13341.5	0.468148
$934$	19889.1	0.696780
$935$	−21259.8	−0.743603
$936$	−13503.9	−0.471568
$937$	−14719.5	−0.513197	−0.256599	−	0.966518i	$-0.582602\pi$
$937$	−14719.5	−0.513197	−0.256599	+	0.966518i	$0.582602\pi$
$938$	−438.612	−0.0152678
$939$	19442.2	0.675691
$940$	−4894.74	−0.169839
$941$	3694.44	0.127987	0.0639933	−	0.997950i	$-0.479616\pi$
$941$	3694.44	0.127987	0.0639933	+	0.997950i	$0.479616\pi$
$942$	−20245.1	−0.700234
$943$	−28307.4	−0.977535
$944$	−7721.23	−0.266213
$945$	3549.03	0.122169
$946$	−5584.77	−0.191941
$947$	36416.7	1.24961	0.624806	−	0.780780i	$-0.285178\pi$
$947$	36416.7	1.24961	0.624806	+	0.780780i	$0.285178\pi$
$948$	−694.240	−0.0237847
$949$	−26087.4	−0.892342
$950$	−14932.3	−0.509965
$951$	−3758.25	−0.128149
$952$	−16457.6	−0.560289
$953$	20779.4	0.706306	0.353153	−	0.935566i	$-0.385110\pi$
$953$	20779.4	0.706306	0.353153	+	0.935566i	$0.385110\pi$
$954$	−6952.84	−0.235961
$955$	17454.2	0.591419
$956$	−2900.35	−0.0981212
$957$	−697.123	−0.0235473
$958$	−22617.6	−0.762777
$959$	9950.94	0.335071
$960$	32767.0	1.10161
$961$	71789.7	2.40978
$962$	−21753.7	−0.729071
$963$	13845.8	0.463318
$964$	4775.43	0.159550
$965$	25886.2	0.863531
$966$	−5376.00	−0.179058
$967$	56812.8	1.88932	0.944662	−	0.328044i	$-0.106389\pi$
$967$	56812.8	1.88932	0.944662	+	0.328044i	$0.106389\pi$
$968$	2977.32	0.0988582
$969$	−7348.70	−0.243627
$970$	83144.7	2.75218
$971$	−26459.7	−0.874493	−0.437247	−	0.899342i	$-0.644046\pi$
$971$	−26459.7	−0.874493	−0.437247	+	0.899342i	$0.644046\pi$
$972$	−576.464	−0.0190227
$973$	−10951.2	−0.360822
$974$	−10559.2	−0.347371
$975$	−46616.5	−1.53120
$976$	15861.7	0.520204
$977$	−21009.2	−0.687967	−0.343984	−	0.938976i	$-0.611776\pi$
$977$	−21009.2	−0.687967	−0.343984	+	0.938976i	$0.611776\pi$
$978$	10878.2	0.355670
$979$	5093.24	0.166272
$980$	13755.0	0.448355
$981$	7018.04	0.228409
$982$	23147.3	0.752199
$983$	−9076.80	−0.294512	−0.147256	−	0.989098i	$-0.547044\pi$
$983$	−9076.80	−0.294512	−0.147256	+	0.989098i	$0.547044\pi$
$984$	−18657.1	−0.604437
$985$	3003.55	0.0971585
$986$	−4969.76	−0.160517
$987$	2142.13	0.0690828
$988$	3573.20	0.115059
$989$	23969.8	0.770673
$990$	−4577.14	−0.146940
$991$	2629.24	0.0842791	0.0421395	−	0.999112i	$-0.486583\pi$
$991$	2629.24	0.0842791	0.0421395	+	0.999112i	$0.486583\pi$
$992$	32953.5	1.05471
$993$	11404.3	0.364457
$994$	4808.00	0.153421
$995$	25650.6	0.817267
$996$	−7861.40	−0.250098
$997$	−50423.9	−1.60175	−0.800874	−	0.598833i	$-0.795631\pi$
$997$	−50423.9	−1.60175	−0.800874	+	0.598833i	$0.795631\pi$
$998$	17018.0	0.539775
$999$	−4060.27	−0.128590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.a.d.1.1	✓	2
3.2	odd	2		99.4.a.e.1.2		2
4.3	odd	2		528.4.a.o.1.2		2
5.2	odd	4		825.4.c.i.199.2		4
5.3	odd	4		825.4.c.i.199.3		4
5.4	even	2		825.4.a.k.1.2		2
7.6	odd	2		1617.4.a.j.1.1		2
8.3	odd	2		2112.4.a.bh.1.1		2
8.5	even	2		2112.4.a.ba.1.1		2
11.10	odd	2		363.4.a.j.1.2		2
12.11	even	2		1584.4.a.x.1.1		2
15.14	odd	2		2475.4.a.o.1.1		2
33.32	even	2		1089.4.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.a.d.1.1	✓	2	1.1	even	1	trivial
99.4.a.e.1.2		2	3.2	odd	2
363.4.a.j.1.2		2	11.10	odd	2
528.4.a.o.1.2		2	4.3	odd	2
825.4.a.k.1.2		2	5.4	even	2
825.4.c.i.199.2		4	5.2	odd	4
825.4.c.i.199.3		4	5.3	odd	4
1089.4.a.t.1.1		2	33.32	even	2
1584.4.a.x.1.1		2	12.11	even	2
1617.4.a.j.1.1		2	7.6	odd	2
2112.4.a.ba.1.1		2	8.5	even	2
2112.4.a.bh.1.1		2	8.3	odd	2
2475.4.a.o.1.1		2	15.14	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37228 q^{2} +3.00000 q^{3} -2.37228 q^{4} +19.4891 q^{5} -7.11684 q^{6} +6.74456 q^{7} +24.6060 q^{8} +9.00000 q^{9} -46.2337 q^{10} +11.0000 q^{11} -7.11684 q^{12} -60.9783 q^{13} -16.0000 q^{14} +58.4674 q^{15} -39.3940 q^{16} -99.1684 q^{17} -21.3505 q^{18} +24.7011 q^{19} -46.2337 q^{20} +20.2337 q^{21} -26.0951 q^{22} +112.000 q^{23} +73.8179 q^{24} +254.826 q^{25} +144.658 q^{26} +27.0000 q^{27} -16.0000 q^{28} -21.1249 q^{29} -138.701 q^{30} -318.717 q^{31} -103.394 q^{32} +33.0000 q^{33} +235.255 q^{34} +131.446 q^{35} -21.3505 q^{36} -150.380 q^{37} -58.5979 q^{38} -182.935 q^{39} +479.549 q^{40} -252.745 q^{41} -48.0000 q^{42} +214.016 q^{43} -26.0951 q^{44} +175.402 q^{45} -265.696 q^{46} +105.870 q^{47} -118.182 q^{48} -297.511 q^{49} -604.519 q^{50} -297.505 q^{51} +144.658 q^{52} +325.652 q^{53} -64.0516 q^{54} +214.380 q^{55} +165.957 q^{56} +74.1032 q^{57} +50.1143 q^{58} +196.000 q^{59} -138.701 q^{60} -402.641 q^{61} +756.087 q^{62} +60.7011 q^{63} +560.432 q^{64} -1188.41 q^{65} -78.2853 q^{66} +27.4132 q^{67} +235.255 q^{68} +336.000 q^{69} -311.826 q^{70} -300.500 q^{71} +221.454 q^{72} +427.815 q^{73} +356.745 q^{74} +764.478 q^{75} -58.5979 q^{76} +74.1902 q^{77} +433.973 q^{78} +97.5488 q^{79} -767.755 q^{80} +81.0000 q^{81} +599.581 q^{82} +1104.62 q^{83} -48.0000 q^{84} -1932.71 q^{85} -507.707 q^{86} -63.3748 q^{87} +270.666 q^{88} +463.022 q^{89} -416.103 q^{90} -411.272 q^{91} -265.696 q^{92} -956.152 q^{93} -251.152 q^{94} +481.402 q^{95} -310.182 q^{96} -1798.36 q^{97} +705.779 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 6 q^{3} + q^{4} + 16 q^{5} + 3 q^{6} + 2 q^{7} + 9 q^{8} + 18 q^{9} - 58 q^{10} + 22 q^{11} + 3 q^{12} - 76 q^{13} - 32 q^{14} + 48 q^{15} - 119 q^{16} - 26 q^{17} + 9 q^{18} - 54 q^{19}+ \cdots + 198 q^{99}+O(q^{100}) \) 2 * q + q^2 + 6 * q^3 + q^4 + 16 * q^5 + 3 * q^6 + 2 * q^7 + 9 * q^8 + 18 * q^9 - 58 * q^10 + 22 * q^11 + 3 * q^12 - 76 * q^13 - 32 * q^14 + 48 * q^15 - 119 * q^16 - 26 * q^17 + 9 * q^18 - 54 * q^19 - 58 * q^20 + 6 * q^21 + 11 * q^22 + 224 * q^23 + 27 * q^24 + 142 * q^25 + 94 * q^26 + 54 * q^27 - 32 * q^28 + 222 * q^29 - 174 * q^30 - 40 * q^31 - 247 * q^32 + 66 * q^33 + 482 * q^34 + 148 * q^35 + 9 * q^36 - 48 * q^37 - 324 * q^38 - 228 * q^39 + 534 * q^40 - 494 * q^41 - 96 * q^42 - 66 * q^43 + 11 * q^44 + 144 * q^45 + 112 * q^46 - 64 * q^47 - 357 * q^48 - 618 * q^49 - 985 * q^50 - 78 * q^51 + 94 * q^52 - 84 * q^53 + 27 * q^54 + 176 * q^55 + 240 * q^56 - 162 * q^57 + 870 * q^58 + 392 * q^59 - 174 * q^60 - 1104 * q^61 + 1696 * q^62 + 18 * q^63 + 713 * q^64 - 1136 * q^65 + 33 * q^66 + 928 * q^67 + 482 * q^68 + 672 * q^69 - 256 * q^70 + 456 * q^71 + 81 * q^72 - 592 * q^73 + 702 * q^74 + 426 * q^75 - 324 * q^76 + 22 * q^77 + 282 * q^78 - 230 * q^79 - 490 * q^80 + 162 * q^81 - 214 * q^82 + 348 * q^83 - 96 * q^84 - 2188 * q^85 - 1452 * q^86 + 666 * q^87 + 99 * q^88 + 972 * q^89 - 522 * q^90 - 340 * q^91 + 112 * q^92 - 120 * q^93 - 824 * q^94 + 756 * q^95 - 741 * q^96 - 1184 * q^97 - 375 * q^98 + 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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