LMFDB - Embedded newform 322.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,4,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, 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("322.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.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:	$18.9986150218$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 42x^{2} + 26x + 46 $ x^4 - x^3 - 42x^2 + 26x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$6.60395$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -6.60395 q^{3} +4.00000 q^{4} -12.4950 q^{5} +13.2079 q^{6} +7.00000 q^{7} -8.00000 q^{8} +16.6122 q^{9} +24.9900 q^{10} -4.54973 q^{11} -26.4158 q^{12} +69.5312 q^{13} -14.0000 q^{14} +82.5162 q^{15} +16.0000 q^{16} +37.6339 q^{17} -33.2243 q^{18} -8.54171 q^{19} -49.9799 q^{20} -46.2277 q^{21} +9.09945 q^{22} -23.0000 q^{23} +52.8316 q^{24} +31.1246 q^{25} -139.062 q^{26} +68.6008 q^{27} +28.0000 q^{28} +83.9781 q^{29} -165.032 q^{30} +158.085 q^{31} -32.0000 q^{32} +30.0462 q^{33} -75.2679 q^{34} -87.4649 q^{35} +66.4486 q^{36} -107.560 q^{37} +17.0834 q^{38} -459.180 q^{39} +99.9599 q^{40} -311.205 q^{41} +92.4553 q^{42} -67.0402 q^{43} -18.1989 q^{44} -207.569 q^{45} +46.0000 q^{46} -527.877 q^{47} -105.663 q^{48} +49.0000 q^{49} -62.2491 q^{50} -248.533 q^{51} +278.125 q^{52} -279.451 q^{53} -137.202 q^{54} +56.8487 q^{55} -56.0000 q^{56} +56.4090 q^{57} -167.956 q^{58} -72.9596 q^{59} +330.065 q^{60} +439.464 q^{61} -316.169 q^{62} +116.285 q^{63} +64.0000 q^{64} -868.790 q^{65} -60.0923 q^{66} -290.182 q^{67} +150.536 q^{68} +151.891 q^{69} +174.930 q^{70} +18.6115 q^{71} -132.897 q^{72} -456.805 q^{73} +215.120 q^{74} -205.545 q^{75} -34.1669 q^{76} -31.8481 q^{77} +918.361 q^{78} -838.364 q^{79} -199.920 q^{80} -901.564 q^{81} +622.410 q^{82} +65.0265 q^{83} -184.911 q^{84} -470.235 q^{85} +134.080 q^{86} -554.587 q^{87} +36.3978 q^{88} +128.271 q^{89} +415.137 q^{90} +486.718 q^{91} -92.0000 q^{92} -1043.98 q^{93} +1055.75 q^{94} +106.729 q^{95} +211.326 q^{96} +903.996 q^{97} -98.0000 q^{98} -75.5808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 28 q^{7} - 32 q^{8} - 23 q^{9} + 4 q^{10} - 66 q^{11} - 4 q^{12} - 25 q^{13} - 56 q^{14} - 4 q^{15} + 64 q^{16} - 56 q^{17} + 46 q^{18} + 4 q^{19}+ \cdots - 108 q^{99}+O(q^{100}) $ 4 * q - 8 * q^2 - q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 28 * q^7 - 32 * q^8 - 23 * q^9 + 4 * q^10 - 66 * q^11 - 4 * q^12 - 25 * q^13 - 56 * q^14 - 4 * q^15 + 64 * q^16 - 56 * q^17 + 46 * q^18 + 4 * q^19 - 8 * q^20 - 7 * q^21 + 132 * q^22 - 92 * q^23 + 8 * q^24 + 104 * q^25 + 50 * q^26 + 5 * q^27 + 112 * q^28 - 109 * q^29 + 8 * q^30 - 119 * q^31 - 128 * q^32 - 132 * q^33 + 112 * q^34 - 14 * q^35 - 92 * q^36 - 134 * q^37 - 8 * q^38 - 299 * q^39 + 16 * q^40 - 557 * q^41 + 14 * q^42 + 60 * q^43 - 264 * q^44 - 836 * q^45 + 184 * q^46 - 699 * q^47 - 16 * q^48 + 196 * q^49 - 208 * q^50 - 532 * q^51 - 100 * q^52 - 1002 * q^53 - 10 * q^54 - 426 * q^55 - 224 * q^56 - 64 * q^57 + 218 * q^58 - 1482 * q^59 - 16 * q^60 - 132 * q^61 + 238 * q^62 - 161 * q^63 + 256 * q^64 - 2272 * q^65 + 264 * q^66 - 380 * q^67 - 224 * q^68 + 23 * q^69 + 28 * q^70 - 173 * q^71 + 184 * q^72 - 2107 * q^73 + 268 * q^74 - 785 * q^75 + 16 * q^76 - 462 * q^77 + 598 * q^78 - 2184 * q^79 - 32 * q^80 - 560 * q^81 + 1114 * q^82 - 152 * q^83 - 28 * q^84 + 388 * q^85 - 120 * q^86 - 1493 * q^87 + 528 * q^88 + 384 * q^89 + 1672 * q^90 - 175 * q^91 - 368 * q^92 - 1891 * q^93 + 1398 * q^94 - 440 * q^95 + 32 * q^96 + 2756 * q^97 - 392 * q^98 - 108 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−6.60395	−1.27093	−0.635465	−	0.772129i	$-0.719192\pi$
$3$	−6.60395	−1.27093	−0.635465	+	0.772129i	$0.719192\pi$
$4$	4.00000	0.500000
$5$	−12.4950	−1.11759	−0.558793	−	0.829307i	$-0.688735\pi$
$5$	−12.4950	−1.11759	−0.558793	+	0.829307i	$0.688735\pi$
$6$	13.2079	0.898684
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	16.6122	0.615265
$10$	24.9900	0.790252
$11$	−4.54973	−0.124709	−0.0623543	−	0.998054i	$-0.519861\pi$
$11$	−4.54973	−0.124709	−0.0623543	+	0.998054i	$0.519861\pi$
$12$	−26.4158	−0.635465
$13$	69.5312	1.48342	0.741710	−	0.670720i	$-0.234015\pi$
$13$	69.5312	1.48342	0.741710	+	0.670720i	$0.234015\pi$
$14$	−14.0000	−0.267261
$15$	82.5162	1.42037
$16$	16.0000	0.250000
$17$	37.6339	0.536916	0.268458	−	0.963291i	$-0.413486\pi$
$17$	37.6339	0.536916	0.268458	+	0.963291i	$0.413486\pi$
$18$	−33.2243	−0.435058
$19$	−8.54171	−0.103137	−0.0515685	−	0.998669i	$-0.516422\pi$
$19$	−8.54171	−0.103137	−0.0515685	+	0.998669i	$0.516422\pi$
$20$	−49.9799	−0.558793
$21$	−46.2277	−0.480367
$22$	9.09945	0.0881823
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	52.8316	0.449342
$25$	31.1246	0.248996
$26$	−139.062	−1.04894
$27$	68.6008	0.488971
$28$	28.0000	0.188982
$29$	83.9781	0.537736	0.268868	−	0.963177i	$-0.413351\pi$
$29$	83.9781	0.537736	0.268868	+	0.963177i	$0.413351\pi$
$30$	−165.032	−1.00436
$31$	158.085	0.915898	0.457949	−	0.888978i	$-0.348584\pi$
$31$	158.085	0.915898	0.457949	+	0.888978i	$0.348584\pi$
$32$	−32.0000	−0.176777
$33$	30.0462	0.158496
$34$	−75.2679	−0.379657
$35$	−87.4649	−0.422407
$36$	66.4486	0.307633
$37$	−107.560	−0.477912	−0.238956	−	0.971030i	$-0.576805\pi$
$37$	−107.560	−0.477912	−0.238956	+	0.971030i	$0.576805\pi$
$38$	17.0834	0.0729289
$39$	−459.180	−1.88533
$40$	99.9599	0.395126
$41$	−311.205	−1.18542	−0.592708	−	0.805417i	$-0.701941\pi$
$41$	−311.205	−1.18542	−0.592708	+	0.805417i	$0.701941\pi$
$42$	92.4553	0.339671
$43$	−67.0402	−0.237757	−0.118878	−	0.992909i	$-0.537930\pi$
$43$	−67.0402	−0.237757	−0.118878	+	0.992909i	$0.537930\pi$
$44$	−18.1989	−0.0623543
$45$	−207.569	−0.687611
$46$	46.0000	0.147442
$47$	−527.877	−1.63827	−0.819136	−	0.573600i	$-0.805546\pi$
$47$	−527.877	−1.63827	−0.819136	+	0.573600i	$0.805546\pi$
$48$	−105.663	−0.317733
$49$	49.0000	0.142857
$50$	−62.2491	−0.176067
$51$	−248.533	−0.682383
$52$	278.125	0.741710
$53$	−279.451	−0.724255	−0.362127	−	0.932129i	$-0.617949\pi$
$53$	−279.451	−0.724255	−0.362127	+	0.932129i	$0.617949\pi$
$54$	−137.202	−0.345755
$55$	56.8487	0.139372
$56$	−56.0000	−0.133631
$57$	56.4090	0.131080
$58$	−167.956	−0.380237
$59$	−72.9596	−0.160992	−0.0804960	−	0.996755i	$-0.525650\pi$
$59$	−72.9596	−0.160992	−0.0804960	+	0.996755i	$0.525650\pi$
$60$	330.065	0.710187
$61$	439.464	0.922419	0.461209	−	0.887291i	$-0.347416\pi$
$61$	439.464	0.922419	0.461209	+	0.887291i	$0.347416\pi$
$62$	−316.169	−0.647638
$63$	116.285	0.232548
$64$	64.0000	0.125000
$65$	−868.790	−1.65785
$66$	−60.0923	−0.112074
$67$	−290.182	−0.529126	−0.264563	−	0.964368i	$-0.585228\pi$
$67$	−290.182	−0.529126	−0.264563	+	0.964368i	$0.585228\pi$
$68$	150.536	0.268458
$69$	151.891	0.265007
$70$	174.930	0.298687
$71$	18.6115	0.0311095	0.0155548	−	0.999879i	$-0.495049\pi$
$71$	18.6115	0.0311095	0.0155548	+	0.999879i	$0.495049\pi$
$72$	−132.897	−0.217529
$73$	−456.805	−0.732397	−0.366198	−	0.930537i	$-0.619341\pi$
$73$	−456.805	−0.732397	−0.366198	+	0.930537i	$0.619341\pi$
$74$	215.120	0.337935
$75$	−205.545	−0.316457
$76$	−34.1669	−0.0515685
$77$	−31.8481	−0.0471354
$78$	918.361	1.33313
$79$	−838.364	−1.19397	−0.596983	−	0.802254i	$-0.703634\pi$
$79$	−838.364	−1.19397	−0.596983	+	0.802254i	$0.703634\pi$
$80$	−199.920	−0.279396
$81$	−901.564	−1.23671
$82$	622.410	0.838216
$83$	65.0265	0.0859950	0.0429975	−	0.999075i	$-0.486309\pi$
$83$	65.0265	0.0859950	0.0429975	+	0.999075i	$0.486309\pi$
$84$	−184.911	−0.240183
$85$	−470.235	−0.600049
$86$	134.080	0.168119
$87$	−554.587	−0.683425
$88$	36.3978	0.0440911
$89$	128.271	0.152772	0.0763861	−	0.997078i	$-0.475662\pi$
$89$	128.271	0.152772	0.0763861	+	0.997078i	$0.475662\pi$
$90$	415.137	0.486215
$91$	486.718	0.560680
$92$	−92.0000	−0.104257
$93$	−1043.98	−1.16404
$94$	1055.75	1.15843
$95$	106.729	0.115264
$96$	211.326	0.224671
$97$	903.996	0.946256	0.473128	−	0.880994i	$-0.343125\pi$
$97$	903.996	0.946256	0.473128	+	0.880994i	$0.343125\pi$
$98$	−98.0000	−0.101015
$99$	−75.5808	−0.0767288
$100$	124.498	0.124498
$101$	1157.64	1.14049	0.570245	−	0.821474i	$-0.306848\pi$
$101$	1157.64	1.14049	0.570245	+	0.821474i	$0.306848\pi$
$102$	497.065	0.482518
$103$	392.047	0.375044	0.187522	−	0.982260i	$-0.439954\pi$
$103$	392.047	0.375044	0.187522	+	0.982260i	$0.439954\pi$
$104$	−556.249	−0.524469
$105$	577.614	0.536851
$106$	558.901	0.512125
$107$	−1169.19	−1.05635	−0.528175	−	0.849135i	$-0.677124\pi$
$107$	−1169.19	−1.05635	−0.528175	+	0.849135i	$0.677124\pi$
$108$	274.403	0.244486
$109$	1001.00	0.879619	0.439809	−	0.898091i	$-0.355046\pi$
$109$	1001.00	0.879619	0.439809	+	0.898091i	$0.355046\pi$
$110$	−113.697	−0.0985512
$111$	710.321	0.607393
$112$	112.000	0.0944911
$113$	−1055.42	−0.878636	−0.439318	−	0.898332i	$-0.644780\pi$
$113$	−1055.42	−0.878636	−0.439318	+	0.898332i	$0.644780\pi$
$114$	−112.818	−0.0926876
$115$	287.385	0.233033
$116$	335.912	0.268868
$117$	1155.06	0.912697
$118$	145.919	0.113839
$119$	263.438	0.202935
$120$	−660.130	−0.502178
$121$	−1310.30	−0.984448
$122$	−878.927	−0.652249
$123$	2055.18	1.50658
$124$	632.339	0.457949
$125$	1172.97	0.839310
$126$	−232.570	−0.164437
$127$	−1801.28	−1.25857	−0.629283	−	0.777176i	$-0.716652\pi$
$127$	−1801.28	−1.25857	−0.629283	+	0.777176i	$0.716652\pi$
$128$	−128.000	−0.0883883
$129$	442.730	0.302172
$130$	1737.58	1.17228
$131$	−522.855	−0.348718	−0.174359	−	0.984682i	$-0.555785\pi$
$131$	−522.855	−0.348718	−0.174359	+	0.984682i	$0.555785\pi$
$132$	120.185	0.0792480
$133$	−59.7920	−0.0389821
$134$	580.365	0.374148
$135$	−857.165	−0.546467
$136$	−301.072	−0.189828
$137$	659.840	0.411489	0.205744	−	0.978606i	$-0.434038\pi$
$137$	659.840	0.411489	0.205744	+	0.978606i	$0.434038\pi$
$138$	−303.782	−0.187389
$139$	1486.78	0.907244	0.453622	−	0.891194i	$-0.350132\pi$
$139$	1486.78	0.907244	0.453622	+	0.891194i	$0.350132\pi$
$140$	−349.859	−0.211204
$141$	3486.07	2.08213
$142$	−37.2230	−0.0219978
$143$	−316.348	−0.184995
$144$	265.795	0.153816
$145$	−1049.30	−0.600965
$146$	913.610	0.517883
$147$	−323.594	−0.181562
$148$	−430.240	−0.238956
$149$	1290.59	0.709594	0.354797	−	0.934943i	$-0.384550\pi$
$149$	1290.59	0.709594	0.354797	+	0.934943i	$0.384550\pi$
$150$	411.090	0.223769
$151$	1644.17	0.886098	0.443049	−	0.896497i	$-0.353897\pi$
$151$	1644.17	0.886098	0.443049	+	0.896497i	$0.353897\pi$
$152$	68.3337	0.0364644
$153$	625.181	0.330346
$154$	63.6962	0.0333298
$155$	−1975.27	−1.02359
$156$	−1836.72	−0.942663
$157$	1164.70	0.592057	0.296029	−	0.955179i	$-0.404338\pi$
$157$	1164.70	0.592057	0.296029	+	0.955179i	$0.404338\pi$
$158$	1676.73	0.844262
$159$	1845.48	0.920478
$160$	399.839	0.197563
$161$	−161.000	−0.0788110
$162$	1803.13	0.874489
$163$	−3256.16	−1.56468	−0.782339	−	0.622853i	$-0.785974\pi$
$163$	−3256.16	−1.56468	−0.782339	+	0.622853i	$0.785974\pi$
$164$	−1244.82	−0.592708
$165$	−375.426	−0.177133
$166$	−130.053	−0.0608076
$167$	51.0032	0.0236332	0.0118166	−	0.999930i	$-0.496239\pi$
$167$	51.0032	0.0236332	0.0118166	+	0.999930i	$0.496239\pi$
$168$	369.821	0.169835
$169$	2637.58	1.20054
$170$	940.471	0.424299
$171$	−141.896	−0.0634566
$172$	−268.161	−0.118878
$173$	−1654.30	−0.727017	−0.363509	−	0.931591i	$-0.618421\pi$
$173$	−1654.30	−0.727017	−0.363509	+	0.931591i	$0.618421\pi$
$174$	1109.17	0.483254
$175$	217.872	0.0941118
$176$	−72.7956	−0.0311771
$177$	481.822	0.204610
$178$	−256.542	−0.108026
$179$	−2361.53	−0.986086	−0.493043	−	0.870005i	$-0.664115\pi$
$179$	−2361.53	−0.986086	−0.493043	+	0.870005i	$0.664115\pi$
$180$	−830.275	−0.343806
$181$	2.78442	0.00114345	0.000571724	−	1.00000i	$-0.499818\pi$
$181$	2.78442	0.00114345	0.000571724		1.00000i	$0.499818\pi$
$182$	−973.436	−0.396461
$183$	−2902.20	−1.17233
$184$	184.000	0.0737210
$185$	1343.96	0.534108
$186$	2087.97	0.823103
$187$	−171.224	−0.0669580
$188$	−2111.51	−0.819136
$189$	480.205	0.184814
$190$	−213.457	−0.0815042
$191$	−4766.45	−1.80570	−0.902849	−	0.429958i	$-0.858528\pi$
$191$	−4766.45	−1.80570	−0.902849	+	0.429958i	$0.858528\pi$
$192$	−422.653	−0.158866
$193$	−1845.15	−0.688169	−0.344084	−	0.938939i	$-0.611811\pi$
$193$	−1845.15	−0.688169	−0.344084	+	0.938939i	$0.611811\pi$
$194$	−1807.99	−0.669104
$195$	5737.45	2.10701
$196$	196.000	0.0714286
$197$	−252.367	−0.0912710	−0.0456355	−	0.998958i	$-0.514531\pi$
$197$	−252.367	−0.0912710	−0.0456355	+	0.998958i	$0.514531\pi$
$198$	151.162	0.0542555
$199$	−2685.75	−0.956722	−0.478361	−	0.878163i	$-0.658769\pi$
$199$	−2685.75	−0.956722	−0.478361	+	0.878163i	$0.658769\pi$
$200$	−248.996	−0.0880335
$201$	1916.35	0.672482
$202$	−2315.28	−0.806449
$203$	587.846	0.203245
$204$	−994.131	−0.341192
$205$	3888.50	1.32480
$206$	−784.093	−0.265196
$207$	−382.080	−0.128292
$208$	1112.50	0.370855
$209$	38.8625	0.0128621
$210$	−1155.23	−0.379611
$211$	−3654.66	−1.19240	−0.596202	−	0.802834i	$-0.703324\pi$
$211$	−3654.66	−1.19240	−0.596202	+	0.802834i	$0.703324\pi$
$212$	−1117.80	−0.362127
$213$	−122.909	−0.0395381
$214$	2338.37	0.746952
$215$	837.666	0.265713
$216$	−548.806	−0.172877
$217$	1106.59	0.346177
$218$	−2002.00	−0.621984
$219$	3016.72	0.930825
$220$	227.395	0.0696862
$221$	2616.73	0.796472
$222$	−1420.64	−0.429492
$223$	−6181.45	−1.85623	−0.928117	−	0.372288i	$-0.878573\pi$
$223$	−6181.45	−1.85623	−0.928117	+	0.372288i	$0.878573\pi$
$224$	−224.000	−0.0668153
$225$	517.046	0.153199
$226$	2110.85	0.621289
$227$	−6442.43	−1.88370	−0.941848	−	0.336038i	$-0.890913\pi$
$227$	−6442.43	−1.88370	−0.941848	+	0.336038i	$0.890913\pi$
$228$	225.636	0.0655400
$229$	2241.04	0.646691	0.323346	−	0.946281i	$-0.395192\pi$
$229$	2241.04	0.646691	0.323346	+	0.946281i	$0.395192\pi$
$230$	−574.769	−0.164779
$231$	210.323	0.0599058
$232$	−671.824	−0.190118
$233$	2393.50	0.672976	0.336488	−	0.941688i	$-0.390761\pi$
$233$	2393.50	0.672976	0.336488	+	0.941688i	$0.390761\pi$
$234$	−2310.13	−0.645374
$235$	6595.81	1.83091
$236$	−291.838	−0.0804960
$237$	5536.51	1.51745
$238$	−526.875	−0.143497
$239$	−1340.72	−0.362863	−0.181431	−	0.983404i	$-0.558073\pi$
$239$	−1340.72	−0.362863	−0.181431	+	0.983404i	$0.558073\pi$
$240$	1320.26	0.355093
$241$	4849.48	1.29619	0.648096	−	0.761558i	$-0.275565\pi$
$241$	4849.48	1.29619	0.648096	+	0.761558i	$0.275565\pi$
$242$	2620.60	0.696110
$243$	4101.67	1.08281
$244$	1757.85	0.461209
$245$	−612.254	−0.159655
$246$	−4110.37	−1.06531
$247$	−593.915	−0.152996
$248$	−1264.68	−0.323819
$249$	−429.432	−0.109294
$250$	−2345.94	−0.593482
$251$	5121.56	1.28793	0.643964	−	0.765056i	$-0.277289\pi$
$251$	5121.56	1.28793	0.643964	+	0.765056i	$0.277289\pi$
$252$	465.141	0.116274
$253$	104.644	0.0260035
$254$	3602.57	0.889941
$255$	3105.41	0.762621
$256$	256.000	0.0625000
$257$	−6432.43	−1.56126	−0.780631	−	0.624992i	$-0.785102\pi$
$257$	−6432.43	−1.56126	−0.780631	+	0.624992i	$0.785102\pi$
$258$	−885.460	−0.213668
$259$	−752.920	−0.180634
$260$	−3475.16	−0.828925
$261$	1395.06	0.330850
$262$	1045.71	0.246581
$263$	−4259.92	−0.998776	−0.499388	−	0.866378i	$-0.666442\pi$
$263$	−4259.92	−0.998776	−0.499388	+	0.866378i	$0.666442\pi$
$264$	−240.369	−0.0560368
$265$	3491.73	0.809416
$266$	119.584	0.0275645
$267$	−847.097	−0.194163
$268$	−1160.73	−0.264563
$269$	−5682.64	−1.28802	−0.644009	−	0.765018i	$-0.722730\pi$
$269$	−5682.64	−1.28802	−0.644009	+	0.765018i	$0.722730\pi$
$270$	1714.33	0.386411
$271$	−3835.26	−0.859688	−0.429844	−	0.902903i	$-0.641431\pi$
$271$	−3835.26	−0.859688	−0.429844	+	0.902903i	$0.641431\pi$
$272$	602.143	0.134229
$273$	−3214.26	−0.712586
$274$	−1319.68	−0.290966
$275$	−141.608	−0.0310520
$276$	607.563	0.132504
$277$	3210.70	0.696433	0.348217	−	0.937414i	$-0.386787\pi$
$277$	3210.70	0.696433	0.348217	+	0.937414i	$0.386787\pi$
$278$	−2973.56	−0.641518
$279$	2626.13	0.563520
$280$	699.719	0.149344
$281$	7147.06	1.51729	0.758644	−	0.651505i	$-0.225862\pi$
$281$	7147.06	1.51729	0.758644	+	0.651505i	$0.225862\pi$
$282$	−6972.14	−1.47229
$283$	−9010.23	−1.89259	−0.946294	−	0.323306i	$-0.895206\pi$
$283$	−9010.23	−1.89259	−0.946294	+	0.323306i	$0.895206\pi$
$284$	74.4459	0.0155548
$285$	−704.830	−0.146493
$286$	632.695	0.130811
$287$	−2178.44	−0.448045
$288$	−531.589	−0.108765
$289$	−3496.69	−0.711721
$290$	2098.61	0.424947
$291$	−5969.94	−1.20263
$292$	−1827.22	−0.366198
$293$	−5420.30	−1.08074	−0.540371	−	0.841427i	$-0.681716\pi$
$293$	−5420.30	−1.08074	−0.540371	+	0.841427i	$0.681716\pi$
$294$	647.187	0.128383
$295$	911.629	0.179922
$296$	860.480	0.168967
$297$	−312.115	−0.0609789
$298$	−2581.19	−0.501759
$299$	−1599.22	−0.309315
$300$	−822.180	−0.158229
$301$	−469.281	−0.0898635
$302$	−3288.34	−0.626566
$303$	−7645.00	−1.44948
$304$	−136.667	−0.0257843
$305$	−5491.09	−1.03088
$306$	−1250.36	−0.233590
$307$	1585.49	0.294751	0.147376	−	0.989081i	$-0.452917\pi$
$307$	1585.49	0.294751	0.147376	+	0.989081i	$0.452917\pi$
$308$	−127.392	−0.0235677
$309$	−2589.06	−0.476655
$310$	3950.53	0.723790
$311$	5198.07	0.947766	0.473883	−	0.880588i	$-0.342852\pi$
$311$	5198.07	0.947766	0.473883	+	0.880588i	$0.342852\pi$
$312$	3673.44	0.666563
$313$	−9254.83	−1.67129	−0.835645	−	0.549269i	$-0.814906\pi$
$313$	−9254.83	−1.67129	−0.835645	+	0.549269i	$0.814906\pi$
$314$	−2329.40	−0.418648
$315$	−1452.98	−0.259893
$316$	−3353.46	−0.596983
$317$	−2329.84	−0.412798	−0.206399	−	0.978468i	$-0.566174\pi$
$317$	−2329.84	−0.412798	−0.206399	+	0.978468i	$0.566174\pi$
$318$	−3690.96	−0.650876
$319$	−382.077	−0.0670602
$320$	−799.679	−0.139698
$321$	7721.25	1.34255
$322$	322.000	0.0557278
$323$	−321.458	−0.0553759
$324$	−3606.26	−0.618357
$325$	2164.13	0.369367
$326$	6512.33	1.10639
$327$	−6610.56	−1.11793
$328$	2489.64	0.419108
$329$	−3695.14	−0.619208
$330$	750.853	0.125252
$331$	−4025.17	−0.668408	−0.334204	−	0.942501i	$-0.608467\pi$
$331$	−4025.17	−0.668408	−0.334204	+	0.942501i	$0.608467\pi$
$332$	260.106	0.0429975
$333$	−1786.80	−0.294043
$334$	−102.006	−0.0167112
$335$	3625.82	0.591343
$336$	−739.642	−0.120092
$337$	466.579	0.0754189	0.0377095	−	0.999289i	$-0.487994\pi$
$337$	466.579	0.0754189	0.0377095	+	0.999289i	$0.487994\pi$
$338$	−5275.16	−0.848908
$339$	6969.96	1.11669
$340$	−1880.94	−0.300025
$341$	−719.242	−0.114220
$342$	283.793	0.0448706
$343$	343.000	0.0539949
$344$	536.321	0.0840596
$345$	−1897.87	−0.296168
$346$	3308.60	0.514079
$347$	11083.8	1.71473	0.857363	−	0.514711i	$-0.172101\pi$
$347$	11083.8	1.71473	0.857363	+	0.514711i	$0.172101\pi$
$348$	−2218.35	−0.341712
$349$	4958.34	0.760499	0.380249	−	0.924884i	$-0.375838\pi$
$349$	4958.34	0.760499	0.380249	+	0.924884i	$0.375838\pi$
$350$	−435.744	−0.0665471
$351$	4769.89	0.725350
$352$	145.591	0.0220456
$353$	−2135.45	−0.321979	−0.160990	−	0.986956i	$-0.551469\pi$
$353$	−2135.45	−0.321979	−0.160990	+	0.986956i	$0.551469\pi$
$354$	−963.643	−0.144681
$355$	−232.550	−0.0347675
$356$	513.085	0.0763861
$357$	−1739.73	−0.257917
$358$	4723.07	0.697268
$359$	4260.14	0.626299	0.313150	−	0.949704i	$-0.398616\pi$
$359$	4260.14	0.626299	0.313150	+	0.949704i	$0.398616\pi$
$360$	1660.55	0.243107
$361$	−6786.04	−0.989363
$362$	−5.56883	−0.000808540 0
$363$	8653.16	1.25117
$364$	1946.87	0.280340
$365$	5707.77	0.818516
$366$	5804.39	0.828963
$367$	213.711	0.0303968	0.0151984	−	0.999884i	$-0.495162\pi$
$367$	213.711	0.0303968	0.0151984	+	0.999884i	$0.495162\pi$
$368$	−368.000	−0.0521286
$369$	−5169.79	−0.729345
$370$	−2687.92	−0.377671
$371$	−1956.15	−0.273743
$372$	−4175.93	−0.582022
$373$	6927.85	0.961691	0.480845	−	0.876805i	$-0.340330\pi$
$373$	6927.85	0.961691	0.480845	+	0.876805i	$0.340330\pi$
$374$	342.448	0.0473465
$375$	−7746.25	−1.06671
$376$	4223.01	0.579216
$377$	5839.09	0.797688
$378$	−960.411	−0.130683
$379$	9270.50	1.25645	0.628224	−	0.778033i	$-0.283782\pi$
$379$	9270.50	1.25645	0.628224	+	0.778033i	$0.283782\pi$
$380$	426.914	0.0576322
$381$	11895.6	1.59955
$382$	9532.90	1.27682
$383$	−6499.04	−0.867064	−0.433532	−	0.901138i	$-0.642733\pi$
$383$	−6499.04	−0.867064	−0.433532	+	0.901138i	$0.642733\pi$
$384$	845.306	0.112335
$385$	397.941	0.0526778
$386$	3690.29	0.486609
$387$	−1113.68	−0.146283
$388$	3615.98	0.473128
$389$	−3776.36	−0.492208	−0.246104	−	0.969243i	$-0.579150\pi$
$389$	−3776.36	−0.492208	−0.246104	+	0.969243i	$0.579150\pi$
$390$	−11474.9	−1.48988
$391$	−865.581	−0.111955
$392$	−392.000	−0.0505076
$393$	3452.91	0.443196
$394$	504.734	0.0645384
$395$	10475.3	1.33436
$396$	−302.323	−0.0383644
$397$	11250.4	1.42227	0.711137	−	0.703053i	$-0.248180\pi$
$397$	11250.4	1.42227	0.711137	+	0.703053i	$0.248180\pi$
$398$	5371.50	0.676505
$399$	394.863	0.0495436
$400$	497.993	0.0622491
$401$	−10381.8	−1.29288	−0.646438	−	0.762966i	$-0.723742\pi$
$401$	−10381.8	−1.29288	−0.646438	+	0.762966i	$0.723742\pi$
$402$	−3832.70	−0.475517
$403$	10991.8	1.35866
$404$	4630.56	0.570245
$405$	11265.0	1.38213
$406$	−1175.69	−0.143716
$407$	489.368	0.0595997
$408$	1988.26	0.241259
$409$	−25.0944	−0.00303384	−0.00151692	−	0.999999i	$-0.500483\pi$
$409$	−25.0944	−0.00303384	−0.00151692	+	0.999999i	$0.500483\pi$
$410$	−7777.00	−0.936778
$411$	−4357.55	−0.522974
$412$	1568.19	0.187522
$413$	−510.717	−0.0608493
$414$	764.159	0.0907159
$415$	−812.505	−0.0961067
$416$	−2225.00	−0.262234
$417$	−9818.61	−1.15304
$418$	−77.7249	−0.00909486
$419$	−281.528	−0.0328247	−0.0164123	−	0.999865i	$-0.505224\pi$
$419$	−281.528	−0.0328247	−0.0164123	+	0.999865i	$0.505224\pi$
$420$	2310.45	0.268425
$421$	−4136.42	−0.478853	−0.239426	−	0.970915i	$-0.576959\pi$
$421$	−4136.42	−0.478853	−0.239426	+	0.970915i	$0.576959\pi$
$422$	7309.32	0.843157
$423$	−8769.17	−1.00797
$424$	2235.61	0.256063
$425$	1171.34	0.133690
$426$	245.819	0.0279576
$427$	3076.25	0.348642
$428$	−4676.74	−0.528175
$429$	2089.14	0.235116
$430$	−1675.33	−0.187888
$431$	1488.64	0.166369	0.0831846	−	0.996534i	$-0.473491\pi$
$431$	1488.64	0.166369	0.0831846	+	0.996534i	$0.473491\pi$
$432$	1097.61	0.122243
$433$	14018.0	1.55580	0.777902	−	0.628385i	$-0.216284\pi$
$433$	14018.0	1.55580	0.777902	+	0.628385i	$0.216284\pi$
$434$	−2213.19	−0.244784
$435$	6929.55	0.763785
$436$	4004.00	0.439809
$437$	196.459	0.0215056
$438$	−6033.43	−0.658193
$439$	16037.7	1.74359	0.871795	−	0.489871i	$-0.162956\pi$
$439$	16037.7	1.74359	0.871795	+	0.489871i	$0.162956\pi$
$440$	−454.790	−0.0492756
$441$	813.996	0.0878950
$442$	−5233.46	−0.563191
$443$	7819.36	0.838621	0.419311	−	0.907843i	$-0.362272\pi$
$443$	7819.36	0.838621	0.419311	+	0.907843i	$0.362272\pi$
$444$	2841.28	0.303697
$445$	−1602.75	−0.170736
$446$	12362.9	1.31256
$447$	−8523.02	−0.901845
$448$	448.000	0.0472456
$449$	5908.45	0.621017	0.310509	−	0.950571i	$-0.399501\pi$
$449$	5908.45	0.621017	0.310509	+	0.950571i	$0.399501\pi$
$450$	−1034.09	−0.108328
$451$	1415.90	0.147832
$452$	−4221.69	−0.439318
$453$	−10858.0	−1.12617
$454$	12884.9	1.33197
$455$	−6081.53	−0.626608
$456$	−451.272	−0.0463438
$457$	2558.51	0.261886	0.130943	−	0.991390i	$-0.458199\pi$
$457$	2558.51	0.261886	0.130943	+	0.991390i	$0.458199\pi$
$458$	−4482.09	−0.457280
$459$	2581.72	0.262536
$460$	1149.54	0.116516
$461$	−6595.33	−0.666323	−0.333162	−	0.942870i	$-0.608115\pi$
$461$	−6595.33	−0.666323	−0.333162	+	0.942870i	$0.608115\pi$
$462$	−420.646	−0.0423598
$463$	−12883.6	−1.29320	−0.646601	−	0.762829i	$-0.723810\pi$
$463$	−12883.6	−1.29320	−0.646601	+	0.762829i	$0.723810\pi$
$464$	1343.65	0.134434
$465$	13044.6	1.30092
$466$	−4787.00	−0.475866
$467$	7779.89	0.770901	0.385450	−	0.922729i	$-0.374046\pi$
$467$	7779.89	0.770901	0.385450	+	0.922729i	$0.374046\pi$
$468$	4620.25	0.456349
$469$	−2031.28	−0.199991
$470$	−13191.6	−1.29465
$471$	−7691.61	−0.752464
$472$	583.677	0.0569193
$473$	305.014	0.0296503
$474$	−11073.0	−1.07300
$475$	−265.857	−0.0256808
$476$	1053.75	0.101468
$477$	−4642.28	−0.445609
$478$	2681.45	0.256583
$479$	2432.92	0.232073	0.116036	−	0.993245i	$-0.462981\pi$
$479$	2432.92	0.232073	0.116036	+	0.993245i	$0.462981\pi$
$480$	−2640.52	−0.251089
$481$	−7478.77	−0.708945
$482$	−9698.96	−0.916546
$483$	1063.24	0.100163
$484$	−5241.20	−0.492224
$485$	−11295.4	−1.05752
$486$	−8203.33	−0.765660
$487$	−612.347	−0.0569776	−0.0284888	−	0.999594i	$-0.509069\pi$
$487$	−612.347	−0.0569776	−0.0284888	+	0.999594i	$0.509069\pi$
$488$	−3515.71	−0.326124
$489$	21503.6	1.98860
$490$	1224.51	0.112893
$491$	−9410.64	−0.864962	−0.432481	−	0.901643i	$-0.642362\pi$
$491$	−9410.64	−0.864962	−0.432481	+	0.901643i	$0.642362\pi$
$492$	8220.73	0.753291
$493$	3160.42	0.288719
$494$	1187.83	0.108184
$495$	944.380	0.0857510
$496$	2529.35	0.228975
$497$	130.280	0.0117583
$498$	858.863	0.0772823
$499$	2349.14	0.210745	0.105373	−	0.994433i	$-0.466396\pi$
$499$	2349.14	0.210745	0.105373	+	0.994433i	$0.466396\pi$
$500$	4691.89	0.419655
$501$	−336.823	−0.0300362
$502$	−10243.1	−0.910703
$503$	−16551.1	−1.46715	−0.733577	−	0.679607i	$-0.762150\pi$
$503$	−16551.1	−1.46715	−0.733577	+	0.679607i	$0.762150\pi$
$504$	−930.281	−0.0822183
$505$	−14464.7	−1.27460
$506$	−209.287	−0.0183873
$507$	−17418.5	−1.52580
$508$	−7205.13	−0.629283
$509$	11312.1	0.985068	0.492534	−	0.870293i	$-0.336071\pi$
$509$	11312.1	0.985068	0.492534	+	0.870293i	$0.336071\pi$
$510$	−6210.82	−0.539255
$511$	−3197.63	−0.276820
$512$	−512.000	−0.0441942
$513$	−585.968	−0.0504310
$514$	12864.9	1.10398
$515$	−4898.61	−0.419143
$516$	1770.92	0.151086
$517$	2401.69	0.204306
$518$	1505.84	0.127727
$519$	10924.9	0.923989
$520$	6950.32	0.586138
$521$	−11666.9	−0.981067	−0.490533	−	0.871422i	$-0.663198\pi$
$521$	−11666.9	−0.981067	−0.490533	+	0.871422i	$0.663198\pi$
$522$	−2790.11	−0.233946
$523$	9668.20	0.808338	0.404169	−	0.914684i	$-0.367561\pi$
$523$	9668.20	0.808338	0.404169	+	0.914684i	$0.367561\pi$
$524$	−2091.42	−0.174359
$525$	−1438.82	−0.119610
$526$	8519.85	0.706241
$527$	5949.35	0.491760
$528$	480.739	0.0396240
$529$	529.000	0.0434783
$530$	−6983.46	−0.572344
$531$	−1212.02	−0.0990528
$532$	−239.168	−0.0194911
$533$	−21638.4	−1.75847
$534$	1694.19	0.137294
$535$	14609.0	1.18056
$536$	2321.46	0.187074
$537$	15595.5	1.25325
$538$	11365.3	0.910766
$539$	−222.937	−0.0178155
$540$	−3428.66	−0.273234
$541$	10017.7	0.796105	0.398052	−	0.917363i	$-0.369686\pi$
$541$	10017.7	0.796105	0.398052	+	0.917363i	$0.369686\pi$
$542$	7670.52	0.607891
$543$	−18.3882	−0.00145324
$544$	−1204.29	−0.0949142
$545$	−12507.5	−0.983049
$546$	6428.52	0.503874
$547$	−14202.0	−1.11012	−0.555059	−	0.831811i	$-0.687304\pi$
$547$	−14202.0	−1.11012	−0.555059	+	0.831811i	$0.687304\pi$
$548$	2639.36	0.205744
$549$	7300.44	0.567532
$550$	283.216	0.0219571
$551$	−717.316	−0.0554604
$552$	−1215.13	−0.0936943
$553$	−5868.55	−0.451277
$554$	−6421.39	−0.492453
$555$	−8875.45	−0.678814
$556$	5947.11	0.453622
$557$	13660.8	1.03919	0.519593	−	0.854414i	$-0.326083\pi$
$557$	13660.8	1.03919	0.519593	+	0.854414i	$0.326083\pi$
$558$	−5252.26	−0.398469
$559$	−4661.38	−0.352693
$560$	−1399.44	−0.105602
$561$	1130.76	0.0850990
$562$	−14294.1	−1.07288
$563$	12003.8	0.898581	0.449290	−	0.893386i	$-0.351677\pi$
$563$	12003.8	0.898581	0.449290	+	0.893386i	$0.351677\pi$
$564$	13944.3	1.04106
$565$	13187.5	0.981950
$566$	18020.5	1.33826
$567$	−6310.95	−0.467434
$568$	−148.892	−0.0109989
$569$	−24889.7	−1.83379	−0.916897	−	0.399124i	$-0.869314\pi$
$569$	−24889.7	−1.83379	−0.916897	+	0.399124i	$0.869314\pi$
$570$	1409.66	0.103586
$571$	−477.361	−0.0349858	−0.0174929	−	0.999847i	$-0.505568\pi$
$571$	−477.361	−0.0349858	−0.0174929	+	0.999847i	$0.505568\pi$
$572$	−1265.39	−0.0924976
$573$	31477.4	2.29492
$574$	4356.87	0.316816
$575$	−715.865	−0.0519194
$576$	1063.18	0.0769082
$577$	−26449.3	−1.90831	−0.954157	−	0.299306i	$-0.903245\pi$
$577$	−26449.3	−1.90831	−0.954157	+	0.299306i	$0.903245\pi$
$578$	6993.37	0.503263
$579$	12185.3	0.874615
$580$	−4197.22	−0.300483
$581$	455.185	0.0325031
$582$	11939.9	0.850385
$583$	1271.42	0.0903208
$584$	3654.44	0.258941
$585$	−14432.5	−1.02002
$586$	10840.6	0.764200
$587$	−17676.4	−1.24290	−0.621450	−	0.783454i	$-0.713456\pi$
$587$	−17676.4	−1.24290	−0.621450	+	0.783454i	$0.713456\pi$
$588$	−1294.37	−0.0907808
$589$	−1350.31	−0.0944630
$590$	−1823.26	−0.127224
$591$	1666.62	0.115999
$592$	−1720.96	−0.119478
$593$	19732.4	1.36646	0.683230	−	0.730203i	$-0.260574\pi$
$593$	19732.4	1.36646	0.683230	+	0.730203i	$0.260574\pi$
$594$	624.229	0.0431186
$595$	−3291.65	−0.226797
$596$	5162.37	0.354797
$597$	17736.6	1.21593
$598$	3198.43	0.218718
$599$	5194.44	0.354322	0.177161	−	0.984182i	$-0.443309\pi$
$599$	5194.44	0.354322	0.177161	+	0.984182i	$0.443309\pi$
$600$	1644.36	0.111885
$601$	−5279.89	−0.358355	−0.179177	−	0.983817i	$-0.557344\pi$
$601$	−5279.89	−0.358355	−0.179177	+	0.983817i	$0.557344\pi$
$602$	938.562	0.0635431
$603$	−4820.56	−0.325553
$604$	6576.69	0.443049
$605$	16372.2	1.10020
$606$	15290.0	1.02494
$607$	23328.5	1.55993	0.779964	−	0.625825i	$-0.215238\pi$
$607$	23328.5	1.55993	0.779964	+	0.625825i	$0.215238\pi$
$608$	273.335	0.0182322
$609$	−3882.11	−0.258310
$610$	10982.2	0.728943
$611$	−36703.9	−2.43025
$612$	2500.72	0.165173
$613$	−5023.54	−0.330993	−0.165497	−	0.986210i	$-0.552923\pi$
$613$	−5023.54	−0.330993	−0.165497	+	0.986210i	$0.552923\pi$
$614$	−3170.98	−0.208421
$615$	−25679.5	−1.68373
$616$	254.785	0.0166649
$617$	−10234.1	−0.667762	−0.333881	−	0.942615i	$-0.608358\pi$
$617$	−10234.1	−0.667762	−0.333881	+	0.942615i	$0.608358\pi$
$618$	5178.11	0.337046
$619$	−23782.3	−1.54425	−0.772125	−	0.635471i	$-0.780806\pi$
$619$	−23782.3	−1.54425	−0.772125	+	0.635471i	$0.780806\pi$
$620$	−7901.06	−0.511797
$621$	−1577.82	−0.101958
$622$	−10396.1	−0.670172
$623$	897.899	0.0577425
$624$	−7346.88	−0.471331
$625$	−18546.8	−1.18700
$626$	18509.7	1.18178
$627$	−256.646	−0.0163468
$628$	4658.79	0.296029
$629$	−4047.91	−0.256599
$630$	2905.96	0.183772
$631$	−5629.02	−0.355131	−0.177565	−	0.984109i	$-0.556822\pi$
$631$	−5629.02	−0.355131	−0.177565	+	0.984109i	$0.556822\pi$
$632$	6706.91	0.422131
$633$	24135.2	1.51546
$634$	4659.68	0.291892
$635$	22507.0	1.40656
$636$	7381.91	0.460239
$637$	3407.03	0.211917
$638$	764.154	0.0474187
$639$	309.177	0.0191406
$640$	1599.36	0.0987815
$641$	−8450.03	−0.520680	−0.260340	−	0.965517i	$-0.583835\pi$
$641$	−8450.03	−0.520680	−0.260340	+	0.965517i	$0.583835\pi$
$642$	−15442.5	−0.949325
$643$	−25034.8	−1.53542	−0.767712	−	0.640795i	$-0.778605\pi$
$643$	−25034.8	−1.53542	−0.767712	+	0.640795i	$0.778605\pi$
$644$	−644.000	−0.0394055
$645$	−5531.90	−0.337703
$646$	642.917	0.0391567
$647$	−12594.1	−0.765262	−0.382631	−	0.923901i	$-0.624982\pi$
$647$	−12594.1	−0.765262	−0.382631	+	0.923901i	$0.624982\pi$
$648$	7212.52	0.437244
$649$	331.946	0.0200771
$650$	−4328.25	−0.261182
$651$	−7307.88	−0.439967
$652$	−13024.7	−0.782339
$653$	−26759.9	−1.60367	−0.801834	−	0.597547i	$-0.796142\pi$
$653$	−26759.9	−1.60367	−0.801834	+	0.597547i	$0.796142\pi$
$654$	13221.1	0.790499
$655$	6533.06	0.389722
$656$	−4979.28	−0.296354
$657$	−7588.51	−0.450618
$658$	7390.28	0.437846
$659$	4901.36	0.289727	0.144863	−	0.989452i	$-0.453726\pi$
$659$	4901.36	0.289727	0.144863	+	0.989452i	$0.453726\pi$
$660$	−1501.71	−0.0885664
$661$	−29815.6	−1.75445	−0.877226	−	0.480077i	$-0.840609\pi$
$661$	−29815.6	−1.75445	−0.877226	+	0.480077i	$0.840609\pi$
$662$	8050.33	0.472636
$663$	−17280.8	−1.01226
$664$	−520.212	−0.0304038
$665$	747.100	0.0435658
$666$	3573.61	0.207920
$667$	−1931.50	−0.112126
$668$	204.013	0.0118166
$669$	40822.0	2.35915
$670$	−7251.65	−0.418143
$671$	−1999.44	−0.115034
$672$	1479.28	0.0849176
$673$	26068.9	1.49314	0.746571	−	0.665306i	$-0.231699\pi$
$673$	26068.9	1.49314	0.746571	+	0.665306i	$0.231699\pi$
$674$	−933.158	−0.0533292
$675$	2135.17	0.121752
$676$	10550.3	0.600269
$677$	395.976	0.0224795	0.0112397	−	0.999937i	$-0.496422\pi$
$677$	395.976	0.0224795	0.0112397	+	0.999937i	$0.496422\pi$
$678$	−13939.9	−0.789616
$679$	6327.97	0.357651
$680$	3761.88	0.212149
$681$	42545.5	2.39405
$682$	1438.48	0.0807660
$683$	20914.9	1.17172	0.585861	−	0.810411i	$-0.300756\pi$
$683$	20914.9	1.17172	0.585861	+	0.810411i	$0.300756\pi$
$684$	−567.585	−0.0317283
$685$	−8244.69	−0.459874
$686$	−686.000	−0.0381802
$687$	−14799.7	−0.821900
$688$	−1072.64	−0.0594391
$689$	−19430.5	−1.07437
$690$	3795.75	0.209423
$691$	11800.8	0.649674	0.324837	−	0.945770i	$-0.394691\pi$
$691$	11800.8	0.649674	0.324837	+	0.945770i	$0.394691\pi$
$692$	−6617.19	−0.363509
$693$	−529.065	−0.0290008
$694$	−22167.6	−1.21250
$695$	−18577.3	−1.01392
$696$	4436.70	0.241627
$697$	−11711.9	−0.636469
$698$	−9916.69	−0.537754
$699$	−15806.6	−0.855307
$700$	871.488	0.0470559
$701$	18463.5	0.994803	0.497402	−	0.867520i	$-0.334288\pi$
$701$	18463.5	0.994803	0.497402	+	0.867520i	$0.334288\pi$
$702$	−9539.78	−0.512900
$703$	918.746	0.0492904
$704$	−291.182	−0.0155886
$705$	−43558.4	−2.32696
$706$	4270.90	0.227674
$707$	8103.49	0.431065
$708$	1927.29	0.102305
$709$	14466.1	0.766271	0.383135	−	0.923692i	$-0.374844\pi$
$709$	14466.1	0.766271	0.383135	+	0.923692i	$0.374844\pi$
$710$	465.100	0.0245844
$711$	−13927.0	−0.734606
$712$	−1026.17	−0.0540131
$713$	−3635.95	−0.190978
$714$	3479.46	0.182375
$715$	3952.76	0.206748
$716$	−9446.14	−0.493043
$717$	8854.07	0.461174
$718$	−8520.27	−0.442860
$719$	22849.5	1.18518	0.592589	−	0.805505i	$-0.298106\pi$
$719$	22849.5	1.18518	0.592589	+	0.805505i	$0.298106\pi$
$720$	−3321.10	−0.171903
$721$	2744.33	0.141753
$722$	13572.1	0.699585
$723$	−32025.7	−1.64737
$724$	11.1377	0.000571724 0
$725$	2613.78	0.133894
$726$	−17306.3	−0.884707
$727$	−20393.5	−1.04038	−0.520188	−	0.854051i	$-0.674138\pi$
$727$	−20393.5	−1.04038	−0.520188	+	0.854051i	$0.674138\pi$
$728$	−3893.74	−0.198230
$729$	−2744.96	−0.139458
$730$	−11415.5	−0.578778
$731$	−2522.99	−0.127655
$732$	−11608.8	−0.586165
$733$	−6878.47	−0.346606	−0.173303	−	0.984869i	$-0.555444\pi$
$733$	−6878.47	−0.346606	−0.173303	+	0.984869i	$0.555444\pi$
$734$	−427.423	−0.0214938
$735$	4043.30	0.202910
$736$	736.000	0.0368605
$737$	1320.25	0.0659865
$738$	10339.6	0.515725
$739$	2479.80	0.123438	0.0617192	−	0.998094i	$-0.480342\pi$
$739$	2479.80	0.123438	0.0617192	+	0.998094i	$0.480342\pi$
$740$	5375.84	0.267054
$741$	3922.19	0.194447
$742$	3912.31	0.193565
$743$	13453.0	0.664259	0.332129	−	0.943234i	$-0.392233\pi$
$743$	13453.0	0.664259	0.332129	+	0.943234i	$0.392233\pi$
$744$	8351.87	0.411551
$745$	−16125.9	−0.793032
$746$	−13855.7	−0.680018
$747$	1080.23	0.0529097
$748$	−684.896	−0.0334790
$749$	−8184.30	−0.399263
$750$	15492.5	0.754275
$751$	−14526.4	−0.705829	−0.352915	−	0.935656i	$-0.614809\pi$
$751$	−14526.4	−0.705829	−0.352915	+	0.935656i	$0.614809\pi$
$752$	−8446.03	−0.409568
$753$	−33822.5	−1.63687
$754$	−11678.2	−0.564051
$755$	−20543.9	−0.990290
$756$	1920.82	0.0924069
$757$	−8492.68	−0.407756	−0.203878	−	0.978996i	$-0.565355\pi$
$757$	−8492.68	−0.407756	−0.203878	+	0.978996i	$0.565355\pi$
$758$	−18541.0	−0.888443
$759$	−691.062	−0.0330487
$760$	−853.828	−0.0407521
$761$	24953.2	1.18864	0.594320	−	0.804229i	$-0.297421\pi$
$761$	24953.2	1.18864	0.594320	+	0.804229i	$0.297421\pi$
$762$	−23791.2	−1.13105
$763$	7007.00	0.332465
$764$	−19065.8	−0.902849
$765$	−7811.63	−0.369189
$766$	12998.1	0.613107
$767$	−5072.97	−0.238819
$768$	−1690.61	−0.0794332
$769$	29111.4	1.36513	0.682565	−	0.730825i	$-0.260865\pi$
$769$	29111.4	1.36513	0.682565	+	0.730825i	$0.260865\pi$
$770$	−795.882	−0.0372488
$771$	42479.5	1.98426
$772$	−7380.59	−0.344084
$773$	22408.1	1.04264	0.521322	−	0.853360i	$-0.325439\pi$
$773$	22408.1	1.04264	0.521322	+	0.853360i	$0.325439\pi$
$774$	2227.36	0.103438
$775$	4920.32	0.228055
$776$	−7231.97	−0.334552
$777$	4972.25	0.229573
$778$	7552.71	0.348043
$779$	2658.22	0.122260
$780$	22949.8	1.05351
$781$	−84.6771	−0.00387962
$782$	1731.16	0.0791639
$783$	5760.96	0.262937
$784$	784.000	0.0357143
$785$	−14552.9	−0.661675
$786$	−6905.82	−0.313387
$787$	−10072.6	−0.456225	−0.228112	−	0.973635i	$-0.573255\pi$
$787$	−10072.6	−0.456225	−0.228112	+	0.973635i	$0.573255\pi$
$788$	−1009.47	−0.0456355
$789$	28132.3	1.26938
$790$	−20950.7	−0.943534
$791$	−7387.96	−0.332093
$792$	604.646	0.0271277
$793$	30556.4	1.36834
$794$	−22500.9	−1.00570
$795$	−23059.2	−1.02871
$796$	−10743.0	−0.478361
$797$	3266.57	0.145179	0.0725897	−	0.997362i	$-0.476874\pi$
$797$	3266.57	0.145179	0.0725897	+	0.997362i	$0.476874\pi$
$798$	−789.727	−0.0350326
$799$	−19866.1	−0.879614
$800$	−995.986	−0.0440168
$801$	2130.86	0.0939954
$802$	20763.7	0.914202
$803$	2078.34	0.0913361
$804$	7665.40	0.336241
$805$	2011.69	0.0880780
$806$	−21983.6	−0.960720
$807$	37527.9	1.63698
$808$	−9261.13	−0.403224
$809$	1038.67	0.0451391	0.0225696	−	0.999745i	$-0.492815\pi$
$809$	1038.67	0.0451391	0.0225696	+	0.999745i	$0.492815\pi$
$810$	−22530.1	−0.977316
$811$	−43445.1	−1.88109	−0.940544	−	0.339672i	$-0.889684\pi$
$811$	−43445.1	−1.88109	−0.940544	+	0.339672i	$0.889684\pi$
$812$	2351.39	0.101622
$813$	25327.9	1.09260
$814$	−978.737	−0.0421434
$815$	40685.7	1.74866
$816$	−3976.52	−0.170596
$817$	572.638	0.0245215
$818$	50.1888	0.00214525
$819$	8085.44	0.344967
$820$	15554.0	0.662402
$821$	20499.6	0.871428	0.435714	−	0.900085i	$-0.356496\pi$
$821$	20499.6	0.871428	0.435714	+	0.900085i	$0.356496\pi$
$822$	8715.10	0.369798
$823$	−4443.50	−0.188203	−0.0941013	−	0.995563i	$-0.529998\pi$
$823$	−4443.50	−0.188203	−0.0941013	+	0.995563i	$0.529998\pi$
$824$	−3136.37	−0.132598
$825$	935.174	0.0394649
$826$	1021.43	0.0430269
$827$	20075.8	0.844139	0.422070	−	0.906563i	$-0.361304\pi$
$827$	20075.8	0.844139	0.422070	+	0.906563i	$0.361304\pi$
$828$	−1528.32	−0.0641458
$829$	−40501.1	−1.69682	−0.848408	−	0.529342i	$-0.822439\pi$
$829$	−40501.1	−1.69682	−0.848408	+	0.529342i	$0.822439\pi$
$830$	1625.01	0.0679577
$831$	−21203.3	−0.885119
$832$	4449.99	0.185428
$833$	1844.06	0.0767023
$834$	19637.2	0.815325
$835$	−637.284	−0.0264121
$836$	155.450	0.00643103
$837$	10844.7	0.447848
$838$	563.056	0.0232106
$839$	18290.7	0.752639	0.376319	−	0.926490i	$-0.377190\pi$
$839$	18290.7	0.752639	0.376319	+	0.926490i	$0.377190\pi$
$840$	−4620.91	−0.189805
$841$	−17336.7	−0.710840
$842$	8272.85	0.338600
$843$	−47198.8	−1.92837
$844$	−14618.6	−0.596202
$845$	−32956.5	−1.34170
$846$	17538.3	0.712743
$847$	−9172.10	−0.372086
$848$	−4471.21	−0.181064
$849$	59503.1	2.40535
$850$	−2342.68	−0.0945332
$851$	2473.88	0.0996516
$852$	−491.637	−0.0197690
$853$	−7534.66	−0.302440	−0.151220	−	0.988500i	$-0.548320\pi$
$853$	−7534.66	−0.302440	−0.151220	+	0.988500i	$0.548320\pi$
$854$	−6152.49	−0.246527
$855$	1772.99	0.0709182
$856$	9353.49	0.373476
$857$	−2592.92	−0.103352	−0.0516758	−	0.998664i	$-0.516456\pi$
$857$	−2592.92	−0.103352	−0.0516758	+	0.998664i	$0.516456\pi$
$858$	−4178.29	−0.166252
$859$	12781.5	0.507682	0.253841	−	0.967246i	$-0.418306\pi$
$859$	12781.5	0.507682	0.253841	+	0.967246i	$0.418306\pi$
$860$	3350.66	0.132857
$861$	14386.3	0.569435
$862$	−2977.27	−0.117641
$863$	−24270.2	−0.957321	−0.478660	−	0.878000i	$-0.658877\pi$
$863$	−24270.2	−0.957321	−0.478660	+	0.878000i	$0.658877\pi$
$864$	−2195.22	−0.0864387
$865$	20670.4	0.812504
$866$	−28036.1	−1.10012
$867$	23091.9	0.904549
$868$	4426.37	0.173089
$869$	3814.33	0.148898
$870$	−13859.1	−0.540078
$871$	−20176.7	−0.784916
$872$	−8008.00	−0.310992
$873$	15017.3	0.582199
$874$	−392.919	−0.0152067
$875$	8210.80	0.317229
$876$	12066.9	0.465413
$877$	15375.5	0.592012	0.296006	−	0.955186i	$-0.404345\pi$
$877$	15375.5	0.592012	0.296006	+	0.955186i	$0.404345\pi$
$878$	−32075.3	−1.23290
$879$	35795.4	1.37355
$880$	909.580	0.0348431
$881$	7494.59	0.286605	0.143303	−	0.989679i	$-0.454228\pi$
$881$	7494.59	0.286605	0.143303	+	0.989679i	$0.454228\pi$
$882$	−1627.99	−0.0621512
$883$	−35896.0	−1.36806	−0.684029	−	0.729455i	$-0.739774\pi$
$883$	−35896.0	−1.36806	−0.684029	+	0.729455i	$0.739774\pi$
$884$	10466.9	0.398236
$885$	−6020.35	−0.228669
$886$	−15638.7	−0.592995
$887$	−4210.74	−0.159395	−0.0796973	−	0.996819i	$-0.525395\pi$
$887$	−4210.74	−0.159395	−0.0796973	+	0.996819i	$0.525395\pi$
$888$	−5682.57	−0.214746
$889$	−12609.0	−0.475694
$890$	3205.49	0.120729
$891$	4101.87	0.154229
$892$	−24725.8	−0.928117
$893$	4508.97	0.168966
$894$	17046.0	0.637701
$895$	29507.3	1.10203
$896$	−896.000	−0.0334077
$897$	10561.1	0.393118
$898$	−11816.9	−0.439126
$899$	13275.6	0.492511
$900$	2068.18	0.0765994
$901$	−10516.8	−0.388864
$902$	−2831.80	−0.104533
$903$	3099.11	0.114210
$904$	8443.38	0.310645
$905$	−34.7912	−0.00127790
$906$	21716.1	0.796322
$907$	9560.33	0.349995	0.174998	−	0.984569i	$-0.444008\pi$
$907$	9560.33	0.349995	0.174998	+	0.984569i	$0.444008\pi$
$908$	−25769.7	−0.941848
$909$	19230.9	0.701704
$910$	12163.1	0.443079
$911$	−31138.7	−1.13246	−0.566231	−	0.824247i	$-0.691599\pi$
$911$	−31138.7	−1.13246	−0.566231	+	0.824247i	$0.691599\pi$
$912$	902.545	0.0327700
$913$	−295.853	−0.0107243
$914$	−5117.02	−0.185181
$915$	36262.9	1.31018
$916$	8964.17	0.323346
$917$	−3659.98	−0.131803
$918$	−5163.43	−0.185641
$919$	14589.4	0.523677	0.261839	−	0.965112i	$-0.415671\pi$
$919$	14589.4	0.523677	0.261839	+	0.965112i	$0.415671\pi$
$920$	−2299.08	−0.0823895
$921$	−10470.5	−0.374609
$922$	13190.7	0.471162
$923$	1294.08	0.0461485
$924$	841.293	0.0299529
$925$	−3347.76	−0.118998
$926$	25767.2	0.914431
$927$	6512.74	0.230751
$928$	−2687.30	−0.0950591
$929$	13340.9	0.471153	0.235577	−	0.971856i	$-0.424302\pi$
$929$	13340.9	0.471153	0.235577	+	0.971856i	$0.424302\pi$
$930$	−26089.1	−0.919888
$931$	−418.544	−0.0147339
$932$	9574.01	0.336488
$933$	−34327.8	−1.20455
$934$	−15559.8	−0.545109
$935$	2139.44	0.0748313
$936$	−9240.50	−0.322687
$937$	−16885.0	−0.588697	−0.294349	−	0.955698i	$-0.595103\pi$
$937$	−16885.0	−0.588697	−0.294349	+	0.955698i	$0.595103\pi$
$938$	4062.55	0.141415
$939$	61118.5	2.12410
$940$	26383.2	0.915454
$941$	−14688.4	−0.508852	−0.254426	−	0.967092i	$-0.581887\pi$
$941$	−14688.4	−0.508852	−0.254426	+	0.967092i	$0.581887\pi$
$942$	15383.2	0.532072
$943$	7157.72	0.247176
$944$	−1167.35	−0.0402480
$945$	−6000.16	−0.206545
$946$	−610.029	−0.0209659
$947$	43778.4	1.50223	0.751113	−	0.660173i	$-0.229517\pi$
$947$	43778.4	1.50223	0.751113	+	0.660173i	$0.229517\pi$
$948$	22146.1	0.758724
$949$	−31762.2	−1.08645
$950$	531.714	0.0181590
$951$	15386.2	0.524638
$952$	−2107.50	−0.0717484
$953$	54902.3	1.86617	0.933085	−	0.359656i	$-0.117106\pi$
$953$	54902.3	1.86617	0.933085	+	0.359656i	$0.117106\pi$
$954$	9284.56	0.315093
$955$	59556.7	2.01802
$956$	−5362.90	−0.181431
$957$	2523.22	0.0852289
$958$	−4865.84	−0.164100
$959$	4618.88	0.155528
$960$	5281.04	0.177547
$961$	−4800.24	−0.161130
$962$	14957.5	0.501300
$963$	−19422.7	−0.649936
$964$	19397.9	0.648096
$965$	23055.1	0.769087
$966$	−2126.47	−0.0708262
$967$	3286.84	0.109305	0.0546523	−	0.998505i	$-0.482595\pi$
$967$	3286.84	0.109305	0.0546523	+	0.998505i	$0.482595\pi$
$968$	10482.4	0.348055
$969$	2122.89	0.0703789
$970$	22590.8	0.747781
$971$	49862.4	1.64795	0.823975	−	0.566626i	$-0.191751\pi$
$971$	49862.4	1.64795	0.823975	+	0.566626i	$0.191751\pi$
$972$	16406.7	0.541403
$973$	10407.4	0.342906
$974$	1224.69	0.0402892
$975$	−14291.8	−0.469439
$976$	7031.42	0.230605
$977$	−6244.06	−0.204468	−0.102234	−	0.994760i	$-0.532599\pi$
$977$	−6244.06	−0.204468	−0.102234	+	0.994760i	$0.532599\pi$
$978$	−43007.1	−1.40615
$979$	−583.599	−0.0190520
$980$	−2449.02	−0.0798275
$981$	16628.8	0.541199
$982$	18821.3	0.611620
$983$	59620.5	1.93449	0.967243	−	0.253854i	$-0.0816982\pi$
$983$	59620.5	1.93449	0.967243	+	0.253854i	$0.0816982\pi$
$984$	−16441.5	−0.532657
$985$	3153.32	0.102003
$986$	−6320.85	−0.204155
$987$	24402.5	0.786971
$988$	−2375.66	−0.0764978
$989$	1541.92	0.0495757
$990$	−1888.76	−0.0606351
$991$	45346.5	1.45356	0.726781	−	0.686869i	$-0.241016\pi$
$991$	45346.5	1.45356	0.726781	+	0.686869i	$0.241016\pi$
$992$	−5058.71	−0.161909
$993$	26582.0	0.849501
$994$	−260.561	−0.00831437
$995$	33558.4	1.06922
$996$	−1717.73	−0.0546468
$997$	−41002.8	−1.30248	−0.651240	−	0.758872i	$-0.725751\pi$
$997$	−41002.8	−1.30248	−0.651240	+	0.758872i	$0.725751\pi$
$998$	−4698.28	−0.149019
$999$	−7378.70	−0.233685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.a.f.1.1	✓	4
7.6	odd	2		2254.4.a.j.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.a.f.1.1	✓	4	1.1	even	1	trivial
2254.4.a.j.1.4		4	7.6	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -6.60395 q^{3} +4.00000 q^{4} -12.4950 q^{5} +13.2079 q^{6} +7.00000 q^{7} -8.00000 q^{8} +16.6122 q^{9} +24.9900 q^{10} -4.54973 q^{11} -26.4158 q^{12} +69.5312 q^{13} -14.0000 q^{14} +82.5162 q^{15} +16.0000 q^{16} +37.6339 q^{17} -33.2243 q^{18} -8.54171 q^{19} -49.9799 q^{20} -46.2277 q^{21} +9.09945 q^{22} -23.0000 q^{23} +52.8316 q^{24} +31.1246 q^{25} -139.062 q^{26} +68.6008 q^{27} +28.0000 q^{28} +83.9781 q^{29} -165.032 q^{30} +158.085 q^{31} -32.0000 q^{32} +30.0462 q^{33} -75.2679 q^{34} -87.4649 q^{35} +66.4486 q^{36} -107.560 q^{37} +17.0834 q^{38} -459.180 q^{39} +99.9599 q^{40} -311.205 q^{41} +92.4553 q^{42} -67.0402 q^{43} -18.1989 q^{44} -207.569 q^{45} +46.0000 q^{46} -527.877 q^{47} -105.663 q^{48} +49.0000 q^{49} -62.2491 q^{50} -248.533 q^{51} +278.125 q^{52} -279.451 q^{53} -137.202 q^{54} +56.8487 q^{55} -56.0000 q^{56} +56.4090 q^{57} -167.956 q^{58} -72.9596 q^{59} +330.065 q^{60} +439.464 q^{61} -316.169 q^{62} +116.285 q^{63} +64.0000 q^{64} -868.790 q^{65} -60.0923 q^{66} -290.182 q^{67} +150.536 q^{68} +151.891 q^{69} +174.930 q^{70} +18.6115 q^{71} -132.897 q^{72} -456.805 q^{73} +215.120 q^{74} -205.545 q^{75} -34.1669 q^{76} -31.8481 q^{77} +918.361 q^{78} -838.364 q^{79} -199.920 q^{80} -901.564 q^{81} +622.410 q^{82} +65.0265 q^{83} -184.911 q^{84} -470.235 q^{85} +134.080 q^{86} -554.587 q^{87} +36.3978 q^{88} +128.271 q^{89} +415.137 q^{90} +486.718 q^{91} -92.0000 q^{92} -1043.98 q^{93} +1055.75 q^{94} +106.729 q^{95} +211.326 q^{96} +903.996 q^{97} -98.0000 q^{98} -75.5808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 28 q^{7} - 32 q^{8} - 23 q^{9} + 4 q^{10} - 66 q^{11} - 4 q^{12} - 25 q^{13} - 56 q^{14} - 4 q^{15} + 64 q^{16} - 56 q^{17} + 46 q^{18} + 4 q^{19}+ \cdots - 108 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 28 * q^7 - 32 * q^8 - 23 * q^9 + 4 * q^10 - 66 * q^11 - 4 * q^12 - 25 * q^13 - 56 * q^14 - 4 * q^15 + 64 * q^16 - 56 * q^17 + 46 * q^18 + 4 * q^19 - 8 * q^20 - 7 * q^21 + 132 * q^22 - 92 * q^23 + 8 * q^24 + 104 * q^25 + 50 * q^26 + 5 * q^27 + 112 * q^28 - 109 * q^29 + 8 * q^30 - 119 * q^31 - 128 * q^32 - 132 * q^33 + 112 * q^34 - 14 * q^35 - 92 * q^36 - 134 * q^37 - 8 * q^38 - 299 * q^39 + 16 * q^40 - 557 * q^41 + 14 * q^42 + 60 * q^43 - 264 * q^44 - 836 * q^45 + 184 * q^46 - 699 * q^47 - 16 * q^48 + 196 * q^49 - 208 * q^50 - 532 * q^51 - 100 * q^52 - 1002 * q^53 - 10 * q^54 - 426 * q^55 - 224 * q^56 - 64 * q^57 + 218 * q^58 - 1482 * q^59 - 16 * q^60 - 132 * q^61 + 238 * q^62 - 161 * q^63 + 256 * q^64 - 2272 * q^65 + 264 * q^66 - 380 * q^67 - 224 * q^68 + 23 * q^69 + 28 * q^70 - 173 * q^71 + 184 * q^72 - 2107 * q^73 + 268 * q^74 - 785 * q^75 + 16 * q^76 - 462 * q^77 + 598 * q^78 - 2184 * q^79 - 32 * q^80 - 560 * q^81 + 1114 * q^82 - 152 * q^83 - 28 * q^84 + 388 * q^85 - 120 * q^86 - 1493 * q^87 + 528 * q^88 + 384 * q^89 + 1672 * q^90 - 175 * q^91 - 368 * q^92 - 1891 * q^93 + 1398 * q^94 - 440 * q^95 + 32 * q^96 + 2756 * q^97 - 392 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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