LMFDB - Embedded newform 2023.4.a.l.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2023,4,Mod(1,2023)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2023, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2023.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,3,3,65,-12,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 76 x^{10} + 195 x^{9} + 2126 x^{8} - 4299 x^{7} - 26508 x^{6} + 35641 x^{5} + \cdots + 17280 $ x^12 - 3x^11 - 76x^10 + 195x^9 + 2126x^8 - 4299x^7 - 26508x^6 + 35641x^5 + 137633x^4 - 72318x^3 - 196104x^2 - 42272*x + 17280
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$5.43473$ of defining polynomial
Character	$\chi$	$=$	2023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.43473 q^{2} +5.22551 q^{3} +21.5363 q^{4} -10.5392 q^{5} +28.3992 q^{6} -7.00000 q^{7} +73.5664 q^{8} +0.305909 q^{9} -57.2779 q^{10} +64.6024 q^{11} +112.538 q^{12} +66.6746 q^{13} -38.0431 q^{14} -55.0728 q^{15} +227.523 q^{16} +1.66253 q^{18} +34.1490 q^{19} -226.976 q^{20} -36.5785 q^{21} +351.097 q^{22} -180.191 q^{23} +384.422 q^{24} -13.9245 q^{25} +362.359 q^{26} -139.490 q^{27} -150.754 q^{28} +85.0745 q^{29} -299.306 q^{30} +175.861 q^{31} +647.996 q^{32} +337.580 q^{33} +73.7746 q^{35} +6.58815 q^{36} -247.618 q^{37} +185.591 q^{38} +348.409 q^{39} -775.333 q^{40} +148.720 q^{41} -198.795 q^{42} +186.861 q^{43} +1391.30 q^{44} -3.22404 q^{45} -979.288 q^{46} +199.660 q^{47} +1188.92 q^{48} +49.0000 q^{49} -75.6762 q^{50} +1435.93 q^{52} +425.750 q^{53} -758.092 q^{54} -680.859 q^{55} -514.965 q^{56} +178.446 q^{57} +462.357 q^{58} +551.016 q^{59} -1186.07 q^{60} -558.213 q^{61} +955.760 q^{62} -2.14136 q^{63} +1701.50 q^{64} -702.700 q^{65} +1834.66 q^{66} +490.599 q^{67} -941.587 q^{69} +400.946 q^{70} -341.890 q^{71} +22.5046 q^{72} +932.646 q^{73} -1345.74 q^{74} -72.7628 q^{75} +735.445 q^{76} -452.217 q^{77} +1893.51 q^{78} +96.3239 q^{79} -2397.92 q^{80} -737.166 q^{81} +808.253 q^{82} -191.735 q^{83} -787.768 q^{84} +1015.54 q^{86} +444.557 q^{87} +4752.56 q^{88} +21.0193 q^{89} -17.5218 q^{90} -466.723 q^{91} -3880.64 q^{92} +918.965 q^{93} +1085.10 q^{94} -359.905 q^{95} +3386.11 q^{96} +779.904 q^{97} +266.302 q^{98} +19.7624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} + 65 q^{4} - 12 q^{5} - 22 q^{6} - 84 q^{7} + 78 q^{8} + 233 q^{9} + 36 q^{10} + 4 q^{11} + 6 q^{12} + 98 q^{13} - 21 q^{14} - 196 q^{15} + 429 q^{16} + 603 q^{18} - 37 q^{19} + 54 q^{20}+ \cdots + 5140 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 3 * q^3 + 65 * q^4 - 12 * q^5 - 22 * q^6 - 84 * q^7 + 78 * q^8 + 233 * q^9 + 36 * q^10 + 4 * q^11 + 6 * q^12 + 98 * q^13 - 21 * q^14 - 196 * q^15 + 429 * q^16 + 603 * q^18 - 37 * q^19 + 54 * q^20 - 21 * q^21 + 70 * q^22 - 369 * q^23 - 652 * q^24 + 590 * q^25 + 638 * q^26 + 501 * q^27 - 455 * q^28 + 144 * q^29 - 160 * q^30 + 67 * q^31 + 417 * q^32 + 628 * q^33 + 84 * q^35 + 999 * q^36 - 345 * q^37 - 190 * q^38 + 6 * q^39 - 466 * q^40 - 156 * q^41 + 154 * q^42 - 763 * q^43 + 1046 * q^44 + 832 * q^45 - 395 * q^46 + 561 * q^47 + 532 * q^48 + 588 * q^49 + 1923 * q^50 + 3138 * q^52 + 1156 * q^53 - 1682 * q^54 - 156 * q^55 - 546 * q^56 - 501 * q^57 - 2305 * q^58 - 473 * q^59 - 1292 * q^60 + 1850 * q^61 + 202 * q^62 - 1631 * q^63 - 712 * q^64 + 1718 * q^65 + 2142 * q^66 - 834 * q^67 + 1316 * q^69 - 252 * q^70 - 3179 * q^71 + 2046 * q^72 + 1012 * q^73 - 2695 * q^74 - 3841 * q^75 + 3272 * q^76 - 28 * q^77 + 970 * q^78 - 3897 * q^79 - 1616 * q^80 + 3448 * q^81 + 4758 * q^82 + 675 * q^83 - 42 * q^84 + 77 * q^86 + 805 * q^87 + 5398 * q^88 + 4078 * q^89 + 13384 * q^90 - 686 * q^91 - 3393 * q^92 + 3671 * q^93 + 958 * q^94 - 4126 * q^95 - 2320 * q^96 + 1474 * q^97 + 147 * q^98 + 5140 * 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 $

$2$	5.43473	1.92147	0.960734	−	0.277470i	$-0.0894959\pi$
$2$	5.43473	1.92147	0.960734	+	0.277470i	$0.0894959\pi$
$3$	5.22551	1.00565	0.502825	−	0.864389i	$-0.332294\pi$
$3$	5.22551	1.00565	0.502825	+	0.864389i	$0.332294\pi$
$4$	21.5363	2.69204
$5$	−10.5392	−0.942658	−0.471329	−	0.881958i	$-0.656226\pi$
$5$	−10.5392	−0.942658	−0.471329	+	0.881958i	$0.656226\pi$
$6$	28.3992	1.93232
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	73.5664	3.25121
$9$	0.305909	0.0113300
$10$	−57.2779	−1.81129
$11$	64.6024	1.77076	0.885379	−	0.464869i	$-0.153899\pi$
$11$	64.6024	1.77076	0.885379	+	0.464869i	$0.153899\pi$
$12$	112.538	2.70725
$13$	66.6746	1.42248	0.711239	−	0.702950i	$-0.248134\pi$
$13$	66.6746	1.42248	0.711239	+	0.702950i	$0.248134\pi$
$14$	−38.0431	−0.726247
$15$	−55.0728	−0.947983
$16$	227.523	3.55505
$17$	0	0
$17$	0	0
$18$	1.66253	0.0217701
$19$	34.1490	0.412333	0.206166	−	0.978517i	$-0.433901\pi$
$19$	34.1490	0.412333	0.206166	+	0.978517i	$0.433901\pi$
$20$	−226.976	−2.53767
$21$	−36.5785	−0.380100
$22$	351.097	3.40246
$23$	−180.191	−1.63358	−0.816790	−	0.576936i	$-0.804248\pi$
$23$	−180.191	−1.63358	−0.816790	+	0.576936i	$0.804248\pi$
$24$	384.422	3.26957
$25$	−13.9245	−0.111396
$26$	362.359	2.73325
$27$	−139.490	−0.994255
$28$	−150.754	−1.01750
$29$	85.0745	0.544756	0.272378	−	0.962190i	$-0.412190\pi$
$29$	85.0745	0.544756	0.272378	+	0.962190i	$0.412190\pi$
$30$	−299.306	−1.82152
$31$	175.861	1.01889	0.509446	−	0.860503i	$-0.329850\pi$
$31$	175.861	1.01889	0.509446	+	0.860503i	$0.329850\pi$
$32$	647.996	3.57971
$33$	337.580	1.78076
$34$	0	0
$35$	73.7746	0.356291
$36$	6.58815	0.0305007
$37$	−247.618	−1.10022	−0.550111	−	0.835091i	$-0.685415\pi$
$37$	−247.618	−1.10022	−0.550111	+	0.835091i	$0.685415\pi$
$38$	185.591	0.792285
$39$	348.409	1.43051
$40$	−775.333	−3.06477
$41$	148.720	0.566492	0.283246	−	0.959047i	$-0.408589\pi$
$41$	148.720	0.566492	0.283246	+	0.959047i	$0.408589\pi$
$42$	−198.795	−0.730349
$43$	186.861	0.662698	0.331349	−	0.943508i	$-0.392496\pi$
$43$	186.861	0.662698	0.331349	+	0.943508i	$0.392496\pi$
$44$	1391.30	4.76696
$45$	−3.22404	−0.0106803
$46$	−979.288	−3.13887
$47$	199.660	0.619648	0.309824	−	0.950794i	$-0.399730\pi$
$47$	199.660	0.619648	0.309824	+	0.950794i	$0.399730\pi$
$48$	1188.92	3.57513
$49$	49.0000	0.142857
$50$	−75.6762	−0.214045
$51$	0	0
$52$	1435.93	3.82937
$53$	425.750	1.10342	0.551710	−	0.834036i	$-0.313975\pi$
$53$	425.750	1.10342	0.551710	+	0.834036i	$0.313975\pi$
$54$	−758.092	−1.91043
$55$	−680.859	−1.66922
$56$	−514.965	−1.22884
$57$	178.446	0.414662
$58$	462.357	1.04673
$59$	551.016	1.21587	0.607934	−	0.793987i	$-0.291998\pi$
$59$	551.016	1.21587	0.607934	+	0.793987i	$0.291998\pi$
$60$	−1186.07	−2.55201
$61$	−558.213	−1.17167	−0.585835	−	0.810430i	$-0.699233\pi$
$61$	−558.213	−1.17167	−0.585835	+	0.810430i	$0.699233\pi$
$62$	955.760	1.95777
$63$	−2.14136	−0.00428232
$64$	1701.50	3.32325
$65$	−702.700	−1.34091
$66$	1834.66	3.42168
$67$	490.599	0.894570	0.447285	−	0.894392i	$-0.352391\pi$
$67$	490.599	0.894570	0.447285	+	0.894392i	$0.352391\pi$
$68$	0	0
$69$	−941.587	−1.64281
$70$	400.946	0.684602
$71$	−341.890	−0.571477	−0.285739	−	0.958308i	$-0.592239\pi$
$71$	−341.890	−0.571477	−0.285739	+	0.958308i	$0.592239\pi$
$72$	22.5046	0.0368360
$73$	932.646	1.49531	0.747657	−	0.664085i	$-0.231179\pi$
$73$	932.646	1.49531	0.747657	+	0.664085i	$0.231179\pi$
$74$	−1345.74	−2.11404
$75$	−72.7628	−0.112026
$76$	735.445	1.11002
$77$	−452.217	−0.669284
$78$	1893.51	2.74869
$79$	96.3239	0.137181	0.0685904	−	0.997645i	$-0.478150\pi$
$79$	96.3239	0.137181	0.0685904	+	0.997645i	$0.478150\pi$
$80$	−2397.92	−3.35119
$81$	−737.166	−1.01120
$82$	808.253	1.08850
$83$	−191.735	−0.253562	−0.126781	−	0.991931i	$-0.540464\pi$
$83$	−191.735	−0.253562	−0.126781	+	0.991931i	$0.540464\pi$
$84$	−787.768	−1.02324
$85$	0	0
$86$	1015.54	1.27335
$87$	444.557	0.547834
$88$	4752.56	5.75710
$89$	21.0193	0.0250342	0.0125171	−	0.999922i	$-0.496016\pi$
$89$	21.0193	0.0250342	0.0125171	+	0.999922i	$0.496016\pi$
$90$	−17.5218	−0.0205218
$91$	−466.723	−0.537646
$92$	−3880.64	−4.39766
$93$	918.965	1.02465
$94$	1085.10	1.19063
$95$	−359.905	−0.388689
$96$	3386.11	3.59993
$97$	779.904	0.816364	0.408182	−	0.912901i	$-0.366163\pi$
$97$	779.904	0.816364	0.408182	+	0.912901i	$0.366163\pi$
$98$	266.302	0.274496
$99$	19.7624	0.0200626
$100$	−299.884	−0.299884
$101$	−1732.11	−1.70645	−0.853225	−	0.521543i	$-0.825357\pi$
$101$	−1732.11	−1.70645	−0.853225	+	0.521543i	$0.825357\pi$
$102$	0	0
$103$	−1046.93	−1.00153	−0.500764	−	0.865584i	$-0.666948\pi$
$103$	−1046.93	−1.00153	−0.500764	+	0.865584i	$0.666948\pi$
$104$	4905.01	4.62477
$105$	385.510	0.358304
$106$	2313.84	2.12019
$107$	−1039.89	−0.939532	−0.469766	−	0.882791i	$-0.655662\pi$
$107$	−1039.89	−0.939532	−0.469766	+	0.882791i	$0.655662\pi$
$108$	−3004.11	−2.67658
$109$	−1692.55	−1.48731	−0.743654	−	0.668565i	$-0.766909\pi$
$109$	−1692.55	−1.48731	−0.743654	+	0.668565i	$0.766909\pi$
$110$	−3700.29	−3.20735
$111$	−1293.93	−1.10644
$112$	−1592.66	−1.34368
$113$	−1061.03	−0.883300	−0.441650	−	0.897188i	$-0.645607\pi$
$113$	−1061.03	−0.883300	−0.441650	+	0.897188i	$0.645607\pi$
$114$	969.806	0.796760
$115$	1899.07	1.53991
$116$	1832.19	1.46651
$117$	20.3964	0.0161166
$118$	2994.63	2.33625
$119$	0	0
$120$	−4051.51	−3.08209
$121$	2842.47	2.13559
$122$	−3033.74	−2.25133
$123$	777.137	0.569692
$124$	3787.41	2.74290
$125$	1464.16	1.04767
$126$	−11.6377	−0.00822834
$127$	−1218.82	−0.851599	−0.425800	−	0.904817i	$-0.640007\pi$
$127$	−1218.82	−0.851599	−0.425800	+	0.904817i	$0.640007\pi$
$128$	4063.24	2.80581
$129$	976.443	0.666442
$130$	−3818.99	−2.57652
$131$	2147.01	1.43195	0.715975	−	0.698126i	$-0.245983\pi$
$131$	2147.01	1.43195	0.715975	+	0.698126i	$0.245983\pi$
$132$	7270.24	4.79389
$133$	−239.043	−0.155847
$134$	2666.27	1.71889
$135$	1470.12	0.937242
$136$	0	0
$137$	−880.855	−0.549318	−0.274659	−	0.961542i	$-0.588565\pi$
$137$	−880.855	−0.549318	−0.274659	+	0.961542i	$0.588565\pi$
$138$	−5117.27	−3.15660
$139$	−604.930	−0.369133	−0.184567	−	0.982820i	$-0.559088\pi$
$139$	−604.930	−0.369133	−0.184567	+	0.982820i	$0.559088\pi$
$140$	1588.84	0.959151
$141$	1043.33	0.623148
$142$	−1858.08	−1.09808
$143$	4307.34	2.51887
$144$	69.6013	0.0402785
$145$	−896.620	−0.513519
$146$	5068.68	2.87320
$147$	256.050	0.143664
$148$	−5332.79	−2.96184
$149$	832.868	0.457928	0.228964	−	0.973435i	$-0.426466\pi$
$149$	832.868	0.457928	0.228964	+	0.973435i	$0.426466\pi$
$150$	−395.446	−0.215254
$151$	−2031.83	−1.09502	−0.547510	−	0.836799i	$-0.684424\pi$
$151$	−2031.83	−1.09502	−0.547510	+	0.836799i	$0.684424\pi$
$152$	2512.22	1.34058
$153$	0	0
$154$	−2457.68	−1.28601
$155$	−1853.44	−0.960466
$156$	7503.45	3.85100
$157$	2464.96	1.25303	0.626513	−	0.779411i	$-0.284481\pi$
$157$	2464.96	1.25303	0.626513	+	0.779411i	$0.284481\pi$
$158$	523.495	0.263589
$159$	2224.76	1.10965
$160$	−6829.38	−3.37444
$161$	1261.33	0.617435
$162$	−4006.30	−1.94299
$163$	−343.866	−0.165237	−0.0826185	−	0.996581i	$-0.526328\pi$
$163$	−343.866	−0.165237	−0.0826185	+	0.996581i	$0.526328\pi$
$164$	3202.88	1.52502
$165$	−3557.84	−1.67865
$166$	−1042.03	−0.487211
$167$	−304.776	−0.141223	−0.0706116	−	0.997504i	$-0.522495\pi$
$167$	−304.776	−0.141223	−0.0706116	+	0.997504i	$0.522495\pi$
$168$	−2690.95	−1.23578
$169$	2248.51	1.02345
$170$	0	0
$171$	10.4465	0.00467171
$172$	4024.30	1.78401
$173$	−164.827	−0.0724368	−0.0362184	−	0.999344i	$-0.511531\pi$
$173$	−164.827	−0.0724368	−0.0362184	+	0.999344i	$0.511531\pi$
$174$	2416.05	1.05264
$175$	97.4718	0.0421039
$176$	14698.5	6.29513
$177$	2879.34	1.22274
$178$	114.234	0.0481024
$179$	−1523.97	−0.636350	−0.318175	−	0.948032i	$-0.603070\pi$
$179$	−1523.97	−0.636350	−0.318175	+	0.948032i	$0.603070\pi$
$180$	−69.4341	−0.0287517
$181$	−276.555	−0.113570	−0.0567849	−	0.998386i	$-0.518085\pi$
$181$	−276.555	−0.113570	−0.0567849	+	0.998386i	$0.518085\pi$
$182$	−2536.51	−1.03307
$183$	−2916.95	−1.17829
$184$	−13256.0	−5.31110
$185$	2609.71	1.03713
$186$	4994.33	1.96883
$187$	0	0
$188$	4299.95	1.66812
$189$	976.431	0.375793
$190$	−1955.99	−0.746853
$191$	−802.057	−0.303847	−0.151924	−	0.988392i	$-0.548547\pi$
$191$	−802.057	−0.303847	−0.151924	+	0.988392i	$0.548547\pi$
$192$	8891.21	3.34202
$193$	−1915.04	−0.714238	−0.357119	−	0.934059i	$-0.616241\pi$
$193$	−1915.04	−0.714238	−0.357119	+	0.934059i	$0.616241\pi$
$194$	4238.57	1.56862
$195$	−3671.96	−1.34849
$196$	1055.28	0.384577
$197$	−2996.23	−1.08362	−0.541809	−	0.840502i	$-0.682260\pi$
$197$	−2996.23	−1.08362	−0.541809	+	0.840502i	$0.682260\pi$
$198$	107.404	0.0385497
$199$	454.246	0.161812	0.0809062	−	0.996722i	$-0.474219\pi$
$199$	454.246	0.161812	0.0809062	+	0.996722i	$0.474219\pi$
$200$	−1024.38	−0.362172
$201$	2563.63	0.899623
$202$	−9413.56	−3.27889
$203$	−595.521	−0.205898
$204$	0	0
$205$	−1567.39	−0.534008
$206$	−5689.81	−1.92441
$207$	−55.1218	−0.0185084
$208$	15170.0	5.05698
$209$	2206.11	0.730142
$210$	2095.14	0.688470
$211$	1323.79	0.431912	0.215956	−	0.976403i	$-0.430713\pi$
$211$	1323.79	0.431912	0.215956	+	0.976403i	$0.430713\pi$
$212$	9169.10	2.97045
$213$	−1786.55	−0.574706
$214$	−5651.52	−1.80528
$215$	−1969.37	−0.624698
$216$	−10261.8	−3.23253
$217$	−1231.03	−0.385105
$218$	−9198.54	−2.85781
$219$	4873.54	1.50376
$220$	−14663.2	−4.49361
$221$	0	0
$222$	−7032.17	−2.12598
$223$	−5389.26	−1.61835	−0.809174	−	0.587569i	$-0.800085\pi$
$223$	−5389.26	−1.61835	−0.809174	+	0.587569i	$0.800085\pi$
$224$	−4535.97	−1.35300
$225$	−4.25964	−0.00126212
$226$	−5766.39	−1.69723
$227$	−3973.06	−1.16168	−0.580839	−	0.814018i	$-0.697276\pi$
$227$	−3973.06	−1.16168	−0.580839	+	0.814018i	$0.697276\pi$
$228$	3843.07	1.11629
$229$	6571.66	1.89637	0.948183	−	0.317725i	$-0.102919\pi$
$229$	6571.66	1.89637	0.948183	+	0.317725i	$0.102919\pi$
$230$	10320.9	2.95888
$231$	−2363.06	−0.673065
$232$	6258.62	1.77111
$233$	−2089.69	−0.587554	−0.293777	−	0.955874i	$-0.594912\pi$
$233$	−2089.69	−0.587554	−0.293777	+	0.955874i	$0.594912\pi$
$234$	110.849	0.0309676
$235$	−2104.27	−0.584116
$236$	11866.9	3.27317
$237$	503.341	0.137956
$238$	0	0
$239$	5242.27	1.41880	0.709402	−	0.704804i	$-0.248965\pi$
$239$	5242.27	1.41880	0.709402	+	0.704804i	$0.248965\pi$
$240$	−12530.3	−3.37012
$241$	−2572.51	−0.687592	−0.343796	−	0.939044i	$-0.611713\pi$
$241$	−2572.51	−0.687592	−0.343796	+	0.939044i	$0.611713\pi$
$242$	15448.0	4.10346
$243$	−85.8315	−0.0226588
$244$	−12021.9	−3.15419
$245$	−516.422	−0.134665
$246$	4223.53	1.09464
$247$	2276.87	0.586535
$248$	12937.5	3.31263
$249$	−1001.91	−0.254994
$250$	7957.31	2.01306
$251$	591.174	0.148664	0.0743318	−	0.997234i	$-0.476318\pi$
$251$	591.174	0.148664	0.0743318	+	0.997234i	$0.476318\pi$
$252$	−46.1171	−0.0115282
$253$	−11640.7	−2.89267
$254$	−6623.98	−1.63632
$255$	0	0
$256$	8470.63	2.06802
$257$	4304.04	1.04466	0.522332	−	0.852742i	$-0.325062\pi$
$257$	4304.04	1.04466	0.522332	+	0.852742i	$0.325062\pi$
$258$	5306.71	1.28055
$259$	1733.33	0.415845
$260$	−15133.6	−3.60979
$261$	26.0250	0.00617206
$262$	11668.4	2.75145
$263$	−8028.67	−1.88239	−0.941196	−	0.337860i	$-0.890297\pi$
$263$	−8028.67	−1.88239	−0.941196	+	0.337860i	$0.890297\pi$
$264$	24834.5	5.78962
$265$	−4487.08	−1.04015
$266$	−1299.14	−0.299456
$267$	109.836	0.0251756
$268$	10565.7	2.40822
$269$	−6063.95	−1.37444	−0.687222	−	0.726447i	$-0.741170\pi$
$269$	−6063.95	−1.37444	−0.687222	+	0.726447i	$0.741170\pi$
$270$	7989.71	1.80088
$271$	−7777.74	−1.74341	−0.871705	−	0.490032i	$-0.836985\pi$
$271$	−7777.74	−1.74341	−0.871705	+	0.490032i	$0.836985\pi$
$272$	0	0
$273$	−2438.86	−0.540684
$274$	−4787.21	−1.05550
$275$	−899.559	−0.197256
$276$	−20278.3	−4.42251
$277$	2547.88	0.552661	0.276330	−	0.961063i	$-0.410882\pi$
$277$	2547.88	0.552661	0.276330	+	0.961063i	$0.410882\pi$
$278$	−3287.63	−0.709278
$279$	53.7975	0.0115440
$280$	5427.33	1.15838
$281$	−1463.24	−0.310639	−0.155320	−	0.987864i	$-0.549641\pi$
$281$	−1463.24	−0.310639	−0.155320	+	0.987864i	$0.549641\pi$
$282$	5670.20	1.19736
$283$	−798.572	−0.167739	−0.0838696	−	0.996477i	$-0.526728\pi$
$283$	−798.572	−0.167739	−0.0838696	+	0.996477i	$0.526728\pi$
$284$	−7363.06	−1.53844
$285$	−1880.68	−0.390885
$286$	23409.2	4.83992
$287$	−1041.04	−0.214114
$288$	198.228	0.0405579
$289$	0	0
$290$	−4872.89	−0.986710
$291$	4075.39	0.820975
$292$	20085.8	4.02545
$293$	−687.871	−0.137153	−0.0685766	−	0.997646i	$-0.521846\pi$
$293$	−687.871	−0.137153	−0.0685766	+	0.997646i	$0.521846\pi$
$294$	1391.56	0.276046
$295$	−5807.29	−1.14615
$296$	−18216.4	−3.57705
$297$	−9011.39	−1.76059
$298$	4526.42	0.879894
$299$	−12014.1	−2.32373
$300$	−1567.04	−0.301578
$301$	−1308.03	−0.250476
$302$	−11042.5	−2.10405
$303$	−9051.15	−1.71609
$304$	7769.69	1.46586
$305$	5883.14	1.10448
$306$	0	0
$307$	−2898.89	−0.538920	−0.269460	−	0.963012i	$-0.586845\pi$
$307$	−2898.89	−0.538920	−0.269460	+	0.963012i	$0.586845\pi$
$308$	−9739.09	−1.80174
$309$	−5470.76	−1.00719
$310$	−10073.0	−1.84551
$311$	10436.9	1.90297	0.951484	−	0.307698i	$-0.0995585\pi$
$311$	10436.9	1.90297	0.951484	+	0.307698i	$0.0995585\pi$
$312$	25631.2	4.65089
$313$	−2156.11	−0.389362	−0.194681	−	0.980867i	$-0.562367\pi$
$313$	−2156.11	−0.389362	−0.194681	+	0.980867i	$0.562367\pi$
$314$	13396.4	2.40765
$315$	22.5683	0.00403676
$316$	2074.46	0.369297
$317$	5739.94	1.01699	0.508497	−	0.861064i	$-0.330201\pi$
$317$	5739.94	1.01699	0.508497	+	0.861064i	$0.330201\pi$
$318$	12091.0	2.13216
$319$	5496.01	0.964632
$320$	−17932.5	−3.13268
$321$	−5433.95	−0.944839
$322$	6855.01	1.18638
$323$	0	0
$324$	−15875.9	−2.72220
$325$	−928.414	−0.158459
$326$	−1868.82	−0.317498
$327$	−8844.41	−1.49571
$328$	10940.8	1.84178
$329$	−1397.62	−0.234205
$330$	−19335.9	−3.22547
$331$	−400.586	−0.0665202	−0.0332601	−	0.999447i	$-0.510589\pi$
$331$	−400.586	−0.0665202	−0.0332601	+	0.999447i	$0.510589\pi$
$332$	−4129.26	−0.682598
$333$	−75.7486	−0.0124655
$334$	−1656.38	−0.271356
$335$	−5170.54	−0.843273
$336$	−8322.46	−1.35127
$337$	1857.70	0.300283	0.150142	−	0.988665i	$-0.452027\pi$
$337$	1857.70	0.300283	0.150142	+	0.988665i	$0.452027\pi$
$338$	12220.0	1.96652
$339$	−5544.39	−0.888289
$340$	0	0
$341$	11361.1	1.80421
$342$	56.7739	0.00897655
$343$	−343.000	−0.0539949
$344$	13746.7	2.15457
$345$	9923.60	1.54861
$346$	−895.792	−0.139185
$347$	6879.42	1.06428	0.532142	−	0.846655i	$-0.321387\pi$
$347$	6879.42	1.06428	0.532142	+	0.846655i	$0.321387\pi$
$348$	9574.13	1.47479
$349$	−8937.02	−1.37074	−0.685369	−	0.728196i	$-0.740359\pi$
$349$	−8937.02	−1.37074	−0.685369	+	0.728196i	$0.740359\pi$
$350$	529.733	0.0809013
$351$	−9300.45	−1.41431
$352$	41862.1	6.33880
$353$	5562.13	0.838646	0.419323	−	0.907837i	$-0.362267\pi$
$353$	5562.13	0.838646	0.419323	+	0.907837i	$0.362267\pi$
$354$	15648.4	2.34945
$355$	3603.26	0.538708
$356$	452.678	0.0673930
$357$	0	0
$358$	−8282.35	−1.22273
$359$	−12245.0	−1.80018	−0.900090	−	0.435703i	$-0.856500\pi$
$359$	−12245.0	−1.80018	−0.900090	+	0.435703i	$0.856500\pi$
$360$	−237.181	−0.0347237
$361$	−5692.84	−0.829982
$362$	−1503.00	−0.218221
$363$	14853.3	2.14765
$364$	−10051.5	−1.44737
$365$	−9829.37	−1.40957
$366$	−15852.8	−2.26405
$367$	5493.09	0.781299	0.390650	−	0.920539i	$-0.372250\pi$
$367$	5493.09	0.781299	0.390650	+	0.920539i	$0.372250\pi$
$368$	−40997.5	−5.80745
$369$	45.4947	0.00641832
$370$	14183.1	1.99282
$371$	−2980.25	−0.417054
$372$	19791.1	2.75839
$373$	−6030.22	−0.837086	−0.418543	−	0.908197i	$-0.637459\pi$
$373$	−6030.22	−0.837086	−0.418543	+	0.908197i	$0.637459\pi$
$374$	0	0
$375$	7650.97	1.05358
$376$	14688.3	2.01460
$377$	5672.31	0.774904
$378$	5306.64	0.722075
$379$	−4622.40	−0.626482	−0.313241	−	0.949674i	$-0.601415\pi$
$379$	−4622.40	−0.626482	−0.313241	+	0.949674i	$0.601415\pi$
$380$	−7751.03	−1.04637
$381$	−6368.97	−0.856410
$382$	−4358.97	−0.583833
$383$	−8035.87	−1.07210	−0.536049	−	0.844187i	$-0.680084\pi$
$383$	−8035.87	−1.07210	−0.536049	+	0.844187i	$0.680084\pi$
$384$	21232.5	2.82166
$385$	4766.02	0.630906
$386$	−10407.8	−1.37239
$387$	57.1624	0.00750834
$388$	16796.3	2.19768
$389$	8420.03	1.09746	0.548730	−	0.835999i	$-0.315111\pi$
$389$	8420.03	1.09746	0.548730	+	0.835999i	$0.315111\pi$
$390$	−19956.1	−2.59107
$391$	0	0
$392$	3604.75	0.464458
$393$	11219.2	1.44004
$394$	−16283.7	−2.08214
$395$	−1015.18	−0.129315
$396$	425.610	0.0540094
$397$	−6130.85	−0.775060	−0.387530	−	0.921857i	$-0.626672\pi$
$397$	−6130.85	−0.775060	−0.387530	+	0.921857i	$0.626672\pi$
$398$	2468.71	0.310917
$399$	−1249.12	−0.156728
$400$	−3168.15	−0.396019
$401$	−7963.78	−0.991751	−0.495875	−	0.868394i	$-0.665153\pi$
$401$	−7963.78	−0.991751	−0.495875	+	0.868394i	$0.665153\pi$
$402$	13932.6	1.72860
$403$	11725.5	1.44935
$404$	−37303.3	−4.59383
$405$	7769.16	0.953217
$406$	−3236.50	−0.395627
$407$	−15996.7	−1.94823
$408$	0	0
$409$	−4182.03	−0.505594	−0.252797	−	0.967519i	$-0.581351\pi$
$409$	−4182.03	−0.505594	−0.252797	+	0.967519i	$0.581351\pi$
$410$	−8518.37	−1.02608
$411$	−4602.91	−0.552421
$412$	−22547.1	−2.69616
$413$	−3857.12	−0.459555
$414$	−299.573	−0.0355633
$415$	2020.74	0.239022
$416$	43204.9	5.09206
$417$	−3161.07	−0.371218
$418$	11989.6	1.40295
$419$	2117.96	0.246943	0.123472	−	0.992348i	$-0.460597\pi$
$419$	2117.96	0.246943	0.123472	+	0.992348i	$0.460597\pi$
$420$	8302.47	0.964569
$421$	−13463.8	−1.55863	−0.779316	−	0.626631i	$-0.784433\pi$
$421$	−13463.8	−1.55863	−0.779316	+	0.626631i	$0.784433\pi$
$422$	7194.45	0.829906
$423$	61.0778	0.00702058
$424$	31320.9	3.58745
$425$	0	0
$426$	−9709.42	−1.10428
$427$	3907.49	0.442850
$428$	−22395.4	−2.52926
$429$	22508.0	2.53310
$430$	−10703.0	−1.20034
$431$	−7789.96	−0.870601	−0.435301	−	0.900285i	$-0.643358\pi$
$431$	−7789.96	−0.870601	−0.435301	+	0.900285i	$0.643358\pi$
$432$	−31737.2	−3.53462
$433$	−14741.8	−1.63614	−0.818068	−	0.575122i	$-0.804955\pi$
$433$	−14741.8	−1.63614	−0.818068	+	0.575122i	$0.804955\pi$
$434$	−6690.32	−0.739967
$435$	−4685.29	−0.516419
$436$	−36451.2	−4.00389
$437$	−6153.33	−0.673579
$438$	26486.4	2.88943
$439$	9291.43	1.01015	0.505075	−	0.863076i	$-0.331465\pi$
$439$	9291.43	1.01015	0.505075	+	0.863076i	$0.331465\pi$
$440$	−50088.4	−5.42698
$441$	14.9895	0.00161856
$442$	0	0
$443$	−1971.56	−0.211449	−0.105724	−	0.994395i	$-0.533716\pi$
$443$	−1971.56	−0.211449	−0.105724	+	0.994395i	$0.533716\pi$
$444$	−27866.5	−2.97858
$445$	−221.527	−0.0235986
$446$	−29289.2	−3.10961
$447$	4352.16	0.460515
$448$	−11910.5	−1.25607
$449$	−13088.4	−1.37568	−0.687838	−	0.725864i	$-0.741440\pi$
$449$	−13088.4	−1.37568	−0.687838	+	0.725864i	$0.741440\pi$
$450$	−23.1500	−0.00242512
$451$	9607.66	1.00312
$452$	−22850.6	−2.37788
$453$	−10617.3	−1.10121
$454$	−21592.5	−2.23213
$455$	4918.90	0.506816
$456$	13127.6	1.34815
$457$	13830.5	1.41568	0.707839	−	0.706374i	$-0.249670\pi$
$457$	13830.5	1.41568	0.707839	+	0.706374i	$0.249670\pi$
$458$	35715.2	3.64381
$459$	0	0
$460$	40899.0	4.14549
$461$	3116.28	0.314837	0.157418	−	0.987532i	$-0.449683\pi$
$461$	3116.28	0.314837	0.157418	+	0.987532i	$0.449683\pi$
$462$	−12842.6	−1.29327
$463$	10225.4	1.02638	0.513190	−	0.858275i	$-0.328463\pi$
$463$	10225.4	1.02638	0.513190	+	0.858275i	$0.328463\pi$
$464$	19356.4	1.93663
$465$	−9685.18	−0.965892
$466$	−11356.9	−1.12897
$467$	6707.56	0.664644	0.332322	−	0.943166i	$-0.392168\pi$
$467$	6707.56	0.664644	0.332322	+	0.943166i	$0.392168\pi$
$468$	439.263	0.0433866
$469$	−3434.19	−0.338116
$470$	−11436.1	−1.12236
$471$	12880.7	1.26010
$472$	40536.3	3.95304
$473$	12071.7	1.17348
$474$	2735.53	0.265078
$475$	−475.510	−0.0459324
$476$	0	0
$477$	130.241	0.0125017
$478$	28490.3	2.72619
$479$	17403.2	1.66007	0.830036	−	0.557710i	$-0.188320\pi$
$479$	17403.2	1.66007	0.830036	+	0.557710i	$0.188320\pi$
$480$	−35687.0	−3.39350
$481$	−16509.9	−1.56504
$482$	−13980.9	−1.32119
$483$	6591.11	0.620923
$484$	61216.3	5.74909
$485$	−8219.59	−0.769551
$486$	−466.471	−0.0435382
$487$	14643.4	1.36254	0.681268	−	0.732034i	$-0.261429\pi$
$487$	14643.4	1.36254	0.681268	+	0.732034i	$0.261429\pi$
$488$	−41065.7	−3.80934
$489$	−1796.87	−0.166170
$490$	−2806.62	−0.258755
$491$	160.937	0.0147923	0.00739613	−	0.999973i	$-0.497646\pi$
$491$	160.937	0.0147923	0.00739613	+	0.999973i	$0.497646\pi$
$492$	16736.7	1.53363
$493$	0	0
$494$	12374.2	1.12701
$495$	−208.281	−0.0189122
$496$	40012.5	3.62221
$497$	2393.23	0.215998
$498$	−5445.12	−0.489963
$499$	−719.655	−0.0645615	−0.0322807	−	0.999479i	$-0.510277\pi$
$499$	−719.655	−0.0645615	−0.0322807	+	0.999479i	$0.510277\pi$
$500$	31532.6	2.82036
$501$	−1592.61	−0.142021
$502$	3212.87	0.285652
$503$	−3554.49	−0.315084	−0.157542	−	0.987512i	$-0.550357\pi$
$503$	−3554.49	−0.315084	−0.157542	+	0.987512i	$0.550357\pi$
$504$	−157.532	−0.0139227
$505$	18255.1	1.60860
$506$	−63264.3	−5.55818
$507$	11749.6	1.02923
$508$	−26249.0	−2.29254
$509$	−4737.28	−0.412527	−0.206263	−	0.978497i	$-0.566130\pi$
$509$	−4737.28	−0.412527	−0.206263	+	0.978497i	$0.566130\pi$
$510$	0	0
$511$	−6528.52	−0.565176
$512$	13529.7	1.16784
$513$	−4763.45	−0.409964
$514$	23391.3	2.00729
$515$	11033.9	0.944099
$516$	21029.0	1.79409
$517$	12898.5	1.09725
$518$	9420.18	0.799033
$519$	−861.305	−0.0728460
$520$	−51695.1	−4.35957
$521$	558.439	0.0469590	0.0234795	−	0.999724i	$-0.492526\pi$
$521$	558.439	0.0469590	0.0234795	+	0.999724i	$0.492526\pi$
$522$	141.439	0.0118594
$523$	−20801.7	−1.73919	−0.869593	−	0.493769i	$-0.835619\pi$
$523$	−20801.7	−1.73919	−0.869593	+	0.493769i	$0.835619\pi$
$524$	46238.8	3.85487
$525$	509.340	0.0423417
$526$	−43633.7	−3.61696
$527$	0	0
$528$	76807.2	6.33069
$529$	20301.6	1.66858
$530$	−24386.1	−1.99861
$531$	168.561	0.0137757
$532$	−5148.12	−0.419547
$533$	9915.85	0.805822
$534$	596.932	0.0483741
$535$	10959.6	0.885657
$536$	36091.6	2.90843
$537$	−7963.50	−0.639945
$538$	−32955.9	−2.64095
$539$	3165.52	0.252966
$540$	31661.0	2.52310
$541$	14320.8	1.13808	0.569038	−	0.822311i	$-0.307316\pi$
$541$	14320.8	1.13808	0.569038	+	0.822311i	$0.307316\pi$
$542$	−42269.9	−3.34991
$543$	−1445.14	−0.114211
$544$	0	0
$545$	17838.1	1.40202
$546$	−13254.6	−1.03891
$547$	12017.1	0.939334	0.469667	−	0.882844i	$-0.344374\pi$
$547$	12017.1	0.939334	0.469667	+	0.882844i	$0.344374\pi$
$548$	−18970.4	−1.47879
$549$	−170.762	−0.0132750
$550$	−4888.86	−0.379021
$551$	2905.21	0.224621
$552$	−69269.1	−5.34110
$553$	−674.267	−0.0518495
$554$	13847.0	1.06192
$555$	13637.0	1.04299
$556$	−13028.0	−0.993722
$557$	−1072.46	−0.0815826	−0.0407913	−	0.999168i	$-0.512988\pi$
$557$	−1072.46	−0.0815826	−0.0407913	+	0.999168i	$0.512988\pi$
$558$	292.375	0.0221814
$559$	12458.9	0.942674
$560$	16785.4	1.26663
$561$	0	0
$562$	−7952.33	−0.596884
$563$	−8076.90	−0.604620	−0.302310	−	0.953210i	$-0.597758\pi$
$563$	−8076.90	−0.604620	−0.302310	+	0.953210i	$0.597758\pi$
$564$	22469.4	1.67754
$565$	11182.4	0.832649
$566$	−4340.03	−0.322306
$567$	5160.16	0.382198
$568$	−25151.6	−1.85799
$569$	−1762.48	−0.129854	−0.0649271	−	0.997890i	$-0.520681\pi$
$569$	−1762.48	−0.129854	−0.0649271	+	0.997890i	$0.520681\pi$
$570$	−10221.0	−0.751072
$571$	2378.41	0.174314	0.0871569	−	0.996195i	$-0.472222\pi$
$571$	2378.41	0.174314	0.0871569	+	0.996195i	$0.472222\pi$
$572$	92764.3	6.78089
$573$	−4191.15	−0.305564
$574$	−5657.77	−0.411413
$575$	2509.07	0.181975
$576$	520.504	0.0376522
$577$	−10838.1	−0.781970	−0.390985	−	0.920397i	$-0.627866\pi$
$577$	−10838.1	−0.781970	−0.390985	+	0.920397i	$0.627866\pi$
$578$	0	0
$579$	−10007.1	−0.718273
$580$	−19309.9	−1.38241
$581$	1342.14	0.0958373
$582$	22148.7	1.57748
$583$	27504.5	1.95389
$584$	68611.4	4.86157
$585$	−214.962	−0.0151924
$586$	−3738.40	−0.263536
$587$	6455.58	0.453919	0.226959	−	0.973904i	$-0.427122\pi$
$587$	6455.58	0.453919	0.226959	+	0.973904i	$0.427122\pi$
$588$	5514.37	0.386750
$589$	6005.50	0.420123
$590$	−31561.1	−2.20229
$591$	−15656.8	−1.08974
$592$	−56338.9	−3.91134
$593$	−11556.4	−0.800274	−0.400137	−	0.916455i	$-0.631037\pi$
$593$	−11556.4	−0.800274	−0.400137	+	0.916455i	$0.631037\pi$
$594$	−48974.5	−3.38291
$595$	0	0
$596$	17936.9	1.23276
$597$	2373.67	0.162727
$598$	−65293.7	−4.46498
$599$	20334.5	1.38705	0.693526	−	0.720431i	$-0.256056\pi$
$599$	20334.5	1.38705	0.693526	+	0.720431i	$0.256056\pi$
$600$	−5352.90	−0.364218
$601$	13583.9	0.921964	0.460982	−	0.887409i	$-0.347497\pi$
$601$	13583.9	0.921964	0.460982	+	0.887409i	$0.347497\pi$
$602$	−7108.78	−0.481283
$603$	150.078	0.0101354
$604$	−43758.2	−2.94784
$605$	−29957.4	−2.01313
$606$	−49190.6	−3.29741
$607$	19329.7	1.29253	0.646267	−	0.763111i	$-0.276329\pi$
$607$	19329.7	1.29253	0.646267	+	0.763111i	$0.276329\pi$
$608$	22128.4	1.47603
$609$	−3111.90	−0.207062
$610$	31973.3	2.12223
$611$	13312.3	0.881436
$612$	0	0
$613$	−1472.93	−0.0970490	−0.0485245	−	0.998822i	$-0.515452\pi$
$613$	−1472.93	−0.0970490	−0.0485245	+	0.998822i	$0.515452\pi$
$614$	−15754.7	−1.03552
$615$	−8190.43	−0.537024
$616$	−33267.9	−2.17598
$617$	6443.07	0.420402	0.210201	−	0.977658i	$-0.432588\pi$
$617$	6443.07	0.420402	0.210201	+	0.977658i	$0.432588\pi$
$618$	−29732.1	−1.93528
$619$	−7397.28	−0.480326	−0.240163	−	0.970733i	$-0.577201\pi$
$619$	−7397.28	−0.480326	−0.240163	+	0.970733i	$0.577201\pi$
$620$	−39916.4	−2.58561
$621$	25134.8	1.62419
$622$	56721.9	3.65649
$623$	−147.135	−0.00946202
$624$	79271.0	5.08554
$625$	−13690.5	−0.876194
$626$	−11717.9	−0.748148
$627$	11528.0	0.734267
$628$	53086.2	3.37320
$629$	0	0
$630$	122.653	0.00775651
$631$	−24685.2	−1.55737	−0.778686	−	0.627414i	$-0.784113\pi$
$631$	−24685.2	−1.55737	−0.778686	+	0.627414i	$0.784113\pi$
$632$	7086.20	0.446003
$633$	6917.48	0.434352
$634$	31195.0	1.95412
$635$	12845.5	0.802767
$636$	47913.2	2.98723
$637$	3267.06	0.203211
$638$	29869.4	1.85351
$639$	−104.587	−0.00647481
$640$	−42823.5	−2.64492
$641$	−15914.8	−0.980649	−0.490324	−	0.871540i	$-0.663122\pi$
$641$	−15914.8	−0.980649	−0.490324	+	0.871540i	$0.663122\pi$
$642$	−29532.1	−1.81548
$643$	14705.4	0.901901	0.450951	−	0.892549i	$-0.351085\pi$
$643$	14705.4	0.901901	0.450951	+	0.892549i	$0.351085\pi$
$644$	27164.5	1.66216
$645$	−10291.0	−0.628227
$646$	0	0
$647$	−4403.14	−0.267551	−0.133775	−	0.991012i	$-0.542710\pi$
$647$	−4403.14	−0.267551	−0.133775	+	0.991012i	$0.542710\pi$
$648$	−54230.6	−3.28762
$649$	35597.0	2.15301
$650$	−5045.68	−0.304474
$651$	−6432.75	−0.387280
$652$	−7405.60	−0.444825
$653$	−2775.10	−0.166306	−0.0831531	−	0.996537i	$-0.526499\pi$
$653$	−2775.10	−0.166306	−0.0831531	+	0.996537i	$0.526499\pi$
$654$	−48067.0	−2.87396
$655$	−22627.9	−1.34984
$656$	33837.2	2.01390
$657$	285.304	0.0169418
$658$	−7595.70	−0.450017
$659$	−10531.7	−0.622546	−0.311273	−	0.950321i	$-0.600755\pi$
$659$	−10531.7	−0.622546	−0.311273	+	0.950321i	$0.600755\pi$
$660$	−76622.7	−4.51899
$661$	−12767.3	−0.751270	−0.375635	−	0.926768i	$-0.622575\pi$
$661$	−12767.3	−0.751270	−0.375635	+	0.926768i	$0.622575\pi$
$662$	−2177.08	−0.127817
$663$	0	0
$664$	−14105.2	−0.824381
$665$	2519.33	0.146911
$666$	−411.674	−0.0239520
$667$	−15329.6	−0.889902
$668$	−6563.75	−0.380179
$669$	−28161.6	−1.62749
$670$	−28100.5	−1.62032
$671$	−36061.9	−2.07475
$672$	−23702.7	−1.36064
$673$	−14462.9	−0.828384	−0.414192	−	0.910190i	$-0.635936\pi$
$673$	−14462.9	−0.828384	−0.414192	+	0.910190i	$0.635936\pi$
$674$	10096.1	0.576985
$675$	1942.34	0.110756
$676$	48424.6	2.75516
$677$	9503.00	0.539483	0.269742	−	0.962933i	$-0.413062\pi$
$677$	9503.00	0.539483	0.269742	+	0.962933i	$0.413062\pi$
$678$	−30132.3	−1.70682
$679$	−5459.33	−0.308556
$680$	0	0
$681$	−20761.2	−1.16824
$682$	61744.4	3.46674
$683$	11291.7	0.632600	0.316300	−	0.948659i	$-0.397559\pi$
$683$	11291.7	0.632600	0.316300	+	0.948659i	$0.397559\pi$
$684$	224.979	0.0125764
$685$	9283.54	0.517819
$686$	−1864.11	−0.103750
$687$	34340.3	1.90708
$688$	42515.2	2.35592
$689$	28386.7	1.56959
$690$	53932.1	2.97560
$691$	8279.56	0.455817	0.227908	−	0.973683i	$-0.426811\pi$
$691$	8279.56	0.455817	0.227908	+	0.973683i	$0.426811\pi$
$692$	−3549.77	−0.195003
$693$	−138.337	−0.00758295
$694$	37387.8	2.04499
$695$	6375.50	0.347966
$696$	32704.4	1.78112
$697$	0	0
$698$	−48570.3	−2.63383
$699$	−10919.7	−0.590874
$700$	2099.19	0.113345
$701$	−15744.7	−0.848315	−0.424157	−	0.905589i	$-0.639430\pi$
$701$	−15744.7	−0.848315	−0.424157	+	0.905589i	$0.639430\pi$
$702$	−50545.5	−2.71755
$703$	−8455.93	−0.453658
$704$	109921.	5.88467
$705$	−10995.9	−0.587415
$706$	30228.7	1.61143
$707$	12124.8	0.644977
$708$	62010.4	3.29166
$709$	−28550.2	−1.51231	−0.756154	−	0.654394i	$-0.772924\pi$
$709$	−28550.2	−1.51231	−0.756154	+	0.654394i	$0.772924\pi$
$710$	19582.8	1.03511
$711$	29.4663	0.00155425
$712$	1546.31	0.0813912
$713$	−31688.6	−1.66444
$714$	0	0
$715$	−45396.1	−2.37443
$716$	−32820.7	−1.71308
$717$	27393.5	1.42682
$718$	−66548.2	−3.45899
$719$	27719.6	1.43778	0.718891	−	0.695123i	$-0.244650\pi$
$719$	27719.6	1.43778	0.718891	+	0.695123i	$0.244650\pi$
$720$	−733.544	−0.0379688
$721$	7328.54	0.378542
$722$	−30939.1	−1.59478
$723$	−13442.7	−0.691477
$724$	−5955.98	−0.305735
$725$	−1184.62	−0.0606839
$726$	80723.9	4.12664
$727$	10694.7	0.545590	0.272795	−	0.962072i	$-0.412052\pi$
$727$	10694.7	0.545590	0.272795	+	0.962072i	$0.412052\pi$
$728$	−34335.1	−1.74800
$729$	19455.0	0.988415
$730$	−53420.0	−2.70844
$731$	0	0
$732$	−62820.4	−3.17200
$733$	15531.0	0.782608	0.391304	−	0.920261i	$-0.372024\pi$
$733$	15531.0	0.782608	0.391304	+	0.920261i	$0.372024\pi$
$734$	29853.5	1.50124
$735$	−2698.57	−0.135426
$736$	−116763.	−5.84773
$737$	31693.8	1.58407
$738$	247.252	0.0123326
$739$	7026.05	0.349740	0.174870	−	0.984592i	$-0.444050\pi$
$739$	7026.05	0.349740	0.174870	+	0.984592i	$0.444050\pi$
$740$	56203.6	2.79201
$741$	11897.8	0.589848
$742$	−16196.9	−0.801356
$743$	23896.5	1.17992	0.589958	−	0.807434i	$-0.299144\pi$
$743$	23896.5	1.17992	0.589958	+	0.807434i	$0.299144\pi$
$744$	67604.9	3.33134
$745$	−8777.79	−0.431669
$746$	−32772.6	−1.60843
$747$	−58.6533	−0.00287284
$748$	0	0
$749$	7279.23	0.355110
$750$	41581.0	2.02443
$751$	−5576.12	−0.270939	−0.135470	−	0.990781i	$-0.543254\pi$
$751$	−5576.12	−0.270939	−0.135470	+	0.990781i	$0.543254\pi$
$752$	45427.3	2.20288
$753$	3089.18	0.149503
$754$	30827.5	1.48895
$755$	21413.9	1.03223
$756$	21028.7	1.01165
$757$	−8472.56	−0.406791	−0.203395	−	0.979097i	$-0.565198\pi$
$757$	−8472.56	−0.406791	−0.203395	+	0.979097i	$0.565198\pi$
$758$	−25121.5	−1.20377
$759$	−60828.7	−2.90902
$760$	−26476.9	−1.26371
$761$	12055.8	0.574273	0.287137	−	0.957890i	$-0.407297\pi$
$761$	12055.8	0.574273	0.287137	+	0.957890i	$0.407297\pi$
$762$	−34613.7	−1.64557
$763$	11847.8	0.562149
$764$	−17273.4	−0.817969
$765$	0	0
$766$	−43672.8	−2.06000
$767$	36738.8	1.72955
$768$	44263.3	2.07971
$769$	3250.06	0.152406	0.0762030	−	0.997092i	$-0.475720\pi$
$769$	3250.06	0.152406	0.0762030	+	0.997092i	$0.475720\pi$
$770$	25902.0	1.21227
$771$	22490.8	1.05057
$772$	−41243.0	−1.92276
$773$	36682.0	1.70681	0.853403	−	0.521252i	$-0.174535\pi$
$773$	36682.0	1.70681	0.853403	+	0.521252i	$0.174535\pi$
$774$	310.662	0.0144270
$775$	−2448.79	−0.113501
$776$	57374.7	2.65417
$777$	9057.52	0.418194
$778$	45760.6	2.10874
$779$	5078.64	0.233583
$780$	−79080.6	−3.63018
$781$	−22086.9	−1.01195
$782$	0	0
$783$	−11867.0	−0.541627
$784$	11148.6	0.507864
$785$	−25978.8	−1.18118
$786$	60973.5	2.76699
$787$	−4957.43	−0.224540	−0.112270	−	0.993678i	$-0.535812\pi$
$787$	−4957.43	−0.224540	−0.112270	+	0.993678i	$0.535812\pi$
$788$	−64527.9	−2.91715
$789$	−41953.9	−1.89303
$790$	−5517.24	−0.248474
$791$	7427.18	0.333856
$792$	1453.85	0.0652277
$793$	−37218.7	−1.66668
$794$	−33319.6	−1.48925
$795$	−23447.3	−1.04602
$796$	9782.80	0.435606
$797$	1587.25	0.0705435	0.0352718	−	0.999378i	$-0.488770\pi$
$797$	1587.25	0.0705435	0.0352718	+	0.999378i	$0.488770\pi$
$798$	−6788.64	−0.301147
$799$	0	0
$800$	−9023.05	−0.398766
$801$	6.42998	0.000283636 0
$802$	−43281.0	−1.90562
$803$	60251.1	2.64784
$804$	55211.1	2.42182
$805$	−13293.5	−0.582030
$806$	63725.0	2.78488
$807$	−31687.2	−1.38221
$808$	−127425.	−5.54802
$809$	−39593.5	−1.72068	−0.860342	−	0.509717i	$-0.829750\pi$
$809$	−39593.5	−1.72068	−0.860342	+	0.509717i	$0.829750\pi$
$810$	42223.3	1.83158
$811$	−24364.8	−1.05495	−0.527475	−	0.849571i	$-0.676861\pi$
$811$	−24364.8	−1.05495	−0.527475	+	0.849571i	$0.676861\pi$
$812$	−12825.3	−0.554287
$813$	−40642.6	−1.75326
$814$	−86938.0	−3.74346
$815$	3624.08	0.155762
$816$	0	0
$817$	6381.12	0.273252
$818$	−22728.2	−0.971484
$819$	−142.774	−0.00609151
$820$	−33755.9	−1.43757
$821$	−3226.74	−0.137167	−0.0685833	−	0.997645i	$-0.521848\pi$
$821$	−3226.74	−0.137167	−0.0685833	+	0.997645i	$0.521848\pi$
$822$	−25015.6	−1.06146
$823$	32631.1	1.38208	0.691038	−	0.722818i	$-0.257154\pi$
$823$	32631.1	1.38208	0.691038	+	0.722818i	$0.257154\pi$
$824$	−77019.1	−3.25618
$825$	−4700.65	−0.198370
$826$	−20962.4	−0.883021
$827$	21602.3	0.908326	0.454163	−	0.890919i	$-0.349938\pi$
$827$	21602.3	0.908326	0.454163	+	0.890919i	$0.349938\pi$
$828$	−1187.12	−0.0498253
$829$	1356.54	0.0568329	0.0284164	−	0.999596i	$-0.490954\pi$
$829$	1356.54	0.0568329	0.0284164	+	0.999596i	$0.490954\pi$
$830$	10982.2	0.459273
$831$	13313.9	0.555783
$832$	113447.	4.72725
$833$	0	0
$834$	−17179.6	−0.713284
$835$	3212.10	0.133125
$836$	47511.5	1.96557
$837$	−24530.9	−1.01304
$838$	11510.6	0.474494
$839$	−27957.8	−1.15043	−0.575216	−	0.818002i	$-0.695082\pi$
$839$	−27957.8	−1.15043	−0.575216	+	0.818002i	$0.695082\pi$
$840$	28360.6	1.16492
$841$	−17151.3	−0.703241
$842$	−73172.0	−2.99486
$843$	−7646.17	−0.312394
$844$	28509.6	1.16273
$845$	−23697.6	−0.964758
$846$	331.942	0.0134898
$847$	−19897.3	−0.807176
$848$	96868.0	3.92271
$849$	−4172.94	−0.168687
$850$	0	0
$851$	44618.5	1.79730
$852$	−38475.7	−1.54713
$853$	22197.0	0.890987	0.445494	−	0.895285i	$-0.353028\pi$
$853$	22197.0	0.890987	0.445494	+	0.895285i	$0.353028\pi$
$854$	21236.2	0.850922
$855$	−110.098	−0.00440383
$856$	−76500.9	−3.05461
$857$	28620.6	1.14079	0.570397	−	0.821369i	$-0.306790\pi$
$857$	28620.6	1.14079	0.570397	+	0.821369i	$0.306790\pi$
$858$	122325.	4.86726
$859$	−20146.1	−0.800207	−0.400103	−	0.916470i	$-0.631026\pi$
$859$	−20146.1	−0.800207	−0.400103	+	0.916470i	$0.631026\pi$
$860$	−42413.0	−1.68171
$861$	−5439.96	−0.215323
$862$	−42336.4	−1.67283
$863$	−18676.5	−0.736680	−0.368340	−	0.929691i	$-0.620074\pi$
$863$	−18676.5	−0.736680	−0.368340	+	0.929691i	$0.620074\pi$
$864$	−90389.1	−3.55914
$865$	1737.15	0.0682832
$866$	−80117.9	−3.14378
$867$	0	0
$868$	−26511.9	−1.03672
$869$	6222.75	0.242914
$870$	−25463.3	−0.992284
$871$	32710.5	1.27251
$872$	−124514.	−4.83554
$873$	238.579	0.00924936
$874$	−33441.7	−1.29426
$875$	−10249.1	−0.395981
$876$	104958.	4.04819
$877$	26947.5	1.03757	0.518786	−	0.854904i	$-0.326384\pi$
$877$	26947.5	1.03757	0.518786	+	0.854904i	$0.326384\pi$
$878$	50496.4	1.94097
$879$	−3594.48	−0.137928
$880$	−154911.	−5.93415
$881$	−35309.6	−1.35030	−0.675148	−	0.737683i	$-0.735920\pi$
$881$	−35309.6	−1.35030	−0.675148	+	0.737683i	$0.735920\pi$
$882$	81.4641	0.00311002
$883$	42421.3	1.61675	0.808374	−	0.588669i	$-0.200348\pi$
$883$	42421.3	1.61675	0.808374	+	0.588669i	$0.200348\pi$
$884$	0	0
$885$	−30346.0	−1.15262
$886$	−10714.9	−0.406292
$887$	−31687.1	−1.19949	−0.599745	−	0.800191i	$-0.704731\pi$
$887$	−31687.1	−1.19949	−0.599745	+	0.800191i	$0.704731\pi$
$888$	−95189.9	−3.59725
$889$	8531.77	0.321874
$890$	−1203.94	−0.0453441
$891$	−47622.7	−1.79059
$892$	−116065.	−4.35666
$893$	6818.21	0.255501
$894$	23652.8	0.884864
$895$	16061.4	0.599860
$896$	−28442.7	−1.06050
$897$	−62780.0	−2.33686
$898$	−71131.8	−2.64332
$899$	14961.3	0.555047
$900$	−91.7370	−0.00339767
$901$	0	0
$902$	52215.1	1.92746
$903$	−6835.10	−0.251891
$904$	−78055.8	−2.87179
$905$	2914.68	0.107058
$906$	−57702.4	−2.11593
$907$	5302.73	0.194128	0.0970640	−	0.995278i	$-0.469055\pi$
$907$	5302.73	0.194128	0.0970640	+	0.995278i	$0.469055\pi$
$908$	−85565.1	−3.12729
$909$	−529.868	−0.0193340
$910$	26732.9	0.973832
$911$	12477.8	0.453797	0.226899	−	0.973918i	$-0.427141\pi$
$911$	12477.8	0.453797	0.226899	+	0.973918i	$0.427141\pi$
$912$	40600.6	1.47414
$913$	−12386.5	−0.448996
$914$	75165.2	2.72018
$915$	30742.4	1.11072
$916$	141530.	5.10510
$917$	−15029.1	−0.541226
$918$	0	0
$919$	42043.4	1.50912	0.754561	−	0.656230i	$-0.227850\pi$
$919$	42043.4	1.50912	0.754561	+	0.656230i	$0.227850\pi$
$920$	139708.	5.00655
$921$	−15148.2	−0.541964
$922$	16936.2	0.604949
$923$	−22795.4	−0.812914
$924$	−50891.7	−1.81192
$925$	3447.97	0.122561
$926$	55572.3	1.97216
$927$	−320.266	−0.0113473
$928$	55127.9	1.95007
$929$	−10450.4	−0.369071	−0.184535	−	0.982826i	$-0.559078\pi$
$929$	−10450.4	−0.369071	−0.184535	+	0.982826i	$0.559078\pi$
$930$	−52636.4	−1.85593
$931$	1673.30	0.0589047
$932$	−45004.3	−1.58172
$933$	54538.2	1.91372
$934$	36453.8	1.27709
$935$	0	0
$936$	1500.49	0.0523984
$937$	855.668	0.0298329	0.0149165	−	0.999889i	$-0.495252\pi$
$937$	855.668	0.0298329	0.0149165	+	0.999889i	$0.495252\pi$
$938$	−18663.9	−0.649679
$939$	−11266.8	−0.391562
$940$	−45318.2	−1.57246
$941$	53778.5	1.86305	0.931525	−	0.363678i	$-0.118479\pi$
$941$	53778.5	1.86305	0.931525	+	0.363678i	$0.118479\pi$
$942$	70003.0	2.42125
$943$	−26797.9	−0.925409
$944$	125369.	4.32247
$945$	−10290.8	−0.354244
$946$	65606.3	2.25480
$947$	8730.15	0.299569	0.149784	−	0.988719i	$-0.452142\pi$
$947$	8730.15	0.299569	0.149784	+	0.988719i	$0.452142\pi$
$948$	10840.1	0.371383
$949$	62183.8	2.12705
$950$	−2584.27	−0.0882577
$951$	29994.1	1.02274
$952$	0	0
$953$	39579.2	1.34533	0.672664	−	0.739948i	$-0.265150\pi$
$953$	39579.2	1.34533	0.672664	+	0.739948i	$0.265150\pi$
$954$	707.823	0.0240216
$955$	8453.07	0.286424
$956$	112899.	3.81948
$957$	28719.4	0.970081
$958$	94582.0	3.18978
$959$	6165.99	0.207623
$960$	−93706.5	−3.15038
$961$	1136.23	0.0381401
$962$	−89726.8	−3.00718
$963$	−318.111	−0.0106448
$964$	−55402.4	−1.85103
$965$	20183.1	0.673282
$966$	35820.9	1.19308
$967$	10343.2	0.343965	0.171983	−	0.985100i	$-0.444983\pi$
$967$	10343.2	0.343965	0.171983	+	0.985100i	$0.444983\pi$
$968$	209110.	6.94323
$969$	0	0
$970$	−44671.3	−1.47867
$971$	38341.3	1.26718	0.633590	−	0.773669i	$-0.281581\pi$
$971$	38341.3	1.26718	0.633590	+	0.773669i	$0.281581\pi$
$972$	−1848.50	−0.0609985
$973$	4234.51	0.139519
$974$	79582.9	2.61807
$975$	−4851.43	−0.159354
$976$	−127006.	−4.16534
$977$	26902.6	0.880952	0.440476	−	0.897764i	$-0.354810\pi$
$977$	26902.6	0.880952	0.440476	+	0.897764i	$0.354810\pi$
$978$	−9765.52	−0.319291
$979$	1357.90	0.0443295
$980$	−11121.8	−0.362525
$981$	−517.764	−0.0168511
$982$	874.651	0.0284229
$983$	46559.6	1.51070	0.755351	−	0.655320i	$-0.227466\pi$
$983$	46559.6	1.51070	0.755351	+	0.655320i	$0.227466\pi$
$984$	57171.2	1.85218
$985$	31578.0	1.02148
$986$	0	0
$987$	−7303.28	−0.235528
$988$	49035.5	1.57898
$989$	−33670.6	−1.08257
$990$	−1131.95	−0.0363392
$991$	−2533.96	−0.0812250	−0.0406125	−	0.999175i	$-0.512931\pi$
$991$	−2533.96	−0.0812250	−0.0406125	+	0.999175i	$0.512931\pi$
$992$	113957.	3.64733
$993$	−2093.26	−0.0668960
$994$	13006.6	0.415034
$995$	−4787.41	−0.152534
$996$	−21577.5	−0.686454
$997$	−21324.1	−0.677374	−0.338687	−	0.940899i	$-0.609983\pi$
$997$	−21324.1	−0.677374	−0.338687	+	0.940899i	$0.609983\pi$
$998$	−3911.13	−0.124053
$999$	34540.3	1.09390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.l.1.12	yes	12
17.16	even	2		2023.4.a.k.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2023.4.a.k.1.12	✓	12	17.16	even	2
2023.4.a.l.1.12	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q+5.43473 q^{2} +5.22551 q^{3} +21.5363 q^{4} -10.5392 q^{5} +28.3992 q^{6} -7.00000 q^{7} +73.5664 q^{8} +0.305909 q^{9} -57.2779 q^{10} +64.6024 q^{11} +112.538 q^{12} +66.6746 q^{13} -38.0431 q^{14} -55.0728 q^{15} +227.523 q^{16} +1.66253 q^{18} +34.1490 q^{19} -226.976 q^{20} -36.5785 q^{21} +351.097 q^{22} -180.191 q^{23} +384.422 q^{24} -13.9245 q^{25} +362.359 q^{26} -139.490 q^{27} -150.754 q^{28} +85.0745 q^{29} -299.306 q^{30} +175.861 q^{31} +647.996 q^{32} +337.580 q^{33} +73.7746 q^{35} +6.58815 q^{36} -247.618 q^{37} +185.591 q^{38} +348.409 q^{39} -775.333 q^{40} +148.720 q^{41} -198.795 q^{42} +186.861 q^{43} +1391.30 q^{44} -3.22404 q^{45} -979.288 q^{46} +199.660 q^{47} +1188.92 q^{48} +49.0000 q^{49} -75.6762 q^{50} +1435.93 q^{52} +425.750 q^{53} -758.092 q^{54} -680.859 q^{55} -514.965 q^{56} +178.446 q^{57} +462.357 q^{58} +551.016 q^{59} -1186.07 q^{60} -558.213 q^{61} +955.760 q^{62} -2.14136 q^{63} +1701.50 q^{64} -702.700 q^{65} +1834.66 q^{66} +490.599 q^{67} -941.587 q^{69} +400.946 q^{70} -341.890 q^{71} +22.5046 q^{72} +932.646 q^{73} -1345.74 q^{74} -72.7628 q^{75} +735.445 q^{76} -452.217 q^{77} +1893.51 q^{78} +96.3239 q^{79} -2397.92 q^{80} -737.166 q^{81} +808.253 q^{82} -191.735 q^{83} -787.768 q^{84} +1015.54 q^{86} +444.557 q^{87} +4752.56 q^{88} +21.0193 q^{89} -17.5218 q^{90} -466.723 q^{91} -3880.64 q^{92} +918.965 q^{93} +1085.10 q^{94} -359.905 q^{95} +3386.11 q^{96} +779.904 q^{97} +266.302 q^{98} +19.7624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} + 65 q^{4} - 12 q^{5} - 22 q^{6} - 84 q^{7} + 78 q^{8} + 233 q^{9} + 36 q^{10} + 4 q^{11} + 6 q^{12} + 98 q^{13} - 21 q^{14} - 196 q^{15} + 429 q^{16} + 603 q^{18} - 37 q^{19} + 54 q^{20}+ \cdots + 5140 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 + 65 * q^4 - 12 * q^5 - 22 * q^6 - 84 * q^7 + 78 * q^8 + 233 * q^9 + 36 * q^10 + 4 * q^11 + 6 * q^12 + 98 * q^13 - 21 * q^14 - 196 * q^15 + 429 * q^16 + 603 * q^18 - 37 * q^19 + 54 * q^20 - 21 * q^21 + 70 * q^22 - 369 * q^23 - 652 * q^24 + 590 * q^25 + 638 * q^26 + 501 * q^27 - 455 * q^28 + 144 * q^29 - 160 * q^30 + 67 * q^31 + 417 * q^32 + 628 * q^33 + 84 * q^35 + 999 * q^36 - 345 * q^37 - 190 * q^38 + 6 * q^39 - 466 * q^40 - 156 * q^41 + 154 * q^42 - 763 * q^43 + 1046 * q^44 + 832 * q^45 - 395 * q^46 + 561 * q^47 + 532 * q^48 + 588 * q^49 + 1923 * q^50 + 3138 * q^52 + 1156 * q^53 - 1682 * q^54 - 156 * q^55 - 546 * q^56 - 501 * q^57 - 2305 * q^58 - 473 * q^59 - 1292 * q^60 + 1850 * q^61 + 202 * q^62 - 1631 * q^63 - 712 * q^64 + 1718 * q^65 + 2142 * q^66 - 834 * q^67 + 1316 * q^69 - 252 * q^70 - 3179 * q^71 + 2046 * q^72 + 1012 * q^73 - 2695 * q^74 - 3841 * q^75 + 3272 * q^76 - 28 * q^77 + 970 * q^78 - 3897 * q^79 - 1616 * q^80 + 3448 * q^81 + 4758 * q^82 + 675 * q^83 - 42 * q^84 + 77 * q^86 + 805 * q^87 + 5398 * q^88 + 4078 * q^89 + 13384 * q^90 - 686 * q^91 - 3393 * q^92 + 3671 * q^93 + 958 * q^94 - 4126 * q^95 - 2320 * q^96 + 1474 * q^97 + 147 * q^98 + 5140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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