LMFDB - Embedded newform 2366.4.a.bd.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,4,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2366.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:	$139.598519074$
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} - 6 x^{11} - 219 x^{10} + 1022 x^{9} + 17084 x^{8} - 65540 x^{7} - 566763 x^{6} + 1871300 x^{5} + \cdots + 543166 $ x^12 - 6x^11 - 219x^10 + 1022x^9 + 17084x^8 - 65540x^7 - 566763x^6 + 1871300x^5 + 6589295x^4 - 20167176x^3 + 8073768x^2 + 5594524*x + 543166
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 13 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$6.59050$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +4.85845 q^{3} +4.00000 q^{4} -13.8421 q^{5} -9.71690 q^{6} +7.00000 q^{7} -8.00000 q^{8} -3.39547 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +4.85845 q^{3} +4.00000 q^{4} -13.8421 q^{5} -9.71690 q^{6} +7.00000 q^{7} -8.00000 q^{8} -3.39547 q^{9} +27.6843 q^{10} -51.8429 q^{11} +19.4338 q^{12} -14.0000 q^{14} -67.2513 q^{15} +16.0000 q^{16} -105.787 q^{17} +6.79094 q^{18} +48.0058 q^{19} -55.3685 q^{20} +34.0091 q^{21} +103.686 q^{22} +22.8487 q^{23} -38.8676 q^{24} +66.6045 q^{25} -147.675 q^{27} +28.0000 q^{28} +233.181 q^{29} +134.503 q^{30} -123.298 q^{31} -32.0000 q^{32} -251.876 q^{33} +211.574 q^{34} -96.8949 q^{35} -13.5819 q^{36} -187.074 q^{37} -96.0117 q^{38} +110.737 q^{40} -354.907 q^{41} -68.0183 q^{42} +72.8028 q^{43} -207.372 q^{44} +47.0005 q^{45} -45.6974 q^{46} -470.316 q^{47} +77.7352 q^{48} +49.0000 q^{49} -133.209 q^{50} -513.961 q^{51} +159.833 q^{53} +295.350 q^{54} +717.616 q^{55} -56.0000 q^{56} +233.234 q^{57} -466.361 q^{58} -320.826 q^{59} -269.005 q^{60} +478.752 q^{61} +246.596 q^{62} -23.7683 q^{63} +64.0000 q^{64} +503.752 q^{66} +343.671 q^{67} -423.148 q^{68} +111.009 q^{69} +193.790 q^{70} +147.749 q^{71} +27.1637 q^{72} -779.080 q^{73} +374.149 q^{74} +323.595 q^{75} +192.023 q^{76} -362.900 q^{77} +962.115 q^{79} -221.474 q^{80} -625.793 q^{81} +709.815 q^{82} -1097.00 q^{83} +136.037 q^{84} +1464.32 q^{85} -145.606 q^{86} +1132.90 q^{87} +414.743 q^{88} +709.491 q^{89} -94.0010 q^{90} +91.3948 q^{92} -599.037 q^{93} +940.631 q^{94} -664.503 q^{95} -155.470 q^{96} -355.024 q^{97} -98.0000 q^{98} +176.031 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} + 6 q^{3} + 48 q^{4} - 28 q^{5} - 12 q^{6} + 84 q^{7} - 96 q^{8} + 162 q^{9}+O(q^{10}) $ 12 * q - 24 * q^2 + 6 * q^3 + 48 * q^4 - 28 * q^5 - 12 * q^6 + 84 * q^7 - 96 * q^8 + 162 * q^9	\( 12 q - 24 q^{2} + 6 q^{3} + 48 q^{4} - 28 q^{5} - 12 q^{6} + 84 q^{7} - 96 q^{8} + 162 q^{9} + 56 q^{10} - 6 q^{11} + 24 q^{12} - 168 q^{14} + 138 q^{15} + 192 q^{16} - 56 q^{17} - 324 q^{18} - 158 q^{19} - 112 q^{20} + 42 q^{21} + 12 q^{22} + 414 q^{23} - 48 q^{24} + 478 q^{25} + 390 q^{27} + 336 q^{28} + 222 q^{29} - 276 q^{30} + 200 q^{31} - 384 q^{32} - 844 q^{33} + 112 q^{34} - 196 q^{35} + 648 q^{36} + 560 q^{37} + 316 q^{38} + 224 q^{40} + 66 q^{41} - 84 q^{42} + 484 q^{43} - 24 q^{44} - 542 q^{45} - 828 q^{46} - 618 q^{47} + 96 q^{48} + 588 q^{49} - 956 q^{50} + 992 q^{51} + 504 q^{53} - 780 q^{54} + 2584 q^{55} - 672 q^{56} + 1164 q^{57} - 444 q^{58} - 1460 q^{59} + 552 q^{60} - 2 q^{61} - 400 q^{62} + 1134 q^{63} + 768 q^{64} + 1688 q^{66} - 334 q^{67} - 224 q^{68} + 4660 q^{69} + 392 q^{70} + 196 q^{71} - 1296 q^{72} - 490 q^{73} - 1120 q^{74} - 338 q^{75} - 632 q^{76} - 42 q^{77} + 2942 q^{79} - 448 q^{80} + 2824 q^{81} - 132 q^{82} - 236 q^{83} + 168 q^{84} - 1352 q^{85} - 968 q^{86} + 1456 q^{87} + 48 q^{88} - 3566 q^{89} + 1084 q^{90} + 1656 q^{92} - 1884 q^{93} + 1236 q^{94} + 5754 q^{95} - 192 q^{96} - 3032 q^{97} - 1176 q^{98} - 3670 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 6 * q^3 + 48 * q^4 - 28 * q^5 - 12 * q^6 + 84 * q^7 - 96 * q^8 + 162 * q^9 + 56 * q^10 - 6 * q^11 + 24 * q^12 - 168 * q^14 + 138 * q^15 + 192 * q^16 - 56 * q^17 - 324 * q^18 - 158 * q^19 - 112 * q^20 + 42 * q^21 + 12 * q^22 + 414 * q^23 - 48 * q^24 + 478 * q^25 + 390 * q^27 + 336 * q^28 + 222 * q^29 - 276 * q^30 + 200 * q^31 - 384 * q^32 - 844 * q^33 + 112 * q^34 - 196 * q^35 + 648 * q^36 + 560 * q^37 + 316 * q^38 + 224 * q^40 + 66 * q^41 - 84 * q^42 + 484 * q^43 - 24 * q^44 - 542 * q^45 - 828 * q^46 - 618 * q^47 + 96 * q^48 + 588 * q^49 - 956 * q^50 + 992 * q^51 + 504 * q^53 - 780 * q^54 + 2584 * q^55 - 672 * q^56 + 1164 * q^57 - 444 * q^58 - 1460 * q^59 + 552 * q^60 - 2 * q^61 - 400 * q^62 + 1134 * q^63 + 768 * q^64 + 1688 * q^66 - 334 * q^67 - 224 * q^68 + 4660 * q^69 + 392 * q^70 + 196 * q^71 - 1296 * q^72 - 490 * q^73 - 1120 * q^74 - 338 * q^75 - 632 * q^76 - 42 * q^77 + 2942 * q^79 - 448 * q^80 + 2824 * q^81 - 132 * q^82 - 236 * q^83 + 168 * q^84 - 1352 * q^85 - 968 * q^86 + 1456 * q^87 + 48 * q^88 - 3566 * q^89 + 1084 * q^90 + 1656 * q^92 - 1884 * q^93 + 1236 * q^94 + 5754 * q^95 - 192 * q^96 - 3032 * q^97 - 1176 * q^98 - 3670 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	4.85845	0.935009	0.467505	−	0.883991i	$-0.345153\pi$
$3$	4.85845	0.935009	0.467505	+	0.883991i	$0.345153\pi$
$4$	4.00000	0.500000
$5$	−13.8421	−1.23808	−0.619039	−	0.785360i	$-0.712478\pi$
$5$	−13.8421	−1.23808	−0.619039	+	0.785360i	$0.712478\pi$
$6$	−9.71690	−0.661151
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	−3.39547	−0.125758
$10$	27.6843	0.875453
$11$	−51.8429	−1.42102	−0.710510	−	0.703687i	$-0.751536\pi$
$11$	−51.8429	−1.42102	−0.710510	+	0.703687i	$0.751536\pi$
$12$	19.4338	0.467505
$13$	0	0
$13$	0	0
$14$	−14.0000	−0.267261
$15$	−67.2513	−1.15761
$16$	16.0000	0.250000
$17$	−105.787	−1.50924	−0.754621	−	0.656161i	$-0.772179\pi$
$17$	−105.787	−1.50924	−0.754621	+	0.656161i	$0.772179\pi$
$18$	6.79094	0.0889244
$19$	48.0058	0.579647	0.289824	−	0.957080i	$-0.406403\pi$
$19$	48.0058	0.579647	0.289824	+	0.957080i	$0.406403\pi$
$20$	−55.3685	−0.619039
$21$	34.0091	0.353400
$22$	103.686	1.00481
$23$	22.8487	0.207143	0.103571	−	0.994622i	$-0.466973\pi$
$23$	22.8487	0.207143	0.103571	+	0.994622i	$0.466973\pi$
$24$	−38.8676	−0.330576
$25$	66.6045	0.532836
$26$	0	0
$27$	−147.675	−1.05259
$28$	28.0000	0.188982
$29$	233.181	1.49312	0.746561	−	0.665316i	$-0.231703\pi$
$29$	233.181	1.49312	0.746561	+	0.665316i	$0.231703\pi$
$30$	134.503	0.818557
$31$	−123.298	−0.714354	−0.357177	−	0.934037i	$-0.616261\pi$
$31$	−123.298	−0.714354	−0.357177	+	0.934037i	$0.616261\pi$
$32$	−32.0000	−0.176777
$33$	−251.876	−1.32867
$34$	211.574	1.06720
$35$	−96.8949	−0.467949
$36$	−13.5819	−0.0628790
$37$	−187.074	−0.831212	−0.415606	−	0.909545i	$-0.636430\pi$
$37$	−187.074	−0.831212	−0.415606	+	0.909545i	$0.636430\pi$
$38$	−96.0117	−0.409872
$39$	0	0
$40$	110.737	0.437727
$41$	−354.907	−1.35188	−0.675942	−	0.736955i	$-0.736263\pi$
$41$	−354.907	−1.35188	−0.675942	+	0.736955i	$0.736263\pi$
$42$	−68.0183	−0.249892
$43$	72.8028	0.258193	0.129097	−	0.991632i	$-0.458792\pi$
$43$	72.8028	0.258193	0.129097	+	0.991632i	$0.458792\pi$
$44$	−207.372	−0.710510
$45$	47.0005	0.155698
$46$	−45.6974	−0.146472
$47$	−470.316	−1.45963	−0.729815	−	0.683645i	$-0.760394\pi$
$47$	−470.316	−1.45963	−0.729815	+	0.683645i	$0.760394\pi$
$48$	77.7352	0.233752
$49$	49.0000	0.142857
$50$	−133.209	−0.376772
$51$	−513.961	−1.41115
$52$	0	0
$53$	159.833	0.414242	0.207121	−	0.978315i	$-0.433591\pi$
$53$	159.833	0.414242	0.207121	+	0.978315i	$0.433591\pi$
$54$	295.350	0.744296
$55$	717.616	1.75933
$56$	−56.0000	−0.133631
$57$	233.234	0.541975
$58$	−466.361	−1.05580
$59$	−320.826	−0.707931	−0.353966	−	0.935258i	$-0.615167\pi$
$59$	−320.826	−0.707931	−0.353966	+	0.935258i	$0.615167\pi$
$60$	−269.005	−0.578807
$61$	478.752	1.00488	0.502442	−	0.864611i	$-0.332435\pi$
$61$	478.752	1.00488	0.502442	+	0.864611i	$0.332435\pi$
$62$	246.596	0.505124
$63$	−23.7683	−0.0475321
$64$	64.0000	0.125000
$65$	0	0
$66$	503.752	0.939509
$67$	343.671	0.626658	0.313329	−	0.949645i	$-0.398556\pi$
$67$	343.671	0.626658	0.313329	+	0.949645i	$0.398556\pi$
$68$	−423.148	−0.754621
$69$	111.009	0.193680
$70$	193.790	0.330890
$71$	147.749	0.246966	0.123483	−	0.992347i	$-0.460594\pi$
$71$	147.749	0.246966	0.123483	+	0.992347i	$0.460594\pi$
$72$	27.1637	0.0444622
$73$	−779.080	−1.24910	−0.624551	−	0.780984i	$-0.714718\pi$
$73$	−779.080	−1.24910	−0.624551	+	0.780984i	$0.714718\pi$
$74$	374.149	0.587755
$75$	323.595	0.498207
$76$	192.023	0.289824
$77$	−362.900	−0.537095
$78$	0	0
$79$	962.115	1.37021	0.685104	−	0.728445i	$-0.259757\pi$
$79$	962.115	1.37021	0.685104	+	0.728445i	$0.259757\pi$
$80$	−221.474	−0.309519
$81$	−625.793	−0.858427
$82$	709.815	0.955926
$83$	−1097.00	−1.45074	−0.725369	−	0.688361i	$-0.758331\pi$
$83$	−1097.00	−1.45074	−0.725369	+	0.688361i	$0.758331\pi$
$84$	136.037	0.176700
$85$	1464.32	1.86856
$86$	−145.606	−0.182570
$87$	1132.90	1.39608
$88$	414.743	0.502406
$89$	709.491	0.845010	0.422505	−	0.906361i	$-0.361151\pi$
$89$	709.491	0.845010	0.422505	+	0.906361i	$0.361151\pi$
$90$	−94.0010	−0.110095
$91$	0	0
$92$	91.3948	0.103571
$93$	−599.037	−0.667927
$94$	940.631	1.03211
$95$	−664.503	−0.717648
$96$	−155.470	−0.165288
$97$	−355.024	−0.371621	−0.185811	−	0.982586i	$-0.559491\pi$
$97$	−355.024	−0.371621	−0.185811	+	0.982586i	$0.559491\pi$
$98$	−98.0000	−0.101015
$99$	176.031	0.178705
$100$	266.418	0.266418
$101$	−476.630	−0.469569	−0.234785	−	0.972047i	$-0.575438\pi$
$101$	−476.630	−0.469569	−0.234785	+	0.972047i	$0.575438\pi$
$102$	1027.92	0.997837
$103$	−1564.39	−1.49655	−0.748274	−	0.663390i	$-0.769117\pi$
$103$	−1564.39	−1.49655	−0.748274	+	0.663390i	$0.769117\pi$
$104$	0	0
$105$	−470.759	−0.437537
$106$	−319.667	−0.292913
$107$	1641.19	1.48280	0.741399	−	0.671064i	$-0.234162\pi$
$107$	1641.19	1.48280	0.741399	+	0.671064i	$0.234162\pi$
$108$	−590.699	−0.526297
$109$	1828.38	1.60667	0.803335	−	0.595527i	$-0.203057\pi$
$109$	1828.38	1.60667	0.803335	+	0.595527i	$0.203057\pi$
$110$	−1435.23	−1.24404
$111$	−908.891	−0.777191
$112$	112.000	0.0944911
$113$	−638.758	−0.531764	−0.265882	−	0.964006i	$-0.585663\pi$
$113$	−638.758	−0.531764	−0.265882	+	0.964006i	$0.585663\pi$
$114$	−466.468	−0.383234
$115$	−316.275	−0.256459
$116$	932.723	0.746561
$117$	0	0
$118$	641.651	0.500583
$119$	−740.509	−0.570440
$120$	538.010	0.409278
$121$	1356.68	1.01930
$122$	−957.504	−0.710560
$123$	−1724.30	−1.26402
$124$	−493.192	−0.357177
$125$	808.318	0.578385
$126$	47.5366	0.0336103
$127$	−1940.17	−1.35561	−0.677805	−	0.735242i	$-0.737068\pi$
$127$	−1940.17	−1.35561	−0.677805	+	0.735242i	$0.737068\pi$
$128$	−128.000	−0.0883883
$129$	353.709	0.241413
$130$	0	0
$131$	698.893	0.466126	0.233063	−	0.972462i	$-0.425125\pi$
$131$	698.893	0.466126	0.233063	+	0.972462i	$0.425125\pi$
$132$	−1007.50	−0.664333
$133$	336.041	0.219086
$134$	−687.342	−0.443114
$135$	2044.13	1.30319
$136$	846.296	0.533598
$137$	2273.06	1.41752	0.708761	−	0.705448i	$-0.249254\pi$
$137$	2273.06	1.41752	0.708761	+	0.705448i	$0.249254\pi$
$138$	−222.019	−0.136953
$139$	−2107.46	−1.28599	−0.642993	−	0.765872i	$-0.722308\pi$
$139$	−2107.46	−1.28599	−0.642993	+	0.765872i	$0.722308\pi$
$140$	−387.580	−0.233975
$141$	−2285.00	−1.36477
$142$	−295.498	−0.174631
$143$	0	0
$144$	−54.3275	−0.0314395
$145$	−3227.72	−1.84860
$146$	1558.16	0.883249
$147$	238.064	0.133573
$148$	−748.297	−0.415606
$149$	1089.78	0.599180	0.299590	−	0.954068i	$-0.403150\pi$
$149$	1089.78	0.599180	0.299590	+	0.954068i	$0.403150\pi$
$150$	−647.189	−0.352285
$151$	2968.18	1.59965	0.799826	−	0.600232i	$-0.204925\pi$
$151$	2968.18	1.59965	0.799826	+	0.600232i	$0.204925\pi$
$152$	−384.047	−0.204936
$153$	359.196	0.189799
$154$	725.800	0.379783
$155$	1706.71	0.884425
$156$	0	0
$157$	3026.87	1.53866	0.769332	−	0.638849i	$-0.220589\pi$
$157$	3026.87	1.53866	0.769332	+	0.638849i	$0.220589\pi$
$158$	−1924.23	−0.968883
$159$	776.543	0.387320
$160$	442.948	0.218863
$161$	159.941	0.0782926
$162$	1251.59	0.606999
$163$	−469.542	−0.225628	−0.112814	−	0.993616i	$-0.535986\pi$
$163$	−469.542	−0.225628	−0.112814	+	0.993616i	$0.535986\pi$
$164$	−1419.63	−0.675942
$165$	3486.50	1.64499
$166$	2194.00	1.02583
$167$	1376.82	0.637974	0.318987	−	0.947759i	$-0.396657\pi$
$167$	1376.82	0.637974	0.318987	+	0.947759i	$0.396657\pi$
$168$	−272.073	−0.124946
$169$	0	0
$170$	−2928.63	−1.32127
$171$	−163.002	−0.0728953
$172$	291.211	0.129097
$173$	346.341	0.152207	0.0761035	−	0.997100i	$-0.475752\pi$
$173$	346.341	0.152207	0.0761035	+	0.997100i	$0.475752\pi$
$174$	−2265.79	−0.987180
$175$	466.232	0.201393
$176$	−829.486	−0.355255
$177$	−1558.71	−0.661922
$178$	−1418.98	−0.597512
$179$	1807.66	0.754811	0.377406	−	0.926048i	$-0.376816\pi$
$179$	1807.66	0.754811	0.377406	+	0.926048i	$0.376816\pi$
$180$	188.002	0.0778491
$181$	2138.29	0.878110	0.439055	−	0.898460i	$-0.355313\pi$
$181$	2138.29	0.878110	0.439055	+	0.898460i	$0.355313\pi$
$182$	0	0
$183$	2325.99	0.939575
$184$	−182.790	−0.0732360
$185$	2589.51	1.02910
$186$	1198.07	0.472296
$187$	5484.30	2.14466
$188$	−1881.26	−0.729815
$189$	−1033.72	−0.397843
$190$	1329.01	0.507454
$191$	−2405.05	−0.911115	−0.455558	−	0.890206i	$-0.650560\pi$
$191$	−2405.05	−0.911115	−0.455558	+	0.890206i	$0.650560\pi$
$192$	310.941	0.116876
$193$	−1341.73	−0.500412	−0.250206	−	0.968193i	$-0.580498\pi$
$193$	−1341.73	−0.500412	−0.250206	+	0.968193i	$0.580498\pi$
$194$	710.049	0.262776
$195$	0	0
$196$	196.000	0.0714286
$197$	−4329.75	−1.56590	−0.782949	−	0.622086i	$-0.786285\pi$
$197$	−4329.75	−1.56590	−0.782949	+	0.622086i	$0.786285\pi$
$198$	−352.062	−0.126363
$199$	1853.27	0.660176	0.330088	−	0.943950i	$-0.392921\pi$
$199$	1853.27	0.660176	0.330088	+	0.943950i	$0.392921\pi$
$200$	−532.836	−0.188386
$201$	1669.71	0.585931
$202$	953.260	0.332035
$203$	1632.26	0.564347
$204$	−2055.84	−0.705577
$205$	4912.67	1.67374
$206$	3128.79	1.05822
$207$	−77.5820	−0.0260499
$208$	0	0
$209$	−2488.76	−0.823690
$210$	941.518	0.309385
$211$	−1358.15	−0.443121	−0.221561	−	0.975147i	$-0.571115\pi$
$211$	−1358.15	−0.443121	−0.221561	+	0.975147i	$0.571115\pi$
$212$	639.334	0.207121
$213$	717.831	0.230915
$214$	−3282.37	−1.04850
$215$	−1007.75	−0.319663
$216$	1181.40	0.372148
$217$	−863.086	−0.270000
$218$	−3656.76	−1.13609
$219$	−3785.12	−1.16792
$220$	2870.46	0.879666
$221$	0	0
$222$	1817.78	0.549557
$223$	6094.90	1.83025	0.915123	−	0.403175i	$-0.132093\pi$
$223$	6094.90	1.83025	0.915123	+	0.403175i	$0.132093\pi$
$224$	−224.000	−0.0668153
$225$	−226.154	−0.0670085
$226$	1277.52	0.376014
$227$	−5436.03	−1.58943	−0.794717	−	0.606980i	$-0.792381\pi$
$227$	−5436.03	−1.58943	−0.794717	+	0.606980i	$0.792381\pi$
$228$	932.936	0.270988
$229$	3794.17	1.09487	0.547437	−	0.836847i	$-0.315604\pi$
$229$	3794.17	1.09487	0.547437	+	0.836847i	$0.315604\pi$
$230$	632.549	0.181344
$231$	−1763.13	−0.502189
$232$	−1865.45	−0.527899
$233$	1070.66	0.301035	0.150518	−	0.988607i	$-0.451906\pi$
$233$	1070.66	0.301035	0.150518	+	0.988607i	$0.451906\pi$
$234$	0	0
$235$	6510.17	1.80713
$236$	−1283.30	−0.353966
$237$	4674.39	1.28116
$238$	1481.02	0.403362
$239$	5205.17	1.40876	0.704382	−	0.709821i	$-0.251224\pi$
$239$	5205.17	1.40876	0.704382	+	0.709821i	$0.251224\pi$
$240$	−1076.02	−0.289403
$241$	3077.22	0.822494	0.411247	−	0.911524i	$-0.365093\pi$
$241$	3077.22	0.822494	0.411247	+	0.911524i	$0.365093\pi$
$242$	−2713.37	−0.720752
$243$	946.836	0.249957
$244$	1915.01	0.502442
$245$	−678.264	−0.176868
$246$	3448.60	0.893799
$247$	0	0
$248$	986.384	0.252562
$249$	−5329.71	−1.35645
$250$	−1616.64	−0.408980
$251$	1338.28	0.336540	0.168270	−	0.985741i	$-0.446182\pi$
$251$	1338.28	0.336540	0.168270	+	0.985741i	$0.446182\pi$
$252$	−95.0731	−0.0237660
$253$	−1184.54	−0.294354
$254$	3880.34	0.958561
$255$	7114.31	1.74712
$256$	256.000	0.0625000
$257$	−5716.43	−1.38747	−0.693737	−	0.720228i	$-0.744037\pi$
$257$	−5716.43	−1.38747	−0.693737	+	0.720228i	$0.744037\pi$
$258$	−707.417	−0.170705
$259$	−1309.52	−0.314169
$260$	0	0
$261$	−791.758	−0.187772
$262$	−1397.79	−0.329601
$263$	−5068.87	−1.18844	−0.594220	−	0.804303i	$-0.702539\pi$
$263$	−5068.87	−1.18844	−0.594220	+	0.804303i	$0.702539\pi$
$264$	2015.01	0.469754
$265$	−2212.43	−0.512863
$266$	−672.082	−0.154917
$267$	3447.03	0.790092
$268$	1374.68	0.313329
$269$	−6243.48	−1.41514	−0.707568	−	0.706645i	$-0.750208\pi$
$269$	−6243.48	−1.41514	−0.707568	+	0.706645i	$0.750208\pi$
$270$	−4088.27	−0.921497
$271$	4648.16	1.04190	0.520951	−	0.853587i	$-0.325577\pi$
$271$	4648.16	1.04190	0.520951	+	0.853587i	$0.325577\pi$
$272$	−1692.59	−0.377310
$273$	0	0
$274$	−4546.12	−1.00234
$275$	−3452.97	−0.757171
$276$	444.037	0.0968402
$277$	−2699.24	−0.585493	−0.292746	−	0.956190i	$-0.594569\pi$
$277$	−2699.24	−0.585493	−0.292746	+	0.956190i	$0.594569\pi$
$278$	4214.91	0.909330
$279$	418.654	0.0898358
$280$	775.159	0.165445
$281$	−3742.77	−0.794573	−0.397286	−	0.917695i	$-0.630048\pi$
$281$	−3742.77	−0.794573	−0.397286	+	0.917695i	$0.630048\pi$
$282$	4570.01	0.965036
$283$	−5419.64	−1.13839	−0.569194	−	0.822203i	$-0.692745\pi$
$283$	−5419.64	−1.13839	−0.569194	+	0.822203i	$0.692745\pi$
$284$	590.996	0.123483
$285$	−3228.45	−0.671007
$286$	0	0
$287$	−2484.35	−0.510964
$288$	108.655	0.0222311
$289$	6277.88	1.27781
$290$	6455.43	1.30716
$291$	−1724.87	−0.347469
$292$	−3116.32	−0.624551
$293$	2507.16	0.499897	0.249948	−	0.968259i	$-0.419586\pi$
$293$	2507.16	0.499897	0.249948	+	0.968259i	$0.419586\pi$
$294$	−476.128	−0.0944502
$295$	4440.91	0.876474
$296$	1496.59	0.293878
$297$	7655.89	1.49576
$298$	−2179.55	−0.423684
$299$	0	0
$300$	1294.38	0.249103
$301$	509.619	0.0975879
$302$	−5936.37	−1.13112
$303$	−2315.68	−0.439051
$304$	768.093	0.144912
$305$	−6626.95	−1.24412
$306$	−718.393	−0.134208
$307$	3558.50	0.661545	0.330773	−	0.943710i	$-0.392691\pi$
$307$	3558.50	0.661545	0.330773	+	0.943710i	$0.392691\pi$
$308$	−1451.60	−0.268547
$309$	−7600.53	−1.39929
$310$	−3413.41	−0.625383
$311$	−790.495	−0.144131	−0.0720657	−	0.997400i	$-0.522959\pi$
$311$	−790.495	−0.144131	−0.0720657	+	0.997400i	$0.522959\pi$
$312$	0	0
$313$	6589.31	1.18994	0.594968	−	0.803749i	$-0.297165\pi$
$313$	6589.31	1.18994	0.594968	+	0.803749i	$0.297165\pi$
$314$	−6053.73	−1.08800
$315$	329.004	0.0588484
$316$	3848.46	0.685104
$317$	9740.30	1.72577	0.862886	−	0.505398i	$-0.168654\pi$
$317$	9740.30	1.72577	0.862886	+	0.505398i	$0.168654\pi$
$318$	−1553.09	−0.273876
$319$	−12088.8	−2.12176
$320$	−885.896	−0.154760
$321$	7973.62	1.38643
$322$	−319.882	−0.0553612
$323$	−5078.39	−0.874828
$324$	−2503.17	−0.429213
$325$	0	0
$326$	939.084	0.159543
$327$	8883.09	1.50225
$328$	2839.26	0.477963
$329$	−3292.21	−0.551688
$330$	−6973.00	−1.16318
$331$	1309.24	0.217410	0.108705	−	0.994074i	$-0.465330\pi$
$331$	1309.24	0.217410	0.108705	+	0.994074i	$0.465330\pi$
$332$	−4387.99	−0.725369
$333$	635.205	0.104532
$334$	−2753.64	−0.451116
$335$	−4757.14	−0.775851
$336$	544.146	0.0883501
$337$	−7265.34	−1.17439	−0.587194	−	0.809446i	$-0.699767\pi$
$337$	−7265.34	−1.17439	−0.587194	+	0.809446i	$0.699767\pi$
$338$	0	0
$339$	−3103.38	−0.497204
$340$	5857.27	0.934279
$341$	6392.12	1.01511
$342$	326.005	0.0515448
$343$	343.000	0.0539949
$344$	−582.422	−0.0912852
$345$	−1536.60	−0.239791
$346$	−692.682	−0.107627
$347$	2244.17	0.347186	0.173593	−	0.984817i	$-0.444462\pi$
$347$	2244.17	0.347186	0.173593	+	0.984817i	$0.444462\pi$
$348$	4531.59	0.698042
$349$	7509.56	1.15180	0.575899	−	0.817521i	$-0.304652\pi$
$349$	7509.56	1.15180	0.575899	+	0.817521i	$0.304652\pi$
$350$	−932.463	−0.142406
$351$	0	0
$352$	1658.97	0.251203
$353$	−8419.25	−1.26944	−0.634719	−	0.772743i	$-0.718884\pi$
$353$	−8419.25	−1.26944	−0.634719	+	0.772743i	$0.718884\pi$
$354$	3117.43	0.468049
$355$	−2045.16	−0.305763
$356$	2837.96	0.422505
$357$	−3597.72	−0.533366
$358$	−3615.33	−0.533732
$359$	3581.38	0.526513	0.263256	−	0.964726i	$-0.415203\pi$
$359$	3581.38	0.526513	0.263256	+	0.964726i	$0.415203\pi$
$360$	−376.004	−0.0550476
$361$	−4554.44	−0.664009
$362$	−4276.58	−0.620918
$363$	6591.38	0.953052
$364$	0	0
$365$	10784.1	1.54649
$366$	−4651.98	−0.664380
$367$	−7202.07	−1.02437	−0.512187	−	0.858874i	$-0.671164\pi$
$367$	−7202.07	−1.02437	−0.512187	+	0.858874i	$0.671164\pi$
$368$	365.579	0.0517857
$369$	1205.08	0.170010
$370$	−5179.01	−0.727687
$371$	1118.83	0.156569
$372$	−2396.15	−0.333964
$373$	4731.06	0.656743	0.328372	−	0.944549i	$-0.393500\pi$
$373$	4731.06	0.656743	0.328372	+	0.944549i	$0.393500\pi$
$374$	−10968.6	−1.51651
$375$	3927.17	0.540795
$376$	3762.52	0.516057
$377$	0	0
$378$	2067.45	0.281318
$379$	6574.68	0.891079	0.445539	−	0.895262i	$-0.353012\pi$
$379$	6574.68	0.891079	0.445539	+	0.895262i	$0.353012\pi$
$380$	−2658.01	−0.358824
$381$	−9426.23	−1.26751
$382$	4810.09	0.644256
$383$	−5046.06	−0.673215	−0.336608	−	0.941645i	$-0.609280\pi$
$383$	−5046.06	−0.673215	−0.336608	+	0.941645i	$0.609280\pi$
$384$	−621.882	−0.0826439
$385$	5023.31	0.664965
$386$	2683.45	0.353845
$387$	−247.199	−0.0324699
$388$	−1420.10	−0.185811
$389$	8101.69	1.05597	0.527985	−	0.849254i	$-0.322948\pi$
$389$	8101.69	1.05597	0.527985	+	0.849254i	$0.322948\pi$
$390$	0	0
$391$	−2417.10	−0.312629
$392$	−392.000	−0.0505076
$393$	3395.54	0.435832
$394$	8659.50	1.10726
$395$	−13317.7	−1.69642
$396$	704.123	0.0893523
$397$	1924.21	0.243258	0.121629	−	0.992576i	$-0.461188\pi$
$397$	1924.21	0.243258	0.121629	+	0.992576i	$0.461188\pi$
$398$	−3706.55	−0.466815
$399$	1632.64	0.204847
$400$	1065.67	0.133209
$401$	−12535.6	−1.56109	−0.780544	−	0.625101i	$-0.785058\pi$
$401$	−12535.6	−1.56109	−0.780544	+	0.625101i	$0.785058\pi$
$402$	−3339.42	−0.414316
$403$	0	0
$404$	−1906.52	−0.234785
$405$	8662.31	1.06280
$406$	−3264.53	−0.399054
$407$	9698.47	1.18117
$408$	4111.69	0.498919
$409$	−5310.06	−0.641970	−0.320985	−	0.947084i	$-0.604014\pi$
$409$	−5310.06	−0.641970	−0.320985	+	0.947084i	$0.604014\pi$
$410$	−9825.35	−1.18351
$411$	11043.5	1.32540
$412$	−6257.58	−0.748274
$413$	−2245.78	−0.267573
$414$	155.164	0.0184200
$415$	15184.8	1.79613
$416$	0	0
$417$	−10239.0	−1.20241
$418$	4977.52	0.582437
$419$	12040.8	1.40389	0.701947	−	0.712229i	$-0.252314\pi$
$419$	12040.8	1.40389	0.701947	+	0.712229i	$0.252314\pi$
$420$	−1883.04	−0.218768
$421$	−4855.80	−0.562131	−0.281066	−	0.959689i	$-0.590688\pi$
$421$	−4855.80	−0.562131	−0.281066	+	0.959689i	$0.590688\pi$
$422$	2716.29	0.313334
$423$	1596.94	0.183560
$424$	−1278.67	−0.146457
$425$	−7045.89	−0.804179
$426$	−1435.66	−0.163282
$427$	3351.26	0.379810
$428$	6564.75	0.741399
$429$	0	0
$430$	2015.49	0.226036
$431$	12615.6	1.40991	0.704954	−	0.709253i	$-0.250968\pi$
$431$	12615.6	1.40991	0.704954	+	0.709253i	$0.250968\pi$
$432$	−2362.80	−0.263148
$433$	10733.9	1.19131	0.595655	−	0.803240i	$-0.296892\pi$
$433$	10733.9	1.19131	0.595655	+	0.803240i	$0.296892\pi$
$434$	1726.17	0.190919
$435$	−15681.7	−1.72846
$436$	7313.52	0.803335
$437$	1096.87	0.120070
$438$	7570.25	0.825846
$439$	−1434.13	−0.155916	−0.0779580	−	0.996957i	$-0.524840\pi$
$439$	−1434.13	−0.155916	−0.0779580	+	0.996957i	$0.524840\pi$
$440$	−5740.93	−0.622018
$441$	−166.378	−0.0179654
$442$	0	0
$443$	1155.06	0.123879	0.0619395	−	0.998080i	$-0.480271\pi$
$443$	1155.06	0.123879	0.0619395	+	0.998080i	$0.480271\pi$
$444$	−3635.57	−0.388595
$445$	−9820.87	−1.04619
$446$	−12189.8	−1.29418
$447$	5294.62	0.560239
$448$	448.000	0.0472456
$449$	−4988.94	−0.524371	−0.262185	−	0.965018i	$-0.584443\pi$
$449$	−4988.94	−0.524371	−0.262185	+	0.965018i	$0.584443\pi$
$450$	452.307	0.0473821
$451$	18399.4	1.92105
$452$	−2555.03	−0.265882
$453$	14420.8	1.49569
$454$	10872.1	1.12390
$455$	0	0
$456$	−1865.87	−0.191617
$457$	15322.2	1.56836	0.784181	−	0.620532i	$-0.213083\pi$
$457$	15322.2	1.56836	0.784181	+	0.620532i	$0.213083\pi$
$458$	−7588.35	−0.774193
$459$	15622.1	1.58862
$460$	−1265.10	−0.128229
$461$	−11903.8	−1.20264	−0.601319	−	0.799009i	$-0.705358\pi$
$461$	−11903.8	−1.20264	−0.601319	+	0.799009i	$0.705358\pi$
$462$	3526.26	0.355101
$463$	−15221.5	−1.52787	−0.763936	−	0.645292i	$-0.776736\pi$
$463$	−15221.5	−1.52787	−0.763936	+	0.645292i	$0.776736\pi$
$464$	3730.89	0.373281
$465$	8291.95	0.826946
$466$	−2141.32	−0.212864
$467$	8807.37	0.872712	0.436356	−	0.899774i	$-0.356269\pi$
$467$	8807.37	0.872712	0.436356	+	0.899774i	$0.356269\pi$
$468$	0	0
$469$	2405.70	0.236854
$470$	−13020.3	−1.27784
$471$	14705.9	1.43867
$472$	2566.60	0.250291
$473$	−3774.30	−0.366898
$474$	−9348.78	−0.905915
$475$	3197.41	0.308857
$476$	−2962.04	−0.285220
$477$	−542.709	−0.0520942
$478$	−10410.3	−0.996147
$479$	−10143.7	−0.967590	−0.483795	−	0.875181i	$-0.660742\pi$
$479$	−10143.7	−0.967590	−0.483795	+	0.875181i	$0.660742\pi$
$480$	2152.04	0.204639
$481$	0	0
$482$	−6154.44	−0.581591
$483$	777.065	0.0732043
$484$	5426.74	0.509648
$485$	4914.29	0.460096
$486$	−1893.67	−0.176746
$487$	9386.36	0.873381	0.436691	−	0.899612i	$-0.356150\pi$
$487$	9386.36	0.873381	0.436691	+	0.899612i	$0.356150\pi$
$488$	−3830.02	−0.355280
$489$	−2281.25	−0.210964
$490$	1356.53	0.125065
$491$	11886.9	1.09256	0.546281	−	0.837602i	$-0.316043\pi$
$491$	11886.9	1.09256	0.546281	+	0.837602i	$0.316043\pi$
$492$	−6897.20	−0.632012
$493$	−24667.5	−2.25348
$494$	0	0
$495$	−2436.64	−0.221250
$496$	−1972.77	−0.178588
$497$	1034.24	0.0933443
$498$	10659.4	0.959157
$499$	5665.99	0.508306	0.254153	−	0.967164i	$-0.418203\pi$
$499$	5665.99	0.508306	0.254153	+	0.967164i	$0.418203\pi$
$500$	3233.27	0.289193
$501$	6689.22	0.596511
$502$	−2676.56	−0.237970
$503$	6305.31	0.558926	0.279463	−	0.960156i	$-0.409844\pi$
$503$	6305.31	0.558926	0.279463	+	0.960156i	$0.409844\pi$
$504$	190.146	0.0168051
$505$	6597.58	0.581363
$506$	2369.08	0.208140
$507$	0	0
$508$	−7760.69	−0.677805
$509$	−6832.62	−0.594992	−0.297496	−	0.954723i	$-0.596151\pi$
$509$	−6832.62	−0.594992	−0.297496	+	0.954723i	$0.596151\pi$
$510$	−14228.6	−1.23540
$511$	−5453.56	−0.472116
$512$	−512.000	−0.0441942
$513$	−7089.25	−0.610133
$514$	11432.9	0.981092
$515$	21654.5	1.85284
$516$	1414.83	0.120707
$517$	24382.5	2.07416
$518$	2619.04	0.222151
$519$	1682.68	0.142315
$520$	0	0
$521$	17145.8	1.44178	0.720892	−	0.693047i	$-0.243732\pi$
$521$	17145.8	1.44178	0.720892	+	0.693047i	$0.243732\pi$
$522$	1583.52	0.132775
$523$	−9121.38	−0.762620	−0.381310	−	0.924447i	$-0.624527\pi$
$523$	−9121.38	−0.762620	−0.381310	+	0.924447i	$0.624527\pi$
$524$	2795.57	0.233063
$525$	2265.16	0.188304
$526$	10137.7	0.840354
$527$	13043.3	1.07813
$528$	−4030.02	−0.332167
$529$	−11644.9	−0.957092
$530$	4424.87	0.362649
$531$	1089.35	0.0890280
$532$	1344.16	0.109543
$533$	0	0
$534$	−6894.05	−0.558680
$535$	−22717.5	−1.83582
$536$	−2749.37	−0.221557
$537$	8782.45	0.705755
$538$	12487.0	1.00065
$539$	−2540.30	−0.203003
$540$	8176.54	0.651597
$541$	14595.4	1.15990	0.579950	−	0.814652i	$-0.303072\pi$
$541$	14595.4	1.15990	0.579950	+	0.814652i	$0.303072\pi$
$542$	−9296.31	−0.736736
$543$	10388.8	0.821041
$544$	3385.18	0.266799
$545$	−25308.7	−1.98918
$546$	0	0
$547$	6798.55	0.531417	0.265708	−	0.964053i	$-0.414394\pi$
$547$	6798.55	0.531417	0.265708	+	0.964053i	$0.414394\pi$
$548$	9092.24	0.708761
$549$	−1625.59	−0.126372
$550$	6905.94	0.535401
$551$	11194.0	0.865484
$552$	−888.074	−0.0684764
$553$	6734.81	0.517890
$554$	5398.47	0.414006
$555$	12581.0	0.962222
$556$	−8429.82	−0.642993
$557$	−1050.99	−0.0799498	−0.0399749	−	0.999201i	$-0.512728\pi$
$557$	−1050.99	−0.0799498	−0.0399749	+	0.999201i	$0.512728\pi$
$558$	−837.309	−0.0635235
$559$	0	0
$560$	−1550.32	−0.116987
$561$	26645.2	2.00528
$562$	7485.54	0.561848
$563$	−8634.05	−0.646326	−0.323163	−	0.946343i	$-0.604746\pi$
$563$	−8634.05	−0.646326	−0.323163	+	0.946343i	$0.604746\pi$
$564$	−9140.02	−0.682383
$565$	8841.78	0.658365
$566$	10839.3	0.804962
$567$	−4380.55	−0.324455
$568$	−1181.99	−0.0873156
$569$	−17056.1	−1.25664	−0.628321	−	0.777954i	$-0.716258\pi$
$569$	−17056.1	−1.25664	−0.628321	+	0.777954i	$0.716258\pi$
$570$	6456.91	0.474474
$571$	−10954.2	−0.802833	−0.401416	−	0.915896i	$-0.631482\pi$
$571$	−10954.2	−0.802833	−0.401416	+	0.915896i	$0.631482\pi$
$572$	0	0
$573$	−11684.8	−0.851901
$574$	4968.70	0.361306
$575$	1521.83	0.110373
$576$	−217.310	−0.0157198
$577$	5216.96	0.376404	0.188202	−	0.982130i	$-0.439734\pi$
$577$	5216.96	0.376404	0.188202	+	0.982130i	$0.439734\pi$
$578$	−12555.8	−0.903549
$579$	−6518.71	−0.467890
$580$	−12910.9	−0.924301
$581$	−7678.99	−0.548327
$582$	3449.74	0.245698
$583$	−8286.22	−0.588645
$584$	6232.64	0.441624
$585$	0	0
$586$	−5014.31	−0.353480
$587$	1205.16	0.0847399	0.0423699	−	0.999102i	$-0.486509\pi$
$587$	1205.16	0.0847399	0.0423699	+	0.999102i	$0.486509\pi$
$588$	952.256	0.0667864
$589$	−5919.02	−0.414073
$590$	−8881.82	−0.619760
$591$	−21035.9	−1.46413
$592$	−2993.19	−0.207803
$593$	3957.51	0.274057	0.137028	−	0.990567i	$-0.456245\pi$
$593$	3957.51	0.274057	0.137028	+	0.990567i	$0.456245\pi$
$594$	−15311.8	−1.05766
$595$	10250.2	0.706249
$596$	4359.10	0.299590
$597$	9004.04	0.617271
$598$	0	0
$599$	18807.0	1.28286	0.641432	−	0.767180i	$-0.278341\pi$
$599$	18807.0	1.28286	0.641432	+	0.767180i	$0.278341\pi$
$600$	−2588.76	−0.176143
$601$	1149.80	0.0780388	0.0390194	−	0.999238i	$-0.487577\pi$
$601$	1149.80	0.0780388	0.0390194	+	0.999238i	$0.487577\pi$
$602$	−1019.24	−0.0690051
$603$	−1166.92	−0.0788073
$604$	11872.7	0.799826
$605$	−18779.4	−1.26197
$606$	4631.37	0.310456
$607$	10560.1	0.706128	0.353064	−	0.935599i	$-0.385140\pi$
$607$	10560.1	0.706128	0.353064	+	0.935599i	$0.385140\pi$
$608$	−1536.19	−0.102468
$609$	7930.28	0.527670
$610$	13253.9	0.879729
$611$	0	0
$612$	1436.79	0.0948997
$613$	−28888.4	−1.90341	−0.951707	−	0.307008i	$-0.900672\pi$
$613$	−28888.4	−1.90341	−0.951707	+	0.307008i	$0.900672\pi$
$614$	−7117.00	−0.467783
$615$	23868.0	1.56496
$616$	2903.20	0.189892
$617$	27432.2	1.78992	0.894958	−	0.446151i	$-0.147205\pi$
$617$	27432.2	1.78992	0.894958	+	0.446151i	$0.147205\pi$
$618$	15201.1	0.989444
$619$	3690.47	0.239633	0.119816	−	0.992796i	$-0.461769\pi$
$619$	3690.47	0.239633	0.119816	+	0.992796i	$0.461769\pi$
$620$	6826.82	0.442213
$621$	−3374.18	−0.218037
$622$	1580.99	0.101916
$623$	4966.44	0.319384
$624$	0	0
$625$	−19514.4	−1.24892
$626$	−13178.6	−0.841412
$627$	−12091.5	−0.770157
$628$	12107.5	0.769332
$629$	19790.0	1.25450
$630$	−658.007	−0.0416121
$631$	−7976.61	−0.503239	−0.251619	−	0.967826i	$-0.580963\pi$
$631$	−7976.61	−0.503239	−0.251619	+	0.967826i	$0.580963\pi$
$632$	−7696.92	−0.484442
$633$	−6598.48	−0.414322
$634$	−19480.6	−1.22031
$635$	26856.1	1.67835
$636$	3106.17	0.193660
$637$	0	0
$638$	24177.5	1.50031
$639$	−501.677	−0.0310580
$640$	1771.79	0.109432
$641$	3729.99	0.229837	0.114919	−	0.993375i	$-0.463339\pi$
$641$	3729.99	0.229837	0.114919	+	0.993375i	$0.463339\pi$
$642$	−15947.2	−0.980354
$643$	21830.9	1.33892	0.669462	−	0.742846i	$-0.266525\pi$
$643$	21830.9	1.33892	0.669462	+	0.742846i	$0.266525\pi$
$644$	639.764	0.0391463
$645$	−4896.08	−0.298888
$646$	10156.8	0.618597
$647$	6708.66	0.407642	0.203821	−	0.979008i	$-0.434664\pi$
$647$	6708.66	0.407642	0.203821	+	0.979008i	$0.434664\pi$
$648$	5006.35	0.303500
$649$	16632.5	1.00598
$650$	0	0
$651$	−4193.26	−0.252453
$652$	−1878.17	−0.112814
$653$	24968.6	1.49632	0.748159	−	0.663519i	$-0.230938\pi$
$653$	24968.6	1.49632	0.748159	+	0.663519i	$0.230938\pi$
$654$	−17766.2	−1.06225
$655$	−9674.17	−0.577101
$656$	−5678.52	−0.337971
$657$	2645.34	0.157085
$658$	6584.42	0.390102
$659$	25676.0	1.51775	0.758874	−	0.651237i	$-0.225750\pi$
$659$	25676.0	1.51775	0.758874	+	0.651237i	$0.225750\pi$
$660$	13946.0	0.822496
$661$	10584.5	0.622829	0.311414	−	0.950274i	$-0.399197\pi$
$661$	10584.5	0.622829	0.311414	+	0.950274i	$0.399197\pi$
$662$	−2618.49	−0.153732
$663$	0	0
$664$	8775.99	0.512913
$665$	−4651.52	−0.271245
$666$	−1270.41	−0.0739150
$667$	5327.88	0.309290
$668$	5507.29	0.318987
$669$	29611.8	1.71130
$670$	9514.27	0.548610
$671$	−24819.9	−1.42796
$672$	−1088.29	−0.0624729
$673$	−5615.04	−0.321611	−0.160805	−	0.986986i	$-0.551409\pi$
$673$	−5615.04	−0.321611	−0.160805	+	0.986986i	$0.551409\pi$
$674$	14530.7	0.830417
$675$	−9835.81	−0.560860
$676$	0	0
$677$	22934.3	1.30197	0.650986	−	0.759090i	$-0.274356\pi$
$677$	22934.3	1.30197	0.650986	+	0.759090i	$0.274356\pi$
$678$	6206.75	0.351577
$679$	−2485.17	−0.140460
$680$	−11714.5	−0.660635
$681$	−26410.7	−1.48614
$682$	−12784.2	−0.717792
$683$	−9747.92	−0.546111	−0.273055	−	0.961998i	$-0.588034\pi$
$683$	−9747.92	−0.546111	−0.273055	+	0.961998i	$0.588034\pi$
$684$	−652.009	−0.0364476
$685$	−31464.0	−1.75500
$686$	−686.000	−0.0381802
$687$	18433.8	1.02372
$688$	1164.84	0.0645484
$689$	0	0
$690$	3073.21	0.169558
$691$	13732.4	0.756014	0.378007	−	0.925803i	$-0.376610\pi$
$691$	13732.4	0.756014	0.378007	+	0.925803i	$0.376610\pi$
$692$	1385.36	0.0761035
$693$	1232.22	0.0675440
$694$	−4488.35	−0.245498
$695$	29171.7	1.59215
$696$	−9063.17	−0.493590
$697$	37544.6	2.04032
$698$	−15019.1	−0.814445
$699$	5201.74	0.281471
$700$	1864.93	0.100697
$701$	−19528.0	−1.05216	−0.526078	−	0.850436i	$-0.676338\pi$
$701$	−19528.0	−1.05216	−0.526078	+	0.850436i	$0.676338\pi$
$702$	0	0
$703$	−8980.66	−0.481809
$704$	−3317.94	−0.177627
$705$	31629.3	1.68969
$706$	16838.5	0.897628
$707$	−3336.41	−0.177480
$708$	−6234.86	−0.330961
$709$	1305.38	0.0691460	0.0345730	−	0.999402i	$-0.488993\pi$
$709$	1305.38	0.0691460	0.0345730	+	0.999402i	$0.488993\pi$
$710$	4090.32	0.216207
$711$	−3266.83	−0.172315
$712$	−5675.93	−0.298756
$713$	−2817.20	−0.147973
$714$	7195.45	0.377147
$715$	0	0
$716$	7230.66	0.377406
$717$	25289.1	1.31721
$718$	−7162.76	−0.372301
$719$	20578.6	1.06739	0.533693	−	0.845678i	$-0.320804\pi$
$719$	20578.6	1.06739	0.533693	+	0.845678i	$0.320804\pi$
$720$	752.008	0.0389246
$721$	−10950.8	−0.565642
$722$	9108.88	0.469525
$723$	14950.5	0.769039
$724$	8553.17	0.439055
$725$	15530.9	0.795590
$726$	−13182.8	−0.673909
$727$	−19534.4	−0.996548	−0.498274	−	0.867020i	$-0.666033\pi$
$727$	−19534.4	−0.996548	−0.498274	+	0.867020i	$0.666033\pi$
$728$	0	0
$729$	21496.6	1.09214
$730$	−21568.3	−1.09353
$731$	−7701.58	−0.389676
$732$	9303.97	0.469788
$733$	23047.0	1.16134	0.580669	−	0.814140i	$-0.302791\pi$
$733$	23047.0	1.16134	0.580669	+	0.814140i	$0.302791\pi$
$734$	14404.1	0.724341
$735$	−3295.31	−0.165373
$736$	−731.158	−0.0366180
$737$	−17816.9	−0.890493
$738$	−2410.15	−0.120215
$739$	7582.68	0.377447	0.188724	−	0.982030i	$-0.439565\pi$
$739$	7582.68	0.377447	0.188724	+	0.982030i	$0.439565\pi$
$740$	10358.0	0.514552
$741$	0	0
$742$	−2237.67	−0.110711
$743$	−2781.28	−0.137329	−0.0686645	−	0.997640i	$-0.521874\pi$
$743$	−2781.28	−0.137329	−0.0686645	+	0.997640i	$0.521874\pi$
$744$	4792.30	0.236148
$745$	−15084.8	−0.741832
$746$	−9462.13	−0.464388
$747$	3724.82	0.182442
$748$	21937.2	1.07233
$749$	11488.3	0.560445
$750$	−7854.34	−0.382400
$751$	26274.8	1.27667	0.638337	−	0.769757i	$-0.279623\pi$
$751$	26274.8	1.27667	0.638337	+	0.769757i	$0.279623\pi$
$752$	−7525.05	−0.364907
$753$	6501.97	0.314668
$754$	0	0
$755$	−41086.0	−1.98049
$756$	−4134.90	−0.198922
$757$	−37501.6	−1.80055	−0.900276	−	0.435320i	$-0.856635\pi$
$757$	−37501.6	−1.80055	−0.900276	+	0.435320i	$0.856635\pi$
$758$	−13149.4	−0.630088
$759$	−5755.04	−0.275224
$760$	5316.02	0.253727
$761$	−7853.66	−0.374107	−0.187053	−	0.982350i	$-0.559894\pi$
$761$	−7853.66	−0.374107	−0.187053	+	0.982350i	$0.559894\pi$
$762$	18852.5	0.896263
$763$	12798.7	0.607264
$764$	−9620.18	−0.455558
$765$	−4972.04	−0.234986
$766$	10092.1	0.476035
$767$	0	0
$768$	1243.76	0.0584381
$769$	−36073.7	−1.69161	−0.845806	−	0.533490i	$-0.820880\pi$
$769$	−36073.7	−1.69161	−0.845806	+	0.533490i	$0.820880\pi$
$770$	−10046.6	−0.470201
$771$	−27773.0	−1.29730
$772$	−5366.91	−0.250206
$773$	14832.4	0.690149	0.345075	−	0.938575i	$-0.387854\pi$
$773$	14832.4	0.690149	0.345075	+	0.938575i	$0.387854\pi$
$774$	494.399	0.0229597
$775$	−8212.20	−0.380634
$776$	2840.20	0.131388
$777$	−6362.24	−0.293750
$778$	−16203.4	−0.746683
$779$	−17037.6	−0.783615
$780$	0	0
$781$	−7659.73	−0.350943
$782$	4834.19	0.221062
$783$	−34434.9	−1.57165
$784$	784.000	0.0357143
$785$	−41898.3	−1.90499
$786$	−6791.07	−0.308180
$787$	−13747.7	−0.622684	−0.311342	−	0.950298i	$-0.600778\pi$
$787$	−13747.7	−0.622684	−0.311342	+	0.950298i	$0.600778\pi$
$788$	−17319.0	−0.782949
$789$	−24626.8	−1.11120
$790$	26635.4	1.19955
$791$	−4471.31	−0.200988
$792$	−1408.25	−0.0631816
$793$	0	0
$794$	−3848.43	−0.172010
$795$	−10749.0	−0.479532
$796$	7413.10	0.330088
$797$	281.955	0.0125312	0.00626560	−	0.999980i	$-0.498006\pi$
$797$	281.955	0.0125312	0.00626560	+	0.999980i	$0.498006\pi$
$798$	−3265.28	−0.144849
$799$	49753.3	2.20293
$800$	−2131.34	−0.0941930
$801$	−2409.05	−0.106267
$802$	25071.1	1.10386
$803$	40389.8	1.77500
$804$	6678.83	0.292965
$805$	−2213.92	−0.0969323
$806$	0	0
$807$	−30333.6	−1.32317
$808$	3813.04	0.166018
$809$	3977.34	0.172850	0.0864252	−	0.996258i	$-0.472456\pi$
$809$	3977.34	0.172850	0.0864252	+	0.996258i	$0.472456\pi$
$810$	−17324.6	−0.751512
$811$	−8748.05	−0.378774	−0.189387	−	0.981903i	$-0.560650\pi$
$811$	−8748.05	−0.378774	−0.189387	+	0.981903i	$0.560650\pi$
$812$	6529.06	0.282174
$813$	22582.8	0.974188
$814$	−19396.9	−0.835212
$815$	6499.46	0.279345
$816$	−8223.37	−0.352789
$817$	3494.96	0.149661
$818$	10620.1	0.453941
$819$	0	0
$820$	19650.7	0.836868
$821$	−10646.7	−0.452586	−0.226293	−	0.974059i	$-0.572661\pi$
$821$	−10646.7	−0.452586	−0.226293	+	0.974059i	$0.572661\pi$
$822$	−22087.1	−0.937197
$823$	−4003.17	−0.169552	−0.0847762	−	0.996400i	$-0.527018\pi$
$823$	−4003.17	−0.169552	−0.0847762	+	0.996400i	$0.527018\pi$
$824$	12515.2	0.529109
$825$	−16776.1	−0.707961
$826$	4491.56	0.189203
$827$	36320.0	1.52717	0.763585	−	0.645708i	$-0.223437\pi$
$827$	36320.0	1.52717	0.763585	+	0.645708i	$0.223437\pi$
$828$	−310.328	−0.0130249
$829$	−12103.1	−0.507065	−0.253532	−	0.967327i	$-0.581592\pi$
$829$	−12103.1	−0.507065	−0.253532	+	0.967327i	$0.581592\pi$
$830$	−30369.6	−1.27005
$831$	−13114.1	−0.547441
$832$	0	0
$833$	−5183.56	−0.215606
$834$	20477.9	0.850231
$835$	−19058.1	−0.789861
$836$	−9955.04	−0.411845
$837$	18208.0	0.751925
$838$	−24081.6	−0.992703
$839$	−34851.0	−1.43408	−0.717039	−	0.697033i	$-0.754503\pi$
$839$	−34851.0	−1.43408	−0.717039	+	0.697033i	$0.754503\pi$
$840$	3766.07	0.154693
$841$	29984.2	1.22942
$842$	9711.60	0.397487
$843$	−18184.1	−0.742933
$844$	−5432.58	−0.221561
$845$	0	0
$846$	−3193.88	−0.129797
$847$	9496.79	0.385258
$848$	2557.33	0.103560
$849$	−26331.0	−1.06440
$850$	14091.8	0.568640
$851$	−4274.41	−0.172180
$852$	2871.32	0.115458
$853$	−14775.3	−0.593081	−0.296541	−	0.955020i	$-0.595833\pi$
$853$	−14775.3	−0.593081	−0.296541	+	0.955020i	$0.595833\pi$
$854$	−6702.53	−0.268566
$855$	2256.30	0.0902500
$856$	−13129.5	−0.524249
$857$	−42512.0	−1.69450	−0.847248	−	0.531198i	$-0.821742\pi$
$857$	−42512.0	−1.69450	−0.847248	+	0.531198i	$0.821742\pi$
$858$	0	0
$859$	−9574.43	−0.380297	−0.190149	−	0.981755i	$-0.560897\pi$
$859$	−9574.43	−0.380297	−0.190149	+	0.981755i	$0.560897\pi$
$860$	−4030.98	−0.159832
$861$	−12070.1	−0.477756
$862$	−25231.1	−0.996955
$863$	48476.2	1.91211	0.956053	−	0.293194i	$-0.0947181\pi$
$863$	48476.2	1.91211	0.956053	+	0.293194i	$0.0947181\pi$
$864$	4725.60	0.186074
$865$	−4794.10	−0.188444
$866$	−21467.8	−0.842384
$867$	30500.8	1.19476
$868$	−3452.34	−0.135000
$869$	−49878.8	−1.94709
$870$	31363.4	1.22221
$871$	0	0
$872$	−14627.0	−0.568044
$873$	1205.47	0.0467344
$874$	−2193.74	−0.0849021
$875$	5658.22	0.218609
$876$	−15140.5	−0.583961
$877$	−39895.5	−1.53612	−0.768058	−	0.640380i	$-0.778777\pi$
$877$	−39895.5	−1.53612	−0.768058	+	0.640380i	$0.778777\pi$
$878$	2868.25	0.110249
$879$	12180.9	0.467408
$880$	11481.9	0.439833
$881$	−34536.7	−1.32074	−0.660369	−	0.750942i	$-0.729600\pi$
$881$	−34536.7	−1.32074	−0.660369	+	0.750942i	$0.729600\pi$
$882$	332.756	0.0127035
$883$	3167.28	0.120711	0.0603553	−	0.998177i	$-0.480777\pi$
$883$	3167.28	0.120711	0.0603553	+	0.998177i	$0.480777\pi$
$884$	0	0
$885$	21575.9	0.819511
$886$	−2310.11	−0.0875957
$887$	21597.6	0.817561	0.408781	−	0.912633i	$-0.365954\pi$
$887$	21597.6	0.817561	0.408781	+	0.912633i	$0.365954\pi$
$888$	7271.13	0.274778
$889$	−13581.2	−0.512372
$890$	19641.7	0.739767
$891$	32442.9	1.21984
$892$	24379.6	0.915123
$893$	−22577.9	−0.846070
$894$	−10589.2	−0.396149
$895$	−25021.9	−0.934515
$896$	−896.000	−0.0334077
$897$	0	0
$898$	9977.87	0.370786
$899$	−28750.7	−1.06662
$900$	−904.614	−0.0335042
$901$	−16908.3	−0.625191
$902$	−36798.8	−1.35839
$903$	2475.96	0.0912456
$904$	5110.07	0.188007
$905$	−29598.5	−1.08717
$906$	−28841.5	−1.05761
$907$	−15400.3	−0.563790	−0.281895	−	0.959445i	$-0.590963\pi$
$907$	−15400.3	−0.563790	−0.281895	+	0.959445i	$0.590963\pi$
$908$	−21744.1	−0.794717
$909$	1618.38	0.0590521
$910$	0	0
$911$	49710.6	1.80789	0.903945	−	0.427650i	$-0.140658\pi$
$911$	49710.6	1.80789	0.903945	+	0.427650i	$0.140658\pi$
$912$	3731.74	0.135494
$913$	56871.5	2.06153
$914$	−30644.4	−1.10900
$915$	−32196.7	−1.16327
$916$	15176.7	0.547437
$917$	4892.25	0.176179
$918$	−31244.2	−1.12332
$919$	−16580.4	−0.595142	−0.297571	−	0.954700i	$-0.596177\pi$
$919$	−16580.4	−0.595142	−0.297571	+	0.954700i	$0.596177\pi$
$920$	2530.20	0.0906719
$921$	17288.8	0.618551
$922$	23807.6	0.850393
$923$	0	0
$924$	−7052.53	−0.251094
$925$	−12460.0	−0.442900
$926$	30443.1	1.08037
$927$	5311.85	0.188203
$928$	−7461.78	−0.263949
$929$	−21186.5	−0.748232	−0.374116	−	0.927382i	$-0.622054\pi$
$929$	−21186.5	−0.748232	−0.374116	+	0.927382i	$0.622054\pi$
$930$	−16583.9	−0.584739
$931$	2352.29	0.0828067
$932$	4282.64	0.150518
$933$	−3840.58	−0.134764
$934$	−17614.7	−0.617101
$935$	−75914.4	−2.65526
$936$	0	0
$937$	−37667.5	−1.31328	−0.656640	−	0.754204i	$-0.728023\pi$
$937$	−37667.5	−1.31328	−0.656640	+	0.754204i	$0.728023\pi$
$938$	−4811.39	−0.167481
$939$	32013.8	1.11260
$940$	26040.7	0.903567
$941$	−3401.39	−0.117834	−0.0589172	−	0.998263i	$-0.518765\pi$
$941$	−3401.39	−0.117834	−0.0589172	+	0.998263i	$0.518765\pi$
$942$	−29411.8	−1.01729
$943$	−8109.17	−0.280033
$944$	−5133.21	−0.176983
$945$	14308.9	0.492561
$946$	7548.61	0.259436
$947$	8950.65	0.307135	0.153568	−	0.988138i	$-0.450924\pi$
$947$	8950.65	0.307135	0.153568	+	0.988138i	$0.450924\pi$
$948$	18697.6	0.640578
$949$	0	0
$950$	−6394.81	−0.218395
$951$	47322.8	1.61361
$952$	5924.07	0.201681
$953$	−26947.3	−0.915960	−0.457980	−	0.888963i	$-0.651427\pi$
$953$	−26947.3	−0.915960	−0.457980	+	0.888963i	$0.651427\pi$
$954$	1085.42	0.0368362
$955$	33291.0	1.12803
$956$	20820.7	0.704382
$957$	−58732.6	−1.98386
$958$	20287.3	0.684190
$959$	15911.4	0.535773
$960$	−4304.08	−0.144702
$961$	−14588.6	−0.489699
$962$	0	0
$963$	−5572.60	−0.186474
$964$	12308.9	0.411247
$965$	18572.3	0.619549
$966$	−1554.13	−0.0517633
$967$	−7549.32	−0.251054	−0.125527	−	0.992090i	$-0.540062\pi$
$967$	−7549.32	−0.251054	−0.125527	+	0.992090i	$0.540062\pi$
$968$	−10853.5	−0.360376
$969$	−24673.1	−0.817972
$970$	−9828.59	−0.325337
$971$	−46922.7	−1.55080	−0.775398	−	0.631473i	$-0.782451\pi$
$971$	−46922.7	−1.55080	−0.775398	+	0.631473i	$0.782451\pi$
$972$	3787.35	0.124979
$973$	−14752.2	−0.486057
$974$	−18772.7	−0.617574
$975$	0	0
$976$	7660.03	0.251221
$977$	2568.52	0.0841086	0.0420543	−	0.999115i	$-0.486610\pi$
$977$	2568.52	0.0841086	0.0420543	+	0.999115i	$0.486610\pi$
$978$	4562.49	0.149174
$979$	−36782.1	−1.20078
$980$	−2713.06	−0.0884341
$981$	−6208.21	−0.202052
$982$	−23773.8	−0.772559
$983$	−49875.4	−1.61829	−0.809144	−	0.587610i	$-0.800069\pi$
$983$	−49875.4	−1.61829	−0.809144	+	0.587610i	$0.800069\pi$
$984$	13794.4	0.446900
$985$	59932.9	1.93870
$986$	49335.0	1.59345
$987$	−15995.0	−0.515833
$988$	0	0
$989$	1663.45	0.0534829
$990$	4873.28	0.156448
$991$	−26464.3	−0.848299	−0.424150	−	0.905592i	$-0.639427\pi$
$991$	−26464.3	−0.848299	−0.424150	+	0.905592i	$0.639427\pi$
$992$	3945.53	0.126281
$993$	6360.90	0.203280
$994$	−2068.49	−0.0660044
$995$	−25653.3	−0.817350
$996$	−21318.8	−0.678226
$997$	−22873.6	−0.726592	−0.363296	−	0.931674i	$-0.618349\pi$
$997$	−22873.6	−0.726592	−0.363296	+	0.931674i	$0.618349\pi$
$998$	−11332.0	−0.359426
$999$	27626.2	0.874928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.4.a.bd.1.9		12
13.2	odd	12		182.4.m.b.43.2	✓	24
13.7	odd	12		182.4.m.b.127.2	yes	24
13.12	even	2		2366.4.a.bg.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.4.m.b.43.2	✓	24	13.2	odd	12
182.4.m.b.127.2	yes	24	13.7	odd	12
2366.4.a.bd.1.9		12	1.1	even	1	trivial
2366.4.a.bg.1.9		12	13.12	even	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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +4.85845 q^{3} +4.00000 q^{4} -13.8421 q^{5} -9.71690 q^{6} +7.00000 q^{7} -8.00000 q^{8} -3.39547 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +4.85845 q^{3} +4.00000 q^{4} -13.8421 q^{5} -9.71690 q^{6} +7.00000 q^{7} -8.00000 q^{8} -3.39547 q^{9} +27.6843 q^{10} -51.8429 q^{11} +19.4338 q^{12} -14.0000 q^{14} -67.2513 q^{15} +16.0000 q^{16} -105.787 q^{17} +6.79094 q^{18} +48.0058 q^{19} -55.3685 q^{20} +34.0091 q^{21} +103.686 q^{22} +22.8487 q^{23} -38.8676 q^{24} +66.6045 q^{25} -147.675 q^{27} +28.0000 q^{28} +233.181 q^{29} +134.503 q^{30} -123.298 q^{31} -32.0000 q^{32} -251.876 q^{33} +211.574 q^{34} -96.8949 q^{35} -13.5819 q^{36} -187.074 q^{37} -96.0117 q^{38} +110.737 q^{40} -354.907 q^{41} -68.0183 q^{42} +72.8028 q^{43} -207.372 q^{44} +47.0005 q^{45} -45.6974 q^{46} -470.316 q^{47} +77.7352 q^{48} +49.0000 q^{49} -133.209 q^{50} -513.961 q^{51} +159.833 q^{53} +295.350 q^{54} +717.616 q^{55} -56.0000 q^{56} +233.234 q^{57} -466.361 q^{58} -320.826 q^{59} -269.005 q^{60} +478.752 q^{61} +246.596 q^{62} -23.7683 q^{63} +64.0000 q^{64} +503.752 q^{66} +343.671 q^{67} -423.148 q^{68} +111.009 q^{69} +193.790 q^{70} +147.749 q^{71} +27.1637 q^{72} -779.080 q^{73} +374.149 q^{74} +323.595 q^{75} +192.023 q^{76} -362.900 q^{77} +962.115 q^{79} -221.474 q^{80} -625.793 q^{81} +709.815 q^{82} -1097.00 q^{83} +136.037 q^{84} +1464.32 q^{85} -145.606 q^{86} +1132.90 q^{87} +414.743 q^{88} +709.491 q^{89} -94.0010 q^{90} +91.3948 q^{92} -599.037 q^{93} +940.631 q^{94} -664.503 q^{95} -155.470 q^{96} -355.024 q^{97} -98.0000 q^{98} +176.031 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} + 6 q^{3} + 48 q^{4} - 28 q^{5} - 12 q^{6} + 84 q^{7} - 96 q^{8} + 162 q^{9}+O(q^{10}) \) 12 * q - 24 * q^2 + 6 * q^3 + 48 * q^4 - 28 * q^5 - 12 * q^6 + 84 * q^7 - 96 * q^8 + 162 * q^9	\( 12 q - 24 q^{2} + 6 q^{3} + 48 q^{4} - 28 q^{5} - 12 q^{6} + 84 q^{7} - 96 q^{8} + 162 q^{9} + 56 q^{10} - 6 q^{11} + 24 q^{12} - 168 q^{14} + 138 q^{15} + 192 q^{16} - 56 q^{17} - 324 q^{18} - 158 q^{19} - 112 q^{20} + 42 q^{21} + 12 q^{22} + 414 q^{23} - 48 q^{24} + 478 q^{25} + 390 q^{27} + 336 q^{28} + 222 q^{29} - 276 q^{30} + 200 q^{31} - 384 q^{32} - 844 q^{33} + 112 q^{34} - 196 q^{35} + 648 q^{36} + 560 q^{37} + 316 q^{38} + 224 q^{40} + 66 q^{41} - 84 q^{42} + 484 q^{43} - 24 q^{44} - 542 q^{45} - 828 q^{46} - 618 q^{47} + 96 q^{48} + 588 q^{49} - 956 q^{50} + 992 q^{51} + 504 q^{53} - 780 q^{54} + 2584 q^{55} - 672 q^{56} + 1164 q^{57} - 444 q^{58} - 1460 q^{59} + 552 q^{60} - 2 q^{61} - 400 q^{62} + 1134 q^{63} + 768 q^{64} + 1688 q^{66} - 334 q^{67} - 224 q^{68} + 4660 q^{69} + 392 q^{70} + 196 q^{71} - 1296 q^{72} - 490 q^{73} - 1120 q^{74} - 338 q^{75} - 632 q^{76} - 42 q^{77} + 2942 q^{79} - 448 q^{80} + 2824 q^{81} - 132 q^{82} - 236 q^{83} + 168 q^{84} - 1352 q^{85} - 968 q^{86} + 1456 q^{87} + 48 q^{88} - 3566 q^{89} + 1084 q^{90} + 1656 q^{92} - 1884 q^{93} + 1236 q^{94} + 5754 q^{95} - 192 q^{96} - 3032 q^{97} - 1176 q^{98} - 3670 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 + 6 * q^3 + 48 * q^4 - 28 * q^5 - 12 * q^6 + 84 * q^7 - 96 * q^8 + 162 * q^9 + 56 * q^10 - 6 * q^11 + 24 * q^12 - 168 * q^14 + 138 * q^15 + 192 * q^16 - 56 * q^17 - 324 * q^18 - 158 * q^19 - 112 * q^20 + 42 * q^21 + 12 * q^22 + 414 * q^23 - 48 * q^24 + 478 * q^25 + 390 * q^27 + 336 * q^28 + 222 * q^29 - 276 * q^30 + 200 * q^31 - 384 * q^32 - 844 * q^33 + 112 * q^34 - 196 * q^35 + 648 * q^36 + 560 * q^37 + 316 * q^38 + 224 * q^40 + 66 * q^41 - 84 * q^42 + 484 * q^43 - 24 * q^44 - 542 * q^45 - 828 * q^46 - 618 * q^47 + 96 * q^48 + 588 * q^49 - 956 * q^50 + 992 * q^51 + 504 * q^53 - 780 * q^54 + 2584 * q^55 - 672 * q^56 + 1164 * q^57 - 444 * q^58 - 1460 * q^59 + 552 * q^60 - 2 * q^61 - 400 * q^62 + 1134 * q^63 + 768 * q^64 + 1688 * q^66 - 334 * q^67 - 224 * q^68 + 4660 * q^69 + 392 * q^70 + 196 * q^71 - 1296 * q^72 - 490 * q^73 - 1120 * q^74 - 338 * q^75 - 632 * q^76 - 42 * q^77 + 2942 * q^79 - 448 * q^80 + 2824 * q^81 - 132 * q^82 - 236 * q^83 + 168 * q^84 - 1352 * q^85 - 968 * q^86 + 1456 * q^87 + 48 * q^88 - 3566 * q^89 + 1084 * q^90 + 1656 * q^92 - 1884 * q^93 + 1236 * q^94 + 5754 * q^95 - 192 * q^96 - 3032 * q^97 - 1176 * q^98 - 3670 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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