LMFDB - Embedded newform 1150.4.a.bb.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, 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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 179x^{7} + 380x^{6} + 10197x^{5} - 8259x^{4} - 205207x^{3} - 105750x^{2} + 525560x + 178000 $ x^9 - 3x^8 - 179x^7 + 380x^6 + 10197x^5 - 8259x^4 - 205207x^3 - 105750x^2 + 525560x + 178000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$6.93776$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +6.93776 q^{3} +4.00000 q^{4} +13.8755 q^{6} -7.91891 q^{7} +8.00000 q^{8} +21.1325 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +6.93776 q^{3} +4.00000 q^{4} +13.8755 q^{6} -7.91891 q^{7} +8.00000 q^{8} +21.1325 q^{9} +26.0634 q^{11} +27.7510 q^{12} +31.1013 q^{13} -15.8378 q^{14} +16.0000 q^{16} +24.1764 q^{17} +42.2649 q^{18} +85.8889 q^{19} -54.9395 q^{21} +52.1267 q^{22} -23.0000 q^{23} +55.5020 q^{24} +62.2026 q^{26} -40.7076 q^{27} -31.6757 q^{28} +195.331 q^{29} -9.44106 q^{31} +32.0000 q^{32} +180.821 q^{33} +48.3527 q^{34} +84.5298 q^{36} -126.450 q^{37} +171.778 q^{38} +215.773 q^{39} -102.646 q^{41} -109.879 q^{42} +112.883 q^{43} +104.253 q^{44} -46.0000 q^{46} +162.846 q^{47} +111.004 q^{48} -280.291 q^{49} +167.730 q^{51} +124.405 q^{52} +88.3105 q^{53} -81.4152 q^{54} -63.3513 q^{56} +595.876 q^{57} +390.663 q^{58} -397.344 q^{59} +414.542 q^{61} -18.8821 q^{62} -167.346 q^{63} +64.0000 q^{64} +361.643 q^{66} +570.237 q^{67} +96.7055 q^{68} -159.568 q^{69} +212.342 q^{71} +169.060 q^{72} +942.373 q^{73} -252.899 q^{74} +343.556 q^{76} -206.394 q^{77} +431.546 q^{78} +673.719 q^{79} -852.996 q^{81} -205.292 q^{82} +194.627 q^{83} -219.758 q^{84} +225.766 q^{86} +1355.16 q^{87} +208.507 q^{88} -273.267 q^{89} -246.288 q^{91} -92.0000 q^{92} -65.4998 q^{93} +325.692 q^{94} +222.008 q^{96} +123.204 q^{97} -560.582 q^{98} +550.783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) $ 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * 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
$3$	6.93776	1.33517	0.667586	−	0.744533i	$-0.267328\pi$
$3$	6.93776	1.33517	0.667586	+	0.744533i	$0.267328\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	13.8755	0.944109
$7$	−7.91891	−0.427581	−0.213791	−	0.976880i	$-0.568581\pi$
$7$	−7.91891	−0.427581	−0.213791	+	0.976880i	$0.568581\pi$
$8$	8.00000	0.353553
$9$	21.1325	0.782683
$10$	0	0
$11$	26.0634	0.714400	0.357200	−	0.934028i	$-0.383731\pi$
$11$	26.0634	0.714400	0.357200	+	0.934028i	$0.383731\pi$
$12$	27.7510	0.667586
$13$	31.1013	0.663534	0.331767	−	0.943361i	$-0.392355\pi$
$13$	31.1013	0.663534	0.331767	+	0.943361i	$0.392355\pi$
$14$	−15.8378	−0.302346
$15$	0	0
$16$	16.0000	0.250000
$17$	24.1764	0.344919	0.172460	−	0.985017i	$-0.444829\pi$
$17$	24.1764	0.344919	0.172460	+	0.985017i	$0.444829\pi$
$18$	42.2649	0.553441
$19$	85.8889	1.03707	0.518533	−	0.855057i	$-0.326478\pi$
$19$	85.8889	1.03707	0.518533	+	0.855057i	$0.326478\pi$
$20$	0	0
$21$	−54.9395	−0.570894
$22$	52.1267	0.505157
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	55.5020	0.472054
$25$	0	0
$26$	62.2026	0.469190
$27$	−40.7076	−0.290155
$28$	−31.6757	−0.213791
$29$	195.331	1.25076	0.625382	−	0.780319i	$-0.284943\pi$
$29$	195.331	1.25076	0.625382	+	0.780319i	$0.284943\pi$
$30$	0	0
$31$	−9.44106	−0.0546989	−0.0273494	−	0.999626i	$-0.508707\pi$
$31$	−9.44106	−0.0546989	−0.0273494	+	0.999626i	$0.508707\pi$
$32$	32.0000	0.176777
$33$	180.821	0.953847
$34$	48.3527	0.243895
$35$	0	0
$36$	84.5298	0.391342
$37$	−126.450	−0.561843	−0.280921	−	0.959731i	$-0.590640\pi$
$37$	−126.450	−0.561843	−0.280921	+	0.959731i	$0.590640\pi$
$38$	171.778	0.733317
$39$	215.773	0.885932
$40$	0	0
$41$	−102.646	−0.390991	−0.195496	−	0.980705i	$-0.562632\pi$
$41$	−102.646	−0.390991	−0.195496	+	0.980705i	$0.562632\pi$
$42$	−109.879	−0.403683
$43$	112.883	0.400338	0.200169	−	0.979761i	$-0.435851\pi$
$43$	112.883	0.400338	0.200169	+	0.979761i	$0.435851\pi$
$44$	104.253	0.357200
$45$	0	0
$46$	−46.0000	−0.147442
$47$	162.846	0.505394	0.252697	−	0.967545i	$-0.418682\pi$
$47$	162.846	0.505394	0.252697	+	0.967545i	$0.418682\pi$
$48$	111.004	0.333793
$49$	−280.291	−0.817174
$50$	0	0
$51$	167.730	0.460527
$52$	124.405	0.331767
$53$	88.3105	0.228875	0.114438	−	0.993430i	$-0.463493\pi$
$53$	88.3105	0.228875	0.114438	+	0.993430i	$0.463493\pi$
$54$	−81.4152	−0.205171
$55$	0	0
$56$	−63.3513	−0.151173
$57$	595.876	1.38466
$58$	390.663	0.884423
$59$	−397.344	−0.876775	−0.438388	−	0.898786i	$-0.644450\pi$
$59$	−397.344	−0.876775	−0.438388	+	0.898786i	$0.644450\pi$
$60$	0	0
$61$	414.542	0.870110	0.435055	−	0.900404i	$-0.356729\pi$
$61$	414.542	0.870110	0.435055	+	0.900404i	$0.356729\pi$
$62$	−18.8821	−0.0386779
$63$	−167.346	−0.334661
$64$	64.0000	0.125000
$65$	0	0
$66$	361.643	0.674472
$67$	570.237	1.03978	0.519892	−	0.854232i	$-0.325972\pi$
$67$	570.237	1.03978	0.519892	+	0.854232i	$0.325972\pi$
$68$	96.7055	0.172460
$69$	−159.568	−0.278403
$70$	0	0
$71$	212.342	0.354935	0.177467	−	0.984127i	$-0.443210\pi$
$71$	212.342	0.354935	0.177467	+	0.984127i	$0.443210\pi$
$72$	169.060	0.276720
$73$	942.373	1.51091	0.755455	−	0.655200i	$-0.227416\pi$
$73$	942.373	1.51091	0.755455	+	0.655200i	$0.227416\pi$
$74$	−252.899	−0.397283
$75$	0	0
$76$	343.556	0.518533
$77$	−206.394	−0.305464
$78$	431.546	0.626449
$79$	673.719	0.959485	0.479743	−	0.877409i	$-0.340730\pi$
$79$	673.719	0.959485	0.479743	+	0.877409i	$0.340730\pi$
$80$	0	0
$81$	−852.996	−1.17009
$82$	−205.292	−0.276473
$83$	194.627	0.257387	0.128694	−	0.991684i	$-0.458922\pi$
$83$	194.627	0.257387	0.128694	+	0.991684i	$0.458922\pi$
$84$	−219.758	−0.285447
$85$	0	0
$86$	225.766	0.283081
$87$	1355.16	1.66998
$88$	208.507	0.252579
$89$	−273.267	−0.325463	−0.162732	−	0.986670i	$-0.552030\pi$
$89$	−273.267	−0.325463	−0.162732	+	0.986670i	$0.552030\pi$
$90$	0	0
$91$	−246.288	−0.283715
$92$	−92.0000	−0.104257
$93$	−65.4998	−0.0730324
$94$	325.692	0.357367
$95$	0	0
$96$	222.008	0.236027
$97$	123.204	0.128964	0.0644820	−	0.997919i	$-0.479460\pi$
$97$	123.204	0.128964	0.0644820	+	0.997919i	$0.479460\pi$
$98$	−560.582	−0.577830
$99$	550.783	0.559149
$100$	0	0
$101$	1714.30	1.68890	0.844450	−	0.535634i	$-0.179927\pi$
$101$	1714.30	1.68890	0.844450	+	0.535634i	$0.179927\pi$
$102$	335.459	0.325642
$103$	−1659.24	−1.58728	−0.793641	−	0.608386i	$-0.791817\pi$
$103$	−1659.24	−1.58728	−0.793641	+	0.608386i	$0.791817\pi$
$104$	248.810	0.234595
$105$	0	0
$106$	176.621	0.161839
$107$	586.313	0.529729	0.264865	−	0.964286i	$-0.414673\pi$
$107$	586.313	0.529729	0.264865	+	0.964286i	$0.414673\pi$
$108$	−162.830	−0.145077
$109$	−679.092	−0.596745	−0.298373	−	0.954449i	$-0.596444\pi$
$109$	−679.092	−0.596745	−0.298373	+	0.954449i	$0.596444\pi$
$110$	0	0
$111$	−877.277	−0.750157
$112$	−126.703	−0.106895
$113$	1030.68	0.858035	0.429017	−	0.903296i	$-0.358860\pi$
$113$	1030.68	0.858035	0.429017	+	0.903296i	$0.358860\pi$
$114$	1191.75	0.979104
$115$	0	0
$116$	781.326	0.625382
$117$	657.247	0.519337
$118$	−794.687	−0.619974
$119$	−191.451	−0.147481
$120$	0	0
$121$	−651.701	−0.489632
$122$	829.084	0.615260
$123$	−712.134	−0.522041
$124$	−37.7643	−0.0273494
$125$	0	0
$126$	−334.692	−0.236641
$127$	241.705	0.168880	0.0844402	−	0.996429i	$-0.473090\pi$
$127$	241.705	0.168880	0.0844402	+	0.996429i	$0.473090\pi$
$128$	128.000	0.0883883
$129$	783.156	0.534519
$130$	0	0
$131$	1522.31	1.01530	0.507651	−	0.861563i	$-0.330514\pi$
$131$	1522.31	1.01530	0.507651	+	0.861563i	$0.330514\pi$
$132$	723.285	0.476924
$133$	−680.147	−0.443430
$134$	1140.47	0.735239
$135$	0	0
$136$	193.411	0.121947
$137$	−2816.66	−1.75652	−0.878260	−	0.478184i	$-0.841295\pi$
$137$	−2816.66	−1.75652	−0.878260	+	0.478184i	$0.841295\pi$
$138$	−319.137	−0.196860
$139$	−1131.35	−0.690360	−0.345180	−	0.938536i	$-0.612182\pi$
$139$	−1131.35	−0.690360	−0.345180	+	0.938536i	$0.612182\pi$
$140$	0	0
$141$	1129.79	0.674788
$142$	424.684	0.250977
$143$	810.605	0.474029
$144$	338.119	0.195671
$145$	0	0
$146$	1884.75	1.06837
$147$	−1944.59	−1.09107
$148$	−505.798	−0.280921
$149$	−1671.85	−0.919218	−0.459609	−	0.888121i	$-0.652011\pi$
$149$	−1671.85	−0.919218	−0.459609	+	0.888121i	$0.652011\pi$
$150$	0	0
$151$	1088.06	0.586390	0.293195	−	0.956053i	$-0.405281\pi$
$151$	1088.06	0.586390	0.293195	+	0.956053i	$0.405281\pi$
$152$	687.111	0.366659
$153$	510.906	0.269963
$154$	−412.787	−0.215996
$155$	0	0
$156$	863.093	0.442966
$157$	−1600.28	−0.813481	−0.406740	−	0.913544i	$-0.633335\pi$
$157$	−1600.28	−0.813481	−0.406740	+	0.913544i	$0.633335\pi$
$158$	1347.44	0.678459
$159$	612.677	0.305588
$160$	0	0
$161$	182.135	0.0891568
$162$	−1705.99	−0.827379
$163$	−530.195	−0.254773	−0.127387	−	0.991853i	$-0.540659\pi$
$163$	−530.195	−0.254773	−0.127387	+	0.991853i	$0.540659\pi$
$164$	−410.585	−0.195496
$165$	0	0
$166$	389.255	0.182000
$167$	−4009.99	−1.85810	−0.929049	−	0.369957i	$-0.879372\pi$
$167$	−4009.99	−1.85810	−0.929049	+	0.369957i	$0.879372\pi$
$168$	−439.516	−0.201842
$169$	−1229.71	−0.559722
$170$	0	0
$171$	1815.04	0.811695
$172$	451.532	0.200169
$173$	−833.108	−0.366127	−0.183064	−	0.983101i	$-0.558601\pi$
$173$	−833.108	−0.366127	−0.183064	+	0.983101i	$0.558601\pi$
$174$	2710.32	1.18086
$175$	0	0
$176$	417.014	0.178600
$177$	−2756.67	−1.17065
$178$	−546.533	−0.230137
$179$	−3037.70	−1.26843	−0.634214	−	0.773157i	$-0.718676\pi$
$179$	−3037.70	−1.26843	−0.634214	+	0.773157i	$0.718676\pi$
$180$	0	0
$181$	3578.15	1.46940	0.734701	−	0.678391i	$-0.237322\pi$
$181$	3578.15	1.46940	0.734701	+	0.678391i	$0.237322\pi$
$182$	−492.577	−0.200617
$183$	2875.99	1.16175
$184$	−184.000	−0.0737210
$185$	0	0
$186$	−131.000	−0.0516417
$187$	630.118	0.246411
$188$	651.384	0.252697
$189$	322.360	0.124065
$190$	0	0
$191$	277.836	0.105254	0.0526269	−	0.998614i	$-0.483241\pi$
$191$	277.836	0.105254	0.0526269	+	0.998614i	$0.483241\pi$
$192$	444.016	0.166896
$193$	−252.013	−0.0939911	−0.0469955	−	0.998895i	$-0.514965\pi$
$193$	−252.013	−0.0939911	−0.0469955	+	0.998895i	$0.514965\pi$
$194$	246.409	0.0911914
$195$	0	0
$196$	−1121.16	−0.408587
$197$	−5403.14	−1.95410	−0.977051	−	0.213007i	$-0.931674\pi$
$197$	−5403.14	−1.95410	−0.977051	+	0.213007i	$0.931674\pi$
$198$	1101.57	0.395378
$199$	−370.081	−0.131831	−0.0659155	−	0.997825i	$-0.520997\pi$
$199$	−370.081	−0.131831	−0.0659155	+	0.997825i	$0.520997\pi$
$200$	0	0
$201$	3956.17	1.38829
$202$	3428.59	1.19423
$203$	−1546.81	−0.534803
$204$	670.919	0.230263
$205$	0	0
$206$	−3318.49	−1.12238
$207$	−486.046	−0.163201
$208$	497.621	0.165884
$209$	2238.56	0.740881
$210$	0	0
$211$	−3696.35	−1.20601	−0.603003	−	0.797739i	$-0.706029\pi$
$211$	−3696.35	−1.20601	−0.603003	+	0.797739i	$0.706029\pi$
$212$	353.242	0.114438
$213$	1473.18	0.473899
$214$	1172.63	0.374575
$215$	0	0
$216$	−325.661	−0.102585
$217$	74.7630	0.0233882
$218$	−1358.18	−0.421963
$219$	6537.96	2.01732
$220$	0	0
$221$	751.916	0.228866
$222$	−1754.55	−0.530441
$223$	−3757.60	−1.12837	−0.564187	−	0.825647i	$-0.690810\pi$
$223$	−3757.60	−1.12837	−0.564187	+	0.825647i	$0.690810\pi$
$224$	−253.405	−0.0755864
$225$	0	0
$226$	2061.35	0.606722
$227$	−1181.85	−0.345559	−0.172779	−	0.984961i	$-0.555275\pi$
$227$	−1181.85	−0.345559	−0.172779	+	0.984961i	$0.555275\pi$
$228$	2383.51	0.692331
$229$	1884.22	0.543725	0.271863	−	0.962336i	$-0.412360\pi$
$229$	1884.22	0.543725	0.271863	+	0.962336i	$0.412360\pi$
$230$	0	0
$231$	−1431.91	−0.407847
$232$	1562.65	0.442212
$233$	−3172.45	−0.891992	−0.445996	−	0.895035i	$-0.647150\pi$
$233$	−3172.45	−0.891992	−0.445996	+	0.895035i	$0.647150\pi$
$234$	1314.49	0.367227
$235$	0	0
$236$	−1589.37	−0.438388
$237$	4674.10	1.28108
$238$	−382.901	−0.104285
$239$	3542.75	0.958833	0.479417	−	0.877587i	$-0.340848\pi$
$239$	3542.75	0.958833	0.479417	+	0.877587i	$0.340848\pi$
$240$	0	0
$241$	3241.84	0.866494	0.433247	−	0.901275i	$-0.357368\pi$
$241$	3241.84	0.866494	0.433247	+	0.901275i	$0.357368\pi$
$242$	−1303.40	−0.346222
$243$	−4818.77	−1.27212
$244$	1658.17	0.435055
$245$	0	0
$246$	−1424.27	−0.369138
$247$	2671.26	0.688130
$248$	−75.5285	−0.0193390
$249$	1350.28	0.343656
$250$	0	0
$251$	−1387.91	−0.349021	−0.174511	−	0.984655i	$-0.555834\pi$
$251$	−1387.91	−0.349021	−0.174511	+	0.984655i	$0.555834\pi$
$252$	−669.384	−0.167330
$253$	−599.458	−0.148963
$254$	483.409	0.119417
$255$	0	0
$256$	256.000	0.0625000
$257$	−7582.04	−1.84029	−0.920146	−	0.391577i	$-0.871930\pi$
$257$	−7582.04	−1.84029	−0.920146	+	0.391577i	$0.871930\pi$
$258$	1566.31	0.377962
$259$	1001.34	0.240233
$260$	0	0
$261$	4127.83	0.978951
$262$	3044.61	0.717927
$263$	6956.05	1.63091	0.815453	−	0.578824i	$-0.196488\pi$
$263$	6956.05	1.63091	0.815453	+	0.578824i	$0.196488\pi$
$264$	1446.57	0.337236
$265$	0	0
$266$	−1360.29	−0.313553
$267$	−1895.86	−0.434549
$268$	2280.95	0.519892
$269$	−43.9099	−0.00995254	−0.00497627	−	0.999988i	$-0.501584\pi$
$269$	−43.9099	−0.00995254	−0.00497627	+	0.999988i	$0.501584\pi$
$270$	0	0
$271$	−1084.19	−0.243025	−0.121513	−	0.992590i	$-0.538775\pi$
$271$	−1084.19	−0.243025	−0.121513	+	0.992590i	$0.538775\pi$
$272$	386.822	0.0862299
$273$	−1708.69	−0.378808
$274$	−5633.31	−1.24205
$275$	0	0
$276$	−638.274	−0.139201
$277$	−4591.13	−0.995864	−0.497932	−	0.867216i	$-0.665907\pi$
$277$	−4591.13	−0.995864	−0.497932	+	0.867216i	$0.665907\pi$
$278$	−2262.70	−0.488158
$279$	−199.513	−0.0428119
$280$	0	0
$281$	9070.95	1.92572	0.962860	−	0.270001i	$-0.0870241\pi$
$281$	9070.95	1.92572	0.962860	+	0.270001i	$0.0870241\pi$
$282$	2259.57	0.477147
$283$	−7419.01	−1.55835	−0.779177	−	0.626803i	$-0.784363\pi$
$283$	−7419.01	−1.55835	−0.779177	+	0.626803i	$0.784363\pi$
$284$	849.368	0.177467
$285$	0	0
$286$	1621.21	0.335189
$287$	812.847	0.167181
$288$	676.238	0.138360
$289$	−4328.50	−0.881031
$290$	0	0
$291$	854.762	0.172189
$292$	3769.49	0.755455
$293$	−6597.77	−1.31552	−0.657758	−	0.753230i	$-0.728495\pi$
$293$	−6597.77	−1.31552	−0.657758	+	0.753230i	$0.728495\pi$
$294$	−3889.18	−0.771502
$295$	0	0
$296$	−1011.60	−0.198641
$297$	−1060.98	−0.207287
$298$	−3343.71	−0.649986
$299$	−715.330	−0.138356
$300$	0	0
$301$	−893.912	−0.171177
$302$	2176.12	0.414640
$303$	11893.4	2.25497
$304$	1374.22	0.259267
$305$	0	0
$306$	1021.81	0.190892
$307$	8826.83	1.64096	0.820479	−	0.571677i	$-0.193707\pi$
$307$	8826.83	1.64096	0.820479	+	0.571677i	$0.193707\pi$
$308$	−825.574	−0.152732
$309$	−11511.4	−2.11930
$310$	0	0
$311$	−8623.45	−1.57232	−0.786159	−	0.618024i	$-0.787933\pi$
$311$	−8623.45	−1.57232	−0.786159	+	0.618024i	$0.787933\pi$
$312$	1726.19	0.313224
$313$	−2287.24	−0.413044	−0.206522	−	0.978442i	$-0.566214\pi$
$313$	−2287.24	−0.413044	−0.206522	+	0.978442i	$0.566214\pi$
$314$	−3200.57	−0.575218
$315$	0	0
$316$	2694.88	0.479743
$317$	9394.91	1.66458	0.832288	−	0.554343i	$-0.187030\pi$
$317$	9394.91	1.66458	0.832288	+	0.554343i	$0.187030\pi$
$318$	1225.35	0.216083
$319$	5091.00	0.893545
$320$	0	0
$321$	4067.70	0.707280
$322$	364.270	0.0630434
$323$	2076.48	0.357705
$324$	−3411.98	−0.585045
$325$	0	0
$326$	−1060.39	−0.180152
$327$	−4711.37	−0.796757
$328$	−821.170	−0.138236
$329$	−1289.56	−0.216097
$330$	0	0
$331$	−5163.63	−0.857458	−0.428729	−	0.903433i	$-0.641038\pi$
$331$	−5163.63	−0.857458	−0.428729	+	0.903433i	$0.641038\pi$
$332$	778.510	0.128694
$333$	−2672.19	−0.439745
$334$	−8019.98	−1.31387
$335$	0	0
$336$	−879.032	−0.142724
$337$	2671.64	0.431850	0.215925	−	0.976410i	$-0.430723\pi$
$337$	2671.64	0.431850	0.215925	+	0.976410i	$0.430723\pi$
$338$	−2459.42	−0.395783
$339$	7150.59	1.14562
$340$	0	0
$341$	−246.066	−0.0390769
$342$	3630.09	0.573955
$343$	4935.79	0.776990
$344$	903.065	0.141541
$345$	0	0
$346$	−1666.22	−0.258891
$347$	−1894.60	−0.293105	−0.146553	−	0.989203i	$-0.546818\pi$
$347$	−1894.60	−0.293105	−0.146553	+	0.989203i	$0.546818\pi$
$348$	5420.65	0.834992
$349$	7079.29	1.08580	0.542902	−	0.839796i	$-0.317325\pi$
$349$	7079.29	1.08580	0.542902	+	0.839796i	$0.317325\pi$
$350$	0	0
$351$	−1266.06	−0.192528
$352$	834.028	0.126289
$353$	−8321.95	−1.25477	−0.627383	−	0.778711i	$-0.715874\pi$
$353$	−8321.95	−1.25477	−0.627383	+	0.778711i	$0.715874\pi$
$354$	−5513.35	−0.827771
$355$	0	0
$356$	−1093.07	−0.162732
$357$	−1328.24	−0.196913
$358$	−6075.41	−0.896914
$359$	11795.5	1.73410	0.867052	−	0.498218i	$-0.166012\pi$
$359$	11795.5	1.73410	0.867052	+	0.498218i	$0.166012\pi$
$360$	0	0
$361$	517.909	0.0755079
$362$	7156.30	1.03902
$363$	−4521.34	−0.653743
$364$	−985.154	−0.141857
$365$	0	0
$366$	5751.98	0.821478
$367$	3058.56	0.435029	0.217515	−	0.976057i	$-0.430205\pi$
$367$	3058.56	0.435029	0.217515	+	0.976057i	$0.430205\pi$
$368$	−368.000	−0.0521286
$369$	−2169.17	−0.306022
$370$	0	0
$371$	−699.324	−0.0978627
$372$	−261.999	−0.0365162
$373$	1391.63	0.193180	0.0965898	−	0.995324i	$-0.469207\pi$
$373$	1391.63	0.193180	0.0965898	+	0.995324i	$0.469207\pi$
$374$	1260.24	0.174239
$375$	0	0
$376$	1302.77	0.178684
$377$	6075.06	0.829924
$378$	644.720	0.0877271
$379$	−12851.0	−1.74172	−0.870861	−	0.491529i	$-0.836438\pi$
$379$	−12851.0	−1.74172	−0.870861	+	0.491529i	$0.836438\pi$
$380$	0	0
$381$	1676.89	0.225484
$382$	555.671	0.0744257
$383$	−3190.96	−0.425719	−0.212860	−	0.977083i	$-0.568278\pi$
$383$	−3190.96	−0.425719	−0.212860	+	0.977083i	$0.568278\pi$
$384$	888.033	0.118014
$385$	0	0
$386$	−504.026	−0.0664617
$387$	2385.50	0.313338
$388$	492.818	0.0644820
$389$	3213.28	0.418817	0.209409	−	0.977828i	$-0.432846\pi$
$389$	3213.28	0.418817	0.209409	+	0.977828i	$0.432846\pi$
$390$	0	0
$391$	−556.056	−0.0719207
$392$	−2242.33	−0.288915
$393$	10561.4	1.35560
$394$	−10806.3	−1.38176
$395$	0	0
$396$	2203.13	0.279575
$397$	9509.10	1.20214	0.601068	−	0.799198i	$-0.294742\pi$
$397$	9509.10	1.20214	0.601068	+	0.799198i	$0.294742\pi$
$398$	−740.162	−0.0932185
$399$	−4718.69	−0.592056
$400$	0	0
$401$	4895.24	0.609618	0.304809	−	0.952414i	$-0.401407\pi$
$401$	4895.24	0.609618	0.304809	+	0.952414i	$0.401407\pi$
$402$	7912.33	0.981670
$403$	−293.629	−0.0362946
$404$	6857.19	0.844450
$405$	0	0
$406$	−3093.62	−0.378163
$407$	−3295.70	−0.401381
$408$	1341.84	0.162821
$409$	12163.6	1.47055	0.735273	−	0.677771i	$-0.237054\pi$
$409$	12163.6	1.47055	0.735273	+	0.677771i	$0.237054\pi$
$410$	0	0
$411$	−19541.3	−2.34526
$412$	−6636.97	−0.793641
$413$	3146.53	0.374893
$414$	−972.093	−0.115400
$415$	0	0
$416$	995.242	0.117297
$417$	−7849.05	−0.921749
$418$	4477.11	0.523882
$419$	−4863.74	−0.567087	−0.283543	−	0.958959i	$-0.591510\pi$
$419$	−4863.74	−0.567087	−0.283543	+	0.958959i	$0.591510\pi$
$420$	0	0
$421$	11133.7	1.28889	0.644444	−	0.764652i	$-0.277089\pi$
$421$	11133.7	1.28889	0.644444	+	0.764652i	$0.277089\pi$
$422$	−7392.70	−0.852775
$423$	3441.33	0.395563
$424$	706.484	0.0809196
$425$	0	0
$426$	2946.35	0.335097
$427$	−3282.72	−0.372042
$428$	2345.25	0.264865
$429$	5623.78	0.632910
$430$	0	0
$431$	−6878.61	−0.768749	−0.384374	−	0.923177i	$-0.625583\pi$
$431$	−6878.61	−0.768749	−0.384374	+	0.923177i	$0.625583\pi$
$432$	−651.322	−0.0725387
$433$	−653.858	−0.0725691	−0.0362846	−	0.999341i	$-0.511552\pi$
$433$	−653.858	−0.0725691	−0.0362846	+	0.999341i	$0.511552\pi$
$434$	149.526	0.0165380
$435$	0	0
$436$	−2716.37	−0.298373
$437$	−1975.45	−0.216243
$438$	13075.9	1.42646
$439$	−5747.82	−0.624894	−0.312447	−	0.949935i	$-0.601149\pi$
$439$	−5747.82	−0.624894	−0.312447	+	0.949935i	$0.601149\pi$
$440$	0	0
$441$	−5923.23	−0.639589
$442$	1503.83	0.161833
$443$	−7623.07	−0.817568	−0.408784	−	0.912631i	$-0.634047\pi$
$443$	−7623.07	−0.817568	−0.408784	+	0.912631i	$0.634047\pi$
$444$	−3509.11	−0.375078
$445$	0	0
$446$	−7515.20	−0.797881
$447$	−11598.9	−1.22731
$448$	−506.810	−0.0534476
$449$	−2230.35	−0.234425	−0.117212	−	0.993107i	$-0.537396\pi$
$449$	−2230.35	−0.234425	−0.117212	+	0.993107i	$0.537396\pi$
$450$	0	0
$451$	−2675.31	−0.279324
$452$	4122.71	0.429017
$453$	7548.68	0.782931
$454$	−2363.69	−0.244347
$455$	0	0
$456$	4767.01	0.489552
$457$	−7898.29	−0.808460	−0.404230	−	0.914657i	$-0.632461\pi$
$457$	−7898.29	−0.808460	−0.404230	+	0.914657i	$0.632461\pi$
$458$	3768.45	0.384472
$459$	−984.162	−0.100080
$460$	0	0
$461$	802.317	0.0810578	0.0405289	−	0.999178i	$-0.487096\pi$
$461$	802.317	0.0810578	0.0405289	+	0.999178i	$0.487096\pi$
$462$	−2863.82	−0.288391
$463$	−13041.6	−1.30906	−0.654530	−	0.756036i	$-0.727134\pi$
$463$	−13041.6	−1.30906	−0.654530	+	0.756036i	$0.727134\pi$
$464$	3125.30	0.312691
$465$	0	0
$466$	−6344.90	−0.630733
$467$	−10282.8	−1.01891	−0.509454	−	0.860498i	$-0.670153\pi$
$467$	−10282.8	−1.01891	−0.509454	+	0.860498i	$0.670153\pi$
$468$	2628.99	0.259669
$469$	−4515.66	−0.444592
$470$	0	0
$471$	−11102.4	−1.08614
$472$	−3178.75	−0.309987
$473$	2942.12	0.286001
$474$	9348.20	0.905859
$475$	0	0
$476$	−765.802	−0.0737405
$477$	1866.22	0.179137
$478$	7085.49	0.677997
$479$	9397.63	0.896427	0.448214	−	0.893927i	$-0.352060\pi$
$479$	9397.63	0.896427	0.448214	+	0.893927i	$0.352060\pi$
$480$	0	0
$481$	−3932.75	−0.372802
$482$	6483.67	0.612704
$483$	1263.61	0.119040
$484$	−2606.80	−0.244816
$485$	0	0
$486$	−9637.54	−0.899522
$487$	1301.80	0.121130	0.0605650	−	0.998164i	$-0.480710\pi$
$487$	1301.80	0.121130	0.0605650	+	0.998164i	$0.480710\pi$
$488$	3316.34	0.307630
$489$	−3678.36	−0.340166
$490$	0	0
$491$	9405.16	0.864458	0.432229	−	0.901764i	$-0.357727\pi$
$491$	9405.16	0.864458	0.432229	+	0.901764i	$0.357727\pi$
$492$	−2848.54	−0.261020
$493$	4722.40	0.431413
$494$	5342.51	0.486581
$495$	0	0
$496$	−151.057	−0.0136747
$497$	−1681.52	−0.151763
$498$	2700.56	0.243002
$499$	−11196.8	−1.00449	−0.502243	−	0.864727i	$-0.667492\pi$
$499$	−11196.8	−1.00449	−0.502243	+	0.864727i	$0.667492\pi$
$500$	0	0
$501$	−27820.3	−2.48088
$502$	−2775.83	−0.246795
$503$	−5258.38	−0.466122	−0.233061	−	0.972462i	$-0.574874\pi$
$503$	−5258.38	−0.466122	−0.233061	+	0.972462i	$0.574874\pi$
$504$	−1338.77	−0.118320
$505$	0	0
$506$	−1198.92	−0.105333
$507$	−8531.42	−0.747325
$508$	966.819	0.0844402
$509$	10444.2	0.909494	0.454747	−	0.890621i	$-0.349730\pi$
$509$	10444.2	0.909494	0.454747	+	0.890621i	$0.349730\pi$
$510$	0	0
$511$	−7462.57	−0.646037
$512$	512.000	0.0441942
$513$	−3496.33	−0.300910
$514$	−15164.1	−1.30128
$515$	0	0
$516$	3132.62	0.267260
$517$	4244.31	0.361054
$518$	2002.69	0.169871
$519$	−5779.90	−0.488843
$520$	0	0
$521$	3545.70	0.298157	0.149079	−	0.988825i	$-0.452369\pi$
$521$	3545.70	0.298157	0.149079	+	0.988825i	$0.452369\pi$
$522$	8255.66	0.692223
$523$	−6584.42	−0.550510	−0.275255	−	0.961371i	$-0.588762\pi$
$523$	−6584.42	−0.550510	−0.275255	+	0.961371i	$0.588762\pi$
$524$	6089.23	0.507651
$525$	0	0
$526$	13912.1	1.15322
$527$	−228.251	−0.0188667
$528$	2893.14	0.238462
$529$	529.000	0.0434783
$530$	0	0
$531$	−8396.85	−0.686237
$532$	−2720.59	−0.221715
$533$	−3192.43	−0.259436
$534$	−3791.72	−0.307273
$535$	0	0
$536$	4561.90	0.367619
$537$	−21074.8	−1.69357
$538$	−87.8198	−0.00703751
$539$	−7305.32	−0.583790
$540$	0	0
$541$	−19460.6	−1.54654	−0.773270	−	0.634077i	$-0.781380\pi$
$541$	−19460.6	−1.54654	−0.773270	+	0.634077i	$0.781380\pi$
$542$	−2168.38	−0.171845
$543$	24824.3	1.96190
$544$	773.644	0.0609737
$545$	0	0
$546$	−3417.38	−0.267858
$547$	11958.1	0.934715	0.467358	−	0.884068i	$-0.345206\pi$
$547$	11958.1	0.934715	0.467358	+	0.884068i	$0.345206\pi$
$548$	−11266.6	−0.878260
$549$	8760.29	0.681020
$550$	0	0
$551$	16776.8	1.29713
$552$	−1276.55	−0.0984302
$553$	−5335.13	−0.410258
$554$	−9182.26	−0.704182
$555$	0	0
$556$	−4525.41	−0.345180
$557$	−21613.7	−1.64417	−0.822084	−	0.569366i	$-0.807189\pi$
$557$	−21613.7	−1.64417	−0.822084	+	0.569366i	$0.807189\pi$
$558$	−399.026	−0.0302726
$559$	3510.81	0.265638
$560$	0	0
$561$	4371.60	0.329000
$562$	18141.9	1.36169
$563$	21645.8	1.62036	0.810178	−	0.586183i	$-0.199370\pi$
$563$	21645.8	1.62036	0.810178	+	0.586183i	$0.199370\pi$
$564$	4519.14	0.337394
$565$	0	0
$566$	−14838.0	−1.10192
$567$	6754.80	0.500308
$568$	1698.74	0.125488
$569$	6365.08	0.468960	0.234480	−	0.972121i	$-0.424661\pi$
$569$	6365.08	0.468960	0.234480	+	0.972121i	$0.424661\pi$
$570$	0	0
$571$	−7995.66	−0.586004	−0.293002	−	0.956112i	$-0.594654\pi$
$571$	−7995.66	−0.586004	−0.293002	+	0.956112i	$0.594654\pi$
$572$	3242.42	0.237015
$573$	1927.56	0.140532
$574$	1625.69	0.118214
$575$	0	0
$576$	1352.48	0.0978354
$577$	2134.90	0.154033	0.0770166	−	0.997030i	$-0.475461\pi$
$577$	2134.90	0.154033	0.0770166	+	0.997030i	$0.475461\pi$
$578$	−8657.01	−0.622983
$579$	−1748.40	−0.125494
$580$	0	0
$581$	−1541.24	−0.110054
$582$	1709.52	0.121756
$583$	2301.67	0.163509
$584$	7538.99	0.534187
$585$	0	0
$586$	−13195.5	−0.930210
$587$	−1249.40	−0.0878506	−0.0439253	−	0.999035i	$-0.513986\pi$
$587$	−1249.40	−0.0878506	−0.0439253	+	0.999035i	$0.513986\pi$
$588$	−7778.36	−0.545534
$589$	−810.883	−0.0567264
$590$	0	0
$591$	−37485.7	−2.60906
$592$	−2023.19	−0.140461
$593$	1353.24	0.0937114	0.0468557	−	0.998902i	$-0.485080\pi$
$593$	1353.24	0.0937114	0.0468557	+	0.998902i	$0.485080\pi$
$594$	−2121.96	−0.146574
$595$	0	0
$596$	−6687.41	−0.459609
$597$	−2567.53	−0.176017
$598$	−1430.66	−0.0978328
$599$	−14112.2	−0.962621	−0.481311	−	0.876550i	$-0.659839\pi$
$599$	−14112.2	−0.962621	−0.481311	+	0.876550i	$0.659839\pi$
$600$	0	0
$601$	−1755.49	−0.119148	−0.0595740	−	0.998224i	$-0.518974\pi$
$601$	−1755.49	−0.119148	−0.0595740	+	0.998224i	$0.518974\pi$
$602$	−1787.82	−0.121040
$603$	12050.5	0.813822
$604$	4352.23	0.293195
$605$	0	0
$606$	23786.7	1.59451
$607$	−3511.11	−0.234780	−0.117390	−	0.993086i	$-0.537453\pi$
$607$	−3511.11	−0.234780	−0.117390	+	0.993086i	$0.537453\pi$
$608$	2748.45	0.183329
$609$	−10731.4	−0.714053
$610$	0	0
$611$	5064.72	0.335346
$612$	2043.62	0.134981
$613$	22164.0	1.46035	0.730177	−	0.683258i	$-0.239437\pi$
$613$	22164.0	1.46035	0.730177	+	0.683258i	$0.239437\pi$
$614$	17653.7	1.16033
$615$	0	0
$616$	−1651.15	−0.107998
$617$	−19395.7	−1.26555	−0.632773	−	0.774337i	$-0.718084\pi$
$617$	−19395.7	−1.26555	−0.632773	+	0.774337i	$0.718084\pi$
$618$	−23022.9	−1.49857
$619$	−26735.5	−1.73601	−0.868006	−	0.496553i	$-0.834599\pi$
$619$	−26735.5	−1.73601	−0.868006	+	0.496553i	$0.834599\pi$
$620$	0	0
$621$	936.275	0.0605015
$622$	−17246.9	−1.11180
$623$	2163.98	0.139162
$624$	3452.37	0.221483
$625$	0	0
$626$	−4574.49	−0.292066
$627$	15530.5	0.989203
$628$	−6401.13	−0.406740
$629$	−3057.09	−0.193791
$630$	0	0
$631$	27135.2	1.71194	0.855971	−	0.517024i	$-0.172960\pi$
$631$	27135.2	1.71194	0.855971	+	0.517024i	$0.172960\pi$
$632$	5389.75	0.339229
$633$	−25644.4	−1.61023
$634$	18789.8	1.17703
$635$	0	0
$636$	2450.71	0.152794
$637$	−8717.41	−0.542223
$638$	10182.0	0.631832
$639$	4487.31	0.277802
$640$	0	0
$641$	23224.1	1.43104	0.715519	−	0.698593i	$-0.246190\pi$
$641$	23224.1	1.43104	0.715519	+	0.698593i	$0.246190\pi$
$642$	8135.40	0.500122
$643$	−20562.7	−1.26114	−0.630571	−	0.776132i	$-0.717179\pi$
$643$	−20562.7	−1.26114	−0.630571	+	0.776132i	$0.717179\pi$
$644$	728.540	0.0445784
$645$	0	0
$646$	4152.97	0.252935
$647$	10859.9	0.659886	0.329943	−	0.944001i	$-0.392970\pi$
$647$	10859.9	0.659886	0.329943	+	0.944001i	$0.392970\pi$
$648$	−6823.97	−0.413689
$649$	−10356.1	−0.626369
$650$	0	0
$651$	518.687	0.0312273
$652$	−2120.78	−0.127387
$653$	−14197.6	−0.850833	−0.425417	−	0.904998i	$-0.639872\pi$
$653$	−14197.6	−0.850833	−0.425417	+	0.904998i	$0.639872\pi$
$654$	−9422.75	−0.563392
$655$	0	0
$656$	−1642.34	−0.0977478
$657$	19914.7	1.18256
$658$	−2579.13	−0.152804
$659$	−13523.1	−0.799372	−0.399686	−	0.916652i	$-0.630881\pi$
$659$	−13523.1	−0.799372	−0.399686	+	0.916652i	$0.630881\pi$
$660$	0	0
$661$	−21824.4	−1.28422	−0.642110	−	0.766612i	$-0.721941\pi$
$661$	−21824.4	−1.28422	−0.642110	+	0.766612i	$0.721941\pi$
$662$	−10327.3	−0.606314
$663$	5216.61	0.305575
$664$	1557.02	0.0910001
$665$	0	0
$666$	−5344.38	−0.310947
$667$	−4492.62	−0.260802
$668$	−16040.0	−0.929049
$669$	−26069.3	−1.50657
$670$	0	0
$671$	10804.4	0.621607
$672$	−1758.06	−0.100921
$673$	−22835.5	−1.30794	−0.653970	−	0.756520i	$-0.726898\pi$
$673$	−22835.5	−1.30794	−0.653970	+	0.756520i	$0.726898\pi$
$674$	5343.28	0.305364
$675$	0	0
$676$	−4918.84	−0.279861
$677$	2429.32	0.137912	0.0689560	−	0.997620i	$-0.478033\pi$
$677$	2429.32	0.137912	0.0689560	+	0.997620i	$0.478033\pi$
$678$	14301.2	0.810078
$679$	−975.645	−0.0551426
$680$	0	0
$681$	−8199.36	−0.461381
$682$	−492.132	−0.0276315
$683$	−25006.5	−1.40095	−0.700473	−	0.713679i	$-0.747028\pi$
$683$	−25006.5	−1.40095	−0.700473	+	0.713679i	$0.747028\pi$
$684$	7260.17	0.405848
$685$	0	0
$686$	9871.57	0.549415
$687$	13072.3	0.725966
$688$	1806.13	0.100084
$689$	2746.57	0.151867
$690$	0	0
$691$	5801.05	0.319367	0.159683	−	0.987168i	$-0.448953\pi$
$691$	5801.05	0.319367	0.159683	+	0.987168i	$0.448953\pi$
$692$	−3332.43	−0.183064
$693$	−4361.60	−0.239082
$694$	−3789.20	−0.207257
$695$	0	0
$696$	10841.3	0.590428
$697$	−2481.61	−0.134861
$698$	14158.6	0.767780
$699$	−22009.7	−1.19096
$700$	0	0
$701$	13399.4	0.721953	0.360976	−	0.932575i	$-0.382444\pi$
$701$	13399.4	0.721953	0.360976	+	0.932575i	$0.382444\pi$
$702$	−2532.12	−0.136138
$703$	−10860.6	−0.582669
$704$	1668.06	0.0893000
$705$	0	0
$706$	−16643.9	−0.887254
$707$	−13575.4	−0.722142
$708$	−11026.7	−0.585323
$709$	19519.4	1.03394	0.516972	−	0.856002i	$-0.327059\pi$
$709$	19519.4	1.03394	0.516972	+	0.856002i	$0.327059\pi$
$710$	0	0
$711$	14237.3	0.750973
$712$	−2186.13	−0.115069
$713$	217.144	0.0114055
$714$	−2656.47	−0.139238
$715$	0	0
$716$	−12150.8	−0.634214
$717$	24578.7	1.28021
$718$	23591.0	1.22620
$719$	5506.10	0.285595	0.142798	−	0.989752i	$-0.454390\pi$
$719$	5506.10	0.285595	0.142798	+	0.989752i	$0.454390\pi$
$720$	0	0
$721$	13139.4	0.678692
$722$	1035.82	0.0533921
$723$	22491.1	1.15692
$724$	14312.6	0.734701
$725$	0	0
$726$	−9042.68	−0.462266
$727$	15276.5	0.779334	0.389667	−	0.920956i	$-0.372590\pi$
$727$	15276.5	0.779334	0.389667	+	0.920956i	$0.372590\pi$
$728$	−1970.31	−0.100308
$729$	−10400.6	−0.528403
$730$	0	0
$731$	2729.10	0.138084
$732$	11504.0	0.580873
$733$	−14668.7	−0.739155	−0.369578	−	0.929200i	$-0.620498\pi$
$733$	−14668.7	−0.739155	−0.369578	+	0.929200i	$0.620498\pi$
$734$	6117.13	0.307612
$735$	0	0
$736$	−736.000	−0.0368605
$737$	14862.3	0.742822
$738$	−4338.33	−0.216391
$739$	15650.4	0.779040	0.389520	−	0.921018i	$-0.372641\pi$
$739$	15650.4	0.779040	0.389520	+	0.921018i	$0.372641\pi$
$740$	0	0
$741$	18532.5	0.918771
$742$	−1398.65	−0.0691994
$743$	27285.2	1.34724	0.673618	−	0.739079i	$-0.264739\pi$
$743$	27285.2	1.34724	0.673618	+	0.739079i	$0.264739\pi$
$744$	−523.998	−0.0258208
$745$	0	0
$746$	2783.26	0.136599
$747$	4112.96	0.201453
$748$	2520.47	0.123205
$749$	−4642.97	−0.226502
$750$	0	0
$751$	30412.1	1.47770	0.738852	−	0.673868i	$-0.235368\pi$
$751$	30412.1	1.47770	0.738852	+	0.673868i	$0.235368\pi$
$752$	2605.53	0.126348
$753$	−9629.01	−0.466004
$754$	12150.1	0.586845
$755$	0	0
$756$	1289.44	0.0620324
$757$	−4567.26	−0.219286	−0.109643	−	0.993971i	$-0.534971\pi$
$757$	−4567.26	−0.219286	−0.109643	+	0.993971i	$0.534971\pi$
$758$	−25702.0	−1.23158
$759$	−4158.89	−0.198891
$760$	0	0
$761$	−5690.93	−0.271085	−0.135543	−	0.990772i	$-0.543278\pi$
$761$	−5690.93	−0.271085	−0.135543	+	0.990772i	$0.543278\pi$
$762$	3353.78	0.159442
$763$	5377.67	0.255157
$764$	1111.34	0.0526269
$765$	0	0
$766$	−6381.92	−0.301029
$767$	−12357.9	−0.581771
$768$	1776.07	0.0834482
$769$	3068.42	0.143888	0.0719441	−	0.997409i	$-0.477080\pi$
$769$	3068.42	0.143888	0.0719441	+	0.997409i	$0.477080\pi$
$770$	0	0
$771$	−52602.4	−2.45710
$772$	−1008.05	−0.0469955
$773$	−6371.71	−0.296474	−0.148237	−	0.988952i	$-0.547360\pi$
$773$	−6371.71	−0.296474	−0.148237	+	0.988952i	$0.547360\pi$
$774$	4770.99	0.221563
$775$	0	0
$776$	985.635	0.0455957
$777$	6947.08	0.320753
$778$	6426.57	0.296149
$779$	−8816.17	−0.405484
$780$	0	0
$781$	5534.35	0.253565
$782$	−1112.11	−0.0508556
$783$	−7951.48	−0.362915
$784$	−4484.65	−0.204294
$785$	0	0
$786$	21122.8	0.958556
$787$	15087.2	0.683355	0.341677	−	0.939817i	$-0.389005\pi$
$787$	15087.2	0.683355	0.341677	+	0.939817i	$0.389005\pi$
$788$	−21612.6	−0.977051
$789$	48259.3	2.17754
$790$	0	0
$791$	−8161.84	−0.366880
$792$	4406.26	0.197689
$793$	12892.8	0.577348
$794$	19018.2	0.850039
$795$	0	0
$796$	−1480.32	−0.0659155
$797$	10434.5	0.463749	0.231874	−	0.972746i	$-0.425514\pi$
$797$	10434.5	0.463749	0.231874	+	0.972746i	$0.425514\pi$
$798$	−9437.39	−0.418646
$799$	3937.02	0.174320
$800$	0	0
$801$	−5774.80	−0.254735
$802$	9790.48	0.431065
$803$	24561.4	1.07939
$804$	15824.7	0.694145
$805$	0	0
$806$	−587.259	−0.0256641
$807$	−304.636	−0.0132884
$808$	13714.4	0.597116
$809$	26505.2	1.15188	0.575941	−	0.817491i	$-0.304636\pi$
$809$	26505.2	1.15188	0.575941	+	0.817491i	$0.304636\pi$
$810$	0	0
$811$	21013.2	0.909832	0.454916	−	0.890534i	$-0.349669\pi$
$811$	21013.2	0.909832	0.454916	+	0.890534i	$0.349669\pi$
$812$	−6187.25	−0.267401
$813$	−7521.85	−0.324481
$814$	−6591.41	−0.283819
$815$	0	0
$816$	2683.68	0.115132
$817$	9695.41	0.415177
$818$	24327.3	1.03983
$819$	−5204.68	−0.222059
$820$	0	0
$821$	−32097.0	−1.36443	−0.682213	−	0.731154i	$-0.738982\pi$
$821$	−32097.0	−1.36443	−0.682213	+	0.731154i	$0.738982\pi$
$822$	−39082.5	−1.65835
$823$	17377.4	0.736014	0.368007	−	0.929823i	$-0.380040\pi$
$823$	17377.4	0.736014	0.368007	+	0.929823i	$0.380040\pi$
$824$	−13273.9	−0.561189
$825$	0	0
$826$	6293.06	0.265089
$827$	19307.9	0.811850	0.405925	−	0.913906i	$-0.366949\pi$
$827$	19307.9	0.811850	0.405925	+	0.913906i	$0.366949\pi$
$828$	−1944.19	−0.0816004
$829$	−22276.9	−0.933305	−0.466652	−	0.884441i	$-0.654540\pi$
$829$	−22276.9	−0.933305	−0.466652	+	0.884441i	$0.654540\pi$
$830$	0	0
$831$	−31852.1	−1.32965
$832$	1990.48	0.0829418
$833$	−6776.41	−0.281859
$834$	−15698.1	−0.651775
$835$	0	0
$836$	8954.22	0.370440
$837$	384.323	0.0158711
$838$	−9727.49	−0.400991
$839$	−5345.55	−0.219963	−0.109981	−	0.993934i	$-0.535079\pi$
$839$	−5345.55	−0.219963	−0.109981	+	0.993934i	$0.535079\pi$
$840$	0	0
$841$	13765.4	0.564408
$842$	22267.3	0.911381
$843$	62932.0	2.57117
$844$	−14785.4	−0.603003
$845$	0	0
$846$	6882.67	0.279706
$847$	5160.76	0.209358
$848$	1412.97	0.0572188
$849$	−51471.3	−2.08067
$850$	0	0
$851$	2908.34	0.117152
$852$	5892.71	0.236949
$853$	−22834.0	−0.916557	−0.458278	−	0.888809i	$-0.651534\pi$
$853$	−22834.0	−0.916557	−0.458278	+	0.888809i	$0.651534\pi$
$854$	−6565.45	−0.263074
$855$	0	0
$856$	4690.51	0.187288
$857$	20655.1	0.823296	0.411648	−	0.911343i	$-0.364953\pi$
$857$	20655.1	0.823296	0.411648	+	0.911343i	$0.364953\pi$
$858$	11247.6	0.447535
$859$	40869.9	1.62336	0.811679	−	0.584104i	$-0.198554\pi$
$859$	40869.9	1.62336	0.811679	+	0.584104i	$0.198554\pi$
$860$	0	0
$861$	5639.33	0.223215
$862$	−13757.2	−0.543588
$863$	−11570.5	−0.456390	−0.228195	−	0.973615i	$-0.573282\pi$
$863$	−11570.5	−0.456390	−0.228195	+	0.973615i	$0.573282\pi$
$864$	−1302.64	−0.0512926
$865$	0	0
$866$	−1307.72	−0.0513141
$867$	−30030.1	−1.17633
$868$	299.052	0.0116941
$869$	17559.4	0.685457
$870$	0	0
$871$	17735.1	0.689933
$872$	−5432.74	−0.210981
$873$	2603.61	0.100938
$874$	−3950.89	−0.152907
$875$	0	0
$876$	26151.8	1.00866
$877$	27923.3	1.07515	0.537573	−	0.843217i	$-0.319341\pi$
$877$	27923.3	1.07515	0.537573	+	0.843217i	$0.319341\pi$
$878$	−11495.6	−0.441867
$879$	−45773.7	−1.75644
$880$	0	0
$881$	25303.0	0.967626	0.483813	−	0.875171i	$-0.339251\pi$
$881$	25303.0	0.967626	0.483813	+	0.875171i	$0.339251\pi$
$882$	−11846.5	−0.452258
$883$	28720.3	1.09458	0.547290	−	0.836943i	$-0.315659\pi$
$883$	28720.3	1.09458	0.547290	+	0.836943i	$0.315659\pi$
$884$	3007.67	0.114433
$885$	0	0
$886$	−15246.1	−0.578108
$887$	4810.15	0.182085	0.0910423	−	0.995847i	$-0.470980\pi$
$887$	4810.15	0.182085	0.0910423	+	0.995847i	$0.470980\pi$
$888$	−7018.21	−0.265220
$889$	−1914.04	−0.0722101
$890$	0	0
$891$	−22231.9	−0.835913
$892$	−15030.4	−0.564187
$893$	13986.7	0.524127
$894$	−23197.8	−0.867842
$895$	0	0
$896$	−1013.62	−0.0377932
$897$	−4962.78	−0.184730
$898$	−4460.70	−0.165763
$899$	−1844.14	−0.0684153
$900$	0	0
$901$	2135.03	0.0789435
$902$	−5350.61	−0.197512
$903$	−6201.74	−0.228550
$904$	8245.42	0.303361
$905$	0	0
$906$	15097.4	0.553616
$907$	−34526.0	−1.26397	−0.631983	−	0.774983i	$-0.717759\pi$
$907$	−34526.0	−1.26397	−0.631983	+	0.774983i	$0.717759\pi$
$908$	−4727.38	−0.172779
$909$	36227.3	1.32187
$910$	0	0
$911$	8466.48	0.307911	0.153956	−	0.988078i	$-0.450799\pi$
$911$	8466.48	0.307911	0.153956	+	0.988078i	$0.450799\pi$
$912$	9534.02	0.346166
$913$	5072.65	0.183878
$914$	−15796.6	−0.571668
$915$	0	0
$916$	7536.90	0.271863
$917$	−12055.0	−0.434124
$918$	−1968.32	−0.0707673
$919$	42002.8	1.50766	0.753832	−	0.657067i	$-0.228203\pi$
$919$	42002.8	1.50766	0.753832	+	0.657067i	$0.228203\pi$
$920$	0	0
$921$	61238.4	2.19096
$922$	1604.63	0.0573165
$923$	6604.11	0.235511
$924$	−5727.63	−0.203924
$925$	0	0
$926$	−26083.2	−0.925646
$927$	−35063.9	−1.24234
$928$	6250.60	0.221106
$929$	−4758.59	−0.168056	−0.0840282	−	0.996463i	$-0.526779\pi$
$929$	−4758.59	−0.168056	−0.0840282	+	0.996463i	$0.526779\pi$
$930$	0	0
$931$	−24073.9	−0.847465
$932$	−12689.8	−0.445996
$933$	−59827.4	−2.09932
$934$	−20565.6	−0.720477
$935$	0	0
$936$	5257.97	0.183613
$937$	−36812.9	−1.28348	−0.641742	−	0.766920i	$-0.721788\pi$
$937$	−36812.9	−1.28348	−0.641742	+	0.766920i	$0.721788\pi$
$938$	−9031.32	−0.314374
$939$	−15868.3	−0.551484
$940$	0	0
$941$	−44659.5	−1.54714	−0.773570	−	0.633711i	$-0.781531\pi$
$941$	−44659.5	−1.54714	−0.773570	+	0.633711i	$0.781531\pi$
$942$	−22204.7	−0.768015
$943$	2360.86	0.0815273
$944$	−6357.50	−0.219194
$945$	0	0
$946$	5884.23	0.202233
$947$	29127.5	0.999491	0.499746	−	0.866172i	$-0.333427\pi$
$947$	29127.5	0.999491	0.499746	+	0.866172i	$0.333427\pi$
$948$	18696.4	0.640539
$949$	29309.0	1.00254
$950$	0	0
$951$	65179.6	2.22250
$952$	−1531.60	−0.0521424
$953$	5740.19	0.195113	0.0975566	−	0.995230i	$-0.468897\pi$
$953$	5740.19	0.195113	0.0975566	+	0.995230i	$0.468897\pi$
$954$	3732.44	0.126669
$955$	0	0
$956$	14171.0	0.479417
$957$	35320.1	1.19304
$958$	18795.3	0.633870
$959$	22304.9	0.751055
$960$	0	0
$961$	−29701.9	−0.997008
$962$	−7865.49	−0.263611
$963$	12390.2	0.414610
$964$	12967.3	0.433247
$965$	0	0
$966$	2527.22	0.0841738
$967$	12438.6	0.413647	0.206824	−	0.978378i	$-0.433687\pi$
$967$	12438.6	0.413647	0.206824	+	0.978378i	$0.433687\pi$
$968$	−5213.60	−0.173111
$969$	14406.1	0.477597
$970$	0	0
$971$	50415.2	1.66622	0.833110	−	0.553107i	$-0.186558\pi$
$971$	50415.2	1.66622	0.833110	+	0.553107i	$0.186558\pi$
$972$	−19275.1	−0.636058
$973$	8959.08	0.295185
$974$	2603.60	0.0856518
$975$	0	0
$976$	6632.68	0.217527
$977$	17531.7	0.574093	0.287046	−	0.957917i	$-0.407327\pi$
$977$	17531.7	0.574093	0.287046	+	0.957917i	$0.407327\pi$
$978$	−7356.72	−0.240534
$979$	−7122.25	−0.232511
$980$	0	0
$981$	−14350.9	−0.467063
$982$	18810.3	0.611264
$983$	−22303.0	−0.723656	−0.361828	−	0.932245i	$-0.617847\pi$
$983$	−22303.0	−0.723656	−0.361828	+	0.932245i	$0.617847\pi$
$984$	−5697.07	−0.184569
$985$	0	0
$986$	9444.81	0.305055
$987$	−8946.67	−0.288526
$988$	10685.0	0.344065
$989$	−2596.31	−0.0834762
$990$	0	0
$991$	−44522.1	−1.42714	−0.713568	−	0.700586i	$-0.752922\pi$
$991$	−44522.1	−1.42714	−0.713568	+	0.700586i	$0.752922\pi$
$992$	−302.114	−0.00966949
$993$	−35824.0	−1.14485
$994$	−3363.04	−0.107313
$995$	0	0
$996$	5401.11	0.171828
$997$	−42042.4	−1.33550	−0.667751	−	0.744385i	$-0.732743\pi$
$997$	−42042.4	−1.33550	−0.667751	+	0.744385i	$0.732743\pi$
$998$	−22393.6	−0.710279
$999$	5147.46	0.163022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.bb.1.7		9
5.2	odd	4		230.4.b.b.139.12	yes	18
5.3	odd	4		230.4.b.b.139.7	✓	18
5.4	even	2		1150.4.a.ba.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.b.139.7	✓	18	5.3	odd	4
230.4.b.b.139.12	yes	18	5.2	odd	4
1150.4.a.ba.1.3		9	5.4	even	2
1150.4.a.bb.1.7		9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +6.93776 q^{3} +4.00000 q^{4} +13.8755 q^{6} -7.91891 q^{7} +8.00000 q^{8} +21.1325 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +6.93776 q^{3} +4.00000 q^{4} +13.8755 q^{6} -7.91891 q^{7} +8.00000 q^{8} +21.1325 q^{9} +26.0634 q^{11} +27.7510 q^{12} +31.1013 q^{13} -15.8378 q^{14} +16.0000 q^{16} +24.1764 q^{17} +42.2649 q^{18} +85.8889 q^{19} -54.9395 q^{21} +52.1267 q^{22} -23.0000 q^{23} +55.5020 q^{24} +62.2026 q^{26} -40.7076 q^{27} -31.6757 q^{28} +195.331 q^{29} -9.44106 q^{31} +32.0000 q^{32} +180.821 q^{33} +48.3527 q^{34} +84.5298 q^{36} -126.450 q^{37} +171.778 q^{38} +215.773 q^{39} -102.646 q^{41} -109.879 q^{42} +112.883 q^{43} +104.253 q^{44} -46.0000 q^{46} +162.846 q^{47} +111.004 q^{48} -280.291 q^{49} +167.730 q^{51} +124.405 q^{52} +88.3105 q^{53} -81.4152 q^{54} -63.3513 q^{56} +595.876 q^{57} +390.663 q^{58} -397.344 q^{59} +414.542 q^{61} -18.8821 q^{62} -167.346 q^{63} +64.0000 q^{64} +361.643 q^{66} +570.237 q^{67} +96.7055 q^{68} -159.568 q^{69} +212.342 q^{71} +169.060 q^{72} +942.373 q^{73} -252.899 q^{74} +343.556 q^{76} -206.394 q^{77} +431.546 q^{78} +673.719 q^{79} -852.996 q^{81} -205.292 q^{82} +194.627 q^{83} -219.758 q^{84} +225.766 q^{86} +1355.16 q^{87} +208.507 q^{88} -273.267 q^{89} -246.288 q^{91} -92.0000 q^{92} -65.4998 q^{93} +325.692 q^{94} +222.008 q^{96} +123.204 q^{97} -560.582 q^{98} +550.783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9}+O(q^{10}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9	\( 9 q + 18 q^{2} + 3 q^{3} + 36 q^{4} + 6 q^{6} + 44 q^{7} + 72 q^{8} + 124 q^{9} + 81 q^{11} + 12 q^{12} + 59 q^{13} + 88 q^{14} + 144 q^{16} + 110 q^{17} + 248 q^{18} + 221 q^{19} + 142 q^{21} + 162 q^{22} - 207 q^{23} + 24 q^{24} + 118 q^{26} + 336 q^{27} + 176 q^{28} + 205 q^{29} + 336 q^{31} + 288 q^{32} + 437 q^{33} + 220 q^{34} + 496 q^{36} - 5 q^{37} + 442 q^{38} - 44 q^{39} + 360 q^{41} + 284 q^{42} + 366 q^{43} + 324 q^{44} - 414 q^{46} - 122 q^{47} + 48 q^{48} + 457 q^{49} + 1025 q^{51} + 236 q^{52} + 631 q^{53} + 672 q^{54} + 352 q^{56} - 384 q^{57} + 410 q^{58} + 797 q^{59} + 211 q^{61} + 672 q^{62} + 2447 q^{63} + 576 q^{64} + 874 q^{66} + 111 q^{67} + 440 q^{68} - 69 q^{69} + 2912 q^{71} + 992 q^{72} + 98 q^{73} - 10 q^{74} + 884 q^{76} + 942 q^{77} - 88 q^{78} + 1184 q^{79} + 2093 q^{81} + 720 q^{82} + 2375 q^{83} + 568 q^{84} + 732 q^{86} - 1534 q^{87} + 648 q^{88} + 2588 q^{89} + 2677 q^{91} - 828 q^{92} + 1402 q^{93} - 244 q^{94} + 96 q^{96} - 593 q^{97} + 914 q^{98} - 1753 q^{99}+O(q^{100}) \) 9 * q + 18 * q^2 + 3 * q^3 + 36 * q^4 + 6 * q^6 + 44 * q^7 + 72 * q^8 + 124 * q^9 + 81 * q^11 + 12 * q^12 + 59 * q^13 + 88 * q^14 + 144 * q^16 + 110 * q^17 + 248 * q^18 + 221 * q^19 + 142 * q^21 + 162 * q^22 - 207 * q^23 + 24 * q^24 + 118 * q^26 + 336 * q^27 + 176 * q^28 + 205 * q^29 + 336 * q^31 + 288 * q^32 + 437 * q^33 + 220 * q^34 + 496 * q^36 - 5 * q^37 + 442 * q^38 - 44 * q^39 + 360 * q^41 + 284 * q^42 + 366 * q^43 + 324 * q^44 - 414 * q^46 - 122 * q^47 + 48 * q^48 + 457 * q^49 + 1025 * q^51 + 236 * q^52 + 631 * q^53 + 672 * q^54 + 352 * q^56 - 384 * q^57 + 410 * q^58 + 797 * q^59 + 211 * q^61 + 672 * q^62 + 2447 * q^63 + 576 * q^64 + 874 * q^66 + 111 * q^67 + 440 * q^68 - 69 * q^69 + 2912 * q^71 + 992 * q^72 + 98 * q^73 - 10 * q^74 + 884 * q^76 + 942 * q^77 - 88 * q^78 + 1184 * q^79 + 2093 * q^81 + 720 * q^82 + 2375 * q^83 + 568 * q^84 + 732 * q^86 - 1534 * q^87 + 648 * q^88 + 2588 * q^89 + 2677 * q^91 - 828 * q^92 + 1402 * q^93 - 244 * q^94 + 96 * q^96 - 593 * q^97 + 914 * q^98 - 1753 * q^99

Introduction

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