LMFDB - Embedded newform 1075.4.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,4,Mod(1,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, 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("1075.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1075.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:	$63.4270532562$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 $ x^6 - 32x^4 - 16x^3 + 251x^2 + 276x + 60
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$4.31455$ of defining polynomial
Character	$\chi$	$=$	1075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} +O(q^{10})$	\(q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} +0.597776 q^{11} +21.2147 q^{12} -34.9021 q^{13} -32.6318 q^{14} -78.9723 q^{16} -91.3552 q^{17} +77.7863 q^{18} -24.0324 q^{19} -69.9399 q^{21} +1.98136 q^{22} -127.719 q^{23} -118.058 q^{24} -115.685 q^{26} -25.0908 q^{27} -29.3999 q^{28} +285.724 q^{29} -192.699 q^{31} -128.812 q^{32} +4.24666 q^{33} -302.802 q^{34} +70.0821 q^{36} -363.399 q^{37} -79.6565 q^{38} -247.948 q^{39} +191.586 q^{41} -231.820 q^{42} +43.0000 q^{43} +1.78512 q^{44} -423.330 q^{46} +458.267 q^{47} -561.027 q^{48} -246.076 q^{49} -648.995 q^{51} -104.227 q^{52} +583.068 q^{53} -83.1648 q^{54} +163.607 q^{56} -170.728 q^{57} +947.047 q^{58} +416.589 q^{59} -30.9376 q^{61} -638.710 q^{62} -231.044 q^{63} +204.825 q^{64} +14.0758 q^{66} -16.1466 q^{67} -272.811 q^{68} -907.324 q^{69} -219.461 q^{71} -390.000 q^{72} -1031.07 q^{73} -1204.50 q^{74} -71.7670 q^{76} -5.88512 q^{77} -821.836 q^{78} +445.438 q^{79} -811.887 q^{81} +635.022 q^{82} -298.511 q^{83} -208.859 q^{84} +142.526 q^{86} +2029.81 q^{87} -9.93402 q^{88} +846.185 q^{89} +343.612 q^{91} -381.402 q^{92} -1368.95 q^{93} +1518.95 q^{94} -915.091 q^{96} +259.068 q^{97} -815.631 q^{98} +14.0287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * 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 $

$2$	3.31455	1.17187	0.585936	−	0.810357i	$-0.300727\pi$
$2$	3.31455	1.17187	0.585936	+	0.810357i	$0.300727\pi$
$3$	7.10409	1.36718	0.683592	−	0.729865i	$-0.260417\pi$
$3$	7.10409	1.36718	0.683592	+	0.729865i	$0.260417\pi$
$4$	2.98627	0.373283
$5$	0	0
$5$	0	0
$6$	23.5469	1.60216
$7$	−9.84502	−0.531581	−0.265791	−	0.964031i	$-0.585633\pi$
$7$	−9.84502	−0.531581	−0.265791	+	0.964031i	$0.585633\pi$
$8$	−16.6183	−0.734432
$9$	23.4681	0.869190
$10$	0	0
$11$	0.597776	0.0163851	0.00819256	−	0.999966i	$-0.497392\pi$
$11$	0.597776	0.0163851	0.00819256	+	0.999966i	$0.497392\pi$
$12$	21.2147	0.510347
$13$	−34.9021	−0.744623	−0.372311	−	0.928108i	$-0.621435\pi$
$13$	−34.9021	−0.744623	−0.372311	+	0.928108i	$0.621435\pi$
$14$	−32.6318	−0.622945
$15$	0	0
$16$	−78.9723	−1.23394
$17$	−91.3552	−1.30335	−0.651673	−	0.758500i	$-0.725933\pi$
$17$	−91.3552	−1.30335	−0.651673	+	0.758500i	$0.725933\pi$
$18$	77.7863	1.01858
$19$	−24.0324	−0.290179	−0.145089	−	0.989419i	$-0.546347\pi$
$19$	−24.0324	−0.290179	−0.145089	+	0.989419i	$0.546347\pi$
$20$	0	0
$21$	−69.9399	−0.726769
$22$	1.98136	0.0192013
$23$	−127.719	−1.15788	−0.578938	−	0.815371i	$-0.696533\pi$
$23$	−127.719	−1.15788	−0.578938	+	0.815371i	$0.696533\pi$
$24$	−118.058	−1.00410
$25$	0	0
$26$	−115.685	−0.872602
$27$	−25.0908	−0.178842
$28$	−29.3999	−0.198430
$29$	285.724	1.82957	0.914786	−	0.403939i	$-0.132359\pi$
$29$	285.724	1.82957	0.914786	+	0.403939i	$0.132359\pi$
$30$	0	0
$31$	−192.699	−1.11644	−0.558221	−	0.829692i	$-0.688516\pi$
$31$	−192.699	−1.11644	−0.558221	+	0.829692i	$0.688516\pi$
$32$	−128.812	−0.711591
$33$	4.24666	0.0224015
$34$	−302.802	−1.52735
$35$	0	0
$36$	70.0821	0.324454
$37$	−363.399	−1.61466	−0.807329	−	0.590101i	$-0.799088\pi$
$37$	−363.399	−1.61466	−0.807329	+	0.590101i	$0.799088\pi$
$38$	−79.6565	−0.340053
$39$	−247.948	−1.01804
$40$	0	0
$41$	191.586	0.729774	0.364887	−	0.931052i	$-0.381108\pi$
$41$	191.586	0.729774	0.364887	+	0.931052i	$0.381108\pi$
$42$	−231.820	−0.851680
$43$	43.0000	0.152499
$43$	43.0000	0.152499
$44$	1.78512	0.00611629
$45$	0	0
$46$	−423.330	−1.35688
$47$	458.267	1.42223	0.711117	−	0.703073i	$-0.248189\pi$
$47$	458.267	1.42223	0.711117	+	0.703073i	$0.248189\pi$
$48$	−561.027	−1.68703
$49$	−246.076	−0.717422
$50$	0	0
$51$	−648.995	−1.78191
$52$	−104.227	−0.277955
$53$	583.068	1.51114	0.755572	−	0.655066i	$-0.227359\pi$
$53$	583.068	1.51114	0.755572	+	0.655066i	$0.227359\pi$
$54$	−83.1648	−0.209580
$55$	0	0
$56$	163.607	0.390410
$57$	−170.728	−0.396728
$58$	947.047	2.14402
$59$	416.589	0.919243	0.459621	−	0.888115i	$-0.347985\pi$
$59$	416.589	0.919243	0.459621	+	0.888115i	$0.347985\pi$
$60$	0	0
$61$	−30.9376	−0.0649369	−0.0324685	−	0.999473i	$-0.510337\pi$
$61$	−30.9376	−0.0649369	−0.0324685	+	0.999473i	$0.510337\pi$
$62$	−638.710	−1.30833
$63$	−231.044	−0.462045
$64$	204.825	0.400049
$65$	0	0
$66$	14.0758	0.0262516
$67$	−16.1466	−0.0294421	−0.0147210	−	0.999892i	$-0.504686\pi$
$67$	−16.1466	−0.0294421	−0.0147210	+	0.999892i	$0.504686\pi$
$68$	−272.811	−0.486517
$69$	−907.324	−1.58303
$70$	0	0
$71$	−219.461	−0.366835	−0.183418	−	0.983035i	$-0.558716\pi$
$71$	−219.461	−0.366835	−0.183418	+	0.983035i	$0.558716\pi$
$72$	−390.000	−0.638360
$73$	−1031.07	−1.65311	−0.826557	−	0.562853i	$-0.809704\pi$
$73$	−1031.07	−1.65311	−0.826557	+	0.562853i	$0.809704\pi$
$74$	−1204.50	−1.89217
$75$	0	0
$76$	−71.7670	−0.108319
$77$	−5.88512	−0.00871002
$78$	−821.836	−1.19301
$79$	445.438	0.634375	0.317188	−	0.948363i	$-0.397262\pi$
$79$	445.438	0.634375	0.317188	+	0.948363i	$0.397262\pi$
$80$	0	0
$81$	−811.887	−1.11370
$82$	635.022	0.855201
$83$	−298.511	−0.394769	−0.197384	−	0.980326i	$-0.563245\pi$
$83$	−298.511	−0.394769	−0.197384	+	0.980326i	$0.563245\pi$
$84$	−208.859	−0.271291
$85$	0	0
$86$	142.526	0.178709
$87$	2029.81	2.50136
$88$	−9.93402	−0.0120338
$89$	846.185	1.00781	0.503907	−	0.863758i	$-0.331895\pi$
$89$	846.185	1.00781	0.503907	+	0.863758i	$0.331895\pi$
$90$	0	0
$91$	343.612	0.395827
$92$	−381.402	−0.432216
$93$	−1368.95	−1.52638
$94$	1518.95	1.66668
$95$	0	0
$96$	−915.091	−0.972876
$97$	259.068	0.271179	0.135590	−	0.990765i	$-0.456707\pi$
$97$	259.068	0.271179	0.135590	+	0.990765i	$0.456707\pi$
$98$	−815.631	−0.840726
$99$	14.0287	0.0142418
$100$	0	0
$101$	−1182.01	−1.16450	−0.582252	−	0.813009i	$-0.697828\pi$
$101$	−1182.01	−1.16450	−0.582252	+	0.813009i	$0.697828\pi$
$102$	−2151.13	−2.08817
$103$	−319.565	−0.305706	−0.152853	−	0.988249i	$-0.548846\pi$
$103$	−319.565	−0.305706	−0.152853	+	0.988249i	$0.548846\pi$
$104$	580.013	0.546874
$105$	0	0
$106$	1932.61	1.77087
$107$	−1647.14	−1.48818	−0.744089	−	0.668081i	$-0.767116\pi$
$107$	−1647.14	−1.48818	−0.744089	+	0.668081i	$0.767116\pi$
$108$	−74.9279	−0.0667587
$109$	−560.538	−0.492567	−0.246283	−	0.969198i	$-0.579209\pi$
$109$	−560.538	−0.492567	−0.246283	+	0.969198i	$0.579209\pi$
$110$	0	0
$111$	−2581.62	−2.20753
$112$	777.484	0.655941
$113$	65.6852	0.0546827	0.0273414	−	0.999626i	$-0.491296\pi$
$113$	65.6852	0.0546827	0.0273414	+	0.999626i	$0.491296\pi$
$114$	−565.887	−0.464914
$115$	0	0
$116$	853.248	0.682949
$117$	−819.086	−0.647218
$118$	1380.81	1.07723
$119$	899.393	0.692834
$120$	0	0
$121$	−1330.64	−0.999732
$122$	−102.544	−0.0760977
$123$	1361.05	0.997734
$124$	−575.450	−0.416749
$125$	0	0
$126$	−765.808	−0.541457
$127$	1906.92	1.33238	0.666189	−	0.745783i	$-0.267924\pi$
$127$	1906.92	1.33238	0.666189	+	0.745783i	$0.267924\pi$
$128$	1709.40	1.18040
$129$	305.476	0.208493
$130$	0	0
$131$	−1536.09	−1.02449	−0.512246	−	0.858839i	$-0.671186\pi$
$131$	−1536.09	−1.02449	−0.512246	+	0.858839i	$0.671186\pi$
$132$	12.6817	0.00836209
$133$	236.599	0.154254
$134$	−53.5187	−0.0345023
$135$	0	0
$136$	1518.17	0.957218
$137$	1695.38	1.05727	0.528634	−	0.848850i	$-0.322704\pi$
$137$	1695.38	1.05727	0.528634	+	0.848850i	$0.322704\pi$
$138$	−3007.38	−1.85511
$139$	947.580	0.578221	0.289110	−	0.957296i	$-0.406641\pi$
$139$	947.580	0.578221	0.289110	+	0.957296i	$0.406641\pi$
$140$	0	0
$141$	3255.57	1.94446
$142$	−727.417	−0.429884
$143$	−20.8636	−0.0122007
$144$	−1853.33	−1.07253
$145$	0	0
$146$	−3417.53	−1.93724
$147$	−1748.14	−0.980847
$148$	−1085.21	−0.602725
$149$	3084.10	1.69570	0.847850	−	0.530236i	$-0.177897\pi$
$149$	3084.10	1.69570	0.847850	+	0.530236i	$0.177897\pi$
$150$	0	0
$151$	−2346.83	−1.26478	−0.632391	−	0.774649i	$-0.717926\pi$
$151$	−2346.83	−1.26478	−0.632391	+	0.774649i	$0.717926\pi$
$152$	399.377	0.213117
$153$	−2143.93	−1.13285
$154$	−19.5066	−0.0102070
$155$	0	0
$156$	−740.438	−0.380016
$157$	−1582.73	−0.804556	−0.402278	−	0.915517i	$-0.631782\pi$
$157$	−1582.73	−0.804556	−0.402278	+	0.915517i	$0.631782\pi$
$158$	1476.43	0.743406
$159$	4142.17	2.06601
$160$	0	0
$161$	1257.39	0.615505
$162$	−2691.04	−1.30511
$163$	820.887	0.394459	0.197229	−	0.980357i	$-0.436806\pi$
$163$	820.887	0.394459	0.197229	+	0.980357i	$0.436806\pi$
$164$	572.127	0.272412
$165$	0	0
$166$	−989.430	−0.462618
$167$	−1690.58	−0.783358	−0.391679	−	0.920102i	$-0.628106\pi$
$167$	−1690.58	−0.783358	−0.391679	+	0.920102i	$0.628106\pi$
$168$	1162.28	0.533762
$169$	−978.845	−0.445537
$170$	0	0
$171$	−563.994	−0.252221
$172$	128.409	0.0569252
$173$	−1390.24	−0.610973	−0.305486	−	0.952196i	$-0.598819\pi$
$173$	−1390.24	−0.610973	−0.305486	+	0.952196i	$0.598819\pi$
$174$	6727.91	2.93127
$175$	0	0
$176$	−47.2078	−0.0202183
$177$	2959.49	1.25677
$178$	2804.73	1.18103
$179$	693.895	0.289744	0.144872	−	0.989450i	$-0.453723\pi$
$179$	693.895	0.289744	0.144872	+	0.989450i	$0.453723\pi$
$180$	0	0
$181$	−2355.50	−0.967309	−0.483655	−	0.875259i	$-0.660691\pi$
$181$	−2355.50	−0.967309	−0.483655	+	0.875259i	$0.660691\pi$
$182$	1138.92	0.463859
$183$	−219.783	−0.0887807
$184$	2122.46	0.850381
$185$	0	0
$186$	−4537.46	−1.78872
$187$	−54.6100	−0.0213555
$188$	1368.51	0.530897
$189$	247.020	0.0950689
$190$	0	0
$191$	−2168.09	−0.821349	−0.410674	−	0.911782i	$-0.634707\pi$
$191$	−2168.09	−0.821349	−0.410674	+	0.911782i	$0.634707\pi$
$192$	1455.10	0.546940
$193$	−1305.00	−0.486717	−0.243358	−	0.969936i	$-0.578249\pi$
$193$	−1305.00	−0.486717	−0.243358	+	0.969936i	$0.578249\pi$
$194$	858.695	0.317787
$195$	0	0
$196$	−734.847	−0.267802
$197$	4800.27	1.73607	0.868033	−	0.496507i	$-0.165384\pi$
$197$	4800.27	1.73607	0.868033	+	0.496507i	$0.165384\pi$
$198$	46.4988	0.0166895
$199$	−2113.34	−0.752816	−0.376408	−	0.926454i	$-0.622841\pi$
$199$	−2113.34	−0.752816	−0.376408	+	0.926454i	$0.622841\pi$
$200$	0	0
$201$	−114.707	−0.0402527
$202$	−3917.85	−1.36465
$203$	−2812.96	−0.972566
$204$	−1938.07	−0.665158
$205$	0	0
$206$	−1059.22	−0.358248
$207$	−2997.31	−1.00641
$208$	2756.30	0.918822
$209$	−14.3660	−0.00475462
$210$	0	0
$211$	5564.31	1.81546	0.907732	−	0.419551i	$-0.137812\pi$
$211$	5564.31	1.81546	0.907732	+	0.419551i	$0.137812\pi$
$212$	1741.20	0.564085
$213$	−1559.07	−0.501531
$214$	−5459.53	−1.74395
$215$	0	0
$216$	416.966	0.131347
$217$	1897.12	0.593480
$218$	−1857.93	−0.577225
$219$	−7324.80	−2.26011
$220$	0	0
$221$	3188.49	0.970501
$222$	−8556.91	−2.58695
$223$	1709.75	0.513422	0.256711	−	0.966488i	$-0.417361\pi$
$223$	1709.75	0.513422	0.256711	+	0.966488i	$0.417361\pi$
$224$	1268.15	0.378268
$225$	0	0
$226$	217.717	0.0640811
$227$	−347.506	−0.101607	−0.0508035	−	0.998709i	$-0.516178\pi$
$227$	−347.506	−0.101607	−0.0508035	+	0.998709i	$0.516178\pi$
$228$	−509.840	−0.148092
$229$	713.508	0.205895	0.102947	−	0.994687i	$-0.467173\pi$
$229$	713.508	0.205895	0.102947	+	0.994687i	$0.467173\pi$
$230$	0	0
$231$	−41.8084	−0.0119082
$232$	−4748.24	−1.34370
$233$	6539.93	1.83882	0.919410	−	0.393300i	$-0.128667\pi$
$233$	6539.93	1.83882	0.919410	+	0.393300i	$0.128667\pi$
$234$	−2714.91	−0.758457
$235$	0	0
$236$	1244.05	0.343138
$237$	3164.43	0.867307
$238$	2981.09	0.811913
$239$	−2561.41	−0.693238	−0.346619	−	0.938006i	$-0.612670\pi$
$239$	−2561.41	−0.693238	−0.346619	+	0.938006i	$0.612670\pi$
$240$	0	0
$241$	−4656.80	−1.24469	−0.622346	−	0.782742i	$-0.713820\pi$
$241$	−4656.80	−1.24469	−0.622346	+	0.782742i	$0.713820\pi$
$242$	−4410.49	−1.17156
$243$	−5090.27	−1.34379
$244$	−92.3879	−0.0242399
$245$	0	0
$246$	4511.26	1.16922
$247$	838.779	0.216074
$248$	3202.32	0.819950
$249$	−2120.65	−0.539721
$250$	0	0
$251$	6104.04	1.53499	0.767497	−	0.641053i	$-0.221502\pi$
$251$	6104.04	1.53499	0.767497	+	0.641053i	$0.221502\pi$
$252$	−689.959	−0.172474
$253$	−76.3471	−0.0189720
$254$	6320.60	1.56138
$255$	0	0
$256$	4027.29	0.983225
$257$	−682.439	−0.165640	−0.0828199	−	0.996565i	$-0.526393\pi$
$257$	−682.439	−0.165640	−0.0828199	+	0.996565i	$0.526393\pi$
$258$	1012.52	0.244328
$259$	3577.67	0.858322
$260$	0	0
$261$	6705.40	1.59024
$262$	−5091.44	−1.20057
$263$	−1671.87	−0.391984	−0.195992	−	0.980605i	$-0.562793\pi$
$263$	−1671.87	−0.391984	−0.195992	+	0.980605i	$0.562793\pi$
$264$	−70.5722	−0.0164523
$265$	0	0
$266$	784.220	0.180766
$267$	6011.38	1.37787
$268$	−48.2180	−0.0109902
$269$	−261.999	−0.0593843	−0.0296921	−	0.999559i	$-0.509453\pi$
$269$	−261.999	−0.0593843	−0.0296921	+	0.999559i	$0.509453\pi$
$270$	0	0
$271$	4620.04	1.03560	0.517800	−	0.855502i	$-0.326751\pi$
$271$	4620.04	1.03560	0.517800	+	0.855502i	$0.326751\pi$
$272$	7214.53	1.60825
$273$	2441.05	0.541168
$274$	5619.41	1.23898
$275$	0	0
$276$	−2709.51	−0.590918
$277$	−5163.93	−1.12011	−0.560055	−	0.828456i	$-0.689220\pi$
$277$	−5163.93	−1.12011	−0.560055	+	0.828456i	$0.689220\pi$
$278$	3140.81	0.677601
$279$	−4522.28	−0.970400
$280$	0	0
$281$	−5275.67	−1.12000	−0.560000	−	0.828493i	$-0.689199\pi$
$281$	−5275.67	−1.12000	−0.560000	+	0.828493i	$0.689199\pi$
$282$	10790.8	2.27865
$283$	5028.34	1.05620	0.528098	−	0.849183i	$-0.322905\pi$
$283$	5028.34	1.05620	0.528098	+	0.849183i	$0.322905\pi$
$284$	−655.371	−0.136933
$285$	0	0
$286$	−69.1537	−0.0142977
$287$	−1886.17	−0.387934
$288$	−3022.97	−0.618508
$289$	3432.77	0.698711
$290$	0	0
$291$	1840.44	0.370751
$292$	−3079.04	−0.617080
$293$	−8840.69	−1.76273	−0.881363	−	0.472439i	$-0.843374\pi$
$293$	−8840.69	−1.76273	−0.881363	+	0.472439i	$0.843374\pi$
$294$	−5794.32	−1.14943
$295$	0	0
$296$	6039.06	1.18586
$297$	−14.9987	−0.00293035
$298$	10222.4	1.98714
$299$	4457.64	0.862181
$300$	0	0
$301$	−423.336	−0.0810654
$302$	−7778.68	−1.48216
$303$	−8397.14	−1.59209
$304$	1897.89	0.358064
$305$	0	0
$306$	−7106.18	−1.32756
$307$	−6565.15	−1.22050	−0.610249	−	0.792209i	$-0.708931\pi$
$307$	−6565.15	−1.22050	−0.610249	+	0.792209i	$0.708931\pi$
$308$	−17.5745	−0.00325131
$309$	−2270.22	−0.417956
$310$	0	0
$311$	1250.31	0.227969	0.113985	−	0.993483i	$-0.463639\pi$
$311$	1250.31	0.227969	0.113985	+	0.993483i	$0.463639\pi$
$312$	4120.46	0.747677
$313$	2968.85	0.536132	0.268066	−	0.963401i	$-0.413615\pi$
$313$	2968.85	0.536132	0.268066	+	0.963401i	$0.413615\pi$
$314$	−5246.03	−0.942837
$315$	0	0
$316$	1330.20	0.236802
$317$	−1054.32	−0.186803	−0.0934013	−	0.995629i	$-0.529774\pi$
$317$	−1054.32	−0.186803	−0.0934013	+	0.995629i	$0.529774\pi$
$318$	13729.4	2.42110
$319$	170.799	0.0299778
$320$	0	0
$321$	−11701.4	−2.03461
$322$	4167.69	0.721293
$323$	2195.48	0.378204
$324$	−2424.51	−0.415725
$325$	0	0
$326$	2720.87	0.462255
$327$	−3982.11	−0.673429
$328$	−3183.83	−0.535969
$329$	−4511.64	−0.756033
$330$	0	0
$331$	−2881.73	−0.478532	−0.239266	−	0.970954i	$-0.576907\pi$
$331$	−2881.73	−0.478532	−0.239266	+	0.970954i	$0.576907\pi$
$332$	−891.432	−0.147361
$333$	−8528.28	−1.40344
$334$	−5603.51	−0.917995
$335$	0	0
$336$	5523.32	0.896791
$337$	6147.77	0.993740	0.496870	−	0.867825i	$-0.334483\pi$
$337$	6147.77	0.993740	0.496870	+	0.867825i	$0.334483\pi$
$338$	−3244.43	−0.522112
$339$	466.634	0.0747613
$340$	0	0
$341$	−115.191	−0.0182930
$342$	−1869.39	−0.295570
$343$	5799.46	0.912949
$344$	−714.586	−0.112000
$345$	0	0
$346$	−4608.04	−0.715982
$347$	−1404.42	−0.217271	−0.108636	−	0.994082i	$-0.534648\pi$
$347$	−1404.42	−0.217271	−0.108636	+	0.994082i	$0.534648\pi$
$348$	6061.55	0.933716
$349$	−4472.14	−0.685926	−0.342963	−	0.939349i	$-0.611430\pi$
$349$	−4472.14	−0.685926	−0.342963	+	0.939349i	$0.611430\pi$
$350$	0	0
$351$	875.721	0.133170
$352$	−77.0007	−0.0116595
$353$	−2146.48	−0.323642	−0.161821	−	0.986820i	$-0.551737\pi$
$353$	−2146.48	−0.323642	−0.161821	+	0.986820i	$0.551737\pi$
$354$	9809.38	1.47278
$355$	0	0
$356$	2526.93	0.376200
$357$	6389.37	0.947231
$358$	2299.95	0.339543
$359$	1960.49	0.288219	0.144109	−	0.989562i	$-0.453968\pi$
$359$	1960.49	0.288219	0.144109	+	0.989562i	$0.453968\pi$
$360$	0	0
$361$	−6281.45	−0.915796
$362$	−7807.43	−1.13356
$363$	−9453.01	−1.36682
$364$	1026.12	0.147756
$365$	0	0
$366$	−728.484	−0.104040
$367$	−13485.2	−1.91804	−0.959021	−	0.283337i	$-0.908559\pi$
$367$	−13485.2	−1.91804	−0.959021	+	0.283337i	$0.908559\pi$
$368$	10086.2	1.42875
$369$	4496.16	0.634312
$370$	0	0
$371$	−5740.32	−0.803295
$372$	−4088.05	−0.569773
$373$	12034.5	1.67057	0.835285	−	0.549817i	$-0.185303\pi$
$373$	12034.5	1.67057	0.835285	+	0.549817i	$0.185303\pi$
$374$	−181.008	−0.0250259
$375$	0	0
$376$	−7615.60	−1.04453
$377$	−9972.36	−1.36234
$378$	818.760	0.111409
$379$	−10185.1	−1.38041	−0.690204	−	0.723615i	$-0.742479\pi$
$379$	−10185.1	−1.38041	−0.690204	+	0.723615i	$0.742479\pi$
$380$	0	0
$381$	13546.9	1.82160
$382$	−7186.26	−0.962515
$383$	−13508.3	−1.80219	−0.901097	−	0.433618i	$-0.857237\pi$
$383$	−13508.3	−1.80219	−0.901097	+	0.433618i	$0.857237\pi$
$384$	12143.7	1.61382
$385$	0	0
$386$	−4325.51	−0.570369
$387$	1009.13	0.132550
$388$	773.646	0.101227
$389$	−6651.52	−0.866954	−0.433477	−	0.901165i	$-0.642714\pi$
$389$	−6651.52	−0.866954	−0.433477	+	0.901165i	$0.642714\pi$
$390$	0	0
$391$	11667.7	1.50911
$392$	4089.35	0.526897
$393$	−10912.5	−1.40067
$394$	15910.7	2.03445
$395$	0	0
$396$	41.8934	0.00531622
$397$	8308.29	1.05033	0.525165	−	0.851000i	$-0.324004\pi$
$397$	8308.29	1.05033	0.525165	+	0.851000i	$0.324004\pi$
$398$	−7004.77	−0.882204
$399$	1680.82	0.210893
$400$	0	0
$401$	2963.57	0.369061	0.184530	−	0.982827i	$-0.440924\pi$
$401$	2963.57	0.369061	0.184530	+	0.982827i	$0.440924\pi$
$402$	−380.202	−0.0471710
$403$	6725.59	0.831328
$404$	−3529.81	−0.434690
$405$	0	0
$406$	−9323.70	−1.13972
$407$	−217.231	−0.0264564
$408$	10785.2	1.30869
$409$	−9951.28	−1.20308	−0.601540	−	0.798843i	$-0.705446\pi$
$409$	−9951.28	−1.20308	−0.601540	+	0.798843i	$0.705446\pi$
$410$	0	0
$411$	12044.1	1.44548
$412$	−954.308	−0.114115
$413$	−4101.33	−0.488652
$414$	−9934.76	−1.17939
$415$	0	0
$416$	4495.80	0.529867
$417$	6731.70	0.790534
$418$	−47.6168	−0.00557180
$419$	5281.70	0.615818	0.307909	−	0.951416i	$-0.400371\pi$
$419$	5281.70	0.615818	0.307909	+	0.951416i	$0.400371\pi$
$420$	0	0
$421$	−1668.54	−0.193159	−0.0965795	−	0.995325i	$-0.530790\pi$
$421$	−1668.54	−0.193159	−0.0965795	+	0.995325i	$0.530790\pi$
$422$	18443.2	2.12749
$423$	10754.7	1.23619
$424$	−9689.60	−1.10983
$425$	0	0
$426$	−5167.64	−0.587730
$427$	304.581	0.0345192
$428$	−4918.80	−0.555512
$429$	−148.217	−0.0166806
$430$	0	0
$431$	−10348.7	−1.15657	−0.578284	−	0.815835i	$-0.696278\pi$
$431$	−10348.7	−1.15657	−0.578284	+	0.815835i	$0.696278\pi$
$432$	1981.48	0.220681
$433$	−2968.27	−0.329436	−0.164718	−	0.986341i	$-0.552671\pi$
$433$	−2968.27	−0.329436	−0.164718	+	0.986341i	$0.552671\pi$
$434$	6288.12	0.695482
$435$	0	0
$436$	−1673.91	−0.183867
$437$	3069.38	0.335991
$438$	−24278.4	−2.64856
$439$	−9224.53	−1.00288	−0.501438	−	0.865194i	$-0.667196\pi$
$439$	−9224.53	−1.00288	−0.501438	+	0.865194i	$0.667196\pi$
$440$	0	0
$441$	−5774.93	−0.623575
$442$	10568.4	1.13730
$443$	10115.5	1.08488	0.542438	−	0.840096i	$-0.317501\pi$
$443$	10115.5	1.08488	0.542438	+	0.840096i	$0.317501\pi$
$444$	−7709.40	−0.824036
$445$	0	0
$446$	5667.05	0.601665
$447$	21909.7	2.31833
$448$	−2016.51	−0.212659
$449$	14386.0	1.51207	0.756034	−	0.654532i	$-0.227134\pi$
$449$	14386.0	1.51207	0.756034	+	0.654532i	$0.227134\pi$
$450$	0	0
$451$	114.526	0.0119574
$452$	196.154	0.0204121
$453$	−16672.1	−1.72919
$454$	−1151.83	−0.119070
$455$	0	0
$456$	2837.21	0.291369
$457$	10031.8	1.02684	0.513421	−	0.858137i	$-0.328378\pi$
$457$	10031.8	1.02684	0.513421	+	0.858137i	$0.328378\pi$
$458$	2364.96	0.241282
$459$	2292.18	0.233093
$460$	0	0
$461$	−124.788	−0.0126072	−0.00630362	−	0.999980i	$-0.502007\pi$
$461$	−124.788	−0.0126072	−0.00630362	+	0.999980i	$0.502007\pi$
$462$	−138.576	−0.0139549
$463$	−15438.9	−1.54969	−0.774847	−	0.632148i	$-0.782173\pi$
$463$	−15438.9	−1.54969	−0.774847	+	0.632148i	$0.782173\pi$
$464$	−22564.3	−2.25759
$465$	0	0
$466$	21677.0	2.15486
$467$	12014.7	1.19052	0.595259	−	0.803534i	$-0.297049\pi$
$467$	12014.7	1.19052	0.595259	+	0.803534i	$0.297049\pi$
$468$	−2446.01	−0.241596
$469$	158.963	0.0156508
$470$	0	0
$471$	−11243.8	−1.09998
$472$	−6923.00	−0.675121
$473$	25.7044	0.00249871
$474$	10488.7	1.01637
$475$	0	0
$476$	2685.83	0.258623
$477$	13683.5	1.31347
$478$	−8489.93	−0.812386
$479$	6241.39	0.595358	0.297679	−	0.954666i	$-0.403788\pi$
$479$	6241.39	0.595358	0.297679	+	0.954666i	$0.403788\pi$
$480$	0	0
$481$	12683.4	1.20231
$482$	−15435.2	−1.45862
$483$	8932.63	0.841508
$484$	−3973.65	−0.373183
$485$	0	0
$486$	−16872.0	−1.57475
$487$	−924.180	−0.0859930	−0.0429965	−	0.999075i	$-0.513690\pi$
$487$	−924.180	−0.0859930	−0.0429965	+	0.999075i	$0.513690\pi$
$488$	514.130	0.0476917
$489$	5831.65	0.539297
$490$	0	0
$491$	−7044.15	−0.647451	−0.323725	−	0.946151i	$-0.604935\pi$
$491$	−7044.15	−0.647451	−0.323725	+	0.946151i	$0.604935\pi$
$492$	4064.44	0.372438
$493$	−26102.3	−2.38457
$494$	2780.18	0.253211
$495$	0	0
$496$	15217.9	1.37763
$497$	2160.60	0.195003
$498$	−7029.00	−0.632484
$499$	−3981.76	−0.357210	−0.178605	−	0.983921i	$-0.557158\pi$
$499$	−3981.76	−0.357210	−0.178605	+	0.983921i	$0.557158\pi$
$500$	0	0
$501$	−12010.0	−1.07099
$502$	20232.2	1.79882
$503$	11650.2	1.03272	0.516358	−	0.856373i	$-0.327288\pi$
$503$	11650.2	1.03272	0.516358	+	0.856373i	$0.327288\pi$
$504$	3839.56	0.339340
$505$	0	0
$506$	−253.057	−0.0222327
$507$	−6953.80	−0.609131
$508$	5694.58	0.497354
$509$	11408.7	0.993481	0.496740	−	0.867899i	$-0.334530\pi$
$509$	11408.7	0.993481	0.496740	+	0.867899i	$0.334530\pi$
$510$	0	0
$511$	10150.9	0.878764
$512$	−326.513	−0.0281836
$513$	602.991	0.0518961
$514$	−2261.98	−0.194108
$515$	0	0
$516$	912.233	0.0778271
$517$	273.941	0.0233035
$518$	11858.4	1.00584
$519$	−9876.42	−0.835312
$520$	0	0
$521$	15272.4	1.28425	0.642127	−	0.766598i	$-0.278052\pi$
$521$	15272.4	1.28425	0.642127	+	0.766598i	$0.278052\pi$
$522$	22225.4	1.86356
$523$	20831.4	1.74167	0.870835	−	0.491575i	$-0.163579\pi$
$523$	20831.4	1.74167	0.870835	+	0.491575i	$0.163579\pi$
$524$	−4587.16	−0.382426
$525$	0	0
$526$	−5541.50	−0.459355
$527$	17604.0	1.45511
$528$	−335.369	−0.0276421
$529$	4145.03	0.340678
$530$	0	0
$531$	9776.57	0.798996
$532$	706.548	0.0575803
$533$	−6686.75	−0.543406
$534$	19925.0	1.61468
$535$	0	0
$536$	268.328	0.0216232
$537$	4929.50	0.396133
$538$	−868.410	−0.0695907
$539$	−147.098	−0.0117550
$540$	0	0
$541$	−1411.76	−0.112192	−0.0560962	−	0.998425i	$-0.517865\pi$
$541$	−1411.76	−0.112192	−0.0560962	+	0.998425i	$0.517865\pi$
$542$	15313.4	1.21359
$543$	−16733.7	−1.32249
$544$	11767.6	0.927450
$545$	0	0
$546$	8090.99	0.634180
$547$	328.281	0.0256605	0.0128302	−	0.999918i	$-0.495916\pi$
$547$	328.281	0.0256605	0.0128302	+	0.999918i	$0.495916\pi$
$548$	5062.84	0.394661
$549$	−726.047	−0.0564425
$550$	0	0
$551$	−6866.62	−0.530903
$552$	15078.2	1.16263
$553$	−4385.34	−0.337222
$554$	−17116.1	−1.31262
$555$	0	0
$556$	2829.73	0.215840
$557$	1908.49	0.145180	0.0725901	−	0.997362i	$-0.476874\pi$
$557$	1908.49	0.145180	0.0725901	+	0.997362i	$0.476874\pi$
$558$	−14989.3	−1.13718
$559$	−1500.79	−0.113554
$560$	0	0
$561$	−387.954	−0.0291969
$562$	−17486.5	−1.31250
$563$	−3413.23	−0.255507	−0.127753	−	0.991806i	$-0.540777\pi$
$563$	−3413.23	−0.255507	−0.127753	+	0.991806i	$0.540777\pi$
$564$	9721.99	0.725833
$565$	0	0
$566$	16666.7	1.23773
$567$	7993.04	0.592021
$568$	3647.07	0.269415
$569$	−15405.8	−1.13505	−0.567527	−	0.823355i	$-0.692100\pi$
$569$	−15405.8	−1.13505	−0.567527	+	0.823355i	$0.692100\pi$
$570$	0	0
$571$	18819.2	1.37926	0.689632	−	0.724160i	$-0.257772\pi$
$571$	18819.2	1.37926	0.689632	+	0.724160i	$0.257772\pi$
$572$	−62.3044	−0.00455433
$573$	−15402.3	−1.12293
$574$	−6251.81	−0.454609
$575$	0	0
$576$	4806.86	0.347719
$577$	−8098.53	−0.584309	−0.292154	−	0.956371i	$-0.594372\pi$
$577$	−8098.53	−0.584309	−0.292154	+	0.956371i	$0.594372\pi$
$578$	11378.1	0.818799
$579$	−9270.87	−0.665431
$580$	0	0
$581$	2938.84	0.209852
$582$	6100.25	0.434473
$583$	348.545	0.0247603
$584$	17134.6	1.21410
$585$	0	0
$586$	−29303.0	−2.06569
$587$	3631.44	0.255342	0.127671	−	0.991817i	$-0.459250\pi$
$587$	3631.44	0.255342	0.127671	+	0.991817i	$0.459250\pi$
$588$	−5220.42	−0.366134
$589$	4631.00	0.323968
$590$	0	0
$591$	34101.5	2.37352
$592$	28698.4	1.99240
$593$	14298.2	0.990147	0.495073	−	0.868851i	$-0.335141\pi$
$593$	14298.2	0.990147	0.495073	+	0.868851i	$0.335141\pi$
$594$	−49.7140	−0.00343399
$595$	0	0
$596$	9209.95	0.632977
$597$	−15013.3	−1.02924
$598$	14775.1	1.01037
$599$	−27823.6	−1.89790	−0.948949	−	0.315430i	$-0.897851\pi$
$599$	−27823.6	−1.89790	−0.948949	+	0.315430i	$0.897851\pi$
$600$	0	0
$601$	3557.15	0.241430	0.120715	−	0.992687i	$-0.461481\pi$
$601$	3557.15	0.241430	0.120715	+	0.992687i	$0.461481\pi$
$602$	−1403.17	−0.0949982
$603$	−378.930	−0.0255907
$604$	−7008.25	−0.472122
$605$	0	0
$606$	−27832.8	−1.86572
$607$	−19170.9	−1.28192	−0.640958	−	0.767576i	$-0.721463\pi$
$607$	−19170.9	−1.28192	−0.640958	+	0.767576i	$0.721463\pi$
$608$	3095.65	0.206489
$609$	−19983.5	−1.32968
$610$	0	0
$611$	−15994.5	−1.05903
$612$	−6402.36	−0.422876
$613$	−4287.83	−0.282518	−0.141259	−	0.989973i	$-0.545115\pi$
$613$	−4287.83	−0.282518	−0.141259	+	0.989973i	$0.545115\pi$
$614$	−21760.6	−1.43027
$615$	0	0
$616$	97.8006	0.00639692
$617$	10569.5	0.689649	0.344824	−	0.938667i	$-0.387938\pi$
$617$	10569.5	0.689649	0.344824	+	0.938667i	$0.387938\pi$
$618$	−7524.77	−0.489791
$619$	19947.5	1.29525	0.647624	−	0.761960i	$-0.275763\pi$
$619$	19947.5	1.29525	0.647624	+	0.761960i	$0.275763\pi$
$620$	0	0
$621$	3204.56	0.207077
$622$	4144.21	0.267150
$623$	−8330.71	−0.535735
$624$	19581.0	1.25620
$625$	0	0
$626$	9840.42	0.628278
$627$	−102.057	−0.00650043
$628$	−4726.44	−0.300328
$629$	33198.3	2.10446
$630$	0	0
$631$	8854.29	0.558611	0.279306	−	0.960202i	$-0.409896\pi$
$631$	8854.29	0.558611	0.279306	+	0.960202i	$0.409896\pi$
$632$	−7402.41	−0.465905
$633$	39529.4	2.48207
$634$	−3494.60	−0.218909
$635$	0	0
$636$	12369.6	0.771207
$637$	8588.55	0.534208
$638$	566.122	0.0351301
$639$	−5150.35	−0.318849
$640$	0	0
$641$	10022.5	0.617571	0.308786	−	0.951132i	$-0.400077\pi$
$641$	10022.5	0.617571	0.308786	+	0.951132i	$0.400077\pi$
$642$	−38785.0	−2.38430
$643$	5806.52	0.356123	0.178061	−	0.984019i	$-0.443017\pi$
$643$	5806.52	0.356123	0.178061	+	0.984019i	$0.443017\pi$
$644$	3754.91	0.229758
$645$	0	0
$646$	7277.04	0.443206
$647$	−8583.93	−0.521591	−0.260795	−	0.965394i	$-0.583985\pi$
$647$	−8583.93	−0.521591	−0.260795	+	0.965394i	$0.583985\pi$
$648$	13492.2	0.817936
$649$	249.027	0.0150619
$650$	0	0
$651$	13477.3	0.811395
$652$	2451.39	0.147245
$653$	−17048.8	−1.02170	−0.510849	−	0.859670i	$-0.670669\pi$
$653$	−17048.8	−1.02170	−0.510849	+	0.859670i	$0.670669\pi$
$654$	−13198.9	−0.789172
$655$	0	0
$656$	−15130.0	−0.900499
$657$	−24197.2	−1.43687
$658$	−14954.1	−0.885974
$659$	−2694.69	−0.159287	−0.0796437	−	0.996823i	$-0.525378\pi$
$659$	−2694.69	−0.159287	−0.0796437	+	0.996823i	$0.525378\pi$
$660$	0	0
$661$	−29666.8	−1.74570	−0.872848	−	0.487992i	$-0.837730\pi$
$661$	−29666.8	−1.74570	−0.872848	+	0.487992i	$0.837730\pi$
$662$	−9551.64	−0.560778
$663$	22651.3	1.32685
$664$	4960.74	0.289931
$665$	0	0
$666$	−28267.5	−1.64466
$667$	−36492.2	−2.11842
$668$	−5048.52	−0.292415
$669$	12146.2	0.701942
$670$	0	0
$671$	−18.4938	−0.00106400
$672$	9009.09	0.517162
$673$	−17932.8	−1.02713	−0.513564	−	0.858051i	$-0.671675\pi$
$673$	−17932.8	−1.02713	−0.513564	+	0.858051i	$0.671675\pi$
$674$	20377.1	1.16454
$675$	0	0
$676$	−2923.09	−0.166312
$677$	−2440.74	−0.138560	−0.0692801	−	0.997597i	$-0.522070\pi$
$677$	−2440.74	−0.138560	−0.0692801	+	0.997597i	$0.522070\pi$
$678$	1546.68	0.0876106
$679$	−2550.53	−0.144154
$680$	0	0
$681$	−2468.72	−0.138915
$682$	−381.806	−0.0214371
$683$	12722.2	0.712737	0.356369	−	0.934345i	$-0.384015\pi$
$683$	12722.2	0.712737	0.356369	+	0.934345i	$0.384015\pi$
$684$	−1684.24	−0.0941497
$685$	0	0
$686$	19222.6	1.06986
$687$	5068.83	0.281496
$688$	−3395.81	−0.188175
$689$	−20350.3	−1.12523
$690$	0	0
$691$	−5584.80	−0.307461	−0.153731	−	0.988113i	$-0.549129\pi$
$691$	−5584.80	−0.307461	−0.153731	+	0.988113i	$0.549129\pi$
$692$	−4151.64	−0.228066
$693$	−138.113	−0.00757066
$694$	−4655.02	−0.254614
$695$	0	0
$696$	−33731.9	−1.83708
$697$	−17502.4	−0.951148
$698$	−14823.1	−0.803817
$699$	46460.3	2.51400
$700$	0	0
$701$	19891.2	1.07173	0.535864	−	0.844304i	$-0.319986\pi$
$701$	19891.2	1.07173	0.535864	+	0.844304i	$0.319986\pi$
$702$	2902.63	0.156058
$703$	8733.33	0.468540
$704$	122.440	0.00655486
$705$	0	0
$706$	−7114.62	−0.379266
$707$	11637.0	0.619028
$708$	8837.82	0.469132
$709$	−14613.5	−0.774078	−0.387039	−	0.922063i	$-0.626502\pi$
$709$	−14613.5	−0.774078	−0.387039	+	0.922063i	$0.626502\pi$
$710$	0	0
$711$	10453.6	0.551392
$712$	−14062.1	−0.740170
$713$	24611.2	1.29270
$714$	21177.9	1.11003
$715$	0	0
$716$	2072.16	0.108157
$717$	−18196.5	−0.947783
$718$	6498.14	0.337755
$719$	−11027.7	−0.571995	−0.285998	−	0.958230i	$-0.592325\pi$
$719$	−11027.7	−0.571995	−0.285998	+	0.958230i	$0.592325\pi$
$720$	0	0
$721$	3146.13	0.162508
$722$	−20820.2	−1.07320
$723$	−33082.3	−1.70172
$724$	−7034.15	−0.361080
$725$	0	0
$726$	−31332.5	−1.60173
$727$	−1650.84	−0.0842178	−0.0421089	−	0.999113i	$-0.513408\pi$
$727$	−1650.84	−0.0842178	−0.0421089	+	0.999113i	$0.513408\pi$
$728$	−5710.24	−0.290708
$729$	−14240.8	−0.723506
$730$	0	0
$731$	−3928.27	−0.198758
$732$	−656.332	−0.0331403
$733$	28314.8	1.42678	0.713391	−	0.700767i	$-0.247159\pi$
$733$	28314.8	1.42678	0.713391	+	0.700767i	$0.247159\pi$
$734$	−44697.4	−2.24770
$735$	0	0
$736$	16451.7	0.823935
$737$	−9.65204	−0.000482412 0
$738$	14902.8	0.743332
$739$	−28963.4	−1.44172	−0.720862	−	0.693078i	$-0.756254\pi$
$739$	−28963.4	−1.44172	−0.720862	+	0.693078i	$0.756254\pi$
$740$	0	0
$741$	5958.76	0.295413
$742$	−19026.6	−0.941359
$743$	15510.4	0.765844	0.382922	−	0.923781i	$-0.374918\pi$
$743$	15510.4	0.765844	0.382922	+	0.923781i	$0.374918\pi$
$744$	22749.6	1.12102
$745$	0	0
$746$	39889.0	1.95769
$747$	−7005.48	−0.343129
$748$	−163.080	−0.00797165
$749$	16216.1	0.791087
$750$	0	0
$751$	−2901.63	−0.140988	−0.0704941	−	0.997512i	$-0.522458\pi$
$751$	−2901.63	−0.140988	−0.0704941	+	0.997512i	$0.522458\pi$
$752$	−36190.4	−1.75496
$753$	43363.6	2.09862
$754$	−33053.9	−1.59649
$755$	0	0
$756$	737.666	0.0354876
$757$	−9260.00	−0.444598	−0.222299	−	0.974979i	$-0.571356\pi$
$757$	−9260.00	−0.444598	−0.222299	+	0.974979i	$0.571356\pi$
$758$	−33759.2	−1.61766
$759$	−542.377	−0.0259381
$760$	0	0
$761$	−6418.29	−0.305733	−0.152866	−	0.988247i	$-0.548850\pi$
$761$	−6418.29	−0.305733	−0.152866	+	0.988247i	$0.548850\pi$
$762$	44902.1	2.13469
$763$	5518.50	0.261839
$764$	−6474.50	−0.306596
$765$	0	0
$766$	−44773.9	−2.11194
$767$	−14539.8	−0.684489
$768$	28610.2	1.34425
$769$	5335.88	0.250217	0.125108	−	0.992143i	$-0.460072\pi$
$769$	5335.88	0.250217	0.125108	+	0.992143i	$0.460072\pi$
$770$	0	0
$771$	−4848.11	−0.226460
$772$	−3897.09	−0.181683
$773$	−20062.9	−0.933520	−0.466760	−	0.884384i	$-0.654579\pi$
$773$	−20062.9	−0.933520	−0.466760	+	0.884384i	$0.654579\pi$
$774$	3344.81	0.155332
$775$	0	0
$776$	−4305.27	−0.199162
$777$	25416.1	1.17348
$778$	−22046.8	−1.01596
$779$	−4604.26	−0.211765
$780$	0	0
$781$	−131.189	−0.00601064
$782$	38673.4	1.76849
$783$	−7169.04	−0.327204
$784$	19433.2	0.885257
$785$	0	0
$786$	−36170.1	−1.64140
$787$	−17182.2	−0.778248	−0.389124	−	0.921185i	$-0.627222\pi$
$787$	−17182.2	−0.778248	−0.389124	+	0.921185i	$0.627222\pi$
$788$	14334.9	0.648045
$789$	−11877.1	−0.535914
$790$	0	0
$791$	−646.672	−0.0290683
$792$	−233.133	−0.0104596
$793$	1079.79	0.0483535
$794$	27538.3	1.23085
$795$	0	0
$796$	−6310.99	−0.281014
$797$	3342.90	0.148572	0.0742859	−	0.997237i	$-0.476332\pi$
$797$	3342.90	0.148572	0.0742859	+	0.997237i	$0.476332\pi$
$798$	5571.17	0.247140
$799$	−41865.0	−1.85366
$800$	0	0
$801$	19858.4	0.875981
$802$	9822.90	0.432492
$803$	−616.348	−0.0270865
$804$	−342.545	−0.0150257
$805$	0	0
$806$	22292.3	0.974210
$807$	−1861.27	−0.0811892
$808$	19643.1	0.855248
$809$	−10782.5	−0.468596	−0.234298	−	0.972165i	$-0.575279\pi$
$809$	−10782.5	−0.468596	−0.234298	+	0.972165i	$0.575279\pi$
$810$	0	0
$811$	−22440.1	−0.971612	−0.485806	−	0.874067i	$-0.661474\pi$
$811$	−22440.1	−0.971612	−0.485806	+	0.874067i	$0.661474\pi$
$812$	−8400.24	−0.363043
$813$	32821.2	1.41586
$814$	−720.024	−0.0310035
$815$	0	0
$816$	51252.7	2.19878
$817$	−1033.39	−0.0442519
$818$	−32984.1	−1.40985
$819$	8063.92	0.344049
$820$	0	0
$821$	−10938.7	−0.464996	−0.232498	−	0.972597i	$-0.574690\pi$
$821$	−10938.7	−0.464996	−0.232498	+	0.972597i	$0.574690\pi$
$822$	39920.8	1.69392
$823$	37928.5	1.60645	0.803223	−	0.595678i	$-0.203117\pi$
$823$	37928.5	1.60645	0.803223	+	0.595678i	$0.203117\pi$
$824$	5310.63	0.224520
$825$	0	0
$826$	−13594.1	−0.572637
$827$	−36038.1	−1.51532	−0.757660	−	0.652650i	$-0.773657\pi$
$827$	−36038.1	−1.51532	−0.757660	+	0.652650i	$0.773657\pi$
$828$	−8950.78	−0.375678
$829$	29221.5	1.22425	0.612127	−	0.790760i	$-0.290314\pi$
$829$	29221.5	1.22425	0.612127	+	0.790760i	$0.290314\pi$
$830$	0	0
$831$	−36685.0	−1.53139
$832$	−7148.82	−0.297886
$833$	22480.3	0.935048
$834$	22312.6	0.926404
$835$	0	0
$836$	−42.9006	−0.00177482
$837$	4834.97	0.199667
$838$	17506.5	0.721660
$839$	−6285.44	−0.258638	−0.129319	−	0.991603i	$-0.541279\pi$
$839$	−6285.44	−0.258638	−0.129319	+	0.991603i	$0.541279\pi$
$840$	0	0
$841$	57249.1	2.34733
$842$	−5530.48	−0.226357
$843$	−37478.8	−1.53125
$844$	16616.5	0.677682
$845$	0	0
$846$	35646.9	1.44866
$847$	13100.2	0.531438
$848$	−46046.3	−1.86466
$849$	35721.8	1.44401
$850$	0	0
$851$	46412.8	1.86958
$852$	−4655.81	−0.187213
$853$	35129.3	1.41009	0.705044	−	0.709164i	$-0.250927\pi$
$853$	35129.3	1.41009	0.705044	+	0.709164i	$0.250927\pi$
$854$	1009.55	0.0404521
$855$	0	0
$856$	27372.6	1.09296
$857$	−32983.7	−1.31470	−0.657352	−	0.753584i	$-0.728324\pi$
$857$	−32983.7	−1.31470	−0.657352	+	0.753584i	$0.728324\pi$
$858$	−491.274	−0.0195476
$859$	−35152.9	−1.39628	−0.698139	−	0.715962i	$-0.745988\pi$
$859$	−35152.9	−1.39628	−0.698139	+	0.715962i	$0.745988\pi$
$860$	0	0
$861$	−13399.5	−0.530377
$862$	−34301.4	−1.35535
$863$	−24925.6	−0.983173	−0.491587	−	0.870829i	$-0.663583\pi$
$863$	−24925.6	−0.983173	−0.491587	+	0.870829i	$0.663583\pi$
$864$	3231.99	0.127262
$865$	0	0
$866$	−9838.48	−0.386057
$867$	24386.7	0.955266
$868$	5665.31	0.221536
$869$	266.272	0.0103943
$870$	0	0
$871$	563.549	0.0219232
$872$	9315.17	0.361756
$873$	6079.84	0.235706
$874$	10173.6	0.393739
$875$	0	0
$876$	−21873.8	−0.843661
$877$	−2057.63	−0.0792261	−0.0396131	−	0.999215i	$-0.512613\pi$
$877$	−2057.63	−0.0792261	−0.0396131	+	0.999215i	$0.512613\pi$
$878$	−30575.2	−1.17524
$879$	−62805.1	−2.40997
$880$	0	0
$881$	17912.5	0.685004	0.342502	−	0.939517i	$-0.388726\pi$
$881$	17912.5	0.685004	0.342502	+	0.939517i	$0.388726\pi$
$882$	−19141.3	−0.730750
$883$	27215.2	1.03722	0.518610	−	0.855011i	$-0.326450\pi$
$883$	27215.2	1.03722	0.518610	+	0.855011i	$0.326450\pi$
$884$	9521.67	0.362272
$885$	0	0
$886$	33528.2	1.27133
$887$	−25313.0	−0.958206	−0.479103	−	0.877759i	$-0.659038\pi$
$887$	−25313.0	−0.958206	−0.479103	+	0.877759i	$0.659038\pi$
$888$	42902.1	1.62128
$889$	−18773.7	−0.708267
$890$	0	0
$891$	−485.327	−0.0182481
$892$	5105.76	0.191652
$893$	−11013.2	−0.412703
$894$	72621.0	2.71679
$895$	0	0
$896$	−16829.1	−0.627477
$897$	31667.5	1.17876
$898$	47683.3	1.77195
$899$	−55058.6	−2.04261
$900$	0	0
$901$	−53266.3	−1.96954
$902$	379.601	0.0140126
$903$	−3007.42	−0.110831
$904$	−1091.58	−0.0401607
$905$	0	0
$906$	−55260.5	−2.02639
$907$	−45998.9	−1.68398	−0.841989	−	0.539495i	$-0.818615\pi$
$907$	−45998.9	−1.68398	−0.841989	+	0.539495i	$0.818615\pi$
$908$	−1037.75	−0.0379282
$909$	−27739.7	−1.01217
$910$	0	0
$911$	−46592.7	−1.69449	−0.847247	−	0.531199i	$-0.821742\pi$
$911$	−46592.7	−1.69449	−0.847247	+	0.531199i	$0.821742\pi$
$912$	13482.8	0.489539
$913$	−178.443	−0.00646833
$914$	33250.9	1.20333
$915$	0	0
$916$	2130.72	0.0768571
$917$	15122.8	0.544601
$918$	7597.54	0.273155
$919$	33168.1	1.19055	0.595274	−	0.803523i	$-0.297043\pi$
$919$	33168.1	1.19055	0.595274	+	0.803523i	$0.297043\pi$
$920$	0	0
$921$	−46639.5	−1.66865
$922$	−413.615	−0.0147741
$923$	7659.66	0.273154
$924$	−124.851	−0.00444513
$925$	0	0
$926$	−51173.2	−1.81604
$927$	−7499.60	−0.265716
$928$	−36804.6	−1.30191
$929$	19909.9	0.703148	0.351574	−	0.936160i	$-0.385647\pi$
$929$	19909.9	0.703148	0.351574	+	0.936160i	$0.385647\pi$
$930$	0	0
$931$	5913.78	0.208181
$932$	19530.0	0.686401
$933$	8882.29	0.311675
$934$	39823.2	1.39514
$935$	0	0
$936$	13611.8	0.475338
$937$	−26262.2	−0.915634	−0.457817	−	0.889046i	$-0.651369\pi$
$937$	−26262.2	−0.915634	−0.457817	+	0.889046i	$0.651369\pi$
$938$	526.893	0.0183408
$939$	21091.0	0.732991
$940$	0	0
$941$	42227.8	1.46290	0.731449	−	0.681896i	$-0.238845\pi$
$941$	42227.8	1.46290	0.731449	+	0.681896i	$0.238845\pi$
$942$	−37268.3	−1.28903
$943$	−24469.1	−0.844988
$944$	−32899.0	−1.13429
$945$	0	0
$946$	85.1986	0.00292817
$947$	35227.0	1.20879	0.604394	−	0.796685i	$-0.293415\pi$
$947$	35227.0	1.20879	0.604394	+	0.796685i	$0.293415\pi$
$948$	9449.83	0.323751
$949$	35986.4	1.23095
$950$	0	0
$951$	−7489.98	−0.255393
$952$	−14946.4	−0.508839
$953$	−49209.9	−1.67268	−0.836340	−	0.548211i	$-0.815309\pi$
$953$	−49209.9	−1.67268	−0.836340	+	0.548211i	$0.815309\pi$
$954$	45354.8	1.53922
$955$	0	0
$956$	−7649.06	−0.258774
$957$	1213.37	0.0409851
$958$	20687.4	0.697683
$959$	−16691.0	−0.562024
$960$	0	0
$961$	7341.79	0.246443
$962$	42039.7	1.40895
$963$	−38655.3	−1.29351
$964$	−13906.4	−0.464623
$965$	0	0
$966$	29607.7	0.986140
$967$	−13452.5	−0.447366	−0.223683	−	0.974662i	$-0.571808\pi$
$967$	−13452.5	−0.447366	−0.223683	+	0.974662i	$0.571808\pi$
$968$	22113.0	0.734234
$969$	15596.9	0.517074
$970$	0	0
$971$	37322.8	1.23352	0.616758	−	0.787152i	$-0.288446\pi$
$971$	37322.8	1.23352	0.616758	+	0.787152i	$0.288446\pi$
$972$	−15200.9	−0.501614
$973$	−9328.95	−0.307371
$974$	−3063.24	−0.100773
$975$	0	0
$976$	2443.21	0.0801285
$977$	45153.4	1.47859	0.739297	−	0.673380i	$-0.235158\pi$
$977$	45153.4	1.47859	0.739297	+	0.673380i	$0.235158\pi$
$978$	19329.3	0.631987
$979$	505.829	0.0165132
$980$	0	0
$981$	−13154.8	−0.428134
$982$	−23348.2	−0.758729
$983$	15802.7	0.512745	0.256372	−	0.966578i	$-0.417473\pi$
$983$	15802.7	0.512745	0.256372	+	0.966578i	$0.417473\pi$
$984$	−22618.2	−0.732767
$985$	0	0
$986$	−86517.6	−2.79440
$987$	−32051.1	−1.03364
$988$	2504.82	0.0806568
$989$	−5491.90	−0.176575
$990$	0	0
$991$	27570.0	0.883744	0.441872	−	0.897078i	$-0.354315\pi$
$991$	27570.0	0.883744	0.441872	+	0.897078i	$0.354315\pi$
$992$	24821.9	0.794451
$993$	−20472.1	−0.654241
$994$	7161.43	0.228518
$995$	0	0
$996$	−6332.82	−0.201469
$997$	14969.8	0.475526	0.237763	−	0.971323i	$-0.423586\pi$
$997$	14969.8	0.475526	0.237763	+	0.971323i	$0.423586\pi$
$998$	−13197.7	−0.418605
$999$	9117.97	0.288768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.4.a.b.1.6		6
5.4	even	2		43.4.a.b.1.1	✓	6
15.14	odd	2		387.4.a.h.1.6		6
20.19	odd	2		688.4.a.i.1.6		6
35.34	odd	2		2107.4.a.c.1.1		6
215.214	odd	2		1849.4.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.a.b.1.1	✓	6	5.4	even	2
387.4.a.h.1.6		6	15.14	odd	2
688.4.a.i.1.6		6	20.19	odd	2
1075.4.a.b.1.6		6	1.1	even	1	trivial
1849.4.a.c.1.6		6	215.214	odd	2
2107.4.a.c.1.1		6	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} +O(q^{10})\)	\(q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} +0.597776 q^{11} +21.2147 q^{12} -34.9021 q^{13} -32.6318 q^{14} -78.9723 q^{16} -91.3552 q^{17} +77.7863 q^{18} -24.0324 q^{19} -69.9399 q^{21} +1.98136 q^{22} -127.719 q^{23} -118.058 q^{24} -115.685 q^{26} -25.0908 q^{27} -29.3999 q^{28} +285.724 q^{29} -192.699 q^{31} -128.812 q^{32} +4.24666 q^{33} -302.802 q^{34} +70.0821 q^{36} -363.399 q^{37} -79.6565 q^{38} -247.948 q^{39} +191.586 q^{41} -231.820 q^{42} +43.0000 q^{43} +1.78512 q^{44} -423.330 q^{46} +458.267 q^{47} -561.027 q^{48} -246.076 q^{49} -648.995 q^{51} -104.227 q^{52} +583.068 q^{53} -83.1648 q^{54} +163.607 q^{56} -170.728 q^{57} +947.047 q^{58} +416.589 q^{59} -30.9376 q^{61} -638.710 q^{62} -231.044 q^{63} +204.825 q^{64} +14.0758 q^{66} -16.1466 q^{67} -272.811 q^{68} -907.324 q^{69} -219.461 q^{71} -390.000 q^{72} -1031.07 q^{73} -1204.50 q^{74} -71.7670 q^{76} -5.88512 q^{77} -821.836 q^{78} +445.438 q^{79} -811.887 q^{81} +635.022 q^{82} -298.511 q^{83} -208.859 q^{84} +142.526 q^{86} +2029.81 q^{87} -9.93402 q^{88} +846.185 q^{89} +343.612 q^{91} -381.402 q^{92} -1368.95 q^{93} +1518.95 q^{94} -915.091 q^{96} +259.068 q^{97} -815.631 q^{98} +14.0287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9	\( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} - 28 q^{11} + 157 q^{12} - 56 q^{13} - 184 q^{14} - 54 q^{16} - 19 q^{17} + 81 q^{18} - 75 q^{19} - 18 q^{21} + 504 q^{22} - 131 q^{23} - 567 q^{24} + 44 q^{26} - 238 q^{27} + 404 q^{28} + 515 q^{29} + 237 q^{31} - 558 q^{32} - 540 q^{33} - 107 q^{34} + 73 q^{36} - 269 q^{37} - 527 q^{38} + 290 q^{39} + 471 q^{41} - 362 q^{42} + 258 q^{43} - 428 q^{44} - 67 q^{46} - 415 q^{47} + 989 q^{48} + 350 q^{49} - 1241 q^{51} + 8 q^{52} - 450 q^{53} + 402 q^{54} - 780 q^{56} + 1000 q^{57} + 1055 q^{58} + 356 q^{59} - 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 156 q^{66} + 632 q^{67} - 571 q^{68} - 1130 q^{69} - 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 1005 q^{76} - 2660 q^{77} - 2222 q^{78} - 1613 q^{79} - 102 q^{81} - 1673 q^{82} + 682 q^{83} + 3758 q^{84} - 258 q^{86} - 449 q^{87} + 608 q^{88} + 3378 q^{89} - 3900 q^{91} - 3491 q^{92} - 1879 q^{93} + 3197 q^{94} - 591 q^{96} + 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 7 * q^3 + 22 * q^4 - 3 * q^6 - 8 * q^7 - 54 * q^8 + 81 * q^9 - 28 * q^11 + 157 * q^12 - 56 * q^13 - 184 * q^14 - 54 * q^16 - 19 * q^17 + 81 * q^18 - 75 * q^19 - 18 * q^21 + 504 * q^22 - 131 * q^23 - 567 * q^24 + 44 * q^26 - 238 * q^27 + 404 * q^28 + 515 * q^29 + 237 * q^31 - 558 * q^32 - 540 * q^33 - 107 * q^34 + 73 * q^36 - 269 * q^37 - 527 * q^38 + 290 * q^39 + 471 * q^41 - 362 * q^42 + 258 * q^43 - 428 * q^44 - 67 * q^46 - 415 * q^47 + 989 * q^48 + 350 * q^49 - 1241 * q^51 + 8 * q^52 - 450 * q^53 + 402 * q^54 - 780 * q^56 + 1000 * q^57 + 1055 * q^58 + 356 * q^59 - 1328 * q^61 - 1603 * q^62 + 2290 * q^63 + 466 * q^64 + 156 * q^66 + 632 * q^67 - 571 * q^68 - 1130 * q^69 - 144 * q^71 - 567 * q^72 - 864 * q^73 + 1207 * q^74 + 1005 * q^76 - 2660 * q^77 - 2222 * q^78 - 1613 * q^79 - 102 * q^81 - 1673 * q^82 + 682 * q^83 + 3758 * q^84 - 258 * q^86 - 449 * q^87 + 608 * q^88 + 3378 * q^89 - 3900 * q^91 - 3491 * q^92 - 1879 * q^93 + 3197 * q^94 - 591 * q^96 + 55 * q^97 - 2398 * q^98 - 1612 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more