LMFDB - Embedded newform 1075.6.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,6,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, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1075.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 6 $
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:	$172.412606299$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-8.36207 q^{2} -24.1411 q^{3} +37.9243 q^{4} +201.870 q^{6} +224.337 q^{7} -49.5390 q^{8} +339.794 q^{9} +O(q^{10})$	\(q-8.36207 q^{2} -24.1411 q^{3} +37.9243 q^{4} +201.870 q^{6} +224.337 q^{7} -49.5390 q^{8} +339.794 q^{9} +623.217 q^{11} -915.534 q^{12} -843.925 q^{13} -1875.92 q^{14} -799.327 q^{16} +831.902 q^{17} -2841.38 q^{18} +1329.81 q^{19} -5415.74 q^{21} -5211.39 q^{22} -2417.03 q^{23} +1195.93 q^{24} +7056.96 q^{26} -2336.71 q^{27} +8507.80 q^{28} +3.12463 q^{29} +8048.60 q^{31} +8269.28 q^{32} -15045.2 q^{33} -6956.43 q^{34} +12886.4 q^{36} +11303.6 q^{37} -11120.0 q^{38} +20373.3 q^{39} +20350.8 q^{41} +45286.8 q^{42} -1849.00 q^{43} +23635.0 q^{44} +20211.4 q^{46} -296.033 q^{47} +19296.7 q^{48} +33519.9 q^{49} -20083.1 q^{51} -32005.2 q^{52} -17668.3 q^{53} +19539.7 q^{54} -11113.4 q^{56} -32103.1 q^{57} -26.1284 q^{58} -10938.0 q^{59} +12062.3 q^{61} -67303.0 q^{62} +76228.2 q^{63} -43569.9 q^{64} +125809. q^{66} +58445.7 q^{67} +31549.3 q^{68} +58349.8 q^{69} +68615.5 q^{71} -16833.1 q^{72} -45157.8 q^{73} -94521.5 q^{74} +50432.0 q^{76} +139810. q^{77} -170363. q^{78} +80029.7 q^{79} -26159.1 q^{81} -170175. q^{82} +83932.9 q^{83} -205388. q^{84} +15461.5 q^{86} -75.4321 q^{87} -30873.6 q^{88} -95051.8 q^{89} -189323. q^{91} -91664.0 q^{92} -194302. q^{93} +2475.45 q^{94} -199630. q^{96} -165262. q^{97} -280296. q^{98} +211765. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) $ 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * 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 $

$2$	−8.36207	−1.47822	−0.739110	−	0.673585i	$-0.764754\pi$
$2$	−8.36207	−1.47822	−0.739110	+	0.673585i	$0.764754\pi$
$3$	−24.1411	−1.54865	−0.774327	−	0.632786i	$-0.781911\pi$
$3$	−24.1411	−1.54865	−0.774327	+	0.632786i	$0.781911\pi$
$4$	37.9243	1.18513
$5$	0	0
$5$	0	0
$6$	201.870	2.28925
$7$	224.337	1.73043	0.865217	−	0.501397i	$-0.167181\pi$
$7$	224.337	1.73043	0.865217	+	0.501397i	$0.167181\pi$
$8$	−49.5390	−0.273667
$9$	339.794	1.39833
$10$	0	0
$11$	623.217	1.55295	0.776475	−	0.630147i	$-0.217006\pi$
$11$	623.217	1.55295	0.776475	+	0.630147i	$0.217006\pi$
$12$	−915.534	−1.83536
$13$	−843.925	−1.38499	−0.692493	−	0.721425i	$-0.743488\pi$
$13$	−843.925	−1.38499	−0.692493	+	0.721425i	$0.743488\pi$
$14$	−1875.92	−2.55796
$15$	0	0
$16$	−799.327	−0.780593
$17$	831.902	0.698152	0.349076	−	0.937094i	$-0.386496\pi$
$17$	831.902	0.698152	0.349076	+	0.937094i	$0.386496\pi$
$18$	−2841.38	−2.06704
$19$	1329.81	0.845094	0.422547	−	0.906341i	$-0.361136\pi$
$19$	1329.81	0.845094	0.422547	+	0.906341i	$0.361136\pi$
$20$	0	0
$21$	−5415.74	−2.67984
$22$	−5211.39	−2.29560
$23$	−2417.03	−0.952713	−0.476357	−	0.879252i	$-0.658043\pi$
$23$	−2417.03	−0.952713	−0.476357	+	0.879252i	$0.658043\pi$
$24$	1195.93	0.423816
$25$	0	0
$26$	7056.96	2.04731
$27$	−2336.71	−0.616873
$28$	8507.80	2.05079
$29$	3.12463	0.000689928 0	0.000344964	−	1.00000i	$-0.499890\pi$
$29$	3.12463	0.000689928 0	0.000344964		1.00000i	$0.499890\pi$
$30$	0	0
$31$	8048.60	1.50424	0.752118	−	0.659028i	$-0.229032\pi$
$31$	8048.60	1.50424	0.752118	+	0.659028i	$0.229032\pi$
$32$	8269.28	1.42755
$33$	−15045.2	−2.40498
$34$	−6956.43	−1.03202
$35$	0	0
$36$	12886.4	1.65720
$37$	11303.6	1.35741	0.678707	−	0.734409i	$-0.262541\pi$
$37$	11303.6	1.35741	0.678707	+	0.734409i	$0.262541\pi$
$38$	−11120.0	−1.24923
$39$	20373.3	2.14486
$40$	0	0
$41$	20350.8	1.89070	0.945350	−	0.326058i	$-0.105720\pi$
$41$	20350.8	1.89070	0.945350	+	0.326058i	$0.105720\pi$
$42$	45286.8	3.96140
$43$	−1849.00	−0.152499
$43$	−1849.00	−0.152499
$44$	23635.0	1.84045
$45$	0	0
$46$	20211.4	1.40832
$47$	−296.033	−0.0195477	−0.00977384	−	0.999952i	$-0.503111\pi$
$47$	−296.033	−0.0195477	−0.00977384	+	0.999952i	$0.503111\pi$
$48$	19296.7	1.20887
$49$	33519.9	1.99440
$50$	0	0
$51$	−20083.1	−1.08120
$52$	−32005.2	−1.64139
$53$	−17668.3	−0.863985	−0.431992	−	0.901877i	$-0.642189\pi$
$53$	−17668.3	−0.863985	−0.431992	+	0.901877i	$0.642189\pi$
$54$	19539.7	0.911873
$55$	0	0
$56$	−11113.4	−0.473563
$57$	−32103.1	−1.30876
$58$	−26.1284	−0.00101987
$59$	−10938.0	−0.409080	−0.204540	−	0.978858i	$-0.565570\pi$
$59$	−10938.0	−0.409080	−0.204540	+	0.978858i	$0.565570\pi$
$60$	0	0
$61$	12062.3	0.415055	0.207528	−	0.978229i	$-0.433458\pi$
$61$	12062.3	0.415055	0.207528	+	0.978229i	$0.433458\pi$
$62$	−67303.0	−2.22359
$63$	76228.2	2.41972
$64$	−43569.9	−1.32965
$65$	0	0
$66$	125809.	3.55509
$67$	58445.7	1.59062	0.795308	−	0.606205i	$-0.207309\pi$
$67$	58445.7	1.59062	0.795308	+	0.606205i	$0.207309\pi$
$68$	31549.3	0.827403
$69$	58349.8	1.47542
$70$	0	0
$71$	68615.5	1.61539	0.807693	−	0.589603i	$-0.200716\pi$
$71$	68615.5	1.61539	0.807693	+	0.589603i	$0.200716\pi$
$72$	−16833.1	−0.382676
$73$	−45157.8	−0.991802	−0.495901	−	0.868379i	$-0.665162\pi$
$73$	−45157.8	−0.991802	−0.495901	+	0.868379i	$0.665162\pi$
$74$	−94521.5	−2.00656
$75$	0	0
$76$	50432.0	1.00155
$77$	139810.	2.68728
$78$	−170363.	−3.17058
$79$	80029.7	1.44272	0.721362	−	0.692558i	$-0.243516\pi$
$79$	80029.7	1.44272	0.721362	+	0.692558i	$0.243516\pi$
$80$	0	0
$81$	−26159.1	−0.443006
$82$	−170175.	−2.79487
$83$	83932.9	1.33732	0.668662	−	0.743566i	$-0.266867\pi$
$83$	83932.9	1.33732	0.668662	+	0.743566i	$0.266867\pi$
$84$	−205388.	−3.17597
$85$	0	0
$86$	15461.5	0.225426
$87$	−75.4321	−0.00106846
$88$	−30873.6	−0.424992
$89$	−95051.8	−1.27199	−0.635997	−	0.771691i	$-0.719411\pi$
$89$	−95051.8	−1.27199	−0.635997	+	0.771691i	$0.719411\pi$
$90$	0	0
$91$	−189323.	−2.39663
$92$	−91664.0	−1.12909
$93$	−194302.	−2.32954
$94$	2475.45	0.0288958
$95$	0	0
$96$	−199630.	−2.21079
$97$	−165262.	−1.78338	−0.891688	−	0.452650i	$-0.850479\pi$
$97$	−165262.	−1.78338	−0.891688	+	0.452650i	$0.850479\pi$
$98$	−280296.	−2.94816
$99$	211765.	2.17154
$100$	0	0
$101$	130012.	1.26818	0.634088	−	0.773261i	$-0.281376\pi$
$101$	130012.	1.26818	0.634088	+	0.773261i	$0.281376\pi$
$102$	167936.	1.59824
$103$	130355.	1.21070	0.605349	−	0.795960i	$-0.293033\pi$
$103$	130355.	1.21070	0.605349	+	0.795960i	$0.293033\pi$
$104$	41807.2	0.379025
$105$	0	0
$106$	147744.	1.27716
$107$	40647.4	0.343221	0.171610	−	0.985165i	$-0.445103\pi$
$107$	40647.4	0.343221	0.171610	+	0.985165i	$0.445103\pi$
$108$	−88618.0	−0.731076
$109$	−32224.2	−0.259786	−0.129893	−	0.991528i	$-0.541463\pi$
$109$	−32224.2	−0.259786	−0.129893	+	0.991528i	$0.541463\pi$
$110$	0	0
$111$	−272882.	−2.10216
$112$	−179318.	−1.35076
$113$	35500.0	0.261537	0.130768	−	0.991413i	$-0.458256\pi$
$113$	35500.0	0.261537	0.130768	+	0.991413i	$0.458256\pi$
$114$	268448.	1.93463
$115$	0	0
$116$	118.499	0.000817656 0
$117$	−286760.	−1.93667
$118$	91464.3	0.604709
$119$	186626.	1.20811
$120$	0	0
$121$	227349.	1.41166
$122$	−100866.	−0.613543
$123$	−491292.	−2.92804
$124$	305237.	1.78272
$125$	0	0
$126$	−637426.	−3.57687
$127$	−561.292	−0.00308802	−0.00154401	−	0.999999i	$-0.500491\pi$
$127$	−561.292	−0.00308802	−0.00154401	+	0.999999i	$0.500491\pi$
$128$	99717.3	0.537954
$129$	44636.9	0.236167
$130$	0	0
$131$	146812.	0.747452	0.373726	−	0.927539i	$-0.378080\pi$
$131$	146812.	0.747452	0.373726	+	0.927539i	$0.378080\pi$
$132$	−570577.	−2.85022
$133$	298325.	1.46238
$134$	−488727.	−2.35128
$135$	0	0
$136$	−41211.6	−0.191061
$137$	−222968.	−1.01494	−0.507471	−	0.861669i	$-0.669419\pi$
$137$	−222968.	−1.01494	−0.507471	+	0.861669i	$0.669419\pi$
$138$	−487925.	−2.18100
$139$	313611.	1.37675	0.688373	−	0.725357i	$-0.258325\pi$
$139$	313611.	1.37675	0.688373	+	0.725357i	$0.258325\pi$
$140$	0	0
$141$	7146.56	0.0302726
$142$	−573768.	−2.38790
$143$	−525948.	−2.15082
$144$	−271606.	−1.09153
$145$	0	0
$146$	377612.	1.46610
$147$	−809209.	−3.08864
$148$	428681.	1.60872
$149$	−80015.7	−0.295263	−0.147632	−	0.989042i	$-0.547165\pi$
$149$	−80015.7	−0.295263	−0.147632	+	0.989042i	$0.547165\pi$
$150$	0	0
$151$	308534.	1.10119	0.550593	−	0.834774i	$-0.314402\pi$
$151$	308534.	1.10119	0.550593	+	0.834774i	$0.314402\pi$
$152$	−65877.4	−0.231274
$153$	282675.	0.976246
$154$	−1.16911e6	−3.97239
$155$	0	0
$156$	772642.	2.54195
$157$	178212.	0.577016	0.288508	−	0.957478i	$-0.406841\pi$
$157$	178212.	0.577016	0.288508	+	0.957478i	$0.406841\pi$
$158$	−669214.	−2.13266
$159$	426534.	1.33801
$160$	0	0
$161$	−542228.	−1.64861
$162$	218744.	0.654860
$163$	422016.	1.24411	0.622057	−	0.782972i	$-0.286297\pi$
$163$	422016.	1.24411	0.622057	+	0.782972i	$0.286297\pi$
$164$	771790.	2.24073
$165$	0	0
$166$	−701853.	−1.97686
$167$	87306.1	0.242244	0.121122	−	0.992638i	$-0.461351\pi$
$167$	87306.1	0.242244	0.121122	+	0.992638i	$0.461351\pi$
$168$	268290.	0.733385
$169$	340916.	0.918186
$170$	0	0
$171$	451861.	1.18172
$172$	−70121.9	−0.180731
$173$	137164.	0.348436	0.174218	−	0.984707i	$-0.444260\pi$
$173$	137164.	0.348436	0.174218	+	0.984707i	$0.444260\pi$
$174$	630.769	0.00157942
$175$	0	0
$176$	−498154.	−1.21222
$177$	264056.	0.633523
$178$	794830.	1.88029
$179$	−193464.	−0.451301	−0.225651	−	0.974208i	$-0.572451\pi$
$179$	−193464.	−0.451301	−0.225651	+	0.974208i	$0.572451\pi$
$180$	0	0
$181$	−570635.	−1.29468	−0.647340	−	0.762202i	$-0.724119\pi$
$181$	−570635.	−1.29468	−0.647340	+	0.762202i	$0.724119\pi$
$182$	1.58313e6	3.54274
$183$	−291198.	−0.642777
$184$	119737.	0.260726
$185$	0	0
$186$	1.62477e6	3.44357
$187$	518456.	1.08420
$188$	−11226.8	−0.0231666
$189$	−524210.	−1.06746
$190$	0	0
$191$	−367339.	−0.728591	−0.364296	−	0.931283i	$-0.618690\pi$
$191$	−367339.	−0.728591	−0.364296	+	0.931283i	$0.618690\pi$
$192$	1.05183e6	2.05916
$193$	−97686.8	−0.188774	−0.0943871	−	0.995536i	$-0.530089\pi$
$193$	−97686.8	−0.188774	−0.0943871	+	0.995536i	$0.530089\pi$
$194$	1.38193e6	2.63622
$195$	0	0
$196$	1.27122e6	2.36363
$197$	−129398.	−0.237553	−0.118777	−	0.992921i	$-0.537897\pi$
$197$	−129398.	−0.237553	−0.118777	+	0.992921i	$0.537897\pi$
$198$	−1.77080e6	−3.21001
$199$	−493673.	−0.883704	−0.441852	−	0.897088i	$-0.645678\pi$
$199$	−493673.	−0.883704	−0.441852	+	0.897088i	$0.645678\pi$
$200$	0	0
$201$	−1.41094e6	−2.46331
$202$	−1.08717e6	−1.87464
$203$	700.969	0.00119388
$204$	−761635.	−1.28136
$205$	0	0
$206$	−1.09004e6	−1.78968
$207$	−821291.	−1.33221
$208$	674572.	1.08111
$209$	828759.	1.31239
$210$	0	0
$211$	−536229.	−0.829171	−0.414586	−	0.910010i	$-0.636073\pi$
$211$	−536229.	−0.829171	−0.414586	+	0.910010i	$0.636073\pi$
$212$	−670059.	−1.02394
$213$	−1.65646e6	−2.50167
$214$	−339897.	−0.507356
$215$	0	0
$216$	115758.	0.168818
$217$	1.80560e6	2.60298
$218$	269461.	0.384021
$219$	1.09016e6	1.53596
$220$	0	0
$221$	−702063.	−0.966931
$222$	2.28186e6	3.10746
$223$	−466931.	−0.628768	−0.314384	−	0.949296i	$-0.601798\pi$
$223$	−466931.	−0.628768	−0.314384	+	0.949296i	$0.601798\pi$
$224$	1.85510e6	2.47029
$225$	0	0
$226$	−296854.	−0.386609
$227$	1.13007e6	1.45559	0.727795	−	0.685795i	$-0.240545\pi$
$227$	1.13007e6	1.45559	0.727795	+	0.685795i	$0.240545\pi$
$228$	−1.21748e6	−1.55105
$229$	−1.45628e6	−1.83508	−0.917542	−	0.397639i	$-0.869830\pi$
$229$	−1.45628e6	−1.83508	−0.917542	+	0.397639i	$0.869830\pi$
$230$	0	0
$231$	−3.37518e6	−4.16167
$232$	−154.791	−0.000188811 0
$233$	−156262.	−0.188566	−0.0942829	−	0.995545i	$-0.530056\pi$
$233$	−156262.	−0.188566	−0.0942829	+	0.995545i	$0.530056\pi$
$234$	2.39791e6	2.86282
$235$	0	0
$236$	−414815.	−0.484814
$237$	−1.93201e6	−2.23428
$238$	−1.56058e6	−1.78585
$239$	920680.	1.04259	0.521296	−	0.853376i	$-0.325449\pi$
$239$	920680.	1.04259	0.521296	+	0.853376i	$0.325449\pi$
$240$	0	0
$241$	−1.69368e6	−1.87840	−0.939199	−	0.343374i	$-0.888430\pi$
$241$	−1.69368e6	−1.87840	−0.939199	+	0.343374i	$0.888430\pi$
$242$	−1.90111e6	−2.08674
$243$	1.19933e6	1.30294
$244$	457454.	0.491896
$245$	0	0
$246$	4.10822e6	4.32828
$247$	−1.12226e6	−1.17044
$248$	−398720.	−0.411660
$249$	−2.02623e6	−2.07105
$250$	0	0
$251$	701178.	0.702496	0.351248	−	0.936282i	$-0.385757\pi$
$251$	701178.	0.702496	0.351248	+	0.936282i	$0.385757\pi$
$252$	2.89090e6	2.86768
$253$	−1.50633e6	−1.47952
$254$	4693.56	0.00456477
$255$	0	0
$256$	560392.	0.534432
$257$	887984.	0.838633	0.419317	−	0.907840i	$-0.362270\pi$
$257$	887984.	0.838633	0.419317	+	0.907840i	$0.362270\pi$
$258$	−373257.	−0.349107
$259$	2.53581e6	2.34892
$260$	0	0
$261$	1061.73	0.000964746 0
$262$	−1.22765e6	−1.10490
$263$	−683096.	−0.608965	−0.304482	−	0.952518i	$-0.598483\pi$
$263$	−683096.	−0.608965	−0.304482	+	0.952518i	$0.598483\pi$
$264$	745323.	0.658165
$265$	0	0
$266$	−2.49461e6	−2.16172
$267$	2.29466e6	1.96988
$268$	2.21651e6	1.88509
$269$	377900.	0.318417	0.159209	−	0.987245i	$-0.449106\pi$
$269$	377900.	0.318417	0.159209	+	0.987245i	$0.449106\pi$
$270$	0	0
$271$	−2.01049e6	−1.66295	−0.831474	−	0.555564i	$-0.812502\pi$
$271$	−2.01049e6	−1.66295	−0.831474	+	0.555564i	$0.812502\pi$
$272$	−664962.	−0.544972
$273$	4.57048e6	3.71155
$274$	1.86447e6	1.50031
$275$	0	0
$276$	2.21287e6	1.74857
$277$	288011.	0.225533	0.112766	−	0.993622i	$-0.464029\pi$
$277$	288011.	0.225533	0.112766	+	0.993622i	$0.464029\pi$
$278$	−2.62243e6	−2.03513
$279$	2.73486e6	2.10342
$280$	0	0
$281$	−521323.	−0.393859	−0.196930	−	0.980418i	$-0.563097\pi$
$281$	−521323.	−0.393859	−0.196930	+	0.980418i	$0.563097\pi$
$282$	−59760.1	−0.0447495
$283$	−839975.	−0.623448	−0.311724	−	0.950173i	$-0.600906\pi$
$283$	−839975.	−0.623448	−0.311724	+	0.950173i	$0.600906\pi$
$284$	2.60219e6	1.91445
$285$	0	0
$286$	4.39802e6	3.17938
$287$	4.56544e6	3.27173
$288$	2.80985e6	1.99619
$289$	−727796.	−0.512584
$290$	0	0
$291$	3.98960e6	2.76183
$292$	−1.71257e6	−1.17542
$293$	467350.	0.318034	0.159017	−	0.987276i	$-0.449168\pi$
$293$	467350.	0.318034	0.159017	+	0.987276i	$0.449168\pi$
$294$	6.76666e6	4.56569
$295$	0	0
$296$	−559969.	−0.371480
$297$	−1.45628e6	−0.957973
$298$	669097.	0.436464
$299$	2.03979e6	1.31949
$300$	0	0
$301$	−414798.	−0.263889
$302$	−2.57998e6	−1.62779
$303$	−3.13863e6	−1.96397
$304$	−1.06295e6	−0.659674
$305$	0	0
$306$	−2.36375e6	−1.44311
$307$	203823.	0.123426	0.0617131	−	0.998094i	$-0.480344\pi$
$307$	203823.	0.123426	0.0617131	+	0.998094i	$0.480344\pi$
$308$	5.30221e6	3.18478
$309$	−3.14693e6	−1.87495
$310$	0	0
$311$	−455828.	−0.267239	−0.133620	−	0.991033i	$-0.542660\pi$
$311$	−455828.	−0.267239	−0.133620	+	0.991033i	$0.542660\pi$
$312$	−1.00927e6	−0.586979
$313$	−328669.	−0.189626	−0.0948131	−	0.995495i	$-0.530225\pi$
$313$	−328669.	−0.189626	−0.0948131	+	0.995495i	$0.530225\pi$
$314$	−1.49022e6	−0.852956
$315$	0	0
$316$	3.03507e6	1.70982
$317$	787288.	0.440033	0.220017	−	0.975496i	$-0.429389\pi$
$317$	787288.	0.440033	0.220017	+	0.975496i	$0.429389\pi$
$318$	−3.56670e6	−1.97788
$319$	1947.32	0.00107142
$320$	0	0
$321$	−981275.	−0.531530
$322$	4.53415e6	2.43700
$323$	1.10627e6	0.590004
$324$	−992063.	−0.525021
$325$	0	0
$326$	−3.52893e6	−1.83907
$327$	777928.	0.402319
$328$	−1.00816e6	−0.517422
$329$	−66411.0	−0.0338260
$330$	0	0
$331$	168885.	0.0847269	0.0423634	−	0.999102i	$-0.486511\pi$
$331$	168885.	0.0847269	0.0423634	+	0.999102i	$0.486511\pi$
$332$	3.18309e6	1.58491
$333$	3.84089e6	1.89811
$334$	−730060.	−0.358090
$335$	0	0
$336$	4.32895e6	2.09187
$337$	−1.84716e6	−0.885994	−0.442997	−	0.896523i	$-0.646085\pi$
$337$	−1.84716e6	−0.885994	−0.442997	+	0.896523i	$0.646085\pi$
$338$	−2.85077e6	−1.35728
$339$	−857011.	−0.405030
$340$	0	0
$341$	5.01603e6	2.33600
$342$	−3.77849e6	−1.74684
$343$	3.74932e6	1.72075
$344$	91597.7	0.0417338
$345$	0	0
$346$	−1.14697e6	−0.515065
$347$	−1.03888e6	−0.463173	−0.231587	−	0.972814i	$-0.574392\pi$
$347$	−1.03888e6	−0.463173	−0.231587	+	0.972814i	$0.574392\pi$
$348$	−2860.71	−0.00126627
$349$	−4.24443e6	−1.86533	−0.932665	−	0.360744i	$-0.882523\pi$
$349$	−4.24443e6	−1.86533	−0.932665	+	0.360744i	$0.882523\pi$
$350$	0	0
$351$	1.97201e6	0.854360
$352$	5.15356e6	2.21692
$353$	3.29606e6	1.40786	0.703928	−	0.710272i	$-0.251428\pi$
$353$	3.29606e6	1.40786	0.703928	+	0.710272i	$0.251428\pi$
$354$	−2.20805e6	−0.936486
$355$	0	0
$356$	−3.60477e6	−1.50748
$357$	−4.50536e6	−1.87094
$358$	1.61776e6	0.667122
$359$	1.51208e6	0.619212	0.309606	−	0.950865i	$-0.399803\pi$
$359$	1.51208e6	0.619212	0.309606	+	0.950865i	$0.399803\pi$
$360$	0	0
$361$	−707709.	−0.285816
$362$	4.77169e6	1.91382
$363$	−5.48845e6	−2.18617
$364$	−7.17994e6	−2.84032
$365$	0	0
$366$	2.43502e6	0.950165
$367$	−1.14344e6	−0.443146	−0.221573	−	0.975144i	$-0.571119\pi$
$367$	−1.14344e6	−0.443146	−0.221573	+	0.975144i	$0.571119\pi$
$368$	1.93200e6	0.743681
$369$	6.91509e6	2.64382
$370$	0	0
$371$	−3.96366e6	−1.49507
$372$	−7.36877e6	−2.76082
$373$	4.54625e6	1.69192	0.845962	−	0.533243i	$-0.179027\pi$
$373$	4.54625e6	1.69192	0.845962	+	0.533243i	$0.179027\pi$
$374$	−4.33536e6	−1.60268
$375$	0	0
$376$	14665.2	0.00534956
$377$	−2636.95	−0.000955541 0
$378$	4.38348e6	1.57794
$379$	−2.73356e6	−0.977532	−0.488766	−	0.872415i	$-0.662553\pi$
$379$	−2.73356e6	−0.977532	−0.488766	+	0.872415i	$0.662553\pi$
$380$	0	0
$381$	13550.2	0.00478227
$382$	3.07172e6	1.07702
$383$	5.28114e6	1.83963	0.919815	−	0.392352i	$-0.128339\pi$
$383$	5.28114e6	1.83963	0.919815	+	0.392352i	$0.128339\pi$
$384$	−2.40729e6	−0.833105
$385$	0	0
$386$	816864.	0.279050
$387$	−628279.	−0.213243
$388$	−6.26743e6	−2.11354
$389$	572811.	0.191928	0.0959638	−	0.995385i	$-0.469407\pi$
$389$	572811.	0.191928	0.0959638	+	0.995385i	$0.469407\pi$
$390$	0	0
$391$	−2.01073e6	−0.665138
$392$	−1.66054e6	−0.545802
$393$	−3.54420e6	−1.15754
$394$	1.08203e6	0.351156
$395$	0	0
$396$	8.03104e6	2.57356
$397$	−4.75009e6	−1.51260	−0.756302	−	0.654222i	$-0.772996\pi$
$397$	−4.75009e6	−1.51260	−0.756302	+	0.654222i	$0.772996\pi$
$398$	4.12813e6	1.30631
$399$	−7.20189e6	−2.26472
$400$	0	0
$401$	−3.28710e6	−1.02083	−0.510413	−	0.859929i	$-0.670507\pi$
$401$	−3.28710e6	−1.02083	−0.510413	+	0.859929i	$0.670507\pi$
$402$	1.17984e7	3.64132
$403$	−6.79241e6	−2.08335
$404$	4.93060e6	1.50296
$405$	0	0
$406$	−5861.56	−0.00176481
$407$	7.04460e6	2.10800
$408$	994895.	0.295888
$409$	1.60418e6	0.474181	0.237091	−	0.971488i	$-0.423806\pi$
$409$	1.60418e6	0.474181	0.237091	+	0.971488i	$0.423806\pi$
$410$	0	0
$411$	5.38270e6	1.57179
$412$	4.94363e6	1.43484
$413$	−2.45379e6	−0.707885
$414$	6.86770e6	1.96929
$415$	0	0
$416$	−6.97865e6	−1.97714
$417$	−7.57091e6	−2.13210
$418$	−6.93015e6	−1.94000
$419$	955879.	0.265992	0.132996	−	0.991117i	$-0.457540\pi$
$419$	955879.	0.265992	0.132996	+	0.991117i	$0.457540\pi$
$420$	0	0
$421$	2.67103e6	0.734470	0.367235	−	0.930128i	$-0.380304\pi$
$421$	2.67103e6	0.734470	0.367235	+	0.930128i	$0.380304\pi$
$422$	4.48399e6	1.22570
$423$	−100590.	−0.0273341
$424$	875272.	0.236444
$425$	0	0
$426$	1.38514e7	3.69802
$427$	2.70602e6	0.718226
$428$	1.54152e6	0.406762
$429$	1.26970e7	3.33087
$430$	0	0
$431$	107690.	0.0279244	0.0139622	−	0.999903i	$-0.495556\pi$
$431$	107690.	0.0279244	0.0139622	+	0.999903i	$0.495556\pi$
$432$	1.86780e6	0.481526
$433$	−1.60432e6	−0.411218	−0.205609	−	0.978634i	$-0.565917\pi$
$433$	−1.60432e6	−0.411218	−0.205609	+	0.978634i	$0.565917\pi$
$434$	−1.50985e7	−3.84778
$435$	0	0
$436$	−1.22208e6	−0.307881
$437$	−3.21418e6	−0.805132
$438$	−9.11599e6	−2.27048
$439$	3.03140e6	0.750726	0.375363	−	0.926878i	$-0.377518\pi$
$439$	3.03140e6	0.750726	0.375363	+	0.926878i	$0.377518\pi$
$440$	0	0
$441$	1.13899e7	2.78883
$442$	5.87070e6	1.42934
$443$	315626.	0.0764124	0.0382062	−	0.999270i	$-0.487836\pi$
$443$	315626.	0.0764124	0.0382062	+	0.999270i	$0.487836\pi$
$444$	−1.03488e7	−2.49134
$445$	0	0
$446$	3.90451e6	0.929457
$447$	1.93167e6	0.457261
$448$	−9.77431e6	−2.30087
$449$	−1.01809e6	−0.238325	−0.119163	−	0.992875i	$-0.538021\pi$
$449$	−1.01809e6	−0.238325	−0.119163	+	0.992875i	$0.538021\pi$
$450$	0	0
$451$	1.26830e7	2.93616
$452$	1.34631e6	0.309956
$453$	−7.44836e6	−1.70536
$454$	−9.44969e6	−2.15168
$455$	0	0
$456$	1.59035e6	0.358164
$457$	−4.74886e6	−1.06365	−0.531826	−	0.846854i	$-0.678494\pi$
$457$	−4.74886e6	−1.06365	−0.531826	+	0.846854i	$0.678494\pi$
$458$	1.21775e7	2.71266
$459$	−1.94391e6	−0.430671
$460$	0	0
$461$	5.86019e6	1.28428	0.642140	−	0.766588i	$-0.278047\pi$
$461$	5.86019e6	1.28428	0.642140	+	0.766588i	$0.278047\pi$
$462$	2.82235e7	6.15185
$463$	−7.21977e6	−1.56520	−0.782602	−	0.622523i	$-0.786108\pi$
$463$	−7.21977e6	−1.56520	−0.782602	+	0.622523i	$0.786108\pi$
$464$	−2497.60	−0.000538553 0
$465$	0	0
$466$	1.30667e6	0.278742
$467$	1.27932e6	0.271449	0.135725	−	0.990747i	$-0.456664\pi$
$467$	1.27932e6	0.271449	0.135725	+	0.990747i	$0.456664\pi$
$468$	−1.08752e7	−2.29521
$469$	1.31115e7	2.75246
$470$	0	0
$471$	−4.30224e6	−0.893598
$472$	541858.	0.111952
$473$	−1.15233e6	−0.236823
$474$	1.61556e7	3.30276
$475$	0	0
$476$	7.07766e6	1.43177
$477$	−6.00359e6	−1.20813
$478$	−7.69879e6	−1.54118
$479$	−7.90785e6	−1.57478	−0.787390	−	0.616456i	$-0.788568\pi$
$479$	−7.90785e6	−1.57478	−0.787390	+	0.616456i	$0.788568\pi$
$480$	0	0
$481$	−9.53939e6	−1.88000
$482$	1.41626e7	2.77668
$483$	1.30900e7	2.55312
$484$	8.62203e6	1.67300
$485$	0	0
$486$	−1.00289e7	−1.92603
$487$	−8.63488e6	−1.64981	−0.824905	−	0.565272i	$-0.808771\pi$
$487$	−8.63488e6	−1.64981	−0.824905	+	0.565272i	$0.808771\pi$
$488$	−597555.	−0.113587
$489$	−1.01879e7	−1.92670
$490$	0	0
$491$	−6.58814e6	−1.23327	−0.616636	−	0.787248i	$-0.711505\pi$
$491$	−6.58814e6	−1.23327	−0.616636	+	0.787248i	$0.711505\pi$
$492$	−1.86319e7	−3.47012
$493$	2599.39	0.000481675 0
$494$	9.38440e6	1.73017
$495$	0	0
$496$	−6.43346e6	−1.17420
$497$	1.53930e7	2.79532
$498$	1.69435e7	3.06147
$499$	3.64907e6	0.656041	0.328021	−	0.944671i	$-0.393618\pi$
$499$	3.64907e6	0.656041	0.328021	+	0.944671i	$0.393618\pi$
$500$	0	0
$501$	−2.10767e6	−0.375153
$502$	−5.86330e6	−1.03844
$503$	3.44859e6	0.607746	0.303873	−	0.952713i	$-0.401720\pi$
$503$	3.44859e6	0.607746	0.303873	+	0.952713i	$0.401720\pi$
$504$	−3.77627e6	−0.662196
$505$	0	0
$506$	1.25961e7	2.18705
$507$	−8.23010e6	−1.42195
$508$	−21286.6	−0.00365971
$509$	5.86750e6	1.00383	0.501913	−	0.864918i	$-0.332630\pi$
$509$	5.86750e6	1.00383	0.501913	+	0.864918i	$0.332630\pi$
$510$	0	0
$511$	−1.01305e7	−1.71625
$512$	−7.87699e6	−1.32796
$513$	−3.10738e6	−0.521315
$514$	−7.42538e6	−1.23968
$515$	0	0
$516$	1.69282e6	0.279890
$517$	−184493.	−0.0303566
$518$	−2.12046e7	−3.47221
$519$	−3.31128e6	−0.539607
$520$	0	0
$521$	3.14321e6	0.507316	0.253658	−	0.967294i	$-0.418366\pi$
$521$	3.14321e6	0.507316	0.253658	+	0.967294i	$0.418366\pi$
$522$	−8878.27	−0.00142611
$523$	8.02440e6	1.28280	0.641399	−	0.767208i	$-0.278354\pi$
$523$	8.02440e6	1.28280	0.641399	+	0.767208i	$0.278354\pi$
$524$	5.56773e6	0.885830
$525$	0	0
$526$	5.71210e6	0.900184
$527$	6.69565e6	1.05019
$528$	1.20260e7	1.87731
$529$	−594319.	−0.0923379
$530$	0	0
$531$	−3.71666e6	−0.572028
$532$	1.13137e7	1.73311
$533$	−1.71746e7	−2.61859
$534$	−1.91881e7	−2.91191
$535$	0	0
$536$	−2.89534e6	−0.435299
$537$	4.67043e6	0.698909
$538$	−3.16003e6	−0.470691
$539$	2.08902e7	3.09721
$540$	0	0
$541$	470290.	0.0690833	0.0345416	−	0.999403i	$-0.489003\pi$
$541$	470290.	0.0690833	0.0345416	+	0.999403i	$0.489003\pi$
$542$	1.68119e7	2.45820
$543$	1.37758e7	2.00501
$544$	6.87923e6	0.996650
$545$	0	0
$546$	−3.82186e7	−5.48648
$547$	8.63758e6	1.23431	0.617154	−	0.786842i	$-0.288285\pi$
$547$	8.63758e6	1.23431	0.617154	+	0.786842i	$0.288285\pi$
$548$	−8.45589e6	−1.20284
$549$	4.09870e6	0.580384
$550$	0	0
$551$	4155.16	0.000583054 0
$552$	−2.89059e6	−0.403775
$553$	1.79536e7	2.49654
$554$	−2.40837e6	−0.333387
$555$	0	0
$556$	1.18934e7	1.63163
$557$	−7.93744e6	−1.08403	−0.542017	−	0.840368i	$-0.682339\pi$
$557$	−7.93744e6	−1.08403	−0.542017	+	0.840368i	$0.682339\pi$
$558$	−2.28691e7	−3.10931
$559$	1.56042e6	0.211208
$560$	0	0
$561$	−1.25161e7	−1.67904
$562$	4.35934e6	0.582211
$563$	−4.11060e6	−0.546555	−0.273277	−	0.961935i	$-0.588108\pi$
$563$	−4.11060e6	−0.546555	−0.273277	+	0.961935i	$0.588108\pi$
$564$	271028.	0.0358770
$565$	0	0
$566$	7.02393e6	0.921593
$567$	−5.86844e6	−0.766593
$568$	−3.39914e6	−0.442078
$569$	−9.83986e6	−1.27411	−0.637057	−	0.770816i	$-0.719849\pi$
$569$	−9.83986e6	−1.27411	−0.637057	+	0.770816i	$0.719849\pi$
$570$	0	0
$571$	6.43917e6	0.826494	0.413247	−	0.910619i	$-0.364395\pi$
$571$	6.43917e6	0.826494	0.413247	+	0.910619i	$0.364395\pi$
$572$	−1.99462e7	−2.54900
$573$	8.86798e6	1.12834
$574$	−3.81765e7	−4.83634
$575$	0	0
$576$	−1.48048e7	−1.85928
$577$	8.47384e6	1.05960	0.529798	−	0.848124i	$-0.322268\pi$
$577$	8.47384e6	1.05960	0.529798	+	0.848124i	$0.322268\pi$
$578$	6.08588e6	0.757712
$579$	2.35827e6	0.292346
$580$	0	0
$581$	1.88292e7	2.31415
$582$	−3.33614e7	−4.08259
$583$	−1.10112e7	−1.34173
$584$	2.23707e6	0.271424
$585$	0	0
$586$	−3.90802e6	−0.470124
$587$	3.99832e6	0.478941	0.239470	−	0.970904i	$-0.423026\pi$
$587$	3.99832e6	0.478941	0.239470	+	0.970904i	$0.423026\pi$
$588$	−3.06886e7	−3.66045
$589$	1.07031e7	1.27122
$590$	0	0
$591$	3.12381e6	0.367888
$592$	−9.03527e6	−1.05959
$593$	−536631.	−0.0626670	−0.0313335	−	0.999509i	$-0.509975\pi$
$593$	−536631.	−0.0626670	−0.0313335	+	0.999509i	$0.509975\pi$
$594$	1.21775e7	1.41609
$595$	0	0
$596$	−3.03454e6	−0.349926
$597$	1.19178e7	1.36855
$598$	−1.70569e7	−1.95050
$599$	−1.40226e7	−1.59684	−0.798419	−	0.602102i	$-0.794330\pi$
$599$	−1.40226e7	−1.59684	−0.798419	+	0.602102i	$0.794330\pi$
$600$	0	0
$601$	−2.78826e6	−0.314882	−0.157441	−	0.987528i	$-0.550324\pi$
$601$	−2.78826e6	−0.314882	−0.157441	+	0.987528i	$0.550324\pi$
$602$	3.46857e6	0.390085
$603$	1.98595e7	2.22420
$604$	1.17009e7	1.30505
$605$	0	0
$606$	2.62455e7	2.90317
$607$	−1.29016e7	−1.42125	−0.710625	−	0.703571i	$-0.751588\pi$
$607$	−1.29016e7	−1.42125	−0.710625	+	0.703571i	$0.751588\pi$
$608$	1.09966e7	1.20642
$609$	−16922.2	−0.00184890
$610$	0	0
$611$	249829.	0.0270733
$612$	1.07202e7	1.15698
$613$	−3.78135e6	−0.406439	−0.203220	−	0.979133i	$-0.565141\pi$
$613$	−3.78135e6	−0.406439	−0.203220	+	0.979133i	$0.565141\pi$
$614$	−1.70438e6	−0.182451
$615$	0	0
$616$	−6.92607e6	−0.735420
$617$	−1.81217e7	−1.91640	−0.958201	−	0.286097i	$-0.907642\pi$
$617$	−1.81217e7	−1.91640	−0.958201	+	0.286097i	$0.907642\pi$
$618$	2.63148e7	2.77159
$619$	1.19507e7	1.25363	0.626813	−	0.779170i	$-0.284359\pi$
$619$	1.19507e7	1.25363	0.626813	+	0.779170i	$0.284359\pi$
$620$	0	0
$621$	5.64790e6	0.587703
$622$	3.81167e6	0.395038
$623$	−2.13236e7	−2.20110
$624$	−1.62849e7	−1.67427
$625$	0	0
$626$	2.74836e6	0.280309
$627$	−2.00072e7	−2.03244
$628$	6.75856e6	0.683840
$629$	9.40349e6	0.947681
$630$	0	0
$631$	8.06443e6	0.806306	0.403153	−	0.915133i	$-0.367914\pi$
$631$	8.06443e6	0.806306	0.403153	+	0.915133i	$0.367914\pi$
$632$	−3.96459e6	−0.394826
$633$	1.29452e7	1.28410
$634$	−6.58336e6	−0.650465
$635$	0	0
$636$	1.61760e7	1.58572
$637$	−2.82883e7	−2.76222
$638$	−16283.7	−0.00158380
$639$	2.33151e7	2.25884
$640$	0	0
$641$	783733.	0.0753396	0.0376698	−	0.999290i	$-0.488006\pi$
$641$	783733.	0.0753396	0.0376698	+	0.999290i	$0.488006\pi$
$642$	8.20549e6	0.785719
$643$	−1.86322e7	−1.77720	−0.888601	−	0.458681i	$-0.848322\pi$
$643$	−1.86322e7	−1.77720	−0.888601	+	0.458681i	$0.848322\pi$
$644$	−2.05636e7	−1.95382
$645$	0	0
$646$	−9.25071e6	−0.872155
$647$	−9.54586e6	−0.896509	−0.448254	−	0.893906i	$-0.647954\pi$
$647$	−9.54586e6	−0.896509	−0.448254	+	0.893906i	$0.647954\pi$
$648$	1.29589e6	0.121236
$649$	−6.81675e6	−0.635281
$650$	0	0
$651$	−4.35891e7	−4.03112
$652$	1.60047e7	1.47444
$653$	1.68708e7	1.54829	0.774147	−	0.633005i	$-0.218179\pi$
$653$	1.68708e7	1.54829	0.774147	+	0.633005i	$0.218179\pi$
$654$	−6.50509e6	−0.594715
$655$	0	0
$656$	−1.62670e7	−1.47587
$657$	−1.53443e7	−1.38687
$658$	555334.	0.0500022
$659$	1.43315e6	0.128552	0.0642761	−	0.997932i	$-0.479526\pi$
$659$	1.43315e6	0.128552	0.0642761	+	0.997932i	$0.479526\pi$
$660$	0	0
$661$	−1.92644e7	−1.71495	−0.857476	−	0.514523i	$-0.827969\pi$
$661$	−1.92644e7	−1.71495	−0.857476	+	0.514523i	$0.827969\pi$
$662$	−1.41223e6	−0.125245
$663$	1.69486e7	1.49744
$664$	−4.15795e6	−0.365982
$665$	0	0
$666$	−3.21178e7	−2.80582
$667$	−7552.32	−0.000657303 0
$668$	3.31102e6	0.287092
$669$	1.12722e7	0.973744
$670$	0	0
$671$	7.51744e6	0.644561
$672$	−4.47843e7	−3.82562
$673$	−3.87425e6	−0.329724	−0.164862	−	0.986317i	$-0.552718\pi$
$673$	−3.87425e6	−0.329724	−0.164862	+	0.986317i	$0.552718\pi$
$674$	1.54461e7	1.30969
$675$	0	0
$676$	1.29290e7	1.08817
$677$	−1.76566e7	−1.48059	−0.740296	−	0.672281i	$-0.765315\pi$
$677$	−1.76566e7	−1.48059	−0.740296	+	0.672281i	$0.765315\pi$
$678$	7.16639e6	0.598723
$679$	−3.70743e7	−3.08602
$680$	0	0
$681$	−2.72810e7	−2.25420
$682$	−4.19444e7	−3.45313
$683$	6.67516e6	0.547533	0.273766	−	0.961796i	$-0.411730\pi$
$683$	6.67516e6	0.547533	0.273766	+	0.961796i	$0.411730\pi$
$684$	1.71365e7	1.40049
$685$	0	0
$686$	−3.13521e7	−2.54364
$687$	3.51562e7	2.84191
$688$	1.47796e6	0.119039
$689$	1.49108e7	1.19661
$690$	0	0
$691$	2.89543e6	0.230684	0.115342	−	0.993326i	$-0.463204\pi$
$691$	2.89543e6	0.230684	0.115342	+	0.993326i	$0.463204\pi$
$692$	5.20182e6	0.412943
$693$	4.75067e7	3.75770
$694$	8.68723e6	0.684672
$695$	0	0
$696$	3736.83	0.000292402 0
$697$	1.69299e7	1.32000
$698$	3.54922e7	2.75737
$699$	3.77233e6	0.292023
$700$	0	0
$701$	−5.82907e6	−0.448027	−0.224013	−	0.974586i	$-0.571916\pi$
$701$	−5.82907e6	−0.448027	−0.224013	+	0.974586i	$0.571916\pi$
$702$	−1.64901e7	−1.26293
$703$	1.50316e7	1.14714
$704$	−2.71535e7	−2.06488
$705$	0	0
$706$	−2.75619e7	−2.08112
$707$	2.91664e7	2.19449
$708$	1.00141e7	0.750809
$709$	−9.06576e6	−0.677312	−0.338656	−	0.940910i	$-0.609972\pi$
$709$	−9.06576e6	−0.677312	−0.338656	+	0.940910i	$0.609972\pi$
$710$	0	0
$711$	2.71936e7	2.01740
$712$	4.70877e6	0.348103
$713$	−1.94537e7	−1.43311
$714$	3.76742e7	2.76566
$715$	0	0
$716$	−7.33696e6	−0.534852
$717$	−2.22263e7	−1.61461
$718$	−1.26441e7	−0.915332
$719$	−8.67478e6	−0.625801	−0.312900	−	0.949786i	$-0.601301\pi$
$719$	−8.67478e6	−0.625801	−0.312900	+	0.949786i	$0.601301\pi$
$720$	0	0
$721$	2.92435e7	2.09503
$722$	5.91791e6	0.422499
$723$	4.08872e7	2.90899
$724$	−2.16409e7	−1.53437
$725$	0	0
$726$	4.58948e7	3.23163
$727$	−1.13012e6	−0.0793027	−0.0396513	−	0.999214i	$-0.512625\pi$
$727$	−1.13012e6	−0.0793027	−0.0396513	+	0.999214i	$0.512625\pi$
$728$	9.37889e6	0.655878
$729$	−2.25965e7	−1.57479
$730$	0	0
$731$	−1.53819e6	−0.106467
$732$	−1.10435e7	−0.761776
$733$	5.86047e6	0.402877	0.201439	−	0.979501i	$-0.435438\pi$
$733$	5.86047e6	0.402877	0.201439	+	0.979501i	$0.435438\pi$
$734$	9.56150e6	0.655067
$735$	0	0
$736$	−1.99871e7	−1.36005
$737$	3.64244e7	2.47015
$738$	−5.78245e7	−3.90814
$739$	−1.93147e7	−1.30100	−0.650500	−	0.759506i	$-0.725441\pi$
$739$	−1.93147e7	−1.30100	−0.650500	+	0.759506i	$0.725441\pi$
$740$	0	0
$741$	2.70926e7	1.81261
$742$	3.31444e7	2.21004
$743$	1.77415e7	1.17901	0.589507	−	0.807763i	$-0.299322\pi$
$743$	1.77415e7	1.17901	0.589507	+	0.807763i	$0.299322\pi$
$744$	9.62554e6	0.637519
$745$	0	0
$746$	−3.80161e7	−2.50104
$747$	2.85199e7	1.87002
$748$	1.96620e7	1.28492
$749$	9.11871e6	0.593921
$750$	0	0
$751$	1.42116e7	0.919481	0.459740	−	0.888053i	$-0.347942\pi$
$751$	1.42116e7	0.919481	0.459740	+	0.888053i	$0.347942\pi$
$752$	236627.	0.0152588
$753$	−1.69272e7	−1.08792
$754$	22050.4	0.00141250
$755$	0	0
$756$	−1.98803e7	−1.26508
$757$	−1.63609e7	−1.03769	−0.518844	−	0.854869i	$-0.673637\pi$
$757$	−1.63609e7	−1.03769	−0.518844	+	0.854869i	$0.673637\pi$
$758$	2.28583e7	1.44501
$759$	3.63646e7	2.29126
$760$	0	0
$761$	−8.75525e6	−0.548033	−0.274017	−	0.961725i	$-0.588352\pi$
$761$	−8.75525e6	−0.548033	−0.274017	+	0.961725i	$0.588352\pi$
$762$	−113308.	−0.00706924
$763$	−7.22906e6	−0.449543
$764$	−1.39311e7	−0.863478
$765$	0	0
$766$	−4.41613e7	−2.71938
$767$	9.23085e6	0.566570
$768$	−1.35285e7	−0.827650
$769$	1.38755e7	0.846123	0.423061	−	0.906101i	$-0.360956\pi$
$769$	1.38755e7	0.846123	0.423061	+	0.906101i	$0.360956\pi$
$770$	0	0
$771$	−2.14369e7	−1.29875
$772$	−3.70470e6	−0.223723
$773$	−1.25987e7	−0.758362	−0.379181	−	0.925323i	$-0.623794\pi$
$773$	−1.25987e7	−0.758362	−0.379181	+	0.925323i	$0.623794\pi$
$774$	5.25371e6	0.315220
$775$	0	0
$776$	8.18691e6	0.488051
$777$	−6.12173e7	−3.63766
$778$	−4.78989e6	−0.283711
$779$	2.70627e7	1.59782
$780$	0	0
$781$	4.27624e7	2.50862
$782$	1.68139e7	0.983221
$783$	−7301.36	−0.000425598 0
$784$	−2.67934e7	−1.55682
$785$	0	0
$786$	2.96369e7	1.71110
$787$	1.98717e6	0.114366	0.0571830	−	0.998364i	$-0.481788\pi$
$787$	1.98717e6	0.114366	0.0571830	+	0.998364i	$0.481788\pi$
$788$	−4.90731e6	−0.281532
$789$	1.64907e7	0.943076
$790$	0	0
$791$	7.96396e6	0.452572
$792$	−1.04906e7	−0.594278
$793$	−1.01797e7	−0.574846
$794$	3.97206e7	2.23596
$795$	0	0
$796$	−1.87222e7	−1.04731
$797$	9.51484e6	0.530586	0.265293	−	0.964168i	$-0.414531\pi$
$797$	9.51484e6	0.530586	0.265293	+	0.964168i	$0.414531\pi$
$798$	6.02228e7	3.34775
$799$	−246270.	−0.0136472
$800$	0	0
$801$	−3.22980e7	−1.77867
$802$	2.74869e7	1.50900
$803$	−2.81431e7	−1.54022
$804$	−5.35090e7	−2.91936
$805$	0	0
$806$	5.67986e7	3.07964
$807$	−9.12294e6	−0.493118
$808$	−6.44066e6	−0.347058
$809$	1.06038e7	0.569625	0.284813	−	0.958583i	$-0.408069\pi$
$809$	1.06038e7	0.569625	0.284813	+	0.958583i	$0.408069\pi$
$810$	0	0
$811$	1.88217e7	1.00486	0.502430	−	0.864618i	$-0.332439\pi$
$811$	1.88217e7	1.00486	0.502430	+	0.864618i	$0.332439\pi$
$812$	26583.7	0.00141490
$813$	4.85355e7	2.57533
$814$	−5.89074e7	−3.11608
$815$	0	0
$816$	1.60529e7	0.843974
$817$	−2.45882e6	−0.128876
$818$	−1.34143e7	−0.700944
$819$	−6.43309e7	−3.35127
$820$	0	0
$821$	1.40465e7	0.727297	0.363648	−	0.931536i	$-0.381531\pi$
$821$	1.40465e7	0.727297	0.363648	+	0.931536i	$0.381531\pi$
$822$	−4.50105e7	−2.32346
$823$	−2.04864e7	−1.05430	−0.527152	−	0.849771i	$-0.676740\pi$
$823$	−2.04864e7	−1.05430	−0.527152	+	0.849771i	$0.676740\pi$
$824$	−6.45768e6	−0.331328
$825$	0	0
$826$	2.05188e7	1.04641
$827$	8.52320e6	0.433350	0.216675	−	0.976244i	$-0.430479\pi$
$827$	8.52320e6	0.433350	0.216675	+	0.976244i	$0.430479\pi$
$828$	−3.11469e7	−1.57884
$829$	9.76291e6	0.493393	0.246697	−	0.969093i	$-0.420655\pi$
$829$	9.76291e6	0.493393	0.246697	+	0.969093i	$0.420655\pi$
$830$	0	0
$831$	−6.95291e6	−0.349272
$832$	3.67697e7	1.84154
$833$	2.78853e7	1.39240
$834$	6.33085e7	3.15171
$835$	0	0
$836$	3.14301e7	1.55536
$837$	−1.88072e7	−0.927922
$838$	−7.99313e6	−0.393194
$839$	2.77668e7	1.36182	0.680911	−	0.732366i	$-0.261584\pi$
$839$	2.77668e7	1.36182	0.680911	+	0.732366i	$0.261584\pi$
$840$	0	0
$841$	−2.05111e7	−1.00000
$842$	−2.23354e7	−1.08571
$843$	1.25853e7	0.609952
$844$	−2.03361e7	−0.982678
$845$	0	0
$846$	841142.	0.0404058
$847$	5.10026e7	2.44278
$848$	1.41228e7	0.674420
$849$	2.02779e7	0.965505
$850$	0	0
$851$	−2.73211e7	−1.29323
$852$	−6.28198e7	−2.96482
$853$	4.69577e6	0.220971	0.110485	−	0.993878i	$-0.464759\pi$
$853$	4.69577e6	0.220971	0.110485	+	0.993878i	$0.464759\pi$
$854$	−2.26279e7	−1.06170
$855$	0	0
$856$	−2.01363e6	−0.0939283
$857$	2.10349e7	0.978337	0.489168	−	0.872189i	$-0.337300\pi$
$857$	2.10349e7	0.978337	0.489168	+	0.872189i	$0.337300\pi$
$858$	−1.06173e8	−4.92375
$859$	−5.68083e6	−0.262681	−0.131341	−	0.991337i	$-0.541928\pi$
$859$	−5.68083e6	−0.262681	−0.131341	+	0.991337i	$0.541928\pi$
$860$	0	0
$861$	−1.10215e8	−5.06678
$862$	−900514.	−0.0412784
$863$	−3.35927e6	−0.153539	−0.0767694	−	0.997049i	$-0.524461\pi$
$863$	−3.35927e6	−0.153539	−0.0767694	+	0.997049i	$0.524461\pi$
$864$	−1.93229e7	−0.880620
$865$	0	0
$866$	1.34155e7	0.607870
$867$	1.75698e7	0.793815
$868$	6.84759e7	3.08488
$869$	4.98759e7	2.24048
$870$	0	0
$871$	−4.93238e7	−2.20298
$872$	1.59635e6	0.0710949
$873$	−5.61549e7	−2.49375
$874$	2.68772e7	1.19016
$875$	0	0
$876$	4.13435e7	1.82032
$877$	2.91005e7	1.27762	0.638809	−	0.769365i	$-0.279427\pi$
$877$	2.91005e7	1.27762	0.638809	+	0.769365i	$0.279427\pi$
$878$	−2.53488e7	−1.10974
$879$	−1.12824e7	−0.492525
$880$	0	0
$881$	−2.34116e6	−0.101623	−0.0508114	−	0.998708i	$-0.516181\pi$
$881$	−2.34116e6	−0.101623	−0.0508114	+	0.998708i	$0.516181\pi$
$882$	−9.52428e7	−4.12250
$883$	2.95554e7	1.27566	0.637830	−	0.770178i	$-0.279832\pi$
$883$	2.95554e7	1.27566	0.637830	+	0.770178i	$0.279832\pi$
$884$	−2.66252e7	−1.14594
$885$	0	0
$886$	−2.63929e6	−0.112954
$887$	−3.66410e7	−1.56372	−0.781858	−	0.623456i	$-0.785728\pi$
$887$	−3.66410e7	−1.56372	−0.781858	+	0.623456i	$0.785728\pi$
$888$	1.35183e7	0.575293
$889$	−125918.	−0.00534361
$890$	0	0
$891$	−1.63028e7	−0.687967
$892$	−1.77080e7	−0.745174
$893$	−393667.	−0.0165196
$894$	−1.61528e7	−0.675932
$895$	0	0
$896$	2.23702e7	0.930895
$897$	−4.92428e7	−2.04344
$898$	8.51334e6	0.352297
$899$	25148.9	0.00103781
$900$	0	0
$901$	−1.46983e7	−0.603193
$902$	−1.06056e8	−4.34029
$903$	1.00137e7	0.408672
$904$	−1.75864e6	−0.0715740
$905$	0	0
$906$	6.22837e7	2.52089
$907$	−4.44766e7	−1.79520	−0.897602	−	0.440807i	$-0.854692\pi$
$907$	−4.44766e7	−1.79520	−0.897602	+	0.440807i	$0.854692\pi$
$908$	4.28569e7	1.72507
$909$	4.41772e7	1.77333
$910$	0	0
$911$	1.26869e7	0.506478	0.253239	−	0.967404i	$-0.418504\pi$
$911$	1.26869e7	0.506478	0.253239	+	0.967404i	$0.418504\pi$
$912$	2.56609e7	1.02161
$913$	5.23084e7	2.07680
$914$	3.97103e7	1.57231
$915$	0	0
$916$	−5.52283e7	−2.17482
$917$	3.29353e7	1.29342
$918$	1.62552e7	0.636626
$919$	2.83616e7	1.10775	0.553875	−	0.832600i	$-0.313148\pi$
$919$	2.83616e7	1.10775	0.553875	+	0.832600i	$0.313148\pi$
$920$	0	0
$921$	−4.92051e6	−0.191144
$922$	−4.90034e7	−1.89845
$923$	−5.79063e7	−2.23729
$924$	−1.28001e8	−4.93213
$925$	0	0
$926$	6.03722e7	2.31371
$927$	4.42940e7	1.69295
$928$	25838.5	0.000984910 0
$929$	−1.27953e7	−0.486419	−0.243210	−	0.969974i	$-0.578200\pi$
$929$	−1.27953e7	−0.486419	−0.243210	+	0.969974i	$0.578200\pi$
$930$	0	0
$931$	4.45751e7	1.68546
$932$	−5.92611e6	−0.223475
$933$	1.10042e7	0.413861
$934$	−1.06978e7	−0.401261
$935$	0	0
$936$	1.42058e7	0.530002
$937$	170070.	0.00632817	0.00316408	−	0.999995i	$-0.498993\pi$
$937$	170070.	0.00632817	0.00316408	+	0.999995i	$0.498993\pi$
$938$	−1.09639e8	−4.06874
$939$	7.93445e6	0.293665
$940$	0	0
$941$	2.19281e7	0.807284	0.403642	−	0.914917i	$-0.367744\pi$
$941$	2.19281e7	0.807284	0.403642	+	0.914917i	$0.367744\pi$
$942$	3.59756e7	1.32093
$943$	−4.91885e7	−1.80129
$944$	8.74304e6	0.319325
$945$	0	0
$946$	9.63586e6	0.350076
$947$	3.10023e7	1.12336	0.561680	−	0.827354i	$-0.310155\pi$
$947$	3.10023e7	1.12336	0.561680	+	0.827354i	$0.310155\pi$
$948$	−7.32699e7	−2.64792
$949$	3.81098e7	1.37363
$950$	0	0
$951$	−1.90060e7	−0.681459
$952$	−9.24528e6	−0.330619
$953$	3.55137e7	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$953$	3.55137e7	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$954$	5.02025e7	1.78589
$955$	0	0
$956$	3.49161e7	1.23561
$957$	−47010.6	−0.00165927
$958$	6.61260e7	2.32787
$959$	−5.00199e7	−1.75629
$960$	0	0
$961$	3.61508e7	1.26273
$962$	7.97691e7	2.77905
$963$	1.38117e7	0.479936
$964$	−6.42314e7	−2.22615
$965$	0	0
$966$	−1.09459e8	−3.77407
$967$	2.48343e6	0.0854054	0.0427027	−	0.999088i	$-0.486403\pi$
$967$	2.48343e6	0.0854054	0.0427027	+	0.999088i	$0.486403\pi$
$968$	−1.12626e7	−0.386324
$969$	−2.67066e7	−0.913712
$970$	0	0
$971$	3.17595e6	0.108100	0.0540499	−	0.998538i	$-0.482787\pi$
$971$	3.17595e6	0.108100	0.0540499	+	0.998538i	$0.482787\pi$
$972$	4.54837e7	1.54415
$973$	7.03543e7	2.38237
$974$	7.22055e7	2.43878
$975$	0	0
$976$	−9.64173e6	−0.323989
$977$	7.62420e6	0.255540	0.127770	−	0.991804i	$-0.459218\pi$
$977$	7.62420e6	0.255540	0.127770	+	0.991804i	$0.459218\pi$
$978$	8.51923e7	2.84809
$979$	−5.92379e7	−1.97535
$980$	0	0
$981$	−1.09496e7	−0.363266
$982$	5.50905e7	1.82305
$983$	4.35760e7	1.43835	0.719173	−	0.694831i	$-0.244521\pi$
$983$	4.35760e7	1.43835	0.719173	+	0.694831i	$0.244521\pi$
$984$	2.43381e7	0.801308
$985$	0	0
$986$	−21736.3	−0.000712021 0
$987$	1.60324e6	0.0523847
$988$	−4.25608e7	−1.38713
$989$	4.46908e6	0.145287
$990$	0	0
$991$	5.75068e7	1.86010	0.930048	−	0.367438i	$-0.119765\pi$
$991$	5.75068e7	1.86010	0.930048	+	0.367438i	$0.119765\pi$
$992$	6.65561e7	2.14738
$993$	−4.07707e6	−0.131213
$994$	−1.28717e8	−4.13210
$995$	0	0
$996$	−7.68434e7	−2.45447
$997$	−4.21441e6	−0.134276	−0.0671380	−	0.997744i	$-0.521387\pi$
$997$	−4.21441e6	−0.134276	−0.0671380	+	0.997744i	$0.521387\pi$
$998$	−3.05138e7	−0.969773
$999$	−2.64132e7	−0.837352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.6.a.i.1.6	✓	37
5.4	even	2		1075.6.a.j.1.32	yes	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.6.a.i.1.6	✓	37	1.1	even	1	trivial
1075.6.a.j.1.32	yes	37	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1075.a (trivial)

\(f(q)\)	\(=\)	\(q-8.36207 q^{2} -24.1411 q^{3} +37.9243 q^{4} +201.870 q^{6} +224.337 q^{7} -49.5390 q^{8} +339.794 q^{9} +O(q^{10})\)	\(q-8.36207 q^{2} -24.1411 q^{3} +37.9243 q^{4} +201.870 q^{6} +224.337 q^{7} -49.5390 q^{8} +339.794 q^{9} +623.217 q^{11} -915.534 q^{12} -843.925 q^{13} -1875.92 q^{14} -799.327 q^{16} +831.902 q^{17} -2841.38 q^{18} +1329.81 q^{19} -5415.74 q^{21} -5211.39 q^{22} -2417.03 q^{23} +1195.93 q^{24} +7056.96 q^{26} -2336.71 q^{27} +8507.80 q^{28} +3.12463 q^{29} +8048.60 q^{31} +8269.28 q^{32} -15045.2 q^{33} -6956.43 q^{34} +12886.4 q^{36} +11303.6 q^{37} -11120.0 q^{38} +20373.3 q^{39} +20350.8 q^{41} +45286.8 q^{42} -1849.00 q^{43} +23635.0 q^{44} +20211.4 q^{46} -296.033 q^{47} +19296.7 q^{48} +33519.9 q^{49} -20083.1 q^{51} -32005.2 q^{52} -17668.3 q^{53} +19539.7 q^{54} -11113.4 q^{56} -32103.1 q^{57} -26.1284 q^{58} -10938.0 q^{59} +12062.3 q^{61} -67303.0 q^{62} +76228.2 q^{63} -43569.9 q^{64} +125809. q^{66} +58445.7 q^{67} +31549.3 q^{68} +58349.8 q^{69} +68615.5 q^{71} -16833.1 q^{72} -45157.8 q^{73} -94521.5 q^{74} +50432.0 q^{76} +139810. q^{77} -170363. q^{78} +80029.7 q^{79} -26159.1 q^{81} -170175. q^{82} +83932.9 q^{83} -205388. q^{84} +15461.5 q^{86} -75.4321 q^{87} -30873.6 q^{88} -95051.8 q^{89} -189323. q^{91} -91664.0 q^{92} -194302. q^{93} +2475.45 q^{94} -199630. q^{96} -165262. q^{97} -280296. q^{98} +211765. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9}+O(q^{10}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9	\( 37 q + 630 q^{4} + 291 q^{6} - 213 q^{8} + 3535 q^{9} + 675 q^{11} + 4446 q^{12} - 1241 q^{13} + 2375 q^{14} + 10518 q^{16} - 1153 q^{17} + 6680 q^{18} + 4065 q^{19} + 9953 q^{21} - 9283 q^{22} + 360 q^{23} + 2265 q^{24} + 23695 q^{26} - 1323 q^{27} + 30375 q^{28} + 19290 q^{29} + 23291 q^{31} - 8166 q^{32} + 10388 q^{33} - 13153 q^{34} + 148705 q^{36} - 13501 q^{37} + 8127 q^{38} - 1327 q^{39} + 38345 q^{41} + 21835 q^{42} - 68413 q^{43} + 47768 q^{44} + 48755 q^{46} - 84859 q^{47} + 208720 q^{48} + 107255 q^{49} + 62027 q^{51} - 128320 q^{52} + 53559 q^{53} + 44158 q^{54} + 107538 q^{56} - 104239 q^{57} + 85186 q^{58} + 48186 q^{59} + 82364 q^{61} - 206506 q^{62} + 75269 q^{63} + 161467 q^{64} + 91969 q^{66} - 38168 q^{67} - 95991 q^{68} + 287103 q^{69} + 155302 q^{71} - 9979 q^{72} - 31927 q^{73} + 59946 q^{74} + 225407 q^{76} + 80007 q^{77} + 67815 q^{78} + 150174 q^{79} + 417489 q^{81} - 60603 q^{82} - 266568 q^{83} + 586273 q^{84} + 57554 q^{87} - 323054 q^{88} + 334356 q^{89} + 51747 q^{91} + 258529 q^{92} + 285287 q^{93} + 302744 q^{94} + 287282 q^{96} + 78640 q^{97} + 397117 q^{98} + 362152 q^{99}+O(q^{100}) \) 37 * q + 630 * q^4 + 291 * q^6 - 213 * q^8 + 3535 * q^9 + 675 * q^11 + 4446 * q^12 - 1241 * q^13 + 2375 * q^14 + 10518 * q^16 - 1153 * q^17 + 6680 * q^18 + 4065 * q^19 + 9953 * q^21 - 9283 * q^22 + 360 * q^23 + 2265 * q^24 + 23695 * q^26 - 1323 * q^27 + 30375 * q^28 + 19290 * q^29 + 23291 * q^31 - 8166 * q^32 + 10388 * q^33 - 13153 * q^34 + 148705 * q^36 - 13501 * q^37 + 8127 * q^38 - 1327 * q^39 + 38345 * q^41 + 21835 * q^42 - 68413 * q^43 + 47768 * q^44 + 48755 * q^46 - 84859 * q^47 + 208720 * q^48 + 107255 * q^49 + 62027 * q^51 - 128320 * q^52 + 53559 * q^53 + 44158 * q^54 + 107538 * q^56 - 104239 * q^57 + 85186 * q^58 + 48186 * q^59 + 82364 * q^61 - 206506 * q^62 + 75269 * q^63 + 161467 * q^64 + 91969 * q^66 - 38168 * q^67 - 95991 * q^68 + 287103 * q^69 + 155302 * q^71 - 9979 * q^72 - 31927 * q^73 + 59946 * q^74 + 225407 * q^76 + 80007 * q^77 + 67815 * q^78 + 150174 * q^79 + 417489 * q^81 - 60603 * q^82 - 266568 * q^83 + 586273 * q^84 + 57554 * q^87 - 323054 * q^88 + 334356 * q^89 + 51747 * q^91 + 258529 * q^92 + 285287 * q^93 + 302744 * q^94 + 287282 * q^96 + 78640 * q^97 + 397117 * q^98 + 362152 * q^99

Introduction

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Modular forms

Varieties

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Database

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