LMFDB - Embedded newform 1617.4.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.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:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 38x^{5} + 73x^{4} + 383x^{3} - 256x^{2} - 676x - 224 $ x^7 - 3x^6 - 38x^5 + 73x^4 + 383x^3 - 256x^2 - 676x - 224
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.462025$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46203 q^{2} -3.00000 q^{3} -5.86248 q^{4} +13.7188 q^{5} +4.38608 q^{6} +20.2673 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.46203 q^{2} -3.00000 q^{3} -5.86248 q^{4} +13.7188 q^{5} +4.38608 q^{6} +20.2673 q^{8} +9.00000 q^{9} -20.0572 q^{10} +11.0000 q^{11} +17.5874 q^{12} +54.9610 q^{13} -41.1563 q^{15} +17.2686 q^{16} +67.0036 q^{17} -13.1582 q^{18} +22.5852 q^{19} -80.4260 q^{20} -16.0823 q^{22} +193.284 q^{23} -60.8019 q^{24} +63.2045 q^{25} -80.3544 q^{26} -27.0000 q^{27} +227.940 q^{29} +60.1715 q^{30} +68.6947 q^{31} -187.385 q^{32} -33.0000 q^{33} -97.9610 q^{34} -52.7623 q^{36} +301.478 q^{37} -33.0202 q^{38} -164.883 q^{39} +278.042 q^{40} -366.280 q^{41} -67.4146 q^{43} -64.4873 q^{44} +123.469 q^{45} -282.586 q^{46} +594.558 q^{47} -51.8057 q^{48} -92.4066 q^{50} -201.011 q^{51} -322.208 q^{52} +192.711 q^{53} +39.4747 q^{54} +150.906 q^{55} -67.7557 q^{57} -333.254 q^{58} +630.764 q^{59} +241.278 q^{60} -321.750 q^{61} -100.433 q^{62} +135.814 q^{64} +753.998 q^{65} +48.2468 q^{66} -794.875 q^{67} -392.808 q^{68} -579.851 q^{69} +501.559 q^{71} +182.406 q^{72} -882.308 q^{73} -440.769 q^{74} -189.614 q^{75} -132.405 q^{76} +241.063 q^{78} -449.968 q^{79} +236.903 q^{80} +81.0000 q^{81} +535.511 q^{82} -87.9363 q^{83} +919.207 q^{85} +98.5619 q^{86} -683.820 q^{87} +222.940 q^{88} -761.292 q^{89} -180.515 q^{90} -1133.12 q^{92} -206.084 q^{93} -869.258 q^{94} +309.841 q^{95} +562.156 q^{96} -1373.22 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9} - 49 q^{10} + 77 q^{11} - 90 q^{12} + 92 q^{13} - 60 q^{15} + 218 q^{16} + 170 q^{17} - 36 q^{18} + 76 q^{19} + 569 q^{20} - 44 q^{22} - 56 q^{23} + 117 q^{24} + 53 q^{25} + 109 q^{26} - 189 q^{27} - 472 q^{29} + 147 q^{30} + 290 q^{31} - 1046 q^{32} - 231 q^{33} + 344 q^{34} + 270 q^{36} - 66 q^{37} + 385 q^{38} - 276 q^{39} - 800 q^{40} - 166 q^{41} - 76 q^{43} + 330 q^{44} + 180 q^{45} - 528 q^{46} + 1082 q^{47} - 654 q^{48} - 569 q^{50} - 510 q^{51} + 1065 q^{52} - 150 q^{53} + 108 q^{54} + 220 q^{55} - 228 q^{57} + 1457 q^{58} + 1284 q^{59} - 1707 q^{60} - 764 q^{61} - 296 q^{62} + 1661 q^{64} + 2722 q^{65} + 132 q^{66} - 658 q^{67} - 360 q^{68} + 168 q^{69} - 272 q^{71} - 351 q^{72} + 1658 q^{73} + 613 q^{74} - 159 q^{75} - 1757 q^{76} - 327 q^{78} + 792 q^{79} + 5079 q^{80} + 567 q^{81} + 3208 q^{82} - 770 q^{83} - 776 q^{85} - 478 q^{86} + 1416 q^{87} - 429 q^{88} + 656 q^{89} - 441 q^{90} - 3916 q^{92} - 870 q^{93} - 849 q^{94} - 1636 q^{95} + 3138 q^{96} + 608 q^{97} + 693 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9 - 49 * q^10 + 77 * q^11 - 90 * q^12 + 92 * q^13 - 60 * q^15 + 218 * q^16 + 170 * q^17 - 36 * q^18 + 76 * q^19 + 569 * q^20 - 44 * q^22 - 56 * q^23 + 117 * q^24 + 53 * q^25 + 109 * q^26 - 189 * q^27 - 472 * q^29 + 147 * q^30 + 290 * q^31 - 1046 * q^32 - 231 * q^33 + 344 * q^34 + 270 * q^36 - 66 * q^37 + 385 * q^38 - 276 * q^39 - 800 * q^40 - 166 * q^41 - 76 * q^43 + 330 * q^44 + 180 * q^45 - 528 * q^46 + 1082 * q^47 - 654 * q^48 - 569 * q^50 - 510 * q^51 + 1065 * q^52 - 150 * q^53 + 108 * q^54 + 220 * q^55 - 228 * q^57 + 1457 * q^58 + 1284 * q^59 - 1707 * q^60 - 764 * q^61 - 296 * q^62 + 1661 * q^64 + 2722 * q^65 + 132 * q^66 - 658 * q^67 - 360 * q^68 + 168 * q^69 - 272 * q^71 - 351 * q^72 + 1658 * q^73 + 613 * q^74 - 159 * q^75 - 1757 * q^76 - 327 * q^78 + 792 * q^79 + 5079 * q^80 + 567 * q^81 + 3208 * q^82 - 770 * q^83 - 776 * q^85 - 478 * q^86 + 1416 * q^87 - 429 * q^88 + 656 * q^89 - 441 * q^90 - 3916 * q^92 - 870 * q^93 - 849 * q^94 - 1636 * q^95 + 3138 * q^96 + 608 * q^97 + 693 * 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 $

$2$	−1.46203	−0.516904	−0.258452	−	0.966024i	$-0.583212\pi$
$2$	−1.46203	−0.516904	−0.258452	+	0.966024i	$0.583212\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.86248	−0.732810
$5$	13.7188	1.22704	0.613522	−	0.789678i	$-0.289752\pi$
$5$	13.7188	1.22704	0.613522	+	0.789678i	$0.289752\pi$
$6$	4.38608	0.298435
$7$	0	0
$7$	0	0
$8$	20.2673	0.895696
$9$	9.00000	0.333333
$10$	−20.0572	−0.634264
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	17.5874	0.423088
$13$	54.9610	1.17257	0.586287	−	0.810104i	$-0.300589\pi$
$13$	54.9610	1.17257	0.586287	+	0.810104i	$0.300589\pi$
$14$	0	0
$15$	−41.1563	−0.708434
$16$	17.2686	0.269821
$17$	67.0036	0.955927	0.477964	−	0.878380i	$-0.341375\pi$
$17$	67.0036	0.955927	0.477964	+	0.878380i	$0.341375\pi$
$18$	−13.1582	−0.172301
$19$	22.5852	0.272706	0.136353	−	0.990660i	$-0.456462\pi$
$19$	22.5852	0.272706	0.136353	+	0.990660i	$0.456462\pi$
$20$	−80.4260	−0.899190
$21$	0	0
$22$	−16.0823	−0.155852
$23$	193.284	1.75228	0.876140	−	0.482057i	$-0.160110\pi$
$23$	193.284	1.75228	0.876140	+	0.482057i	$0.160110\pi$
$24$	−60.8019	−0.517131
$25$	63.2045	0.505636
$26$	−80.3544	−0.606108
$27$	−27.0000	−0.192450
$28$	0	0
$29$	227.940	1.45957	0.729783	−	0.683679i	$-0.239621\pi$
$29$	227.940	1.45957	0.729783	+	0.683679i	$0.239621\pi$
$30$	60.1715	0.366192
$31$	68.6947	0.397998	0.198999	−	0.980000i	$-0.436231\pi$
$31$	68.6947	0.397998	0.198999	+	0.980000i	$0.436231\pi$
$32$	−187.385	−1.03517
$33$	−33.0000	−0.174078
$34$	−97.9610	−0.494123
$35$	0	0
$36$	−52.7623	−0.244270
$37$	301.478	1.33953	0.669767	−	0.742572i	$-0.266394\pi$
$37$	301.478	1.33953	0.669767	+	0.742572i	$0.266394\pi$
$38$	−33.0202	−0.140963
$39$	−164.883	−0.676985
$40$	278.042	1.09906
$41$	−366.280	−1.39520	−0.697602	−	0.716485i	$-0.745750\pi$
$41$	−366.280	−1.39520	−0.697602	+	0.716485i	$0.745750\pi$
$42$	0	0
$43$	−67.4146	−0.239084	−0.119542	−	0.992829i	$-0.538143\pi$
$43$	−67.4146	−0.239084	−0.119542	+	0.992829i	$0.538143\pi$
$44$	−64.4873	−0.220951
$45$	123.469	0.409015
$46$	−282.586	−0.905760
$47$	594.558	1.84522	0.922608	−	0.385739i	$-0.126054\pi$
$47$	594.558	1.84522	0.922608	+	0.385739i	$0.126054\pi$
$48$	−51.8057	−0.155781
$49$	0	0
$50$	−92.4066	−0.261365
$51$	−201.011	−0.551905
$52$	−322.208	−0.859274
$53$	192.711	0.499450	0.249725	−	0.968317i	$-0.419660\pi$
$53$	192.711	0.499450	0.249725	+	0.968317i	$0.419660\pi$
$54$	39.4747	0.0994782
$55$	150.906	0.369968
$56$	0	0
$57$	−67.7557	−0.157447
$58$	−333.254	−0.754455
$59$	630.764	1.39184	0.695919	−	0.718120i	$-0.254997\pi$
$59$	630.764	1.39184	0.695919	+	0.718120i	$0.254997\pi$
$60$	241.278	0.519148
$61$	−321.750	−0.675341	−0.337671	−	0.941264i	$-0.609639\pi$
$61$	−321.750	−0.675341	−0.337671	+	0.941264i	$0.609639\pi$
$62$	−100.433	−0.205727
$63$	0	0
$64$	135.814	0.265261
$65$	753.998	1.43880
$66$	48.2468	0.0899814
$67$	−794.875	−1.44939	−0.724697	−	0.689067i	$-0.758020\pi$
$67$	−794.875	−1.44939	−0.724697	+	0.689067i	$0.758020\pi$
$68$	−392.808	−0.700513
$69$	−579.851	−1.01168
$70$	0	0
$71$	501.559	0.838367	0.419184	−	0.907901i	$-0.362316\pi$
$71$	501.559	0.838367	0.419184	+	0.907901i	$0.362316\pi$
$72$	182.406	0.298565
$73$	−882.308	−1.41461	−0.707304	−	0.706910i	$-0.750089\pi$
$73$	−882.308	−1.41461	−0.707304	+	0.706910i	$0.750089\pi$
$74$	−440.769	−0.692410
$75$	−189.614	−0.291929
$76$	−132.405	−0.199841
$77$	0	0
$78$	241.063	0.349936
$79$	−449.968	−0.640827	−0.320414	−	0.947278i	$-0.603822\pi$
$79$	−449.968	−0.640827	−0.320414	+	0.947278i	$0.603822\pi$
$80$	236.903	0.331083
$81$	81.0000	0.111111
$82$	535.511	0.721186
$83$	−87.9363	−0.116292	−0.0581462	−	0.998308i	$-0.518519\pi$
$83$	−87.9363	−0.116292	−0.0581462	+	0.998308i	$0.518519\pi$
$84$	0	0
$85$	919.207	1.17296
$86$	98.5619	0.123584
$87$	−683.820	−0.842681
$88$	222.940	0.270063
$89$	−761.292	−0.906705	−0.453353	−	0.891331i	$-0.649772\pi$
$89$	−761.292	−0.906705	−0.453353	+	0.891331i	$0.649772\pi$
$90$	−180.515	−0.211421
$91$	0	0
$92$	−1133.12	−1.28409
$93$	−206.084	−0.229784
$94$	−869.258	−0.953799
$95$	309.841	0.334622
$96$	562.156	0.597655
$97$	−1373.22	−1.43741	−0.718706	−	0.695314i	$-0.755265\pi$
$97$	−1373.22	−1.43741	−0.718706	+	0.695314i	$0.755265\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	−370.536	−0.370536
$101$	1021.01	1.00588	0.502941	−	0.864321i	$-0.332251\pi$
$101$	1021.01	1.00588	0.502941	+	0.864321i	$0.332251\pi$
$102$	293.883	0.285282
$103$	−626.037	−0.598886	−0.299443	−	0.954114i	$-0.596801\pi$
$103$	−626.037	−0.598886	−0.299443	+	0.954114i	$0.596801\pi$
$104$	1113.91	1.05027
$105$	0	0
$106$	−281.748	−0.258168
$107$	867.215	0.783522	0.391761	−	0.920067i	$-0.371866\pi$
$107$	867.215	0.783522	0.391761	+	0.920067i	$0.371866\pi$
$108$	158.287	0.141029
$109$	1438.48	1.26405	0.632025	−	0.774948i	$-0.282224\pi$
$109$	1438.48	1.26405	0.632025	+	0.774948i	$0.282224\pi$
$110$	−220.629	−0.191238
$111$	−904.435	−0.773380
$112$	0	0
$113$	−1799.22	−1.49784	−0.748922	−	0.662659i	$-0.769428\pi$
$113$	−1799.22	−1.49784	−0.748922	+	0.662659i	$0.769428\pi$
$114$	99.0605	0.0813848
$115$	2651.61	2.15012
$116$	−1336.29	−1.06958
$117$	494.649	0.390858
$118$	−922.193	−0.719447
$119$	0	0
$120$	−834.127	−0.634542
$121$	121.000	0.0909091
$122$	470.406	0.349087
$123$	1098.84	0.805521
$124$	−402.722	−0.291657
$125$	−847.757	−0.606606
$126$	0	0
$127$	−840.811	−0.587480	−0.293740	−	0.955885i	$-0.594900\pi$
$127$	−840.811	−0.587480	−0.293740	+	0.955885i	$0.594900\pi$
$128$	1300.52	0.898054
$129$	202.244	0.138035
$130$	−1102.36	−0.743721
$131$	424.411	0.283061	0.141530	−	0.989934i	$-0.454798\pi$
$131$	424.411	0.283061	0.141530	+	0.989934i	$0.454798\pi$
$132$	193.462	0.127566
$133$	0	0
$134$	1162.13	0.749198
$135$	−370.407	−0.236145
$136$	1357.98	0.856221
$137$	−1629.91	−1.01644	−0.508222	−	0.861226i	$-0.669697\pi$
$137$	−1629.91	−1.01644	−0.508222	+	0.861226i	$0.669697\pi$
$138$	847.757	0.522941
$139$	238.960	0.145816	0.0729078	−	0.997339i	$-0.476772\pi$
$139$	238.960	0.145816	0.0729078	+	0.997339i	$0.476772\pi$
$140$	0	0
$141$	−1783.67	−1.06534
$142$	−733.292	−0.433355
$143$	604.571	0.353544
$144$	155.417	0.0899404
$145$	3127.06	1.79095
$146$	1289.96	0.731216
$147$	0	0
$148$	−1767.41	−0.981624
$149$	−2552.35	−1.40333	−0.701667	−	0.712505i	$-0.747561\pi$
$149$	−2552.35	−1.40333	−0.701667	+	0.712505i	$0.747561\pi$
$150$	277.220	0.150899
$151$	−1863.59	−1.00435	−0.502176	−	0.864766i	$-0.667467\pi$
$151$	−1863.59	−1.00435	−0.502176	+	0.864766i	$0.667467\pi$
$152$	457.741	0.244261
$153$	603.033	0.318642
$154$	0	0
$155$	942.407	0.488361
$156$	966.624	0.496102
$157$	585.425	0.297592	0.148796	−	0.988868i	$-0.452460\pi$
$157$	585.425	0.297592	0.148796	+	0.988868i	$0.452460\pi$
$158$	657.864	0.331246
$159$	−578.132	−0.288358
$160$	−2570.70	−1.27020
$161$	0	0
$162$	−118.424	−0.0574338
$163$	−3057.99	−1.46945	−0.734724	−	0.678366i	$-0.762688\pi$
$163$	−3057.99	−1.46945	−0.734724	+	0.678366i	$0.762688\pi$
$164$	2147.31	1.02242
$165$	−452.719	−0.213601
$166$	128.565	0.0601120
$167$	3075.42	1.42505	0.712525	−	0.701647i	$-0.247552\pi$
$167$	3075.42	1.42505	0.712525	+	0.701647i	$0.247552\pi$
$168$	0	0
$169$	823.716	0.374927
$170$	−1343.90	−0.606310
$171$	203.267	0.0909018
$172$	395.217	0.175204
$173$	2279.37	1.00172	0.500859	−	0.865529i	$-0.333017\pi$
$173$	2279.37	1.00172	0.500859	+	0.865529i	$0.333017\pi$
$174$	999.762	0.435585
$175$	0	0
$176$	189.954	0.0813542
$177$	−1892.29	−0.803579
$178$	1113.03	0.468679
$179$	3359.74	1.40290	0.701450	−	0.712719i	$-0.252537\pi$
$179$	3359.74	1.40290	0.701450	+	0.712719i	$0.252537\pi$
$180$	−723.834	−0.299730
$181$	−2429.40	−0.997655	−0.498828	−	0.866701i	$-0.666236\pi$
$181$	−2429.40	−0.997655	−0.498828	+	0.866701i	$0.666236\pi$
$182$	0	0
$183$	965.249	0.389909
$184$	3917.34	1.56951
$185$	4135.91	1.64367
$186$	301.300	0.118776
$187$	737.040	0.288223
$188$	−3485.58	−1.35219
$189$	0	0
$190$	−452.996	−0.172967
$191$	−335.824	−0.127222	−0.0636110	−	0.997975i	$-0.520262\pi$
$191$	−335.824	−0.127222	−0.0636110	+	0.997975i	$0.520262\pi$
$192$	−407.441	−0.153149
$193$	−1834.22	−0.684094	−0.342047	−	0.939683i	$-0.611120\pi$
$193$	−1834.22	−0.684094	−0.342047	+	0.939683i	$0.611120\pi$
$194$	2007.68	0.743004
$195$	−2261.99	−0.830691
$196$	0	0
$197$	−1795.85	−0.649489	−0.324744	−	0.945802i	$-0.605278\pi$
$197$	−1795.85	−0.649489	−0.324744	+	0.945802i	$0.605278\pi$
$198$	−144.740	−0.0519508
$199$	1707.58	0.608278	0.304139	−	0.952628i	$-0.401631\pi$
$199$	1707.58	0.608278	0.304139	+	0.952628i	$0.401631\pi$
$200$	1280.99	0.452897
$201$	2384.62	0.836808
$202$	−1492.74	−0.519944
$203$	0	0
$204$	1178.42	0.404442
$205$	−5024.91	−1.71198
$206$	915.282	0.309567
$207$	1739.55	0.584093
$208$	949.098	0.316385
$209$	248.437	0.0822238
$210$	0	0
$211$	5758.96	1.87897	0.939486	−	0.342586i	$-0.111303\pi$
$211$	5758.96	1.87897	0.939486	+	0.342586i	$0.111303\pi$
$212$	−1129.76	−0.366002
$213$	−1504.68	−0.484032
$214$	−1267.89	−0.405005
$215$	−924.845	−0.293367
$216$	−547.217	−0.172377
$217$	0	0
$218$	−2103.09	−0.653392
$219$	2646.93	0.816724
$220$	−884.686	−0.271116
$221$	3682.59	1.12089
$222$	1322.31	0.399763
$223$	1389.41	0.417226	0.208613	−	0.977998i	$-0.433105\pi$
$223$	1389.41	0.417226	0.208613	+	0.977998i	$0.433105\pi$
$224$	0	0
$225$	568.841	0.168545
$226$	2630.50	0.774241
$227$	5741.39	1.67872	0.839360	−	0.543576i	$-0.182930\pi$
$227$	5741.39	1.67872	0.839360	+	0.543576i	$0.182930\pi$
$228$	397.216	0.115379
$229$	3928.69	1.13369	0.566846	−	0.823824i	$-0.308164\pi$
$229$	3928.69	1.13369	0.566846	+	0.823824i	$0.308164\pi$
$230$	−3876.73	−1.11141
$231$	0	0
$232$	4619.73	1.30733
$233$	1746.32	0.491008	0.245504	−	0.969396i	$-0.421046\pi$
$233$	1746.32	0.491008	0.245504	+	0.969396i	$0.421046\pi$
$234$	−723.190	−0.202036
$235$	8156.60	2.26416
$236$	−3697.84	−1.01995
$237$	1349.90	0.369982
$238$	0	0
$239$	−741.876	−0.200786	−0.100393	−	0.994948i	$-0.532010\pi$
$239$	−741.876	−0.200786	−0.100393	+	0.994948i	$0.532010\pi$
$240$	−710.710	−0.191151
$241$	5684.46	1.51937	0.759685	−	0.650291i	$-0.225353\pi$
$241$	5684.46	1.51937	0.759685	+	0.650291i	$0.225353\pi$
$242$	−176.905	−0.0469913
$243$	−243.000	−0.0641500
$244$	1886.25	0.494897
$245$	0	0
$246$	−1606.53	−0.416377
$247$	1241.31	0.319767
$248$	1392.26	0.356485
$249$	263.809	0.0671414
$250$	1239.44	0.313557
$251$	3415.78	0.858972	0.429486	−	0.903074i	$-0.358695\pi$
$251$	3415.78	0.858972	0.429486	+	0.903074i	$0.358695\pi$
$252$	0	0
$253$	2126.12	0.528332
$254$	1229.29	0.303671
$255$	−2757.62	−0.677212
$256$	−2987.90	−0.729469
$257$	3890.50	0.944291	0.472145	−	0.881521i	$-0.343480\pi$
$257$	3890.50	0.944291	0.472145	+	0.881521i	$0.343480\pi$
$258$	−295.686	−0.0713511
$259$	0	0
$260$	−4420.30	−1.05437
$261$	2051.46	0.486522
$262$	−620.500	−0.146315
$263$	−3467.04	−0.812878	−0.406439	−	0.913678i	$-0.633230\pi$
$263$	−3467.04	−0.812878	−0.406439	+	0.913678i	$0.633230\pi$
$264$	−668.821	−0.155921
$265$	2643.75	0.612847
$266$	0	0
$267$	2283.88	0.523486
$268$	4659.94	1.06213
$269$	−3515.07	−0.796720	−0.398360	−	0.917229i	$-0.630420\pi$
$269$	−3515.07	−0.796720	−0.398360	+	0.917229i	$0.630420\pi$
$270$	541.544	0.122064
$271$	−1975.55	−0.442827	−0.221413	−	0.975180i	$-0.571067\pi$
$271$	−1975.55	−0.442827	−0.221413	+	0.975180i	$0.571067\pi$
$272$	1157.06	0.257930
$273$	0	0
$274$	2382.97	0.525404
$275$	695.250	0.152455
$276$	3399.37	0.741369
$277$	−4600.69	−0.997936	−0.498968	−	0.866620i	$-0.666288\pi$
$277$	−4600.69	−0.997936	−0.498968	+	0.866620i	$0.666288\pi$
$278$	−349.366	−0.0753726
$279$	618.252	0.132666
$280$	0	0
$281$	−3985.40	−0.846081	−0.423041	−	0.906111i	$-0.639037\pi$
$281$	−3985.40	−0.846081	−0.423041	+	0.906111i	$0.639037\pi$
$282$	2607.77	0.550676
$283$	−3223.74	−0.677143	−0.338572	−	0.940941i	$-0.609944\pi$
$283$	−3223.74	−0.677143	−0.338572	+	0.940941i	$0.609944\pi$
$284$	−2940.38	−0.614364
$285$	−929.524	−0.193194
$286$	−883.899	−0.182748
$287$	0	0
$288$	−1686.47	−0.345056
$289$	−423.514	−0.0862027
$290$	−4571.83	−0.925750
$291$	4119.65	0.829890
$292$	5172.52	1.03664
$293$	−4142.15	−0.825893	−0.412947	−	0.910755i	$-0.635500\pi$
$293$	−4142.15	−0.825893	−0.412947	+	0.910755i	$0.635500\pi$
$294$	0	0
$295$	8653.31	1.70785
$296$	6110.15	1.19982
$297$	−297.000	−0.0580259
$298$	3731.60	0.725389
$299$	10623.1	2.05468
$300$	1111.61	0.213929
$301$	0	0
$302$	2724.62	0.519153
$303$	−3063.02	−0.580746
$304$	390.014	0.0735818
$305$	−4414.01	−0.828673
$306$	−881.649	−0.164708
$307$	1061.53	0.197345	0.0986724	−	0.995120i	$-0.468540\pi$
$307$	1061.53	0.197345	0.0986724	+	0.995120i	$0.468540\pi$
$308$	0	0
$309$	1878.11	0.345767
$310$	−1377.82	−0.252436
$311$	3487.67	0.635910	0.317955	−	0.948106i	$-0.397004\pi$
$311$	3487.67	0.635910	0.317955	+	0.948106i	$0.397004\pi$
$312$	−3341.74	−0.606373
$313$	5230.61	0.944574	0.472287	−	0.881445i	$-0.343429\pi$
$313$	5230.61	0.944574	0.472287	+	0.881445i	$0.343429\pi$
$314$	−855.905	−0.153827
$315$	0	0
$316$	2637.93	0.469605
$317$	−5303.56	−0.939677	−0.469839	−	0.882752i	$-0.655688\pi$
$317$	−5303.56	−0.939677	−0.469839	+	0.882752i	$0.655688\pi$
$318$	845.244	0.149053
$319$	2507.34	0.440076
$320$	1863.20	0.325487
$321$	−2601.64	−0.452366
$322$	0	0
$323$	1513.29	0.260687
$324$	−474.861	−0.0814234
$325$	3473.79	0.592896
$326$	4470.85	0.759563
$327$	−4315.44	−0.729799
$328$	−7423.51	−1.24968
$329$	0	0
$330$	661.887	0.110411
$331$	7484.85	1.24291	0.621457	−	0.783448i	$-0.286541\pi$
$331$	7484.85	1.24291	0.621457	+	0.783448i	$0.286541\pi$
$332$	515.525	0.0852203
$333$	2713.30	0.446511
$334$	−4496.34	−0.736614
$335$	−10904.7	−1.77847
$336$	0	0
$337$	11676.3	1.88738	0.943689	−	0.330834i	$-0.107330\pi$
$337$	11676.3	1.88738	0.943689	+	0.330834i	$0.107330\pi$
$338$	−1204.29	−0.193801
$339$	5397.66	0.864780
$340$	−5388.84	−0.859561
$341$	755.642	0.120001
$342$	−297.181	−0.0469875
$343$	0	0
$344$	−1366.31	−0.214147
$345$	−7954.84	−1.24137
$346$	−3332.50	−0.517792
$347$	−11537.1	−1.78485	−0.892424	−	0.451198i	$-0.850997\pi$
$347$	−11537.1	−1.78485	−0.892424	+	0.451198i	$0.850997\pi$
$348$	4008.88	0.617525
$349$	5859.17	0.898665	0.449333	−	0.893365i	$-0.351662\pi$
$349$	5859.17	0.898665	0.449333	+	0.893365i	$0.351662\pi$
$350$	0	0
$351$	−1483.95	−0.225662
$352$	−2061.24	−0.312115
$353$	−5283.86	−0.796689	−0.398345	−	0.917236i	$-0.630415\pi$
$353$	−5283.86	−0.796689	−0.398345	+	0.917236i	$0.630415\pi$
$354$	2766.58	0.415373
$355$	6880.77	1.02871
$356$	4463.06	0.664443
$357$	0	0
$358$	−4912.03	−0.725164
$359$	−5103.38	−0.750268	−0.375134	−	0.926971i	$-0.622403\pi$
$359$	−5103.38	−0.750268	−0.375134	+	0.926971i	$0.622403\pi$
$360$	2502.38	0.366353
$361$	−6348.91	−0.925632
$362$	3551.84	0.515692
$363$	−363.000	−0.0524864
$364$	0	0
$365$	−12104.2	−1.73579
$366$	−1411.22	−0.201545
$367$	−1014.41	−0.144282	−0.0721412	−	0.997394i	$-0.522983\pi$
$367$	−1014.41	−0.144282	−0.0721412	+	0.997394i	$0.522983\pi$
$368$	3337.73	0.472802
$369$	−3296.52	−0.465068
$370$	−6046.81	−0.849617
$371$	0	0
$372$	1208.16	0.168388
$373$	2803.52	0.389170	0.194585	−	0.980886i	$-0.437664\pi$
$373$	2803.52	0.389170	0.194585	+	0.980886i	$0.437664\pi$
$374$	−1077.57	−0.148984
$375$	2543.27	0.350224
$376$	12050.1	1.65275
$377$	12527.8	1.71145
$378$	0	0
$379$	−10212.2	−1.38408	−0.692041	−	0.721858i	$-0.743288\pi$
$379$	−10212.2	−1.38408	−0.692041	+	0.721858i	$0.743288\pi$
$380$	−1816.44	−0.245214
$381$	2522.43	0.339182
$382$	490.984	0.0657615
$383$	8761.82	1.16895	0.584475	−	0.811411i	$-0.301300\pi$
$383$	8761.82	1.16895	0.584475	+	0.811411i	$0.301300\pi$
$384$	−3901.56	−0.518491
$385$	0	0
$386$	2681.68	0.353611
$387$	−606.732	−0.0796948
$388$	8050.45	1.05335
$389$	−6254.93	−0.815264	−0.407632	−	0.913146i	$-0.633645\pi$
$389$	−6254.93	−0.815264	−0.407632	+	0.913146i	$0.633645\pi$
$390$	3307.09	0.429387
$391$	12950.7	1.67505
$392$	0	0
$393$	−1273.23	−0.163425
$394$	2625.58	0.335723
$395$	−6173.00	−0.786323
$396$	−580.386	−0.0736502
$397$	−8228.13	−1.04020	−0.520098	−	0.854106i	$-0.674105\pi$
$397$	−8228.13	−1.04020	−0.520098	+	0.854106i	$0.674105\pi$
$398$	−2496.53	−0.314422
$399$	0	0
$400$	1091.45	0.136431
$401$	6969.81	0.867970	0.433985	−	0.900920i	$-0.357107\pi$
$401$	6969.81	0.867970	0.433985	+	0.900920i	$0.357107\pi$
$402$	−3486.38	−0.432549
$403$	3775.53	0.466682
$404$	−5985.64	−0.737121
$405$	1111.22	0.136338
$406$	0	0
$407$	3316.26	0.403884
$408$	−4073.95	−0.494339
$409$	−12959.4	−1.56675	−0.783374	−	0.621550i	$-0.786503\pi$
$409$	−12959.4	−1.56675	−0.783374	+	0.621550i	$0.786503\pi$
$410$	7346.55	0.884927
$411$	4889.74	0.586845
$412$	3670.13	0.438870
$413$	0	0
$414$	−2543.27	−0.301920
$415$	−1206.38	−0.142696
$416$	−10298.9	−1.21381
$417$	−716.881	−0.0841866
$418$	−363.222	−0.0425018
$419$	−11013.5	−1.28411	−0.642056	−	0.766658i	$-0.721918\pi$
$419$	−11013.5	−1.28411	−0.642056	+	0.766658i	$0.721918\pi$
$420$	0	0
$421$	2276.93	0.263589	0.131795	−	0.991277i	$-0.457926\pi$
$421$	2276.93	0.263589	0.131795	+	0.991277i	$0.457926\pi$
$422$	−8419.75	−0.971248
$423$	5351.02	0.615072
$424$	3905.73	0.447356
$425$	4234.93	0.483352
$426$	2199.88	0.250198
$427$	0	0
$428$	−5084.03	−0.574173
$429$	−1813.71	−0.204119
$430$	1352.15	0.151643
$431$	3788.40	0.423389	0.211695	−	0.977336i	$-0.432102\pi$
$431$	3788.40	0.423389	0.211695	+	0.977336i	$0.432102\pi$
$432$	−466.251	−0.0519271
$433$	4650.91	0.516186	0.258093	−	0.966120i	$-0.416906\pi$
$433$	4650.91	0.516186	0.258093	+	0.966120i	$0.416906\pi$
$434$	0	0
$435$	−9381.17	−1.03401
$436$	−8433.06	−0.926308
$437$	4365.35	0.477856
$438$	−3869.87	−0.422168
$439$	3355.78	0.364835	0.182418	−	0.983221i	$-0.441608\pi$
$439$	3355.78	0.364835	0.182418	+	0.983221i	$0.441608\pi$
$440$	3058.47	0.331379
$441$	0	0
$442$	−5384.04	−0.579395
$443$	3866.66	0.414696	0.207348	−	0.978267i	$-0.433517\pi$
$443$	3866.66	0.414696	0.207348	+	0.978267i	$0.433517\pi$
$444$	5302.23	0.566741
$445$	−10444.0	−1.11257
$446$	−2031.35	−0.215666
$447$	7657.06	0.810216
$448$	0	0
$449$	−7207.30	−0.757536	−0.378768	−	0.925492i	$-0.623652\pi$
$449$	−7207.30	−0.757536	−0.378768	+	0.925492i	$0.623652\pi$
$450$	−831.660	−0.0871218
$451$	−4029.08	−0.420670
$452$	10547.9	1.09763
$453$	5590.78	0.579862
$454$	−8394.06	−0.867737
$455$	0	0
$456$	−1373.22	−0.141024
$457$	15201.1	1.55597	0.777986	−	0.628282i	$-0.216242\pi$
$457$	15201.1	1.55597	0.777986	+	0.628282i	$0.216242\pi$
$458$	−5743.85	−0.586010
$459$	−1809.10	−0.183968
$460$	−15545.0	−1.57563
$461$	−7824.22	−0.790477	−0.395239	−	0.918578i	$-0.629338\pi$
$461$	−7824.22	−0.790477	−0.395239	+	0.918578i	$0.629338\pi$
$462$	0	0
$463$	2531.64	0.254116	0.127058	−	0.991895i	$-0.459447\pi$
$463$	2531.64	0.254116	0.127058	+	0.991895i	$0.459447\pi$
$464$	3936.20	0.393822
$465$	−2827.22	−0.281955
$466$	−2553.16	−0.253804
$467$	10851.1	1.07522	0.537612	−	0.843192i	$-0.319327\pi$
$467$	10851.1	1.07522	0.537612	+	0.843192i	$0.319327\pi$
$468$	−2899.87	−0.286425
$469$	0	0
$470$	−11925.1	−1.17035
$471$	−1756.27	−0.171815
$472$	12783.9	1.24667
$473$	−741.561	−0.0720867
$474$	−1973.59	−0.191245
$475$	1427.49	0.137890
$476$	0	0
$477$	1734.40	0.166483
$478$	1084.64	0.103787
$479$	−4732.87	−0.451462	−0.225731	−	0.974190i	$-0.572477\pi$
$479$	−4732.87	−0.451462	−0.225731	+	0.974190i	$0.572477\pi$
$480$	7712.09	0.733348
$481$	16569.6	1.57070
$482$	−8310.82	−0.785369
$483$	0	0
$484$	−709.360	−0.0666191
$485$	−18838.8	−1.76377
$486$	355.272	0.0331594
$487$	−3354.58	−0.312137	−0.156068	−	0.987746i	$-0.549882\pi$
$487$	−3354.58	−0.312137	−0.156068	+	0.987746i	$0.549882\pi$
$488$	−6521.00	−0.604901
$489$	9173.96	0.848386
$490$	0	0
$491$	7860.53	0.722487	0.361243	−	0.932472i	$-0.382352\pi$
$491$	7860.53	0.722487	0.361243	+	0.932472i	$0.382352\pi$
$492$	−6441.94	−0.590294
$493$	15272.8	1.39524
$494$	−1814.82	−0.165289
$495$	1358.16	0.123323
$496$	1186.26	0.107388
$497$	0	0
$498$	−385.695	−0.0347057
$499$	13603.0	1.22035	0.610173	−	0.792268i	$-0.291100\pi$
$499$	13603.0	1.22035	0.610173	+	0.792268i	$0.291100\pi$
$500$	4969.96	0.444527
$501$	−9226.26	−0.822753
$502$	−4993.95	−0.444006
$503$	−13196.9	−1.16983	−0.584913	−	0.811096i	$-0.698872\pi$
$503$	−13196.9	−1.16983	−0.584913	+	0.811096i	$0.698872\pi$
$504$	0	0
$505$	14007.0	1.23426
$506$	−3108.44	−0.273097
$507$	−2471.15	−0.216464
$508$	4929.24	0.430511
$509$	−6458.72	−0.562432	−0.281216	−	0.959644i	$-0.590738\pi$
$509$	−6458.72	−0.562432	−0.281216	+	0.959644i	$0.590738\pi$
$510$	4031.71	0.350053
$511$	0	0
$512$	−6035.77	−0.520988
$513$	−609.801	−0.0524822
$514$	−5688.01	−0.488108
$515$	−8588.46	−0.734860
$516$	−1185.65	−0.101154
$517$	6540.13	0.556353
$518$	0	0
$519$	−6838.11	−0.578342
$520$	15281.5	1.28873
$521$	−7148.33	−0.601102	−0.300551	−	0.953766i	$-0.597171\pi$
$521$	−7148.33	−0.601102	−0.300551	+	0.953766i	$0.597171\pi$
$522$	−2999.29	−0.251485
$523$	−17061.6	−1.42648	−0.713242	−	0.700918i	$-0.752774\pi$
$523$	−17061.6	−1.42648	−0.713242	+	0.700918i	$0.752774\pi$
$524$	−2488.10	−0.207430
$525$	0	0
$526$	5068.90	0.420180
$527$	4602.79	0.380457
$528$	−569.863	−0.0469699
$529$	25191.6	2.07048
$530$	−3865.23	−0.316783
$531$	5676.88	0.463946
$532$	0	0
$533$	−20131.1	−1.63598
$534$	−3339.08	−0.270592
$535$	11897.1	0.961415
$536$	−16110.0	−1.29822
$537$	−10079.2	−0.809964
$538$	5139.12	0.411827
$539$	0	0
$540$	2171.50	0.173049
$541$	−989.286	−0.0786187	−0.0393094	−	0.999227i	$-0.512516\pi$
$541$	−989.286	−0.0786187	−0.0393094	+	0.999227i	$0.512516\pi$
$542$	2888.30	0.228899
$543$	7288.19	0.575997
$544$	−12555.5	−0.989546
$545$	19734.2	1.55104
$546$	0	0
$547$	−10611.5	−0.829464	−0.414732	−	0.909944i	$-0.636125\pi$
$547$	−10611.5	−0.829464	−0.414732	+	0.909944i	$0.636125\pi$
$548$	9555.34	0.744861
$549$	−2895.75	−0.225114
$550$	−1016.47	−0.0788046
$551$	5148.08	0.398032
$552$	−11752.0	−0.906157
$553$	0	0
$554$	6726.32	0.515837
$555$	−12407.7	−0.948971
$556$	−1400.90	−0.106855
$557$	3196.28	0.243143	0.121572	−	0.992583i	$-0.461207\pi$
$557$	3196.28	0.243143	0.121572	+	0.992583i	$0.461207\pi$
$558$	−903.900	−0.0685756
$559$	−3705.18	−0.280344
$560$	0	0
$561$	−2211.12	−0.166406
$562$	5826.75	0.437343
$563$	17843.7	1.33574	0.667871	−	0.744277i	$-0.267206\pi$
$563$	17843.7	1.33574	0.667871	+	0.744277i	$0.267206\pi$
$564$	10456.7	0.780689
$565$	−24683.1	−1.83792
$566$	4713.19	0.350018
$567$	0	0
$568$	10165.2	0.750923
$569$	−12057.5	−0.888362	−0.444181	−	0.895937i	$-0.646505\pi$
$569$	−12057.5	−0.888362	−0.444181	+	0.895937i	$0.646505\pi$
$570$	1358.99	0.0998627
$571$	−8636.71	−0.632986	−0.316493	−	0.948595i	$-0.602505\pi$
$571$	−8636.71	−0.632986	−0.316493	+	0.948595i	$0.602505\pi$
$572$	−3544.29	−0.259081
$573$	1007.47	0.0734516
$574$	0	0
$575$	12216.4	0.886016
$576$	1222.32	0.0884204
$577$	−18584.4	−1.34086	−0.670431	−	0.741972i	$-0.733891\pi$
$577$	−18584.4	−1.34086	−0.670431	+	0.741972i	$0.733891\pi$
$578$	619.188	0.0445585
$579$	5502.67	0.394962
$580$	−18332.3	−1.31243
$581$	0	0
$582$	−6023.03	−0.428973
$583$	2119.82	0.150590
$584$	−17882.0	−1.26706
$585$	6785.98	0.479599
$586$	6055.92	0.426908
$587$	24215.3	1.70268	0.851338	−	0.524618i	$-0.175792\pi$
$587$	24215.3	1.70268	0.851338	+	0.524618i	$0.175792\pi$
$588$	0	0
$589$	1551.49	0.108536
$590$	−12651.4	−0.882793
$591$	5387.56	0.374983
$592$	5206.10	0.361435
$593$	−15317.9	−1.06076	−0.530379	−	0.847761i	$-0.677950\pi$
$593$	−15317.9	−1.06076	−0.530379	+	0.847761i	$0.677950\pi$
$594$	434.221	0.0299938
$595$	0	0
$596$	14963.1	1.02838
$597$	−5122.75	−0.351190
$598$	−15531.2	−1.06207
$599$	−18631.8	−1.27091	−0.635456	−	0.772137i	$-0.719188\pi$
$599$	−18631.8	−1.27091	−0.635456	+	0.772137i	$0.719188\pi$
$600$	−3842.96	−0.261480
$601$	8727.44	0.592345	0.296173	−	0.955134i	$-0.404290\pi$
$601$	8727.44	0.592345	0.296173	+	0.955134i	$0.404290\pi$
$602$	0	0
$603$	−7153.87	−0.483131
$604$	10925.3	0.735999
$605$	1659.97	0.111549
$606$	4478.22	0.300190
$607$	−24801.9	−1.65845	−0.829223	−	0.558917i	$-0.811217\pi$
$607$	−24801.9	−1.65845	−0.829223	+	0.558917i	$0.811217\pi$
$608$	−4232.14	−0.282296
$609$	0	0
$610$	6453.39	0.428345
$611$	32677.5	2.16365
$612$	−3535.27	−0.233504
$613$	−24667.8	−1.62532	−0.812661	−	0.582736i	$-0.801982\pi$
$613$	−24667.8	−1.62532	−0.812661	+	0.582736i	$0.801982\pi$
$614$	−1551.99	−0.102008
$615$	15074.7	0.988410
$616$	0	0
$617$	−16915.6	−1.10372	−0.551860	−	0.833937i	$-0.686082\pi$
$617$	−16915.6	−1.10372	−0.551860	+	0.833937i	$0.686082\pi$
$618$	−2745.85	−0.178728
$619$	−6621.95	−0.429982	−0.214991	−	0.976616i	$-0.568972\pi$
$619$	−6621.95	−0.429982	−0.214991	+	0.976616i	$0.568972\pi$
$620$	−5524.84	−0.357876
$621$	−5218.66	−0.337226
$622$	−5099.07	−0.328704
$623$	0	0
$624$	−2847.29	−0.182665
$625$	−19530.8	−1.24997
$626$	−7647.29	−0.488254
$627$	−745.312	−0.0474719
$628$	−3432.04	−0.218079
$629$	20200.1	1.28050
$630$	0	0
$631$	8668.35	0.546881	0.273440	−	0.961889i	$-0.411838\pi$
$631$	8668.35	0.546881	0.273440	+	0.961889i	$0.411838\pi$
$632$	−9119.63	−0.573987
$633$	−17276.9	−1.08483
$634$	7753.94	0.485723
$635$	−11534.9	−0.720864
$636$	3389.29	0.211311
$637$	0	0
$638$	−3665.79	−0.227477
$639$	4514.03	0.279456
$640$	17841.5	1.10195
$641$	−6330.64	−0.390086	−0.195043	−	0.980795i	$-0.562485\pi$
$641$	−6330.64	−0.390086	−0.195043	+	0.980795i	$0.562485\pi$
$642$	3803.67	0.233830
$643$	26710.4	1.63819	0.819096	−	0.573657i	$-0.194476\pi$
$643$	26710.4	1.63819	0.819096	+	0.573657i	$0.194476\pi$
$644$	0	0
$645$	2774.54	0.169376
$646$	−2212.47	−0.134750
$647$	6461.96	0.392652	0.196326	−	0.980539i	$-0.437099\pi$
$647$	6461.96	0.392652	0.196326	+	0.980539i	$0.437099\pi$
$648$	1641.65	0.0995218
$649$	6938.41	0.419655
$650$	−5078.76	−0.306470
$651$	0	0
$652$	17927.4	1.07683
$653$	9719.26	0.582456	0.291228	−	0.956654i	$-0.405936\pi$
$653$	9719.26	0.582456	0.291228	+	0.956654i	$0.405936\pi$
$654$	6309.28	0.377236
$655$	5822.40	0.347328
$656$	−6325.13	−0.376456
$657$	−7940.78	−0.471536
$658$	0	0
$659$	−15394.4	−0.909983	−0.454992	−	0.890496i	$-0.650358\pi$
$659$	−15394.4	−0.909983	−0.454992	+	0.890496i	$0.650358\pi$
$660$	2654.06	0.156529
$661$	−9816.01	−0.577607	−0.288804	−	0.957388i	$-0.593258\pi$
$661$	−9816.01	−0.577607	−0.288804	+	0.957388i	$0.593258\pi$
$662$	−10943.0	−0.642467
$663$	−11047.8	−0.647149
$664$	−1782.23	−0.104163
$665$	0	0
$666$	−3966.92	−0.230803
$667$	44057.1	2.55757
$668$	−18029.6	−1.04429
$669$	−4168.22	−0.240886
$670$	15942.9	0.919298
$671$	−3539.25	−0.203623
$672$	0	0
$673$	19396.0	1.11094	0.555469	−	0.831537i	$-0.312539\pi$
$673$	19396.0	1.11094	0.555469	+	0.831537i	$0.312539\pi$
$674$	−17071.0	−0.975593
$675$	−1706.52	−0.0973098
$676$	−4829.02	−0.274751
$677$	−8027.38	−0.455712	−0.227856	−	0.973695i	$-0.573172\pi$
$677$	−8027.38	−0.455712	−0.227856	+	0.973695i	$0.573172\pi$
$678$	−7891.51	−0.447008
$679$	0	0
$680$	18629.8	1.05062
$681$	−17224.2	−0.969210
$682$	−1104.77	−0.0620289
$683$	21500.9	1.20455	0.602275	−	0.798289i	$-0.294261\pi$
$683$	21500.9	1.20455	0.602275	+	0.798289i	$0.294261\pi$
$684$	−1191.65	−0.0666138
$685$	−22360.4	−1.24722
$686$	0	0
$687$	−11786.1	−0.654537
$688$	−1164.15	−0.0645101
$689$	10591.6	0.585642
$690$	11630.2	0.641671
$691$	19045.2	1.04850	0.524249	−	0.851565i	$-0.324346\pi$
$691$	19045.2	1.04850	0.524249	+	0.851565i	$0.324346\pi$
$692$	−13362.8	−0.734069
$693$	0	0
$694$	16867.5	0.922595
$695$	3278.24	0.178922
$696$	−13859.2	−0.754786
$697$	−24542.1	−1.33371
$698$	−8566.25	−0.464524
$699$	−5238.95	−0.283484
$700$	0	0
$701$	22024.5	1.18667	0.593334	−	0.804957i	$-0.297812\pi$
$701$	22024.5	1.18667	0.593334	+	0.804957i	$0.297812\pi$
$702$	2169.57	0.116645
$703$	6808.95	0.365298
$704$	1493.95	0.0799793
$705$	−24469.8	−1.30721
$706$	7725.13	0.411812
$707$	0	0
$708$	11093.5	0.588871
$709$	33441.1	1.77138	0.885690	−	0.464278i	$-0.153686\pi$
$709$	33441.1	1.77138	0.885690	+	0.464278i	$0.153686\pi$
$710$	−10059.9	−0.531746
$711$	−4049.71	−0.213609
$712$	−15429.3	−0.812133
$713$	13277.6	0.697403
$714$	0	0
$715$	8293.97	0.433814
$716$	−19696.4	−1.02806
$717$	2225.63	0.115924
$718$	7461.27	0.387817
$719$	−14889.6	−0.772306	−0.386153	−	0.922435i	$-0.626196\pi$
$719$	−14889.6	−0.772306	−0.386153	+	0.922435i	$0.626196\pi$
$720$	2132.13	0.110361
$721$	0	0
$722$	9282.26	0.478463
$723$	−17053.4	−0.877209
$724$	14242.3	0.731092
$725$	14406.8	0.738009
$726$	530.715	0.0271304
$727$	8295.96	0.423219	0.211609	−	0.977354i	$-0.432130\pi$
$727$	8295.96	0.423219	0.211609	+	0.977354i	$0.432130\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	17696.6	0.897235
$731$	−4517.02	−0.228547
$732$	−5658.76	−0.285729
$733$	−9274.06	−0.467320	−0.233660	−	0.972318i	$-0.575070\pi$
$733$	−9274.06	−0.467320	−0.233660	+	0.972318i	$0.575070\pi$
$734$	1483.09	0.0745802
$735$	0	0
$736$	−36218.5	−1.81390
$737$	−8743.62	−0.437009
$738$	4819.60	0.240395
$739$	3253.57	0.161955	0.0809774	−	0.996716i	$-0.474196\pi$
$739$	3253.57	0.161955	0.0809774	+	0.996716i	$0.474196\pi$
$740$	−24246.7	−1.20450
$741$	−3723.92	−0.184618
$742$	0	0
$743$	−32025.6	−1.58130	−0.790649	−	0.612269i	$-0.790257\pi$
$743$	−32025.6	−1.58130	−0.790649	+	0.612269i	$0.790257\pi$
$744$	−4176.77	−0.205817
$745$	−35015.1	−1.72195
$746$	−4098.81	−0.201164
$747$	−791.427	−0.0387641
$748$	−4320.88	−0.211213
$749$	0	0
$750$	−3718.33	−0.181032
$751$	−16661.7	−0.809579	−0.404790	−	0.914410i	$-0.632655\pi$
$751$	−16661.7	−0.809579	−0.404790	+	0.914410i	$0.632655\pi$
$752$	10267.2	0.497878
$753$	−10247.3	−0.495928
$754$	−18316.0	−0.884654
$755$	−25566.2	−1.23238
$756$	0	0
$757$	19376.1	0.930297	0.465149	−	0.885233i	$-0.346001\pi$
$757$	19376.1	0.930297	0.465149	+	0.885233i	$0.346001\pi$
$758$	14930.5	0.715437
$759$	−6378.36	−0.305033
$760$	6279.65	0.299719
$761$	25481.6	1.21381	0.606904	−	0.794775i	$-0.292411\pi$
$761$	25481.6	1.21381	0.606904	+	0.794775i	$0.292411\pi$
$762$	−3687.86	−0.175324
$763$	0	0
$764$	1968.76	0.0932296
$765$	8272.86	0.390988
$766$	−12810.0	−0.604235
$767$	34667.5	1.63203
$768$	8963.71	0.421159
$769$	−10748.5	−0.504032	−0.252016	−	0.967723i	$-0.581094\pi$
$769$	−10748.5	−0.504032	−0.252016	+	0.967723i	$0.581094\pi$
$770$	0	0
$771$	−11671.5	−0.545187
$772$	10753.1	0.501311
$773$	21154.1	0.984295	0.492148	−	0.870512i	$-0.336212\pi$
$773$	21154.1	0.984295	0.492148	+	0.870512i	$0.336212\pi$
$774$	887.057	0.0411946
$775$	4341.82	0.201242
$776$	−27831.4	−1.28748
$777$	0	0
$778$	9144.87	0.421413
$779$	−8272.52	−0.380480
$780$	13260.9	0.608739
$781$	5517.15	0.252777
$782$	−18934.3	−0.865841
$783$	−6154.38	−0.280894
$784$	0	0
$785$	8031.30	0.365159
$786$	1861.50	0.0844752
$787$	−24195.9	−1.09592	−0.547960	−	0.836504i	$-0.684596\pi$
$787$	−24195.9	−1.09592	−0.547960	+	0.836504i	$0.684596\pi$
$788$	10528.2	0.475952
$789$	10401.1	0.469315
$790$	9025.09	0.406453
$791$	0	0
$792$	2006.46	0.0900209
$793$	−17683.7	−0.791887
$794$	12029.7	0.537682
$795$	−7931.26	−0.353828
$796$	−10010.7	−0.445753
$797$	20929.4	0.930183	0.465091	−	0.885263i	$-0.346021\pi$
$797$	20929.4	0.930183	0.465091	+	0.885263i	$0.346021\pi$
$798$	0	0
$799$	39837.5	1.76389
$800$	−11843.6	−0.523419
$801$	−6851.63	−0.302235
$802$	−10190.0	−0.448657
$803$	−9705.39	−0.426520
$804$	−13979.8	−0.613222
$805$	0	0
$806$	−5519.92	−0.241230
$807$	10545.2	0.459986
$808$	20693.1	0.900965
$809$	1599.64	0.0695182	0.0347591	−	0.999396i	$-0.488934\pi$
$809$	1599.64	0.0695182	0.0347591	+	0.999396i	$0.488934\pi$
$810$	−1624.63	−0.0704737
$811$	−7923.58	−0.343076	−0.171538	−	0.985178i	$-0.554874\pi$
$811$	−7923.58	−0.343076	−0.171538	+	0.985178i	$0.554874\pi$
$812$	0	0
$813$	5926.65	0.255666
$814$	−4848.46	−0.208769
$815$	−41951.8	−1.80308
$816$	−3471.17	−0.148916
$817$	−1522.57	−0.0651997
$818$	18946.9	0.809859
$819$	0	0
$820$	29458.5	1.25455
$821$	−18571.2	−0.789452	−0.394726	−	0.918799i	$-0.629160\pi$
$821$	−18571.2	−0.789452	−0.394726	+	0.918799i	$0.629160\pi$
$822$	−7148.92	−0.303342
$823$	10412.5	0.441016	0.220508	−	0.975385i	$-0.429229\pi$
$823$	10412.5	0.441016	0.220508	+	0.975385i	$0.429229\pi$
$824$	−12688.1	−0.536420
$825$	−2085.75	−0.0880200
$826$	0	0
$827$	−24177.9	−1.01663	−0.508313	−	0.861172i	$-0.669731\pi$
$827$	−24177.9	−1.01663	−0.508313	+	0.861172i	$0.669731\pi$
$828$	−10198.1	−0.428029
$829$	1346.51	0.0564128	0.0282064	−	0.999602i	$-0.491020\pi$
$829$	1346.51	0.0564128	0.0282064	+	0.999602i	$0.491020\pi$
$830$	1763.76	0.0737600
$831$	13802.1	0.576159
$832$	7464.46	0.311038
$833$	0	0
$834$	1048.10	0.0435164
$835$	42191.0	1.74860
$836$	−1456.46	−0.0602545
$837$	−1854.76	−0.0765947
$838$	16102.0	0.663763
$839$	16560.1	0.681429	0.340715	−	0.940167i	$-0.389331\pi$
$839$	16560.1	0.681429	0.340715	+	0.940167i	$0.389331\pi$
$840$	0	0
$841$	27567.7	1.13033
$842$	−3328.94	−0.136250
$843$	11956.2	0.488485
$844$	−33761.8	−1.37693
$845$	11300.4	0.460052
$846$	−7823.32	−0.317933
$847$	0	0
$848$	3327.84	0.134762
$849$	9671.22	0.390949
$850$	−6191.58	−0.249846
$851$	58270.8	2.34724
$852$	8821.14	0.354703
$853$	−27176.2	−1.09085	−0.545426	−	0.838159i	$-0.683632\pi$
$853$	−27176.2	−1.09085	−0.545426	+	0.838159i	$0.683632\pi$
$854$	0	0
$855$	2788.57	0.111541
$856$	17576.1	0.701797
$857$	−27644.5	−1.10189	−0.550944	−	0.834543i	$-0.685732\pi$
$857$	−27644.5	−1.10189	−0.550944	+	0.834543i	$0.685732\pi$
$858$	2651.70	0.105510
$859$	36388.9	1.44537	0.722686	−	0.691176i	$-0.242907\pi$
$859$	36388.9	1.44537	0.722686	+	0.691176i	$0.242907\pi$
$860$	5421.89	0.214982
$861$	0	0
$862$	−5538.73	−0.218851
$863$	−30092.8	−1.18699	−0.593495	−	0.804838i	$-0.702252\pi$
$863$	−30092.8	−1.18699	−0.593495	+	0.804838i	$0.702252\pi$
$864$	5059.41	0.199218
$865$	31270.1	1.22915
$866$	−6799.75	−0.266819
$867$	1270.54	0.0497692
$868$	0	0
$869$	−4949.65	−0.193217
$870$	13715.5	0.534482
$871$	−43687.1	−1.69952
$872$	29154.1	1.13220
$873$	−12358.9	−0.479137
$874$	−6382.26	−0.247006
$875$	0	0
$876$	−15517.6	−0.598504
$877$	−7469.36	−0.287597	−0.143798	−	0.989607i	$-0.545932\pi$
$877$	−7469.36	−0.287597	−0.143798	+	0.989607i	$0.545932\pi$
$878$	−4906.24	−0.188585
$879$	12426.4	0.476830
$880$	2605.94	0.0998251
$881$	23264.7	0.889678	0.444839	−	0.895610i	$-0.353261\pi$
$881$	23264.7	0.889678	0.444839	+	0.895610i	$0.353261\pi$
$882$	0	0
$883$	2667.22	0.101653	0.0508263	−	0.998708i	$-0.483815\pi$
$883$	2667.22	0.101653	0.0508263	+	0.998708i	$0.483815\pi$
$884$	−21589.1	−0.821403
$885$	−25959.9	−0.986026
$886$	−5653.15	−0.214358
$887$	−17744.3	−0.671697	−0.335849	−	0.941916i	$-0.609023\pi$
$887$	−17744.3	−0.671697	−0.335849	+	0.941916i	$0.609023\pi$
$888$	−18330.5	−0.692714
$889$	0	0
$890$	15269.4	0.575090
$891$	891.000	0.0335013
$892$	−8145.36	−0.305748
$893$	13428.2	0.503201
$894$	−11194.8	−0.418804
$895$	46091.5	1.72142
$896$	0	0
$897$	−31869.2	−1.18627
$898$	10537.3	0.391573
$899$	15658.3	0.580904
$900$	−3334.82	−0.123512
$901$	12912.3	0.477438
$902$	5890.62	0.217446
$903$	0	0
$904$	−36465.3	−1.34161
$905$	−33328.3	−1.22417
$906$	−8173.86	−0.299733
$907$	−46752.8	−1.71158	−0.855790	−	0.517324i	$-0.826928\pi$
$907$	−46752.8	−1.71158	−0.855790	+	0.517324i	$0.826928\pi$
$908$	−33658.8	−1.23018
$909$	9189.07	0.335294
$910$	0	0
$911$	−36958.9	−1.34413	−0.672064	−	0.740493i	$-0.734592\pi$
$911$	−36958.9	−1.34413	−0.672064	+	0.740493i	$0.734592\pi$
$912$	−1170.04	−0.0424824
$913$	−967.300	−0.0350635
$914$	−22224.4	−0.804288
$915$	13242.0	0.478435
$916$	−23031.9	−0.830781
$917$	0	0
$918$	2644.95	0.0950940
$919$	−31473.0	−1.12970	−0.564852	−	0.825192i	$-0.691067\pi$
$919$	−31473.0	−1.12970	−0.564852	+	0.825192i	$0.691067\pi$
$920$	53741.0	1.92586
$921$	−3184.60	−0.113937
$922$	11439.2	0.408601
$923$	27566.2	0.983047
$924$	0	0
$925$	19054.8	0.677317
$926$	−3701.33	−0.131353
$927$	−5634.34	−0.199629
$928$	−42712.6	−1.51090
$929$	−10458.1	−0.369343	−0.184671	−	0.982800i	$-0.559122\pi$
$929$	−10458.1	−0.369343	−0.184671	+	0.982800i	$0.559122\pi$
$930$	4133.47	0.145744
$931$	0	0
$932$	−10237.7	−0.359816
$933$	−10463.0	−0.367143
$934$	−15864.6	−0.555787
$935$	10111.3	0.353662
$936$	10025.2	0.350090
$937$	−32261.2	−1.12479	−0.562395	−	0.826868i	$-0.690120\pi$
$937$	−32261.2	−1.12479	−0.562395	+	0.826868i	$0.690120\pi$
$938$	0	0
$939$	−15691.8	−0.545350
$940$	−47817.9	−1.65920
$941$	45317.7	1.56994	0.784970	−	0.619534i	$-0.212678\pi$
$941$	45317.7	1.56994	0.784970	+	0.619534i	$0.212678\pi$
$942$	2567.72	0.0888118
$943$	−70796.0	−2.44479
$944$	10892.4	0.375548
$945$	0	0
$946$	1084.18	0.0372619
$947$	27645.8	0.948646	0.474323	−	0.880351i	$-0.342693\pi$
$947$	27645.8	0.948646	0.474323	+	0.880351i	$0.342693\pi$
$948$	−7913.79	−0.271126
$949$	−48492.6	−1.65873
$950$	−2087.02	−0.0712758
$951$	15910.7	0.542523
$952$	0	0
$953$	−34309.8	−1.16621	−0.583107	−	0.812395i	$-0.698163\pi$
$953$	−34309.8	−1.16621	−0.583107	+	0.812395i	$0.698163\pi$
$954$	−2535.73	−0.0860559
$955$	−4607.09	−0.156107
$956$	4349.23	0.147138
$957$	−7522.02	−0.254078
$958$	6919.57	0.233362
$959$	0	0
$960$	−5589.59	−0.187920
$961$	−25072.0	−0.841598
$962$	−24225.1	−0.811901
$963$	7804.93	0.261174
$964$	−33325.1	−1.11341
$965$	−25163.3	−0.839413
$966$	0	0
$967$	−26158.8	−0.869916	−0.434958	−	0.900451i	$-0.643237\pi$
$967$	−26158.8	−0.869916	−0.434958	+	0.900451i	$0.643237\pi$
$968$	2452.34	0.0814270
$969$	−4539.88	−0.150508
$970$	27542.8	0.911698
$971$	−33487.3	−1.10676	−0.553378	−	0.832930i	$-0.686662\pi$
$971$	−33487.3	−1.10676	−0.553378	+	0.832930i	$0.686662\pi$
$972$	1424.58	0.0470098
$973$	0	0
$974$	4904.48	0.161345
$975$	−10421.4	−0.342308
$976$	−5556.15	−0.182221
$977$	−25952.9	−0.849854	−0.424927	−	0.905228i	$-0.639700\pi$
$977$	−25952.9	−0.849854	−0.424927	+	0.905228i	$0.639700\pi$
$978$	−13412.6	−0.438534
$979$	−8374.21	−0.273382
$980$	0	0
$981$	12946.3	0.421350
$982$	−11492.3	−0.373456
$983$	2225.76	0.0722183	0.0361092	−	0.999348i	$-0.488504\pi$
$983$	2225.76	0.0722183	0.0361092	+	0.999348i	$0.488504\pi$
$984$	22270.5	0.721503
$985$	−24636.9	−0.796951
$986$	−22329.2	−0.721204
$987$	0	0
$988$	−7277.14	−0.234329
$989$	−13030.1	−0.418943
$990$	−1985.66	−0.0637459
$991$	−11209.5	−0.359315	−0.179657	−	0.983729i	$-0.557499\pi$
$991$	−11209.5	−0.359315	−0.179657	+	0.983729i	$0.557499\pi$
$992$	−12872.4	−0.411995
$993$	−22454.5	−0.717596
$994$	0	0
$995$	23425.9	0.746384
$996$	−1546.58	−0.0492019
$997$	−13132.4	−0.417158	−0.208579	−	0.978006i	$-0.566884\pi$
$997$	−13132.4	−0.417158	−0.208579	+	0.978006i	$0.566884\pi$
$998$	−19887.9	−0.630802
$999$	−8139.91	−0.257793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.q.1.4	✓	7
7.6	odd	2		1617.4.a.r.1.4	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.q.1.4	✓	7	1.1	even	1	trivial
1617.4.a.r.1.4	yes	7	7.6	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46203 q^{2} -3.00000 q^{3} -5.86248 q^{4} +13.7188 q^{5} +4.38608 q^{6} +20.2673 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.46203 q^{2} -3.00000 q^{3} -5.86248 q^{4} +13.7188 q^{5} +4.38608 q^{6} +20.2673 q^{8} +9.00000 q^{9} -20.0572 q^{10} +11.0000 q^{11} +17.5874 q^{12} +54.9610 q^{13} -41.1563 q^{15} +17.2686 q^{16} +67.0036 q^{17} -13.1582 q^{18} +22.5852 q^{19} -80.4260 q^{20} -16.0823 q^{22} +193.284 q^{23} -60.8019 q^{24} +63.2045 q^{25} -80.3544 q^{26} -27.0000 q^{27} +227.940 q^{29} +60.1715 q^{30} +68.6947 q^{31} -187.385 q^{32} -33.0000 q^{33} -97.9610 q^{34} -52.7623 q^{36} +301.478 q^{37} -33.0202 q^{38} -164.883 q^{39} +278.042 q^{40} -366.280 q^{41} -67.4146 q^{43} -64.4873 q^{44} +123.469 q^{45} -282.586 q^{46} +594.558 q^{47} -51.8057 q^{48} -92.4066 q^{50} -201.011 q^{51} -322.208 q^{52} +192.711 q^{53} +39.4747 q^{54} +150.906 q^{55} -67.7557 q^{57} -333.254 q^{58} +630.764 q^{59} +241.278 q^{60} -321.750 q^{61} -100.433 q^{62} +135.814 q^{64} +753.998 q^{65} +48.2468 q^{66} -794.875 q^{67} -392.808 q^{68} -579.851 q^{69} +501.559 q^{71} +182.406 q^{72} -882.308 q^{73} -440.769 q^{74} -189.614 q^{75} -132.405 q^{76} +241.063 q^{78} -449.968 q^{79} +236.903 q^{80} +81.0000 q^{81} +535.511 q^{82} -87.9363 q^{83} +919.207 q^{85} +98.5619 q^{86} -683.820 q^{87} +222.940 q^{88} -761.292 q^{89} -180.515 q^{90} -1133.12 q^{92} -206.084 q^{93} -869.258 q^{94} +309.841 q^{95} +562.156 q^{96} -1373.22 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9	\( 7 q - 4 q^{2} - 21 q^{3} + 30 q^{4} + 20 q^{5} + 12 q^{6} - 39 q^{8} + 63 q^{9} - 49 q^{10} + 77 q^{11} - 90 q^{12} + 92 q^{13} - 60 q^{15} + 218 q^{16} + 170 q^{17} - 36 q^{18} + 76 q^{19} + 569 q^{20} - 44 q^{22} - 56 q^{23} + 117 q^{24} + 53 q^{25} + 109 q^{26} - 189 q^{27} - 472 q^{29} + 147 q^{30} + 290 q^{31} - 1046 q^{32} - 231 q^{33} + 344 q^{34} + 270 q^{36} - 66 q^{37} + 385 q^{38} - 276 q^{39} - 800 q^{40} - 166 q^{41} - 76 q^{43} + 330 q^{44} + 180 q^{45} - 528 q^{46} + 1082 q^{47} - 654 q^{48} - 569 q^{50} - 510 q^{51} + 1065 q^{52} - 150 q^{53} + 108 q^{54} + 220 q^{55} - 228 q^{57} + 1457 q^{58} + 1284 q^{59} - 1707 q^{60} - 764 q^{61} - 296 q^{62} + 1661 q^{64} + 2722 q^{65} + 132 q^{66} - 658 q^{67} - 360 q^{68} + 168 q^{69} - 272 q^{71} - 351 q^{72} + 1658 q^{73} + 613 q^{74} - 159 q^{75} - 1757 q^{76} - 327 q^{78} + 792 q^{79} + 5079 q^{80} + 567 q^{81} + 3208 q^{82} - 770 q^{83} - 776 q^{85} - 478 q^{86} + 1416 q^{87} - 429 q^{88} + 656 q^{89} - 441 q^{90} - 3916 q^{92} - 870 q^{93} - 849 q^{94} - 1636 q^{95} + 3138 q^{96} + 608 q^{97} + 693 q^{99}+O(q^{100}) \) 7 * q - 4 * q^2 - 21 * q^3 + 30 * q^4 + 20 * q^5 + 12 * q^6 - 39 * q^8 + 63 * q^9 - 49 * q^10 + 77 * q^11 - 90 * q^12 + 92 * q^13 - 60 * q^15 + 218 * q^16 + 170 * q^17 - 36 * q^18 + 76 * q^19 + 569 * q^20 - 44 * q^22 - 56 * q^23 + 117 * q^24 + 53 * q^25 + 109 * q^26 - 189 * q^27 - 472 * q^29 + 147 * q^30 + 290 * q^31 - 1046 * q^32 - 231 * q^33 + 344 * q^34 + 270 * q^36 - 66 * q^37 + 385 * q^38 - 276 * q^39 - 800 * q^40 - 166 * q^41 - 76 * q^43 + 330 * q^44 + 180 * q^45 - 528 * q^46 + 1082 * q^47 - 654 * q^48 - 569 * q^50 - 510 * q^51 + 1065 * q^52 - 150 * q^53 + 108 * q^54 + 220 * q^55 - 228 * q^57 + 1457 * q^58 + 1284 * q^59 - 1707 * q^60 - 764 * q^61 - 296 * q^62 + 1661 * q^64 + 2722 * q^65 + 132 * q^66 - 658 * q^67 - 360 * q^68 + 168 * q^69 - 272 * q^71 - 351 * q^72 + 1658 * q^73 + 613 * q^74 - 159 * q^75 - 1757 * q^76 - 327 * q^78 + 792 * q^79 + 5079 * q^80 + 567 * q^81 + 3208 * q^82 - 770 * q^83 - 776 * q^85 - 478 * q^86 + 1416 * q^87 - 429 * q^88 + 656 * q^89 - 441 * q^90 - 3916 * q^92 - 870 * q^93 - 849 * q^94 - 1636 * q^95 + 3138 * q^96 + 608 * q^97 + 693 * q^99

Introduction

L-functions

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