LMFDB - Embedded newform 637.4.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,4,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("637.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	637.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:	$37.5842166737$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5364412.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 27x^{2} - 24x + 76 $ x^4 - 27x^2 - 24x + 76
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$5.36970$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.36970 q^{2} +7.65388 q^{3} +11.0943 q^{4} +22.2654 q^{5} +33.4452 q^{6} +13.5212 q^{8} +31.5819 q^{9} +O(q^{10})$	\(q+4.36970 q^{2} +7.65388 q^{3} +11.0943 q^{4} +22.2654 q^{5} +33.4452 q^{6} +13.5212 q^{8} +31.5819 q^{9} +97.2930 q^{10} -29.6363 q^{11} +84.9145 q^{12} +13.0000 q^{13} +170.416 q^{15} -29.6708 q^{16} -68.8257 q^{17} +138.004 q^{18} -16.7771 q^{19} +247.019 q^{20} -129.502 q^{22} -144.108 q^{23} +103.490 q^{24} +370.746 q^{25} +56.8061 q^{26} +35.0694 q^{27} -62.5699 q^{29} +744.669 q^{30} +0.369192 q^{31} -237.822 q^{32} -226.833 q^{33} -300.748 q^{34} +350.379 q^{36} -433.781 q^{37} -73.3108 q^{38} +99.5005 q^{39} +301.055 q^{40} +281.633 q^{41} +342.213 q^{43} -328.794 q^{44} +703.183 q^{45} -629.709 q^{46} +254.917 q^{47} -227.097 q^{48} +1620.05 q^{50} -526.784 q^{51} +144.226 q^{52} -188.630 q^{53} +153.243 q^{54} -659.863 q^{55} -128.410 q^{57} -273.412 q^{58} -56.4514 q^{59} +1890.65 q^{60} +156.806 q^{61} +1.61326 q^{62} -801.846 q^{64} +289.450 q^{65} -991.192 q^{66} -183.455 q^{67} -763.574 q^{68} -1102.99 q^{69} +751.276 q^{71} +427.026 q^{72} -311.543 q^{73} -1895.50 q^{74} +2837.65 q^{75} -186.130 q^{76} +434.788 q^{78} +234.345 q^{79} -660.630 q^{80} -584.295 q^{81} +1230.65 q^{82} -290.255 q^{83} -1532.43 q^{85} +1495.37 q^{86} -478.903 q^{87} -400.719 q^{88} +390.646 q^{89} +3072.70 q^{90} -1598.78 q^{92} +2.82575 q^{93} +1113.91 q^{94} -373.548 q^{95} -1820.26 q^{96} +739.433 q^{97} -935.971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * 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 $

$2$	4.36970	1.54492	0.772462	−	0.635061i	$-0.219025\pi$
$2$	4.36970	1.54492	0.772462	+	0.635061i	$0.219025\pi$
$3$	7.65388	1.47299	0.736495	−	0.676443i	$-0.236479\pi$
$3$	7.65388	1.47299	0.736495	+	0.676443i	$0.236479\pi$
$4$	11.0943	1.38679
$5$	22.2654	1.99147	0.995737	−	0.0922357i	$-0.0294013\pi$
$5$	22.2654	1.99147	0.995737	+	0.0922357i	$0.0294013\pi$
$6$	33.4452	2.27566
$7$	0	0
$7$	0	0
$8$	13.5212	0.597559
$9$	31.5819	1.16970
$10$	97.2930	3.07668
$11$	−29.6363	−0.812335	−0.406167	−	0.913799i	$-0.633135\pi$
$11$	−29.6363	−0.812335	−0.406167	+	0.913799i	$0.633135\pi$
$12$	84.9145	2.04273
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	0	0
$15$	170.416	2.93342
$16$	−29.6708	−0.463606
$17$	−68.8257	−0.981923	−0.490961	−	0.871181i	$-0.663354\pi$
$17$	−68.8257	−0.981923	−0.490961	+	0.871181i	$0.663354\pi$
$18$	138.004	1.80710
$19$	−16.7771	−0.202575	−0.101287	−	0.994857i	$-0.532296\pi$
$19$	−16.7771	−0.202575	−0.101287	+	0.994857i	$0.532296\pi$
$20$	247.019	2.76175
$21$	0	0
$22$	−129.502	−1.25500
$23$	−144.108	−1.30646	−0.653230	−	0.757160i	$-0.726587\pi$
$23$	−144.108	−1.30646	−0.653230	+	0.757160i	$0.726587\pi$
$24$	103.490	0.880199
$25$	370.746	2.96597
$26$	56.8061	0.428485
$27$	35.0694	0.249967
$28$	0	0
$29$	−62.5699	−0.400653	−0.200327	−	0.979729i	$-0.564200\pi$
$29$	−62.5699	−0.400653	−0.200327	+	0.979729i	$0.564200\pi$
$30$	744.669	4.53191
$31$	0.369192	0.00213899	0.00106950	−	0.999999i	$-0.499660\pi$
$31$	0.369192	0.00213899	0.00106950	+	0.999999i	$0.499660\pi$
$32$	−237.822	−1.31379
$33$	−226.833	−1.19656
$34$	−300.748	−1.51700
$35$	0	0
$36$	350.379	1.62213
$37$	−433.781	−1.92738	−0.963692	−	0.267015i	$-0.913963\pi$
$37$	−433.781	−1.92738	−0.963692	+	0.267015i	$0.913963\pi$
$38$	−73.3108	−0.312963
$39$	99.5005	0.408534
$40$	301.055	1.19002
$41$	281.633	1.07277	0.536386	−	0.843973i	$-0.319789\pi$
$41$	281.633	1.07277	0.536386	+	0.843973i	$0.319789\pi$
$42$	0	0
$43$	342.213	1.21365	0.606826	−	0.794835i	$-0.292442\pi$
$43$	342.213	1.21365	0.606826	+	0.794835i	$0.292442\pi$
$44$	−328.794	−1.12654
$45$	703.183	2.32943
$46$	−629.709	−2.01838
$47$	254.917	0.791139	0.395569	−	0.918436i	$-0.370547\pi$
$47$	254.917	0.791139	0.395569	+	0.918436i	$0.370547\pi$
$48$	−227.097	−0.682887
$49$	0	0
$50$	1620.05	4.58220
$51$	−526.784	−1.44636
$52$	144.226	0.384626
$53$	−188.630	−0.488873	−0.244437	−	0.969665i	$-0.578603\pi$
$53$	−188.630	−0.488873	−0.244437	+	0.969665i	$0.578603\pi$
$54$	153.243	0.386180
$55$	−659.863	−1.61774
$56$	0	0
$57$	−128.410	−0.298391
$58$	−273.412	−0.618979
$59$	−56.4514	−0.124565	−0.0622826	−	0.998059i	$-0.519838\pi$
$59$	−56.4514	−0.124565	−0.0622826	+	0.998059i	$0.519838\pi$
$60$	1890.65	4.06804
$61$	156.806	0.329130	0.164565	−	0.986366i	$-0.447378\pi$
$61$	156.806	0.329130	0.164565	+	0.986366i	$0.447378\pi$
$62$	1.61326	0.00330458
$63$	0	0
$64$	−801.846	−1.56611
$65$	289.450	0.552336
$66$	−991.192	−1.84860
$67$	−183.455	−0.334516	−0.167258	−	0.985913i	$-0.553491\pi$
$67$	−183.455	−0.334516	−0.167258	+	0.985913i	$0.553491\pi$
$68$	−763.574	−1.36172
$69$	−1102.99	−1.92440
$70$	0	0
$71$	751.276	1.25578	0.627888	−	0.778304i	$-0.283920\pi$
$71$	751.276	1.25578	0.627888	+	0.778304i	$0.283920\pi$
$72$	427.026	0.698965
$73$	−311.543	−0.499498	−0.249749	−	0.968311i	$-0.580348\pi$
$73$	−311.543	−0.499498	−0.249749	+	0.968311i	$0.580348\pi$
$74$	−1895.50	−2.97766
$75$	2837.65	4.36885
$76$	−186.130	−0.280929
$77$	0	0
$78$	434.788	0.631154
$79$	234.345	0.333745	0.166873	−	0.985978i	$-0.446633\pi$
$79$	234.345	0.333745	0.166873	+	0.985978i	$0.446633\pi$
$80$	−660.630	−0.923259
$81$	−584.295	−0.801501
$82$	1230.65	1.65735
$83$	−290.255	−0.383851	−0.191926	−	0.981409i	$-0.561473\pi$
$83$	−290.255	−0.383851	−0.191926	+	0.981409i	$0.561473\pi$
$84$	0	0
$85$	−1532.43	−1.95547
$86$	1495.37	1.87500
$87$	−478.903	−0.590158
$88$	−400.719	−0.485418
$89$	390.646	0.465263	0.232632	−	0.972565i	$-0.425266\pi$
$89$	390.646	0.465263	0.232632	+	0.972565i	$0.425266\pi$
$90$	3072.70	3.59879
$91$	0	0
$92$	−1598.78	−1.81178
$93$	2.82575	0.00315072
$94$	1113.91	1.22225
$95$	−373.548	−0.403423
$96$	−1820.26	−1.93521
$97$	739.433	0.774000	0.387000	−	0.922080i	$-0.373511\pi$
$97$	739.433	0.774000	0.387000	+	0.922080i	$0.373511\pi$
$98$	0	0
$99$	−935.971	−0.950188
$100$	4113.17	4.11317
$101$	1129.43	1.11270	0.556351	−	0.830948i	$-0.312201\pi$
$101$	1129.43	1.11270	0.556351	+	0.830948i	$0.312201\pi$
$102$	−2301.89	−2.23452
$103$	601.210	0.575135	0.287568	−	0.957760i	$-0.407153\pi$
$103$	601.210	0.575135	0.287568	+	0.957760i	$0.407153\pi$
$104$	175.776	0.165733
$105$	0	0
$106$	−824.256	−0.755272
$107$	1885.73	1.70374	0.851869	−	0.523755i	$-0.175469\pi$
$107$	1885.73	1.70374	0.851869	+	0.523755i	$0.175469\pi$
$108$	389.071	0.346651
$109$	500.691	0.439977	0.219988	−	0.975502i	$-0.429398\pi$
$109$	500.691	0.439977	0.219988	+	0.975502i	$0.429398\pi$
$110$	−2883.41	−2.49929
$111$	−3320.11	−2.83902
$112$	0	0
$113$	−16.7610	−0.0139534	−0.00697672	−	0.999976i	$-0.502221\pi$
$113$	−16.7610	−0.0139534	−0.00697672	+	0.999976i	$0.502221\pi$
$114$	−561.113	−0.460991
$115$	−3208.61	−2.60178
$116$	−694.170	−0.555621
$117$	410.565	0.324417
$118$	−246.676	−0.192444
$119$	0	0
$120$	2304.24	1.75289
$121$	−452.689	−0.340112
$122$	685.195	0.508480
$123$	2155.58	1.58018
$124$	4.09593	0.00296633
$125$	5471.63	3.91518
$126$	0	0
$127$	1858.56	1.29859	0.649295	−	0.760537i	$-0.275064\pi$
$127$	1858.56	1.29859	0.649295	+	0.760537i	$0.275064\pi$
$128$	−1601.25	−1.10572
$129$	2619.26	1.78770
$130$	1264.81	0.853316
$131$	1851.92	1.23514	0.617568	−	0.786517i	$-0.288118\pi$
$131$	1851.92	1.23514	0.617568	+	0.786517i	$0.288118\pi$
$132$	−2516.55	−1.65938
$133$	0	0
$134$	−801.644	−0.516802
$135$	780.833	0.497803
$136$	−930.608	−0.586757
$137$	1859.77	1.15979	0.579893	−	0.814693i	$-0.303094\pi$
$137$	1859.77	1.15979	0.579893	+	0.814693i	$0.303094\pi$
$138$	−4819.72	−2.97306
$139$	−430.419	−0.262645	−0.131322	−	0.991340i	$-0.541922\pi$
$139$	−430.419	−0.262645	−0.131322	+	0.991340i	$0.541922\pi$
$140$	0	0
$141$	1951.11	1.16534
$142$	3282.86	1.94008
$143$	−385.272	−0.225301
$144$	−937.059	−0.542280
$145$	−1393.14	−0.797891
$146$	−1361.35	−0.771687
$147$	0	0
$148$	−4812.51	−2.67288
$149$	−2899.56	−1.59424	−0.797119	−	0.603822i	$-0.793644\pi$
$149$	−2899.56	−1.59424	−0.797119	+	0.603822i	$0.793644\pi$
$150$	12399.7	6.74953
$151$	−395.073	−0.212918	−0.106459	−	0.994317i	$-0.533951\pi$
$151$	−395.073	−0.212918	−0.106459	+	0.994317i	$0.533951\pi$
$152$	−226.846	−0.121051
$153$	−2173.65	−1.14856
$154$	0	0
$155$	8.22019	0.00425975
$156$	1103.89	0.566550
$157$	−2000.48	−1.01691	−0.508457	−	0.861088i	$-0.669784\pi$
$157$	−2000.48	−1.01691	−0.508457	+	0.861088i	$0.669784\pi$
$158$	1024.02	0.515611
$159$	−1443.75	−0.720106
$160$	−5295.20	−2.61639
$161$	0	0
$162$	−2553.19	−1.23826
$163$	3251.15	1.56227	0.781134	−	0.624363i	$-0.214642\pi$
$163$	3251.15	1.56227	0.781134	+	0.624363i	$0.214642\pi$
$164$	3124.52	1.48771
$165$	−5050.51	−2.38292
$166$	−1268.33	−0.593021
$167$	−810.306	−0.375469	−0.187735	−	0.982220i	$-0.560115\pi$
$167$	−810.306	−0.375469	−0.187735	+	0.982220i	$0.560115\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−6696.26	−3.02106
$171$	−529.852	−0.236952
$172$	3796.62	1.68308
$173$	−1895.69	−0.833102	−0.416551	−	0.909112i	$-0.636761\pi$
$173$	−1895.69	−0.833102	−0.416551	+	0.909112i	$0.636761\pi$
$174$	−2092.66	−0.911749
$175$	0	0
$176$	879.332	0.376603
$177$	−432.073	−0.183483
$178$	1707.01	0.718796
$179$	−277.740	−0.115974	−0.0579868	−	0.998317i	$-0.518468\pi$
$179$	−277.740	−0.115974	−0.0579868	+	0.998317i	$0.518468\pi$
$180$	7801.33	3.23042
$181$	−1273.75	−0.523077	−0.261539	−	0.965193i	$-0.584230\pi$
$181$	−1273.75	−0.523077	−0.261539	+	0.965193i	$0.584230\pi$
$182$	0	0
$183$	1200.17	0.484805
$184$	−1948.51	−0.780687
$185$	−9658.30	−3.83834
$186$	12.3477	0.00486762
$187$	2039.74	0.797650
$188$	2828.13	1.09714
$189$	0	0
$190$	−1632.29	−0.623258
$191$	1315.49	0.498353	0.249176	−	0.968458i	$-0.419840\pi$
$191$	1315.49	0.498353	0.249176	+	0.968458i	$0.419840\pi$
$192$	−6137.24	−2.30686
$193$	−3924.54	−1.46370	−0.731852	−	0.681464i	$-0.761344\pi$
$193$	−3924.54	−1.46370	−0.731852	+	0.681464i	$0.761344\pi$
$194$	3231.10	1.19577
$195$	2215.41	0.813585
$196$	0	0
$197$	−1538.23	−0.556315	−0.278158	−	0.960535i	$-0.589724\pi$
$197$	−1538.23	−0.556315	−0.278158	+	0.960535i	$0.589724\pi$
$198$	−4089.92	−1.46797
$199$	5076.75	1.80845	0.904225	−	0.427056i	$-0.140449\pi$
$199$	5076.75	1.80845	0.904225	+	0.427056i	$0.140449\pi$
$200$	5012.94	1.77234
$201$	−1404.14	−0.492739
$202$	4935.29	1.71904
$203$	0	0
$204$	−5844.30	−2.00580
$205$	6270.65	2.13640
$206$	2627.11	0.888540
$207$	−4551.20	−1.52817
$208$	−385.720	−0.128581
$209$	497.211	0.164559
$210$	0	0
$211$	−3620.11	−1.18113	−0.590565	−	0.806990i	$-0.701095\pi$
$211$	−3620.11	−1.18113	−0.590565	+	0.806990i	$0.701095\pi$
$212$	−2092.72	−0.677964
$213$	5750.18	1.84975
$214$	8240.06	2.63215
$215$	7619.50	2.41696
$216$	474.181	0.149370
$217$	0	0
$218$	2187.87	0.679731
$219$	−2384.52	−0.735756
$220$	−7320.73	−2.24347
$221$	−894.734	−0.272336
$222$	−14507.9	−4.38607
$223$	1119.95	0.336311	0.168155	−	0.985761i	$-0.446219\pi$
$223$	1119.95	0.336311	0.168155	+	0.985761i	$0.446219\pi$
$224$	0	0
$225$	11708.9	3.46930
$226$	−73.2405	−0.0215570
$227$	−1897.96	−0.554942	−0.277471	−	0.960734i	$-0.589496\pi$
$227$	−1897.96	−0.554942	−0.277471	+	0.960734i	$0.589496\pi$
$228$	−1424.62	−0.413805
$229$	1851.04	0.534150	0.267075	−	0.963676i	$-0.413943\pi$
$229$	1851.04	0.534150	0.267075	+	0.963676i	$0.413943\pi$
$230$	−14020.7	−4.01955
$231$	0	0
$232$	−846.022	−0.239414
$233$	−5576.26	−1.56787	−0.783933	−	0.620845i	$-0.786789\pi$
$233$	−5576.26	−1.56787	−0.783933	+	0.620845i	$0.786789\pi$
$234$	1794.05	0.501199
$235$	5675.83	1.57553
$236$	−626.290	−0.172746
$237$	1793.65	0.491604
$238$	0	0
$239$	−2856.49	−0.773099	−0.386550	−	0.922269i	$-0.626333\pi$
$239$	−2856.49	−0.773099	−0.386550	+	0.922269i	$0.626333\pi$
$240$	−5056.39	−1.35995
$241$	−2052.45	−0.548588	−0.274294	−	0.961646i	$-0.588444\pi$
$241$	−2052.45	−0.548588	−0.274294	+	0.961646i	$0.588444\pi$
$242$	−1978.12	−0.525447
$243$	−5419.00	−1.43057
$244$	1739.65	0.456433
$245$	0	0
$246$	9419.26	2.44126
$247$	−218.102	−0.0561842
$248$	4.99192	0.00127818
$249$	−2221.58	−0.565409
$250$	23909.4	6.04865
$251$	5817.11	1.46284	0.731419	−	0.681928i	$-0.238858\pi$
$251$	5817.11	1.46284	0.731419	+	0.681928i	$0.238858\pi$
$252$	0	0
$253$	4270.83	1.06128
$254$	8121.37	2.00622
$255$	−11729.0	−2.88039
$256$	−582.232	−0.142147
$257$	1586.76	0.385134	0.192567	−	0.981284i	$-0.438319\pi$
$257$	1586.76	0.385134	0.192567	+	0.981284i	$0.438319\pi$
$258$	11445.4	2.76186
$259$	0	0
$260$	3211.24	0.765973
$261$	−1976.08	−0.468644
$262$	8092.34	1.90819
$263$	−2396.72	−0.561933	−0.280966	−	0.959718i	$-0.590655\pi$
$263$	−2396.72	−0.561933	−0.280966	+	0.959718i	$0.590655\pi$
$264$	−3067.06	−0.715016
$265$	−4199.91	−0.973579
$266$	0	0
$267$	2989.96	0.685328
$268$	−2035.31	−0.463903
$269$	−2312.68	−0.524188	−0.262094	−	0.965042i	$-0.584413\pi$
$269$	−2312.68	−0.524188	−0.262094	+	0.965042i	$0.584413\pi$
$270$	3412.01	0.769067
$271$	−2424.88	−0.543546	−0.271773	−	0.962361i	$-0.587610\pi$
$271$	−2424.88	−0.543546	−0.271773	+	0.962361i	$0.587610\pi$
$272$	2042.11	0.455225
$273$	0	0
$274$	8126.63	1.79178
$275$	−10987.6	−2.40936
$276$	−12236.9	−2.66874
$277$	−8159.10	−1.76979	−0.884897	−	0.465786i	$-0.845772\pi$
$277$	−8159.10	−1.76979	−0.884897	+	0.465786i	$0.845772\pi$
$278$	−1880.80	−0.405766
$279$	11.6598	0.00250198
$280$	0	0
$281$	−4210.52	−0.893874	−0.446937	−	0.894565i	$-0.647485\pi$
$281$	−4210.52	−0.893874	−0.446937	+	0.894565i	$0.647485\pi$
$282$	8525.76	1.80036
$283$	4511.44	0.947624	0.473812	−	0.880626i	$-0.342878\pi$
$283$	4511.44	0.947624	0.473812	+	0.880626i	$0.342878\pi$
$284$	8334.89	1.74150
$285$	−2859.09	−0.594238
$286$	−1683.52	−0.348073
$287$	0	0
$288$	−7510.88	−1.53675
$289$	−176.021	−0.0358276
$290$	−6087.62	−1.23268
$291$	5659.53	1.14009
$292$	−3456.36	−0.692699
$293$	1075.06	0.214355	0.107177	−	0.994240i	$-0.465819\pi$
$293$	1075.06	0.214355	0.107177	+	0.994240i	$0.465819\pi$
$294$	0	0
$295$	−1256.91	−0.248069
$296$	−5865.25	−1.15173
$297$	−1039.33	−0.203057
$298$	−12670.2	−2.46298
$299$	−1873.40	−0.362347
$300$	31481.8	6.05867
$301$	0	0
$302$	−1726.35	−0.328942
$303$	8644.55	1.63900
$304$	497.789	0.0939149
$305$	3491.34	0.655454
$306$	−9498.20	−1.77443
$307$	1104.20	0.205276	0.102638	−	0.994719i	$-0.467272\pi$
$307$	1104.20	0.205276	0.102638	+	0.994719i	$0.467272\pi$
$308$	0	0
$309$	4601.59	0.847169
$310$	35.9198	0.00658099
$311$	−7738.31	−1.41093	−0.705465	−	0.708745i	$-0.749262\pi$
$311$	−7738.31	−1.41093	−0.705465	+	0.708745i	$0.749262\pi$
$312$	1345.37	0.244123
$313$	−4821.02	−0.870607	−0.435304	−	0.900284i	$-0.643359\pi$
$313$	−4821.02	−0.870607	−0.435304	+	0.900284i	$0.643359\pi$
$314$	−8741.49	−1.57105
$315$	0	0
$316$	2599.90	0.462834
$317$	923.668	0.163654	0.0818270	−	0.996647i	$-0.473924\pi$
$317$	923.668	0.163654	0.0818270	+	0.996647i	$0.473924\pi$
$318$	−6308.76	−1.11251
$319$	1854.34	0.325465
$320$	−17853.4	−3.11886
$321$	14433.1	2.50959
$322$	0	0
$323$	1154.69	0.198913
$324$	−6482.34	−1.11151
$325$	4819.70	0.822612
$326$	14206.6	2.41358
$327$	3832.23	0.648082
$328$	3808.02	0.641045
$329$	0	0
$330$	−22069.3	−3.68143
$331$	−5444.50	−0.904099	−0.452050	−	0.891993i	$-0.649307\pi$
$331$	−5444.50	−0.904099	−0.452050	+	0.891993i	$0.649307\pi$
$332$	−3220.18	−0.532321
$333$	−13699.6	−2.25446
$334$	−3540.80	−0.580072
$335$	−4084.69	−0.666180
$336$	0	0
$337$	4828.99	0.780569	0.390285	−	0.920694i	$-0.372377\pi$
$337$	4828.99	0.780569	0.390285	+	0.920694i	$0.372377\pi$
$338$	738.480	0.118840
$339$	−128.287	−0.0205533
$340$	−17001.2	−2.71183
$341$	−10.9415	−0.00173758
$342$	−2315.30	−0.366073
$343$	0	0
$344$	4627.14	0.725229
$345$	−24558.4	−3.83240
$346$	−8283.60	−1.28708
$347$	3766.14	0.582642	0.291321	−	0.956625i	$-0.405905\pi$
$347$	3766.14	0.582642	0.291321	+	0.956625i	$0.405905\pi$
$348$	−5313.10	−0.818425
$349$	−6791.47	−1.04166	−0.520829	−	0.853661i	$-0.674377\pi$
$349$	−6791.47	−1.04166	−0.520829	+	0.853661i	$0.674377\pi$
$350$	0	0
$351$	455.902	0.0693284
$352$	7048.17	1.06724
$353$	−2667.76	−0.402240	−0.201120	−	0.979567i	$-0.564458\pi$
$353$	−2667.76	−0.402240	−0.201120	+	0.979567i	$0.564458\pi$
$354$	−1888.03	−0.283468
$355$	16727.4	2.50085
$356$	4333.95	0.645222
$357$	0	0
$358$	−1213.64	−0.179170
$359$	1846.13	0.271407	0.135704	−	0.990749i	$-0.456671\pi$
$359$	1846.13	0.271407	0.135704	+	0.990749i	$0.456671\pi$
$360$	9507.89	1.39197
$361$	−6577.53	−0.958963
$362$	−5565.90	−0.808114
$363$	−3464.83	−0.500982
$364$	0	0
$365$	−6936.62	−0.994738
$366$	5244.40	0.748987
$367$	−2301.86	−0.327401	−0.163700	−	0.986510i	$-0.552343\pi$
$367$	−2301.86	−0.327401	−0.163700	+	0.986510i	$0.552343\pi$
$368$	4275.79	0.605682
$369$	8894.50	1.25482
$370$	−42203.9	−5.92994
$371$	0	0
$372$	31.3498	0.00436938
$373$	11580.5	1.60755	0.803773	−	0.594937i	$-0.202823\pi$
$373$	11580.5	1.60755	0.803773	+	0.594937i	$0.202823\pi$
$374$	8913.06	1.23231
$375$	41879.2	5.76702
$376$	3446.79	0.472752
$377$	−813.409	−0.111121
$378$	0	0
$379$	−8180.87	−1.10877	−0.554384	−	0.832261i	$-0.687046\pi$
$379$	−8180.87	−1.10877	−0.554384	+	0.832261i	$0.687046\pi$
$380$	−4144.25	−0.559462
$381$	14225.2	1.91281
$382$	5748.29	0.769917
$383$	7826.24	1.04413	0.522066	−	0.852905i	$-0.325162\pi$
$383$	7826.24	1.04413	0.522066	+	0.852905i	$0.325162\pi$
$384$	−12255.8	−1.62871
$385$	0	0
$386$	−17149.1	−2.26131
$387$	10807.8	1.41961
$388$	8203.49	1.07337
$389$	−1815.99	−0.236695	−0.118347	−	0.992972i	$-0.537760\pi$
$389$	−1815.99	−0.236695	−0.118347	+	0.992972i	$0.537760\pi$
$390$	9680.70	1.25693
$391$	9918.33	1.28284
$392$	0	0
$393$	14174.4	1.81934
$394$	−6721.59	−0.859464
$395$	5217.78	0.664645
$396$	−10384.0	−1.31771
$397$	4659.64	0.589069	0.294535	−	0.955641i	$-0.404835\pi$
$397$	4659.64	0.589069	0.294535	+	0.955641i	$0.404835\pi$
$398$	22183.9	2.79392
$399$	0	0
$400$	−11000.3	−1.37504
$401$	−13483.6	−1.67915	−0.839574	−	0.543246i	$-0.817195\pi$
$401$	−13483.6	−1.67915	−0.839574	+	0.543246i	$0.817195\pi$
$402$	−6135.69	−0.761244
$403$	4.79949	0.000593250 0
$404$	12530.3	1.54308
$405$	−13009.5	−1.59617
$406$	0	0
$407$	12855.7	1.56568
$408$	−7122.76	−0.864287
$409$	−6357.37	−0.768586	−0.384293	−	0.923211i	$-0.625555\pi$
$409$	−6357.37	−0.768586	−0.384293	+	0.923211i	$0.625555\pi$
$410$	27400.9	3.30057
$411$	14234.4	1.70835
$412$	6670.01	0.797591
$413$	0	0
$414$	−19887.4	−2.36090
$415$	−6462.64	−0.764430
$416$	−3091.69	−0.364381
$417$	−3294.37	−0.386873
$418$	2172.66	0.254231
$419$	−11986.3	−1.39754	−0.698772	−	0.715344i	$-0.746270\pi$
$419$	−11986.3	−1.39754	−0.698772	+	0.715344i	$0.746270\pi$
$420$	0	0
$421$	9704.56	1.12345	0.561723	−	0.827325i	$-0.310139\pi$
$421$	9704.56	1.12345	0.561723	+	0.827325i	$0.310139\pi$
$422$	−15818.8	−1.82475
$423$	8050.78	0.925395
$424$	−2550.50	−0.292131
$425$	−25516.9	−2.91235
$426$	25126.6	2.85772
$427$	0	0
$428$	20920.8	2.36272
$429$	−2948.83	−0.331866
$430$	33295.0	3.73401
$431$	−2841.90	−0.317610	−0.158805	−	0.987310i	$-0.550764\pi$
$431$	−2841.90	−0.317610	−0.158805	+	0.987310i	$0.550764\pi$
$432$	−1040.54	−0.115886
$433$	−2188.21	−0.242861	−0.121430	−	0.992600i	$-0.538748\pi$
$433$	−2188.21	−0.242861	−0.121430	+	0.992600i	$0.538748\pi$
$434$	0	0
$435$	−10662.9	−1.17529
$436$	5554.82	0.610155
$437$	2417.71	0.264656
$438$	−10419.6	−1.13669
$439$	−10929.2	−1.18820	−0.594100	−	0.804391i	$-0.702492\pi$
$439$	−10929.2	−1.18820	−0.594100	+	0.804391i	$0.702492\pi$
$440$	−8922.15	−0.966698
$441$	0	0
$442$	−3909.72	−0.420739
$443$	15563.0	1.66913	0.834563	−	0.550913i	$-0.185720\pi$
$443$	15563.0	1.66913	0.834563	+	0.550913i	$0.185720\pi$
$444$	−36834.4	−3.93712
$445$	8697.88	0.926560
$446$	4893.84	0.519574
$447$	−22192.9	−2.34830
$448$	0	0
$449$	−7554.08	−0.793985	−0.396993	−	0.917822i	$-0.629946\pi$
$449$	−7554.08	−0.793985	−0.396993	+	0.917822i	$0.629946\pi$
$450$	51164.3	5.35980
$451$	−8346.56	−0.871450
$452$	−185.951	−0.0193505
$453$	−3023.84	−0.313626
$454$	−8293.51	−0.857343
$455$	0	0
$456$	−1736.26	−0.178306
$457$	6062.28	0.620529	0.310264	−	0.950650i	$-0.399582\pi$
$457$	6062.28	0.620529	0.310264	+	0.950650i	$0.399582\pi$
$458$	8088.51	0.825221
$459$	−2413.68	−0.245448
$460$	−35597.4	−3.60812
$461$	13224.9	1.33610	0.668051	−	0.744115i	$-0.267129\pi$
$461$	13224.9	1.33610	0.668051	+	0.744115i	$0.267129\pi$
$462$	0	0
$463$	6308.80	0.633250	0.316625	−	0.948551i	$-0.397450\pi$
$463$	6308.80	0.633250	0.316625	+	0.948551i	$0.397450\pi$
$464$	1856.50	0.185745
$465$	62.9164	0.00627457
$466$	−24366.6	−2.42223
$467$	−818.162	−0.0810707	−0.0405353	−	0.999178i	$-0.512906\pi$
$467$	−818.162	−0.0810707	−0.0405353	+	0.999178i	$0.512906\pi$
$468$	4554.93	0.449897
$469$	0	0
$470$	24801.7	2.43408
$471$	−15311.4	−1.49790
$472$	−763.292	−0.0744351
$473$	−10141.9	−0.985892
$474$	7837.72	0.759490
$475$	−6220.04	−0.600831
$476$	0	0
$477$	−5957.29	−0.571835
$478$	−12482.0	−1.19438
$479$	−9195.58	−0.877154	−0.438577	−	0.898694i	$-0.644517\pi$
$479$	−9195.58	−0.877154	−0.438577	+	0.898694i	$0.644517\pi$
$480$	−40528.8	−3.85391
$481$	−5639.16	−0.534560
$482$	−8968.58	−0.847527
$483$	0	0
$484$	−5022.27	−0.471663
$485$	16463.7	1.54140
$486$	−23679.4	−2.21012
$487$	−16423.4	−1.52816	−0.764080	−	0.645121i	$-0.776807\pi$
$487$	−16423.4	−1.52816	−0.764080	+	0.645121i	$0.776807\pi$
$488$	2120.20	0.196674
$489$	24883.9	2.30121
$490$	0	0
$491$	761.593	0.0700004	0.0350002	−	0.999387i	$-0.488857\pi$
$491$	761.593	0.0700004	0.0350002	+	0.999387i	$0.488857\pi$
$492$	23914.7	2.19138
$493$	4306.42	0.393411
$494$	−953.041	−0.0868003
$495$	−20839.7	−1.89228
$496$	−10.9542	−0.000991650 0
$497$	0	0
$498$	−9707.65	−0.873514
$499$	1226.49	0.110031	0.0550153	−	0.998486i	$-0.482479\pi$
$499$	1226.49	0.110031	0.0550153	+	0.998486i	$0.482479\pi$
$500$	60704.0	5.42953
$501$	−6201.99	−0.553063
$502$	25419.0	2.25997
$503$	−1239.97	−0.109916	−0.0549580	−	0.998489i	$-0.517502\pi$
$503$	−1239.97	−0.109916	−0.0549580	+	0.998489i	$0.517502\pi$
$504$	0	0
$505$	25147.2	2.21592
$506$	18662.3	1.63960
$507$	1293.51	0.113307
$508$	20619.5	1.80087
$509$	9563.78	0.832823	0.416411	−	0.909176i	$-0.363288\pi$
$509$	9563.78	0.832823	0.416411	+	0.909176i	$0.363288\pi$
$510$	−51252.4	−4.44999
$511$	0	0
$512$	10265.8	0.886114
$513$	−588.362	−0.0506371
$514$	6933.68	0.595003
$515$	13386.1	1.14537
$516$	29058.9	2.47916
$517$	−7554.81	−0.642670
$518$	0	0
$519$	−14509.4	−1.22715
$520$	3913.71	0.330053
$521$	21095.1	1.77388	0.886940	−	0.461884i	$-0.152826\pi$
$521$	21095.1	1.77388	0.886940	+	0.461884i	$0.152826\pi$
$522$	−8634.87	−0.724019
$523$	−16158.7	−1.35100	−0.675500	−	0.737360i	$-0.736072\pi$
$523$	−16158.7	−1.35100	−0.675500	+	0.737360i	$0.736072\pi$
$524$	20545.8	1.71287
$525$	0	0
$526$	−10473.0	−0.868143
$527$	−25.4099	−0.00210033
$528$	6730.30	0.554733
$529$	8600.09	0.706838
$530$	−18352.4	−1.50411
$531$	−1782.84	−0.145704
$532$	0	0
$533$	3661.23	0.297533
$534$	13065.2	1.05878
$535$	41986.4	3.39295
$536$	−2480.53	−0.199893
$537$	−2125.79	−0.170828
$538$	−10105.7	−0.809830
$539$	0	0
$540$	8662.80	0.690347
$541$	−1819.41	−0.144589	−0.0722944	−	0.997383i	$-0.523032\pi$
$541$	−1819.41	−0.144589	−0.0722944	+	0.997383i	$0.523032\pi$
$542$	−10596.0	−0.839737
$543$	−9749.12	−0.770487
$544$	16368.3	1.29004
$545$	11148.1	0.876203
$546$	0	0
$547$	15208.3	1.18878	0.594389	−	0.804178i	$-0.297394\pi$
$547$	15208.3	1.18878	0.594389	+	0.804178i	$0.297394\pi$
$548$	20632.8	1.60838
$549$	4952.22	0.384983
$550$	−48012.3	−3.72228
$551$	1049.74	0.0811623
$552$	−14913.7	−1.14994
$553$	0	0
$554$	−35652.9	−2.73420
$555$	−73923.5	−5.65383
$556$	−4775.20	−0.364233
$557$	9899.79	0.753084	0.376542	−	0.926400i	$-0.377113\pi$
$557$	9899.79	0.753084	0.376542	+	0.926400i	$0.377113\pi$
$558$	50.9498	0.00386537
$559$	4448.77	0.336607
$560$	0	0
$561$	15611.9	1.17493
$562$	−18398.7	−1.38097
$563$	−11688.4	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$563$	−11688.4	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$564$	21646.2	1.61608
$565$	−373.189	−0.0277879
$566$	19713.7	1.46401
$567$	0	0
$568$	10158.2	0.750400
$569$	−11068.1	−0.815460	−0.407730	−	0.913102i	$-0.633680\pi$
$569$	−11068.1	−0.815460	−0.407730	+	0.913102i	$0.633680\pi$
$570$	−12493.4	−0.918052
$571$	14939.1	1.09489	0.547446	−	0.836841i	$-0.315600\pi$
$571$	14939.1	1.09489	0.547446	+	0.836841i	$0.315600\pi$
$572$	−4274.33	−0.312445
$573$	10068.6	0.734068
$574$	0	0
$575$	−53427.5	−3.87492
$576$	−25323.8	−1.83187
$577$	19280.1	1.39106	0.695528	−	0.718499i	$-0.255171\pi$
$577$	19280.1	1.39106	0.695528	+	0.718499i	$0.255171\pi$
$578$	−769.159	−0.0553508
$579$	−30038.0	−2.15602
$580$	−15455.9	−1.10651
$581$	0	0
$582$	24730.5	1.76136
$583$	5590.29	0.397129
$584$	−4212.44	−0.298480
$585$	9141.37	0.646067
$586$	4697.71	0.331162
$587$	1953.73	0.137375	0.0686876	−	0.997638i	$-0.478119\pi$
$587$	1953.73	0.137375	0.0686876	+	0.997638i	$0.478119\pi$
$588$	0	0
$589$	−6.19396	−0.000433307 0
$590$	−5492.33	−0.383247
$591$	−11773.4	−0.819447
$592$	12870.6	0.893546
$593$	−16528.3	−1.14458	−0.572291	−	0.820051i	$-0.693945\pi$
$593$	−16528.3	−1.14458	−0.572291	+	0.820051i	$0.693945\pi$
$594$	−4541.55	−0.313707
$595$	0	0
$596$	−32168.7	−2.21087
$597$	38856.9	2.66383
$598$	−8186.22	−0.559798
$599$	−10330.5	−0.704665	−0.352333	−	0.935875i	$-0.614611\pi$
$599$	−10330.5	−0.704665	−0.352333	+	0.935875i	$0.614611\pi$
$600$	38368.5	2.61064
$601$	−3872.28	−0.262818	−0.131409	−	0.991328i	$-0.541950\pi$
$601$	−3872.28	−0.262818	−0.131409	+	0.991328i	$0.541950\pi$
$602$	0	0
$603$	−5793.86	−0.391284
$604$	−4383.06	−0.295272
$605$	−10079.3	−0.677324
$606$	37774.1	2.53213
$607$	25485.2	1.70414	0.852069	−	0.523429i	$-0.175347\pi$
$607$	25485.2	1.70414	0.852069	+	0.523429i	$0.175347\pi$
$608$	3989.96	0.266142
$609$	0	0
$610$	15256.1	1.01263
$611$	3313.93	0.219422
$612$	−24115.1	−1.59280
$613$	10392.7	0.684759	0.342379	−	0.939562i	$-0.388767\pi$
$613$	10392.7	0.684759	0.342379	+	0.939562i	$0.388767\pi$
$614$	4825.01	0.317136
$615$	47994.8	3.14689
$616$	0	0
$617$	8288.40	0.540808	0.270404	−	0.962747i	$-0.412843\pi$
$617$	8288.40	0.540808	0.270404	+	0.962747i	$0.412843\pi$
$618$	20107.6	1.30881
$619$	−4901.44	−0.318264	−0.159132	−	0.987257i	$-0.550870\pi$
$619$	−4901.44	−0.318264	−0.159132	+	0.987257i	$0.550870\pi$
$620$	91.1973	0.00590738
$621$	−5053.78	−0.326572
$622$	−33814.1	−2.17978
$623$	0	0
$624$	−2952.25	−0.189399
$625$	75484.5	4.83101
$626$	−21066.4	−1.34502
$627$	3805.59	0.242393
$628$	−22193.9	−1.41024
$629$	29855.3	1.89254
$630$	0	0
$631$	4670.73	0.294673	0.147337	−	0.989086i	$-0.452930\pi$
$631$	4670.73	0.294673	0.147337	+	0.989086i	$0.452930\pi$
$632$	3168.63	0.199433
$633$	−27707.9	−1.73979
$634$	4036.15	0.252833
$635$	41381.6	2.58611
$636$	−16017.4	−0.998635
$637$	0	0
$638$	8102.92	0.502818
$639$	23726.7	1.46888
$640$	−35652.5	−2.20201
$641$	20182.4	1.24361	0.621806	−	0.783171i	$-0.286399\pi$
$641$	20182.4	1.24361	0.621806	+	0.783171i	$0.286399\pi$
$642$	63068.5	3.87712
$643$	14088.9	0.864095	0.432048	−	0.901851i	$-0.357791\pi$
$643$	14088.9	0.864095	0.432048	+	0.901851i	$0.357791\pi$
$644$	0	0
$645$	58318.8	3.56015
$646$	5045.67	0.307305
$647$	−14169.9	−0.861012	−0.430506	−	0.902588i	$-0.641665\pi$
$647$	−14169.9	−0.861012	−0.430506	+	0.902588i	$0.641665\pi$
$648$	−7900.37	−0.478944
$649$	1673.01	0.101189
$650$	21060.7	1.27087
$651$	0	0
$652$	36069.3	2.16654
$653$	26754.7	1.60336	0.801680	−	0.597753i	$-0.203940\pi$
$653$	26754.7	1.60336	0.801680	+	0.597753i	$0.203940\pi$
$654$	16745.7	1.00124
$655$	41233.6	2.45974
$656$	−8356.26	−0.497343
$657$	−9839.13	−0.584263
$658$	0	0
$659$	−5079.36	−0.300248	−0.150124	−	0.988667i	$-0.547967\pi$
$659$	−5079.36	−0.300248	−0.150124	+	0.988667i	$0.547967\pi$
$660$	−56032.0	−3.30461
$661$	2412.80	0.141978	0.0709888	−	0.997477i	$-0.477385\pi$
$661$	2412.80	0.141978	0.0709888	+	0.997477i	$0.477385\pi$
$662$	−23790.9	−1.39676
$663$	−6848.19	−0.401149
$664$	−3924.61	−0.229374
$665$	0	0
$666$	−59863.4	−3.48297
$667$	9016.82	0.523437
$668$	−8989.79	−0.520697
$669$	8571.95	0.495382
$670$	−17848.9	−1.02920
$671$	−4647.14	−0.267364
$672$	0	0
$673$	−10049.3	−0.575591	−0.287795	−	0.957692i	$-0.592922\pi$
$673$	−10049.3	−0.575591	−0.287795	+	0.957692i	$0.592922\pi$
$674$	21101.3	1.20592
$675$	13001.8	0.741395
$676$	1874.94	0.106676
$677$	8441.71	0.479234	0.239617	−	0.970868i	$-0.422978\pi$
$677$	8441.71	0.479234	0.239617	+	0.970868i	$0.422978\pi$
$678$	−560.574	−0.0317533
$679$	0	0
$680$	−20720.3	−1.16851
$681$	−14526.7	−0.817424
$682$	−47.8111	−0.00268443
$683$	−6276.05	−0.351605	−0.175802	−	0.984425i	$-0.556252\pi$
$683$	−6276.05	−0.351605	−0.175802	+	0.984425i	$0.556252\pi$
$684$	−5878.34	−0.328602
$685$	41408.4	2.30968
$686$	0	0
$687$	14167.7	0.786798
$688$	−10153.7	−0.562656
$689$	−2452.19	−0.135589
$690$	−107313.	−5.92076
$691$	22660.3	1.24752	0.623761	−	0.781615i	$-0.285604\pi$
$691$	22660.3	1.24752	0.623761	+	0.781615i	$0.285604\pi$
$692$	−21031.4	−1.15534
$693$	0	0
$694$	16456.9	0.900137
$695$	−9583.43	−0.523050
$696$	−6475.35	−0.352654
$697$	−19383.6	−1.05338
$698$	−29676.7	−1.60928
$699$	−42680.0	−2.30945
$700$	0	0
$701$	−7379.11	−0.397582	−0.198791	−	0.980042i	$-0.563702\pi$
$701$	−7379.11	−0.397582	−0.198791	+	0.980042i	$0.563702\pi$
$702$	1992.16	0.107107
$703$	7277.58	0.390440
$704$	23763.8	1.27220
$705$	43442.1	2.32074
$706$	−11657.3	−0.621430
$707$	0	0
$708$	−4793.55	−0.254453
$709$	6689.19	0.354327	0.177163	−	0.984181i	$-0.443308\pi$
$709$	6689.19	0.354327	0.177163	+	0.984181i	$0.443308\pi$
$710$	73094.0	3.86362
$711$	7401.06	0.390382
$712$	5282.02	0.278022
$713$	−53.2035	−0.00279451
$714$	0	0
$715$	−8578.22	−0.448682
$716$	−3081.33	−0.160831
$717$	−21863.2	−1.13877
$718$	8067.06	0.419303
$719$	17434.4	0.904303	0.452152	−	0.891941i	$-0.350657\pi$
$719$	17434.4	0.904303	0.452152	+	0.891941i	$0.350657\pi$
$720$	−20864.0	−1.07994
$721$	0	0
$722$	−28741.9	−1.48153
$723$	−15709.2	−0.808065
$724$	−14131.4	−0.725397
$725$	−23197.6	−1.18833
$726$	−15140.3	−0.773978
$727$	29783.1	1.51939	0.759693	−	0.650282i	$-0.225349\pi$
$727$	29783.1	1.51939	0.759693	+	0.650282i	$0.225349\pi$
$728$	0	0
$729$	−25700.4	−1.30572
$730$	−30311.0	−1.53679
$731$	−23553.1	−1.19171
$732$	13315.1	0.672322
$733$	16782.9	0.845690	0.422845	−	0.906202i	$-0.361032\pi$
$733$	16782.9	0.845690	0.422845	+	0.906202i	$0.361032\pi$
$734$	−10058.4	−0.505809
$735$	0	0
$736$	34272.1	1.71642
$737$	5436.93	0.271739
$738$	38866.3	1.93860
$739$	−28765.0	−1.43185	−0.715926	−	0.698176i	$-0.753995\pi$
$739$	−28765.0	−1.43185	−0.715926	+	0.698176i	$0.753995\pi$
$740$	−107152.	−5.32296
$741$	−1669.33	−0.0827588
$742$	0	0
$743$	17390.0	0.858653	0.429326	−	0.903149i	$-0.358751\pi$
$743$	17390.0	0.858653	0.429326	+	0.903149i	$0.358751\pi$
$744$	38.2076	0.00188274
$745$	−64559.8	−3.17489
$746$	50603.2	2.48353
$747$	−9166.82	−0.448991
$748$	22629.5	1.10617
$749$	0	0
$750$	183000.	8.90961
$751$	11869.3	0.576721	0.288360	−	0.957522i	$-0.406890\pi$
$751$	11869.3	0.576721	0.288360	+	0.957522i	$0.406890\pi$
$752$	−7563.59	−0.366776
$753$	44523.5	2.15475
$754$	−3554.36	−0.171674
$755$	−8796.44	−0.424020
$756$	0	0
$757$	−11924.0	−0.572504	−0.286252	−	0.958154i	$-0.592410\pi$
$757$	−11924.0	−0.572504	−0.286252	+	0.958154i	$0.592410\pi$
$758$	−35748.0	−1.71296
$759$	32688.4	1.56326
$760$	−5050.82	−0.241069
$761$	4332.02	0.206354	0.103177	−	0.994663i	$-0.467099\pi$
$761$	4332.02	0.206354	0.103177	+	0.994663i	$0.467099\pi$
$762$	62160.0	2.95515
$763$	0	0
$764$	14594.4	0.691110
$765$	−48397.0	−2.28732
$766$	34198.4	1.61310
$767$	−733.869	−0.0345482
$768$	−4456.34	−0.209381
$769$	−4011.68	−0.188121	−0.0940603	−	0.995567i	$-0.529985\pi$
$769$	−4011.68	−0.188121	−0.0940603	+	0.995567i	$0.529985\pi$
$770$	0	0
$771$	12144.9	0.567299
$772$	−43540.1	−2.02985
$773$	−6244.31	−0.290546	−0.145273	−	0.989392i	$-0.546406\pi$
$773$	−6244.31	−0.290546	−0.145273	+	0.989392i	$0.546406\pi$
$774$	47226.7	2.19319
$775$	136.877	0.00634419
$776$	9998.03	0.462511
$777$	0	0
$778$	−7935.33	−0.365675
$779$	−4724.97	−0.217317
$780$	24578.5	1.12827
$781$	−22265.1	−1.02011
$782$	43340.2	1.98189
$783$	−2194.29	−0.100150
$784$	0	0
$785$	−44541.3	−2.02516
$786$	61937.8	2.81075
$787$	−30033.9	−1.36035	−0.680173	−	0.733052i	$-0.738095\pi$
$787$	−30033.9	−1.36035	−0.680173	+	0.733052i	$0.738095\pi$
$788$	−17065.6	−0.771492
$789$	−18344.2	−0.827722
$790$	22800.1	1.02683
$791$	0	0
$792$	−12655.5	−0.567794
$793$	2038.47	0.0912842
$794$	20361.2	0.910067
$795$	−32145.6	−1.43407
$796$	56323.1	2.50794
$797$	−22799.5	−1.01330	−0.506650	−	0.862152i	$-0.669117\pi$
$797$	−22799.5	−1.01330	−0.506650	+	0.862152i	$0.669117\pi$
$798$	0	0
$799$	−17544.9	−0.776837
$800$	−88171.7	−3.89668
$801$	12337.4	0.544219
$802$	−58919.3	−2.59415
$803$	9232.99	0.405760
$804$	−15578.0	−0.683325
$805$	0	0
$806$	20.9724	0.000916526 0
$807$	−17701.0	−0.772124
$808$	15271.3	0.664905
$809$	14408.1	0.626158	0.313079	−	0.949727i	$-0.398640\pi$
$809$	14408.1	0.626158	0.313079	+	0.949727i	$0.398640\pi$
$810$	−56847.8	−2.46596
$811$	−2369.85	−0.102610	−0.0513050	−	0.998683i	$-0.516338\pi$
$811$	−2369.85	−0.102610	−0.0513050	+	0.998683i	$0.516338\pi$
$812$	0	0
$813$	−18559.7	−0.800638
$814$	56175.5	2.41886
$815$	72388.0	3.11122
$816$	15630.1	0.670542
$817$	−5741.34	−0.245856
$818$	−27779.8	−1.18741
$819$	0	0
$820$	69568.6	2.96273
$821$	10524.8	0.447402	0.223701	−	0.974658i	$-0.428186\pi$
$821$	10524.8	0.447402	0.223701	+	0.974658i	$0.428186\pi$
$822$	62200.3	2.63927
$823$	−29723.0	−1.25891	−0.629453	−	0.777038i	$-0.716721\pi$
$823$	−29723.0	−1.25891	−0.629453	+	0.777038i	$0.716721\pi$
$824$	8129.09	0.343677
$825$	−84097.4	−3.54897
$826$	0	0
$827$	−16178.2	−0.680253	−0.340127	−	0.940380i	$-0.610470\pi$
$827$	−16178.2	−0.680253	−0.340127	+	0.940380i	$0.610470\pi$
$828$	−50492.5	−2.11924
$829$	6591.47	0.276153	0.138077	−	0.990422i	$-0.455908\pi$
$829$	6591.47	0.276153	0.138077	+	0.990422i	$0.455908\pi$
$830$	−28239.8	−1.18099
$831$	−62448.8	−2.60689
$832$	−10424.0	−0.434360
$833$	0	0
$834$	−14395.4	−0.597690
$835$	−18041.8	−0.747738
$836$	5516.21	0.228208
$837$	12.9473	0.000534678 0
$838$	−52376.7	−2.15910
$839$	27270.5	1.12215	0.561074	−	0.827766i	$-0.310388\pi$
$839$	27270.5	1.12215	0.561074	+	0.827766i	$0.310388\pi$
$840$	0	0
$841$	−20474.0	−0.839477
$842$	42406.0	1.73564
$843$	−32226.8	−1.31667
$844$	−40162.6	−1.63798
$845$	3762.85	0.153190
$846$	35179.5	1.42966
$847$	0	0
$848$	5596.79	0.226645
$849$	34530.1	1.39584
$850$	−111501.	−4.49936
$851$	62511.3	2.51805
$852$	63794.3	2.56521
$853$	41132.1	1.65104	0.825519	−	0.564374i	$-0.190883\pi$
$853$	41132.1	1.65104	0.825519	+	0.564374i	$0.190883\pi$
$854$	0	0
$855$	−11797.3	−0.471884
$856$	25497.3	1.01808
$857$	16481.5	0.656941	0.328470	−	0.944514i	$-0.393467\pi$
$857$	16481.5	0.656941	0.328470	+	0.944514i	$0.393467\pi$
$858$	−12885.5	−0.512708
$859$	−9478.06	−0.376469	−0.188235	−	0.982124i	$-0.560277\pi$
$859$	−9478.06	−0.376469	−0.188235	+	0.982124i	$0.560277\pi$
$860$	84533.1	3.35181
$861$	0	0
$862$	−12418.3	−0.490682
$863$	27485.0	1.08413	0.542064	−	0.840337i	$-0.317643\pi$
$863$	27485.0	1.08413	0.542064	+	0.840337i	$0.317643\pi$
$864$	−8340.28	−0.328405
$865$	−42208.2	−1.65910
$866$	−9561.84	−0.375201
$867$	−1347.24	−0.0527736
$868$	0	0
$869$	−6945.12	−0.271113
$870$	−46593.9	−1.81573
$871$	−2384.91	−0.0927781
$872$	6769.95	0.262912
$873$	23352.7	0.905348
$874$	10564.7	0.408873
$875$	0	0
$876$	−26454.6	−1.02034
$877$	−16319.3	−0.628351	−0.314176	−	0.949365i	$-0.601728\pi$
$877$	−16319.3	−0.628351	−0.314176	+	0.949365i	$0.601728\pi$
$878$	−47757.2	−1.83568
$879$	8228.42	0.315742
$880$	19578.6	0.749995
$881$	−35302.1	−1.35001	−0.675005	−	0.737813i	$-0.735859\pi$
$881$	−35302.1	−1.35001	−0.675005	+	0.737813i	$0.735859\pi$
$882$	0	0
$883$	20248.5	0.771704	0.385852	−	0.922561i	$-0.373907\pi$
$883$	20248.5	0.771704	0.385852	+	0.922561i	$0.373907\pi$
$884$	−9926.46	−0.377673
$885$	−9620.25	−0.365403
$886$	68005.9	2.57867
$887$	−24324.0	−0.920768	−0.460384	−	0.887720i	$-0.652288\pi$
$887$	−24324.0	−0.920768	−0.460384	+	0.887720i	$0.652288\pi$
$888$	−44892.0	−1.69648
$889$	0	0
$890$	38007.2	1.43146
$891$	17316.3	0.651088
$892$	12425.0	0.466392
$893$	−4276.77	−0.160265
$894$	−96976.5	−3.62794
$895$	−6183.98	−0.230958
$896$	0	0
$897$	−14338.8	−0.533733
$898$	−33009.1	−1.22665
$899$	−23.1003	−0.000856995 0
$900$	129902.	4.81118
$901$	12982.6	0.480036
$902$	−36472.0	−1.34632
$903$	0	0
$904$	−226.629	−0.00833801
$905$	−28360.5	−1.04169
$906$	−13213.3	−0.484528
$907$	−38882.0	−1.42344	−0.711718	−	0.702465i	$-0.752083\pi$
$907$	−38882.0	−1.42344	−0.711718	+	0.702465i	$0.752083\pi$
$908$	−21056.5	−0.769587
$909$	35669.7	1.30153
$910$	0	0
$911$	10328.9	0.375644	0.187822	−	0.982203i	$-0.439857\pi$
$911$	10328.9	0.375644	0.187822	+	0.982203i	$0.439857\pi$
$912$	3810.02	0.138336
$913$	8602.10	0.311816
$914$	26490.4	0.958670
$915$	26722.3	0.965477
$916$	20536.1	0.740754
$917$	0	0
$918$	−10547.0	−0.379199
$919$	−7815.30	−0.280526	−0.140263	−	0.990114i	$-0.544795\pi$
$919$	−7815.30	−0.280526	−0.140263	+	0.990114i	$0.544795\pi$
$920$	−43384.4	−1.55472
$921$	8451.39	0.302370
$922$	57788.7	2.06418
$923$	9766.59	0.348290
$924$	0	0
$925$	−160823.	−5.71657
$926$	27567.6	0.978323
$927$	18987.3	0.672736
$928$	14880.5	0.526376
$929$	23252.8	0.821206	0.410603	−	0.911814i	$-0.365318\pi$
$929$	23252.8	0.821206	0.410603	+	0.911814i	$0.365318\pi$
$930$	274.926	0.00969374
$931$	0	0
$932$	−61864.7	−2.17430
$933$	−59228.1	−2.07829
$934$	−3575.12	−0.125248
$935$	45415.6	1.58850
$936$	5551.34	0.193858
$937$	−39999.2	−1.39458	−0.697288	−	0.716791i	$-0.745610\pi$
$937$	−39999.2	−1.39458	−0.697288	+	0.716791i	$0.745610\pi$
$938$	0	0
$939$	−36899.5	−1.28240
$940$	62969.4	2.18493
$941$	−41457.9	−1.43623	−0.718113	−	0.695926i	$-0.754994\pi$
$941$	−41457.9	−1.43623	−0.718113	+	0.695926i	$0.754994\pi$
$942$	−66906.3	−2.31415
$943$	−40585.5	−1.40153
$944$	1674.96	0.0577492
$945$	0	0
$946$	−44317.3	−1.52313
$947$	18775.7	0.644274	0.322137	−	0.946693i	$-0.395599\pi$
$947$	18775.7	0.644274	0.322137	+	0.946693i	$0.395599\pi$
$948$	19899.3	0.681750
$949$	−4050.06	−0.138536
$950$	−27179.7	−0.928239
$951$	7069.64	0.241061
$952$	0	0
$953$	51791.1	1.76042	0.880208	−	0.474588i	$-0.157403\pi$
$953$	51791.1	1.76042	0.880208	+	0.474588i	$0.157403\pi$
$954$	−26031.6	−0.883442
$955$	29289.8	0.992456
$956$	−31690.7	−1.07213
$957$	14192.9	0.479406
$958$	−40182.0	−1.35514
$959$	0	0
$960$	−136648.	−4.59405
$961$	−29790.9	−0.999995
$962$	−24641.5	−0.825855
$963$	59554.8	1.99286
$964$	−22770.5	−0.760776
$965$	−87381.4	−2.91493
$966$	0	0
$967$	−21401.1	−0.711698	−0.355849	−	0.934543i	$-0.615808\pi$
$967$	−21401.1	−0.711698	−0.355849	+	0.934543i	$0.615808\pi$
$968$	−6120.91	−0.203237
$969$	8837.89	0.292997
$970$	71941.6	2.38135
$971$	4449.09	0.147042	0.0735212	−	0.997294i	$-0.476576\pi$
$971$	4449.09	0.147042	0.0735212	+	0.997294i	$0.476576\pi$
$972$	−60120.0	−1.98390
$973$	0	0
$974$	−71765.3	−2.36089
$975$	36889.4	1.21170
$976$	−4652.55	−0.152586
$977$	−33998.3	−1.11331	−0.556654	−	0.830744i	$-0.687915\pi$
$977$	−33998.3	−1.11331	−0.556654	+	0.830744i	$0.687915\pi$
$978$	108735.	3.55519
$979$	−11577.3	−0.377950
$980$	0	0
$981$	15812.8	0.514641
$982$	3327.93	0.108145
$983$	−4647.71	−0.150803	−0.0754013	−	0.997153i	$-0.524024\pi$
$983$	−4647.71	−0.150803	−0.0754013	+	0.997153i	$0.524024\pi$
$984$	29146.1	0.944252
$985$	−34249.2	−1.10789
$986$	18817.8	0.607789
$987$	0	0
$988$	−2419.69	−0.0779156
$989$	−49315.7	−1.58559
$990$	−91063.5	−2.92342
$991$	−13175.0	−0.422318	−0.211159	−	0.977452i	$-0.567724\pi$
$991$	−13175.0	−0.422318	−0.211159	+	0.977452i	$0.567724\pi$
$992$	−87.8020	−0.00281020
$993$	−41671.6	−1.33173
$994$	0	0
$995$	113036.	3.60148
$996$	−24646.9	−0.784103
$997$	−40608.7	−1.28996	−0.644979	−	0.764200i	$-0.723134\pi$
$997$	−40608.7	−1.28996	−0.644979	+	0.764200i	$0.723134\pi$
$998$	5359.40	0.169989
$999$	−15212.5	−0.481782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.4.a.d.1.4		4
7.6	odd	2		91.4.a.b.1.4	✓	4
21.20	even	2		819.4.a.h.1.1		4
28.27	even	2		1456.4.a.s.1.4		4
35.34	odd	2		2275.4.a.h.1.1		4
91.90	odd	2		1183.4.a.e.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.4.a.b.1.4	✓	4	7.6	odd	2
637.4.a.d.1.4		4	1.1	even	1	trivial
819.4.a.h.1.1		4	21.20	even	2
1183.4.a.e.1.1		4	91.90	odd	2
1456.4.a.s.1.4		4	28.27	even	2
2275.4.a.h.1.1		4	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+4.36970 q^{2} +7.65388 q^{3} +11.0943 q^{4} +22.2654 q^{5} +33.4452 q^{6} +13.5212 q^{8} +31.5819 q^{9} +O(q^{10})\)	\(q+4.36970 q^{2} +7.65388 q^{3} +11.0943 q^{4} +22.2654 q^{5} +33.4452 q^{6} +13.5212 q^{8} +31.5819 q^{9} +97.2930 q^{10} -29.6363 q^{11} +84.9145 q^{12} +13.0000 q^{13} +170.416 q^{15} -29.6708 q^{16} -68.8257 q^{17} +138.004 q^{18} -16.7771 q^{19} +247.019 q^{20} -129.502 q^{22} -144.108 q^{23} +103.490 q^{24} +370.746 q^{25} +56.8061 q^{26} +35.0694 q^{27} -62.5699 q^{29} +744.669 q^{30} +0.369192 q^{31} -237.822 q^{32} -226.833 q^{33} -300.748 q^{34} +350.379 q^{36} -433.781 q^{37} -73.3108 q^{38} +99.5005 q^{39} +301.055 q^{40} +281.633 q^{41} +342.213 q^{43} -328.794 q^{44} +703.183 q^{45} -629.709 q^{46} +254.917 q^{47} -227.097 q^{48} +1620.05 q^{50} -526.784 q^{51} +144.226 q^{52} -188.630 q^{53} +153.243 q^{54} -659.863 q^{55} -128.410 q^{57} -273.412 q^{58} -56.4514 q^{59} +1890.65 q^{60} +156.806 q^{61} +1.61326 q^{62} -801.846 q^{64} +289.450 q^{65} -991.192 q^{66} -183.455 q^{67} -763.574 q^{68} -1102.99 q^{69} +751.276 q^{71} +427.026 q^{72} -311.543 q^{73} -1895.50 q^{74} +2837.65 q^{75} -186.130 q^{76} +434.788 q^{78} +234.345 q^{79} -660.630 q^{80} -584.295 q^{81} +1230.65 q^{82} -290.255 q^{83} -1532.43 q^{85} +1495.37 q^{86} -478.903 q^{87} -400.719 q^{88} +390.646 q^{89} +3072.70 q^{90} -1598.78 q^{92} +2.82575 q^{93} +1113.91 q^{94} -373.548 q^{95} -1820.26 q^{96} +739.433 q^{97} -935.971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9	\( 4 q - 4 q^{2} + 5 q^{3} + 26 q^{4} + 36 q^{5} + 45 q^{6} - 30 q^{8} + 21 q^{9} + 44 q^{10} - 95 q^{11} + 17 q^{12} + 52 q^{13} - 16 q^{15} + 58 q^{16} + 146 q^{17} + 65 q^{18} + 48 q^{19} + 474 q^{20} - 143 q^{22} - 121 q^{23} + 469 q^{24} + 506 q^{25} - 52 q^{26} + 83 q^{27} - 440 q^{29} + 1548 q^{30} + 283 q^{31} - 114 q^{32} - 227 q^{33} - 1234 q^{34} + 755 q^{36} - 209 q^{37} - 440 q^{38} + 65 q^{39} - 754 q^{40} + 93 q^{41} + 526 q^{43} + 217 q^{44} + 768 q^{45} - 841 q^{46} + 783 q^{47} - 1407 q^{48} + 446 q^{50} - 672 q^{51} + 338 q^{52} - 340 q^{53} + 199 q^{54} - 756 q^{55} - 1014 q^{57} + 1916 q^{58} + 922 q^{59} - 396 q^{60} + 141 q^{61} - 1745 q^{62} - 1510 q^{64} + 468 q^{65} - 503 q^{66} - 523 q^{67} + 1710 q^{68} - 1595 q^{69} + 1468 q^{71} - 9 q^{72} + 47 q^{73} - 2249 q^{74} + 1547 q^{75} + 1382 q^{76} + 585 q^{78} + 1025 q^{79} + 2538 q^{80} - 1772 q^{81} + 1561 q^{82} + 1190 q^{83} - 568 q^{85} + 738 q^{86} - 720 q^{87} - 555 q^{88} + 2962 q^{89} + 1960 q^{90} - 599 q^{92} - 763 q^{93} - 317 q^{94} + 2082 q^{95} + 45 q^{96} - 2715 q^{97} + 586 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 5 * q^3 + 26 * q^4 + 36 * q^5 + 45 * q^6 - 30 * q^8 + 21 * q^9 + 44 * q^10 - 95 * q^11 + 17 * q^12 + 52 * q^13 - 16 * q^15 + 58 * q^16 + 146 * q^17 + 65 * q^18 + 48 * q^19 + 474 * q^20 - 143 * q^22 - 121 * q^23 + 469 * q^24 + 506 * q^25 - 52 * q^26 + 83 * q^27 - 440 * q^29 + 1548 * q^30 + 283 * q^31 - 114 * q^32 - 227 * q^33 - 1234 * q^34 + 755 * q^36 - 209 * q^37 - 440 * q^38 + 65 * q^39 - 754 * q^40 + 93 * q^41 + 526 * q^43 + 217 * q^44 + 768 * q^45 - 841 * q^46 + 783 * q^47 - 1407 * q^48 + 446 * q^50 - 672 * q^51 + 338 * q^52 - 340 * q^53 + 199 * q^54 - 756 * q^55 - 1014 * q^57 + 1916 * q^58 + 922 * q^59 - 396 * q^60 + 141 * q^61 - 1745 * q^62 - 1510 * q^64 + 468 * q^65 - 503 * q^66 - 523 * q^67 + 1710 * q^68 - 1595 * q^69 + 1468 * q^71 - 9 * q^72 + 47 * q^73 - 2249 * q^74 + 1547 * q^75 + 1382 * q^76 + 585 * q^78 + 1025 * q^79 + 2538 * q^80 - 1772 * q^81 + 1561 * q^82 + 1190 * q^83 - 568 * q^85 + 738 * q^86 - 720 * q^87 - 555 * q^88 + 2962 * q^89 + 1960 * q^90 - 599 * q^92 - 763 * q^93 - 317 * q^94 + 2082 * q^95 + 45 * q^96 - 2715 * q^97 + 586 * q^99

Introduction

L-functions

Modular forms

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Database

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