LMFDB - Embedded newform 1617.4.a.n.1.2

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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 30x^{3} + 11x^{2} + 185x + 162 $ x^5 - x^4 - 30x^3 + 11x^2 + 185*x + 162
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.63074$ 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)

$f(q)$	$=$	$q-3.63074 q^{2} +3.00000 q^{3} +5.18226 q^{4} -21.1113 q^{5} -10.8922 q^{6} +10.2305 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.63074 q^{2} +3.00000 q^{3} +5.18226 q^{4} -21.1113 q^{5} -10.8922 q^{6} +10.2305 q^{8} +9.00000 q^{9} +76.6494 q^{10} +11.0000 q^{11} +15.5468 q^{12} -87.3602 q^{13} -63.3338 q^{15} -78.6023 q^{16} +28.2691 q^{17} -32.6766 q^{18} +97.9284 q^{19} -109.404 q^{20} -39.9381 q^{22} -112.065 q^{23} +30.6914 q^{24} +320.685 q^{25} +317.182 q^{26} +27.0000 q^{27} +14.9213 q^{29} +229.948 q^{30} -138.440 q^{31} +203.540 q^{32} +33.0000 q^{33} -102.638 q^{34} +46.6403 q^{36} +206.944 q^{37} -355.552 q^{38} -262.081 q^{39} -215.978 q^{40} -321.063 q^{41} +285.198 q^{43} +57.0048 q^{44} -190.001 q^{45} +406.877 q^{46} +303.300 q^{47} -235.807 q^{48} -1164.32 q^{50} +84.8072 q^{51} -452.723 q^{52} -554.639 q^{53} -98.0299 q^{54} -232.224 q^{55} +293.785 q^{57} -54.1752 q^{58} +693.110 q^{59} -328.212 q^{60} -156.761 q^{61} +502.638 q^{62} -110.184 q^{64} +1844.28 q^{65} -119.814 q^{66} +584.667 q^{67} +146.498 q^{68} -336.194 q^{69} +363.745 q^{71} +92.0743 q^{72} +747.424 q^{73} -751.360 q^{74} +962.055 q^{75} +507.490 q^{76} +951.546 q^{78} +419.344 q^{79} +1659.39 q^{80} +81.0000 q^{81} +1165.70 q^{82} -1178.20 q^{83} -596.796 q^{85} -1035.48 q^{86} +44.7638 q^{87} +112.535 q^{88} +397.908 q^{89} +689.845 q^{90} -580.748 q^{92} -415.319 q^{93} -1101.20 q^{94} -2067.39 q^{95} +610.621 q^{96} +1333.21 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} + 15 q^{3} + 21 q^{4} - 21 q^{5} - 3 q^{6} - 42 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - q^2 + 15 * q^3 + 21 * q^4 - 21 * q^5 - 3 * q^6 - 42 * q^8 + 45 * q^9	\( 5 q - q^{2} + 15 q^{3} + 21 q^{4} - 21 q^{5} - 3 q^{6} - 42 q^{8} + 45 q^{9} + 23 q^{10} + 55 q^{11} + 63 q^{12} - 101 q^{13} - 63 q^{15} - 7 q^{16} + 20 q^{17} - 9 q^{18} - 237 q^{19} - 85 q^{20} - 11 q^{22} - 80 q^{23} - 126 q^{24} + 486 q^{25} - 165 q^{26} + 135 q^{27} - 11 q^{29} + 69 q^{30} - 316 q^{31} + 453 q^{32} + 165 q^{33} - 936 q^{34} + 189 q^{36} + 319 q^{37} - 89 q^{38} - 303 q^{39} - 624 q^{40} - 1190 q^{41} + 88 q^{43} + 231 q^{44} - 189 q^{45} + 1000 q^{46} - 377 q^{47} - 21 q^{48} - 644 q^{50} + 60 q^{51} - 1001 q^{52} - 992 q^{53} - 27 q^{54} - 231 q^{55} - 711 q^{57} + 721 q^{58} - 71 q^{59} - 255 q^{60} + 574 q^{61} - 272 q^{62} - 1380 q^{64} + 589 q^{65} - 33 q^{66} - 527 q^{67} + 2974 q^{68} - 240 q^{69} - 1156 q^{71} - 378 q^{72} - 1061 q^{73} - 1609 q^{74} + 1458 q^{75} - 2399 q^{76} - 495 q^{78} + 588 q^{79} + 1643 q^{80} + 405 q^{81} + 2602 q^{82} + 212 q^{83} + 1918 q^{85} - 4760 q^{86} - 33 q^{87} - 462 q^{88} - 1030 q^{89} + 207 q^{90} - 1174 q^{92} - 948 q^{93} + 1799 q^{94} - 3593 q^{95} + 1359 q^{96} - 2488 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q - q^2 + 15 * q^3 + 21 * q^4 - 21 * q^5 - 3 * q^6 - 42 * q^8 + 45 * q^9 + 23 * q^10 + 55 * q^11 + 63 * q^12 - 101 * q^13 - 63 * q^15 - 7 * q^16 + 20 * q^17 - 9 * q^18 - 237 * q^19 - 85 * q^20 - 11 * q^22 - 80 * q^23 - 126 * q^24 + 486 * q^25 - 165 * q^26 + 135 * q^27 - 11 * q^29 + 69 * q^30 - 316 * q^31 + 453 * q^32 + 165 * q^33 - 936 * q^34 + 189 * q^36 + 319 * q^37 - 89 * q^38 - 303 * q^39 - 624 * q^40 - 1190 * q^41 + 88 * q^43 + 231 * q^44 - 189 * q^45 + 1000 * q^46 - 377 * q^47 - 21 * q^48 - 644 * q^50 + 60 * q^51 - 1001 * q^52 - 992 * q^53 - 27 * q^54 - 231 * q^55 - 711 * q^57 + 721 * q^58 - 71 * q^59 - 255 * q^60 + 574 * q^61 - 272 * q^62 - 1380 * q^64 + 589 * q^65 - 33 * q^66 - 527 * q^67 + 2974 * q^68 - 240 * q^69 - 1156 * q^71 - 378 * q^72 - 1061 * q^73 - 1609 * q^74 + 1458 * q^75 - 2399 * q^76 - 495 * q^78 + 588 * q^79 + 1643 * q^80 + 405 * q^81 + 2602 * q^82 + 212 * q^83 + 1918 * q^85 - 4760 * q^86 - 33 * q^87 - 462 * q^88 - 1030 * q^89 + 207 * q^90 - 1174 * q^92 - 948 * q^93 + 1799 * q^94 - 3593 * q^95 + 1359 * q^96 - 2488 * q^97 + 495 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.63074	−1.28366	−0.641830	−	0.766847i	$-0.721824\pi$
$2$	−3.63074	−1.28366	−0.641830	+	0.766847i	$0.721824\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.18226	0.647782
$5$	−21.1113	−1.88825	−0.944124	−	0.329590i	$-0.893089\pi$
$5$	−21.1113	−1.88825	−0.944124	+	0.329590i	$0.893089\pi$
$6$	−10.8922	−0.741121
$7$	0	0
$7$	0	0
$8$	10.2305	0.452128
$9$	9.00000	0.333333
$10$	76.6494	2.42387
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	15.5468	0.373997
$13$	−87.3602	−1.86380	−0.931898	−	0.362719i	$-0.881848\pi$
$13$	−87.3602	−1.86380	−0.931898	+	0.362719i	$0.881848\pi$
$14$	0	0
$15$	−63.3338	−1.09018
$16$	−78.6023	−1.22816
$17$	28.2691	0.403309	0.201655	−	0.979457i	$-0.435368\pi$
$17$	28.2691	0.403309	0.201655	+	0.979457i	$0.435368\pi$
$18$	−32.6766	−0.427887
$19$	97.9284	1.18244	0.591219	−	0.806511i	$-0.298647\pi$
$19$	97.9284	1.18244	0.591219	+	0.806511i	$0.298647\pi$
$20$	−109.404	−1.22317
$21$	0	0
$22$	−39.9381	−0.387038
$23$	−112.065	−1.01596	−0.507980	−	0.861369i	$-0.669608\pi$
$23$	−112.065	−1.01596	−0.507980	+	0.861369i	$0.669608\pi$
$24$	30.6914	0.261036
$25$	320.685	2.56548
$26$	317.182	2.39248
$27$	27.0000	0.192450
$28$	0	0
$29$	14.9213	0.0955451	0.0477725	−	0.998858i	$-0.484788\pi$
$29$	14.9213	0.0955451	0.0477725	+	0.998858i	$0.484788\pi$
$30$	229.948	1.39942
$31$	−138.440	−0.802081	−0.401040	−	0.916060i	$-0.631351\pi$
$31$	−138.440	−0.802081	−0.401040	+	0.916060i	$0.631351\pi$
$32$	203.540	1.12441
$33$	33.0000	0.174078
$34$	−102.638	−0.517712
$35$	0	0
$36$	46.6403	0.215927
$37$	206.944	0.919498	0.459749	−	0.888049i	$-0.347939\pi$
$37$	206.944	0.919498	0.459749	+	0.888049i	$0.347939\pi$
$38$	−355.552	−1.51785
$39$	−262.081	−1.07606
$40$	−215.978	−0.853729
$41$	−321.063	−1.22297	−0.611483	−	0.791257i	$-0.709427\pi$
$41$	−321.063	−1.22297	−0.611483	+	0.791257i	$0.709427\pi$
$42$	0	0
$43$	285.198	1.01145	0.505724	−	0.862696i	$-0.331226\pi$
$43$	285.198	1.01145	0.505724	+	0.862696i	$0.331226\pi$
$44$	57.0048	0.195314
$45$	−190.001	−0.629416
$46$	406.877	1.30415
$47$	303.300	0.941293	0.470647	−	0.882322i	$-0.344021\pi$
$47$	303.300	0.941293	0.470647	+	0.882322i	$0.344021\pi$
$48$	−235.807	−0.709079
$49$	0	0
$50$	−1164.32	−3.29320
$51$	84.8072	0.232851
$52$	−452.723	−1.20733
$53$	−554.639	−1.43746	−0.718732	−	0.695287i	$-0.755277\pi$
$53$	−554.639	−1.43746	−0.718732	+	0.695287i	$0.755277\pi$
$54$	−98.0299	−0.247040
$55$	−232.224	−0.569328
$56$	0	0
$57$	293.785	0.682681
$58$	−54.1752	−0.122647
$59$	693.110	1.52941	0.764705	−	0.644380i	$-0.222885\pi$
$59$	693.110	1.52941	0.764705	+	0.644380i	$0.222885\pi$
$60$	−328.212	−0.706200
$61$	−156.761	−0.329037	−0.164518	−	0.986374i	$-0.552607\pi$
$61$	−156.761	−0.329037	−0.164518	+	0.986374i	$0.552607\pi$
$62$	502.638	1.02960
$63$	0	0
$64$	−110.184	−0.215203
$65$	1844.28	3.51931
$66$	−119.814	−0.223456
$67$	584.667	1.06610	0.533048	−	0.846085i	$-0.321047\pi$
$67$	584.667	1.06610	0.533048	+	0.846085i	$0.321047\pi$
$68$	146.498	0.261257
$69$	−336.194	−0.586565
$70$	0	0
$71$	363.745	0.608008	0.304004	−	0.952671i	$-0.401676\pi$
$71$	363.745	0.608008	0.304004	+	0.952671i	$0.401676\pi$
$72$	92.0743	0.150709
$73$	747.424	1.19835	0.599173	−	0.800619i	$-0.295496\pi$
$73$	747.424	1.19835	0.599173	+	0.800619i	$0.295496\pi$
$74$	−751.360	−1.18032
$75$	962.055	1.48118
$76$	507.490	0.765962
$77$	0	0
$78$	951.546	1.38130
$79$	419.344	0.597213	0.298607	−	0.954376i	$-0.403478\pi$
$79$	419.344	0.597213	0.298607	+	0.954376i	$0.403478\pi$
$80$	1659.39	2.31907
$81$	81.0000	0.111111
$82$	1165.70	1.56987
$83$	−1178.20	−1.55812	−0.779061	−	0.626948i	$-0.784304\pi$
$83$	−1178.20	−1.55812	−0.779061	+	0.626948i	$0.784304\pi$
$84$	0	0
$85$	−596.796	−0.761548
$86$	−1035.48	−1.29835
$87$	44.7638	0.0551630
$88$	112.535	0.136322
$89$	397.908	0.473911	0.236956	−	0.971520i	$-0.423850\pi$
$89$	397.908	0.473911	0.236956	+	0.971520i	$0.423850\pi$
$90$	689.845	0.807956
$91$	0	0
$92$	−580.748	−0.658121
$93$	−415.319	−0.463082
$94$	−1101.20	−1.20830
$95$	−2067.39	−2.23274
$96$	610.621	0.649180
$97$	1333.21	1.39553	0.697766	−	0.716325i	$-0.254177\pi$
$97$	1333.21	1.39553	0.697766	+	0.716325i	$0.254177\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	1661.87	1.66187
$101$	−747.399	−0.736326	−0.368163	−	0.929761i	$-0.620013\pi$
$101$	−747.399	−0.736326	−0.368163	+	0.929761i	$0.620013\pi$
$102$	−307.913	−0.298901
$103$	−548.716	−0.524918	−0.262459	−	0.964943i	$-0.584533\pi$
$103$	−548.716	−0.524918	−0.262459	+	0.964943i	$0.584533\pi$
$104$	−893.737	−0.842674
$105$	0	0
$106$	2013.75	1.84521
$107$	273.875	0.247444	0.123722	−	0.992317i	$-0.460517\pi$
$107$	273.875	0.247444	0.123722	+	0.992317i	$0.460517\pi$
$108$	139.921	0.124666
$109$	2026.77	1.78100	0.890500	−	0.454983i	$-0.150355\pi$
$109$	2026.77	1.78100	0.890500	+	0.454983i	$0.150355\pi$
$110$	843.144	0.730824
$111$	620.833	0.530872
$112$	0	0
$113$	−1048.04	−0.872490	−0.436245	−	0.899828i	$-0.643692\pi$
$113$	−1048.04	−0.872490	−0.436245	+	0.899828i	$0.643692\pi$
$114$	−1066.66	−0.876330
$115$	2365.83	1.91839
$116$	77.3258	0.0618924
$117$	−786.242	−0.621266
$118$	−2516.50	−1.96324
$119$	0	0
$120$	−647.935	−0.492901
$121$	121.000	0.0909091
$122$	569.160	0.422371
$123$	−963.189	−0.706080
$124$	−717.431	−0.519574
$125$	−4131.16	−2.95602
$126$	0	0
$127$	−905.819	−0.632901	−0.316451	−	0.948609i	$-0.602491\pi$
$127$	−905.819	−0.632901	−0.316451	+	0.948609i	$0.602491\pi$
$128$	−1228.27	−0.848166
$129$	855.593	0.583959
$130$	−6696.11	−4.51760
$131$	−1887.45	−1.25883	−0.629416	−	0.777069i	$-0.716706\pi$
$131$	−1887.45	−1.25883	−0.629416	+	0.777069i	$0.716706\pi$
$132$	171.015	0.112764
$133$	0	0
$134$	−2122.77	−1.36850
$135$	−570.004	−0.363394
$136$	289.206	0.182347
$137$	690.753	0.430767	0.215383	−	0.976530i	$-0.430900\pi$
$137$	690.753	0.430767	0.215383	+	0.976530i	$0.430900\pi$
$138$	1220.63	0.752950
$139$	1466.05	0.894592	0.447296	−	0.894386i	$-0.352387\pi$
$139$	1466.05	0.894592	0.447296	+	0.894386i	$0.352387\pi$
$140$	0	0
$141$	909.899	0.543456
$142$	−1320.66	−0.780476
$143$	−960.962	−0.561956
$144$	−707.420	−0.409387
$145$	−315.006	−0.180413
$146$	−2713.70	−1.53827
$147$	0	0
$148$	1072.44	0.595634
$149$	1367.88	0.752088	0.376044	−	0.926602i	$-0.377284\pi$
$149$	1367.88	0.752088	0.376044	+	0.926602i	$0.377284\pi$
$150$	−3492.97	−1.90133
$151$	93.9161	0.0506145	0.0253072	−	0.999680i	$-0.491944\pi$
$151$	93.9161	0.0506145	0.0253072	+	0.999680i	$0.491944\pi$
$152$	1001.85	0.534613
$153$	254.422	0.134436
$154$	0	0
$155$	2922.64	1.51453
$156$	−1358.17	−0.697055
$157$	72.3063	0.0367558	0.0183779	−	0.999831i	$-0.494150\pi$
$157$	72.3063	0.0367558	0.0183779	+	0.999831i	$0.494150\pi$
$158$	−1522.53	−0.766619
$159$	−1663.92	−0.829920
$160$	−4296.99	−2.12317
$161$	0	0
$162$	−294.090	−0.142629
$163$	34.3598	0.0165108	0.00825542	−	0.999966i	$-0.497372\pi$
$163$	34.3598	0.0165108	0.00825542	+	0.999966i	$0.497372\pi$
$164$	−1663.83	−0.792216
$165$	−696.671	−0.328702
$166$	4277.73	2.00010
$167$	−379.079	−0.175653	−0.0878263	−	0.996136i	$-0.527992\pi$
$167$	−379.079	−0.175653	−0.0878263	+	0.996136i	$0.527992\pi$
$168$	0	0
$169$	5434.80	2.47374
$170$	2166.81	0.977569
$171$	881.356	0.394146
$172$	1477.97	0.655198
$173$	1398.29	0.614507	0.307253	−	0.951628i	$-0.400590\pi$
$173$	1398.29	0.614507	0.307253	+	0.951628i	$0.400590\pi$
$174$	−162.525	−0.0708105
$175$	0	0
$176$	−864.625	−0.370304
$177$	2079.33	0.883006
$178$	−1444.70	−0.608341
$179$	−2591.03	−1.08191	−0.540956	−	0.841051i	$-0.681938\pi$
$179$	−2591.03	−1.08191	−0.540956	+	0.841051i	$0.681938\pi$
$180$	−984.636	−0.407725
$181$	−3408.35	−1.39967	−0.699837	−	0.714303i	$-0.746744\pi$
$181$	−3408.35	−1.39967	−0.699837	+	0.714303i	$0.746744\pi$
$182$	0	0
$183$	−470.284	−0.189969
$184$	−1146.48	−0.459344
$185$	−4368.85	−1.73624
$186$	1507.92	0.594439
$187$	310.960	0.121602
$188$	1571.78	0.609753
$189$	0	0
$190$	7506.16	2.86607
$191$	−2785.74	−1.05533	−0.527667	−	0.849451i	$-0.676933\pi$
$191$	−2785.74	−1.05533	−0.527667	+	0.849451i	$0.676933\pi$
$192$	−330.551	−0.124247
$193$	−4931.75	−1.83935	−0.919677	−	0.392676i	$-0.871549\pi$
$193$	−4931.75	−1.83935	−0.919677	+	0.392676i	$0.871549\pi$
$194$	−4840.53	−1.79139
$195$	5532.85	2.03188
$196$	0	0
$197$	28.9860	0.0104831	0.00524154	−	0.999986i	$-0.498332\pi$
$197$	28.9860	0.0104831	0.00524154	+	0.999986i	$0.498332\pi$
$198$	−359.443	−0.129013
$199$	499.588	0.177964	0.0889821	−	0.996033i	$-0.471639\pi$
$199$	499.588	0.177964	0.0889821	+	0.996033i	$0.471639\pi$
$200$	3280.76	1.15992
$201$	1754.00	0.615511
$202$	2713.61	0.945192
$203$	0	0
$204$	439.493	0.150837
$205$	6778.04	2.30926
$206$	1992.24	0.673816
$207$	−1008.58	−0.338654
$208$	6866.71	2.28904
$209$	1077.21	0.356518
$210$	0	0
$211$	3435.50	1.12090	0.560450	−	0.828189i	$-0.310628\pi$
$211$	3435.50	1.12090	0.560450	+	0.828189i	$0.310628\pi$
$212$	−2874.29	−0.931164
$213$	1091.23	0.351034
$214$	−994.369	−0.317634
$215$	−6020.88	−1.90986
$216$	276.223	0.0870120
$217$	0	0
$218$	−7358.66	−2.28620
$219$	2242.27	0.691866
$220$	−1203.44	−0.368801
$221$	−2469.59	−0.751687
$222$	−2254.08	−0.681459
$223$	707.522	0.212463	0.106231	−	0.994341i	$-0.466122\pi$
$223$	707.522	0.212463	0.106231	+	0.994341i	$0.466122\pi$
$224$	0	0
$225$	2886.17	0.855160
$226$	3805.16	1.11998
$227$	500.427	0.146319	0.0731596	−	0.997320i	$-0.476692\pi$
$227$	500.427	0.146319	0.0731596	+	0.997320i	$0.476692\pi$
$228$	1522.47	0.442228
$229$	−3362.25	−0.970236	−0.485118	−	0.874449i	$-0.661223\pi$
$229$	−3362.25	−0.970236	−0.485118	+	0.874449i	$0.661223\pi$
$230$	−8589.69	−2.46255
$231$	0	0
$232$	152.652	0.0431986
$233$	−2963.07	−0.833122	−0.416561	−	0.909108i	$-0.636765\pi$
$233$	−2963.07	−0.833122	−0.416561	+	0.909108i	$0.636765\pi$
$234$	2854.64	0.797494
$235$	−6403.03	−1.77740
$236$	3591.88	0.990725
$237$	1258.03	0.344801
$238$	0	0
$239$	−844.179	−0.228474	−0.114237	−	0.993454i	$-0.536442\pi$
$239$	−844.179	−0.228474	−0.114237	+	0.993454i	$0.536442\pi$
$240$	4978.18	1.33892
$241$	−3616.63	−0.966672	−0.483336	−	0.875435i	$-0.660575\pi$
$241$	−3616.63	−0.966672	−0.483336	+	0.875435i	$0.660575\pi$
$242$	−439.319	−0.116696
$243$	243.000	0.0641500
$244$	−812.378	−0.213144
$245$	0	0
$246$	3497.09	0.906366
$247$	−8555.04	−2.20382
$248$	−1416.30	−0.362643
$249$	−3534.60	−0.899582
$250$	14999.2	3.79452
$251$	6190.73	1.55679	0.778397	−	0.627772i	$-0.216033\pi$
$251$	6190.73	1.55679	0.778397	+	0.627772i	$0.216033\pi$
$252$	0	0
$253$	−1232.71	−0.306324
$254$	3288.79	0.812430
$255$	−1790.39	−0.439680
$256$	5341.01	1.30396
$257$	4990.16	1.21120	0.605598	−	0.795771i	$-0.292934\pi$
$257$	4990.16	1.21120	0.605598	+	0.795771i	$0.292934\pi$
$258$	−3106.43	−0.749605
$259$	0	0
$260$	9557.55	2.27975
$261$	134.291	0.0318484
$262$	6852.82	1.61591
$263$	−672.993	−0.157789	−0.0788946	−	0.996883i	$-0.525139\pi$
$263$	−672.993	−0.157789	−0.0788946	+	0.996883i	$0.525139\pi$
$264$	337.606	0.0787053
$265$	11709.1	2.71429
$266$	0	0
$267$	1193.72	0.273613
$268$	3029.89	0.690598
$269$	3558.01	0.806453	0.403226	−	0.915100i	$-0.367889\pi$
$269$	3558.01	0.806453	0.403226	+	0.915100i	$0.367889\pi$
$270$	2069.53	0.466474
$271$	−3305.52	−0.740944	−0.370472	−	0.928844i	$-0.620804\pi$
$271$	−3305.52	−0.740944	−0.370472	+	0.928844i	$0.620804\pi$
$272$	−2222.01	−0.495328
$273$	0	0
$274$	−2507.94	−0.552958
$275$	3527.54	0.773522
$276$	−1742.24	−0.379967
$277$	1428.48	0.309851	0.154926	−	0.987926i	$-0.450486\pi$
$277$	1428.48	0.309851	0.154926	+	0.987926i	$0.450486\pi$
$278$	−5322.83	−1.14835
$279$	−1245.96	−0.267360
$280$	0	0
$281$	−7156.92	−1.51938	−0.759691	−	0.650284i	$-0.774650\pi$
$281$	−7156.92	−1.51938	−0.759691	+	0.650284i	$0.774650\pi$
$282$	−3303.60	−0.697612
$283$	2470.58	0.518942	0.259471	−	0.965751i	$-0.416452\pi$
$283$	2470.58	0.518942	0.259471	+	0.965751i	$0.416452\pi$
$284$	1885.02	0.393857
$285$	−6202.17	−1.28907
$286$	3489.00	0.721360
$287$	0	0
$288$	1831.86	0.374804
$289$	−4113.86	−0.837342
$290$	1143.71	0.231589
$291$	3999.62	0.805711
$292$	3873.34	0.776268
$293$	−4544.57	−0.906131	−0.453066	−	0.891477i	$-0.649670\pi$
$293$	−4544.57	−0.906131	−0.453066	+	0.891477i	$0.649670\pi$
$294$	0	0
$295$	−14632.4	−2.88791
$296$	2117.14	0.415730
$297$	297.000	0.0580259
$298$	−4966.41	−0.965425
$299$	9789.99	1.89354
$300$	4985.62	0.959483
$301$	0	0
$302$	−340.985	−0.0649717
$303$	−2242.20	−0.425118
$304$	−7697.39	−1.45222
$305$	3309.43	0.621303
$306$	−923.738	−0.172571
$307$	−6711.77	−1.24776	−0.623878	−	0.781522i	$-0.714444\pi$
$307$	−6711.77	−1.24776	−0.623878	+	0.781522i	$0.714444\pi$
$308$	0	0
$309$	−1646.15	−0.303062
$310$	−10611.3	−1.94414
$311$	3627.08	0.661328	0.330664	−	0.943749i	$-0.392727\pi$
$311$	3627.08	0.661328	0.330664	+	0.943749i	$0.392727\pi$
$312$	−2681.21	−0.486518
$313$	−4355.14	−0.786475	−0.393238	−	0.919437i	$-0.628645\pi$
$313$	−4355.14	−0.786475	−0.393238	+	0.919437i	$0.628645\pi$
$314$	−262.525	−0.0471820
$315$	0	0
$316$	2173.15	0.386864
$317$	−9227.18	−1.63486	−0.817429	−	0.576029i	$-0.804602\pi$
$317$	−9227.18	−1.63486	−0.817429	+	0.576029i	$0.804602\pi$
$318$	6041.25	1.06534
$319$	164.134	0.0288079
$320$	2326.12	0.406356
$321$	821.626	0.142862
$322$	0	0
$323$	2768.35	0.476888
$324$	419.763	0.0719758
$325$	−28015.1	−4.78154
$326$	−124.751	−0.0211943
$327$	6080.30	1.02826
$328$	−3284.63	−0.552937
$329$	0	0
$330$	2529.43	0.421941
$331$	837.223	0.139027	0.0695135	−	0.997581i	$-0.477855\pi$
$331$	837.223	0.139027	0.0695135	+	0.997581i	$0.477855\pi$
$332$	−6105.73	−1.00932
$333$	1862.50	0.306499
$334$	1376.34	0.225478
$335$	−12343.0	−2.01305
$336$	0	0
$337$	−9563.00	−1.54579	−0.772893	−	0.634536i	$-0.781191\pi$
$337$	−9563.00	−1.54579	−0.772893	+	0.634536i	$0.781191\pi$
$338$	−19732.3	−3.17544
$339$	−3144.12	−0.503732
$340$	−3092.75	−0.493317
$341$	−1522.84	−0.241837
$342$	−3199.97	−0.505949
$343$	0	0
$344$	2917.71	0.457303
$345$	7097.48	1.10758
$346$	−5076.81	−0.788818
$347$	−7584.04	−1.17329	−0.586646	−	0.809843i	$-0.699552\pi$
$347$	−7584.04	−1.17329	−0.586646	+	0.809843i	$0.699552\pi$
$348$	231.977	0.0357336
$349$	1800.32	0.276128	0.138064	−	0.990423i	$-0.455912\pi$
$349$	1800.32	0.276128	0.138064	+	0.990423i	$0.455912\pi$
$350$	0	0
$351$	−2358.73	−0.358688
$352$	2238.94	0.339023
$353$	−9042.84	−1.36346	−0.681731	−	0.731603i	$-0.738772\pi$
$353$	−9042.84	−1.36346	−0.681731	+	0.731603i	$0.738772\pi$
$354$	−7549.50	−1.13348
$355$	−7679.11	−1.14807
$356$	2062.06	0.306991
$357$	0	0
$358$	9407.33	1.38881
$359$	8915.34	1.31068	0.655339	−	0.755335i	$-0.272526\pi$
$359$	8915.34	1.31068	0.655339	+	0.755335i	$0.272526\pi$
$360$	−1943.80	−0.284576
$361$	2730.97	0.398159
$362$	12374.8	1.79671
$363$	363.000	0.0524864
$364$	0	0
$365$	−15779.1	−2.26278
$366$	1707.48	0.243856
$367$	11721.9	1.66724	0.833622	−	0.552335i	$-0.186263\pi$
$367$	11721.9	1.66724	0.833622	+	0.552335i	$0.186263\pi$
$368$	8808.53	1.24776
$369$	−2889.57	−0.407655
$370$	15862.2	2.22874
$371$	0	0
$372$	−2152.29	−0.299976
$373$	−8089.21	−1.12291	−0.561453	−	0.827509i	$-0.689757\pi$
$373$	−8089.21	−1.12291	−0.561453	+	0.827509i	$0.689757\pi$
$374$	−1129.01	−0.156096
$375$	−12393.5	−1.70666
$376$	3102.90	0.425585
$377$	−1303.52	−0.178077
$378$	0	0
$379$	−10580.4	−1.43398	−0.716989	−	0.697084i	$-0.754480\pi$
$379$	−10580.4	−1.43398	−0.716989	+	0.697084i	$0.754480\pi$
$380$	−10713.8	−1.44633
$381$	−2717.46	−0.365406
$382$	10114.3	1.35469
$383$	−10512.0	−1.40245	−0.701224	−	0.712941i	$-0.747363\pi$
$383$	−10512.0	−1.40245	−0.701224	+	0.712941i	$0.747363\pi$
$384$	−3684.82	−0.489689
$385$	0	0
$386$	17905.9	2.36110
$387$	2566.78	0.337149
$388$	6909.02	0.904001
$389$	1019.47	0.132878	0.0664388	−	0.997790i	$-0.478836\pi$
$389$	1019.47	0.132878	0.0664388	+	0.997790i	$0.478836\pi$
$390$	−20088.3	−2.60824
$391$	−3167.96	−0.409746
$392$	0	0
$393$	−5662.34	−0.726787
$394$	−105.241	−0.0134567
$395$	−8852.87	−1.12769
$396$	513.044	0.0651046
$397$	−11793.5	−1.49093	−0.745467	−	0.666543i	$-0.767773\pi$
$397$	−11793.5	−1.49093	−0.745467	+	0.666543i	$0.767773\pi$
$398$	−1813.87	−0.228445
$399$	0	0
$400$	−25206.6	−3.15082
$401$	−5342.21	−0.665280	−0.332640	−	0.943054i	$-0.607939\pi$
$401$	−5342.21	−0.665280	−0.332640	+	0.943054i	$0.607939\pi$
$402$	−6368.31	−0.790106
$403$	12094.1	1.49492
$404$	−3873.21	−0.476979
$405$	−1710.01	−0.209805
$406$	0	0
$407$	2276.39	0.277239
$408$	867.619	0.105278
$409$	8535.63	1.03193	0.515965	−	0.856610i	$-0.327433\pi$
$409$	8535.63	1.03193	0.515965	+	0.856610i	$0.327433\pi$
$410$	−24609.3	−2.96431
$411$	2072.26	0.248703
$412$	−2843.59	−0.340033
$413$	0	0
$414$	3661.90	0.434716
$415$	24873.3	2.94212
$416$	−17781.3	−2.09568
$417$	4398.14	0.516493
$418$	−3911.08	−0.457648
$419$	−4300.54	−0.501420	−0.250710	−	0.968062i	$-0.580664\pi$
$419$	−4300.54	−0.501420	−0.250710	+	0.968062i	$0.580664\pi$
$420$	0	0
$421$	−5917.77	−0.685070	−0.342535	−	0.939505i	$-0.611285\pi$
$421$	−5917.77	−0.685070	−0.342535	+	0.939505i	$0.611285\pi$
$422$	−12473.4	−1.43885
$423$	2729.70	0.313764
$424$	−5674.23	−0.649917
$425$	9065.47	1.03468
$426$	−3961.99	−0.450608
$427$	0	0
$428$	1419.29	0.160290
$429$	−2882.89	−0.324445
$430$	21860.2	2.45161
$431$	8110.20	0.906391	0.453196	−	0.891411i	$-0.350284\pi$
$431$	8110.20	0.906391	0.453196	+	0.891411i	$0.350284\pi$
$432$	−2122.26	−0.236360
$433$	4242.54	0.470862	0.235431	−	0.971891i	$-0.424350\pi$
$433$	4242.54	0.470862	0.235431	+	0.971891i	$0.424350\pi$
$434$	0	0
$435$	−945.019	−0.104161
$436$	10503.2	1.15370
$437$	−10974.3	−1.20131
$438$	−8141.10	−0.888120
$439$	595.983	0.0647944	0.0323972	−	0.999475i	$-0.489686\pi$
$439$	595.983	0.0647944	0.0323972	+	0.999475i	$0.489686\pi$
$440$	−2375.76	−0.257409
$441$	0	0
$442$	8966.44	0.964910
$443$	−4284.60	−0.459521	−0.229760	−	0.973247i	$-0.573794\pi$
$443$	−4284.60	−0.459521	−0.229760	+	0.973247i	$0.573794\pi$
$444$	3217.31	0.343890
$445$	−8400.33	−0.894862
$446$	−2568.83	−0.272730
$447$	4103.64	0.434218
$448$	0	0
$449$	−704.286	−0.0740252	−0.0370126	−	0.999315i	$-0.511784\pi$
$449$	−704.286	−0.0740252	−0.0370126	+	0.999315i	$0.511784\pi$
$450$	−10478.9	−1.09773
$451$	−3531.69	−0.368738
$452$	−5431.22	−0.565184
$453$	281.748	0.0292223
$454$	−1816.92	−0.187824
$455$	0	0
$456$	3005.56	0.308659
$457$	−7013.21	−0.717865	−0.358932	−	0.933364i	$-0.616859\pi$
$457$	−7013.21	−0.717865	−0.358932	+	0.933364i	$0.616859\pi$
$458$	12207.5	1.24545
$459$	763.265	0.0776169
$460$	12260.3	1.24270
$461$	−1032.99	−0.104363	−0.0521813	−	0.998638i	$-0.516617\pi$
$461$	−1032.99	−0.104363	−0.0521813	+	0.998638i	$0.516617\pi$
$462$	0	0
$463$	12593.3	1.26406	0.632029	−	0.774945i	$-0.282222\pi$
$463$	12593.3	1.26406	0.632029	+	0.774945i	$0.282222\pi$
$464$	−1172.84	−0.117345
$465$	8767.91	0.874413
$466$	10758.1	1.06944
$467$	18527.1	1.83583	0.917914	−	0.396779i	$-0.129872\pi$
$467$	18527.1	1.83583	0.917914	+	0.396779i	$0.129872\pi$
$468$	−4074.51	−0.402445
$469$	0	0
$470$	23247.7	2.28157
$471$	216.919	0.0212210
$472$	7090.85	0.691489
$473$	3137.17	0.304963
$474$	−4567.58	−0.442607
$475$	31404.2	3.03352
$476$	0	0
$477$	−4991.76	−0.479155
$478$	3064.99	0.293283
$479$	15402.2	1.46920	0.734599	−	0.678501i	$-0.237370\pi$
$479$	15402.2	1.46920	0.734599	+	0.678501i	$0.237370\pi$
$480$	−12891.0	−1.22581
$481$	−18078.7	−1.71376
$482$	13131.0	1.24088
$483$	0	0
$484$	627.053	0.0588893
$485$	−28145.7	−2.63511
$486$	−882.269	−0.0823468
$487$	6816.82	0.634291	0.317146	−	0.948377i	$-0.397276\pi$
$487$	6816.82	0.634291	0.317146	+	0.948377i	$0.397276\pi$
$488$	−1603.74	−0.148767
$489$	103.079	0.00953254
$490$	0	0
$491$	6232.66	0.572864	0.286432	−	0.958101i	$-0.407531\pi$
$491$	6232.66	0.572864	0.286432	+	0.958101i	$0.407531\pi$
$492$	−4991.49	−0.457386
$493$	421.810	0.0385342
$494$	31061.1	2.82896
$495$	−2090.01	−0.189776
$496$	10881.7	0.985084
$497$	0	0
$498$	12833.2	1.15476
$499$	−19244.6	−1.72646	−0.863232	−	0.504807i	$-0.831564\pi$
$499$	−19244.6	−1.72646	−0.863232	+	0.504807i	$0.831564\pi$
$500$	−21408.7	−1.91486
$501$	−1137.24	−0.101413
$502$	−22476.9	−1.99839
$503$	−7177.94	−0.636280	−0.318140	−	0.948044i	$-0.603058\pi$
$503$	−7177.94	−0.636280	−0.318140	+	0.948044i	$0.603058\pi$
$504$	0	0
$505$	15778.5	1.39037
$506$	4475.65	0.393215
$507$	16304.4	1.42821
$508$	−4694.19	−0.409982
$509$	−15314.2	−1.33357	−0.666787	−	0.745248i	$-0.732331\pi$
$509$	−15314.2	−1.33357	−0.666787	+	0.745248i	$0.732331\pi$
$510$	6500.43	0.564399
$511$	0	0
$512$	−9565.62	−0.825674
$513$	2644.07	0.227560
$514$	−18118.0	−1.55476
$515$	11584.1	0.991176
$516$	4433.90	0.378278
$517$	3336.29	0.283811
$518$	0	0
$519$	4194.86	0.354786
$520$	18867.9	1.59118
$521$	−9650.62	−0.811519	−0.405760	−	0.913980i	$-0.632993\pi$
$521$	−9650.62	−0.811519	−0.405760	+	0.913980i	$0.632993\pi$
$522$	−487.576	−0.0408825
$523$	13116.1	1.09661	0.548305	−	0.836278i	$-0.315273\pi$
$523$	13116.1	1.09661	0.548305	+	0.836278i	$0.315273\pi$
$524$	−9781.23	−0.815449
$525$	0	0
$526$	2443.46	0.202548
$527$	−3913.56	−0.323487
$528$	−2593.87	−0.213795
$529$	391.484	0.0321759
$530$	−42512.8	−3.48422
$531$	6237.99	0.509804
$532$	0	0
$533$	28048.1	2.27936
$534$	−4334.09	−0.351226
$535$	−5781.85	−0.467236
$536$	5981.42	0.482011
$537$	−7773.08	−0.624642
$538$	−12918.2	−1.03521
$539$	0	0
$540$	−2953.91	−0.235400
$541$	18625.5	1.48017	0.740086	−	0.672512i	$-0.234785\pi$
$541$	18625.5	1.48017	0.740086	+	0.672512i	$0.234785\pi$
$542$	12001.5	0.951121
$543$	−10225.1	−0.808102
$544$	5753.90	0.453486
$545$	−42787.6	−3.36297
$546$	0	0
$547$	−6967.57	−0.544628	−0.272314	−	0.962208i	$-0.587789\pi$
$547$	−6967.57	−0.544628	−0.272314	+	0.962208i	$0.587789\pi$
$548$	3579.66	0.279043
$549$	−1410.85	−0.109679
$550$	−12807.6	−0.992939
$551$	1461.21	0.112976
$552$	−3439.43	−0.265202
$553$	0	0
$554$	−5186.42	−0.397744
$555$	−13106.6	−1.00242
$556$	7597.43	0.579501
$557$	−17230.7	−1.31075	−0.655374	−	0.755305i	$-0.727489\pi$
$557$	−17230.7	−1.31075	−0.655374	+	0.755305i	$0.727489\pi$
$558$	4523.75	0.343200
$559$	−24914.9	−1.88513
$560$	0	0
$561$	932.879	0.0702071
$562$	25984.9	1.95037
$563$	20751.0	1.55338	0.776688	−	0.629885i	$-0.216898\pi$
$563$	20751.0	1.55338	0.776688	+	0.629885i	$0.216898\pi$
$564$	4715.33	0.352041
$565$	22125.5	1.64748
$566$	−8970.01	−0.666145
$567$	0	0
$568$	3721.29	0.274897
$569$	−15953.4	−1.17540	−0.587700	−	0.809079i	$-0.699966\pi$
$569$	−15953.4	−1.17540	−0.587700	+	0.809079i	$0.699966\pi$
$570$	22518.5	1.65473
$571$	10837.6	0.794291	0.397145	−	0.917756i	$-0.370001\pi$
$571$	10837.6	0.794291	0.397145	+	0.917756i	$0.370001\pi$
$572$	−4979.95	−0.364025
$573$	−8357.21	−0.609297
$574$	0	0
$575$	−35937.5	−2.60643
$576$	−991.654	−0.0717342
$577$	−9613.09	−0.693584	−0.346792	−	0.937942i	$-0.612729\pi$
$577$	−9613.09	−0.693584	−0.346792	+	0.937942i	$0.612729\pi$
$578$	14936.3	1.07486
$579$	−14795.3	−1.06195
$580$	−1632.44	−0.116868
$581$	0	0
$582$	−14521.6	−1.03426
$583$	−6101.03	−0.433412
$584$	7646.50	0.541806
$585$	16598.6	1.17310
$586$	16500.1	1.16316
$587$	−2169.43	−0.152542	−0.0762708	−	0.997087i	$-0.524301\pi$
$587$	−2169.43	−0.152542	−0.0762708	+	0.997087i	$0.524301\pi$
$588$	0	0
$589$	−13557.2	−0.948411
$590$	53126.5	3.70709
$591$	86.9580	0.00605241
$592$	−16266.3	−1.12929
$593$	−4688.62	−0.324686	−0.162343	−	0.986734i	$-0.551905\pi$
$593$	−4688.62	−0.324686	−0.162343	+	0.986734i	$0.551905\pi$
$594$	−1078.33	−0.0744855
$595$	0	0
$596$	7088.71	0.487189
$597$	1498.76	0.102748
$598$	−35544.9	−2.43067
$599$	941.884	0.0642476	0.0321238	−	0.999484i	$-0.489773\pi$
$599$	941.884	0.0642476	0.0321238	+	0.999484i	$0.489773\pi$
$600$	9842.29	0.669683
$601$	8131.21	0.551879	0.275939	−	0.961175i	$-0.411011\pi$
$601$	8131.21	0.551879	0.275939	+	0.961175i	$0.411011\pi$
$602$	0	0
$603$	5262.00	0.355365
$604$	486.698	0.0327872
$605$	−2554.46	−0.171659
$606$	8140.83	0.545707
$607$	27616.5	1.84666	0.923328	−	0.384011i	$-0.125458\pi$
$607$	27616.5	1.84666	0.923328	+	0.384011i	$0.125458\pi$
$608$	19932.4	1.32955
$609$	0	0
$610$	−12015.7	−0.797542
$611$	−26496.3	−1.75438
$612$	1318.48	0.0870855
$613$	7289.82	0.480315	0.240158	−	0.970734i	$-0.422801\pi$
$613$	7289.82	0.480315	0.240158	+	0.970734i	$0.422801\pi$
$614$	24368.7	1.60169
$615$	20334.1	1.33325
$616$	0	0
$617$	−13672.2	−0.892094	−0.446047	−	0.895010i	$-0.647169\pi$
$617$	−13672.2	−0.892094	−0.446047	+	0.895010i	$0.647169\pi$
$618$	5976.73	0.389028
$619$	−20157.3	−1.30887	−0.654435	−	0.756118i	$-0.727094\pi$
$619$	−20157.3	−1.30887	−0.654435	+	0.756118i	$0.727094\pi$
$620$	15145.9	0.981084
$621$	−3025.75	−0.195522
$622$	−13169.0	−0.848920
$623$	0	0
$624$	20600.1	1.32158
$625$	47128.3	3.01621
$626$	15812.4	1.00957
$627$	3231.64	0.205836
$628$	374.710	0.0238098
$629$	5850.12	0.370842
$630$	0	0
$631$	−21955.4	−1.38515	−0.692576	−	0.721345i	$-0.743524\pi$
$631$	−21955.4	−1.38515	−0.692576	+	0.721345i	$0.743524\pi$
$632$	4290.09	0.270017
$633$	10306.5	0.647151
$634$	33501.5	2.09860
$635$	19123.0	1.19507
$636$	−8622.86	−0.537608
$637$	0	0
$638$	−595.927	−0.0369796
$639$	3273.70	0.202669
$640$	25930.4	1.60155
$641$	3575.87	0.220340	0.110170	−	0.993913i	$-0.464860\pi$
$641$	3575.87	0.220340	0.110170	+	0.993913i	$0.464860\pi$
$642$	−2983.11	−0.183386
$643$	−6676.04	−0.409452	−0.204726	−	0.978819i	$-0.565630\pi$
$643$	−6676.04	−0.409452	−0.204726	+	0.978819i	$0.565630\pi$
$644$	0	0
$645$	−18062.6	−1.10266
$646$	−10051.1	−0.612162
$647$	12366.4	0.751430	0.375715	−	0.926735i	$-0.377397\pi$
$647$	12366.4	0.751430	0.375715	+	0.926735i	$0.377397\pi$
$648$	828.669	0.0502364
$649$	7624.21	0.461135
$650$	101716.	6.13786
$651$	0	0
$652$	178.061	0.0106954
$653$	19797.3	1.18642	0.593208	−	0.805049i	$-0.297861\pi$
$653$	19797.3	1.18642	0.593208	+	0.805049i	$0.297861\pi$
$654$	−22076.0	−1.31994
$655$	39846.4	2.37699
$656$	25236.3	1.50200
$657$	6726.81	0.399449
$658$	0	0
$659$	−893.599	−0.0528220	−0.0264110	−	0.999651i	$-0.508408\pi$
$659$	−893.599	−0.0528220	−0.0264110	+	0.999651i	$0.508408\pi$
$660$	−3610.33	−0.212927
$661$	−16418.8	−0.966137	−0.483068	−	0.875583i	$-0.660478\pi$
$661$	−16418.8	−0.966137	−0.483068	+	0.875583i	$0.660478\pi$
$662$	−3039.74	−0.178463
$663$	−7408.78	−0.433986
$664$	−12053.5	−0.704470
$665$	0	0
$666$	−6762.24	−0.393441
$667$	−1672.14	−0.0970700
$668$	−1964.48	−0.113785
$669$	2122.57	0.122665
$670$	44814.4	2.58408
$671$	−1724.38	−0.0992083
$672$	0	0
$673$	−17447.6	−0.999339	−0.499670	−	0.866216i	$-0.666545\pi$
$673$	−17447.6	−0.999339	−0.499670	+	0.866216i	$0.666545\pi$
$674$	34720.8	1.98426
$675$	8658.50	0.493727
$676$	28164.6	1.60244
$677$	23669.4	1.34371	0.671853	−	0.740685i	$-0.265499\pi$
$677$	23669.4	1.34371	0.671853	+	0.740685i	$0.265499\pi$
$678$	11415.5	0.646621
$679$	0	0
$680$	−6105.51	−0.344317
$681$	1501.28	0.0844775
$682$	5529.02	0.310436
$683$	−15236.3	−0.853586	−0.426793	−	0.904349i	$-0.640357\pi$
$683$	−15236.3	−0.853586	−0.426793	+	0.904349i	$0.640357\pi$
$684$	4567.41	0.255321
$685$	−14582.7	−0.813394
$686$	0	0
$687$	−10086.8	−0.560166
$688$	−22417.2	−1.24222
$689$	48453.4	2.67914
$690$	−25769.1	−1.42176
$691$	8336.36	0.458944	0.229472	−	0.973315i	$-0.426300\pi$
$691$	8336.36	0.458944	0.229472	+	0.973315i	$0.426300\pi$
$692$	7246.28	0.398067
$693$	0	0
$694$	27535.7	1.50611
$695$	−30950.1	−1.68921
$696$	457.955	0.0249407
$697$	−9076.15	−0.493234
$698$	−6536.48	−0.354455
$699$	−8889.22	−0.481003
$700$	0	0
$701$	798.786	0.0430381	0.0215191	−	0.999768i	$-0.493150\pi$
$701$	798.786	0.0430381	0.0215191	+	0.999768i	$0.493150\pi$
$702$	8563.91	0.460433
$703$	20265.7	1.08725
$704$	−1212.02	−0.0648860
$705$	−19209.1	−1.02618
$706$	32832.2	1.75022
$707$	0	0
$708$	10775.6	0.571995
$709$	−22352.2	−1.18400	−0.591999	−	0.805939i	$-0.701661\pi$
$709$	−22352.2	−1.18400	−0.591999	+	0.805939i	$0.701661\pi$
$710$	27880.9	1.47373
$711$	3774.09	0.199071
$712$	4070.79	0.214268
$713$	15514.2	0.814883
$714$	0	0
$715$	20287.1	1.06111
$716$	−13427.4	−0.700844
$717$	−2532.54	−0.131910
$718$	−32369.3	−1.68247
$719$	−13763.8	−0.713914	−0.356957	−	0.934121i	$-0.616186\pi$
$719$	−13763.8	−0.713914	−0.356957	+	0.934121i	$0.616186\pi$
$720$	14934.5	0.773024
$721$	0	0
$722$	−9915.44	−0.511100
$723$	−10849.9	−0.558108
$724$	−17663.0	−0.906684
$725$	4785.02	0.245119
$726$	−1317.96	−0.0673747
$727$	−16014.2	−0.816966	−0.408483	−	0.912766i	$-0.633942\pi$
$727$	−16014.2	−0.816966	−0.408483	+	0.912766i	$0.633942\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	57289.6	2.90463
$731$	8062.27	0.407926
$732$	−2437.13	−0.123059
$733$	−21073.3	−1.06188	−0.530942	−	0.847408i	$-0.678162\pi$
$733$	−21073.3	−1.06188	−0.530942	+	0.847408i	$0.678162\pi$
$734$	−42559.2	−2.14017
$735$	0	0
$736$	−22809.7	−1.14236
$737$	6431.33	0.321440
$738$	10491.3	0.523291
$739$	4570.10	0.227488	0.113744	−	0.993510i	$-0.463716\pi$
$739$	4570.10	0.227488	0.113744	+	0.993510i	$0.463716\pi$
$740$	−22640.5	−1.12471
$741$	−25665.1	−1.27238
$742$	0	0
$743$	7122.27	0.351670	0.175835	−	0.984420i	$-0.443737\pi$
$743$	7122.27	0.351670	0.175835	+	0.984420i	$0.443737\pi$
$744$	−4248.91	−0.209372
$745$	−28877.7	−1.42013
$746$	29369.8	1.44143
$747$	−10603.8	−0.519374
$748$	1611.47	0.0787718
$749$	0	0
$750$	44997.5	2.19077
$751$	31096.8	1.51097	0.755485	−	0.655166i	$-0.227401\pi$
$751$	31096.8	1.51097	0.755485	+	0.655166i	$0.227401\pi$
$752$	−23840.0	−1.15606
$753$	18572.2	0.898816
$754$	4732.75	0.228590
$755$	−1982.69	−0.0955727
$756$	0	0
$757$	2783.78	0.133657	0.0668284	−	0.997764i	$-0.478712\pi$
$757$	2783.78	0.133657	0.0668284	+	0.997764i	$0.478712\pi$
$758$	38414.6	1.84074
$759$	−3698.13	−0.176856
$760$	−21150.4	−1.00948
$761$	−22236.2	−1.05922	−0.529608	−	0.848243i	$-0.677661\pi$
$761$	−22236.2	−1.05922	−0.529608	+	0.848243i	$0.677661\pi$
$762$	9866.38	0.469057
$763$	0	0
$764$	−14436.4	−0.683626
$765$	−5371.16	−0.253849
$766$	38166.3	1.80027
$767$	−60550.2	−2.85051
$768$	16023.0	0.752841
$769$	28682.5	1.34502	0.672508	−	0.740090i	$-0.265217\pi$
$769$	28682.5	1.34502	0.672508	+	0.740090i	$0.265217\pi$
$770$	0	0
$771$	14970.5	0.699284
$772$	−25557.6	−1.19150
$773$	−27245.4	−1.26772	−0.633861	−	0.773447i	$-0.718531\pi$
$773$	−27245.4	−1.26772	−0.633861	+	0.773447i	$0.718531\pi$
$774$	−9319.30	−0.432785
$775$	−44395.6	−2.05772
$776$	13639.3	0.630959
$777$	0	0
$778$	−3701.45	−0.170570
$779$	−31441.2	−1.44608
$780$	28672.7	1.31621
$781$	4001.19	0.183321
$782$	11502.0	0.525975
$783$	402.874	0.0183877
$784$	0	0
$785$	−1526.48	−0.0694042
$786$	20558.5	0.932947
$787$	33427.2	1.51404	0.757020	−	0.653391i	$-0.226654\pi$
$787$	33427.2	1.51404	0.757020	+	0.653391i	$0.226654\pi$
$788$	150.213	0.00679075
$789$	−2018.98	−0.0910996
$790$	32142.5	1.44757
$791$	0	0
$792$	1012.82	0.0454405
$793$	13694.7	0.613258
$794$	42819.2	1.91385
$795$	35127.4	1.56710
$796$	2589.00	0.115282
$797$	6592.94	0.293016	0.146508	−	0.989209i	$-0.453197\pi$
$797$	6592.94	0.293016	0.146508	+	0.989209i	$0.453197\pi$
$798$	0	0
$799$	8574.00	0.379632
$800$	65272.4	2.88466
$801$	3581.17	0.157970
$802$	19396.2	0.853993
$803$	8221.66	0.361315
$804$	9089.68	0.398717
$805$	0	0
$806$	−43910.6	−1.91896
$807$	10674.0	0.465606
$808$	−7646.25	−0.332913
$809$	22661.3	0.984830	0.492415	−	0.870361i	$-0.336114\pi$
$809$	22661.3	0.984830	0.492415	+	0.870361i	$0.336114\pi$
$810$	6208.60	0.269319
$811$	−2938.33	−0.127224	−0.0636121	−	0.997975i	$-0.520262\pi$
$811$	−2938.33	−0.127224	−0.0636121	+	0.997975i	$0.520262\pi$
$812$	0	0
$813$	−9916.56	−0.427784
$814$	−8264.96	−0.355881
$815$	−725.379	−0.0311766
$816$	−6666.04	−0.285978
$817$	27928.9	1.19597
$818$	−30990.6	−1.32465
$819$	0	0
$820$	35125.6	1.49590
$821$	27511.4	1.16949	0.584747	−	0.811216i	$-0.301194\pi$
$821$	27511.4	1.16949	0.584747	+	0.811216i	$0.301194\pi$
$822$	−7523.83	−0.319250
$823$	25092.9	1.06280	0.531400	−	0.847121i	$-0.321666\pi$
$823$	25092.9	1.06280	0.531400	+	0.847121i	$0.321666\pi$
$824$	−5613.63	−0.237330
$825$	10582.6	0.446593
$826$	0	0
$827$	10259.3	0.431382	0.215691	−	0.976462i	$-0.430800\pi$
$827$	10259.3	0.431382	0.215691	+	0.976462i	$0.430800\pi$
$828$	−5226.73	−0.219374
$829$	40456.9	1.69497	0.847483	−	0.530823i	$-0.178117\pi$
$829$	40456.9	1.69497	0.847483	+	0.530823i	$0.178117\pi$
$830$	−90308.3	−3.77668
$831$	4285.43	0.178893
$832$	9625.67	0.401094
$833$	0	0
$834$	−15968.5	−0.663001
$835$	8002.83	0.331676
$836$	5582.39	0.230946
$837$	−3737.87	−0.154361
$838$	15614.1	0.643652
$839$	−11387.0	−0.468563	−0.234281	−	0.972169i	$-0.575274\pi$
$839$	−11387.0	−0.468563	−0.234281	+	0.972169i	$0.575274\pi$
$840$	0	0
$841$	−24166.4	−0.990871
$842$	21485.9	0.879396
$843$	−21470.8	−0.877215
$844$	17803.7	0.726099
$845$	−114736.	−4.67103
$846$	−9910.81	−0.402767
$847$	0	0
$848$	43595.9	1.76544
$849$	7411.73	0.299611
$850$	−32914.4	−1.32818
$851$	−23191.1	−0.934173
$852$	5655.06	0.227393
$853$	−8058.93	−0.323485	−0.161742	−	0.986833i	$-0.551711\pi$
$853$	−8058.93	−0.323485	−0.161742	+	0.986833i	$0.551711\pi$
$854$	0	0
$855$	−18606.5	−0.744245
$856$	2801.87	0.111876
$857$	−4025.02	−0.160434	−0.0802170	−	0.996777i	$-0.525561\pi$
$857$	−4025.02	−0.160434	−0.0802170	+	0.996777i	$0.525561\pi$
$858$	10467.0	0.416477
$859$	4319.84	0.171584	0.0857922	−	0.996313i	$-0.472658\pi$
$859$	4319.84	0.171584	0.0857922	+	0.996313i	$0.472658\pi$
$860$	−31201.8	−1.23718
$861$	0	0
$862$	−29446.0	−1.16350
$863$	11967.7	0.472055	0.236028	−	0.971746i	$-0.424154\pi$
$863$	11967.7	0.472055	0.236028	+	0.971746i	$0.424154\pi$
$864$	5495.59	0.216393
$865$	−29519.6	−1.16034
$866$	−15403.5	−0.604427
$867$	−12341.6	−0.483439
$868$	0	0
$869$	4612.78	0.180067
$870$	3431.12	0.133708
$871$	−51076.6	−1.98699
$872$	20734.8	0.805239
$873$	11998.9	0.465178
$874$	39844.8	1.54207
$875$	0	0
$876$	11620.0	0.448179
$877$	−3248.36	−0.125074	−0.0625368	−	0.998043i	$-0.519919\pi$
$877$	−3248.36	−0.125074	−0.0625368	+	0.998043i	$0.519919\pi$
$878$	−2163.86	−0.0831740
$879$	−13633.7	−0.523155
$880$	18253.3	0.699226
$881$	−1264.38	−0.0483518	−0.0241759	−	0.999708i	$-0.507696\pi$
$881$	−1264.38	−0.0483518	−0.0241759	+	0.999708i	$0.507696\pi$
$882$	0	0
$883$	−11524.4	−0.439216	−0.219608	−	0.975588i	$-0.570478\pi$
$883$	−11524.4	−0.439216	−0.219608	+	0.975588i	$0.570478\pi$
$884$	−12798.1	−0.486929
$885$	−43897.3	−1.66733
$886$	15556.3	0.589868
$887$	−24949.8	−0.944457	−0.472228	−	0.881476i	$-0.656550\pi$
$887$	−24949.8	−0.944457	−0.472228	+	0.881476i	$0.656550\pi$
$888$	6351.41	0.240022
$889$	0	0
$890$	30499.4	1.14870
$891$	891.000	0.0335013
$892$	3666.56	0.137630
$893$	29701.6	1.11302
$894$	−14899.2	−0.557388
$895$	54699.8	2.04292
$896$	0	0
$897$	29370.0	1.09324
$898$	2557.08	0.0950231
$899$	−2065.69	−0.0766349
$900$	14956.9	0.553958
$901$	−15679.1	−0.579743
$902$	12822.7	0.473334
$903$	0	0
$904$	−10722.0	−0.394477
$905$	71954.6	2.64293
$906$	−1022.95	−0.0375115
$907$	40615.8	1.48691	0.743454	−	0.668787i	$-0.233186\pi$
$907$	40615.8	1.48691	0.743454	+	0.668787i	$0.233186\pi$
$908$	2593.34	0.0947830
$909$	−6726.59	−0.245442
$910$	0	0
$911$	−14594.0	−0.530760	−0.265380	−	0.964144i	$-0.585497\pi$
$911$	−14594.0	−0.530760	−0.265380	+	0.964144i	$0.585497\pi$
$912$	−23092.2	−0.838441
$913$	−12960.2	−0.469792
$914$	25463.1	0.921494
$915$	9928.29	0.358710
$916$	−17424.1	−0.628502
$917$	0	0
$918$	−2771.22	−0.0996337
$919$	28339.1	1.01721	0.508607	−	0.860999i	$-0.330161\pi$
$919$	28339.1	1.01721	0.508607	+	0.860999i	$0.330161\pi$
$920$	24203.5	0.867355
$921$	−20135.3	−0.720392
$922$	3750.51	0.133966
$923$	−31776.8	−1.13320
$924$	0	0
$925$	66363.9	2.35895
$926$	−45722.9	−1.62262
$927$	−4938.44	−0.174973
$928$	3037.08	0.107432
$929$	−25916.5	−0.915276	−0.457638	−	0.889139i	$-0.651304\pi$
$929$	−25916.5	−0.915276	−0.457638	+	0.889139i	$0.651304\pi$
$930$	−31834.0	−1.12245
$931$	0	0
$932$	−15355.4	−0.539682
$933$	10881.2	0.381818
$934$	−67267.0	−2.35658
$935$	−6564.75	−0.229615
$936$	−8043.63	−0.280891
$937$	2004.67	0.0698930	0.0349465	−	0.999389i	$-0.488874\pi$
$937$	2004.67	0.0698930	0.0349465	+	0.999389i	$0.488874\pi$
$938$	0	0
$939$	−13065.4	−0.454072
$940$	−33182.2	−1.15137
$941$	36486.7	1.26401	0.632004	−	0.774965i	$-0.282233\pi$
$941$	36486.7	1.26401	0.632004	+	0.774965i	$0.282233\pi$
$942$	−787.575	−0.0272405
$943$	35979.8	1.24249
$944$	−54480.0	−1.87836
$945$	0	0
$946$	−11390.3	−0.391468
$947$	−26275.1	−0.901611	−0.450806	−	0.892622i	$-0.648863\pi$
$947$	−26275.1	−0.901611	−0.450806	+	0.892622i	$0.648863\pi$
$948$	6519.44	0.223356
$949$	−65295.1	−2.23347
$950$	−114020.	−3.89401
$951$	−27681.5	−0.943886
$952$	0	0
$953$	−25800.3	−0.876971	−0.438485	−	0.898738i	$-0.644485\pi$
$953$	−25800.3	−0.876971	−0.438485	+	0.898738i	$0.644485\pi$
$954$	18123.8	0.615072
$955$	58810.4	1.99273
$956$	−4374.75	−0.148002
$957$	492.401	0.0166323
$958$	−55921.5	−1.88595
$959$	0	0
$960$	6978.35	0.234610
$961$	−10625.4	−0.356666
$962$	65639.0	2.19988
$963$	2464.88	0.0824814
$964$	−18742.3	−0.626193
$965$	104115.	3.47316
$966$	0	0
$967$	−24454.9	−0.813254	−0.406627	−	0.913594i	$-0.633295\pi$
$967$	−24454.9	−0.813254	−0.406627	+	0.913594i	$0.633295\pi$
$968$	1237.89	0.0411025
$969$	8305.04	0.275331
$970$	102190.	3.38259
$971$	57692.0	1.90672	0.953359	−	0.301839i	$-0.0976004\pi$
$971$	57692.0	1.90672	0.953359	+	0.301839i	$0.0976004\pi$
$972$	1259.29	0.0415553
$973$	0	0
$974$	−24750.1	−0.814214
$975$	−84045.3	−2.76062
$976$	12321.8	0.404110
$977$	−6855.66	−0.224495	−0.112248	−	0.993680i	$-0.535805\pi$
$977$	−6855.66	−0.224495	−0.112248	+	0.993680i	$0.535805\pi$
$978$	−374.254	−0.0122365
$979$	4376.98	0.142890
$980$	0	0
$981$	18240.9	0.593667
$982$	−22629.2	−0.735362
$983$	8142.33	0.264191	0.132096	−	0.991237i	$-0.457829\pi$
$983$	8142.33	0.264191	0.132096	+	0.991237i	$0.457829\pi$
$984$	−9853.89	−0.319238
$985$	−611.931	−0.0197947
$986$	−1531.48	−0.0494648
$987$	0	0
$988$	−44334.4	−1.42760
$989$	−31960.6	−1.02759
$990$	7588.29	0.243608
$991$	11895.7	0.381312	0.190656	−	0.981657i	$-0.438938\pi$
$991$	11895.7	0.381312	0.190656	+	0.981657i	$0.438938\pi$
$992$	−28178.1	−0.901870
$993$	2511.67	0.0802672
$994$	0	0
$995$	−10546.9	−0.336041
$996$	−18317.2	−0.582734
$997$	44608.5	1.41702	0.708509	−	0.705702i	$-0.249368\pi$
$997$	44608.5	1.41702	0.708509	+	0.705702i	$0.249368\pi$
$998$	69872.0	2.21619
$999$	5587.49	0.176957

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.n.1.2		5
7.6	odd	2		231.4.a.k.1.2	✓	5
21.20	even	2		693.4.a.p.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.k.1.2	✓	5	7.6	odd	2
693.4.a.p.1.4		5	21.20	even	2
1617.4.a.n.1.2		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-3.63074 q^{2} +3.00000 q^{3} +5.18226 q^{4} -21.1113 q^{5} -10.8922 q^{6} +10.2305 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.63074 q^{2} +3.00000 q^{3} +5.18226 q^{4} -21.1113 q^{5} -10.8922 q^{6} +10.2305 q^{8} +9.00000 q^{9} +76.6494 q^{10} +11.0000 q^{11} +15.5468 q^{12} -87.3602 q^{13} -63.3338 q^{15} -78.6023 q^{16} +28.2691 q^{17} -32.6766 q^{18} +97.9284 q^{19} -109.404 q^{20} -39.9381 q^{22} -112.065 q^{23} +30.6914 q^{24} +320.685 q^{25} +317.182 q^{26} +27.0000 q^{27} +14.9213 q^{29} +229.948 q^{30} -138.440 q^{31} +203.540 q^{32} +33.0000 q^{33} -102.638 q^{34} +46.6403 q^{36} +206.944 q^{37} -355.552 q^{38} -262.081 q^{39} -215.978 q^{40} -321.063 q^{41} +285.198 q^{43} +57.0048 q^{44} -190.001 q^{45} +406.877 q^{46} +303.300 q^{47} -235.807 q^{48} -1164.32 q^{50} +84.8072 q^{51} -452.723 q^{52} -554.639 q^{53} -98.0299 q^{54} -232.224 q^{55} +293.785 q^{57} -54.1752 q^{58} +693.110 q^{59} -328.212 q^{60} -156.761 q^{61} +502.638 q^{62} -110.184 q^{64} +1844.28 q^{65} -119.814 q^{66} +584.667 q^{67} +146.498 q^{68} -336.194 q^{69} +363.745 q^{71} +92.0743 q^{72} +747.424 q^{73} -751.360 q^{74} +962.055 q^{75} +507.490 q^{76} +951.546 q^{78} +419.344 q^{79} +1659.39 q^{80} +81.0000 q^{81} +1165.70 q^{82} -1178.20 q^{83} -596.796 q^{85} -1035.48 q^{86} +44.7638 q^{87} +112.535 q^{88} +397.908 q^{89} +689.845 q^{90} -580.748 q^{92} -415.319 q^{93} -1101.20 q^{94} -2067.39 q^{95} +610.621 q^{96} +1333.21 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} + 15 q^{3} + 21 q^{4} - 21 q^{5} - 3 q^{6} - 42 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - q^2 + 15 * q^3 + 21 * q^4 - 21 * q^5 - 3 * q^6 - 42 * q^8 + 45 * q^9	\( 5 q - q^{2} + 15 q^{3} + 21 q^{4} - 21 q^{5} - 3 q^{6} - 42 q^{8} + 45 q^{9} + 23 q^{10} + 55 q^{11} + 63 q^{12} - 101 q^{13} - 63 q^{15} - 7 q^{16} + 20 q^{17} - 9 q^{18} - 237 q^{19} - 85 q^{20} - 11 q^{22} - 80 q^{23} - 126 q^{24} + 486 q^{25} - 165 q^{26} + 135 q^{27} - 11 q^{29} + 69 q^{30} - 316 q^{31} + 453 q^{32} + 165 q^{33} - 936 q^{34} + 189 q^{36} + 319 q^{37} - 89 q^{38} - 303 q^{39} - 624 q^{40} - 1190 q^{41} + 88 q^{43} + 231 q^{44} - 189 q^{45} + 1000 q^{46} - 377 q^{47} - 21 q^{48} - 644 q^{50} + 60 q^{51} - 1001 q^{52} - 992 q^{53} - 27 q^{54} - 231 q^{55} - 711 q^{57} + 721 q^{58} - 71 q^{59} - 255 q^{60} + 574 q^{61} - 272 q^{62} - 1380 q^{64} + 589 q^{65} - 33 q^{66} - 527 q^{67} + 2974 q^{68} - 240 q^{69} - 1156 q^{71} - 378 q^{72} - 1061 q^{73} - 1609 q^{74} + 1458 q^{75} - 2399 q^{76} - 495 q^{78} + 588 q^{79} + 1643 q^{80} + 405 q^{81} + 2602 q^{82} + 212 q^{83} + 1918 q^{85} - 4760 q^{86} - 33 q^{87} - 462 q^{88} - 1030 q^{89} + 207 q^{90} - 1174 q^{92} - 948 q^{93} + 1799 q^{94} - 3593 q^{95} + 1359 q^{96} - 2488 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q - q^2 + 15 * q^3 + 21 * q^4 - 21 * q^5 - 3 * q^6 - 42 * q^8 + 45 * q^9 + 23 * q^10 + 55 * q^11 + 63 * q^12 - 101 * q^13 - 63 * q^15 - 7 * q^16 + 20 * q^17 - 9 * q^18 - 237 * q^19 - 85 * q^20 - 11 * q^22 - 80 * q^23 - 126 * q^24 + 486 * q^25 - 165 * q^26 + 135 * q^27 - 11 * q^29 + 69 * q^30 - 316 * q^31 + 453 * q^32 + 165 * q^33 - 936 * q^34 + 189 * q^36 + 319 * q^37 - 89 * q^38 - 303 * q^39 - 624 * q^40 - 1190 * q^41 + 88 * q^43 + 231 * q^44 - 189 * q^45 + 1000 * q^46 - 377 * q^47 - 21 * q^48 - 644 * q^50 + 60 * q^51 - 1001 * q^52 - 992 * q^53 - 27 * q^54 - 231 * q^55 - 711 * q^57 + 721 * q^58 - 71 * q^59 - 255 * q^60 + 574 * q^61 - 272 * q^62 - 1380 * q^64 + 589 * q^65 - 33 * q^66 - 527 * q^67 + 2974 * q^68 - 240 * q^69 - 1156 * q^71 - 378 * q^72 - 1061 * q^73 - 1609 * q^74 + 1458 * q^75 - 2399 * q^76 - 495 * q^78 + 588 * q^79 + 1643 * q^80 + 405 * q^81 + 2602 * q^82 + 212 * q^83 + 1918 * q^85 - 4760 * q^86 - 33 * q^87 - 462 * q^88 - 1030 * q^89 + 207 * q^90 - 1174 * q^92 - 948 * q^93 + 1799 * q^94 - 3593 * q^95 + 1359 * q^96 - 2488 * q^97 + 495 * q^99

Introduction

L-functions

Modular forms

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Database

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