LMFDB - Embedded newform 1617.4.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$5$
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} - 28x^{3} - 11x^{2} + 108x - 64 $ x^5 - 28x^3 - 11x^2 + 108*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.1
Root			$5.15106$ 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)

$f(q)$	$=$	$q-4.15106 q^{2} -3.00000 q^{3} +9.23129 q^{4} -3.26204 q^{5} +12.4532 q^{6} -5.11115 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.15106 q^{2} -3.00000 q^{3} +9.23129 q^{4} -3.26204 q^{5} +12.4532 q^{6} -5.11115 q^{8} +9.00000 q^{9} +13.5409 q^{10} +11.0000 q^{11} -27.6939 q^{12} -19.4744 q^{13} +9.78612 q^{15} -52.6336 q^{16} -67.3291 q^{17} -37.3595 q^{18} +1.34582 q^{19} -30.1128 q^{20} -45.6616 q^{22} -102.218 q^{23} +15.3335 q^{24} -114.359 q^{25} +80.8392 q^{26} -27.0000 q^{27} +284.892 q^{29} -40.6228 q^{30} +110.709 q^{31} +259.374 q^{32} -33.0000 q^{33} +279.487 q^{34} +83.0816 q^{36} +43.4522 q^{37} -5.58656 q^{38} +58.4231 q^{39} +16.6728 q^{40} -324.422 q^{41} +340.787 q^{43} +101.544 q^{44} -29.3584 q^{45} +424.315 q^{46} -198.515 q^{47} +157.901 q^{48} +474.711 q^{50} +201.987 q^{51} -179.773 q^{52} +284.605 q^{53} +112.079 q^{54} -35.8824 q^{55} -4.03745 q^{57} -1182.60 q^{58} -861.612 q^{59} +90.3385 q^{60} -260.954 q^{61} -459.558 q^{62} -655.610 q^{64} +63.5261 q^{65} +136.985 q^{66} +890.274 q^{67} -621.534 q^{68} +306.655 q^{69} -480.915 q^{71} -46.0004 q^{72} -57.2651 q^{73} -180.373 q^{74} +343.077 q^{75} +12.4236 q^{76} -242.518 q^{78} -791.455 q^{79} +171.693 q^{80} +81.0000 q^{81} +1346.69 q^{82} +1020.86 q^{83} +219.630 q^{85} -1414.63 q^{86} -854.677 q^{87} -56.2227 q^{88} -421.812 q^{89} +121.868 q^{90} -943.607 q^{92} -332.126 q^{93} +824.048 q^{94} -4.39010 q^{95} -778.123 q^{96} +712.669 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9} - 55 q^{10} + 55 q^{11} - 63 q^{12} - 111 q^{13} + 21 q^{15} + 201 q^{16} - 136 q^{17} + 45 q^{18} - 111 q^{19} - 219 q^{20} + 55 q^{22} - 28 q^{23} - 180 q^{24} + 190 q^{25} + q^{26} - 135 q^{27} + 61 q^{29} + 165 q^{30} + 280 q^{31} + 535 q^{32} - 165 q^{33} + 572 q^{34} + 189 q^{36} - 41 q^{37} - 267 q^{38} + 333 q^{39} + 336 q^{40} - 426 q^{41} + 424 q^{43} + 231 q^{44} - 63 q^{45} + 140 q^{46} - 75 q^{47} - 603 q^{48} + 490 q^{50} + 408 q^{51} + 269 q^{52} + 1500 q^{53} - 135 q^{54} - 77 q^{55} + 333 q^{57} - 1767 q^{58} - 757 q^{59} + 657 q^{60} - 658 q^{61} + 568 q^{62} - 748 q^{64} + 537 q^{65} - 165 q^{66} - 583 q^{67} + 1650 q^{68} + 84 q^{69} - 764 q^{71} + 540 q^{72} - 875 q^{73} - 825 q^{74} - 570 q^{75} - 213 q^{76} - 3 q^{78} - 244 q^{79} + 2577 q^{80} + 405 q^{81} + 2006 q^{82} - 924 q^{83} - 1402 q^{85} + 1272 q^{86} - 183 q^{87} + 660 q^{88} + 1110 q^{89} - 495 q^{90} - 2046 q^{92} - 840 q^{93} + 3349 q^{94} + 1923 q^{95} - 1605 q^{96} + 852 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9 - 55 * q^10 + 55 * q^11 - 63 * q^12 - 111 * q^13 + 21 * q^15 + 201 * q^16 - 136 * q^17 + 45 * q^18 - 111 * q^19 - 219 * q^20 + 55 * q^22 - 28 * q^23 - 180 * q^24 + 190 * q^25 + q^26 - 135 * q^27 + 61 * q^29 + 165 * q^30 + 280 * q^31 + 535 * q^32 - 165 * q^33 + 572 * q^34 + 189 * q^36 - 41 * q^37 - 267 * q^38 + 333 * q^39 + 336 * q^40 - 426 * q^41 + 424 * q^43 + 231 * q^44 - 63 * q^45 + 140 * q^46 - 75 * q^47 - 603 * q^48 + 490 * q^50 + 408 * q^51 + 269 * q^52 + 1500 * q^53 - 135 * q^54 - 77 * q^55 + 333 * q^57 - 1767 * q^58 - 757 * q^59 + 657 * q^60 - 658 * q^61 + 568 * q^62 - 748 * q^64 + 537 * q^65 - 165 * q^66 - 583 * q^67 + 1650 * q^68 + 84 * q^69 - 764 * q^71 + 540 * q^72 - 875 * q^73 - 825 * q^74 - 570 * q^75 - 213 * q^76 - 3 * q^78 - 244 * q^79 + 2577 * q^80 + 405 * q^81 + 2006 * q^82 - 924 * q^83 - 1402 * q^85 + 1272 * q^86 - 183 * q^87 + 660 * q^88 + 1110 * q^89 - 495 * q^90 - 2046 * q^92 - 840 * q^93 + 3349 * q^94 + 1923 * q^95 - 1605 * q^96 + 852 * 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 $

$2$	−4.15106	−1.46762	−0.733810	−	0.679354i	$-0.762260\pi$
$2$	−4.15106	−1.46762	−0.733810	+	0.679354i	$0.762260\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	9.23129	1.15391
$5$	−3.26204	−0.291766	−0.145883	−	0.989302i	$-0.546602\pi$
$5$	−3.26204	−0.291766	−0.145883	+	0.989302i	$0.546602\pi$
$6$	12.4532	0.847331
$7$	0	0
$7$	0	0
$8$	−5.11115	−0.225883
$9$	9.00000	0.333333
$10$	13.5409	0.428202
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−27.6939	−0.666211
$13$	−19.4744	−0.415478	−0.207739	−	0.978184i	$-0.566610\pi$
$13$	−19.4744	−0.415478	−0.207739	+	0.978184i	$0.566610\pi$
$14$	0	0
$15$	9.78612	0.168451
$16$	−52.6336	−0.822400
$17$	−67.3291	−0.960570	−0.480285	−	0.877112i	$-0.659467\pi$
$17$	−67.3291	−0.960570	−0.480285	+	0.877112i	$0.659467\pi$
$18$	−37.3595	−0.489207
$19$	1.34582	0.0162501	0.00812503	−	0.999967i	$-0.497414\pi$
$19$	1.34582	0.0162501	0.00812503	+	0.999967i	$0.497414\pi$
$20$	−30.1128	−0.336672
$21$	0	0
$22$	−45.6616	−0.442504
$23$	−102.218	−0.926696	−0.463348	−	0.886176i	$-0.653352\pi$
$23$	−102.218	−0.926696	−0.463348	+	0.886176i	$0.653352\pi$
$24$	15.3335	0.130414
$25$	−114.359	−0.914873
$26$	80.8392	0.609764
$27$	−27.0000	−0.192450
$28$	0	0
$29$	284.892	1.82425	0.912124	−	0.409915i	$-0.134442\pi$
$29$	284.892	1.82425	0.912124	+	0.409915i	$0.134442\pi$
$30$	−40.6228	−0.247222
$31$	110.709	0.641414	0.320707	−	0.947178i	$-0.396080\pi$
$31$	110.709	0.641414	0.320707	+	0.947178i	$0.396080\pi$
$32$	259.374	1.43285
$33$	−33.0000	−0.174078
$34$	279.487	1.40975
$35$	0	0
$36$	83.0816	0.384637
$37$	43.4522	0.193068	0.0965338	−	0.995330i	$-0.469224\pi$
$37$	43.4522	0.193068	0.0965338	+	0.995330i	$0.469224\pi$
$38$	−5.58656	−0.0238489
$39$	58.4231	0.239876
$40$	16.6728	0.0659050
$41$	−324.422	−1.23576	−0.617880	−	0.786272i	$-0.712008\pi$
$41$	−324.422	−1.23576	−0.617880	+	0.786272i	$0.712008\pi$
$42$	0	0
$43$	340.787	1.20859	0.604297	−	0.796759i	$-0.293454\pi$
$43$	340.787	1.20859	0.604297	+	0.796759i	$0.293454\pi$
$44$	101.544	0.347917
$45$	−29.3584	−0.0972553
$46$	424.315	1.36004
$47$	−198.515	−0.616094	−0.308047	−	0.951371i	$-0.599675\pi$
$47$	−198.515	−0.616094	−0.308047	+	0.951371i	$0.599675\pi$
$48$	157.901	0.474813
$49$	0	0
$50$	474.711	1.34269
$51$	201.987	0.554586
$52$	−179.773	−0.479425
$53$	284.605	0.737613	0.368806	−	0.929506i	$-0.379767\pi$
$53$	284.605	0.737613	0.368806	+	0.929506i	$0.379767\pi$
$54$	112.079	0.282444
$55$	−35.8824	−0.0879707
$56$	0	0
$57$	−4.03745	−0.00938198
$58$	−1182.60	−2.67730
$59$	−861.612	−1.90123	−0.950613	−	0.310377i	$-0.899545\pi$
$59$	−861.612	−1.90123	−0.950613	+	0.310377i	$0.899545\pi$
$60$	90.3385	0.194378
$61$	−260.954	−0.547733	−0.273867	−	0.961768i	$-0.588303\pi$
$61$	−260.954	−0.547733	−0.273867	+	0.961768i	$0.588303\pi$
$62$	−459.558	−0.941353
$63$	0	0
$64$	−655.610	−1.28049
$65$	63.5261	0.121222
$66$	136.985	0.255480
$67$	890.274	1.62335	0.811674	−	0.584111i	$-0.198557\pi$
$67$	890.274	1.62335	0.811674	+	0.584111i	$0.198557\pi$
$68$	−621.534	−1.10841
$69$	306.655	0.535028
$70$	0	0
$71$	−480.915	−0.803861	−0.401930	−	0.915670i	$-0.631661\pi$
$71$	−480.915	−0.803861	−0.401930	+	0.915670i	$0.631661\pi$
$72$	−46.0004	−0.0752944
$73$	−57.2651	−0.0918133	−0.0459067	−	0.998946i	$-0.514618\pi$
$73$	−57.2651	−0.0918133	−0.0459067	+	0.998946i	$0.514618\pi$
$74$	−180.373	−0.283350
$75$	343.077	0.528202
$76$	12.4236	0.0187511
$77$	0	0
$78$	−242.518	−0.352048
$79$	−791.455	−1.12716	−0.563580	−	0.826061i	$-0.690576\pi$
$79$	−791.455	−1.12716	−0.563580	+	0.826061i	$0.690576\pi$
$80$	171.693	0.239948
$81$	81.0000	0.111111
$82$	1346.69	1.81363
$83$	1020.86	1.35004	0.675021	−	0.737798i	$-0.264134\pi$
$83$	1020.86	1.35004	0.675021	+	0.737798i	$0.264134\pi$
$84$	0	0
$85$	219.630	0.280262
$86$	−1414.63	−1.77376
$87$	−854.677	−1.05323
$88$	−56.2227	−0.0681063
$89$	−421.812	−0.502382	−0.251191	−	0.967938i	$-0.580822\pi$
$89$	−421.812	−0.502382	−0.251191	+	0.967938i	$0.580822\pi$
$90$	121.868	0.142734
$91$	0	0
$92$	−943.607	−1.06932
$93$	−332.126	−0.370321
$94$	824.048	0.904193
$95$	−4.39010	−0.00474121
$96$	−778.123	−0.827259
$97$	712.669	0.745985	0.372992	−	0.927834i	$-0.378332\pi$
$97$	712.669	0.745985	0.372992	+	0.927834i	$0.378332\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	−1055.68	−1.05568
$101$	−886.490	−0.873357	−0.436679	−	0.899618i	$-0.643845\pi$
$101$	−886.490	−0.873357	−0.436679	+	0.899618i	$0.643845\pi$
$102$	−838.461	−0.813921
$103$	−745.793	−0.713448	−0.356724	−	0.934210i	$-0.616106\pi$
$103$	−745.793	−0.713448	−0.356724	+	0.934210i	$0.616106\pi$
$104$	99.5364	0.0938495
$105$	0	0
$106$	−1181.41	−1.08254
$107$	−1470.90	−1.32894	−0.664472	−	0.747313i	$-0.731343\pi$
$107$	−1470.90	−1.32894	−0.664472	+	0.747313i	$0.731343\pi$
$108$	−249.245	−0.222070
$109$	1157.15	1.01683	0.508416	−	0.861112i	$-0.330231\pi$
$109$	1157.15	1.01683	0.508416	+	0.861112i	$0.330231\pi$
$110$	148.950	0.129108
$111$	−130.357	−0.111468
$112$	0	0
$113$	−207.183	−0.172479	−0.0862395	−	0.996274i	$-0.527485\pi$
$113$	−207.183	−0.172479	−0.0862395	+	0.996274i	$0.527485\pi$
$114$	16.7597	0.0137692
$115$	333.441	0.270378
$116$	2629.92	2.10502
$117$	−175.269	−0.138493
$118$	3576.60	2.79028
$119$	0	0
$120$	−50.0184	−0.0380503
$121$	121.000	0.0909091
$122$	1083.23	0.803865
$123$	973.265	0.713466
$124$	1021.98	0.740135
$125$	780.799	0.558694
$126$	0	0
$127$	615.933	0.430356	0.215178	−	0.976575i	$-0.430967\pi$
$127$	615.933	0.430356	0.215178	+	0.976575i	$0.430967\pi$
$128$	646.479	0.446415
$129$	−1022.36	−0.697782
$130$	−263.701	−0.177908
$131$	−2271.14	−1.51474	−0.757369	−	0.652987i	$-0.773516\pi$
$131$	−2271.14	−1.51474	−0.757369	+	0.652987i	$0.773516\pi$
$132$	−304.633	−0.200870
$133$	0	0
$134$	−3695.58	−2.38246
$135$	88.0751	0.0561503
$136$	344.129	0.216977
$137$	−1979.81	−1.23465	−0.617323	−	0.786710i	$-0.711783\pi$
$137$	−1979.81	−1.23465	−0.617323	+	0.786710i	$0.711783\pi$
$138$	−1272.94	−0.785219
$139$	370.611	0.226150	0.113075	−	0.993586i	$-0.463930\pi$
$139$	370.611	0.226150	0.113075	+	0.993586i	$0.463930\pi$
$140$	0	0
$141$	595.546	0.355702
$142$	1996.31	1.17976
$143$	−214.218	−0.125271
$144$	−473.703	−0.274133
$145$	−929.330	−0.532253
$146$	237.711	0.134747
$147$	0	0
$148$	401.120	0.222783
$149$	−418.304	−0.229992	−0.114996	−	0.993366i	$-0.536685\pi$
$149$	−418.304	−0.229992	−0.114996	+	0.993366i	$0.536685\pi$
$150$	−1424.13	−0.775200
$151$	−1686.68	−0.909005	−0.454503	−	0.890745i	$-0.650183\pi$
$151$	−1686.68	−0.909005	−0.454503	+	0.890745i	$0.650183\pi$
$152$	−6.87867	−0.00367062
$153$	−605.962	−0.320190
$154$	0	0
$155$	−361.136	−0.187143
$156$	539.320	0.276796
$157$	514.971	0.261778	0.130889	−	0.991397i	$-0.458217\pi$
$157$	514.971	0.261778	0.130889	+	0.991397i	$0.458217\pi$
$158$	3285.38	1.65424
$159$	−853.815	−0.425861
$160$	−846.090	−0.418058
$161$	0	0
$162$	−336.236	−0.163069
$163$	−1688.10	−0.811181	−0.405591	−	0.914055i	$-0.632934\pi$
$163$	−1688.10	−0.811181	−0.405591	+	0.914055i	$0.632934\pi$
$164$	−2994.83	−1.42596
$165$	107.647	0.0507899
$166$	−4237.63	−1.98135
$167$	−1445.06	−0.669594	−0.334797	−	0.942290i	$-0.608668\pi$
$167$	−1445.06	−0.669594	−0.334797	+	0.942290i	$0.608668\pi$
$168$	0	0
$169$	−1817.75	−0.827378
$170$	−911.698	−0.411318
$171$	12.1123	0.00541669
$172$	3145.90	1.39461
$173$	3367.85	1.48008	0.740038	−	0.672565i	$-0.234808\pi$
$173$	3367.85	1.48008	0.740038	+	0.672565i	$0.234808\pi$
$174$	3547.81	1.54574
$175$	0	0
$176$	−578.970	−0.247963
$177$	2584.84	1.09767
$178$	1750.97	0.737306
$179$	2318.20	0.967990	0.483995	−	0.875071i	$-0.339185\pi$
$179$	2318.20	0.967990	0.483995	+	0.875071i	$0.339185\pi$
$180$	−271.016	−0.112224
$181$	−2835.47	−1.16441	−0.582207	−	0.813041i	$-0.697811\pi$
$181$	−2835.47	−1.16441	−0.582207	+	0.813041i	$0.697811\pi$
$182$	0	0
$183$	782.862	0.316234
$184$	522.454	0.209325
$185$	−141.743	−0.0563305
$186$	1378.67	0.543490
$187$	−740.620	−0.289623
$188$	−1832.55	−0.710918
$189$	0	0
$190$	18.2236	0.00695830
$191$	−438.009	−0.165933	−0.0829666	−	0.996552i	$-0.526439\pi$
$191$	−438.009	−0.165933	−0.0829666	+	0.996552i	$0.526439\pi$
$192$	1966.83	0.739290
$193$	1394.12	0.519955	0.259977	−	0.965615i	$-0.416285\pi$
$193$	1394.12	0.519955	0.259977	+	0.965615i	$0.416285\pi$
$194$	−2958.33	−1.09482
$195$	−190.578	−0.0699877
$196$	0	0
$197$	−765.521	−0.276858	−0.138429	−	0.990372i	$-0.544205\pi$
$197$	−765.521	−0.276858	−0.138429	+	0.990372i	$0.544205\pi$
$198$	−410.955	−0.147501
$199$	2461.98	0.877010	0.438505	−	0.898729i	$-0.355508\pi$
$199$	2461.98	0.877010	0.438505	+	0.898729i	$0.355508\pi$
$200$	584.507	0.206654
$201$	−2670.82	−0.937241
$202$	3679.87	1.28176
$203$	0	0
$204$	1864.60	0.639943
$205$	1058.28	0.360553
$206$	3095.83	1.04707
$207$	−919.965	−0.308899
$208$	1025.01	0.341689
$209$	14.8040	0.00489958
$210$	0	0
$211$	4441.44	1.44910	0.724552	−	0.689220i	$-0.242047\pi$
$211$	4441.44	1.44910	0.724552	+	0.689220i	$0.242047\pi$
$212$	2627.27	0.851140
$213$	1442.74	0.464109
$214$	6105.78	1.95039
$215$	−1111.66	−0.352626
$216$	138.001	0.0434712
$217$	0	0
$218$	−4803.39	−1.49232
$219$	171.795	0.0530084
$220$	−331.241	−0.101510
$221$	1311.19	0.399096
$222$	541.118	0.163592
$223$	3889.49	1.16798	0.583989	−	0.811761i	$-0.301491\pi$
$223$	3889.49	1.16798	0.583989	+	0.811761i	$0.301491\pi$
$224$	0	0
$225$	−1029.23	−0.304958
$226$	860.028	0.253134
$227$	−188.302	−0.0550576	−0.0275288	−	0.999621i	$-0.508764\pi$
$227$	−188.302	−0.0550576	−0.0275288	+	0.999621i	$0.508764\pi$
$228$	−37.2708	−0.0108260
$229$	3501.22	1.01034	0.505168	−	0.863021i	$-0.331431\pi$
$229$	3501.22	1.01034	0.505168	+	0.863021i	$0.331431\pi$
$230$	−1384.13	−0.396813
$231$	0	0
$232$	−1456.13	−0.412067
$233$	−2464.65	−0.692980	−0.346490	−	0.938054i	$-0.612627\pi$
$233$	−2464.65	−0.692980	−0.346490	+	0.938054i	$0.612627\pi$
$234$	727.553	0.203255
$235$	647.565	0.179755
$236$	−7953.79	−2.19385
$237$	2374.37	0.650766
$238$	0	0
$239$	−7215.07	−1.95274	−0.976369	−	0.216110i	$-0.930663\pi$
$239$	−7215.07	−1.95274	−0.976369	+	0.216110i	$0.930663\pi$
$240$	−515.079	−0.138534
$241$	−1911.83	−0.511004	−0.255502	−	0.966809i	$-0.582241\pi$
$241$	−1911.83	−0.511004	−0.255502	+	0.966809i	$0.582241\pi$
$242$	−502.278	−0.133420
$243$	−243.000	−0.0641500
$244$	−2408.94	−0.632035
$245$	0	0
$246$	−4040.08	−1.04710
$247$	−26.2089	−0.00675155
$248$	−565.848	−0.144885
$249$	−3062.57	−0.779447
$250$	−3241.14	−0.819951
$251$	−131.469	−0.0330606	−0.0165303	−	0.999863i	$-0.505262\pi$
$251$	−131.469	−0.0330606	−0.0165303	+	0.999863i	$0.505262\pi$
$252$	0	0
$253$	−1124.40	−0.279409
$254$	−2556.77	−0.631599
$255$	−658.890	−0.161809
$256$	2561.31	0.625319
$257$	4231.71	1.02711	0.513554	−	0.858057i	$-0.328328\pi$
$257$	4231.71	1.02711	0.513554	+	0.858057i	$0.328328\pi$
$258$	4243.88	1.02408
$259$	0	0
$260$	586.428	0.139880
$261$	2564.03	0.608082
$262$	9427.65	2.22306
$263$	383.018	0.0898018	0.0449009	−	0.998991i	$-0.485703\pi$
$263$	383.018	0.0898018	0.0449009	+	0.998991i	$0.485703\pi$
$264$	168.668	0.0393212
$265$	−928.393	−0.215210
$266$	0	0
$267$	1265.44	0.290050
$268$	8218.38	1.87320
$269$	2567.02	0.581835	0.290918	−	0.956748i	$-0.406039\pi$
$269$	2567.02	0.581835	0.290918	+	0.956748i	$0.406039\pi$
$270$	−365.605	−0.0824074
$271$	4120.83	0.923700	0.461850	−	0.886958i	$-0.347186\pi$
$271$	4120.83	0.923700	0.461850	+	0.886958i	$0.347186\pi$
$272$	3543.77	0.789973
$273$	0	0
$274$	8218.30	1.81199
$275$	−1257.95	−0.275845
$276$	2830.82	0.617375
$277$	−655.149	−0.142109	−0.0710543	−	0.997472i	$-0.522636\pi$
$277$	−655.149	−0.142109	−0.0710543	+	0.997472i	$0.522636\pi$
$278$	−1538.43	−0.331902
$279$	996.377	0.213805
$280$	0	0
$281$	7702.19	1.63514	0.817570	−	0.575830i	$-0.195321\pi$
$281$	7702.19	1.63514	0.817570	+	0.575830i	$0.195321\pi$
$282$	−2472.15	−0.522036
$283$	4348.16	0.913326	0.456663	−	0.889640i	$-0.349045\pi$
$283$	4348.16	0.913326	0.456663	+	0.889640i	$0.349045\pi$
$284$	−4439.47	−0.927584
$285$	13.1703	0.00273734
$286$	889.231	0.183851
$287$	0	0
$288$	2334.37	0.477618
$289$	−379.796	−0.0773044
$290$	3857.70	0.781145
$291$	−2138.01	−0.430695
$292$	−528.631	−0.105944
$293$	−5082.77	−1.01344	−0.506721	−	0.862110i	$-0.669143\pi$
$293$	−5082.77	−1.01344	−0.506721	+	0.862110i	$0.669143\pi$
$294$	0	0
$295$	2810.61	0.554713
$296$	−222.091	−0.0436107
$297$	−297.000	−0.0580259
$298$	1736.40	0.337541
$299$	1990.64	0.385022
$300$	3167.05	0.609498
$301$	0	0
$302$	7001.50	1.33408
$303$	2659.47	0.504233
$304$	−70.8351	−0.0133641
$305$	851.242	0.159810
$306$	2515.38	0.469918
$307$	6510.02	1.21025	0.605124	−	0.796131i	$-0.293123\pi$
$307$	6510.02	1.21025	0.605124	+	0.796131i	$0.293123\pi$
$308$	0	0
$309$	2237.38	0.411910
$310$	1499.10	0.274655
$311$	−9851.98	−1.79632	−0.898158	−	0.439672i	$-0.855095\pi$
$311$	−9851.98	−1.79632	−0.898158	+	0.439672i	$0.855095\pi$
$312$	−298.609	−0.0541840
$313$	−3402.74	−0.614487	−0.307244	−	0.951631i	$-0.599407\pi$
$313$	−3402.74	−0.614487	−0.307244	+	0.951631i	$0.599407\pi$
$314$	−2137.67	−0.384191
$315$	0	0
$316$	−7306.15	−1.30064
$317$	2467.52	0.437192	0.218596	−	0.975815i	$-0.429852\pi$
$317$	2467.52	0.437192	0.218596	+	0.975815i	$0.429852\pi$
$318$	3544.23	0.625003
$319$	3133.82	0.550031
$320$	2138.63	0.373602
$321$	4412.69	0.767266
$322$	0	0
$323$	−90.6125	−0.0156093
$324$	747.734	0.128212
$325$	2227.07	0.380110
$326$	7007.42	1.19051
$327$	−3471.44	−0.587068
$328$	1658.17	0.279137
$329$	0	0
$330$	−446.850	−0.0745403
$331$	6382.69	1.05989	0.529947	−	0.848031i	$-0.322212\pi$
$331$	6382.69	1.05989	0.529947	+	0.848031i	$0.322212\pi$
$332$	9423.82	1.55783
$333$	391.070	0.0643559
$334$	5998.53	0.982710
$335$	−2904.11	−0.473637
$336$	0	0
$337$	4926.96	0.796405	0.398202	−	0.917298i	$-0.369634\pi$
$337$	4926.96	0.796405	0.398202	+	0.917298i	$0.369634\pi$
$338$	7545.58	1.21428
$339$	621.548	0.0995808
$340$	2027.47	0.323397
$341$	1217.79	0.193394
$342$	−50.2790	−0.00794965
$343$	0	0
$344$	−1741.81	−0.273001
$345$	−1000.32	−0.156103
$346$	−13980.2	−2.17219
$347$	5130.03	0.793644	0.396822	−	0.917896i	$-0.370113\pi$
$347$	5130.03	0.793644	0.396822	+	0.917896i	$0.370113\pi$
$348$	−7889.77	−1.21533
$349$	4659.10	0.714602	0.357301	−	0.933989i	$-0.383697\pi$
$349$	4659.10	0.714602	0.357301	+	0.933989i	$0.383697\pi$
$350$	0	0
$351$	525.808	0.0799588
$352$	2853.12	0.432022
$353$	2899.39	0.437164	0.218582	−	0.975819i	$-0.429857\pi$
$353$	2899.39	0.437164	0.218582	+	0.975819i	$0.429857\pi$
$354$	−10729.8	−1.61097
$355$	1568.76	0.234539
$356$	−3893.87	−0.579704
$357$	0	0
$358$	−9622.97	−1.42064
$359$	2198.77	0.323250	0.161625	−	0.986852i	$-0.448326\pi$
$359$	2198.77	0.323250	0.161625	+	0.986852i	$0.448326\pi$
$360$	150.055	0.0219683
$361$	−6857.19	−0.999736
$362$	11770.2	1.70892
$363$	−363.000	−0.0524864
$364$	0	0
$365$	186.801	0.0267880
$366$	−3249.70	−0.464111
$367$	1134.51	0.161366	0.0806828	−	0.996740i	$-0.474290\pi$
$367$	1134.51	0.161366	0.0806828	+	0.996740i	$0.474290\pi$
$368$	5380.12	0.762115
$369$	−2919.80	−0.411920
$370$	588.383	0.0826718
$371$	0	0
$372$	−3065.95	−0.427317
$373$	9706.48	1.34741	0.673703	−	0.739002i	$-0.264703\pi$
$373$	9706.48	1.34741	0.673703	+	0.739002i	$0.264703\pi$
$374$	3074.36	0.425057
$375$	−2342.40	−0.322562
$376$	1014.64	0.139165
$377$	−5548.09	−0.757935
$378$	0	0
$379$	302.591	0.0410107	0.0205053	−	0.999790i	$-0.493472\pi$
$379$	302.591	0.0410107	0.0205053	+	0.999790i	$0.493472\pi$
$380$	−40.5263	−0.00547094
$381$	−1847.80	−0.248466
$382$	1818.20	0.243527
$383$	14013.6	1.86961	0.934807	−	0.355157i	$-0.115572\pi$
$383$	14013.6	1.86961	0.934807	+	0.355157i	$0.115572\pi$
$384$	−1939.44	−0.257738
$385$	0	0
$386$	−5787.09	−0.763097
$387$	3067.08	0.402865
$388$	6578.85	0.860800
$389$	11301.7	1.47306	0.736529	−	0.676406i	$-0.236463\pi$
$389$	11301.7	1.47306	0.736529	+	0.676406i	$0.236463\pi$
$390$	791.102	0.102715
$391$	6882.27	0.890157
$392$	0	0
$393$	6813.43	0.874535
$394$	3177.72	0.406323
$395$	2581.76	0.328867
$396$	913.898	0.115972
$397$	3670.15	0.463979	0.231989	−	0.972718i	$-0.425477\pi$
$397$	3670.15	0.463979	0.231989	+	0.972718i	$0.425477\pi$
$398$	−10219.8	−1.28712
$399$	0	0
$400$	6019.13	0.752392
$401$	3074.76	0.382908	0.191454	−	0.981502i	$-0.438680\pi$
$401$	3074.76	0.382908	0.191454	+	0.981502i	$0.438680\pi$
$402$	11086.7	1.37551
$403$	−2155.98	−0.266493
$404$	−8183.45	−1.00778
$405$	−264.225	−0.0324184
$406$	0	0
$407$	477.974	0.0582121
$408$	−1032.39	−0.125272
$409$	−10464.0	−1.26506	−0.632532	−	0.774534i	$-0.717984\pi$
$409$	−10464.0	−1.26506	−0.632532	+	0.774534i	$0.717984\pi$
$410$	−4392.97	−0.529154
$411$	5939.43	0.712823
$412$	−6884.63	−0.823256
$413$	0	0
$414$	3818.83	0.453346
$415$	−3330.07	−0.393896
$416$	−5051.15	−0.595320
$417$	−1111.83	−0.130568
$418$	−61.4521	−0.00719072
$419$	3179.46	0.370708	0.185354	−	0.982672i	$-0.440657\pi$
$419$	3179.46	0.370708	0.185354	+	0.982672i	$0.440657\pi$
$420$	0	0
$421$	5886.95	0.681502	0.340751	−	0.940154i	$-0.389319\pi$
$421$	5886.95	0.681502	0.340751	+	0.940154i	$0.389319\pi$
$422$	−18436.7	−2.12674
$423$	−1786.64	−0.205365
$424$	−1454.66	−0.166614
$425$	7699.69	0.878800
$426$	−5988.92	−0.681136
$427$	0	0
$428$	−13578.3	−1.53348
$429$	642.654	0.0723254
$430$	4614.57	0.517522
$431$	−14719.7	−1.64507	−0.822534	−	0.568716i	$-0.807440\pi$
$431$	−14719.7	−1.64507	−0.822534	+	0.568716i	$0.807440\pi$
$432$	1421.11	0.158271
$433$	14842.9	1.64736	0.823679	−	0.567056i	$-0.191918\pi$
$433$	14842.9	1.64736	0.823679	+	0.567056i	$0.191918\pi$
$434$	0	0
$435$	2787.99	0.307296
$436$	10682.0	1.17333
$437$	−137.567	−0.0150589
$438$	−713.132	−0.0777963
$439$	11734.9	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$439$	11734.9	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$440$	183.401	0.0198711
$441$	0	0
$442$	−5442.83	−0.585722
$443$	−4105.38	−0.440299	−0.220149	−	0.975466i	$-0.570654\pi$
$443$	−4105.38	−0.440299	−0.220149	+	0.975466i	$0.570654\pi$
$444$	−1203.36	−0.128624
$445$	1375.97	0.146578
$446$	−16145.5	−1.71415
$447$	1254.91	0.132786
$448$	0	0
$449$	10076.3	1.05909	0.529545	−	0.848282i	$-0.322363\pi$
$449$	10076.3	1.05909	0.529545	+	0.848282i	$0.322363\pi$
$450$	4272.40	0.447562
$451$	−3568.64	−0.372596
$452$	−1912.56	−0.199025
$453$	5060.03	0.524815
$454$	781.654	0.0808036
$455$	0	0
$456$	20.6360	0.00211923
$457$	−4586.99	−0.469519	−0.234760	−	0.972053i	$-0.575430\pi$
$457$	−4586.99	−0.469519	−0.234760	+	0.972053i	$0.575430\pi$
$458$	−14533.8	−1.48279
$459$	1817.88	0.184862
$460$	3078.09	0.311992
$461$	−12235.3	−1.23612	−0.618062	−	0.786129i	$-0.712082\pi$
$461$	−12235.3	−1.23612	−0.618062	+	0.786129i	$0.712082\pi$
$462$	0	0
$463$	−11153.9	−1.11958	−0.559791	−	0.828634i	$-0.689119\pi$
$463$	−11153.9	−1.11958	−0.559791	+	0.828634i	$0.689119\pi$
$464$	−14994.9	−1.50026
$465$	1083.41	0.108047
$466$	10230.9	1.01703
$467$	4522.19	0.448099	0.224049	−	0.974578i	$-0.428072\pi$
$467$	4522.19	0.448099	0.224049	+	0.974578i	$0.428072\pi$
$468$	−1617.96	−0.159808
$469$	0	0
$470$	−2688.08	−0.263812
$471$	−1544.91	−0.151138
$472$	4403.83	0.429455
$473$	3748.66	0.364405
$474$	−9856.13	−0.955078
$475$	−153.906	−0.0148667
$476$	0	0
$477$	2561.44	0.245871
$478$	29950.2	2.86588
$479$	14121.2	1.34700	0.673502	−	0.739185i	$-0.264789\pi$
$479$	14121.2	1.34700	0.673502	+	0.739185i	$0.264789\pi$
$480$	2538.27	0.241366
$481$	−846.204	−0.0802153
$482$	7936.13	0.749960
$483$	0	0
$484$	1116.99	0.104901
$485$	−2324.75	−0.217653
$486$	1008.71	0.0941479
$487$	−14730.9	−1.37068	−0.685341	−	0.728223i	$-0.740347\pi$
$487$	−14730.9	−1.37068	−0.685341	+	0.728223i	$0.740347\pi$
$488$	1333.78	0.123724
$489$	5064.31	0.468336
$490$	0	0
$491$	9517.11	0.874748	0.437374	−	0.899280i	$-0.355909\pi$
$491$	9517.11	0.874748	0.437374	+	0.899280i	$0.355909\pi$
$492$	8984.49	0.823277
$493$	−19181.5	−1.75232
$494$	108.795	0.00990871
$495$	−322.942	−0.0293236
$496$	−5826.99	−0.527499
$497$	0	0
$498$	12712.9	1.14393
$499$	18020.6	1.61666	0.808328	−	0.588732i	$-0.200373\pi$
$499$	18020.6	1.61666	0.808328	+	0.588732i	$0.200373\pi$
$500$	7207.78	0.644684
$501$	4335.18	0.386590
$502$	545.734	0.0485205
$503$	−21207.7	−1.87993	−0.939963	−	0.341277i	$-0.889141\pi$
$503$	−21207.7	−1.87993	−0.939963	+	0.341277i	$0.889141\pi$
$504$	0	0
$505$	2891.77	0.254816
$506$	4667.46	0.410067
$507$	5453.25	0.477687
$508$	5685.85	0.496592
$509$	−9282.22	−0.808305	−0.404152	−	0.914692i	$-0.632433\pi$
$509$	−9282.22	−0.808305	−0.404152	+	0.914692i	$0.632433\pi$
$510$	2735.09	0.237474
$511$	0	0
$512$	−15804.0	−1.36415
$513$	−36.3370	−0.00312733
$514$	−17566.1	−1.50741
$515$	2432.81	0.208160
$516$	−9437.71	−0.805179
$517$	−2183.67	−0.185759
$518$	0	0
$519$	−10103.6	−0.854522
$520$	−324.692	−0.0273821
$521$	9502.88	0.799096	0.399548	−	0.916712i	$-0.369167\pi$
$521$	9502.88	0.799096	0.399548	+	0.916712i	$0.369167\pi$
$522$	−10643.4	−0.892434
$523$	7836.98	0.655234	0.327617	−	0.944811i	$-0.393754\pi$
$523$	7836.98	0.655234	0.327617	+	0.944811i	$0.393754\pi$
$524$	−20965.6	−1.74787
$525$	0	0
$526$	−1589.93	−0.131795
$527$	−7453.90	−0.616123
$528$	1736.91	0.143162
$529$	−1718.40	−0.141235
$530$	3853.81	0.315847
$531$	−7754.51	−0.633742
$532$	0	0
$533$	6317.90	0.513431
$534$	−5252.90	−0.425684
$535$	4798.12	0.387740
$536$	−4550.33	−0.366687
$537$	−6954.59	−0.558869
$538$	−10655.8	−0.853914
$539$	0	0
$540$	813.047	0.0647925
$541$	7070.29	0.561877	0.280939	−	0.959726i	$-0.409354\pi$
$541$	7070.29	0.561877	0.280939	+	0.959726i	$0.409354\pi$
$542$	−17105.8	−1.35564
$543$	8506.42	0.672275
$544$	−17463.4	−1.37636
$545$	−3774.66	−0.296677
$546$	0	0
$547$	−24983.4	−1.95286	−0.976429	−	0.215839i	$-0.930751\pi$
$547$	−24983.4	−1.95286	−0.976429	+	0.215839i	$0.930751\pi$
$548$	−18276.2	−1.42467
$549$	−2348.58	−0.182578
$550$	5221.82	0.404835
$551$	383.412	0.0296441
$552$	−1567.36	−0.120854
$553$	0	0
$554$	2719.56	0.208562
$555$	425.229	0.0325224
$556$	3421.22	0.260957
$557$	2707.47	0.205959	0.102980	−	0.994683i	$-0.467162\pi$
$557$	2707.47	0.205959	0.102980	+	0.994683i	$0.467162\pi$
$558$	−4136.02	−0.313784
$559$	−6636.61	−0.502144
$560$	0	0
$561$	2221.86	0.167214
$562$	−31972.2	−2.39976
$563$	12885.5	0.964580	0.482290	−	0.876012i	$-0.339805\pi$
$563$	12885.5	0.964580	0.482290	+	0.876012i	$0.339805\pi$
$564$	5497.65	0.410449
$565$	675.839	0.0503234
$566$	−18049.5	−1.34042
$567$	0	0
$568$	2458.03	0.181579
$569$	1753.12	0.129164	0.0645822	−	0.997912i	$-0.479429\pi$
$569$	1753.12	0.129164	0.0645822	+	0.997912i	$0.479429\pi$
$570$	−54.6707	−0.00401738
$571$	9829.16	0.720381	0.360191	−	0.932879i	$-0.382712\pi$
$571$	9829.16	0.720381	0.360191	+	0.932879i	$0.382712\pi$
$572$	−1977.51	−0.144552
$573$	1314.03	0.0958016
$574$	0	0
$575$	11689.6	0.847809
$576$	−5900.49	−0.426829
$577$	8662.96	0.625033	0.312516	−	0.949912i	$-0.398828\pi$
$577$	8662.96	0.625033	0.312516	+	0.949912i	$0.398828\pi$
$578$	1576.56	0.113454
$579$	−4182.37	−0.300196
$580$	−8578.92	−0.614173
$581$	0	0
$582$	8874.99	0.632096
$583$	3130.65	0.222399
$584$	292.691	0.0207391
$585$	571.735	0.0404074
$586$	21098.9	1.48735
$587$	26091.9	1.83463	0.917315	−	0.398161i	$-0.130352\pi$
$587$	26091.9	1.83463	0.917315	+	0.398161i	$0.130352\pi$
$588$	0	0
$589$	148.993	0.0104230
$590$	−11667.0	−0.814108
$591$	2296.56	0.159844
$592$	−2287.05	−0.158779
$593$	6071.64	0.420459	0.210230	−	0.977652i	$-0.432579\pi$
$593$	6071.64	0.420459	0.210230	+	0.977652i	$0.432579\pi$
$594$	1232.86	0.0851600
$595$	0	0
$596$	−3861.48	−0.265390
$597$	−7385.93	−0.506342
$598$	−8263.25	−0.565066
$599$	−19267.5	−1.31427	−0.657136	−	0.753772i	$-0.728232\pi$
$599$	−19267.5	−1.31427	−0.657136	+	0.753772i	$0.728232\pi$
$600$	−1753.52	−0.119312
$601$	2993.29	0.203160	0.101580	−	0.994827i	$-0.467610\pi$
$601$	2993.29	0.203160	0.101580	+	0.994827i	$0.467610\pi$
$602$	0	0
$603$	8012.47	0.541116
$604$	−15570.2	−1.04891
$605$	−394.707	−0.0265242
$606$	−11039.6	−0.740023
$607$	19757.4	1.32113	0.660566	−	0.750768i	$-0.270316\pi$
$607$	19757.4	1.32113	0.660566	+	0.750768i	$0.270316\pi$
$608$	349.070	0.0232840
$609$	0	0
$610$	−3533.56	−0.234540
$611$	3865.96	0.255974
$612$	−5593.81	−0.369471
$613$	−19518.0	−1.28601	−0.643004	−	0.765862i	$-0.722312\pi$
$613$	−19518.0	−1.28601	−0.643004	+	0.765862i	$0.722312\pi$
$614$	−27023.5	−1.77619
$615$	−3174.83	−0.208165
$616$	0	0
$617$	−5107.95	−0.333288	−0.166644	−	0.986017i	$-0.553293\pi$
$617$	−5107.95	−0.333288	−0.166644	+	0.986017i	$0.553293\pi$
$618$	−9287.49	−0.604527
$619$	−11473.8	−0.745025	−0.372513	−	0.928027i	$-0.621504\pi$
$619$	−11473.8	−0.745025	−0.372513	+	0.928027i	$0.621504\pi$
$620$	−3333.75	−0.215946
$621$	2759.90	0.178343
$622$	40896.1	2.63631
$623$	0	0
$624$	−3075.02	−0.197274
$625$	11747.9	0.751865
$626$	14125.0	0.901834
$627$	−44.4119	−0.00282877
$628$	4753.84	0.302069
$629$	−2925.60	−0.185455
$630$	0	0
$631$	−10334.6	−0.652004	−0.326002	−	0.945369i	$-0.605702\pi$
$631$	−10334.6	−0.652004	−0.326002	+	0.945369i	$0.605702\pi$
$632$	4045.25	0.254606
$633$	−13324.3	−0.836641
$634$	−10242.8	−0.641632
$635$	−2009.20	−0.125563
$636$	−7881.81	−0.491406
$637$	0	0
$638$	−13008.7	−0.807237
$639$	−4328.23	−0.267954
$640$	−2108.84	−0.130249
$641$	17973.8	1.10752	0.553762	−	0.832675i	$-0.313192\pi$
$641$	17973.8	1.10752	0.553762	+	0.832675i	$0.313192\pi$
$642$	−18317.3	−1.12606
$643$	15688.5	0.962201	0.481101	−	0.876665i	$-0.340237\pi$
$643$	15688.5	0.962201	0.481101	+	0.876665i	$0.340237\pi$
$644$	0	0
$645$	3334.98	0.203589
$646$	376.138	0.0229086
$647$	−27368.9	−1.66303	−0.831517	−	0.555500i	$-0.812527\pi$
$647$	−27368.9	−1.66303	−0.831517	+	0.555500i	$0.812527\pi$
$648$	−414.003	−0.0250981
$649$	−9477.74	−0.573241
$650$	−9244.70	−0.557857
$651$	0	0
$652$	−15583.4	−0.936031
$653$	−3101.76	−0.185882	−0.0929411	−	0.995672i	$-0.529627\pi$
$653$	−3101.76	−0.185882	−0.0929411	+	0.995672i	$0.529627\pi$
$654$	14410.2	0.861593
$655$	7408.56	0.441949
$656$	17075.5	1.01629
$657$	−515.386	−0.0306044
$658$	0	0
$659$	23699.9	1.40093	0.700467	−	0.713685i	$-0.252975\pi$
$659$	23699.9	1.40093	0.700467	+	0.713685i	$0.252975\pi$
$660$	993.724	0.0586070
$661$	10463.7	0.615721	0.307860	−	0.951432i	$-0.400387\pi$
$661$	10463.7	0.615721	0.307860	+	0.951432i	$0.400387\pi$
$662$	−26494.9	−1.55552
$663$	−3933.57	−0.230418
$664$	−5217.75	−0.304952
$665$	0	0
$666$	−1623.35	−0.0944500
$667$	−29121.2	−1.69052
$668$	−13339.8	−0.772652
$669$	−11668.5	−0.674333
$670$	12055.1	0.695120
$671$	−2870.49	−0.165148
$672$	0	0
$673$	−393.578	−0.0225428	−0.0112714	−	0.999936i	$-0.503588\pi$
$673$	−393.578	−0.0225428	−0.0112714	+	0.999936i	$0.503588\pi$
$674$	−20452.1	−1.16882
$675$	3087.70	0.176067
$676$	−16780.2	−0.954721
$677$	−26792.0	−1.52098	−0.760488	−	0.649352i	$-0.775040\pi$
$677$	−26792.0	−1.52098	−0.760488	+	0.649352i	$0.775040\pi$
$678$	−2580.08	−0.146147
$679$	0	0
$680$	−1122.56	−0.0633064
$681$	564.907	0.0317875
$682$	−5055.13	−0.283829
$683$	19910.7	1.11547	0.557733	−	0.830021i	$-0.311671\pi$
$683$	19910.7	1.11547	0.557733	+	0.830021i	$0.311671\pi$
$684$	111.813	0.00625038
$685$	6458.22	0.360227
$686$	0	0
$687$	−10503.7	−0.583318
$688$	−17936.9	−0.993948
$689$	−5542.50	−0.306462
$690$	4152.39	0.229100
$691$	19143.7	1.05392	0.526962	−	0.849889i	$-0.323331\pi$
$691$	19143.7	1.05392	0.526962	+	0.849889i	$0.323331\pi$
$692$	31089.6	1.70788
$693$	0	0
$694$	−21295.1	−1.16477
$695$	−1208.95	−0.0659827
$696$	4368.38	0.237907
$697$	21843.0	1.18703
$698$	−19340.2	−1.04876
$699$	7393.94	0.400092
$700$	0	0
$701$	−1211.07	−0.0652517	−0.0326258	−	0.999468i	$-0.510387\pi$
$701$	−1211.07	−0.0652517	−0.0326258	+	0.999468i	$0.510387\pi$
$702$	−2182.66	−0.117349
$703$	58.4787	0.00313736
$704$	−7211.71	−0.386082
$705$	−1942.69	−0.103782
$706$	−12035.5	−0.641591
$707$	0	0
$708$	23861.4	1.26662
$709$	−4768.03	−0.252563	−0.126282	−	0.991994i	$-0.540304\pi$
$709$	−4768.03	−0.252563	−0.126282	+	0.991994i	$0.540304\pi$
$710$	−6512.03	−0.344214
$711$	−7123.10	−0.375720
$712$	2155.94	0.113480
$713$	−11316.4	−0.594396
$714$	0	0
$715$	698.787	0.0365499
$716$	21399.9	1.11697
$717$	21645.2	1.12741
$718$	−9127.24	−0.474409
$719$	16722.3	0.867366	0.433683	−	0.901066i	$-0.357214\pi$
$719$	16722.3	0.867366	0.433683	+	0.901066i	$0.357214\pi$
$720$	1545.24	0.0799827
$721$	0	0
$722$	28464.6	1.46723
$723$	5735.50	0.295028
$724$	−26175.1	−1.34363
$725$	−32580.0	−1.66895
$726$	1506.83	0.0770301
$727$	37538.4	1.91502	0.957511	−	0.288395i	$-0.0931217\pi$
$727$	37538.4	1.91502	0.957511	+	0.288395i	$0.0931217\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−775.422	−0.0393146
$731$	−22944.9	−1.16094
$732$	7226.82	0.364906
$733$	22182.9	1.11779	0.558897	−	0.829237i	$-0.311225\pi$
$733$	22182.9	1.11779	0.558897	+	0.829237i	$0.311225\pi$
$734$	−4709.44	−0.236824
$735$	0	0
$736$	−26512.8	−1.32782
$737$	9793.02	0.489458
$738$	12120.2	0.604542
$739$	−32657.5	−1.62561	−0.812805	−	0.582536i	$-0.802060\pi$
$739$	−32657.5	−1.62561	−0.812805	+	0.582536i	$0.802060\pi$
$740$	−1308.47	−0.0650004
$741$	78.6267	0.00389801
$742$	0	0
$743$	16584.4	0.818871	0.409435	−	0.912339i	$-0.365726\pi$
$743$	16584.4	0.818871	0.409435	+	0.912339i	$0.365726\pi$
$744$	1697.54	0.0836492
$745$	1364.52	0.0671037
$746$	−40292.2	−1.97748
$747$	9187.71	0.450014
$748$	−6836.88	−0.334199
$749$	0	0
$750$	9723.43	0.473399
$751$	−12948.9	−0.629178	−0.314589	−	0.949228i	$-0.601867\pi$
$751$	−12948.9	−0.629178	−0.314589	+	0.949228i	$0.601867\pi$
$752$	10448.6	0.506676
$753$	394.406	0.0190876
$754$	23030.5	1.11236
$755$	5502.01	0.265217
$756$	0	0
$757$	16725.4	0.803032	0.401516	−	0.915852i	$-0.368483\pi$
$757$	16725.4	0.803032	0.401516	+	0.915852i	$0.368483\pi$
$758$	−1256.07	−0.0601881
$759$	3373.21	0.161317
$760$	22.4385	0.00107096
$761$	−12601.5	−0.600267	−0.300133	−	0.953897i	$-0.597031\pi$
$761$	−12601.5	−0.600267	−0.300133	+	0.953897i	$0.597031\pi$
$762$	7670.32	0.364654
$763$	0	0
$764$	−4043.39	−0.191472
$765$	1976.67	0.0934205
$766$	−58171.3	−2.74388
$767$	16779.3	0.789918
$768$	−7683.92	−0.361028
$769$	−32194.4	−1.50970	−0.754851	−	0.655896i	$-0.772291\pi$
$769$	−32194.4	−1.50970	−0.754851	+	0.655896i	$0.772291\pi$
$770$	0	0
$771$	−12695.1	−0.593002
$772$	12869.6	0.599982
$773$	11246.4	0.523294	0.261647	−	0.965164i	$-0.415734\pi$
$773$	11246.4	0.523294	0.261647	+	0.965164i	$0.415734\pi$
$774$	−12731.6	−0.591253
$775$	−12660.5	−0.586812
$776$	−3642.56	−0.168505
$777$	0	0
$778$	−46914.1	−2.16189
$779$	−436.612	−0.0200812
$780$	−1759.28	−0.0807596
$781$	−5290.06	−0.242373
$782$	−28568.7	−1.30641
$783$	−7692.09	−0.351077
$784$	0	0
$785$	−1679.86	−0.0763779
$786$	−28283.0	−1.28349
$787$	−18425.7	−0.834568	−0.417284	−	0.908776i	$-0.637018\pi$
$787$	−18425.7	−0.834568	−0.417284	+	0.908776i	$0.637018\pi$
$788$	−7066.74	−0.319470
$789$	−1149.05	−0.0518471
$790$	−10717.0	−0.482652
$791$	0	0
$792$	−506.004	−0.0227021
$793$	5081.91	0.227571
$794$	−15235.0	−0.680945
$795$	2785.18	0.124252
$796$	22727.2	1.01199
$797$	−560.363	−0.0249047	−0.0124524	−	0.999922i	$-0.503964\pi$
$797$	−560.363	−0.0249047	−0.0124524	+	0.999922i	$0.503964\pi$
$798$	0	0
$799$	13365.8	0.591802
$800$	−29661.8	−1.31088
$801$	−3796.31	−0.167461
$802$	−12763.5	−0.561963
$803$	−629.916	−0.0276828
$804$	−24655.1	−1.08149
$805$	0	0
$806$	8949.59	0.391111
$807$	−7701.05	−0.335923
$808$	4530.99	0.197277
$809$	10913.6	0.474291	0.237145	−	0.971474i	$-0.423788\pi$
$809$	10913.6	0.474291	0.237145	+	0.971474i	$0.423788\pi$
$810$	1096.81	0.0475779
$811$	33661.7	1.45749	0.728744	−	0.684787i	$-0.240105\pi$
$811$	33661.7	1.45749	0.728744	+	0.684787i	$0.240105\pi$
$812$	0	0
$813$	−12362.5	−0.533298
$814$	−1984.10	−0.0854333
$815$	5506.67	0.236675
$816$	−10631.3	−0.456091
$817$	458.637	0.0196397
$818$	43436.6	1.85663
$819$	0	0
$820$	9769.26	0.416046
$821$	−16200.3	−0.688665	−0.344332	−	0.938848i	$-0.611895\pi$
$821$	−16200.3	−0.688665	−0.344332	+	0.938848i	$0.611895\pi$
$822$	−24654.9	−1.04615
$823$	−1176.78	−0.0498421	−0.0249211	−	0.999689i	$-0.507933\pi$
$823$	−1176.78	−0.0498421	−0.0249211	+	0.999689i	$0.507933\pi$
$824$	3811.86	0.161156
$825$	3773.85	0.159259
$826$	0	0
$827$	23152.3	0.973500	0.486750	−	0.873541i	$-0.338182\pi$
$827$	23152.3	0.973500	0.486750	+	0.873541i	$0.338182\pi$
$828$	−8492.47	−0.356442
$829$	−11196.6	−0.469087	−0.234543	−	0.972106i	$-0.575359\pi$
$829$	−11196.6	−0.469087	−0.234543	+	0.972106i	$0.575359\pi$
$830$	13823.3	0.578090
$831$	1965.45	0.0820464
$832$	12767.6	0.532014
$833$	0	0
$834$	4615.28	0.191624
$835$	4713.85	0.195365
$836$	136.660	0.00565368
$837$	−2989.13	−0.123440
$838$	−13198.1	−0.544059
$839$	87.2457	0.00359006	0.00179503	−	0.999998i	$-0.499429\pi$
$839$	87.2457	0.00359006	0.00179503	+	0.999998i	$0.499429\pi$
$840$	0	0
$841$	56774.6	2.32788
$842$	−24437.1	−1.00019
$843$	−23106.6	−0.944048
$844$	41000.2	1.67214
$845$	5929.57	0.241401
$846$	7416.44	0.301398
$847$	0	0
$848$	−14979.8	−0.606613
$849$	−13044.5	−0.527309
$850$	−31961.9	−1.28974
$851$	−4441.62	−0.178915
$852$	13318.4	0.535541
$853$	−35342.2	−1.41863	−0.709317	−	0.704890i	$-0.750997\pi$
$853$	−35342.2	−1.41863	−0.709317	+	0.704890i	$0.750997\pi$
$854$	0	0
$855$	−39.5109	−0.00158040
$856$	7517.98	0.300186
$857$	−5285.04	−0.210658	−0.105329	−	0.994437i	$-0.533590\pi$
$857$	−5285.04	−0.210658	−0.105329	+	0.994437i	$0.533590\pi$
$858$	−2667.69	−0.106146
$859$	−28186.3	−1.11956	−0.559781	−	0.828640i	$-0.689115\pi$
$859$	−28186.3	−1.11956	−0.559781	+	0.828640i	$0.689115\pi$
$860$	−10262.1	−0.406900
$861$	0	0
$862$	61102.4	2.41434
$863$	−253.364	−0.00999377	−0.00499689	−	0.999988i	$-0.501591\pi$
$863$	−253.364	−0.00999377	−0.00499689	+	0.999988i	$0.501591\pi$
$864$	−7003.11	−0.275753
$865$	−10986.1	−0.431835
$866$	−61613.9	−2.41770
$867$	1139.39	0.0446317
$868$	0	0
$869$	−8706.01	−0.339852
$870$	−11573.1	−0.450995
$871$	−17337.5	−0.674466
$872$	−5914.36	−0.229685
$873$	6414.02	0.248662
$874$	571.049	0.0221007
$875$	0	0
$876$	1585.89	0.0611670
$877$	23610.3	0.909081	0.454541	−	0.890726i	$-0.349803\pi$
$877$	23610.3	0.909081	0.454541	+	0.890726i	$0.349803\pi$
$878$	−48712.4	−1.87240
$879$	15248.3	0.585111
$880$	1888.62	0.0723471
$881$	−41686.9	−1.59417	−0.797087	−	0.603864i	$-0.793627\pi$
$881$	−41686.9	−1.59417	−0.797087	+	0.603864i	$0.793627\pi$
$882$	0	0
$883$	41675.0	1.58831	0.794153	−	0.607718i	$-0.207915\pi$
$883$	41675.0	1.58831	0.794153	+	0.607718i	$0.207915\pi$
$884$	12104.0	0.460521
$885$	−8431.84	−0.320264
$886$	17041.7	0.646191
$887$	32053.6	1.21337	0.606683	−	0.794944i	$-0.292500\pi$
$887$	32053.6	1.21337	0.606683	+	0.794944i	$0.292500\pi$
$888$	666.273	0.0251787
$889$	0	0
$890$	−5711.72	−0.215121
$891$	891.000	0.0335013
$892$	35905.0	1.34774
$893$	−267.165	−0.0100116
$894$	−5209.21	−0.194879
$895$	−7562.05	−0.282426
$896$	0	0
$897$	−5971.91	−0.222292
$898$	−41827.5	−1.55434
$899$	31540.0	1.17010
$900$	−9501.14	−0.351894
$901$	−19162.2	−0.708529
$902$	14813.6	0.546829
$903$	0	0
$904$	1058.94	0.0389601
$905$	9249.42	0.339736
$906$	−21004.5	−0.770229
$907$	27388.2	1.00266	0.501329	−	0.865257i	$-0.332845\pi$
$907$	27388.2	1.00266	0.501329	+	0.865257i	$0.332845\pi$
$908$	−1738.27	−0.0635315
$909$	−7978.41	−0.291119
$910$	0	0
$911$	40504.2	1.47307	0.736533	−	0.676402i	$-0.236462\pi$
$911$	40504.2	1.47307	0.736533	+	0.676402i	$0.236462\pi$
$912$	212.505	0.00771574
$913$	11229.4	0.407053
$914$	19040.9	0.689076
$915$	−2553.73	−0.0922662
$916$	32320.7	1.16584
$917$	0	0
$918$	−7546.15	−0.271307
$919$	40628.6	1.45834	0.729170	−	0.684332i	$-0.239906\pi$
$919$	40628.6	1.45834	0.729170	+	0.684332i	$0.239906\pi$
$920$	−1704.27	−0.0610739
$921$	−19530.0	−0.698737
$922$	50789.3	1.81416
$923$	9365.51	0.333986
$924$	0	0
$925$	−4969.16	−0.176632
$926$	46300.6	1.64312
$927$	−6712.14	−0.237816
$928$	73893.8	2.61388
$929$	12898.7	0.455536	0.227768	−	0.973715i	$-0.426857\pi$
$929$	12898.7	0.455536	0.227768	+	0.973715i	$0.426857\pi$
$930$	−4497.29	−0.158572
$931$	0	0
$932$	−22751.9	−0.799637
$933$	29555.9	1.03710
$934$	−18771.9	−0.657639
$935$	2415.93	0.0845020
$936$	895.828	0.0312832
$937$	−36137.0	−1.25992	−0.629959	−	0.776628i	$-0.716928\pi$
$937$	−36137.0	−1.25992	−0.629959	+	0.776628i	$0.716928\pi$
$938$	0	0
$939$	10208.2	0.354774
$940$	5977.86	0.207421
$941$	22452.2	0.777812	0.388906	−	0.921277i	$-0.372853\pi$
$941$	22452.2	0.777812	0.388906	+	0.921277i	$0.372853\pi$
$942$	6413.02	0.221813
$943$	33161.9	1.14517
$944$	45349.8	1.56357
$945$	0	0
$946$	−15560.9	−0.534808
$947$	37101.4	1.27311	0.636554	−	0.771233i	$-0.280359\pi$
$947$	37101.4	1.27311	0.636554	+	0.771233i	$0.280359\pi$
$948$	21918.5	0.750926
$949$	1115.20	0.0381464
$950$	638.874	0.0218187
$951$	−7402.57	−0.252413
$952$	0	0
$953$	−18105.1	−0.615406	−0.307703	−	0.951482i	$-0.599560\pi$
$953$	−18105.1	−0.615406	−0.307703	+	0.951482i	$0.599560\pi$
$954$	−10632.7	−0.360845
$955$	1428.80	0.0484136
$956$	−66604.4	−2.25329
$957$	−9401.45	−0.317561
$958$	−58618.0	−1.97689
$959$	0	0
$960$	−6415.88	−0.215699
$961$	−17534.6	−0.588588
$962$	3512.64	0.117726
$963$	−13238.1	−0.442981
$964$	−17648.7	−0.589653
$965$	−4547.69	−0.151705
$966$	0	0
$967$	135.876	0.00451860	0.00225930	−	0.999997i	$-0.499281\pi$
$967$	135.876	0.00451860	0.00225930	+	0.999997i	$0.499281\pi$
$968$	−618.449	−0.0205348
$969$	271.838	0.00901205
$970$	9650.19	0.319432
$971$	26451.5	0.874221	0.437111	−	0.899408i	$-0.356002\pi$
$971$	26451.5	0.874221	0.437111	+	0.899408i	$0.356002\pi$
$972$	−2243.20	−0.0740234
$973$	0	0
$974$	61148.9	2.01164
$975$	−6681.21	−0.219456
$976$	13734.9	0.450456
$977$	1085.27	0.0355383	0.0177692	−	0.999842i	$-0.494344\pi$
$977$	1085.27	0.0355383	0.0177692	+	0.999842i	$0.494344\pi$
$978$	−21022.3	−0.687339
$979$	−4639.93	−0.151474
$980$	0	0
$981$	10414.3	0.338944
$982$	−39506.1	−1.28380
$983$	32820.0	1.06490	0.532449	−	0.846462i	$-0.321272\pi$
$983$	32820.0	1.06490	0.532449	+	0.846462i	$0.321272\pi$
$984$	−4974.51	−0.161160
$985$	2497.16	0.0807778
$986$	79623.7	2.57174
$987$	0	0
$988$	−241.942	−0.00779068
$989$	−34834.7	−1.12000
$990$	1340.55	0.0430359
$991$	17462.8	0.559762	0.279881	−	0.960035i	$-0.409705\pi$
$991$	17462.8	0.559762	0.279881	+	0.960035i	$0.409705\pi$
$992$	28715.0	0.919053
$993$	−19148.1	−0.611930
$994$	0	0
$995$	−8031.07	−0.255881
$996$	−28271.5	−0.899413
$997$	8012.91	0.254535	0.127267	−	0.991868i	$-0.459379\pi$
$997$	8012.91	0.254535	0.127267	+	0.991868i	$0.459379\pi$
$998$	−74804.5	−2.37264
$999$	−1173.21	−0.0371559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.p.1.1		5
7.6	odd	2		231.4.a.l.1.1	✓	5
21.20	even	2		693.4.a.n.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.l.1.1	✓	5	7.6	odd	2
693.4.a.n.1.5		5	21.20	even	2
1617.4.a.p.1.1		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)

\(f(q)\)	\(=\)	\(q-4.15106 q^{2} -3.00000 q^{3} +9.23129 q^{4} -3.26204 q^{5} +12.4532 q^{6} -5.11115 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.15106 q^{2} -3.00000 q^{3} +9.23129 q^{4} -3.26204 q^{5} +12.4532 q^{6} -5.11115 q^{8} +9.00000 q^{9} +13.5409 q^{10} +11.0000 q^{11} -27.6939 q^{12} -19.4744 q^{13} +9.78612 q^{15} -52.6336 q^{16} -67.3291 q^{17} -37.3595 q^{18} +1.34582 q^{19} -30.1128 q^{20} -45.6616 q^{22} -102.218 q^{23} +15.3335 q^{24} -114.359 q^{25} +80.8392 q^{26} -27.0000 q^{27} +284.892 q^{29} -40.6228 q^{30} +110.709 q^{31} +259.374 q^{32} -33.0000 q^{33} +279.487 q^{34} +83.0816 q^{36} +43.4522 q^{37} -5.58656 q^{38} +58.4231 q^{39} +16.6728 q^{40} -324.422 q^{41} +340.787 q^{43} +101.544 q^{44} -29.3584 q^{45} +424.315 q^{46} -198.515 q^{47} +157.901 q^{48} +474.711 q^{50} +201.987 q^{51} -179.773 q^{52} +284.605 q^{53} +112.079 q^{54} -35.8824 q^{55} -4.03745 q^{57} -1182.60 q^{58} -861.612 q^{59} +90.3385 q^{60} -260.954 q^{61} -459.558 q^{62} -655.610 q^{64} +63.5261 q^{65} +136.985 q^{66} +890.274 q^{67} -621.534 q^{68} +306.655 q^{69} -480.915 q^{71} -46.0004 q^{72} -57.2651 q^{73} -180.373 q^{74} +343.077 q^{75} +12.4236 q^{76} -242.518 q^{78} -791.455 q^{79} +171.693 q^{80} +81.0000 q^{81} +1346.69 q^{82} +1020.86 q^{83} +219.630 q^{85} -1414.63 q^{86} -854.677 q^{87} -56.2227 q^{88} -421.812 q^{89} +121.868 q^{90} -943.607 q^{92} -332.126 q^{93} +824.048 q^{94} -4.39010 q^{95} -778.123 q^{96} +712.669 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9	\( 5 q + 5 q^{2} - 15 q^{3} + 21 q^{4} - 7 q^{5} - 15 q^{6} + 60 q^{8} + 45 q^{9} - 55 q^{10} + 55 q^{11} - 63 q^{12} - 111 q^{13} + 21 q^{15} + 201 q^{16} - 136 q^{17} + 45 q^{18} - 111 q^{19} - 219 q^{20} + 55 q^{22} - 28 q^{23} - 180 q^{24} + 190 q^{25} + q^{26} - 135 q^{27} + 61 q^{29} + 165 q^{30} + 280 q^{31} + 535 q^{32} - 165 q^{33} + 572 q^{34} + 189 q^{36} - 41 q^{37} - 267 q^{38} + 333 q^{39} + 336 q^{40} - 426 q^{41} + 424 q^{43} + 231 q^{44} - 63 q^{45} + 140 q^{46} - 75 q^{47} - 603 q^{48} + 490 q^{50} + 408 q^{51} + 269 q^{52} + 1500 q^{53} - 135 q^{54} - 77 q^{55} + 333 q^{57} - 1767 q^{58} - 757 q^{59} + 657 q^{60} - 658 q^{61} + 568 q^{62} - 748 q^{64} + 537 q^{65} - 165 q^{66} - 583 q^{67} + 1650 q^{68} + 84 q^{69} - 764 q^{71} + 540 q^{72} - 875 q^{73} - 825 q^{74} - 570 q^{75} - 213 q^{76} - 3 q^{78} - 244 q^{79} + 2577 q^{80} + 405 q^{81} + 2006 q^{82} - 924 q^{83} - 1402 q^{85} + 1272 q^{86} - 183 q^{87} + 660 q^{88} + 1110 q^{89} - 495 q^{90} - 2046 q^{92} - 840 q^{93} + 3349 q^{94} + 1923 q^{95} - 1605 q^{96} + 852 q^{97} + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 15 * q^3 + 21 * q^4 - 7 * q^5 - 15 * q^6 + 60 * q^8 + 45 * q^9 - 55 * q^10 + 55 * q^11 - 63 * q^12 - 111 * q^13 + 21 * q^15 + 201 * q^16 - 136 * q^17 + 45 * q^18 - 111 * q^19 - 219 * q^20 + 55 * q^22 - 28 * q^23 - 180 * q^24 + 190 * q^25 + q^26 - 135 * q^27 + 61 * q^29 + 165 * q^30 + 280 * q^31 + 535 * q^32 - 165 * q^33 + 572 * q^34 + 189 * q^36 - 41 * q^37 - 267 * q^38 + 333 * q^39 + 336 * q^40 - 426 * q^41 + 424 * q^43 + 231 * q^44 - 63 * q^45 + 140 * q^46 - 75 * q^47 - 603 * q^48 + 490 * q^50 + 408 * q^51 + 269 * q^52 + 1500 * q^53 - 135 * q^54 - 77 * q^55 + 333 * q^57 - 1767 * q^58 - 757 * q^59 + 657 * q^60 - 658 * q^61 + 568 * q^62 - 748 * q^64 + 537 * q^65 - 165 * q^66 - 583 * q^67 + 1650 * q^68 + 84 * q^69 - 764 * q^71 + 540 * q^72 - 875 * q^73 - 825 * q^74 - 570 * q^75 - 213 * q^76 - 3 * q^78 - 244 * q^79 + 2577 * q^80 + 405 * q^81 + 2006 * q^82 - 924 * q^83 - 1402 * q^85 + 1272 * q^86 - 183 * q^87 + 660 * q^88 + 1110 * q^89 - 495 * q^90 - 2046 * q^92 - 840 * q^93 + 3349 * q^94 + 1923 * q^95 - 1605 * q^96 + 852 * q^97 + 495 * q^99

Introduction

L-functions

Modular forms

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Database

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