LMFDB - Embedded newform 2523.2.a.r.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,2,Mod(1,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2523.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.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:	$20.1462564300$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 $ x^9 - 4x^8 - 6x^7 + 33x^6 + 6x^5 - 90x^4 + 21x^3 + 84x^2 - 36x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.58860$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.58860 q^{2} +1.00000 q^{3} +4.70087 q^{4} -1.14894 q^{5} +2.58860 q^{6} +2.76526 q^{7} +6.99148 q^{8} +1.00000 q^{9} -2.97416 q^{10} -4.35418 q^{11} +4.70087 q^{12} +5.62914 q^{13} +7.15816 q^{14} -1.14894 q^{15} +8.69643 q^{16} +2.41516 q^{17} +2.58860 q^{18} +1.87296 q^{19} -5.40103 q^{20} +2.76526 q^{21} -11.2712 q^{22} -8.82048 q^{23} +6.99148 q^{24} -3.67993 q^{25} +14.5716 q^{26} +1.00000 q^{27} +12.9991 q^{28} -2.97416 q^{30} +1.56053 q^{31} +8.52865 q^{32} -4.35418 q^{33} +6.25190 q^{34} -3.17713 q^{35} +4.70087 q^{36} +7.76330 q^{37} +4.84834 q^{38} +5.62914 q^{39} -8.03281 q^{40} +3.16072 q^{41} +7.15816 q^{42} -1.46397 q^{43} -20.4684 q^{44} -1.14894 q^{45} -22.8327 q^{46} +0.357351 q^{47} +8.69643 q^{48} +0.646666 q^{49} -9.52588 q^{50} +2.41516 q^{51} +26.4618 q^{52} -1.63498 q^{53} +2.58860 q^{54} +5.00270 q^{55} +19.3333 q^{56} +1.87296 q^{57} -4.85026 q^{59} -5.40103 q^{60} +1.55510 q^{61} +4.03961 q^{62} +2.76526 q^{63} +4.68444 q^{64} -6.46755 q^{65} -11.2712 q^{66} -9.66950 q^{67} +11.3534 q^{68} -8.82048 q^{69} -8.22432 q^{70} -8.18108 q^{71} +6.99148 q^{72} +11.3786 q^{73} +20.0961 q^{74} -3.67993 q^{75} +8.80452 q^{76} -12.0404 q^{77} +14.5716 q^{78} -8.13075 q^{79} -9.99170 q^{80} +1.00000 q^{81} +8.18185 q^{82} -0.481835 q^{83} +12.9991 q^{84} -2.77488 q^{85} -3.78965 q^{86} -30.4421 q^{88} -1.99621 q^{89} -2.97416 q^{90} +15.5660 q^{91} -41.4639 q^{92} +1.56053 q^{93} +0.925040 q^{94} -2.15192 q^{95} +8.52865 q^{96} +4.63516 q^{97} +1.67396 q^{98} -4.35418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - q^99

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 $

$2$	2.58860	1.83042	0.915210	−	0.402978i	$-0.132025\pi$
$2$	2.58860	1.83042	0.915210	+	0.402978i	$0.132025\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.70087	2.35043
$5$	−1.14894	−0.513823	−0.256911	−	0.966435i	$-0.582705\pi$
$5$	−1.14894	−0.513823	−0.256911	+	0.966435i	$0.582705\pi$
$6$	2.58860	1.05679
$7$	2.76526	1.04517	0.522585	−	0.852587i	$-0.324968\pi$
$7$	2.76526	1.04517	0.522585	+	0.852587i	$0.324968\pi$
$8$	6.99148	2.47186
$9$	1.00000	0.333333
$10$	−2.97416	−0.940511
$11$	−4.35418	−1.31283	−0.656417	−	0.754399i	$-0.727929\pi$
$11$	−4.35418	−1.31283	−0.656417	+	0.754399i	$0.727929\pi$
$12$	4.70087	1.35702
$13$	5.62914	1.56124	0.780621	−	0.625005i	$-0.214903\pi$
$13$	5.62914	1.56124	0.780621	+	0.625005i	$0.214903\pi$
$14$	7.15816	1.91310
$15$	−1.14894	−0.296656
$16$	8.69643	2.17411
$17$	2.41516	0.585763	0.292881	−	0.956149i	$-0.405386\pi$
$17$	2.41516	0.585763	0.292881	+	0.956149i	$0.405386\pi$
$18$	2.58860	0.610140
$19$	1.87296	0.429686	0.214843	−	0.976649i	$-0.431076\pi$
$19$	1.87296	0.429686	0.214843	+	0.976649i	$0.431076\pi$
$20$	−5.40103	−1.20771
$21$	2.76526	0.603429
$22$	−11.2712	−2.40304
$23$	−8.82048	−1.83920	−0.919598	−	0.392860i	$-0.871486\pi$
$23$	−8.82048	−1.83920	−0.919598	+	0.392860i	$0.871486\pi$
$24$	6.99148	1.42713
$25$	−3.67993	−0.735986
$26$	14.5716	2.85773
$27$	1.00000	0.192450
$28$	12.9991	2.45660
$29$	0	0
$29$	0	0
$30$	−2.97416	−0.543004
$31$	1.56053	0.280280	0.140140	−	0.990132i	$-0.455245\pi$
$31$	1.56053	0.280280	0.140140	+	0.990132i	$0.455245\pi$
$32$	8.52865	1.50767
$33$	−4.35418	−0.757965
$34$	6.25190	1.07219
$35$	−3.17713	−0.537032
$36$	4.70087	0.783478
$37$	7.76330	1.27628	0.638139	−	0.769921i	$-0.279705\pi$
$37$	7.76330	1.27628	0.638139	+	0.769921i	$0.279705\pi$
$38$	4.84834	0.786505
$39$	5.62914	0.901383
$40$	−8.03281	−1.27010
$41$	3.16072	0.493622	0.246811	−	0.969064i	$-0.420617\pi$
$41$	3.16072	0.493622	0.246811	+	0.969064i	$0.420617\pi$
$42$	7.15816	1.10453
$43$	−1.46397	−0.223254	−0.111627	−	0.993750i	$-0.535606\pi$
$43$	−1.46397	−0.223254	−0.111627	+	0.993750i	$0.535606\pi$
$44$	−20.4684	−3.08573
$45$	−1.14894	−0.171274
$46$	−22.8327	−3.36650
$47$	0.357351	0.0521250	0.0260625	−	0.999660i	$-0.491703\pi$
$47$	0.357351	0.0521250	0.0260625	+	0.999660i	$0.491703\pi$
$48$	8.69643	1.25522
$49$	0.646666	0.0923809
$50$	−9.52588	−1.34716
$51$	2.41516	0.338190
$52$	26.4618	3.66960
$53$	−1.63498	−0.224582	−0.112291	−	0.993675i	$-0.535819\pi$
$53$	−1.63498	−0.224582	−0.112291	+	0.993675i	$0.535819\pi$
$54$	2.58860	0.352264
$55$	5.00270	0.674563
$56$	19.3333	2.58352
$57$	1.87296	0.248079
$58$	0	0
$59$	−4.85026	−0.631450	−0.315725	−	0.948851i	$-0.602248\pi$
$59$	−4.85026	−0.631450	−0.315725	+	0.948851i	$0.602248\pi$
$60$	−5.40103	−0.697270
$61$	1.55510	0.199110	0.0995551	−	0.995032i	$-0.468258\pi$
$61$	1.55510	0.199110	0.0995551	+	0.995032i	$0.468258\pi$
$62$	4.03961	0.513030
$63$	2.76526	0.348390
$64$	4.68444	0.585555
$65$	−6.46755	−0.802201
$66$	−11.2712	−1.38739
$67$	−9.66950	−1.18132	−0.590659	−	0.806922i	$-0.701132\pi$
$67$	−9.66950	−1.18132	−0.590659	+	0.806922i	$0.701132\pi$
$68$	11.3534	1.37680
$69$	−8.82048	−1.06186
$70$	−8.22432	−0.982994
$71$	−8.18108	−0.970915	−0.485458	−	0.874260i	$-0.661347\pi$
$71$	−8.18108	−0.970915	−0.485458	+	0.874260i	$0.661347\pi$
$72$	6.99148	0.823954
$73$	11.3786	1.33177	0.665884	−	0.746055i	$-0.268054\pi$
$73$	11.3786	1.33177	0.665884	+	0.746055i	$0.268054\pi$
$74$	20.0961	2.33612
$75$	−3.67993	−0.424922
$76$	8.80452	1.00995
$77$	−12.0404	−1.37213
$78$	14.5716	1.64991
$79$	−8.13075	−0.914781	−0.457391	−	0.889266i	$-0.651216\pi$
$79$	−8.13075	−0.914781	−0.457391	+	0.889266i	$0.651216\pi$
$80$	−9.99170	−1.11711
$81$	1.00000	0.111111
$82$	8.18185	0.903535
$83$	−0.481835	−0.0528882	−0.0264441	−	0.999650i	$-0.508418\pi$
$83$	−0.481835	−0.0528882	−0.0264441	+	0.999650i	$0.508418\pi$
$84$	12.9991	1.41832
$85$	−2.77488	−0.300978
$86$	−3.78965	−0.408648
$87$	0	0
$88$	−30.4421	−3.24514
$89$	−1.99621	−0.211598	−0.105799	−	0.994388i	$-0.533740\pi$
$89$	−1.99621	−0.211598	−0.105799	+	0.994388i	$0.533740\pi$
$90$	−2.97416	−0.313504
$91$	15.5660	1.63176
$92$	−41.4639	−4.32291
$93$	1.56053	0.161820
$94$	0.925040	0.0954106
$95$	−2.15192	−0.220782
$96$	8.52865	0.870452
$97$	4.63516	0.470629	0.235315	−	0.971919i	$-0.424388\pi$
$97$	4.63516	0.470629	0.235315	+	0.971919i	$0.424388\pi$
$98$	1.67396	0.169096
$99$	−4.35418	−0.437611
$100$	−17.2989	−1.72989
$101$	−1.89907	−0.188964	−0.0944822	−	0.995527i	$-0.530120\pi$
$101$	−1.89907	−0.188964	−0.0944822	+	0.995527i	$0.530120\pi$
$102$	6.25190	0.619030
$103$	−8.22122	−0.810061	−0.405030	−	0.914303i	$-0.632739\pi$
$103$	−8.22122	−0.810061	−0.405030	+	0.914303i	$0.632739\pi$
$104$	39.3560	3.85917
$105$	−3.17713	−0.310056
$106$	−4.23233	−0.411080
$107$	4.45778	0.430950	0.215475	−	0.976509i	$-0.430870\pi$
$107$	4.45778	0.430950	0.215475	+	0.976509i	$0.430870\pi$
$108$	4.70087	0.452341
$109$	17.5256	1.67865	0.839324	−	0.543631i	$-0.182951\pi$
$109$	17.5256	1.67865	0.839324	+	0.543631i	$0.182951\pi$
$110$	12.9500	1.23473
$111$	7.76330	0.736859
$112$	24.0479	2.27231
$113$	7.93117	0.746102	0.373051	−	0.927811i	$-0.378312\pi$
$113$	7.93117	0.746102	0.373051	+	0.927811i	$0.378312\pi$
$114$	4.84834	0.454089
$115$	10.1342	0.945021
$116$	0	0
$117$	5.62914	0.520414
$118$	−12.5554	−1.15582
$119$	6.67855	0.612222
$120$	−8.03281	−0.733292
$121$	7.95884	0.723531
$122$	4.02554	0.364455
$123$	3.16072	0.284993
$124$	7.33587	0.658780
$125$	9.97274	0.891989
$126$	7.15816	0.637700
$127$	−3.35542	−0.297745	−0.148873	−	0.988856i	$-0.547564\pi$
$127$	−3.35542	−0.297745	−0.148873	+	0.988856i	$0.547564\pi$
$128$	−4.93114	−0.435855
$129$	−1.46397	−0.128896
$130$	−16.7419	−1.46836
$131$	−8.69320	−0.759528	−0.379764	−	0.925083i	$-0.623995\pi$
$131$	−8.69320	−0.759528	−0.379764	+	0.925083i	$0.623995\pi$
$132$	−20.4684	−1.78155
$133$	5.17921	0.449095
$134$	−25.0305	−2.16231
$135$	−1.14894	−0.0988852
$136$	16.8856	1.44792
$137$	3.22382	0.275429	0.137715	−	0.990472i	$-0.456024\pi$
$137$	3.22382	0.275429	0.137715	+	0.990472i	$0.456024\pi$
$138$	−22.8327	−1.94365
$139$	−22.4884	−1.90744	−0.953721	−	0.300693i	$-0.902782\pi$
$139$	−22.4884	−1.90744	−0.953721	+	0.300693i	$0.902782\pi$
$140$	−14.9352	−1.26226
$141$	0.357351	0.0300944
$142$	−21.1776	−1.77718
$143$	−24.5102	−2.04965
$144$	8.69643	0.724703
$145$	0	0
$146$	29.4548	2.43769
$147$	0.646666	0.0533361
$148$	36.4942	2.99981
$149$	1.28934	0.105627	0.0528133	−	0.998604i	$-0.483181\pi$
$149$	1.28934	0.105627	0.0528133	+	0.998604i	$0.483181\pi$
$150$	−9.52588	−0.777785
$151$	6.55195	0.533190	0.266595	−	0.963809i	$-0.414101\pi$
$151$	6.55195	0.533190	0.266595	+	0.963809i	$0.414101\pi$
$152$	13.0947	1.06212
$153$	2.41516	0.195254
$154$	−31.1679	−2.51158
$155$	−1.79296	−0.144014
$156$	26.4618	2.11864
$157$	−24.1178	−1.92481	−0.962407	−	0.271612i	$-0.912443\pi$
$157$	−24.1178	−1.92481	−0.962407	+	0.271612i	$0.912443\pi$
$158$	−21.0473	−1.67443
$159$	−1.63498	−0.129663
$160$	−9.79893	−0.774674
$161$	−24.3909	−1.92227
$162$	2.58860	0.203380
$163$	16.1434	1.26445	0.632223	−	0.774786i	$-0.282143\pi$
$163$	16.1434	1.26445	0.632223	+	0.774786i	$0.282143\pi$
$164$	14.8581	1.16023
$165$	5.00270	0.389459
$166$	−1.24728	−0.0968076
$167$	−5.42045	−0.419447	−0.209723	−	0.977761i	$-0.567256\pi$
$167$	−5.42045	−0.419447	−0.209723	+	0.977761i	$0.567256\pi$
$168$	19.3333	1.49159
$169$	18.6872	1.43747
$170$	−7.18307	−0.550916
$171$	1.87296	0.143229
$172$	−6.88195	−0.524744
$173$	−11.2923	−0.858537	−0.429268	−	0.903177i	$-0.641229\pi$
$173$	−11.2923	−0.858537	−0.429268	+	0.903177i	$0.641229\pi$
$174$	0	0
$175$	−10.1760	−0.769231
$176$	−37.8658	−2.85424
$177$	−4.85026	−0.364568
$178$	−5.16739	−0.387312
$179$	−10.6541	−0.796323	−0.398161	−	0.917315i	$-0.630352\pi$
$179$	−10.6541	−0.796323	−0.398161	+	0.917315i	$0.630352\pi$
$180$	−5.40103	−0.402569
$181$	−12.2934	−0.913763	−0.456882	−	0.889527i	$-0.651034\pi$
$181$	−12.2934	−0.913763	−0.456882	+	0.889527i	$0.651034\pi$
$182$	40.2943	2.98681
$183$	1.55510	0.114956
$184$	−61.6682	−4.54624
$185$	−8.91958	−0.655781
$186$	4.03961	0.296198
$187$	−10.5160	−0.769009
$188$	1.67986	0.122516
$189$	2.76526	0.201143
$190$	−5.57047	−0.404124
$191$	−1.68311	−0.121786	−0.0608929	−	0.998144i	$-0.519395\pi$
$191$	−1.68311	−0.121786	−0.0608929	+	0.998144i	$0.519395\pi$
$192$	4.68444	0.338071
$193$	10.5761	0.761284	0.380642	−	0.924722i	$-0.375703\pi$
$193$	10.5761	0.761284	0.380642	+	0.924722i	$0.375703\pi$
$194$	11.9986	0.861449
$195$	−6.46755	−0.463151
$196$	3.03989	0.217135
$197$	−12.1150	−0.863161	−0.431581	−	0.902074i	$-0.642044\pi$
$197$	−12.1150	−0.863161	−0.431581	+	0.902074i	$0.642044\pi$
$198$	−11.2712	−0.801012
$199$	4.99592	0.354151	0.177076	−	0.984197i	$-0.443336\pi$
$199$	4.99592	0.354151	0.177076	+	0.984197i	$0.443336\pi$
$200$	−25.7282	−1.81926
$201$	−9.66950	−0.682034
$202$	−4.91594	−0.345884
$203$	0	0
$204$	11.3534	0.794894
$205$	−3.63149	−0.253634
$206$	−21.2815	−1.48275
$207$	−8.82048	−0.613066
$208$	48.9534	3.39431
$209$	−8.15518	−0.564106
$210$	−8.22432	−0.567532
$211$	−19.2108	−1.32253	−0.661263	−	0.750154i	$-0.729979\pi$
$211$	−19.2108	−1.32253	−0.661263	+	0.750154i	$0.729979\pi$
$212$	−7.68585	−0.527866
$213$	−8.18108	−0.560558
$214$	11.5394	0.788819
$215$	1.68202	0.114713
$216$	6.99148	0.475710
$217$	4.31528	0.292941
$218$	45.3668	3.07263
$219$	11.3786	0.768897
$220$	23.5170	1.58552
$221$	13.5953	0.914517
$222$	20.0961	1.34876
$223$	−21.2442	−1.42262	−0.711308	−	0.702881i	$-0.751897\pi$
$223$	−21.2442	−1.42262	−0.711308	+	0.702881i	$0.751897\pi$
$224$	23.5840	1.57577
$225$	−3.67993	−0.245329
$226$	20.5307	1.36568
$227$	19.7559	1.31125	0.655624	−	0.755088i	$-0.272406\pi$
$227$	19.7559	1.31125	0.655624	+	0.755088i	$0.272406\pi$
$228$	8.80452	0.583094
$229$	20.7139	1.36881	0.684405	−	0.729102i	$-0.260062\pi$
$229$	20.7139	1.36881	0.684405	+	0.729102i	$0.260062\pi$
$230$	26.2335	1.72978
$231$	−12.0404	−0.792202
$232$	0	0
$233$	20.7745	1.36098	0.680492	−	0.732756i	$-0.261766\pi$
$233$	20.7745	1.36098	0.680492	+	0.732756i	$0.261766\pi$
$234$	14.5716	0.952575
$235$	−0.410576	−0.0267830
$236$	−22.8004	−1.48418
$237$	−8.13075	−0.528149
$238$	17.2881	1.12062
$239$	−2.27481	−0.147145	−0.0735727	−	0.997290i	$-0.523440\pi$
$239$	−2.27481	−0.147145	−0.0735727	+	0.997290i	$0.523440\pi$
$240$	−9.99170	−0.644961
$241$	11.7783	0.758706	0.379353	−	0.925252i	$-0.376147\pi$
$241$	11.7783	0.758706	0.379353	+	0.925252i	$0.376147\pi$
$242$	20.6023	1.32437
$243$	1.00000	0.0641500
$244$	7.31032	0.467995
$245$	−0.742982	−0.0474674
$246$	8.18185	0.521656
$247$	10.5431	0.670843
$248$	10.9104	0.692814
$249$	−0.481835	−0.0305350
$250$	25.8155	1.63271
$251$	−1.42714	−0.0900805	−0.0450402	−	0.998985i	$-0.514342\pi$
$251$	−1.42714	−0.0900805	−0.0450402	+	0.998985i	$0.514342\pi$
$252$	12.9991	0.818868
$253$	38.4059	2.41456
$254$	−8.68585	−0.544999
$255$	−2.77488	−0.173770
$256$	−22.1337	−1.38335
$257$	−28.6450	−1.78683	−0.893414	−	0.449234i	$-0.851697\pi$
$257$	−28.6450	−1.78683	−0.893414	+	0.449234i	$0.851697\pi$
$258$	−3.78965	−0.235933
$259$	21.4675	1.33393
$260$	−30.4031	−1.88552
$261$	0	0
$262$	−22.5032	−1.39025
$263$	18.5023	1.14090	0.570451	−	0.821332i	$-0.306769\pi$
$263$	18.5023	1.14090	0.570451	+	0.821332i	$0.306769\pi$
$264$	−30.4421	−1.87358
$265$	1.87850	0.115396
$266$	13.4069	0.822032
$267$	−1.99621	−0.122166
$268$	−45.4550	−2.77661
$269$	−28.7074	−1.75032	−0.875160	−	0.483834i	$-0.839244\pi$
$269$	−28.7074	−1.75032	−0.875160	+	0.483834i	$0.839244\pi$
$270$	−2.97416	−0.181001
$271$	1.80441	0.109610	0.0548050	−	0.998497i	$-0.482546\pi$
$271$	1.80441	0.109610	0.0548050	+	0.998497i	$0.482546\pi$
$272$	21.0033	1.27351
$273$	15.5660	0.942099
$274$	8.34518	0.504151
$275$	16.0231	0.966227
$276$	−41.4639	−2.49583
$277$	−14.1949	−0.852890	−0.426445	−	0.904513i	$-0.640234\pi$
$277$	−14.1949	−0.852890	−0.426445	+	0.904513i	$0.640234\pi$
$278$	−58.2136	−3.49142
$279$	1.56053	0.0934268
$280$	−22.2128	−1.32747
$281$	18.8216	1.12280	0.561400	−	0.827545i	$-0.310263\pi$
$281$	18.8216	1.12280	0.561400	+	0.827545i	$0.310263\pi$
$282$	0.925040	0.0550853
$283$	21.8832	1.30082	0.650410	−	0.759584i	$-0.274597\pi$
$283$	21.8832	1.30082	0.650410	+	0.759584i	$0.274597\pi$
$284$	−38.4582	−2.28207
$285$	−2.15192	−0.127469
$286$	−63.4473	−3.75172
$287$	8.74022	0.515919
$288$	8.52865	0.502556
$289$	−11.1670	−0.656882
$290$	0	0
$291$	4.63516	0.271718
$292$	53.4895	3.13023
$293$	0.00776592	0.000453690 0	0.000226845	−	1.00000i	$-0.499928\pi$
$293$	0.00776592	0.000453690 0	0.000226845		1.00000i	$0.499928\pi$
$294$	1.67396	0.0976275
$295$	5.57267	0.324453
$296$	54.2769	3.15478
$297$	−4.35418	−0.252655
$298$	3.33758	0.193341
$299$	−49.6517	−2.87143
$300$	−17.2989	−0.998751
$301$	−4.04827	−0.233338
$302$	16.9604	0.975961
$303$	−1.89907	−0.109099
$304$	16.2880	0.934183
$305$	−1.78672	−0.102307
$306$	6.25190	0.357397
$307$	0.214941	0.0122673	0.00613367	−	0.999981i	$-0.498048\pi$
$307$	0.214941	0.0122673	0.00613367	+	0.999981i	$0.498048\pi$
$308$	−56.6005	−3.22511
$309$	−8.22122	−0.467689
$310$	−4.64127	−0.263607
$311$	28.2266	1.60058	0.800291	−	0.599612i	$-0.204678\pi$
$311$	28.2266	1.60058	0.800291	+	0.599612i	$0.204678\pi$
$312$	39.3560	2.22809
$313$	−10.2302	−0.578244	−0.289122	−	0.957292i	$-0.593363\pi$
$313$	−10.2302	−0.578244	−0.289122	+	0.957292i	$0.593363\pi$
$314$	−62.4316	−3.52322
$315$	−3.17713	−0.179011
$316$	−38.2216	−2.15013
$317$	23.7789	1.33555	0.667777	−	0.744361i	$-0.267246\pi$
$317$	23.7789	1.33555	0.667777	+	0.744361i	$0.267246\pi$
$318$	−4.23233	−0.237337
$319$	0	0
$320$	−5.38216	−0.300872
$321$	4.45778	0.248809
$322$	−63.1384	−3.51857
$323$	4.52349	0.251694
$324$	4.70087	0.261159
$325$	−20.7148	−1.14905
$326$	41.7888	2.31447
$327$	17.5256	0.969168
$328$	22.0981	1.22016
$329$	0.988168	0.0544795
$330$	12.9500	0.712874
$331$	−7.07856	−0.389073	−0.194536	−	0.980895i	$-0.562320\pi$
$331$	−7.07856	−0.389073	−0.194536	+	0.980895i	$0.562320\pi$
$332$	−2.26504	−0.124310
$333$	7.76330	0.425426
$334$	−14.0314	−0.767763
$335$	11.1097	0.606987
$336$	24.0479	1.31192
$337$	−7.02402	−0.382623	−0.191311	−	0.981529i	$-0.561274\pi$
$337$	−7.02402	−0.382623	−0.191311	+	0.981529i	$0.561274\pi$
$338$	48.3737	2.63118
$339$	7.93117	0.430762
$340$	−13.0444	−0.707429
$341$	−6.79484	−0.367961
$342$	4.84834	0.262168
$343$	−17.5686	−0.948617
$344$	−10.2353	−0.551852
$345$	10.1342	0.545608
$346$	−29.2313	−1.57148
$347$	10.0795	0.541094	0.270547	−	0.962707i	$-0.412795\pi$
$347$	10.0795	0.541094	0.270547	+	0.962707i	$0.412795\pi$
$348$	0	0
$349$	−1.64246	−0.0879187	−0.0439593	−	0.999033i	$-0.513997\pi$
$349$	−1.64246	−0.0879187	−0.0439593	+	0.999033i	$0.513997\pi$
$350$	−26.3416	−1.40802
$351$	5.62914	0.300461
$352$	−37.1353	−1.97932
$353$	24.1232	1.28395	0.641975	−	0.766726i	$-0.278115\pi$
$353$	24.1232	1.28395	0.641975	+	0.766726i	$0.278115\pi$
$354$	−12.5554	−0.667312
$355$	9.39959	0.498878
$356$	−9.38391	−0.497346
$357$	6.67855	0.353466
$358$	−27.5792	−1.45760
$359$	−12.8958	−0.680612	−0.340306	−	0.940315i	$-0.610531\pi$
$359$	−12.8958	−0.680612	−0.340306	+	0.940315i	$0.610531\pi$
$360$	−8.03281	−0.423366
$361$	−15.4920	−0.815370
$362$	−31.8228	−1.67257
$363$	7.95884	0.417731
$364$	73.1739	3.83535
$365$	−13.0734	−0.684293
$366$	4.02554	0.210418
$367$	−31.7420	−1.65692	−0.828459	−	0.560050i	$-0.810782\pi$
$367$	−31.7420	−1.65692	−0.828459	+	0.560050i	$0.810782\pi$
$368$	−76.7067	−3.99861
$369$	3.16072	0.164541
$370$	−23.0893	−1.20035
$371$	−4.52116	−0.234727
$372$	7.33587	0.380347
$373$	4.75511	0.246210	0.123105	−	0.992394i	$-0.460715\pi$
$373$	4.75511	0.246210	0.123105	+	0.992394i	$0.460715\pi$
$374$	−27.2218	−1.40761
$375$	9.97274	0.514990
$376$	2.49841	0.128846
$377$	0	0
$378$	7.15816	0.368176
$379$	2.11960	0.108877	0.0544383	−	0.998517i	$-0.482663\pi$
$379$	2.11960	0.108877	0.0544383	+	0.998517i	$0.482663\pi$
$380$	−10.1159	−0.518934
$381$	−3.35542	−0.171903
$382$	−4.35691	−0.222919
$383$	14.6407	0.748103	0.374051	−	0.927408i	$-0.377968\pi$
$383$	14.6407	0.748103	0.374051	+	0.927408i	$0.377968\pi$
$384$	−4.93114	−0.251641
$385$	13.8338	0.705034
$386$	27.3773	1.39347
$387$	−1.46397	−0.0744179
$388$	21.7893	1.10618
$389$	1.93401	0.0980583	0.0490292	−	0.998797i	$-0.484387\pi$
$389$	1.93401	0.0980583	0.0490292	+	0.998797i	$0.484387\pi$
$390$	−16.7419	−0.847761
$391$	−21.3029	−1.07733
$392$	4.52115	0.228353
$393$	−8.69320	−0.438514
$394$	−31.3611	−1.57995
$395$	9.34177	0.470035
$396$	−20.4684	−1.02858
$397$	−30.0191	−1.50662	−0.753309	−	0.657667i	$-0.771543\pi$
$397$	−30.0191	−1.50662	−0.753309	+	0.657667i	$0.771543\pi$
$398$	12.9324	0.648245
$399$	5.17921	0.259285
$400$	−32.0023	−1.60011
$401$	15.7085	0.784444	0.392222	−	0.919871i	$-0.371707\pi$
$401$	15.7085	0.784444	0.392222	+	0.919871i	$0.371707\pi$
$402$	−25.0305	−1.24841
$403$	8.78446	0.437585
$404$	−8.92728	−0.444149
$405$	−1.14894	−0.0570914
$406$	0	0
$407$	−33.8027	−1.67554
$408$	16.8856	0.835959
$409$	−4.87216	−0.240913	−0.120456	−	0.992719i	$-0.538436\pi$
$409$	−4.87216	−0.240913	−0.120456	+	0.992719i	$0.538436\pi$
$410$	−9.40048	−0.464257
$411$	3.22382	0.159019
$412$	−38.6469	−1.90399
$413$	−13.4122	−0.659973
$414$	−22.8327	−1.12217
$415$	0.553600	0.0271752
$416$	48.0090	2.35383
$417$	−22.4884	−1.10126
$418$	−21.1105	−1.03255
$419$	19.0131	0.928853	0.464426	−	0.885612i	$-0.346261\pi$
$419$	19.0131	0.928853	0.464426	+	0.885612i	$0.346261\pi$
$420$	−14.9352	−0.728766
$421$	12.5171	0.610047	0.305023	−	0.952345i	$-0.401336\pi$
$421$	12.5171	0.610047	0.305023	+	0.952345i	$0.401336\pi$
$422$	−49.7292	−2.42078
$423$	0.357351	0.0173750
$424$	−11.4310	−0.555136
$425$	−8.88763	−0.431113
$426$	−21.1776	−1.02606
$427$	4.30026	0.208104
$428$	20.9554	1.01292
$429$	−24.5102	−1.18337
$430$	4.35409	0.209973
$431$	35.3970	1.70501	0.852507	−	0.522716i	$-0.175081\pi$
$431$	35.3970	1.70501	0.852507	+	0.522716i	$0.175081\pi$
$432$	8.69643	0.418407
$433$	5.85494	0.281371	0.140685	−	0.990054i	$-0.455069\pi$
$433$	5.85494	0.281371	0.140685	+	0.990054i	$0.455069\pi$
$434$	11.1706	0.536204
$435$	0	0
$436$	82.3856	3.94555
$437$	−16.5204	−0.790277
$438$	29.4548	1.40740
$439$	24.8297	1.18506	0.592530	−	0.805549i	$-0.298129\pi$
$439$	24.8297	1.18506	0.592530	+	0.805549i	$0.298129\pi$
$440$	34.9762	1.66743
$441$	0.646666	0.0307936
$442$	35.1928	1.67395
$443$	23.7488	1.12834	0.564170	−	0.825659i	$-0.309196\pi$
$443$	23.7488	1.12834	0.564170	+	0.825659i	$0.309196\pi$
$444$	36.4942	1.73194
$445$	2.29353	0.108724
$446$	−54.9928	−2.60398
$447$	1.28934	0.0609835
$448$	12.9537	0.612005
$449$	6.44854	0.304325	0.152163	−	0.988355i	$-0.451376\pi$
$449$	6.44854	0.304325	0.152163	+	0.988355i	$0.451376\pi$
$450$	−9.52588	−0.449054
$451$	−13.7623	−0.648043
$452$	37.2834	1.75366
$453$	6.55195	0.307837
$454$	51.1403	2.40013
$455$	−17.8845	−0.838437
$456$	13.0947	0.613217
$457$	−2.62569	−0.122824	−0.0614122	−	0.998112i	$-0.519560\pi$
$457$	−2.62569	−0.122824	−0.0614122	+	0.998112i	$0.519560\pi$
$458$	53.6200	2.50550
$459$	2.41516	0.112730
$460$	47.6396	2.22121
$461$	−7.15794	−0.333378	−0.166689	−	0.986009i	$-0.553308\pi$
$461$	−7.15794	−0.333378	−0.166689	+	0.986009i	$0.553308\pi$
$462$	−31.1679	−1.45006
$463$	−18.2411	−0.847737	−0.423868	−	0.905724i	$-0.639328\pi$
$463$	−18.2411	−0.847737	−0.423868	+	0.905724i	$0.639328\pi$
$464$	0	0
$465$	−1.79296	−0.0831467
$466$	53.7770	2.49117
$467$	35.4677	1.64125	0.820624	−	0.571468i	$-0.193626\pi$
$467$	35.4677	1.64125	0.820624	+	0.571468i	$0.193626\pi$
$468$	26.4618	1.22320
$469$	−26.7387	−1.23468
$470$	−1.06282	−0.0490241
$471$	−24.1178	−1.11129
$472$	−33.9105	−1.56086
$473$	6.37440	0.293095
$474$	−21.0473	−0.966734
$475$	−6.89235	−0.316243
$476$	31.3950	1.43899
$477$	−1.63498	−0.0748608
$478$	−5.88859	−0.269338
$479$	26.1004	1.19256	0.596280	−	0.802777i	$-0.296645\pi$
$479$	26.1004	1.19256	0.596280	+	0.802777i	$0.296645\pi$
$480$	−9.79893	−0.447258
$481$	43.7006	1.99258
$482$	30.4893	1.38875
$483$	−24.3909	−1.10983
$484$	37.4135	1.70061
$485$	−5.32553	−0.241820
$486$	2.58860	0.117421
$487$	22.1493	1.00368	0.501839	−	0.864961i	$-0.332657\pi$
$487$	22.1493	1.00368	0.501839	+	0.864961i	$0.332657\pi$
$488$	10.8724	0.492173
$489$	16.1434	0.730029
$490$	−1.92329	−0.0868852
$491$	−11.7483	−0.530193	−0.265096	−	0.964222i	$-0.585404\pi$
$491$	−11.7483	−0.530193	−0.265096	+	0.964222i	$0.585404\pi$
$492$	14.8581	0.669856
$493$	0	0
$494$	27.2920	1.22792
$495$	5.00270	0.224854
$496$	13.5711	0.609359
$497$	−22.6228	−1.01477
$498$	−1.24728	−0.0558919
$499$	−16.3753	−0.733060	−0.366530	−	0.930406i	$-0.619454\pi$
$499$	−16.3753	−0.733060	−0.366530	+	0.930406i	$0.619454\pi$
$500$	46.8805	2.09656
$501$	−5.42045	−0.242168
$502$	−3.69431	−0.164885
$503$	14.8354	0.661476	0.330738	−	0.943723i	$-0.392702\pi$
$503$	14.8354	0.661476	0.330738	+	0.943723i	$0.392702\pi$
$504$	19.3333	0.861172
$505$	2.18192	0.0970942
$506$	99.4177	4.41965
$507$	18.6872	0.829927
$508$	−15.7734	−0.699831
$509$	31.5733	1.39946	0.699732	−	0.714406i	$-0.253303\pi$
$509$	31.5733	1.39946	0.699732	+	0.714406i	$0.253303\pi$
$510$	−7.18307	−0.318072
$511$	31.4649	1.39192
$512$	−47.4330	−2.09626
$513$	1.87296	0.0826931
$514$	−74.1507	−3.27065
$515$	9.44571	0.416228
$516$	−6.88195	−0.302961
$517$	−1.55597	−0.0684314
$518$	55.5709	2.44165
$519$	−11.2923	−0.495676
$520$	−45.2178	−1.98293
$521$	−8.03875	−0.352184	−0.176092	−	0.984374i	$-0.556346\pi$
$521$	−8.03875	−0.352184	−0.176092	+	0.984374i	$0.556346\pi$
$522$	0	0
$523$	−1.48633	−0.0649927	−0.0324963	−	0.999472i	$-0.510346\pi$
$523$	−1.48633	−0.0649927	−0.0324963	+	0.999472i	$0.510346\pi$
$524$	−40.8656	−1.78522
$525$	−10.1760	−0.444116
$526$	47.8951	2.08833
$527$	3.76894	0.164178
$528$	−37.8658	−1.64790
$529$	54.8008	2.38264
$530$	4.86270	0.211222
$531$	−4.85026	−0.210483
$532$	24.3468	1.05557
$533$	17.7921	0.770663
$534$	−5.16739	−0.223615
$535$	−5.12173	−0.221432
$536$	−67.6041	−2.92005
$537$	−10.6541	−0.459757
$538$	−74.3120	−3.20382
$539$	−2.81570	−0.121281
$540$	−5.40103	−0.232423
$541$	38.8306	1.66946	0.834728	−	0.550662i	$-0.185625\pi$
$541$	38.8306	1.66946	0.834728	+	0.550662i	$0.185625\pi$
$542$	4.67090	0.200632
$543$	−12.2934	−0.527561
$544$	20.5981	0.883135
$545$	−20.1359	−0.862528
$546$	40.2943	1.72444
$547$	−17.3495	−0.741809	−0.370905	−	0.928671i	$-0.620952\pi$
$547$	−17.3495	−0.741809	−0.370905	+	0.928671i	$0.620952\pi$
$548$	15.1547	0.647378
$549$	1.55510	0.0663700
$550$	41.4774	1.76860
$551$	0	0
$552$	−61.6682	−2.62477
$553$	−22.4837	−0.956102
$554$	−36.7450	−1.56115
$555$	−8.91958	−0.378615
$556$	−105.715	−4.48332
$557$	30.4259	1.28919	0.644593	−	0.764526i	$-0.277027\pi$
$557$	30.4259	1.28919	0.644593	+	0.764526i	$0.277027\pi$
$558$	4.03961	0.171010
$559$	−8.24091	−0.348553
$560$	−27.6296	−1.16757
$561$	−10.5160	−0.443987
$562$	48.7215	2.05519
$563$	−12.1911	−0.513793	−0.256897	−	0.966439i	$-0.582700\pi$
$563$	−12.1911	−0.513793	−0.256897	+	0.966439i	$0.582700\pi$
$564$	1.67986	0.0707349
$565$	−9.11246	−0.383364
$566$	56.6469	2.38104
$567$	2.76526	0.116130
$568$	−57.1978	−2.39997
$569$	−3.15785	−0.132384	−0.0661920	−	0.997807i	$-0.521085\pi$
$569$	−3.15785	−0.132384	−0.0661920	+	0.997807i	$0.521085\pi$
$570$	−5.57047	−0.233321
$571$	24.3414	1.01865	0.509327	−	0.860573i	$-0.329894\pi$
$571$	24.3414	1.01865	0.509327	+	0.860573i	$0.329894\pi$
$572$	−115.219	−4.81757
$573$	−1.68311	−0.0703130
$574$	22.6250	0.944347
$575$	32.4588	1.35362
$576$	4.68444	0.195185
$577$	7.99079	0.332661	0.166330	−	0.986070i	$-0.446808\pi$
$577$	7.99079	0.332661	0.166330	+	0.986070i	$0.446808\pi$
$578$	−28.9069	−1.20237
$579$	10.5761	0.439528
$580$	0	0
$581$	−1.33240	−0.0552772
$582$	11.9986	0.497358
$583$	7.11901	0.294839
$584$	79.5535	3.29195
$585$	−6.46755	−0.267400
$586$	0.0201029	0.000830443 0
$587$	−42.3655	−1.74861	−0.874305	−	0.485377i	$-0.838682\pi$
$587$	−42.3655	−1.74861	−0.874305	+	0.485377i	$0.838682\pi$
$588$	3.03989	0.125363
$589$	2.92281	0.120432
$590$	14.4254	0.593886
$591$	−12.1150	−0.498347
$592$	67.5130	2.77477
$593$	−26.3761	−1.08314	−0.541569	−	0.840656i	$-0.682169\pi$
$593$	−26.3761	−1.08314	−0.541569	+	0.840656i	$0.682169\pi$
$594$	−11.2712	−0.462464
$595$	−7.67327	−0.314573
$596$	6.06100	0.248268
$597$	4.99592	0.204469
$598$	−128.528	−5.25592
$599$	6.35768	0.259768	0.129884	−	0.991529i	$-0.458540\pi$
$599$	6.35768	0.259768	0.129884	+	0.991529i	$0.458540\pi$
$600$	−25.7282	−1.05035
$601$	−16.9016	−0.689430	−0.344715	−	0.938707i	$-0.612024\pi$
$601$	−16.9016	−0.689430	−0.344715	+	0.938707i	$0.612024\pi$
$602$	−10.4794	−0.427107
$603$	−9.66950	−0.393772
$604$	30.7999	1.25323
$605$	−9.14425	−0.371767
$606$	−4.91594	−0.199696
$607$	−7.41550	−0.300986	−0.150493	−	0.988611i	$-0.548086\pi$
$607$	−7.41550	−0.300986	−0.150493	+	0.988611i	$0.548086\pi$
$608$	15.9738	0.647823
$609$	0	0
$610$	−4.62511	−0.187265
$611$	2.01158	0.0813797
$612$	11.3534	0.458932
$613$	−28.9255	−1.16829	−0.584145	−	0.811649i	$-0.698570\pi$
$613$	−28.9255	−1.16829	−0.584145	+	0.811649i	$0.698570\pi$
$614$	0.556398	0.0224544
$615$	−3.63149	−0.146436
$616$	−84.1804	−3.39173
$617$	−34.9128	−1.40554	−0.702768	−	0.711419i	$-0.748053\pi$
$617$	−34.9128	−1.40554	−0.702768	+	0.711419i	$0.748053\pi$
$618$	−21.2815	−0.856067
$619$	45.1342	1.81410	0.907048	−	0.421028i	$-0.138331\pi$
$619$	45.1342	1.81410	0.907048	+	0.421028i	$0.138331\pi$
$620$	−8.42849	−0.338496
$621$	−8.82048	−0.353954
$622$	73.0674	2.92974
$623$	−5.52003	−0.221155
$624$	48.9534	1.95970
$625$	6.94155	0.277662
$626$	−26.4819	−1.05843
$627$	−8.15518	−0.325687
$628$	−113.375	−4.52415
$629$	18.7496	0.747596
$630$	−8.22432	−0.327665
$631$	29.2602	1.16483	0.582415	−	0.812892i	$-0.302108\pi$
$631$	29.2602	1.16483	0.582415	+	0.812892i	$0.302108\pi$
$632$	−56.8460	−2.26121
$633$	−19.2108	−0.763561
$634$	61.5540	2.44462
$635$	3.85518	0.152988
$636$	−7.68585	−0.304764
$637$	3.64017	0.144229
$638$	0	0
$639$	−8.18108	−0.323638
$640$	5.66560	0.223952
$641$	17.7234	0.700031	0.350016	−	0.936744i	$-0.386176\pi$
$641$	17.7234	0.700031	0.350016	+	0.936744i	$0.386176\pi$
$642$	11.5394	0.455425
$643$	38.4443	1.51609	0.758047	−	0.652200i	$-0.226154\pi$
$643$	38.4443	1.51609	0.758047	+	0.652200i	$0.226154\pi$
$644$	−114.659	−4.51818
$645$	1.68202	0.0662295
$646$	11.7095	0.460705
$647$	40.5910	1.59580	0.797899	−	0.602792i	$-0.205945\pi$
$647$	40.5910	1.59580	0.797899	+	0.602792i	$0.205945\pi$
$648$	6.99148	0.274651
$649$	21.1189	0.828989
$650$	−53.6225	−2.10325
$651$	4.31528	0.169129
$652$	75.8879	2.97200
$653$	−26.6169	−1.04160	−0.520800	−	0.853679i	$-0.674366\pi$
$653$	−26.6169	−1.04160	−0.520800	+	0.853679i	$0.674366\pi$
$654$	45.3668	1.77398
$655$	9.98798	0.390263
$656$	27.4870	1.07319
$657$	11.3786	0.443923
$658$	2.55798	0.0997203
$659$	−23.1105	−0.900259	−0.450130	−	0.892963i	$-0.648622\pi$
$659$	−23.1105	−0.900259	−0.450130	+	0.892963i	$0.648622\pi$
$660$	23.5170	0.915399
$661$	23.4613	0.912537	0.456269	−	0.889842i	$-0.349186\pi$
$661$	23.4613	0.912537	0.456269	+	0.889842i	$0.349186\pi$
$662$	−18.3236	−0.712166
$663$	13.5953	0.527997
$664$	−3.36874	−0.130732
$665$	−5.95062	−0.230755
$666$	20.0961	0.778708
$667$	0	0
$668$	−25.4808	−0.985882
$669$	−21.2442	−0.821348
$670$	28.7586	1.11104
$671$	−6.77118	−0.261398
$672$	23.5840	0.909771
$673$	−26.9621	−1.03931	−0.519656	−	0.854376i	$-0.673940\pi$
$673$	−26.9621	−1.03931	−0.519656	+	0.854376i	$0.673940\pi$
$674$	−18.1824	−0.700360
$675$	−3.67993	−0.141641
$676$	87.8460	3.37869
$677$	33.5314	1.28872	0.644358	−	0.764724i	$-0.277125\pi$
$677$	33.5314	1.28872	0.644358	+	0.764724i	$0.277125\pi$
$678$	20.5307	0.788475
$679$	12.8174	0.491888
$680$	−19.4005	−0.743976
$681$	19.7559	0.757049
$682$	−17.5891	−0.673523
$683$	−12.3343	−0.471957	−0.235979	−	0.971758i	$-0.575830\pi$
$683$	−12.3343	−0.471957	−0.235979	+	0.971758i	$0.575830\pi$
$684$	8.80452	0.336649
$685$	−3.70398	−0.141522
$686$	−45.4782	−1.73637
$687$	20.7139	0.790283
$688$	−12.7313	−0.485378
$689$	−9.20355	−0.350627
$690$	26.2335	0.998691
$691$	2.02123	0.0768913	0.0384457	−	0.999261i	$-0.487759\pi$
$691$	2.02123	0.0768913	0.0384457	+	0.999261i	$0.487759\pi$
$692$	−53.0836	−2.01793
$693$	−12.0404	−0.457378
$694$	26.0918	0.990429
$695$	25.8379	0.980087
$696$	0	0
$697$	7.63365	0.289145
$698$	−4.25167	−0.160928
$699$	20.7745	0.785764
$700$	−47.8359	−1.80803
$701$	−33.6980	−1.27275	−0.636377	−	0.771378i	$-0.719568\pi$
$701$	−33.6980	−1.27275	−0.636377	+	0.771378i	$0.719568\pi$
$702$	14.5716	0.549970
$703$	14.5403	0.548398
$704$	−20.3969	−0.768737
$705$	−0.410576	−0.0154632
$706$	62.4455	2.35017
$707$	−5.25142	−0.197500
$708$	−22.8004	−0.856893
$709$	12.6531	0.475198	0.237599	−	0.971363i	$-0.423640\pi$
$709$	12.6531	0.475198	0.237599	+	0.971363i	$0.423640\pi$
$710$	24.3318	0.913157
$711$	−8.13075	−0.304927
$712$	−13.9564	−0.523040
$713$	−13.7647	−0.515490
$714$	17.2881	0.646992
$715$	28.1609	1.05316
$716$	−50.0834	−1.87170
$717$	−2.27481	−0.0849545
$718$	−33.3820	−1.24581
$719$	13.3377	0.497411	0.248706	−	0.968579i	$-0.419995\pi$
$719$	13.3377	0.497411	0.248706	+	0.968579i	$0.419995\pi$
$720$	−9.99170	−0.372369
$721$	−22.7338	−0.846651
$722$	−40.1027	−1.49247
$723$	11.7783	0.438039
$724$	−57.7898	−2.14774
$725$	0	0
$726$	20.6023	0.764622
$727$	−41.7683	−1.54910	−0.774551	−	0.632512i	$-0.782024\pi$
$727$	−41.7683	−1.54910	−0.774551	+	0.632512i	$0.782024\pi$
$728$	108.830	4.03349
$729$	1.00000	0.0370370
$730$	−33.8418	−1.25254
$731$	−3.53573	−0.130774
$732$	7.31032	0.270197
$733$	−42.5635	−1.57212	−0.786059	−	0.618152i	$-0.787882\pi$
$733$	−42.5635	−1.57212	−0.786059	+	0.618152i	$0.787882\pi$
$734$	−82.1674	−3.03285
$735$	−0.742982	−0.0274053
$736$	−75.2268	−2.77290
$737$	42.1027	1.55087
$738$	8.18185	0.301178
$739$	22.2405	0.818129	0.409064	−	0.912506i	$-0.365855\pi$
$739$	22.2405	0.818129	0.409064	+	0.912506i	$0.365855\pi$
$740$	−41.9298	−1.54137
$741$	10.5431	0.387312
$742$	−11.7035	−0.429648
$743$	−28.0714	−1.02984	−0.514920	−	0.857238i	$-0.672178\pi$
$743$	−28.0714	−1.02984	−0.514920	+	0.857238i	$0.672178\pi$
$744$	10.9104	0.399996
$745$	−1.48137	−0.0542733
$746$	12.3091	0.450668
$747$	−0.481835	−0.0176294
$748$	−49.4345	−1.80750
$749$	12.3269	0.450416
$750$	25.8155	0.942648
$751$	28.5813	1.04295	0.521473	−	0.853268i	$-0.325383\pi$
$751$	28.5813	1.04295	0.521473	+	0.853268i	$0.325383\pi$
$752$	3.10768	0.113325
$753$	−1.42714	−0.0520080
$754$	0	0
$755$	−7.52781	−0.273965
$756$	12.9991	0.472774
$757$	−21.4521	−0.779689	−0.389844	−	0.920881i	$-0.627471\pi$
$757$	−21.4521	−0.779689	−0.389844	+	0.920881i	$0.627471\pi$
$758$	5.48680	0.199290
$759$	38.4059	1.39405
$760$	−15.0451	−0.545743
$761$	−21.4222	−0.776553	−0.388277	−	0.921543i	$-0.626929\pi$
$761$	−21.4222	−0.776553	−0.388277	+	0.921543i	$0.626929\pi$
$762$	−8.68585	−0.314655
$763$	48.4629	1.75447
$764$	−7.91209	−0.286249
$765$	−2.77488	−0.100326
$766$	37.8989	1.36934
$767$	−27.3028	−0.985846
$768$	−22.1337	−0.798679
$769$	−22.7152	−0.819130	−0.409565	−	0.912281i	$-0.634320\pi$
$769$	−22.7152	−0.819130	−0.409565	+	0.912281i	$0.634320\pi$
$770$	35.8101	1.29051
$771$	−28.6450	−1.03163
$772$	49.7168	1.78935
$773$	−0.180228	−0.00648235	−0.00324118	−	0.999995i	$-0.501032\pi$
$773$	−0.180228	−0.00648235	−0.00324118	+	0.999995i	$0.501032\pi$
$774$	−3.78965	−0.136216
$775$	−5.74266	−0.206282
$776$	32.4066	1.16333
$777$	21.4675	0.770144
$778$	5.00639	0.179488
$779$	5.91989	0.212102
$780$	−30.4031	−1.08861
$781$	35.6219	1.27465
$782$	−55.1447	−1.97197
$783$	0	0
$784$	5.62369	0.200846
$785$	27.7100	0.989013
$786$	−22.5032	−0.802664
$787$	44.4923	1.58598	0.792989	−	0.609236i	$-0.208524\pi$
$787$	44.4923	1.58598	0.792989	+	0.609236i	$0.208524\pi$
$788$	−56.9513	−2.02880
$789$	18.5023	0.658700
$790$	24.1821	0.860362
$791$	21.9318	0.779803
$792$	−30.4421	−1.08171
$793$	8.75387	0.310859
$794$	−77.7076	−2.75774
$795$	1.87850	0.0666236
$796$	23.4851	0.832409
$797$	−2.28072	−0.0807872	−0.0403936	−	0.999184i	$-0.512861\pi$
$797$	−2.28072	−0.0807872	−0.0403936	+	0.999184i	$0.512861\pi$
$798$	13.4069	0.474600
$799$	0.863060	0.0305329
$800$	−31.3849	−1.10962
$801$	−1.99621	−0.0705325
$802$	40.6630	1.43586
$803$	−49.5446	−1.74839
$804$	−45.4550	−1.60308
$805$	28.0238	0.987708
$806$	22.7395	0.800964
$807$	−28.7074	−1.01055
$808$	−13.2773	−0.467094
$809$	11.4774	0.403523	0.201761	−	0.979435i	$-0.435333\pi$
$809$	11.4774	0.403523	0.201761	+	0.979435i	$0.435333\pi$
$810$	−2.97416	−0.104501
$811$	27.4524	0.963985	0.481993	−	0.876175i	$-0.339913\pi$
$811$	27.4524	0.963985	0.481993	+	0.876175i	$0.339913\pi$
$812$	0	0
$813$	1.80441	0.0632834
$814$	−87.5019	−3.06694
$815$	−18.5478	−0.649701
$816$	21.0033	0.735262
$817$	−2.74196	−0.0959290
$818$	−12.6121	−0.440971
$819$	15.5660	0.543921
$820$	−17.0711	−0.596150
$821$	−25.1785	−0.878734	−0.439367	−	0.898308i	$-0.644797\pi$
$821$	−25.1785	−0.878734	−0.439367	+	0.898308i	$0.644797\pi$
$822$	8.34518	0.291072
$823$	2.12913	0.0742169	0.0371085	−	0.999311i	$-0.488185\pi$
$823$	2.12913	0.0742169	0.0371085	+	0.999311i	$0.488185\pi$
$824$	−57.4785	−2.00236
$825$	16.0231	0.557852
$826$	−34.7190	−1.20803
$827$	−18.3427	−0.637837	−0.318918	−	0.947782i	$-0.603320\pi$
$827$	−18.3427	−0.637837	−0.318918	+	0.947782i	$0.603320\pi$
$828$	−41.4639	−1.44097
$829$	52.9373	1.83859	0.919295	−	0.393570i	$-0.128760\pi$
$829$	52.9373	1.83859	0.919295	+	0.393570i	$0.128760\pi$
$830$	1.43305	0.0497419
$831$	−14.1949	−0.492416
$832$	26.3694	0.914194
$833$	1.56180	0.0541133
$834$	−58.2136	−2.01577
$835$	6.22778	0.215521
$836$	−38.3364	−1.32589
$837$	1.56053	0.0539400
$838$	49.2175	1.70019
$839$	−26.8505	−0.926984	−0.463492	−	0.886101i	$-0.653404\pi$
$839$	−26.8505	−0.926984	−0.463492	+	0.886101i	$0.653404\pi$
$840$	−22.2128	−0.766415
$841$	0	0
$842$	32.4018	1.11664
$843$	18.8216	0.648249
$844$	−90.3075	−3.10851
$845$	−21.4705	−0.738607
$846$	0.925040	0.0318035
$847$	22.0083	0.756213
$848$	−14.2185	−0.488266
$849$	21.8832	0.751028
$850$	−23.0065	−0.789118
$851$	−68.4760	−2.34733
$852$	−38.4582	−1.31756
$853$	39.8554	1.36462	0.682311	−	0.731062i	$-0.260975\pi$
$853$	39.8554	1.36462	0.682311	+	0.731062i	$0.260975\pi$
$854$	11.1317	0.380918
$855$	−2.15192	−0.0735941
$856$	31.1665	1.06525
$857$	50.9827	1.74154	0.870768	−	0.491694i	$-0.163622\pi$
$857$	50.9827	1.74154	0.870768	+	0.491694i	$0.163622\pi$
$858$	−63.4473	−2.16606
$859$	14.8714	0.507404	0.253702	−	0.967282i	$-0.418352\pi$
$859$	14.8714	0.507404	0.253702	+	0.967282i	$0.418352\pi$
$860$	7.90696	0.269625
$861$	8.74022	0.297866
$862$	91.6288	3.12089
$863$	−20.4603	−0.696478	−0.348239	−	0.937406i	$-0.613220\pi$
$863$	−20.4603	−0.696478	−0.348239	+	0.937406i	$0.613220\pi$
$864$	8.52865	0.290151
$865$	12.9742	0.441136
$866$	15.1561	0.515026
$867$	−11.1670	−0.379251
$868$	20.2856	0.688538
$869$	35.4027	1.20096
$870$	0	0
$871$	−54.4309	−1.84432
$872$	122.530	4.14939
$873$	4.63516	0.156876
$874$	−42.7647	−1.44654
$875$	27.5772	0.932280
$876$	53.4895	1.80724
$877$	−15.4211	−0.520732	−0.260366	−	0.965510i	$-0.583843\pi$
$877$	−15.4211	−0.520732	−0.260366	+	0.965510i	$0.583843\pi$
$878$	64.2744	2.16916
$879$	0.00776592	0.000261938 0
$880$	43.5056	1.46657
$881$	55.0390	1.85431	0.927155	−	0.374678i	$-0.122247\pi$
$881$	55.0390	1.85431	0.927155	+	0.374678i	$0.122247\pi$
$882$	1.67396	0.0563652
$883$	37.9954	1.27865	0.639324	−	0.768938i	$-0.279214\pi$
$883$	37.9954	1.27865	0.639324	+	0.768938i	$0.279214\pi$
$884$	63.9096	2.14951
$885$	5.57267	0.187323
$886$	61.4762	2.06533
$887$	18.2699	0.613444	0.306722	−	0.951799i	$-0.400768\pi$
$887$	18.2699	0.613444	0.306722	+	0.951799i	$0.400768\pi$
$888$	54.2769	1.82141
$889$	−9.27861	−0.311195
$890$	5.93703	0.199010
$891$	−4.35418	−0.145870
$892$	−99.8661	−3.34376
$893$	0.669303	0.0223974
$894$	3.33758	0.111625
$895$	12.2409	0.409169
$896$	−13.6359	−0.455543
$897$	−49.6517	−1.65782
$898$	16.6927	0.557043
$899$	0	0
$900$	−17.2989	−0.576629
$901$	−3.94875	−0.131552
$902$	−35.6252	−1.18619
$903$	−4.04827	−0.134718
$904$	55.4506	1.84426
$905$	14.1244	0.469512
$906$	16.9604	0.563472
$907$	25.2735	0.839192	0.419596	−	0.907711i	$-0.362172\pi$
$907$	25.2735	0.839192	0.419596	+	0.907711i	$0.362172\pi$
$908$	92.8701	3.08200
$909$	−1.89907	−0.0629882
$910$	−46.2958	−1.53469
$911$	34.3336	1.13752	0.568762	−	0.822502i	$-0.307422\pi$
$911$	34.3336	1.13752	0.568762	+	0.822502i	$0.307422\pi$
$912$	16.2880	0.539351
$913$	2.09799	0.0694334
$914$	−6.79686	−0.224820
$915$	−1.78672	−0.0590671
$916$	97.3731	3.21730
$917$	−24.0390	−0.793836
$918$	6.25190	0.206343
$919$	−26.8764	−0.886572	−0.443286	−	0.896380i	$-0.646187\pi$
$919$	−26.8764	−0.886572	−0.443286	+	0.896380i	$0.646187\pi$
$920$	70.8532	2.33596
$921$	0.214941	0.00708256
$922$	−18.5291	−0.610222
$923$	−46.0524	−1.51583
$924$	−56.6005	−1.86202
$925$	−28.5684	−0.939323
$926$	−47.2190	−1.55171
$927$	−8.22122	−0.270020
$928$	0	0
$929$	−27.4218	−0.899679	−0.449839	−	0.893109i	$-0.648519\pi$
$929$	−27.4218	−0.899679	−0.449839	+	0.893109i	$0.648519\pi$
$930$	−4.64127	−0.152193
$931$	1.21118	0.0396947
$932$	97.6582	3.19890
$933$	28.2266	0.924097
$934$	91.8118	3.00417
$935$	12.0823	0.395134
$936$	39.3560	1.28639
$937$	−10.3107	−0.336836	−0.168418	−	0.985716i	$-0.553866\pi$
$937$	−10.3107	−0.336836	−0.168418	+	0.985716i	$0.553866\pi$
$938$	−69.2158	−2.25998
$939$	−10.2302	−0.333849
$940$	−1.93006	−0.0629517
$941$	16.9225	0.551657	0.275828	−	0.961207i	$-0.411048\pi$
$941$	16.9225	0.551657	0.275828	+	0.961207i	$0.411048\pi$
$942$	−62.4316	−2.03413
$943$	−27.8791	−0.907867
$944$	−42.1800	−1.37284
$945$	−3.17713	−0.103352
$946$	16.5008	0.536487
$947$	−21.2231	−0.689659	−0.344829	−	0.938665i	$-0.612063\pi$
$947$	−21.2231	−0.689659	−0.344829	+	0.938665i	$0.612063\pi$
$948$	−38.2216	−1.24138
$949$	64.0519	2.07921
$950$	−17.8416	−0.578857
$951$	23.7789	0.771082
$952$	46.6929	1.51333
$953$	−8.78444	−0.284556	−0.142278	−	0.989827i	$-0.545443\pi$
$953$	−8.78444	−0.284556	−0.142278	+	0.989827i	$0.545443\pi$
$954$	−4.23233	−0.137027
$955$	1.93380	0.0625763
$956$	−10.6936	−0.345856
$957$	0	0
$958$	67.5637	2.18288
$959$	8.91469	0.287870
$960$	−5.38216	−0.173708
$961$	−28.5647	−0.921443
$962$	113.124	3.64725
$963$	4.45778	0.143650
$964$	55.3682	1.78329
$965$	−12.1513	−0.391165
$966$	−63.1384	−2.03145
$967$	−25.9334	−0.833961	−0.416981	−	0.908915i	$-0.636912\pi$
$967$	−25.9334	−0.833961	−0.416981	+	0.908915i	$0.636912\pi$
$968$	55.6441	1.78847
$969$	4.52349	0.145316
$970$	−13.7857	−0.442632
$971$	−58.1391	−1.86577	−0.932886	−	0.360172i	$-0.882718\pi$
$971$	−58.1391	−1.86577	−0.932886	+	0.360172i	$0.882718\pi$
$972$	4.70087	0.150780
$973$	−62.1863	−1.99360
$974$	57.3357	1.83715
$975$	−20.7148	−0.663406
$976$	13.5238	0.432887
$977$	29.9259	0.957414	0.478707	−	0.877975i	$-0.341106\pi$
$977$	29.9259	0.957414	0.478707	+	0.877975i	$0.341106\pi$
$978$	41.7888	1.33626
$979$	8.69184	0.277792
$980$	−3.49266	−0.111569
$981$	17.5256	0.559549
$982$	−30.4117	−0.970475
$983$	−40.2091	−1.28247	−0.641236	−	0.767344i	$-0.721578\pi$
$983$	−40.2091	−1.28247	−0.641236	+	0.767344i	$0.721578\pi$
$984$	22.0981	0.704462
$985$	13.9195	0.443512
$986$	0	0
$987$	0.988168	0.0314537
$988$	49.5619	1.57677
$989$	12.9129	0.410608
$990$	12.9500	0.411578
$991$	39.1707	1.24430	0.622149	−	0.782898i	$-0.286260\pi$
$991$	39.1707	1.24430	0.622149	+	0.782898i	$0.286260\pi$
$992$	13.3093	0.422569
$993$	−7.07856	−0.224631
$994$	−58.5615	−1.85746
$995$	−5.74002	−0.181971
$996$	−2.26504	−0.0717706
$997$	34.4756	1.09185	0.545927	−	0.837833i	$-0.316177\pi$
$997$	34.4756	1.09185	0.545927	+	0.837833i	$0.316177\pi$
$998$	−42.3892	−1.34181
$999$	7.76330	0.245620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.r.1.8		9
3.2	odd	2		7569.2.a.bj.1.2		9
29.16	even	7		87.2.g.a.82.3	yes	18
29.20	even	7		87.2.g.a.52.3	✓	18
29.28	even	2		2523.2.a.o.1.2		9
87.20	odd	14		261.2.k.c.226.1		18
87.74	odd	14		261.2.k.c.82.1		18
87.86	odd	2		7569.2.a.bm.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.52.3	✓	18	29.20	even	7
87.2.g.a.82.3	yes	18	29.16	even	7
261.2.k.c.82.1		18	87.74	odd	14
261.2.k.c.226.1		18	87.20	odd	14
2523.2.a.o.1.2		9	29.28	even	2
2523.2.a.r.1.8		9	1.1	even	1	trivial
7569.2.a.bj.1.2		9	3.2	odd	2
7569.2.a.bm.1.8		9	87.86	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q+2.58860 q^{2} +1.00000 q^{3} +4.70087 q^{4} -1.14894 q^{5} +2.58860 q^{6} +2.76526 q^{7} +6.99148 q^{8} +1.00000 q^{9} -2.97416 q^{10} -4.35418 q^{11} +4.70087 q^{12} +5.62914 q^{13} +7.15816 q^{14} -1.14894 q^{15} +8.69643 q^{16} +2.41516 q^{17} +2.58860 q^{18} +1.87296 q^{19} -5.40103 q^{20} +2.76526 q^{21} -11.2712 q^{22} -8.82048 q^{23} +6.99148 q^{24} -3.67993 q^{25} +14.5716 q^{26} +1.00000 q^{27} +12.9991 q^{28} -2.97416 q^{30} +1.56053 q^{31} +8.52865 q^{32} -4.35418 q^{33} +6.25190 q^{34} -3.17713 q^{35} +4.70087 q^{36} +7.76330 q^{37} +4.84834 q^{38} +5.62914 q^{39} -8.03281 q^{40} +3.16072 q^{41} +7.15816 q^{42} -1.46397 q^{43} -20.4684 q^{44} -1.14894 q^{45} -22.8327 q^{46} +0.357351 q^{47} +8.69643 q^{48} +0.646666 q^{49} -9.52588 q^{50} +2.41516 q^{51} +26.4618 q^{52} -1.63498 q^{53} +2.58860 q^{54} +5.00270 q^{55} +19.3333 q^{56} +1.87296 q^{57} -4.85026 q^{59} -5.40103 q^{60} +1.55510 q^{61} +4.03961 q^{62} +2.76526 q^{63} +4.68444 q^{64} -6.46755 q^{65} -11.2712 q^{66} -9.66950 q^{67} +11.3534 q^{68} -8.82048 q^{69} -8.22432 q^{70} -8.18108 q^{71} +6.99148 q^{72} +11.3786 q^{73} +20.0961 q^{74} -3.67993 q^{75} +8.80452 q^{76} -12.0404 q^{77} +14.5716 q^{78} -8.13075 q^{79} -9.99170 q^{80} +1.00000 q^{81} +8.18185 q^{82} -0.481835 q^{83} +12.9991 q^{84} -2.77488 q^{85} -3.78965 q^{86} -30.4421 q^{88} -1.99621 q^{89} -2.97416 q^{90} +15.5660 q^{91} -41.4639 q^{92} +1.56053 q^{93} +0.925040 q^{94} -2.15192 q^{95} +8.52865 q^{96} +4.63516 q^{97} +1.67396 q^{98} -4.35418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - q^99

Introduction

L-functions

Modular forms

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Database

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