LMFDB - Embedded newform 1075.2.b.j.474.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1075,2,Mod(474,1075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1075, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1075.474");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1075 = 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1075.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$8.58391821729$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 23x^{10} + 205x^{8} + 890x^{6} + 1942x^{4} + 1980x^{2} + 729 $ x^12 + 23x^10 + 205x^8 + 890x^6 + 1942x^4 + 1980*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			474.3
Root			$-2.22264i$ of defining polynomial
Character	$\chi$	$=$	1075.474
Dual form			1075.2.b.j.474.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22264i q^{2} +2.75173i q^{3} -2.94015 q^{4} +6.11612 q^{6} -1.28250i q^{7} +2.08961i q^{8} -4.57203 q^{9} +O(q^{10})$	\(q-2.22264i q^{2} +2.75173i q^{3} -2.94015 q^{4} +6.11612 q^{6} -1.28250i q^{7} +2.08961i q^{8} -4.57203 q^{9} +0.693556 q^{11} -8.09050i q^{12} -4.64521i q^{13} -2.85053 q^{14} -1.23583 q^{16} +1.40938i q^{17} +10.1620i q^{18} +3.40938 q^{19} +3.52909 q^{21} -1.54153i q^{22} -3.45400i q^{23} -5.75006 q^{24} -10.3247 q^{26} -4.32581i q^{27} +3.77073i q^{28} +1.86953 q^{29} -4.95166 q^{31} +6.92603i q^{32} +1.90848i q^{33} +3.13256 q^{34} +13.4425 q^{36} -11.0438i q^{37} -7.57785i q^{38} +12.7824 q^{39} +7.25520 q^{41} -7.84391i q^{42} -1.00000i q^{43} -2.03916 q^{44} -7.67702 q^{46} -13.1468i q^{47} -3.40067i q^{48} +5.35520 q^{49} -3.87825 q^{51} +13.6576i q^{52} -6.42885i q^{53} -9.61475 q^{54} +2.67992 q^{56} +9.38171i q^{57} -4.15530i q^{58} -0.115236 q^{59} +13.8835 q^{61} +11.0058i q^{62} +5.86362i q^{63} +12.9225 q^{64} +4.24187 q^{66} -9.51474i q^{67} -4.14379i q^{68} +9.50449 q^{69} -0.745588 q^{71} -9.55378i q^{72} +4.37747i q^{73} -24.5465 q^{74} -10.0241 q^{76} -0.889483i q^{77} -28.4107i q^{78} -17.3421 q^{79} -1.81261 q^{81} -16.1257i q^{82} -10.8096i q^{83} -10.3760 q^{84} -2.22264 q^{86} +5.14445i q^{87} +1.44926i q^{88} -1.62510 q^{89} -5.95747 q^{91} +10.1553i q^{92} -13.6256i q^{93} -29.2206 q^{94} -19.0586 q^{96} +8.69891i q^{97} -11.9027i q^{98} -3.17096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{4} + 22 q^{6} - 24 q^{9}+O(q^{10}) $ 12 * q - 22 * q^4 + 22 * q^6 - 24 * q^9	$ 12 q - 22 q^{4} + 22 q^{6} - 24 q^{9} - 12 q^{11} - 34 q^{14} + 10 q^{16} + 10 q^{19} + 38 q^{21} - 18 q^{24} + 28 q^{26} - 36 q^{29} - 24 q^{31} - 2 q^{34} - 20 q^{36} + 6 q^{39} - 18 q^{44} - 28 q^{46} - 2 q^{51} - 24 q^{54} + 40 q^{56} - 42 q^{59} - 16 q^{61} - 12 q^{64} + 2 q^{66} - 74 q^{69} + 28 q^{71} - 4 q^{74} - 114 q^{76} + 62 q^{79} + 124 q^{81} - 42 q^{84} - 2 q^{86} - 80 q^{89} + 22 q^{91} - 70 q^{94} - 100 q^{96} + 106 q^{99}+O(q^{100}) $ 12 * q - 22 * q^4 + 22 * q^6 - 24 * q^9 - 12 * q^11 - 34 * q^14 + 10 * q^16 + 10 * q^19 + 38 * q^21 - 18 * q^24 + 28 * q^26 - 36 * q^29 - 24 * q^31 - 2 * q^34 - 20 * q^36 + 6 * q^39 - 18 * q^44 - 28 * q^46 - 2 * q^51 - 24 * q^54 + 40 * q^56 - 42 * q^59 - 16 * q^61 - 12 * q^64 + 2 * q^66 - 74 * q^69 + 28 * q^71 - 4 * q^74 - 114 * q^76 + 62 * q^79 + 124 * q^81 - 42 * q^84 - 2 * q^86 - 80 * q^89 + 22 * q^91 - 70 * q^94 - 100 * q^96 + 106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1075\mathbb{Z}\right)^\times$.

$n$	$302$	$476$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 2.22264i	− 1.57165i	−0.618451	−	0.785823i	$-0.712239\pi$
$2$	− 2.22264i	− 1.57165i	0.618451	−	0.785823i	$-0.287761\pi$
$3$	2.75173i	1.58871i	0.607451	+	0.794357i	$0.292192\pi$
$3$	2.75173i	1.58871i	−0.607451	+	0.794357i	$0.707808\pi$
$4$	−2.94015	−1.47007
$5$	0	0
$5$	0	0
$6$	6.11612	2.49690
$7$	− 1.28250i	− 0.484738i	−0.970184	−	0.242369i	$-0.922076\pi$
$7$	− 1.28250i	− 0.484738i	0.970184	−	0.242369i	$-0.0779245\pi$
$8$	2.08961i	0.738790i
$9$	−4.57203	−1.52401
$10$	0	0
$11$	0.693556	0.209115	0.104557	−	0.994519i	$-0.466657\pi$
$11$	0.693556	0.209115	0.104557	+	0.994519i	$0.466657\pi$
$12$	− 8.09050i	− 2.33553i
$13$	− 4.64521i	− 1.28835i	−0.764878	−	0.644175i	$-0.777201\pi$
$13$	− 4.64521i	− 1.28835i	0.764878	−	0.644175i	$-0.222799\pi$
$14$	−2.85053	−0.761837
$15$	0	0
$16$	−1.23583	−0.308957
$17$	1.40938i	0.341826i	0.985286	+	0.170913i	$0.0546717\pi$
$17$	1.40938i	0.341826i	−0.985286	+	0.170913i	$0.945328\pi$
$18$	10.1620i	2.39521i
$19$	3.40938	0.782166	0.391083	−	0.920355i	$-0.372101\pi$
$19$	3.40938	0.782166	0.391083	+	0.920355i	$0.372101\pi$
$20$	0	0
$21$	3.52909	0.770110
$22$	− 1.54153i	− 0.328655i
$23$	− 3.45400i	− 0.720209i	−0.932912	−	0.360105i	$-0.882741\pi$
$23$	− 3.45400i	− 0.720209i	0.932912	−	0.360105i	$-0.117259\pi$
$24$	−5.75006	−1.17373
$25$	0	0
$26$	−10.3247	−2.02483
$27$	− 4.32581i	− 0.832503i
$28$	3.77073i	0.712601i
$29$	1.86953	0.347163	0.173582	−	0.984819i	$-0.444466\pi$
$29$	1.86953	0.347163	0.173582	+	0.984819i	$0.444466\pi$
$30$	0	0
$31$	−4.95166	−0.889344	−0.444672	−	0.895694i	$-0.646680\pi$
$31$	−4.95166	−0.889344	−0.444672	+	0.895694i	$0.646680\pi$
$32$	6.92603i	1.22436i
$33$	1.90848i	0.332224i
$34$	3.13256	0.537229
$35$	0	0
$36$	13.4425	2.24041
$37$	− 11.0438i	− 1.81559i	−0.419409	−	0.907797i	$-0.637763\pi$
$37$	− 11.0438i	− 1.81559i	0.419409	−	0.907797i	$-0.362237\pi$
$38$	− 7.57785i	− 1.22929i
$39$	12.7824	2.04682
$40$	0	0
$41$	7.25520	1.13307	0.566536	−	0.824037i	$-0.308283\pi$
$41$	7.25520	1.13307	0.566536	+	0.824037i	$0.308283\pi$
$42$	− 7.84391i	− 1.21034i
$43$	− 1.00000i	− 0.152499i
$43$	− 1.00000i	− 0.152499i
$44$	−2.03916	−0.307414
$45$	0	0
$46$	−7.67702	−1.13191
$47$	− 13.1468i	− 1.91765i	−0.283992	−	0.958827i	$-0.591659\pi$
$47$	− 13.1468i	− 1.91765i	0.283992	−	0.958827i	$-0.408341\pi$
$48$	− 3.40067i	− 0.490844i
$49$	5.35520	0.765029
$50$	0	0
$51$	−3.87825	−0.543063
$52$	13.6576i	1.89397i
$53$	− 6.42885i	− 0.883071i	−0.897244	−	0.441535i	$-0.854434\pi$
$53$	− 6.42885i	− 0.883071i	0.897244	−	0.441535i	$-0.145566\pi$
$54$	−9.61475	−1.30840
$55$	0	0
$56$	2.67992	0.358120
$57$	9.38171i	1.24264i
$58$	− 4.15530i	− 0.545618i
$59$	−0.115236	−0.0150025	−0.00750124	−	0.999972i	$-0.502388\pi$
$59$	−0.115236	−0.0150025	−0.00750124	+	0.999972i	$0.502388\pi$
$60$	0	0
$61$	13.8835	1.77760	0.888800	−	0.458295i	$-0.151540\pi$
$61$	13.8835	1.77760	0.888800	+	0.458295i	$0.151540\pi$
$62$	11.0058i	1.39773i
$63$	5.86362i	0.738746i
$64$	12.9225	1.61531
$65$	0	0
$66$	4.24187	0.522138
$67$	− 9.51474i	− 1.16241i	−0.813757	−	0.581205i	$-0.802581\pi$
$67$	− 9.51474i	− 1.16241i	0.813757	−	0.581205i	$-0.197419\pi$
$68$	− 4.14379i	− 0.502509i
$69$	9.50449	1.14421
$70$	0	0
$71$	−0.745588	−0.0884850	−0.0442425	−	0.999021i	$-0.514087\pi$
$71$	−0.745588	−0.0884850	−0.0442425	+	0.999021i	$0.514087\pi$
$72$	− 9.55378i	− 1.12592i
$73$	4.37747i	0.512345i	0.966631	+	0.256172i	$0.0824614\pi$
$73$	4.37747i	0.512345i	−0.966631	+	0.256172i	$0.917539\pi$
$74$	−24.5465	−2.85347
$75$	0	0
$76$	−10.0241	−1.14984
$77$	− 0.889483i	− 0.101366i
$78$	− 28.4107i	− 3.21688i
$79$	−17.3421	−1.95114	−0.975570	−	0.219688i	$-0.929496\pi$
$79$	−17.3421	−1.95114	−0.975570	+	0.219688i	$0.929496\pi$
$80$	0	0
$81$	−1.81261	−0.201402
$82$	− 16.1257i	− 1.78079i
$83$	− 10.8096i	− 1.18651i	−0.805016	−	0.593253i	$-0.797844\pi$
$83$	− 10.8096i	− 1.18651i	0.805016	−	0.593253i	$-0.202156\pi$
$84$	−10.3760	−1.13212
$85$	0	0
$86$	−2.22264	−0.239674
$87$	5.14445i	0.551543i
$88$	1.44926i	0.154492i
$89$	−1.62510	−0.172260	−0.0861300	−	0.996284i	$-0.527450\pi$
$89$	−1.62510	−0.172260	−0.0861300	+	0.996284i	$0.527450\pi$
$90$	0	0
$91$	−5.95747	−0.624512
$92$	10.1553i	1.05876i
$93$	− 13.6256i	− 1.41291i
$94$	−29.2206	−3.01387
$95$	0	0
$96$	−19.0586	−1.94516
$97$	8.69891i	0.883241i	0.897202	+	0.441620i	$0.145596\pi$
$97$	8.69891i	0.883241i	−0.897202	+	0.441620i	$0.854404\pi$
$98$	− 11.9027i	− 1.20236i
$99$	−3.17096	−0.318693
$100$	0	0
$101$	14.0265	1.39569	0.697845	−	0.716249i	$-0.254142\pi$
$101$	14.0265	1.39569	0.697845	+	0.716249i	$0.254142\pi$
$102$	8.61996i	0.853503i
$103$	7.40859i	0.729990i	0.931009	+	0.364995i	$0.118929\pi$
$103$	7.40859i	0.729990i	−0.931009	+	0.364995i	$0.881071\pi$
$104$	9.70669	0.951820
$105$	0	0
$106$	−14.2891	−1.38788
$107$	13.5123i	1.30629i	0.757235	+	0.653143i	$0.226550\pi$
$107$	13.5123i	1.30629i	−0.757235	+	0.653143i	$0.773450\pi$
$108$	12.7185i	1.22384i
$109$	0.548567	0.0525432	0.0262716	−	0.999655i	$-0.491637\pi$
$109$	0.548567	0.0525432	0.0262716	+	0.999655i	$0.491637\pi$
$110$	0	0
$111$	30.3897	2.88446
$112$	1.58495i	0.149763i
$113$	− 8.15217i	− 0.766892i	−0.923563	−	0.383446i	$-0.874737\pi$
$113$	− 8.15217i	− 0.766892i	0.923563	−	0.383446i	$-0.125263\pi$
$114$	20.8522	1.95299
$115$	0	0
$116$	−5.49670	−0.510356
$117$	21.2381i	1.96346i
$118$	0.256129i	0.0235786i
$119$	1.80753	0.165696
$120$	0	0
$121$	−10.5190	−0.956271
$122$	− 30.8581i	− 2.79376i
$123$	19.9644i	1.80013i
$124$	14.5586	1.30740
$125$	0	0
$126$	13.0327	1.16105
$127$	16.8976i	1.49942i	0.661766	+	0.749710i	$0.269807\pi$
$127$	16.8976i	1.49942i	−0.661766	+	0.749710i	$0.730193\pi$
$128$	− 14.8699i	− 1.31433i
$129$	2.75173	0.242277
$130$	0	0
$131$	4.21818	0.368544	0.184272	−	0.982875i	$-0.441007\pi$
$131$	4.21818	0.368544	0.184272	+	0.982875i	$0.441007\pi$
$132$	− 5.61121i	− 0.488393i
$133$	− 4.37252i	− 0.379146i
$134$	−21.1479	−1.82690
$135$	0	0
$136$	−2.94507	−0.252537
$137$	7.91281i	0.676037i	0.941140	+	0.338018i	$0.109757\pi$
$137$	7.91281i	0.676037i	−0.941140	+	0.338018i	$0.890243\pi$
$138$	− 21.1251i	− 1.79829i
$139$	4.17765	0.354344	0.177172	−	0.984180i	$-0.443305\pi$
$139$	4.17765	0.354344	0.177172	+	0.984180i	$0.443305\pi$
$140$	0	0
$141$	36.1764	3.04660
$142$	1.65718i	0.139067i
$143$	− 3.22171i	− 0.269413i
$144$	5.65025	0.470854
$145$	0	0
$146$	9.72957	0.805225
$147$	14.7361i	1.21541i
$148$	32.4705i	2.66906i
$149$	−2.40576	−0.197087	−0.0985437	−	0.995133i	$-0.531418\pi$
$149$	−2.40576	−0.197087	−0.0985437	+	0.995133i	$0.531418\pi$
$150$	0	0
$151$	−4.95459	−0.403199	−0.201599	−	0.979468i	$-0.564614\pi$
$151$	−4.95459	−0.403199	−0.201599	+	0.979468i	$0.564614\pi$
$152$	7.12429i	0.577856i
$153$	− 6.44375i	− 0.520946i
$154$	−1.97700	−0.159312
$155$	0	0
$156$	−37.5821	−3.00897
$157$	22.3846i	1.78649i	0.449571	+	0.893245i	$0.351577\pi$
$157$	22.3846i	1.78649i	−0.449571	+	0.893245i	$0.648423\pi$
$158$	38.5454i	3.06650i
$159$	17.6905	1.40295
$160$	0	0
$161$	−4.42975	−0.349113
$162$	4.02880i	0.316532i
$163$	9.96144i	0.780240i	0.920764	+	0.390120i	$0.127566\pi$
$163$	9.96144i	0.780240i	−0.920764	+	0.390120i	$0.872434\pi$
$164$	−21.3314	−1.66570
$165$	0	0
$166$	−24.0258	−1.86477
$167$	− 24.6610i	− 1.90833i	−0.299283	−	0.954164i	$-0.596748\pi$
$167$	− 24.6610i	− 1.90833i	0.299283	−	0.954164i	$-0.403252\pi$
$168$	7.37443i	0.568950i
$169$	−8.57799	−0.659845
$170$	0	0
$171$	−15.5878	−1.19203
$172$	2.94015i	0.224184i
$173$	8.89437i	0.676226i	0.941106	+	0.338113i	$0.109789\pi$
$173$	8.89437i	0.676226i	−0.941106	+	0.338113i	$0.890211\pi$
$174$	11.4343	0.866831
$175$	0	0
$176$	−0.857116	−0.0646075
$177$	− 0.317099i	− 0.0238347i
$178$	3.61201i	0.270732i
$179$	−5.14937	−0.384882	−0.192441	−	0.981309i	$-0.561640\pi$
$179$	−5.14937	−0.384882	−0.192441	+	0.981309i	$0.561640\pi$
$180$	0	0
$181$	−11.2822	−0.838598	−0.419299	−	0.907848i	$-0.637724\pi$
$181$	−11.2822	−0.838598	−0.419299	+	0.907848i	$0.637724\pi$
$182$	13.2413i	0.981513i
$183$	38.2037i	2.82410i
$184$	7.21753	0.532083
$185$	0	0
$186$	−30.2849	−2.22060
$187$	0.977486i	0.0714808i
$188$	38.6534i	2.81909i
$189$	−5.54784	−0.403546
$190$	0	0
$191$	6.40030	0.463109	0.231555	−	0.972822i	$-0.425619\pi$
$191$	6.40030	0.463109	0.231555	+	0.972822i	$0.425619\pi$
$192$	35.5591i	2.56626i
$193$	− 6.52294i	− 0.469532i	−0.972052	−	0.234766i	$-0.924568\pi$
$193$	− 6.52294i	− 0.469532i	0.972052	−	0.234766i	$-0.0754324\pi$
$194$	19.3346	1.38814
$195$	0	0
$196$	−15.7451	−1.12465
$197$	− 2.09409i	− 0.149198i	−0.997214	−	0.0745989i	$-0.976232\pi$
$197$	− 2.09409i	− 0.149198i	0.997214	−	0.0745989i	$-0.0237676\pi$
$198$	7.04792i	0.500874i
$199$	−13.5231	−0.958629	−0.479314	−	0.877643i	$-0.659115\pi$
$199$	−13.5231	−0.958629	−0.479314	+	0.877643i	$0.659115\pi$
$200$	0	0
$201$	26.1820	1.84674
$202$	− 31.1759i	− 2.19353i
$203$	− 2.39767i	− 0.168283i
$204$	11.4026	0.798343
$205$	0	0
$206$	16.4667	1.14729
$207$	15.7918i	1.09761i
$208$	5.74068i	0.398045i
$209$	2.36460	0.163563
$210$	0	0
$211$	−18.2501	−1.25639	−0.628196	−	0.778055i	$-0.716206\pi$
$211$	−18.2501	−1.25639	−0.628196	+	0.778055i	$0.716206\pi$
$212$	18.9018i	1.29818i
$213$	− 2.05166i	− 0.140577i
$214$	30.0331	2.05302
$215$	0	0
$216$	9.03928	0.615045
$217$	6.35048i	0.431099i
$218$	− 1.21927i	− 0.0825793i
$219$	−12.0456	−0.813969
$220$	0	0
$221$	6.54688	0.440391
$222$	− 67.5454i	− 4.53335i
$223$	− 5.41236i	− 0.362438i	−0.983443	−	0.181219i	$-0.941996\pi$
$223$	− 5.41236i	− 0.362438i	0.983443	−	0.181219i	$-0.0580043\pi$
$224$	8.88261	0.593495
$225$	0	0
$226$	−18.1194	−1.20528
$227$	6.82156i	0.452763i	0.974039	+	0.226381i	$0.0726896\pi$
$227$	6.82156i	0.452763i	−0.974039	+	0.226381i	$0.927310\pi$
$228$	− 27.5836i	− 1.82677i
$229$	−12.4920	−0.825492	−0.412746	−	0.910846i	$-0.635430\pi$
$229$	−12.4920	−0.825492	−0.412746	+	0.910846i	$0.635430\pi$
$230$	0	0
$231$	2.44762	0.161042
$232$	3.90660i	0.256481i
$233$	10.1763i	0.666669i	0.942809	+	0.333334i	$0.108174\pi$
$233$	10.1763i	0.666669i	−0.942809	+	0.333334i	$0.891826\pi$
$234$	47.2046	3.08586
$235$	0	0
$236$	0.338812	0.0220548
$237$	− 47.7209i	− 3.09980i
$238$	− 4.01750i	− 0.260416i
$239$	2.97578	0.192487	0.0962436	−	0.995358i	$-0.469317\pi$
$239$	2.97578	0.192487	0.0962436	+	0.995358i	$0.469317\pi$
$240$	0	0
$241$	3.40795	0.219525	0.109763	−	0.993958i	$-0.464991\pi$
$241$	3.40795	0.219525	0.109763	+	0.993958i	$0.464991\pi$
$242$	23.3800i	1.50292i
$243$	− 17.9653i	− 1.15247i
$244$	−40.8195	−2.61320
$245$	0	0
$246$	44.3737	2.82916
$247$	− 15.8373i	− 1.00770i
$248$	− 10.3470i	− 0.657038i
$249$	29.7451	1.88502
$250$	0	0
$251$	16.4879	1.04071	0.520354	−	0.853951i	$-0.325800\pi$
$251$	16.4879	1.04071	0.520354	+	0.853951i	$0.325800\pi$
$252$	− 17.2399i	− 1.08601i
$253$	− 2.39554i	− 0.150607i
$254$	37.5574	2.35656
$255$	0	0
$256$	−7.20570	−0.450356
$257$	5.59551i	0.349038i	0.984654	+	0.174519i	$0.0558371\pi$
$257$	5.59551i	0.349038i	−0.984654	+	0.174519i	$0.944163\pi$
$258$	− 6.11612i	− 0.380773i
$259$	−14.1637	−0.880088
$260$	0	0
$261$	−8.54756	−0.529081
$262$	− 9.37550i	− 0.579221i
$263$	− 17.2017i	− 1.06070i	−0.847778	−	0.530351i	$-0.822060\pi$
$263$	− 17.2017i	− 1.06070i	0.847778	−	0.530351i	$-0.177940\pi$
$264$	−3.98799	−0.245444
$265$	0	0
$266$	−9.71856	−0.595883
$267$	− 4.47183i	− 0.273672i
$268$	27.9747i	1.70883i
$269$	−30.0165	−1.83014	−0.915070	−	0.403294i	$-0.867865\pi$
$269$	−30.0165	−1.83014	−0.915070	+	0.403294i	$0.867865\pi$
$270$	0	0
$271$	−9.51143	−0.577778	−0.288889	−	0.957363i	$-0.593286\pi$
$271$	−9.51143	−0.577778	−0.288889	+	0.957363i	$0.593286\pi$
$272$	− 1.74176i	− 0.105609i
$273$	− 16.3934i	− 0.992171i
$274$	17.5874	1.06249
$275$	0	0
$276$	−27.9446	−1.68207
$277$	− 18.4915i	− 1.11105i	−0.831500	−	0.555524i	$-0.812518\pi$
$277$	− 18.4915i	− 1.11105i	0.831500	−	0.555524i	$-0.187482\pi$
$278$	− 9.28543i	− 0.556903i
$279$	22.6391	1.35537
$280$	0	0
$281$	24.5302	1.46335	0.731674	−	0.681654i	$-0.238739\pi$
$281$	24.5302	1.46335	0.731674	+	0.681654i	$0.238739\pi$
$282$	− 80.4073i	− 4.78818i
$283$	20.9654i	1.24626i	0.782117	+	0.623131i	$0.214140\pi$
$283$	20.9654i	1.24626i	−0.782117	+	0.623131i	$0.785860\pi$
$284$	2.19214	0.130080
$285$	0	0
$286$	−7.16072	−0.423422
$287$	− 9.30477i	− 0.549243i
$288$	− 31.6660i	− 1.86594i
$289$	15.0136	0.883155
$290$	0	0
$291$	−23.9371	−1.40322
$292$	− 12.8704i	− 0.753184i
$293$	− 30.2734i	− 1.76859i	−0.466927	−	0.884296i	$-0.654639\pi$
$293$	− 30.2734i	− 1.76859i	0.466927	−	0.884296i	$-0.345361\pi$
$294$	32.7531	1.91020
$295$	0	0
$296$	23.0773	1.34134
$297$	− 3.00019i	− 0.174089i
$298$	5.34715i	0.309752i
$299$	−16.0446	−0.927882
$300$	0	0
$301$	−1.28250	−0.0739219
$302$	11.0123i	0.633686i
$303$	38.5972i	2.21735i
$304$	−4.21341	−0.241656
$305$	0	0
$306$	−14.3222	−0.818743
$307$	30.2420i	1.72600i	0.505204	+	0.863000i	$0.331417\pi$
$307$	30.2420i	1.72600i	−0.505204	+	0.863000i	$0.668583\pi$
$308$	2.61521i	0.149015i
$309$	−20.3865	−1.15975
$310$	0	0
$311$	12.9367	0.733570	0.366785	−	0.930306i	$-0.380458\pi$
$311$	12.9367	0.733570	0.366785	+	0.930306i	$0.380458\pi$
$312$	26.7102i	1.51217i
$313$	5.52011i	0.312015i	0.987756	+	0.156007i	$0.0498624\pi$
$313$	5.52011i	0.312015i	−0.987756	+	0.156007i	$0.950138\pi$
$314$	49.7531	2.80773
$315$	0	0
$316$	50.9884	2.86832
$317$	− 9.80213i	− 0.550542i	−0.961367	−	0.275271i	$-0.911232\pi$
$317$	− 9.80213i	− 0.550542i	0.961367	−	0.275271i	$-0.0887677\pi$
$318$	− 39.3197i	− 2.20494i
$319$	1.29662	0.0725970
$320$	0	0
$321$	−37.1823	−2.07531
$322$	9.84575i	0.548682i
$323$	4.80513i	0.267364i
$324$	5.32935	0.296075
$325$	0	0
$326$	22.1407	1.22626
$327$	1.50951i	0.0834761i
$328$	15.1606i	0.837102i
$329$	−16.8607	−0.929560
$330$	0	0
$331$	21.8234	1.19952	0.599761	−	0.800179i	$-0.295262\pi$
$331$	21.8234	1.19952	0.599761	+	0.800179i	$0.295262\pi$
$332$	31.7818i	1.74425i
$333$	50.4928i	2.76699i
$334$	−54.8127	−2.99922
$335$	0	0
$336$	−4.36135	−0.237931
$337$	0.342893i	0.0186786i	0.999956	+	0.00933930i	$0.00297283\pi$
$337$	0.342893i	0.0186786i	−0.999956	+	0.00933930i	$0.997027\pi$
$338$	19.0658i	1.03704i
$339$	22.4326	1.21837
$340$	0	0
$341$	−3.43425	−0.185975
$342$	34.6462i	1.87345i
$343$	− 15.8455i	− 0.855577i
$344$	2.08961	0.112664
$345$	0	0
$346$	19.7690	1.06279
$347$	27.4280i	1.47241i	0.676757	+	0.736207i	$0.263385\pi$
$347$	27.4280i	1.47241i	−0.676757	+	0.736207i	$0.736615\pi$
$348$	− 15.1254i	− 0.810809i
$349$	12.6075	0.674864	0.337432	−	0.941350i	$-0.390442\pi$
$349$	12.6075	0.674864	0.337432	+	0.941350i	$0.390442\pi$
$350$	0	0
$351$	−20.0943	−1.07256
$352$	4.80359i	0.256032i
$353$	− 21.4021i	− 1.13912i	−0.821950	−	0.569559i	$-0.807114\pi$
$353$	− 21.4021i	− 1.13912i	0.821950	−	0.569559i	$-0.192886\pi$
$354$	−0.704799	−0.0374597
$355$	0	0
$356$	4.77802	0.253235
$357$	4.97384i	0.263243i
$358$	11.4452i	0.604898i
$359$	32.1457	1.69659	0.848294	−	0.529526i	$-0.177630\pi$
$359$	32.1457	1.69659	0.848294	+	0.529526i	$0.177630\pi$
$360$	0	0
$361$	−7.37611	−0.388216
$362$	25.0763i	1.31798i
$363$	− 28.9454i	− 1.51924i
$364$	17.5158	0.918079
$365$	0	0
$366$	84.9132	4.43848
$367$	30.9304i	1.61455i	0.590172	+	0.807277i	$0.299060\pi$
$367$	30.9304i	1.61455i	−0.590172	+	0.807277i	$0.700940\pi$
$368$	4.26855i	0.222514i
$369$	−33.1710	−1.72681
$370$	0	0
$371$	−8.24498	−0.428058
$372$	40.0614i	2.07709i
$373$	− 34.9509i	− 1.80969i	−0.425744	−	0.904844i	$-0.639988\pi$
$373$	− 34.9509i	− 1.80969i	0.425744	−	0.904844i	$-0.360012\pi$
$374$	2.17260	0.112343
$375$	0	0
$376$	27.4717	1.41674
$377$	− 8.68437i	− 0.447268i
$378$	12.3309i	0.634232i
$379$	−29.8762	−1.53464	−0.767319	−	0.641266i	$-0.778410\pi$
$379$	−29.8762	−1.53464	−0.767319	+	0.641266i	$0.778410\pi$
$380$	0	0
$381$	−46.4977	−2.38215
$382$	− 14.2256i	− 0.727844i
$383$	16.3808i	0.837021i	0.908212	+	0.418511i	$0.137448\pi$
$383$	16.3808i	0.837021i	−0.908212	+	0.418511i	$0.862552\pi$
$384$	40.9181	2.08809
$385$	0	0
$386$	−14.4982	−0.737938
$387$	4.57203i	0.232409i
$388$	− 25.5761i	− 1.29843i
$389$	6.66512	0.337935	0.168968	−	0.985622i	$-0.445957\pi$
$389$	6.66512	0.337935	0.168968	+	0.985622i	$0.445957\pi$
$390$	0	0
$391$	4.86801	0.246186
$392$	11.1903i	0.565196i
$393$	11.6073i	0.585510i
$394$	−4.65442	−0.234486
$395$	0	0
$396$	9.32309	0.468503
$397$	− 12.8793i	− 0.646392i	−0.946332	−	0.323196i	$-0.895243\pi$
$397$	− 12.8793i	− 0.646392i	0.946332	−	0.323196i	$-0.104757\pi$
$398$	30.0571i	1.50663i
$399$	12.0320	0.602354
$400$	0	0
$401$	0.182243	0.00910076	0.00455038	−	0.999990i	$-0.498552\pi$
$401$	0.182243	0.00910076	0.00455038	+	0.999990i	$0.498552\pi$
$402$	− 58.1933i	− 2.90242i
$403$	23.0015i	1.14579i
$404$	−41.2400	−2.05177
$405$	0	0
$406$	−5.32916	−0.264482
$407$	− 7.65951i	− 0.379668i
$408$	− 8.10403i	− 0.401209i
$409$	16.1153	0.796850	0.398425	−	0.917201i	$-0.369557\pi$
$409$	16.1153	0.796850	0.398425	+	0.917201i	$0.369557\pi$
$410$	0	0
$411$	−21.7739	−1.07403
$412$	− 21.7824i	− 1.07314i
$413$	0.147790i	0.00727228i
$414$	35.0996	1.72505
$415$	0	0
$416$	32.1729	1.57741
$417$	11.4958i	0.562951i
$418$	− 5.25566i	− 0.257063i
$419$	−9.46633	−0.462460	−0.231230	−	0.972899i	$-0.574275\pi$
$419$	−9.46633	−0.462460	−0.231230	+	0.972899i	$0.574275\pi$
$420$	0	0
$421$	21.4059	1.04326	0.521629	−	0.853172i	$-0.325325\pi$
$421$	21.4059	1.04326	0.521629	+	0.853172i	$0.325325\pi$
$422$	40.5636i	1.97460i
$423$	60.1075i	2.92252i
$424$	13.4338	0.652404
$425$	0	0
$426$	−4.56011	−0.220938
$427$	− 17.8055i	− 0.861671i
$428$	− 39.7282i	− 1.92034i
$429$	8.86529	0.428020
$430$	0	0
$431$	5.93385	0.285824	0.142912	−	0.989735i	$-0.454353\pi$
$431$	5.93385	0.285824	0.142912	+	0.989735i	$0.454353\pi$
$432$	5.34596i	0.257208i
$433$	− 19.3301i	− 0.928946i	−0.885587	−	0.464473i	$-0.846244\pi$
$433$	− 19.3301i	− 0.928946i	0.885587	−	0.464473i	$-0.153756\pi$
$434$	14.1149	0.677535
$435$	0	0
$436$	−1.61287	−0.0772424
$437$	− 11.7760i	− 0.563323i
$438$	26.7732i	1.27927i
$439$	−19.4454	−0.928079	−0.464039	−	0.885815i	$-0.653600\pi$
$439$	−19.4454	−0.928079	−0.464039	+	0.885815i	$0.653600\pi$
$440$	0	0
$441$	−24.4842	−1.16591
$442$	− 14.5514i	− 0.692139i
$443$	41.1661i	1.95586i	0.208928	+	0.977931i	$0.433003\pi$
$443$	41.1661i	1.95586i	−0.208928	+	0.977931i	$0.566997\pi$
$444$	−89.3501	−4.24037
$445$	0	0
$446$	−12.0297	−0.569625
$447$	− 6.62001i	− 0.313116i
$448$	− 16.5730i	− 0.783001i
$449$	6.96894	0.328884	0.164442	−	0.986387i	$-0.447418\pi$
$449$	6.96894	0.328884	0.164442	+	0.986387i	$0.447418\pi$
$450$	0	0
$451$	5.03188	0.236942
$452$	23.9686i	1.12739i
$453$	− 13.6337i	− 0.640568i
$454$	15.1619	0.711583
$455$	0	0
$456$	−19.6041	−0.918048
$457$	27.5917i	1.29069i	0.763893	+	0.645343i	$0.223285\pi$
$457$	27.5917i	1.29069i	−0.763893	+	0.645343i	$0.776715\pi$
$458$	27.7652i	1.29738i
$459$	6.09673	0.284571
$460$	0	0
$461$	0.124899	0.00581714	0.00290857	−	0.999996i	$-0.499074\pi$
$461$	0.124899	0.00581714	0.00290857	+	0.999996i	$0.499074\pi$
$462$	− 5.44019i	− 0.253100i
$463$	18.2120i	0.846383i	0.906040	+	0.423192i	$0.139090\pi$
$463$	18.2120i	0.846383i	−0.906040	+	0.423192i	$0.860910\pi$
$464$	−2.31042	−0.107259
$465$	0	0
$466$	22.6182	1.04777
$467$	− 9.04241i	− 0.418433i	−0.977869	−	0.209216i	$-0.932909\pi$
$467$	− 9.04241i	− 0.418433i	0.977869	−	0.209216i	$-0.0670913\pi$
$468$	− 62.4430i	− 2.88643i
$469$	−12.2026	−0.563465
$470$	0	0
$471$	−61.5966	−2.83822
$472$	− 0.240799i	− 0.0110837i
$473$	− 0.693556i	− 0.0318897i
$474$	−106.067	−4.87180
$475$	0	0
$476$	−5.31440	−0.243585
$477$	29.3929i	1.34581i
$478$	− 6.61410i	− 0.302522i
$479$	20.7568	0.948404	0.474202	−	0.880416i	$-0.342737\pi$
$479$	20.7568	0.948404	0.474202	+	0.880416i	$0.342737\pi$
$480$	0	0
$481$	−51.3009	−2.33912
$482$	− 7.57466i	− 0.345016i
$483$	− 12.1895i	− 0.554641i
$484$	30.9274	1.40579
$485$	0	0
$486$	−39.9304	−1.81128
$487$	12.1736i	0.551638i	0.961210	+	0.275819i	$0.0889490\pi$
$487$	12.1736i	0.551638i	−0.961210	+	0.275819i	$0.911051\pi$
$488$	29.0111i	1.31327i
$489$	−27.4112	−1.23958
$490$	0	0
$491$	30.6391	1.38272	0.691361	−	0.722510i	$-0.257012\pi$
$491$	30.6391	1.38272	0.691361	+	0.722510i	$0.257012\pi$
$492$	− 58.6982i	− 2.64632i
$493$	2.63489i	0.118669i
$494$	−35.2007	−1.58375
$495$	0	0
$496$	6.11939	0.274769
$497$	0.956214i	0.0428921i
$498$	− 66.1127i	− 2.96258i
$499$	−14.1460	−0.633261	−0.316631	−	0.948549i	$-0.602552\pi$
$499$	−14.1460	−0.633261	−0.316631	+	0.948549i	$0.602552\pi$
$500$	0	0
$501$	67.8606	3.03179
$502$	− 36.6468i	− 1.63563i
$503$	− 11.6127i	− 0.517785i	−0.965906	−	0.258892i	$-0.916643\pi$
$503$	− 11.6127i	− 0.517785i	0.965906	−	0.258892i	$-0.0833575\pi$
$504$	−12.2527	−0.545778
$505$	0	0
$506$	−5.32444	−0.236700
$507$	− 23.6043i	− 1.04831i
$508$	− 49.6815i	− 2.20426i
$509$	−24.4918	−1.08558	−0.542790	−	0.839868i	$-0.682632\pi$
$509$	−24.4918	−1.08558	−0.542790	+	0.839868i	$0.682632\pi$
$510$	0	0
$511$	5.61410	0.248353
$512$	− 13.7242i	− 0.606529i
$513$	− 14.7484i	− 0.651156i
$514$	12.4368	0.548565
$515$	0	0
$516$	−8.09050	−0.356164
$517$	− 9.11802i	− 0.401010i
$518$	31.4808i	1.38319i
$519$	−24.4749	−1.07433
$520$	0	0
$521$	3.88839	0.170354	0.0851768	−	0.996366i	$-0.472854\pi$
$521$	3.88839	0.170354	0.0851768	+	0.996366i	$0.472854\pi$
$522$	18.9982i	0.831528i
$523$	− 24.1125i	− 1.05437i	−0.849751	−	0.527184i	$-0.823248\pi$
$523$	− 24.1125i	− 1.05437i	0.849751	−	0.527184i	$-0.176752\pi$
$524$	−12.4021	−0.541786
$525$	0	0
$526$	−38.2333	−1.66705
$527$	− 6.97878i	− 0.304000i
$528$	− 2.35855i	− 0.102643i
$529$	11.0699	0.481298
$530$	0	0
$531$	0.526864	0.0228640
$532$	12.8559i	0.557372i
$533$	− 33.7019i	− 1.45979i
$534$	−9.93929	−0.430115
$535$	0	0
$536$	19.8821	0.858777
$537$	− 14.1697i	− 0.611467i
$538$	66.7161i	2.87633i
$539$	3.71413	0.159979
$540$	0	0
$541$	10.8764	0.467612	0.233806	−	0.972283i	$-0.424882\pi$
$541$	10.8764	0.467612	0.233806	+	0.972283i	$0.424882\pi$
$542$	21.1405i	0.908063i
$543$	− 31.0455i	− 1.33229i
$544$	−9.76143	−0.418518
$545$	0	0
$546$	−36.4366	−1.55934
$547$	19.6772i	0.841337i	0.907214	+	0.420669i	$0.138204\pi$
$547$	19.6772i	0.841337i	−0.907214	+	0.420669i	$0.861796\pi$
$548$	− 23.2648i	− 0.993824i
$549$	−63.4758	−2.70908
$550$	0	0
$551$	6.37395	0.271539
$552$	19.8607i	0.845328i
$553$	22.2412i	0.945792i
$554$	−41.1001	−1.74618
$555$	0	0
$556$	−12.2829	−0.520911
$557$	21.9055i	0.928166i	0.885792	+	0.464083i	$0.153616\pi$
$557$	21.9055i	0.928166i	−0.885792	+	0.464083i	$0.846384\pi$
$558$	− 50.3187i	− 2.13016i
$559$	−4.64521	−0.196472
$560$	0	0
$561$	−2.68978	−0.113563
$562$	− 54.5219i	− 2.29987i
$563$	41.7251i	1.75850i	0.476357	+	0.879252i	$0.341957\pi$
$563$	41.7251i	1.75850i	−0.476357	+	0.879252i	$0.658043\pi$
$564$	−106.364	−4.47873
$565$	0	0
$566$	46.5986	1.95869
$567$	2.32467i	0.0976270i
$568$	− 1.55799i	− 0.0653718i
$569$	32.6060	1.36691	0.683456	−	0.729991i	$-0.260476\pi$
$569$	32.6060	1.36691	0.683456	+	0.729991i	$0.260476\pi$
$570$	0	0
$571$	−21.5649	−0.902461	−0.451231	−	0.892407i	$-0.649015\pi$
$571$	−21.5649	−0.902461	−0.451231	+	0.892407i	$0.649015\pi$
$572$	9.47231i	0.396057i
$573$	17.6119i	0.735748i
$574$	−20.6812	−0.863216
$575$	0	0
$576$	−59.0819	−2.46174
$577$	− 38.9705i	− 1.62236i	−0.584796	−	0.811181i	$-0.698825\pi$
$577$	− 38.9705i	− 1.62236i	0.584796	−	0.811181i	$-0.301175\pi$
$578$	− 33.3700i	− 1.38801i
$579$	17.9494	0.745952
$580$	0	0
$581$	−13.8632	−0.575145
$582$	53.2036i	2.20536i
$583$	− 4.45877i	− 0.184663i
$584$	−9.14723	−0.378515
$585$	0	0
$586$	−67.2870	−2.77960
$587$	22.5462i	0.930580i	0.885158	+	0.465290i	$0.154050\pi$
$587$	22.5462i	0.930580i	−0.885158	+	0.465290i	$0.845950\pi$
$588$	− 43.3263i	− 1.78674i
$589$	−16.8821	−0.695614
$590$	0	0
$591$	5.76238	0.237033
$592$	13.6483i	0.560941i
$593$	− 16.9573i	− 0.696351i	−0.937429	−	0.348175i	$-0.886801\pi$
$593$	− 16.9573i	− 0.696351i	0.937429	−	0.348175i	$-0.113199\pi$
$594$	−6.66836	−0.273606
$595$	0	0
$596$	7.07329	0.289733
$597$	− 37.2120i	− 1.52299i
$598$	35.6614i	1.45830i
$599$	40.9904	1.67482	0.837411	−	0.546573i	$-0.184068\pi$
$599$	40.9904	1.67482	0.837411	+	0.546573i	$0.184068\pi$
$600$	0	0
$601$	33.5073	1.36679	0.683395	−	0.730049i	$-0.260503\pi$
$601$	33.5073	1.36679	0.683395	+	0.730049i	$0.260503\pi$
$602$	2.85053i	0.116179i
$603$	43.5017i	1.77153i
$604$	14.5672	0.592732
$605$	0	0
$606$	85.7879	3.48489
$607$	21.3526i	0.866676i	0.901231	+	0.433338i	$0.142664\pi$
$607$	21.3526i	0.866676i	−0.901231	+	0.433338i	$0.857336\pi$
$608$	23.6135i	0.957654i
$609$	6.59774	0.267354
$610$	0	0
$611$	−61.0695	−2.47061
$612$	18.9456i	0.765829i
$613$	12.0340i	0.486050i	0.970020	+	0.243025i	$0.0781396\pi$
$613$	12.0340i	0.486050i	−0.970020	+	0.243025i	$0.921860\pi$
$614$	67.2171	2.71266
$615$	0	0
$616$	1.85868	0.0748882
$617$	− 18.0232i	− 0.725587i	−0.931870	−	0.362793i	$-0.881823\pi$
$617$	− 18.0232i	− 0.725587i	0.931870	−	0.362793i	$-0.118177\pi$
$618$	45.3119i	1.82271i
$619$	−8.00253	−0.321649	−0.160825	−	0.986983i	$-0.551415\pi$
$619$	−8.00253	−0.321649	−0.160825	+	0.986983i	$0.551415\pi$
$620$	0	0
$621$	−14.9414	−0.599577
$622$	− 28.7536i	− 1.15291i
$623$	2.08418i	0.0835010i
$624$	−15.7968	−0.632379
$625$	0	0
$626$	12.2692	0.490377
$627$	6.50674i	0.259854i
$628$	− 65.8142i	− 2.62627i
$629$	15.5650	0.620617
$630$	0	0
$631$	−4.94373	−0.196807	−0.0984035	−	0.995147i	$-0.531374\pi$
$631$	−4.94373	−0.196807	−0.0984035	+	0.995147i	$0.531374\pi$
$632$	− 36.2383i	− 1.44148i
$633$	− 50.2195i	− 1.99605i
$634$	−21.7866	−0.865258
$635$	0	0
$636$	−52.0126	−2.06244
$637$	− 24.8760i	− 0.985625i
$638$	− 2.88193i	− 0.114097i
$639$	3.40885	0.134852
$640$	0	0
$641$	27.4749	1.08519	0.542596	−	0.839994i	$-0.317442\pi$
$641$	27.4749	1.08519	0.542596	+	0.839994i	$0.317442\pi$
$642$	82.6430i	3.26166i
$643$	− 36.1442i	− 1.42539i	−0.701476	−	0.712693i	$-0.747475\pi$
$643$	− 36.1442i	− 1.42539i	0.701476	−	0.712693i	$-0.252525\pi$
$644$	13.0241	0.513222
$645$	0	0
$646$	10.6801	0.420203
$647$	− 14.0123i	− 0.550882i	−0.961318	−	0.275441i	$-0.911176\pi$
$647$	− 14.0123i	− 0.550882i	0.961318	−	0.275441i	$-0.0888238\pi$
$648$	− 3.78766i	− 0.148793i
$649$	−0.0799228	−0.00313724
$650$	0	0
$651$	−17.4748	−0.684893
$652$	− 29.2881i	− 1.14701i
$653$	35.5834i	1.39249i	0.717806	+	0.696243i	$0.245146\pi$
$653$	35.5834i	1.39249i	−0.717806	+	0.696243i	$0.754854\pi$
$654$	3.35510	0.131195
$655$	0	0
$656$	−8.96618	−0.350070
$657$	− 20.0140i	− 0.780819i
$658$	37.4753i	1.46094i
$659$	−29.4542	−1.14737	−0.573687	−	0.819074i	$-0.694487\pi$
$659$	−29.4542	−1.14737	−0.573687	+	0.819074i	$0.694487\pi$
$660$	0	0
$661$	29.6136	1.15184	0.575918	−	0.817508i	$-0.304645\pi$
$661$	29.6136	1.15184	0.575918	+	0.817508i	$0.304645\pi$
$662$	− 48.5056i	− 1.88522i
$663$	18.0153i	0.699655i
$664$	22.5878	0.876578
$665$	0	0
$666$	112.227	4.34872
$667$	− 6.45737i	− 0.250030i
$668$	72.5071i	2.80538i
$669$	14.8934	0.575811
$670$	0	0
$671$	9.62898	0.371723
$672$	24.4426i	0.942893i
$673$	42.6874i	1.64548i	0.568418	+	0.822740i	$0.307555\pi$
$673$	42.6874i	1.64548i	−0.568418	+	0.822740i	$0.692445\pi$
$674$	0.762130	0.0293561
$675$	0	0
$676$	25.2205	0.970021
$677$	− 16.7330i	− 0.643103i	−0.946892	−	0.321552i	$-0.895796\pi$
$677$	− 16.7330i	− 0.643103i	0.946892	−	0.321552i	$-0.104204\pi$
$678$	− 49.8597i	− 1.91485i
$679$	11.1563	0.428141
$680$	0	0
$681$	−18.7711	−0.719310
$682$	7.63311i	0.292287i
$683$	7.23929i	0.277004i	0.990362	+	0.138502i	$0.0442287\pi$
$683$	7.23929i	0.277004i	−0.990362	+	0.138502i	$0.955771\pi$
$684$	45.8305	1.75237
$685$	0	0
$686$	−35.2189	−1.34466
$687$	− 34.3745i	− 1.31147i
$688$	1.23583i	0.0471155i
$689$	−29.8634	−1.13770
$690$	0	0
$691$	−12.9188	−0.491454	−0.245727	−	0.969339i	$-0.579027\pi$
$691$	−12.9188	−0.491454	−0.245727	+	0.969339i	$0.579027\pi$
$692$	− 26.1507i	− 0.994102i
$693$	4.06675i	0.154483i
$694$	60.9627	2.31411
$695$	0	0
$696$	−10.7499	−0.407474
$697$	10.2254i	0.387313i
$698$	− 28.0220i	− 1.06065i
$699$	−28.0023	−1.05915
$700$	0	0
$701$	−25.2475	−0.953586	−0.476793	−	0.879016i	$-0.658201\pi$
$701$	−25.2475	−0.953586	−0.476793	+	0.879016i	$0.658201\pi$
$702$	44.6625i	1.68568i
$703$	− 37.6527i	− 1.42010i
$704$	8.96244	0.337785
$705$	0	0
$706$	−47.5693	−1.79029
$707$	− 17.9890i	− 0.676544i
$708$	0.932319i	0.0350387i
$709$	14.3734	0.539805	0.269903	−	0.962888i	$-0.413008\pi$
$709$	14.3734	0.539805	0.269903	+	0.962888i	$0.413008\pi$
$710$	0	0
$711$	79.2887	2.97356
$712$	− 3.39582i	− 0.127264i
$713$	17.1030i	0.640514i
$714$	11.0551	0.413726
$715$	0	0
$716$	15.1399	0.565804
$717$	8.18856i	0.305807i
$718$	− 71.4486i	− 2.66644i
$719$	−27.1379	−1.01207	−0.506036	−	0.862512i	$-0.668890\pi$
$719$	−27.1379	−1.01207	−0.506036	+	0.862512i	$0.668890\pi$
$720$	0	0
$721$	9.50150	0.353854
$722$	16.3945i	0.610139i
$723$	9.37777i	0.348763i
$724$	33.1713	1.23280
$725$	0	0
$726$	−64.3354	−2.38771
$727$	− 14.8556i	− 0.550962i	−0.961306	−	0.275481i	$-0.911163\pi$
$727$	− 14.8556i	− 0.550962i	0.961306	−	0.275481i	$-0.0888371\pi$
$728$	− 12.4488i	− 0.461383i
$729$	43.9978	1.62955
$730$	0	0
$731$	1.40938	0.0521279
$732$	− 112.324i	− 4.15163i
$733$	− 42.4037i	− 1.56622i	−0.621885	−	0.783108i	$-0.713633\pi$
$733$	− 42.4037i	− 1.56622i	0.621885	−	0.783108i	$-0.286367\pi$
$734$	68.7473	2.53751
$735$	0	0
$736$	23.9225	0.881797
$737$	− 6.59900i	− 0.243077i
$738$	73.7273i	2.71394i
$739$	35.1324	1.29237	0.646183	−	0.763182i	$-0.276364\pi$
$739$	35.1324	1.29237	0.646183	+	0.763182i	$0.276364\pi$
$740$	0	0
$741$	43.5800	1.60095
$742$	18.3257i	0.672756i
$743$	− 10.9468i	− 0.401599i	−0.979632	−	0.200799i	$-0.935646\pi$
$743$	− 10.9468i	− 0.401599i	0.979632	−	0.200799i	$-0.0643539\pi$
$744$	28.4723	1.04385
$745$	0	0
$746$	−77.6833	−2.84419
$747$	49.4217i	1.80825i
$748$	− 2.87395i	− 0.105082i
$749$	17.3295	0.633207
$750$	0	0
$751$	28.9469	1.05629	0.528143	−	0.849155i	$-0.322888\pi$
$751$	28.9469	1.05629	0.528143	+	0.849155i	$0.322888\pi$
$752$	16.2471i	0.592472i
$753$	45.3703i	1.65339i
$754$	−19.3023	−0.702947
$755$	0	0
$756$	16.3115	0.593243
$757$	17.4955i	0.635883i	0.948110	+	0.317942i	$0.102992\pi$
$757$	17.4955i	0.635883i	−0.948110	+	0.317942i	$0.897008\pi$
$758$	66.4042i	2.41191i
$759$	6.59190	0.239271
$760$	0	0
$761$	44.4522	1.61139	0.805695	−	0.592330i	$-0.201792\pi$
$761$	44.4522	1.61139	0.805695	+	0.592330i	$0.201792\pi$
$762$	103.348i	3.74390i
$763$	− 0.703535i	− 0.0254697i
$764$	−18.8178	−0.680805
$765$	0	0
$766$	36.4087	1.31550
$767$	0.535297i	0.0193284i
$768$	− 19.8281i	− 0.715487i
$769$	−13.4830	−0.486209	−0.243105	−	0.970000i	$-0.578166\pi$
$769$	−13.4830	−0.486209	−0.243105	+	0.970000i	$0.578166\pi$
$770$	0	0
$771$	−15.3973	−0.554522
$772$	19.1784i	0.690246i
$773$	35.2197i	1.26676i	0.773840	+	0.633382i	$0.218334\pi$
$773$	35.2197i	1.26676i	−0.773840	+	0.633382i	$0.781666\pi$
$774$	10.1620	0.365266
$775$	0	0
$776$	−18.1774	−0.652529
$777$	− 38.9747i	− 1.39821i
$778$	− 14.8142i	− 0.531114i
$779$	24.7358	0.886250
$780$	0	0
$781$	−0.517107	−0.0185035
$782$	− 10.8199i	− 0.386918i
$783$	− 8.08724i	− 0.289015i
$784$	−6.61811	−0.236361
$785$	0	0
$786$	25.7989	0.920216
$787$	24.7248i	0.881344i	0.897668	+	0.440672i	$0.145260\pi$
$787$	24.7248i	0.881344i	−0.897668	+	0.440672i	$0.854740\pi$
$788$	6.15693i	0.219332i
$789$	47.3345	1.68515
$790$	0	0
$791$	−10.4551	−0.371742
$792$	− 6.62608i	− 0.235447i
$793$	− 64.4918i	− 2.29017i
$794$	−28.6260	−1.01590
$795$	0	0
$796$	39.7600	1.40926
$797$	40.1286i	1.42143i	0.703481	+	0.710714i	$0.251628\pi$
$797$	40.1286i	1.42143i	−0.703481	+	0.710714i	$0.748372\pi$
$798$	− 26.7429i	− 0.946688i
$799$	18.5288	0.655503
$800$	0	0
$801$	7.43000	0.262526
$802$	− 0.405060i	− 0.0143032i
$803$	3.03602i	0.107139i
$804$	−76.9790	−2.71484
$805$	0	0
$806$	51.1241	1.80077
$807$	− 82.5975i	− 2.90757i
$808$	29.3100i	1.03112i
$809$	−23.2556	−0.817623	−0.408812	−	0.912619i	$-0.634057\pi$
$809$	−23.2556	−0.817623	−0.408812	+	0.912619i	$0.634057\pi$
$810$	0	0
$811$	−5.51345	−0.193604	−0.0968018	−	0.995304i	$-0.530861\pi$
$811$	−5.51345	−0.193604	−0.0968018	+	0.995304i	$0.530861\pi$
$812$	7.04950i	0.247389i
$813$	− 26.1729i	− 0.917924i
$814$	−17.0244	−0.596704
$815$	0	0
$816$	4.79285	0.167783
$817$	− 3.40938i	− 0.119279i
$818$	− 35.8186i	− 1.25237i
$819$	27.2377	0.951764
$820$	0	0
$821$	48.8688	1.70553	0.852767	−	0.522291i	$-0.174923\pi$
$821$	48.8688	1.70553	0.852767	+	0.522291i	$0.174923\pi$
$822$	48.3957i	1.68799i
$823$	− 13.3239i	− 0.464444i	−0.972663	−	0.232222i	$-0.925400\pi$
$823$	− 13.3239i	− 0.464444i	0.972663	−	0.232222i	$-0.0745995\pi$
$824$	−15.4811	−0.539310
$825$	0	0
$826$	0.328485	0.0114295
$827$	20.1530i	0.700789i	0.936602	+	0.350395i	$0.113953\pi$
$827$	20.1530i	0.700789i	−0.936602	+	0.350395i	$0.886047\pi$
$828$	− 46.4303i	− 1.61356i
$829$	−31.4314	−1.09166	−0.545828	−	0.837897i	$-0.683785\pi$
$829$	−31.4314	−1.09166	−0.545828	+	0.837897i	$0.683785\pi$
$830$	0	0
$831$	50.8838	1.76514
$832$	− 60.0275i	− 2.08108i
$833$	7.54753i	0.261506i
$834$	25.5510	0.884760
$835$	0	0
$836$	−6.95227	−0.240449
$837$	21.4199i	0.740382i
$838$	21.0403i	0.726824i
$839$	−21.4592	−0.740855	−0.370428	−	0.928861i	$-0.620789\pi$
$839$	−21.4592	−0.740855	−0.370428	+	0.928861i	$0.620789\pi$
$840$	0	0
$841$	−25.5049	−0.879478
$842$	− 47.5776i	− 1.63963i
$843$	67.5005i	2.32484i
$844$	53.6581	1.84699
$845$	0	0
$846$	133.598	4.59318
$847$	13.4906i	0.463541i
$848$	7.94496i	0.272831i
$849$	−57.6911	−1.97995
$850$	0	0
$851$	−38.1454	−1.30761
$852$	6.03218i	0.206659i
$853$	47.8736i	1.63916i	0.572964	+	0.819580i	$0.305793\pi$
$853$	47.8736i	1.63916i	−0.572964	+	0.819580i	$0.694207\pi$
$854$	−39.5754	−1.35424
$855$	0	0
$856$	−28.2355	−0.965070
$857$	− 55.5048i	− 1.89601i	−0.318260	−	0.948003i	$-0.603098\pi$
$857$	− 55.5048i	− 1.89601i	0.318260	−	0.948003i	$-0.396902\pi$
$858$	− 19.7044i	− 0.672697i
$859$	35.7010	1.21810	0.609051	−	0.793131i	$-0.291550\pi$
$859$	35.7010	1.21810	0.609051	+	0.793131i	$0.291550\pi$
$860$	0	0
$861$	25.6042	0.872590
$862$	− 13.1888i	− 0.449214i
$863$	21.1893i	0.721292i	0.932703	+	0.360646i	$0.117444\pi$
$863$	21.1893i	0.721292i	−0.932703	+	0.360646i	$0.882556\pi$
$864$	29.9607	1.01928
$865$	0	0
$866$	−42.9640	−1.45998
$867$	41.3135i	1.40308i
$868$	− 18.6714i	− 0.633747i
$869$	−12.0277	−0.408013
$870$	0	0
$871$	−44.1980	−1.49759
$872$	1.14629i	0.0388184i
$873$	− 39.7717i	− 1.34607i
$874$	−26.1739	−0.885346
$875$	0	0
$876$	35.4159	1.19659
$877$	− 21.5794i	− 0.728684i	−0.931265	−	0.364342i	$-0.881294\pi$
$877$	− 21.5794i	− 0.728684i	0.931265	−	0.364342i	$-0.118706\pi$
$878$	43.2202i	1.45861i
$879$	83.3043	2.80979
$880$	0	0
$881$	6.32151	0.212977	0.106489	−	0.994314i	$-0.466039\pi$
$881$	6.32151	0.212977	0.106489	+	0.994314i	$0.466039\pi$
$882$	54.4196i	1.83240i
$883$	− 28.1139i	− 0.946108i	−0.881033	−	0.473054i	$-0.843152\pi$
$883$	− 28.1139i	− 0.946108i	0.881033	−	0.473054i	$-0.156848\pi$
$884$	−19.2488	−0.647407
$885$	0	0
$886$	91.4977	3.07392
$887$	− 39.6532i	− 1.33142i	−0.746209	−	0.665712i	$-0.768128\pi$
$887$	− 39.6532i	− 1.33142i	0.746209	−	0.665712i	$-0.231872\pi$
$888$	63.5027i	2.13101i
$889$	21.6711	0.726827
$890$	0	0
$891$	−1.25715	−0.0421161
$892$	15.9131i	0.532811i
$893$	− 44.8224i	− 1.49992i
$894$	−14.7139	−0.492107
$895$	0	0
$896$	−19.0707	−0.637106
$897$	− 44.1504i	− 1.47414i
$898$	− 15.4895i	− 0.516890i
$899$	−9.25727	−0.308747
$900$	0	0
$901$	9.06072	0.301856
$902$	− 11.1841i	− 0.372389i
$903$	− 3.52909i	− 0.117441i
$904$	17.0349	0.566572
$905$	0	0
$906$	−30.3029	−1.00675
$907$	29.9919i	0.995863i	0.867216	+	0.497932i	$0.165907\pi$
$907$	29.9919i	0.995863i	−0.867216	+	0.497932i	$0.834093\pi$
$908$	− 20.0564i	− 0.665595i
$909$	−64.1297	−2.12705
$910$	0	0
$911$	−5.77941	−0.191480	−0.0957402	−	0.995406i	$-0.530522\pi$
$911$	−5.77941	−0.191480	−0.0957402	+	0.995406i	$0.530522\pi$
$912$	− 11.5942i	− 0.383922i
$913$	− 7.49705i	− 0.248116i
$914$	61.3265	2.02850
$915$	0	0
$916$	36.7282	1.21353
$917$	− 5.40980i	− 0.178647i
$918$	− 13.5509i	− 0.447245i
$919$	44.9594	1.48307	0.741537	−	0.670912i	$-0.234097\pi$
$919$	44.9594	1.48307	0.741537	+	0.670912i	$0.234097\pi$
$920$	0	0
$921$	−83.2178	−2.74212
$922$	− 0.277607i	− 0.00914249i
$923$	3.46341i	0.114000i
$924$	−7.19636	−0.236743
$925$	0	0
$926$	40.4788	1.33022
$927$	− 33.8723i	− 1.11251i
$928$	12.9484i	0.425053i
$929$	35.9826	1.18055	0.590276	−	0.807202i	$-0.299019\pi$
$929$	35.9826	1.18055	0.590276	+	0.807202i	$0.299019\pi$
$930$	0	0
$931$	18.2579	0.598380
$932$	− 29.9197i	− 0.980052i
$933$	35.5982i	1.16543i
$934$	−20.0981	−0.657628
$935$	0	0
$936$	−44.3793	−1.45058
$937$	− 21.4420i	− 0.700479i	−0.936660	−	0.350240i	$-0.886100\pi$
$937$	− 21.4420i	− 0.700479i	0.936660	−	0.350240i	$-0.113900\pi$
$938$	27.1221i	0.885568i
$939$	−15.1899	−0.495702
$940$	0	0
$941$	−19.4037	−0.632542	−0.316271	−	0.948669i	$-0.602431\pi$
$941$	−19.4037	−0.632542	−0.316271	+	0.948669i	$0.602431\pi$
$942$	136.907i	4.46068i
$943$	− 25.0595i	− 0.816049i
$944$	0.142412	0.00463512
$945$	0	0
$946$	−1.54153	−0.0501194
$947$	− 46.9421i	− 1.52541i	−0.646744	−	0.762707i	$-0.723870\pi$
$947$	− 46.9421i	− 1.52541i	0.646744	−	0.762707i	$-0.276130\pi$
$948$	140.306i	4.55694i
$949$	20.3343	0.660079
$950$	0	0
$951$	26.9728	0.874654
$952$	3.77704i	0.122414i
$953$	− 47.5086i	− 1.53896i	−0.638673	−	0.769478i	$-0.720516\pi$
$953$	− 47.5086i	− 1.53896i	0.638673	−	0.769478i	$-0.279484\pi$
$954$	65.3300	2.11514
$955$	0	0
$956$	−8.74924	−0.282971
$957$	3.56796i	0.115336i
$958$	− 46.1351i	− 1.49056i
$959$	10.1481	0.327701
$960$	0	0
$961$	−6.48111	−0.209068
$962$	114.024i	3.67627i
$963$	− 61.7788i	− 1.99079i
$964$	−10.0199	−0.322718
$965$	0	0
$966$	−27.0929	−0.871699
$967$	2.95900i	0.0951549i	0.998868	+	0.0475774i	$0.0151501\pi$
$967$	2.95900i	0.0951549i	−0.998868	+	0.0475774i	$0.984850\pi$
$968$	− 21.9806i	− 0.706483i
$969$	−13.2224	−0.424766
$970$	0	0
$971$	17.5287	0.562522	0.281261	−	0.959631i	$-0.409247\pi$
$971$	17.5287	0.562522	0.281261	+	0.959631i	$0.409247\pi$
$972$	52.8205i	1.69422i
$973$	− 5.35782i	− 0.171764i
$974$	27.0576	0.866980
$975$	0	0
$976$	−17.1576	−0.549202
$977$	− 25.9865i	− 0.831383i	−0.909506	−	0.415691i	$-0.863540\pi$
$977$	− 25.9865i	− 0.831383i	0.909506	−	0.415691i	$-0.136460\pi$
$978$	60.9254i	1.94818i
$979$	−1.12710	−0.0360221
$980$	0	0
$981$	−2.50807	−0.0800764
$982$	− 68.0997i	− 2.17315i
$983$	− 14.0898i	− 0.449396i	−0.974428	−	0.224698i	$-0.927860\pi$
$983$	− 14.0898i	− 0.449396i	0.974428	−	0.224698i	$-0.0721396\pi$
$984$	−41.7178	−1.32991
$985$	0	0
$986$	5.85641	0.186506
$987$	− 46.3961i	− 1.47680i
$988$	46.5640i	1.48140i
$989$	−3.45400	−0.109831
$990$	0	0
$991$	5.00189	0.158890	0.0794451	−	0.996839i	$-0.474685\pi$
$991$	5.00189	0.158890	0.0794451	+	0.996839i	$0.474685\pi$
$992$	− 34.2953i	− 1.08888i
$993$	60.0521i	1.90570i
$994$	2.12532	0.0674112
$995$	0	0
$996$	−87.4549	−2.77111
$997$	− 12.7777i	− 0.404674i	−0.979316	−	0.202337i	$-0.935146\pi$
$997$	− 12.7777i	− 0.404674i	0.979316	−	0.202337i	$-0.0648536\pi$
$998$	31.4415i	0.995263i
$999$	−47.7736	−1.51149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1075.2.b.j.474.3		12
5.2	odd	4		1075.2.a.r.1.5	yes	6
5.3	odd	4		1075.2.a.q.1.2	✓	6
5.4	even	2	inner	1075.2.b.j.474.10		12
15.2	even	4		9675.2.a.cj.1.2		6
15.8	even	4		9675.2.a.ck.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1075.2.a.q.1.2	✓	6	5.3	odd	4
1075.2.a.r.1.5	yes	6	5.2	odd	4
1075.2.b.j.474.3		12	1.1	even	1	trivial
1075.2.b.j.474.10		12	5.4	even	2	inner
9675.2.a.cj.1.2		6	15.2	even	4
9675.2.a.ck.1.5		6	15.8	even	4

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:	\( N \)	\(=\)	\( 1075 = 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1075.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.22264i q^{2} +2.75173i q^{3} -2.94015 q^{4} +6.11612 q^{6} -1.28250i q^{7} +2.08961i q^{8} -4.57203 q^{9} +O(q^{10})\)	\(q-2.22264i q^{2} +2.75173i q^{3} -2.94015 q^{4} +6.11612 q^{6} -1.28250i q^{7} +2.08961i q^{8} -4.57203 q^{9} +0.693556 q^{11} -8.09050i q^{12} -4.64521i q^{13} -2.85053 q^{14} -1.23583 q^{16} +1.40938i q^{17} +10.1620i q^{18} +3.40938 q^{19} +3.52909 q^{21} -1.54153i q^{22} -3.45400i q^{23} -5.75006 q^{24} -10.3247 q^{26} -4.32581i q^{27} +3.77073i q^{28} +1.86953 q^{29} -4.95166 q^{31} +6.92603i q^{32} +1.90848i q^{33} +3.13256 q^{34} +13.4425 q^{36} -11.0438i q^{37} -7.57785i q^{38} +12.7824 q^{39} +7.25520 q^{41} -7.84391i q^{42} -1.00000i q^{43} -2.03916 q^{44} -7.67702 q^{46} -13.1468i q^{47} -3.40067i q^{48} +5.35520 q^{49} -3.87825 q^{51} +13.6576i q^{52} -6.42885i q^{53} -9.61475 q^{54} +2.67992 q^{56} +9.38171i q^{57} -4.15530i q^{58} -0.115236 q^{59} +13.8835 q^{61} +11.0058i q^{62} +5.86362i q^{63} +12.9225 q^{64} +4.24187 q^{66} -9.51474i q^{67} -4.14379i q^{68} +9.50449 q^{69} -0.745588 q^{71} -9.55378i q^{72} +4.37747i q^{73} -24.5465 q^{74} -10.0241 q^{76} -0.889483i q^{77} -28.4107i q^{78} -17.3421 q^{79} -1.81261 q^{81} -16.1257i q^{82} -10.8096i q^{83} -10.3760 q^{84} -2.22264 q^{86} +5.14445i q^{87} +1.44926i q^{88} -1.62510 q^{89} -5.95747 q^{91} +10.1553i q^{92} -13.6256i q^{93} -29.2206 q^{94} -19.0586 q^{96} +8.69891i q^{97} -11.9027i q^{98} -3.17096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{4} + 22 q^{6} - 24 q^{9}+O(q^{10}) \) 12 * q - 22 * q^4 + 22 * q^6 - 24 * q^9	\( 12 q - 22 q^{4} + 22 q^{6} - 24 q^{9} - 12 q^{11} - 34 q^{14} + 10 q^{16} + 10 q^{19} + 38 q^{21} - 18 q^{24} + 28 q^{26} - 36 q^{29} - 24 q^{31} - 2 q^{34} - 20 q^{36} + 6 q^{39} - 18 q^{44} - 28 q^{46} - 2 q^{51} - 24 q^{54} + 40 q^{56} - 42 q^{59} - 16 q^{61} - 12 q^{64} + 2 q^{66} - 74 q^{69} + 28 q^{71} - 4 q^{74} - 114 q^{76} + 62 q^{79} + 124 q^{81} - 42 q^{84} - 2 q^{86} - 80 q^{89} + 22 q^{91} - 70 q^{94} - 100 q^{96} + 106 q^{99}+O(q^{100}) \) 12 * q - 22 * q^4 + 22 * q^6 - 24 * q^9 - 12 * q^11 - 34 * q^14 + 10 * q^16 + 10 * q^19 + 38 * q^21 - 18 * q^24 + 28 * q^26 - 36 * q^29 - 24 * q^31 - 2 * q^34 - 20 * q^36 + 6 * q^39 - 18 * q^44 - 28 * q^46 - 2 * q^51 - 24 * q^54 + 40 * q^56 - 42 * q^59 - 16 * q^61 - 12 * q^64 + 2 * q^66 - 74 * q^69 + 28 * q^71 - 4 * q^74 - 114 * q^76 + 62 * q^79 + 124 * q^81 - 42 * q^84 - 2 * q^86 - 80 * q^89 + 22 * q^91 - 70 * q^94 - 100 * q^96 + 106 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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