LMFDB - Embedded newform 1650.2.c.k.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1650,2,Mod(199,1650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1650, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1650.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1650.c (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:	$13.1753163335$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1650.199
Dual form			1650.2.c.k.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +1.00000 q^{11} -1.00000i q^{12} +4.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} +7.00000i q^{17} +1.00000i q^{18} -5.00000 q^{19} +3.00000 q^{21} -1.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000i q^{27} +3.00000i q^{28} +10.0000 q^{29} +2.00000 q^{31} -1.00000i q^{32} +1.00000i q^{33} +7.00000 q^{34} +1.00000 q^{36} +7.00000i q^{37} +5.00000i q^{38} -4.00000 q^{39} -3.00000 q^{41} -3.00000i q^{42} +4.00000i q^{43} -1.00000 q^{44} -1.00000 q^{46} -13.0000i q^{47} +1.00000i q^{48} -2.00000 q^{49} -7.00000 q^{51} -4.00000i q^{52} +4.00000i q^{53} -1.00000 q^{54} +3.00000 q^{56} -5.00000i q^{57} -10.0000i q^{58} +5.00000 q^{59} +12.0000 q^{61} -2.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} +1.00000 q^{66} +12.0000i q^{67} -7.00000i q^{68} +1.00000 q^{69} -3.00000 q^{71} -1.00000i q^{72} +4.00000i q^{73} +7.00000 q^{74} +5.00000 q^{76} -3.00000i q^{77} +4.00000i q^{78} +15.0000 q^{79} +1.00000 q^{81} +3.00000i q^{82} +14.0000i q^{83} -3.00000 q^{84} +4.00000 q^{86} +10.0000i q^{87} +1.00000i q^{88} +12.0000 q^{91} +1.00000i q^{92} +2.00000i q^{93} -13.0000 q^{94} +1.00000 q^{96} +7.00000i q^{97} +2.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} + 2 q^{11} - 6 q^{14} + 2 q^{16} - 10 q^{19} + 6 q^{21} - 2 q^{24} + 8 q^{26} + 20 q^{29} + 4 q^{31} + 14 q^{34} + 2 q^{36} - 8 q^{39} - 6 q^{41} - 2 q^{44} - 2 q^{46} - 4 q^{49} - 14 q^{51} - 2 q^{54} + 6 q^{56} + 10 q^{59} + 24 q^{61} - 2 q^{64} + 2 q^{66} + 2 q^{69} - 6 q^{71} + 14 q^{74} + 10 q^{76} + 30 q^{79} + 2 q^{81} - 6 q^{84} + 8 q^{86} + 24 q^{91} - 26 q^{94} + 2 q^{96} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 + 2 * q^11 - 6 * q^14 + 2 * q^16 - 10 * q^19 + 6 * q^21 - 2 * q^24 + 8 * q^26 + 20 * q^29 + 4 * q^31 + 14 * q^34 + 2 * q^36 - 8 * q^39 - 6 * q^41 - 2 * q^44 - 2 * q^46 - 4 * q^49 - 14 * q^51 - 2 * q^54 + 6 * q^56 + 10 * q^59 + 24 * q^61 - 2 * q^64 + 2 * q^66 + 2 * q^69 - 6 * q^71 + 14 * q^74 + 10 * q^76 + 30 * q^79 + 2 * q^81 - 6 * q^84 + 8 * q^86 + 24 * q^91 - 26 * q^94 + 2 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1650\mathbb{Z}\right)^\times$.

$n$	$551$	$727$	$1201$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	− 3.00000i	− 1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$	− 3.00000i	− 1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	− 1.00000i	− 0.288675i
$13$	4.00000i	1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$	4.00000i	1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000i	1.69775i	0.528594	+	0.848875i	$0.322719\pi$
$17$	7.00000i	1.69775i	−0.528594	+	0.848875i	$0.677281\pi$
$18$	1.00000i	0.235702i
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	− 1.00000i	− 0.213201i
$23$	− 1.00000i	− 0.208514i	−0.994550	−	0.104257i	$-0.966753\pi$
$23$	− 1.00000i	− 0.208514i	0.994550	−	0.104257i	$-0.0332465\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	− 1.00000i	− 0.192450i
$28$	3.00000i	0.566947i
$29$	10.0000	1.85695	0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000	1.85695	0.928477	+	0.371391i	$0.121119\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	− 1.00000i	− 0.176777i
$33$	1.00000i	0.174078i
$34$	7.00000	1.20049
$35$	0	0
$36$	1.00000	0.166667
$37$	7.00000i	1.15079i	0.817875	+	0.575396i	$0.195152\pi$
$37$	7.00000i	1.15079i	−0.817875	+	0.575396i	$0.804848\pi$
$38$	5.00000i	0.811107i
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	− 3.00000i	− 0.462910i
$43$	4.00000i	0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$	4.00000i	0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 13.0000i	− 1.89624i	−0.317905	−	0.948122i	$-0.602979\pi$
$47$	− 13.0000i	− 1.89624i	0.317905	−	0.948122i	$-0.397021\pi$
$48$	1.00000i	0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	−7.00000	−0.980196
$52$	− 4.00000i	− 0.554700i
$53$	4.00000i	0.549442i	0.961524	+	0.274721i	$0.0885855\pi$
$53$	4.00000i	0.549442i	−0.961524	+	0.274721i	$0.911414\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	− 5.00000i	− 0.662266i
$58$	− 10.0000i	− 1.31306i
$59$	5.00000	0.650945	0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000	0.650945	0.325472	+	0.945552i	$0.394477\pi$
$60$	0	0
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	− 2.00000i	− 0.254000i
$63$	3.00000i	0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	12.0000i	1.46603i	0.680211	+	0.733017i	$0.261888\pi$
$67$	12.0000i	1.46603i	−0.680211	+	0.733017i	$0.738112\pi$
$68$	− 7.00000i	− 0.848875i
$69$	1.00000	0.120386
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	− 1.00000i	− 0.117851i
$73$	4.00000i	0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$	4.00000i	0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	7.00000	0.813733
$75$	0	0
$76$	5.00000	0.573539
$77$	− 3.00000i	− 0.341882i
$78$	4.00000i	0.452911i
$79$	15.0000	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	3.00000i	0.331295i
$83$	14.0000i	1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$	14.0000i	1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$	−3.00000	−0.327327
$85$	0	0
$86$	4.00000	0.431331
$87$	10.0000i	1.07211i
$88$	1.00000i	0.106600i
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	12.0000	1.25794
$92$	1.00000i	0.104257i
$93$	2.00000i	0.207390i
$94$	−13.0000	−1.34085
$95$	0	0
$96$	1.00000	0.102062
$97$	7.00000i	0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$	7.00000i	0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$	2.00000i	0.202031i
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	7.00000i	0.693103i
$103$	14.0000i	1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$	14.0000i	1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	4.00000	0.388514
$107$	2.00000i	0.193347i	0.995316	+	0.0966736i	$0.0308203\pi$
$107$	2.00000i	0.193347i	−0.995316	+	0.0966736i	$0.969180\pi$
$108$	1.00000i	0.0962250i
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	− 3.00000i	− 0.283473i
$113$	4.00000i	0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$	4.00000i	0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$	−5.00000	−0.468293
$115$	0	0
$116$	−10.0000	−0.928477
$117$	− 4.00000i	− 0.369800i
$118$	− 5.00000i	− 0.460287i
$119$	21.0000	1.92507
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 12.0000i	− 1.08643i
$123$	− 3.00000i	− 0.270501i
$124$	−2.00000	−0.179605
$125$	0	0
$126$	3.00000	0.267261
$127$	− 13.0000i	− 1.15356i	−0.816898	−	0.576782i	$-0.804308\pi$
$127$	− 13.0000i	− 1.15356i	0.816898	−	0.576782i	$-0.195692\pi$
$128$	1.00000i	0.0883883i
$129$	−4.00000	−0.352180
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	− 1.00000i	− 0.0870388i
$133$	15.0000i	1.30066i
$134$	12.0000	1.03664
$135$	0	0
$136$	−7.00000	−0.600245
$137$	2.00000i	0.170872i	0.996344	+	0.0854358i	$0.0272282\pi$
$137$	2.00000i	0.170872i	−0.996344	+	0.0854358i	$0.972772\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	13.0000	1.09480
$142$	3.00000i	0.251754i
$143$	4.00000i	0.334497i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	4.00000	0.331042
$147$	− 2.00000i	− 0.164957i
$148$	− 7.00000i	− 0.575396i
$149$	5.00000	0.409616	0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000	0.409616	0.204808	+	0.978802i	$0.434343\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	− 5.00000i	− 0.405554i
$153$	− 7.00000i	− 0.565916i
$154$	−3.00000	−0.241747
$155$	0	0
$156$	4.00000	0.320256
$157$	22.0000i	1.75579i	0.478852	+	0.877896i	$0.341053\pi$
$157$	22.0000i	1.75579i	−0.478852	+	0.877896i	$0.658947\pi$
$158$	− 15.0000i	− 1.19334i
$159$	−4.00000	−0.317221
$160$	0	0
$161$	−3.00000	−0.236433
$162$	− 1.00000i	− 0.0785674i
$163$	4.00000i	0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$	4.00000i	0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	14.0000	1.08661
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	3.00000i	0.231455i
$169$	−3.00000	−0.230769
$170$	0	0
$171$	5.00000	0.382360
$172$	− 4.00000i	− 0.304997i
$173$	− 21.0000i	− 1.59660i	−0.602260	−	0.798300i	$-0.705733\pi$
$173$	− 21.0000i	− 1.59660i	0.602260	−	0.798300i	$-0.294267\pi$
$174$	10.0000	0.758098
$175$	0	0
$176$	1.00000	0.0753778
$177$	5.00000i	0.375823i
$178$	0	0
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	0	0
$181$	−23.0000	−1.70958	−0.854788	−	0.518977i	$-0.826313\pi$
$181$	−23.0000	−1.70958	−0.854788	+	0.518977i	$0.826313\pi$
$182$	− 12.0000i	− 0.889499i
$183$	12.0000i	0.887066i
$184$	1.00000	0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	7.00000i	0.511891i
$188$	13.0000i	0.948122i
$189$	−3.00000	−0.218218
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	4.00000i	0.287926i	0.989583	+	0.143963i	$0.0459847\pi$
$193$	4.00000i	0.287926i	−0.989583	+	0.143963i	$0.954015\pi$
$194$	7.00000	0.502571
$195$	0	0
$196$	2.00000	0.142857
$197$	− 23.0000i	− 1.63868i	−0.573306	−	0.819341i	$-0.694340\pi$
$197$	− 23.0000i	− 1.63868i	0.573306	−	0.819341i	$-0.305660\pi$
$198$	1.00000i	0.0710669i
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−12.0000	−0.846415
$202$	3.00000i	0.211079i
$203$	− 30.0000i	− 2.10559i
$204$	7.00000	0.490098
$205$	0	0
$206$	14.0000	0.975426
$207$	1.00000i	0.0695048i
$208$	4.00000i	0.277350i
$209$	−5.00000	−0.345857
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	− 4.00000i	− 0.274721i
$213$	− 3.00000i	− 0.205557i
$214$	2.00000	0.136717
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 6.00000i	− 0.407307i
$218$	0	0
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−28.0000	−1.88348
$222$	7.00000i	0.469809i
$223$	4.00000i	0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$	4.00000i	0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	4.00000	0.266076
$227$	− 18.0000i	− 1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$	− 18.0000i	− 1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$	5.00000i	0.331133i
$229$	−5.00000	−0.330409	−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000	−0.330409	−0.165205	+	0.986259i	$0.552828\pi$
$230$	0	0
$231$	3.00000	0.197386
$232$	10.0000i	0.656532i
$233$	− 21.0000i	− 1.37576i	−0.725826	−	0.687878i	$-0.758542\pi$
$233$	− 21.0000i	− 1.37576i	0.725826	−	0.687878i	$-0.241458\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	−5.00000	−0.325472
$237$	15.0000i	0.974355i
$238$	− 21.0000i	− 1.36123i
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	− 1.00000i	− 0.0642824i
$243$	1.00000i	0.0641500i
$244$	−12.0000	−0.768221
$245$	0	0
$246$	−3.00000	−0.191273
$247$	− 20.0000i	− 1.27257i
$248$	2.00000i	0.127000i
$249$	−14.0000	−0.887214
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	− 3.00000i	− 0.188982i
$253$	− 1.00000i	− 0.0628695i
$254$	−13.0000	−0.815693
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000i	0.124757i	0.998053	+	0.0623783i	$0.0198685\pi$
$257$	2.00000i	0.124757i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	4.00000i	0.249029i
$259$	21.0000	1.30488
$260$	0	0
$261$	−10.0000	−0.618984
$262$	18.0000i	1.11204i
$263$	− 6.00000i	− 0.369976i	−0.982741	−	0.184988i	$-0.940775\pi$
$263$	− 6.00000i	− 0.369976i	0.982741	−	0.184988i	$-0.0592246\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	15.0000	0.919709
$267$	0	0
$268$	− 12.0000i	− 0.733017i
$269$	10.0000	0.609711	0.304855	−	0.952399i	$-0.401392\pi$
$269$	10.0000	0.609711	0.304855	+	0.952399i	$0.401392\pi$
$270$	0	0
$271$	−3.00000	−0.182237	−0.0911185	−	0.995840i	$-0.529044\pi$
$271$	−3.00000	−0.182237	−0.0911185	+	0.995840i	$0.529044\pi$
$272$	7.00000i	0.424437i
$273$	12.0000i	0.726273i
$274$	2.00000	0.120824
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	− 8.00000i	− 0.480673i	−0.970690	−	0.240337i	$-0.922742\pi$
$277$	− 8.00000i	− 0.480673i	0.970690	−	0.240337i	$-0.0772579\pi$
$278$	− 20.0000i	− 1.19952i
$279$	−2.00000	−0.119737
$280$	0	0
$281$	17.0000	1.01413	0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000	1.01413	0.507067	+	0.861906i	$0.330729\pi$
$282$	− 13.0000i	− 0.774139i
$283$	− 31.0000i	− 1.84276i	−0.388664	−	0.921379i	$-0.627063\pi$
$283$	− 31.0000i	− 1.84276i	0.388664	−	0.921379i	$-0.372937\pi$
$284$	3.00000	0.178017
$285$	0	0
$286$	4.00000	0.236525
$287$	9.00000i	0.531253i
$288$	1.00000i	0.0589256i
$289$	−32.0000	−1.88235
$290$	0	0
$291$	−7.00000	−0.410347
$292$	− 4.00000i	− 0.234082i
$293$	9.00000i	0.525786i	0.964825	+	0.262893i	$0.0846766\pi$
$293$	9.00000i	0.525786i	−0.964825	+	0.262893i	$0.915323\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	−7.00000	−0.406867
$297$	− 1.00000i	− 0.0580259i
$298$	− 5.00000i	− 0.289642i
$299$	4.00000	0.231326
$300$	0	0
$301$	12.0000	0.691669
$302$	8.00000i	0.460348i
$303$	− 3.00000i	− 0.172345i
$304$	−5.00000	−0.286770
$305$	0	0
$306$	−7.00000	−0.400163
$307$	12.0000i	0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$	12.0000i	0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$	3.00000i	0.170941i
$309$	−14.0000	−0.796432
$310$	0	0
$311$	−8.00000	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$312$	− 4.00000i	− 0.226455i
$313$	9.00000i	0.508710i	0.967111	+	0.254355i	$0.0818632\pi$
$313$	9.00000i	0.508710i	−0.967111	+	0.254355i	$0.918137\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	−15.0000	−0.843816
$317$	12.0000i	0.673987i	0.941507	+	0.336994i	$0.109410\pi$
$317$	12.0000i	0.673987i	−0.941507	+	0.336994i	$0.890590\pi$
$318$	4.00000i	0.224309i
$319$	10.0000	0.559893
$320$	0	0
$321$	−2.00000	−0.111629
$322$	3.00000i	0.167183i
$323$	− 35.0000i	− 1.94745i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	− 3.00000i	− 0.165647i
$329$	−39.0000	−2.15014
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	− 14.0000i	− 0.768350i
$333$	− 7.00000i	− 0.383598i
$334$	−8.00000	−0.437741
$335$	0	0
$336$	3.00000	0.163663
$337$	− 8.00000i	− 0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$	− 8.00000i	− 0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$	3.00000i	0.163178i
$339$	−4.00000	−0.217250
$340$	0	0
$341$	2.00000	0.108306
$342$	− 5.00000i	− 0.270369i
$343$	− 15.0000i	− 0.809924i
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−21.0000	−1.12897
$347$	− 8.00000i	− 0.429463i	−0.976673	−	0.214731i	$-0.931112\pi$
$347$	− 8.00000i	− 0.429463i	0.976673	−	0.214731i	$-0.0688876\pi$
$348$	− 10.0000i	− 0.536056i
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	0	0
$351$	4.00000	0.213504
$352$	− 1.00000i	− 0.0533002i
$353$	4.00000i	0.212899i	0.994318	+	0.106449i	$0.0339482\pi$
$353$	4.00000i	0.212899i	−0.994318	+	0.106449i	$0.966052\pi$
$354$	5.00000	0.265747
$355$	0	0
$356$	0	0
$357$	21.0000i	1.11144i
$358$	15.0000i	0.792775i
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	23.0000i	1.20885i
$363$	1.00000i	0.0524864i
$364$	−12.0000	−0.628971
$365$	0	0
$366$	12.0000	0.627250
$367$	22.0000i	1.14839i	0.818718	+	0.574195i	$0.194685\pi$
$367$	22.0000i	1.14839i	−0.818718	+	0.574195i	$0.805315\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	3.00000	0.156174
$370$	0	0
$371$	12.0000	0.623009
$372$	− 2.00000i	− 0.103695i
$373$	34.0000i	1.76045i	0.474554	+	0.880227i	$0.342610\pi$
$373$	34.0000i	1.76045i	−0.474554	+	0.880227i	$0.657390\pi$
$374$	7.00000	0.361961
$375$	0	0
$376$	13.0000	0.670424
$377$	40.0000i	2.06010i
$378$	3.00000i	0.154303i
$379$	−30.0000	−1.54100	−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000	−1.54100	−0.770498	+	0.637442i	$0.779993\pi$
$380$	0	0
$381$	13.0000	0.666010
$382$	3.00000i	0.153493i
$383$	24.0000i	1.22634i	0.789950	+	0.613171i	$0.210106\pi$
$383$	24.0000i	1.22634i	−0.789950	+	0.613171i	$0.789894\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	4.00000	0.203595
$387$	− 4.00000i	− 0.203331i
$388$	− 7.00000i	− 0.355371i
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	7.00000	0.354005
$392$	− 2.00000i	− 0.101015i
$393$	− 18.0000i	− 0.907980i
$394$	−23.0000	−1.15872
$395$	0	0
$396$	1.00000	0.0502519
$397$	22.0000i	1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$	22.0000i	1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$	0	0
$399$	−15.0000	−0.750939
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	12.0000i	0.598506i
$403$	8.00000i	0.398508i
$404$	3.00000	0.149256
$405$	0	0
$406$	−30.0000	−1.48888
$407$	7.00000i	0.346977i
$408$	− 7.00000i	− 0.346552i
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	0	0
$411$	−2.00000	−0.0986527
$412$	− 14.0000i	− 0.689730i
$413$	− 15.0000i	− 0.738102i
$414$	1.00000	0.0491473
$415$	0	0
$416$	4.00000	0.196116
$417$	20.0000i	0.979404i
$418$	5.00000i	0.244558i
$419$	35.0000	1.70986	0.854931	−	0.518742i	$-0.173599\pi$
$419$	35.0000	1.70986	0.854931	+	0.518742i	$0.173599\pi$
$420$	0	0
$421$	−13.0000	−0.633581	−0.316791	−	0.948495i	$-0.602605\pi$
$421$	−13.0000	−0.633581	−0.316791	+	0.948495i	$0.602605\pi$
$422$	− 12.0000i	− 0.584151i
$423$	13.0000i	0.632082i
$424$	−4.00000	−0.194257
$425$	0	0
$426$	−3.00000	−0.145350
$427$	− 36.0000i	− 1.74216i
$428$	− 2.00000i	− 0.0966736i
$429$	−4.00000	−0.193122
$430$	0	0
$431$	−18.0000	−0.867029	−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000	−0.867029	−0.433515	+	0.901146i	$0.642727\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 26.0000i	− 1.24948i	−0.780833	−	0.624740i	$-0.785205\pi$
$433$	− 26.0000i	− 1.24948i	0.780833	−	0.624740i	$-0.214795\pi$
$434$	−6.00000	−0.288009
$435$	0	0
$436$	0	0
$437$	5.00000i	0.239182i
$438$	4.00000i	0.191127i
$439$	−5.00000	−0.238637	−0.119318	−	0.992856i	$-0.538071\pi$
$439$	−5.00000	−0.238637	−0.119318	+	0.992856i	$0.538071\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	28.0000i	1.33182i
$443$	− 11.0000i	− 0.522626i	−0.965254	−	0.261313i	$-0.915845\pi$
$443$	− 11.0000i	− 0.522626i	0.965254	−	0.261313i	$-0.0841554\pi$
$444$	7.00000	0.332205
$445$	0	0
$446$	4.00000	0.189405
$447$	5.00000i	0.236492i
$448$	3.00000i	0.141737i
$449$	20.0000	0.943858	0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000	0.943858	0.471929	+	0.881636i	$0.343558\pi$
$450$	0	0
$451$	−3.00000	−0.141264
$452$	− 4.00000i	− 0.188144i
$453$	− 8.00000i	− 0.375873i
$454$	−18.0000	−0.844782
$455$	0	0
$456$	5.00000	0.234146
$457$	− 38.0000i	− 1.77757i	−0.458329	−	0.888783i	$-0.651552\pi$
$457$	− 38.0000i	− 1.77757i	0.458329	−	0.888783i	$-0.348448\pi$
$458$	5.00000i	0.233635i
$459$	7.00000	0.326732
$460$	0	0
$461$	42.0000	1.95614	0.978068	−	0.208288i	$-0.0667892\pi$
$461$	42.0000	1.95614	0.978068	+	0.208288i	$0.0667892\pi$
$462$	− 3.00000i	− 0.139573i
$463$	− 26.0000i	− 1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$	− 26.0000i	− 1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$	10.0000	0.464238
$465$	0	0
$466$	−21.0000	−0.972806
$467$	12.0000i	0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$	12.0000i	0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$	4.00000i	0.184900i
$469$	36.0000	1.66233
$470$	0	0
$471$	−22.0000	−1.01371
$472$	5.00000i	0.230144i
$473$	4.00000i	0.183920i
$474$	15.0000	0.688973
$475$	0	0
$476$	−21.0000	−0.962533
$477$	− 4.00000i	− 0.183147i
$478$	− 20.0000i	− 0.914779i
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	−28.0000	−1.27669
$482$	18.0000i	0.819878i
$483$	− 3.00000i	− 0.136505i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	1.00000	0.0453609
$487$	2.00000i	0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$	2.00000i	0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	12.0000i	0.543214i
$489$	−4.00000	−0.180886
$490$	0	0
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	3.00000i	0.135250i
$493$	70.0000i	3.15264i
$494$	−20.0000	−0.899843
$495$	0	0
$496$	2.00000	0.0898027
$497$	9.00000i	0.403705i
$498$	14.0000i	0.627355i
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	8.00000	0.357414
$502$	8.00000i	0.357057i
$503$	− 36.0000i	− 1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$	− 36.0000i	− 1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−1.00000	−0.0444554
$507$	− 3.00000i	− 0.133235i
$508$	13.0000i	0.576782i
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	− 1.00000i	− 0.0441942i
$513$	5.00000i	0.220755i
$514$	2.00000	0.0882162
$515$	0	0
$516$	4.00000	0.176090
$517$	− 13.0000i	− 0.571739i
$518$	− 21.0000i	− 0.922687i
$519$	21.0000	0.921798
$520$	0	0
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	10.0000i	0.437688i
$523$	39.0000i	1.70535i	0.522441	+	0.852675i	$0.325022\pi$
$523$	39.0000i	1.70535i	−0.522441	+	0.852675i	$0.674978\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	−6.00000	−0.261612
$527$	14.0000i	0.609850i
$528$	1.00000i	0.0435194i
$529$	22.0000	0.956522
$530$	0	0
$531$	−5.00000	−0.216982
$532$	− 15.0000i	− 0.650332i
$533$	− 12.0000i	− 0.519778i
$534$	0	0
$535$	0	0
$536$	−12.0000	−0.518321
$537$	− 15.0000i	− 0.647298i
$538$	− 10.0000i	− 0.431131i
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	32.0000	1.37579	0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000	1.37579	0.687894	+	0.725811i	$0.258536\pi$
$542$	3.00000i	0.128861i
$543$	− 23.0000i	− 0.987024i
$544$	7.00000	0.300123
$545$	0	0
$546$	12.0000	0.513553
$547$	17.0000i	0.726868i	0.931620	+	0.363434i	$0.118396\pi$
$547$	17.0000i	0.726868i	−0.931620	+	0.363434i	$0.881604\pi$
$548$	− 2.00000i	− 0.0854358i
$549$	−12.0000	−0.512148
$550$	0	0
$551$	−50.0000	−2.13007
$552$	1.00000i	0.0425628i
$553$	− 45.0000i	− 1.91359i
$554$	−8.00000	−0.339887
$555$	0	0
$556$	−20.0000	−0.848189
$557$	2.00000i	0.0847427i	0.999102	+	0.0423714i	$0.0134913\pi$
$557$	2.00000i	0.0847427i	−0.999102	+	0.0423714i	$0.986509\pi$
$558$	2.00000i	0.0846668i
$559$	−16.0000	−0.676728
$560$	0	0
$561$	−7.00000	−0.295540
$562$	− 17.0000i	− 0.717102i
$563$	14.0000i	0.590030i	0.955493	+	0.295015i	$0.0953246\pi$
$563$	14.0000i	0.590030i	−0.955493	+	0.295015i	$0.904675\pi$
$564$	−13.0000	−0.547399
$565$	0	0
$566$	−31.0000	−1.30303
$567$	− 3.00000i	− 0.125988i
$568$	− 3.00000i	− 0.125877i
$569$	−35.0000	−1.46728	−0.733638	−	0.679540i	$-0.762179\pi$
$569$	−35.0000	−1.46728	−0.733638	+	0.679540i	$0.762179\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	− 4.00000i	− 0.167248i
$573$	− 3.00000i	− 0.125327i
$574$	9.00000	0.375653
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 3.00000i	− 0.124892i	−0.998048	−	0.0624458i	$-0.980110\pi$
$577$	− 3.00000i	− 0.124892i	0.998048	−	0.0624458i	$-0.0198901\pi$
$578$	32.0000i	1.33102i
$579$	−4.00000	−0.166234
$580$	0	0
$581$	42.0000	1.74245
$582$	7.00000i	0.290159i
$583$	4.00000i	0.165663i
$584$	−4.00000	−0.165521
$585$	0	0
$586$	9.00000	0.371787
$587$	− 33.0000i	− 1.36206i	−0.732257	−	0.681028i	$-0.761533\pi$
$587$	− 33.0000i	− 1.36206i	0.732257	−	0.681028i	$-0.238467\pi$
$588$	2.00000i	0.0824786i
$589$	−10.0000	−0.412043
$590$	0	0
$591$	23.0000	0.946094
$592$	7.00000i	0.287698i
$593$	14.0000i	0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$	14.0000i	0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−5.00000	−0.204808
$597$	0	0
$598$	− 4.00000i	− 0.163572i
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	− 12.0000i	− 0.489083i
$603$	− 12.0000i	− 0.488678i
$604$	8.00000	0.325515
$605$	0	0
$606$	−3.00000	−0.121867
$607$	− 8.00000i	− 0.324710i	−0.986732	−	0.162355i	$-0.948091\pi$
$607$	− 8.00000i	− 0.324710i	0.986732	−	0.162355i	$-0.0519090\pi$
$608$	5.00000i	0.202777i
$609$	30.0000	1.21566
$610$	0	0
$611$	52.0000	2.10369
$612$	7.00000i	0.282958i
$613$	44.0000i	1.77714i	0.458738	+	0.888572i	$0.348302\pi$
$613$	44.0000i	1.77714i	−0.458738	+	0.888572i	$0.651698\pi$
$614$	12.0000	0.484281
$615$	0	0
$616$	3.00000	0.120873
$617$	− 18.0000i	− 0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$	− 18.0000i	− 0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$	14.0000i	0.563163i
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	8.00000i	0.320771i
$623$	0	0
$624$	−4.00000	−0.160128
$625$	0	0
$626$	9.00000	0.359712
$627$	− 5.00000i	− 0.199681i
$628$	− 22.0000i	− 0.877896i
$629$	−49.0000	−1.95376
$630$	0	0
$631$	−18.0000	−0.716569	−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000	−0.716569	−0.358284	+	0.933613i	$0.616638\pi$
$632$	15.0000i	0.596668i
$633$	12.0000i	0.476957i
$634$	12.0000	0.476581
$635$	0	0
$636$	4.00000	0.158610
$637$	− 8.00000i	− 0.316972i
$638$	− 10.0000i	− 0.395904i
$639$	3.00000	0.118678
$640$	0	0
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	2.00000i	0.0789337i
$643$	− 46.0000i	− 1.81406i	−0.421063	−	0.907031i	$-0.638343\pi$
$643$	− 46.0000i	− 1.81406i	0.421063	−	0.907031i	$-0.361657\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−35.0000	−1.37706
$647$	7.00000i	0.275198i	0.990488	+	0.137599i	$0.0439386\pi$
$647$	7.00000i	0.275198i	−0.990488	+	0.137599i	$0.956061\pi$
$648$	1.00000i	0.0392837i
$649$	5.00000	0.196267
$650$	0	0
$651$	6.00000	0.235159
$652$	− 4.00000i	− 0.156652i
$653$	− 6.00000i	− 0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$	− 6.00000i	− 0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	0	0
$655$	0	0
$656$	−3.00000	−0.117130
$657$	− 4.00000i	− 0.156055i
$658$	39.0000i	1.52038i
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	17.0000	0.661223	0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000	0.661223	0.330612	+	0.943767i	$0.392745\pi$
$662$	− 12.0000i	− 0.466393i
$663$	− 28.0000i	− 1.08743i
$664$	−14.0000	−0.543305
$665$	0	0
$666$	−7.00000	−0.271244
$667$	− 10.0000i	− 0.387202i
$668$	8.00000i	0.309529i
$669$	−4.00000	−0.154649
$670$	0	0
$671$	12.0000	0.463255
$672$	− 3.00000i	− 0.115728i
$673$	24.0000i	0.925132i	0.886585	+	0.462566i	$0.153071\pi$
$673$	24.0000i	0.925132i	−0.886585	+	0.462566i	$0.846929\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	3.00000	0.115385
$677$	− 38.0000i	− 1.46046i	−0.683202	−	0.730229i	$-0.739413\pi$
$677$	− 38.0000i	− 1.46046i	0.683202	−	0.730229i	$-0.260587\pi$
$678$	4.00000i	0.153619i
$679$	21.0000	0.805906
$680$	0	0
$681$	18.0000	0.689761
$682$	− 2.00000i	− 0.0765840i
$683$	19.0000i	0.727015i	0.931591	+	0.363507i	$0.118421\pi$
$683$	19.0000i	0.727015i	−0.931591	+	0.363507i	$0.881579\pi$
$684$	−5.00000	−0.191180
$685$	0	0
$686$	−15.0000	−0.572703
$687$	− 5.00000i	− 0.190762i
$688$	4.00000i	0.152499i
$689$	−16.0000	−0.609551
$690$	0	0
$691$	32.0000	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$692$	21.0000i	0.798300i
$693$	3.00000i	0.113961i
$694$	−8.00000	−0.303676
$695$	0	0
$696$	−10.0000	−0.379049
$697$	− 21.0000i	− 0.795432i
$698$	30.0000i	1.13552i
$699$	21.0000	0.794293
$700$	0	0
$701$	−13.0000	−0.491003	−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000	−0.491003	−0.245502	+	0.969396i	$0.578953\pi$
$702$	− 4.00000i	− 0.150970i
$703$	− 35.0000i	− 1.32005i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	4.00000	0.150542
$707$	9.00000i	0.338480i
$708$	− 5.00000i	− 0.187912i
$709$	35.0000	1.31445	0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000	1.31445	0.657226	+	0.753693i	$0.271730\pi$
$710$	0	0
$711$	−15.0000	−0.562544
$712$	0	0
$713$	− 2.00000i	− 0.0749006i
$714$	21.0000	0.785905
$715$	0	0
$716$	15.0000	0.560576
$717$	20.0000i	0.746914i
$718$	10.0000i	0.373197i
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	42.0000	1.56416
$722$	− 6.00000i	− 0.223297i
$723$	− 18.0000i	− 0.669427i
$724$	23.0000	0.854788
$725$	0	0
$726$	1.00000	0.0371135
$727$	32.0000i	1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$	32.0000i	1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$	12.0000i	0.444750i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−28.0000	−1.03562
$732$	− 12.0000i	− 0.443533i
$733$	− 16.0000i	− 0.590973i	−0.955347	−	0.295487i	$-0.904518\pi$
$733$	− 16.0000i	− 0.590973i	0.955347	−	0.295487i	$-0.0954818\pi$
$734$	22.0000	0.812035
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	12.0000i	0.442026i
$738$	− 3.00000i	− 0.110432i
$739$	−15.0000	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$740$	0	0
$741$	20.0000	0.734718
$742$	− 12.0000i	− 0.440534i
$743$	44.0000i	1.61420i	0.590412	+	0.807102i	$0.298965\pi$
$743$	44.0000i	1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$	−2.00000	−0.0733236
$745$	0	0
$746$	34.0000	1.24483
$747$	− 14.0000i	− 0.512233i
$748$	− 7.00000i	− 0.255945i
$749$	6.00000	0.219235
$750$	0	0
$751$	−28.0000	−1.02173	−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000	−1.02173	−0.510867	+	0.859660i	$0.670676\pi$
$752$	− 13.0000i	− 0.474061i
$753$	− 8.00000i	− 0.291536i
$754$	40.0000	1.45671
$755$	0	0
$756$	3.00000	0.109109
$757$	2.00000i	0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$	2.00000i	0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	30.0000i	1.08965i
$759$	1.00000	0.0362977
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	− 13.0000i	− 0.470940i
$763$	0	0
$764$	3.00000	0.108536
$765$	0	0
$766$	24.0000	0.867155
$767$	20.0000i	0.722158i
$768$	1.00000i	0.0360844i
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	− 4.00000i	− 0.143963i
$773$	− 16.0000i	− 0.575480i	−0.957709	−	0.287740i	$-0.907096\pi$
$773$	− 16.0000i	− 0.575480i	0.957709	−	0.287740i	$-0.0929039\pi$
$774$	−4.00000	−0.143777
$775$	0	0
$776$	−7.00000	−0.251285
$777$	21.0000i	0.753371i
$778$	− 10.0000i	− 0.358517i
$779$	15.0000	0.537431
$780$	0	0
$781$	−3.00000	−0.107348
$782$	− 7.00000i	− 0.250319i
$783$	− 10.0000i	− 0.357371i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	−18.0000	−0.642039
$787$	− 23.0000i	− 0.819861i	−0.912117	−	0.409931i	$-0.865553\pi$
$787$	− 23.0000i	− 0.819861i	0.912117	−	0.409931i	$-0.134447\pi$
$788$	23.0000i	0.819341i
$789$	6.00000	0.213606
$790$	0	0
$791$	12.0000	0.426671
$792$	− 1.00000i	− 0.0355335i
$793$	48.0000i	1.70453i
$794$	22.0000	0.780751
$795$	0	0
$796$	0	0
$797$	42.0000i	1.48772i	0.668338	+	0.743858i	$0.267006\pi$
$797$	42.0000i	1.48772i	−0.668338	+	0.743858i	$0.732994\pi$
$798$	15.0000i	0.530994i
$799$	91.0000	3.21935
$800$	0	0
$801$	0	0
$802$	− 12.0000i	− 0.423735i
$803$	4.00000i	0.141157i
$804$	12.0000	0.423207
$805$	0	0
$806$	8.00000	0.281788
$807$	10.0000i	0.352017i
$808$	− 3.00000i	− 0.105540i
$809$	45.0000	1.58212	0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000	1.58212	0.791058	+	0.611741i	$0.209531\pi$
$810$	0	0
$811$	37.0000	1.29925	0.649623	−	0.760257i	$-0.274927\pi$
$811$	37.0000	1.29925	0.649623	+	0.760257i	$0.274927\pi$
$812$	30.0000i	1.05279i
$813$	− 3.00000i	− 0.105215i
$814$	7.00000	0.245350
$815$	0	0
$816$	−7.00000	−0.245049
$817$	− 20.0000i	− 0.699711i
$818$	20.0000i	0.699284i
$819$	−12.0000	−0.419314
$820$	0	0
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	2.00000i	0.0697580i
$823$	24.0000i	0.836587i	0.908312	+	0.418294i	$0.137372\pi$
$823$	24.0000i	0.836587i	−0.908312	+	0.418294i	$0.862628\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	−15.0000	−0.521917
$827$	− 48.0000i	− 1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$	− 48.0000i	− 1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	−10.0000	−0.347314	−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000	−0.347314	−0.173657	+	0.984806i	$0.555558\pi$
$830$	0	0
$831$	8.00000	0.277517
$832$	− 4.00000i	− 0.138675i
$833$	− 14.0000i	− 0.485071i
$834$	20.0000	0.692543
$835$	0	0
$836$	5.00000	0.172929
$837$	− 2.00000i	− 0.0691301i
$838$	− 35.0000i	− 1.20905i
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	13.0000i	0.448010i
$843$	17.0000i	0.585511i
$844$	−12.0000	−0.413057
$845$	0	0
$846$	13.0000	0.446949
$847$	− 3.00000i	− 0.103081i
$848$	4.00000i	0.137361i
$849$	31.0000	1.06392
$850$	0	0
$851$	7.00000	0.239957
$852$	3.00000i	0.102778i
$853$	− 26.0000i	− 0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$	− 26.0000i	− 0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−36.0000	−1.23189
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	− 33.0000i	− 1.12726i	−0.826028	−	0.563629i	$-0.809405\pi$
$857$	− 33.0000i	− 1.12726i	0.826028	−	0.563629i	$-0.190595\pi$
$858$	4.00000i	0.136558i
$859$	−40.0000	−1.36478	−0.682391	−	0.730987i	$-0.739060\pi$
$859$	−40.0000	−1.36478	−0.682391	+	0.730987i	$0.739060\pi$
$860$	0	0
$861$	−9.00000	−0.306719
$862$	18.0000i	0.613082i
$863$	− 16.0000i	− 0.544646i	−0.962206	−	0.272323i	$-0.912208\pi$
$863$	− 16.0000i	− 0.544646i	0.962206	−	0.272323i	$-0.0877920\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−26.0000	−0.883516
$867$	− 32.0000i	− 1.08678i
$868$	6.00000i	0.203653i
$869$	15.0000	0.508840
$870$	0	0
$871$	−48.0000	−1.62642
$872$	0	0
$873$	− 7.00000i	− 0.236914i
$874$	5.00000	0.169128
$875$	0	0
$876$	4.00000	0.135147
$877$	− 58.0000i	− 1.95852i	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	− 58.0000i	− 1.95852i	0.202606	−	0.979260i	$-0.435059\pi$
$878$	5.00000i	0.168742i
$879$	−9.00000	−0.303562
$880$	0	0
$881$	52.0000	1.75192	0.875962	−	0.482380i	$-0.160227\pi$
$881$	52.0000	1.75192	0.875962	+	0.482380i	$0.160227\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	14.0000i	0.471138i	0.971858	+	0.235569i	$0.0756953\pi$
$883$	14.0000i	0.471138i	−0.971858	+	0.235569i	$0.924305\pi$
$884$	28.0000	0.941742
$885$	0	0
$886$	−11.0000	−0.369552
$887$	− 8.00000i	− 0.268614i	−0.990940	−	0.134307i	$-0.957119\pi$
$887$	− 8.00000i	− 0.268614i	0.990940	−	0.134307i	$-0.0428808\pi$
$888$	− 7.00000i	− 0.234905i
$889$	−39.0000	−1.30802
$890$	0	0
$891$	1.00000	0.0335013
$892$	− 4.00000i	− 0.133930i
$893$	65.0000i	2.17514i
$894$	5.00000	0.167225
$895$	0	0
$896$	3.00000	0.100223
$897$	4.00000i	0.133556i
$898$	− 20.0000i	− 0.667409i
$899$	20.0000	0.667037
$900$	0	0
$901$	−28.0000	−0.932815
$902$	3.00000i	0.0998891i
$903$	12.0000i	0.399335i
$904$	−4.00000	−0.133038
$905$	0	0
$906$	−8.00000	−0.265782
$907$	− 38.0000i	− 1.26177i	−0.775877	−	0.630885i	$-0.782692\pi$
$907$	− 38.0000i	− 1.26177i	0.775877	−	0.630885i	$-0.217308\pi$
$908$	18.0000i	0.597351i
$909$	3.00000	0.0995037
$910$	0	0
$911$	37.0000	1.22586	0.612932	−	0.790135i	$-0.289990\pi$
$911$	37.0000	1.22586	0.612932	+	0.790135i	$0.289990\pi$
$912$	− 5.00000i	− 0.165567i
$913$	14.0000i	0.463332i
$914$	−38.0000	−1.25693
$915$	0	0
$916$	5.00000	0.165205
$917$	54.0000i	1.78324i
$918$	− 7.00000i	− 0.231034i
$919$	55.0000	1.81428	0.907141	−	0.420826i	$-0.138260\pi$
$919$	55.0000	1.81428	0.907141	+	0.420826i	$0.138260\pi$
$920$	0	0
$921$	−12.0000	−0.395413
$922$	− 42.0000i	− 1.38320i
$923$	− 12.0000i	− 0.394985i
$924$	−3.00000	−0.0986928
$925$	0	0
$926$	−26.0000	−0.854413
$927$	− 14.0000i	− 0.459820i
$928$	− 10.0000i	− 0.328266i
$929$	−20.0000	−0.656179	−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000	−0.656179	−0.328089	+	0.944647i	$0.606405\pi$
$930$	0	0
$931$	10.0000	0.327737
$932$	21.0000i	0.687878i
$933$	− 8.00000i	− 0.261908i
$934$	12.0000	0.392652
$935$	0	0
$936$	4.00000	0.130744
$937$	− 18.0000i	− 0.588034i	−0.955800	−	0.294017i	$-0.905008\pi$
$937$	− 18.0000i	− 0.588034i	0.955800	−	0.294017i	$-0.0949923\pi$
$938$	− 36.0000i	− 1.17544i
$939$	−9.00000	−0.293704
$940$	0	0
$941$	17.0000	0.554184	0.277092	−	0.960843i	$-0.410629\pi$
$941$	17.0000	0.554184	0.277092	+	0.960843i	$0.410629\pi$
$942$	22.0000i	0.716799i
$943$	3.00000i	0.0976934i
$944$	5.00000	0.162736
$945$	0	0
$946$	4.00000	0.130051
$947$	− 53.0000i	− 1.72227i	−0.508378	−	0.861134i	$-0.669755\pi$
$947$	− 53.0000i	− 1.72227i	0.508378	−	0.861134i	$-0.330245\pi$
$948$	− 15.0000i	− 0.487177i
$949$	−16.0000	−0.519382
$950$	0	0
$951$	−12.0000	−0.389127
$952$	21.0000i	0.680614i
$953$	49.0000i	1.58727i	0.608397	+	0.793633i	$0.291813\pi$
$953$	49.0000i	1.58727i	−0.608397	+	0.793633i	$0.708187\pi$
$954$	−4.00000	−0.129505
$955$	0	0
$956$	−20.0000	−0.646846
$957$	10.0000i	0.323254i
$958$	0	0
$959$	6.00000	0.193750
$960$	0	0
$961$	−27.0000	−0.870968
$962$	28.0000i	0.902756i
$963$	− 2.00000i	− 0.0644491i
$964$	18.0000	0.579741
$965$	0	0
$966$	−3.00000	−0.0965234
$967$	− 8.00000i	− 0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$	− 8.00000i	− 0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$	1.00000i	0.0321412i
$969$	35.0000	1.12436
$970$	0	0
$971$	−3.00000	−0.0962746	−0.0481373	−	0.998841i	$-0.515328\pi$
$971$	−3.00000	−0.0962746	−0.0481373	+	0.998841i	$0.515328\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 60.0000i	− 1.92351i
$974$	2.00000	0.0640841
$975$	0	0
$976$	12.0000	0.384111
$977$	− 38.0000i	− 1.21573i	−0.794041	−	0.607864i	$-0.792027\pi$
$977$	− 38.0000i	− 1.21573i	0.794041	−	0.607864i	$-0.207973\pi$
$978$	4.00000i	0.127906i
$979$	0	0
$980$	0	0
$981$	0	0
$982$	18.0000i	0.574403i
$983$	− 31.0000i	− 0.988746i	−0.869250	−	0.494373i	$-0.835398\pi$
$983$	− 31.0000i	− 0.988746i	0.869250	−	0.494373i	$-0.164602\pi$
$984$	3.00000	0.0956365
$985$	0	0
$986$	70.0000	2.22925
$987$	− 39.0000i	− 1.24138i
$988$	20.0000i	0.636285i
$989$	4.00000	0.127193
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	− 2.00000i	− 0.0635001i
$993$	12.0000i	0.380808i
$994$	9.00000	0.285463
$995$	0	0
$996$	14.0000	0.443607
$997$	2.00000i	0.0633406i	0.999498	+	0.0316703i	$0.0100827\pi$
$997$	2.00000i	0.0633406i	−0.999498	+	0.0316703i	$0.989917\pi$
$998$	− 20.0000i	− 0.633089i
$999$	7.00000	0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1650.2.c.k.199.1		2
3.2	odd	2		4950.2.c.l.199.2		2
5.2	odd	4		1650.2.a.s.1.1	yes	1
5.3	odd	4		1650.2.a.a.1.1	✓	1
5.4	even	2	inner	1650.2.c.k.199.2		2
15.2	even	4		4950.2.a.r.1.1		1
15.8	even	4		4950.2.a.z.1.1		1
15.14	odd	2		4950.2.c.l.199.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1650.2.a.a.1.1	✓	1	5.3	odd	4
1650.2.a.s.1.1	yes	1	5.2	odd	4
1650.2.c.k.199.1		2	1.1	even	1	trivial
1650.2.c.k.199.2		2	5.4	even	2	inner
4950.2.a.r.1.1		1	15.2	even	4
4950.2.a.z.1.1		1	15.8	even	4
4950.2.c.l.199.1		2	15.14	odd	2
4950.2.c.l.199.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +1.00000 q^{11} -1.00000i q^{12} +4.00000i q^{13} -3.00000 q^{14} +1.00000 q^{16} +7.00000i q^{17} +1.00000i q^{18} -5.00000 q^{19} +3.00000 q^{21} -1.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +4.00000 q^{26} -1.00000i q^{27} +3.00000i q^{28} +10.0000 q^{29} +2.00000 q^{31} -1.00000i q^{32} +1.00000i q^{33} +7.00000 q^{34} +1.00000 q^{36} +7.00000i q^{37} +5.00000i q^{38} -4.00000 q^{39} -3.00000 q^{41} -3.00000i q^{42} +4.00000i q^{43} -1.00000 q^{44} -1.00000 q^{46} -13.0000i q^{47} +1.00000i q^{48} -2.00000 q^{49} -7.00000 q^{51} -4.00000i q^{52} +4.00000i q^{53} -1.00000 q^{54} +3.00000 q^{56} -5.00000i q^{57} -10.0000i q^{58} +5.00000 q^{59} +12.0000 q^{61} -2.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} +1.00000 q^{66} +12.0000i q^{67} -7.00000i q^{68} +1.00000 q^{69} -3.00000 q^{71} -1.00000i q^{72} +4.00000i q^{73} +7.00000 q^{74} +5.00000 q^{76} -3.00000i q^{77} +4.00000i q^{78} +15.0000 q^{79} +1.00000 q^{81} +3.00000i q^{82} +14.0000i q^{83} -3.00000 q^{84} +4.00000 q^{86} +10.0000i q^{87} +1.00000i q^{88} +12.0000 q^{91} +1.00000i q^{92} +2.00000i q^{93} -13.0000 q^{94} +1.00000 q^{96} +7.00000i q^{97} +2.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} + 2 q^{11} - 6 q^{14} + 2 q^{16} - 10 q^{19} + 6 q^{21} - 2 q^{24} + 8 q^{26} + 20 q^{29} + 4 q^{31} + 14 q^{34} + 2 q^{36} - 8 q^{39} - 6 q^{41} - 2 q^{44} - 2 q^{46} - 4 q^{49} - 14 q^{51} - 2 q^{54} + 6 q^{56} + 10 q^{59} + 24 q^{61} - 2 q^{64} + 2 q^{66} + 2 q^{69} - 6 q^{71} + 14 q^{74} + 10 q^{76} + 30 q^{79} + 2 q^{81} - 6 q^{84} + 8 q^{86} + 24 q^{91} - 26 q^{94} + 2 q^{96} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 + 2 * q^11 - 6 * q^14 + 2 * q^16 - 10 * q^19 + 6 * q^21 - 2 * q^24 + 8 * q^26 + 20 * q^29 + 4 * q^31 + 14 * q^34 + 2 * q^36 - 8 * q^39 - 6 * q^41 - 2 * q^44 - 2 * q^46 - 4 * q^49 - 14 * q^51 - 2 * q^54 + 6 * q^56 + 10 * q^59 + 24 * q^61 - 2 * q^64 + 2 * q^66 + 2 * q^69 - 6 * q^71 + 14 * q^74 + 10 * q^76 + 30 * q^79 + 2 * q^81 - 6 * q^84 + 8 * q^86 + 24 * q^91 - 26 * q^94 + 2 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more