LMFDB - Embedded newform 2550.2.d.h.2449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2550,2,Mod(2449,2550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2550, 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("2550.2449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2550.d (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:	$20.3618525154$
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			2449.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	2550.2449
Dual form			2550.2.d.h.2449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} -1.00000i q^{12} +2.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +1.00000i q^{17} -1.00000i q^{18} -8.00000 q^{19} +4.00000 q^{21} +2.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} -1.00000i q^{27} +4.00000i q^{28} +4.00000 q^{29} -2.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} -3.00000i q^{37} -8.00000i q^{38} -2.00000 q^{39} -1.00000 q^{41} +4.00000i q^{42} -6.00000i q^{43} -2.00000 q^{44} -1.00000 q^{46} -4.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{51} -2.00000i q^{52} -13.0000i q^{53} +1.00000 q^{54} -4.00000 q^{56} -8.00000i q^{57} +4.00000i q^{58} -15.0000 q^{59} +5.00000 q^{61} -2.00000i q^{62} +4.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +10.0000i q^{67} -1.00000i q^{68} -1.00000 q^{69} -1.00000 q^{71} +1.00000i q^{72} -16.0000i q^{73} +3.00000 q^{74} +8.00000 q^{76} -8.00000i q^{77} -2.00000i q^{78} -12.0000 q^{79} +1.00000 q^{81} -1.00000i q^{82} -11.0000i q^{83} -4.00000 q^{84} +6.00000 q^{86} +4.00000i q^{87} -2.00000i q^{88} +2.00000 q^{89} +8.00000 q^{91} -1.00000i q^{92} -2.00000i q^{93} +4.00000 q^{94} -1.00000 q^{96} -9.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{11} + 8 q^{14} + 2 q^{16} - 16 q^{19} + 8 q^{21} + 2 q^{24} - 4 q^{26} + 8 q^{29} - 4 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} - 2 q^{41} - 4 q^{44} - 2 q^{46} - 18 q^{49} - 2 q^{51} + 2 q^{54} - 8 q^{56} - 30 q^{59} + 10 q^{61} - 2 q^{64} - 4 q^{66} - 2 q^{69} - 2 q^{71} + 6 q^{74} + 16 q^{76} - 24 q^{79} + 2 q^{81} - 8 q^{84} + 12 q^{86} + 4 q^{89} + 16 q^{91} + 8 q^{94} - 2 q^{96} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 8 * q^14 + 2 * q^16 - 16 * q^19 + 8 * q^21 + 2 * q^24 - 4 * q^26 + 8 * q^29 - 4 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 - 2 * q^41 - 4 * q^44 - 2 * q^46 - 18 * q^49 - 2 * q^51 + 2 * q^54 - 8 * q^56 - 30 * q^59 + 10 * q^61 - 2 * q^64 - 4 * q^66 - 2 * q^69 - 2 * q^71 + 6 * q^74 + 16 * q^76 - 24 * q^79 + 2 * q^81 - 8 * q^84 + 12 * q^86 + 4 * q^89 + 16 * q^91 + 8 * q^94 - 2 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2550\mathbb{Z}\right)^\times$.

$n$	$751$	$851$	$1327$
$\chi(n)$	$1$	$1$	$-1$

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
$7$	− 4.00000i	− 1.51186i	−0.654654	−	0.755929i	$-0.727186\pi$
$7$	− 4.00000i	− 1.51186i	0.654654	−	0.755929i	$-0.272814\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	− 1.00000i	− 0.288675i
$13$	2.00000i	0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$	2.00000i	0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000i	0.242536i
$17$	1.00000i	0.242536i
$18$	− 1.00000i	− 0.235702i
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	2.00000i	0.426401i
$23$	1.00000i	0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$	1.00000i	0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$	1.00000	0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	− 1.00000i	− 0.192450i
$28$	4.00000i	0.755929i
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000i	0.176777i
$33$	2.00000i	0.348155i
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	− 3.00000i	− 0.493197i	−0.969118	−	0.246598i	$-0.920687\pi$
$37$	− 3.00000i	− 0.493197i	0.969118	−	0.246598i	$-0.0793129\pi$
$38$	− 8.00000i	− 1.29777i
$39$	−2.00000	−0.320256
$40$	0	0
$41$	−1.00000	−0.156174	−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000	−0.156174	−0.0780869	+	0.996947i	$0.524881\pi$
$42$	4.00000i	0.617213i
$43$	− 6.00000i	− 0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$	− 6.00000i	− 0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 4.00000i	− 0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$47$	− 4.00000i	− 0.583460i	0.956501	−	0.291730i	$-0.0942309\pi$
$48$	1.00000i	0.144338i
$49$	−9.00000	−1.28571
$50$	0	0
$51$	−1.00000	−0.140028
$52$	− 2.00000i	− 0.277350i
$53$	− 13.0000i	− 1.78569i	−0.450367	−	0.892844i	$-0.648707\pi$
$53$	− 13.0000i	− 1.78569i	0.450367	−	0.892844i	$-0.351293\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.00000	−0.534522
$57$	− 8.00000i	− 1.05963i
$58$	4.00000i	0.525226i
$59$	−15.0000	−1.95283	−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−15.0000	−1.95283	−0.976417	+	0.215894i	$0.930733\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	− 2.00000i	− 0.254000i
$63$	4.00000i	0.503953i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	10.0000i	1.22169i	0.791748	+	0.610847i	$0.209171\pi$
$67$	10.0000i	1.22169i	−0.791748	+	0.610847i	$0.790829\pi$
$68$	− 1.00000i	− 0.121268i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	1.00000i	0.117851i
$73$	− 16.0000i	− 1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	− 16.0000i	− 1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	8.00000	0.917663
$77$	− 8.00000i	− 0.911685i
$78$	− 2.00000i	− 0.226455i
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 1.00000i	− 0.110432i
$83$	− 11.0000i	− 1.20741i	−0.797209	−	0.603703i	$-0.793691\pi$
$83$	− 11.0000i	− 1.20741i	0.797209	−	0.603703i	$-0.206309\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	6.00000	0.646997
$87$	4.00000i	0.428845i
$88$	− 2.00000i	− 0.213201i
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	− 1.00000i	− 0.104257i
$93$	− 2.00000i	− 0.207390i
$94$	4.00000	0.412568
$95$	0	0
$96$	−1.00000	−0.102062
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	− 9.00000i	− 0.909137i
$99$	−2.00000	−0.201008
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	− 1.00000i	− 0.0990148i
$103$	3.00000i	0.295599i	0.989017	+	0.147799i	$0.0472190\pi$
$103$	3.00000i	0.295599i	−0.989017	+	0.147799i	$0.952781\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	13.0000	1.26267
$107$	− 12.0000i	− 1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$	− 12.0000i	− 1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	1.00000i	0.0962250i
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	− 4.00000i	− 0.377964i
$113$	− 15.0000i	− 1.41108i	−0.708669	−	0.705541i	$-0.750704\pi$
$113$	− 15.0000i	− 1.41108i	0.708669	−	0.705541i	$-0.249296\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	−4.00000	−0.371391
$117$	− 2.00000i	− 0.184900i
$118$	− 15.0000i	− 1.38086i
$119$	4.00000	0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	5.00000i	0.452679i
$123$	− 1.00000i	− 0.0901670i
$124$	2.00000	0.179605
$125$	0	0
$126$	−4.00000	−0.356348
$127$	− 16.0000i	− 1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$	− 16.0000i	− 1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	6.00000	0.528271
$130$	0	0
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	− 2.00000i	− 0.174078i
$133$	32.0000i	2.77475i
$134$	−10.0000	−0.863868
$135$	0	0
$136$	1.00000	0.0857493
$137$	− 12.0000i	− 1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$	− 12.0000i	− 1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	− 1.00000i	− 0.0839181i
$143$	4.00000i	0.334497i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	16.0000	1.32417
$147$	− 9.00000i	− 0.742307i
$148$	3.00000i	0.246598i
$149$	−1.00000	−0.0819232	−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000	−0.0819232	−0.0409616	+	0.999161i	$0.513042\pi$
$150$	0	0
$151$	1.00000	0.0813788	0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000	0.0813788	0.0406894	+	0.999172i	$0.487045\pi$
$152$	8.00000i	0.648886i
$153$	− 1.00000i	− 0.0808452i
$154$	8.00000	0.644658
$155$	0	0
$156$	2.00000	0.160128
$157$	14.0000i	1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$	14.0000i	1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$	− 12.0000i	− 0.954669i
$159$	13.0000	1.03097
$160$	0	0
$161$	4.00000	0.315244
$162$	1.00000i	0.0785674i
$163$	− 7.00000i	− 0.548282i	−0.961689	−	0.274141i	$-0.911606\pi$
$163$	− 7.00000i	− 0.548282i	0.961689	−	0.274141i	$-0.0883936\pi$
$164$	1.00000	0.0780869
$165$	0	0
$166$	11.0000	0.853766
$167$	24.0000i	1.85718i	0.371113	+	0.928588i	$0.378976\pi$
$167$	24.0000i	1.85718i	−0.371113	+	0.928588i	$0.621024\pi$
$168$	− 4.00000i	− 0.308607i
$169$	9.00000	0.692308
$170$	0	0
$171$	8.00000	0.611775
$172$	6.00000i	0.457496i
$173$	8.00000i	0.608229i	0.952636	+	0.304114i	$0.0983605\pi$
$173$	8.00000i	0.608229i	−0.952636	+	0.304114i	$0.901639\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	2.00000	0.150756
$177$	− 15.0000i	− 1.12747i
$178$	2.00000i	0.149906i
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	0	0
$181$	11.0000	0.817624	0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000	0.817624	0.408812	+	0.912619i	$0.365943\pi$
$182$	8.00000i	0.592999i
$183$	5.00000i	0.369611i
$184$	1.00000	0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	2.00000i	0.146254i
$188$	4.00000i	0.291730i
$189$	−4.00000	−0.290957
$190$	0	0
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	24.0000i	1.72756i	0.503871	+	0.863779i	$0.331909\pi$
$193$	24.0000i	1.72756i	−0.503871	+	0.863779i	$0.668091\pi$
$194$	0	0
$195$	0	0
$196$	9.00000	0.642857
$197$	− 2.00000i	− 0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$	− 2.00000i	− 0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	− 2.00000i	− 0.142134i
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	0	0
$201$	−10.0000	−0.705346
$202$	− 10.0000i	− 0.703598i
$203$	− 16.0000i	− 1.12298i
$204$	1.00000	0.0700140
$205$	0	0
$206$	−3.00000	−0.209020
$207$	− 1.00000i	− 0.0695048i
$208$	2.00000i	0.138675i
$209$	−16.0000	−1.10674
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	13.0000i	0.892844i
$213$	− 1.00000i	− 0.0685189i
$214$	12.0000	0.820303
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	8.00000i	0.543075i
$218$	2.00000i	0.135457i
$219$	16.0000	1.08118
$220$	0	0
$221$	−2.00000	−0.134535
$222$	3.00000i	0.201347i
$223$	17.0000i	1.13840i	0.822198	+	0.569202i	$0.192748\pi$
$223$	17.0000i	1.13840i	−0.822198	+	0.569202i	$0.807252\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	15.0000	0.997785
$227$	22.0000i	1.46019i	0.683345	+	0.730096i	$0.260525\pi$
$227$	22.0000i	1.46019i	−0.683345	+	0.730096i	$0.739475\pi$
$228$	8.00000i	0.529813i
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	0	0
$231$	8.00000	0.526361
$232$	− 4.00000i	− 0.262613i
$233$	3.00000i	0.196537i	0.995160	+	0.0982683i	$0.0313303\pi$
$233$	3.00000i	0.196537i	−0.995160	+	0.0982683i	$0.968670\pi$
$234$	2.00000	0.130744
$235$	0	0
$236$	15.0000	0.976417
$237$	− 12.0000i	− 0.779484i
$238$	4.00000i	0.259281i
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	− 7.00000i	− 0.449977i
$243$	1.00000i	0.0641500i
$244$	−5.00000	−0.320092
$245$	0	0
$246$	1.00000	0.0637577
$247$	− 16.0000i	− 1.01806i
$248$	2.00000i	0.127000i
$249$	11.0000	0.697097
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	− 4.00000i	− 0.251976i
$253$	2.00000i	0.125739i
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 12.0000i	− 0.748539i	−0.927320	−	0.374270i	$-0.877893\pi$
$257$	− 12.0000i	− 0.748539i	0.927320	−	0.374270i	$-0.122107\pi$
$258$	6.00000i	0.373544i
$259$	−12.0000	−0.745644
$260$	0	0
$261$	−4.00000	−0.247594
$262$	8.00000i	0.494242i
$263$	4.00000i	0.246651i	0.992366	+	0.123325i	$0.0393559\pi$
$263$	4.00000i	0.246651i	−0.992366	+	0.123325i	$0.960644\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	−32.0000	−1.96205
$267$	2.00000i	0.122398i
$268$	− 10.0000i	− 0.610847i
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	−21.0000	−1.27566	−0.637830	−	0.770178i	$-0.720168\pi$
$271$	−21.0000	−1.27566	−0.637830	+	0.770178i	$0.720168\pi$
$272$	1.00000i	0.0606339i
$273$	8.00000i	0.484182i
$274$	12.0000	0.724947
$275$	0	0
$276$	1.00000	0.0601929
$277$	− 31.0000i	− 1.86261i	−0.364241	−	0.931305i	$-0.618672\pi$
$277$	− 31.0000i	− 1.86261i	0.364241	−	0.931305i	$-0.381328\pi$
$278$	− 1.00000i	− 0.0599760i
$279$	2.00000	0.119737
$280$	0	0
$281$	−2.00000	−0.119310	−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000	−0.119310	−0.0596550	+	0.998219i	$0.519000\pi$
$282$	4.00000i	0.238197i
$283$	− 7.00000i	− 0.416107i	−0.978117	−	0.208053i	$-0.933287\pi$
$283$	− 7.00000i	− 0.416107i	0.978117	−	0.208053i	$-0.0667128\pi$
$284$	1.00000	0.0593391
$285$	0	0
$286$	−4.00000	−0.236525
$287$	4.00000i	0.236113i
$288$	− 1.00000i	− 0.0589256i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	0	0
$292$	16.0000i	0.936329i
$293$	− 31.0000i	− 1.81104i	−0.424304	−	0.905520i	$-0.639481\pi$
$293$	− 31.0000i	− 1.81104i	0.424304	−	0.905520i	$-0.360519\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	−3.00000	−0.174371
$297$	− 2.00000i	− 0.116052i
$298$	− 1.00000i	− 0.0579284i
$299$	−2.00000	−0.115663
$300$	0	0
$301$	−24.0000	−1.38334
$302$	1.00000i	0.0575435i
$303$	− 10.0000i	− 0.574485i
$304$	−8.00000	−0.458831
$305$	0	0
$306$	1.00000	0.0571662
$307$	− 22.0000i	− 1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$	− 22.0000i	− 1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	8.00000i	0.455842i
$309$	−3.00000	−0.170664
$310$	0	0
$311$	5.00000	0.283524	0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000	0.283524	0.141762	+	0.989901i	$0.454723\pi$
$312$	2.00000i	0.113228i
$313$	20.0000i	1.13047i	0.824931	+	0.565233i	$0.191214\pi$
$313$	20.0000i	1.13047i	−0.824931	+	0.565233i	$0.808786\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	12.0000	0.675053
$317$	− 26.0000i	− 1.46031i	−0.683284	−	0.730153i	$-0.739449\pi$
$317$	− 26.0000i	− 1.46031i	0.683284	−	0.730153i	$-0.260551\pi$
$318$	13.0000i	0.729004i
$319$	8.00000	0.447914
$320$	0	0
$321$	12.0000	0.669775
$322$	4.00000i	0.222911i
$323$	− 8.00000i	− 0.445132i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	7.00000	0.387694
$327$	2.00000i	0.110600i
$328$	1.00000i	0.0552158i
$329$	−16.0000	−0.882109
$330$	0	0
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	11.0000i	0.603703i
$333$	3.00000i	0.164399i
$334$	−24.0000	−1.31322
$335$	0	0
$336$	4.00000	0.218218
$337$	26.0000i	1.41631i	0.706057	+	0.708155i	$0.250472\pi$
$337$	26.0000i	1.41631i	−0.706057	+	0.708155i	$0.749528\pi$
$338$	9.00000i	0.489535i
$339$	15.0000	0.814688
$340$	0	0
$341$	−4.00000	−0.216612
$342$	8.00000i	0.432590i
$343$	8.00000i	0.431959i
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−8.00000	−0.430083
$347$	− 16.0000i	− 0.858925i	−0.903085	−	0.429463i	$-0.858703\pi$
$347$	− 16.0000i	− 0.858925i	0.903085	−	0.429463i	$-0.141297\pi$
$348$	− 4.00000i	− 0.214423i
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	2.00000i	0.106600i
$353$	16.0000i	0.851594i	0.904819	+	0.425797i	$0.140006\pi$
$353$	16.0000i	0.851594i	−0.904819	+	0.425797i	$0.859994\pi$
$354$	15.0000	0.797241
$355$	0	0
$356$	−2.00000	−0.106000
$357$	4.00000i	0.211702i
$358$	− 9.00000i	− 0.475665i
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	11.0000i	0.578147i
$363$	− 7.00000i	− 0.367405i
$364$	−8.00000	−0.419314
$365$	0	0
$366$	−5.00000	−0.261354
$367$	− 2.00000i	− 0.104399i	−0.998637	−	0.0521996i	$-0.983377\pi$
$367$	− 2.00000i	− 0.104399i	0.998637	−	0.0521996i	$-0.0166232\pi$
$368$	1.00000i	0.0521286i
$369$	1.00000	0.0520579
$370$	0	0
$371$	−52.0000	−2.69971
$372$	2.00000i	0.103695i
$373$	4.00000i	0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$	4.00000i	0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	−4.00000	−0.206284
$377$	8.00000i	0.412021i
$378$	− 4.00000i	− 0.205738i
$379$	1.00000	0.0513665	0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000	0.0513665	0.0256833	+	0.999670i	$0.491824\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	10.0000i	0.511645i
$383$	− 20.0000i	− 1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$383$	− 20.0000i	− 1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−24.0000	−1.22157
$387$	6.00000i	0.304997i
$388$	0	0
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	−1.00000	−0.0505722
$392$	9.00000i	0.454569i
$393$	8.00000i	0.403547i
$394$	2.00000	0.100759
$395$	0	0
$396$	2.00000	0.100504
$397$	21.0000i	1.05396i	0.849878	+	0.526980i	$0.176676\pi$
$397$	21.0000i	1.05396i	−0.849878	+	0.526980i	$0.823324\pi$
$398$	− 10.0000i	− 0.501255i
$399$	−32.0000	−1.60200
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	− 10.0000i	− 0.498755i
$403$	− 4.00000i	− 0.199254i
$404$	10.0000	0.497519
$405$	0	0
$406$	16.0000	0.794067
$407$	− 6.00000i	− 0.297409i
$408$	1.00000i	0.0495074i
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	− 3.00000i	− 0.147799i
$413$	60.0000i	2.95241i
$414$	1.00000	0.0491473
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	− 1.00000i	− 0.0489702i
$418$	− 16.0000i	− 0.782586i
$419$	−24.0000	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$420$	0	0
$421$	−24.0000	−1.16969	−0.584844	−	0.811146i	$-0.698844\pi$
$421$	−24.0000	−1.16969	−0.584844	+	0.811146i	$0.698844\pi$
$422$	4.00000i	0.194717i
$423$	4.00000i	0.194487i
$424$	−13.0000	−0.631336
$425$	0	0
$426$	1.00000	0.0484502
$427$	− 20.0000i	− 0.967868i
$428$	12.0000i	0.580042i
$429$	−4.00000	−0.193122
$430$	0	0
$431$	−28.0000	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$431$	−28.0000	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	14.0000i	0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$	14.0000i	0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$	−8.00000	−0.384012
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	− 8.00000i	− 0.382692i
$438$	16.0000i	0.764510i
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	− 2.00000i	− 0.0951303i
$443$	− 39.0000i	− 1.85295i	−0.376361	−	0.926473i	$-0.622825\pi$
$443$	− 39.0000i	− 1.85295i	0.376361	−	0.926473i	$-0.377175\pi$
$444$	−3.00000	−0.142374
$445$	0	0
$446$	−17.0000	−0.804973
$447$	− 1.00000i	− 0.0472984i
$448$	4.00000i	0.188982i
$449$	42.0000	1.98210	0.991051	−	0.133482i	$-0.0426157\pi$
$449$	42.0000	1.98210	0.991051	+	0.133482i	$0.0426157\pi$
$450$	0	0
$451$	−2.00000	−0.0941763
$452$	15.0000i	0.705541i
$453$	1.00000i	0.0469841i
$454$	−22.0000	−1.03251
$455$	0	0
$456$	−8.00000	−0.374634
$457$	31.0000i	1.45012i	0.688686	+	0.725059i	$0.258188\pi$
$457$	31.0000i	1.45012i	−0.688686	+	0.725059i	$0.741812\pi$
$458$	18.0000i	0.841085i
$459$	1.00000	0.0466760
$460$	0	0
$461$	−1.00000	−0.0465746	−0.0232873	−	0.999729i	$-0.507413\pi$
$461$	−1.00000	−0.0465746	−0.0232873	+	0.999729i	$0.507413\pi$
$462$	8.00000i	0.372194i
$463$	35.0000i	1.62659i	0.581853	+	0.813294i	$0.302328\pi$
$463$	35.0000i	1.62659i	−0.581853	+	0.813294i	$0.697672\pi$
$464$	4.00000	0.185695
$465$	0	0
$466$	−3.00000	−0.138972
$467$	− 3.00000i	− 0.138823i	−0.997588	−	0.0694117i	$-0.977888\pi$
$467$	− 3.00000i	− 0.138823i	0.997588	−	0.0694117i	$-0.0221122\pi$
$468$	2.00000i	0.0924500i
$469$	40.0000	1.84703
$470$	0	0
$471$	−14.0000	−0.645086
$472$	15.0000i	0.690431i
$473$	− 12.0000i	− 0.551761i
$474$	12.0000	0.551178
$475$	0	0
$476$	−4.00000	−0.183340
$477$	13.0000i	0.595229i
$478$	− 6.00000i	− 0.274434i
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	0	0
$481$	6.00000	0.273576
$482$	− 14.0000i	− 0.637683i
$483$	4.00000i	0.182006i
$484$	7.00000	0.318182
$485$	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	$0.985571\pi$
$488$	− 5.00000i	− 0.226339i
$489$	7.00000	0.316551
$490$	0	0
$491$	39.0000	1.76005	0.880023	−	0.474932i	$-0.157527\pi$
$491$	39.0000	1.76005	0.880023	+	0.474932i	$0.157527\pi$
$492$	1.00000i	0.0450835i
$493$	4.00000i	0.180151i
$494$	16.0000	0.719874
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	4.00000i	0.179425i
$498$	11.0000i	0.492922i
$499$	41.0000	1.83541	0.917706	−	0.397260i	$-0.130039\pi$
$499$	41.0000	1.83541	0.917706	+	0.397260i	$0.130039\pi$
$500$	0	0
$501$	−24.0000	−1.07224
$502$	− 4.00000i	− 0.178529i
$503$	− 41.0000i	− 1.82810i	−0.405602	−	0.914050i	$-0.632938\pi$
$503$	− 41.0000i	− 1.82810i	0.405602	−	0.914050i	$-0.367062\pi$
$504$	4.00000	0.178174
$505$	0	0
$506$	−2.00000	−0.0889108
$507$	9.00000i	0.399704i
$508$	16.0000i	0.709885i
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	0	0
$511$	−64.0000	−2.83119
$512$	1.00000i	0.0441942i
$513$	8.00000i	0.353209i
$514$	12.0000	0.529297
$515$	0	0
$516$	−6.00000	−0.264135
$517$	− 8.00000i	− 0.351840i
$518$	− 12.0000i	− 0.527250i
$519$	−8.00000	−0.351161
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	− 4.00000i	− 0.175075i
$523$	− 34.0000i	− 1.48672i	−0.668894	−	0.743358i	$-0.733232\pi$
$523$	− 34.0000i	− 1.48672i	0.668894	−	0.743358i	$-0.266768\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−4.00000	−0.174408
$527$	− 2.00000i	− 0.0871214i
$528$	2.00000i	0.0870388i
$529$	22.0000	0.956522
$530$	0	0
$531$	15.0000	0.650945
$532$	− 32.0000i	− 1.38738i
$533$	− 2.00000i	− 0.0866296i
$534$	−2.00000	−0.0865485
$535$	0	0
$536$	10.0000	0.431934
$537$	− 9.00000i	− 0.388379i
$538$	6.00000i	0.258678i
$539$	−18.0000	−0.775315
$540$	0	0
$541$	15.0000	0.644900	0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000	0.644900	0.322450	+	0.946586i	$0.395494\pi$
$542$	− 21.0000i	− 0.902027i
$543$	11.0000i	0.472055i
$544$	−1.00000	−0.0428746
$545$	0	0
$546$	−8.00000	−0.342368
$547$	− 13.0000i	− 0.555840i	−0.960604	−	0.277920i	$-0.910355\pi$
$547$	− 13.0000i	− 0.555840i	0.960604	−	0.277920i	$-0.0896450\pi$
$548$	12.0000i	0.512615i
$549$	−5.00000	−0.213395
$550$	0	0
$551$	−32.0000	−1.36325
$552$	1.00000i	0.0425628i
$553$	48.0000i	2.04117i
$554$	31.0000	1.31706
$555$	0	0
$556$	1.00000	0.0424094
$557$	31.0000i	1.31351i	0.754103	+	0.656756i	$0.228072\pi$
$557$	31.0000i	1.31351i	−0.754103	+	0.656756i	$0.771928\pi$
$558$	2.00000i	0.0846668i
$559$	12.0000	0.507546
$560$	0	0
$561$	−2.00000	−0.0844401
$562$	− 2.00000i	− 0.0843649i
$563$	15.0000i	0.632175i	0.948730	+	0.316087i	$0.102369\pi$
$563$	15.0000i	0.632175i	−0.948730	+	0.316087i	$0.897631\pi$
$564$	−4.00000	−0.168430
$565$	0	0
$566$	7.00000	0.294232
$567$	− 4.00000i	− 0.167984i
$568$	1.00000i	0.0419591i
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−41.0000	−1.71580	−0.857898	−	0.513820i	$-0.828230\pi$
$571$	−41.0000	−1.71580	−0.857898	+	0.513820i	$0.828230\pi$
$572$	− 4.00000i	− 0.167248i
$573$	10.0000i	0.417756i
$574$	−4.00000	−0.166957
$575$	0	0
$576$	1.00000	0.0416667
$577$	33.0000i	1.37381i	0.726748	+	0.686904i	$0.241031\pi$
$577$	33.0000i	1.37381i	−0.726748	+	0.686904i	$0.758969\pi$
$578$	− 1.00000i	− 0.0415945i
$579$	−24.0000	−0.997406
$580$	0	0
$581$	−44.0000	−1.82543
$582$	0	0
$583$	− 26.0000i	− 1.07681i
$584$	−16.0000	−0.662085
$585$	0	0
$586$	31.0000	1.28060
$587$	− 25.0000i	− 1.03186i	−0.856631	−	0.515930i	$-0.827446\pi$
$587$	− 25.0000i	− 1.03186i	0.856631	−	0.515930i	$-0.172554\pi$
$588$	9.00000i	0.371154i
$589$	16.0000	0.659269
$590$	0	0
$591$	2.00000	0.0822690
$592$	− 3.00000i	− 0.123299i
$593$	− 12.0000i	− 0.492781i	−0.969171	−	0.246390i	$-0.920755\pi$
$593$	− 12.0000i	− 0.492781i	0.969171	−	0.246390i	$-0.0792446\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	1.00000	0.0409616
$597$	− 10.0000i	− 0.409273i
$598$	− 2.00000i	− 0.0817861i
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	− 24.0000i	− 0.978167i
$603$	− 10.0000i	− 0.407231i
$604$	−1.00000	−0.0406894
$605$	0	0
$606$	10.0000	0.406222
$607$	34.0000i	1.38002i	0.723801	+	0.690009i	$0.242393\pi$
$607$	34.0000i	1.38002i	−0.723801	+	0.690009i	$0.757607\pi$
$608$	− 8.00000i	− 0.324443i
$609$	16.0000	0.648353
$610$	0	0
$611$	8.00000	0.323645
$612$	1.00000i	0.0404226i
$613$	26.0000i	1.05013i	0.851062	+	0.525065i	$0.175959\pi$
$613$	26.0000i	1.05013i	−0.851062	+	0.525065i	$0.824041\pi$
$614$	22.0000	0.887848
$615$	0	0
$616$	−8.00000	−0.322329
$617$	− 6.00000i	− 0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$	− 6.00000i	− 0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$	− 3.00000i	− 0.120678i
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	5.00000i	0.200482i
$623$	− 8.00000i	− 0.320513i
$624$	−2.00000	−0.0800641
$625$	0	0
$626$	−20.0000	−0.799361
$627$	− 16.0000i	− 0.638978i
$628$	− 14.0000i	− 0.558661i
$629$	3.00000	0.119618
$630$	0	0
$631$	−7.00000	−0.278666	−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000	−0.278666	−0.139333	+	0.990246i	$0.544496\pi$
$632$	12.0000i	0.477334i
$633$	4.00000i	0.158986i
$634$	26.0000	1.03259
$635$	0	0
$636$	−13.0000	−0.515484
$637$	− 18.0000i	− 0.713186i
$638$	8.00000i	0.316723i
$639$	1.00000	0.0395594
$640$	0	0
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	12.0000i	0.473602i
$643$	29.0000i	1.14365i	0.820376	+	0.571824i	$0.193764\pi$
$643$	29.0000i	1.14365i	−0.820376	+	0.571824i	$0.806236\pi$
$644$	−4.00000	−0.157622
$645$	0	0
$646$	8.00000	0.314756
$647$	38.0000i	1.49393i	0.664861	+	0.746967i	$0.268491\pi$
$647$	38.0000i	1.49393i	−0.664861	+	0.746967i	$0.731509\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−30.0000	−1.17760
$650$	0	0
$651$	−8.00000	−0.313545
$652$	7.00000i	0.274141i
$653$	− 12.0000i	− 0.469596i	−0.972044	−	0.234798i	$-0.924557\pi$
$653$	− 12.0000i	− 0.469596i	0.972044	−	0.234798i	$-0.0754429\pi$
$654$	−2.00000	−0.0782062
$655$	0	0
$656$	−1.00000	−0.0390434
$657$	16.0000i	0.624219i
$658$	− 16.0000i	− 0.623745i
$659$	40.0000	1.55818	0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000	1.55818	0.779089	+	0.626913i	$0.215682\pi$
$660$	0	0
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	10.0000i	0.388661i
$663$	− 2.00000i	− 0.0776736i
$664$	−11.0000	−0.426883
$665$	0	0
$666$	−3.00000	−0.116248
$667$	4.00000i	0.154881i
$668$	− 24.0000i	− 0.928588i
$669$	−17.0000	−0.657258
$670$	0	0
$671$	10.0000	0.386046
$672$	4.00000i	0.154303i
$673$	− 28.0000i	− 1.07932i	−0.841883	−	0.539660i	$-0.818553\pi$
$673$	− 28.0000i	− 1.07932i	0.841883	−	0.539660i	$-0.181447\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	12.0000i	0.461197i	0.973049	+	0.230599i	$0.0740685\pi$
$677$	12.0000i	0.461197i	−0.973049	+	0.230599i	$0.925932\pi$
$678$	15.0000i	0.576072i
$679$	0	0
$680$	0	0
$681$	−22.0000	−0.843042
$682$	− 4.00000i	− 0.153168i
$683$	− 6.00000i	− 0.229584i	−0.993390	−	0.114792i	$-0.963380\pi$
$683$	− 6.00000i	− 0.229584i	0.993390	−	0.114792i	$-0.0366201\pi$
$684$	−8.00000	−0.305888
$685$	0	0
$686$	−8.00000	−0.305441
$687$	18.0000i	0.686743i
$688$	− 6.00000i	− 0.228748i
$689$	26.0000	0.990521
$690$	0	0
$691$	−41.0000	−1.55971	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000	−1.55971	−0.779857	+	0.625958i	$0.784708\pi$
$692$	− 8.00000i	− 0.304114i
$693$	8.00000i	0.303895i
$694$	16.0000	0.607352
$695$	0	0
$696$	4.00000	0.151620
$697$	− 1.00000i	− 0.0378777i
$698$	14.0000i	0.529908i
$699$	−3.00000	−0.113470
$700$	0	0
$701$	−3.00000	−0.113308	−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000	−0.113308	−0.0566542	+	0.998394i	$0.518043\pi$
$702$	2.00000i	0.0754851i
$703$	24.0000i	0.905177i
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−16.0000	−0.602168
$707$	40.0000i	1.50435i
$708$	15.0000i	0.563735i
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	− 2.00000i	− 0.0749532i
$713$	− 2.00000i	− 0.0749006i
$714$	−4.00000	−0.149696
$715$	0	0
$716$	9.00000	0.336346
$717$	− 6.00000i	− 0.224074i
$718$	− 36.0000i	− 1.34351i
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	12.0000	0.446903
$722$	45.0000i	1.67473i
$723$	− 14.0000i	− 0.520666i
$724$	−11.0000	−0.408812
$725$	0	0
$726$	7.00000	0.259794
$727$	44.0000i	1.63187i	0.578144	+	0.815935i	$0.303777\pi$
$727$	44.0000i	1.63187i	−0.578144	+	0.815935i	$0.696223\pi$
$728$	− 8.00000i	− 0.296500i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	6.00000	0.221918
$732$	− 5.00000i	− 0.184805i
$733$	30.0000i	1.10808i	0.832492	+	0.554038i	$0.186914\pi$
$733$	30.0000i	1.10808i	−0.832492	+	0.554038i	$0.813086\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	20.0000i	0.736709i
$738$	1.00000i	0.0368105i
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	− 52.0000i	− 1.90898i
$743$	17.0000i	0.623670i	0.950136	+	0.311835i	$0.100944\pi$
$743$	17.0000i	0.623670i	−0.950136	+	0.311835i	$0.899056\pi$
$744$	−2.00000	−0.0733236
$745$	0	0
$746$	−4.00000	−0.146450
$747$	11.0000i	0.402469i
$748$	− 2.00000i	− 0.0731272i
$749$	−48.0000	−1.75388
$750$	0	0
$751$	−48.0000	−1.75154	−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000	−1.75154	−0.875772	+	0.482724i	$0.839647\pi$
$752$	− 4.00000i	− 0.145865i
$753$	− 4.00000i	− 0.145768i
$754$	−8.00000	−0.291343
$755$	0	0
$756$	4.00000	0.145479
$757$	− 28.0000i	− 1.01768i	−0.860862	−	0.508839i	$-0.830075\pi$
$757$	− 28.0000i	− 1.01768i	0.860862	−	0.508839i	$-0.169925\pi$
$758$	1.00000i	0.0363216i
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	36.0000	1.30500	0.652499	−	0.757789i	$-0.273720\pi$
$761$	36.0000	1.30500	0.652499	+	0.757789i	$0.273720\pi$
$762$	16.0000i	0.579619i
$763$	− 8.00000i	− 0.289619i
$764$	−10.0000	−0.361787
$765$	0	0
$766$	20.0000	0.722629
$767$	− 30.0000i	− 1.08324i
$768$	1.00000i	0.0360844i
$769$	37.0000	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$769$	37.0000	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$770$	0	0
$771$	12.0000	0.432169
$772$	− 24.0000i	− 0.863779i
$773$	− 15.0000i	− 0.539513i	−0.962929	−	0.269756i	$-0.913057\pi$
$773$	− 15.0000i	− 0.539513i	0.962929	−	0.269756i	$-0.0869431\pi$
$774$	−6.00000	−0.215666
$775$	0	0
$776$	0	0
$777$	− 12.0000i	− 0.430498i
$778$	− 9.00000i	− 0.322666i
$779$	8.00000	0.286630
$780$	0	0
$781$	−2.00000	−0.0715656
$782$	− 1.00000i	− 0.0357599i
$783$	− 4.00000i	− 0.142948i
$784$	−9.00000	−0.321429
$785$	0	0
$786$	−8.00000	−0.285351
$787$	− 3.00000i	− 0.106938i	−0.998569	−	0.0534692i	$-0.982972\pi$
$787$	− 3.00000i	− 0.106938i	0.998569	−	0.0534692i	$-0.0170279\pi$
$788$	2.00000i	0.0712470i
$789$	−4.00000	−0.142404
$790$	0	0
$791$	−60.0000	−2.13335
$792$	2.00000i	0.0710669i
$793$	10.0000i	0.355110i
$794$	−21.0000	−0.745262
$795$	0	0
$796$	10.0000	0.354441
$797$	31.0000i	1.09808i	0.835797	+	0.549038i	$0.185006\pi$
$797$	31.0000i	1.09808i	−0.835797	+	0.549038i	$0.814994\pi$
$798$	− 32.0000i	− 1.13279i
$799$	4.00000	0.141510
$800$	0	0
$801$	−2.00000	−0.0706665
$802$	3.00000i	0.105934i
$803$	− 32.0000i	− 1.12926i
$804$	10.0000	0.352673
$805$	0	0
$806$	4.00000	0.140894
$807$	6.00000i	0.211210i
$808$	10.0000i	0.351799i
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	16.0000i	0.561490i
$813$	− 21.0000i	− 0.736502i
$814$	6.00000	0.210300
$815$	0	0
$816$	−1.00000	−0.0350070
$817$	48.0000i	1.67931i
$818$	− 19.0000i	− 0.664319i
$819$	−8.00000	−0.279543
$820$	0	0
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	12.0000i	0.418548i
$823$	− 32.0000i	− 1.11545i	−0.830026	−	0.557725i	$-0.811674\pi$
$823$	− 32.0000i	− 1.11545i	0.830026	−	0.557725i	$-0.188326\pi$
$824$	3.00000	0.104510
$825$	0	0
$826$	−60.0000	−2.08767
$827$	38.0000i	1.32139i	0.750655	+	0.660695i	$0.229738\pi$
$827$	38.0000i	1.32139i	−0.750655	+	0.660695i	$0.770262\pi$
$828$	1.00000i	0.0347524i
$829$	16.0000	0.555703	0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000	0.555703	0.277851	+	0.960624i	$0.410378\pi$
$830$	0	0
$831$	31.0000	1.07538
$832$	− 2.00000i	− 0.0693375i
$833$	− 9.00000i	− 0.311832i
$834$	1.00000	0.0346272
$835$	0	0
$836$	16.0000	0.553372
$837$	2.00000i	0.0691301i
$838$	− 24.0000i	− 0.829066i
$839$	−27.0000	−0.932144	−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000	−0.932144	−0.466072	+	0.884747i	$0.654331\pi$
$840$	0	0
$841$	−13.0000	−0.448276
$842$	− 24.0000i	− 0.827095i
$843$	− 2.00000i	− 0.0688837i
$844$	−4.00000	−0.137686
$845$	0	0
$846$	−4.00000	−0.137523
$847$	28.0000i	0.962091i
$848$	− 13.0000i	− 0.446422i
$849$	7.00000	0.240239
$850$	0	0
$851$	3.00000	0.102839
$852$	1.00000i	0.0342594i
$853$	− 26.0000i	− 0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$	− 26.0000i	− 0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	20.0000	0.684386
$855$	0	0
$856$	−12.0000	−0.410152
$857$	− 7.00000i	− 0.239115i	−0.992827	−	0.119558i	$-0.961852\pi$
$857$	− 7.00000i	− 0.239115i	0.992827	−	0.119558i	$-0.0381477\pi$
$858$	− 4.00000i	− 0.136558i
$859$	44.0000	1.50126	0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000	1.50126	0.750630	+	0.660722i	$0.229750\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	− 28.0000i	− 0.953684i
$863$	40.0000i	1.36162i	0.732462	+	0.680808i	$0.238371\pi$
$863$	40.0000i	1.36162i	−0.732462	+	0.680808i	$0.761629\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−14.0000	−0.475739
$867$	− 1.00000i	− 0.0339618i
$868$	− 8.00000i	− 0.271538i
$869$	−24.0000	−0.814144
$870$	0	0
$871$	−20.0000	−0.677674
$872$	− 2.00000i	− 0.0677285i
$873$	0	0
$874$	8.00000	0.270604
$875$	0	0
$876$	−16.0000	−0.540590
$877$	14.0000i	0.472746i	0.971662	+	0.236373i	$0.0759588\pi$
$877$	14.0000i	0.472746i	−0.971662	+	0.236373i	$0.924041\pi$
$878$	12.0000i	0.404980i
$879$	31.0000	1.04560
$880$	0	0
$881$	33.0000	1.11180	0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000	1.11180	0.555899	+	0.831250i	$0.312374\pi$
$882$	9.00000i	0.303046i
$883$	− 50.0000i	− 1.68263i	−0.540542	−	0.841317i	$-0.681781\pi$
$883$	− 50.0000i	− 1.68263i	0.540542	−	0.841317i	$-0.318219\pi$
$884$	2.00000	0.0672673
$885$	0	0
$886$	39.0000	1.31023
$887$	− 15.0000i	− 0.503651i	−0.967773	−	0.251825i	$-0.918969\pi$
$887$	− 15.0000i	− 0.503651i	0.967773	−	0.251825i	$-0.0810309\pi$
$888$	− 3.00000i	− 0.100673i
$889$	−64.0000	−2.14649
$890$	0	0
$891$	2.00000	0.0670025
$892$	− 17.0000i	− 0.569202i
$893$	32.0000i	1.07084i
$894$	1.00000	0.0334450
$895$	0	0
$896$	−4.00000	−0.133631
$897$	− 2.00000i	− 0.0667781i
$898$	42.0000i	1.40156i
$899$	−8.00000	−0.266815
$900$	0	0
$901$	13.0000	0.433093
$902$	− 2.00000i	− 0.0665927i
$903$	− 24.0000i	− 0.798670i
$904$	−15.0000	−0.498893
$905$	0	0
$906$	−1.00000	−0.0332228
$907$	− 23.0000i	− 0.763702i	−0.924224	−	0.381851i	$-0.875287\pi$
$907$	− 23.0000i	− 0.763702i	0.924224	−	0.381851i	$-0.124713\pi$
$908$	− 22.0000i	− 0.730096i
$909$	10.0000	0.331679
$910$	0	0
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	− 8.00000i	− 0.264906i
$913$	− 22.0000i	− 0.728094i
$914$	−31.0000	−1.02539
$915$	0	0
$916$	−18.0000	−0.594737
$917$	− 32.0000i	− 1.05673i
$918$	1.00000i	0.0330049i
$919$	47.0000	1.55039	0.775193	−	0.631724i	$-0.217652\pi$
$919$	47.0000	1.55039	0.775193	+	0.631724i	$0.217652\pi$
$920$	0	0
$921$	22.0000	0.724925
$922$	− 1.00000i	− 0.0329332i
$923$	− 2.00000i	− 0.0658308i
$924$	−8.00000	−0.263181
$925$	0	0
$926$	−35.0000	−1.15017
$927$	− 3.00000i	− 0.0985329i
$928$	4.00000i	0.131306i
$929$	15.0000	0.492134	0.246067	−	0.969253i	$-0.420862\pi$
$929$	15.0000	0.492134	0.246067	+	0.969253i	$0.420862\pi$
$930$	0	0
$931$	72.0000	2.35970
$932$	− 3.00000i	− 0.0982683i
$933$	5.00000i	0.163693i
$934$	3.00000	0.0981630
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	17.0000i	0.555366i	0.960673	+	0.277683i	$0.0895665\pi$
$937$	17.0000i	0.555366i	−0.960673	+	0.277683i	$0.910434\pi$
$938$	40.0000i	1.30605i
$939$	−20.0000	−0.652675
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	− 14.0000i	− 0.456145i
$943$	− 1.00000i	− 0.0325645i
$944$	−15.0000	−0.488208
$945$	0	0
$946$	12.0000	0.390154
$947$	− 16.0000i	− 0.519930i	−0.965618	−	0.259965i	$-0.916289\pi$
$947$	− 16.0000i	− 0.519930i	0.965618	−	0.259965i	$-0.0837111\pi$
$948$	12.0000i	0.389742i
$949$	32.0000	1.03876
$950$	0	0
$951$	26.0000	0.843108
$952$	− 4.00000i	− 0.129641i
$953$	42.0000i	1.36051i	0.732974	+	0.680257i	$0.238132\pi$
$953$	42.0000i	1.36051i	−0.732974	+	0.680257i	$0.761868\pi$
$954$	−13.0000	−0.420891
$955$	0	0
$956$	6.00000	0.194054
$957$	8.00000i	0.258603i
$958$	16.0000i	0.516937i
$959$	−48.0000	−1.55000
$960$	0	0
$961$	−27.0000	−0.870968
$962$	6.00000i	0.193448i
$963$	12.0000i	0.386695i
$964$	14.0000	0.450910
$965$	0	0
$966$	−4.00000	−0.128698
$967$	− 1.00000i	− 0.0321578i	−0.999871	−	0.0160789i	$-0.994882\pi$
$967$	− 1.00000i	− 0.0321578i	0.999871	−	0.0160789i	$-0.00511830\pi$
$968$	7.00000i	0.224989i
$969$	8.00000	0.256997
$970$	0	0
$971$	25.0000	0.802288	0.401144	−	0.916015i	$-0.368613\pi$
$971$	25.0000	0.802288	0.401144	+	0.916015i	$0.368613\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	4.00000i	0.128234i
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	5.00000	0.160046
$977$	18.0000i	0.575871i	0.957650	+	0.287936i	$0.0929689\pi$
$977$	18.0000i	0.575871i	−0.957650	+	0.287936i	$0.907031\pi$
$978$	7.00000i	0.223835i
$979$	4.00000	0.127841
$980$	0	0
$981$	−2.00000	−0.0638551
$982$	39.0000i	1.24454i
$983$	− 8.00000i	− 0.255160i	−0.991828	−	0.127580i	$-0.959279\pi$
$983$	− 8.00000i	− 0.255160i	0.991828	−	0.127580i	$-0.0407210\pi$
$984$	−1.00000	−0.0318788
$985$	0	0
$986$	−4.00000	−0.127386
$987$	− 16.0000i	− 0.509286i
$988$	16.0000i	0.509028i
$989$	6.00000	0.190789
$990$	0	0
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	− 2.00000i	− 0.0635001i
$993$	10.0000i	0.317340i
$994$	−4.00000	−0.126872
$995$	0	0
$996$	−11.0000	−0.348548
$997$	− 50.0000i	− 1.58352i	−0.610835	−	0.791758i	$-0.709166\pi$
$997$	− 50.0000i	− 1.58352i	0.610835	−	0.791758i	$-0.290834\pi$
$998$	41.0000i	1.29783i
$999$	−3.00000	−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2550.2.d.h.2449.2		2
5.2	odd	4		2550.2.a.q.1.1	✓	1
5.3	odd	4		2550.2.a.t.1.1	yes	1
5.4	even	2	inner	2550.2.d.h.2449.1		2
15.2	even	4		7650.2.a.cj.1.1		1
15.8	even	4		7650.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2550.2.a.q.1.1	✓	1	5.2	odd	4
2550.2.a.t.1.1	yes	1	5.3	odd	4
2550.2.d.h.2449.1		2	5.4	even	2	inner
2550.2.d.h.2449.2		2	1.1	even	1	trivial
7650.2.a.c.1.1		1	15.8	even	4
7650.2.a.cj.1.1		1	15.2	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:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -4.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} -1.00000i q^{12} +2.00000i q^{13} +4.00000 q^{14} +1.00000 q^{16} +1.00000i q^{17} -1.00000i q^{18} -8.00000 q^{19} +4.00000 q^{21} +2.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} -2.00000 q^{26} -1.00000i q^{27} +4.00000i q^{28} +4.00000 q^{29} -2.00000 q^{31} +1.00000i q^{32} +2.00000i q^{33} -1.00000 q^{34} +1.00000 q^{36} -3.00000i q^{37} -8.00000i q^{38} -2.00000 q^{39} -1.00000 q^{41} +4.00000i q^{42} -6.00000i q^{43} -2.00000 q^{44} -1.00000 q^{46} -4.00000i q^{47} +1.00000i q^{48} -9.00000 q^{49} -1.00000 q^{51} -2.00000i q^{52} -13.0000i q^{53} +1.00000 q^{54} -4.00000 q^{56} -8.00000i q^{57} +4.00000i q^{58} -15.0000 q^{59} +5.00000 q^{61} -2.00000i q^{62} +4.00000i q^{63} -1.00000 q^{64} -2.00000 q^{66} +10.0000i q^{67} -1.00000i q^{68} -1.00000 q^{69} -1.00000 q^{71} +1.00000i q^{72} -16.0000i q^{73} +3.00000 q^{74} +8.00000 q^{76} -8.00000i q^{77} -2.00000i q^{78} -12.0000 q^{79} +1.00000 q^{81} -1.00000i q^{82} -11.0000i q^{83} -4.00000 q^{84} +6.00000 q^{86} +4.00000i q^{87} -2.00000i q^{88} +2.00000 q^{89} +8.00000 q^{91} -1.00000i q^{92} -2.00000i q^{93} +4.00000 q^{94} -1.00000 q^{96} -9.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} + 4 q^{11} + 8 q^{14} + 2 q^{16} - 16 q^{19} + 8 q^{21} + 2 q^{24} - 4 q^{26} + 8 q^{29} - 4 q^{31} - 2 q^{34} + 2 q^{36} - 4 q^{39} - 2 q^{41} - 4 q^{44} - 2 q^{46} - 18 q^{49} - 2 q^{51} + 2 q^{54} - 8 q^{56} - 30 q^{59} + 10 q^{61} - 2 q^{64} - 4 q^{66} - 2 q^{69} - 2 q^{71} + 6 q^{74} + 16 q^{76} - 24 q^{79} + 2 q^{81} - 8 q^{84} + 12 q^{86} + 4 q^{89} + 16 q^{91} + 8 q^{94} - 2 q^{96} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 + 4 * q^11 + 8 * q^14 + 2 * q^16 - 16 * q^19 + 8 * q^21 + 2 * q^24 - 4 * q^26 + 8 * q^29 - 4 * q^31 - 2 * q^34 + 2 * q^36 - 4 * q^39 - 2 * q^41 - 4 * q^44 - 2 * q^46 - 18 * q^49 - 2 * q^51 + 2 * q^54 - 8 * q^56 - 30 * q^59 + 10 * q^61 - 2 * q^64 - 4 * q^66 - 2 * q^69 - 2 * q^71 + 6 * q^74 + 16 * q^76 - 24 * q^79 + 2 * q^81 - 8 * q^84 + 12 * q^86 + 4 * q^89 + 16 * q^91 + 8 * q^94 - 2 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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