LMFDB - Embedded newform 1183.2.c.i.337.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.3
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.i.337.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38595i q^{2} -2.82577 q^{3} +0.0791355 q^{4} -0.518957i q^{5} +3.91639i q^{6} +1.00000i q^{7} -2.88158i q^{8} +4.98500 q^{9} +O(q^{10})$	\(q-1.38595i q^{2} -2.82577 q^{3} +0.0791355 q^{4} -0.518957i q^{5} +3.91639i q^{6} +1.00000i q^{7} -2.88158i q^{8} +4.98500 q^{9} -0.719250 q^{10} +1.62416i q^{11} -0.223619 q^{12} +1.38595 q^{14} +1.46646i q^{15} -3.83547 q^{16} -1.94825 q^{17} -6.90897i q^{18} -2.49115i q^{19} -0.0410679i q^{20} -2.82577i q^{21} +2.25101 q^{22} +9.14058 q^{23} +8.14270i q^{24} +4.73068 q^{25} -5.60916 q^{27} +0.0791355i q^{28} -5.22996 q^{29} +2.03244 q^{30} -5.79391i q^{31} -0.447392i q^{32} -4.58951i q^{33} +2.70019i q^{34} +0.518957 q^{35} +0.394491 q^{36} -10.2293i q^{37} -3.45262 q^{38} -1.49542 q^{40} +4.20903i q^{41} -3.91639 q^{42} +0.997311 q^{43} +0.128529i q^{44} -2.58700i q^{45} -12.6684i q^{46} -4.51725i q^{47} +10.8382 q^{48} -1.00000 q^{49} -6.55650i q^{50} +5.50532 q^{51} -8.89651 q^{53} +7.77403i q^{54} +0.842869 q^{55} +2.88158 q^{56} +7.03944i q^{57} +7.24847i q^{58} +6.20526i q^{59} +0.116049i q^{60} -13.4707 q^{61} -8.03008 q^{62} +4.98500i q^{63} -8.29100 q^{64} -6.36084 q^{66} -8.37266i q^{67} -0.154176 q^{68} -25.8292 q^{69} -0.719250i q^{70} +5.19809i q^{71} -14.3647i q^{72} -11.8395i q^{73} -14.1773 q^{74} -13.3678 q^{75} -0.197139i q^{76} -1.62416 q^{77} +0.982310 q^{79} +1.99044i q^{80} +0.895217 q^{81} +5.83352 q^{82} +8.91851i q^{83} -0.223619i q^{84} +1.01106i q^{85} -1.38223i q^{86} +14.7787 q^{87} +4.68015 q^{88} -12.0190i q^{89} -3.58546 q^{90} +0.723345 q^{92} +16.3723i q^{93} -6.26070 q^{94} -1.29280 q^{95} +1.26423i q^{96} -4.42228i q^{97} +1.38595i q^{98} +8.09643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 + 8 * q^9	$ 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42} - 4 q^{43} + 4 q^{48} - 12 q^{49} + 52 q^{51} - 44 q^{53} + 12 q^{55} + 24 q^{56} - 28 q^{61} + 8 q^{62} - 52 q^{64} - 52 q^{66} + 16 q^{68} - 8 q^{69} - 12 q^{74} - 92 q^{75} + 8 q^{77} - 56 q^{79} - 4 q^{81} - 28 q^{82} + 4 q^{87} + 28 q^{88} + 24 q^{90} + 24 q^{92} - 8 q^{94} + 44 q^{95}+O(q^{100}) $ 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 1.38595i	− 0.980016i	−0.871718	−	0.490008i	$-0.836994\pi$
$2$	− 1.38595i	− 0.980016i	0.871718	−	0.490008i	$-0.163006\pi$
$3$	−2.82577	−1.63146	−0.815731	−	0.578432i	$-0.803665\pi$
$3$	−2.82577	−1.63146	−0.815731	+	0.578432i	$0.803665\pi$
$4$	0.0791355	0.0395678
$5$	− 0.518957i	− 0.232085i	−0.993244	−	0.116042i	$-0.962979\pi$
$5$	− 0.518957i	− 0.232085i	0.993244	−	0.116042i	$-0.0370208\pi$
$6$	3.91639i	1.59886i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 2.88158i	− 1.01879i
$9$	4.98500	1.66167
$10$	−0.719250	−0.227447
$11$	1.62416i	0.489702i	0.969561	+	0.244851i	$0.0787391\pi$
$11$	1.62416i	0.489702i	−0.969561	+	0.244851i	$0.921261\pi$
$12$	−0.223619	−0.0645533
$13$	0	0
$13$	0	0
$14$	1.38595	0.370411
$15$	1.46646i	0.378637i
$16$	−3.83547	−0.958867
$17$	−1.94825	−0.472521	−0.236260	−	0.971690i	$-0.575922\pi$
$17$	−1.94825	−0.472521	−0.236260	+	0.971690i	$0.575922\pi$
$18$	− 6.90897i	− 1.62846i
$19$	− 2.49115i	− 0.571510i	−0.958303	−	0.285755i	$-0.907756\pi$
$19$	− 2.49115i	− 0.571510i	0.958303	−	0.285755i	$-0.0922444\pi$
$20$	− 0.0410679i	− 0.00918307i
$21$	− 2.82577i	− 0.616634i
$22$	2.25101	0.479916
$23$	9.14058	1.90594	0.952971	−	0.303060i	$-0.0980083\pi$
$23$	9.14058	1.90594	0.952971	+	0.303060i	$0.0980083\pi$
$24$	8.14270i	1.66212i
$25$	4.73068	0.946137
$26$	0	0
$27$	−5.60916	−1.07948
$28$	0.0791355i	0.0149552i
$29$	−5.22996	−0.971179	−0.485589	−	0.874187i	$-0.661395\pi$
$29$	−5.22996	−0.971179	−0.485589	+	0.874187i	$0.661395\pi$
$30$	2.03244	0.371071
$31$	− 5.79391i	− 1.04062i	−0.853978	−	0.520308i	$-0.825817\pi$
$31$	− 5.79391i	− 1.04062i	0.853978	−	0.520308i	$-0.174183\pi$
$32$	− 0.447392i	− 0.0790885i
$33$	− 4.58951i	− 0.798931i
$34$	2.70019i	0.463078i
$35$	0.518957	0.0877197
$36$	0.394491	0.0657484
$37$	− 10.2293i	− 1.68168i	−0.541284	−	0.840840i	$-0.682062\pi$
$37$	− 10.2293i	− 1.68168i	0.541284	−	0.840840i	$-0.317938\pi$
$38$	−3.45262	−0.560089
$39$	0	0
$40$	−1.49542	−0.236446
$41$	4.20903i	0.657340i	0.944445	+	0.328670i	$0.106600\pi$
$41$	4.20903i	0.657340i	−0.944445	+	0.328670i	$0.893400\pi$
$42$	−3.91639	−0.604312
$43$	0.997311	0.152088	0.0760442	−	0.997104i	$-0.475771\pi$
$43$	0.997311	0.152088	0.0760442	+	0.997104i	$0.475771\pi$
$44$	0.128529i	0.0193764i
$45$	− 2.58700i	− 0.385647i
$46$	− 12.6684i	− 1.86786i
$47$	− 4.51725i	− 0.658909i	−0.944171	−	0.329455i	$-0.893135\pi$
$47$	− 4.51725i	− 0.658909i	0.944171	−	0.329455i	$-0.106865\pi$
$48$	10.8382	1.56435
$49$	−1.00000	−0.142857
$50$	− 6.55650i	− 0.927230i
$51$	5.50532	0.770899
$52$	0	0
$53$	−8.89651	−1.22203	−0.611015	−	0.791619i	$-0.709238\pi$
$53$	−8.89651	−1.22203	−0.611015	+	0.791619i	$0.709238\pi$
$54$	7.77403i	1.05791i
$55$	0.842869	0.113652
$56$	2.88158	0.385068
$57$	7.03944i	0.932397i
$58$	7.24847i	0.951771i
$59$	6.20526i	0.807856i	0.914791	+	0.403928i	$0.132355\pi$
$59$	6.20526i	0.807856i	−0.914791	+	0.403928i	$0.867645\pi$
$60$	0.116049i	0.0149818i
$61$	−13.4707	−1.72475	−0.862375	−	0.506270i	$-0.831024\pi$
$61$	−13.4707	−1.72475	−0.862375	+	0.506270i	$0.831024\pi$
$62$	−8.03008	−1.01982
$63$	4.98500i	0.628051i
$64$	−8.29100	−1.03637
$65$	0	0
$66$	−6.36084	−0.782965
$67$	− 8.37266i	− 1.02288i	−0.859318	−	0.511442i	$-0.829112\pi$
$67$	− 8.37266i	− 1.02288i	0.859318	−	0.511442i	$-0.170888\pi$
$68$	−0.154176	−0.0186966
$69$	−25.8292	−3.10947
$70$	− 0.719250i	− 0.0859668i
$71$	5.19809i	0.616900i	0.951241	+	0.308450i	$0.0998103\pi$
$71$	5.19809i	0.616900i	−0.951241	+	0.308450i	$0.900190\pi$
$72$	− 14.3647i	− 1.69289i
$73$	− 11.8395i	− 1.38571i	−0.721076	−	0.692856i	$-0.756352\pi$
$73$	− 11.8395i	− 1.38571i	0.721076	−	0.692856i	$-0.243648\pi$
$74$	−14.1773	−1.64807
$75$	−13.3678	−1.54359
$76$	− 0.197139i	− 0.0226134i
$77$	−1.62416	−0.185090
$78$	0	0
$79$	0.982310	0.110518	0.0552592	−	0.998472i	$-0.482401\pi$
$79$	0.982310	0.110518	0.0552592	+	0.998472i	$0.482401\pi$
$80$	1.99044i	0.222538i
$81$	0.895217	0.0994686
$82$	5.83352	0.644204
$83$	8.91851i	0.978934i	0.872022	+	0.489467i	$0.162809\pi$
$83$	8.91851i	0.978934i	−0.872022	+	0.489467i	$0.837191\pi$
$84$	− 0.223619i	− 0.0243989i
$85$	1.01106i	0.109665i
$86$	− 1.38223i	− 0.149049i
$87$	14.7787	1.58444
$88$	4.68015	0.498906
$89$	− 12.0190i	− 1.27401i	−0.770860	−	0.637005i	$-0.780173\pi$
$89$	− 12.0190i	− 1.27401i	0.770860	−	0.637005i	$-0.219827\pi$
$90$	−3.58546	−0.377941
$91$	0	0
$92$	0.723345	0.0754139
$93$	16.3723i	1.69773i
$94$	−6.26070	−0.645742
$95$	−1.29280	−0.132639
$96$	1.26423i	0.129030i
$97$	− 4.42228i	− 0.449015i	−0.974472	−	0.224507i	$-0.927923\pi$
$97$	− 4.42228i	− 0.449015i	0.974472	−	0.224507i	$-0.0720773\pi$
$98$	1.38595i	0.140002i
$99$	8.09643i	0.813722i
$100$	0.374365	0.0374365
$101$	−18.3026	−1.82118	−0.910591	−	0.413309i	$-0.864373\pi$
$101$	−18.3026	−1.82118	−0.910591	+	0.413309i	$0.864373\pi$
$102$	− 7.63012i	− 0.755494i
$103$	−5.02046	−0.494680	−0.247340	−	0.968929i	$-0.579556\pi$
$103$	−5.02046	−0.494680	−0.247340	+	0.968929i	$0.579556\pi$
$104$	0	0
$105$	−1.46646	−0.143111
$106$	12.3301i	1.19761i
$107$	6.14456	0.594017	0.297008	−	0.954875i	$-0.404011\pi$
$107$	6.14456	0.594017	0.297008	+	0.954875i	$0.404011\pi$
$108$	−0.443884	−0.0427127
$109$	− 11.8962i	− 1.13945i	−0.821834	−	0.569727i	$-0.807049\pi$
$109$	− 11.8962i	− 1.13945i	0.821834	−	0.569727i	$-0.192951\pi$
$110$	− 1.16818i	− 0.111381i
$111$	28.9056i	2.74359i
$112$	− 3.83547i	− 0.362418i
$113$	3.55612	0.334532	0.167266	−	0.985912i	$-0.446506\pi$
$113$	3.55612	0.334532	0.167266	+	0.985912i	$0.446506\pi$
$114$	9.75633	0.913764
$115$	− 4.74357i	− 0.442340i
$116$	−0.413875	−0.0384274
$117$	0	0
$118$	8.60020	0.791713
$119$	− 1.94825i	− 0.178596i
$120$	4.22571	0.385753
$121$	8.36211	0.760191
$122$	18.6698i	1.69028i
$123$	− 11.8938i	− 1.07243i
$124$	− 0.458504i	− 0.0411749i
$125$	− 5.04981i	− 0.451668i
$126$	6.90897	0.615500
$127$	1.42350	0.126315	0.0631575	−	0.998004i	$-0.479883\pi$
$127$	1.42350	0.126315	0.0631575	+	0.998004i	$0.479883\pi$
$128$	10.5961i	0.936576i
$129$	−2.81818	−0.248127
$130$	0	0
$131$	8.67374	0.757828	0.378914	−	0.925432i	$-0.376298\pi$
$131$	8.67374	0.757828	0.378914	+	0.925432i	$0.376298\pi$
$132$	− 0.363193i	− 0.0316119i
$133$	2.49115	0.216011
$134$	−11.6041	−1.00244
$135$	2.91091i	0.250531i
$136$	5.61405i	0.481401i
$137$	− 8.51784i	− 0.727728i	−0.931452	−	0.363864i	$-0.881457\pi$
$137$	− 8.51784i	− 0.727728i	0.931452	−	0.363864i	$-0.118543\pi$
$138$	35.7981i	3.04733i
$139$	−5.03844	−0.427355	−0.213677	−	0.976904i	$-0.568544\pi$
$139$	−5.03844	−0.427355	−0.213677	+	0.976904i	$0.568544\pi$
$140$	0.0410679	0.00347087
$141$	12.7647i	1.07499i
$142$	7.20431	0.604572
$143$	0	0
$144$	−19.1198	−1.59332
$145$	2.71412i	0.225396i
$146$	−16.4090	−1.35802
$147$	2.82577	0.233066
$148$	− 0.809498i	− 0.0665403i
$149$	− 3.36490i	− 0.275663i	−0.990456	−	0.137832i	$-0.955987\pi$
$149$	− 3.36490i	− 0.275663i	0.990456	−	0.137832i	$-0.0440133\pi$
$150$	18.5272i	1.51274i
$151$	12.6566i	1.02998i	0.857196	+	0.514991i	$0.172205\pi$
$151$	12.6566i	1.02998i	−0.857196	+	0.514991i	$0.827795\pi$
$152$	−7.17847	−0.582251
$153$	−9.71204	−0.785172
$154$	2.25101i	0.181391i
$155$	−3.00679	−0.241511
$156$	0	0
$157$	10.3691	0.827547	0.413773	−	0.910380i	$-0.364211\pi$
$157$	10.3691	0.827547	0.413773	+	0.910380i	$0.364211\pi$
$158$	− 1.36143i	− 0.108310i
$159$	25.1395	1.99369
$160$	−0.232177	−0.0183552
$161$	9.14058i	0.720379i
$162$	− 1.24073i	− 0.0974808i
$163$	− 15.7534i	− 1.23390i	−0.787002	−	0.616950i	$-0.788368\pi$
$163$	− 15.7534i	− 1.23390i	0.787002	−	0.616950i	$-0.211632\pi$
$164$	0.333084i	0.0260095i
$165$	−2.38176	−0.185420
$166$	12.3606	0.959371
$167$	− 16.3986i	− 1.26896i	−0.772939	−	0.634481i	$-0.781214\pi$
$167$	− 16.3986i	− 1.26896i	0.772939	−	0.634481i	$-0.218786\pi$
$168$	−8.14270	−0.628223
$169$	0	0
$170$	1.40128	0.107473
$171$	− 12.4184i	− 0.949659i
$172$	0.0789227	0.00601780
$173$	0.301355	0.0229116	0.0114558	−	0.999934i	$-0.496353\pi$
$173$	0.301355	0.0229116	0.0114558	+	0.999934i	$0.496353\pi$
$174$	− 20.4825i	− 1.55278i
$175$	4.73068i	0.357606i
$176$	− 6.22941i	− 0.469559i
$177$	− 17.5347i	− 1.31799i
$178$	−16.6577	−1.24855
$179$	9.81582	0.733669	0.366834	−	0.930286i	$-0.380442\pi$
$179$	9.81582	0.733669	0.366834	+	0.930286i	$0.380442\pi$
$180$	− 0.204724i	− 0.0152592i
$181$	12.4320	0.924062	0.462031	−	0.886864i	$-0.347121\pi$
$181$	12.4320	0.924062	0.462031	+	0.886864i	$0.347121\pi$
$182$	0	0
$183$	38.0652	2.81386
$184$	− 26.3393i	− 1.94176i
$185$	−5.30854	−0.390292
$186$	22.6912	1.66380
$187$	− 3.16427i	− 0.231395i
$188$	− 0.357475i	− 0.0260716i
$189$	− 5.60916i	− 0.408006i
$190$	1.79176i	0.129988i
$191$	−12.2469	−0.886156	−0.443078	−	0.896483i	$-0.646114\pi$
$191$	−12.2469	−0.886156	−0.443078	+	0.896483i	$0.646114\pi$
$192$	23.4285	1.69081
$193$	− 11.6338i	− 0.837422i	−0.908119	−	0.418711i	$-0.862482\pi$
$193$	− 11.6338i	− 0.837422i	0.908119	−	0.418711i	$-0.137518\pi$
$194$	−6.12908	−0.440042
$195$	0	0
$196$	−0.0791355	−0.00565254
$197$	− 1.80114i	− 0.128326i	−0.997939	−	0.0641631i	$-0.979562\pi$
$197$	− 1.80114i	− 0.128326i	0.997939	−	0.0641631i	$-0.0204378\pi$
$198$	11.2213	0.797461
$199$	−6.59313	−0.467375	−0.233687	−	0.972312i	$-0.575079\pi$
$199$	−6.59313	−0.467375	−0.233687	+	0.972312i	$0.575079\pi$
$200$	− 13.6319i	− 0.963918i
$201$	23.6592i	1.66879i
$202$	25.3666i	1.78479i
$203$	− 5.22996i	− 0.367071i
$204$	0.435667	0.0305028
$205$	2.18431	0.152559
$206$	6.95811i	0.484795i
$207$	45.5658	3.16704
$208$	0	0
$209$	4.04603	0.279870
$210$	2.03244i	0.140252i
$211$	10.7199	0.737990	0.368995	−	0.929431i	$-0.379702\pi$
$211$	10.7199	0.737990	0.368995	+	0.929431i	$0.379702\pi$
$212$	−0.704030	−0.0483530
$213$	− 14.6886i	− 1.00645i
$214$	− 8.51607i	− 0.582146i
$215$	− 0.517562i	− 0.0352974i
$216$	16.1633i	1.09977i
$217$	5.79391	0.393316
$218$	−16.4876	−1.11668
$219$	33.4558i	2.26074i
$220$	0.0667009	0.00449697
$221$	0	0
$222$	40.0617	2.68877
$223$	− 12.8878i	− 0.863034i	−0.902105	−	0.431517i	$-0.857979\pi$
$223$	− 12.8878i	− 0.863034i	0.902105	−	0.431517i	$-0.142021\pi$
$224$	0.447392	0.0298926
$225$	23.5825	1.57216
$226$	− 4.92862i	− 0.327847i
$227$	0.699155i	0.0464045i	0.999731	+	0.0232023i	$0.00738617\pi$
$227$	0.699155i	0.0464045i	−0.999731	+	0.0232023i	$0.992614\pi$
$228$	0.557070i	0.0368929i
$229$	18.2868i	1.20843i	0.796822	+	0.604214i	$0.206513\pi$
$229$	18.2868i	1.20843i	−0.796822	+	0.604214i	$0.793487\pi$
$230$	−6.57436	−0.433501
$231$	4.58951	0.301967
$232$	15.0706i	0.989431i
$233$	−26.7796	−1.75439	−0.877194	−	0.480137i	$-0.840587\pi$
$233$	−26.7796	−1.75439	−0.877194	+	0.480137i	$0.840587\pi$
$234$	0	0
$235$	−2.34426	−0.152923
$236$	0.491057i	0.0319651i
$237$	−2.77579	−0.180307
$238$	−2.70019	−0.175027
$239$	16.6177i	1.07491i	0.843293	+	0.537454i	$0.180614\pi$
$239$	16.6177i	1.07491i	−0.843293	+	0.537454i	$0.819386\pi$
$240$	− 5.62454i	− 0.363063i
$241$	− 17.4129i	− 1.12166i	−0.827931	−	0.560830i	$-0.810482\pi$
$241$	− 17.4129i	− 1.12166i	0.827931	−	0.560830i	$-0.189518\pi$
$242$	− 11.5895i	− 0.745000i
$243$	14.2978	0.917204
$244$	−1.06601	−0.0682445
$245$	0.518957i	0.0331549i
$246$	−16.4842	−1.05099
$247$	0	0
$248$	−16.6956	−1.06017
$249$	− 25.2017i	− 1.59709i
$250$	−6.99879	−0.442642
$251$	6.44982	0.407109	0.203554	−	0.979064i	$-0.434751\pi$
$251$	6.44982	0.407109	0.203554	+	0.979064i	$0.434751\pi$
$252$	0.394491i	0.0248506i
$253$	14.8458i	0.933345i
$254$	− 1.97290i	− 0.123791i
$255$	− 2.85703i	− 0.178914i
$256$	−1.89624	−0.118515
$257$	3.67156	0.229025	0.114513	−	0.993422i	$-0.463469\pi$
$257$	3.67156	0.229025	0.114513	+	0.993422i	$0.463469\pi$
$258$	3.90586i	0.243168i
$259$	10.2293	0.635615
$260$	0	0
$261$	−26.0713	−1.61377
$262$	− 12.0214i	− 0.742684i
$263$	18.3193	1.12961	0.564807	−	0.825223i	$-0.308950\pi$
$263$	18.3193	1.12961	0.564807	+	0.825223i	$0.308950\pi$
$264$	−13.2250	−0.813945
$265$	4.61690i	0.283614i
$266$	− 3.45262i	− 0.211694i
$267$	33.9629i	2.07850i
$268$	− 0.662575i	− 0.0404732i
$269$	27.5429	1.67932	0.839661	−	0.543111i	$-0.182754\pi$
$269$	27.5429	1.67932	0.839661	+	0.543111i	$0.182754\pi$
$270$	4.03439	0.245525
$271$	6.51923i	0.396015i	0.980201	+	0.198007i	$0.0634470\pi$
$271$	6.51923i	0.396015i	−0.980201	+	0.198007i	$0.936553\pi$
$272$	7.47246	0.453084
$273$	0	0
$274$	−11.8053	−0.713186
$275$	7.68338i	0.463325i
$276$	−2.04401	−0.123035
$277$	−5.44186	−0.326970	−0.163485	−	0.986546i	$-0.552273\pi$
$277$	−5.44186	−0.326970	−0.163485	+	0.986546i	$0.552273\pi$
$278$	6.98304i	0.418815i
$279$	− 28.8826i	− 1.72916i
$280$	− 1.49542i	− 0.0893683i
$281$	3.54237i	0.211320i	0.994402	+	0.105660i	$0.0336955\pi$
$281$	3.54237i	0.211320i	−0.994402	+	0.105660i	$0.966304\pi$
$282$	17.6913	1.05350
$283$	14.1391	0.840484	0.420242	−	0.907412i	$-0.361945\pi$
$283$	14.1391	0.840484	0.420242	+	0.907412i	$0.361945\pi$
$284$	0.411354i	0.0244094i
$285$	3.65317	0.216395
$286$	0	0
$287$	−4.20903	−0.248451
$288$	− 2.23025i	− 0.131419i
$289$	−13.2043	−0.776724
$290$	3.76165	0.220891
$291$	12.4964i	0.732551i
$292$	− 0.936928i	− 0.0548295i
$293$	8.34931i	0.487772i	0.969804	+	0.243886i	$0.0784222\pi$
$293$	8.34931i	0.487772i	−0.969804	+	0.243886i	$0.921578\pi$
$294$	− 3.91639i	− 0.228408i
$295$	3.22027	0.187491
$296$	−29.4765	−1.71328
$297$	− 9.11017i	− 0.528626i
$298$	−4.66359	−0.270155
$299$	0	0
$300$	−1.05787	−0.0610762
$301$	0.997311i	0.0574840i
$302$	17.5415	1.00940
$303$	51.7192	2.97119
$304$	9.55474i	0.548002i
$305$	6.99073i	0.400288i
$306$	13.4604i	0.769481i
$307$	− 8.33362i	− 0.475625i	−0.971311	−	0.237813i	$-0.923570\pi$
$307$	− 8.33362i	− 0.475625i	0.971311	−	0.237813i	$-0.0764304\pi$
$308$	−0.128529	−0.00732360
$309$	14.1867	0.807052
$310$	4.16727i	0.236685i
$311$	14.6227	0.829176	0.414588	−	0.910009i	$-0.363926\pi$
$311$	14.6227	0.829176	0.414588	+	0.910009i	$0.363926\pi$
$312$	0	0
$313$	17.1328	0.968404	0.484202	−	0.874956i	$-0.339110\pi$
$313$	17.1328	0.968404	0.484202	+	0.874956i	$0.339110\pi$
$314$	− 14.3711i	− 0.811009i
$315$	2.58700	0.145761
$316$	0.0777356	0.00437297
$317$	14.0000i	0.786320i	0.919470	+	0.393160i	$0.128618\pi$
$317$	14.0000i	0.786320i	−0.919470	+	0.393160i	$0.871382\pi$
$318$	− 34.8422i	− 1.95385i
$319$	− 8.49428i	− 0.475589i
$320$	4.30267i	0.240527i
$321$	−17.3631	−0.969116
$322$	12.6684	0.705983
$323$	4.85340i	0.270050i
$324$	0.0708435	0.00393575
$325$	0	0
$326$	−21.8334	−1.20924
$327$	33.6161i	1.85897i
$328$	12.1287	0.669694
$329$	4.51725	0.249044
$330$	3.30100i	0.181714i
$331$	− 6.91996i	− 0.380355i	−0.981750	−	0.190178i	$-0.939094\pi$
$331$	− 6.91996i	− 0.380355i	0.981750	−	0.190178i	$-0.0609064\pi$
$332$	0.705771i	0.0387342i
$333$	− 50.9928i	− 2.79439i
$334$	−22.7277	−1.24360
$335$	−4.34505	−0.237395
$336$	10.8382i	0.591270i
$337$	11.1559	0.607703	0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559	0.607703	0.303852	+	0.952719i	$0.401727\pi$
$338$	0	0
$339$	−10.0488	−0.545776
$340$	0.0800108i	0.00433919i
$341$	9.41023	0.509593
$342$	−17.2113	−0.930682
$343$	− 1.00000i	− 0.0539949i
$344$	− 2.87383i	− 0.154947i
$345$	13.4043i	0.721661i
$346$	− 0.417663i	− 0.0224537i
$347$	−4.92511	−0.264393	−0.132197	−	0.991223i	$-0.542203\pi$
$347$	−4.92511	−0.264393	−0.132197	+	0.991223i	$0.542203\pi$
$348$	1.16952	0.0626928
$349$	1.52335i	0.0815430i	0.999168	+	0.0407715i	$0.0129816\pi$
$349$	1.52335i	0.0815430i	−0.999168	+	0.0407715i	$0.987018\pi$
$350$	6.55650	0.350460
$351$	0	0
$352$	0.726636	0.0387298
$353$	17.9280i	0.954212i	0.878846	+	0.477106i	$0.158314\pi$
$353$	17.9280i	0.954212i	−0.878846	+	0.477106i	$0.841686\pi$
$354$	−24.3022	−1.29165
$355$	2.69759	0.143173
$356$	− 0.951129i	− 0.0504097i
$357$	5.50532i	0.291373i
$358$	− 13.6043i	− 0.719007i
$359$	− 20.0014i	− 1.05563i	−0.849359	−	0.527816i	$-0.823011\pi$
$359$	− 20.0014i	− 1.05563i	0.849359	−	0.527816i	$-0.176989\pi$
$360$	−7.45466	−0.392895
$361$	12.7941	0.673376
$362$	− 17.2301i	− 0.905596i
$363$	−23.6294	−1.24022
$364$	0	0
$365$	−6.14421	−0.321602
$366$	− 52.7566i	− 2.75763i
$367$	27.4157	1.43109	0.715544	−	0.698568i	$-0.246179\pi$
$367$	27.4157	1.43109	0.715544	+	0.698568i	$0.246179\pi$
$368$	−35.0584	−1.82754
$369$	20.9820i	1.09228i
$370$	7.35739i	0.382492i
$371$	− 8.89651i	− 0.461884i
$372$	1.29563i	0.0671752i
$373$	−15.8929	−0.822901	−0.411451	−	0.911432i	$-0.634978\pi$
$373$	−15.8929	−0.822901	−0.411451	+	0.911432i	$0.634978\pi$
$374$	−4.38553	−0.226771
$375$	14.2696i	0.736880i
$376$	−13.0168	−0.671292
$377$	0	0
$378$	−7.77403	−0.399853
$379$	8.77900i	0.450947i	0.974249	+	0.225474i	$0.0723929\pi$
$379$	8.77900i	0.450947i	−0.974249	+	0.225474i	$0.927607\pi$
$380$	−0.102307	−0.00524822
$381$	−4.02249	−0.206078
$382$	16.9736i	0.868447i
$383$	− 7.96237i	− 0.406858i	−0.979090	−	0.203429i	$-0.934791\pi$
$383$	− 7.96237i	− 0.406858i	0.979090	−	0.203429i	$-0.0652086\pi$
$384$	− 29.9423i	− 1.52799i
$385$	0.842869i	0.0429566i
$386$	−16.1240	−0.820688
$387$	4.97159	0.252720
$388$	− 0.349960i	− 0.0177665i
$389$	−32.0434	−1.62467	−0.812333	−	0.583194i	$-0.801803\pi$
$389$	−32.0434	−1.62467	−0.812333	+	0.583194i	$0.801803\pi$
$390$	0	0
$391$	−17.8082	−0.900598
$392$	2.88158i	0.145542i
$393$	−24.5100	−1.23637
$394$	−2.49630	−0.125762
$395$	− 0.509777i	− 0.0256496i
$396$	0.640716i	0.0321972i
$397$	− 6.43457i	− 0.322942i	−0.986877	−	0.161471i	$-0.948376\pi$
$397$	− 6.43457i	− 0.322942i	0.986877	−	0.161471i	$-0.0516238\pi$
$398$	9.13777i	0.458035i
$399$	−7.03944	−0.352413
$400$	−18.1444	−0.907219
$401$	− 0.533577i	− 0.0266456i	−0.999911	−	0.0133228i	$-0.995759\pi$
$401$	− 0.533577i	− 0.0266456i	0.999911	−	0.0133228i	$-0.00424090\pi$
$402$	32.7906	1.63545
$403$	0	0
$404$	−1.44839	−0.0720601
$405$	− 0.464579i	− 0.0230851i
$406$	−7.24847	−0.359736
$407$	16.6139	0.823522
$408$	− 15.8640i	− 0.785387i
$409$	39.7528i	1.96565i	0.184547	+	0.982824i	$0.440918\pi$
$409$	39.7528i	1.96565i	−0.184547	+	0.982824i	$0.559082\pi$
$410$	− 3.02735i	− 0.149510i
$411$	24.0695i	1.18726i
$412$	−0.397296	−0.0195734
$413$	−6.20526	−0.305341
$414$	− 63.1520i	− 3.10375i
$415$	4.62832	0.227195
$416$	0	0
$417$	14.2375	0.697213
$418$	− 5.60761i	− 0.274277i
$419$	23.8176	1.16357	0.581783	−	0.813344i	$-0.302355\pi$
$419$	23.8176	1.16357	0.581783	+	0.813344i	$0.302355\pi$
$420$	−0.116049	−0.00566260
$421$	− 23.2419i	− 1.13274i	−0.824151	−	0.566370i	$-0.808347\pi$
$421$	− 23.2419i	− 1.13274i	0.824151	−	0.566370i	$-0.191653\pi$
$422$	− 14.8573i	− 0.723243i
$423$	− 22.5185i	− 1.09489i
$424$	25.6360i	1.24500i
$425$	−9.21657	−0.447069
$426$	−20.3578	−0.986336
$427$	− 13.4707i	− 0.651894i
$428$	0.486253	0.0235039
$429$	0	0
$430$	−0.717316	−0.0345920
$431$	− 2.70689i	− 0.130386i	−0.997873	−	0.0651932i	$-0.979234\pi$
$431$	− 2.70689i	− 0.130386i	0.997873	−	0.0651932i	$-0.0207664\pi$
$432$	21.5137	1.03508
$433$	5.81890	0.279638	0.139819	−	0.990177i	$-0.455348\pi$
$433$	5.81890	0.279638	0.139819	+	0.990177i	$0.455348\pi$
$434$	− 8.03008i	− 0.385456i
$435$	− 7.66950i	− 0.367724i
$436$	− 0.941416i	− 0.0450856i
$437$	− 22.7706i	− 1.08927i
$438$	46.3682	2.21556
$439$	−38.1702	−1.82176	−0.910882	−	0.412668i	$-0.864597\pi$
$439$	−38.1702	−1.82176	−0.910882	+	0.412668i	$0.864597\pi$
$440$	− 2.42880i	− 0.115788i
$441$	−4.98500	−0.237381
$442$	0	0
$443$	−31.6740	−1.50488	−0.752440	−	0.658661i	$-0.771123\pi$
$443$	−31.6740	−1.50488	−0.752440	+	0.658661i	$0.771123\pi$
$444$	2.28746i	0.108558i
$445$	−6.23734	−0.295678
$446$	−17.8619	−0.845787
$447$	9.50845i	0.449734i
$448$	− 8.29100i	− 0.391713i
$449$	− 31.4049i	− 1.48209i	−0.671455	−	0.741045i	$-0.734331\pi$
$449$	− 31.4049i	− 1.48209i	0.671455	−	0.741045i	$-0.265669\pi$
$450$	− 32.6842i	− 1.54075i
$451$	−6.83614	−0.321901
$452$	0.281416	0.0132367
$453$	− 35.7648i	− 1.68037i
$454$	0.968995	0.0454772
$455$	0	0
$456$	20.2847	0.949920
$457$	31.8281i	1.48886i	0.667702	+	0.744429i	$0.267278\pi$
$457$	31.8281i	1.48886i	−0.667702	+	0.744429i	$0.732722\pi$
$458$	25.3447	1.18428
$459$	10.9281	0.510078
$460$	− 0.375385i	− 0.0175024i
$461$	− 1.16631i	− 0.0543203i	−0.999631	−	0.0271601i	$-0.991354\pi$
$461$	− 1.16631i	− 0.0543203i	0.999631	−	0.0271601i	$-0.00864640\pi$
$462$	− 6.36084i	− 0.295933i
$463$	20.3441i	0.945469i	0.881205	+	0.472734i	$0.156733\pi$
$463$	20.3441i	0.945469i	−0.881205	+	0.472734i	$0.843267\pi$
$464$	20.0593	0.931231
$465$	8.49651	0.394016
$466$	37.1152i	1.71933i
$467$	1.56939	0.0726229	0.0363114	−	0.999341i	$-0.488439\pi$
$467$	1.56939	0.0726229	0.0363114	+	0.999341i	$0.488439\pi$
$468$	0	0
$469$	8.37266	0.386614
$470$	3.24903i	0.149867i
$471$	−29.3008	−1.35011
$472$	17.8810	0.823039
$473$	1.61979i	0.0744781i
$474$	3.84711i	0.176703i
$475$	− 11.7849i	− 0.540727i
$476$	− 0.154176i	− 0.00706665i
$477$	−44.3491	−2.03060
$478$	23.0313	1.05343
$479$	7.71918i	0.352699i	0.984328	+	0.176349i	$0.0564288\pi$
$479$	7.71918i	0.352699i	−0.984328	+	0.176349i	$0.943571\pi$
$480$	0.656080	0.0299458
$481$	0	0
$482$	−24.1334	−1.09925
$483$	− 25.8292i	− 1.17527i
$484$	0.661740	0.0300791
$485$	−2.29498	−0.104209
$486$	− 19.8161i	− 0.898875i
$487$	0.0761801i	0.00345205i	0.999999	+	0.00172602i	$0.000549411\pi$
$487$	0.0761801i	0.00345205i	−0.999999	+	0.00172602i	$0.999451\pi$
$488$	38.8170i	1.75716i
$489$	44.5155i	2.01306i
$490$	0.719250	0.0324924
$491$	−1.78715	−0.0806529	−0.0403264	−	0.999187i	$-0.512840\pi$
$491$	−1.78715	−0.0806529	−0.0403264	+	0.999187i	$0.512840\pi$
$492$	− 0.941220i	− 0.0424335i
$493$	10.1893	0.458902
$494$	0	0
$495$	4.20170	0.188852
$496$	22.2223i	0.997813i
$497$	−5.19809	−0.233166
$498$	−34.9284	−1.56518
$499$	− 8.33493i	− 0.373123i	−0.982443	−	0.186561i	$-0.940266\pi$
$499$	− 8.33493i	− 0.373123i	0.982443	−	0.186561i	$-0.0597343\pi$
$500$	− 0.399619i	− 0.0178715i
$501$	46.3387i	2.07026i
$502$	− 8.93914i	− 0.398973i
$503$	1.44048	0.0642277	0.0321138	−	0.999484i	$-0.489776\pi$
$503$	1.44048	0.0642277	0.0321138	+	0.999484i	$0.489776\pi$
$504$	14.3647	0.639854
$505$	9.49829i	0.422668i
$506$	20.5755	0.914693
$507$	0	0
$508$	0.112649	0.00499801
$509$	14.8256i	0.657135i	0.944480	+	0.328568i	$0.106566\pi$
$509$	14.8256i	0.657135i	−0.944480	+	0.328568i	$0.893434\pi$
$510$	−3.95970	−0.175339
$511$	11.8395	0.523750
$512$	23.8204i	1.05272i
$513$	13.9733i	0.616935i
$514$	− 5.08860i	− 0.224449i
$515$	2.60540i	0.114808i
$516$	−0.223018	−0.00981781
$517$	7.33674	0.322670
$518$	− 14.1773i	− 0.622913i
$519$	−0.851561	−0.0373794
$520$	0	0
$521$	−0.334388	−0.0146498	−0.00732489	−	0.999973i	$-0.502332\pi$
$521$	−0.334388	−0.0146498	−0.00732489	+	0.999973i	$0.502332\pi$
$522$	36.1336i	1.58153i
$523$	−32.5065	−1.42141	−0.710705	−	0.703490i	$-0.751624\pi$
$523$	−32.5065	−1.42141	−0.710705	+	0.703490i	$0.751624\pi$
$524$	0.686401	0.0299856
$525$	− 13.3678i	− 0.583420i
$526$	− 25.3896i	− 1.10704i
$527$	11.2880i	0.491713i
$528$	17.6029i	0.766068i
$529$	60.5502	2.63262
$530$	6.39881	0.277947
$531$	30.9332i	1.34239i
$532$	0.197139	0.00854706
$533$	0	0
$534$	47.0710	2.03696
$535$	− 3.18876i	− 0.137862i
$536$	−24.1265	−1.04211
$537$	−27.7373	−1.19695
$538$	− 38.1732i	− 1.64576i
$539$	− 1.62416i	− 0.0699575i
$540$	0.230357i	0.00991297i
$541$	10.6015i	0.455796i	0.973685	+	0.227898i	$0.0731852\pi$
$541$	10.6015i	0.455796i	−0.973685	+	0.227898i	$0.926815\pi$
$542$	9.03534	0.388101
$543$	−35.1300	−1.50757
$544$	0.871633i	0.0373709i
$545$	−6.17364	−0.264450
$546$	0	0
$547$	10.2327	0.437519	0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327	0.437519	0.218760	+	0.975779i	$0.429799\pi$
$548$	− 0.674064i	− 0.0287946i
$549$	−67.1515	−2.86596
$550$	10.6488	0.454067
$551$	13.0286i	0.555038i
$552$	74.4290i	3.16791i
$553$	0.982310i	0.0417721i
$554$	7.54216i	0.320436i
$555$	15.0007	0.636746
$556$	−0.398720	−0.0169095
$557$	31.9930i	1.35559i	0.735253	+	0.677793i	$0.237063\pi$
$557$	31.9930i	1.35559i	−0.735253	+	0.677793i	$0.762937\pi$
$558$	−40.0300	−1.69460
$559$	0	0
$560$	−1.99044	−0.0841115
$561$	8.94152i	0.377511i
$562$	4.90956	0.207097
$563$	−10.7913	−0.454800	−0.227400	−	0.973801i	$-0.573022\pi$
$563$	−10.7913	−0.454800	−0.227400	+	0.973801i	$0.573022\pi$
$564$	1.01014i	0.0425348i
$565$	− 1.84547i	− 0.0776397i
$566$	− 19.5962i	− 0.823688i
$567$	0.895217i	0.0375956i
$568$	14.9787	0.628494
$569$	24.6014	1.03134	0.515672	−	0.856786i	$-0.327542\pi$
$569$	24.6014	1.03134	0.515672	+	0.856786i	$0.327542\pi$
$570$	− 5.06312i	− 0.212071i
$571$	−16.5724	−0.693534	−0.346767	−	0.937951i	$-0.612721\pi$
$571$	−16.5724	−0.693534	−0.346767	+	0.937951i	$0.612721\pi$
$572$	0	0
$573$	34.6070	1.44573
$574$	5.83352i	0.243486i
$575$	43.2412	1.80328
$576$	−41.3306	−1.72211
$577$	− 14.6611i	− 0.610348i	−0.952297	−	0.305174i	$-0.901285\pi$
$577$	− 14.6611i	− 0.610348i	0.952297	−	0.305174i	$-0.0987147\pi$
$578$	18.3005i	0.761202i
$579$	32.8746i	1.36622i
$580$	0.214784i	0.00891840i
$581$	−8.91851	−0.370002
$582$	17.3194	0.717912
$583$	− 14.4493i	− 0.598431i
$584$	−34.1166	−1.41175
$585$	0	0
$586$	11.5717	0.478024
$587$	35.3336i	1.45837i	0.684315	+	0.729186i	$0.260101\pi$
$587$	35.3336i	1.45837i	−0.684315	+	0.729186i	$0.739899\pi$
$588$	0.223619	0.00922190
$589$	−14.4335	−0.594723
$590$	− 4.46313i	− 0.183744i
$591$	5.08963i	0.209359i
$592$	39.2340i	1.61251i
$593$	16.4294i	0.674675i	0.941384	+	0.337338i	$0.109526\pi$
$593$	16.4294i	0.674675i	−0.941384	+	0.337338i	$0.890474\pi$
$594$	−12.6263	−0.518062
$595$	−1.01106	−0.0414494
$596$	− 0.266283i	− 0.0109074i
$597$	18.6307	0.762504
$598$	0	0
$599$	12.0819	0.493653	0.246826	−	0.969060i	$-0.420612\pi$
$599$	12.0819	0.493653	0.246826	+	0.969060i	$0.420612\pi$
$600$	38.5206i	1.57259i
$601$	7.81486	0.318775	0.159387	−	0.987216i	$-0.449048\pi$
$601$	7.81486	0.318775	0.159387	+	0.987216i	$0.449048\pi$
$602$	1.38223	0.0563353
$603$	− 41.7377i	− 1.69969i
$604$	1.00159i	0.0407541i
$605$	− 4.33957i	− 0.176429i
$606$	− 71.6803i	− 2.91181i
$607$	35.5649	1.44354	0.721768	−	0.692135i	$-0.243330\pi$
$607$	35.5649	1.44354	0.721768	+	0.692135i	$0.243330\pi$
$608$	−1.11452	−0.0451999
$609$	14.7787i	0.598862i
$610$	9.68882	0.392289
$611$	0	0
$612$	−0.768568	−0.0310675
$613$	− 11.9368i	− 0.482122i	−0.970510	−	0.241061i	$-0.922505\pi$
$613$	− 11.9368i	− 0.482122i	0.970510	−	0.241061i	$-0.0774954\pi$
$614$	−11.5500	−0.466120
$615$	−6.17236	−0.248893
$616$	4.68015i	0.188569i
$617$	23.5702i	0.948901i	0.880282	+	0.474450i	$0.157353\pi$
$617$	23.5702i	0.948901i	−0.880282	+	0.474450i	$0.842647\pi$
$618$	− 19.6621i	− 0.790924i
$619$	28.5571i	1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$619$	28.5571i	1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$620$	−0.237944	−0.00955606
$621$	−51.2710	−2.05743
$622$	− 20.2663i	− 0.812607i
$623$	12.0190	0.481530
$624$	0	0
$625$	21.0328	0.841311
$626$	− 23.7453i	− 0.949052i
$627$	−11.4332	−0.456597
$628$	0.820567	0.0327442
$629$	19.9292i	0.794628i
$630$	− 3.58546i	− 0.142848i
$631$	44.9925i	1.79112i	0.444938	+	0.895561i	$0.353226\pi$
$631$	44.9925i	1.79112i	−0.444938	+	0.895561i	$0.646774\pi$
$632$	− 2.83061i	− 0.112596i
$633$	−30.2921	−1.20400
$634$	19.4034	0.770607
$635$	− 0.738735i	− 0.0293158i
$636$	1.98943	0.0788860
$637$	0	0
$638$	−11.7727	−0.466085
$639$	25.9125i	1.02508i
$640$	5.49894	0.217365
$641$	2.53300	0.100048	0.0500238	−	0.998748i	$-0.484070\pi$
$641$	2.53300	0.100048	0.0500238	+	0.998748i	$0.484070\pi$
$642$	24.0645i	0.949749i
$643$	− 18.3771i	− 0.724721i	−0.932038	−	0.362360i	$-0.881971\pi$
$643$	− 18.3771i	− 0.724721i	0.932038	−	0.362360i	$-0.118029\pi$
$644$	0.723345i	0.0285038i
$645$	1.46251i	0.0575863i
$646$	6.72658	0.264654
$647$	−20.9287	−0.822791	−0.411396	−	0.911457i	$-0.634959\pi$
$647$	−20.9287	−0.822791	−0.411396	+	0.911457i	$0.634959\pi$
$648$	− 2.57964i	− 0.101338i
$649$	−10.0783	−0.395609
$650$	0	0
$651$	−16.3723	−0.641680
$652$	− 1.24665i	− 0.0488227i
$653$	−48.1160	−1.88292	−0.941461	−	0.337121i	$-0.890547\pi$
$653$	−48.1160	−1.88292	−0.941461	+	0.337121i	$0.890547\pi$
$654$	46.5903	1.82183
$655$	− 4.50130i	− 0.175880i
$656$	− 16.1436i	− 0.630302i
$657$	− 59.0200i	− 2.30259i
$658$	− 6.26070i	− 0.244068i
$659$	−2.21638	−0.0863379	−0.0431690	−	0.999068i	$-0.513745\pi$
$659$	−2.21638	−0.0863379	−0.0431690	+	0.999068i	$0.513745\pi$
$660$	−0.188482	−0.00733664
$661$	− 0.637434i	− 0.0247933i	−0.999923	−	0.0123966i	$-0.996054\pi$
$661$	− 0.637434i	− 0.0247933i	0.999923	−	0.0123966i	$-0.00394608\pi$
$662$	−9.59073	−0.372754
$663$	0	0
$664$	25.6994	0.997331
$665$	− 1.29280i	− 0.0501327i
$666$	−70.6736	−2.73855
$667$	−47.8048	−1.85101
$668$	− 1.29771i	− 0.0502100i
$669$	36.4181i	1.40801i
$670$	6.02203i	0.232651i
$671$	− 21.8786i	− 0.844614i
$672$	−1.26423	−0.0487687
$673$	−15.4069	−0.593891	−0.296945	−	0.954895i	$-0.595968\pi$
$673$	−15.4069	−0.593891	−0.296945	+	0.954895i	$0.595968\pi$
$674$	− 15.4616i	− 0.595559i
$675$	−26.5352	−1.02134
$676$	0	0
$677$	−11.6812	−0.448945	−0.224473	−	0.974480i	$-0.572066\pi$
$677$	−11.6812	−0.448945	−0.224473	+	0.974480i	$0.572066\pi$
$678$	13.9272i	0.534869i
$679$	4.42228	0.169712
$680$	2.91345	0.111726
$681$	− 1.97565i	− 0.0757072i
$682$	− 13.0421i	− 0.499409i
$683$	− 22.9114i	− 0.876680i	−0.898809	−	0.438340i	$-0.855567\pi$
$683$	− 22.9114i	− 0.876680i	0.898809	−	0.438340i	$-0.144433\pi$
$684$	− 0.982737i	− 0.0375759i
$685$	−4.42039	−0.168895
$686$	−1.38595	−0.0529159
$687$	− 51.6745i	− 1.97150i
$688$	−3.82515	−0.145833
$689$	0	0
$690$	18.5777	0.707239
$691$	− 47.2325i	− 1.79681i	−0.439167	−	0.898405i	$-0.644726\pi$
$691$	− 47.2325i	− 1.79681i	0.439167	−	0.898405i	$-0.355274\pi$
$692$	0.0238479	0.000906560 0
$693$	−8.09643	−0.307558
$694$	6.82596i	0.259110i
$695$	2.61473i	0.0991825i
$696$	− 42.5860i	− 1.61422i
$697$	− 8.20026i	− 0.310607i
$698$	2.11129	0.0799135
$699$	75.6730	2.86222
$700$	0.374365i	0.0141497i
$701$	12.2098	0.461158	0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098	0.461158	0.230579	+	0.973054i	$0.425938\pi$
$702$	0	0
$703$	−25.4827	−0.961097
$704$	− 13.4659i	− 0.507515i
$705$	6.62435	0.249488
$706$	24.8474	0.935144
$707$	− 18.3026i	− 0.688342i
$708$	− 1.38762i	− 0.0521498i
$709$	17.8875i	0.671778i	0.941902	+	0.335889i	$0.109037\pi$
$709$	17.8875i	0.671778i	−0.941902	+	0.335889i	$0.890963\pi$
$710$	− 3.73873i	− 0.140312i
$711$	4.89681	0.183645
$712$	−34.6337	−1.29795
$713$	− 52.9597i	− 1.98336i
$714$	7.63012	0.285550
$715$	0	0
$716$	0.776780	0.0290296
$717$	− 46.9578i	− 1.75367i
$718$	−27.7210	−1.03454
$719$	−9.12634	−0.340355	−0.170178	−	0.985413i	$-0.554434\pi$
$719$	−9.12634	−0.340355	−0.170178	+	0.985413i	$0.554434\pi$
$720$	9.92235i	0.369784i
$721$	− 5.02046i	− 0.186972i
$722$	− 17.7321i	− 0.659920i
$723$	49.2048i	1.82995i
$724$	0.983812	0.0365631
$725$	−24.7413	−0.918868
$726$	32.7493i	1.21544i
$727$	33.6859	1.24934	0.624670	−	0.780889i	$-0.285233\pi$
$727$	33.6859	1.24934	0.624670	+	0.780889i	$0.285233\pi$
$728$	0	0
$729$	−43.0880	−1.59585
$730$	8.51558i	0.315176i
$731$	−1.94301	−0.0718650
$732$	3.01231	0.111338
$733$	− 46.4344i	− 1.71509i	−0.514406	−	0.857547i	$-0.671987\pi$
$733$	− 46.4344i	− 1.71509i	0.514406	−	0.857547i	$-0.328013\pi$
$734$	− 37.9968i	− 1.40249i
$735$	− 1.46646i	− 0.0540910i
$736$	− 4.08942i	− 0.150738i
$737$	13.5985	0.500908
$738$	29.0801	1.07045
$739$	− 1.85025i	− 0.0680627i	−0.999421	−	0.0340314i	$-0.989165\pi$
$739$	− 1.85025i	− 0.0680627i	0.999421	−	0.0340314i	$-0.0108346\pi$
$740$	−0.420095	−0.0154430
$741$	0	0
$742$	−12.3301	−0.452654
$743$	33.1509i	1.21619i	0.793865	+	0.608094i	$0.208066\pi$
$743$	33.1509i	1.21619i	−0.793865	+	0.608094i	$0.791934\pi$
$744$	47.1781	1.72963
$745$	−1.74624	−0.0639773
$746$	22.0268i	0.806457i
$747$	44.4588i	1.62666i
$748$	− 0.250407i	− 0.00915577i
$749$	6.14456i	0.224517i
$750$	19.7770	0.722154
$751$	20.7743	0.758064	0.379032	−	0.925384i	$-0.376257\pi$
$751$	20.7743	0.758064	0.379032	+	0.925384i	$0.376257\pi$
$752$	17.3258i	0.631806i
$753$	−18.2257	−0.664182
$754$	0	0
$755$	6.56824	0.239043
$756$	− 0.443884i	− 0.0161439i
$757$	43.6150	1.58521	0.792607	−	0.609733i	$-0.208723\pi$
$757$	43.6150	1.58521	0.792607	+	0.609733i	$0.208723\pi$
$758$	12.1673	0.441936
$759$	− 41.9508i	− 1.52272i
$760$	3.72532i	0.135131i
$761$	− 12.3902i	− 0.449145i	−0.974457	−	0.224573i	$-0.927901\pi$
$761$	− 12.3902i	− 0.449145i	0.974457	−	0.224573i	$-0.0720986\pi$
$762$	5.57497i	0.201960i
$763$	11.8962	0.430673
$764$	−0.969167	−0.0350632
$765$	5.04013i	0.182226i
$766$	−11.0355	−0.398728
$767$	0	0
$768$	5.35835	0.193353
$769$	− 5.55359i	− 0.200268i	−0.994974	−	0.100134i	$-0.968073\pi$
$769$	− 5.55359i	− 0.200268i	0.994974	−	0.100134i	$-0.0319271\pi$
$770$	1.16818	0.0420982
$771$	−10.3750	−0.373646
$772$	− 0.920651i	− 0.0331349i
$773$	− 43.8042i	− 1.57553i	−0.615977	−	0.787764i	$-0.711239\pi$
$773$	− 43.8042i	− 1.57553i	0.615977	−	0.787764i	$-0.288761\pi$
$774$	− 6.89039i	− 0.247670i
$775$	− 27.4092i	− 0.984566i
$776$	−12.7432	−0.457454
$777$	−28.9056	−1.03698
$778$	44.4107i	1.59220i
$779$	10.4853	0.375677
$780$	0	0
$781$	−8.44253	−0.302098
$782$	24.6813i	0.882600i
$783$	29.3357	1.04837
$784$	3.83547	0.136981
$785$	− 5.38113i	− 0.192061i
$786$	33.9697i	1.21166i
$787$	− 24.8009i	− 0.884057i	−0.897001	−	0.442029i	$-0.854259\pi$
$787$	− 24.8009i	− 0.884057i	0.897001	−	0.442029i	$-0.145741\pi$
$788$	− 0.142535i	− 0.00507758i
$789$	−51.7661	−1.84292
$790$	−0.706526	−0.0251371
$791$	3.55612i	0.126441i
$792$	23.3305	0.829015
$793$	0	0
$794$	−8.91801	−0.316489
$795$	− 13.0463i	− 0.462706i
$796$	−0.521751	−0.0184930
$797$	16.4715	0.583451	0.291725	−	0.956502i	$-0.405771\pi$
$797$	16.4715	0.583451	0.291725	+	0.956502i	$0.405771\pi$
$798$	9.75633i	0.345370i
$799$	8.80076i	0.311348i
$800$	− 2.11647i	− 0.0748285i
$801$	− 59.9146i	− 2.11698i
$802$	−0.739513	−0.0261131
$803$	19.2293	0.678587
$804$	1.87229i	0.0660305i
$805$	4.74357	0.167189
$806$	0	0
$807$	−77.8301	−2.73975
$808$	52.7406i	1.85541i
$809$	1.38194	0.0485863	0.0242932	−	0.999705i	$-0.492266\pi$
$809$	1.38194	0.0485863	0.0242932	+	0.999705i	$0.492266\pi$
$810$	−0.643885	−0.0226238
$811$	6.83571i	0.240034i	0.992772	+	0.120017i	$0.0382950\pi$
$811$	6.83571i	0.240034i	−0.992772	+	0.120017i	$0.961705\pi$
$812$	− 0.413875i	− 0.0145242i
$813$	− 18.4219i	− 0.646083i
$814$	− 23.0261i	− 0.807066i
$815$	−8.17533	−0.286369
$816$	−21.1155	−0.739190
$817$	− 2.48446i	− 0.0869201i
$818$	55.0954	1.92637
$819$	0	0
$820$	0.172856	0.00603640
$821$	− 10.5425i	− 0.367936i	−0.982932	−	0.183968i	$-0.941106\pi$
$821$	− 10.5425i	− 0.367936i	0.982932	−	0.183968i	$-0.0588943\pi$
$822$	33.3592	1.16353
$823$	−14.8330	−0.517047	−0.258524	−	0.966005i	$-0.583236\pi$
$823$	−14.8330	−0.517047	−0.258524	+	0.966005i	$0.583236\pi$
$824$	14.4669i	0.503977i
$825$	− 21.7115i	− 0.755898i
$826$	8.60020i	0.299239i
$827$	55.6758i	1.93604i	0.250879	+	0.968018i	$0.419280\pi$
$827$	55.6758i	1.93604i	−0.250879	+	0.968018i	$0.580720\pi$
$828$	3.60587	0.125313
$829$	0.0464848	0.00161448	0.000807242	−	1.00000i	$-0.499743\pi$
$829$	0.0464848	0.00161448	0.000807242		1.00000i	$0.499743\pi$
$830$	− 6.41464i	− 0.222655i
$831$	15.3775	0.533438
$832$	0	0
$833$	1.94825	0.0675030
$834$	− 19.7325i	− 0.683280i
$835$	−8.51016	−0.294506
$836$	0.320185	0.0110738
$837$	32.4990i	1.12333i
$838$	− 33.0100i	− 1.14031i
$839$	− 25.5475i	− 0.881999i	−0.897507	−	0.440999i	$-0.854624\pi$
$839$	− 25.5475i	− 0.881999i	0.897507	−	0.440999i	$-0.145376\pi$
$840$	4.22571i	0.145801i
$841$	−1.64755	−0.0568120
$842$	−32.2121	−1.11010
$843$	− 10.0099i	− 0.344761i
$844$	0.848327	0.0292006
$845$	0	0
$846$	−31.2096	−1.07301
$847$	8.36211i	0.287325i
$848$	34.1223	1.17176
$849$	−39.9540	−1.37122
$850$	12.7737i	0.438135i
$851$	− 93.5013i	− 3.20518i
$852$	− 1.16239i	− 0.0398229i
$853$	− 22.6671i	− 0.776105i	−0.921637	−	0.388053i	$-0.873148\pi$
$853$	− 22.6671i	− 0.776105i	0.921637	−	0.388053i	$-0.126852\pi$
$854$	−18.6698	−0.638867
$855$	−6.44462	−0.220401
$856$	− 17.7061i	− 0.605181i
$857$	37.0535	1.26572	0.632862	−	0.774264i	$-0.281880\pi$
$857$	37.0535	1.26572	0.632862	+	0.774264i	$0.281880\pi$
$858$	0	0
$859$	−4.24339	−0.144782	−0.0723912	−	0.997376i	$-0.523063\pi$
$859$	−4.24339	−0.144782	−0.0723912	+	0.997376i	$0.523063\pi$
$860$	− 0.0409575i	− 0.00139664i
$861$	11.8938	0.405339
$862$	−3.75162	−0.127781
$863$	7.50051i	0.255320i	0.991818	+	0.127660i	$0.0407467\pi$
$863$	7.50051i	0.255320i	−0.991818	+	0.127660i	$0.959253\pi$
$864$	2.50949i	0.0853746i
$865$	− 0.156390i	− 0.00531743i
$866$	− 8.06472i	− 0.274050i
$867$	37.3124	1.26720
$868$	0.458504	0.0155626
$869$	1.59543i	0.0541212i
$870$	−10.6296	−0.360376
$871$	0	0
$872$	−34.2800	−1.16087
$873$	− 22.0451i	− 0.746113i
$874$	−31.5590	−1.06750
$875$	5.04981	0.170715
$876$	2.64755i	0.0894523i
$877$	28.2897i	0.955274i	0.878557	+	0.477637i	$0.158507\pi$
$877$	28.2897i	0.955274i	−0.878557	+	0.477637i	$0.841493\pi$
$878$	52.9021i	1.78536i
$879$	− 23.5933i	− 0.795781i
$880$	−3.23280	−0.108978
$881$	39.5721	1.33322	0.666609	−	0.745408i	$-0.267745\pi$
$881$	39.5721	1.33322	0.666609	+	0.745408i	$0.267745\pi$
$882$	6.90897i	0.232637i
$883$	−28.3609	−0.954419	−0.477209	−	0.878790i	$-0.658352\pi$
$883$	−28.3609	−0.954419	−0.477209	+	0.878790i	$0.658352\pi$
$884$	0	0
$885$	−9.09974	−0.305884
$886$	43.8987i	1.47481i
$887$	−43.7186	−1.46793	−0.733963	−	0.679189i	$-0.762331\pi$
$887$	−43.7186	−1.46793	−0.733963	+	0.679189i	$0.762331\pi$
$888$	83.2938	2.79516
$889$	1.42350i	0.0477426i
$890$	8.64465i	0.289769i
$891$	1.45398i	0.0487100i
$892$	− 1.01989i	− 0.0341483i
$893$	−11.2532	−0.376573
$894$	13.1783	0.440747
$895$	− 5.09399i	− 0.170273i
$896$	−10.5961	−0.353992
$897$	0	0
$898$	−43.5257	−1.45247
$899$	30.3019i	1.01062i
$900$	1.86621	0.0622070
$901$	17.3326	0.577434
$902$	9.47456i	0.315468i
$903$	− 2.81818i	− 0.0937830i
$904$	− 10.2473i	− 0.340819i
$905$	− 6.45167i	− 0.214461i
$906$	−49.5683	−1.64679
$907$	36.6985	1.21855	0.609277	−	0.792957i	$-0.291460\pi$
$907$	36.6985	1.21855	0.609277	+	0.792957i	$0.291460\pi$
$908$	0.0553280i	0.00183612i
$909$	−91.2387	−3.02620
$910$	0	0
$911$	−35.5211	−1.17686	−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211	−1.17686	−0.588432	+	0.808546i	$0.700255\pi$
$912$	− 26.9995i	− 0.894044i
$913$	−14.4851	−0.479386
$914$	44.1123	1.45911
$915$	− 19.7542i	− 0.653054i
$916$	1.44714i	0.0478148i
$917$	8.67374i	0.286432i
$918$	− 15.1458i	− 0.499885i
$919$	21.9334	0.723516	0.361758	−	0.932272i	$-0.382177\pi$
$919$	21.9334	0.723516	0.361758	+	0.932272i	$0.382177\pi$
$920$	−13.6690	−0.450653
$921$	23.5489i	0.775964i
$922$	−1.61644	−0.0532348
$923$	0	0
$924$	0.363193	0.0119482
$925$	− 48.3914i	− 1.59110i
$926$	28.1959	0.926575
$927$	−25.0270	−0.821993
$928$	2.33984i	0.0768090i
$929$	15.5172i	0.509102i	0.967059	+	0.254551i	$0.0819276\pi$
$929$	15.5172i	0.509102i	−0.967059	+	0.254551i	$0.918072\pi$
$930$	− 11.7758i	− 0.386142i
$931$	2.49115i	0.0816443i
$932$	−2.11922	−0.0694172
$933$	−41.3204	−1.35277
$934$	− 2.17510i	− 0.0711716i
$935$	−1.64212	−0.0537031
$936$	0	0
$937$	40.8110	1.33324	0.666618	−	0.745399i	$-0.267741\pi$
$937$	40.8110	1.33324	0.666618	+	0.745399i	$0.267741\pi$
$938$	− 11.6041i	− 0.378888i
$939$	−48.4135	−1.57991
$940$	−0.185514	−0.00605081
$941$	51.5936i	1.68190i	0.541109	+	0.840952i	$0.318004\pi$
$941$	51.5936i	1.68190i	−0.541109	+	0.840952i	$0.681996\pi$
$942$	40.6096i	1.32313i
$943$	38.4730i	1.25285i
$944$	− 23.8001i	− 0.774627i
$945$	−2.91091	−0.0946920
$946$	2.24495	0.0729898
$947$	− 4.98209i	− 0.161896i	−0.996718	−	0.0809482i	$-0.974205\pi$
$947$	− 4.98209i	− 0.161896i	0.996718	−	0.0809482i	$-0.0257948\pi$
$948$	−0.219663	−0.00713433
$949$	0	0
$950$	−16.3333	−0.529921
$951$	− 39.5609i	− 1.28285i
$952$	−5.61405	−0.181953
$953$	−30.2325	−0.979328	−0.489664	−	0.871911i	$-0.662881\pi$
$953$	−30.2325	−0.979328	−0.489664	+	0.871911i	$0.662881\pi$
$954$	61.4657i	1.99003i
$955$	6.35562i	0.205663i
$956$	1.31505i	0.0425317i
$957$	24.0029i	0.775904i
$958$	10.6984	0.345650
$959$	8.51784	0.275055
$960$	− 12.1584i	− 0.392410i
$961$	−2.56939	−0.0828835
$962$	0	0
$963$	30.6306	0.987058
$964$	− 1.37798i	− 0.0443816i
$965$	−6.03746	−0.194353
$966$	−35.7981	−1.15178
$967$	29.9990i	0.964703i	0.875978	+	0.482352i	$0.160217\pi$
$967$	29.9990i	0.964703i	−0.875978	+	0.482352i	$0.839783\pi$
$968$	− 24.0961i	− 0.774478i
$969$	− 13.7146i	− 0.440577i
$970$	3.18073i	0.102127i
$971$	44.1240	1.41601	0.708003	−	0.706209i	$-0.249596\pi$
$971$	44.1240	1.41601	0.708003	+	0.706209i	$0.249596\pi$
$972$	1.13146	0.0362917
$973$	− 5.03844i	− 0.161525i
$974$	0.105582	0.00338306
$975$	0	0
$976$	51.6665	1.65380
$977$	− 15.0024i	− 0.479970i	−0.970777	−	0.239985i	$-0.922858\pi$
$977$	− 15.0024i	− 0.479970i	0.970777	−	0.239985i	$-0.0771425\pi$
$978$	61.6964	1.97283
$979$	19.5207	0.623886
$980$	0.0410679i	0.00131187i
$981$	− 59.3028i	− 1.89339i
$982$	2.47690i	0.0790411i
$983$	− 6.01856i	− 0.191962i	−0.995383	−	0.0959812i	$-0.969401\pi$
$983$	− 6.01856i	− 0.191962i	0.995383	−	0.0959812i	$-0.0305989\pi$
$984$	−34.2729	−1.09258
$985$	−0.934717	−0.0297825
$986$	− 14.1219i	− 0.449732i
$987$	−12.7647	−0.406306
$988$	0	0
$989$	9.11600	0.289872
$990$	− 5.82336i	− 0.185078i
$991$	33.8400	1.07496	0.537482	−	0.843275i	$-0.319376\pi$
$991$	33.8400	1.07496	0.537482	+	0.843275i	$0.319376\pi$
$992$	−2.59215	−0.0823008
$993$	19.5542i	0.620535i
$994$	7.20431i	0.228507i
$995$	3.42155i	0.108471i
$996$	− 1.99435i	− 0.0631934i
$997$	26.3215	0.833610	0.416805	−	0.908996i	$-0.363150\pi$
$997$	26.3215	0.833610	0.416805	+	0.908996i	$0.363150\pi$
$998$	−11.5518	−0.365666
$999$	57.3775i	1.81534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.i.337.3		12
13.5	odd	4		1183.2.a.p.1.1		6
13.8	odd	4		1183.2.a.m.1.6		6
13.9	even	3		91.2.q.a.36.2	✓	12
13.10	even	6		91.2.q.a.43.2	yes	12
13.12	even	2	inner	1183.2.c.i.337.10		12
39.23	odd	6		819.2.ct.a.316.5		12
39.35	odd	6		819.2.ct.a.127.5		12
52.23	odd	6		1456.2.cc.c.225.1		12
52.35	odd	6		1456.2.cc.c.673.1		12
91.9	even	3		637.2.u.h.361.5		12
91.10	odd	6		637.2.u.i.30.5		12
91.23	even	6		637.2.k.h.459.5		12
91.34	even	4		8281.2.a.by.1.6		6
91.48	odd	6		637.2.q.h.491.2		12
91.61	odd	6		637.2.u.i.361.5		12
91.62	odd	6		637.2.q.h.589.2		12
91.74	even	3		637.2.k.h.569.2		12
91.75	odd	6		637.2.k.g.459.5		12
91.83	even	4		8281.2.a.ch.1.1		6
91.87	odd	6		637.2.k.g.569.2		12
91.88	even	6		637.2.u.h.30.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	13.9	even	3
91.2.q.a.43.2	yes	12	13.10	even	6
637.2.k.g.459.5		12	91.75	odd	6
637.2.k.g.569.2		12	91.87	odd	6
637.2.k.h.459.5		12	91.23	even	6
637.2.k.h.569.2		12	91.74	even	3
637.2.q.h.491.2		12	91.48	odd	6
637.2.q.h.589.2		12	91.62	odd	6
637.2.u.h.30.5		12	91.88	even	6
637.2.u.h.361.5		12	91.9	even	3
637.2.u.i.30.5		12	91.10	odd	6
637.2.u.i.361.5		12	91.61	odd	6
819.2.ct.a.127.5		12	39.35	odd	6
819.2.ct.a.316.5		12	39.23	odd	6
1183.2.a.m.1.6		6	13.8	odd	4
1183.2.a.p.1.1		6	13.5	odd	4
1183.2.c.i.337.3		12	1.1	even	1	trivial
1183.2.c.i.337.10		12	13.12	even	2	inner
1456.2.cc.c.225.1		12	52.23	odd	6
1456.2.cc.c.673.1		12	52.35	odd	6
8281.2.a.by.1.6		6	91.34	even	4
8281.2.a.ch.1.1		6	91.83	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.38595i q^{2} -2.82577 q^{3} +0.0791355 q^{4} -0.518957i q^{5} +3.91639i q^{6} +1.00000i q^{7} -2.88158i q^{8} +4.98500 q^{9} +O(q^{10})\)	\(q-1.38595i q^{2} -2.82577 q^{3} +0.0791355 q^{4} -0.518957i q^{5} +3.91639i q^{6} +1.00000i q^{7} -2.88158i q^{8} +4.98500 q^{9} -0.719250 q^{10} +1.62416i q^{11} -0.223619 q^{12} +1.38595 q^{14} +1.46646i q^{15} -3.83547 q^{16} -1.94825 q^{17} -6.90897i q^{18} -2.49115i q^{19} -0.0410679i q^{20} -2.82577i q^{21} +2.25101 q^{22} +9.14058 q^{23} +8.14270i q^{24} +4.73068 q^{25} -5.60916 q^{27} +0.0791355i q^{28} -5.22996 q^{29} +2.03244 q^{30} -5.79391i q^{31} -0.447392i q^{32} -4.58951i q^{33} +2.70019i q^{34} +0.518957 q^{35} +0.394491 q^{36} -10.2293i q^{37} -3.45262 q^{38} -1.49542 q^{40} +4.20903i q^{41} -3.91639 q^{42} +0.997311 q^{43} +0.128529i q^{44} -2.58700i q^{45} -12.6684i q^{46} -4.51725i q^{47} +10.8382 q^{48} -1.00000 q^{49} -6.55650i q^{50} +5.50532 q^{51} -8.89651 q^{53} +7.77403i q^{54} +0.842869 q^{55} +2.88158 q^{56} +7.03944i q^{57} +7.24847i q^{58} +6.20526i q^{59} +0.116049i q^{60} -13.4707 q^{61} -8.03008 q^{62} +4.98500i q^{63} -8.29100 q^{64} -6.36084 q^{66} -8.37266i q^{67} -0.154176 q^{68} -25.8292 q^{69} -0.719250i q^{70} +5.19809i q^{71} -14.3647i q^{72} -11.8395i q^{73} -14.1773 q^{74} -13.3678 q^{75} -0.197139i q^{76} -1.62416 q^{77} +0.982310 q^{79} +1.99044i q^{80} +0.895217 q^{81} +5.83352 q^{82} +8.91851i q^{83} -0.223619i q^{84} +1.01106i q^{85} -1.38223i q^{86} +14.7787 q^{87} +4.68015 q^{88} -12.0190i q^{89} -3.58546 q^{90} +0.723345 q^{92} +16.3723i q^{93} -6.26070 q^{94} -1.29280 q^{95} +1.26423i q^{96} -4.42228i q^{97} +1.38595i q^{98} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 + 8 * q^9	\( 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42} - 4 q^{43} + 4 q^{48} - 12 q^{49} + 52 q^{51} - 44 q^{53} + 12 q^{55} + 24 q^{56} - 28 q^{61} + 8 q^{62} - 52 q^{64} - 52 q^{66} + 16 q^{68} - 8 q^{69} - 12 q^{74} - 92 q^{75} + 8 q^{77} - 56 q^{79} - 4 q^{81} - 28 q^{82} + 4 q^{87} + 28 q^{88} + 24 q^{90} + 24 q^{92} - 8 q^{94} + 44 q^{95}+O(q^{100}) \) 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * q^95

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