LMFDB - Embedded newform 1183.2.c.f.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:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.3
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.f.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.470683i q^{2} +2.24914 q^{3} +1.77846 q^{4} -0.529317i q^{5} -1.05863i q^{6} -1.00000i q^{7} -1.77846i q^{8} +2.05863 q^{9} +O(q^{10})$	\(q-0.470683i q^{2} +2.24914 q^{3} +1.77846 q^{4} -0.529317i q^{5} -1.05863i q^{6} -1.00000i q^{7} -1.77846i q^{8} +2.05863 q^{9} -0.249141 q^{10} -2.24914i q^{11} +4.00000 q^{12} -0.470683 q^{14} -1.19051i q^{15} +2.71982 q^{16} +1.30777 q^{17} -0.968964i q^{18} +1.47068i q^{19} -0.941367i q^{20} -2.24914i q^{21} -1.05863 q^{22} -5.83709 q^{23} -4.00000i q^{24} +4.71982 q^{25} -2.11727 q^{27} -1.77846i q^{28} +5.22154 q^{29} -0.560352 q^{30} +7.02760i q^{31} -4.83709i q^{32} -5.05863i q^{33} -0.615547i q^{34} -0.529317 q^{35} +3.66119 q^{36} -2.36641i q^{37} +0.692226 q^{38} -0.941367 q^{40} -6.49828i q^{41} -1.05863 q^{42} -11.3940 q^{43} -4.00000i q^{44} -1.08967i q^{45} +2.74742i q^{46} +8.58451i q^{47} +6.11727 q^{48} -1.00000 q^{49} -2.22154i q^{50} +2.94137 q^{51} +11.2767 q^{53} +0.996562i q^{54} -1.19051 q^{55} -1.77846 q^{56} +3.30777i q^{57} -2.45769i q^{58} -12.1725i q^{59} -2.11727i q^{60} -2.00000 q^{61} +3.30777 q^{62} -2.05863i q^{63} +3.16291 q^{64} -2.38101 q^{66} +15.9379i q^{67} +2.32582 q^{68} -13.1284 q^{69} +0.249141i q^{70} -1.19051i q^{71} -3.66119i q^{72} +7.64315i q^{73} -1.11383 q^{74} +10.6155 q^{75} +2.61555i q^{76} -2.24914 q^{77} -1.33881 q^{79} -1.43965i q^{80} -10.9379 q^{81} -3.05863 q^{82} +16.3500i q^{83} -4.00000i q^{84} -0.692226i q^{85} +5.36297i q^{86} +11.7440 q^{87} -4.00000 q^{88} +6.91033i q^{89} -0.512889 q^{90} -10.3810 q^{92} +15.8061i q^{93} +4.04059 q^{94} +0.778457 q^{95} -10.8793i q^{96} +3.47068i q^{97} +0.470683i q^{98} -4.63016i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9	$ 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9} + 16 q^{10} + 24 q^{12} - 2 q^{14} - 2 q^{16} - 8 q^{17} - 8 q^{22} - 20 q^{23} + 10 q^{25} - 16 q^{27} + 48 q^{29} - 40 q^{30} - 4 q^{35} + 2 q^{36} + 20 q^{38} - 4 q^{40} - 8 q^{42} - 20 q^{43} + 40 q^{48} - 6 q^{49} + 16 q^{51} + 16 q^{53} + 12 q^{55} + 6 q^{56} - 12 q^{61} + 4 q^{62} + 34 q^{64} + 24 q^{66} + 44 q^{68} + 12 q^{69} + 60 q^{74} + 32 q^{75} + 4 q^{77} - 28 q^{79} + 6 q^{81} - 20 q^{82} - 52 q^{87} - 24 q^{88} + 56 q^{90} - 24 q^{92} - 20 q^{94} - 12 q^{95}+O(q^{100}) $ 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9 + 16 * q^10 + 24 * q^12 - 2 * q^14 - 2 * q^16 - 8 * q^17 - 8 * q^22 - 20 * q^23 + 10 * q^25 - 16 * q^27 + 48 * q^29 - 40 * q^30 - 4 * q^35 + 2 * q^36 + 20 * q^38 - 4 * q^40 - 8 * q^42 - 20 * q^43 + 40 * q^48 - 6 * q^49 + 16 * q^51 + 16 * q^53 + 12 * q^55 + 6 * q^56 - 12 * q^61 + 4 * q^62 + 34 * q^64 + 24 * q^66 + 44 * q^68 + 12 * q^69 + 60 * q^74 + 32 * q^75 + 4 * q^77 - 28 * q^79 + 6 * q^81 - 20 * q^82 - 52 * q^87 - 24 * q^88 + 56 * q^90 - 24 * q^92 - 20 * q^94 - 12 * 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 $

$2$	− 0.470683i	− 0.332823i	−0.986056	−	0.166412i	$-0.946782\pi$
$2$	− 0.470683i	− 0.332823i	0.986056	−	0.166412i	$-0.0532181\pi$
$3$	2.24914	1.29854	0.649271	−	0.760557i	$-0.275074\pi$
$3$	2.24914	1.29854	0.649271	+	0.760557i	$0.275074\pi$
$4$	1.77846	0.889229
$5$	− 0.529317i	− 0.236718i	−0.992971	−	0.118359i	$-0.962237\pi$
$5$	− 0.529317i	− 0.236718i	0.992971	−	0.118359i	$-0.0377633\pi$
$6$	− 1.05863i	− 0.432185i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.77846i	− 0.628780i
$9$	2.05863	0.686211
$10$	−0.249141	−0.0787852
$11$	− 2.24914i	− 0.678141i	−0.940761	−	0.339071i	$-0.889887\pi$
$11$	− 2.24914i	− 0.678141i	0.940761	−	0.339071i	$-0.110113\pi$
$12$	4.00000	1.15470
$13$	0	0
$13$	0	0
$14$	−0.470683	−0.125795
$15$	− 1.19051i	− 0.307388i
$16$	2.71982	0.679956
$17$	1.30777	0.317182	0.158591	−	0.987344i	$-0.449305\pi$
$17$	1.30777	0.317182	0.158591	+	0.987344i	$0.449305\pi$
$18$	− 0.968964i	− 0.228387i
$19$	1.47068i	0.337398i	0.985668	+	0.168699i	$0.0539566\pi$
$19$	1.47068i	0.337398i	−0.985668	+	0.168699i	$0.946043\pi$
$20$	− 0.941367i	− 0.210496i
$21$	− 2.24914i	− 0.490803i
$22$	−1.05863	−0.225701
$23$	−5.83709	−1.21712	−0.608559	−	0.793509i	$-0.708252\pi$
$23$	−5.83709	−1.21712	−0.608559	+	0.793509i	$0.708252\pi$
$24$	− 4.00000i	− 0.816497i
$25$	4.71982	0.943965
$26$	0	0
$27$	−2.11727	−0.407468
$28$	− 1.77846i	− 0.336097i
$29$	5.22154	0.969616	0.484808	−	0.874621i	$-0.338889\pi$
$29$	5.22154	0.969616	0.484808	+	0.874621i	$0.338889\pi$
$30$	−0.560352	−0.102306
$31$	7.02760i	1.26219i	0.775704	+	0.631097i	$0.217395\pi$
$31$	7.02760i	1.26219i	−0.775704	+	0.631097i	$0.782605\pi$
$32$	− 4.83709i	− 0.855085i
$33$	− 5.05863i	− 0.880595i
$34$	− 0.615547i	− 0.105566i
$35$	−0.529317	−0.0894708
$36$	3.66119	0.610198
$37$	− 2.36641i	− 0.389035i	−0.980899	−	0.194517i	$-0.937686\pi$
$37$	− 2.36641i	− 0.389035i	0.980899	−	0.194517i	$-0.0623141\pi$
$38$	0.692226	0.112294
$39$	0	0
$40$	−0.941367	−0.148843
$41$	− 6.49828i	− 1.01486i	−0.861693	−	0.507431i	$-0.830595\pi$
$41$	− 6.49828i	− 1.01486i	0.861693	−	0.507431i	$-0.169405\pi$
$42$	−1.05863	−0.163351
$43$	−11.3940	−1.73757	−0.868785	−	0.495190i	$-0.835098\pi$
$43$	−11.3940	−1.73757	−0.868785	+	0.495190i	$0.835098\pi$
$44$	− 4.00000i	− 0.603023i
$45$	− 1.08967i	− 0.162438i
$46$	2.74742i	0.405085i
$47$	8.58451i	1.25218i	0.779751	+	0.626090i	$0.215346\pi$
$47$	8.58451i	1.25218i	−0.779751	+	0.626090i	$0.784654\pi$
$48$	6.11727	0.882951
$49$	−1.00000	−0.142857
$50$	− 2.22154i	− 0.314174i
$51$	2.94137	0.411874
$52$	0	0
$53$	11.2767	1.54898	0.774490	−	0.632587i	$-0.218007\pi$
$53$	11.2767	1.54898	0.774490	+	0.632587i	$0.218007\pi$
$54$	0.996562i	0.135615i
$55$	−1.19051	−0.160528
$56$	−1.77846	−0.237656
$57$	3.30777i	0.438125i
$58$	− 2.45769i	− 0.322711i
$59$	− 12.1725i	− 1.58472i	−0.610054	−	0.792360i	$-0.708852\pi$
$59$	− 12.1725i	− 1.58472i	0.610054	−	0.792360i	$-0.291148\pi$
$60$	− 2.11727i	− 0.273338i
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	3.30777	0.420088
$63$	− 2.05863i	− 0.259363i
$64$	3.16291	0.395364
$65$	0	0
$66$	−2.38101	−0.293083
$67$	15.9379i	1.94713i	0.228415	+	0.973564i	$0.426646\pi$
$67$	15.9379i	1.94713i	−0.228415	+	0.973564i	$0.573354\pi$
$68$	2.32582	0.282047
$69$	−13.1284	−1.58048
$70$	0.249141i	0.0297780i
$71$	− 1.19051i	− 0.141287i	−0.997502	−	0.0706436i	$-0.977495\pi$
$71$	− 1.19051i	− 0.141287i	0.997502	−	0.0706436i	$-0.0225053\pi$
$72$	− 3.66119i	− 0.431475i
$73$	7.64315i	0.894562i	0.894393	+	0.447281i	$0.147608\pi$
$73$	7.64315i	0.894562i	−0.894393	+	0.447281i	$0.852392\pi$
$74$	−1.11383	−0.129480
$75$	10.6155	1.22578
$76$	2.61555i	0.300024i
$77$	−2.24914	−0.256313
$78$	0	0
$79$	−1.33881	−0.150628	−0.0753139	−	0.997160i	$-0.523996\pi$
$79$	−1.33881	−0.150628	−0.0753139	+	0.997160i	$0.523996\pi$
$80$	− 1.43965i	− 0.160958i
$81$	−10.9379	−1.21533
$82$	−3.05863	−0.337770
$83$	16.3500i	1.79464i	0.441377	+	0.897322i	$0.354490\pi$
$83$	16.3500i	1.79464i	−0.441377	+	0.897322i	$0.645510\pi$
$84$	− 4.00000i	− 0.436436i
$85$	− 0.692226i	− 0.0750825i
$86$	5.36297i	0.578304i
$87$	11.7440	1.25909
$88$	−4.00000	−0.426401
$89$	6.91033i	0.732494i	0.930518	+	0.366247i	$0.119357\pi$
$89$	6.91033i	0.732494i	−0.930518	+	0.366247i	$0.880643\pi$
$90$	−0.512889	−0.0540632
$91$	0	0
$92$	−10.3810	−1.08230
$93$	15.8061i	1.63901i
$94$	4.04059	0.416755
$95$	0.778457	0.0798680
$96$	− 10.8793i	− 1.11036i
$97$	3.47068i	0.352395i	0.984355	+	0.176197i	$0.0563797\pi$
$97$	3.47068i	0.352395i	−0.984355	+	0.176197i	$0.943620\pi$
$98$	0.470683i	0.0475462i
$99$	− 4.63016i	− 0.465348i
$100$	8.39400	0.839400
$101$	−7.75086	−0.771239	−0.385620	−	0.922658i	$-0.626012\pi$
$101$	−7.75086	−0.771239	−0.385620	+	0.922658i	$0.626012\pi$
$102$	− 1.38445i	− 0.137081i
$103$	16.9966	1.67472	0.837361	−	0.546651i	$-0.184098\pi$
$103$	16.9966	1.67472	0.837361	+	0.546651i	$0.184098\pi$
$104$	0	0
$105$	−1.19051	−0.116182
$106$	− 5.30777i	− 0.515537i
$107$	−5.55691	−0.537207	−0.268604	−	0.963251i	$-0.586562\pi$
$107$	−5.55691	−0.537207	−0.268604	+	0.963251i	$0.586562\pi$
$108$	−3.76547	−0.362332
$109$	− 7.92332i	− 0.758917i	−0.925209	−	0.379458i	$-0.876110\pi$
$109$	− 7.92332i	− 0.758917i	0.925209	−	0.379458i	$-0.123890\pi$
$110$	0.560352i	0.0534275i
$111$	− 5.32238i	− 0.505178i
$112$	− 2.71982i	− 0.256999i
$113$	−9.89229	−0.930588	−0.465294	−	0.885156i	$-0.654051\pi$
$113$	−9.89229	−0.930588	−0.465294	+	0.885156i	$0.654051\pi$
$114$	1.55691	0.145818
$115$	3.08967i	0.288113i
$116$	9.28629	0.862210
$117$	0	0
$118$	−5.72938	−0.527432
$119$	− 1.30777i	− 0.119883i
$120$	−2.11727	−0.193279
$121$	5.94137	0.540124
$122$	0.941367i	0.0852273i
$123$	− 14.6155i	− 1.31784i
$124$	12.4983i	1.12238i
$125$	− 5.14486i	− 0.460171i
$126$	−0.968964	−0.0863222
$127$	−0.824101	−0.0731271	−0.0365635	−	0.999331i	$-0.511641\pi$
$127$	−0.824101	−0.0731271	−0.0365635	+	0.999331i	$0.511641\pi$
$128$	− 11.1629i	− 0.986671i
$129$	−25.6267	−2.25631
$130$	0	0
$131$	10.6155	0.927485	0.463742	−	0.885970i	$-0.346506\pi$
$131$	10.6155	0.927485	0.463742	+	0.885970i	$0.346506\pi$
$132$	− 8.99656i	− 0.783050i
$133$	1.47068	0.127524
$134$	7.50172	0.648050
$135$	1.12070i	0.0964549i
$136$	− 2.32582i	− 0.199437i
$137$	11.3630i	0.970804i	0.874291	+	0.485402i	$0.161327\pi$
$137$	11.3630i	0.970804i	−0.874291	+	0.485402i	$0.838673\pi$
$138$	6.17934i	0.526020i
$139$	−13.9233	−1.18096	−0.590480	−	0.807052i	$-0.701062\pi$
$139$	−13.9233	−1.18096	−0.590480	+	0.807052i	$0.701062\pi$
$140$	−0.941367	−0.0795600
$141$	19.3078i	1.62601i
$142$	−0.560352	−0.0470237
$143$	0	0
$144$	5.59912	0.466593
$145$	− 2.76385i	− 0.229525i
$146$	3.59750	0.297731
$147$	−2.24914	−0.185506
$148$	− 4.20855i	− 0.345941i
$149$	− 9.30777i	− 0.762523i	−0.924467	−	0.381261i	$-0.875490\pi$
$149$	− 9.30777i	− 0.762523i	0.924467	−	0.381261i	$-0.124510\pi$
$150$	− 4.99656i	− 0.407968i
$151$	7.07324i	0.575612i	0.957689	+	0.287806i	$0.0929259\pi$
$151$	7.07324i	0.575612i	−0.957689	+	0.287806i	$0.907074\pi$
$152$	2.61555	0.212149
$153$	2.69223	0.217654
$154$	1.05863i	0.0853071i
$155$	3.71982	0.298783
$156$	0	0
$157$	−6.04059	−0.482091	−0.241046	−	0.970514i	$-0.577490\pi$
$157$	−6.04059	−0.482091	−0.241046	+	0.970514i	$0.577490\pi$
$158$	0.630155i	0.0501325i
$159$	25.3630	2.01141
$160$	−2.56035	−0.202414
$161$	5.83709i	0.460027i
$162$	5.14830i	0.404489i
$163$	6.38101i	0.499800i	0.968272	+	0.249900i	$0.0803977\pi$
$163$	6.38101i	0.499800i	−0.968272	+	0.249900i	$0.919602\pi$
$164$	− 11.5569i	− 0.902443i
$165$	−2.67762	−0.208452
$166$	7.69566	0.597299
$167$	− 16.5845i	− 1.28335i	−0.766977	−	0.641674i	$-0.778240\pi$
$167$	− 16.5845i	− 1.28335i	0.766977	−	0.641674i	$-0.221760\pi$
$168$	−4.00000	−0.308607
$169$	0	0
$170$	−0.325819	−0.0249892
$171$	3.02760i	0.231526i
$172$	−20.2637	−1.54510
$173$	23.3009	1.77153	0.885767	−	0.464130i	$-0.153633\pi$
$173$	23.3009	1.77153	0.885767	+	0.464130i	$0.153633\pi$
$174$	− 5.52770i	− 0.419054i
$175$	− 4.71982i	− 0.356785i
$176$	− 6.11727i	− 0.461106i
$177$	− 27.3776i	− 2.05782i
$178$	3.25258	0.243791
$179$	−21.0422	−1.57277	−0.786384	−	0.617738i	$-0.788049\pi$
$179$	−21.0422	−1.57277	−0.786384	+	0.617738i	$0.788049\pi$
$180$	− 1.93793i	− 0.144445i
$181$	−16.7474	−1.24483	−0.622413	−	0.782689i	$-0.713848\pi$
$181$	−16.7474	−1.24483	−0.622413	+	0.782689i	$0.713848\pi$
$182$	0	0
$183$	−4.49828	−0.332523
$184$	10.3810i	0.765299i
$185$	−1.25258	−0.0920914
$186$	7.43965	0.545501
$187$	− 2.94137i	− 0.215094i
$188$	15.2672i	1.11347i
$189$	2.11727i	0.154008i
$190$	− 0.366407i	− 0.0265819i
$191$	−7.43965	−0.538314	−0.269157	−	0.963096i	$-0.586745\pi$
$191$	−7.43965	−0.538314	−0.269157	+	0.963096i	$0.586745\pi$
$192$	7.11383	0.513396
$193$	− 1.50172i	− 0.108096i	−0.998538	−	0.0540480i	$-0.982788\pi$
$193$	− 1.50172i	− 0.108096i	0.998538	−	0.0540480i	$-0.0172124\pi$
$194$	1.63359	0.117285
$195$	0	0
$196$	−1.77846	−0.127033
$197$	− 23.9931i	− 1.70944i	−0.519090	−	0.854720i	$-0.673729\pi$
$197$	− 23.9931i	− 1.70944i	0.519090	−	0.854720i	$-0.326271\pi$
$198$	−2.17934	−0.154879
$199$	2.01461	0.142812	0.0714059	−	0.997447i	$-0.477251\pi$
$199$	2.01461	0.142812	0.0714059	+	0.997447i	$0.477251\pi$
$200$	− 8.39400i	− 0.593546i
$201$	35.8466i	2.52843i
$202$	3.64820i	0.256687i
$203$	− 5.22154i	− 0.366480i
$204$	5.23109	0.366250
$205$	−3.43965	−0.240235
$206$	− 8.00000i	− 0.557386i
$207$	−12.0164	−0.835199
$208$	0	0
$209$	3.30777	0.228803
$210$	0.560352i	0.0386680i
$211$	10.1008	0.695370	0.347685	−	0.937611i	$-0.386968\pi$
$211$	10.1008	0.695370	0.347685	+	0.937611i	$0.386968\pi$
$212$	20.0552	1.37740
$213$	− 2.67762i	− 0.183467i
$214$	2.61555i	0.178795i
$215$	6.03104i	0.411313i
$216$	3.76547i	0.256208i
$217$	7.02760	0.477064
$218$	−3.72938	−0.252585
$219$	17.1905i	1.16163i
$220$	−2.11727	−0.142746
$221$	0	0
$222$	−2.50516	−0.168135
$223$	− 10.1414i	− 0.679120i	−0.940584	−	0.339560i	$-0.889722\pi$
$223$	− 10.1414i	− 0.679120i	0.940584	−	0.339560i	$-0.110278\pi$
$224$	−4.83709	−0.323192
$225$	9.71639	0.647759
$226$	4.65613i	0.309721i
$227$	5.38445i	0.357379i	0.983906	+	0.178689i	$0.0571857\pi$
$227$	5.38445i	0.357379i	−0.983906	+	0.178689i	$0.942814\pi$
$228$	5.88273i	0.389594i
$229$	3.32238i	0.219549i	0.993957	+	0.109775i	$0.0350129\pi$
$229$	3.32238i	0.219549i	−0.993957	+	0.109775i	$0.964987\pi$
$230$	1.45426	0.0958908
$231$	−5.05863	−0.332834
$232$	− 9.28629i	− 0.609675i
$233$	−13.7198	−0.898816	−0.449408	−	0.893327i	$-0.648365\pi$
$233$	−13.7198	−0.898816	−0.449408	+	0.893327i	$0.648365\pi$
$234$	0	0
$235$	4.54392	0.296413
$236$	− 21.6482i	− 1.40918i
$237$	−3.01117	−0.195597
$238$	−0.615547	−0.0399000
$239$	3.50172i	0.226507i	0.993566	+	0.113254i	$0.0361273\pi$
$239$	3.50172i	0.226507i	−0.993566	+	0.113254i	$0.963873\pi$
$240$	− 3.23797i	− 0.209010i
$241$	1.58795i	0.102289i	0.998691	+	0.0511444i	$0.0162869\pi$
$241$	1.58795i	0.102289i	−0.998691	+	0.0511444i	$0.983713\pi$
$242$	− 2.79650i	− 0.179766i
$243$	−18.2491	−1.17068
$244$	−3.55691	−0.227708
$245$	0.529317i	0.0338168i
$246$	−6.87930	−0.438608
$247$	0	0
$248$	12.4983	0.793642
$249$	36.7734i	2.33042i
$250$	−2.42160	−0.153156
$251$	4.92676	0.310974	0.155487	−	0.987838i	$-0.450305\pi$
$251$	4.92676	0.310974	0.155487	+	0.987838i	$0.450305\pi$
$252$	− 3.66119i	− 0.230633i
$253$	13.1284i	0.825378i
$254$	0.387890i	0.0243384i
$255$	− 1.55691i	− 0.0974978i
$256$	1.07162	0.0669764
$257$	8.01461	0.499938	0.249969	−	0.968254i	$-0.419580\pi$
$257$	8.01461	0.499938	0.249969	+	0.968254i	$0.419580\pi$
$258$	12.0621i	0.750952i
$259$	−2.36641	−0.147041
$260$	0	0
$261$	10.7492	0.665361
$262$	− 4.99656i	− 0.308689i
$263$	1.60256	0.0988179	0.0494090	−	0.998779i	$-0.484266\pi$
$263$	1.60256	0.0988179	0.0494090	+	0.998779i	$0.484266\pi$
$264$	−8.99656	−0.553700
$265$	− 5.96896i	− 0.366671i
$266$	− 0.692226i	− 0.0424431i
$267$	15.5423i	0.951174i
$268$	28.3449i	1.73144i
$269$	−11.8207	−0.720719	−0.360359	−	0.932814i	$-0.617346\pi$
$269$	−11.8207	−0.720719	−0.360359	+	0.932814i	$0.617346\pi$
$270$	0.527497	0.0321024
$271$	21.8827i	1.32928i	0.747163	+	0.664641i	$0.231415\pi$
$271$	21.8827i	1.32928i	−0.747163	+	0.664641i	$0.768585\pi$
$272$	3.55691	0.215670
$273$	0	0
$274$	5.34836	0.323106
$275$	− 10.6155i	− 0.640142i
$276$	−23.3484	−1.40541
$277$	10.2181	0.613946	0.306973	−	0.951718i	$-0.400684\pi$
$277$	10.2181	0.613946	0.306973	+	0.951718i	$0.400684\pi$
$278$	6.55348i	0.393051i
$279$	14.4672i	0.866131i
$280$	0.941367i	0.0562574i
$281$	1.54231i	0.0920063i	0.998941	+	0.0460031i	$0.0146484\pi$
$281$	1.54231i	0.0920063i	−0.998941	+	0.0460031i	$0.985352\pi$
$282$	9.08785	0.541174
$283$	−15.8466	−0.941985	−0.470993	−	0.882137i	$-0.656104\pi$
$283$	−15.8466	−0.941985	−0.470993	+	0.882137i	$0.656104\pi$
$284$	− 2.11727i	− 0.125637i
$285$	1.75086	0.103712
$286$	0	0
$287$	−6.49828	−0.383581
$288$	− 9.95779i	− 0.586769i
$289$	−15.2897	−0.899396
$290$	−1.30090	−0.0763914
$291$	7.80605i	0.457599i
$292$	13.5930i	0.795470i
$293$	11.0828i	0.647464i	0.946149	+	0.323732i	$0.104938\pi$
$293$	11.0828i	0.647464i	−0.946149	+	0.323732i	$0.895062\pi$
$294$	1.05863i	0.0617407i
$295$	−6.44309	−0.375131
$296$	−4.20855	−0.244617
$297$	4.76203i	0.276321i
$298$	−4.38101	−0.253785
$299$	0	0
$300$	18.8793	1.09000
$301$	11.3940i	0.656740i
$302$	3.32926	0.191577
$303$	−17.4328	−1.00149
$304$	4.00000i	0.229416i
$305$	1.05863i	0.0606172i
$306$	− 1.26719i	− 0.0724402i
$307$	20.4121i	1.16498i	0.812839	+	0.582489i	$0.197921\pi$
$307$	20.4121i	1.16498i	−0.812839	+	0.582489i	$0.802079\pi$
$308$	−4.00000	−0.227921
$309$	38.2277	2.17470
$310$	− 1.75086i	− 0.0994421i
$311$	1.92332	0.109062	0.0545308	−	0.998512i	$-0.482634\pi$
$311$	1.92332	0.109062	0.0545308	+	0.998512i	$0.482634\pi$
$312$	0	0
$313$	−14.3664	−0.812037	−0.406019	−	0.913865i	$-0.633083\pi$
$313$	−14.3664	−0.812037	−0.406019	+	0.913865i	$0.633083\pi$
$314$	2.84320i	0.160451i
$315$	−1.08967	−0.0613959
$316$	−2.38101	−0.133943
$317$	− 15.5569i	− 0.873763i	−0.899519	−	0.436882i	$-0.856083\pi$
$317$	− 15.5569i	− 0.873763i	0.899519	−	0.436882i	$-0.143917\pi$
$318$	− 11.9379i	− 0.669446i
$319$	− 11.7440i	− 0.657537i
$320$	− 1.67418i	− 0.0935895i
$321$	−12.4983	−0.697586
$322$	2.74742	0.153108
$323$	1.92332i	0.107016i
$324$	−19.4526	−1.08070
$325$	0	0
$326$	3.00344	0.166345
$327$	− 17.8207i	− 0.985485i
$328$	−11.5569	−0.638124
$329$	8.58451	0.473279
$330$	1.26031i	0.0693778i
$331$	− 31.5500i	− 1.73415i	−0.498180	−	0.867073i	$-0.665998\pi$
$331$	− 31.5500i	− 1.73415i	0.498180	−	0.867073i	$-0.334002\pi$
$332$	29.0777i	1.59585i
$333$	− 4.87156i	− 0.266960i
$334$	−7.80605	−0.427128
$335$	8.43621	0.460919
$336$	− 6.11727i	− 0.333724i
$337$	8.42666	0.459029	0.229515	−	0.973305i	$-0.426286\pi$
$337$	8.42666	0.459029	0.229515	+	0.973305i	$0.426286\pi$
$338$	0	0
$339$	−22.2491	−1.20841
$340$	− 1.23109i	− 0.0667655i
$341$	15.8061	0.855946
$342$	1.42504	0.0770573
$343$	1.00000i	0.0539949i
$344$	20.2637i	1.09255i
$345$	6.94910i	0.374127i
$346$	− 10.9673i	− 0.589608i
$347$	19.3484	1.03867	0.519337	−	0.854569i	$-0.326179\pi$
$347$	19.3484	1.03867	0.519337	+	0.854569i	$0.326179\pi$
$348$	20.8862	1.11962
$349$	27.2553i	1.45894i	0.684013	+	0.729470i	$0.260233\pi$
$349$	27.2553i	1.45894i	−0.684013	+	0.729470i	$0.739767\pi$
$350$	−2.22154	−0.118746
$351$	0	0
$352$	−10.8793	−0.579868
$353$	25.6742i	1.36650i	0.730185	+	0.683249i	$0.239434\pi$
$353$	25.6742i	1.36650i	−0.730185	+	0.683249i	$0.760566\pi$
$354$	−12.8862	−0.684892
$355$	−0.630155	−0.0334452
$356$	12.2897i	0.651354i
$357$	− 2.94137i	− 0.155674i
$358$	9.90422i	0.523454i
$359$	− 23.4182i	− 1.23596i	−0.786192	−	0.617982i	$-0.787951\pi$
$359$	− 23.4182i	− 1.23596i	0.786192	−	0.617982i	$-0.212049\pi$
$360$	−1.93793	−0.102138
$361$	16.8371	0.886163
$362$	7.88273i	0.414307i
$363$	13.3630	0.701374
$364$	0	0
$365$	4.04564	0.211759
$366$	2.11727i	0.110671i
$367$	−14.6854	−0.766569	−0.383285	−	0.923630i	$-0.625207\pi$
$367$	−14.6854	−0.766569	−0.383285	+	0.923630i	$0.625207\pi$
$368$	−15.8759	−0.827586
$369$	− 13.3776i	− 0.696409i
$370$	0.589568i	0.0306502i
$371$	− 11.2767i	− 0.585459i
$372$	28.1104i	1.45746i
$373$	−23.6673	−1.22545	−0.612723	−	0.790298i	$-0.709926\pi$
$373$	−23.6673	−1.22545	−0.612723	+	0.790298i	$0.709926\pi$
$374$	−1.38445	−0.0715883
$375$	− 11.5715i	− 0.597551i
$376$	15.2672	0.787345
$377$	0	0
$378$	0.996562	0.0512576
$379$	32.7405i	1.68177i	0.541215	+	0.840884i	$0.317965\pi$
$379$	32.7405i	1.68177i	−0.541215	+	0.840884i	$0.682035\pi$
$380$	1.38445	0.0710209
$381$	−1.85352	−0.0949586
$382$	3.50172i	0.179164i
$383$	22.6155i	1.15560i	0.816178	+	0.577800i	$0.196089\pi$
$383$	22.6155i	1.15560i	−0.816178	+	0.577800i	$0.803911\pi$
$384$	− 25.1070i	− 1.28123i
$385$	1.19051i	0.0606739i
$386$	−0.706834	−0.0359769
$387$	−23.4561	−1.19234
$388$	6.17246i	0.313359i
$389$	−38.0483	−1.92913	−0.964563	−	0.263852i	$-0.915007\pi$
$389$	−38.0483	−1.92913	−0.964563	+	0.263852i	$0.915007\pi$
$390$	0	0
$391$	−7.63359	−0.386047
$392$	1.77846i	0.0898256i
$393$	23.8759	1.20438
$394$	−11.2932	−0.568941
$395$	0.708654i	0.0356562i
$396$	− 8.23453i	− 0.413801i
$397$	− 11.7052i	− 0.587468i	−0.955887	−	0.293734i	$-0.905102\pi$
$397$	− 11.7052i	− 0.587468i	0.955887	−	0.293734i	$-0.0948980\pi$
$398$	− 0.948243i	− 0.0475311i
$399$	3.30777	0.165596
$400$	12.8371	0.641855
$401$	3.55691i	0.177624i	0.996048	+	0.0888119i	$0.0283070\pi$
$401$	3.55691i	0.177624i	−0.996048	+	0.0888119i	$0.971693\pi$
$402$	16.8724	0.841520
$403$	0	0
$404$	−13.7846	−0.685808
$405$	5.78963i	0.287689i
$406$	−2.45769	−0.121973
$407$	−5.32238	−0.263821
$408$	− 5.23109i	− 0.258978i
$409$	− 5.26213i	− 0.260196i	−0.991501	−	0.130098i	$-0.958471\pi$
$409$	− 5.26213i	− 0.260196i	0.991501	−	0.130098i	$-0.0415291\pi$
$410$	1.61899i	0.0799560i
$411$	25.5569i	1.26063i
$412$	30.2277	1.48921
$413$	−12.1725	−0.598968
$414$	5.65593i	0.277974i
$415$	8.65432	0.424824
$416$	0	0
$417$	−31.3155	−1.53353
$418$	− 1.55691i	− 0.0761512i
$419$	26.0337	1.27183	0.635915	−	0.771759i	$-0.280623\pi$
$419$	26.0337	1.27183	0.635915	+	0.771759i	$0.280623\pi$
$420$	−2.11727	−0.103312
$421$	− 22.2423i	− 1.08402i	−0.840372	−	0.542011i	$-0.817663\pi$
$421$	− 22.2423i	− 1.08402i	0.840372	−	0.542011i	$-0.182337\pi$
$422$	− 4.75430i	− 0.231436i
$423$	17.6724i	0.859260i
$424$	− 20.0552i	− 0.973966i
$425$	6.17246	0.299408
$426$	−1.26031	−0.0610622
$427$	2.00000i	0.0967868i
$428$	−9.88273	−0.477700
$429$	0	0
$430$	2.83871	0.136895
$431$	− 27.6742i	− 1.33302i	−0.745497	−	0.666509i	$-0.767788\pi$
$431$	− 27.6742i	− 1.33302i	0.745497	−	0.666509i	$-0.232212\pi$
$432$	−5.75859	−0.277060
$433$	12.7880	0.614552	0.307276	−	0.951620i	$-0.400582\pi$
$433$	12.7880	0.614552	0.307276	+	0.951620i	$0.400582\pi$
$434$	− 3.30777i	− 0.158778i
$435$	− 6.21629i	− 0.298048i
$436$	− 14.0913i	− 0.674850i
$437$	− 8.58451i	− 0.410653i
$438$	8.09129	0.386617
$439$	18.1656	0.866996	0.433498	−	0.901155i	$-0.357279\pi$
$439$	18.1656	0.866996	0.433498	+	0.901155i	$0.357279\pi$
$440$	2.11727i	0.100937i
$441$	−2.05863	−0.0980302
$442$	0	0
$443$	0.107714	0.00511767	0.00255883	−	0.999997i	$-0.499185\pi$
$443$	0.107714	0.00511767	0.00255883	+	0.999997i	$0.499185\pi$
$444$	− 9.46563i	− 0.449219i
$445$	3.65775	0.173394
$446$	−4.77340	−0.226027
$447$	− 20.9345i	− 0.990167i
$448$	− 3.16291i	− 0.149433i
$449$	− 22.1725i	− 1.04638i	−0.852215	−	0.523192i	$-0.824741\pi$
$449$	− 22.1725i	− 1.04638i	0.852215	−	0.523192i	$-0.175259\pi$
$450$	− 4.57334i	− 0.215589i
$451$	−14.6155	−0.688219
$452$	−17.5930	−0.827505
$453$	15.9087i	0.747457i
$454$	2.53437	0.118944
$455$	0	0
$456$	5.88273	0.275484
$457$	− 4.35953i	− 0.203930i	−0.994788	−	0.101965i	$-0.967487\pi$
$457$	− 4.35953i	− 0.203930i	0.994788	−	0.101965i	$-0.0325130\pi$
$458$	1.56379	0.0730711
$459$	−2.76891	−0.129241
$460$	5.49484i	0.256198i
$461$	− 32.3810i	− 1.50813i	−0.656797	−	0.754067i	$-0.728089\pi$
$461$	− 32.3810i	− 1.50813i	0.656797	−	0.754067i	$-0.271911\pi$
$462$	2.38101i	0.110775i
$463$	8.36641i	0.388820i	0.980920	+	0.194410i	$0.0622792\pi$
$463$	8.36641i	0.388820i	−0.980920	+	0.194410i	$0.937721\pi$
$464$	14.2017	0.659296
$465$	8.36641	0.387983
$466$	6.45769i	0.299147i
$467$	19.5423	0.904310	0.452155	−	0.891939i	$-0.350655\pi$
$467$	19.5423	0.904310	0.452155	+	0.891939i	$0.350655\pi$
$468$	0	0
$469$	15.9379	0.735945
$470$	− 2.13875i	− 0.0986532i
$471$	−13.5861	−0.626016
$472$	−21.6482	−0.996439
$473$	25.6267i	1.17832i
$474$	1.41731i	0.0650991i
$475$	6.94137i	0.318492i
$476$	− 2.32582i	− 0.106604i
$477$	23.2147	1.06293
$478$	1.64820	0.0753870
$479$	− 28.5224i	− 1.30322i	−0.758553	−	0.651612i	$-0.774093\pi$
$479$	− 28.5224i	− 1.30322i	0.758553	−	0.651612i	$-0.225907\pi$
$480$	−5.75859	−0.262843
$481$	0	0
$482$	0.747422	0.0340441
$483$	13.1284i	0.597365i
$484$	10.5665	0.480294
$485$	1.83709	0.0834180
$486$	8.58957i	0.389631i
$487$	− 24.8241i	− 1.12489i	−0.826836	−	0.562444i	$-0.809861\pi$
$487$	− 24.8241i	− 1.12489i	0.826836	−	0.562444i	$-0.190139\pi$
$488$	3.55691i	0.161014i
$489$	14.3518i	0.649011i
$490$	0.249141	0.0112550
$491$	−29.1690	−1.31638	−0.658190	−	0.752852i	$-0.728678\pi$
$491$	−29.1690	−1.31638	−0.658190	+	0.752852i	$0.728678\pi$
$492$	− 25.9931i	− 1.17186i
$493$	6.82860	0.307545
$494$	0	0
$495$	−2.45082	−0.110156
$496$	19.1138i	0.858236i
$497$	−1.19051	−0.0534016
$498$	17.3086	0.775618
$499$	33.3009i	1.49075i	0.666644	+	0.745376i	$0.267730\pi$
$499$	33.3009i	1.49075i	−0.666644	+	0.745376i	$0.732270\pi$
$500$	− 9.14992i	− 0.409197i
$501$	− 37.3009i	− 1.66648i
$502$	− 2.31894i	− 0.103500i
$503$	−12.3258	−0.549581	−0.274791	−	0.961504i	$-0.588609\pi$
$503$	−12.3258	−0.549581	−0.274791	+	0.961504i	$0.588609\pi$
$504$	−3.66119	−0.163082
$505$	4.10266i	0.182566i
$506$	6.17934	0.274705
$507$	0	0
$508$	−1.46563	−0.0650267
$509$	− 23.7052i	− 1.05072i	−0.850882	−	0.525358i	$-0.823932\pi$
$509$	− 23.7052i	− 1.05072i	0.850882	−	0.525358i	$-0.176068\pi$
$510$	−0.732814	−0.0324495
$511$	7.64315	0.338113
$512$	− 22.8302i	− 1.00896i
$513$	− 3.11383i	− 0.137479i
$514$	− 3.77234i	− 0.166391i
$515$	− 8.99656i	− 0.396436i
$516$	−45.5760	−2.00637
$517$	19.3078	0.849155
$518$	1.11383i	0.0489388i
$519$	52.4070	2.30041
$520$	0	0
$521$	43.9018	1.92337	0.961687	−	0.274149i	$-0.0883962\pi$
$521$	43.9018	1.92337	0.961687	+	0.274149i	$0.0883962\pi$
$522$	− 5.05949i	− 0.221448i
$523$	37.4328	1.63682	0.818410	−	0.574634i	$-0.194856\pi$
$523$	37.4328	1.63682	0.818410	+	0.574634i	$0.194856\pi$
$524$	18.8793	0.824746
$525$	− 10.6155i	− 0.463300i
$526$	− 0.754297i	− 0.0328889i
$527$	9.19051i	0.400345i
$528$	− 13.7586i	− 0.598766i
$529$	11.0716	0.481375
$530$	−2.80949	−0.122037
$531$	− 25.0586i	− 1.08745i
$532$	2.61555	0.113398
$533$	0	0
$534$	7.31551	0.316573
$535$	2.94137i	0.127166i
$536$	28.3449	1.22431
$537$	−47.3269	−2.04231
$538$	5.56379i	0.239872i
$539$	2.24914i	0.0968773i
$540$	1.99312i	0.0857704i
$541$	− 34.9751i	− 1.50370i	−0.659336	−	0.751848i	$-0.729163\pi$
$541$	− 34.9751i	− 1.50370i	0.659336	−	0.751848i	$-0.270837\pi$
$542$	10.2998	0.442416
$543$	−37.6673	−1.61646
$544$	− 6.32582i	− 0.271217i
$545$	−4.19395	−0.179649
$546$	0	0
$547$	6.50783	0.278255	0.139127	−	0.990274i	$-0.455570\pi$
$547$	6.50783	0.278255	0.139127	+	0.990274i	$0.455570\pi$
$548$	20.2086i	0.863267i
$549$	−4.11727	−0.175721
$550$	−4.99656	−0.213054
$551$	7.67924i	0.327146i
$552$	23.3484i	0.993772i
$553$	1.33881i	0.0569320i
$554$	− 4.80949i	− 0.204336i
$555$	−2.81722	−0.119585
$556$	−24.7620	−1.05014
$557$	− 43.4328i	− 1.84031i	−0.391559	−	0.920153i	$-0.628064\pi$
$557$	− 43.4328i	− 1.84031i	0.391559	−	0.920153i	$-0.371936\pi$
$558$	6.80949	0.288269
$559$	0	0
$560$	−1.43965	−0.0608362
$561$	− 6.61555i	− 0.279309i
$562$	0.725938	0.0306218
$563$	33.8827	1.42799	0.713993	−	0.700152i	$-0.246885\pi$
$563$	33.8827	1.42799	0.713993	+	0.700152i	$0.246885\pi$
$564$	34.3380i	1.44589i
$565$	5.23615i	0.220287i
$566$	7.45875i	0.313515i
$567$	10.9379i	0.459350i
$568$	−2.11727	−0.0888385
$569$	−19.2147	−0.805521	−0.402760	−	0.915305i	$-0.631949\pi$
$569$	−19.2147	−0.805521	−0.402760	+	0.915305i	$0.631949\pi$
$570$	− 0.824101i	− 0.0345178i
$571$	−20.8268	−0.871573	−0.435787	−	0.900050i	$-0.643530\pi$
$571$	−20.8268	−0.871573	−0.435787	+	0.900050i	$0.643530\pi$
$572$	0	0
$573$	−16.7328	−0.699023
$574$	3.05863i	0.127665i
$575$	−27.5500	−1.14892
$576$	6.51127	0.271303
$577$	− 28.6448i	− 1.19250i	−0.802800	−	0.596249i	$-0.796657\pi$
$577$	− 28.6448i	− 1.19250i	0.802800	−	0.596249i	$-0.203343\pi$
$578$	7.19662i	0.299340i
$579$	− 3.37758i	− 0.140367i
$580$	− 4.91539i	− 0.204100i
$581$	16.3500	0.678311
$582$	3.67418	0.152300
$583$	− 25.3630i	− 1.05043i
$584$	13.5930	0.562483
$585$	0	0
$586$	5.21649	0.215491
$587$	4.32076i	0.178337i	0.996017	+	0.0891685i	$0.0284210\pi$
$587$	4.32076i	0.178337i	−0.996017	+	0.0891685i	$0.971579\pi$
$588$	−4.00000	−0.164957
$589$	−10.3354	−0.425862
$590$	3.03265i	0.124852i
$591$	− 53.9639i	− 2.21978i
$592$	− 6.43621i	− 0.264527i
$593$	− 15.9690i	− 0.655767i	−0.944718	−	0.327883i	$-0.893665\pi$
$593$	− 15.9690i	− 0.655767i	0.944718	−	0.327883i	$-0.106335\pi$
$594$	2.24141	0.0919661
$595$	−0.692226	−0.0283785
$596$	− 16.5535i	− 0.678057i
$597$	4.53114	0.185447
$598$	0	0
$599$	−16.8697	−0.689279	−0.344640	−	0.938735i	$-0.611999\pi$
$599$	−16.8697	−0.689279	−0.344640	+	0.938735i	$0.611999\pi$
$600$	− 18.8793i	− 0.770744i
$601$	−15.3415	−0.625792	−0.312896	−	0.949787i	$-0.601299\pi$
$601$	−15.3415	−0.625792	−0.312896	+	0.949787i	$0.601299\pi$
$602$	5.36297	0.218578
$603$	32.8103i	1.33614i
$604$	12.5795i	0.511851i
$605$	− 3.14486i	− 0.127857i
$606$	8.20532i	0.333318i
$607$	35.8353	1.45451	0.727254	−	0.686368i	$-0.240796\pi$
$607$	35.8353	1.45451	0.727254	+	0.686368i	$0.240796\pi$
$608$	7.11383	0.288504
$609$	− 11.7440i	− 0.475890i
$610$	0.498281	0.0201748
$611$	0	0
$612$	4.78801	0.193544
$613$	− 19.6673i	− 0.794355i	−0.917742	−	0.397177i	$-0.869990\pi$
$613$	− 19.6673i	− 0.794355i	0.917742	−	0.397177i	$-0.130010\pi$
$614$	9.60761	0.387732
$615$	−7.73625	−0.311956
$616$	4.00000i	0.161165i
$617$	41.4588i	1.66907i	0.550958	+	0.834533i	$0.314263\pi$
$617$	41.4588i	1.66907i	−0.550958	+	0.834533i	$0.685737\pi$
$618$	− 17.9931i	− 0.723790i
$619$	10.8793i	0.437276i	0.975806	+	0.218638i	$0.0701614\pi$
$619$	10.8793i	0.437276i	−0.975806	+	0.218638i	$0.929839\pi$
$620$	6.61555	0.265687
$621$	12.3587	0.495937
$622$	− 0.905275i	− 0.0362982i
$623$	6.91033	0.276857
$624$	0	0
$625$	20.8759	0.835034
$626$	6.76203i	0.270265i
$627$	7.43965	0.297111
$628$	−10.7429	−0.428689
$629$	− 3.09472i	− 0.123395i
$630$	0.512889i	0.0204340i
$631$	− 31.4396i	− 1.25159i	−0.779987	−	0.625796i	$-0.784774\pi$
$631$	− 31.4396i	− 1.25159i	0.779987	−	0.625796i	$-0.215226\pi$
$632$	2.38101i	0.0947117i
$633$	22.7182	0.902968
$634$	−7.32238	−0.290809
$635$	0.436210i	0.0173105i
$636$	45.1070	1.78861
$637$	0	0
$638$	−5.52770	−0.218844
$639$	− 2.45082i	− 0.0969529i
$640$	−5.90871	−0.233562
$641$	−3.04221	−0.120160	−0.0600799	−	0.998194i	$-0.519136\pi$
$641$	−3.04221	−0.120160	−0.0600799	+	0.998194i	$0.519136\pi$
$642$	5.88273i	0.232173i
$643$	− 8.02922i	− 0.316641i	−0.987388	−	0.158321i	$-0.949392\pi$
$643$	− 8.02922i	− 0.316641i	0.987388	−	0.158321i	$-0.0506080\pi$
$644$	10.3810i	0.409069i
$645$	13.5646i	0.534107i
$646$	0.905275	0.0356176
$647$	−7.07324	−0.278078	−0.139039	−	0.990287i	$-0.544401\pi$
$647$	−7.07324	−0.278078	−0.139039	+	0.990287i	$0.544401\pi$
$648$	19.4526i	0.764172i
$649$	−27.3776	−1.07466
$650$	0	0
$651$	15.8061	0.619488
$652$	11.3484i	0.444436i
$653$	−15.7586	−0.616681	−0.308341	−	0.951276i	$-0.599774\pi$
$653$	−15.7586	−0.616681	−0.308341	+	0.951276i	$0.599774\pi$
$654$	−8.38789	−0.327992
$655$	− 5.61899i	− 0.219552i
$656$	− 17.6742i	− 0.690061i
$657$	15.7344i	0.613859i
$658$	− 4.04059i	− 0.157518i
$659$	−12.2181	−0.475950	−0.237975	−	0.971271i	$-0.576484\pi$
$659$	−12.2181	−0.475950	−0.237975	+	0.971271i	$0.576484\pi$
$660$	−4.76203	−0.185362
$661$	3.73443i	0.145253i	0.997359	+	0.0726263i	$0.0231380\pi$
$661$	3.73443i	0.145253i	−0.997359	+	0.0726263i	$0.976862\pi$
$662$	−14.8501	−0.577165
$663$	0	0
$664$	29.0777	1.12844
$665$	− 0.778457i	− 0.0301873i
$666$	−2.29296	−0.0888506
$667$	−30.4786	−1.18014
$668$	− 29.4948i	− 1.14119i
$669$	− 22.8095i	− 0.881866i
$670$	− 3.97078i	− 0.153405i
$671$	4.49828i	0.173654i
$672$	−10.8793	−0.419678
$673$	5.65775	0.218090	0.109045	−	0.994037i	$-0.465221\pi$
$673$	5.65775	0.218090	0.109045	+	0.994037i	$0.465221\pi$
$674$	− 3.96629i	− 0.152776i
$675$	−9.99312	−0.384636
$676$	0	0
$677$	9.39906	0.361235	0.180618	−	0.983553i	$-0.442190\pi$
$677$	9.39906	0.361235	0.180618	+	0.983553i	$0.442190\pi$
$678$	10.4723i	0.402186i
$679$	3.47068	0.133193
$680$	−1.23109	−0.0472103
$681$	12.1104i	0.464071i
$682$	− 7.43965i	− 0.284879i
$683$	− 20.7328i	− 0.793319i	−0.917966	−	0.396660i	$-0.870169\pi$
$683$	− 20.7328i	− 0.793319i	0.917966	−	0.396660i	$-0.129831\pi$
$684$	5.38445i	0.205880i
$685$	6.01461	0.229806
$686$	0.470683	0.0179708
$687$	7.47250i	0.285094i
$688$	−30.9897	−1.18147
$689$	0	0
$690$	3.27083	0.124518
$691$	− 16.0862i	− 0.611949i	−0.952040	−	0.305975i	$-0.901018\pi$
$691$	− 16.0862i	− 0.611949i	0.952040	−	0.305975i	$-0.0989822\pi$
$692$	41.4396	1.57530
$693$	−4.63016	−0.175885
$694$	− 9.10695i	− 0.345695i
$695$	7.36984i	0.279554i
$696$	− 20.8862i	− 0.791688i
$697$	− 8.49828i	− 0.321895i
$698$	12.8286	0.485570
$699$	−30.8578	−1.16715
$700$	− 8.39400i	− 0.317264i
$701$	6.98013	0.263636	0.131818	−	0.991274i	$-0.457919\pi$
$701$	6.98013	0.263636	0.131818	+	0.991274i	$0.457919\pi$
$702$	0	0
$703$	3.48024	0.131260
$704$	− 7.11383i	− 0.268112i
$705$	10.2199	0.384905
$706$	12.0844	0.454803
$707$	7.75086i	0.291501i
$708$	− 48.6898i	− 1.82988i
$709$	8.39239i	0.315183i	0.987504	+	0.157591i	$0.0503729\pi$
$709$	8.39239i	0.315183i	−0.987504	+	0.157591i	$0.949627\pi$
$710$	0.296604i	0.0111313i
$711$	−2.75612	−0.103362
$712$	12.2897	0.460577
$713$	− 41.0207i	− 1.53624i
$714$	−1.38445	−0.0518118
$715$	0	0
$716$	−37.4227	−1.39855
$717$	7.87586i	0.294129i
$718$	−11.0225	−0.411358
$719$	5.16129	0.192484	0.0962418	−	0.995358i	$-0.469318\pi$
$719$	5.16129	0.192484	0.0962418	+	0.995358i	$0.469318\pi$
$720$	− 2.96371i	− 0.110451i
$721$	− 16.9966i	− 0.632985i
$722$	− 7.92494i	− 0.294936i
$723$	3.57152i	0.132826i
$724$	−29.7846	−1.10693
$725$	24.6448	0.915284
$726$	− 6.28973i	− 0.233434i
$727$	40.4362	1.49970	0.749848	−	0.661610i	$-0.230127\pi$
$727$	40.4362	1.49970	0.749848	+	0.661610i	$0.230127\pi$
$728$	0	0
$729$	−8.23109	−0.304855
$730$	− 1.90422i	− 0.0704782i
$731$	−14.9008	−0.551125
$732$	−8.00000	−0.295689
$733$	39.1311i	1.44534i	0.691193	+	0.722670i	$0.257085\pi$
$733$	39.1311i	1.44534i	−0.691193	+	0.722670i	$0.742915\pi$
$734$	6.91215i	0.255132i
$735$	1.19051i	0.0439125i
$736$	28.2345i	1.04074i
$737$	35.8466	1.32043
$738$	−6.29660	−0.231781
$739$	− 7.13531i	− 0.262477i	−0.991351	−	0.131238i	$-0.958105\pi$
$739$	− 7.13531i	− 0.262477i	0.991351	−	0.131238i	$-0.0418953\pi$
$740$	−2.22766	−0.0818903
$741$	0	0
$742$	−5.30777	−0.194855
$743$	− 13.8827i	− 0.509308i	−0.967032	−	0.254654i	$-0.918038\pi$
$743$	− 13.8827i	− 0.509308i	0.967032	−	0.254654i	$-0.0819616\pi$
$744$	28.1104	1.03058
$745$	−4.92676	−0.180502
$746$	11.1398i	0.407857i
$747$	33.6586i	1.23150i
$748$	− 5.23109i	− 0.191268i
$749$	5.55691i	0.203045i
$750$	−5.44652	−0.198879
$751$	37.3251	1.36201	0.681005	−	0.732278i	$-0.261543\pi$
$751$	37.3251	1.36201	0.681005	+	0.732278i	$0.261543\pi$
$752$	23.3484i	0.851427i
$753$	11.0810	0.403813
$754$	0	0
$755$	3.74398	0.136258
$756$	3.76547i	0.136949i
$757$	−7.10428	−0.258209	−0.129105	−	0.991631i	$-0.541210\pi$
$757$	−7.10428	−0.258209	−0.129105	+	0.991631i	$0.541210\pi$
$758$	15.4104	0.559732
$759$	29.5277i	1.07179i
$760$	− 1.38445i	− 0.0502194i
$761$	− 25.9621i	− 0.941125i	−0.882367	−	0.470562i	$-0.844051\pi$
$761$	− 25.9621i	− 0.941125i	0.882367	−	0.470562i	$-0.155949\pi$
$762$	0.872420i	0.0316044i
$763$	−7.92332	−0.286843
$764$	−13.2311	−0.478684
$765$	− 1.42504i	− 0.0515224i
$766$	10.6448	0.384611
$767$	0	0
$768$	2.41023	0.0869717
$769$	21.4638i	0.774005i	0.922079	+	0.387002i	$0.126489\pi$
$769$	21.4638i	0.774005i	−0.922079	+	0.387002i	$0.873511\pi$
$770$	0.560352	0.0201937
$771$	18.0260	0.649190
$772$	− 2.67074i	− 0.0961221i
$773$	40.4914i	1.45637i	0.685378	+	0.728187i	$0.259637\pi$
$773$	40.4914i	1.45637i	−0.685378	+	0.728187i	$0.740363\pi$
$774$	11.0404i	0.396838i
$775$	33.1690i	1.19147i
$776$	6.17246	0.221578
$777$	−5.32238	−0.190939
$778$	17.9087i	0.642058i
$779$	9.55691	0.342412
$780$	0	0
$781$	−2.67762	−0.0958127
$782$	3.59301i	0.128486i
$783$	−11.0554	−0.395088
$784$	−2.71982	−0.0971366
$785$	3.19738i	0.114119i
$786$	− 11.2380i	− 0.400845i
$787$	− 5.02072i	− 0.178969i	−0.995988	−	0.0894847i	$-0.971478\pi$
$787$	− 5.02072i	− 0.178969i	0.995988	−	0.0894847i	$-0.0285220\pi$
$788$	− 42.6707i	− 1.52008i
$789$	3.60438	0.128319
$790$	0.333552	0.0118672
$791$	9.89229i	0.351729i
$792$	−8.23453	−0.292601
$793$	0	0
$794$	−5.50945	−0.195523
$795$	− 13.4250i	− 0.476137i
$796$	3.58289	0.126992
$797$	−19.7002	−0.697815	−0.348908	−	0.937157i	$-0.613447\pi$
$797$	−19.7002	−0.697815	−0.348908	+	0.937157i	$0.613447\pi$
$798$	− 1.55691i	− 0.0551142i
$799$	11.2266i	0.397169i
$800$	− 22.8302i	− 0.807170i
$801$	14.2258i	0.502645i
$802$	1.67418	0.0591174
$803$	17.1905	0.606640
$804$	63.7517i	2.24835i
$805$	3.08967	0.108897
$806$	0	0
$807$	−26.5863	−0.935883
$808$	13.7846i	0.484940i
$809$	−2.57678	−0.0905947	−0.0452974	−	0.998974i	$-0.514424\pi$
$809$	−2.57678	−0.0905947	−0.0452974	+	0.998974i	$0.514424\pi$
$810$	2.72508	0.0957496
$811$	− 41.2311i	− 1.44782i	−0.689895	−	0.723910i	$-0.742343\pi$
$811$	− 41.2311i	− 1.44782i	0.689895	−	0.723910i	$-0.257657\pi$
$812$	− 9.28629i	− 0.325885i
$813$	49.2173i	1.72613i
$814$	2.50516i	0.0878057i
$815$	3.37758	0.118311
$816$	8.00000	0.280056
$817$	− 16.7570i	− 0.586252i
$818$	−2.47680	−0.0865992
$819$	0	0
$820$	−6.11727	−0.213624
$821$	− 5.26719i	− 0.183826i	−0.995767	−	0.0919130i	$-0.970702\pi$
$821$	− 5.26719i	− 0.183826i	0.995767	−	0.0919130i	$-0.0292982\pi$
$822$	12.0292	0.419567
$823$	−36.0191	−1.25555	−0.627774	−	0.778396i	$-0.716034\pi$
$823$	−36.0191	−1.25555	−0.627774	+	0.778396i	$0.716034\pi$
$824$	− 30.2277i	− 1.05303i
$825$	− 23.8759i	− 0.831251i
$826$	5.72938i	0.199350i
$827$	− 16.3157i	− 0.567353i	−0.958920	−	0.283676i	$-0.908446\pi$
$827$	− 16.3157i	− 0.567353i	0.958920	−	0.283676i	$-0.0915541\pi$
$828$	−21.3707	−0.742683
$829$	30.3956	1.05568	0.527842	−	0.849343i	$-0.323001\pi$
$829$	30.3956	1.05568	0.527842	+	0.849343i	$0.323001\pi$
$830$	− 4.07344i	− 0.141391i
$831$	22.9820	0.797235
$832$	0	0
$833$	−1.30777	−0.0453117
$834$	14.7397i	0.510394i
$835$	−8.77846	−0.303791
$836$	5.88273	0.203459
$837$	− 14.8793i	− 0.514304i
$838$	− 12.2536i	− 0.423295i
$839$	29.8398i	1.03018i	0.857135	+	0.515092i	$0.172242\pi$
$839$	29.8398i	1.03018i	−0.857135	+	0.515092i	$0.827758\pi$
$840$	2.11727i	0.0730526i
$841$	−1.73549	−0.0598445
$842$	−10.4691	−0.360788
$843$	3.46886i	0.119474i
$844$	17.9639	0.618343
$845$	0	0
$846$	8.31809	0.285982
$847$	− 5.94137i	− 0.204148i
$848$	30.6707	1.05324
$849$	−35.6413	−1.22321
$850$	− 2.90528i	− 0.0996501i
$851$	13.8129i	0.473501i
$852$	− 4.76203i	− 0.163144i
$853$	− 0.203497i	− 0.00696761i	−0.999994	−	0.00348380i	$-0.998891\pi$
$853$	− 0.203497i	− 0.00696761i	0.999994	−	0.00348380i	$-0.00110893\pi$
$854$	0.941367	0.0322129
$855$	1.60256	0.0548063
$856$	9.88273i	0.337785i
$857$	12.6155	0.430939	0.215469	−	0.976511i	$-0.430872\pi$
$857$	12.6155	0.430939	0.215469	+	0.976511i	$0.430872\pi$
$858$	0	0
$859$	−27.9671	−0.954227	−0.477113	−	0.878842i	$-0.658317\pi$
$859$	−27.9671	−0.954227	−0.477113	+	0.878842i	$0.658317\pi$
$860$	10.7259i	0.365751i
$861$	−14.6155	−0.498097
$862$	−13.0258	−0.443660
$863$	2.76891i	0.0942546i	0.998889	+	0.0471273i	$0.0150066\pi$
$863$	2.76891i	0.0942546i	−0.998889	+	0.0471273i	$0.984993\pi$
$864$	10.2414i	0.348420i
$865$	− 12.3336i	− 0.419353i
$866$	− 6.01910i	− 0.204537i
$867$	−34.3887	−1.16790
$868$	12.4983	0.424219
$869$	3.01117i	0.102147i
$870$	−2.92590	−0.0991974
$871$	0	0
$872$	−14.0913	−0.477191
$873$	7.14486i	0.241817i
$874$	−4.04059	−0.136675
$875$	−5.14486	−0.173928
$876$	30.5726i	1.03295i
$877$	− 6.71133i	− 0.226626i	−0.993559	−	0.113313i	$-0.963854\pi$
$877$	− 6.71133i	− 0.226626i	0.993559	−	0.113313i	$-0.0361462\pi$
$878$	− 8.55024i	− 0.288557i
$879$	24.9268i	0.840759i
$880$	−3.23797	−0.109152
$881$	18.3741	0.619040	0.309520	−	0.950893i	$-0.399832\pi$
$881$	18.3741	0.619040	0.309520	+	0.950893i	$0.399832\pi$
$882$	0.968964i	0.0326267i
$883$	−9.93105	−0.334207	−0.167103	−	0.985939i	$-0.553441\pi$
$883$	−9.93105	−0.334207	−0.167103	+	0.985939i	$0.553441\pi$
$884$	0	0
$885$	−14.4914	−0.487123
$886$	− 0.0506994i	− 0.00170328i
$887$	−51.3776	−1.72509	−0.862545	−	0.505980i	$-0.831131\pi$
$887$	−51.3776	−1.72509	−0.862545	+	0.505980i	$0.831131\pi$
$888$	−9.46563	−0.317646
$889$	0.824101i	0.0276394i
$890$	− 1.72164i	− 0.0577096i
$891$	24.6009i	0.824162i
$892$	− 18.0361i	− 0.603893i
$893$	−12.6251	−0.422483
$894$	−9.85352	−0.329551
$895$	11.1380i	0.372302i
$896$	−11.1629	−0.372927
$897$	0	0
$898$	−10.4362	−0.348261
$899$	36.6949i	1.22384i
$900$	17.2802	0.576006
$901$	14.7474	0.491308
$902$	6.87930i	0.229055i
$903$	25.6267i	0.852804i
$904$	17.5930i	0.585135i
$905$	8.86469i	0.294672i
$906$	7.48797	0.248771
$907$	−4.34225	−0.144182	−0.0720910	−	0.997398i	$-0.522967\pi$
$907$	−4.34225	−0.144182	−0.0720910	+	0.997398i	$0.522967\pi$
$908$	9.57602i	0.317791i
$909$	−15.9562	−0.529233
$910$	0	0
$911$	31.4853	1.04315	0.521577	−	0.853204i	$-0.325344\pi$
$911$	31.4853	1.04315	0.521577	+	0.853204i	$0.325344\pi$
$912$	8.99656i	0.297906i
$913$	36.7734	1.21702
$914$	−2.05196	−0.0678728
$915$	2.38101i	0.0787139i
$916$	5.90871i	0.195229i
$917$	− 10.6155i	− 0.350556i
$918$	1.30328i	0.0430146i
$919$	43.4588	1.43357	0.716786	−	0.697293i	$-0.245612\pi$
$919$	43.4588	1.43357	0.716786	+	0.697293i	$0.245612\pi$
$920$	5.49484	0.181160
$921$	45.9096i	1.51277i
$922$	−15.2412	−0.501942
$923$	0	0
$924$	−8.99656	−0.295965
$925$	− 11.1690i	− 0.367235i
$926$	3.93793	0.129408
$927$	34.9897	1.14921
$928$	− 25.2571i	− 0.829104i
$929$	− 4.40517i	− 0.144529i	−0.997385	−	0.0722645i	$-0.976977\pi$
$929$	− 4.40517i	− 0.144529i	0.997385	−	0.0722645i	$-0.0230226\pi$
$930$	− 3.93793i	− 0.129130i
$931$	− 1.47068i	− 0.0481997i
$932$	−24.4001	−0.799252
$933$	4.32582	0.141621
$934$	− 9.19824i	− 0.300976i
$935$	−1.55691	−0.0509165
$936$	0	0
$937$	−34.0990	−1.11397	−0.556983	−	0.830524i	$-0.688041\pi$
$937$	−34.0990	−1.11397	−0.556983	+	0.830524i	$0.688041\pi$
$938$	− 7.50172i	− 0.244940i
$939$	−32.3121	−1.05446
$940$	8.08117	0.263579
$941$	− 44.4672i	− 1.44959i	−0.688964	−	0.724795i	$-0.741934\pi$
$941$	− 44.4672i	− 1.44959i	0.688964	−	0.724795i	$-0.258066\pi$
$942$	6.39477i	0.208353i
$943$	37.9311i	1.23521i
$944$	− 33.1070i	− 1.07754i
$945$	1.12070	0.0364565
$946$	12.0621	0.392172
$947$	57.9311i	1.88251i	0.337702	+	0.941253i	$0.390350\pi$
$947$	57.9311i	1.88251i	−0.337702	+	0.941253i	$0.609650\pi$
$948$	−5.35524	−0.173930
$949$	0	0
$950$	3.26719	0.106002
$951$	− 34.9897i	− 1.13462i
$952$	−2.32582	−0.0753802
$953$	−35.3060	−1.14367	−0.571836	−	0.820368i	$-0.693769\pi$
$953$	−35.3060	−1.14367	−0.571836	+	0.820368i	$0.693769\pi$
$954$	− 10.9268i	− 0.353767i
$955$	3.93793i	0.127428i
$956$	6.22766i	0.201417i
$957$	− 26.4139i	− 0.853839i
$958$	−13.4250	−0.433743
$959$	11.3630	0.366929
$960$	− 3.76547i	− 0.121530i
$961$	−18.3871	−0.593133
$962$	0	0
$963$	−11.4396	−0.368638
$964$	2.82410i	0.0909582i
$965$	−0.794885	−0.0255882
$966$	6.17934	0.198817
$967$	− 23.7148i	− 0.762616i	−0.924448	−	0.381308i	$-0.875474\pi$
$967$	− 23.7148i	− 0.762616i	0.924448	−	0.381308i	$-0.124526\pi$
$968$	− 10.5665i	− 0.339619i
$969$	4.32582i	0.138965i
$970$	− 0.864688i	− 0.0277635i
$971$	−23.9379	−0.768205	−0.384102	−	0.923291i	$-0.625489\pi$
$971$	−23.9379	−0.768205	−0.384102	+	0.923291i	$0.625489\pi$
$972$	−32.4553	−1.04100
$973$	13.9233i	0.446361i
$974$	−11.6843	−0.374389
$975$	0	0
$976$	−5.43965	−0.174119
$977$	16.1871i	0.517870i	0.965895	+	0.258935i	$0.0833716\pi$
$977$	16.1871i	0.517870i	−0.965895	+	0.258935i	$0.916628\pi$
$978$	6.75515	0.216006
$979$	15.5423	0.496734
$980$	0.941367i	0.0300709i
$981$	− 16.3112i	− 0.520777i
$982$	13.7294i	0.438122i
$983$	45.7243i	1.45838i	0.684312	+	0.729190i	$0.260103\pi$
$983$	45.7243i	1.45838i	−0.684312	+	0.729190i	$0.739897\pi$
$984$	−25.9931	−0.828631
$985$	−12.7000	−0.404654
$986$	− 3.21411i	− 0.102358i
$987$	19.3078	0.614573
$988$	0	0
$989$	66.5078	2.11483
$990$	1.15356i	0.0366625i
$991$	−5.40356	−0.171650	−0.0858248	−	0.996310i	$-0.527353\pi$
$991$	−5.40356	−0.171650	−0.0858248	+	0.996310i	$0.527353\pi$
$992$	33.9931	1.07928
$993$	− 70.9605i	− 2.25186i
$994$	0.560352i	0.0177733i
$995$	− 1.06637i	− 0.0338061i
$996$	65.3999i	2.07228i
$997$	6.04832	0.191552	0.0957761	−	0.995403i	$-0.469467\pi$
$997$	6.04832	0.191552	0.0957761	+	0.995403i	$0.469467\pi$
$998$	15.6742	0.496158
$999$	5.01031i	0.158519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.f.337.3		6
13.5	odd	4		1183.2.a.i.1.2		3
13.8	odd	4		91.2.a.d.1.2	✓	3
13.12	even	2	inner	1183.2.c.f.337.4		6
39.8	even	4		819.2.a.i.1.2		3
52.47	even	4		1456.2.a.t.1.1		3
65.34	odd	4		2275.2.a.m.1.2		3
91.34	even	4		637.2.a.j.1.2		3
91.47	even	12		637.2.e.i.508.2		6
91.60	odd	12		637.2.e.j.79.2		6
91.73	even	12		637.2.e.i.79.2		6
91.83	even	4		8281.2.a.bg.1.2		3
91.86	odd	12		637.2.e.j.508.2		6
104.21	odd	4		5824.2.a.by.1.1		3
104.99	even	4		5824.2.a.bs.1.3		3
273.125	odd	4		5733.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.2	✓	3	13.8	odd	4
637.2.a.j.1.2		3	91.34	even	4
637.2.e.i.79.2		6	91.73	even	12
637.2.e.i.508.2		6	91.47	even	12
637.2.e.j.79.2		6	91.60	odd	12
637.2.e.j.508.2		6	91.86	odd	12
819.2.a.i.1.2		3	39.8	even	4
1183.2.a.i.1.2		3	13.5	odd	4
1183.2.c.f.337.3		6	1.1	even	1	trivial
1183.2.c.f.337.4		6	13.12	even	2	inner
1456.2.a.t.1.1		3	52.47	even	4
2275.2.a.m.1.2		3	65.34	odd	4
5733.2.a.x.1.2		3	273.125	odd	4
5824.2.a.bs.1.3		3	104.99	even	4
5824.2.a.by.1.1		3	104.21	odd	4
8281.2.a.bg.1.2		3	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)

\(f(q)\)	\(=\)	\(q-0.470683i q^{2} +2.24914 q^{3} +1.77846 q^{4} -0.529317i q^{5} -1.05863i q^{6} -1.00000i q^{7} -1.77846i q^{8} +2.05863 q^{9} +O(q^{10})\)	\(q-0.470683i q^{2} +2.24914 q^{3} +1.77846 q^{4} -0.529317i q^{5} -1.05863i q^{6} -1.00000i q^{7} -1.77846i q^{8} +2.05863 q^{9} -0.249141 q^{10} -2.24914i q^{11} +4.00000 q^{12} -0.470683 q^{14} -1.19051i q^{15} +2.71982 q^{16} +1.30777 q^{17} -0.968964i q^{18} +1.47068i q^{19} -0.941367i q^{20} -2.24914i q^{21} -1.05863 q^{22} -5.83709 q^{23} -4.00000i q^{24} +4.71982 q^{25} -2.11727 q^{27} -1.77846i q^{28} +5.22154 q^{29} -0.560352 q^{30} +7.02760i q^{31} -4.83709i q^{32} -5.05863i q^{33} -0.615547i q^{34} -0.529317 q^{35} +3.66119 q^{36} -2.36641i q^{37} +0.692226 q^{38} -0.941367 q^{40} -6.49828i q^{41} -1.05863 q^{42} -11.3940 q^{43} -4.00000i q^{44} -1.08967i q^{45} +2.74742i q^{46} +8.58451i q^{47} +6.11727 q^{48} -1.00000 q^{49} -2.22154i q^{50} +2.94137 q^{51} +11.2767 q^{53} +0.996562i q^{54} -1.19051 q^{55} -1.77846 q^{56} +3.30777i q^{57} -2.45769i q^{58} -12.1725i q^{59} -2.11727i q^{60} -2.00000 q^{61} +3.30777 q^{62} -2.05863i q^{63} +3.16291 q^{64} -2.38101 q^{66} +15.9379i q^{67} +2.32582 q^{68} -13.1284 q^{69} +0.249141i q^{70} -1.19051i q^{71} -3.66119i q^{72} +7.64315i q^{73} -1.11383 q^{74} +10.6155 q^{75} +2.61555i q^{76} -2.24914 q^{77} -1.33881 q^{79} -1.43965i q^{80} -10.9379 q^{81} -3.05863 q^{82} +16.3500i q^{83} -4.00000i q^{84} -0.692226i q^{85} +5.36297i q^{86} +11.7440 q^{87} -4.00000 q^{88} +6.91033i q^{89} -0.512889 q^{90} -10.3810 q^{92} +15.8061i q^{93} +4.04059 q^{94} +0.778457 q^{95} -10.8793i q^{96} +3.47068i q^{97} +0.470683i q^{98} -4.63016i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9	\( 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9} + 16 q^{10} + 24 q^{12} - 2 q^{14} - 2 q^{16} - 8 q^{17} - 8 q^{22} - 20 q^{23} + 10 q^{25} - 16 q^{27} + 48 q^{29} - 40 q^{30} - 4 q^{35} + 2 q^{36} + 20 q^{38} - 4 q^{40} - 8 q^{42} - 20 q^{43} + 40 q^{48} - 6 q^{49} + 16 q^{51} + 16 q^{53} + 12 q^{55} + 6 q^{56} - 12 q^{61} + 4 q^{62} + 34 q^{64} + 24 q^{66} + 44 q^{68} + 12 q^{69} + 60 q^{74} + 32 q^{75} + 4 q^{77} - 28 q^{79} + 6 q^{81} - 20 q^{82} - 52 q^{87} - 24 q^{88} + 56 q^{90} - 24 q^{92} - 20 q^{94} - 12 q^{95}+O(q^{100}) \) 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9 + 16 * q^10 + 24 * q^12 - 2 * q^14 - 2 * q^16 - 8 * q^17 - 8 * q^22 - 20 * q^23 + 10 * q^25 - 16 * q^27 + 48 * q^29 - 40 * q^30 - 4 * q^35 + 2 * q^36 + 20 * q^38 - 4 * q^40 - 8 * q^42 - 20 * q^43 + 40 * q^48 - 6 * q^49 + 16 * q^51 + 16 * q^53 + 12 * q^55 + 6 * q^56 - 12 * q^61 + 4 * q^62 + 34 * q^64 + 24 * q^66 + 44 * q^68 + 12 * q^69 + 60 * q^74 + 32 * q^75 + 4 * q^77 - 28 * q^79 + 6 * q^81 - 20 * q^82 - 52 * q^87 - 24 * q^88 + 56 * q^90 - 24 * q^92 - 20 * q^94 - 12 * q^95

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