LMFDB - Embedded newform 1183.2.c.f.337.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(337,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [6,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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	$0.0532181\pi$
$2$	0.470683i	0.332823i	−0.986056	+	0.166412i	$0.946782\pi$
$3$	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	$0.0377633\pi$
$5$	0.529317i	0.236718i	−0.992971	+	0.118359i	$0.962237\pi$
$6$	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	$0.110113\pi$
$11$	2.24914i	0.678141i	−0.940761	+	0.339071i	$0.889887\pi$
$12$	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	$-0.946043\pi$
$19$	− 1.47068i	− 0.337398i	0.985668	−	0.168699i	$-0.0539566\pi$
$20$	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	$-0.782605\pi$
$31$	− 7.02760i	− 1.26219i	0.775704	−	0.631097i	$-0.217395\pi$
$32$	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	$0.0623141\pi$
$37$	2.36641i	0.389035i	−0.980899	+	0.194517i	$0.937686\pi$
$38$	0.692226	0.112294
$39$	0	0
$40$	−0.941367	−0.148843
$41$	6.49828i	1.01486i	0.861693	+	0.507431i	$0.169405\pi$
$41$	6.49828i	1.01486i	−0.861693	+	0.507431i	$0.830595\pi$
$42$	−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	$-0.784654\pi$
$47$	− 8.58451i	− 1.25218i	0.779751	−	0.626090i	$-0.215346\pi$
$48$	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	$0.291148\pi$
$59$	12.1725i	1.58472i	−0.610054	+	0.792360i	$0.708852\pi$
$60$	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	$-0.573354\pi$
$67$	− 15.9379i	− 1.94713i	0.228415	−	0.973564i	$-0.426646\pi$
$68$	2.32582	0.282047
$69$	−13.1284	−1.58048
$70$	− 0.249141i	− 0.0297780i
$71$	1.19051i	0.141287i	0.997502	+	0.0706436i	$0.0225053\pi$
$71$	1.19051i	0.141287i	−0.997502	+	0.0706436i	$0.977495\pi$
$72$	3.66119i	0.431475i
$73$	− 7.64315i	− 0.894562i	−0.894393	−	0.447281i	$-0.852392\pi$
$73$	− 7.64315i	− 0.894562i	0.894393	−	0.447281i	$-0.147608\pi$
$74$	−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	$-0.645510\pi$
$83$	− 16.3500i	− 1.79464i	0.441377	−	0.897322i	$-0.354490\pi$
$84$	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	$-0.880643\pi$
$89$	− 6.91033i	− 0.732494i	0.930518	−	0.366247i	$-0.119357\pi$
$90$	−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	$-0.943620\pi$
$97$	− 3.47068i	− 0.352395i	0.984355	−	0.176197i	$-0.0563797\pi$
$98$	− 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	$0.123890\pi$
$109$	7.92332i	0.758917i	−0.925209	+	0.379458i	$0.876110\pi$
$110$	− 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	$-0.838673\pi$
$137$	− 11.3630i	− 0.970804i	0.874291	−	0.485402i	$-0.161327\pi$
$138$	− 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	$0.124510\pi$
$149$	9.30777i	0.762523i	−0.924467	+	0.381261i	$0.875490\pi$
$150$	4.99656i	0.407968i
$151$	− 7.07324i	− 0.575612i	−0.957689	−	0.287806i	$-0.907074\pi$
$151$	− 7.07324i	− 0.575612i	0.957689	−	0.287806i	$-0.0929259\pi$
$152$	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	$-0.919602\pi$
$163$	− 6.38101i	− 0.499800i	0.968272	−	0.249900i	$-0.0803977\pi$
$164$	11.5569i	0.902443i
$165$	−2.67762	−0.208452
$166$	7.69566	0.597299
$167$	16.5845i	1.28335i	0.766977	+	0.641674i	$0.221760\pi$
$167$	16.5845i	1.28335i	−0.766977	+	0.641674i	$0.778240\pi$
$168$	−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	$0.0172124\pi$
$193$	1.50172i	0.108096i	−0.998538	+	0.0540480i	$0.982788\pi$
$194$	1.63359	0.117285
$195$	0	0
$196$	−1.77846	−0.127033
$197$	23.9931i	1.70944i	0.519090	+	0.854720i	$0.326271\pi$
$197$	23.9931i	1.70944i	−0.519090	+	0.854720i	$0.673729\pi$
$198$	−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	$0.110278\pi$
$223$	10.1414i	0.679120i	−0.940584	+	0.339560i	$0.889722\pi$
$224$	−4.83709	−0.323192
$225$	9.71639	0.647759
$226$	− 4.65613i	− 0.309721i
$227$	− 5.38445i	− 0.357379i	−0.983906	−	0.178689i	$-0.942814\pi$
$227$	− 5.38445i	− 0.357379i	0.983906	−	0.178689i	$-0.0571857\pi$
$228$	− 5.88273i	− 0.389594i
$229$	− 3.32238i	− 0.219549i	−0.993957	−	0.109775i	$-0.964987\pi$
$229$	− 3.32238i	− 0.219549i	0.993957	−	0.109775i	$-0.0350129\pi$
$230$	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	$-0.963873\pi$
$239$	− 3.50172i	− 0.226507i	0.993566	−	0.113254i	$-0.0361273\pi$
$240$	3.23797i	0.209010i
$241$	− 1.58795i	− 0.102289i	−0.998691	−	0.0511444i	$-0.983713\pi$
$241$	− 1.58795i	− 0.102289i	0.998691	−	0.0511444i	$-0.0162869\pi$
$242$	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	$-0.768585\pi$
$271$	− 21.8827i	− 1.32928i	0.747163	−	0.664641i	$-0.231415\pi$
$272$	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	$-0.985352\pi$
$281$	− 1.54231i	− 0.0920063i	0.998941	−	0.0460031i	$-0.0146484\pi$
$282$	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	$-0.895062\pi$
$293$	− 11.0828i	− 0.647464i	0.946149	−	0.323732i	$-0.104938\pi$
$294$	− 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	$-0.802079\pi$
$307$	− 20.4121i	− 1.16498i	0.812839	−	0.582489i	$-0.197921\pi$
$308$	−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	$0.143917\pi$
$317$	15.5569i	0.873763i	−0.899519	+	0.436882i	$0.856083\pi$
$318$	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	$0.334002\pi$
$331$	31.5500i	1.73415i	−0.498180	+	0.867073i	$0.665998\pi$
$332$	− 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	$-0.739767\pi$
$349$	− 27.2553i	− 1.45894i	0.684013	−	0.729470i	$-0.260233\pi$
$350$	−2.22154	−0.118746
$351$	0	0
$352$	−10.8793	−0.579868
$353$	− 25.6742i	− 1.36650i	−0.730185	−	0.683249i	$-0.760566\pi$
$353$	− 25.6742i	− 1.36650i	0.730185	−	0.683249i	$-0.239434\pi$
$354$	−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	$0.212049\pi$
$359$	23.4182i	1.23596i	−0.786192	+	0.617982i	$0.787951\pi$
$360$	−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	$-0.682035\pi$
$379$	− 32.7405i	− 1.68177i	0.541215	−	0.840884i	$-0.317965\pi$
$380$	1.38445	0.0710209
$381$	−1.85352	−0.0949586
$382$	− 3.50172i	− 0.179164i
$383$	− 22.6155i	− 1.15560i	−0.816178	−	0.577800i	$-0.803911\pi$
$383$	− 22.6155i	− 1.15560i	0.816178	−	0.577800i	$-0.196089\pi$
$384$	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	$0.0948980\pi$
$397$	11.7052i	0.587468i	−0.955887	+	0.293734i	$0.905102\pi$
$398$	0.948243i	0.0475311i
$399$	3.30777	0.165596
$400$	12.8371	0.641855
$401$	− 3.55691i	− 0.177624i	−0.996048	−	0.0888119i	$-0.971693\pi$
$401$	− 3.55691i	− 0.177624i	0.996048	−	0.0888119i	$-0.0283070\pi$
$402$	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	$0.0415291\pi$
$409$	5.26213i	0.260196i	−0.991501	+	0.130098i	$0.958471\pi$
$410$	− 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	$0.182337\pi$
$421$	22.2423i	1.08402i	−0.840372	+	0.542011i	$0.817663\pi$
$422$	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	$0.232212\pi$
$431$	27.6742i	1.33302i	−0.745497	+	0.666509i	$0.767788\pi$
$432$	−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	$0.175259\pi$
$449$	22.1725i	1.04638i	−0.852215	+	0.523192i	$0.824741\pi$
$450$	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	$0.0325130\pi$
$457$	4.35953i	0.203930i	−0.994788	+	0.101965i	$0.967487\pi$
$458$	1.56379	0.0730711
$459$	−2.76891	−0.129241
$460$	− 5.49484i	− 0.256198i
$461$	32.3810i	1.50813i	0.656797	+	0.754067i	$0.271911\pi$
$461$	32.3810i	1.50813i	−0.656797	+	0.754067i	$0.728089\pi$
$462$	− 2.38101i	− 0.110775i
$463$	− 8.36641i	− 0.388820i	−0.980920	−	0.194410i	$-0.937721\pi$
$463$	− 8.36641i	− 0.388820i	0.980920	−	0.194410i	$-0.0622792\pi$
$464$	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	$0.225907\pi$
$479$	28.5224i	1.30322i	−0.758553	+	0.651612i	$0.774093\pi$
$480$	−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	$0.190139\pi$
$487$	24.8241i	1.12489i	−0.826836	+	0.562444i	$0.809861\pi$
$488$	− 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	$-0.732270\pi$
$499$	− 33.3009i	− 1.49075i	0.666644	−	0.745376i	$-0.267730\pi$
$500$	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	$0.176068\pi$
$509$	23.7052i	1.05072i	−0.850882	+	0.525358i	$0.823932\pi$
$510$	−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	$0.270837\pi$
$541$	34.9751i	1.50370i	−0.659336	+	0.751848i	$0.729163\pi$
$542$	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	$0.371936\pi$
$557$	43.4328i	1.84031i	−0.391559	+	0.920153i	$0.628064\pi$
$558$	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	$0.203343\pi$
$577$	28.6448i	1.19250i	−0.802800	+	0.596249i	$0.796657\pi$
$578$	− 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	$-0.971579\pi$
$587$	− 4.32076i	− 0.178337i	0.996017	−	0.0891685i	$-0.0284210\pi$
$588$	−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	$0.106335\pi$
$593$	15.9690i	0.655767i	−0.944718	+	0.327883i	$0.893665\pi$
$594$	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	$0.130010\pi$
$613$	19.6673i	0.794355i	−0.917742	+	0.397177i	$0.869990\pi$
$614$	9.60761	0.387732
$615$	−7.73625	−0.311956
$616$	− 4.00000i	− 0.161165i
$617$	− 41.4588i	− 1.66907i	−0.550958	−	0.834533i	$-0.685737\pi$
$617$	− 41.4588i	− 1.66907i	0.550958	−	0.834533i	$-0.314263\pi$
$618$	17.9931i	0.723790i
$619$	− 10.8793i	− 0.437276i	−0.975806	−	0.218638i	$-0.929839\pi$
$619$	− 10.8793i	− 0.437276i	0.975806	−	0.218638i	$-0.0701614\pi$
$620$	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	$0.215226\pi$
$631$	31.4396i	1.25159i	−0.779987	+	0.625796i	$0.784774\pi$
$632$	− 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	$0.0506080\pi$
$643$	8.02922i	0.316641i	−0.987388	+	0.158321i	$0.949392\pi$
$644$	− 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	$-0.976862\pi$
$661$	− 3.73443i	− 0.145253i	0.997359	−	0.0726263i	$-0.0231380\pi$
$662$	−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	$0.129831\pi$
$683$	20.7328i	0.793319i	−0.917966	+	0.396660i	$0.870169\pi$
$684$	− 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	$0.0989822\pi$
$691$	16.0862i	0.611949i	−0.952040	+	0.305975i	$0.901018\pi$
$692$	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	$-0.949627\pi$
$709$	− 8.39239i	− 0.315183i	0.987504	−	0.157591i	$-0.0503729\pi$
$710$	− 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	$-0.742915\pi$
$733$	− 39.1311i	− 1.44534i	0.691193	−	0.722670i	$-0.257085\pi$
$734$	− 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	$0.0418953\pi$
$739$	7.13531i	0.262477i	−0.991351	+	0.131238i	$0.958105\pi$
$740$	−2.22766	−0.0818903
$741$	0	0
$742$	−5.30777	−0.194855
$743$	13.8827i	0.509308i	0.967032	+	0.254654i	$0.0819616\pi$
$743$	13.8827i	0.509308i	−0.967032	+	0.254654i	$0.918038\pi$
$744$	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	$0.155949\pi$
$761$	25.9621i	0.941125i	−0.882367	+	0.470562i	$0.844051\pi$
$762$	− 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	$-0.873511\pi$
$769$	− 21.4638i	− 0.774005i	0.922079	−	0.387002i	$-0.126489\pi$
$770$	0.560352	0.0201937
$771$	18.0260	0.649190
$772$	2.67074i	0.0961221i
$773$	− 40.4914i	− 1.45637i	−0.685378	−	0.728187i	$-0.740363\pi$
$773$	− 40.4914i	− 1.45637i	0.685378	−	0.728187i	$-0.259637\pi$
$774$	− 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	$0.0285220\pi$
$787$	5.02072i	0.178969i	−0.995988	+	0.0894847i	$0.971478\pi$
$788$	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	$0.257657\pi$
$811$	41.2311i	1.44782i	−0.689895	+	0.723910i	$0.742343\pi$
$812$	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	$0.0292982\pi$
$821$	5.26719i	0.183826i	−0.995767	+	0.0919130i	$0.970702\pi$
$822$	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	$0.0915541\pi$
$827$	16.3157i	0.567353i	−0.958920	+	0.283676i	$0.908446\pi$
$828$	−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	$-0.827758\pi$
$839$	− 29.8398i	− 1.03018i	0.857135	−	0.515092i	$-0.172242\pi$
$840$	− 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	$0.00110893\pi$
$853$	0.203497i	0.00696761i	−0.999994	+	0.00348380i	$0.998891\pi$
$854$	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	$-0.984993\pi$
$863$	− 2.76891i	− 0.0942546i	0.998889	−	0.0471273i	$-0.0150066\pi$
$864$	− 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	$0.0361462\pi$
$877$	6.71133i	0.226626i	−0.993559	+	0.113313i	$0.963854\pi$
$878$	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	$0.0230226\pi$
$929$	4.40517i	0.144529i	−0.997385	+	0.0722645i	$0.976977\pi$
$930$	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	$0.258066\pi$
$941$	44.4672i	1.44959i	−0.688964	+	0.724795i	$0.741934\pi$
$942$	− 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	$-0.609650\pi$
$947$	− 57.9311i	− 1.88251i	0.337702	−	0.941253i	$-0.390350\pi$
$948$	−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	$0.124526\pi$
$967$	23.7148i	0.762616i	−0.924448	+	0.381308i	$0.875474\pi$
$968$	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	$-0.916628\pi$
$977$	− 16.1871i	− 0.517870i	0.965895	−	0.258935i	$-0.0833716\pi$
$978$	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	$-0.739897\pi$
$983$	− 45.7243i	− 1.45838i	0.684312	−	0.729190i	$-0.260103\pi$
$984$	−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.337.4		6
13.5	odd	4		91.2.a.d.1.2	✓	3
13.8	odd	4		1183.2.a.i.1.2		3
13.12	even	2	inner	1183.2.c.f.337.3		6
39.5	even	4		819.2.a.i.1.2		3
52.31	even	4		1456.2.a.t.1.1		3
65.44	odd	4		2275.2.a.m.1.2		3
91.5	even	12		637.2.e.i.508.2		6
91.18	odd	12		637.2.e.j.79.2		6
91.31	even	12		637.2.e.i.79.2		6
91.34	even	4		8281.2.a.bg.1.2		3
91.44	odd	12		637.2.e.j.508.2		6
91.83	even	4		637.2.a.j.1.2		3
104.5	odd	4		5824.2.a.by.1.1		3
104.83	even	4		5824.2.a.bs.1.3		3
273.83	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	13.5	odd	4
637.2.a.j.1.2		3	91.83	even	4
637.2.e.i.79.2		6	91.31	even	12
637.2.e.i.508.2		6	91.5	even	12
637.2.e.j.79.2		6	91.18	odd	12
637.2.e.j.508.2		6	91.44	odd	12
819.2.a.i.1.2		3	39.5	even	4
1183.2.a.i.1.2		3	13.8	odd	4
1183.2.c.f.337.3		6	13.12	even	2	inner
1183.2.c.f.337.4		6	1.1	even	1	trivial
1456.2.a.t.1.1		3	52.31	even	4
2275.2.a.m.1.2		3	65.44	odd	4
5733.2.a.x.1.2		3	273.83	odd	4
5824.2.a.bs.1.3		3	104.83	even	4
5824.2.a.by.1.1		3	104.5	odd	4
8281.2.a.bg.1.2		3	91.34	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more