LMFDB - Embedded newform 1183.2.c.f.337.6

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			337.6
Root			$-0.671462 + 1.24464i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.f.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.34292i q^{2} -1.14637 q^{3} -3.48929 q^{4} -1.34292i q^{5} -2.68585i q^{6} +1.00000i q^{7} -3.48929i q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+2.34292i q^{2} -1.14637 q^{3} -3.48929 q^{4} -1.34292i q^{5} -2.68585i q^{6} +1.00000i q^{7} -3.48929i q^{8} -1.68585 q^{9} +3.14637 q^{10} -1.14637i q^{11} +4.00000 q^{12} -2.34292 q^{14} +1.53948i q^{15} +1.19656 q^{16} -5.83221 q^{17} -3.94981i q^{18} -3.34292i q^{19} +4.68585i q^{20} -1.14637i q^{21} +2.68585 q^{22} +3.17513 q^{23} +4.00000i q^{24} +3.19656 q^{25} +5.37169 q^{27} -3.48929i q^{28} +10.4893 q^{29} -3.60688 q^{30} +1.63565i q^{31} -4.17513i q^{32} +1.31415i q^{33} -13.6644i q^{34} +1.34292 q^{35} +5.88240 q^{36} -8.51806i q^{37} +7.83221 q^{38} -4.68585 q^{40} -0.292731i q^{41} +2.68585 q^{42} +8.15371 q^{43} +4.00000i q^{44} +2.26396i q^{45} +7.43910i q^{46} +10.6142i q^{47} -1.37169 q^{48} -1.00000 q^{49} +7.48929i q^{50} +6.68585 q^{51} -0.782020 q^{53} +12.5855i q^{54} -1.53948 q^{55} +3.48929 q^{56} +3.83221i q^{57} +24.5756i q^{58} -12.6430i q^{59} -5.37169i q^{60} -2.00000 q^{61} -3.83221 q^{62} -1.68585i q^{63} +12.1751 q^{64} -3.07896 q^{66} -6.10038i q^{67} +20.3503 q^{68} -3.63986 q^{69} +3.14637i q^{70} +1.53948i q^{71} +5.88240i q^{72} +15.3001i q^{73} +19.9572 q^{74} -3.66442 q^{75} +11.6644i q^{76} +1.14637 q^{77} +0.882404 q^{79} -1.60688i q^{80} -1.10038 q^{81} +0.685846 q^{82} -12.1292i q^{83} +4.00000i q^{84} +7.83221i q^{85} +19.1035i q^{86} -12.0246 q^{87} -4.00000 q^{88} -5.73604i q^{89} -5.30429 q^{90} -11.0790 q^{92} -1.87506i q^{93} -24.8683 q^{94} -4.48929 q^{95} +4.78623i q^{96} -5.34292i q^{97} -2.34292i q^{98} +1.93260i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.34292i	1.65670i	0.560213	+	0.828348i	$0.310719\pi$
$2$	2.34292i	1.65670i	−0.560213	+	0.828348i	$0.689281\pi$
$3$	−1.14637	−0.661854	−0.330927	−	0.943656i	$-0.607361\pi$
$3$	−1.14637	−0.661854	−0.330927	+	0.943656i	$0.607361\pi$
$4$	−3.48929	−1.74464
$5$	− 1.34292i	− 0.600573i	−0.953849	−	0.300287i	$-0.902918\pi$
$5$	− 1.34292i	− 0.600573i	0.953849	−	0.300287i	$-0.0970824\pi$
$6$	− 2.68585i	− 1.09649i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 3.48929i	− 1.23365i
$9$	−1.68585	−0.561949
$10$	3.14637	0.994968
$11$	− 1.14637i	− 0.345642i	−0.984953	−	0.172821i	$-0.944712\pi$
$11$	− 1.14637i	− 0.345642i	0.984953	−	0.172821i	$-0.0552882\pi$
$12$	4.00000	1.15470
$13$	0	0
$13$	0	0
$14$	−2.34292	−0.626173
$15$	1.53948i	0.397492i
$16$	1.19656	0.299139
$17$	−5.83221	−1.41452	−0.707260	−	0.706954i	$-0.750069\pi$
$17$	−5.83221	−1.41452	−0.707260	+	0.706954i	$0.750069\pi$
$18$	− 3.94981i	− 0.930979i
$19$	− 3.34292i	− 0.766919i	−0.923558	−	0.383460i	$-0.874733\pi$
$19$	− 3.34292i	− 0.766919i	0.923558	−	0.383460i	$-0.125267\pi$
$20$	4.68585i	1.04779i
$21$	− 1.14637i	− 0.250157i
$22$	2.68585	0.572624
$23$	3.17513	0.662061	0.331031	−	0.943620i	$-0.392604\pi$
$23$	3.17513	0.662061	0.331031	+	0.943620i	$0.392604\pi$
$24$	4.00000i	0.816497i
$25$	3.19656	0.639312
$26$	0	0
$27$	5.37169	1.03378
$28$	− 3.48929i	− 0.659414i
$29$	10.4893	1.94781	0.973906	−	0.226952i	$-0.0728760\pi$
$29$	10.4893	1.94781	0.973906	+	0.226952i	$0.0728760\pi$
$30$	−3.60688	−0.658524
$31$	1.63565i	0.293772i	0.989153	+	0.146886i	$0.0469251\pi$
$31$	1.63565i	0.293772i	−0.989153	+	0.146886i	$0.953075\pi$
$32$	− 4.17513i	− 0.738067i
$33$	1.31415i	0.228765i
$34$	− 13.6644i	− 2.34343i
$35$	1.34292	0.226995
$36$	5.88240	0.980401
$37$	− 8.51806i	− 1.40036i	−0.713966	−	0.700180i	$-0.753103\pi$
$37$	− 8.51806i	− 1.40036i	0.713966	−	0.700180i	$-0.246897\pi$
$38$	7.83221	1.27055
$39$	0	0
$40$	−4.68585	−0.740897
$41$	− 0.292731i	− 0.0457169i	−0.999739	−	0.0228584i	$-0.992723\pi$
$41$	− 0.292731i	− 0.0457169i	0.999739	−	0.0228584i	$-0.00727670\pi$
$42$	2.68585	0.414435
$43$	8.15371	1.24343	0.621715	−	0.783244i	$-0.286436\pi$
$43$	8.15371	1.24343	0.621715	+	0.783244i	$0.286436\pi$
$44$	4.00000i	0.603023i
$45$	2.26396i	0.337491i
$46$	7.43910i	1.09683i
$47$	10.6142i	1.54824i	0.633036	+	0.774122i	$0.281809\pi$
$47$	10.6142i	1.54824i	−0.633036	+	0.774122i	$0.718191\pi$
$48$	−1.37169	−0.197987
$49$	−1.00000	−0.142857
$50$	7.48929i	1.05915i
$51$	6.68585	0.936206
$52$	0	0
$53$	−0.782020	−0.107419	−0.0537093	−	0.998557i	$-0.517104\pi$
$53$	−0.782020	−0.107419	−0.0537093	+	0.998557i	$0.517104\pi$
$54$	12.5855i	1.71266i
$55$	−1.53948	−0.207584
$56$	3.48929	0.466276
$57$	3.83221i	0.507589i
$58$	24.5756i	3.22693i
$59$	− 12.6430i	− 1.64598i	−0.568057	−	0.822989i	$-0.692305\pi$
$59$	− 12.6430i	− 1.64598i	0.568057	−	0.822989i	$-0.307695\pi$
$60$	− 5.37169i	− 0.693482i
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	−3.83221	−0.486691
$63$	− 1.68585i	− 0.212397i
$64$	12.1751	1.52189
$65$	0	0
$66$	−3.07896	−0.378994
$67$	− 6.10038i	− 0.745281i	−0.927976	−	0.372640i	$-0.878453\pi$
$67$	− 6.10038i	− 0.745281i	0.927976	−	0.372640i	$-0.121547\pi$
$68$	20.3503	2.46783
$69$	−3.63986	−0.438188
$70$	3.14637i	0.376063i
$71$	1.53948i	0.182703i	0.995819	+	0.0913514i	$0.0291186\pi$
$71$	1.53948i	0.182703i	−0.995819	+	0.0913514i	$0.970881\pi$
$72$	5.88240i	0.693248i
$73$	15.3001i	1.79074i	0.445324	+	0.895369i	$0.353088\pi$
$73$	15.3001i	1.79074i	−0.445324	+	0.895369i	$0.646912\pi$
$74$	19.9572	2.31997
$75$	−3.66442	−0.423131
$76$	11.6644i	1.33800i
$77$	1.14637	0.130640
$78$	0	0
$79$	0.882404	0.0992782	0.0496391	−	0.998767i	$-0.484193\pi$
$79$	0.882404	0.0992782	0.0496391	+	0.998767i	$0.484193\pi$
$80$	− 1.60688i	− 0.179655i
$81$	−1.10038	−0.122265
$82$	0.685846	0.0757390
$83$	− 12.1292i	− 1.33135i	−0.746243	−	0.665674i	$-0.768144\pi$
$83$	− 12.1292i	− 1.33135i	0.746243	−	0.665674i	$-0.231856\pi$
$84$	4.00000i	0.436436i
$85$	7.83221i	0.849523i
$86$	19.1035i	2.05999i
$87$	−12.0246	−1.28917
$88$	−4.00000	−0.426401
$89$	− 5.73604i	− 0.608019i	−0.952669	−	0.304009i	$-0.901675\pi$
$89$	− 5.73604i	− 0.608019i	0.952669	−	0.304009i	$-0.0983254\pi$
$90$	−5.30429	−0.559121
$91$	0	0
$92$	−11.0790	−1.15506
$93$	− 1.87506i	− 0.194434i
$94$	−24.8683	−2.56497
$95$	−4.48929	−0.460591
$96$	4.78623i	0.488493i
$97$	− 5.34292i	− 0.542492i	−0.962510	−	0.271246i	$-0.912564\pi$
$97$	− 5.34292i	− 0.542492i	0.962510	−	0.271246i	$-0.0874356\pi$
$98$	− 2.34292i	− 0.236671i
$99$	1.93260i	0.194233i
$100$	−11.1537	−1.11537
$101$	−11.1464	−1.10910	−0.554552	−	0.832149i	$-0.687111\pi$
$101$	−11.1464	−1.10910	−0.554552	+	0.832149i	$0.687111\pi$
$102$	15.6644i	1.55101i
$103$	3.41454	0.336444	0.168222	−	0.985749i	$-0.446197\pi$
$103$	3.41454	0.336444	0.168222	+	0.985749i	$0.446197\pi$
$104$	0	0
$105$	−1.53948	−0.150238
$106$	− 1.83221i	− 0.177960i
$107$	4.97858	0.481297	0.240649	−	0.970612i	$-0.422640\pi$
$107$	4.97858	0.481297	0.240649	+	0.970612i	$0.422640\pi$
$108$	−18.7434	−1.80358
$109$	− 13.4966i	− 1.29274i	−0.763023	−	0.646372i	$-0.776286\pi$
$109$	− 13.4966i	− 1.29274i	0.763023	−	0.646372i	$-0.223714\pi$
$110$	− 3.60688i	− 0.343903i
$111$	9.76481i	0.926835i
$112$	1.19656i	0.113064i
$113$	16.4464	1.54715	0.773576	−	0.633704i	$-0.218466\pi$
$113$	16.4464	1.54715	0.773576	+	0.633704i	$0.218466\pi$
$114$	−8.97858	−0.840921
$115$	− 4.26396i	− 0.397616i
$116$	−36.6002	−3.39824
$117$	0	0
$118$	29.6216	2.72689
$119$	− 5.83221i	− 0.534638i
$120$	5.37169	0.490366
$121$	9.68585	0.880531
$122$	− 4.68585i	− 0.424237i
$123$	0.335577i	0.0302579i
$124$	− 5.70727i	− 0.512528i
$125$	− 11.0073i	− 0.984527i
$126$	3.94981	0.351877
$127$	−12.0575	−1.06993	−0.534967	−	0.844873i	$-0.679676\pi$
$127$	−12.0575	−1.06993	−0.534967	+	0.844873i	$0.679676\pi$
$128$	20.1751i	1.78325i
$129$	−9.34713	−0.822969
$130$	0	0
$131$	−3.66442	−0.320162	−0.160081	−	0.987104i	$-0.551176\pi$
$131$	−3.66442	−0.320162	−0.160081	+	0.987104i	$0.551176\pi$
$132$	− 4.58546i	− 0.399113i
$133$	3.34292	0.289868
$134$	14.2927	1.23470
$135$	− 7.21377i	− 0.620862i
$136$	20.3503i	1.74502i
$137$	13.1035i	1.11951i	0.828658	+	0.559755i	$0.189105\pi$
$137$	13.1035i	1.11951i	−0.828658	+	0.559755i	$0.810895\pi$
$138$	− 8.52792i	− 0.725945i
$139$	7.49663	0.635856	0.317928	−	0.948115i	$-0.397013\pi$
$139$	7.49663	0.635856	0.317928	+	0.948115i	$0.397013\pi$
$140$	−4.68585	−0.396026
$141$	− 12.1678i	− 1.02471i
$142$	−3.60688	−0.302683
$143$	0	0
$144$	−2.01721	−0.168101
$145$	− 14.0863i	− 1.16980i
$146$	−35.8469	−2.96671
$147$	1.14637	0.0945506
$148$	29.7220i	2.44313i
$149$	2.16779i	0.177592i	0.996050	+	0.0887961i	$0.0283019\pi$
$149$	2.16779i	0.177592i	−0.996050	+	0.0887961i	$0.971698\pi$
$150$	− 8.58546i	− 0.701000i
$151$	− 14.9112i	− 1.21345i	−0.794910	−	0.606727i	$-0.792482\pi$
$151$	− 14.9112i	− 1.21345i	0.794910	−	0.606727i	$-0.207518\pi$
$152$	−11.6644	−0.946110
$153$	9.83221	0.794887
$154$	2.68585i	0.216432i
$155$	2.19656	0.176432
$156$	0	0
$157$	22.8683	1.82509	0.912546	−	0.408975i	$-0.134114\pi$
$157$	22.8683	1.82509	0.912546	+	0.408975i	$0.134114\pi$
$158$	2.06740i	0.164474i
$159$	0.896480	0.0710955
$160$	−5.60688	−0.443263
$161$	3.17513i	0.250236i
$162$	− 2.57812i	− 0.202556i
$163$	− 7.07896i	− 0.554467i	−0.960803	−	0.277234i	$-0.910582\pi$
$163$	− 7.07896i	− 0.554467i	0.960803	−	0.277234i	$-0.0894176\pi$
$164$	1.02142i	0.0797597i
$165$	1.76481	0.137390
$166$	28.4177	2.20564
$167$	− 2.61423i	− 0.202295i	−0.994871	−	0.101148i	$-0.967749\pi$
$167$	− 2.61423i	− 0.202295i	0.994871	−	0.101148i	$-0.0322514\pi$
$168$	−4.00000	−0.308607
$169$	0	0
$170$	−18.3503	−1.40740
$171$	5.63565i	0.430969i
$172$	−28.4507	−2.16934
$173$	−11.0031	−0.836553	−0.418276	−	0.908320i	$-0.637366\pi$
$173$	−11.0031	−0.836553	−0.418276	+	0.908320i	$0.637366\pi$
$174$	− 28.1726i	− 2.13576i
$175$	3.19656i	0.241637i
$176$	− 1.37169i	− 0.103395i
$177$	14.4935i	1.08940i
$178$	13.4391	1.00730
$179$	−23.9614	−1.79096	−0.895478	−	0.445105i	$-0.853166\pi$
$179$	−23.9614	−1.79096	−0.895478	+	0.445105i	$0.853166\pi$
$180$	− 7.89962i	− 0.588803i
$181$	−6.56090	−0.487668	−0.243834	−	0.969817i	$-0.578405\pi$
$181$	−6.56090	−0.487668	−0.243834	+	0.969817i	$0.578405\pi$
$182$	0	0
$183$	2.29273	0.169484
$184$	− 11.0790i	− 0.816752i
$185$	−11.4391	−0.841019
$186$	4.39312	0.322119
$187$	6.68585i	0.488917i
$188$	− 37.0361i	− 2.70114i
$189$	5.37169i	0.390733i
$190$	− 10.5181i	− 0.763060i
$191$	−4.39312	−0.317875	−0.158937	−	0.987289i	$-0.550807\pi$
$191$	−4.39312	−0.317875	−0.158937	+	0.987289i	$0.550807\pi$
$192$	−13.9572	−1.00727
$193$	8.29273i	0.596924i	0.954422	+	0.298462i	$0.0964736\pi$
$193$	8.29273i	0.596924i	−0.954422	+	0.298462i	$0.903526\pi$
$194$	12.5181	0.898744
$195$	0	0
$196$	3.48929	0.249235
$197$	− 3.17092i	− 0.225919i	−0.993600	−	0.112959i	$-0.963967\pi$
$197$	− 3.17092i	− 0.225919i	0.993600	−	0.112959i	$-0.0360330\pi$
$198$	−4.52792	−0.321786
$199$	13.5970	0.963867	0.481934	−	0.876208i	$-0.339935\pi$
$199$	13.5970	0.963867	0.481934	+	0.876208i	$0.339935\pi$
$200$	− 11.1537i	− 0.788687i
$201$	6.99327i	0.493267i
$202$	− 26.1151i	− 1.83745i
$203$	10.4893i	0.736204i
$204$	−23.3288	−1.63335
$205$	−0.393115	−0.0274564
$206$	8.00000i	0.557386i
$207$	−5.35279	−0.372045
$208$	0	0
$209$	−3.83221	−0.265080
$210$	− 3.60688i	− 0.248899i
$211$	9.27552	0.638553	0.319277	−	0.947662i	$-0.396560\pi$
$211$	9.27552	0.638553	0.319277	+	0.947662i	$0.396560\pi$
$212$	2.72869	0.187407
$213$	− 1.76481i	− 0.120923i
$214$	11.6644i	0.797364i
$215$	− 10.9498i	− 0.746771i
$216$	− 18.7434i	− 1.27533i
$217$	−1.63565	−0.111035
$218$	31.6216	2.14168
$219$	− 17.5395i	− 1.18521i
$220$	5.37169	0.362159
$221$	0	0
$222$	−22.8782	−1.53548
$223$	− 19.5928i	− 1.31203i	−0.754747	−	0.656016i	$-0.772240\pi$
$223$	− 19.5928i	− 1.31203i	0.754747	−	0.656016i	$-0.227760\pi$
$224$	4.17513	0.278963
$225$	−5.38890	−0.359260
$226$	38.5328i	2.56316i
$227$	− 19.6644i	− 1.30517i	−0.757714	−	0.652587i	$-0.773684\pi$
$227$	− 19.6644i	− 1.30517i	0.757714	−	0.652587i	$-0.226316\pi$
$228$	− 13.3717i	− 0.885562i
$229$	− 7.76481i	− 0.513113i	−0.966529	−	0.256556i	$-0.917412\pi$
$229$	− 7.76481i	− 0.513113i	0.966529	−	0.256556i	$-0.0825880\pi$
$230$	9.99013	0.658730
$231$	−1.31415	−0.0864650
$232$	− 36.6002i	− 2.40292i
$233$	−12.1966	−0.799023	−0.399512	−	0.916728i	$-0.630820\pi$
$233$	−12.1966	−0.799023	−0.399512	+	0.916728i	$0.630820\pi$
$234$	0	0
$235$	14.2541	0.929835
$236$	44.1151i	2.87165i
$237$	−1.01156	−0.0657077
$238$	13.6644	0.885733
$239$	− 10.2927i	− 0.665781i	−0.942965	−	0.332891i	$-0.891976\pi$
$239$	− 10.2927i	− 0.665781i	0.942965	−	0.332891i	$-0.108024\pi$
$240$	1.84208i	0.118906i
$241$	4.02877i	0.259516i	0.991546	+	0.129758i	$0.0414200\pi$
$241$	4.02877i	0.259516i	−0.991546	+	0.129758i	$0.958580\pi$
$242$	22.6932i	1.45877i
$243$	−14.8536	−0.952861
$244$	6.97858	0.446758
$245$	1.34292i	0.0857962i
$246$	−0.786230	−0.0501282
$247$	0	0
$248$	5.70727	0.362412
$249$	13.9044i	0.881158i
$250$	25.7894	1.63106
$251$	−2.91117	−0.183752	−0.0918758	−	0.995770i	$-0.529286\pi$
$251$	−2.91117	−0.183752	−0.0918758	+	0.995770i	$0.529286\pi$
$252$	5.88240i	0.370557i
$253$	− 3.63986i	− 0.228836i
$254$	− 28.2499i	− 1.77256i
$255$	− 8.97858i	− 0.562260i
$256$	−22.9185	−1.43241
$257$	19.5970	1.22243	0.611214	−	0.791465i	$-0.290681\pi$
$257$	19.5970	1.22243	0.611214	+	0.791465i	$0.290681\pi$
$258$	− 21.8996i	− 1.36341i
$259$	8.51806	0.529286
$260$	0	0
$261$	−17.6833	−1.09457
$262$	− 8.58546i	− 0.530412i
$263$	7.56825	0.466678	0.233339	−	0.972395i	$-0.425035\pi$
$263$	7.56825	0.466678	0.233339	+	0.972395i	$0.425035\pi$
$264$	4.58546	0.282216
$265$	1.05019i	0.0645128i
$266$	7.83221i	0.480224i
$267$	6.57560i	0.402420i
$268$	21.2860i	1.30025i
$269$	−9.47208	−0.577523	−0.288761	−	0.957401i	$-0.593243\pi$
$269$	−9.47208	−0.577523	−0.288761	+	0.957401i	$0.593243\pi$
$270$	16.9013	1.02858
$271$	− 29.3717i	− 1.78420i	−0.451835	−	0.892102i	$-0.649230\pi$
$271$	− 29.3717i	− 1.78420i	0.451835	−	0.892102i	$-0.350770\pi$
$272$	−6.97858	−0.423138
$273$	0	0
$274$	−30.7005	−1.85469
$275$	− 3.66442i	− 0.220973i
$276$	12.7005	0.764483
$277$	1.90383	0.114390	0.0571949	−	0.998363i	$-0.481784\pi$
$277$	1.90383	0.114390	0.0571949	+	0.998363i	$0.481784\pi$
$278$	17.5640i	1.05342i
$279$	− 2.75746i	− 0.165085i
$280$	− 4.68585i	− 0.280033i
$281$	20.5756i	1.22744i	0.789525	+	0.613719i	$0.210327\pi$
$281$	20.5756i	1.22744i	−0.789525	+	0.613719i	$0.789673\pi$
$282$	28.5082	1.69764
$283$	26.9933	1.60458	0.802292	−	0.596932i	$-0.203614\pi$
$283$	26.9933	1.60458	0.802292	+	0.596932i	$0.203614\pi$
$284$	− 5.37169i	− 0.318751i
$285$	5.14637	0.304844
$286$	0	0
$287$	0.292731	0.0172794
$288$	7.03863i	0.414756i
$289$	17.0147	1.00086
$290$	33.0031	1.93801
$291$	6.12494i	0.359050i
$292$	− 53.3864i	− 3.12420i
$293$	14.9070i	0.870874i	0.900219	+	0.435437i	$0.143406\pi$
$293$	14.9070i	0.870874i	−0.900219	+	0.435437i	$0.856594\pi$
$294$	2.68585i	0.156642i
$295$	−16.9786	−0.988531
$296$	−29.7220	−1.72755
$297$	− 6.15792i	− 0.357319i
$298$	−5.07896	−0.294216
$299$	0	0
$300$	12.7862	0.738213
$301$	8.15371i	0.469972i
$302$	34.9357	2.01033
$303$	12.7778	0.734066
$304$	− 4.00000i	− 0.229416i
$305$	2.68585i	0.153791i
$306$	23.0361i	1.31689i
$307$	− 26.0288i	− 1.48554i	−0.669546	−	0.742770i	$-0.733512\pi$
$307$	− 26.0288i	− 1.48554i	0.669546	−	0.742770i	$-0.266488\pi$
$308$	−4.00000	−0.227921
$309$	−3.91431	−0.222677
$310$	5.14637i	0.292294i
$311$	−19.4966	−1.10555	−0.552776	−	0.833330i	$-0.686432\pi$
$311$	−19.4966	−1.10555	−0.552776	+	0.833330i	$0.686432\pi$
$312$	0	0
$313$	−3.48194	−0.196811	−0.0984055	−	0.995146i	$-0.531374\pi$
$313$	−3.48194	−0.196811	−0.0984055	+	0.995146i	$0.531374\pi$
$314$	53.5787i	3.02362i
$315$	−2.26396	−0.127560
$316$	−3.07896	−0.173205
$317$	5.02142i	0.282031i	0.990007	+	0.141016i	$0.0450368\pi$
$317$	5.02142i	0.282031i	−0.990007	+	0.141016i	$0.954963\pi$
$318$	2.10038i	0.117784i
$319$	− 12.0246i	− 0.673246i
$320$	− 16.3503i	− 0.914008i
$321$	−5.70727	−0.318549
$322$	−7.43910	−0.414565
$323$	19.4966i	1.08482i
$324$	3.83956	0.213309
$325$	0	0
$326$	16.5855	0.918584
$327$	15.4721i	0.855608i
$328$	−1.02142	−0.0563986
$329$	−10.6142	−0.585182
$330$	4.13481i	0.227614i
$331$	− 6.14950i	− 0.338007i	−0.985615	−	0.169004i	$-0.945945\pi$
$331$	− 6.14950i	− 0.338007i	0.985615	−	0.169004i	$-0.0540549\pi$
$332$	42.3221i	2.32273i
$333$	14.3601i	0.786931i
$334$	6.12494	0.335142
$335$	−8.19235	−0.447596
$336$	− 1.37169i	− 0.0748320i
$337$	25.6258	1.39593	0.697963	−	0.716134i	$-0.254090\pi$
$337$	25.6258	1.39593	0.697963	+	0.716134i	$0.254090\pi$
$338$	0	0
$339$	−18.8536	−1.02399
$340$	− 27.3288i	− 1.48211i
$341$	1.87506	0.101540
$342$	−13.2039	−0.713985
$343$	− 1.00000i	− 0.0539949i
$344$	− 28.4507i	− 1.53396i
$345$	4.88806i	0.263164i
$346$	− 25.7795i	− 1.38591i
$347$	−16.7005	−0.896532	−0.448266	−	0.893900i	$-0.647958\pi$
$347$	−16.7005	−0.896532	−0.448266	+	0.893900i	$0.647958\pi$
$348$	41.9572	2.24914
$349$	23.5500i	1.26060i	0.776351	+	0.630300i	$0.217068\pi$
$349$	23.5500i	1.26060i	−0.776351	+	0.630300i	$0.782932\pi$
$350$	−7.48929	−0.400319
$351$	0	0
$352$	−4.78623	−0.255107
$353$	− 7.64973i	− 0.407154i	−0.979059	−	0.203577i	$-0.934743\pi$
$353$	− 7.64973i	− 0.407154i	0.979059	−	0.203577i	$-0.0652567\pi$
$354$	−33.9572	−1.80480
$355$	2.06740	0.109726
$356$	20.0147i	1.06078i
$357$	6.68585i	0.353853i
$358$	− 56.1396i	− 2.96707i
$359$	− 18.3748i	− 0.969786i	−0.874573	−	0.484893i	$-0.838858\pi$
$359$	− 18.3748i	− 0.969786i	0.874573	−	0.484893i	$-0.161142\pi$
$360$	7.89962	0.416346
$361$	7.82487	0.411835
$362$	− 15.3717i	− 0.807918i
$363$	−11.1035	−0.582784
$364$	0	0
$365$	20.5468	1.07547
$366$	5.37169i	0.280783i
$367$	5.33871	0.278679	0.139339	−	0.990245i	$-0.455502\pi$
$367$	5.33871	0.278679	0.139339	+	0.990245i	$0.455502\pi$
$368$	3.79923	0.198049
$369$	0.493499i	0.0256906i
$370$	− 26.8009i	− 1.39331i
$371$	− 0.782020i	− 0.0406004i
$372$	6.54262i	0.339219i
$373$	21.5212	1.11433	0.557163	−	0.830403i	$-0.311890\pi$
$373$	21.5212	1.11433	0.557163	+	0.830403i	$0.311890\pi$
$374$	−15.6644	−0.809988
$375$	12.6184i	0.651614i
$376$	37.0361	1.90999
$377$	0	0
$378$	−12.5855	−0.647326
$379$	4.61002i	0.236801i	0.992966	+	0.118400i	$0.0377766\pi$
$379$	4.61002i	0.236801i	−0.992966	+	0.118400i	$0.962223\pi$
$380$	15.6644	0.803568
$381$	13.8223	0.708140
$382$	− 10.2927i	− 0.526622i
$383$	− 8.33558i	− 0.425928i	−0.977060	−	0.212964i	$-0.931688\pi$
$383$	− 8.33558i	− 0.425928i	0.977060	−	0.212964i	$-0.0683117\pi$
$384$	− 23.1281i	− 1.18025i
$385$	− 1.53948i	− 0.0784592i
$386$	−19.4292	−0.988922
$387$	−13.7459	−0.698744
$388$	18.6430i	0.946455i
$389$	6.44223	0.326634	0.163317	−	0.986574i	$-0.447781\pi$
$389$	6.44223	0.326634	0.163317	+	0.986574i	$0.447781\pi$
$390$	0	0
$391$	−18.5181	−0.936498
$392$	3.48929i	0.176236i
$393$	4.20077	0.211901
$394$	7.42923	0.374279
$395$	− 1.18500i	− 0.0596238i
$396$	− 6.74338i	− 0.338868i
$397$	− 1.40046i	− 0.0702872i	−0.999382	−	0.0351436i	$-0.988811\pi$
$397$	− 1.40046i	− 0.0702872i	0.999382	−	0.0351436i	$-0.0111889\pi$
$398$	31.8568i	1.59684i
$399$	−3.83221	−0.191851
$400$	3.82487	0.191243
$401$	6.97858i	0.348494i	0.984702	+	0.174247i	$0.0557490\pi$
$401$	6.97858i	0.348494i	−0.984702	+	0.174247i	$0.944251\pi$
$402$	−16.3847	−0.817194
$403$	0	0
$404$	38.8929	1.93499
$405$	1.47773i	0.0734291i
$406$	−24.5756	−1.21967
$407$	−9.76481	−0.484024
$408$	− 23.3288i	− 1.15495i
$409$	− 18.3790i	− 0.908785i	−0.890802	−	0.454392i	$-0.849856\pi$
$409$	− 18.3790i	− 0.908785i	0.890802	−	0.454392i	$-0.150144\pi$
$410$	− 0.921039i	− 0.0454869i
$411$	− 15.0214i	− 0.740952i
$412$	−11.9143	−0.586976
$413$	12.6430	0.622121
$414$	− 12.5412i	− 0.616365i
$415$	−16.2885	−0.799572
$416$	0	0
$417$	−8.59388	−0.420844
$418$	− 8.97858i	− 0.439157i
$419$	−30.0393	−1.46751	−0.733757	−	0.679412i	$-0.762235\pi$
$419$	−30.0393	−1.46751	−0.733757	+	0.679412i	$0.762235\pi$
$420$	5.37169	0.262112
$421$	− 8.31729i	− 0.405360i	−0.979245	−	0.202680i	$-0.935035\pi$
$421$	− 8.31729i	− 0.405360i	0.979245	−	0.202680i	$-0.0649651\pi$
$422$	21.7318i	1.05789i
$423$	− 17.8940i	− 0.870034i
$424$	2.72869i	0.132517i
$425$	−18.6430	−0.904318
$426$	4.13481	0.200332
$427$	− 2.00000i	− 0.0967868i
$428$	−17.3717	−0.839692
$429$	0	0
$430$	25.6546	1.23717
$431$	9.64973i	0.464811i	0.972619	+	0.232406i	$0.0746597\pi$
$431$	9.64973i	0.464811i	−0.972619	+	0.232406i	$0.925340\pi$
$432$	6.42754	0.309245
$433$	−26.3074	−1.26425	−0.632127	−	0.774865i	$-0.717818\pi$
$433$	−26.3074	−1.26425	−0.632127	+	0.774865i	$0.717818\pi$
$434$	− 3.83221i	− 0.183952i
$435$	16.1481i	0.774240i
$436$	47.0937i	2.25538i
$437$	− 10.6142i	− 0.507748i
$438$	41.0937	1.96353
$439$	−33.8139	−1.61385	−0.806925	−	0.590654i	$-0.798870\pi$
$439$	−33.8139	−1.61385	−0.806925	+	0.590654i	$0.798870\pi$
$440$	5.37169i	0.256085i
$441$	1.68585	0.0802784
$442$	0	0
$443$	26.4464	1.25651	0.628254	−	0.778008i	$-0.283770\pi$
$443$	26.4464	1.25651	0.628254	+	0.778008i	$0.283770\pi$
$444$	− 34.0722i	− 1.61700i
$445$	−7.70306	−0.365160
$446$	45.9044	2.17364
$447$	− 2.48508i	− 0.117540i
$448$	12.1751i	0.575221i
$449$	− 2.64300i	− 0.124731i	−0.998053	−	0.0623655i	$-0.980136\pi$
$449$	− 2.64300i	− 0.124731i	0.998053	−	0.0623655i	$-0.0198644\pi$
$450$	− 12.6258i	− 0.595185i
$451$	−0.335577	−0.0158017
$452$	−57.3864	−2.69923
$453$	17.0937i	0.803130i
$454$	46.0722	2.16228
$455$	0	0
$456$	13.3717	0.626187
$457$	− 33.6890i	− 1.57590i	−0.615737	−	0.787952i	$-0.711141\pi$
$457$	− 33.6890i	− 1.57590i	0.615737	−	0.787952i	$-0.288859\pi$
$458$	18.1923	0.850073
$459$	−31.3288	−1.46231
$460$	14.8782i	0.693699i
$461$	33.0790i	1.54064i	0.637657	+	0.770320i	$0.279904\pi$
$461$	33.0790i	1.54064i	−0.637657	+	0.770320i	$0.720096\pi$
$462$	− 3.07896i	− 0.143246i
$463$	2.51806i	0.117024i	0.998287	+	0.0585120i	$0.0186356\pi$
$463$	2.51806i	0.117024i	−0.998287	+	0.0585120i	$0.981364\pi$
$464$	12.5510	0.582667
$465$	−2.51806	−0.116772
$466$	− 28.5756i	− 1.32374i
$467$	−2.57560	−0.119184	−0.0595922	−	0.998223i	$-0.518980\pi$
$467$	−2.57560	−0.119184	−0.0595922	+	0.998223i	$0.518980\pi$
$468$	0	0
$469$	6.10038	0.281690
$470$	33.3963i	1.54045i
$471$	−26.2155	−1.20794
$472$	−44.1151	−2.03056
$473$	− 9.34713i	− 0.429782i
$474$	− 2.37000i	− 0.108858i
$475$	− 10.6858i	− 0.490300i
$476$	20.3503i	0.932753i
$477$	1.31836	0.0603638
$478$	24.1151	1.10300
$479$	− 0.513847i	− 0.0234783i	−0.999931	−	0.0117391i	$-0.996263\pi$
$479$	− 0.513847i	− 0.0234783i	0.999931	−	0.0117391i	$-0.00373677\pi$
$480$	6.42754	0.293376
$481$	0	0
$482$	−9.43910	−0.429939
$483$	− 3.63986i	− 0.165620i
$484$	−33.7967	−1.53621
$485$	−7.17513	−0.325806
$486$	− 34.8009i	− 1.57860i
$487$	36.0575i	1.63392i	0.576692	+	0.816962i	$0.304343\pi$
$487$	36.0575i	1.63392i	−0.576692	+	0.816962i	$0.695657\pi$
$488$	6.97858i	0.315905i
$489$	8.11508i	0.366976i
$490$	−3.14637	−0.142138
$491$	9.22846	0.416475	0.208237	−	0.978078i	$-0.433227\pi$
$491$	9.22846	0.416475	0.208237	+	0.978078i	$0.433227\pi$
$492$	− 1.17092i	− 0.0527893i
$493$	−61.1758	−2.75522
$494$	0	0
$495$	2.59533	0.116651
$496$	1.95715i	0.0878788i
$497$	−1.53948	−0.0690551
$498$	−32.5770	−1.45981
$499$	1.00314i	0.0449065i	0.999748	+	0.0224533i	$0.00714769\pi$
$499$	1.00314i	0.0449065i	−0.999748	+	0.0224533i	$0.992852\pi$
$500$	38.4078i	1.71765i
$501$	2.99686i	0.133890i
$502$	− 6.82065i	− 0.304421i
$503$	−30.3503	−1.35325	−0.676626	−	0.736327i	$-0.736559\pi$
$503$	−30.3503	−1.35325	−0.676626	+	0.736327i	$0.736559\pi$
$504$	−5.88240	−0.262023
$505$	14.9687i	0.666099i
$506$	8.52792	0.379112
$507$	0	0
$508$	42.0722	1.86665
$509$	10.5995i	0.469816i	0.972018	+	0.234908i	$0.0754789\pi$
$509$	10.5995i	0.469816i	−0.972018	+	0.234908i	$0.924521\pi$
$510$	21.0361	0.931495
$511$	−15.3001	−0.676836
$512$	− 13.3461i	− 0.589818i
$513$	− 17.9572i	− 0.792828i
$514$	45.9143i	2.02519i
$515$	− 4.58546i	− 0.202060i
$516$	32.6148	1.43579
$517$	12.1678	0.535139
$518$	19.9572i	0.876867i
$519$	12.6136	0.553676
$520$	0	0
$521$	−16.2646	−0.712564	−0.356282	−	0.934378i	$-0.615956\pi$
$521$	−16.2646	−0.712564	−0.356282	+	0.934378i	$0.615956\pi$
$522$	− 41.4307i	− 1.81337i
$523$	7.22219	0.315804	0.157902	−	0.987455i	$-0.449527\pi$
$523$	7.22219	0.315804	0.157902	+	0.987455i	$0.449527\pi$
$524$	12.7862	0.558569
$525$	− 3.66442i	− 0.159929i
$526$	17.7318i	0.773144i
$527$	− 9.53948i	− 0.415546i
$528$	1.57246i	0.0684326i
$529$	−12.9185	−0.561675
$530$	−2.46052	−0.106878
$531$	21.3142i	0.924955i
$532$	−11.6644	−0.505717
$533$	0	0
$534$	−15.4061	−0.666688
$535$	− 6.68585i	− 0.289054i
$536$	−21.2860	−0.919415
$537$	27.4685	1.18535
$538$	− 22.1923i	− 0.956780i
$539$	1.14637i	0.0493775i
$540$	25.1709i	1.08318i
$541$	− 17.3534i	− 0.746081i	−0.927815	−	0.373041i	$-0.878315\pi$
$541$	− 17.3534i	− 0.746081i	0.927815	−	0.373041i	$-0.121685\pi$
$542$	68.8156	2.95588
$543$	7.52119	0.322765
$544$	24.3503i	1.04401i
$545$	−18.1249	−0.776387
$546$	0	0
$547$	−34.1109	−1.45848	−0.729238	−	0.684261i	$-0.760125\pi$
$547$	−34.1109	−1.45848	−0.729238	+	0.684261i	$0.760125\pi$
$548$	− 45.7220i	− 1.95315i
$549$	3.37169	0.143900
$550$	8.58546	0.366085
$551$	− 35.0649i	− 1.49381i
$552$	12.7005i	0.540571i
$553$	0.882404i	0.0375236i
$554$	4.46052i	0.189509i
$555$	13.1134	0.556632
$556$	−26.1579	−1.10934
$557$	13.2222i	0.560242i	0.959965	+	0.280121i	$0.0903746\pi$
$557$	13.2222i	0.560242i	−0.959965	+	0.280121i	$0.909625\pi$
$558$	6.46052	0.273496
$559$	0	0
$560$	1.60688	0.0679033
$561$	− 7.66442i	− 0.323592i
$562$	−48.2070	−2.03349
$563$	41.3717	1.74361	0.871804	−	0.489854i	$-0.162950\pi$
$563$	41.3717	1.74361	0.871804	+	0.489854i	$0.162950\pi$
$564$	42.4569i	1.78776i
$565$	− 22.0863i	− 0.929178i
$566$	63.2432i	2.65831i
$567$	− 1.10038i	− 0.0462118i
$568$	5.37169	0.225391
$569$	2.68164	0.112420	0.0562100	−	0.998419i	$-0.482098\pi$
$569$	2.68164	0.112420	0.0562100	+	0.998419i	$0.482098\pi$
$570$	12.0575i	0.505035i
$571$	28.9315	1.21075	0.605373	−	0.795942i	$-0.293024\pi$
$571$	28.9315	1.21075	0.605373	+	0.795942i	$0.293024\pi$
$572$	0	0
$573$	5.03612	0.210387
$574$	0.685846i	0.0286267i
$575$	10.1495	0.423263
$576$	−20.5254	−0.855225
$577$	37.5296i	1.56238i	0.624294	+	0.781189i	$0.285387\pi$
$577$	37.5296i	1.56238i	−0.624294	+	0.781189i	$0.714613\pi$
$578$	39.8641i	1.65813i
$579$	− 9.50650i	− 0.395077i
$580$	49.1512i	2.04089i
$581$	12.1292	0.503202
$582$	−14.3503	−0.594838
$583$	0.896480i	0.0371284i
$584$	53.3864	2.20914
$585$	0	0
$586$	−34.9259	−1.44277
$587$	23.0649i	0.951990i	0.879448	+	0.475995i	$0.157912\pi$
$587$	23.0649i	0.951990i	−0.879448	+	0.475995i	$0.842088\pi$
$588$	−4.00000	−0.164957
$589$	5.46787	0.225299
$590$	− 39.7795i	− 1.63770i
$591$	3.63504i	0.149525i
$592$	− 10.1923i	− 0.418903i
$593$	11.0502i	0.453777i	0.973921	+	0.226889i	$0.0728553\pi$
$593$	11.0502i	0.453777i	−0.973921	+	0.226889i	$0.927145\pi$
$594$	14.4275	0.591969
$595$	−7.83221	−0.321089
$596$	− 7.56404i	− 0.309835i
$597$	−15.5872	−0.637940
$598$	0	0
$599$	−44.6044	−1.82248	−0.911242	−	0.411870i	$-0.864876\pi$
$599$	−44.6044	−1.82248	−0.911242	+	0.411870i	$0.864876\pi$
$600$	12.7862i	0.521996i
$601$	47.8715	1.95272	0.976359	−	0.216156i	$-0.0693520\pi$
$601$	47.8715	1.95272	0.976359	+	0.216156i	$0.0693520\pi$
$602$	−19.1035	−0.778601
$603$	10.2843i	0.418809i
$604$	52.0294i	2.11705i
$605$	− 13.0073i	− 0.528824i
$606$	29.9374i	1.21612i
$607$	45.0691	1.82930	0.914649	−	0.404249i	$-0.132467\pi$
$607$	45.0691	1.82930	0.914649	+	0.404249i	$0.132467\pi$
$608$	−13.9572	−0.566037
$609$	− 12.0246i	− 0.487260i
$610$	−6.29273	−0.254785
$611$	0	0
$612$	−34.3074	−1.38680
$613$	− 25.5212i	− 1.03079i	−0.856952	−	0.515396i	$-0.827645\pi$
$613$	− 25.5212i	− 1.03079i	0.856952	−	0.515396i	$-0.172355\pi$
$614$	60.9834	2.46109
$615$	0.450654	0.0181721
$616$	− 4.00000i	− 0.161165i
$617$	29.2432i	1.17729i	0.808393	+	0.588643i	$0.200337\pi$
$617$	29.2432i	1.17729i	−0.808393	+	0.588643i	$0.799663\pi$
$618$	− 9.17092i	− 0.368909i
$619$	− 4.78623i	− 0.192375i	−0.995363	−	0.0961874i	$-0.969335\pi$
$619$	− 4.78623i	− 0.192375i	0.995363	−	0.0961874i	$-0.0306648\pi$
$620$	−7.66442	−0.307811
$621$	17.0558	0.684428
$622$	− 45.6791i	− 1.83157i
$623$	5.73604	0.229810
$624$	0	0
$625$	1.20077	0.0480307
$626$	− 8.15792i	− 0.326056i
$627$	4.39312	0.175444
$628$	−79.7942	−3.18413
$629$	49.6791i	1.98084i
$630$	− 5.30429i	− 0.211328i
$631$	28.3931i	1.13031i	0.824984	+	0.565156i	$0.191184\pi$
$631$	28.3931i	1.13031i	−0.824984	+	0.565156i	$0.808816\pi$
$632$	− 3.07896i	− 0.122475i
$633$	−10.6331	−0.422629
$634$	−11.7648	−0.467240
$635$	16.1923i	0.642574i
$636$	−3.12808	−0.124036
$637$	0	0
$638$	28.1726	1.11536
$639$	− 2.59533i	− 0.102670i
$640$	27.0937	1.07097
$641$	−5.96137	−0.235460	−0.117730	−	0.993046i	$-0.537562\pi$
$641$	−5.96137	−0.235460	−0.117730	+	0.993046i	$0.537562\pi$
$642$	− 13.3717i	− 0.527739i
$643$	31.1940i	1.23017i	0.788460	+	0.615086i	$0.210879\pi$
$643$	31.1940i	1.23017i	−0.788460	+	0.615086i	$0.789121\pi$
$644$	− 11.0790i	− 0.436572i
$645$	12.5525i	0.494253i
$646$	−45.6791	−1.79722
$647$	−14.9112	−0.586219	−0.293109	−	0.956079i	$-0.594690\pi$
$647$	−14.9112	−0.586219	−0.293109	+	0.956079i	$0.594690\pi$
$648$	3.83956i	0.150832i
$649$	−14.4935	−0.568920
$650$	0	0
$651$	1.87506	0.0734893
$652$	24.7005i	0.967348i
$653$	−3.57246	−0.139801	−0.0699006	−	0.997554i	$-0.522268\pi$
$653$	−3.57246	−0.139801	−0.0699006	+	0.997554i	$0.522268\pi$
$654$	−36.2499	−1.41748
$655$	4.92104i	0.192281i
$656$	− 0.350269i	− 0.0136757i
$657$	− 25.7936i	− 1.00630i
$658$	− 24.8683i	− 0.969468i
$659$	−3.90383	−0.152071	−0.0760357	−	0.997105i	$-0.524226\pi$
$659$	−3.90383	−0.152071	−0.0760357	+	0.997105i	$0.524226\pi$
$660$	−6.15792	−0.239697
$661$	− 13.7936i	− 0.536508i	−0.963348	−	0.268254i	$-0.913553\pi$
$661$	− 13.7936i	− 0.536508i	0.963348	−	0.268254i	$-0.0864466\pi$
$662$	14.4078	0.559975
$663$	0	0
$664$	−42.3221	−1.64242
$665$	− 4.48929i	− 0.174087i
$666$	−33.6447	−1.30371
$667$	33.3049	1.28957
$668$	9.12181i	0.352933i
$669$	22.4605i	0.868374i
$670$	− 19.1940i	− 0.741530i
$671$	2.29273i	0.0885099i
$672$	−4.78623	−0.184633
$673$	−5.70306	−0.219837	−0.109918	−	0.993941i	$-0.535059\pi$
$673$	−5.70306	−0.219837	−0.109918	+	0.993941i	$0.535059\pi$
$674$	60.0393i	2.31263i
$675$	17.1709	0.660909
$676$	0	0
$677$	35.2614	1.35521	0.677604	−	0.735427i	$-0.263019\pi$
$677$	35.2614	1.35521	0.677604	+	0.735427i	$0.263019\pi$
$678$	− 44.1726i	− 1.69644i
$679$	5.34292	0.205043
$680$	27.3288	1.04801
$681$	22.5426i	0.863835i
$682$	4.39312i	0.168221i
$683$	− 1.03612i	− 0.0396459i	−0.999804	−	0.0198229i	$-0.993690\pi$
$683$	− 1.03612i	− 0.0396459i	0.999804	−	0.0198229i	$-0.00631025\pi$
$684$	− 19.6644i	− 0.751888i
$685$	17.5970	0.672348
$686$	2.34292	0.0894532
$687$	8.90131i	0.339606i
$688$	9.75639	0.371959
$689$	0	0
$690$	−11.4523	−0.435983
$691$	3.67850i	0.139937i	0.997549	+	0.0699684i	$0.0222898\pi$
$691$	3.67850i	0.139937i	−0.997549	+	0.0699684i	$0.977710\pi$
$692$	38.3931	1.45949
$693$	−1.93260	−0.0734132
$694$	− 39.1281i	− 1.48528i
$695$	− 10.0674i	− 0.381878i
$696$	41.9572i	1.59038i
$697$	1.70727i	0.0646674i
$698$	−55.1758	−2.08843
$699$	13.9817	0.528837
$700$	− 11.1537i	− 0.421571i
$701$	0.0617493	0.00233224	0.00116612	−	0.999999i	$-0.499629\pi$
$701$	0.0617493	0.00233224	0.00116612	+	0.999999i	$0.499629\pi$
$702$	0	0
$703$	−28.4752	−1.07396
$704$	− 13.9572i	− 0.526030i
$705$	−16.3404	−0.615415
$706$	17.9227	0.674531
$707$	− 11.1464i	− 0.419202i
$708$	− 50.5720i	− 1.90061i
$709$	42.9834i	1.61428i	0.590363	+	0.807138i	$0.298985\pi$
$709$	42.9834i	1.61428i	−0.590363	+	0.807138i	$0.701015\pi$
$710$	4.84377i	0.181783i
$711$	−1.48760	−0.0557892
$712$	−20.0147	−0.750082
$713$	5.19342i	0.194495i
$714$	−15.6644	−0.586226
$715$	0	0
$716$	83.6081	3.12458
$717$	11.7992i	0.440650i
$718$	43.0508	1.60664
$719$	−17.6546	−0.658404	−0.329202	−	0.944260i	$-0.606780\pi$
$719$	−17.6546	−0.658404	−0.329202	+	0.944260i	$0.606780\pi$
$720$	2.70896i	0.100957i
$721$	3.41454i	0.127164i
$722$	18.3331i	0.682286i
$723$	− 4.61844i	− 0.171762i
$724$	22.8929	0.850807
$725$	33.5296	1.24526
$726$	− 26.0147i	− 0.965496i
$727$	23.8077	0.882977	0.441488	−	0.897267i	$-0.354451\pi$
$727$	23.8077	0.882977	0.441488	+	0.897267i	$0.354451\pi$
$728$	0	0
$729$	20.3288	0.752920
$730$	48.1396i	1.78173i
$731$	−47.5542	−1.75885
$732$	−8.00000	−0.295689
$733$	31.3492i	1.15791i	0.815360	+	0.578954i	$0.196539\pi$
$733$	31.3492i	1.15791i	−0.815360	+	0.578954i	$0.803461\pi$
$734$	12.5082i	0.461686i
$735$	− 1.53948i	− 0.0567846i
$736$	− 13.2566i	− 0.488645i
$737$	−6.99327	−0.257600
$738$	−1.15623	−0.0425615
$739$	24.8108i	0.912680i	0.889806	+	0.456340i	$0.150840\pi$
$739$	24.8108i	0.912680i	−0.889806	+	0.456340i	$0.849160\pi$
$740$	39.9143	1.46728
$741$	0	0
$742$	1.83221	0.0672626
$743$	21.3717i	0.784051i	0.919954	+	0.392026i	$0.128226\pi$
$743$	21.3717i	0.784051i	−0.919954	+	0.392026i	$0.871774\pi$
$744$	−6.54262	−0.239864
$745$	2.91117	0.106657
$746$	50.4225i	1.84610i
$747$	20.4479i	0.748149i
$748$	− 23.3288i	− 0.852987i
$749$	4.97858i	0.181913i
$750$	−29.5640	−1.07953
$751$	−19.2243	−0.701503	−0.350751	−	0.936469i	$-0.614074\pi$
$751$	−19.2243	−0.701503	−0.350751	+	0.936469i	$0.614074\pi$
$752$	12.7005i	0.463141i
$753$	3.33727	0.121617
$754$	0	0
$755$	−20.0246	−0.728768
$756$	− 18.7434i	− 0.681690i
$757$	−19.8610	−0.721860	−0.360930	−	0.932593i	$-0.617541\pi$
$757$	−19.8610	−0.721860	−0.360930	+	0.932593i	$0.617541\pi$
$758$	−10.8009	−0.392307
$759$	4.17262i	0.151456i
$760$	15.6644i	0.568208i
$761$	− 6.12073i	− 0.221876i	−0.993827	−	0.110938i	$-0.964614\pi$
$761$	− 6.12073i	− 0.221876i	0.993827	−	0.110938i	$-0.0353856\pi$
$762$	32.3847i	1.17317i
$763$	13.4966	0.488611
$764$	15.3288	0.554578
$765$	− 13.2039i	− 0.477388i
$766$	19.5296	0.705634
$767$	0	0
$768$	26.2730	0.948045
$769$	3.82800i	0.138041i	0.997615	+	0.0690206i	$0.0219874\pi$
$769$	3.82800i	0.138041i	−0.997615	+	0.0690206i	$0.978013\pi$
$770$	3.60688	0.129983
$771$	−22.4653	−0.809070
$772$	− 28.9357i	− 1.04142i
$773$	− 6.53635i	− 0.235096i	−0.993067	−	0.117548i	$-0.962497\pi$
$773$	− 6.53635i	− 0.235096i	0.993067	−	0.117548i	$-0.0375034\pi$
$774$	− 32.2056i	− 1.15761i
$775$	5.22846i	0.187812i
$776$	−18.6430	−0.669245
$777$	−9.76481	−0.350311
$778$	15.0937i	0.541134i
$779$	−0.978577	−0.0350612
$780$	0	0
$781$	1.76481	0.0631498
$782$	− 43.3864i	− 1.55149i
$783$	56.3452	2.01361
$784$	−1.19656	−0.0427342
$785$	− 30.7104i	− 1.09610i
$786$	9.84208i	0.351055i
$787$	− 30.8066i	− 1.09814i	−0.835778	−	0.549068i	$-0.814983\pi$
$787$	− 30.8066i	− 1.09814i	0.835778	−	0.549068i	$-0.185017\pi$
$788$	11.0643i	0.394148i
$789$	−8.67598	−0.308873
$790$	2.77636	0.0987786
$791$	16.4464i	0.584768i
$792$	6.74338	0.239616
$793$	0	0
$794$	3.28117	0.116444
$795$	− 1.20390i	− 0.0426981i
$796$	−47.4439	−1.68161
$797$	38.8156	1.37492	0.687460	−	0.726222i	$-0.258726\pi$
$797$	38.8156	1.37492	0.687460	+	0.726222i	$0.258726\pi$
$798$	− 8.97858i	− 0.317838i
$799$	− 61.9044i	− 2.19002i
$800$	− 13.3461i	− 0.471854i
$801$	9.67008i	0.341675i
$802$	−16.3503	−0.577348
$803$	17.5395	0.618955
$804$	− 24.4015i	− 0.860576i
$805$	4.26396	0.150285
$806$	0	0
$807$	10.8585	0.382236
$808$	38.8929i	1.36825i
$809$	1.04033	0.0365759	0.0182880	−	0.999833i	$-0.494178\pi$
$809$	1.04033	0.0365759	0.0182880	+	0.999833i	$0.494178\pi$
$810$	−3.46221	−0.121650
$811$	12.6712i	0.444944i	0.974939	+	0.222472i	$0.0714127\pi$
$811$	12.6712i	0.444944i	−0.974939	+	0.222472i	$0.928587\pi$
$812$	− 36.6002i	− 1.28441i
$813$	33.6707i	1.18088i
$814$	− 22.8782i	− 0.801880i
$815$	−9.50650	−0.332998
$816$	8.00000	0.280056
$817$	− 27.2572i	− 0.953610i
$818$	43.0607	1.50558
$819$	0	0
$820$	1.37169	0.0479016
$821$	27.0361i	0.943567i	0.881714	+	0.471783i	$0.156390\pi$
$821$	27.0361i	0.943567i	−0.881714	+	0.471783i	$0.843610\pi$
$822$	35.1940	1.22753
$823$	31.6363	1.10277	0.551386	−	0.834251i	$-0.314099\pi$
$823$	31.6363	1.10277	0.551386	+	0.834251i	$0.314099\pi$
$824$	− 11.9143i	− 0.415055i
$825$	4.20077i	0.146252i
$826$	29.6216i	1.03067i
$827$	− 56.4800i	− 1.96400i	−0.188872	−	0.982002i	$-0.560483\pi$
$827$	− 56.4800i	− 1.96400i	0.188872	−	0.982002i	$-0.439517\pi$
$828$	18.6774	0.649085
$829$	42.6760	1.48220	0.741099	−	0.671396i	$-0.234305\pi$
$829$	42.6760	1.48220	0.741099	+	0.671396i	$0.234305\pi$
$830$	− 38.1627i	− 1.32465i
$831$	−2.18248	−0.0757094
$832$	0	0
$833$	5.83221	0.202074
$834$	− 20.1348i	− 0.697211i
$835$	−3.51071	−0.121493
$836$	13.3717	0.462470
$837$	8.78623i	0.303697i
$838$	− 70.3797i	− 2.43122i
$839$	40.1642i	1.38662i	0.720639	+	0.693311i	$0.243849\pi$
$839$	40.1642i	1.38662i	−0.720639	+	0.693311i	$0.756151\pi$
$840$	5.37169i	0.185341i
$841$	81.0252	2.79397
$842$	19.4868	0.671558
$843$	− 23.5872i	− 0.812385i
$844$	−32.3650	−1.11405
$845$	0	0
$846$	41.9242	1.44138
$847$	9.68585i	0.332810i
$848$	−0.935731	−0.0321331
$849$	−30.9442	−1.06200
$850$	− 43.6791i	− 1.49818i
$851$	− 27.0460i	− 0.927124i
$852$	6.15792i	0.210967i
$853$	− 19.6932i	− 0.674282i	−0.941454	−	0.337141i	$-0.890540\pi$
$853$	− 19.6932i	− 0.674282i	0.941454	−	0.337141i	$-0.109460\pi$
$854$	4.68585	0.160346
$855$	7.56825	0.258829
$856$	− 17.3717i	− 0.593752i
$857$	−1.66442	−0.0568556	−0.0284278	−	0.999596i	$-0.509050\pi$
$857$	−1.66442	−0.0568556	−0.0284278	+	0.999596i	$0.509050\pi$
$858$	0	0
$859$	−41.2944	−1.40895	−0.704474	−	0.709730i	$-0.748817\pi$
$859$	−41.2944	−1.40895	−0.704474	+	0.709730i	$0.748817\pi$
$860$	38.2070i	1.30285i
$861$	−0.335577	−0.0114364
$862$	−22.6086	−0.770051
$863$	− 31.3288i	− 1.06645i	−0.845975	−	0.533223i	$-0.820981\pi$
$863$	− 31.3288i	− 1.06645i	0.845975	−	0.533223i	$-0.179019\pi$
$864$	− 22.4275i	− 0.763000i
$865$	14.7764i	0.502411i
$866$	− 61.6363i	− 2.09449i
$867$	−19.5051	−0.662426
$868$	5.70727	0.193717
$869$	− 1.01156i	− 0.0343147i
$870$	−37.8337	−1.28268
$871$	0	0
$872$	−47.0937	−1.59479
$873$	9.00735i	0.304852i
$874$	24.8683	0.841184
$875$	11.0073	0.372116
$876$	61.2003i	2.06777i
$877$	− 53.8041i	− 1.81683i	−0.418065	−	0.908417i	$-0.637292\pi$
$877$	− 53.8041i	− 1.81683i	0.418065	−	0.908417i	$-0.362708\pi$
$878$	− 79.2234i	− 2.67366i
$879$	− 17.0888i	− 0.576392i
$880$	−1.84208	−0.0620964
$881$	−8.09196	−0.272625	−0.136313	−	0.990666i	$-0.543525\pi$
$881$	−8.09196	−0.272625	−0.136313	+	0.990666i	$0.543525\pi$
$882$	3.94981i	0.132997i
$883$	27.0705	0.910996	0.455498	−	0.890237i	$-0.349461\pi$
$883$	27.0705	0.910996	0.455498	+	0.890237i	$0.349461\pi$
$884$	0	0
$885$	19.4637	0.654264
$886$	61.9620i	2.08165i
$887$	−38.4935	−1.29249	−0.646243	−	0.763132i	$-0.723661\pi$
$887$	−38.4935	−1.29249	−0.646243	+	0.763132i	$0.723661\pi$
$888$	34.0722	1.14339
$889$	− 12.0575i	− 0.404397i
$890$	− 18.0477i	− 0.604959i
$891$	1.26144i	0.0422599i
$892$	68.3650i	2.28903i
$893$	35.4826	1.18738
$894$	5.82235	0.194728
$895$	32.1783i	1.07560i
$896$	−20.1751	−0.674004
$897$	0	0
$898$	6.19235	0.206641
$899$	17.1568i	0.572213i
$900$	18.8034	0.626781
$901$	4.56090	0.151946
$902$	− 0.786230i	− 0.0261786i
$903$	− 9.34713i	− 0.311053i
$904$	− 57.3864i	− 1.90864i
$905$	8.81079i	0.292881i
$906$	−40.0491	−1.33054
$907$	−15.7031	−0.521411	−0.260706	−	0.965418i	$-0.583955\pi$
$907$	−15.7031	−0.521411	−0.260706	+	0.965418i	$0.583955\pi$
$908$	68.6148i	2.27706i
$909$	18.7911	0.623260
$910$	0	0
$911$	44.9399	1.48893	0.744463	−	0.667663i	$-0.232705\pi$
$911$	44.9399	1.48893	0.744463	+	0.667663i	$0.232705\pi$
$912$	4.58546i	0.151840i
$913$	−13.9044	−0.460170
$914$	78.9307	2.61080
$915$	− 3.07896i	− 0.101787i
$916$	27.0937i	0.895200i
$917$	− 3.66442i	− 0.121010i
$918$	− 73.4011i	− 2.42260i
$919$	−27.2432	−0.898669	−0.449334	−	0.893364i	$-0.648339\pi$
$919$	−27.2432	−0.898669	−0.449334	+	0.893364i	$0.648339\pi$
$920$	−14.8782	−0.490519
$921$	29.8385i	0.983211i
$922$	−77.5015	−2.55237
$923$	0	0
$924$	4.58546	0.150851
$925$	− 27.2285i	− 0.895266i
$926$	−5.89962	−0.193873
$927$	−5.75639	−0.189065
$928$	− 43.7942i	− 1.43761i
$929$	− 17.1422i	− 0.562416i	−0.959647	−	0.281208i	$-0.909265\pi$
$929$	− 17.1422i	− 0.562416i	0.959647	−	0.281208i	$-0.0907351\pi$
$930$	− 5.89962i	− 0.193456i
$931$	3.34292i	0.109560i
$932$	42.5573	1.39401
$933$	22.3503	0.731715
$934$	− 6.03442i	− 0.197452i
$935$	8.97858	0.293631
$936$	0	0
$937$	−51.5197	−1.68308	−0.841538	−	0.540197i	$-0.818350\pi$
$937$	−51.5197	−1.68308	−0.841538	+	0.540197i	$0.818350\pi$
$938$	14.2927i	0.466674i
$939$	3.99158	0.130260
$940$	−49.7367	−1.62223
$941$	32.7575i	1.06786i	0.845528	+	0.533931i	$0.179286\pi$
$941$	32.7575i	1.06786i	−0.845528	+	0.533931i	$0.820714\pi$
$942$	− 61.4208i	− 2.00120i
$943$	− 0.929460i	− 0.0302674i
$944$	− 15.1281i	− 0.492377i
$945$	7.21377	0.234664
$946$	21.8996	0.712018
$947$	− 20.9295i	− 0.680116i	−0.940404	−	0.340058i	$-0.889553\pi$
$947$	− 20.9295i	− 0.680116i	0.940404	−	0.340058i	$-0.110447\pi$
$948$	3.52962	0.114637
$949$	0	0
$950$	25.0361	0.812279
$951$	− 5.75639i	− 0.186664i
$952$	−20.3503	−0.659556
$953$	−46.4120	−1.50343	−0.751716	−	0.659487i	$-0.770774\pi$
$953$	−46.4120	−1.50343	−0.751716	+	0.659487i	$0.770774\pi$
$954$	3.08883i	0.100004i
$955$	5.89962i	0.190907i
$956$	35.9143i	1.16155i
$957$	13.7845i	0.445591i
$958$	1.20390	0.0388964
$959$	−13.1035	−0.423135
$960$	18.7434i	0.604940i
$961$	28.3246	0.913698
$962$	0	0
$963$	−8.39312	−0.270464
$964$	− 14.0575i	− 0.452763i
$965$	11.1365	0.358497
$966$	8.52792	0.274381
$967$	− 23.2186i	− 0.746660i	−0.927699	−	0.373330i	$-0.878216\pi$
$967$	− 23.2186i	− 0.746660i	0.927699	−	0.373330i	$-0.121784\pi$
$968$	− 33.7967i	− 1.08627i
$969$	− 22.3503i	− 0.717994i
$970$	− 16.8108i	− 0.539762i
$971$	−14.1004	−0.452503	−0.226251	−	0.974069i	$-0.572647\pi$
$971$	−14.1004	−0.452503	−0.226251	+	0.974069i	$0.572647\pi$
$972$	51.8286	1.66240
$973$	7.49663i	0.240331i
$974$	−84.4800	−2.70692
$975$	0	0
$976$	−2.39312	−0.0766018
$977$	− 2.95402i	− 0.0945074i	−0.998883	−	0.0472537i	$-0.984953\pi$
$977$	− 2.95402i	− 0.0945074i	0.998883	−	0.0472537i	$-0.0150469\pi$
$978$	−19.0130	−0.607969
$979$	−6.57560	−0.210157
$980$	− 4.68585i	− 0.149684i
$981$	22.7533i	0.726455i
$982$	21.6216i	0.689972i
$983$	35.0367i	1.11750i	0.829337	+	0.558749i	$0.188719\pi$
$983$	35.0367i	1.11750i	−0.829337	+	0.558749i	$0.811281\pi$
$984$	1.17092	0.0373277
$985$	−4.25831	−0.135681
$986$	− 143.330i	− 4.56456i
$987$	12.1678	0.387305
$988$	0	0
$989$	25.8891	0.823227
$990$	6.08065i	0.193256i
$991$	47.9718	1.52388	0.761938	−	0.647650i	$-0.224248\pi$
$991$	47.9718	1.52388	0.761938	+	0.647650i	$0.224248\pi$
$992$	6.82908	0.216823
$993$	7.04958i	0.223712i
$994$	− 3.60688i	− 0.114403i
$995$	− 18.2598i	− 0.578873i
$996$	− 48.5166i	− 1.53731i
$997$	−38.4422	−1.21748	−0.608739	−	0.793371i	$-0.708324\pi$
$997$	−38.4422	−1.21748	−0.608739	+	0.793371i	$0.708324\pi$
$998$	−2.35027	−0.0743965
$999$	− 45.7564i	− 1.44767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.f.337.6		6
13.5	odd	4		91.2.a.d.1.3	✓	3
13.8	odd	4		1183.2.a.i.1.1		3
13.12	even	2	inner	1183.2.c.f.337.1		6
39.5	even	4		819.2.a.i.1.1		3
52.31	even	4		1456.2.a.t.1.2		3
65.44	odd	4		2275.2.a.m.1.1		3
91.5	even	12		637.2.e.i.508.1		6
91.18	odd	12		637.2.e.j.79.1		6
91.31	even	12		637.2.e.i.79.1		6
91.34	even	4		8281.2.a.bg.1.1		3
91.44	odd	12		637.2.e.j.508.1		6
91.83	even	4		637.2.a.j.1.3		3
104.5	odd	4		5824.2.a.by.1.2		3
104.83	even	4		5824.2.a.bs.1.2		3
273.83	odd	4		5733.2.a.x.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.3	✓	3	13.5	odd	4
637.2.a.j.1.3		3	91.83	even	4
637.2.e.i.79.1		6	91.31	even	12
637.2.e.i.508.1		6	91.5	even	12
637.2.e.j.79.1		6	91.18	odd	12
637.2.e.j.508.1		6	91.44	odd	12
819.2.a.i.1.1		3	39.5	even	4
1183.2.a.i.1.1		3	13.8	odd	4
1183.2.c.f.337.1		6	13.12	even	2	inner
1183.2.c.f.337.6		6	1.1	even	1	trivial
1456.2.a.t.1.2		3	52.31	even	4
2275.2.a.m.1.1		3	65.44	odd	4
5733.2.a.x.1.1		3	273.83	odd	4
5824.2.a.bs.1.2		3	104.83	even	4
5824.2.a.by.1.2		3	104.5	odd	4
8281.2.a.bg.1.1		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.34292i q^{2} -1.14637 q^{3} -3.48929 q^{4} -1.34292i q^{5} -2.68585i q^{6} +1.00000i q^{7} -3.48929i q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+2.34292i q^{2} -1.14637 q^{3} -3.48929 q^{4} -1.34292i q^{5} -2.68585i q^{6} +1.00000i q^{7} -3.48929i q^{8} -1.68585 q^{9} +3.14637 q^{10} -1.14637i q^{11} +4.00000 q^{12} -2.34292 q^{14} +1.53948i q^{15} +1.19656 q^{16} -5.83221 q^{17} -3.94981i q^{18} -3.34292i q^{19} +4.68585i q^{20} -1.14637i q^{21} +2.68585 q^{22} +3.17513 q^{23} +4.00000i q^{24} +3.19656 q^{25} +5.37169 q^{27} -3.48929i q^{28} +10.4893 q^{29} -3.60688 q^{30} +1.63565i q^{31} -4.17513i q^{32} +1.31415i q^{33} -13.6644i q^{34} +1.34292 q^{35} +5.88240 q^{36} -8.51806i q^{37} +7.83221 q^{38} -4.68585 q^{40} -0.292731i q^{41} +2.68585 q^{42} +8.15371 q^{43} +4.00000i q^{44} +2.26396i q^{45} +7.43910i q^{46} +10.6142i q^{47} -1.37169 q^{48} -1.00000 q^{49} +7.48929i q^{50} +6.68585 q^{51} -0.782020 q^{53} +12.5855i q^{54} -1.53948 q^{55} +3.48929 q^{56} +3.83221i q^{57} +24.5756i q^{58} -12.6430i q^{59} -5.37169i q^{60} -2.00000 q^{61} -3.83221 q^{62} -1.68585i q^{63} +12.1751 q^{64} -3.07896 q^{66} -6.10038i q^{67} +20.3503 q^{68} -3.63986 q^{69} +3.14637i q^{70} +1.53948i q^{71} +5.88240i q^{72} +15.3001i q^{73} +19.9572 q^{74} -3.66442 q^{75} +11.6644i q^{76} +1.14637 q^{77} +0.882404 q^{79} -1.60688i q^{80} -1.10038 q^{81} +0.685846 q^{82} -12.1292i q^{83} +4.00000i q^{84} +7.83221i q^{85} +19.1035i q^{86} -12.0246 q^{87} -4.00000 q^{88} -5.73604i q^{89} -5.30429 q^{90} -11.0790 q^{92} -1.87506i q^{93} -24.8683 q^{94} -4.48929 q^{95} +4.78623i q^{96} -5.34292i q^{97} -2.34292i q^{98} +1.93260i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9}+O(q^{10}) \) 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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