LMFDB - Embedded newform 605.2.e.a.362.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("605.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 $ x^20 + 67x^16 + 1315x^12 + 9193x^8 + 16040x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			362.6
Root			$0.125683 - 0.125683i$ of defining polynomial
Character	$\chi$	$=$	605.362
Dual form			605.2.e.a.483.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125683 - 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} -0.416692i q^{6} +(-3.15683 + 3.15683i) q^{7} +(0.498761 + 0.498761i) q^{8} -2.49602i q^{9} +O(q^{10})$	\(q+(0.125683 - 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} -0.416692i q^{6} +(-3.15683 + 3.15683i) q^{7} +(0.498761 + 0.498761i) q^{8} -2.49602i q^{9} +(0.371061 - 0.142393i) q^{10} +(3.26305 + 3.26305i) q^{12} +(1.97128 + 1.97128i) q^{13} +0.793518i q^{14} +(4.89416 - 1.87811i) q^{15} -3.81144 q^{16} +(2.20398 - 2.20398i) q^{17} +(-0.313707 - 0.313707i) q^{18} -1.24889 q^{19} +(-1.79067 + 4.02078i) q^{20} +10.4662i q^{21} +(1.27860 - 1.27860i) q^{23} +1.65360 q^{24} +(3.34488 + 3.71642i) q^{25} +0.495512 q^{26} +(0.835455 + 0.835455i) q^{27} +(-6.21392 - 6.21392i) q^{28} +7.47247 q^{29} +(0.379066 - 0.851158i) q^{30} -5.13483 q^{31} +(-1.47655 + 1.47655i) q^{32} -0.554006i q^{34} +(-9.32008 + 3.57654i) q^{35} +4.91318 q^{36} +(-1.75014 - 1.75014i) q^{37} +(-0.156964 + 0.156964i) q^{38} +6.53563 q^{39} +(0.565073 + 1.47252i) q^{40} -10.8036i q^{41} +(1.31542 + 1.31542i) q^{42} +(-4.31967 - 4.31967i) q^{43} +(2.27064 - 5.09851i) q^{45} -0.321395i q^{46} +(2.65013 + 2.65013i) q^{47} +(-6.31828 + 6.31828i) q^{48} -12.9311i q^{49} +(0.887484 + 0.0466955i) q^{50} -7.30714i q^{51} +(-3.88028 + 3.88028i) q^{52} +(0.315424 - 0.315424i) q^{53} +0.210005 q^{54} -3.14900 q^{56} +(-2.07030 + 2.07030i) q^{57} +(0.939161 - 0.939161i) q^{58} -11.3112i q^{59} +(3.69689 + 9.63370i) q^{60} +1.38079i q^{61} +(-0.645360 + 0.645360i) q^{62} +(7.87950 + 7.87950i) q^{63} -7.25173i q^{64} +(2.23337 + 5.81993i) q^{65} +(0.721404 + 0.721404i) q^{67} +(4.33834 + 4.33834i) q^{68} -4.23909i q^{69} +(-0.721865 + 1.62088i) q^{70} +3.52812 q^{71} +(1.24492 - 1.24492i) q^{72} +(6.58997 + 6.58997i) q^{73} -0.439926 q^{74} +(11.7056 + 0.615897i) q^{75} -2.45832i q^{76} +(0.821417 - 0.821417i) q^{78} +6.02093 q^{79} +(-7.78547 - 3.46728i) q^{80} +10.2579 q^{81} +(-1.35783 - 1.35783i) q^{82} +(-3.45287 - 3.45287i) q^{83} -20.6018 q^{84} +(6.50695 - 2.49701i) q^{85} -1.08582 q^{86} +(12.3872 - 12.3872i) q^{87} +2.57764i q^{89} +(-0.355415 - 0.926175i) q^{90} -12.4460 q^{91} +(2.51680 + 2.51680i) q^{92} +(-8.51207 + 8.51207i) q^{93} +0.666152 q^{94} +(-2.55105 - 1.13612i) q^{95} +4.89541i q^{96} +(-4.62327 - 4.62327i) q^{97} +(-1.62522 - 1.62522i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^3 + 4 * q^5	$ 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.125683	−	0.125683i	0.0888712	−	0.0888712i	−0.661274	−	0.750145i	$-0.729984\pi$
$2$	0.125683	−	0.125683i	0.0888712	−	0.0888712i	0.750145	+	0.661274i	$0.229984\pi$
$3$	1.65771	−	1.65771i	0.957081	−	0.957081i	−0.0420355	−	0.999116i	$-0.513384\pi$
$3$	1.65771	−	1.65771i	0.957081	−	0.957081i	0.999116	+	0.0420355i	$0.0133843\pi$
$4$			1.96841i			0.984204i
$5$	2.04266	+	0.909702i	0.913503	+	0.406831i
$5$	2.04266	+	0.909702i	0.913503	+	0.406831i
$6$		−	0.416692i		−	0.170114i
$7$	−3.15683	+	3.15683i	−1.19317	+	1.19317i	−0.216996	+	0.976173i	$0.569626\pi$
$7$	−3.15683	+	3.15683i	−1.19317	+	1.19317i	−0.976173	+	0.216996i	$0.930374\pi$
$8$	0.498761	+	0.498761i	0.176339	+	0.176339i
$9$		−	2.49602i		−	0.832007i
$10$	0.371061	−	0.142393i	0.117340	−	0.0450285i
$11$		0			0
$11$		0			0
$12$	3.26305	+	3.26305i	0.941962	+	0.941962i
$13$	1.97128	+	1.97128i	0.546735	+	0.546735i	0.925495	−	0.378760i	$-0.123649\pi$
$13$	1.97128	+	1.97128i	0.546735	+	0.546735i	−0.378760	+	0.925495i	$0.623649\pi$
$14$			0.793518i			0.212077i
$15$	4.89416	−	1.87811i	1.26367	−	0.484926i
$16$	−3.81144			−0.952861
$17$	2.20398	−	2.20398i	0.534545	−	0.534545i	−0.387377	−	0.921921i	$-0.626619\pi$
$17$	2.20398	−	2.20398i	0.534545	−	0.534545i	0.921921	+	0.387377i	$0.126619\pi$
$18$	−0.313707	−	0.313707i	−0.0739414	−	0.0739414i
$19$	−1.24889			−0.286514			−0.143257	−	0.989685i	$-0.545758\pi$
$19$	−1.24889			−0.286514			−0.143257	+	0.989685i	$0.545758\pi$
$20$	−1.79067	+	4.02078i	−0.400405	+	0.899073i
$21$			10.4662i			2.28392i
$22$		0			0
$23$	1.27860	−	1.27860i	0.266606	−	0.266606i	−0.561125	−	0.827731i	$-0.689631\pi$
$23$	1.27860	−	1.27860i	0.266606	−	0.266606i	0.827731	+	0.561125i	$0.189631\pi$
$24$	1.65360			0.337540
$25$	3.34488	+	3.71642i	0.668977	+	0.743283i
$26$	0.495512			0.0971780
$27$	0.835455	+	0.835455i	0.160783	+	0.160783i
$28$	−6.21392	−	6.21392i	−1.17432	−	1.17432i
$29$	7.47247			1.38760			0.693801	−	0.720167i	$-0.255935\pi$
$29$	7.47247			1.38760			0.693801	+	0.720167i	$0.255935\pi$
$30$	0.379066	−	0.851158i	0.0692076	−	0.155400i
$31$	−5.13483			−0.922243			−0.461121	−	0.887337i	$-0.652553\pi$
$31$	−5.13483			−0.922243			−0.461121	+	0.887337i	$0.652553\pi$
$32$	−1.47655	+	1.47655i	−0.261020	+	0.261020i
$33$		0			0
$34$		−	0.554006i		−	0.0950112i
$35$	−9.32008	+	3.57654i	−1.57538	+	0.604545i
$36$	4.91318			0.818864
$37$	−1.75014	−	1.75014i	−0.287722	−	0.287722i	0.548457	−	0.836179i	$-0.315215\pi$
$37$	−1.75014	−	1.75014i	−0.287722	−	0.287722i	−0.836179	+	0.548457i	$0.815215\pi$
$38$	−0.156964	+	0.156964i	−0.0254629	+	0.0254629i
$39$	6.53563			1.04654
$40$	0.565073	+	1.47252i	0.0893458	+	0.232826i
$41$		−	10.8036i		−	1.68724i	−0.536938	−	0.843621i	$-0.680419\pi$
$41$		−	10.8036i		−	1.68724i	0.536938	−	0.843621i	$-0.319581\pi$
$42$	1.31542	+	1.31542i	0.202974	+	0.202974i
$43$	−4.31967	−	4.31967i	−0.658744	−	0.658744i	0.296339	−	0.955083i	$-0.404234\pi$
$43$	−4.31967	−	4.31967i	−0.658744	−	0.658744i	−0.955083	+	0.296339i	$0.904234\pi$
$44$		0			0
$45$	2.27064	−	5.09851i	0.338486	−	0.760041i
$46$		−	0.321395i		−	0.0473871i
$47$	2.65013	+	2.65013i	0.386561	+	0.386561i	0.873459	−	0.486898i	$-0.161872\pi$
$47$	2.65013	+	2.65013i	0.386561	+	0.386561i	−0.486898	+	0.873459i	$0.661872\pi$
$48$	−6.31828	+	6.31828i	−0.911965	+	0.911965i
$49$		−	12.9311i		−	1.84730i
$50$	0.887484	+	0.0466955i	0.125509	+	0.00660374i
$51$		−	7.30714i		−	1.02320i
$52$	−3.88028	+	3.88028i	−0.538099	+	0.538099i
$53$	0.315424	−	0.315424i	0.0433269	−	0.0433269i	−0.685111	−	0.728438i	$-0.740247\pi$
$53$	0.315424	−	0.315424i	0.0433269	−	0.0433269i	0.728438	+	0.685111i	$0.240247\pi$
$54$	0.210005			0.0285780
$55$		0			0
$56$	−3.14900			−0.420803
$57$	−2.07030	+	2.07030i	−0.274217	+	0.274217i
$58$	0.939161	−	0.939161i	0.123318	−	0.123318i
$59$		−	11.3112i		−	1.47259i	−0.676662	−	0.736294i	$-0.736574\pi$
$59$		−	11.3112i		−	1.47259i	0.676662	−	0.736294i	$-0.263426\pi$
$60$	3.69689	+	9.63370i	0.477266	+	1.24371i
$61$			1.38079i			0.176793i	0.996085	+	0.0883963i	$0.0281742\pi$
$61$			1.38079i			0.176793i	−0.996085	+	0.0883963i	$0.971826\pi$
$62$	−0.645360	+	0.645360i	−0.0819608	+	0.0819608i
$63$	7.87950	+	7.87950i	0.992724	+	0.992724i
$64$		−	7.25173i		−	0.906467i
$65$	2.23337	+	5.81993i	0.277015	+	0.721873i
$66$		0			0
$67$	0.721404	+	0.721404i	0.0881335	+	0.0881335i	0.749799	−	0.661666i	$-0.230150\pi$
$67$	0.721404	+	0.721404i	0.0881335	+	0.0881335i	−0.661666	+	0.749799i	$0.730150\pi$
$68$	4.33834	+	4.33834i	0.526101	+	0.526101i
$69$		−	4.23909i		−	0.510326i
$70$	−0.721865	+	1.62088i	−0.0862794	+	0.193733i
$71$	3.52812			0.418711			0.209355	−	0.977840i	$-0.432863\pi$
$71$	3.52812			0.418711			0.209355	+	0.977840i	$0.432863\pi$
$72$	1.24492	−	1.24492i	0.146715	−	0.146715i
$73$	6.58997	+	6.58997i	0.771298	+	0.771298i	0.978333	−	0.207036i	$-0.0663816\pi$
$73$	6.58997	+	6.58997i	0.771298	+	0.771298i	−0.207036	+	0.978333i	$0.566382\pi$
$74$	−0.439926			−0.0511404
$75$	11.7056	+	0.615897i	1.35165	+	0.0711177i
$76$		−	2.45832i		−	0.281989i
$77$		0			0
$78$	0.821417	−	0.821417i	0.0930072	−	0.0930072i
$79$	6.02093			0.677407			0.338704	−	0.940893i	$-0.390012\pi$
$79$	6.02093			0.677407			0.338704	+	0.940893i	$0.390012\pi$
$80$	−7.78547	−	3.46728i	−0.870442	−	0.387654i
$81$	10.2579			1.13977
$82$	−1.35783	−	1.35783i	−0.149947	−	0.149947i
$83$	−3.45287	−	3.45287i	−0.379002	−	0.379002i	0.491740	−	0.870742i	$-0.336361\pi$
$83$	−3.45287	−	3.45287i	−0.379002	−	0.379002i	−0.870742	+	0.491740i	$0.836361\pi$
$84$	−20.6018			−2.24784
$85$	6.50695	−	2.49701i	0.705778	−	0.270839i
$86$	−1.08582			−0.117087
$87$	12.3872	−	12.3872i	1.32805	−	1.32805i
$88$		0			0
$89$			2.57764i			0.273229i	0.990624	+	0.136615i	$0.0436222\pi$
$89$			2.57764i			0.273229i	−0.990624	+	0.136615i	$0.956378\pi$
$90$	−0.355415	−	0.926175i	−0.0374640	−	0.0976274i
$91$	−12.4460			−1.30469
$92$	2.51680	+	2.51680i	0.262394	+	0.262394i
$93$	−8.51207	+	8.51207i	−0.882660	+	0.882660i
$94$	0.666152			0.0687083
$95$	−2.55105	−	1.13612i	−0.261732	−	0.116563i
$96$			4.89541i			0.499635i
$97$	−4.62327	−	4.62327i	−0.469422	−	0.469422i	0.432306	−	0.901727i	$-0.357700\pi$
$97$	−4.62327	−	4.62327i	−0.469422	−	0.469422i	−0.901727	+	0.432306i	$0.857700\pi$
$98$	−1.62522	−	1.62522i	−0.164172	−	0.164172i
$99$		0			0
$100$	−7.31542	+	6.58409i	−0.731542	+	0.658409i
$101$		−	12.1812i		−	1.21208i	−0.795435	−	0.606039i	$-0.792758\pi$
$101$		−	12.1812i		−	1.21208i	0.795435	−	0.606039i	$-0.207242\pi$
$102$	−0.918382	−	0.918382i	−0.0909334	−	0.0909334i
$103$	−9.08246	+	9.08246i	−0.894921	+	0.894921i	−0.994981	−	0.100060i	$-0.968096\pi$
$103$	−9.08246	+	9.08246i	−0.894921	+	0.894921i	0.100060	+	0.994981i	$0.468096\pi$
$104$			1.96640i			0.192821i
$105$	−9.52115	+	21.3789i	−0.929169	+	2.08637i
$106$		−	0.0792869i		−	0.00770102i
$107$	−7.07404	+	7.07404i	−0.683873	+	0.683873i	−0.960871	−	0.276998i	$-0.910661\pi$
$107$	−7.07404	+	7.07404i	−0.683873	+	0.683873i	0.276998	+	0.960871i	$0.410661\pi$
$108$	−1.64452	+	1.64452i	−0.158244	+	0.158244i
$109$	−8.79661			−0.842562			−0.421281	−	0.906930i	$-0.638419\pi$
$109$	−8.79661			−0.842562			−0.421281	+	0.906930i	$0.638419\pi$
$110$		0			0
$111$	−5.80247			−0.550746
$112$	12.0321	−	12.0321i	1.13692	−	1.13692i
$113$	−6.95236	+	6.95236i	−0.654023	+	0.654023i	−0.953959	−	0.299936i	$-0.903035\pi$
$113$	−6.95236	+	6.95236i	−0.654023	+	0.654023i	0.299936	+	0.953959i	$0.403035\pi$
$114$			0.520401i			0.0487400i
$115$	3.77487	−	1.44859i	0.352009	−	0.135082i
$116$			14.7089i			1.36568i
$117$	4.92036	−	4.92036i	0.454887	−	0.454887i
$118$	−1.42162	−	1.42162i	−0.130871	−	0.130871i
$119$			13.9152i			1.27560i
$120$	3.37774	+	1.50429i	0.308344	+	0.137322i
$121$		0			0
$122$	0.173542	+	0.173542i	0.0157118	+	0.0157118i
$123$	−17.9093	−	17.9093i	−1.61483	−	1.61483i
$124$		−	10.1074i		−	0.907675i
$125$	3.45161	+	10.6342i	0.308721	+	0.951153i
$126$	1.98064			0.176449
$127$	5.46777	−	5.46777i	0.485186	−	0.485186i	−0.421597	−	0.906783i	$-0.638530\pi$
$127$	5.46777	−	5.46777i	0.485186	−	0.485186i	0.906783	+	0.421597i	$0.138530\pi$
$128$	−3.86453	−	3.86453i	−0.341579	−	0.341579i
$129$	−14.3216			−1.26094
$130$	1.01216	+	0.450769i	0.0887724	+	0.0395350i
$131$		−	19.6002i		−	1.71248i	−0.516578	−	0.856240i	$-0.672794\pi$
$131$		−	19.6002i		−	1.71248i	0.516578	−	0.856240i	$-0.327206\pi$
$132$		0			0
$133$	3.94252	−	3.94252i	0.341860	−	0.341860i
$134$	0.181336			0.0156651
$135$	0.946531	+	2.46656i	0.0814644	+	0.212288i
$136$	2.19852			0.188522
$137$	−5.79590	−	5.79590i	−0.495177	−	0.495177i	0.414756	−	0.909933i	$-0.363867\pi$
$137$	−5.79590	−	5.79590i	−0.495177	−	0.495177i	−0.909933	+	0.414756i	$0.863867\pi$
$138$	−0.532781	−	0.532781i	−0.0453533	−	0.0453533i
$139$	12.4159			1.05310			0.526550	−	0.850144i	$-0.323485\pi$
$139$	12.4159			1.05310			0.526550	+	0.850144i	$0.323485\pi$
$140$	−7.04008	−	18.3457i	−0.594995	−	1.55050i
$141$	8.78631			0.739941
$142$	0.443424	−	0.443424i	0.0372113	−	0.0372113i
$143$		0			0
$144$			9.51344i			0.792787i
$145$	15.2637	+	6.79772i	1.26758	+	0.564520i
$146$	1.65649			0.137092
$147$	−21.4361	−	21.4361i	−1.76802	−	1.76802i
$148$	3.44500	−	3.44500i	0.283177	−	0.283177i
$149$	1.49550			0.122516			0.0612581	−	0.998122i	$-0.480489\pi$
$149$	1.49550			0.122516			0.0612581	+	0.998122i	$0.480489\pi$
$150$	1.54860	−	1.39379i	0.126443	−	0.113802i
$151$			5.93157i			0.482704i	0.970438	+	0.241352i	$0.0775909\pi$
$151$			5.93157i			0.482704i	−0.970438	+	0.241352i	$0.922409\pi$
$152$	−0.622896	−	0.622896i	−0.0505235	−	0.0505235i
$153$	−5.50119	−	5.50119i	−0.444745	−	0.444745i
$154$		0			0
$155$	−10.4887	−	4.67117i	−0.842472	−	0.375197i
$156$			12.8648i			1.03001i
$157$	−8.26778	−	8.26778i	−0.659841	−	0.659841i	0.295501	−	0.955342i	$-0.404513\pi$
$157$	−8.26778	−	8.26778i	−0.659841	−	0.659841i	−0.955342	+	0.295501i	$0.904513\pi$
$158$	0.756727	−	0.756727i	0.0602020	−	0.0602020i
$159$		−	1.04577i		−	0.0829346i
$160$	−4.35932	+	1.67287i	−0.344634	+	0.132252i
$161$			8.07261i			0.636211i
$162$	1.28925	−	1.28925i	0.101293	−	0.101293i
$163$	−4.84865	+	4.84865i	−0.379776	+	0.379776i	−0.871021	−	0.491245i	$-0.836542\pi$
$163$	−4.84865	+	4.84865i	−0.379776	+	0.379776i	0.491245	+	0.871021i	$0.336542\pi$
$164$	21.2659			1.66059
$165$		0			0
$166$	−0.867933			−0.0673647
$167$	−8.83234	+	8.83234i	−0.683467	+	0.683467i	−0.960780	−	0.277312i	$-0.910556\pi$
$167$	−8.83234	+	8.83234i	−0.683467	+	0.683467i	0.277312	+	0.960780i	$0.410556\pi$
$168$	−5.22014	+	5.22014i	−0.402743	+	0.402743i
$169$		−	5.22810i		−	0.402162i
$170$	0.503980	−	1.13164i	0.0386535	−	0.0867931i
$171$			3.11725i			0.238382i
$172$	8.50288	−	8.50288i	0.648339	−	0.648339i
$173$	16.7036	+	16.7036i	1.26995	+	1.26995i	0.946114	+	0.323834i	$0.104972\pi$
$173$	16.7036	+	16.7036i	1.26995	+	1.26995i	0.323834	+	0.946114i	$0.395028\pi$
$174$		−	3.11372i		−	0.236050i
$175$	−22.2913	−	1.17287i	−1.68506	−	0.0886606i
$176$		0			0
$177$	−18.7506	−	18.7506i	−1.40938	−	1.40938i
$178$	0.323965	+	0.323965i	0.0242822	+	0.0242822i
$179$			19.3159i			1.44374i	0.692029	+	0.721870i	$0.256717\pi$
$179$			19.3159i			1.44374i	−0.692029	+	0.721870i	$0.743283\pi$
$180$	10.0359	+	4.46954i	0.748035	+	0.333140i
$181$	13.4648			1.00083			0.500417	−	0.865785i	$-0.333180\pi$
$181$	13.4648			1.00083			0.500417	+	0.865785i	$0.333180\pi$
$182$	−1.56425	+	1.56425i	−0.115950	+	0.115950i
$183$	2.28896	+	2.28896i	0.169205	+	0.169205i
$184$	1.27543			0.0940257
$185$	−1.98283	−	5.16705i	−0.145781	−	0.379889i
$186$			2.13964i			0.156886i
$187$		0			0
$188$	−5.21654	+	5.21654i	−0.380455	+	0.380455i
$189$	−5.27477			−0.383683
$190$	−0.463413	+	0.177833i	−0.0336195	+	0.0129013i
$191$	−13.3527			−0.966168			−0.483084	−	0.875574i	$-0.660484\pi$
$191$	−13.3527			−0.966168			−0.483084	+	0.875574i	$0.660484\pi$
$192$	−12.0213	−	12.0213i	−0.867562	−	0.867562i
$193$	−2.28334	−	2.28334i	−0.164358	−	0.164358i	0.620136	−	0.784494i	$-0.287077\pi$
$193$	−2.28334	−	2.28334i	−0.164358	−	0.164358i	−0.784494	+	0.620136i	$0.787077\pi$
$194$	−1.16213			−0.0834361
$195$	13.3500	+	5.94548i	0.956017	+	0.425765i
$196$	25.4537			1.81812
$197$	−3.61891	+	3.61891i	−0.257837	+	0.257837i	−0.824174	−	0.566337i	$-0.808360\pi$
$197$	−3.61891	+	3.61891i	−0.257837	+	0.257837i	0.566337	+	0.824174i	$0.308360\pi$
$198$		0			0
$199$		−	7.26740i		−	0.515173i	−0.966255	−	0.257586i	$-0.917073\pi$
$199$		−	7.26740i		−	0.515173i	0.966255	−	0.257586i	$-0.0829272\pi$
$200$	−0.185307	+	3.52190i	−0.0131032	+	0.249036i
$201$	2.39176			0.168702
$202$	−1.53097	−	1.53097i	−0.107719	−	0.107719i
$203$	−23.5893	+	23.5893i	−1.65564	+	1.65564i
$204$	14.3834			1.00704
$205$	9.82808	−	22.0681i	0.686423	−	1.54130i
$206$			2.28302i			0.159065i
$207$	−3.19140	−	3.19140i	−0.221818	−	0.221818i
$208$	−7.51343	−	7.51343i	−0.520962	−	0.520962i
$209$		0			0
$210$	1.49031	+	3.88360i	0.102841	+	0.267994i
$211$			14.3789i			0.989886i	0.868925	+	0.494943i	$0.164811\pi$
$211$			14.3789i			0.989886i	−0.868925	+	0.494943i	$0.835189\pi$
$212$	0.620884	+	0.620884i	0.0426425	+	0.0426425i
$213$	5.84861	−	5.84861i	0.400740	−	0.400740i
$214$			1.77817i			0.121553i
$215$	−4.89399	−	12.7532i	−0.333767	−	0.869763i
$216$			0.833384i			0.0567046i
$217$	16.2098	−	16.2098i	1.10039	−	1.10039i
$218$	−1.10558	+	1.10558i	−0.0748795	+	0.0748795i
$219$	21.8485			1.47639
$220$		0			0
$221$	8.68934			0.584508
$222$	−0.729271	+	0.729271i	−0.0489455	+	0.0489455i
$223$	7.68134	−	7.68134i	0.514381	−	0.514381i	−0.401485	−	0.915866i	$-0.631506\pi$
$223$	7.68134	−	7.68134i	0.514381	−	0.514381i	0.915866	+	0.401485i	$0.131506\pi$
$224$		−	9.32245i		−	0.622883i
$225$	9.27625	−	8.34889i	0.618417	−	0.556593i
$226$			1.74758i			0.116248i
$227$	−10.9700	+	10.9700i	−0.728106	+	0.728106i	−0.970242	−	0.242137i	$-0.922152\pi$
$227$	−10.9700	+	10.9700i	−0.728106	+	0.728106i	0.242137	+	0.970242i	$0.422152\pi$
$228$	−4.07519	−	4.07519i	−0.269886	−	0.269886i
$229$		−	20.6756i		−	1.36628i	−0.730286	−	0.683142i	$-0.760613\pi$
$229$		−	20.6756i		−	1.36628i	0.730286	−	0.683142i	$-0.239387\pi$
$230$	0.292374	−	0.656500i	0.0192786	−	0.0432883i
$231$		0			0
$232$	3.72697	+	3.72697i	0.244688	+	0.244688i
$233$	−13.0750	−	13.0750i	−0.856571	−	0.856571i	0.134362	−	0.990932i	$-0.457102\pi$
$233$	−13.0750	−	13.0750i	−0.856571	−	0.856571i	−0.990932	+	0.134362i	$0.957102\pi$
$234$		−	1.23681i		−	0.0808527i
$235$	3.00247	+	7.82413i	0.195860	+	0.510390i
$236$	22.2650			1.44933
$237$	9.98096	−	9.98096i	0.648333	−	0.648333i
$238$	1.74890	+	1.74890i	0.113364	+	0.113364i
$239$	−16.6078			−1.07427			−0.537134	−	0.843497i	$-0.680493\pi$
$239$	−16.6078			−1.07427			−0.537134	+	0.843497i	$0.680493\pi$
$240$	−18.6538	+	7.15831i	−1.20410	+	0.462067i
$241$			13.5493i			0.872789i	0.899755	+	0.436395i	$0.143745\pi$
$241$			13.5493i			0.872789i	−0.899755	+	0.436395i	$0.856255\pi$
$242$		0			0
$243$	14.4984	−	14.4984i	0.930070	−	0.930070i
$244$	−2.71796			−0.174000
$245$	11.7635	−	26.4138i	0.751540	−	1.68752i
$246$	−4.50178			−0.287023
$247$	−2.46191	−	2.46191i	−0.156647	−	0.156647i
$248$	−2.56105	−	2.56105i	−0.162627	−	0.162627i
$249$	−11.4477			−0.725471
$250$	1.77035	+	0.902730i	0.111966	+	0.0570936i
$251$	−6.59073			−0.416003			−0.208002	−	0.978128i	$-0.566696\pi$
$251$	−6.59073			−0.416003			−0.208002	+	0.978128i	$0.566696\pi$
$252$	−15.5101	+	15.5101i	−0.977043	+	0.977043i
$253$		0			0
$254$		−	1.37441i		−	0.0862381i
$255$	6.64732	−	14.9260i	0.416272	−	0.934701i
$256$	13.5321			0.845753
$257$	11.1970	+	11.1970i	0.698451	+	0.698451i	0.964076	−	0.265626i	$-0.0855785\pi$
$257$	11.1970	+	11.1970i	0.698451	+	0.698451i	−0.265626	+	0.964076i	$0.585578\pi$
$258$	−1.79997	+	1.79997i	−0.112061	+	0.112061i
$259$	11.0498			0.686601
$260$	−11.4560	+	4.39618i	−0.710470	+	0.272640i
$261$		−	18.6514i		−	1.15449i
$262$	−2.46341	−	2.46341i	−0.152190	−	0.152190i
$263$	21.0043	+	21.0043i	1.29518	+	1.29518i	0.931541	+	0.363637i	$0.118465\pi$
$263$	21.0043	+	21.0043i	1.29518	+	1.29518i	0.363637	+	0.931541i	$0.381535\pi$
$264$		0			0
$265$	0.931246	−	0.357361i	0.0572060	−	0.0219525i
$266$		−	0.991014i		−	0.0607630i
$267$	4.27298	+	4.27298i	0.261502	+	0.261502i
$268$	−1.42002	+	1.42002i	−0.0867413	+	0.0867413i
$269$			4.29801i			0.262054i	0.991379	+	0.131027i	$0.0418275\pi$
$269$			4.29801i			0.262054i	−0.991379	+	0.131027i	$0.958173\pi$
$270$	0.428967	+	0.191042i	0.0261061	+	0.0116264i
$271$			20.8238i			1.26495i	0.774579	+	0.632477i	$0.217962\pi$
$271$			20.8238i			1.26495i	−0.774579	+	0.632477i	$0.782038\pi$
$272$	−8.40036	+	8.40036i	−0.509347	+	0.509347i
$273$	−20.6319	+	20.6319i	−1.24870	+	1.24870i
$274$	−1.45689			−0.0880140
$275$		0			0
$276$	8.34425			0.502265
$277$	6.87337	−	6.87337i	0.412981	−	0.412981i	−0.469795	−	0.882776i	$-0.655672\pi$
$277$	6.87337	−	6.87337i	0.412981	−	0.412981i	0.882776	+	0.469795i	$0.155672\pi$
$278$	1.56046	−	1.56046i	0.0935903	−	0.0935903i
$279$			12.8166i			0.767312i
$280$	−6.43233	−	2.86466i	−0.384405	−	0.171196i
$281$		−	0.853512i		−	0.0509163i	−0.999676	−	0.0254581i	$-0.991896\pi$
$281$		−	0.853512i		−	0.0509163i	0.999676	−	0.0254581i	$-0.00810445\pi$
$282$	1.10429	−	1.10429i	0.0657594	−	0.0657594i
$283$	−6.87072	−	6.87072i	−0.408422	−	0.408422i	0.472766	−	0.881188i	$-0.343256\pi$
$283$	−6.87072	−	6.87072i	−0.408422	−	0.408422i	−0.881188	+	0.472766i	$0.843256\pi$
$284$			6.94478i			0.412097i
$285$	−6.11225	+	2.34555i	−0.362059	+	0.138938i
$286$		0			0
$287$	34.1052	+	34.1052i	2.01316	+	2.01316i
$288$	3.68551	+	3.68551i	0.217171	+	0.217171i
$289$			7.28491i			0.428524i
$290$	2.77274	−	1.06403i	0.162821	−	0.0624817i
$291$	−15.3281			−0.898549
$292$	−12.9717	+	12.9717i	−0.759114	+	0.759114i
$293$	−18.8718	−	18.8718i	−1.10250	−	1.10250i	−0.994108	−	0.108395i	$-0.965429\pi$
$293$	−18.8718	−	18.8718i	−1.10250	−	1.10250i	−0.108395	−	0.994108i	$-0.534571\pi$
$294$	−5.38829			−0.314251
$295$	10.2898	−	23.1048i	0.599095	−	1.34521i
$296$		−	1.74581i		−	0.101473i
$297$		0			0
$298$	0.187959	−	0.187959i	0.0108882	−	0.0108882i
$299$	5.04094			0.291525
$300$	−1.21234	+	23.0414i	−0.0699943	+	1.33030i
$301$	27.2729			1.57199
$302$	0.745497	+	0.745497i	0.0428985	+	0.0428985i
$303$	−20.1930	−	20.1930i	−1.16006	−	1.16006i
$304$	4.76006			0.273008
$305$	−1.25611	+	2.82049i	−0.0719247	+	0.161501i
$306$	−1.38281			−0.0790500
$307$	−4.08294	+	4.08294i	−0.233026	+	0.233026i	−0.813954	−	0.580929i	$-0.802689\pi$
$307$	−4.08294	+	4.08294i	−0.233026	+	0.233026i	0.580929	+	0.813954i	$0.302689\pi$
$308$		0			0
$309$			30.1122i			1.71302i
$310$	−1.90533	+	0.731163i	−0.108216	+	0.0415272i
$311$	−0.766768			−0.0434794			−0.0217397	−	0.999764i	$-0.506921\pi$
$311$	−0.766768			−0.0434794			−0.0217397	+	0.999764i	$0.506921\pi$
$312$	3.25972	+	3.25972i	0.184545	+	0.184545i
$313$	18.9656	−	18.9656i	1.07200	−	1.07200i	0.0748001	−	0.997199i	$-0.476168\pi$
$313$	18.9656	−	18.9656i	1.07200	−	1.07200i	0.997199	−	0.0748001i	$-0.0238319\pi$
$314$	−2.07824			−0.117282
$315$	8.92710	+	23.2631i	0.502985	+	1.31073i
$316$			11.8516i			0.666707i
$317$	13.4304	+	13.4304i	0.754329	+	0.754329i	0.975284	−	0.220955i	$-0.0709174\pi$
$317$	13.4304	+	13.4304i	0.754329	+	0.754329i	−0.220955	+	0.975284i	$0.570917\pi$
$318$	−0.131435	−	0.131435i	−0.00737050	−	0.00737050i
$319$		0			0
$320$	6.59692	−	14.8128i	0.368779	−	0.828060i
$321$			23.4534i			1.30904i
$322$	1.01459	+	1.01459i	0.0565408	+	0.0565408i
$323$	−2.75253	+	2.75253i	−0.153155	+	0.153155i
$324$			20.1918i			1.12177i
$325$	−0.732399	+	13.9198i	−0.0406262	+	0.772132i
$326$			1.21878i			0.0675022i
$327$	−14.5822	+	14.5822i	−0.806400	+	0.806400i
$328$	5.38842	−	5.38842i	0.297526	−	0.297526i
$329$	−16.7320			−0.922465
$330$		0			0
$331$	−0.0204452			−0.00112377			−0.000561885	−	1.00000i	$-0.500179\pi$
$331$	−0.0204452			−0.00112377			−0.000561885		1.00000i	$0.500179\pi$
$332$	6.79666	−	6.79666i	0.373015	−	0.373015i
$333$	−4.36839	+	4.36839i	−0.239386	+	0.239386i
$334$			2.22015i			0.121481i
$335$	0.817317	+	2.12984i	0.0446548	+	0.116366i
$336$		−	39.8914i		−	2.17625i
$337$	−11.1779	+	11.1779i	−0.608899	+	0.608899i	−0.942658	−	0.333760i	$-0.891683\pi$
$337$	−11.1779	+	11.1779i	−0.608899	+	0.608899i	0.333760	+	0.942658i	$0.391683\pi$
$338$	−0.657083	−	0.657083i	−0.0357406	−	0.0357406i
$339$			23.0500i			1.25191i
$340$	4.91513	+	12.8083i	0.266561	+	0.694629i
$341$		0			0
$342$	0.391784	+	0.391784i	0.0211853	+	0.0211853i
$343$	18.7235	+	18.7235i	1.01097	+	1.01097i
$344$		−	4.30897i		−	0.232324i
$345$	3.85631	−	8.65900i	0.207617	−	0.466185i
$346$	4.19870			0.225724
$347$	15.4800	−	15.4800i	0.831008	−	0.831008i	−0.156647	−	0.987655i	$-0.550068\pi$
$347$	15.4800	−	15.4800i	0.831008	−	0.831008i	0.987655	+	0.156647i	$0.0500683\pi$
$348$	24.3831	+	24.3831i	1.30707	+	1.30707i
$349$	27.9856			1.49804			0.749018	−	0.662549i	$-0.230526\pi$
$349$	27.9856			1.49804			0.749018	+	0.662549i	$0.230526\pi$
$350$	−2.94904	+	2.65422i	−0.157633	+	0.141874i
$351$			3.29383i			0.175812i
$352$		0			0
$353$	−9.36952	+	9.36952i	−0.498689	+	0.498689i	−0.911030	−	0.412340i	$-0.864711\pi$
$353$	−9.36952	+	9.36952i	−0.498689	+	0.498689i	0.412340	+	0.911030i	$0.364711\pi$
$354$	−4.71327			−0.250507
$355$	7.20673	+	3.20954i	0.382494	+	0.170345i
$356$	−5.07384			−0.268913
$357$	23.0674	+	23.0674i	1.22086	+	1.22086i
$358$	2.42768	+	2.42768i	0.128307	+	0.128307i
$359$	1.69815			0.0896252			0.0448126	−	0.998995i	$-0.485731\pi$
$359$	1.69815			0.0896252			0.0448126	+	0.998995i	$0.485731\pi$
$360$	3.67544	−	1.41043i	0.193713	−	0.0743363i
$361$	−17.4403			−0.917910
$362$	1.69230	−	1.69230i	0.0889453	−	0.0889453i
$363$		0			0
$364$		−	24.4988i		−	1.28408i
$365$	7.46613	+	19.4559i	0.390795	+	1.01837i
$366$	0.575366			0.0300748
$367$	15.1500	+	15.1500i	0.790825	+	0.790825i	0.981628	−	0.190803i	$-0.0611092\pi$
$367$	15.1500	+	15.1500i	0.790825	+	0.790825i	−0.190803	+	0.981628i	$0.561109\pi$
$368$	−4.87330	+	4.87330i	−0.254038	+	0.254038i
$369$	−26.9661			−1.40380
$370$	−0.898617	−	0.400202i	−0.0467169	−	0.0208055i
$371$			1.99148i			0.103393i
$372$	−16.7552	−	16.7552i	−0.868718	−	0.868718i
$373$	6.29327	+	6.29327i	0.325853	+	0.325853i	0.851007	−	0.525154i	$-0.175992\pi$
$373$	6.29327	+	6.29327i	0.325853	+	0.325853i	−0.525154	+	0.851007i	$0.675992\pi$
$374$		0			0
$375$	23.3502	+	11.9067i	1.20580	+	0.614858i
$376$			2.64356i			0.136331i
$377$	14.7303	+	14.7303i	0.758651	+	0.758651i
$378$	−0.662948	+	0.662948i	−0.0340984	+	0.0340984i
$379$		−	32.3401i		−	1.66120i	−0.556871	−	0.830599i	$-0.687998\pi$
$379$		−	32.3401i		−	1.66120i	0.556871	−	0.830599i	$-0.312002\pi$
$380$	2.23634	−	5.02150i	0.114722	−	0.257597i
$381$		−	18.1280i		−	0.928724i
$382$	−1.67821	+	1.67821i	−0.0858645	+	0.0858645i
$383$	16.2896	−	16.2896i	0.832358	−	0.832358i	−0.155481	−	0.987839i	$-0.549693\pi$
$383$	16.2896	−	16.2896i	0.832358	−	0.832358i	0.987839	+	0.155481i	$0.0496926\pi$
$384$	−12.8125			−0.653838
$385$		0			0
$386$	−0.573952			−0.0292134
$387$	−10.7820	+	10.7820i	−0.548079	+	0.548079i
$388$	9.10047	−	9.10047i	0.462007	−	0.462007i
$389$		−	14.3543i		−	0.727792i	−0.931440	−	0.363896i	$-0.881446\pi$
$389$		−	14.3543i		−	0.727792i	0.931440	−	0.363896i	$-0.118554\pi$
$390$	2.42512	−	0.930627i	0.122801	−	0.0471241i
$391$		−	5.63601i		−	0.285025i
$392$	6.44953	−	6.44953i	0.325750	−	0.325750i
$393$	−32.4915	−	32.4915i	−1.63898	−	1.63898i
$394$			0.909671i			0.0458286i
$395$	12.2987	+	5.47725i	0.618814	+	0.275590i
$396$		0			0
$397$	−8.05942	−	8.05942i	−0.404491	−	0.404491i	0.475321	−	0.879812i	$-0.342332\pi$
$397$	−8.05942	−	8.05942i	−0.404491	−	0.404491i	−0.879812	+	0.475321i	$0.842332\pi$
$398$	−0.913388	−	0.913388i	−0.0457840	−	0.0457840i
$399$		−	13.0711i		−	0.654375i
$400$	−12.7488	−	14.1649i	−0.637442	−	0.708246i
$401$	−22.3236			−1.11479			−0.557395	−	0.830248i	$-0.688199\pi$
$401$	−22.3236			−1.11479			−0.557395	+	0.830248i	$0.688199\pi$
$402$	0.300603	−	0.300603i	0.0149927	−	0.0149927i
$403$	−10.1222	−	10.1222i	−0.504222	−	0.504222i
$404$	23.9776			1.19293
$405$	20.9534	+	9.33168i	1.04119	+	0.463695i
$406$			5.92954i			0.294278i
$407$		0			0
$408$	3.64452	−	3.64452i	0.180430	−	0.180430i
$409$	−2.81860			−0.139371			−0.0696855	−	0.997569i	$-0.522200\pi$
$409$	−2.81860			−0.139371			−0.0696855	+	0.997569i	$0.522200\pi$
$410$	−1.53836	−	4.00880i	−0.0759741	−	0.197981i
$411$	−19.2159			−0.947849
$412$	−17.8780	−	17.8780i	−0.880785	−	0.880785i
$413$	35.7074	+	35.7074i	1.75704	+	1.75704i
$414$	−0.802209			−0.0394264
$415$	−3.91194	−	10.1941i	−0.192030	−	0.500409i
$416$	−5.82141			−0.285418
$417$	20.5819	−	20.5819i	1.00790	−	1.00790i
$418$		0			0
$419$		−	24.7639i		−	1.20980i	−0.796303	−	0.604898i	$-0.793214\pi$
$419$		−	24.7639i		−	1.20980i	0.796303	−	0.604898i	$-0.206786\pi$
$420$	−42.0824	−	18.7415i	−2.05341	−	0.914491i
$421$	28.6112			1.39443			0.697213	−	0.716864i	$-0.254423\pi$
$421$	28.6112			1.39443			0.697213	+	0.716864i	$0.254423\pi$
$422$	1.80718	+	1.80718i	0.0879724	+	0.0879724i
$423$	6.61478	−	6.61478i	0.321621	−	0.321621i
$424$	0.314643			0.0152804
$425$	15.5630	+	0.818856i	0.754916	+	0.0397203i
$426$		−	1.47014i		−	0.0712285i
$427$	−4.35893	−	4.35893i	−0.210943	−	0.210943i
$428$	−13.9246	−	13.9246i	−0.673070	−	0.673070i
$429$		0			0
$430$	−2.21795	−	0.987771i	−0.106959	−	0.0476346i
$431$		−	33.8869i		−	1.63228i	−0.577857	−	0.816138i	$-0.696111\pi$
$431$		−	33.8869i		−	1.63228i	0.577857	−	0.816138i	$-0.303889\pi$
$432$	−3.18429	−	3.18429i	−0.153204	−	0.153204i
$433$	−1.88692	+	1.88692i	−0.0906795	+	0.0906795i	−0.750991	−	0.660312i	$-0.770424\pi$
$433$	−1.88692	+	1.88692i	−0.0906795	+	0.0906795i	0.660312	+	0.750991i	$0.270424\pi$
$434$		−	4.07458i		−	0.195586i
$435$	36.5714	−	14.0341i	1.75347	−	0.672884i
$436$		−	17.3153i		−	0.829253i
$437$	−1.59682	+	1.59682i	−0.0763864	+	0.0763864i
$438$	2.74599	−	2.74599i	0.131208	−	0.131208i
$439$	−25.1409			−1.19991			−0.599956	−	0.800033i	$-0.704815\pi$
$439$	−25.1409			−1.19991			−0.599956	+	0.800033i	$0.704815\pi$
$440$		0			0
$441$	−32.2763			−1.53697
$442$	1.09210	−	1.09210i	0.0519460	−	0.0519460i
$443$	8.85103	−	8.85103i	0.420525	−	0.420525i	−0.464859	−	0.885385i	$-0.653895\pi$
$443$	8.85103	−	8.85103i	0.420525	−	0.420525i	0.885385	+	0.464859i	$0.153895\pi$
$444$		−	11.4216i		−	0.542046i
$445$	−2.34488	+	5.26522i	−0.111158	+	0.249596i
$446$		−	1.93083i		−	0.0914273i
$447$	2.47911	−	2.47911i	0.117258	−	0.117258i
$448$	22.8925	+	22.8925i	1.08157	+	1.08157i
$449$		−	12.1995i		−	0.575731i	−0.957671	−	0.287865i	$-0.907054\pi$
$449$		−	12.1995i		−	0.575731i	0.957671	−	0.287865i	$-0.0929455\pi$
$450$	0.116553	−	2.21518i	0.00549436	−	0.104425i
$451$		0			0
$452$	−13.6851	−	13.6851i	−0.643692	−	0.643692i
$453$	9.83284	+	9.83284i	0.461987	+	0.461987i
$454$			2.75749i			0.129415i
$455$	−25.4229	−	11.3221i	−1.19184	−	0.530790i
$456$	−2.06516			−0.0967102
$457$	−21.3621	+	21.3621i	−0.999277	+	0.999277i	−1.00000		0.000722482i	$-0.999770\pi$
$457$	−21.3621	+	21.3621i	−0.999277	+	0.999277i	0.000722482		1.00000i	$0.499770\pi$
$458$	−2.59857	−	2.59857i	−0.121423	−	0.121423i
$459$	3.68266			0.171892
$460$	2.85141	+	7.43049i	0.132948	+	0.346448i
$461$			16.7546i			0.780340i	0.920743	+	0.390170i	$0.127584\pi$
$461$			16.7546i			0.780340i	−0.920743	+	0.390170i	$0.872416\pi$
$462$		0			0
$463$	−15.7524	+	15.7524i	−0.732077	+	0.732077i	−0.971031	−	0.238954i	$-0.923195\pi$
$463$	−15.7524	+	15.7524i	−0.732077	+	0.732077i	0.238954	+	0.971031i	$0.423195\pi$
$464$	−28.4809			−1.32219
$465$	−25.1307	+	9.64377i	−1.16541	+	0.447219i
$466$	−3.28660			−0.152249
$467$	22.8580	+	22.8580i	1.05774	+	1.05774i	0.998228	+	0.0595134i	$0.0189549\pi$
$467$	22.8580	+	22.8580i	1.05774	+	1.05774i	0.0595134	+	0.998228i	$0.481045\pi$
$468$	9.68527	+	9.68527i	0.447702	+	0.447702i
$469$	−4.55469			−0.210316
$470$	1.36072	+	0.606000i	0.0627653	+	0.0279527i
$471$	−27.4112			−1.26304
$472$	5.64156	−	5.64156i	0.259674	−	0.259674i
$473$		0			0
$474$		−	2.50887i		−	0.115236i
$475$	−4.17738	−	4.64139i	−0.191671	−	0.212961i
$476$	−27.3908			−1.25545
$477$	−0.787305	−	0.787305i	−0.0360482	−	0.0360482i
$478$	−2.08732	+	2.08732i	−0.0954716	+	0.0954716i
$479$	−19.0743			−0.871526			−0.435763	−	0.900061i	$-0.643521\pi$
$479$	−19.0743			−0.871526			−0.435763	+	0.900061i	$0.643521\pi$
$480$	−4.45336	+	9.99963i	−0.203267	+	0.456418i
$481$		−	6.90005i		−	0.314615i
$482$	1.70292	+	1.70292i	0.0775658	+	0.0775658i
$483$	13.3821	+	13.3821i	0.608905	+	0.608905i
$484$		0			0
$485$	−5.23794	−	13.6495i	−0.237843	−	0.619794i
$486$		−	3.64439i		−	0.165313i
$487$	−19.5034	−	19.5034i	−0.883785	−	0.883785i	0.110132	−	0.993917i	$-0.464873\pi$
$487$	−19.5034	−	19.5034i	−0.883785	−	0.883785i	−0.993917	+	0.110132i	$0.964873\pi$
$488$	−0.688686	+	0.688686i	−0.0311753	+	0.0311753i
$489$			16.0753i			0.726952i
$490$	−1.84130	−	4.79823i	−0.0831813	−	0.216762i
$491$		−	37.3349i		−	1.68490i	−0.538775	−	0.842449i	$-0.681113\pi$
$491$		−	37.3349i		−	1.68490i	0.538775	−	0.842449i	$-0.318887\pi$
$492$	35.2528	−	35.2528i	1.58932	−	1.58932i
$493$	16.4692	−	16.4692i	0.741735	−	0.741735i
$494$	−0.618839			−0.0278429
$495$		0			0
$496$	19.5711			0.878769
$497$	−11.1377	+	11.1377i	−0.499592	+	0.499592i
$498$	−1.43878	+	1.43878i	−0.0644734	+	0.0644734i
$499$			14.1177i			0.631993i	0.948760	+	0.315996i	$0.102339\pi$
$499$			14.1177i			0.631993i	−0.948760	+	0.315996i	$0.897661\pi$
$500$	−20.9325	+	6.79417i	−0.936128	+	0.303845i
$501$			29.2830i			1.30827i
$502$	−0.828342	+	0.828342i	−0.0369707	+	0.0369707i
$503$	8.84744	+	8.84744i	0.394488	+	0.394488i	0.876284	−	0.481796i	$-0.160015\pi$
$503$	8.84744	+	8.84744i	0.394488	+	0.394488i	−0.481796	+	0.876284i	$0.660015\pi$
$504$			7.85997i			0.350111i
$505$	11.0813	−	24.8821i	0.493111	−	1.10724i
$506$		0			0
$507$	−8.66669	−	8.66669i	−0.384901	−	0.384901i
$508$	10.7628	+	10.7628i	0.477522	+	0.477522i
$509$		−	2.12688i		−	0.0942725i	−0.998888	−	0.0471363i	$-0.984991\pi$
$509$		−	2.12688i		−	0.0942725i	0.998888	−	0.0471363i	$-0.0150095\pi$
$510$	−1.04048	−	2.71139i	−0.0460734	−	0.120063i
$511$	−41.6068			−1.84058
$512$	9.42980	−	9.42980i	0.416742	−	0.416742i
$513$	−1.04339	−	1.04339i	−0.0460667	−	0.0460667i
$514$	2.81455			0.124144
$515$	−26.8147	+	10.2900i	−1.18160	+	0.453432i
$516$		−	28.1907i		−	1.24102i
$517$		0			0
$518$	1.38877	−	1.38877i	0.0610191	−	0.0610191i
$519$	55.3794			2.43089
$520$	−1.78883	+	4.01667i	−0.0784456	+	0.176143i
$521$	24.8668			1.08944			0.544718	−	0.838619i	$-0.316637\pi$
$521$	24.8668			1.08944			0.544718	+	0.838619i	$0.316637\pi$
$522$	−2.34416	−	2.34416i	−0.102601	−	0.102601i
$523$	−13.6144	−	13.6144i	−0.595318	−	0.595318i	0.343745	−	0.939063i	$-0.388304\pi$
$523$	−13.6144	−	13.6144i	−0.595318	−	0.595318i	−0.939063	+	0.343745i	$0.888304\pi$
$524$	38.5812			1.68543
$525$	−38.8968	+	35.0083i	−1.69760	+	1.52789i
$526$	5.27975			0.230208
$527$	−11.3171	+	11.3171i	−0.492980	+	0.492980i
$528$		0			0
$529$			19.7304i			0.857843i
$530$	0.0721275	−	0.161956i	0.00313302	−	0.00703491i
$531$	−28.2329			−1.22520
$532$	7.76049	+	7.76049i	0.336460	+	0.336460i
$533$	21.2970	−	21.2970i	0.922475	−	0.922475i
$534$	1.07408			0.0464800
$535$	−20.8851	+	8.01455i	−0.902941	+	0.346499i
$536$			0.719616i			0.0310827i
$537$	32.0202	+	32.0202i	1.38178	+	1.38178i
$538$	0.540186	+	0.540186i	0.0232891	+	0.0232891i
$539$		0			0
$540$	−4.85520	+	1.86316i	−0.208934	+	0.0801776i
$541$		−	33.4198i		−	1.43683i	−0.695616	−	0.718414i	$-0.744868\pi$
$541$		−	33.4198i		−	1.43683i	0.695616	−	0.718414i	$-0.255132\pi$
$542$	2.61719	+	2.61719i	0.112418	+	0.112418i
$543$	22.3208	−	22.3208i	0.957879	−	0.957879i
$544$			6.50860i			0.279054i
$545$	−17.9684	−	8.00229i	−0.769683	−	0.342781i
$546$			5.18614i			0.221946i
$547$	−20.4901	+	20.4901i	−0.876093	+	0.876093i	−0.993128	−	0.117035i	$-0.962661\pi$
$547$	−20.4901	+	20.4901i	−0.876093	+	0.876093i	0.117035	+	0.993128i	$0.462661\pi$
$548$	11.4087	−	11.4087i	0.487355	−	0.487355i
$549$	3.44649			0.147093
$550$		0			0
$551$	−9.33227			−0.397568
$552$	2.11429	−	2.11429i	0.0899902	−	0.0899902i
$553$	−19.0070	+	19.0070i	−0.808261	+	0.808261i
$554$		−	1.72773i		−	0.0734042i
$555$	−11.8524	−	5.27852i	−0.503108	−	0.224061i
$556$			24.4395i			1.03647i
$557$	−13.6444	+	13.6444i	−0.578131	+	0.578131i	−0.934388	−	0.356257i	$-0.884053\pi$
$557$	−13.6444	+	13.6444i	−0.578131	+	0.578131i	0.356257	+	0.934388i	$0.384053\pi$
$558$	1.61083	+	1.61083i	0.0681919	+	0.0681919i
$559$		−	17.0306i		−	0.720317i
$560$	35.5230	−	13.6318i	1.50112	−	0.576047i
$561$		0			0
$562$	−0.107272	−	0.107272i	−0.00452499	−	0.00452499i
$563$	0.755686	+	0.755686i	0.0318484	+	0.0318484i	0.722852	−	0.691003i	$-0.242831\pi$
$563$	0.755686	+	0.755686i	0.0318484	+	0.0318484i	−0.691003	+	0.722852i	$0.742831\pi$
$564$			17.2950i			0.728252i
$565$	−20.5258	+	7.87670i	−0.863529	+	0.331375i
$566$	−1.72706			−0.0725939
$567$	−32.3826	+	32.3826i	−1.35994	+	1.35994i
$568$	1.75969	+	1.75969i	0.0738348	+	0.0738348i
$569$	−7.88940			−0.330741			−0.165371	−	0.986232i	$-0.552882\pi$
$569$	−7.88940			−0.330741			−0.165371	+	0.986232i	$0.552882\pi$
$570$	−0.473410	+	1.06300i	−0.0198290	+	0.0445242i
$571$		−	12.2418i		−	0.512302i	−0.966637	−	0.256151i	$-0.917546\pi$
$571$		−	12.2418i		−	0.512302i	0.966637	−	0.256151i	$-0.0824544\pi$
$572$		0			0
$573$	−22.1350	+	22.1350i	−0.924701	+	0.924701i
$574$	8.57287			0.357825
$575$	9.02855	+	0.475043i	0.376517	+	0.0198106i
$576$	−18.1005			−0.754186
$577$	32.8802	+	32.8802i	1.36882	+	1.36882i	0.862124	+	0.506697i	$0.169134\pi$
$577$	32.8802	+	32.8802i	1.36882	+	1.36882i	0.506697	+	0.862124i	$0.330866\pi$
$578$	0.915589	+	0.915589i	0.0380835	+	0.0380835i
$579$	−7.57022			−0.314608
$580$	−13.3807	+	30.0451i	−0.555603	+	1.24756i
$581$	21.8002			0.904426
$582$	−1.92648	+	1.92648i	−0.0798551	+	0.0798551i
$583$		0			0
$584$			6.57364i			0.272019i
$585$	14.5267	−	5.57453i	0.600603	−	0.230479i
$586$	−4.74372			−0.195961
$587$	−3.86005	−	3.86005i	−0.159321	−	0.159321i	0.622945	−	0.782266i	$-0.285936\pi$
$587$	−3.86005	−	3.86005i	−0.159321	−	0.159321i	−0.782266	+	0.622945i	$0.785936\pi$
$588$	42.1949	−	42.1949i	1.74009	−	1.74009i
$589$	6.41282			0.264236
$590$	−1.61063	−	4.19713i	−0.0663085	−	0.172793i
$591$			11.9982i			0.493541i
$592$	6.67057	+	6.67057i	0.274159	+	0.274159i
$593$	−28.4741	−	28.4741i	−1.16929	−	1.16929i	−0.982376	−	0.186913i	$-0.940152\pi$
$593$	−28.4741	−	28.4741i	−1.16929	−	1.16929i	−0.186913	−	0.982376i	$-0.559848\pi$
$594$		0			0
$595$	−12.6587	+	28.4239i	−0.518955	+	1.16527i
$596$			2.94376i			0.120581i
$597$	−12.0473	−	12.0473i	−0.493062	−	0.493062i
$598$	0.633560	−	0.633560i	0.0259082	−	0.0259082i
$599$		−	6.94646i		−	0.283825i	−0.989879	−	0.141912i	$-0.954675\pi$
$599$		−	6.94646i		−	0.283825i	0.989879	−	0.141912i	$-0.0453251\pi$
$600$	5.53111	+	6.14548i	0.225807	+	0.250888i
$601$			24.2943i			0.990985i	0.868612	+	0.495493i	$0.165012\pi$
$601$			24.2943i			0.990985i	−0.868612	+	0.495493i	$0.834988\pi$
$602$	3.42774	−	3.42774i	0.139704	−	0.139704i
$603$	1.80064	−	1.80064i	0.0733277	−	0.0733277i
$604$	−11.6757			−0.475079
$605$		0			0
$606$	−5.07582			−0.206191
$607$	2.84537	−	2.84537i	0.115490	−	0.115490i	−0.647000	−	0.762490i	$-0.723977\pi$
$607$	2.84537	−	2.84537i	0.115490	−	0.115490i	0.762490	+	0.647000i	$0.223977\pi$
$608$	1.84405	−	1.84405i	0.0747861	−	0.0747861i
$609$			78.2085i			3.16917i
$610$	0.196615	+	0.512358i	0.00796071	+	0.0207448i
$611$			10.4483i			0.422693i
$612$	10.8286	−	10.8286i	0.437719	−	0.437719i
$613$	−32.5918	−	32.5918i	−1.31637	−	1.31637i	−0.916628	−	0.399742i	$-0.869100\pi$
$613$	−32.5918	−	32.5918i	−1.31637	−	1.31637i	−0.399742	−	0.916628i	$-0.630900\pi$
$614$			1.02631i			0.0414185i
$615$	−20.2904	−	52.8747i	−0.818188	−	2.13211i
$616$		0			0
$617$	6.94955	+	6.94955i	0.279778	+	0.279778i	0.833021	−	0.553242i	$-0.186610\pi$
$617$	6.94955	+	6.94955i	0.279778	+	0.279778i	−0.553242	+	0.833021i	$0.686610\pi$
$618$	3.78459	+	3.78459i	0.152238	+	0.152238i
$619$		−	20.8324i		−	0.837324i	−0.908142	−	0.418662i	$-0.862499\pi$
$619$		−	20.8324i		−	0.837324i	0.908142	−	0.418662i	$-0.137501\pi$
$620$	9.19476	−	20.6460i	0.369270	−	0.829164i
$621$	2.13642			0.0857315
$622$	−0.0963696	+	0.0963696i	−0.00386407	+	0.00386407i
$623$	−8.13715	−	8.13715i	−0.326008	−	0.326008i
$624$	−24.9102			−0.997206
$625$	−2.62352	+	24.8620i	−0.104941	+	0.994478i
$626$		−	4.76730i		−	0.190540i
$627$		0			0
$628$	16.2744	−	16.2744i	0.649418	−	0.649418i
$629$	−7.71458			−0.307600
$630$	4.04576	+	1.80179i	0.161187	+	0.0717850i
$631$	−30.3096			−1.20661			−0.603304	−	0.797511i	$-0.706149\pi$
$631$	−30.3096			−1.20661			−0.603304	+	0.797511i	$0.706149\pi$
$632$	3.00300	+	3.00300i	0.119453	+	0.119453i
$633$	23.8361	+	23.8361i	0.947401	+	0.947401i
$634$	3.37595			0.134076
$635$	16.1428	−	6.19472i	0.640608	−	0.245830i
$636$	2.05849			0.0816246
$637$	25.4909	−	25.4909i	1.00998	−	1.00998i
$638$		0			0
$639$		−	8.80625i		−	0.348370i
$640$	−4.37833	−	11.4095i	−0.173069	−	0.450999i
$641$	−33.8177			−1.33572			−0.667859	−	0.744288i	$-0.732789\pi$
$641$	−33.8177			−1.33572			−0.667859	+	0.744288i	$0.732789\pi$
$642$	2.94769	+	2.94769i	0.116336	+	0.116336i
$643$	−8.93302	+	8.93302i	−0.352284	+	0.352284i	−0.860959	−	0.508675i	$-0.830136\pi$
$643$	−8.93302	+	8.93302i	−0.352284	+	0.352284i	0.508675	+	0.860959i	$0.330136\pi$
$644$	−15.8902			−0.626161
$645$	−29.2540	−	13.0284i	−1.15188	−	0.512991i
$646$			0.691891i			0.0272221i
$647$	6.53948	+	6.53948i	0.257094	+	0.257094i	0.823871	−	0.566777i	$-0.191810\pi$
$647$	6.53948	+	6.53948i	0.257094	+	0.257094i	−0.566777	+	0.823871i	$0.691810\pi$
$648$	5.11626	+	5.11626i	0.200986	+	0.200986i
$649$		0			0
$650$	1.65743	+	1.84153i	0.0650098	+	0.0722308i
$651$		−	53.7423i		−	2.10633i
$652$	−9.54412	−	9.54412i	−0.373777	−	0.373777i
$653$	−2.95335	+	2.95335i	−0.115573	+	0.115573i	−0.762528	−	0.646955i	$-0.776042\pi$
$653$	−2.95335	+	2.95335i	−0.115573	+	0.115573i	0.646955	+	0.762528i	$0.276042\pi$
$654$			3.66548i			0.143331i
$655$	17.8304	−	40.0365i	0.696691	−	1.56436i
$656$			41.1774i			1.60771i
$657$	16.4487	−	16.4487i	0.641725	−	0.641725i
$658$	−2.10293	+	2.10293i	−0.0819806	+	0.0819806i
$659$	16.5191			0.643494			0.321747	−	0.946826i	$-0.395730\pi$
$659$	16.5191			0.643494			0.321747	+	0.946826i	$0.395730\pi$
$660$		0			0
$661$	35.6112			1.38512			0.692558	−	0.721362i	$-0.256484\pi$
$661$	35.6112			1.38512			0.692558	+	0.721362i	$0.256484\pi$
$662$	−0.00256961	+	0.00256961i	−9.98707e−5	+	9.98707e-5i
$663$	14.4044	−	14.4044i	0.559422	−	0.559422i
$664$		−	3.44431i		−	0.133665i
$665$	11.6397	−	4.46669i	0.451369	−	0.173211i
$666$			1.09806i			0.0425491i
$667$	9.55427	−	9.55427i	0.369943	−	0.369943i
$668$	−17.3857	−	17.3857i	−0.672671	−	0.672671i
$669$		−	25.4669i		−	0.984608i
$670$	0.370407	+	0.164962i	0.0143101	+	0.00637304i
$671$		0			0
$672$	−15.4539	−	15.4539i	−0.596149	−	0.596149i
$673$	−4.53251	−	4.53251i	−0.174716	−	0.174716i	0.614332	−	0.789048i	$-0.289426\pi$
$673$	−4.53251	−	4.53251i	−0.174716	−	0.174716i	−0.789048	+	0.614332i	$0.789426\pi$
$674$			2.80974i			0.108227i
$675$	−0.310400	+	5.89940i	−0.0119473	+	0.227068i
$676$	10.2910			0.395809
$677$	−19.5446	+	19.5446i	−0.751162	+	0.751162i	−0.974696	−	0.223534i	$-0.928240\pi$
$677$	−19.5446	+	19.5446i	−0.751162	+	0.751162i	0.223534	+	0.974696i	$0.428240\pi$
$678$	2.89699	+	2.89699i	0.111258	+	0.111258i
$679$	29.1897			1.12020
$680$	4.49082	+	2.00000i	0.172215	+	0.0766965i
$681$			36.3703i			1.39371i
$682$		0			0
$683$	−5.39890	+	5.39890i	−0.206583	+	0.206583i	−0.802814	−	0.596230i	$-0.796665\pi$
$683$	−5.39890	+	5.39890i	−0.206583	+	0.206583i	0.596230	+	0.802814i	$0.296665\pi$
$684$	−6.13601			−0.234616
$685$	−6.56648	−	17.1116i	−0.250892	−	0.653800i
$686$	4.70644			0.179693
$687$	−34.2742	−	34.2742i	−1.30764	−	1.30764i
$688$	16.4642	+	16.4642i	0.627692	+	0.627692i
$689$	1.24358			0.0473766
$690$	−0.603616	−	1.57296i	−0.0229793	−	0.0598815i
$691$	−25.3818			−0.965570			−0.482785	−	0.875739i	$-0.660375\pi$
$691$	−25.3818			−0.965570			−0.482785	+	0.875739i	$0.660375\pi$
$692$	−32.8794	+	32.8794i	−1.24989	+	1.24989i
$693$		0			0
$694$		−	3.89113i		−	0.147705i
$695$	25.3613	+	11.2947i	0.962011	+	0.428434i
$696$	12.3565			0.468372
$697$	−23.8110	−	23.8110i	−0.901906	−	0.901906i
$698$	3.51731	−	3.51731i	0.133132	−	0.133132i
$699$	−43.3491			−1.63961
$700$	2.30869	−	43.8784i	0.0872601	−	1.65845i
$701$			31.0378i			1.17228i	0.810210	+	0.586140i	$0.199353\pi$
$701$			31.0378i			1.17228i	−0.810210	+	0.586140i	$0.800647\pi$
$702$	0.413978	+	0.413978i	0.0156246	+	0.0156246i
$703$	2.18573	+	2.18573i	0.0824364	+	0.0824364i
$704$		0			0
$705$	17.9474	+	7.99293i	0.675938	+	0.301031i
$706$			2.35518i			0.0886382i
$707$	38.4540	+	38.4540i	1.44621	+	1.44621i
$708$	36.9089	−	36.9089i	1.38712	−	1.38712i
$709$			49.7760i			1.86938i	0.355467	+	0.934689i	$0.384322\pi$
$709$			49.7760i			1.86938i	−0.355467	+	0.934689i	$0.615678\pi$
$710$	1.30915	−	0.502379i	0.0491314	−	0.0188539i
$711$		−	15.0284i		−	0.563607i
$712$	−1.28562	+	1.28562i	−0.0481808	+	0.0481808i
$713$	−6.56537	+	6.56537i	−0.245875	+	0.245875i
$714$	5.79835			0.216998
$715$		0			0
$716$	−38.0216			−1.42093
$717$	−27.5309	+	27.5309i	−1.02816	+	1.02816i
$718$	0.213429	−	0.213429i	0.00796510	−	0.00796510i
$719$			36.4841i			1.36063i	0.732921	+	0.680314i	$0.238157\pi$
$719$			36.4841i			1.36063i	−0.732921	+	0.680314i	$0.761843\pi$
$720$	−8.65440	+	19.4327i	−0.322530	+	0.724213i
$721$		−	57.3435i		−	2.13558i
$722$	−2.19194	+	2.19194i	−0.0815757	+	0.0815757i
$723$	22.4609	+	22.4609i	0.835330	+	0.835330i
$724$			26.5043i			0.985025i
$725$	24.9945	+	27.7708i	0.928273	+	1.03138i
$726$		0			0
$727$	−17.4528	−	17.4528i	−0.647287	−	0.647287i	0.305050	−	0.952336i	$-0.401327\pi$
$727$	−17.4528	−	17.4528i	−0.647287	−	0.647287i	−0.952336	+	0.305050i	$0.901327\pi$
$728$	−6.20757	−	6.20757i	−0.230068	−	0.230068i
$729$		−	17.2944i		−	0.640532i
$730$	3.38364	+	1.50692i	0.125234	+	0.0557734i
$731$	−19.0410			−0.704256
$732$	−4.50560	+	4.50560i	−0.166532	+	0.166532i
$733$	6.58997	+	6.58997i	0.243406	+	0.243406i	0.818258	−	0.574852i	$-0.194940\pi$
$733$	6.58997	+	6.58997i	0.243406	+	0.243406i	−0.574852	+	0.818258i	$0.694940\pi$
$734$	3.80820			0.140563
$735$	−24.2860	−	63.2869i	−0.895804	−	2.33437i
$736$			3.77583i			0.139179i
$737$		0			0
$738$	−3.38917	+	3.38917i	−0.124757	+	0.124757i
$739$	−36.2605			−1.33387			−0.666933	−	0.745118i	$-0.732393\pi$
$739$	−36.2605			−1.33387			−0.666933	+	0.745118i	$0.732393\pi$
$740$	10.1709	−	3.90302i	0.373888	−	0.143478i
$741$	−8.16227			−0.299848
$742$	0.250295	+	0.250295i	0.00918862	+	0.00918862i
$743$	29.6603	+	29.6603i	1.08813	+	1.08813i	0.995721	+	0.0924088i	$0.0294567\pi$
$743$	29.6603	+	29.6603i	1.08813	+	1.08813i	0.0924088	+	0.995721i	$0.470543\pi$
$744$	−8.49097			−0.311294
$745$	3.05479	+	1.36046i	0.111919	+	0.0498435i
$746$	1.58191			0.0579180
$747$	−8.61843	+	8.61843i	−0.315332	+	0.315332i
$748$		0			0
$749$		−	44.6630i		−	1.63195i
$750$	4.43119	−	1.43826i	0.161804	−	0.0525178i
$751$	−18.2399			−0.665584			−0.332792	−	0.943000i	$-0.607991\pi$
$751$	−18.2399			−0.665584			−0.332792	+	0.943000i	$0.607991\pi$
$752$	−10.1008	−	10.1008i	−0.368339	−	0.368339i
$753$	−10.9255	+	10.9255i	−0.398149	+	0.398149i
$754$	3.70270			0.134844
$755$	−5.39596	+	12.1162i	−0.196379	+	0.440952i
$756$		−	10.3829i		−	0.377622i
$757$	13.9623	+	13.9623i	0.507468	+	0.507468i	0.913748	−	0.406281i	$-0.133174\pi$
$757$	13.9623	+	13.9623i	0.507468	+	0.507468i	−0.406281	+	0.913748i	$0.633174\pi$
$758$	−4.06459	−	4.06459i	−0.147633	−	0.147633i
$759$		0			0
$760$	−0.705712	−	1.83901i	−0.0255989	−	0.0667080i
$761$			44.1709i			1.60119i	0.599203	+	0.800597i	$0.295484\pi$
$761$			44.1709i			1.60119i	−0.599203	+	0.800597i	$0.704516\pi$
$762$	−2.27837	−	2.27837i	−0.0825368	−	0.0825368i
$763$	27.7694	−	27.7694i	1.00532	−	1.00532i
$764$		−	26.2836i		−	0.950907i
$765$	−6.23259	−	16.2415i	−0.225340	−	0.587212i
$766$		−	4.09464i		−	0.147945i
$767$	22.2975	−	22.2975i	0.805115	−	0.805115i
$768$	22.4323	−	22.4323i	0.809454	−	0.809454i
$769$	19.2821			0.695332			0.347666	−	0.937618i	$-0.386974\pi$
$769$	19.2821			0.695332			0.347666	+	0.937618i	$0.386974\pi$
$770$		0			0
$771$	37.1229			1.33695
$772$	4.49453	−	4.49453i	0.161762	−	0.161762i
$773$	−20.3097	+	20.3097i	−0.730490	+	0.730490i	−0.970717	−	0.240227i	$-0.922778\pi$
$773$	−20.3097	+	20.3097i	−0.730490	+	0.730490i	0.240227	+	0.970717i	$0.422778\pi$
$774$			2.71022i			0.0974170i
$775$	−17.1754	−	19.0832i	−0.616959	−	0.685488i
$776$		−	4.61181i		−	0.165554i
$777$	18.3174	−	18.3174i	0.657133	−	0.657133i
$778$	−1.80409	−	1.80409i	−0.0646797	−	0.0646797i
$779$			13.4925i			0.483419i
$780$	−11.7031	+	26.2783i	−0.419039	+	0.940915i
$781$		0			0
$782$	−0.708350	−	0.708350i	−0.0253305	−	0.0253305i
$783$	6.24291	+	6.24291i	0.223103	+	0.223103i
$784$			49.2862i			1.76022i
$785$	−9.36701	−	24.4095i	−0.334323	−	0.871211i
$786$	−8.16726			−0.291317
$787$	30.2941	−	30.2941i	1.07987	−	1.07987i	0.0833458	−	0.996521i	$-0.473439\pi$
$787$	30.2941	−	30.2941i	1.07987	−	1.07987i	0.996521	−	0.0833458i	$-0.0265606\pi$
$788$	−7.12350	−	7.12350i	−0.253764	−	0.253764i
$789$	69.6380			2.47918
$790$	2.23413	−	0.857336i	0.0794868	−	0.0305027i
$791$		−	43.8948i		−	1.56072i
$792$		0			0
$793$	−2.72193	+	2.72193i	−0.0966587	+	0.0966587i
$794$	−2.02586			−0.0718952
$795$	0.951336	−	2.13614i	0.0337404	−	0.0757611i
$796$	14.3052			0.507035
$797$	−5.70581	−	5.70581i	−0.202110	−	0.202110i	0.598793	−	0.800904i	$-0.295647\pi$
$797$	−5.70581	−	5.70581i	−0.202110	−	0.202110i	−0.800904	+	0.598793i	$0.795647\pi$
$798$	−1.64282	−	1.64282i	−0.0581551	−	0.0581551i
$799$	11.6817			0.413268
$800$	−10.4264	−	0.548591i	−0.368629	−	0.0193956i
$801$	6.43383			0.227328
$802$	−2.80570	+	2.80570i	−0.0990727	+	0.0990727i
$803$		0			0
$804$			4.70796i			0.166037i
$805$	−7.34368	+	16.4896i	−0.258831	+	0.581181i
$806$	−2.54437			−0.0896217
$807$	7.12486	+	7.12486i	0.250807	+	0.250807i
$808$	6.07552	−	6.07552i	0.213736	−	0.213736i
$809$	25.7993			0.907054			0.453527	−	0.891243i	$-0.350166\pi$
$809$	25.7993			0.907054			0.453527	+	0.891243i	$0.350166\pi$
$810$	3.80632	−	1.46066i	0.133740	−	0.0513223i
$811$		−	5.32931i		−	0.187137i	−0.995613	−	0.0935687i	$-0.970173\pi$
$811$		−	5.32931i		−	0.187137i	0.995613	−	0.0935687i	$-0.0298275\pi$
$812$	−46.4333	−	46.4333i	−1.62949	−	1.62949i
$813$	34.5198	+	34.5198i	1.21066	+	1.21066i
$814$		0			0
$815$	−14.3150	+	5.49329i	−0.501431	+	0.192422i
$816$			27.8508i			0.974972i
$817$	5.39479	+	5.39479i	0.188740	+	0.188740i
$818$	−0.354250	+	0.354250i	−0.0123861	+	0.0123861i
$819$			31.0654i			1.08551i
$820$	43.4390	+	19.3457i	1.51696	+	0.675580i
$821$			1.07893i			0.0376548i	0.999823	+	0.0188274i	$0.00599330\pi$
$821$			1.07893i			0.0376548i	−0.999823	+	0.0188274i	$0.994007\pi$
$822$	−2.41511	+	2.41511i	−0.0842365	+	0.0842365i
$823$	−28.2971	+	28.2971i	−0.986374	+	0.986374i	−0.999908	−	0.0135342i	$-0.995692\pi$
$823$	−28.2971	+	28.2971i	−0.986374	+	0.986374i	0.0135342	+	0.999908i	$0.495692\pi$
$824$	−9.05995			−0.315618
$825$		0			0
$826$	8.97561			0.312301
$827$	2.04606	−	2.04606i	0.0711485	−	0.0711485i	−0.670637	−	0.741786i	$-0.733979\pi$
$827$	2.04606	−	2.04606i	0.0711485	−	0.0711485i	0.741786	+	0.670637i	$0.233979\pi$
$828$	6.28198	−	6.28198i	0.218314	−	0.218314i
$829$		−	40.5134i		−	1.40709i	−0.710651	−	0.703545i	$-0.751600\pi$
$829$		−	40.5134i		−	1.40709i	0.710651	−	0.703545i	$-0.248400\pi$
$830$	−1.77289	−	0.789561i	−0.0615379	−	0.0274061i
$831$		−	22.7882i		−	0.790512i
$832$	14.2952	−	14.2952i	0.495597	−	0.495597i
$833$	−28.5000	−	28.5000i	−0.987465	−	0.987465i
$834$		−	5.17359i		−	0.179147i
$835$	−26.0762	+	10.0066i	−0.902406	+	0.346294i
$836$		0			0
$837$	−4.28992	−	4.28992i	−0.148281	−	0.148281i
$838$	−3.11240	−	3.11240i	−0.107516	−	0.107516i
$839$		−	42.0635i		−	1.45219i	−0.687593	−	0.726096i	$-0.741333\pi$
$839$		−	42.0635i		−	1.45219i	0.687593	−	0.726096i	$-0.258667\pi$
$840$	−15.4117	+	5.91417i	−0.531755	+	0.204058i
$841$	26.8378			0.925440
$842$	3.59594	−	3.59594i	0.123924	−	0.123924i
$843$	−1.41488	−	1.41488i	−0.0487310	−	0.0487310i
$844$	−28.3036			−0.974250
$845$	4.75602	−	10.6792i	0.163612	−	0.367376i
$846$		−	1.66273i		−	0.0571658i
$847$		0			0
$848$	−1.20222	+	1.20222i	−0.0412845	+	0.0412845i
$849$	−22.7794			−0.781785
$850$	2.05892	−	1.85308i	0.0706203	−	0.0635603i
$851$	−4.47545			−0.153417
$852$	11.5124	+	11.5124i	0.394410	+	0.394410i
$853$	−19.2871	−	19.2871i	−0.660379	−	0.660379i	0.295091	−	0.955469i	$-0.404650\pi$
$853$	−19.2871	−	19.2871i	−0.660379	−	0.660379i	−0.955469	+	0.295091i	$0.904650\pi$
$854$	−1.09568			−0.0374936
$855$	−2.83577	+	6.36746i	−0.0969812	+	0.217763i
$856$	−7.05651			−0.241186
$857$	−23.4018	+	23.4018i	−0.799391	+	0.799391i	−0.982999	−	0.183608i	$-0.941222\pi$
$857$	−23.4018	+	23.4018i	−0.799391	+	0.799391i	0.183608	+	0.982999i	$0.441222\pi$
$858$		0			0
$859$			31.9233i			1.08921i	0.838693	+	0.544605i	$0.183321\pi$
$859$			31.9233i			1.08921i	−0.838693	+	0.544605i	$0.816679\pi$
$860$	25.1035	−	9.63336i	0.856024	−	0.328495i
$861$	113.073			3.85352
$862$	−4.25901	−	4.25901i	−0.145062	−	0.145062i
$863$	20.4630	−	20.4630i	0.696569	−	0.696569i	−0.267100	−	0.963669i	$-0.586065\pi$
$863$	20.4630	−	20.4630i	0.696569	−	0.696569i	0.963669	+	0.267100i	$0.0860654\pi$
$864$	−2.46719			−0.0839355
$865$	18.9243	+	49.3149i	0.643447	+	1.67676i
$866$			0.474306i			0.0161176i
$867$	12.0763	+	12.0763i	0.410132	+	0.410132i
$868$	31.9074	+	31.9074i	1.08301	+	1.08301i
$869$		0			0
$870$	2.83256	−	6.36025i	0.0960326	−	0.215633i
$871$			2.84418i			0.0963714i
$872$	−4.38740	−	4.38740i	−0.148576	−	0.148576i
$873$	−11.5398	+	11.5398i	−0.390562	+	0.390562i
$874$			0.401386i			0.0135771i
$875$	−44.4665	−	22.6742i	−1.50324	−	0.766529i
$876$			43.0068i			1.45307i
$877$	−1.40135	+	1.40135i	−0.0473204	+	0.0473204i	−0.730371	−	0.683051i	$-0.760653\pi$
$877$	−1.40135	+	1.40135i	−0.0473204	+	0.0473204i	0.683051	+	0.730371i	$0.260653\pi$
$878$	−3.15979	+	3.15979i	−0.106638	+	0.106638i
$879$	−62.5680			−2.11037
$880$		0			0
$881$	25.3007			0.852401			0.426201	−	0.904629i	$-0.359852\pi$
$881$	25.3007			0.852401			0.426201	+	0.904629i	$0.359852\pi$
$882$	−4.05658	+	4.05658i	−0.136592	+	0.136592i
$883$	2.89490	−	2.89490i	0.0974212	−	0.0974212i	−0.656716	−	0.754138i	$-0.728055\pi$
$883$	2.89490	−	2.89490i	0.0974212	−	0.0974212i	0.754138	+	0.656716i	$0.228055\pi$
$884$			17.1042i			0.575275i
$885$	−21.2436	−	55.3586i	−0.714096	−	1.86086i
$886$		−	2.22485i		−	0.0747452i
$887$	14.1709	−	14.1709i	0.475813	−	0.475813i	−0.427977	−	0.903790i	$-0.640773\pi$
$887$	14.1709	−	14.1709i	0.475813	−	0.475813i	0.903790	+	0.427977i	$0.140773\pi$
$888$	−2.89404	−	2.89404i	−0.0971178	−	0.0971178i
$889$			34.5216i			1.15782i
$890$	0.367037	+	0.956460i	0.0123031	+	0.0320606i
$891$		0			0
$892$	15.1200	+	15.1200i	0.506256	+	0.506256i
$893$	−3.30971	−	3.30971i	−0.110755	−	0.110755i
$894$		−	0.623164i		−	0.0208417i
$895$	−17.5717	+	39.4558i	−0.587359	+	1.31886i
$896$	24.3993			0.815123
$897$	8.35644	−	8.35644i	0.279013	−	0.279013i
$898$	−1.53327	−	1.53327i	−0.0511659	−	0.0511659i
$899$	−38.3698			−1.27971
$900$	16.4340	+	18.2594i	0.547801	+	0.608648i
$901$		−	1.39038i		−	0.0463203i
$902$		0			0
$903$	45.2107	−	45.2107i	1.50452	−	1.50452i
$904$	−6.93513			−0.230659
$905$	27.5040	+	12.2490i	0.914265	+	0.407171i
$906$	2.47164			0.0821147
$907$	8.81403	+	8.81403i	0.292665	+	0.292665i	0.838132	−	0.545467i	$-0.183648\pi$
$907$	8.81403	+	8.81403i	0.292665	+	0.292665i	−0.545467	+	0.838132i	$0.683648\pi$
$908$	−21.5935	−	21.5935i	−0.716604	−	0.716604i
$909$	−30.4046			−1.00846
$910$	−4.61822	+	1.77222i	−0.153092	+	0.0587485i
$911$	31.0467			1.02862			0.514311	−	0.857604i	$-0.328048\pi$
$911$	31.0467			1.02862			0.514311	+	0.857604i	$0.328048\pi$
$912$	7.89082	−	7.89082i	0.261291	−	0.261291i
$913$		0			0
$914$			5.36970i			0.177614i
$915$	2.59328	+	6.75783i	0.0857313	+	0.223407i
$916$	40.6980			1.34470
$917$	61.8745	+	61.8745i	2.04328	+	2.04328i
$918$	0.462847	−	0.462847i	0.0152762	−	0.0152762i
$919$	−22.0347			−0.726859			−0.363429	−	0.931622i	$-0.618394\pi$
$919$	−22.0347			−0.726859			−0.363429	+	0.931622i	$0.618394\pi$
$920$	2.60526	+	1.16026i	0.0858928	+	0.0382526i
$921$			13.5367i			0.446049i
$922$	2.10577	+	2.10577i	0.0693497	+	0.0693497i
$923$	6.95491	+	6.95491i	0.228924	+	0.228924i
$924$		0			0
$925$	0.650239	−	12.3583i	0.0213797	−	0.406338i
$926$			3.95962i			0.130121i
$927$	22.6700	+	22.6700i	0.744580	+	0.744580i
$928$	−11.0335	+	11.0335i	−0.362193	+	0.362193i
$929$			19.8981i			0.652835i	0.945226	+	0.326417i	$0.105841\pi$
$929$			19.8981i			0.652835i	−0.945226	+	0.326417i	$0.894159\pi$
$930$	−1.94644	+	4.37055i	−0.0638262	+	0.143316i
$931$			16.1495i			0.529278i
$932$	25.7369	−	25.7369i	0.843040	−	0.843040i
$933$	−1.27108	+	1.27108i	−0.0416133	+	0.0416133i
$934$	5.74571			0.188005
$935$		0			0
$936$	4.90816			0.160428
$937$	−8.24405	+	8.24405i	−0.269321	+	0.269321i	−0.828827	−	0.559505i	$-0.810991\pi$
$937$	−8.24405	+	8.24405i	−0.269321	+	0.269321i	0.559505	+	0.828827i	$0.310991\pi$
$938$	−0.572447	+	0.572447i	−0.0186911	+	0.0186911i
$939$		−	62.8790i		−	2.05198i
$940$	−15.4011	+	5.91009i	−0.502328	+	0.192766i
$941$		−	0.127366i		−	0.00415202i	−0.999998	−	0.00207601i	$-0.999339\pi$
$941$		−	0.127366i		−	0.00415202i	0.999998	−	0.00207601i	$-0.000660816\pi$
$942$	−3.44512	+	3.44512i	−0.112248	+	0.112248i
$943$	−13.8135	−	13.8135i	−0.449829	−	0.449829i
$944$			43.1118i			1.40317i
$945$	−10.7745	−	4.79847i	−0.350496	−	0.156094i
$946$		0			0
$947$	41.6247	+	41.6247i	1.35262	+	1.35262i	0.882718	+	0.469903i	$0.155711\pi$
$947$	41.6247	+	41.6247i	1.35262	+	1.35262i	0.469903	+	0.882718i	$0.344289\pi$
$948$	19.6466	+	19.6466i	0.638092	+	0.638092i
$949$			25.9814i			0.843391i
$950$	−1.10837	−	0.0583174i	−0.0359602	−	0.00189207i
$951$	44.5276			1.44391
$952$	−6.94035	+	6.94035i	−0.224938	+	0.224938i
$953$	29.8434	+	29.8434i	0.966723	+	0.966723i	0.999464	−	0.0327407i	$-0.0104235\pi$
$953$	29.8434	+	29.8434i	0.966723	+	0.966723i	−0.0327407	+	0.999464i	$0.510424\pi$
$954$	−0.197902			−0.00640730
$955$	−27.2750	−	12.1470i	−0.882598	−	0.393068i
$956$		−	32.6909i		−	1.05730i
$957$		0			0
$958$	−2.39731	+	2.39731i	−0.0774536	+	0.0774536i
$959$	36.5933			1.18166
$960$	−13.6196	−	35.4911i	−0.439569	−	1.14547i
$961$	−4.63353			−0.149469
$962$	−0.867218	−	0.867218i	−0.0279602	−	0.0279602i
$963$	17.6569	+	17.6569i	0.568987	+	0.568987i
$964$	−26.6706			−0.859002
$965$	−2.58691	−	6.74122i	−0.0832756	−	0.217008i
$966$	3.36379			0.108228
$967$	−1.28318	+	1.28318i	−0.0412643	+	0.0412643i	−0.727438	−	0.686174i	$-0.759289\pi$
$967$	−1.28318	+	1.28318i	−0.0412643	+	0.0412643i	0.686174	+	0.727438i	$0.259289\pi$
$968$		0			0
$969$			9.12579i			0.293163i
$970$	−2.37383	−	1.05719i	−0.0762192	−	0.0339444i
$971$	−35.0831			−1.12587			−0.562934	−	0.826502i	$-0.690328\pi$
$971$	−35.0831			−1.12587			−0.562934	+	0.826502i	$0.690328\pi$
$972$	28.5387	+	28.5387i	0.915378	+	0.915378i
$973$	−39.1947	+	39.1947i	−1.25653	+	1.25653i
$974$	−4.90250			−0.157086
$975$	21.8609	+	24.2891i	0.700110	+	0.777875i
$976$		−	5.26282i		−	0.168459i
$977$	−36.6633	−	36.6633i	−1.17296	−	1.17296i	−0.981500	−	0.191461i	$-0.938677\pi$
$977$	−36.6633	−	36.6633i	−1.17296	−	1.17296i	−0.191461	−	0.981500i	$-0.561323\pi$
$978$	2.02039	+	2.02039i	0.0646051	+	0.0646051i
$979$		0			0
$980$	51.9931	+	23.1553i	1.66086	+	0.739669i
$981$			21.9565i			0.701017i
$982$	−4.69235	−	4.69235i	−0.149739	−	0.149739i
$983$	0.552530	−	0.552530i	0.0176230	−	0.0176230i	−0.698240	−	0.715863i	$-0.746033\pi$
$983$	0.552530	−	0.552530i	0.0176230	−	0.0176230i	0.715863	+	0.698240i	$0.246033\pi$
$984$		−	17.8649i		−	0.569513i
$985$	−10.6843	+	4.10006i	−0.340431	+	0.130639i
$986$		−	4.13979i		−	0.131838i
$987$	−27.7368	+	27.7368i	−0.882874	+	0.882874i
$988$	4.84604	−	4.84604i	0.154173	−	0.154173i
$989$	−11.0462			−0.351250
$990$		0			0
$991$	−27.7886			−0.882735			−0.441368	−	0.897326i	$-0.645507\pi$
$991$	−27.7886			−0.882735			−0.441368	+	0.897326i	$0.645507\pi$
$992$	7.58186	−	7.58186i	0.240724	−	0.240724i
$993$	−0.0338922	+	0.0338922i	−0.00107554	+	0.00107554i
$994$			2.79963i			0.0887987i
$995$	6.61117	−	14.8448i	0.209588	−	0.470612i
$996$		−	22.5338i		−	0.714011i
$997$	−33.4795	+	33.4795i	−1.06031	+	1.06031i	−0.0622463	+	0.998061i	$0.519826\pi$
$997$	−33.4795	+	33.4795i	−1.06031	+	1.06031i	−0.998061	+	0.0622463i	$0.980174\pi$
$998$	1.77435	+	1.77435i	0.0561660	+	0.0561660i
$999$		−	2.92433i		−	0.0925217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.a.362.6	yes	20
5.3	odd	4	inner	605.2.e.a.483.5	yes	20
11.2	odd	10		605.2.m.f.282.6		80
11.3	even	5		605.2.m.f.112.5		80
11.4	even	5		605.2.m.f.457.6		80
11.5	even	5		605.2.m.f.602.5		80
11.6	odd	10		605.2.m.f.602.6		80
11.7	odd	10		605.2.m.f.457.5		80
11.8	odd	10		605.2.m.f.112.6		80
11.9	even	5		605.2.m.f.282.5		80
11.10	odd	2	inner	605.2.e.a.362.5	✓	20
55.3	odd	20		605.2.m.f.233.5		80
55.8	even	20		605.2.m.f.233.6		80
55.13	even	20		605.2.m.f.403.5		80
55.18	even	20		605.2.m.f.578.5		80
55.28	even	20		605.2.m.f.118.5		80
55.38	odd	20		605.2.m.f.118.6		80
55.43	even	4	inner	605.2.e.a.483.6	yes	20
55.48	odd	20		605.2.m.f.578.6		80
55.53	odd	20		605.2.m.f.403.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.a.362.5	✓	20	11.10	odd	2	inner
605.2.e.a.362.6	yes	20	1.1	even	1	trivial
605.2.e.a.483.5	yes	20	5.3	odd	4	inner
605.2.e.a.483.6	yes	20	55.43	even	4	inner
605.2.m.f.112.5		80	11.3	even	5
605.2.m.f.112.6		80	11.8	odd	10
605.2.m.f.118.5		80	55.28	even	20
605.2.m.f.118.6		80	55.38	odd	20
605.2.m.f.233.5		80	55.3	odd	20
605.2.m.f.233.6		80	55.8	even	20
605.2.m.f.282.5		80	11.9	even	5
605.2.m.f.282.6		80	11.2	odd	10
605.2.m.f.403.5		80	55.13	even	20
605.2.m.f.403.6		80	55.53	odd	20
605.2.m.f.457.5		80	11.7	odd	10
605.2.m.f.457.6		80	11.4	even	5
605.2.m.f.578.5		80	55.18	even	20
605.2.m.f.578.6		80	55.48	odd	20
605.2.m.f.602.5		80	11.5	even	5
605.2.m.f.602.6		80	11.6	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.125683 - 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} -0.416692i q^{6} +(-3.15683 + 3.15683i) q^{7} +(0.498761 + 0.498761i) q^{8} -2.49602i q^{9} +O(q^{10})\)	\(q+(0.125683 - 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} -0.416692i q^{6} +(-3.15683 + 3.15683i) q^{7} +(0.498761 + 0.498761i) q^{8} -2.49602i q^{9} +(0.371061 - 0.142393i) q^{10} +(3.26305 + 3.26305i) q^{12} +(1.97128 + 1.97128i) q^{13} +0.793518i q^{14} +(4.89416 - 1.87811i) q^{15} -3.81144 q^{16} +(2.20398 - 2.20398i) q^{17} +(-0.313707 - 0.313707i) q^{18} -1.24889 q^{19} +(-1.79067 + 4.02078i) q^{20} +10.4662i q^{21} +(1.27860 - 1.27860i) q^{23} +1.65360 q^{24} +(3.34488 + 3.71642i) q^{25} +0.495512 q^{26} +(0.835455 + 0.835455i) q^{27} +(-6.21392 - 6.21392i) q^{28} +7.47247 q^{29} +(0.379066 - 0.851158i) q^{30} -5.13483 q^{31} +(-1.47655 + 1.47655i) q^{32} -0.554006i q^{34} +(-9.32008 + 3.57654i) q^{35} +4.91318 q^{36} +(-1.75014 - 1.75014i) q^{37} +(-0.156964 + 0.156964i) q^{38} +6.53563 q^{39} +(0.565073 + 1.47252i) q^{40} -10.8036i q^{41} +(1.31542 + 1.31542i) q^{42} +(-4.31967 - 4.31967i) q^{43} +(2.27064 - 5.09851i) q^{45} -0.321395i q^{46} +(2.65013 + 2.65013i) q^{47} +(-6.31828 + 6.31828i) q^{48} -12.9311i q^{49} +(0.887484 + 0.0466955i) q^{50} -7.30714i q^{51} +(-3.88028 + 3.88028i) q^{52} +(0.315424 - 0.315424i) q^{53} +0.210005 q^{54} -3.14900 q^{56} +(-2.07030 + 2.07030i) q^{57} +(0.939161 - 0.939161i) q^{58} -11.3112i q^{59} +(3.69689 + 9.63370i) q^{60} +1.38079i q^{61} +(-0.645360 + 0.645360i) q^{62} +(7.87950 + 7.87950i) q^{63} -7.25173i q^{64} +(2.23337 + 5.81993i) q^{65} +(0.721404 + 0.721404i) q^{67} +(4.33834 + 4.33834i) q^{68} -4.23909i q^{69} +(-0.721865 + 1.62088i) q^{70} +3.52812 q^{71} +(1.24492 - 1.24492i) q^{72} +(6.58997 + 6.58997i) q^{73} -0.439926 q^{74} +(11.7056 + 0.615897i) q^{75} -2.45832i q^{76} +(0.821417 - 0.821417i) q^{78} +6.02093 q^{79} +(-7.78547 - 3.46728i) q^{80} +10.2579 q^{81} +(-1.35783 - 1.35783i) q^{82} +(-3.45287 - 3.45287i) q^{83} -20.6018 q^{84} +(6.50695 - 2.49701i) q^{85} -1.08582 q^{86} +(12.3872 - 12.3872i) q^{87} +2.57764i q^{89} +(-0.355415 - 0.926175i) q^{90} -12.4460 q^{91} +(2.51680 + 2.51680i) q^{92} +(-8.51207 + 8.51207i) q^{93} +0.666152 q^{94} +(-2.55105 - 1.13612i) q^{95} +4.89541i q^{96} +(-4.62327 - 4.62327i) q^{97} +(-1.62522 - 1.62522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^3 + 4 * q^5	\( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^5 - 16 * q^12 + 16 * q^15 + 12 * q^16 + 16 * q^20 + 12 * q^23 + 16 * q^25 + 56 * q^26 - 20 * q^27 - 16 * q^31 - 20 * q^36 - 72 * q^37 - 32 * q^38 - 32 * q^42 - 28 * q^45 + 16 * q^47 - 104 * q^48 - 52 * q^53 - 32 * q^56 + 12 * q^58 + 112 * q^60 + 28 * q^67 + 104 * q^70 + 24 * q^71 + 64 * q^75 + 104 * q^78 + 44 * q^80 + 100 * q^81 - 124 * q^82 + 128 * q^86 - 16 * q^92 - 132 * q^93 + 32 * q^97

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