LMFDB - Embedded newform 784.2.m.k.197.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.10
Character	$\chi$	$=$	784.197
Dual form			784.2.m.k.589.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +O(q^{10})$	\(q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +(0.307296 + 1.37014i) q^{10} +(-1.38191 - 1.38191i) q^{11} +(3.80628 + 1.36417i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(-2.54083 + 3.08937i) q^{16} +5.67771 q^{17} +(0.822907 - 1.29876i) q^{18} +(0.451363 - 0.451363i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +6.84381i q^{23} +(3.51444 + 4.51068i) q^{24} -4.01414i q^{25} +(4.10432 - 0.920521i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(2.39797 + 1.51938i) q^{30} -7.89385 q^{31} +(-5.37368 + 1.76737i) q^{32} -3.95101 q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(-7.03159 - 7.03159i) q^{37} +(0.880843 - 0.197556i) q^{38} -6.01306i q^{39} +(-2.21532 + 1.72604i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(1.31872 - 3.67947i) q^{44} +(0.763301 - 0.763301i) q^{45} +(-5.18019 + 8.17564i) q^{46} -0.289185 q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(8.11653 - 8.11653i) q^{51} +(5.59980 + 2.00697i) q^{52} +(-5.58365 - 5.58365i) q^{53} +(1.19684 + 5.33633i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(-0.404540 + 0.0907305i) q^{58} +(-9.84923 - 9.84923i) q^{59} +(1.71458 + 3.63012i) q^{60} +(2.64783 - 2.64783i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +2.95319 q^{65} +(-4.71989 - 2.99058i) q^{66} +(-7.35474 + 7.35474i) q^{67} +(4.84966 + 10.2677i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(3.05160 + 0.378828i) q^{72} +0.358849i q^{73} +(-3.07764 - 13.7223i) q^{74} +(-5.73839 - 5.73839i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +7.69906 q^{79} +(-3.95290 + 0.385121i) q^{80} +11.0796 q^{81} +(1.81812 - 2.86946i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(1.60013 + 7.13449i) q^{86} +0.592673i q^{87} +(4.36039 - 3.39734i) q^{88} -17.5887i q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(-11.2846 + 11.2846i) q^{93} +(-0.345462 - 0.218889i) q^{94} +0.633794 q^{95} +(-5.15536 + 10.2084i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.19460	+	0.756916i	0.844713	+	0.535220i
$2$	1.19460	+	0.756916i	0.844713	+	0.535220i
$3$	1.42954	−	1.42954i	0.825347	−	0.825347i	−0.161522	−	0.986869i	$-0.551640\pi$
$3$	1.42954	−	1.42954i	0.825347	−	0.825347i	0.986869	+	0.161522i	$0.0516403\pi$
$4$	0.854157	+	1.80843i	0.427079	+	0.904214i
$5$	0.702089	+	0.702089i	0.313984	+	0.313984i	0.846451	−	0.532467i	$-0.178735\pi$
$5$	0.702089	+	0.702089i	0.313984	+	0.313984i	−0.532467	+	0.846451i	$0.678735\pi$
$6$	2.78978	−	0.625694i	1.13892	−	0.255439i
$7$		0			0
$7$		0			0
$8$	−0.348448	+	2.80688i	−0.123195	+	0.992382i
$9$		−	1.08719i		−	0.362395i
$10$	0.307296	+	1.37014i	0.0971756	+	0.433277i
$11$	−1.38191	−	1.38191i	−0.416663	−	0.416663i	0.467389	−	0.884052i	$-0.345195\pi$
$11$	−1.38191	−	1.38191i	−0.416663	−	0.416663i	−0.884052	+	0.467389i	$0.845195\pi$
$12$	3.80628	+	1.36417i	1.09878	+	0.393803i
$13$	2.10314	−	2.10314i	0.583307	−	0.583307i	−0.352504	−	0.935810i	$-0.614670\pi$
$13$	2.10314	−	2.10314i	0.583307	−	0.583307i	0.935810	+	0.352504i	$0.114670\pi$
$14$		0			0
$15$	2.00733			0.518291
$16$	−2.54083	+	3.08937i	−0.635208	+	0.772341i
$17$	5.67771			1.37705			0.688523	−	0.725214i	$-0.258259\pi$
$17$	5.67771			1.37705			0.688523	+	0.725214i	$0.258259\pi$
$18$	0.822907	−	1.29876i	0.193961	−	0.306120i
$19$	0.451363	−	0.451363i	0.103550	−	0.103550i	−0.653434	−	0.756984i	$-0.726672\pi$
$19$	0.451363	−	0.451363i	0.103550	−	0.103550i	0.756984	+	0.653434i	$0.226672\pi$
$20$	−0.669984	+	1.86937i	−0.149813	+	0.418005i
$21$		0			0
$22$	−0.604848	−	2.69683i	−0.128954	−	0.574967i
$23$			6.84381i			1.42703i	0.700639	+	0.713516i	$0.252899\pi$
$23$			6.84381i			1.42703i	−0.700639	+	0.713516i	$0.747101\pi$
$24$	3.51444	+	4.51068i	0.717381	+	0.920738i
$25$		−	4.01414i		−	0.802828i
$26$	4.10432	−	0.920521i	0.804924	−	0.180529i
$27$	2.73445	+	2.73445i	0.526245	+	0.526245i
$28$		0			0
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	−0.726092	−	0.687598i	$-0.758665\pi$
$29$	−0.207295	+	0.207295i	−0.0384937	+	0.0384937i	0.687598	+	0.726092i	$0.258665\pi$
$30$	2.39797	+	1.51938i	0.437807	+	0.277400i
$31$	−7.89385			−1.41778			−0.708889	−	0.705320i	$-0.750803\pi$
$31$	−7.89385			−1.41778			−0.708889	+	0.705320i	$0.750803\pi$
$32$	−5.37368	+	1.76737i	−0.949941	+	0.312431i
$33$	−3.95101			−0.687783
$34$	6.78261	+	4.29755i	1.16321	+	0.737023i
$35$		0			0
$36$	1.96610	−	0.928627i	0.327683	−	0.154771i
$37$	−7.03159	−	7.03159i	−1.15599	−	1.15599i	−0.985331	−	0.170655i	$-0.945412\pi$
$37$	−7.03159	−	7.03159i	−1.15599	−	1.15599i	−0.170655	−	0.985331i	$-0.554588\pi$
$38$	0.880843	−	0.197556i	0.142892	−	0.0320478i
$39$		−	6.01306i		−	0.962861i
$40$	−2.21532	+	1.72604i	−0.350273	+	0.272911i
$41$		−	2.40202i		−	0.375132i	−0.982252	−	0.187566i	$-0.939940\pi$
$41$		−	2.40202i		−	0.375132i	0.982252	−	0.187566i	$-0.0600599\pi$
$42$		0			0
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	0.928599	−	0.371085i	$-0.121014\pi$
$43$	3.65586	+	3.65586i	0.557514	+	0.557514i	−0.371085	+	0.928599i	$0.621014\pi$
$44$	1.31872	−	3.67947i	0.198805	−	0.554700i
$45$	0.763301	−	0.763301i	0.113786	−	0.113786i
$46$	−5.18019	+	8.17564i	−0.763777	+	1.20543i
$47$	−0.289185			−0.0421820			−0.0210910	−	0.999778i	$-0.506714\pi$
$47$	−0.289185			−0.0421820			−0.0210910	+	0.999778i	$0.506714\pi$
$48$	0.784155	+	8.04861i	0.113183	+	1.16172i
$49$		0			0
$50$	3.03837	−	4.79531i	0.429690	−	0.678159i
$51$	8.11653	−	8.11653i	1.13654	−	1.13654i
$52$	5.59980	+	2.00697i	0.776552	+	0.278316i
$53$	−5.58365	−	5.58365i	−0.766973	−	0.766973i	0.210599	−	0.977572i	$-0.432458\pi$
$53$	−5.58365	−	5.58365i	−0.766973	−	0.766973i	−0.977572	+	0.210599i	$0.932458\pi$
$54$	1.19684	+	5.33633i	0.162869	+	0.726183i
$55$		−	1.94045i		−	0.261651i
$56$		0			0
$57$		−	1.29048i		−	0.170929i
$58$	−0.404540	+	0.0907305i	−0.0531187	+	0.0119135i
$59$	−9.84923	−	9.84923i	−1.28226	−	1.28226i	−0.939378	−	0.342883i	$-0.888597\pi$
$59$	−9.84923	−	9.84923i	−1.28226	−	1.28226i	−0.342883	−	0.939378i	$-0.611403\pi$
$60$	1.71458	+	3.63012i	0.221351	+	0.468646i
$61$	2.64783	−	2.64783i	0.339020	−	0.339020i	−0.516978	−	0.855999i	$-0.672943\pi$
$61$	2.64783	−	2.64783i	0.339020	−	0.339020i	0.855999	+	0.516978i	$0.172943\pi$
$62$	−9.43003	−	5.97498i	−1.19761	−	0.758823i
$63$		0			0
$64$	−7.75717	−	1.95611i	−0.969646	−	0.244513i
$65$	2.95319			0.366298
$66$	−4.71989	−	2.99058i	−0.580979	−	0.368115i
$67$	−7.35474	+	7.35474i	−0.898525	+	0.898525i	−0.995306	−	0.0967807i	$-0.969145\pi$
$67$	−7.35474	+	7.35474i	−0.898525	+	0.898525i	0.0967807	+	0.995306i	$0.469145\pi$
$68$	4.84966	+	10.2677i	0.588107	+	1.24515i
$69$	9.78352	+	9.78352i	1.17780	+	1.17780i
$70$		0			0
$71$			11.5947i			1.37603i	0.725695	+	0.688017i	$0.241518\pi$
$71$			11.5947i			1.37603i	−0.725695	+	0.688017i	$0.758482\pi$
$72$	3.05160	+	0.378828i	0.359634	+	0.0446453i
$73$			0.358849i			0.0420001i	0.999779	+	0.0210000i	$0.00668501\pi$
$73$			0.358849i			0.0420001i	−0.999779	+	0.0210000i	$0.993315\pi$
$74$	−3.07764	−	13.7223i	−0.357769	−	1.59518i
$75$	−5.73839	−	5.73839i	−0.662612	−	0.662612i
$76$	1.20179	+	0.430722i	0.137855	+	0.0494073i
$77$		0			0
$78$	4.55138	−	7.18323i	0.515342	−	0.813341i
$79$	7.69906			0.866211			0.433106	−	0.901343i	$-0.357418\pi$
$79$	7.69906			0.866211			0.433106	+	0.901343i	$0.357418\pi$
$80$	−3.95290	+	0.385121i	−0.441948	+	0.0430578i
$81$	11.0796			1.23106
$82$	1.81812	−	2.86946i	0.200778	−	0.316879i
$83$	0.424001	−	0.424001i	0.0465402	−	0.0465402i	−0.683454	−	0.729994i	$-0.739523\pi$
$83$	0.424001	−	0.424001i	0.0465402	−	0.0465402i	0.729994	+	0.683454i	$0.239523\pi$
$84$		0			0
$85$	3.98626	+	3.98626i	0.432371	+	0.432371i
$86$	1.60013	+	7.13449i	0.172546	+	0.769332i
$87$			0.592673i			0.0635412i
$88$	4.36039	−	3.39734i	0.464820	−	0.362158i
$89$		−	17.5887i		−	1.86440i	−0.361940	−	0.932201i	$-0.617885\pi$
$89$		−	17.5887i		−	1.86440i	0.361940	−	0.932201i	$-0.382115\pi$
$90$	1.48960	−	0.334088i	0.157017	−	0.0352160i
$91$		0			0
$92$	−12.3765	+	5.84569i	−1.29034	+	0.609455i
$93$	−11.2846	+	11.2846i	−1.17016	+	1.17016i
$94$	−0.345462	−	0.218889i	−0.0356317	−	0.0225767i
$95$	0.633794			0.0650259
$96$	−5.15536	+	10.2084i	−0.526167	+	1.04189i
$97$	−12.2678			−1.24560			−0.622802	−	0.782379i	$-0.714006\pi$
$97$	−12.2678			−1.24560			−0.622802	+	0.782379i	$0.714006\pi$
$98$		0			0
$99$	−1.50240	+	1.50240i	−0.150997	+	0.150997i
$100$	7.25929	−	3.42871i	0.725929	−	0.342871i
$101$	0.855455	+	0.855455i	0.0851209	+	0.0851209i	0.748385	−	0.663264i	$-0.230829\pi$
$101$	0.855455	+	0.855455i	0.0851209	+	0.0851209i	−0.663264	+	0.748385i	$0.730829\pi$
$102$	15.8396	−	3.55251i	1.56835	−	0.351751i
$103$			5.84488i			0.575913i	0.957643	+	0.287956i	$0.0929759\pi$
$103$			5.84488i			0.575913i	−0.957643	+	0.287956i	$0.907024\pi$
$104$	5.17043	+	6.63611i	0.507003	+	0.650724i
$105$		0			0
$106$	−2.44390	−	10.8966i	−0.237372	−	1.05837i
$107$	−2.65363	−	2.65363i	−0.256536	−	0.256536i	0.567108	−	0.823644i	$-0.308062\pi$
$107$	−2.65363	−	2.65363i	−0.256536	−	0.256536i	−0.823644	+	0.567108i	$0.808062\pi$
$108$	−2.60941	+	7.28071i	−0.251090	+	0.700587i
$109$	−7.08373	+	7.08373i	−0.678499	+	0.678499i	−0.959660	−	0.281162i	$-0.909280\pi$
$109$	−7.08373	+	7.08373i	−0.678499	+	0.678499i	0.281162	+	0.959660i	$0.409280\pi$
$110$	1.46876	−	2.31807i	0.140041	−	0.221020i
$111$	−20.1039			−1.90818
$112$		0			0
$113$	5.07461			0.477379			0.238689	−	0.971096i	$-0.423282\pi$
$113$	5.07461			0.477379			0.238689	+	0.971096i	$0.423282\pi$
$114$	0.976788	−	1.54162i	0.0914846	−	0.144386i
$115$	−4.80496	+	4.80496i	−0.448065	+	0.448065i
$116$	−0.551940	−	0.197815i	−0.0512463	−	0.0183667i
$117$	−2.28650	−	2.28650i	−0.211387	−	0.211387i
$118$	−4.31089	−	19.2210i	−0.396850	−	1.76943i
$119$		0			0
$120$	−0.699452	+	5.63435i	−0.0638509	+	0.514343i
$121$		−	7.18063i		−	0.652784i
$122$	5.16730	−	1.15893i	0.467825	−	0.104924i
$123$	−3.43379	−	3.43379i	−0.309614	−	0.309614i
$124$	−6.74259	−	14.2755i	−0.605503	−	1.28197i
$125$	6.32873	−	6.32873i	0.566059	−	0.566059i
$126$		0			0
$127$	−11.1710			−0.991270			−0.495635	−	0.868531i	$-0.665065\pi$
$127$	−11.1710			−0.991270			−0.495635	+	0.868531i	$0.665065\pi$
$128$	−7.78614	−	8.20829i	−0.688204	−	0.725518i
$129$	10.4524			0.920285
$130$	3.52789	+	2.23531i	0.309416	+	0.196050i
$131$	8.91555	−	8.91555i	0.778956	−	0.778956i	−0.200698	−	0.979653i	$-0.564321\pi$
$131$	8.91555	−	8.91555i	0.778956	−	0.778956i	0.979653	+	0.200698i	$0.0643209\pi$
$132$	−3.37478	−	7.14512i	−0.293737	−	0.621903i
$133$		0			0
$134$	−14.3529	+	3.21909i	−1.23990	+	0.278087i
$135$			3.83966i			0.330465i
$136$	−1.97839	+	15.9367i	−0.169645	+	1.36656i
$137$			16.2033i			1.38434i	0.721733	+	0.692172i	$0.243346\pi$
$137$			16.2033i			1.38434i	−0.721733	+	0.692172i	$0.756654\pi$
$138$	4.28213	+	19.0927i	0.364519	+	1.62528i
$139$	−10.5018	−	10.5018i	−0.890748	−	0.890748i	0.103846	−	0.994593i	$-0.466885\pi$
$139$	−10.5018	−	10.5018i	−0.890748	−	0.890748i	−0.994593	+	0.103846i	$0.966885\pi$
$140$		0			0
$141$	−0.413403	+	0.413403i	−0.0348148	+	0.0348148i
$142$	−8.77618	+	13.8510i	−0.736481	+	1.16235i
$143$	−5.81272			−0.486084
$144$	3.35871	+	2.76235i	0.279893	+	0.230196i
$145$	−0.291079			−0.0241728
$146$	−0.271618	+	0.428682i	−0.0224793	+	0.0354780i
$147$		0			0
$148$	6.71005	−	18.7222i	0.551562	−	1.53896i
$149$	7.04183	+	7.04183i	0.576889	+	0.576889i	0.934045	−	0.357156i	$-0.116254\pi$
$149$	7.04183	+	7.04183i	0.576889	+	0.576889i	−0.357156	+	0.934045i	$0.616254\pi$
$150$	−2.51162	−	11.1986i	−0.205073	−	0.914360i
$151$			10.3650i			0.843494i	0.906713	+	0.421747i	$0.138583\pi$
$151$			10.3650i			0.843494i	−0.906713	+	0.421747i	$0.861417\pi$
$152$	1.10964	+	1.42420i	0.0900041	+	0.115518i
$153$		−	6.17272i		−	0.499035i
$154$		0			0
$155$	−5.54219	−	5.54219i	−0.445159	−	0.445159i
$156$	10.8742	−	5.13610i	0.870633	−	0.411217i
$157$	2.91731	−	2.91731i	0.232827	−	0.232827i	−0.581045	−	0.813872i	$-0.697356\pi$
$157$	2.91731	−	2.91731i	0.232827	−	0.232827i	0.813872	+	0.581045i	$0.197356\pi$
$158$	9.19732	+	5.82754i	0.731700	+	0.463614i
$159$	−15.9641			−1.26604
$160$	−5.01366	−	2.53195i	−0.396364	−	0.200168i
$161$		0			0
$162$	13.2357	+	8.38631i	1.03990	+	0.658891i
$163$	5.84382	−	5.84382i	0.457723	−	0.457723i	−0.440184	−	0.897907i	$-0.645087\pi$
$163$	5.84382	−	5.84382i	0.457723	−	0.457723i	0.897907	+	0.440184i	$0.145087\pi$
$164$	4.34388	−	2.05170i	0.339200	−	0.160211i
$165$	−2.77396	−	2.77396i	−0.215953	−	0.215953i
$166$	0.827446	−	0.185580i	0.0642223	−	0.0144038i
$167$			8.92669i			0.690768i	0.938462	+	0.345384i	$0.112251\pi$
$167$			8.92669i			0.690768i	−0.938462	+	0.345384i	$0.887749\pi$
$168$		0			0
$169$			4.15359i			0.319507i
$170$	1.74474	+	7.77926i	0.133815	+	0.596642i
$171$	−0.490715	−	0.490715i	−0.0375259	−	0.0375259i
$172$	−3.48869	+	9.73405i	−0.266010	+	0.742214i
$173$	−3.85339	+	3.85339i	−0.292968	+	0.292968i	−0.838252	−	0.545284i	$-0.816422\pi$
$173$	−3.85339	+	3.85339i	−0.292968	+	0.292968i	0.545284	+	0.838252i	$0.316422\pi$
$174$	−0.448604	+	0.708010i	−0.0340086	+	0.0536741i
$175$		0			0
$176$	7.78045	−	0.758029i	0.586473	−	0.0571386i
$177$	−28.1598			−2.11662
$178$	13.3132	−	21.0116i	0.997866	−	1.57488i
$179$	6.89914	−	6.89914i	0.515666	−	0.515666i	−0.400591	−	0.916257i	$-0.631195\pi$
$179$	6.89914	−	6.89914i	0.515666	−	0.515666i	0.916257	+	0.400591i	$0.131195\pi$
$180$	2.03235	+	0.728396i	0.151483	+	0.0542915i
$181$	8.42976	+	8.42976i	0.626579	+	0.626579i	0.947206	−	0.320627i	$-0.103894\pi$
$181$	8.42976	+	8.42976i	0.626579	+	0.626579i	−0.320627	+	0.947206i	$0.603894\pi$
$182$		0			0
$183$		−	7.57038i		−	0.559619i
$184$	−19.2098	−	2.38471i	−1.41616	−	0.175803i
$185$		−	9.87361i		−	0.725922i
$186$	−22.0221	+	4.93914i	−1.61474	+	0.362155i
$187$	−7.84611	−	7.84611i	−0.573764	−	0.573764i
$188$	−0.247010	−	0.522971i	−0.0180150	−	0.0381416i
$189$		0			0
$190$	0.757132	+	0.479728i	0.0549282	+	0.0348032i
$191$	−4.93044			−0.356754			−0.178377	−	0.983962i	$-0.557085\pi$
$191$	−4.93044			−0.356754			−0.178377	+	0.983962i	$0.557085\pi$
$192$	−13.8855	+	8.29286i	−1.00210	+	0.598486i
$193$	21.9087			1.57702			0.788510	−	0.615022i	$-0.210853\pi$
$193$	21.9087			1.57702			0.788510	+	0.615022i	$0.210853\pi$
$194$	−14.6551	−	9.28568i	−1.05218	−	0.666673i
$195$	4.22171	−	4.22171i	0.302323	−	0.302323i
$196$		0			0
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	0.924375	−	0.381484i	$-0.124587\pi$
$197$	7.61984	+	7.61984i	0.542891	+	0.542891i	−0.381484	+	0.924375i	$0.624587\pi$
$198$	−2.93196	+	0.657581i	−0.208365	+	0.0467323i
$199$			3.57622i			0.253511i	0.991934	+	0.126756i	$0.0404564\pi$
$199$			3.57622i			0.253511i	−0.991934	+	0.126756i	$0.959544\pi$
$200$	11.2672	+	1.39872i	0.796713	+	0.0989045i
$201$			21.0278i			1.48319i
$202$	0.374422	+	1.66944i	0.0263443	+	0.117461i
$203$		0			0
$204$	21.6110	+	7.74537i	1.51307	+	0.542285i
$205$	1.68643	−	1.68643i	0.117785	−	0.117785i
$206$	−4.42408	+	6.98232i	−0.308240	+	0.486481i
$207$	7.44049			0.517149
$208$	1.15365	+	11.8411i	0.0799911	+	0.821033i
$209$	−1.24749			−0.0862906
$210$		0			0
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	−0.407901	−	0.913026i	$-0.633739\pi$
$211$	7.33737	−	7.33737i	0.505126	−	0.505126i	0.913026	+	0.407901i	$0.133739\pi$
$212$	5.32832	−	14.8669i	0.365950	−	1.02107i
$213$	16.5751	+	16.5751i	1.13570	+	1.13570i
$214$	−1.16146	−	5.17861i	−0.0793959	−	0.354002i
$215$			5.13349i			0.350101i
$216$	−8.62809	+	6.72246i	−0.587067	+	0.457406i
$217$		0			0
$218$	−13.8240	+	3.10047i	−0.936283	+	0.209990i
$219$	0.512990	+	0.512990i	0.0346646	+	0.0346646i
$220$	3.50917	−	1.65745i	0.236588	−	0.111745i
$221$	11.9410	−	11.9410i	0.803241	−	0.803241i
$222$	−24.0162	−	15.2170i	−1.61186	−	1.02130i
$223$	−4.26037			−0.285295			−0.142648	−	0.989774i	$-0.545562\pi$
$223$	−4.26037			−0.285295			−0.142648	+	0.989774i	$0.545562\pi$
$224$		0			0
$225$	−4.36411			−0.290941
$226$	6.06214	+	3.84105i	0.403248	+	0.255503i
$227$	−3.42116	+	3.42116i	−0.227071	+	0.227071i	−0.811468	−	0.584397i	$-0.801331\pi$
$227$	−3.42116	+	3.42116i	−0.227071	+	0.227071i	0.584397	+	0.811468i	$0.301331\pi$
$228$	2.33375	−	1.10228i	0.154556	−	0.0730001i
$229$	13.8716	+	13.8716i	0.916663	+	0.916663i	0.996785	−	0.0801224i	$-0.0255311\pi$
$229$	13.8716	+	13.8716i	0.916663	+	0.916663i	−0.0801224	+	0.996785i	$0.525531\pi$
$230$	−9.37698	+	2.10308i	−0.618300	+	0.138673i
$231$		0			0
$232$	−0.509620	−	0.654083i	−0.0334582	−	0.0429427i
$233$		−	5.06546i		−	0.331849i	−0.986138	−	0.165925i	$-0.946939\pi$
$233$		−	5.06546i		−	0.331849i	0.986138	−	0.165925i	$-0.0530608\pi$
$234$	−1.00078	−	4.46216i	−0.0654228	−	0.291700i
$235$	−0.203034	−	0.203034i	−0.0132445	−	0.0132445i
$236$	9.39884	−	26.2244i	0.611813	−	1.70707i
$237$	11.0061	−	11.0061i	0.714925	−	0.714925i
$238$		0			0
$239$	−9.32494			−0.603181			−0.301590	−	0.953438i	$-0.597517\pi$
$239$	−9.32494			−0.603181			−0.301590	+	0.953438i	$0.597517\pi$
$240$	−5.10029	+	6.20139i	−0.329223	+	0.400298i
$241$	−25.7325			−1.65758			−0.828789	−	0.559562i	$-0.810969\pi$
$241$	−25.7325			−1.65758			−0.828789	+	0.559562i	$0.810969\pi$
$242$	5.43513	−	8.57801i	0.349383	−	0.551415i
$243$	7.63539	−	7.63539i	0.489810	−	0.489810i
$244$	7.05008	+	2.52675i	0.451335	+	0.161759i
$245$		0			0
$246$	−1.50293	−	6.70110i	−0.0958232	−	0.427247i
$247$		−	1.89856i		−	0.120802i
$248$	2.75060	−	22.1571i	0.174663	−	1.40698i
$249$		−	1.21226i		−	0.0768236i
$250$	12.3506	−	2.77001i	0.781123	−	0.175191i
$251$	3.64372	+	3.64372i	0.229990	+	0.229990i	0.812688	−	0.582699i	$-0.198003\pi$
$251$	3.64372	+	3.64372i	0.229990	+	0.229990i	−0.582699	+	0.812688i	$0.698003\pi$
$252$		0			0
$253$	9.45755	−	9.45755i	0.594591	−	0.594591i
$254$	−13.3450	−	8.45554i	−0.837338	−	0.530548i
$255$	11.3971			0.713711
$256$	−3.08836	−	15.6991i	−0.193023	−	0.981194i
$257$	3.75548			0.234260			0.117130	−	0.993117i	$-0.462631\pi$
$257$	3.75548			0.234260			0.117130	+	0.993117i	$0.462631\pi$
$258$	12.4865	+	7.91160i	0.777376	+	0.492555i
$259$		0			0
$260$	2.52249	+	5.34063i	0.156438	+	0.331212i
$261$	0.225368	+	0.225368i	0.0139499	+	0.0139499i
$262$	17.3989	−	3.90223i	1.07491	−	0.241081i
$263$		−	18.8507i		−	1.16238i	−0.813767	−	0.581191i	$-0.802587\pi$
$263$		−	18.8507i		−	1.16238i	0.813767	−	0.581191i	$-0.197413\pi$
$264$	1.37672	−	11.0900i	0.0847315	−	0.682543i
$265$		−	7.84044i		−	0.481634i
$266$		0			0
$267$	−25.1439	−	25.1439i	−1.53878	−	1.53878i
$268$	−19.5826	−	7.01842i	−1.19620	−	0.428718i
$269$	12.1259	−	12.1259i	0.739330	−	0.739330i	−0.233118	−	0.972448i	$-0.574893\pi$
$269$	12.1259	−	12.1259i	0.739330	−	0.739330i	0.972448	+	0.233118i	$0.0748930\pi$
$270$	−2.90630	+	4.58687i	−0.176872	+	0.279148i
$271$	−5.31215			−0.322690			−0.161345	−	0.986898i	$-0.551583\pi$
$271$	−5.31215			−0.322690			−0.161345	+	0.986898i	$0.551583\pi$
$272$	−14.4261	+	17.5405i	−0.874711	+	1.06355i
$273$		0			0
$274$	−12.2646	+	19.3566i	−0.740929	+	1.16937i
$275$	−5.54720	+	5.54720i	−0.334509	+	0.334509i
$276$	−9.33613	+	26.0495i	−0.561969	+	1.56799i
$277$	−10.7488	−	10.7488i	−0.645834	−	0.645834i	0.306149	−	0.951984i	$-0.400959\pi$
$277$	−10.7488	−	10.7488i	−0.645834	−	0.645834i	−0.951984	+	0.306149i	$0.900959\pi$
$278$	−4.59650	−	20.4944i	−0.275680	−	1.22917i
$279$			8.58208i			0.513795i
$280$		0			0
$281$		−	3.15786i		−	0.188382i	−0.995554	−	0.0941910i	$-0.969974\pi$
$281$		−	3.15786i		−	0.188382i	0.995554	−	0.0941910i	$-0.0300264\pi$
$282$	−0.806763	+	0.180941i	−0.0480420	+	0.0107749i
$283$	9.98203	+	9.98203i	0.593370	+	0.593370i	0.938540	−	0.345170i	$-0.112179\pi$
$283$	9.98203	+	9.98203i	0.593370	+	0.593370i	−0.345170	+	0.938540i	$0.612179\pi$
$284$	−20.9681	+	9.90367i	−1.24423	+	0.587674i
$285$	0.906035	−	0.906035i	0.0536689	−	0.0536689i
$286$	−6.94390	−	4.39974i	−0.410602	−	0.260162i
$287$		0			0
$288$	1.92146	+	5.84218i	0.113223	+	0.344254i
$289$	15.2364			0.896258
$290$	−0.347724	−	0.220322i	−0.0204190	−	0.0129378i
$291$	−17.5373	+	17.5373i	−1.02806	+	1.02806i
$292$	−0.648952	+	0.306513i	−0.0379771	+	0.0179373i
$293$	10.9335	+	10.9335i	0.638743	+	0.638743i	0.950245	−	0.311502i	$-0.100832\pi$
$293$	10.9335	+	10.9335i	0.638743	+	0.638743i	−0.311502	+	0.950245i	$0.600832\pi$
$294$		0			0
$295$		−	13.8301i		−	0.805219i
$296$	22.1870	−	17.2867i	1.28959	−	1.00477i
$297$		−	7.55755i		−	0.438534i
$298$	3.08213	+	13.7423i	0.178543	+	0.796068i
$299$	14.3935	+	14.3935i	0.832398	+	0.832398i
$300$	5.47598	−	15.2789i	0.316156	−	0.882131i
$301$		0			0
$302$	−7.84545	+	12.3821i	−0.451455	+	0.712510i
$303$	2.44582			0.140509
$304$	0.247588	+	2.54126i	0.0142002	+	0.145751i
$305$	3.71803			0.212894
$306$	4.67223	−	7.37396i	0.267094	−	0.421541i
$307$	14.7735	−	14.7735i	0.843170	−	0.843170i	−0.146100	−	0.989270i	$-0.546672\pi$
$307$	14.7735	−	14.7735i	0.843170	−	0.843170i	0.989270	+	0.146100i	$0.0466721\pi$
$308$		0			0
$309$	8.35550	+	8.35550i	0.475328	+	0.475328i
$310$	−2.42575	−	10.8157i	−0.137773	−	0.614290i
$311$			8.73588i			0.495366i	0.968841	+	0.247683i	$0.0796692\pi$
$311$			8.73588i			0.495366i	−0.968841	+	0.247683i	$0.920331\pi$
$312$	16.8780	+	2.09524i	0.955526	+	0.118620i
$313$			4.11784i			0.232754i	0.993205	+	0.116377i	$0.0371281\pi$
$313$			4.11784i			0.232754i	−0.993205	+	0.116377i	$0.962872\pi$
$314$	5.69319	−	1.27687i	0.321285	−	0.0720581i
$315$		0			0
$316$	6.57621	+	13.9232i	0.369940	+	0.783241i
$317$	17.2736	−	17.2736i	0.970182	−	0.970182i	−0.0293866	−	0.999568i	$-0.509355\pi$
$317$	17.2736	−	17.2736i	0.970182	−	0.970182i	0.999568	+	0.0293866i	$0.00935539\pi$
$318$	−19.0708	−	12.0835i	−1.06944	−	0.677609i
$319$	0.572927			0.0320777
$320$	−4.07286	−	6.81959i	−0.227680	−	0.381226i
$321$	−7.58695			−0.423462
$322$		0			0
$323$	2.56271	−	2.56271i	0.142593	−	0.142593i
$324$	9.46371	+	20.0366i	0.525762	+	1.11315i
$325$	−8.44231	−	8.44231i	−0.468295	−	0.468295i
$326$	11.4043	−	2.55777i	0.631627	−	0.141662i
$327$			20.2530i			1.11999i
$328$	6.74218	+	0.836979i	0.372274	+	0.0462144i
$329$		0			0
$330$	−1.21413	−	5.41344i	−0.0668357	−	0.298000i
$331$	5.16464	+	5.16464i	0.283874	+	0.283874i	0.834652	−	0.550778i	$-0.185669\pi$
$331$	5.16464	+	5.16464i	0.283874	+	0.283874i	−0.550778	+	0.834652i	$0.685669\pi$
$332$	1.12894	+	0.404612i	0.0619586	+	0.0222060i
$333$	−7.64464	+	7.64464i	−0.418924	+	0.418924i
$334$	−6.75675	+	10.6639i	−0.369713	+	0.583500i
$335$	−10.3274			−0.564245
$336$		0			0
$337$	−9.53985			−0.519669			−0.259834	−	0.965653i	$-0.583668\pi$
$337$	−9.53985			−0.519669			−0.259834	+	0.965653i	$0.583668\pi$
$338$	−3.14392	+	4.96189i	−0.171006	+	0.269891i
$339$	7.25436	−	7.25436i	0.394003	−	0.394003i
$340$	−3.80397	+	10.6138i	−0.206299	+	0.575612i
$341$	10.9086	+	10.9086i	0.590735	+	0.590735i
$342$	−0.214780	−	0.957639i	−0.0116140	−	0.0517832i
$343$		0			0
$344$	−11.5355	+	8.98769i	−0.621950	+	0.484584i
$345$			13.7378i			0.739619i
$346$	−7.51997	+	1.68658i	−0.404276	+	0.0906714i
$347$	6.46084	+	6.46084i	0.346836	+	0.346836i	0.858930	−	0.512094i	$-0.171130\pi$
$347$	6.46084	+	6.46084i	0.346836	+	0.346836i	−0.512094	+	0.858930i	$0.671130\pi$
$348$	−1.07181	+	0.506236i	−0.0574549	+	0.0271371i
$349$	−24.4862	+	24.4862i	−1.31072	+	1.31072i	−0.389831	+	0.920887i	$0.627467\pi$
$349$	−24.4862	+	24.4862i	−1.31072	+	1.31072i	−0.920887	+	0.389831i	$0.872533\pi$
$350$		0			0
$351$	11.5019			0.613925
$352$	9.86832	+	4.98360i	0.525983	+	0.265627i
$353$	26.0704			1.38759			0.693793	−	0.720175i	$-0.255938\pi$
$353$	26.0704			1.38759			0.693793	+	0.720175i	$0.255938\pi$
$354$	−33.6398	−	21.3146i	−1.78794	−	1.13286i
$355$	−8.14049	+	8.14049i	−0.432052	+	0.432052i
$356$	31.8080	−	15.0236i	1.68582	−	0.796247i
$357$		0			0
$358$	13.4638	−	3.01967i	0.711584	−	0.159595i
$359$			3.48419i			0.183889i	0.995764	+	0.0919443i	$0.0293082\pi$
$359$			3.48419i			0.183889i	−0.995764	+	0.0919443i	$0.970692\pi$
$360$	1.87652	+	2.40847i	0.0989015	+	0.126937i
$361$			18.5925i			0.978555i
$362$	3.68961	+	16.4508i	0.193921	+	0.864637i
$363$	−10.2650	−	10.2650i	−0.538773	−	0.538773i
$364$		0			0
$365$	−0.251944	+	0.251944i	−0.0131873	+	0.0131873i
$366$	5.73014	−	9.04361i	0.299519	−	0.472717i
$367$	−24.4561			−1.27660			−0.638298	−	0.769789i	$-0.720361\pi$
$367$	−24.4561			−1.27660			−0.638298	+	0.769789i	$0.720361\pi$
$368$	−21.1430	−	17.3890i	−1.10216	−	0.906462i
$369$	−2.61144			−0.135946
$370$	7.47349	−	11.7951i	0.388528	−	0.613196i
$371$		0			0
$372$	−30.0462	−	10.7686i	−1.55782	−	0.558324i
$373$	25.9873	+	25.9873i	1.34557	+	1.34557i	0.890410	+	0.455160i	$0.150418\pi$
$373$	25.9873	+	25.9873i	1.34557	+	1.34557i	0.455160	+	0.890410i	$0.349582\pi$
$374$	−3.43415	−	15.3118i	−0.177576	−	0.791756i
$375$		−	18.0944i		−	0.934390i
$376$	0.100766	−	0.811708i	0.00519661	−	0.0418607i
$377$			0.871940i			0.0449072i
$378$		0			0
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	0.998864	−	0.0476420i	$-0.0151707\pi$
$379$	18.5183	+	18.5183i	0.951222	+	0.951222i	−0.0476420	+	0.998864i	$0.515171\pi$
$380$	0.541360	+	1.14617i	0.0277712	+	0.0587973i
$381$	−15.9695	+	15.9695i	−0.818142	+	0.818142i
$382$	−5.88992	−	3.73193i	−0.301355	−	0.190942i
$383$	15.7957			0.807123			0.403562	−	0.914953i	$-0.367772\pi$
$383$	15.7957			0.807123			0.403562	+	0.914953i	$0.367772\pi$
$384$	−22.8647	−	0.603494i	−1.16681	−	0.0307969i
$385$		0			0
$386$	26.1722	+	16.5830i	1.33213	+	0.844053i
$387$	3.97460	−	3.97460i	0.202040	−	0.202040i
$388$	−10.4786	−	22.1854i	−0.531971	−	1.12629i
$389$	4.03146	+	4.03146i	0.204403	+	0.204403i	0.801883	−	0.597481i	$-0.203831\pi$
$389$	4.03146	+	4.03146i	0.204403	+	0.204403i	−0.597481	+	0.801883i	$0.703831\pi$
$390$	8.23875	−	1.84779i	0.417185	−	0.0935666i
$391$			38.8572i			1.96509i
$392$		0			0
$393$		−	25.4903i		−	1.28582i
$394$	3.33512	+	14.8703i	0.168021	+	0.749154i
$395$	5.40543	+	5.40543i	0.271976	+	0.271976i
$396$	−4.00026	−	1.43369i	−0.201021	−	0.0720458i
$397$	−0.711500	+	0.711500i	−0.0357092	+	0.0357092i	−0.724736	−	0.689027i	$-0.758038\pi$
$397$	−0.711500	+	0.711500i	−0.0357092	+	0.0357092i	0.689027	+	0.724736i	$0.258038\pi$
$398$	−2.70690	+	4.27216i	−0.135684	+	0.214144i
$399$		0			0
$400$	12.4012	+	10.1993i	0.620058	+	0.509963i
$401$	−17.4064			−0.869232			−0.434616	−	0.900616i	$-0.643116\pi$
$401$	−17.4064			−0.869232			−0.434616	+	0.900616i	$0.643116\pi$
$402$	−15.9163	+	25.1199i	−0.793833	+	1.25287i
$403$	−16.6019	+	16.6019i	−0.826999	+	0.826999i
$404$	−0.816336	+	2.27772i	−0.0406142	+	0.113321i
$405$	7.77886	+	7.77886i	0.386535	+	0.386535i
$406$		0			0
$407$			19.4341i			0.963313i
$408$	19.9539	+	25.6103i	0.987867	+	1.26790i
$409$			38.1750i			1.88763i	0.330474	+	0.943815i	$0.392792\pi$
$409$			38.1750i			1.88763i	−0.330474	+	0.943815i	$0.607208\pi$
$410$	3.29110	−	0.738131i	0.162536	−	0.0364537i
$411$	23.1633	+	23.1633i	1.14256	+	1.14256i
$412$	−10.5700	+	4.99245i	−0.520749	+	0.245960i
$413$		0			0
$414$	8.88843	+	5.63182i	0.436843	+	0.276789i
$415$	0.595373			0.0292257
$416$	−7.58456	+	15.0186i	−0.371864	+	0.736350i
$417$	−30.0254			−1.47035
$418$	−1.49025	−	0.944244i	−0.0728907	−	0.0461845i
$419$	27.0004	−	27.0004i	1.31905	−	1.31905i	0.404529	−	0.914525i	$-0.367435\pi$
$419$	27.0004	−	27.0004i	1.31905	−	1.31905i	0.914525	−	0.404529i	$-0.132565\pi$
$420$		0			0
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	0.0647277	−	0.997903i	$-0.479382\pi$
$421$	−19.1472	−	19.1472i	−0.933175	−	0.933175i	−0.997903	+	0.0647277i	$0.979382\pi$
$422$	14.3190	−	3.21148i	0.697039	−	0.156333i
$423$			0.314398i			0.0152865i
$424$	17.6182	−	13.7270i	0.855618	−	0.666643i
$425$		−	22.7911i		−	1.10553i
$426$	7.25471	+	32.3466i	0.351492	+	1.56720i
$427$		0			0
$428$	2.53228	−	7.06551i	0.122402	−	0.341524i
$429$	−8.30954	+	8.30954i	−0.401188	+	0.401188i
$430$	−3.88562	+	6.13248i	−0.187381	+	0.295735i
$431$	1.25711			0.0605528			0.0302764	−	0.999542i	$-0.490361\pi$
$431$	1.25711			0.0605528			0.0302764	+	0.999542i	$0.490361\pi$
$432$	−15.3955	+	1.49994i	−0.740716	+	0.0721660i
$433$	9.16885			0.440627			0.220313	−	0.975429i	$-0.429292\pi$
$433$	9.16885			0.440627			0.220313	+	0.975429i	$0.429292\pi$
$434$		0			0
$435$	−0.416110	+	0.416110i	−0.0199509	+	0.0199509i
$436$	−18.8611	−	6.75981i	−0.903281	−	0.323736i
$437$	3.08904	+	3.08904i	0.147769	+	0.147769i
$438$	0.224530	+	1.00111i	0.0107284	+	0.0478349i
$439$		−	7.96586i		−	0.380190i	−0.981766	−	0.190095i	$-0.939120\pi$
$439$		−	7.96586i		−	0.380190i	0.981766	−	0.190095i	$-0.0608796\pi$
$440$	5.44663	+	0.676148i	0.259658	+	0.0322341i
$441$		0			0
$442$	23.3032	−	5.22645i	1.10842	−	0.248597i
$443$	17.6930	+	17.6930i	0.840621	+	0.840621i	0.988940	−	0.148319i	$-0.0473861\pi$
$443$	17.6930	+	17.6930i	0.840621	+	0.840621i	−0.148319	+	0.988940i	$0.547386\pi$
$444$	−17.1719	−	36.3565i	−0.814943	−	1.72540i
$445$	12.3489	−	12.3489i	0.585393	−	0.585393i
$446$	−5.08945	−	3.22474i	−0.240992	−	0.152696i
$447$	20.1332			0.952267
$448$		0			0
$449$	−8.33038			−0.393135			−0.196567	−	0.980490i	$-0.562979\pi$
$449$	−8.33038			−0.393135			−0.196567	+	0.980490i	$0.562979\pi$
$450$	−5.21339	−	3.30327i	−0.245761	−	0.155717i
$451$	−3.31938	+	3.31938i	−0.156304	+	0.156304i
$452$	4.33451	+	9.17706i	0.203878	+	0.431653i
$453$	14.8173	+	14.8173i	0.696175	+	0.696175i
$454$	−6.67647	+	1.49740i	−0.313342	+	0.0702766i
$455$		0			0
$456$	3.62224	+	0.449667i	0.169627	+	0.0210576i
$457$			14.4728i			0.677010i	0.940965	+	0.338505i	$0.109921\pi$
$457$			14.4728i			0.677010i	−0.940965	+	0.338505i	$0.890079\pi$
$458$	6.07145	+	27.0707i	0.283700	+	1.26493i
$459$	15.5254	+	15.5254i	0.724664	+	0.724664i
$460$	−12.7936	−	4.58524i	−0.596506	−	0.213788i
$461$	4.23021	−	4.23021i	0.197020	−	0.197020i	−0.601701	−	0.798721i	$-0.705510\pi$
$461$	4.23021	−	4.23021i	0.197020	−	0.197020i	0.798721	+	0.601701i	$0.205510\pi$
$462$		0			0
$463$	−25.1987			−1.17108			−0.585542	−	0.810642i	$-0.699118\pi$
$463$	−25.1987			−1.17108			−0.585542	+	0.810642i	$0.699118\pi$
$464$	−0.113708	−	1.16711i	−0.00527878	−	0.0541817i
$465$	−15.8456			−0.734822
$466$	3.83412	−	6.05121i	0.177612	−	0.280317i
$467$	−10.8645	+	10.8645i	−0.502747	+	0.502747i	−0.912291	−	0.409543i	$-0.865688\pi$
$467$	−10.8645	+	10.8645i	−0.502747	+	0.502747i	0.409543	+	0.912291i	$0.365688\pi$
$468$	2.18195	−	6.08802i	0.100860	−	0.281419i
$469$		0			0
$470$	−0.0888655	−	0.396224i	−0.00409906	−	0.0182765i
$471$		−	8.34085i		−	0.384326i
$472$	31.0776	−	24.2137i	1.43046	−	1.11453i
$473$		−	10.1042i		−	0.464591i
$474$	21.4787	−	4.81725i	0.986548	−	0.221264i
$475$	−1.81183	−	1.81183i	−0.0831326	−	0.0831326i
$476$		0			0
$477$	−6.07046	+	6.07046i	−0.277947	+	0.277947i
$478$	−11.1396	−	7.05820i	−0.509514	−	0.322834i
$479$	20.8293			0.951717			0.475859	−	0.879522i	$-0.342137\pi$
$479$	20.8293			0.951717			0.475859	+	0.879522i	$0.342137\pi$
$480$	−10.7868	+	3.54771i	−0.492346	+	0.161930i
$481$	−29.5769			−1.34859
$482$	−30.7402	−	19.4773i	−1.40018	−	0.887169i
$483$		0			0
$484$	12.9857	−	6.13339i	0.590257	−	0.278790i
$485$	−8.61308	−	8.61308i	−0.391100	−	0.391100i
$486$	14.9006	−	3.34192i	0.675905	−	0.151593i
$487$		−	0.222431i		−	0.0100793i	−0.999987	−	0.00503966i	$-0.998396\pi$
$487$		−	0.222431i		−	0.0100793i	0.999987	−	0.00503966i	$-0.00160418\pi$
$488$	6.50952	+	8.35479i	0.294672	+	0.378203i
$489$		−	16.7080i		−	0.755561i
$490$		0			0
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	0.986033	−	0.166547i	$-0.0532618\pi$
$491$	18.1586	+	18.1586i	0.819486	+	0.819486i	−0.166547	+	0.986033i	$0.553262\pi$
$492$	3.27676	−	9.14275i	0.147728	−	0.412187i
$493$	−1.17696	+	1.17696i	−0.0530076	+	0.0530076i
$494$	1.43705	−	2.26803i	0.0646559	−	0.102043i
$495$	−2.10963			−0.0948209
$496$	20.0569	−	24.3870i	0.900583	−	1.09501i
$497$		0			0
$498$	0.917575	−	1.44816i	0.0411175	−	0.0648938i
$499$	2.48274	−	2.48274i	0.111143	−	0.111143i	−0.649348	−	0.760491i	$-0.724958\pi$
$499$	2.48274	−	2.48274i	0.111143	−	0.111143i	0.760491	+	0.649348i	$0.224958\pi$
$500$	16.8508	+	6.03933i	0.753591	+	0.270087i
$501$	12.7611	+	12.7611i	0.570123	+	0.570123i
$502$	1.59481	+	7.11079i	0.0711800	+	0.317370i
$503$			7.65278i			0.341220i	0.985339	+	0.170610i	$0.0545739\pi$
$503$			7.65278i			0.341220i	−0.985339	+	0.170610i	$0.945426\pi$
$504$		0			0
$505$			1.20121i			0.0534532i
$506$	18.4566	−	4.13946i	0.820496	−	0.184021i
$507$	5.93773	+	5.93773i	0.263704	+	0.263704i
$508$	−9.54183	−	20.2020i	−0.423350	−	0.896321i
$509$	22.6006	−	22.6006i	1.00175	−	1.00175i	0.00175431	−	0.999998i	$-0.499442\pi$
$509$	22.6006	−	22.6006i	1.00175	−	1.00175i	0.999998	−	0.00175431i	$-0.000558414\pi$
$510$	13.6150	+	8.62661i	0.602881	+	0.381993i
$511$		0			0
$512$	8.19353	−	21.0918i	0.362106	−	0.932137i
$513$	2.46846			0.108985
$514$	4.48631	+	2.84258i	0.197883	+	0.125381i
$515$	−4.10363	+	4.10363i	−0.180827	+	0.180827i
$516$	8.92802	+	18.9025i	0.393034	+	0.832135i
$517$	0.399629	+	0.399629i	0.0175757	+	0.0175757i
$518$		0			0
$519$			11.0172i			0.483600i
$520$	−1.02903	+	8.28925i	−0.0451261	+	0.363508i
$521$		−	2.76916i		−	0.121319i	−0.998159	−	0.0606595i	$-0.980680\pi$
$521$		−	2.76916i		−	0.121319i	0.998159	−	0.0606595i	$-0.0193204\pi$
$522$	0.0986408	+	0.439809i	0.00431739	+	0.0192499i
$523$	−15.6353	−	15.6353i	−0.683686	−	0.683686i	0.277143	−	0.960829i	$-0.410612\pi$
$523$	−15.6353	−	15.6353i	−0.683686	−	0.683686i	−0.960829	+	0.277143i	$0.910612\pi$
$524$	23.7384	+	8.50786i	1.03702	+	0.371668i
$525$		0			0
$526$	14.2684	−	22.5191i	0.622131	−	0.981879i
$527$	−44.8190			−1.95235
$528$	10.0388	−	12.2061i	0.436885	−	0.531203i
$529$	−23.8377			−1.03642
$530$	5.93455	−	9.36622i	0.257780	−	0.406843i
$531$	−10.7079	+	10.7079i	−0.464685	+	0.464685i
$532$		0			0
$533$	−5.05178	−	5.05178i	−0.218817	−	0.218817i
$534$	−11.0052	−	49.0687i	−0.476240	−	2.12341i
$535$		−	3.72617i		−	0.161096i
$536$	−18.0811	−	23.2066i	−0.780987	−	1.00237i
$537$		−	19.7252i		−	0.851207i
$538$	23.6640	−	5.30737i	1.02023	−	0.228817i
$539$		0			0
$540$	−6.94375	+	3.27967i	−0.298811	+	0.141135i
$541$	23.6185	−	23.6185i	1.01544	−	1.01544i	0.0155590	−	0.999879i	$-0.495047\pi$
$541$	23.6185	−	23.6185i	1.01544	−	1.01544i	0.999879	−	0.0155590i	$-0.00495280\pi$
$542$	−6.34592	−	4.02085i	−0.272580	−	0.172710i
$543$	24.1014			1.03429
$544$	−30.5102	+	10.0346i	−1.30811	+	0.430232i
$545$	−9.94683			−0.426075
$546$		0			0
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	−0.629462	−	0.777032i	$-0.716724\pi$
$547$	3.45137	−	3.45137i	0.147570	−	0.147570i	0.777032	+	0.629462i	$0.216724\pi$
$548$	−29.3026	+	13.8402i	−1.25174	+	0.591224i
$549$	−2.87868	−	2.87868i	−0.122859	−	0.122859i
$550$	−10.8255	+	2.42794i	−0.461599	+	0.103528i
$551$			0.187130i			0.00797201i
$552$	−30.8702	+	24.0521i	−1.31392	+	1.02373i
$553$		0			0
$554$	−4.70464	−	20.9765i	−0.199881	−	0.891208i
$555$	−14.1147	−	14.1147i	−0.599138	−	0.599138i
$556$	10.0215	−	27.9618i	0.425008	−	1.18585i
$557$	−15.5967	+	15.5967i	−0.660853	+	0.660853i	−0.955581	−	0.294728i	$-0.904771\pi$
$557$	−15.5967	+	15.5967i	−0.660853	+	0.660853i	0.294728	+	0.955581i	$0.404771\pi$
$558$	−6.49591	+	10.2522i	−0.274994	+	0.434009i
$559$	15.3776			0.650403
$560$		0			0
$561$	−22.4327			−0.947109
$562$	2.39023	−	3.77239i	0.100826	−	0.159129i
$563$	19.5230	−	19.5230i	0.822798	−	0.822798i	−0.163710	−	0.986508i	$-0.552346\pi$
$563$	19.5230	−	19.5230i	0.822798	−	0.822798i	0.986508	+	0.163710i	$0.0523462\pi$
$564$	−1.10072	−	0.394498i	−0.0463487	−	0.0166114i
$565$	3.56283	+	3.56283i	0.149889	+	0.149889i
$566$	4.36902	+	19.4801i	0.183644	+	0.818811i
$567$		0			0
$568$	−32.5448	−	4.04014i	−1.36555	−	0.169521i
$569$		−	35.0633i		−	1.46993i	−0.678105	−	0.734965i	$-0.737198\pi$
$569$		−	35.0633i		−	1.46993i	0.678105	−	0.734965i	$-0.262802\pi$
$570$	1.76815	−	0.396561i	0.0740595	−	0.0166101i
$571$	−0.913269	−	0.913269i	−0.0382191	−	0.0382191i	0.687739	−	0.725958i	$-0.258603\pi$
$571$	−0.913269	−	0.913269i	−0.0382191	−	0.0382191i	−0.725958	+	0.687739i	$0.758603\pi$
$572$	−4.96498	−	10.5119i	−0.207596	−	0.439524i
$573$	−7.04827	+	7.04827i	−0.294446	+	0.294446i
$574$		0			0
$575$	27.4720			1.14566
$576$	−2.12665	+	8.43348i	−0.0886104	+	0.351395i
$577$	−15.3294			−0.638171			−0.319086	−	0.947726i	$-0.603376\pi$
$577$	−15.3294			−0.638171			−0.319086	+	0.947726i	$0.603376\pi$
$578$	18.2014	+	11.5327i	0.757080	+	0.479695i
$579$	31.3194	−	31.3194i	1.30159	−	1.30159i
$580$	−0.248627	−	0.526395i	−0.0103237	−	0.0218574i
$581$		0			0
$582$	−34.2244	+	7.67588i	−1.41865	+	0.318176i
$583$			15.4322i			0.639138i
$584$	−1.00725	−	0.125040i	−0.0416801	−	0.00517420i
$585$		−	3.21066i		−	0.132744i
$586$	4.78547	+	21.3370i	0.197686	+	0.881423i
$587$	27.8270	+	27.8270i	1.14854	+	1.14854i	0.986840	+	0.161702i	$0.0516982\pi$
$587$	27.8270	+	27.8270i	1.14854	+	1.14854i	0.161702	+	0.986840i	$0.448302\pi$
$588$		0			0
$589$	−3.56299	+	3.56299i	−0.146810	+	0.146810i
$590$	10.4682	−	16.5215i	0.430969	−	0.680178i
$591$	21.7858			0.896148
$592$	39.5892	−	3.85708i	1.62711	−	0.158525i
$593$	−17.7962			−0.730803			−0.365401	−	0.930850i	$-0.619068\pi$
$593$	−17.7962			−0.730803			−0.365401	+	0.930850i	$0.619068\pi$
$594$	5.72043	−	9.02828i	0.234712	−	0.370435i
$595$		0			0
$596$	−6.71981	+	18.7495i	−0.275254	+	0.768008i
$597$	5.11236	+	5.11236i	0.209235	+	0.209235i
$598$	6.29987	+	28.0892i	0.257621	+	1.14865i
$599$		−	19.1935i		−	0.784226i	−0.919917	−	0.392113i	$-0.871744\pi$
$599$		−	19.1935i		−	0.784226i	0.919917	−	0.392113i	$-0.128256\pi$
$600$	18.1065	−	14.1074i	0.739195	−	0.575934i
$601$			26.9530i			1.09944i	0.835351	+	0.549718i	$0.185265\pi$
$601$			26.9530i			1.09944i	−0.835351	+	0.549718i	$0.814735\pi$
$602$		0			0
$603$	7.99597	+	7.99597i	0.325621	+	0.325621i
$604$	−18.7444	+	8.85337i	−0.762700	+	0.360238i
$605$	5.04144	−	5.04144i	0.204964	−	0.204964i
$606$	2.92178	+	1.85128i	0.118689	+	0.0752030i
$607$	29.4551			1.19555			0.597773	−	0.801665i	$-0.296052\pi$
$607$	29.4551			1.19555			0.597773	+	0.801665i	$0.296052\pi$
$608$	−1.62775	+	3.22320i	−0.0660140	+	0.130718i
$609$		0			0
$610$	4.44157	+	2.81424i	0.179834	+	0.113945i
$611$	−0.608197	+	0.608197i	−0.0246050	+	0.0246050i
$612$	11.1629	−	5.27247i	0.451235	−	0.213127i
$613$	−17.6491	−	17.6491i	−0.712839	−	0.712839i	0.254289	−	0.967128i	$-0.418159\pi$
$613$	−17.6491	−	17.6491i	−0.712839	−	0.712839i	−0.967128	+	0.254289i	$0.918159\pi$
$614$	28.8308	−	6.46620i	1.16352	−	0.260955i
$615$		−	4.82165i		−	0.194428i
$616$		0			0
$617$			10.8407i			0.436431i	0.975901	+	0.218216i	$0.0700236\pi$
$617$			10.8407i			0.436431i	−0.975901	+	0.218216i	$0.929976\pi$
$618$	3.65711	+	16.3059i	0.147110	+	0.655921i
$619$	−14.1990	−	14.1990i	−0.570707	−	0.570707i	0.361619	−	0.932326i	$-0.382224\pi$
$619$	−14.1990	−	14.1990i	−0.570707	−	0.570707i	−0.932326	+	0.361619i	$0.882224\pi$
$620$	5.28875	−	14.7566i	0.212401	−	0.592638i
$621$	−18.7141	+	18.7141i	−0.750969	+	0.750969i
$622$	−6.61232	+	10.4359i	−0.265130	+	0.418442i
$623$		0			0
$624$	18.5766	+	15.2782i	0.743657	+	0.611616i
$625$	−11.1840			−0.447361
$626$	−3.11686	+	4.91919i	−0.124575	+	0.196610i
$627$	−1.78334	+	1.78334i	−0.0712197	+	0.0712197i
$628$	7.76760	+	2.78391i	0.309961	+	0.111090i
$629$	−39.9233	−	39.9233i	−1.59185	−	1.59185i
$630$		0			0
$631$		−	5.71697i		−	0.227589i	−0.993504	−	0.113794i	$-0.963699\pi$
$631$		−	5.71697i		−	0.227589i	0.993504	−	0.113794i	$-0.0363005\pi$
$632$	−2.68272	+	21.6103i	−0.106713	+	0.859613i
$633$		−	20.9782i		−	0.833808i
$634$	33.7098	−	7.56045i	1.33879	−	0.300264i
$635$	−7.84307	−	7.84307i	−0.311243	−	0.311243i
$636$	−13.6359	−	28.8700i	−0.540698	−	1.14477i
$637$		0			0
$638$	0.684421	+	0.433657i	0.0270965	+	0.0171687i
$639$	12.6055			0.498668
$640$	0.296393	−	11.2295i	0.0117160	−	0.443886i
$641$	29.6950			1.17288			0.586441	−	0.809992i	$-0.300528\pi$
$641$	29.6950			1.17288			0.586441	+	0.809992i	$0.300528\pi$
$642$	−9.06340	−	5.74268i	−0.357704	−	0.226646i
$643$	−3.53512	+	3.53512i	−0.139412	+	0.139412i	−0.773368	−	0.633957i	$-0.781430\pi$
$643$	−3.53512	+	3.53512i	−0.139412	+	0.139412i	0.633957	+	0.773368i	$0.281430\pi$
$644$		0			0
$645$	7.33854	+	7.33854i	0.288955	+	0.288955i
$646$	5.00117	−	1.12167i	0.196768	−	0.0441314i
$647$		−	14.7556i		−	0.580104i	−0.957011	−	0.290052i	$-0.906327\pi$
$647$		−	14.7556i		−	0.580104i	0.957011	−	0.290052i	$-0.0936726\pi$
$648$	−3.86066	+	31.0991i	−0.151661	+	1.22169i
$649$			27.2216i			1.06854i
$650$	−3.69510	−	16.4753i	−0.144934	−	0.646216i
$651$		0			0
$652$	15.5597	+	5.57659i	0.609364	+	0.218396i
$653$	−7.00360	+	7.00360i	−0.274072	+	0.274072i	−0.830737	−	0.556665i	$-0.812081\pi$
$653$	−7.00360	+	7.00360i	−0.274072	+	0.274072i	0.556665	+	0.830737i	$0.312081\pi$
$654$	−15.3298	+	24.1943i	−0.599443	+	0.946073i
$655$	12.5190			0.489159
$656$	7.42071	+	6.10312i	0.289730	+	0.238287i
$657$	0.390135			0.0152206
$658$		0			0
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	−0.587722	−	0.809063i	$-0.699975\pi$
$659$	5.68205	−	5.68205i	0.221341	−	0.221341i	0.809063	+	0.587722i	$0.199975\pi$
$660$	2.64711	−	7.38591i	0.103039	−	0.287496i
$661$	6.78275	+	6.78275i	0.263819	+	0.263819i	0.826603	−	0.562785i	$-0.190270\pi$
$661$	6.78275	+	6.78275i	0.263819	+	0.263819i	−0.562785	+	0.826603i	$0.690270\pi$
$662$	2.26050	+	10.0789i	0.0878569	+	0.391727i
$663$		−	34.1404i		−	1.32590i
$664$	1.04238	+	1.33786i	0.0404521	+	0.0519192i
$665$		0			0
$666$	−14.9187	+	3.34597i	−0.578086	+	0.129654i
$667$	−1.41869	−	1.41869i	−0.0549317	−	0.0549317i
$668$	−16.1433	+	7.62479i	−0.624602	+	0.295012i
$669$	−6.09037	+	6.09037i	−0.235467	+	0.235467i
$670$	−12.3371	−	7.81695i	−0.476625	−	0.301995i
$671$	−7.31815			−0.282514
$672$		0			0
$673$	3.24280			0.125001			0.0625004	−	0.998045i	$-0.480093\pi$
$673$	3.24280			0.125001			0.0625004	+	0.998045i	$0.480093\pi$
$674$	−11.3963	−	7.22086i	−0.438971	−	0.278137i
$675$	10.9765	−	10.9765i	0.422485	−	0.422485i
$676$	−7.51147	+	3.54782i	−0.288903	+	0.136454i
$677$	−23.7096	−	23.7096i	−0.911234	−	0.911234i	0.0851352	−	0.996369i	$-0.472868\pi$
$677$	−23.7096	−	23.7096i	−0.911234	−	0.911234i	−0.996369	+	0.0851352i	$0.972868\pi$
$678$	14.1570	−	3.17515i	0.543698	−	0.121941i
$679$		0			0
$680$	−12.5780	+	9.79995i	−0.482343	+	0.375811i
$681$			9.78140i			0.374824i
$682$	4.77458	+	21.2884i	0.182828	+	0.815175i
$683$	13.1530	+	13.1530i	0.503284	+	0.503284i	0.912457	−	0.409173i	$-0.134183\pi$
$683$	13.1530	+	13.1530i	0.503284	+	0.503284i	−0.409173	+	0.912457i	$0.634183\pi$
$684$	0.468275	−	1.30657i	0.0179049	−	0.0499580i
$685$	−11.3762	+	11.3762i	−0.434662	+	0.434662i
$686$		0			0
$687$	39.6602			1.51313
$688$	−20.5832	+	2.00537i	−0.784728	+	0.0764540i
$689$	−23.4864			−0.894761
$690$	−10.3984	+	16.4112i	−0.395859	+	0.624765i
$691$	−15.3221	+	15.3221i	−0.582878	+	0.582878i	−0.935693	−	0.352815i	$-0.885225\pi$
$691$	−15.3221	+	15.3221i	−0.582878	+	0.582878i	0.352815	+	0.935693i	$0.385225\pi$
$692$	−10.2600	−	3.67718i	−0.390026	−	0.139786i
$693$		0			0
$694$	2.82783	+	12.6085i	0.107343	+	0.478611i
$695$		−	14.7463i		−	0.559361i
$696$	−1.66356	−	0.206516i	−0.0630572	−	0.00782797i
$697$		−	13.6380i		−	0.516574i
$698$	−47.7853	+	10.7173i	−1.80870	+	0.405657i
$699$	−7.24128	−	7.24128i	−0.273891	−	0.273891i
$700$		0			0
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	−0.607202	−	0.794547i	$-0.707708\pi$
$701$	4.96023	−	4.96023i	0.187345	−	0.187345i	0.794547	+	0.607202i	$0.207708\pi$
$702$	13.7402	+	8.70595i	0.518590	+	0.328585i
$703$	−6.34759			−0.239404
$704$	8.01657	+	13.4229i	0.302136	+	0.505895i
$705$	−0.580491			−0.0218626
$706$	31.1438	+	19.7331i	1.17211	+	0.742664i
$707$		0			0
$708$	−24.0529	−	50.9250i	−0.903963	−	1.91388i
$709$	−10.2322	−	10.2322i	−0.384277	−	0.384277i	0.488363	−	0.872640i	$-0.337594\pi$
$709$	−10.2322	−	10.2322i	−0.384277	−	0.384277i	−0.872640	+	0.488363i	$0.837594\pi$
$710$	−15.8863	+	3.56300i	−0.596203	+	0.133717i
$711$		−	8.37030i		−	0.313911i
$712$	49.3695	+	6.12877i	1.85020	+	0.229685i
$713$		−	54.0240i		−	2.02321i
$714$		0			0
$715$	−4.08105	−	4.08105i	−0.152623	−	0.152623i
$716$	18.3696	+	6.58365i	0.686503	+	0.246043i
$717$	−13.3304	+	13.3304i	−0.497833	+	0.497833i
$718$	−2.63724	+	4.16223i	−0.0984209	+	0.155333i
$719$	−33.1292			−1.23551			−0.617756	−	0.786370i	$-0.711958\pi$
$719$	−33.1292			−1.23551			−0.617756	+	0.786370i	$0.711958\pi$
$720$	0.418698	+	4.29753i	0.0156039	+	0.160160i
$721$		0			0
$722$	−14.0730	+	22.2107i	−0.523742	+	0.826598i
$723$	−36.7857	+	36.7857i	−1.36808	+	1.36808i
$724$	−8.04428	+	22.4450i	−0.298963	+	0.834160i
$725$	0.832110	+	0.832110i	0.0309038	+	0.0309038i
$726$	−4.49288	−	20.0324i	−0.166746	−	0.743471i
$727$		−	23.5496i		−	0.873406i	−0.899606	−	0.436703i	$-0.856146\pi$
$727$		−	23.5496i		−	0.873406i	0.899606	−	0.436703i	$-0.143854\pi$
$728$		0			0
$729$			11.4085i			0.422538i
$730$	−0.491673	+	0.110273i	−0.0181977	+	0.00408138i
$731$	20.7569	+	20.7569i	0.767723	+	0.767723i
$732$	13.6905	−	6.46630i	0.506015	−	0.239001i
$733$	−1.26479	+	1.26479i	−0.0467162	+	0.0467162i	−0.730079	−	0.683363i	$-0.760517\pi$
$733$	−1.26479	+	1.26479i	−0.0467162	+	0.0467162i	0.683363	+	0.730079i	$0.260517\pi$
$734$	−29.2153	−	18.5112i	−1.07836	−	0.683260i
$735$		0			0
$736$	−12.0956	−	36.7764i	−0.445849	−	1.35560i
$737$	20.3272			0.748764
$738$	−3.11963	−	1.97664i	−0.114835	−	0.0727610i
$739$	16.5610	−	16.5610i	0.609206	−	0.609206i	−0.333532	−	0.942739i	$-0.608241\pi$
$739$	16.5610	−	16.5610i	0.609206	−	0.609206i	0.942739	+	0.333532i	$0.108241\pi$
$740$	17.8557	−	8.43362i	0.656389	−	0.310026i
$741$	−2.71407	−	2.71407i	−0.0997039	−	0.0997039i
$742$		0			0
$743$		−	13.9219i		−	0.510747i	−0.966843	−	0.255373i	$-0.917802\pi$
$743$		−	13.9219i		−	0.510747i	0.966843	−	0.255373i	$-0.0821984\pi$
$744$	−27.7424	−	35.6066i	−1.01709	−	1.30540i
$745$			9.88798i			0.362268i
$746$	11.3743	+	50.7147i	0.416444	+	1.85680i
$747$	−0.460968	−	0.460968i	−0.0168659	−	0.0168659i
$748$	7.48732	−	20.8909i	0.273763	−	0.763848i
$749$		0			0
$750$	13.6959	−	21.6156i	0.500104	−	0.789291i
$751$	−9.07708			−0.331227			−0.165614	−	0.986191i	$-0.552960\pi$
$751$	−9.07708			−0.331227			−0.165614	+	0.986191i	$0.552960\pi$
$752$	0.734770	−	0.893399i	0.0267943	−	0.0325789i
$753$	10.4177			0.379642
$754$	−0.659985	+	1.04162i	−0.0240352	+	0.0379337i
$755$	−7.27718	+	7.27718i	−0.264844	+	0.264844i
$756$		0			0
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	0.686078	−	0.727528i	$-0.259331\pi$
$757$	−1.14043	−	1.14043i	−0.0414496	−	0.0414496i	−0.727528	+	0.686078i	$0.759331\pi$
$758$	8.10525	+	36.1389i	0.294396	+	1.31262i
$759$		−	27.0400i		−	0.981488i
$760$	−0.220844	+	1.77898i	−0.00801087	+	0.0645305i
$761$		−	8.78122i		−	0.318319i	−0.987253	−	0.159159i	$-0.949122\pi$
$761$		−	8.78122i		−	0.318319i	0.987253	−	0.159159i	$-0.0508784\pi$
$762$	−31.1648	+	6.98966i	−1.12898	+	0.253209i
$763$		0			0
$764$	−4.21137	−	8.91635i	−0.152362	−	0.322582i
$765$	4.33380	−	4.33380i	0.156689	−	0.156689i
$766$	18.8696	+	11.9560i	0.681787	+	0.431989i
$767$	−41.4287			−1.49590
$768$	−26.8575	−	18.0276i	−0.969136	−	0.650515i
$769$	−29.8204			−1.07535			−0.537676	−	0.843152i	$-0.680697\pi$
$769$	−29.8204			−1.07535			−0.537676	+	0.843152i	$0.680697\pi$
$770$		0			0
$771$	5.36862	−	5.36862i	0.193346	−	0.193346i
$772$	18.7134	+	39.6202i	0.673511	+	1.42596i
$773$	−32.6111	−	32.6111i	−1.17294	−	1.17294i	−0.981505	−	0.191435i	$-0.938686\pi$
$773$	−32.6111	−	32.6111i	−1.17294	−	1.17294i	−0.191435	−	0.981505i	$-0.561314\pi$
$774$	7.75651	−	1.73964i	0.278802	−	0.0625299i
$775$			31.6870i			1.13823i
$776$	4.27469	−	34.4342i	0.153452	−	1.23612i
$777$		0			0
$778$	1.76452	+	7.86746i	0.0632611	+	0.282062i
$779$	−1.08418	−	1.08418i	−0.0388448	−	0.0388448i
$780$	11.2407	+	4.02866i	0.402480	+	0.144249i
$781$	16.0228	−	16.0228i	0.573342	−	0.573342i
$782$	−29.4116	+	46.4189i	−1.05176	+	1.65994i
$783$	−1.13367			−0.0405142
$784$		0			0
$785$	4.09643			0.146208
$786$	19.2940	−	30.4509i	0.688195	−	1.08615i
$787$	−18.5275	+	18.5275i	−0.660435	+	0.660435i	−0.955482	−	0.295048i	$-0.904664\pi$
$787$	−18.5275	+	18.5275i	−0.660435	+	0.660435i	0.295048	+	0.955482i	$0.404664\pi$
$788$	−7.27140	+	20.2885i	−0.259033	+	0.722748i
$789$	−26.9479	−	26.9479i	−0.959369	−	0.959369i
$790$	2.36589	+	10.5488i	0.0841746	+	0.375309i
$791$		0			0
$792$	−3.69354	−	4.74056i	−0.131244	−	0.168448i
$793$		−	11.1375i		−	0.395506i
$794$	−1.38851	+	0.311415i	−0.0492762	+	0.0110517i
$795$	−11.2082	−	11.2082i	−0.397515	−	0.397515i
$796$	−6.46734	+	3.05465i	−0.229229	+	0.108269i
$797$	16.7419	−	16.7419i	0.593028	−	0.593028i	−0.345420	−	0.938448i	$-0.612264\pi$
$797$	16.7419	−	16.7419i	0.593028	−	0.593028i	0.938448	+	0.345420i	$0.112264\pi$
$798$		0			0
$799$	−1.64191			−0.0580866
$800$	7.09449	+	21.5707i	0.250828	+	0.762639i
$801$	−19.1222			−0.675650
$802$	−20.7937	−	13.1751i	−0.734252	−	0.465231i
$803$	0.495898	−	0.495898i	0.0174999	−	0.0174999i
$804$	−38.0274	+	17.9611i	−1.34112	+	0.633439i
$805$		0			0
$806$	−32.3989	+	7.26645i	−1.14120	+	0.255950i
$807$		−	34.6690i		−	1.22041i
$808$	−2.69924	+	2.10308i	−0.0949590	+	0.0739860i
$809$			35.5325i			1.24926i	0.780923	+	0.624628i	$0.214749\pi$
$809$			35.5325i			1.24926i	−0.780923	+	0.624628i	$0.785251\pi$
$810$	3.40472	+	15.1806i	0.119629	+	0.533392i
$811$	−29.5602	−	29.5602i	−1.03800	−	1.03800i	−0.999249	−	0.0387507i	$-0.987662\pi$
$811$	−29.5602	−	29.5602i	−1.03800	−	1.03800i	−0.0387507	−	0.999249i	$-0.512338\pi$
$812$		0			0
$813$	−7.59395	+	7.59395i	−0.266331	+	0.266331i
$814$	−14.7100	+	23.2161i	−0.515584	+	0.813722i
$815$	8.20576			0.287435
$816$	4.45220	+	45.6976i	0.155858	+	1.59974i
$817$	3.30024			0.115461
$818$	−28.8952	+	45.6040i	−1.01030	+	1.59451i
$819$		0			0
$820$	4.49027	+	1.60931i	0.156807	+	0.0561996i
$821$	5.59033	+	5.59033i	0.195104	+	0.195104i	0.797897	−	0.602794i	$-0.205946\pi$
$821$	5.59033	+	5.59033i	0.195104	+	0.195104i	−0.602794	+	0.797897i	$0.705946\pi$
$822$	10.1383	+	45.2037i	0.353615	+	1.57666i
$823$			49.8955i			1.73925i	0.493716	+	0.869623i	$0.335638\pi$
$823$			49.8955i			1.73925i	−0.493716	+	0.869623i	$0.664362\pi$
$824$	−16.4059	−	2.03664i	−0.571526	−	0.0709497i
$825$			15.8599i			0.552171i
$826$		0			0
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	0.551758	−	0.834004i	$-0.313957\pi$
$827$	−8.11672	−	8.11672i	−0.282246	−	0.282246i	−0.834004	+	0.551758i	$0.813957\pi$
$828$	6.35535	+	13.4556i	0.220864	+	0.467614i
$829$	5.02945	−	5.02945i	0.174680	−	0.174680i	−0.614352	−	0.789032i	$-0.710583\pi$
$829$	5.02945	−	5.02945i	0.174680	−	0.174680i	0.789032	+	0.614352i	$0.210583\pi$
$830$	0.711235	+	0.450647i	0.0246873	+	0.0156422i
$831$	−30.7318			−1.06607
$832$	−20.4284	+	12.2005i	−0.708227	+	0.422975i
$833$		0			0
$834$	−35.8685	−	22.7267i	−1.24202	−	0.786962i
$835$	−6.26733	+	6.26733i	−0.216890	+	0.216890i
$836$	−1.06555	−	2.25599i	−0.0368529	−	0.0780252i
$837$	−21.5853	−	21.5853i	−0.746099	−	0.746099i
$838$	52.6918	−	11.8177i	1.82021	−	0.408237i
$839$			3.57060i			0.123271i	0.998099	+	0.0616354i	$0.0196316\pi$
$839$			3.57060i			0.123271i	−0.998099	+	0.0616354i	$0.980368\pi$
$840$		0			0
$841$			28.9141i			0.997036i
$842$	−8.38049	−	37.3661i	−0.288811	−	1.28772i
$843$	−4.51429	−	4.51429i	−0.155480	−	0.155480i
$844$	19.5364	+	7.00185i	0.672470	+	0.241014i
$845$	−2.91619	+	2.91619i	−0.100320	+	0.100320i
$846$	−0.237973	+	0.375581i	−0.00818167	+	0.0129127i
$847$		0			0
$848$	31.4370	−	3.06283i	1.07955	−	0.105178i
$849$	28.5395			0.979473
$850$	17.2510	−	27.2264i	0.591703	−	0.933857i
$851$	48.1228	−	48.1228i	1.64963	−	1.64963i
$852$	−15.8171	+	44.1325i	−0.541885	+	1.51196i
$853$	−13.8958	−	13.8958i	−0.475784	−	0.475784i	0.427996	−	0.903780i	$-0.359220\pi$
$853$	−13.8958	−	13.8958i	−0.475784	−	0.475784i	−0.903780	+	0.427996i	$0.859220\pi$
$854$		0			0
$855$		−	0.689051i		−	0.0235650i
$856$	8.37307	−	6.52377i	0.286186	−	0.222978i
$857$		−	40.2114i		−	1.37360i	−0.726848	−	0.686798i	$-0.759016\pi$
$857$		−	40.2114i		−	1.37360i	0.726848	−	0.686798i	$-0.240984\pi$
$858$	−16.2162	+	3.63699i	−0.553613	+	0.124165i
$859$	−18.3327	−	18.3327i	−0.625502	−	0.625502i	0.321431	−	0.946933i	$-0.395836\pi$
$859$	−18.3327	−	18.3327i	−0.625502	−	0.625502i	−0.946933	+	0.321431i	$0.895836\pi$
$860$	−9.28354	+	4.38480i	−0.316566	+	0.149521i
$861$		0			0
$862$	1.50175	+	0.951526i	0.0511497	+	0.0324091i
$863$	16.4582			0.560243			0.280121	−	0.959965i	$-0.409625\pi$
$863$	16.4582			0.560243			0.280121	+	0.959965i	$0.409625\pi$
$864$	−19.5268	−	9.86125i	−0.664317	−	0.335487i
$865$	−5.41085			−0.183974
$866$	10.9531	+	6.94004i	0.372203	+	0.235832i
$867$	21.7811	−	21.7811i	0.739724	−	0.739724i
$868$		0			0
$869$	−10.6394	−	10.6394i	−0.360918	−	0.360918i
$870$	−0.812046	+	0.182126i	−0.0275309	+	0.00617466i
$871$			30.9361i			1.04823i
$872$	−17.4149	−	22.3515i	−0.589742	−	0.756918i
$873$			13.3374i			0.451401i
$874$	1.35204	+	6.02832i	0.0457333	+	0.203911i
$875$		0			0
$876$	−0.489531	+	1.36588i	−0.0165397	+	0.0461488i
$877$	16.1432	−	16.1432i	0.545118	−	0.545118i	−0.379906	−	0.925025i	$-0.624044\pi$
$877$	16.1432	−	16.1432i	0.545118	−	0.545118i	0.925025	+	0.379906i	$0.124044\pi$
$878$	6.02949	−	9.51605i	0.203485	−	0.321151i
$879$	31.2599			1.05437
$880$	5.99477	+	4.93037i	0.202084	+	0.166203i
$881$	−5.29761			−0.178481			−0.0892405	−	0.996010i	$-0.528444\pi$
$881$	−5.29761			−0.178481			−0.0892405	+	0.996010i	$0.528444\pi$
$882$		0			0
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.0351900	+	0.999381i	$0.511204\pi$
$883$	−30.7426	+	30.7426i	−1.03457	+	1.03457i	−0.999381	+	0.0351900i	$0.988796\pi$
$884$	31.7940	+	11.3950i	1.06935	+	0.383255i
$885$	−19.7707	−	19.7707i	−0.664585	−	0.664585i
$886$	7.74403	+	34.5283i	0.260166	+	1.16000i
$887$			5.82199i			0.195483i	0.995212	+	0.0977417i	$0.0311619\pi$
$887$			5.82199i			0.195483i	−0.995212	+	0.0977417i	$0.968838\pi$
$888$	7.00518	−	56.4293i	0.235078	−	1.89364i
$889$		0			0
$890$	24.0991	−	5.40496i	0.807802	−	0.181175i
$891$	−15.3110	−	15.3110i	−0.512939	−	0.512939i
$892$	−3.63902	−	7.70457i	−0.121843	−	0.257968i
$893$	−0.130527	+	0.130527i	−0.00436793	+	0.00436793i
$894$	24.0512	+	15.2391i	0.804392	+	0.509672i
$895$	9.68763			0.323822
$896$		0			0
$897$	41.1522			1.37403
$898$	−9.95150	−	6.30539i	−0.332086	−	0.210414i
$899$	1.63635	−	1.63635i	0.0545754	−	0.0545754i
$900$	−3.72764	−	7.89219i	−0.124255	−	0.263073i
$901$	−31.7023	−	31.7023i	−1.05616	−	1.05616i
$902$	−6.47784	+	1.45285i	−0.215688	+	0.0483748i
$903$		0			0
$904$	−1.76824	+	14.2438i	−0.0588107	+	0.473742i
$905$			11.8369i			0.393471i
$906$	6.48534	+	28.9162i	0.215461	+	0.960675i
$907$	−14.8840	−	14.8840i	−0.494214	−	0.494214i	0.415417	−	0.909631i	$-0.363636\pi$
$907$	−14.8840	−	14.8840i	−0.494214	−	0.494214i	−0.909631	+	0.415417i	$0.863636\pi$
$908$	−9.10914	−	3.26472i	−0.302298	−	0.108343i
$909$	0.930037	−	0.930037i	0.0308474	−	0.0308474i
$910$		0			0
$911$	−46.3231			−1.53475			−0.767376	−	0.641197i	$-0.778438\pi$
$911$	−46.3231			−1.53475			−0.767376	+	0.641197i	$0.778438\pi$
$912$	3.98678	+	3.27890i	0.132015	+	0.108575i
$913$	−1.17187			−0.0387831
$914$	−10.9547	+	17.2893i	−0.362350	+	0.571879i
$915$	5.31508	−	5.31508i	0.175711	−	0.175711i
$916$	−13.2373	+	36.9344i	−0.437373	+	1.22035i
$917$		0			0
$918$	6.79529	+	30.2982i	0.224278	+	0.999988i
$919$		−	14.8697i		−	0.490505i	−0.969459	−	0.245253i	$-0.921129\pi$
$919$		−	14.8697i		−	0.490505i	0.969459	−	0.245253i	$-0.0788709\pi$
$920$	−11.8127	−	15.1612i	−0.389453	−	0.499852i
$921$		−	42.2388i		−	1.39182i
$922$	8.25533	−	1.85151i	0.271875	−	0.0609763i
$923$	24.3852	+	24.3852i	0.802649	+	0.802649i
$924$		0			0
$925$	−28.2258	+	28.2258i	−0.928058	+	0.928058i
$926$	−30.1025	−	19.0733i	−0.989230	−	0.626788i
$927$	6.35446			0.208708
$928$	0.747567	−	1.48030i	0.0245401	−	0.0485933i
$929$	51.7008			1.69625			0.848124	−	0.529798i	$-0.177732\pi$
$929$	51.7008			1.69625			0.848124	+	0.529798i	$0.177732\pi$
$930$	−18.9292	−	11.9938i	−0.620713	−	0.393291i
$931$		0			0
$932$	9.16052	−	4.32670i	0.300063	−	0.141726i
$933$	12.4883	+	12.4883i	0.408849	+	0.408849i
$934$	−21.2022	+	4.75525i	−0.693758	+	0.155596i
$935$		−	11.0173i		−	0.360305i
$936$	7.21468	−	5.62122i	0.235819	−	0.183735i
$937$			50.1408i			1.63803i	0.573773	+	0.819014i	$0.305479\pi$
$937$			50.1408i			1.63803i	−0.573773	+	0.819014i	$0.694521\pi$
$938$		0			0
$939$	5.88663	+	5.88663i	0.192103	+	0.192103i
$940$	0.193749	−	0.540595i	0.00631941	−	0.0176323i
$941$	−31.7068	+	31.7068i	−1.03361	+	1.03361i	−0.0341962	+	0.999415i	$0.510887\pi$
$941$	−31.7068	+	31.7068i	−1.03361	+	1.03361i	−0.999415	+	0.0341962i	$0.989113\pi$
$942$	6.31332	−	9.96401i	0.205699	−	0.324645i
$943$	16.4389			0.535326
$944$	55.4531	−	5.40265i	1.80485	−	0.175841i
$945$		0			0
$946$	7.64801	−	12.0705i	0.248658	−	0.392445i
$947$	1.16699	−	1.16699i	0.0379222	−	0.0379222i	−0.687891	−	0.725814i	$-0.741463\pi$
$947$	1.16699	−	1.16699i	0.0379222	−	0.0379222i	0.725814	+	0.687891i	$0.241463\pi$
$948$	29.3048	+	10.5028i	0.951775	+	0.341116i
$949$	0.754710	+	0.754710i	0.0244989	+	0.0244989i
$950$	−0.793018	−	3.53583i	−0.0257289	−	0.114717i
$951$		−	49.3867i		−	1.60147i
$952$		0			0
$953$		−	40.9510i		−	1.32653i	−0.748384	−	0.663266i	$-0.769170\pi$
$953$		−	40.9510i		−	1.32653i	0.748384	−	0.663266i	$-0.230830\pi$
$954$	−11.8466	+	2.65697i	−0.383548	+	0.0860225i
$955$	−3.46161	−	3.46161i	−0.112015	−	0.112015i
$956$	−7.96497	−	16.8635i	−0.257606	−	0.545405i
$957$	0.819023	−	0.819023i	0.0264753	−	0.0264753i
$958$	24.8828	+	15.7661i	0.803927	+	0.509378i
$959$		0			0
$960$	−15.5712	−	3.92656i	−0.502559	−	0.126729i
$961$	31.3129			1.01009
$962$	−35.3326	−	22.3872i	−1.13917	−	0.721792i
$963$	−2.88498	+	2.88498i	−0.0929673	+	0.0929673i
$964$	−21.9796	−	46.5354i	−0.707916	−	1.49881i
$965$	15.3818	+	15.3818i	0.495159	+	0.495159i
$966$		0			0
$967$			14.6315i			0.470518i	0.971933	+	0.235259i	$0.0755938\pi$
$967$			14.6315i			0.470518i	−0.971933	+	0.235259i	$0.924406\pi$
$968$	20.1552	+	2.50208i	0.647812	+	0.0804198i
$969$		−	7.32699i		−	0.235377i
$970$	−3.76985	−	16.8086i	−0.121042	−	0.539692i
$971$	−17.2723	−	17.2723i	−0.554295	−	0.554295i	0.373382	−	0.927678i	$-0.378198\pi$
$971$	−17.2723	−	17.2723i	−0.554295	−	0.554295i	−0.927678	+	0.373382i	$0.878198\pi$
$972$	20.3299	+	7.28623i	0.652081	+	0.233706i
$973$		0			0
$974$	0.168362	−	0.265717i	0.00539466	−	0.00851413i
$975$	−24.1373			−0.773012
$976$	1.45243	+	14.9078i	0.0464912	+	0.477188i
$977$	−5.71563			−0.182859			−0.0914295	−	0.995812i	$-0.529144\pi$
$977$	−5.71563			−0.182859			−0.0914295	+	0.995812i	$0.529144\pi$
$978$	12.6465	−	19.9594i	0.404391	−	0.638232i
$979$	−24.3061	+	24.3061i	−0.776827	+	0.776827i
$980$		0			0
$981$	7.70133	+	7.70133i	0.245885	+	0.245885i
$982$	7.94781	+	35.4369i	0.253625	+	1.13084i
$983$		−	21.5599i		−	0.687654i	−0.939033	−	0.343827i	$-0.888277\pi$
$983$		−	21.5599i		−	0.687654i	0.939033	−	0.343827i	$-0.111723\pi$
$984$	10.8347	−	8.44173i	0.345399	−	0.269113i
$985$			10.6996i			0.340918i
$986$	−2.29686	+	0.515141i	−0.0731469	+	0.0164054i
$987$		0			0
$988$	3.43341	−	1.62167i	0.109231	−	0.0515921i
$989$	−25.0200	+	25.0200i	−0.795590	+	0.795590i
$990$	−2.52018	−	1.59681i	−0.0800964	−	0.0507501i
$991$	−34.7621			−1.10426			−0.552128	−	0.833759i	$-0.686184\pi$
$991$	−34.7621			−1.10426			−0.552128	+	0.833759i	$0.686184\pi$
$992$	42.4190	−	13.9514i	1.34680	−	0.442957i
$993$	14.7661			0.468590
$994$		0			0
$995$	−2.51082	+	2.51082i	−0.0795985	+	0.0795985i
$996$	2.19228	−	1.03546i	0.0694650	−	0.0328097i
$997$	−3.62794	−	3.62794i	−0.114898	−	0.114898i	0.647320	−	0.762218i	$-0.275890\pi$
$997$	−3.62794	−	3.62794i	−0.114898	−	0.114898i	−0.762218	+	0.647320i	$0.775890\pi$
$998$	4.84512	−	1.08667i	0.153370	−	0.0343978i
$999$		−	38.4551i		−	1.21666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.k.197.10		24
7.2	even	3		784.2.x.o.165.7		48
7.3	odd	6		112.2.w.c.37.3	✓	48
7.4	even	3		784.2.x.o.373.3		48
7.5	odd	6		112.2.w.c.53.7	yes	48
7.6	odd	2		784.2.m.j.197.10		24
16.13	even	4	inner	784.2.m.k.589.10		24
28.3	even	6		448.2.ba.c.177.3		48
28.19	even	6		448.2.ba.c.305.10		48
56.3	even	6		896.2.ba.e.737.10		48
56.5	odd	6		896.2.ba.f.865.10		48
56.19	even	6		896.2.ba.e.865.3		48
56.45	odd	6		896.2.ba.f.737.3		48
112.3	even	12		448.2.ba.c.401.10		48
112.5	odd	12		896.2.ba.f.417.3		48
112.13	odd	4		784.2.m.j.589.10		24
112.19	even	12		448.2.ba.c.81.3		48
112.45	odd	12		112.2.w.c.93.7	yes	48
112.59	even	12		896.2.ba.e.289.3		48
112.61	odd	12		112.2.w.c.109.3	yes	48
112.75	even	12		896.2.ba.e.417.10		48
112.93	even	12		784.2.x.o.557.3		48
112.101	odd	12		896.2.ba.f.289.10		48
112.109	even	12		784.2.x.o.765.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.3	✓	48	7.3	odd	6
112.2.w.c.53.7	yes	48	7.5	odd	6
112.2.w.c.93.7	yes	48	112.45	odd	12
112.2.w.c.109.3	yes	48	112.61	odd	12
448.2.ba.c.81.3		48	112.19	even	12
448.2.ba.c.177.3		48	28.3	even	6
448.2.ba.c.305.10		48	28.19	even	6
448.2.ba.c.401.10		48	112.3	even	12
784.2.m.j.197.10		24	7.6	odd	2
784.2.m.j.589.10		24	112.13	odd	4
784.2.m.k.197.10		24	1.1	even	1	trivial
784.2.m.k.589.10		24	16.13	even	4	inner
784.2.x.o.165.7		48	7.2	even	3
784.2.x.o.373.3		48	7.4	even	3
784.2.x.o.557.3		48	112.93	even	12
784.2.x.o.765.7		48	112.109	even	12
896.2.ba.e.289.3		48	112.59	even	12
896.2.ba.e.417.10		48	112.75	even	12
896.2.ba.e.737.10		48	56.3	even	6
896.2.ba.e.865.3		48	56.19	even	6
896.2.ba.f.289.10		48	112.101	odd	12
896.2.ba.f.417.3		48	112.5	odd	12
896.2.ba.f.737.3		48	56.45	odd	6
896.2.ba.f.865.10		48	56.5	odd	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +O(q^{10})\)	\(q+(1.19460 + 0.756916i) q^{2} +(1.42954 - 1.42954i) q^{3} +(0.854157 + 1.80843i) q^{4} +(0.702089 + 0.702089i) q^{5} +(2.78978 - 0.625694i) q^{6} +(-0.348448 + 2.80688i) q^{8} -1.08719i q^{9} +(0.307296 + 1.37014i) q^{10} +(-1.38191 - 1.38191i) q^{11} +(3.80628 + 1.36417i) q^{12} +(2.10314 - 2.10314i) q^{13} +2.00733 q^{15} +(-2.54083 + 3.08937i) q^{16} +5.67771 q^{17} +(0.822907 - 1.29876i) q^{18} +(0.451363 - 0.451363i) q^{19} +(-0.669984 + 1.86937i) q^{20} +(-0.604848 - 2.69683i) q^{22} +6.84381i q^{23} +(3.51444 + 4.51068i) q^{24} -4.01414i q^{25} +(4.10432 - 0.920521i) q^{26} +(2.73445 + 2.73445i) q^{27} +(-0.207295 + 0.207295i) q^{29} +(2.39797 + 1.51938i) q^{30} -7.89385 q^{31} +(-5.37368 + 1.76737i) q^{32} -3.95101 q^{33} +(6.78261 + 4.29755i) q^{34} +(1.96610 - 0.928627i) q^{36} +(-7.03159 - 7.03159i) q^{37} +(0.880843 - 0.197556i) q^{38} -6.01306i q^{39} +(-2.21532 + 1.72604i) q^{40} -2.40202i q^{41} +(3.65586 + 3.65586i) q^{43} +(1.31872 - 3.67947i) q^{44} +(0.763301 - 0.763301i) q^{45} +(-5.18019 + 8.17564i) q^{46} -0.289185 q^{47} +(0.784155 + 8.04861i) q^{48} +(3.03837 - 4.79531i) q^{50} +(8.11653 - 8.11653i) q^{51} +(5.59980 + 2.00697i) q^{52} +(-5.58365 - 5.58365i) q^{53} +(1.19684 + 5.33633i) q^{54} -1.94045i q^{55} -1.29048i q^{57} +(-0.404540 + 0.0907305i) q^{58} +(-9.84923 - 9.84923i) q^{59} +(1.71458 + 3.63012i) q^{60} +(2.64783 - 2.64783i) q^{61} +(-9.43003 - 5.97498i) q^{62} +(-7.75717 - 1.95611i) q^{64} +2.95319 q^{65} +(-4.71989 - 2.99058i) q^{66} +(-7.35474 + 7.35474i) q^{67} +(4.84966 + 10.2677i) q^{68} +(9.78352 + 9.78352i) q^{69} +11.5947i q^{71} +(3.05160 + 0.378828i) q^{72} +0.358849i q^{73} +(-3.07764 - 13.7223i) q^{74} +(-5.73839 - 5.73839i) q^{75} +(1.20179 + 0.430722i) q^{76} +(4.55138 - 7.18323i) q^{78} +7.69906 q^{79} +(-3.95290 + 0.385121i) q^{80} +11.0796 q^{81} +(1.81812 - 2.86946i) q^{82} +(0.424001 - 0.424001i) q^{83} +(3.98626 + 3.98626i) q^{85} +(1.60013 + 7.13449i) q^{86} +0.592673i q^{87} +(4.36039 - 3.39734i) q^{88} -17.5887i q^{89} +(1.48960 - 0.334088i) q^{90} +(-12.3765 + 5.84569i) q^{92} +(-11.2846 + 11.2846i) q^{93} +(-0.345462 - 0.218889i) q^{94} +0.633794 q^{95} +(-5.15536 + 10.2084i) q^{96} -12.2678 q^{97} +(-1.50240 + 1.50240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27} + 12 q^{29} + 4 q^{30} + 28 q^{31} - 16 q^{32} + 16 q^{33} + 22 q^{34} - 36 q^{36} + 24 q^{37} + 20 q^{38} + 26 q^{40} - 20 q^{43} - 6 q^{44} - 28 q^{45} + 14 q^{46} - 20 q^{47} - 28 q^{48} + 28 q^{50} - 24 q^{51} - 16 q^{52} + 16 q^{53} + 64 q^{54} + 6 q^{58} - 20 q^{59} - 46 q^{60} + 8 q^{61} - 12 q^{62} + 40 q^{64} - 8 q^{65} - 20 q^{66} - 48 q^{67} + 20 q^{69} + 32 q^{72} + 8 q^{74} - 4 q^{75} + 18 q^{76} + 58 q^{78} + 36 q^{79} - 28 q^{80} + 2 q^{82} + 4 q^{83} + 20 q^{86} + 42 q^{88} + 10 q^{90} + 38 q^{92} - 8 q^{93} - 72 q^{94} + 4 q^{95} - 120 q^{96} + 24 q^{97} - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

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