LMFDB - Embedded newform 784.2.m.k.589.10

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			589.10
Character	$\chi$	$=$	784.589
Dual form			784.2.m.k.197.10

$q$-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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	0.986869	−	0.161522i	$-0.0516403\pi$
$3$	1.42954	+	1.42954i	0.825347	+	0.825347i	−0.161522	+	0.986869i	$0.551640\pi$
$4$	0.854157	−	1.80843i	0.427079	−	0.904214i
$5$	0.702089	−	0.702089i	0.313984	−	0.313984i	−0.532467	−	0.846451i	$-0.678735\pi$
$5$	0.702089	−	0.702089i	0.313984	−	0.313984i	0.846451	+	0.532467i	$0.178735\pi$
$6$	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	−0.884052	−	0.467389i	$-0.845195\pi$
$11$	−1.38191	+	1.38191i	−0.416663	+	0.416663i	0.467389	+	0.884052i	$0.345195\pi$
$12$	3.80628	−	1.36417i	1.09878	−	0.393803i
$13$	2.10314	+	2.10314i	0.583307	+	0.583307i	0.935810	−	0.352504i	$-0.114670\pi$
$13$	2.10314	+	2.10314i	0.583307	+	0.583307i	−0.352504	+	0.935810i	$0.614670\pi$
$14$		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	0.756984	−	0.653434i	$-0.226672\pi$
$19$	0.451363	+	0.451363i	0.103550	+	0.103550i	−0.653434	+	0.756984i	$0.726672\pi$
$20$	−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	$-0.747101\pi$
$23$		−	6.84381i		−	1.42703i	0.700639	−	0.713516i	$-0.252899\pi$
$24$	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	0.687598	−	0.726092i	$-0.258665\pi$
$29$	−0.207295	−	0.207295i	−0.0384937	−	0.0384937i	−0.726092	+	0.687598i	$0.758665\pi$
$30$	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	−0.170655	+	0.985331i	$0.554588\pi$
$37$	−7.03159	+	7.03159i	−1.15599	+	1.15599i	−0.985331	+	0.170655i	$0.945412\pi$
$38$	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	$0.0600599\pi$
$41$			2.40202i			0.375132i	−0.982252	+	0.187566i	$0.939940\pi$
$42$		0			0
$43$	3.65586	−	3.65586i	0.557514	−	0.557514i	−0.371085	−	0.928599i	$-0.621014\pi$
$43$	3.65586	−	3.65586i	0.557514	−	0.557514i	0.928599	+	0.371085i	$0.121014\pi$
$44$	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	−0.977572	−	0.210599i	$-0.932458\pi$
$53$	−5.58365	+	5.58365i	−0.766973	+	0.766973i	0.210599	+	0.977572i	$0.432458\pi$
$54$	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	−0.342883	+	0.939378i	$0.611403\pi$
$59$	−9.84923	+	9.84923i	−1.28226	+	1.28226i	−0.939378	+	0.342883i	$0.888597\pi$
$60$	1.71458	−	3.63012i	0.221351	−	0.468646i
$61$	2.64783	+	2.64783i	0.339020	+	0.339020i	0.855999	−	0.516978i	$-0.172943\pi$
$61$	2.64783	+	2.64783i	0.339020	+	0.339020i	−0.516978	+	0.855999i	$0.672943\pi$
$62$	−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	0.0967807	−	0.995306i	$-0.469145\pi$
$67$	−7.35474	−	7.35474i	−0.898525	−	0.898525i	−0.995306	+	0.0967807i	$0.969145\pi$
$68$	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	$-0.758482\pi$
$71$		−	11.5947i		−	1.37603i	0.725695	−	0.688017i	$-0.241518\pi$
$72$	3.05160	−	0.378828i	0.359634	−	0.0446453i
$73$		−	0.358849i		−	0.0420001i	−0.999779	−	0.0210000i	$-0.993315\pi$
$73$		−	0.358849i		−	0.0420001i	0.999779	−	0.0210000i	$-0.00668501\pi$
$74$	−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	0.729994	−	0.683454i	$-0.239523\pi$
$83$	0.424001	+	0.424001i	0.0465402	+	0.0465402i	−0.683454	+	0.729994i	$0.739523\pi$
$84$		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	$0.382115\pi$
$89$			17.5887i			1.86440i	−0.361940	+	0.932201i	$0.617885\pi$
$90$	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	−0.663264	−	0.748385i	$-0.730829\pi$
$101$	0.855455	−	0.855455i	0.0851209	−	0.0851209i	0.748385	+	0.663264i	$0.230829\pi$
$102$	15.8396	+	3.55251i	1.56835	+	0.351751i
$103$		−	5.84488i		−	0.575913i	−0.957643	−	0.287956i	$-0.907024\pi$
$103$		−	5.84488i		−	0.575913i	0.957643	−	0.287956i	$-0.0929759\pi$
$104$	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	−0.823644	−	0.567108i	$-0.808062\pi$
$107$	−2.65363	+	2.65363i	−0.256536	+	0.256536i	0.567108	+	0.823644i	$0.308062\pi$
$108$	−2.60941	−	7.28071i	−0.251090	−	0.700587i
$109$	−7.08373	−	7.08373i	−0.678499	−	0.678499i	0.281162	−	0.959660i	$-0.409280\pi$
$109$	−7.08373	−	7.08373i	−0.678499	−	0.678499i	−0.959660	+	0.281162i	$0.909280\pi$
$110$	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	0.979653	−	0.200698i	$-0.0643209\pi$
$131$	8.91555	+	8.91555i	0.778956	+	0.778956i	−0.200698	+	0.979653i	$0.564321\pi$
$132$	−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	$-0.756654\pi$
$137$		−	16.2033i		−	1.38434i	0.721733	−	0.692172i	$-0.243346\pi$
$138$	4.28213	−	19.0927i	0.364519	−	1.62528i
$139$	−10.5018	+	10.5018i	−0.890748	+	0.890748i	−0.994593	−	0.103846i	$-0.966885\pi$
$139$	−10.5018	+	10.5018i	−0.890748	+	0.890748i	0.103846	+	0.994593i	$0.466885\pi$
$140$		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	−0.357156	−	0.934045i	$-0.616254\pi$
$149$	7.04183	−	7.04183i	0.576889	−	0.576889i	0.934045	+	0.357156i	$0.116254\pi$
$150$	−2.51162	+	11.1986i	−0.205073	+	0.914360i
$151$		−	10.3650i		−	0.843494i	−0.906713	−	0.421747i	$-0.861417\pi$
$151$		−	10.3650i		−	0.843494i	0.906713	−	0.421747i	$-0.138583\pi$
$152$	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	0.813872	−	0.581045i	$-0.197356\pi$
$157$	2.91731	+	2.91731i	0.232827	+	0.232827i	−0.581045	+	0.813872i	$0.697356\pi$
$158$	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	0.897907	−	0.440184i	$-0.145087\pi$
$163$	5.84382	+	5.84382i	0.457723	+	0.457723i	−0.440184	+	0.897907i	$0.645087\pi$
$164$	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	$-0.887749\pi$
$167$		−	8.92669i		−	0.690768i	0.938462	−	0.345384i	$-0.112251\pi$
$168$		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	0.545284	−	0.838252i	$-0.316422\pi$
$173$	−3.85339	−	3.85339i	−0.292968	−	0.292968i	−0.838252	+	0.545284i	$0.816422\pi$
$174$	−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	0.916257	−	0.400591i	$-0.131195\pi$
$179$	6.89914	+	6.89914i	0.515666	+	0.515666i	−0.400591	+	0.916257i	$0.631195\pi$
$180$	2.03235	−	0.728396i	0.151483	−	0.0542915i
$181$	8.42976	−	8.42976i	0.626579	−	0.626579i	−0.320627	−	0.947206i	$-0.603894\pi$
$181$	8.42976	−	8.42976i	0.626579	−	0.626579i	0.947206	+	0.320627i	$0.103894\pi$
$182$		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	−0.381484	−	0.924375i	$-0.624587\pi$
$197$	7.61984	−	7.61984i	0.542891	−	0.542891i	0.924375	+	0.381484i	$0.124587\pi$
$198$	−2.93196	−	0.657581i	−0.208365	−	0.0467323i
$199$		−	3.57622i		−	0.253511i	−0.991934	−	0.126756i	$-0.959544\pi$
$199$		−	3.57622i		−	0.253511i	0.991934	−	0.126756i	$-0.0404564\pi$
$200$	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	0.913026	−	0.407901i	$-0.133739\pi$
$211$	7.33737	+	7.33737i	0.505126	+	0.505126i	−0.407901	+	0.913026i	$0.633739\pi$
$212$	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	0.584397	−	0.811468i	$-0.301331\pi$
$227$	−3.42116	−	3.42116i	−0.227071	−	0.227071i	−0.811468	+	0.584397i	$0.801331\pi$
$228$	2.33375	+	1.10228i	0.154556	+	0.0730001i
$229$	13.8716	−	13.8716i	0.916663	−	0.916663i	−0.0801224	−	0.996785i	$-0.525531\pi$
$229$	13.8716	−	13.8716i	0.916663	−	0.916663i	0.996785	+	0.0801224i	$0.0255311\pi$
$230$	−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	$0.0530608\pi$
$233$			5.06546i			0.331849i	−0.986138	+	0.165925i	$0.946939\pi$
$234$	−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	−0.582699	−	0.812688i	$-0.698003\pi$
$251$	3.64372	−	3.64372i	0.229990	−	0.229990i	0.812688	+	0.582699i	$0.198003\pi$
$252$		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	$0.197413\pi$
$263$			18.8507i			1.16238i	−0.813767	+	0.581191i	$0.802587\pi$
$264$	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	0.972448	−	0.233118i	$-0.0748930\pi$
$269$	12.1259	+	12.1259i	0.739330	+	0.739330i	−0.233118	+	0.972448i	$0.574893\pi$
$270$	−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	−0.951984	−	0.306149i	$-0.900959\pi$
$277$	−10.7488	+	10.7488i	−0.645834	+	0.645834i	0.306149	+	0.951984i	$0.400959\pi$
$278$	−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	$0.0300264\pi$
$281$			3.15786i			0.188382i	−0.995554	+	0.0941910i	$0.969974\pi$
$282$	−0.806763	−	0.180941i	−0.0480420	−	0.0107749i
$283$	9.98203	−	9.98203i	0.593370	−	0.593370i	−0.345170	−	0.938540i	$-0.612179\pi$
$283$	9.98203	−	9.98203i	0.593370	−	0.593370i	0.938540	+	0.345170i	$0.112179\pi$
$284$	−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	−0.311502	−	0.950245i	$-0.600832\pi$
$293$	10.9335	−	10.9335i	0.638743	−	0.638743i	0.950245	+	0.311502i	$0.100832\pi$
$294$		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	0.989270	−	0.146100i	$-0.0466721\pi$
$307$	14.7735	+	14.7735i	0.843170	+	0.843170i	−0.146100	+	0.989270i	$0.546672\pi$
$308$		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	$-0.920331\pi$
$311$		−	8.73588i		−	0.495366i	0.968841	−	0.247683i	$-0.0796692\pi$
$312$	16.8780	−	2.09524i	0.955526	−	0.118620i
$313$		−	4.11784i		−	0.232754i	−0.993205	−	0.116377i	$-0.962872\pi$
$313$		−	4.11784i		−	0.232754i	0.993205	−	0.116377i	$-0.0371281\pi$
$314$	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	0.999568	−	0.0293866i	$-0.00935539\pi$
$317$	17.2736	+	17.2736i	0.970182	+	0.970182i	−0.0293866	+	0.999568i	$0.509355\pi$
$318$	−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	−0.550778	−	0.834652i	$-0.685669\pi$
$331$	5.16464	−	5.16464i	0.283874	−	0.283874i	0.834652	+	0.550778i	$0.185669\pi$
$332$	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	−0.512094	−	0.858930i	$-0.671130\pi$
$347$	6.46084	−	6.46084i	0.346836	−	0.346836i	0.858930	+	0.512094i	$0.171130\pi$
$348$	−1.07181	−	0.506236i	−0.0574549	−	0.0271371i
$349$	−24.4862	−	24.4862i	−1.31072	−	1.31072i	−0.920887	−	0.389831i	$-0.872533\pi$
$349$	−24.4862	−	24.4862i	−1.31072	−	1.31072i	−0.389831	−	0.920887i	$-0.627467\pi$
$350$		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	$-0.970692\pi$
$359$		−	3.48419i		−	0.183889i	0.995764	−	0.0919443i	$-0.0293082\pi$
$360$	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	0.455160	−	0.890410i	$-0.349582\pi$
$373$	25.9873	−	25.9873i	1.34557	−	1.34557i	0.890410	−	0.455160i	$-0.150418\pi$
$374$	−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	−0.0476420	−	0.998864i	$-0.515171\pi$
$379$	18.5183	−	18.5183i	0.951222	−	0.951222i	0.998864	+	0.0476420i	$0.0151707\pi$
$380$	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	−0.597481	−	0.801883i	$-0.703831\pi$
$389$	4.03146	−	4.03146i	0.204403	−	0.204403i	0.801883	+	0.597481i	$0.203831\pi$
$390$	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	0.689027	−	0.724736i	$-0.258038\pi$
$397$	−0.711500	−	0.711500i	−0.0357092	−	0.0357092i	−0.724736	+	0.689027i	$0.758038\pi$
$398$	−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	$-0.607208\pi$
$409$		−	38.1750i		−	1.88763i	0.330474	−	0.943815i	$-0.392792\pi$
$410$	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	0.914525	+	0.404529i	$0.132565\pi$
$419$	27.0004	+	27.0004i	1.31905	+	1.31905i	0.404529	+	0.914525i	$0.367435\pi$
$420$		0			0
$421$	−19.1472	+	19.1472i	−0.933175	+	0.933175i	−0.997903	−	0.0647277i	$-0.979382\pi$
$421$	−19.1472	+	19.1472i	−0.933175	+	0.933175i	0.0647277	+	0.997903i	$0.479382\pi$
$422$	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	$0.0608796\pi$
$439$			7.96586i			0.380190i	−0.981766	+	0.190095i	$0.939120\pi$
$440$	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	−0.148319	−	0.988940i	$-0.547386\pi$
$443$	17.6930	−	17.6930i	0.840621	−	0.840621i	0.988940	+	0.148319i	$0.0473861\pi$
$444$	−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	$-0.890079\pi$
$457$		−	14.4728i		−	0.677010i	0.940965	−	0.338505i	$-0.109921\pi$
$458$	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	0.798721	−	0.601701i	$-0.205510\pi$
$461$	4.23021	+	4.23021i	0.197020	+	0.197020i	−0.601701	+	0.798721i	$0.705510\pi$
$462$		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	0.409543	−	0.912291i	$-0.365688\pi$
$467$	−10.8645	−	10.8645i	−0.502747	−	0.502747i	−0.912291	+	0.409543i	$0.865688\pi$
$468$	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	$0.00160418\pi$
$487$			0.222431i			0.0100793i	−0.999987	+	0.00503966i	$0.998396\pi$
$488$	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	−0.166547	−	0.986033i	$-0.553262\pi$
$491$	18.1586	−	18.1586i	0.819486	−	0.819486i	0.986033	+	0.166547i	$0.0532618\pi$
$492$	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	0.760491	−	0.649348i	$-0.224958\pi$
$499$	2.48274	+	2.48274i	0.111143	+	0.111143i	−0.649348	+	0.760491i	$0.724958\pi$
$500$	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	$-0.945426\pi$
$503$		−	7.65278i		−	0.341220i	0.985339	−	0.170610i	$-0.0545739\pi$
$504$		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	0.999998	+	0.00175431i	$0.000558414\pi$
$509$	22.6006	+	22.6006i	1.00175	+	1.00175i	0.00175431	+	0.999998i	$0.499442\pi$
$510$	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	$0.0193204\pi$
$521$			2.76916i			0.121319i	−0.998159	+	0.0606595i	$0.980680\pi$
$522$	0.0986408	−	0.439809i	0.00431739	−	0.0192499i
$523$	−15.6353	+	15.6353i	−0.683686	+	0.683686i	−0.960829	−	0.277143i	$-0.910612\pi$
$523$	−15.6353	+	15.6353i	−0.683686	+	0.683686i	0.277143	+	0.960829i	$0.410612\pi$
$524$	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	0.999879	+	0.0155590i	$0.00495280\pi$
$541$	23.6185	+	23.6185i	1.01544	+	1.01544i	0.0155590	+	0.999879i	$0.495047\pi$
$542$	−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	0.777032	−	0.629462i	$-0.216724\pi$
$547$	3.45137	+	3.45137i	0.147570	+	0.147570i	−0.629462	+	0.777032i	$0.716724\pi$
$548$	−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	0.294728	−	0.955581i	$-0.404771\pi$
$557$	−15.5967	−	15.5967i	−0.660853	−	0.660853i	−0.955581	+	0.294728i	$0.904771\pi$
$558$	−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	0.986508	−	0.163710i	$-0.0523462\pi$
$563$	19.5230	+	19.5230i	0.822798	+	0.822798i	−0.163710	+	0.986508i	$0.552346\pi$
$564$	−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	$0.262802\pi$
$569$			35.0633i			1.46993i	−0.678105	+	0.734965i	$0.737198\pi$
$570$	1.76815	+	0.396561i	0.0740595	+	0.0166101i
$571$	−0.913269	+	0.913269i	−0.0382191	+	0.0382191i	−0.725958	−	0.687739i	$-0.758603\pi$
$571$	−0.913269	+	0.913269i	−0.0382191	+	0.0382191i	0.687739	+	0.725958i	$0.258603\pi$
$572$	−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	0.161702	−	0.986840i	$-0.448302\pi$
$587$	27.8270	−	27.8270i	1.14854	−	1.14854i	0.986840	−	0.161702i	$-0.0516982\pi$
$588$		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	$0.128256\pi$
$599$			19.1935i			0.784226i	−0.919917	+	0.392113i	$0.871744\pi$
$600$	18.1065	+	14.1074i	0.739195	+	0.575934i
$601$		−	26.9530i		−	1.09944i	−0.835351	−	0.549718i	$-0.814735\pi$
$601$		−	26.9530i		−	1.09944i	0.835351	−	0.549718i	$-0.185265\pi$
$602$		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	−0.967128	−	0.254289i	$-0.918159\pi$
$613$	−17.6491	+	17.6491i	−0.712839	+	0.712839i	0.254289	+	0.967128i	$0.418159\pi$
$614$	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	$-0.929976\pi$
$617$		−	10.8407i		−	0.436431i	0.975901	−	0.218216i	$-0.0700236\pi$
$618$	3.65711	−	16.3059i	0.147110	−	0.655921i
$619$	−14.1990	+	14.1990i	−0.570707	+	0.570707i	−0.932326	−	0.361619i	$-0.882224\pi$
$619$	−14.1990	+	14.1990i	−0.570707	+	0.570707i	0.361619	+	0.932326i	$0.382224\pi$
$620$	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	$0.0363005\pi$
$631$			5.71697i			0.227589i	−0.993504	+	0.113794i	$0.963699\pi$
$632$	−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	0.633957	−	0.773368i	$-0.281430\pi$
$643$	−3.53512	−	3.53512i	−0.139412	−	0.139412i	−0.773368	+	0.633957i	$0.781430\pi$
$644$		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	$0.0936726\pi$
$647$			14.7556i			0.580104i	−0.957011	+	0.290052i	$0.906327\pi$
$648$	−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	0.556665	−	0.830737i	$-0.312081\pi$
$653$	−7.00360	−	7.00360i	−0.274072	−	0.274072i	−0.830737	+	0.556665i	$0.812081\pi$
$654$	−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	0.809063	−	0.587722i	$-0.199975\pi$
$659$	5.68205	+	5.68205i	0.221341	+	0.221341i	−0.587722	+	0.809063i	$0.699975\pi$
$660$	2.64711	+	7.38591i	0.103039	+	0.287496i
$661$	6.78275	−	6.78275i	0.263819	−	0.263819i	−0.562785	−	0.826603i	$-0.690270\pi$
$661$	6.78275	−	6.78275i	0.263819	−	0.263819i	0.826603	+	0.562785i	$0.190270\pi$
$662$	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	−0.996369	−	0.0851352i	$-0.972868\pi$
$677$	−23.7096	+	23.7096i	−0.911234	+	0.911234i	0.0851352	+	0.996369i	$0.472868\pi$
$678$	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	−0.409173	−	0.912457i	$-0.634183\pi$
$683$	13.1530	−	13.1530i	0.503284	−	0.503284i	0.912457	+	0.409173i	$0.134183\pi$
$684$	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	0.352815	−	0.935693i	$-0.385225\pi$
$691$	−15.3221	−	15.3221i	−0.582878	−	0.582878i	−0.935693	+	0.352815i	$0.885225\pi$
$692$	−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	0.794547	−	0.607202i	$-0.207708\pi$
$701$	4.96023	+	4.96023i	0.187345	+	0.187345i	−0.607202	+	0.794547i	$0.707708\pi$
$702$	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	−0.872640	−	0.488363i	$-0.837594\pi$
$709$	−10.2322	+	10.2322i	−0.384277	+	0.384277i	0.488363	+	0.872640i	$0.337594\pi$
$710$	−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	$0.143854\pi$
$727$			23.5496i			0.873406i	−0.899606	+	0.436703i	$0.856146\pi$
$728$		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	0.683363	−	0.730079i	$-0.260517\pi$
$733$	−1.26479	−	1.26479i	−0.0467162	−	0.0467162i	−0.730079	+	0.683363i	$0.760517\pi$
$734$	−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	0.942739	−	0.333532i	$-0.108241\pi$
$739$	16.5610	+	16.5610i	0.609206	+	0.609206i	−0.333532	+	0.942739i	$0.608241\pi$
$740$	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	$0.0821984\pi$
$743$			13.9219i			0.510747i	−0.966843	+	0.255373i	$0.917802\pi$
$744$	−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	−0.727528	−	0.686078i	$-0.759331\pi$
$757$	−1.14043	+	1.14043i	−0.0414496	+	0.0414496i	0.686078	+	0.727528i	$0.259331\pi$
$758$	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	$0.0508784\pi$
$761$			8.78122i			0.318319i	−0.987253	+	0.159159i	$0.949122\pi$
$762$	−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	−0.191435	+	0.981505i	$0.561314\pi$
$773$	−32.6111	+	32.6111i	−1.17294	+	1.17294i	−0.981505	+	0.191435i	$0.938686\pi$
$774$	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	0.295048	−	0.955482i	$-0.404664\pi$
$787$	−18.5275	−	18.5275i	−0.660435	−	0.660435i	−0.955482	+	0.295048i	$0.904664\pi$
$788$	−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	0.938448	−	0.345420i	$-0.112264\pi$
$797$	16.7419	+	16.7419i	0.593028	+	0.593028i	−0.345420	+	0.938448i	$0.612264\pi$
$798$		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	$-0.785251\pi$
$809$		−	35.5325i		−	1.24926i	0.780923	−	0.624628i	$-0.214749\pi$
$810$	3.40472	−	15.1806i	0.119629	−	0.533392i
$811$	−29.5602	+	29.5602i	−1.03800	+	1.03800i	−0.0387507	+	0.999249i	$0.512338\pi$
$811$	−29.5602	+	29.5602i	−1.03800	+	1.03800i	−0.999249	+	0.0387507i	$0.987662\pi$
$812$		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	−0.602794	−	0.797897i	$-0.705946\pi$
$821$	5.59033	−	5.59033i	0.195104	−	0.195104i	0.797897	+	0.602794i	$0.205946\pi$
$822$	10.1383	−	45.2037i	0.353615	−	1.57666i
$823$		−	49.8955i		−	1.73925i	−0.493716	−	0.869623i	$-0.664362\pi$
$823$		−	49.8955i		−	1.73925i	0.493716	−	0.869623i	$-0.335638\pi$
$824$	−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	−0.834004	−	0.551758i	$-0.813957\pi$
$827$	−8.11672	+	8.11672i	−0.282246	+	0.282246i	0.551758	+	0.834004i	$0.313957\pi$
$828$	6.35535	−	13.4556i	0.220864	−	0.467614i
$829$	5.02945	+	5.02945i	0.174680	+	0.174680i	0.789032	−	0.614352i	$-0.210583\pi$
$829$	5.02945	+	5.02945i	0.174680	+	0.174680i	−0.614352	+	0.789032i	$0.710583\pi$
$830$	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	$-0.980368\pi$
$839$		−	3.57060i		−	0.123271i	0.998099	−	0.0616354i	$-0.0196316\pi$
$840$		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	−0.903780	−	0.427996i	$-0.859220\pi$
$853$	−13.8958	+	13.8958i	−0.475784	+	0.475784i	0.427996	+	0.903780i	$0.359220\pi$
$854$		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	$0.240984\pi$
$857$			40.2114i			1.37360i	−0.726848	+	0.686798i	$0.759016\pi$
$858$	−16.2162	−	3.63699i	−0.553613	−	0.124165i
$859$	−18.3327	+	18.3327i	−0.625502	+	0.625502i	−0.946933	−	0.321431i	$-0.895836\pi$
$859$	−18.3327	+	18.3327i	−0.625502	+	0.625502i	0.321431	+	0.946933i	$0.395836\pi$
$860$	−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	0.925025	−	0.379906i	$-0.124044\pi$
$877$	16.1432	+	16.1432i	0.545118	+	0.545118i	−0.379906	+	0.925025i	$0.624044\pi$
$878$	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	−0.999381	−	0.0351900i	$-0.988796\pi$
$883$	−30.7426	−	30.7426i	−1.03457	−	1.03457i	−0.0351900	−	0.999381i	$-0.511204\pi$
$884$	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	$-0.968838\pi$
$887$		−	5.82199i		−	0.195483i	0.995212	−	0.0977417i	$-0.0311619\pi$
$888$	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	−0.909631	−	0.415417i	$-0.863636\pi$
$907$	−14.8840	+	14.8840i	−0.494214	+	0.494214i	0.415417	+	0.909631i	$0.363636\pi$
$908$	−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	$0.0788709\pi$
$919$			14.8697i			0.490505i	−0.969459	+	0.245253i	$0.921129\pi$
$920$	−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	$-0.694521\pi$
$937$		−	50.1408i		−	1.63803i	0.573773	−	0.819014i	$-0.305479\pi$
$938$		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	−0.999415	−	0.0341962i	$-0.989113\pi$
$941$	−31.7068	−	31.7068i	−1.03361	−	1.03361i	−0.0341962	−	0.999415i	$-0.510887\pi$
$942$	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	0.725814	−	0.687891i	$-0.241463\pi$
$947$	1.16699	+	1.16699i	0.0379222	+	0.0379222i	−0.687891	+	0.725814i	$0.741463\pi$
$948$	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	$0.230830\pi$
$953$			40.9510i			1.32653i	−0.748384	+	0.663266i	$0.769170\pi$
$954$	−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	$-0.924406\pi$
$967$		−	14.6315i		−	0.470518i	0.971933	−	0.235259i	$-0.0755938\pi$
$968$	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	−0.927678	−	0.373382i	$-0.878198\pi$
$971$	−17.2723	+	17.2723i	−0.554295	+	0.554295i	0.373382	+	0.927678i	$0.378198\pi$
$972$	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	$0.111723\pi$
$983$			21.5599i			0.687654i	−0.939033	+	0.343827i	$0.888277\pi$
$984$	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	−0.762218	−	0.647320i	$-0.775890\pi$
$997$	−3.62794	+	3.62794i	−0.114898	+	0.114898i	0.647320	+	0.762218i	$0.275890\pi$
$998$	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.589.10		24
7.2	even	3		784.2.x.o.557.3		48
7.3	odd	6		112.2.w.c.93.7	yes	48
7.4	even	3		784.2.x.o.765.7		48
7.5	odd	6		112.2.w.c.109.3	yes	48
7.6	odd	2		784.2.m.j.589.10		24
16.5	even	4	inner	784.2.m.k.197.10		24
28.3	even	6		448.2.ba.c.401.10		48
28.19	even	6		448.2.ba.c.81.3		48
56.3	even	6		896.2.ba.e.289.3		48
56.5	odd	6		896.2.ba.f.417.3		48
56.19	even	6		896.2.ba.e.417.10		48
56.45	odd	6		896.2.ba.f.289.10		48
112.3	even	12		896.2.ba.e.737.10		48
112.5	odd	12		112.2.w.c.53.7	yes	48
112.19	even	12		896.2.ba.e.865.3		48
112.37	even	12		784.2.x.o.165.7		48
112.45	odd	12		896.2.ba.f.737.3		48
112.53	even	12		784.2.x.o.373.3		48
112.59	even	12		448.2.ba.c.177.3		48
112.61	odd	12		896.2.ba.f.865.10		48
112.69	odd	4		784.2.m.j.197.10		24
112.75	even	12		448.2.ba.c.305.10		48
112.101	odd	12		112.2.w.c.37.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.3	✓	48	112.101	odd	12
112.2.w.c.53.7	yes	48	112.5	odd	12
112.2.w.c.93.7	yes	48	7.3	odd	6
112.2.w.c.109.3	yes	48	7.5	odd	6
448.2.ba.c.81.3		48	28.19	even	6
448.2.ba.c.177.3		48	112.59	even	12
448.2.ba.c.305.10		48	112.75	even	12
448.2.ba.c.401.10		48	28.3	even	6
784.2.m.j.197.10		24	112.69	odd	4
784.2.m.j.589.10		24	7.6	odd	2
784.2.m.k.197.10		24	16.5	even	4	inner
784.2.m.k.589.10		24	1.1	even	1	trivial
784.2.x.o.165.7		48	112.37	even	12
784.2.x.o.373.3		48	112.53	even	12
784.2.x.o.557.3		48	7.2	even	3
784.2.x.o.765.7		48	7.4	even	3
896.2.ba.e.289.3		48	56.3	even	6
896.2.ba.e.417.10		48	56.19	even	6
896.2.ba.e.737.10		48	112.3	even	12
896.2.ba.e.865.3		48	112.19	even	12
896.2.ba.f.289.10		48	56.45	odd	6
896.2.ba.f.417.3		48	56.5	odd	6
896.2.ba.f.737.3		48	112.45	odd	12
896.2.ba.f.865.10		48	112.61	odd	12

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more