LMFDB - Embedded newform 304.2.k.b.229.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.34
Character	$\chi$	$=$	304.229
Dual form			304.2.k.b.77.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41380 + 0.0343004i) q^{2} +(-1.89015 + 1.89015i) q^{3} +(1.99765 + 0.0969877i) q^{4} +(-1.06645 - 1.06645i) q^{5} +(-2.73712 + 2.60746i) q^{6} +4.02959i q^{7} +(2.82094 + 0.205641i) q^{8} -4.14533i q^{9} +O(q^{10})$	\(q+(1.41380 + 0.0343004i) q^{2} +(-1.89015 + 1.89015i) q^{3} +(1.99765 + 0.0969877i) q^{4} +(-1.06645 - 1.06645i) q^{5} +(-2.73712 + 2.60746i) q^{6} +4.02959i q^{7} +(2.82094 + 0.205641i) q^{8} -4.14533i q^{9} +(-1.47117 - 1.54433i) q^{10} +(0.552303 + 0.552303i) q^{11} +(-3.95917 + 3.59253i) q^{12} +(-4.37311 + 4.37311i) q^{13} +(-0.138217 + 5.69702i) q^{14} +4.03151 q^{15} +(3.98119 + 0.387494i) q^{16} +0.608142 q^{17} +(0.142187 - 5.86066i) q^{18} +(-0.707107 + 0.707107i) q^{19} +(-2.02696 - 2.23383i) q^{20} +(-7.61653 - 7.61653i) q^{21} +(0.761901 + 0.799789i) q^{22} +0.900783i q^{23} +(-5.72070 + 4.94331i) q^{24} -2.72536i q^{25} +(-6.33269 + 6.03269i) q^{26} +(2.16485 + 2.16485i) q^{27} +(-0.390820 + 8.04970i) q^{28} +(6.34029 - 6.34029i) q^{29} +(5.69974 + 0.138282i) q^{30} +7.50604 q^{31} +(5.61530 + 0.684395i) q^{32} -2.08787 q^{33} +(0.859789 + 0.0208595i) q^{34} +(4.29737 - 4.29737i) q^{35} +(0.402046 - 8.28092i) q^{36} +(4.12547 + 4.12547i) q^{37} +(-1.02396 + 0.975452i) q^{38} -16.5317i q^{39} +(-2.78909 - 3.22771i) q^{40} +3.15335i q^{41} +(-10.5070 - 11.0295i) q^{42} +(-4.34630 - 4.34630i) q^{43} +(1.04974 + 1.15687i) q^{44} +(-4.42080 + 4.42080i) q^{45} +(-0.0308972 + 1.27353i) q^{46} +12.4949 q^{47} +(-8.25746 + 6.79262i) q^{48} -9.23758 q^{49} +(0.0934808 - 3.85310i) q^{50} +(-1.14948 + 1.14948i) q^{51} +(-9.16006 + 8.31179i) q^{52} +(0.257543 + 0.257543i) q^{53} +(2.98641 + 3.13492i) q^{54} -1.17801i q^{55} +(-0.828649 + 11.3672i) q^{56} -2.67308i q^{57} +(9.18136 - 8.74641i) q^{58} +(-3.92257 - 3.92257i) q^{59} +(8.05354 + 0.391007i) q^{60} +(4.73541 - 4.73541i) q^{61} +(10.6120 + 0.257460i) q^{62} +16.7040 q^{63} +(7.91542 + 1.16020i) q^{64} +9.32743 q^{65} +(-2.95183 - 0.0716148i) q^{66} +(-9.32201 + 9.32201i) q^{67} +(1.21485 + 0.0589822i) q^{68} +(-1.70262 - 1.70262i) q^{69} +(6.22301 - 5.92820i) q^{70} +0.270319i q^{71} +(0.852451 - 11.6937i) q^{72} -12.3210i q^{73} +(5.69107 + 5.97408i) q^{74} +(5.15133 + 5.15133i) q^{75} +(-1.48113 + 1.34397i) q^{76} +(-2.22555 + 2.22555i) q^{77} +(0.567043 - 23.3724i) q^{78} -1.74353 q^{79} +(-3.83250 - 4.65899i) q^{80} +4.25220 q^{81} +(-0.108161 + 4.45820i) q^{82} +(-2.77691 + 2.77691i) q^{83} +(-14.4764 - 15.9538i) q^{84} +(-0.648554 - 0.648554i) q^{85} +(-5.99571 - 6.29387i) q^{86} +23.9682i q^{87} +(1.44444 + 1.67159i) q^{88} +10.4507i q^{89} +(-6.40176 + 6.09849i) q^{90} +(-17.6218 - 17.6218i) q^{91} +(-0.0873649 + 1.79945i) q^{92} +(-14.1875 + 14.1875i) q^{93} +(17.6653 + 0.428582i) q^{94} +1.50819 q^{95} +(-11.9074 + 9.32015i) q^{96} -3.49540 q^{97} +(-13.0601 - 0.316853i) q^{98} +(2.28948 - 2.28948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.41380	+	0.0343004i	0.999706	+	0.0242540i
$2$	1.41380	+	0.0343004i	0.999706	+	0.0242540i
$3$	−1.89015	+	1.89015i	−1.09128	+	1.09128i	−0.0958864	+	0.995392i	$0.530569\pi$
$3$	−1.89015	+	1.89015i	−1.09128	+	1.09128i	−0.995392	+	0.0958864i	$0.969431\pi$
$4$	1.99765	+	0.0969877i	0.998823	+	0.0484938i
$5$	−1.06645	−	1.06645i	−0.476932	−	0.476932i	0.427217	−	0.904149i	$-0.359494\pi$
$5$	−1.06645	−	1.06645i	−0.476932	−	0.476932i	−0.904149	+	0.427217i	$0.859494\pi$
$6$	−2.73712	+	2.60746i	−1.11743	+	1.06449i
$7$			4.02959i			1.52304i	0.648141	+	0.761521i	$0.275547\pi$
$7$			4.02959i			1.52304i	−0.648141	+	0.761521i	$0.724453\pi$
$8$	2.82094	+	0.205641i	0.997353	+	0.0727051i
$9$		−	4.14533i		−	1.38178i
$10$	−1.47117	−	1.54433i	−0.465224	−	0.488359i
$11$	0.552303	+	0.552303i	0.166526	+	0.166526i	0.785450	−	0.618925i	$-0.212431\pi$
$11$	0.552303	+	0.552303i	0.166526	+	0.166526i	−0.618925	+	0.785450i	$0.712431\pi$
$12$	−3.95917	+	3.59253i	−1.14292	+	1.03707i
$13$	−4.37311	+	4.37311i	−1.21288	+	1.21288i	−0.242807	+	0.970075i	$0.578068\pi$
$13$	−4.37311	+	4.37311i	−1.21288	+	1.21288i	−0.970075	+	0.242807i	$0.921932\pi$
$14$	−0.138217	+	5.69702i	−0.0369399	+	1.52259i
$15$	4.03151			1.04093
$16$	3.98119	+	0.387494i	0.995297	+	0.0968735i
$17$	0.608142			0.147496			0.0737480	−	0.997277i	$-0.476504\pi$
$17$	0.608142			0.147496			0.0737480	+	0.997277i	$0.476504\pi$
$18$	0.142187	−	5.86066i	0.0335137	−	1.38137i
$19$	−0.707107	+	0.707107i	−0.162221	+	0.162221i
$19$	−0.707107	+	0.707107i	−0.162221	+	0.162221i
$20$	−2.02696	−	2.23383i	−0.453243	−	0.499499i
$21$	−7.61653	−	7.61653i	−1.66206	−	1.66206i
$22$	0.761901	+	0.799789i	0.162438	+	0.170516i
$23$			0.900783i			0.187826i	0.995580	+	0.0939132i	$0.0299376\pi$
$23$			0.900783i			0.187826i	−0.995580	+	0.0939132i	$0.970062\pi$
$24$	−5.72070	+	4.94331i	−1.16773	+	1.00905i
$25$		−	2.72536i		−	0.545071i
$26$	−6.33269	+	6.03269i	−1.24194	+	1.18311i
$27$	2.16485	+	2.16485i	0.416626	+	0.416626i
$28$	−0.390820	+	8.04970i	−0.0738581	+	1.52125i
$29$	6.34029	−	6.34029i	1.17736	−	1.17736i	0.196949	−	0.980414i	$-0.436897\pi$
$29$	6.34029	−	6.34029i	1.17736	−	1.17736i	0.980414	−	0.196949i	$-0.0631033\pi$
$30$	5.69974	+	0.138282i	1.04063	+	0.0252468i
$31$	7.50604			1.34813			0.674063	−	0.738674i	$-0.264548\pi$
$31$	7.50604			1.34813			0.674063	+	0.738674i	$0.264548\pi$
$32$	5.61530	+	0.684395i	0.992654	+	0.120985i
$33$	−2.08787			−0.363452
$34$	0.859789	+	0.0208595i	0.147453	+	0.00357738i
$35$	4.29737	−	4.29737i	0.726387	−	0.726387i
$36$	0.402046	−	8.28092i	0.0670077	−	1.38015i
$37$	4.12547	+	4.12547i	0.678223	+	0.678223i	0.959598	−	0.281375i	$-0.0907905\pi$
$37$	4.12547	+	4.12547i	0.678223	+	0.678223i	−0.281375	+	0.959598i	$0.590790\pi$
$38$	−1.02396	+	0.975452i	−0.166108	+	0.158239i
$39$		−	16.5317i		−	2.64718i
$40$	−2.78909	−	3.22771i	−0.440995	−	0.510345i
$41$			3.15335i			0.492471i	0.969210	+	0.246236i	$0.0791937\pi$
$41$			3.15335i			0.492471i	−0.969210	+	0.246236i	$0.920806\pi$
$42$	−10.5070	−	11.0295i	−1.62126	−	1.70189i
$43$	−4.34630	−	4.34630i	−0.662805	−	0.662805i	0.293235	−	0.956040i	$-0.405268\pi$
$43$	−4.34630	−	4.34630i	−0.662805	−	0.662805i	−0.956040	+	0.293235i	$0.905268\pi$
$44$	1.04974	+	1.15687i	0.158254	+	0.174405i
$45$	−4.42080	+	4.42080i	−0.659015	+	0.659015i
$46$	−0.0308972	+	1.27353i	−0.00455555	+	0.187771i
$47$	12.4949			1.82258			0.911288	−	0.411770i	$-0.135089\pi$
$47$	12.4949			1.82258			0.911288	+	0.411770i	$0.135089\pi$
$48$	−8.25746	+	6.79262i	−1.19186	+	0.980430i
$49$	−9.23758			−1.31965
$50$	0.0934808	−	3.85310i	0.0132202	−	0.544911i
$51$	−1.14948	+	1.14948i	−0.160959	+	0.160959i
$52$	−9.16006	+	8.31179i	−1.27027	+	1.15264i
$53$	0.257543	+	0.257543i	0.0353763	+	0.0353763i	0.724574	−	0.689197i	$-0.242037\pi$
$53$	0.257543	+	0.257543i	0.0353763	+	0.0353763i	−0.689197	+	0.724574i	$0.742037\pi$
$54$	2.98641	+	3.13492i	0.406399	+	0.426609i
$55$		−	1.17801i		−	0.158843i
$56$	−0.828649	+	11.3672i	−0.110733	+	1.51901i
$57$		−	2.67308i		−	0.354058i
$58$	9.18136	−	8.74641i	1.20557	−	1.14846i
$59$	−3.92257	−	3.92257i	−0.510675	−	0.510675i	0.404059	−	0.914733i	$-0.367599\pi$
$59$	−3.92257	−	3.92257i	−0.510675	−	0.510675i	−0.914733	+	0.404059i	$0.867599\pi$
$60$	8.05354	+	0.391007i	1.03971	+	0.0504788i
$61$	4.73541	−	4.73541i	0.606307	−	0.606307i	−0.335672	−	0.941979i	$-0.608963\pi$
$61$	4.73541	−	4.73541i	0.606307	−	0.606307i	0.941979	+	0.335672i	$0.108963\pi$
$62$	10.6120	+	0.257460i	1.34773	+	0.0326975i
$63$	16.7040			2.10451
$64$	7.91542	+	1.16020i	0.989428	+	0.145025i
$65$	9.32743			1.15692
$66$	−2.95183	−	0.0716148i	−0.363345	−	0.00881518i
$67$	−9.32201	+	9.32201i	−1.13886	+	1.13886i	−0.150211	+	0.988654i	$0.547995\pi$
$67$	−9.32201	+	9.32201i	−1.13886	+	1.13886i	−0.988654	+	0.150211i	$0.952005\pi$
$68$	1.21485	+	0.0589822i	0.147322	+	0.00715265i
$69$	−1.70262	−	1.70262i	−0.204971	−	0.204971i
$70$	6.22301	−	5.92820i	0.743792	−	0.708556i
$71$			0.270319i			0.0320809i	0.999871	+	0.0160405i	$0.00510605\pi$
$71$			0.270319i			0.0320809i	−0.999871	+	0.0160405i	$0.994894\pi$
$72$	0.852451	−	11.6937i	0.100462	−	1.37812i
$73$		−	12.3210i		−	1.44206i	−0.692903	−	0.721031i	$-0.743669\pi$
$73$		−	12.3210i		−	1.44206i	0.692903	−	0.721031i	$-0.256331\pi$
$74$	5.69107	+	5.97408i	0.661574	+	0.694473i
$75$	5.15133	+	5.15133i	0.594825	+	0.594825i
$76$	−1.48113	+	1.34397i	−0.169897	+	0.154164i
$77$	−2.22555	+	2.22555i	−0.253625	+	0.253625i
$78$	0.567043	−	23.3724i	0.0642049	−	2.64641i
$79$	−1.74353			−0.196162			−0.0980810	−	0.995178i	$-0.531270\pi$
$79$	−1.74353			−0.196162			−0.0980810	+	0.995178i	$0.531270\pi$
$80$	−3.83250	−	4.65899i	−0.428487	−	0.520891i
$81$	4.25220			0.472467
$82$	−0.108161	+	4.45820i	−0.0119444	+	0.492326i
$83$	−2.77691	+	2.77691i	−0.304805	+	0.304805i	−0.842890	−	0.538085i	$-0.819148\pi$
$83$	−2.77691	+	2.77691i	−0.304805	+	0.304805i	0.538085	+	0.842890i	$0.319148\pi$
$84$	−14.4764	−	15.9538i	−1.57951	−	1.74071i
$85$	−0.648554	−	0.648554i	−0.0703456	−	0.0703456i
$86$	−5.99571	−	6.29387i	−0.646534	−	0.678686i
$87$			23.9682i			2.56966i
$88$	1.44444	+	1.67159i	0.153978	+	0.178192i
$89$			10.4507i			1.10778i	0.832591	+	0.553888i	$0.186856\pi$
$89$			10.4507i			1.10778i	−0.832591	+	0.553888i	$0.813144\pi$
$90$	−6.40176	+	6.09849i	−0.674804	+	0.642837i
$91$	−17.6218	−	17.6218i	−1.84727	−	1.84727i
$92$	−0.0873649	+	1.79945i	−0.00910842	+	0.187605i
$93$	−14.1875	+	14.1875i	−1.47118	+	1.47118i
$94$	17.6653	+	0.428582i	1.82204	+	0.0442048i
$95$	1.50819			0.154737
$96$	−11.9074	+	9.32015i	−1.21529	+	0.951234i
$97$	−3.49540			−0.354904			−0.177452	−	0.984129i	$-0.556785\pi$
$97$	−3.49540			−0.354904			−0.177452	+	0.984129i	$0.556785\pi$
$98$	−13.0601	−	0.316853i	−1.31927	−	0.0320070i
$99$	2.28948	−	2.28948i	0.230102	−	0.230102i
$100$	0.264326	−	5.44430i	0.0264326	−	0.544430i
$101$	−12.3075	−	12.3075i	−1.22464	−	1.22464i	−0.965965	−	0.258673i	$-0.916715\pi$
$101$	−12.3075	−	12.3075i	−1.22464	−	1.22464i	−0.258673	−	0.965965i	$-0.583285\pi$
$102$	−1.66456	+	1.58570i	−0.164816	+	0.157008i
$103$			5.57914i			0.549729i	0.961483	+	0.274865i	$0.0886330\pi$
$103$			5.57914i			0.549729i	−0.961483	+	0.274865i	$0.911367\pi$
$104$	−13.2356	+	11.4370i	−1.29785	+	1.12149i
$105$			16.2453i			1.58538i
$106$	0.355280	+	0.372948i	0.0345079	+	0.0362239i
$107$	4.04485	+	4.04485i	0.391031	+	0.391031i	0.875055	−	0.484024i	$-0.160825\pi$
$107$	4.04485	+	4.04485i	0.391031	+	0.391031i	−0.484024	+	0.875055i	$0.660825\pi$
$108$	4.11465	+	4.53458i	0.395932	+	0.436340i
$109$	3.65197	−	3.65197i	0.349796	−	0.349796i	−0.510238	−	0.860033i	$-0.670443\pi$
$109$	3.65197	−	3.65197i	0.349796	−	0.349796i	0.860033	+	0.510238i	$0.170443\pi$
$110$	0.0404062	−	1.66547i	0.00385258	−	0.158796i
$111$	−15.5955			−1.48026
$112$	−1.56144	+	16.0425i	−0.147542	+	1.51588i
$113$	−4.70937			−0.443020			−0.221510	−	0.975158i	$-0.571099\pi$
$113$	−4.70937			−0.443020			−0.221510	+	0.975158i	$0.571099\pi$
$114$	0.0916876	−	3.77919i	0.00858733	−	0.353953i
$115$	0.960643	−	0.960643i	0.0895804	−	0.0895804i
$116$	13.2806	−	12.0507i	1.23307	−	1.11888i
$117$	18.1280	+	18.1280i	1.67593	+	1.67593i
$118$	−5.41117	−	5.68026i	−0.498138	−	0.522910i
$119$			2.45056i			0.224643i
$120$	11.3727	+	0.829044i	1.03818	+	0.0756810i
$121$		−	10.3899i		−	0.944538i
$122$	6.85734	−	6.53249i	0.620835	−	0.591424i
$123$	−5.96031	−	5.96031i	−0.537423	−	0.537423i
$124$	14.9944	+	0.727993i	1.34654	+	0.0653757i
$125$	−8.23873	+	8.23873i	−0.736894	+	0.736894i
$126$	23.6161	+	0.572954i	2.10389	+	0.0510428i
$127$	−15.6940			−1.39262			−0.696311	−	0.717741i	$-0.745176\pi$
$127$	−15.6940			−1.39262			−0.696311	+	0.717741i	$0.745176\pi$
$128$	11.1510	+	1.91179i	0.985619	+	0.168980i
$129$	16.4303			1.44661
$130$	13.1871	+	0.319934i	1.15658	+	0.0280601i
$131$	1.22078	−	1.22078i	0.106660	−	0.106660i	−0.651763	−	0.758423i	$-0.725970\pi$
$131$	1.22078	−	1.22078i	0.106660	−	0.106660i	0.758423	+	0.651763i	$0.225970\pi$
$132$	−4.17083	−	0.202498i	−0.363024	−	0.0176252i
$133$	−2.84935	−	2.84935i	−0.247070	−	0.247070i
$134$	−13.4992	+	12.8597i	−1.16615	+	1.11091i
$135$		−	4.61743i		−	0.397405i
$136$	1.71553	+	0.125059i	0.147106	+	0.0107237i
$137$			0.501149i			0.0428160i	0.999771	+	0.0214080i	$0.00681491\pi$
$137$			0.501149i			0.0428160i	−0.999771	+	0.0214080i	$0.993185\pi$
$138$	−2.34875	−	2.46555i	−0.199939	−	0.209882i
$139$	9.02230	+	9.02230i	0.765261	+	0.765261i	0.977268	−	0.212007i	$-0.0679999\pi$
$139$	9.02230	+	9.02230i	0.765261	+	0.765261i	−0.212007	+	0.977268i	$0.568000\pi$
$140$	9.00141	−	8.16783i	0.760758	−	0.690308i
$141$	−23.6173	+	23.6173i	−1.98894	+	1.98894i
$142$	−0.00927203	+	0.382176i	−0.000778092	+	0.0320715i
$143$	−4.83056			−0.403952
$144$	1.60629	−	16.5034i	0.133858	−	1.37528i
$145$	−13.5232			−1.12304
$146$	0.422614	−	17.4194i	0.0349758	−	1.44164i
$147$	17.4604	−	17.4604i	1.44011	−	1.44011i
$148$	7.84111	+	8.64135i	0.644535	+	0.710315i
$149$	15.6712	+	15.6712i	1.28383	+	1.28383i	0.938469	+	0.345363i	$0.112244\pi$
$149$	15.6712	+	15.6712i	1.28383	+	1.28383i	0.345363	+	0.938469i	$0.387756\pi$
$150$	7.10625	+	7.45964i	0.580223	+	0.609077i
$151$			12.8059i			1.04213i	0.853516	+	0.521066i	$0.174466\pi$
$151$			12.8059i			1.04213i	−0.853516	+	0.521066i	$0.825534\pi$
$152$	−2.14012	+	1.84930i	−0.173586	+	0.149998i
$153$		−	2.52095i		−	0.203807i
$154$	−3.22282	+	3.07015i	−0.259702	+	0.247399i
$155$	−8.00484	−	8.00484i	−0.642964	−	0.642964i
$156$	1.60337	−	33.0244i	0.128372	−	2.64407i
$157$	13.3219	−	13.3219i	1.06320	−	1.06320i	0.0653374	−	0.997863i	$-0.479188\pi$
$157$	13.3219	−	13.3219i	1.06320	−	1.06320i	0.997863	−	0.0653374i	$-0.0208124\pi$
$158$	−2.46499	−	0.0598036i	−0.196104	−	0.00475772i
$159$	−0.973591			−0.0772108
$160$	−5.25858	−	6.71833i	−0.415727	−	0.531130i
$161$	−3.62979			−0.286067
$162$	6.01176	+	0.145852i	0.472328	+	0.0114592i
$163$	2.50875	−	2.50875i	0.196501	−	0.196501i	−0.601997	−	0.798498i	$-0.705628\pi$
$163$	2.50875	−	2.50875i	0.196501	−	0.196501i	0.798498	+	0.601997i	$0.205628\pi$
$164$	−0.305836	+	6.29929i	−0.0238818	+	0.491892i
$165$	2.22662	+	2.22662i	0.173342	+	0.173342i
$166$	−4.02123	+	3.83074i	−0.312108	+	0.297323i
$167$		−	13.2280i		−	1.02361i	−0.859101	−	0.511806i	$-0.828977\pi$
$167$		−	13.2280i		−	1.02361i	0.859101	−	0.511806i	$-0.171023\pi$
$168$	−19.9195	−	23.0520i	−1.53682	−	1.77850i
$169$		−	25.2481i		−	1.94216i
$170$	−0.894679	−	0.939170i	−0.0686187	−	0.0720311i
$171$	2.93119	+	2.93119i	0.224154	+	0.224154i
$172$	−8.26084	−	9.10392i	−0.629883	−	0.694167i
$173$	2.64423	−	2.64423i	0.201037	−	0.201037i	−0.599407	−	0.800444i	$-0.704597\pi$
$173$	2.64423	−	2.64423i	0.201037	−	0.201037i	0.800444	+	0.599407i	$0.204597\pi$
$174$	−0.822119	+	33.8862i	−0.0623247	+	2.56891i
$175$	10.9821			0.830166
$176$	1.98481	+	2.41284i	0.149611	+	0.181874i
$177$	14.8285			1.11458
$178$	−0.358464	+	14.7752i	−0.0268680	+	1.10745i
$179$	−5.58253	+	5.58253i	−0.417258	+	0.417258i	−0.884257	−	0.467000i	$-0.845335\pi$
$179$	−5.58253	+	5.58253i	−0.417258	+	0.417258i	0.467000	+	0.884257i	$0.345335\pi$
$180$	−9.25997	+	8.40244i	−0.690197	+	0.626281i
$181$	12.3479	+	12.3479i	0.917815	+	0.917815i	0.996870	−	0.0790555i	$-0.0251904\pi$
$181$	12.3479	+	12.3479i	0.917815	+	0.917815i	−0.0790555	+	0.996870i	$0.525190\pi$
$182$	−24.3093	−	25.5181i	−1.80192	−	1.89153i
$183$			17.9013i			1.32330i
$184$	−0.185238	+	2.54106i	−0.0136559	+	0.187329i
$185$		−	8.79924i		−	0.646933i
$186$	−20.5450	+	19.5717i	−1.50643	+	1.43507i
$187$	0.335879	+	0.335879i	0.0245619	+	0.0245619i
$188$	24.9605	+	1.21186i	1.82043	+	0.0883837i
$189$	−8.72347	+	8.72347i	−0.634539	+	0.634539i
$190$	2.13228	+	0.0517316i	0.154692	+	0.00375300i
$191$	2.01504			0.145804			0.0729018	−	0.997339i	$-0.476774\pi$
$191$	2.01504			0.145804			0.0729018	+	0.997339i	$0.476774\pi$
$192$	−17.1543	+	12.7684i	−1.23800	+	0.921479i
$193$	2.51436			0.180987			0.0904937	−	0.995897i	$-0.471155\pi$
$193$	2.51436			0.180987			0.0904937	+	0.995897i	$0.471155\pi$
$194$	−4.94179	−	0.119894i	−0.354800	−	0.00860786i
$195$	−17.6302	+	17.6302i	−1.26253	+	1.26253i
$196$	−18.4534	−	0.895932i	−1.31810	−	0.0639951i
$197$	8.73121	+	8.73121i	0.622073	+	0.622073i	0.946061	−	0.323988i	$-0.105024\pi$
$197$	8.73121	+	8.73121i	0.622073	+	0.622073i	−0.323988	+	0.946061i	$0.605024\pi$
$198$	3.31539	−	3.15833i	0.235615	−	0.224453i
$199$			3.61211i			0.256056i	0.991771	+	0.128028i	$0.0408647\pi$
$199$			3.61211i			0.256056i	−0.991771	+	0.128028i	$0.959135\pi$
$200$	0.560445	−	7.68807i	0.0396295	−	0.543629i
$201$		−	35.2400i		−	2.48564i
$202$	−16.9781	−	17.8224i	−1.19458	−	1.25398i
$203$	25.5488	+	25.5488i	1.79317	+	1.79317i
$204$	−2.40774	+	2.18477i	−0.168575	+	0.152964i
$205$	3.36290	−	3.36290i	0.234875	−	0.234875i
$206$	−0.191367	+	7.88778i	−0.0133332	+	0.549567i
$207$	3.73405			0.259534
$208$	−19.1047	+	15.7156i	−1.32467	+	1.08968i
$209$	−0.781075			−0.0540281
$210$	−0.557222	+	22.9676i	−0.0384519	+	1.58492i
$211$	3.51585	−	3.51585i	0.242041	−	0.242041i	−0.575653	−	0.817694i	$-0.695252\pi$
$211$	3.51585	−	3.51585i	0.242041	−	0.242041i	0.817694	+	0.575653i	$0.195252\pi$
$212$	0.489502	+	0.539459i	0.0336191	+	0.0370502i
$213$	−0.510943	−	0.510943i	−0.0350092	−	0.0350092i
$214$	5.57986	+	5.85734i	0.381432	+	0.400400i
$215$			9.27026i			0.632226i
$216$	5.66174	+	6.55211i	0.385233	+	0.445815i
$217$			30.2463i			2.05325i
$218$	5.28841	−	5.03789i	0.358177	−	0.341209i
$219$	23.2885	+	23.2885i	1.57369	+	1.57369i
$220$	0.114252	−	2.35325i	0.00770290	−	0.158656i
$221$	−2.65947	+	2.65947i	−0.178895	+	0.178895i
$222$	−22.0489	−	0.534932i	−1.47982	−	0.0359023i
$223$	−25.9333			−1.73663			−0.868313	−	0.496017i	$-0.834795\pi$
$223$	−25.9333			−1.73663			−0.868313	+	0.496017i	$0.834795\pi$
$224$	−2.75783	+	22.6274i	−0.184265	+	1.51185i
$225$	−11.2975			−0.753168
$226$	−6.65809	−	0.161533i	−0.442890	−	0.0107450i
$227$	15.5390	−	15.5390i	1.03136	−	1.03136i	0.0318692	−	0.999492i	$-0.489854\pi$
$227$	15.5390	−	15.5390i	1.03136	−	1.03136i	0.999492	−	0.0318692i	$-0.0101460\pi$
$228$	0.259255	−	5.33986i	0.0171696	−	0.353641i
$229$	−7.93339	−	7.93339i	−0.524253	−	0.524253i	0.394600	−	0.918853i	$-0.370883\pi$
$229$	−7.93339	−	7.93339i	−0.524253	−	0.524253i	−0.918853	+	0.394600i	$0.870883\pi$
$230$	1.39111	−	1.32520i	0.0917268	−	0.0873814i
$231$		−	8.41326i		−	0.553552i
$232$	19.1894	−	16.5818i	1.25985	−	1.08865i
$233$		−	13.0596i		−	0.855564i	−0.903882	−	0.427782i	$-0.859295\pi$
$233$		−	13.0596i		−	0.855564i	0.903882	−	0.427782i	$-0.140705\pi$
$234$	25.0075	+	26.2511i	1.63479	+	1.71609i
$235$	−13.3253	−	13.3253i	−0.869245	−	0.869245i
$236$	−7.45546	−	8.21634i	−0.485309	−	0.534838i
$237$	3.29553	−	3.29553i	0.214067	−	0.214067i
$238$	−0.0840552	+	3.46460i	−0.00544849	+	0.224576i
$239$	3.88146			0.251071			0.125535	−	0.992089i	$-0.459935\pi$
$239$	3.88146			0.251071			0.125535	+	0.992089i	$0.459935\pi$
$240$	16.0502	+	1.56219i	1.03604	+	0.100839i
$241$	−21.7242			−1.39938			−0.699689	−	0.714448i	$-0.746678\pi$
$241$	−21.7242			−1.39938			−0.699689	+	0.714448i	$0.746678\pi$
$242$	0.356379	−	14.6892i	0.0229089	−	0.944261i
$243$	−14.5319	+	14.5319i	−0.932220	+	0.932220i
$244$	9.91896	−	9.00041i	0.634996	−	0.576192i
$245$	9.85145	+	9.85145i	0.629386	+	0.629386i
$246$	−8.22223	−	8.63111i	−0.524230	−	0.550300i
$247$		−	6.18451i		−	0.393511i
$248$	21.1741	+	1.54355i	1.34456	+	0.0980155i
$249$		−	10.4975i		−	0.665255i
$250$	−11.9305	+	11.3653i	−0.754550	+	0.718805i
$251$	−20.9875	−	20.9875i	−1.32472	−	1.32472i	−0.909909	−	0.414807i	$-0.863849\pi$
$251$	−20.9875	−	20.9875i	−1.32472	−	1.32472i	−0.414807	−	0.909909i	$-0.636151\pi$
$252$	33.3687	+	1.62008i	2.10203	+	0.102056i
$253$	−0.497505	+	0.497505i	−0.0312779	+	0.0312779i
$254$	−22.1882	−	0.538312i	−1.39221	−	0.0337767i
$255$	2.45173			0.153533
$256$	15.6997	+	3.08537i	0.981231	+	0.192836i
$257$	3.05424			0.190518			0.0952590	−	0.995453i	$-0.469632\pi$
$257$	3.05424			0.190518			0.0952590	+	0.995453i	$0.469632\pi$
$258$	23.2292	+	0.563567i	1.44618	+	0.0350862i
$259$	−16.6239	+	16.6239i	−1.03296	+	1.03296i
$260$	18.6329	+	0.904645i	1.15556	+	0.0561037i
$261$	−26.2826	−	26.2826i	−1.62685	−	1.62685i
$262$	1.76781	−	1.68406i	0.109216	−	0.104042i
$263$		−	19.3970i		−	1.19607i	−0.801469	−	0.598036i	$-0.795948\pi$
$263$		−	19.3970i		−	1.19607i	0.801469	−	0.598036i	$-0.204052\pi$
$264$	−5.88976	−	0.429352i	−0.362490	−	0.0264248i
$265$		−	0.549315i		−	0.0337442i
$266$	−3.93067	−	4.12614i	−0.241005	−	0.252990i
$267$	−19.7535	−	19.7535i	−1.20889	−	1.20889i
$268$	−19.5262	+	17.7180i	−1.19275	+	1.08230i
$269$	12.1781	−	12.1781i	0.742514	−	0.742514i	−0.230547	−	0.973061i	$-0.574052\pi$
$269$	12.1781	−	12.1781i	0.742514	−	0.742514i	0.973061	+	0.230547i	$0.0740516\pi$
$270$	0.158380	−	6.52811i	0.00963868	−	0.397288i
$271$	−18.7432			−1.13857			−0.569285	−	0.822140i	$-0.692780\pi$
$271$	−18.7432			−1.13857			−0.569285	+	0.822140i	$0.692780\pi$
$272$	2.42113	+	0.235651i	0.146802	+	0.0142885i
$273$	66.6158			4.03177
$274$	−0.0171896	+	0.708523i	−0.00103846	+	0.0428035i
$275$	1.50522	−	1.50522i	0.0907684	−	0.0907684i
$276$	−3.23609	−	3.56636i	−0.194790	−	0.214670i
$277$	4.84631	+	4.84631i	0.291187	+	0.291187i	0.837549	−	0.546362i	$-0.183988\pi$
$277$	4.84631	+	4.84631i	0.291187	+	0.291187i	−0.546362	+	0.837549i	$0.683988\pi$
$278$	12.4462	+	13.0652i	0.746476	+	0.783597i
$279$		−	31.1151i		−	1.86281i
$280$	13.0063	−	11.2389i	0.777277	−	0.671653i
$281$			7.27330i			0.433889i	0.976184	+	0.216944i	$0.0696090\pi$
$281$			7.27330i			0.433889i	−0.976184	+	0.216944i	$0.930391\pi$
$282$	−34.2002	+	32.5800i	−2.03659	+	1.94011i
$283$	−4.02007	−	4.02007i	−0.238968	−	0.238968i	0.577455	−	0.816423i	$-0.304046\pi$
$283$	−4.02007	−	4.02007i	−0.238968	−	0.238968i	−0.816423	+	0.577455i	$0.804046\pi$
$284$	−0.0262176	+	0.540001i	−0.00155573	+	0.0320432i
$285$	−2.85071	+	2.85071i	−0.168861	+	0.168861i
$286$	−6.82944	−	0.165690i	−0.403833	−	0.00979747i
$287$	−12.7067			−0.750054
$288$	2.83704	−	23.2773i	0.167174	−	1.37163i
$289$	−16.6302			−0.978245
$290$	−19.1191	−	0.463853i	−1.12271	−	0.0272384i
$291$	6.60683	−	6.60683i	0.387299	−	0.387299i
$292$	1.19498	−	24.6130i	0.0699311	−	1.44036i
$293$	13.2722	+	13.2722i	0.775370	+	0.775370i	0.979040	−	0.203670i	$-0.0652869\pi$
$293$	13.2722	+	13.2722i	0.775370	+	0.775370i	−0.203670	+	0.979040i	$0.565287\pi$
$294$	25.2844	−	24.0866i	1.47462	−	1.40476i
$295$			8.36646i			0.487114i
$296$	10.7893	+	12.4861i	0.627118	+	0.725738i
$297$			2.39131i			0.138758i
$298$	21.6183	+	22.6934i	1.25232	+	1.31459i
$299$	−3.93922	−	3.93922i	−0.227811	−	0.227811i
$300$	9.79093	+	10.7902i	0.565280	+	0.622970i
$301$	17.5138	−	17.5138i	1.00948	−	1.00948i
$302$	−0.439249	+	18.1050i	−0.0252759	+	1.04183i
$303$	46.5259			2.67284
$304$	−3.08912	+	2.54112i	−0.177173	+	0.145743i
$305$	−10.1002			−0.578335
$306$	0.0864696	−	3.56411i	0.00494314	−	0.203747i
$307$	14.4957	−	14.4957i	0.827315	−	0.827315i	−0.159830	−	0.987145i	$-0.551094\pi$
$307$	14.4957	−	14.4957i	0.827315	−	0.827315i	0.987145	+	0.159830i	$0.0510945\pi$
$308$	−4.66172	+	4.23002i	−0.265626	+	0.241028i
$309$	−10.5454	−	10.5454i	−0.599908	−	0.599908i
$310$	−11.0427	−	11.5918i	−0.627181	−	0.658370i
$311$			5.20251i			0.295007i	0.989062	+	0.147504i	$0.0471238\pi$
$311$			5.20251i			0.295007i	−0.989062	+	0.147504i	$0.952876\pi$
$312$	3.39959	−	46.6348i	0.192464	−	2.64018i
$313$		−	25.8149i		−	1.45914i	−0.683904	−	0.729572i	$-0.739719\pi$
$313$		−	25.8149i		−	1.45914i	0.683904	−	0.729572i	$-0.260281\pi$
$314$	19.2914	−	18.3775i	1.08867	−	1.03710i
$315$	−17.8140	−	17.8140i	−1.00371	−	1.00371i
$316$	−3.48295	−	0.169100i	−0.195931	−	0.00951265i
$317$	13.8188	−	13.8188i	0.776142	−	0.776142i	−0.203030	−	0.979172i	$-0.565079\pi$
$317$	13.8188	−	13.8188i	0.776142	−	0.776142i	0.979172	+	0.203030i	$0.0650790\pi$
$318$	−1.37646	−	0.0333946i	−0.0771881	−	0.00187267i
$319$	7.00353			0.392122
$320$	−7.20412	−	9.67873i	−0.402723	−	0.541057i
$321$	−15.2908			−0.853447
$322$	−5.13178	−	0.124503i	−0.285983	−	0.00693829i
$323$	−0.430021	+	0.430021i	−0.0239270	+	0.0239270i
$324$	8.49440	+	0.412411i	0.471911	+	0.0229117i
$325$	11.9183	+	11.9183i	0.661107	+	0.661107i
$326$	3.63292	−	3.46082i	0.201209	−	0.191677i
$327$			13.8056i			0.763449i
$328$	−0.648459	+	8.89543i	−0.0358051	+	0.491168i
$329$			50.3495i			2.77586i
$330$	3.07161	+	3.22436i	0.169087	+	0.177495i
$331$	−12.6291	−	12.6291i	−0.694160	−	0.694160i	0.268985	−	0.963144i	$-0.413312\pi$
$331$	−12.6291	−	12.6291i	−0.694160	−	0.694160i	−0.963144	+	0.268985i	$0.913312\pi$
$332$	−5.81661	+	5.27796i	−0.319228	+	0.289665i
$333$	17.1014	−	17.1014i	0.937154	−	0.937154i
$334$	0.453725	−	18.7017i	0.0248267	−	1.02331i
$335$	19.8830			1.08632
$336$	−27.3715	−	33.2742i	−1.49324	−	1.81526i
$337$	−11.1511			−0.607438			−0.303719	−	0.952762i	$-0.598228\pi$
$337$	−11.1511			−0.607438			−0.303719	+	0.952762i	$0.598228\pi$
$338$	0.866021	−	35.6958i	0.0471054	−	1.94159i
$339$	8.90141	−	8.90141i	0.483458	−	0.483458i
$340$	−1.23268	−	1.35848i	−0.0668515	−	0.0736742i
$341$	4.14561	+	4.14561i	0.224497	+	0.224497i
$342$	4.04357	+	4.24466i	0.218651	+	0.229525i
$343$		−	9.01654i		−	0.486847i
$344$	−11.3669	−	13.1544i	−0.612862	−	0.709240i
$345$			3.63152i			0.195514i
$346$	3.82910	−	3.64771i	0.205854	−	0.196102i
$347$	−10.3939	−	10.3939i	−0.557974	−	0.557974i	0.370756	−	0.928730i	$-0.379099\pi$
$347$	−10.3939	−	10.3939i	−0.557974	−	0.557974i	−0.928730	+	0.370756i	$0.879099\pi$
$348$	−2.32462	+	47.8800i	−0.124613	+	2.56664i
$349$	−10.9522	+	10.9522i	−0.586258	+	0.586258i	−0.936616	−	0.350358i	$-0.886060\pi$
$349$	−10.9522	+	10.9522i	−0.586258	+	0.586258i	0.350358	+	0.936616i	$0.386060\pi$
$350$	15.5264	+	0.376689i	0.829922	+	0.0201349i
$351$	−18.9343			−1.01064
$352$	2.72335	+	3.47934i	0.145155	+	0.185450i
$353$	28.2593			1.50409			0.752045	−	0.659111i	$-0.229067\pi$
$353$	28.2593			1.50409			0.752045	+	0.659111i	$0.229067\pi$
$354$	20.9645	+	0.508623i	1.11425	+	0.0270330i
$355$	0.288282	−	0.288282i	0.0153004	−	0.0153004i
$356$	−1.01359	+	20.8769i	−0.0537203	+	1.10647i
$357$	−4.63193	−	4.63193i	−0.245148	−	0.245148i
$358$	−8.08405	+	7.70108i	−0.427255	+	0.407015i
$359$		−	6.64825i		−	0.350881i	−0.984490	−	0.175441i	$-0.943865\pi$
$359$		−	6.64825i		−	0.350881i	0.984490	−	0.175441i	$-0.0561350\pi$
$360$	−13.3799	+	11.5617i	−0.705184	+	0.609357i
$361$		−	1.00000i		−	0.0526316i
$362$	17.0339	+	17.8810i	0.895284	+	0.939805i
$363$	19.6385	+	19.6385i	1.03075	+	1.03075i
$364$	−33.4931	−	36.9113i	−1.75551	−	1.93468i
$365$	−13.1397	+	13.1397i	−0.687765	+	0.687765i
$366$	−0.614021	+	25.3088i	−0.0320954	+	1.32291i
$367$	−8.84035			−0.461462			−0.230731	−	0.973018i	$-0.574112\pi$
$367$	−8.84035			−0.461462			−0.230731	+	0.973018i	$0.574112\pi$
$368$	−0.349048	+	3.58619i	−0.0181954	+	0.186943i
$369$	13.0717			0.680486
$370$	0.301817	−	12.4403i	0.0156907	−	0.646742i
$371$	−1.03779	+	1.03779i	−0.0538795	+	0.0538795i
$372$	−29.7177	+	26.9657i	−1.54079	+	1.39811i
$373$	−8.66241	−	8.66241i	−0.448522	−	0.448522i	0.446341	−	0.894863i	$-0.352727\pi$
$373$	−8.66241	−	8.66241i	−0.448522	−	0.448522i	−0.894863	+	0.446341i	$0.852727\pi$
$374$	0.463343	+	0.486385i	0.0239589	+	0.0251504i
$375$		−	31.1449i		−	1.60831i
$376$	35.2475	+	2.56947i	1.81775	+	0.132511i
$377$			55.4536i			2.85600i
$378$	−12.6324	+	12.0340i	−0.649743	+	0.618962i
$379$	8.58240	+	8.58240i	0.440848	+	0.440848i	0.892297	−	0.451449i	$-0.149093\pi$
$379$	8.58240	+	8.58240i	0.440848	+	0.440848i	−0.451449	+	0.892297i	$0.649093\pi$
$380$	3.01284	+	0.146276i	0.154555	+	0.00750380i
$381$	29.6641	−	29.6641i	1.51974	−	1.51974i
$382$	2.84887	+	0.0691169i	0.145761	+	0.00353633i
$383$	−29.4894			−1.50684			−0.753420	−	0.657540i	$-0.771597\pi$
$383$	−29.4894			−1.50684			−0.753420	+	0.657540i	$0.771597\pi$
$384$	−24.6907	+	17.4635i	−1.25999	+	0.891181i
$385$	4.74690			0.241924
$386$	3.55479	+	0.0862435i	0.180934	+	0.00438968i
$387$	−18.0169	+	18.0169i	−0.915850	+	0.915850i
$388$	−6.98258	−	0.339011i	−0.354487	−	0.0172107i
$389$	−9.54195	−	9.54195i	−0.483796	−	0.483796i	0.422546	−	0.906342i	$-0.361137\pi$
$389$	−9.54195	−	9.54195i	−0.483796	−	0.483796i	−0.906342	+	0.422546i	$0.861137\pi$
$390$	−25.5303	+	24.3209i	−1.29278	+	1.23153i
$391$			0.547804i			0.0277036i
$392$	−26.0587	−	1.89963i	−1.31616	−	0.0959456i
$393$			4.61492i			0.232792i
$394$	12.0447	+	12.6437i	0.606803	+	0.636978i
$395$	1.85939	+	1.85939i	0.0935560	+	0.0935560i
$396$	4.79563	−	4.35152i	0.240989	−	0.218672i
$397$	−16.2249	+	16.2249i	−0.814306	+	0.814306i	−0.985276	−	0.170970i	$-0.945310\pi$
$397$	−16.2249	+	16.2249i	−0.814306	+	0.814306i	0.170970	+	0.985276i	$0.445310\pi$
$398$	−0.123897	+	5.10680i	−0.00621039	+	0.255981i
$399$	10.7714			0.539244
$400$	1.05606	−	10.8502i	0.0528030	−	0.542508i
$401$	10.8292			0.540783			0.270392	−	0.962750i	$-0.412847\pi$
$401$	10.8292			0.540783			0.270392	+	0.962750i	$0.412847\pi$
$402$	1.20875	−	49.8222i	0.0602868	−	2.48491i
$403$	−32.8247	+	32.8247i	−1.63512	+	1.63512i
$404$	−23.3923	−	25.7796i	−1.16381	−	1.28258i
$405$	−4.53478	−	4.53478i	−0.225335	−	0.225335i
$406$	35.2445	+	36.9971i	1.74915	+	1.83614i
$407$			4.55702i			0.225883i
$408$	−3.47899	+	3.00623i	−0.172236	+	0.148831i
$409$			19.3955i			0.959048i	0.877529	+	0.479524i	$0.159191\pi$
$409$			19.3955i			0.959048i	−0.877529	+	0.479524i	$0.840809\pi$
$410$	4.86981	−	4.63911i	0.240503	−	0.229110i
$411$	−0.947247	−	0.947247i	−0.0467242	−	0.0467242i
$412$	−0.541108	+	11.1452i	−0.0266585	+	0.549082i
$413$	15.8063	−	15.8063i	0.777779	−	0.777779i
$414$	5.27919	+	0.128079i	0.259458	+	0.00629476i
$415$	5.92288			0.290743
$416$	−27.5492	+	21.5634i	−1.35071	+	1.05723i
$417$	−34.1070			−1.67023
$418$	−1.10428	−	0.0267912i	−0.0540122	−	0.00131040i
$419$	7.01113	−	7.01113i	0.342516	−	0.342516i	−0.514796	−	0.857313i	$-0.672132\pi$
$419$	7.01113	−	7.01113i	0.342516	−	0.342516i	0.857313	+	0.514796i	$0.172132\pi$
$420$	−1.57560	+	32.4524i	−0.0768813	+	1.58352i
$421$	4.19487	+	4.19487i	0.204445	+	0.204445i	0.801902	−	0.597456i	$-0.203822\pi$
$421$	4.19487	+	4.19487i	0.204445	+	0.204445i	−0.597456	+	0.801902i	$0.703822\pi$
$422$	5.09130	−	4.85011i	0.247841	−	0.236100i
$423$		−	51.7957i		−	2.51840i
$424$	0.673553	+	0.779476i	0.0327106	+	0.0378547i
$425$		−	1.65740i		−	0.0803959i
$426$	−0.704844	−	0.739895i	−0.0341498	−	0.0358480i
$427$	19.0818	+	19.0818i	0.923431	+	0.923431i
$428$	7.68789	+	8.47249i	0.371608	+	0.409533i
$429$	9.13049	−	9.13049i	0.440824	−	0.440824i
$430$	−0.317974	+	13.1063i	−0.0153340	+	0.632040i
$431$	1.34988			0.0650215			0.0325107	−	0.999471i	$-0.489650\pi$
$431$	1.34988			0.0650215			0.0325107	+	0.999471i	$0.489650\pi$
$432$	7.77982	+	9.45756i	0.374307	+	0.455027i
$433$	29.1510			1.40091			0.700454	−	0.713698i	$-0.252981\pi$
$433$	29.1510			1.40091			0.700454	+	0.713698i	$0.252981\pi$
$434$	−1.03746	+	42.7621i	−0.0497996	+	2.05265i
$435$	25.5610	−	25.5610i	1.22555	−	1.22555i
$436$	7.64955	−	6.94116i	0.366347	−	0.332421i
$437$	−0.636950	−	0.636950i	−0.0304695	−	0.0304695i
$438$	32.1264	+	33.7240i	1.53506	+	1.61140i
$439$			4.37163i			0.208646i	0.994543	+	0.104323i	$0.0332676\pi$
$439$			4.37163i			0.208646i	−0.994543	+	0.104323i	$0.966732\pi$
$440$	0.242247	−	3.32310i	0.0115487	−	0.158423i
$441$			38.2929i			1.82347i
$442$	−3.85117	+	3.66873i	−0.183182	+	0.174504i
$443$	−20.5023	−	20.5023i	−0.974092	−	0.974092i	0.0255807	−	0.999673i	$-0.491857\pi$
$443$	−20.5023	−	20.5023i	−0.974092	−	0.974092i	−0.999673	+	0.0255807i	$0.991857\pi$
$444$	−31.1543	−	1.51257i	−1.47852	−	0.0717835i
$445$	11.1452	−	11.1452i	0.528334	−	0.528334i
$446$	−36.6645	−	0.889524i	−1.73611	−	0.0421202i
$447$	−59.2417			−2.80204
$448$	−4.67514	+	31.8959i	−0.220880	+	1.50694i
$449$	−8.68234			−0.409745			−0.204873	−	0.978789i	$-0.565678\pi$
$449$	−8.68234			−0.409745			−0.204873	+	0.978789i	$0.565678\pi$
$450$	−15.9724	−	0.387509i	−0.752946	−	0.0182674i
$451$	−1.74161	+	1.74161i	−0.0820091	+	0.0820091i
$452$	−9.40766	−	0.456751i	−0.442499	−	0.0214837i
$453$	−24.2051	−	24.2051i	−1.13726	−	1.13726i
$454$	22.5020	−	21.4360i	1.05607	−	1.00604i
$455$			37.5857i			1.76204i
$456$	0.549694	−	7.54059i	0.0257418	−	0.353121i
$457$			25.4118i			1.18871i	0.804202	+	0.594356i	$0.202593\pi$
$457$			25.4118i			1.18871i	−0.804202	+	0.594356i	$0.797407\pi$
$458$	−10.9441	−	11.4883i	−0.511384	−	0.536814i
$459$	1.31654	+	1.31654i	0.0614507	+	0.0614507i
$460$	2.01220	−	1.82586i	0.0938191	−	0.0851309i
$461$	−4.47785	+	4.47785i	−0.208554	+	0.208554i	−0.803653	−	0.595098i	$-0.797113\pi$
$461$	−4.47785	+	4.47785i	−0.208554	+	0.208554i	0.595098	+	0.803653i	$0.297113\pi$
$462$	0.288578	−	11.8947i	0.0134259	−	0.553389i
$463$	−14.9185			−0.693320			−0.346660	−	0.937991i	$-0.612684\pi$
$463$	−14.9185			−0.693320			−0.346660	+	0.937991i	$0.612684\pi$
$464$	27.6987	−	22.7851i	1.28588	−	1.05777i
$465$	30.2607			1.40331
$466$	0.447950	−	18.4637i	0.0207509	−	0.855313i
$467$	21.1197	−	21.1197i	0.977301	−	0.977301i	−0.0224468	−	0.999748i	$-0.507146\pi$
$467$	21.1197	−	21.1197i	0.977301	−	0.977301i	0.999748	+	0.0224468i	$0.00714563\pi$
$468$	34.4551	+	37.9715i	1.59269	+	1.75523i
$469$	−37.5639	−	37.5639i	−1.73454	−	1.73454i
$470$	−18.3822	−	19.2963i	−0.847907	−	0.890072i
$471$			50.3606i			2.32050i
$472$	−10.2587	−	11.8720i	−0.472194	−	0.546452i
$473$		−	4.80095i		−	0.220748i
$474$	4.77224	−	4.54617i	0.219196	−	0.208812i
$475$	1.92712	+	1.92712i	0.0884223	+	0.0884223i
$476$	−0.237674	+	4.89535i	−0.0108938	+	0.224378i
$477$	1.06760	−	1.06760i	0.0488822	−	0.0488822i
$478$	5.48760	+	0.133136i	0.250997	+	0.00608948i
$479$	27.6920			1.26528			0.632641	−	0.774446i	$-0.281971\pi$
$479$	27.6920			1.26528			0.632641	+	0.774446i	$0.281971\pi$
$480$	22.6382	+	2.75915i	1.03329	+	0.125937i
$481$	−36.0822			−1.64521
$482$	−30.7136	−	0.745148i	−1.39897	−	0.0339406i
$483$	6.86084	−	6.86084i	0.312179	−	0.312179i
$484$	1.00769	−	20.7554i	0.0458043	−	0.943427i
$485$	3.72768	+	3.72768i	0.169265	+	0.169265i
$486$	−21.0436	+	20.0467i	−0.954556	+	0.909335i
$487$		−	35.2062i		−	1.59534i	−0.603091	−	0.797672i	$-0.706065\pi$
$487$		−	35.2062i		−	1.59534i	0.603091	−	0.797672i	$-0.293935\pi$
$488$	14.3321	−	12.3845i	0.648785	−	0.560621i
$489$			9.48384i			0.428874i
$490$	13.5900	+	14.2659i	0.613936	+	0.644466i
$491$	21.0214	+	21.0214i	0.948681	+	0.948681i	0.998746	−	0.0500647i	$-0.0159428\pi$
$491$	21.0214	+	21.0214i	0.948681	+	0.948681i	−0.0500647	+	0.998746i	$0.515943\pi$
$492$	−11.3285	−	12.4847i	−0.510729	−	0.562853i
$493$	3.85580	−	3.85580i	0.173656	−	0.173656i
$494$	0.212131	−	8.74364i	0.00954423	−	0.393395i
$495$	−4.88325			−0.219486
$496$	29.8830	+	2.90855i	1.34178	+	0.130598i
$497$	−1.08927			−0.0488605
$498$	0.360070	−	14.8414i	0.0161351	−	0.665059i
$499$	−0.953966	+	0.953966i	−0.0427054	+	0.0427054i	−0.728137	−	0.685432i	$-0.759614\pi$
$499$	−0.953966	+	0.953966i	−0.0427054	+	0.0427054i	0.685432	+	0.728137i	$0.259614\pi$
$500$	−17.2571	+	15.6590i	−0.771762	+	0.700292i
$501$	25.0029	+	25.0029i	1.11705	+	1.11705i
$502$	−28.9521	−	30.3919i	−1.29220	−	1.35646i
$503$		−	4.28185i		−	0.190918i	−0.995433	−	0.0954592i	$-0.969568\pi$
$503$		−	4.28185i		−	0.190918i	0.995433	−	0.0954592i	$-0.0304320\pi$
$504$	47.1210	+	3.43503i	2.09894	+	0.153008i
$505$			26.2506i			1.16814i
$506$	−0.720437	+	0.686307i	−0.0320273	+	0.0305101i
$507$	47.7228	+	47.7228i	2.11944	+	2.11944i
$508$	−31.3512	−	1.52213i	−1.39098	−	0.0675335i
$509$	−21.8211	+	21.8211i	−0.967202	+	0.967202i	−0.999479	−	0.0322767i	$-0.989724\pi$
$509$	−21.8211	+	21.8211i	−0.967202	+	0.967202i	0.0322767	+	0.999479i	$0.489724\pi$
$510$	3.46625	+	0.0840953i	0.153488	+	0.00372380i
$511$	49.6485			2.19632
$512$	22.0904	+	4.90060i	0.976265	+	0.216578i
$513$	−3.06157			−0.135171
$514$	4.31807	+	0.104762i	0.190462	+	0.00462083i
$515$	5.94989	−	5.94989i	0.262184	−	0.262184i
$516$	32.8220	+	1.59354i	1.44491	+	0.0701517i
$517$	6.90100	+	6.90100i	0.303506	+	0.303506i
$518$	−24.0731	+	22.9327i	−1.05771	+	1.00760i
$519$			9.99598i			0.438775i
$520$	26.3121	+	1.91810i	1.15386	+	0.0841143i
$521$		−	32.0921i		−	1.40598i	−0.711199	−	0.702991i	$-0.751848\pi$
$521$		−	32.0921i		−	1.40598i	0.711199	−	0.702991i	$-0.248152\pi$
$522$	−36.2568	−	38.0598i	−1.58692	−	1.66583i
$523$	23.2846	+	23.2846i	1.01816	+	1.01816i	0.999832	+	0.0183319i	$0.00583556\pi$
$523$	23.2846	+	23.2846i	1.01816	+	1.01816i	0.0183319	+	0.999832i	$0.494164\pi$
$524$	2.55709	−	2.32029i	0.111707	−	0.101362i
$525$	−20.7578	+	20.7578i	−0.905943	+	0.905943i
$526$	0.665326	−	27.4235i	0.0290096	−	1.19572i
$527$	4.56474			0.198843
$528$	−8.31221	−	0.809038i	−0.361742	−	0.0352089i
$529$	22.1886			0.964721
$530$	0.0188417	−	0.776621i	0.000818433	−	0.0337342i
$531$	−16.2603	+	16.2603i	−0.705639	+	0.705639i
$532$	−5.41564	−	5.96835i	−0.234798	−	0.258761i
$533$	−13.7900	−	13.7900i	−0.597309	−	0.597309i
$534$	−27.2498	−	28.6049i	−1.17922	−	1.23786i
$535$		−	8.62729i		−	0.372990i
$536$	−28.2138	+	24.3799i	−1.21865	+	1.05305i
$537$		−	21.1036i		−	0.910689i
$538$	17.6351	−	16.7997i	0.760304	−	0.724287i
$539$	−5.10195	−	5.10195i	−0.219756	−	0.219756i
$540$	0.447834	−	9.22399i	0.0192717	−	0.396938i
$541$	−12.1744	+	12.1744i	−0.523420	+	0.523420i	−0.918602	−	0.395183i	$-0.870681\pi$
$541$	−12.1744	+	12.1744i	−0.523420	+	0.523420i	0.395183	+	0.918602i	$0.370681\pi$
$542$	−26.4991	−	0.642900i	−1.13823	−	0.0276149i
$543$	−46.6789			−2.00318
$544$	3.41490	+	0.416209i	0.146413	+	0.0178448i
$545$	−7.78931			−0.333658
$546$	94.1812	+	2.28495i	4.03058	+	0.0977868i
$547$	−10.7020	+	10.7020i	−0.457584	+	0.457584i	−0.897862	−	0.440277i	$-0.854880\pi$
$547$	−10.7020	+	10.7020i	−0.457584	+	0.457584i	0.440277	+	0.897862i	$0.354880\pi$
$548$	−0.0486053	+	1.00112i	−0.00207631	+	0.0427657i
$549$	−19.6299	−	19.6299i	−0.837782	−	0.837782i
$550$	2.17971	−	2.07645i	0.0929432	−	0.0885402i
$551$			8.96653i			0.381987i
$552$	−4.45285	−	5.15311i	−0.189526	−	0.219331i
$553$		−	7.02569i		−	0.298763i
$554$	6.68547	+	7.01793i	0.284038	+	0.298163i
$555$	16.6319	+	16.6319i	0.705984	+	0.705984i
$556$	17.1483	+	18.8984i	0.727251	+	0.801472i
$557$	10.6604	−	10.6604i	0.451695	−	0.451695i	−0.444222	−	0.895917i	$-0.646520\pi$
$557$	10.6604	−	10.6604i	0.451695	−	0.451695i	0.895917	+	0.444222i	$0.146520\pi$
$558$	1.06726	−	43.9904i	0.0451807	−	1.86226i
$559$	38.0137			1.60781
$560$	18.7738	−	15.4434i	0.793339	−	0.652603i
$561$	−1.26972			−0.0536077
$562$	−0.249477	+	10.2830i	−0.0105236	+	0.433761i
$563$	12.8332	−	12.8332i	0.540854	−	0.540854i	−0.382926	−	0.923779i	$-0.625083\pi$
$563$	12.8332	−	12.8332i	0.540854	−	0.540854i	0.923779	+	0.382926i	$0.125083\pi$
$564$	−49.4697	+	44.8885i	−2.08305	+	1.89015i
$565$	5.02232	+	5.02232i	0.211291	+	0.211291i
$566$	−5.54567	−	5.82145i	−0.233102	−	0.244694i
$567$			17.1346i			0.719587i
$568$	−0.0555886	+	0.762553i	−0.00233244	+	0.0319960i
$569$		−	15.4815i		−	0.649020i	−0.945882	−	0.324510i	$-0.894801\pi$
$569$		−	15.4815i		−	0.649020i	0.945882	−	0.324510i	$-0.105199\pi$
$570$	−4.12811	+	3.93255i	−0.172907	+	0.164716i
$571$	17.8262	+	17.8262i	0.746004	+	0.746004i	0.973726	−	0.227722i	$-0.0731277\pi$
$571$	17.8262	+	17.8262i	0.746004	+	0.746004i	−0.227722	+	0.973726i	$0.573128\pi$
$572$	−9.64976	−	0.468505i	−0.403477	−	0.0195892i
$573$	−3.80874	+	3.80874i	−0.159112	+	0.159112i
$574$	−17.9647	−	0.435845i	−0.749833	−	0.0181918i
$575$	2.45496			0.102379
$576$	4.80943	−	32.8121i	0.200393	−	1.36717i
$577$	−5.29423			−0.220401			−0.110201	−	0.993909i	$-0.535149\pi$
$577$	−5.29423			−0.220401			−0.110201	+	0.993909i	$0.535149\pi$
$578$	−23.5117	−	0.570421i	−0.977957	−	0.0237264i
$579$	−4.75251	+	4.75251i	−0.197508	+	0.197508i
$580$	−27.0147	−	1.31159i	−1.12172	−	0.0544607i
$581$	−11.1898	−	11.1898i	−0.464231	−	0.464231i
$582$	9.56734	−	9.11411i	0.396579	−	0.377792i
$583$			0.284484i			0.0117821i
$584$	2.53370	−	34.7568i	0.104845	−	1.43824i
$585$		−	38.6653i		−	1.59861i
$586$	18.3090	+	19.2194i	0.756336	+	0.793948i
$587$	−27.4763	−	27.4763i	−1.13407	−	1.13407i	−0.989494	−	0.144574i	$-0.953819\pi$
$587$	−27.4763	−	27.4763i	−1.13407	−	1.13407i	−0.144574	−	0.989494i	$-0.546181\pi$
$588$	36.5732	−	33.1863i	1.50825	−	1.36858i
$589$	−5.30757	+	5.30757i	−0.218695	+	0.218695i
$590$	−0.286973	+	11.8285i	−0.0118145	+	0.486971i
$591$	−33.0066			−1.35771
$592$	14.8257	+	18.0229i	0.609331	+	0.740735i
$593$	−26.3502			−1.08207			−0.541036	−	0.841000i	$-0.681968\pi$
$593$	−26.3502			−1.08207			−0.541036	+	0.841000i	$0.681968\pi$
$594$	−0.0820230	+	3.38083i	−0.00336544	+	0.138717i
$595$	2.61341	−	2.61341i	0.107139	−	0.107139i
$596$	29.7856	+	32.8254i	1.22006	+	1.34458i
$597$	−6.82744	−	6.82744i	−0.279428	−	0.279428i
$598$	−5.43415	−	5.70438i	−0.222219	−	0.233269i
$599$		−	18.7420i		−	0.765776i	−0.923795	−	0.382888i	$-0.874930\pi$
$599$		−	18.7420i		−	0.765776i	0.923795	−	0.382888i	$-0.125070\pi$
$600$	13.4723	+	15.5909i	0.550004	+	0.636497i
$601$			6.35121i			0.259071i	0.991575	+	0.129536i	$0.0413486\pi$
$601$			6.35121i			0.259071i	−0.991575	+	0.129536i	$0.958651\pi$
$602$	25.3617	−	24.1603i	1.03367	−	0.984699i
$603$	38.6429	+	38.6429i	1.57366	+	1.57366i
$604$	−1.24202	+	25.5817i	−0.0505370	+	1.04091i
$605$	−11.0804	+	11.0804i	−0.450481	+	0.450481i
$606$	65.7782	+	1.59586i	2.67206	+	0.0648273i
$607$	21.4722			0.871531			0.435765	−	0.900060i	$-0.356478\pi$
$607$	21.4722			0.871531			0.435765	+	0.900060i	$0.356478\pi$
$608$	−4.45456	+	3.48668i	−0.180656	+	0.141403i
$609$	−96.5820			−3.91370
$610$	−14.2796	−	0.346441i	−0.578165	−	0.0140270i
$611$	−54.6418	+	54.6418i	−2.21057	+	2.21057i
$612$	0.244501	−	5.03597i	0.00988337	−	0.203567i
$613$	29.5806	+	29.5806i	1.19475	+	1.19475i	0.975717	+	0.219033i	$0.0702904\pi$
$613$	29.5806	+	29.5806i	1.19475	+	1.19475i	0.219033	+	0.975717i	$0.429710\pi$
$614$	20.9912	−	19.9968i	0.847137	−	0.807006i
$615$			12.7128i			0.512629i
$616$	−6.73582	+	5.82049i	−0.271394	+	0.234514i
$617$		−	17.8609i		−	0.719051i	−0.933135	−	0.359525i	$-0.882939\pi$
$617$		−	17.8609i		−	0.719051i	0.933135	−	0.359525i	$-0.117061\pi$
$618$	−14.5474	−	15.2708i	−0.585181	−	0.614281i
$619$	−3.98730	−	3.98730i	−0.160263	−	0.160263i	0.622420	−	0.782683i	$-0.286150\pi$
$619$	−3.98730	−	3.98730i	−0.160263	−	0.160263i	−0.782683	+	0.622420i	$0.786150\pi$
$620$	−15.2145	−	16.7672i	−0.611028	−	0.673388i
$621$	−1.95006	+	1.95006i	−0.0782534	+	0.0782534i
$622$	−0.178448	+	7.35530i	−0.00715513	+	0.294921i
$623$	−42.1122			−1.68719
$624$	6.40592	−	65.8156i	0.256442	−	2.63473i
$625$	3.94565			0.157826
$626$	0.885462	−	36.4971i	0.0353902	−	1.45872i
$627$	1.47635	−	1.47635i	0.0589597	−	0.0589597i
$628$	27.9044	−	25.3203i	1.11351	−	1.01039i
$629$	2.50887	+	2.50887i	0.100035	+	0.100035i
$630$	−24.5744	−	25.7964i	−0.979067	−	1.02775i
$631$			30.3473i			1.20811i	0.796944	+	0.604053i	$0.206448\pi$
$631$			30.3473i			1.20811i	−0.796944	+	0.604053i	$0.793552\pi$
$632$	−4.91838	−	0.358540i	−0.195643	−	0.0142620i
$633$			13.2910i			0.528269i
$634$	20.0110	−	19.0630i	0.794738	−	0.757089i
$635$	16.7370	+	16.7370i	0.664186	+	0.664186i
$636$	−1.94489	−	0.0944263i	−0.0771199	−	0.00374425i
$637$	40.3969	−	40.3969i	1.60059	−	1.60059i
$638$	9.90157	+	0.240224i	0.392007	+	0.00951055i
$639$	1.12056			0.0443287
$640$	−9.85319	−	13.9309i	−0.389481	−	0.550666i
$641$	−26.6647			−1.05319			−0.526595	−	0.850116i	$-0.676532\pi$
$641$	−26.6647			−1.05319			−0.526595	+	0.850116i	$0.676532\pi$
$642$	−21.6180	−	0.524479i	−0.853196	−	0.0206995i
$643$	−17.4776	+	17.4776i	−0.689250	+	0.689250i	−0.962066	−	0.272816i	$-0.912045\pi$
$643$	−17.4776	+	17.4776i	−0.689250	+	0.689250i	0.272816	+	0.962066i	$0.412045\pi$
$644$	−7.25103	−	0.352044i	−0.285731	−	0.0138725i
$645$	−17.5222	−	17.5222i	−0.689935	−	0.689935i
$646$	−0.622713	+	0.593213i	−0.0245003	+	0.0233396i
$647$			21.9528i			0.863055i	0.902100	+	0.431528i	$0.142025\pi$
$647$			21.9528i			0.863055i	−0.902100	+	0.431528i	$0.857975\pi$
$648$	11.9952	+	0.874428i	0.471217	+	0.0343508i
$649$		−	4.33289i		−	0.170081i
$650$	16.4412	+	17.2588i	0.644878	+	0.676947i
$651$	−57.1700	−	57.1700i	−2.24067	−	2.24067i
$652$	5.25492	−	4.76829i	0.205799	−	0.186741i
$653$	−20.4948	+	20.4948i	−0.802024	+	0.802024i	−0.983412	−	0.181387i	$-0.941941\pi$
$653$	−20.4948	+	20.4948i	−0.802024	+	0.802024i	0.181387	+	0.983412i	$0.441941\pi$
$654$	−0.473536	+	19.5183i	−0.0185167	+	0.763224i
$655$	−2.60381			−0.101739
$656$	−1.22191	+	12.5541i	−0.0477074	+	0.490155i
$657$	−51.0746			−1.99261
$658$	−1.72701	+	71.1840i	−0.0673258	+	2.77504i
$659$	36.1034	−	36.1034i	1.40639	−	1.40639i	0.628905	−	0.777482i	$-0.283504\pi$
$659$	36.1034	−	36.1034i	1.40639	−	1.40639i	0.777482	−	0.628905i	$-0.216496\pi$
$660$	4.23204	+	4.66395i	0.164732	+	0.181544i
$661$	−6.46495	−	6.46495i	−0.251457	−	0.251457i	0.570111	−	0.821568i	$-0.306900\pi$
$661$	−6.46495	−	6.46495i	−0.251457	−	0.251457i	−0.821568	+	0.570111i	$0.806900\pi$
$662$	−17.4218	−	18.2882i	−0.677119	−	0.710792i
$663$		−	10.0536i		−	0.390449i
$664$	−8.40454	+	7.26245i	−0.326159	+	0.281838i
$665$			6.07739i			0.235671i
$666$	24.7646	−	23.5914i	0.959608	−	0.914148i
$667$	5.71123	+	5.71123i	0.221140	+	0.221140i
$668$	1.28295	−	26.4249i	0.0496389	−	1.02241i
$669$	49.0179	−	49.0179i	1.89514	−	1.89514i
$670$	28.1105	+	0.681994i	1.08600	+	0.0263477i
$671$	5.23077			0.201932
$672$	−37.5564	−	47.9818i	−1.44877	−	1.85094i
$673$	4.15503			0.160165			0.0800823	−	0.996788i	$-0.474482\pi$
$673$	4.15503			0.160165			0.0800823	+	0.996788i	$0.474482\pi$
$674$	−15.7654	−	0.382487i	−0.607259	−	0.0147328i
$675$	5.90000	−	5.90000i	0.227091	−	0.227091i
$676$	2.44876	−	50.4369i	0.0941830	−	1.93988i
$677$	−2.06257	−	2.06257i	−0.0792710	−	0.0792710i	0.666360	−	0.745631i	$-0.267852\pi$
$677$	−2.06257	−	2.06257i	−0.0792710	−	0.0792710i	−0.745631	+	0.666360i	$0.767852\pi$
$678$	12.8901	−	12.2795i	0.495042	−	0.471590i
$679$		−	14.0850i		−	0.540534i
$680$	−1.69616	−	1.96290i	−0.0650449	−	0.0752739i
$681$			58.7422i			2.25100i
$682$	5.71886	+	6.00325i	0.218986	+	0.229876i
$683$	10.6287	+	10.6287i	0.406695	+	0.406695i	0.880584	−	0.473890i	$-0.157150\pi$
$683$	10.6287	+	10.6287i	0.406695	+	0.406695i	−0.473890	+	0.880584i	$0.657150\pi$
$684$	5.57120	+	6.13978i	0.213020	+	0.234760i
$685$	0.534452	−	0.534452i	0.0204204	−	0.0204204i
$686$	0.309271	−	12.7476i	0.0118080	−	0.486704i
$687$	29.9906			1.14421
$688$	−15.6193	−	18.9876i	−0.595479	−	0.723896i
$689$	−2.25253			−0.0858145
$690$	−0.124563	+	5.13423i	−0.00474202	+	0.195457i
$691$	16.9758	−	16.9758i	0.645790	−	0.645790i	−0.306183	−	0.951973i	$-0.599052\pi$
$691$	16.9758	−	16.9758i	0.645790	−	0.645790i	0.951973	+	0.306183i	$0.0990519\pi$
$692$	5.53869	−	5.02578i	0.210550	−	0.191051i
$693$	9.22567	+	9.22567i	0.350454	+	0.350454i
$694$	−14.3384	−	15.0514i	−0.544277	−	0.571343i
$695$		−	19.2437i		−	0.729956i
$696$	−4.92885	+	67.6129i	−0.186827	+	2.56286i
$697$			1.91769i			0.0726375i
$698$	−15.8599	+	15.1085i	−0.600305	+	0.571866i
$699$	24.6847	+	24.6847i	0.933659	+	0.933659i
$700$	21.9383	+	1.06512i	0.829189	+	0.0402579i
$701$	−8.20712	+	8.20712i	−0.309979	+	0.309979i	−0.844901	−	0.534922i	$-0.820341\pi$
$701$	−8.20712	+	8.20712i	−0.309979	+	0.309979i	0.534922	+	0.844901i	$0.320341\pi$
$702$	−26.7692	−	0.649454i	−1.01034	−	0.0245120i
$703$	−5.83429			−0.220045
$704$	3.73093	+	5.01250i	0.140615	+	0.188916i
$705$	50.3735			1.89718
$706$	39.9529	+	0.969305i	1.50365	+	0.0364803i
$707$	49.5940	−	49.5940i	1.86517	−	1.86517i
$708$	29.6221	+	1.43818i	1.11327	+	0.0540501i
$709$	2.94396	+	2.94396i	0.110563	+	0.110563i	0.760224	−	0.649661i	$-0.225089\pi$
$709$	2.94396	+	2.94396i	0.110563	+	0.110563i	−0.649661	+	0.760224i	$0.725089\pi$
$710$	0.417460	−	0.397684i	0.0156670	−	0.0149248i
$711$			7.22750i			0.271052i
$712$	−2.14910	+	29.4809i	−0.0805409	+	1.10484i
$713$			6.76132i			0.253213i
$714$	−6.38973	−	6.70748i	−0.239130	−	0.251021i
$715$	5.15157	+	5.15157i	0.192658	+	0.192658i
$716$	−11.6934	+	10.6105i	−0.437001	+	0.396532i
$717$	−7.33654	+	7.33654i	−0.273988	+	0.273988i
$718$	0.228038	−	9.39928i	0.00851029	−	0.350778i
$719$	11.3521			0.423362			0.211681	−	0.977339i	$-0.432106\pi$
$719$	11.3521			0.423362			0.211681	+	0.977339i	$0.432106\pi$
$720$	−19.3131	+	15.8870i	−0.719756	+	0.592074i
$721$	−22.4816			−0.837260
$722$	0.0343004	−	1.41380i	0.00127653	−	0.0526161i
$723$	41.0620	−	41.0620i	1.52711	−	1.52711i
$724$	23.4692	+	25.8644i	0.872226	+	0.961243i
$725$	−17.2796	−	17.2796i	−0.641747	−	0.641747i
$726$	27.0913	+	28.4385i	1.00545	+	1.05545i
$727$			7.72299i			0.286430i	0.989692	+	0.143215i	$0.0457440\pi$
$727$			7.72299i			0.286430i	−0.989692	+	0.143215i	$0.954256\pi$
$728$	−46.0864	−	53.3339i	−1.70807	−	1.97669i
$729$		−	42.1782i		−	1.56216i
$730$	−19.0276	+	18.1262i	−0.704244	+	0.670882i
$731$	−2.64317	−	2.64317i	−0.0977611	−	0.0977611i
$732$	−1.73620	+	35.7604i	−0.0641719	+	1.32174i
$733$	25.6965	−	25.6965i	0.949122	−	0.949122i	−0.0496448	−	0.998767i	$-0.515809\pi$
$733$	25.6965	−	25.6965i	0.949122	−	0.949122i	0.998767	+	0.0496448i	$0.0158089\pi$
$734$	−12.4985	−	0.303228i	−0.461327	−	0.0111923i
$735$	−37.2414			−1.37367
$736$	−0.616491	+	5.05817i	−0.0227242	+	0.186447i
$737$	−10.2972			−0.379300
$738$	18.4807	+	0.448365i	0.680286	+	0.0165045i
$739$	−14.2617	+	14.2617i	−0.524627	+	0.524627i	−0.918965	−	0.394338i	$-0.870974\pi$
$739$	−14.2617	+	14.2617i	−0.524627	+	0.524627i	0.394338	+	0.918965i	$0.370974\pi$
$740$	0.853417	−	17.5778i	0.0313722	−	0.646172i
$741$	11.6896	+	11.6896i	0.429430	+	0.429430i
$742$	−1.50283	+	1.43163i	−0.0551705	+	0.0525569i
$743$			19.0364i			0.698379i	0.937052	+	0.349190i	$0.113543\pi$
$743$			19.0364i			0.698379i	−0.937052	+	0.349190i	$0.886457\pi$
$744$	−42.9398	+	37.1047i	−1.57425	+	1.36032i
$745$		−	33.4251i		−	1.22460i
$746$	−11.9498	−	12.5440i	−0.437512	−	0.459269i
$747$	11.5112	+	11.5112i	0.421173	+	0.421173i
$748$	0.638391	+	0.703543i	0.0233419	+	0.0257241i
$749$	−16.2991	+	16.2991i	−0.595556	+	0.595556i
$750$	1.06828	−	44.0325i	0.0390081	−	1.60784i
$751$	−30.0230			−1.09556			−0.547778	−	0.836624i	$-0.684526\pi$
$751$	−30.0230			−1.09556			−0.547778	+	0.836624i	$0.684526\pi$
$752$	49.7447	+	4.84172i	1.81400	+	0.176559i
$753$	79.3389			2.89127
$754$	−1.90208	+	78.4001i	−0.0692697	+	2.85516i
$755$	13.6569	−	13.6569i	0.497027	−	0.497027i
$756$	−18.2725	+	16.5803i	−0.664564	+	0.603021i
$757$	18.8213	+	18.8213i	0.684071	+	0.684071i	0.960915	−	0.276844i	$-0.0892884\pi$
$757$	18.8213	+	18.8213i	0.684071	+	0.684071i	−0.276844	+	0.960915i	$0.589288\pi$
$758$	11.8394	+	12.4282i	0.430026	+	0.451411i
$759$		−	1.88072i		−	0.0682658i
$760$	4.25452	+	0.310146i	0.154328	+	0.0112502i
$761$			0.500291i			0.0181355i	0.999959	+	0.00906777i	$0.00288640\pi$
$761$			0.500291i			0.0181355i	−0.999959	+	0.00906777i	$0.997114\pi$
$762$	42.9565	−	40.9215i	1.55615	−	1.48243i
$763$	14.7159	+	14.7159i	0.532753	+	0.532753i
$764$	4.02535	+	0.195434i	0.145632	+	0.00707057i
$765$	−2.68847	+	2.68847i	−0.0972020	+	0.0972020i
$766$	−41.6921	−	1.01150i	−1.50640	−	0.0365470i
$767$	34.3076			1.23878
$768$	−35.5066	+	23.8430i	−1.28123	+	0.860359i
$769$	−6.22678			−0.224543			−0.112272	−	0.993678i	$-0.535813\pi$
$769$	−6.22678			−0.224543			−0.112272	+	0.993678i	$0.535813\pi$
$770$	6.71115	+	0.162820i	0.241853	+	0.00586764i
$771$	−5.77297	+	5.77297i	−0.207908	+	0.207908i
$772$	5.02280	+	0.243862i	0.180775	+	0.00877677i
$773$	−22.7785	−	22.7785i	−0.819287	−	0.819287i	0.166718	−	0.986005i	$-0.446683\pi$
$773$	−22.7785	−	22.7785i	−0.819287	−	0.819287i	−0.986005	+	0.166718i	$0.946683\pi$
$774$	−26.0902	+	24.8542i	−0.937793	+	0.893367i
$775$		−	20.4566i		−	0.734824i
$776$	−9.86032	−	0.718798i	−0.353965	−	0.0258033i
$777$		−	62.8435i		−	2.25450i
$778$	−13.1631	−	13.8177i	−0.471920	−	0.495388i
$779$	−2.22976	−	2.22976i	−0.0798893	−	0.0798893i
$780$	−36.9289	+	33.5091i	−1.32227	+	1.19982i
$781$	−0.149298	+	0.149298i	−0.00534229	+	0.00534229i
$782$	−0.0187899	+	0.774484i	−0.000671925	+	0.0276955i
$783$	27.4516			0.981041
$784$	−36.7765	−	3.57951i	−1.31345	−	0.127840i
$785$	−28.4143			−1.01415
$786$	−0.158294	+	6.52456i	−0.00564615	+	0.232723i
$787$	15.6427	−	15.6427i	0.557601	−	0.557601i	−0.371023	−	0.928624i	$-0.620993\pi$
$787$	15.6427	−	15.6427i	0.557601	−	0.557601i	0.928624	+	0.371023i	$0.120993\pi$
$788$	16.5951	+	18.2887i	0.591175	+	0.651508i
$789$	36.6633	+	36.6633i	1.30525	+	1.30525i
$790$	2.56502	+	2.69258i	0.0912593	+	0.0957976i
$791$		−	18.9768i		−	0.674738i
$792$	6.92930	−	5.98768i	0.246222	−	0.212763i
$793$			41.4169i			1.47076i
$794$	−23.4953	+	22.3822i	−0.833817	+	0.794316i
$795$	1.03829	+	1.03829i	0.0368243	+	0.0368243i
$796$	−0.350330	+	7.21573i	−0.0124171	+	0.255755i
$797$	−31.3227	+	31.3227i	−1.10951	+	1.10951i	−0.116291	+	0.993215i	$0.537100\pi$
$797$	−31.3227	+	31.3227i	−1.10951	+	1.10951i	−0.993215	+	0.116291i	$0.962900\pi$
$798$	15.2286	+	0.369463i	0.539086	+	0.0130789i
$799$	7.59870			0.268823
$800$	1.86522	−	15.3037i	0.0659455	−	0.541067i
$801$	43.3218			1.53070
$802$	15.3103	+	0.371445i	0.540624	+	0.0131162i
$803$	6.80491	−	6.80491i	0.240140	−	0.240140i
$804$	3.41785	−	70.3971i	0.120538	−	2.48271i
$805$	3.87100	+	3.87100i	0.136435	+	0.136435i
$806$	−47.5334	+	45.2816i	−1.67429	+	1.59498i
$807$			46.0370i			1.62058i
$808$	−32.1877	−	37.2495i	−1.13236	−	1.31043i
$809$			42.4127i			1.49115i	0.666421	+	0.745575i	$0.267825\pi$
$809$			42.4127i			1.49115i	−0.666421	+	0.745575i	$0.732175\pi$
$810$	−6.25571	−	6.56680i	−0.219803	−	0.230734i
$811$	−14.3351	−	14.3351i	−0.503374	−	0.503374i	0.409111	−	0.912485i	$-0.365839\pi$
$811$	−14.3351	−	14.3351i	−0.503374	−	0.503374i	−0.912485	+	0.409111i	$0.865839\pi$
$812$	48.5595	+	53.5153i	1.70410	+	1.87802i
$813$	35.4275	−	35.4275i	1.24250	−	1.24250i
$814$	−0.156308	+	6.44270i	−0.00547858	+	0.225817i
$815$	−5.35094			−0.187435
$816$	−5.02171	+	4.13087i	−0.175795	+	0.144610i
$817$	6.14660			0.215042
$818$	−0.665275	+	27.4214i	−0.0232608	+	0.958765i
$819$	−73.0484	+	73.0484i	−2.55252	+	2.55252i
$820$	7.04405	−	6.39173i	0.245989	−	0.223209i
$821$	0.414946	+	0.414946i	0.0144817	+	0.0144817i	0.714311	−	0.699829i	$-0.246740\pi$
$821$	0.414946	+	0.414946i	0.0144817	+	0.0144817i	−0.699829	+	0.714311i	$0.746740\pi$
$822$	−1.30672	−	1.37171i	−0.0455772	−	0.0478437i
$823$		−	24.2381i		−	0.844888i	−0.906389	−	0.422444i	$-0.861172\pi$
$823$		−	24.2381i		−	0.844888i	0.906389	−	0.422444i	$-0.138828\pi$
$824$	−1.14730	+	15.7384i	−0.0399681	+	0.548274i
$825$			5.69020i			0.198107i
$826$	22.8891	−	21.8048i	0.796414	−	0.758685i
$827$	−13.1438	−	13.1438i	−0.457056	−	0.457056i	0.440632	−	0.897688i	$-0.354754\pi$
$827$	−13.1438	−	13.1438i	−0.457056	−	0.457056i	−0.897688	+	0.440632i	$0.854754\pi$
$828$	7.45931	+	0.362157i	0.259229	+	0.0125858i
$829$	13.6134	−	13.6134i	0.472814	−	0.472814i	−0.430010	−	0.902824i	$-0.641490\pi$
$829$	13.6134	−	13.6134i	0.472814	−	0.472814i	0.902824	+	0.430010i	$0.141490\pi$
$830$	8.37376	+	0.203157i	0.290657	+	0.00705169i
$831$	−18.3205			−0.635531
$832$	−39.6887	+	29.5413i	−1.37596	+	1.02416i
$833$	−5.61776			−0.194644
$834$	−48.2204	−	1.16988i	−1.66974	−	0.0405098i
$835$	−14.1070	+	14.1070i	−0.488194	+	0.488194i
$836$	−1.56031	−	0.0757546i	−0.0539645	−	0.00262003i
$837$	16.2495	+	16.2495i	0.561664	+	0.561664i
$838$	10.1528	−	9.67184i	0.350723	−	0.334108i
$839$			29.7619i			1.02750i	0.857941	+	0.513748i	$0.171743\pi$
$839$			29.7619i			1.02750i	−0.857941	+	0.513748i	$0.828257\pi$
$840$	−3.34071	+	45.8271i	−0.115265	+	1.58119i
$841$		−	51.3986i		−	1.77237i
$842$	5.78681	+	6.07458i	0.199427	+	0.209344i
$843$	−13.7476	−	13.7476i	−0.473493	−	0.473493i
$844$	7.36443	−	6.68244i	0.253494	−	0.230019i
$845$	−26.9259	+	26.9259i	−0.926281	+	0.926281i
$846$	1.77662	−	73.2287i	0.0610813	−	2.51765i
$847$	41.8671			1.43857
$848$	0.925531	+	1.12512i	0.0317829	+	0.0386369i
$849$	15.1971			0.521562
$850$	0.0568496	−	2.34323i	0.00194992	−	0.0803722i
$851$	−3.71615	+	3.71615i	−0.127388	+	0.127388i
$852$	−0.971128	−	1.07024i	−0.0332703	−	0.0366657i
$853$	−2.40701	−	2.40701i	−0.0824143	−	0.0824143i	0.664698	−	0.747112i	$-0.268560\pi$
$853$	−2.40701	−	2.40701i	−0.0824143	−	0.0824143i	−0.747112	+	0.664698i	$0.768560\pi$
$854$	26.3232	+	27.6323i	0.900763	+	0.945557i
$855$		−	6.25196i		−	0.213813i
$856$	10.5785	+	12.2421i	0.361566	+	0.418426i
$857$			42.4913i			1.45148i	0.687972	+	0.725738i	$0.258501\pi$
$857$			42.4913i			1.45148i	−0.687972	+	0.725738i	$0.741499\pi$
$858$	13.2218	−	12.5955i	0.451386	−	0.430003i
$859$	−36.3033	−	36.3033i	−1.23865	−	1.23865i	−0.960552	−	0.278102i	$-0.910295\pi$
$859$	−36.3033	−	36.3033i	−1.23865	−	1.23865i	−0.278102	−	0.960552i	$-0.589705\pi$
$860$	−0.899100	+	18.5187i	−0.0306591	+	0.631482i
$861$	24.0176	−	24.0176i	0.818518	−	0.818518i
$862$	1.90846	+	0.0463014i	0.0650023	+	0.00157703i
$863$	−40.3605			−1.37389			−0.686943	−	0.726711i	$-0.741048\pi$
$863$	−40.3605			−1.37389			−0.686943	+	0.726711i	$0.741048\pi$
$864$	10.6747	+	13.6379i	0.363160	+	0.463972i
$865$	−5.63989			−0.191762
$866$	41.2136	+	0.999891i	1.40049	+	0.0339777i
$867$	31.4335	−	31.4335i	1.06754	−	1.06754i
$868$	−2.93351	+	60.4214i	−0.0995700	+	2.05083i
$869$	−0.962955	−	0.962955i	−0.0326660	−	0.0326660i
$870$	37.0148	−	35.2613i	1.25492	−	1.19547i
$871$		−	81.5323i		−	2.76262i
$872$	11.0530	−	9.55101i	0.374302	−	0.323438i
$873$			14.4896i			0.490399i
$874$	−0.878671	−	0.922366i	−0.0297215	−	0.0311995i
$875$	−33.1987	−	33.1987i	−1.12232	−	1.12232i
$876$	44.2635	+	48.7809i	1.49552	+	1.64815i
$877$	−12.7663	+	12.7663i	−0.431087	+	0.431087i	−0.888998	−	0.457911i	$-0.848598\pi$
$877$	−12.7663	+	12.7663i	−0.431087	+	0.431087i	0.457911	+	0.888998i	$0.348598\pi$
$878$	−0.149949	+	6.18060i	−0.00506052	+	0.208585i
$879$	−50.1729			−1.69229
$880$	0.456472	−	4.68988i	0.0153877	−	0.158096i
$881$	−53.9328			−1.81704			−0.908521	−	0.417839i	$-0.862788\pi$
$881$	−53.9328			−1.81704			−0.908521	+	0.417839i	$0.862788\pi$
$882$	−1.31346	+	54.1384i	−0.0442265	+	1.82293i
$883$	−34.7449	+	34.7449i	−1.16926	+	1.16926i	−0.186874	+	0.982384i	$0.559836\pi$
$883$	−34.7449	+	34.7449i	−1.16926	+	1.16926i	−0.982384	+	0.186874i	$0.940164\pi$
$884$	−5.57062	+	5.05474i	−0.187360	+	0.170009i
$885$	−15.8139	−	15.8139i	−0.531577	−	0.531577i
$886$	−28.2828	−	29.6893i	−0.950180	−	0.997431i
$887$		−	45.2215i		−	1.51839i	−0.650864	−	0.759195i	$-0.725593\pi$
$887$		−	45.2215i		−	1.51839i	0.650864	−	0.759195i	$-0.274407\pi$
$888$	−43.9940	−	3.20708i	−1.47634	−	0.107622i
$889$		−	63.2405i		−	2.12102i
$890$	16.1394	−	15.3748i	0.540993	−	0.515364i
$891$	2.34851	+	2.34851i	0.0786779	+	0.0786779i
$892$	−51.8057	−	2.51521i	−1.73458	−	0.0842156i
$893$	−8.83526	+	8.83526i	−0.295661	+	0.295661i
$894$	−83.7558	−	2.03202i	−2.80121	−	0.0679608i
$895$	11.9070			0.398007
$896$	−7.70374	+	44.9340i	−0.257364	+	1.50114i
$897$	14.8914			0.497211
$898$	−12.2751	−	0.297808i	−0.409625	−	0.00993798i
$899$	47.5905	−	47.5905i	1.58723	−	1.58723i
$900$	−22.5684	−	1.09572i	−0.752282	−	0.0365240i
$901$	0.156623	+	0.156623i	0.00521786	+	0.00521786i
$902$	−2.52202	+	2.40254i	−0.0839740	+	0.0799959i
$903$			66.2075i			2.20325i
$904$	−13.2849	−	0.968439i	−0.441848	−	0.0322098i
$905$		−	26.3370i		−	0.875471i
$906$	−33.3909	−	35.0514i	−1.10934	−	1.16451i
$907$	11.5383	+	11.5383i	0.383123	+	0.383123i	0.872226	−	0.489103i	$-0.162676\pi$
$907$	11.5383	+	11.5383i	0.383123	+	0.383123i	−0.489103	+	0.872226i	$0.662676\pi$
$908$	32.5486	−	29.5344i	1.08016	−	0.980133i
$909$	−51.0185	+	51.0185i	−1.69218	+	1.69218i
$910$	−1.28920	+	53.1386i	−0.0427367	+	1.76153i
$911$	28.5045			0.944395			0.472198	−	0.881493i	$-0.343461\pi$
$911$	28.5045			0.944395			0.472198	+	0.881493i	$0.343461\pi$
$912$	1.03580	−	10.6420i	0.0342988	−	0.352392i
$913$	−3.06739			−0.101516
$914$	−0.871634	+	35.9271i	−0.0288311	+	1.18836i
$915$	19.0909	−	19.0909i	0.631125	−	0.631125i
$916$	−15.0787	−	16.6175i	−0.498213	−	0.549059i
$917$	4.91925	+	4.91925i	0.162448	+	0.162448i
$918$	1.81616	+	1.90648i	0.0599422	+	0.0629231i
$919$		−	5.64101i		−	0.186080i	−0.995662	−	0.0930399i	$-0.970342\pi$
$919$		−	5.64101i		−	0.186080i	0.995662	−	0.0930399i	$-0.0296584\pi$
$920$	2.90747	−	2.51237i	0.0958563	−	0.0828304i
$921$			54.7982i			1.80566i
$922$	−6.48437	+	6.17718i	−0.213551	+	0.203435i
$923$	−1.18213	−	1.18213i	−0.0389103	−	0.0389103i
$924$	0.815983	−	16.8067i	0.0268439	−	0.552901i
$925$	11.2434	−	11.2434i	0.369680	−	0.369680i
$926$	−21.0917	−	0.511709i	−0.693116	−	0.0168158i
$927$	23.1274			0.759604
$928$	39.9419	−	31.2634i	1.31116	−	1.02627i
$929$	14.2171			0.466448			0.233224	−	0.972423i	$-0.425072\pi$
$929$	14.2171			0.466448			0.233224	+	0.972423i	$0.425072\pi$
$930$	42.7825	+	1.03795i	1.40289	+	0.0340359i
$931$	6.53196	−	6.53196i	0.214076	−	0.214076i
$932$	1.26662	−	26.0885i	0.0414896	−	0.854558i
$933$	−9.83353	−	9.83353i	−0.321935	−	0.321935i
$934$	30.5833	−	29.1345i	1.00072	−	0.953310i
$935$		−	0.716397i		−	0.0234287i
$936$	47.4102	+	54.8659i	1.54965	+	1.79335i
$937$		−	19.4713i		−	0.636101i	−0.948074	−	0.318051i	$-0.896972\pi$
$937$		−	19.4713i		−	0.636101i	0.948074	−	0.318051i	$-0.103028\pi$
$938$	−51.8193	−	54.3962i	−1.69196	−	1.77610i
$939$	48.7940	+	48.7940i	1.59233	+	1.59233i
$940$	−25.3268	−	27.9116i	−0.826069	−	0.910375i
$941$	38.1234	−	38.1234i	1.24279	−	1.24279i	0.283947	−	0.958840i	$-0.408356\pi$
$941$	38.1234	−	38.1234i	1.24279	−	1.24279i	0.958840	−	0.283947i	$-0.0916441\pi$
$942$	−1.72739	+	71.1998i	−0.0562814	+	2.31981i
$943$	−2.84049			−0.0924990
$944$	−14.0965	−	17.1364i	−0.458802	−	0.557744i
$945$	18.6063			0.605264
$946$	0.164675	−	6.78758i	0.00535404	−	0.220683i
$947$	8.23030	−	8.23030i	0.267449	−	0.267449i	−0.560623	−	0.828071i	$-0.689438\pi$
$947$	8.23030	−	8.23030i	0.267449	−	0.267449i	0.828071	+	0.560623i	$0.189438\pi$
$948$	6.90292	−	6.26367i	0.224196	−	0.203435i
$949$	53.8810	+	53.8810i	1.74905	+	1.74905i
$950$	2.65845	+	2.79066i	0.0862516	+	0.0905408i
$951$			52.2393i			1.69397i
$952$	−0.503936	+	6.91289i	−0.0163327	+	0.224048i
$953$		−	13.2093i		−	0.427890i	−0.976846	−	0.213945i	$-0.931369\pi$
$953$		−	13.2093i		−	0.427890i	0.976846	−	0.213945i	$-0.0686314\pi$
$954$	1.54599	−	1.47276i	0.0500534	−	0.0476822i
$955$	−2.14895	−	2.14895i	−0.0695384	−	0.0695384i
$956$	7.75379	+	0.376454i	0.250775	+	0.0121754i
$957$	−13.2377	+	13.2377i	−0.427915	+	0.427915i
$958$	39.1509	+	0.949848i	1.26491	+	0.0306882i
$959$	−2.01942			−0.0652106
$960$	31.9111	+	4.67737i	1.02993	+	0.150961i
$961$	25.3407			0.817441
$962$	−51.0130	−	1.23764i	−1.64472	−	0.0399030i
$963$	16.7673	−	16.7673i	0.540318	−	0.540318i
$964$	−43.3972	−	2.10698i	−1.39773	−	0.0678612i
$965$	−2.68144	−	2.68144i	−0.0863187	−	0.0863187i
$966$	9.93517	−	9.46451i	0.319659	−	0.304516i
$967$		−	9.64759i		−	0.310246i	−0.987895	−	0.155123i	$-0.950423\pi$
$967$		−	9.64759i		−	0.310246i	0.987895	−	0.155123i	$-0.0495773\pi$
$968$	2.13659	−	29.3094i	0.0686727	−	0.942039i
$969$		−	1.62561i		−	0.0522221i
$970$	5.14232	+	5.39805i	0.165110	+	0.173321i
$971$	1.09782	+	1.09782i	0.0352307	+	0.0352307i	0.724503	−	0.689272i	$-0.242069\pi$
$971$	1.09782	+	1.09782i	0.0352307	+	0.0352307i	−0.689272	+	0.724503i	$0.742069\pi$
$972$	−30.4390	+	27.6201i	−0.976330	+	0.885916i
$973$	−36.3562	+	36.3562i	−1.16552	+	1.16552i
$974$	1.20759	−	49.7744i	0.0386936	−	1.59488i
$975$	−45.0547			−1.44290
$976$	20.6875	−	17.0176i	0.662191	−	0.544721i
$977$	0.637383			0.0203917			0.0101958	−	0.999948i	$-0.496755\pi$
$977$	0.637383			0.0203917			0.0101958	+	0.999948i	$0.496755\pi$
$978$	−0.325300	+	13.4082i	−0.0104019	+	0.428748i
$979$	−5.77197	+	5.77197i	−0.184473	+	0.184473i
$980$	18.7242	+	20.6352i	0.598124	+	0.659167i
$981$	−15.1386	−	15.1386i	−0.483340	−	0.483340i
$982$	28.9989	+	30.4410i	0.925393	+	0.971412i
$983$			17.4766i			0.557418i	0.960376	+	0.278709i	$0.0899065\pi$
$983$			17.4766i			0.557418i	−0.960376	+	0.278709i	$0.910093\pi$
$984$	−15.5880	−	18.0394i	−0.496927	−	0.575074i
$985$		−	18.6229i		−	0.593374i
$986$	5.58357	−	5.31906i	0.177817	−	0.169393i
$987$	−95.1681	−	95.1681i	−3.02923	−	3.02923i
$988$	0.599821	−	12.3545i	0.0190828	−	0.393048i
$989$	3.91508	−	3.91508i	0.124492	−	0.124492i
$990$	−6.90392	−	0.167497i	−0.219421	−	0.00532342i
$991$	−13.2083			−0.419576			−0.209788	−	0.977747i	$-0.567277\pi$
$991$	−13.2083			−0.419576			−0.209788	+	0.977747i	$0.567277\pi$
$992$	42.1487	+	5.13710i	1.33822	+	0.163103i
$993$	47.7419			1.51504
$994$	−1.54001	−	0.0373625i	−0.0488462	−	0.00118507i
$995$	3.85215	−	3.85215i	0.122121	−	0.122121i
$996$	1.01813	−	20.9704i	0.0322608	−	0.664472i
$997$	14.8543	+	14.8543i	0.470440	+	0.470440i	0.902057	−	0.431617i	$-0.142057\pi$
$997$	14.8543	+	14.8543i	0.470440	+	0.470440i	−0.431617	+	0.902057i	$0.642057\pi$
$998$	−1.38144	+	1.31599i	−0.0437286	+	0.0416570i
$999$			17.8621i			0.565131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.229.34	yes	68
4.3	odd	2		1216.2.k.b.305.30		68
16.3	odd	4		1216.2.k.b.913.30		68
16.13	even	4	inner	304.2.k.b.77.34	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.34	✓	68	16.13	even	4	inner
304.2.k.b.229.34	yes	68	1.1	even	1	trivial
1216.2.k.b.305.30		68	4.3	odd	2
1216.2.k.b.913.30		68	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41380 + 0.0343004i) q^{2} +(-1.89015 + 1.89015i) q^{3} +(1.99765 + 0.0969877i) q^{4} +(-1.06645 - 1.06645i) q^{5} +(-2.73712 + 2.60746i) q^{6} +4.02959i q^{7} +(2.82094 + 0.205641i) q^{8} -4.14533i q^{9} +O(q^{10})\)	\(q+(1.41380 + 0.0343004i) q^{2} +(-1.89015 + 1.89015i) q^{3} +(1.99765 + 0.0969877i) q^{4} +(-1.06645 - 1.06645i) q^{5} +(-2.73712 + 2.60746i) q^{6} +4.02959i q^{7} +(2.82094 + 0.205641i) q^{8} -4.14533i q^{9} +(-1.47117 - 1.54433i) q^{10} +(0.552303 + 0.552303i) q^{11} +(-3.95917 + 3.59253i) q^{12} +(-4.37311 + 4.37311i) q^{13} +(-0.138217 + 5.69702i) q^{14} +4.03151 q^{15} +(3.98119 + 0.387494i) q^{16} +0.608142 q^{17} +(0.142187 - 5.86066i) q^{18} +(-0.707107 + 0.707107i) q^{19} +(-2.02696 - 2.23383i) q^{20} +(-7.61653 - 7.61653i) q^{21} +(0.761901 + 0.799789i) q^{22} +0.900783i q^{23} +(-5.72070 + 4.94331i) q^{24} -2.72536i q^{25} +(-6.33269 + 6.03269i) q^{26} +(2.16485 + 2.16485i) q^{27} +(-0.390820 + 8.04970i) q^{28} +(6.34029 - 6.34029i) q^{29} +(5.69974 + 0.138282i) q^{30} +7.50604 q^{31} +(5.61530 + 0.684395i) q^{32} -2.08787 q^{33} +(0.859789 + 0.0208595i) q^{34} +(4.29737 - 4.29737i) q^{35} +(0.402046 - 8.28092i) q^{36} +(4.12547 + 4.12547i) q^{37} +(-1.02396 + 0.975452i) q^{38} -16.5317i q^{39} +(-2.78909 - 3.22771i) q^{40} +3.15335i q^{41} +(-10.5070 - 11.0295i) q^{42} +(-4.34630 - 4.34630i) q^{43} +(1.04974 + 1.15687i) q^{44} +(-4.42080 + 4.42080i) q^{45} +(-0.0308972 + 1.27353i) q^{46} +12.4949 q^{47} +(-8.25746 + 6.79262i) q^{48} -9.23758 q^{49} +(0.0934808 - 3.85310i) q^{50} +(-1.14948 + 1.14948i) q^{51} +(-9.16006 + 8.31179i) q^{52} +(0.257543 + 0.257543i) q^{53} +(2.98641 + 3.13492i) q^{54} -1.17801i q^{55} +(-0.828649 + 11.3672i) q^{56} -2.67308i q^{57} +(9.18136 - 8.74641i) q^{58} +(-3.92257 - 3.92257i) q^{59} +(8.05354 + 0.391007i) q^{60} +(4.73541 - 4.73541i) q^{61} +(10.6120 + 0.257460i) q^{62} +16.7040 q^{63} +(7.91542 + 1.16020i) q^{64} +9.32743 q^{65} +(-2.95183 - 0.0716148i) q^{66} +(-9.32201 + 9.32201i) q^{67} +(1.21485 + 0.0589822i) q^{68} +(-1.70262 - 1.70262i) q^{69} +(6.22301 - 5.92820i) q^{70} +0.270319i q^{71} +(0.852451 - 11.6937i) q^{72} -12.3210i q^{73} +(5.69107 + 5.97408i) q^{74} +(5.15133 + 5.15133i) q^{75} +(-1.48113 + 1.34397i) q^{76} +(-2.22555 + 2.22555i) q^{77} +(0.567043 - 23.3724i) q^{78} -1.74353 q^{79} +(-3.83250 - 4.65899i) q^{80} +4.25220 q^{81} +(-0.108161 + 4.45820i) q^{82} +(-2.77691 + 2.77691i) q^{83} +(-14.4764 - 15.9538i) q^{84} +(-0.648554 - 0.648554i) q^{85} +(-5.99571 - 6.29387i) q^{86} +23.9682i q^{87} +(1.44444 + 1.67159i) q^{88} +10.4507i q^{89} +(-6.40176 + 6.09849i) q^{90} +(-17.6218 - 17.6218i) q^{91} +(-0.0873649 + 1.79945i) q^{92} +(-14.1875 + 14.1875i) q^{93} +(17.6653 + 0.428582i) q^{94} +1.50819 q^{95} +(-11.9074 + 9.32015i) q^{96} -3.49540 q^{97} +(-13.0601 - 0.316853i) q^{98} +(2.28948 - 2.28948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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