LMFDB - Embedded newform 304.2.k.b.77.4

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			77.4
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33638 + 0.462685i) q^{2} +(0.227569 + 0.227569i) q^{3} +(1.57185 - 1.23665i) q^{4} +(-2.67518 + 2.67518i) q^{5} +(-0.409413 - 0.198827i) q^{6} -4.39636i q^{7} +(-1.52841 + 2.37991i) q^{8} -2.89642i q^{9} +O(q^{10})$	\(q+(-1.33638 + 0.462685i) q^{2} +(0.227569 + 0.227569i) q^{3} +(1.57185 - 1.23665i) q^{4} +(-2.67518 + 2.67518i) q^{5} +(-0.409413 - 0.198827i) q^{6} -4.39636i q^{7} +(-1.52841 + 2.37991i) q^{8} -2.89642i q^{9} +(2.33730 - 4.81283i) q^{10} +(2.02533 - 2.02533i) q^{11} +(0.639127 + 0.0762802i) q^{12} +(1.66455 + 1.66455i) q^{13} +(2.03413 + 5.87522i) q^{14} -1.21758 q^{15} +(0.941394 - 3.88764i) q^{16} +4.30895 q^{17} +(1.34013 + 3.87074i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.896708 + 7.51323i) q^{20} +(1.00048 - 1.00048i) q^{21} +(-1.76953 + 3.64371i) q^{22} -1.00039i q^{23} +(-0.889413 + 0.193775i) q^{24} -9.31318i q^{25} +(-2.99464 - 1.45432i) q^{26} +(1.34185 - 1.34185i) q^{27} +(-5.43675 - 6.91039i) q^{28} +(-3.73350 - 3.73350i) q^{29} +(1.62715 - 0.563355i) q^{30} +10.1761 q^{31} +(0.540691 + 5.63095i) q^{32} +0.921807 q^{33} +(-5.75841 + 1.99369i) q^{34} +(11.7610 + 11.7610i) q^{35} +(-3.58186 - 4.55273i) q^{36} +(-4.90117 + 4.90117i) q^{37} +(1.27213 + 0.617799i) q^{38} +0.757602i q^{39} +(-2.27791 - 10.4555i) q^{40} -9.29118i q^{41} +(-0.874115 + 1.79992i) q^{42} +(5.74417 - 5.74417i) q^{43} +(0.678881 - 5.68813i) q^{44} +(7.74846 + 7.74846i) q^{45} +(0.462863 + 1.33690i) q^{46} -4.84582 q^{47} +(1.09894 - 0.670476i) q^{48} -12.3279 q^{49} +(4.30907 + 12.4460i) q^{50} +(0.980585 + 0.980585i) q^{51} +(4.67489 + 0.557950i) q^{52} +(3.75205 - 3.75205i) q^{53} +(-1.17237 + 2.41407i) q^{54} +10.8363i q^{55} +(10.4629 + 6.71943i) q^{56} -0.321832i q^{57} +(6.71682 + 3.26195i) q^{58} +(-3.38755 + 3.38755i) q^{59} +(-1.91384 + 1.50572i) q^{60} +(-7.04771 - 7.04771i) q^{61} +(-13.5992 + 4.70833i) q^{62} -12.7337 q^{63} +(-3.32793 - 7.27495i) q^{64} -8.90595 q^{65} +(-1.23189 + 0.426506i) q^{66} +(-1.62249 - 1.62249i) q^{67} +(6.77300 - 5.32866i) q^{68} +(0.227657 - 0.227657i) q^{69} +(-21.1589 - 10.2756i) q^{70} +2.97588i q^{71} +(6.89323 + 4.42692i) q^{72} +13.7046i q^{73} +(4.28215 - 8.81754i) q^{74} +(2.11939 - 2.11939i) q^{75} +(-1.98591 - 0.237019i) q^{76} +(-8.90408 - 8.90408i) q^{77} +(-0.350531 - 1.01245i) q^{78} -5.25301 q^{79} +(7.88175 + 12.9185i) q^{80} -8.07855 q^{81} +(4.29889 + 12.4166i) q^{82} +(2.32686 + 2.32686i) q^{83} +(0.335355 - 2.80983i) q^{84} +(-11.5272 + 11.5272i) q^{85} +(-5.01868 + 10.3342i) q^{86} -1.69926i q^{87} +(1.72457 + 7.91564i) q^{88} -3.66579i q^{89} +(-13.9400 - 6.76982i) q^{90} +(7.31796 - 7.31796i) q^{91} +(-1.23713 - 1.57245i) q^{92} +(2.31577 + 2.31577i) q^{93} +(6.47588 - 2.24209i) q^{94} +3.78328 q^{95} +(-1.15839 + 1.40448i) q^{96} +4.82769 q^{97} +(16.4749 - 5.70395i) q^{98} +(-5.86622 - 5.86622i) 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 $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.33638	+	0.462685i	−0.944966	+	0.327168i
$2$	−1.33638	+	0.462685i	−0.944966	+	0.327168i
$3$	0.227569	+	0.227569i	0.131387	+	0.131387i	0.769742	−	0.638355i	$-0.220385\pi$
$3$	0.227569	+	0.227569i	0.131387	+	0.131387i	−0.638355	+	0.769742i	$0.720385\pi$
$4$	1.57185	−	1.23665i	0.785923	−	0.618325i
$5$	−2.67518	+	2.67518i	−1.19638	+	1.19638i	−0.221133	+	0.975244i	$0.570976\pi$
$5$	−2.67518	+	2.67518i	−1.19638	+	1.19638i	−0.975244	+	0.221133i	$0.929024\pi$
$6$	−0.409413	−	0.198827i	−0.167142	−	0.0811708i
$7$		−	4.39636i		−	1.66167i	−0.556522	−	0.830833i	$-0.687864\pi$
$7$		−	4.39636i		−	1.66167i	0.556522	−	0.830833i	$-0.312136\pi$
$8$	−1.52841	+	2.37991i	−0.540374	+	0.841425i
$9$		−	2.89642i		−	0.965475i
$10$	2.33730	−	4.81283i	0.739120	−	1.52195i
$11$	2.02533	−	2.02533i	0.610660	−	0.610660i	−0.332458	−	0.943118i	$-0.607878\pi$
$11$	2.02533	−	2.02533i	0.610660	−	0.610660i	0.943118	+	0.332458i	$0.107878\pi$
$12$	0.639127	+	0.0762802i	0.184500	+	0.0220202i
$13$	1.66455	+	1.66455i	0.461664	+	0.461664i	0.899200	−	0.437537i	$-0.144149\pi$
$13$	1.66455	+	1.66455i	0.461664	+	0.461664i	−0.437537	+	0.899200i	$0.644149\pi$
$14$	2.03413	+	5.87522i	0.543644	+	1.57022i
$15$	−1.21758			−0.314377
$16$	0.941394	−	3.88764i	0.235349	−	0.971911i
$17$	4.30895			1.04507			0.522537	−	0.852617i	$-0.324986\pi$
$17$	4.30895			1.04507			0.522537	+	0.852617i	$0.324986\pi$
$18$	1.34013	+	3.87074i	0.315872	+	0.912341i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−0.896708	+	7.51323i	−0.200510	+	1.68001i
$21$	1.00048	−	1.00048i	0.218322	−	0.218322i
$22$	−1.76953	+	3.64371i	−0.377265	+	0.776842i
$23$		−	1.00039i		−	0.208595i	−0.994546	−	0.104297i	$-0.966741\pi$
$23$		−	1.00039i		−	0.208595i	0.994546	−	0.104297i	$-0.0332594\pi$
$24$	−0.889413	+	0.193775i	−0.181551	+	0.0395542i
$25$		−	9.31318i		−	1.86264i
$26$	−2.99464	−	1.45432i	−0.587298	−	0.285215i
$27$	1.34185	−	1.34185i	0.258238	−	0.258238i
$28$	−5.43675	−	6.91039i	−1.02745	−	1.30594i
$29$	−3.73350	−	3.73350i	−0.693293	−	0.693293i	0.269662	−	0.962955i	$-0.413088\pi$
$29$	−3.73350	−	3.73350i	−0.693293	−	0.693293i	−0.962955	+	0.269662i	$0.913088\pi$
$30$	1.62715	−	0.563355i	0.297076	−	0.102854i
$31$	10.1761			1.82768			0.913841	−	0.406072i	$-0.133102\pi$
$31$	10.1761			1.82768			0.913841	+	0.406072i	$0.133102\pi$
$32$	0.540691	+	5.63095i	0.0955815	+	0.995422i
$33$	0.921807			0.160466
$34$	−5.75841	+	1.99369i	−0.987559	+	0.341914i
$35$	11.7610	+	11.7610i	1.98798	+	1.98798i
$36$	−3.58186	−	4.55273i	−0.596977	−	0.758788i
$37$	−4.90117	+	4.90117i	−0.805747	+	0.805747i	−0.983987	−	0.178240i	$-0.942960\pi$
$37$	−4.90117	+	4.90117i	−0.805747	+	0.805747i	0.178240	+	0.983987i	$0.442960\pi$
$38$	1.27213	+	0.617799i	0.206367	+	0.100220i
$39$			0.757602i			0.121313i
$40$	−2.27791	−	10.4555i	−0.360170	−	1.65315i
$41$		−	9.29118i		−	1.45104i	−0.688202	−	0.725519i	$-0.741600\pi$
$41$		−	9.29118i		−	1.45104i	0.688202	−	0.725519i	$-0.258400\pi$
$42$	−0.874115	+	1.79992i	−0.134879	+	0.277734i
$43$	5.74417	−	5.74417i	0.875978	−	0.875978i	−0.117138	−	0.993116i	$-0.537372\pi$
$43$	5.74417	−	5.74417i	0.875978	−	0.875978i	0.993116	+	0.117138i	$0.0373720\pi$
$44$	0.678881	−	5.68813i	0.102345	−	0.857518i
$45$	7.74846	+	7.74846i	1.15507	+	1.15507i
$46$	0.462863	+	1.33690i	0.0682455	+	0.197115i
$47$	−4.84582			−0.706836			−0.353418	−	0.935466i	$-0.614981\pi$
$47$	−4.84582			−0.706836			−0.353418	+	0.935466i	$0.614981\pi$
$48$	1.09894	−	0.670476i	0.158618	−	0.0967749i
$49$	−12.3279			−1.76113
$50$	4.30907	+	12.4460i	0.609394	+	1.76013i
$51$	0.980585	+	0.980585i	0.137309	+	0.137309i
$52$	4.67489	+	0.557950i	0.648290	+	0.0773737i
$53$	3.75205	−	3.75205i	0.515383	−	0.515383i	−0.400788	−	0.916171i	$-0.631264\pi$
$53$	3.75205	−	3.75205i	0.515383	−	0.515383i	0.916171	+	0.400788i	$0.131264\pi$
$54$	−1.17237	+	2.41407i	−0.159539	+	0.328514i
$55$			10.8363i			1.46116i
$56$	10.4629	+	6.71943i	1.39817	+	0.897922i
$57$		−	0.321832i		−	0.0426276i
$58$	6.71682	+	3.26195i	0.881962	+	0.428316i
$59$	−3.38755	+	3.38755i	−0.441022	+	0.441022i	−0.892355	−	0.451333i	$-0.850949\pi$
$59$	−3.38755	+	3.38755i	−0.441022	+	0.441022i	0.451333	+	0.892355i	$0.350949\pi$
$60$	−1.91384	+	1.50572i	−0.247076	+	0.194387i
$61$	−7.04771	−	7.04771i	−0.902367	−	0.902367i	0.0932736	−	0.995641i	$-0.470267\pi$
$61$	−7.04771	−	7.04771i	−0.902367	−	0.902367i	−0.995641	+	0.0932736i	$0.970267\pi$
$62$	−13.5992	+	4.70833i	−1.72710	+	0.597959i
$63$	−12.7337			−1.60430
$64$	−3.32793	−	7.27495i	−0.415991	−	0.909369i
$65$	−8.90595			−1.10465
$66$	−1.23189	+	0.426506i	−0.151635	+	0.0524993i
$67$	−1.62249	−	1.62249i	−0.198219	−	0.198219i	0.601017	−	0.799236i	$-0.294762\pi$
$67$	−1.62249	−	1.62249i	−0.198219	−	0.198219i	−0.799236	+	0.601017i	$0.794762\pi$
$68$	6.77300	−	5.32866i	0.821347	−	0.646195i
$69$	0.227657	−	0.227657i	0.0274067	−	0.0274067i
$70$	−21.1589	−	10.2756i	−2.52898	−	1.22817i
$71$			2.97588i			0.353171i	0.984285	+	0.176586i	$0.0565053\pi$
$71$			2.97588i			0.353171i	−0.984285	+	0.176586i	$0.943495\pi$
$72$	6.89323	+	4.42692i	0.812374	+	0.521718i
$73$			13.7046i			1.60400i	0.597324	+	0.802000i	$0.296231\pi$
$73$			13.7046i			1.60400i	−0.597324	+	0.802000i	$0.703769\pi$
$74$	4.28215	−	8.81754i	0.497790	−	1.02502i
$75$	2.11939	−	2.11939i	0.244727	−	0.244727i
$76$	−1.98591	−	0.237019i	−0.227799	−	0.0271879i
$77$	−8.90408	−	8.90408i	−1.01471	−	1.01471i
$78$	−0.350531	−	1.01245i	−0.0396898	−	0.114637i
$79$	−5.25301			−0.591010			−0.295505	−	0.955341i	$-0.595488\pi$
$79$	−5.25301			−0.591010			−0.295505	+	0.955341i	$0.595488\pi$
$80$	7.88175	+	12.9185i	0.881206	+	1.44434i
$81$	−8.07855			−0.897616
$82$	4.29889	+	12.4166i	0.474733	+	1.37118i
$83$	2.32686	+	2.32686i	0.255407	+	0.255407i	0.823183	−	0.567776i	$-0.192196\pi$
$83$	2.32686	+	2.32686i	0.255407	+	0.255407i	−0.567776	+	0.823183i	$0.692196\pi$
$84$	0.335355	−	2.80983i	0.0365902	−	0.306578i
$85$	−11.5272	+	11.5272i	−1.25030	+	1.25030i
$86$	−5.01868	+	10.3342i	−0.541178	+	1.11436i
$87$		−	1.69926i		−	0.182180i
$88$	1.72457	+	7.91564i	0.183840	+	0.843810i
$89$		−	3.66579i		−	0.388573i	−0.980945	−	0.194286i	$-0.937761\pi$
$89$		−	3.66579i		−	0.388573i	0.980945	−	0.194286i	$-0.0622391\pi$
$90$	−13.9400	−	6.76982i	−1.46941	−	0.713602i
$91$	7.31796	−	7.31796i	0.767131	−	0.767131i
$92$	−1.23713	−	1.57245i	−0.128979	−	0.163939i
$93$	2.31577	+	2.31577i	0.240134	+	0.240134i
$94$	6.47588	−	2.24209i	0.667936	−	0.231254i
$95$	3.78328			0.388156
$96$	−1.15839	+	1.40448i	−0.118227	+	0.143344i
$97$	4.82769			0.490178			0.245089	−	0.969501i	$-0.421183\pi$
$97$	4.82769			0.490178			0.245089	+	0.969501i	$0.421183\pi$
$98$	16.4749	−	5.70395i	1.66421	−	0.576186i
$99$	−5.86622	−	5.86622i	−0.589577	−	0.589577i
$100$	−11.5171	−	14.6389i	−1.15171	−	1.46389i
$101$	0.374330	−	0.374330i	0.0372472	−	0.0372472i	−0.688238	−	0.725485i	$-0.741615\pi$
$101$	0.374330	−	0.374330i	0.0372472	−	0.0372472i	0.725485	+	0.688238i	$0.241615\pi$
$102$	−1.76414	−	0.856736i	−0.174676	−	0.0848295i
$103$			14.5146i			1.43017i	0.699038	+	0.715084i	$0.253612\pi$
$103$			14.5146i			1.43017i	−0.699038	+	0.715084i	$0.746388\pi$
$104$	−6.50560	+	1.41736i	−0.637926	+	0.138984i
$105$			5.35291i			0.522390i
$106$	−3.27816	+	6.75019i	−0.318403	+	0.655636i
$107$	3.51434	−	3.51434i	0.339744	−	0.339744i	−0.516527	−	0.856271i	$-0.672775\pi$
$107$	3.51434	−	3.51434i	0.339744	−	0.339744i	0.856271	+	0.516527i	$0.172775\pi$
$108$	0.449780	−	3.76857i	0.0432801	−	0.362630i
$109$	10.1285	+	10.1285i	0.970134	+	0.970134i	0.999567	−	0.0294323i	$-0.00936994\pi$
$109$	10.1285	+	10.1285i	0.970134	+	0.970134i	−0.0294323	+	0.999567i	$0.509370\pi$
$110$	−5.01377	−	14.4814i	−0.478044	−	1.38075i
$111$	−2.23071			−0.211730
$112$	−17.0915	−	4.13870i	−1.61499	−	0.391071i
$113$	−3.15167			−0.296484			−0.148242	−	0.988951i	$-0.547361\pi$
$113$	−3.15167			−0.296484			−0.148242	+	0.988951i	$0.547361\pi$
$114$	0.148907	+	0.430091i	0.0139464	+	0.0402817i
$115$	2.67621	+	2.67621i	0.249558	+	0.249558i
$116$	−10.4855	−	1.25145i	−0.973555	−	0.116194i
$117$	4.82125	−	4.82125i	0.445725	−	0.445725i
$118$	2.95970	−	6.09444i	0.272463	−	0.561039i
$119$		−	18.9437i		−	1.73656i
$120$	1.86096	−	2.89772i	0.169881	−	0.264525i
$121$			2.79606i			0.254188i
$122$	12.6793	+	6.15758i	1.14793	+	0.557481i
$123$	2.11439	−	2.11439i	0.190648	−	0.190648i
$124$	15.9953	−	12.5843i	1.43642	−	1.13010i
$125$	11.5385	+	11.5385i	1.03204	+	1.03204i
$126$	17.0171	−	5.89170i	1.51601	−	0.524874i
$127$	4.72470			0.419249			0.209625	−	0.977782i	$-0.432776\pi$
$127$	4.72470			0.419249			0.209625	+	0.977782i	$0.432776\pi$
$128$	7.81340	+	8.18234i	0.690614	+	0.723224i
$129$	2.61439			0.230185
$130$	11.9018	−	4.12065i	1.04385	−	0.361405i
$131$	7.12660	+	7.12660i	0.622654	+	0.622654i	0.946209	−	0.323555i	$-0.104878\pi$
$131$	7.12660	+	7.12660i	0.622654	+	0.622654i	−0.323555	+	0.946209i	$0.604878\pi$
$132$	1.44894	−	1.13995i	0.126114	−	0.0992201i
$133$	−3.10869	+	3.10869i	−0.269558	+	0.269558i
$134$	2.91897	+	1.41757i	0.252161	+	0.122459i
$135$			7.17936i			0.617901i
$136$	−6.58584	+	10.2549i	−0.564731	+	0.879351i
$137$			13.0928i			1.11860i	0.828966	+	0.559299i	$0.188929\pi$
$137$			13.0928i			1.11860i	−0.828966	+	0.559299i	$0.811071\pi$
$138$	−0.198904	+	0.409571i	−0.0169318	+	0.0348650i
$139$	10.2338	−	10.2338i	0.868021	−	0.868021i	−0.124232	−	0.992253i	$-0.539647\pi$
$139$	10.2338	−	10.2338i	0.868021	−	0.868021i	0.992253	+	0.124232i	$0.0396467\pi$
$140$	33.0308	+	3.94225i	2.79161	+	0.333181i
$141$	−1.10276	−	1.10276i	−0.0928692	−	0.0928692i
$142$	−1.37689	−	3.97691i	−0.115546	−	0.333735i
$143$	6.74254			0.563839
$144$	−11.2603	−	2.72668i	−0.938356	−	0.227223i
$145$	19.9756			1.65888
$146$	−6.34091	−	18.3146i	−0.524777	−	1.51573i
$147$	−2.80546	−	2.80546i	−0.231391	−	0.231391i
$148$	−1.64285	+	13.7649i	−0.135041	+	1.13147i
$149$	6.44260	−	6.44260i	0.527798	−	0.527798i	−0.392117	−	0.919915i	$-0.628257\pi$
$149$	6.44260	−	6.44260i	0.527798	−	0.527798i	0.919915	+	0.392117i	$0.128257\pi$
$150$	−1.85171	+	3.81294i	−0.151192	+	0.311325i
$151$		−	11.6346i		−	0.946809i	−0.880845	−	0.473405i	$-0.843025\pi$
$151$		−	11.6346i		−	0.946809i	0.880845	−	0.473405i	$-0.156975\pi$
$152$	2.76360	−	0.602101i	0.224157	−	0.0488368i
$153$		−	12.4805i		−	1.00899i
$154$	16.0191	+	7.77948i	1.29085	+	0.626889i
$155$	−27.2229	+	27.2229i	−2.18660	+	2.18660i
$156$	0.936888	+	1.19083i	0.0750111	+	0.0953429i
$157$	−4.67527	−	4.67527i	−0.373127	−	0.373127i	0.495488	−	0.868615i	$-0.334989\pi$
$157$	−4.67527	−	4.67527i	−0.373127	−	0.373127i	−0.868615	+	0.495488i	$0.834989\pi$
$158$	7.02004	−	2.43049i	0.558485	−	0.193359i
$159$	1.70770			0.135429
$160$	−16.5103	−	13.6174i	−1.30525	−	1.07655i
$161$	−4.39805			−0.346615
$162$	10.7960	−	3.73782i	0.848217	−	0.293671i
$163$	−5.18458	−	5.18458i	−0.406088	−	0.406088i	0.474284	−	0.880372i	$-0.342707\pi$
$163$	−5.18458	−	5.18458i	−0.406088	−	0.406088i	−0.880372	+	0.474284i	$0.842707\pi$
$164$	−11.4899	−	14.6043i	−0.897213	−	1.14040i
$165$	−2.46600	+	2.46600i	−0.191978	+	0.191978i
$166$	−4.18619	−	2.03298i	−0.324911	−	0.157790i
$167$			7.00542i			0.542096i	0.962566	+	0.271048i	$0.0873701\pi$
$167$			7.00542i			0.542096i	−0.962566	+	0.271048i	$0.912630\pi$
$168$	0.851904	+	3.91018i	0.0657258	+	0.301677i
$169$		−	7.45853i		−	0.573733i
$170$	10.0713	−	20.7383i	0.772435	−	1.59055i
$171$	−2.04808	+	2.04808i	−0.156621	+	0.156621i
$172$	1.92542	−	16.1325i	0.146812	−	1.23009i
$173$	4.60026	+	4.60026i	0.349751	+	0.349751i	0.860017	−	0.510266i	$-0.170453\pi$
$173$	4.60026	+	4.60026i	0.349751	+	0.349751i	−0.510266	+	0.860017i	$0.670453\pi$
$174$	0.786222	+	2.27086i	0.0596033	+	0.172154i
$175$	−40.9440			−3.09508
$176$	−5.96713	−	9.78040i	−0.449790	−	0.737226i
$177$	−1.54181			−0.115889
$178$	1.69611	+	4.89890i	0.127128	+	0.367188i
$179$	−5.69533	−	5.69533i	−0.425689	−	0.425689i	0.461468	−	0.887157i	$-0.347323\pi$
$179$	−5.69533	−	5.69533i	−0.425689	−	0.425689i	−0.887157	+	0.461468i	$0.847323\pi$
$180$	21.7615	+	2.59725i	1.62201	+	0.193587i
$181$	−6.45972	+	6.45972i	−0.480147	+	0.480147i	−0.905179	−	0.425031i	$-0.860263\pi$
$181$	−6.45972	+	6.45972i	−0.480147	+	0.480147i	0.425031	+	0.905179i	$0.360263\pi$
$182$	−6.39370	+	13.1655i	−0.473932	+	0.975893i
$183$		−	3.20769i		−	0.237119i
$184$	2.38083	+	1.52900i	0.175517	+	0.112719i
$185$		−	26.2230i		−	1.92796i
$186$	−4.16623	−	2.02329i	−0.305483	−	0.148355i
$187$	8.72705	−	8.72705i	0.638185	−	0.638185i
$188$	−7.61688	+	5.99259i	−0.555518	+	0.437054i
$189$	−5.89923	−	5.89923i	−0.429106	−	0.429106i
$190$	−5.05591	+	1.75047i	−0.366794	+	0.126992i
$191$	3.96124			0.286625			0.143313	−	0.989677i	$-0.454225\pi$
$191$	3.96124			0.286625			0.143313	+	0.989677i	$0.454225\pi$
$192$	0.898221	−	2.41289i	0.0648235	−	0.174135i
$193$	4.46556			0.321438			0.160719	−	0.987000i	$-0.448619\pi$
$193$	4.46556			0.321438			0.160719	+	0.987000i	$0.448619\pi$
$194$	−6.45165	+	2.23370i	−0.463201	+	0.160370i
$195$	−2.02672	−	2.02672i	−0.145137	−	0.145137i
$196$	−19.3776	+	15.2453i	−1.38411	+	1.08895i
$197$	−13.6729	+	13.6729i	−0.974150	+	0.974150i	−0.999674	−	0.0255237i	$-0.991875\pi$
$197$	−13.6729	+	13.6729i	−0.974150	+	0.974150i	0.0255237	+	0.999674i	$0.491875\pi$
$198$	10.5537	+	5.12531i	0.750021	+	0.364240i
$199$		−	7.37356i		−	0.522698i	−0.965244	−	0.261349i	$-0.915833\pi$
$199$		−	7.37356i		−	0.522698i	0.965244	−	0.261349i	$-0.0841673\pi$
$200$	22.1645	+	14.2344i	1.56727	+	1.00652i
$201$		−	0.738457i		−	0.0520868i
$202$	−0.327052	+	0.673446i	−0.0230113	+	0.0473835i
$203$	−16.4138	+	16.4138i	−1.15202	+	1.15202i
$204$	2.75397	+	0.328687i	0.192816	+	0.0230127i
$205$	24.8556	+	24.8556i	1.73599	+	1.73599i
$206$	−6.71570	−	19.3971i	−0.467905	−	1.35146i
$207$	−2.89754			−0.201393
$208$	8.03818	−	4.90419i	0.557348	−	0.340044i
$209$	−2.86425			−0.198124
$210$	−2.47671	−	7.15354i	−0.170909	−	0.493641i
$211$	15.3355	+	15.3355i	1.05574	+	1.05574i	0.998352	+	0.0573888i	$0.0182775\pi$
$211$	15.3355	+	15.3355i	1.05574	+	1.05574i	0.0573888	+	0.998352i	$0.481723\pi$
$212$	1.25767	−	10.5376i	0.0863770	−	0.723725i
$213$	−0.677218	+	0.677218i	−0.0464022	+	0.0464022i
$214$	−3.07048	+	6.32255i	−0.209894	+	0.432200i
$215$			30.7334i			2.09600i
$216$	1.14258	+	5.24436i	0.0777427	+	0.356833i
$217$		−	44.7378i		−	3.03700i
$218$	−18.2219	−	8.84926i	−1.23414	−	0.599348i
$219$	−3.11874	+	3.11874i	−0.210745	+	0.210745i
$220$	13.4007	+	17.0329i	0.903472	+	1.14836i
$221$	7.17247	+	7.17247i	0.482472	+	0.482472i
$222$	2.98109	−	1.03212i	0.200078	−	0.0692712i
$223$	14.3163			0.958687			0.479344	−	0.877627i	$-0.340875\pi$
$223$	14.3163			0.958687			0.479344	+	0.877627i	$0.340875\pi$
$224$	24.7557	−	2.37707i	1.65406	−	0.158825i
$225$	−26.9749			−1.79833
$226$	4.21184	−	1.45823i	0.280167	−	0.0970000i
$227$	3.59813	+	3.59813i	0.238816	+	0.238816i	0.816360	−	0.577544i	$-0.195989\pi$
$227$	3.59813	+	3.59813i	0.238816	+	0.238816i	−0.577544	+	0.816360i	$0.695989\pi$
$228$	−0.397993	−	0.505870i	−0.0263577	−	0.0335020i
$229$	0.525546	−	0.525546i	0.0347290	−	0.0347290i	−0.689529	−	0.724258i	$-0.742182\pi$
$229$	0.525546	−	0.525546i	0.0347290	−	0.0347290i	0.724258	+	0.689529i	$0.242182\pi$
$230$	−4.81469	−	2.33820i	−0.317471	−	0.154177i
$231$		−	4.05259i		−	0.266641i
$232$	14.5917	−	3.17907i	0.957992	−	0.208716i
$233$			22.6573i			1.48433i	0.670218	+	0.742164i	$0.266201\pi$
$233$			22.6573i			1.48433i	−0.670218	+	0.742164i	$0.733799\pi$
$234$	−4.21232	+	8.67376i	−0.275368	+	0.567021i
$235$	12.9634	−	12.9634i	0.845642	−	0.845642i
$236$	−1.13549	+	9.51393i	−0.0739142	+	0.619304i
$237$	−1.19542	−	1.19542i	−0.0776512	−	0.0776512i
$238$	8.76495	+	25.3160i	0.568148	+	1.64099i
$239$	−15.2944			−0.989315			−0.494657	−	0.869088i	$-0.664706\pi$
$239$	−15.2944			−0.989315			−0.494657	+	0.869088i	$0.664706\pi$
$240$	−1.14622	+	4.73351i	−0.0739882	+	0.305547i
$241$	14.8849			0.958819			0.479409	−	0.877591i	$-0.340851\pi$
$241$	14.8849			0.958819			0.479409	+	0.877591i	$0.340851\pi$
$242$	−1.29370	−	3.73662i	−0.0831620	−	0.240199i
$243$	−5.86397	−	5.86397i	−0.376174	−	0.376174i
$244$	−19.7935	−	2.36236i	−1.26715	−	0.151235i
$245$	32.9795	−	32.9795i	2.10698	−	2.10698i
$246$	−1.84734	+	3.80393i	−0.117782	+	0.242530i
$247$		−	2.35403i		−	0.149783i
$248$	−15.5533	+	24.2182i	−0.987633	+	1.53786i
$249$			1.05905i			0.0671143i
$250$	−20.7586	−	10.0812i	−1.31289	−	0.637591i
$251$	7.80300	−	7.80300i	0.492521	−	0.492521i	−0.416579	−	0.909100i	$-0.636771\pi$
$251$	7.80300	−	7.80300i	0.492521	−	0.492521i	0.909100	+	0.416579i	$0.136771\pi$
$252$	−20.0154	+	15.7471i	−1.26085	+	0.991977i
$253$	−2.02611	−	2.02611i	−0.127381	−	0.127381i
$254$	−6.31401	+	2.18605i	−0.396177	+	0.137165i
$255$	−5.24648			−0.328547
$256$	−14.2276	−	7.31961i	−0.889222	−	0.457476i
$257$	25.2472			1.57487			0.787437	−	0.616395i	$-0.211407\pi$
$257$	25.2472			1.57487			0.787437	+	0.616395i	$0.211407\pi$
$258$	−3.49383	+	1.20964i	−0.217517	+	0.0753089i
$259$	21.5473	+	21.5473i	1.33888	+	1.33888i
$260$	−13.9988	+	11.0135i	−0.868167	+	0.683031i
$261$	−10.8138	+	10.8138i	−0.669357	+	0.669357i
$262$	−12.8212	−	6.22650i	−0.792099	−	0.384675i
$263$		−	13.1351i		−	0.809945i	−0.914329	−	0.404972i	$-0.867281\pi$
$263$		−	13.1351i		−	0.809945i	0.914329	−	0.404972i	$-0.132719\pi$
$264$	−1.40890	+	2.19382i	−0.0867117	+	0.135020i
$265$			20.0748i			1.23318i
$266$	2.71606	−	5.59275i	0.166532	−	0.342914i
$267$	0.834221	−	0.834221i	0.0510535	−	0.0510535i
$268$	−4.55675	−	0.543850i	−0.278348	−	0.0332209i
$269$	−6.91043	−	6.91043i	−0.421336	−	0.421336i	0.464327	−	0.885664i	$-0.346296\pi$
$269$	−6.91043	−	6.91043i	−0.421336	−	0.421336i	−0.885664	+	0.464327i	$0.846296\pi$
$270$	−3.32178	−	9.59438i	−0.202157	−	0.583895i
$271$	24.2494			1.47305			0.736524	−	0.676412i	$-0.236466\pi$
$271$	24.2494			1.47305			0.736524	+	0.676412i	$0.236466\pi$
$272$	4.05642	−	16.7517i	0.245957	−	1.01572i
$273$	3.33069			0.201582
$274$	−6.05786	−	17.4971i	−0.365969	−	1.05704i
$275$	−18.8623	−	18.8623i	−1.13744	−	1.13744i
$276$	0.0763096	−	0.639374i	0.00459330	−	0.0384858i
$277$	−5.94145	+	5.94145i	−0.356987	+	0.356987i	−0.862701	−	0.505714i	$-0.831229\pi$
$277$	−5.94145	+	5.94145i	−0.356987	+	0.356987i	0.505714	+	0.862701i	$0.331229\pi$
$278$	−8.94128	+	18.4113i	−0.536262	+	1.10424i
$279$		−	29.4743i		−	1.76458i
$280$	−45.9659	+	10.0145i	−2.74699	+	0.598482i
$281$			13.3583i			0.796887i	0.917193	+	0.398443i	$0.130449\pi$
$281$			13.3583i			0.796887i	−0.917193	+	0.398443i	$0.869551\pi$
$282$	1.98394	+	0.963481i	0.118142	+	0.0573745i
$283$	−8.67373	+	8.67373i	−0.515600	+	0.515600i	−0.916237	−	0.400637i	$-0.868789\pi$
$283$	−8.67373	+	8.67373i	−0.515600	+	0.515600i	0.400637	+	0.916237i	$0.368789\pi$
$284$	3.68012	+	4.67761i	0.218375	+	0.277565i
$285$	0.860958	+	0.860958i	0.0509987	+	0.0509987i
$286$	−9.01062	+	3.11967i	−0.532809	+	0.184470i
$287$	−40.8473			−2.41114
$288$	16.3096	−	1.56607i	0.961054	−	0.0922815i
$289$	1.56704			0.0921789
$290$	−26.6950	+	9.24239i	−1.56759	+	0.542732i
$291$	1.09863	+	1.09863i	0.0644031	+	0.0644031i
$292$	16.9478	+	21.5415i	0.991794	+	1.26062i
$293$	−17.5565	+	17.5565i	−1.02566	+	1.02566i	−0.0259972	+	0.999662i	$0.508276\pi$
$293$	−17.5565	+	17.5565i	−1.02566	+	1.02566i	−0.999662	+	0.0259972i	$0.991724\pi$
$294$	5.04722	+	2.45113i	0.294360	+	0.142953i
$295$		−	18.1246i		−	1.05526i
$296$	−4.17334	−	19.1553i	−0.242571	−	1.11338i
$297$		−	5.43536i		−	0.315392i
$298$	−5.62889	+	11.5907i	−0.326073	+	0.671430i
$299$	1.66519	−	1.66519i	0.0963006	−	0.0963006i
$300$	0.710411	−	5.95231i	0.0410156	−	0.343657i
$301$	−25.2534	−	25.2534i	−1.45558	−	1.45558i
$302$	5.38315	+	15.5483i	0.309765	+	0.894703i
$303$	0.170372			0.00978762
$304$	−3.41465	+	2.08331i	−0.195843	+	0.119486i
$305$	37.7078			2.15914
$306$	5.77456	+	16.6788i	0.330110	+	0.953464i
$307$	−11.5903	−	11.5903i	−0.661494	−	0.661494i	0.294238	−	0.955732i	$-0.404934\pi$
$307$	−11.5903	−	11.5903i	−0.661494	−	0.661494i	−0.955732	+	0.294238i	$0.904934\pi$
$308$	−25.0071	−	2.98460i	−1.42491	−	0.170064i
$309$	−3.30308	+	3.30308i	−0.187906	+	0.187906i
$310$	23.7846	−	48.9759i	1.35088	−	2.78164i
$311$			0.569510i			0.0322939i	0.999870	+	0.0161470i	$0.00513996\pi$
$311$			0.569510i			0.0322939i	−0.999870	+	0.0161470i	$0.994860\pi$
$312$	−1.80302	−	1.15793i	−0.102076	−	0.0655546i
$313$			13.5726i			0.767171i	0.923505	+	0.383585i	$0.125311\pi$
$313$			13.5726i			0.767171i	−0.923505	+	0.383585i	$0.874689\pi$
$314$	8.41113	+	4.08478i	0.474667	+	0.230517i
$315$	34.0650	−	34.0650i	1.91934	−	1.91934i
$316$	−8.25692	+	6.49614i	−0.464488	+	0.365436i
$317$	0.753000	+	0.753000i	0.0422927	+	0.0422927i	0.727937	−	0.685644i	$-0.240479\pi$
$317$	0.753000	+	0.753000i	0.0422927	+	0.0422927i	−0.685644	+	0.727937i	$0.740479\pi$
$318$	−2.28214	+	0.790128i	−0.127976	+	0.0443082i
$319$	−15.1231			−0.846733
$320$	28.3646	+	10.5590i	1.58563	+	0.590266i
$321$	1.59951			0.0892761
$322$	5.87748	−	2.03491i	0.327539	−	0.113401i
$323$	−3.04689	−	3.04689i	−0.169533	−	0.169533i
$324$	−12.6982	+	9.99033i	−0.705457	+	0.555019i
$325$	15.5023	−	15.5023i	0.859911	−	0.859911i
$326$	9.32742	+	4.52977i	0.516598	+	0.250881i
$327$			4.60987i			0.254927i
$328$	22.1122	+	14.2007i	1.22094	+	0.784104i
$329$			21.3040i			1.17453i
$330$	2.15454	−	4.43650i	0.118604	−	0.244221i
$331$	−23.5920	+	23.5920i	−1.29673	+	1.29673i	−0.366196	+	0.930538i	$0.619340\pi$
$331$	−23.5920	+	23.5920i	−1.29673	+	1.29673i	−0.930538	+	0.366196i	$0.880660\pi$
$332$	6.53499	+	0.779954i	0.358654	+	0.0428055i
$333$	14.1959	+	14.1959i	0.777929	+	0.777929i
$334$	−3.24130	−	9.36193i	−0.177356	−	0.512262i
$335$	8.68090			0.474288
$336$	−2.94765	−	4.83134i	−0.160808	−	0.263571i
$337$	−3.23675			−0.176317			−0.0881586	−	0.996106i	$-0.528098\pi$
$337$	−3.23675			−0.176317			−0.0881586	+	0.996106i	$0.528098\pi$
$338$	3.45095	+	9.96747i	0.187707	+	0.542159i
$339$	−0.717223	−	0.717223i	−0.0389542	−	0.0389542i
$340$	−3.86387	+	32.3741i	−0.209548	+	1.75573i
$341$	20.6100	−	20.6100i	1.11609	−	1.11609i
$342$	1.78941	−	3.68464i	0.0967600	−	0.199243i
$343$			23.4235i			1.26475i
$344$	4.89115	+	22.4500i	0.263713	+	1.21042i
$345$			1.21805i			0.0655775i
$346$	−8.27619	−	4.01924i	−0.444931	−	0.216076i
$347$	−5.51073	+	5.51073i	−0.295832	+	0.295832i	−0.839379	−	0.543547i	$-0.817081\pi$
$347$	−5.51073	+	5.51073i	−0.295832	+	0.295832i	0.543547	+	0.839379i	$0.317081\pi$
$348$	−2.10139	−	2.67097i	−0.112646	−	0.143179i
$349$	20.3320	+	20.3320i	1.08835	+	1.08835i	0.995699	+	0.0926462i	$0.0295326\pi$
$349$	20.3320	+	20.3320i	1.08835	+	1.08835i	0.0926462	+	0.995699i	$0.470467\pi$
$350$	54.7170	−	18.9442i	2.92474	−	1.01261i
$351$	4.46714			0.238438
$352$	12.4996	+	10.3095i	0.666232	+	0.549497i
$353$	−5.44129			−0.289611			−0.144805	−	0.989460i	$-0.546256\pi$
$353$	−5.44129			−0.289611			−0.144805	+	0.989460i	$0.546256\pi$
$354$	2.06045	−	0.713371i	0.109511	−	0.0379152i
$355$	−7.96100	−	7.96100i	−0.422526	−	0.422526i
$356$	−4.53330	−	5.76205i	−0.240264	−	0.305388i
$357$	4.31100	−	4.31100i	0.228162	−	0.228162i
$358$	10.2463	+	4.97600i	0.541533	+	0.262990i
$359$		−	17.2613i		−	0.911015i	−0.890232	−	0.455508i	$-0.849458\pi$
$359$		−	17.2613i		−	0.911015i	0.890232	−	0.455508i	$-0.150542\pi$
$360$	−30.2834	+	6.59780i	−1.59608	+	0.347735i
$361$			1.00000i			0.0526316i
$362$	5.64385	−	11.6215i	0.296634	−	0.610812i
$363$	−0.636298	+	0.636298i	−0.0333970	+	0.0333970i
$364$	2.45295	−	20.5525i	0.128569	−	1.07724i
$365$	−36.6622	−	36.6622i	−1.91899	−	1.91899i
$366$	1.48415	+	4.28670i	0.0775777	+	0.224069i
$367$	−0.865480			−0.0451777			−0.0225888	−	0.999745i	$-0.507191\pi$
$367$	−0.865480			−0.0451777			−0.0225888	+	0.999745i	$0.507191\pi$
$368$	−3.88914	−	0.941757i	−0.202736	−	0.0490925i
$369$	−26.9112			−1.40094
$370$	12.1330	+	35.0440i	0.630765	+	1.82185i
$371$	−16.4953	−	16.4953i	−0.856394	−	0.856394i
$372$	6.50383	+	0.776235i	0.337208	+	0.0402459i
$373$	7.67303	−	7.67303i	0.397295	−	0.397295i	−0.479983	−	0.877278i	$-0.659357\pi$
$373$	7.67303	−	7.67303i	0.397295	−	0.397295i	0.877278	+	0.479983i	$0.159357\pi$
$374$	−7.62482	+	15.7006i	−0.394270	+	0.811857i
$375$			5.25163i			0.271193i
$376$	7.40640	−	11.5326i	0.381956	−	0.594749i
$377$		−	12.4292i		−	0.640136i
$378$	10.6131	+	5.15415i	0.545880	+	0.265101i
$379$	−7.99335	+	7.99335i	−0.410591	+	0.410591i	−0.881944	−	0.471354i	$-0.843766\pi$
$379$	−7.99335	+	7.99335i	−0.410591	+	0.410591i	0.471354	+	0.881944i	$0.343766\pi$
$380$	5.94672	−	4.67859i	0.305061	−	0.240007i
$381$	1.07520	+	1.07520i	0.0550840	+	0.0550840i
$382$	−5.29374	+	1.83281i	−0.270851	+	0.0937745i
$383$	28.1053			1.43611			0.718056	−	0.695985i	$-0.245032\pi$
$383$	28.1053			1.43611			0.718056	+	0.695985i	$0.245032\pi$
$384$	−0.0839600	+	3.64014i	−0.00428456	+	0.185760i
$385$	47.6400			2.42796
$386$	−5.96770	+	2.06615i	−0.303748	+	0.105164i
$387$	−16.6376	−	16.6376i	−0.845734	−	0.845734i
$388$	7.58838	−	5.97016i	0.385242	−	0.303089i
$389$	15.6028	−	15.6028i	0.791093	−	0.791093i	−0.190579	−	0.981672i	$-0.561037\pi$
$389$	15.6028	−	15.6028i	0.791093	−	0.791093i	0.981672	+	0.190579i	$0.0610366\pi$
$390$	3.64621	+	1.77074i	0.184633	+	0.0896652i
$391$		−	4.31061i		−	0.217997i
$392$	18.8421	−	29.3394i	0.951672	−	1.48186i
$393$			3.24359i			0.163618i
$394$	11.9460	−	24.5984i	0.601829	−	1.23925i
$395$	14.0528	−	14.0528i	0.707071	−	0.707071i
$396$	−16.4752	−	1.96633i	−0.827912	−	0.0988117i
$397$	−10.4509	−	10.4509i	−0.524517	−	0.524517i	0.394415	−	0.918932i	$-0.370947\pi$
$397$	−10.4509	−	10.4509i	−0.524517	−	0.524517i	−0.918932	+	0.394415i	$0.870947\pi$
$398$	3.41164	+	9.85391i	0.171010	+	0.493932i
$399$	−1.41489			−0.0708329
$400$	−36.2063	−	8.76737i	−1.81032	−	0.438369i
$401$	−31.8665			−1.59134			−0.795670	−	0.605731i	$-0.792881\pi$
$401$	−31.8665			−1.59134			−0.795670	+	0.605731i	$0.792881\pi$
$402$	0.341673	+	0.986863i	0.0170411	+	0.0492202i
$403$	16.9387	+	16.9387i	0.843774	+	0.843774i
$404$	0.125474	−	1.05130i	0.00624255	−	0.0523044i
$405$	21.6116	−	21.6116i	1.07389	−	1.07389i
$406$	14.3407	−	29.5295i	0.711717	−	1.46553i
$407$			19.8530i			0.984076i
$408$	−3.83244	+	0.834967i	−0.189734	+	0.0413370i
$409$			36.3968i			1.79971i	0.436191	+	0.899854i	$0.356327\pi$
$409$			36.3968i			1.79971i	−0.436191	+	0.899854i	$0.643673\pi$
$410$	−44.7169	−	21.7163i	−2.20841	−	1.07249i
$411$	−2.97953	+	2.97953i	−0.146969	+	0.146969i
$412$	17.9495	+	22.8147i	0.884309	+	1.12400i
$413$	14.8929	+	14.8929i	0.732831	+	0.732831i
$414$	3.87223	−	1.34065i	0.190310	−	0.0658893i
$415$	−12.4496			−0.611125
$416$	−8.47301	+	10.2730i	−0.415423	+	0.503676i
$417$	4.65781			0.228094
$418$	3.82774	−	1.32525i	0.187221	−	0.0648199i
$419$	17.6691	+	17.6691i	0.863192	+	0.863192i	0.991707	−	0.128516i	$-0.0410212\pi$
$419$	17.6691	+	17.6691i	0.863192	+	0.863192i	−0.128516	+	0.991707i	$0.541021\pi$
$420$	6.61967	+	8.41394i	0.323007	+	0.410558i
$421$	−13.6022	+	13.6022i	−0.662932	+	0.662932i	−0.956070	−	0.293138i	$-0.905300\pi$
$421$	−13.6022	+	13.6022i	−0.662932	+	0.662932i	0.293138	+	0.956070i	$0.405300\pi$
$422$	−27.5897	−	13.3986i	−1.34304	−	0.652235i
$423$			14.0356i			0.682432i
$424$	3.19486	+	14.6642i	0.155156	+	0.712156i
$425$		−	40.1300i		−	1.94659i
$426$	0.591685	−	1.21836i	0.0286672	−	0.0590298i
$427$	−30.9842	+	30.9842i	−1.49943	+	1.49943i
$428$	1.17799	−	9.87001i	0.0569403	−	0.477085i
$429$	1.53440	+	1.53440i	0.0740813	+	0.0740813i
$430$	−14.2199	−	41.0716i	−0.685743	−	1.98065i
$431$	15.5501			0.749020			0.374510	−	0.927223i	$-0.377811\pi$
$431$	15.5501			0.749020			0.374510	+	0.927223i	$0.377811\pi$
$432$	−3.95341	−	6.47982i	−0.190209	−	0.311761i
$433$	−2.21799			−0.106590			−0.0532950	−	0.998579i	$-0.516972\pi$
$433$	−2.21799			−0.106590			−0.0532950	+	0.998579i	$0.516972\pi$
$434$	20.6995	+	59.7868i	0.993608	+	2.86986i
$435$	4.54583	+	4.54583i	0.217956	+	0.217956i
$436$	28.4458	+	3.39503i	1.36231	+	0.162592i
$437$	−0.707379	+	0.707379i	−0.0338385	+	0.0338385i
$438$	2.72484	−	5.61084i	0.130198	−	0.268096i
$439$		−	40.0184i		−	1.90997i	−0.296649	−	0.954987i	$-0.595869\pi$
$439$		−	40.0184i		−	1.90997i	0.296649	−	0.954987i	$-0.404131\pi$
$440$	−25.7893	−	16.5622i	−1.22946	−	0.789573i
$441$			35.7069i			1.70033i
$442$	−12.9038	−	6.26658i	−0.613770	−	0.298071i
$443$	21.2067	−	21.2067i	1.00756	−	1.00756i	0.00759015	−	0.999971i	$-0.497584\pi$
$443$	21.2067	−	21.2067i	1.00756	−	1.00756i	0.999971	−	0.00759015i	$-0.00241604\pi$
$444$	−3.50633	+	2.75861i	−0.166403	+	0.130918i
$445$	9.80664	+	9.80664i	0.464879	+	0.464879i
$446$	−19.1320	+	6.62392i	−0.905927	+	0.313652i
$447$	2.93227			0.138692
$448$	−31.9833	+	14.6308i	−1.51107	+	0.691238i
$449$	−3.16929			−0.149568			−0.0747841	−	0.997200i	$-0.523827\pi$
$449$	−3.16929			−0.149568			−0.0747841	+	0.997200i	$0.523827\pi$
$450$	36.0489	−	12.4809i	1.69936	−	0.588355i
$451$	−18.8177	−	18.8177i	−0.886092	−	0.886092i
$452$	−4.95393	+	3.89751i	−0.233013	+	0.183323i
$453$	2.64768	−	2.64768i	0.124399	−	0.124399i
$454$	−6.47329	−	3.14368i	−0.303806	−	0.147540i
$455$			39.1537i			1.83556i
$456$	0.765930	+	0.491891i	0.0358680	+	0.0230349i
$457$			15.8367i			0.740811i	0.928870	+	0.370406i	$0.120781\pi$
$457$			15.8367i			0.740811i	−0.928870	+	0.370406i	$0.879219\pi$
$458$	−0.459169	+	0.945493i	−0.0214555	+	0.0441800i
$459$	5.78194	−	5.78194i	0.269878	−	0.269878i
$460$	7.51613	+	0.897053i	0.350441	+	0.0418253i
$461$	−2.95667	−	2.95667i	−0.137706	−	0.137706i	0.634894	−	0.772599i	$-0.281044\pi$
$461$	−2.95667	−	2.95667i	−0.137706	−	0.137706i	−0.772599	+	0.634894i	$0.781044\pi$
$462$	1.87507	+	5.41582i	0.0872363	+	0.251967i
$463$	38.3541			1.78246			0.891232	−	0.453547i	$-0.149842\pi$
$463$	38.3541			1.78246			0.891232	+	0.453547i	$0.149842\pi$
$464$	−18.0292	+	10.9998i	−0.836985	+	0.510654i
$465$	−12.3902			−0.574582
$466$	−10.4832	−	30.2788i	−0.485624	−	1.40264i
$467$	1.19127	+	1.19127i	0.0551253	+	0.0551253i	0.734132	−	0.679007i	$-0.237589\pi$
$467$	1.19127	+	1.19127i	0.0551253	+	0.0551253i	−0.679007	+	0.734132i	$0.737589\pi$
$468$	1.61606	−	13.5405i	0.0747024	−	0.625908i
$469$	−7.13304	+	7.13304i	−0.329373	+	0.329373i
$470$	−11.3262	+	23.3221i	−0.522436	+	1.07577i
$471$		−	2.12789i		−	0.0980482i
$472$	−2.88450	−	13.2396i	−0.132770	−	0.609404i
$473$		−	23.2677i		−	1.06985i
$474$	2.15065	+	1.04444i	0.0987827	+	0.0479728i
$475$	−6.58541	+	6.58541i	−0.302159	+	0.302159i
$476$	−23.4267	−	29.7765i	−1.07376	−	1.36480i
$477$	−10.8675	−	10.8675i	−0.497589	−	0.497589i
$478$	20.4392	−	7.07651i	0.934869	−	0.323672i
$479$	8.59819			0.392861			0.196431	−	0.980518i	$-0.437065\pi$
$479$	8.59819			0.392861			0.196431	+	0.980518i	$0.437065\pi$
$480$	−0.658333	−	6.85613i	−0.0300487	−	0.312938i
$481$	−16.3165			−0.743968
$482$	−19.8919	+	6.88701i	−0.906051	+	0.313694i
$483$	−1.00086	−	1.00086i	−0.0455408	−	0.0455408i
$484$	3.45775	+	4.39498i	0.157171	+	0.199772i
$485$	−12.9149	+	12.9149i	−0.586437	+	0.586437i
$486$	10.5497	+	5.12334i	0.478543	+	0.232400i
$487$		−	5.87262i		−	0.266114i	−0.991108	−	0.133057i	$-0.957521\pi$
$487$		−	5.87262i		−	0.266114i	0.991108	−	0.133057i	$-0.0424793\pi$
$488$	27.5447	−	6.00112i	1.24689	−	0.271658i
$489$		−	2.35970i		−	0.106710i
$490$	−28.8141	+	59.3323i	−1.30169	+	2.68036i
$491$	−23.9757	+	23.9757i	−1.08201	+	1.08201i	−0.0856842	+	0.996322i	$0.527308\pi$
$491$	−23.9757	+	23.9757i	−1.08201	+	1.08201i	−0.996322	+	0.0856842i	$0.972692\pi$
$492$	0.708733	−	5.93825i	0.0319521	−	0.267717i
$493$	−16.0875	−	16.0875i	−0.724542	−	0.724542i
$494$	1.08918	+	3.14589i	0.0490043	+	0.141540i
$495$	31.3864			1.41071
$496$	9.57972	−	39.5611i	0.430142	−	1.77634i
$497$	13.0830			0.586853
$498$	−0.490005	−	1.41529i	−0.0219576	−	0.0634208i
$499$	−9.66955	−	9.66955i	−0.432869	−	0.432869i	0.456734	−	0.889603i	$-0.349019\pi$
$499$	−9.66955	−	9.66955i	−0.432869	−	0.432869i	−0.889603	+	0.456734i	$0.849019\pi$
$500$	32.4059	+	3.86766i	1.44924	+	0.172967i
$501$	−1.59422	+	1.59422i	−0.0712244	+	0.0712244i
$502$	−6.81747	+	14.0381i	−0.304279	+	0.626553i
$503$		−	13.5513i		−	0.604221i	−0.953273	−	0.302110i	$-0.902309\pi$
$503$		−	13.5513i		−	0.604221i	0.953273	−	0.302110i	$-0.0976911\pi$
$504$	19.4623	−	30.3051i	0.866921	−	1.34989i
$505$			2.00280i			0.0891235i
$506$	3.64512	+	1.77021i	0.162045	+	0.0786956i
$507$	1.69733	−	1.69733i	0.0753812	−	0.0753812i
$508$	7.42650	−	5.84280i	0.329498	−	0.259232i
$509$	−22.6930	−	22.6930i	−1.00585	−	1.00585i	−0.999983	−	0.00586588i	$-0.998133\pi$
$509$	−22.6930	−	22.6930i	−1.00585	−	1.00585i	−0.00586588	−	0.999983i	$-0.501867\pi$
$510$	7.01131	−	2.42747i	0.310466	−	0.107490i
$511$	60.2502			2.66531
$512$	22.4002	+	3.19894i	0.989956	+	0.141374i
$513$	−1.89766			−0.0837836
$514$	−33.7399	+	11.6815i	−1.48820	+	0.515248i
$515$	−38.8292	−	38.8292i	−1.71102	−	1.71102i
$516$	4.10942	−	3.23309i	0.180907	−	0.142329i
$517$	−9.81440	+	9.81440i	−0.431637	+	0.431637i
$518$	−38.7651	−	18.8258i	−1.70324	−	0.827160i
$519$			2.09376i			0.0919057i
$520$	13.6119	−	21.1954i	0.596923	−	0.929478i
$521$		−	2.17318i		−	0.0952086i	−0.998866	−	0.0476043i	$-0.984841\pi$
$521$		−	2.17318i		−	0.0952086i	0.998866	−	0.0476043i	$-0.0151586\pi$
$522$	9.44800	−	19.4548i	0.413528	−	0.851512i
$523$	−7.89745	+	7.89745i	−0.345331	+	0.345331i	−0.858367	−	0.513036i	$-0.828521\pi$
$523$	−7.89745	+	7.89745i	−0.345331	+	0.345331i	0.513036	+	0.858367i	$0.328521\pi$
$524$	20.0150	+	2.38880i	0.874360	+	0.104355i
$525$	−9.31761	−	9.31761i	−0.406654	−	0.406654i
$526$	6.07741	+	17.5535i	0.264988	+	0.765370i
$527$	43.8483			1.91006
$528$	0.867783	−	3.58366i	0.0377654	−	0.155959i
$529$	21.9992			0.956488
$530$	−9.28831	−	26.8276i	−0.403458	−	1.16532i
$531$	9.81179	+	9.81179i	0.425796	+	0.425796i
$532$	−1.04202	+	8.73075i	−0.0451772	+	0.378526i
$533$	15.4657	−	15.4657i	0.669892	−	0.669892i
$534$	−0.728858	+	1.50082i	−0.0315408	+	0.0649469i
$535$			18.8030i			0.812925i
$536$	6.34120	−	1.38155i	0.273898	−	0.0596738i
$537$		−	2.59216i		−	0.111860i
$538$	12.4323	+	6.03763i	0.535996	+	0.260301i
$539$	−24.9682	+	24.9682i	−1.07545	+	1.07545i
$540$	8.87835	+	11.2848i	0.382063	+	0.485622i
$541$	29.2913	+	29.2913i	1.25933	+	1.25933i	0.951413	+	0.307919i	$0.0996325\pi$
$541$	29.2913	+	29.2913i	1.25933	+	1.25933i	0.307919	+	0.951413i	$0.400367\pi$
$542$	−32.4065	+	11.2198i	−1.39198	+	0.481933i
$543$	−2.94007			−0.126170
$544$	2.32981	+	24.2635i	0.0998897	+	1.04029i
$545$	−54.1911			−2.32129
$546$	−4.45108	+	1.54106i	−0.190489	+	0.0659512i
$547$	−1.41222	−	1.41222i	−0.0603820	−	0.0603820i	0.676271	−	0.736653i	$-0.263595\pi$
$547$	−1.41222	−	1.41222i	−0.0603820	−	0.0603820i	−0.736653	+	0.676271i	$0.763595\pi$
$548$	16.1913	+	20.5799i	0.691656	+	0.879131i
$549$	−20.4132	+	20.4132i	−0.871213	+	0.871213i
$550$	33.9345	+	16.4800i	1.44697	+	0.702708i
$551$			5.27996i			0.224934i
$552$	0.193850	+	0.889756i	0.00825079	+	0.0378705i
$553$			23.0941i			0.982061i
$554$	5.19104	−	10.6891i	0.220546	−	0.454136i
$555$	5.96756	−	5.96756i	0.253309	−	0.253309i
$556$	3.43033	−	28.7416i	0.145478	−	1.21892i
$557$	−0.206338	−	0.206338i	−0.00874281	−	0.00874281i	0.702722	−	0.711465i	$-0.251968\pi$
$557$	−0.206338	−	0.206338i	−0.00874281	−	0.00874281i	−0.711465	+	0.702722i	$0.751968\pi$
$558$	13.6373	+	39.3890i	0.577314	+	1.66747i
$559$	19.1229			0.808814
$560$	56.7945	−	34.6510i	2.40001	−	1.46427i
$561$	3.97202			0.167699
$562$	−6.18067	−	17.8518i	−0.260716	−	0.753031i
$563$	−26.0294	−	26.0294i	−1.09701	−	1.09701i	−0.994759	−	0.102251i	$-0.967395\pi$
$563$	−26.0294	−	26.0294i	−1.09701	−	1.09701i	−0.102251	−	0.994759i	$-0.532605\pi$
$564$	−3.09710	−	0.369640i	−0.130411	−	0.0155647i
$565$	8.43128	−	8.43128i	0.354707	−	0.354707i
$566$	7.57823	−	15.6046i	0.318537	−	0.655912i
$567$			35.5162i			1.49154i
$568$	−7.08231	−	4.54836i	−0.297167	−	0.190845i
$569$			12.9086i			0.541156i	0.962698	+	0.270578i	$0.0872149\pi$
$569$			12.9086i			0.541156i	−0.962698	+	0.270578i	$0.912785\pi$
$570$	−1.54892	−	0.752218i	−0.0648772	−	0.0315069i
$571$	7.51687	−	7.51687i	0.314571	−	0.314571i	−0.532106	−	0.846678i	$-0.678599\pi$
$571$	7.51687	−	7.51687i	0.314571	−	0.314571i	0.846678	+	0.532106i	$0.178599\pi$
$572$	10.5982	−	8.33816i	0.443134	−	0.348636i
$573$	0.901456	+	0.901456i	0.0376589	+	0.0376589i
$574$	54.5877	−	18.8994i	2.27845	−	0.788848i
$575$	−9.31677			−0.388536
$576$	−21.0713	+	9.63909i	−0.877973	+	0.401629i
$577$	−47.5099			−1.97786			−0.988932	−	0.148367i	$-0.952598\pi$
$577$	−47.5099			−1.97786			−0.988932	+	0.148367i	$0.952598\pi$
$578$	−2.09417	+	0.725047i	−0.0871060	+	0.0301580i
$579$	1.01622	+	1.01622i	0.0422328	+	0.0422328i
$580$	31.3985	−	24.7028i	1.30375	−	1.02573i
$581$	10.2297	−	10.2297i	0.424400	−	0.424400i
$582$	−1.97652	−	0.959876i	−0.0819293	−	0.0397881i
$583$		−	15.1983i		−	0.629448i
$584$	−32.6157	−	20.9462i	−1.34965	−	0.866761i
$585$			25.7954i			1.06651i
$586$	15.3391	−	31.5853i	0.633651	−	1.30478i
$587$	4.03778	−	4.03778i	0.166657	−	0.166657i	−0.618851	−	0.785508i	$-0.712402\pi$
$587$	4.03778	−	4.03778i	0.166657	−	0.166657i	0.785508	+	0.618851i	$0.212402\pi$
$588$	−7.87912	−	0.940377i	−0.324930	−	0.0387805i
$589$	−7.19559	−	7.19559i	−0.296489	−	0.296489i
$590$	8.38600	+	24.2215i	0.345246	+	0.997182i
$591$	−6.22304			−0.255982
$592$	14.4401	+	23.6679i	0.593483	+	0.972746i
$593$	−12.9856			−0.533254			−0.266627	−	0.963800i	$-0.585909\pi$
$593$	−12.9856			−0.533254			−0.266627	+	0.963800i	$0.585909\pi$
$594$	2.51486	+	7.26373i	0.103186	+	0.298035i
$595$	50.6777	+	50.6777i	2.07758	+	2.07758i
$596$	2.15953	−	18.0940i	0.0884577	−	0.741159i
$597$	1.67800	−	1.67800i	0.0686758	−	0.0686758i
$598$	−1.45488	+	2.99580i	−0.0594944	+	0.122507i
$599$		−	10.7708i		−	0.440085i	−0.975490	−	0.220042i	$-0.929380\pi$
$599$		−	10.7708i		−	0.440085i	0.975490	−	0.220042i	$-0.0706195\pi$
$600$	1.80466	+	8.28327i	0.0736750	+	0.338163i
$601$			20.1676i			0.822654i	0.911488	+	0.411327i	$0.134935\pi$
$601$			20.1676i			0.822654i	−0.911488	+	0.411327i	$0.865065\pi$
$602$	45.4326	+	22.0639i	1.85170	+	0.899257i
$603$	−4.69942	+	4.69942i	−0.191375	+	0.191375i
$604$	−14.3879	−	18.2878i	−0.585436	−	0.744119i
$605$	−7.47998	−	7.47998i	−0.304104	−	0.304104i
$606$	−0.227683	+	0.0788286i	−0.00924898	+	0.00320219i
$607$	−30.9682			−1.25696			−0.628481	−	0.777825i	$-0.716323\pi$
$607$	−30.9682			−1.25696			−0.628481	+	0.777825i	$0.716323\pi$
$608$	3.59936	−	4.36401i	0.145973	−	0.176984i
$609$	−7.47055			−0.302722
$610$	−50.3921	+	17.4468i	−2.04032	+	0.706402i
$611$	−8.06612	−	8.06612i	−0.326320	−	0.326320i
$612$	−15.4341	−	19.6175i	−0.623885	−	0.792990i
$613$	27.8822	−	27.8822i	1.12615	−	1.12615i	0.135355	−	0.990797i	$-0.456783\pi$
$613$	27.8822	−	27.8822i	1.12615	−	1.12615i	0.990797	−	0.135355i	$-0.0432175\pi$
$614$	20.8518	+	10.1264i	0.841509	+	0.408670i
$615$			11.3127i			0.456174i
$616$	34.8000	−	7.58181i	1.40213	−	0.305480i
$617$		−	24.2307i		−	0.975493i	−0.872985	−	0.487747i	$-0.837819\pi$
$617$		−	24.2307i		−	0.975493i	0.872985	−	0.487747i	$-0.162181\pi$
$618$	2.88590	−	5.94247i	0.116088	−	0.239041i
$619$	−17.7690	+	17.7690i	−0.714197	+	0.714197i	−0.967411	−	0.253213i	$-0.918513\pi$
$619$	−17.7690	+	17.7690i	−0.714197	+	0.714197i	0.253213	+	0.967411i	$0.418513\pi$
$620$	−9.12499	+	76.4554i	−0.366468	+	3.07052i
$621$	−1.34236	−	1.34236i	−0.0538672	−	0.0538672i
$622$	−0.263504	−	0.761084i	−0.0105655	−	0.0305167i
$623$	−16.1161			−0.645678
$624$	2.94529	+	0.713202i	0.117906	+	0.0285509i
$625$	−15.1694			−0.606776
$626$	−6.27985	−	18.1383i	−0.250993	−	0.724950i
$627$	−0.651816	−	0.651816i	−0.0260310	−	0.0260310i
$628$	−13.1305	−	1.56713i	−0.523962	−	0.0625352i
$629$	−21.1189	+	21.1189i	−0.842065	+	0.842065i
$630$	−29.7625	+	61.2852i	−1.18577	+	2.44166i
$631$			17.4714i			0.695526i	0.937582	+	0.347763i	$0.113059\pi$
$631$			17.4714i			0.695526i	−0.937582	+	0.347763i	$0.886941\pi$
$632$	8.02875	−	12.5017i	0.319367	−	0.497291i
$633$			6.97979i			0.277422i
$634$	−1.35470	−	0.657896i	−0.0538020	−	0.0261284i
$635$	−12.6394	+	12.6394i	−0.501580	+	0.501580i
$636$	2.68424	−	2.11183i	0.106437	−	0.0837394i
$637$	−20.5205	−	20.5205i	−0.813051	−	0.813051i
$638$	20.2103	−	6.99725i	0.800135	−	0.277024i
$639$	8.61940			0.340978
$640$	−42.7915	−	0.986987i	−1.69148	−	0.0390141i
$641$	2.26693			0.0895382			0.0447691	−	0.998997i	$-0.485745\pi$
$641$	2.26693			0.0895382			0.0447691	+	0.998997i	$0.485745\pi$
$642$	−2.13756	+	0.740071i	−0.0843629	+	0.0292083i
$643$	25.6063	+	25.6063i	1.00981	+	1.00981i	0.999951	+	0.00986080i	$0.00313884\pi$
$643$	25.6063	+	25.6063i	1.00981	+	1.00981i	0.00986080	+	0.999951i	$0.496861\pi$
$644$	−6.91305	+	5.43885i	−0.272412	+	0.214321i
$645$	−6.99397	+	6.99397i	−0.275387	+	0.275387i
$646$	5.48156	+	2.66206i	0.215669	+	0.104737i
$647$			10.4115i			0.409317i	0.978833	+	0.204658i	$0.0656083\pi$
$647$			10.4115i			0.409317i	−0.978833	+	0.204658i	$0.934392\pi$
$648$	12.3473	−	19.2262i	0.485049	−	0.755277i
$649$			13.7218i			0.538629i
$650$	−13.5443	+	27.8897i	−0.531252	+	1.09392i
$651$	10.1809	−	10.1809i	0.399023	−	0.399023i
$652$	−14.5609	−	1.73785i	−0.570248	−	0.0680594i
$653$	−10.2793	−	10.2793i	−0.402258	−	0.402258i	0.476770	−	0.879028i	$-0.341808\pi$
$653$	−10.2793	−	10.2793i	−0.402258	−	0.402258i	−0.879028	+	0.476770i	$0.841808\pi$
$654$	−2.13292	−	6.16056i	−0.0834037	−	0.240897i
$655$	−38.1299			−1.48986
$656$	−36.1208	−	8.74666i	−1.41028	−	0.341500i
$657$	39.6943			1.54862
$658$	−9.85702	−	28.4703i	−0.384267	−	1.10989i
$659$	24.4316	+	24.4316i	0.951719	+	0.951719i	0.998887	−	0.0471677i	$-0.0150195\pi$
$659$	24.4316	+	24.4316i	0.951719	+	0.951719i	−0.0471677	+	0.998887i	$0.515020\pi$
$660$	−0.826591	+	6.92575i	−0.0321750	+	0.269584i
$661$	4.58322	−	4.58322i	0.178266	−	0.178266i	−0.612333	−	0.790600i	$-0.709769\pi$
$661$	4.58322	−	4.58322i	0.178266	−	0.178266i	0.790600	+	0.612333i	$0.209769\pi$
$662$	20.6123	−	42.4436i	0.801120	−	1.64962i
$663$			3.26447i			0.126781i
$664$	−9.09413	+	1.98132i	−0.352921	+	0.0768903i
$665$		−	16.6326i		−	0.644986i
$666$	−25.5393	−	12.4029i	−0.989630	−	0.480603i
$667$	−3.73494	+	3.73494i	−0.144617	+	0.144617i
$668$	8.66325	+	11.0114i	0.335191	+	0.426045i
$669$	3.25794	+	3.25794i	0.125959	+	0.125959i
$670$	−11.6010	+	4.01652i	−0.448186	+	0.155172i
$671$	−28.5479			−1.10208
$672$	6.17458	+	5.09269i	0.238190	+	0.196455i
$673$	−28.0938			−1.08293			−0.541467	−	0.840722i	$-0.682131\pi$
$673$	−28.0938			−1.08293			−0.541467	+	0.840722i	$0.682131\pi$
$674$	4.32555	−	1.49760i	0.166614	−	0.0576853i
$675$	−12.4968	−	12.4968i	−0.481004	−	0.481004i
$676$	−9.22360	−	11.7237i	−0.354754	−	0.450910i
$677$	10.8054	−	10.8054i	0.415284	−	0.415284i	−0.468290	−	0.883575i	$-0.655130\pi$
$677$	10.8054	−	10.8054i	0.415284	−	0.415284i	0.883575	+	0.468290i	$0.155130\pi$
$678$	1.29033	+	0.626637i	0.0495550	+	0.0240658i
$679$		−	21.2242i		−	0.814511i
$680$	−9.81541	−	45.0520i	−0.376404	−	1.72767i
$681$			1.63765i			0.0627548i
$682$	−18.0069	+	37.0788i	−0.689521	+	1.41982i
$683$	13.8954	−	13.8954i	0.531695	−	0.531695i	−0.389382	−	0.921076i	$-0.627311\pi$
$683$	13.8954	−	13.8954i	0.531695	−	0.531695i	0.921076	+	0.389382i	$0.127311\pi$
$684$	−0.686507	+	5.75203i	−0.0262493	+	0.219934i
$685$	−35.0257	−	35.0257i	−1.33826	−	1.33826i
$686$	−10.8377	−	31.3028i	−0.413786	−	1.19515i
$687$	0.239196			0.00912590
$688$	−16.9238	−	27.7388i	−0.645212	−	1.05753i
$689$	12.4909			0.475867
$690$	−0.563572	−	1.62778i	−0.0214548	−	0.0619685i
$691$	−10.1250	−	10.1250i	−0.385174	−	0.385174i	0.487788	−	0.872962i	$-0.337804\pi$
$691$	−10.1250	−	10.1250i	−0.385174	−	0.385174i	−0.872962	+	0.487788i	$0.837804\pi$
$692$	12.9198	+	1.54199i	0.491137	+	0.0586175i
$693$	−25.7900	+	25.7900i	−0.979681	+	0.979681i
$694$	4.81472	−	9.91419i	0.182764	−	0.376338i
$695$			54.7546i			2.07696i
$696$	4.04408	+	2.59716i	0.153291	+	0.0984453i
$697$		−	40.0352i		−	1.51644i
$698$	−36.5786	−	17.7640i	−1.38452	−	0.672378i
$699$	−5.15610	+	5.15610i	−0.195022	+	0.195022i
$700$	−64.3577	+	50.6334i	−2.43249	+	1.91376i
$701$	23.3962	+	23.3962i	0.883663	+	0.883663i	0.993905	−	0.110241i	$-0.0351624\pi$
$701$	23.3962	+	23.3962i	0.883663	+	0.883663i	−0.110241	+	0.993905i	$0.535162\pi$
$702$	−5.96982	+	2.06688i	−0.225316	+	0.0780094i
$703$	6.93130			0.261419
$704$	−21.4743	−	7.99403i	−0.809345	−	0.301286i
$705$	5.90017			0.222213
$706$	7.27166	−	2.51761i	0.273672	−	0.0947513i
$707$	−1.64569	−	1.64569i	−0.0618925	−	0.0618925i
$708$	−2.42348	+	1.90668i	−0.0910800	+	0.0716572i
$709$	−29.4212	+	29.4212i	−1.10493	+	1.10493i	−0.111129	+	0.993806i	$0.535447\pi$
$709$	−29.4212	+	29.4212i	−1.10493	+	1.10493i	−0.993806	+	0.111129i	$0.964553\pi$
$710$	14.3224	+	6.95552i	0.537510	+	0.261036i
$711$			15.2150i			0.570605i
$712$	8.72424	+	5.60283i	0.326955	+	0.209975i
$713$		−	10.1800i		−	0.381245i
$714$	−3.76652	+	7.75578i	−0.140958	+	0.290253i
$715$	−18.0375	+	18.0375i	−0.674564	+	0.674564i
$716$	−15.9953	−	1.90905i	−0.597773	−	0.0713444i
$717$	−3.48055	−	3.48055i	−0.129983	−	0.129983i
$718$	7.98653	+	23.0677i	0.298055	+	0.860878i
$719$	9.47760			0.353455			0.176727	−	0.984260i	$-0.443449\pi$
$719$	9.47760			0.353455			0.176727	+	0.984260i	$0.443449\pi$
$720$	37.4176	−	22.8289i	1.39447	−	0.850783i
$721$	63.8114			2.37646
$722$	−0.462685	−	1.33638i	−0.0172194	−	0.0497351i
$723$	3.38734	+	3.38734i	0.125977	+	0.125977i
$724$	−2.16527	+	18.1421i	−0.0804715	+	0.674246i
$725$	−34.7707	+	34.7707i	−1.29135	+	1.29135i
$726$	0.555933	−	1.14474i	0.0206326	−	0.0424855i
$727$		−	35.4252i		−	1.31385i	−0.753957	−	0.656923i	$-0.771858\pi$
$727$		−	35.4252i		−	1.31385i	0.753957	−	0.656923i	$-0.228142\pi$
$728$	6.23124	+	28.6009i	0.230945	+	1.06002i
$729$			21.5667i			0.798768i
$730$	65.9579	+	32.0318i	2.44121	+	1.18555i
$731$	24.7513	−	24.7513i	0.915461	−	0.915461i
$732$	−3.96678	−	5.04199i	−0.146617	−	0.186357i
$733$	−5.82127	−	5.82127i	−0.215013	−	0.215013i	0.591380	−	0.806393i	$-0.298583\pi$
$733$	−5.82127	−	5.82127i	−0.215013	−	0.215013i	−0.806393	+	0.591380i	$0.798583\pi$
$734$	1.15661	−	0.400445i	0.0426914	−	0.0147807i
$735$	15.0102			0.553661
$736$	5.63313	−	0.540899i	0.207640	−	0.0199378i
$737$	−6.57215			−0.242088
$738$	35.9637	−	12.4514i	1.32384	−	0.458343i
$739$	23.4233	+	23.4233i	0.861642	+	0.861642i	0.991529	−	0.129887i	$-0.0414615\pi$
$739$	23.4233	+	23.4233i	0.861642	+	0.861642i	−0.129887	+	0.991529i	$0.541462\pi$
$740$	−32.4287	−	41.2185i	−1.19210	−	1.51522i
$741$	0.535705	−	0.535705i	0.0196796	−	0.0196796i
$742$	29.6762	+	14.4119i	1.08945	+	0.529079i
$743$		−	28.1401i		−	1.03236i	−0.856480	−	0.516180i	$-0.827354\pi$
$743$		−	28.1401i		−	1.03236i	0.856480	−	0.516180i	$-0.172646\pi$
$744$	−9.05076	+	1.97188i	−0.331817	+	0.0722925i
$745$			34.4702i			1.26289i
$746$	−6.70392	+	13.8043i	−0.245448	+	0.505412i
$747$	6.73959	−	6.73959i	0.246589	−	0.246589i
$748$	2.92527	−	24.5099i	0.106958	−	0.896170i
$749$	−15.4503	−	15.4503i	−0.564542	−	0.564542i
$750$	−2.42985	−	7.01820i	−0.0887256	−	0.256268i
$751$	−26.8303			−0.979053			−0.489527	−	0.871988i	$-0.662830\pi$
$751$	−26.8303			−0.979053			−0.489527	+	0.871988i	$0.662830\pi$
$752$	−4.56183	+	18.8388i	−0.166353	+	0.686982i
$753$	3.55145			0.129422
$754$	5.75081	+	16.6102i	0.209432	+	0.604907i
$755$	31.1246	+	31.1246i	1.13274	+	1.13274i
$756$	−16.5680	−	1.97739i	−0.602571	−	0.0719171i
$757$	13.8135	−	13.8135i	0.502059	−	0.502059i	−0.410018	−	0.912077i	$-0.634478\pi$
$757$	13.8135	−	13.8135i	0.502059	−	0.502059i	0.912077	+	0.410018i	$0.134478\pi$
$758$	6.98378	−	14.3806i	0.253662	−	0.522326i
$759$		−	0.922162i		−	0.0334724i
$760$	−5.78240	+	9.00385i	−0.209750	+	0.326604i
$761$			1.46541i			0.0531210i	0.999647	+	0.0265605i	$0.00845547\pi$
$761$			1.46541i			0.0531210i	−0.999647	+	0.0265605i	$0.991545\pi$
$762$	−1.93435	−	0.939399i	−0.0700742	−	0.0340308i
$763$	44.5285	−	44.5285i	1.61204	−	1.61204i
$764$	6.22645	−	4.89866i	0.225265	−	0.177227i
$765$	33.3877	+	33.3877i	1.20714	+	1.20714i
$766$	−37.5594	+	13.0039i	−1.35708	+	0.469849i
$767$	−11.2775			−0.407208
$768$	−1.57204	−	4.90347i	−0.0567260	−	0.176939i
$769$	19.3550			0.697960			0.348980	−	0.937130i	$-0.386528\pi$
$769$	19.3550			0.697960			0.348980	+	0.937130i	$0.386528\pi$
$770$	−63.6654	+	22.0423i	−2.29434	+	0.794350i
$771$	5.74548	+	5.74548i	0.206918	+	0.206918i
$772$	7.01916	−	5.52233i	0.252625	−	0.198753i
$773$	12.5827	−	12.5827i	0.452568	−	0.452568i	−0.443638	−	0.896206i	$-0.646313\pi$
$773$	12.5827	−	12.5827i	0.452568	−	0.452568i	0.896206	+	0.443638i	$0.146313\pi$
$774$	29.9321	+	14.5362i	1.07589	+	0.522493i
$775$		−	94.7719i		−	3.40431i
$776$	−7.37869	+	11.4895i	−0.264879	+	0.412448i
$777$			9.80700i			0.351824i
$778$	−13.6321	+	28.0705i	−0.488736	+	1.00638i
$779$	−6.56986	+	6.56986i	−0.235390	+	0.235390i
$780$	−5.69204	−	0.679347i	−0.203808	−	0.0243245i
$781$	6.02713	+	6.02713i	0.215668	+	0.215668i
$782$	1.99445	+	5.76063i	0.0713216	+	0.206000i
$783$	−10.0196			−0.358070
$784$	−11.6054	+	47.9266i	−0.414480	+	1.71167i
$785$	25.0144			0.892801
$786$	−1.50076	−	4.33468i	−0.0535304	−	0.154613i
$787$	−11.9606	−	11.9606i	−0.426351	−	0.426351i	0.461033	−	0.887383i	$-0.347479\pi$
$787$	−11.9606	−	11.9606i	−0.426351	−	0.426351i	−0.887383	+	0.461033i	$0.847479\pi$
$788$	−4.58308	+	38.4001i	−0.163265	+	1.36795i
$789$	2.98915	−	2.98915i	0.106416	−	0.106416i
$790$	−12.2779	+	25.2819i	−0.436827	+	0.899489i
$791$			13.8558i			0.492657i
$792$	22.9271	−	4.99508i	0.814677	−	0.177492i
$793$		−	23.4626i		−	0.833180i
$794$	18.8019	+	9.13096i	0.667256	+	0.324046i
$795$	−4.56841	+	4.56841i	−0.162025	+	0.162025i
$796$	−9.11851	−	11.5901i	−0.323197	−	0.410800i
$797$	−27.9924	−	27.9924i	−0.991540	−	0.991540i	0.00842418	−	0.999965i	$-0.497318\pi$
$797$	−27.9924	−	27.9924i	−0.991540	−	0.991540i	−0.999965	+	0.00842418i	$0.997318\pi$
$798$	1.89083	−	0.654647i	0.0669347	−	0.0231742i
$799$	−20.8804			−0.738695
$800$	52.4421	−	5.03555i	1.85411	−	0.178034i
$801$	−10.6177			−0.375157
$802$	42.5859	−	14.7442i	1.50376	−	0.520635i
$803$	27.7563	+	27.7563i	0.979500	+	0.979500i
$804$	−0.913213	−	1.16074i	−0.0322065	−	0.0409362i
$805$	11.7656	−	11.7656i	0.414682	−	0.414682i
$806$	−30.4738	−	14.7993i	−1.07339	−	0.521283i
$807$		−	3.14520i		−	0.110716i
$808$	0.318742	+	1.46300i	0.0112133	+	0.0514682i
$809$			13.1003i			0.460583i	0.973122	+	0.230292i	$0.0739680\pi$
$809$			13.1003i			0.460583i	−0.973122	+	0.230292i	$0.926032\pi$
$810$	−18.8820	+	38.8807i	−0.663446	+	1.36613i
$811$	−10.6982	+	10.6982i	−0.375664	+	0.375664i	−0.869535	−	0.493871i	$-0.835581\pi$
$811$	−10.6982	+	10.6982i	−0.375664	+	0.375664i	0.493871	+	0.869535i	$0.335581\pi$
$812$	−5.50182	+	46.0980i	−0.193076	+	1.61772i
$813$	5.51842	+	5.51842i	0.193540	+	0.193540i
$814$	−9.18568	−	26.5312i	−0.321958	−	0.929919i
$815$	27.7394			0.971668
$816$	4.73528	−	2.88905i	0.165768	−	0.101137i
$817$	−8.12348			−0.284205
$818$	−16.8403	−	48.6402i	−0.588806	−	1.70066i
$819$	−21.1959	−	21.1959i	−0.740645	−	0.740645i
$820$	69.8068	+	8.33147i	2.43776	+	0.290948i
$821$	19.9290	−	19.9290i	0.695527	−	0.695527i	−0.267916	−	0.963442i	$-0.586335\pi$
$821$	19.9290	−	19.9290i	0.695527	−	0.695527i	0.963442	+	0.267916i	$0.0863348\pi$
$822$	2.60321	−	5.36038i	0.0907975	−	0.186965i
$823$		−	25.0441i		−	0.872984i	−0.899708	−	0.436492i	$-0.856221\pi$
$823$		−	25.0441i		−	0.872984i	0.899708	−	0.436492i	$-0.143779\pi$
$824$	−34.5435	−	22.1843i	−1.20338	−	0.772826i
$825$		−	8.58495i		−	0.298890i
$826$	−26.7933	−	13.0119i	−0.932260	−	0.452742i
$827$	−1.80361	+	1.80361i	−0.0627178	+	0.0627178i	−0.737770	−	0.675052i	$-0.764121\pi$
$827$	−1.80361	+	1.80361i	−0.0627178	+	0.0627178i	0.675052	+	0.737770i	$0.264121\pi$
$828$	−4.55449	+	3.58324i	−0.158279	+	0.124526i
$829$	−1.15862	−	1.15862i	−0.0402406	−	0.0402406i	0.686700	−	0.726941i	$-0.259059\pi$
$829$	−1.15862	−	1.15862i	−0.0402406	−	0.0402406i	−0.726941	+	0.686700i	$0.759059\pi$
$830$	16.6374	−	5.76023i	0.577493	−	0.199940i
$831$	−2.70419			−0.0938072
$832$	6.57002	−	17.6490i	0.227774	−	0.611870i
$833$	−53.1205			−1.84051
$834$	−6.22462	+	2.15510i	−0.215541	+	0.0746249i
$835$	−18.7408	−	18.7408i	−0.648551	−	0.648551i
$836$	−4.50216	+	3.54208i	−0.155710	+	0.122505i
$837$	13.6548	−	13.6548i	0.471978	−	0.471978i
$838$	−31.7879	−	15.4375i	−1.09810	−	0.533279i
$839$		−	34.0557i		−	1.17573i	−0.808958	−	0.587866i	$-0.799968\pi$
$839$		−	34.0557i		−	1.17573i	0.808958	−	0.587866i	$-0.200032\pi$
$840$	−12.7394	−	8.18143i	−0.439552	−	0.282286i
$841$		−	1.12199i		−	0.0386892i
$842$	11.8843	−	24.4713i	0.409558	−	0.843338i
$843$	−3.03993	+	3.03993i	−0.104701	+	0.104701i
$844$	43.0697	+	5.14039i	1.48252	+	0.176940i
$845$	19.9529	+	19.9529i	0.686402	+	0.686402i
$846$	−6.49404	−	18.7569i	−0.223270	−	0.644875i
$847$	12.2925			0.422375
$848$	−11.0545	−	18.1188i	−0.379612	−	0.622201i
$849$	−3.94775			−0.135486
$850$	18.5676	+	53.6291i	0.636862	+	1.83946i
$851$	4.90306	+	4.90306i	0.168075	+	0.168075i
$852$	−0.227000	+	1.90196i	−0.00777690	+	0.0651602i
$853$	−26.1963	+	26.1963i	−0.896945	+	0.896945i	−0.995165	−	0.0982195i	$-0.968685\pi$
$853$	−26.1963	+	26.1963i	−0.896945	+	0.896945i	0.0982195	+	0.995165i	$0.468685\pi$
$854$	27.0709	−	55.7428i	0.926347	−	1.90748i
$855$		−	10.9580i		−	0.374755i
$856$	2.99246	+	13.7352i	0.102280	+	0.469458i
$857$			46.6402i			1.59320i	0.604508	+	0.796599i	$0.293370\pi$
$857$			46.6402i			1.59320i	−0.604508	+	0.796599i	$0.706630\pi$
$858$	−2.76048	−	1.34060i	−0.0942413	−	0.0457673i
$859$	11.2221	−	11.2221i	0.382892	−	0.382892i	−0.489251	−	0.872143i	$-0.662730\pi$
$859$	11.2221	−	11.2221i	0.382892	−	0.382892i	0.872143	+	0.489251i	$0.162730\pi$
$860$	38.0064	+	48.3081i	1.29601	+	1.64729i
$861$	−9.29560	−	9.29560i	−0.316793	−	0.316793i
$862$	−20.7809	+	7.19478i	−0.707799	+	0.245055i
$863$	−15.6352			−0.532227			−0.266114	−	0.963942i	$-0.585740\pi$
$863$	−15.6352			−0.532227			−0.266114	+	0.963942i	$0.585740\pi$
$864$	8.28139	+	6.83035i	0.281739	+	0.232373i
$865$	−24.6131			−0.836869
$866$	2.96409	−	1.02623i	0.100724	−	0.0348728i
$867$	0.356611	+	0.356611i	0.0121111	+	0.0121111i
$868$	−55.3250	−	70.3208i	−1.87785	−	2.38684i
$869$	−10.6391	+	10.6391i	−0.360907	+	0.360907i
$870$	−8.17825	−	3.97168i	−0.277269	−	0.134653i
$871$		−	5.40143i		−	0.183021i
$872$	−39.5854	+	8.62441i	−1.34053	+	0.292059i
$873$		−	13.9830i		−	0.473254i
$874$	0.618037	−	1.27262i	0.0209054	−	0.0430472i
$875$	50.7275	−	50.7275i	1.71490	−	1.71490i
$876$	−1.04539	+	8.75898i	−0.0353204	+	0.295938i
$877$	−14.3124	−	14.3124i	−0.483296	−	0.483296i	0.422887	−	0.906183i	$-0.361017\pi$
$877$	−14.3124	−	14.3124i	−0.483296	−	0.483296i	−0.906183	+	0.422887i	$0.861017\pi$
$878$	18.5159	+	53.4799i	0.624882	+	1.80486i
$879$	−7.99062			−0.269517
$880$	42.1275	+	10.2012i	1.42012	+	0.343882i
$881$	8.02585			0.270398			0.135199	−	0.990818i	$-0.456833\pi$
$881$	8.02585			0.270398			0.135199	+	0.990818i	$0.456833\pi$
$882$	−16.5211	−	47.7182i	−0.556293	−	1.60676i
$883$	−8.50315	−	8.50315i	−0.286154	−	0.286154i	0.549403	−	0.835557i	$-0.314855\pi$
$883$	−8.50315	−	8.50315i	−0.286154	−	0.286154i	−0.835557	+	0.549403i	$0.814855\pi$
$884$	20.1438	+	2.40418i	0.677511	+	0.0808612i
$885$	4.12461	−	4.12461i	0.138647	−	0.138647i
$886$	−18.5283	+	38.1523i	−0.622470	+	1.28175i
$887$			59.4731i			1.99691i	0.0555406	+	0.998456i	$0.482312\pi$
$887$			59.4731i			1.99691i	−0.0555406	+	0.998456i	$0.517688\pi$
$888$	3.40944	−	5.30889i	0.114413	−	0.178155i
$889$		−	20.7715i		−	0.696652i
$890$	−17.6428	−	8.56806i	−0.591389	−	0.287202i
$891$	−16.3617	+	16.3617i	−0.548139	+	0.548139i
$892$	22.5029	−	17.7042i	0.753454	−	0.592780i
$893$	3.42651	+	3.42651i	0.114664	+	0.114664i
$894$	−3.91865	+	1.35672i	−0.131059	+	0.0453755i
$895$	30.4721			1.01857
$896$	35.9725	−	34.3505i	1.20176	−	1.14757i
$897$	0.757894			0.0253053
$898$	4.23539	−	1.46638i	0.141337	−	0.0489339i
$899$	−37.9925	−	37.9925i	−1.26712	−	1.26712i
$900$	−42.4004	+	33.3585i	−1.41335	+	1.11195i
$901$	16.1674	−	16.1674i	0.538613	−	0.538613i
$902$	33.8544	+	16.4410i	1.12723	+	0.547426i
$903$		−	11.4938i		−	0.382490i
$904$	4.81704	−	7.50068i	0.160212	−	0.249469i
$905$		−	34.5618i		−	1.14887i
$906$	−2.31327	+	4.76335i	−0.0768533	+	0.158252i
$907$	−5.10934	+	5.10934i	−0.169653	+	0.169653i	−0.786827	−	0.617174i	$-0.788277\pi$
$907$	−5.10934	+	5.10934i	−0.169653	+	0.169653i	0.617174	+	0.786827i	$0.288277\pi$
$908$	10.1053	+	1.20608i	0.335357	+	0.0400250i
$909$	−1.08422	−	1.08422i	−0.0359613	−	0.0359613i
$910$	−18.1158	−	52.3244i	−0.600534	−	1.73454i
$911$	0.585347			0.0193934			0.00969670	−	0.999953i	$-0.496913\pi$
$911$	0.585347			0.0193934			0.00969670	+	0.999953i	$0.496913\pi$
$912$	−1.25117	−	0.302970i	−0.0414303	−	0.0100324i
$913$	9.42535			0.311933
$914$	−7.32742	−	21.1640i	−0.242369	−	0.700042i
$915$	8.58114	+	8.58114i	0.283684	+	0.283684i
$916$	0.176160	−	1.47599i	0.00582050	−	0.0487682i
$917$	31.3311	−	31.3311i	1.03464	−	1.03464i
$918$	−5.05168	+	10.4021i	−0.166730	+	0.343321i
$919$		−	26.1480i		−	0.862543i	−0.902222	−	0.431272i	$-0.858065\pi$
$919$		−	26.1480i		−	0.862543i	0.902222	−	0.431272i	$-0.141935\pi$
$920$	−10.4595	+	2.27879i	−0.344839	+	0.0751295i
$921$		−	5.27520i		−	0.173824i
$922$	5.31925	+	2.58324i	0.175180	+	0.0850744i
$923$	−4.95350	+	4.95350i	−0.163046	+	0.163046i
$924$	−5.01163	−	6.37004i	−0.164871	−	0.209559i
$925$	45.6455	+	45.6455i	1.50081	+	1.50081i
$926$	−51.2558	+	17.7459i	−1.68437	+	0.583165i
$927$	42.0405			1.38079
$928$	19.0045	−	23.0418i	0.623853	−	0.756385i
$929$	−9.37281			−0.307512			−0.153756	−	0.988109i	$-0.549137\pi$
$929$	−9.37281			−0.307512			−0.153756	+	0.988109i	$0.549137\pi$
$930$	16.5581	−	5.73276i	0.542960	−	0.187985i
$931$	8.71717	+	8.71717i	0.285694	+	0.285694i
$932$	28.0191	+	35.6137i	0.917797	+	1.16657i
$933$	−0.129603	+	0.129603i	−0.00424301	+	0.00424301i
$934$	−2.14317	−	1.04081i	−0.0701267	−	0.0340563i
$935$			46.6929i			1.52702i
$936$	4.10529	+	18.8430i	0.134186	+	0.615902i
$937$		−	40.6229i		−	1.32709i	−0.748135	−	0.663547i	$-0.769050\pi$
$937$		−	40.6229i		−	1.32709i	0.748135	−	0.663547i	$-0.230950\pi$
$938$	6.23213	−	12.8328i	0.203486	−	0.419007i
$939$	−3.08872	+	3.08872i	−0.100796	+	0.100796i
$940$	4.34529	−	36.4078i	0.141728	−	1.18749i
$941$	37.9630	+	37.9630i	1.23756	+	1.23756i	0.960996	+	0.276561i	$0.0891948\pi$
$941$	37.9630	+	37.9630i	1.23756	+	1.23756i	0.276561	+	0.960996i	$0.410805\pi$
$942$	0.984545	+	2.84368i	0.0320782	+	0.0926522i
$943$	−9.29476			−0.302679
$944$	9.98058	+	16.3586i	0.324840	+	0.532428i
$945$	31.5630			1.02674
$946$	10.7656	+	31.0946i	0.350020	+	1.01097i
$947$	31.1416	+	31.1416i	1.01196	+	1.01196i	0.999928	+	0.0120371i	$0.00383163\pi$
$947$	31.1416	+	31.1416i	1.01196	+	1.01196i	0.0120371	+	0.999928i	$0.496168\pi$
$948$	−3.35734	−	0.400701i	−0.109041	−	0.0130142i
$949$	−22.8120	+	22.8120i	−0.740509	+	0.740509i
$950$	5.75367	−	11.8476i	0.186674	−	0.384387i
$951$			0.342720i			0.0111134i
$952$	45.0842	+	28.9537i	1.46119	+	0.938394i
$953$			44.3858i			1.43780i	0.695115	+	0.718899i	$0.255353\pi$
$953$			44.3858i			1.43780i	−0.695115	+	0.718899i	$0.744647\pi$
$954$	19.5514	+	9.49494i	0.633000	+	0.307410i
$955$	−10.5970	+	10.5970i	−0.342912	+	0.342912i
$956$	−24.0405	+	18.9139i	−0.777525	+	0.611718i
$957$	−3.44156	−	3.44156i	−0.111250	−	0.111250i
$958$	−11.4905	+	3.97825i	−0.371241	+	0.128532i
$959$	57.5608			1.85873
$960$	4.05201	+	8.85782i	0.130778	+	0.285885i
$961$	72.5531			2.34042
$962$	21.8051	−	7.54940i	0.703025	−	0.243402i
$963$	−10.1790	−	10.1790i	−0.328015	−	0.328015i
$964$	23.3967	−	18.4074i	0.753557	−	0.592861i
$965$	−11.9462	+	11.9462i	−0.384561	+	0.384561i
$966$	1.80062	+	0.874452i	0.0579340	+	0.0281350i
$967$			21.6551i			0.696383i	0.937424	+	0.348191i	$0.113204\pi$
$967$			21.6551i			0.696383i	−0.937424	+	0.348191i	$0.886796\pi$
$968$	−6.65438	−	4.27353i	−0.213880	−	0.137356i
$969$		−	1.38676i		−	0.0445490i
$970$	11.2838	−	23.2349i	0.362300	−	0.746027i
$971$	11.7855	−	11.7855i	0.378215	−	0.378215i	−0.492243	−	0.870458i	$-0.663823\pi$
$971$	11.7855	−	11.7855i	0.378215	−	0.378215i	0.870458	+	0.492243i	$0.163823\pi$
$972$	−16.4689	−	1.96557i	−0.528241	−	0.0630458i
$973$	−44.9915	−	44.9915i	−1.44236	−	1.44236i
$974$	2.71717	+	7.84808i	0.0870638	+	0.251469i
$975$	7.05568			0.225963
$976$	−34.0337	+	20.7643i	−1.08939	+	0.664650i
$977$	22.8900			0.732315			0.366158	−	0.930553i	$-0.380673\pi$
$977$	22.8900			0.732315			0.366158	+	0.930553i	$0.380673\pi$
$978$	1.09180	+	3.15347i	0.0349119	+	0.100837i
$979$	−7.42444	−	7.42444i	−0.237286	−	0.237286i
$980$	11.0546	−	92.6226i	0.353125	−	2.95872i
$981$	29.3364	−	29.3364i	0.936640	−	0.936640i
$982$	20.9475	−	43.1339i	0.668462	−	1.37646i
$983$			36.6424i			1.16871i	0.811498	+	0.584355i	$0.198653\pi$
$983$			36.6424i			1.16871i	−0.811498	+	0.584355i	$0.801347\pi$
$984$	1.80040	+	8.26370i	0.0573946	+	0.263437i
$985$		−	73.1547i		−	2.33090i
$986$	28.9424	+	14.0556i	0.921715	+	0.447621i
$987$	−4.84813	+	4.84813i	−0.154318	+	0.154318i
$988$	−2.91111	−	3.70017i	−0.0926148	−	0.117718i
$989$	−5.74638	−	5.74638i	−0.182724	−	0.182724i
$990$	−41.9443	+	14.5220i	−1.33308	+	0.461540i
$991$	6.19048			0.196647			0.0983235	−	0.995155i	$-0.468652\pi$
$991$	6.19048			0.196647			0.0983235	+	0.995155i	$0.468652\pi$
$992$	5.50212	+	57.3012i	0.174693	+	1.81931i
$993$	−10.7376			−0.340749
$994$	−17.4839	+	6.05331i	−0.554556	+	0.191999i
$995$	19.7256	+	19.7256i	0.625344	+	0.625344i
$996$	1.30967	+	1.66466i	0.0414985	+	0.0527467i
$997$	6.76247	−	6.76247i	0.214169	−	0.214169i	−0.591867	−	0.806036i	$-0.701609\pi$
$997$	6.76247	−	6.76247i	0.214169	−	0.214169i	0.806036	+	0.591867i	$0.201609\pi$
$998$	17.3962	+	8.44828i	0.550667	+	0.267426i
$999$			13.1532i			0.416150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.4	✓	68
4.3	odd	2		1216.2.k.b.913.17		68
16.5	even	4	inner	304.2.k.b.229.4	yes	68
16.11	odd	4		1216.2.k.b.305.17		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.4	✓	68	1.1	even	1	trivial
304.2.k.b.229.4	yes	68	16.5	even	4	inner
1216.2.k.b.305.17		68	16.11	odd	4
1216.2.k.b.913.17		68	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.33638 + 0.462685i) q^{2} +(0.227569 + 0.227569i) q^{3} +(1.57185 - 1.23665i) q^{4} +(-2.67518 + 2.67518i) q^{5} +(-0.409413 - 0.198827i) q^{6} -4.39636i q^{7} +(-1.52841 + 2.37991i) q^{8} -2.89642i q^{9} +O(q^{10})\)	\(q+(-1.33638 + 0.462685i) q^{2} +(0.227569 + 0.227569i) q^{3} +(1.57185 - 1.23665i) q^{4} +(-2.67518 + 2.67518i) q^{5} +(-0.409413 - 0.198827i) q^{6} -4.39636i q^{7} +(-1.52841 + 2.37991i) q^{8} -2.89642i q^{9} +(2.33730 - 4.81283i) q^{10} +(2.02533 - 2.02533i) q^{11} +(0.639127 + 0.0762802i) q^{12} +(1.66455 + 1.66455i) q^{13} +(2.03413 + 5.87522i) q^{14} -1.21758 q^{15} +(0.941394 - 3.88764i) q^{16} +4.30895 q^{17} +(1.34013 + 3.87074i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.896708 + 7.51323i) q^{20} +(1.00048 - 1.00048i) q^{21} +(-1.76953 + 3.64371i) q^{22} -1.00039i q^{23} +(-0.889413 + 0.193775i) q^{24} -9.31318i q^{25} +(-2.99464 - 1.45432i) q^{26} +(1.34185 - 1.34185i) q^{27} +(-5.43675 - 6.91039i) q^{28} +(-3.73350 - 3.73350i) q^{29} +(1.62715 - 0.563355i) q^{30} +10.1761 q^{31} +(0.540691 + 5.63095i) q^{32} +0.921807 q^{33} +(-5.75841 + 1.99369i) q^{34} +(11.7610 + 11.7610i) q^{35} +(-3.58186 - 4.55273i) q^{36} +(-4.90117 + 4.90117i) q^{37} +(1.27213 + 0.617799i) q^{38} +0.757602i q^{39} +(-2.27791 - 10.4555i) q^{40} -9.29118i q^{41} +(-0.874115 + 1.79992i) q^{42} +(5.74417 - 5.74417i) q^{43} +(0.678881 - 5.68813i) q^{44} +(7.74846 + 7.74846i) q^{45} +(0.462863 + 1.33690i) q^{46} -4.84582 q^{47} +(1.09894 - 0.670476i) q^{48} -12.3279 q^{49} +(4.30907 + 12.4460i) q^{50} +(0.980585 + 0.980585i) q^{51} +(4.67489 + 0.557950i) q^{52} +(3.75205 - 3.75205i) q^{53} +(-1.17237 + 2.41407i) q^{54} +10.8363i q^{55} +(10.4629 + 6.71943i) q^{56} -0.321832i q^{57} +(6.71682 + 3.26195i) q^{58} +(-3.38755 + 3.38755i) q^{59} +(-1.91384 + 1.50572i) q^{60} +(-7.04771 - 7.04771i) q^{61} +(-13.5992 + 4.70833i) q^{62} -12.7337 q^{63} +(-3.32793 - 7.27495i) q^{64} -8.90595 q^{65} +(-1.23189 + 0.426506i) q^{66} +(-1.62249 - 1.62249i) q^{67} +(6.77300 - 5.32866i) q^{68} +(0.227657 - 0.227657i) q^{69} +(-21.1589 - 10.2756i) q^{70} +2.97588i q^{71} +(6.89323 + 4.42692i) q^{72} +13.7046i q^{73} +(4.28215 - 8.81754i) q^{74} +(2.11939 - 2.11939i) q^{75} +(-1.98591 - 0.237019i) q^{76} +(-8.90408 - 8.90408i) q^{77} +(-0.350531 - 1.01245i) q^{78} -5.25301 q^{79} +(7.88175 + 12.9185i) q^{80} -8.07855 q^{81} +(4.29889 + 12.4166i) q^{82} +(2.32686 + 2.32686i) q^{83} +(0.335355 - 2.80983i) q^{84} +(-11.5272 + 11.5272i) q^{85} +(-5.01868 + 10.3342i) q^{86} -1.69926i q^{87} +(1.72457 + 7.91564i) q^{88} -3.66579i q^{89} +(-13.9400 - 6.76982i) q^{90} +(7.31796 - 7.31796i) q^{91} +(-1.23713 - 1.57245i) q^{92} +(2.31577 + 2.31577i) q^{93} +(6.47588 - 2.24209i) q^{94} +3.78328 q^{95} +(-1.15839 + 1.40448i) q^{96} +4.82769 q^{97} +(16.4749 - 5.70395i) q^{98} +(-5.86622 - 5.86622i) 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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