LMFDB - Embedded newform 804.2.j.a.499.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.18
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.278040 + 1.38661i) q^{2} -1.00000 q^{3} +(-1.84539 + 0.771067i) q^{4} +3.05041i q^{5} +(-0.278040 - 1.38661i) q^{6} +(-1.90650 + 3.30215i) q^{7} +(-1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.278040 + 1.38661i) q^{2} -1.00000 q^{3} +(-1.84539 + 0.771067i) q^{4} +3.05041i q^{5} +(-0.278040 - 1.38661i) q^{6} +(-1.90650 + 3.30215i) q^{7} +(-1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +(-4.22974 + 0.848137i) q^{10} +(-1.71453 + 2.96965i) q^{11} +(1.84539 - 0.771067i) q^{12} +(1.47575 - 0.852022i) q^{13} +(-5.10889 - 1.72544i) q^{14} -3.05041i q^{15} +(2.81091 - 2.84584i) q^{16} +(0.669958 + 1.16040i) q^{17} +(0.278040 + 1.38661i) q^{18} +(-1.55431 + 0.897384i) q^{19} +(-2.35207 - 5.62920i) q^{20} +(1.90650 - 3.30215i) q^{21} +(-4.59447 - 1.55171i) q^{22} +(4.68399 - 2.70430i) q^{23} +(1.58226 + 2.34445i) q^{24} -4.30502 q^{25} +(1.59174 + 1.80939i) q^{26} -1.00000 q^{27} +(0.972048 - 7.56379i) q^{28} +(0.926578 - 1.60488i) q^{29} +(4.22974 - 0.848137i) q^{30} +(-1.04111 + 1.80326i) q^{31} +(4.72762 + 3.10639i) q^{32} +(1.71453 - 2.96965i) q^{33} +(-1.42275 + 1.25161i) q^{34} +(-10.0729 - 5.81561i) q^{35} +(-1.84539 + 0.771067i) q^{36} +(-2.73181 - 4.73163i) q^{37} +(-1.67649 - 1.90572i) q^{38} +(-1.47575 + 0.852022i) q^{39} +(7.15154 - 4.82656i) q^{40} +(5.78819 + 3.34181i) q^{41} +(5.10889 + 1.72544i) q^{42} -10.2838 q^{43} +(0.874171 - 6.80218i) q^{44} +3.05041i q^{45} +(5.05215 + 5.74297i) q^{46} +(1.21783 + 0.703117i) q^{47} +(-2.81091 + 2.84584i) q^{48} +(-3.76948 - 6.52893i) q^{49} +(-1.19697 - 5.96940i) q^{50} +(-0.669958 - 1.16040i) q^{51} +(-2.06636 + 2.71021i) q^{52} +2.63461i q^{53} +(-0.278040 - 1.38661i) q^{54} +(-9.05867 - 5.23003i) q^{55} +(10.7583 - 0.755183i) q^{56} +(1.55431 - 0.897384i) q^{57} +(2.48297 + 0.838584i) q^{58} -9.62440i q^{59} +(2.35207 + 5.62920i) q^{60} +(5.08331 - 2.93485i) q^{61} +(-2.78989 - 0.942240i) q^{62} +(-1.90650 + 3.30215i) q^{63} +(-2.99289 + 7.41907i) q^{64} +(2.59902 + 4.50164i) q^{65} +(4.59447 + 1.55171i) q^{66} +(4.09995 + 7.08452i) q^{67} +(-2.13108 - 1.62481i) q^{68} +(-4.68399 + 2.70430i) q^{69} +(5.26332 - 15.5842i) q^{70} +(-10.4497 - 6.03316i) q^{71} +(-1.58226 - 2.34445i) q^{72} +(1.59216 + 2.75770i) q^{73} +(5.80139 - 5.10354i) q^{74} +4.30502 q^{75} +(2.17637 - 2.85450i) q^{76} +(-6.53750 - 11.3233i) q^{77} +(-1.59174 - 1.80939i) q^{78} +(-4.93575 + 8.54897i) q^{79} +(8.68098 + 8.57444i) q^{80} +1.00000 q^{81} +(-3.02445 + 8.95513i) q^{82} +(11.9041 - 6.87285i) q^{83} +(-0.972048 + 7.56379i) q^{84} +(-3.53970 + 2.04365i) q^{85} +(-2.85931 - 14.2597i) q^{86} +(-0.926578 + 1.60488i) q^{87} +(9.67504 - 0.679142i) q^{88} -2.62544 q^{89} +(-4.22974 + 0.848137i) q^{90} +6.49752i q^{91} +(-6.55857 + 8.60215i) q^{92} +(1.04111 - 1.80326i) q^{93} +(-0.636344 + 1.88416i) q^{94} +(-2.73739 - 4.74130i) q^{95} +(-4.72762 - 3.10639i) q^{96} +(-12.3915 + 7.15423i) q^{97} +(8.00503 - 7.04211i) q^{98} +(-1.71453 + 2.96965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.278040	+	1.38661i	0.196604	+	0.980483i
$2$	0.278040	+	1.38661i	0.196604	+	0.980483i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.84539	+	0.771067i	−0.922694	+	0.385534i
$5$			3.05041i			1.36419i	0.731265	+	0.682093i	$0.238930\pi$
$5$			3.05041i			1.36419i	−0.731265	+	0.682093i	$0.761070\pi$
$6$	−0.278040	−	1.38661i	−0.113509	−	0.566082i
$7$	−1.90650	+	3.30215i	−0.720589	+	1.24810i	0.240175	+	0.970730i	$0.422795\pi$
$7$	−1.90650	+	3.30215i	−0.720589	+	1.24810i	−0.960764	+	0.277367i	$0.910538\pi$
$8$	−1.58226	−	2.34445i	−0.559414	−	0.828888i
$9$	1.00000			0.333333
$10$	−4.22974	+	0.848137i	−1.33756	+	0.268204i
$11$	−1.71453	+	2.96965i	−0.516950	+	0.895384i	0.482856	+	0.875700i	$0.339600\pi$
$11$	−1.71453	+	2.96965i	−0.516950	+	0.895384i	−0.999806	+	0.0196845i	$0.993734\pi$
$12$	1.84539	−	0.771067i	0.532718	−	0.222588i
$13$	1.47575	−	0.852022i	0.409298	−	0.236308i	−0.281190	−	0.959652i	$-0.590729\pi$
$13$	1.47575	−	0.852022i	0.409298	−	0.236308i	0.690488	+	0.723344i	$0.257396\pi$
$14$	−5.10889	−	1.72544i	−1.36541	−	0.461145i
$15$		−	3.05041i		−	0.787613i
$16$	2.81091	−	2.84584i	0.702728	−	0.711459i
$17$	0.669958	+	1.16040i	0.162489	+	0.281439i	0.935761	−	0.352636i	$-0.114715\pi$
$17$	0.669958	+	1.16040i	0.162489	+	0.281439i	−0.773272	+	0.634075i	$0.781381\pi$
$18$	0.278040	+	1.38661i	0.0655346	+	0.326828i
$19$	−1.55431	+	0.897384i	−0.356584	+	0.205874i	−0.667581	−	0.744537i	$-0.732670\pi$
$19$	−1.55431	+	0.897384i	−0.356584	+	0.205874i	0.310997	+	0.950411i	$0.399337\pi$
$20$	−2.35207	−	5.62920i	−0.525940	−	1.25873i
$21$	1.90650	−	3.30215i	0.416032	−	0.720589i
$22$	−4.59447	−	1.55171i	−0.979544	−	0.330825i
$23$	4.68399	−	2.70430i	0.976679	−	0.563886i	0.0754128	−	0.997152i	$-0.475973\pi$
$23$	4.68399	−	2.70430i	0.976679	−	0.563886i	0.901266	+	0.433267i	$0.142639\pi$
$24$	1.58226	+	2.34445i	0.322978	+	0.478559i
$25$	−4.30502			−0.861005
$26$	1.59174	+	1.80939i	0.312166	+	0.354851i
$27$	−1.00000			−0.192450
$28$	0.972048	−	7.56379i	0.183700	−	1.42942i
$29$	0.926578	−	1.60488i	0.172061	−	0.298019i	−0.767079	−	0.641553i	$-0.778291\pi$
$29$	0.926578	−	1.60488i	0.172061	−	0.298019i	0.939140	+	0.343534i	$0.111624\pi$
$30$	4.22974	−	0.848137i	0.772242	−	0.154848i
$31$	−1.04111	+	1.80326i	−0.186989	+	0.323874i	−0.944245	−	0.329244i	$-0.893206\pi$
$31$	−1.04111	+	1.80326i	−0.186989	+	0.323874i	0.757256	+	0.653118i	$0.226540\pi$
$32$	4.72762	+	3.10639i	0.835732	+	0.549137i
$33$	1.71453	−	2.96965i	0.298461	−	0.516950i
$34$	−1.42275	+	1.25161i	−0.244000	+	0.214649i
$35$	−10.0729	−	5.81561i	−1.70264	−	0.983018i
$36$	−1.84539	+	0.771067i	−0.307565	+	0.128511i
$37$	−2.73181	−	4.73163i	−0.449106	−	0.777875i	0.549222	−	0.835677i	$-0.314924\pi$
$37$	−2.73181	−	4.73163i	−0.449106	−	0.777875i	−0.998328	+	0.0578015i	$0.981591\pi$
$38$	−1.67649	−	1.90572i	−0.271962	−	0.309149i
$39$	−1.47575	+	0.852022i	−0.236308	+	0.136433i
$40$	7.15154	−	4.82656i	1.13076	−	0.763146i
$41$	5.78819	+	3.34181i	0.903963	+	0.521903i	0.878484	−	0.477772i	$-0.158555\pi$
$41$	5.78819	+	3.34181i	0.903963	+	0.521903i	0.0254794	+	0.999675i	$0.491889\pi$
$42$	5.10889	+	1.72544i	0.788319	+	0.266242i
$43$	−10.2838			−1.56827			−0.784134	−	0.620592i	$-0.786893\pi$
$43$	−10.2838			−1.56827			−0.784134	+	0.620592i	$0.786893\pi$
$44$	0.874171	−	6.80218i	0.131786	−	1.02547i
$45$			3.05041i			0.454729i
$46$	5.05215	+	5.74297i	0.744899	+	0.846755i
$47$	1.21783	+	0.703117i	0.177639	+	0.102560i	0.586183	−	0.810179i	$-0.300630\pi$
$47$	1.21783	+	0.703117i	0.177639	+	0.102560i	−0.408544	+	0.912739i	$0.633963\pi$
$48$	−2.81091	+	2.84584i	−0.405720	+	0.410761i
$49$	−3.76948	−	6.52893i	−0.538497	−	0.932704i
$50$	−1.19697	−	5.96940i	−0.169277	−	0.844201i
$51$	−0.669958	−	1.16040i	−0.0938129	−	0.162489i
$52$	−2.06636	+	2.71021i	−0.286552	+	0.375839i
$53$			2.63461i			0.361892i	0.983493	+	0.180946i	$0.0579159\pi$
$53$			2.63461i			0.361892i	−0.983493	+	0.180946i	$0.942084\pi$
$54$	−0.278040	−	1.38661i	−0.0378364	−	0.188694i
$55$	−9.05867	−	5.23003i	−1.22147	−	0.705217i
$56$	10.7583	−	0.755183i	1.43764	−	0.100916i
$57$	1.55431	−	0.897384i	0.205874	−	0.118861i
$58$	2.48297	+	0.838584i	0.326030	+	0.110111i
$59$		−	9.62440i		−	1.25299i	−0.779425	−	0.626495i	$-0.784489\pi$
$59$		−	9.62440i		−	1.25299i	0.779425	−	0.626495i	$-0.215511\pi$
$60$	2.35207	+	5.62920i	0.303651	+	0.726726i
$61$	5.08331	−	2.93485i	0.650851	−	0.375769i	−0.137931	−	0.990442i	$-0.544045\pi$
$61$	5.08331	−	2.93485i	0.650851	−	0.375769i	0.788782	+	0.614673i	$0.210712\pi$
$62$	−2.78989	−	0.942240i	−0.354316	−	0.119665i
$63$	−1.90650	+	3.30215i	−0.240196	+	0.416032i
$64$	−2.99289	+	7.41907i	−0.374111	+	0.927384i
$65$	2.59902	+	4.50164i	0.322369	+	0.558359i
$66$	4.59447	+	1.55171i	0.565540	+	0.191002i
$67$	4.09995	+	7.08452i	0.500889	+	0.865512i
$67$	4.09995	+	7.08452i	0.500889	+	0.865512i
$68$	−2.13108	−	1.62481i	−0.258431	−	0.197037i
$69$	−4.68399	+	2.70430i	−0.563886	+	0.325560i
$70$	5.26332	−	15.5842i	0.629087	−	1.86267i
$71$	−10.4497	−	6.03316i	−1.24016	−	0.716005i	−0.271031	−	0.962571i	$-0.587365\pi$
$71$	−10.4497	−	6.03316i	−1.24016	−	0.716005i	−0.969126	+	0.246566i	$0.920698\pi$
$72$	−1.58226	−	2.34445i	−0.186471	−	0.276296i
$73$	1.59216	+	2.75770i	0.186348	+	0.322764i	0.944030	−	0.329860i	$-0.107002\pi$
$73$	1.59216	+	2.75770i	0.186348	+	0.322764i	−0.757682	+	0.652624i	$0.773668\pi$
$74$	5.80139	−	5.10354i	0.674397	−	0.593275i
$75$	4.30502			0.497101
$76$	2.17637	−	2.85450i	0.249647	−	0.327434i
$77$	−6.53750	−	11.3233i	−0.745018	−	1.29041i
$78$	−1.59174	−	1.80939i	−0.180229	−	0.204873i
$79$	−4.93575	+	8.54897i	−0.555315	+	0.961835i	0.442563	+	0.896737i	$0.354069\pi$
$79$	−4.93575	+	8.54897i	−0.555315	+	0.961835i	−0.997879	+	0.0650974i	$0.979264\pi$
$80$	8.68098	+	8.57444i	0.970563	+	0.958652i
$81$	1.00000			0.111111
$82$	−3.02445	+	8.95513i	−0.333995	+	0.988929i
$83$	11.9041	−	6.87285i	1.30665	−	0.754393i	0.325112	−	0.945676i	$-0.394598\pi$
$83$	11.9041	−	6.87285i	1.30665	−	0.754393i	0.981535	+	0.191283i	$0.0612647\pi$
$84$	−0.972048	+	7.56379i	−0.106059	+	0.825277i
$85$	−3.53970	+	2.04365i	−0.383935	+	0.221665i
$86$	−2.85931	−	14.2597i	−0.308328	−	1.53766i
$87$	−0.926578	+	1.60488i	−0.0993396	+	0.172061i
$88$	9.67504	−	0.679142i	1.03136	−	0.0723968i
$89$	−2.62544			−0.278296			−0.139148	−	0.990272i	$-0.544436\pi$
$89$	−2.62544			−0.278296			−0.139148	+	0.990272i	$0.544436\pi$
$90$	−4.22974	+	0.848137i	−0.445854	+	0.0894015i
$91$			6.49752i			0.681125i
$92$	−6.55857	+	8.60215i	−0.683778	+	0.896836i
$93$	1.04111	−	1.80326i	0.107958	−	0.186989i
$94$	−0.636344	+	1.88416i	−0.0656339	+	0.194336i
$95$	−2.73739	−	4.74130i	−0.280851	−	0.486447i
$96$	−4.72762	−	3.10639i	−0.482510	−	0.317044i
$97$	−12.3915	+	7.15423i	−1.25817	+	0.726402i	−0.972718	−	0.231992i	$-0.925476\pi$
$97$	−12.3915	+	7.15423i	−1.25817	+	0.726402i	−0.285448	+	0.958394i	$0.592142\pi$
$98$	8.00503	−	7.04211i	0.808630	−	0.711360i
$99$	−1.71453	+	2.96965i	−0.172317	+	0.298461i
$100$	7.94444	−	3.31946i	0.794444	−	0.331946i
$101$	−11.7399	−	6.77804i	−1.16816	−	0.674440i	−0.214917	−	0.976632i	$-0.568948\pi$
$101$	−11.7399	−	6.77804i	−1.16816	−	0.674440i	−0.953247	+	0.302192i	$0.902282\pi$
$102$	1.42275	−	1.25161i	0.140873	−	0.123928i
$103$	8.83844	+	5.10287i	0.870877	+	0.502801i	0.867640	−	0.497194i	$-0.165636\pi$
$103$	8.83844	+	5.10287i	0.870877	+	0.502801i	0.00323750	+	0.999995i	$0.498969\pi$
$104$	−4.33254	−	2.11169i	−0.424841	−	0.207068i
$105$	10.0729	+	5.81561i	0.983018	+	0.567546i
$106$	−3.65318	+	0.732527i	−0.354829	+	0.0711493i
$107$			5.18115i			0.500881i	0.968132	+	0.250441i	$0.0805755\pi$
$107$			5.18115i			0.500881i	−0.968132	+	0.250441i	$0.919425\pi$
$108$	1.84539	−	0.771067i	0.177573	−	0.0741960i
$109$			15.1608i			1.45215i	0.687618	+	0.726073i	$0.258657\pi$
$109$			15.1608i			1.45215i	−0.687618	+	0.726073i	$0.741343\pi$
$110$	4.73335	−	14.0150i	0.451307	−	1.33628i
$111$	2.73181	+	4.73163i	0.259292	+	0.449106i
$112$	4.03839	+	14.7076i	0.381592	+	1.38974i
$113$	15.5947	+	9.00363i	1.46703	+	0.846990i	0.999319	−	0.0368913i	$-0.0117455\pi$
$113$	15.5947	+	9.00363i	1.46703	+	0.846990i	0.467711	+	0.883882i	$0.345079\pi$
$114$	1.67649	+	1.90572i	0.157017	+	0.178487i
$115$	8.24923	+	14.2881i	0.769245	+	1.33237i
$116$	−0.472425	+	3.67608i	−0.0438636	+	0.341316i
$117$	1.47575	−	0.852022i	0.136433	−	0.0787695i
$118$	13.3453	−	2.67597i	1.22854	−	0.246343i
$119$	−5.10910			−0.468350
$120$	−7.15154	+	4.82656i	−0.652843	+	0.440602i
$121$	−0.379231	−	0.656847i	−0.0344755	−	0.0597133i
$122$	5.48286	+	6.23257i	0.496395	+	0.564271i
$123$	−5.78819	−	3.34181i	−0.521903	−	0.301321i
$124$	0.530821	−	4.13047i	0.0476691	−	0.370928i
$125$			2.11996i			0.189615i
$126$	−5.10889	−	1.72544i	−0.455136	−	0.153715i
$127$	−14.4999	−	8.37151i	−1.28666	−	0.742851i	−0.308600	−	0.951192i	$-0.599860\pi$
$127$	−14.4999	−	8.37151i	−1.28666	−	0.742851i	−0.978056	+	0.208340i	$0.933194\pi$
$128$	−11.1195	−	2.08718i	−0.982836	−	0.184482i
$129$	10.2838			0.905440
$130$	−5.51939	+	4.85547i	−0.484083	+	0.425853i
$131$			10.9676i			0.958241i	0.877749	+	0.479120i	$0.159044\pi$
$131$			10.9676i			0.958241i	−0.877749	+	0.479120i	$0.840956\pi$
$132$	−0.874171	+	6.80218i	−0.0760868	+	0.592054i
$133$		−	6.84345i		−	0.593402i
$134$	−8.68353	+	7.65482i	−0.750143	+	0.661276i
$135$		−	3.05041i		−	0.262538i
$136$	1.66045	−	3.40674i	0.142383	−	0.292126i
$137$			0.0295386i			0.00252365i	0.999999	+	0.00126183i	$0.000401652\pi$
$137$			0.0295386i			0.00252365i	−0.999999	+	0.00126183i	$0.999598\pi$
$138$	−5.05215	−	5.74297i	−0.430068	−	0.488874i
$139$	−9.42510			−0.799427			−0.399713	−	0.916640i	$-0.630890\pi$
$139$	−9.42510			−0.799427			−0.399713	+	0.916640i	$0.630890\pi$
$140$	23.0727	+	2.96515i	1.95000	+	0.250601i
$141$	−1.21783	−	0.703117i	−0.102560	−	0.0592131i
$142$	5.46021	−	16.1672i	0.458211	−	1.35672i
$143$			5.84327i			0.488639i
$144$	2.81091	−	2.84584i	0.234243	−	0.237153i
$145$	4.89555	+	2.82645i	0.406553	+	0.234724i
$146$	−3.38117	+	2.97445i	−0.279828	+	0.246168i
$147$	3.76948	+	6.52893i	0.310901	+	0.538497i
$148$	8.68965	+	6.62528i	0.714285	+	0.544595i
$149$	0.963142			0.0789037			0.0394518	−	0.999221i	$-0.487439\pi$
$149$	0.963142			0.0789037			0.0394518	+	0.999221i	$0.487439\pi$
$150$	1.19697	+	5.96940i	0.0977321	+	0.487399i
$151$	16.7349	−	9.66190i	1.36187	−	0.786274i	0.371994	−	0.928235i	$-0.378674\pi$
$151$	16.7349	−	9.66190i	1.36187	−	0.786274i	0.989872	+	0.141961i	$0.0453408\pi$
$152$	4.56321	+	2.22412i	0.370125	+	0.180400i
$153$	0.669958	+	1.16040i	0.0541629	+	0.0938129i
$154$	13.8833	−	12.2133i	1.11875	−	0.984176i
$155$	−5.50068	−	3.17582i	−0.441825	−	0.255088i
$156$	2.06636	−	2.71021i	0.165441	−	0.216991i
$157$	−4.70405	−	8.14765i	−0.375424	−	0.650253i	0.614967	−	0.788553i	$-0.289169\pi$
$157$	−4.70405	−	8.14765i	−0.375424	−	0.650253i	−0.990390	+	0.138300i	$0.955836\pi$
$158$	−13.2264	−	4.46702i	−1.05224	−	0.355377i
$159$		−	2.63461i		−	0.208938i
$160$	−9.47577	+	14.4212i	−0.749125	+	1.14009i
$161$			20.6230i			1.62532i
$162$	0.278040	+	1.38661i	0.0218449	+	0.108943i
$163$	11.5865	+	6.68947i	0.907525	+	0.523960i	0.879634	−	0.475651i	$-0.157787\pi$
$163$	11.5865	+	6.68947i	0.907525	+	0.523960i	0.0278913	+	0.999611i	$0.491121\pi$
$164$	−13.2582	−	1.70386i	−1.03529	−	0.133049i
$165$	9.05867	+	5.23003i	0.705217	+	0.407157i
$166$	12.8398	+	14.5955i	0.996561	+	1.13283i
$167$	20.3646	+	11.7575i	1.57586	+	0.909822i	0.995428	+	0.0955127i	$0.0304490\pi$
$167$	20.3646	+	11.7575i	1.57586	+	0.909822i	0.580431	+	0.814310i	$0.302884\pi$
$168$	−10.7583	+	0.755183i	−0.830022	+	0.0582636i
$169$	−5.04812	+	8.74359i	−0.388317	+	0.672584i
$170$	−3.81793	−	4.33998i	−0.292822	−	0.332861i
$171$	−1.55431	+	0.897384i	−0.118861	+	0.0686247i
$172$	18.9776	−	7.92952i	1.44703	−	0.604620i
$173$	−11.2095	−	19.4154i	−0.852239	−	1.47612i	−0.879183	−	0.476485i	$-0.841911\pi$
$173$	−11.2095	−	19.4154i	−0.852239	−	1.47612i	0.0269430	−	0.999637i	$-0.491423\pi$
$174$	−2.48297	−	0.838584i	−0.188234	−	0.0635729i
$175$	8.20752	−	14.2159i	0.620431	−	1.07462i
$176$	3.63176	+	13.2267i	0.273754	+	0.997000i
$177$			9.62440i			0.723414i
$178$	−0.729976	−	3.64046i	−0.0547140	−	0.272864i
$179$	−3.10081			−0.231766			−0.115883	−	0.993263i	$-0.536970\pi$
$179$	−3.10081			−0.231766			−0.115883	+	0.993263i	$0.536970\pi$
$180$	−2.35207	−	5.62920i	−0.175313	−	0.419575i
$181$	−13.2249	+	22.9062i	−0.982997	+	1.70260i	−0.332479	+	0.943111i	$0.607885\pi$
$181$	−13.2249	+	22.9062i	−0.982997	+	1.70260i	−0.650518	+	0.759491i	$0.725448\pi$
$182$	−9.00954	+	1.80657i	−0.667832	+	0.133912i
$183$	−5.08331	+	2.93485i	−0.375769	+	0.216950i
$184$	−13.7514	−	6.70246i	−1.01377	−	0.494112i
$185$	14.4334	−	8.33314i	1.06117	−	0.612665i
$186$	2.78989	+	0.942240i	0.204565	+	0.0690884i
$187$	−4.59465			−0.335994
$188$	−2.78953	−	0.358491i	−0.203447	−	0.0261457i
$189$	1.90650	−	3.30215i	0.138677	−	0.240196i
$190$	5.81324	−	5.11397i	0.421737	−	0.371007i
$191$	2.21515	+	3.83674i	0.160282	+	0.277617i	0.934970	−	0.354727i	$-0.115426\pi$
$191$	2.21515	+	3.83674i	0.160282	+	0.277617i	−0.774688	+	0.632344i	$0.782093\pi$
$192$	2.99289	−	7.41907i	0.215993	−	0.535425i
$193$	11.0688			0.796753			0.398377	−	0.917222i	$-0.369574\pi$
$193$	11.0688			0.796753			0.398377	+	0.917222i	$0.369574\pi$
$194$	−13.3655	−	15.1930i	−0.959586	−	1.09080i
$195$	−2.59902	−	4.50164i	−0.186120	−	0.322369i
$196$	11.9904	+	9.14188i	0.856456	+	0.652991i
$197$	−23.7894	−	13.7348i	−1.69493	−	0.978565i	−0.950431	−	0.310937i	$-0.899357\pi$
$197$	−23.7894	−	13.7348i	−1.69493	−	0.978565i	−0.744495	−	0.667628i	$-0.767309\pi$
$198$	−4.59447	−	1.55171i	−0.326515	−	0.110275i
$199$	−7.11906	+	4.11019i	−0.504657	+	0.291364i	−0.730635	−	0.682769i	$-0.760776\pi$
$199$	−7.11906	+	4.11019i	−0.504657	+	0.291364i	0.225978	+	0.974133i	$0.427442\pi$
$200$	6.81168	+	10.0929i	0.481658	+	0.713677i
$201$	−4.09995	−	7.08452i	−0.289188	−	0.499703i
$202$	6.13435	−	18.1633i	0.431611	−	1.27796i
$203$	3.53304	+	6.11941i	0.247971	+	0.429498i
$204$	2.13108	+	1.62481i	0.149205	+	0.113759i
$205$	−10.1939	+	17.6564i	−0.711974	+	1.23317i
$206$	−4.61827	+	13.6743i	−0.321770	+	0.952733i
$207$	4.68399	−	2.70430i	0.325560	−	0.187962i
$208$	1.72347	−	6.59469i	0.119501	−	0.457259i
$209$		−	6.15437i		−	0.425707i
$210$	−5.26332	+	15.5842i	−0.363204	+	1.07541i
$211$	−13.7604	+	7.94455i	−0.947302	+	0.546925i	−0.892242	−	0.451558i	$-0.850868\pi$
$211$	−13.7604	+	7.94455i	−0.947302	+	0.546925i	−0.0550604	+	0.998483i	$0.517535\pi$
$212$	−2.03146	−	4.86188i	−0.139521	−	0.333915i
$213$	10.4497	+	6.03316i	0.716005	+	0.413386i
$214$	−7.18425	+	1.44057i	−0.491105	+	0.0984752i
$215$		−	31.3699i		−	2.13941i
$216$	1.58226	+	2.34445i	0.107659	+	0.159520i
$217$	−3.96975	−	6.87582i	−0.269484	−	0.466761i
$218$	−21.0222	+	4.21532i	−1.42380	+	0.285498i
$219$	−1.59216	−	2.75770i	−0.107588	−	0.186348i
$220$	20.7495	+	2.66658i	1.39893	+	0.179781i
$221$	1.97738	+	1.14164i	0.133013	+	0.0767949i
$222$	−5.80139	+	5.10354i	−0.389363	+	0.342527i
$223$		−	20.1734i		−	1.35091i	−0.737402	−	0.675454i	$-0.763948\pi$
$223$		−	20.1734i		−	1.35091i	0.737402	−	0.675454i	$-0.236052\pi$
$224$	−19.2710	+	9.68899i	−1.28760	+	0.647373i
$225$	−4.30502			−0.287002
$226$	−8.14858	+	24.1272i	−0.542036	+	1.60492i
$227$	11.9488	+	6.89864i	0.793069	+	0.457879i	0.841042	−	0.540970i	$-0.181943\pi$
$227$	11.9488	+	6.89864i	0.793069	+	0.457879i	−0.0479727	+	0.998849i	$0.515276\pi$
$228$	−2.17637	+	2.85450i	−0.144134	+	0.189044i
$229$	−19.9089	+	11.4944i	−1.31562	+	0.759572i	−0.983020	−	0.183497i	$-0.941258\pi$
$229$	−19.9089	+	11.4944i	−1.31562	+	0.759572i	−0.332597	+	0.943069i	$0.607925\pi$
$230$	−17.5184	+	15.4112i	−1.15513	+	1.01618i
$231$	6.53750	+	11.3233i	0.430136	+	0.745018i
$232$	−5.22865	+	0.367027i	−0.343278	+	0.0240965i
$233$	−11.8039	−	6.81500i	−0.773301	−	0.446466i	0.0607498	−	0.998153i	$-0.480651\pi$
$233$	−11.8039	−	6.81500i	−0.773301	−	0.446466i	−0.834051	+	0.551687i	$0.813984\pi$
$234$	1.59174	+	1.80939i	0.104055	+	0.118284i
$235$	−2.14480	+	3.71490i	−0.139911	+	0.242333i
$236$	7.42106	+	17.7607i	0.483070	+	1.15613i
$237$	4.93575	−	8.54897i	0.320612	−	0.555315i
$238$	−1.42053	−	7.08434i	−0.0920795	−	0.459209i
$239$	3.59665	−	6.22958i	0.232648	−	0.402958i	−0.725938	−	0.687760i	$-0.758594\pi$
$239$	3.59665	−	6.22958i	0.232648	−	0.402958i	0.958587	+	0.284801i	$0.0919276\pi$
$240$	−8.68098	−	8.57444i	−0.560355	−	0.553478i
$241$	−2.11223			−0.136061			−0.0680304	−	0.997683i	$-0.521671\pi$
$241$	−2.11223			−0.136061			−0.0680304	+	0.997683i	$0.521671\pi$
$242$	0.805350	−	0.708475i	0.0517699	−	0.0455425i
$243$	−1.00000			−0.0641500
$244$	−7.11771	+	9.33551i	−0.455665	+	0.597645i
$245$	19.9159	−	11.4985i	1.27238	−	0.734610i
$246$	3.02445	−	8.95513i	0.192832	−	0.570958i
$247$	−1.52918	+	2.64862i	−0.0972995	+	0.168528i
$248$	5.87496	−	0.412394i	0.373060	−	0.0261871i
$249$	−11.9041	+	6.87285i	−0.754393	+	0.435549i
$250$	−2.93957	+	0.589435i	−0.185915	+	0.0372791i
$251$	−4.93278	−	8.54383i	−0.311355	−	0.539282i	0.667301	−	0.744788i	$-0.267449\pi$
$251$	−4.93278	−	8.54383i	−0.311355	−	0.539282i	−0.978656	+	0.205506i	$0.934116\pi$
$252$	0.972048	−	7.56379i	0.0612333	−	0.476474i
$253$			18.5464i			1.16600i
$254$	7.57649	−	22.4333i	0.475391	−	1.40759i
$255$	3.53970	−	2.04365i	0.221665	−	0.127978i
$256$	−0.197562	−	15.9988i	−0.0123476	−	0.999924i
$257$	0.903181	−	1.56436i	0.0563389	−	0.0975818i	−0.836480	−	0.547997i	$-0.815391\pi$
$257$	0.903181	−	1.56436i	0.0563389	−	0.0975818i	0.892819	+	0.450415i	$0.148724\pi$
$258$	2.85931	+	14.2597i	0.178013	+	0.887768i
$259$	20.8328			1.29448
$260$	−8.26726	−	6.30324i	−0.512714	−	0.390911i
$261$	0.926578	−	1.60488i	0.0573538	−	0.0993396i
$262$	−15.2078	+	3.04942i	−0.939539	+	0.188394i
$263$			16.6218i			1.02495i	0.858703	+	0.512473i	$0.171270\pi$
$263$			16.6218i			1.02495i	−0.858703	+	0.512473i	$0.828730\pi$
$264$	−9.67504	+	0.679142i	−0.595458	+	0.0417983i
$265$	−8.03665			−0.493688
$266$	9.48921	−	1.90275i	0.581821	−	0.116665i
$267$	2.62544			0.160674
$268$	−13.0286	−	9.91234i	−0.795851	−	0.605493i
$269$	−11.3463			−0.691799			−0.345899	−	0.938272i	$-0.612426\pi$
$269$	−11.3463			−0.691799			−0.345899	+	0.938272i	$0.612426\pi$
$270$	4.22974	−	0.848137i	0.257414	−	0.0516160i
$271$	0.663016			0.0402753			0.0201377	−	0.999797i	$-0.493590\pi$
$271$	0.663016			0.0402753			0.0201377	+	0.999797i	$0.493590\pi$
$272$	5.18550	+	1.35519i	0.314417	+	0.0821707i
$273$		−	6.49752i		−	0.393248i
$274$	−0.0409586	+	0.00821290i	−0.00247440	+	0.000496160i
$275$	7.38110	−	12.7844i	0.445097	−	0.770930i
$276$	6.55857	−	8.60215i	0.394780	−	0.517789i
$277$	−6.08139			−0.365396			−0.182698	−	0.983169i	$-0.558483\pi$
$277$	−6.08139			−0.365396			−0.182698	+	0.983169i	$0.558483\pi$
$278$	−2.62056	−	13.0690i	−0.157170	−	0.783824i
$279$	−1.04111	+	1.80326i	−0.0623297	+	0.107958i
$280$	2.30362	+	32.8173i	0.137668	+	1.96121i
$281$	22.3068	−	12.8789i	1.33071	−	0.768288i	0.345305	−	0.938490i	$-0.387775\pi$
$281$	22.3068	−	12.8789i	1.33071	−	0.768288i	0.985409	+	0.170202i	$0.0544420\pi$
$282$	0.636344	−	1.88416i	0.0378937	−	0.112200i
$283$		−	16.9654i		−	1.00849i	−0.863561	−	0.504244i	$-0.831771\pi$
$283$		−	16.9654i		−	1.00849i	0.863561	−	0.504244i	$-0.168229\pi$
$284$	23.9358	+	3.07607i	1.42033	+	0.182531i
$285$	2.73739	+	4.74130i	0.162149	+	0.280851i
$286$	−8.10236	+	1.62466i	−0.479102	+	0.0960684i
$287$	−22.0704	+	12.7423i	−1.30277	+	0.752156i
$288$	4.72762	+	3.10639i	0.278577	+	0.183046i
$289$	7.60231	−	13.1676i	0.447195	−	0.774564i
$290$	−2.55803	+	7.57410i	−0.150213	+	0.444766i
$291$	12.3915	−	7.15423i	0.726402	−	0.419389i
$292$	−5.06452	−	3.86136i	−0.296378	−	0.225969i
$293$	5.39347			0.315090			0.157545	−	0.987512i	$-0.449642\pi$
$293$	5.39347			0.315090			0.157545	+	0.987512i	$0.449642\pi$
$294$	−8.00503	+	7.04211i	−0.466863	+	0.410704i
$295$	29.3584			1.70931
$296$	−6.77063	+	13.8913i	−0.393535	+	0.807414i
$297$	1.71453	−	2.96965i	0.0994872	−	0.172317i
$298$	0.267792	+	1.33550i	0.0155128	+	0.0773637i
$299$	4.60825	−	7.98172i	0.266502	−	0.461595i
$300$	−7.94444	+	3.31946i	−0.458672	+	0.191649i
$301$	19.6061	−	33.9588i	1.13008	−	1.95735i
$302$	18.0503	+	20.5184i	1.03868	+	1.18070i
$303$	11.7399	+	6.77804i	0.674440	+	0.389388i
$304$	−1.81523	+	6.94579i	−0.104111	+	0.398368i
$305$	8.95251	+	15.5062i	0.512619	+	0.887882i
$306$	−1.42275	+	1.25161i	−0.0813333	+	0.0715498i
$307$	7.63838	−	4.41002i	0.435945	−	0.251693i	−0.265931	−	0.963992i	$-0.585679\pi$
$307$	7.63838	−	4.41002i	0.435945	−	0.251693i	0.701876	+	0.712299i	$0.252346\pi$
$308$	20.7952	+	15.8550i	1.18492	+	0.903422i
$309$	−8.83844	−	5.10287i	−0.502801	−	0.290292i
$310$	2.87422	−	8.51031i	0.163245	−	0.483353i
$311$	9.77865			0.554497			0.277248	−	0.960798i	$-0.410578\pi$
$311$	9.77865			0.554497			0.277248	+	0.960798i	$0.410578\pi$
$312$	4.33254	+	2.11169i	0.245282	+	0.119551i
$313$			0.848936i			0.0479847i	0.999712	+	0.0239923i	$0.00763773\pi$
$313$			0.848936i			0.0479847i	−0.999712	+	0.0239923i	$0.992362\pi$
$314$	9.98972	−	8.78806i	0.563752	−	0.495939i
$315$	−10.0729	−	5.81561i	−0.567546	−	0.327673i
$316$	2.51654	−	19.5820i	0.141567	−	1.10157i
$317$	5.74790	+	9.95565i	0.322834	+	0.559165i	0.981072	−	0.193645i	$-0.0620310\pi$
$317$	5.74790	+	9.95565i	0.322834	+	0.559165i	−0.658237	+	0.752810i	$0.728698\pi$
$318$	3.65318	−	0.732527i	0.204860	−	0.0410781i
$319$	3.17729	+	5.50324i	0.177894	+	0.308122i
$320$	−22.6312	−	9.12955i	−1.26512	−	0.510357i
$321$		−	5.18115i		−	0.289184i
$322$	−28.5961	+	5.73401i	−1.59360	+	0.319544i
$323$	−2.08265	−	1.20242i	−0.115882	−	0.0669044i
$324$	−1.84539	+	0.771067i	−0.102522	+	0.0428371i
$325$	−6.35312	+	3.66798i	−0.352408	+	0.203463i
$326$	−6.05420	+	17.9259i	−0.335311	+	0.992826i
$327$		−	15.1608i		−	0.838397i
$328$	−1.32372	−	18.8577i	−0.0730905	−	1.04124i
$329$	−4.64360	+	2.68098i	−0.256010	+	0.147807i
$330$	−4.73335	+	14.0150i	−0.260562	+	0.771502i
$331$	−16.0007	+	27.7140i	−0.879478	+	1.52330i	−0.0275625	+	0.999620i	$0.508775\pi$
$331$	−16.0007	+	27.7140i	−0.879478	+	1.52330i	−0.851915	+	0.523680i	$0.824559\pi$
$332$	−16.6683	+	21.8619i	−0.914791	+	1.19983i
$333$	−2.73181	−	4.73163i	−0.149702	−	0.259292i
$334$	−10.6409	+	31.5068i	−0.582245	+	1.72398i
$335$	−21.6107	+	12.5065i	−1.18072	+	0.683306i
$336$	−4.03839	−	14.7076i	−0.220312	−	0.802368i
$337$	5.50941	−	3.18086i	0.300117	−	0.173273i	−0.342378	−	0.939562i	$-0.611233\pi$
$337$	5.50941	−	3.18086i	0.300117	−	0.173273i	0.642495	+	0.766290i	$0.277899\pi$
$338$	−13.5276	−	4.56871i	−0.735802	−	0.248505i
$339$	−15.5947	−	9.00363i	−0.846990	−	0.489010i
$340$	4.95634	−	6.50067i	0.268795	−	0.352549i
$341$	−3.57003	−	6.18348i	−0.193328	−	0.334854i
$342$	−1.67649	−	1.90572i	−0.0906539	−	0.103050i
$343$	2.05504			0.110962
$344$	16.2717	+	24.1099i	0.877312	+	1.29992i
$345$	−8.24923	−	14.2881i	−0.444124	−	0.769245i
$346$	23.8049	−	20.9414i	1.27976	−	1.12582i
$347$	6.46555	−	11.1987i	0.347089	−	0.601176i	−0.638642	−	0.769504i	$-0.720503\pi$
$347$	6.46555	−	11.1987i	0.347089	−	0.601176i	0.985731	+	0.168328i	$0.0538368\pi$
$348$	0.472425	−	3.67608i	0.0253247	−	0.197059i
$349$	−8.74340			−0.468024			−0.234012	−	0.972234i	$-0.575185\pi$
$349$	−8.74340			−0.468024			−0.234012	+	0.972234i	$0.575185\pi$
$350$	21.9939	+	7.42808i	1.17562	+	0.397048i
$351$	−1.47575	+	0.852022i	−0.0787695	+	0.0454776i
$352$	−17.3305	+	8.71339i	−0.923721	+	0.464425i
$353$	23.3107	−	13.4585i	1.24071	−	0.716322i	0.271468	−	0.962448i	$-0.412491\pi$
$353$	23.3107	−	13.4585i	1.24071	−	0.716322i	0.969238	+	0.246126i	$0.0791576\pi$
$354$	−13.3453	+	2.67597i	−0.709295	+	0.142226i
$355$	18.4036	−	31.8761i	0.976764	−	1.69181i
$356$	4.84495	−	2.02439i	0.256782	−	0.107292i
$357$	5.10910			0.270402
$358$	−0.862150	−	4.29963i	−0.0455661	−	0.227242i
$359$		−	18.8160i		−	0.993071i	−0.868016	−	0.496535i	$-0.834605\pi$
$359$		−	18.8160i		−	0.993071i	0.868016	−	0.496535i	$-0.165395\pi$
$360$	7.15154	−	4.82656i	0.376919	−	0.254382i
$361$	−7.88940	+	13.6648i	−0.415232	+	0.719203i
$362$	−35.4390	−	11.9689i	−1.86263	−	0.629074i
$363$	0.379231	+	0.656847i	0.0199044	+	0.0344755i
$364$	−5.01002	−	11.9904i	−0.262597	−	0.628470i
$365$	−8.41212	+	4.85674i	−0.440310	+	0.254213i
$366$	−5.48286	−	6.23257i	−0.286594	−	0.325782i
$367$	10.3476	−	17.9226i	0.540140	−	0.935551i	−0.458755	−	0.888563i	$-0.651704\pi$
$367$	10.3476	−	17.9226i	0.540140	−	0.935551i	0.998895	−	0.0469878i	$-0.0149622\pi$
$368$	5.47027	−	20.9314i	0.285158	−	1.09112i
$369$	5.78819	+	3.34181i	0.301321	+	0.173968i
$370$	15.5679	+	17.6966i	0.809337	+	0.920004i
$371$	−8.69989	−	5.02288i	−0.451676	−	0.260775i
$372$	−0.530821	+	4.13047i	−0.0275218	+	0.214155i
$373$	−14.0000	−	8.08289i	−0.724891	−	0.418516i	0.0916590	−	0.995790i	$-0.470783\pi$
$373$	−14.0000	−	8.08289i	−0.724891	−	0.418516i	−0.816550	+	0.577274i	$0.804116\pi$
$374$	−1.27750	−	6.37100i	−0.0660578	−	0.329437i
$375$		−	2.11996i		−	0.109474i
$376$	−0.278511	−	3.96767i	−0.0143631	−	0.204617i
$377$		−	3.15786i		−	0.162638i
$378$	5.10889	+	1.72544i	0.262773	+	0.0887473i
$379$	5.70277	+	9.87748i	0.292931	+	0.507372i	0.974502	−	0.224381i	$-0.0720359\pi$
$379$	5.70277	+	9.87748i	0.292931	+	0.507372i	−0.681570	+	0.731753i	$0.738703\pi$
$380$	8.70741	+	6.63883i	0.446681	+	0.340565i
$381$	14.4999	+	8.37151i	0.742851	+	0.428885i
$382$	−4.70418	+	4.13832i	−0.240687	+	0.211735i
$383$	13.9838	+	24.2206i	0.714538	+	1.23762i	0.963137	+	0.269010i	$0.0866963\pi$
$383$	13.9838	+	24.2206i	0.714538	+	1.23762i	−0.248600	+	0.968606i	$0.579970\pi$
$384$	11.1195	+	2.08718i	0.567441	+	0.106511i
$385$	34.5407	−	19.9421i	1.76036	−	1.01634i
$386$	3.07758	+	15.3482i	0.156645	+	0.781203i
$387$	−10.2838			−0.522756
$388$	17.3507	−	22.7570i	0.880849	−	1.15531i
$389$	14.4378	+	25.0069i	0.732024	+	1.26790i	0.956017	+	0.293311i	$0.0947572\pi$
$389$	14.4378	+	25.0069i	0.732024	+	1.26790i	−0.223993	+	0.974591i	$0.571909\pi$
$390$	5.51939	−	4.85547i	0.279485	−	0.245866i
$391$	6.27615	+	3.62354i	0.317398	+	0.183250i
$392$	−9.34244	+	19.1678i	−0.471864	+	0.968122i
$393$		−	10.9676i		−	0.553241i
$394$	12.4305	−	36.8055i	0.626238	−	1.85424i
$395$	−26.0779	−	15.0561i	−1.31212	−	0.757554i
$396$	0.874171	−	6.80218i	0.0439287	−	0.341822i
$397$	38.0941			1.91189			0.955945	−	0.293545i	$-0.0948352\pi$
$397$	38.0941			1.91189			0.955945	+	0.293545i	$0.0948352\pi$
$398$	−7.67863	−	8.72859i	−0.384895	−	0.437524i
$399$			6.84345i			0.342601i
$400$	−12.1010	+	12.2514i	−0.605052	+	0.612570i
$401$			22.1666i			1.10695i	0.832867	+	0.553473i	$0.186698\pi$
$401$			22.1666i			1.10695i	−0.832867	+	0.553473i	$0.813302\pi$
$402$	8.68353	−	7.65482i	0.433095	−	0.381788i
$403$			3.54820i			0.176748i
$404$	26.8910	+	3.45585i	1.33788	+	0.171935i
$405$			3.05041i			0.151576i
$406$	−7.50292	+	6.60040i	−0.372364	+	0.327572i
$407$	18.7351			0.928663
$408$	−1.66045	+	3.40674i	−0.0822047	+	0.168659i
$409$	−19.0661	−	11.0078i	−0.942758	−	0.544302i	−0.0519345	−	0.998650i	$-0.516539\pi$
$409$	−19.0661	−	11.0078i	−0.942758	−	0.544302i	−0.890824	+	0.454349i	$0.849872\pi$
$410$	−27.3169	−	9.22583i	−1.34908	−	0.455631i
$411$		−	0.0295386i		−	0.00145703i
$412$	−20.2450	−	2.60175i	−0.997400	−	0.128179i
$413$	31.7812	+	18.3489i	1.56385	+	0.902891i
$414$	5.05215	+	5.74297i	0.248300	+	0.282252i
$415$	20.9650	+	36.3125i	1.02913	+	1.78251i
$416$	9.62347	+	0.556204i	0.471830	+	0.0272702i
$417$	9.42510			0.461549
$418$	8.53372	−	1.71116i	0.417398	−	0.0836956i
$419$	10.2786	−	5.93435i	0.502142	−	0.289912i	−0.227456	−	0.973788i	$-0.573041\pi$
$419$	10.2786	−	5.93435i	0.502142	−	0.289912i	0.729598	+	0.683877i	$0.239707\pi$
$420$	−23.0727	−	2.96515i	−1.12583	−	0.144684i
$421$	−15.9573	−	27.6388i	−0.777709	−	1.34703i	−0.933259	−	0.359204i	$-0.883048\pi$
$421$	−15.9573	−	27.6388i	−0.777709	−	1.34703i	0.155550	−	0.987828i	$-0.450285\pi$
$422$	−14.8419	−	16.8714i	−0.722494	−	0.821286i
$423$	1.21783	+	0.703117i	0.0592131	+	0.0341867i
$424$	6.17671	−	4.16865i	0.299968	−	0.202447i
$425$	−2.88419	−	4.99556i	−0.139904	−	0.242320i
$426$	−5.46021	+	16.1672i	−0.264548	+	0.783304i
$427$			22.3812i			1.08310i
$428$	−3.99502	−	9.56124i	−0.193107	−	0.462160i
$429$		−	5.84327i		−	0.282116i
$430$	43.4979	−	8.72209i	2.09766	−	0.420616i
$431$	20.7144	+	11.9595i	0.997779	+	0.576068i	0.907590	−	0.419857i	$-0.137920\pi$
$431$	20.7144	+	11.9595i	0.997779	+	0.576068i	0.0901886	+	0.995925i	$0.471253\pi$
$432$	−2.81091	+	2.84584i	−0.135240	+	0.136920i
$433$	−3.71030	−	2.14214i	−0.178305	−	0.102945i	0.408191	−	0.912897i	$-0.366160\pi$
$433$	−3.71030	−	2.14214i	−0.178305	−	0.102945i	−0.586496	+	0.809952i	$0.699493\pi$
$434$	8.43034	−	7.41626i	0.404669	−	0.355992i
$435$	−4.89555	−	2.82645i	−0.234724	−	0.135518i
$436$	−11.6900	−	27.9776i	−0.559851	−	1.33989i
$437$	−4.85359	+	8.40667i	−0.232179	+	0.402145i
$438$	3.38117	−	2.97445i	0.161559	−	0.142125i
$439$	30.1261	−	17.3933i	1.43784	−	0.830138i	0.440142	−	0.897928i	$-0.354928\pi$
$439$	30.1261	−	17.3933i	1.43784	−	0.830138i	0.997700	+	0.0677898i	$0.0215947\pi$
$440$	2.07166	+	29.5129i	0.0987627	+	1.40697i
$441$	−3.76948	−	6.52893i	−0.179499	−	0.310901i
$442$	−1.03322	+	3.05927i	−0.0491453	+	0.145515i
$443$	9.36281	−	16.2169i	0.444840	−	0.770486i	−0.553201	−	0.833048i	$-0.686594\pi$
$443$	9.36281	−	16.2169i	0.444840	−	0.770486i	0.998041	+	0.0625619i	$0.0199271\pi$
$444$	−8.68965	−	6.62528i	−0.412393	−	0.314422i
$445$		−	8.00867i		−	0.379647i
$446$	27.9726	−	5.60900i	1.32454	−	0.265594i
$447$	−0.963142			−0.0455551
$448$	−18.7930	−	24.0274i	−0.887884	−	1.13519i
$449$	7.56224	−	13.0982i	0.356884	−	0.618141i	−0.630555	−	0.776145i	$-0.717172\pi$
$449$	7.56224	−	13.0982i	0.356884	−	0.618141i	0.987439	+	0.158004i	$0.0505058\pi$
$450$	−1.19697	−	5.96940i	−0.0564256	−	0.281400i
$451$	−19.8481	+	11.4593i	−0.934608	+	0.539596i
$452$	−35.7208	−	4.59059i	−1.68016	−	0.215923i
$453$	−16.7349	+	9.66190i	−0.786274	+	0.453955i
$454$	−6.24350	+	18.4864i	−0.293022	+	0.867612i
$455$	−19.8201			−0.929182
$456$	−4.56321	−	2.22412i	−0.213692	−	0.104154i
$457$	0.910513	−	1.57706i	0.0425920	−	0.0737715i	−0.843944	−	0.536432i	$-0.819772\pi$
$457$	0.910513	−	1.57706i	0.0425920	−	0.0737715i	0.886536	+	0.462661i	$0.153105\pi$
$458$	−21.4738	−	24.4100i	−1.00340	−	1.14061i
$459$	−0.669958	−	1.16040i	−0.0312710	−	0.0541629i
$460$	−26.2401	−	20.0064i	−1.22345	−	0.932801i
$461$	−24.2007			−1.12714			−0.563570	−	0.826069i	$-0.690572\pi$
$461$	−24.2007			−1.12714			−0.563570	+	0.826069i	$0.690572\pi$
$462$	−13.8833	+	12.2133i	−0.645911	+	0.568214i
$463$	−11.0035	−	19.0586i	−0.511376	−	0.885729i	−0.999913	−	0.0131858i	$-0.995803\pi$
$463$	−11.0035	−	19.0586i	−0.511376	−	0.885729i	0.488537	−	0.872543i	$-0.337531\pi$
$464$	−1.96270	−	7.14807i	−0.0911160	−	0.331841i
$465$	5.50068	+	3.17582i	0.255088	+	0.147275i
$466$	6.16780	−	18.2623i	0.285718	−	0.845986i
$467$	22.2494	−	12.8457i	1.02958	−	0.594429i	0.112716	−	0.993627i	$-0.464045\pi$
$467$	22.2494	−	12.8457i	1.02958	−	0.594429i	0.916864	+	0.399199i	$0.130712\pi$
$468$	−2.06636	+	2.71021i	−0.0955174	+	0.125280i
$469$	−31.2107	+	0.0320384i	−1.44118	+	0.00147940i
$470$	−5.74746	−	1.94111i	−0.265111	−	0.0895368i
$471$	4.70405	+	8.14765i	0.216751	+	0.375424i
$472$	−22.5639	+	15.2283i	−1.03859	+	0.700941i
$473$	17.6319	−	30.5394i	0.810717	−	1.40420i
$474$	13.2264	+	4.46702i	0.607511	+	0.205177i
$475$	6.69136	−	3.86326i	0.307021	−	0.177258i
$476$	9.42827	−	3.93946i	0.432144	−	0.180565i
$477$			2.63461i			0.120631i
$478$	9.63803	+	3.25509i	0.440833	+	0.148884i
$479$	−23.2487	+	13.4227i	−1.06226	+	0.613297i	−0.926057	−	0.377384i	$-0.876824\pi$
$479$	−23.2487	+	13.4227i	−1.06226	+	0.613297i	−0.136204	+	0.990681i	$0.543490\pi$
$480$	9.47577	−	14.4212i	0.432508	−	0.658234i
$481$	−8.06291	−	4.65512i	−0.367637	−	0.212255i
$482$	−0.587285	−	2.92885i	−0.0267501	−	0.133405i
$483$		−	20.6230i		−	0.938378i
$484$	1.20630	+	0.919724i	0.0548318	+	0.0418057i
$485$	−21.8234	−	37.7992i	−0.990948	−	1.71637i
$486$	−0.278040	−	1.38661i	−0.0126121	−	0.0628980i
$487$	6.25747	+	10.8383i	0.283553	+	0.491128i	0.972257	−	0.233914i	$-0.0751535\pi$
$487$	6.25747	+	10.8383i	0.283553	+	0.491128i	−0.688704	+	0.725042i	$0.741820\pi$
$488$	−14.9237	−	7.27386i	−0.675566	−	0.329272i
$489$	−11.5865	−	6.68947i	−0.523960	−	0.302508i
$490$	21.4813	+	24.4186i	0.970428	+	1.10312i
$491$			40.0582i			1.80780i	0.427740	+	0.903902i	$0.359310\pi$
$491$			40.0582i			1.80780i	−0.427740	+	0.903902i	$0.640690\pi$
$492$	13.2582	+	1.70386i	0.597727	+	0.0768158i
$493$	2.48307			0.111832
$494$	−4.09779	−	1.38396i	−0.184368	−	0.0622673i
$495$	−9.05867	−	5.23003i	−0.407157	−	0.235072i
$496$	2.20530	+	8.03162i	0.0990210	+	0.360631i
$497$	39.8449	−	23.0044i	1.78729	−	1.03189i
$498$	−12.8398	−	14.5955i	−0.575365	−	0.654039i
$499$	5.52402	+	9.56789i	0.247289	+	0.428318i	0.962773	−	0.270312i	$-0.0871269\pi$
$499$	5.52402	+	9.56789i	0.247289	+	0.428318i	−0.715483	+	0.698630i	$0.753794\pi$
$500$	−1.63463	−	3.91216i	−0.0731031	−	0.174957i
$501$	−20.3646	−	11.7575i	−0.909822	−	0.525286i
$502$	10.4755	−	9.21539i	0.467543	−	0.411303i
$503$	−11.9613	+	20.7176i	−0.533329	+	0.923753i	0.465913	+	0.884830i	$0.345726\pi$
$503$	−11.9613	+	20.7176i	−0.533329	+	0.923753i	−0.999242	+	0.0389223i	$0.987608\pi$
$504$	10.7583	−	0.755183i	0.479213	−	0.0336385i
$505$	20.6758	−	35.8116i	0.920062	−	1.59359i
$506$	−25.7167	+	5.15665i	−1.14325	+	0.229241i
$507$	5.04812	−	8.74359i	0.224195	−	0.388317i
$508$	33.2129	+	4.26830i	1.47358	+	0.189375i
$509$	−27.8071			−1.23253			−0.616265	−	0.787539i	$-0.711355\pi$
$509$	−27.8071			−1.23253			−0.616265	+	0.787539i	$0.711355\pi$
$510$	3.81793	+	4.33998i	0.169061	+	0.192178i
$511$	−12.1418			−0.537121
$512$	22.1292	−	4.72224i	0.977981	−	0.208696i
$513$	1.55431	−	0.897384i	0.0686247	−	0.0396205i
$514$	2.42027	+	0.817409i	0.106754	+	0.0360543i
$515$	−15.5659	+	26.9609i	−0.685915	+	1.18804i
$516$	−18.9776	+	7.92952i	−0.835444	+	0.349078i
$517$	−4.17603	+	2.41103i	−0.183661	+	0.106037i
$518$	5.79234	+	28.8870i	0.254501	+	1.26922i
$519$	11.2095	+	19.4154i	0.492041	+	0.852239i
$520$	6.44153	−	13.2160i	0.282480	−	0.579562i
$521$			23.3181i			1.02158i	0.859704	+	0.510792i	$0.170648\pi$
$521$			23.3181i			1.02158i	−0.859704	+	0.510792i	$0.829352\pi$
$522$	2.48297	+	0.838584i	0.108677	+	0.0367038i
$523$	−12.7846	+	7.38117i	−0.559030	+	0.322756i	−0.752756	−	0.658299i	$-0.771276\pi$
$523$	−12.7846	+	7.38117i	−0.559030	+	0.322756i	0.193726	+	0.981056i	$0.437943\pi$
$524$	−8.45673	−	20.2394i	−0.369434	−	0.884163i
$525$	−8.20752	+	14.2159i	−0.358206	+	0.620431i
$526$	−23.0480	+	4.62153i	−1.00494	+	0.201508i
$527$	−2.79000			−0.121534
$528$	−3.63176	−	13.2267i	−0.158052	−	0.575618i
$529$	3.12648	−	5.41522i	0.135934	−	0.235444i
$530$	−2.23451	−	11.1437i	−0.0970609	−	0.484052i
$531$		−	9.62440i		−	0.417663i
$532$	5.27676	+	12.6288i	0.228776	+	0.547528i
$533$	11.3892			0.493321
$534$	0.729976	+	3.64046i	0.0315892	+	0.157538i
$535$	−15.8047			−0.683295
$536$	10.1221	−	20.8217i	0.437208	−	0.899360i
$537$	3.10081			0.133810
$538$	−3.15474	−	15.7330i	−0.136010	−	0.678297i
$539$	25.8515			1.11350
$540$	2.35207	+	5.62920i	0.101217	+	0.242242i
$541$			14.8487i			0.638394i	0.947688	+	0.319197i	$0.103413\pi$
$541$			14.8487i			0.638394i	−0.947688	+	0.319197i	$0.896587\pi$
$542$	0.184345	+	0.919346i	0.00791829	+	0.0394893i
$543$	13.2249	−	22.9062i	0.567534	−	0.982997i
$544$	−0.437352	+	7.56708i	−0.0187513	+	0.324436i
$545$	−46.2469			−1.98100
$546$	9.00954	−	1.80657i	0.385573	−	0.0773141i
$547$	5.38731	−	9.33109i	0.230345	−	0.398968i	−0.727565	−	0.686039i	$-0.759348\pi$
$547$	5.38731	−	9.33109i	0.230345	−	0.398968i	0.957910	+	0.287070i	$0.0926813\pi$
$548$	−0.0227762	−	0.0545101i	−0.000972952	−	0.00232856i
$549$	5.08331	−	2.93485i	0.216950	−	0.125256i
$550$	19.7793	+	6.68014i	0.843392	+	0.284842i
$551$			3.32599i			0.141692i
$552$	13.7514	+	6.70246i	0.585298	+	0.285275i
$553$	−18.8200	−	32.5972i	−0.800308	−	1.38617i
$554$	−1.69087	−	8.43254i	−0.0718382	−	0.358264i
$555$	−14.4334	+	8.33314i	−0.612665	+	0.353722i
$556$	17.3930	−	7.26739i	0.737626	−	0.308206i
$557$	−19.1782	+	33.2177i	−0.812608	+	1.40748i	0.0984241	+	0.995145i	$0.468620\pi$
$557$	−19.1782	+	33.2177i	−0.812608	+	1.40748i	−0.911033	+	0.412334i	$0.864714\pi$
$558$	−2.78989	−	0.942240i	−0.118105	−	0.0398882i
$559$	−15.1763	+	8.76205i	−0.641889	+	0.370595i
$560$	−44.8644	+	12.3188i	−1.89587	+	0.520562i
$561$	4.59465			0.193986
$562$	24.0602	+	27.3501i	1.01492	+	1.15369i
$563$	−22.4845			−0.947610			−0.473805	−	0.880630i	$-0.657120\pi$
$563$	−22.4845			−0.947610			−0.473805	+	0.880630i	$0.657120\pi$
$564$	2.78953	+	0.358491i	0.117460	+	0.0150952i
$565$	−27.4648	+	47.5704i	−1.15545	+	2.00130i
$566$	23.5244	−	4.71706i	0.988805	−	0.198273i
$567$	−1.90650	+	3.30215i	−0.0800654	+	0.138677i
$568$	2.38980	+	34.0450i	0.100274	+	1.42849i
$569$	−13.8985	+	24.0729i	−0.582655	+	1.00919i	0.412509	+	0.910954i	$0.364653\pi$
$569$	−13.8985	+	24.0729i	−0.582655	+	1.00919i	−0.995163	+	0.0982337i	$0.968681\pi$
$570$	−5.81324	+	5.11397i	−0.243490	+	0.214201i
$571$	−34.7904	−	20.0863i	−1.45593	−	0.840583i	−0.457126	−	0.889402i	$-0.651121\pi$
$571$	−34.7904	−	20.0863i	−1.45593	−	0.840583i	−0.998808	+	0.0488187i	$0.984454\pi$
$572$	−4.50556	−	10.7831i	−0.188387	−	0.450864i
$573$	−2.21515	−	3.83674i	−0.0925390	−	0.160282i
$574$	−23.8051	−	27.0602i	−0.993606	−	1.12947i
$575$	−20.1647	+	11.6421i	−0.840925	+	0.485508i
$576$	−2.99289	+	7.41907i	−0.124704	+	0.309128i
$577$	10.9114	+	6.29969i	0.454247	+	0.262260i	0.709622	−	0.704582i	$-0.248866\pi$
$577$	10.9114	+	6.29969i	0.454247	+	0.262260i	−0.255375	+	0.966842i	$0.582199\pi$
$578$	20.3721	+	6.88034i	0.847367	+	0.286185i
$579$	−11.0688			−0.460006
$580$	−11.2136	−	1.44109i	−0.465618	−	0.0598381i
$581$			52.4123i			2.17443i
$582$	13.3655	+	15.1930i	0.554017	+	0.629772i
$583$	−7.82388	−	4.51712i	−0.324032	−	0.187080i
$584$	3.94607	−	8.09613i	0.163290	−	0.335020i
$585$	2.59902	+	4.50164i	0.107456	+	0.186120i
$586$	1.49960	+	7.47866i	0.0619480	+	0.308941i
$587$	3.77482	+	6.53817i	0.155803	+	0.269859i	0.933351	−	0.358964i	$-0.116870\pi$
$587$	3.77482	+	6.53817i	0.155803	+	0.269859i	−0.777548	+	0.628824i	$0.783537\pi$
$588$	−11.9904	−	9.14188i	−0.494475	−	0.377005i
$589$		−	3.73710i		−	0.153985i
$590$	8.16281	+	40.7087i	0.336058	+	1.67595i
$591$	23.7894	+	13.7348i	0.978565	+	0.564975i
$592$	−21.1443	−	5.52591i	−0.869026	−	0.227114i
$593$	−3.95331	+	2.28244i	−0.162343	+	0.0937288i	−0.578970	−	0.815349i	$-0.696545\pi$
$593$	−3.95331	+	2.28244i	−0.162343	+	0.0937288i	0.416627	+	0.909077i	$0.363212\pi$
$594$	4.59447	+	1.55171i	0.188513	+	0.0636673i
$595$		−	15.5849i		−	0.638917i
$596$	−1.77737	+	0.742647i	−0.0728039	+	0.0304200i
$597$	7.11906	−	4.11019i	0.291364	−	0.168219i
$598$	12.3488	+	4.17062i	0.504981	+	0.170549i
$599$	11.5114	−	19.9384i	0.470344	−	0.814660i	−0.529081	−	0.848572i	$-0.677463\pi$
$599$	11.5114	−	19.9384i	0.470344	−	0.814660i	0.999425	+	0.0339114i	$0.0107964\pi$
$600$	−6.81168	−	10.0929i	−0.278086	−	0.412041i
$601$	13.3878	+	23.1883i	0.546100	+	0.945872i	0.998537	+	0.0540762i	$0.0172214\pi$
$601$	13.3878	+	23.1883i	0.546100	+	0.945872i	−0.452437	+	0.891796i	$0.649445\pi$
$602$	52.5389	+	17.7442i	2.14133	+	0.723198i
$603$	4.09995	+	7.08452i	0.166963	+	0.288504i
$604$	−23.4324	+	30.7337i	−0.953451	+	1.25054i
$605$	2.00365	−	1.15681i	0.0814601	−	0.0470310i
$606$	−6.13435	+	18.1633i	−0.249191	+	0.737832i
$607$	−13.3060	−	7.68223i	−0.540074	−	0.311812i	0.205035	−	0.978755i	$-0.434269\pi$
$607$	−13.3060	−	7.68223i	−0.540074	−	0.311812i	−0.745109	+	0.666943i	$0.767603\pi$
$608$	−10.1358	−	0.585817i	−0.411062	−	0.0237580i
$609$	−3.53304	−	6.11941i	−0.143166	−	0.247971i
$610$	−19.0119	+	16.7250i	−0.769770	+	0.677175i
$611$	2.39628			0.0969433
$612$	−2.13108	−	1.62481i	−0.0861438	−	0.0656790i
$613$	−6.20004	−	10.7388i	−0.250417	−	0.433735i	0.713224	−	0.700937i	$-0.247234\pi$
$613$	−6.20004	−	10.7388i	−0.250417	−	0.433735i	−0.963641	+	0.267201i	$0.913901\pi$
$614$	8.23876	+	9.36530i	0.332489	+	0.377953i
$615$	10.1939	−	17.6564i	0.411058	−	0.711974i
$616$	−16.2028	+	33.2433i	−0.652831	+	1.33941i
$617$	29.5101			1.18803			0.594015	−	0.804454i	$-0.297542\pi$
$617$	29.5101			1.18803			0.594015	+	0.804454i	$0.297542\pi$
$618$	4.61827	−	13.6743i	0.185774	−	0.550061i
$619$	0.744242	−	0.429688i	0.0299136	−	0.0172706i	−0.484969	−	0.874532i	$-0.661169\pi$
$619$	0.744242	−	0.429688i	0.0299136	−	0.0172706i	0.514882	+	0.857261i	$0.327836\pi$
$620$	12.5997	+	1.61922i	0.506014	+	0.0650296i
$621$	−4.68399	+	2.70430i	−0.187962	+	0.108520i
$622$	2.71886	+	13.5592i	0.109016	+	0.543674i
$623$	5.00539	−	8.66960i	0.200537	−	0.347340i
$624$	−1.72347	+	6.59469i	−0.0689942	+	0.263999i
$625$	−27.9919			−1.11968
$626$	−1.17715	+	0.236038i	−0.0470482	+	0.00943398i
$627$			6.15437i			0.245782i
$628$	14.9632	+	11.4084i	0.597096	+	0.455246i
$629$	3.66039	−	6.33999i	0.145949	−	0.252792i
$630$	5.26332	−	15.5842i	0.209696	−	0.620890i
$631$	−1.10350	−	1.91133i	−0.0439298	−	0.0760887i	0.843224	−	0.537562i	$-0.180654\pi$
$631$	−1.10350	−	1.91133i	−0.0439298	−	0.0760887i	−0.887154	+	0.461473i	$0.847321\pi$
$632$	27.8523	−	1.95510i	1.10790	−	0.0777697i
$633$	13.7604	−	7.94455i	0.546925	−	0.315767i
$634$	−12.2065	+	10.7382i	−0.484782	+	0.426468i
$635$	25.5366	−	44.2306i	1.01339	−	1.75524i
$636$	2.03146	+	4.86188i	0.0805527	+	0.192786i
$637$	−11.1256	−	6.42336i	−0.440812	−	0.254503i
$638$	−6.74744	+	5.93579i	−0.267134	+	0.235000i
$639$	−10.4497	−	6.03316i	−0.413386	−	0.238668i
$640$	6.36676	−	33.9191i	0.251668	−	1.34077i
$641$	−5.00162	−	2.88769i	−0.197552	−	0.114057i	0.397961	−	0.917402i	$-0.369718\pi$
$641$	−5.00162	−	2.88769i	−0.197552	−	0.114057i	−0.595513	+	0.803346i	$0.703051\pi$
$642$	7.18425	−	1.44057i	0.283540	−	0.0568547i
$643$		−	3.10268i		−	0.122358i	−0.998127	−	0.0611789i	$-0.980514\pi$
$643$		−	3.10268i		−	0.122358i	0.998127	−	0.0611789i	$-0.0194860\pi$
$644$	−15.9017	−	38.0574i	−0.626615	−	1.49967i
$645$			31.3699i			1.23519i
$646$	1.08823	−	3.22215i	0.0428158	−	0.126774i
$647$	12.8565	+	22.2680i	0.505439	+	0.875447i	0.999980	+	0.00629223i	$0.00200289\pi$
$647$	12.8565	+	22.2680i	0.505439	+	0.875447i	−0.494541	+	0.869154i	$0.664664\pi$
$648$	−1.58226	−	2.34445i	−0.0621572	−	0.0920987i
$649$	28.5811	+	16.5013i	1.12191	+	0.647734i
$650$	−6.85248	−	7.78947i	−0.268777	−	0.305528i
$651$	3.96975	+	6.87582i	0.155587	+	0.269484i
$652$	−26.5396	−	3.41070i	−1.03937	−	0.133573i
$653$	42.1746	−	24.3495i	1.65042	−	0.952870i	0.673520	−	0.739169i	$-0.264781\pi$
$653$	42.1746	−	24.3495i	1.65042	−	0.952870i	0.976899	−	0.213701i	$-0.0685519\pi$
$654$	21.0222	−	4.21532i	0.822034	−	0.164832i
$655$	−33.4556			−1.30722
$656$	25.7803	−	7.07870i	1.00655	−	0.276377i
$657$	1.59216	+	2.75770i	0.0621160	+	0.107588i
$658$	−5.00859	−	5.69345i	−0.195255	−	0.221954i
$659$	9.73696	+	5.62163i	0.379298	+	0.218988i	0.677513	−	0.735511i	$-0.263058\pi$
$659$	9.73696	+	5.62163i	0.379298	+	0.218988i	−0.298215	+	0.954499i	$0.596391\pi$
$660$	−20.7495	−	2.66658i	−0.807672	−	0.103797i
$661$		−	4.12358i		−	0.160389i	−0.996779	−	0.0801944i	$-0.974446\pi$
$661$		−	4.12358i		−	0.160389i	0.996779	−	0.0801944i	$-0.0255541\pi$
$662$	−42.8774	−	14.4812i	−1.66648	−	0.562826i
$663$	−1.97738	−	1.14164i	−0.0767949	−	0.0443376i
$664$	−34.9485	−	17.0340i	−1.35626	−	0.661046i
$665$	20.8753			0.809511
$666$	5.80139	−	5.10354i	0.224799	−	0.197758i
$667$		−	10.0230i		−	0.388092i
$668$	−46.6464	−	5.99468i	−1.80480	−	0.231941i
$669$			20.1734i			0.779947i
$670$	−23.3504	−	26.4884i	−0.902104	−	1.02333i
$671$			20.1276i			0.777016i
$672$	19.2710	−	9.68899i	0.743394	−	0.373761i
$673$			33.7116i			1.29949i	0.760154	+	0.649743i	$0.225124\pi$
$673$			33.7116i			1.29949i	−0.760154	+	0.649743i	$0.774876\pi$
$674$	5.94246	+	6.75502i	0.228895	+	0.260193i
$675$	4.30502			0.165700
$676$	2.57383	−	20.0278i	0.0989936	−	0.770298i
$677$	4.94639	+	2.85580i	0.190105	+	0.109757i	0.592032	−	0.805915i	$-0.298326\pi$
$677$	4.94639	+	2.85580i	0.190105	+	0.109757i	−0.401927	+	0.915672i	$0.631659\pi$
$678$	8.14858	−	24.1272i	0.312944	−	0.926601i
$679$		−	54.5582i		−	2.09375i
$680$	10.3920	+	5.06507i	0.398514	+	0.194237i
$681$	−11.9488	−	6.89864i	−0.457879	−	0.264356i
$682$	7.58148	−	6.66951i	0.290310	−	0.255389i
$683$	12.3397	+	21.3730i	0.472166	+	0.817815i	0.999493	−	0.0318472i	$-0.0101390\pi$
$683$	12.3397	+	21.3730i	0.472166	+	0.817815i	−0.527327	+	0.849662i	$0.676806\pi$
$684$	2.17637	−	2.85450i	0.0832156	−	0.109145i
$685$	−0.0901049			−0.00344273
$686$	0.571383	+	2.84954i	0.0218155	+	0.108796i
$687$	19.9089	−	11.4944i	0.759572	−	0.438539i
$688$	−28.9069	+	29.2661i	−1.10207	+	1.11576i
$689$	2.24475	+	3.88802i	0.0855181	+	0.148122i
$690$	17.5184	−	15.4112i	0.666915	−	0.586693i
$691$	−27.0601	−	15.6232i	−1.02941	−	0.594333i	−0.112598	−	0.993641i	$-0.535917\pi$
$691$	−27.0601	−	15.6232i	−1.02941	−	0.594333i	−0.916817	+	0.399308i	$0.869250\pi$
$692$	35.6563	+	27.1856i	1.35545	+	1.03344i
$693$	−6.53750	−	11.3233i	−0.248339	−	0.430136i
$694$	17.3259	+	5.85154i	0.657682	+	0.222121i
$695$		−	28.7505i		−	1.09057i
$696$	5.22865	−	0.367027i	0.198192	−	0.0139121i
$697$			8.95550i			0.339214i
$698$	−2.43102	−	12.1237i	−0.0920153	−	0.458889i
$699$	11.8039	+	6.81500i	0.446466	+	0.257767i
$700$	−4.18469	+	32.5623i	−0.158166	+	1.23074i
$701$	7.44701	+	4.29954i	0.281270	+	0.162391i	0.633998	−	0.773335i	$-0.281413\pi$
$701$	7.44701	+	4.29954i	0.281270	+	0.162391i	−0.352728	+	0.935726i	$0.614746\pi$
$702$	−1.59174	−	1.80939i	−0.0600764	−	0.0682911i
$703$	8.49218	+	4.90296i	0.320289	+	0.184919i
$704$	−16.9007	−	21.6081i	−0.636968	−	0.814385i
$705$	2.14480	−	3.71490i	0.0807777	−	0.139911i
$706$	25.1430	+	28.5810i	0.946269	+	1.07566i
$707$	44.7642	−	25.8446i	1.68353	−	0.971988i
$708$	−7.42106	−	17.7607i	−0.278900	−	0.667490i
$709$	12.2133	+	21.1540i	0.458679	+	0.794455i	0.998891	−	0.0470735i	$-0.0149895\pi$
$709$	12.2133	+	21.1540i	0.458679	+	0.794455i	−0.540213	+	0.841529i	$0.681656\pi$
$710$	49.3167	+	16.6559i	1.85082	+	0.625085i
$711$	−4.93575	+	8.54897i	−0.185105	+	0.320612i
$712$	4.15413	+	6.15521i	0.155683	+	0.230676i
$713$			11.2619i			0.421762i
$714$	1.42053	+	7.08434i	0.0531621	+	0.265125i
$715$	−17.8244			−0.666595
$716$	5.72220	−	2.39094i	0.213849	−	0.0893535i
$717$	−3.59665	+	6.22958i	−0.134319	+	0.232648i
$718$	26.0905	−	5.23160i	0.973689	−	0.195242i
$719$	9.43992	−	5.45014i	0.352050	−	0.203256i	−0.313538	−	0.949576i	$-0.601514\pi$
$719$	9.43992	−	5.45014i	0.352050	−	0.203256i	0.665588	+	0.746320i	$0.268181\pi$
$720$	8.68098	+	8.57444i	0.323521	+	0.319551i
$721$	−33.7009	+	19.4573i	−1.25509	+	0.724626i
$722$	−21.1414	−	7.14017i	−0.786802	−	0.265730i
$723$	2.11223			0.0785548
$724$	6.74284	−	52.4680i	0.250596	−	1.94996i
$725$	−3.98894	+	6.90905i	−0.148146	+	0.256596i
$726$	−0.805350	+	0.708475i	−0.0298894	+	0.0262940i
$727$	−5.60679	−	9.71125i	−0.207944	−	0.360170i	0.743122	−	0.669156i	$-0.233344\pi$
$727$	−5.60679	−	9.71125i	−0.207944	−	0.360170i	−0.951067	+	0.308985i	$0.900011\pi$
$728$	15.2331	−	10.2808i	0.564577	−	0.381031i
$729$	1.00000			0.0370370
$730$	−9.07332	−	10.3140i	−0.335818	−	0.381737i
$731$	−6.88973	−	11.9334i	−0.254826	−	0.441371i
$732$	7.11771	−	9.33551i	0.263078	−	0.345050i
$733$	−20.3455	−	11.7465i	−0.751478	−	0.433866i	0.0747500	−	0.997202i	$-0.476184\pi$
$733$	−20.3455	−	11.7465i	−0.751478	−	0.433866i	−0.826228	+	0.563337i	$0.809517\pi$
$734$	27.7287	+	9.36492i	1.02349	+	0.345666i
$735$	−19.9159	+	11.4985i	−0.734610	+	0.424127i
$736$	30.5447	+	1.76538i	1.12589	+	0.0650728i
$737$	−28.0681	+	0.0288124i	−1.03390	+	0.00106132i
$738$	−3.02445	+	8.95513i	−0.111332	+	0.329643i
$739$	19.8760	+	34.4262i	0.731150	+	1.26639i	0.956392	+	0.292086i	$0.0943492\pi$
$739$	19.8760	+	34.4262i	0.731150	+	1.26639i	−0.225243	+	0.974303i	$0.572317\pi$
$740$	−20.2099	+	26.5070i	−0.742929	+	0.974418i
$741$	1.52918	−	2.64862i	0.0561759	−	0.0972995i
$742$	4.54587	−	13.4599i	0.166884	−	0.494130i
$743$	−25.1460	+	14.5181i	−0.922519	+	0.532616i	−0.884438	−	0.466658i	$-0.845458\pi$
$743$	−25.1460	+	14.5181i	−0.922519	+	0.532616i	−0.0380809	+	0.999275i	$0.512124\pi$
$744$	−5.87496	+	0.412394i	−0.215386	+	0.0151191i
$745$			2.93798i			0.107639i
$746$	7.31528	−	21.6599i	0.267832	−	0.793026i
$747$	11.9041	−	6.87285i	0.435549	−	0.251464i
$748$	8.47892	−	3.54279i	0.310020	−	0.129537i
$749$	−17.1090	−	9.87787i	−0.625148	−	0.360929i
$750$	2.93957	−	0.589435i	0.107338	−	0.0215231i
$751$			17.0296i			0.621420i	0.950505	+	0.310710i	$0.100567\pi$
$751$			17.0296i			0.621420i	−0.950505	+	0.310710i	$0.899433\pi$
$752$	5.42418	−	1.48936i	0.197799	−	0.0543113i
$753$	4.93278	+	8.54383i	0.179761	+	0.311355i
$754$	4.37873	−	0.878012i	0.159464	−	0.0319753i
$755$	29.4728	+	51.0484i	1.07262	+	1.85784i
$756$	−0.972048	+	7.56379i	−0.0353530	+	0.275092i
$757$	37.6520	+	21.7384i	1.36849	+	0.790096i	0.990735	−	0.135811i	$-0.0433640\pi$
$757$	37.6520	+	21.7384i	1.36849	+	0.790096i	0.377752	+	0.925907i	$0.376697\pi$
$758$	−12.1106	+	10.6539i	−0.439878	+	0.386966i
$759$		−	18.5464i		−	0.673193i
$760$	−6.78447	+	13.9197i	−0.246099	+	0.504919i
$761$	24.6851			0.894834			0.447417	−	0.894325i	$-0.352344\pi$
$761$	24.6851			0.894834			0.447417	+	0.894325i	$0.352344\pi$
$762$	−7.57649	+	22.4333i	−0.274467	+	0.812674i
$763$	−50.0634	−	28.9041i	−1.81242	−	1.04640i
$764$	−7.04619	−	5.37225i	−0.254922	−	0.194361i
$765$	−3.53970	+	2.04365i	−0.127978	+	0.0738883i
$766$	−29.6966	+	26.1244i	−1.07298	+	0.943912i
$767$	−8.20020	−	14.2032i	−0.296092	−	0.512847i
$768$	0.197562	+	15.9988i	0.00712889	+	0.577306i
$769$	20.5653	+	11.8734i	0.741604	+	0.428165i	0.822652	−	0.568545i	$-0.192493\pi$
$769$	20.5653	+	11.8734i	0.741604	+	0.428165i	−0.0810482	+	0.996710i	$0.525827\pi$
$770$	37.2556	+	42.3499i	1.34260	+	1.52618i
$771$	−0.903181	+	1.56436i	−0.0325273	+	0.0563389i
$772$	−20.4263	+	8.53483i	−0.735159	+	0.307175i
$773$	3.43737	−	5.95370i	0.123634	−	0.214140i	−0.797564	−	0.603234i	$-0.793879\pi$
$773$	3.43737	−	5.95370i	0.123634	−	0.214140i	0.921198	+	0.389094i	$0.127212\pi$
$774$	−2.85931	−	14.2597i	−0.102776	−	0.512553i
$775$	4.48201	−	7.76306i	0.160998	−	0.278857i
$776$	36.3793	+	17.7314i	1.30594	+	0.636519i
$777$	−20.8328			−0.747371
$778$	−30.6607	+	26.9725i	−1.09924	+	0.967011i
$779$	−11.9956			−0.429785
$780$	8.26726	+	6.30324i	0.296016	+	0.225692i
$781$	35.8328	−	20.6881i	1.28220	−	0.740278i
$782$	−3.27942	+	9.71007i	−0.117272	+	0.347231i
$783$	−0.926578	+	1.60488i	−0.0331132	+	0.0573538i
$784$	−29.1759	−	7.62492i	−1.04200	−	0.272318i
$785$	24.8537	−	14.3493i	0.887066	−	0.512148i
$786$	15.2078	−	3.04942i	0.542443	−	0.108769i
$787$	4.70785	+	8.15424i	0.167817	+	0.290667i	0.937652	−	0.347575i	$-0.112995\pi$
$787$	4.70785	+	8.15424i	0.167817	+	0.290667i	−0.769835	+	0.638243i	$0.779662\pi$
$788$	54.4911	+	7.00284i	1.94117	+	0.249466i
$789$		−	16.6218i		−	0.591753i
$790$	13.6263	−	40.3461i	0.484800	−	1.43545i
$791$	−59.4627	+	34.3308i	−2.11425	+	1.22066i
$792$	9.67504	−	0.679142i	0.343788	−	0.0241323i
$793$	5.00112	−	8.66219i	0.177595	−	0.307603i
$794$	10.5917	+	52.8218i	0.375885	+	1.87458i
$795$	8.03665			0.285031
$796$	9.96820	−	13.0742i	0.353313	−	0.463402i
$797$	−14.3367	+	24.8318i	−0.507831	+	0.879589i	0.492128	+	0.870523i	$0.336219\pi$
$797$	−14.3367	+	24.8318i	−0.507831	+	0.879589i	−0.999959	+	0.00906590i	$0.997114\pi$
$798$	−9.48921	+	1.90275i	−0.335914	+	0.0673567i
$799$			1.88423i			0.0666594i
$800$	−20.3525	−	13.3731i	−0.719570	−	0.472810i
$801$	−2.62544			−0.0927653
$802$	−30.7365	+	6.16320i	−1.08534	+	0.217630i
$803$	−10.9192			−0.385330
$804$	13.0286	+	9.91234i	0.459485	+	0.349581i
$805$	−62.9086			−2.21724
$806$	−4.91998	+	0.986541i	−0.173299	+	0.0347494i
$807$	11.3463			0.399410
$808$	2.68485	+	38.2483i	0.0944526	+	1.34557i
$809$			4.14471i			0.145720i	0.997342	+	0.0728601i	$0.0232126\pi$
$809$			4.14471i			0.145720i	−0.997342	+	0.0728601i	$0.976787\pi$
$810$	−4.22974	+	0.848137i	−0.148618	+	0.0298005i
$811$	24.0870	−	41.7199i	0.845809	−	1.46498i	−0.0391069	−	0.999235i	$-0.512451\pi$
$811$	24.0870	−	41.7199i	0.845809	−	1.46498i	0.884916	−	0.465750i	$-0.154215\pi$
$812$	−11.2383	−	8.56847i	−0.394387	−	0.300694i
$813$	−0.663016			−0.0232530
$814$	5.20910	+	25.9783i	0.182579	+	0.910538i
$815$	−20.4057	+	35.3436i	−0.714779	+	1.23803i
$816$	−5.18550	−	1.35519i	−0.181529	−	0.0474413i
$817$	15.9843	−	9.22854i	0.559220	−	0.322866i
$818$	9.96244	−	29.4979i	0.348329	−	1.03137i
$819$			6.49752i			0.227042i
$820$	5.19747	−	40.4430i	0.181503	−	1.41233i
$821$	27.8028	+	48.1558i	0.970323	+	1.68065i	0.694576	+	0.719419i	$0.255592\pi$
$821$	27.8028	+	48.1558i	0.970323	+	1.68065i	0.275747	+	0.961230i	$0.411075\pi$
$822$	0.0409586	−	0.00821290i	0.00142859	−	0.000286458i
$823$	−8.75976	+	5.05745i	−0.305346	+	0.176292i	−0.644842	−	0.764316i	$-0.723077\pi$
$823$	−8.75976	+	5.05745i	−0.305346	+	0.176292i	0.339496	+	0.940608i	$0.389744\pi$
$824$	−2.02130	−	28.7954i	−0.0704153	−	1.00313i
$825$	−7.38110	+	12.7844i	−0.256977	+	0.445097i
$826$	−16.6064	+	49.1700i	−0.577810	+	1.71084i
$827$	10.6998	−	6.17754i	0.372069	−	0.214814i	−0.302293	−	0.953215i	$-0.597752\pi$
$827$	10.6998	−	6.17754i	0.372069	−	0.214814i	0.674362	+	0.738401i	$0.264419\pi$
$828$	−6.55857	+	8.60215i	−0.227926	+	0.298945i
$829$	27.5422			0.956581			0.478290	−	0.878202i	$-0.341257\pi$
$829$	27.5422			0.956581			0.478290	+	0.878202i	$0.341257\pi$
$830$	−44.5222	+	39.1667i	−1.54539	+	1.35950i
$831$	6.08139			0.210961
$832$	1.90447	+	13.4987i	0.0660256	+	0.467982i
$833$	5.05078	−	8.74821i	0.174999	−	0.303108i
$834$	2.62056	+	13.0690i	0.0907424	+	0.452541i
$835$	−35.8652	+	62.1204i	−1.24117	+	2.14977i
$836$	4.74543	+	11.3572i	0.164124	+	0.392797i
$837$	1.04111	−	1.80326i	0.0359861	−	0.0623297i
$838$	11.0865	+	12.6024i	0.382977	+	0.435344i
$839$	−44.5141	−	25.7002i	−1.53680	−	0.887271i	−0.999023	−	0.0441824i	$-0.985932\pi$
$839$	−44.5141	−	25.7002i	−1.53680	−	0.887271i	−0.537775	−	0.843089i	$-0.680735\pi$
$840$	−2.30362	−	32.8173i	−0.0794824	−	1.13230i
$841$	12.7829	+	22.1406i	0.440790	+	0.763470i
$842$	33.8875	−	29.8112i	1.16784	−	1.02736i
$843$	−22.3068	+	12.8789i	−0.768288	+	0.443572i
$844$	19.2674	−	25.2709i	0.663212	−	0.869861i
$845$	−26.6716	−	15.3988i	−0.917530	−	0.529736i
$846$	−0.636344	+	1.88416i	−0.0218780	+	0.0647787i
$847$	2.89201			0.0993707
$848$	7.49767	+	7.40565i	0.257471	+	0.254311i
$849$			16.9654i			0.582251i
$850$	6.12498	−	5.38821i	0.210085	−	0.184814i
$851$	−25.5915	−	14.7753i	−0.877265	−	0.506489i
$852$	−23.9358	−	3.07607i	−0.820027	−	0.105384i
$853$	−3.21193	−	5.56323i	−0.109974	−	0.190481i	0.805785	−	0.592208i	$-0.201744\pi$
$853$	−3.21193	−	5.56323i	−0.109974	−	0.190481i	−0.915760	+	0.401727i	$0.868410\pi$
$854$	−31.0340	+	6.22285i	−1.06196	+	0.212942i
$855$	−2.73739	−	4.74130i	−0.0936168	−	0.162149i
$856$	12.1470	−	8.19795i	0.415174	−	0.280200i
$857$		−	3.96978i		−	0.135605i	−0.997699	−	0.0678025i	$-0.978401\pi$
$857$		−	3.96978i		−	0.135605i	0.997699	−	0.0678025i	$-0.0215988\pi$
$858$	8.10236	−	1.62466i	0.276610	−	0.0554651i
$859$	24.5884	+	14.1961i	0.838946	+	0.484366i	0.856906	−	0.515473i	$-0.172384\pi$
$859$	24.5884	+	14.1961i	0.838946	+	0.484366i	−0.0179597	+	0.999839i	$0.505717\pi$
$860$	24.1883	+	57.8896i	0.824814	+	1.97402i
$861$	22.0704	−	12.7423i	0.752156	−	0.434257i
$862$	−10.8237	+	32.0481i	−0.368658	+	1.09156i
$863$			20.0465i			0.682390i	0.939993	+	0.341195i	$0.110832\pi$
$863$			20.0465i			0.682390i	−0.939993	+	0.341195i	$0.889168\pi$
$864$	−4.72762	−	3.10639i	−0.160837	−	0.105681i
$865$	59.2249	−	34.1935i	2.01371	−	1.16261i
$866$	1.93871	−	5.74034i	0.0658800	−	0.195065i
$867$	−7.60231	+	13.1676i	−0.258188	+	0.447195i
$868$	12.6274	+	9.62760i	0.428604	+	0.326782i
$869$	−16.9250	−	29.3150i	−0.574141	−	0.994442i
$870$	2.55803	−	7.57410i	0.0867253	−	0.256786i
$871$	12.0867	+	6.96170i	0.409541	+	0.235888i
$872$	35.5438	−	23.9884i	1.20367	−	0.812351i
$873$	−12.3915	+	7.15423i	−0.419389	+	0.242134i
$874$	−13.0063	−	4.39266i	−0.439944	−	0.148584i
$875$	−7.00045	−	4.04171i	−0.236658	−	0.136635i
$876$	5.06452	+	3.86136i	0.171114	+	0.130463i
$877$	7.49256	+	12.9775i	0.253006	+	0.438219i	0.964352	−	0.264623i	$-0.0852475\pi$
$877$	7.49256	+	12.9775i	0.253006	+	0.438219i	−0.711346	+	0.702842i	$0.751914\pi$
$878$	32.4941	+	36.9372i	1.09662	+	1.24657i
$879$	−5.39347			−0.181917
$880$	−40.3469	+	11.0784i	−1.36009	+	0.373451i
$881$	−5.77524	−	10.0030i	−0.194573	−	0.337010i	0.752188	−	0.658949i	$-0.228999\pi$
$881$	−5.77524	−	10.0030i	−0.194573	−	0.337010i	−0.946760	+	0.321939i	$0.895665\pi$
$882$	8.00503	−	7.04211i	0.269543	−	0.237120i
$883$	−10.8739	+	18.8342i	−0.365937	+	0.633822i	−0.988926	−	0.148409i	$-0.952585\pi$
$883$	−10.8739	+	18.8342i	−0.365937	+	0.633822i	0.622989	+	0.782231i	$0.285918\pi$
$884$	−4.52930	−	0.582076i	−0.152337	−	0.0195773i
$885$	−29.3584			−0.986872
$886$	25.0897	+	8.47365i	0.842906	+	0.284678i
$887$	6.65860	−	3.84435i	0.223574	−	0.129081i	−0.384030	−	0.923321i	$-0.625464\pi$
$887$	6.65860	−	3.84435i	0.223574	−	0.129081i	0.607604	+	0.794240i	$0.292131\pi$
$888$	6.77063	−	13.8913i	0.227208	−	0.466160i
$889$	55.2880	−	31.9206i	1.85430	−	1.07058i
$890$	11.1049	−	2.22673i	0.372238	−	0.0746402i
$891$	−1.71453	+	2.96965i	−0.0574389	+	0.0994872i
$892$	15.5550	+	37.2277i	0.520820	+	1.24647i
$893$	−2.52386			−0.0844578
$894$	−0.267792	−	1.33550i	−0.00895630	−	0.0446660i
$895$		−	9.45877i		−	0.316172i
$896$	28.0915	−	32.7391i	0.938472	−	1.09374i
$897$	−4.60825	+	7.98172i	−0.153865	+	0.266502i
$898$	20.2647	+	6.84407i	0.676242	+	0.228390i
$899$	1.92934	+	3.34172i	0.0643471	+	0.111453i
$900$	7.94444	−	3.31946i	0.264815	−	0.110649i
$901$	−3.05721	+	1.76508i	−0.101850	+	0.0588033i
$902$	−21.4081	−	24.3354i	−0.712813	−	0.810281i
$903$	−19.6061	+	33.9588i	−0.652450	+	1.13008i
$904$	−3.56643	−	50.8072i	−0.118618	−	1.68982i
$905$	−69.8733	−	40.3413i	−2.32267	−	1.34099i
$906$	−18.0503	−	20.5184i	−0.599680	−	0.681679i
$907$	31.2791	+	18.0590i	1.03861	+	0.599640i	0.919438	−	0.393234i	$-0.128644\pi$
$907$	31.2791	+	18.0590i	1.03861	+	0.599640i	0.119168	+	0.992874i	$0.461977\pi$
$908$	−27.3695	−	3.51734i	−0.908288	−	0.116727i
$909$	−11.7399	−	6.77804i	−0.389388	−	0.224813i
$910$	−5.51079	−	27.4828i	−0.182681	−	0.911047i
$911$		−	31.2491i		−	1.03533i	−0.855584	−	0.517665i	$-0.826802\pi$
$911$		−	31.2491i		−	1.03533i	0.855584	−	0.517665i	$-0.173198\pi$
$912$	1.81523	−	6.94579i	0.0601083	−	0.229998i
$913$			47.1348i			1.55993i
$914$	2.43992	+	0.824045i	0.0807055	+	0.0272570i
$915$	−8.95251	−	15.5062i	−0.295961	−	0.512619i
$916$	27.8767	−	36.5628i	0.921072	−	1.20807i
$917$	−36.2166	−	20.9097i	−1.19598	−	0.690498i
$918$	1.42275	−	1.25161i	0.0469578	−	0.0413093i
$919$	10.0334	+	17.3784i	0.330973	+	0.573261i	0.982703	−	0.185189i	$-0.0592899\pi$
$919$	10.0334	+	17.3784i	0.330973	+	0.573261i	−0.651730	+	0.758451i	$0.725957\pi$
$920$	20.4453	−	41.9474i	0.674060	−	1.38297i
$921$	−7.63838	+	4.41002i	−0.251693	+	0.145315i
$922$	−6.72876	−	33.5570i	−0.221600	−	1.10514i
$923$	−20.5616			−0.676792
$924$	−20.7952	−	15.8550i	−0.684113	−	0.521591i
$925$	11.7605	+	20.3698i	0.386683	+	0.669754i
$926$	23.3675	−	20.5566i	0.767904	−	0.675533i
$927$	8.83844	+	5.10287i	0.290292	+	0.167600i
$928$	9.36589	−	4.70895i	0.307450	−	0.154579i
$929$		−	24.0572i		−	0.789292i	−0.918833	−	0.394646i	$-0.870867\pi$
$929$		−	24.0572i		−	0.789292i	0.918833	−	0.394646i	$-0.129133\pi$
$930$	−2.87422	+	8.51031i	−0.0942494	+	0.279064i
$931$	11.7179	+	6.76534i	0.384039	+	0.221725i
$932$	27.0376	+	3.47470i	0.885648	+	0.113817i
$933$	−9.77865			−0.320139
$934$	23.9983	+	27.2797i	0.785247	+	0.892619i
$935$		−	14.0156i		−	0.458359i
$936$	−4.33254	−	2.11169i	−0.141614	−	0.0690227i
$937$		−	56.4036i		−	1.84263i	−0.388823	−	0.921313i	$-0.627118\pi$
$937$		−	56.4036i		−	1.84263i	0.388823	−	0.921313i	$-0.372882\pi$
$938$	−8.72225	−	43.2683i	−0.284792	−	1.41276i
$939$		−	0.848936i		−	0.0277040i
$940$	1.09355	−	8.50921i	0.0356675	−	0.277540i
$941$			16.1905i			0.527796i	0.964551	+	0.263898i	$0.0850082\pi$
$941$			16.1905i			0.527796i	−0.964551	+	0.263898i	$0.914992\pi$
$942$	−9.98972	+	8.78806i	−0.325483	+	0.286330i
$943$	36.1491			1.17718
$944$	−27.3895	−	27.0533i	−0.891451	−	0.880511i
$945$	10.0729	+	5.81561i	0.327673	+	0.189182i
$946$	47.2487	+	15.9575i	1.53619	+	0.518822i
$947$			41.2682i			1.34103i	0.741894	+	0.670517i	$0.233928\pi$
$947$			41.2682i			1.34103i	−0.741894	+	0.670517i	$0.766072\pi$
$948$	−2.51654	+	19.5820i	−0.0817335	+	0.635993i
$949$	4.69924	+	2.71311i	0.152544	+	0.0880712i
$950$	7.21731	+	8.20418i	0.234160	+	0.266179i
$951$	−5.74790	−	9.95565i	−0.186388	−	0.322834i
$952$	8.08393	+	11.9780i	0.262002	+	0.388210i
$953$	6.15674			0.199436			0.0997182	−	0.995016i	$-0.468206\pi$
$953$	6.15674			0.199436			0.0997182	+	0.995016i	$0.468206\pi$
$954$	−3.65318	+	0.732527i	−0.118276	+	0.0237164i
$955$	−11.7037	+	6.75711i	−0.378721	+	0.218655i
$956$	−1.83379	+	14.2693i	−0.0593090	+	0.461501i
$957$	−3.17729	−	5.50324i	−0.102707	−	0.177894i
$958$	−25.0761	−	28.5049i	−0.810172	−	0.920952i
$959$	−0.0975409	−	0.0563153i	−0.00314976	−	0.00181852i
$960$	22.6312	+	9.12955i	0.730420	+	0.294655i
$961$	13.3322	+	23.0920i	0.430070	+	0.744903i
$962$	4.21304	−	12.4744i	0.135834	−	0.402192i
$963$			5.18115i			0.166960i
$964$	3.89789	−	1.62867i	0.125543	−	0.0524560i
$965$			33.7646i			1.08692i
$966$	28.5961	−	5.73401i	0.920064	−	0.184489i
$967$	24.7218	+	14.2731i	0.795000	+	0.458993i	0.841720	−	0.539915i	$-0.181544\pi$
$967$	24.7218	+	14.2731i	0.795000	+	0.458993i	−0.0467201	+	0.998908i	$0.514877\pi$
$968$	−0.939901	+	1.92839i	−0.0302096	+	0.0619808i
$969$	2.08265	+	1.20242i	0.0669044	+	0.0386273i
$970$	46.3451	−	40.7702i	1.48805	−	1.30905i
$971$	30.7302	+	17.7421i	0.986178	+	0.569370i	0.904130	−	0.427258i	$-0.140520\pi$
$971$	30.7302	+	17.7421i	0.986178	+	0.569370i	0.0820483	+	0.996628i	$0.473854\pi$
$972$	1.84539	−	0.771067i	0.0591908	−	0.0247320i
$973$	17.9690	−	31.1231i	0.576058	−	0.997762i
$974$	−13.2886	+	11.6902i	−0.425795	+	0.374577i
$975$	6.35312	−	3.66798i	0.203463	−	0.117469i
$976$	5.93663	−	22.7159i	0.190027	−	0.727117i
$977$	21.8634	+	37.8686i	0.699474	+	1.21152i	0.968649	+	0.248433i	$0.0799155\pi$
$977$	21.8634	+	37.8686i	0.699474	+	1.21152i	−0.269176	+	0.963091i	$0.586751\pi$
$978$	6.05420	−	17.9259i	0.193592	−	0.573208i
$979$	4.50139	−	7.79664i	0.143865	−	0.249182i
$980$	−27.8865	+	36.5757i	−0.890802	+	1.16837i
$981$			15.1608i			0.484049i
$982$	−55.5453	+	11.1378i	−1.77252	+	0.355421i
$983$	3.51330			0.112057			0.0560284	−	0.998429i	$-0.482156\pi$
$983$	3.51330			0.112057			0.0560284	+	0.998429i	$0.482156\pi$
$984$	1.32372	+	18.8577i	0.0421988	+	0.601163i
$985$	41.8969	−	72.5675i	1.33495	−	2.31219i
$986$	0.690394	+	3.44306i	0.0219866	+	0.109649i
$987$	4.64360	−	2.68098i	0.147807	−	0.0853366i
$988$	0.779669	−	6.06684i	0.0248046	−	0.193012i
$989$	−48.1693	+	27.8105i	−1.53169	+	0.884324i
$990$	4.73335	−	14.0150i	0.150436	−	0.445427i
$991$	−21.9743			−0.698037			−0.349019	−	0.937116i	$-0.613485\pi$
$991$	−21.9743			−0.698037			−0.349019	+	0.937116i	$0.613485\pi$
$992$	−10.5236	+	5.29101i	−0.334124	+	0.167990i
$993$	16.0007	−	27.7140i	0.507767	−	0.879478i
$994$	42.9767	+	48.8532i	1.36314	+	1.54953i
$995$	−12.5378	−	21.7161i	−0.397475	−	0.688446i
$996$	16.6683	−	21.8619i	0.528155	−	0.692722i
$997$	6.46346			0.204700			0.102350	−	0.994748i	$-0.467364\pi$
$997$	6.46346			0.204700			0.102350	+	0.994748i	$0.467364\pi$
$998$	−11.7311	+	10.3199i	−0.371340	+	0.326672i
$999$	2.73181	+	4.73163i	0.0864306	+	0.149702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.18	✓	68
4.3	odd	2		804.2.j.b.499.7	yes	68
67.38	odd	6		804.2.j.b.775.7	yes	68
268.239	even	6	inner	804.2.j.a.775.18	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.18	✓	68	1.1	even	1	trivial
804.2.j.a.775.18	yes	68	268.239	even	6	inner
804.2.j.b.499.7	yes	68	4.3	odd	2
804.2.j.b.775.7	yes	68	67.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.278040 + 1.38661i) q^{2} -1.00000 q^{3} +(-1.84539 + 0.771067i) q^{4} +3.05041i q^{5} +(-0.278040 - 1.38661i) q^{6} +(-1.90650 + 3.30215i) q^{7} +(-1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.278040 + 1.38661i) q^{2} -1.00000 q^{3} +(-1.84539 + 0.771067i) q^{4} +3.05041i q^{5} +(-0.278040 - 1.38661i) q^{6} +(-1.90650 + 3.30215i) q^{7} +(-1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +(-4.22974 + 0.848137i) q^{10} +(-1.71453 + 2.96965i) q^{11} +(1.84539 - 0.771067i) q^{12} +(1.47575 - 0.852022i) q^{13} +(-5.10889 - 1.72544i) q^{14} -3.05041i q^{15} +(2.81091 - 2.84584i) q^{16} +(0.669958 + 1.16040i) q^{17} +(0.278040 + 1.38661i) q^{18} +(-1.55431 + 0.897384i) q^{19} +(-2.35207 - 5.62920i) q^{20} +(1.90650 - 3.30215i) q^{21} +(-4.59447 - 1.55171i) q^{22} +(4.68399 - 2.70430i) q^{23} +(1.58226 + 2.34445i) q^{24} -4.30502 q^{25} +(1.59174 + 1.80939i) q^{26} -1.00000 q^{27} +(0.972048 - 7.56379i) q^{28} +(0.926578 - 1.60488i) q^{29} +(4.22974 - 0.848137i) q^{30} +(-1.04111 + 1.80326i) q^{31} +(4.72762 + 3.10639i) q^{32} +(1.71453 - 2.96965i) q^{33} +(-1.42275 + 1.25161i) q^{34} +(-10.0729 - 5.81561i) q^{35} +(-1.84539 + 0.771067i) q^{36} +(-2.73181 - 4.73163i) q^{37} +(-1.67649 - 1.90572i) q^{38} +(-1.47575 + 0.852022i) q^{39} +(7.15154 - 4.82656i) q^{40} +(5.78819 + 3.34181i) q^{41} +(5.10889 + 1.72544i) q^{42} -10.2838 q^{43} +(0.874171 - 6.80218i) q^{44} +3.05041i q^{45} +(5.05215 + 5.74297i) q^{46} +(1.21783 + 0.703117i) q^{47} +(-2.81091 + 2.84584i) q^{48} +(-3.76948 - 6.52893i) q^{49} +(-1.19697 - 5.96940i) q^{50} +(-0.669958 - 1.16040i) q^{51} +(-2.06636 + 2.71021i) q^{52} +2.63461i q^{53} +(-0.278040 - 1.38661i) q^{54} +(-9.05867 - 5.23003i) q^{55} +(10.7583 - 0.755183i) q^{56} +(1.55431 - 0.897384i) q^{57} +(2.48297 + 0.838584i) q^{58} -9.62440i q^{59} +(2.35207 + 5.62920i) q^{60} +(5.08331 - 2.93485i) q^{61} +(-2.78989 - 0.942240i) q^{62} +(-1.90650 + 3.30215i) q^{63} +(-2.99289 + 7.41907i) q^{64} +(2.59902 + 4.50164i) q^{65} +(4.59447 + 1.55171i) q^{66} +(4.09995 + 7.08452i) q^{67} +(-2.13108 - 1.62481i) q^{68} +(-4.68399 + 2.70430i) q^{69} +(5.26332 - 15.5842i) q^{70} +(-10.4497 - 6.03316i) q^{71} +(-1.58226 - 2.34445i) q^{72} +(1.59216 + 2.75770i) q^{73} +(5.80139 - 5.10354i) q^{74} +4.30502 q^{75} +(2.17637 - 2.85450i) q^{76} +(-6.53750 - 11.3233i) q^{77} +(-1.59174 - 1.80939i) q^{78} +(-4.93575 + 8.54897i) q^{79} +(8.68098 + 8.57444i) q^{80} +1.00000 q^{81} +(-3.02445 + 8.95513i) q^{82} +(11.9041 - 6.87285i) q^{83} +(-0.972048 + 7.56379i) q^{84} +(-3.53970 + 2.04365i) q^{85} +(-2.85931 - 14.2597i) q^{86} +(-0.926578 + 1.60488i) q^{87} +(9.67504 - 0.679142i) q^{88} -2.62544 q^{89} +(-4.22974 + 0.848137i) q^{90} +6.49752i q^{91} +(-6.55857 + 8.60215i) q^{92} +(1.04111 - 1.80326i) q^{93} +(-0.636344 + 1.88416i) q^{94} +(-2.73739 - 4.74130i) q^{95} +(-4.72762 - 3.10639i) q^{96} +(-12.3915 + 7.15423i) q^{97} +(8.00503 - 7.04211i) q^{98} +(-1.71453 + 2.96965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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