LMFDB - Embedded newform 804.2.j.b.499.7

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			499.7
Character	$\chi$	$=$	804.499
Dual form			804.2.j.b.775.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06182 - 0.934096i) q^{2} +1.00000 q^{3} +(0.254930 + 1.98369i) q^{4} +3.05041i q^{5} +(-1.06182 - 0.934096i) q^{6} +(1.90650 - 3.30215i) q^{7} +(1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.06182 - 0.934096i) q^{2} +1.00000 q^{3} +(0.254930 + 1.98369i) q^{4} +3.05041i q^{5} +(-1.06182 - 0.934096i) q^{6} +(1.90650 - 3.30215i) q^{7} +(1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +(2.84938 - 3.23900i) q^{10} +(1.71453 - 2.96965i) q^{11} +(0.254930 + 1.98369i) q^{12} +(1.47575 - 0.852022i) q^{13} +(-5.10889 + 1.72544i) q^{14} +3.05041i q^{15} +(-3.87002 + 1.01140i) q^{16} +(0.669958 + 1.16040i) q^{17} +(-1.06182 - 0.934096i) q^{18} +(1.55431 - 0.897384i) q^{19} +(-6.05106 + 0.777642i) 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} +(-2.36285 - 0.473793i) q^{26} +1.00000 q^{27} +(7.03646 + 2.94008i) q^{28} +(0.926578 - 1.60488i) q^{29} +(2.84938 - 3.23900i) q^{30} +(1.04111 - 1.80326i) q^{31} +(5.05402 + 2.54104i) q^{32} +(1.71453 - 2.96965i) q^{33} +(0.372550 - 1.85794i) q^{34} +(10.0729 + 5.81561i) q^{35} +(0.254930 + 1.98369i) q^{36} +(-2.73181 - 4.73163i) q^{37} +(-2.48865 - 0.499017i) 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} +(6.32795 + 2.64404i) q^{44} +3.05041i q^{45} +(7.49963 + 1.50381i) q^{46} +(-1.21783 - 0.703117i) q^{47} +(-3.87002 + 1.01140i) q^{48} +(-3.76948 - 6.52893i) q^{49} +(4.57117 + 4.02131i) q^{50} +(0.669958 + 1.16040i) q^{51} +(2.06636 + 2.71021i) q^{52} +2.63461i q^{53} +(-1.06182 - 0.934096i) q^{54} +(9.05867 + 5.23003i) q^{55} +(-4.72515 - 9.69457i) q^{56} +(1.55431 - 0.897384i) q^{57} +(-2.48297 + 0.838584i) q^{58} +9.62440i q^{59} +(-6.05106 + 0.777642i) 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} +(-1.51910 + 7.57592i) q^{74} -4.30502 q^{75} +(2.17637 + 2.85450i) q^{76} +(-6.53750 - 11.3233i) q^{77} +(-2.36285 - 0.473793i) q^{78} +(4.93575 - 8.54897i) q^{79} +(-3.08520 - 11.8052i) q^{80} +1.00000 q^{81} +(-3.02445 - 8.95513i) q^{82} +(-11.9041 + 6.87285i) q^{83} +(7.03646 + 2.94008i) q^{84} +(-3.53970 + 2.04365i) q^{85} +(-10.9196 - 9.60607i) q^{86} +(0.926578 - 1.60488i) q^{87} +(-4.24937 - 8.71840i) q^{88} -2.62544 q^{89} +(2.84938 - 3.23900i) 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} +(5.05402 + 2.54104i) q^{96} +(-12.3915 + 7.15423i) q^{97} +(-2.09613 + 10.4536i) 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} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 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} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * 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 $

$2$	−1.06182	−	0.934096i	−0.750821	−	0.660505i
$2$	−1.06182	−	0.934096i	−0.750821	−	0.660505i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.254930	+	1.98369i	0.127465	+	0.991843i
$5$			3.05041i			1.36419i	0.731265	+	0.682093i	$0.238930\pi$
$5$			3.05041i			1.36419i	−0.731265	+	0.682093i	$0.761070\pi$
$6$	−1.06182	−	0.934096i	−0.433487	−	0.381343i
$7$	1.90650	−	3.30215i	0.720589	−	1.24810i	−0.240175	−	0.970730i	$-0.577205\pi$
$7$	1.90650	−	3.30215i	0.720589	−	1.24810i	0.960764	−	0.277367i	$-0.0894618\pi$
$8$	1.58226	−	2.34445i	0.559414	−	0.828888i
$9$	1.00000			0.333333
$10$	2.84938	−	3.23900i	0.901053	−	1.02426i
$11$	1.71453	−	2.96965i	0.516950	−	0.895384i	−0.482856	−	0.875700i	$-0.660400\pi$
$11$	1.71453	−	2.96965i	0.516950	−	0.895384i	0.999806	−	0.0196845i	$-0.00626619\pi$
$12$	0.254930	+	1.98369i	0.0735920	+	0.572641i
$13$	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
$16$	−3.87002	+	1.01140i	−0.967505	+	0.252851i
$17$	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	$0.781381\pi$
$18$	−1.06182	−	0.934096i	−0.250274	−	0.220168i
$19$	1.55431	−	0.897384i	0.356584	−	0.205874i	−0.310997	−	0.950411i	$-0.600663\pi$
$19$	1.55431	−	0.897384i	0.356584	−	0.205874i	0.667581	+	0.744537i	$0.267330\pi$
$20$	−6.05106	+	0.777642i	−1.35306	+	0.173886i
$21$	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	−0.901266	−	0.433267i	$-0.857361\pi$
$23$	−4.68399	+	2.70430i	−0.976679	+	0.563886i	−0.0754128	+	0.997152i	$0.524027\pi$
$24$	1.58226	−	2.34445i	0.322978	−	0.478559i
$25$	−4.30502			−0.861005
$26$	−2.36285	−	0.473793i	−0.463393	−	0.0929184i
$27$	1.00000			0.192450
$28$	7.03646	+	2.94008i	1.32977	+	0.555623i
$29$	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	$0.111624\pi$
$30$	2.84938	−	3.23900i	0.520223	−	0.591357i
$31$	1.04111	−	1.80326i	0.186989	−	0.323874i	−0.757256	−	0.653118i	$-0.773460\pi$
$31$	1.04111	−	1.80326i	0.186989	−	0.323874i	0.944245	+	0.329244i	$0.106794\pi$
$32$	5.05402	+	2.54104i	0.893433	+	0.449197i
$33$	1.71453	−	2.96965i	0.298461	−	0.516950i
$34$	0.372550	−	1.85794i	0.0638918	−	0.318635i
$35$	10.0729	+	5.81561i	1.70264	+	0.983018i
$36$	0.254930	+	1.98369i	0.0424883	+	0.330614i
$37$	−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	$0.981591\pi$
$38$	−2.48865	−	0.499017i	−0.403712	−	0.0809513i
$39$	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	$-0.213107\pi$
$43$	10.2838			1.56827			0.784134	+	0.620592i	$0.213107\pi$
$44$	6.32795	+	2.64404i	0.953974	+	0.398604i
$45$			3.05041i			0.454729i
$46$	7.49963	+	1.50381i	1.10576	+	0.221724i
$47$	−1.21783	−	0.703117i	−0.177639	−	0.102560i	0.408544	−	0.912739i	$-0.366037\pi$
$47$	−1.21783	−	0.703117i	−0.177639	−	0.102560i	−0.586183	+	0.810179i	$0.699370\pi$
$48$	−3.87002	+	1.01140i	−0.558589	+	0.145983i
$49$	−3.76948	−	6.52893i	−0.538497	−	0.932704i
$50$	4.57117	+	4.02131i	0.646461	+	0.568698i
$51$	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	$0.942084\pi$
$54$	−1.06182	−	0.934096i	−0.144496	−	0.127114i
$55$	9.05867	+	5.23003i	1.22147	+	0.705217i
$56$	−4.72515	−	9.69457i	−0.631425	−	1.29549i
$57$	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	$0.215511\pi$
$59$			9.62440i			1.25299i	−0.779425	+	0.626495i	$0.784489\pi$
$60$	−6.05106	+	0.777642i	−0.781189	+	0.100393i
$61$	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	0.969126	−	0.246566i	$-0.0793021\pi$
$71$	10.4497	+	6.03316i	1.24016	+	0.716005i	0.271031	+	0.962571i	$0.412635\pi$
$72$	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	$0.773668\pi$
$74$	−1.51910	+	7.57592i	−0.176592	+	0.880683i
$75$	−4.30502			−0.497101
$76$	2.17637	+	2.85450i	0.249647	+	0.327434i
$77$	−6.53750	−	11.3233i	−0.745018	−	1.29041i
$78$	−2.36285	−	0.473793i	−0.267540	−	0.0536464i
$79$	4.93575	−	8.54897i	0.555315	−	0.961835i	−0.442563	−	0.896737i	$-0.645931\pi$
$79$	4.93575	−	8.54897i	0.555315	−	0.961835i	0.997879	−	0.0650974i	$-0.0207358\pi$
$80$	−3.08520	−	11.8052i	−0.344935	−	1.31986i
$81$	1.00000			0.111111
$82$	−3.02445	−	8.95513i	−0.333995	−	0.988929i
$83$	−11.9041	+	6.87285i	−1.30665	+	0.754393i	−0.981535	−	0.191283i	$-0.938735\pi$
$83$	−11.9041	+	6.87285i	−1.30665	+	0.754393i	−0.325112	+	0.945676i	$0.605402\pi$
$84$	7.03646	+	2.94008i	0.767741	+	0.320789i
$85$	−3.53970	+	2.04365i	−0.383935	+	0.221665i
$86$	−10.9196	−	9.60607i	−1.17749	−	1.03585i
$87$	0.926578	−	1.60488i	0.0993396	−	0.172061i
$88$	−4.24937	−	8.71840i	−0.452984	−	0.929385i
$89$	−2.62544			−0.278296			−0.139148	−	0.990272i	$-0.544436\pi$
$89$	−2.62544			−0.278296			−0.139148	+	0.990272i	$0.544436\pi$
$90$	2.84938	−	3.23900i	0.300351	−	0.341420i
$91$		−	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
$96$	5.05402	+	2.54104i	0.515824	+	0.259344i
$97$	−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	$0.592142\pi$
$98$	−2.09613	+	10.4536i	−0.211741	+	1.05597i
$99$	1.71453	−	2.96965i	0.172317	−	0.298461i
$100$	−1.09748	−	8.53982i	−0.109748	−	0.853982i
$101$	−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	$0.902282\pi$
$102$	0.372550	−	1.85794i	0.0368880	−	0.183964i
$103$	−8.83844	−	5.10287i	−0.870877	−	0.502801i	−0.00323750	−	0.999995i	$-0.501031\pi$
$103$	−8.83844	−	5.10287i	−0.870877	−	0.502801i	−0.867640	+	0.497194i	$0.834364\pi$
$104$	0.337494	−	4.80794i	0.0330940	−	0.471457i
$105$	10.0729	+	5.81561i	0.983018	+	0.567546i
$106$	2.46098	−	2.79749i	0.239031	−	0.271716i
$107$		−	5.18115i		−	0.500881i	−0.968132	−	0.250441i	$-0.919425\pi$
$107$		−	5.18115i		−	0.500881i	0.968132	−	0.250441i	$-0.0805755\pi$
$108$	0.254930	+	1.98369i	0.0245307	+	0.190880i
$109$			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	$0.345079\pi$
$114$	−2.48865	−	0.499017i	−0.233083	−	0.0467372i
$115$	−8.24923	−	14.2881i	−0.769245	−	1.33237i
$116$	3.41979	+	1.42891i	0.317520	+	0.132671i
$117$	1.47575	−	0.852022i	0.136433	−	0.0787695i
$118$	8.99011	−	10.2194i	0.827607	−	0.940772i
$119$	5.10910			0.468350
$120$	7.15154	+	4.82656i	0.652843	+	0.440602i
$121$	−0.379231	−	0.656847i	−0.0344755	−	0.0597133i
$122$	−8.13900	−	1.63201i	−0.736870	−	0.147755i
$123$	5.78819	+	3.34181i	0.521903	+	0.301321i
$124$	3.84251	+	1.60553i	0.345067	+	0.144181i
$125$			2.11996i			0.189615i
$126$	−5.10889	+	1.72544i	−0.455136	+	0.153715i
$127$	14.4999	+	8.37151i	1.28666	+	0.742851i	0.978056	−	0.208340i	$-0.0668062\pi$
$127$	14.4999	+	8.37151i	1.28666	+	0.742851i	0.308600	+	0.951192i	$0.400140\pi$
$128$	−3.75221	+	10.6734i	−0.331652	+	0.943402i
$129$	10.2838			0.905440
$130$	1.44526	−	7.20767i	0.126758	−	0.632154i
$131$		−	10.9676i		−	0.958241i	−0.877749	−	0.479120i	$-0.840956\pi$
$131$		−	10.9676i		−	0.958241i	0.877749	−	0.479120i	$-0.159044\pi$
$132$	6.32795	+	2.64404i	0.550777	+	0.230134i
$133$		−	6.84345i		−	0.593402i
$134$	−2.26420	+	11.3522i	−0.195597	+	0.980684i
$135$			3.05041i			0.262538i
$136$	3.78055	+	0.265377i	0.324180	+	0.0227559i
$137$			0.0295386i			0.00252365i	0.999999	+	0.00126183i	$0.000401652\pi$
$137$			0.0295386i			0.00252365i	−0.999999	+	0.00126183i	$0.999598\pi$
$138$	7.49963	+	1.50381i	0.638411	+	0.128013i
$139$	9.42510			0.799427			0.399713	−	0.916640i	$-0.369110\pi$
$139$	9.42510			0.799427			0.399713	+	0.916640i	$0.369110\pi$
$140$	−8.96845	+	21.4641i	−0.757973	+	1.81405i
$141$	−1.21783	−	0.703117i	−0.102560	−	0.0592131i
$142$	−5.46021	−	16.1672i	−0.458211	−	1.35672i
$143$		−	5.84327i		−	0.488639i
$144$	−3.87002	+	1.01140i	−0.322502	+	0.0842835i
$145$	4.89555	+	2.82645i	0.406553	+	0.234724i
$146$	0.885366	−	4.41541i	0.0732734	−	0.365422i
$147$	−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	$0.487439\pi$
$150$	4.57117	+	4.02131i	0.373234	+	0.328338i
$151$	−16.7349	+	9.66190i	−1.36187	+	0.786274i	−0.989872	−	0.141961i	$-0.954659\pi$
$151$	−16.7349	+	9.66190i	−1.36187	+	0.786274i	−0.371994	+	0.928235i	$0.621326\pi$
$152$	0.355462	−	5.06391i	0.0288318	−	0.410737i
$153$	0.669958	+	1.16040i	0.0541629	+	0.0938129i
$154$	−3.63537	+	18.1300i	−0.292947	+	1.46095i
$155$	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
$160$	−7.75123	+	15.4168i	−0.612789	+	1.21881i
$161$			20.6230i			1.62532i
$162$	−1.06182	−	0.934096i	−0.0834246	−	0.0733895i
$163$	−11.5865	−	6.68947i	−0.907525	−	0.523960i	−0.0278913	−	0.999611i	$-0.508879\pi$
$163$	−11.5865	−	6.68947i	−0.907525	−	0.523960i	−0.879634	+	0.475651i	$0.842213\pi$
$164$	−5.15352	+	12.3339i	−0.402423	+	0.963114i
$165$	9.05867	+	5.23003i	0.705217	+	0.407157i
$166$	19.0599	+	3.82185i	1.47934	+	0.296633i
$167$	−20.3646	−	11.7575i	−1.57586	−	0.909822i	−0.995428	−	0.0955127i	$-0.969551\pi$
$167$	−20.3646	−	11.7575i	−1.57586	−	0.909822i	−0.580431	−	0.814310i	$-0.697116\pi$
$168$	−4.72515	−	9.69457i	−0.364553	−	0.747952i
$169$	−5.04812	+	8.74359i	−0.388317	+	0.672584i
$170$	5.66750	+	1.13643i	0.434677	+	0.0871604i
$171$	1.55431	−	0.897384i	0.118861	−	0.0686247i
$172$	2.62165	+	20.3999i	0.199899	+	1.55548i
$173$	−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
$178$	2.78775	+	2.45241i	0.208950	+	0.183816i
$179$	3.10081			0.231766			0.115883	−	0.993263i	$-0.463030\pi$
$179$	3.10081			0.231766			0.115883	+	0.993263i	$0.463030\pi$
$180$	−6.05106	+	0.777642i	−0.451020	+	0.0579620i
$181$	−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	$0.725448\pi$
$182$	−6.06931	+	6.89921i	−0.449887	+	0.511403i
$183$	5.08331	−	2.93485i	0.375769	−	0.216950i
$184$	−1.07120	+	15.2603i	−0.0789699	+	1.12500i
$185$	14.4334	−	8.33314i	1.06117	−	0.612665i
$186$	−2.78989	+	0.942240i	−0.204565	+	0.0690884i
$187$	4.59465			0.335994
$188$	1.08430	−	2.59505i	0.0790807	−	0.189263i
$189$	1.90650	−	3.30215i	0.138677	−	0.240196i
$190$	1.52221	−	7.59140i	0.110433	−	0.550738i
$191$	−2.21515	−	3.83674i	−0.160282	−	0.277617i	0.774688	−	0.632344i	$-0.217907\pi$
$191$	−2.21515	−	3.83674i	−0.160282	−	0.277617i	−0.934970	+	0.354727i	$0.884574\pi$
$192$	−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	$0.369574\pi$
$194$	19.8403	+	3.97833i	1.42445	+	0.285627i
$195$	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	−0.225978	−	0.974133i	$-0.572558\pi$
$199$	7.11906	−	4.11019i	0.504657	−	0.291364i	0.730635	+	0.682769i	$0.239224\pi$
$200$	−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
$208$	−4.84943	+	4.78992i	−0.336248	+	0.332121i
$209$		−	6.15437i		−	0.425707i
$210$	−5.26332	−	15.5842i	−0.363204	−	1.07541i
$211$	13.7604	−	7.94455i	0.947302	−	0.546925i	0.0550604	−	0.998483i	$-0.482465\pi$
$211$	13.7604	−	7.94455i	0.947302	−	0.546925i	0.892242	+	0.451558i	$0.149132\pi$
$212$	−5.22624	+	0.671641i	−0.358940	+	0.0461285i
$213$	10.4497	+	6.03316i	0.716005	+	0.413386i
$214$	−4.83969	+	5.50146i	−0.330835	+	0.376072i
$215$			31.3699i			2.13941i
$216$	1.58226	−	2.34445i	0.107659	−	0.159520i
$217$	−3.96975	−	6.87582i	−0.269484	−	0.466761i
$218$	14.1617	−	16.0981i	0.959150	−	1.09030i
$219$	1.59216	+	2.75770i	0.107588	+	0.186348i
$220$	−8.06541	+	19.3029i	−0.543770	+	1.30140i
$221$	1.97738	+	1.14164i	0.133013	+	0.0767949i
$222$	−1.51910	+	7.57592i	−0.101956	+	0.508462i
$223$			20.1734i			1.35091i	0.737402	+	0.675454i	$0.236052\pi$
$223$			20.1734i			1.35091i	−0.737402	+	0.675454i	$0.763948\pi$
$224$	18.0264	−	11.8447i	1.20444	−	0.791404i
$225$	−4.30502			−0.287002
$226$	−8.14858	−	24.1272i	−0.542036	−	1.60492i
$227$	−11.9488	−	6.89864i	−0.793069	−	0.457879i	0.0479727	−	0.998849i	$-0.484724\pi$
$227$	−11.9488	−	6.89864i	−0.793069	−	0.457879i	−0.841042	+	0.540970i	$0.818057\pi$
$228$	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	$0.607925\pi$
$230$	−4.58723	+	22.8770i	−0.302473	+	1.50846i
$231$	−6.53750	−	11.3233i	−0.430136	−	0.745018i
$232$	−2.29647	−	4.71166i	−0.150771	−	0.309336i
$233$	−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	$0.813984\pi$
$234$	−2.36285	−	0.473793i	−0.154464	−	0.0309728i
$235$	2.14480	−	3.71490i	0.139911	−	0.242333i
$236$	−19.0918	+	2.45355i	−1.24277	+	0.159712i
$237$	4.93575	−	8.54897i	0.320612	−	0.555315i
$238$	−5.42495	−	4.77239i	−0.351647	−	0.309348i
$239$	−3.59665	+	6.22958i	−0.232648	+	0.402958i	−0.958587	−	0.284801i	$-0.908072\pi$
$239$	−3.59665	+	6.22958i	−0.232648	+	0.402958i	0.725938	+	0.687760i	$0.241406\pi$
$240$	−3.08520	−	11.8052i	−0.199149	−	0.762020i
$241$	−2.11223			−0.136061			−0.0680304	−	0.997683i	$-0.521671\pi$
$241$	−2.11223			−0.136061			−0.0680304	+	0.997683i	$0.521671\pi$
$242$	−0.210882	+	1.05169i	−0.0135560	+	0.0676053i
$243$	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
$248$	−2.58033	−	5.29406i	−0.163851	−	0.336173i
$249$	−11.9041	+	6.87285i	−0.754393	+	0.435549i
$250$	1.98025	−	2.25102i	0.125242	−	0.142367i
$251$	4.93278	+	8.54383i	0.311355	+	0.539282i	0.978656	−	0.205506i	$-0.0658840\pi$
$251$	4.93278	+	8.54383i	0.311355	+	0.539282i	−0.667301	+	0.744788i	$0.732551\pi$
$252$	7.03646	+	2.94008i	0.443255	+	0.185208i
$253$			18.5464i			1.16600i
$254$	−7.57649	−	22.4333i	−0.475391	−	1.40759i
$255$	−3.53970	+	2.04365i	−0.221665	+	0.127978i
$256$	13.9541	−	7.82830i	0.872133	−	0.489269i
$257$	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	$0.148724\pi$
$258$	−10.9196	−	9.60607i	−0.679824	−	0.598048i
$259$	−20.8328			−1.29448
$260$	−8.26726	+	6.30324i	−0.512714	+	0.390911i
$261$	0.926578	−	1.60488i	0.0573538	−	0.0993396i
$262$	−10.2448	+	11.6456i	−0.632923	+	0.719468i
$263$		−	16.6218i		−	1.02495i	−0.858703	−	0.512473i	$-0.828730\pi$
$263$		−	16.6218i		−	1.02495i	0.858703	−	0.512473i	$-0.171270\pi$
$264$	−4.24937	−	8.71840i	−0.261530	−	0.536581i
$265$	−8.03665			−0.493688
$266$	−6.39243	+	7.26652i	−0.391945	+	0.445539i
$267$	−2.62544			−0.160674
$268$	13.0083	−	9.93907i	0.794606	−	0.607125i
$269$	−11.3463			−0.691799			−0.345899	−	0.938272i	$-0.612426\pi$
$269$	−11.3463			−0.691799			−0.345899	+	0.938272i	$0.612426\pi$
$270$	2.84938	−	3.23900i	0.173408	−	0.197119i
$271$	−0.663016			−0.0402753			−0.0201377	−	0.999797i	$-0.506410\pi$
$271$	−0.663016			−0.0402753			−0.0201377	+	0.999797i	$0.506410\pi$
$272$	−3.76638	−	3.81318i	−0.228371	−	0.231208i
$273$		−	6.49752i		−	0.393248i
$274$	0.0275919	−	0.0313647i	0.00166689	−	0.00189481i
$275$	−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	$0.558483\pi$
$278$	−10.0078	−	8.80395i	−0.600227	−	0.528026i
$279$	1.04111	−	1.80326i	0.0623297	−	0.107958i
$280$	29.5724	−	14.4137i	1.76729	−	0.861381i
$281$	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	$0.168229\pi$
$283$			16.9654i			1.00849i	−0.863561	+	0.504244i	$0.831771\pi$
$284$	−9.30395	+	22.2671i	−0.552088	+	1.32131i
$285$	2.73739	+	4.74130i	0.162149	+	0.280851i
$286$	−5.45818	+	6.20451i	−0.322749	+	0.366881i
$287$	22.0704	−	12.7423i	1.30277	−	0.752156i
$288$	5.05402	+	2.54104i	0.297811	+	0.149732i
$289$	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	$0.449642\pi$
$294$	−2.09613	+	10.4536i	−0.122249	+	0.609667i
$295$	−29.3584			−1.70931
$296$	−15.4155	−	1.08210i	−0.896008	−	0.0628955i
$297$	1.71453	−	2.96965i	0.0994872	−	0.172317i
$298$	−1.02268	−	0.899667i	−0.0592425	−	0.0521163i
$299$	−4.60825	+	7.98172i	−0.266502	+	0.461595i
$300$	−1.09748	−	8.53982i	−0.0633630	−	0.493047i
$301$	19.6061	−	33.9588i	1.13008	−	1.95735i
$302$	26.7946	+	5.37279i	1.54186	+	0.309169i
$303$	−11.7399	−	6.77804i	−0.674440	−	0.389388i
$304$	−5.10761	+	5.04493i	−0.292942	+	0.289347i
$305$	8.95251	+	15.5062i	0.512619	+	0.887882i
$306$	0.372550	−	1.85794i	0.0212973	−	0.106212i
$307$	−7.63838	+	4.41002i	−0.435945	+	0.251693i	−0.701876	−	0.712299i	$-0.747654\pi$
$307$	−7.63838	+	4.41002i	−0.435945	+	0.251693i	0.265931	+	0.963992i	$0.414321\pi$
$308$	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	$-0.589422\pi$
$311$	−9.77865			−0.554497			−0.277248	+	0.960798i	$0.589422\pi$
$312$	0.337494	−	4.80794i	0.0191069	−	0.272196i
$313$			0.848936i			0.0479847i	0.999712	+	0.0239923i	$0.00763773\pi$
$313$			0.848936i			0.0479847i	−0.999712	+	0.0239923i	$0.992362\pi$
$314$	−2.61583	+	13.0454i	−0.147620	+	0.736193i
$315$	10.0729	+	5.81561i	0.567546	+	0.327673i
$316$	18.2168	+	7.61159i	1.02477	+	0.428186i
$317$	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	$0.728698\pi$
$318$	2.46098	−	2.79749i	0.138005	−	0.156875i
$319$	−3.17729	−	5.50324i	−0.177894	−	0.308122i
$320$	22.6312	−	9.12955i	1.26512	−	0.510357i
$321$		−	5.18115i		−	0.289184i
$322$	19.2638	−	21.8979i	1.07353	−	1.22032i
$323$	2.08265	+	1.20242i	0.115882	+	0.0669044i
$324$	0.254930	+	1.98369i	0.0141628	+	0.110205i
$325$	−6.35312	+	3.66798i	−0.352408	+	0.203463i
$326$	6.05420	+	17.9259i	0.335311	+	0.992826i
$327$			15.1608i			0.838397i
$328$	16.9931	−	8.28249i	0.938290	−	0.457324i
$329$	−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	$-0.491225\pi$
$331$	16.0007	−	27.7140i	0.879478	−	1.52330i	0.851915	−	0.523680i	$-0.175441\pi$
$332$	−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
$342$	−2.48865	−	0.499017i	−0.134571	−	0.0269838i
$343$	−2.05504			−0.110962
$344$	16.2717	−	24.1099i	0.877312	−	1.29992i
$345$	−8.24923	−	14.2881i	−0.444124	−	0.769245i
$346$	−6.23336	+	31.0864i	−0.335107	+	1.67121i
$347$	−6.46555	+	11.1987i	−0.347089	+	0.601176i	−0.985731	−	0.168328i	$-0.946163\pi$
$347$	−6.46555	+	11.1987i	−0.347089	+	0.601176i	0.638642	+	0.769504i	$0.279497\pi$
$348$	3.41979	+	1.42891i	0.183320	+	0.0765975i
$349$	−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
$352$	16.2113	−	10.6520i	0.864064	−	0.567753i
$353$	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	$0.0791576\pi$
$354$	8.99011	−	10.2194i	0.477819	−	0.543155i
$355$	−18.4036	+	31.8761i	−0.976764	+	1.69181i
$356$	−0.669303	−	5.20804i	−0.0354730	−	0.276026i
$357$	5.10910			0.270402
$358$	−3.29251	−	2.89646i	−0.174015	−	0.153083i
$359$			18.8160i			0.993071i	0.868016	+	0.496535i	$0.165395\pi$
$359$			18.8160i			0.993071i	−0.868016	+	0.496535i	$0.834605\pi$
$360$	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
$364$	12.8890	−	1.65641i	0.675569	−	0.0868196i
$365$	−8.41212	+	4.85674i	−0.440310	+	0.254213i
$366$	−8.13900	−	1.63201i	−0.425432	−	0.0853066i
$367$	−10.3476	+	17.9226i	−0.540140	+	0.935551i	0.458755	+	0.888563i	$0.348296\pi$
$367$	−10.3476	+	17.9226i	−0.540140	+	0.935551i	−0.998895	+	0.0469878i	$0.985038\pi$
$368$	15.3920	−	15.2031i	0.802363	−	0.792516i
$369$	5.78819	+	3.34181i	0.301321	+	0.173968i
$370$	−23.1097	−	4.63389i	−1.20142	−	0.240905i
$371$	8.69989	+	5.02288i	0.451676	+	0.260775i
$372$	3.84251	+	1.60553i	0.199225	+	0.0832430i
$373$	−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	$0.804116\pi$
$374$	−4.87870	−	4.29185i	−0.252272	−	0.221926i
$375$			2.11996i			0.109474i
$376$	−3.57536	+	1.74264i	−0.184385	+	0.0898695i
$377$		−	3.15786i		−	0.162638i
$378$	−5.10889	+	1.72544i	−0.262773	+	0.0887473i
$379$	−5.70277	−	9.87748i	−0.292931	−	0.507372i	0.681570	−	0.731753i	$-0.261297\pi$
$379$	−5.70277	−	9.87748i	−0.292931	−	0.507372i	−0.974502	+	0.224381i	$0.927964\pi$
$380$	−8.70741	+	6.63883i	−0.446681	+	0.340565i
$381$	14.4999	+	8.37151i	0.742851	+	0.428885i
$382$	−1.23180	+	6.14309i	−0.0630242	+	0.314308i
$383$	−13.9838	−	24.2206i	−0.714538	−	1.23762i	−0.963137	−	0.269010i	$-0.913304\pi$
$383$	−13.9838	−	24.2206i	−0.714538	−	1.23762i	0.248600	−	0.968606i	$-0.420030\pi$
$384$	−3.75221	+	10.6734i	−0.191479	+	0.544673i
$385$	34.5407	−	19.9421i	1.76036	−	1.01634i
$386$	−11.7531	−	10.3394i	−0.598219	−	0.526260i
$387$	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	$0.571909\pi$
$390$	1.44526	−	7.20767i	0.0731837	−	0.364975i
$391$	−6.27615	−	3.62354i	−0.317398	−	0.183250i
$392$	−21.2710	−	1.49313i	−1.07435	−	0.0754143i
$393$		−	10.9676i		−	0.553241i
$394$	12.4305	+	36.8055i	0.626238	+	1.85424i
$395$	26.0779	+	15.0561i	1.31212	+	0.757554i
$396$	6.32795	+	2.64404i	0.317991	+	0.132868i
$397$	38.0941			1.91189			0.955945	−	0.293545i	$-0.0948352\pi$
$397$	38.0941			1.91189			0.955945	+	0.293545i	$0.0948352\pi$
$398$	−11.3985	−	2.28560i	−0.571355	−	0.114567i
$399$		−	6.84345i		−	0.342601i
$400$	16.6605	−	4.35411i	0.833027	−	0.217706i
$401$			22.1666i			1.10695i	0.832867	+	0.553473i	$0.186698\pi$
$401$			22.1666i			1.10695i	−0.832867	+	0.553473i	$0.813302\pi$
$402$	−2.26420	+	11.3522i	−0.112928	+	0.566198i
$403$		−	3.54820i		−	0.176748i
$404$	10.4526	−	25.0162i	0.520039	−	1.24460i
$405$			3.05041i			0.151576i
$406$	−1.96465	+	9.79792i	−0.0975041	+	0.486263i
$407$	−18.7351			−0.928663
$408$	3.78055	+	0.265377i	0.187165	+	0.0131381i
$409$	−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
$412$	7.86932	−	18.8336i	0.387693	−	0.927863i
$413$	31.7812	+	18.3489i	1.56385	+	0.902891i
$414$	7.49963	+	1.50381i	0.368587	+	0.0739081i
$415$	−20.9650	−	36.3125i	−1.02913	−	1.78251i
$416$	9.62347	−	0.556204i	0.471830	−	0.0272702i
$417$	9.42510			0.461549
$418$	−5.74877	+	6.53484i	−0.281182	+	0.319630i
$419$	−10.2786	+	5.93435i	−0.502142	+	0.289912i	−0.729598	−	0.683877i	$-0.760293\pi$
$419$	−10.2786	+	5.93435i	−0.502142	+	0.289912i	0.227456	+	0.973788i	$0.426959\pi$
$420$	−8.96845	+	21.4641i	−0.437616	+	1.04734i
$421$	−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	$-0.450285\pi$
$422$	−22.0320	−	4.41780i	−1.07250	−	0.215055i
$423$	−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
$428$	10.2778	−	1.32083i	0.496795	−	0.0638448i
$429$		−	5.84327i		−	0.282116i
$430$	29.3025	−	33.3092i	1.41309	−	1.60631i
$431$	−20.7144	−	11.9595i	−0.997779	−	0.576068i	−0.0901886	−	0.995925i	$-0.528747\pi$
$431$	−20.7144	−	11.9595i	−0.997779	−	0.576068i	−0.907590	+	0.419857i	$0.862080\pi$
$432$	−3.87002	+	1.01140i	−0.186196	+	0.0486611i
$433$	−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	$0.699493\pi$
$434$	−2.20750	+	11.0090i	−0.105963	+	0.528450i
$435$	4.89555	+	2.82645i	0.234724	+	0.135518i
$436$	−30.0744	+	3.86495i	−1.44030	+	0.185098i
$437$	−4.85359	+	8.40667i	−0.232179	+	0.402145i
$438$	0.885366	−	4.41541i	0.0423044	−	0.210976i
$439$	−30.1261	+	17.3933i	−1.43784	+	0.830138i	−0.997700	−	0.0677898i	$-0.978405\pi$
$439$	−30.1261	+	17.3933i	−1.43784	+	0.830138i	−0.440142	+	0.897928i	$0.645072\pi$
$440$	26.5947	−	12.9623i	1.26785	−	0.617955i
$441$	−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	−0.998041	−	0.0625619i	$-0.980073\pi$
$443$	−9.36281	+	16.2169i	−0.444840	+	0.770486i	0.553201	+	0.833048i	$0.313406\pi$
$444$	8.68965	−	6.62528i	0.412393	−	0.314422i
$445$		−	8.00867i		−	0.379647i
$446$	18.8438	−	21.4205i	0.892282	−	1.01429i
$447$	0.963142			0.0455551
$448$	−30.2049	−	4.26147i	−1.42705	−	0.201336i
$449$	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	$0.0505058\pi$
$450$	4.57117	+	4.02131i	0.215487	+	0.189566i
$451$	19.8481	−	11.4593i	0.934608	−	0.539596i
$452$	−13.8848	+	33.2304i	−0.653086	+	1.56303i
$453$	−16.7349	+	9.66190i	−0.786274	+	0.453955i
$454$	6.24350	+	18.4864i	0.293022	+	0.867612i
$455$	19.8201			0.929182
$456$	0.355462	−	5.06391i	0.0166461	−	0.237139i
$457$	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	$0.153105\pi$
$458$	31.8766	+	6.39181i	1.48950	+	0.298670i
$459$	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	$0.690572\pi$
$462$	−3.63537	+	18.1300i	−0.169133	+	0.843482i
$463$	11.0035	+	19.0586i	0.511376	+	0.885729i	0.999913	+	0.0131858i	$0.00419730\pi$
$463$	11.0035	+	19.0586i	0.511376	+	0.885729i	−0.488537	+	0.872543i	$0.662469\pi$
$464$	−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	−0.916864	−	0.399199i	$-0.869288\pi$
$467$	−22.2494	+	12.8457i	−1.02958	+	0.594429i	−0.112716	+	0.993627i	$0.535955\pi$
$468$	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
$476$	1.30246	+	10.1348i	0.0596983	+	0.464530i
$477$			2.63461i			0.120631i
$478$	9.63803	−	3.25509i	0.440833	−	0.148884i
$479$	23.2487	−	13.4227i	1.06226	−	0.613297i	0.136204	−	0.990681i	$-0.456510\pi$
$479$	23.2487	−	13.4227i	1.06226	−	0.613297i	0.926057	+	0.377384i	$0.123176\pi$
$480$	−7.75123	+	15.4168i	−0.353794	+	0.703680i
$481$	−8.06291	−	4.65512i	−0.367637	−	0.212255i
$482$	2.24281	+	1.97303i	0.102157	+	0.0898689i
$483$			20.6230i			0.938378i
$484$	1.20630	−	0.919724i	0.0548318	−	0.0418057i
$485$	−21.8234	−	37.7992i	−0.990948	−	1.71637i
$486$	−1.06182	−	0.934096i	−0.0481652	−	0.0423714i
$487$	−6.25747	−	10.8383i	−0.283553	−	0.491128i	0.688704	−	0.725042i	$-0.258180\pi$
$487$	−6.25747	−	10.8383i	−0.283553	−	0.491128i	−0.972257	+	0.233914i	$0.924847\pi$
$488$	1.16252	−	16.5613i	0.0526249	−	0.749693i
$489$	−11.5865	−	6.68947i	−0.523960	−	0.302508i
$490$	−31.8878	−	6.39407i	−1.44055	−	0.288854i
$491$		−	40.0582i		−	1.80780i	−0.427740	−	0.903902i	$-0.640690\pi$
$491$		−	40.0582i		−	1.80780i	0.427740	−	0.903902i	$-0.359310\pi$
$492$	−5.15352	+	12.3339i	−0.232339	+	0.556054i
$493$	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
$498$	19.0599	+	3.82185i	0.854097	+	0.171261i
$499$	−5.52402	−	9.56789i	−0.247289	−	0.428318i	0.715483	−	0.698630i	$-0.246206\pi$
$499$	−5.52402	−	9.56789i	−0.247289	−	0.428318i	−0.962773	+	0.270312i	$0.912873\pi$
$500$	−4.20534	+	0.540442i	−0.188069	+	0.0241693i
$501$	−20.3646	−	11.7575i	−0.909822	−	0.525286i
$502$	2.74302	−	13.6797i	0.122427	−	0.610556i
$503$	11.9613	−	20.7176i	0.533329	−	0.923753i	−0.465913	−	0.884830i	$-0.654274\pi$
$503$	11.9613	−	20.7176i	0.533329	−	0.923753i	0.999242	−	0.0389223i	$-0.0123925\pi$
$504$	−4.72515	−	9.69457i	−0.210475	−	0.431830i
$505$	20.6758	−	35.8116i	0.920062	−	1.59359i
$506$	17.3241	−	19.6930i	0.770152	−	0.875460i
$507$	−5.04812	+	8.74359i	−0.224195	+	0.388317i
$508$	−12.9100	+	30.8974i	−0.572788	+	1.37085i
$509$	−27.8071			−1.23253			−0.616265	−	0.787539i	$-0.711355\pi$
$509$	−27.8071			−1.23253			−0.616265	+	0.787539i	$0.711355\pi$
$510$	5.66750	+	1.13643i	0.250961	+	0.0503221i
$511$	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
$516$	2.62165	+	20.3999i	0.115412	+	0.898054i
$517$	−4.17603	+	2.41103i	−0.183661	+	0.106037i
$518$	22.1207	+	19.4598i	0.971927	+	0.855014i
$519$	−11.2095	−	19.4154i	−0.492041	−	0.852239i
$520$	14.6662	+	1.02950i	0.643155	+	0.0451464i
$521$			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	−0.193726	−	0.981056i	$-0.562057\pi$
$523$	12.7846	−	7.38117i	0.559030	−	0.322756i	0.752756	+	0.658299i	$0.228724\pi$
$524$	21.7562	−	2.79596i	0.950425	−	0.122142i
$525$	−8.20752	+	14.2159i	−0.358206	+	0.620431i
$526$	−15.5264	+	17.6494i	−0.676982	+	0.769551i
$527$	2.79000			0.121534
$528$	−3.63176	+	13.2267i	−0.158052	+	0.575618i
$529$	3.12648	−	5.41522i	0.135934	−	0.235444i
$530$	8.53349	+	7.50700i	0.370671	+	0.326083i
$531$			9.62440i			0.417663i
$532$	13.5752	−	1.74460i	0.588562	−	0.0756380i
$533$	11.3892			0.493321
$534$	2.78775	+	2.45241i	0.120638	+	0.106126i
$535$	15.8047			0.683295
$536$	−23.0965	−	1.59744i	−0.997617	−	0.0689989i
$537$	3.10081			0.133810
$538$	12.0478	+	10.5986i	0.519417	+	0.456937i
$539$	−25.8515			−1.11350
$540$	−6.05106	+	0.777642i	−0.260396	+	0.0334644i
$541$			14.8487i			0.638394i	0.947688	+	0.319197i	$0.103413\pi$
$541$			14.8487i			0.638394i	−0.947688	+	0.319197i	$0.896587\pi$
$542$	0.704005	+	0.619320i	0.0302396	+	0.0266021i
$543$	−13.2249	+	22.9062i	−0.567534	+	0.982997i
$544$	0.437352	+	7.56708i	0.0187513	+	0.324436i
$545$	−46.2469			−1.98100
$546$	−6.06931	+	6.89921i	−0.259742	+	0.295259i
$547$	−5.38731	+	9.33109i	−0.230345	+	0.398968i	−0.957910	−	0.287070i	$-0.907319\pi$
$547$	−5.38731	+	9.33109i	−0.230345	+	0.398968i	0.727565	+	0.686039i	$0.240652\pi$
$548$	−0.0585953	+	0.00753027i	−0.00250307	+	0.000321677i
$549$	5.08331	−	2.93485i	0.216950	−	0.125256i
$550$	19.7793	−	6.68014i	0.843392	−	0.284842i
$551$		−	3.32599i		−	0.141692i
$552$	−1.07120	+	15.2603i	−0.0455933	+	0.649521i
$553$	−18.8200	−	32.5972i	−0.800308	−	1.38617i
$554$	6.45736	+	5.68061i	0.274347	+	0.241346i
$555$	14.4334	−	8.33314i	0.612665	−	0.353722i
$556$	2.40274	+	18.6964i	0.101899	+	0.792906i
$557$	−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
$562$	−35.7160	−	7.16168i	−1.50659	−	0.302097i
$563$	22.4845			0.947610			0.473805	−	0.880630i	$-0.342880\pi$
$563$	22.4845			0.947610			0.473805	+	0.880630i	$0.342880\pi$
$564$	1.08430	−	2.59505i	0.0456573	−	0.109271i
$565$	−27.4648	+	47.5704i	−1.15545	+	2.00130i
$566$	15.8473	−	18.0142i	0.666112	−	0.757194i
$567$	1.90650	−	3.30215i	0.0800654	−	0.138677i
$568$	30.6787	−	14.9529i	1.28725	−	0.627408i
$569$	−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	$0.968681\pi$
$570$	1.52221	−	7.59140i	0.0637583	−	0.317969i
$571$	34.7904	+	20.0863i	1.45593	+	0.840583i	0.998808	−	0.0488187i	$-0.0155457\pi$
$571$	34.7904	+	20.0863i	1.45593	+	0.840583i	0.457126	+	0.889402i	$0.348879\pi$
$572$	11.5912	−	1.48963i	0.484653	−	0.0622844i
$573$	−2.21515	−	3.83674i	−0.0925390	−	0.160282i
$574$	−35.3373	−	7.08575i	−1.47495	−	0.295754i
$575$	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
$580$	−4.35876	+	10.4318i	−0.180988	+	0.433156i
$581$			52.4123i			2.17443i
$582$	19.8403	+	3.97833i	0.822407	+	0.164907i
$583$	7.82388	+	4.51712i	0.324032	+	0.187080i
$584$	8.98449	+	0.630669i	0.371781	+	0.0260973i
$585$	2.59902	+	4.50164i	0.107456	+	0.186120i
$586$	−5.72691	−	5.03802i	−0.236576	−	0.208119i
$587$	−3.77482	−	6.53817i	−0.155803	−	0.269859i	0.777548	−	0.628824i	$-0.216463\pi$
$587$	−3.77482	−	6.53817i	−0.155803	−	0.269859i	−0.933351	+	0.358964i	$0.883130\pi$
$588$	11.9904	−	9.14188i	0.494475	−	0.377005i
$589$		−	3.73710i		−	0.153985i
$590$	31.1734	+	27.4236i	1.28339	+	1.12901i
$591$	−23.7894	−	13.7348i	−0.978565	−	0.564975i
$592$	15.3577	+	15.5486i	0.631199	+	0.639042i
$593$	−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
$596$	0.245534	+	1.91057i	0.0100575	+	0.0782601i
$597$	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	−0.999425	−	0.0339114i	$-0.989204\pi$
$599$	−11.5114	+	19.9384i	−0.470344	+	0.814660i	0.529081	+	0.848572i	$0.322537\pi$
$600$	−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	0.745109	−	0.666943i	$-0.232397\pi$
$607$	13.3060	+	7.68223i	0.540074	+	0.311812i	−0.205035	+	0.978755i	$0.565731\pi$
$608$	10.1358	−	0.585817i	0.411062	−	0.0237580i
$609$	−3.53304	−	6.11941i	−0.143166	−	0.247971i
$610$	4.97831	−	24.8273i	0.201566	−	1.00523i
$611$	−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	$0.913901\pi$
$614$	12.2300	+	2.45232i	0.493561	+	0.0989677i
$615$	−10.1939	+	17.6564i	−0.411058	+	0.711974i
$616$	−36.8909	−	2.58957i	−1.48638	−	0.104337i
$617$	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	−0.514882	−	0.857261i	$-0.672164\pi$
$619$	−0.744242	+	0.429688i	−0.0299136	+	0.0172706i	0.484969	+	0.874532i	$0.338831\pi$
$620$	−4.89754	+	11.7212i	−0.196690	+	0.470736i
$621$	−4.68399	+	2.70430i	−0.187962	+	0.108520i
$622$	10.3832	+	9.13420i	0.416328	+	0.366248i
$623$	−5.00539	+	8.66960i	−0.200537	+	0.347340i
$624$	−4.84943	+	4.78992i	−0.194133	+	0.191750i
$625$	−27.9919			−1.11968
$626$	0.792988	−	0.901418i	0.0316942	−	0.0360279i
$627$		−	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	0.887154	−	0.461473i	$-0.152679\pi$
$631$	1.10350	+	1.91133i	0.0439298	+	0.0760887i	−0.843224	+	0.537562i	$0.819346\pi$
$632$	−12.2330	−	25.0983i	−0.486602	−	0.998359i
$633$	13.7604	−	7.94455i	0.546925	−	0.315767i
$634$	3.19629	−	15.9402i	0.126941	−	0.633067i
$635$	−25.5366	+	44.2306i	−1.01339	+	1.75524i
$636$	−5.22624	+	0.671641i	−0.207234	+	0.0266323i
$637$	−11.1256	−	6.42336i	−0.440812	−	0.254503i
$638$	−1.76683	+	8.81135i	−0.0699494	+	0.348845i
$639$	10.4497	+	6.03316i	0.413386	+	0.238668i
$640$	−32.5582	−	11.4458i	−1.28698	−	0.452435i
$641$	−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	$0.703051\pi$
$642$	−4.83969	+	5.50146i	−0.191008	+	0.217125i
$643$			3.10268i			0.122358i	0.998127	+	0.0611789i	$0.0194860\pi$
$643$			3.10268i			0.122358i	−0.998127	+	0.0611789i	$0.980514\pi$
$644$	−40.9095	+	5.25742i	−1.61206	+	0.207171i
$645$			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	$-0.997997\pi$
$647$	−12.8565	−	22.2680i	−0.505439	−	0.875447i	0.494541	−	0.869154i	$-0.335336\pi$
$648$	1.58226	−	2.34445i	0.0621572	−	0.0920987i
$649$	28.5811	+	16.5013i	1.12191	+	0.647734i
$650$	10.1721	+	2.03969i	0.398984	+	0.0800032i
$651$	−3.96975	−	6.87582i	−0.155587	−	0.269484i
$652$	10.3161	−	24.6893i	0.404008	−	0.966909i
$653$	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	$-0.0685519\pi$
$654$	14.1617	−	16.0981i	0.553766	−	0.629486i
$655$	33.4556			1.30722
$656$	−25.7803	−	7.07870i	−1.00655	−	0.276377i
$657$	1.59216	+	2.75770i	0.0621160	+	0.107588i
$658$	7.43497	+	1.49084i	0.289845	+	0.0581190i
$659$	−9.73696	−	5.62163i	−0.379298	−	0.218988i	0.298215	−	0.954499i	$-0.403609\pi$
$659$	−9.73696	−	5.62163i	−0.379298	−	0.218988i	−0.677513	+	0.735511i	$0.736942\pi$
$660$	−8.06541	+	19.3029i	−0.313945	+	0.751363i
$661$		−	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
$664$	−2.72240	+	38.7833i	−0.105650	+	1.50508i
$665$	20.8753			0.809511
$666$	−1.51910	+	7.57592i	−0.0588641	+	0.293561i
$667$			10.0230i			0.388092i
$668$	18.1316	−	43.3943i	0.701534	−	1.67898i
$669$			20.1734i			0.779947i
$670$	−34.6290	−	6.90676i	−1.33784	−	0.266831i
$671$		−	20.1276i		−	0.777016i
$672$	18.0264	−	11.8447i	0.695383	−	0.456917i
$673$			33.7116i			1.29949i	0.760154	+	0.649743i	$0.225124\pi$
$673$			33.7116i			1.29949i	−0.760154	+	0.649743i	$0.774876\pi$
$674$	−8.82125	−	1.76881i	−0.339782	−	0.0681321i
$675$	−4.30502			−0.165700
$676$	−18.6315	−	7.78487i	−0.716595	−	0.299418i
$677$	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
$680$	−0.809509	+	11.5322i	−0.0310433	+	0.442242i
$681$	−11.9488	−	6.89864i	−0.457879	−	0.264356i
$682$	−1.98522	+	9.90050i	−0.0760181	+	0.379110i
$683$	−12.3397	−	21.3730i	−0.472166	−	0.817815i	0.527327	−	0.849662i	$-0.323194\pi$
$683$	−12.3397	−	21.3730i	−0.472166	−	0.817815i	−0.999493	+	0.0318472i	$0.989861\pi$
$684$	2.17637	+	2.85450i	0.0832156	+	0.109145i
$685$	−0.0901049			−0.00344273
$686$	2.18208	+	1.91960i	0.0833124	+	0.0732908i
$687$	−19.9089	+	11.4944i	−0.759572	+	0.438539i
$688$	−39.7986	+	10.4011i	−1.51731	+	0.396537i
$689$	2.24475	+	3.88802i	0.0855181	+	0.148122i
$690$	−4.58723	+	22.8770i	−0.174633	+	0.870912i
$691$	27.0601	+	15.6232i	1.02941	+	0.594333i	0.916817	−	0.399308i	$-0.130750\pi$
$691$	27.0601	+	15.6232i	1.02941	+	0.594333i	0.112598	+	0.993641i	$0.464083\pi$
$692$	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
$696$	−2.29647	−	4.71166i	−0.0870476	−	0.178595i
$697$			8.95550i			0.339214i
$698$	9.28394	+	8.16718i	0.351402	+	0.309132i
$699$	−11.8039	−	6.81500i	−0.446466	−	0.257767i
$700$	−30.2921	−	12.6571i	−1.14493	−	0.478394i
$701$	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	$0.614746\pi$
$702$	−2.36285	−	0.473793i	−0.0891800	−	0.0178821i
$703$	−8.49218	−	4.90296i	−0.320289	−	0.184919i
$704$	−27.1635	−	3.83238i	−1.02376	−	0.144438i
$705$	2.14480	−	3.71490i	0.0807777	−	0.139911i
$706$	−37.3233	−	7.48398i	−1.40468	−	0.281663i
$707$	−44.7642	+	25.8446i	−1.68353	+	0.971988i
$708$	−19.0918	+	2.45355i	−0.717513	+	0.0922100i
$709$	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
$714$	−5.42495	−	4.77239i	−0.203024	−	0.178602i
$715$	17.8244			0.666595
$716$	0.790491	+	6.15104i	0.0295420	+	0.229875i
$717$	−3.59665	+	6.22958i	−0.134319	+	0.232648i
$718$	17.5760	−	19.9792i	0.655929	−	0.745619i
$719$	−9.43992	+	5.45014i	−0.352050	+	0.203256i	−0.665588	−	0.746320i	$-0.731819\pi$
$719$	−9.43992	+	5.45014i	−0.352050	+	0.203256i	0.313538	+	0.949576i	$0.398486\pi$
$720$	−3.08520	−	11.8052i	−0.114978	−	0.439953i
$721$	−33.7009	+	19.4573i	−1.25509	+	0.724626i
$722$	21.1414	−	7.14017i	0.786802	−	0.265730i
$723$	−2.11223			−0.0785548
$724$	−48.8100	−	20.3945i	−1.81401	−	0.757957i
$725$	−3.98894	+	6.90905i	−0.148146	+	0.256596i
$726$	−0.210882	+	1.05169i	−0.00782658	+	0.0390319i
$727$	5.60679	+	9.71125i	0.207944	+	0.360170i	0.951067	−	0.308985i	$-0.0999893\pi$
$727$	5.60679	+	9.71125i	0.207944	+	0.360170i	−0.743122	+	0.669156i	$0.766656\pi$
$728$	−15.2331	−	10.2808i	−0.564577	−	0.381031i
$729$	1.00000			0.0370370
$730$	13.4688	+	2.70073i	0.498503	+	0.0999586i
$731$	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	$-0.905651\pi$
$739$	−19.8760	−	34.4262i	−0.731150	−	1.26639i	0.225243	−	0.974303i	$-0.427683\pi$
$740$	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	0.0380809	−	0.999275i	$-0.487876\pi$
$743$	25.1460	−	14.5181i	0.922519	−	0.532616i	0.884438	+	0.466658i	$0.154542\pi$
$744$	−2.58033	−	5.29406i	−0.0945996	−	0.194090i
$745$			2.93798i			0.107639i
$746$	7.31528	+	21.6599i	0.267832	+	0.793026i
$747$	−11.9041	+	6.87285i	−0.435549	+	0.251464i
$748$	1.17132	+	9.11435i	0.0428275	+	0.333254i
$749$	−17.1090	−	9.87787i	−0.625148	−	0.360929i
$750$	1.98025	−	2.25102i	0.0723085	−	0.0821957i
$751$		−	17.0296i		−	0.621420i	−0.950505	−	0.310710i	$-0.899433\pi$
$751$		−	17.0296i		−	0.621420i	0.950505	−	0.310710i	$-0.100567\pi$
$752$	5.42418	+	1.48936i	0.197799	+	0.0543113i
$753$	4.93278	+	8.54383i	0.179761	+	0.311355i
$754$	−2.94975	+	3.35309i	−0.107423	+	0.122112i
$755$	−29.4728	−	51.0484i	−1.07262	−	1.85784i
$756$	7.03646	+	2.94008i	0.255914	+	0.106930i
$757$	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	$0.376697\pi$
$758$	−3.17119	+	15.8151i	−0.115183	+	0.574429i
$759$			18.5464i			0.673193i
$760$	15.4470	+	1.08431i	0.560322	+	0.0393320i
$761$	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
$766$	−7.77610	+	38.7802i	−0.280962	+	1.40118i
$767$	8.20020	+	14.2032i	0.296092	+	0.512847i
$768$	13.9541	−	7.82830i	0.503526	−	0.282479i
$769$	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	$0.525827\pi$
$770$	−55.3039	−	11.0894i	−1.99301	−	0.399634i
$771$	0.903181	−	1.56436i	0.0325273	−	0.0563389i
$772$	2.82178	+	21.9571i	0.101558	+	0.790254i
$773$	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	$0.127212\pi$
$774$	−10.9196	−	9.60607i	−0.392496	−	0.345283i
$775$	−4.48201	+	7.76306i	−0.160998	+	0.278857i
$776$	−2.83386	+	40.3711i	−0.101730	+	1.44924i
$777$	−20.8328			−0.747371
$778$	8.02855	−	40.0392i	0.287837	−	1.43547i
$779$	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
$784$	21.1913	+	21.4546i	0.756833	+	0.766237i
$785$	24.8537	−	14.3493i	0.887066	−	0.512148i
$786$	−10.2448	+	11.6456i	−0.365418	+	0.415385i
$787$	−4.70785	−	8.15424i	−0.167817	−	0.290667i	0.769835	−	0.638243i	$-0.220338\pi$
$787$	−4.70785	−	8.15424i	−0.167817	−	0.290667i	−0.937652	+	0.347575i	$0.887005\pi$
$788$	21.1809	−	50.6921i	0.754540	−	1.80583i
$789$		−	16.6218i		−	0.591753i
$790$	−13.6263	−	40.3461i	−0.484800	−	1.43545i
$791$	59.4627	−	34.3308i	2.11425	−	1.22066i
$792$	−4.24937	−	8.71840i	−0.150995	−	0.309795i
$793$	5.00112	−	8.66219i	0.177595	−	0.307603i
$794$	−40.4492	−	35.5836i	−1.43549	−	1.26281i
$795$	−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	$0.997114\pi$
$798$	−6.39243	+	7.26652i	−0.226290	+	0.257232i
$799$		−	1.88423i		−	0.0666594i
$800$	−21.7577	−	10.9392i	−0.769250	−	0.386761i
$801$	−2.62544			−0.0927653
$802$	20.7057	−	23.5370i	0.731144	−	0.831119i
$803$	10.9192			0.385330
$804$	13.0083	−	9.93907i	0.458766	−	0.350524i
$805$	−62.9086			−2.21724
$806$	−3.31436	+	3.76755i	−0.116743	+	0.132706i
$807$	−11.3463			−0.399410
$808$	−34.4664	+	16.7990i	−1.21252	+	0.590986i
$809$			4.14471i			0.145720i	0.997342	+	0.0728601i	$0.0232126\pi$
$809$			4.14471i			0.145720i	−0.997342	+	0.0728601i	$0.976787\pi$
$810$	2.84938	−	3.23900i	0.100117	−	0.113807i
$811$	−24.0870	+	41.7199i	−0.845809	+	1.46498i	0.0391069	+	0.999235i	$0.487549\pi$
$811$	−24.0870	+	41.7199i	−0.845809	+	1.46498i	−0.884916	+	0.465750i	$0.845785\pi$
$812$	11.2383	−	8.56847i	0.394387	−	0.300694i
$813$	−0.663016			−0.0232530
$814$	19.8933	+	17.5004i	0.697260	+	0.613387i
$815$	20.4057	−	35.3436i	0.714779	−	1.23803i
$816$	−3.76638	−	3.81318i	−0.131850	−	0.133488i
$817$	15.9843	−	9.22854i	0.559220	−	0.322866i
$818$	9.96244	+	29.4979i	0.348329	+	1.03137i
$819$		−	6.49752i		−	0.227042i
$820$	−37.6234	−	15.7204i	−1.31387	−	0.548980i
$821$	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	$0.411075\pi$
$822$	0.0275919	−	0.0313647i	0.000962377	−	0.00109397i
$823$	8.75976	−	5.05745i	0.305346	−	0.176292i	−0.339496	−	0.940608i	$-0.610256\pi$
$823$	8.75976	−	5.05745i	0.305346	−	0.176292i	0.644842	+	0.764316i	$0.276923\pi$
$824$	−25.9482	+	12.6472i	−0.903947	+	0.440586i
$825$	−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	−0.674362	−	0.738401i	$-0.735581\pi$
$827$	−10.6998	+	6.17754i	−0.372069	+	0.214814i	0.302293	+	0.953215i	$0.402248\pi$
$828$	−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	$0.341257\pi$
$830$	−11.6582	+	58.1407i	−0.404663	+	2.01809i
$831$	−6.08139			−0.210961
$832$	−10.7380	−	8.39866i	−0.372272	−	0.291171i
$833$	5.05078	−	8.74821i	0.174999	−	0.303108i
$834$	−10.0078	−	8.80395i	−0.346541	−	0.304856i
$835$	35.8652	−	62.1204i	1.24117	−	2.14977i
$836$	12.2083	−	1.56893i	0.422234	−	0.0542627i
$837$	1.04111	−	1.80326i	0.0359861	−	0.0623297i
$838$	16.4573	+	3.29997i	0.568507	+	0.113996i
$839$	44.5141	+	25.7002i	1.53680	+	0.887271i	0.999023	+	0.0441824i	$0.0140683\pi$
$839$	44.5141	+	25.7002i	1.53680	+	0.887271i	0.537775	+	0.843089i	$0.319265\pi$
$840$	29.5724	−	14.4137i	1.02035	−	0.497319i
$841$	12.7829	+	22.1406i	0.440790	+	0.763470i
$842$	−8.87351	+	44.2531i	−0.305801	+	1.52506i
$843$	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
$848$	−2.66465	−	10.1960i	−0.0915045	−	0.350132i
$849$			16.9654i			0.582251i
$850$	−1.60384	+	7.99849i	−0.0550112	+	0.274346i
$851$	25.5915	+	14.7753i	0.877265	+	0.506489i
$852$	−9.30395	+	22.2671i	−0.318748	+	0.762857i
$853$	−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	$0.868410\pi$
$854$	−20.9061	+	23.7648i	−0.715393	+	0.813214i
$855$	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	$-0.0215988\pi$
$858$	−5.45818	+	6.20451i	−0.186339	+	0.211819i
$859$	−24.5884	−	14.1961i	−0.838946	−	0.484366i	0.0179597	−	0.999839i	$-0.494283\pi$
$859$	−24.5884	−	14.1961i	−0.838946	−	0.484366i	−0.856906	+	0.515473i	$0.827616\pi$
$860$	−62.2281	+	7.99713i	−2.12196	+	0.272700i
$861$	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	$-0.889168\pi$
$863$		−	20.0465i		−	0.682390i	0.939993	−	0.341195i	$-0.110832\pi$
$864$	5.05402	+	2.54104i	0.171941	+	0.0864480i
$865$	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	$0.751914\pi$
$878$	48.2356	+	9.67208i	1.62787	+	0.326417i
$879$	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	$0.895665\pi$
$882$	−2.09613	+	10.4536i	−0.0705804	+	0.351991i
$883$	10.8739	−	18.8342i	0.365937	−	0.633822i	−0.622989	−	0.782231i	$-0.714082\pi$
$883$	10.8739	−	18.8342i	0.365937	−	0.633822i	0.988926	+	0.148409i	$0.0474151\pi$
$884$	−1.76056	+	4.21353i	−0.0592140	+	0.141716i
$885$	−29.3584			−0.986872
$886$	25.0897	−	8.47365i	0.842906	−	0.284678i
$887$	−6.65860	+	3.84435i	−0.223574	+	0.129081i	−0.607604	−	0.794240i	$-0.707869\pi$
$887$	−6.65860	+	3.84435i	−0.223574	+	0.129081i	0.384030	+	0.923321i	$0.374536\pi$
$888$	−15.4155	−	1.08210i	−0.517311	−	0.0363128i
$889$	55.2880	−	31.9206i	1.85430	−	1.07058i
$890$	−7.48087	+	8.50378i	−0.250759	+	0.285047i
$891$	1.71453	−	2.96965i	0.0574389	−	0.0994872i
$892$	−40.0176	+	5.14279i	−1.33989	+	0.172193i
$893$	−2.52386			−0.0844578
$894$	−1.02268	−	0.899667i	−0.0342037	−	0.0300894i
$895$			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
$900$	−1.09748	−	8.53982i	−0.0365827	−	0.284661i
$901$	−3.05721	+	1.76508i	−0.101850	+	0.0588033i
$902$	−31.7792	−	6.37228i	−1.05813	−	0.212174i
$903$	19.6061	−	33.9588i	0.652450	−	1.13008i
$904$	45.7835	−	22.3150i	1.52274	−	0.742185i
$905$	−69.8733	−	40.3413i	−2.32267	−	1.34099i
$906$	26.7946	+	5.37279i	0.890191	+	0.178499i
$907$	−31.2791	−	18.0590i	−1.03861	−	0.599640i	−0.119168	−	0.992874i	$-0.538023\pi$
$907$	−31.2791	−	18.0590i	−1.03861	−	0.599640i	−0.919438	+	0.393234i	$0.871356\pi$
$908$	10.6386	−	25.4613i	0.353055	−	0.844964i
$909$	−11.7399	−	6.77804i	−0.389388	−	0.224813i
$910$	−21.0454	−	18.5139i	−0.697649	−	0.613730i
$911$			31.2491i			1.03533i	0.855584	+	0.517665i	$0.173198\pi$
$911$			31.2491i			1.03533i	−0.855584	+	0.517665i	$0.826802\pi$
$912$	−5.10761	+	5.04493i	−0.169130	+	0.167054i
$913$			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
$918$	0.372550	−	1.85794i	0.0122960	−	0.0613213i
$919$	−10.0334	−	17.3784i	−0.330973	−	0.573261i	0.651730	−	0.758451i	$-0.274043\pi$
$919$	−10.0334	−	17.3784i	−0.330973	−	0.573261i	−0.982703	+	0.185189i	$0.940710\pi$
$920$	−46.5502	−	3.26760i	−1.53471	−	0.107730i
$921$	−7.63838	+	4.41002i	−0.251693	+	0.145315i
$922$	25.6968	+	22.6058i	0.846280	+	0.744482i
$923$	20.5616			0.676792
$924$	20.7952	−	15.8550i	0.684113	−	0.521591i
$925$	11.7605	+	20.3698i	0.386683	+	0.669754i
$926$	6.11882	−	30.5152i	0.201077	−	1.00279i
$927$	−8.83844	−	5.10287i	−0.290292	−	0.167600i
$928$	8.76102	−	5.75662i	0.287594	−	0.188970i
$929$		−	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
$932$	10.5096	−	25.1526i	0.344255	−	0.823902i
$933$	−9.77865			−0.320139
$934$	35.6240	+	7.14324i	1.16565	+	0.233734i
$935$			14.0156i			0.458359i
$936$	0.337494	−	4.80794i	0.0110313	−	0.157152i
$937$		−	56.4036i		−	1.84263i	−0.388823	−	0.921313i	$-0.627118\pi$
$937$		−	56.4036i		−	1.84263i	0.388823	−	0.921313i	$-0.372882\pi$
$938$	33.1701	+	29.1198i	1.08304	+	0.950795i
$939$			0.848936i			0.0277040i
$940$	7.91596	+	3.30757i	0.258190	+	0.107881i
$941$			16.1905i			0.527796i	0.964551	+	0.263898i	$0.0850082\pi$
$941$			16.1905i			0.527796i	−0.964551	+	0.263898i	$0.914992\pi$
$942$	−2.61583	+	13.0454i	−0.0852282	+	0.425041i
$943$	−36.1491			−1.17718
$944$	−9.73414	−	37.2466i	−0.316819	−	1.21227i
$945$	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	$-0.766072\pi$
$947$		−	41.2682i		−	1.34103i	0.741894	−	0.670517i	$-0.233928\pi$
$948$	18.2168	+	7.61159i	0.591653	+	0.247213i
$949$	4.69924	+	2.71311i	0.152544	+	0.0880712i
$950$	10.7137	+	2.14828i	0.347598	+	0.0696994i
$951$	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	$0.468206\pi$
$954$	2.46098	−	2.79749i	0.0796771	−	0.0905720i
$955$	11.7037	−	6.75711i	0.378721	−	0.218655i
$956$	−13.2744	−	5.54652i	−0.429326	−	0.179387i
$957$	−3.17729	−	5.50324i	−0.102707	−	0.177894i
$958$	−37.2240	−	7.46407i	−1.20265	−	0.241153i
$959$	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
$964$	−0.538471	−	4.19001i	−0.0173430	−	0.134951i
$965$			33.7646i			1.08692i
$966$	19.2638	−	21.8979i	0.619804	−	0.704554i
$967$	−24.7218	−	14.2731i	−0.795000	−	0.458993i	0.0467201	−	0.998908i	$-0.485123\pi$
$967$	−24.7218	−	14.2731i	−0.795000	−	0.458993i	−0.841720	+	0.539915i	$0.818456\pi$
$968$	−2.13999	−	0.150217i	−0.0687818	−	0.00482815i
$969$	2.08265	+	1.20242i	0.0669044	+	0.0386273i
$970$	−12.1355	+	60.5211i	−0.389649	+	1.94322i
$971$	−30.7302	−	17.7421i	−0.986178	−	0.569370i	−0.0820483	−	0.996628i	$-0.526146\pi$
$971$	−30.7302	−	17.7421i	−0.986178	−	0.569370i	−0.904130	+	0.427258i	$0.859480\pi$
$972$	0.254930	+	1.98369i	0.00817688	+	0.0636268i
$973$	17.9690	−	31.1231i	0.576058	−	0.997762i
$974$	−3.47965	+	17.3534i	−0.111495	+	0.556038i
$975$	−6.35312	+	3.66798i	−0.203463	+	0.117469i
$976$	−16.7042	+	16.4992i	−0.534688	+	0.528127i
$977$	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
$982$	−37.4182	+	42.5347i	−1.19406	+	1.35734i
$983$	−3.51330			−0.112057			−0.0560284	−	0.998429i	$-0.517844\pi$
$983$	−3.51330			−0.112057			−0.0560284	+	0.998429i	$0.517844\pi$
$984$	16.9931	−	8.28249i	0.541722	−	0.264036i
$985$	41.8969	−	72.5675i	1.33495	−	2.31219i
$986$	−2.63658	−	2.31943i	−0.0839659	−	0.0738657i
$987$	−4.64360	+	2.68098i	−0.147807	+	0.0853366i
$988$	5.64387	+	2.35820i	0.179555	+	0.0750245i
$989$	−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	$-0.386515\pi$
$991$	21.9743			0.698037			0.349019	+	0.937116i	$0.386515\pi$
$992$	9.84394	−	6.46819i	0.312546	−	0.205365i
$993$	16.0007	−	27.7140i	0.507767	−	0.879478i
$994$	−63.7965	−	12.7923i	−2.02350	−	0.405747i
$995$	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	$0.467364\pi$
$998$	−3.07180	+	15.3194i	−0.0972361	+	0.484926i
$999$	−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.b.499.7	yes	68
4.3	odd	2		804.2.j.a.499.18	✓	68
67.38	odd	6		804.2.j.a.775.18	yes	68
268.239	even	6	inner	804.2.j.b.775.7	yes	68

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

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)

\(f(q)\)	\(=\)	\(q+(-1.06182 - 0.934096i) q^{2} +1.00000 q^{3} +(0.254930 + 1.98369i) q^{4} +3.05041i q^{5} +(-1.06182 - 0.934096i) q^{6} +(1.90650 - 3.30215i) q^{7} +(1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.06182 - 0.934096i) q^{2} +1.00000 q^{3} +(0.254930 + 1.98369i) q^{4} +3.05041i q^{5} +(-1.06182 - 0.934096i) q^{6} +(1.90650 - 3.30215i) q^{7} +(1.58226 - 2.34445i) q^{8} +1.00000 q^{9} +(2.84938 - 3.23900i) q^{10} +(1.71453 - 2.96965i) q^{11} +(0.254930 + 1.98369i) q^{12} +(1.47575 - 0.852022i) q^{13} +(-5.10889 + 1.72544i) q^{14} +3.05041i q^{15} +(-3.87002 + 1.01140i) q^{16} +(0.669958 + 1.16040i) q^{17} +(-1.06182 - 0.934096i) q^{18} +(1.55431 - 0.897384i) q^{19} +(-6.05106 + 0.777642i) 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} +(-2.36285 - 0.473793i) q^{26} +1.00000 q^{27} +(7.03646 + 2.94008i) q^{28} +(0.926578 - 1.60488i) q^{29} +(2.84938 - 3.23900i) q^{30} +(1.04111 - 1.80326i) q^{31} +(5.05402 + 2.54104i) q^{32} +(1.71453 - 2.96965i) q^{33} +(0.372550 - 1.85794i) q^{34} +(10.0729 + 5.81561i) q^{35} +(0.254930 + 1.98369i) q^{36} +(-2.73181 - 4.73163i) q^{37} +(-2.48865 - 0.499017i) 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} +(6.32795 + 2.64404i) q^{44} +3.05041i q^{45} +(7.49963 + 1.50381i) q^{46} +(-1.21783 - 0.703117i) q^{47} +(-3.87002 + 1.01140i) q^{48} +(-3.76948 - 6.52893i) q^{49} +(4.57117 + 4.02131i) q^{50} +(0.669958 + 1.16040i) q^{51} +(2.06636 + 2.71021i) q^{52} +2.63461i q^{53} +(-1.06182 - 0.934096i) q^{54} +(9.05867 + 5.23003i) q^{55} +(-4.72515 - 9.69457i) q^{56} +(1.55431 - 0.897384i) q^{57} +(-2.48297 + 0.838584i) q^{58} +9.62440i q^{59} +(-6.05106 + 0.777642i) 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} +(-1.51910 + 7.57592i) q^{74} -4.30502 q^{75} +(2.17637 + 2.85450i) q^{76} +(-6.53750 - 11.3233i) q^{77} +(-2.36285 - 0.473793i) q^{78} +(4.93575 - 8.54897i) q^{79} +(-3.08520 - 11.8052i) q^{80} +1.00000 q^{81} +(-3.02445 - 8.95513i) q^{82} +(-11.9041 + 6.87285i) q^{83} +(7.03646 + 2.94008i) q^{84} +(-3.53970 + 2.04365i) q^{85} +(-10.9196 - 9.60607i) q^{86} +(0.926578 - 1.60488i) q^{87} +(-4.24937 - 8.71840i) q^{88} -2.62544 q^{89} +(2.84938 - 3.23900i) 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} +(5.05402 + 2.54104i) q^{96} +(-12.3915 + 7.15423i) q^{97} +(-2.09613 + 10.4536i) 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	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

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