LMFDB - Embedded newform 451.2.j.a.379.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [451,2,Mod(119,451)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(451, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 8]))

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

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

chi := DirichletCharacter("451.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 451 = 11 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	451.j (of order $5$, degree $4$, 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:	$3.60125313116$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			379.10
Character	$\chi$	$=$	451.379
Dual form			451.2.j.a.119.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.506048 + 1.55746i) q^{2} +(-2.55608 - 1.85710i) q^{3} +(-0.551548 - 0.400723i) q^{4} -4.00839 q^{5} +(4.18585 - 3.04120i) q^{6} +(-0.366381 + 1.12760i) q^{7} +(-1.74648 + 1.26889i) q^{8} +(2.15767 + 6.64064i) q^{9} +O(q^{10})$	\(q+(-0.506048 + 1.55746i) q^{2} +(-2.55608 - 1.85710i) q^{3} +(-0.551548 - 0.400723i) q^{4} -4.00839 q^{5} +(4.18585 - 3.04120i) q^{6} +(-0.366381 + 1.12760i) q^{7} +(-1.74648 + 1.26889i) q^{8} +(2.15767 + 6.64064i) q^{9} +(2.02844 - 6.24289i) q^{10} +(-3.29351 - 0.390874i) q^{11} +(0.665618 + 2.04856i) q^{12} +(1.05979 - 3.26171i) q^{13} +(-1.57079 - 1.14124i) q^{14} +(10.2458 + 7.44399i) q^{15} +(-1.51379 - 4.65896i) q^{16} +(-2.86066 - 2.07839i) q^{17} -11.4344 q^{18} +3.72211 q^{19} +(2.21082 + 1.60626i) q^{20} +(3.03058 - 2.20184i) q^{21} +(2.27544 - 4.93170i) q^{22} +(6.71397 + 4.87798i) q^{23} +6.82062 q^{24} +11.0672 q^{25} +(4.54366 + 3.30116i) q^{26} +(3.88814 - 11.9665i) q^{27} +(0.653934 - 0.475111i) q^{28} +(2.29564 + 1.66788i) q^{29} +(-16.7785 + 12.1903i) q^{30} -4.60923 q^{31} +3.70462 q^{32} +(7.69259 + 7.11549i) q^{33} +(4.68463 - 3.40358i) q^{34} +(1.46860 - 4.51988i) q^{35} +(1.47100 - 4.52726i) q^{36} +(0.860841 + 0.625437i) q^{37} +(-1.88357 + 5.79702i) q^{38} +(-8.76624 + 6.36904i) q^{39} +(7.00059 - 5.08622i) q^{40} +(5.65841 + 2.99707i) q^{41} +(1.89565 + 5.83422i) q^{42} +(-6.73539 - 4.89355i) q^{43} +(1.65990 + 1.53537i) q^{44} +(-8.64880 - 26.6183i) q^{45} +(-10.9948 + 7.98821i) q^{46} +(-3.79369 - 11.6758i) q^{47} +(-4.78280 + 14.7199i) q^{48} +(4.52586 + 3.28823i) q^{49} +(-5.60053 + 17.2367i) q^{50} +(3.45229 + 10.6251i) q^{51} +(-1.89157 + 1.37430i) q^{52} +(-0.375183 + 0.272587i) q^{53} +(16.6697 + 12.1112i) q^{54} +(13.2017 + 1.56678i) q^{55} +(-0.790933 - 2.43424i) q^{56} +(-9.51402 - 6.91234i) q^{57} +(-3.75935 + 2.73133i) q^{58} -0.165535 q^{59} +(-2.66806 - 8.21144i) q^{60} +(1.98076 + 6.09614i) q^{61} +(2.33249 - 7.17867i) q^{62} -8.27854 q^{63} +(1.15286 - 3.54813i) q^{64} +(-4.24806 + 13.0742i) q^{65} +(-14.9749 + 8.38008i) q^{66} +(-1.33916 - 4.12152i) q^{67} +(0.744931 + 2.29266i) q^{68} +(-8.10253 - 24.9370i) q^{69} +(6.29633 + 4.57455i) q^{70} +(2.71507 + 1.97262i) q^{71} +(-12.1946 - 8.85990i) q^{72} +(-7.51212 + 5.45787i) q^{73} +(-1.40972 + 1.02422i) q^{74} +(-28.2887 - 20.5529i) q^{75} +(-2.05292 - 1.49154i) q^{76} +(1.64743 - 3.57057i) q^{77} +(-5.48337 - 16.8761i) q^{78} +(0.520090 + 1.60067i) q^{79} +(6.06785 + 18.6749i) q^{80} +(-15.2148 + 11.0542i) q^{81} +(-7.53122 + 7.29606i) q^{82} +(1.87484 - 5.77016i) q^{83} -2.55384 q^{84} +(11.4666 + 8.33099i) q^{85} +(11.0299 - 8.01370i) q^{86} +(-2.77042 - 8.52647i) q^{87} +(6.24804 - 3.49646i) q^{88} +(6.26931 - 4.55492i) q^{89} +45.8335 q^{90} +(3.28963 + 2.39005i) q^{91} +(-1.74835 - 5.38088i) q^{92} +(11.7816 + 8.55981i) q^{93} +20.1043 q^{94} -14.9197 q^{95} +(-9.46931 - 6.87986i) q^{96} +(-1.08173 + 0.785923i) q^{97} +(-7.41157 + 5.38482i) q^{98} +(-4.51067 - 22.7144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + q^{2} - 7 q^{3} - 39 q^{4} - 6 q^{5} + 6 q^{6} - q^{7} + 3 q^{8} - 45 q^{9}+O(q^{10}) $ 160 * q + q^2 - 7 * q^3 - 39 * q^4 - 6 * q^5 + 6 * q^6 - q^7 + 3 * q^8 - 45 * q^9	\( 160 q + q^{2} - 7 q^{3} - 39 q^{4} - 6 q^{5} + 6 q^{6} - q^{7} + 3 q^{8} - 45 q^{9} + 12 q^{10} + 5 q^{11} + 7 q^{12} + 11 q^{13} - 10 q^{14} - 6 q^{15} - 21 q^{16} - 20 q^{17} - 6 q^{18} - 48 q^{19} - 27 q^{20} + 11 q^{21} + 10 q^{22} + 5 q^{23} + 26 q^{24} + 126 q^{25} + 5 q^{26} + 11 q^{27} + 17 q^{28} + 11 q^{29} - 24 q^{30} + 2 q^{31} - 28 q^{32} + q^{33} - 29 q^{34} - 41 q^{35} - 67 q^{36} - 6 q^{37} - 69 q^{38} + 19 q^{39} + 33 q^{40} - 13 q^{41} + 46 q^{42} - 7 q^{43} + 20 q^{44} - 53 q^{45} + 29 q^{46} - q^{47} - 21 q^{48} - 7 q^{49} + 13 q^{50} - 9 q^{51} - 109 q^{52} - 3 q^{53} + 69 q^{54} - 75 q^{55} + 11 q^{56} + 38 q^{57} - 19 q^{58} + 10 q^{59} + 92 q^{60} + 7 q^{61} - 7 q^{62} - 112 q^{63} + 11 q^{64} - 41 q^{65} + 62 q^{66} - 43 q^{67} + 11 q^{68} - 10 q^{69} + 73 q^{70} - 31 q^{71} - 19 q^{72} - 30 q^{73} + 151 q^{74} - 78 q^{75} - 62 q^{76} + 18 q^{77} + 50 q^{78} - 22 q^{79} + 24 q^{80} - 58 q^{81} + 35 q^{82} + 22 q^{83} + 66 q^{84} + 6 q^{85} - 10 q^{86} + 46 q^{87} + 60 q^{88} - 13 q^{89} - 440 q^{90} + 54 q^{91} + 103 q^{92} + 25 q^{93} + 106 q^{94} - 28 q^{95} + 94 q^{96} + 29 q^{97} + 35 q^{98} + 40 q^{99}+O(q^{100}) \) 160 * q + q^2 - 7 * q^3 - 39 * q^4 - 6 * q^5 + 6 * q^6 - q^7 + 3 * q^8 - 45 * q^9 + 12 * q^10 + 5 * q^11 + 7 * q^12 + 11 * q^13 - 10 * q^14 - 6 * q^15 - 21 * q^16 - 20 * q^17 - 6 * q^18 - 48 * q^19 - 27 * q^20 + 11 * q^21 + 10 * q^22 + 5 * q^23 + 26 * q^24 + 126 * q^25 + 5 * q^26 + 11 * q^27 + 17 * q^28 + 11 * q^29 - 24 * q^30 + 2 * q^31 - 28 * q^32 + q^33 - 29 * q^34 - 41 * q^35 - 67 * q^36 - 6 * q^37 - 69 * q^38 + 19 * q^39 + 33 * q^40 - 13 * q^41 + 46 * q^42 - 7 * q^43 + 20 * q^44 - 53 * q^45 + 29 * q^46 - q^47 - 21 * q^48 - 7 * q^49 + 13 * q^50 - 9 * q^51 - 109 * q^52 - 3 * q^53 + 69 * q^54 - 75 * q^55 + 11 * q^56 + 38 * q^57 - 19 * q^58 + 10 * q^59 + 92 * q^60 + 7 * q^61 - 7 * q^62 - 112 * q^63 + 11 * q^64 - 41 * q^65 + 62 * q^66 - 43 * q^67 + 11 * q^68 - 10 * q^69 + 73 * q^70 - 31 * q^71 - 19 * q^72 - 30 * q^73 + 151 * q^74 - 78 * q^75 - 62 * q^76 + 18 * q^77 + 50 * q^78 - 22 * q^79 + 24 * q^80 - 58 * q^81 + 35 * q^82 + 22 * q^83 + 66 * q^84 + 6 * q^85 - 10 * q^86 + 46 * q^87 + 60 * q^88 - 13 * q^89 - 440 * q^90 + 54 * q^91 + 103 * q^92 + 25 * q^93 + 106 * q^94 - 28 * q^95 + 94 * q^96 + 29 * q^97 + 35 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/451\mathbb{Z}\right)^\times$.

$n$	$288$	$375$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.506048	+	1.55746i	−0.357830	+	1.10129i	0.596521	+	0.802598i	$0.296549\pi$
$2$	−0.506048	+	1.55746i	−0.357830	+	1.10129i	−0.954350	+	0.298689i	$0.903451\pi$
$3$	−2.55608	−	1.85710i	−1.47575	−	1.07220i	−0.978894	−	0.204368i	$-0.934486\pi$
$3$	−2.55608	−	1.85710i	−1.47575	−	1.07220i	−0.496860	−	0.867831i	$-0.665514\pi$
$4$	−0.551548	−	0.400723i	−0.275774	−	0.200362i
$5$	−4.00839			−1.79261			−0.896304	−	0.443441i	$-0.853758\pi$
$5$	−4.00839			−1.79261			−0.896304	+	0.443441i	$0.853758\pi$
$6$	4.18585	−	3.04120i	1.70887	−	1.24156i
$7$	−0.366381	+	1.12760i	−0.138479	+	0.426194i	−0.996115	−	0.0880628i	$-0.971932\pi$
$7$	−0.366381	+	1.12760i	−0.138479	+	0.426194i	0.857636	+	0.514257i	$0.171932\pi$
$8$	−1.74648	+	1.26889i	−0.617475	+	0.448622i
$9$	2.15767	+	6.64064i	0.719225	+	2.21355i
$10$	2.02844	−	6.24289i	0.641448	−	1.97418i
$11$	−3.29351	−	0.390874i	−0.993031	−	0.117853i
$11$	−3.29351	−	0.390874i	−0.993031	−	0.117853i
$12$	0.665618	+	2.04856i	0.192147	+	0.591369i
$13$	1.05979	−	3.26171i	0.293934	−	0.904635i	−0.689644	−	0.724149i	$-0.742233\pi$
$13$	1.05979	−	3.26171i	0.293934	−	0.904635i	0.983578	−	0.180486i	$-0.0577671\pi$
$14$	−1.57079	−	1.14124i	−0.419811	−	0.305010i
$15$	10.2458	+	7.44399i	2.64545	+	1.92203i
$16$	−1.51379	−	4.65896i	−0.378447	−	1.16474i
$17$	−2.86066	−	2.07839i	−0.693811	−	0.504083i	0.184100	−	0.982908i	$-0.441063\pi$
$17$	−2.86066	−	2.07839i	−0.693811	−	0.504083i	−0.877911	+	0.478824i	$0.841063\pi$
$18$	−11.4344			−2.69511
$19$	3.72211			0.853911			0.426956	−	0.904273i	$-0.359586\pi$
$19$	3.72211			0.853911			0.426956	+	0.904273i	$0.359586\pi$
$20$	2.21082	+	1.60626i	0.494354	+	0.359170i
$21$	3.03058	−	2.20184i	0.661326	−	0.480481i
$22$	2.27544	−	4.93170i	0.485126	−	1.05144i
$23$	6.71397	+	4.87798i	1.39996	+	1.01713i	0.994688	+	0.102933i	$0.0328226\pi$
$23$	6.71397	+	4.87798i	1.39996	+	1.01713i	0.405270	+	0.914197i	$0.367177\pi$
$24$	6.82062			1.39225
$25$	11.0672			2.21344
$26$	4.54366	+	3.30116i	0.891084	+	0.647411i
$27$	3.88814	−	11.9665i	0.748273	−	2.30295i
$28$	0.653934	−	0.475111i	0.123582	−	0.0897875i
$29$	2.29564	+	1.66788i	0.426289	+	0.309717i	0.780163	−	0.625576i	$-0.215136\pi$
$29$	2.29564	+	1.66788i	0.426289	+	0.309717i	−0.353874	+	0.935293i	$0.615136\pi$
$30$	−16.7785	+	12.1903i	−3.06333	+	2.22564i
$31$	−4.60923			−0.827842			−0.413921	−	0.910313i	$-0.635841\pi$
$31$	−4.60923			−0.827842			−0.413921	+	0.910313i	$0.635841\pi$
$32$	3.70462			0.654891
$33$	7.69259	+	7.11549i	1.33911	+	1.23865i
$34$	4.68463	−	3.40358i	0.803407	−	0.583709i
$35$	1.46860	−	4.51988i	0.248238	−	0.763999i
$36$	1.47100	−	4.52726i	0.245166	−	0.754543i
$37$	0.860841	+	0.625437i	0.141521	+	0.102821i	0.656293	−	0.754506i	$-0.272123\pi$
$37$	0.860841	+	0.625437i	0.141521	+	0.102821i	−0.514772	+	0.857327i	$0.672123\pi$
$38$	−1.88357	+	5.79702i	−0.305555	+	0.940401i
$39$	−8.76624	+	6.36904i	−1.40372	+	1.01986i
$40$	7.00059	−	5.08622i	1.10689	−	0.804203i
$41$	5.65841	+	2.99707i	0.883695	+	0.468063i
$41$	5.65841	+	2.99707i	0.883695	+	0.468063i
$42$	1.89565	+	5.83422i	0.292506	+	0.900240i
$43$	−6.73539	−	4.89355i	−1.02714	−	0.746259i	−0.0594041	−	0.998234i	$-0.518920\pi$
$43$	−6.73539	−	4.89355i	−1.02714	−	0.746259i	−0.967734	+	0.251975i	$0.918920\pi$
$44$	1.65990	+	1.53537i	0.250239	+	0.231466i
$45$	−8.64880	−	26.6183i	−1.28929	−	3.96802i
$46$	−10.9948	+	7.98821i	−1.62110	+	1.17780i
$47$	−3.79369	−	11.6758i	−0.553366	−	1.70309i	−0.700220	−	0.713928i	$-0.746915\pi$
$47$	−3.79369	−	11.6758i	−0.553366	−	1.70309i	0.146853	−	0.989158i	$-0.453085\pi$
$48$	−4.78280	+	14.7199i	−0.690337	+	2.12464i
$49$	4.52586	+	3.28823i	0.646552	+	0.469747i
$50$	−5.60053	+	17.2367i	−0.792035	+	2.43763i
$51$	3.45229	+	10.6251i	0.483417	+	1.48781i
$52$	−1.89157	+	1.37430i	−0.262313	+	0.190582i
$53$	−0.375183	+	0.272587i	−0.0515354	+	0.0374427i	−0.613255	−	0.789885i	$-0.710140\pi$
$53$	−0.375183	+	0.272587i	−0.0515354	+	0.0374427i	0.561719	+	0.827328i	$0.310140\pi$
$54$	16.6697	+	12.1112i	2.26845	+	1.64813i
$55$	13.2017	+	1.56678i	1.78011	+	0.211264i
$56$	−0.790933	−	2.43424i	−0.105693	−	0.325289i
$57$	−9.51402	−	6.91234i	−1.26016	−	0.915562i
$58$	−3.75935	+	2.73133i	−0.493627	+	0.358641i
$59$	−0.165535			−0.0215508			−0.0107754	−	0.999942i	$-0.503430\pi$
$59$	−0.165535			−0.0215508			−0.0107754	+	0.999942i	$0.503430\pi$
$60$	−2.66806	−	8.21144i	−0.344445	−	1.06009i
$61$	1.98076	+	6.09614i	0.253610	+	0.780531i	0.994100	+	0.108464i	$0.0345932\pi$
$61$	1.98076	+	6.09614i	0.253610	+	0.780531i	−0.740491	+	0.672067i	$0.765407\pi$
$62$	2.33249	−	7.17867i	0.296227	−	0.911692i
$63$	−8.27854			−1.04300
$64$	1.15286	−	3.54813i	0.144107	−	0.443517i
$65$	−4.24806	+	13.0742i	−0.526908	+	1.62165i
$66$	−14.9749	+	8.38008i	−1.84328	+	1.03152i
$67$	−1.33916	−	4.12152i	−0.163605	−	0.503523i	0.835326	−	0.549755i	$-0.185279\pi$
$67$	−1.33916	−	4.12152i	−0.163605	−	0.503523i	−0.998931	+	0.0462314i	$0.985279\pi$
$68$	0.744931	+	2.29266i	0.0903361	+	0.278026i
$69$	−8.10253	−	24.9370i	−0.975430	−	3.00207i
$70$	6.29633	+	4.57455i	0.752555	+	0.546764i
$71$	2.71507	+	1.97262i	0.322220	+	0.234106i	0.737122	−	0.675760i	$-0.236184\pi$
$71$	2.71507	+	1.97262i	0.322220	+	0.234106i	−0.414902	+	0.909866i	$0.636184\pi$
$72$	−12.1946	−	8.85990i	−1.43715	−	1.04415i
$73$	−7.51212	+	5.45787i	−0.879227	+	0.638796i	−0.933047	−	0.359755i	$-0.882860\pi$
$73$	−7.51212	+	5.45787i	−0.879227	+	0.638796i	0.0538201	+	0.998551i	$0.482860\pi$
$74$	−1.40972	+	1.02422i	−0.163876	+	0.119063i
$75$	−28.2887	−	20.5529i	−3.26649	−	2.37325i
$76$	−2.05292	−	1.49154i	−0.235486	−	0.171091i
$77$	1.64743	−	3.57057i	0.187742	−	0.406904i
$78$	−5.48337	−	16.8761i	−0.620869	−	1.91084i
$79$	0.520090	+	1.60067i	0.0585147	+	0.180090i	0.976042	−	0.217584i	$-0.0698176\pi$
$79$	0.520090	+	1.60067i	0.0585147	+	0.180090i	−0.917527	+	0.397674i	$0.869818\pi$
$80$	6.06785	+	18.6749i	0.678406	+	2.08792i
$81$	−15.2148	+	11.0542i	−1.69053	+	1.22824i
$82$	−7.53122	+	7.29606i	−0.831685	+	0.805715i
$83$	1.87484	−	5.77016i	0.205790	−	0.633358i	−0.793890	−	0.608062i	$-0.791947\pi$
$83$	1.87484	−	5.77016i	0.205790	−	0.633358i	0.999680	−	0.0252957i	$-0.00805273\pi$
$84$	−2.55384			−0.278646
$85$	11.4666	+	8.33099i	1.24373	+	0.903623i
$86$	11.0299	−	8.01370i	1.18939	−	0.864140i
$87$	−2.77042	−	8.52647i	−0.297020	−	0.914133i
$88$	6.24804	−	3.49646i	0.666043	−	0.372724i
$89$	6.26931	−	4.55492i	0.664545	−	0.482820i	−0.203650	−	0.979044i	$-0.565280\pi$
$89$	6.26931	−	4.55492i	0.664545	−	0.482820i	0.868195	+	0.496224i	$0.165280\pi$
$90$	45.8335			4.83127
$91$	3.28963	+	2.39005i	0.344847	+	0.250546i
$92$	−1.74835	−	5.38088i	−0.182279	−	0.560996i
$93$	11.7816	+	8.55981i	1.22169	+	0.887611i
$94$	20.1043			2.07360
$95$	−14.9197			−1.53073
$96$	−9.46931	−	6.87986i	−0.966458	−	0.702173i
$97$	−1.08173	+	0.785923i	−0.109833	+	0.0797984i	−0.641346	−	0.767252i	$-0.721624\pi$
$97$	−1.08173	+	0.785923i	−0.109833	+	0.0797984i	0.531513	+	0.847050i	$0.321624\pi$
$98$	−7.41157	+	5.38482i	−0.748682	+	0.543949i
$99$	−4.51067	−	22.7144i	−0.453339	−	2.28288i
$100$	−6.10409	−	4.43488i	−0.610409	−	0.443488i
$101$	8.87288	+	6.44652i	0.882884	+	0.641453i	0.934013	−	0.357239i	$-0.116282\pi$
$101$	8.87288	+	6.44652i	0.882884	+	0.641453i	−0.0511286	+	0.998692i	$0.516282\pi$
$102$	−18.2951			−1.81148
$103$	−0.851156	+	2.61959i	−0.0838669	+	0.258116i	−0.984193	−	0.177101i	$-0.943328\pi$
$103$	−0.851156	+	2.61959i	−0.0838669	+	0.258116i	0.900326	+	0.435216i	$0.143328\pi$
$104$	2.28785	+	7.04128i	0.224342	+	0.690454i
$105$	−12.1477	+	8.82585i	−1.18550	+	0.861314i
$106$	−0.234681	−	0.722273i	−0.0227942	−	0.0701534i
$107$	1.90662			0.184320			0.0921600	−	0.995744i	$-0.470623\pi$
$107$	1.90662			0.184320			0.0921600	+	0.995744i	$0.470623\pi$
$108$	−6.93974	+	5.04201i	−0.667777	+	0.485168i
$109$	3.24662			0.310970			0.155485	−	0.987838i	$-0.450306\pi$
$109$	3.24662			0.310970			0.155485	+	0.987838i	$0.450306\pi$
$110$	−9.12087	+	19.7682i	−0.869641	+	1.88482i
$111$	−1.03888	−	3.19734i	−0.0986059	−	0.303478i
$112$	5.80808			0.548812
$113$	−2.72654	+	1.98095i	−0.256491	+	0.186352i	−0.708599	−	0.705612i	$-0.750672\pi$
$113$	−2.72654	+	1.98095i	−0.256491	+	0.186352i	0.452108	+	0.891963i	$0.350672\pi$
$114$	15.5802	−	11.3197i	1.45922	−	1.06019i
$115$	−26.9122	−	19.5529i	−2.50958	−	1.82331i
$116$	−0.597797	−	1.83983i	−0.0555041	−	0.170824i
$117$	23.9465			2.21385
$118$	0.0837684	−	0.257813i	0.00771151	−	0.0237336i
$119$	3.39169	−	2.46421i	0.310916	−	0.225893i
$120$	−27.3397			−2.49576
$121$	10.6944	+	2.57470i	0.972221	+	0.234063i
$122$	−10.4968			−0.950337
$123$	−8.89749	−	18.1690i	−0.802260	−	1.63824i
$124$	2.54221	+	1.84703i	0.228297	+	0.165868i
$125$	−24.3197			−2.17522
$126$	4.18934	−	12.8935i	0.373216	−	1.14864i
$127$	4.86708			0.431883			0.215942	−	0.976406i	$-0.430718\pi$
$127$	4.86708			0.431883			0.215942	+	0.976406i	$0.430718\pi$
$128$	10.9369	+	7.94609i	0.966691	+	0.702342i
$129$	8.12839	+	25.0166i	0.715665	+	2.20259i
$130$	−18.2128	−	13.2323i	−1.59736	−	1.16055i
$131$	3.99627	−	12.2993i	0.349156	−	1.07459i	−0.610165	−	0.792274i	$-0.708897\pi$
$131$	3.99627	−	12.2993i	0.349156	−	1.07459i	0.959321	−	0.282317i	$-0.0911032\pi$
$132$	−1.39149	−	7.00713i	−0.121114	−	0.609893i
$133$	−1.36371	+	4.19707i	−0.118249	+	0.363932i
$134$	7.09676			0.613066
$135$	−15.5852	+	47.9663i	−1.34136	+	4.12828i
$136$	7.63334			0.654554
$137$	7.21060	−	22.1919i	0.616043	−	1.89599i	0.231746	−	0.972776i	$-0.425556\pi$
$137$	7.21060	−	22.1919i	0.616043	−	1.89599i	0.384297	−	0.923210i	$-0.374444\pi$
$138$	42.9386			3.65517
$139$	−2.32798	+	7.16478i	−0.197457	+	0.607709i	0.802483	+	0.596675i	$0.203512\pi$
$139$	−2.32798	+	7.16478i	−0.197457	+	0.607709i	−0.999939	+	0.0110332i	$0.996488\pi$
$140$	−2.62122	+	1.90443i	−0.221534	+	0.160954i
$141$	−11.9861	+	36.8895i	−1.00941	+	3.10665i
$142$	−4.44622	+	3.23037i	−0.373118	+	0.271086i
$143$	−4.76536	+	10.3282i	−0.398499	+	0.863689i
$144$	27.6722	−	20.1050i	2.30602	−	1.67542i
$145$	−9.20182	−	6.68551i	−0.764169	−	0.555201i
$146$	−4.69890	−	14.4617i	−0.388884	−	1.19686i
$147$	−5.46189	−	16.8100i	−0.450489	−	1.38646i
$148$	−0.224168	−	0.689917i	−0.0184265	−	0.0567109i
$149$	−5.37362			−0.440224			−0.220112	−	0.975475i	$-0.570642\pi$
$149$	−5.37362			−0.440224			−0.220112	+	0.975475i	$0.570642\pi$
$150$	46.3257	−	33.6576i	3.78248	−	2.74813i
$151$	−5.97718	−	18.3959i	−0.486416	−	1.49703i	−0.829919	−	0.557883i	$-0.811614\pi$
$151$	−5.97718	−	18.3959i	−0.486416	−	1.49703i	0.343503	−	0.939151i	$-0.388386\pi$
$152$	−6.50061	+	4.72297i	−0.527269	+	0.383083i
$153$	7.62946	−	23.4811i	0.616805	−	1.89833i
$154$	4.72732	+	4.37268i	0.380939	+	0.352361i
$155$	18.4756			1.48400
$156$	7.38722			0.591451
$157$	18.4413			1.47178			0.735889	−	0.677103i	$-0.236765\pi$
$157$	18.4413			1.47178			0.735889	+	0.677103i	$0.236765\pi$
$158$	−2.75616			−0.219269
$159$	1.46522			0.116200
$160$	−14.8496			−1.17396
$161$	−7.96030	+	5.78350i	−0.627360	+	0.455804i
$162$	−9.51698	−	29.2903i	−0.747725	−	2.30126i
$163$	−0.722378	−	2.22325i	−0.0565810	−	0.174139i	0.918772	−	0.394789i	$-0.129182\pi$
$163$	−0.722378	−	2.22325i	−0.0565810	−	0.174139i	−0.975353	+	0.220650i	$0.929182\pi$
$164$	−1.91989	−	3.92048i	−0.149918	−	0.306138i
$165$	−30.8349	−	28.5217i	−2.40049	−	2.22041i
$166$	8.03801	+	5.83996i	0.623871	+	0.453268i
$167$	−1.81396	−	5.58280i	−0.140369	−	0.432010i	0.856018	−	0.516946i	$-0.172931\pi$
$167$	−1.81396	−	5.58280i	−0.140369	−	0.432010i	−0.996386	+	0.0849364i	$0.972931\pi$
$168$	−2.49894	+	7.69096i	−0.192798	+	0.593371i
$169$	1.00165	+	0.727742i	0.0770501	+	0.0559802i
$170$	−18.7778	+	13.6429i	−1.44019	+	1.04636i
$171$	8.03110	+	24.7172i	0.614154	+	1.89017i
$172$	1.75393	+	5.39806i	0.133736	+	0.411598i
$173$	−5.52312	−	4.01278i	−0.419915	−	0.305086i	0.357688	−	0.933841i	$-0.383565\pi$
$173$	−5.52312	−	4.01278i	−0.419915	−	0.305086i	−0.777604	+	0.628755i	$0.783565\pi$
$174$	14.6816			1.11301
$175$	−4.05481	+	12.4794i	−0.306515	+	0.943356i
$176$	3.16461	+	15.9360i	0.238541	+	1.20122i
$177$	0.423120	+	0.307415i	0.0318036	+	0.0231067i
$178$	3.92151	+	12.0692i	0.293930	+	0.904622i
$179$	−1.98417	+	6.10665i	−0.148304	+	0.456432i	−0.997421	−	0.0717721i	$-0.977135\pi$
$179$	−1.98417	+	6.10665i	−0.148304	+	0.456432i	0.849117	+	0.528204i	$0.177135\pi$
$180$	−5.89633	+	18.1470i	−0.439486	+	1.35260i
$181$	1.80073	+	1.30831i	0.133848	+	0.0972459i	0.652694	−	0.757621i	$-0.273639\pi$
$181$	1.80073	+	1.30831i	0.133848	+	0.0972459i	−0.518847	+	0.854867i	$0.673639\pi$
$182$	−5.38711	+	3.91397i	−0.399319	+	0.290122i
$183$	6.25818	−	19.2607i	0.462618	−	1.42379i
$184$	−17.9155			−1.32075
$185$	−3.45059	−	2.50700i	−0.253692	−	0.184318i
$186$	−19.2936	+	14.0176i	−1.41467	+	1.02782i
$187$	8.60921	+	7.96335i	0.629568	+	0.582338i
$188$	−2.58635	+	7.95996i	−0.188629	+	0.580540i
$189$	12.0689	+	8.76857i	0.877884	+	0.637820i
$190$	7.55007	−	23.2367i	0.547740	−	1.68577i
$191$	5.72415	−	4.15884i	0.414185	−	0.300923i	−0.361109	−	0.932524i	$-0.617602\pi$
$191$	5.72415	−	4.15884i	0.414185	−	0.300923i	0.775294	+	0.631601i	$0.217602\pi$
$192$	−9.53604	+	6.92834i	−0.688205	+	0.500010i
$193$	23.8390			1.71597			0.857986	−	0.513673i	$-0.171716\pi$
$193$	23.8390			1.71597			0.857986	+	0.513673i	$0.171716\pi$
$194$	−0.676632	−	2.08246i	−0.0485794	−	0.149512i
$195$	35.1385	−	25.5296i	2.51632	−	1.82821i
$196$	−1.17856	−	3.62723i	−0.0841829	−	0.259088i
$197$	−2.02513	+	6.23271i	−0.144285	+	0.444062i	−0.996918	−	0.0784469i	$-0.975004\pi$
$197$	−2.02513	+	6.23271i	−0.144285	+	0.444062i	0.852634	+	0.522509i	$0.175004\pi$
$198$	37.6593	+	4.46941i	2.67633	+	0.317627i
$199$	3.49818	+	2.54158i	0.247980	+	0.180168i	0.704831	−	0.709375i	$-0.251023\pi$
$199$	3.49818	+	2.54158i	0.247980	+	0.180168i	−0.456851	+	0.889543i	$0.651023\pi$
$200$	−19.3287	+	14.0431i	−1.36674	+	0.992998i
$201$	−4.23107	+	13.0219i	−0.298437	+	0.918493i
$202$	−14.5303	+	10.5569i	−1.02235	+	0.742778i
$203$	−2.72179	+	1.97749i	−0.191032	+	0.138793i
$204$	2.35360	−	7.24364i	0.164785	−	0.507156i
$205$	−22.6811	−	12.0134i	−1.58412	−	0.839054i
$206$	−3.64916	−	2.65127i	−0.254249	−	0.184723i
$207$	−17.9064	+	55.1101i	−1.24458	+	3.83042i
$208$	−16.8005			−1.16490
$209$	−12.2588	−	1.45488i	−0.847960	−	0.100636i
$210$	−7.59852	−	23.3859i	−0.524348	−	1.61378i
$211$	2.68852	−	8.27442i	0.185086	−	0.569635i	−0.814864	−	0.579652i	$-0.803189\pi$
$211$	2.68852	−	8.27442i	0.185086	−	0.569635i	0.999950	+	0.0100171i	$0.00318859\pi$
$212$	0.316163			0.0217142
$213$	−3.27660	−	10.0843i	−0.224509	−	0.690967i
$214$	−0.964841	+	2.96948i	−0.0659552	+	0.202989i
$215$	26.9981	+	19.6153i	1.84125	+	1.33775i
$216$	8.39361	+	25.8329i	0.571113	+	1.75770i
$217$	1.68873	−	5.19739i	0.114639	−	0.352822i
$218$	−1.64295	+	5.05647i	−0.111274	+	0.342467i
$219$	29.3374			1.98244
$220$	−6.65352	−	6.15437i	−0.448580	−	0.414928i
$221$	−9.81080	+	7.12796i	−0.659945	+	0.479478i
$222$	5.50543			0.369500
$223$	4.09981	+	12.6179i	0.274544	+	0.844959i	0.989340	+	0.145626i	$0.0465196\pi$
$223$	4.09981	+	12.6179i	0.274544	+	0.844959i	−0.714796	+	0.699333i	$0.753480\pi$
$224$	−1.35730	+	4.17735i	−0.0906886	+	0.279111i
$225$	23.8794	+	73.4933i	1.59196	+	4.89955i
$226$	−1.70548	−	5.24891i	−0.113447	−	0.349153i
$227$	−3.92070	+	12.0667i	−0.260226	+	0.800893i	0.732529	+	0.680736i	$0.238340\pi$
$227$	−3.92070	+	12.0667i	−0.260226	+	0.800893i	−0.992755	+	0.120157i	$0.961660\pi$
$228$	2.47750	+	7.62498i	0.164077	+	0.504976i
$229$	5.84106			0.385988			0.192994	−	0.981200i	$-0.438180\pi$
$229$	5.84106			0.385988			0.192994	+	0.981200i	$0.438180\pi$
$230$	44.0716	−	32.0199i	2.90599	−	2.11133i
$231$	−10.8419	+	6.06722i	−0.713343	+	0.399194i
$232$	−6.12565			−0.402169
$233$	−8.39878	+	25.8488i	−0.550222	+	1.69341i	0.158016	+	0.987437i	$0.449490\pi$
$233$	−8.39878	+	25.8488i	−0.550222	+	1.69341i	−0.708238	+	0.705974i	$0.750510\pi$
$234$	−12.1181	+	37.2956i	−0.792183	+	2.43809i
$235$	15.2066	+	46.8011i	0.991968	+	3.05296i
$236$	0.0913003	+	0.0663335i	0.00594314	+	0.00431794i
$237$	1.64322	−	5.05731i	0.106739	−	0.328507i
$238$	2.12153	+	6.52941i	0.137519	+	0.423239i
$239$	17.4237			1.12704			0.563522	−	0.826101i	$-0.309446\pi$
$239$	17.4237			1.12704			0.563522	+	0.826101i	$0.309446\pi$
$240$	19.1713	−	59.0032i	1.23750	−	3.80864i
$241$	−1.67747	−	5.16272i	−0.108055	−	0.332560i	0.882380	−	0.470537i	$-0.155940\pi$
$241$	−1.67747	−	5.16272i	−0.108055	−	0.332560i	−0.990435	+	0.137977i	$0.955940\pi$
$242$	−9.42187	+	15.3532i	−0.605661	+	0.986940i
$243$	21.6721			1.39026
$244$	1.35038	−	4.15605i	0.0864493	−	0.266064i
$245$	−18.1414	−	13.1805i	−1.15901	−	0.842072i
$246$	32.7999	−	4.66307i	2.09125	−	0.297306i
$247$	3.94467	−	12.1404i	0.250993	−	0.772478i
$248$	8.04994	−	5.84863i	0.511172	−	0.371388i
$249$	−15.5080	+	11.2672i	−0.982781	+	0.714032i
$250$	12.3069	−	37.8769i	0.778360	−	2.39554i
$251$	19.8699	−	14.4363i	1.25418	−	0.911213i	0.255720	−	0.966751i	$-0.417687\pi$
$251$	19.8699	−	14.4363i	1.25418	−	0.911213i	0.998457	+	0.0555383i	$0.0176875\pi$
$252$	4.56601	+	3.31740i	0.287632	+	0.208977i
$253$	−20.2058	−	18.6900i	−1.27033	−	1.17503i
$254$	−2.46297	+	7.58025i	−0.154541	+	0.475627i
$255$	−13.8381	−	42.5894i	−0.866578	−	2.66705i
$256$	−11.8738	+	8.62683i	−0.742113	+	0.539177i
$257$	−1.18721	−	3.65385i	−0.0740561	−	0.227921i	0.907176	−	0.420751i	$-0.138233\pi$
$257$	−1.18721	−	3.65385i	−0.0740561	−	0.227921i	−0.981232	+	0.192830i	$0.938233\pi$
$258$	−43.0756			−2.68177
$259$	−1.02064	+	0.741540i	−0.0634196	+	0.0460770i
$260$	7.58214	−	5.50875i	0.470225	−	0.341638i
$261$	−6.12254	+	18.8432i	−0.378976	+	1.16637i
$262$	17.1332	+	12.4480i	1.05850	+	0.769042i
$263$	4.00681	−	12.3317i	0.247071	−	0.760405i	−0.748218	−	0.663453i	$-0.769090\pi$
$263$	4.00681	−	12.3317i	0.247071	−	0.760405i	0.995289	−	0.0969527i	$-0.0309096\pi$
$264$	−22.4638	−	2.66600i	−1.38255	−	0.164081i
$265$	1.50388	−	1.09263i	0.0923828	−	0.0671200i
$266$	−5.84665	−	4.24784i	−0.358481	−	0.260452i
$267$	−24.4838			−1.49838
$268$	−0.912975	+	2.80985i	−0.0557688	+	0.171639i
$269$	13.0980	−	9.51626i	0.798600	−	0.580217i	−0.111903	−	0.993719i	$-0.535695\pi$
$269$	13.0980	−	9.51626i	0.798600	−	0.580217i	0.910503	+	0.413502i	$0.135695\pi$
$270$	−66.8185	−	48.5465i	−4.06644	−	2.95445i
$271$	−1.25360	+	3.85818i	−0.0761507	+	0.234368i	−0.981885	−	0.189478i	$-0.939320\pi$
$271$	−1.25360	+	3.85818i	−0.0761507	+	0.234368i	0.905734	+	0.423846i	$0.139320\pi$
$272$	−5.35270	+	16.4739i	−0.324555	+	0.998878i
$273$	−3.96998	−	12.2183i	−0.240274	−	0.739488i
$274$	30.9140	+	22.4604i	1.86759	+	1.35688i
$275$	−36.4500	−	4.32588i	−2.19802	−	0.260861i
$276$	−5.52391	+	17.0008i	−0.332500	+	1.02333i
$277$	21.8797			1.31463			0.657313	−	0.753618i	$-0.271693\pi$
$277$	21.8797			1.31463			0.657313	+	0.753618i	$0.271693\pi$
$278$	−9.98075	−	7.25144i	−0.598606	−	0.434913i
$279$	−9.94522	−	30.6082i	−0.595405	−	1.83247i
$280$	3.17037	+	9.75739i	0.189466	+	0.583116i
$281$	−15.5163	+	11.2732i	−0.925623	+	0.672505i	−0.944917	−	0.327309i	$-0.893858\pi$
$281$	−15.5163	+	11.2732i	−0.925623	+	0.672505i	0.0192942	+	0.999814i	$0.493858\pi$
$282$	−51.3882	−	37.3357i	−3.06012	−	2.22331i
$283$	7.53987	−	23.2053i	0.448199	−	1.37941i	−0.430739	−	0.902477i	$-0.641747\pi$
$283$	7.53987	−	23.2053i	0.448199	−	1.37941i	0.878938	−	0.476937i	$-0.158253\pi$
$284$	−0.707020	−	2.17598i	−0.0419539	−	0.129121i
$285$	38.1359	+	27.7074i	2.25898	+	1.64124i
$286$	−13.6742	−	12.6484i	−0.808575	−	0.747916i
$287$	−5.45264	+	5.28238i	−0.321859	+	0.311809i
$288$	7.99337	+	24.6011i	0.471014	+	1.44963i
$289$	−1.38963	−	4.27685i	−0.0817432	−	0.251580i
$290$	15.0689	−	10.9482i	0.884879	−	0.642902i
$291$	4.22453			0.247646
$292$	6.33039			0.370458
$293$	19.2166			1.12265			0.561323	−	0.827597i	$-0.310293\pi$
$293$	19.2166			1.12265			0.561323	+	0.827597i	$0.310293\pi$
$294$	28.9448			1.68809
$295$	0.663527			0.0386321
$296$	−2.29706			−0.133514
$297$	−17.4830	+	37.8919i	−1.01447	+	2.19871i
$298$	2.71931	−	8.36917i	0.157525	−	0.484813i
$299$	23.0260	−	16.7293i	1.33163	−	0.967483i
$300$	7.36653	+	22.6718i	0.425307	+	1.30896i
$301$	7.98571	−	5.80196i	0.460289	−	0.334419i
$302$	31.6755			1.82272
$303$	−10.7079	−	32.9557i	−0.615156	−	1.89325i
$304$	−5.63448	−	17.3412i	−0.323160	−	0.994584i
$305$	−7.93965	−	24.4357i	−0.454623	−	1.39918i
$306$	32.7098	+	23.7651i	1.86990	+	1.35856i
$307$	−6.82819	+	4.96097i	−0.389706	+	0.283138i	−0.765335	−	0.643632i	$-0.777427\pi$
$307$	−6.82819	+	4.96097i	−0.389706	+	0.283138i	0.375629	+	0.926770i	$0.377427\pi$
$308$	−2.33945	+	1.30918i	−0.133302	+	0.0745973i
$309$	7.04046	−	5.11520i	0.400518	−	0.290993i
$310$	−9.34954	+	28.7749i	−0.531018	+	1.63431i
$311$	13.2012	−	9.59120i	0.748569	−	0.543867i	−0.146814	−	0.989164i	$-0.546902\pi$
$311$	13.2012	−	9.59120i	0.748569	−	0.543867i	0.895383	+	0.445297i	$0.146902\pi$
$312$	7.22844	−	22.2469i	0.409230	−	1.25948i
$313$	−30.6962			−1.73505			−0.867526	−	0.497392i	$-0.834291\pi$
$313$	−30.6962			−1.73505			−0.867526	+	0.497392i	$0.834291\pi$
$314$	−9.33219	+	28.7215i	−0.526646	+	1.62085i
$315$	33.1836			1.86969
$316$	0.354572	−	1.09126i	0.0199462	−	0.0613881i
$317$	0.880715			0.0494659			0.0247329	−	0.999694i	$-0.492126\pi$
$317$	0.880715			0.0494659			0.0247329	+	0.999694i	$0.492126\pi$
$318$	−0.741472	+	2.28202i	−0.0415797	+	0.127969i
$319$	−6.90878	−	6.39048i	−0.386817	−	0.357798i
$320$	−4.62111	+	14.2223i	−0.258328	+	0.795051i
$321$	−4.87348	−	3.54079i	−0.272011	−	0.197628i
$322$	−4.97925	−	15.3245i	−0.277483	−	0.854003i
$323$	−10.6477	−	7.73599i	−0.592453	−	0.430442i
$324$	12.8213			0.712297
$325$	11.7289	−	36.0980i	0.650605	−	2.00236i
$326$	3.82817			0.212023
$327$	−8.29863	−	6.02931i	−0.458915	−	0.333422i
$328$	−13.6853	+	1.94559i	−0.755643	+	0.107427i
$329$	14.5556			0.802475
$330$	60.0252	−	33.5907i	3.30428	−	1.84910i
$331$	−17.5370			−0.963923			−0.481962	−	0.876192i	$-0.660076\pi$
$331$	−17.5370			−0.963923			−0.481962	+	0.876192i	$0.660076\pi$
$332$	−3.34630	+	2.43123i	−0.183652	+	0.133431i
$333$	−2.29589	+	7.06602i	−0.125814	+	0.387216i
$334$	9.61291			0.525995
$335$	5.36788	+	16.5207i	0.293279	+	0.902620i
$336$	−14.8459	−	10.7862i	−0.809912	−	0.588436i
$337$	24.0838	−	17.4979i	1.31193	−	0.953173i	0.311934	−	0.950104i	$-0.399023\pi$
$337$	24.0838	−	17.4979i	1.31193	−	0.953173i	0.999995	−	0.00306897i	$-0.000976885\pi$
$338$	−1.64031	+	1.19175i	−0.0892211	+	0.0648229i
$339$	10.6481			0.578324
$340$	−2.98597	−	9.18989i	−0.161937	−	0.498392i
$341$	15.1806	+	1.80163i	0.822073	+	0.0975637i
$342$	−42.5600			−2.30138
$343$	−12.0804	+	8.77692i	−0.652280	+	0.473909i
$344$	17.9726			0.969020
$345$	32.4781	+	99.9574i	1.74856	+	5.38153i
$346$	9.04469	−	6.57136i	0.486246	−	0.353278i
$347$	6.87200	+	21.1498i	0.368908	+	1.13538i	0.947497	+	0.319764i	$0.103604\pi$
$347$	6.87200	+	21.1498i	0.368908	+	1.13538i	−0.578589	+	0.815619i	$0.696396\pi$
$348$	−1.88873	+	5.81293i	−0.101247	+	0.311606i
$349$	−20.2530			−1.08412			−0.542060	−	0.840340i	$-0.682355\pi$
$349$	−20.2530			−1.08412			−0.542060	+	0.840340i	$0.682355\pi$
$350$	−17.3842	−	12.6304i	−0.929226	−	0.675122i
$351$	−34.9105	−	25.3640i	−1.86338	−	1.35383i
$352$	−12.2012	−	1.44804i	−0.650327	−	0.0771808i
$353$	17.9063	−	13.0097i	0.953056	−	0.692436i	0.00152856	−	0.999999i	$-0.499513\pi$
$353$	17.9063	−	13.0097i	0.953056	−	0.692436i	0.951528	+	0.307563i	$0.0995134\pi$
$354$	−0.692903	+	0.503424i	−0.0368274	+	0.0267567i
$355$	−10.8831	−	7.90702i	−0.577614	−	0.419661i
$356$	−5.28308			−0.280003
$357$	−13.2457			−0.701038
$358$	−8.50675	−	6.18051i	−0.449595	−	0.326650i
$359$	−5.96795	−	18.3675i	−0.314976	−	0.969398i	−0.975764	−	0.218825i	$-0.929778\pi$
$359$	−5.96795	−	18.3675i	−0.314976	−	0.969398i	0.660788	−	0.750573i	$-0.270222\pi$
$360$	48.8808	+	35.5140i	2.57624	+	1.87175i
$361$	−5.14588			−0.270836
$362$	−2.94889	+	2.14250i	−0.154990	+	0.112607i
$363$	−22.5544	−	26.4418i	−1.18380	−	1.38783i
$364$	−0.856638	−	2.63646i	−0.0449000	−	0.138188i
$365$	30.1115	−	21.8773i	1.57611	−	1.14511i
$366$	26.8307	+	19.4937i	1.40246	+	1.01895i
$367$	−4.03828			−0.210796			−0.105398	−	0.994430i	$-0.533612\pi$
$367$	−4.03828			−0.210796			−0.105398	+	0.994430i	$0.533612\pi$
$368$	12.5628	−	38.6643i	0.654881	−	2.01552i
$369$	−7.69344	+	44.0421i	−0.400504	+	2.29274i
$370$	5.65070	−	4.10547i	0.293766	−	0.213433i
$371$	−0.169910	−	0.522929i	−0.00882129	−	0.0271491i
$372$	−3.06799	−	9.44229i	−0.159068	−	0.489560i
$373$	7.99166	+	24.5958i	0.413793	+	1.27352i	0.913326	+	0.407228i	$0.133505\pi$
$373$	7.99166	+	24.5958i	0.413793	+	1.27352i	−0.499534	+	0.866294i	$0.666495\pi$
$374$	−16.7592	+	9.37863i	−0.866600	+	0.484957i
$375$	62.1632	+	45.1642i	3.21009	+	2.33227i
$376$	21.4409	+	15.5777i	1.10573	+	0.803361i
$377$	7.87303	−	5.72009i	0.405482	−	0.294600i
$378$	−19.7641	+	14.3595i	−1.01656	+	0.738571i
$379$	−27.8024	−	20.1997i	−1.42812	−	1.03759i	−0.990364	−	0.138491i	$-0.955775\pi$
$379$	−27.8024	−	20.1997i	−1.42812	−	1.03759i	−0.437752	−	0.899096i	$-0.644225\pi$
$380$	8.22892	+	5.97866i	0.422135	+	0.306699i
$381$	−12.4406	−	9.03866i	−0.637354	−	0.463064i
$382$	3.58051	+	11.0197i	0.183195	+	0.563815i
$383$	5.42685	+	16.7021i	0.277299	+	0.853438i	0.988602	+	0.150553i	$0.0481053\pi$
$383$	5.42685	+	16.7021i	0.277299	+	0.853438i	−0.711303	+	0.702885i	$0.751895\pi$
$384$	−13.1988	−	40.6217i	−0.673548	−	2.07297i
$385$	−6.60355	+	14.3122i	−0.336548	+	0.729419i
$386$	−12.0637	+	37.1282i	−0.614026	+	1.88978i
$387$	17.9635	−	55.2860i	0.913137	−	2.81035i
$388$	0.911564			0.0462776
$389$	9.33169	−	28.7200i	0.473135	−	1.45616i	−0.375321	−	0.926895i	$-0.622467\pi$
$389$	9.33169	−	28.7200i	0.473135	−	1.45616i	0.848456	−	0.529266i	$-0.177533\pi$
$390$	21.9795	+	67.6459i	1.11297	+	3.42538i
$391$	−9.06801	−	27.9085i	−0.458589	−	1.41139i
$392$	−12.0768			−0.609968
$393$	−33.0558	+	24.0164i	−1.66744	+	1.21147i
$394$	−8.68235	−	6.30810i	−0.437411	−	0.317797i
$395$	−2.08472	−	6.41612i	−0.104894	−	0.322830i
$396$	−6.61433	+	14.3356i	−0.332383	+	0.720391i
$397$	−6.29792	−	4.57571i	−0.316084	−	0.229648i	0.418419	−	0.908254i	$-0.362584\pi$
$397$	−6.29792	−	4.57571i	−0.316084	−	0.229648i	−0.734503	+	0.678606i	$0.762584\pi$
$398$	−5.72864	+	4.16210i	−0.287151	+	0.208627i
$399$	11.2801	−	8.19550i	0.564714	−	0.410288i
$400$	−16.7534	−	51.5616i	−0.837669	−	2.57808i
$401$	2.57496	−	7.92491i	0.128587	−	0.395751i	−0.865950	−	0.500130i	$-0.833286\pi$
$401$	2.57496	−	7.92491i	0.128587	−	0.395751i	0.994538	+	0.104379i	$0.0332855\pi$
$402$	−18.1399	−	13.1794i	−0.904735	−	0.657329i
$403$	−4.88483	+	15.0340i	−0.243331	+	0.748895i
$404$	−2.31055	−	7.11113i	−0.114954	−	0.353792i
$405$	60.9868	−	44.3095i	3.03046	−	2.20176i
$406$	−1.70250	−	5.23976i	−0.0844938	−	0.260045i
$407$	−2.59072	−	2.39637i	−0.128417	−	0.118783i
$408$	−19.5114	−	14.1759i	−0.965960	−	0.701811i
$409$	5.63962	+	17.3570i	0.278861	+	0.858247i	0.988172	+	0.153351i	$0.0490064\pi$
$409$	5.63962	+	17.3570i	0.278861	+	0.858247i	−0.709310	+	0.704896i	$0.750994\pi$
$410$	30.1881	−	29.2455i	1.49088	−	1.44433i
$411$	−59.6436	+	43.3336i	−2.94200	+	2.13749i
$412$	1.51918	−	1.10375i	0.0748447	−	0.0543779i
$413$	0.0606487	−	0.186658i	0.00298433	−	0.00918482i
$414$	−76.7700	−	55.7767i	−3.77304	−	2.74128i
$415$	−7.51509	+	23.1291i	−0.368901	+	1.13536i
$416$	3.92613	−	12.0834i	0.192494	−	0.592437i
$417$	19.2562	−	13.9905i	0.942981	−	0.685116i
$418$	8.46946	−	18.3563i	0.414255	−	0.897837i
$419$	−16.0642			−0.784786			−0.392393	−	0.919798i	$-0.628353\pi$
$419$	−16.0642			−0.784786			−0.392393	+	0.919798i	$0.628353\pi$
$420$	10.2368			0.499504
$421$	−12.8990	+	9.37171i	−0.628661	+	0.456749i	−0.855936	−	0.517082i	$-0.827018\pi$
$421$	−12.8990	+	9.37171i	−0.628661	+	0.456749i	0.227275	+	0.973831i	$0.427018\pi$
$422$	11.5265	+	8.37451i	0.561102	+	0.407665i
$423$	69.3490	−	50.3850i	3.37186	−	2.44980i
$424$	0.309368	−	0.952136i	0.0150242	−	0.0462398i
$425$	−31.6595	−	23.0019i	−1.53571	−	1.11576i
$426$	17.3640			0.841289
$427$	−7.59975			−0.367777
$428$	−1.05159	−	0.764027i	−0.0508307	−	0.0369306i
$429$	31.3612	−	17.5500i	1.51413	−	0.847323i
$430$	−44.2122	+	32.1221i	−2.13210	+	1.54906i
$431$	−7.88889	−	5.73162i	−0.379995	−	0.276082i	0.381349	−	0.924431i	$-0.375460\pi$
$431$	−7.88889	−	5.73162i	−0.379995	−	0.276082i	−0.761343	+	0.648349i	$0.775460\pi$
$432$	−61.6371			−2.96552
$433$	10.4850			0.503875			0.251937	−	0.967744i	$-0.418932\pi$
$433$	10.4850			0.503875			0.251937	+	0.967744i	$0.418932\pi$
$434$	7.24012	+	5.26026i	0.347537	+	0.252500i
$435$	11.1049	+	34.1774i	0.532440	+	1.63868i
$436$	−1.79067	−	1.30100i	−0.0857574	−	0.0623064i
$437$	24.9901	+	18.1564i	1.19544	+	0.868538i
$438$	−14.8461	+	45.6917i	−0.709375	+	2.18323i
$439$	−2.09843	−	6.45830i	−0.100153	−	0.308238i	0.888410	−	0.459052i	$-0.151811\pi$
$439$	−2.09843	−	6.45830i	−0.100153	−	0.308238i	−0.988562	+	0.150814i	$0.951811\pi$
$440$	−25.0446	+	14.0152i	−1.19395	+	0.668148i
$441$	−12.0706	+	37.1495i	−0.574791	+	1.76903i
$442$	−6.13675	−	18.8870i	−0.291895	−	0.898361i
$443$	4.77959	−	3.47257i	0.227085	−	0.164987i	−0.468425	−	0.883503i	$-0.655178\pi$
$443$	4.77959	−	3.47257i	0.227085	−	0.164987i	0.695510	+	0.718516i	$0.255178\pi$
$444$	−0.708256	+	2.17979i	−0.0336123	+	0.103448i
$445$	−25.1298	+	18.2579i	−1.19127	+	0.865507i
$446$	−21.7266			−1.02878
$447$	13.7354	+	9.97936i	0.649663	+	0.472008i
$448$	3.57851	+	2.59994i	0.169068	+	0.122835i
$449$	−3.62352	+	11.1521i	−0.171005	+	0.526298i	−0.999428	−	0.0338036i	$-0.989238\pi$
$449$	−3.62352	+	11.1521i	−0.171005	+	0.526298i	0.828424	+	0.560102i	$0.189238\pi$
$450$	−126.547			−5.96547
$451$	−17.4646	−	12.0826i	−0.822374	−	0.568948i
$452$	2.29763			0.108071
$453$	−18.8848	+	58.1216i	−0.887287	+	2.73079i
$454$	−16.8092	−	12.2126i	−0.788897	−	0.573167i
$455$	−13.1861	−	9.58027i	−0.618175	−	0.449130i
$456$	25.3871			1.18886
$457$	10.9300	−	7.94113i	0.511285	−	0.371470i	−0.302026	−	0.953300i	$-0.597663\pi$
$457$	10.9300	−	7.94113i	0.511285	−	0.371470i	0.813311	+	0.581829i	$0.197663\pi$
$458$	−2.95586	+	9.09720i	−0.138118	+	0.425084i
$459$	−35.9936	+	26.1509i	−1.68004	+	1.22062i
$460$	7.00809	+	21.5687i	0.326754	+	1.00564i
$461$	−8.65651	+	26.6420i	−0.403174	+	1.24084i	0.519237	+	0.854630i	$0.326216\pi$
$461$	−8.65651	+	26.6420i	−0.403174	+	1.24084i	−0.922411	+	0.386211i	$0.873784\pi$
$462$	−3.96291	−	19.9560i	−0.184371	−	0.928439i
$463$	0.922761	+	2.83997i	0.0428844	+	0.131984i	0.970206	−	0.242280i	$-0.0778952\pi$
$463$	0.922761	+	2.83997i	0.0428844	+	0.131984i	−0.927322	+	0.374264i	$0.877895\pi$
$464$	4.29547	−	13.2201i	0.199412	−	0.613727i
$465$	−47.2252	−	34.3111i	−2.19001	−	1.59114i
$466$	−36.0081	−	26.1614i	−1.66804	−	1.21191i
$467$	−0.0221580	−	0.0681953i	−0.00102535	−	0.00315570i	0.950543	−	0.310594i	$-0.100528\pi$
$467$	−0.0221580	−	0.0681953i	−0.00102535	−	0.00315570i	−0.951568	+	0.307439i	$0.900528\pi$
$468$	−13.2076	−	9.59592i	−0.610524	−	0.443571i
$469$	5.13808			0.237255
$470$	−80.5858			−3.71715
$471$	−47.1375	−	34.2474i	−2.17198	−	1.57804i
$472$	0.289103	−	0.210046i	0.0133071	−	0.00966815i
$473$	20.2703	+	18.7497i	0.932031	+	0.862110i
$474$	7.04498	+	5.11848i	0.323587	+	0.235100i
$475$	41.1934			1.89008
$476$	−2.85814			−0.131003
$477$	−2.61967	−	1.90330i	−0.119947	−	0.0871463i
$478$	−8.81721	+	27.1366i	−0.403290	+	1.24120i
$479$	14.9777	−	10.8819i	0.684349	−	0.497209i	−0.190448	−	0.981697i	$-0.560994\pi$
$479$	14.9777	−	10.8819i	0.684349	−	0.497209i	0.874798	+	0.484488i	$0.160994\pi$
$480$	37.9567	+	27.5772i	1.73248	+	1.25872i
$481$	2.95231	−	2.14498i	0.134614	−	0.0978025i
$482$	8.88958			0.404909
$483$	31.0877			1.41454
$484$	−4.86675	−	5.70558i	−0.221216	−	0.259344i
$485$	4.33600	−	3.15029i	0.196888	−	0.143047i
$486$	−10.9671	+	33.7532i	−0.497478	+	1.53108i
$487$	6.74218	−	20.7503i	0.305518	−	0.940286i	−0.673966	−	0.738762i	$-0.735411\pi$
$487$	6.74218	−	20.7503i	0.305518	−	0.940286i	0.979484	−	0.201524i	$-0.0645894\pi$
$488$	−11.1947	−	8.13343i	−0.506761	−	0.368183i
$489$	−2.28235	+	7.02434i	−0.103211	+	0.317652i
$490$	29.7085	−	21.5845i	1.34209	−	0.975088i
$491$	−3.36807	+	2.44704i	−0.151999	+	0.110433i	−0.661185	−	0.750223i	$-0.729946\pi$
$491$	−3.36807	+	2.44704i	−0.151999	+	0.110433i	0.509187	+	0.860656i	$0.329946\pi$
$492$	−2.37334	+	13.5865i	−0.106998	+	0.612527i
$493$	−3.10053	−	9.54245i	−0.139641	−	0.429771i
$494$	16.9120	+	12.2873i	0.760907	+	0.552831i
$495$	18.0805	+	91.0482i	0.812659	+	4.09231i
$496$	6.97739	+	21.4742i	0.313294	+	0.964221i
$497$	−3.21908	+	2.33880i	−0.144396	+	0.104910i
$498$	−9.70041	−	29.8548i	−0.434686	−	1.33783i
$499$	0.216630	−	0.666720i	0.00969770	−	0.0298465i	−0.946091	−	0.323902i	$-0.895005\pi$
$499$	0.216630	−	0.666720i	0.00969770	−	0.0298465i	0.955788	+	0.294056i	$0.0950051\pi$
$500$	13.4135	+	9.74548i	0.599870	+	0.435831i
$501$	−5.73119	+	17.6388i	−0.256051	+	0.788043i
$502$	12.4288	+	38.2519i	0.554725	+	1.70727i
$503$	5.07800	−	3.68938i	0.226417	−	0.164501i	−0.468794	−	0.883308i	$-0.655311\pi$
$503$	5.07800	−	3.68938i	0.226417	−	0.164501i	0.695210	+	0.718806i	$0.255311\pi$
$504$	14.4583	−	10.5046i	0.644026	−	0.467912i
$505$	−35.5660	−	25.8402i	−1.58267	−	1.14987i
$506$	39.3340	−	22.0117i	1.74861	−	0.978538i
$507$	−1.20881	−	3.72034i	−0.0536852	−	0.165226i
$508$	−2.68443	−	1.95035i	−0.119102	−	0.0865328i
$509$	3.62083	−	2.63069i	0.160491	−	0.116603i	−0.504641	−	0.863329i	$-0.668375\pi$
$509$	3.62083	−	2.63069i	0.160491	−	0.116603i	0.665132	+	0.746726i	$0.268375\pi$
$510$	73.3338			3.24728
$511$	−3.40202	−	10.4704i	−0.150497	−	0.463181i
$512$	0.927833	+	2.85558i	0.0410048	+	0.126200i
$513$	14.4721	−	44.5405i	0.638959	−	1.96651i
$514$	6.29150			0.277506
$515$	3.41177	−	10.5003i	0.150340	−	0.462700i
$516$	5.54154	−	17.0551i	0.243953	−	0.750809i
$517$	7.93079	+	39.9371i	0.348796	+	1.75643i
$518$	−0.638421	−	1.96486i	−0.0280506	−	0.0863309i
$519$	6.66540	+	20.5140i	0.292579	+	0.900465i
$520$	−9.17060	−	28.2242i	−0.402157	−	1.23771i
$521$	−18.3403	−	13.3250i	−0.803503	−	0.583779i	0.108437	−	0.994103i	$-0.465415\pi$
$521$	−18.3403	−	13.3250i	−0.803503	−	0.583779i	−0.911940	+	0.410324i	$0.865415\pi$
$522$	−26.2492	−	19.0712i	−1.14890	−	0.834722i
$523$	36.0731	+	26.2086i	1.57737	+	1.14602i	0.919637	+	0.392770i	$0.128483\pi$
$523$	36.0731	+	26.2086i	1.57737	+	1.14602i	0.657730	+	0.753254i	$0.271517\pi$
$524$	−7.13274	+	5.18224i	−0.311595	+	0.226387i
$525$	33.5400	−	24.3682i	1.46381	−	1.06352i
$526$	17.1784	+	12.4809i	0.749015	+	0.544191i
$527$	13.1854	+	9.57977i	0.574366	+	0.417301i
$528$	21.5058	−	46.6108i	0.935921	−	2.02847i
$529$	14.1752	+	43.6269i	0.616315	+	1.89682i
$530$	0.940693	+	2.89515i	0.0408611	+	0.125757i
$531$	−0.357170	−	1.09926i	−0.0154998	−	0.0477036i
$532$	2.43401	−	1.76842i	0.105528	−	0.0766705i
$533$	15.7723	−	15.2798i	0.683174	−	0.661842i
$534$	12.3900	−	38.1324i	0.536167	−	1.65015i
$535$	−7.64248			−0.330413
$536$	7.56859	+	5.49890i	0.326913	+	0.237516i
$537$	16.4124	−	11.9243i	0.708246	−	0.514571i
$538$	8.19293	+	25.2153i	0.353222	+	1.08711i
$539$	−13.6207	−	12.5989i	−0.586685	−	0.542672i
$540$	27.8172	−	20.2104i	1.19706	−	0.869716i
$541$	25.2596			1.08599			0.542997	−	0.839735i	$-0.317290\pi$
$541$	25.2596			1.08599			0.542997	+	0.839735i	$0.317290\pi$
$542$	−5.37456	−	3.90485i	−0.230857	−	0.167728i
$543$	−2.17316	−	6.68829i	−0.0932592	−	0.287022i
$544$	−10.5976	−	7.69964i	−0.454370	−	0.330119i
$545$	−13.0137			−0.557447
$546$	21.0385			0.900366
$547$	32.9269	+	23.9228i	1.40785	+	1.02286i	0.993631	+	0.112687i	$0.0359457\pi$
$547$	32.9269	+	23.9228i	1.40785	+	1.02286i	0.414220	+	0.910177i	$0.364054\pi$
$548$	−12.8698	+	9.35047i	−0.549771	+	0.399432i
$549$	−36.2084	+	26.3070i	−1.54534	+	1.12275i
$550$	25.1828	−	54.5801i	1.07380	−	2.32730i
$551$	8.54462	+	6.20803i	0.364013	+	0.264471i
$552$	45.7934	+	33.2709i	1.94910	+	1.41610i
$553$	−1.99548			−0.0848563
$554$	−11.0722	+	34.0767i	−0.470412	+	1.44778i
$555$	4.16423	+	12.8162i	0.176762	+	0.544017i
$556$	4.15508	−	3.01885i	0.176215	−	0.128028i
$557$	2.87336	+	8.84329i	0.121748	+	0.374702i	0.993295	−	0.115611i	$-0.0368825\pi$
$557$	2.87336	+	8.84329i	0.121748	+	0.374702i	−0.871546	+	0.490313i	$0.836882\pi$
$558$	52.7037			2.23113
$559$	−23.0994	+	16.7827i	−0.977002	+	0.709834i
$560$	−23.2811			−0.983805
$561$	−7.21710	−	36.3432i	−0.304706	−	1.53441i
$562$	−9.70557	−	29.8707i	−0.409405	−	1.26002i
$563$	−33.0671			−1.39361			−0.696807	−	0.717259i	$-0.745397\pi$
$563$	−33.0671			−1.39361			−0.696807	+	0.717259i	$0.745397\pi$
$564$	21.3934	−	15.5432i	0.900824	−	0.654487i
$565$	10.9290	−	7.94041i	0.459788	−	0.334055i
$566$	32.3257	+	23.4860i	1.35875	+	0.987191i
$567$	−6.89034	−	21.2063i	−0.289367	−	0.890580i
$568$	−7.24487			−0.303988
$569$	−4.11179	+	12.6548i	−0.172375	+	0.530517i	−0.999504	−	0.0314961i	$-0.989973\pi$
$569$	−4.11179	+	12.6548i	−0.172375	+	0.530517i	0.827129	+	0.562013i	$0.189973\pi$
$570$	−62.4516	+	45.3737i	−2.61581	+	1.90050i
$571$	22.6224			0.946716			0.473358	−	0.880870i	$-0.343042\pi$
$571$	22.6224			0.946716			0.473358	+	0.880870i	$0.343042\pi$
$572$	6.76708	−	3.78692i	0.282946	−	0.158339i
$573$	−22.3548			−0.933884
$574$	−5.46777	−	11.1654i	−0.228220	−	0.466034i
$575$	74.3048	+	53.9856i	3.09873	+	2.25136i
$576$	26.0494			1.08539
$577$	4.53018	−	13.9425i	0.188594	−	0.580432i	−0.811398	−	0.584494i	$-0.801293\pi$
$577$	4.53018	−	13.9425i	0.188594	−	0.580432i	0.999992	+	0.00406193i	$0.00129296\pi$
$578$	7.36423			0.306312
$579$	−60.9345	−	44.2715i	−2.53235	−	1.83986i
$580$	2.39620	+	7.37476i	0.0994970	+	0.306220i
$581$	5.81956	+	4.22815i	0.241436	+	0.175413i
$582$	−2.13781	+	6.57951i	−0.0886152	+	0.272730i
$583$	1.34222	−	0.751118i	0.0555890	−	0.0311081i
$584$	6.19432	−	19.0642i	0.256323	−	0.788881i
$585$	−95.9870			−3.96857
$586$	−9.72452	+	29.9290i	−0.401716	+	1.23635i
$587$	−3.38887			−0.139874			−0.0699368	−	0.997551i	$-0.522280\pi$
$587$	−3.38887			−0.139874			−0.0699368	+	0.997551i	$0.522280\pi$
$588$	−3.72365	+	11.4602i	−0.153561	+	0.472611i
$589$	−17.1561			−0.706904
$590$	−0.335777	+	1.03341i	−0.0138237	+	0.0425450i
$591$	16.7512	−	12.1704i	0.689051	−	0.500625i
$592$	1.61076	−	4.95740i	0.0662017	−	0.203748i
$593$	−30.8269	+	22.3971i	−1.26591	+	0.919737i	−0.999032	−	0.0439930i	$-0.985992\pi$
$593$	−30.8269	+	22.3971i	−1.26591	+	0.919737i	−0.266878	+	0.963730i	$0.585992\pi$
$594$	−50.1677	−	46.4042i	−2.05841	−	1.90399i
$595$	−13.5952	+	9.87751i	−0.557350	+	0.404938i
$596$	2.96381	+	2.15333i	0.121402	+	0.0882040i
$597$	−4.22167	−	12.9930i	−0.172781	−	0.531766i
$598$	14.4030	+	44.3277i	0.588981	+	1.81270i
$599$	2.97034	+	9.14176i	0.121365	+	0.373522i	0.993221	−	0.116239i	$-0.0370839\pi$
$599$	2.97034	+	9.14176i	0.121365	+	0.373522i	−0.871857	+	0.489761i	$0.837084\pi$
$600$	75.4852			3.08167
$601$	−16.5444	+	12.0202i	−0.674861	+	0.490315i	−0.871649	−	0.490131i	$-0.836949\pi$
$601$	−16.5444	+	12.0202i	−0.674861	+	0.490315i	0.196788	+	0.980446i	$0.436949\pi$
$602$	4.99514	+	15.3735i	0.203587	+	0.626575i
$603$	24.4800	−	17.7858i	0.996904	−	0.724293i
$604$	−4.07495	+	12.5414i	−0.165807	+	0.510302i
$605$	−42.8675	−	10.3204i	−1.74281	−	0.419584i
$606$	56.7457			2.30514
$607$	−39.2465			−1.59297			−0.796484	−	0.604659i	$-0.793309\pi$
$607$	−39.2465			−1.59297			−0.796484	+	0.604659i	$0.793309\pi$
$608$	13.7890			0.559218
$609$	10.6295			0.430730
$610$	42.0754			1.70358
$611$	−42.1035			−1.70332
$612$	−13.6174	+	9.89363i	−0.550452	+	0.399926i
$613$	−1.92959	−	5.93867i	−0.0779354	−	0.239861i	0.904497	−	0.426480i	$-0.140247\pi$
$613$	−1.92959	−	5.93867i	−0.0779354	−	0.239861i	−0.982432	+	0.186620i	$0.940247\pi$
$614$	−4.27110	−	13.1451i	−0.172368	−	0.530493i
$615$	35.6646	+	72.8284i	1.43814	+	2.93673i
$616$	1.65346	+	8.32636i	0.0666200	+	0.335478i
$617$	−7.97571	−	5.79469i	−0.321090	−	0.233285i	0.415551	−	0.909570i	$-0.363589\pi$
$617$	−7.97571	−	5.79469i	−0.321090	−	0.233285i	−0.736640	+	0.676285i	$0.763589\pi$
$618$	4.40388	+	13.5537i	0.177150	+	0.545211i
$619$	−7.68344	+	23.6472i	−0.308824	+	0.950462i	0.669399	+	0.742903i	$0.266552\pi$
$619$	−7.68344	+	23.6472i	−0.308824	+	0.950462i	−0.978223	+	0.207558i	$0.933448\pi$
$620$	−10.1902	−	7.40360i	−0.409248	−	0.297336i
$621$	84.4771	−	61.3762i	3.38995	−	2.46294i
$622$	8.25745	+	25.4138i	0.331094	+	1.01900i
$623$	2.83919	+	8.73813i	0.113750	+	0.350086i
$624$	42.9433	+	31.2002i	1.71911	+	1.24901i
$625$	42.1470			1.68588
$626$	15.5337	−	47.8079i	0.620853	−	1.91079i
$627$	28.6327	+	26.4847i	1.14348	+	1.05770i
$628$	−10.1713	−	7.38986i	−0.405878	−	0.294888i
$629$	−1.16267	−	3.57832i	−0.0463586	−	0.142677i
$630$	−16.7925	+	51.6820i	−0.669030	+	2.05906i
$631$	8.39392	−	25.8338i	0.334157	−	1.02843i	−0.632979	−	0.774169i	$-0.718168\pi$
$631$	8.39392	−	25.8338i	0.334157	−	1.02843i	0.967136	−	0.254260i	$-0.0818319\pi$
$632$	−2.93941	−	2.13561i	−0.116923	−	0.0849499i
$633$	−22.2385	+	16.1572i	−0.883902	+	0.642192i
$634$	−0.445684	+	1.37167i	−0.0177004	+	0.0544761i
$635$	−19.5092			−0.774197
$636$	−0.808140	−	0.587148i	−0.0320448	−	0.0232819i
$637$	15.5217	−	11.2772i	0.614993	−	0.446819i
$638$	13.4491	−	7.52622i	0.532454	−	0.297966i
$639$	−7.24119	+	22.2861i	−0.286457	+	0.881624i
$640$	−43.8392	−	31.8511i	−1.73290	−	1.25902i
$641$	8.88919	−	27.3581i	0.351102	−	1.08058i	−0.607133	−	0.794600i	$-0.707681\pi$
$641$	8.88919	−	27.3581i	0.351102	−	1.08058i	0.958235	−	0.285981i	$-0.0923194\pi$
$642$	7.98083	−	5.79841i	0.314978	−	0.228845i
$643$	−17.4872	+	12.7052i	−0.689629	+	0.501045i	−0.876538	−	0.481332i	$-0.840153\pi$
$643$	−17.4872	+	12.7052i	−0.689629	+	0.501045i	0.186909	+	0.982377i	$0.440153\pi$
$644$	6.70807			0.264335
$645$	−32.5818	−	100.276i	−1.28291	−	3.94838i
$646$	17.4367	−	12.6685i	0.686038	−	0.498436i
$647$	3.99588	+	12.2980i	0.157094	+	0.483486i	0.998367	−	0.0571246i	$-0.0181932\pi$
$647$	3.99588	+	12.2980i	0.157094	+	0.483486i	−0.841273	+	0.540611i	$0.818193\pi$
$648$	12.5458	−	38.6119i	0.492844	−	1.51682i
$649$	0.545190	+	0.0647032i	0.0214006	+	0.00253982i
$650$	50.2856	+	36.5346i	1.97236	+	1.43300i
$651$	−13.9686	+	10.1488i	−0.547474	+	0.397763i
$652$	−0.492482	+	1.51570i	−0.0192871	+	0.0593595i
$653$	9.21156	−	6.69259i	0.360476	−	0.261901i	−0.392774	−	0.919635i	$-0.628485\pi$
$653$	9.21156	−	6.69259i	0.360476	−	0.261901i	0.753251	+	0.657733i	$0.228485\pi$
$654$	13.5899	−	9.87363i	0.531406	−	0.386089i
$655$	−16.0186	+	49.3003i	−0.625900	+	1.92632i
$656$	5.39758	−	30.8992i	0.210740	−	1.20641i
$657$	−52.4524	−	38.1089i	−2.04636	−	1.48677i
$658$	−7.36582	+	22.6697i	−0.287150	+	0.883756i
$659$	−22.2510			−0.866777			−0.433389	−	0.901207i	$-0.642682\pi$
$659$	−22.2510			−0.866777			−0.433389	+	0.901207i	$0.642682\pi$
$660$	5.57764	+	28.0873i	0.217109	+	1.09330i
$661$	−8.64929	−	26.6198i	−0.336418	−	1.03539i	−0.966019	−	0.258471i	$-0.916781\pi$
$661$	−8.64929	−	26.6198i	−0.336418	−	1.03539i	0.629601	−	0.776919i	$-0.283219\pi$
$662$	8.87458	−	27.3132i	0.344920	−	1.06156i
$663$	38.3145			1.48801
$664$	4.04735	+	12.4565i	0.157068	+	0.483404i
$665$	5.46629	−	16.8235i	0.211974	−	0.652387i
$666$	−9.84318	−	7.15149i	−0.381416	−	0.277115i
$667$	7.27695	+	22.3962i	0.281765	+	0.867183i
$668$	−1.23667	+	3.80608i	−0.0478482	+	0.147262i
$669$	12.9533	−	39.8662i	0.500805	−	1.54132i
$670$	−28.4466			−1.09899
$671$	−4.14082	−	20.8519i	−0.159855	−	0.804980i
$672$	11.2271	−	8.15699i	0.433096	−	0.314663i
$673$	−5.56596			−0.214552			−0.107276	−	0.994229i	$-0.534213\pi$
$673$	−5.56596			−0.214552			−0.107276	+	0.994229i	$0.534213\pi$
$674$	15.0647	+	46.3643i	0.580269	+	1.78588i
$675$	43.0309	−	132.435i	1.65626	−	5.09744i
$676$	−0.260836	−	0.802770i	−0.0100321	−	0.0308758i
$677$	1.43933	+	4.42980i	0.0553179	+	0.170251i	0.974898	−	0.222651i	$-0.0714711\pi$
$677$	1.43933	+	4.42980i	0.0553179	+	0.170251i	−0.919580	+	0.392902i	$0.871471\pi$
$678$	−5.38843	+	16.5839i	−0.206942	+	0.636901i
$679$	−0.489885	−	1.50771i	−0.0188001	−	0.0578606i
$680$	−30.5974			−1.17336
$681$	32.4307	−	23.5623i	1.24275	−	0.902908i
$682$	−10.4880	+	22.7313i	−0.401608	+	0.870427i
$683$	−34.5873			−1.32345			−0.661724	−	0.749747i	$-0.730175\pi$
$683$	−34.5873			−1.32345			−0.661724	+	0.749747i	$0.730175\pi$
$684$	5.47521	−	16.8510i	0.209350	−	0.644313i
$685$	−28.9029	+	88.9540i	−1.10432	+	3.39876i
$686$	−7.55640	−	23.2562i	−0.288505	−	0.887927i
$687$	−14.9302	−	10.8475i	−0.569624	−	0.413856i
$688$	−12.6029	+	38.7877i	−0.480481	+	1.47877i
$689$	0.491481	+	1.51262i	0.0187239	+	0.0576264i
$690$	−172.115			−6.55229
$691$	12.3243	−	37.9302i	0.468838	−	1.44293i	−0.385254	−	0.922811i	$-0.625886\pi$
$691$	12.3243	−	37.9302i	0.468838	−	1.44293i	0.854091	−	0.520123i	$-0.174114\pi$
$692$	1.43825	+	4.42649i	0.0546741	+	0.168270i
$693$	27.2655	+	3.23587i	1.03573	+	0.122921i
$694$	−36.4175			−1.38239
$695$	9.33145	−	28.7192i	0.353962	−	1.08938i
$696$	15.6577	+	11.3760i	0.593503	+	0.431205i
$697$	−9.95769	−	20.3339i	−0.377174	−	0.770203i
$698$	10.2490	−	31.5432i	0.387930	−	1.19393i
$699$	69.4718	−	50.4742i	2.62766	−	1.90911i
$700$	7.23722	−	5.25815i	0.273541	−	0.198739i
$701$	8.08705	−	24.8894i	0.305444	−	0.940059i	−0.674068	−	0.738670i	$-0.735454\pi$
$701$	8.08705	−	24.8894i	0.305444	−	0.940059i	0.979511	−	0.201389i	$-0.0645456\pi$
$702$	57.1696	−	41.5361i	2.15773	−	1.56768i
$703$	3.20415	+	2.32795i	0.120847	+	0.0878002i
$704$	−5.18382	+	11.2352i	−0.195373	+	0.423442i
$705$	48.0451	−	147.867i	1.80948	−	5.56901i
$706$	11.2006	+	34.4718i	0.421539	+	1.29736i
$707$	−10.5200	+	7.64322i	−0.395645	+	0.287453i
$708$	−0.110183	−	0.339108i	−0.00414092	−	0.0127445i
$709$	46.8557			1.75970			0.879850	−	0.475251i	$-0.157643\pi$
$709$	46.8557			1.75970			0.879850	+	0.475251i	$0.157643\pi$
$710$	17.8222	−	12.9486i	0.668855	−	0.485951i
$711$	−9.50730	+	6.90746i	−0.356552	+	0.259050i
$712$	−5.16953	+	15.9102i	−0.193736	+	0.596259i
$713$	−30.9462	−	22.4837i	−1.15895	−	0.842023i
$714$	6.70297	−	20.6296i	0.250852	−	0.772044i
$715$	19.1014	−	41.3996i	0.714352	−	1.54826i
$716$	3.54144	−	2.57301i	0.132350	−	0.0961578i
$717$	−44.5363	−	32.3575i	−1.66324	−	1.20841i
$718$	31.6266			1.18029
$719$	1.99680	−	6.14553i	0.0744682	−	0.229190i	−0.906893	−	0.421360i	$-0.861553\pi$
$719$	1.99680	−	6.14553i	0.0744682	−	0.229190i	0.981362	+	0.192171i	$0.0615527\pi$
$720$	−110.921	+	80.5888i	−4.13378	+	3.00337i
$721$	−2.64201	−	1.91953i	−0.0983937	−	0.0714872i
$722$	2.60406	−	8.01448i	0.0969132	−	0.298268i
$723$	−5.29994	+	16.3116i	−0.197107	+	0.606633i
$724$	−0.468921	−	1.44319i	−0.0174273	−	0.0536358i
$725$	25.4063	+	18.4588i	0.943566	+	0.685541i
$726$	52.5955	−	21.7466i	1.95200	−	0.807092i
$727$	−7.97372	+	24.5406i	−0.295729	+	0.910160i	0.687247	+	0.726424i	$0.258819\pi$
$727$	−7.97372	+	24.5406i	−0.295729	+	0.910160i	−0.982976	+	0.183736i	$0.941181\pi$
$728$	−8.77800			−0.325334
$729$	−9.75122	−	7.08468i	−0.361156	−	0.262395i
$730$	18.8350	+	57.9683i	0.697116	+	2.14550i
$731$	9.09695	+	27.9975i	0.336463	+	1.03553i
$732$	−11.1699	+	8.11540i	−0.412851	+	0.299954i
$733$	3.95548	+	2.87382i	0.146099	+	0.106147i	0.658434	−	0.752639i	$-0.271219\pi$
$733$	3.95548	+	2.87382i	0.146099	+	0.106147i	−0.512335	+	0.858786i	$0.671219\pi$
$734$	2.04356	−	6.28944i	0.0754293	−	0.232147i
$735$	21.8934	+	67.3810i	0.807550	+	2.48538i
$736$	24.8727	+	18.0711i	0.916820	+	0.666109i
$737$	2.79955	+	14.0977i	0.103123	+	0.519296i
$738$	−64.7004	−	34.2696i	−2.38165	−	1.26148i
$739$	3.07048	+	9.44996i	0.112949	+	0.347623i	0.991514	−	0.130001i	$-0.0414982\pi$
$739$	3.07048	+	9.44996i	0.112949	+	0.347623i	−0.878564	+	0.477624i	$0.841498\pi$
$740$	0.898552	+	2.76546i	0.0330314	+	0.101660i
$741$	−32.6289	+	23.7063i	−1.19865	+	0.870873i
$742$	0.900421			0.0330555
$743$	28.8006			1.05659			0.528295	−	0.849061i	$-0.322832\pi$
$743$	28.8006			1.05659			0.528295	+	0.849061i	$0.322832\pi$
$744$	−31.4378			−1.15257
$745$	21.5396			0.789149
$746$	−42.3510			−1.55058
$747$	42.3628			1.54998
$748$	−1.55730	−	7.84208i	−0.0569404	−	0.286735i
$749$	−0.698549	+	2.14991i	−0.0255244	+	0.0785561i
$750$	−101.799	+	73.9612i	−3.71717	+	2.70068i
$751$	1.59882	+	4.92065i	0.0583416	+	0.179557i	0.975980	−	0.217859i	$-0.0699072\pi$
$751$	1.59882	+	4.92065i	0.0583416	+	0.179557i	−0.917639	+	0.397416i	$0.869907\pi$
$752$	−48.6541	+	35.3493i	−1.77423	+	1.28905i
$753$	−77.5988			−2.82786
$754$	4.92466	+	15.1565i	0.179345	+	0.551968i
$755$	23.9589	+	73.7378i	0.871953	+	2.68360i
$756$	−3.14281	−	9.67258i	−0.114303	−	0.351788i
$757$	−16.2627	−	11.8155i	−0.591077	−	0.429442i	0.251624	−	0.967825i	$-0.419036\pi$
$757$	−16.2627	−	11.8155i	−0.591077	−	0.429442i	−0.842700	+	0.538383i	$0.819036\pi$
$758$	45.5294	−	33.0791i	1.65370	−	1.20149i
$759$	16.9385	+	85.2975i	0.614830	+	3.09610i
$760$	26.0570	−	18.9315i	0.945186	−	0.686718i
$761$	−4.71396	+	14.5081i	−0.170881	+	0.525917i	−0.999421	−	0.0340119i	$-0.989172\pi$
$761$	−4.71396	+	14.5081i	−0.170881	+	0.525917i	0.828541	+	0.559929i	$0.189172\pi$
$762$	20.3729	−	14.8018i	0.738031	−	0.536211i
$763$	−1.18950	+	3.66091i	−0.0430628	+	0.132534i
$764$	−4.82368			−0.174515
$765$	−30.5819	+	94.1213i	−1.10569	+	3.40296i
$766$	−28.7590			−1.03911
$767$	−0.175432	+	0.539925i	−0.00633450	+	0.0194956i
$768$	46.3713			1.67328
$769$	11.1720	−	34.3840i	0.402874	−	1.23992i	−0.519783	−	0.854298i	$-0.673987\pi$
$769$	11.1720	−	34.3840i	0.402874	−	1.23992i	0.922657	−	0.385621i	$-0.126013\pi$
$770$	−18.9490	−	17.5274i	−0.682873	−	0.631644i
$771$	−3.75098	+	11.5443i	−0.135088	+	0.415759i
$772$	−13.1484	−	9.55286i	−0.473220	−	0.343815i
$773$	−2.35090	−	7.23533i	−0.0845561	−	0.260237i	0.899835	−	0.436230i	$-0.143686\pi$
$773$	−2.35090	−	7.23533i	−0.0845561	−	0.260237i	−0.984391	+	0.175993i	$0.943686\pi$
$774$	77.0151	+	55.9547i	2.76825	+	2.01125i
$775$	−51.0113			−1.83238
$776$	0.891970	−	2.74520i	0.0320199	−	0.0985470i
$777$	3.98596			0.142995
$778$	40.0078	+	29.0674i	1.43435	+	1.04212i
$779$	21.0612	+	11.1554i	0.754597	+	0.399684i
$780$	−29.6109			−1.06024
$781$	−8.17108	−	7.55809i	−0.292384	−	0.270450i
$782$	48.0550			1.71844
$783$	28.8844	−	20.9857i	1.03224	−	0.749969i
$784$	8.46854	−	26.0635i	0.302448	−	0.930838i
$785$	−73.9200			−2.63832
$786$	−20.6767	−	63.6364i	−0.737514	−	2.26983i
$787$	−18.5662	−	13.4891i	−0.661813	−	0.480836i	0.205461	−	0.978665i	$-0.434130\pi$
$787$	−18.5662	−	13.4891i	−0.661813	−	0.480836i	−0.867275	+	0.497830i	$0.834130\pi$
$788$	3.61455	−	2.62612i	0.128763	−	0.0935517i
$789$	−33.1430	+	24.0798i	−1.17992	+	0.857263i
$790$	11.0478			0.393063
$791$	−1.23477	−	3.80024i	−0.0439034	−	0.135121i
$792$	36.7000	+	33.9467i	1.30408	+	1.20625i
$793$	21.9830			0.780640
$794$	10.3135	−	7.49320i	0.366013	−	0.265924i
$795$	−5.87318			−0.208300
$796$	−0.910946	−	2.80360i	−0.0322876	−	0.0993711i
$797$	−10.6214	+	7.71689i	−0.376229	+	0.273346i	−0.759789	−	0.650170i	$-0.774698\pi$
$797$	−10.6214	+	7.71689i	−0.376229	+	0.273346i	0.383560	+	0.923516i	$0.374698\pi$
$798$	7.05584	+	21.7156i	0.249774	+	0.768725i
$799$	−13.4143	+	41.2851i	−0.474565	+	1.46056i
$800$	40.9998			1.44956
$801$	43.7747	+	31.8042i	1.54670	+	1.12374i
$802$	11.0396	+	8.02076i	0.389823	+	0.283223i
$803$	26.8746	−	15.0393i	0.948383	−	0.530724i
$804$	7.55181	−	5.48671i	0.266332	−	0.193501i
$805$	31.9080	−	23.1825i	1.12461	−	0.817077i
$806$	−20.9428	−	15.2158i	−0.737677	−	0.535954i
$807$	−51.1523			−1.80064
$808$	−23.6763			−0.832929
$809$	33.7205	+	24.4994i	1.18555	+	0.861353i	0.992787	−	0.119892i	$-0.0382550\pi$
$809$	33.7205	+	24.4994i	1.18555	+	0.861353i	0.192763	+	0.981245i	$0.438255\pi$
$810$	38.1478	+	117.407i	1.34038	+	4.12526i
$811$	12.0981	+	8.78980i	0.424822	+	0.308652i	0.779575	−	0.626309i	$-0.215435\pi$
$811$	12.0981	+	8.78980i	0.424822	+	0.308652i	−0.354753	+	0.934960i	$0.615435\pi$
$812$	2.29362			0.0804904
$813$	10.3693	−	7.53376i	0.363668	−	0.264221i
$814$	5.04326	−	2.82226i	0.176766	−	0.0989200i
$815$	2.89558	+	8.91166i	0.101428	+	0.312162i
$816$	44.2757	−	32.1682i	1.54996	−	1.12611i
$817$	−25.0699	−	18.2143i	−0.877084	−	0.637239i
$818$	−29.8866			−1.04496
$819$	−8.77354	+	27.0022i	−0.306572	+	0.943533i
$820$	7.69567	+	15.7148i	0.268744	+	0.548785i
$821$	−0.315154	+	0.228973i	−0.0109990	+	0.00799121i	−0.593271	−	0.805003i	$-0.702164\pi$
$821$	−0.315154	+	0.228973i	−0.0109990	+	0.00799121i	0.582272	+	0.812994i	$0.302164\pi$
$822$	−37.3076	−	114.821i	−1.30125	−	4.00485i
$823$	−0.0639882	−	0.196936i	−0.00223049	−	0.00686474i	0.949935	−	0.312447i	$-0.101149\pi$
$823$	−0.0639882	−	0.196936i	−0.00223049	−	0.00686474i	−0.952166	+	0.305583i	$0.901149\pi$
$824$	−1.83745	−	5.65509i	−0.0640106	−	0.197004i
$825$	85.1355	+	78.7486i	2.96404	+	2.74167i
$826$	0.260020	+	0.188915i	0.00904724	+	0.00657320i
$827$	−8.54075	−	6.20522i	−0.296991	−	0.215777i	0.429303	−	0.903160i	$-0.358759\pi$
$827$	−8.54075	−	6.20522i	−0.296991	−	0.215777i	−0.726294	+	0.687384i	$0.758759\pi$
$828$	31.9601	−	23.2204i	1.11069	−	0.806964i
$829$	−20.4309	+	14.8439i	−0.709596	+	0.515551i	−0.883043	−	0.469292i	$-0.844509\pi$
$829$	−20.4309	+	14.8439i	−0.709596	+	0.515551i	0.173448	+	0.984843i	$0.444509\pi$
$830$	−32.2195	−	23.4088i	−1.11835	−	0.812532i
$831$	−55.9264	−	40.6329i	−1.94007	−	1.40954i
$832$	−10.3512	−	7.52057i	−0.358862	−	0.260729i
$833$	−6.11271	−	18.8130i	−0.211793	−	0.651832i
$834$	12.0450	+	37.0706i	0.417083	+	1.28365i
$835$	7.27107	+	22.3780i	0.251626	+	0.774424i
$836$	6.17832	+	5.71483i	0.213682	+	0.197651i
$837$	−17.9213	+	55.1562i	−0.619452	+	1.90648i
$838$	8.12924	−	25.0192i	0.280820	−	0.864274i
$839$	−18.4361			−0.636484			−0.318242	−	0.948009i	$-0.603093\pi$
$839$	−18.4361			−0.636484			−0.318242	+	0.948009i	$0.603093\pi$
$840$	10.0167	−	30.8284i	0.345611	−	1.06368i
$841$	−6.47336	−	19.9229i	−0.223219	−	0.686998i
$842$	−8.06848	−	24.8322i	−0.278058	−	0.855775i
$843$	60.5964			2.08705
$844$	−4.79860	+	3.48639i	−0.165175	+	0.120006i
$845$	−4.01501	−	2.91708i	−0.138121	−	0.100350i
$846$	43.3785	+	133.505i	1.49138	+	4.59000i
$847$	−6.82148	+	11.1158i	−0.234389	+	0.381942i
$848$	1.83792	+	1.33533i	0.0631144	+	0.0458553i
$849$	−62.3672	+	45.3124i	−2.14044	+	1.55512i
$850$	51.8457	−	37.6681i	1.77829	−	1.29201i
$851$	2.72878	+	8.39833i	0.0935415	+	0.287891i
$852$	−2.23382	+	6.87500i	−0.0765295	+	0.235534i
$853$	18.8043	+	13.6621i	0.643845	+	0.467781i	0.861169	−	0.508318i	$-0.169733\pi$
$853$	18.8043	+	13.6621i	0.643845	+	0.467781i	−0.217324	+	0.976100i	$0.569733\pi$
$854$	3.84584	−	11.8363i	0.131602	−	0.405029i
$855$	−32.1918	−	99.0762i	−1.10094	−	3.38833i
$856$	−3.32988	+	2.41930i	−0.113813	+	0.0826900i
$857$	−8.10217	−	24.9359i	−0.276765	−	0.851794i	−0.988747	−	0.149597i	$-0.952202\pi$
$857$	−8.10217	−	24.9359i	−0.276765	−	0.851794i	0.711982	−	0.702197i	$-0.247798\pi$
$858$	11.4631	+	57.7248i	0.391344	+	1.97069i
$859$	42.7519	+	31.0610i	1.45867	+	1.05979i	0.983706	+	0.179786i	$0.0575406\pi$
$859$	42.7519	+	31.0610i	1.45867	+	1.05979i	0.474969	+	0.880003i	$0.342459\pi$
$860$	−7.03046	−	21.6375i	−0.239737	−	0.737833i
$861$	23.7473	−	3.37608i	0.809306	−	0.115057i
$862$	12.9189	−	9.38613i	0.440019	−	0.319693i
$863$	15.2869	−	11.1066i	0.520372	−	0.378072i	−0.296372	−	0.955073i	$-0.595777\pi$
$863$	15.2869	−	11.1066i	0.520372	−	0.378072i	0.816744	+	0.577000i	$0.195777\pi$
$864$	14.4041	−	44.3312i	0.490037	−	1.50818i
$865$	22.1388	+	16.0848i	0.752743	+	0.546900i
$866$	−5.30589	+	16.3299i	−0.180301	+	0.554911i
$867$	−4.39054	+	13.5127i	−0.149110	+	0.458915i
$868$	−3.01413	+	2.18990i	−0.102306	+	0.0743299i
$869$	−1.08726	−	5.47512i	−0.0368828	−	0.185731i
$870$	−58.8494			−1.99518
$871$	−14.8624			−0.503594
$872$	−5.67017	+	4.11962i	−0.192016	+	0.139508i
$873$	−7.55305	−	5.48761i	−0.255632	−	0.185728i
$874$	−40.9240	+	29.7330i	−1.38427	+	1.00573i
$875$	8.91029	−	27.4230i	0.301223	−	0.927068i
$876$	−16.1810	−	11.7562i	−0.546705	−	0.397204i
$877$	54.3043			1.83373			0.916864	−	0.399200i	$-0.130712\pi$
$877$	54.3043			1.83373			0.916864	+	0.399200i	$0.130712\pi$
$878$	11.1204			0.375296
$879$	−49.1192	−	35.6872i	−1.65675	−	1.20370i
$880$	−12.6850	−	63.8778i	−0.427611	−	2.15332i
$881$	30.2611	−	21.9860i	1.01952	−	0.740726i	0.0533374	−	0.998577i	$-0.483014\pi$
$881$	30.2611	−	21.9860i	1.01952	−	0.740726i	0.966185	+	0.257850i	$0.0830141\pi$
$882$	−51.7504	−	37.5989i	−1.74253	−	1.26602i
$883$	−31.5275			−1.06099			−0.530493	−	0.847690i	$-0.677993\pi$
$883$	−31.5275			−1.06099			−0.530493	+	0.847690i	$0.677993\pi$
$884$	8.26746			0.278065
$885$	−1.69603	−	1.23224i	−0.0570114	−	0.0414212i
$886$	2.98968	+	9.20128i	0.100440	+	0.309123i
$887$	33.2511	+	24.1583i	1.11646	+	0.811157i	0.983669	−	0.179987i	$-0.0576056\pi$
$887$	33.2511	+	24.1583i	1.11646	+	0.811157i	0.132793	+	0.991144i	$0.457606\pi$
$888$	5.87147	+	4.26587i	0.197033	+	0.143153i
$889$	−1.78320	+	5.48814i	−0.0598068	+	0.184066i
$890$	−15.7190	−	48.3780i	−0.526900	−	1.62163i
$891$	54.4308	−	30.4600i	1.82350	−	1.02045i
$892$	2.79505	−	8.60229i	0.0935853	−	0.288026i
$893$	−14.1205	−	43.4585i	−0.472525	−	1.45428i
$894$	−22.4932	+	16.3423i	−0.752284	+	0.546567i
$895$	7.95333	−	24.4778i	0.265851	−	0.818204i
$896$	−12.9671	+	9.42116i	−0.433201	+	0.314739i
$897$	−89.9243			−3.00249
$898$	−15.5351	−	11.2869i	−0.518415	−	0.376650i
$899$	−10.5811	−	7.68764i	−0.352900	−	0.256397i
$900$	16.2798	−	50.1041i	0.542660	−	1.67014i
$901$	1.63981			0.0546301
$902$	27.6560	−	21.0859i	0.920844	−	0.702083i
$903$	−31.1870			−1.03784
$904$	2.24824	−	6.91938i	0.0747754	−	0.230135i
$905$	−7.21805	−	5.24422i	−0.239936	−	0.174324i
$906$	−80.9651	−	58.8246i	−2.68989	−	1.95432i
$907$	−56.0092			−1.85975			−0.929877	−	0.367870i	$-0.880087\pi$
$907$	−56.0092			−1.85975			−0.929877	+	0.367870i	$0.880087\pi$
$908$	6.99785	−	5.08423i	0.232232	−	0.168726i
$909$	−23.6643	+	72.8311i	−0.784894	+	2.41565i
$910$	21.5937	−	15.6887i	0.715823	−	0.520076i
$911$	−9.15925	−	28.1893i	−0.303459	−	0.933952i	−0.980248	−	0.197774i	$-0.936629\pi$
$911$	−9.15925	−	28.1893i	−0.303459	−	0.933952i	0.676788	−	0.736178i	$-0.263371\pi$
$912$	−17.8021	+	54.7892i	−0.589486	+	1.81425i
$913$	−8.43021	+	18.2713i	−0.278999	+	0.604691i
$914$	6.83683	+	21.0416i	0.226142	+	0.695995i
$915$	−25.0852	+	77.2044i	−0.829292	+	2.55230i
$916$	−3.22163	−	2.34065i	−0.106446	−	0.0773372i
$917$	12.4046	+	9.01243i	0.409634	+	0.297617i
$918$	−22.5143	−	69.2920i	−0.743084	−	2.28698i
$919$	18.7164	+	13.5983i	0.617398	+	0.448566i	0.852012	−	0.523523i	$-0.175383\pi$
$919$	18.7164	+	13.5983i	0.617398	+	0.448566i	−0.234614	+	0.972089i	$0.575383\pi$
$920$	71.8122			2.36758
$921$	26.6665			0.878689
$922$	−37.1131	−	26.9642i	−1.22225	−	0.888020i
$923$	9.31151	−	6.76521i	0.306492	−	0.222680i
$924$	8.41109	+	0.998229i	0.276705	+	0.0328393i
$925$	9.52710	+	6.92184i	0.313249	+	0.227589i
$926$	−4.89008			−0.160698
$927$	−19.2323			−0.631670
$928$	8.50447	+	6.17886i	0.279173	+	0.202831i
$929$	8.75142	−	26.9341i	0.287125	−	0.883680i	−0.698629	−	0.715484i	$-0.746206\pi$
$929$	8.75142	−	26.9341i	0.287125	−	0.883680i	0.985754	−	0.168195i	$-0.0537939\pi$
$930$	77.3362	−	56.1880i	2.53595	−	1.84248i
$931$	16.8458	+	12.2392i	0.552098	+	0.401122i
$932$	14.9905	−	10.8913i	0.491031	−	0.356755i
$933$	−51.5551			−1.68784
$934$	0.117424			0.00384223
$935$	−34.5091	−	31.9202i	−1.12857	−	1.04390i
$936$	−41.8222	+	30.3856i	−1.36700	+	0.993184i
$937$	7.08264	−	21.7981i	0.231380	−	0.712114i	−0.766201	−	0.642601i	$-0.777855\pi$
$937$	7.08264	−	21.7981i	0.231380	−	0.712114i	0.997581	−	0.0695131i	$-0.0221446\pi$
$938$	−2.60012	+	8.00233i	−0.0848968	+	0.261285i
$939$	78.4620	+	57.0060i	2.56051	+	1.86032i
$940$	10.3671	−	31.9067i	0.338138	−	1.04068i
$941$	46.6971	−	33.9275i	1.52228	−	1.10600i	0.561942	−	0.827177i	$-0.310055\pi$
$941$	46.6971	−	33.9275i	1.52228	−	1.10600i	0.960341	−	0.278827i	$-0.0899455\pi$
$942$	77.1926	−	56.0837i	2.51507	−	1.82731i
$943$	23.3707	+	47.7238i	0.761055	+	1.55410i
$944$	0.250584	+	0.771219i	0.00815582	+	0.0251010i
$945$	−48.3769	−	35.1479i	−1.57370	−	1.14336i
$946$	−39.4595	+	22.0819i	−1.28294	+	0.717945i
$947$	−16.4011	−	50.4775i	−0.532966	−	1.64030i	−0.748004	−	0.663694i	$-0.768988\pi$
$947$	−16.4011	−	50.4775i	−0.532966	−	1.64030i	0.215039	−	0.976606i	$-0.431012\pi$
$948$	−2.93289	+	2.13087i	−0.0952560	+	0.0692075i
$949$	9.84069	+	30.2865i	0.319442	+	0.983142i
$950$	−20.8458	+	64.1568i	−0.676328	+	2.08152i
$951$	−2.25118	−	1.63558i	−0.0729995	−	0.0530372i
$952$	−2.79671	+	8.60739i	−0.0906419	+	0.278967i
$953$	6.19583	+	19.0688i	0.200703	+	0.617699i	0.999863	+	0.0165806i	$0.00527801\pi$
$953$	6.19583	+	19.0688i	0.200703	+	0.617699i	−0.799160	+	0.601118i	$0.794722\pi$
$954$	4.28999	−	3.11686i	0.138894	−	0.100912i
$955$	−22.9446	+	16.6702i	−0.742471	+	0.539436i
$956$	−9.60999	−	6.98207i	−0.310809	−	0.225816i
$957$	5.79162	+	29.1649i	0.187217	+	0.942767i
$958$	9.36871	+	28.8339i	0.302689	+	0.931581i
$959$	22.3819	+	16.2614i	0.722750	+	0.525108i
$960$	38.2242	−	27.7715i	1.23368	−	0.896321i
$961$	−9.75499			−0.314677
$962$	1.84670	+	5.68354i	0.0595399	+	0.183245i
$963$	4.11387	+	12.6612i	0.132567	+	0.408001i
$964$	−1.14362	+	3.51969i	−0.0368334	+	0.113361i
$965$	−95.5562			−3.07606
$966$	−15.7319	+	48.4177i	−0.506165	+	1.55782i
$967$	5.34513	−	16.4506i	0.171888	−	0.529017i	−0.827590	−	0.561333i	$-0.810289\pi$
$967$	5.34513	−	16.4506i	0.171888	−	0.529017i	0.999478	+	0.0323168i	$0.0102885\pi$
$968$	−21.9447	+	9.07344i	−0.705328	+	0.291631i
$969$	12.8498	+	39.5477i	0.412795	+	1.27045i
$970$	2.71221	+	8.34732i	0.0870838	+	0.268016i
$971$	2.28362	+	7.02826i	0.0732849	+	0.225548i	0.980989	−	0.194063i	$-0.0621666\pi$
$971$	2.28362	+	7.02826i	0.0732849	+	0.225548i	−0.907704	+	0.419611i	$0.862167\pi$
$972$	−11.9532	−	8.68449i	−0.383398	−	0.278555i
$973$	−7.22611	−	5.25008i	−0.231658	−	0.168310i
$974$	28.9058	+	21.0013i	0.926202	+	0.672925i
$975$	−97.0177	+	70.4875i	−3.10705	+	2.25741i
$976$	25.4032	−	18.4565i	0.813137	−	0.590779i
$977$	12.3532	+	8.97515i	0.395215	+	0.287141i	0.767589	−	0.640942i	$-0.221456\pi$
$977$	12.3532	+	8.97515i	0.395215	+	0.287141i	−0.372374	+	0.928083i	$0.621456\pi$
$978$	−9.78512	−	7.10931i	−0.312894	−	0.227331i
$979$	−22.4284	+	12.5512i	−0.716816	+	0.401137i
$980$	4.72413	+	14.5394i	0.150907	+	0.464443i
$981$	7.00515	+	21.5596i	0.223657	+	0.688346i
$982$	−2.10676	−	6.48393i	−0.0672293	−	0.206911i
$983$	43.4968	−	31.6023i	1.38733	−	1.00796i	0.391181	−	0.920314i	$-0.372067\pi$
$983$	43.4968	−	31.6023i	1.38733	−	1.00796i	0.996152	−	0.0876431i	$-0.0279335\pi$
$984$	38.5938	+	20.4419i	1.23033	+	0.651663i
$985$	8.11751	−	24.9831i	0.258645	−	0.796029i
$986$	16.4310			0.523268
$987$	−37.2053	−	27.0312i	−1.18426	−	0.860413i
$988$	−7.04063	+	5.11531i	−0.223992	+	0.162740i
$989$	−21.3506	−	65.7103i	−0.678908	−	2.08946i
$990$	−150.953	−	17.9151i	−4.79760	−	0.569380i
$991$	18.1022	−	13.1520i	0.575034	−	0.417787i	−0.261896	−	0.965096i	$-0.584348\pi$
$991$	18.1022	−	13.1520i	0.575034	−	0.417787i	0.836931	+	0.547309i	$0.184348\pi$
$992$	−17.0755			−0.542146
$993$	44.8261	+	32.5681i	1.42251	+	1.03352i
$994$	−2.01357	−	6.19712i	−0.0638664	−	0.196561i
$995$	−14.0221	−	10.1876i	−0.444530	−	0.322970i
$996$	13.0685			0.414090
$997$	−9.09660			−0.288092			−0.144046	−	0.989571i	$-0.546011\pi$
$997$	−9.09660			−0.288092			−0.144046	+	0.989571i	$0.546011\pi$
$998$	0.928760	+	0.674784i	0.0293994	+	0.0213599i
$999$	10.8313	−	7.86944i	0.342689	−	0.248978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	451.2.j.a.379.10	yes	160
11.9	even	5		451.2.h.a.174.31	✓	160
41.37	even	5		451.2.h.a.324.31	yes	160
451.119	even	5	inner	451.2.j.a.119.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
451.2.h.a.174.31	✓	160	11.9	even	5
451.2.h.a.324.31	yes	160	41.37	even	5
451.2.j.a.119.10	yes	160	451.119	even	5	inner
451.2.j.a.379.10	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 451 = 11 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	451.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.506048 + 1.55746i) q^{2} +(-2.55608 - 1.85710i) q^{3} +(-0.551548 - 0.400723i) q^{4} -4.00839 q^{5} +(4.18585 - 3.04120i) q^{6} +(-0.366381 + 1.12760i) q^{7} +(-1.74648 + 1.26889i) q^{8} +(2.15767 + 6.64064i) q^{9} +O(q^{10})\)	\(q+(-0.506048 + 1.55746i) q^{2} +(-2.55608 - 1.85710i) q^{3} +(-0.551548 - 0.400723i) q^{4} -4.00839 q^{5} +(4.18585 - 3.04120i) q^{6} +(-0.366381 + 1.12760i) q^{7} +(-1.74648 + 1.26889i) q^{8} +(2.15767 + 6.64064i) q^{9} +(2.02844 - 6.24289i) q^{10} +(-3.29351 - 0.390874i) q^{11} +(0.665618 + 2.04856i) q^{12} +(1.05979 - 3.26171i) q^{13} +(-1.57079 - 1.14124i) q^{14} +(10.2458 + 7.44399i) q^{15} +(-1.51379 - 4.65896i) q^{16} +(-2.86066 - 2.07839i) q^{17} -11.4344 q^{18} +3.72211 q^{19} +(2.21082 + 1.60626i) q^{20} +(3.03058 - 2.20184i) q^{21} +(2.27544 - 4.93170i) q^{22} +(6.71397 + 4.87798i) q^{23} +6.82062 q^{24} +11.0672 q^{25} +(4.54366 + 3.30116i) q^{26} +(3.88814 - 11.9665i) q^{27} +(0.653934 - 0.475111i) q^{28} +(2.29564 + 1.66788i) q^{29} +(-16.7785 + 12.1903i) q^{30} -4.60923 q^{31} +3.70462 q^{32} +(7.69259 + 7.11549i) q^{33} +(4.68463 - 3.40358i) q^{34} +(1.46860 - 4.51988i) q^{35} +(1.47100 - 4.52726i) q^{36} +(0.860841 + 0.625437i) q^{37} +(-1.88357 + 5.79702i) q^{38} +(-8.76624 + 6.36904i) q^{39} +(7.00059 - 5.08622i) q^{40} +(5.65841 + 2.99707i) q^{41} +(1.89565 + 5.83422i) q^{42} +(-6.73539 - 4.89355i) q^{43} +(1.65990 + 1.53537i) q^{44} +(-8.64880 - 26.6183i) q^{45} +(-10.9948 + 7.98821i) q^{46} +(-3.79369 - 11.6758i) q^{47} +(-4.78280 + 14.7199i) q^{48} +(4.52586 + 3.28823i) q^{49} +(-5.60053 + 17.2367i) q^{50} +(3.45229 + 10.6251i) q^{51} +(-1.89157 + 1.37430i) q^{52} +(-0.375183 + 0.272587i) q^{53} +(16.6697 + 12.1112i) q^{54} +(13.2017 + 1.56678i) q^{55} +(-0.790933 - 2.43424i) q^{56} +(-9.51402 - 6.91234i) q^{57} +(-3.75935 + 2.73133i) q^{58} -0.165535 q^{59} +(-2.66806 - 8.21144i) q^{60} +(1.98076 + 6.09614i) q^{61} +(2.33249 - 7.17867i) q^{62} -8.27854 q^{63} +(1.15286 - 3.54813i) q^{64} +(-4.24806 + 13.0742i) q^{65} +(-14.9749 + 8.38008i) q^{66} +(-1.33916 - 4.12152i) q^{67} +(0.744931 + 2.29266i) q^{68} +(-8.10253 - 24.9370i) q^{69} +(6.29633 + 4.57455i) q^{70} +(2.71507 + 1.97262i) q^{71} +(-12.1946 - 8.85990i) q^{72} +(-7.51212 + 5.45787i) q^{73} +(-1.40972 + 1.02422i) q^{74} +(-28.2887 - 20.5529i) q^{75} +(-2.05292 - 1.49154i) q^{76} +(1.64743 - 3.57057i) q^{77} +(-5.48337 - 16.8761i) q^{78} +(0.520090 + 1.60067i) q^{79} +(6.06785 + 18.6749i) q^{80} +(-15.2148 + 11.0542i) q^{81} +(-7.53122 + 7.29606i) q^{82} +(1.87484 - 5.77016i) q^{83} -2.55384 q^{84} +(11.4666 + 8.33099i) q^{85} +(11.0299 - 8.01370i) q^{86} +(-2.77042 - 8.52647i) q^{87} +(6.24804 - 3.49646i) q^{88} +(6.26931 - 4.55492i) q^{89} +45.8335 q^{90} +(3.28963 + 2.39005i) q^{91} +(-1.74835 - 5.38088i) q^{92} +(11.7816 + 8.55981i) q^{93} +20.1043 q^{94} -14.9197 q^{95} +(-9.46931 - 6.87986i) q^{96} +(-1.08173 + 0.785923i) q^{97} +(-7.41157 + 5.38482i) q^{98} +(-4.51067 - 22.7144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + q^{2} - 7 q^{3} - 39 q^{4} - 6 q^{5} + 6 q^{6} - q^{7} + 3 q^{8} - 45 q^{9}+O(q^{10}) \) 160 * q + q^2 - 7 * q^3 - 39 * q^4 - 6 * q^5 + 6 * q^6 - q^7 + 3 * q^8 - 45 * q^9	\( 160 q + q^{2} - 7 q^{3} - 39 q^{4} - 6 q^{5} + 6 q^{6} - q^{7} + 3 q^{8} - 45 q^{9} + 12 q^{10} + 5 q^{11} + 7 q^{12} + 11 q^{13} - 10 q^{14} - 6 q^{15} - 21 q^{16} - 20 q^{17} - 6 q^{18} - 48 q^{19} - 27 q^{20} + 11 q^{21} + 10 q^{22} + 5 q^{23} + 26 q^{24} + 126 q^{25} + 5 q^{26} + 11 q^{27} + 17 q^{28} + 11 q^{29} - 24 q^{30} + 2 q^{31} - 28 q^{32} + q^{33} - 29 q^{34} - 41 q^{35} - 67 q^{36} - 6 q^{37} - 69 q^{38} + 19 q^{39} + 33 q^{40} - 13 q^{41} + 46 q^{42} - 7 q^{43} + 20 q^{44} - 53 q^{45} + 29 q^{46} - q^{47} - 21 q^{48} - 7 q^{49} + 13 q^{50} - 9 q^{51} - 109 q^{52} - 3 q^{53} + 69 q^{54} - 75 q^{55} + 11 q^{56} + 38 q^{57} - 19 q^{58} + 10 q^{59} + 92 q^{60} + 7 q^{61} - 7 q^{62} - 112 q^{63} + 11 q^{64} - 41 q^{65} + 62 q^{66} - 43 q^{67} + 11 q^{68} - 10 q^{69} + 73 q^{70} - 31 q^{71} - 19 q^{72} - 30 q^{73} + 151 q^{74} - 78 q^{75} - 62 q^{76} + 18 q^{77} + 50 q^{78} - 22 q^{79} + 24 q^{80} - 58 q^{81} + 35 q^{82} + 22 q^{83} + 66 q^{84} + 6 q^{85} - 10 q^{86} + 46 q^{87} + 60 q^{88} - 13 q^{89} - 440 q^{90} + 54 q^{91} + 103 q^{92} + 25 q^{93} + 106 q^{94} - 28 q^{95} + 94 q^{96} + 29 q^{97} + 35 q^{98} + 40 q^{99}+O(q^{100}) \) 160 * q + q^2 - 7 * q^3 - 39 * q^4 - 6 * q^5 + 6 * q^6 - q^7 + 3 * q^8 - 45 * q^9 + 12 * q^10 + 5 * q^11 + 7 * q^12 + 11 * q^13 - 10 * q^14 - 6 * q^15 - 21 * q^16 - 20 * q^17 - 6 * q^18 - 48 * q^19 - 27 * q^20 + 11 * q^21 + 10 * q^22 + 5 * q^23 + 26 * q^24 + 126 * q^25 + 5 * q^26 + 11 * q^27 + 17 * q^28 + 11 * q^29 - 24 * q^30 + 2 * q^31 - 28 * q^32 + q^33 - 29 * q^34 - 41 * q^35 - 67 * q^36 - 6 * q^37 - 69 * q^38 + 19 * q^39 + 33 * q^40 - 13 * q^41 + 46 * q^42 - 7 * q^43 + 20 * q^44 - 53 * q^45 + 29 * q^46 - q^47 - 21 * q^48 - 7 * q^49 + 13 * q^50 - 9 * q^51 - 109 * q^52 - 3 * q^53 + 69 * q^54 - 75 * q^55 + 11 * q^56 + 38 * q^57 - 19 * q^58 + 10 * q^59 + 92 * q^60 + 7 * q^61 - 7 * q^62 - 112 * q^63 + 11 * q^64 - 41 * q^65 + 62 * q^66 - 43 * q^67 + 11 * q^68 - 10 * q^69 + 73 * q^70 - 31 * q^71 - 19 * q^72 - 30 * q^73 + 151 * q^74 - 78 * q^75 - 62 * q^76 + 18 * q^77 + 50 * q^78 - 22 * q^79 + 24 * q^80 - 58 * q^81 + 35 * q^82 + 22 * q^83 + 66 * q^84 + 6 * q^85 - 10 * q^86 + 46 * q^87 + 60 * q^88 - 13 * q^89 - 440 * q^90 + 54 * q^91 + 103 * q^92 + 25 * q^93 + 106 * q^94 - 28 * q^95 + 94 * q^96 + 29 * q^97 + 35 * q^98 + 40 * q^99

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