LMFDB - Embedded newform 380.2.k.d.343.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.4
Character	$\chi$	$=$	380.343
Dual form			380.2.k.d.267.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34528 - 0.436150i) q^{2} +(1.71881 - 1.71881i) q^{3} +(1.61955 + 1.17349i) q^{4} +(-0.923046 - 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(0.323011 + 0.323011i) q^{7} +(-1.66692 - 2.28503i) q^{8} -2.90860i q^{9} +O(q^{10})$	\(q+(-1.34528 - 0.436150i) q^{2} +(1.71881 - 1.71881i) q^{3} +(1.61955 + 1.17349i) q^{4} +(-0.923046 - 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(0.323011 + 0.323011i) q^{7} +(-1.66692 - 2.28503i) q^{8} -2.90860i q^{9} +(0.353464 + 3.14246i) q^{10} -0.665839i q^{11} +(4.80068 - 0.766690i) q^{12} +(-3.14627 - 3.14627i) q^{13} +(-0.293659 - 0.575422i) q^{14} +(-5.08716 - 1.91409i) q^{15} +(1.24586 + 3.80103i) q^{16} +(1.48371 - 1.48371i) q^{17} +(-1.26858 + 3.91287i) q^{18} -1.00000 q^{19} +(0.895077 - 4.38165i) q^{20} +1.11039 q^{21} +(-0.290406 + 0.895738i) q^{22} +(4.04683 - 4.04683i) q^{23} +(-6.79265 - 1.06241i) q^{24} +(-3.29597 + 3.75986i) q^{25} +(2.86037 + 5.60486i) q^{26} +(0.157107 + 0.157107i) q^{27} +(0.144082 + 0.902182i) q^{28} -1.94446i q^{29} +(6.00882 + 4.79375i) q^{30} +7.94906i q^{31} +(-0.0182060 - 5.65682i) q^{32} +(-1.14445 - 1.14445i) q^{33} +(-2.64312 + 1.34888i) q^{34} +(0.359710 - 0.956019i) q^{35} +(3.41320 - 4.71060i) q^{36} +(-2.86508 + 2.86508i) q^{37} +(1.34528 + 0.436150i) q^{38} -10.8157 q^{39} +(-3.11518 + 5.50415i) q^{40} +0.378665 q^{41} +(-1.49378 - 0.484296i) q^{42} +(6.48324 - 6.48324i) q^{43} +(0.781353 - 1.07836i) q^{44} +(-5.92382 + 2.68477i) q^{45} +(-7.20914 + 3.67909i) q^{46} +(0.849686 + 0.849686i) q^{47} +(8.67463 + 4.39185i) q^{48} -6.79133i q^{49} +(6.07386 - 3.62052i) q^{50} -5.10041i q^{51} +(-1.40343 - 8.78765i) q^{52} +(-7.26036 - 7.26036i) q^{53} +(-0.142830 - 0.279874i) q^{54} +(-1.35609 + 0.614600i) q^{55} +(0.199656 - 1.27653i) q^{56} +(-1.71881 + 1.71881i) q^{57} +(-0.848077 + 2.61584i) q^{58} +0.564667 q^{59} +(-5.99274 - 9.06967i) q^{60} -6.86731 q^{61} +(3.46699 - 10.6937i) q^{62} +(0.939510 - 0.939510i) q^{63} +(-2.44273 + 7.61794i) q^{64} +(-3.50374 + 9.31205i) q^{65} +(1.04045 + 2.03875i) q^{66} +(11.3195 + 11.3195i) q^{67} +(4.14404 - 0.661821i) q^{68} -13.9114i q^{69} +(-0.900878 + 1.12922i) q^{70} +0.795606i q^{71} +(-6.64623 + 4.84841i) q^{72} +(8.57222 + 8.57222i) q^{73} +(5.10393 - 2.60472i) q^{74} +(0.797343 + 12.1276i) q^{75} +(-1.61955 - 1.17349i) q^{76} +(0.215073 - 0.215073i) q^{77} +(14.5501 + 4.71726i) q^{78} +9.50896 q^{79} +(6.59142 - 6.04592i) q^{80} +9.26586 q^{81} +(-0.509409 - 0.165155i) q^{82} +(8.07466 - 8.07466i) q^{83} +(1.79833 + 1.30303i) q^{84} +(-4.39134 - 1.65228i) q^{85} +(-11.5494 + 5.89410i) q^{86} +(-3.34215 - 3.34215i) q^{87} +(-1.52146 + 1.10990i) q^{88} +16.8328i q^{89} +(9.14015 - 1.02808i) q^{90} -2.03257i q^{91} +(11.3029 - 1.80513i) q^{92} +(13.6629 + 13.6629i) q^{93} +(-0.772473 - 1.51366i) q^{94} +(0.923046 + 2.03666i) q^{95} +(-9.75428 - 9.69170i) q^{96} +(2.53220 - 2.53220i) q^{97} +(-2.96204 + 9.13622i) q^{98} -1.93665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	$ 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.34528	−	0.436150i	−0.951255	−	0.308405i
$2$	−1.34528	−	0.436150i	−0.951255	−	0.308405i
$3$	1.71881	−	1.71881i	0.992354	−	0.992354i	−0.00761727	−	0.999971i	$-0.502425\pi$
$3$	1.71881	−	1.71881i	0.992354	−	0.992354i	0.999971	+	0.00761727i	$0.00242468\pi$
$4$	1.61955	+	1.17349i	0.809773	+	0.586743i
$5$	−0.923046	−	2.03666i	−0.412799	−	0.910822i
$5$	−0.923046	−	2.03666i	−0.412799	−	0.910822i
$6$	−3.06193	+	1.56262i	−1.25003	+	0.637935i
$7$	0.323011	+	0.323011i	0.122087	+	0.122087i	0.765510	−	0.643424i	$-0.222487\pi$
$7$	0.323011	+	0.323011i	0.122087	+	0.122087i	−0.643424	+	0.765510i	$0.722487\pi$
$8$	−1.66692	−	2.28503i	−0.589346	−	0.807880i
$9$		−	2.90860i		−	0.969532i
$10$	0.353464	+	3.14246i	0.111775	+	0.993734i
$11$		−	0.665839i		−	0.200758i	−0.994949	−	0.100379i	$-0.967994\pi$
$11$		−	0.665839i		−	0.200758i	0.994949	−	0.100379i	$-0.0320055\pi$
$12$	4.80068	−	0.766690i	1.38584	−	0.221324i
$13$	−3.14627	−	3.14627i	−0.872620	−	0.872620i	0.120138	−	0.992757i	$-0.461666\pi$
$13$	−3.14627	−	3.14627i	−0.872620	−	0.872620i	−0.992757	+	0.120138i	$0.961666\pi$
$14$	−0.293659	−	0.575422i	−0.0784836	−	0.153788i
$15$	−5.08716	−	1.91409i	−1.31350	−	0.494215i
$16$	1.24586	+	3.80103i	0.311465	+	0.950258i
$17$	1.48371	−	1.48371i	0.359852	−	0.359852i	−0.503907	−	0.863758i	$-0.668104\pi$
$17$	1.48371	−	1.48371i	0.359852	−	0.359852i	0.863758	+	0.503907i	$0.168104\pi$
$18$	−1.26858	+	3.91287i	−0.299008	+	0.922272i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.895077	−	4.38165i	0.200145	−	0.979766i
$21$	1.11039			0.242307
$22$	−0.290406	+	0.895738i	−0.0619147	+	0.190972i
$23$	4.04683	−	4.04683i	0.843823	−	0.843823i	−0.145531	−	0.989354i	$-0.546489\pi$
$23$	4.04683	−	4.04683i	0.843823	−	0.843823i	0.989354	+	0.145531i	$0.0464890\pi$
$24$	−6.79265	−	1.06241i	−1.38654	−	0.216863i
$25$	−3.29597	+	3.75986i	−0.659194	+	0.751973i
$26$	2.86037	+	5.60486i	0.560964	+	1.09920i
$27$	0.157107	+	0.157107i	0.0302352	+	0.0302352i
$28$	0.144082	+	0.902182i	0.0272290	+	0.170496i
$29$		−	1.94446i		−	0.361077i	−0.983568	−	0.180539i	$-0.942216\pi$
$29$		−	1.94446i		−	0.361077i	0.983568	−	0.180539i	$-0.0577841\pi$
$30$	6.00882	+	4.79375i	1.09706	+	0.875215i
$31$			7.94906i			1.42769i	0.700302	+	0.713847i	$0.253049\pi$
$31$			7.94906i			1.42769i	−0.700302	+	0.713847i	$0.746951\pi$
$32$	−0.0182060	−	5.65682i	−0.00321840	−	0.999995i
$33$	−1.14445	−	1.14445i	−0.199223	−	0.199223i
$34$	−2.64312	+	1.34888i	−0.453291	+	0.231331i
$35$	0.359710	−	0.956019i	0.0608021	−	0.161597i
$36$	3.41320	−	4.71060i	0.568866	−	0.785101i
$37$	−2.86508	+	2.86508i	−0.471016	+	0.471016i	−0.902243	−	0.431228i	$-0.858081\pi$
$37$	−2.86508	+	2.86508i	−0.471016	+	0.471016i	0.431228	+	0.902243i	$0.358081\pi$
$38$	1.34528	+	0.436150i	0.218233	+	0.0707529i
$39$	−10.8157			−1.73189
$40$	−3.11518	+	5.50415i	−0.492554	+	0.870282i
$41$	0.378665			0.0591375			0.0295687	−	0.999563i	$-0.490587\pi$
$41$	0.378665			0.0591375			0.0295687	+	0.999563i	$0.490587\pi$
$42$	−1.49378	−	0.484296i	−0.230496	−	0.0747285i
$43$	6.48324	−	6.48324i	0.988685	−	0.988685i	−0.0112515	−	0.999937i	$-0.503582\pi$
$43$	6.48324	−	6.48324i	0.988685	−	0.988685i	0.999937	+	0.0112515i	$0.00358153\pi$
$44$	0.781353	−	1.07836i	0.117793	−	0.162568i
$45$	−5.92382	+	2.68477i	−0.883071	+	0.400222i
$46$	−7.20914	+	3.67909i	−1.06293	+	0.542452i
$47$	0.849686	+	0.849686i	0.123939	+	0.123939i	0.766356	−	0.642416i	$-0.222068\pi$
$47$	0.849686	+	0.849686i	0.123939	+	0.123939i	−0.642416	+	0.766356i	$0.722068\pi$
$48$	8.67463	+	4.39185i	1.25207	+	0.633909i
$49$		−	6.79133i		−	0.970190i
$50$	6.07386	−	3.62052i	0.858974	−	0.512019i
$51$		−	5.10041i		−	0.714200i
$52$	−1.40343	−	8.78765i	−0.194620	−	1.21863i
$53$	−7.26036	−	7.26036i	−0.997287	−	0.997287i	0.00270956	−	0.999996i	$-0.499138\pi$
$53$	−7.26036	−	7.26036i	−0.997287	−	0.997287i	−0.999996	+	0.00270956i	$0.999138\pi$
$54$	−0.142830	−	0.279874i	−0.0194367	−	0.0380861i
$55$	−1.35609	+	0.614600i	−0.182855	+	0.0828726i
$56$	0.199656	−	1.27653i	0.0266801	−	0.170583i
$57$	−1.71881	+	1.71881i	−0.227662	+	0.227662i
$58$	−0.848077	+	2.61584i	−0.111358	+	0.343477i
$59$	0.564667			0.0735134			0.0367567	−	0.999324i	$-0.488297\pi$
$59$	0.564667			0.0735134			0.0367567	+	0.999324i	$0.488297\pi$
$60$	−5.99274	−	9.06967i	−0.773660	−	1.17089i
$61$	−6.86731			−0.879269			−0.439634	−	0.898177i	$-0.644892\pi$
$61$	−6.86731			−0.879269			−0.439634	+	0.898177i	$0.644892\pi$
$62$	3.46699	−	10.6937i	0.440308	−	1.35810i
$63$	0.939510	−	0.939510i	0.118367	−	0.118367i
$64$	−2.44273	+	7.61794i	−0.305342	+	0.952243i
$65$	−3.50374	+	9.31205i	−0.434585	+	1.15502i
$66$	1.04045	+	2.03875i	0.128070	+	0.250953i
$67$	11.3195	+	11.3195i	1.38290	+	1.38290i	0.839428	+	0.543472i	$0.182890\pi$
$67$	11.3195	+	11.3195i	1.38290	+	1.38290i	0.543472	+	0.839428i	$0.317110\pi$
$68$	4.14404	−	0.661821i	0.502539	−	0.0802576i
$69$		−	13.9114i		−	1.67474i
$70$	−0.900878	+	1.12922i	−0.107676	+	0.134968i
$71$			0.795606i			0.0944210i	0.998885	+	0.0472105i	$0.0150332\pi$
$71$			0.795606i			0.0944210i	−0.998885	+	0.0472105i	$0.984967\pi$
$72$	−6.64623	+	4.84841i	−0.783266	+	0.571390i
$73$	8.57222	+	8.57222i	1.00330	+	1.00330i	0.999995	+	0.00330820i	$0.00105303\pi$
$73$	8.57222	+	8.57222i	1.00330	+	1.00330i	0.00330820	+	0.999995i	$0.498947\pi$
$74$	5.10393	−	2.60472i	0.593320	−	0.302793i
$75$	0.797343	+	12.1276i	0.0920693	+	1.40038i
$76$	−1.61955	−	1.17349i	−0.185775	−	0.134608i
$77$	0.215073	−	0.215073i	0.0245099	−	0.0245099i
$78$	14.5501	+	4.71726i	1.64747	+	0.534125i
$79$	9.50896			1.06984			0.534921	−	0.844902i	$-0.320342\pi$
$79$	9.50896			1.06984			0.534921	+	0.844902i	$0.320342\pi$
$80$	6.59142	−	6.04592i	0.736944	−	0.675954i
$81$	9.26586			1.02954
$82$	−0.509409	−	0.165155i	−0.0562548	−	0.0182383i
$83$	8.07466	−	8.07466i	0.886309	−	0.886309i	−0.107857	−	0.994166i	$-0.534399\pi$
$83$	8.07466	−	8.07466i	0.886309	−	0.886309i	0.994166	+	0.107857i	$0.0343989\pi$
$84$	1.79833	+	1.30303i	0.196213	+	0.142172i
$85$	−4.39134	−	1.65228i	−0.476307	−	0.179215i
$86$	−11.5494	+	5.89410i	−1.24541	+	0.635577i
$87$	−3.34215	−	3.34215i	−0.358316	−	0.358316i
$88$	−1.52146	+	1.10990i	−0.162188	+	0.118316i
$89$			16.8328i			1.78427i	0.451769	+	0.892135i	$0.350793\pi$
$89$			16.8328i			1.78427i	−0.451769	+	0.892135i	$0.649207\pi$
$90$	9.14015	−	1.02808i	0.963456	−	0.108370i
$91$		−	2.03257i		−	0.213071i
$92$	11.3029	−	1.80513i	1.17841	−	0.188198i
$93$	13.6629	+	13.6629i	1.41678	+	1.41678i
$94$	−0.772473	−	1.51366i	−0.0796745	−	0.156122i
$95$	0.923046	+	2.03666i	0.0947026	+	0.208957i
$96$	−9.75428	−	9.69170i	−0.995542	−	0.989155i
$97$	2.53220	−	2.53220i	0.257106	−	0.257106i	−0.566770	−	0.823876i	$-0.691807\pi$
$97$	2.53220	−	2.53220i	0.257106	−	0.257106i	0.823876	+	0.566770i	$0.191807\pi$
$98$	−2.96204	+	9.13622i	−0.299211	+	0.922898i
$99$	−1.93665			−0.194641
$100$	−9.75013	+	2.22150i	−0.975013	+	0.222150i
$101$	8.60157			0.855888			0.427944	−	0.903805i	$-0.359238\pi$
$101$	8.60157			0.855888			0.427944	+	0.903805i	$0.359238\pi$
$102$	−2.22455	+	6.86147i	−0.220263	+	0.679387i
$103$	−3.00558	+	3.00558i	−0.296148	+	0.296148i	−0.839503	−	0.543355i	$-0.817154\pi$
$103$	−3.00558	+	3.00558i	−0.296148	+	0.296148i	0.543355	+	0.839503i	$0.317154\pi$
$104$	−1.94474	+	12.4339i	−0.190697	+	1.21925i
$105$	−1.02494	−	2.26148i	−0.100024	−	0.220698i
$106$	6.60059	+	12.9338i	0.641106	+	1.25624i
$107$	−0.608998	−	0.608998i	−0.0588740	−	0.0588740i	0.677057	−	0.735931i	$-0.263255\pi$
$107$	−0.608998	−	0.608998i	−0.0588740	−	0.0588740i	−0.735931	+	0.677057i	$0.763255\pi$
$108$	0.0700790	+	0.438804i	0.00674335	+	0.0422240i
$109$		−	12.6039i		−	1.20723i	−0.797274	−	0.603617i	$-0.793726\pi$
$109$		−	12.6039i		−	1.20723i	0.797274	−	0.603617i	$-0.206274\pi$
$110$	2.09237	−	0.235350i	0.199500	−	0.0224398i
$111$			9.84903i			0.934828i
$112$	−0.825350	+	1.63020i	−0.0779882	+	0.154040i
$113$	8.21770	+	8.21770i	0.773056	+	0.773056i	0.978640	−	0.205583i	$-0.0659091\pi$
$113$	8.21770	+	8.21770i	0.773056	+	0.773056i	−0.205583	+	0.978640i	$0.565909\pi$
$114$	3.06193	−	1.56262i	0.286776	−	0.146352i
$115$	−11.9774	−	4.50661i	−1.11690	−	0.420243i
$116$	2.28180	−	3.14914i	0.211860	−	0.292391i
$117$	−9.15124	+	9.15124i	−0.846032	+	0.846032i
$118$	−0.759634	−	0.246280i	−0.0699300	−	0.0226719i
$119$	0.958508			0.0878663
$120$	4.10616	+	14.8150i	0.374840	+	1.35242i
$121$	10.5567			0.959696
$122$	9.23844	+	2.99518i	0.836409	+	0.271171i
$123$	0.650851	−	0.650851i	0.0586853	−	0.0586853i
$124$	−9.32812	+	12.8739i	−0.837690	+	1.15611i
$125$	10.6999	+	3.24224i	0.957028	+	0.289995i
$126$	−1.67367	+	0.854134i	−0.149102	+	0.0760923i
$127$	−1.00113	−	1.00113i	−0.0888362	−	0.0888362i	0.661292	−	0.750128i	$-0.270008\pi$
$127$	−1.00113	−	1.00113i	−0.0888362	−	0.0888362i	−0.750128	+	0.661292i	$0.770008\pi$
$128$	6.60872	−	9.18285i	0.584134	−	0.811657i
$129$		−	22.2869i		−	1.96225i
$130$	8.77495	−	10.9991i	0.769614	−	0.964689i
$131$		−	10.2560i		−	0.896075i	−0.894015	−	0.448037i	$-0.852123\pi$
$131$		−	10.2560i		−	0.896075i	0.894015	−	0.448037i	$-0.147877\pi$
$132$	−0.510492	−	3.19648i	−0.0444326	−	0.278218i
$133$	−0.323011	−	0.323011i	−0.0280086	−	0.0280086i
$134$	−10.2909	−	20.1649i	−0.888997	−	1.74198i
$135$	0.174956	−	0.464990i	0.0150578	−	0.0400200i
$136$	−5.86354	−	0.917090i	−0.502794	−	0.0786398i
$137$	−11.0516	+	11.0516i	−0.944202	+	0.944202i	−0.998523	−	0.0543216i	$-0.982700\pi$
$137$	−11.0516	+	11.0516i	−0.944202	+	0.944202i	0.0543216	+	0.998523i	$0.482700\pi$
$138$	−6.06748	+	18.7148i	−0.516498	+	1.59311i
$139$	9.20366			0.780644			0.390322	−	0.920678i	$-0.372364\pi$
$139$	9.20366			0.780644			0.390322	+	0.920678i	$0.372364\pi$
$140$	1.70444	−	1.12620i	0.144052	−	0.0951815i
$141$	2.92089			0.245984
$142$	0.347004	−	1.07031i	0.0291199	−	0.0898185i
$143$	−2.09491	+	2.09491i	−0.175185	+	0.175185i
$144$	11.0557	−	3.62370i	0.921305	−	0.301975i
$145$	−3.96021	+	1.79483i	−0.328877	+	0.149052i
$146$	−7.79325	−	15.2708i	−0.644974	−	1.26382i
$147$	−11.6730	−	11.6730i	−0.962771	−	0.962771i
$148$	−8.00225	+	1.27799i	−0.657781	+	0.105051i
$149$			22.1531i			1.81485i	0.420215	+	0.907425i	$0.361955\pi$
$149$			22.1531i			1.81485i	−0.420215	+	0.907425i	$0.638045\pi$
$150$	4.21681	−	16.6628i	0.344301	−	1.36051i
$151$			0.248045i			0.0201856i	0.999949	+	0.0100928i	$0.00321269\pi$
$151$			0.248045i			0.0201856i	−0.999949	+	0.0100928i	$0.996787\pi$
$152$	1.66692	+	2.28503i	0.135205	+	0.185340i
$153$	−4.31550	−	4.31550i	−0.348888	−	0.348888i
$154$	−0.383138	+	0.195529i	−0.0308741	+	0.0157562i
$155$	16.1895	−	7.33736i	1.30038	−	0.589351i
$156$	−17.5165	−	12.6921i	−1.40244	−	1.01618i
$157$	11.8130	−	11.8130i	0.942781	−	0.942781i	−0.0556683	−	0.998449i	$-0.517729\pi$
$157$	11.8130	−	11.8130i	0.942781	−	0.942781i	0.998449	+	0.0556683i	$0.0177289\pi$
$158$	−12.7922	−	4.14733i	−1.01769	−	0.329944i
$159$	−24.9583			−1.97932
$160$	−11.5042	+	5.25859i	−0.909489	+	0.415728i
$161$	2.61435			0.206039
$162$	−12.4652	−	4.04131i	−0.979355	−	0.317515i
$163$	−6.88031	+	6.88031i	−0.538908	+	0.538908i	−0.923208	−	0.384301i	$-0.874443\pi$
$163$	−6.88031	+	6.88031i	−0.538908	+	0.538908i	0.384301	+	0.923208i	$0.374443\pi$
$164$	0.613265	+	0.444358i	0.0478879	+	0.0346985i
$165$	−1.27447	+	3.38723i	−0.0992176	+	0.263696i
$166$	−14.3844	+	7.34090i	−1.11645	+	0.569764i
$167$	−8.95374	−	8.95374i	−0.692861	−	0.692861i	0.269999	−	0.962860i	$-0.412976\pi$
$167$	−8.95374	−	8.95374i	−0.692861	−	0.692861i	−0.962860	+	0.269999i	$0.912976\pi$
$168$	−1.85093	−	2.53727i	−0.142803	−	0.195755i
$169$			6.79809i			0.522930i
$170$	5.18693	+	4.13805i	0.397819	+	0.317374i
$171$			2.90860i			0.222426i
$172$	18.1079	−	2.89191i	1.38072	−	0.220506i
$173$	−7.68917	−	7.68917i	−0.584597	−	0.584597i	0.351566	−	0.936163i	$-0.385649\pi$
$173$	−7.68917	−	7.68917i	−0.584597	−	0.584597i	−0.936163	+	0.351566i	$0.885649\pi$
$174$	3.03844	+	5.95380i	0.230344	+	0.451357i
$175$	−2.27912	+	0.149843i	−0.172285	+	0.0113271i
$176$	2.53087	−	0.829541i	0.190772	−	0.0625290i
$177$	0.970554	−	0.970554i	0.0729513	−	0.0729513i
$178$	7.34161	−	22.6447i	0.550277	−	1.69730i
$179$	−11.9377			−0.892269			−0.446134	−	0.894966i	$-0.647200\pi$
$179$	−11.9377			−0.892269			−0.446134	+	0.894966i	$0.647200\pi$
$180$	−12.7444	−	2.60342i	−0.949915	−	0.194047i
$181$	−16.5433			−1.22965			−0.614827	−	0.788662i	$-0.710774\pi$
$181$	−16.5433			−1.22965			−0.614827	+	0.788662i	$0.710774\pi$
$182$	−0.886504	+	2.73437i	−0.0657120	+	0.202685i
$183$	−11.8036	+	11.8036i	−0.872546	+	0.872546i
$184$	−15.9929	−	2.50138i	−1.17901	−	0.184404i
$185$	8.47979	+	3.19059i	0.623446	+	0.234577i
$186$	−12.4213	−	24.3395i	−0.910776	−	1.78466i
$187$	−0.987909	−	0.987909i	−0.0722431	−	0.0722431i
$188$	0.379011	+	2.37320i	0.0276422	+	0.173083i
$189$			0.101495i			0.00738265i
$190$	−0.353464	−	3.14246i	−0.0256430	−	0.227978i
$191$		−	5.07533i		−	0.367238i	−0.982997	−	0.183619i	$-0.941219\pi$
$191$		−	5.07533i		−	0.367238i	0.982997	−	0.183619i	$-0.0587812\pi$
$192$	8.89519	+	17.2924i	0.641955	+	1.24797i
$193$	−11.3183	−	11.3183i	−0.814711	−	0.814711i	0.170625	−	0.985336i	$-0.445421\pi$
$193$	−11.3183	−	11.3183i	−0.814711	−	0.814711i	−0.985336	+	0.170625i	$0.945421\pi$
$194$	−4.51094	+	2.30210i	−0.323867	+	0.165281i
$195$	9.98337	+	22.0279i	0.714924	+	1.57745i
$196$	7.96953	−	10.9989i	0.569252	−	0.785633i
$197$	4.90003	−	4.90003i	0.349113	−	0.349113i	−0.510666	−	0.859779i	$-0.670601\pi$
$197$	4.90003	−	4.90003i	0.349113	−	0.349113i	0.859779	+	0.510666i	$0.170601\pi$
$198$	2.60534	+	0.844672i	0.185153	+	0.0600283i
$199$	18.6186			1.31984			0.659919	−	0.751336i	$-0.270590\pi$
$199$	18.6186			1.31984			0.659919	+	0.751336i	$0.270590\pi$
$200$	14.0855	+	1.26399i	0.995998	+	0.0893776i
$201$	38.9121			2.74465
$202$	−11.5715	−	3.75158i	−0.814168	−	0.263960i
$203$	0.628083	−	0.628083i	0.0440828	−	0.0440828i
$204$	5.98526	−	8.26035i	0.419052	−	0.578340i
$205$	−0.349525	−	0.771211i	−0.0244119	−	0.0538637i
$206$	5.35422	−	2.73245i	0.373046	−	0.190379i
$207$	−11.7706	−	11.7706i	−0.818113	−	0.818113i
$208$	8.03927	−	15.8789i	0.557423	−	1.10100i
$209$			0.665839i			0.0460570i
$210$	0.392483	+	3.48935i	0.0270839	+	0.240788i
$211$			17.5026i			1.20493i	0.798147	+	0.602463i	$0.205814\pi$
$211$			17.5026i			1.20493i	−0.798147	+	0.602463i	$0.794186\pi$
$212$	−3.23855	−	20.2784i	−0.222425	−	1.39273i
$213$	1.36749	+	1.36749i	0.0936991	+	0.0936991i
$214$	0.553657	+	1.08489i	0.0378472	+	0.0741613i
$215$	−19.1885	−	7.21983i	−1.30864	−	0.492388i
$216$	0.0971089	−	0.620879i	0.00660742	−	0.0422455i
$217$	−2.56764	+	2.56764i	−0.174303	+	0.174303i
$218$	−5.49719	+	16.9557i	−0.372317	+	1.14839i
$219$	29.4680			1.99126
$220$	−2.91747	−	0.595977i	−0.196696	−	0.0401808i
$221$	−9.33630			−0.628027
$222$	4.29565	−	13.2497i	0.288305	−	0.889260i
$223$	−8.70816	+	8.70816i	−0.583142	+	0.583142i	−0.935765	−	0.352624i	$-0.885290\pi$
$223$	−8.70816	+	8.70816i	−0.583142	+	0.583142i	0.352624	+	0.935765i	$0.385290\pi$
$224$	1.82134	−	1.83310i	0.121693	−	0.122479i
$225$	10.9359	+	9.58664i	0.729062	+	0.639110i
$226$	−7.47094	−	14.6392i	−0.496960	−	0.973788i
$227$	−5.72919	−	5.72919i	−0.380260	−	0.380260i	0.490936	−	0.871196i	$-0.336655\pi$
$227$	−5.72919	−	5.72919i	−0.380260	−	0.380260i	−0.871196	+	0.490936i	$0.836655\pi$
$228$	−4.80068	+	0.766690i	−0.317933	+	0.0507753i
$229$			10.0081i			0.661351i	0.943745	+	0.330675i	$0.107277\pi$
$229$			10.0081i			0.661351i	−0.943745	+	0.330675i	$0.892723\pi$
$230$	14.1474	+	11.2866i	0.932854	+	0.744217i
$231$		−	0.739340i		−	0.0486450i
$232$	−4.44315	+	3.24127i	−0.291707	+	0.212800i
$233$	−11.9694	−	11.9694i	−0.784142	−	0.784142i	0.196385	−	0.980527i	$-0.437080\pi$
$233$	−11.9694	−	11.9694i	−0.784142	−	0.784142i	−0.980527	+	0.196385i	$0.937080\pi$
$234$	16.3023	−	8.31965i	1.06571	−	0.543872i
$235$	0.946222	−	2.51482i	0.0617247	−	0.164049i
$236$	0.914504	+	0.662629i	0.0595292	+	0.0431335i
$237$	16.3441	−	16.3441i	1.06166	−	1.06166i
$238$	−1.28946	−	0.418054i	−0.0835833	−	0.0270984i
$239$	3.14892			0.203687			0.101843	−	0.994800i	$-0.467526\pi$
$239$	3.14892			0.203687			0.101843	+	0.994800i	$0.467526\pi$
$240$	0.937617	−	21.7212i	0.0605229	−	1.40209i
$241$	11.0868			0.714164			0.357082	−	0.934073i	$-0.383772\pi$
$241$	11.0868			0.714164			0.357082	+	0.934073i	$0.383772\pi$
$242$	−14.2016	−	4.60429i	−0.912916	−	0.295975i
$243$	15.4549	−	15.4549i	0.991433	−	0.991433i
$244$	−11.1219	−	8.05869i	−0.712008	−	0.515905i
$245$	−13.8316	+	6.26871i	−0.883670	+	0.400493i
$246$	−1.15945	+	0.591707i	−0.0739235	+	0.0377259i
$247$	3.14627	+	3.14627i	0.200193	+	0.200193i
$248$	18.1639	−	13.2505i	1.15341	−	0.841406i
$249$		−	27.7576i		−	1.75906i
$250$	−12.9802	−	9.02848i	−0.820942	−	0.571011i
$251$			23.7489i			1.49901i	0.661996	+	0.749507i	$0.269709\pi$
$251$			23.7489i			1.49901i	−0.661996	+	0.749507i	$0.730291\pi$
$252$	2.62408	−	0.419077i	0.165302	−	0.0263994i
$253$	−2.69454	−	2.69454i	−0.169404	−	0.169404i
$254$	0.910158	+	1.78345i	0.0571084	+	0.111903i
$255$	−10.3878	+	4.70792i	−0.650510	+	0.294821i
$256$	−12.8957	+	9.47109i	−0.805980	+	0.591943i
$257$	8.59420	−	8.59420i	0.536091	−	0.536091i	−0.386287	−	0.922379i	$-0.626243\pi$
$257$	8.59420	−	8.59420i	0.536091	−	0.536091i	0.922379	+	0.386287i	$0.126243\pi$
$258$	−9.72043	+	29.9821i	−0.605168	+	1.86660i
$259$	−1.85091			−0.115010
$260$	−16.6020	+	10.9697i	−1.02961	+	0.680312i
$261$	−5.65565			−0.350076
$262$	−4.47318	+	13.7972i	−0.276354	+	0.852396i
$263$	−19.7478	+	19.7478i	−1.21770	+	1.21770i	−0.249268	+	0.968435i	$0.580190\pi$
$263$	−19.7478	+	19.7478i	−1.21770	+	1.21770i	−0.968435	+	0.249268i	$0.919810\pi$
$264$	−0.707392	+	4.52281i	−0.0435370	+	0.278359i
$265$	−8.08523	+	21.4885i	−0.496672	+	1.32003i
$266$	0.293659	+	0.575422i	0.0180054	+	0.0352814i
$267$	28.9323	+	28.9323i	1.77063	+	1.77063i
$268$	5.04918	+	31.6158i	0.308428	+	1.93124i
$269$		−	1.08328i		−	0.0660485i	−0.999455	−	0.0330243i	$-0.989486\pi$
$269$		−	1.08328i		−	0.0660485i	0.999455	−	0.0330243i	$-0.0105139\pi$
$270$	−0.438170	+	0.549234i	−0.0266662	+	0.0334253i
$271$			27.0809i			1.64505i	0.568732	+	0.822523i	$0.307434\pi$
$271$			27.0809i			1.64505i	−0.568732	+	0.822523i	$0.692566\pi$
$272$	7.48810	+	3.79113i	0.454033	+	0.229871i
$273$	−3.49359	−	3.49359i	−0.211442	−	0.211442i
$274$	19.6876	−	10.0473i	1.18937	−	0.606981i
$275$	2.50346	+	2.19458i	0.150964	+	0.132338i
$276$	16.3249	−	22.5302i	0.982643	−	1.35616i
$277$	−4.92017	+	4.92017i	−0.295624	+	0.295624i	−0.839297	−	0.543673i	$-0.817033\pi$
$277$	−4.92017	+	4.92017i	−0.295624	+	0.295624i	0.543673	+	0.839297i	$0.317033\pi$
$278$	−12.3815	−	4.01418i	−0.742592	−	0.240754i
$279$	23.1206			1.38419
$280$	−2.78414	+	0.771662i	−0.166384	+	0.0461156i
$281$	−23.8097			−1.42037			−0.710185	−	0.704015i	$-0.751389\pi$
$281$	−23.8097			−1.42037			−0.710185	+	0.704015i	$0.751389\pi$
$282$	−3.92941	−	1.27395i	−0.233993	−	0.0758625i
$283$	−0.250284	+	0.250284i	−0.0148778	+	0.0148778i	−0.714507	−	0.699629i	$-0.753349\pi$
$283$	−0.250284	+	0.250284i	−0.0148778	+	0.0148778i	0.699629	+	0.714507i	$0.253349\pi$
$284$	−0.933633	+	1.28852i	−0.0554009	+	0.0764596i
$285$	5.08716	+	1.91409i	0.301338	+	0.113381i
$286$	3.73193	−	1.90454i	0.220674	−	0.112618i
$287$	0.122313	+	0.122313i	0.00721991	+	0.00721991i
$288$	−16.4534	+	0.0529540i	−0.969527	+	0.00312034i
$289$			12.5972i			0.741014i
$290$	6.11039	−	0.687297i	0.358815	−	0.0403595i
$291$		−	8.70474i		−	0.510281i
$292$	3.82372	+	23.9425i	0.223766	+	1.40113i
$293$	−2.57593	−	2.57593i	−0.150487	−	0.150487i	0.627848	−	0.778336i	$-0.283936\pi$
$293$	−2.57593	−	2.57593i	−0.150487	−	0.150487i	−0.778336	+	0.627848i	$0.783936\pi$
$294$	10.6122	+	20.7946i	0.618918	+	1.21276i
$295$	−0.521214	−	1.15003i	−0.0303462	−	0.0669576i
$296$	11.3227	+	1.77093i	0.658116	+	0.102933i
$297$	0.104608	−	0.104608i	0.00606996	−	0.00606996i
$298$	9.66206	−	29.8020i	0.559708	−	1.72639i
$299$	−25.4649			−1.47267
$300$	−12.9403	+	20.5769i	−0.747106	+	1.18801i
$301$	4.18832			0.241411
$302$	0.108185	−	0.333689i	0.00622533	−	0.0192016i
$303$	14.7844	−	14.7844i	0.849344	−	0.849344i
$304$	−1.24586	−	3.80103i	−0.0714549	−	0.218004i
$305$	6.33884	+	13.9864i	0.362961	+	0.800858i
$306$	3.92334	+	7.68776i	0.224283	+	0.439480i
$307$	−13.0381	−	13.0381i	−0.744123	−	0.744123i	0.229246	−	0.973369i	$-0.426374\pi$
$307$	−13.0381	−	13.0381i	−0.744123	−	0.744123i	−0.973369	+	0.229246i	$0.926374\pi$
$308$	0.600707	−	0.0959356i	0.0342285	−	0.00546644i
$309$			10.3320i			0.587768i
$310$	−24.9796	+	2.80971i	−1.41875	+	0.159581i
$311$		−	6.68856i		−	0.379274i	−0.981854	−	0.189637i	$-0.939269\pi$
$311$		−	6.68856i		−	0.379274i	0.981854	−	0.189637i	$-0.0607311\pi$
$312$	18.0289	+	24.7142i	1.02069	+	1.39916i
$313$	−13.5578	−	13.5578i	−0.766331	−	0.766331i	0.211128	−	0.977458i	$-0.432286\pi$
$313$	−13.5578	−	13.5578i	−0.766331	−	0.766331i	−0.977458	+	0.211128i	$0.932286\pi$
$314$	−21.0440	+	10.7395i	−1.18758	+	0.606067i
$315$	−2.78067	−	1.04625i	−0.156673	−	0.0589496i
$316$	15.4002	+	11.1586i	0.866329	+	0.627722i
$317$	−12.9940	+	12.9940i	−0.729818	+	0.729818i	−0.970583	−	0.240765i	$-0.922602\pi$
$317$	−12.9940	+	12.9940i	−0.729818	+	0.729818i	0.240765	+	0.970583i	$0.422602\pi$
$318$	33.5759	+	10.8856i	1.88284	+	0.610432i
$319$	−1.29470			−0.0724891
$320$	17.7699	−	2.05670i	0.993369	−	0.114973i
$321$	−2.09350			−0.116848
$322$	−3.51702	−	1.14025i	−0.195996	−	0.0635435i
$323$	−1.48371	+	1.48371i	−0.0825556	+	0.0825556i
$324$	15.0065	+	10.8734i	0.833694	+	0.604076i
$325$	22.1996	−	1.45954i	1.23141	−	0.0809605i
$326$	12.2568	−	6.25508i	0.678840	−	0.346437i
$327$	−21.6637	−	21.6637i	−1.19800	−	1.19800i
$328$	−0.631205	−	0.865260i	−0.0348525	−	0.0477760i
$329$			0.548917i			0.0302628i
$330$	3.19186	−	4.00091i	0.175706	−	0.220243i
$331$		−	14.8683i		−	0.817236i	−0.912705	−	0.408618i	$-0.866011\pi$
$331$		−	14.8683i		−	0.817236i	0.912705	−	0.408618i	$-0.133989\pi$
$332$	22.5528	−	3.60178i	1.23775	−	0.197673i
$333$	8.33335	+	8.33335i	0.456665	+	0.456665i
$334$	8.14009	+	15.9504i	0.445406	+	0.872769i
$335$	12.6056	−	33.5025i	0.688716	−	1.83043i
$336$	1.38339	+	4.22062i	0.0754700	+	0.230254i
$337$	−17.4555	+	17.4555i	−0.950859	+	0.950859i	−0.998848	−	0.0479886i	$-0.984719\pi$
$337$	−17.4555	+	17.4555i	−0.950859	+	0.950859i	0.0479886	+	0.998848i	$0.484719\pi$
$338$	2.96499	−	9.14532i	0.161274	−	0.497440i
$339$	28.2493			1.53429
$340$	−5.17305	−	7.82911i	−0.280548	−	0.424593i
$341$	5.29279			0.286621
$342$	1.26858	−	3.91287i	0.0685972	−	0.211584i
$343$	4.45476	−	4.45476i	0.240534	−	0.240534i
$344$	−25.6215	−	4.00734i	−1.38142	−	0.216061i
$345$	−28.3329	+	12.8409i	−1.52539	+	0.691331i
$346$	6.99044	+	13.6977i	0.375808	+	0.736393i
$347$	16.4481	+	16.4481i	0.882982	+	0.882982i	0.993837	−	0.110855i	$-0.0353588\pi$
$347$	16.4481	+	16.4481i	0.882982	+	0.882982i	−0.110855	+	0.993837i	$0.535359\pi$
$348$	−1.49080	−	9.33474i	−0.0799152	−	0.500395i
$349$		−	29.9956i		−	1.60563i	−0.596229	−	0.802814i	$-0.703335\pi$
$349$		−	29.9956i		−	1.60563i	0.596229	−	0.802814i	$-0.296665\pi$
$350$	3.13140	+	0.792456i	0.167380	+	0.0423586i
$351$		−	0.988602i		−	0.0527677i
$352$	−3.76653	+	0.0121223i	−0.200757	+	0.000646119i
$353$	−23.2559	−	23.2559i	−1.23778	−	1.23778i	−0.960905	−	0.276879i	$-0.910700\pi$
$353$	−23.2559	−	23.2559i	−1.23778	−	1.23778i	−0.276879	−	0.960905i	$-0.589300\pi$
$354$	−1.72897	+	0.882357i	−0.0918938	+	0.0468968i
$355$	1.62038	−	0.734381i	0.0860008	−	0.0389769i
$356$	−19.7530	+	27.2614i	−1.04691	+	1.44485i
$357$	1.64749	−	1.64749i	0.0871945	−	0.0871945i
$358$	16.0596	+	5.20665i	0.848775	+	0.275180i
$359$	18.1714			0.959050			0.479525	−	0.877528i	$-0.340809\pi$
$359$	18.1714			0.959050			0.479525	+	0.877528i	$0.340809\pi$
$360$	16.0093	+	9.06081i	0.843766	+	0.477547i
$361$	1.00000			0.0526316
$362$	22.2553	+	7.21536i	1.16971	+	0.379231i
$363$	18.1449	−	18.1449i	0.952358	−	0.952358i
$364$	2.38519	−	3.29183i	0.125018	−	0.172539i
$365$	9.54615	−	25.3713i	0.499668	−	1.32799i
$366$	21.0272	−	10.7310i	1.09911	−	0.560916i
$367$	−19.9274	−	19.9274i	−1.04020	−	1.04020i	−0.999157	−	0.0410456i	$-0.986931\pi$
$367$	−19.9274	−	19.9274i	−1.04020	−	1.04020i	−0.0410456	−	0.999157i	$-0.513069\pi$
$368$	20.4239	+	10.3404i	1.06467	+	0.539028i
$369$		−	1.10138i		−	0.0573357i
$370$	−10.0161	−	7.99069i	−0.520712	−	0.415416i
$371$		−	4.69036i		−	0.243511i
$372$	6.09447	+	38.1609i	0.315984	+	1.97855i
$373$	25.6623	+	25.6623i	1.32874	+	1.32874i	0.906466	+	0.422279i	$0.138770\pi$
$373$	25.6623	+	25.6623i	1.32874	+	1.32874i	0.422279	+	0.906466i	$0.361230\pi$
$374$	0.898136	+	1.75989i	0.0464415	+	0.0910017i
$375$	23.9639	−	12.8183i	1.23749	−	0.661933i
$376$	0.525198	−	3.35792i	0.0270850	−	0.173172i
$377$	−6.11781	+	6.11781i	−0.315083	+	0.315083i
$378$	0.0442669	−	0.136538i	0.00227684	−	0.00702278i
$379$	12.3650			0.635150			0.317575	−	0.948233i	$-0.397131\pi$
$379$	12.3650			0.635150			0.317575	+	0.948233i	$0.397131\pi$
$380$	−0.895077	+	4.38165i	−0.0459165	+	0.224774i
$381$	−3.44151			−0.176314
$382$	−2.21361	+	6.82773i	−0.113258	+	0.349337i
$383$	−16.8608	+	16.8608i	−0.861545	+	0.861545i	−0.991518	−	0.129973i	$-0.958511\pi$
$383$	−16.8608	+	16.8608i	−0.861545	+	0.861545i	0.129973	+	0.991518i	$0.458511\pi$
$384$	−4.42443	−	27.1427i	−0.225783	−	1.38512i
$385$	−0.636554	−	0.239509i	−0.0324418	−	0.0122065i
$386$	10.2898	+	20.1628i	0.523737	+	1.02626i
$387$	−18.8571	−	18.8571i	−0.958562	−	0.958562i
$388$	7.07253	−	1.12951i	0.359053	−	0.0573424i
$389$			37.0728i			1.87966i	0.341637	+	0.939832i	$0.389019\pi$
$389$			37.0728i			1.87966i	−0.341637	+	0.939832i	$0.610981\pi$
$390$	−3.82296	−	33.9879i	−0.193583	−	1.72104i
$391$		−	12.0086i		−	0.607302i
$392$	−15.5184	+	11.3206i	−0.783797	+	0.571778i
$393$	−17.6282	−	17.6282i	−0.889223	−	0.889223i
$394$	−8.72905	+	4.45475i	−0.439763	+	0.224427i
$395$	−8.77721	−	19.3665i	−0.441629	−	0.974435i
$396$	−3.13650	−	2.27264i	−0.157615	−	0.114204i
$397$	−1.43078	+	1.43078i	−0.0718089	+	0.0718089i	−0.742099	−	0.670290i	$-0.766170\pi$
$397$	−1.43078	+	1.43078i	−0.0718089	+	0.0718089i	0.670290	+	0.742099i	$0.266170\pi$
$398$	−25.0472	−	8.12051i	−1.25550	−	0.407045i
$399$	−1.11039			−0.0555890
$400$	−18.3977	−	7.84383i	−0.919884	−	0.392191i
$401$	13.4835			0.673334			0.336667	−	0.941624i	$-0.390700\pi$
$401$	13.4835			0.673334			0.336667	+	0.941624i	$0.390700\pi$
$402$	−52.3476	−	16.9715i	−2.61086	−	0.846463i
$403$	25.0099	−	25.0099i	1.24583	−	1.24583i
$404$	13.9306	+	10.0938i	0.693075	+	0.502187i
$405$	−8.55282	−	18.8714i	−0.424993	−	0.937728i
$406$	−1.11888	+	0.571008i	−0.0555293	+	0.0283386i
$407$	1.90768	+	1.90768i	0.0945601	+	0.0945601i
$408$	−11.6546	+	8.50199i	−0.576988	+	0.420911i
$409$		−	33.7262i		−	1.66765i	−0.552027	−	0.833826i	$-0.686146\pi$
$409$		−	33.7262i		−	1.66765i	0.552027	−	0.833826i	$-0.313854\pi$
$410$	0.133844	+	1.18994i	0.00661011	+	0.0587669i
$411$			37.9911i			1.87396i
$412$	−8.39467	+	1.34067i	−0.413576	+	0.0660499i
$413$	0.182394	+	0.182394i	0.00897502	+	0.00897502i
$414$	10.7010	+	20.9685i	0.525924	+	1.03054i
$415$	−23.8986	−	8.99206i	−1.17314	−	0.441403i
$416$	−17.7406	+	17.8552i	−0.869807	+	0.875424i
$417$	15.8193	−	15.8193i	0.774675	−	0.774675i
$418$	0.290406	−	0.895738i	0.0142042	−	0.0438120i
$419$	3.79083			0.185194			0.0925970	−	0.995704i	$-0.470483\pi$
$419$	3.79083			0.185194			0.0925970	+	0.995704i	$0.470483\pi$
$420$	0.993884	−	4.86533i	0.0484966	−	0.237404i
$421$	13.7408			0.669686			0.334843	−	0.942274i	$-0.391317\pi$
$421$	13.7408			0.669686			0.334843	+	0.942274i	$0.391317\pi$
$422$	7.63374	−	23.5458i	0.371605	−	1.14619i
$423$	2.47139	−	2.47139i	0.120163	−	0.120163i
$424$	−4.48768	+	28.6926i	−0.217941	+	1.39344i
$425$	0.688282	+	10.4688i	0.0333866	+	0.507811i
$426$	−1.24323	−	2.43609i	−0.0602345	−	0.118029i
$427$	−2.21822	−	2.21822i	−0.107347	−	0.107347i
$428$	−0.271649	−	1.70095i	−0.0131307	−	0.0822185i
$429$			7.20150i			0.347691i
$430$	22.6649	+	18.0817i	1.09300	+	0.871979i
$431$		−	22.9069i		−	1.10339i	−0.834046	−	0.551694i	$-0.813981\pi$
$431$		−	22.9069i		−	1.10339i	0.834046	−	0.551694i	$-0.186019\pi$
$432$	−0.401435	+	0.792901i	−0.0193140	+	0.0381485i
$433$	−8.24824	−	8.24824i	−0.396385	−	0.396385i	0.480571	−	0.876956i	$-0.340430\pi$
$433$	−8.24824	−	8.24824i	−0.396385	−	0.396385i	−0.876956	+	0.480571i	$0.840430\pi$
$434$	4.57406	−	2.33431i	0.219562	−	0.112051i
$435$	−3.72187	+	9.89179i	−0.178450	+	0.474275i
$436$	14.7905	−	20.4126i	0.708336	−	0.977585i
$437$	−4.04683	+	4.04683i	−0.193586	+	0.193586i
$438$	−39.6426	−	12.8525i	−1.89420	−	0.614115i
$439$	−12.9690			−0.618975			−0.309487	−	0.950904i	$-0.600157\pi$
$439$	−12.9690			−0.618975			−0.309487	+	0.950904i	$0.600157\pi$
$440$	3.66487	+	2.07421i	0.174716	+	0.0988841i
$441$	−19.7532			−0.940630
$442$	12.5599	+	4.07203i	0.597414	+	0.193687i
$443$	−23.2730	+	23.2730i	−1.10574	+	1.10574i	−0.112031	+	0.993705i	$0.535736\pi$
$443$	−23.2730	+	23.2730i	−1.10574	+	1.10574i	−0.993705	+	0.112031i	$0.964264\pi$
$444$	−11.5577	+	15.9510i	−0.548504	+	0.756999i
$445$	34.2826	−	15.5374i	1.62515	−	0.736545i
$446$	15.5130	−	7.91683i	0.734560	−	0.374873i
$447$	38.0768	+	38.0768i	1.80097	+	1.80097i
$448$	−3.24971	+	1.67165i	−0.153535	+	0.0789781i
$449$		−	7.25236i		−	0.342260i	−0.985248	−	0.171130i	$-0.945258\pi$
$449$		−	7.25236i		−	0.342260i	0.985248	−	0.171130i	$-0.0547418\pi$
$450$	−10.5306	−	17.6664i	−0.496419	−	0.832802i
$451$		−	0.252130i		−	0.0118723i
$452$	3.66558	+	22.9523i	0.172415	+	1.07959i
$453$	0.426341	+	0.426341i	0.0200312	+	0.0200312i
$454$	5.20857	+	10.2061i	0.244450	+	0.478998i
$455$	−4.13965	+	1.87615i	−0.194070	+	0.0879554i
$456$	6.79265	+	1.06241i	0.318095	+	0.0497518i
$457$	−22.3426	+	22.3426i	−1.04515	+	1.04515i	−0.0462135	+	0.998932i	$0.514715\pi$
$457$	−22.3426	+	22.3426i	−1.04515	+	1.04515i	−0.998932	+	0.0462135i	$0.985285\pi$
$458$	4.36501	−	13.4636i	0.203964	−	0.629113i
$459$	0.466201			0.0217604
$460$	−14.1096	−	21.3540i	−0.657862	−	0.995636i
$461$	0.00705621			0.000328641			0.000164320	−	1.00000i	$-0.499948\pi$
$461$	0.00705621			0.000328641			0.000164320		1.00000i	$0.499948\pi$
$462$	−0.322463	+	0.994617i	−0.0150023	+	0.0462738i
$463$	−6.48079	+	6.48079i	−0.301188	+	0.301188i	−0.841478	−	0.540291i	$-0.818314\pi$
$463$	−6.48079	+	6.48079i	−0.301188	+	0.301188i	0.540291	+	0.841478i	$0.318314\pi$
$464$	7.39095	−	2.42252i	0.343116	−	0.112463i
$465$	15.2152	−	40.4382i	0.705588	−	1.87528i
$466$	10.8817	+	21.3226i	0.504086	+	0.987752i
$467$	−24.1145	−	24.1145i	−1.11589	−	1.11589i	−0.992339	−	0.123547i	$-0.960573\pi$
$467$	−24.1145	−	24.1145i	−1.11589	−	1.11589i	−0.123547	−	0.992339i	$-0.539427\pi$
$468$	−25.5597	+	4.08200i	−1.18150	+	0.188690i
$469$			7.31267i			0.337668i
$470$	−2.36977	+	2.97044i	−0.109309	+	0.137016i
$471$		−	40.6086i		−	1.87114i
$472$	−0.941257	−	1.29028i	−0.0433249	−	0.0593900i
$473$	−4.31679	−	4.31679i	−0.198486	−	0.198486i
$474$	−29.1158	+	14.8588i	−1.33733	+	0.682489i
$475$	3.29597	−	3.75986i	0.151230	−	0.172514i
$476$	1.55235	+	1.12480i	0.0711518	+	0.0515550i
$477$	−21.1174	+	21.1174i	−0.966901	+	0.966901i
$478$	−4.23617	−	1.37340i	−0.193758	−	0.0628179i
$479$	−18.5538			−0.847743			−0.423872	−	0.905722i	$-0.639329\pi$
$479$	−18.5538			−0.847743			−0.423872	+	0.905722i	$0.639329\pi$
$480$	−10.7350	+	28.8120i	−0.489985	+	1.31508i
$481$	18.0286			0.822035
$482$	−14.9148	−	4.83551i	−0.679352	−	0.220252i
$483$	4.49356	−	4.49356i	0.204464	−	0.204464i
$484$	17.0970	+	12.3881i	0.777136	+	0.563095i
$485$	−7.49458	−	2.81990i	−0.340311	−	0.128045i
$486$	−27.5318	+	14.0505i	−1.24887	+	0.637343i
$487$	26.4040	+	26.4040i	1.19648	+	1.19648i	0.975213	+	0.221268i	$0.0710197\pi$
$487$	26.4040	+	26.4040i	1.19648	+	1.19648i	0.221268	+	0.975213i	$0.428980\pi$
$488$	11.4473	+	15.6920i	0.518194	+	0.710344i
$489$			23.6519i			1.06957i
$490$	21.3415	−	2.40049i	0.964110	−	0.108443i
$491$			29.3852i			1.32614i	0.748559	+	0.663068i	$0.230746\pi$
$491$			29.3852i			1.32614i	−0.748559	+	0.663068i	$0.769254\pi$
$492$	1.81785	−	0.290318i	0.0819550	−	0.0130886i
$493$	−2.88501	−	2.88501i	−0.129934	−	0.129934i
$494$	−2.86037	−	5.60486i	−0.128694	−	0.252175i
$495$	1.78762	+	3.94431i	0.0803477	+	0.177283i
$496$	−30.2146	+	9.90341i	−1.35668	+	0.444676i
$497$	−0.256990	+	0.256990i	−0.0115276	+	0.0115276i
$498$	−12.1065	+	37.3417i	−0.542504	+	1.67332i
$499$	21.6258			0.968103			0.484051	−	0.875040i	$-0.339165\pi$
$499$	21.6258			0.968103			0.484051	+	0.875040i	$0.339165\pi$
$500$	13.5243	+	17.8072i	0.604823	+	0.796360i
$501$	−30.7795			−1.37513
$502$	10.3581	−	31.9488i	0.462303	−	1.42595i
$503$	−5.45937	+	5.45937i	−0.243421	+	0.243421i	−0.818264	−	0.574843i	$-0.805063\pi$
$503$	−5.45937	+	5.45937i	−0.243421	+	0.243421i	0.574843	+	0.818264i	$0.305063\pi$
$504$	−3.71290	−	0.580718i	−0.165386	−	0.0258672i
$505$	−7.93965	−	17.5185i	−0.353310	−	0.779562i
$506$	2.44968	+	4.80012i	0.108901	+	0.213392i
$507$	11.6846	+	11.6846i	0.518932	+	0.518932i
$508$	−0.446565	−	2.79620i	−0.0198131	−	0.124061i
$509$			10.0786i			0.446727i	0.974735	+	0.223364i	$0.0717038\pi$
$509$			10.0786i			0.446727i	−0.974735	+	0.223364i	$0.928296\pi$
$510$	16.0278	−	1.80281i	0.709725	−	0.0798299i
$511$			5.53785i			0.244980i
$512$	21.4791	−	7.11681i	0.949250	−	0.314521i
$513$	−0.157107	−	0.157107i	−0.00693643	−	0.00693643i
$514$	−15.3099	+	7.81322i	−0.675293	+	0.344627i
$515$	8.89563	+	3.34705i	0.391988	+	0.147489i
$516$	26.1534	−	36.0946i	1.15134	−	1.58898i
$517$	0.565754	−	0.565754i	0.0248818	−	0.0248818i
$518$	2.48998	+	0.807273i	0.109404	+	0.0354695i
$519$	−26.4324			−1.16025
$520$	27.1188	−	7.51633i	1.18924	−	0.329613i
$521$	2.30389			0.100935			0.0504677	−	0.998726i	$-0.483929\pi$
$521$	2.30389			0.100935			0.0504677	+	0.998726i	$0.483929\pi$
$522$	7.60842	+	2.46671i	0.333012	+	0.107965i
$523$	−18.0133	+	18.0133i	−0.787666	+	0.787666i	−0.981111	−	0.193445i	$-0.938034\pi$
$523$	−18.0133	+	18.0133i	−0.787666	+	0.787666i	0.193445	+	0.981111i	$0.438034\pi$
$524$	12.0353	−	16.6101i	0.525766	−	0.725617i
$525$	−3.65981	+	4.17491i	−0.159727	+	0.182208i
$526$	35.1793	−	17.9533i	1.53389	−	0.782801i
$527$	11.7941	+	11.7941i	0.513758	+	0.513758i
$528$	2.92426	−	5.77590i	0.127262	−	0.251364i
$529$		−	9.75370i		−	0.424074i
$530$	20.2491	−	25.3817i	0.879565	−	1.10251i
$531$		−	1.64239i		−	0.0712736i
$532$	−0.144082	−	0.902182i	−0.00624676	−	0.0391145i
$533$	−1.19138	−	1.19138i	−0.0516045	−	0.0516045i
$534$	−26.3031	−	51.5408i	−1.13825	−	2.23039i
$535$	−0.678188	+	1.80245i	−0.0293206	+	0.0779269i
$536$	6.99668	−	44.7342i	0.302211	−	1.93222i
$537$	−20.5187	+	20.5187i	−0.885446	+	0.885446i
$538$	−0.472471	+	1.45731i	−0.0203697	+	0.0628290i
$539$	−4.52193			−0.194773
$540$	0.829009	−	0.547764i	0.0356749	−	0.0235720i
$541$	8.88031			0.381795			0.190897	−	0.981610i	$-0.438860\pi$
$541$	8.88031			0.381795			0.190897	+	0.981610i	$0.438860\pi$
$542$	11.8113	−	36.4313i	0.507340	−	1.56486i
$543$	−28.4347	+	28.4347i	−1.22025	+	1.22025i
$544$	−8.42008	−	8.36606i	−0.361008	−	0.358692i
$545$	−25.6698	+	11.6340i	−1.09958	+	0.498345i
$546$	3.17612	+	6.22358i	0.135925	+	0.266344i
$547$	22.2527	+	22.2527i	0.951457	+	0.951457i	0.998875	−	0.0474184i	$-0.0150994\pi$
$547$	22.2527	+	22.2527i	0.951457	+	0.951457i	−0.0474184	+	0.998875i	$0.515099\pi$
$548$	−30.8675	+	4.92967i	−1.31859	+	0.210585i
$549$			19.9742i			0.852479i
$550$	−2.41068	−	4.04421i	−0.102792	−	0.172446i
$551$			1.94446i			0.0828368i
$552$	−31.7881	+	23.1893i	−1.35299	+	0.987003i
$553$	3.07150	+	3.07150i	0.130614	+	0.130614i
$554$	8.76493	−	4.47306i	0.372386	−	0.190042i
$555$	20.0591	−	9.09111i	0.851462	−	0.385896i
$556$	14.9058	+	10.8004i	0.632145	+	0.458038i
$557$	21.1979	−	21.1979i	0.898183	−	0.898183i	−0.0970919	−	0.995275i	$-0.530954\pi$
$557$	21.1979	−	21.1979i	0.898183	−	0.898183i	0.995275	+	0.0970919i	$0.0309541\pi$
$558$	−31.1037	−	10.0841i	−1.31672	−	0.426892i
$559$	−40.7961			−1.72549
$560$	4.08201	+	0.176204i	0.172496	+	0.00744599i
$561$	−3.39605			−0.143381
$562$	32.0307	+	10.3846i	1.35113	+	0.438049i
$563$	7.32244	−	7.32244i	0.308604	−	0.308604i	−0.535764	−	0.844368i	$-0.679976\pi$
$563$	7.32244	−	7.32244i	0.308604	−	0.308604i	0.844368	+	0.535764i	$0.179976\pi$
$564$	4.73052	+	3.42763i	0.199191	+	0.144329i
$565$	9.15135	−	24.3220i	0.385000	−	1.02323i
$566$	0.445862	−	0.227540i	0.0187410	−	0.00956421i
$567$	2.99298	+	2.99298i	0.125693	+	0.125693i
$568$	1.81798	−	1.32621i	0.0762809	−	0.0556467i
$569$		−	4.10754i		−	0.172197i	−0.996287	−	0.0860985i	$-0.972560\pi$
$569$		−	4.10754i		−	0.172197i	0.996287	−	0.0860985i	$-0.0274400\pi$
$570$	−6.00882	−	4.79375i	−0.251682	−	0.200788i
$571$		−	16.0964i		−	0.673612i	−0.941574	−	0.336806i	$-0.890653\pi$
$571$		−	16.0964i		−	0.673612i	0.941574	−	0.336806i	$-0.109347\pi$
$572$	−5.85115	+	0.934455i	−0.244649	+	0.0390715i
$573$	−8.72351	−	8.72351i	−0.364430	−	0.364430i
$574$	−0.111198	−	0.217892i	−0.00464132	−	0.00909463i
$575$	1.87730	+	28.5538i	0.0782888	+	1.19077i
$576$	22.1575	+	7.10492i	0.923230	+	0.296038i
$577$	15.6097	−	15.6097i	0.649839	−	0.649839i	−0.303115	−	0.952954i	$-0.598027\pi$
$577$	15.6097	−	15.6097i	0.649839	−	0.649839i	0.952954	+	0.303115i	$0.0980267\pi$
$578$	5.49428	−	16.9468i	0.228532	−	0.704893i
$579$	−38.9080			−1.61696
$580$	−8.51994	−	1.74044i	−0.353771	−	0.0722679i
$581$	5.21642			0.216413
$582$	−3.79657	+	11.7103i	−0.157373	+	0.485407i
$583$	−4.83423	+	4.83423i	−0.200213	+	0.200213i
$584$	5.29856	−	33.8770i	0.219256	−	1.40184i
$585$	27.0850	+	10.1909i	1.11983	+	0.421344i
$586$	2.34185	+	4.58883i	0.0967408	+	0.189563i
$587$	−2.99516	−	2.99516i	−0.123623	−	0.123623i	0.642588	−	0.766212i	$-0.277861\pi$
$587$	−2.99516	−	2.99516i	−0.123623	−	0.123623i	−0.766212	+	0.642588i	$0.777861\pi$
$588$	−5.20684	−	32.6030i	−0.214727	−	1.34453i
$589$		−	7.94906i		−	0.327536i
$590$	0.199590	+	1.77444i	0.00821698	+	0.0730527i
$591$		−	16.8444i		−	0.692886i
$592$	−14.4597	−	7.32076i	−0.594291	−	0.300882i
$593$	−12.0584	−	12.0584i	−0.495180	−	0.495180i	0.414754	−	0.909934i	$-0.363868\pi$
$593$	−12.0584	−	12.0584i	−0.495180	−	0.495180i	−0.909934	+	0.414754i	$0.863868\pi$
$594$	−0.186351	+	0.0951018i	−0.00764608	+	0.00390208i
$595$	−0.884748	−	1.95216i	−0.0362711	−	0.0800306i
$596$	−25.9963	+	35.8779i	−1.06485	+	1.46962i
$597$	32.0018	−	32.0018i	1.30975	−	1.30975i
$598$	34.2574	+	11.1065i	1.40089	+	0.454179i
$599$	12.8351			0.524429			0.262215	−	0.965010i	$-0.415547\pi$
$599$	12.8351			0.524429			0.262215	+	0.965010i	$0.415547\pi$
$600$	26.3829	−	22.0378i	1.07708	−	0.899688i
$601$	−5.86790			−0.239357			−0.119678	−	0.992813i	$-0.538186\pi$
$601$	−5.86790			−0.239357			−0.119678	+	0.992813i	$0.538186\pi$
$602$	−5.63446	−	1.82674i	−0.229643	−	0.0744523i
$603$	32.9239	−	32.9239i	1.34076	−	1.34076i
$604$	−0.291077	+	0.401720i	−0.0118438	+	0.0163457i
$605$	−9.74429	−	21.5003i	−0.396162	−	0.874113i
$606$	−26.3374	+	13.4409i	−1.06988	+	0.546001i
$607$	32.9098	+	32.9098i	1.33577	+	1.33577i	0.900117	+	0.435649i	$0.143481\pi$
$607$	32.9098	+	32.9098i	1.33577	+	1.33577i	0.435649	+	0.900117i	$0.356519\pi$
$608$	0.0182060	+	5.65682i	0.000738352	+	0.229415i
$609$		−	2.15911i		−	0.0874914i
$610$	−2.42735	−	21.5803i	−0.0982805	−	0.873759i
$611$		−	5.34669i		−	0.216304i
$612$	−1.92497	−	12.0533i	−0.0778123	−	0.487227i
$613$	2.57292	+	2.57292i	0.103919	+	0.103919i	0.757155	−	0.653236i	$-0.226589\pi$
$613$	2.57292	+	2.57292i	0.103919	+	0.103919i	−0.653236	+	0.757155i	$0.726589\pi$
$614$	11.8533	+	23.2264i	0.478360	+	0.937341i
$615$	−1.92633	−	0.724797i	−0.0776771	−	0.0292266i
$616$	−0.849961	−	0.132939i	−0.0342459	−	0.00535625i
$617$	5.95239	−	5.95239i	0.239634	−	0.239634i	−0.577064	−	0.816699i	$-0.695802\pi$
$617$	5.95239	−	5.95239i	0.239634	−	0.239634i	0.816699	+	0.577064i	$0.195802\pi$
$618$	4.50631	−	13.8994i	0.181270	−	0.559117i
$619$	−12.1365			−0.487805			−0.243903	−	0.969800i	$-0.578428\pi$
$619$	−12.1365			−0.487805			−0.243903	+	0.969800i	$0.578428\pi$
$620$	34.8300	+	7.11503i	1.39881	+	0.285746i
$621$	1.27157			0.0510263
$622$	−2.91722	+	8.99798i	−0.116970	+	0.360786i
$623$	−5.43718	+	5.43718i	−0.217836	+	0.217836i
$624$	−13.4748	−	41.1107i	−0.539424	−	1.64575i
$625$	−3.27316	−	24.7848i	−0.130926	−	0.991392i
$626$	12.3257	+	24.1522i	0.492636	+	0.965316i
$627$	1.14445	+	1.14445i	0.0457049	+	0.0457049i
$628$	32.9941	−	5.26931i	1.31661	−	0.210268i
$629$			8.50187i			0.338992i
$630$	3.28446	+	2.62029i	0.130856	+	0.104395i
$631$		−	7.53890i		−	0.300119i	−0.988677	−	0.150059i	$-0.952053\pi$
$631$		−	7.53890i		−	0.300119i	0.988677	−	0.150059i	$-0.0479465\pi$
$632$	−15.8507	−	21.7283i	−0.630507	−	0.864304i
$633$	30.0835	+	30.0835i	1.19571	+	1.19571i
$634$	23.1480	−	11.8132i	0.919323	−	0.469164i
$635$	−1.11488	+	2.96306i	−0.0442425	+	0.117585i
$636$	−40.4211	−	29.2882i	−1.60280	−	1.16135i
$637$	−21.3674	+	21.3674i	−0.846606	+	0.846606i
$638$	1.74173	+	0.564682i	0.0689556	+	0.0223560i
$639$	2.31410			0.0915442
$640$	−24.8025	−	4.98352i	−0.980405	−	0.196991i
$641$	−8.28659			−0.327301			−0.163650	−	0.986518i	$-0.552327\pi$
$641$	−8.28659			−0.327301			−0.163650	+	0.986518i	$0.552327\pi$
$642$	2.81634	+	0.913080i	0.111152	+	0.0360364i
$643$	24.9239	−	24.9239i	0.982903	−	0.982903i	−0.0169536	−	0.999856i	$-0.505397\pi$
$643$	24.9239	−	24.9239i	0.982903	−	0.982903i	0.999856	+	0.0169536i	$0.00539676\pi$
$644$	4.23405	+	3.06790i	0.166845	+	0.120892i
$645$	−45.3908	+	20.5718i	−1.78726	+	0.810015i
$646$	2.64312	−	1.34888i	0.103992	−	0.0530709i
$647$	16.2883	+	16.2883i	0.640358	+	0.640358i	0.950643	−	0.310286i	$-0.100425\pi$
$647$	16.2883	+	16.2883i	0.640358	+	0.640358i	−0.310286	+	0.950643i	$0.600425\pi$
$648$	−15.4455	−	21.1728i	−0.606756	−	0.831745i
$649$		−	0.375977i		−	0.0147584i
$650$	−30.5012	−	7.71887i	−1.19636	−	0.302759i
$651$			8.82655i			0.345940i
$652$	−19.2169	+	3.06903i	−0.752593	+	0.120192i
$653$	35.8880	+	35.8880i	1.40441	+	1.40441i	0.785337	+	0.619069i	$0.212490\pi$
$653$	35.8880	+	35.8880i	1.40441	+	1.40441i	0.619069	+	0.785337i	$0.287510\pi$
$654$	19.6950	+	38.5923i	0.770137	+	1.50908i
$655$	−20.8881	+	9.46680i	−0.816165	+	0.369899i
$656$	0.471763	+	1.43932i	0.0184192	+	0.0561958i
$657$	24.9331	−	24.9331i	0.972734	−	0.972734i
$658$	0.239410	−	0.738446i	0.00933318	−	0.0287876i
$659$	−18.4068			−0.717027			−0.358513	−	0.933525i	$-0.616716\pi$
$659$	−18.4068			−0.717027			−0.358513	+	0.933525i	$0.616716\pi$
$660$	−6.03894	+	3.99020i	−0.235065	+	0.155318i
$661$	−20.1755			−0.784734			−0.392367	−	0.919809i	$-0.628344\pi$
$661$	−20.1755			−0.784734			−0.392367	+	0.919809i	$0.628344\pi$
$662$	−6.48482	+	20.0020i	−0.252040	+	0.777400i
$663$	−16.0473	+	16.0473i	−0.623225	+	0.623225i
$664$	−31.9107	−	4.99101i	−1.23838	−	0.193689i
$665$	−0.359710	+	0.956019i	−0.0139490	+	0.0370728i
$666$	−7.57608	−	14.8453i	−0.293567	−	0.575242i
$667$	−7.86891	−	7.86891i	−0.304685	−	0.304685i
$668$	−3.99390	−	25.0081i	−0.154529	−	0.967592i
$669$			29.9353i			1.15737i
$670$	−31.5701	+	39.5722i	−1.21966	+	1.52881i
$671$			4.57252i			0.176520i
$672$	−0.0202158	−	6.28128i	−0.000779840	−	0.242305i
$673$	3.18320	+	3.18320i	0.122703	+	0.122703i	0.765792	−	0.643089i	$-0.222347\pi$
$673$	3.18320	+	3.18320i	0.122703	+	0.122703i	−0.643089	+	0.765792i	$0.722347\pi$
$674$	31.0956	−	15.8692i	1.19776	−	0.611260i
$675$	−1.10852	+	0.0728808i	−0.0426669	+	0.00280518i
$676$	−7.97747	+	11.0098i	−0.306826	+	0.423455i
$677$	0.872720	−	0.872720i	0.0335413	−	0.0335413i	−0.690137	−	0.723679i	$-0.742450\pi$
$677$	0.872720	−	0.872720i	0.0335413	−	0.0335413i	0.723679	+	0.690137i	$0.242450\pi$
$678$	−38.0032	−	12.3209i	−1.45950	−	0.473183i
$679$	1.63586			0.0627786
$680$	3.54452	+	12.7886i	0.135926	+	0.490419i
$681$	−19.6947			−0.754704
$682$	−7.12028	−	2.30845i	−0.272650	−	0.0883952i
$683$	−19.5540	+	19.5540i	−0.748215	+	0.748215i	−0.974144	−	0.225929i	$-0.927458\pi$
$683$	−19.5540	+	19.5540i	−0.748215	+	0.748215i	0.225929	+	0.974144i	$0.427458\pi$
$684$	−3.41320	+	4.71060i	−0.130507	+	0.180114i
$685$	32.7095	+	12.3072i	1.24977	+	0.470235i
$686$	−7.93583	+	4.04994i	−0.302991	+	0.154628i
$687$	17.2019	+	17.2019i	0.656294	+	0.656294i
$688$	32.7202	+	16.5658i	1.24745	+	0.631565i
$689$			45.6862i			1.74050i
$690$	43.7162	−	4.91720i	1.66425	−	0.187195i
$691$		−	49.4492i		−	1.88113i	−0.339607	−	0.940567i	$-0.610294\pi$
$691$		−	49.4492i		−	1.88113i	0.339607	−	0.940567i	$-0.389706\pi$
$692$	−3.42983	−	21.4761i	−0.130382	−	0.816399i
$693$	−0.625562	−	0.625562i	−0.0237631	−	0.0237631i
$694$	−14.9535	−	29.3012i	−0.567625	−	1.11226i
$695$	−8.49541	−	18.7447i	−0.322249	−	0.711028i
$696$	−2.06581	+	13.2080i	−0.0783043	+	0.500649i
$697$	0.561827	−	0.561827i	0.0212807	−	0.0212807i
$698$	−13.0826	+	40.3524i	−0.495183	+	1.52736i
$699$	−41.1462			−1.55629
$700$	−3.86697	−	2.43183i	−0.146158	−	0.0919147i
$701$	−39.1086			−1.47711			−0.738555	−	0.674193i	$-0.764492\pi$
$701$	−39.1086			−1.47711			−0.738555	+	0.674193i	$0.764492\pi$
$702$	−0.431179	+	1.32995i	−0.0162738	+	0.0501955i
$703$	2.86508	−	2.86508i	0.108058	−	0.108058i
$704$	5.07232	+	1.62647i	0.191170	+	0.0612997i
$705$	−2.69612	−	5.94887i	−0.101542	−	0.224047i
$706$	21.1425	+	41.4286i	0.795710	+	1.55919i
$707$	2.77841	+	2.77841i	0.104493	+	0.104493i
$708$	2.71079	−	0.432925i	0.101878	−	0.0162703i
$709$		−	20.4872i		−	0.769413i	−0.923039	−	0.384707i	$-0.874303\pi$
$709$		−	20.4872i		−	0.769413i	0.923039	−	0.384707i	$-0.125697\pi$
$710$	−2.50016	+	0.281218i	−0.0938293	+	0.0105539i
$711$		−	27.6577i		−	1.03725i
$712$	38.4634	−	28.0589i	1.44148	−	1.05155i
$713$	32.1685	+	32.1685i	1.20472	+	1.20472i
$714$	−2.93489	+	1.49778i	−0.109835	+	0.0560530i
$715$	6.20032	+	2.33292i	0.231879	+	0.0872463i
$716$	−19.3337	−	14.0088i	−0.722535	−	0.523533i
$717$	5.41238	−	5.41238i	0.202129	−	0.202129i
$718$	−24.4456	−	7.92546i	−0.912301	−	0.295776i
$719$	13.8492			0.516489			0.258245	−	0.966080i	$-0.416856\pi$
$719$	13.8492			0.516489			0.258245	+	0.966080i	$0.416856\pi$
$720$	−17.5851	−	19.1718i	−0.655359	−	0.714490i
$721$	−1.94167			−0.0723116
$722$	−1.34528	−	0.436150i	−0.0500661	−	0.0162318i
$723$	19.0561	−	19.0561i	0.708703	−	0.708703i
$724$	−26.7926	−	19.4133i	−0.995741	−	0.721491i
$725$	7.31091	+	6.40888i	0.271520	+	0.238020i
$726$	−32.3238	+	16.4960i	−1.19965	+	0.612224i
$727$	−10.3882	−	10.3882i	−0.385275	−	0.385275i	0.487723	−	0.872998i	$-0.337828\pi$
$727$	−10.3882	−	10.3882i	−0.385275	−	0.385275i	−0.872998	+	0.487723i	$0.837828\pi$
$728$	−4.64448	+	3.38813i	−0.172136	+	0.125572i
$729$		−	25.3304i		−	0.938164i
$730$	−23.9079	+	29.9679i	−0.884871	+	1.10916i
$731$		−	19.2385i		−	0.711560i
$732$	−32.9678	+	5.26510i	−1.21852	+	0.194604i
$733$	9.18018	+	9.18018i	0.339078	+	0.339078i	0.856020	−	0.516942i	$-0.172930\pi$
$733$	9.18018	+	9.18018i	0.339078	+	0.339078i	−0.516942	+	0.856020i	$0.672930\pi$
$734$	18.1166	+	35.4993i	0.668695	+	1.31030i
$735$	−12.9992	+	34.5486i	−0.479482	+	1.27434i
$736$	−22.9659	−	22.8185i	−0.846534	−	0.841103i
$737$	7.53697	−	7.53697i	0.277628	−	0.277628i
$738$	−0.480368	+	1.48167i	−0.0176826	+	0.0545409i
$739$	7.09627			0.261041			0.130520	−	0.991446i	$-0.458335\pi$
$739$	7.09627			0.261041			0.130520	+	0.991446i	$0.458335\pi$
$740$	9.98929	+	15.1182i	0.367214	+	0.555757i
$741$	10.8157			0.397324
$742$	−2.04570	+	6.30983i	−0.0751000	+	0.231641i
$743$	4.52085	−	4.52085i	0.165854	−	0.165854i	−0.619300	−	0.785154i	$-0.712584\pi$
$743$	4.52085	−	4.52085i	0.165854	−	0.165854i	0.785154	+	0.619300i	$0.212584\pi$
$744$	8.44515	−	53.9952i	0.309614	−	1.97956i
$745$	45.1183	−	20.4483i	1.65301	−	0.749168i
$746$	−23.3303	−	45.7156i	−0.854184	−	1.67377i
$747$	−23.4859	−	23.4859i	−0.859305	−	0.859305i
$748$	−0.440666	−	2.75926i	−0.0161124	−	0.100889i
$749$		−	0.393426i		−	0.0143755i
$750$	−37.8287	+	6.79230i	−1.38131	+	0.248020i
$751$			32.3004i			1.17866i	0.807894	+	0.589328i	$0.200608\pi$
$751$			32.3004i			1.17866i	−0.807894	+	0.589328i	$0.799392\pi$
$752$	−2.17109	+	4.28827i	−0.0791717	+	0.156377i
$753$	40.8197	+	40.8197i	1.48755	+	1.48755i
$754$	10.8984	−	5.56187i	0.396898	−	0.202551i
$755$	0.505183	−	0.228957i	0.0183855	−	0.00833259i
$756$	−0.119103	+	0.164375i	−0.00433172	+	0.00597827i
$757$	22.8717	−	22.8717i	0.831285	−	0.831285i	−0.156407	−	0.987693i	$-0.549991\pi$
$757$	22.8717	−	22.8717i	0.831285	−	0.831285i	0.987693	+	0.156407i	$0.0499913\pi$
$758$	−16.6344	−	5.39302i	−0.604190	−	0.195883i
$759$	−9.26278			−0.336218
$760$	3.11518	−	5.50415i	0.113000	−	0.199656i
$761$	−21.6152			−0.783550			−0.391775	−	0.920061i	$-0.628139\pi$
$761$	−21.6152			−0.783550			−0.391775	+	0.920061i	$0.628139\pi$
$762$	4.62979	+	1.50102i	0.167720	+	0.0543760i
$763$	4.07120	−	4.07120i	0.147387	−	0.147387i
$764$	5.95583	−	8.21973i	0.215474	−	0.297379i
$765$	−4.80580	+	12.7726i	−0.173754	+	0.461795i
$766$	30.0363	−	15.3286i	1.08525	−	0.553845i
$767$	−1.77660	−	1.77660i	−0.0641492	−	0.0641492i
$768$	−5.88619	+	38.4442i	−0.212399	+	1.38723i
$769$			23.8575i			0.860322i	0.902752	+	0.430161i	$0.141543\pi$
$769$			23.8575i			0.860322i	−0.902752	+	0.430161i	$0.858457\pi$
$770$	0.751881	+	0.599839i	0.0270959	+	0.0216167i
$771$		−	29.5435i		−	1.06398i
$772$	−5.04864	−	31.6124i	−0.181705	−	1.13776i
$773$	−8.40856	−	8.40856i	−0.302435	−	0.302435i	0.539531	−	0.841966i	$-0.318602\pi$
$773$	−8.40856	−	8.40856i	−0.302435	−	0.302435i	−0.841966	+	0.539531i	$0.818602\pi$
$774$	17.1435	+	33.5926i	0.616212	+	1.20746i
$775$	−29.8874	−	26.1999i	−1.07359	−	0.941128i
$776$	−10.0072	−	1.56517i	−0.359236	−	0.0561865i
$777$	−3.18135	+	3.18135i	−0.114130	+	0.114130i
$778$	16.1693	−	49.8732i	0.579697	−	1.78804i
$779$	−0.378665			−0.0135671
$780$	−9.68087	+	47.3905i	−0.346631	+	1.69685i
$781$	0.529745			0.0189558
$782$	−5.23756	+	16.1549i	−0.187295	+	0.577699i
$783$	0.305488	−	0.305488i	0.0109172	−	0.0109172i
$784$	25.8140	−	8.46103i	0.921930	−	0.302180i
$785$	−34.9631	−	13.1551i	−1.24788	−	0.469527i
$786$	16.0263	+	31.4033i	0.571637	+	1.12012i
$787$	−27.0454	−	27.0454i	−0.964063	−	0.964063i	0.0353136	−	0.999376i	$-0.488757\pi$
$787$	−27.0454	−	27.0454i	−0.964063	−	0.964063i	−0.999376	+	0.0353136i	$0.988757\pi$
$788$	13.6859	−	2.18570i	0.487541	−	0.0778625i
$789$			67.8854i			2.41678i
$790$	3.36108	+	29.8815i	0.119582	+	1.06314i
$791$			5.30882i			0.188760i
$792$	3.22826	+	4.42532i	0.114711	+	0.157247i
$793$	21.6064	+	21.6064i	0.767267	+	0.767267i
$794$	2.54883	−	1.30076i	0.0904548	−	0.0461624i
$795$	23.0377	+	50.8316i	0.817062	+	1.80281i
$796$	30.1537	+	21.8487i	1.06877	+	0.774407i
$797$	33.6565	−	33.6565i	1.19217	−	1.19217i	0.215718	−	0.976456i	$-0.430791\pi$
$797$	33.6565	−	33.6565i	1.19217	−	1.19217i	0.976456	−	0.215718i	$-0.0692091\pi$
$798$	1.49378	+	0.484296i	0.0528793	+	0.0171439i
$799$	2.52137			0.0891997
$800$	21.3289	+	18.5763i	0.754090	+	0.656771i
$801$	48.9597			1.72991
$802$	−18.1391	−	5.88083i	−0.640512	−	0.207659i
$803$	5.70772	−	5.70772i	0.201421	−	0.201421i
$804$	63.0200	+	45.6629i	2.22254	+	1.61041i
$805$	−2.41316	−	5.32454i	−0.0850528	−	0.187665i
$806$	−44.5534	+	22.7372i	−1.56933	+	0.800885i
$807$	−1.86194	−	1.86194i	−0.0655435	−	0.0655435i
$808$	−14.3382	−	19.6549i	−0.504415	−	0.691455i
$809$		−	16.4325i		−	0.577737i	−0.957369	−	0.288868i	$-0.906721\pi$
$809$		−	16.4325i		−	0.577737i	0.957369	−	0.288868i	$-0.0932790\pi$
$810$	3.27515	+	29.1176i	0.115077	+	1.02309i
$811$			20.9394i			0.735283i	0.929968	+	0.367641i	$0.119835\pi$
$811$			20.9394i			0.735283i	−0.929968	+	0.367641i	$0.880165\pi$
$812$	1.75426	−	0.280162i	0.0615623	−	0.00983177i
$813$	46.5468	+	46.5468i	1.63247	+	1.63247i
$814$	−1.73432	−	3.39839i	−0.0607880	−	0.119114i
$815$	20.3637	+	7.66201i	0.713309	+	0.268388i
$816$	19.3868	−	6.35439i	0.678674	−	0.222448i
$817$	−6.48324	+	6.48324i	−0.226820	+	0.226820i
$818$	−14.7097	+	45.3711i	−0.514312	+	1.58636i
$819$	−5.91191			−0.206579
$820$	0.338934	−	1.65918i	0.0118361	−	0.0579409i
$821$	30.0440			1.04854			0.524272	−	0.851551i	$-0.324337\pi$
$821$	30.0440			1.04854			0.524272	+	0.851551i	$0.324337\pi$
$822$	16.5698	−	51.1086i	0.577940	−	1.78262i
$823$	−10.1299	+	10.1299i	−0.353106	+	0.353106i	−0.861264	−	0.508158i	$-0.830327\pi$
$823$	−10.1299	+	10.1299i	−0.353106	+	0.353106i	0.508158	+	0.861264i	$0.330327\pi$
$824$	11.8779	+	1.85777i	0.413786	+	0.0647185i
$825$	8.07504	−	0.530902i	0.281137	−	0.0184836i
$826$	−0.165819	−	0.324922i	−0.00576959	−	0.0113055i
$827$	−26.4200	−	26.4200i	−0.918713	−	0.918713i	0.0782233	−	0.996936i	$-0.475075\pi$
$827$	−26.4200	−	26.4200i	−0.918713	−	0.918713i	−0.996936	+	0.0782233i	$0.975075\pi$
$828$	−5.25039	−	32.8757i	−0.182464	−	1.14251i
$829$		−	23.2743i		−	0.808351i	−0.914682	−	0.404175i	$-0.867559\pi$
$829$		−	23.2743i		−	0.808351i	0.914682	−	0.404175i	$-0.132441\pi$
$830$	28.2284	+	22.5202i	0.979823	+	0.781688i
$831$			16.9136i			0.586728i
$832$	31.6537	−	16.2826i	1.09739	−	0.564499i
$833$	−10.0763	−	10.0763i	−0.349124	−	0.349124i
$834$	−28.1810	+	14.3818i	−0.975828	+	0.498000i
$835$	−9.97101	+	26.5004i	−0.345061	+	0.917086i
$836$	−0.781353	+	1.07836i	−0.0270236	+	0.0372957i
$837$	−1.24885	+	1.24885i	−0.0431666	+	0.0431666i
$838$	−5.09971	−	1.65337i	−0.176167	−	0.0571147i
$839$	52.2635			1.80434			0.902168	−	0.431385i	$-0.141975\pi$
$839$	52.2635			1.80434			0.902168	+	0.431385i	$0.141975\pi$
$840$	−3.45907	+	6.11174i	−0.119349	+	0.210875i
$841$	25.2191			0.869623
$842$	−18.4852	−	5.99306i	−0.637043	−	0.206534i
$843$	−40.9243	+	40.9243i	−1.40951	+	1.40951i
$844$	−20.5390	+	28.3462i	−0.706982	+	0.975716i
$845$	13.8454	−	6.27495i	0.476296	−	0.215865i
$846$	−4.40261	+	2.24681i	−0.151365	+	0.0772470i
$847$	3.40992	+	3.40992i	0.117166	+	0.117166i
$848$	18.5515	−	36.6422i	0.637060	−	1.25830i
$849$			0.860379i			0.0295281i
$850$	3.64003	−	14.3836i	0.124852	−	0.493354i
$851$			23.1890i			0.794908i
$852$	0.609983	+	3.81945i	0.0208977	+	0.130852i
$853$	−16.0917	−	16.0917i	−0.550969	−	0.550969i	0.375752	−	0.926720i	$-0.377385\pi$
$853$	−16.0917	−	16.0917i	−0.550969	−	0.550969i	−0.926720	+	0.375752i	$0.877385\pi$
$854$	2.01665	+	3.95160i	0.0690082	+	0.135221i
$855$	5.92382	−	2.68477i	0.202590	−	0.0918172i
$856$	−0.376426	+	2.40673i	−0.0128660	+	0.0822604i
$857$	−17.1500	+	17.1500i	−0.585833	+	0.585833i	−0.936500	−	0.350667i	$-0.885955\pi$
$857$	−17.1500	+	17.1500i	−0.585833	+	0.585833i	0.350667	+	0.936500i	$0.385955\pi$
$858$	3.14093	−	9.68801i	0.107230	−	0.330743i
$859$	24.0866			0.821826			0.410913	−	0.911675i	$-0.365210\pi$
$859$	24.0866			0.821826			0.410913	+	0.911675i	$0.365210\pi$
$860$	−22.6043	−	34.2103i	−0.770800	−	1.16656i
$861$	0.420465			0.0143294
$862$	−9.99087	+	30.8162i	−0.340290	+	1.04960i
$863$	32.7301	−	32.7301i	1.11415	−	1.11415i	0.121562	−	0.992584i	$-0.461210\pi$
$863$	32.7301	−	32.7301i	1.11415	−	1.11415i	0.992584	−	0.121562i	$-0.0387904\pi$
$864$	0.885865	−	0.891586i	0.0301378	−	0.0303324i
$865$	−8.56276	+	22.7577i	−0.291143	+	0.773784i
$866$	7.49871	+	14.6936i	0.254816	+	0.499311i
$867$	21.6522	+	21.6522i	0.735348	+	0.735348i
$868$	−7.17150	+	1.14532i	−0.243417	+	0.0388747i
$869$		−	6.33143i		−	0.214779i
$870$	9.32125	−	11.6839i	0.316020	−	0.396122i
$871$		−	71.2286i		−	2.41349i
$872$	−28.8003	+	21.0097i	−0.975301	+	0.711479i
$873$	−7.36516	−	7.36516i	−0.249273	−	0.249273i
$874$	7.20914	−	3.67909i	0.243853	−	0.124447i
$875$	2.40891	+	4.50347i	0.0814360	+	0.152245i
$876$	47.7248	+	34.5803i	1.61247	+	1.16836i
$877$	−40.5285	+	40.5285i	−1.36855	+	1.36855i	−0.506037	+	0.862512i	$0.668890\pi$
$877$	−40.5285	+	40.5285i	−1.36855	+	1.36855i	−0.862512	+	0.506037i	$0.831110\pi$
$878$	17.4469	+	5.65641i	0.588803	+	0.190895i
$879$	−8.85504			−0.298673
$880$	−4.02561	−	4.38882i	−0.135703	−	0.147947i
$881$	11.8098			0.397881			0.198941	−	0.980012i	$-0.436250\pi$
$881$	11.8098			0.397881			0.198941	+	0.980012i	$0.436250\pi$
$882$	26.5736	+	8.61537i	0.894779	+	0.290095i
$883$	−0.785490	+	0.785490i	−0.0264338	+	0.0264338i	−0.720200	−	0.693766i	$-0.755950\pi$
$883$	−0.785490	+	0.785490i	−0.0264338	+	0.0264338i	0.693766	+	0.720200i	$0.255950\pi$
$884$	−15.1206	−	10.9560i	−0.508560	−	0.368491i
$885$	−2.87255	−	1.08082i	−0.0965599	−	0.0363314i
$886$	41.4593	−	21.1582i	1.39285	−	0.710823i
$887$	0.832759	+	0.832759i	0.0279613	+	0.0279613i	0.720949	−	0.692988i	$-0.243706\pi$
$887$	0.832759	+	0.832759i	0.0279613	+	0.0279613i	−0.692988	+	0.720949i	$0.743706\pi$
$888$	22.5053	−	16.4176i	0.755229	−	0.550938i
$889$		−	0.646755i		−	0.0216915i
$890$	−52.8963	+	5.94978i	−1.77309	+	0.199437i
$891$		−	6.16957i		−	0.206688i
$892$	−24.3222	+	3.88436i	−0.814367	+	0.130058i
$893$	−0.849686	−	0.849686i	−0.0284337	−	0.0284337i
$894$	−34.6167	−	67.8312i	−1.15776	−	2.26861i
$895$	11.0191	+	24.3131i	0.368328	+	0.812698i
$896$	5.10086	−	0.831474i	0.170408	−	0.0277776i
$897$	−43.7692	+	43.7692i	−1.46141	+	1.46141i
$898$	−3.16312	+	9.75644i	−0.105555	+	0.325577i
$899$	15.4566			0.515508
$900$	6.46143	+	28.3592i	0.215381	+	0.945306i
$901$	−21.5445			−0.717751
$902$	−0.109966	+	0.339184i	−0.00366148	+	0.0112936i
$903$	7.19892	−	7.19892i	0.239565	−	0.239565i
$904$	5.07942	−	32.4760i	0.168939	−	1.08014i
$905$	15.2702	+	33.6931i	0.507600	+	1.12000i
$906$	−0.387598	−	0.759495i	−0.0128771	−	0.0252325i
$907$	−6.94748	−	6.94748i	−0.230687	−	0.230687i	0.582292	−	0.812980i	$-0.302156\pi$
$907$	−6.94748	−	6.94748i	−0.230687	−	0.230687i	−0.812980	+	0.582292i	$0.802156\pi$
$908$	−2.55556	−	16.0018i	−0.0848092	−	0.531039i
$909$		−	25.0185i		−	0.829811i
$910$	6.38726	−	0.718439i	0.211736	−	0.0238160i
$911$		−	29.0624i		−	0.962880i	−0.876479	−	0.481440i	$-0.840114\pi$
$911$		−	29.0624i		−	0.962880i	0.876479	−	0.481440i	$-0.159886\pi$
$912$	−8.67463	−	4.39185i	−0.287246	−	0.145429i
$913$	−5.37642	−	5.37642i	−0.177934	−	0.177934i
$914$	39.8018	−	20.3123i	1.31653	−	0.671872i
$915$	34.9351	+	13.1446i	1.15492	+	0.434548i
$916$	−11.7443	+	16.2085i	−0.388043	+	0.535544i
$917$	3.31282	−	3.31282i	0.109399	−	0.109399i
$918$	−0.627170	−	0.203334i	−0.0206997	−	0.00671101i
$919$	54.8935			1.81077			0.905385	−	0.424592i	$-0.139582\pi$
$919$	54.8935			1.81077			0.905385	+	0.424592i	$0.139582\pi$
$920$	9.66773	+	34.8810i	0.318736	+	1.14999i
$921$	−44.8199			−1.47687
$922$	−0.00949257	−	0.00307757i	−0.000312621	−	0.000101354i
$923$	2.50319	−	2.50319i	0.0823936	−	0.0823936i
$924$	0.867605	−	1.19739i	0.0285421	−	0.0393914i
$925$	−1.32909	−	20.2155i	−0.0437002	−	0.664682i
$926$	11.5451	−	5.89186i	0.379394	−	0.193619i
$927$	8.74201	+	8.74201i	0.287125	+	0.287125i
$928$	−10.9995	+	0.0354009i	−0.361075	+	0.00116209i
$929$			7.99522i			0.262315i	0.991362	+	0.131157i	$0.0418693\pi$
$929$			7.99522i			0.262315i	−0.991362	+	0.131157i	$0.958131\pi$
$930$	−38.1058	+	47.7645i	−1.24954	+	1.56626i
$931$			6.79133i			0.222577i
$932$	−5.33907	−	33.4309i	−0.174887	−	1.09507i
$933$	−11.4964	−	11.4964i	−0.376374	−	0.376374i
$934$	21.9232	+	42.9582i	0.717348	+	1.40564i
$935$	−1.10015	+	2.92392i	−0.0359787	+	0.0956224i
$936$	36.1653	+	5.65645i	1.18210	+	0.184887i
$937$	11.0007	−	11.0007i	0.359379	−	0.359379i	−0.504205	−	0.863584i	$-0.668214\pi$
$937$	11.0007	−	11.0007i	0.359379	−	0.359379i	0.863584	+	0.504205i	$0.168214\pi$
$938$	3.18942	−	9.83757i	0.104138	−	0.321208i
$939$	−46.6064			−1.52094
$940$	4.48356	−	2.96249i	0.146238	−	0.0966258i
$941$	−43.2923			−1.41129			−0.705644	−	0.708566i	$-0.749342\pi$
$941$	−43.2923			−1.41129			−0.705644	+	0.708566i	$0.749342\pi$
$942$	−17.7114	+	54.6298i	−0.577070	+	1.77994i
$943$	1.53239	−	1.53239i	0.0499016	−	0.0499016i
$944$	0.703495	+	2.14632i	0.0228968	+	0.0698567i
$945$	0.206710	−	0.0936842i	0.00672428	−	0.00304755i
$946$	3.92452	+	7.69006i	0.127597	+	0.250025i
$947$	26.8841	+	26.8841i	0.873617	+	0.873617i	0.992865	−	0.119248i	$-0.0380483\pi$
$947$	26.8841	+	26.8841i	0.873617	+	0.873617i	−0.119248	+	0.992865i	$0.538048\pi$
$948$	45.6495	−	7.29042i	1.48263	−	0.236782i
$949$		−	53.9411i		−	1.75100i
$950$	−6.07386	+	3.62052i	−0.197062	+	0.117465i
$951$			44.6685i			1.44848i
$952$	−1.59776	−	2.19022i	−0.0517837	−	0.0709855i
$953$	−10.3968	−	10.3968i	−0.336785	−	0.336785i	0.518371	−	0.855156i	$-0.326539\pi$
$953$	−10.3968	−	10.3968i	−0.336785	−	0.336785i	−0.855156	+	0.518371i	$0.826539\pi$
$954$	37.6192	−	19.1985i	1.21797	−	0.621573i
$955$	−10.3367	+	4.68476i	−0.334488	+	0.151595i
$956$	5.09982	+	3.69521i	0.164940	+	0.119512i
$957$	−2.22533	+	2.22533i	−0.0719348	+	0.0719348i
$958$	24.9600	+	8.09223i	0.806420	+	0.261448i
$959$	−7.13959			−0.230549
$960$	27.0080	−	34.0781i	0.871679	−	1.09987i
$961$	−32.1876			−1.03831
$962$	−24.2535	−	7.86319i	−0.781965	−	0.253520i
$963$	−1.77133	+	1.77133i	−0.0570802	+	0.0570802i
$964$	17.9556	+	13.0102i	0.578311	+	0.419031i
$965$	−12.6042	+	33.4989i	−0.405745	+	1.07837i
$966$	−8.00495	+	4.08522i	−0.257555	+	0.131440i
$967$	−20.6729	−	20.6729i	−0.664794	−	0.664794i	0.291712	−	0.956506i	$-0.405775\pi$
$967$	−20.6729	−	20.6729i	−0.664794	−	0.664794i	−0.956506	+	0.291712i	$0.905775\pi$
$968$	−17.5971	−	24.1223i	−0.565594	−	0.775320i
$969$			5.10041i			0.163849i
$970$	8.85240	+	7.06231i	0.284233	+	0.226757i
$971$			27.3691i			0.878317i	0.898410	+	0.439158i	$0.144723\pi$
$971$			27.3691i			0.878317i	−0.898410	+	0.439158i	$0.855277\pi$
$972$	43.1660	−	6.89381i	1.38455	−	0.221119i
$973$	2.97289	+	2.97289i	0.0953064	+	0.0953064i
$974$	−24.0047	−	47.0369i	−0.769159	−	1.50716i
$975$	35.6482	−	40.6655i	1.14165	−	1.30234i
$976$	−8.55570	−	26.1029i	−0.273861	−	0.835532i
$977$	−2.07325	+	2.07325i	−0.0663293	+	0.0663293i	−0.739493	−	0.673164i	$-0.764935\pi$
$977$	−2.07325	+	2.07325i	−0.0663293	+	0.0663293i	0.673164	+	0.739493i	$0.264935\pi$
$978$	10.3158	−	31.8183i	0.329862	−	1.01744i
$979$	11.2079			0.358206
$980$	−29.7572	−	6.07876i	−0.950559	−	0.194179i
$981$	−36.6596			−1.17045
$982$	12.8164	−	39.5313i	0.408986	−	1.26149i
$983$	4.42510	−	4.42510i	0.141139	−	0.141139i	−0.633007	−	0.774146i	$-0.718180\pi$
$983$	4.42510	−	4.42510i	0.141139	−	0.141139i	0.774146	+	0.633007i	$0.218180\pi$
$984$	−2.57214	−	0.402296i	−0.0819967	−	0.0128247i
$985$	−14.5026	−	5.45674i	−0.462093	−	0.173866i
$986$	2.62284	+	5.13944i	0.0835283	+	0.163673i
$987$	0.943482	+	0.943482i	0.0300314	+	0.0300314i
$988$	1.40343	+	8.78765i	0.0446489	+	0.279572i
$989$		−	52.4732i		−	1.66855i
$990$	−0.684538	−	6.08586i	−0.0217561	−	0.193421i
$991$			12.1670i			0.386497i	0.981150	+	0.193248i	$0.0619023\pi$
$991$			12.1670i			0.386497i	−0.981150	+	0.193248i	$0.938098\pi$
$992$	44.9665	−	0.144721i	1.42769	−	0.00459489i
$993$	−25.5558	−	25.5558i	−0.810988	−	0.810988i
$994$	0.457809	−	0.233637i	0.0145208	−	0.00741050i
$995$	−17.1858	−	37.9198i	−0.544828	−	1.20214i
$996$	32.5731	−	44.9547i	1.03212	−	1.42444i
$997$	−23.4777	+	23.4777i	−0.743545	+	0.743545i	−0.973258	−	0.229714i	$-0.926221\pi$
$997$	−23.4777	+	23.4777i	−0.743545	+	0.743545i	0.229714	+	0.973258i	$0.426221\pi$
$998$	−29.0927	−	9.43209i	−0.920913	−	0.298568i
$999$	−0.900246			−0.0284825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.d.343.4	yes	52
4.3	odd	2		380.2.k.c.343.17	yes	52
5.2	odd	4		380.2.k.c.267.17	✓	52
20.7	even	4	inner	380.2.k.d.267.4	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.17	✓	52	5.2	odd	4
380.2.k.c.343.17	yes	52	4.3	odd	2
380.2.k.d.267.4	yes	52	20.7	even	4	inner
380.2.k.d.343.4	yes	52	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34528 - 0.436150i) q^{2} +(1.71881 - 1.71881i) q^{3} +(1.61955 + 1.17349i) q^{4} +(-0.923046 - 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(0.323011 + 0.323011i) q^{7} +(-1.66692 - 2.28503i) q^{8} -2.90860i q^{9} +O(q^{10})\)	\(q+(-1.34528 - 0.436150i) q^{2} +(1.71881 - 1.71881i) q^{3} +(1.61955 + 1.17349i) q^{4} +(-0.923046 - 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(0.323011 + 0.323011i) q^{7} +(-1.66692 - 2.28503i) q^{8} -2.90860i q^{9} +(0.353464 + 3.14246i) q^{10} -0.665839i q^{11} +(4.80068 - 0.766690i) q^{12} +(-3.14627 - 3.14627i) q^{13} +(-0.293659 - 0.575422i) q^{14} +(-5.08716 - 1.91409i) q^{15} +(1.24586 + 3.80103i) q^{16} +(1.48371 - 1.48371i) q^{17} +(-1.26858 + 3.91287i) q^{18} -1.00000 q^{19} +(0.895077 - 4.38165i) q^{20} +1.11039 q^{21} +(-0.290406 + 0.895738i) q^{22} +(4.04683 - 4.04683i) q^{23} +(-6.79265 - 1.06241i) q^{24} +(-3.29597 + 3.75986i) q^{25} +(2.86037 + 5.60486i) q^{26} +(0.157107 + 0.157107i) q^{27} +(0.144082 + 0.902182i) q^{28} -1.94446i q^{29} +(6.00882 + 4.79375i) q^{30} +7.94906i q^{31} +(-0.0182060 - 5.65682i) q^{32} +(-1.14445 - 1.14445i) q^{33} +(-2.64312 + 1.34888i) q^{34} +(0.359710 - 0.956019i) q^{35} +(3.41320 - 4.71060i) q^{36} +(-2.86508 + 2.86508i) q^{37} +(1.34528 + 0.436150i) q^{38} -10.8157 q^{39} +(-3.11518 + 5.50415i) q^{40} +0.378665 q^{41} +(-1.49378 - 0.484296i) q^{42} +(6.48324 - 6.48324i) q^{43} +(0.781353 - 1.07836i) q^{44} +(-5.92382 + 2.68477i) q^{45} +(-7.20914 + 3.67909i) q^{46} +(0.849686 + 0.849686i) q^{47} +(8.67463 + 4.39185i) q^{48} -6.79133i q^{49} +(6.07386 - 3.62052i) q^{50} -5.10041i q^{51} +(-1.40343 - 8.78765i) q^{52} +(-7.26036 - 7.26036i) q^{53} +(-0.142830 - 0.279874i) q^{54} +(-1.35609 + 0.614600i) q^{55} +(0.199656 - 1.27653i) q^{56} +(-1.71881 + 1.71881i) q^{57} +(-0.848077 + 2.61584i) q^{58} +0.564667 q^{59} +(-5.99274 - 9.06967i) q^{60} -6.86731 q^{61} +(3.46699 - 10.6937i) q^{62} +(0.939510 - 0.939510i) q^{63} +(-2.44273 + 7.61794i) q^{64} +(-3.50374 + 9.31205i) q^{65} +(1.04045 + 2.03875i) q^{66} +(11.3195 + 11.3195i) q^{67} +(4.14404 - 0.661821i) q^{68} -13.9114i q^{69} +(-0.900878 + 1.12922i) q^{70} +0.795606i q^{71} +(-6.64623 + 4.84841i) q^{72} +(8.57222 + 8.57222i) q^{73} +(5.10393 - 2.60472i) q^{74} +(0.797343 + 12.1276i) q^{75} +(-1.61955 - 1.17349i) q^{76} +(0.215073 - 0.215073i) q^{77} +(14.5501 + 4.71726i) q^{78} +9.50896 q^{79} +(6.59142 - 6.04592i) q^{80} +9.26586 q^{81} +(-0.509409 - 0.165155i) q^{82} +(8.07466 - 8.07466i) q^{83} +(1.79833 + 1.30303i) q^{84} +(-4.39134 - 1.65228i) q^{85} +(-11.5494 + 5.89410i) q^{86} +(-3.34215 - 3.34215i) q^{87} +(-1.52146 + 1.10990i) q^{88} +16.8328i q^{89} +(9.14015 - 1.02808i) q^{90} -2.03257i q^{91} +(11.3029 - 1.80513i) q^{92} +(13.6629 + 13.6629i) q^{93} +(-0.772473 - 1.51366i) q^{94} +(0.923046 + 2.03666i) q^{95} +(-9.75428 - 9.69170i) q^{96} +(2.53220 - 2.53220i) q^{97} +(-2.96204 + 9.13622i) q^{98} -1.93665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

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