LMFDB - Embedded newform 380.2.k.c.267.17

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			267.17
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.436150 - 1.34528i) q^{2} +(-1.71881 - 1.71881i) q^{3} +(-1.61955 - 1.17349i) q^{4} +(-0.923046 + 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(-0.323011 + 0.323011i) q^{7} +(-2.28503 + 1.66692i) q^{8} +2.90860i q^{9} +O(q^{10})$	\(q+(0.436150 - 1.34528i) 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} +(-2.28503 + 1.66692i) q^{8} +2.90860i q^{9} +(2.33729 + 2.13004i) q^{10} -0.665839i q^{11} +(0.766690 + 4.80068i) 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} +(3.91287 + 1.26858i) q^{18} +1.00000 q^{19} +(3.88491 - 2.21528i) q^{20} +1.11039 q^{21} +(-0.895738 - 0.290406i) 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} +(0.902182 - 0.144082i) q^{28} +1.94446i q^{29} +(-0.356212 - 7.67848i) q^{30} +7.94906i q^{31} +(5.65682 - 0.0182060i) 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} +(0.436150 - 1.34528i) q^{38} +10.8157 q^{39} +(-1.28577 - 6.19248i) q^{40} +0.378665 q^{41} +(0.484296 - 1.49378i) 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} +(4.39185 - 8.67463i) q^{48} +6.79133i q^{49} +(-6.49560 + 2.79413i) q^{50} -5.10041i q^{51} +(8.78765 - 1.40343i) 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} +(2.61584 + 0.848077i) q^{58} -0.564667 q^{59} +(-10.4851 - 2.86977i) q^{60} -6.86731 q^{61} +(10.6937 + 3.46699i) 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} +(-0.661821 - 4.14404i) q^{68} +13.9114i q^{69} +(-1.44300 + 0.0669421i) q^{70} +0.795606i q^{71} +(-4.84841 - 6.64623i) 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} +(4.71726 - 14.5501i) q^{78} -9.50896 q^{79} +(-8.89139 - 0.971137i) q^{80} +9.26586 q^{81} +(0.165155 - 0.509409i) 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} +(1.10990 + 1.52146i) q^{88} -16.8328i q^{89} +(-6.19544 + 6.79822i) q^{90} -2.03257i q^{91} +(1.80513 + 11.3029i) 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} +(9.13622 + 2.96204i) 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} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 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 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.436150	−	1.34528i	0.308405	−	0.951255i
$2$	0.436150	−	1.34528i	0.308405	−	0.951255i
$3$	−1.71881	−	1.71881i	−0.992354	−	0.992354i	0.00761727	−	0.999971i	$-0.497575\pi$
$3$	−1.71881	−	1.71881i	−0.992354	−	0.992354i	−0.999971	+	0.00761727i	$0.997575\pi$
$4$	−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	$-0.777513\pi$
$7$	−0.323011	+	0.323011i	−0.122087	+	0.122087i	0.643424	+	0.765510i	$0.277513\pi$
$8$	−2.28503	+	1.66692i	−0.807880	+	0.589346i
$9$			2.90860i			0.969532i
$10$	2.33729	+	2.13004i	0.739115	+	0.673579i
$11$		−	0.665839i		−	0.200758i	−0.994949	−	0.100379i	$-0.967994\pi$
$11$		−	0.665839i		−	0.200758i	0.994949	−	0.100379i	$-0.0320055\pi$
$12$	0.766690	+	4.80068i	0.221324	+	1.38584i
$13$	−3.14627	+	3.14627i	−0.872620	+	0.872620i	−0.992757	−	0.120138i	$-0.961666\pi$
$13$	−3.14627	+	3.14627i	−0.872620	+	0.872620i	0.120138	+	0.992757i	$0.461666\pi$
$14$	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	0.863758	−	0.503907i	$-0.168104\pi$
$17$	1.48371	+	1.48371i	0.359852	+	0.359852i	−0.503907	+	0.863758i	$0.668104\pi$
$18$	3.91287	+	1.26858i	0.922272	+	0.299008i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	3.88491	−	2.21528i	0.868692	−	0.495352i
$21$	1.11039			0.242307
$22$	−0.895738	−	0.290406i	−0.190972	−	0.0619147i
$23$	−4.04683	−	4.04683i	−0.843823	−	0.843823i	0.145531	−	0.989354i	$-0.453511\pi$
$23$	−4.04683	−	4.04683i	−0.843823	−	0.843823i	−0.989354	+	0.145531i	$0.953511\pi$
$24$	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
$28$	0.902182	−	0.144082i	0.170496	−	0.0272290i
$29$			1.94446i			0.361077i	0.983568	+	0.180539i	$0.0577841\pi$
$29$			1.94446i			0.361077i	−0.983568	+	0.180539i	$0.942216\pi$
$30$	−0.356212	−	7.67848i	−0.0650351	−	1.40189i
$31$			7.94906i			1.42769i	0.700302	+	0.713847i	$0.253049\pi$
$31$			7.94906i			1.42769i	−0.700302	+	0.713847i	$0.746951\pi$
$32$	5.65682	−	0.0182060i	0.999995	−	0.00321840i
$33$	−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	0.431228	−	0.902243i	$-0.358081\pi$
$37$	−2.86508	−	2.86508i	−0.471016	−	0.471016i	−0.902243	+	0.431228i	$0.858081\pi$
$38$	0.436150	−	1.34528i	0.0707529	−	0.218233i
$39$	10.8157			1.73189
$40$	−1.28577	−	6.19248i	−0.203298	−	0.979117i
$41$	0.378665			0.0591375			0.0295687	−	0.999563i	$-0.490587\pi$
$41$	0.378665			0.0591375			0.0295687	+	0.999563i	$0.490587\pi$
$42$	0.484296	−	1.49378i	0.0747285	−	0.230496i
$43$	−6.48324	−	6.48324i	−0.988685	−	0.988685i	0.0112515	−	0.999937i	$-0.496418\pi$
$43$	−6.48324	−	6.48324i	−0.988685	−	0.988685i	−0.999937	+	0.0112515i	$0.996418\pi$
$44$	−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	$-0.777932\pi$
$47$	−0.849686	+	0.849686i	−0.123939	+	0.123939i	0.642416	+	0.766356i	$0.277932\pi$
$48$	4.39185	−	8.67463i	0.633909	−	1.25207i
$49$			6.79133i			0.970190i
$50$	−6.49560	+	2.79413i	−0.918617	+	0.395150i
$51$		−	5.10041i		−	0.714200i
$52$	8.78765	−	1.40343i	1.21863	−	0.194620i
$53$	−7.26036	+	7.26036i	−0.997287	+	0.997287i	−0.999996	−	0.00270956i	$-0.999138\pi$
$53$	−7.26036	+	7.26036i	−0.997287	+	0.997287i	0.00270956	+	0.999996i	$0.499138\pi$
$54$	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
$58$	2.61584	+	0.848077i	0.343477	+	0.111358i
$59$	−0.564667			−0.0735134			−0.0367567	−	0.999324i	$-0.511703\pi$
$59$	−0.564667			−0.0735134			−0.0367567	+	0.999324i	$0.511703\pi$
$60$	−10.4851	−	2.86977i	−1.35361	−	0.370485i
$61$	−6.86731			−0.879269			−0.439634	−	0.898177i	$-0.644892\pi$
$61$	−6.86731			−0.879269			−0.439634	+	0.898177i	$0.644892\pi$
$62$	10.6937	+	3.46699i	1.35810	+	0.440308i
$63$	−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	−0.543472	+	0.839428i	$0.682890\pi$
$67$	−11.3195	+	11.3195i	−1.38290	+	1.38290i	−0.839428	+	0.543472i	$0.817110\pi$
$68$	−0.661821	−	4.14404i	−0.0802576	−	0.502539i
$69$			13.9114i			1.67474i
$70$	−1.44300	+	0.0669421i	−0.172471	+	0.00800111i
$71$			0.795606i			0.0944210i	0.998885	+	0.0472105i	$0.0150332\pi$
$71$			0.795606i			0.0944210i	−0.998885	+	0.0472105i	$0.984967\pi$
$72$	−4.84841	−	6.64623i	−0.571390	−	0.783266i
$73$	8.57222	−	8.57222i	1.00330	−	1.00330i	0.00330820	−	0.999995i	$-0.498947\pi$
$73$	8.57222	−	8.57222i	1.00330	−	1.00330i	0.999995	−	0.00330820i	$-0.00105303\pi$
$74$	−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
$78$	4.71726	−	14.5501i	0.534125	−	1.64747i
$79$	−9.50896			−1.06984			−0.534921	−	0.844902i	$-0.679658\pi$
$79$	−9.50896			−1.06984			−0.534921	+	0.844902i	$0.679658\pi$
$80$	−8.89139	−	0.971137i	−0.994088	−	0.108576i
$81$	9.26586			1.02954
$82$	0.165155	−	0.509409i	0.0182383	−	0.0562548i
$83$	−8.07466	−	8.07466i	−0.886309	−	0.886309i	0.107857	−	0.994166i	$-0.465601\pi$
$83$	−8.07466	−	8.07466i	−0.886309	−	0.886309i	−0.994166	+	0.107857i	$0.965601\pi$
$84$	−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
$88$	1.10990	+	1.52146i	0.118316	+	0.162188i
$89$		−	16.8328i		−	1.78427i	−0.451769	−	0.892135i	$-0.649207\pi$
$89$		−	16.8328i		−	1.78427i	0.451769	−	0.892135i	$-0.350793\pi$
$90$	−6.19544	+	6.79822i	−0.653056	+	0.716596i
$91$		−	2.03257i		−	0.213071i
$92$	1.80513	+	11.3029i	0.188198	+	1.17841i
$93$	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	0.823876	−	0.566770i	$-0.191807\pi$
$97$	2.53220	+	2.53220i	0.257106	+	0.257106i	−0.566770	+	0.823876i	$0.691807\pi$
$98$	9.13622	+	2.96204i	0.922898	+	0.299211i
$99$	1.93665			0.194641
$100$	0.925826	+	9.95705i	0.0925826	+	0.995705i
$101$	8.60157			0.855888			0.427944	−	0.903805i	$-0.359238\pi$
$101$	8.60157			0.855888			0.427944	+	0.903805i	$0.359238\pi$
$102$	−6.86147	−	2.22455i	−0.679387	−	0.220263i
$103$	3.00558	+	3.00558i	0.296148	+	0.296148i	0.839503	−	0.543355i	$-0.182846\pi$
$103$	3.00558	+	3.00558i	0.296148	+	0.296148i	−0.543355	+	0.839503i	$0.682846\pi$
$104$	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	$-0.736745\pi$
$107$	0.608998	−	0.608998i	0.0588740	−	0.0588740i	0.735931	+	0.677057i	$0.236745\pi$
$108$	0.438804	−	0.0700790i	0.0422240	−	0.00674335i
$109$			12.6039i			1.20723i	0.797274	+	0.603617i	$0.206274\pi$
$109$			12.6039i			1.20723i	−0.797274	+	0.603617i	$0.793726\pi$
$110$	1.41827	−	1.55626i	0.135226	−	0.148383i
$111$			9.84903i			0.934828i
$112$	−1.63020	−	0.825350i	−0.154040	−	0.0779882i
$113$	8.21770	−	8.21770i	0.773056	−	0.773056i	−0.205583	−	0.978640i	$-0.565909\pi$
$113$	8.21770	−	8.21770i	0.773056	−	0.773056i	0.978640	+	0.205583i	$0.0659091\pi$
$114$	−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
$118$	−0.246280	+	0.759634i	−0.0226719	+	0.0699300i
$119$	−0.958508			−0.0878663
$120$	−8.43369	+	12.8537i	−0.769887	+	1.17337i
$121$	10.5567			0.959696
$122$	−2.99518	+	9.23844i	−0.271171	+	0.836409i
$123$	−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	$-0.729992\pi$
$127$	1.00113	−	1.00113i	0.0888362	−	0.0888362i	0.750128	+	0.661292i	$0.229992\pi$
$128$	−9.18285	−	6.60872i	−0.811657	−	0.584134i
$129$			22.2869i			1.96225i
$130$	−14.0555	+	0.652046i	−1.23274	+	0.0571882i
$131$		−	10.2560i		−	0.896075i	−0.894015	−	0.448037i	$-0.852123\pi$
$131$		−	10.2560i		−	0.896075i	0.894015	−	0.448037i	$-0.147877\pi$
$132$	3.19648	−	0.510492i	0.278218	−	0.0444326i
$133$	−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	0.0543216	−	0.998523i	$-0.482700\pi$
$137$	−11.0516	−	11.0516i	−0.944202	−	0.944202i	−0.998523	+	0.0543216i	$0.982700\pi$
$138$	18.7148	+	6.06748i	1.59311	+	0.516498i
$139$	−9.20366			−0.780644			−0.390322	−	0.920678i	$-0.627636\pi$
$139$	−9.20366			−0.780644			−0.390322	+	0.920678i	$0.627636\pi$
$140$	−0.539309	+	1.97043i	−0.0455799	+	0.166532i
$141$	2.92089			0.245984
$142$	1.07031	+	0.347004i	0.0898185	+	0.0291199i
$143$	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
$148$	1.27799	+	8.00225i	0.105051	+	0.657781i
$149$		−	22.1531i		−	1.81485i	−0.420215	−	0.907425i	$-0.638045\pi$
$149$		−	22.1531i		−	1.81485i	0.420215	−	0.907425i	$-0.361955\pi$
$150$	15.9673	+	6.36211i	1.30372	+	0.519464i
$151$			0.248045i			0.0201856i	0.999949	+	0.0100928i	$0.00321269\pi$
$151$			0.248045i			0.0201856i	−0.999949	+	0.0100928i	$0.996787\pi$
$152$	−2.28503	+	1.66692i	−0.185340	+	0.135205i
$153$	−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	0.998449	−	0.0556683i	$-0.0177289\pi$
$157$	11.8130	+	11.8130i	0.942781	+	0.942781i	−0.0556683	+	0.998449i	$0.517729\pi$
$158$	−4.14733	+	12.7922i	−0.329944	+	1.01769i
$159$	24.9583			1.97932
$160$	−5.18443	+	11.5378i	−0.409865	+	0.912146i
$161$	2.61435			0.206039
$162$	4.04131	−	12.4652i	0.317515	−	0.979355i
$163$	6.88031	+	6.88031i	0.538908	+	0.538908i	0.923208	−	0.384301i	$-0.125557\pi$
$163$	6.88031	+	6.88031i	0.538908	+	0.538908i	−0.384301	+	0.923208i	$0.625557\pi$
$164$	−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	$-0.587024\pi$
$167$	8.95374	−	8.95374i	0.692861	−	0.692861i	0.962860	+	0.269999i	$0.0870235\pi$
$168$	−2.53727	+	1.85093i	−0.195755	+	0.142803i
$169$		−	6.79809i		−	0.522930i
$170$	0.307489	+	6.62821i	0.0235833	+	0.508360i
$171$			2.90860i			0.222426i
$172$	2.89191	+	18.1079i	0.220506	+	1.38072i
$173$	−7.68917	+	7.68917i	−0.584597	+	0.584597i	−0.936163	−	0.351566i	$-0.885649\pi$
$173$	−7.68917	+	7.68917i	−0.584597	+	0.584597i	0.351566	+	0.936163i	$0.385649\pi$
$174$	−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
$178$	−22.6447	−	7.34161i	−1.69730	−	0.550277i
$179$	11.9377			0.892269			0.446134	−	0.894966i	$-0.352800\pi$
$179$	11.9377			0.892269			0.446134	+	0.894966i	$0.352800\pi$
$180$	6.44336	+	11.2996i	0.480260	+	0.842225i
$181$	−16.5433			−1.22965			−0.614827	−	0.788662i	$-0.710774\pi$
$181$	−16.5433			−1.22965			−0.614827	+	0.788662i	$0.710774\pi$
$182$	−2.73437	−	0.886504i	−0.202685	−	0.0657120i
$183$	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
$188$	2.37320	−	0.379011i	0.173083	−	0.0276422i
$189$		−	0.101495i		−	0.00738265i
$190$	2.33729	+	2.13004i	0.169565	+	0.154530i
$191$		−	5.07533i		−	0.367238i	−0.982997	−	0.183619i	$-0.941219\pi$
$191$		−	5.07533i		−	0.367238i	0.982997	−	0.183619i	$-0.0587812\pi$
$192$	−17.2924	+	8.89519i	−1.24797	+	0.641955i
$193$	−11.3183	+	11.3183i	−0.814711	+	0.814711i	−0.985336	−	0.170625i	$-0.945421\pi$
$193$	−11.3183	+	11.3183i	−0.814711	+	0.814711i	0.170625	+	0.985336i	$0.445421\pi$
$194$	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	0.859779	−	0.510666i	$-0.170601\pi$
$197$	4.90003	+	4.90003i	0.349113	+	0.349113i	−0.510666	+	0.859779i	$0.670601\pi$
$198$	0.844672	−	2.60534i	0.0600283	−	0.185153i
$199$	−18.6186			−1.31984			−0.659919	−	0.751336i	$-0.729410\pi$
$199$	−18.6186			−1.31984			−0.659919	+	0.751336i	$0.729410\pi$
$200$	13.7988	+	3.09728i	0.975723	+	0.219010i
$201$	38.9121			2.74465
$202$	3.75158	−	11.5715i	0.263960	−	0.814168i
$203$	−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
$208$	−15.8789	−	8.03927i	−1.10100	−	0.557423i
$209$		−	0.665839i		−	0.0460570i
$210$	2.59530	+	2.36518i	0.179093	+	0.163213i
$211$			17.5026i			1.20493i	0.798147	+	0.602463i	$0.205814\pi$
$211$			17.5026i			1.20493i	−0.798147	+	0.602463i	$0.794186\pi$
$212$	20.2784	−	3.23855i	1.39273	−	0.222425i
$213$	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
$218$	16.9557	+	5.49719i	1.14839	+	0.372317i
$219$	−29.4680			−1.99126
$220$	−1.47502	−	2.58672i	−0.0994459	−	0.174397i
$221$	−9.33630			−0.628027
$222$	13.2497	+	4.29565i	0.889260	+	0.288305i
$223$	8.70816	+	8.70816i	0.583142	+	0.583142i	0.935765	−	0.352624i	$-0.114710\pi$
$223$	8.70816	+	8.70816i	0.583142	+	0.583142i	−0.352624	+	0.935765i	$0.614710\pi$
$224$	−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	$-0.663345\pi$
$227$	5.72919	−	5.72919i	0.380260	−	0.380260i	0.871196	+	0.490936i	$0.163345\pi$
$228$	0.766690	+	4.80068i	0.0507753	+	0.317933i
$229$		−	10.0081i		−	0.661351i	−0.943745	−	0.330675i	$-0.892723\pi$
$229$		−	10.0081i		−	0.661351i	0.943745	−	0.330675i	$-0.107277\pi$
$230$	−0.838680	−	18.0785i	−0.0553009	−	1.19206i
$231$		−	0.739340i		−	0.0486450i
$232$	−3.24127	−	4.44315i	−0.212800	−	0.291707i
$233$	−11.9694	+	11.9694i	−0.784142	+	0.784142i	−0.980527	−	0.196385i	$-0.937080\pi$
$233$	−11.9694	+	11.9694i	−0.784142	+	0.784142i	0.196385	+	0.980527i	$0.437080\pi$
$234$	−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
$238$	−0.418054	+	1.28946i	−0.0270984	+	0.0835833i
$239$	−3.14892			−0.203687			−0.101843	−	0.994800i	$-0.532474\pi$
$239$	−3.14892			−0.203687			−0.101843	+	0.994800i	$0.532474\pi$
$240$	13.6134	+	16.9518i	0.878741	+	1.09423i
$241$	11.0868			0.714164			0.357082	−	0.934073i	$-0.383772\pi$
$241$	11.0868			0.714164			0.357082	+	0.934073i	$0.383772\pi$
$242$	4.60429	−	14.2016i	0.295975	−	0.912916i
$243$	−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
$248$	−13.2505	−	18.1639i	−0.841406	−	1.15341i
$249$			27.7576i			1.75906i
$250$	0.305045	−	15.8084i	0.0192927	−	0.999814i
$251$			23.7489i			1.49901i	0.661996	+	0.749507i	$0.269709\pi$
$251$			23.7489i			1.49901i	−0.661996	+	0.749507i	$0.730291\pi$
$252$	0.419077	+	2.62408i	0.0263994	+	0.165302i
$253$	−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	0.922379	−	0.386287i	$-0.126243\pi$
$257$	8.59420	+	8.59420i	0.536091	+	0.536091i	−0.386287	+	0.922379i	$0.626243\pi$
$258$	29.9821	+	9.72043i	1.86660	+	0.605168i
$259$	1.85091			0.115010
$260$	−5.25311	+	19.1929i	−0.325784	+	1.19029i
$261$	−5.65565			−0.350076
$262$	−13.7972	−	4.47318i	−0.852396	−	0.276354i
$263$	19.7478	+	19.7478i	1.21770	+	1.21770i	0.968435	+	0.249268i	$0.0801899\pi$
$263$	19.7478	+	19.7478i	1.21770	+	1.21770i	0.249268	+	0.968435i	$0.419810\pi$
$264$	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
$268$	31.6158	−	5.04918i	1.93124	−	0.308428i
$269$			1.08328i			0.0660485i	0.999455	+	0.0330243i	$0.0105139\pi$
$269$			1.08328i			0.0660485i	−0.999455	+	0.0330243i	$0.989486\pi$
$270$	−0.701848	+	0.0325594i	−0.0427131	+	0.00198150i
$271$			27.0809i			1.64505i	0.568732	+	0.822523i	$0.307434\pi$
$271$			27.0809i			1.64505i	−0.568732	+	0.822523i	$0.692566\pi$
$272$	−3.79113	+	7.48810i	−0.229871	+	0.454033i
$273$	−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	0.543673	−	0.839297i	$-0.317033\pi$
$277$	−4.92017	−	4.92017i	−0.295624	−	0.295624i	−0.839297	+	0.543673i	$0.817033\pi$
$278$	−4.01418	+	12.3815i	−0.240754	+	0.742592i
$279$	−23.1206			−1.38419
$280$	2.41556	+	1.58492i	0.144357	+	0.0947174i
$281$	−23.8097			−1.42037			−0.710185	−	0.704015i	$-0.751389\pi$
$281$	−23.8097			−1.42037			−0.710185	+	0.704015i	$0.751389\pi$
$282$	1.27395	−	3.92941i	0.0758625	−	0.233993i
$283$	0.250284	+	0.250284i	0.0148778	+	0.0148778i	0.714507	−	0.699629i	$-0.246651\pi$
$283$	0.250284	+	0.250284i	0.0148778	+	0.0148778i	−0.699629	+	0.714507i	$0.746651\pi$
$284$	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
$288$	0.0529540	+	16.4534i	0.00312034	+	0.969527i
$289$		−	12.5972i		−	0.741014i
$290$	−4.14179	+	4.54476i	−0.243214	+	0.266878i
$291$		−	8.70474i		−	0.510281i
$292$	−23.9425	+	3.82372i	−1.40113	+	0.223766i
$293$	−2.57593	+	2.57593i	−0.150487	+	0.150487i	−0.778336	−	0.627848i	$-0.783936\pi$
$293$	−2.57593	+	2.57593i	−0.150487	+	0.150487i	0.627848	+	0.778336i	$0.283936\pi$
$294$	−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
$298$	−29.8020	−	9.66206i	−1.72639	−	0.559708i
$299$	25.4649			1.47267
$300$	15.5229	−	18.7056i	0.896217	−	1.07997i
$301$	4.18832			0.241411
$302$	0.333689	+	0.108185i	0.0192016	+	0.00622533i
$303$	−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	$-0.573626\pi$
$307$	13.0381	−	13.0381i	0.744123	−	0.744123i	0.973369	+	0.229246i	$0.0736260\pi$
$308$	−0.0959356	−	0.600707i	−0.00546644	−	0.0342285i
$309$		−	10.3320i		−	0.587768i
$310$	−16.9319	+	18.5793i	−0.961665	+	1.05523i
$311$		−	6.68856i		−	0.379274i	−0.981854	−	0.189637i	$-0.939269\pi$
$311$		−	6.68856i		−	0.379274i	0.981854	−	0.189637i	$-0.0607311\pi$
$312$	−24.7142	+	18.0289i	−1.39916	+	1.02069i
$313$	−13.5578	+	13.5578i	−0.766331	+	0.766331i	−0.977458	−	0.211128i	$-0.932286\pi$
$313$	−13.5578	+	13.5578i	−0.766331	+	0.766331i	0.211128	+	0.977458i	$0.432286\pi$
$314$	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	0.240765	−	0.970583i	$-0.422602\pi$
$317$	−12.9940	−	12.9940i	−0.729818	−	0.729818i	−0.970583	+	0.240765i	$0.922602\pi$
$318$	10.8856	−	33.5759i	0.610432	−	1.88284i
$319$	1.29470			0.0724891
$320$	13.2604	+	12.0067i	0.741279	+	0.671197i
$321$	−2.09350			−0.116848
$322$	1.14025	−	3.51702i	0.0635435	−	0.195996i
$323$	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
$328$	−0.865260	+	0.631205i	−0.0477760	+	0.0348525i
$329$		−	0.548917i		−	0.0302628i
$330$	−5.11263	+	0.237180i	−0.281441	+	0.0130563i
$331$		−	14.8683i		−	0.817236i	−0.912705	−	0.408618i	$-0.866011\pi$
$331$		−	14.8683i		−	0.817236i	0.912705	−	0.408618i	$-0.133989\pi$
$332$	3.60178	+	22.5528i	0.197673	+	1.23775i
$333$	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	0.0479886	−	0.998848i	$-0.484719\pi$
$337$	−17.4555	−	17.4555i	−0.950859	−	0.950859i	−0.998848	+	0.0479886i	$0.984719\pi$
$338$	−9.14532	−	2.96499i	−0.497440	−	0.161274i
$339$	−28.2493			−1.53429
$340$	9.05090	+	2.47724i	0.490854	+	0.134347i
$341$	5.29279			0.286621
$342$	3.91287	+	1.26858i	0.211584	+	0.0685972i
$343$	−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	$-0.964641\pi$
$347$	−16.4481	+	16.4481i	−0.882982	+	0.882982i	0.110855	+	0.993837i	$0.464641\pi$
$348$	−9.33474	+	1.49080i	−0.500395	+	0.0799152i
$349$			29.9956i			1.60563i	0.596229	+	0.802814i	$0.296665\pi$
$349$			29.9956i			1.60563i	−0.596229	+	0.802814i	$0.703335\pi$
$350$	1.19562	−	3.00069i	0.0639084	−	0.160394i
$351$		−	0.988602i		−	0.0527677i
$352$	−0.0121223	−	3.76653i	−0.000646119	−	0.200757i
$353$	−23.2559	+	23.2559i	−1.23778	+	1.23778i	−0.276879	+	0.960905i	$0.589300\pi$
$353$	−23.2559	+	23.2559i	−1.23778	+	1.23778i	−0.960905	+	0.276879i	$0.910700\pi$
$354$	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
$358$	5.20665	−	16.0596i	0.275180	−	0.848775i
$359$	−18.1714			−0.959050			−0.479525	−	0.877528i	$-0.659191\pi$
$359$	−18.1714			−0.959050			−0.479525	+	0.877528i	$0.659191\pi$
$360$	18.0114	−	3.73978i	0.949285	−	0.197103i
$361$	1.00000			0.0526316
$362$	−7.21536	+	22.2553i	−0.379231	+	1.16971i
$363$	−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	0.0410456	−	0.999157i	$-0.486931\pi$
$367$	19.9274	−	19.9274i	1.04020	−	1.04020i	0.999157	−	0.0410456i	$-0.0130689\pi$
$368$	10.3404	−	20.4239i	0.539028	−	1.06467i
$369$			1.10138i			0.0573357i
$370$	−0.593769	−	12.7992i	−0.0308686	−	0.665401i
$371$		−	4.69036i		−	0.243511i
$372$	−38.1609	+	6.09447i	−1.97855	+	0.315984i
$373$	25.6623	−	25.6623i	1.32874	−	1.32874i	0.422279	−	0.906466i	$-0.361230\pi$
$373$	25.6623	−	25.6623i	1.32874	−	1.32874i	0.906466	−	0.422279i	$-0.138770\pi$
$374$	−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
$378$	−0.136538	−	0.0442669i	−0.00702278	−	0.00227684i
$379$	−12.3650			−0.635150			−0.317575	−	0.948233i	$-0.602869\pi$
$379$	−12.3650			−0.635150			−0.317575	+	0.948233i	$0.602869\pi$
$380$	3.88491	−	2.21528i	0.199292	−	0.113642i
$381$	−3.44151			−0.176314
$382$	−6.82773	−	2.21361i	−0.349337	−	0.113258i
$383$	16.8608	+	16.8608i	0.861545	+	0.861545i	0.991518	−	0.129973i	$-0.0414889\pi$
$383$	16.8608	+	16.8608i	0.861545	+	0.861545i	−0.129973	+	0.991518i	$0.541489\pi$
$384$	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
$388$	−1.12951	−	7.07253i	−0.0573424	−	0.359053i
$389$		−	37.0728i		−	1.87966i	−0.341637	−	0.939832i	$-0.610981\pi$
$389$		−	37.0728i		−	1.87966i	0.341637	−	0.939832i	$-0.389019\pi$
$390$	25.2794	+	23.0379i	1.28007	+	1.16657i
$391$		−	12.0086i		−	0.607302i
$392$	−11.3206	−	15.5184i	−0.571778	−	0.783797i
$393$	−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	0.670290	−	0.742099i	$-0.266170\pi$
$397$	−1.43078	−	1.43078i	−0.0718089	−	0.0718089i	−0.742099	+	0.670290i	$0.766170\pi$
$398$	−8.12051	+	25.0472i	−0.407045	+	1.25550i
$399$	1.11039			0.0555890
$400$	10.1850	−	17.2123i	0.509252	−	0.860617i
$401$	13.4835			0.673334			0.336667	−	0.941624i	$-0.390700\pi$
$401$	13.4835			0.673334			0.336667	+	0.941624i	$0.390700\pi$
$402$	16.9715	−	52.3476i	0.846463	−	2.61086i
$403$	−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
$408$	8.50199	+	11.6546i	0.420911	+	0.576988i
$409$			33.7262i			1.66765i	0.552027	+	0.833826i	$0.313854\pi$
$409$			33.7262i			1.66765i	−0.552027	+	0.833826i	$0.686146\pi$
$410$	0.885048	+	0.806572i	0.0437094	+	0.0398338i
$411$			37.9911i			1.87396i
$412$	−1.34067	−	8.39467i	−0.0660499	−	0.413576i
$413$	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
$418$	−0.895738	−	0.290406i	−0.0438120	−	0.0142042i
$419$	−3.79083			−0.185194			−0.0925970	−	0.995704i	$-0.529517\pi$
$419$	−3.79083			−0.185194			−0.0925970	+	0.995704i	$0.529517\pi$
$420$	4.31376	−	2.45982i	0.210490	−	0.120027i
$421$	13.7408			0.669686			0.334843	−	0.942274i	$-0.391317\pi$
$421$	13.7408			0.669686			0.334843	+	0.942274i	$0.391317\pi$
$422$	23.5458	+	7.63374i	1.14619	+	0.371605i
$423$	−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
$428$	−1.70095	+	0.271649i	−0.0822185	+	0.0131307i
$429$		−	7.20150i		−	0.347691i
$430$	−1.34361	−	28.9628i	−0.0647947	−	1.39671i
$431$		−	22.9069i		−	1.10339i	−0.834046	−	0.551694i	$-0.813981\pi$
$431$		−	22.9069i		−	1.10339i	0.834046	−	0.551694i	$-0.186019\pi$
$432$	−0.792901	−	0.401435i	−0.0381485	−	0.0193140i
$433$	−8.24824	+	8.24824i	−0.396385	+	0.396385i	−0.876956	−	0.480571i	$-0.840430\pi$
$433$	−8.24824	+	8.24824i	−0.396385	+	0.396385i	0.480571	+	0.876956i	$0.340430\pi$
$434$	−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
$438$	−12.8525	+	39.6426i	−0.614115	+	1.89420i
$439$	12.9690			0.618975			0.309487	−	0.950904i	$-0.399843\pi$
$439$	12.9690			0.618975			0.309487	+	0.950904i	$0.399843\pi$
$440$	−4.12319	+	0.856113i	−0.196565	+	0.0408136i
$441$	−19.7532			−0.940630
$442$	−4.07203	+	12.5599i	−0.193687	+	0.597414i
$443$	23.2730	+	23.2730i	1.10574	+	1.10574i	0.993705	+	0.112031i	$0.0357355\pi$
$443$	23.2730	+	23.2730i	1.10574	+	1.10574i	0.112031	+	0.993705i	$0.464264\pi$
$444$	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
$448$	1.67165	+	3.24971i	0.0789781	+	0.153535i
$449$			7.25236i			0.342260i	0.985248	+	0.171130i	$0.0547418\pi$
$449$			7.25236i			0.342260i	−0.985248	+	0.171130i	$0.945258\pi$
$450$	−8.12700	−	18.8931i	−0.383110	−	0.890628i
$451$		−	0.252130i		−	0.0118723i
$452$	−22.9523	+	3.66558i	−1.07959	+	0.172415i
$453$	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	−0.998932	−	0.0462135i	$-0.985285\pi$
$457$	−22.3426	−	22.3426i	−1.04515	−	1.04515i	−0.0462135	−	0.998932i	$-0.514715\pi$
$458$	−13.4636	−	4.36501i	−0.629113	−	0.203964i
$459$	−0.466201			−0.0217604
$460$	−24.6865	−	6.75670i	−1.15101	−	0.315033i
$461$	0.00705621			0.000328641			0.000164320	−	1.00000i	$-0.499948\pi$
$461$	0.00705621			0.000328641			0.000164320		1.00000i	$0.499948\pi$
$462$	−0.994617	−	0.322463i	−0.0462738	−	0.0150023i
$463$	6.48079	+	6.48079i	0.301188	+	0.301188i	0.841478	−	0.540291i	$-0.181686\pi$
$463$	6.48079	+	6.48079i	0.301188	+	0.301188i	−0.540291	+	0.841478i	$0.681686\pi$
$464$	−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	0.123547	−	0.992339i	$-0.460573\pi$
$467$	24.1145	−	24.1145i	1.11589	−	1.11589i	0.992339	−	0.123547i	$-0.0394270\pi$
$468$	4.08200	+	25.5597i	0.188690	+	1.18150i
$469$		−	7.31267i		−	0.337668i
$470$	−3.79583	+	0.176092i	−0.175089	+	0.00812252i
$471$		−	40.6086i		−	1.87114i
$472$	1.29028	−	0.941257i	0.0593900	−	0.0433249i
$473$	−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
$478$	−1.37340	+	4.23617i	−0.0628179	+	0.193758i
$479$	18.5538			0.847743			0.423872	−	0.905722i	$-0.360671\pi$
$479$	18.5538			0.847743			0.423872	+	0.905722i	$0.360671\pi$
$480$	28.7424	−	10.9203i	1.31190	−	0.498440i
$481$	18.0286			0.822035
$482$	4.83551	−	14.9148i	0.220252	−	0.679352i
$483$	−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	−0.221268	+	0.975213i	$0.571020\pi$
$487$	−26.4040	+	26.4040i	−1.19648	+	1.19648i	−0.975213	+	0.221268i	$0.928980\pi$
$488$	15.6920	−	11.4473i	0.710344	−	0.518194i
$489$		−	23.6519i		−	1.06957i
$490$	−14.4658	+	15.8733i	−0.653499	+	0.717082i
$491$			29.3852i			1.32614i	0.748559	+	0.663068i	$0.230746\pi$
$491$			29.3852i			1.32614i	−0.748559	+	0.663068i	$0.769254\pi$
$492$	0.290318	+	1.81785i	0.0130886	+	0.0819550i
$493$	−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
$498$	37.3417	+	12.1065i	1.67332	+	0.542504i
$499$	−21.6258			−0.968103			−0.484051	−	0.875040i	$-0.660835\pi$
$499$	−21.6258			−0.968103			−0.484051	+	0.875040i	$0.660835\pi$
$500$	−21.1337	−	7.30523i	−0.945128	−	0.326700i
$501$	−30.7795			−1.37513
$502$	31.9488	+	10.3581i	1.42595	+	0.462303i
$503$	5.45937	+	5.45937i	0.243421	+	0.243421i	0.818264	−	0.574843i	$-0.194937\pi$
$503$	5.45937	+	5.45937i	0.243421	+	0.243421i	−0.574843	+	0.818264i	$0.694937\pi$
$504$	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
$508$	−2.79620	+	0.446565i	−0.124061	+	0.0198131i
$509$		−	10.0786i		−	0.446727i	−0.974735	−	0.223364i	$-0.928296\pi$
$509$		−	10.0786i		−	0.446727i	0.974735	−	0.223364i	$-0.0717038\pi$
$510$	10.8641	−	11.9211i	0.481070	−	0.527876i
$511$			5.53785i			0.244980i
$512$	7.11681	+	21.4791i	0.314521	+	0.949250i
$513$	−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
$518$	0.807273	−	2.48998i	0.0354695	−	0.109404i
$519$	26.4324			1.16025
$520$	23.5286	+	15.4379i	1.03180	+	0.676995i
$521$	2.30389			0.100935			0.0504677	−	0.998726i	$-0.483929\pi$
$521$	2.30389			0.100935			0.0504677	+	0.998726i	$0.483929\pi$
$522$	−2.46671	+	7.60842i	−0.107965	+	0.333012i
$523$	18.0133	+	18.0133i	0.787666	+	0.787666i	0.981111	−	0.193445i	$-0.0619662\pi$
$523$	18.0133	+	18.0133i	0.787666	+	0.787666i	−0.193445	+	0.981111i	$0.561966\pi$
$524$	−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
$528$	−5.77590	−	2.92426i	−0.251364	−	0.127262i
$529$			9.75370i			0.424074i
$530$	−32.4344	+	1.50466i	−1.40886	+	0.0653584i
$531$		−	1.64239i		−	0.0712736i
$532$	0.902182	−	0.144082i	0.0391145	−	0.00624676i
$533$	−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
$538$	1.45731	+	0.472471i	0.0628290	+	0.0203697i
$539$	4.52193			0.194773
$540$	−0.262310	+	0.958382i	−0.0112880	+	0.0412422i
$541$	8.88031			0.381795			0.190897	−	0.981610i	$-0.438860\pi$
$541$	8.88031			0.381795			0.190897	+	0.981610i	$0.438860\pi$
$542$	36.4313	+	11.8113i	1.56486	+	0.507340i
$543$	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	$-0.984901\pi$
$547$	−22.2527	+	22.2527i	−0.951457	+	0.951457i	0.0474184	+	0.998875i	$0.484901\pi$
$548$	4.92967	+	30.8675i	0.210585	+	1.31859i
$549$		−	19.9742i		−	0.852479i
$550$	1.86044	+	4.32502i	0.0793294	+	0.184420i
$551$			1.94446i			0.0828368i
$552$	−23.1893	−	31.7881i	−0.987003	−	1.35299i
$553$	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	0.995275	−	0.0970919i	$-0.0309541\pi$
$557$	21.1979	+	21.1979i	0.898183	+	0.898183i	−0.0970919	+	0.995275i	$0.530954\pi$
$558$	−10.0841	+	31.1037i	−0.426892	+	1.31672i
$559$	40.7961			1.72549
$560$	3.18571	−	2.55833i	0.134621	−	0.108109i
$561$	−3.39605			−0.143381
$562$	−10.3846	+	32.0307i	−0.438049	+	1.35113i
$563$	−7.32244	−	7.32244i	−0.308604	−	0.308604i	0.535764	−	0.844368i	$-0.320024\pi$
$563$	−7.32244	−	7.32244i	−0.308604	−	0.308604i	−0.844368	+	0.535764i	$0.820024\pi$
$564$	−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
$568$	−1.32621	−	1.81798i	−0.0556467	−	0.0762809i
$569$			4.10754i			0.172197i	0.996287	+	0.0860985i	$0.0274400\pi$
$569$			4.10754i			0.172197i	−0.996287	+	0.0860985i	$0.972560\pi$
$570$	−0.356212	−	7.67848i	−0.0149201	−	0.321616i
$571$		−	16.0964i		−	0.673612i	−0.941574	−	0.336806i	$-0.890653\pi$
$571$		−	16.0964i		−	0.673612i	0.941574	−	0.336806i	$-0.109347\pi$
$572$	−0.934455	−	5.85115i	−0.0390715	−	0.244649i
$573$	−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	0.952954	−	0.303115i	$-0.0980267\pi$
$577$	15.6097	+	15.6097i	0.649839	+	0.649839i	−0.303115	+	0.952954i	$0.598027\pi$
$578$	−16.9468	−	5.49428i	−0.704893	−	0.228532i
$579$	38.9080			1.61696
$580$	4.30753	+	7.55405i	0.178860	+	0.313665i
$581$	5.21642			0.216413
$582$	−11.7103	−	3.79657i	−0.485407	−	0.157373i
$583$	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	$-0.722139\pi$
$587$	2.99516	−	2.99516i	0.123623	−	0.123623i	0.766212	+	0.642588i	$0.222139\pi$
$588$	−32.6030	+	5.20684i	−1.34453	+	0.214727i
$589$			7.94906i			0.327536i
$590$	−1.31979	−	1.20277i	−0.0543349	−	0.0495171i
$591$		−	16.8444i		−	0.692886i
$592$	7.32076	−	14.4597i	0.300882	−	0.594291i
$593$	−12.0584	+	12.0584i	−0.495180	+	0.495180i	−0.909934	−	0.414754i	$-0.863868\pi$
$593$	−12.0584	+	12.0584i	−0.495180	+	0.495180i	0.414754	+	0.909934i	$0.363868\pi$
$594$	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
$598$	11.1065	−	34.2574i	0.454179	−	1.40089i
$599$	−12.8351			−0.524429			−0.262215	−	0.965010i	$-0.584453\pi$
$599$	−12.8351			−0.524429			−0.262215	+	0.965010i	$0.584453\pi$
$600$	−18.3939	−	29.0411i	−0.750926	−	1.18560i
$601$	−5.86790			−0.239357			−0.119678	−	0.992813i	$-0.538186\pi$
$601$	−5.86790			−0.239357			−0.119678	+	0.992813i	$0.538186\pi$
$602$	1.82674	−	5.63446i	0.0744523	−	0.229643i
$603$	−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	−0.435649	+	0.900117i	$0.643481\pi$
$607$	−32.9098	+	32.9098i	−1.33577	+	1.33577i	−0.900117	+	0.435649i	$0.856519\pi$
$608$	5.65682	−	0.0182060i	0.229415	−	0.000738352i
$609$			2.15911i			0.0874914i
$610$	−16.0509	−	14.6277i	−0.649881	−	0.592257i
$611$		−	5.34669i		−	0.216304i
$612$	12.0533	−	1.92497i	0.487227	−	0.0778123i
$613$	2.57292	−	2.57292i	0.103919	−	0.103919i	−0.653236	−	0.757155i	$-0.726589\pi$
$613$	2.57292	−	2.57292i	0.103919	−	0.103919i	0.757155	+	0.653236i	$0.226589\pi$
$614$	−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	0.816699	−	0.577064i	$-0.195802\pi$
$617$	5.95239	+	5.95239i	0.239634	+	0.239634i	−0.577064	+	0.816699i	$0.695802\pi$
$618$	−13.8994	−	4.50631i	−0.559117	−	0.181270i
$619$	12.1365			0.487805			0.243903	−	0.969800i	$-0.421572\pi$
$619$	12.1365			0.487805			0.243903	+	0.969800i	$0.421572\pi$
$620$	17.6094	+	30.8814i	0.707212	+	1.24023i
$621$	1.27157			0.0510263
$622$	−8.99798	−	2.91722i	−0.360786	−	0.116970i
$623$	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
$628$	−5.26931	−	32.9941i	−0.210268	−	1.31661i
$629$		−	8.50187i		−	0.338992i
$630$	−0.194707	−	4.19710i	−0.00775733	−	0.167217i
$631$		−	7.53890i		−	0.300119i	−0.988677	−	0.150059i	$-0.952053\pi$
$631$		−	7.53890i		−	0.300119i	0.988677	−	0.150059i	$-0.0479465\pi$
$632$	21.7283	−	15.8507i	0.864304	−	0.630507i
$633$	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
$638$	0.564682	−	1.74173i	0.0223560	−	0.0689556i
$639$	−2.31410			−0.0915442
$640$	21.9359	−	12.6022i	0.867093	−	0.498145i
$641$	−8.28659			−0.327301			−0.163650	−	0.986518i	$-0.552327\pi$
$641$	−8.28659			−0.327301			−0.163650	+	0.986518i	$0.552327\pi$
$642$	−0.913080	+	2.81634i	−0.0360364	+	0.111152i
$643$	−24.9239	−	24.9239i	−0.982903	−	0.982903i	0.0169536	−	0.999856i	$-0.494603\pi$
$643$	−24.9239	−	24.9239i	−0.982903	−	0.982903i	−0.999856	+	0.0169536i	$0.994603\pi$
$644$	−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	$-0.899575\pi$
$647$	−16.2883	+	16.2883i	−0.640358	+	0.640358i	0.310286	+	0.950643i	$0.399575\pi$
$648$	−21.1728	+	15.4455i	−0.831745	+	0.606756i
$649$			0.375977i			0.0147584i
$650$	11.6458	−	29.2281i	0.456787	−	1.14642i
$651$			8.82655i			0.345940i
$652$	−3.06903	−	19.2169i	−0.120192	−	0.752593i
$653$	35.8880	−	35.8880i	1.40441	−	1.40441i	0.619069	−	0.785337i	$-0.287510\pi$
$653$	35.8880	−	35.8880i	1.40441	−	1.40441i	0.785337	−	0.619069i	$-0.212490\pi$
$654$	−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
$658$	−0.738446	−	0.239410i	−0.0287876	−	0.00933318i
$659$	18.4068			0.717027			0.358513	−	0.933525i	$-0.383284\pi$
$659$	18.4068			0.717027			0.358513	+	0.933525i	$0.383284\pi$
$660$	−1.91080	+	6.98135i	−0.0743778	+	0.271749i
$661$	−20.1755			−0.784734			−0.392367	−	0.919809i	$-0.628344\pi$
$661$	−20.1755			−0.784734			−0.392367	+	0.919809i	$0.628344\pi$
$662$	−20.0020	−	6.48482i	−0.777400	−	0.252040i
$663$	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
$668$	−25.0081	+	3.99390i	−0.967592	+	0.154529i
$669$		−	29.9353i		−	1.15737i
$670$	−50.5680	+	2.34590i	−1.95361	+	0.0906300i
$671$			4.57252i			0.176520i
$672$	6.28128	−	0.0202158i	0.242305	−	0.000779840i
$673$	3.18320	−	3.18320i	0.122703	−	0.122703i	−0.643089	−	0.765792i	$-0.722347\pi$
$673$	3.18320	−	3.18320i	0.122703	−	0.122703i	0.765792	+	0.643089i	$0.222347\pi$
$674$	−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	0.723679	−	0.690137i	$-0.242450\pi$
$677$	0.872720	+	0.872720i	0.0335413	+	0.0335413i	−0.690137	+	0.723679i	$0.742450\pi$
$678$	−12.3209	+	38.0032i	−0.473183	+	1.45950i
$679$	−1.63586			−0.0627786
$680$	7.28012	−	11.0955i	0.279180	−	0.425494i
$681$	−19.6947			−0.754704
$682$	2.30845	−	7.12028i	0.0883952	−	0.272650i
$683$	19.5540	+	19.5540i	0.748215	+	0.748215i	0.974144	−	0.225929i	$-0.0725418\pi$
$683$	19.5540	+	19.5540i	0.748215	+	0.748215i	−0.225929	+	0.974144i	$0.572542\pi$
$684$	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
$688$	16.5658	−	32.7202i	0.631565	−	1.24745i
$689$		−	45.6862i		−	1.74050i
$690$	−29.6320	+	32.5151i	−1.12807	+	1.23783i
$691$		−	49.4492i		−	1.88113i	−0.339607	−	0.940567i	$-0.610294\pi$
$691$		−	49.4492i		−	1.88113i	0.339607	−	0.940567i	$-0.389706\pi$
$692$	21.4761	−	3.42983i	0.816399	−	0.130382i
$693$	−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
$698$	40.3524	+	13.0826i	1.52736	+	0.495183i
$699$	41.1462			1.55629
$700$	−3.51529	−	2.91719i	−0.132866	−	0.110259i
$701$	−39.1086			−1.47711			−0.738555	−	0.674193i	$-0.764492\pi$
$701$	−39.1086			−1.47711			−0.738555	+	0.674193i	$0.764492\pi$
$702$	−1.32995	−	0.431179i	−0.0501955	−	0.0162738i
$703$	−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
$708$	−0.432925	−	2.71079i	−0.0162703	−	0.101878i
$709$			20.4872i			0.769413i	0.923039	+	0.384707i	$0.125697\pi$
$709$			20.4872i			0.769413i	−0.923039	+	0.384707i	$0.874303\pi$
$710$	−1.69468	+	1.85956i	−0.0636000	+	0.0697880i
$711$		−	27.6577i		−	1.03725i
$712$	28.0589	+	38.4634i	1.05155	+	1.44148i
$713$	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
$718$	−7.92546	+	24.4456i	−0.295776	+	0.912301i
$719$	−13.8492			−0.516489			−0.258245	−	0.966080i	$-0.583144\pi$
$719$	−13.8492			−0.516489			−0.258245	+	0.966080i	$0.583144\pi$
$720$	2.82464	−	25.8615i	0.105268	−	0.963800i
$721$	−1.94167			−0.0723116
$722$	0.436150	−	1.34528i	0.0162318	−	0.0500661i
$723$	−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	$-0.662172\pi$
$727$	10.3882	−	10.3882i	0.385275	−	0.385275i	0.872998	+	0.487723i	$0.162172\pi$
$728$	3.38813	+	4.64448i	0.125572	+	0.172136i
$729$			25.3304i			0.938164i
$730$	38.2950	−	1.77654i	1.41736	−	0.0657527i
$731$		−	19.2385i		−	0.711560i
$732$	−5.26510	−	32.9678i	−0.194604	−	1.21852i
$733$	9.18018	−	9.18018i	0.339078	−	0.339078i	−0.516942	−	0.856020i	$-0.672930\pi$
$733$	9.18018	−	9.18018i	0.339078	−	0.339078i	0.856020	+	0.516942i	$0.172930\pi$
$734$	−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
$738$	1.48167	+	0.480368i	0.0545409	+	0.0176826i
$739$	−7.09627			−0.261041			−0.130520	−	0.991446i	$-0.541665\pi$
$739$	−7.09627			−0.261041			−0.130520	+	0.991446i	$0.541665\pi$
$740$	−17.4775	−	4.78361i	−0.642486	−	0.175849i
$741$	10.8157			0.397324
$742$	−6.30983	−	2.04570i	−0.231641	−	0.0751000i
$743$	−4.52085	−	4.52085i	−0.165854	−	0.165854i	0.619300	−	0.785154i	$-0.287416\pi$
$743$	−4.52085	−	4.52085i	−0.165854	−	0.165854i	−0.785154	+	0.619300i	$0.787416\pi$
$744$	−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
$748$	−2.75926	+	0.440666i	−0.100889	+	0.0161124i
$749$			0.393426i			0.0143755i
$750$	−27.6960	+	26.6474i	−1.01131	+	0.973024i
$751$			32.3004i			1.17866i	0.807894	+	0.589328i	$0.200608\pi$
$751$			32.3004i			1.17866i	−0.807894	+	0.589328i	$0.799392\pi$
$752$	−4.28827	−	2.17109i	−0.156377	−	0.0791717i
$753$	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	0.987693	−	0.156407i	$-0.0499913\pi$
$757$	22.8717	+	22.8717i	0.831285	+	0.831285i	−0.156407	+	0.987693i	$0.549991\pi$
$758$	−5.39302	+	16.6344i	−0.195883	+	0.604190i
$759$	9.26278			0.336218
$760$	−1.28577	−	6.19248i	−0.0466397	−	0.224625i
$761$	−21.6152			−0.783550			−0.391775	−	0.920061i	$-0.628139\pi$
$761$	−21.6152			−0.783550			−0.391775	+	0.920061i	$0.628139\pi$
$762$	−1.50102	+	4.62979i	−0.0543760	+	0.167720i
$763$	−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
$768$	38.4442	+	5.88619i	1.38723	+	0.212399i
$769$		−	23.8575i		−	0.860322i	−0.902752	−	0.430161i	$-0.858457\pi$
$769$		−	23.8575i		−	0.860322i	0.902752	−	0.430161i	$-0.141543\pi$
$770$	0.0445726	+	0.960805i	0.00160629	+	0.0346250i
$771$		−	29.5435i		−	1.06398i
$772$	31.6124	−	5.04864i	1.13776	−	0.181705i
$773$	−8.40856	+	8.40856i	−0.302435	+	0.302435i	−0.841966	−	0.539531i	$-0.818602\pi$
$773$	−8.40856	+	8.40856i	−0.302435	+	0.302435i	0.539531	+	0.841966i	$0.318602\pi$
$774$	−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
$778$	−49.8732	−	16.1693i	−1.78804	−	0.579697i
$779$	0.378665			0.0135671
$780$	42.0179	−	23.9598i	1.50448	−	0.857898i
$781$	0.529745			0.0189558
$782$	−16.1549	−	5.23756i	−0.577699	−	0.187295i
$783$	−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	$-0.511243\pi$
$787$	27.0454	−	27.0454i	0.964063	−	0.964063i	0.999376	+	0.0353136i	$0.0112430\pi$
$788$	−2.18570	−	13.6859i	−0.0778625	−	0.487541i
$789$		−	67.8854i		−	2.41678i
$790$	−22.2252	−	20.2545i	−0.790736	−	0.720623i
$791$			5.30882i			0.188760i
$792$	−4.42532	+	3.22826i	−0.157247	+	0.114711i
$793$	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	0.976456	+	0.215718i	$0.0692091\pi$
$797$	33.6565	+	33.6565i	1.19217	+	1.19217i	0.215718	+	0.976456i	$0.430791\pi$
$798$	0.484296	−	1.49378i	0.0171439	−	0.0528793i
$799$	−2.52137			−0.0891997
$800$	−18.7132	−	21.2089i	−0.661611	−	0.749847i
$801$	48.9597			1.72991
$802$	5.88083	−	18.1391i	0.207659	−	0.640512i
$803$	−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
$808$	−19.6549	+	14.3382i	−0.691455	+	0.504415i
$809$			16.4325i			0.577737i	0.957369	+	0.288868i	$0.0932790\pi$
$809$			16.4325i			0.577737i	−0.957369	+	0.288868i	$0.906721\pi$
$810$	21.6570	+	19.7367i	0.760949	+	0.693476i
$811$			20.9394i			0.735283i	0.929968	+	0.367641i	$0.119835\pi$
$811$			20.9394i			0.735283i	−0.929968	+	0.367641i	$0.880165\pi$
$812$	0.280162	+	1.75426i	0.00983177	+	0.0615623i
$813$	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
$818$	45.3711	+	14.7097i	1.58636	+	0.514312i
$819$	5.91191			0.206579
$820$	1.47108	−	0.838849i	0.0513723	−	0.0292939i
$821$	30.0440			1.04854			0.524272	−	0.851551i	$-0.324337\pi$
$821$	30.0440			1.04854			0.524272	+	0.851551i	$0.324337\pi$
$822$	51.1086	+	16.5698i	1.78262	+	0.577940i
$823$	10.1299	+	10.1299i	0.353106	+	0.353106i	0.861264	−	0.508158i	$-0.169673\pi$
$823$	10.1299	+	10.1299i	0.353106	+	0.353106i	−0.508158	+	0.861264i	$0.669673\pi$
$824$	−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	$-0.524925\pi$
$827$	26.4200	−	26.4200i	0.918713	−	0.918713i	0.996936	+	0.0782233i	$0.0249247\pi$
$828$	−32.8757	+	5.25039i	−1.14251	+	0.182464i
$829$			23.2743i			0.808351i	0.914682	+	0.404175i	$0.132441\pi$
$829$			23.2743i			0.808351i	−0.914682	+	0.404175i	$0.867559\pi$
$830$	−1.67342	−	36.0722i	−0.0580854	−	1.25208i
$831$			16.9136i			0.586728i
$832$	16.2826	+	31.6537i	0.564499	+	1.09739i
$833$	−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
$838$	−1.65337	+	5.09971i	−0.0571147	+	0.176167i
$839$	−52.2635			−1.80434			−0.902168	−	0.431385i	$-0.858025\pi$
$839$	−52.2635			−1.80434			−0.902168	+	0.431385i	$0.858025\pi$
$840$	−1.42770	−	6.87606i	−0.0492604	−	0.237247i
$841$	25.2191			0.869623
$842$	5.99306	−	18.4852i	0.206534	−	0.637043i
$843$	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
$848$	−36.6422	−	18.5515i	−1.25830	−	0.637060i
$849$		−	0.860379i		−	0.0295281i
$850$	−13.7832	−	5.49189i	−0.472761	−	0.188370i
$851$			23.1890i			0.794908i
$852$	−3.81945	+	0.609983i	−0.130852	+	0.0208977i
$853$	−16.0917	+	16.0917i	−0.550969	+	0.550969i	−0.926720	−	0.375752i	$-0.877385\pi$
$853$	−16.0917	+	16.0917i	−0.550969	+	0.550969i	0.375752	+	0.926720i	$0.377385\pi$
$854$	−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	0.350667	−	0.936500i	$-0.385955\pi$
$857$	−17.1500	−	17.1500i	−0.585833	−	0.585833i	−0.936500	+	0.350667i	$0.885955\pi$
$858$	−9.68801	−	3.14093i	−0.330743	−	0.107230i
$859$	−24.0866			−0.821826			−0.410913	−	0.911675i	$-0.634790\pi$
$859$	−24.0866			−0.821826			−0.410913	+	0.911675i	$0.634790\pi$
$860$	−39.5490	−	10.8246i	−1.34861	−	0.369116i
$861$	0.420465			0.0143294
$862$	−30.8162	−	9.99087i	−1.04960	−	0.340290i
$863$	−32.7301	−	32.7301i	−1.11415	−	1.11415i	−0.992584	−	0.121562i	$-0.961210\pi$
$863$	−32.7301	−	32.7301i	−1.11415	−	1.11415i	−0.121562	−	0.992584i	$-0.538790\pi$
$864$	−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
$868$	1.14532	+	7.17150i	0.0388747	+	0.243417i
$869$			6.33143i			0.214779i
$870$	14.9305	−	0.692640i	0.506191	−	0.0234827i
$871$		−	71.2286i		−	2.41349i
$872$	−21.0097	−	28.8003i	−0.711479	−	0.975301i
$873$	−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	−0.862512	−	0.506037i	$-0.831110\pi$
$877$	−40.5285	−	40.5285i	−1.36855	−	1.36855i	−0.506037	−	0.862512i	$-0.668890\pi$
$878$	5.65641	−	17.4469i	0.190895	−	0.588803i
$879$	8.85504			0.298673
$880$	−0.646620	+	5.92023i	−0.0217976	+	0.199571i
$881$	11.8098			0.397881			0.198941	−	0.980012i	$-0.436250\pi$
$881$	11.8098			0.397881			0.198941	+	0.980012i	$0.436250\pi$
$882$	−8.61537	+	26.5736i	−0.290095	+	0.894779i
$883$	0.785490	+	0.785490i	0.0264338	+	0.0264338i	0.720200	−	0.693766i	$-0.244050\pi$
$883$	0.785490	+	0.785490i	0.0264338	+	0.0264338i	−0.693766	+	0.720200i	$0.744050\pi$
$884$	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	$-0.756294\pi$
$887$	−0.832759	+	0.832759i	−0.0279613	+	0.0279613i	0.692988	+	0.720949i	$0.256294\pi$
$888$	−16.4176	−	22.5053i	−0.550938	−	0.755229i
$889$			0.646755i			0.0216915i
$890$	35.8545	−	39.3430i	1.20185	−	1.31878i
$891$		−	6.16957i		−	0.206688i
$892$	−3.88436	−	24.3222i	−0.130058	−	0.814367i
$893$	−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
$898$	9.75644	+	3.16312i	0.325577	+	0.105555i
$899$	−15.4566			−0.515508
$900$	−28.9610	+	2.69285i	−0.965368	+	0.0897618i
$901$	−21.5445			−0.717751
$902$	−0.339184	−	0.109966i	−0.0112936	−	0.00366148i
$903$	−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	$-0.697844\pi$
$907$	6.94748	−	6.94748i	0.230687	−	0.230687i	0.812980	+	0.582292i	$0.197844\pi$
$908$	−16.0018	+	2.55556i	−0.531039	+	0.0848092i
$909$			25.0185i			0.829811i
$910$	4.32945	−	4.75069i	0.143520	−	0.157484i
$911$		−	29.0624i		−	0.962880i	−0.876479	−	0.481440i	$-0.840114\pi$
$911$		−	29.0624i		−	0.962880i	0.876479	−	0.481440i	$-0.159886\pi$
$912$	4.39185	−	8.67463i	0.145429	−	0.287246i
$913$	−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
$918$	−0.203334	+	0.627170i	−0.00671101	+	0.0206997i
$919$	−54.8935			−1.81077			−0.905385	−	0.424592i	$-0.860418\pi$
$919$	−54.8935			−1.81077			−0.905385	+	0.424592i	$0.860418\pi$
$920$	−19.8566	+	30.2632i	−0.654654	+	0.997748i
$921$	−44.8199			−1.47687
$922$	0.00307757	−	0.00949257i	0.000101354	−	0.000312621i
$923$	−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
$928$	0.0354009	+	10.9995i	0.00116209	+	0.361075i
$929$		−	7.99522i		−	0.262315i	−0.991362	−	0.131157i	$-0.958131\pi$
$929$		−	7.99522i		−	0.262315i	0.991362	−	0.131157i	$-0.0418693\pi$
$930$	61.0367	−	2.83155i	2.00147	−	0.0928502i
$931$			6.79133i			0.222577i
$932$	33.4309	−	5.33907i	1.09507	−	0.174887i
$933$	−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	0.863584	−	0.504205i	$-0.168214\pi$
$937$	11.0007	+	11.0007i	0.359379	+	0.359379i	−0.504205	+	0.863584i	$0.668214\pi$
$938$	−9.83757	−	3.18942i	−0.321208	−	0.104138i
$939$	46.6064			1.52094
$940$	−1.41866	+	5.18325i	−0.0462716	+	0.169059i
$941$	−43.2923			−1.41129			−0.705644	−	0.708566i	$-0.749342\pi$
$941$	−43.2923			−1.41129			−0.705644	+	0.708566i	$0.749342\pi$
$942$	−54.6298	−	17.7114i	−1.77994	−	0.577070i
$943$	−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	$-0.961952\pi$
$947$	−26.8841	+	26.8841i	−0.873617	+	0.873617i	0.119248	+	0.992865i	$0.461952\pi$
$948$	−7.29042	−	45.6495i	−0.236782	−	1.48263i
$949$			53.9411i			1.75100i
$950$	−6.49560	+	2.79413i	−0.210745	+	0.0906536i
$951$			44.6685i			1.44848i
$952$	2.19022	−	1.59776i	0.0709855	−	0.0517837i
$953$	−10.3968	+	10.3968i	−0.336785	+	0.336785i	−0.855156	−	0.518371i	$-0.826539\pi$
$953$	−10.3968	+	10.3968i	−0.336785	+	0.336785i	0.518371	+	0.855156i	$0.326539\pi$
$954$	−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
$958$	8.09223	−	24.9600i	0.261448	−	0.806420i
$959$	7.13959			0.230549
$960$	−2.15482	−	43.4293i	−0.0695466	−	1.40168i
$961$	−32.1876			−1.03831
$962$	7.86319	−	24.2535i	0.253520	−	0.781965i
$963$	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	$-0.594225\pi$
$967$	20.6729	−	20.6729i	0.664794	−	0.664794i	0.956506	+	0.291712i	$0.0942248\pi$
$968$	−24.1223	+	17.5971i	−0.775320	+	0.565594i
$969$		−	5.10041i		−	0.163849i
$970$	0.524783	+	11.3122i	0.0168498	+	0.363213i
$971$			27.3691i			0.878317i	0.898410	+	0.439158i	$0.144723\pi$
$971$			27.3691i			0.878317i	−0.898410	+	0.439158i	$0.855277\pi$
$972$	6.89381	+	43.1660i	0.221119	+	1.38455i
$973$	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	0.673164	−	0.739493i	$-0.264935\pi$
$977$	−2.07325	−	2.07325i	−0.0663293	−	0.0663293i	−0.739493	+	0.673164i	$0.764935\pi$
$978$	−31.8183	−	10.3158i	−1.01744	−	0.329862i
$979$	−11.2079			−0.358206
$980$	15.0447	+	26.3837i	0.480586	+	0.842796i
$981$	−36.6596			−1.17045
$982$	39.5313	+	12.8164i	1.26149	+	0.408986i
$983$	−4.42510	−	4.42510i	−0.141139	−	0.141139i	0.633007	−	0.774146i	$-0.281820\pi$
$983$	−4.42510	−	4.42510i	−0.141139	−	0.141139i	−0.774146	+	0.633007i	$0.781820\pi$
$984$	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
$988$	8.78765	−	1.40343i	0.279572	−	0.0446489i
$989$			52.4732i			1.66855i
$990$	4.52652	+	4.12516i	0.143862	+	0.131106i
$991$			12.1670i			0.386497i	0.981150	+	0.193248i	$0.0619023\pi$
$991$			12.1670i			0.386497i	−0.981150	+	0.193248i	$0.938098\pi$
$992$	0.144721	+	44.9665i	0.00459489	+	1.42769i
$993$	−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	0.229714	−	0.973258i	$-0.426221\pi$
$997$	−23.4777	−	23.4777i	−0.743545	−	0.743545i	−0.973258	+	0.229714i	$0.926221\pi$
$998$	−9.43209	+	29.0927i	−0.298568	+	0.920913i
$999$	0.900246			0.0284825

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.17	✓	52	1.1	even	1	trivial
380.2.k.c.343.17	yes	52	20.3	even	4	inner
380.2.k.d.267.4	yes	52	4.3	odd	2
380.2.k.d.343.4	yes	52	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.436150 - 1.34528i) q^{2} +(-1.71881 - 1.71881i) q^{3} +(-1.61955 - 1.17349i) q^{4} +(-0.923046 + 2.03666i) q^{5} +(-3.06193 + 1.56262i) q^{6} +(-0.323011 + 0.323011i) q^{7} +(-2.28503 + 1.66692i) q^{8} +2.90860i q^{9} +O(q^{10})\)	\(q+(0.436150 - 1.34528i) 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} +(-2.28503 + 1.66692i) q^{8} +2.90860i q^{9} +(2.33729 + 2.13004i) q^{10} -0.665839i q^{11} +(0.766690 + 4.80068i) 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} +(3.91287 + 1.26858i) q^{18} +1.00000 q^{19} +(3.88491 - 2.21528i) q^{20} +1.11039 q^{21} +(-0.895738 - 0.290406i) 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} +(0.902182 - 0.144082i) q^{28} +1.94446i q^{29} +(-0.356212 - 7.67848i) q^{30} +7.94906i q^{31} +(5.65682 - 0.0182060i) 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} +(0.436150 - 1.34528i) q^{38} +10.8157 q^{39} +(-1.28577 - 6.19248i) q^{40} +0.378665 q^{41} +(0.484296 - 1.49378i) 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} +(4.39185 - 8.67463i) q^{48} +6.79133i q^{49} +(-6.49560 + 2.79413i) q^{50} -5.10041i q^{51} +(8.78765 - 1.40343i) 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} +(2.61584 + 0.848077i) q^{58} -0.564667 q^{59} +(-10.4851 - 2.86977i) q^{60} -6.86731 q^{61} +(10.6937 + 3.46699i) 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} +(-0.661821 - 4.14404i) q^{68} +13.9114i q^{69} +(-1.44300 + 0.0669421i) q^{70} +0.795606i q^{71} +(-4.84841 - 6.64623i) 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} +(4.71726 - 14.5501i) q^{78} -9.50896 q^{79} +(-8.89139 - 0.971137i) q^{80} +9.26586 q^{81} +(0.165155 - 0.509409i) 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} +(1.10990 + 1.52146i) q^{88} -16.8328i q^{89} +(-6.19544 + 6.79822i) q^{90} -2.03257i q^{91} +(1.80513 + 11.3029i) 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} +(9.13622 + 2.96204i) 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	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more