LMFDB - Embedded newform 380.2.k.d.267.4

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			267.4
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.4

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	0.999971	−	0.00761727i	$-0.00242468\pi$
$3$	1.71881	+	1.71881i	0.992354	+	0.992354i	−0.00761727	+	0.999971i	$0.502425\pi$
$4$	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	−0.643424	−	0.765510i	$-0.722487\pi$
$7$	0.323011	−	0.323011i	0.122087	−	0.122087i	0.765510	+	0.643424i	$0.222487\pi$
$8$	−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	$0.0320055\pi$
$11$			0.665839i			0.200758i	−0.994949	+	0.100379i	$0.967994\pi$
$12$	4.80068	+	0.766690i	1.38584	+	0.221324i
$13$	−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	$0.668104\pi$
$18$	−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	0.989354	−	0.145531i	$-0.0464890\pi$
$23$	4.04683	+	4.04683i	0.843823	+	0.843823i	−0.145531	+	0.989354i	$0.546489\pi$
$24$	−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	$0.0577841\pi$
$29$			1.94446i			0.361077i	−0.983568	+	0.180539i	$0.942216\pi$
$30$	6.00882	−	4.79375i	1.09706	−	0.875215i
$31$		−	7.94906i		−	1.42769i	−0.700302	−	0.713847i	$-0.746951\pi$
$31$		−	7.94906i		−	1.42769i	0.700302	−	0.713847i	$-0.253049\pi$
$32$	−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	0.431228	−	0.902243i	$-0.358081\pi$
$37$	−2.86508	−	2.86508i	−0.471016	−	0.471016i	−0.902243	+	0.431228i	$0.858081\pi$
$38$	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	0.999937	−	0.0112515i	$-0.00358153\pi$
$43$	6.48324	+	6.48324i	0.988685	+	0.988685i	−0.0112515	+	0.999937i	$0.503582\pi$
$44$	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	−0.642416	−	0.766356i	$-0.722068\pi$
$47$	0.849686	−	0.849686i	0.123939	−	0.123939i	0.766356	+	0.642416i	$0.222068\pi$
$48$	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	−0.999996	−	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
$58$	−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	0.543472	−	0.839428i	$-0.317110\pi$
$67$	11.3195	−	11.3195i	1.38290	−	1.38290i	0.839428	−	0.543472i	$-0.182890\pi$
$68$	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	$-0.984967\pi$
$71$		−	0.795606i		−	0.0944210i	0.998885	−	0.0472105i	$-0.0150332\pi$
$72$	−6.64623	−	4.84841i	−0.783266	−	0.571390i
$73$	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
$78$	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	0.994166	−	0.107857i	$-0.0343989\pi$
$83$	8.07466	+	8.07466i	0.886309	+	0.886309i	−0.107857	+	0.994166i	$0.534399\pi$
$84$	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	$-0.649207\pi$
$89$		−	16.8328i		−	1.78427i	0.451769	−	0.892135i	$-0.350793\pi$
$90$	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	0.823876	−	0.566770i	$-0.191807\pi$
$97$	2.53220	+	2.53220i	0.257106	+	0.257106i	−0.566770	+	0.823876i	$0.691807\pi$
$98$	−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	0.543355	−	0.839503i	$-0.317154\pi$
$103$	−3.00558	−	3.00558i	−0.296148	−	0.296148i	−0.839503	+	0.543355i	$0.817154\pi$
$104$	−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	−0.735931	−	0.677057i	$-0.763255\pi$
$107$	−0.608998	+	0.608998i	−0.0588740	+	0.0588740i	0.677057	+	0.735931i	$0.263255\pi$
$108$	0.0700790	−	0.438804i	0.00674335	−	0.0422240i
$109$			12.6039i			1.20723i	0.797274	+	0.603617i	$0.206274\pi$
$109$			12.6039i			1.20723i	−0.797274	+	0.603617i	$0.793726\pi$
$110$	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	−0.205583	−	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
$118$	−0.759634	+	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	−0.750128	−	0.661292i	$-0.770008\pi$
$127$	−1.00113	+	1.00113i	−0.0888362	+	0.0888362i	0.661292	+	0.750128i	$0.270008\pi$
$128$	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	$0.147877\pi$
$131$			10.2560i			0.896075i	−0.894015	+	0.448037i	$0.852123\pi$
$132$	−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	0.0543216	−	0.998523i	$-0.482700\pi$
$137$	−11.0516	−	11.0516i	−0.944202	−	0.944202i	−0.998523	+	0.0543216i	$0.982700\pi$
$138$	−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	$-0.638045\pi$
$149$		−	22.1531i		−	1.81485i	0.420215	−	0.907425i	$-0.361955\pi$
$150$	4.21681	+	16.6628i	0.344301	+	1.36051i
$151$		−	0.248045i		−	0.0201856i	−0.999949	−	0.0100928i	$-0.996787\pi$
$151$		−	0.248045i		−	0.0201856i	0.999949	−	0.0100928i	$-0.00321269\pi$
$152$	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	0.998449	−	0.0556683i	$-0.0177289\pi$
$157$	11.8130	+	11.8130i	0.942781	+	0.942781i	−0.0556683	+	0.998449i	$0.517729\pi$
$158$	−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	0.384301	−	0.923208i	$-0.374443\pi$
$163$	−6.88031	−	6.88031i	−0.538908	−	0.538908i	−0.923208	+	0.384301i	$0.874443\pi$
$164$	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	−0.962860	−	0.269999i	$-0.912976\pi$
$167$	−8.95374	+	8.95374i	−0.692861	+	0.692861i	0.269999	+	0.962860i	$0.412976\pi$
$168$	−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	−0.936163	−	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
$178$	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	$0.0587812\pi$
$191$			5.07533i			0.367238i	−0.982997	+	0.183619i	$0.941219\pi$
$192$	8.89519	−	17.2924i	0.641955	−	1.24797i
$193$	−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	$0.670601\pi$
$198$	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	$-0.794186\pi$
$211$		−	17.5026i		−	1.20493i	0.798147	−	0.602463i	$-0.205814\pi$
$212$	−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	0.352624	−	0.935765i	$-0.385290\pi$
$223$	−8.70816	−	8.70816i	−0.583142	−	0.583142i	−0.935765	+	0.352624i	$0.885290\pi$
$224$	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	−0.871196	−	0.490936i	$-0.836655\pi$
$227$	−5.72919	+	5.72919i	−0.380260	+	0.380260i	0.490936	+	0.871196i	$0.336655\pi$
$228$	−4.80068	−	0.766690i	−0.317933	−	0.0507753i
$229$		−	10.0081i		−	0.661351i	−0.943745	−	0.330675i	$-0.892723\pi$
$229$		−	10.0081i		−	0.661351i	0.943745	−	0.330675i	$-0.107277\pi$
$230$	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	−0.980527	−	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
$238$	−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	$-0.730291\pi$
$251$		−	23.7489i		−	1.49901i	0.661996	−	0.749507i	$-0.269709\pi$
$252$	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	0.922379	−	0.386287i	$-0.126243\pi$
$257$	8.59420	+	8.59420i	0.536091	+	0.536091i	−0.386287	+	0.922379i	$0.626243\pi$
$258$	−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	−0.968435	−	0.249268i	$-0.919810\pi$
$263$	−19.7478	−	19.7478i	−1.21770	−	1.21770i	−0.249268	−	0.968435i	$-0.580190\pi$
$264$	−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	$0.0105139\pi$
$269$			1.08328i			0.0660485i	−0.999455	+	0.0330243i	$0.989486\pi$
$270$	−0.438170	−	0.549234i	−0.0266662	−	0.0334253i
$271$		−	27.0809i		−	1.64505i	−0.568732	−	0.822523i	$-0.692566\pi$
$271$		−	27.0809i		−	1.64505i	0.568732	−	0.822523i	$-0.307434\pi$
$272$	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	0.543673	−	0.839297i	$-0.317033\pi$
$277$	−4.92017	−	4.92017i	−0.295624	−	0.295624i	−0.839297	+	0.543673i	$0.817033\pi$
$278$	−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	0.699629	−	0.714507i	$-0.253349\pi$
$283$	−0.250284	−	0.250284i	−0.0148778	−	0.0148778i	−0.714507	+	0.699629i	$0.753349\pi$
$284$	−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	−0.778336	−	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
$298$	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	−0.973369	−	0.229246i	$-0.926374\pi$
$307$	−13.0381	+	13.0381i	−0.744123	+	0.744123i	0.229246	+	0.973369i	$0.426374\pi$
$308$	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	$0.0607311\pi$
$311$			6.68856i			0.379274i	−0.981854	+	0.189637i	$0.939269\pi$
$312$	18.0289	−	24.7142i	1.02069	−	1.39916i
$313$	−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	$0.922602\pi$
$318$	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	$0.133989\pi$
$331$			14.8683i			0.817236i	−0.912705	+	0.408618i	$0.866011\pi$
$332$	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	0.0479886	−	0.998848i	$-0.484719\pi$
$337$	−17.4555	−	17.4555i	−0.950859	−	0.950859i	−0.998848	+	0.0479886i	$0.984719\pi$
$338$	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	−0.110855	−	0.993837i	$-0.535359\pi$
$347$	16.4481	−	16.4481i	0.882982	−	0.882982i	0.993837	+	0.110855i	$0.0353588\pi$
$348$	−1.49080	+	9.33474i	−0.0799152	+	0.500395i
$349$			29.9956i			1.60563i	0.596229	+	0.802814i	$0.296665\pi$
$349$			29.9956i			1.60563i	−0.596229	+	0.802814i	$0.703335\pi$
$350$	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	−0.276879	+	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
$358$	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	−0.0410456	+	0.999157i	$0.513069\pi$
$367$	−19.9274	+	19.9274i	−1.04020	+	1.04020i	−0.999157	+	0.0410456i	$0.986931\pi$
$368$	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	0.422279	−	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
$378$	0.0442669	+	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	0.129973	−	0.991518i	$-0.458511\pi$
$383$	−16.8608	−	16.8608i	−0.861545	−	0.861545i	−0.991518	+	0.129973i	$0.958511\pi$
$384$	−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	$-0.610981\pi$
$389$		−	37.0728i		−	1.87966i	0.341637	−	0.939832i	$-0.389019\pi$
$390$	−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	0.670290	−	0.742099i	$-0.266170\pi$
$397$	−1.43078	−	1.43078i	−0.0718089	−	0.0718089i	−0.742099	+	0.670290i	$0.766170\pi$
$398$	−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	$0.313854\pi$
$409$			33.7262i			1.66765i	−0.552027	+	0.833826i	$0.686146\pi$
$410$	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	$0.186019\pi$
$431$			22.9069i			1.10339i	−0.834046	+	0.551694i	$0.813981\pi$
$432$	−0.401435	−	0.792901i	−0.0193140	−	0.0381485i
$433$	−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
$438$	−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	−0.993705	−	0.112031i	$-0.964264\pi$
$443$	−23.2730	−	23.2730i	−1.10574	−	1.10574i	−0.112031	−	0.993705i	$-0.535736\pi$
$444$	−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	$0.0547418\pi$
$449$			7.25236i			0.342260i	−0.985248	+	0.171130i	$0.945258\pi$
$450$	−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	−0.998932	−	0.0462135i	$-0.985285\pi$
$457$	−22.3426	−	22.3426i	−1.04515	−	1.04515i	−0.0462135	−	0.998932i	$-0.514715\pi$
$458$	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	0.540291	−	0.841478i	$-0.318314\pi$
$463$	−6.48079	−	6.48079i	−0.301188	−	0.301188i	−0.841478	+	0.540291i	$0.818314\pi$
$464$	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	$0.539427\pi$
$467$	−24.1145	+	24.1145i	−1.11589	+	1.11589i	−0.992339	+	0.123547i	$0.960573\pi$
$468$	−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	0.221268	−	0.975213i	$-0.428980\pi$
$487$	26.4040	−	26.4040i	1.19648	−	1.19648i	0.975213	−	0.221268i	$-0.0710197\pi$
$488$	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	$-0.769254\pi$
$491$		−	29.3852i		−	1.32614i	0.748559	−	0.663068i	$-0.230746\pi$
$492$	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	0.574843	−	0.818264i	$-0.305063\pi$
$503$	−5.45937	−	5.45937i	−0.243421	−	0.243421i	−0.818264	+	0.574843i	$0.805063\pi$
$504$	−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	$-0.928296\pi$
$509$		−	10.0786i		−	0.446727i	0.974735	−	0.223364i	$-0.0717038\pi$
$510$	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	0.193445	−	0.981111i	$-0.438034\pi$
$523$	−18.0133	−	18.0133i	−0.787666	−	0.787666i	−0.981111	+	0.193445i	$0.938034\pi$
$524$	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	−0.0474184	−	0.998875i	$-0.515099\pi$
$547$	22.2527	−	22.2527i	0.951457	−	0.951457i	0.998875	+	0.0474184i	$0.0150994\pi$
$548$	−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	0.995275	−	0.0970919i	$-0.0309541\pi$
$557$	21.1979	+	21.1979i	0.898183	+	0.898183i	−0.0970919	+	0.995275i	$0.530954\pi$
$558$	−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	0.844368	−	0.535764i	$-0.179976\pi$
$563$	7.32244	+	7.32244i	0.308604	+	0.308604i	−0.535764	+	0.844368i	$0.679976\pi$
$564$	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	$0.0274400\pi$
$569$			4.10754i			0.172197i	−0.996287	+	0.0860985i	$0.972560\pi$
$570$	−6.00882	+	4.79375i	−0.251682	+	0.200788i
$571$			16.0964i			0.673612i	0.941574	+	0.336806i	$0.109347\pi$
$571$			16.0964i			0.673612i	−0.941574	+	0.336806i	$0.890653\pi$
$572$	−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	0.952954	−	0.303115i	$-0.0980267\pi$
$577$	15.6097	+	15.6097i	0.649839	+	0.649839i	−0.303115	+	0.952954i	$0.598027\pi$
$578$	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	−0.766212	−	0.642588i	$-0.777861\pi$
$587$	−2.99516	+	2.99516i	−0.123623	+	0.123623i	0.642588	+	0.766212i	$0.277861\pi$
$588$	−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	−0.909934	−	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
$598$	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	0.435649	−	0.900117i	$-0.356519\pi$
$607$	32.9098	−	32.9098i	1.33577	−	1.33577i	0.900117	−	0.435649i	$-0.143481\pi$
$608$	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	−0.653236	−	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	$0.695802\pi$
$618$	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	$0.0479465\pi$
$631$			7.53890i			0.300119i	−0.988677	+	0.150059i	$0.952053\pi$
$632$	−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	0.999856	−	0.0169536i	$-0.00539676\pi$
$643$	24.9239	+	24.9239i	0.982903	+	0.982903i	−0.0169536	+	0.999856i	$0.505397\pi$
$644$	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	−0.310286	−	0.950643i	$-0.600425\pi$
$647$	16.2883	−	16.2883i	0.640358	−	0.640358i	0.950643	+	0.310286i	$0.100425\pi$
$648$	−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	0.619069	−	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
$658$	0.239410	+	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	−0.643089	−	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	$0.742450\pi$
$678$	−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	0.225929	−	0.974144i	$-0.427458\pi$
$683$	−19.5540	−	19.5540i	−0.748215	−	0.748215i	−0.974144	+	0.225929i	$0.927458\pi$
$684$	−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	$0.389706\pi$
$691$			49.4492i			1.88113i	−0.339607	+	0.940567i	$0.610294\pi$
$692$	−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	$0.125697\pi$
$709$			20.4872i			0.769413i	−0.923039	+	0.384707i	$0.874303\pi$
$710$	−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	−0.872998	−	0.487723i	$-0.837828\pi$
$727$	−10.3882	+	10.3882i	−0.385275	+	0.385275i	0.487723	+	0.872998i	$0.337828\pi$
$728$	−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	−0.516942	−	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
$738$	−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	0.785154	−	0.619300i	$-0.212584\pi$
$743$	4.52085	+	4.52085i	0.165854	+	0.165854i	−0.619300	+	0.785154i	$0.712584\pi$
$744$	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	$-0.799392\pi$
$751$		−	32.3004i		−	1.17866i	0.807894	−	0.589328i	$-0.200608\pi$
$752$	−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	0.987693	−	0.156407i	$-0.0499913\pi$
$757$	22.8717	+	22.8717i	0.831285	+	0.831285i	−0.156407	+	0.987693i	$0.549991\pi$
$758$	−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	$-0.858457\pi$
$769$		−	23.8575i		−	0.860322i	0.902752	−	0.430161i	$-0.141543\pi$
$770$	0.751881	−	0.599839i	0.0270959	−	0.0216167i
$771$			29.5435i

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

Introduction

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