LMFDB - Embedded newform 403.2.k.e.287.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.6
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.285917 + 0.879963i) q^{2} +(-0.982047 - 3.02243i) q^{3} +(0.925448 + 0.672377i) q^{4} -3.20777 q^{5} +2.94041 q^{6} +(3.53175 + 2.56597i) q^{7} +(-2.35335 + 1.70981i) q^{8} +(-5.74362 + 4.17298i) q^{9} +O(q^{10})$	\(q+(-0.285917 + 0.879963i) q^{2} +(-0.982047 - 3.02243i) q^{3} +(0.925448 + 0.672377i) q^{4} -3.20777 q^{5} +2.94041 q^{6} +(3.53175 + 2.56597i) q^{7} +(-2.35335 + 1.70981i) q^{8} +(-5.74362 + 4.17298i) q^{9} +(0.917156 - 2.82271i) q^{10} +(2.91008 + 2.11430i) q^{11} +(1.12338 - 3.45741i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-3.26775 + 2.37416i) q^{14} +(3.15018 + 9.69525i) q^{15} +(-0.124726 - 0.383868i) q^{16} +(6.01051 - 4.36689i) q^{17} +(-2.02987 - 6.24730i) q^{18} +(-0.151293 + 0.465631i) q^{19} +(-2.96862 - 2.15683i) q^{20} +(4.28711 - 13.1944i) q^{21} +(-2.69255 + 1.95625i) q^{22} +(0.998169 - 0.725212i) q^{23} +(7.47888 + 5.43373i) q^{24} +5.28976 q^{25} -0.925248 q^{26} +(10.5400 + 7.65773i) q^{27} +(1.54315 + 4.74934i) q^{28} +(-0.157079 + 0.483439i) q^{29} -9.43215 q^{30} +(3.23500 + 4.53153i) q^{31} -5.44435 q^{32} +(3.53249 - 10.8719i) q^{33} +(2.12419 + 6.53759i) q^{34} +(-11.3290 - 8.23102i) q^{35} -8.12124 q^{36} +3.70182 q^{37} +(-0.366481 - 0.266264i) q^{38} +(2.57103 - 1.86796i) q^{39} +(7.54900 - 5.48467i) q^{40} +(-1.14497 + 3.52387i) q^{41} +(10.3848 + 7.54500i) q^{42} +(0.114848 - 0.353467i) q^{43} +(1.27152 + 3.91335i) q^{44} +(18.4242 - 13.3860i) q^{45} +(0.352766 + 1.08570i) q^{46} +(2.17893 + 6.70605i) q^{47} +(-1.03773 + 0.753952i) q^{48} +(3.72596 + 11.4673i) q^{49} +(-1.51243 + 4.65479i) q^{50} +(-19.1012 - 13.8778i) q^{51} +(-0.353490 + 1.08793i) q^{52} +(-8.10271 + 5.88696i) q^{53} +(-9.75207 + 7.08530i) q^{54} +(-9.33487 - 6.78218i) q^{55} -12.6988 q^{56} +1.55591 q^{57} +(-0.380496 - 0.276447i) q^{58} +(-0.125995 - 0.387773i) q^{59} +(-3.60354 + 11.0906i) q^{60} -4.19075 q^{61} +(-4.91252 + 1.55104i) q^{62} -30.9928 q^{63} +(1.80609 - 5.55856i) q^{64} +(-0.991254 - 3.05077i) q^{65} +(8.55685 + 6.21691i) q^{66} +5.80795 q^{67} +8.49861 q^{68} +(-3.17215 - 2.30470i) q^{69} +(10.4822 - 7.61574i) q^{70} +(-7.90103 + 5.74044i) q^{71} +(6.38174 - 19.6410i) q^{72} +(4.57861 + 3.32655i) q^{73} +(-1.05842 + 3.25747i) q^{74} +(-5.19479 - 15.9879i) q^{75} +(-0.453093 + 0.329192i) q^{76} +(4.85247 + 14.9344i) q^{77} +(0.908637 + 2.79650i) q^{78} +(2.70104 - 1.96242i) q^{79} +(0.400092 + 1.23136i) q^{80} +(6.21261 - 19.1205i) q^{81} +(-2.77351 - 2.01507i) q^{82} +(4.93941 - 15.2019i) q^{83} +(12.8391 - 9.32815i) q^{84} +(-19.2803 + 14.0080i) q^{85} +(0.278201 + 0.202125i) q^{86} +1.61542 q^{87} -10.4635 q^{88} +(-2.54472 - 1.84885i) q^{89} +(6.51135 + 20.0399i) q^{90} +(-1.34901 + 4.15182i) q^{91} +1.41137 q^{92} +(10.5193 - 14.2277i) q^{93} -6.52407 q^{94} +(0.485312 - 1.49364i) q^{95} +(5.34661 + 16.4552i) q^{96} +(2.48437 + 1.80500i) q^{97} -11.1561 q^{98} -25.5374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.285917	+	0.879963i	−0.202174	+	0.622228i	0.797644	+	0.603129i	$0.206080\pi$
$2$	−0.285917	+	0.879963i	−0.202174	+	0.622228i	−0.999818	+	0.0190986i	$0.993920\pi$
$3$	−0.982047	−	3.02243i	−0.566985	−	1.74500i	−0.661978	−	0.749523i	$-0.730283\pi$
$3$	−0.982047	−	3.02243i	−0.566985	−	1.74500i	0.0949929	−	0.995478i	$-0.469717\pi$
$4$	0.925448	+	0.672377i	0.462724	+	0.336189i
$5$	−3.20777			−1.43456			−0.717278	−	0.696787i	$-0.754612\pi$
$5$	−3.20777			−1.43456			−0.717278	+	0.696787i	$0.754612\pi$
$6$	2.94041			1.20042
$7$	3.53175	+	2.56597i	1.33488	+	0.969845i	0.999616	+	0.0277194i	$0.00882448\pi$
$7$	3.53175	+	2.56597i	1.33488	+	0.969845i	0.335261	+	0.942125i	$0.391176\pi$
$8$	−2.35335	+	1.70981i	−0.832035	+	0.604509i
$9$	−5.74362	+	4.17298i	−1.91454	+	1.39099i
$10$	0.917156	−	2.82271i	0.290030	−	0.892621i
$11$	2.91008	+	2.11430i	0.877424	+	0.637486i	0.932569	−	0.360993i	$-0.117562\pi$
$11$	2.91008	+	2.11430i	0.877424	+	0.637486i	−0.0551451	+	0.998478i	$0.517562\pi$
$12$	1.12338	−	3.45741i	0.324292	−	0.998068i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−3.26775	+	2.37416i	−0.873342	+	0.634520i
$15$	3.15018	+	9.69525i	0.813372	+	2.50330i
$16$	−0.124726	−	0.383868i	−0.0311815	−	0.0959669i
$17$	6.01051	−	4.36689i	1.45776	−	1.05913i	0.473823	−	0.880620i	$-0.342874\pi$
$17$	6.01051	−	4.36689i	1.45776	−	1.05913i	0.983939	−	0.178506i	$-0.0571263\pi$
$18$	−2.02987	−	6.24730i	−0.478445	−	1.47250i
$19$	−0.151293	+	0.465631i	−0.0347089	+	0.106823i	−0.966910	−	0.255118i	$-0.917886\pi$
$19$	−0.151293	+	0.465631i	−0.0347089	+	0.106823i	0.932201	+	0.361941i	$0.117886\pi$
$20$	−2.96862	−	2.15683i	−0.663803	−	0.482281i
$21$	4.28711	−	13.1944i	0.935525	−	2.87925i
$22$	−2.69255	+	1.95625i	−0.574053	+	0.417074i
$23$	0.998169	−	0.725212i	0.208133	−	0.151217i	−0.478836	−	0.877904i	$-0.658941\pi$
$23$	0.998169	−	0.725212i	0.208133	−	0.151217i	0.686968	+	0.726687i	$0.258941\pi$
$24$	7.47888	+	5.43373i	1.52662	+	1.10915i
$25$	5.28976			1.05795
$26$	−0.925248			−0.181456
$27$	10.5400	+	7.65773i	2.02842	+	1.47373i
$28$	1.54315	+	4.74934i	0.291629	+	0.897541i
$29$	−0.157079	+	0.483439i	−0.0291688	+	0.0897723i	−0.964581	−	0.263786i	$-0.915029\pi$
$29$	−0.157079	+	0.483439i	−0.0291688	+	0.0897723i	0.935412	+	0.353559i	$0.115029\pi$
$30$	−9.43215			−1.72207
$31$	3.23500	+	4.53153i	0.581023	+	0.813887i
$31$	3.23500	+	4.53153i	0.581023	+	0.813887i
$32$	−5.44435			−0.962435
$33$	3.53249	−	10.8719i	0.614927	−	1.89255i
$34$	2.12419	+	6.53759i	0.364296	+	1.12119i
$35$	−11.3290	−	8.23102i	−1.91496	−	1.39130i
$36$	−8.12124			−1.35354
$37$	3.70182			0.608576			0.304288	−	0.952580i	$-0.401581\pi$
$37$	3.70182			0.608576			0.304288	+	0.952580i	$0.401581\pi$
$38$	−0.366481	−	0.266264i	−0.0594511	−	0.0431937i
$39$	2.57103	−	1.86796i	0.411695	−	0.299114i
$40$	7.54900	−	5.48467i	1.19360	−	0.867202i
$41$	−1.14497	+	3.52387i	−0.178815	+	0.550336i	−0.999787	−	0.0206322i	$-0.993432\pi$
$41$	−1.14497	+	3.52387i	−0.178815	+	0.550336i	0.820972	+	0.570968i	$0.193432\pi$
$42$	10.3848	+	7.54500i	1.60241	+	1.16422i
$43$	0.114848	−	0.353467i	0.0175142	−	0.0539032i	−0.941917	−	0.335844i	$-0.890978\pi$
$43$	0.114848	−	0.353467i	0.0175142	−	0.0539032i	0.959432	+	0.281941i	$0.0909783\pi$
$44$	1.27152	+	3.91335i	0.191689	+	0.589960i
$45$	18.4242	−	13.3860i	2.74651	−	1.99546i
$46$	0.352766	+	1.08570i	0.0520125	+	0.160078i
$47$	2.17893	+	6.70605i	0.317829	+	0.978178i	0.974574	+	0.224065i	$0.0719328\pi$
$47$	2.17893	+	6.70605i	0.317829	+	0.978178i	−0.656745	+	0.754113i	$0.728067\pi$
$48$	−1.03773	+	0.753952i	−0.149783	+	0.108824i
$49$	3.72596	+	11.4673i	0.532280	+	1.63819i
$50$	−1.51243	+	4.65479i	−0.213890	+	0.658287i
$51$	−19.1012	−	13.8778i	−2.67471	−	1.94329i
$52$	−0.353490	+	1.08793i	−0.0490202	+	0.150869i
$53$	−8.10271	+	5.88696i	−1.11299	+	0.808637i	−0.983132	−	0.182896i	$-0.941453\pi$
$53$	−8.10271	+	5.88696i	−1.11299	+	0.808637i	−0.129861	+	0.991532i	$0.541453\pi$
$54$	−9.75207	+	7.08530i	−1.32709	+	0.964187i
$55$	−9.33487	−	6.78218i	−1.25871	−	0.914509i
$56$	−12.6988			−1.69694
$57$	1.55591			0.206086
$58$	−0.380496	−	0.276447i	−0.0499616	−	0.0362993i
$59$	−0.125995	−	0.387773i	−0.0164032	−	0.0504838i	0.942520	−	0.334150i	$-0.108449\pi$
$59$	−0.125995	−	0.387773i	−0.0164032	−	0.0504838i	−0.958923	+	0.283666i	$0.908449\pi$
$60$	−3.60354	+	11.0906i	−0.465215	+	1.43178i
$61$	−4.19075			−0.536571			−0.268285	−	0.963339i	$-0.586457\pi$
$61$	−4.19075			−0.536571			−0.268285	+	0.963339i	$0.586457\pi$
$62$	−4.91252	+	1.55104i	−0.623891	+	0.196982i
$63$	−30.9928			−3.90472
$64$	1.80609	−	5.55856i	0.225761	−	0.694821i
$65$	−0.991254	−	3.05077i	−0.122950	−	0.378401i
$66$	8.55685	+	6.21691i	1.05327	+	0.765249i
$67$	5.80795			0.709554			0.354777	−	0.934951i	$-0.384557\pi$
$67$	5.80795			0.709554			0.354777	+	0.934951i	$0.384557\pi$
$68$	8.49861			1.03061
$69$	−3.17215	−	2.30470i	−0.381882	−	0.277454i
$70$	10.4822	−	7.61574i	1.25286	−	0.910255i
$71$	−7.90103	+	5.74044i	−0.937680	+	0.681265i	−0.947861	−	0.318684i	$-0.896759\pi$
$71$	−7.90103	+	5.74044i	−0.937680	+	0.681265i	0.0101810	+	0.999948i	$0.496759\pi$
$72$	6.38174	−	19.6410i	0.752096	−	2.31471i
$73$	4.57861	+	3.32655i	0.535885	+	0.389343i	0.822555	−	0.568686i	$-0.192548\pi$
$73$	4.57861	+	3.32655i	0.535885	+	0.389343i	−0.286669	+	0.958030i	$0.592548\pi$
$74$	−1.05842	+	3.25747i	−0.123038	+	0.378673i
$75$	−5.19479	−	15.9879i	−0.599843	−	1.84613i
$76$	−0.453093	+	0.329192i	−0.0519734	+	0.0377609i
$77$	4.85247	+	14.9344i	0.552990	+	1.70193i
$78$	0.908637	+	2.79650i	0.102883	+	0.316641i
$79$	2.70104	−	1.96242i	0.303891	−	0.220790i	−0.425380	−	0.905015i	$-0.639859\pi$
$79$	2.70104	−	1.96242i	0.303891	−	0.220790i	0.729271	+	0.684225i	$0.239859\pi$
$80$	0.400092	+	1.23136i	0.0447317	+	0.137670i
$81$	6.21261	−	19.1205i	0.690290	−	2.12450i
$82$	−2.77351	−	2.01507i	−0.306283	−	0.222527i
$83$	4.93941	−	15.2019i	0.542170	−	1.66863i	−0.185454	−	0.982653i	$-0.559375\pi$
$83$	4.93941	−	15.2019i	0.542170	−	1.66863i	0.727624	−	0.685976i	$-0.240625\pi$
$84$	12.8391	−	9.32815i	1.40086	−	1.01778i
$85$	−19.2803	+	14.0080i	−2.09124	+	1.51938i
$86$	0.278201	+	0.202125i	0.0299991	+	0.0217957i
$87$	1.61542			0.173191
$88$	−10.4635			−1.11541
$89$	−2.54472	−	1.84885i	−0.269740	−	0.195978i	0.444690	−	0.895685i	$-0.353314\pi$
$89$	−2.54472	−	1.84885i	−0.269740	−	0.195978i	−0.714430	+	0.699707i	$0.753314\pi$
$90$	6.51135	+	20.0399i	0.686357	+	2.11239i
$91$	−1.34901	+	4.15182i	−0.141415	+	0.435229i
$92$	1.41137			0.147145
$93$	10.5193	−	14.2277i	1.09080	−	1.47535i
$94$	−6.52407			−0.672906
$95$	0.485312	−	1.49364i	0.0497919	−	0.153244i
$96$	5.34661	+	16.4552i	0.545686	+	1.67945i
$97$	2.48437	+	1.80500i	0.252249	+	0.183270i	0.706723	−	0.707490i	$-0.250173\pi$
$97$	2.48437	+	1.80500i	0.252249	+	0.183270i	−0.454474	+	0.890760i	$0.650173\pi$
$98$	−11.1561			−1.12694
$99$	−25.5374			−2.56660
$100$	4.89540	+	3.55671i	0.489540	+	0.355671i
$101$	9.34420	−	6.78896i	0.929782	−	0.675527i	−0.0161571	−	0.999869i	$-0.505143\pi$
$101$	9.34420	−	6.78896i	0.929782	−	0.675527i	0.945940	+	0.324343i	$0.105143\pi$
$102$	17.6734	−	12.8404i	1.74992	−	1.27139i
$103$	−0.348418	+	1.07232i	−0.0343306	+	0.105659i	−0.966753	−	0.255710i	$-0.917691\pi$
$103$	−0.348418	+	1.07232i	−0.0343306	+	0.105659i	0.932423	+	0.361369i	$0.117691\pi$
$104$	−2.35335	−	1.70981i	−0.230765	−	0.167661i
$105$	−13.7521	+	42.3245i	−1.34206	+	4.13044i
$106$	−2.86360	−	8.81327i	−0.278138	−	0.856020i
$107$	−0.650560	+	0.472660i	−0.0628920	+	0.0456937i	−0.618787	−	0.785559i	$-0.712376\pi$
$107$	−0.650560	+	0.472660i	−0.0628920	+	0.0456937i	0.555895	+	0.831252i	$0.312376\pi$
$108$	4.60530	+	14.1737i	0.443145	+	1.36386i
$109$	−4.64790	−	14.3048i	−0.445188	−	1.37015i	−0.882278	−	0.470729i	$-0.843991\pi$
$109$	−4.64790	−	14.3048i	−0.445188	−	1.37015i	0.437090	−	0.899418i	$-0.356009\pi$
$110$	8.63707	−	6.27520i	0.823512	−	0.598316i
$111$	−3.63537	−	11.1885i	−0.345054	−	1.06197i
$112$	0.544490	−	1.67577i	0.0514495	−	0.158345i
$113$	1.40293	+	1.01929i	0.131977	+	0.0958868i	0.651815	−	0.758378i	$-0.274008\pi$
$113$	1.40293	+	1.01929i	0.131977	+	0.0958868i	−0.519838	+	0.854265i	$0.674008\pi$
$114$	−0.444863	+	1.36915i	−0.0416652	+	0.128232i
$115$	−3.20189	+	2.32631i	−0.298578	+	0.216930i
$116$	−0.470421	+	0.341781i	−0.0436775	+	0.0317336i
$117$	−5.74362	−	4.17298i	−0.530998	−	0.385792i
$118$	0.377250			0.0347287
$119$	32.4329			2.97312
$120$	−23.9905	−	17.4301i	−2.19002	−	1.59114i
$121$	0.599140	+	1.84396i	0.0544673	+	0.167633i
$122$	1.19821	−	3.68771i	0.108481	−	0.333869i
$123$	11.7751			1.06172
$124$	−0.0530734	+	6.36884i	−0.00476613	+	0.571938i
$125$	−0.929476			−0.0831348
$126$	8.86137	−	27.2725i	0.789434	−	2.42963i
$127$	2.08773	+	6.42539i	0.185256	+	0.570161i	0.999953	−	0.00972714i	$-0.00309630\pi$
$127$	2.08773	+	6.42539i	0.185256	+	0.570161i	−0.814696	+	0.579888i	$0.803096\pi$
$128$	−4.43421	−	3.22164i	−0.391932	−	0.284756i
$129$	−1.18112			−0.103991
$130$	2.96798			0.260309
$131$	3.38295	+	2.45786i	0.295570	+	0.214744i	0.725680	−	0.688032i	$-0.241525\pi$
$131$	3.38295	+	2.45786i	0.295570	+	0.214744i	−0.430110	+	0.902776i	$0.641525\pi$
$132$	10.5791	−	7.68619i	0.920795	−	0.668997i
$133$	−1.72912	+	1.25628i	−0.149934	+	0.108933i
$134$	−1.66059	+	5.11078i	−0.143453	+	0.441504i
$135$	−33.8097	−	24.5642i	−2.90988	−	2.11415i
$136$	−6.67828	+	20.5536i	−0.572658	+	1.76246i
$137$	−5.93613	−	18.2695i	−0.507157	−	1.56087i	−0.797113	−	0.603830i	$-0.793641\pi$
$137$	−5.93613	−	18.2695i	−0.507157	−	1.56087i	0.289956	−	0.957040i	$-0.406359\pi$
$138$	2.93503	−	2.13242i	0.249846	−	0.181524i
$139$	−6.27551	−	19.3140i	−0.532282	−	1.63820i	−0.749450	−	0.662061i	$-0.769682\pi$
$139$	−6.27551	−	19.3140i	−0.532282	−	1.63820i	0.217168	−	0.976134i	$-0.430318\pi$
$140$	−4.95007	−	15.2348i	−0.418358	−	1.28757i
$141$	18.1288	−	13.1713i	1.52672	−	1.10922i
$142$	−2.79233	−	8.59391i	−0.234327	−	0.721185i
$143$	−1.11155	+	3.42101i	−0.0929528	+	0.286079i
$144$	2.31825	+	1.68431i	0.193188	+	0.140359i
$145$	0.503872	−	1.55076i	0.0418443	−	0.128783i
$146$	−4.23635	+	3.07789i	−0.350602	+	0.254728i
$147$	31.0001	−	22.5229i	2.55685	−	1.85766i
$148$	3.42584	+	2.48902i	0.281603	+	0.204596i
$149$	−18.6434			−1.52732			−0.763662	−	0.645616i	$-0.776601\pi$
$149$	−18.6434			−1.52732			−0.763662	+	0.645616i	$0.776601\pi$
$150$	15.5541			1.26998
$151$	−8.62522	−	6.26659i	−0.701911	−	0.509968i	0.178643	−	0.983914i	$-0.442829\pi$
$151$	−8.62522	−	6.26659i	−0.701911	−	0.509968i	−0.880554	+	0.473946i	$0.842829\pi$
$152$	−0.440096	−	1.35448i	−0.0356965	−	0.109862i
$153$	−16.2991	+	50.1635i	−1.31770	+	4.05548i
$154$	−14.5291			−1.17079
$155$	−10.3771	−	14.5361i	−0.833511	−	1.16757i
$156$	3.63533			0.291060
$157$	−0.398835	+	1.22749i	−0.0318305	+	0.0979642i	−0.965710	−	0.259625i	$-0.916401\pi$
$157$	−0.398835	+	1.22749i	−0.0318305	+	0.0979642i	0.933879	+	0.357589i	$0.116401\pi$
$158$	0.954585	+	2.93791i	0.0759427	+	0.233728i
$159$	25.7502	+	18.7086i	2.04212	+	1.48369i
$160$	17.4642			1.38067
$161$	5.38615			0.424488
$162$	15.0490	+	10.9337i	1.18236	+	0.859036i
$163$	−0.222573	+	0.161709i	−0.0174332	+	0.0126660i	−0.596468	−	0.802637i	$-0.703430\pi$
$163$	−0.222573	+	0.161709i	−0.0174332	+	0.0126660i	0.579035	+	0.815303i	$0.303430\pi$
$164$	−3.42898	+	2.49130i	−0.267759	+	0.194538i
$165$	−11.3314	+	34.8744i	−0.882147	+	2.71497i
$166$	11.9649	+	8.69299i	0.928655	+	0.674707i
$167$	−0.660097	+	2.03157i	−0.0510798	+	0.157207i	−0.973343	−	0.229356i	$-0.926338\pi$
$167$	−0.660097	+	2.03157i	−0.0510798	+	0.157207i	0.922263	+	0.386564i	$0.126338\pi$
$168$	12.4708	+	38.3811i	0.962142	+	2.96117i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	−6.81391	−	20.9711i	−0.522603	−	1.60841i
$171$	−1.07410	−	3.30575i	−0.0821387	−	0.252797i
$172$	0.343949	−	0.249894i	0.0262259	−	0.0190542i
$173$	3.63258	+	11.1799i	0.276180	+	0.849995i	0.988905	+	0.148551i	$0.0474609\pi$
$173$	3.63258	+	11.1799i	0.276180	+	0.849995i	−0.712725	+	0.701444i	$0.752539\pi$
$174$	−0.461876	+	1.42151i	−0.0350147	+	0.107764i
$175$	18.6821	+	13.5733i	1.41223	+	1.02605i
$176$	0.448648	−	1.38080i	0.0338181	−	0.104081i
$177$	−1.04828	+	0.761624i	−0.0787939	+	0.0572471i
$178$	2.35450	−	1.71064i	0.176477	−	0.128218i
$179$	−3.10323	−	2.25463i	−0.231946	−	0.168519i	0.465742	−	0.884921i	$-0.345788\pi$
$179$	−3.10323	−	2.25463i	−0.231946	−	0.168519i	−0.697688	+	0.716402i	$0.745788\pi$
$180$	26.0510			1.94173
$181$	−24.8551			−1.84746			−0.923731	−	0.383041i	$-0.874877\pi$
$181$	−24.8551			−1.84746			−0.923731	+	0.383041i	$0.874877\pi$
$182$	−3.26775	−	2.37416i	−0.242221	−	0.175984i
$183$	4.11552	+	12.6663i	0.304228	+	0.936317i
$184$	−1.10907	+	3.41336i	−0.0817615	+	0.251636i
$185$	−11.8746			−0.873036
$186$	9.51223	+	13.3246i	0.697471	+	0.977004i
$187$	26.7240			1.95425
$188$	−2.49251	+	7.67116i	−0.181785	+	0.559477i
$189$	17.5750	+	54.0904i	1.27840	+	3.93450i
$190$	1.17558	+	0.854112i	0.0852859	+	0.0619638i
$191$	14.1301			1.02242			0.511210	−	0.859456i	$-0.329197\pi$
$191$	14.1301			1.02242			0.511210	+	0.859456i	$0.329197\pi$
$192$	−18.5740			−1.34047
$193$	−1.05199	−	0.764312i	−0.0757236	−	0.0550164i	0.549279	−	0.835639i	$-0.314902\pi$
$193$	−1.05199	−	0.764312i	−0.0757236	−	0.0550164i	−0.625003	+	0.780622i	$0.714902\pi$
$194$	−2.29866	+	1.67007i	−0.165034	+	0.119904i
$195$	−8.24727	+	5.99199i	−0.590599	+	0.429096i
$196$	−4.26219	+	13.1177i	−0.304442	+	0.936976i
$197$	20.3496	+	14.7848i	1.44985	+	1.05338i	0.985867	+	0.167529i	$0.0535789\pi$
$197$	20.3496	+	14.7848i	1.44985	+	1.05338i	0.463980	+	0.885846i	$0.346421\pi$
$198$	7.30157	−	22.4719i	0.518900	−	1.59701i
$199$	−5.82171	−	17.9174i	−0.412690	−	1.27013i	−0.914301	−	0.405036i	$-0.867259\pi$
$199$	−5.82171	−	17.9174i	−0.412690	−	1.27013i	0.501611	−	0.865093i	$-0.332741\pi$
$200$	−12.4487	+	9.04448i	−0.880253	+	0.639541i
$201$	−5.70368	−	17.5541i	−0.402307	−	1.23817i
$202$	3.30236	+	10.1636i	0.232353	+	0.715110i
$203$	−1.79525	+	1.30433i	−0.126002	+	0.0915457i
$204$	−8.34603	−	25.6864i	−0.584339	−	1.79841i
$205$	3.67281	−	11.3037i	0.256520	−	0.789488i
$206$	−0.843983	−	0.613189i	−0.0588031	−	0.0427229i
$207$	−2.70680	+	8.33068i	−0.188136	+	0.579023i
$208$	0.326537	−	0.237243i	0.0226413	−	0.0164499i
$209$	−1.42476	+	1.03515i	−0.0985526	+	0.0716027i
$210$	−33.3120	−	24.2026i	−2.29875	−	1.67014i
$211$	−18.0767			−1.24445			−0.622225	−	0.782838i	$-0.713771\pi$
$211$	−18.0767			−1.24445			−0.622225	+	0.782838i	$0.713771\pi$
$212$	−11.4569			−0.786863
$213$	25.1093	+	18.2429i	1.72046	+	1.24999i
$214$	−0.229917	−	0.707610i	−0.0157168	−	0.0483713i
$215$	−0.368407	+	1.13384i	−0.0251251	+	0.0773272i
$216$	−37.8975			−2.57860
$217$	−0.202542	+	24.3051i	−0.0137495	+	1.64994i
$218$	13.9166			0.942549
$219$	5.55787	−	17.1054i	0.375566	−	1.15587i
$220$	−4.07875	−	12.5531i	−0.274989	−	0.846330i
$221$	6.01051	+	4.36689i	0.404310	+	0.293749i
$222$	10.8849			0.730545
$223$	−4.76057			−0.318791			−0.159396	−	0.987215i	$-0.550955\pi$
$223$	−4.76057			−0.318791			−0.159396	+	0.987215i	$0.550955\pi$
$224$	−19.2281	−	13.9700i	−1.28473	−	0.933412i
$225$	−30.3824	+	22.0741i	−2.02549	+	1.47160i
$226$	−1.29806	+	0.943097i	−0.0863457	+	0.0627339i
$227$	2.93265	−	9.02576i	0.194647	−	0.599061i	−0.805334	−	0.592821i	$-0.798014\pi$
$227$	2.93265	−	9.02576i	0.194647	−	0.599061i	0.999981	−	0.00623920i	$-0.00198601\pi$
$228$	1.43992	+	1.04616i	0.0953609	+	0.0692837i
$229$	−2.14033	+	6.58727i	−0.141437	+	0.435299i	−0.996536	−	0.0831666i	$-0.973497\pi$
$229$	−2.14033	+	6.58727i	−0.141437	+	0.435299i	0.855098	+	0.518466i	$0.173497\pi$
$230$	−1.13159	−	3.48268i	−0.0746149	−	0.229641i
$231$	40.3727	−	29.3325i	2.65633	−	1.92994i
$232$	−0.456927	−	1.40628i	−0.0299987	−	0.0923265i
$233$	7.01168	+	21.5797i	0.459350	+	1.41374i	0.865951	+	0.500129i	$0.166714\pi$
$233$	7.01168	+	21.5797i	0.459350	+	1.41374i	−0.406600	+	0.913606i	$0.633286\pi$
$234$	5.31427	−	3.86104i	0.347405	−	0.252404i
$235$	−6.98949	−	21.5114i	−0.455944	−	1.40325i
$236$	0.144128	−	0.443580i	0.00938193	−	0.0288746i
$237$	−8.58384	−	6.23653i	−0.557580	−	0.405106i
$238$	−9.27313	+	28.5398i	−0.601088	+	1.84996i
$239$	−8.48500	+	6.16471i	−0.548849	+	0.398762i	−0.827361	−	0.561671i	$-0.810159\pi$
$239$	−8.48500	+	6.16471i	−0.548849	+	0.398762i	0.278512	+	0.960433i	$0.410159\pi$
$240$	3.32878	−	2.41850i	0.214872	−	0.156114i
$241$	10.1330	+	7.36203i	0.652722	+	0.474230i	0.864197	−	0.503153i	$-0.167827\pi$
$241$	10.1330	+	7.36203i	0.652722	+	0.474230i	−0.211476	+	0.977383i	$0.567827\pi$
$242$	−1.79392			−0.115318
$243$	−24.8070			−1.59137
$244$	−3.87832	−	2.81777i	−0.248284	−	0.180389i
$245$	−11.9520	−	36.7845i	−0.763586	−	2.35008i
$246$	−3.36670	+	10.3616i	−0.214653	+	0.660633i
$247$	−0.489594			−0.0311521
$248$	−15.3611	−	5.13305i	−0.975434	−	0.325949i
$249$	−50.7975			−3.21916
$250$	0.265753	−	0.817904i	0.0168077	−	0.0517288i
$251$	−3.07058	−	9.45029i	−0.193814	−	0.596497i	−0.999988	−	0.00481945i	$-0.998466\pi$
$251$	−3.07058	−	9.45029i	−0.193814	−	0.596497i	0.806175	−	0.591677i	$-0.201534\pi$
$252$	−28.6822	−	20.8388i	−1.80681	−	1.31272i
$253$	4.43807			0.279019
$254$	−6.25102			−0.392224
$255$	61.2722	+	44.5169i	3.83702	+	2.78775i
$256$	13.5595	−	9.85158i	0.847471	−	0.615724i
$257$	20.3156	−	14.7601i	1.26725	−	0.920711i	0.268160	−	0.963374i	$-0.413584\pi$
$257$	20.3156	−	14.7601i	1.26725	−	0.920711i	0.999089	+	0.0426638i	$0.0135844\pi$
$258$	0.337701	−	1.03934i	0.0210244	−	0.0647064i
$259$	13.0739	+	9.49876i	0.812374	+	0.590224i
$260$	1.13391	−	3.48982i	0.0703222	−	0.216430i
$261$	−1.11518	−	3.43217i	−0.0690280	−	0.212446i
$262$	−3.13007	+	2.27413i	−0.193376	+	0.140496i
$263$	5.52330	+	16.9990i	0.340582	+	1.04820i	0.963907	+	0.266240i	$0.0857812\pi$
$263$	5.52330	+	16.9990i	0.340582	+	1.04820i	−0.623325	+	0.781963i	$0.714219\pi$
$264$	10.2757	+	31.6252i	0.632423	+	1.94640i
$265$	25.9916	−	18.8840i	1.59665	−	1.16003i
$266$	−0.611095	−	1.88076i	−0.0374686	−	0.115317i
$267$	−3.08898	+	9.50691i	−0.189043	+	0.581813i
$268$	5.37495	+	3.90513i	0.328328	+	0.238544i
$269$	0.943199	−	2.90287i	0.0575079	−	0.176991i	−0.918176	−	0.396172i	$-0.870338\pi$
$269$	0.943199	−	2.90287i	0.0575079	−	0.176991i	0.975684	+	0.219181i	$0.0703384\pi$
$270$	31.2824	−	22.7280i	1.90378	−	1.38318i
$271$	16.1782	−	11.7541i	0.982754	−	0.714012i	0.0244314	−	0.999702i	$-0.492222\pi$
$271$	16.1782	−	11.7541i	0.982754	−	0.714012i	0.958322	+	0.285689i	$0.0922225\pi$
$272$	−2.42597	−	1.76257i	−0.147096	−	0.106872i
$273$	13.8734			0.839656
$274$	17.7737			1.07375
$275$	15.3936	+	11.1841i	0.928272	+	0.674429i
$276$	−1.38603	−	4.26577i	−0.0834293	−	0.256769i
$277$	2.24630	−	6.91339i	0.134967	−	0.415385i	−0.860618	−	0.509251i	$-0.829922\pi$
$277$	2.24630	−	6.91339i	0.134967	−	0.415385i	0.995585	+	0.0938657i	$0.0299224\pi$
$278$	18.7899			1.12694
$279$	−37.4906	−	12.5278i	−2.24450	−	0.750019i
$280$	40.7347			2.43436
$281$	−4.65905	+	14.3391i	−0.277936	+	0.855399i	0.710492	+	0.703705i	$0.248473\pi$
$281$	−4.65905	+	14.3391i	−0.277936	+	0.855399i	−0.988428	+	0.151693i	$0.951527\pi$
$282$	6.40694	+	19.7185i	0.381528	+	1.17422i
$283$	−24.7658	−	17.9934i	−1.47218	−	1.06960i	−0.979976	−	0.199117i	$-0.936193\pi$
$283$	−24.7658	−	17.9934i	−1.47218	−	1.06960i	−0.492200	−	0.870482i	$-0.663807\pi$
$284$	−11.1717			−0.662920
$285$	−4.99101			−0.295642
$286$	−2.69255	−	1.95625i	−0.159214	−	0.115676i
$287$	−13.0859	+	9.50747i	−0.772437	+	0.561208i
$288$	31.2703	−	22.7192i	1.84262	−	1.33874i
$289$	11.8032	−	36.3264i	0.694305	−	2.13685i
$290$	1.22054	+	0.886777i	0.0716728	+	0.0520733i
$291$	3.01572	−	9.28142i	0.176784	−	0.544087i
$292$	2.00056	+	6.15710i	0.117074	+	0.360317i
$293$	17.7378	−	12.8872i	1.03625	−	0.752881i	0.0667012	−	0.997773i	$-0.478753\pi$
$293$	17.7378	−	12.8872i	1.03625	−	0.752881i	0.969550	+	0.244892i	$0.0787526\pi$
$294$	10.9559	+	33.7187i	0.638959	+	1.96651i
$295$	0.404163	+	1.24389i	0.0235313	+	0.0724218i
$296$	−8.71169	+	6.32941i	−0.506357	+	0.367890i
$297$	14.4814	+	44.5693i	0.840298	+	2.58617i
$298$	5.33046	−	16.4055i	0.308785	−	0.950343i
$299$	0.998169	+	0.725212i	0.0577256	+	0.0419401i
$300$	5.94241	−	18.2889i	0.343085	−	1.05591i
$301$	1.31260	−	0.953660i	0.0756570	−	0.0549681i
$302$	7.98047	−	5.79815i	0.459224	−	0.333646i
$303$	−29.6956	−	21.5751i	−1.70597	−	1.23946i
$304$	0.197611			0.0113338
$305$	13.4429			0.769741
$306$	−39.4818	−	28.6852i	−2.25702	−	1.63982i
$307$	−8.98364	−	27.6488i	−0.512723	−	1.57800i	−0.787387	−	0.616459i	$-0.788567\pi$
$307$	−8.98364	−	27.6488i	−0.512723	−	1.57800i	0.274664	−	0.961540i	$-0.411433\pi$
$308$	−5.55082	+	17.0837i	−0.316287	+	0.973432i
$309$	3.58317			0.203840
$310$	15.7582	−	4.97537i	0.895007	−	0.282582i
$311$	5.56554			0.315593			0.157796	−	0.987472i	$-0.449561\pi$
$311$	5.56554			0.315593			0.157796	+	0.987472i	$0.449561\pi$
$312$	−2.85668	+	8.79195i	−0.161728	+	0.497746i
$313$	−7.38343	−	22.7239i	−0.417336	−	1.28443i	−0.910145	−	0.414291i	$-0.864030\pi$
$313$	−7.38343	−	22.7239i	−0.417336	−	1.28443i	0.492809	−	0.870138i	$-0.335970\pi$
$314$	−0.966110	−	0.701920i	−0.0545207	−	0.0396116i
$315$	99.4176			5.60154
$316$	3.81916			0.214845
$317$	−18.8426	−	13.6900i	−1.05831	−	0.768906i	−0.0845338	−	0.996421i	$-0.526940\pi$
$317$	−18.8426	−	13.6900i	−1.05831	−	0.768906i	−0.973775	+	0.227515i	$0.926940\pi$
$318$	−23.8253	+	17.3101i	−1.33606	+	0.970702i
$319$	−1.47925	+	1.07474i	−0.0828219	+	0.0601736i
$320$	−5.79350	+	17.8306i	−0.323867	+	0.996759i
$321$	2.06746	+	1.50210i	0.115394	+	0.0838390i
$322$	−1.53999	+	4.73962i	−0.0858206	+	0.264129i
$323$	1.12401	+	3.45936i	0.0625418	+	0.192484i
$324$	18.6056	−	13.5178i	1.03365	−	0.750987i
$325$	1.63463	+	5.03086i	0.0906727	+	0.279062i
$326$	−0.0786601	−	0.242091i	−0.00435658	−	0.0134082i
$327$	−38.6707	+	28.0959i	−2.13849	+	1.55371i
$328$	−3.33062	−	10.2506i	−0.183903	−	0.565994i
$329$	−9.51208	+	29.2752i	−0.524418	+	1.61399i
$330$	−27.4484	−	19.9424i	−1.51098	−	1.09779i
$331$	0.427169	−	1.31469i	0.0234793	−	0.0722619i	−0.938630	−	0.344925i	$-0.887904\pi$
$331$	0.427169	−	1.31469i	0.0234793	−	0.0722619i	0.962110	+	0.272663i	$0.0879044\pi$
$332$	14.7926	−	10.7475i	0.811849	−	0.589843i
$333$	−21.2619	+	15.4476i	−1.16514	+	0.846526i
$334$	−1.59897	−	1.16172i	−0.0874919	−	0.0635666i
$335$	−18.6305			−1.01790
$336$	−5.59961			−0.305484
$337$	23.2327	+	16.8795i	1.26557	+	0.919487i	0.999017	−	0.0443339i	$-0.0141165\pi$
$337$	23.2327	+	16.8795i	1.26557	+	0.919487i	0.266549	+	0.963821i	$0.414117\pi$
$338$	−0.285917	−	0.879963i	−0.0155519	−	0.0478637i
$339$	1.70299	−	5.24126i	0.0924937	−	0.284666i
$340$	−27.2615			−1.47846
$341$	−0.166890	+	20.0269i	−0.00903761	+	1.08452i
$342$	3.21604			0.173904
$343$	−6.82256	+	20.9977i	−0.368384	+	1.13377i
$344$	0.334083	+	1.02820i	0.0180125	+	0.0554369i
$345$	10.1755	+	7.39295i	0.547832	+	0.398023i
$346$	−10.8765			−0.584727
$347$	15.1117			0.811238			0.405619	−	0.914042i	$-0.367056\pi$
$347$	15.1117			0.811238			0.405619	+	0.914042i	$0.367056\pi$
$348$	1.49499	+	1.08617i	0.0801396	+	0.0582248i
$349$	0.972479	−	0.706547i	0.0520556	−	0.0378206i	−0.561453	−	0.827509i	$-0.689758\pi$
$349$	0.972479	−	0.706547i	0.0520556	−	0.0378206i	0.613509	+	0.789688i	$0.289758\pi$
$350$	−17.2856	+	12.5587i	−0.923953	+	0.671291i
$351$	−4.02591	+	12.3905i	−0.214887	+	0.661354i
$352$	−15.8435	−	11.5110i	−0.844463	−	0.613538i
$353$	5.93366	−	18.2619i	0.315817	−	0.971984i	−0.659600	−	0.751617i	$-0.729274\pi$
$353$	5.93366	−	18.2619i	0.315817	−	0.971984i	0.975417	−	0.220367i	$-0.0707256\pi$
$354$	−0.370478	−	1.14021i	−0.0196907	−	0.0606017i
$355$	25.3447	−	18.4140i	1.34515	−	0.977312i
$356$	−1.11188	−	3.42203i	−0.0589298	−	0.181367i
$357$	−31.8506	−	98.0262i	−1.68572	−	5.18810i
$358$	2.87126	−	2.08609i	0.151751	−	0.110253i
$359$	−0.934200	−	2.87517i	−0.0493052	−	0.151746i	0.923373	−	0.383905i	$-0.125421\pi$
$359$	−0.934200	−	2.87517i	−0.0493052	−	0.151746i	−0.972678	+	0.232159i	$0.925421\pi$
$360$	−20.4711	+	63.0037i	−1.07892	+	3.32059i
$361$	15.1774	+	11.0270i	0.798811	+	0.580370i
$362$	7.10649	−	21.8715i	0.373509	−	1.14954i
$363$	4.98487	−	3.62172i	0.261638	−	0.190091i
$364$	−4.04003	+	2.93525i	−0.211755	+	0.153849i
$365$	−14.6871	−	10.6708i	−0.768758	−	0.558535i
$366$	−12.3225			−0.644109
$367$	−0.848006			−0.0442656			−0.0221328	−	0.999755i	$-0.507046\pi$
$367$	−0.848006			−0.0442656			−0.0221328	+	0.999755i	$0.507046\pi$
$368$	−0.402883	−	0.292712i	−0.0210017	−	0.0152587i
$369$	−8.12875	−	25.0177i	−0.423166	−	1.30237i
$370$	3.39515	−	10.4492i	0.176505	−	0.543228i
$371$	−43.7225			−2.26996
$372$	19.3015	−	6.09409i	1.00074	−	0.315964i
$373$	27.5454			1.42625			0.713124	−	0.701038i	$-0.247280\pi$
$373$	27.5454			1.42625			0.713124	+	0.701038i	$0.247280\pi$
$374$	−7.64085	+	23.5161i	−0.395099	+	1.21599i
$375$	0.912789	+	2.80928i	0.0471362	+	0.145070i
$376$	−16.5939	−	12.0561i	−0.855763	−	0.621748i
$377$	−0.508317			−0.0261797
$378$	−52.6225			−2.70661
$379$	5.31121	+	3.85882i	0.272819	+	0.198214i	0.715779	−	0.698327i	$-0.246072\pi$
$379$	5.31121	+	3.85882i	0.272819	+	0.198214i	−0.442960	+	0.896541i	$0.646072\pi$
$380$	1.45342	−	1.05597i	0.0745587	−	0.0541701i
$381$	17.3700	−	12.6201i	0.889894	−	0.646546i
$382$	−4.04005	+	12.4340i	−0.206707	+	0.636179i
$383$	−12.1452	−	8.82401i	−0.620591	−	0.450886i	0.232537	−	0.972588i	$-0.425297\pi$
$383$	−12.1452	−	8.82401i	−0.620591	−	0.450886i	−0.853128	+	0.521702i	$0.825297\pi$
$384$	−5.38258	+	16.5659i	−0.274679	+	0.845375i
$385$	−15.5656	−	47.9059i	−0.793296	−	2.44151i
$386$	0.973347	−	0.707178i	0.0495421	−	0.0359944i
$387$	0.815366	+	2.50944i	0.0414474	+	0.127562i
$388$	1.08551	+	3.34086i	0.0551086	+	0.169607i
$389$	19.6234	−	14.2573i	0.994947	−	0.722871i	0.0339483	−	0.999424i	$-0.489192\pi$
$389$	19.6234	−	14.2573i	0.994947	−	0.722871i	0.960999	+	0.276552i	$0.0891918\pi$
$390$	−2.91469	−	8.97051i	−0.147591	−	0.454239i
$391$	2.83258	−	8.71778i	0.143250	−	0.440877i
$392$	−28.3754	−	20.6160i	−1.43318	−	1.04126i
$393$	4.10649	−	12.6385i	0.207145	−	0.637527i
$394$	−18.8284	+	13.6796i	−0.948561	+	0.689170i
$395$	−8.66432	+	6.29499i	−0.435949	+	0.316736i
$396$	−23.6335	−	17.1707i	−1.18763	−	0.862862i
$397$	8.71678			0.437483			0.218741	−	0.975783i	$-0.429805\pi$
$397$	8.71678			0.437483			0.218741	+	0.975783i	$0.429805\pi$
$398$	17.4312			0.873745
$399$	5.49510	+	3.99243i	0.275099	+	0.199871i
$400$	−0.659771	−	2.03057i	−0.0329886	−	0.101528i
$401$	−9.73783	+	29.9700i	−0.486284	+	1.49663i	0.343829	+	0.939032i	$0.388276\pi$
$401$	−9.73783	+	29.9700i	−0.486284	+	1.49663i	−0.830113	+	0.557596i	$0.811724\pi$
$402$	17.0778			0.851761
$403$	−3.31007	+	4.47699i	−0.164886	+	0.223015i
$404$	13.2123			0.657337
$405$	−19.9286	+	61.3339i	−0.990260	+	3.04771i
$406$	−0.634465	−	1.95268i	−0.0314880	−	0.0969101i
$407$	10.7726	+	7.82677i	0.533979	+	0.387958i
$408$	68.6803			3.40018
$409$	−17.5637			−0.868471			−0.434235	−	0.900799i	$-0.642981\pi$
$409$	−17.5637			−0.868471			−0.434235	+	0.900799i	$0.642981\pi$
$410$	8.89676	+	6.46387i	0.439380	+	0.319228i
$411$	−49.3888	+	35.8831i	−2.43617	+	1.76998i
$412$	−1.04345	+	0.758108i	−0.0514069	+	0.0373493i
$413$	0.550030	−	1.69282i	0.0270652	−	0.0832982i
$414$	−6.55677	−	4.76377i	−0.322248	−	0.234127i
$415$	−15.8445	+	48.7642i	−0.777774	+	2.39374i
$416$	−1.68240	−	5.17789i	−0.0824863	−	0.253867i
$417$	−52.2125	+	37.9346i	−2.55686	+	1.85767i
$418$	−0.503529	−	1.54970i	−0.0246284	−	0.0757984i
$419$	3.43742	+	10.5793i	0.167929	+	0.516832i	0.999240	−	0.0389751i	$-0.0124093\pi$
$419$	3.43742	+	10.5793i	0.167929	+	0.516832i	−0.831311	+	0.555807i	$0.812409\pi$
$420$	−41.1848	+	29.9225i	−2.00961	+	1.46007i
$421$	11.5455	+	35.5335i	0.562694	+	1.73180i	0.674704	+	0.738088i	$0.264271\pi$
$421$	11.5455	+	35.5335i	0.562694	+	1.73180i	−0.112010	+	0.993707i	$0.535729\pi$
$422$	5.16844	−	15.9068i	0.251596	−	0.774332i
$423$	−40.4992	−	29.4244i	−1.96914	−	1.43066i
$424$	9.00293	−	27.7082i	0.437221	−	1.34563i
$425$	31.7941	−	23.0998i	1.54224	−	1.12050i
$426$	−23.2323	+	16.8792i	−1.12561	+	0.817802i
$427$	−14.8007	−	10.7533i	−0.716256	−	0.520390i
$428$	−0.919865			−0.0444634
$429$	11.4314			0.551911
$430$	−0.892402	−	0.648368i	−0.0430355	−	0.0312671i
$431$	0.555951	+	1.71104i	0.0267792	+	0.0824180i	0.963553	−	0.267518i	$-0.0862034\pi$
$431$	0.555951	+	1.71104i	0.0267792	+	0.0824180i	−0.936774	+	0.349936i	$0.886203\pi$
$432$	1.62495	−	5.00107i	0.0781802	−	0.240614i
$433$	−18.5443			−0.891182			−0.445591	−	0.895237i	$-0.647006\pi$
$433$	−18.5443			−0.891182			−0.445591	+	0.895237i	$0.647006\pi$
$434$	−21.3297	−	7.12749i	−1.02386	−	0.342131i
$435$	−5.18188			−0.248452
$436$	5.31681	−	16.3634i	0.254629	−	0.783667i
$437$	0.186666	+	0.574498i	0.00892943	+	0.0274820i
$438$	13.4630	+	9.78143i	0.643286	+	0.467375i
$439$	0.364098			0.0173774			0.00868872	−	0.999962i	$-0.497234\pi$
$439$	0.364098			0.0173774			0.00868872	+	0.999962i	$0.497234\pi$
$440$	33.5645			1.60012
$441$	−69.2535	−	50.3156i	−3.29778	−	2.39598i
$442$	−5.56121	+	4.04045i	−0.264520	+	0.192185i
$443$	10.6185	−	7.71476i	0.504498	−	0.366539i	−0.306234	−	0.951956i	$-0.599069\pi$
$443$	10.6185	−	7.71476i	0.504498	−	0.366539i	0.810733	+	0.585417i	$0.199069\pi$
$444$	4.15855	−	12.7987i	0.197356	−	0.607400i
$445$	8.16288	+	5.93068i	0.386957	+	0.281141i
$446$	1.36113	−	4.18912i	0.0644513	−	0.198361i
$447$	18.3087	+	56.3483i	0.865970	+	2.66518i
$448$	20.6417	−	14.9971i	0.975231	−	0.708547i
$449$	−3.48849	−	10.7365i	−0.164632	−	0.506686i	0.834377	−	0.551195i	$-0.185828\pi$
$449$	−3.48849	−	10.7365i	−0.164632	−	0.506686i	−0.999009	+	0.0445087i	$0.985828\pi$
$450$	−10.7375	−	33.0467i	−0.506172	−	1.55784i
$451$	−10.7825	+	7.83394i	−0.507728	+	0.368886i
$452$	0.612994	+	1.88660i	0.0288328	+	0.0887382i
$453$	−10.4700	+	32.2232i	−0.491922	+	1.51398i
$454$	7.10384	+	5.16124i	0.333400	+	0.242229i
$455$	4.32730	−	13.3181i	0.202867	−	0.624361i
$456$	−3.66161	+	2.66032i	−0.171471	+	0.124581i
$457$	1.81613	−	1.31950i	0.0849550	−	0.0617234i	−0.544497	−	0.838763i	$-0.683279\pi$
$457$	1.81613	−	1.31950i	0.0849550	−	0.0617234i	0.629452	+	0.777039i	$0.283279\pi$
$458$	−5.18460	−	3.76683i	−0.242260	−	0.176012i
$459$	96.7909			4.51781
$460$	−4.52734			−0.211088
$461$	26.0928	+	18.9576i	1.21526	+	0.882941i	0.995698	−	0.0926563i	$-0.0295358\pi$
$461$	26.0928	+	18.9576i	1.21526	+	0.882941i	0.219566	+	0.975598i	$0.429536\pi$
$462$	14.2683	+	43.9132i	0.663819	+	2.04303i
$463$	1.08199	−	3.33002i	0.0502842	−	0.154759i	−0.922761	−	0.385372i	$-0.874073\pi$
$463$	1.08199	−	3.33002i	0.0502842	−	0.154759i	0.973046	+	0.230613i	$0.0740731\pi$
$464$	0.205168			0.00952470
$465$	−33.7435	+	45.6393i	−1.56482	+	2.11647i
$466$	−20.9941			−0.972534
$467$	3.19064	−	9.81977i	0.147645	−	0.454405i	−0.849697	−	0.527272i	$-0.823215\pi$
$467$	3.19064	−	9.81977i	0.147645	−	0.454405i	0.997342	+	0.0728672i	$0.0232149\pi$
$468$	−2.50960	−	7.72376i	−0.116006	−	0.357031i
$469$	20.5122	+	14.9030i	0.947167	+	0.688157i
$470$	20.9277			0.965322
$471$	4.10167			0.188995
$472$	0.959530	+	0.697139i	0.0441659	+	0.0320884i
$473$	1.08155	−	0.785795i	0.0497299	−	0.0361309i
$474$	7.94218	−	5.77033i	0.364796	−	0.265040i
$475$	−0.800302	+	2.46308i	−0.0367204	+	0.113014i
$476$	30.0150	+	21.8071i	1.37573	+	0.999529i
$477$	21.9727	−	67.6250i	1.00606	−	3.09633i
$478$	−2.99871	−	9.22908i	−0.137158	−	0.422128i
$479$	1.79017	−	1.30064i	0.0817952	−	0.0594277i	−0.546136	−	0.837696i	$-0.683902\pi$
$479$	1.79017	−	1.30064i	0.0817952	−	0.0594277i	0.627931	+	0.778269i	$0.283902\pi$
$480$	−17.1507	−	52.7844i	−0.782818	−	2.40927i
$481$	1.14393	+	3.52064i	0.0521585	+	0.160528i
$482$	−9.37550	+	6.81170i	−0.427043	+	0.310265i
$483$	−5.28946	−	16.2793i	−0.240679	−	0.740733i
$484$	−0.685366	+	2.10934i	−0.0311530	+	0.0958791i
$485$	−7.96927	−	5.79001i	−0.361866	−	0.262911i
$486$	7.09276	−	21.8293i	0.321734	−	0.990195i
$487$	7.50595	−	5.45339i	0.340127	−	0.247117i	−0.404589	−	0.914499i	$-0.632585\pi$
$487$	7.50595	−	5.45339i	0.340127	−	0.247117i	0.744715	+	0.667382i	$0.232585\pi$
$488$	9.86231	−	7.16539i	0.446446	−	0.324362i
$489$	0.707330	+	0.513905i	0.0319866	+	0.0232396i
$490$	35.7863			1.61666
$491$	−9.05969			−0.408858			−0.204429	−	0.978881i	$-0.565534\pi$
$491$	−9.05969			−0.408858			−0.204429	+	0.978881i	$0.565534\pi$
$492$	10.8972	+	7.91729i	0.491284	+	0.356939i
$493$	1.16700	+	3.59166i	0.0525590	+	0.161760i
$494$	0.139983	−	0.430824i	0.00629815	−	0.0193837i
$495$	81.9178			3.68193
$496$	1.33602	−	1.80701i	0.0599890	−	0.0811373i
$497$	−42.6343			−1.91241
$498$	14.5239	−	44.6999i	0.650831	−	2.00305i
$499$	−2.88741	−	8.88653i	−0.129258	−	0.397816i	0.865395	−	0.501091i	$-0.167068\pi$
$499$	−2.88741	−	8.88653i	−0.129258	−	0.397816i	−0.994653	+	0.103275i	$0.967068\pi$
$500$	−0.860181	−	0.624958i	−0.0384685	−	0.0279490i
$501$	6.78852			0.303289
$502$	9.19384			0.410341
$503$	−28.2442	−	20.5206i	−1.25935	−	0.914969i	−0.260621	−	0.965441i	$-0.583927\pi$
$503$	−28.2442	−	20.5206i	−1.25935	−	0.914969i	−0.998725	+	0.0504724i	$0.983927\pi$
$504$	72.9369	−	52.9918i	3.24887	−	2.36044i
$505$	−29.9740	+	21.7774i	−1.33383	+	0.969081i
$506$	−1.26892	+	3.90534i	−0.0564104	+	0.173613i
$507$	2.57103	+	1.86796i	0.114184	+	0.0829592i
$508$	−2.38819	+	7.35011i	−0.105959	+	0.326108i
$509$	13.0314	+	40.1064i	0.577605	+	1.77768i	0.627133	+	0.778912i	$0.284228\pi$
$509$	13.0314	+	40.1064i	0.577605	+	1.77768i	−0.0495286	+	0.998773i	$0.515772\pi$
$510$	−56.6920	+	41.1891i	−2.51036	+	1.82389i
$511$	7.63467	+	23.4971i	0.337738	+	1.03945i
$512$	1.40469	+	4.32318i	0.0620789	+	0.191059i
$513$	−5.16030	+	3.74917i	−0.227833	+	0.165530i
$514$	7.17979	+	22.0971i	0.316687	+	0.974662i
$515$	1.11764	−	3.43975i	0.0492492	−	0.151573i
$516$	−1.09306	−	0.794155i	−0.0481193	−	0.0349607i
$517$	−7.83774	+	24.1221i	−0.344703	+	1.06089i
$518$	−12.0966	+	8.78871i	−0.531495	+	0.386154i
$519$	30.2232	−	21.9584i	1.32665	−	0.963869i
$520$	7.54900	+	5.48467i	0.331045	+	0.240519i
$521$	−10.7505			−0.470989			−0.235495	−	0.971876i	$-0.575671\pi$
$521$	−10.7505			−0.470989			−0.235495	+	0.971876i	$0.575671\pi$
$522$	3.33904			0.146146
$523$	−11.5897	−	8.42039i	−0.506781	−	0.368198i	0.304820	−	0.952410i	$-0.401404\pi$
$523$	−11.5897	−	8.42039i	−0.506781	−	0.368198i	−0.811601	+	0.584212i	$0.801404\pi$
$524$	1.47814	+	4.54924i	0.0645728	+	0.198734i
$525$	22.6778	−	69.7951i	0.989740	−	3.04611i
$526$	−16.5377			−0.721077
$527$	39.2327	+	13.1099i	1.70900	+	0.571076i
$528$	−4.61395			−0.200797
$529$	−6.63698	+	20.4265i	−0.288564	+	0.888110i
$530$	9.18577	+	28.2709i	0.399004	+	1.22801i
$531$	2.34184	+	1.70145i	0.101627	+	0.0738365i
$532$	−2.44491			−0.106000
$533$	−3.70522			−0.160491
$534$	−7.48253	−	5.43638i	−0.323801	−	0.235255i
$535$	2.08684	−	1.51618i	0.0902221	−	0.0655502i
$536$	−13.6681	+	9.93049i	−0.590374	+	0.428932i
$537$	−3.76694	+	11.5934i	−0.162555	+	0.500294i
$538$	2.28474	+	1.65996i	0.0985022	+	0.0715660i
$539$	−13.4025	+	41.2487i	−0.577287	+	1.77671i
$540$	−14.7727	−	45.4658i	−0.635717	−	1.95653i
$541$	−10.1890	+	7.40271i	−0.438058	+	0.318267i	−0.784863	−	0.619670i	$-0.787267\pi$
$541$	−10.1890	+	7.40271i	−0.438058	+	0.318267i	0.346805	+	0.937937i	$0.387267\pi$
$542$	5.71758	+	17.5969i	0.245591	+	0.755851i
$543$	24.4088	+	75.1227i	1.04748	+	3.22382i
$544$	−32.7233	+	23.7749i	−1.40300	+	1.01934i
$545$	14.9094	+	45.8863i	0.638647	+	1.96555i
$546$	−3.96664	+	12.2081i	−0.169757	+	0.522457i
$547$	2.06911	+	1.50330i	0.0884688	+	0.0642763i	0.631140	−	0.775669i	$-0.282587\pi$
$547$	2.06911	+	1.50330i	0.0884688	+	0.0642763i	−0.542672	+	0.839945i	$0.682587\pi$
$548$	6.79043	−	20.8988i	0.290073	−	0.892752i
$549$	24.0701	−	17.4879i	1.02729	−	0.746367i
$550$	−14.2429	+	10.3481i	−0.607321	+	0.441244i
$551$	−0.201339	−	0.146281i	−0.00857734	−	0.00623180i
$552$	11.4058			0.485463
$553$	14.5749			0.619789
$554$	5.44127	+	3.95332i	0.231178	+	0.167960i
$555$	11.6614	+	35.8901i	0.494999	+	1.52345i
$556$	7.17866	−	22.0936i	0.304443	−	0.936979i
$557$	0.530931			0.0224963			0.0112481	−	0.999937i	$-0.496420\pi$
$557$	0.530931			0.0224963			0.0112481	+	0.999937i	$0.496420\pi$
$558$	21.7432	−	29.4084i	0.920463	−	1.24496i
$559$	0.371657			0.0157194
$560$	−1.74660	+	5.37547i	−0.0738072	+	0.227155i
$561$	−26.2442	−	80.7714i	−1.10803	−	3.41017i
$562$	−11.2858	−	8.19959i	−0.476061	−	0.345879i
$563$	6.00123			0.252922			0.126461	−	0.991972i	$-0.459638\pi$
$563$	6.00123			0.252922			0.126461	+	0.991972i	$0.459638\pi$
$564$	25.6333			1.07936
$565$	−4.50028	−	3.26965i	−0.189328	−	0.137555i
$566$	22.9145	−	16.6484i	0.963170	−	0.699784i
$567$	71.0039	−	51.5873i	2.98188	−	2.16646i
$568$	8.77885	−	27.0185i	0.368352	−	1.13367i
$569$	−20.8937	−	15.1802i	−0.875910	−	0.636386i	0.0562560	−	0.998416i	$-0.482084\pi$
$569$	−20.8937	−	15.1802i	−0.875910	−	0.636386i	−0.932166	+	0.362030i	$0.882084\pi$
$570$	1.42702	−	4.39190i	0.0597711	−	0.183957i
$571$	−3.37851	−	10.3980i	−0.141386	−	0.435142i	0.855142	−	0.518393i	$-0.173470\pi$
$571$	−3.37851	−	10.3980i	−0.141386	−	0.435142i	−0.996529	+	0.0832513i	$0.973470\pi$
$572$	−3.32889	+	2.41858i	−0.139188	+	0.101126i
$573$	−13.8765	−	42.7074i	−0.579698	−	1.78413i
$574$	−4.62473	−	14.2335i	−0.193033	−	0.594093i
$575$	5.28007	−	3.83620i	0.220194	−	0.159980i
$576$	12.8223	+	39.4630i	0.534263	+	1.64429i
$577$	−10.4708	+	32.2257i	−0.435903	+	1.34157i	0.456255	+	0.889849i	$0.349190\pi$
$577$	−10.4708	+	32.2257i	−0.435903	+	1.34157i	−0.892158	+	0.451723i	$0.850810\pi$
$578$	28.5912	+	20.7727i	1.18924	+	0.864031i
$579$	−1.27698	+	3.93014i	−0.0530695	+	0.163331i
$580$	1.50900	−	1.09635i	0.0626578	−	0.0455236i
$581$	56.4524	−	41.0151i	2.34204	−	1.70159i
$582$	7.30506	+	5.30744i	0.302805	+	0.220000i
$583$	−36.0264			−1.49206
$584$	−16.4628			−0.681237
$585$	18.4242	+	13.3860i	0.761746	+	0.553441i
$586$	6.26876	+	19.2933i	0.258960	+	0.796997i
$587$	−13.8346	+	42.5786i	−0.571017	+	1.75741i	0.0783422	+	0.996927i	$0.475037\pi$
$587$	−13.8346	+	42.5786i	−0.571017	+	1.75741i	−0.649359	+	0.760482i	$0.724963\pi$
$588$	43.8329			1.80764
$589$	−2.59945	+	0.820730i	−0.107109	+	0.0338176i
$590$	−1.21013			−0.0498203
$591$	24.7019	−	76.0246i	1.01610	−	3.12723i
$592$	−0.461714	−	1.42101i	−0.0189763	−	0.0584032i
$593$	−20.4891	−	14.8862i	−0.841388	−	0.611304i	0.0813702	−	0.996684i	$-0.474070\pi$
$593$	−20.4891	−	14.8862i	−0.841388	−	0.611304i	−0.922758	+	0.385380i	$0.874070\pi$
$594$	−43.3598			−1.77907
$595$	−104.037			−4.26511
$596$	−17.2535	−	12.5354i	−0.706729	−	0.513469i
$597$	−48.4368	+	35.1914i	−1.98239	+	1.44029i
$598$	−0.923553	+	0.671001i	−0.0377669	+	0.0274393i
$599$	−4.15660	+	12.7927i	−0.169834	+	0.522696i	−0.999360	−	0.0357727i	$-0.988611\pi$
$599$	−4.15660	+	12.7927i	−0.169834	+	0.522696i	0.829526	+	0.558468i	$0.188611\pi$
$600$	39.5615	+	28.7431i	1.61509	+	1.17343i
$601$	8.22456	−	25.3126i	0.335487	−	1.03252i	−0.630995	−	0.775787i	$-0.717353\pi$
$601$	8.22456	−	25.3126i	0.335487	−	1.03252i	0.966482	−	0.256735i	$-0.0826468\pi$
$602$	0.463890	+	1.42771i	0.0189068	+	0.0581890i
$603$	−33.3586	+	24.2365i	−1.35847	+	0.986986i
$604$	−3.76868	−	11.5988i	−0.153345	−	0.471949i
$605$	−1.92190	−	5.91500i	−0.0781364	−	0.240479i
$606$	27.4758	−	19.9623i	1.11613	−	0.810914i
$607$	−14.5463	−	44.7690i	−0.590417	−	1.81712i	−0.576332	−	0.817216i	$-0.695516\pi$
$607$	−14.5463	−	44.7690i	−0.590417	−	1.81712i	−0.0140853	−	0.999901i	$-0.504484\pi$
$608$	0.823691	−	2.53506i	0.0334051	−	0.102810i
$609$	5.70526	+	4.14511i	0.231189	+	0.167968i
$610$	−3.84357	+	11.8293i	−0.155622	+	0.478954i
$611$	−5.70451	+	4.14457i	−0.230780	+	0.167671i
$612$	−48.8128	+	35.4645i	−1.97314	+	1.43357i
$613$	23.8926	+	17.3590i	0.965014	+	0.701124i	0.954310	−	0.298819i	$-0.0965927\pi$
$613$	23.8926	+	17.3590i	0.965014	+	0.701124i	0.0107043	+	0.999943i	$0.496593\pi$
$614$	26.8985			1.08553
$615$	−37.7717			−1.52310
$616$	−36.9545	−	26.8490i	−1.48894	−	1.08178i
$617$	−11.2455	−	34.6100i	−0.452725	−	1.39335i	−0.873785	−	0.486313i	$-0.838342\pi$
$617$	−11.2455	−	34.6100i	−0.452725	−	1.39335i	0.421060	−	0.907033i	$-0.361658\pi$
$618$	−1.02449	+	3.15306i	−0.0412111	+	0.126835i
$619$	13.9413			0.560349			0.280174	−	0.959949i	$-0.409608\pi$
$619$	13.9413			0.560349			0.280174	+	0.959949i	$0.409608\pi$
$620$	0.170247	−	20.4297i	0.00683729	−	0.820478i
$621$	16.0741			0.645033
$622$	−1.59128	+	4.89747i	−0.0638047	+	0.196371i
$623$	−4.24324	−	13.0594i	−0.170002	−	0.523212i
$624$	−1.03773	−	0.753952i	−0.0415423	−	0.0301823i
$625$	−23.4672			−0.938690
$626$	22.1072			0.883582
$627$	4.52784	+	3.28967i	0.180825	+	0.131377i
$628$	−1.19444	+	0.867808i	−0.0476632	+	0.0346293i
$629$	22.2498	−	16.1654i	0.887159	−	0.644559i
$630$	−28.4252	+	87.4838i	−1.13249	+	3.48544i
$631$	19.3657	+	14.0700i	0.770938	+	0.560119i	0.902246	−	0.431222i	$-0.141918\pi$
$631$	19.3657	+	14.0700i	0.770938	+	0.560119i	−0.131308	+	0.991342i	$0.541918\pi$
$632$	−3.00113	+	9.23654i	−0.119379	+	0.367410i
$633$	17.7522	+	54.6356i	0.705585	+	2.17157i
$634$	17.4341	−	12.6666i	0.692397	−	0.503056i
$635$	−6.69696	−	20.6111i	−0.265761	−	0.817928i
$636$	11.2512	+	34.6277i	0.446140	+	1.37308i
$637$	−9.75469	+	7.08720i	−0.386495	+	0.280805i
$638$	−0.522785	−	1.60897i	−0.0206973	−	0.0636996i
$639$	21.4258	−	65.9418i	0.847591	−	2.60862i
$640$	14.2239	+	10.3343i	0.562249	+	0.408498i
$641$	3.33400	−	10.2610i	0.131685	−	0.405285i	−0.863375	−	0.504563i	$-0.831653\pi$
$641$	3.33400	−	10.2610i	0.131685	−	0.405285i	0.995060	+	0.0992786i	$0.0316535\pi$
$642$	−1.91291	+	1.38981i	−0.0754967	+	0.0548516i
$643$	−20.3420	+	14.7794i	−0.802212	+	0.582841i	−0.911562	−	0.411162i	$-0.865123\pi$
$643$	−20.3420	+	14.7794i	−0.802212	+	0.582841i	0.109350	+	0.994003i	$0.465123\pi$
$644$	4.98461	+	3.62153i	0.196421	+	0.142708i
$645$	3.78874			0.149182
$646$	−3.36548			−0.132413
$647$	23.8465	+	17.3255i	0.937503	+	0.681136i	0.947818	−	0.318811i	$-0.103284\pi$
$647$	23.8465	+	17.3255i	0.937503	+	0.681136i	−0.0103153	+	0.999947i	$0.503284\pi$
$648$	18.0719	+	55.6195i	0.709931	+	2.18494i
$649$	0.453213	−	1.39485i	0.0177902	−	0.0547525i
$650$	−4.89434			−0.191972
$651$	73.6595	−	23.2566i	2.88694	−	0.911499i
$652$	−0.314709			−0.0123249
$653$	2.94436	−	9.06180i	0.115222	−	0.354616i	−0.876772	−	0.480907i	$-0.840307\pi$
$653$	2.94436	−	9.06180i	0.115222	−	0.354616i	0.991993	+	0.126291i	$0.0403075\pi$
$654$	−13.6667	−	42.0619i	−0.534412	−	1.64475i
$655$	−10.8517	−	7.88423i	−0.424012	−	0.308063i
$656$	1.49551			0.0583898
$657$	−40.1794			−1.56755
$658$	−23.0414	−	16.7406i	−0.898247	−	0.652615i
$659$	−22.5693	+	16.3975i	−0.879174	+	0.638757i	−0.933033	−	0.359791i	$-0.882848\pi$
$659$	−22.5693	+	16.3975i	−0.879174	+	0.638757i	0.0538588	+	0.998549i	$0.482848\pi$
$660$	−33.9354	+	24.6555i	−1.32093	+	0.959713i
$661$	11.3941	−	35.0674i	0.443178	−	1.36396i	−0.441291	−	0.897364i	$-0.645479\pi$
$661$	11.3941	−	35.0674i	0.443178	−	1.36396i	0.884469	−	0.466598i	$-0.154521\pi$
$662$	1.03474	+	0.751786i	0.0402165	+	0.0292190i
$663$	7.29602	−	22.4548i	0.283354	−	0.872073i
$664$	14.3683	+	44.2209i	0.557596	+	1.71611i
$665$	5.54662	−	4.02986i	0.215089	−	0.156271i
$666$	−7.51422	−	23.1264i	−0.291170	−	0.896130i
$667$	0.193804	+	0.596469i	0.00750414	+	0.0230954i
$668$	−1.97687	+	1.43628i	−0.0764872	+	0.0555712i
$669$	4.67510	+	14.3885i	0.180750	+	0.556291i
$670$	5.32679	−	16.3942i	0.205792	−	0.633363i
$671$	−12.1954	−	8.86051i	−0.470800	−	0.342056i
$672$	−23.3406	+	71.8348i	−0.900381	+	2.77109i
$673$	19.3336	−	14.0467i	0.745254	−	0.541459i	−0.149098	−	0.988822i	$-0.547637\pi$
$673$	19.3336	−	14.0467i	0.745254	−	0.541459i	0.894352	+	0.447363i	$0.147637\pi$
$674$	−21.4960	+	15.6178i	−0.827995	+	0.601574i
$675$	55.7538	+	40.5075i	2.14597	+	1.55914i
$676$	−1.14392			−0.0439968
$677$	−32.1405			−1.23526			−0.617629	−	0.786470i	$-0.711907\pi$
$677$	−32.1405			−1.23526			−0.617629	+	0.786470i	$0.711907\pi$
$678$	4.12520	+	2.99713i	0.158427	+	0.115104i
$679$	4.14260	+	12.7496i	0.158978	+	0.489285i
$680$	21.4224	−	65.9313i	0.821510	−	2.52835i
$681$	−30.1597			−1.15572
$682$	−17.5752	−	5.87289i	−0.672990	−	0.224885i
$683$	−18.1841			−0.695794			−0.347897	−	0.937533i	$-0.613104\pi$
$683$	−18.1841			−0.695794			−0.347897	+	0.937533i	$0.613104\pi$
$684$	1.22868	−	3.78150i	0.0469799	−	0.144589i
$685$	19.0417	+	58.6043i	0.727546	+	2.23916i
$686$	−16.5265	−	12.0072i	−0.630985	−	0.458437i
$687$	22.0115			0.839790
$688$	−0.150009			−0.00571904
$689$	−8.10271	−	5.88696i	−0.308689	−	0.224275i
$690$	−9.41488	+	6.84031i	−0.358418	+	0.260406i
$691$	−8.55121	+	6.21282i	−0.325303	+	0.236347i	−0.738435	−	0.674325i	$-0.764435\pi$
$691$	−8.55121	+	6.21282i	−0.325303	+	0.236347i	0.413132	+	0.910671i	$0.364435\pi$
$692$	−4.15537	+	12.7889i	−0.157963	+	0.486161i
$693$	−90.1916	−	65.5280i	−3.42610	−	2.48920i
$694$	−4.32069	+	13.2977i	−0.164011	+	0.504775i
$695$	20.1304	+	61.9549i	0.763588	+	2.35008i
$696$	−3.80165	+	2.76206i	−0.144101	+	0.104696i
$697$	8.50647	+	26.1802i	0.322205	+	0.991646i
$698$	0.343687	+	1.05776i	0.0130087	+	0.0400368i
$699$	58.3374	−	42.3846i	2.20652	−	1.60313i
$700$	8.16291	+	25.1229i	0.308529	+	0.949555i
$701$	12.4301	−	38.2558i	0.469478	−	1.44490i	−0.383785	−	0.923422i	$-0.625380\pi$
$701$	12.4301	−	38.2558i	0.469478	−	1.44490i	0.853263	−	0.521481i	$-0.174620\pi$
$702$	−9.75207	−	7.08530i	−0.368068	−	0.267417i
$703$	−0.560059	+	1.72368i	−0.0211230	+	0.0650100i
$704$	17.0083	−	12.3573i	0.641026	−	0.465733i
$705$	−58.1528	+	42.2505i	−2.19016	+	1.59125i
$706$	14.3733	+	10.4428i	0.540945	+	0.393020i
$707$	50.4216			1.89630
$708$	−1.48223			−0.0557057
$709$	−17.0559	−	12.3919i	−0.640549	−	0.465386i	0.219490	−	0.975615i	$-0.429561\pi$
$709$	−17.0559	−	12.3919i	−0.640549	−	0.465386i	−0.860039	+	0.510229i	$0.829561\pi$
$710$	8.95714	+	27.5672i	0.336155	+	1.03458i
$711$	−7.32461	+	22.5428i	−0.274694	+	0.845422i
$712$	9.14981			0.342904
$713$	6.51540	+	2.17717i	0.244004	+	0.0815357i
$714$	95.3661			3.56899
$715$	3.56560	−	10.9738i	0.133346	−	0.410397i
$716$	−1.35592	−	4.17308i	−0.0506730	−	0.155955i
$717$	26.9651	+	19.5913i	1.00703	+	0.731650i
$718$	2.79715			0.104389
$719$	−41.3656			−1.54268			−0.771338	−	0.636426i	$-0.780412\pi$
$719$	−41.3656			−1.54268			−0.771338	+	0.636426i	$0.780412\pi$
$720$	−7.43641	−	5.40287i	−0.277139	−	0.201353i
$721$	−3.98206	+	2.89314i	−0.148300	+	0.107746i
$722$	−14.0429	+	10.2027i	−0.522621	+	0.379706i
$723$	12.3002	−	37.8560i	0.457448	−	1.40788i
$724$	−23.0021	−	16.7120i	−0.854865	−	0.621096i
$725$	−0.830908	+	2.55727i	−0.0308592	+	0.0949747i
$726$	1.76172	+	5.42201i	0.0653835	+	0.201230i
$727$	−0.643007	+	0.467172i	−0.0238478	+	0.0173264i	−0.599645	−	0.800266i	$-0.704692\pi$
$727$	−0.643007	+	0.467172i	−0.0238478	+	0.0173264i	0.575798	+	0.817592i	$0.304692\pi$
$728$	−3.92414	−	12.0772i	−0.145438	−	0.447613i
$729$	5.72383	+	17.6161i	0.211994	+	0.652449i
$730$	13.5892	−	9.87313i	0.502959	−	0.365421i
$731$	−0.853254	−	2.62604i	−0.0315587	−	0.0971278i
$732$	−4.70781	+	14.4891i	−0.174006	+	0.535534i
$733$	−30.6808	−	22.2909i	−1.13322	−	0.823334i	−0.147062	−	0.989127i	$-0.546982\pi$
$733$	−30.6808	−	22.2909i	−1.13322	−	0.823334i	−0.986161	+	0.165793i	$0.946982\pi$
$734$	0.242460	−	0.746214i	0.00894935	−	0.0275433i
$735$	−99.4411	+	72.2482i	−3.66794	+	2.66492i
$736$	−5.43438	+	3.94831i	−0.200314	+	0.145537i
$737$	16.9016	+	12.2797i	0.622579	+	0.452330i
$738$	24.3388			0.895925
$739$	−38.4187			−1.41325			−0.706627	−	0.707587i	$-0.749784\pi$
$739$	−38.4187			−1.41325			−0.706627	+	0.707587i	$0.749784\pi$
$740$	−10.9893	−	7.98420i	−0.403975	−	0.293505i
$741$	0.480804	+	1.47976i	0.0176628	+	0.0543604i
$742$	12.5010	−	38.4742i	0.458927	−	1.41243i
$743$	−11.0652			−0.405943			−0.202972	−	0.979185i	$-0.565060\pi$
$743$	−11.0652			−0.405943			−0.202972	+	0.979185i	$0.565060\pi$
$744$	−0.428906	+	51.4689i	−0.0157244	+	1.88694i
$745$	59.8035			2.19103
$746$	−7.87572	+	24.2390i	−0.288350	+	0.887451i
$747$	35.0673	+	107.926i	1.28305	+	3.94881i
$748$	24.7317	+	17.9686i	0.904279	+	0.656997i
$749$	−3.51045			−0.128269
$750$	−2.73304			−0.0997966
$751$	1.90608	+	1.38485i	0.0695539	+	0.0505339i	0.622019	−	0.783002i	$-0.286313\pi$
$751$	1.90608	+	1.38485i	0.0695539	+	0.0505339i	−0.552465	+	0.833536i	$0.686313\pi$
$752$	2.30247	−	1.67284i	0.0839623	−	0.0610022i
$753$	−25.5474	+	18.5613i	−0.930998	+	0.676410i
$754$	0.145337	−	0.447300i	0.00529285	−	0.0162897i
$755$	27.6677	+	20.1018i	1.00693	+	0.731578i
$756$	−20.1044	+	61.8749i	−0.731189	+	2.25037i
$757$	3.52613	+	10.8523i	0.128160	+	0.394434i	0.994463	−	0.105083i	$-0.0335108\pi$
$757$	3.52613	+	10.8523i	0.128160	+	0.394434i	−0.866304	+	0.499517i	$0.833511\pi$
$758$	−4.91419	+	3.57037i	−0.178491	+	0.129682i
$759$	−4.35840	−	13.4138i	−0.158200	−	0.486889i
$760$	1.41172	+	4.34484i	0.0512086	+	0.157604i
$761$	−9.57817	+	6.95895i	−0.347209	+	0.252262i	−0.747697	−	0.664040i	$-0.768840\pi$
$761$	−9.57817	+	6.95895i	−0.347209	+	0.252262i	0.400489	+	0.916302i	$0.368840\pi$
$762$	6.13880	+	18.8933i	0.222385	+	0.684431i
$763$	20.2903	−	62.4472i	0.734559	−	2.26074i
$764$	13.0767	+	9.50078i	0.473099	+	0.343726i
$765$	52.2837	−	160.913i	1.89032	−	5.81781i
$766$	11.2373	−	8.16440i	0.406021	−	0.294992i
$767$	0.329860	−	0.239657i	0.0119105	−	0.00865352i
$768$	−43.0918	−	31.3080i	−1.55494	−	1.12973i
$769$	24.5510			0.885330			0.442665	−	0.896687i	$-0.354033\pi$
$769$	24.5510			0.885330			0.442665	+	0.896687i	$0.354033\pi$
$770$	46.6059			1.67956
$771$	−64.5623	−	46.9072i	−2.32515	−	1.68932i
$772$	−0.459651	−	1.41466i	−0.0165432	−	0.0509148i
$773$	−0.121482	+	0.373884i	−0.00436941	+	0.0134477i	−0.953217	−	0.302285i	$-0.902250\pi$
$773$	−0.121482	+	0.373884i	−0.00436941	+	0.0134477i	0.948848	+	0.315733i	$0.102250\pi$
$774$	−2.44134			−0.0877522
$775$	17.1124	+	23.9707i	0.614695	+	0.861053i
$776$	−8.93279			−0.320669
$777$	15.8701	−	48.8432i	0.569338	−	1.75224i
$778$	6.93518	+	21.3443i	0.248638	+	0.765230i
$779$	−1.46760	−	1.06627i	−0.0525821	−	0.0382032i
$780$	−11.6613			−0.417541
$781$	−35.1297			−1.25704
$782$	6.86144	+	4.98513i	0.245365	+	0.178268i
$783$	−5.35764	+	3.89256i	−0.191467	+	0.139109i
$784$	3.93721	−	2.86055i	0.140615	−	0.102163i
$785$	1.27937	−	3.93749i	0.0456626	−	0.140535i
$786$	9.94727	+	7.22712i	0.354807	+	0.257783i
$787$	6.78540	−	20.8833i	0.241873	−	0.744410i	−0.754262	−	0.656574i	$-0.772005\pi$
$787$	6.78540	−	20.8833i	0.241873	−	0.744410i	0.996135	−	0.0878356i	$-0.0279950\pi$
$788$	8.89148	+	27.3652i	0.316746	+	0.974844i
$789$	45.9541	−	33.3876i	1.63601	−	1.18863i
$790$	−3.06208	−	9.42413i	−0.108944	−	0.335295i
$791$	2.33935	+	7.19976i	0.0831775	+	0.255994i
$792$	60.0984	−	43.6640i	2.13550	−	1.55153i
$793$	−1.29501	−	3.98564i	−0.0459873	−	0.141534i
$794$	−2.49228	+	7.67045i	−0.0884477	+	0.272214i
$795$	−82.6005	−	60.0128i	−2.92954	−	2.12843i
$796$	6.65955	−	20.4960i	0.236041	−	0.726461i
$797$	34.4496	−	25.0291i	1.22027	−	0.886577i	0.224146	−	0.974556i	$-0.428041\pi$
$797$	34.4496	−	25.0291i	1.22027	−	0.886577i	0.996122	+	0.0879790i	$0.0280409\pi$
$798$	−5.08433	+	3.69398i	−0.179983	+	0.130766i
$799$	42.3810	+	30.7916i	1.49933	+	1.08933i
$800$	−28.7993			−1.01821
$801$	22.3311			0.789032
$802$	−23.5882	−	17.1379i	−0.832930	−	0.605159i
$803$	6.29080	+	19.3611i	0.221998	+	0.683238i
$804$	6.52453	−	20.0805i	0.230103	−	0.708183i
$805$	−17.2775			−0.608953
$806$	−2.99318	−	4.19279i	−0.105430	−	0.147685i
$807$	−9.69999			−0.341456
$808$	−10.3824	+	31.9536i	−0.365250	+	1.12412i
$809$	4.39498	+	13.5263i	0.154519	+	0.475561i	0.998112	−	0.0614225i	$-0.0195637\pi$
$809$	4.39498	+	13.5263i	0.154519	+	0.475561i	−0.843593	+	0.536984i	$0.819564\pi$
$810$	−48.2737	−	35.0729i	−1.69616	−	1.23234i
$811$	−28.2686			−0.992645			−0.496322	−	0.868138i	$-0.665317\pi$
$811$	−28.2686			−0.992645			−0.496322	+	0.868138i	$0.665317\pi$
$812$	−2.53841			−0.0890807
$813$	−51.4138	−	37.3543i	−1.80316	−	1.31007i
$814$	−9.96734	+	7.24170i	−0.349355	+	0.253821i
$815$	0.713961	−	0.518723i	0.0250090	−	0.0181701i
$816$	−2.94483	+	9.06327i	−0.103090	+	0.317278i
$817$	0.147209	+	0.106954i	0.00515021	+	0.00374184i
$818$	5.02178	−	15.4554i	0.175582	−	0.540387i
$819$	−9.57730	−	29.4759i	−0.334658	−	1.02997i
$820$	10.9994	−	7.99152i	0.384115	−	0.279076i
$821$	1.65626	+	5.09743i	0.0578038	+	0.177902i	0.975790	−	0.218712i	$-0.0701854\pi$
$821$	1.65626	+	5.09743i	0.0578038	+	0.177902i	−0.917986	+	0.396613i	$0.870185\pi$
$822$	−17.4547	−	53.7199i	−0.608801	−	1.87370i
$823$	23.4645	−	17.0480i	0.817922	−	0.594255i	−0.0981946	−	0.995167i	$-0.531307\pi$
$823$	23.4645	−	17.0480i	0.817922	−	0.594255i	0.916116	+	0.400912i	$0.131307\pi$
$824$	−1.01351	−	3.11927i	−0.0353074	−	0.108665i
$825$	18.6860	−	57.5096i	0.650563	−	2.00223i
$826$	1.33235	+	0.968012i	0.0463586	+	0.0336815i
$827$	2.52340	−	7.76623i	0.0877472	−	0.270058i	−0.897549	−	0.440916i	$-0.854654\pi$
$827$	2.52340	−	7.76623i	0.0877472	−	0.270058i	0.985296	+	0.170857i	$0.0546538\pi$
$828$	−8.10637	+	5.88962i	−0.281716	+	0.204678i
$829$	−9.71291	+	7.05684i	−0.337343	+	0.245094i	−0.743540	−	0.668691i	$-0.766855\pi$
$829$	−9.71291	+	7.05684i	−0.337343	+	0.245094i	0.406197	+	0.913786i	$0.366855\pi$
$830$	−38.3805	−	27.8851i	−1.33221	−	0.967905i
$831$	−23.1012			−0.801372
$832$	5.84462			0.202626
$833$	72.4714	+	52.6536i	2.51099	+	1.82434i
$834$	−18.4526	−	56.7912i	−0.638961	−	1.96652i
$835$	2.11743	−	6.51679i	0.0732769	−	0.225523i
$836$	−2.01455			−0.0696747
$837$	−0.604455	+	72.5349i	−0.0208930	+	2.50717i
$838$	−10.2922			−0.355538
$839$	3.05406	−	9.39942i	0.105438	−	0.324504i	−0.884395	−	0.466739i	$-0.845429\pi$
$839$	3.05406	−	9.39942i	0.105438	−	0.324504i	0.989833	+	0.142235i	$0.0454288\pi$
$840$	−40.0034	−	123.118i	−1.38025	−	4.24796i
$841$	23.2525	+	16.8939i	0.801809	+	0.582548i
$842$	−34.5692			−1.19133
$843$	47.9143			1.65026
$844$	−16.7290	−	12.1544i	−0.575837	−	0.418370i
$845$	2.59514	−	1.88548i	0.0892754	−	0.0648624i
$846$	37.4718	−	27.2248i	1.28831	−	0.936009i
$847$	−2.61554	+	8.04980i	−0.0898709	+	0.276594i
$848$	3.27043	+	2.37611i	0.112307	+	0.0815960i
$849$	−30.0627	+	92.5234i	−1.03175	+	3.17540i
$850$	11.2365	+	34.5823i	0.385407	+	1.18616i
$851$	3.69504	−	2.68461i	0.126664	−	0.0920271i
$852$	10.9712	+	33.7658i	0.375866	+	1.15680i
$853$	16.7894	+	51.6723i	0.574857	+	1.76923i	0.636667	+	0.771139i	$0.280313\pi$
$853$	16.7894	+	51.6723i	0.574857	+	1.76923i	−0.0618103	+	0.998088i	$0.519687\pi$
$854$	13.6943	−	9.94950i	0.468610	−	0.340465i
$855$	3.44547	+	10.6041i	0.117833	+	0.362652i
$856$	0.722838	−	2.22467i	0.0247061	−	0.0760376i
$857$	24.8988	+	18.0901i	0.850527	+	0.617944i	0.925291	−	0.379257i	$-0.123820\pi$
$857$	24.8988	+	18.0901i	0.850527	+	0.617944i	−0.0747639	+	0.997201i	$0.523820\pi$
$858$	−3.26842	+	10.0592i	−0.111582	+	0.343415i
$859$	25.1408	−	18.2659i	0.857793	−	0.623223i	−0.0694906	−	0.997583i	$-0.522137\pi$
$859$	25.1408	−	18.2659i	0.857793	−	0.623223i	0.927284	+	0.374359i	$0.122137\pi$
$860$	−1.10331	+	0.801600i	−0.0376225	+	0.0273343i
$861$	41.5866	+	30.2145i	1.41727	+	1.02971i
$862$	−1.66461			−0.0566968
$863$	−35.3421			−1.20306			−0.601530	−	0.798850i	$-0.705442\pi$
$863$	−35.3421			−1.20306			−0.601530	+	0.798850i	$0.705442\pi$
$864$	−57.3833	−	41.6914i	−1.95222	−	1.41837i
$865$	−11.6525	−	35.8626i	−0.396196	−	1.21937i
$866$	5.30213	−	16.3183i	0.180174	−	0.554518i
$867$	−121.385			−4.12247
$868$	−16.5297	+	22.3570i	−0.561054	+	0.758845i
$869$	12.0094			0.407392
$870$	1.48159	−	4.55986i	0.0502306	−	0.154594i
$871$	1.79476	+	5.52369i	0.0608130	+	0.187163i
$872$	35.3965	+	25.7171i	1.19868	+	0.870891i
$873$	−21.8015			−0.737869
$874$	−0.558908			−0.0189053
$875$	−3.28268	−	2.38501i	−0.110975	−	0.0806279i
$876$	16.6448	−	12.0931i	0.562374	−	0.408589i
$877$	−6.40074	+	4.65041i	−0.216138	+	0.157033i	−0.690586	−	0.723250i	$-0.742647\pi$
$877$	−6.40074	+	4.65041i	−0.216138	+	0.157033i	0.474449	+	0.880283i	$0.342647\pi$
$878$	−0.104102	+	0.320393i	−0.00351327	+	0.0108127i
$879$	−56.3701	−	40.9553i	−1.90132	−	1.38139i
$880$	−1.43916	+	4.42927i	−0.0485140	+	0.149311i
$881$	−2.32491	−	7.15535i	−0.0783283	−	0.241070i	0.904223	−	0.427060i	$-0.140451\pi$
$881$	−2.32491	−	7.15535i	−0.0783283	−	0.241070i	−0.982552	+	0.185990i	$0.940451\pi$
$882$	64.0766	−	46.5544i	2.15757	−	1.56757i
$883$	−4.29506	−	13.2188i	−0.144540	−	0.444849i	0.852411	−	0.522872i	$-0.175139\pi$
$883$	−4.29506	−	13.2188i	−0.144540	−	0.444849i	−0.996952	+	0.0780226i	$0.975139\pi$
$884$	2.62621	+	8.08265i	0.0883291	+	0.271849i
$885$	3.36265	−	2.44311i	0.113034	−	0.0821242i
$886$	3.75270	+	11.5496i	0.126075	+	0.388018i
$887$	−2.82691	+	8.70033i	−0.0949183	+	0.292129i	−0.987232	−	0.159287i	$-0.949081\pi$
$887$	−2.82691	+	8.70033i	−0.0949183	+	0.292129i	0.892314	+	0.451415i	$0.149081\pi$
$888$	27.6855	+	20.1147i	0.929065	+	0.675005i
$889$	−9.11398	+	28.0499i	−0.305673	+	0.940764i
$890$	−7.55268	+	5.48735i	−0.253167	+	0.183936i
$891$	58.5056	−	42.5068i	1.96001	−	1.42403i
$892$	−4.40566	−	3.20090i	−0.147512	−	0.107174i
$893$	−3.45220			−0.115524
$894$	−54.8192			−1.83343
$895$	9.95443	+	7.23231i	0.332740	+	0.241750i
$896$	−7.39390	−	22.7561i	−0.247013	−	0.760227i
$897$	1.21165	−	3.72909i	0.0404560	−	0.124511i
$898$	10.4451			0.348558
$899$	−2.69887	+	0.852117i	−0.0900122	+	0.0284197i
$900$	−42.9594			−1.43198
$901$	−22.9937	+	70.7673i	−0.766030	+	2.35760i
$902$	−3.81068	−	11.7281i	−0.126882	−	0.390501i
$903$	−4.17141	−	3.03070i	−0.138816	−	0.100856i
$904$	−5.04439			−0.167774
$905$	79.7292			2.65029
$906$	−25.3617	−	18.4264i	−0.842586	−	0.612175i
$907$	−19.8375	+	14.4128i	−0.658693	+	0.478569i	−0.866221	−	0.499660i	$-0.833458\pi$
$907$	−19.8375	+	14.4128i	−0.658693	+	0.478569i	0.207528	+	0.978229i	$0.433458\pi$
$908$	8.78273	−	6.38102i	0.291465	−	0.211762i
$909$	−25.3393	+	77.9864i	−0.840452	+	2.58664i
$910$	10.4822	+	7.61574i	0.347480	+	0.252459i
$911$	4.89421	−	15.0628i	0.162152	−	0.499053i	−0.836663	−	0.547718i	$-0.815497\pi$
$911$	4.89421	−	15.0628i	0.162152	−	0.499053i	0.998815	+	0.0486647i	$0.0154966\pi$
$912$	−0.194063	−	0.597265i	−0.00642608	−	0.0197774i
$913$	46.5155	−	33.7955i	1.53944	−	1.11847i
$914$	0.641844	+	1.97539i	0.0212303	+	0.0653402i
$915$	−13.2016	−	40.6304i	−0.436432	−	1.34320i
$916$	−6.40990	+	4.65706i	−0.211789	+	0.153874i
$917$	5.64096	+	17.3611i	0.186281	+	0.573314i
$918$	−27.6742	+	85.1724i	−0.913385	+	2.81111i
$919$	7.68105	+	5.58061i	0.253374	+	0.184087i	0.707221	−	0.706993i	$-0.249949\pi$
$919$	7.68105	+	5.58061i	0.253374	+	0.184087i	−0.453847	+	0.891080i	$0.649949\pi$
$920$	3.55763	−	10.9492i	0.117291	−	0.360986i
$921$	−74.7442	+	54.3048i	−2.46290	+	1.78940i
$922$	−24.1423	+	17.5404i	−0.795086	+	0.577663i
$923$	−7.90103	−	5.74044i	−0.260066	−	0.188949i
$924$	57.0854			1.87797
$925$	19.5817			0.643844
$926$	2.62093	+	1.90422i	0.0861292	+	0.0625765i
$927$	−2.47359	−	7.61294i	−0.0812434	−	0.250042i
$928$	0.855192	−	2.63201i	0.0280730	−	0.0864000i
$929$	34.5845			1.13468			0.567341	−	0.823483i	$-0.307972\pi$
$929$	34.5845			1.13468			0.567341	+	0.823483i	$0.307972\pi$
$930$	−30.5130	−	42.7421i	−1.00056	−	1.40157i
$931$	−5.90326			−0.193471
$932$	−8.02078	+	24.6854i	−0.262729	+	0.808597i
$933$	−5.46562	−	16.8215i	−0.178937	−	0.550710i
$934$	7.72877	+	5.61528i	0.252893	+	0.183738i
$935$	−85.7243			−2.80348
$936$	20.6518			0.675024
$937$	−6.44426	−	4.68203i	−0.210525	−	0.152955i	0.477526	−	0.878617i	$-0.341534\pi$
$937$	−6.44426	−	4.68203i	−0.210525	−	0.152955i	−0.688051	+	0.725662i	$0.741534\pi$
$938$	−18.9789	+	13.7890i	−0.619683	+	0.450226i
$939$	−61.4304	+	44.6318i	−2.00471	+	1.45650i
$940$	7.99539	−	24.6073i	0.260781	−	0.802601i
$941$	32.2159	+	23.4062i	1.05021	+	0.763020i	0.972252	−	0.233937i	$-0.0751609\pi$
$941$	32.2159	+	23.4062i	1.05021	+	0.763020i	0.0779552	+	0.996957i	$0.475161\pi$
$942$	−1.17274	+	3.60932i	−0.0382099	+	0.117598i
$943$	1.41267	+	4.34777i	0.0460030	+	0.141583i
$944$	−0.133139	+	0.0967310i	−0.00433330	+	0.00314833i
$945$	−56.3766	−	173.509i	−1.83393	−	5.64426i
$946$	0.382235	+	1.17640i	0.0124275	+	0.0382480i
$947$	−13.8461	+	10.0598i	−0.449937	+	0.326899i	−0.789571	−	0.613659i	$-0.789697\pi$
$947$	−13.8461	+	10.0598i	−0.449937	+	0.326899i	0.339634	+	0.940558i	$0.389697\pi$
$948$	−3.75060	−	11.5432i	−0.121814	−	0.374904i
$949$	−1.74887	+	5.38247i	−0.0567708	+	0.174723i
$950$	−1.93860	−	1.40847i	−0.0628964	−	0.0456969i
$951$	−22.8727	+	70.3948i	−0.741697	+	2.28271i
$952$	−76.3260	+	55.4541i	−2.47374	+	1.79728i
$953$	32.7067	−	23.7628i	1.05947	−	0.769752i	0.0854825	−	0.996340i	$-0.472757\pi$
$953$	32.7067	−	23.7628i	1.05947	−	0.769752i	0.973991	+	0.226587i	$0.0727568\pi$
$954$	53.2251	+	38.6703i	1.72323	+	1.25200i
$955$	−45.3262			−1.46672
$956$	−11.9974			−0.388025
$957$	4.70100	+	3.41548i	0.151962	+	0.110407i
$958$	0.632671	+	1.94716i	0.0204407	+	0.0629100i
$959$	25.9141	−	79.7553i	0.836809	−	2.57543i
$960$	59.5812			1.92297
$961$	−10.0695	+	29.3190i	−0.324824	+	0.945775i
$962$	−3.42510			−0.110430
$963$	1.76417	−	5.42955i	0.0568495	−	0.174965i
$964$	4.42747	+	13.6264i	0.142599	+	0.438875i
$965$	3.37452	+	2.45173i	0.108630	+	0.0789241i
$966$	15.8375			0.509564
$967$	22.7612			0.731951			0.365976	−	0.930624i	$-0.380735\pi$
$967$	22.7612			0.731951			0.365976	+	0.930624i	$0.380735\pi$
$968$	−4.56281	−	3.31508i	−0.146654	−	0.106551i
$969$	9.35183	−	6.79450i	0.300424	−	0.218271i
$970$	7.37355	−	5.35720i	0.236750	−	0.172009i
$971$	−7.40273	+	22.7833i	−0.237565	+	0.731149i	0.759206	+	0.650850i	$0.225588\pi$
$971$	−7.40273	+	22.7833i	−0.237565	+	0.731149i	−0.996771	+	0.0802990i	$0.974412\pi$
$972$	−22.9576	−	16.6797i	−0.736366	−	0.535001i
$973$	27.3957	−	84.3151i	0.878264	−	2.70302i
$974$	2.65270	+	8.16417i	0.0849980	+	0.261597i
$975$	13.6001	−	9.88108i	0.435553	−	0.316448i
$976$	0.522696	+	1.60869i	0.0167311	+	0.0514930i
$977$	−2.54250	−	7.82500i	−0.0813416	−	0.250344i	0.902113	−	0.431501i	$-0.142016\pi$
$977$	−2.54250	−	7.82500i	−0.0813416	−	0.250344i	−0.983454	+	0.181157i	$0.942016\pi$
$978$	−0.654455	+	0.475490i	−0.0209272	+	0.0152045i
$979$	−3.49634	−	10.7606i	−0.111743	−	0.343911i
$980$	13.6721	−	42.0784i	0.436739	−	1.34414i
$981$	86.3893	+	62.7655i	2.75820	+	2.00395i
$982$	2.59032	−	7.97219i	0.0826605	−	0.254403i
$983$	0.732682	−	0.532325i	0.0233689	−	0.0169785i	−0.576039	−	0.817422i	$-0.695403\pi$
$983$	0.732682	−	0.532325i	0.0233689	−	0.0169785i	0.599408	+	0.800443i	$0.295403\pi$
$984$	−27.7109	+	20.1331i	−0.883391	+	0.641821i
$985$	−65.2766	−	47.4263i	−2.07989	−	1.51113i
$986$	−3.49419			−0.111278
$987$	97.8235			3.11375
$988$	−0.453093	−	0.329192i	−0.0144148	−	0.0104730i
$989$	−0.141700	−	0.436109i	−0.00450581	−	0.0138675i
$990$	−23.4217	+	72.0847i	−0.744391	+	2.29100i
$991$	11.8662			0.376944			0.188472	−	0.982079i	$-0.439647\pi$
$991$	11.8662			0.376944			0.188472	+	0.982079i	$0.439647\pi$
$992$	−17.6125	−	24.6713i	−0.559197	−	0.783313i
$993$	−4.39306			−0.139410
$994$	12.1899	−	37.5166i	0.386639	−	1.18995i
$995$	18.6747	+	57.4747i	0.592027	+	1.82207i
$996$	−47.0105	−	34.1551i	−1.48958	−	1.08225i
$997$	−58.1488			−1.84159			−0.920795	−	0.390046i	$-0.872459\pi$
$997$	−58.1488			−1.84159			−0.920795	+	0.390046i	$0.872459\pi$
$998$	8.64537			0.273665
$999$	39.0171	+	28.3476i	1.23445	+	0.896877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.6	yes	68
31.4	even	5	inner	403.2.k.e.66.6	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.6	✓	68	31.4	even	5	inner
403.2.k.e.287.6	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.285917 + 0.879963i) q^{2} +(-0.982047 - 3.02243i) q^{3} +(0.925448 + 0.672377i) q^{4} -3.20777 q^{5} +2.94041 q^{6} +(3.53175 + 2.56597i) q^{7} +(-2.35335 + 1.70981i) q^{8} +(-5.74362 + 4.17298i) q^{9} +O(q^{10})\)	\(q+(-0.285917 + 0.879963i) q^{2} +(-0.982047 - 3.02243i) q^{3} +(0.925448 + 0.672377i) q^{4} -3.20777 q^{5} +2.94041 q^{6} +(3.53175 + 2.56597i) q^{7} +(-2.35335 + 1.70981i) q^{8} +(-5.74362 + 4.17298i) q^{9} +(0.917156 - 2.82271i) q^{10} +(2.91008 + 2.11430i) q^{11} +(1.12338 - 3.45741i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-3.26775 + 2.37416i) q^{14} +(3.15018 + 9.69525i) q^{15} +(-0.124726 - 0.383868i) q^{16} +(6.01051 - 4.36689i) q^{17} +(-2.02987 - 6.24730i) q^{18} +(-0.151293 + 0.465631i) q^{19} +(-2.96862 - 2.15683i) q^{20} +(4.28711 - 13.1944i) q^{21} +(-2.69255 + 1.95625i) q^{22} +(0.998169 - 0.725212i) q^{23} +(7.47888 + 5.43373i) q^{24} +5.28976 q^{25} -0.925248 q^{26} +(10.5400 + 7.65773i) q^{27} +(1.54315 + 4.74934i) q^{28} +(-0.157079 + 0.483439i) q^{29} -9.43215 q^{30} +(3.23500 + 4.53153i) q^{31} -5.44435 q^{32} +(3.53249 - 10.8719i) q^{33} +(2.12419 + 6.53759i) q^{34} +(-11.3290 - 8.23102i) q^{35} -8.12124 q^{36} +3.70182 q^{37} +(-0.366481 - 0.266264i) q^{38} +(2.57103 - 1.86796i) q^{39} +(7.54900 - 5.48467i) q^{40} +(-1.14497 + 3.52387i) q^{41} +(10.3848 + 7.54500i) q^{42} +(0.114848 - 0.353467i) q^{43} +(1.27152 + 3.91335i) q^{44} +(18.4242 - 13.3860i) q^{45} +(0.352766 + 1.08570i) q^{46} +(2.17893 + 6.70605i) q^{47} +(-1.03773 + 0.753952i) q^{48} +(3.72596 + 11.4673i) q^{49} +(-1.51243 + 4.65479i) q^{50} +(-19.1012 - 13.8778i) q^{51} +(-0.353490 + 1.08793i) q^{52} +(-8.10271 + 5.88696i) q^{53} +(-9.75207 + 7.08530i) q^{54} +(-9.33487 - 6.78218i) q^{55} -12.6988 q^{56} +1.55591 q^{57} +(-0.380496 - 0.276447i) q^{58} +(-0.125995 - 0.387773i) q^{59} +(-3.60354 + 11.0906i) q^{60} -4.19075 q^{61} +(-4.91252 + 1.55104i) q^{62} -30.9928 q^{63} +(1.80609 - 5.55856i) q^{64} +(-0.991254 - 3.05077i) q^{65} +(8.55685 + 6.21691i) q^{66} +5.80795 q^{67} +8.49861 q^{68} +(-3.17215 - 2.30470i) q^{69} +(10.4822 - 7.61574i) q^{70} +(-7.90103 + 5.74044i) q^{71} +(6.38174 - 19.6410i) q^{72} +(4.57861 + 3.32655i) q^{73} +(-1.05842 + 3.25747i) q^{74} +(-5.19479 - 15.9879i) q^{75} +(-0.453093 + 0.329192i) q^{76} +(4.85247 + 14.9344i) q^{77} +(0.908637 + 2.79650i) q^{78} +(2.70104 - 1.96242i) q^{79} +(0.400092 + 1.23136i) q^{80} +(6.21261 - 19.1205i) q^{81} +(-2.77351 - 2.01507i) q^{82} +(4.93941 - 15.2019i) q^{83} +(12.8391 - 9.32815i) q^{84} +(-19.2803 + 14.0080i) q^{85} +(0.278201 + 0.202125i) q^{86} +1.61542 q^{87} -10.4635 q^{88} +(-2.54472 - 1.84885i) q^{89} +(6.51135 + 20.0399i) q^{90} +(-1.34901 + 4.15182i) q^{91} +1.41137 q^{92} +(10.5193 - 14.2277i) q^{93} -6.52407 q^{94} +(0.485312 - 1.49364i) q^{95} +(5.34661 + 16.4552i) q^{96} +(2.48437 + 1.80500i) q^{97} -11.1561 q^{98} -25.5374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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