LMFDB - Embedded newform 403.2.h.a.118.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.10
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.352077 q^{2} +(-1.65894 - 2.87336i) q^{3} -1.87604 q^{4} +(1.09161 - 1.89072i) q^{5} +(-0.584073 - 1.01164i) q^{6} +(-1.14275 - 1.97930i) q^{7} -1.36466 q^{8} +(-4.00415 + 6.93538i) q^{9} +O(q^{10})$	\(q+0.352077 q^{2} +(-1.65894 - 2.87336i) q^{3} -1.87604 q^{4} +(1.09161 - 1.89072i) q^{5} +(-0.584073 - 1.01164i) q^{6} +(-1.14275 - 1.97930i) q^{7} -1.36466 q^{8} +(-4.00415 + 6.93538i) q^{9} +(0.384330 - 0.665679i) q^{10} +(1.46731 - 2.54145i) q^{11} +(3.11224 + 5.39055i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.402336 - 0.696866i) q^{14} -7.24364 q^{15} +3.27162 q^{16} +(1.85069 + 3.20548i) q^{17} +(-1.40977 + 2.44179i) q^{18} +(0.373487 + 0.646898i) q^{19} +(-2.04790 + 3.54707i) q^{20} +(-3.79150 + 6.56707i) q^{21} +(0.516605 - 0.894787i) q^{22} -7.68978 q^{23} +(2.26389 + 3.92118i) q^{24} +(0.116781 + 0.202271i) q^{25} +(0.176038 - 0.304907i) q^{26} +16.6169 q^{27} +(2.14385 + 3.71325i) q^{28} +5.11832 q^{29} -2.55032 q^{30} +(-5.56377 - 0.210991i) q^{31} +3.88119 q^{32} -9.73669 q^{33} +(0.651584 + 1.12858i) q^{34} -4.98974 q^{35} +(7.51195 - 13.0111i) q^{36} +(-3.95073 - 6.84287i) q^{37} +(0.131496 + 0.227758i) q^{38} -3.31787 q^{39} +(-1.48968 + 2.58020i) q^{40} +(-2.63374 + 4.56176i) q^{41} +(-1.33490 + 2.31211i) q^{42} +(-2.99467 - 5.18692i) q^{43} +(-2.75273 + 4.76787i) q^{44} +(8.74192 + 15.1414i) q^{45} -2.70739 q^{46} -5.63971 q^{47} +(-5.42741 - 9.40055i) q^{48} +(0.888247 - 1.53849i) q^{49} +(0.0411160 + 0.0712150i) q^{50} +(6.14034 - 10.6354i) q^{51} +(-0.938021 + 1.62470i) q^{52} +(2.20199 - 3.81396i) q^{53} +5.85042 q^{54} +(-3.20345 - 5.54854i) q^{55} +(1.55947 + 2.70108i) q^{56} +(1.23918 - 2.14633i) q^{57} +1.80204 q^{58} +(-2.14122 - 3.70871i) q^{59} +13.5894 q^{60} +3.34127 q^{61} +(-1.95887 - 0.0742850i) q^{62} +18.3029 q^{63} -5.17676 q^{64} +(-1.09161 - 1.89072i) q^{65} -3.42806 q^{66} +(5.54348 - 9.60159i) q^{67} +(-3.47197 - 6.01362i) q^{68} +(12.7569 + 22.0955i) q^{69} -1.75677 q^{70} +(-1.53632 + 2.66099i) q^{71} +(5.46431 - 9.46447i) q^{72} +(-1.48966 + 2.58017i) q^{73} +(-1.39096 - 2.40921i) q^{74} +(0.387466 - 0.671110i) q^{75} +(-0.700677 - 1.21361i) q^{76} -6.70707 q^{77} -1.16815 q^{78} +(6.59593 + 11.4245i) q^{79} +(3.57133 - 6.18572i) q^{80} +(-15.5539 - 26.9402i) q^{81} +(-0.927277 + 1.60609i) q^{82} +(6.61777 - 11.4623i) q^{83} +(7.11301 - 12.3201i) q^{84} +8.08090 q^{85} +(-1.05435 - 1.82619i) q^{86} +(-8.49097 - 14.7068i) q^{87} +(-2.00238 + 3.46823i) q^{88} -8.82102 q^{89} +(3.07783 + 5.33095i) q^{90} -2.28550 q^{91} +14.4264 q^{92} +(8.62368 + 16.3367i) q^{93} -1.98561 q^{94} +1.63080 q^{95} +(-6.43865 - 11.1521i) q^{96} +0.0441635 q^{97} +(0.312731 - 0.541666i) q^{98} +(11.7506 + 20.3527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.352077			0.248956			0.124478	−	0.992222i	$-0.460274\pi$
$2$	0.352077			0.248956			0.124478	+	0.992222i	$0.460274\pi$
$3$	−1.65894	−	2.87336i	−0.957788	−	1.65894i	−0.727855	−	0.685731i	$-0.759483\pi$
$3$	−1.65894	−	2.87336i	−0.957788	−	1.65894i	−0.229932	−	0.973207i	$-0.573851\pi$
$4$	−1.87604			−0.938021
$5$	1.09161	−	1.89072i	0.488182	−	0.845556i	−0.511725	−	0.859149i	$-0.670993\pi$
$5$	1.09161	−	1.89072i	0.488182	−	0.845556i	0.999908	+	0.0135927i	$0.00432682\pi$
$6$	−0.584073	−	1.01164i	−0.238447	−	0.413002i
$7$	−1.14275	−	1.97930i	−0.431919	−	0.748105i	0.565120	−	0.825009i	$-0.308830\pi$
$7$	−1.14275	−	1.97930i	−0.431919	−	0.748105i	−0.997039	+	0.0769036i	$0.975497\pi$
$8$	−1.36466			−0.482482
$9$	−4.00415	+	6.93538i	−1.33472	+	2.31179i
$10$	0.384330	−	0.665679i	0.121536	−	0.210506i
$11$	1.46731	−	2.54145i	0.442410	−	0.766277i	−0.555458	−	0.831545i	$-0.687457\pi$
$11$	1.46731	−	2.54145i	0.442410	−	0.766277i	0.997868	+	0.0652679i	$0.0207902\pi$
$12$	3.11224	+	5.39055i	0.898425	+	1.55612i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.402336	−	0.696866i	−0.107529	−	0.186245i
$15$	−7.24364			−1.87030
$16$	3.27162			0.817904
$17$	1.85069	+	3.20548i	0.448857	+	0.777444i	0.998312	−	0.0580799i	$-0.0184978\pi$
$17$	1.85069	+	3.20548i	0.448857	+	0.777444i	−0.549455	+	0.835524i	$0.685164\pi$
$18$	−1.40977	+	2.44179i	−0.332285	+	0.575535i
$19$	0.373487	+	0.646898i	0.0856837	+	0.148409i	0.905682	−	0.423957i	$-0.139359\pi$
$19$	0.373487	+	0.646898i	0.0856837	+	0.148409i	−0.819999	+	0.572365i	$0.806026\pi$
$20$	−2.04790	+	3.54707i	−0.457925	+	0.793150i
$21$	−3.79150	+	6.56707i	−0.827373	+	1.43305i
$22$	0.516605	−	0.894787i	0.110141	−	0.190769i
$23$	−7.68978			−1.60343			−0.801715	−	0.597706i	$-0.796079\pi$
$23$	−7.68978			−1.60343			−0.801715	+	0.597706i	$0.796079\pi$
$24$	2.26389	+	3.92118i	0.462115	+	0.800407i
$25$	0.116781	+	0.202271i	0.0233563	+	0.0404542i
$26$	0.176038	−	0.304907i	0.0345240	−	0.0597973i
$27$	16.6169			3.19792
$28$	2.14385	+	3.71325i	0.405149	+	0.701738i
$29$	5.11832			0.950448			0.475224	−	0.879865i	$-0.342367\pi$
$29$	5.11832			0.950448			0.475224	+	0.879865i	$0.342367\pi$
$30$	−2.55032			−0.465622
$31$	−5.56377	−	0.210991i	−0.999282	−	0.0378951i
$31$	−5.56377	−	0.210991i	−0.999282	−	0.0378951i
$32$	3.88119			0.686104
$33$	−9.73669			−1.69494
$34$	0.651584	+	1.12858i	0.111746	+	0.193549i
$35$	−4.98974			−0.843420
$36$	7.51195	−	13.0111i	1.25199	−	2.16851i
$37$	−3.95073	−	6.84287i	−0.649496	−	1.12496i	−0.983243	−	0.182298i	$-0.941647\pi$
$37$	−3.95073	−	6.84287i	−0.649496	−	1.12496i	0.333747	−	0.942663i	$-0.391687\pi$
$38$	0.131496	+	0.227758i	0.0213315	+	0.0369472i
$39$	−3.31787			−0.531285
$40$	−1.48968	+	2.58020i	−0.235539	+	0.407965i
$41$	−2.63374	+	4.56176i	−0.411320	+	0.712428i	−0.995034	−	0.0995315i	$-0.968266\pi$
$41$	−2.63374	+	4.56176i	−0.411320	+	0.712428i	0.583714	+	0.811959i	$0.301599\pi$
$42$	−1.33490	+	2.31211i	−0.205979	+	0.356767i
$43$	−2.99467	−	5.18692i	−0.456683	−	0.790998i	0.542100	−	0.840314i	$-0.317629\pi$
$43$	−2.99467	−	5.18692i	−0.456683	−	0.790998i	−0.998783	+	0.0493159i	$0.984296\pi$
$44$	−2.75273	+	4.76787i	−0.414990	+	0.718784i
$45$	8.74192	+	15.1414i	1.30317	+	2.25715i
$46$	−2.70739			−0.399183
$47$	−5.63971			−0.822637			−0.411318	−	0.911492i	$-0.634932\pi$
$47$	−5.63971			−0.822637			−0.411318	+	0.911492i	$0.634932\pi$
$48$	−5.42741	−	9.40055i	−0.783379	−	1.35685i
$49$	0.888247	−	1.53849i	0.126892	−	0.219784i
$50$	0.0411160	+	0.0712150i	0.00581468	+	0.0100713i
$51$	6.14034	−	10.6354i	0.859820	−	1.48925i
$52$	−0.938021	+	1.62470i	−0.130080	+	0.225305i
$53$	2.20199	−	3.81396i	0.302467	−	0.523888i	−0.674227	−	0.738524i	$-0.735523\pi$
$53$	2.20199	−	3.81396i	0.302467	−	0.523888i	0.976694	+	0.214636i	$0.0688564\pi$
$54$	5.85042			0.796141
$55$	−3.20345	−	5.54854i	−0.431954	−	0.748166i
$56$	1.55947	+	2.70108i	0.208393	+	0.360947i
$57$	1.23918	−	2.14633i	0.164134	−	0.284288i
$58$	1.80204			0.236620
$59$	−2.14122	−	3.70871i	−0.278763	−	0.482832i	0.692314	−	0.721596i	$-0.256591\pi$
$59$	−2.14122	−	3.70871i	−0.278763	−	0.482832i	−0.971078	+	0.238764i	$0.923258\pi$
$60$	13.5894			1.75438
$61$	3.34127			0.427806			0.213903	−	0.976855i	$-0.431382\pi$
$61$	3.34127			0.427806			0.213903	+	0.976855i	$0.431382\pi$
$62$	−1.95887	−	0.0742850i	−0.248777	−	0.00943420i
$63$	18.3029			2.30595
$64$	−5.17676			−0.647095
$65$	−1.09161	−	1.89072i	−0.135397	−	0.234515i
$66$	−3.42806			−0.421965
$67$	5.54348	−	9.60159i	0.677244	−	1.17302i	−0.298564	−	0.954390i	$-0.596508\pi$
$67$	5.54348	−	9.60159i	0.677244	−	1.17302i	0.975808	−	0.218631i	$-0.0701591\pi$
$68$	−3.47197	−	6.01362i	−0.421038	−	0.729259i
$69$	12.7569	+	22.0955i	1.53575	+	2.65999i
$70$	−1.75677			−0.209974
$71$	−1.53632	+	2.66099i	−0.182328	+	0.315802i	−0.942673	−	0.333718i	$-0.891697\pi$
$71$	−1.53632	+	2.66099i	−0.182328	+	0.315802i	0.760345	+	0.649520i	$0.225030\pi$
$72$	5.46431	−	9.46447i	0.643976	−	1.11540i
$73$	−1.48966	+	2.58017i	−0.174352	+	0.301987i	−0.939937	−	0.341348i	$-0.889116\pi$
$73$	−1.48966	+	2.58017i	−0.174352	+	0.301987i	0.765585	+	0.643335i	$0.222450\pi$
$74$	−1.39096	−	2.40921i	−0.161696	−	0.280065i
$75$	0.387466	−	0.671110i	0.0447407	−	0.0774932i
$76$	−0.700677	−	1.21361i	−0.0803731	−	0.139210i
$77$	−6.70707			−0.764341
$78$	−1.16815			−0.132267
$79$	6.59593	+	11.4245i	0.742100	+	1.28535i	0.951538	+	0.307533i	$0.0995033\pi$
$79$	6.59593	+	11.4245i	0.742100	+	1.28535i	−0.209438	+	0.977822i	$0.567163\pi$
$80$	3.57133	−	6.18572i	0.399286	−	0.691584i
$81$	−15.5539	−	26.9402i	−1.72821	−	2.99335i
$82$	−0.927277	+	1.60609i	−0.102401	+	0.177363i
$83$	6.61777	−	11.4623i	0.726395	−	1.25815i	−0.232002	−	0.972715i	$-0.574528\pi$
$83$	6.61777	−	11.4623i	0.726395	−	1.25815i	0.958397	−	0.285438i	$-0.0921389\pi$
$84$	7.11301	−	12.3201i	0.776093	−	1.34423i
$85$	8.08090			0.876497
$86$	−1.05435	−	1.82619i	−0.113694	−	0.196924i
$87$	−8.49097	−	14.7068i	−0.910328	−	1.57673i
$88$	−2.00238	+	3.46823i	−0.213455	+	0.369715i
$89$	−8.82102			−0.935026			−0.467513	−	0.883986i	$-0.654850\pi$
$89$	−8.82102			−0.935026			−0.467513	+	0.883986i	$0.654850\pi$
$90$	3.07783	+	5.33095i	0.324431	+	0.561932i
$91$	−2.28550			−0.239585
$92$	14.4264			1.50405
$93$	8.62368	+	16.3367i	0.894234	+	1.69404i
$94$	−1.98561			−0.204800
$95$	1.63080			0.167317
$96$	−6.43865	−	11.1521i	−0.657142	−	1.13820i
$97$	0.0441635			0.00448412			0.00224206	−	0.999997i	$-0.499286\pi$
$97$	0.0441635			0.00448412			0.00224206	+	0.999997i	$0.499286\pi$
$98$	0.312731	−	0.541666i	0.0315906	−	0.0547165i
$99$	11.7506	+	20.3527i	1.18098	+	2.04552i
$100$	−0.219087	−	0.379469i	−0.0219087	−	0.0379469i
$101$	−17.5047			−1.74179			−0.870894	−	0.491471i	$-0.836459\pi$
$101$	−17.5047			−1.74179			−0.870894	+	0.491471i	$0.836459\pi$
$102$	2.16187	−	3.74447i	0.214057	−	0.370758i
$103$	−3.75220	+	6.49901i	−0.369716	+	0.640366i	−0.989521	−	0.144389i	$-0.953878\pi$
$103$	−3.75220	+	6.49901i	−0.369716	+	0.640366i	0.619805	+	0.784756i	$0.287212\pi$
$104$	−0.682332	+	1.18183i	−0.0669082	+	0.115888i
$105$	8.27767	+	14.3373i	0.807818	+	1.39918i
$106$	0.775271	−	1.34281i	0.0753009	−	0.130425i
$107$	1.60809	+	2.78530i	0.155460	+	0.269265i	0.933227	−	0.359288i	$-0.116981\pi$
$107$	1.60809	+	2.78530i	0.155460	+	0.269265i	−0.777766	+	0.628554i	$0.783647\pi$
$108$	−31.1740			−2.99972
$109$	−19.4001			−1.85819			−0.929095	−	0.369842i	$-0.879412\pi$
$109$	−19.4001			−1.85819			−0.929095	+	0.369842i	$0.879412\pi$
$110$	−1.12786	−	1.95351i	−0.107537	−	0.186260i
$111$	−13.1080	+	22.7038i	−1.24416	+	2.15495i
$112$	−3.73864	−	6.47551i	−0.353268	−	0.611879i
$113$	8.31555	−	14.4029i	0.782261	−	1.35492i	−0.148361	−	0.988933i	$-0.547400\pi$
$113$	8.31555	−	14.4029i	0.782261	−	1.35492i	0.930622	−	0.365982i	$-0.119267\pi$
$114$	0.436287	−	0.755671i	0.0408620	−	0.0707751i
$115$	−8.39423	+	14.5392i	−0.782766	+	1.35579i
$116$	−9.60219			−0.891541
$117$	4.00415	+	6.93538i	0.370183	+	0.641176i
$118$	−0.753875	−	1.30575i	−0.0693998	−	0.120204i
$119$	4.22974	−	7.32613i	0.387740	−	0.671585i
$120$	9.88514			0.902385
$121$	1.19401	+	2.06809i	0.108546	+	0.188008i
$122$	1.17638			0.106505
$123$	17.4768			1.57583
$124$	10.4379	+	0.395828i	0.937347	+	0.0355464i
$125$	11.4260			1.02197
$126$	6.44404			0.574081
$127$	7.21981	+	12.5051i	0.640654	+	1.10965i	0.985287	+	0.170908i	$0.0546701\pi$
$127$	7.21981	+	12.5051i	0.640654	+	1.10965i	−0.344633	+	0.938738i	$0.611997\pi$
$128$	−9.58499			−0.847202
$129$	−9.93594	+	17.2095i	−0.874810	+	1.51522i
$130$	−0.384330	−	0.665679i	−0.0337080	−	0.0583839i
$131$	−2.60086	−	4.50483i	−0.227239	−	0.393589i	0.729750	−	0.683714i	$-0.239636\pi$
$131$	−2.60086	−	4.50483i	−0.227239	−	0.393589i	−0.956989	+	0.290125i	$0.906303\pi$
$132$	18.2664			1.58989
$133$	0.853603	−	1.47848i	0.0740168	−	0.128201i
$134$	1.95173	−	3.38050i	0.168604	−	0.292030i
$135$	18.1391	−	31.4179i	1.56117	−	2.70402i
$136$	−2.52557	−	4.37441i	−0.216565	−	0.375102i
$137$	4.92213	−	8.52538i	0.420526	−	0.728372i	−0.575465	−	0.817826i	$-0.695179\pi$
$137$	4.92213	−	8.52538i	0.420526	−	0.728372i	0.995991	+	0.0894542i	$0.0285123\pi$
$138$	4.49139	+	7.77932i	0.382333	+	0.662220i
$139$	6.68623			0.567119			0.283559	−	0.958955i	$-0.408485\pi$
$139$	6.68623			0.567119			0.283559	+	0.958955i	$0.408485\pi$
$140$	9.36096			0.791146
$141$	9.35593	+	16.2049i	0.787911	+	1.36470i
$142$	−0.540904	+	0.936874i	−0.0453917	+	0.0786207i
$143$	−1.46731	−	2.54145i	−0.122703	−	0.212527i
$144$	−13.1000	+	22.6899i	−1.09167	+	1.89083i
$145$	5.58720	−	9.67732i	0.463992	−	0.803658i
$146$	−0.524476	+	0.908420i	−0.0434060	+	0.0751813i
$147$	−5.89418			−0.486144
$148$	7.41174	+	12.8375i	0.609241	+	1.05524i
$149$	−6.52086	−	11.2945i	−0.534210	−	0.925279i	−0.999201	−	0.0399636i	$-0.987276\pi$
$149$	−6.52086	−	11.2945i	−0.534210	−	0.925279i	0.464991	−	0.885315i	$-0.346058\pi$
$150$	0.136418	−	0.236282i	0.0111385	−	0.0192924i
$151$	9.53586			0.776017			0.388008	−	0.921656i	$-0.373163\pi$
$151$	9.53586			0.776017			0.388008	+	0.921656i	$0.373163\pi$
$152$	−0.509684	−	0.882798i	−0.0413408	−	0.0716044i
$153$	−29.6417			−2.39639
$154$	−2.36140			−0.190287
$155$	−6.47238	+	10.2892i	−0.519874	+	0.826449i
$156$	6.22447			0.498357
$157$	−3.99415			−0.318768			−0.159384	−	0.987217i	$-0.550951\pi$
$157$	−3.99415			−0.318768			−0.159384	+	0.987217i	$0.550951\pi$
$158$	2.32227	+	4.02229i	0.184750	+	0.319997i
$159$	−14.6119			−1.15880
$160$	4.23674	−	7.33825i	0.334944	−	0.580139i
$161$	8.78749	+	15.2204i	0.692552	+	1.19953i
$162$	−5.47618	−	9.48501i	−0.430249	−	0.745213i
$163$	−9.40333			−0.736525			−0.368263	−	0.929722i	$-0.620047\pi$
$163$	−9.40333			−0.736525			−0.368263	+	0.929722i	$0.620047\pi$
$164$	4.94100	−	8.55806i	0.385827	−	0.668272i
$165$	−10.6287	+	18.4094i	−0.827440	+	1.43317i
$166$	2.32996	−	4.03562i	0.180840	−	0.313224i
$167$	5.15906	+	8.93576i	0.399220	+	0.691470i	0.993630	−	0.112693i	$-0.0359476\pi$
$167$	5.15906	+	8.93576i	0.399220	+	0.691470i	−0.594410	+	0.804162i	$0.702614\pi$
$168$	5.17412	−	8.96185i	0.399192	−	0.691421i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	2.84510			0.218209
$171$	−5.98198			−0.457453
$172$	5.61813	+	9.73088i	0.428378	+	0.741973i
$173$	3.03767	−	5.26141i	0.230950	−	0.400017i	−0.727138	−	0.686491i	$-0.759150\pi$
$173$	3.03767	−	5.26141i	0.230950	−	0.400017i	0.958088	+	0.286474i	$0.0924833\pi$
$174$	−2.98947	−	5.17792i	−0.226631	−	0.392537i
$175$	0.266904	−	0.462291i	0.0201760	−	0.0349459i
$176$	4.80047	−	8.31466i	0.361849	−	0.626741i
$177$	−7.10431	+	12.3050i	−0.533992	+	0.924902i
$178$	−3.10567			−0.232780
$179$	−8.01130	−	13.8760i	−0.598793	−	1.03714i	−0.993000	−	0.118118i	$-0.962314\pi$
$179$	−8.01130	−	13.8760i	−0.598793	−	1.03714i	0.394207	−	0.919022i	$-0.371019\pi$
$180$	−16.4002	−	28.4060i	−1.22240	−	2.11726i
$181$	−5.52837	+	9.57542i	−0.410920	+	0.711735i	−0.994991	−	0.0999681i	$-0.968126\pi$
$181$	−5.52837	+	9.57542i	−0.410920	+	0.711735i	0.584070	+	0.811703i	$0.301459\pi$
$182$	−0.804671			−0.0596462
$183$	−5.54295	−	9.60068i	−0.409747	−	0.709703i
$184$	10.4940			0.773626
$185$	−17.2506			−1.26829
$186$	3.03620	+	5.75179i	0.222625	+	0.421741i
$187$	10.8621			0.794316
$188$	10.5803			0.771650
$189$	−18.9889	−	32.8898i	−1.38124	−	2.39238i
$190$	0.574168			0.0416546
$191$	8.96385	−	15.5258i	0.648601	−	1.12341i	−0.334856	−	0.942269i	$-0.608688\pi$
$191$	8.96385	−	15.5258i	0.648601	−	1.12341i	0.983457	−	0.181141i	$-0.0579791\pi$
$192$	8.58792	+	14.8747i	0.619780	+	1.07349i
$193$	−6.75142	−	11.6938i	−0.485978	−	0.841739i	0.513892	−	0.857855i	$-0.328203\pi$
$193$	−6.75142	−	11.6938i	−0.485978	−	0.841739i	−0.999870	+	0.0161162i	$0.994870\pi$
$194$	0.0155489			0.00111635
$195$	−3.62182	+	6.27318i	−0.259364	+	0.449232i
$196$	−1.66639	+	2.88627i	−0.119028	+	0.206162i
$197$	−8.39729	+	14.5445i	−0.598282	+	1.03626i	0.394793	+	0.918770i	$0.370816\pi$
$197$	−8.39729	+	14.5445i	−0.598282	+	1.03626i	−0.993075	+	0.117485i	$0.962517\pi$
$198$	4.13713	+	7.16571i	0.294013	+	0.509245i
$199$	3.69388	−	6.39799i	0.261852	−	0.453541i	−0.704882	−	0.709325i	$-0.749000\pi$
$199$	3.69388	−	6.39799i	0.261852	−	0.453541i	0.966734	+	0.255783i	$0.0823334\pi$
$200$	−0.159367	−	0.276032i	−0.0112690	−	0.0195184i
$201$	−36.7851			−2.59462
$202$	−6.16301			−0.433628
$203$	−5.84896	−	10.1307i	−0.410516	−	0.711035i
$204$	−11.5195	+	19.9524i	−0.806529	+	1.39695i
$205$	5.75002	+	9.95932i	0.401599	+	0.695589i
$206$	−1.32106	+	2.28815i	−0.0920429	+	0.159423i
$207$	30.7910	−	53.3316i	2.14012	−	3.70680i
$208$	1.63581	−	2.83330i	0.113423	−	0.196454i
$209$	2.19208			0.151629
$210$	2.91437	+	5.04784i	0.201111	+	0.348334i
$211$	11.7223	+	20.3036i	0.806995	+	1.39776i	0.914936	+	0.403599i	$0.132241\pi$
$211$	11.7223	+	20.3036i	0.806995	+	1.39776i	−0.107941	+	0.994157i	$0.534426\pi$
$212$	−4.13103	+	7.15516i	−0.283720	+	0.491418i
$213$	10.1947			0.698527
$214$	0.566173	+	0.980640i	0.0387028	+	0.0670352i
$215$	−13.0760			−0.891778
$216$	−22.6765			−1.54294
$217$	5.94038	+	11.2535i	0.403259	+	0.763935i
$218$	−6.83031			−0.462607
$219$	9.88504			0.667969
$220$	6.00981	+	10.4093i	0.405182	+	0.701795i
$221$	3.70137			0.248981
$222$	−4.61503	+	7.99347i	−0.309741	+	0.536487i
$223$	−14.5331	−	25.1721i	−0.973211	−	1.68565i	−0.685716	−	0.727869i	$-0.740511\pi$
$223$	−14.5331	−	25.1721i	−0.973211	−	1.68565i	−0.287495	−	0.957782i	$-0.592823\pi$
$224$	−4.43523	−	7.68204i	−0.296341	−	0.513278i
$225$	−1.87044			−0.124696
$226$	2.92771	−	5.07094i	0.194748	−	0.337314i
$227$	5.80795	−	10.0597i	0.385487	−	0.667683i	−0.606350	−	0.795198i	$-0.707367\pi$
$227$	5.80795	−	10.0597i	0.385487	−	0.667683i	0.991837	+	0.127515i	$0.0407001\pi$
$228$	−2.32476	+	4.02660i	−0.153961	+	0.266668i
$229$	10.0793	+	17.4579i	0.666059	+	1.15365i	0.978997	+	0.203874i	$0.0653533\pi$
$229$	10.0793	+	17.4579i	0.666059	+	1.15365i	−0.312938	+	0.949773i	$0.601313\pi$
$230$	−2.95541	+	5.11893i	−0.194874	+	0.337532i
$231$	11.1266	+	19.2718i	0.732077	+	1.26799i
$232$	−6.98479			−0.458574
$233$	23.8617			1.56323			0.781615	−	0.623761i	$-0.214396\pi$
$233$	23.8617			1.56323			0.781615	+	0.623761i	$0.214396\pi$
$234$	1.40977	+	2.44179i	0.0921593	+	0.159625i
$235$	−6.15636	+	10.6631i	−0.401597	+	0.695586i
$236$	4.01702	+	6.95769i	0.261486	+	0.452907i
$237$	21.8845	−	37.9050i	1.42155	−	2.46219i
$238$	1.48919	−	2.57936i	0.0965301	−	0.167195i
$239$	7.78235	−	13.4794i	0.503398	−	0.871911i	−0.496594	−	0.867983i	$-0.665416\pi$
$239$	7.78235	−	13.4794i	0.503398	−	0.871911i	0.999992	−	0.00392832i	$-0.00125043\pi$
$240$	−23.6984			−1.52973
$241$	12.4267	+	21.5237i	0.800473	+	1.38646i	0.919305	+	0.393546i	$0.128752\pi$
$241$	12.4267	+	21.5237i	0.800473	+	1.38646i	−0.118831	+	0.992914i	$0.537915\pi$
$242$	0.420383	+	0.728125i	0.0270232	+	0.0468056i
$243$	−26.6807	+	46.2122i	−1.71156	+	2.96452i
$244$	−6.26836			−0.401291
$245$	−1.93924	−	3.35885i	−0.123893	−	0.214589i
$246$	6.15318			0.392312
$247$	0.746973			0.0475288
$248$	7.59267	+	0.287932i	0.482135	+	0.0182837i
$249$	−43.9139			−2.78293
$250$	4.02283			0.254426
$251$	2.65133	+	4.59224i	0.167351	+	0.289860i	0.937488	−	0.348019i	$-0.113145\pi$
$251$	2.65133	+	4.59224i	0.167351	+	0.289860i	−0.770137	+	0.637879i	$0.779812\pi$
$252$	−34.3371			−2.16303
$253$	−11.2833	+	19.5432i	−0.709374	+	1.22867i
$254$	2.54193	+	4.40274i	0.159495	+	0.276253i
$255$	−13.4057	−	23.2194i	−0.839498	−	1.45405i
$256$	6.97886			0.436179
$257$	9.48972	−	16.4367i	0.591953	−	1.02529i	−0.402016	−	0.915632i	$-0.631691\pi$
$257$	9.48972	−	16.4367i	0.591953	−	1.02529i	0.993969	−	0.109660i	$-0.0349761\pi$
$258$	−3.49821	+	6.05908i	−0.217789	+	0.377222i
$259$	−9.02939	+	15.6394i	−0.561059	+	0.971783i
$260$	2.04790	+	3.54707i	0.127006	+	0.219980i
$261$	−20.4945	+	35.4975i	−1.26858	+	2.19724i
$262$	−0.915704	−	1.58605i	−0.0565724	−	0.0979862i
$263$	3.89504			0.240179			0.120089	−	0.992763i	$-0.461682\pi$
$263$	3.89504			0.240179			0.120089	+	0.992763i	$0.461682\pi$
$264$	13.2873			0.817778
$265$	−4.80743	−	8.32671i	−0.295318	−	0.511506i
$266$	0.300534	−	0.520540i	0.0184269	−	0.0319164i
$267$	14.6335	+	25.3460i	0.895556	+	1.55115i
$268$	−10.3998	+	18.0130i	−0.635269	+	1.10032i
$269$	10.6694	−	18.4799i	0.650525	−	1.12674i	−0.332471	−	0.943114i	$-0.607882\pi$
$269$	10.6694	−	18.4799i	0.650525	−	1.12674i	0.982996	−	0.183628i	$-0.0587843\pi$
$270$	6.38637	−	11.0615i	0.388662	−	0.673182i
$271$	6.28200			0.381604			0.190802	−	0.981629i	$-0.438891\pi$
$271$	6.28200			0.381604			0.190802	+	0.981629i	$0.438891\pi$
$272$	6.05474	+	10.4871i	0.367122	+	0.635875i
$273$	3.79150	+	6.56707i	0.229472	+	0.397457i
$274$	1.73297	−	3.00159i	0.104692	−	0.181333i
$275$	0.685417			0.0413322
$276$	−23.9324	−	41.4522i	−1.44056	−	2.49513i
$277$	9.80791			0.589300			0.294650	−	0.955605i	$-0.404797\pi$
$277$	9.80791			0.589300			0.294650	+	0.955605i	$0.404797\pi$
$278$	2.35407			0.141187
$279$	23.7414	−	37.7420i	1.42136	−	2.25955i
$280$	6.80932			0.406935
$281$	−12.0813			−0.720713			−0.360356	−	0.932815i	$-0.617345\pi$
$281$	−12.0813			−0.720713			−0.360356	+	0.932815i	$0.617345\pi$
$282$	3.29401	+	5.70538i	0.196155	+	0.339751i
$283$	−11.3927			−0.677225			−0.338612	−	0.940926i	$-0.609958\pi$
$283$	−11.3927			−0.677225			−0.338612	+	0.940926i	$0.609958\pi$
$284$	2.88221	−	4.99213i	0.171028	−	0.296229i
$285$	−2.70540	−	4.68590i	−0.160254	−	0.277568i
$286$	−0.516605	−	0.894787i	−0.0305475	−	0.0529098i
$287$	12.0388			0.710628
$288$	−15.5408	+	26.9175i	−0.915753	+	1.58613i
$289$	1.64992	−	2.85775i	0.0970542	−	0.168103i
$290$	1.96712	−	3.40716i	0.115514	−	0.200075i
$291$	−0.0732645	−	0.126898i	−0.00429484	−	0.00743888i
$292$	2.79467	−	4.84052i	0.163546	−	0.283270i
$293$	−2.86939	−	4.96993i	−0.167632	−	0.290346i	0.769955	−	0.638098i	$-0.220279\pi$
$293$	−2.86939	−	4.96993i	−0.167632	−	0.290346i	−0.937587	+	0.347752i	$0.886945\pi$
$294$	−2.07520			−0.121028
$295$	−9.34951			−0.544349
$296$	5.39142	+	9.33821i	0.313370	+	0.542773i
$297$	24.3821	−	42.2310i	1.41479	−	2.45049i
$298$	−2.29584	−	3.97652i	−0.132995	−	0.230354i
$299$	−3.84489	+	6.65955i	−0.222356	+	0.385131i
$300$	−0.726902	+	1.25903i	−0.0419677	+	0.0726902i
$301$	−6.84431	+	11.8547i	−0.394500	+	0.683294i
$302$	3.35735			0.193194
$303$	29.0393	+	50.2975i	1.66826	+	2.88952i
$304$	1.22191	+	2.11640i	0.0700811	+	0.121384i
$305$	3.64736	−	6.31741i	0.208847	−	0.361734i
$306$	−10.4361			−0.596595
$307$	−3.52715	−	6.10920i	−0.201305	−	0.348671i	0.747644	−	0.664100i	$-0.231185\pi$
$307$	−3.52715	−	6.10920i	−0.201305	−	0.348671i	−0.948949	+	0.315429i	$0.897852\pi$
$308$	12.5827			0.716968
$309$	24.8987			1.41644
$310$	−2.27877	+	3.62259i	−0.129426	+	0.205749i
$311$	−26.8200			−1.52082			−0.760412	−	0.649441i	$-0.775003\pi$
$311$	−26.8200			−1.52082			−0.760412	+	0.649441i	$0.775003\pi$
$312$	4.52778			0.256335
$313$	−0.580126	−	1.00481i	−0.0327907	−	0.0567951i	0.849164	−	0.528129i	$-0.177106\pi$
$313$	−0.580126	−	1.00481i	−0.0327907	−	0.0567951i	−0.881955	+	0.471334i	$0.843773\pi$
$314$	−1.40625			−0.0793591
$315$	19.9797	−	34.6058i	1.12573	−	1.94981i
$316$	−12.3742	−	21.4328i	−0.696105	−	1.20569i
$317$	−8.35985	−	14.4797i	−0.469536	−	0.813260i	0.529857	−	0.848087i	$-0.322245\pi$
$317$	−8.35985	−	14.4797i	−0.469536	−	0.813260i	−0.999393	+	0.0348266i	$0.988912\pi$
$318$	−5.14450			−0.288489
$319$	7.51016	−	13.0080i	0.420488	−	0.728307i
$320$	−5.65099	+	9.78781i	−0.315900	+	0.547155i
$321$	5.33546	−	9.24128i	0.297796	−	0.515798i
$322$	3.09387	+	5.35874i	0.172415	+	0.298631i
$323$	−1.38241	+	2.39441i	−0.0769195	+	0.133229i
$324$	29.1798	+	50.5409i	1.62110	+	2.80783i
$325$	0.233563			0.0129557
$326$	−3.31069			−0.183362
$327$	32.1835	+	55.7434i	1.77975	+	3.08262i
$328$	3.59416	−	6.22528i	0.198455	−	0.343733i
$329$	6.44478	+	11.1627i	0.355312	+	0.615419i
$330$	−3.74210	+	6.48151i	−0.205996	+	0.356796i
$331$	15.5234	−	26.8872i	0.853241	−	1.47786i	−0.0250265	−	0.999687i	$-0.507967\pi$
$331$	15.5234	−	26.8872i	0.853241	−	1.47786i	0.878267	−	0.478170i	$-0.158700\pi$
$332$	−12.4152	+	21.5038i	−0.681374	+	1.18017i
$333$	63.2772			3.46757
$334$	1.81639	+	3.14607i	0.0993882	+	0.172145i
$335$	−12.1026	−	20.9624i	−0.661237	−	1.14530i
$336$	−12.4043	+	21.4849i	−0.676712	+	1.17210i
$337$	6.33966			0.345343			0.172672	−	0.984979i	$-0.444760\pi$
$337$	6.33966			0.345343			0.172672	+	0.984979i	$0.444760\pi$
$338$	−0.176038	−	0.304907i	−0.00957523	−	0.0165848i
$339$	−55.1799			−2.99696
$340$	−15.1601			−0.822172
$341$	−8.69999	+	13.8305i	−0.471131	+	0.748961i
$342$	−2.10612			−0.113886
$343$	−20.0587			−1.08307
$344$	4.08672	+	7.07840i	0.220341	+	0.381642i
$345$	55.7020			2.99890
$346$	1.06949	−	1.85242i	0.0574964	−	0.0995866i
$347$	10.0371	+	17.3848i	0.538820	+	0.933264i	0.998968	+	0.0454213i	$0.0144630\pi$
$347$	10.0371	+	17.3848i	0.538820	+	0.933264i	−0.460148	+	0.887842i	$0.652204\pi$
$348$	15.9294	+	27.5906i	0.853907	+	1.47901i
$349$	23.3526			1.25004			0.625018	−	0.780610i	$-0.285092\pi$
$349$	23.3526			1.25004			0.625018	+	0.780610i	$0.285092\pi$
$350$	0.0939706	−	0.162762i	0.00502294	−	0.00869998i
$351$	8.30844	−	14.3906i	0.443472	−	0.768116i
$352$	5.69490	−	9.86386i	0.303539	−	0.525746i
$353$	−9.75431	−	16.8950i	−0.519170	−	0.899228i	−0.999752	−	0.0222786i	$-0.992908\pi$
$353$	−9.75431	−	16.8950i	−0.519170	−	0.899228i	0.480582	−	0.876950i	$-0.340425\pi$
$354$	−2.50126	+	4.33231i	−0.132941	+	0.230260i
$355$	3.35413	+	5.80952i	0.178019	+	0.308338i
$356$	16.5486			0.877074
$357$	−28.0675			−1.48549
$358$	−2.82059	−	4.88541i	−0.149073	−	0.258202i
$359$	7.87554	−	13.6408i	0.415655	−	0.719936i	−0.579842	−	0.814729i	$-0.696886\pi$
$359$	7.87554	−	13.6408i	0.415655	−	0.719936i	0.995497	+	0.0947930i	$0.0302189\pi$
$360$	−11.9298	−	20.6630i	−0.628755	−	1.08904i
$361$	9.22102	−	15.9713i	0.485317	−	0.840593i
$362$	−1.94641	+	3.37128i	−0.102301	+	0.177191i
$363$	3.96157	−	6.86165i	0.207929	−	0.360143i
$364$	4.28769			0.224736
$365$	3.25226	+	5.63308i	0.170231	+	0.294849i
$366$	−1.95155	−	3.38018i	−0.102009	−	0.176685i
$367$	−3.01230	+	5.21746i	−0.157241	+	0.272349i	−0.933873	−	0.357605i	$-0.883593\pi$
$367$	−3.01230	+	5.21746i	−0.157241	+	0.272349i	0.776632	+	0.629955i	$0.216927\pi$
$368$	−25.1580			−1.31145
$369$	−21.0917	−	36.5319i	−1.09799	−	1.90178i
$370$	−6.07354			−0.315748
$371$	−10.0653			−0.522565
$372$	−16.1784	−	30.6484i	−0.838811	−	1.58905i
$373$	19.5522			1.01237			0.506187	−	0.862424i	$-0.331055\pi$
$373$	19.5522			1.01237			0.506187	+	0.862424i	$0.331055\pi$
$374$	3.82430			0.197750
$375$	−18.9550	−	32.8311i	−0.978833	−	1.69539i
$376$	7.69631			0.396907
$377$	2.55916	−	4.43260i	0.131803	−	0.228290i
$378$	−6.68556	−	11.5797i	−0.343868	−	0.595597i
$379$	−9.10388	−	15.7684i	−0.467635	−	0.809968i	0.531681	−	0.846945i	$-0.321561\pi$
$379$	−9.10388	−	15.7684i	−0.467635	−	0.809968i	−0.999316	+	0.0369769i	$0.988227\pi$
$380$	−3.05946			−0.156947
$381$	23.9544	−	41.4903i	1.22722	−	2.12561i
$382$	3.15596	−	5.46629i	0.161473	−	0.279680i
$383$	−8.47108	+	14.6723i	−0.432852	+	0.749722i	−0.997118	−	0.0758716i	$-0.975826\pi$
$383$	−8.47108	+	14.6723i	−0.432852	+	0.749722i	0.564266	+	0.825593i	$0.309159\pi$
$384$	15.9009	+	27.5412i	0.811440	+	1.40545i
$385$	−7.32149	+	12.6812i	−0.373138	+	0.646294i
$386$	−2.37702	−	4.11712i	−0.120987	−	0.209556i
$387$	47.9644			2.43817
$388$	−0.0828526			−0.00420620
$389$	−7.36100	−	12.7496i	−0.373218	−	0.646432i	0.616841	−	0.787088i	$-0.288412\pi$
$389$	−7.36100	−	12.7496i	−0.373218	−	0.646432i	−0.990059	+	0.140656i	$0.955079\pi$
$390$	−1.27516	+	2.20864i	−0.0645702	+	0.111839i
$391$	−14.2314	−	24.6495i	−0.719711	−	1.24658i
$392$	−1.21216	+	2.09952i	−0.0612232	+	0.106042i
$393$	−8.62934	+	14.9465i	−0.435293	+	0.753949i
$394$	−2.95649	+	5.12079i	−0.148946	+	0.257982i
$395$	28.8007			1.44912
$396$	−22.0447	−	38.1825i	−1.10779	−	1.91874i
$397$	−2.22400	−	3.85207i	−0.111619	−	0.193330i	0.804804	−	0.593541i	$-0.202270\pi$
$397$	−2.22400	−	3.85207i	−0.111619	−	0.193330i	−0.916423	+	0.400211i	$0.868937\pi$
$398$	1.30053	−	2.25258i	0.0651896	−	0.112912i
$399$	−5.66430			−0.283570
$400$	0.382064	+	0.661754i	0.0191032	+	0.0330877i
$401$	−9.40764			−0.469795			−0.234898	−	0.972020i	$-0.575475\pi$
$401$	−9.40764			−0.469795			−0.234898	+	0.972020i	$0.575475\pi$
$402$	−12.9512			−0.645947
$403$	−2.96461	+	4.71287i	−0.147678	+	0.234765i
$404$	32.8396			1.63383
$405$	−67.9152			−3.37473
$406$	−2.05928	−	3.56678i	−0.102200	−	0.177016i
$407$	−23.1878			−1.14937
$408$	−8.37951	+	14.5137i	−0.414847	+	0.718537i
$409$	13.5835	+	23.5274i	0.671662	+	1.16335i	0.977433	+	0.211248i	$0.0677527\pi$
$409$	13.5835	+	23.5274i	0.671662	+	1.16335i	−0.305770	+	0.952105i	$0.598914\pi$
$410$	2.02445	+	3.50645i	0.0999803	+	0.173171i
$411$	−32.6620			−1.61110
$412$	7.03929	−	12.1924i	0.346801	−	0.600677i
$413$	−4.89376	+	8.47625i	−0.240806	+	0.417089i
$414$	10.8408	−	18.7768i	0.532796	−	0.922830i
$415$	−14.4480	−	25.0247i	−0.709226	−	1.22842i
$416$	1.94059	−	3.36121i	0.0951455	−	0.164797i
$417$	−11.0920	−	19.2120i	−0.543179	−	0.940814i
$418$	0.771781			0.0377490
$419$	−9.93186			−0.485203			−0.242602	−	0.970126i	$-0.578001\pi$
$419$	−9.93186			−0.485203			−0.242602	+	0.970126i	$0.578001\pi$
$420$	−15.5293	−	26.8975i	−0.757750	−	1.31246i
$421$	0.482166	−	0.835136i	0.0234993	−	0.0407020i	−0.854037	−	0.520213i	$-0.825853\pi$
$421$	0.482166	−	0.835136i	0.0234993	−	0.0407020i	0.877536	+	0.479511i	$0.159186\pi$
$422$	4.12714	+	7.14842i	0.200906	+	0.347980i
$423$	22.5822	−	39.1136i	1.09799	−	1.90177i
$424$	−3.00498	+	5.20478i	−0.145935	+	0.252767i
$425$	−0.432251	+	0.748681i	−0.0209673	+	0.0363164i
$426$	3.58930			0.173902
$427$	−3.81823	−	6.61337i	−0.184777	−	0.320044i
$428$	−3.01685	−	5.22534i	−0.145825	−	0.252577i
$429$	−4.86835	+	8.43222i	−0.235046	+	0.407112i
$430$	−4.60376			−0.222013
$431$	0.476999	+	0.826186i	0.0229762	+	0.0397960i	0.877285	−	0.479970i	$-0.159352\pi$
$431$	0.476999	+	0.826186i	0.0229762	+	0.0397960i	−0.854309	+	0.519766i	$0.826019\pi$
$432$	54.3641			2.61559
$433$	24.3958			1.17239			0.586194	−	0.810171i	$-0.300626\pi$
$433$	24.3958			1.17239			0.586194	+	0.810171i	$0.300626\pi$
$434$	2.09147	+	3.96209i	0.100394	+	0.190186i
$435$	−37.0753			−1.77762
$436$	36.3953			1.74302
$437$	−2.87203	−	4.97450i	−0.137388	−	0.237963i
$438$	3.48029			0.166295
$439$	−13.8464	+	23.9827i	−0.660853	+	1.14463i	0.319539	+	0.947573i	$0.396472\pi$
$439$	−13.8464	+	23.9827i	−0.660853	+	1.14463i	−0.980392	+	0.197058i	$0.936861\pi$
$440$	4.37164	+	7.57190i	0.208410	+	0.360976i
$441$	7.11334	+	12.3207i	0.338730	+	0.586698i
$442$	1.30317			0.0619853
$443$	−4.15451	+	7.19582i	−0.197387	+	0.341884i	−0.947680	−	0.319221i	$-0.896579\pi$
$443$	−4.15451	+	7.19582i	−0.197387	+	0.341884i	0.750294	+	0.661105i	$0.229912\pi$
$444$	24.5912	−	42.5932i	1.16705	−	2.02138i
$445$	−9.62910	+	16.6781i	−0.456463	+	0.790617i
$446$	−5.11678	−	8.86253i	−0.242287	−	0.419653i
$447$	−21.6354	+	37.4736i	−1.02332	+	1.77244i
$448$	5.91574	+	10.2464i	0.279492	+	0.484095i
$449$	2.05010			0.0967500			0.0483750	−	0.998829i	$-0.484596\pi$
$449$	2.05010			0.0967500			0.0483750	+	0.998829i	$0.484596\pi$
$450$	−0.658538			−0.0310438
$451$	7.72901	+	13.3870i	0.363945	+	0.630371i
$452$	−15.6003	+	27.0205i	−0.733777	+	1.27094i
$453$	−15.8194	−	27.4000i	−0.743260	−	1.28736i
$454$	2.04484	−	3.54177i	0.0959692	−	0.166224i
$455$	−2.49487	+	4.32124i	−0.116961	+	0.202583i
$456$	−1.69107	+	2.92901i	−0.0791915	+	0.137164i
$457$	33.4349			1.56402			0.782009	−	0.623267i	$-0.214195\pi$
$457$	33.4349			1.56402			0.782009	+	0.623267i	$0.214195\pi$
$458$	3.54869	+	6.14650i	0.165819	+	0.287207i
$459$	30.7526	+	53.2651i	1.43541	+	2.48620i
$460$	15.7479	−	27.2762i	0.734251	−	1.27176i
$461$	16.6215			0.774139			0.387069	−	0.922051i	$-0.373487\pi$
$461$	16.6215			0.774139			0.387069	+	0.922051i	$0.373487\pi$
$462$	3.91742	+	6.78517i	0.182255	+	0.315675i
$463$	30.4730			1.41620			0.708101	−	0.706111i	$-0.249552\pi$
$463$	30.4730			1.41620			0.708101	+	0.706111i	$0.249552\pi$
$464$	16.7452			0.777376
$465$	40.3019	+	1.52834i	1.86896	+	0.0708751i
$466$	8.40114			0.389175
$467$	21.7888			1.00827			0.504133	−	0.863626i	$-0.331812\pi$
$467$	21.7888			1.00827			0.504133	+	0.863626i	$0.331812\pi$
$468$	−7.51195	−	13.0111i	−0.347240	−	0.601437i
$469$	−25.3392			−1.17006
$470$	−2.16751	+	3.75424i	−0.0999798	+	0.173170i
$471$	6.62605	+	11.4766i	0.305312	+	0.528816i
$472$	2.92205	+	5.06114i	0.134498	+	0.232958i
$473$	−17.5764			−0.808165
$474$	7.70501	−	13.3455i	0.353903	−	0.612978i
$475$	−0.0872325	+	0.151091i	−0.00400250	+	0.00693254i
$476$	−7.93517	+	13.7441i	−0.363708	+	0.629961i
$477$	17.6342	+	30.5433i	0.807415	+	1.39848i
$478$	2.73998	−	4.74579i	0.125324	−	0.217067i
$479$	1.09560	+	1.89764i	0.0500594	+	0.0867055i	0.889969	−	0.456020i	$-0.150726\pi$
$479$	1.09560	+	1.89764i	0.0500594	+	0.0867055i	−0.839910	+	0.542726i	$0.817392\pi$
$480$	−28.1139			−1.28322
$481$	−7.90146			−0.360276
$482$	4.37515	+	7.57798i	0.199283	+	0.345167i
$483$	29.1558	−	50.4993i	1.32663	−	2.29780i
$484$	−2.24001	−	3.87981i	−0.101819	−	0.176355i
$485$	0.0482093	−	0.0835009i	0.00218907	−	0.00379158i
$486$	−9.39364	+	16.2703i	−0.426104	+	0.738034i
$487$	1.19825	−	2.07543i	0.0542978	−	0.0940465i	−0.837599	−	0.546286i	$-0.816041\pi$
$487$	1.19825	−	2.07543i	0.0542978	−	0.0940465i	0.891897	+	0.452239i	$0.149375\pi$
$488$	−4.55971			−0.206408
$489$	15.5995	+	27.0192i	0.705435	+	1.22185i
$490$	−0.682760	−	1.18257i	−0.0308439	−	0.0534233i
$491$	−0.481273	+	0.833589i	−0.0217195	+	0.0376193i	−0.876681	−	0.481072i	$-0.840247\pi$
$491$	−0.481273	+	0.833589i	−0.0217195	+	0.0376193i	0.854961	+	0.518692i	$0.173581\pi$
$492$	−32.7872			−1.47816
$493$	9.47241	+	16.4067i	0.426616	+	0.738920i
$494$	0.262992			0.0118326
$495$	51.3084			2.30614
$496$	−18.2025	−	0.690281i	−0.817317	−	0.0309945i
$497$	7.02254			0.315004
$498$	−15.4611			−0.692826
$499$	−3.43170	−	5.94387i	−0.153624	−	0.266084i	0.778933	−	0.627107i	$-0.215761\pi$
$499$	−3.43170	−	5.94387i	−0.153624	−	0.266084i	−0.932557	+	0.361023i	$0.882428\pi$
$500$	−21.4357			−0.958632
$501$	17.1171	−	29.6477i	0.764736	−	1.32456i
$502$	0.933473	+	1.61682i	0.0416629	+	0.0721623i
$503$	2.90805	+	5.03689i	0.129664	+	0.224584i	0.923546	−	0.383487i	$-0.125277\pi$
$503$	2.90805	+	5.03689i	0.129664	+	0.224584i	−0.793883	+	0.608071i	$0.791944\pi$
$504$	−24.9774			−1.11258
$505$	−19.1083	+	33.0966i	−0.850310	+	1.47278i
$506$	−3.97258	+	6.88071i	−0.176603	+	0.305885i
$507$	−1.65894	+	2.87336i	−0.0736760	+	0.127611i
$508$	−13.5447	−	23.4600i	−0.600947	−	1.04087i
$509$	13.9192	−	24.1087i	0.616957	−	1.06860i	−0.373081	−	0.927799i	$-0.621699\pi$
$509$	13.9192	−	24.1087i	0.616957	−	1.06860i	0.990038	−	0.140801i	$-0.0449679\pi$
$510$	−4.71984	−	8.17500i	−0.208998	−	0.361995i
$511$	6.80925			0.301224
$512$	21.6271			0.955791
$513$	6.20618	+	10.7494i	0.274010	+	0.474599i
$514$	3.34111	−	5.78697i	0.147370	−	0.255252i
$515$	8.19187	+	14.1887i	0.360977	+	0.625231i
$516$	18.6402	−	32.2858i	0.820591	−	1.42130i
$517$	−8.27520	+	14.3331i	−0.363943	+	0.630368i
$518$	−3.17904	+	5.50626i	−0.139679	+	0.241931i
$519$	−20.1572			−0.884805
$520$	1.48968	+	2.58020i	0.0653268	+	0.113149i
$521$	−0.847147	−	1.46730i	−0.0371142	−	0.0642836i	0.846872	−	0.531797i	$-0.178483\pi$
$521$	−0.847147	−	1.46730i	−0.0371142	−	0.0642836i	−0.883986	+	0.467514i	$0.845150\pi$
$522$	−7.21564	+	12.4979i	−0.315820	+	0.547016i
$523$	−38.0307			−1.66297			−0.831484	−	0.555549i	$-0.812508\pi$
$523$	−38.0307			−1.66297			−0.831484	+	0.555549i	$0.812508\pi$
$524$	4.87933	+	8.45125i	0.213155	+	0.369194i
$525$	−1.77111			−0.0772974
$526$	1.37135			0.0597939
$527$	−9.62046	−	18.2250i	−0.419074	−	0.793895i
$528$	−31.8547			−1.38630
$529$	36.1327			1.57099
$530$	−1.69258	−	2.93164i	−0.0735212	−	0.127342i
$531$	34.2951			1.48828
$532$	−1.60140	+	2.77370i	−0.0694293	+	0.120255i
$533$	2.63374	+	4.56176i	0.114080	+	0.197592i
$534$	5.15212	+	8.92373i	0.222954	+	0.386168i
$535$	7.02164			0.303572
$536$	−7.56499	+	13.1029i	−0.326758	+	0.565961i
$537$	−26.5805	+	46.0388i	−1.14703	+	1.98672i
$538$	3.75645	−	6.50636i	0.161952	−	0.280509i
$539$	−2.60666	−	4.51487i	−0.112277	−	0.194469i
$540$	−34.0298	+	58.9413i	−1.46441	+	2.53643i
$541$	−11.2753	−	19.5295i	−0.484765	−	0.839637i	0.515082	−	0.857141i	$-0.327761\pi$
$541$	−11.2753	−	19.5295i	−0.484765	−	0.839637i	−0.999847	+	0.0175039i	$0.994428\pi$
$542$	2.21175			0.0950026
$543$	36.6849			1.57430
$544$	7.18286	+	12.4411i	0.307963	+	0.533407i
$545$	−21.1773	+	36.6801i	−0.907135	+	1.57120i
$546$	1.33490	+	2.31211i	0.0571284	+	0.0989493i
$547$	−8.68607	+	15.0447i	−0.371389	+	0.643265i	−0.989780	−	0.142606i	$-0.954452\pi$
$547$	−8.68607	+	15.0447i	−0.371389	+	0.643265i	0.618390	+	0.785871i	$0.287785\pi$
$548$	−9.23412	+	15.9940i	−0.394462	+	0.683228i
$549$	−13.3789	+	23.1730i	−0.570999	+	0.988999i
$550$	0.241319			0.0102899
$551$	1.91162	+	3.31103i	0.0814379	+	0.141055i
$552$	−17.4088	−	30.1530i	−0.740969	−	1.28340i
$553$	15.0750	−	26.1106i	0.641054	−	1.11034i
$554$	3.45314			0.146710
$555$	28.6177	+	49.5673i	1.21475	+	2.10401i
$556$	−12.5436			−0.531969
$557$	−22.2395			−0.942318			−0.471159	−	0.882048i	$-0.656164\pi$
$557$	−22.2395			−0.942318			−0.471159	+	0.882048i	$0.656164\pi$
$558$	8.35880	−	13.2881i	0.353856	−	0.562529i
$559$	−5.98934			−0.253322
$560$	−16.3245			−0.689837
$561$	−18.0196	−	31.2108i	−0.760787	−	1.31772i
$562$	−4.25356			−0.179426
$563$	7.34763	−	12.7265i	0.309666	−	0.536357i	−0.668623	−	0.743601i	$-0.733116\pi$
$563$	7.34763	−	12.7265i	0.309666	−	0.536357i	0.978289	+	0.207244i	$0.0664495\pi$
$564$	−17.5521	−	30.4012i	−0.739077	−	1.28012i
$565$	−18.1546	−	31.4448i	−0.763772	−	1.32289i
$566$	−4.01110			−0.168599
$567$	−35.5485	+	61.5718i	−1.49290	+	2.58577i
$568$	2.09657	−	3.63136i	0.0879700	−	0.152369i
$569$	11.4891	−	19.8997i	0.481647	−	0.834238i	−0.518131	−	0.855301i	$-0.673372\pi$
$569$	11.4891	−	19.8997i	0.481647	−	0.834238i	0.999778	+	0.0210638i	$0.00670531\pi$
$570$	−0.952509	−	1.64979i	−0.0398962	−	0.0691023i
$571$	−12.7921	+	22.1566i	−0.535334	+	0.927226i	0.463813	+	0.885933i	$0.346481\pi$
$571$	−12.7921	+	22.1566i	−0.535334	+	0.927226i	−0.999147	+	0.0412932i	$0.986852\pi$
$572$	2.75273	+	4.76787i	0.115098	+	0.199355i
$573$	−59.4819			−2.48489
$574$	4.23858			0.176915
$575$	−0.898023	−	1.55542i	−0.0374501	−	0.0648655i
$576$	20.7285	−	35.9028i	0.863687	−	1.49595i
$577$	−11.6553	−	20.1876i	−0.485218	−	0.840423i	0.514637	−	0.857408i	$-0.327927\pi$
$577$	−11.6553	−	20.1876i	−0.485218	−	0.840423i	−0.999856	+	0.0169852i	$0.994593\pi$
$578$	0.580899	−	1.00615i	0.0241622	−	0.0418502i
$579$	−22.4004	+	38.7986i	−0.930928	+	1.61241i
$580$	−10.4818	+	18.1551i	−0.435234	+	0.753848i
$581$	−30.2498			−1.25497
$582$	−0.0257947	−	0.0446778i	−0.00106923	−	0.00185195i
$583$	−6.46201	−	11.1925i	−0.267629	−	0.463547i
$584$	2.03289	−	3.52107i	0.0841217	−	0.145703i
$585$	17.4838			0.722868
$586$	−1.01025	−	1.74980i	−0.0417329	−	0.0722834i
$587$	39.4175			1.62694			0.813468	−	0.581610i	$-0.197577\pi$
$587$	39.4175			1.62694			0.813468	+	0.581610i	$0.197577\pi$
$588$	11.0577			0.456013
$589$	−1.94150	−	3.67799i	−0.0799982	−	0.151549i
$590$	−3.29174			−0.135519
$591$	55.7223			2.29211
$592$	−12.9253	−	22.3872i	−0.531226	−	0.920110i
$593$	−26.7765			−1.09958			−0.549789	−	0.835303i	$-0.685292\pi$
$593$	−26.7765			−1.09958			−0.549789	+	0.835303i	$0.685292\pi$
$594$	8.58437	−	14.8686i	0.352221	−	0.610065i
$595$	−9.23445	−	15.9945i	−0.378575	−	0.655712i
$596$	12.2334	+	21.1889i	0.501100	+	0.867931i
$597$	−24.5117			−1.00320
$598$	−1.35370	+	2.34467i	−0.0553568	+	0.0958807i
$599$	−15.6103	+	27.0379i	−0.637822	+	1.10474i	0.348088	+	0.937462i	$0.386831\pi$
$599$	−15.6103	+	27.0379i	−0.637822	+	1.10474i	−0.985910	+	0.167278i	$0.946502\pi$
$600$	−0.528761	+	0.915840i	−0.0215866	+	0.0373890i
$601$	−1.22713	−	2.12545i	−0.0500557	−	0.0866990i	0.839912	−	0.542723i	$-0.182607\pi$
$601$	−1.22713	−	2.12545i	−0.0500557	−	0.0866990i	−0.889968	+	0.456024i	$0.849273\pi$
$602$	−2.40972	+	4.17376i	−0.0982130	+	0.170110i
$603$	44.3938	+	76.8923i	1.80786	+	3.13130i
$604$	−17.8897			−0.727920
$605$	5.21356			0.211962
$606$	10.2241	+	17.7086i	0.415324	+	0.719362i
$607$	0.0202721	−	0.0351123i	0.000822819	−	0.00142516i	−0.865614	−	0.500712i	$-0.833071\pi$
$607$	0.0202721	−	0.0351123i	0.000822819	−	0.00142516i	0.866437	+	0.499287i	$0.166405\pi$
$608$	1.44957	+	2.51073i	0.0587879	+	0.101824i
$609$	−19.4061	+	33.6124i	−0.786375	+	1.36204i
$610$	1.28415	−	2.22421i	0.0519937	−	0.0900557i
$611$	−2.81986	+	4.88413i	−0.114079	+	0.197591i
$612$	55.6090			2.24786
$613$	−2.40415	−	4.16411i	−0.0971026	−	0.168187i	0.813382	−	0.581731i	$-0.197624\pi$
$613$	−2.40415	−	4.16411i	−0.0971026	−	0.168187i	−0.910484	+	0.413544i	$0.864291\pi$
$614$	−1.24183	−	2.15091i	−0.0501161	−	0.0868036i
$615$	19.0778	−	33.0438i	0.769292	−	1.33245i
$616$	9.15289			0.368781
$617$	17.8145	+	30.8557i	0.717186	+	1.24220i	0.962110	+	0.272660i	$0.0879035\pi$
$617$	17.8145	+	30.8557i	0.717186	+	1.24220i	−0.244924	+	0.969542i	$0.578763\pi$
$618$	8.76625			0.352630
$619$	15.6890			0.630594			0.315297	−	0.948993i	$-0.397896\pi$
$619$	15.6890			0.630594			0.315297	+	0.948993i	$0.397896\pi$
$620$	12.1425	−	19.3030i	0.487653	−	0.775227i
$621$	−127.780			−5.12764
$622$	−9.44271			−0.378618
$623$	10.0802	+	17.4594i	0.403855	+	0.699498i
$624$	−10.8548			−0.434540
$625$	11.8888	−	20.5920i	0.475553	−	0.823681i
$626$	−0.204249	−	0.353769i	−0.00816342	−	0.0141395i
$627$	−3.63652	−	6.29865i	−0.145229	−	0.251544i
$628$	7.49319			0.299011
$629$	14.6231	−	25.3280i	0.583062	−	1.00989i
$630$	7.03437	−	12.1839i	0.280256	−	0.485418i
$631$	−17.7504	+	30.7447i	−0.706634	+	1.22393i	0.259465	+	0.965753i	$0.416454\pi$
$631$	−17.7504	+	30.7447i	−0.706634	+	1.22393i	−0.966099	+	0.258173i	$0.916879\pi$
$632$	−9.00123	−	15.5906i	−0.358050	−	0.620160i
$633$	38.8931	−	67.3648i	1.54586	−	2.67751i
$634$	−2.94331	−	5.09796i	−0.116894	−	0.202466i
$635$	31.5248			1.25102
$636$	27.4125			1.08698
$637$	−0.888247	−	1.53849i	−0.0351936	−	0.0609571i
$638$	2.64415	−	4.57981i	0.104683	−	0.181316i
$639$	−12.3033	−	21.3100i	−0.486712	−	0.843011i
$640$	−10.4631	+	18.1226i	−0.413589	+	0.716357i
$641$	−6.96210	+	12.0587i	−0.274986	+	0.476291i	−0.970132	−	0.242579i	$-0.922007\pi$
$641$	−6.96210	+	12.0587i	−0.274986	+	0.476291i	0.695145	+	0.718869i	$0.255340\pi$
$642$	1.87849	−	3.25364i	0.0741381	−	0.128411i
$643$	−31.9792			−1.26114			−0.630568	−	0.776134i	$-0.717178\pi$
$643$	−31.9792			−1.26114			−0.630568	+	0.776134i	$0.717178\pi$
$644$	−16.4857	−	28.5541i	−0.649628	−	1.12519i
$645$	21.6923	+	37.5722i	0.854134	+	1.47940i
$646$	−0.486716	+	0.843016i	−0.0191496	+	0.0331680i
$647$	−29.4068			−1.15610			−0.578051	−	0.816001i	$-0.696187\pi$
$647$	−29.4068			−1.15610			−0.578051	+	0.816001i	$0.696187\pi$
$648$	21.2259	+	36.7643i	0.833832	+	1.44424i
$649$	−12.5673			−0.493311
$650$	0.0822320			0.00322540
$651$	22.4806	−	35.7377i	0.881084	−	1.40067i
$652$	17.6410			0.690876
$653$	−39.8877			−1.56093			−0.780464	−	0.625201i	$-0.785017\pi$
$653$	−39.8877			−1.56093			−0.780464	+	0.625201i	$0.785017\pi$
$654$	11.3311	+	19.6260i	0.443079	+	0.767436i
$655$	−11.3565			−0.443735
$656$	−8.61657	+	14.9243i	−0.336421	+	0.582698i
$657$	−11.9297	−	20.6628i	−0.465421	−	0.806132i
$658$	2.26906	+	3.93012i	0.0884571	+	0.153212i
$659$	−34.2900			−1.33575			−0.667875	−	0.744273i	$-0.732796\pi$
$659$	−34.2900			−1.33575			−0.667875	+	0.744273i	$0.732796\pi$
$660$	19.9398	−	34.5368i	0.776156	−	1.34434i
$661$	−14.1793	+	24.5592i	−0.551510	+	0.955243i	0.446656	+	0.894706i	$0.352615\pi$
$661$	−14.1793	+	24.5592i	−0.551510	+	0.955243i	−0.998166	+	0.0605374i	$0.980719\pi$
$662$	5.46541	−	9.46637i	0.212419	−	0.367921i
$663$	−6.14034	−	10.6354i	−0.238471	−	0.413044i
$664$	−9.03104	+	15.6422i	−0.350472	+	0.607036i
$665$	−1.86360	−	3.22785i	−0.0722674	−	0.125171i
$666$	22.2784			0.863272
$667$	−39.3588			−1.52398
$668$	−9.67862	−	16.7639i	−0.374477	−	0.648613i
$669$	−48.2191	+	83.5180i	−1.86426	+	3.22899i
$670$	−4.26105	−	7.38036i	−0.164619	−	0.285128i
$671$	4.90267	−	8.49168i	0.189266	−	0.327818i
$672$	−14.7155	+	25.4880i	−0.567664	+	0.983222i
$673$	16.5678	−	28.6963i	0.638643	−	1.10616i	−0.347088	−	0.937833i	$-0.612829\pi$
$673$	16.5678	−	28.6963i	0.638643	−	1.10616i	0.985731	−	0.168329i	$-0.0538372\pi$
$674$	2.23205			0.0859753
$675$	1.94054	+	3.36112i	0.0746915	+	0.129369i
$676$	0.938021	+	1.62470i	0.0360777	+	0.0624885i
$677$	8.63181	−	14.9507i	0.331748	−	0.574604i	−0.651107	−	0.758986i	$-0.725695\pi$
$677$	8.63181	−	14.9507i	0.331748	−	0.574604i	0.982855	+	0.184382i	$0.0590285\pi$
$678$	−19.4276			−0.746111
$679$	−0.0504678	−	0.0874129i	−0.00193678	−	0.00335460i
$680$	−11.0277			−0.422894
$681$	−38.5401			−1.47686
$682$	−3.06306	+	4.86938i	−0.117291	+	0.186458i
$683$	0.0682291			0.00261071			0.00130536	−	0.999999i	$-0.499584\pi$
$683$	0.0682291			0.00261071			0.00130536	+	0.999999i	$0.499584\pi$
$684$	11.2224			0.429101
$685$	−10.7461	−	18.6128i	−0.410587	−	0.711157i
$686$	−7.06219			−0.269636
$687$	33.4418	−	57.9230i	1.27589	−	2.20990i
$688$	−9.79741	−	16.9696i	−0.373523	−	0.646961i
$689$	−2.20199	−	3.81396i	−0.0838893	−	0.145300i
$690$	19.6114			0.746593
$691$	4.61036	−	7.98538i	0.175386	−	0.303778i	−0.764908	−	0.644139i	$-0.777216\pi$
$691$	4.61036	−	7.98538i	0.175386	−	0.303778i	0.940295	+	0.340361i	$0.110549\pi$
$692$	−5.69880	+	9.87062i	−0.216636	+	0.375225i
$693$	26.8561	−	46.5161i	1.02018	−	1.76700i
$694$	3.53383	+	6.12077i	0.134142	+	0.232341i
$695$	7.29875	−	12.6418i	0.276857	−	0.479531i
$696$	11.5873	+	20.0698i	0.439217	+	0.760745i
$697$	−19.4969			−0.738497
$698$	8.22190			0.311204
$699$	−39.5850	−	68.5632i	−1.49724	−	2.59330i
$700$	−0.500722	+	0.867277i	−0.0189255	+	0.0327800i
$701$	−6.31232	−	10.9333i	−0.238413	−	0.412943i	0.721846	−	0.692054i	$-0.243294\pi$
$701$	−6.31232	−	10.9333i	−0.238413	−	0.412943i	−0.960259	+	0.279110i	$0.909961\pi$
$702$	2.92521	−	5.06661i	0.110405	−	0.191227i
$703$	2.95109	−	5.11144i	0.111302	−	0.192782i
$704$	−7.59590	+	13.1565i	−0.286281	+	0.495854i
$705$	40.8521			1.53858
$706$	−3.43427	−	5.94832i	−0.129250	−	0.223868i
$707$	20.0035	+	34.6472i	0.752311	+	1.30304i
$708$	13.3280	−	23.0847i	0.500896	−	0.867578i
$709$	1.17037			0.0439543			0.0219772	−	0.999758i	$-0.493004\pi$
$709$	1.17037			0.0439543			0.0219772	+	0.999758i	$0.493004\pi$
$710$	1.18091	+	2.04540i	0.0443188	+	0.0767624i
$711$	−105.644			−3.96197
$712$	12.0377			0.451133
$713$	42.7841	+	1.62247i	1.60228	+	0.0607621i
$714$	−9.88192			−0.369821
$715$	−6.40691			−0.239605
$716$	15.0295	+	26.0319i	0.561680	+	0.972858i
$717$	−51.6417			−1.92859
$718$	2.77280	−	4.80262i	0.103480	−	0.179232i
$719$	11.0495	+	19.1383i	0.412078	+	0.713739i	0.995117	−	0.0987048i	$-0.0314700\pi$
$719$	11.0495	+	19.1383i	0.412078	+	0.713739i	−0.583039	+	0.812444i	$0.698137\pi$
$720$	28.6002	+	49.5370i	1.06587	+	1.84614i
$721$	17.1513			0.638748
$722$	3.24651	−	5.62311i	0.120822	−	0.209271i
$723$	41.2302	−	71.4128i	1.53337	−	2.65587i
$724$	10.3715	−	17.9639i	0.385452	−	0.667622i
$725$	0.597724	+	1.03529i	0.0221989	+	0.0384497i
$726$	1.39478	−	2.41583i	0.0517651	−	0.0896597i
$727$	−8.68325	−	15.0398i	−0.322044	−	0.557797i	0.658866	−	0.752261i	$-0.271037\pi$
$727$	−8.68325	−	15.0398i	−0.322044	−	0.557797i	−0.980910	+	0.194464i	$0.937703\pi$
$728$	3.11894			0.115596
$729$	83.7226			3.10084
$730$	1.14505	+	1.98328i	0.0423800	+	0.0734044i
$731$	11.0844	−	19.1987i	0.409971	−	0.710090i
$732$	10.3988	+	18.0113i	0.384351	+	0.665716i
$733$	5.59048	−	9.68300i	0.206489	−	0.357650i	−0.744117	−	0.668049i	$-0.767130\pi$
$733$	5.59048	−	9.68300i	0.206489	−	0.357650i	0.950606	+	0.310400i	$0.100463\pi$
$734$	−1.06056	+	1.83695i	−0.0391461	+	0.0678030i
$735$	−6.43414	+	11.1443i	−0.237327	+	0.411062i
$736$	−29.8455			−1.10012
$737$	−16.2680	−	28.1770i	−0.599239	−	1.03791i
$738$	−7.42590	−	12.8620i	−0.273351	−	0.473458i
$739$	15.4721	−	26.7984i	0.569149	−	0.985795i	−0.427502	−	0.904015i	$-0.640606\pi$
$739$	15.4721	−	26.7984i	0.569149	−	0.985795i	0.996650	−	0.0817801i	$-0.0260605\pi$
$740$	32.3629			1.18968
$741$	−1.23918	−	2.14633i	−0.0455225	−	0.0788472i
$742$	−3.54376			−0.130096
$743$	23.9164			0.877407			0.438704	−	0.898632i	$-0.355438\pi$
$743$	23.9164			0.877407			0.438704	+	0.898632i	$0.355438\pi$
$744$	−11.7684	−	22.2942i	−0.431452	−	0.817344i
$745$	−28.4729			−1.04317
$746$	6.88387			0.252036
$747$	52.9970	+	91.7936i	1.93906	+	3.35855i
$748$	−20.3778			−0.745085
$749$	3.67530	−	6.36581i	0.134293	−	0.232601i
$750$	−6.67362	−	11.5591i	−0.243686	−	0.422077i
$751$	22.3281	+	38.6733i	0.814763	+	1.41121i	0.909498	+	0.415708i	$0.136466\pi$
$751$	22.3281	+	38.6733i	0.814763	+	1.41121i	−0.0947354	+	0.995502i	$0.530201\pi$
$752$	−18.4510			−0.672838
$753$	8.79679	−	15.2365i	0.320573	−	0.555248i
$754$	0.901021	−	1.56061i	0.0328132	−	0.0568342i
$755$	10.4094	−	18.0296i	0.378838	−	0.656166i
$756$	35.6240	+	61.7026i	1.29563	+	2.24410i
$757$	−25.6749	+	44.4703i	−0.933171	+	1.61630i	−0.155307	+	0.987866i	$0.549637\pi$
$757$	−25.6749	+	44.4703i	−0.933171	+	1.61630i	−0.777864	+	0.628433i	$0.783697\pi$
$758$	−3.20527	−	5.55168i	−0.116421	−	0.201646i
$759$	74.8730			2.71772
$760$	−2.22550			−0.0807274
$761$	−13.8829	−	24.0459i	−0.503254	−	0.871662i	−0.999993	−	0.00376158i	$-0.998803\pi$
$761$	−13.8829	−	24.0459i	−0.503254	−	0.871662i	0.496739	−	0.867900i	$-0.334531\pi$
$762$	8.43379	−	14.6078i	0.305524	−	0.529183i
$763$	22.1694	+	38.3986i	0.802587	+	1.39012i
$764$	−16.8166	+	29.1271i	−0.608402	+	1.05378i
$765$	−32.3571	+	56.0441i	−1.16987	+	2.02628i
$766$	−2.98247	+	5.16579i	−0.107761	+	0.186648i
$767$	−4.28245			−0.154630
$768$	−11.5775	−	20.0528i	−0.417767	−	0.723594i
$769$	15.9407	+	27.6101i	0.574835	+	0.995644i	0.996059	+	0.0886876i	$0.0282673\pi$
$769$	15.9407	+	27.6101i	0.574835	+	0.995644i	−0.421224	+	0.906957i	$0.638399\pi$
$770$	−2.57773	+	4.46475i	−0.0928948	+	0.160899i
$771$	−62.9714			−2.26786
$772$	12.6660	+	21.9381i	0.455858	+	0.789569i
$773$	−22.8860			−0.823153			−0.411576	−	0.911375i	$-0.635022\pi$
$773$	−22.8860			−0.823153			−0.411576	+	0.911375i	$0.635022\pi$
$774$	16.8871			0.606996
$775$	−0.607067	−	1.15003i	−0.0218065	−	0.0413103i
$776$	−0.0602684			−0.00216351
$777$	59.9168			2.14950
$778$	−2.59164	−	4.48885i	−0.0929147	−	0.160933i
$779$	−3.93466			−0.140974
$780$	6.79469	−	11.7687i	0.243289	−	0.421389i
$781$	4.50853	+	7.80900i	0.161328	+	0.279428i
$782$	−5.01053	−	8.67850i	−0.179176	−	0.310343i
$783$	85.0505			3.03946
$784$	2.90600	−	5.03334i	0.103786	−	0.179762i
$785$	−4.36005	+	7.55183i	−0.155617	+	0.269536i
$786$	−3.03819	+	5.26230i	−0.108369	+	0.187700i
$787$	1.77473	+	3.07393i	0.0632624	+	0.109574i	0.895922	−	0.444212i	$-0.146516\pi$
$787$	1.77473	+	3.07393i	0.0632624	+	0.109574i	−0.832659	+	0.553785i	$0.813183\pi$
$788$	15.7537	−	27.2862i	0.561201	−	0.972029i
$789$	−6.46163	−	11.1919i	−0.230040	−	0.398441i
$790$	10.1401			0.360767
$791$	−38.0104			−1.35149
$792$	−16.0357	−	27.7746i	−0.569803	−	0.986927i
$793$	1.67063	−	2.89362i	0.0593260	−	0.102756i
$794$	−0.783017	−	1.35623i	−0.0277882	−	0.0481306i
$795$	−15.9505	+	27.6270i	−0.565704	+	0.979828i
$796$	−6.92987	+	12.0029i	−0.245623	+	0.425431i
$797$	−0.234955	+	0.406955i	−0.00832255	+	0.0144151i	−0.870157	−	0.492775i	$-0.835983\pi$
$797$	−0.234955	+	0.406955i	−0.00832255	+	0.0144151i	0.861834	+	0.507190i	$0.169316\pi$
$798$	−1.99427			−0.0705963
$799$	−10.4373	−	18.0780i	−0.369247	−	0.639554i
$800$	0.453250	+	0.785053i	0.0160248	+	0.0277558i
$801$	35.3206	−	61.1771i	1.24799	−	2.16159i
$802$	−3.31221			−0.116958
$803$	4.37160	+	7.57183i	0.154270	+	0.267204i
$804$	69.0105			2.43381
$805$	38.3700			1.35237
$806$	−1.04377	+	1.65929i	−0.0367652	+	0.0584460i
$807$	−70.7995			−2.49226
$808$	23.8881			0.840381
$809$	−10.4307	−	18.0666i	−0.366725	−	0.635186i	0.622326	−	0.782758i	$-0.286188\pi$
$809$	−10.4307	−	18.0666i	−0.366725	−	0.635186i	−0.989051	+	0.147571i	$0.952854\pi$
$810$	−23.9114			−0.840160
$811$	−6.29864	+	10.9096i	−0.221175	+	0.383087i	−0.955165	−	0.296074i	$-0.904323\pi$
$811$	−6.29864	+	10.9096i	−0.221175	+	0.383087i	0.733990	+	0.679160i	$0.237656\pi$
$812$	10.9729	+	19.0056i	0.385073	+	0.666966i
$813$	−10.4214	−	18.0505i	−0.365496	−	0.633058i
$814$	−8.16387			−0.286144
$815$	−10.2648	+	17.7791i	−0.359559	+	0.622774i
$816$	20.0889	−	34.7949i	0.703251	−	1.21807i
$817$	2.23694	−	3.87449i	0.0782606	−	0.135551i
$818$	4.78244	+	8.28344i	0.167214	+	0.289624i
$819$	9.15147	−	15.8508i	0.319778	−	0.553872i
$820$	−10.7873	−	18.6841i	−0.376708	−	0.652477i
$821$	51.0288			1.78092			0.890458	−	0.455065i	$-0.150384\pi$
$821$	51.0288			1.78092			0.890458	+	0.455065i	$0.150384\pi$
$822$	−11.4995			−0.401092
$823$	14.7004	+	25.4619i	0.512425	+	0.887545i	0.999896	+	0.0144065i	$0.00458589\pi$
$823$	14.7004	+	25.4619i	0.512425	+	0.887545i	−0.487472	+	0.873139i	$0.662081\pi$
$824$	5.12050	−	8.86896i	0.178381	−	0.308965i
$825$	−1.13706	−	1.96945i	−0.0395875	−	0.0685675i
$826$	−1.72298	+	2.98429i	−0.0599501	+	0.103837i
$827$	0.292267	−	0.506221i	0.0101631	−	0.0176030i	−0.860899	−	0.508776i	$-0.830098\pi$
$827$	0.292267	−	0.506221i	0.0101631	−	0.0176030i	0.871062	+	0.491173i	$0.163432\pi$
$828$	−57.7652	+	100.052i	−2.00748	+	3.47706i
$829$	−38.5313			−1.33825			−0.669123	−	0.743152i	$-0.733330\pi$
$829$	−38.5313			−1.33825			−0.669123	+	0.743152i	$0.733330\pi$
$830$	−5.08682	−	8.81062i	−0.176566	−	0.305821i
$831$	−16.2707	−	28.1817i	−0.564424	−	0.977612i
$832$	−2.58838	+	4.48320i	−0.0897359	+	0.155427i
$833$	6.57546			0.227826
$834$	−3.90525	−	6.76409i	−0.135228	−	0.234221i
$835$	22.5267			0.779569
$836$	−4.11244			−0.142232
$837$	−92.4524	−	3.50601i	−3.19562	−	0.121185i
$838$	−3.49678			−0.120794
$839$	−6.97914			−0.240947			−0.120473	−	0.992717i	$-0.538441\pi$
$839$	−6.97914			−0.240947			−0.120473	+	0.992717i	$0.538441\pi$
$840$	−11.2962	−	19.5657i	−0.389757	−	0.675079i
$841$	−2.80279			−0.0966479
$842$	0.169759	−	0.294032i	0.00585030	−	0.0101330i
$843$	20.0422	+	34.7141i	0.690290	+	1.19562i
$844$	−21.9915	−	38.0904i	−0.756978	−	1.31113i
$845$	−2.18322			−0.0751050
$846$	7.95068	−	13.7710i	0.273350	−	0.473456i
$847$	2.72891	−	4.72661i	0.0937664	−	0.162408i
$848$	7.20408	−	12.4778i	0.247389	−	0.428491i
$849$	18.8998	+	32.7353i	0.648638	+	1.12347i
$850$	−0.152186	+	0.263593i	−0.00521992	+	0.00904117i
$851$	30.3802	+	52.6201i	1.04142	+	1.80379i
$852$	−19.1256			−0.655233
$853$	45.4936			1.55767			0.778835	−	0.627229i	$-0.215811\pi$
$853$	45.4936			1.55767			0.778835	+	0.627229i	$0.215811\pi$
$854$	−1.34431	−	2.32842i	−0.0460014	−	0.0796767i
$855$	−6.52998	+	11.3103i	−0.223321	+	0.386803i
$856$	−2.19451	−	3.80100i	−0.0750068	−	0.129916i
$857$	−14.4405	+	25.0118i	−0.493280	+	0.854385i	−0.999970	−	0.00774277i	$-0.997535\pi$
$857$	−14.4405	+	25.0118i	−0.493280	+	0.854385i	0.506690	+	0.862128i	$0.330869\pi$
$858$	−1.71403	+	2.96879i	−0.0585161	+	0.101353i
$859$	11.6235	−	20.1325i	0.396588	−	0.686910i	−0.596715	−	0.802454i	$-0.703528\pi$
$859$	11.6235	−	20.1325i	0.396588	−	0.686910i	0.993302	+	0.115543i	$0.0368608\pi$
$860$	24.5312			0.836506
$861$	−19.9716	−	34.5919i	−0.680631	−	1.17889i
$862$	0.167940	+	0.290881i	0.00572007	+	0.00990745i
$863$	−3.56482	+	6.17444i	−0.121348	+	0.210181i	−0.920299	−	0.391215i	$-0.872055\pi$
$863$	−3.56482	+	6.17444i	−0.121348	+	0.210181i	0.798952	+	0.601395i	$0.205388\pi$
$864$	64.4933			2.19411
$865$	−6.63190	−	11.4868i	−0.225491	−	0.390563i
$866$	8.58919			0.291873
$867$	−10.9485			−0.371829
$868$	−11.1444	−	21.1120i	−0.378265	−	0.716588i
$869$	38.7131			1.31325
$870$	−13.0533			−0.442550
$871$	−5.54348	−	9.60159i	−0.187834	−	0.325337i
$872$	26.4746			0.896542
$873$	−0.176837	+	0.306291i	−0.00598503	+	0.0103664i
$874$	−1.01118	−	1.75141i	−0.0342035	−	0.0592422i
$875$	−13.0571	−	22.6155i	−0.441409	−	0.764543i
$876$	−18.5448			−0.626569
$877$	−2.48889	+	4.31088i	−0.0840438	+	0.145568i	−0.904983	−	0.425447i	$-0.860117\pi$
$877$	−2.48889	+	4.31088i	−0.0840438	+	0.145568i	0.820940	+	0.571015i	$0.193450\pi$
$878$	−4.87500	+	8.44374i	−0.164523	+	0.284962i
$879$	−9.52028	+	16.4896i	−0.321111	+	0.556181i
$880$	−10.4805	−	18.1527i	−0.353297	−	0.611928i
$881$	−10.0807	+	17.4603i	−0.339627	+	0.588251i	−0.984362	−	0.176155i	$-0.943634\pi$
$881$	−10.0807	+	17.4603i	−0.339627	+	0.588251i	0.644736	+	0.764406i	$0.276967\pi$
$882$	2.50444	+	4.33782i	0.0843289	+	0.146062i
$883$	−0.0751132			−0.00252776			−0.00126388	−	0.999999i	$-0.500402\pi$
$883$	−0.0751132			−0.00252776			−0.00126388	+	0.999999i	$0.500402\pi$
$884$	−6.94393			−0.233550
$885$	15.5102	+	26.8645i	0.521371	+	0.903042i
$886$	−1.46271	+	2.53348i	−0.0491405	+	0.0851139i
$887$	19.5569	+	33.8736i	0.656657	+	1.13736i	0.981476	+	0.191587i	$0.0613635\pi$
$887$	19.5569	+	33.8736i	0.656657	+	1.13736i	−0.324818	+	0.945776i	$0.605303\pi$
$888$	17.8881	−	30.9830i	0.600284	−	1.03972i
$889$	16.5009	−	28.5803i	0.553421	−	0.958553i
$890$	−3.39018	+	5.87197i	−0.113639	+	0.196829i
$891$	−91.2897			−3.05832
$892$	27.2648	+	47.2240i	0.912893	+	1.58118i
$893$	−2.10636	−	3.64832i	−0.0704866	−	0.122086i
$894$	−7.61732	+	13.1936i	−0.254761	+	0.441260i
$895$	−34.9808			−1.16928
$896$	10.9532	+	18.9716i	0.365922	+	0.633796i
$897$	25.5137			0.851879
$898$	0.721791			0.0240865
$899$	−28.4771	−	1.07992i	−0.949766	−	0.0360173i
$900$	3.50902			0.116967
$901$	16.3008			0.543058
$902$	2.72120	+	4.71326i	0.0906062	+	0.156934i
$903$	45.4172			1.51139
$904$	−11.3479	+	19.6552i	−0.377427	+	0.653722i
$905$	12.0696	+	20.9052i	0.401208	+	0.694913i
$906$	−5.56964	−	9.64690i	−0.185039	−	0.320497i
$907$	14.1098			0.468507			0.234253	−	0.972176i	$-0.424735\pi$
$907$	14.1098			0.468507			0.234253	+	0.972176i	$0.424735\pi$
$908$	−10.8960	+	18.8723i	−0.361595	+	0.626301i
$909$	70.0916	−	121.402i	2.32479	−	4.02665i
$910$	−0.878386	+	1.52141i	−0.0291182	+	0.0504342i
$911$	−1.19183	−	2.06432i	−0.0394872	−	0.0683939i	0.845606	−	0.533807i	$-0.179239\pi$
$911$	−1.19183	−	2.06432i	−0.0394872	−	0.0683939i	−0.885094	+	0.465413i	$0.845906\pi$
$912$	4.05413	−	7.02196i	0.134246	−	0.232520i
$913$	−19.4206	−	33.6375i	−0.642729	−	1.11324i
$914$	11.7716			0.389371
$915$	−24.2029			−0.800125
$916$	−18.9092	−	32.7517i	−0.624777	−	1.08215i
$917$	−5.94427	+	10.2958i	−0.196297	+	0.339997i
$918$	10.8273	+	18.7534i	0.357354	+	0.618955i
$919$	7.13527	−	12.3586i	0.235371	−	0.407674i	−0.724010	−	0.689790i	$-0.757703\pi$
$919$	7.13527	−	12.3586i	0.235371	−	0.407674i	0.959380	+	0.282116i	$0.0910362\pi$
$920$	11.4553	−	19.8412i	0.377670	−	0.654144i
$921$	−11.7026	+	20.2696i	−0.385615	+	0.667905i
$922$	5.85203			0.192726
$923$	1.53632	+	2.66099i	0.0505687	+	0.0875876i
$924$	−20.8740	−	36.1548i	−0.686703	−	1.18941i
$925$	0.922743	−	1.59824i	0.0303396	−	0.0525497i
$926$	10.7288			0.352572
$927$	−30.0487	−	52.0459i	−0.986930	−	1.70941i
$928$	19.8652			0.652106
$929$	43.3228			1.42137			0.710687	−	0.703508i	$-0.248384\pi$
$929$	43.3228			1.42137			0.710687	+	0.703508i	$0.248384\pi$
$930$	14.1894	+	0.538094i	0.465288	+	0.0176448i
$931$	1.32699			0.0434904
$932$	−44.7655			−1.46634
$933$	44.4927	+	77.0637i	1.45663	+	2.52295i
$934$	7.67133			0.251014
$935$	11.8572	−	20.5372i	0.387771	−	0.671639i
$936$	−5.46431	−	9.46447i	−0.178607	−	0.309356i
$937$	26.4515	+	45.8154i	0.864134	+	1.49672i	0.867904	+	0.496732i	$0.165467\pi$
$937$	26.4515	+	45.8154i	0.864134	+	1.49672i	−0.00376999	+	0.999993i	$0.501200\pi$
$938$	−8.92136			−0.291293
$939$	−1.92478	+	3.33382i	−0.0628130	+	0.108795i
$940$	11.5496	−	20.0045i	0.376706	−	0.652474i
$941$	−9.67011	+	16.7491i	−0.315237	+	0.546006i	−0.979488	−	0.201504i	$-0.935417\pi$
$941$	−9.67011	+	16.7491i	−0.315237	+	0.546006i	0.664251	+	0.747509i	$0.268751\pi$
$942$	2.33288	+	4.04066i	0.0760092	+	0.131652i
$943$	20.2528	−	35.0790i	0.659523	−	1.14233i
$944$	−7.00526	−	12.1335i	−0.228002	−	0.394911i
$945$	−82.9139			−2.69719
$946$	−6.18825			−0.201197
$947$	5.96499	+	10.3317i	0.193836	+	0.335734i	0.946518	−	0.322650i	$-0.104574\pi$
$947$	5.96499	+	10.3317i	0.193836	+	0.335734i	−0.752682	+	0.658384i	$0.771240\pi$
$948$	−41.0562	+	71.1114i	−1.33344	+	2.30959i
$949$	1.48966	+	2.58017i	0.0483566	+	0.0837560i
$950$	−0.0307125	+	0.0531957i	−0.000996447	+	0.00172590i
$951$	−27.7369	+	48.0418i	−0.899432	+	1.55786i
$952$	−5.77218	+	9.99770i	−0.187077	+	0.324027i
$953$	13.0184			0.421706			0.210853	−	0.977518i	$-0.432376\pi$
$953$	13.0184			0.421706			0.210853	+	0.977518i	$0.432376\pi$
$954$	6.20859	+	10.7536i	0.201011	+	0.348161i
$955$	−19.5700	−	33.8963i	−0.633271	−	1.09686i
$956$	−14.6000	+	25.2880i	−0.472198	+	0.817871i
$957$	−49.8355			−1.61095
$958$	0.385737	+	0.668115i	0.0124626	+	0.0215858i
$959$	−22.4990			−0.726532
$960$	37.4986			1.21026
$961$	30.9110	+	2.34781i	0.997128	+	0.0757357i
$962$	−2.78192			−0.0896927
$963$	−25.7562			−0.829981
$964$	−23.3130	−	40.3793i	−0.750861	−	1.30053i
$965$	−29.4796			−0.948983
$966$	10.2651	−	17.7796i	0.330274	−	0.572051i
$967$	−1.39621	−	2.41830i	−0.0448990	−	0.0777673i	0.842703	−	0.538379i	$-0.180963\pi$
$967$	−1.39621	−	2.41830i	−0.0448990	−	0.0777673i	−0.887602	+	0.460612i	$0.847630\pi$
$968$	−1.62942	−	2.82224i	−0.0523716	−	0.0907103i
$969$	9.17335			0.294690
$970$	0.0169734	−	0.0293987i	0.000544982	−	0.000943936i
$971$	8.61195	−	14.9163i	0.276371	−	0.478688i	−0.694109	−	0.719869i	$-0.744202\pi$
$971$	8.61195	−	14.9163i	0.276371	−	0.478688i	0.970480	+	0.241182i	$0.0775350\pi$
$972$	50.0540	−	86.6961i	1.60548	−	2.78078i
$973$	−7.64069	−	13.2341i	−0.244949	−	0.424264i
$974$	0.421875	−	0.730709i	0.0135178	−	0.0234134i
$975$	−0.387466	−	0.671110i	−0.0124088	−	0.0214927i
$976$	10.9314			0.349904
$977$	45.6547			1.46062			0.730311	−	0.683114i	$-0.239375\pi$
$977$	45.6547			1.46062			0.730311	+	0.683114i	$0.239375\pi$
$978$	5.49223	+	9.51282i	0.175622	+	0.304187i
$979$	−12.9432	+	22.4182i	−0.413665	+	0.716489i
$980$	3.63809	+	6.30135i	0.116214	+	0.201289i
$981$	77.6807	−	134.547i	2.48015	−	4.29575i
$982$	−0.169445	+	0.293487i	−0.00540720	+	0.00936555i
$983$	−9.09069	+	15.7455i	−0.289948	+	0.502205i	−0.973797	−	0.227419i	$-0.926971\pi$
$983$	−9.09069	+	15.7455i	−0.289948	+	0.502205i	0.683849	+	0.729624i	$0.260305\pi$
$984$	−23.8500			−0.760309
$985$	18.3331	+	31.7539i	0.584141	+	1.01176i
$986$	3.33501	+	5.77641i	0.106208	+	0.183958i
$987$	21.3830	−	37.0364i	0.680627	−	1.17888i
$988$	−1.40135			−0.0445830
$989$	23.0284	+	39.8863i	0.732259	+	1.26831i
$990$	18.0645			0.574127
$991$	27.0225			0.858397			0.429198	−	0.903210i	$-0.358796\pi$
$991$	27.0225			0.858397			0.429198	+	0.903210i	$0.358796\pi$
$992$	−21.5940	−	0.818895i	−0.685611	−	0.0259999i
$993$	−103.009			−3.26890
$994$	2.47247			0.0784221
$995$	−8.06454	−	13.9682i	−0.255663	−	0.442822i
$996$	82.3843			2.61045
$997$	−20.9896	+	36.3551i	−0.664748	+	1.15138i	0.314606	+	0.949222i	$0.398128\pi$
$997$	−20.9896	+	36.3551i	−0.664748	+	1.15138i	−0.979354	+	0.202155i	$0.935206\pi$
$998$	−1.20822	−	2.09270i	−0.0382455	−	0.0662432i
$999$	−65.6488	−	113.707i	−2.07704	−	3.59753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.10	✓	30
31.5	even	3	inner	403.2.h.a.222.10	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.10	✓	30	1.1	even	1	trivial
403.2.h.a.222.10	yes	30	31.5	even	3	inner

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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.352077 q^{2} +(-1.65894 - 2.87336i) q^{3} -1.87604 q^{4} +(1.09161 - 1.89072i) q^{5} +(-0.584073 - 1.01164i) q^{6} +(-1.14275 - 1.97930i) q^{7} -1.36466 q^{8} +(-4.00415 + 6.93538i) q^{9} +O(q^{10})\)	\(q+0.352077 q^{2} +(-1.65894 - 2.87336i) q^{3} -1.87604 q^{4} +(1.09161 - 1.89072i) q^{5} +(-0.584073 - 1.01164i) q^{6} +(-1.14275 - 1.97930i) q^{7} -1.36466 q^{8} +(-4.00415 + 6.93538i) q^{9} +(0.384330 - 0.665679i) q^{10} +(1.46731 - 2.54145i) q^{11} +(3.11224 + 5.39055i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.402336 - 0.696866i) q^{14} -7.24364 q^{15} +3.27162 q^{16} +(1.85069 + 3.20548i) q^{17} +(-1.40977 + 2.44179i) q^{18} +(0.373487 + 0.646898i) q^{19} +(-2.04790 + 3.54707i) q^{20} +(-3.79150 + 6.56707i) q^{21} +(0.516605 - 0.894787i) q^{22} -7.68978 q^{23} +(2.26389 + 3.92118i) q^{24} +(0.116781 + 0.202271i) q^{25} +(0.176038 - 0.304907i) q^{26} +16.6169 q^{27} +(2.14385 + 3.71325i) q^{28} +5.11832 q^{29} -2.55032 q^{30} +(-5.56377 - 0.210991i) q^{31} +3.88119 q^{32} -9.73669 q^{33} +(0.651584 + 1.12858i) q^{34} -4.98974 q^{35} +(7.51195 - 13.0111i) q^{36} +(-3.95073 - 6.84287i) q^{37} +(0.131496 + 0.227758i) q^{38} -3.31787 q^{39} +(-1.48968 + 2.58020i) q^{40} +(-2.63374 + 4.56176i) q^{41} +(-1.33490 + 2.31211i) q^{42} +(-2.99467 - 5.18692i) q^{43} +(-2.75273 + 4.76787i) q^{44} +(8.74192 + 15.1414i) q^{45} -2.70739 q^{46} -5.63971 q^{47} +(-5.42741 - 9.40055i) q^{48} +(0.888247 - 1.53849i) q^{49} +(0.0411160 + 0.0712150i) q^{50} +(6.14034 - 10.6354i) q^{51} +(-0.938021 + 1.62470i) q^{52} +(2.20199 - 3.81396i) q^{53} +5.85042 q^{54} +(-3.20345 - 5.54854i) q^{55} +(1.55947 + 2.70108i) q^{56} +(1.23918 - 2.14633i) q^{57} +1.80204 q^{58} +(-2.14122 - 3.70871i) q^{59} +13.5894 q^{60} +3.34127 q^{61} +(-1.95887 - 0.0742850i) q^{62} +18.3029 q^{63} -5.17676 q^{64} +(-1.09161 - 1.89072i) q^{65} -3.42806 q^{66} +(5.54348 - 9.60159i) q^{67} +(-3.47197 - 6.01362i) q^{68} +(12.7569 + 22.0955i) q^{69} -1.75677 q^{70} +(-1.53632 + 2.66099i) q^{71} +(5.46431 - 9.46447i) q^{72} +(-1.48966 + 2.58017i) q^{73} +(-1.39096 - 2.40921i) q^{74} +(0.387466 - 0.671110i) q^{75} +(-0.700677 - 1.21361i) q^{76} -6.70707 q^{77} -1.16815 q^{78} +(6.59593 + 11.4245i) q^{79} +(3.57133 - 6.18572i) q^{80} +(-15.5539 - 26.9402i) q^{81} +(-0.927277 + 1.60609i) q^{82} +(6.61777 - 11.4623i) q^{83} +(7.11301 - 12.3201i) q^{84} +8.08090 q^{85} +(-1.05435 - 1.82619i) q^{86} +(-8.49097 - 14.7068i) q^{87} +(-2.00238 + 3.46823i) q^{88} -8.82102 q^{89} +(3.07783 + 5.33095i) q^{90} -2.28550 q^{91} +14.4264 q^{92} +(8.62368 + 16.3367i) q^{93} -1.98561 q^{94} +1.63080 q^{95} +(-6.43865 - 11.1521i) q^{96} +0.0441635 q^{97} +(0.312731 - 0.541666i) q^{98} +(11.7506 + 20.3527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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