LMFDB - Embedded newform 252.2.bi.c.223.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.33
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05092 - 0.946342i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(0.208875 - 1.98906i) q^{4} +(0.416111 - 0.240242i) q^{5} +(0.100346 + 2.44743i) q^{6} +(2.63514 + 0.236713i) q^{7} +(-1.66282 - 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +O(q^{10})$	\(q+(1.05092 - 0.946342i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(0.208875 - 1.98906i) q^{4} +(0.416111 - 0.240242i) q^{5} +(0.100346 + 2.44743i) q^{6} +(2.63514 + 0.236713i) q^{7} +(-1.66282 - 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +(0.209950 - 0.646259i) q^{10} +(2.31311 + 1.33548i) q^{11} +(2.42156 + 2.47710i) q^{12} +(5.48694 - 3.16789i) q^{13} +(2.99334 - 2.24498i) q^{14} +(-0.139573 + 0.820435i) q^{15} +(-3.91274 - 0.830933i) q^{16} +2.37005i q^{17} +(-3.37460 - 2.57140i) q^{18} -4.20225 q^{19} +(-0.390941 - 0.877852i) q^{20} +(-3.22835 + 3.25235i) q^{21} +(3.69472 - 0.785512i) q^{22} +(-4.15320 + 2.39785i) q^{23} +(4.88906 + 0.311614i) q^{24} +(-2.38457 + 4.13019i) q^{25} +(2.76845 - 8.52173i) q^{26} +(4.54623 + 2.51631i) q^{27} +(1.02125 - 5.19202i) q^{28} +(1.45060 - 2.51250i) q^{29} +(0.629731 + 0.994297i) q^{30} +(-3.14399 - 5.44556i) q^{31} +(-4.89833 + 2.82954i) q^{32} +(-4.33762 + 1.60843i) q^{33} +(2.24287 + 2.49074i) q^{34} +(1.15338 - 0.534572i) q^{35} +(-5.97986 + 0.491180i) q^{36} +4.69467 q^{37} +(-4.41624 + 3.97676i) q^{38} +(-1.84044 + 10.8185i) q^{39} +(-1.24160 - 0.552590i) q^{40} +(-10.1295 + 5.84827i) q^{41} +(-0.314913 + 6.47309i) q^{42} +(-1.16280 - 0.671344i) q^{43} +(3.13950 - 4.32198i) q^{44} +(-0.939786 - 1.09297i) q^{45} +(-2.09550 + 6.45030i) q^{46} +(-3.72876 + 6.45840i) q^{47} +(5.43291 - 4.29924i) q^{48} +(6.88793 + 1.24754i) q^{49} +(1.40258 + 6.59713i) q^{50} +(-3.16049 - 2.61967i) q^{51} +(-5.15504 - 11.5756i) q^{52} -8.99689 q^{53} +(7.15902 - 1.65783i) q^{54} +1.28335 q^{55} +(-3.84016 - 6.42286i) q^{56} +(4.64485 - 5.60375i) q^{57} +(-0.853225 - 4.01321i) q^{58} +(0.140454 + 0.243273i) q^{59} +(1.60274 + 0.448988i) q^{60} +(9.52219 + 5.49764i) q^{61} +(-8.45745 - 2.74757i) q^{62} +(-0.768666 - 7.89995i) q^{63} +(-2.47005 + 7.60913i) q^{64} +(1.52212 - 2.63639i) q^{65} +(-3.03638 + 5.79520i) q^{66} +(-1.89068 + 1.09159i) q^{67} +(4.71417 + 0.495044i) q^{68} +(1.39308 - 8.18874i) q^{69} +(0.706224 - 1.65328i) q^{70} +0.198757i q^{71} +(-5.81955 + 6.17518i) q^{72} -4.84941i q^{73} +(4.93373 - 4.44276i) q^{74} +(-2.87194 - 7.74506i) q^{75} +(-0.877746 + 8.35854i) q^{76} +(5.77925 + 4.06671i) q^{77} +(8.30379 + 13.1110i) q^{78} +(3.42117 + 1.97521i) q^{79} +(-1.82776 + 0.594244i) q^{80} +(-8.38060 + 3.28110i) q^{81} +(-5.11086 + 15.7321i) q^{82} +(5.09429 - 8.82356i) q^{83} +(5.79480 + 7.10072i) q^{84} +(0.569384 + 0.986203i) q^{85} +(-1.85733 + 0.394877i) q^{86} +(1.74707 + 4.71152i) q^{87} +(-0.790698 - 7.51310i) q^{88} +2.67188i q^{89} +(-2.02196 - 0.259268i) q^{90} +(15.2087 - 7.04900i) q^{91} +(3.90197 + 8.76182i) q^{92} +(10.7369 + 1.82656i) q^{93} +(2.19322 + 10.3160i) q^{94} +(-1.74860 + 1.00956i) q^{95} +(1.64102 - 9.65956i) q^{96} +(1.87526 + 1.08268i) q^{97} +(8.41929 - 5.20727i) q^{98} +(2.64962 - 7.56210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.05092	−	0.946342i	0.743114	−	0.669165i
$2$	1.05092	−	0.946342i	0.743114	−	0.669165i
$3$	−1.10533	+	1.33351i	−0.638160	+	0.769904i
$3$	−1.10533	+	1.33351i	−0.638160	+	0.769904i
$4$	0.208875	−	1.98906i	0.104438	−	0.994531i
$5$	0.416111	−	0.240242i	0.186091	−	0.107439i	−0.404061	−	0.914732i	$-0.632402\pi$
$5$	0.416111	−	0.240242i	0.186091	−	0.107439i	0.590151	+	0.807293i	$0.299068\pi$
$6$	0.100346	+	2.44743i	0.0409661	+	0.999161i
$7$	2.63514	+	0.236713i	0.995990	+	0.0894690i
$7$	2.63514	+	0.236713i	0.995990	+	0.0894690i
$8$	−1.66282	−	2.28802i	−0.587896	−	0.808937i
$9$	−0.556509	−	2.94793i	−0.185503	−	0.982644i
$10$	0.209950	−	0.646259i	0.0663919	−	0.204365i
$11$	2.31311	+	1.33548i	0.697429	+	0.402661i	0.806389	−	0.591385i	$-0.201419\pi$
$11$	2.31311	+	1.33548i	0.697429	+	0.402661i	−0.108960	+	0.994046i	$0.534752\pi$
$12$	2.42156	+	2.47710i	0.699045	+	0.715077i
$13$	5.48694	−	3.16789i	1.52180	−	0.878614i	0.522136	−	0.852862i	$-0.325135\pi$
$13$	5.48694	−	3.16789i	1.52180	−	0.878614i	0.999668	−	0.0257515i	$-0.00819785\pi$
$14$	2.99334	−	2.24498i	0.800004	−	0.599995i
$15$	−0.139573	+	0.820435i	−0.0360376	+	0.211835i
$16$	−3.91274	−	0.830933i	−0.978186	−	0.207733i
$17$			2.37005i			0.574821i	0.957808	+	0.287410i	$0.0927944\pi$
$17$			2.37005i			0.574821i	−0.957808	+	0.287410i	$0.907206\pi$
$18$	−3.37460	−	2.57140i	−0.795400	−	0.606085i
$19$	−4.20225			−0.964062			−0.482031	−	0.876154i	$-0.660101\pi$
$19$	−4.20225			−0.964062			−0.482031	+	0.876154i	$0.660101\pi$
$20$	−0.390941	−	0.877852i	−0.0874170	−	0.196294i
$21$	−3.22835	+	3.25235i	−0.704484	+	0.709720i
$22$	3.69472	−	0.785512i	0.787716	−	0.167472i
$23$	−4.15320	+	2.39785i	−0.866001	+	0.499986i	−0.866017	−	0.500014i	$-0.833328\pi$
$23$	−4.15320	+	2.39785i	−0.866001	+	0.499986i	1.59909e−5		1.00000i	$0.499995\pi$
$24$	4.88906	+	0.311614i	0.997975	+	0.0636080i
$25$	−2.38457	+	4.13019i	−0.476914	+	0.826038i
$26$	2.76845	−	8.52173i	0.542937	−	1.67125i
$27$	4.54623	+	2.51631i	0.874921	+	0.484265i
$28$	1.02125	−	5.19202i	0.192999	−	0.981199i
$29$	1.45060	−	2.51250i	0.269369	−	0.466560i	−0.699330	−	0.714799i	$-0.746518\pi$
$29$	1.45060	−	2.51250i	0.269369	−	0.466560i	0.968699	+	0.248238i	$0.0798516\pi$
$30$	0.629731	+	0.994297i	0.114973	+	0.181533i
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	−0.997080	−	0.0763698i	$-0.975667\pi$
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	0.432402	−	0.901681i	$-0.357666\pi$
$32$	−4.89833	+	2.82954i	−0.865911	+	0.500198i
$33$	−4.33762	+	1.60843i	−0.755082	+	0.279991i
$34$	2.24287	+	2.49074i	0.384650	+	0.427158i
$35$	1.15338	−	0.534572i	0.194957	−	0.0903592i
$36$	−5.97986	+	0.491180i	−0.996644	+	0.0818634i
$37$	4.69467			0.771799			0.385900	−	0.922541i	$-0.373891\pi$
$37$	4.69467			0.771799			0.385900	+	0.922541i	$0.373891\pi$
$38$	−4.41624	+	3.97676i	−0.716408	+	0.645116i
$39$	−1.84044	+	10.8185i	−0.294707	+	1.73234i
$40$	−1.24160	−	0.552590i	−0.196314	−	0.0873722i
$41$	−10.1295	+	5.84827i	−1.58196	+	0.913347i	−0.587390	+	0.809304i	$0.699845\pi$
$41$	−10.1295	+	5.84827i	−1.58196	+	0.913347i	−0.994573	+	0.104043i	$0.966822\pi$
$42$	−0.314913	+	6.47309i	−0.0485921	+	0.998819i
$43$	−1.16280	−	0.671344i	−0.177326	−	0.102379i	0.408710	−	0.912664i	$-0.365979\pi$
$43$	−1.16280	−	0.671344i	−0.177326	−	0.102379i	−0.586036	+	0.810285i	$0.699312\pi$
$44$	3.13950	−	4.32198i	0.473297	−	0.651562i
$45$	−0.939786	−	1.09297i	−0.140095	−	0.162930i
$46$	−2.09550	+	6.45030i	−0.308965	+	0.951044i
$47$	−3.72876	+	6.45840i	−0.543895	+	0.942054i	0.454780	+	0.890604i	$0.349718\pi$
$47$	−3.72876	+	6.45840i	−0.543895	+	0.942054i	−0.998676	+	0.0514505i	$0.983616\pi$
$48$	5.43291	−	4.29924i	0.784174	−	0.620541i
$49$	6.88793	+	1.24754i	0.983991	+	0.178220i
$50$	1.40258	+	6.59713i	0.198354	+	0.932975i
$51$	−3.16049	−	2.61967i	−0.442557	−	0.366828i
$52$	−5.15504	−	11.5756i	−0.714875	−	1.60524i
$53$	−8.99689			−1.23582			−0.617909	−	0.786250i	$-0.712020\pi$
$53$	−8.99689			−1.23582			−0.617909	+	0.786250i	$0.712020\pi$
$54$	7.15902	−	1.65783i	0.974219	−	0.225602i
$55$	1.28335			0.173047
$56$	−3.84016	−	6.42286i	−0.513164	−	0.858291i
$57$	4.64485	−	5.60375i	0.615226	−	0.742235i
$58$	−0.853225	−	4.01321i	−0.112034	−	0.526960i
$59$	0.140454	+	0.243273i	0.0182855	+	0.0316715i	0.875023	−	0.484081i	$-0.160846\pi$
$59$	0.140454	+	0.243273i	0.0182855	+	0.0316715i	−0.856738	+	0.515752i	$0.827513\pi$
$60$	1.60274	+	0.448988i	0.206913	+	0.0579641i
$61$	9.52219	+	5.49764i	1.21919	+	0.703900i	0.964745	−	0.263186i	$-0.0847735\pi$
$61$	9.52219	+	5.49764i	1.21919	+	0.703900i	0.254446	+	0.967087i	$0.418107\pi$
$62$	−8.45745	−	2.74757i	−1.07410	−	0.348941i
$63$	−0.768666	−	7.89995i	−0.0968428	−	0.995300i
$64$	−2.47005	+	7.60913i	−0.308757	+	0.951141i
$65$	1.52212	−	2.63639i	0.188796	−	0.327003i
$66$	−3.03638	+	5.79520i	−0.373752	+	0.713339i
$67$	−1.89068	+	1.09159i	−0.230984	+	0.133358i	−0.611026	−	0.791611i	$-0.709243\pi$
$67$	−1.89068	+	1.09159i	−0.230984	+	0.133358i	0.380042	+	0.924969i	$0.375909\pi$
$68$	4.71417	+	0.495044i	0.571677	+	0.0600330i
$69$	1.39308	−	8.18874i	0.167707	−	0.985809i
$70$	0.706224	−	1.65328i	0.0844099	−	0.197605i
$71$			0.198757i			0.0235881i	0.999930	+	0.0117940i	$0.00375425\pi$
$71$			0.198757i			0.0235881i	−0.999930	+	0.0117940i	$0.996246\pi$
$72$	−5.81955	+	6.17518i	−0.685840	+	0.727752i
$73$		−	4.84941i		−	0.567580i	−0.958886	−	0.283790i	$-0.908408\pi$
$73$		−	4.84941i		−	0.567580i	0.958886	−	0.283790i	$-0.0915919\pi$
$74$	4.93373	−	4.44276i	0.573535	−	0.516461i
$75$	−2.87194	−	7.74506i	−0.331623	−	0.894322i
$76$	−0.877746	+	8.35854i	−0.100684	+	0.958790i
$77$	5.77925	+	4.06671i	0.658607	+	0.463444i
$78$	8.30379	+	13.1110i	0.940219	+	1.48453i
$79$	3.42117	+	1.97521i	0.384912	+	0.222229i	0.679953	−	0.733256i	$-0.262000\pi$
$79$	3.42117	+	1.97521i	0.384912	+	0.222229i	−0.295041	+	0.955484i	$0.595333\pi$
$80$	−1.82776	+	0.594244i	−0.204350	+	0.0664385i
$81$	−8.38060	+	3.28110i	−0.931177	+	0.364567i
$82$	−5.11086	+	15.7321i	−0.564400	+	1.73731i
$83$	5.09429	−	8.82356i	0.559171	−	0.968512i	−0.438395	−	0.898782i	$-0.644453\pi$
$83$	5.09429	−	8.82356i	0.559171	−	0.968512i	0.997566	−	0.0697297i	$-0.0222137\pi$
$84$	5.79480	+	7.10072i	0.632265	+	0.774753i
$85$	0.569384	+	0.986203i	0.0617584	+	0.106969i
$86$	−1.85733	+	0.394877i	−0.200282	+	0.0425807i
$87$	1.74707	+	4.71152i	0.187306	+	0.505128i
$88$	−0.790698	−	7.51310i	−0.0842887	−	0.800899i
$89$			2.67188i			0.283219i	0.989923	+	0.141609i	$0.0452277\pi$
$89$			2.67188i			0.283219i	−0.989923	+	0.141609i	$0.954772\pi$
$90$	−2.02196	−	0.259268i	−0.213134	−	0.0273293i
$91$	15.2087	−	7.04900i	1.59431	−	0.738936i
$92$	3.90197	+	8.76182i	0.406809	+	0.913483i
$93$	10.7369	+	1.82656i	1.11336	+	0.189406i
$94$	2.19322	+	10.3160i	0.226213	+	1.06401i
$95$	−1.74860	+	1.00956i	−0.179403	+	0.103578i
$96$	1.64102	−	9.65956i	0.167486	−	0.985874i
$97$	1.87526	+	1.08268i	0.190403	+	0.109929i	0.592171	−	0.805812i	$-0.298271\pi$
$97$	1.87526	+	1.08268i	0.190403	+	0.109929i	−0.401768	+	0.915741i	$0.631604\pi$
$98$	8.41929	−	5.20727i	0.850476	−	0.526013i
$99$	2.64962	−	7.56210i	0.266297	−	0.760019i
$100$	7.71713	+	5.60575i	0.771713	+	0.560575i
$101$	4.50341	+	2.60004i	0.448106	+	0.258714i	0.707030	−	0.707184i	$-0.250035\pi$
$101$	4.50341	+	2.60004i	0.448106	+	0.258714i	−0.258924	+	0.965898i	$0.583368\pi$
$102$	−5.80053	+	0.237825i	−0.574338	+	0.0235482i
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	0.804946	−	0.593348i	$-0.202194\pi$
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	−0.916328	+	0.400429i	$0.868861\pi$
$104$	−16.3720	−	7.28659i	−1.60541	−	0.714509i
$105$	−0.562002	+	2.12892i	−0.0548458	+	0.207762i
$106$	−9.45503	+	8.51413i	−0.918354	+	0.826966i
$107$		−	14.8308i		−	1.43375i	−0.697204	−	0.716873i	$-0.745573\pi$
$107$		−	14.8308i		−	1.43375i	0.697204	−	0.716873i	$-0.254427\pi$
$108$	5.95470	−	8.51713i	0.572991	−	0.819561i
$109$	−10.9535			−1.04916			−0.524578	−	0.851363i	$-0.675777\pi$
$109$	−10.9535			−1.04916			−0.524578	+	0.851363i	$0.675777\pi$
$110$	1.34870	−	1.21449i	0.128593	−	0.115797i
$111$	−5.18914	+	6.26040i	−0.492532	+	0.594211i
$112$	−10.1139	−	3.11582i	−0.955677	−	0.294417i
$113$	−4.72782	−	8.18882i	−0.444756	−	0.770339i	0.553280	−	0.832996i	$-0.313376\pi$
$113$	−4.72782	−	8.18882i	−0.444756	−	0.770339i	−0.998035	+	0.0626563i	$0.980043\pi$
$114$	−0.421679	−	10.2847i	−0.0394939	−	0.963253i
$115$	−1.15213	+	1.99554i	−0.107436	+	0.186085i
$116$	−4.69454	−	3.41013i	−0.435877	−	0.316622i
$117$	−12.3922	−	14.4122i	−1.14566	−	1.33241i
$118$	0.377825	+	0.122744i	0.0347816	+	0.0112995i
$119$	−0.561020	+	6.24541i	−0.0514286	+	0.572516i
$120$	2.10925	−	1.04489i	0.192548	−	0.0953850i
$121$	−1.93301	−	3.34807i	−0.175728	−	0.304370i
$122$	15.2097	−	3.23365i	1.37702	−	0.292761i
$123$	3.39766	−	19.9721i	0.306357	−	1.80082i
$124$	−11.4883	+	5.11616i	−1.03168	+	0.459445i
$125$			4.69391i			0.419836i
$126$	−8.28386	−	7.57481i	−0.737985	−	0.674818i
$127$		−	1.45847i		−	0.129419i	−0.997904	−	0.0647093i	$-0.979388\pi$
$127$		−	1.45847i		−	0.129419i	0.997904	−	0.0647093i	$-0.0206120\pi$
$128$	4.60500	+	10.3341i	0.407028	+	0.913415i
$129$	2.18052	−	0.808556i	0.191984	−	0.0711894i
$130$	−0.895294	−	4.21108i	−0.0785224	−	0.369336i
$131$	6.19426	+	10.7288i	0.541195	+	0.937377i	0.998836	+	0.0482400i	$0.0153612\pi$
$131$	6.19426	+	10.7288i	0.541195	+	0.937377i	−0.457641	+	0.889137i	$0.651305\pi$
$132$	2.29324	+	8.96375i	0.199601	+	0.780194i
$133$	−11.0735	−	0.994726i	−0.960196	−	0.0862537i
$134$	−0.953947	+	2.93640i	−0.0824085	+	0.253667i
$135$	2.49626	−	0.0451274i	0.214844	−	0.00388394i
$136$	5.42271	−	3.94096i	0.464994	−	0.337935i
$137$	−4.45878	+	7.72284i	−0.380939	+	0.659806i	−0.991197	−	0.132397i	$-0.957733\pi$
$137$	−4.45878	+	7.72284i	−0.380939	+	0.659806i	0.610257	+	0.792203i	$0.291066\pi$
$138$	−6.28533	−	9.92406i	−0.535043	−	0.844792i
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	0.918444	−	0.395551i	$-0.129446\pi$
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	−0.801779	+	0.597621i	$0.796113\pi$
$140$	−0.822385	−	2.40580i	−0.0695042	−	0.203327i
$141$	−4.49086	−	12.1110i	−0.378198	−	1.01993i
$142$	0.188092	+	0.208878i	0.0157843	+	0.0175286i
$143$	16.9225			1.41513
$144$	−0.272057	+	11.9969i	−0.0226714	+	0.999743i
$145$		−	1.39397i		−	0.115763i
$146$	−4.58919	−	5.09635i	−0.379804	−	0.421777i
$147$	−9.27703	+	7.80620i	−0.765156	+	0.643845i
$148$	0.980601	−	9.33799i	0.0806049	−	0.767578i
$149$	−0.0762596	−	0.132086i	−0.00624743	−	0.0108209i	0.862885	−	0.505401i	$-0.168655\pi$
$149$	−0.0762596	−	0.132086i	−0.00624743	−	0.0108209i	−0.869132	+	0.494580i	$0.835322\pi$
$150$	−10.3477	−	5.42162i	−0.844882	−	0.442674i
$151$	10.8876	+	6.28594i	0.886017	+	0.511542i	0.872638	−	0.488368i	$-0.162408\pi$
$151$	10.8876	+	6.28594i	0.886017	+	0.511542i	0.0133797	+	0.999910i	$0.495741\pi$
$152$	6.98759	+	9.61482i	0.566768	+	0.779865i
$153$	6.98674	−	1.31895i	0.564844	−	0.106631i
$154$	9.92204	−	1.19535i	0.799541	−	0.0963240i
$155$	−2.61650	−	1.51064i	−0.210162	−	0.121337i
$156$	21.1342	+	5.92047i	1.69209	+	0.474017i
$157$	−9.96123	+	5.75112i	−0.794993	+	0.458989i	−0.841717	−	0.539919i	$-0.818455\pi$
$157$	−9.96123	+	5.75112i	−0.794993	+	0.458989i	0.0467246	+	0.998908i	$0.485122\pi$
$158$	5.46461	−	1.16180i	0.434741	−	0.0924278i
$159$	9.94450	−	11.9975i	0.788650	−	0.951461i
$160$	−1.35848	+	2.35419i	−0.107397	+	0.186115i
$161$	−11.5119	+	5.33556i	−0.907262	+	0.420501i
$162$	−5.70232	+	11.3791i	−0.448016	+	0.894025i
$163$		−	19.9710i		−	1.56425i	−0.623121	−	0.782126i	$-0.714135\pi$
$163$		−	19.9710i		−	1.56425i	0.623121	−	0.782126i	$-0.285865\pi$
$164$	9.51678	+	21.3698i	0.743135	+	1.66870i
$165$	−1.41852	+	1.71136i	−0.110431	+	0.133229i
$166$	−2.99641	−	14.0938i	−0.232566	−	1.09389i
$167$	−10.9749	−	19.0090i	−0.849260	−	1.47096i	−0.881870	−	0.471493i	$-0.843715\pi$
$167$	−10.9749	−	19.0090i	−0.849260	−	1.47096i	0.0326095	−	0.999468i	$-0.489618\pi$
$168$	12.8096	+	1.97845i	0.988282	+	0.152641i
$169$	13.5710	−	23.5057i	1.04392	−	1.80813i
$170$	1.53166	+	0.497590i	0.117473	+	0.0381634i
$171$	2.33859	+	12.3879i	0.178836	+	0.947329i
$172$	−1.57823	+	2.17266i	−0.120339	+	0.165664i
$173$	13.2462	+	7.64770i	1.00709	+	0.581444i	0.910339	−	0.413864i	$-0.135821\pi$
$173$	13.2462	+	7.64770i	1.00709	+	0.581444i	0.0967521	+	0.995309i	$0.469155\pi$
$174$	6.29475	+	3.29812i	0.477204	+	0.250029i
$175$	−7.26134	+	10.3192i	−0.548906	+	0.780057i
$176$	−7.94092	−	7.14741i	−0.598569	−	0.538756i
$177$	−0.479655	−	0.0815993i	−0.0360531	−	0.00613338i
$178$	2.52851	+	2.80794i	0.189520	+	0.210464i
$179$			10.6967i			0.799512i	0.916622	+	0.399756i	$0.130905\pi$
$179$			10.6967i			0.799512i	−0.916622	+	0.399756i	$0.869095\pi$
$180$	−2.37028	+	1.64100i	−0.176671	+	0.122313i
$181$			7.23452i			0.537738i	0.963177	+	0.268869i	$0.0866498\pi$
$181$			7.23452i			0.537738i	−0.963177	+	0.268869i	$0.913350\pi$
$182$	9.31245	−	21.8006i	0.690284	−	1.61597i
$183$	−17.8563	+	6.62127i	−1.31997	+	0.489458i
$184$	12.3923	+	5.51539i	0.913576	+	0.406600i
$185$	1.95350	−	1.12786i	0.143624	−	0.0829216i
$186$	13.0122	−	8.24116i	0.954097	−	0.604271i
$187$	−3.16514	+	5.48218i	−0.231458	+	0.400897i
$188$	12.0673	+	8.76573i	0.880099	+	0.639307i
$189$	11.3843	+	7.70699i	0.828086	+	0.560601i
$190$	−0.882260	+	2.71574i	−0.0640059	+	0.197020i
$191$	17.2598	+	9.96493i	1.24887	+	0.721037i	0.970885	−	0.239547i	$-0.0769990\pi$
$191$	17.2598	+	9.96493i	1.24887	+	0.721037i	0.277988	+	0.960584i	$0.410332\pi$
$192$	−7.41665	−	11.7044i	−0.535251	−	0.844693i
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	0.999884	+	0.0152396i	$0.00485112\pi$
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	−0.486744	+	0.873545i	$0.661816\pi$
$194$	2.99533	−	0.636820i	0.215052	−	0.0457210i
$195$	1.83322	+	4.94383i	0.131279	+	0.354035i
$196$	3.92016	−	13.4400i	0.280011	−	0.959997i
$197$	11.9516			0.851517			0.425759	−	0.904837i	$-0.360007\pi$
$197$	11.9516			0.851517			0.425759	+	0.904837i	$0.360007\pi$
$198$	−4.37178	−	10.4546i	−0.310689	−	0.742978i
$199$	−21.9514			−1.55610			−0.778048	−	0.628205i	$-0.783790\pi$
$199$	−21.9514			−1.55610			−0.778048	+	0.628205i	$0.783790\pi$
$200$	13.4151	−	1.41184i	0.948588	−	0.0998319i
$201$	0.634177	−	3.72781i	0.0447314	−	0.262939i
$202$	7.19326	−	1.52932i	0.506116	−	0.107602i
$203$	4.41726	−	6.27743i	0.310031	−	0.440589i
$204$	−5.87085	+	5.73922i	−0.411041	+	0.401826i
$205$	−2.81000	+	4.86706i	−0.196259	+	0.339930i
$206$	−3.04082	−	0.987869i	−0.211864	−	0.0688281i
$207$	9.37998	+	10.9089i	0.651954	+	0.758222i
$208$	−24.1013	+	7.83585i	−1.67112	+	0.543318i
$209$	−9.72027	−	5.61200i	−0.672365	−	0.388190i
$210$	1.42407	+	2.76918i	0.0982700	+	0.191091i
$211$	−8.92341	+	5.15194i	−0.614313	+	0.354674i	−0.774652	−	0.632388i	$-0.782075\pi$
$211$	−8.92341	+	5.15194i	−0.614313	+	0.354674i	0.160338	+	0.987062i	$0.448741\pi$
$212$	−1.87923	+	17.8954i	−0.129066	+	1.22906i
$213$	−0.265044	−	0.219691i	−0.0181605	−	0.0150530i
$214$	−14.0350	−	15.5860i	−0.959411	−	1.06544i
$215$	−0.645139			−0.0439981
$216$	−1.80219	−	14.5860i	−0.122623	−	0.992453i
$217$	−6.99583	−	15.0940i	−0.474908	−	1.02465i
$218$	−11.5113	+	10.3658i	−0.779642	+	0.702058i
$219$	6.46674	+	5.36017i	0.436982	+	0.362207i
$220$	0.268060	−	2.55266i	0.0180726	−	0.172100i
$221$	7.50804	+	13.0043i	0.505046	+	0.874765i
$222$	0.471092	+	11.4899i	0.0316176	+	0.771151i
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	−0.999839	−	0.0179449i	$-0.994288\pi$
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	0.515460	+	0.856914i	$0.327621\pi$
$224$	−13.5776	+	6.29675i	−0.907191	+	0.420719i
$225$	13.5026	+	4.73105i	0.900170	+	0.315404i
$226$	−12.7180	−	4.13168i	−0.845988	−	0.274835i
$227$	9.67633	−	16.7599i	0.642240	−	1.11239i	−0.342691	−	0.939448i	$-0.611338\pi$
$227$	9.67633	−	16.7599i	0.642240	−	1.11239i	0.984932	−	0.172945i	$-0.0553282\pi$
$228$	−10.1760	−	10.4094i	−0.673923	−	0.689379i
$229$	−17.0595	+	9.84933i	−1.12733	+	0.650862i	−0.943261	−	0.332052i	$-0.892259\pi$
$229$	−17.0595	+	9.84933i	−1.12733	+	0.650862i	−0.184065	+	0.982914i	$0.558926\pi$
$230$	0.677669	+	3.18747i	0.0446842	+	0.210175i
$231$	−11.8110	+	3.21166i	−0.777104	+	0.211312i
$232$	−8.16074	+	0.858857i	−0.535779	+	0.0563868i
$233$	7.34808			0.481389			0.240694	−	0.970601i	$-0.422625\pi$
$233$	7.34808			0.481389			0.240694	+	0.970601i	$0.422625\pi$
$234$	−26.6621	−	3.41878i	−1.74296	−	0.223492i
$235$			3.58321i			0.233743i
$236$	0.513223	−	0.228558i	0.0334080	−	0.0148778i
$237$	−6.41548	+	2.37892i	−0.416730	+	0.154527i
$238$	5.32070	+	7.09435i	0.344890	+	0.459859i
$239$	−8.34611	+	4.81863i	−0.539865	+	0.311691i	−0.745024	−	0.667037i	$-0.767562\pi$
$239$	−8.34611	+	4.81863i	−0.539865	+	0.311691i	0.205159	+	0.978729i	$0.434229\pi$
$240$	1.22784	−	3.09417i	0.0792567	−	0.199728i
$241$	3.56210	+	2.05658i	0.229455	+	0.132476i	0.610321	−	0.792154i	$-0.291041\pi$
$241$	3.56210	+	2.05658i	0.229455	+	0.132476i	−0.380865	+	0.924630i	$0.624374\pi$
$242$	−5.19986	−	1.68928i	−0.334260	−	0.108591i
$243$	4.88791	−	14.8023i	0.313559	−	0.949569i
$244$	12.9241	−	17.7919i	0.827381	−	1.13901i
$245$	3.16586	−	1.13565i	0.202259	−	0.0725542i
$246$	−15.3297	−	24.2044i	−0.977387	−	1.54322i
$247$	−23.0575	+	13.3123i	−1.46711	+	0.847038i
$248$	−7.23163	+	16.2485i	−0.459209	+	1.03178i
$249$	6.13548	+	16.5462i	0.388820	+	1.04857i
$250$	4.44204	+	4.93293i	0.280939	+	0.311986i
$251$	−3.31816			−0.209441			−0.104720	−	0.994502i	$-0.533395\pi$
$251$	−3.31816			−0.209441			−0.104720	+	0.994502i	$0.533395\pi$
$252$	−15.8740	−	0.121179i	−0.999971	−	0.00763359i
$253$	−12.8091			−0.805300
$254$	−1.38021	−	1.53274i	−0.0866023	−	0.0961728i
$255$	−1.94447	−	0.330795i	−0.121767	−	0.0207152i
$256$	14.6191	+	6.50245i	0.913694	+	0.406403i
$257$	14.9497	−	8.63121i	0.932537	−	0.538400i	0.0449237	−	0.998990i	$-0.485696\pi$
$257$	14.9497	−	8.63121i	0.932537	−	0.538400i	0.887613	+	0.460590i	$0.152362\pi$
$258$	1.52639	−	2.91325i	0.0950287	−	0.181371i
$259$	12.3711	+	1.11129i	0.768704	+	0.0690521i
$260$	−4.92600	−	3.57826i	−0.305498	−	0.221915i
$261$	−8.21396	−	2.87802i	−0.508431	−	0.178145i
$262$	16.6628	+	5.41322i	1.02943	+	0.334430i
$263$	−11.4455	−	6.60806i	−0.705760	−	0.407471i	0.103729	−	0.994606i	$-0.466922\pi$
$263$	−11.4455	−	6.60806i	−0.705760	−	0.407471i	−0.809489	+	0.587135i	$0.800256\pi$
$264$	10.8928	+	7.25002i	0.670405	+	0.446208i
$265$	−3.74371	+	2.16143i	−0.229974	+	0.132776i
$266$	−12.5788	+	9.43395i	−0.771253	+	0.578433i
$267$	−3.56298	−	2.95330i	−0.218051	−	0.180739i
$268$	1.77632	+	3.98869i	0.108506	+	0.243648i
$269$		−	27.5600i		−	1.68036i	−0.542304	−	0.840182i	$-0.682448\pi$
$269$		−	27.5600i		−	1.68036i	0.542304	−	0.840182i	$-0.317552\pi$
$270$	2.58067	−	2.40974i	0.157054	−	0.146652i
$271$	21.2467			1.29065			0.645323	−	0.763910i	$-0.276723\pi$
$271$	21.2467			1.29065			0.645323	+	0.763910i	$0.276723\pi$
$272$	1.96935	−	9.27338i	0.119409	−	0.562281i
$273$	−7.41069	+	28.0725i	−0.448516	+	1.69902i
$274$	2.62261	+	12.3356i	0.158438	+	0.745223i
$275$	−11.0315	+	6.36906i	−0.665227	+	0.384069i
$276$	−15.9969	−	4.48134i	−0.962903	−	0.269745i
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	−0.561140	−	0.827721i	$-0.689637\pi$
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	0.997397	+	0.0721016i	$0.0229706\pi$
$278$	3.70004	+	1.20203i	0.221914	+	0.0720930i
$279$	−14.3035	+	12.2988i	−0.856326	+	0.736309i
$280$	−3.14097	−	1.75005i	−0.187709	−	0.104586i
$281$	6.35647	−	11.0097i	0.379195	−	0.656785i	−0.611750	−	0.791051i	$-0.709534\pi$
$281$	6.35647	−	11.0097i	0.379195	−	0.656785i	0.990945	+	0.134266i	$0.0428676\pi$
$282$	−16.1807	−	8.47781i	−0.963545	−	0.504846i
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	−0.989516	−	0.144425i	$-0.953867\pi$
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	0.369682	−	0.929158i	$-0.379467\pi$
$284$	0.395340	+	0.0415154i	0.0234591	+	0.00246348i
$285$	0.586520	−	3.44767i	0.0347425	−	0.204222i
$286$	17.7843	−	16.0145i	1.05161	−	0.946958i
$287$	−28.0770	+	13.0132i	−1.65733	+	0.768147i
$288$	11.0673	+	12.8653i	0.652145	+	0.758094i
$289$	11.3829			0.669581
$290$	−1.31918	−	1.46496i	−0.0774647	−	0.0860253i
$291$	−3.51653	+	1.30396i	−0.206143	+	0.0764396i
$292$	−9.64577	−	1.01292i	−0.564476	−	0.0592768i
$293$	5.80807	−	3.35329i	0.339311	−	0.195901i	−0.320656	−	0.947196i	$-0.603903\pi$
$293$	5.80807	−	3.35329i	0.339311	−	0.195901i	0.659967	+	0.751294i	$0.270570\pi$
$294$	−2.36210	+	16.9829i	−0.137761	+	0.990466i
$295$	0.116889	+	0.0674857i	0.00680552	+	0.00392917i
$296$	−7.80640	−	10.7415i	−0.453738	−	0.624336i
$297$	7.15545	+	11.8919i	0.415201	+	0.690037i
$298$	−0.205141	−	0.0666440i	−0.0118835	−	0.00386058i
$299$	−15.1922	+	26.3137i	−0.878590	+	1.52176i
$300$	−16.0053	+	4.09471i	−0.924066	+	0.236408i
$301$	−2.90523	−	2.04434i	−0.167455	−	0.117834i
$302$	17.3906	−	3.69732i	1.00072	−	0.212757i
$303$	−8.44492	+	3.13145i	−0.485148	+	0.179897i
$304$	16.4423	+	3.49179i	0.943031	+	0.200268i
$305$	5.28305			0.302507
$306$	6.09434	−	7.99795i	0.348390	−	0.457213i
$307$	12.0792			0.689397			0.344699	−	0.938713i	$-0.387981\pi$
$307$	12.0792			0.689397			0.344699	+	0.938713i	$0.387981\pi$
$308$	9.29608	−	10.6459i	0.529693	−	0.606604i
$309$	3.86037	+	0.656729i	0.219609	+	0.0373600i
$310$	−4.17932	+	0.888541i	−0.237369	+	0.0504657i
$311$	−1.01185	−	1.75258i	−0.0573769	−	0.0993797i	0.835910	−	0.548866i	$-0.184940\pi$
$311$	−1.01185	−	1.75258i	−0.0573769	−	0.0993797i	−0.893287	+	0.449486i	$0.851607\pi$
$312$	27.8131	−	13.7782i	1.57461	−	0.780036i
$313$	−16.8337	−	9.71892i	−0.951495	−	0.549346i	−0.0579500	−	0.998319i	$-0.518456\pi$
$313$	−16.8337	−	9.71892i	−0.951495	−	0.549346i	−0.893545	+	0.448974i	$0.851790\pi$
$314$	−5.02596	+	15.4707i	−0.283631	+	0.873062i
$315$	−2.21775	−	3.10259i	−0.124956	−	0.174811i
$316$	4.64342	−	6.39235i	0.261213	−	0.359598i
$317$	−5.21828	+	9.03832i	−0.293088	+	0.507643i	−0.974538	−	0.224222i	$-0.928016\pi$
$317$	−5.21828	+	9.03832i	−0.293088	+	0.507643i	0.681451	+	0.731864i	$0.261349\pi$
$318$	−0.902802	−	22.0193i	−0.0506266	−	1.23478i
$319$	6.71078	−	3.87447i	0.375731	−	0.216929i
$320$	0.800215	+	3.75965i	0.0447334	+	0.210171i
$321$	19.7770	+	16.3928i	1.10385	+	0.914959i
$322$	−7.04881	+	16.5014i	−0.392815	+	0.919587i
$323$		−	9.95953i		−	0.554163i
$324$	4.77581	+	17.3549i	0.265323	+	0.964160i
$325$			30.2162i			1.67609i
$326$	−18.8994	−	20.9880i	−1.04674	−	1.16242i
$327$	12.1072	−	14.6066i	0.669529	−	0.807748i
$328$	30.2245	+	13.4519i	1.66887	+	0.742755i
$329$	−11.3546	+	16.1361i	−0.625999	+	0.889614i
$330$	0.128779	+	3.14091i	0.00708904	+	0.172901i
$331$	31.2751	+	18.0567i	1.71903	+	0.992484i	0.920704	+	0.390261i	$0.127615\pi$
$331$	31.2751	+	18.0567i	1.71903	+	0.992484i	0.798328	+	0.602223i	$0.205718\pi$
$332$	−16.4866	−	11.9759i	−0.904817	−	0.657262i
$333$	−2.61262	−	13.8396i	−0.143171	−	0.758404i
$334$	−29.5227	−	9.59103i	−1.61541	−	0.524798i
$335$	−0.524489	+	0.908442i	−0.0286559	+	0.0496335i
$336$	15.3342	−	10.0431i	0.836548	−	0.547894i
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	0.949123	−	0.314905i	$-0.101973\pi$
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	−0.747278	+	0.664512i	$0.768639\pi$
$338$	−7.98233	−	37.5455i	−0.434182	−	2.04221i
$339$	16.1457	+	2.74671i	0.876912	+	0.149181i
$340$	2.08055	−	0.926548i	0.112834	−	0.0502491i
$341$		−	16.7949i		−	0.909495i
$342$	14.1809	+	10.8057i	0.766815	+	0.584303i
$343$	17.8554	+	4.91791i	0.964099	+	0.265542i
$344$	0.397484	+	3.77684i	0.0214309	+	0.203633i
$345$	−1.38760	−	3.74210i	−0.0747061	−	0.201468i
$346$	21.1581	−	4.49830i	1.13747	−	0.241830i
$347$	24.8678	−	14.3574i	1.33497	−	0.770747i	0.348915	−	0.937154i	$-0.386550\pi$
$347$	24.8678	−	14.3574i	1.33497	−	0.770747i	0.986057	+	0.166408i	$0.0532168\pi$
$348$	9.73644	−	2.49092i	0.521928	−	0.133527i
$349$	0.744758	+	0.429986i	0.0398660	+	0.0230166i	0.519801	−	0.854288i	$-0.326006\pi$
$349$	0.744758	+	0.429986i	0.0398660	+	0.0230166i	−0.479935	+	0.877304i	$0.659340\pi$
$350$	2.13436	+	17.7164i	0.114087	+	0.946980i
$351$	32.9163	−	0.595060i	1.75694	−	0.0317620i
$352$	−15.1092	+	0.00344740i	−0.805322	+	0.000183747i
$353$	−27.7159	−	16.0018i	−1.47517	−	0.851690i	−0.475562	−	0.879682i	$-0.657755\pi$
$353$	−27.7159	−	16.0018i	−1.47517	−	0.851690i	−0.999608	+	0.0279920i	$0.991089\pi$
$354$	−0.581301	+	0.368163i	−0.0308958	+	0.0195676i
$355$	0.0477497	+	0.0827049i	0.00253429	+	0.00438952i
$356$	5.31454	+	0.558090i	0.281670	+	0.0295787i
$357$	−7.70822	−	7.65134i	−0.407962	−	0.404952i
$358$	10.1228	+	11.2414i	0.535005	+	0.594129i
$359$			5.52163i			0.291421i	0.989327	+	0.145710i	$0.0465468\pi$
$359$			5.52163i			0.291421i	−0.989327	+	0.145710i	$0.953453\pi$
$360$	−0.938040	+	3.96766i	−0.0494390	+	0.209114i
$361$	−1.34111			−0.0705845
$362$	6.84633	+	7.60292i	0.359835	+	0.399601i
$363$	6.60130	+	1.12302i	0.346478	+	0.0589432i
$364$	−10.8442	−	31.7235i	−0.568389	−	1.66276i
$365$	−1.16503	−	2.01789i	−0.0609805	−	0.105621i
$366$	−12.4996	+	23.8566i	−0.653364	+	1.24700i
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	0.393886	+	0.919159i	$0.371131\pi$
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	−0.992958	+	0.118465i	$0.962203\pi$
$368$	18.2428	−	5.93114i	0.950974	−	0.309182i
$369$	22.8775	+	26.6065i	1.19095	+	1.38508i
$370$	0.985644	−	3.03397i	0.0512412	−	0.157729i
$371$	−23.7081	−	2.12968i	−1.23086	−	0.110567i
$372$	5.87581	−	20.9748i	0.304647	−	1.08749i
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	−0.953032	−	0.302871i	$-0.902055\pi$
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	0.214222	−	0.976785i	$-0.431278\pi$
$374$	1.86170	+	8.75665i	0.0962663	+	0.452796i
$375$	−6.25938	−	5.18830i	−0.323233	−	0.267923i
$376$	20.9772	−	2.20769i	1.08182	−	0.113853i
$377$		−	18.3813i		−	0.946685i
$378$	19.2575	−	2.67399i	0.990497	−	0.137535i
$379$		−	13.3942i		−	0.688014i	−0.938967	−	0.344007i	$-0.888216\pi$
$379$		−	13.3942i		−	0.688014i	0.938967	−	0.344007i	$-0.111784\pi$
$380$	1.64283	+	3.68895i	0.0842754	+	0.189239i
$381$	1.94489	+	1.61209i	0.0996398	+	0.0825898i
$382$	27.5689	−	5.86127i	1.41055	−	0.299889i
$383$	11.1930	+	19.3869i	0.571937	+	0.990625i	0.996367	+	0.0851637i	$0.0271413\pi$
$383$	11.1930	+	19.3869i	0.571937	+	0.990625i	−0.424430	+	0.905461i	$0.639525\pi$
$384$	−18.8707	−	5.28174i	−0.962991	−	0.269533i
$385$	3.38180	+	0.303785i	0.172353	+	0.0154823i
$386$	19.1766	+	6.22990i	0.976064	+	0.317093i
$387$	−1.33197	+	3.80147i	−0.0677076	+	0.193239i
$388$	2.54521	−	3.50386i	0.129214	−	0.177881i
$389$	13.5306	−	23.4357i	0.686029	−	1.18824i	−0.287083	−	0.957906i	$-0.592686\pi$
$389$	13.5306	−	23.4357i	0.686029	−	1.18824i	0.973112	−	0.230332i	$-0.0739811\pi$
$390$	6.60512	+	3.46073i	0.334463	+	0.175241i
$391$	−5.68302	−	9.84327i	−0.287402	−	0.497796i
$392$	−8.59900	−	17.8342i	−0.434315	−	0.900761i
$393$	−21.1536	−	3.59867i	−1.06706	−	0.181529i
$394$	12.5602	−	11.3103i	0.632775	−	0.569805i
$395$	1.89812			0.0955046
$396$	−14.4880	−	6.84980i	−0.728052	−	0.344216i
$397$			11.6658i			0.585487i	0.956191	+	0.292744i	$0.0945683\pi$
$397$			11.6658i			0.585487i	−0.956191	+	0.292744i	$0.905432\pi$
$398$	−23.0692	+	20.7735i	−1.15636	+	1.04128i
$399$	13.5663	−	13.6672i	0.679166	−	0.684214i
$400$	12.7621	−	14.1790i	0.638106	−	0.708948i
$401$	−8.33464	−	14.4360i	−0.416212	−	0.720901i	0.579343	−	0.815084i	$-0.303309\pi$
$401$	−8.33464	−	14.4360i	−0.416212	−	0.720901i	−0.995555	+	0.0941835i	$0.969976\pi$
$402$	−2.86131	−	4.51778i	−0.142709	−	0.225327i
$403$	−34.5018	−	19.9196i	−1.71866	−	0.992268i
$404$	6.11230	−	8.41447i	0.304098	−	0.418636i
$405$	−2.69900	+	3.37867i	−0.134114	+	0.167888i
$406$	−1.29839	−	10.7773i	−0.0644380	−	0.534870i
$407$	10.8593	+	6.26962i	0.538275	+	0.310773i
$408$	−0.738540	+	11.5873i	−0.0365632	+	0.573657i
$409$	−0.589282	+	0.340222i	−0.0291381	+	0.0168229i	−0.514498	−	0.857491i	$-0.672022\pi$
$409$	−0.589282	+	0.340222i	−0.0291381	+	0.0168229i	0.485360	+	0.874314i	$0.338688\pi$
$410$	1.65281	+	7.77412i	0.0816265	+	0.383937i
$411$	−5.37009	−	14.4821i	−0.264887	−	0.714349i
$412$	−4.13053	+	1.83948i	−0.203497	+	0.0906247i
$413$	0.312530	+	0.674306i	0.0153786	+	0.0331804i
$414$	20.1812	+	2.58775i	0.991852	+	0.127181i
$415$		−	4.89544i		−	0.240308i
$416$	−17.9132	+	31.0429i	−0.878267	+	1.52200i
$417$	−4.69726	−	0.799101i	−0.230026	−	0.0391322i
$418$	−15.5261	+	3.30092i	−0.759407	+	0.161453i
$419$	5.19926	+	9.00538i	0.254000	+	0.439941i	0.964624	−	0.263631i	$-0.0849202\pi$
$419$	5.19926	+	9.00538i	0.254000	+	0.439941i	−0.710623	+	0.703573i	$0.751587\pi$
$420$	4.11717	+	1.56254i	0.200897	+	0.0762440i
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	−0.937384	−	0.348298i	$-0.886760\pi$
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	0.770327	+	0.637649i	$0.220093\pi$
$422$	−4.50232	+	13.8589i	−0.219170	+	0.674640i
$423$	21.1140	+	7.39797i	1.02660	+	0.359701i
$424$	14.9602	+	20.5850i	0.726532	+	0.999698i
$425$	−9.78875	−	5.65154i	−0.474824	−	0.274140i
$426$	−0.486444	+	0.0199444i	−0.0235683	+	0.000966312i
$427$	23.7909	+	16.7411i	1.15132	+	0.810157i
$428$	−29.4993	−	3.09778i	−1.42590	−	0.149737i
$429$	−18.7049	+	22.5664i	−0.903083	+	1.08952i
$430$	−0.677991	+	0.610522i	−0.0326956	+	0.0294420i
$431$		−	15.2572i		−	0.734914i	−0.930040	−	0.367457i	$-0.880228\pi$
$431$		−	15.2572i		−	0.734914i	0.930040	−	0.367457i	$-0.119772\pi$
$432$	−15.6973	−	13.6233i	−0.755238	−	0.655451i
$433$		−	34.6459i		−	1.66498i	−0.554042	−	0.832489i	$-0.686915\pi$
$433$		−	34.6459i		−	1.66498i	0.554042	−	0.832489i	$-0.313085\pi$
$434$	−21.6362	−	9.24221i	−1.03857	−	0.443640i
$435$	1.85888	+	1.54080i	0.0891266	+	0.0738755i
$436$	−2.28792	+	21.7872i	−0.109571	+	1.04342i
$437$	17.4528	−	10.0764i	0.834879	−	0.482018i
$438$	11.8686	−	0.486619i	0.567104	−	0.0232515i
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	−0.682149	−	0.731213i	$-0.738955\pi$
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	0.974324	+	0.225152i	$0.0722878\pi$
$440$	−2.13398	−	2.93632i	−0.101733	−	0.139984i
$441$	−0.155525	−	20.9994i	−0.00740597	−	0.999973i
$442$	20.1969	+	6.56135i	0.960668	+	0.312091i
$443$	−24.2468	−	13.9989i	−1.15200	−	0.665108i	−0.202627	−	0.979256i	$-0.564948\pi$
$443$	−24.2468	−	13.9989i	−1.15200	−	0.665108i	−0.949374	+	0.314148i	$0.898281\pi$
$444$	11.3684	+	11.6292i	0.539522	+	0.551896i
$445$	0.641897	+	1.11180i	0.0304288	+	0.0527043i
$446$	4.25456	+	20.0116i	0.201459	+	0.947579i
$447$	0.260429	+	0.0443045i	0.0123179	+	0.00209553i
$448$	−8.31011	+	19.4664i	−0.392616	+	0.919703i
$449$	23.8270			1.12446			0.562232	−	0.826979i	$-0.309943\pi$
$449$	23.8270			1.12446			0.562232	+	0.826979i	$0.309943\pi$
$450$	18.6673	−	7.80606i	0.879986	−	0.367981i
$451$	−31.2409			−1.47108
$452$	−17.2756	+	7.69348i	−0.812576	+	0.361871i
$453$	−20.4167	+	7.57069i	−0.959260	+	0.355702i
$454$	−5.69151	−	26.7705i	−0.267116	−	1.25640i
$455$	4.63506	−	6.58694i	0.217295	−	0.308801i
$456$	−20.5450	−	1.30948i	−0.962110	−	0.0613220i
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	0.440607	+	0.897700i	$0.354763\pi$
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	−0.997735	+	0.0672735i	$0.978570\pi$
$458$	−8.60742	+	26.4950i	−0.402198	+	1.23803i
$459$	−5.96378	+	10.7748i	−0.278366	+	0.502923i
$460$	3.72861	+	2.70847i	0.173847	+	0.126283i
$461$	−0.317557	−	0.183341i	−0.0147901	−	0.00853906i	0.492587	−	0.870263i	$-0.336051\pi$
$461$	−0.317557	−	0.183341i	−0.0147901	−	0.00853906i	−0.507377	+	0.861724i	$0.669385\pi$
$462$	−9.37307	+	14.5524i	−0.436075	+	0.677039i
$463$	14.3509	−	8.28549i	0.666943	−	0.385060i	−0.127974	−	0.991777i	$-0.540848\pi$
$463$	14.3509	−	8.28549i	0.666943	−	0.385060i	0.794917	+	0.606718i	$0.207514\pi$
$464$	−7.76353	+	8.62544i	−0.360413	+	0.400426i
$465$	4.90654	−	1.81939i	0.227535	−	0.0843721i
$466$	7.72226	−	6.95379i	0.357727	−	0.322128i
$467$	−26.1463			−1.20991			−0.604953	−	0.796261i	$-0.706808\pi$
$467$	−26.1463			−1.20991			−0.604953	+	0.796261i	$0.706808\pi$
$468$	−31.2551	+	21.6386i	−1.44477	+	1.00024i
$469$	−5.24061	+	2.42893i	−0.241989	+	0.112158i
$470$	3.39094	+	3.76568i	0.156413	+	0.173698i
$471$	3.34122	−	19.6403i	0.153955	−	0.904976i
$472$	0.323064	−	0.725880i	0.0148702	−	0.0334113i
$473$	−1.79313	−	3.10579i	−0.0824480	−	0.142804i
$474$	−4.49090	+	8.57129i	−0.206274	+	0.393692i
$475$	10.0205	−	17.3561i	0.459774	−	0.796352i
$476$	12.3053	+	2.42042i	0.564014	+	0.110940i
$477$	5.00685	+	26.5222i	0.229248	+	1.21437i
$478$	−4.21104	+	12.9623i	−0.192609	+	0.592880i
$479$	19.0772	−	33.0427i	0.871661	−	1.50976i	0.0113840	−	0.999935i	$-0.496376\pi$
$479$	19.0772	−	33.0427i	0.871661	−	1.50976i	0.860277	−	0.509826i	$-0.170290\pi$
$480$	−1.63778	−	4.41369i	−0.0747541	−	0.201456i
$481$	25.7594	−	14.8722i	1.17453	−	0.678113i
$482$	5.68972	−	1.20966i	0.259160	−	0.0550985i
$483$	5.60933	−	21.2487i	0.255233	−	0.966851i
$484$	−7.06328	+	3.14555i	−0.321058	+	0.142979i
$485$	1.04042			0.0472430
$486$	−8.87123	−	20.1817i	−0.402407	−	0.915461i
$487$		−	8.93817i		−	0.405027i	−0.979279	−	0.202514i	$-0.935089\pi$
$487$		−	8.93817i		−	0.405027i	0.979279	−	0.202514i	$-0.0649110\pi$
$488$	−3.25500	−	30.9285i	−0.147347	−	1.40007i
$489$	26.6316	+	22.0745i	1.20432	+	0.998243i
$490$	2.25235	−	4.18947i	0.101751	−	0.189261i
$491$	8.03087	−	4.63662i	0.362428	−	0.209248i	−0.307717	−	0.951478i	$-0.599565\pi$
$491$	8.03087	−	4.63662i	0.362428	−	0.209248i	0.670145	+	0.742230i	$0.266232\pi$
$492$	−39.0160	−	10.9298i	−1.75898	−	0.492755i
$493$	5.95475	+	3.43798i	0.268189	+	0.154839i
$494$	−11.6337	+	35.8104i	−0.523425	+	1.61119i
$495$	−0.714194	−	3.78322i	−0.0321007	−	0.170043i
$496$	7.77675	+	23.9195i	0.349186	+	1.07402i
$497$	−0.0470482	+	0.523752i	−0.00211040	+	0.0234935i
$498$	22.1063	+	11.5825i	0.990606	+	0.519025i
$499$	−15.0365	+	8.68131i	−0.673125	+	0.388629i	−0.797260	−	0.603636i	$-0.793718\pi$
$499$	−15.0365	+	8.68131i	−0.673125	+	0.388629i	0.124135	+	0.992265i	$0.460385\pi$
$500$	9.33648	+	0.980442i	0.417540	+	0.0438467i
$501$	37.4795	+	6.37605i	1.67446	+	0.284861i
$502$	−3.48713	+	3.14012i	−0.155638	+	0.140150i
$503$	6.23388			0.277955			0.138978	−	0.990296i	$-0.455618\pi$
$503$	6.23388			0.277955			0.138978	+	0.990296i	$0.455618\pi$
$504$	−16.7971	+	14.8949i	−0.748201	+	0.663472i
$505$	2.49856			0.111184
$506$	−13.4613	+	12.1218i	−0.598430	+	0.538878i
$507$	16.3447	+	44.0786i	0.725895	+	1.95760i
$508$	−2.90099	−	0.304639i	−0.128711	−	0.0135162i
$509$	3.52873	−	2.03731i	0.156408	−	0.0903023i	−0.419753	−	0.907638i	$-0.637883\pi$
$509$	3.52873	−	2.03731i	0.156408	−	0.0903023i	0.576161	+	0.817336i	$0.304550\pi$
$510$	−2.35653	+	1.49249i	−0.104349	+	0.0660887i
$511$	1.14792	−	12.7789i	0.0507808	−	0.565304i
$512$	21.5171	−	7.00109i	0.950930	−	0.309408i
$513$	−19.1044	−	10.5742i	−0.843478	−	0.466861i
$514$	7.54290	−	23.2183i	0.332703	−	1.02411i
$515$	−0.940746	−	0.543140i	−0.0414542	−	0.0239336i
$516$	−1.15281	−	4.50608i	−0.0507497	−	0.198369i
$517$	−17.2501	+	9.95933i	−0.758657	+	0.438011i
$518$	14.0527	−	10.5394i	0.617442	−	0.463076i
$519$	−24.8397	+	9.21077i	−1.09034	+	0.404308i
$520$	−8.56311	+	0.901204i	−0.375517	+	0.0395204i
$521$			27.2193i			1.19250i	0.802798	+	0.596251i	$0.203344\pi$
$521$			27.2193i			1.19250i	−0.802798	+	0.596251i	$0.796656\pi$
$522$	−11.3558	+	4.74863i	−0.497031	+	0.207842i
$523$	−3.44794			−0.150768			−0.0753838	−	0.997155i	$-0.524018\pi$
$523$	−3.44794			−0.150768			−0.0753838	+	0.997155i	$0.524018\pi$
$524$	22.6340	−	10.0798i	0.988772	−	0.440338i
$525$	−5.73460	−	21.0891i	−0.250279	−	0.920406i
$526$	−18.2818	+	3.88679i	−0.797125	+	0.169472i
$527$	12.9062	−	7.45141i	0.562204	−	0.324589i
$528$	18.3085	−	2.68909i	0.796774	−	0.117028i
$529$	−0.000637027		0.00110336i	−2.76968e−5		4.79723e-5i
$530$	−1.88889	+	5.81432i	−0.0820483	+	0.252558i
$531$	0.638988	−	0.549432i	0.0277297	−	0.0238433i
$532$	−4.29156	+	21.8181i	−0.186063	+	0.945937i
$533$	−37.0533	+	64.1783i	−1.60496	+	2.77987i
$534$	−6.53925	+	0.268113i	−0.282981	+	0.0116024i
$535$	−3.56297	−	6.17125i	−0.154041	−	0.266806i
$536$	5.64143	+	2.51080i	0.243673	+	0.108450i
$537$	−14.2642	−	11.8234i	−0.615547	−	0.510217i
$538$	−26.0812	−	28.9634i	−1.12444	−	1.24870i
$539$	14.2665	+	12.0844i	0.614502	+	0.520511i
$540$	0.431646	−	4.97464i	0.0185751	−	0.214074i
$541$	5.99277			0.257649			0.128825	−	0.991667i	$-0.458880\pi$
$541$	5.99277			0.257649			0.128825	+	0.991667i	$0.458880\pi$
$542$	22.3286	−	20.1066i	0.959097	−	0.863654i
$543$	−9.64732	−	7.99651i	−0.414006	−	0.343163i
$544$	−6.70615	−	11.6093i	−0.287524	−	0.497744i
$545$	−4.55787	+	2.63149i	−0.195238	+	0.112721i
$546$	18.7781	+	36.5151i	0.803628	+	1.56270i
$547$	5.72221	+	3.30372i	0.244664	+	0.141257i	0.617319	−	0.786713i	$-0.288219\pi$
$547$	5.72221	+	3.30372i	0.244664	+	0.141257i	−0.372654	+	0.927970i	$0.621552\pi$
$548$	14.4299	+	10.4819i	0.616414	+	0.447765i
$549$	10.9075	−	31.1302i	0.465520	−	1.32861i
$550$	−5.56598	+	17.1330i	−0.237334	+	0.730553i
$551$	−6.09576	+	10.5582i	−0.259688	+	0.449793i
$552$	−21.0524	+	10.4290i	−0.896051	+	0.443889i
$553$	8.54771	+	6.01480i	0.363485	+	0.255775i
$554$	−4.27070	−	20.0876i	−0.181445	−	0.853439i
$555$	−0.655249	+	3.85167i	−0.0278138	+	0.163494i
$556$	5.02599	−	2.23826i	0.213149	−	0.0949235i
$557$	6.08351			0.257767			0.128883	−	0.991660i	$-0.458861\pi$
$557$	6.08351			0.257767			0.128883	+	0.991660i	$0.458861\pi$
$558$	−3.39299	+	26.4610i	−0.143637	+	1.12018i
$559$	−8.50697			−0.359806
$560$	−4.95707	+	1.13326i	−0.209474	+	0.0478891i
$561$	−3.81205	−	10.2804i	−0.160945	−	0.434037i
$562$	−3.73881	−	17.5858i	−0.157712	−	0.741810i
$563$	−13.1561	−	22.7871i	−0.554465	−	0.960361i	−0.997945	−	0.0640767i	$-0.979590\pi$
$563$	−13.1561	−	22.7871i	−0.554465	−	0.960361i	0.443480	−	0.896284i	$-0.353744\pi$
$564$	−25.0275	+	6.40291i	−1.05385	+	0.269611i
$565$	−3.93459	−	2.27164i	−0.165530	−	0.0955686i
$566$	−28.0496	−	9.11244i	−1.17901	−	0.383024i
$567$	−22.8607	+	6.66236i	−0.960060	+	0.279793i
$568$	0.454759	−	0.330497i	0.0190813	−	0.0138673i
$569$	−0.683478	+	1.18382i	−0.0286529	+	0.0496283i	−0.879996	−	0.474981i	$-0.842455\pi$
$569$	−0.683478	+	1.18382i	−0.0286529	+	0.0496283i	0.851343	+	0.524609i	$0.175788\pi$
$570$	−2.64629	−	4.17828i	−0.110841	−	0.175009i
$571$	14.6500	−	8.45818i	0.613083	−	0.353964i	−0.161088	−	0.986940i	$-0.551500\pi$
$571$	14.6500	−	8.45818i	0.613083	−	0.353964i	0.774171	+	0.632976i	$0.218167\pi$
$572$	3.53470	−	33.6600i	0.147793	−	1.40740i
$573$	−32.3660	+	12.0016i	−1.35211	+	0.501375i
$574$	−17.1918	+	40.2464i	−0.717572	+	1.67985i
$575$		−	22.8713i		−	0.953801i
$576$	23.8058	+	3.04700i	0.991908	+	0.126958i
$577$			0.277722i			0.0115617i	0.999983	+	0.00578087i	$0.00184012\pi$
$577$			0.277722i			0.0115617i	−0.999983	+	0.00578087i	$0.998160\pi$
$578$	11.9625	−	10.7721i	0.497575	−	0.448060i
$579$	−24.3450	−	4.14159i	−1.01174	−	0.172119i
$580$	−2.77270	−	0.291167i	−0.115130	−	0.0120901i
$581$	15.5128	−	22.0455i	0.643580	−	0.914599i
$582$	−2.46161	+	4.69821i	−0.102037	+	0.194747i
$583$	−20.8108	−	12.0151i	−0.861896	−	0.497616i
$584$	−11.0955	+	8.06369i	−0.459136	+	0.333678i
$585$	−8.61896	−	3.01993i	−0.356350	−	0.124859i
$586$	2.93047	−	9.02046i	0.121057	−	0.372632i
$587$	13.6979	−	23.7254i	0.565372	−	0.979253i	−0.431643	−	0.902044i	$-0.642066\pi$
$587$	13.6979	−	23.7254i	0.565372	−	0.979253i	0.997015	−	0.0772082i	$-0.0246006\pi$
$588$	13.5893	+	20.0831i	0.560413	+	0.828214i
$589$	13.2118	+	22.8836i	0.544385	+	0.942902i
$590$	0.186706	−	0.0396944i	0.00768654	−	0.00163419i
$591$	−13.2104	+	15.9376i	−0.543404	+	0.655586i
$592$	−18.3690	−	3.90095i	−0.754963	−	0.160328i
$593$			32.0154i			1.31471i	0.753579	+	0.657357i	$0.228326\pi$
$593$			32.0154i			1.31471i	−0.753579	+	0.657357i	$0.771674\pi$
$594$	18.7736	+	5.72595i	0.770291	+	0.234939i
$595$	1.26696	+	2.73356i	0.0519403	+	0.112065i
$596$	−0.278655	+	0.124096i	−0.0114142	+	0.00508316i
$597$	24.2635	−	29.2725i	0.993038	−	1.19804i
$598$	8.93591	+	42.0307i	0.365417	+	1.71876i
$599$	−15.8709	+	9.16306i	−0.648467	+	0.374392i	−0.787869	−	0.615843i	$-0.788815\pi$
$599$	−15.8709	+	9.16306i	−0.648467	+	0.374392i	0.139402	+	0.990236i	$0.455482\pi$
$600$	−12.9453	+	19.4497i	−0.528490	+	0.794030i
$601$	−19.1583	−	11.0611i	−0.781485	−	0.451190i	0.0554716	−	0.998460i	$-0.482334\pi$
$601$	−19.1583	−	11.0611i	−0.781485	−	0.451190i	−0.836956	+	0.547270i	$0.815667\pi$
$602$	−4.98781	+	0.600902i	−0.203288	+	0.0244910i
$603$	4.27010	+	4.96612i	0.173892	+	0.202236i
$604$	14.7773	−	20.3431i	0.601279	−	0.827748i
$605$	−1.60869	−	0.928780i	−0.0654027	−	0.0377603i
$606$	−5.91153	+	11.2827i	−0.240140	+	0.458328i
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	0.980832	−	0.194853i	$-0.0624230\pi$
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	−0.659164	+	0.751999i	$0.729090\pi$
$608$	20.5840	−	11.8905i	0.834792	−	0.482221i
$609$	3.48851	+	12.8291i	0.141362	+	0.519861i
$610$	5.55208	−	4.99957i	0.224797	−	0.202427i
$611$			47.2491i			1.91150i
$612$	−1.16412	−	14.1726i	−0.0470568	−	0.572891i
$613$	24.5067			0.989818			0.494909	−	0.868945i	$-0.335201\pi$
$613$	24.5067			0.989818			0.494909	+	0.868945i	$0.335201\pi$
$614$	12.6943	−	11.4311i	0.512301	−	0.461320i
$615$	−3.38432	−	9.12686i	−0.136469	−	0.368030i
$616$	−0.305156	−	19.9852i	−0.0122951	−	0.805228i
$617$	−15.9608	−	27.6449i	−0.642557	−	1.11294i	−0.984860	−	0.173352i	$-0.944540\pi$
$617$	−15.9608	−	27.6449i	−0.642557	−	1.11294i	0.342303	−	0.939590i	$-0.388793\pi$
$618$	4.67843	−	2.96305i	0.188194	−	0.119192i
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	−0.870560	−	0.492062i	$-0.836243\pi$
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	0.861418	+	0.507897i	$0.169577\pi$
$620$	−3.55128	+	4.88885i	−0.142623	+	0.196341i
$621$	−24.9151	+	0.450415i	−0.999809	+	0.0180745i
$622$	−2.72192	−	0.884267i	−0.109139	−	0.0354559i
$623$	−0.632468	+	7.04078i	−0.0253393	+	0.282083i
$624$	16.1906	−	40.8005i	0.648142	−	1.63333i
$625$	−10.7952	−	18.6978i	−0.431807	−	0.747911i
$626$	−26.8883	+	5.71657i	−1.07467	+	0.228480i
$627$	18.2277	−	6.75901i	0.727946	−	0.269929i
$628$	9.35868	+	21.0148i	0.373452	+	0.838581i
$629$			11.1266i			0.443646i
$630$	−5.26679	−	1.16183i	−0.209834	−	0.0462885i
$631$			28.8331i			1.14783i	0.818916	+	0.573913i	$0.194575\pi$
$631$			28.8331i			1.14783i	−0.818916	+	0.573913i	$0.805425\pi$
$632$	−1.16947	−	11.1121i	−0.0465190	−	0.442017i
$633$	2.99311	−	17.5940i	0.118966	−	0.699301i
$634$	3.06933	+	14.4368i	0.121899	+	0.573360i
$635$	−0.350386	−	0.606887i	−0.0139046	−	0.0240836i
$636$	−21.7865	−	22.2862i	−0.863893	−	0.883706i
$637$	41.7458	−	14.9750i	1.65403	−	0.593331i
$638$	3.38593	−	10.4225i	0.134050	−	0.412629i
$639$	0.585921	−	0.110610i	0.0231787	−	0.00437566i
$640$	4.39888	+	3.19383i	0.173881	+	0.126247i
$641$	3.90266	−	6.75961i	0.154146	−	0.266989i	−0.778602	−	0.627518i	$-0.784071\pi$
$641$	3.90266	−	6.75961i	0.154146	−	0.266989i	0.932748	+	0.360530i	$0.117404\pi$
$642$	36.2973	−	1.48821i	1.43254	−	0.0587349i
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	0.907165	−	0.420776i	$-0.138242\pi$
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	−0.817985	+	0.575240i	$0.804909\pi$
$644$	8.20821	+	24.0123i	0.323449	+	0.946216i
$645$	0.713089	−	0.860301i	0.0280779	−	0.0338743i
$646$	−9.42511	−	10.4667i	−0.370826	−	0.411806i
$647$	32.4931			1.27744			0.638718	−	0.769441i	$-0.279465\pi$
$647$	32.4931			1.27744			0.638718	+	0.769441i	$0.279465\pi$
$648$	21.4426	+	13.7191i	0.842347	+	0.538936i
$649$			0.750290i			0.0294515i
$650$	28.5948	+	31.7548i	1.12158	+	1.24553i
$651$	27.8608	+	7.35480i	1.09195	+	0.288257i
$652$	−39.7236	−	4.17146i	−1.55570	−	0.163367i
$653$	3.99865	+	6.92587i	0.156479	+	0.271030i	0.933597	−	0.358325i	$-0.116652\pi$
$653$	3.99865	+	6.92587i	0.156479	+	0.271030i	−0.777117	+	0.629356i	$0.783319\pi$
$654$	−1.09914	−	26.8080i	−0.0429798	−	1.04827i
$655$	5.15500	+	2.97624i	0.201422	+	0.116291i
$656$	44.4937	−	14.4658i	1.73719	−	0.564796i
$657$	−14.2957	+	2.69874i	−0.557729	+	0.105288i
$658$	3.33751	+	27.7031i	0.130110	+	1.07998i
$659$	6.89888	+	3.98307i	0.268742	+	0.155158i	0.628316	−	0.777958i	$-0.283745\pi$
$659$	6.89888	+	3.98307i	0.268742	+	0.155158i	−0.359574	+	0.933117i	$0.617078\pi$
$660$	3.10771	+	3.17898i	0.120967	+	0.123742i
$661$	−0.220771	+	0.127462i	−0.00858700	+	0.00495771i	−0.504287	−	0.863536i	$-0.668245\pi$
$661$	−0.220771	+	0.127462i	−0.00858700	+	0.00495771i	0.495700	+	0.868494i	$0.334911\pi$
$662$	49.9554	−	10.6207i	1.94157	−	0.412787i
$663$	−25.6402	−	4.36194i	−0.995784	−	0.169404i
$664$	−28.6594	+	3.01619i	−1.11220	+	0.117051i
$665$	−4.84679	+	2.24641i	−0.187950	+	0.0871119i
$666$	−15.8426	−	12.0719i	−0.613889	−	0.467776i
$667$			13.9132i			0.538723i
$668$	−40.1025	+	17.8592i	−1.55161	+	0.690992i
$669$	−8.71170	−	23.4938i	−0.336814	−	0.908321i
$670$	0.308499	+	1.45105i	0.0119184	+	0.0560589i
$671$	14.6839	+	25.4333i	0.566867	+	0.981842i
$672$	6.61087	−	25.0658i	0.255020	−	0.966936i
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	−0.869822	−	0.493365i	$-0.835767\pi$
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	0.862178	+	0.506606i	$0.169100\pi$
$674$	9.96762	+	3.23817i	0.383938	+	0.124730i
$675$	−21.2336	+	12.7765i	−0.817283	+	0.491766i
$676$	−43.9197	−	31.9034i	−1.68922	−	1.22705i
$677$	43.1462	+	24.9105i	1.65824	+	0.957388i	0.973525	+	0.228582i	$0.0734090\pi$
$677$	43.1462	+	24.9105i	1.65824	+	0.957388i	0.684720	+	0.728806i	$0.259924\pi$
$678$	19.5672	−	12.3927i	0.751473	−	0.475940i
$679$	4.68528	+	3.29691i	0.179804	+	0.126524i
$680$	1.30967	−	2.94264i	0.0502234	−	0.112845i
$681$	11.6540	+	31.4286i	0.446583	+	1.20435i
$682$	−15.8937	−	17.6501i	−0.608602	−	0.675859i
$683$			28.4508i			1.08864i	0.838878	+	0.544320i	$0.183212\pi$
$683$			28.4508i			1.08864i	−0.838878	+	0.544320i	$0.816788\pi$
$684$	25.1289	−	2.06406i	0.960826	−	0.0789214i
$685$			4.28474i			0.163712i
$686$	23.4186	−	11.7289i	0.894127	−	0.447813i
$687$	5.72215	−	33.6358i	0.218314	−	1.28329i
$688$	3.99190	+	3.59301i	0.152190	+	0.136982i
$689$	−49.3654	+	28.5011i	−1.88067	+	1.08581i
$690$	−4.99957	−	2.61951i	−0.190330	−	0.0997230i
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	−0.958227	−	0.286008i	$-0.907672\pi$
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	0.726804	+	0.686845i	$0.241005\pi$
$692$	17.9786	−	24.7501i	0.683443	−	0.940859i
$693$	8.77218	−	19.3000i	0.333227	−	0.733146i
$694$	12.5471	−	38.6219i	0.476281	−	1.46607i
$695$	1.14469	+	0.660887i	0.0434206	+	0.0250689i
$696$	7.87498	−	11.8318i	0.298500	−	0.448482i
$697$	−13.8607	−	24.0074i	−0.525011	−	0.909345i
$698$	1.18960	−	0.252913i	0.0450269	−	0.00957291i
$699$	−8.12202	+	9.79875i	−0.307203	+	0.370623i
$700$	19.0088	+	16.5987i	0.718465	+	0.627371i
$701$	−9.67651			−0.365477			−0.182738	−	0.983162i	$-0.558496\pi$
$701$	−9.67651			−0.365477			−0.182738	+	0.983162i	$0.558496\pi$
$702$	34.0293	−	31.7754i	1.28435	−	1.19929i
$703$	−19.7282			−0.744062
$704$	−15.8753	+	14.3021i	−0.598323	+	0.539029i
$705$	−4.77826	−	3.96062i	−0.179960	−	0.149166i
$706$	−44.2705	+	9.41209i	−1.66614	+	0.354229i
$707$	11.2516	+	7.91749i	0.423162	+	0.297768i
$708$	−0.262494	+	0.937019i	−0.00986513	+	0.0352153i
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	0.0377999	+	0.999285i	$0.487965\pi$
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	−0.884306	+	0.466907i	$0.845368\pi$
$710$	0.128448	+	0.0417289i	0.00482058	+	0.00156606i
$711$	3.91888	−	11.1846i	0.146970	−	0.419455i
$712$	6.11331	−	4.44286i	0.229106	−	0.166503i
$713$	26.1153	+	15.0776i	0.978024	+	0.564662i
$714$	−15.3415	−	0.746358i	−0.574142	−	0.0279317i
$715$	7.04166	−	4.06550i	0.263343	−	0.152041i
$716$	21.2765	+	2.23429i	0.795140	+	0.0834992i
$717$	2.79947	−	16.4558i	0.104548	−	0.614553i
$718$	5.22535	+	5.80281i	0.195008	+	0.216559i
$719$	−12.1609			−0.453526			−0.226763	−	0.973950i	$-0.572814\pi$
$719$	−12.1609			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$720$	2.76895	+	5.05741i	0.103193	+	0.188478i
$721$	−2.51531	−	5.42696i	−0.0936749	−	0.202111i
$722$	−1.40940	+	1.26914i	−0.0524524	+	0.0472326i
$723$	−6.67976	+	2.47691i	−0.248423	+	0.0921174i
$724$	14.3899	+	1.51111i	0.534797	+	0.0561601i
$725$	6.91809	+	11.9825i	0.256931	+	0.445018i
$726$	8.00021	−	5.06688i	0.296916	−	0.188050i
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	−0.667276	−	0.744810i	$-0.732540\pi$
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	0.978663	+	0.205473i	$0.0658733\pi$
$728$	−41.4177	−	23.0767i	−1.53504	−	0.855278i
$729$	14.3363	+	22.8795i	0.530975	+	0.847387i
$730$	−3.13397	−	1.01813i	−0.115993	−	0.0376827i
$731$	1.59112	−	2.75589i	0.0588496	−	0.101930i
$732$	9.44038	+	36.9003i	0.348927	+	1.36387i
$733$	18.4832	−	10.6713i	0.682693	−	0.394153i	−0.118176	−	0.992993i	$-0.537705\pi$
$733$	18.4832	−	10.6713i	0.682693	−	0.394153i	0.800869	+	0.598840i	$0.204371\pi$
$734$	6.75040	+	31.7510i	0.249162	+	1.17195i
$735$	−1.98490	+	5.47698i	−0.0732140	+	0.202021i
$736$	13.5589	−	23.4971i	0.499789	−	0.866115i
$737$	−5.83114			−0.214793
$738$	49.2212	+	6.31144i	1.81186	+	0.232327i
$739$			50.5558i			1.85973i	0.367907	+	0.929863i	$0.380074\pi$
$739$			50.5558i			1.85973i	−0.367907	+	0.929863i	$0.619926\pi$
$740$	−1.83534	−	4.12122i	−0.0674684	−	0.151499i
$741$	7.73400	−	45.4618i	0.284116	−	1.67008i
$742$	−26.9307	+	20.1978i	−0.988659	+	0.741485i
$743$	−32.1395	+	18.5558i	−1.17909	+	0.680745i	−0.955803	−	0.294009i	$-0.905011\pi$
$743$	−32.1395	+	18.5558i	−1.17909	+	0.680745i	−0.223282	+	0.974754i	$0.571677\pi$
$744$	−13.6743	−	27.6034i	−0.501323	−	1.01199i
$745$	−0.0634650	−	0.0366415i	−0.00232518	−	0.00134244i
$746$	−38.3835	−	12.4696i	−1.40532	−	0.456545i
$747$	−28.8463	−	10.1072i	−1.05543	−	0.369804i
$748$	10.2433	+	7.44075i	0.374532	+	0.272061i
$749$	3.51063	−	39.0812i	0.128276	−	1.42800i
$750$	−11.4880	+	0.471015i	−0.419484	+	0.0171990i
$751$	37.8228	−	21.8370i	1.38017	−	0.796843i	0.387993	−	0.921662i	$-0.373168\pi$
$751$	37.8228	−	21.8370i	1.38017	−	0.796843i	0.992180	+	0.124819i	$0.0398350\pi$
$752$	19.9562	−	22.1717i	0.727726	−	0.808519i
$753$	3.66765	−	4.42481i	0.133657	−	0.161249i
$754$	−17.3950	−	19.3173i	−0.633488	−	0.703495i
$755$	6.04058			0.219839
$756$	17.7076	−	21.0343i	0.644019	−	0.765010i
$757$	−53.5207			−1.94524			−0.972622	−	0.232392i	$-0.925345\pi$
$757$	−53.5207			−1.94524			−0.972622	+	0.232392i	$0.925345\pi$
$758$	−12.6755	−	14.0763i	−0.460394	−	0.511273i
$759$	14.1582	−	17.0811i	0.513910	−	0.620003i
$760$	5.21749	+	2.32212i	0.189258	+	0.0842322i
$761$	−19.6964	+	11.3717i	−0.713994	+	0.412225i	−0.812538	−	0.582908i	$-0.801915\pi$
$761$	−19.6964	+	11.3717i	−0.713994	+	0.412225i	0.0985439	+	0.995133i	$0.468582\pi$
$762$	3.56951	−	0.146352i	0.129310	−	0.00530177i
$763$	−28.8640	−	2.59283i	−1.04495	−	0.0938669i
$764$	23.4260	−	32.2493i	0.847524	−	1.16674i
$765$	2.59039	−	2.22734i	0.0936558	−	0.0805295i
$766$	30.1096	+	9.78170i	1.08791	+	0.353427i
$767$	1.54132	+	0.889883i	0.0556540	+	0.0321318i
$768$	−24.8300	+	12.3074i	−0.895974	+	0.444106i
$769$	9.86460	−	5.69533i	0.355726	−	0.205379i	−0.311478	−	0.950253i	$-0.600824\pi$
$769$	9.86460	−	5.69533i	0.355726	−	0.205379i	0.667204	+	0.744875i	$0.267491\pi$
$770$	3.84150	−	2.88109i	0.138438	−	0.103827i
$771$	−5.01447	+	29.4759i	−0.180592	+	1.06155i
$772$	26.0488	−	11.6005i	0.937515	−	0.417511i
$773$			30.6663i			1.10299i	0.834178	+	0.551495i	$0.185942\pi$
$773$			30.6663i			1.10299i	−0.834178	+	0.551495i	$0.814058\pi$
$774$	2.19769	+	5.25554i	0.0789945	+	0.188907i
$775$	29.9883			1.07721
$776$	−0.641025	−	6.09092i	−0.0230114	−	0.218651i
$777$	−15.1560	+	15.2687i	−0.543720	+	0.547762i
$778$	−7.95856	−	37.4337i	−0.285328	−	1.34206i
$779$	42.5667	−	24.5759i	1.52511	−	0.880523i
$780$	10.2165	−	2.61374i	0.365809	−	0.0935868i
$781$	−0.265435	+	0.459746i	−0.00949800	+	0.0164510i
$782$	−15.2875	−	4.96644i	−0.546680	−	0.177600i
$783$	12.9170	−	7.77226i	0.461615	−	0.277758i
$784$	−25.9141	−	10.6047i	−0.925503	−	0.378740i
$785$	−2.76332	+	4.78621i	−0.0986271	+	0.170827i
$786$	−25.6364	+	16.2366i	−0.914420	+	0.579141i
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	0.638059	−	0.769988i	$-0.279738\pi$
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	−0.985858	+	0.167581i	$0.946404\pi$
$788$	2.49640	−	23.7725i	0.0889305	−	0.846861i
$789$	21.4629	−	7.95865i	0.764101	−	0.283335i
$790$	1.99477	−	1.79627i	0.0709708	−	0.0639083i
$791$	−10.5201	−	22.6978i	−0.374050	−	0.807042i
$792$	−21.7081	+	6.51203i	−0.771362	+	0.231395i
$793$	69.6636			2.47383
$794$	11.0398	+	12.2598i	0.391787	+	0.435084i
$795$	1.25572	−	7.38136i	0.0445359	−	0.261790i
$796$	−4.58511	+	43.6628i	−0.162515	+	1.54759i
$797$	25.9632	−	14.9898i	0.919663	−	0.530968i	0.0361355	−	0.999347i	$-0.488495\pi$
$797$	25.9632	−	14.9898i	0.919663	−	0.530968i	0.883528	+	0.468379i	$0.155162\pi$
$798$	1.32334	−	27.2015i	0.0468458	−	0.962923i
$799$	−15.3067	−	8.83733i	−0.541512	−	0.312642i
$800$	−0.00615553	−	26.9783i	−0.000217631	−	0.953827i
$801$	7.87652	−	1.48692i	0.278303	−	0.0525379i
$802$	−22.4205	−	7.28372i	−0.791694	−	0.257197i
$803$	6.47626	−	11.2172i	0.228542	−	0.395847i
$804$	−7.28238	−	2.04007i	−0.256830	−	0.0719476i
$805$	−3.50839	+	4.98581i	−0.123654	+	0.175727i
$806$	−55.1095	+	11.7165i	−1.94115	+	0.412697i
$807$	36.7516	+	30.4628i	1.29372	+	1.07234i
$808$	−1.53941	−	14.6273i	−0.0541564	−	0.514586i
$809$	−54.5869			−1.91917			−0.959586	−	0.281415i	$-0.909196\pi$
$809$	−54.5869			−1.91917			−0.959586	+	0.281415i	$0.909196\pi$
$810$	0.360936	+	6.10490i	0.0126820	+	0.214504i
$811$	−17.5107			−0.614883			−0.307442	−	0.951567i	$-0.599473\pi$
$811$	−17.5107			−0.614883			−0.307442	+	0.951567i	$0.599473\pi$
$812$	−11.5635	−	10.0974i	−0.405801	−	0.354350i
$813$	−23.4845	+	28.3327i	−0.823639	+	0.993672i
$814$	17.3455	−	3.68772i	0.607959	−	0.129255i
$815$	−4.79788	−	8.31016i	−0.168062	−	0.291092i
$816$	10.1894	+	12.8763i	0.356700	+	0.450759i
$817$	4.88638	+	2.82115i	0.170953	+	0.0986997i
$818$	−0.297323	+	0.915209i	−0.0103957	+	0.0319995i
$819$	−29.2438	−	40.9115i	−1.02186	−	1.42956i
$820$	9.09395	+	6.60587i	0.317575	+	0.230687i
$821$	−9.47071	+	16.4037i	−0.330530	+	0.572495i	−0.982616	−	0.185650i	$-0.940561\pi$
$821$	−9.47071	+	16.4037i	−0.330530	+	0.572495i	0.652086	+	0.758145i	$0.273894\pi$
$822$	−19.3485	−	10.1376i	−0.674858	−	0.353590i
$823$	−8.43975	+	4.87269i	−0.294191	+	0.169851i	−0.639831	−	0.768516i	$-0.720995\pi$
$823$	−8.43975	+	4.87269i	−0.294191	+	0.169851i	0.345639	+	0.938367i	$0.387662\pi$
$824$	−2.60009	+	5.84204i	−0.0905783	+	0.203517i
$825$	3.70023	−	21.7506i	0.128825	−	0.757258i
$826$	0.966568	+	0.412883i	0.0336312	+	0.0143661i
$827$			38.9872i			1.35572i	0.735193	+	0.677858i	$0.237092\pi$
$827$			38.9872i			1.35572i	−0.735193	+	0.677858i	$0.762908\pi$
$828$	23.6578	−	16.3788i	0.822164	−	0.569202i
$829$			8.11853i			0.281968i	0.990012	+	0.140984i	$0.0450266\pi$
$829$			8.11853i			0.281968i	−0.990012	+	0.140984i	$0.954973\pi$
$830$	−4.63276	−	5.14473i	−0.160805	−	0.178576i
$831$	8.74475	+	23.5829i	0.303352	+	0.818082i
$832$	10.5518	+	49.5757i	0.365819	+	1.71873i
$833$	−2.95673	+	16.3247i	−0.102445	+	0.565618i
$834$	−5.69267	+	3.60542i	−0.197121	+	0.124845i
$835$	−9.13352	−	5.27324i	−0.316078	−	0.182488i
$836$	−13.1929	+	18.1620i	−0.456288	+	0.628147i
$837$	−0.590572	−	32.6680i	−0.0204132	−	1.12917i
$838$	13.9862	+	4.54368i	0.483144	+	0.156959i
$839$	−13.5859	+	23.5314i	−0.469036	+	0.812394i	−0.999373	−	0.0353923i	$-0.988732\pi$
$839$	−13.5859	+	23.5314i	−0.469036	+	0.812394i	0.530337	+	0.847787i	$0.322065\pi$
$840$	5.80552	−	2.25415i	0.200309	−	0.0777754i
$841$	10.2915	+	17.8255i	0.354881	+	0.614672i
$842$	2.01615	+	9.48311i	0.0694811	+	0.326810i
$843$	7.65563	+	20.6458i	0.263674	+	0.711078i
$844$	8.38364	+	18.8253i	0.288577	+	0.647995i
$845$		−	13.0413i		−	0.448635i
$846$	29.1902	−	12.2064i	1.00358	−	0.419663i
$847$	−4.30122	−	9.28021i	−0.147792	−	0.318872i
$848$	35.2025	+	7.47581i	1.20886	+	0.256720i
$849$	35.6093	+	6.05789i	1.22211	+	0.207906i
$850$	−15.6355	+	3.32417i	−0.536293	+	0.114018i
$851$	−19.4979	+	11.2571i	−0.668379	+	0.385889i
$852$	−0.492340	+	0.481302i	−0.0168673	+	0.0164891i
$853$	20.4384	+	11.8001i	0.699797	+	0.404028i	0.807272	−	0.590180i	$-0.200943\pi$
$853$	20.4384	+	11.8001i	0.699797	+	0.404028i	−0.107475	+	0.994208i	$0.534276\pi$
$854$	40.8452	−	4.92079i	1.39769	−	0.168386i
$855$	3.94921	+	4.59293i	0.135060	+	0.157075i
$856$	−33.9331	+	24.6609i	−1.15981	+	0.842893i
$857$	13.6342	+	7.87173i	0.465737	+	0.268893i	0.714453	−	0.699683i	$-0.246675\pi$
$857$	13.6342	+	7.87173i	0.465737	+	0.268893i	−0.248717	+	0.968576i	$0.580009\pi$
$858$	1.69811	+	41.4168i	0.0579725	+	1.41395i
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	0.998754	−	0.0499024i	$-0.0158910\pi$
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	−0.542594	+	0.839995i	$0.682558\pi$
$860$	−0.134754	+	1.28322i	−0.00459506	+	0.0437575i
$861$	13.6810	−	51.8249i	0.466246	−	1.76619i
$862$	−14.4385	−	16.0341i	−0.491778	−	0.546125i
$863$		−	50.8477i		−	1.73088i	−0.501015	−	0.865438i	$-0.667040\pi$
$863$		−	50.8477i		−	1.73088i	0.501015	−	0.865438i	$-0.332960\pi$
$864$	−29.3890	+	0.538001i	−0.999832	+	0.0183032i
$865$	7.34919			0.249880
$866$	−32.7869	−	36.4102i	−1.11414	−	1.23727i
$867$	−12.5818	+	15.1792i	−0.427300	+	0.515513i
$868$	−31.4842	+	10.7624i	−1.06864	+	0.365299i
$869$	5.27570	+	9.13778i	0.178966	+	0.309978i
$870$	3.41166	−	0.139880i	0.115666	−	0.00474237i
$871$	−6.91604	+	11.9789i	−0.234341	+	0.405891i
$872$	18.2137	+	25.0618i	0.616794	+	0.848700i
$873$	2.14807	−	6.13064i	0.0727011	−	0.207491i
$874$	8.80582	−	27.1057i	0.297861	−	0.916866i
$875$	−1.11111	+	12.3691i	−0.0375623	+	0.418152i
$876$	12.0125	−	11.7431i	0.405864	−	0.396764i
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	0.957604	−	0.288087i	$-0.0930192\pi$
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	−0.728293	+	0.685266i	$0.759686\pi$
$878$	−3.60074	−	16.9363i	−0.121519	−	0.571574i
$879$	−1.94816	+	11.4516i	−0.0657097	+	0.386253i
$880$	−5.02141	−	1.06638i	−0.169272	−	0.0359475i
$881$			5.11905i			0.172465i	0.996275	+	0.0862325i	$0.0274828\pi$
$881$			5.11905i			0.172465i	−0.996275	+	0.0862325i	$0.972517\pi$
$882$	−20.0361	−	21.9216i	−0.674650	−	0.738138i
$883$			36.5196i			1.22898i	0.788924	+	0.614491i	$0.210639\pi$
$883$			36.5196i			1.22898i	−0.788924	+	0.614491i	$0.789361\pi$
$884$	27.4346	−	12.2177i	0.922727	−	0.410925i
$885$	−0.219193	+	0.0812788i	−0.00736810	+	0.00273216i
$886$	−38.7293	+	8.23400i	−1.30113	+	0.276627i
$887$	−16.1245	−	27.9284i	−0.541407	−	0.937744i	−0.998824	−	0.0484917i	$-0.984559\pi$
$887$	−16.1245	−	27.9284i	−0.541407	−	0.937744i	0.457417	−	0.889252i	$-0.348775\pi$
$888$	22.9525	+	1.46293i	0.770236	+	0.0490926i
$889$	0.345239	−	3.84328i	0.0115789	−	0.128899i
$890$	1.72673	+	0.560960i	0.0578800	+	0.0188034i
$891$	−23.7671	−	3.60253i	−0.796227	−	0.120689i
$892$	23.4091	+	17.0044i	0.783793	+	0.569350i
$893$	15.6692	−	27.1398i	0.524349	−	0.908199i
$894$	0.315618	−	0.199895i	0.0105559	−	0.00668548i
$895$	2.56981	+	4.45103i	0.0858991	+	0.148782i
$896$	9.68861	+	28.3219i	0.323674	+	0.946169i
$897$	−18.2973	−	49.3443i	−0.610929	−	1.64756i
$898$	25.0403	−	22.5485i	0.835606	−	0.752452i
$899$	−18.2427			−0.608426
$900$	12.2307	−	25.8692i	0.407690	−	0.862308i
$901$		−	21.3231i		−	0.710374i
$902$	−32.8318	+	29.5646i	−1.09318	+	0.984392i
$903$	5.93737	−	1.61450i	0.197583	−	0.0537273i
$904$	−10.8747	+	24.4339i	−0.361686	+	0.812658i
$905$	1.73803	+	3.01036i	0.0577742	+	0.100068i
$906$	−14.2919	+	27.2774i	−0.474816	+	0.906230i
$907$	24.3819	+	14.0769i	0.809588	+	0.467416i	0.846813	−	0.531891i	$-0.178518\pi$
$907$	24.3819	+	14.0769i	0.809588	+	0.467416i	−0.0372246	+	0.999307i	$0.511852\pi$
$908$	−31.3153	−	22.7475i	−1.03924	−	0.754904i
$909$	5.15856	−	14.7227i	0.171099	−	0.488320i
$910$	−1.36241	−	11.3087i	−0.0451634	−	0.374880i
$911$	33.2831	+	19.2160i	1.10272	+	0.636655i	0.936934	−	0.349507i	$-0.113651\pi$
$911$	33.2831	+	19.2160i	1.10272	+	0.636655i	0.165785	+	0.986162i	$0.446984\pi$
$912$	−22.8305	+	18.0665i	−0.755992	+	0.598240i
$913$	23.5673	−	13.6066i	0.779964	−	0.450312i
$914$	7.00535	+	32.9502i	0.231717	+	1.08990i
$915$	−5.83949	+	7.04501i	−0.193048	+	0.232901i
$916$	16.0276	+	35.9898i	0.529567	+	1.18914i
$917$	13.7831	+	29.7381i	0.455158	+	0.982038i
$918$	3.92914	+	16.9672i	0.129681	+	0.560002i
$919$		−	17.3398i		−	0.571988i	−0.958231	−	0.285994i	$-0.907676\pi$
$919$		−	17.3398i		−	0.571988i	0.958231	−	0.285994i	$-0.0923238\pi$
$920$	6.48162	−	0.682143i	0.213693	−	0.0224896i
$921$	−13.3515	+	16.1078i	−0.439946	+	0.530769i
$922$	−0.507231	+	0.107839i	−0.0167048	+	0.00355150i
$923$	0.629639	+	1.09057i	0.0207248	+	0.0358964i
$924$	3.92118	+	24.1636i	0.128997	+	0.794923i
$925$	−11.1948	+	19.3899i	−0.368081	+	0.637536i
$926$	7.24077	−	22.2883i	0.237946	−	0.732438i
$927$	−5.14272	+	4.42195i	−0.168909	+	0.145236i
$928$	0.00374457	+	16.4116i	0.000122922	+	0.538738i
$929$	−48.7835	−	28.1651i	−1.60053	−	0.924068i	−0.991380	−	0.131016i	$-0.958176\pi$
$929$	−48.7835	−	28.1651i	−1.60053	−	0.924068i	−0.609153	−	0.793053i	$-0.708490\pi$
$930$	3.43463	−	6.55530i	0.112626	−	0.214957i
$931$	−28.9448	−	5.24248i	−0.948628	−	0.171815i
$932$	1.53483	−	14.6158i	0.0502751	−	0.478756i
$933$	3.45551	+	0.587855i	0.113128	+	0.0192455i
$934$	−27.4777	+	24.7433i	−0.899099	+	0.809627i
$935$			3.04160i			0.0994708i
$936$	−12.3692	+	52.3185i	−0.404301	+	1.71009i
$937$			36.1315i			1.18036i	0.807270	+	0.590182i	$0.200944\pi$
$937$			36.1315i			1.18036i	−0.807270	+	0.590182i	$0.799056\pi$
$938$	−3.20887	+	7.51202i	−0.104773	+	0.245276i
$939$	31.5670	−	11.7053i	1.03015	−	0.381989i
$940$	7.12724	+	0.748445i	0.232465	+	0.0244116i
$941$	−12.0974	+	6.98446i	−0.394365	+	0.227687i	−0.684050	−	0.729435i	$-0.739783\pi$
$941$	−12.0974	+	6.98446i	−0.394365	+	0.227687i	0.289684	+	0.957122i	$0.406450\pi$
$942$	−15.0750	−	23.8023i	−0.491172	−	0.775522i
$943$	28.0466	−	48.5781i	0.913321	−	1.58192i
$944$	−0.347416	−	1.06857i	−0.0113074	−	0.0347791i
$945$	6.58867	+	0.471979i	0.214330	+	0.0153535i
$946$	−4.82357	−	1.56703i	−0.156828	−	0.0509485i
$947$	11.0539	+	6.38196i	0.359203	+	0.207386i	0.668731	−	0.743505i	$-0.266838\pi$
$947$	11.0539	+	6.38196i	0.359203	+	0.207386i	−0.309528	+	0.950890i	$0.600171\pi$
$948$	3.39178	+	13.2577i	0.110160	+	0.430590i
$949$	−15.3624	−	26.6084i	−0.498684	−	0.863746i
$950$	−5.89398	−	27.7228i	−0.191226	−	0.899445i
$951$	−6.28481	−	16.9489i	−0.203799	−	0.549606i
$952$	15.2225	−	9.10137i	0.493363	−	0.294977i
$953$	−3.91673			−0.126875			−0.0634377	−	0.997986i	$-0.520206\pi$
$953$	−3.91673			−0.126875			−0.0634377	+	0.997986i	$0.520206\pi$
$954$	30.3609	+	23.1346i	0.982970	+	0.749010i
$955$	9.57597			0.309871
$956$	7.84126	+	17.6074i	0.253604	+	0.569465i
$957$	−2.25095	+	13.2315i	−0.0727627	+	0.427712i
$958$	−11.2210	−	52.7789i	−0.362535	−	1.70521i
$959$	−13.5776	+	19.2953i	−0.438444	+	0.623078i
$960$	−5.89804	−	3.08855i	−0.190358	−	0.0996824i
$961$	−4.26940	+	7.39481i	−0.137722	+	0.238542i
$962$	12.9969	−	40.0067i	0.419038	−	1.28987i
$963$	−43.7201	+	8.25345i	−1.40886	+	0.265964i
$964$	4.83470	−	6.65568i	0.155715	−	0.214365i
$965$	5.93272	+	3.42526i	0.190981	+	0.110263i
$966$	−14.2136	−	27.6391i	−0.457315	−	0.889274i
$967$	20.2799	−	11.7086i	0.652158	−	0.376524i	−0.137125	−	0.990554i	$-0.543786\pi$
$967$	20.2799	−	11.7086i	0.652158	−	0.376524i	0.789283	+	0.614030i	$0.210453\pi$
$968$	−4.44620	+	9.99001i	−0.142906	+	0.321091i
$969$	13.2811	+	11.0085i	0.426652	+	0.353645i
$970$	1.09340	−	0.984592i	0.0351070	−	0.0316133i
$971$	25.1209			0.806167			0.403084	−	0.915163i	$-0.367938\pi$
$971$	25.1209			0.806167			0.403084	+	0.915163i	$0.367938\pi$
$972$	−28.4218	−	12.8142i	−0.911628	−	0.411015i
$973$	3.06060	+	6.60347i	0.0981184	+	0.211698i
$974$	−8.45856	−	9.39332i	−0.271030	−	0.300982i
$975$	−40.2936	−	33.3987i	−1.29043	−	1.06962i
$976$	−32.6897	−	29.4231i	−1.04637	−	0.941812i
$977$	−1.21770	−	2.10911i	−0.0389575	−	0.0674764i	0.845889	−	0.533359i	$-0.179070\pi$
$977$	−1.21770	−	2.10911i	−0.0389575	−	0.0674764i	−0.884847	+	0.465882i	$0.845737\pi$
$978$	48.8778	−	2.00401i	1.56294	−	0.0640813i
$979$	−3.56823	+	6.18036i	−0.114041	+	0.197525i
$980$	−1.59762	−	6.53430i	−0.0510340	−	0.208731i
$981$	6.09572	+	32.2902i	0.194621	+	1.03095i
$982$	4.05199	−	12.4727i	0.129304	−	0.398019i
$983$	9.60279	−	16.6325i	0.306281	−	0.530495i	−0.671264	−	0.741218i	$-0.734248\pi$
$983$	9.60279	−	16.6325i	0.306281	−	0.530495i	0.977546	+	0.210723i	$0.0675818\pi$
$984$	−51.3462	+	25.4361i	−1.63686	+	0.810872i
$985$	4.97320	−	2.87128i	0.158459	−	0.0914865i
$986$	9.51149	−	2.02218i	0.302907	−	0.0643994i
$987$	−8.96722	−	32.9772i	−0.285430	−	1.04968i
$988$	21.6628	+	48.6434i	0.689184	+	1.54755i
$989$	6.43913			0.204752
$990$	−4.33078	−	3.30000i	−0.137641	−	0.104881i
$991$		−	29.4493i		−	0.935489i	−0.883864	−	0.467745i	$-0.845067\pi$
$991$		−	29.4493i		−	0.935489i	0.883864	−	0.467745i	$-0.154933\pi$
$992$	30.8088	+	17.7781i	0.978180	+	0.564455i
$993$	−58.6479	+	21.7472i	−1.86113	+	0.690125i
$994$	0.446204	+	0.594946i	0.0141527	+	0.0188705i
$995$	−9.13423	+	5.27365i	−0.289575	+	0.167186i
$996$	34.1930	−	8.74776i	1.08345	−	0.277183i
$997$	−13.3933	−	7.73264i	−0.424171	−	0.244895i	0.272689	−	0.962102i	$-0.412087\pi$
$997$	−13.3933	−	7.73264i	−0.424171	−	0.244895i	−0.696860	+	0.717207i	$0.745420\pi$
$998$	−7.58668	+	23.3530i	−0.240152	+	0.739227i
$999$	21.3430	+	11.8133i	0.675264	+	0.373755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.223.33	yes	80
3.2	odd	2		756.2.bi.c.559.7		80
4.3	odd	2	inner	252.2.bi.c.223.24	yes	80
7.6	odd	2	inner	252.2.bi.c.223.34	yes	80
9.4	even	3	inner	252.2.bi.c.139.23	✓	80
9.5	odd	6		756.2.bi.c.307.18		80
12.11	even	2		756.2.bi.c.559.17		80
21.20	even	2		756.2.bi.c.559.8		80
28.27	even	2	inner	252.2.bi.c.223.23	yes	80
36.23	even	6		756.2.bi.c.307.8		80
36.31	odd	6	inner	252.2.bi.c.139.34	yes	80
63.13	odd	6	inner	252.2.bi.c.139.24	yes	80
63.41	even	6		756.2.bi.c.307.17		80
84.83	odd	2		756.2.bi.c.559.18		80
252.139	even	6	inner	252.2.bi.c.139.33	yes	80
252.167	odd	6		756.2.bi.c.307.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.23	✓	80	9.4	even	3	inner
252.2.bi.c.139.24	yes	80	63.13	odd	6	inner
252.2.bi.c.139.33	yes	80	252.139	even	6	inner
252.2.bi.c.139.34	yes	80	36.31	odd	6	inner
252.2.bi.c.223.23	yes	80	28.27	even	2	inner
252.2.bi.c.223.24	yes	80	4.3	odd	2	inner
252.2.bi.c.223.33	yes	80	1.1	even	1	trivial
252.2.bi.c.223.34	yes	80	7.6	odd	2	inner
756.2.bi.c.307.7		80	252.167	odd	6
756.2.bi.c.307.8		80	36.23	even	6
756.2.bi.c.307.17		80	63.41	even	6
756.2.bi.c.307.18		80	9.5	odd	6
756.2.bi.c.559.7		80	3.2	odd	2
756.2.bi.c.559.8		80	21.20	even	2
756.2.bi.c.559.17		80	12.11	even	2
756.2.bi.c.559.18		80	84.83	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05092 - 0.946342i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(0.208875 - 1.98906i) q^{4} +(0.416111 - 0.240242i) q^{5} +(0.100346 + 2.44743i) q^{6} +(2.63514 + 0.236713i) q^{7} +(-1.66282 - 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +O(q^{10})\)	\(q+(1.05092 - 0.946342i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(0.208875 - 1.98906i) q^{4} +(0.416111 - 0.240242i) q^{5} +(0.100346 + 2.44743i) q^{6} +(2.63514 + 0.236713i) q^{7} +(-1.66282 - 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +(0.209950 - 0.646259i) q^{10} +(2.31311 + 1.33548i) q^{11} +(2.42156 + 2.47710i) q^{12} +(5.48694 - 3.16789i) q^{13} +(2.99334 - 2.24498i) q^{14} +(-0.139573 + 0.820435i) q^{15} +(-3.91274 - 0.830933i) q^{16} +2.37005i q^{17} +(-3.37460 - 2.57140i) q^{18} -4.20225 q^{19} +(-0.390941 - 0.877852i) q^{20} +(-3.22835 + 3.25235i) q^{21} +(3.69472 - 0.785512i) q^{22} +(-4.15320 + 2.39785i) q^{23} +(4.88906 + 0.311614i) q^{24} +(-2.38457 + 4.13019i) q^{25} +(2.76845 - 8.52173i) q^{26} +(4.54623 + 2.51631i) q^{27} +(1.02125 - 5.19202i) q^{28} +(1.45060 - 2.51250i) q^{29} +(0.629731 + 0.994297i) q^{30} +(-3.14399 - 5.44556i) q^{31} +(-4.89833 + 2.82954i) q^{32} +(-4.33762 + 1.60843i) q^{33} +(2.24287 + 2.49074i) q^{34} +(1.15338 - 0.534572i) q^{35} +(-5.97986 + 0.491180i) q^{36} +4.69467 q^{37} +(-4.41624 + 3.97676i) q^{38} +(-1.84044 + 10.8185i) q^{39} +(-1.24160 - 0.552590i) q^{40} +(-10.1295 + 5.84827i) q^{41} +(-0.314913 + 6.47309i) q^{42} +(-1.16280 - 0.671344i) q^{43} +(3.13950 - 4.32198i) q^{44} +(-0.939786 - 1.09297i) q^{45} +(-2.09550 + 6.45030i) q^{46} +(-3.72876 + 6.45840i) q^{47} +(5.43291 - 4.29924i) q^{48} +(6.88793 + 1.24754i) q^{49} +(1.40258 + 6.59713i) q^{50} +(-3.16049 - 2.61967i) q^{51} +(-5.15504 - 11.5756i) q^{52} -8.99689 q^{53} +(7.15902 - 1.65783i) q^{54} +1.28335 q^{55} +(-3.84016 - 6.42286i) q^{56} +(4.64485 - 5.60375i) q^{57} +(-0.853225 - 4.01321i) q^{58} +(0.140454 + 0.243273i) q^{59} +(1.60274 + 0.448988i) q^{60} +(9.52219 + 5.49764i) q^{61} +(-8.45745 - 2.74757i) q^{62} +(-0.768666 - 7.89995i) q^{63} +(-2.47005 + 7.60913i) q^{64} +(1.52212 - 2.63639i) q^{65} +(-3.03638 + 5.79520i) q^{66} +(-1.89068 + 1.09159i) q^{67} +(4.71417 + 0.495044i) q^{68} +(1.39308 - 8.18874i) q^{69} +(0.706224 - 1.65328i) q^{70} +0.198757i q^{71} +(-5.81955 + 6.17518i) q^{72} -4.84941i q^{73} +(4.93373 - 4.44276i) q^{74} +(-2.87194 - 7.74506i) q^{75} +(-0.877746 + 8.35854i) q^{76} +(5.77925 + 4.06671i) q^{77} +(8.30379 + 13.1110i) q^{78} +(3.42117 + 1.97521i) q^{79} +(-1.82776 + 0.594244i) q^{80} +(-8.38060 + 3.28110i) q^{81} +(-5.11086 + 15.7321i) q^{82} +(5.09429 - 8.82356i) q^{83} +(5.79480 + 7.10072i) q^{84} +(0.569384 + 0.986203i) q^{85} +(-1.85733 + 0.394877i) q^{86} +(1.74707 + 4.71152i) q^{87} +(-0.790698 - 7.51310i) q^{88} +2.67188i q^{89} +(-2.02196 - 0.259268i) q^{90} +(15.2087 - 7.04900i) q^{91} +(3.90197 + 8.76182i) q^{92} +(10.7369 + 1.82656i) q^{93} +(2.19322 + 10.3160i) q^{94} +(-1.74860 + 1.00956i) q^{95} +(1.64102 - 9.65956i) q^{96} +(1.87526 + 1.08268i) q^{97} +(8.41929 - 5.20727i) q^{98} +(2.64962 - 7.56210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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