LMFDB - Embedded newform 285.2.k.d.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(77,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("285.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.4
Character	$\chi$	$=$	285.77
Dual form			285.2.k.d.248.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43829 + 1.43829i) q^{2} +(-1.69247 - 0.368185i) q^{3} -2.13738i q^{4} +(-2.18737 + 0.464149i) q^{5} +(2.96382 - 1.90470i) q^{6} +(-1.23221 - 1.23221i) q^{7} +(0.197591 + 0.197591i) q^{8} +(2.72888 + 1.24628i) q^{9} +O(q^{10})$	\(q+(-1.43829 + 1.43829i) q^{2} +(-1.69247 - 0.368185i) q^{3} -2.13738i q^{4} +(-2.18737 + 0.464149i) q^{5} +(2.96382 - 1.90470i) q^{6} +(-1.23221 - 1.23221i) q^{7} +(0.197591 + 0.197591i) q^{8} +(2.72888 + 1.24628i) q^{9} +(2.47849 - 3.81366i) q^{10} +0.351554i q^{11} +(-0.786952 + 3.61744i) q^{12} +(0.181358 - 0.181358i) q^{13} +3.54456 q^{14} +(3.87293 + 0.0197996i) q^{15} +3.70637 q^{16} +(1.52282 - 1.52282i) q^{17} +(-5.71745 + 2.13241i) q^{18} +1.00000i q^{19} +(0.992062 + 4.67523i) q^{20} +(1.63179 + 2.53915i) q^{21} +(-0.505639 - 0.505639i) q^{22} +(3.86668 + 3.86668i) q^{23} +(-0.261666 - 0.407167i) q^{24} +(4.56913 - 2.03053i) q^{25} +0.521694i q^{26} +(-4.15967 - 3.11402i) q^{27} +(-2.63370 + 2.63370i) q^{28} +7.70264 q^{29} +(-5.59889 + 5.54194i) q^{30} -4.22453 q^{31} +(-5.72603 + 5.72603i) q^{32} +(0.129437 - 0.594994i) q^{33} +4.38052i q^{34} +(3.26722 + 2.12336i) q^{35} +(2.66378 - 5.83265i) q^{36} +(1.89968 + 1.89968i) q^{37} +(-1.43829 - 1.43829i) q^{38} +(-0.373716 + 0.240169i) q^{39} +(-0.523916 - 0.340492i) q^{40} -6.12012i q^{41} +(-5.99904 - 1.30505i) q^{42} +(-0.226097 + 0.226097i) q^{43} +0.751405 q^{44} +(-6.54752 - 1.45947i) q^{45} -11.1228 q^{46} +(8.19848 - 8.19848i) q^{47} +(-6.27290 - 1.36463i) q^{48} -3.96332i q^{49} +(-3.65126 + 9.49225i) q^{50} +(-3.13800 + 2.01664i) q^{51} +(-0.387632 - 0.387632i) q^{52} +(2.43700 + 2.43700i) q^{53} +(10.4617 - 1.50395i) q^{54} +(-0.163174 - 0.768978i) q^{55} -0.486948i q^{56} +(0.368185 - 1.69247i) q^{57} +(-11.0787 + 11.0787i) q^{58} -5.37432 q^{59} +(0.0423193 - 8.27792i) q^{60} +11.0661 q^{61} +(6.07611 - 6.07611i) q^{62} +(-1.82687 - 4.89823i) q^{63} -9.05869i q^{64} +(-0.312520 + 0.480874i) q^{65} +(0.669607 + 1.04194i) q^{66} +(-5.18430 - 5.18430i) q^{67} +(-3.25484 - 3.25484i) q^{68} +(-5.12056 - 7.96787i) q^{69} +(-7.75324 + 1.64520i) q^{70} -14.9920i q^{71} +(0.292948 + 0.785457i) q^{72} +(6.94178 - 6.94178i) q^{73} -5.46459 q^{74} +(-8.48071 + 1.75431i) q^{75} +2.13738 q^{76} +(0.433189 - 0.433189i) q^{77} +(0.192080 - 0.882948i) q^{78} -3.78981i q^{79} +(-8.10718 + 1.72031i) q^{80} +(5.89356 + 6.80191i) q^{81} +(8.80253 + 8.80253i) q^{82} +(7.19514 + 7.19514i) q^{83} +(5.42713 - 3.48775i) q^{84} +(-2.62415 + 4.03778i) q^{85} -0.650387i q^{86} +(-13.0364 - 2.83600i) q^{87} +(-0.0694641 + 0.0694641i) q^{88} -17.9313 q^{89} +(11.5164 - 7.31811i) q^{90} -0.446943 q^{91} +(8.26455 - 8.26455i) q^{92} +(7.14987 + 1.55541i) q^{93} +23.5837i q^{94} +(-0.464149 - 2.18737i) q^{95} +(11.7994 - 7.58287i) q^{96} +(9.20451 + 9.20451i) q^{97} +(5.70042 + 5.70042i) q^{98} +(-0.438136 + 0.959350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.43829	+	1.43829i	−1.01703	+	1.01703i	−0.0171749	+	0.999853i	$0.505467\pi$
$2$	−1.43829	+	1.43829i	−1.01703	+	1.01703i	−0.999853	+	0.0171749i	$0.994533\pi$
$3$	−1.69247	−	0.368185i	−0.977145	−	0.212572i
$3$	−1.69247	−	0.368185i	−0.977145	−	0.212572i
$4$		−	2.13738i		−	1.06869i
$5$	−2.18737	+	0.464149i	−0.978219	+	0.207574i
$5$	−2.18737	+	0.464149i	−0.978219	+	0.207574i
$6$	2.96382	−	1.90470i	1.20998	−	0.777592i
$7$	−1.23221	−	1.23221i	−0.465731	−	0.465731i	0.434797	−	0.900528i	$-0.356820\pi$
$7$	−1.23221	−	1.23221i	−0.465731	−	0.465731i	−0.900528	+	0.434797i	$0.856820\pi$
$8$	0.197591	+	0.197591i	0.0698591	+	0.0698591i
$9$	2.72888	+	1.24628i	0.909626	+	0.415427i
$10$	2.47849	−	3.81366i	0.783768	−	1.20598i
$11$			0.351554i			0.105998i	0.998595	+	0.0529988i	$0.0168780\pi$
$11$			0.351554i			0.105998i	−0.998595	+	0.0529988i	$0.983122\pi$
$12$	−0.786952	+	3.61744i	−0.227173	+	1.04427i
$13$	0.181358	−	0.181358i	0.0502998	−	0.0502998i	−0.681509	−	0.731809i	$-0.738676\pi$
$13$	0.181358	−	0.181358i	0.0502998	−	0.0502998i	0.731809	+	0.681509i	$0.238676\pi$
$14$	3.54456			0.947323
$15$	3.87293	+	0.0197996i	0.999987	+	0.00511224i
$16$	3.70637			0.926592
$17$	1.52282	−	1.52282i	0.369338	−	0.369338i	−0.497898	−	0.867236i	$-0.665895\pi$
$17$	1.52282	−	1.52282i	0.369338	−	0.369338i	0.867236	+	0.497898i	$0.165895\pi$
$18$	−5.71745	+	2.13241i	−1.34762	+	0.502614i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	0.992062	+	4.67523i	0.221832	+	1.04541i
$21$	1.63179	+	2.53915i	0.356086	+	0.554089i
$22$	−0.505639	−	0.505639i	−0.107803	−	0.107803i
$23$	3.86668	+	3.86668i	0.806258	+	0.806258i	0.984065	−	0.177808i	$-0.0569005\pi$
$23$	3.86668	+	3.86668i	0.806258	+	0.806258i	−0.177808	+	0.984065i	$0.556901\pi$
$24$	−0.261666	−	0.407167i	−0.0534124	−	0.0831125i
$25$	4.56913	−	2.03053i	0.913826	−	0.406105i
$26$			0.521694i			0.102313i
$27$	−4.15967	−	3.11402i	−0.800529	−	0.599294i
$28$	−2.63370	+	2.63370i	−0.497722	+	0.497722i
$29$	7.70264			1.43034			0.715172	−	0.698949i	$-0.246348\pi$
$29$	7.70264			1.43034			0.715172	+	0.698949i	$0.246348\pi$
$30$	−5.59889	+	5.54194i	−1.02221	+	1.01181i
$31$	−4.22453			−0.758747			−0.379374	−	0.925244i	$-0.623861\pi$
$31$	−4.22453			−0.758747			−0.379374	+	0.925244i	$0.623861\pi$
$32$	−5.72603	+	5.72603i	−1.01223	+	1.01223i
$33$	0.129437	−	0.594994i	0.0225321	−	0.103575i
$34$			4.38052i			0.751254i
$35$	3.26722	+	2.12336i	0.552261	+	0.358914i
$36$	2.66378	−	5.83265i	0.443963	−	0.972108i
$37$	1.89968	+	1.89968i	0.312305	+	0.312305i	0.845802	−	0.533497i	$-0.179122\pi$
$37$	1.89968	+	1.89968i	0.312305	+	0.312305i	−0.533497	+	0.845802i	$0.679122\pi$
$38$	−1.43829	−	1.43829i	−0.233322	−	0.233322i
$39$	−0.373716	+	0.240169i	−0.0598425	+	0.0384579i
$40$	−0.523916	−	0.340492i	−0.0828384	−	0.0538366i
$41$		−	6.12012i		−	0.955802i	−0.878414	−	0.477901i	$-0.841398\pi$
$41$		−	6.12012i		−	0.955802i	0.878414	−	0.477901i	$-0.158602\pi$
$42$	−5.99904	−	1.30505i	−0.925672	−	0.201374i
$43$	−0.226097	+	0.226097i	−0.0344794	+	0.0344794i	−0.724136	−	0.689657i	$-0.757761\pi$
$43$	−0.226097	+	0.226097i	−0.0344794	+	0.0344794i	0.689657	+	0.724136i	$0.257761\pi$
$44$	0.751405			0.113279
$45$	−6.54752	−	1.45947i	−0.976046	−	0.217565i
$46$	−11.1228			−1.63997
$47$	8.19848	−	8.19848i	1.19587	−	1.19587i	0.220480	−	0.975391i	$-0.429238\pi$
$47$	8.19848	−	8.19848i	1.19587	−	1.19587i	0.975391	−	0.220480i	$-0.0707624\pi$
$48$	−6.27290	−	1.36463i	−0.905415	−	0.196967i
$49$		−	3.96332i		−	0.566189i
$50$	−3.65126	+	9.49225i	−0.516366	+	1.34241i
$51$	−3.13800	+	2.01664i	−0.439408	+	0.282386i
$52$	−0.387632	−	0.387632i	−0.0537549	−	0.0537549i
$53$	2.43700	+	2.43700i	0.334747	+	0.334747i	0.854386	−	0.519639i	$-0.173933\pi$
$53$	2.43700	+	2.43700i	0.334747	+	0.334747i	−0.519639	+	0.854386i	$0.673933\pi$
$54$	10.4617	−	1.50395i	1.42366	−	0.204662i
$55$	−0.163174	−	0.768978i	−0.0220023	−	0.103689i
$56$		−	0.486948i		−	0.0650711i
$57$	0.368185	−	1.69247i	0.0487673	−	0.224173i
$58$	−11.0787	+	11.0787i	−1.45470	+	1.45470i
$59$	−5.37432			−0.699677			−0.349839	−	0.936810i	$-0.613764\pi$
$59$	−5.37432			−0.699677			−0.349839	+	0.936810i	$0.613764\pi$
$60$	0.0423193	−	8.27792i	0.00546339	−	1.06868i
$61$	11.0661			1.41687			0.708437	−	0.705774i	$-0.249401\pi$
$61$	11.0661			1.41687			0.708437	+	0.705774i	$0.249401\pi$
$62$	6.07611	−	6.07611i	0.771667	−	0.771667i
$63$	−1.82687	−	4.89823i	−0.230164	−	0.617119i
$64$		−	9.05869i		−	1.13234i
$65$	−0.312520	+	0.480874i	−0.0387633	+	0.0596451i
$66$	0.669607	+	1.04194i	0.0824230	+	0.128255i
$67$	−5.18430	−	5.18430i	−0.633363	−	0.633363i	0.315547	−	0.948910i	$-0.397812\pi$
$67$	−5.18430	−	5.18430i	−0.633363	−	0.633363i	−0.948910	+	0.315547i	$0.897812\pi$
$68$	−3.25484	−	3.25484i	−0.394708	−	0.394708i
$69$	−5.12056	−	7.96787i	−0.616443	−	0.959219i
$70$	−7.75324	+	1.64520i	−0.926690	+	0.196639i
$71$		−	14.9920i		−	1.77923i	−0.456714	−	0.889614i	$-0.650974\pi$
$71$		−	14.9920i		−	1.77923i	0.456714	−	0.889614i	$-0.349026\pi$
$72$	0.292948	+	0.785457i	0.0345243	+	0.0925670i
$73$	6.94178	−	6.94178i	0.812474	−	0.812474i	−0.172531	−	0.985004i	$-0.555194\pi$
$73$	6.94178	−	6.94178i	0.812474	−	0.812474i	0.985004	+	0.172531i	$0.0551943\pi$
$74$	−5.46459			−0.635245
$75$	−8.48071	+	1.75431i	−0.979268	+	0.202570i
$76$	2.13738			0.245174
$77$	0.433189	−	0.433189i	0.0493664	−	0.0493664i
$78$	0.192080	−	0.882948i	0.0217488	−	0.0999742i
$79$		−	3.78981i		−	0.426387i	−0.977010	−	0.213193i	$-0.931614\pi$
$79$		−	3.78981i		−	0.426387i	0.977010	−	0.213193i	$-0.0683864\pi$
$80$	−8.10718	+	1.72031i	−0.906411	+	0.192336i
$81$	5.89356	+	6.80191i	0.654840	+	0.755767i
$82$	8.80253	+	8.80253i	0.972077	+	0.972077i
$83$	7.19514	+	7.19514i	0.789769	+	0.789769i	0.981456	−	0.191687i	$-0.0613958\pi$
$83$	7.19514	+	7.19514i	0.789769	+	0.789769i	−0.191687	+	0.981456i	$0.561396\pi$
$84$	5.42713	−	3.48775i	0.592149	−	0.380545i
$85$	−2.62415	+	4.03778i	−0.284629	+	0.437958i
$86$		−	0.650387i		−	0.0701330i
$87$	−13.0364	−	2.83600i	−1.39765	−	0.304051i
$88$	−0.0694641	+	0.0694641i	−0.00740490	+	0.00740490i
$89$	−17.9313			−1.90072			−0.950358	−	0.311160i	$-0.899283\pi$
$89$	−17.9313			−1.90072			−0.950358	+	0.311160i	$0.899283\pi$
$90$	11.5164	−	7.31811i	1.21393	−	0.771396i
$91$	−0.446943			−0.0468524
$92$	8.26455	−	8.26455i	0.861639	−	0.861639i
$93$	7.14987	+	1.55541i	0.741407	+	0.161288i
$94$			23.5837i			2.43247i
$95$	−0.464149	−	2.18737i	−0.0476207	−	0.224419i
$96$	11.7994	−	7.58287i	1.20427	−	0.773923i
$97$	9.20451	+	9.20451i	0.934576	+	0.934576i	0.997987	−	0.0634115i	$-0.0201981\pi$
$97$	9.20451	+	9.20451i	0.934576	+	0.934576i	−0.0634115	+	0.997987i	$0.520198\pi$
$98$	5.70042	+	5.70042i	0.575829	+	0.575829i
$99$	−0.438136	+	0.959350i	−0.0440343	+	0.0964183i
$100$	−4.34000	−	9.76597i	−0.434000	−	0.976597i
$101$		−	5.36602i		−	0.533939i	−0.963705	−	0.266969i	$-0.913978\pi$
$101$		−	5.36602i		−	0.533939i	0.963705	−	0.266969i	$-0.0860222\pi$
$102$	1.61284	−	7.41388i	0.159695	−	0.734084i
$103$	0.661659	−	0.661659i	0.0651952	−	0.0651952i	−0.673757	−	0.738953i	$-0.735321\pi$
$103$	0.661659	−	0.661659i	0.0651952	−	0.0651952i	0.738953	+	0.673757i	$0.235321\pi$
$104$	0.0716697			0.00702779
$105$	−4.74787	−	4.79666i	−0.463344	−	0.468106i
$106$	−7.01024			−0.680894
$107$	−2.98489	+	2.98489i	−0.288560	+	0.288560i	−0.836511	−	0.547950i	$-0.815408\pi$
$107$	−2.98489	+	2.98489i	−0.288560	+	0.288560i	0.547950	+	0.836511i	$0.315408\pi$
$108$	−6.65585	+	8.89079i	−0.640459	+	0.855517i
$109$			15.3648i			1.47168i	0.677154	+	0.735841i	$0.263213\pi$
$109$			15.3648i			1.47168i	−0.677154	+	0.735841i	$0.736787\pi$
$110$	1.34071	+	0.871325i	0.127831	+	0.0830775i
$111$	−2.51570	−	3.91457i	−0.238780	−	0.371555i
$112$	−4.56702	−	4.56702i	−0.431543	−	0.431543i
$113$	12.5987	+	12.5987i	1.18519	+	1.18519i	0.978382	+	0.206807i	$0.0663073\pi$
$113$	12.5987	+	12.5987i	1.18519	+	1.18519i	0.206807	+	0.978382i	$0.433693\pi$
$114$	1.90470	+	2.96382i	0.178392	+	0.277587i
$115$	−10.2525	−	6.66312i	−0.956055	−	0.621339i
$116$		−	16.4635i		−	1.52859i
$117$	0.720929	−	0.268882i	0.0666499	−	0.0248581i
$118$	7.72986	−	7.72986i	0.711591	−	0.711591i
$119$	−3.75286			−0.344024
$120$	0.761346	+	0.769170i	0.0695010	+	0.0702153i
$121$	10.8764			0.988764
$122$	−15.9164	+	15.9164i	−1.44100	+	1.44100i
$123$	−2.25334	+	10.3581i	−0.203177	+	0.933957i
$124$			9.02941i			0.810865i
$125$	−9.05189	+	6.56226i	−0.809626	+	0.586946i
$126$	9.67267	+	4.41752i	0.861710	+	0.393544i
$127$	−2.44477	−	2.44477i	−0.216938	−	0.216938i	0.590269	−	0.807207i	$-0.299022\pi$
$127$	−2.44477	−	2.44477i	−0.216938	−	0.216938i	−0.807207	+	0.590269i	$0.799022\pi$
$128$	1.57700	+	1.57700i	0.139389	+	0.139389i
$129$	0.465906	−	0.299415i	0.0410208	−	0.0263621i
$130$	−0.242144	−	1.14113i	−0.0212374	−	0.100084i
$131$			19.1466i			1.67285i	0.548082	+	0.836424i	$0.315358\pi$
$131$			19.1466i			1.67285i	−0.548082	+	0.836424i	$0.684642\pi$
$132$	−1.27173	−	0.276656i	−0.110690	−	0.0240798i
$133$	1.23221	−	1.23221i	0.106846	−	0.106846i
$134$	14.9131			1.28830
$135$	10.5441	+	4.88080i	0.907491	+	0.420072i
$136$	0.601792			0.0516032
$137$	−3.89420	+	3.89420i	−0.332704	+	0.332704i	−0.853613	−	0.520908i	$-0.825593\pi$
$137$	−3.89420	+	3.89420i	−0.332704	+	0.332704i	0.520908	+	0.853613i	$0.325593\pi$
$138$	18.8250	+	4.09526i	1.60249	+	0.348612i
$139$		−	1.97780i		−	0.167755i	−0.996476	−	0.0838776i	$-0.973270\pi$
$139$		−	1.97780i		−	0.167755i	0.996476	−	0.0838776i	$-0.0267305\pi$
$140$	4.53843	−	6.98329i	0.383567	−	0.590196i
$141$	−16.8942	+	10.8571i	−1.42275	+	0.914332i
$142$	21.5630	+	21.5630i	1.80952	+	1.80952i
$143$	0.0637574	+	0.0637574i	0.00533166	+	0.00533166i
$144$	10.1142	+	4.61918i	0.842853	+	0.384932i
$145$	−16.8485	+	3.57517i	−1.39919	+	0.296902i
$146$			19.9686i			1.65262i
$147$	−1.45924	+	6.70778i	−0.120356	+	0.553249i
$148$	4.06033	−	4.06033i	0.333757	−	0.333757i
$149$	−2.29450			−0.187973			−0.0939866	−	0.995573i	$-0.529961\pi$
$149$	−2.29450			−0.187973			−0.0939866	+	0.995573i	$0.529961\pi$
$150$	9.67454	−	14.7210i	0.789923	−	1.20196i
$151$	11.0214			0.896909			0.448454	−	0.893806i	$-0.351975\pi$
$151$	11.0214			0.896909			0.448454	+	0.893806i	$0.351975\pi$
$152$	−0.197591	+	0.197591i	−0.0160268	+	0.0160268i
$153$	6.05345	−	2.25773i	0.489393	−	0.182526i
$154$			1.24611i			0.100414i
$155$	9.24058	−	1.96081i	0.742221	−	0.157496i
$156$	0.513333	+	0.798774i	0.0410995	+	0.0639531i
$157$	−13.2385	−	13.2385i	−1.05655	−	1.05655i	−0.998302	−	0.0582450i	$-0.981450\pi$
$157$	−13.2385	−	13.2385i	−1.05655	−	1.05655i	−0.0582450	−	0.998302i	$-0.518550\pi$
$158$	5.45086	+	5.45086i	0.433647	+	0.433647i
$159$	−3.22727	−	5.02180i	−0.255939	−	0.398255i
$160$	9.86719	−	15.1827i	0.780070	−	1.20029i
$161$		−	9.52911i		−	0.750999i
$162$	−18.2598	−	1.30646i	−1.43463	−	0.102646i
$163$	4.18678	−	4.18678i	0.327934	−	0.327934i	−0.523867	−	0.851800i	$-0.675511\pi$
$163$	4.18678	−	4.18678i	0.327934	−	0.327934i	0.851800	+	0.523867i	$0.175511\pi$
$164$	−13.0810			−1.02146
$165$	−0.00696064	+	1.36155i	−0.000541885	+	0.105996i
$166$	−20.6975			−1.60643
$167$	9.30946	−	9.30946i	0.720388	−	0.720388i	−0.248296	−	0.968684i	$-0.579871\pi$
$167$	9.30946	−	9.30946i	0.720388	−	0.720388i	0.968684	+	0.248296i	$0.0798706\pi$
$168$	−0.179287	+	0.824142i	−0.0138323	+	0.0635839i
$169$			12.9342i			0.994940i
$170$	−2.03322	−	9.58180i	−0.155940	−	0.734891i
$171$	−1.24628	+	2.72888i	−0.0953056	+	0.208683i
$172$	0.483254	+	0.483254i	0.0368478	+	0.0368478i
$173$	−5.23789	−	5.23789i	−0.398229	−	0.398229i	0.479379	−	0.877608i	$-0.340862\pi$
$173$	−5.23789	−	5.23789i	−0.398229	−	0.398229i	−0.877608	+	0.479379i	$0.840862\pi$
$174$	22.8292	−	14.6712i	1.73068	−	1.11222i
$175$	−8.13216	−	3.12809i	−0.614733	−	0.236462i
$176$			1.30299i			0.0982166i
$177$	9.09586	+	1.97875i	0.683687	+	0.148732i
$178$	25.7905	−	25.7905i	1.93308	−	1.93308i
$179$	−3.71181			−0.277434			−0.138717	−	0.990332i	$-0.544298\pi$
$179$	−3.71181			−0.277434			−0.138717	+	0.990332i	$0.544298\pi$
$180$	−3.11943	+	13.9945i	−0.232509	+	1.04309i
$181$	19.2249			1.42898			0.714488	−	0.699648i	$-0.246660\pi$
$181$	19.2249			1.42898			0.714488	+	0.699648i	$0.246660\pi$
$182$	0.642836	−	0.642836i	0.0476501	−	0.0476501i
$183$	−18.7291	−	4.07439i	−1.38449	−	0.301188i
$184$			1.52804i			0.112649i
$185$	−5.03702	−	3.27355i	−0.370329	−	0.240676i
$186$	−12.5207	+	8.04647i	−0.918066	+	0.589996i
$187$	0.535354	+	0.535354i	0.0391490	+	0.0391490i
$188$	−17.5233	−	17.5233i	−1.27802	−	1.27802i
$189$	1.28846	+	8.96271i	0.0937215	+	0.651941i
$190$	3.81366	+	2.47849i	0.276672	+	0.179809i
$191$		−	20.3995i		−	1.47606i	−0.674770	−	0.738028i	$-0.735757\pi$
$191$		−	20.3995i		−	1.47606i	0.674770	−	0.738028i	$-0.264243\pi$
$192$	−3.33528	+	15.3315i	−0.240703	+	1.10646i
$193$	7.55435	−	7.55435i	0.543774	−	0.543774i	−0.380859	−	0.924633i	$-0.624372\pi$
$193$	7.55435	−	7.55435i	0.543774	−	0.543774i	0.924633	+	0.380859i	$0.124372\pi$
$194$	−26.4776			−1.90098
$195$	0.705980	−	0.698798i	0.0505563	−	0.0500420i
$196$	−8.47112			−0.605080
$197$	14.7537	−	14.7537i	1.05116	−	1.05116i	0.0525373	−	0.998619i	$-0.483269\pi$
$197$	14.7537	−	14.7537i	1.05116	−	1.05116i	0.998619	−	0.0525373i	$-0.0167308\pi$
$198$	−0.749658	−	2.01000i	−0.0532759	−	0.142844i
$199$			4.57329i			0.324192i	0.986775	+	0.162096i	$0.0518254\pi$
$199$			4.57329i			0.324192i	−0.986775	+	0.162096i	$0.948175\pi$
$200$	1.30403	+	0.501606i	0.0922092	+	0.0354689i
$201$	6.86547	+	10.6830i	0.484253	+	0.753523i
$202$	7.71791	+	7.71791i	0.543030	+	0.543030i
$203$	−9.49126	−	9.49126i	−0.666156	−	0.666156i
$204$	4.31032	+	6.70709i	0.301783	+	0.469590i
$205$	2.84065	+	13.3869i	0.198399	+	0.934984i
$206$			1.90332i			0.132611i
$207$	5.73272	+	15.3707i	0.398452	+	1.06833i
$208$	0.672181	−	0.672181i	0.0466074	−	0.0466074i
$209$	−0.351554			−0.0243175
$210$	13.7278	+	0.0701809i	0.947311	+	0.00484294i
$211$	−17.0641			−1.17474			−0.587370	−	0.809319i	$-0.699836\pi$
$211$	−17.0641			−1.17474			−0.587370	+	0.809319i	$0.699836\pi$
$212$	5.20879	−	5.20879i	0.357741	−	0.357741i
$213$	−5.51985	+	25.3735i	−0.378214	+	1.73856i
$214$		−	8.58630i		−	0.586948i
$215$	0.389614	−	0.599499i	0.0265714	−	0.0408855i
$216$	−0.206611	−	1.43722i	−0.0140581	−	0.0977903i
$217$	5.20550	+	5.20550i	0.353372	+	0.353372i
$218$	−22.0991	−	22.0991i	−1.49674	−	1.49674i
$219$	−14.3046	+	9.19286i	−0.966614	+	0.621196i
$220$	−1.64360	+	0.348764i	−0.110811	+	0.0235137i
$221$		−	0.552352i		−	0.0371552i
$222$	9.24863	+	2.01198i	0.620727	+	0.135035i
$223$	16.1518	−	16.1518i	1.08160	−	1.08160i	0.0852434	−	0.996360i	$-0.472833\pi$
$223$	16.1518	−	16.1518i	1.08160	−	1.08160i	0.996360	−	0.0852434i	$-0.0271668\pi$
$224$	14.1113			0.942853
$225$	14.9992	+	0.153365i	0.999948	+	0.0102243i
$226$	−36.2414			−2.41074
$227$	−9.07842	+	9.07842i	−0.602556	+	0.602556i	−0.940990	−	0.338434i	$-0.890103\pi$
$227$	−9.07842	+	9.07842i	−0.602556	+	0.602556i	0.338434	+	0.940990i	$0.390103\pi$
$228$	−3.61744	−	0.786952i	−0.239571	−	0.0521171i
$229$		−	13.3378i		−	0.881388i	−0.897657	−	0.440694i	$-0.854732\pi$
$229$		−	13.3378i		−	0.881388i	0.897657	−	0.440694i	$-0.145268\pi$
$230$	24.3297	−	5.16265i	1.60425	−	0.340415i
$231$	−0.892651	+	0.573663i	−0.0587321	+	0.0377443i
$232$	1.52197	+	1.52197i	0.0999225	+	0.0999225i
$233$	4.65087	+	4.65087i	0.304688	+	0.304688i	0.842845	−	0.538156i	$-0.180879\pi$
$233$	4.65087	+	4.65087i	0.304688	+	0.304688i	−0.538156	+	0.842845i	$0.680879\pi$
$234$	−0.650177	+	1.42364i	−0.0425034	+	0.0930662i
$235$	−14.1278	+	21.7384i	−0.921593	+	1.41806i
$236$			11.4870i			0.747738i
$237$	−1.39535	+	6.41412i	−0.0906379	+	0.416642i
$238$	5.39772	−	5.39772i	0.349882	−	0.349882i
$239$	0.155287			0.0100447			0.00502235	−	0.999987i	$-0.498401\pi$
$239$	0.155287			0.0100447			0.00502235	+	0.999987i	$0.498401\pi$
$240$	14.3545	+	0.0733847i	0.926580	+	0.00473696i
$241$	9.96653			0.642001			0.321000	−	0.947079i	$-0.395981\pi$
$241$	9.96653			0.642001			0.321000	+	0.947079i	$0.395981\pi$
$242$	−15.6435	+	15.6435i	−1.00560	+	1.00560i
$243$	−7.47029	−	13.6819i	−0.479219	−	0.877695i
$244$		−	23.6525i		−	1.51420i
$245$	1.83957	+	8.66923i	0.117526	+	0.553857i
$246$	−11.6570	−	18.1389i	−0.743224	−	1.15650i
$247$	0.181358	+	0.181358i	0.0115396	+	0.0115396i
$248$	−0.834730	−	0.834730i	−0.0530054	−	0.0530054i
$249$	−9.52838	−	14.8267i	−0.603837	−	0.939602i
$250$	3.58082	−	22.4577i	0.226471	−	1.42035i
$251$		−	22.5815i		−	1.42533i	−0.701503	−	0.712667i	$-0.747487\pi$
$251$		−	22.5815i		−	1.42533i	0.701503	−	0.712667i	$-0.252513\pi$
$252$	−10.4694	+	3.90471i	−0.659509	+	0.245974i
$253$	−1.35935	+	1.35935i	−0.0854614	+	0.0854614i
$254$	7.03260			0.441264
$255$	5.92793	−	5.86763i	0.371221	−	0.367445i
$256$	13.5810			0.848813
$257$	−2.95901	+	2.95901i	−0.184578	+	0.184578i	−0.793347	−	0.608769i	$-0.791664\pi$
$257$	−2.95901	+	2.95901i	−0.184578	+	0.184578i	0.608769	+	0.793347i	$0.291664\pi$
$258$	−0.239463	+	1.10076i	−0.0149083	+	0.0685302i
$259$		−	4.68160i		−	0.290900i
$260$	1.02781	+	0.667973i	0.0637421	+	0.0414259i
$261$	21.0196	+	9.59966i	1.30108	+	0.594204i
$262$	−27.5385	−	27.5385i	−1.70133	−	1.70133i
$263$	3.52891	+	3.52891i	0.217602	+	0.217602i	0.807487	−	0.589885i	$-0.200827\pi$
$263$	3.52891	+	3.52891i	0.217602	+	0.217602i	−0.589885	+	0.807487i	$0.700827\pi$
$264$	0.143141	−	0.0919899i	0.00880974	−	0.00566159i
$265$	−6.46173	−	4.19947i	−0.396941	−	0.257972i
$266$			3.54456i			0.217331i
$267$	30.3481	+	6.60205i	1.85728	+	0.404039i
$268$	−11.0808	+	11.0808i	−0.676869	+	0.676869i
$269$	15.2648			0.930711			0.465355	−	0.885124i	$-0.345927\pi$
$269$	15.2648			0.930711			0.465355	+	0.885124i	$0.345927\pi$
$270$	−22.1855	+	8.14548i	−1.35017	+	0.495718i
$271$	−29.1239			−1.76915			−0.884577	−	0.466395i	$-0.845553\pi$
$271$	−29.1239			−1.76915			−0.884577	+	0.466395i	$0.845553\pi$
$272$	5.64413	−	5.64413i	0.342226	−	0.342226i
$273$	0.756436	+	0.164558i	0.0457816	+	0.00995950i
$274$		−	11.2020i		−	0.676739i
$275$	0.713841	+	1.60630i	0.0430462	+	0.0968634i
$276$	−17.0304	+	10.9446i	−1.02511	+	0.658786i
$277$	−7.89347	−	7.89347i	−0.474273	−	0.474273i	0.429022	−	0.903294i	$-0.358858\pi$
$277$	−7.89347	−	7.89347i	−0.474273	−	0.474273i	−0.903294	+	0.429022i	$0.858858\pi$
$278$	2.84466	+	2.84466i	0.170612	+	0.170612i
$279$	−11.5282	−	5.26495i	−0.690177	−	0.315204i
$280$	0.226016	+	1.06513i	0.0135071	+	0.0636538i
$281$			10.3368i			0.616644i	0.951282	+	0.308322i	$0.0997674\pi$
$281$			10.3368i			0.616644i	−0.951282	+	0.308322i	$0.900233\pi$
$282$	8.68316	−	39.9145i	0.517074	−	2.37688i
$283$	−17.9562	+	17.9562i	−1.06739	+	1.06739i	−0.0698264	+	0.997559i	$0.522245\pi$
$283$	−17.9562	+	17.9562i	−1.06739	+	1.06739i	−0.997559	+	0.0698264i	$0.977755\pi$
$284$	−32.0437			−1.90144
$285$	−0.0197996	+	3.87293i	−0.00117283	+	0.229413i
$286$	−0.183404			−0.0108449
$287$	−7.54127	+	7.54127i	−0.445147	+	0.445147i
$288$	−22.7619	+	8.48940i	−1.34126	+	0.500243i
$289$			12.3620i			0.727179i
$290$	19.0909	−	29.3752i	1.12106	−	1.72497i
$291$	−12.1893	−	18.9673i	−0.714552	−	1.11188i
$292$	−14.8372	−	14.8372i	−0.868282	−	0.868282i
$293$	−4.98025	−	4.98025i	−0.290949	−	0.290949i	0.546506	−	0.837455i	$-0.315958\pi$
$293$	−4.98025	−	4.98025i	−0.290949	−	0.290949i	−0.837455	+	0.546506i	$0.815958\pi$
$294$	−7.54895	−	11.7466i	−0.440264	−	0.685074i
$295$	11.7556	−	2.49449i	0.684438	−	0.145235i
$296$			0.750719i			0.0436347i
$297$	1.09475	−	1.46235i	0.0635238	−	0.0848542i
$298$	3.30017	−	3.30017i	0.191174	−	0.191174i
$299$	1.40251			0.0811092
$300$	3.74962	+	18.1265i	0.216485	+	1.04653i
$301$	0.557197			0.0321163
$302$	−15.8520	+	15.8520i	−0.912181	+	0.912181i
$303$	−1.97569	+	9.08180i	−0.113500	+	0.521736i
$304$			3.70637i			0.212575i
$305$	−24.2057	+	5.13634i	−1.38601	+	0.294106i
$306$	−5.45937	+	11.9539i	−0.312091	+	0.683360i
$307$	16.4404	+	16.4404i	0.938304	+	0.938304i	0.998204	−	0.0599002i	$-0.0190782\pi$
$307$	16.4404	+	16.4404i	0.938304	+	0.938304i	−0.0599002	+	0.998204i	$0.519078\pi$
$308$	−0.925888	−	0.925888i	−0.0527574	−	0.0527574i
$309$	−1.36345	+	0.876222i	−0.0775638	+	0.0498465i
$310$	−10.4705	+	16.1109i	−0.594682	+	0.915037i
$311$			16.5978i			0.941176i	0.882353	+	0.470588i	$0.155958\pi$
$311$			16.5978i			0.941176i	−0.882353	+	0.470588i	$0.844042\pi$
$312$	−0.121299	−	0.0263877i	−0.00686718	−	0.00149391i
$313$	−4.89675	+	4.89675i	−0.276781	+	0.276781i	−0.831822	−	0.555042i	$-0.812702\pi$
$313$	−4.89675	+	4.89675i	−0.276781	+	0.276781i	0.555042	+	0.831822i	$0.312702\pi$
$314$	38.0817			2.14908
$315$	6.26954	+	9.86628i	0.353249	+	0.555902i
$316$	−8.10026			−0.455675
$317$	20.4161	−	20.4161i	1.14668	−	1.14668i	0.159480	−	0.987201i	$-0.449018\pi$
$317$	20.4161	−	20.4161i	1.14668	−	1.14668i	0.987201	−	0.159480i	$-0.0509817\pi$
$318$	11.8646	+	2.58107i	0.665333	+	0.144739i
$319$			2.70790i			0.151613i
$320$	4.20458	+	19.8147i	0.235043	+	1.10767i
$321$	6.15082	−	3.95283i	0.343305	−	0.220626i
$322$	13.7057	+	13.7057i	0.763786	+	0.763786i
$323$	1.52282	+	1.52282i	0.0847319	+	0.0847319i
$324$	14.5382	−	12.5968i	0.807681	−	0.699821i
$325$	0.460398	−	1.19690i	0.0255383	−	0.0663923i
$326$			12.0436i			0.667035i
$327$	5.65710	−	26.0044i	0.312838	−	1.43805i
$328$	1.20928	−	1.20928i	0.0667714	−	0.0667714i
$329$	−20.2045			−1.11391
$330$	−1.94829	−	1.96832i	−0.107250	−	0.108352i
$331$	16.2044			0.890676			0.445338	−	0.895363i	$-0.353084\pi$
$331$	16.2044			0.890676			0.445338	+	0.895363i	$0.353084\pi$
$332$	15.3787	−	15.3787i	0.844018	−	0.844018i
$333$	2.81646	+	7.55152i	0.154341	+	0.413821i
$334$			26.7795i			1.46531i
$335$	13.7463	+	8.93367i	0.751038	+	0.488099i
$336$	6.04802	+	9.41104i	0.329946	+	0.513414i
$337$	−10.6952	−	10.6952i	−0.582603	−	0.582603i	0.353015	−	0.935618i	$-0.385156\pi$
$337$	−10.6952	−	10.6952i	−0.582603	−	0.582603i	−0.935618	+	0.353015i	$0.885156\pi$
$338$	−18.6032	−	18.6032i	−1.01188	−	1.01188i
$339$	−16.6843	−	25.9616i	−0.906164	−	1.41004i
$340$	8.63026	+	5.60880i	0.468041	+	0.304180i
$341$		−	1.48515i		−	0.0804255i
$342$	−2.13241	−	5.71745i	−0.115308	−	0.309164i
$343$	−13.5091	+	13.5091i	−0.729423	+	0.729423i
$344$	−0.0893495			−0.00481740
$345$	14.8988	+	15.0519i	0.802125	+	0.810369i
$346$	15.0672			0.810020
$347$	8.24391	−	8.24391i	0.442556	−	0.442556i	−0.450314	−	0.892870i	$-0.648688\pi$
$347$	8.24391	−	8.24391i	0.442556	−	0.442556i	0.892870	+	0.450314i	$0.148688\pi$
$348$	−6.06160	+	27.8638i	−0.324936	+	1.49366i
$349$		−	13.0746i		−	0.699868i	−0.936774	−	0.349934i	$-0.886204\pi$
$349$		−	13.0746i		−	0.699868i	0.936774	−	0.349934i	$-0.113796\pi$
$350$	16.1956	−	7.19732i	0.865689	−	0.384713i
$351$	−1.31915	+	0.189637i	−0.0704108	+	0.0101221i
$352$	−2.01301	−	2.01301i	−0.107294	−	0.107294i
$353$	3.33449	+	3.33449i	0.177477	+	0.177477i	0.790255	−	0.612778i	$-0.209948\pi$
$353$	3.33449	+	3.33449i	0.177477	+	0.177477i	−0.612778	+	0.790255i	$0.709948\pi$
$354$	−15.9285	+	10.2365i	−0.846592	+	0.544064i
$355$	6.95854	+	32.7930i	0.369321	+	1.74047i
$356$			38.3260i			2.03127i
$357$	6.35159	+	1.38175i	0.336162	+	0.0731299i
$358$	5.33868	−	5.33868i	0.282158	−	0.282158i
$359$	31.8869			1.68292			0.841462	−	0.540316i	$-0.181695\pi$
$359$	31.8869			1.68292			0.841462	+	0.540316i	$0.181695\pi$
$360$	−1.00535	−	1.58211i	−0.0529868	−	0.0833845i
$361$	−1.00000			−0.0526316
$362$	−27.6511	+	27.6511i	−1.45331	+	1.45331i
$363$	−18.4079	−	4.00453i	−0.966167	−	0.210184i
$364$			0.955287i			0.0500706i
$365$	−11.9622	+	18.4062i	−0.626129	+	0.963426i
$366$	32.7981	−	21.0777i	1.71438	−	1.10175i
$367$	−0.808859	−	0.808859i	−0.0422221	−	0.0422221i	0.685681	−	0.727903i	$-0.259505\pi$
$367$	−0.808859	−	0.808859i	−0.0422221	−	0.0422221i	−0.727903	+	0.685681i	$0.759505\pi$
$368$	14.3313	+	14.3313i	0.747072	+	0.747072i
$369$	7.62739	−	16.7011i	0.397066	−	0.869423i
$370$	11.9530	−	2.53638i	0.621409	−	0.131860i
$371$		−	6.00578i		−	0.311805i
$372$	3.32450	−	15.2820i	0.172367	−	0.792333i
$373$	−17.3546	+	17.3546i	−0.898586	+	0.898586i	−0.995311	−	0.0967255i	$-0.969163\pi$
$373$	−17.3546	+	17.3546i	−0.898586	+	0.898586i	0.0967255	+	0.995311i	$0.469163\pi$
$374$	−1.53999			−0.0796311
$375$	17.7361	−	7.77363i	0.915890	−	0.401428i
$376$	3.23990			0.167085
$377$	1.39694	−	1.39694i	0.0719460	−	0.0719460i
$378$	−14.7442	−	11.0378i	−0.758360	−	0.567725i
$379$			5.07732i			0.260804i	0.991461	+	0.130402i	$0.0416269\pi$
$379$			5.07732i			0.260804i	−0.991461	+	0.130402i	$0.958373\pi$
$380$	−4.67523	+	0.992062i	−0.239834	+	0.0508917i
$381$	3.23756	+	5.03782i	0.165865	+	0.258095i
$382$	29.3405	+	29.3405i	1.50119	+	1.50119i
$383$	−18.5033	−	18.5033i	−0.945474	−	0.945474i	0.0531142	−	0.998588i	$-0.483085\pi$
$383$	−18.5033	−	18.5033i	−0.945474	−	0.945474i	−0.998588	+	0.0531142i	$0.983085\pi$
$384$	−2.08839	−	3.24965i	−0.106573	−	0.165833i
$385$	−0.746478	+	1.14861i	−0.0380440	+	0.0585384i
$386$			21.7308i			1.10607i
$387$	−0.898771	+	0.335210i	−0.0456871	+	0.0170397i
$388$	19.6735	−	19.6735i	0.998771	−	0.998771i
$389$	−2.18736			−0.110903			−0.0554517	−	0.998461i	$-0.517660\pi$
$389$	−2.18736			−0.110903			−0.0554517	+	0.998461i	$0.517660\pi$
$390$	−0.0103293	+	2.02048i	−0.000523046	+	0.102311i
$391$	11.7765			0.595563
$392$	0.783118	−	0.783118i	0.0395534	−	0.0395534i
$393$	7.04951	−	32.4050i	0.355601	−	1.63462i
$394$			42.4403i			2.13811i
$395$	1.75904	+	8.28970i	0.0885067	+	0.417100i
$396$	2.05049	+	0.936463i	0.103041	+	0.0470590i
$397$	13.4240	+	13.4240i	0.673730	+	0.673730i	0.958574	−	0.284844i	$-0.0919418\pi$
$397$	13.4240	+	13.4240i	0.673730	+	0.673730i	−0.284844	+	0.958574i	$0.591942\pi$
$398$	−6.57774	−	6.57774i	−0.329712	−	0.329712i
$399$	−2.53915	+	1.63179i	−0.127117	+	0.0816917i
$400$	16.9349	−	7.52588i	0.846744	−	0.376294i
$401$		−	30.9472i		−	1.54543i	−0.634753	−	0.772715i	$-0.718898\pi$
$401$		−	30.9472i		−	1.54543i	0.634753	−	0.772715i	$-0.281102\pi$
$402$	−25.2399	−	5.49079i	−1.25885	−	0.273855i
$403$	−0.766154	+	0.766154i	−0.0381648	+	0.0381648i
$404$	−11.4692			−0.570614
$405$	−16.0485	−	12.1428i	−0.797455	−	0.603379i
$406$	27.3024			1.35500
$407$	−0.667840	+	0.667840i	−0.0331036	+	0.0331036i
$408$	−1.01851	−	0.221571i	−0.0504238	−	0.0109694i
$409$		−	19.3750i		−	0.958034i	−0.877806	−	0.479017i	$-0.840993\pi$
$409$		−	19.3750i		−	0.958034i	0.877806	−	0.479017i	$-0.159007\pi$
$410$	−23.3400	−	15.1687i	−1.15268	−	0.749127i
$411$	8.02459	−	5.15702i	0.395824	−	0.254377i
$412$	−1.41422	−	1.41422i	−0.0696734	−	0.0696734i
$413$	6.62229	+	6.62229i	0.325862	+	0.325862i
$414$	−30.3529	−	13.8622i	−1.49176	−	0.681289i
$415$	−19.0780	−	12.3988i	−0.936503	−	0.608632i
$416$			2.07693i			0.101830i
$417$	−0.728198	+	3.34737i	−0.0356600	+	0.163921i
$418$	0.505639	−	0.505639i	0.0247316	−	0.0247316i
$419$	−1.26019			−0.0615642			−0.0307821	−	0.999526i	$-0.509800\pi$
$419$	−1.26019			−0.0615642			−0.0307821	+	0.999526i	$0.509800\pi$
$420$	−10.2523	+	10.1480i	−0.500260	+	0.495171i
$421$	−28.0921			−1.36912			−0.684562	−	0.728955i	$-0.740006\pi$
$421$	−28.0921			−1.36912			−0.684562	+	0.728955i	$0.740006\pi$
$422$	24.5431	−	24.5431i	1.19474	−	1.19474i
$423$	32.5903	−	12.1550i	1.58459	−	0.590999i
$424$			0.963059i			0.0467703i
$425$	3.86584	−	10.0501i	0.187521	−	0.487501i
$426$	−28.5554	−	44.4337i	−1.38351	−	2.15282i
$427$	−13.6358	−	13.6358i	−0.659882	−	0.659882i
$428$	6.37985	+	6.37985i	0.308381	+	0.308381i
$429$	−0.0844326	−	0.131382i	−0.00407645	−	0.00634317i
$430$	0.301876	+	1.42263i	0.0145578	+	0.0686055i
$431$			21.6156i			1.04118i	0.853805	+	0.520592i	$0.174289\pi$
$431$			21.6156i			1.04118i	−0.853805	+	0.520592i	$0.825711\pi$
$432$	−15.4173	−	11.5417i	−0.741764	−	0.555301i
$433$	10.9345	−	10.9345i	0.525478	−	0.525478i	−0.393743	−	0.919221i	$-0.628820\pi$
$433$	10.9345	−	10.9345i	0.525478	−	0.525478i	0.919221	+	0.393743i	$0.128820\pi$
$434$	−14.9741			−0.718779
$435$	29.8318	+	0.152509i	1.43033	+	0.00731226i
$436$	32.8404			1.57277
$437$	−3.86668	+	3.86668i	−0.184968	+	0.184968i
$438$	7.35216	−	33.7962i	0.351300	−	1.61485i
$439$		−	26.4490i		−	1.26234i	−0.775644	−	0.631171i	$-0.782575\pi$
$439$		−	26.4490i		−	1.26234i	0.775644	−	0.631171i	$-0.217425\pi$
$440$	0.119702	−	0.184185i	0.00570655	−	0.00878068i
$441$	4.93941	−	10.8154i	0.235210	−	0.515020i
$442$	0.794445	+	0.794445i	0.0377879	+	0.0377879i
$443$	−6.49327	−	6.49327i	−0.308505	−	0.308505i	0.535825	−	0.844329i	$-0.320001\pi$
$443$	−6.49327	−	6.49327i	−0.308505	−	0.308505i	−0.844329	+	0.535825i	$0.820001\pi$
$444$	−8.36692	+	5.37701i	−0.397077	+	0.255182i
$445$	39.2223	−	8.32280i	1.85932	−	0.394539i
$446$			46.4620i			2.20004i
$447$	3.88337	+	0.844803i	0.183677	+	0.0399578i
$448$	−11.1622	+	11.1622i	−0.527365	+	0.527365i
$449$	22.4309			1.05858			0.529289	−	0.848442i	$-0.322459\pi$
$449$	22.4309			1.05858			0.529289	+	0.848442i	$0.322459\pi$
$450$	−21.7939	+	21.3527i	−1.02737	+	1.00658i
$451$	2.15155			0.101313
$452$	26.9283	−	26.9283i	1.26660	−	1.26660i
$453$	−18.6533	−	4.05792i	−0.876410	−	0.190658i
$454$		−	26.1149i		−	1.22563i
$455$	0.977628	−	0.207448i	0.0458319	−	0.00972532i
$456$	0.407167	−	0.261666i	0.0190673	−	0.0122536i
$457$	−21.2398	−	21.2398i	−0.993558	−	0.993558i	0.00642148	−	0.999979i	$-0.497956\pi$
$457$	−21.2398	−	21.2398i	−0.993558	−	0.993558i	−0.999979	+	0.00642148i	$0.997956\pi$
$458$	19.1837	+	19.1837i	0.896396	+	0.896396i
$459$	−11.0765	+	1.59233i	−0.517008	+	0.0743238i
$460$	−14.2416	+	21.9136i	−0.664018	+	1.02173i
$461$			22.1774i			1.03290i	0.856316	+	0.516452i	$0.172748\pi$
$461$			22.1774i			1.03290i	−0.856316	+	0.516452i	$0.827252\pi$
$462$	0.458798	−	2.10899i	0.0213452	−	0.0981191i
$463$	−4.37335	+	4.37335i	−0.203247	+	0.203247i	−0.801390	−	0.598143i	$-0.795906\pi$
$463$	−4.37335	+	4.37335i	−0.203247	+	0.203247i	0.598143	+	0.801390i	$0.295906\pi$
$464$	28.5488			1.32535
$465$	−16.3613	−	0.0836440i	−0.758738	−	0.00387890i
$466$	−13.3786			−0.619753
$467$	4.51110	−	4.51110i	0.208749	−	0.208749i	−0.594987	−	0.803736i	$-0.702843\pi$
$467$	4.51110	−	4.51110i	0.208749	−	0.208749i	0.803736	+	0.594987i	$0.202843\pi$
$468$	−0.574702	−	1.54090i	−0.0265656	−	0.0712281i
$469$			12.7763i			0.589954i
$470$	−10.9463	−	51.5861i	−0.504916	−	2.37949i
$471$	17.5315	+	27.2799i	0.807808	+	1.25699i
$472$	−1.06192	−	1.06192i	−0.0488788	−	0.0488788i
$473$	−0.0794853	−	0.0794853i	−0.00365474	−	0.00365474i
$474$	−7.21846	−	11.2323i	−0.331555	−	0.515917i
$475$	2.03053	+	4.56913i	0.0931669	+	0.209646i
$476$			8.02129i			0.367655i
$477$	3.61309	+	9.68746i	0.165432	+	0.443558i
$478$	−0.223349	+	0.223349i	−0.0102157	+	0.0102157i
$479$	26.1450			1.19460			0.597298	−	0.802019i	$-0.296241\pi$
$479$	26.1450			1.19460			0.597298	+	0.802019i	$0.296241\pi$
$480$	−22.2899	+	22.0632i	−1.01739	+	1.00704i
$481$	0.689045			0.0314177
$482$	−14.3348	+	14.3348i	−0.652932	+	0.652932i
$483$	−3.50848	+	16.1277i	−0.159641	+	0.733835i
$484$		−	23.2470i		−	1.05668i
$485$	−24.4059	−	15.8614i	−1.10821	−	0.720227i
$486$	30.4231	+	8.93414i	1.38002	+	0.405261i
$487$	9.76706	+	9.76706i	0.442588	+	0.442588i	0.892881	−	0.450293i	$-0.148681\pi$
$487$	9.76706	+	9.76706i	0.442588	+	0.442588i	−0.450293	+	0.892881i	$0.648681\pi$
$488$	2.18657	+	2.18657i	0.0989815	+	0.0989815i
$489$	−8.62749	+	5.54447i	−0.390148	+	0.250729i
$490$	−15.1147	−	9.82306i	−0.682815	−	0.443760i
$491$			27.5380i			1.24277i	0.783505	+	0.621385i	$0.213430\pi$
$491$			27.5380i			1.24277i	−0.783505	+	0.621385i	$0.786570\pi$
$492$	22.1392	+	4.81624i	0.998110	+	0.217133i
$493$	11.7297	−	11.7297i	0.528280	−	0.528280i
$494$	−0.521694			−0.0234721
$495$	0.513082	−	2.30181i	0.0230613	−	0.103459i
$496$	−15.6577			−0.703050
$497$	−18.4733	+	18.4733i	−0.828642	+	0.828642i
$498$	35.0297	+	7.62050i	1.56972	+	0.341483i
$499$			6.35894i			0.284665i	0.989819	+	0.142333i	$0.0454603\pi$
$499$			6.35894i			0.284665i	−0.989819	+	0.142333i	$0.954540\pi$
$500$	14.0260	+	19.3473i	0.627263	+	0.865239i
$501$	−19.1836	+	12.3283i	−0.857058	+	0.550790i
$502$	32.4789	+	32.4789i	1.44960	+	1.44960i
$503$	2.78468	+	2.78468i	0.124163	+	0.124163i	0.766458	−	0.642295i	$-0.222018\pi$
$503$	2.78468	+	2.78468i	0.124163	+	0.124163i	−0.642295	+	0.766458i	$0.722018\pi$
$504$	0.606874	−	1.32882i	0.0270323	−	0.0591904i
$505$	2.49063	+	11.7374i	0.110832	+	0.522309i
$506$		−	3.91028i		−	0.173833i
$507$	4.76219	−	21.8907i	0.211496	−	0.972201i
$508$	−5.22540	+	5.22540i	−0.231840	+	0.231840i
$509$	−6.95758			−0.308389			−0.154195	−	0.988040i	$-0.549278\pi$
$509$	−6.95758			−0.308389			−0.154195	+	0.988040i	$0.549278\pi$
$510$	−0.0867327	+	16.9655i	−0.00384059	+	0.751244i
$511$	−17.1074			−0.756789
$512$	−22.6875	+	22.6875i	−1.00265	+	1.00265i
$513$	3.11402	−	4.15967i	0.137487	−	0.183654i
$514$		−	8.51186i		−	0.375442i
$515$	−1.14018	+	1.75440i	−0.0502424	+	0.0773080i
$516$	−0.639964	−	0.995819i	−0.0281729	−	0.0438385i
$517$	2.88221	+	2.88221i	0.126760	+	0.126760i
$518$	6.73352	+	6.73352i	0.295854	+	0.295854i
$519$	6.93643	+	10.7935i	0.304476	+	0.473780i
$520$	−0.156768	+	0.0332654i	−0.00687472	+	0.00145879i
$521$		−	7.42589i		−	0.325334i	−0.986681	−	0.162667i	$-0.947990\pi$
$521$		−	7.42589i		−	0.325334i	0.986681	−	0.162667i	$-0.0520097\pi$
$522$	−44.0394	+	16.4252i	−1.92755	+	0.718911i
$523$	6.92192	−	6.92192i	0.302674	−	0.302674i	−0.539385	−	0.842059i	$-0.681343\pi$
$523$	6.92192	−	6.92192i	0.302674	−	0.302674i	0.842059	+	0.539385i	$0.181343\pi$
$524$	40.9236			1.78776
$525$	12.6117	+	8.28833i	0.550419	+	0.361732i
$526$	−10.1512			−0.442614
$527$	−6.43319	+	6.43319i	−0.280234	+	0.280234i
$528$	0.479742	−	2.20527i	0.0208781	−	0.0959719i
$529$			6.90235i			0.300102i
$530$	15.3339	−	3.25379i	0.666064	−	0.141336i
$531$	−14.6659	−	6.69792i	−0.636445	−	0.290665i
$532$	−2.63370	−	2.63370i	−0.114185	−	0.114185i
$533$	−1.10994	−	1.10994i	−0.0480766	−	0.0480766i
$534$	−53.1452	+	34.1538i	−2.29982	+	1.47798i
$535$	5.14361	−	7.91448i	0.222378	−	0.342173i
$536$		−	2.04875i		−	0.0884924i
$537$	6.28212	+	1.36664i	0.271093	+	0.0589747i
$538$	−21.9553	+	21.9553i	−0.946558	+	0.946558i
$539$	1.39332			0.0600147
$540$	10.4321	−	22.5367i	0.448927	−	0.969826i
$541$	−17.3801			−0.747227			−0.373613	−	0.927585i	$-0.621881\pi$
$541$	−17.3801			−0.747227			−0.373613	+	0.927585i	$0.621881\pi$
$542$	41.8888	−	41.8888i	1.79928	−	1.79928i
$543$	−32.5375	−	7.07833i	−1.39632	−	0.303760i
$544$			17.4394i			0.747709i
$545$	−7.13156	−	33.6085i	−0.305483	−	1.43963i
$546$	−1.32466	+	0.851294i	−0.0566902	+	0.0364320i
$547$	21.5791	+	21.5791i	0.922657	+	0.922657i	0.997217	−	0.0745593i	$-0.0237550\pi$
$547$	21.5791	+	21.5791i	0.922657	+	0.922657i	−0.0745593	+	0.997217i	$0.523755\pi$
$548$	8.32339	+	8.32339i	0.355557	+	0.355557i
$549$	30.1982	+	13.7915i	1.28883	+	0.588608i
$550$	−3.33704	−	1.28362i	−0.142292	−	0.0547336i
$551$			7.70264i			0.328143i
$552$	0.562603	−	2.58616i	0.0239460	−	0.110074i
$553$	−4.66984	+	4.66984i	−0.198582	+	0.198582i
$554$	22.7063			0.964697
$555$	7.31971	+	7.39493i	0.310704	+	0.313897i
$556$	−4.22732			−0.179278
$557$	−25.3668	+	25.3668i	−1.07483	+	1.07483i	−0.0778623	+	0.996964i	$0.524809\pi$
$557$	−25.3668	+	25.3668i	−1.07483	+	1.07483i	−0.996964	+	0.0778623i	$0.975191\pi$
$558$	24.1535	−	9.00843i	1.02250	−	0.381357i
$559$			0.0820091i			0.00346862i
$560$	12.1095	+	7.86997i	0.511721	+	0.332567i
$561$	−0.708959	−	1.10318i	−0.0299323	−	0.0465762i
$562$	−14.8674	−	14.8674i	−0.627144	−	0.627144i
$563$	−11.4312	−	11.4312i	−0.481769	−	0.481769i	0.423927	−	0.905696i	$-0.360651\pi$
$563$	−11.4312	−	11.4312i	−0.481769	−	0.481769i	−0.905696	+	0.423927i	$0.860651\pi$
$564$	23.2057	+	36.1093i	0.977137	+	1.52048i
$565$	−33.4057	−	21.7103i	−1.40539	−	0.913361i
$566$		−	51.6526i		−	2.17112i
$567$	1.11927	−	15.6435i	0.0470049	−	0.656964i
$568$	2.96230	−	2.96230i	0.124295	−	0.124295i
$569$	−8.91564			−0.373763			−0.186881	−	0.982382i	$-0.559838\pi$
$569$	−8.91564			−0.373763			−0.186881	+	0.982382i	$0.559838\pi$
$570$	−5.54194	−	5.59889i	−0.232126	−	0.234512i
$571$	−22.9887			−0.962047			−0.481024	−	0.876708i	$-0.659735\pi$
$571$	−22.9887			−0.962047			−0.481024	+	0.876708i	$0.659735\pi$
$572$	0.136274	−	0.136274i	0.00569789	−	0.00569789i
$573$	−7.51080	+	34.5255i	−0.313768	+	1.44232i
$574$		−	21.6931i		−	0.905453i
$575$	25.5187	+	9.81596i	1.06420	+	0.409354i
$576$	11.2897	−	24.7201i	0.470404	−	1.03000i
$577$	−31.8440	−	31.8440i	−1.32568	−	1.32568i	−0.909096	−	0.416588i	$-0.863226\pi$
$577$	−31.8440	−	31.8440i	−1.32568	−	1.32568i	−0.416588	−	0.909096i	$-0.636774\pi$
$578$	−17.7803	−	17.7803i	−0.739561	−	0.739561i
$579$	−15.5669	+	10.0041i	−0.646937	+	0.415755i
$580$	7.64150	+	36.0116i	0.317296	+	1.49530i
$581$		−	17.7318i		−	0.735640i
$582$	44.8124	+	9.74865i	1.85753	+	0.404095i
$583$	−0.856737	+	0.856737i	−0.0354824	+	0.0354824i
$584$	2.74327			0.113517
$585$	−1.45213	+	0.922761i	−0.0600384	+	0.0381515i
$586$	14.3261			0.591806
$587$	−16.9188	+	16.9188i	−0.698316	+	0.698316i	−0.964047	−	0.265731i	$-0.914387\pi$
$587$	−16.9188	+	16.9188i	−0.698316	+	0.698316i	0.265731	+	0.964047i	$0.414387\pi$
$588$	14.3371	+	3.11894i	0.591251	+	0.128623i
$589$		−	4.22453i		−	0.174069i
$590$	−13.3202	+	20.4958i	−0.548385	+	0.843800i
$591$	−30.4022	+	19.5380i	−1.25058	+	0.803686i
$592$	7.04090	+	7.04090i	0.289379	+	0.289379i
$593$	19.8094	+	19.8094i	0.813476	+	0.813476i	0.985153	−	0.171678i	$-0.0549187\pi$
$593$	19.8094	+	19.8094i	0.813476	+	0.813476i	−0.171678	+	0.985153i	$0.554919\pi$
$594$	0.528720	+	3.67786i	0.0216937	+	0.150904i
$595$	8.20888	−	1.74189i	0.336531	−	0.0714104i
$596$			4.90423i			0.200885i
$597$	1.68382	−	7.74014i	0.0689141	−	0.316783i
$598$	−2.01722	+	2.01722i	−0.0824902	+	0.0824902i
$599$	12.7792			0.522146			0.261073	−	0.965319i	$-0.415924\pi$
$599$	12.7792			0.522146			0.261073	+	0.965319i	$0.415924\pi$
$600$	−2.02235	−	1.32908i	−0.0825621	−	0.0542594i
$601$	−13.9217			−0.567877			−0.283939	−	0.958842i	$-0.591641\pi$
$601$	−13.9217			−0.567877			−0.283939	+	0.958842i	$0.591641\pi$
$602$	−0.801413	+	0.801413i	−0.0326632	+	0.0326632i
$603$	−7.68623	−	20.6084i	−0.313008	−	0.839240i
$604$		−	23.5569i		−	0.958517i
$605$	−23.7907	+	5.04827i	−0.967229	+	0.205242i
$606$	−10.2207	−	15.9039i	−0.415186	−	0.646052i
$607$	−17.6172	−	17.6172i	−0.715059	−	0.715059i	0.252530	−	0.967589i	$-0.418737\pi$
$607$	−17.6172	−	17.6172i	−0.715059	−	0.715059i	−0.967589	+	0.252530i	$0.918737\pi$
$608$	−5.72603	−	5.72603i	−0.232221	−	0.232221i
$609$	12.5691	+	19.5582i	0.509325	+	0.792537i
$610$	27.4273	−	42.2024i	1.11050	−	1.70873i
$611$		−	2.97373i		−	0.120304i
$612$	−4.82562	−	12.9385i	−0.195064	−	0.523009i
$613$	−1.69012	+	1.69012i	−0.0682631	+	0.0682631i	−0.740414	−	0.672151i	$-0.765371\pi$
$613$	−1.69012	+	1.69012i	−0.0682631	+	0.0682631i	0.672151	+	0.740414i	$0.265371\pi$
$614$	−47.2923			−1.90856
$615$	0.121176	−	23.7028i	0.00488629	−	0.955789i
$616$	0.171189			0.00689739
$617$	−20.3235	+	20.3235i	−0.818194	+	0.818194i	−0.985846	−	0.167652i	$-0.946382\pi$
$617$	−20.3235	+	20.3235i	−0.818194	+	0.818194i	0.167652	+	0.985846i	$0.446382\pi$
$618$	0.700774	−	3.22130i	0.0281893	−	0.129580i
$619$			13.6102i			0.547040i	0.961866	+	0.273520i	$0.0881879\pi$
$619$			13.6102i			0.547040i	−0.961866	+	0.273520i	$0.911812\pi$
$620$	−4.19099	−	19.7506i	−0.168314	−	0.793204i
$621$	−4.04318	−	28.1250i	−0.162247	−	1.12862i
$622$	−23.8726	−	23.8726i	−0.957202	−	0.957202i
$623$	22.0951	+	22.0951i	0.885223	+	0.885223i
$624$	−1.38513	+	0.890157i	−0.0554496	+	0.0356348i
$625$	16.7539	−	18.5555i	0.670157	−	0.742219i
$626$		−	14.0859i		−	0.562987i
$627$	0.594994	+	0.129437i	0.0237618	+	0.00516922i
$628$	−28.2957	+	28.2957i	−1.12912	+	1.12912i
$629$	5.78573			0.230692
$630$	−23.2080	−	5.17317i	−0.924631	−	0.206104i
$631$	34.9196			1.39013			0.695064	−	0.718948i	$-0.255376\pi$
$631$	34.9196			1.39013			0.695064	+	0.718948i	$0.255376\pi$
$632$	0.748833	−	0.748833i	0.0297870	−	0.0297870i
$633$	28.8804	+	6.28274i	1.14789	+	0.249717i
$634$			58.7286i			2.33241i
$635$	6.48234	+	4.21287i	0.257244	+	0.167183i
$636$	−10.7335	+	6.89789i	−0.425611	+	0.273519i
$637$	−0.718782	−	0.718782i	−0.0284792	−	0.0284792i
$638$	−3.89475	−	3.89475i	−0.154195	−	0.154195i
$639$	18.6843	−	40.9114i	0.739140	−	1.61843i
$640$	−4.18144	−	2.71751i	−0.165286	−	0.107419i
$641$		−	6.39096i		−	0.252428i	−0.992003	−	0.126214i	$-0.959717\pi$
$641$		−	6.39096i		−	0.252428i	0.992003	−	0.126214i	$-0.0402825\pi$
$642$	−3.16135	+	14.5320i	−0.124769	+	0.573533i
$643$	27.3839	−	27.3839i	1.07991	−	1.07991i	0.0833979	−	0.996516i	$-0.473423\pi$
$643$	27.3839	−	27.3839i	1.07991	−	1.07991i	0.996516	−	0.0833979i	$-0.0265773\pi$
$644$	−20.3673			−0.802584
$645$	−0.880134	+	0.871181i	−0.0346552	+	0.0343027i
$646$	−4.38052			−0.172349
$647$	−11.9850	+	11.9850i	−0.471178	+	0.471178i	−0.902296	−	0.431118i	$-0.858119\pi$
$647$	−11.9850	+	11.9850i	−0.471178	+	0.471178i	0.431118	+	0.902296i	$0.358119\pi$
$648$	−0.179481	+	2.50851i	−0.00705067	+	0.0985437i
$649$		−	1.88937i		−	0.0741642i
$650$	1.05931	+	2.38369i	0.0415497	+	0.0934959i
$651$	−6.89354	−	10.7267i	−0.270179	−	0.420413i
$652$	−8.94873	−	8.94873i	−0.350459	−	0.350459i
$653$	−2.46174	−	2.46174i	−0.0963354	−	0.0963354i	0.657297	−	0.753632i	$-0.271700\pi$
$653$	−2.46174	−	2.46174i	−0.0963354	−	0.0963354i	−0.753632	+	0.657297i	$0.771700\pi$
$654$	29.2654	+	45.5386i	1.14437	+	1.78070i
$655$	−8.88689	−	41.8807i	−0.347239	−	1.63641i
$656$		−	22.6834i		−	0.885639i
$657$	27.5947	−	10.2919i	1.07657	−	0.401524i
$658$	29.0600	−	29.0600i	1.13288	−	1.13288i
$659$	2.59567			0.101113			0.0505565	−	0.998721i	$-0.483901\pi$
$659$	2.59567			0.101113			0.0505565	+	0.998721i	$0.483901\pi$
$660$	2.91014	+	0.0148775i	0.113277	+	0.000579107i
$661$	36.7087			1.42780			0.713901	−	0.700246i	$-0.246926\pi$
$661$	36.7087			1.42780			0.713901	+	0.700246i	$0.246926\pi$
$662$	−23.3067	+	23.3067i	−0.905842	+	0.905842i
$663$	−0.203368	+	0.934837i	−0.00789816	+	0.0363061i
$664$			2.84339i			0.110345i
$665$	−2.12336	+	3.26722i	−0.0823405	+	0.126697i
$666$	−14.9122	−	6.81042i	−0.577836	−	0.263898i
$667$	29.7836	+	29.7836i	1.15323	+	1.15323i
$668$	−19.8979	−	19.8979i	−0.769871	−	0.769871i
$669$	−33.2832	+	21.3895i	−1.28680	+	0.826965i
$670$	−32.6204	+	6.92190i	−1.26024	+	0.267416i
$671$			3.89035i			0.150185i
$672$	−23.8830	−	5.19559i	−0.921305	−	0.200424i
$673$	−28.8563	+	28.8563i	−1.11233	+	1.11233i	−0.119492	+	0.992835i	$0.538126\pi$
$673$	−28.8563	+	28.8563i	−1.11233	+	1.11233i	−0.992835	+	0.119492i	$0.961874\pi$
$674$	30.7656			1.18505
$675$	−25.3292	−	5.78206i	−0.974921	−	0.222551i
$676$	27.6453			1.06328
$677$	0.0608639	−	0.0608639i	0.00233919	−	0.00233919i	−0.705936	−	0.708275i	$-0.749473\pi$
$677$	0.0608639	−	0.0608639i	0.00233919	−	0.00233919i	0.708275	+	0.705936i	$0.249473\pi$
$678$	61.3373	+	13.3435i	2.35564	+	0.512455i
$679$		−	22.6838i		−	0.870523i
$680$	−1.31634	+	0.279321i	−0.0504793	+	0.0107115i
$681$	18.7075	−	12.0224i	0.716871	−	0.460698i
$682$	2.13608	+	2.13608i	0.0817949	+	0.0817949i
$683$	10.7495	+	10.7495i	0.411318	+	0.411318i	0.882197	−	0.470880i	$-0.156063\pi$
$683$	10.7495	+	10.7495i	0.411318	+	0.411318i	−0.470880	+	0.882197i	$0.656063\pi$
$684$	5.83265	+	2.66378i	0.223017	+	0.101852i
$685$	6.71055	−	10.3255i	0.256397	−	0.394518i
$686$		−	38.8601i		−	1.48369i
$687$	−4.91079	+	22.5738i	−0.187358	+	0.861244i
$688$	−0.837998	+	0.837998i	−0.0319484	+	0.0319484i
$689$	0.883940			0.0336754
$690$	−43.0780	−	0.220228i	−1.63995	−	0.00838393i
$691$	−33.1265			−1.26019			−0.630096	−	0.776517i	$-0.716984\pi$
$691$	−33.1265			−1.26019			−0.630096	+	0.776517i	$0.716984\pi$
$692$	−11.1954	+	11.1954i	−0.425583	+	0.425583i
$693$	1.72199	−	0.642244i	0.0654132	−	0.0243968i
$694$			23.7143i			0.900183i
$695$	0.917996	+	4.32618i	0.0348216	+	0.164101i
$696$	−2.01552	−	3.13626i	−0.0763981	−	0.118880i
$697$	−9.31983	−	9.31983i	−0.353014	−	0.353014i
$698$	18.8051	+	18.8051i	0.711785	+	0.711785i
$699$	−6.15905	−	9.58381i	−0.232957	−	0.362493i
$700$	−6.68592	+	17.3815i	−0.252704	+	0.656959i
$701$		−	43.1763i		−	1.63075i	−0.578936	−	0.815373i	$-0.696532\pi$
$701$		−	43.1763i		−	1.63075i	0.578936	−	0.815373i	$-0.303468\pi$
$702$	1.62457	−	2.17007i	0.0613153	−	0.0819041i
$703$	−1.89968	+	1.89968i	−0.0716477	+	0.0716477i
$704$	3.18462			0.120025
$705$	31.9145	−	31.5898i	1.20197	−	1.18974i
$706$	−9.59196			−0.360998
$707$	−6.61205	+	6.61205i	−0.248672	+	0.248672i
$708$	4.22933	−	19.4413i	0.158948	−	0.730649i
$709$		−	40.3912i		−	1.51692i	−0.651718	−	0.758462i	$-0.725951\pi$
$709$		−	40.3912i		−	1.51692i	0.651718	−	0.758462i	$-0.274049\pi$
$710$	−57.1745	−	37.1576i	−2.14572	−	1.39450i
$711$	4.72317	−	10.3419i	0.177133	−	0.387853i
$712$	−3.54307	−	3.54307i	−0.132782	−	0.132782i
$713$	−16.3349	−	16.3349i	−0.611746	−	0.611746i
$714$	−11.1228	+	7.14810i	−0.416261	+	0.267511i
$715$	−0.169054	−	0.109868i	−0.00632225	−	0.00410882i
$716$			7.93355i			0.296491i
$717$	−0.262818	−	0.0571745i	−0.00981514	−	0.00213522i
$718$	−45.8627	+	45.8627i	−1.71158	+	1.71158i
$719$	−42.5949			−1.58852			−0.794260	−	0.607578i	$-0.792141\pi$
$719$	−42.5949			−1.58852			−0.794260	+	0.607578i	$0.792141\pi$
$720$	−24.2675	−	5.40932i	−0.904397	−	0.201594i
$721$	−1.63060			−0.0607269
$722$	1.43829	−	1.43829i	0.0535278	−	0.0535278i
$723$	−16.8680	−	3.66953i	−0.627328	−	0.136471i
$724$		−	41.0909i		−	1.52713i
$725$	35.1944	−	15.6404i	1.30709	−	0.580870i
$726$	32.2357	−	20.7163i	1.19638	−	0.768856i
$727$	7.35183	+	7.35183i	0.272664	+	0.272664i	0.830172	−	0.557508i	$-0.188242\pi$
$727$	7.35183	+	7.35183i	0.272664	+	0.272664i	−0.557508	+	0.830172i	$0.688242\pi$
$728$	−0.0883121	−	0.0883121i	−0.00327306	−	0.00327306i
$729$	7.60573	+	25.9066i	0.281694	+	0.959504i
$730$	−9.26842	−	43.6787i	−0.343040	−	1.61662i
$731$			0.688609i			0.0254691i
$732$	−8.70851	+	40.0311i	−0.321876	+	1.47959i
$733$	7.73048	−	7.73048i	0.285532	−	0.285532i	−0.549779	−	0.835310i	$-0.685288\pi$
$733$	7.73048	−	7.73048i	0.285532	−	0.285532i	0.835310	+	0.549779i	$0.185288\pi$
$734$	2.32675			0.0858820
$735$	0.0784722	−	15.3497i	0.00289449	−	0.566181i
$736$	−44.2814			−1.63223
$737$	1.82256	−	1.82256i	0.0671350	−	0.0671350i
$738$	13.0506	+	34.9915i	0.480399	+	1.28805i
$739$		−	12.4469i		−	0.457867i	−0.973442	−	0.228933i	$-0.926476\pi$
$739$		−	12.4469i		−	0.457867i	0.973442	−	0.228933i	$-0.0735238\pi$
$740$	−6.99682	+	10.7660i	−0.257208	+	0.395767i
$741$	−0.240169	−	0.373716i	−0.00882284	−	0.0137288i
$742$	8.63808	+	8.63808i	0.317114	+	0.317114i
$743$	17.3581	+	17.3581i	0.636808	+	0.636808i	0.949767	−	0.312959i	$-0.101320\pi$
$743$	17.3581	+	17.3581i	0.636808	+	0.636808i	−0.312959	+	0.949767i	$0.601320\pi$
$744$	1.10542	+	1.72009i	0.0405265	+	0.0630614i
$745$	5.01892	−	1.06499i	0.183879	−	0.0390183i
$746$		−	49.9219i		−	1.82777i
$747$	10.6675	+	28.6018i	0.390303	+	1.04649i
$748$	1.14425	−	1.14425i	0.0418381	−	0.0418381i
$749$	7.35602			0.268783
$750$	−14.3290	+	36.6905i	−0.523222	+	1.33975i
$751$	40.3009			1.47060			0.735300	−	0.677742i	$-0.237041\pi$
$751$	40.3009			1.47060			0.735300	+	0.677742i	$0.237041\pi$
$752$	30.3866	−	30.3866i	1.10809	−	1.10809i
$753$	−8.31419	+	38.2185i	−0.302986	+	1.39276i
$754$			4.01842i			0.146342i
$755$	−24.1078	+	5.11557i	−0.877374	+	0.186175i
$756$	19.1567	−	2.75392i	0.696723	−	0.100159i
$757$	9.15343	+	9.15343i	0.332687	+	0.332687i	0.853606	−	0.520919i	$-0.174411\pi$
$757$	9.15343	+	9.15343i	0.332687	+	0.332687i	−0.520919	+	0.853606i	$0.674411\pi$
$758$	−7.30268	−	7.30268i	−0.265245	−	0.265245i
$759$	2.80114	−	1.80016i	0.101675	−	0.0653415i
$760$	0.340492	−	0.523916i	0.0123510	−	0.0190044i
$761$		−	9.34990i		−	0.338934i	−0.985536	−	0.169467i	$-0.945795\pi$
$761$		−	9.34990i		−	0.338934i	0.985536	−	0.169467i	$-0.0542045\pi$
$762$	−11.9024	−	2.58930i	−0.431180	−	0.0938004i
$763$	18.9327	−	18.9327i	0.685409	−	0.685409i
$764$	−43.6015			−1.57745
$765$	−12.1932	+	7.74818i	−0.440846	+	0.280136i
$766$	53.2264			1.92315
$767$	−0.974679	+	0.974679i	−0.0351936	+	0.0351936i
$768$	−22.9854	−	5.00033i	−0.829413	−	0.180434i
$769$			50.7849i			1.83135i	0.401918	+	0.915676i	$0.368344\pi$
$769$			50.7849i			1.83135i	−0.401918	+	0.915676i	$0.631656\pi$
$770$	−0.578378	−	2.72569i	−0.0208433	−	0.0982269i
$771$	6.09749	−	3.91856i	0.219596	−	0.141124i
$772$	−16.1465	−	16.1465i	−0.581126	−	0.581126i
$773$	−3.46087	−	3.46087i	−0.124479	−	0.124479i	0.642123	−	0.766602i	$-0.278054\pi$
$773$	−3.46087	−	3.46087i	−0.124479	−	0.124479i	−0.766602	+	0.642123i	$0.778054\pi$
$774$	0.810566	−	1.77483i	0.0291352	−	0.0637949i
$775$	−19.3024	+	8.57801i	−0.693363	+	0.308131i
$776$			3.63746i			0.130577i
$777$	−1.72370	+	7.92344i	−0.0618373	+	0.284252i
$778$	3.14606	−	3.14606i	0.112792	−	0.112792i
$779$	6.12012			0.219276
$780$	−1.49360	−	1.50895i	−0.0534793	−	0.0540290i
$781$	5.27052			0.188594
$782$	−16.9381	+	16.9381i	−0.605704	+	0.605704i
$783$	−32.0404	−	23.9862i	−1.14503	−	0.857196i
$784$		−	14.6895i		−	0.524626i
$785$	35.1021	+	22.8128i	1.25285	+	0.814224i
$786$	36.4687	+	56.7472i	1.30079	+	2.02411i
$787$	14.4789	+	14.4789i	0.516117	+	0.516117i	0.916394	−	0.400277i	$-0.131086\pi$
$787$	14.4789	+	14.4789i	0.516117	+	0.516117i	−0.400277	+	0.916394i	$0.631086\pi$
$788$	−31.5342	−	31.5342i	−1.12336	−	1.12336i
$789$	−4.67326	−	7.27184i	−0.166373	−	0.258885i
$790$	−14.4530	−	9.39301i	−0.514216	−	0.334188i
$791$		−	31.0485i		−	1.10396i
$792$	−0.276131	+	0.102987i	−0.00981189	+	0.00365949i
$793$	2.00694	−	2.00694i	0.0712684	−	0.0712684i
$794$	−38.6152			−1.37040
$795$	9.39008	+	9.48658i	0.333032	+	0.336454i
$796$	9.77486			0.346461
$797$	17.9190	−	17.9190i	0.634723	−	0.634723i	−0.314526	−	0.949249i	$-0.601846\pi$
$797$	17.9190	−	17.9190i	0.634723	−	0.634723i	0.949249	+	0.314526i	$0.101846\pi$
$798$	1.30505	−	5.99904i	0.0461984	−	0.212364i
$799$		−	24.9696i		−	0.883361i
$800$	−14.5361	+	37.7898i	−0.513930	+	1.33607i
$801$	−48.9324	−	22.3475i	−1.72894	−	0.789609i
$802$	44.5112	+	44.5112i	1.57175	+	1.57175i
$803$	2.44041	+	2.44041i	0.0861203	+	0.0861203i
$804$	22.8337	−	14.6741i	0.805282	−	0.517516i
$805$	4.42292	+	20.8436i	0.155888	+	0.734642i
$806$		−	2.20391i		−	0.0776294i
$807$	−25.8351	−	5.62027i	−0.909440	−	0.197843i
$808$	1.06028	−	1.06028i	0.0373004	−	0.0373004i
$809$	42.9209			1.50902			0.754509	−	0.656290i	$-0.227875\pi$
$809$	42.9209			1.50902			0.754509	+	0.656290i	$0.227875\pi$
$810$	40.5473	−	5.61756i	1.42469	−	0.197381i
$811$	18.4042			0.646259			0.323130	−	0.946355i	$-0.395265\pi$
$811$	18.4042			0.646259			0.323130	+	0.946355i	$0.395265\pi$
$812$	−20.2864	+	20.2864i	−0.711914	+	0.711914i
$813$	49.2913	+	10.7230i	1.72872	+	0.376072i
$814$		−	1.92110i		−	0.0673345i
$815$	−7.21472	+	11.1013i	−0.252721	+	0.388862i
$816$	−11.6306	+	7.47441i	−0.407152	+	0.261657i
$817$	−0.226097	−	0.226097i	−0.00791012	−	0.00791012i
$818$	27.8670	+	27.8670i	0.974346	+	0.974346i
$819$	−1.21965	−	0.557017i	−0.0426182	−	0.0194638i
$820$	28.6129	−	6.07154i	0.999207	−	0.212027i
$821$			7.35855i			0.256815i	0.991721	+	0.128408i	$0.0409866\pi$
$821$			7.35855i			0.256815i	−0.991721	+	0.128408i	$0.959013\pi$
$822$	−4.12442	+	18.9590i	−0.143856	+	0.661272i
$823$	19.1194	−	19.1194i	0.666459	−	0.666459i	−0.290435	−	0.956895i	$-0.593800\pi$
$823$	19.1194	−	19.1194i	0.666459	−	0.666459i	0.956895	+	0.290435i	$0.0938001\pi$
$824$	0.261476			0.00910895
$825$	−0.616735	−	2.98143i	−0.0214720	−	0.103800i
$826$	−19.0496			−0.662820
$827$	−16.8877	+	16.8877i	−0.587245	+	0.587245i	−0.936884	−	0.349640i	$-0.886304\pi$
$827$	−16.8877	+	16.8877i	−0.587245	+	0.587245i	0.349640	+	0.936884i	$0.386304\pi$
$828$	32.8529	−	12.2530i	1.14172	−	0.425821i
$829$			35.6850i			1.23939i	0.784843	+	0.619695i	$0.212744\pi$
$829$			35.6850i			1.23939i	−0.784843	+	0.619695i	$0.787256\pi$
$830$	45.2729	−	9.60670i	1.57144	−	0.333453i
$831$	10.4532	+	16.2657i	0.362616	+	0.564251i
$832$	−1.64287	−	1.64287i	−0.0569563	−	0.0569563i
$833$	−6.03542	−	6.03542i	−0.209115	−	0.209115i
$834$	−3.76713	−	5.86186i	−0.130445	−	0.202980i
$835$	−16.0422	+	24.6842i	−0.555164	+	0.854231i
$836$			0.751405i			0.0259879i
$837$	17.5726	+	13.1553i	0.607399	+	0.454713i
$838$	1.81252	−	1.81252i	0.0626124	−	0.0626124i
$839$	3.55615			0.122772			0.0613860	−	0.998114i	$-0.480448\pi$
$839$	3.55615			0.122772			0.0613860	+	0.998114i	$0.480448\pi$
$840$	0.00964137	−	1.88592i	0.000332659	−	0.0650703i
$841$	30.3306			1.04588
$842$	40.4047	−	40.4047i	1.39244	−	1.39244i
$843$	3.80587	−	17.4947i	0.131081	−	0.602551i
$844$			36.4724i			1.25543i
$845$	−6.00340	−	28.2919i	−0.206523	−	0.973269i
$846$	−29.3919	+	64.3569i	−1.01051	+	2.21264i
$847$	−13.4020	−	13.4020i	−0.460499	−	0.460499i
$848$	9.03241	+	9.03241i	0.310174	+	0.310174i
$849$	37.0015	−	23.7790i	1.26989	−	0.816095i
$850$	8.89477	+	20.0152i	0.305088	+	0.686515i
$851$			14.6909i			0.503596i
$852$	54.2328	+	11.7980i	1.85798	+	0.404193i
$853$	−23.3945	+	23.3945i	−0.801012	+	0.801012i	−0.983254	−	0.182241i	$-0.941665\pi$
$853$	−23.3945	+	23.3945i	−0.801012	+	0.801012i	0.182241	+	0.983254i	$0.441665\pi$
$854$	39.2246			1.34224
$855$	1.45947	−	6.54752i	0.0499127	−	0.223920i
$856$	−1.17958			−0.0403171
$857$	2.09945	−	2.09945i	0.0717159	−	0.0717159i	−0.670339	−	0.742055i	$-0.733851\pi$
$857$	2.09945	−	2.09945i	0.0717159	−	0.0717159i	0.742055	+	0.670339i	$0.233851\pi$
$858$	0.310404	+	0.0675266i	0.0105970	+	0.00230532i
$859$		−	21.2663i		−	0.725596i	−0.931868	−	0.362798i	$-0.881822\pi$
$859$		−	21.2663i		−	0.725596i	0.931868	−	0.362798i	$-0.118178\pi$
$860$	−1.28136	−	0.832752i	−0.0436939	−	0.0283966i
$861$	15.5399	−	9.98675i	0.529599	−	0.340347i
$862$	−31.0895	−	31.0895i	−1.05891	−	1.05891i
$863$	−12.9433	−	12.9433i	−0.440593	−	0.440593i	0.451618	−	0.892211i	$-0.350847\pi$
$863$	−12.9433	−	12.9433i	−0.440593	−	0.440593i	−0.892211	+	0.451618i	$0.850847\pi$
$864$	41.6494	−	5.98742i	1.41694	−	0.203696i
$865$	13.8883	+	9.02601i	0.472217	+	0.306894i
$866$			31.4540i			1.06885i
$867$	4.55152	−	20.9223i	0.154578	−	0.710560i
$868$	11.1261	−	11.1261i	0.377645	−	0.377645i
$869$	1.33232			0.0451960
$870$	−43.1262	+	42.6875i	−1.46212	+	1.44724i
$871$	−1.88043			−0.0637161
$872$	−3.03595	+	3.03595i	−0.102810	+	0.102810i
$873$	13.6466	+	36.5894i	0.461867	+	1.23836i
$874$		−	11.1228i		−	0.376235i
$875$	19.2399	+	3.06775i	0.650427	+	0.103709i
$876$	19.6486	+	30.5743i	0.663865	+	1.03301i
$877$	10.4997	+	10.4997i	0.354550	+	0.354550i	0.861799	−	0.507249i	$-0.169338\pi$
$877$	10.4997	+	10.4997i	0.354550	+	0.354550i	−0.507249	+	0.861799i	$0.669338\pi$
$878$	38.0414	+	38.0414i	1.28384	+	1.28384i
$879$	6.59524	+	10.2625i	0.222452	+	0.346147i
$880$	−0.604782	−	2.85012i	−0.0203872	−	0.0960774i
$881$		−	11.4045i		−	0.384226i	−0.981373	−	0.192113i	$-0.938466\pi$
$881$		−	11.4045i		−	0.384226i	0.981373	−	0.192113i	$-0.0615340\pi$
$882$	8.45143	+	22.6601i	0.284574	+	0.763005i
$883$	4.83451	−	4.83451i	0.162694	−	0.162694i	−0.621065	−	0.783759i	$-0.713300\pi$
$883$	4.83451	−	4.83451i	0.162694	−	0.162694i	0.783759	+	0.621065i	$0.213300\pi$
$884$	−1.18059			−0.0397074
$885$	−20.8144	−	0.106410i	−0.699668	−	0.00357692i
$886$	18.6785			0.627515
$887$	7.37285	−	7.37285i	0.247556	−	0.247556i	−0.572411	−	0.819967i	$-0.693992\pi$
$887$	7.37285	−	7.37285i	0.247556	−	0.247556i	0.819967	+	0.572411i	$0.193992\pi$
$888$	0.276404	−	1.27057i	0.00927550	−	0.0426374i
$889$			6.02494i			0.202070i
$890$	−44.4426	+	68.3839i	−1.48972	+	2.29223i
$891$	−2.39124	+	2.07191i	−0.0801096	+	0.0694115i
$892$	−34.5225	−	34.5225i	−1.15590	−	1.15590i
$893$	8.19848	+	8.19848i	0.274352	+	0.274352i
$894$	−6.80050	+	4.37035i	−0.227443	+	0.146166i
$895$	8.11909	−	1.72283i	0.271391	−	0.0575880i
$896$		−	3.88639i		−	0.129835i
$897$	−2.37370	−	0.516383i	−0.0792554	−	0.0172415i
$898$	−32.2622	+	32.2622i	−1.07660	+	1.07660i
$899$	−32.5400			−1.08527
$900$	0.327799	−	32.0590i	0.0109266	−	1.06863i
$901$	7.42221			0.247270
$902$	−3.09457	+	3.09457i	−0.103038	+	0.103038i
$903$	−0.943037	−	0.205152i	−0.0313823	−	0.00682702i
$904$			4.97880i			0.165592i
$905$	−42.0519	+	8.92322i	−1.39785	+	0.296618i
$906$	32.6655	−	20.9925i	1.08524	−	0.697429i
$907$	34.1471	+	34.1471i	1.13383	+	1.13383i	0.989534	+	0.144300i	$0.0460932\pi$
$907$	34.1471	+	34.1471i	1.13383	+	1.13383i	0.144300	+	0.989534i	$0.453907\pi$
$908$	19.4040	+	19.4040i	0.643945	+	0.643945i
$909$	6.68757	−	14.6432i	0.221813	−	0.485685i
$910$	−1.10774	+	1.70449i	−0.0367214	+	0.0565032i
$911$			38.3772i			1.27149i	0.771897	+	0.635747i	$0.219308\pi$
$911$			38.3772i			1.27149i	−0.771897	+	0.635747i	$0.780692\pi$
$912$	1.36463	−	6.27290i	0.0451874	−	0.207717i
$913$	−2.52948	+	2.52948i	−0.0837137	+	0.0837137i
$914$	61.0983			2.02095
$915$	42.8584	+	0.219105i	1.41686	+	0.00724339i
$916$	−28.5080			−0.941930
$917$	23.5927	−	23.5927i	0.779098	−	0.779098i
$918$	13.6410	−	18.2215i	0.450222	−	0.601400i
$919$			56.1751i			1.85305i	0.376237	+	0.926523i	$0.377218\pi$
$919$			56.1751i			1.85305i	−0.376237	+	0.926523i	$0.622782\pi$
$920$	−0.709239	−	3.34239i	−0.0233829	−	0.110195i
$921$	−21.7717	−	33.8780i	−0.717403	−	1.11632i
$922$	−31.8976	−	31.8976i	−1.05049	−	1.05049i
$923$	−2.71893	−	2.71893i	−0.0894947	−	0.0894947i
$924$	1.22614	+	1.90793i	0.0403369	+	0.0627664i
$925$	12.5372	+	4.82253i	0.412221	+	0.158564i
$926$		−	12.5803i		−	0.413415i
$927$	2.63020	−	0.980973i	0.0863871	−	0.0322194i
$928$	−44.1055	+	44.1055i	−1.44784	+	1.44784i
$929$	−57.3334			−1.88105			−0.940524	−	0.339726i	$-0.889666\pi$
$929$	−57.3334			−1.88105			−0.940524	+	0.339726i	$0.889666\pi$
$930$	23.6527	−	23.4121i	0.775602	−	0.767712i
$931$	3.96332			0.129893
$932$	9.94067	−	9.94067i	0.325617	−	0.325617i
$933$	6.11108	−	28.0912i	0.200068	−	0.919666i
$934$			12.9766i			0.424607i
$935$	−1.41950	−	0.922530i	−0.0464226	−	0.0301700i
$936$	0.195578	+	0.0893207i	0.00639267	+	0.00291954i
$937$	1.49340	+	1.49340i	0.0487871	+	0.0487871i	0.731079	−	0.682292i	$-0.239017\pi$
$937$	1.49340	+	1.49340i	0.0487871	+	0.0487871i	−0.682292	+	0.731079i	$0.739017\pi$
$938$	−18.3761	−	18.3761i	−0.600000	−	0.600000i
$939$	10.0905	−	6.48467i	0.329291	−	0.211619i
$940$	46.4632	+	30.1964i	1.51546	+	0.984897i
$941$		−	19.5872i		−	0.638525i	−0.947666	−	0.319263i	$-0.896565\pi$
$941$		−	19.5872i		−	0.638525i	0.947666	−	0.319263i	$-0.103435\pi$
$942$	−64.4520	−	14.0211i	−2.09996	−	0.456833i
$943$	23.6645	−	23.6645i	0.770622	−	0.770622i
$944$	−19.9192			−0.648316
$945$	−6.97836	−	19.0067i	−0.227006	−	0.618288i
$946$	0.228646			0.00743394
$947$	6.89430	−	6.89430i	0.224035	−	0.224035i	−0.586160	−	0.810195i	$-0.699361\pi$
$947$	6.89430	−	6.89430i	0.224035	−	0.224035i	0.810195	+	0.586160i	$0.199361\pi$
$948$	13.7094	+	2.98240i	0.445261	+	0.0968637i
$949$		−	2.51790i		−	0.0817345i
$950$	−9.49225	−	3.65126i	−0.307969	−	0.118463i
$951$	−42.0704	+	27.0366i	−1.36423	+	0.876722i
$952$	−0.741533	−	0.741533i	−0.0240332	−	0.0240332i
$953$	−6.10385	−	6.10385i	−0.197723	−	0.197723i	0.601300	−	0.799023i	$-0.294650\pi$
$953$	−6.10385	−	6.10385i	−0.197723	−	0.197723i	−0.799023	+	0.601300i	$0.794650\pi$
$954$	−19.1301	−	8.73673i	−0.619360	−	0.282862i
$955$	9.46841	+	44.6212i	0.306391	+	1.44391i
$956$		−	0.331908i		−	0.0107347i
$957$	0.997008	−	4.58302i	0.0322287	−	0.148148i
$958$	−37.6042	+	37.6042i	−1.21494	+	1.21494i
$959$	9.59694			0.309902
$960$	0.179359	−	35.0837i	0.00578877	−	1.13232i
$961$	−13.1534			−0.424302
$962$	−0.991049	+	0.991049i	−0.0319527	+	0.0319527i
$963$	−11.8654	+	4.42539i	−0.382358	+	0.142606i
$964$		−	21.3023i		−	0.686100i
$965$	−13.0178	+	20.0305i	−0.419057	+	0.644803i
$966$	−18.1501	−	28.2426i	−0.583971	−	0.908690i
$967$	−8.89105	−	8.89105i	−0.285917	−	0.285917i	0.549546	−	0.835463i	$-0.314801\pi$
$967$	−8.89105	−	8.89105i	−0.285917	−	0.285917i	−0.835463	+	0.549546i	$0.814801\pi$
$968$	2.14908	+	2.14908i	0.0690742	+	0.0690742i
$969$	−2.01664	−	3.13800i	−0.0647838	−	0.100807i
$970$	57.9161	−	12.2895i	1.85957	−	0.394593i
$971$		−	52.2284i		−	1.67609i	−0.545603	−	0.838044i	$-0.683699\pi$
$971$		−	52.2284i		−	1.67609i	0.545603	−	0.838044i	$-0.316301\pi$
$972$	−29.2434	+	15.9668i	−0.937984	+	0.512137i
$973$	−2.43707	+	2.43707i	−0.0781288	+	0.0781288i
$974$	−28.0958			−0.900247
$975$	−1.21989	+	1.85621i	−0.0390677	+	0.0594462i
$976$	41.0152			1.31286
$977$	−28.4935	+	28.4935i	−0.911589	+	0.911589i	−0.996397	−	0.0848085i	$-0.972972\pi$
$977$	−28.4935	+	28.4935i	−0.911589	+	0.911589i	0.0848085	+	0.996397i	$0.472972\pi$
$978$	4.43429	−	20.3834i	0.141793	−	0.651790i
$979$		−	6.30383i		−	0.201471i
$980$	18.5294	−	3.93186i	0.591901	−	0.125599i
$981$	−19.1489	+	41.9287i	−0.611377	+	1.33868i
$982$	−39.6077	−	39.6077i	−1.26393	−	1.26393i
$983$	11.3051	+	11.3051i	0.360577	+	0.360577i	0.864025	−	0.503448i	$-0.167936\pi$
$983$	11.3051	+	11.3051i	0.360577	+	0.360577i	−0.503448	+	0.864025i	$0.667936\pi$
$984$	−2.49191	+	1.60143i	−0.0794391	+	0.0510517i
$985$	−25.4238	+	39.1196i	−0.810069	+	1.24645i
$986$			33.7416i			1.07455i
$987$	34.1954	+	7.43900i	1.08845	+	0.236786i
$988$	0.387632	−	0.387632i	0.0123322	−	0.0123322i
$989$	−1.74849			−0.0555986
$990$	2.57271	+	4.04864i	0.0817662	+	0.128674i
$991$	−38.0169			−1.20765			−0.603823	−	0.797118i	$-0.706357\pi$
$991$	−38.0169			−1.20765			−0.603823	+	0.797118i	$0.706357\pi$
$992$	24.1898	−	24.1898i	0.768026	−	0.768026i
$993$	−27.4254	−	5.96623i	−0.870320	−	0.189333i
$994$		−	53.1401i		−	1.68550i
$995$	−2.12269	−	10.0035i	−0.0672937	−	0.317131i
$996$	−31.6902	+	20.3658i	−1.00414	+	0.645314i
$997$	−26.3376	−	26.3376i	−0.834121	−	0.834121i	0.153957	−	0.988078i	$-0.450798\pi$
$997$	−26.3376	−	26.3376i	−0.834121	−	0.834121i	−0.988078	+	0.153957i	$0.950798\pi$
$998$	−9.14603	−	9.14603i	−0.289513	−	0.289513i
$999$	−1.98639	−	13.8177i	−0.0628467	−	0.437172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.77.4	✓	36
3.2	odd	2	inner	285.2.k.d.77.15	yes	36
5.3	odd	4	inner	285.2.k.d.248.15	yes	36
15.8	even	4	inner	285.2.k.d.248.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.4	✓	36	1.1	even	1	trivial
285.2.k.d.77.15	yes	36	3.2	odd	2	inner
285.2.k.d.248.4	yes	36	15.8	even	4	inner
285.2.k.d.248.15	yes	36	5.3	odd	4	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43829 + 1.43829i) q^{2} +(-1.69247 - 0.368185i) q^{3} -2.13738i q^{4} +(-2.18737 + 0.464149i) q^{5} +(2.96382 - 1.90470i) q^{6} +(-1.23221 - 1.23221i) q^{7} +(0.197591 + 0.197591i) q^{8} +(2.72888 + 1.24628i) q^{9} +O(q^{10})\)	\(q+(-1.43829 + 1.43829i) q^{2} +(-1.69247 - 0.368185i) q^{3} -2.13738i q^{4} +(-2.18737 + 0.464149i) q^{5} +(2.96382 - 1.90470i) q^{6} +(-1.23221 - 1.23221i) q^{7} +(0.197591 + 0.197591i) q^{8} +(2.72888 + 1.24628i) q^{9} +(2.47849 - 3.81366i) q^{10} +0.351554i q^{11} +(-0.786952 + 3.61744i) q^{12} +(0.181358 - 0.181358i) q^{13} +3.54456 q^{14} +(3.87293 + 0.0197996i) q^{15} +3.70637 q^{16} +(1.52282 - 1.52282i) q^{17} +(-5.71745 + 2.13241i) q^{18} +1.00000i q^{19} +(0.992062 + 4.67523i) q^{20} +(1.63179 + 2.53915i) q^{21} +(-0.505639 - 0.505639i) q^{22} +(3.86668 + 3.86668i) q^{23} +(-0.261666 - 0.407167i) q^{24} +(4.56913 - 2.03053i) q^{25} +0.521694i q^{26} +(-4.15967 - 3.11402i) q^{27} +(-2.63370 + 2.63370i) q^{28} +7.70264 q^{29} +(-5.59889 + 5.54194i) q^{30} -4.22453 q^{31} +(-5.72603 + 5.72603i) q^{32} +(0.129437 - 0.594994i) q^{33} +4.38052i q^{34} +(3.26722 + 2.12336i) q^{35} +(2.66378 - 5.83265i) q^{36} +(1.89968 + 1.89968i) q^{37} +(-1.43829 - 1.43829i) q^{38} +(-0.373716 + 0.240169i) q^{39} +(-0.523916 - 0.340492i) q^{40} -6.12012i q^{41} +(-5.99904 - 1.30505i) q^{42} +(-0.226097 + 0.226097i) q^{43} +0.751405 q^{44} +(-6.54752 - 1.45947i) q^{45} -11.1228 q^{46} +(8.19848 - 8.19848i) q^{47} +(-6.27290 - 1.36463i) q^{48} -3.96332i q^{49} +(-3.65126 + 9.49225i) q^{50} +(-3.13800 + 2.01664i) q^{51} +(-0.387632 - 0.387632i) q^{52} +(2.43700 + 2.43700i) q^{53} +(10.4617 - 1.50395i) q^{54} +(-0.163174 - 0.768978i) q^{55} -0.486948i q^{56} +(0.368185 - 1.69247i) q^{57} +(-11.0787 + 11.0787i) q^{58} -5.37432 q^{59} +(0.0423193 - 8.27792i) q^{60} +11.0661 q^{61} +(6.07611 - 6.07611i) q^{62} +(-1.82687 - 4.89823i) q^{63} -9.05869i q^{64} +(-0.312520 + 0.480874i) q^{65} +(0.669607 + 1.04194i) q^{66} +(-5.18430 - 5.18430i) q^{67} +(-3.25484 - 3.25484i) q^{68} +(-5.12056 - 7.96787i) q^{69} +(-7.75324 + 1.64520i) q^{70} -14.9920i q^{71} +(0.292948 + 0.785457i) q^{72} +(6.94178 - 6.94178i) q^{73} -5.46459 q^{74} +(-8.48071 + 1.75431i) q^{75} +2.13738 q^{76} +(0.433189 - 0.433189i) q^{77} +(0.192080 - 0.882948i) q^{78} -3.78981i q^{79} +(-8.10718 + 1.72031i) q^{80} +(5.89356 + 6.80191i) q^{81} +(8.80253 + 8.80253i) q^{82} +(7.19514 + 7.19514i) q^{83} +(5.42713 - 3.48775i) q^{84} +(-2.62415 + 4.03778i) q^{85} -0.650387i q^{86} +(-13.0364 - 2.83600i) q^{87} +(-0.0694641 + 0.0694641i) q^{88} -17.9313 q^{89} +(11.5164 - 7.31811i) q^{90} -0.446943 q^{91} +(8.26455 - 8.26455i) q^{92} +(7.14987 + 1.55541i) q^{93} +23.5837i q^{94} +(-0.464149 - 2.18737i) q^{95} +(11.7994 - 7.58287i) q^{96} +(9.20451 + 9.20451i) q^{97} +(5.70042 + 5.70042i) q^{98} +(-0.438136 + 0.959350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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