LMFDB - Embedded newform 930.2.r.b.119.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.12
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.882485 + 1.49038i) q^{3} +1.00000 q^{4} +(1.20301 - 1.88488i) q^{5} +(-0.882485 + 1.49038i) q^{6} +(-3.11576 - 1.79889i) q^{7} +1.00000 q^{8} +(-1.44244 - 2.63047i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.882485 + 1.49038i) q^{3} +1.00000 q^{4} +(1.20301 - 1.88488i) q^{5} +(-0.882485 + 1.49038i) q^{6} +(-3.11576 - 1.79889i) q^{7} +1.00000 q^{8} +(-1.44244 - 2.63047i) q^{9} +(1.20301 - 1.88488i) q^{10} +(0.444351 + 0.769638i) q^{11} +(-0.882485 + 1.49038i) q^{12} +(2.42407 + 4.19861i) q^{13} +(-3.11576 - 1.79889i) q^{14} +(1.74754 + 3.45631i) q^{15} +1.00000 q^{16} +(5.93793 + 3.42826i) q^{17} +(-1.44244 - 2.63047i) q^{18} +(3.55710 - 6.16108i) q^{19} +(1.20301 - 1.88488i) q^{20} +(5.43063 - 3.05617i) q^{21} +(0.444351 + 0.769638i) q^{22} -6.10864i q^{23} +(-0.882485 + 1.49038i) q^{24} +(-2.10555 - 4.53505i) q^{25} +(2.42407 + 4.19861i) q^{26} +(5.19332 + 0.171568i) q^{27} +(-3.11576 - 1.79889i) q^{28} +0.208225 q^{29} +(1.74754 + 3.45631i) q^{30} +(5.55290 - 0.406530i) q^{31} +1.00000 q^{32} +(-1.53918 - 0.0169442i) q^{33} +(5.93793 + 3.42826i) q^{34} +(-7.13897 + 3.70877i) q^{35} +(-1.44244 - 2.63047i) q^{36} +(2.27731 - 3.94442i) q^{37} +(3.55710 - 6.16108i) q^{38} +(-8.39672 - 0.0924355i) q^{39} +(1.20301 - 1.88488i) q^{40} +(7.32942 - 4.23164i) q^{41} +(5.43063 - 3.05617i) q^{42} +(1.70855 - 2.95930i) q^{43} +(0.444351 + 0.769638i) q^{44} +(-6.69338 - 0.445643i) q^{45} -6.10864i q^{46} -3.08276 q^{47} +(-0.882485 + 1.49038i) q^{48} +(2.97199 + 5.14764i) q^{49} +(-2.10555 - 4.53505i) q^{50} +(-10.3495 + 5.82435i) q^{51} +(2.42407 + 4.19861i) q^{52} +(-6.28930 + 3.63113i) q^{53} +(5.19332 + 0.171568i) q^{54} +(1.98523 + 0.0883322i) q^{55} +(-3.11576 - 1.79889i) q^{56} +(6.04324 + 10.7385i) q^{57} +0.208225 q^{58} +(-4.03191 - 2.32782i) q^{59} +(1.74754 + 3.45631i) q^{60} +13.2474i q^{61} +(5.55290 - 0.406530i) q^{62} +(-0.237609 + 10.7907i) q^{63} +1.00000 q^{64} +(10.8301 + 0.481879i) q^{65} +(-1.53918 - 0.0169442i) q^{66} +(-6.17071 + 3.56266i) q^{67} +(5.93793 + 3.42826i) q^{68} +(9.10418 + 5.39079i) q^{69} +(-7.13897 + 3.70877i) q^{70} +(-6.20217 + 3.58082i) q^{71} +(-1.44244 - 2.63047i) q^{72} +(0.840046 + 1.45500i) q^{73} +(2.27731 - 3.94442i) q^{74} +(8.61704 + 0.864055i) q^{75} +(3.55710 - 6.16108i) q^{76} -3.19735i q^{77} +(-8.39672 - 0.0924355i) q^{78} +(-0.516925 - 0.298447i) q^{79} +(1.20301 - 1.88488i) q^{80} +(-4.83873 + 7.58859i) q^{81} +(7.32942 - 4.23164i) q^{82} +(-12.2924 + 7.09701i) q^{83} +(5.43063 - 3.05617i) q^{84} +(13.6052 - 7.06805i) q^{85} +(1.70855 - 2.95930i) q^{86} +(-0.183756 + 0.310334i) q^{87} +(0.444351 + 0.769638i) q^{88} -9.33144 q^{89} +(-6.69338 - 0.445643i) q^{90} -17.4425i q^{91} -6.10864i q^{92} +(-4.29447 + 8.63467i) q^{93} -3.08276 q^{94} +(-7.33368 - 14.1165i) q^{95} +(-0.882485 + 1.49038i) q^{96} -16.4556i q^{97} +(2.97199 + 5.14764i) q^{98} +(1.38356 - 2.27901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.882485	+	1.49038i	−0.509503	+	0.860469i
$3$	−0.882485	+	1.49038i	−0.509503	+	0.860469i
$4$	1.00000			0.500000
$5$	1.20301	−	1.88488i	0.538001	−	0.842944i
$5$	1.20301	−	1.88488i	0.538001	−	0.842944i
$6$	−0.882485	+	1.49038i	−0.360273	+	0.608443i
$7$	−3.11576	−	1.79889i	−1.17765	−	0.679915i	−0.222179	−	0.975006i	$-0.571317\pi$
$7$	−3.11576	−	1.79889i	−1.17765	−	0.679915i	−0.955469	+	0.295091i	$0.904650\pi$
$8$	1.00000			0.353553
$9$	−1.44244	−	2.63047i	−0.480814	−	0.876823i
$10$	1.20301	−	1.88488i	0.380424	−	0.596051i
$11$	0.444351	+	0.769638i	0.133977	+	0.232055i	0.925206	−	0.379465i	$-0.123892\pi$
$11$	0.444351	+	0.769638i	0.133977	+	0.232055i	−0.791229	+	0.611520i	$0.790559\pi$
$12$	−0.882485	+	1.49038i	−0.254751	+	0.430234i
$13$	2.42407	+	4.19861i	0.672316	+	1.16449i	0.977246	+	0.212111i	$0.0680337\pi$
$13$	2.42407	+	4.19861i	0.672316	+	1.16449i	−0.304930	+	0.952375i	$0.598633\pi$
$14$	−3.11576	−	1.79889i	−0.832723	−	0.480773i
$15$	1.74754	+	3.45631i	0.451214	+	0.892416i
$16$	1.00000			0.250000
$17$	5.93793	+	3.42826i	1.44016	+	0.831476i	0.997860	−	0.0653920i	$-0.0208298\pi$
$17$	5.93793	+	3.42826i	1.44016	+	0.831476i	0.442299	+	0.896868i	$0.354163\pi$
$18$	−1.44244	−	2.63047i	−0.339987	−	0.620007i
$19$	3.55710	−	6.16108i	0.816055	−	1.41345i	−0.0925132	−	0.995711i	$-0.529490\pi$
$19$	3.55710	−	6.16108i	0.816055	−	1.41345i	0.908568	−	0.417737i	$-0.137177\pi$
$20$	1.20301	−	1.88488i	0.269001	−	0.421472i
$21$	5.43063	−	3.05617i	1.18506	−	0.666911i
$22$	0.444351	+	0.769638i	0.0947359	+	0.164087i
$23$		−	6.10864i		−	1.27374i	−0.770971	−	0.636870i	$-0.780229\pi$
$23$		−	6.10864i		−	1.27374i	0.770971	−	0.636870i	$-0.219771\pi$
$24$	−0.882485	+	1.49038i	−0.180136	+	0.304222i
$25$	−2.10555	−	4.53505i	−0.421109	−	0.907010i
$26$	2.42407	+	4.19861i	0.475399	+	0.823416i
$27$	5.19332	+	0.171568i	0.999455	+	0.0330183i
$28$	−3.11576	−	1.79889i	−0.588824	−	0.339958i
$29$	0.208225			0.0386665			0.0193332	−	0.999813i	$-0.493846\pi$
$29$	0.208225			0.0386665			0.0193332	+	0.999813i	$0.493846\pi$
$30$	1.74754	+	3.45631i	0.319057	+	0.631033i
$31$	5.55290	−	0.406530i	0.997331	−	0.0730150i
$31$	5.55290	−	0.406530i	0.997331	−	0.0730150i
$32$	1.00000			0.176777
$33$	−1.53918	−	0.0169442i	−0.267937	−	0.00294960i
$34$	5.93793	+	3.42826i	1.01835	+	0.587942i
$35$	−7.13897	+	3.70877i	−1.20671	+	0.626896i
$36$	−1.44244	−	2.63047i	−0.240407	−	0.438411i
$37$	2.27731	−	3.94442i	0.374388	−	0.648459i	−0.615847	−	0.787866i	$-0.711186\pi$
$37$	2.27731	−	3.94442i	0.374388	−	0.648459i	0.990235	+	0.139407i	$0.0445195\pi$
$38$	3.55710	−	6.16108i	0.577038	−	0.999459i
$39$	−8.39672	−	0.0924355i	−1.34455	−	0.0148015i
$40$	1.20301	−	1.88488i	0.190212	−	0.298026i
$41$	7.32942	−	4.23164i	1.14466	−	0.660872i	0.197082	−	0.980387i	$-0.436853\pi$
$41$	7.32942	−	4.23164i	1.14466	−	0.660872i	0.947581	+	0.319515i	$0.103520\pi$
$42$	5.43063	−	3.05617i	0.837965	−	0.471577i
$43$	1.70855	−	2.95930i	0.260551	−	0.451288i	−0.705837	−	0.708374i	$-0.749429\pi$
$43$	1.70855	−	2.95930i	0.260551	−	0.451288i	0.966389	+	0.257086i	$0.0827623\pi$
$44$	0.444351	+	0.769638i	0.0669884	+	0.116027i
$45$	−6.69338	−	0.445643i	−0.997791	−	0.0664325i
$46$		−	6.10864i		−	0.900671i
$47$	−3.08276			−0.449666			−0.224833	−	0.974397i	$-0.572184\pi$
$47$	−3.08276			−0.449666			−0.224833	+	0.974397i	$0.572184\pi$
$48$	−0.882485	+	1.49038i	−0.127376	+	0.215117i
$49$	2.97199	+	5.14764i	0.424570	+	0.735377i
$50$	−2.10555	−	4.53505i	−0.297769	−	0.641353i
$51$	−10.3495	+	5.82435i	−1.44922	+	0.815572i
$52$	2.42407	+	4.19861i	0.336158	+	0.582243i
$53$	−6.28930	+	3.63113i	−0.863902	+	0.498774i	−0.865317	−	0.501225i	$-0.832883\pi$
$53$	−6.28930	+	3.63113i	−0.863902	+	0.498774i	0.00141496	+	0.999999i	$0.499550\pi$
$54$	5.19332	+	0.171568i	0.706721	+	0.0233474i
$55$	1.98523	+	0.0883322i	0.267689	+	0.0119107i
$56$	−3.11576	−	1.79889i	−0.416361	−	0.240386i
$57$	6.04324	+	10.7385i	0.800446	+	1.42235i
$58$	0.208225			0.0273413
$59$	−4.03191	−	2.32782i	−0.524910	−	0.303057i	0.214031	−	0.976827i	$-0.431341\pi$
$59$	−4.03191	−	2.32782i	−0.524910	−	0.303057i	−0.738941	+	0.673770i	$0.764674\pi$
$60$	1.74754	+	3.45631i	0.225607	+	0.446208i
$61$			13.2474i			1.69615i	0.529873	+	0.848077i	$0.322240\pi$
$61$			13.2474i			1.69615i	−0.529873	+	0.848077i	$0.677760\pi$
$62$	5.55290	−	0.406530i	0.705219	−	0.0516294i
$63$	−0.237609	+	10.7907i	−0.0299359	+	1.35950i
$64$	1.00000			0.125000
$65$	10.8301	+	0.481879i	1.34330	+	0.0597698i
$66$	−1.53918	−	0.0169442i	−0.189460	−	0.00208568i
$67$	−6.17071	+	3.56266i	−0.753873	+	0.435249i	−0.827091	−	0.562067i	$-0.810006\pi$
$67$	−6.17071	+	3.56266i	−0.753873	+	0.435249i	0.0732189	+	0.997316i	$0.476673\pi$
$68$	5.93793	+	3.42826i	0.720079	+	0.415738i
$69$	9.10418	+	5.39079i	1.09601	+	0.648974i
$70$	−7.13897	+	3.70877i	−0.853271	+	0.443283i
$71$	−6.20217	+	3.58082i	−0.736062	+	0.424965i	−0.820636	−	0.571452i	$-0.806380\pi$
$71$	−6.20217	+	3.58082i	−0.736062	+	0.424965i	0.0845739	+	0.996417i	$0.473047\pi$
$72$	−1.44244	−	2.63047i	−0.169993	−	0.310004i
$73$	0.840046	+	1.45500i	0.0983200	+	0.170295i	0.910989	−	0.412430i	$-0.135320\pi$
$73$	0.840046	+	1.45500i	0.0983200	+	0.170295i	−0.812669	+	0.582725i	$0.801986\pi$
$74$	2.27731	−	3.94442i	0.264732	−	0.458530i
$75$	8.61704	+	0.864055i	0.995010	+	0.0997724i
$76$	3.55710	−	6.16108i	0.408027	−	0.706724i
$77$		−	3.19735i		−	0.364372i
$78$	−8.39672	−	0.0924355i	−0.950741	−	0.0104663i
$79$	−0.516925	−	0.298447i	−0.0581586	−	0.0335779i	0.470639	−	0.882326i	$-0.344024\pi$
$79$	−0.516925	−	0.298447i	−0.0581586	−	0.0335779i	−0.528797	+	0.848748i	$0.677357\pi$
$80$	1.20301	−	1.88488i	0.134500	−	0.210736i
$81$	−4.83873	+	7.58859i	−0.537636	+	0.843177i
$82$	7.32942	−	4.23164i	0.809399	−	0.467307i
$83$	−12.2924	+	7.09701i	−1.34926	+	0.778998i	−0.988145	−	0.153521i	$-0.950939\pi$
$83$	−12.2924	+	7.09701i	−1.34926	+	0.778998i	−0.361119	+	0.932520i	$0.617605\pi$
$84$	5.43063	−	3.05617i	0.592531	−	0.333455i
$85$	13.6052	−	7.06805i	1.47569	−	0.766638i
$86$	1.70855	−	2.95930i	0.184238	−	0.319109i
$87$	−0.183756	+	0.310334i	−0.0197007	+	0.0332713i
$88$	0.444351	+	0.769638i	0.0473680	+	0.0820437i
$89$	−9.33144			−0.989130			−0.494565	−	0.869141i	$-0.664673\pi$
$89$	−9.33144			−0.989130			−0.494565	+	0.869141i	$0.664673\pi$
$90$	−6.69338	−	0.445643i	−0.705545	−	0.0469749i
$91$		−	17.4425i		−	1.82847i
$92$		−	6.10864i		−	0.636870i
$93$	−4.29447	+	8.63467i	−0.445316	+	0.895374i
$94$	−3.08276			−0.317962
$95$	−7.33368	−	14.1165i	−0.752419	−	1.44833i
$96$	−0.882485	+	1.49038i	−0.0900682	+	0.152111i
$97$		−	16.4556i		−	1.67081i	−0.549636	−	0.835404i	$-0.685234\pi$
$97$		−	16.4556i		−	1.67081i	0.549636	−	0.835404i	$-0.314766\pi$
$98$	2.97199	+	5.14764i	0.300216	+	0.519990i
$99$	1.38356	−	2.27901i	0.139053	−	0.229049i
$100$	−2.10555	−	4.53505i	−0.210555	−	0.453505i
$101$			17.9374i			1.78484i	0.451205	+	0.892420i	$0.350994\pi$
$101$			17.9374i			1.78484i	−0.451205	+	0.892420i	$0.649006\pi$
$102$	−10.3495	+	5.82435i	−1.02476	+	0.576697i
$103$	8.26716	−	4.77304i	0.814587	−	0.470302i	−0.0339592	−	0.999423i	$-0.510812\pi$
$103$	8.26716	−	4.77304i	0.814587	−	0.470302i	0.848546	+	0.529121i	$0.177478\pi$
$104$	2.42407	+	4.19861i	0.237700	+	0.411708i
$105$	0.772577	−	13.9127i	0.0753958	−	1.35774i
$106$	−6.28930	+	3.63113i	−0.610871	+	0.352687i
$107$	1.21085	−	2.09726i	0.117057	−	0.202749i	−0.801543	−	0.597937i	$-0.795987\pi$
$107$	1.21085	−	2.09726i	0.117057	−	0.202749i	0.918600	+	0.395188i	$0.129320\pi$
$108$	5.19332	+	0.171568i	0.499727	+	0.0165091i
$109$	−3.13287			−0.300074			−0.150037	−	0.988680i	$-0.547939\pi$
$109$	−3.13287			−0.300074			−0.150037	+	0.988680i	$0.547939\pi$
$110$	1.98523	+	0.0883322i	0.189285	+	0.00842215i
$111$	3.86898	+	6.87495i	0.367227	+	0.652541i
$112$	−3.11576	−	1.79889i	−0.294412	−	0.169979i
$113$	7.80321	+	13.5156i	0.734064	+	1.27144i	0.955133	+	0.296178i	$0.0957121\pi$
$113$	7.80321	+	13.5156i	0.734064	+	1.27144i	−0.221069	+	0.975258i	$0.570955\pi$
$114$	6.04324	+	10.7385i	0.566001	+	1.00575i
$115$	−11.5141	−	7.34874i	−1.07369	−	0.685274i
$116$	0.208225			0.0193332
$117$	7.54774	−	12.4327i	0.697789	−	1.14940i
$118$	−4.03191	−	2.32782i	−0.371167	−	0.214294i
$119$	−12.3341	−	21.3633i	−1.13067	−	1.95837i
$120$	1.74754	+	3.45631i	0.159528	+	0.315517i
$121$	5.10510	−	8.84230i	0.464100	−	0.803846i
$122$			13.2474i			1.19936i
$123$	−0.161363	+	14.6580i	−0.0145496	+	1.32166i
$124$	5.55290	−	0.406530i	0.498665	−	0.0365075i
$125$	−11.0810	−	1.48699i	−0.991116	−	0.133001i
$126$	−0.237609	+	10.7907i	−0.0211679	+	0.961313i
$127$	3.03420	−	5.25539i	0.269242	−	0.466340i	−0.699424	−	0.714707i	$-0.746560\pi$
$127$	3.03420	−	5.25539i	0.269242	−	0.466340i	0.968666	+	0.248366i	$0.0798936\pi$
$128$	1.00000			0.0883883
$129$	2.90269	+	5.15792i	0.255568	+	0.454129i
$130$	10.8301	+	0.481879i	0.949859	+	0.0422636i
$131$	−8.06862	−	4.65842i	−0.704959	−	0.407008i	0.104233	−	0.994553i	$-0.466761\pi$
$131$	−8.06862	−	4.65842i	−0.704959	−	0.407008i	−0.809192	+	0.587545i	$0.800095\pi$
$132$	−1.53918	−	0.0169442i	−0.133969	−	0.00147480i
$133$	−22.1662	+	12.7976i	−1.92205	+	1.10970i
$134$	−6.17071	+	3.56266i	−0.533068	+	0.307767i
$135$	6.57099	−	9.58239i	0.565540	−	0.824721i
$136$	5.93793	+	3.42826i	0.509173	+	0.293971i
$137$	−2.33899	+	1.35042i	−0.199833	+	0.115374i	−0.596578	−	0.802555i	$-0.703473\pi$
$137$	−2.33899	+	1.35042i	−0.199833	+	0.115374i	0.396744	+	0.917929i	$0.370140\pi$
$138$	9.10418	+	5.39079i	0.774999	+	0.458894i
$139$			0.0933274i			0.00791592i	0.999992	+	0.00395796i	$0.00125986\pi$
$139$			0.0933274i			0.00791592i	−0.999992	+	0.00395796i	$0.998740\pi$
$140$	−7.13897	+	3.70877i	−0.603353	+	0.313448i
$141$	2.72049	−	4.59447i	0.229106	−	0.386924i
$142$	−6.20217	+	3.58082i	−0.520474	+	0.300496i
$143$	−2.15427	+	3.73131i	−0.180149	+	0.312028i
$144$	−1.44244	−	2.63047i	−0.120203	−	0.219206i
$145$	0.250497	−	0.392480i	0.0208026	−	0.0325937i
$146$	0.840046	+	1.45500i	0.0695227	+	0.120417i
$147$	−10.2947	−	0.113329i	−0.849089	−	0.00934722i
$148$	2.27731	−	3.94442i	0.187194	−	0.324230i
$149$	15.6491	+	9.03502i	1.28203	+	0.740178i	0.977218	−	0.212237i	$-0.0680748\pi$
$149$	15.6491	+	9.03502i	1.28203	+	0.740178i	0.304807	+	0.952414i	$0.401408\pi$
$150$	8.61704	+	0.864055i	0.703579	+	0.0705498i
$151$			10.6053i			0.863046i	0.902102	+	0.431523i	$0.142024\pi$
$151$			10.6053i			0.863046i	−0.902102	+	0.431523i	$0.857976\pi$
$152$	3.55710	−	6.16108i	0.288519	−	0.499729i
$153$	0.452827	−	20.5646i	0.0366089	−	1.66255i
$154$		−	3.19735i		−	0.257650i
$155$	5.91392	−	10.9556i	0.475018	−	0.879976i
$156$	−8.39672	−	0.0924355i	−0.672275	−	0.00740077i
$157$		−	16.5883i		−	1.32389i	−0.749554	−	0.661943i	$-0.769732\pi$
$157$		−	16.5883i		−	1.32389i	0.749554	−	0.661943i	$-0.230268\pi$
$158$	−0.516925	−	0.298447i	−0.0411243	−	0.0237431i
$159$	0.138464	−	12.5778i	0.0109809	−	0.997488i
$160$	1.20301	−	1.88488i	0.0951061	−	0.149013i
$161$	−10.9888	+	19.0331i	−0.866036	+	1.50002i
$162$	−4.83873	+	7.58859i	−0.380166	+	0.596216i
$163$			14.9127i			1.16805i	0.811735	+	0.584026i	$0.198523\pi$
$163$			14.9127i			1.16805i	−0.811735	+	0.584026i	$0.801477\pi$
$164$	7.32942	−	4.23164i	0.572332	−	0.330436i
$165$	−1.88359	+	2.88079i	−0.146637	+	0.224269i
$166$	−12.2924	+	7.09701i	−0.954074	+	0.550835i
$167$	6.30505	+	3.64022i	0.487899	+	0.281689i	0.723703	−	0.690112i	$-0.242439\pi$
$167$	6.30505	+	3.64022i	0.487899	+	0.281689i	−0.235803	+	0.971801i	$0.575772\pi$
$168$	5.43063	−	3.05617i	0.418982	−	0.235789i
$169$	−5.25223	+	9.09713i	−0.404018	+	0.699779i
$170$	13.6052	−	7.06805i	1.04347	−	0.542095i
$171$	−21.3374	−	0.469845i	−1.63171	−	0.0359299i
$172$	1.70855	−	2.95930i	0.130276	−	0.225644i
$173$	−1.12708	−	1.95215i	−0.0856900	−	0.148420i	0.819995	−	0.572371i	$-0.193976\pi$
$173$	−1.12708	−	1.95215i	−0.0856900	−	0.148420i	−0.905685	+	0.423951i	$0.860643\pi$
$174$	−0.183756	+	0.310334i	−0.0139305	+	0.0235264i
$175$	−1.59765	+	17.9178i	−0.120771	+	1.35446i
$176$	0.444351	+	0.769638i	0.0334942	+	0.0580137i
$177$	7.02743	−	3.95479i	0.528214	−	0.297260i
$178$	−9.33144			−0.699421
$179$	−2.16360	+	3.74747i	−0.161715	+	0.280099i	−0.935484	−	0.353369i	$-0.885036\pi$
$179$	−2.16360	+	3.74747i	−0.161715	+	0.280099i	0.773769	+	0.633468i	$0.218369\pi$
$180$	−6.69338	−	0.445643i	−0.498895	−	0.0332163i
$181$	−14.7949	+	8.54182i	−1.09969	+	0.634908i	−0.936141	−	0.351626i	$-0.885629\pi$
$181$	−14.7949	+	8.54182i	−1.09969	+	0.634908i	−0.163553	+	0.986535i	$0.552296\pi$
$182$		−	17.4425i		−	1.29292i
$183$	−19.7436	−	11.6906i	−1.45949	−	0.864195i
$184$		−	6.10864i		−	0.450335i
$185$	−4.69514	−	9.03763i	−0.345194	−	0.664460i
$186$	−4.29447	+	8.63467i	−0.314886	+	0.633125i
$187$			6.09340i			0.445594i
$188$	−3.08276			−0.224833
$189$	−15.8725	−	9.87676i	−1.15456	−	0.718429i
$190$	−7.33368	−	14.1165i	−0.532041	−	1.02412i
$191$	−6.92107	+	3.99588i	−0.500791	+	0.289132i	−0.729040	−	0.684471i	$-0.760033\pi$
$191$	−6.92107	+	3.99588i	−0.500791	+	0.289132i	0.228249	+	0.973603i	$0.426700\pi$
$192$	−0.882485	+	1.49038i	−0.0636879	+	0.107559i
$193$	−2.58264	−	1.49109i	−0.185902	−	0.107331i	0.404160	−	0.914688i	$-0.367564\pi$
$193$	−2.58264	−	1.49109i	−0.185902	−	0.107331i	−0.590063	+	0.807357i	$0.700897\pi$
$194$		−	16.4556i		−	1.18144i
$195$	−10.2755	+	15.7156i	−0.735847	+	1.12542i
$196$	2.97199	+	5.14764i	0.212285	+	0.367688i
$197$	3.27825	−	1.89270i	0.233565	−	0.134849i	−0.378650	−	0.925540i	$-0.623612\pi$
$197$	3.27825	−	1.89270i	0.233565	−	0.134849i	0.612216	+	0.790691i	$0.290278\pi$
$198$	1.38356	−	2.27901i	0.0983252	−	0.161962i
$199$	−7.34129	+	4.23850i	−0.520410	+	0.300459i	−0.737102	−	0.675781i	$-0.763807\pi$
$199$	−7.34129	+	4.23850i	−0.520410	+	0.300459i	0.216692	+	0.976240i	$0.430473\pi$
$200$	−2.10555	−	4.53505i	−0.148885	−	0.320676i
$201$	0.135853	−	12.3407i	0.00958232	−	0.870444i
$202$			17.9374i			1.26207i
$203$	−0.648781	−	0.374574i	−0.0455355	−	0.0262899i
$204$	−10.3495	+	5.82435i	−0.724612	+	0.407786i
$205$	0.841206	−	18.9058i	0.0587524	−	1.32044i
$206$	8.26716	−	4.77304i	0.576000	−	0.332554i
$207$	−16.0686	+	8.81136i	−1.11684	+	0.612432i
$208$	2.42407	+	4.19861i	0.168079	+	0.291121i
$209$	6.32240			0.437330
$210$	0.772577	−	13.9127i	0.0533129	−	0.960067i
$211$	4.30904	−	7.46348i	0.296647	−	0.513807i	−0.678720	−	0.734397i	$-0.737465\pi$
$211$	4.30904	−	7.46348i	0.296647	−	0.513807i	0.975367	+	0.220590i	$0.0707983\pi$
$212$	−6.28930	+	3.63113i	−0.431951	+	0.249387i
$213$	0.136545	−	12.4036i	0.00935593	−	0.849879i
$214$	1.21085	−	2.09726i	0.0827721	−	0.143366i
$215$	−3.52252	−	6.78047i	−0.240234	−	0.462424i
$216$	5.19332	+	0.171568i	0.353361	+	0.0116737i
$217$	−18.0328	−	8.72239i	−1.22415	−	0.592115i
$218$	−3.13287			−0.212184
$219$	−2.90983	−	0.0320330i	−0.196628	−	0.00216459i
$220$	1.98523	+	0.0883322i	0.133844	+	0.00595536i
$221$			33.2414i			2.23606i
$222$	3.86898	+	6.87495i	0.259669	+	0.461416i
$223$	7.72422	−	13.3787i	0.517252	−	0.895907i	−0.482547	−	0.875870i	$-0.660288\pi$
$223$	7.72422	−	13.3787i	0.517252	−	0.895907i	0.999799	−	0.0200367i	$-0.00637830\pi$
$224$	−3.11576	−	1.79889i	−0.208181	−	0.120193i
$225$	−8.89217	+	12.0801i	−0.592812	+	0.805341i
$226$	7.80321	+	13.5156i	0.519062	+	0.899041i
$227$	10.3037	+	17.8466i	0.683883	+	1.18452i	0.973786	+	0.227464i	$0.0730434\pi$
$227$	10.3037	+	17.8466i	0.683883	+	1.18452i	−0.289904	+	0.957056i	$0.593623\pi$
$228$	6.04324	+	10.7385i	0.400223	+	0.711173i
$229$	6.36405	+	3.67429i	0.420548	+	0.242804i	0.695312	−	0.718708i	$-0.255266\pi$
$229$	6.36405	+	3.67429i	0.420548	+	0.242804i	−0.274764	+	0.961512i	$0.588600\pi$
$230$	−11.5141	−	7.34874i	−0.759215	−	0.484562i
$231$	4.76525	+	2.82161i	0.313530	+	0.185648i
$232$	0.208225			0.0136707
$233$	27.2543			1.78549			0.892744	−	0.450563i	$-0.148777\pi$
$233$	27.2543			1.78549			0.892744	+	0.450563i	$0.148777\pi$
$234$	7.54774	−	12.4327i	0.493411	−	0.812750i
$235$	−3.70858	+	5.81063i	−0.241921	+	0.379043i
$236$	−4.03191	−	2.32782i	−0.262455	−	0.151528i
$237$	0.900976	−	0.507038i	0.0585247	−	0.0329356i
$238$	−12.3341	−	21.3633i	−0.799502	−	1.38478i
$239$	3.95325	+	6.84724i	0.255715	+	0.442911i	0.965089	−	0.261921i	$-0.0843559\pi$
$239$	3.95325	+	6.84724i	0.255715	+	0.442911i	−0.709375	+	0.704832i	$0.751023\pi$
$240$	1.74754	+	3.45631i	0.112804	+	0.223104i
$241$	−9.30448	−	5.37194i	−0.599354	−	0.346037i	0.169433	−	0.985542i	$-0.445806\pi$
$241$	−9.30448	−	5.37194i	−0.599354	−	0.346037i	−0.768787	+	0.639504i	$0.779140\pi$
$242$	5.10510	−	8.84230i	0.328169	−	0.568405i
$243$	−7.03975	−	13.9083i	−0.451600	−	0.892220i
$244$			13.2474i			0.848077i
$245$	13.2780	+	0.590800i	0.848301	+	0.0377448i
$246$	−0.161363	+	14.6580i	−0.0102881	+	0.934557i
$247$	34.4906			2.19459
$248$	5.55290	−	0.406530i	0.352610	−	0.0258147i
$249$	0.270626	−	24.5833i	0.0171502	−	1.55790i
$250$	−11.0810	−	1.48699i	−0.700825	−	0.0940457i
$251$	1.07603	−	1.86374i	0.0679186	−	0.117638i	−0.830066	−	0.557665i	$-0.811698\pi$
$251$	1.07603	−	1.86374i	0.0679186	−	0.117638i	0.897985	+	0.440026i	$0.145031\pi$
$252$	−0.237609	+	10.7907i	−0.0149679	+	0.679751i
$253$	4.70145	−	2.71438i	0.295577	−	0.170652i
$254$	3.03420	−	5.25539i	0.190383	−	0.329752i
$255$	−1.47235	+	26.5144i	−0.0922023	+	1.66039i
$256$	1.00000			0.0625000
$257$	−14.7563	−	25.5586i	−0.920470	−	1.59430i	−0.798689	−	0.601744i	$-0.794473\pi$
$257$	−14.7563	−	25.5586i	−0.920470	−	1.59430i	−0.121782	−	0.992557i	$-0.538861\pi$
$258$	2.90269	+	5.15792i	0.180714	+	0.321118i
$259$	−14.1911	+	8.19326i	−0.881795	+	0.509104i
$260$	10.8301	+	0.481879i	0.671651	+	0.0298849i
$261$	−0.300353	−	0.547730i	−0.0185914	−	0.0339036i
$262$	−8.06862	−	4.65842i	−0.498481	−	0.287798i
$263$			24.8024i			1.52938i	0.644399	+	0.764690i	$0.277108\pi$
$263$			24.8024i			1.52938i	−0.644399	+	0.764690i	$0.722892\pi$
$264$	−1.53918	−	0.0169442i	−0.0947302	−	0.00104284i
$265$	−0.721830	+	16.2229i	−0.0443417	+	0.996562i
$266$	−22.1662	+	12.7976i	−1.35910	+	0.784674i
$267$	8.23485	−	13.9073i	0.503965	−	0.851116i
$268$	−6.17071	+	3.56266i	−0.376936	+	0.217624i
$269$	5.25141	+	9.09572i	0.320184	+	0.554576i	0.980526	−	0.196390i	$-0.0629218\pi$
$269$	5.25141	+	9.09572i	0.320184	+	0.554576i	−0.660342	+	0.750965i	$0.729588\pi$
$270$	6.57099	−	9.58239i	0.399897	−	0.583166i
$271$			1.36503i			0.0829198i	0.999140	+	0.0414599i	$0.0132009\pi$
$271$			1.36503i			0.0829198i	−0.999140	+	0.0414599i	$0.986799\pi$
$272$	5.93793	+	3.42826i	0.360040	+	0.207869i
$273$	25.9959	+	15.3928i	1.57334	+	0.931612i
$274$	−2.33899	+	1.35042i	−0.141304	+	0.0815816i
$275$	2.55475	−	3.63566i	0.154057	−	0.219239i
$276$	9.10418	+	5.39079i	0.548007	+	0.324487i
$277$	8.45748			0.508161			0.254080	−	0.967183i	$-0.418227\pi$
$277$	8.45748			0.508161			0.254080	+	0.967183i	$0.418227\pi$
$278$			0.0933274i			0.00559740i
$279$	−9.07910	−	14.0203i	−0.543552	−	0.839376i
$280$	−7.13897	+	3.70877i	−0.426635	+	0.221641i
$281$		−	12.6014i		−	0.751737i	−0.926673	−	0.375869i	$-0.877344\pi$
$281$		−	12.6014i		−	0.751737i	0.926673	−	0.375869i	$-0.122656\pi$
$282$	2.72049	−	4.59447i	0.162003	−	0.273596i
$283$		−	27.6941i		−	1.64624i	−0.567865	−	0.823121i	$-0.692231\pi$
$283$		−	27.6941i		−	1.64624i	0.567865	−	0.823121i	$-0.307769\pi$
$284$	−6.20217	+	3.58082i	−0.368031	+	0.212483i
$285$	27.5108	+	1.52768i	1.62960	+	0.0904922i
$286$	−2.15427	+	3.73131i	−0.127385	+	0.220637i
$287$	−30.4490			−1.79735
$288$	−1.44244	−	2.63047i	−0.0849967	−	0.155002i
$289$	15.0060	+	25.9911i	0.882704	+	1.52889i
$290$	0.250497	−	0.392480i	0.0147097	−	0.0230472i
$291$	24.5250	+	14.5218i	1.43768	+	0.851282i
$292$	0.840046	+	1.45500i	0.0491600	+	0.0851476i
$293$	4.37066	−	7.57021i	0.255337	−	0.442256i	−0.709650	−	0.704554i	$-0.751147\pi$
$293$	4.37066	−	7.57021i	0.255337	−	0.442256i	0.964987	+	0.262298i	$0.0844803\pi$
$294$	−10.2947	−	0.113329i	−0.600396	−	0.00660948i
$295$	−9.23809	+	4.79928i	−0.537862	+	0.279425i
$296$	2.27731	−	3.94442i	0.132366	−	0.229265i
$297$	2.17561	+	4.07321i	0.126242	+	0.236352i
$298$	15.6491	+	9.03502i	0.906529	+	0.523385i
$299$	25.6478	−	14.8078i	1.48325	−	0.856356i
$300$	8.61704	+	0.864055i	0.497505	+	0.0498862i
$301$	−10.6469	+	6.14698i	−0.613676	+	0.354306i
$302$			10.6053i			0.610266i
$303$	−26.7335	−	15.8295i	−1.53580	−	0.909381i
$304$	3.55710	−	6.16108i	0.204014	−	0.353362i
$305$	24.9697	+	15.9367i	1.42976	+	0.912533i
$306$	0.452827	−	20.5646i	0.0258864	−	1.17560i
$307$	4.87449	+	2.81429i	0.278202	+	0.160620i	0.632609	−	0.774471i	$-0.281984\pi$
$307$	4.87449	+	2.81429i	0.278202	+	0.160620i	−0.354407	+	0.935091i	$0.615317\pi$
$308$		−	3.19735i		−	0.182186i
$309$	−0.182008	+	16.5333i	−0.0103540	+	0.940547i
$310$	5.91392	−	10.9556i	0.335888	−	0.622237i
$311$			30.9974i			1.75770i	0.477099	+	0.878850i	$0.341688\pi$
$311$			30.9974i			1.75770i	−0.477099	+	0.878850i	$0.658312\pi$
$312$	−8.39672	−	0.0924355i	−0.475370	−	0.00523313i
$313$	3.84231	−	6.65508i	0.217180	−	0.376167i	−0.736764	−	0.676149i	$-0.763647\pi$
$313$	3.84231	−	6.65508i	0.217180	−	0.376167i	0.953945	+	0.299982i	$0.0969807\pi$
$314$		−	16.5883i		−	0.936129i
$315$	20.0533	+	13.4292i	1.12988	+	0.756648i
$316$	−0.516925	−	0.298447i	−0.0290793	−	0.0167889i
$317$	−11.4672	+	19.8618i	−0.644064	+	1.11555i	0.340453	+	0.940262i	$0.389420\pi$
$317$	−11.4672	+	19.8618i	−0.644064	+	1.11555i	−0.984517	+	0.175290i	$0.943914\pi$
$318$	0.138464	−	12.5778i	0.00776466	−	0.705330i
$319$	0.0925251	+	0.160258i	0.00518041	+	0.00897273i
$320$	1.20301	−	1.88488i	0.0672501	−	0.105368i
$321$	2.05714	+	3.65542i	0.114819	+	0.204026i
$322$	−10.9888	+	19.0331i	−0.612380	+	1.06067i
$323$	42.2436	−	24.3893i	2.35050	−	1.35706i
$324$	−4.83873	+	7.58859i	−0.268818	+	0.421588i
$325$	13.9369	−	19.8337i	0.773081	−	1.10017i
$326$			14.9127i			0.825937i
$327$	2.76471	−	4.66915i	0.152889	−	0.258204i
$328$	7.32942	−	4.23164i	0.404700	−	0.233653i
$329$	9.60514	+	5.54553i	0.529549	+	0.305735i
$330$	−1.88359	+	2.88079i	−0.103688	+	0.158582i
$331$	4.12110	−	2.37932i	0.226516	−	0.130779i	−0.382448	−	0.923977i	$-0.624919\pi$
$331$	4.12110	−	2.37932i	0.226516	−	0.130779i	0.608964	+	0.793198i	$0.291585\pi$
$332$	−12.2924	+	7.09701i	−0.674632	+	0.389499i
$333$	−13.6606	−	0.300802i	−0.748595	−	0.0164839i
$334$	6.30505	+	3.64022i	0.344997	+	0.199184i
$335$	−0.708220	+	15.9170i	−0.0386942	+	0.869637i
$336$	5.43063	−	3.05617i	0.296265	−	0.166728i
$337$	−26.5645			−1.44706			−0.723530	−	0.690293i	$-0.757482\pi$
$337$	−26.5645			−1.44706			−0.723530	+	0.690293i	$0.757482\pi$
$338$	−5.25223	+	9.09713i	−0.285684	+	0.494818i
$339$	−27.0295	−	0.297555i	−1.46804	−	0.0161610i
$340$	13.6052	−	7.06805i	0.737847	−	0.383319i
$341$	2.78032	+	4.09308i	0.150563	+	0.221653i
$342$	−21.3374	−	0.469845i	−1.15380	−	0.0254063i
$343$			3.79932i			0.205144i
$344$	1.70855	−	2.95930i	0.0921189	−	0.159555i
$345$	21.1134	−	10.6751i	1.13671	−	0.574730i
$346$	−1.12708	−	1.95215i	−0.0605920	−	0.104948i
$347$	−15.9672	−	9.21867i	−0.857165	−	0.494884i	0.00589720	−	0.999983i	$-0.498123\pi$
$347$	−15.9672	−	9.21867i	−0.857165	−	0.494884i	−0.863062	+	0.505098i	$0.831456\pi$
$348$	−0.183756	+	0.310334i	−0.00985034	+	0.0166357i
$349$	21.7094			1.16208			0.581038	−	0.813876i	$-0.302647\pi$
$349$	21.7094			1.16208			0.581038	+	0.813876i	$0.302647\pi$
$350$	−1.59765	+	17.9178i	−0.0853982	+	0.957746i
$351$	11.8686	+	22.2206i	0.633500	+	1.18605i
$352$	0.444351	+	0.769638i	0.0236840	+	0.0410218i
$353$	−25.1771	−	14.5360i	−1.34004	−	0.773673i	−0.353228	−	0.935537i	$-0.614916\pi$
$353$	−25.1771	−	14.5360i	−1.34004	−	0.773673i	−0.986813	+	0.161864i	$0.948249\pi$
$354$	7.02743	−	3.95479i	0.373504	−	0.210195i
$355$	−0.711830	+	15.9981i	−0.0377800	+	0.849091i
$356$	−9.33144			−0.494565
$357$	42.7240	+	0.470329i	2.26120	+	0.0248925i
$358$	−2.16360	+	3.74747i	−0.114350	+	0.198060i
$359$	4.67591	−	2.69964i	0.246785	−	0.142481i	−0.371506	−	0.928430i	$-0.621159\pi$
$359$	4.67591	−	2.69964i	0.246785	−	0.142481i	0.618291	+	0.785949i	$0.287825\pi$
$360$	−6.69338	−	0.445643i	−0.352772	−	0.0234874i
$361$	−15.8059	−	27.3767i	−0.831891	−	1.44088i
$362$	−14.7949	+	8.54182i	−0.777601	+	0.448948i
$363$	8.67318	+	15.4117i	0.455224	+	0.808906i
$364$		−	17.4425i		−	0.914236i
$365$	3.75309	+	0.166992i	0.196446	+	0.00874077i
$366$	−19.7436	−	11.6906i	−1.03201	−	0.611078i
$367$	2.40676	+	4.16864i	0.125632	+	0.217601i	0.921980	−	0.387238i	$-0.126571\pi$
$367$	2.40676	+	4.16864i	0.125632	+	0.217601i	−0.796348	+	0.604839i	$0.793237\pi$
$368$		−	6.10864i		−	0.318435i
$369$	−21.7035	−	13.1759i	−1.12984	−	0.685911i
$370$	−4.69514	−	9.03763i	−0.244089	−	0.469844i
$371$	26.1280			1.35650
$372$	−4.29447	+	8.63467i	−0.222658	+	0.447687i
$373$			24.7028i			1.27906i	0.768764	+	0.639532i	$0.220872\pi$
$373$			24.7028i			1.27906i	−0.768764	+	0.639532i	$0.779128\pi$
$374$			6.09340i			0.315082i
$375$	11.9950	−	15.2026i	0.619419	−	0.785060i
$376$	−3.08276			−0.158981
$377$	0.504753	+	0.874257i	0.0259961	+	0.0450266i
$378$	−15.8725	−	9.87676i	−0.816395	−	0.508006i
$379$	4.52613	−	7.83948i	0.232492	−	0.402687i	−0.726049	−	0.687643i	$-0.758646\pi$
$379$	4.52613	−	7.83948i	0.232492	−	0.402687i	0.958541	+	0.284956i	$0.0919788\pi$
$380$	−7.33368	−	14.1165i	−0.376210	−	0.724163i
$381$	5.15487	+	9.15990i	0.264092	+	0.469276i
$382$	−6.92107	+	3.99588i	−0.354113	+	0.204447i
$383$	−1.92870	+	1.11354i	−0.0985522	+	0.0568991i	−0.548466	−	0.836173i	$-0.684788\pi$
$383$	−1.92870	+	1.11354i	−0.0985522	+	0.0568991i	0.449914	+	0.893072i	$0.351455\pi$
$384$	−0.882485	+	1.49038i	−0.0450341	+	0.0760554i
$385$	−6.02662	−	3.84643i	−0.307145	−	0.196032i
$386$	−2.58264	−	1.49109i	−0.131453	−	0.0758944i
$387$	−10.2488	−	0.225676i	−0.520977	−	0.0114718i
$388$		−	16.4556i		−	0.835404i
$389$	0.0377830	−	0.0654420i	0.00191567	−	0.00331804i	−0.865066	−	0.501658i	$-0.832724\pi$
$389$	0.0377830	−	0.0654420i	0.00191567	−	0.00331804i	0.866982	+	0.498340i	$0.166057\pi$
$390$	−10.2755	+	15.7156i	−0.520322	+	0.795790i
$391$	20.9420	−	36.2727i	1.05908	−	1.83439i
$392$	2.97199	+	5.14764i	0.150108	+	0.259995i
$393$	14.0632	−	7.91430i	0.709396	−	0.399223i
$394$	3.27825	−	1.89270i	0.165156	−	0.0953527i
$395$	−1.18440	+	0.615308i	−0.0595936	+	0.0309595i
$396$	1.38356	−	2.27901i	0.0695264	−	0.114524i
$397$	2.36830	+	1.36734i	0.118862	+	0.0686248i	0.558252	−	0.829671i	$-0.311472\pi$
$397$	2.36830	+	1.36734i	0.118862	+	0.0686248i	−0.439390	+	0.898296i	$0.644806\pi$
$398$	−7.34129	+	4.23850i	−0.367986	+	0.212457i
$399$	0.488005	−	44.3297i	0.0244308	−	2.21926i
$400$	−2.10555	−	4.53505i	−0.105277	−	0.226752i
$401$	−23.6890			−1.18297			−0.591485	−	0.806316i	$-0.701458\pi$
$401$	−23.6890			−1.18297			−0.591485	+	0.806316i	$0.701458\pi$
$402$	0.135853	−	12.3407i	0.00677572	−	0.615497i
$403$	15.1675	+	22.3290i	0.755546	+	1.11229i
$404$			17.9374i			0.892420i
$405$	8.48257	+	18.2496i	0.421502	+	0.906827i
$406$	−0.648781	−	0.374574i	−0.0321985	−	0.0185898i
$407$	4.04770			0.200637
$408$	−10.3495	+	5.82435i	−0.512378	+	0.288348i
$409$	−20.3042	−	11.7227i	−1.00398	−	0.579648i	−0.0945563	−	0.995520i	$-0.530143\pi$
$409$	−20.3042	−	11.7227i	−1.00398	−	0.579648i	−0.909423	+	0.415872i	$0.863477\pi$
$410$	0.841206	−	18.9058i	0.0415442	−	0.933690i
$411$	0.0514946	−	4.67770i	0.00254004	−	0.230734i
$412$	8.26716	−	4.77304i	0.407294	−	0.235151i
$413$	8.37499	+	14.5059i	0.412106	+	0.713789i
$414$	−16.0686	+	8.81136i	−0.789728	+	0.433055i
$415$	−1.41081	+	31.7074i	−0.0692540	+	1.55646i
$416$	2.42407	+	4.19861i	0.118850	+	0.205854i
$417$	−0.139093	−	0.0823600i	−0.00681141	−	0.00403319i
$418$	6.32240			0.309239
$419$			22.5730i			1.10276i	0.834254	+	0.551380i	$0.185899\pi$
$419$			22.5730i			1.10276i	−0.834254	+	0.551380i	$0.814101\pi$
$420$	0.772577	−	13.9127i	0.0376979	−	0.678870i
$421$	−11.8601	−	20.5423i	−0.578027	−	1.00117i	−0.995706	−	0.0925771i	$-0.970490\pi$
$421$	−11.8601	−	20.5423i	−0.578027	−	1.00117i	0.417679	−	0.908595i	$-0.362844\pi$
$422$	4.30904	−	7.46348i	0.209761	−	0.363317i
$423$	4.44670	+	8.10909i	0.216206	+	0.394278i
$424$	−6.28930	+	3.63113i	−0.305436	+	0.176343i
$425$	3.04476	−	34.1472i	0.147692	−	1.65638i
$426$	0.136545	−	12.4036i	0.00661564	−	0.600956i
$427$	23.8306	−	41.2757i	1.15324	−	1.99747i
$428$	1.21085	−	2.09726i	0.0585287	−	0.101375i
$429$	−3.65994	−	6.50351i	−0.176704	−	0.313992i
$430$	−3.52252	−	6.78047i	−0.169871	−	0.326983i
$431$	5.43983	+	3.14069i	0.262027	+	0.151282i	0.625259	−	0.780417i	$-0.284993\pi$
$431$	5.43983	+	3.14069i	0.262027	+	0.151282i	−0.363232	+	0.931699i	$0.618327\pi$
$432$	5.19332	+	0.171568i	0.249864	+	0.00825457i
$433$	−1.44003			−0.0692034			−0.0346017	−	0.999401i	$-0.511016\pi$
$433$	−1.44003			−0.0692034			−0.0346017	+	0.999401i	$0.511016\pi$
$434$	−18.0328	−	8.72239i	−0.865604	−	0.418688i
$435$	0.363883	+	0.719692i	0.0174469	+	0.0345066i
$436$	−3.13287			−0.150037
$437$	−37.6358	−	21.7291i	−1.80037	−	1.03944i
$438$	−2.90983	−	0.0320330i	−0.139037	−	0.00153059i
$439$	0.711057	+	1.23159i	0.0339369	+	0.0587804i	0.882495	−	0.470322i	$-0.155862\pi$
$439$	0.711057	+	1.23159i	0.0339369	+	0.0587804i	−0.848558	+	0.529102i	$0.822529\pi$
$440$	1.98523	+	0.0883322i	0.0946423	+	0.00421107i
$441$	9.25378	−	15.2429i	0.440656	−	0.725852i
$442$			33.2414i			1.58113i
$443$	−4.10133	−	7.10372i	−0.194860	−	0.337508i	0.751994	−	0.659169i	$-0.229092\pi$
$443$	−4.10133	−	7.10372i	−0.194860	−	0.337508i	−0.946855	+	0.321662i	$0.895759\pi$
$444$	3.86898	+	6.87495i	0.183614	+	0.326270i
$445$	−11.2258	+	17.5886i	−0.532153	+	0.833782i
$446$	7.72422	−	13.3787i	0.365752	−	0.633502i
$447$	−27.2757	+	15.3498i	−1.29010	+	0.726020i
$448$	−3.11576	−	1.79889i	−0.147206	−	0.0849894i
$449$	−9.07385			−0.428221			−0.214111	−	0.976809i	$-0.568685\pi$
$449$	−9.07385			−0.428221			−0.214111	+	0.976809i	$0.568685\pi$
$450$	−8.89217	+	12.0801i	−0.419181	+	0.569462i
$451$	6.51367	+	3.76067i	0.306717	+	0.177083i
$452$	7.80321	+	13.5156i	0.367032	+	0.635718i
$453$	−15.8059	−	9.35900i	−0.742624	−	0.439724i
$454$	10.3037	+	17.8466i	0.483578	+	0.837582i
$455$	−32.8770	−	20.9835i	−1.54130	−	0.983720i
$456$	6.04324	+	10.7385i	0.283001	+	0.502875i
$457$	3.29187			0.153987			0.0769935	−	0.997032i	$-0.475468\pi$
$457$	3.29187			0.153987			0.0769935	+	0.997032i	$0.475468\pi$
$458$	6.36405	+	3.67429i	0.297373	+	0.171688i
$459$	30.2494	+	18.8228i	1.41192	+	0.878574i
$460$	−11.5141	−	7.34874i	−0.536846	−	0.342637i
$461$	−4.60516			−0.214484			−0.107242	−	0.994233i	$-0.534202\pi$
$461$	−4.60516			−0.214484			−0.107242	+	0.994233i	$0.534202\pi$
$462$	4.76525	+	2.82161i	0.221699	+	0.131273i
$463$	2.72875			0.126816			0.0634079	−	0.997988i	$-0.479803\pi$
$463$	2.72875			0.126816			0.0634079	+	0.997988i	$0.479803\pi$
$464$	0.208225			0.00966662
$465$	11.1090	+	18.4821i	0.515169	+	0.857088i
$466$	27.2543			1.26253
$467$	−16.5976			−0.768046			−0.384023	−	0.923323i	$-0.625462\pi$
$467$	−16.5976			−0.768046			−0.384023	+	0.923323i	$0.625462\pi$
$468$	7.54774	−	12.4327i	0.348894	−	0.574701i
$469$	25.6353			1.18373
$470$	−3.70858	+	5.81063i	−0.171064	+	0.268024i
$471$	24.7227	+	14.6389i	1.13916	+	0.674524i
$472$	−4.03191	−	2.32782i	−0.185584	−	0.107147i
$473$	3.03678			0.139631
$474$	0.900976	−	0.507038i	0.0413832	−	0.0232890i
$475$	−35.4304	−	3.15918i	−1.62566	−	0.144953i
$476$	−12.3341	−	21.3633i	−0.565333	−	0.979186i
$477$	18.6235	+	11.3061i	0.852713	+	0.517672i
$478$	3.95325	+	6.84724i	0.180818	+	0.313185i
$479$	−10.0774	−	5.81818i	−0.460447	−	0.265839i	0.251785	−	0.967783i	$-0.418982\pi$
$479$	−10.0774	−	5.81818i	−0.460447	−	0.265839i	−0.712232	+	0.701944i	$0.752316\pi$
$480$	1.74754	+	3.45631i	0.0797641	+	0.157758i
$481$	22.0815			1.00683
$482$	−9.30448	−	5.37194i	−0.423807	−	0.244685i
$483$	−18.6691	−	33.1738i	−0.849471	−	1.50946i
$484$	5.10510	−	8.84230i	0.232050	−	0.401923i
$485$	−31.0168	−	19.7962i	−1.40840	−	0.898897i
$486$	−7.03975	−	13.9083i	−0.319330	−	0.630895i
$487$	13.0103	+	22.5344i	0.589552	+	1.02113i	0.994291	+	0.106701i	$0.0340288\pi$
$487$	13.0103	+	22.5344i	0.589552	+	1.02113i	−0.404740	+	0.914432i	$0.632638\pi$
$488$			13.2474i			0.599681i
$489$	−22.2255	−	13.1602i	−1.00507	−	0.595126i
$490$	13.2780	+	0.590800i	0.599839	+	0.0266896i
$491$	−18.1629	−	31.4591i	−0.819681	−	1.41973i	−0.905917	−	0.423455i	$-0.860817\pi$
$491$	−18.1629	−	31.4591i	−0.819681	−	1.41973i	0.0862357	−	0.996275i	$-0.472516\pi$
$492$	−0.161363	+	14.6580i	−0.00727479	+	0.660832i
$493$	1.23643	+	0.713851i	0.0556859	+	0.0321502i
$494$	34.4906			1.55181
$495$	−2.63123	−	5.34951i	−0.118265	−	0.240442i
$496$	5.55290	−	0.406530i	0.249333	−	0.0182537i
$497$	25.7660			1.15576
$498$	0.270626	−	24.5833i	0.0121270	−	1.10160i
$499$	29.3551	+	16.9482i	1.31412	+	0.758705i	0.982775	−	0.184806i	$-0.0591658\pi$
$499$	29.3551	+	16.9482i	1.31412	+	0.758705i	0.331341	+	0.943511i	$0.392499\pi$
$500$	−11.0810	−	1.48699i	−0.495558	−	0.0665003i
$501$	−10.9894	+	6.18445i	−0.490971	+	0.276301i
$502$	1.07603	−	1.86374i	0.0480257	−	0.0831829i
$503$	−17.8849	+	30.9776i	−0.797450	+	1.38122i	0.123822	+	0.992305i	$0.460485\pi$
$503$	−17.8849	+	30.9776i	−0.797450	+	1.38122i	−0.921272	+	0.388920i	$0.872848\pi$
$504$	−0.237609	+	10.7907i	−0.0105839	+	0.480656i
$505$	33.8099	+	21.5789i	1.50452	+	0.960246i
$506$	4.70145	−	2.71438i	0.209005	−	0.120669i
$507$	−8.92313	−	15.8559i	−0.396290	−	0.704184i
$508$	3.03420	−	5.25539i	0.134621	−	0.233170i
$509$	13.7400	+	23.7983i	0.609013	+	1.05484i	0.991403	+	0.130840i	$0.0417675\pi$
$509$	13.7400	+	23.7983i	0.609013	+	1.05484i	−0.382391	+	0.924001i	$0.624899\pi$
$510$	−1.47235	+	26.5144i	−0.0651969	+	1.17408i
$511$		−	6.04459i		−	0.267397i
$512$	1.00000			0.0441942
$513$	19.5302	−	31.3862i	0.862279	−	1.38573i
$514$	−14.7563	−	25.5586i	−0.650871	−	1.12734i
$515$	0.948831	−	21.3246i	0.0418105	−	0.939674i
$516$	2.90269	+	5.15792i	0.127784	+	0.227065i
$517$	−1.36983	−	2.37261i	−0.0602448	−	0.104347i
$518$	−14.1911	+	8.19326i	−0.623523	+	0.359991i
$519$	3.90407	+	0.0429781i	0.171370	+	0.00188653i
$520$	10.8301	+	0.481879i	0.474929	+	0.0211318i
$521$	6.51605	+	3.76204i	0.285473	+	0.164818i	0.635899	−	0.771773i	$-0.280630\pi$
$521$	6.51605	+	3.76204i	0.285473	+	0.164818i	−0.350425	+	0.936591i	$0.613963\pi$
$522$	−0.300353	−	0.547730i	−0.0131461	−	0.0239735i
$523$	−33.5344			−1.46636			−0.733178	−	0.680036i	$-0.761964\pi$
$523$	−33.5344			−1.46636			−0.733178	+	0.680036i	$0.761964\pi$
$524$	−8.06862	−	4.65842i	−0.352479	−	0.203504i
$525$	−25.2943	−	18.1933i	−1.10394	−	0.794020i
$526$			24.8024i			1.08143i
$527$	34.3664	+	16.6229i	1.49702	+	0.724103i
$528$	−1.53918	−	0.0169442i	−0.0669843	−	0.000737400i
$529$	−14.3155			−0.622415
$530$	−0.721830	+	16.2229i	−0.0313543	+	0.704676i
$531$	−0.307474	+	13.9636i	−0.0133432	+	0.605967i
$532$	−22.1662	+	12.7976i	−0.961025	+	0.554848i
$533$	35.5341	+	20.5156i	1.53915	+	0.888629i
$534$	8.23485	−	13.9073i	0.356357	−	0.601830i
$535$	−2.49641	−	4.80533i	−0.107929	−	0.207752i
$536$	−6.17071	+	3.56266i	−0.266534	+	0.153884i
$537$	−3.67579	−	6.53167i	−0.158622	−	0.281862i
$538$	5.25141	+	9.09572i	0.226405	+	0.392144i
$539$	−2.64121	+	4.57471i	−0.113765	+	0.197047i
$540$	6.57099	−	9.58239i	0.282770	−	0.412360i
$541$	−14.5594	+	25.2177i	−0.625959	+	1.08419i	0.362395	+	0.932025i	$0.381959\pi$
$541$	−14.5594	+	25.2177i	−0.625959	+	1.08419i	−0.988354	+	0.152169i	$0.951374\pi$
$542$			1.36503i			0.0586332i
$543$	0.325720	−	29.5879i	0.0139780	−	1.26974i
$544$	5.93793	+	3.42826i	0.254586	+	0.146986i
$545$	−3.76886	+	5.90508i	−0.161440	+	0.252946i
$546$	25.9959	+	15.3928i	1.11252	+	0.658749i
$547$	−31.4354	+	18.1493i	−1.34408	+	0.776006i	−0.987404	−	0.158221i	$-0.949424\pi$
$547$	−31.4354	+	18.1493i	−1.34408	+	0.776006i	−0.356678	+	0.934227i	$0.616091\pi$
$548$	−2.33899	+	1.35042i	−0.0999167	+	0.0576869i
$549$	34.8468	−	19.1086i	1.48723	−	0.815534i
$550$	2.55475	−	3.63566i	0.108935	−	0.155025i
$551$	0.740679	−	1.28289i	0.0315540	−	0.0546531i
$552$	9.10418	+	5.39079i	0.387500	+	0.229447i
$553$	1.07374	+	1.85978i	0.0456602	+	0.0790858i
$554$	8.45748			0.359324
$555$	17.6129	+	0.978049i	0.747624	+	0.0415159i
$556$			0.0933274i			0.00395796i
$557$		−	13.9269i		−	0.590102i	−0.955482	−	0.295051i	$-0.904663\pi$
$557$		−	13.9269i		−	0.590102i	0.955482	−	0.295051i	$-0.0953366\pi$
$558$	−9.07910	−	14.0203i	−0.384349	−	0.593528i
$559$	16.5666			0.700692
$560$	−7.13897	+	3.70877i	−0.301677	+	0.156724i
$561$	−9.08146	−	5.37734i	−0.383420	−	0.227031i
$562$		−	12.6014i		−	0.531558i
$563$	11.8572	+	20.5373i	0.499722	+	0.865544i	1.00000		0.000320897i	$-0.000102145\pi$
$563$	11.8572	+	20.5373i	0.499722	+	0.865544i	−0.500278	+	0.865865i	$0.666769\pi$
$564$	2.72049	−	4.59447i	0.114553	−	0.193462i
$565$	34.8625	+	1.55119i	1.46668	+	0.0652593i
$566$		−	27.6941i		−	1.16407i
$567$	28.7273	−	14.9399i	1.20644	−	0.627419i
$568$	−6.20217	+	3.58082i	−0.260237	+	0.150248i
$569$	−6.30020	−	10.9123i	−0.264118	−	0.457466i	0.703214	−	0.710978i	$-0.251748\pi$
$569$	−6.30020	−	10.9123i	−0.264118	−	0.457466i	−0.967332	+	0.253512i	$0.918414\pi$
$570$	27.5108	+	1.52768i	1.15230	+	0.0639877i
$571$	−23.6607	+	13.6605i	−0.990169	+	0.571675i	−0.905325	−	0.424720i	$-0.860373\pi$
$571$	−23.6607	+	13.6605i	−0.990169	+	0.571675i	−0.0848444	+	0.996394i	$0.527039\pi$
$572$	−2.15427	+	3.73131i	−0.0900747	+	0.156014i
$573$	0.152373	−	13.8413i	0.00636545	−	0.578229i
$574$	−30.4490			−1.27092
$575$	−27.7030	+	12.8620i	−1.15530	+	0.536384i
$576$	−1.44244	−	2.63047i	−0.0601017	−	0.109603i
$577$	7.29616	+	4.21244i	0.303743	+	0.175366i	0.644123	−	0.764922i	$-0.277222\pi$
$577$	7.29616	+	4.21244i	0.303743	+	0.175366i	−0.340380	+	0.940288i	$0.610556\pi$
$578$	15.0060	+	25.9911i	0.624166	+	1.08109i
$579$	4.50142	−	2.53324i	0.187073	−	0.105278i
$580$	0.250497	−	0.392480i	0.0104013	−	0.0162968i
$581$	51.0669			2.11861
$582$	24.5250	+	14.5218i	1.01659	+	0.601947i
$583$	−5.58931	−	3.22699i	−0.231486	−	0.133648i
$584$	0.840046	+	1.45500i	0.0347614	+	0.0602084i
$585$	−14.3542	−	29.1832i	−0.593471	−	1.20658i
$586$	4.37066	−	7.57021i	0.180550	−	0.312722i
$587$			12.0748i			0.498382i	0.968454	+	0.249191i	$0.0801646\pi$
$587$			12.0748i			0.498382i	−0.968454	+	0.249191i	$0.919835\pi$
$588$	−10.2947	−	0.113329i	−0.424544	−	0.00467361i
$589$	17.2476	−	35.6579i	0.710674	−	1.46926i
$590$	−9.23809	+	4.79928i	−0.380326	+	0.197583i
$591$	−0.0721730	+	6.55610i	−0.00296880	+	0.269682i
$592$	2.27731	−	3.94442i	0.0935970	−	0.162115i
$593$	−1.78234			−0.0731919			−0.0365959	−	0.999330i	$-0.511651\pi$
$593$	−1.78234			−0.0731919			−0.0365959	+	0.999330i	$0.511651\pi$
$594$	2.17561	+	4.07321i	0.0892664	+	0.167126i
$595$	−55.1053	−	2.45189i	−2.25910	−	0.100518i
$596$	15.6491	+	9.03502i	0.641013	+	0.370089i
$597$	0.161624	−	14.6817i	0.00661483	−	0.600882i
$598$	25.6478	−	14.8078i	1.04882	−	0.605535i
$599$	−8.79971	+	5.08052i	−0.359547	+	0.207584i	−0.668882	−	0.743369i	$-0.733227\pi$
$599$	−8.79971	+	5.08052i	−0.359547	+	0.207584i	0.309335	+	0.950953i	$0.399893\pi$
$600$	8.61704	+	0.864055i	0.351789	+	0.0352749i
$601$	−14.8372	−	8.56625i	−0.605221	−	0.349425i	0.165872	−	0.986147i	$-0.446956\pi$
$601$	−14.8372	−	8.56625i	−0.605221	−	0.349425i	−0.771093	+	0.636723i	$0.780290\pi$
$602$	−10.6469	+	6.14698i	−0.433934	+	0.250532i
$603$	18.2724	+	11.0929i	0.744108	+	0.451739i
$604$			10.6053i			0.431523i
$605$	−10.5252	−	20.2599i	−0.427910	−	0.823681i
$606$	−26.7335	−	15.8295i	−1.08597	−	0.643030i
$607$	−1.84689	+	1.06630i	−0.0749628	+	0.0432798i	−0.537013	−	0.843574i	$-0.680447\pi$
$607$	−1.84689	+	1.06630i	−0.0749628	+	0.0432798i	0.462050	+	0.886854i	$0.347114\pi$
$608$	3.55710	−	6.16108i	0.144259	−	0.249865i
$609$	1.13080	−	0.636372i	0.0458221	−	0.0257871i
$610$	24.9697	+	15.9367i	1.01100	+	0.645258i
$611$	−7.47282	−	12.9433i	−0.302318	−	0.523630i
$612$	0.452827	−	20.5646i	0.0183044	−	0.831274i
$613$	−2.50469	+	4.33825i	−0.101163	+	0.175220i	−0.912164	−	0.409825i	$-0.865590\pi$
$613$	−2.50469	+	4.33825i	−0.101163	+	0.175220i	0.811001	+	0.585045i	$0.198923\pi$
$614$	4.87449	+	2.81429i	0.196718	+	0.113575i
$615$	27.4344	+	17.9378i	1.10626	+	0.723321i
$616$		−	3.19735i		−	0.128825i
$617$	20.8759	−	36.1581i	0.840432	−	1.45567i	−0.0490981	−	0.998794i	$-0.515635\pi$
$617$	20.8759	−	36.1581i	0.840432	−	1.45567i	0.889530	−	0.456877i	$-0.151032\pi$
$618$	−0.182008	+	16.5333i	−0.00732142	+	0.665067i
$619$		−	4.34602i		−	0.174681i	−0.996178	−	0.0873407i	$-0.972163\pi$
$619$		−	4.34602i		−	0.174681i	0.996178	−	0.0873407i	$-0.0278369\pi$
$620$	5.91392	−	10.9556i	0.237509	−	0.439988i
$621$	1.04805	−	31.7241i	0.0420567	−	1.27305i
$622$			30.9974i			1.24288i
$623$	29.0746	+	16.7862i	1.16485	+	0.672525i
$624$	−8.39672	−	0.0924355i	−0.336138	−	0.00370038i
$625$	−16.1333	+	19.0975i	−0.645334	+	0.763901i
$626$	3.84231	−	6.65508i	0.153570	−	0.265991i
$627$	−5.57942	+	9.42276i	−0.222821	+	0.376309i
$628$		−	16.5883i		−	0.661943i
$629$	27.0450	−	15.6145i	1.07836	−	0.622589i
$630$	20.0533	+	13.4292i	0.798944	+	0.535031i
$631$	−12.1873	+	7.03634i	−0.485169	+	0.280112i	−0.722568	−	0.691300i	$-0.757038\pi$
$631$	−12.1873	+	7.03634i	−0.485169	+	0.280112i	0.237399	+	0.971412i	$0.423705\pi$
$632$	−0.516925	−	0.298447i	−0.0205622	−	0.0118716i
$633$	7.32073	+	13.0085i	0.290973	+	0.517042i
$634$	−11.4672	+	19.8618i	−0.455422	+	0.788814i
$635$	−6.25561	−	12.0414i	−0.248246	−	0.477847i
$636$	0.138464	−	12.5778i	0.00549044	−	0.498744i
$637$	−14.4086	+	24.9565i	−0.570890	+	0.988811i
$638$	0.0925251	+	0.160258i	0.00366310	+	0.00634468i
$639$	18.3655	+	11.1495i	0.726528	+	0.441066i
$640$	1.20301	−	1.88488i	0.0475530	−	0.0745064i
$641$	7.95197	+	13.7732i	0.314084	+	0.544009i	0.979242	−	0.202693i	$-0.0649694\pi$
$641$	7.95197	+	13.7732i	0.314084	+	0.544009i	−0.665158	+	0.746702i	$0.731636\pi$
$642$	2.05714	+	3.65542i	0.0811890	+	0.144268i
$643$	25.7158			1.01413			0.507065	−	0.861908i	$-0.330730\pi$
$643$	25.7158			1.01413			0.507065	+	0.861908i	$0.330730\pi$
$644$	−10.9888	+	19.0331i	−0.433018	+	0.750009i
$645$	13.2140	+	0.733779i	0.520301	+	0.0288925i
$646$	42.2436	−	24.3893i	1.66205	−	0.959586i
$647$		−	1.11076i		−	0.0436686i	−0.999762	−	0.0218343i	$-0.993049\pi$
$647$		−	1.11076i		−	0.0436686i	0.999762	−	0.0218343i	$-0.00695062\pi$
$648$	−4.83873	+	7.58859i	−0.190083	+	0.298108i
$649$		−	4.13748i		−	0.162410i
$650$	13.9369	−	19.8337i	0.546651	−	0.777940i
$651$	28.9134	−	19.1783i	1.13320	−	0.751658i
$652$			14.9127i			0.584026i
$653$	3.71653			0.145439			0.0727195	−	0.997352i	$-0.476832\pi$
$653$	3.71653			0.145439			0.0727195	+	0.997352i	$0.476832\pi$
$654$	2.76471	−	4.66915i	0.108109	−	0.182578i
$655$	−18.4872	+	9.60427i	−0.722354	+	0.375270i
$656$	7.32942	−	4.23164i	0.286166	−	0.165218i
$657$	2.61562	−	4.30847i	0.102045	−	0.168089i
$658$	9.60514	+	5.54553i	0.374447	+	0.216187i
$659$			22.2369i			0.866225i	0.901340	+	0.433113i	$0.142585\pi$
$659$			22.2369i			0.866225i	−0.901340	+	0.433113i	$0.857415\pi$
$660$	−1.88359	+	2.88079i	−0.0733185	+	0.112135i
$661$	13.7480	+	23.8122i	0.534736	+	0.926189i	0.999176	+	0.0405848i	$0.0129221\pi$
$661$	13.7480	+	23.8122i	0.534736	+	0.926189i	−0.464441	+	0.885604i	$0.653745\pi$
$662$	4.12110	−	2.37932i	0.160171	−	0.0924749i
$663$	−49.5422	−	29.3350i	−1.92406	−	1.13928i
$664$	−12.2924	+	7.09701i	−0.477037	+	0.275417i
$665$	−2.54404	+	57.1762i	−0.0986535	+	2.21720i
$666$	−13.6606	−	0.300802i	−0.529336	−	0.0116558i
$667$		−	1.27197i		−	0.0492511i
$668$	6.30505	+	3.64022i	0.243950	+	0.140844i
$669$	13.1228	+	23.3185i	0.507359	+	0.901546i
$670$	−0.708220	+	15.9170i	−0.0273609	+	0.614926i
$671$	−10.1957	+	5.88649i	−0.393600	+	0.227245i
$672$	5.43063	−	3.05617i	0.209491	−	0.117894i
$673$	23.1347	+	40.0704i	0.891776	+	1.54460i	0.837744	+	0.546063i	$0.183874\pi$
$673$	23.1347	+	40.0704i	0.891776	+	1.54460i	0.0540324	+	0.998539i	$0.482793\pi$
$674$	−26.5645			−1.02323
$675$	−10.1567	−	23.9132i	−0.390932	−	0.920420i
$676$	−5.25223	+	9.09713i	−0.202009	+	0.349889i
$677$	1.08373	−	0.625693i	0.0416512	−	0.0240473i	−0.479030	−	0.877799i	$-0.659011\pi$
$677$	1.08373	−	0.625693i	0.0416512	−	0.0240473i	0.520681	+	0.853751i	$0.325678\pi$
$678$	−27.0295	−	0.297555i	−1.03806	−	0.0114275i
$679$	−29.6017	+	51.2716i	−1.13601	+	1.96762i
$680$	13.6052	−	7.06805i	0.521737	−	0.271047i
$681$	−35.6910	−	0.392906i	−1.36768	−	0.0150562i
$682$	2.78032	+	4.09308i	0.106464	+	0.156732i
$683$	2.52231			0.0965135			0.0482568	−	0.998835i	$-0.484633\pi$
$683$	2.52231			0.0965135			0.0482568	+	0.998835i	$0.484633\pi$
$684$	−21.3374	−	0.469845i	−0.815857	−	0.0179650i
$685$	−0.268448	+	6.03327i	−0.0102569	+	0.230520i
$686$			3.79932i			0.145059i
$687$	−11.0922	+	6.24233i	−0.423196	+	0.238160i
$688$	1.70855	−	2.95930i	0.0651379	−	0.112822i
$689$	−30.4914	−	17.6042i	−1.16163	−	0.670668i
$690$	21.1134	−	10.6751i	0.803773	−	0.406395i
$691$	−6.21777	−	10.7695i	−0.236535	−	0.409691i	0.723183	−	0.690657i	$-0.242679\pi$
$691$	−6.21777	−	10.7695i	−0.236535	−	0.409691i	−0.959718	+	0.280966i	$0.909345\pi$
$692$	−1.12708	−	1.95215i	−0.0428450	−	0.0742098i
$693$	−8.41052	+	4.61199i	−0.319489	+	0.175195i
$694$	−15.9672	−	9.21867i	−0.606107	−	0.349936i
$695$	0.175911	+	0.112273i	0.00667268	+	0.00425878i
$696$	−0.183756	+	0.310334i	−0.00696524	+	0.0117632i
$697$	58.0287			2.19799
$698$	21.7094			0.821712
$699$	−24.0515	+	40.6192i	−0.909712	+	1.53636i
$700$	−1.59765	+	17.9178i	−0.0603856	+	0.677229i
$701$	−43.2340	−	24.9611i	−1.63292	−	0.942769i	−0.983185	−	0.182612i	$-0.941545\pi$
$701$	−43.2340	−	24.9611i	−1.63292	−	0.942769i	−0.649739	−	0.760157i	$-0.725122\pi$
$702$	11.8686	+	22.2206i	0.447952	+	0.838663i
$703$	−16.2013	−	28.0614i	−0.611042	−	1.05836i
$704$	0.444351	+	0.769638i	0.0167471	+	0.0290068i
$705$	−5.38725	−	10.6550i	−0.202896	−	0.401289i
$706$	−25.1771	−	14.5360i	−0.947552	−	0.547069i
$707$	32.2674	−	55.8888i	1.21354	−	2.10191i
$708$	7.02743	−	3.95479i	0.264107	−	0.148630i
$709$			20.1626i			0.757221i	0.925556	+	0.378610i	$0.123598\pi$
$709$			20.1626i			0.757221i	−0.925556	+	0.378610i	$0.876402\pi$
$710$	−0.711830	+	15.9981i	−0.0267145	+	0.600398i
$711$	−0.0394207	+	1.79025i	−0.00147839	+	0.0671394i
$712$	−9.33144			−0.349710
$713$	−2.48335	−	33.9207i	−0.0930021	−	1.27034i
$714$	42.7240	+	0.470329i	1.59891	+	0.0176016i
$715$	4.44147	+	8.54935i	0.166102	+	0.319727i
$716$	−2.16360	+	3.74747i	−0.0808577	+	0.140050i
$717$	−13.6936	−	0.150747i	−0.511398	−	0.00562975i
$718$	4.67591	−	2.69964i	0.174503	−	0.100750i
$719$	−18.1199	+	31.3846i	−0.675760	+	1.17045i	0.300487	+	0.953786i	$0.402851\pi$
$719$	−18.1199	+	31.3846i	−0.675760	+	1.17045i	−0.976246	+	0.216664i	$0.930482\pi$
$720$	−6.69338	−	0.445643i	−0.249448	−	0.0166081i
$721$	−34.3447			−1.27906
$722$	−15.8059	−	27.3767i	−0.588236	−	1.01885i
$723$	16.2173	−	9.12651i	0.603127	−	0.339419i
$724$	−14.7949	+	8.54182i	−0.549847	+	0.317454i
$725$	−0.438428	−	0.944312i	−0.0162828	−	0.0350709i
$726$	8.67318	+	15.4117i	0.321892	+	0.571983i
$727$	−5.69001	−	3.28513i	−0.211031	−	0.121839i	0.390760	−	0.920493i	$-0.372212\pi$
$727$	−5.69001	−	3.28513i	−0.211031	−	0.121839i	−0.601790	+	0.798654i	$0.705546\pi$
$728$		−	17.4425i		−	0.646462i
$729$	26.9411	+	1.78201i	0.997820	+	0.0660005i
$730$	3.75309	+	0.166992i	0.138908	+	0.00618066i
$731$	20.2905	−	11.7147i	0.750471	−	0.433285i
$732$	−19.7436	−	11.6906i	−0.729744	−	0.432098i
$733$	13.5969	−	7.85018i	0.502213	−	0.289953i	−0.227414	−	0.973798i	$-0.573027\pi$
$733$	13.5969	−	7.85018i	0.502213	−	0.289953i	0.729627	+	0.683845i	$0.239694\pi$
$734$	2.40676	+	4.16864i	0.0888352	+	0.153867i
$735$	−12.5982	+	19.2678i	−0.464690	+	0.710705i
$736$		−	6.10864i		−	0.225168i
$737$	−5.48392	−	3.16614i	−0.202003	−	0.116626i
$738$	−21.7035	−	13.1759i	−0.798915	−	0.485012i
$739$	32.0129	−	18.4826i	1.17761	−	0.679895i	0.222151	−	0.975012i	$-0.428692\pi$
$739$	32.0129	−	18.4826i	1.17761	−	0.679895i	0.955461	+	0.295118i	$0.0953589\pi$
$740$	−4.69514	−	9.03763i	−0.172597	−	0.332230i
$741$	−30.4375	+	51.4040i	−1.11815	+	1.88837i
$742$	26.1280			0.959188
$743$			48.0280i			1.76198i	0.473139	+	0.880988i	$0.343121\pi$
$743$			48.0280i			1.76198i	−0.473139	+	0.880988i	$0.656879\pi$
$744$	−4.29447	+	8.63467i	−0.157443	+	0.316562i
$745$	35.8559	−	18.6275i	1.31366	−	0.682459i
$746$			24.7028i			0.904435i
$747$	36.3995	+	22.0977i	1.33179	+	0.808513i
$748$			6.09340i			0.222797i
$749$	−7.54546	+	4.35637i	−0.275705	+	0.159178i
$750$	11.9950	−	15.2026i	0.437996	−	0.555121i
$751$	−3.28045	+	5.68190i	−0.119705	+	0.207335i	−0.919651	−	0.392737i	$-0.871528\pi$
$751$	−3.28045	+	5.68190i	−0.119705	+	0.207335i	0.799946	+	0.600072i	$0.204862\pi$
$752$	−3.08276			−0.112417
$753$	1.82810	+	3.24842i	0.0666195	+	0.118379i
$754$	0.504753	+	0.874257i	0.0183820	+	0.0318386i
$755$	19.9897	+	12.7582i	0.727499	+	0.464320i
$756$	−15.8725	−	9.87676i	−0.577278	−	0.359214i
$757$	−9.71443	−	16.8259i	−0.353077	−	0.611547i	0.633710	−	0.773571i	$-0.281531\pi$
$757$	−9.71443	−	16.8259i	−0.353077	−	0.611547i	−0.986787	+	0.162024i	$0.948198\pi$
$758$	4.52613	−	7.83948i	0.164396	−	0.284743i
$759$	−0.103506	+	9.40232i	−0.00375702	+	0.341283i
$760$	−7.33368	−	14.1165i	−0.266020	−	0.512060i
$761$	14.9000	−	25.8076i	0.540126	−	0.935526i	−0.458770	−	0.888555i	$-0.651710\pi$
$761$	14.9000	−	25.8076i	0.540126	−	0.935526i	0.998896	−	0.0469710i	$-0.0149568\pi$
$762$	5.15487	+	9.15990i	0.186741	+	0.331828i
$763$	9.76127	+	5.63567i	0.353382	+	0.204025i
$764$	−6.92107	+	3.99588i	−0.250396	+	0.144566i
$765$	−38.2170	−	25.5929i	−1.38174	−	0.925312i
$766$	−1.92870	+	1.11354i	−0.0696869	+	0.0402338i
$767$		−	22.5712i		−	0.815000i
$768$	−0.882485	+	1.49038i	−0.0318439	+	0.0537793i
$769$	−14.1978	+	24.5913i	−0.511986	+	0.886787i	0.487917	+	0.872890i	$0.337757\pi$
$769$	−14.1978	+	24.5913i	−0.511986	+	0.886787i	−0.999903	+	0.0138965i	$0.995576\pi$
$770$	−6.02662	−	3.84643i	−0.217184	−	0.138616i
$771$	51.1141	+	0.562691i	1.84083	+	0.0202648i
$772$	−2.58264	−	1.49109i	−0.0929512	−	0.0536654i
$773$		−	5.32890i		−	0.191667i	−0.995397	−	0.0958336i	$-0.969448\pi$
$773$		−	5.32890i		−	0.191667i	0.995397	−	0.0958336i	$-0.0305517\pi$
$774$	−10.2488	−	0.225676i	−0.368386	−	0.00811177i
$775$	−13.5355	−	24.3267i	−0.486211	−	0.873842i
$776$		−	16.4556i		−	0.590720i
$777$	0.312428	−	28.3806i	0.0112083	−	1.01815i
$778$	0.0377830	−	0.0654420i	0.00135459	−	0.00234621i
$779$		−	60.2095i		−	2.15723i
$780$	−10.2755	+	15.7156i	−0.367923	+	0.562709i
$781$	−5.51188	−	3.18228i	−0.197230	−	0.113871i
$782$	20.9420	−	36.2727i	0.748886	−	1.29711i
$783$	1.08138	+	0.0357248i	0.0386454	+	0.00127670i
$784$	2.97199	+	5.14764i	0.106142	+	0.183844i
$785$	−31.2669	−	19.9558i	−1.11596	−	0.712253i
$786$	14.0632	−	7.91430i	0.501619	−	0.282294i
$787$	19.0704	−	33.0310i	0.679788	−	1.17743i	−0.295257	−	0.955418i	$-0.595405\pi$
$787$	19.0704	−	33.0310i	0.679788	−	1.17743i	0.975045	−	0.222009i	$-0.0712614\pi$
$788$	3.27825	−	1.89270i	0.116783	−	0.0674245i
$789$	−36.9648	−	21.8877i	−1.31598	−	0.779223i
$790$	−1.18440	+	0.615308i	−0.0421391	+	0.0218917i
$791$		−	56.1484i		−	1.99641i
$792$	1.38356	−	2.27901i	0.0491626	−	0.0809810i
$793$	−55.6206	+	32.1126i	−1.97515	+	1.14035i
$794$	2.36830	+	1.36734i	0.0840478	+	0.0485250i
$795$	−23.5412	−	15.3922i	−0.834919	−	0.545906i
$796$	−7.34129	+	4.23850i	−0.260205	+	0.150229i
$797$	12.6480	−	7.30232i	0.448015	−	0.258662i	−0.258977	−	0.965884i	$-0.583385\pi$
$797$	12.6480	−	7.30232i	0.448015	−	0.258662i	0.706991	+	0.707222i	$0.250052\pi$
$798$	0.488005	−	44.3297i	0.0172752	−	1.56925i
$799$	−18.3052	−	10.5685i	−0.647591	−	0.373887i
$800$	−2.10555	−	4.53505i	−0.0744423	−	0.160338i
$801$	13.4600	+	24.5460i	0.475587	+	0.867292i
$802$	−23.6890			−0.836486
$803$	−0.746550	+	1.29306i	−0.0263452	+	0.0456312i
$804$	0.135853	−	12.3407i	0.00479116	−	0.435222i
$805$	22.6555	+	43.6095i	0.798503	+	1.53703i
$806$	15.1675	+	22.3290i	0.534252	+	0.786506i
$807$	−18.1903	−	0.200249i	−0.640330	−	0.00704910i
$808$			17.9374i			0.631036i
$809$	−23.6624	+	40.9844i	−0.831924	+	1.44094i	0.0645858	+	0.997912i	$0.479427\pi$
$809$	−23.6624	+	40.9844i	−0.831924	+	1.44094i	−0.896510	+	0.443023i	$0.853906\pi$
$810$	8.48257	+	18.2496i	0.298047	+	0.641224i
$811$	23.9466	+	41.4767i	0.840879	+	1.45645i	0.889152	+	0.457611i	$0.151295\pi$
$811$	23.9466	+	41.4767i	0.840879	+	1.45645i	−0.0482734	+	0.998834i	$0.515372\pi$
$812$	−0.648781	−	0.374574i	−0.0227678	−	0.0131450i
$813$	−2.03441	−	1.20462i	−0.0713500	−	0.0422479i
$814$	4.04770			0.141872
$815$	28.1086	+	17.9401i	0.984602	+	0.628413i
$816$	−10.3495	+	5.82435i	−0.362306	+	0.203893i
$817$	−12.1550	−	21.0530i	−0.425249	−	0.736552i
$818$	−20.3042	−	11.7227i	−0.709921	−	0.409873i
$819$	−45.8820	+	25.1598i	−1.60325	+	0.879155i
$820$	0.841206	−	18.9058i	0.0293762	−	0.660218i
$821$	45.1035			1.57412			0.787061	−	0.616875i	$-0.211602\pi$
$821$	45.1035			1.57412			0.787061	+	0.616875i	$0.211602\pi$
$822$	0.0514946	−	4.67770i	0.00179608	−	0.163153i
$823$	8.14995	−	14.1161i	0.284089	−	0.492057i	−0.688298	−	0.725428i	$-0.741642\pi$
$823$	8.14995	−	14.1161i	0.284089	−	0.492057i	0.972388	+	0.233370i	$0.0749754\pi$
$824$	8.26716	−	4.77304i	0.288000	−	0.166277i
$825$	3.16398	+	7.01595i	0.110156	+	0.244264i
$826$	8.37499	+	14.5059i	0.291403	+	0.504725i
$827$	0.920190	−	0.531272i	0.0319981	−	0.0184741i	−0.483916	−	0.875115i	$-0.660786\pi$
$827$	0.920190	−	0.531272i	0.0319981	−	0.0184741i	0.515914	+	0.856641i	$0.327452\pi$
$828$	−16.0686	+	8.81136i	−0.558422	+	0.306216i
$829$		−	44.4160i		−	1.54263i	−0.636454	−	0.771315i	$-0.719599\pi$
$829$		−	44.4160i		−	1.54263i	0.636454	−	0.771315i	$-0.280401\pi$
$830$	−1.41081	+	31.7074i	−0.0489700	+	1.10058i
$831$	−7.46360	+	12.6048i	−0.258909	+	0.437256i
$832$	2.42407	+	4.19861i	0.0840395	+	0.145561i
$833$			40.7550i			1.41208i
$834$	−0.139093	−	0.0823600i	−0.00481639	−	0.00285189i
$835$	14.4464	−	7.50505i	0.499938	−	0.259723i
$836$	6.32240			0.218665
$837$	28.9077	−	1.15854i	0.999198	−	0.0400450i
$838$			22.5730i			0.779770i
$839$		−	47.8777i		−	1.65292i	−0.562995	−	0.826461i	$-0.690351\pi$
$839$		−	47.8777i		−	1.65292i	0.562995	−	0.826461i	$-0.309649\pi$
$840$	0.772577	−	13.9127i	0.0266564	−	0.480033i
$841$	−28.9566			−0.998505
$842$	−11.8601	−	20.5423i	−0.408727	−	0.707935i
$843$	18.7808	+	11.1206i	0.646846	+	0.383012i
$844$	4.30904	−	7.46348i	0.148323	−	0.256904i
$845$	10.8285	+	20.8437i	0.372513	+	0.717046i
$846$	4.44670	+	8.10909i	0.152881	+	0.278796i
$847$	−31.8126	+	18.3670i	−1.09309	+	0.631098i
$848$	−6.28930	+	3.63113i	−0.215976	+	0.124694i
$849$	41.2746	+	24.4396i	1.41654	+	0.838765i
$850$	3.04476	−	34.1472i	0.104434	−	1.17124i
$851$	−24.0951	−	13.9113i	−0.825969	−	0.476873i
$852$	0.136545	−	12.4036i	0.00467796	−	0.424940i
$853$		−	8.62917i		−	0.295457i	−0.989028	−	0.147729i	$-0.952804\pi$
$853$		−	8.62917i		−	0.295457i	0.989028	−	0.147729i	$-0.0471962\pi$
$854$	23.8306	−	41.2757i	0.815465	−	1.41243i
$855$	−26.5547	+	39.6533i	−0.908151	+	1.35611i
$856$	1.21085	−	2.09726i	0.0413861	−	0.0716828i
$857$	4.91551	+	8.51392i	0.167911	+	0.290830i	0.937685	−	0.347486i	$-0.112965\pi$
$857$	4.91551	+	8.51392i	0.167911	+	0.290830i	−0.769774	+	0.638316i	$0.779631\pi$
$858$	−3.65994	−	6.50351i	−0.124948	−	0.222026i
$859$	3.45563	−	1.99511i	0.117905	−	0.0680723i	−0.439888	−	0.898053i	$-0.644982\pi$
$859$	3.45563	−	1.99511i	0.117905	−	0.0680723i	0.557793	+	0.829980i	$0.311648\pi$
$860$	−3.52252	−	6.78047i	−0.120117	−	0.231212i
$861$	26.8708	−	45.3804i	0.915753	−	1.54656i
$862$	5.43983	+	3.14069i	0.185281	+	0.106972i
$863$	−30.3842	+	17.5423i	−1.03429	+	0.597148i	−0.918211	−	0.396092i	$-0.870366\pi$
$863$	−30.3842	+	17.5423i	−1.03429	+	0.597148i	−0.116080	+	0.993240i	$0.537033\pi$
$864$	5.19332	+	0.171568i	0.176680	+	0.00583686i
$865$	−5.03546	−	0.224051i	−0.171211	−	0.00761796i
$866$	−1.44003			−0.0489342
$867$	−51.9791	−	0.572213i	−1.76530	−	0.0194334i
$868$	−18.0328	−	8.72239i	−0.612074	−	0.296057i
$869$		−	0.530460i		−	0.0179946i
$870$	0.363883	+	0.719692i	0.0123368	+	0.0243998i
$871$	−29.9165	−	17.2723i	−1.01368	−	0.585249i
$872$	−3.13287			−0.106092
$873$	−43.2858	+	23.7362i	−1.46500	+	0.803348i
$874$	−37.6358	−	21.7291i	−1.27305	−	0.734997i
$875$	31.8509	+	24.5666i	1.07676	+	0.830503i
$876$	−2.90983	−	0.0320330i	−0.0983140	−	0.00108229i
$877$	−7.29841	+	4.21374i	−0.246450	+	0.142288i	−0.618138	−	0.786070i	$-0.712113\pi$
$877$	−7.29841	+	4.21374i	−0.246450	+	0.142288i	0.371688	+	0.928358i	$0.378779\pi$
$878$	0.711057	+	1.23159i	0.0239970	+	0.0415640i
$879$	7.42541	+	13.1945i	0.250453	+	0.445040i
$880$	1.98523	+	0.0883322i	0.0669222	+	0.00297768i
$881$	−16.0518	−	27.8025i	−0.540799	−	0.936691i	−0.998858	−	0.0477692i	$-0.984789\pi$
$881$	−16.0518	−	27.8025i	−0.540799	−	0.936691i	0.458060	−	0.888921i	$-0.348545\pi$
$882$	9.25378	−	15.2429i	0.311591	−	0.513255i
$883$	33.7274			1.13502			0.567509	−	0.823367i	$-0.307907\pi$
$883$	33.7274			1.13502			0.567509	+	0.823367i	$0.307907\pi$
$884$			33.2414i			1.11803i
$885$	0.999742	−	18.0035i	0.0336060	−	0.605182i
$886$	−4.10133	−	7.10372i	−0.137787	−	0.238654i
$887$	−16.6124	+	28.7736i	−0.557790	+	0.966121i	0.439890	+	0.898052i	$0.355017\pi$
$887$	−16.6124	+	28.7736i	−0.557790	+	0.966121i	−0.997681	+	0.0680698i	$0.978316\pi$
$888$	3.86898	+	6.87495i	0.129834	+	0.230708i
$889$	−18.9077	+	10.9164i	−0.634144	+	0.366123i
$890$	−11.2258	+	17.5886i	−0.376289	+	0.589573i
$891$	−7.99056	−	0.352071i	−0.267694	−	0.0117948i
$892$	7.72422	−	13.3787i	0.258626	−	0.447953i
$893$	−10.9657	+	18.9931i	−0.366952	+	0.635580i
$894$	−27.2757	+	15.3498i	−0.912235	+	0.513374i
$895$	4.46070	+	8.58637i	0.149105	+	0.287011i
$896$	−3.11576	−	1.79889i	−0.104090	−	0.0600966i
$897$	−0.564656	+	51.2926i	−0.0188533	+	1.71261i
$898$	−9.07385			−0.302798
$899$	1.15626	−	0.0846499i	0.0385633	−	0.00282323i
$900$	−8.89217	+	12.0801i	−0.296406	+	0.402671i
$901$	−49.7939			−1.65887
$902$	6.51367	+	3.76067i	0.216881	+	0.125217i
$903$	0.234399	−	21.2925i	0.00780031	−	0.708569i
$904$	7.80321	+	13.5156i	0.259531	+	0.449521i
$905$	−1.69802	+	38.1624i	−0.0564442	+	1.26856i
$906$	−15.8059	−	9.35900i	−0.525115	−	0.310932i
$907$			9.52988i			0.316435i	0.987404	+	0.158217i	$0.0505746\pi$
$907$			9.52988i			0.316435i	−0.987404	+	0.158217i	$0.949425\pi$
$908$	10.3037	+	17.8466i	0.341941	+	0.592260i
$909$	47.1838	−	25.8737i	1.56499	−	0.858176i
$910$	−32.8770	−	20.9835i	−1.08986	−	0.695595i
$911$	−1.43113	+	2.47879i	−0.0474155	+	0.0821260i	−0.888759	−	0.458375i	$-0.848432\pi$
$911$	−1.43113	+	2.47879i	−0.0474155	+	0.0821260i	0.841344	+	0.540501i	$0.181765\pi$
$912$	6.04324	+	10.7385i	0.200112	+	0.355586i
$913$	−10.9243	−	6.30713i	−0.361540	−	0.208735i
$914$	3.29187			0.108885
$915$	−45.7871	+	23.1504i	−1.51367	+	0.765329i
$916$	6.36405	+	3.67429i	0.210274	+	0.121402i
$917$	16.7599	+	29.0291i	0.553462	+	0.958625i
$918$	30.2494	+	18.8228i	0.998378	+	0.621246i
$919$	−12.5986	−	21.8215i	−0.415590	−	0.719824i	0.579900	−	0.814688i	$-0.303092\pi$
$919$	−12.5986	−	21.8215i	−0.415590	−	0.719824i	−0.995490	+	0.0948641i	$0.969758\pi$
$920$	−11.5141	−	7.34874i	−0.379607	−	0.242281i
$921$	−8.49601	+	4.78126i	−0.279953	+	0.157548i
$922$	−4.60516			−0.151663
$923$	−30.0690	−	17.3603i	−0.989732	−	0.571422i
$924$	4.76525	+	2.82161i	0.156765	+	0.0928242i
$925$	−22.6831	−	2.02256i	−0.745817	−	0.0665014i
$926$	2.72875			0.0896723
$927$	−24.4802	−	14.8617i	−0.804036	−	0.488121i
$928$	0.208225			0.00683533
$929$	10.1595			0.333323			0.166661	−	0.986014i	$-0.446701\pi$
$929$	10.1595			0.333323			0.166661	+	0.986014i	$0.446701\pi$
$930$	11.1090	+	18.4821i	0.364280	+	0.606053i
$931$	42.2867			1.38589
$932$	27.2543			0.892744
$933$	−46.1977	−	27.3547i	−1.51245	−	0.895553i
$934$	−16.5976			−0.543091
$935$	11.4853	+	7.33041i	0.375611	+	0.239730i
$936$	7.54774	−	12.4327i	0.246705	−	0.406375i
$937$	26.5990	+	15.3570i	0.868953	+	0.501690i	0.867000	−	0.498308i	$-0.166045\pi$
$937$	26.5990	+	15.3570i	0.868953	+	0.501690i	0.00195254	+	0.999998i	$0.499378\pi$
$938$	25.6353			0.837023
$939$	6.52779	+	11.5995i	0.213026	+	0.378535i
$940$	−3.70858	+	5.81063i	−0.120960	+	0.189522i
$941$	14.6895	+	25.4430i	0.478865	+	0.829418i	0.999706	−	0.0242352i	$-0.00771505\pi$
$941$	14.6895	+	25.4430i	0.478865	+	0.829418i	−0.520841	+	0.853653i	$0.674382\pi$
$942$	24.7227	+	14.6389i	0.805510	+	0.476960i
$943$	−25.8496	−	44.7728i	−0.841779	−	1.45800i
$944$	−4.03191	−	2.32782i	−0.131228	−	0.0757642i
$945$	−37.7113	+	18.0360i	−1.22675	+	0.586711i
$946$	3.03678			0.0987343
$947$	−9.13018	−	5.27131i	−0.296691	−	0.171295i	0.344264	−	0.938873i	$-0.388128\pi$
$947$	−9.13018	−	5.27131i	−0.296691	−	0.171295i	−0.640955	+	0.767578i	$0.721462\pi$
$948$	0.900976	−	0.507038i	0.0292623	−	0.0164678i
$949$	−4.07266	+	7.05406i	−0.132204	+	0.228984i
$950$	−35.4304	−	3.15918i	−1.14952	−	0.102497i
$951$	−19.4819	−	34.6182i	−0.631745	−	1.12257i
$952$	−12.3341	−	21.3633i	−0.399751	−	0.692389i
$953$		−	31.9897i		−	1.03625i	−0.855306	−	0.518124i	$-0.826631\pi$
$953$		−	31.9897i		−	1.03625i	0.855306	−	0.518124i	$-0.173369\pi$
$954$	18.6235	+	11.3061i	0.602959	+	0.366049i
$955$	−0.794339	+	17.8525i	−0.0257042	+	0.577692i
$956$	3.95325	+	6.84724i	0.127857	+	0.221455i
$957$	−0.320497	−	0.00352820i	−0.0103602	−	0.000114051i
$958$	−10.0774	−	5.81818i	−0.325585	−	0.187977i
$959$	9.71698			0.313778
$960$	1.74754	+	3.45631i	0.0564018	+	0.111552i
$961$	30.6695	−	4.51484i	0.989338	−	0.145640i
$962$	22.0815			0.711935
$963$	−7.26335	−	0.159937i	−0.234058	−	0.00515390i
$964$	−9.30448	−	5.37194i	−0.299677	−	0.173019i
$965$	−5.91746	+	3.07418i	−0.190490	+	0.0989613i
$966$	−18.6691	−	33.1738i	−0.600667	−	1.06735i
$967$	−27.7074	+	47.9906i	−0.891009	+	1.54327i	−0.0523417	+	0.998629i	$0.516668\pi$
$967$	−27.7074	+	47.9906i	−0.891009	+	1.54327i	−0.838667	+	0.544644i	$0.816665\pi$
$968$	5.10510	−	8.84230i	0.164084	−	0.284202i
$969$	−0.930024	+	84.4821i	−0.0298767	+	2.71395i
$970$	−31.0168	−	19.7962i	−0.995888	−	0.635616i
$971$	23.1410	−	13.3605i	0.742630	−	0.428758i	−0.0803947	−	0.996763i	$-0.525618\pi$
$971$	23.1410	−	13.3605i	0.742630	−	0.428758i	0.823025	+	0.568005i	$0.192285\pi$
$972$	−7.03975	−	13.9083i	−0.225800	−	0.446110i
$973$	0.167885	−	0.290786i	0.00538216	−	0.00932217i
$974$	13.0103	+	22.5344i	0.416876	+	0.722050i
$975$	17.2605	+	38.2741i	0.552778	+	1.22575i
$976$			13.2474i			0.424039i
$977$	−12.4548			−0.398465			−0.199232	−	0.979952i	$-0.563845\pi$
$977$	−12.4548			−0.398465			−0.199232	+	0.979952i	$0.563845\pi$
$978$	−22.2255	−	13.1602i	−0.710694	−	0.420817i
$979$	−4.14643	−	7.18183i	−0.132521	−	0.229532i
$980$	13.2780	+	0.590800i	0.424150	+	0.0188724i
$981$	4.51898	+	8.24090i	0.144280	+	0.263112i
$982$	−18.1629	−	31.4591i	−0.579602	−	1.00390i
$983$	25.7998	−	14.8955i	0.822887	−	0.475094i	−0.0285242	−	0.999593i	$-0.509081\pi$
$983$	25.7998	−	14.8955i	0.822887	−	0.475094i	0.851411	+	0.524499i	$0.175747\pi$
$984$	−0.161363	+	14.6580i	−0.00514405	+	0.467278i
$985$	0.376248	−	8.45603i	0.0119883	−	0.269432i
$986$	1.23643	+	0.713851i	0.0393758	+	0.0227337i
$987$	−16.7413	+	9.42143i	−0.532882	+	0.299887i
$988$	34.4906			1.09729
$989$	−18.0773	−	10.4369i	−0.574824	−	0.331875i
$990$	−2.63123	−	5.34951i	−0.0836259	−	0.170018i
$991$		−	16.9143i		−	0.537301i	−0.963238	−	0.268651i	$-0.913422\pi$
$991$		−	16.9143i		−	0.537301i	0.963238	−	0.268651i	$-0.0865777\pi$
$992$	5.55290	−	0.406530i	0.176305	−	0.0129073i
$993$	−0.0907291	+	8.24171i	−0.00287920	+	0.261543i
$994$	25.7660			0.817247
$995$	−0.842568	+	18.9364i	−0.0267112	+	0.600324i
$996$	0.270626	−	24.5833i	0.00857511	−	0.778951i
$997$	25.4051	−	14.6676i	0.804588	−	0.464529i	−0.0404852	−	0.999180i	$-0.512890\pi$
$997$	25.4051	−	14.6676i	0.804588	−	0.464529i	0.845073	+	0.534651i	$0.179557\pi$
$998$	29.3551	+	16.9482i	0.929220	+	0.536485i
$999$	12.5036	−	20.0939i	0.395595	−	0.635744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.12	yes	64
3.2	odd	2		930.2.r.a.119.10	✓	64
5.4	even	2		930.2.r.a.119.21	yes	64
15.14	odd	2	inner	930.2.r.b.119.23	yes	64
31.6	odd	6	inner	930.2.r.b.719.23	yes	64
93.68	even	6		930.2.r.a.719.21	yes	64
155.99	odd	6		930.2.r.a.719.10	yes	64
465.254	even	6	inner	930.2.r.b.719.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.10	✓	64	3.2	odd	2
930.2.r.a.119.21	yes	64	5.4	even	2
930.2.r.a.719.10	yes	64	155.99	odd	6
930.2.r.a.719.21	yes	64	93.68	even	6
930.2.r.b.119.12	yes	64	1.1	even	1	trivial
930.2.r.b.119.23	yes	64	15.14	odd	2	inner
930.2.r.b.719.12	yes	64	465.254	even	6	inner
930.2.r.b.719.23	yes	64	31.6	odd	6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.882485 + 1.49038i) q^{3} +1.00000 q^{4} +(1.20301 - 1.88488i) q^{5} +(-0.882485 + 1.49038i) q^{6} +(-3.11576 - 1.79889i) q^{7} +1.00000 q^{8} +(-1.44244 - 2.63047i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.882485 + 1.49038i) q^{3} +1.00000 q^{4} +(1.20301 - 1.88488i) q^{5} +(-0.882485 + 1.49038i) q^{6} +(-3.11576 - 1.79889i) q^{7} +1.00000 q^{8} +(-1.44244 - 2.63047i) q^{9} +(1.20301 - 1.88488i) q^{10} +(0.444351 + 0.769638i) q^{11} +(-0.882485 + 1.49038i) q^{12} +(2.42407 + 4.19861i) q^{13} +(-3.11576 - 1.79889i) q^{14} +(1.74754 + 3.45631i) q^{15} +1.00000 q^{16} +(5.93793 + 3.42826i) q^{17} +(-1.44244 - 2.63047i) q^{18} +(3.55710 - 6.16108i) q^{19} +(1.20301 - 1.88488i) q^{20} +(5.43063 - 3.05617i) q^{21} +(0.444351 + 0.769638i) q^{22} -6.10864i q^{23} +(-0.882485 + 1.49038i) q^{24} +(-2.10555 - 4.53505i) q^{25} +(2.42407 + 4.19861i) q^{26} +(5.19332 + 0.171568i) q^{27} +(-3.11576 - 1.79889i) q^{28} +0.208225 q^{29} +(1.74754 + 3.45631i) q^{30} +(5.55290 - 0.406530i) q^{31} +1.00000 q^{32} +(-1.53918 - 0.0169442i) q^{33} +(5.93793 + 3.42826i) q^{34} +(-7.13897 + 3.70877i) q^{35} +(-1.44244 - 2.63047i) q^{36} +(2.27731 - 3.94442i) q^{37} +(3.55710 - 6.16108i) q^{38} +(-8.39672 - 0.0924355i) q^{39} +(1.20301 - 1.88488i) q^{40} +(7.32942 - 4.23164i) q^{41} +(5.43063 - 3.05617i) q^{42} +(1.70855 - 2.95930i) q^{43} +(0.444351 + 0.769638i) q^{44} +(-6.69338 - 0.445643i) q^{45} -6.10864i q^{46} -3.08276 q^{47} +(-0.882485 + 1.49038i) q^{48} +(2.97199 + 5.14764i) q^{49} +(-2.10555 - 4.53505i) q^{50} +(-10.3495 + 5.82435i) q^{51} +(2.42407 + 4.19861i) q^{52} +(-6.28930 + 3.63113i) q^{53} +(5.19332 + 0.171568i) q^{54} +(1.98523 + 0.0883322i) q^{55} +(-3.11576 - 1.79889i) q^{56} +(6.04324 + 10.7385i) q^{57} +0.208225 q^{58} +(-4.03191 - 2.32782i) q^{59} +(1.74754 + 3.45631i) q^{60} +13.2474i q^{61} +(5.55290 - 0.406530i) q^{62} +(-0.237609 + 10.7907i) q^{63} +1.00000 q^{64} +(10.8301 + 0.481879i) q^{65} +(-1.53918 - 0.0169442i) q^{66} +(-6.17071 + 3.56266i) q^{67} +(5.93793 + 3.42826i) q^{68} +(9.10418 + 5.39079i) q^{69} +(-7.13897 + 3.70877i) q^{70} +(-6.20217 + 3.58082i) q^{71} +(-1.44244 - 2.63047i) q^{72} +(0.840046 + 1.45500i) q^{73} +(2.27731 - 3.94442i) q^{74} +(8.61704 + 0.864055i) q^{75} +(3.55710 - 6.16108i) q^{76} -3.19735i q^{77} +(-8.39672 - 0.0924355i) q^{78} +(-0.516925 - 0.298447i) q^{79} +(1.20301 - 1.88488i) q^{80} +(-4.83873 + 7.58859i) q^{81} +(7.32942 - 4.23164i) q^{82} +(-12.2924 + 7.09701i) q^{83} +(5.43063 - 3.05617i) q^{84} +(13.6052 - 7.06805i) q^{85} +(1.70855 - 2.95930i) q^{86} +(-0.183756 + 0.310334i) q^{87} +(0.444351 + 0.769638i) q^{88} -9.33144 q^{89} +(-6.69338 - 0.445643i) q^{90} -17.4425i q^{91} -6.10864i q^{92} +(-4.29447 + 8.63467i) q^{93} -3.08276 q^{94} +(-7.33368 - 14.1165i) q^{95} +(-0.882485 + 1.49038i) q^{96} -16.4556i q^{97} +(2.97199 + 5.14764i) q^{98} +(1.38356 - 2.27901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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