LMFDB - Embedded newform 930.2.bf.a.377.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.19
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.609255 + 1.62136i) q^{3} -1.00000i q^{4} +(1.73683 - 1.40835i) q^{5} +(-1.57728 - 0.715666i) q^{6} +(-3.28936 + 0.881380i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.25762 + 1.97564i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.609255 + 1.62136i) q^{3} -1.00000i q^{4} +(1.73683 - 1.40835i) q^{5} +(-1.57728 - 0.715666i) q^{6} +(-3.28936 + 0.881380i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.25762 + 1.97564i) q^{9} +(-0.232271 + 2.22397i) q^{10} +(-2.77080 + 1.59972i) q^{11} +(1.62136 - 0.609255i) q^{12} +(0.287173 + 0.0769478i) q^{13} +(1.70270 - 2.94916i) q^{14} +(3.34160 + 1.95798i) q^{15} -1.00000 q^{16} +(0.735430 + 2.74466i) q^{17} +(0.199385 - 2.99337i) q^{18} +(-3.86767 - 2.23300i) q^{19} +(-1.40835 - 1.73683i) q^{20} +(-3.43309 - 4.79624i) q^{21} +(0.828078 - 3.09043i) q^{22} +(1.91430 + 1.91430i) q^{23} +(-0.715666 + 1.57728i) q^{24} +(1.03313 - 4.89210i) q^{25} +(-0.257472 + 0.148652i) q^{26} +(-4.57869 - 2.45674i) q^{27} +(0.881380 + 3.28936i) q^{28} -0.443792 q^{29} +(-3.74737 + 0.978371i) q^{30} +(-5.55620 + 0.358640i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.28185 - 3.51783i) q^{33} +(-2.46080 - 1.42074i) q^{34} +(-4.47175 + 6.16335i) q^{35} +(1.97564 + 2.25762i) q^{36} +(-11.2384 + 3.01133i) q^{37} +(4.31383 - 1.15589i) q^{38} +(0.0502015 + 0.512492i) q^{39} +(2.22397 + 0.232271i) q^{40} +(0.234078 - 0.135145i) q^{41} +(5.81902 + 0.963895i) q^{42} +(1.42036 + 5.30084i) q^{43} +(1.59972 + 2.77080i) q^{44} +(-1.13870 + 6.61085i) q^{45} -2.70723 q^{46} +(2.98109 - 2.98109i) q^{47} +(-0.609255 - 1.62136i) q^{48} +(3.98085 - 2.29834i) q^{49} +(2.72871 + 4.18977i) q^{50} +(-4.00202 + 2.86460i) q^{51} +(0.0769478 - 0.287173i) q^{52} +(0.886170 - 3.30723i) q^{53} +(4.97480 - 1.50045i) q^{54} +(-2.55944 + 6.68069i) q^{55} +(-2.94916 - 1.70270i) q^{56} +(1.26410 - 7.63136i) q^{57} +(0.313808 - 0.313808i) q^{58} +(-4.37626 + 7.57991i) q^{59} +(1.95798 - 3.34160i) q^{60} -9.78647 q^{61} +(3.67523 - 4.18242i) q^{62} +(5.68481 - 8.48841i) q^{63} +1.00000i q^{64} +(0.607138 - 0.270794i) q^{65} +(5.51521 - 0.540246i) q^{66} +(-0.989853 + 3.69418i) q^{67} +(2.74466 - 0.735430i) q^{68} +(-1.93748 + 4.27007i) q^{69} +(-1.19614 - 7.52015i) q^{70} +(-11.4136 + 6.58964i) q^{71} +(-2.99337 - 0.199385i) q^{72} +(12.8256 + 3.43661i) q^{73} +(5.81744 - 10.0761i) q^{74} +(8.56129 - 1.30546i) q^{75} +(-2.23300 + 3.86767i) q^{76} +(7.70419 - 7.70419i) q^{77} +(-0.397884 - 0.326888i) q^{78} +(3.90126 + 2.25239i) q^{79} +(-1.73683 + 1.40835i) q^{80} +(1.19367 - 8.92049i) q^{81} +(-0.0699563 + 0.261081i) q^{82} +(4.13799 - 15.4432i) q^{83} +(-4.79624 + 3.43309i) q^{84} +(5.14275 + 3.73126i) q^{85} +(-4.75260 - 2.74392i) q^{86} +(-0.270382 - 0.719546i) q^{87} +(-3.09043 - 0.828078i) q^{88} +1.60015 q^{89} +(-3.86940 - 5.47976i) q^{90} -1.01243 q^{91} +(1.91430 - 1.91430i) q^{92} +(-3.96663 - 8.79010i) q^{93} +4.21590i q^{94} +(-9.86232 + 1.56868i) q^{95} +(1.57728 + 0.715666i) q^{96} +(-0.589415 - 0.589415i) q^{97} +(-1.18971 + 4.44006i) q^{98} +(3.09493 - 9.08568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.609255	+	1.62136i	0.351753	+	0.936093i
$3$	0.609255	+	1.62136i	0.351753	+	0.936093i
$4$		−	1.00000i		−	0.500000i
$5$	1.73683	−	1.40835i	0.776732	−	0.629831i
$5$	1.73683	−	1.40835i	0.776732	−	0.629831i
$6$	−1.57728	−	0.715666i	−0.643923	−	0.292170i
$7$	−3.28936	+	0.881380i	−1.24326	+	0.333130i	−0.819729	−	0.572752i	$-0.805876\pi$
$7$	−3.28936	+	0.881380i	−1.24326	+	0.333130i	−0.423530	+	0.905882i	$0.639209\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.25762	+	1.97564i	−0.752539	+	0.658548i
$10$	−0.232271	+	2.22397i	−0.0734505	+	0.703282i
$11$	−2.77080	+	1.59972i	−0.835428	+	0.482335i	−0.855708	−	0.517460i	$-0.826878\pi$
$11$	−2.77080	+	1.59972i	−0.835428	+	0.482335i	0.0202795	+	0.999794i	$0.493544\pi$
$12$	1.62136	−	0.609255i	0.468046	−	0.175877i
$13$	0.287173	+	0.0769478i	0.0796475	+	0.0213415i	0.298423	−	0.954434i	$-0.403539\pi$
$13$	0.287173	+	0.0769478i	0.0796475	+	0.0213415i	−0.218775	+	0.975775i	$0.570206\pi$
$14$	1.70270	−	2.94916i	0.455065	−	0.788195i
$15$	3.34160	+	1.95798i	0.862799	+	0.505548i
$16$	−1.00000			−0.250000
$17$	0.735430	+	2.74466i	0.178368	+	0.665679i	0.995953	+	0.0898712i	$0.0286455\pi$
$17$	0.735430	+	2.74466i	0.178368	+	0.665679i	−0.817585	+	0.575807i	$0.804688\pi$
$18$	0.199385	−	2.99337i	0.0469956	−	0.705543i
$19$	−3.86767	−	2.23300i	−0.887305	−	0.512286i	−0.0142453	−	0.999899i	$-0.504535\pi$
$19$	−3.86767	−	2.23300i	−0.887305	−	0.512286i	−0.873060	+	0.487612i	$0.837868\pi$
$20$	−1.40835	−	1.73683i	−0.314916	−	0.388366i
$21$	−3.43309	−	4.79624i	−0.749162	−	1.04663i
$22$	0.828078	−	3.09043i	0.176547	−	0.658881i
$23$	1.91430	+	1.91430i	0.399160	+	0.399160i	0.877937	−	0.478777i	$-0.158920\pi$
$23$	1.91430	+	1.91430i	0.399160	+	0.399160i	−0.478777	+	0.877937i	$0.658920\pi$
$24$	−0.715666	+	1.57728i	−0.146085	+	0.321962i
$25$	1.03313	−	4.89210i	0.206625	−	0.978420i
$26$	−0.257472	+	0.148652i	−0.0504945	+	0.0291530i
$27$	−4.57869	−	2.45674i	−0.881170	−	0.472800i
$28$	0.881380	+	3.28936i	0.166565	+	0.621630i
$29$	−0.443792			−0.0824101			−0.0412050	−	0.999151i	$-0.513120\pi$
$29$	−0.443792			−0.0824101			−0.0412050	+	0.999151i	$0.513120\pi$
$30$	−3.74737	+	0.978371i	−0.684173	+	0.178625i
$31$	−5.55620	+	0.358640i	−0.997923	+	0.0644136i
$31$	−5.55620	+	0.358640i	−0.997923	+	0.0644136i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−4.28185	−	3.51783i	−0.745375	−	0.612375i
$34$	−2.46080	−	1.42074i	−0.422023	−	0.243655i
$35$	−4.47175	+	6.16335i	−0.755864	+	1.04180i
$36$	1.97564	+	2.25762i	0.329274	+	0.376269i
$37$	−11.2384	+	3.01133i	−1.84759	+	0.495059i	−0.999400	−	0.0346398i	$-0.988972\pi$
$37$	−11.2384	+	3.01133i	−1.84759	+	0.495059i	−0.848186	+	0.529699i	$0.822305\pi$
$38$	4.31383	−	1.15589i	0.699796	−	0.187510i
$39$	0.0502015	+	0.512492i	0.00803868	+	0.0820643i
$40$	2.22397	+	0.232271i	0.351641	+	0.0367252i
$41$	0.234078	−	0.135145i	0.0365569	−	0.0211061i	−0.481610	−	0.876386i	$-0.659948\pi$
$41$	0.234078	−	0.135145i	0.0365569	−	0.0211061i	0.518167	+	0.855279i	$0.326615\pi$
$42$	5.81902	+	0.963895i	0.897894	+	0.148732i
$43$	1.42036	+	5.30084i	0.216602	+	0.808371i	0.985596	+	0.169115i	$0.0540909\pi$
$43$	1.42036	+	5.30084i	0.216602	+	0.808371i	−0.768994	+	0.639256i	$0.779242\pi$
$44$	1.59972	+	2.77080i	0.241167	+	0.417714i
$45$	−1.13870	+	6.61085i	−0.169747	+	0.985488i
$46$	−2.70723			−0.399160
$47$	2.98109	−	2.98109i	0.434837	−	0.434837i	−0.455433	−	0.890270i	$-0.650516\pi$
$47$	2.98109	−	2.98109i	0.434837	−	0.434837i	0.890270	+	0.455433i	$0.150516\pi$
$48$	−0.609255	−	1.62136i	−0.0879384	−	0.234023i
$49$	3.98085	−	2.29834i	0.568693	−	0.328335i
$50$	2.72871	+	4.18977i	0.385897	+	0.592523i
$51$	−4.00202	+	2.86460i	−0.560395	+	0.401124i
$52$	0.0769478	−	0.287173i	0.0106707	−	0.0398237i
$53$	0.886170	−	3.30723i	0.121725	−	0.454283i	−0.877977	−	0.478703i	$-0.841107\pi$
$53$	0.886170	−	3.30723i	0.121725	−	0.454283i	0.999702	+	0.0244196i	$0.00777378\pi$
$54$	4.97480	−	1.50045i	0.676985	−	0.204185i
$55$	−2.55944	+	6.68069i	−0.345114	+	0.900823i
$56$	−2.94916	−	1.70270i	−0.394097	−	0.227532i
$57$	1.26410	−	7.63136i	0.167434	−	1.01080i
$58$	0.313808	−	0.313808i	0.0412050	−	0.0412050i
$59$	−4.37626	+	7.57991i	−0.569741	+	0.986820i	0.426850	+	0.904322i	$0.359623\pi$
$59$	−4.37626	+	7.57991i	−0.569741	+	0.986820i	−0.996591	+	0.0824979i	$0.973710\pi$
$60$	1.95798	−	3.34160i	0.252774	−	0.431399i
$61$	−9.78647			−1.25303			−0.626515	−	0.779410i	$-0.715519\pi$
$61$	−9.78647			−1.25303			−0.626515	+	0.779410i	$0.715519\pi$
$62$	3.67523	−	4.18242i	0.466755	−	0.531168i
$63$	5.68481	−	8.48841i	0.716219	−	1.06944i
$64$			1.00000i			0.125000i
$65$	0.607138	−	0.270794i	0.0753063	−	0.0335878i
$66$	5.51521	−	0.540246i	0.678875	−	0.0664997i
$67$	−0.989853	+	3.69418i	−0.120930	+	0.451316i	−0.999662	−	0.0259991i	$-0.991723\pi$
$67$	−0.989853	+	3.69418i	−0.120930	+	0.451316i	0.878732	+	0.477315i	$0.158390\pi$
$68$	2.74466	−	0.735430i	0.332839	−	0.0891840i
$69$	−1.93748	+	4.27007i	−0.233245	+	0.514057i
$70$	−1.19614	−	7.52015i	−0.142966	−	0.898830i
$71$	−11.4136	+	6.58964i	−1.35454	+	0.782047i	−0.988882	−	0.148701i	$-0.952491\pi$
$71$	−11.4136	+	6.58964i	−1.35454	+	0.782047i	−0.365663	+	0.930747i	$0.619158\pi$
$72$	−2.99337	−	0.199385i	−0.352772	−	0.0234978i
$73$	12.8256	+	3.43661i	1.50112	+	0.402225i	0.913476	−	0.406892i	$-0.133387\pi$
$73$	12.8256	+	3.43661i	1.50112	+	0.402225i	0.587648	+	0.809117i	$0.300054\pi$
$74$	5.81744	−	10.0761i	0.676263	−	1.17132i
$75$	8.56129	−	1.30546i	0.988573	−	0.150742i
$76$	−2.23300	+	3.86767i	−0.256143	+	0.443653i
$77$	7.70419	−	7.70419i	0.877974	−	0.877974i
$78$	−0.397884	−	0.326888i	−0.0450515	−	0.0370128i
$79$	3.90126	+	2.25239i	0.438926	+	0.253414i	0.703142	−	0.711050i	$-0.251780\pi$
$79$	3.90126	+	2.25239i	0.438926	+	0.253414i	−0.264216	+	0.964464i	$0.585113\pi$
$80$	−1.73683	+	1.40835i	−0.194183	+	0.157458i
$81$	1.19367	−	8.92049i	0.132630	−	0.991166i
$82$	−0.0699563	+	0.261081i	−0.00772539	+	0.0288315i
$83$	4.13799	−	15.4432i	0.454204	−	1.69511i	−0.236214	−	0.971701i	$-0.575907\pi$
$83$	4.13799	−	15.4432i	0.454204	−	1.69511i	0.690418	−	0.723411i	$-0.257427\pi$
$84$	−4.79624	+	3.43309i	−0.523313	+	0.374581i
$85$	5.14275	+	3.73126i	0.557809	+	0.404712i
$86$	−4.75260	−	2.74392i	−0.512487	−	0.295884i
$87$	−0.270382	−	0.719546i	−0.0289880	−	0.0771435i
$88$	−3.09043	−	0.828078i	−0.329441	−	0.0882734i
$89$	1.60015			0.169615			0.0848075	−	0.996397i	$-0.472972\pi$
$89$	1.60015			0.169615			0.0848075	+	0.996397i	$0.472972\pi$
$90$	−3.86940	−	5.47976i	−0.407870	−	0.577617i
$91$	−1.01243			−0.106132
$92$	1.91430	−	1.91430i	0.199580	−	0.199580i
$93$	−3.96663	−	8.79010i	−0.411320	−	0.911491i
$94$			4.21590i			0.434837i
$95$	−9.86232	+	1.56868i	−1.01185	+	0.160944i
$96$	1.57728	+	0.715666i	0.160981	+	0.0730424i
$97$	−0.589415	−	0.589415i	−0.0598460	−	0.0598460i	0.676550	−	0.736396i	$-0.263474\pi$
$97$	−0.589415	−	0.589415i	−0.0598460	−	0.0598460i	−0.736396	+	0.676550i	$0.763474\pi$
$98$	−1.18971	+	4.44006i	−0.120179	+	0.448514i
$99$	3.09493	−	9.08568i	0.311052	−	0.913145i
$100$	−4.89210	−	1.03313i	−0.489210	−	0.103313i
$101$		−	13.8400i		−	1.37713i	−0.725176	−	0.688563i	$-0.758242\pi$
$101$		−	13.8400i		−	1.37713i	0.725176	−	0.688563i	$-0.241758\pi$
$102$	0.804281	−	4.85543i	0.0796357	−	0.480759i
$103$	−8.17643	−	2.19087i	−0.805647	−	0.215872i	−0.167585	−	0.985858i	$-0.553597\pi$
$103$	−8.17643	−	2.19087i	−0.805647	−	0.215872i	−0.638062	+	0.769985i	$0.720264\pi$
$104$	0.148652	+	0.257472i	0.0145765	+	0.0252472i
$105$	−12.7174	−	3.49526i	−1.24110	−	0.341103i
$106$	1.71195	+	2.96518i	0.166279	+	0.288004i
$107$	4.24680	+	15.8493i	0.410554	+	1.53221i	0.793577	+	0.608469i	$0.208216\pi$
$107$	4.24680	+	15.8493i	0.410554	+	1.53221i	−0.383023	+	0.923739i	$0.625117\pi$
$108$	−2.45674	+	4.57869i	−0.236400	+	0.440585i
$109$		−	2.02942i		−	0.194383i	−0.995266	−	0.0971917i	$-0.969014\pi$
$109$		−	2.02942i		−	0.194383i	0.995266	−	0.0971917i	$-0.0309860\pi$
$110$	−2.91416	−	6.53375i	−0.277854	−	0.622969i
$111$	−11.7295	−	16.3869i	−1.11332	−	1.55537i
$112$	3.28936	−	0.881380i	0.310815	−	0.0832826i
$113$	1.38606	−	5.17283i	0.130389	−	0.486619i	−0.869585	−	0.493783i	$-0.835614\pi$
$113$	1.38606	−	5.17283i	0.130389	−	0.486619i	0.999974	+	0.00716403i	$0.00228040\pi$
$114$	4.50233	+	6.29004i	0.421682	+	0.589116i
$115$	6.02081	+	0.628812i	0.561444	+	0.0586370i
$116$			0.443792i			0.0412050i
$117$	−0.800348	+	0.393633i	−0.0739922	+	0.0363914i
$118$	−2.26532	−	8.45429i	−0.208540	−	0.778281i
$119$	−4.83818	−	8.37998i	−0.443515	−	0.768191i
$120$	0.978371	+	3.74737i	0.0893127	+	0.342087i
$121$	−0.381773	+	0.661250i	−0.0347066	+	0.0601136i
$122$	6.92008	−	6.92008i	0.626515	−	0.626515i
$123$	0.361733	+	0.297188i	0.0326163	+	0.0267965i
$124$	0.358640	+	5.55620i	0.0322068	+	0.498962i
$125$	−5.09540	−	9.95173i	−0.455747	−	0.890109i
$126$	1.98244	+	10.0220i	0.176610	+	0.892829i
$127$	−0.544992	+	0.146030i	−0.0483602	+	0.0129581i	−0.282918	−	0.959144i	$-0.591302\pi$
$127$	−0.544992	+	0.146030i	−0.0483602	+	0.0129581i	0.234558	+	0.972102i	$0.424636\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−7.72921	+	5.53247i	−0.680519	+	0.487107i
$130$	−0.237832	+	0.620792i	−0.0208592	+	0.0544470i
$131$	14.7091	+	8.49231i	1.28514	+	0.741976i	0.977783	−	0.209618i	$-0.0672220\pi$
$131$	14.7091	+	8.49231i	1.28514	+	0.741976i	0.307357	+	0.951594i	$0.400555\pi$
$132$	−3.51783	+	4.28185i	−0.306188	+	0.372687i
$133$	14.6903	+	3.93625i	1.27381	+	0.341316i
$134$	−1.91225	−	3.31211i	−0.165193	−	0.286123i
$135$	−11.4123	+	2.18145i	−0.982217	+	0.187750i
$136$	−1.42074	+	2.46080i	−0.121828	+	0.211012i
$137$	20.9757	+	5.62041i	1.79207	+	0.480184i	0.992696	−	0.120647i	$-0.0384968\pi$
$137$	20.9757	+	5.62041i	1.79207	+	0.480184i	0.799376	+	0.600831i	$0.205163\pi$
$138$	−1.64940	−	4.38940i	−0.140406	−	0.373651i
$139$			10.9789i			0.931219i	0.884990	+	0.465610i	$0.154165\pi$
$139$			10.9789i			0.931219i	−0.884990	+	0.465610i	$0.845835\pi$
$140$	6.16335	+	4.47175i	0.520898	+	0.377932i
$141$	6.64967	+	3.01718i	0.560003	+	0.254092i
$142$	3.41105	−	12.7302i	0.286249	−	1.06830i
$143$	−0.918794	+	0.246190i	−0.0768334	+	0.0205875i
$144$	2.25762	−	1.97564i	0.188135	−	0.164637i
$145$	−0.770789	+	0.625012i	−0.0640105	+	0.0519044i
$146$	−11.4991	+	6.63903i	−0.951675	+	0.549450i
$147$	6.15180	+	5.05411i	0.507392	+	0.416856i
$148$	3.01133	+	11.2384i	0.247530	+	0.923793i
$149$	2.46227	−	4.26478i	0.201717	−	0.349384i	−0.747365	−	0.664414i	$-0.768681\pi$
$149$	2.46227	−	4.26478i	0.201717	−	0.349384i	0.949082	+	0.315030i	$0.102015\pi$
$150$	−5.13065	+	6.97685i	−0.418916	+	0.569658i
$151$	6.81763			0.554811			0.277405	−	0.960753i	$-0.410526\pi$
$151$	6.81763			0.554811			0.277405	+	0.960753i	$0.410526\pi$
$152$	−1.15589	−	4.31383i	−0.0937549	−	0.349898i
$153$	−7.08279	−	4.74345i	−0.572610	−	0.383485i
$154$			10.8954i			0.877974i
$155$	−9.14507	+	8.44795i	−0.734549	+	0.678555i
$156$	0.512492	−	0.0502015i	0.0410322	−	0.00401934i
$157$	16.8999	+	16.8999i	1.34876	+	1.34876i	0.887012	+	0.461747i	$0.152777\pi$
$157$	16.8999	+	16.8999i	1.34876	+	1.34876i	0.461747	+	0.887012i	$0.347223\pi$
$158$	−4.35129	+	1.16592i	−0.346170	+	0.0927559i
$159$	5.90212	−	0.578147i	0.468068	−	0.0458500i
$160$	0.232271	−	2.22397i	0.0183626	−	0.175820i
$161$	−7.98405	−	4.60960i	−0.629232	−	0.363287i
$162$	5.46369	+	7.15179i	0.429268	+	0.561898i
$163$	−9.46740	+	9.46740i	−0.741544	+	0.741544i	−0.972875	−	0.231331i	$-0.925692\pi$
$163$	−9.46740	+	9.46740i	−0.741544	+	0.741544i	0.231331	+	0.972875i	$0.425692\pi$
$164$	−0.135145	−	0.234078i	−0.0105531	−	0.0182785i
$165$	−12.3911	−	0.0795287i	−0.964649	−	0.00619130i
$166$	7.99399	+	13.8460i	0.620454	+	1.07466i
$167$	1.46502	+	5.46752i	0.113366	+	0.423089i	0.999160	−	0.0409912i	$-0.0130516\pi$
$167$	1.46502	+	5.46752i	0.113366	+	0.423089i	−0.885793	+	0.464080i	$0.846385\pi$
$168$	0.963895	−	5.81902i	0.0743661	−	0.448947i
$169$	−11.1818	−	6.45581i	−0.860137	−	0.496600i
$170$	−6.27487	+	0.998071i	−0.481261	+	0.0765486i
$171$	13.1433	−	2.59988i	1.00510	−	0.198818i
$172$	5.30084	−	1.42036i	0.404185	−	0.108301i
$173$	2.94840	−	11.0036i	0.224162	−	0.836585i	−0.758576	−	0.651585i	$-0.774105\pi$
$173$	2.94840	−	11.0036i	0.224162	−	0.836585i	0.982738	−	0.185001i	$-0.0592288\pi$
$174$	0.699985	+	0.317607i	0.0530657	+	0.0240777i
$175$	0.913477	+	17.0024i	0.0690524	+	1.28526i
$176$	2.77080	−	1.59972i	0.208857	−	0.120584i
$177$	−14.9560	−	2.47740i	−1.12416	−	0.186213i
$178$	−1.13147	+	1.13147i	−0.0848075	+	0.0848075i
$179$	−12.3910	+	21.4618i	−0.926144	+	1.60413i	−0.136433	+	0.990649i	$0.543564\pi$
$179$	−12.3910	+	21.4618i	−0.926144	+	1.60413i	−0.789711	+	0.613479i	$0.789770\pi$
$180$	6.61085	+	1.13870i	0.492744	+	0.0848736i
$181$	5.40408	+	9.36014i	0.401682	+	0.695733i	0.993929	−	0.110023i	$-0.0350924\pi$
$181$	5.40408	+	9.36014i	0.401682	+	0.695733i	−0.592247	+	0.805756i	$0.701759\pi$
$182$	0.715899	−	0.715899i	0.0530660	−	0.0530660i
$183$	−5.96246	−	15.8674i	−0.440757	−	1.17295i
$184$			2.70723i			0.199580i
$185$	−15.2782	+	21.0577i	−1.12328	+	1.54820i
$186$	9.02037	+	3.41071i	0.661406	+	0.250085i
$187$	−6.42843	−	6.42843i	−0.470093	−	0.470093i
$188$	−2.98109	−	2.98109i	−0.217419	−	0.217419i
$189$	17.2263	+	4.04552i	1.25303	+	0.294268i
$190$	5.86448	−	8.08294i	0.425454	−	0.586398i
$191$	−2.55423	+	1.47469i	−0.184818	+	0.106705i	−0.589554	−	0.807729i	$-0.700697\pi$
$191$	−2.55423	+	1.47469i	−0.184818	+	0.106705i	0.404736	+	0.914433i	$0.367363\pi$
$192$	−1.62136	+	0.609255i	−0.117012	+	0.0439692i
$193$	1.32800	+	4.95615i	0.0955914	+	0.356752i	0.997108	−	0.0759917i	$-0.0242122\pi$
$193$	1.32800	+	4.95615i	0.0955914	+	0.356752i	−0.901517	+	0.432744i	$0.857546\pi$
$194$	0.833558			0.0598460
$195$	0.808956	+	0.819408i	0.0579306	+	0.0586790i
$196$	−2.29834	−	3.98085i	−0.164167	−	0.284346i
$197$	16.2205	+	4.34627i	1.15566	+	0.309659i	0.785232	−	0.619201i	$-0.212543\pi$
$197$	16.2205	+	4.34627i	1.15566	+	0.309659i	0.370431	+	0.928860i	$0.379210\pi$
$198$	4.23610	+	8.61299i	0.301047	+	0.612098i
$199$	−0.919312	+	0.530765i	−0.0651683	+	0.0376249i	−0.532230	−	0.846600i	$-0.678646\pi$
$199$	−0.919312	+	0.530765i	−0.0651683	+	0.0376249i	0.467062	+	0.884225i	$0.345313\pi$
$200$	4.18977	−	2.72871i	0.296261	−	0.192949i
$201$	−6.59267	+	0.645790i	−0.465011	+	0.0455505i
$202$	9.78633	+	9.78633i	0.688563	+	0.688563i
$203$	1.45979	−	0.391149i	0.102457	−	0.0274533i
$204$	2.86460	+	4.00202i	0.200562	+	0.280198i
$205$	0.216222	−	0.564387i	0.0151016	−	0.0394185i
$206$	7.33078	−	4.23243i	0.510760	−	0.294887i
$207$	−8.10375	−	0.539783i	−0.563249	−	0.0375175i
$208$	−0.287173	−	0.0769478i	−0.0199119	−	0.00533537i
$209$	14.2887			0.988373
$210$	11.4641	−	6.52107i	0.791099	−	0.449996i
$211$	9.01510	−	15.6146i	0.620625	−	1.07495i	−0.368744	−	0.929531i	$-0.620212\pi$
$211$	9.01510	−	15.6146i	0.620625	−	1.07495i	0.989369	−	0.145424i	$-0.0464545\pi$
$212$	−3.30723	−	0.886170i	−0.227142	−	0.0608624i
$213$	−17.6380	−	14.4908i	−1.20853	−	0.992892i
$214$	−14.2101	−	8.20419i	−0.971381	−	0.560827i
$215$	9.93233	+	7.20629i	0.677379	+	0.491465i
$216$	−1.50045	−	4.97480i	−0.102093	−	0.338492i
$217$	17.9602	−	6.07682i	1.21922	−	0.412521i
$218$	1.43502	+	1.43502i	0.0971917	+	0.0971917i
$219$	2.24208	+	22.8887i	0.151506	+	1.54668i
$220$	6.68069	+	2.55944i	0.450412	+	0.172557i
$221$			0.844783i			0.0568262i
$222$	19.8813	+	3.29325i	1.33434	+	0.221028i
$223$	−5.54563	−	20.6966i	−0.371363	−	1.38595i	−0.858587	−	0.512668i	$-0.828657\pi$
$223$	−5.54563	−	20.6966i	−0.371363	−	1.38595i	0.487224	−	0.873277i	$-0.338010\pi$
$224$	−1.70270	+	2.94916i	−0.113766	+	0.197049i
$225$	7.33264	+	13.0856i	0.488843	+	0.872372i
$226$	2.67765	+	4.63783i	0.178115	+	0.308504i
$227$	−8.77251	−	2.35059i	−0.582252	−	0.156014i	−0.0443421	−	0.999016i	$-0.514119\pi$
$227$	−8.77251	−	2.35059i	−0.582252	−	0.156014i	−0.537910	+	0.843003i	$0.680786\pi$
$228$	−7.63136	−	1.26410i	−0.505399	−	0.0837172i
$229$	−1.05434	−	0.608726i	−0.0696730	−	0.0402257i	0.464759	−	0.885437i	$-0.346141\pi$
$229$	−1.05434	−	0.608726i	−0.0696730	−	0.0402257i	−0.534432	+	0.845212i	$0.679474\pi$
$230$	−4.70199	+	3.81272i	−0.310040	+	0.251403i
$231$	17.1851	+	7.79745i	1.13069	+	0.513034i
$232$	−0.313808	−	0.313808i	−0.0206025	−	0.0206025i
$233$	9.17564	+	9.17564i	0.601116	+	0.601116i	0.940609	−	0.339493i	$-0.110255\pi$
$233$	9.17564	+	9.17564i	0.601116	+	0.601116i	−0.339493	+	0.940609i	$0.610255\pi$
$234$	0.287591	−	0.844272i	0.0188004	−	0.0551918i
$235$	0.979231	−	9.37605i	0.0638780	−	0.611626i
$236$	7.57991	+	4.37626i	0.493410	+	0.284870i
$237$	−1.27508	+	7.69762i	−0.0828252	+	0.500014i
$238$	9.34665	+	2.50443i	0.605853	+	0.162338i
$239$	0.807711	+	1.39900i	0.0522465	+	0.0904936i	0.890966	−	0.454070i	$-0.150029\pi$
$239$	0.807711	+	1.39900i	0.0522465	+	0.0904936i	−0.838719	+	0.544564i	$0.816695\pi$
$240$	−3.34160	−	1.95798i	−0.215700	−	0.126387i
$241$	−6.33139	+	10.9663i	−0.407841	+	0.706401i	−0.994648	−	0.103326i	$-0.967051\pi$
$241$	−6.33139	+	10.9663i	−0.407841	+	0.706401i	0.586807	+	0.809727i	$0.300385\pi$
$242$	−0.197620	−	0.737528i	−0.0127035	−	0.0474101i
$243$	15.1906	−	3.49949i	0.974476	−	0.224492i
$244$			9.78647i			0.626515i
$245$	3.67718	−	9.59823i	0.234926	−	0.613209i
$246$	−0.465927	+	0.0456402i	−0.0297064	+	0.00290992i
$247$	−0.938867	−	0.938867i	−0.0597387	−	0.0597387i
$248$	−4.18242	−	3.67523i	−0.265584	−	0.233377i
$249$	27.5601	−	2.69967i	1.74655	−	0.171085i
$250$	10.6399	+	3.43394i	0.672928	+	0.217181i
$251$	3.74546	+	2.16244i	0.236411	+	0.136492i	0.613526	−	0.789674i	$-0.289751\pi$
$251$	3.74546	+	2.16244i	0.236411	+	0.136492i	−0.377115	+	0.926166i	$0.623084\pi$
$252$	−8.48841	−	5.68481i	−0.534720	−	0.358109i
$253$	−8.36651	−	2.24180i	−0.525998	−	0.140941i
$254$	0.282109	−	0.488627i	0.0177011	−	0.0306592i
$255$	−2.91647	+	10.6115i	−0.182637	+	0.664520i
$256$	1.00000			0.0625000
$257$	−30.1156	−	8.06946i	−1.87856	−	0.503359i	−0.999652	−	0.0263711i	$-0.991605\pi$
$257$	−30.1156	−	8.06946i	−1.87856	−	0.503359i	−0.878910	−	0.476988i	$-0.841728\pi$
$258$	1.55333	−	9.37743i	0.0967061	−	0.583813i
$259$	34.3130	−	19.8106i	2.13211	−	1.23097i
$260$	−0.270794	−	0.607138i	−0.0167939	−	0.0376531i
$261$	1.00191	−	0.876774i	0.0620168	−	0.0542710i
$262$	−16.4059	+	4.39594i	−1.01356	+	0.271582i
$263$	6.35686	+	6.35686i	0.391980	+	0.391980i	0.875393	−	0.483412i	$-0.160603\pi$
$263$	6.35686	+	6.35686i	0.391980	+	0.391980i	−0.483412	+	0.875393i	$0.660603\pi$
$264$	−0.540246	−	5.51521i	−0.0332499	−	0.339437i
$265$	−3.11860	−	6.99212i	−0.191574	−	0.429522i
$266$	−13.1709	+	7.60425i	−0.807563	+	0.466246i
$267$	0.974896	+	2.59441i	0.0596627	+	0.158775i
$268$	3.69418	+	0.989853i	0.225658	+	0.0604649i
$269$	13.0605	+	22.6215i	0.796315	+	1.37926i	0.922001	+	0.387187i	$0.126553\pi$
$269$	13.0605	+	22.6215i	0.796315	+	1.37926i	−0.125686	+	0.992070i	$0.540113\pi$
$270$	6.52722	−	9.61226i	0.397234	−	0.584983i
$271$	−7.77861			−0.472517			−0.236258	−	0.971690i	$-0.575921\pi$
$271$	−7.77861			−0.472517			−0.236258	+	0.971690i	$0.575921\pi$
$272$	−0.735430	−	2.74466i	−0.0445920	−	0.166420i
$273$	−0.616830	−	1.64152i	−0.0373323	−	0.0993493i
$274$	−18.8063	+	10.8578i	−1.13613	+	0.655944i
$275$	4.96341	+	15.2078i	0.299305	+	0.917062i
$276$	4.27007	+	1.93748i	0.257028	+	0.116622i
$277$	4.04388	+	4.04388i	0.242973	+	0.242973i	0.818079	−	0.575106i	$-0.195039\pi$
$277$	4.04388	+	4.04388i	0.242973	+	0.242973i	−0.575106	+	0.818079i	$0.695039\pi$
$278$	−7.76326	−	7.76326i	−0.465610	−	0.465610i
$279$	11.8352	−	11.7867i	0.708557	−	0.705654i
$280$	−7.52015	+	1.19614i	−0.449415	+	0.0714832i
$281$			10.3711i			0.618687i	0.950950	+	0.309343i	$0.100109\pi$
$281$			10.3711i			0.618687i	−0.950950	+	0.309343i	$0.899891\pi$
$282$	−6.83550	+	2.56856i	−0.407048	+	0.152955i
$283$	−0.0860043	+	0.0860043i	−0.00511243	+	0.00511243i	−0.709658	−	0.704546i	$-0.751151\pi$
$283$	−0.0860043	+	0.0860043i	−0.00511243	+	0.00511243i	0.704546	+	0.709658i	$0.251151\pi$
$284$	6.58964	+	11.4136i	0.391023	+	0.677272i
$285$	−8.55207	−	15.0346i	−0.506581	−	0.890575i
$286$	0.475603	−	0.823769i	0.0281230	−	0.0487105i
$287$	−0.650853	+	0.650853i	−0.0384186	+	0.0384186i
$288$	−0.199385	+	2.99337i	−0.0117489	+	0.176386i
$289$	7.73011	−	4.46298i	0.454713	−	0.262528i
$290$	0.103080	−	0.986980i	0.00605306	−	0.0579575i
$291$	0.596550	−	1.31476i	0.0349704	−	0.0770724i
$292$	3.43661	−	12.8256i	0.201113	−	0.750562i
$293$	−16.6793	+	4.46921i	−0.974416	+	0.261094i	−0.710691	−	0.703504i	$-0.751618\pi$
$293$	−16.6793	+	4.46921i	−0.974416	+	0.261094i	−0.263725	+	0.964598i	$0.584951\pi$
$294$	−7.92377	+	0.776179i	−0.462124	+	0.0452677i
$295$	3.07432	+	19.3283i	0.178994	+	1.12534i
$296$	−10.0761	−	5.81744i	−0.585661	−	0.338132i
$297$	16.6168	−	0.517504i	0.964202	−	0.0300286i
$298$	1.27457	+	4.75674i	0.0738336	+	0.275551i
$299$	0.402435	+	0.697038i	0.0232734	+	0.0403107i
$300$	−1.30546	−	8.56129i	−0.0753711	−	0.494287i
$301$	−9.34411	−	16.1845i	−0.538586	−	0.932858i
$302$	−4.82079	+	4.82079i	−0.277405	+	0.277405i
$303$	22.4395	−	8.43206i	1.28912	−	0.484409i
$304$	3.86767	+	2.23300i	0.221826	+	0.128072i
$305$	−16.9974	+	13.7827i	−0.973268	+	0.789197i
$306$	8.36242	−	1.65417i	0.478048	−	0.0945624i
$307$	−16.6000	+	4.44796i	−0.947413	+	0.253859i	−0.699264	−	0.714863i	$-0.746489\pi$
$307$	−16.6000	+	4.44796i	−0.947413	+	0.253859i	−0.248149	+	0.968722i	$0.579822\pi$
$308$	−7.70419	−	7.70419i	−0.438987	−	0.438987i
$309$	−1.42934	−	14.5917i	−0.0813125	−	0.830094i
$310$	0.492938	−	12.4401i	0.0279970	−	0.706552i
$311$		−	14.7583i		−	0.836868i	−0.908247	−	0.418434i	$-0.862579\pi$
$311$		−	14.7583i		−	0.836868i	0.908247	−	0.418434i	$-0.137421\pi$
$312$	−0.326888	+	0.397884i	−0.0185064	+	0.0225258i
$313$	6.63835	+	24.7747i	0.375222	+	1.40035i	0.853020	+	0.521878i	$0.174768\pi$
$313$	6.63835	+	24.7747i	0.375222	+	1.40035i	−0.477798	+	0.878470i	$0.658565\pi$
$314$	−23.9001			−1.34876
$315$	−2.08109	−	22.7491i	−0.117256	−	1.28176i
$316$	2.25239	−	3.90126i	0.126707	−	0.219463i
$317$	−3.59457	−	13.4151i	−0.201891	−	0.753469i	−0.990375	−	0.138412i	$-0.955800\pi$
$317$	−3.59457	−	13.4151i	−0.201891	−	0.753469i	0.788483	−	0.615056i	$-0.210867\pi$
$318$	−3.76462	+	4.58224i	−0.211109	+	0.256959i
$319$	1.22966	−	0.709944i	0.0688477	−	0.0397492i
$320$	1.40835	+	1.73683i	0.0787289	+	0.0970915i
$321$	−23.1100	+	16.5419i	−1.28987	+	0.923276i
$322$	8.90506	−	2.38610i	0.496259	−	0.132972i
$323$	3.28444	−	12.2577i	0.182751	−	0.682036i
$324$	−8.92049	−	1.19367i	−0.495583	−	0.0663149i
$325$	0.673122	−	1.32538i	0.0373381	−	0.0735190i
$326$		−	13.3889i		−	0.741544i
$327$	3.29043	−	1.23644i	0.181961	−	0.0683751i
$328$	0.261081	+	0.0699563i	0.0144158	+	0.00386269i
$329$	−7.17840	+	12.4333i	−0.395758	+	0.685473i
$330$	8.81810	−	8.70563i	0.485420	−	0.479229i
$331$	−12.0705	−	20.9068i	−0.663457	−	1.14914i	−0.979701	−	0.200463i	$-0.935755\pi$
$331$	−12.0705	−	20.9068i	−0.663457	−	1.14914i	0.316245	−	0.948678i	$-0.397578\pi$
$332$	−15.4432	−	4.13799i	−0.847556	−	0.227102i
$333$	19.4227	−	29.0015i	1.06436	−	1.58927i
$334$	−4.90204	−	2.83019i	−0.268228	−	0.154861i
$335$	3.48348	+	7.81020i	0.190323	+	0.426717i
$336$	3.43309	+	4.79624i	0.187290	+	0.261657i
$337$	11.1311	+	11.1311i	0.606348	+	0.606348i	0.941990	−	0.335641i	$-0.108953\pi$
$337$	11.1311	+	11.1311i	0.606348	+	0.606348i	−0.335641	+	0.941990i	$0.608953\pi$
$338$	12.4717	−	3.34177i	0.678369	−	0.181768i
$339$	9.23148	−	0.904277i	0.501385	−	0.0491136i
$340$	3.73126	−	5.14275i	0.202356	−	0.278905i
$341$	14.8214	−	9.88210i	0.802624	−	0.535146i
$342$	−7.45536	+	11.1321i	−0.403139	+	0.601957i
$343$	5.78711	−	5.78711i	0.312475	−	0.312475i
$344$	−2.74392	+	4.75260i	−0.147942	+	0.256243i
$345$	2.64868	+	10.1450i	0.142600	+	0.546189i
$346$	5.69586	+	9.86552i	0.306211	+	0.530374i
$347$	−1.37744	−	5.14067i	−0.0739448	−	0.275966i	0.919047	−	0.394148i	$-0.128960\pi$
$347$	−1.37744	−	5.14067i	−0.0739448	−	0.275966i	−0.992992	+	0.118182i	$0.962293\pi$
$348$	−0.719546	+	0.270382i	−0.0385717	+	0.0144940i
$349$		−	16.5126i		−	0.883899i	−0.897040	−	0.441950i	$-0.854287\pi$
$349$		−	16.5126i		−	0.883899i	0.897040	−	0.441950i	$-0.145713\pi$
$350$	−12.6685	−	11.3766i	−0.677158	−	0.608105i
$351$	−1.12584	−	1.05783i	−0.0600927	−	0.0564628i
$352$	−0.828078	+	3.09043i	−0.0441367	+	0.164720i
$353$	−10.6553	+	2.85509i	−0.567127	+	0.151961i	−0.530979	−	0.847385i	$-0.678176\pi$
$353$	−10.6553	+	2.85509i	−0.567127	+	0.151961i	−0.0361482	+	0.999346i	$0.511509\pi$
$354$	12.3273	−	8.82372i	0.655188	−	0.468975i
$355$	−10.5429	+	27.5194i	−0.559561	+	1.46058i
$356$		−	1.60015i		−	0.0848075i
$357$	10.6393	−	12.9500i	0.563090	−	0.685386i
$358$	−6.41403	−	23.9375i	−0.338992	−	1.26514i
$359$	17.6503	+	30.5713i	0.931549	+	1.61349i	0.780675	+	0.624937i	$0.214876\pi$
$359$	17.6503	+	30.5713i	0.931549	+	1.61349i	0.150874	+	0.988553i	$0.451791\pi$
$360$	−5.47976	+	3.86940i	−0.288809	+	0.203935i
$361$	0.472606	+	0.818578i	0.0248740	+	0.0430831i
$362$	−10.4399	−	2.79736i	−0.548708	−	0.147026i
$363$	−1.30472	−	0.216121i	−0.0684801	−	0.0113434i
$364$			1.01243i			0.0530660i
$365$	27.1158	−	12.0941i	1.41931	−	0.633034i
$366$	15.4360	+	7.00385i	0.806854	+	0.366097i
$367$	−4.37729	+	16.3363i	−0.228493	+	0.852746i	0.752482	+	0.658612i	$0.228856\pi$
$367$	−4.37729	+	16.3363i	−0.228493	+	0.852746i	−0.980975	+	0.194134i	$0.937810\pi$
$368$	−1.91430	−	1.91430i	−0.0997900	−	0.0997900i
$369$	−0.261461	+	0.767562i	−0.0136111	+	0.0399577i
$370$	−4.08675	−	25.6934i	−0.212460	−	1.33574i
$371$			11.6597i			0.605342i
$372$	−8.79010	+	3.96663i	−0.455745	+	0.205660i
$373$	−2.13677	+	2.13677i	−0.110638	+	0.110638i	−0.760258	−	0.649621i	$-0.774928\pi$
$373$	−2.13677	+	2.13677i	−0.110638	+	0.110638i	0.649621	+	0.760258i	$0.274928\pi$
$374$	9.09118			0.470093
$375$	13.0309	−	14.3246i	0.672914	−	0.739720i
$376$	4.21590			0.217419
$377$	−0.127445	−	0.0341488i	−0.00656375	−	0.00175875i
$378$	−15.0414	+	9.32020i	−0.773648	+	0.479379i
$379$	−1.13010	−	0.652462i	−0.0580492	−	0.0335147i	0.470695	−	0.882296i	$-0.344003\pi$
$379$	−1.13010	−	0.652462i	−0.0580492	−	0.0335147i	−0.528744	+	0.848782i	$0.677337\pi$
$380$	1.56868	+	9.86232i	0.0804718	+	0.505926i
$381$	−0.568807	−	0.794659i	−0.0291409	−	0.0407116i
$382$	0.763354	−	2.84888i	0.0390566	−	0.145761i
$383$	−1.35652	+	5.06260i	−0.0693149	+	0.258687i	−0.991884	−	0.127145i	$-0.959419\pi$
$383$	−1.35652	+	5.06260i	−0.0693149	+	0.258687i	0.922569	+	0.385832i	$0.126085\pi$
$384$	0.715666	−	1.57728i	0.0365212	−	0.0804904i
$385$	2.53068	−	24.2310i	0.128975	−	1.23493i
$386$	−4.44357	−	2.56549i	−0.226172	−	0.130580i
$387$	−13.6792	−	9.16115i	−0.695352	−	0.465688i
$388$	−0.589415	+	0.589415i	−0.0299230	+	0.0299230i
$389$	−10.6568	+	18.4582i	−0.540323	+	0.935867i	0.458562	+	0.888662i	$0.348365\pi$
$389$	−10.6568	+	18.4582i	−0.540323	+	0.935867i	−0.998885	+	0.0472048i	$0.984969\pi$
$390$	−1.15143	−	0.00739008i	−0.0583048	−	0.000374211i
$391$	−3.84628	+	6.66196i	−0.194515	+	0.336910i
$392$	4.44006	+	1.18971i	0.224257	+	0.0600895i
$393$	−4.80749	+	29.0227i	−0.242506	+	1.46400i
$394$	−14.5429	+	8.39635i	−0.732661	+	0.423002i
$395$	9.94795	−	1.58231i	0.500536	−	0.0796144i
$396$	−9.08568	−	3.09493i	−0.456572	−	0.155526i
$397$	−15.6264	+	4.18708i	−0.784266	+	0.210143i	−0.628665	−	0.777677i	$-0.716398\pi$
$397$	−15.6264	+	4.18708i	−0.784266	+	0.210143i	−0.155601	+	0.987820i	$0.549731\pi$
$398$	0.274744	−	1.02536i	0.0137717	−	0.0513966i
$399$	2.56805	+	26.2164i	0.128563	+	1.31246i
$400$	−1.03313	+	4.89210i	−0.0516564	+	0.244605i
$401$		−	35.2299i		−	1.75930i	−0.475622	−	0.879650i	$-0.657777\pi$
$401$		−	35.2299i		−	1.75930i	0.475622	−	0.879650i	$-0.342223\pi$
$402$	4.20508	−	5.11836i	0.209730	−	0.255281i
$403$	−1.62319	−	0.324546i	−0.0808567	−	0.0161668i
$404$	−13.8400			−0.688563
$405$	−10.4899	−	17.1744i	−0.521249	−	0.853405i
$406$	−0.755642	+	1.30881i	−0.0375019	+	0.0649552i
$407$	26.3222	−	26.3222i	1.30474	−	1.30474i
$408$	−4.85543	−	0.804281i	−0.240380	−	0.0398179i
$409$	−29.6190	−	17.1006i	−1.46457	−	0.845568i	−0.465350	−	0.885127i	$-0.654072\pi$
$409$	−29.6190	−	17.1006i	−1.46457	−	0.845568i	−0.999217	+	0.0395582i	$0.987405\pi$
$410$	0.246190	+	0.551974i	0.0121584	+	0.0272601i
$411$	3.66681	+	37.4334i	0.180871	+	1.84645i
$412$	−2.19087	+	8.17643i	−0.107936	+	0.402824i
$413$	7.71430	−	28.7902i	0.379596	−	1.41667i
$414$	6.11190	−	5.34853i	0.300383	−	0.262866i
$415$	−14.5624	−	32.6499i	−0.714839	−	1.60272i
$416$	0.257472	−	0.148652i	0.0126236	−	0.00728825i
$417$	−17.8008	+	6.68896i	−0.871707	+	0.327560i
$418$	−10.1037	+	10.1037i	−0.494187	+	0.494187i
$419$	−16.0763			−0.785376			−0.392688	−	0.919672i	$-0.628455\pi$
$419$	−16.0763			−0.785376			−0.392688	+	0.919672i	$0.628455\pi$
$420$	−3.49526	+	12.7174i	−0.170551	+	0.620548i
$421$	6.88605	+	11.9270i	0.335605	+	0.581286i	0.983601	−	0.180359i	$-0.0577258\pi$
$421$	6.88605	+	11.9270i	0.335605	+	0.581286i	−0.647996	+	0.761644i	$0.724392\pi$
$422$	4.66656	+	17.4158i	0.227165	+	0.847790i
$423$	−0.840590	+	12.6197i	−0.0408709	+	0.613593i
$424$	2.96518	−	1.71195i	0.144002	−	0.0831396i
$425$	14.1870	−	0.762212i	0.688169	−	0.0369727i
$426$	22.7185	−	2.22540i	1.10071	−	0.107821i
$427$	32.1912	−	8.62560i	1.55784	−	0.417422i
$428$	15.8493	−	4.24680i	0.766104	−	0.205277i
$429$	−0.958943	−	1.33970i	−0.0462982	−	0.0646815i
$430$	−12.1188	+	1.92760i	−0.584422	+	0.0929572i
$431$	2.93903	+	1.69685i	0.141568	+	0.0817345i	0.569111	−	0.822261i	$-0.307287\pi$
$431$	2.93903	+	1.69685i	0.141568	+	0.0817345i	−0.427543	+	0.903995i	$0.640621\pi$
$432$	4.57869	+	2.45674i	0.220292	+	0.118200i
$433$	−18.5365	+	18.5365i	−0.890807	+	0.890807i	−0.994599	−	0.103792i	$-0.966902\pi$
$433$	−18.5365	+	18.5365i	−0.890807	+	0.890807i	0.103792	+	0.994599i	$0.466902\pi$
$434$	−8.40284	+	16.9968i	−0.403349	+	0.815870i
$435$	−1.48298	−	0.868935i	−0.0711033	−	0.0416622i
$436$	−2.02942			−0.0971917
$437$	−3.12926	−	11.6786i	−0.149693	−	0.558661i
$438$	−17.7702	−	14.5994i	−0.849091	−	0.697585i
$439$	−12.8741	+	7.43286i	−0.614447	+	0.354751i	−0.774704	−	0.632324i	$-0.782101\pi$
$439$	−12.8741	+	7.43286i	−0.614447	+	0.354751i	0.160257	+	0.987075i	$0.448768\pi$
$440$	−6.53375	+	2.91416i	−0.311484	+	0.138927i
$441$	−4.44652	+	13.0535i	−0.211739	+	0.621596i
$442$	−0.597352	−	0.597352i	−0.0284131	−	0.0284131i
$443$	−9.99155	+	37.2890i	−0.474713	+	1.77165i	0.147774	+	0.989021i	$0.452789\pi$
$443$	−9.99155	+	37.2890i	−0.474713	+	1.77165i	−0.622487	+	0.782631i	$0.713877\pi$
$444$	−16.3869	+	11.7295i	−0.777686	+	0.556658i
$445$	2.77917	−	2.25356i	0.131745	−	0.106829i
$446$	18.5560	+	10.7133i	0.878654	+	0.507291i
$447$	8.41489	+	1.39389i	0.398011	+	0.0659287i
$448$	−0.881380	−	3.28936i	−0.0416413	−	0.155407i
$449$	3.78058			0.178417			0.0892083	−	0.996013i	$-0.471566\pi$
$449$	3.78058			0.178417			0.0892083	+	0.996013i	$0.471566\pi$
$450$	−14.4379	−	4.06794i	−0.680607	−	0.191765i
$451$	−0.432390	+	0.748922i	−0.0203605	+	0.0352653i
$452$	−5.17283	−	1.38606i	−0.243309	−	0.0651946i
$453$	4.15367	+	11.0538i	0.195157	+	0.519354i
$454$	7.86521	−	4.54098i	0.369133	−	0.213119i
$455$	−1.75842	+	1.42586i	−0.0824361	+	0.0668452i
$456$	6.29004	−	4.50233i	0.294558	−	0.210841i
$457$	12.8278	+	12.8278i	0.600061	+	0.600061i	0.940329	−	0.340267i	$-0.110518\pi$
$457$	12.8278	+	12.8278i	0.600061	+	0.600061i	−0.340267	+	0.940329i	$0.610518\pi$
$458$	1.17597	−	0.315100i	0.0549494	−	0.0147236i
$459$	3.37561	−	14.3737i	0.157560	−	0.670908i
$460$	0.628812	−	6.02081i	0.0293185	−	0.280722i
$461$		−	22.5784i		−	1.05158i	−0.850614	−	0.525791i	$-0.823769\pi$
$461$		−	22.5784i		−	1.05158i	0.850614	−	0.525791i	$-0.176231\pi$
$462$	−17.6653	+	6.63805i	−0.821865	+	0.308830i
$463$	5.16413	−	5.16413i	0.239998	−	0.239998i	−0.576851	−	0.816849i	$-0.695719\pi$
$463$	5.16413	−	5.16413i	0.239998	−	0.239998i	0.816849	+	0.576851i	$0.195719\pi$
$464$	0.443792			0.0206025
$465$	−19.2688	−	9.68049i	−0.893571	−	0.448922i
$466$	−12.9763			−0.601116
$467$	8.47540	−	8.47540i	0.392195	−	0.392195i	−0.483274	−	0.875469i	$-0.660553\pi$
$467$	8.47540	−	8.47540i	0.392195	−	0.392195i	0.875469	+	0.483274i	$0.160553\pi$
$468$	0.393633	+	0.800348i	0.0181957	+	0.0369961i
$469$		−	13.0239i		−	0.601388i
$470$	5.93745	+	7.32229i	0.273874	+	0.337752i
$471$	−17.1045	+	37.6972i	−0.788133	+	1.73699i
$472$	−8.45429	+	2.26532i	−0.389140	+	0.104270i
$473$	−12.4154	−	12.4154i	−0.570861	−	0.570861i
$474$	−4.54143	−	6.34466i	−0.208595	−	0.291420i
$475$	−14.9199	+	16.6141i	−0.684571	+	0.762306i
$476$	−8.37998	+	4.83818i	−0.384096	+	0.221758i
$477$	4.53328	+	9.21722i	0.207565	+	0.422027i
$478$	−1.56038	−	0.418102i	−0.0713700	−	0.0191235i
$479$	9.50889	−	16.4699i	0.434472	−	0.752528i	−0.562780	−	0.826607i	$-0.690268\pi$
$479$	9.50889	−	16.4699i	0.434472	−	0.752528i	0.997252	+	0.0740786i	$0.0236016\pi$
$480$	3.74737	−	0.978371i	0.171043	−	0.0446563i
$481$	−3.45909			−0.157721
$482$	−3.27737	−	12.2313i	−0.149280	−	0.557121i
$483$	2.60949	−	15.7534i	0.118736	−	0.716807i
$484$	0.661250	+	0.381773i	0.0300568	+	0.0173533i
$485$	−1.85381	−	0.193611i	−0.0841772	−	0.00879143i
$486$	−8.26685	+	13.2159i	−0.374992	+	0.599484i
$487$	4.47527	−	16.7019i	0.202794	−	0.756837i	−0.787317	−	0.616549i	$-0.788530\pi$
$487$	4.47527	−	16.7019i	0.202794	−	0.756837i	0.990111	−	0.140289i	$-0.0448030\pi$
$488$	−6.92008	−	6.92008i	−0.313257	−	0.313257i
$489$	−21.1181	−	9.58201i	−0.954995	−	0.433313i
$490$	4.18682	+	9.38713i	0.189141	+	0.424068i
$491$	7.04962	−	4.07010i	0.318145	−	0.183681i	−0.332421	−	0.943131i	$-0.607865\pi$
$491$	7.04962	−	4.07010i	0.318145	−	0.183681i	0.650565	+	0.759450i	$0.274532\pi$
$492$	0.297188	−	0.361733i	0.0133983	−	0.0163082i
$493$	−0.326378	−	1.21806i	−0.0146993	−	0.0548586i
$494$	1.32776			0.0597387
$495$	−7.42042	−	20.1390i	−0.333523	−	0.905179i
$496$	5.55620	−	0.358640i	0.249481	−	0.0161034i
$497$	31.7354	−	31.7354i	1.42353	−	1.42353i
$498$	−17.5790	+	21.3969i	−0.787732	+	0.958817i
$499$	11.0018	+	6.35190i	0.492508	+	0.284350i	0.725615	−	0.688101i	$-0.241556\pi$
$499$	11.0018	+	6.35190i	0.492508	+	0.284350i	−0.233106	+	0.972451i	$0.574889\pi$
$500$	−9.95173	+	5.09540i	−0.445055	+	0.227873i
$501$	−7.97224	+	5.70643i	−0.356174	+	0.254945i
$502$	−4.17752	+	1.11936i	−0.186452	+	0.0499596i
$503$	15.9015	−	4.26079i	0.709012	−	0.189979i	0.113748	−	0.993510i	$-0.463714\pi$
$503$	15.9015	−	4.26079i	0.709012	−	0.189979i	0.595264	+	0.803530i	$0.297048\pi$
$504$	10.0220	−	1.98244i	0.446415	−	0.0883051i
$505$	−19.4914	−	24.0376i	−0.867357	−	1.06966i
$506$	7.50121	−	4.33083i	0.333469	−	0.192529i
$507$	3.65463	−	22.0629i	0.162308	−	0.979849i
$508$	0.146030	+	0.544992i	0.00647904	+	0.0241801i
$509$	−20.7796	−	35.9914i	−0.921041	−	1.59529i	−0.797807	−	0.602913i	$-0.794007\pi$
$509$	−20.7796	−	35.9914i	−0.921041	−	1.59529i	−0.123234	−	0.992378i	$-0.539327\pi$
$510$	−5.44123	−	9.56575i	−0.240942	−	0.423578i
$511$	−45.2170			−2.00028
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	12.2230	+	19.7261i	0.539658	+	0.870929i
$514$	27.0009	−	15.5890i	1.19096	−	0.687601i
$515$	−17.2865	+	7.71008i	−0.761735	+	0.339747i
$516$	5.53247	+	7.72921i	0.243554	+	0.340260i
$517$	−3.49109	+	13.0289i	−0.153538	+	0.573012i
$518$	−10.2547	+	38.2712i	−0.450568	+	1.68154i
$519$	19.6371	−	1.92356i	0.861971	−	0.0844351i
$520$	0.620792	+	0.237832i	0.0272235	+	0.0104296i
$521$	−2.73764	−	1.58058i	−0.119938	−	0.0692463i	0.438831	−	0.898570i	$-0.355393\pi$
$521$	−2.73764	−	1.58058i	−0.119938	−	0.0692463i	−0.558769	+	0.829323i	$0.688726\pi$
$522$	−0.0884856	+	1.32843i	−0.00387291	+	0.0581439i
$523$	25.0761	−	25.0761i	1.09650	−	1.09650i	0.101684	−	0.994817i	$-0.467577\pi$
$523$	25.0761	−	25.0761i	1.09650	−	1.09650i	0.994817	−	0.101684i	$-0.0324230\pi$
$524$	8.49231	−	14.7091i	0.370988	−	0.642570i
$525$	−27.0105	+	11.8399i	−1.17884	+	0.516735i
$526$	−8.98995			−0.391980
$527$	−5.07054	−	14.9861i	−0.220876	−	0.652807i
$528$	4.28185	+	3.51783i	0.186344	+	0.153094i
$529$		−	15.6709i		−	0.681343i
$530$	7.14936	+	2.73899i	0.310548	+	0.118974i
$531$	−5.09527	−	25.7585i	−0.221116	−	1.11782i
$532$	3.93625	−	14.6903i	0.170658	−	0.636904i
$533$	0.0776201	−	0.0207983i	0.00336210	−	0.000900872i
$534$	−2.52388	−	1.14517i	−0.109219	−	0.0495564i
$535$	29.6972	+	21.5465i	1.28392	+	0.931536i
$536$	−3.31211	+	1.91225i	−0.143061	+	0.0825966i
$537$	−42.3465	−	7.01452i	−1.82739	−	0.302699i
$538$	−25.2310	−	6.76063i	−1.08779	−	0.291471i
$539$	−7.35343	+	12.7365i	−0.316735	+	0.548600i
$540$	2.18145	+	11.4123i	0.0938748	+	0.491108i
$541$	−6.36417	+	11.0231i	−0.273617	+	0.473918i	−0.969785	−	0.243960i	$-0.921553\pi$
$541$	−6.36417	+	11.0231i	−0.273617	+	0.473918i	0.696168	+	0.717879i	$0.254887\pi$
$542$	5.50031	−	5.50031i	0.236258	−	0.236258i
$543$	−11.8837	+	14.4647i	−0.509978	+	0.620738i
$544$	2.46080	+	1.42074i	0.105506	+	0.0609138i
$545$	−2.85813	−	3.52475i	−0.122429	−	0.150984i
$546$	1.59690	+	0.724565i	0.0683408	+	0.0310085i
$547$	−2.93701	+	10.9611i	−0.125578	+	0.468662i	−0.999860	−	0.0167563i	$-0.994666\pi$
$547$	−2.93701	+	10.9611i	−0.125578	+	0.468662i	0.874282	+	0.485418i	$0.161333\pi$
$548$	5.62041	−	20.9757i	0.240092	−	0.896036i
$549$	22.0941	−	19.3346i	0.942953	−	0.825179i
$550$	−14.2632	−	7.24384i	−0.608184	−	0.308879i
$551$	1.71644	+	0.990989i	0.0731229	+	0.0422175i
$552$	−4.38940	+	1.64940i	−0.186825	+	0.0702030i
$553$	−14.8178	−	3.97043i	−0.630119	−	0.168840i
$554$	−5.71890			−0.242973
$555$	−43.4505	−	11.9419i	−1.84437	−	0.506907i
$556$	10.9789			0.465610
$557$	−13.4611	+	13.4611i	−0.570367	+	0.570367i	−0.932231	−	0.361864i	$-0.882140\pi$
$557$	−13.4611	+	13.4611i	−0.570367	+	0.570367i	0.361864	+	0.932231i	$0.382140\pi$
$558$	−0.0342850	+	16.7033i	−0.00145140	+	0.707105i
$559$			1.63155i			0.0690073i
$560$	4.47175	−	6.16335i	0.188966	−	0.260449i
$561$	6.50625	−	14.3394i	0.274694	−	0.605408i
$562$	−7.33346	−	7.33346i	−0.309343	−	0.309343i
$563$	3.27240	−	12.2128i	0.137915	−	0.514706i	−0.862054	−	0.506817i	$-0.830822\pi$
$563$	3.27240	−	12.2128i	0.137915	−	0.514706i	0.999969	−	0.00788931i	$-0.00251127\pi$
$564$	3.01718	−	6.64967i	0.127046	−	0.280002i
$565$	−4.87779	−	10.9363i	−0.205210	−	0.460096i
$566$		−	0.121629i		−	0.00511243i
$567$	3.93595	+	30.3947i	0.165294	+	1.27646i
$568$	−12.7302	−	3.41105i	−0.534148	−	0.143125i
$569$	−12.8027	−	22.1750i	−0.536718	−	0.929623i	−0.999078	−	0.0429304i	$-0.986331\pi$
$569$	−12.8027	−	22.1750i	−0.536718	−	0.929623i	0.462360	−	0.886692i	$-0.347003\pi$
$570$	16.6783	+	4.58387i	0.698578	+	0.191997i
$571$	−9.46485	−	16.3936i	−0.396092	−	0.686051i	0.597148	−	0.802131i	$-0.296300\pi$
$571$	−9.46485	−	16.3936i	−0.396092	−	0.686051i	−0.993240	+	0.116080i	$0.962967\pi$
$572$	0.246190	+	0.918794i	0.0102937	+	0.0384167i
$573$	−3.94718	−	3.24287i	−0.164896	−	0.135473i
$574$		−	0.920445i		−	0.0384186i
$575$	11.3427	−	7.38725i	0.473023	−	0.308070i
$576$	−1.97564	−	2.25762i	−0.0823185	−	0.0940674i
$577$	−37.5637	+	10.0652i	−1.56380	+	0.419018i	−0.933863	−	0.357632i	$-0.883584\pi$
$577$	−37.5637	+	10.0652i	−1.56380	+	0.419018i	−0.629933	+	0.776649i	$0.716918\pi$
$578$	−2.31021	+	8.62182i	−0.0960921	+	0.358621i
$579$	−7.22662	+	5.17272i	−0.300328	+	0.214971i
$580$	0.625012	+	0.770789i	0.0259522	+	0.0320053i
$581$			54.4453i			2.25877i
$582$	0.507849	+	1.35150i	0.0210510	+	0.0560214i
$583$	2.83525	+	10.5813i	0.117424	+	0.438233i
$584$	6.63903	+	11.4991i	0.274725	+	0.475837i
$585$	−0.835694	+	1.81084i	−0.0345517	+	0.0748689i
$586$	8.63385	−	14.9543i	0.356661	−	0.617755i
$587$	−21.8741	+	21.8741i	−0.902840	+	0.902840i	−0.995681	−	0.0928409i	$-0.970405\pi$
$587$	−21.8741	+	21.8741i	−0.902840	+	0.902840i	0.0928409	+	0.995681i	$0.470405\pi$
$588$	5.05411	−	6.15180i	0.208428	−	0.253696i
$589$	22.2904	+	11.0199i	0.918461	+	0.454068i
$590$	−15.8410	−	11.4933i	−0.652165	−	0.473171i
$591$	2.83555	+	28.9473i	0.116639	+	1.19073i
$592$	11.2384	−	3.01133i	0.461896	−	0.123765i
$593$	28.6209	+	28.6209i	1.17532	+	1.17532i	0.980923	+	0.194398i	$0.0622752\pi$
$593$	28.6209	+	28.6209i	1.17532	+	1.17532i	0.194398	+	0.980923i	$0.437725\pi$
$594$	−11.3839	+	12.1157i	−0.467087	+	0.497115i
$595$	−20.2050	−	7.74073i	−0.828324	−	0.317339i
$596$	−4.26478	−	2.46227i	−0.174692	−	0.100859i
$597$	−1.42066	−	1.16716i	−0.0581436	−	0.0477689i
$598$	−0.777445	−	0.208316i	−0.0317921	−	0.00851866i
$599$	7.53618	+	13.0531i	0.307920	+	0.533333i	0.977907	−	0.209039i	$-0.0670337\pi$
$599$	7.53618	+	13.0531i	0.307920	+	0.533333i	−0.669987	+	0.742373i	$0.733700\pi$
$600$	6.97685	+	5.13065i	0.284829	+	0.209458i
$601$	17.4664	−	30.2527i	0.712469	−	1.23403i	−0.251459	−	0.967868i	$-0.580910\pi$
$601$	17.4664	−	30.2527i	0.712469	−	1.23403i	0.963928	−	0.266164i	$-0.0857563\pi$
$602$	18.0514	+	4.83687i	0.735722	+	0.197136i
$603$	−5.06368	−	10.2956i	−0.206209	−	0.419271i
$604$		−	6.81763i		−	0.277405i
$605$	0.268195	+	1.68614i	0.0109037	+	0.0685515i
$606$	−9.90479	+	21.8295i	−0.402355	+	0.886764i
$607$	10.0119	−	37.3648i	0.406369	−	1.51659i	−0.395148	−	0.918617i	$-0.629307\pi$
$607$	10.0119	−	37.3648i	0.406369	−	1.51659i	0.801517	−	0.597972i	$-0.204027\pi$
$608$	−4.31383	+	1.15589i	−0.174949	+	0.0468774i
$609$	1.52358	+	2.12853i	0.0617385	+	0.0862525i
$610$	2.27311	−	21.7648i	0.0920356	−	0.881232i
$611$	1.08548	−	0.626701i	0.0439137	−	0.0253536i
$612$	−4.74345	+	7.08279i	−0.191743	+	0.286305i
$613$	−2.35856	−	8.80225i	−0.0952612	−	0.355520i	0.901798	−	0.432158i	$-0.142248\pi$
$613$	−2.35856	−	8.80225i	−0.0952612	−	0.355520i	−0.997059	+	0.0766388i	$0.975581\pi$
$614$	8.59280	−	14.8832i	0.346777	−	0.600636i
$615$	1.04681	+	0.00671862i	0.0422114	+	0.000270921i
$616$	10.8954			0.438987
$617$	9.41668	+	35.1435i	0.379101	+	1.41483i	0.847259	+	0.531180i	$0.178251\pi$
$617$	9.41668	+	35.1435i	0.379101	+	1.41483i	−0.468158	+	0.883645i	$0.655082\pi$
$618$	11.3286	+	9.30721i	0.455703	+	0.374391i
$619$		−	29.4287i		−	1.18284i	−0.806364	−	0.591420i	$-0.798567\pi$
$619$		−	29.4287i		−	1.18284i	0.806364	−	0.591420i	$-0.201433\pi$
$620$	8.44795	+	9.14507i	0.339278	+	0.367275i
$621$	−4.06206	−	13.4680i	−0.163005	−	0.540450i
$622$	10.4357	+	10.4357i	0.418434	+	0.418434i
$623$	−5.26345	+	1.41034i	−0.210876	+	0.0565039i
$624$	−0.0502015	−	0.512492i	−0.00200967	−	0.0205161i
$625$	−22.8653	−	10.1083i	−0.914612	−	0.404333i
$626$	−22.2124	−	12.8243i	−0.887785	−	0.512563i
$627$	8.70549	+	23.1672i	0.347664	+	0.925209i
$628$	16.8999	−	16.8999i	0.674379	−	0.674379i
$629$	−16.5302	−	28.6311i	−0.659100	−	1.14160i
$630$	17.5576	+	14.6145i	0.699510	+	0.582254i
$631$	−13.7081	−	23.7432i	−0.545713	−	0.945202i	−0.998562	−	0.0536150i	$-0.982926\pi$
$631$	−13.7081	−	23.7432i	−0.545713	−	0.945202i	0.452849	−	0.891587i	$-0.350408\pi$
$632$	1.16592	+	4.35129i	0.0463780	+	0.173085i
$633$	30.8094	+	5.10345i	1.22456	+	0.202844i
$634$	12.0277	+	6.94418i	0.477680	+	0.275789i
$635$	−0.740896	+	1.02117i	−0.0294015	+	0.0405238i
$636$	−0.578147	−	5.90212i	−0.0229250	−	0.234034i
$637$	1.32004	−	0.353705i	0.0523021	−	0.0140143i
$638$	−0.367494	+	1.37151i	−0.0145492	+	0.0542985i
$639$	12.7487	−	37.4261i	0.504333	−	1.48055i
$640$	−2.22397	−	0.232271i	−0.0879102	−	0.00918131i
$641$	13.5475	−	7.82168i	0.535096	−	0.308938i	−0.207993	−	0.978130i	$-0.566693\pi$
$641$	13.5475	−	7.82168i	0.535096	−	0.308938i	0.743089	+	0.669193i	$0.233360\pi$
$642$	4.64439	−	28.0381i	0.183299	−	1.10658i
$643$	−17.7678	+	17.7678i	−0.700693	+	0.700693i	−0.964559	−	0.263866i	$-0.915002\pi$
$643$	−17.7678	+	17.7678i	−0.700693	+	0.700693i	0.263866	+	0.964559i	$0.415002\pi$
$644$	−4.60960	+	7.98405i	−0.181644	+	0.314616i
$645$	−5.63267	+	20.4943i	−0.221786	+	0.806964i
$646$	6.34504	+	10.9899i	0.249642	+	0.432393i
$647$	11.6893	−	11.6893i	0.459552	−	0.459552i	−0.438956	−	0.898508i	$-0.644652\pi$
$647$	11.6893	−	11.6893i	0.459552	−	0.459552i	0.898508	+	0.438956i	$0.144652\pi$
$648$	7.15179	−	5.46369i	0.280949	−	0.214634i
$649$		−	28.0032i		−	1.09922i
$650$	0.461217	+	1.41316i	0.0180904	+	0.0554285i
$651$	20.7951	+	25.4177i	0.815023	+	0.996196i
$652$	9.46740	+	9.46740i	0.370772	+	0.370772i
$653$	−18.3779	−	18.3779i	−0.719183	−	0.719183i	0.249255	−	0.968438i	$-0.419814\pi$
$653$	−18.3779	−	18.3779i	−0.719183	−	0.719183i	−0.968438	+	0.249255i	$0.919814\pi$
$654$	−1.45239	+	3.20097i	−0.0567929	+	0.125168i
$655$	37.5073	−	5.96584i	1.46553	−	0.233105i
$656$	−0.234078	+	0.135145i	−0.00913923	+	0.00527654i
$657$	−35.7448	+	17.5803i	−1.39454	+	0.685872i
$658$	−3.71581	−	13.8676i	−0.144857	−	0.540615i
$659$	−14.7080			−0.572941			−0.286470	−	0.958089i	$-0.592482\pi$
$659$	−14.7080			−0.572941			−0.286470	+	0.958089i	$0.592482\pi$
$660$	−0.0795287	+	12.3911i	−0.00309565	+	0.482325i
$661$	18.6052	+	32.2251i	0.723657	+	1.25341i	0.959525	+	0.281625i	$0.0908734\pi$
$661$	18.6052	+	32.2251i	0.723657	+	1.25341i	−0.235868	+	0.971785i	$0.575793\pi$
$662$	23.3185	+	6.24817i	0.906299	+	0.242842i
$663$	−1.36970	+	0.514688i	−0.0531946	+	0.0199888i
$664$	13.8460	−	7.99399i	0.537329	−	0.310227i
$665$	31.0581	−	13.8524i	1.20438	−	0.537173i
$666$	6.77323	+	34.2411i	0.262457	+	1.32682i
$667$	−0.849552	−	0.849552i	−0.0328948	−	0.0328948i
$668$	5.46752	−	1.46502i	0.211545	−	0.0566832i
$669$	30.1779	−	21.6010i	1.16675	−	0.835141i
$670$	−7.98584	−	3.05945i	−0.308520	−	0.118197i
$671$	27.1164	−	15.6556i	1.04682	−	0.604379i
$672$	−5.81902	−	0.963895i	−0.224474	−	0.0371831i
$673$	9.00979	+	2.41417i	0.347302	+	0.0930592i	0.428253	−	0.903659i	$-0.359129\pi$
$673$	9.00979	+	2.41417i	0.347302	+	0.0930592i	−0.0809513	+	0.996718i	$0.525796\pi$
$674$	−15.7417			−0.606348
$675$	−16.7490	+	19.8613i	−0.644669	+	0.764462i
$676$	−6.45581	+	11.1818i	−0.248300	+	0.430069i
$677$	−8.69451	−	2.32969i	−0.334157	−	0.0895371i	0.0878393	−	0.996135i	$-0.472004\pi$
$677$	−8.69451	−	2.32969i	−0.334157	−	0.0895371i	−0.421996	+	0.906598i	$0.638670\pi$
$678$	−5.88822	+	7.16706i	−0.226136	+	0.275249i
$679$	2.45829	+	1.41930i	0.0943406	+	0.0544676i
$680$	0.998071	+	6.27487i	0.0382743	+	0.240630i
$681$	−1.53355	−	15.6555i	−0.0587656	−	0.599920i
$682$	−3.49262	+	17.4680i	−0.133739	+	0.668885i
$683$	14.6011	+	14.6011i	0.558697	+	0.558697i	0.928936	−	0.370239i	$-0.120724\pi$
$683$	14.6011	+	14.6011i	0.558697	+	0.558697i	−0.370239	+	0.928936i	$0.620724\pi$
$684$	−2.59988	−	13.1433i	−0.0994089	−	0.502548i
$685$	44.3466	−	19.7793i	1.69439	−	0.755728i
$686$			8.18421i			0.312475i
$687$	0.344599	−	2.08034i	0.0131473	−	0.0793700i
$688$	−1.42036	−	5.30084i	−0.0541506	−	0.202093i
$689$	0.508968	−	0.881559i	0.0193901	−	0.0335847i
$690$	−9.04651	−	5.30071i	−0.344395	−	0.201794i
$691$	18.1215	+	31.3873i	0.689373	+	1.19403i	0.972041	+	0.234812i	$0.0754474\pi$
$691$	18.1215	+	31.3873i	0.689373	+	1.19403i	−0.282667	+	0.959218i	$0.591219\pi$
$692$	−11.0036	−	2.94840i	−0.418293	−	0.112081i
$693$	−2.17238	+	32.6138i	−0.0825218	+	1.23890i
$694$	4.60900	+	2.66101i	0.174955	+	0.101011i
$695$	15.4621	+	19.0685i	0.586511	+	0.723308i
$696$	0.317607	−	0.699985i	0.0120389	−	0.0265329i
$697$	0.543077	+	0.543077i	0.0205705	+	0.0205705i
$698$	11.6762	+	11.6762i	0.441950	+	0.441950i
$699$	−9.28671	+	20.4673i	−0.351256	+	0.774145i
$700$	17.0024	−	0.913477i	0.642632	−	0.0345262i
$701$	−20.0931	−	11.6007i	−0.758905	−	0.438154i	0.0699973	−	0.997547i	$-0.477701\pi$
$701$	−20.0931	−	11.6007i	−0.758905	−	0.438154i	−0.828903	+	0.559393i	$0.811034\pi$
$702$	1.54408	−	0.0480882i	0.0582777	−	0.00181497i
$703$	50.1909	+	13.4486i	1.89298	+	0.507224i
$704$	−1.59972	−	2.77080i	−0.0602918	−	0.104429i
$705$	15.7985	−	4.12472i	0.595008	−	0.155346i
$706$	5.51561	−	9.55332i	0.207583	−	0.359544i
$707$	12.1983	+	45.5245i	0.458763	+	1.71213i
$708$	−2.47740	+	14.9560i	−0.0931064	+	0.562082i
$709$			13.1634i			0.494363i	0.968969	+	0.247182i	$0.0795044\pi$
$709$			13.1634i			0.494363i	−0.968969	+	0.247182i	$0.920496\pi$
$710$	−12.0041	−	26.9141i	−0.450507	−	1.01007i
$711$	−13.2575	+	2.62245i	−0.497194	+	0.0983497i
$712$	1.13147	+	1.13147i	0.0424038	+	0.0424038i
$713$	−11.3228	−	9.94971i	−0.424042	−	0.372620i
$714$	1.63391	+	16.6801i	0.0611477	+	0.624238i
$715$	−1.24906	+	1.72157i	−0.0467124	+	0.0643830i
$716$	21.4618	+	12.3910i	0.802064	+	0.463072i
$717$	−1.77618	+	2.16194i	−0.0663325	+	0.0807390i
$718$	−34.0978	−	9.13649i	−1.27252	−	0.340971i
$719$	8.35625	−	14.4735i	0.311636	−	0.539769i	−0.667081	−	0.744985i	$-0.732457\pi$
$719$	8.35625	−	14.4735i	0.311636	−	0.539769i	0.978717	+	0.205217i	$0.0657899\pi$
$720$	1.13870	−	6.61085i	0.0424368	−	0.246372i
$721$	28.8262			1.07354
$722$	−0.913005	−	0.244639i	−0.0339785	−	0.00910452i
$723$	−21.6377	−	3.58420i	−0.804716	−	0.133298i
$724$	9.36014	−	5.40408i	0.347867	−	0.200841i
$725$	−0.458493	+	2.17107i	−0.0170280	+	0.0806317i
$726$	1.07540	−	0.769756i	0.0399118	−	0.0285683i
$727$	−23.4328	+	6.27880i	−0.869074	+	0.232868i	−0.665687	−	0.746231i	$-0.731862\pi$
$727$	−23.4328	+	6.27880i	−0.869074	+	0.232868i	−0.203387	+	0.979098i	$0.565195\pi$
$728$	−0.715899	−	0.715899i	−0.0265330	−	0.0265330i
$729$	14.9289	+	22.4973i	0.552921	+	0.833234i
$730$	−10.6219	+	27.7256i	−0.393136	+	1.02617i
$731$	−13.5045	+	7.79680i	−0.499480	+	0.288375i
$732$	−15.8674	+	5.96246i	−0.586476	+	0.220379i
$733$	−30.8475	−	8.26555i	−1.13938	−	0.305295i	−0.360676	−	0.932691i	$-0.617454\pi$
$733$	−30.8475	−	8.26555i	−1.13938	−	0.305295i	−0.778700	+	0.627396i	$0.784121\pi$
$734$	−8.45627	−	14.6467i	−0.312127	−	0.540619i
$735$	17.8025	+	0.114260i	0.656656	+	0.00421454i
$736$	2.70723			0.0997900
$737$	−3.16698	−	11.8193i	−0.116657	−	0.435371i
$738$	−0.357868	−	0.727629i	−0.0131733	−	0.0267844i
$739$	−11.8761	+	6.85665i	−0.436868	+	0.252226i	−0.702268	−	0.711912i	$-0.747829\pi$
$739$	−11.8761	+	6.85665i	−0.436868	+	0.252226i	0.265400	+	0.964138i	$0.414496\pi$
$740$	21.0577	+	15.2782i	0.774098	+	0.561638i
$741$	0.950232	−	2.09425i	0.0349077	−	0.0769342i
$742$	−8.24466	−	8.24466i	−0.302671	−	0.302671i
$743$	33.4051	+	33.4051i	1.22551	+	1.22551i	0.965644	+	0.259870i	$0.0836797\pi$
$743$	33.4051	+	33.4051i	1.22551	+	1.22551i	0.259870	+	0.965644i	$0.416320\pi$
$744$	3.41071	−	9.02037i	0.125043	−	0.330703i
$745$	−1.72974	−	10.8749i	−0.0633729	−	0.398426i
$746$		−	3.02184i		−	0.110638i
$747$	21.1683	+	43.0400i	0.774506	+	1.57475i
$748$	−6.42843	+	6.42843i	−0.235047	+	0.235047i
$749$	−27.9385	−	48.3909i	−1.02085	−	1.76816i
$750$	0.914779	+	19.3433i	0.0334030	+	0.706317i
$751$	17.8186	−	30.8626i	0.650208	−	1.12619i	−0.332864	−	0.942975i	$-0.608015\pi$
$751$	17.8186	−	30.8626i	0.650208	−	1.12619i	0.983072	−	0.183219i	$-0.0586516\pi$
$752$	−2.98109	+	2.98109i	−0.108709	+	0.108709i
$753$	−1.22416	+	7.39021i	−0.0446108	+	0.269314i
$754$	0.114264	−	0.0659704i	0.00416125	−	0.00240250i
$755$	11.8410	−	9.60157i	0.430939	−	0.349437i
$756$	4.04552	−	17.2263i	0.147134	−	0.626513i
$757$	11.0387	−	41.1971i	0.401209	−	1.49733i	−0.409732	−	0.912206i	$-0.634378\pi$
$757$	11.0387	−	41.1971i	0.401209	−	1.49733i	0.810941	−	0.585128i	$-0.198956\pi$
$758$	1.26046	−	0.337739i	0.0457819	−	0.0122672i
$759$	−1.46257	−	14.9310i	−0.0530881	−	0.541959i
$760$	−8.08294	−	5.86448i	−0.293199	−	0.212727i
$761$	−24.0972	−	13.9125i	−0.873523	−	0.504329i	−0.00500593	−	0.999987i	$-0.501593\pi$
$761$	−24.0972	−	13.9125i	−0.873523	−	0.504329i	−0.868518	+	0.495658i	$0.834927\pi$
$762$	0.964116	+	0.159702i	0.0349262	+	0.00578538i
$763$	1.78869	+	6.67549i	0.0647550	+	0.241669i
$764$	1.47469	+	2.55423i	0.0533523	+	0.0924089i
$765$	−18.9820	+	1.73647i	−0.686295	+	0.0627824i
$766$	−2.62060	−	4.53900i	−0.0946860	−	0.164001i
$767$	−1.84000	+	1.84000i	−0.0664386	+	0.0664386i
$768$	0.609255	+	1.62136i	0.0219846	+	0.0585058i
$769$	21.8280	+	12.6024i	0.787137	+	0.454454i	0.838954	−	0.544203i	$-0.183168\pi$
$769$	21.8280	+	12.6024i	0.787137	+	0.454454i	−0.0518166	+	0.998657i	$0.516501\pi$
$770$	15.3444	+	18.9234i	0.552975	+	0.681950i
$771$	−5.26460	−	53.7447i	−0.189600	−	1.93557i
$772$	4.95615	−	1.32800i	0.178376	−	0.0477957i
$773$	26.6462	+	26.6462i	0.958398	+	0.958398i	0.999169	−	0.0407710i	$-0.0129814\pi$
$773$	26.6462	+	26.6462i	0.958398	+	0.958398i	−0.0407710	+	0.999169i	$0.512981\pi$
$774$	16.1506	−	3.19474i	0.580520	−	0.114832i
$775$	−3.98576	+	27.5520i	−0.143173	+	0.989698i
$776$		−	0.833558i		−	0.0299230i
$777$	53.0256	+	43.5641i	1.90228	+	1.56285i
$778$	−5.51639	−	20.5874i	−0.197772	−	0.738095i
$779$	−1.20712			−0.0432495
$780$	0.819408	−	0.808956i	0.0293395	−	0.0289653i
$781$	21.0832	−	36.5172i	0.754417	−	1.30669i
$782$	−1.99098	−	7.43045i	−0.0711974	−	0.265712i
$783$	2.03199	+	1.09028i	0.0726173	+	0.0389635i
$784$	−3.98085	+	2.29834i	−0.142173	+	0.0820837i
$785$	53.1531	+	5.55129i	1.89711	+	0.198134i
$786$	−17.1228	−	23.9216i	−0.610749	−	0.853255i
$787$	28.4790	−	7.63092i	1.01517	−	0.272013i	0.287380	−	0.957817i	$-0.407216\pi$
$787$	28.4790	−	7.63092i	1.01517	−	0.272013i	0.727786	+	0.685804i	$0.240549\pi$
$788$	4.34627	−	16.2205i	0.154829	−	0.577831i
$789$	−6.43381	+	14.1797i	−0.229050	+	0.504811i
$790$	−5.91540	+	8.15312i	−0.210461	+	0.290075i
$791$			18.2369i			0.648430i
$792$	8.61299	−	4.23610i	0.306049	−	0.150523i
$793$	−2.81041	−	0.753047i	−0.0998006	−	0.0267415i
$794$	8.08881	−	14.0102i	0.287061	−	0.497205i
$795$	9.43672	−	9.31636i	0.334686	−	0.330417i
$796$	0.530765	+	0.919312i	0.0188125	+	0.0325841i
$797$	11.9027	+	3.18932i	0.421616	+	0.112972i	0.463388	−	0.886156i	$-0.346634\pi$
$797$	11.9027	+	3.18932i	0.421616	+	0.112972i	−0.0417722	+	0.999127i	$0.513300\pi$
$798$	−20.3537	−	16.7219i	−0.720513	−	0.591950i
$799$	10.3745	+	5.98971i	0.367023	+	0.211901i
$800$	−2.72871	−	4.18977i	−0.0964743	−	0.148131i
$801$	−3.61251	+	3.16132i	−0.127642	+	0.111700i
$802$	24.9113	+	24.9113i	0.879650	+	0.879650i
$803$	−41.0349	+	10.9953i	−1.44809	+	0.388014i
$804$	0.645790	+	6.59267i	0.0227753	+	0.232506i
$805$	−20.3588	+	3.23824i	−0.717554	+	0.114133i
$806$	1.37726	−	0.918278i	0.0485117	−	0.0323450i
$807$	−28.7204	+	34.9581i	−1.01101	+	1.23058i
$808$	9.78633	−	9.78633i	0.344282	−	0.344282i
$809$	−13.5395	+	23.4511i	−0.476023	+	0.824496i	−0.999623	−	0.0274682i	$-0.991256\pi$
$809$	−13.5395	+	23.4511i	−0.476023	+	0.824496i	0.523599	+	0.851965i	$0.324589\pi$
$810$	19.5617	+	4.72665i	0.687327	+	0.166078i
$811$	−7.25268	−	12.5620i	−0.254676	−	0.441112i	0.710131	−	0.704069i	$-0.248636\pi$
$811$	−7.25268	−	12.5620i	−0.254676	−	0.441112i	−0.964807	+	0.262957i	$0.915302\pi$
$812$	−0.391149	−	1.45979i	−0.0137266	−	0.0512286i
$813$	−4.73915	−	12.6119i	−0.166209	−	0.442319i
$814$			37.2251i			1.30474i
$815$	−3.10986	+	29.7766i	−0.108934	+	1.04303i
$816$	4.00202	−	2.86460i	0.140099	−	0.100281i
$817$	6.34332	−	23.6736i	0.221925	−	0.828234i
$818$	33.0358	−	8.85190i	1.15507	−	0.309500i
$819$	2.28569	−	2.00021i	0.0798684	−	0.0698929i
$820$	−0.564387	−	0.216222i	−0.0197093	−	0.00755081i
$821$			20.3835i			0.711389i	0.934602	+	0.355694i	$0.115756\pi$
$821$			20.3835i			0.711389i	−0.934602	+	0.355694i	$0.884244\pi$
$822$	−29.0622	−	23.8766i	−1.01366	−	0.832791i
$823$	3.19128	+	11.9100i	0.111241	+	0.415157i	0.998978	−	0.0451936i	$-0.0143905\pi$
$823$	3.19128	+	11.9100i	0.111241	+	0.415157i	−0.887737	+	0.460350i	$0.847724\pi$
$824$	−4.23243	−	7.33078i	−0.147444	−	0.255380i
$825$	−21.6333	+	17.3129i	−0.753174	+	0.602757i
$826$	14.9029	+	25.8126i	0.518538	+	0.898134i
$827$	−28.8199	−	7.72226i	−1.00216	−	0.268529i	−0.279813	−	0.960055i	$-0.590272\pi$
$827$	−28.8199	−	7.72226i	−1.00216	−	0.268529i	−0.722352	+	0.691525i	$0.756939\pi$
$828$	−0.539783	+	8.10375i	−0.0187588	+	0.281625i
$829$			40.2598i			1.39828i	0.714984	+	0.699141i	$0.246434\pi$
$829$			40.2598i			1.39828i	−0.714984	+	0.699141i	$0.753566\pi$
$830$	33.3841	+	12.7898i	1.15878	+	0.443940i
$831$	−4.09283	+	9.02033i	−0.141979	+	0.312912i
$832$	−0.0769478	+	0.287173i	−0.00266768	+	0.00995593i
$833$	9.23582	+	9.23582i	0.320002	+	0.320002i
$834$	7.85724	−	17.3168i	0.272074	−	0.599633i
$835$	10.2446	+	7.43287i	0.354530	+	0.257225i
$836$		−	14.2887i		−	0.494187i
$837$	26.3212	+	12.0080i	0.909795	+	0.415058i
$838$	11.3676	−	11.3676i	0.392688	−	0.392688i
$839$	27.3394			0.943862			0.471931	−	0.881636i	$-0.343557\pi$
$839$	27.3394			0.943862			0.471931	+	0.881636i	$0.343557\pi$
$840$	−6.52107	−	11.4641i	−0.224998	−	0.395550i
$841$	−28.8030			−0.993209
$842$	−13.3028	−	3.56448i	−0.458445	−	0.122840i
$843$	−16.8153	+	6.31863i	−0.579148	+	0.217625i
$844$	−15.6146	−	9.01510i	−0.537477	−	0.310313i
$845$	−28.5128	+	4.53520i	−0.980871	+	0.156016i
$846$	−8.32912	−	9.51789i	−0.286361	−	0.327232i
$847$	0.672974	−	2.51157i	0.0231237	−	0.0862986i
$848$	−0.886170	+	3.30723i	−0.0304312	+	0.113571i
$849$	−0.191843	−	0.0870454i	−0.00658402	−	0.00298739i
$850$	−9.49273	+	10.5707i	−0.325598	+	0.362571i
$851$	−27.2784	−	15.7492i	−0.935090	−	0.539874i
$852$	−14.4908	+	17.6380i	−0.496446	+	0.604267i
$853$	−23.9222	+	23.9222i	−0.819081	+	0.819081i	−0.985975	−	0.166894i	$-0.946626\pi$
$853$	−23.9222	+	23.9222i	−0.819081	+	0.819081i	0.166894	+	0.985975i	$0.446626\pi$
$854$	−16.6634	+	28.8618i	−0.570209	+	0.987631i
$855$	19.1662	−	23.0259i	0.655469	−	0.787469i
$856$	−8.20419	+	14.2101i	−0.280414	+	0.485690i
$857$	−0.303507	−	0.0813245i	−0.0103676	−	0.00277799i	0.253632	−	0.967301i	$-0.418375\pi$
$857$	−0.303507	−	0.0813245i	−0.0103676	−	0.00277799i	−0.263999	+	0.964523i	$0.585042\pi$
$858$	1.62539	+	0.269239i	0.0554899	+	0.00919166i
$859$	−5.88108	+	3.39544i	−0.200660	+	0.115851i	−0.596963	−	0.802269i	$-0.703626\pi$
$859$	−5.88108	+	3.39544i	−0.200660	+	0.115851i	0.396303	+	0.918120i	$0.370293\pi$
$860$	7.20629	−	9.93233i	0.245732	−	0.338690i
$861$	−1.45180	−	0.658732i	−0.0494773	−	0.0224495i
$862$	−3.27807	+	0.878355i	−0.111651	+	0.0299169i
$863$	12.2205	−	45.6077i	0.415992	−	1.55250i	−0.366848	−	0.930281i	$-0.619563\pi$
$863$	12.2205	−	45.6077i	0.415992	−	1.55250i	0.782840	−	0.622223i	$-0.213770\pi$
$864$	−4.97480	+	1.50045i	−0.169246	+	0.0510463i
$865$	−10.3760	−	23.2636i	−0.352793	−	0.790987i
$866$		−	26.2146i		−	0.890807i
$867$	11.9457	+	9.81420i	0.405698	+	0.333308i
$868$	−6.07682	−	17.9602i	−0.206261	−	0.609610i
$869$	−14.4128			−0.488921
$870$	1.66305	−	0.434193i	0.0563828	−	0.0147205i
$871$	−0.568518	+	0.984702i	−0.0192635	+	0.0333654i
$872$	1.43502	−	1.43502i	0.0485959	−	0.0485959i
$873$	2.49515	+	0.166199i	0.0844479	+	0.00562500i
$874$	10.4707	+	6.04526i	0.354177	+	0.204484i
$875$	25.5318	+	28.2438i	0.863134	+	0.954814i
$876$	22.8887	−	2.24208i	0.773338	−	0.0757529i
$877$	1.75890	−	6.56429i	0.0593937	−	0.221660i	−0.929850	−	0.367940i	$-0.880063\pi$
$877$	1.75890	−	6.56429i	0.0593937	−	0.221660i	0.989243	+	0.146280i	$0.0467299\pi$
$878$	3.84753	−	14.3592i	0.129848	−	0.484599i
$879$	−17.4082	−	24.3203i	−0.587163	−	0.820303i
$880$	2.55944	−	6.68069i	0.0862786	−	0.225206i
$881$	4.07602	−	2.35329i	0.137325	−	0.0792845i	−0.429764	−	0.902941i	$-0.641403\pi$
$881$	4.07602	−	2.35329i	0.137325	−	0.0792845i	0.567088	+	0.823657i	$0.308070\pi$
$882$	−6.08606	−	12.3744i	−0.204928	−	0.416668i
$883$	17.9138	−	17.9138i	0.602846	−	0.602846i	−0.338221	−	0.941067i	$-0.609825\pi$
$883$	17.9138	−	17.9138i	0.602846	−	0.602846i	0.941067	+	0.338221i	$0.109825\pi$
$884$	0.844783			0.0284131
$885$	−29.4650	+	16.7604i	−0.990457	+	0.563396i
$886$	−19.3022	−	33.4324i	−0.648470	−	1.12318i
$887$	−5.93722	−	22.1580i	−0.199352	−	0.743993i	−0.991097	−	0.133141i	$-0.957494\pi$
$887$	−5.93722	−	22.1580i	−0.199352	−	0.743993i	0.791745	−	0.610852i	$-0.209173\pi$
$888$	3.29325	−	19.8813i	0.110514	−	0.667172i
$889$	1.66397	−	0.960691i	0.0558076	−	0.0322205i
$890$	−0.371667	+	3.55868i	−0.0124583	+	0.119287i
$891$	10.9629	+	26.6264i	0.367271	+	0.892020i
$892$	−20.6966	+	5.54563i	−0.692973	+	0.185681i
$893$	−18.1867	+	4.87311i	−0.608594	+	0.163072i
$894$	−6.93586	+	4.96460i	−0.231970	+	0.166041i
$895$	8.70465	+	54.7261i	0.290964	+	1.82929i
$896$	2.94916	+	1.70270i	0.0985244	+	0.0568831i
$897$	−0.884964	+	1.07717i	−0.0295481	+	0.0359655i
$898$	−2.67327	+	2.67327i	−0.0892083	+	0.0892083i
$899$	2.46580	−	0.159161i	0.0822389	−	0.00530833i
$900$	13.0856	−	7.33264i	0.436186	−	0.244421i
$901$	9.72895			0.324118
$902$	−0.223822	−	0.835313i	−0.00745244	−	0.0278129i
$903$	20.5479	−	25.0106i	0.683792	−	0.832302i
$904$	4.63783	−	2.67765i	0.154252	−	0.0890574i
$905$	22.5682	+	8.64612i	0.750194	+	0.287407i
$906$	−10.7533	−	4.87915i	−0.357255	−	0.162099i
$907$	20.3633	+	20.3633i	0.676153	+	0.676153i	0.959127	−	0.282974i	$-0.0913211\pi$
$907$	20.3633	+	20.3633i	0.676153	+	0.676153i	−0.282974	+	0.959127i	$0.591321\pi$
$908$	−2.35059	+	8.77251i	−0.0780069	+	0.291126i
$909$	27.3428	+	31.2453i	0.906904	+	1.03634i
$910$	0.235159	−	2.25162i	0.00779544	−	0.0746406i
$911$	−47.3081	−	27.3133i	−1.56739	−	0.904931i	−0.996472	−	0.0839222i	$-0.973255\pi$
$911$	−47.3081	−	27.3133i	−1.56739	−	0.904931i	−0.570915	−	0.821009i	$-0.693411\pi$
$912$	−1.26410	+	7.63136i	−0.0418586	+	0.252700i
$913$	13.2393	+	49.4097i	0.438156	+	1.63522i
$914$	−18.1413			−0.600061
$915$	−32.7025	−	19.1617i	−1.08111	−	0.633466i
$916$	−0.608726	+	1.05434i	−0.0201129	+	0.0348365i
$917$	−55.8684	−	14.9699i	−1.84494	−	0.494350i
$918$	7.77684	+	12.5507i	0.256674	+	0.414234i
$919$	−44.0355	+	25.4239i	−1.45260	+	0.838658i	−0.998628	−	0.0523595i	$-0.983326\pi$
$919$	−44.0355	+	25.4239i	−1.45260	+	0.838658i	−0.453970	+	0.891017i	$0.649992\pi$
$920$	3.81272	+	4.70199i	0.125702	+	0.155020i
$921$	−17.3254	−	24.2047i	−0.570891	−	0.797571i
$922$	15.9654	+	15.9654i	0.525791	+	0.525791i
$923$	−3.78474	+	1.01412i	−0.124576	+	0.0333801i
$924$	7.79745	−	17.1851i	0.256517	−	0.565347i
$925$	3.12099	+	58.0906i	0.102618	+	1.91001i
$926$			7.30319i			0.239998i
$927$	22.7876	−	11.2076i	0.748443	−	0.368105i
$928$	−0.313808	+	0.313808i	−0.0103013	+	0.0103013i
$929$	−14.5611			−0.477734			−0.238867	−	0.971052i	$-0.576776\pi$
$929$	−14.5611			−0.477734			−0.238867	+	0.971052i	$0.576776\pi$
$930$	20.4703	−	6.77998i	0.671246	−	0.222324i
$931$	−20.5288			−0.672806
$932$	9.17564	−	9.17564i	0.300558	−	0.300558i
$933$	23.9286	−	8.99158i	0.783386	−	0.294371i
$934$			11.9860i			0.392195i
$935$	−20.2185	−	2.11161i	−0.661216	−	0.0690572i
$936$	−0.844272	−	0.287591i	−0.0275959	−	0.00940021i
$937$	27.5931	−	7.39356i	0.901428	−	0.241537i	0.221799	−	0.975092i	$-0.428807\pi$
$937$	27.5931	−	7.39356i	0.901428	−	0.241537i	0.679630	+	0.733555i	$0.262141\pi$
$938$	9.20929	+	9.20929i	0.300694	+	0.300694i
$939$	−36.1242	+	25.8573i	−1.17887	+	0.843820i
$940$	−9.37605	−	0.979231i	−0.305813	−	0.0319390i
$941$	6.40991	−	3.70076i	0.208957	−	0.120641i	−0.391870	−	0.920021i	$-0.628172\pi$
$941$	6.40991	−	3.70076i	0.208957	−	0.120641i	0.600827	+	0.799379i	$0.294838\pi$
$942$	−14.5612	−	38.7506i	−0.474431	−	1.26256i
$943$	0.706807	+	0.189388i	0.0230168	+	0.00616733i
$944$	4.37626	−	7.57991i	0.142435	−	0.246705i
$945$	35.6165	−	17.2342i	1.15861	−	0.560628i
$946$	17.5580			0.570861
$947$	−13.2563	−	49.4732i	−0.430772	−	1.60766i	−0.750986	−	0.660318i	$-0.770421\pi$
$947$	−13.2563	−	49.4732i	−0.430772	−	1.60766i	0.320214	−	0.947345i	$-0.396245\pi$
$948$	7.69762	+	1.27508i	0.250007	+	0.0414126i
$949$	3.41873	+	1.97380i	0.110977	+	0.0640724i
$950$	−1.19798	−	22.2979i	−0.0388676	−	0.723439i
$951$	19.5607	−	14.0013i	0.634300	−	0.454024i
$952$	2.50443	−	9.34665i	0.0811690	−	0.302927i
$953$	31.0428	+	31.0428i	1.00557	+	1.00557i	0.999984	+	0.00558963i	$0.00177924\pi$
$953$	31.0428	+	31.0428i	1.00557	+	1.00557i	0.00558963	+	0.999984i	$0.498221\pi$
$954$	−9.72307	−	3.31205i	−0.314796	−	0.107231i
$955$	−2.35939	+	6.15852i	−0.0763480	+	0.199285i
$956$	1.39900	−	0.807711i	0.0452468	−	0.0261232i
$957$	1.90025	+	1.56118i	0.0614264	+	0.0504659i
$958$	4.92216	+	18.3698i	0.159028	+	0.593500i
$959$	−73.9501			−2.38797
$960$	−1.95798	+	3.34160i	−0.0631935	+	0.107850i
$961$	30.7428	−	3.98535i	0.991702	−	0.128560i
$962$	2.44594	−	2.44594i	0.0788604	−	0.0788604i
$963$	−40.9002	−	27.3914i	−1.31799	−	0.882677i
$964$	10.9663	+	6.33139i	0.353200	+	0.203920i
$965$	9.28648	+	6.73770i	0.298942	+	0.216894i
$966$	9.29418	+	12.9846i	0.299035	+	0.417771i
$967$	−2.50898	+	0.672279i	−0.0806833	+	0.0216190i	−0.298935	−	0.954274i	$-0.596631\pi$
$967$	−2.50898	+	0.672279i	−0.0806833	+	0.0216190i	0.218252	+	0.975893i	$0.429965\pi$
$968$	−0.737528	+	0.197620i	−0.0237051	+	0.00635175i
$969$	21.8752	−	2.14280i	0.702732	−	0.0688367i
$970$	1.44775	−	1.17394i	0.0464843	−	0.0376929i
$971$	−30.2450	+	17.4619i	−0.970607	+	0.560380i	−0.899421	−	0.437083i	$-0.856012\pi$
$971$	−30.2450	+	17.4619i	−0.970607	+	0.560380i	−0.0711861	+	0.997463i	$0.522678\pi$
$972$	−3.49949	−	15.1906i	−0.112246	−	0.487238i
$973$	−9.67659	−	36.1135i	−0.310217	−	1.15775i
$974$	8.64556	+	14.9746i	0.277022	+	0.479816i
$975$	2.55902	+	0.283878i	0.0819544	+	0.00909138i
$976$	9.78647			0.313257
$977$	−7.74817	+	7.74817i	−0.247886	+	0.247886i	−0.820103	−	0.572217i	$-0.806084\pi$
$977$	−7.74817	+	7.74817i	−0.247886	+	0.247886i	0.572217	+	0.820103i	$0.306084\pi$
$978$	21.7083	−	8.15727i	0.694154	−	0.260841i
$979$	−4.43368	+	2.55979i	−0.141701	+	0.0818112i
$980$	−9.59823	−	3.67718i	−0.306604	−	0.117463i
$981$	4.00942	+	4.58166i	0.128011	+	0.146281i
$982$	−2.10684	+	7.86283i	−0.0672319	+	0.250913i
$983$	0.585999	−	2.18698i	0.0186905	−	0.0697538i	−0.955951	−	0.293527i	$-0.905171\pi$
$983$	0.585999	−	2.18698i	0.0186905	−	0.0697538i	0.974641	+	0.223773i	$0.0718376\pi$
$984$	0.0456402	+	0.465927i	0.00145496	+	0.0148532i
$985$	34.2932	−	15.2954i	1.09267	−	0.487350i
$986$	1.09208	+	0.630514i	0.0347790	+	0.0200796i
$987$	−24.5324	−	4.06369i	−0.780875	−	0.129349i
$988$	−0.938867	+	0.938867i	−0.0298693	+	0.0298693i
$989$	−7.42843	+	12.8664i	−0.236210	+	0.409128i
$990$	19.4874	+	8.99337i	0.619351	+	0.285828i
$991$	0.118751			0.00377224			0.00188612	−	0.999998i	$-0.499400\pi$
$991$	0.118751			0.00377224			0.00188612	+	0.999998i	$0.499400\pi$
$992$	−3.67523	+	4.18242i	−0.116689	+	0.132792i
$993$	26.5434	−	32.3082i	0.842329	−	1.02527i
$994$			44.8806i			1.42353i
$995$	−0.849184	+	2.21655i	−0.0269209	+	0.0702695i
$996$	−2.69967	−	27.5601i	−0.0855423	−	0.873275i
$997$	−10.3950	+	38.7945i	−0.329212	+	1.22863i	0.580798	+	0.814048i	$0.302741\pi$
$997$	−10.3950	+	38.7945i	−0.329212	+	1.22863i	−0.910010	+	0.414587i	$0.863926\pi$
$998$	−12.2709	+	3.28798i	−0.388429	+	0.104079i
$999$	58.8553	+	13.8219i	1.86210	+	0.437307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.19	✓	256
3.2	odd	2	inner	930.2.bf.a.377.51	yes	256
5.3	odd	4	inner	930.2.bf.a.563.36	yes	256
15.8	even	4	inner	930.2.bf.a.563.3	yes	256
31.25	even	3	inner	930.2.bf.a.707.3	yes	256
93.56	odd	6	inner	930.2.bf.a.707.36	yes	256
155.118	odd	12	inner	930.2.bf.a.893.51	yes	256
465.428	even	12	inner	930.2.bf.a.893.19	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.19	✓	256	1.1	even	1	trivial
930.2.bf.a.377.51	yes	256	3.2	odd	2	inner
930.2.bf.a.563.3	yes	256	15.8	even	4	inner
930.2.bf.a.563.36	yes	256	5.3	odd	4	inner
930.2.bf.a.707.3	yes	256	31.25	even	3	inner
930.2.bf.a.707.36	yes	256	93.56	odd	6	inner
930.2.bf.a.893.19	yes	256	465.428	even	12	inner
930.2.bf.a.893.51	yes	256	155.118	odd	12	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.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.609255 + 1.62136i) q^{3} -1.00000i q^{4} +(1.73683 - 1.40835i) q^{5} +(-1.57728 - 0.715666i) q^{6} +(-3.28936 + 0.881380i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.25762 + 1.97564i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.609255 + 1.62136i) q^{3} -1.00000i q^{4} +(1.73683 - 1.40835i) q^{5} +(-1.57728 - 0.715666i) q^{6} +(-3.28936 + 0.881380i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.25762 + 1.97564i) q^{9} +(-0.232271 + 2.22397i) q^{10} +(-2.77080 + 1.59972i) q^{11} +(1.62136 - 0.609255i) q^{12} +(0.287173 + 0.0769478i) q^{13} +(1.70270 - 2.94916i) q^{14} +(3.34160 + 1.95798i) q^{15} -1.00000 q^{16} +(0.735430 + 2.74466i) q^{17} +(0.199385 - 2.99337i) q^{18} +(-3.86767 - 2.23300i) q^{19} +(-1.40835 - 1.73683i) q^{20} +(-3.43309 - 4.79624i) q^{21} +(0.828078 - 3.09043i) q^{22} +(1.91430 + 1.91430i) q^{23} +(-0.715666 + 1.57728i) q^{24} +(1.03313 - 4.89210i) q^{25} +(-0.257472 + 0.148652i) q^{26} +(-4.57869 - 2.45674i) q^{27} +(0.881380 + 3.28936i) q^{28} -0.443792 q^{29} +(-3.74737 + 0.978371i) q^{30} +(-5.55620 + 0.358640i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-4.28185 - 3.51783i) q^{33} +(-2.46080 - 1.42074i) q^{34} +(-4.47175 + 6.16335i) q^{35} +(1.97564 + 2.25762i) q^{36} +(-11.2384 + 3.01133i) q^{37} +(4.31383 - 1.15589i) q^{38} +(0.0502015 + 0.512492i) q^{39} +(2.22397 + 0.232271i) q^{40} +(0.234078 - 0.135145i) q^{41} +(5.81902 + 0.963895i) q^{42} +(1.42036 + 5.30084i) q^{43} +(1.59972 + 2.77080i) q^{44} +(-1.13870 + 6.61085i) q^{45} -2.70723 q^{46} +(2.98109 - 2.98109i) q^{47} +(-0.609255 - 1.62136i) q^{48} +(3.98085 - 2.29834i) q^{49} +(2.72871 + 4.18977i) q^{50} +(-4.00202 + 2.86460i) q^{51} +(0.0769478 - 0.287173i) q^{52} +(0.886170 - 3.30723i) q^{53} +(4.97480 - 1.50045i) q^{54} +(-2.55944 + 6.68069i) q^{55} +(-2.94916 - 1.70270i) q^{56} +(1.26410 - 7.63136i) q^{57} +(0.313808 - 0.313808i) q^{58} +(-4.37626 + 7.57991i) q^{59} +(1.95798 - 3.34160i) q^{60} -9.78647 q^{61} +(3.67523 - 4.18242i) q^{62} +(5.68481 - 8.48841i) q^{63} +1.00000i q^{64} +(0.607138 - 0.270794i) q^{65} +(5.51521 - 0.540246i) q^{66} +(-0.989853 + 3.69418i) q^{67} +(2.74466 - 0.735430i) q^{68} +(-1.93748 + 4.27007i) q^{69} +(-1.19614 - 7.52015i) q^{70} +(-11.4136 + 6.58964i) q^{71} +(-2.99337 - 0.199385i) q^{72} +(12.8256 + 3.43661i) q^{73} +(5.81744 - 10.0761i) q^{74} +(8.56129 - 1.30546i) q^{75} +(-2.23300 + 3.86767i) q^{76} +(7.70419 - 7.70419i) q^{77} +(-0.397884 - 0.326888i) q^{78} +(3.90126 + 2.25239i) q^{79} +(-1.73683 + 1.40835i) q^{80} +(1.19367 - 8.92049i) q^{81} +(-0.0699563 + 0.261081i) q^{82} +(4.13799 - 15.4432i) q^{83} +(-4.79624 + 3.43309i) q^{84} +(5.14275 + 3.73126i) q^{85} +(-4.75260 - 2.74392i) q^{86} +(-0.270382 - 0.719546i) q^{87} +(-3.09043 - 0.828078i) q^{88} +1.60015 q^{89} +(-3.86940 - 5.47976i) q^{90} -1.01243 q^{91} +(1.91430 - 1.91430i) q^{92} +(-3.96663 - 8.79010i) q^{93} +4.21590i q^{94} +(-9.86232 + 1.56868i) q^{95} +(1.57728 + 0.715666i) q^{96} +(-0.589415 - 0.589415i) q^{97} +(-1.18971 + 4.44006i) q^{98} +(3.09493 - 9.08568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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