LMFDB - Embedded newform 285.2.i.f.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Root			$-0.690702 + 1.19633i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.f.106.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.690702 - 1.19633i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0458624 - 0.0794360i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.690702 - 1.19633i) q^{6} -4.36264 q^{7} -2.88952 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.690702 + 1.19633i) q^{10} -4.31625 q^{11} +0.0917248 q^{12} +(3.18132 - 5.51021i) q^{13} +(3.01329 + 5.21916i) q^{14} +(0.500000 - 0.866025i) q^{15} +(1.90407 + 3.29794i) q^{16} +(-2.85821 - 4.95056i) q^{17} +1.38140 q^{18} +(2.97100 + 3.18954i) q^{19} -0.0917248 q^{20} +(-2.18132 - 3.77816i) q^{21} +(2.98124 + 5.16366i) q^{22} +(0.289678 - 0.501738i) q^{23} +(-1.44476 - 2.50239i) q^{24} +(-0.500000 + 0.866025i) q^{25} -8.78938 q^{26} -1.00000 q^{27} +(-0.200081 + 0.346551i) q^{28} +(1.77672 - 3.07737i) q^{29} -1.38140 q^{30} +1.18345 q^{31} +(-0.259229 + 0.448998i) q^{32} +(-2.15812 - 3.73798i) q^{33} +(-3.94834 + 6.83872i) q^{34} +(2.18132 + 3.77816i) q^{35} +(0.0458624 + 0.0794360i) q^{36} -6.54609 q^{37} +(1.76367 - 5.75732i) q^{38} +6.36264 q^{39} +(1.44476 + 2.50239i) q^{40} +(0.381403 + 0.660610i) q^{41} +(-3.01329 + 5.21916i) q^{42} +(3.18132 + 5.51021i) q^{43} +(-0.197954 + 0.342866i) q^{44} +1.00000 q^{45} -0.800326 q^{46} +(1.36632 - 2.36653i) q^{47} +(-1.90407 + 3.29794i) q^{48} +12.0327 q^{49} +1.38140 q^{50} +(2.85821 - 4.95056i) q^{51} +(-0.291806 - 0.505423i) q^{52} +(-2.56853 + 4.44882i) q^{53} +(0.690702 + 1.19633i) q^{54} +(2.15812 + 3.73798i) q^{55} +12.6059 q^{56} +(-1.27672 + 4.16773i) q^{57} -4.90874 q^{58} +(-1.91484 - 3.31660i) q^{59} +(-0.0458624 - 0.0794360i) q^{60} +(6.01053 - 10.4105i) q^{61} +(-0.817411 - 1.41580i) q^{62} +(2.18132 - 3.77816i) q^{63} +8.33247 q^{64} -6.36264 q^{65} +(-2.98124 + 5.16366i) q^{66} +(2.00213 - 3.46779i) q^{67} -0.524337 q^{68} +0.579357 q^{69} +(3.01329 - 5.21916i) q^{70} +(-1.53953 - 2.66654i) q^{71} +(1.44476 - 2.50239i) q^{72} +(-4.04320 - 7.00303i) q^{73} +(4.52140 + 7.83129i) q^{74} -1.00000 q^{75} +(0.389622 - 0.0897246i) q^{76} +18.8303 q^{77} +(-4.39469 - 7.61182i) q^{78} +(-5.66836 - 9.81790i) q^{79} +(1.90407 - 3.29794i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.526872 - 0.912569i) q^{82} +7.67889 q^{83} -0.400163 q^{84} +(-2.85821 + 4.95056i) q^{85} +(4.39469 - 7.61182i) q^{86} +3.55344 q^{87} +12.4719 q^{88} +(-4.92093 + 8.52330i) q^{89} +(-0.690702 - 1.19633i) q^{90} +(-13.8790 + 24.0391i) q^{91} +(-0.0265707 - 0.0460218i) q^{92} +(0.591725 + 1.02490i) q^{93} -3.77487 q^{94} +(1.27672 - 4.16773i) q^{95} -0.518458 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-8.31098 - 14.3950i) q^{98} +(2.15812 - 3.73798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) $ 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Character values

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

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.690702	−	1.19633i	−0.488400	−	0.845933i	0.511511	−	0.859277i	$-0.329086\pi$
$2$	−0.690702	−	1.19633i	−0.488400	−	0.845933i	−0.999911	+	0.0133433i	$0.995753\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.0458624	−	0.0794360i	0.0229312	−	0.0397180i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.690702	−	1.19633i	0.281978	−	0.488400i
$7$	−4.36264			−1.64892			−0.824462	−	0.565917i	$-0.808522\pi$
$7$	−4.36264			−1.64892			−0.824462	+	0.565917i	$0.808522\pi$
$8$	−2.88952			−1.02160
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.690702	+	1.19633i	−0.218419	+	0.378313i
$11$	−4.31625			−1.30140			−0.650699	−	0.759336i	$-0.725524\pi$
$11$	−4.31625			−1.30140			−0.650699	+	0.759336i	$0.725524\pi$
$12$	0.0917248			0.0264787
$13$	3.18132	−	5.51021i	0.882340	−	1.52826i	0.0336075	−	0.999435i	$-0.489300\pi$
$13$	3.18132	−	5.51021i	0.882340	−	1.52826i	0.848732	−	0.528823i	$-0.177366\pi$
$14$	3.01329	+	5.21916i	0.805334	+	1.39488i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	1.90407	+	3.29794i	0.476017	+	0.824486i
$17$	−2.85821	−	4.95056i	−0.693217	−	1.20069i	−0.970778	−	0.239979i	$-0.922860\pi$
$17$	−2.85821	−	4.95056i	−0.693217	−	1.20069i	0.277561	−	0.960708i	$-0.410474\pi$
$18$	1.38140			0.325600
$19$	2.97100	+	3.18954i	0.681594	+	0.731730i
$19$	2.97100	+	3.18954i	0.681594	+	0.731730i
$20$	−0.0917248			−0.0205103
$21$	−2.18132	−	3.77816i	−0.476003	−	0.824462i
$22$	2.98124	+	5.16366i	0.635603	+	1.10090i
$23$	0.289678	−	0.501738i	0.0604021	−	0.104620i	−0.834243	−	0.551397i	$-0.814095\pi$
$23$	0.289678	−	0.501738i	0.0604021	−	0.104620i	0.894645	+	0.446777i	$0.147428\pi$
$24$	−1.44476	−	2.50239i	−0.294910	−	0.510799i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−8.78938			−1.72374
$27$	−1.00000			−0.192450
$28$	−0.200081	+	0.346551i	−0.0378118	+	0.0654920i
$29$	1.77672	−	3.07737i	0.329929	−	0.571454i	−0.652569	−	0.757730i	$-0.726309\pi$
$29$	1.77672	−	3.07737i	0.329929	−	0.571454i	0.982497	+	0.186276i	$0.0596419\pi$
$30$	−1.38140			−0.252209
$31$	1.18345			0.212554			0.106277	−	0.994337i	$-0.466107\pi$
$31$	1.18345			0.212554			0.106277	+	0.994337i	$0.466107\pi$
$32$	−0.259229	+	0.448998i	−0.0458257	+	0.0793724i
$33$	−2.15812	−	3.73798i	−0.375681	−	0.650699i
$34$	−3.94834	+	6.83872i	−0.677134	+	1.17283i
$35$	2.18132	+	3.77816i	0.368711	+	0.638626i
$36$	0.0458624	+	0.0794360i	0.00764374	+	0.0132393i
$37$	−6.54609			−1.07617			−0.538086	−	0.842890i	$-0.680852\pi$
$37$	−6.54609			−1.07617			−0.538086	+	0.842890i	$0.680852\pi$
$38$	1.76367	−	5.75732i	0.286105	−	0.933960i
$39$	6.36264			1.01884
$40$	1.44476	+	2.50239i	0.228436	+	0.395663i
$41$	0.381403	+	0.660610i	0.0595652	+	0.103170i	0.894270	−	0.447527i	$-0.147695\pi$
$41$	0.381403	+	0.660610i	0.0595652	+	0.103170i	−0.834705	+	0.550697i	$0.814362\pi$
$42$	−3.01329	+	5.21916i	−0.464960	+	0.805334i
$43$	3.18132	+	5.51021i	0.485147	+	0.840299i	0.999854	−	0.0170666i	$-0.00543274\pi$
$43$	3.18132	+	5.51021i	0.485147	+	0.840299i	−0.514707	+	0.857366i	$0.672099\pi$
$44$	−0.197954	+	0.342866i	−0.0298426	+	0.0516890i
$45$	1.00000			0.149071
$46$	−0.800326			−0.118002
$47$	1.36632	−	2.36653i	0.199298	−	0.345194i	−0.749003	−	0.662567i	$-0.769467\pi$
$47$	1.36632	−	2.36653i	0.199298	−	0.345194i	0.948301	+	0.317372i	$0.102800\pi$
$48$	−1.90407	+	3.29794i	−0.274829	+	0.476017i
$49$	12.0327			1.71895
$50$	1.38140			0.195360
$51$	2.85821	−	4.95056i	0.400229	−	0.693217i
$52$	−0.291806	−	0.505423i	−0.0404662	−	0.0700896i
$53$	−2.56853	+	4.44882i	−0.352814	+	0.611092i	−0.986741	−	0.162300i	$-0.948109\pi$
$53$	−2.56853	+	4.44882i	−0.352814	+	0.611092i	0.633927	+	0.773393i	$0.281442\pi$
$54$	0.690702	+	1.19633i	0.0939926	+	0.162800i
$55$	2.15812	+	3.73798i	0.291001	+	0.504029i
$56$	12.6059			1.68454
$57$	−1.27672	+	4.16773i	−0.169106	+	0.552029i
$58$	−4.90874			−0.644549
$59$	−1.91484	−	3.31660i	−0.249291	−	0.431785i	0.714038	−	0.700107i	$-0.246864\pi$
$59$	−1.91484	−	3.31660i	−0.249291	−	0.431785i	−0.963329	+	0.268322i	$0.913531\pi$
$60$	−0.0458624	−	0.0794360i	−0.00592081	−	0.0102551i
$61$	6.01053	−	10.4105i	0.769569	−	1.33293i	−0.168227	−	0.985748i	$-0.553804\pi$
$61$	6.01053	−	10.4105i	0.769569	−	1.33293i	0.937797	−	0.347185i	$-0.112862\pi$
$62$	−0.817411	−	1.41580i	−0.103811	−	0.179806i
$63$	2.18132	−	3.77816i	0.274821	−	0.476003i
$64$	8.33247			1.04156
$65$	−6.36264			−0.789189
$66$	−2.98124	+	5.16366i	−0.366965	+	0.635603i
$67$	2.00213	−	3.46779i	0.244599	−	0.423658i	−0.717420	−	0.696641i	$-0.754677\pi$
$67$	2.00213	−	3.46779i	0.244599	−	0.423658i	0.962019	+	0.272983i	$0.0880104\pi$
$68$	−0.524337			−0.0635852
$69$	0.579357			0.0697464
$70$	3.01329	−	5.21916i	0.360156	−	0.623809i
$71$	−1.53953	−	2.66654i	−0.182708	−	0.316460i	0.760094	−	0.649814i	$-0.225153\pi$
$71$	−1.53953	−	2.66654i	−0.182708	−	0.316460i	−0.942802	+	0.333354i	$0.891820\pi$
$72$	1.44476	−	2.50239i	0.170266	−	0.294910i
$73$	−4.04320	−	7.00303i	−0.473221	−	0.819643i	0.526309	−	0.850293i	$-0.323575\pi$
$73$	−4.04320	−	7.00303i	−0.473221	−	0.819643i	−0.999530	+	0.0306504i	$0.990242\pi$
$74$	4.52140	+	7.83129i	0.525602	+	0.910369i
$75$	−1.00000			−0.115470
$76$	0.389622	−	0.0897246i	0.0446927	−	0.0102921i
$77$	18.8303			2.14591
$78$	−4.39469	−	7.61182i	−0.497601	−	0.861869i
$79$	−5.66836	−	9.81790i	−0.637741	−	1.10460i	−0.985927	−	0.167174i	$-0.946536\pi$
$79$	−5.66836	−	9.81790i	−0.637741	−	1.10460i	0.348187	−	0.937425i	$-0.386798\pi$
$80$	1.90407	−	3.29794i	0.212881	−	0.368721i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.526872	−	0.912569i	0.0581833	−	0.100776i
$83$	7.67889			0.842868			0.421434	−	0.906859i	$-0.361527\pi$
$83$	7.67889			0.842868			0.421434	+	0.906859i	$0.361527\pi$
$84$	−0.400163			−0.0436613
$85$	−2.85821	+	4.95056i	−0.310016	+	0.536963i
$86$	4.39469	−	7.61182i	0.473891	−	0.820804i
$87$	3.55344			0.380969
$88$	12.4719			1.32951
$89$	−4.92093	+	8.52330i	−0.521618	+	0.903468i	0.478066	+	0.878324i	$0.341338\pi$
$89$	−4.92093	+	8.52330i	−0.521618	+	0.903468i	−0.999684	+	0.0251445i	$0.991995\pi$
$90$	−0.690702	−	1.19633i	−0.0728063	−	0.126104i
$91$	−13.8790	+	24.0391i	−1.45491	+	2.51998i
$92$	−0.0265707	−	0.0460218i	−0.00277019	−	0.00479811i
$93$	0.591725	+	1.02490i	0.0613590	+	0.106277i
$94$	−3.77487			−0.389348
$95$	1.27672	−	4.16773i	0.130989	−	0.427600i
$96$	−0.518458			−0.0529149
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−8.31098	−	14.3950i	−0.839536	−	1.45412i
$99$	2.15812	−	3.73798i	0.216900	−	0.375681i
$100$	0.0458624	+	0.0794360i	0.00458624	+	0.00794360i
$101$	2.24985	−	3.89685i	0.223868	−	0.387751i	−0.732111	−	0.681185i	$-0.761465\pi$
$101$	2.24985	−	3.89685i	0.223868	−	0.387751i	0.955979	+	0.293434i	$0.0947981\pi$
$102$	−7.89667			−0.781887
$103$	−16.0717			−1.58359			−0.791796	−	0.610785i	$-0.790854\pi$
$103$	−16.0717			−1.58359			−0.791796	+	0.610785i	$0.790854\pi$
$104$	−9.19248	+	15.9218i	−0.901397	+	1.56127i
$105$	−2.18132	+	3.77816i	−0.212875	+	0.368711i
$106$	7.09634			0.689258
$107$	13.6789			1.32239			0.661194	−	0.750215i	$-0.270050\pi$
$107$	13.6789			1.32239			0.661194	+	0.750215i	$0.270050\pi$
$108$	−0.0458624	+	0.0794360i	−0.00441311	+	0.00764374i
$109$	4.48337	+	7.76542i	0.429429	+	0.743792i	0.996823	−	0.0796541i	$-0.0253816\pi$
$109$	4.48337	+	7.76542i	0.429429	+	0.743792i	−0.567394	+	0.823447i	$0.692048\pi$
$110$	2.98124	−	5.16366i	0.284250	−	0.492336i
$111$	−3.27305	−	5.66908i	−0.310664	−	0.538086i
$112$	−8.30677	−	14.3878i	−0.784916	−	1.35951i
$113$	6.42952			0.604838			0.302419	−	0.953175i	$-0.402206\pi$
$113$	6.42952			0.604838			0.302419	+	0.953175i	$0.402206\pi$
$114$	5.86782	−	1.35128i	0.549571	−	0.126559i
$115$	−0.579357			−0.0540253
$116$	−0.162969	−	0.282271i	−0.0151313	−	0.0262082i
$117$	3.18132	+	5.51021i	0.294113	+	0.509419i
$118$	−2.64517	+	4.58156i	−0.243507	+	0.421767i
$119$	12.4693	+	21.5975i	1.14306	+	1.97984i
$120$	−1.44476	+	2.50239i	−0.131888	+	0.228436i
$121$	7.63001			0.693637
$122$	−16.6059			−1.50343
$123$	−0.381403	+	0.660610i	−0.0343900	+	0.0595652i
$124$	0.0542759	−	0.0940086i	0.00487412	−	0.00844222i
$125$	1.00000			0.0894427
$126$	−6.02657			−0.536890
$127$	3.09172	−	5.35502i	0.274346	−	0.475182i	−0.695624	−	0.718406i	$-0.744872\pi$
$127$	3.09172	−	5.35502i	0.274346	−	0.475182i	0.969970	+	0.243225i	$0.0782052\pi$
$128$	−5.23680	−	9.07040i	−0.462872	−	0.801717i
$129$	−3.18132	+	5.51021i	−0.280100	+	0.485147i
$130$	4.39469	+	7.61182i	0.385440	+	0.667601i
$131$	−8.69872	−	15.0666i	−0.760010	−	1.31638i	−0.942845	−	0.333233i	$-0.891860\pi$
$131$	−8.69872	−	15.0666i	−0.760010	−	1.31638i	0.182834	−	0.983144i	$-0.441473\pi$
$132$	−0.395907			−0.0344593
$133$	−12.9614	−	13.9148i	−1.12390	−	1.20657i
$134$	−5.53149			−0.477848
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	8.25883	+	14.3047i	0.708189	+	1.22662i
$137$	−7.85821	+	13.6108i	−0.671372	+	1.16285i	0.306143	+	0.951985i	$0.400961\pi$
$137$	−7.85821	+	13.6108i	−0.671372	+	1.16285i	−0.977515	+	0.210865i	$0.932372\pi$
$138$	−0.400163	−	0.693102i	−0.0340641	−	0.0590008i
$139$	−3.27672	+	5.67545i	−0.277928	+	0.481385i	−0.970870	−	0.239608i	$-0.922981\pi$
$139$	−3.27672	+	5.67545i	−0.277928	+	0.481385i	0.692942	+	0.720994i	$0.256314\pi$
$140$	0.400163			0.0338199
$141$	2.73264			0.230130
$142$	−2.12671	+	3.68357i	−0.178469	+	0.309118i
$143$	−13.7314	+	23.7834i	−1.14828	+	1.98887i
$144$	−3.80814			−0.317345
$145$	−3.55344			−0.295097
$146$	−5.58529	+	9.67401i	−0.462242	+	0.800627i
$147$	6.01633	+	10.4206i	0.496219	+	0.859476i
$148$	−0.300220	+	0.519996i	−0.0246779	+	0.0427434i
$149$	−2.87560	−	4.98069i	−0.235578	−	0.408034i	0.723862	−	0.689945i	$-0.242365\pi$
$149$	−2.87560	−	4.98069i	−0.235578	−	0.408034i	−0.959441	+	0.281911i	$0.909032\pi$
$150$	0.690702	+	1.19633i	0.0563956	+	0.0976800i
$151$	−12.6673			−1.03085			−0.515425	−	0.856935i	$-0.672366\pi$
$151$	−12.6673			−1.03085			−0.515425	+	0.856935i	$0.672366\pi$
$152$	−8.58475	−	9.21622i	−0.696315	−	0.747534i
$153$	5.71641			0.462145
$154$	−13.0061	−	22.5272i	−1.04806	−	1.81529i
$155$	−0.591725	−	1.02490i	−0.0475285	−	0.0823217i
$156$	0.291806	−	0.505423i	0.0233632	−	0.0404662i
$157$	−0.689434	−	1.19414i	−0.0550228	−	0.0953024i	0.837202	−	0.546894i	$-0.184190\pi$
$157$	−0.689434	−	1.19414i	−0.0550228	−	0.0953024i	−0.892225	+	0.451591i	$0.850856\pi$
$158$	−7.83030	+	13.5625i	−0.622945	+	1.07897i
$159$	−5.13706			−0.407395
$160$	0.518458			0.0409877
$161$	−1.26376	+	2.18890i	−0.0995986	+	0.172510i
$162$	−0.690702	+	1.19633i	−0.0542666	+	0.0939926i
$163$	−11.6120			−0.909523			−0.454762	−	0.890613i	$-0.650276\pi$
$163$	−11.6120			−0.909523			−0.454762	+	0.890613i	$0.650276\pi$
$164$	0.0699683			0.00546361
$165$	−2.15812	+	3.73798i	−0.168010	+	0.291001i
$166$	−5.30382	−	9.18649i	−0.411657	−	0.713010i
$167$	10.1557	−	17.5902i	0.785871	−	1.36117i	−0.142606	−	0.989780i	$-0.545548\pi$
$167$	10.1557	−	17.5902i	0.785871	−	1.36117i	0.928477	−	0.371390i	$-0.121119\pi$
$168$	6.30296	+	10.9171i	0.486284	+	0.842269i
$169$	−13.7416	−	23.8012i	−1.05705	−	1.83086i
$170$	7.89667			0.605647
$171$	−4.24772	+	0.978193i	−0.324831	+	0.0748043i
$172$	0.583613			0.0445000
$173$	6.12545	+	10.6096i	0.465709	+	0.806632i	0.999233	−	0.0391527i	$-0.0124659\pi$
$173$	6.12545	+	10.6096i	0.465709	+	0.806632i	−0.533524	+	0.845785i	$0.679133\pi$
$174$	−2.45437	−	4.25109i	−0.186065	−	0.322274i
$175$	2.18132	−	3.77816i	0.164892	−	0.285602i
$176$	−8.21843	−	14.2347i	−0.619488	−	1.07298i
$177$	1.91484	−	3.31660i	0.143928	−	0.249291i
$178$	13.5956			1.01903
$179$	−19.1840			−1.43388			−0.716941	−	0.697134i	$-0.754458\pi$
$179$	−19.1840			−1.43388			−0.716941	+	0.697134i	$0.754458\pi$
$180$	0.0458624	−	0.0794360i	0.00341838	−	0.00592081i
$181$	1.61492	−	2.79713i	0.120036	−	0.207909i	−0.799746	−	0.600339i	$-0.795032\pi$
$181$	1.61492	−	2.79713i	0.120036	−	0.207909i	0.919782	+	0.392430i	$0.128366\pi$
$182$	38.3449			2.84231
$183$	12.0211			0.888622
$184$	−0.837031	+	1.44978i	−0.0617067	+	0.106879i
$185$	3.27305	+	5.66908i	0.240639	+	0.416799i
$186$	0.817411	−	1.41580i	0.0599355	−	0.103811i
$187$	12.3367	+	21.3678i	0.902151	+	1.56257i
$188$	−0.125325	−	0.217070i	−0.00914029	−	0.0158314i
$189$	4.36264			0.317336
$190$	−5.86782	+	1.35128i	−0.425696	+	0.0980320i
$191$	27.5509			1.99352			0.996758	−	0.0804642i	$-0.0256403\pi$
$191$	27.5509			1.99352			0.996758	+	0.0804642i	$0.0256403\pi$
$192$	4.16624	+	7.21613i	0.300672	+	0.520780i
$193$	−11.1233	−	19.2662i	−0.800674	−	1.38681i	−0.919173	−	0.393854i	$-0.871141\pi$
$193$	−11.1233	−	19.2662i	−0.800674	−	1.38681i	0.118499	−	0.992954i	$-0.462192\pi$
$194$	−1.38140	+	2.39266i	−0.0991790	+	0.171783i
$195$	−3.18132	−	5.51021i	−0.227819	−	0.394594i
$196$	0.551847	−	0.955827i	0.0394176	−	0.0682734i
$197$	12.6627			0.902178			0.451089	−	0.892479i	$-0.351036\pi$
$197$	12.6627			0.902178			0.451089	+	0.892479i	$0.351036\pi$
$198$	−5.96248			−0.423735
$199$	4.38478	−	7.59466i	0.310829	−	0.538371i	−0.667713	−	0.744418i	$-0.732727\pi$
$199$	4.38478	−	7.59466i	0.310829	−	0.538371i	0.978542	+	0.206048i	$0.0660602\pi$
$200$	1.44476	−	2.50239i	0.102160	−	0.176946i
$201$	4.00426			0.282438
$202$	−6.21590			−0.437349
$203$	−7.75120	+	13.4255i	−0.544028	+	0.942284i
$204$	−0.262168	−	0.454089i	−0.0183555	−	0.0317926i
$205$	0.381403	−	0.660610i	0.0266384	−	0.0461390i
$206$	11.1008	+	19.2271i	0.773426	+	1.33961i
$207$	0.289678	+	0.501738i	0.0201340	+	0.0348732i
$208$	24.2298			1.68004
$209$	−12.8236	−	13.7668i	−0.887025	−	0.952272i
$210$	6.02657			0.415873
$211$	−3.93389	−	6.81369i	−0.270820	−	0.469074i	0.698252	−	0.715852i	$-0.253962\pi$
$211$	−3.93389	−	6.81369i	−0.270820	−	0.469074i	−0.969072	+	0.246778i	$0.920628\pi$
$212$	0.235598	+	0.408067i	0.0161809	+	0.0280262i
$213$	1.53953	−	2.66654i	0.105487	−	0.182708i
$214$	−9.44803	−	16.3645i	−0.645854	−	1.11865i
$215$	3.18132	−	5.51021i	0.216964	−	0.375793i
$216$	2.88952			0.196607
$217$	−5.16297			−0.350485
$218$	6.19334	−	10.7272i	0.419466	−	0.726536i
$219$	4.04320	−	7.00303i	0.273214	−	0.473221i
$220$	0.395907			0.0266921
$221$	−36.3715			−2.44661
$222$	−4.52140	+	7.83129i	−0.303456	+	0.525602i
$223$	13.6768	+	23.6889i	0.915864	+	1.58632i	0.805631	+	0.592417i	$0.201826\pi$
$223$	13.6768	+	23.6889i	0.915864	+	1.58632i	0.110232	+	0.993906i	$0.464840\pi$
$224$	1.13092	−	1.95882i	0.0755631	−	0.130879i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−4.44088	−	7.69183i	−0.295403	−	0.511653i
$227$	−25.0922			−1.66543			−0.832713	−	0.553704i	$-0.813214\pi$
$227$	−25.0922			−1.66543			−0.832713	+	0.553704i	$0.813214\pi$
$228$	0.272515	+	0.292560i	0.0180477	+	0.0193753i
$229$	4.98530			0.329438			0.164719	−	0.986341i	$-0.447328\pi$
$229$	4.98530			0.329438			0.164719	+	0.986341i	$0.447328\pi$
$230$	0.400163	+	0.693102i	0.0263860	+	0.0457018i
$231$	9.41513	+	16.3075i	0.619470	+	1.07295i
$232$	−5.13386	+	8.89211i	−0.337055	+	0.583796i
$233$	−6.39821	−	11.0820i	−0.419161	−	0.726007i	0.576695	−	0.816960i	$-0.304342\pi$
$233$	−6.39821	−	11.0820i	−0.419161	−	0.726007i	−0.995855	+	0.0909523i	$0.971009\pi$
$234$	4.39469	−	7.61182i	0.287290	−	0.497601i
$235$	−2.73264			−0.178258
$236$	−0.351277			−0.0228662
$237$	5.66836	−	9.81790i	0.368200	−	0.637741i
$238$	17.2252	−	29.8349i	1.11654	−	1.93391i
$239$	12.8049			0.828283			0.414142	−	0.910212i	$-0.364082\pi$
$239$	12.8049			0.828283			0.414142	+	0.910212i	$0.364082\pi$
$240$	3.80814			0.245814
$241$	0.546395	−	0.946383i	0.0351964	−	0.0609619i	−0.847891	−	0.530171i	$-0.822128\pi$
$241$	0.546395	−	0.946383i	0.0351964	−	0.0609619i	0.883087	+	0.469209i	$0.155461\pi$
$242$	−5.27006	−	9.12801i	−0.338772	−	0.586771i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.551315	−	0.954905i	−0.0352943	−	0.0611315i
$245$	−6.01633	−	10.4206i	−0.384369	−	0.665747i
$246$	1.05374			0.0671842
$247$	27.0267	−	6.22389i	1.71967	−	0.396017i
$248$	−3.41960			−0.217145
$249$	3.83945	+	6.65012i	0.243315	+	0.421434i
$250$	−0.690702	−	1.19633i	−0.0436838	−	0.0756626i
$251$	−3.04764	+	5.27867i	−0.192365	+	0.333187i	−0.946034	−	0.324068i	$-0.894949\pi$
$251$	−3.04764	+	5.27867i	−0.192365	+	0.333187i	0.753668	+	0.657255i	$0.228283\pi$
$252$	−0.200081	−	0.346551i	−0.0126039	−	0.0218307i
$253$	−1.25032	+	2.16563i	−0.0786072	+	0.136152i
$254$	−8.54184			−0.535963
$255$	−5.71641			−0.357976
$256$	1.09835	−	1.90239i	0.0686467	−	0.118900i
$257$	−2.31016	+	4.00131i	−0.144104	+	0.249595i	−0.929038	−	0.369984i	$-0.879363\pi$
$257$	−2.31016	+	4.00131i	−0.144104	+	0.249595i	0.784934	+	0.619579i	$0.212697\pi$
$258$	8.78938			0.547203
$259$	28.5583			1.77452
$260$	−0.291806	+	0.505423i	−0.0180971	+	0.0313450i
$261$	1.77672	+	3.07737i	0.109976	+	0.190485i
$262$	−12.0164	+	20.8131i	−0.742378	+	1.28584i
$263$	15.0247	+	26.0236i	0.926465	+	1.60468i	0.789189	+	0.614151i	$0.210501\pi$
$263$	15.0247	+	26.0236i	0.926465	+	1.60468i	0.137276	+	0.990533i	$0.456165\pi$
$264$	6.23593	+	10.8010i	0.383795	+	0.664753i
$265$	5.13706			0.315567
$266$	−7.69425	+	25.1171i	−0.471765	+	1.54003i
$267$	−9.84186			−0.602312
$268$	−0.183645	−	0.318082i	−0.0112179	−	0.0194300i
$269$	0.105639	+	0.182973i	0.00644095	+	0.0111561i	0.869228	−	0.494412i	$-0.164616\pi$
$269$	0.105639	+	0.182973i	0.00644095	+	0.0111561i	−0.862787	+	0.505568i	$0.831283\pi$
$270$	0.690702	−	1.19633i	0.0420348	−	0.0728063i
$271$	3.70364	+	6.41489i	0.224980	+	0.389677i	0.956313	−	0.292343i	$-0.0944350\pi$
$271$	3.70364	+	6.41489i	0.224980	+	0.389677i	−0.731333	+	0.682020i	$0.761102\pi$
$272$	10.8844	−	18.8524i	0.659966	−	1.14309i
$273$	−27.7579			−1.67999
$274$	21.7107			1.31159
$275$	2.15812	−	3.73798i	0.130140	−	0.225409i
$276$	0.0265707	−	0.0460218i	0.00159937	−	0.00277019i
$277$	−29.0668			−1.74646			−0.873229	−	0.487310i	$-0.837978\pi$
$277$	−29.0668			−1.74646			−0.873229	+	0.487310i	$0.837978\pi$
$278$	9.05295			0.542960
$279$	−0.591725	+	1.02490i	−0.0354256	+	0.0613590i
$280$	−6.30296	−	10.9171i	−0.376674	−	0.652419i
$281$	−5.73796	+	9.93843i	−0.342298	+	0.592877i	−0.984859	−	0.173357i	$-0.944539\pi$
$281$	−5.73796	+	9.93843i	−0.342298	+	0.592877i	0.642561	+	0.766234i	$0.277872\pi$
$282$	−1.88744	−	3.26914i	−0.112395	−	0.194674i
$283$	13.6662	+	23.6706i	0.812373	+	1.40707i	0.911199	+	0.411966i	$0.135158\pi$
$283$	13.6662	+	23.6706i	0.812373	+	1.40707i	−0.0988265	+	0.995105i	$0.531509\pi$
$284$	−0.282426			−0.0167589
$285$	4.24772	−	0.978193i	0.251613	−	0.0579431i
$286$	37.9371			2.24327
$287$	−1.66393	−	2.88201i	−0.0982185	−	0.170119i
$288$	−0.259229	−	0.448998i	−0.0152752	−	0.0264575i
$289$	−7.83868	+	13.5770i	−0.461099	+	0.798647i
$290$	2.45437	+	4.25109i	0.144125	+	0.249633i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	−0.741724			−0.0434061
$293$	13.0211			0.760698			0.380349	−	0.924843i	$-0.375804\pi$
$293$	13.0211			0.760698			0.380349	+	0.924843i	$0.375804\pi$
$294$	8.31098	−	14.3950i	0.484706	−	0.839536i
$295$	−1.91484	+	3.31660i	−0.111486	+	0.193100i
$296$	18.9150			1.09941
$297$	4.31625			0.250454
$298$	−3.97236	+	6.88034i	−0.230113	+	0.398567i
$299$	−1.84312	−	3.19238i	−0.106590	−	0.184620i
$300$	−0.0458624	+	0.0794360i	−0.00264787	+	0.00458624i
$301$	−13.8790	−	24.0391i	−0.799971	−	1.38559i
$302$	8.74932	+	15.1543i	0.503467	+	0.872030i
$303$	4.49970			0.258501
$304$	−4.86193	+	15.8713i	−0.278851	+	0.910281i
$305$	−12.0211			−0.688324
$306$	−3.94834	−	6.83872i	−0.225711	−	0.390943i
$307$	−2.01267	−	3.48604i	−0.114869	−	0.198959i	0.802858	−	0.596170i	$-0.203312\pi$
$307$	−2.01267	−	3.48604i	−0.114869	−	0.198959i	−0.917727	+	0.397211i	$0.869978\pi$
$308$	0.863601	−	1.49580i	0.0492082	−	0.0852312i
$309$	−8.03585	−	13.9185i	−0.457144	−	0.791796i
$310$	−0.817411	+	1.41580i	−0.0464258	+	0.0804119i
$311$	15.3578			0.870860			0.435430	−	0.900223i	$-0.356596\pi$
$311$	15.3578			0.870860			0.435430	+	0.900223i	$0.356596\pi$
$312$	−18.3850			−1.04084
$313$	−10.9800	+	19.0179i	−0.620625	+	1.07495i	0.368744	+	0.929531i	$0.379788\pi$
$313$	−10.9800	+	19.0179i	−0.620625	+	1.07495i	−0.989369	+	0.145424i	$0.953546\pi$
$314$	−0.952387	+	1.64958i	−0.0537463	+	0.0930913i
$315$	−4.36264			−0.245807
$316$	−1.03986			−0.0584967
$317$	12.0640	−	20.8954i	0.677580	−	1.17360i	−0.298127	−	0.954526i	$-0.596362\pi$
$317$	12.0640	−	20.8954i	0.677580	−	1.17360i	0.975708	−	0.219077i	$-0.0703046\pi$
$318$	3.54817	+	6.14561i	0.198972	+	0.344629i
$319$	−7.66877	+	13.2827i	−0.429369	+	0.743689i
$320$	−4.16624	−	7.21613i	−0.232900	−	0.403394i
$321$	6.83945	+	11.8463i	0.381741	+	0.661194i
$322$	3.49154			0.194576
$323$	7.29826	−	23.8245i	0.406086	−	1.32563i
$324$	−0.0917248			−0.00509582
$325$	3.18132	+	5.51021i	0.176468	+	0.305652i
$326$	8.02044	+	13.8918i	0.444211	+	0.769396i
$327$	−4.48337	+	7.76542i	−0.247931	+	0.429429i
$328$	−1.10207	−	1.90884i	−0.0608517	−	0.105398i
$329$	−5.96076	+	10.3243i	−0.328627	+	0.569199i
$330$	5.96248			0.328224
$331$	−24.8416			−1.36542			−0.682710	−	0.730690i	$-0.739199\pi$
$331$	−24.8416			−1.36542			−0.682710	+	0.730690i	$0.739199\pi$
$332$	0.352173	−	0.609981i	0.0193280	−	0.0334771i
$333$	3.27305	−	5.66908i	0.179362	−	0.310664i
$334$	−28.0582			−1.53528
$335$	−4.00426			−0.218776
$336$	8.30677	−	14.3878i	0.453172	−	0.784916i
$337$	−0.284651	−	0.493031i	−0.0155059	−	0.0268571i	0.858168	−	0.513368i	$-0.171603\pi$
$337$	−0.284651	−	0.493031i	−0.0155059	−	0.0268571i	−0.873674	+	0.486511i	$0.838269\pi$
$338$	−18.9827	+	32.8790i	−1.03252	+	1.78838i
$339$	3.21476	+	5.56813i	0.174602	+	0.302419i
$340$	0.262168	+	0.454089i	0.0142181	+	0.0246264i
$341$	−5.10806			−0.276617
$342$	4.10415	+	4.40604i	0.221927	+	0.238251i
$343$	−21.9557			−1.18550
$344$	−9.19248	−	15.9218i	−0.495625	−	0.858448i
$345$	−0.289678	−	0.501738i	−0.0155958	−	0.0270127i
$346$	8.46172	−	14.6561i	0.454905	−	0.787918i
$347$	−4.68682	−	8.11782i	−0.251602	−	0.435787i	0.712365	−	0.701809i	$-0.247624\pi$
$347$	−4.68682	−	8.11782i	−0.251602	−	0.435787i	−0.963967	+	0.266022i	$0.914291\pi$
$348$	0.162969	−	0.282271i	0.00873608	−	0.0151313i
$349$	14.8297			0.793815			0.396907	−	0.917859i	$-0.370083\pi$
$349$	14.8297			0.793815			0.396907	+	0.917859i	$0.370083\pi$
$350$	−6.02657			−0.322134
$351$	−3.18132	+	5.51021i	−0.169806	+	0.294113i
$352$	1.11890	−	1.93799i	0.0596375	−	0.103295i
$353$	31.2650			1.66407			0.832034	−	0.554725i	$-0.187176\pi$
$353$	31.2650			1.66407			0.832034	+	0.554725i	$0.187176\pi$
$354$	−5.29033			−0.281178
$355$	−1.53953	+	2.66654i	−0.0817097	+	0.141525i
$356$	0.451372	+	0.781799i	0.0239226	+	0.0414352i
$357$	−12.4693	+	21.5975i	−0.659947	+	1.14306i
$358$	13.2504	+	22.9504i	0.700307	+	1.21297i
$359$	−5.43561	−	9.41475i	−0.286880	−	0.496892i	0.686183	−	0.727429i	$-0.259285\pi$
$359$	−5.43561	−	9.41475i	−0.286880	−	0.496892i	−0.973063	+	0.230537i	$0.925952\pi$
$360$	−2.88952			−0.152291
$361$	−1.34631	+	18.9522i	−0.0708586	+	0.997486i
$362$	−4.46172			−0.234503
$363$	3.81500	+	6.60778i	0.200236	+	0.346819i
$364$	1.27305	+	2.20498i	0.0667258	+	0.115572i
$365$	−4.04320	+	7.00303i	−0.211631	+	0.366555i
$366$	−8.30296	−	14.3812i	−0.434003	−	0.751715i
$367$	9.36477	−	16.2203i	0.488837	−	0.846691i	−0.511080	−	0.859533i	$-0.670755\pi$
$367$	9.36477	−	16.2203i	0.488837	−	0.846691i	0.999918	+	0.0128422i	$0.00408791\pi$
$368$	2.20627			0.115010
$369$	−0.762807			−0.0397101
$370$	4.52140	−	7.83129i	0.235056	−	0.407129i
$371$	11.2056	−	19.4086i	0.581764	−	1.00765i
$372$	0.108552			0.00562815
$373$	29.3275			1.51852			0.759259	−	0.650788i	$-0.225561\pi$
$373$	29.3275			1.51852			0.759259	+	0.650788i	$0.225561\pi$
$374$	17.0420	−	29.5176i	0.881221	−	1.52632i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−3.94800	+	6.83813i	−0.203602	+	0.352650i
$377$	−11.3046	−	19.5802i	−0.582219	−	1.00843i
$378$	−3.01329	−	5.21916i	−0.154987	−	0.268445i
$379$	−10.6486			−0.546980			−0.273490	−	0.961875i	$-0.588178\pi$
$379$	−10.6486			−0.546980			−0.273490	+	0.961875i	$0.588178\pi$
$380$	−0.272515	−	0.292560i	−0.0139797	−	0.0150080i
$381$	6.18345			0.316788
$382$	−19.0295	−	32.9600i	−0.973632	−	1.68638i
$383$	−4.63977	−	8.03632i	−0.237081	−	0.410637i	0.722794	−	0.691063i	$-0.242857\pi$
$383$	−4.63977	−	8.03632i	−0.237081	−	0.410637i	−0.959876	+	0.280426i	$0.909524\pi$
$384$	5.23680	−	9.07040i	0.267239	−	0.462872i
$385$	−9.41513	−	16.3075i	−0.479839	−	0.831106i
$386$	−15.3658	+	26.6143i	−0.782098	+	1.35463i
$387$	−6.36264			−0.323431
$388$	−0.183450			−0.00931325
$389$	−0.666237	+	1.15396i	−0.0337796	+	0.0585079i	−0.882421	−	0.470461i	$-0.844088\pi$
$389$	−0.666237	+	1.15396i	−0.0337796	+	0.0585079i	0.848641	+	0.528969i	$0.177421\pi$
$390$	−4.39469	+	7.61182i	−0.222534	+	0.385440i
$391$	−3.31184			−0.167487
$392$	−34.7686			−1.75608
$393$	8.69872	−	15.0666i	0.438792	−	0.760010i
$394$	−8.74613	−	15.1487i	−0.440623	−	0.763182i
$395$	−5.66836	+	9.81790i	−0.285206	+	0.493992i
$396$	−0.197954	−	0.342866i	−0.00994754	−	0.0172297i
$397$	15.8324	+	27.4225i	0.794605	+	1.37630i	0.923090	+	0.384584i	$0.125655\pi$
$397$	15.8324	+	27.4225i	0.794605	+	1.37630i	−0.128485	+	0.991711i	$0.541011\pi$
$398$	−12.1143			−0.607235
$399$	5.56988	−	18.1823i	0.278843	−	0.910255i
$400$	−3.80814			−0.190407
$401$	2.44425	+	4.23356i	0.122060	+	0.211414i	0.920580	−	0.390554i	$-0.127717\pi$
$401$	2.44425	+	4.23356i	0.122060	+	0.211414i	−0.798520	+	0.601968i	$0.794383\pi$
$402$	−2.76575	−	4.79041i	−0.137943	−	0.238924i
$403$	3.76493	−	6.52106i	0.187545	−	0.324837i
$404$	−0.206367	−	0.357438i	−0.0102671	−	0.0177832i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	21.4151			1.06281
$407$	28.2546			1.40053
$408$	−8.25883	+	14.3047i	−0.408873	+	0.708189i
$409$	11.3941	−	19.7351i	0.563400	−	0.975837i	−0.433797	−	0.901011i	$-0.642826\pi$
$409$	11.3941	−	19.7351i	0.563400	−	0.975837i	0.997197	−	0.0748266i	$-0.0238403\pi$
$410$	−1.05374			−0.0520407
$411$	−15.7164			−0.775233
$412$	−0.737087	+	1.27667i	−0.0363137	+	0.0628972i
$413$	8.35377	+	14.4692i	0.411062	+	0.711980i
$414$	0.400163	−	0.693102i	0.0196669	−	0.0340641i
$415$	−3.83945	−	6.65012i	−0.188471	−	0.326441i
$416$	1.64938	+	2.85682i	0.0808677	+	0.140067i
$417$	−6.55344			−0.320923
$418$	−7.61243	+	24.8500i	−0.372336	+	1.21545i
$419$	30.8809			1.50863			0.754316	−	0.656512i	$-0.227969\pi$
$419$	30.8809			1.50863			0.754316	+	0.656512i	$0.227969\pi$
$420$	0.200081	+	0.346551i	0.00976297	+	0.0169100i
$421$	−13.2891	−	23.0174i	−0.647671	−	1.12180i	−0.983678	−	0.179939i	$-0.942410\pi$
$421$	−13.2891	−	23.0174i	−0.647671	−	1.12180i	0.336007	−	0.941859i	$-0.390923\pi$
$422$	−5.43429	+	9.41246i	−0.264537	+	0.458191i
$423$	1.36632	+	2.36653i	0.0664327	+	0.115065i
$424$	7.42180	−	12.8549i	0.360434	−	0.624291i
$425$	5.71641			0.277287
$426$	−4.25342			−0.206079
$427$	−26.2218	+	45.4175i	−1.26896	+	2.19791i
$428$	0.627347	−	1.08660i	0.0303240	−	0.0525227i
$429$	−27.4628			−1.32591
$430$	−8.78938			−0.423861
$431$	−8.23718	+	14.2672i	−0.396771	+	0.687228i	−0.993325	−	0.115345i	$-0.963203\pi$
$431$	−8.23718	+	14.2672i	−0.396771	+	0.687228i	0.596554	+	0.802573i	$0.296536\pi$
$432$	−1.90407	−	3.29794i	−0.0916095	−	0.158672i
$433$	18.4021	−	31.8733i	0.884346	−	1.53173i	0.0378851	−	0.999282i	$-0.487938\pi$
$433$	18.4021	−	31.8733i	0.884346	−	1.53173i	0.846461	−	0.532450i	$-0.178729\pi$
$434$	3.56607	+	6.17662i	0.171177	+	0.296487i
$435$	−1.77672	−	3.07737i	−0.0851873	−	0.147549i
$436$	0.822473			0.0393893
$437$	2.46095	−	0.566723i	0.117723	−	0.0271100i
$438$	−11.1706			−0.533751
$439$	−4.79140	−	8.29895i	−0.228681	−	0.396087i	0.728736	−	0.684794i	$-0.240108\pi$
$439$	−4.79140	−	8.29895i	−0.228681	−	0.396087i	−0.957417	+	0.288707i	$0.906775\pi$
$440$	−6.23593	−	10.8010i	−0.297287	−	0.514915i
$441$	−6.01633	+	10.4206i	−0.286492	+	0.496219i
$442$	25.1219	+	43.5123i	1.19492	+	2.06967i
$443$	11.1218	−	19.2635i	0.528412	−	0.915236i	−0.471040	−	0.882112i	$-0.656121\pi$
$443$	11.1218	−	19.2635i	0.528412	−	0.915236i	0.999451	−	0.0331236i	$-0.0105455\pi$
$444$	−0.600439			−0.0284956
$445$	9.84186			0.466549
$446$	18.8931	−	32.7239i	0.894616	−	1.54952i
$447$	2.87560	−	4.98069i	0.136011	−	0.235578i
$448$	−36.3516			−1.71745
$449$	−0.491188			−0.0231806			−0.0115903	−	0.999933i	$-0.503689\pi$
$449$	−0.491188			−0.0231806			−0.0115903	+	0.999933i	$0.503689\pi$
$450$	−0.690702	+	1.19633i	−0.0325600	+	0.0563956i
$451$	−1.64623	−	2.85136i	−0.0775180	−	0.134265i
$452$	0.294873	−	0.510736i	0.0138697	−	0.0240230i
$453$	−6.33364	−	10.9702i	−0.297581	−	0.515425i
$454$	17.3312	+	30.0185i	0.813394	+	1.40884i
$455$	27.7579			1.30131
$456$	3.68911	−	12.0427i	0.172758	−	0.563952i
$457$	13.2607			0.620311			0.310156	−	0.950686i	$-0.399619\pi$
$457$	13.2607			0.620311			0.310156	+	0.950686i	$0.399619\pi$
$458$	−3.44336	−	5.96407i	−0.160897	−	0.278683i
$459$	2.85821	+	4.95056i	0.133410	+	0.231072i
$460$	−0.0265707	+	0.0460218i	−0.00123887	+	0.00214578i
$461$	−11.6867	−	20.2420i	−0.544305	−	0.942763i	−0.998650	−	0.0519379i	$-0.983460\pi$
$461$	−11.6867	−	20.2420i	−0.544305	−	0.942763i	0.454346	−	0.890825i	$-0.349873\pi$
$462$	13.0061	−	22.5272i	0.605098	−	1.04806i
$463$	−0.981649			−0.0456211			−0.0228105	−	0.999740i	$-0.507261\pi$
$463$	−0.981649			−0.0456211			−0.0228105	+	0.999740i	$0.507261\pi$
$464$	13.5320			0.628207
$465$	0.591725	−	1.02490i	0.0274406	−	0.0475285i
$466$	−8.83851	+	15.3087i	−0.409436	+	0.709164i
$467$	−18.8498			−0.872264			−0.436132	−	0.899883i	$-0.643652\pi$
$467$	−18.8498			−0.872264			−0.436132	+	0.899883i	$0.643652\pi$
$468$	0.583613			0.0269775
$469$	−8.73457	+	15.1287i	−0.403325	+	0.698579i
$470$	1.88744	+	3.26914i	0.0870610	+	0.150794i
$471$	0.689434	−	1.19414i	0.0317675	−	0.0550228i
$472$	5.53296	+	9.58337i	0.254675	+	0.441110i
$473$	−13.7314	−	23.7834i	−0.631369	−	1.09356i
$474$	−15.6606			−0.719315
$475$	−4.24772	+	0.978193i	−0.194899	+	0.0448826i
$476$	2.28750			0.104847
$477$	−2.56853	−	4.44882i	−0.117605	−	0.203697i
$478$	−8.84440	−	15.3189i	−0.404533	−	0.700672i
$479$	−10.0795	+	17.4583i	−0.460546	+	0.797688i	−0.998988	−	0.0449739i	$-0.985680\pi$
$479$	−10.0795	+	17.4583i	−0.460546	+	0.797688i	0.538443	+	0.842662i	$0.319013\pi$
$480$	0.259229	+	0.448998i	0.0118321	+	0.0204939i
$481$	−20.8252	+	36.0704i	−0.949549	+	1.64467i
$482$	−1.50958			−0.0687596
$483$	−2.52753			−0.115007
$484$	0.349931	−	0.606098i	0.0159059	−	0.0275499i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−1.38140			−0.0626617
$487$	2.79159			0.126499			0.0632494	−	0.997998i	$-0.479854\pi$
$487$	2.79159			0.126499			0.0632494	+	0.997998i	$0.479854\pi$
$488$	−17.3675	+	30.0814i	−0.786190	+	1.36172i
$489$	−5.80601	−	10.0563i	−0.262557	−	0.454762i
$490$	−8.31098	+	14.3950i	−0.375452	+	0.650302i
$491$	−2.88904	−	5.00397i	−0.130381	−	0.225826i	0.793443	−	0.608645i	$-0.208287\pi$
$491$	−2.88904	−	5.00397i	−0.130381	−	0.225826i	−0.923823	+	0.382819i	$0.874953\pi$
$492$	0.0349842	+	0.0605943i	0.00157721	+	0.00273180i
$493$	−20.3129			−0.914849
$494$	−26.1132	−	28.0341i	−1.17489	−	1.26131i
$495$	−4.31625			−0.194001
$496$	2.25337	+	3.90295i	0.101179	+	0.175248i
$497$	6.71641	+	11.6332i	0.301272	+	0.521819i
$498$	5.30382	−	9.18649i	0.237670	−	0.411657i
$499$	−6.39792	−	11.0815i	−0.286410	−	0.496077i	0.686540	−	0.727092i	$-0.259129\pi$
$499$	−6.39792	−	11.0815i	−0.286410	−	0.496077i	−0.972950	+	0.231015i	$0.925795\pi$
$500$	0.0458624	−	0.0794360i	0.00205103	−	0.00355249i
$501$	20.3114			0.907446
$502$	8.42004			0.375805
$503$	−15.8339	+	27.4252i	−0.706000	+	1.22283i	0.260329	+	0.965520i	$0.416169\pi$
$503$	−15.8339	+	27.4252i	−0.706000	+	1.22283i	−0.966329	+	0.257308i	$0.917164\pi$
$504$	−6.30296	+	10.9171i	−0.280756	+	0.486284i
$505$	−4.49970			−0.200234
$506$	3.45440			0.153567
$507$	13.7416	−	23.8012i	0.610287	−	1.05705i
$508$	−0.283588	−	0.491189i	−0.0125822	−	0.0217930i
$509$	2.74405	−	4.75283i	0.121628	−	0.210665i	−0.798782	−	0.601621i	$-0.794522\pi$
$509$	2.74405	−	4.75283i	0.121628	−	0.210665i	0.920410	+	0.390955i	$0.127855\pi$
$510$	3.94834	+	6.83872i	0.174835	+	0.302823i
$511$	17.6391	+	30.5517i	0.780306	+	1.35153i
$512$	−23.9817			−1.05985
$513$	−2.97100	−	3.18954i	−0.131173	−	0.140822i
$514$	6.38252			0.281521
$515$	8.03585	+	13.9185i	0.354102	+	0.613323i
$516$	0.291806	+	0.505423i	0.0128461	+	0.0222500i
$517$	−5.89737	+	10.2145i	−0.259366	+	0.449235i
$518$	−19.7252	−	34.1651i	−0.866678	−	1.50113i
$519$	−6.12545	+	10.6096i	−0.268877	+	0.465709i
$520$	18.3850			0.806234
$521$	8.28086			0.362791			0.181396	−	0.983410i	$-0.441939\pi$
$521$	8.28086			0.362791			0.181396	+	0.983410i	$0.441939\pi$
$522$	2.45437	−	4.25109i	0.107425	−	0.186065i
$523$	−5.77584	+	10.0040i	−0.252560	+	0.437446i	−0.964230	−	0.265067i	$-0.914606\pi$
$523$	−5.77584	+	10.0040i	−0.252560	+	0.437446i	0.711670	+	0.702514i	$0.247939\pi$
$524$	−1.59578			−0.0697118
$525$	4.36264			0.190401
$526$	20.7552	−	35.9491i	0.904970	−	1.56745i
$527$	−3.38254	−	5.85874i	−0.147346	−	0.255211i
$528$	8.21843	−	14.2347i	0.357661	−	0.619488i
$529$	11.3322	+	19.6279i	0.492703	+	0.853387i
$530$	−3.54817	−	6.14561i	−0.154123	−	0.266948i
$531$	3.82968			0.166194
$532$	−1.69978	+	0.391436i	−0.0736948	+	0.0169709i
$533$	4.85347			0.210227
$534$	6.79779	+	11.7741i	0.294169	+	0.509516i
$535$	−6.83945	−	11.8463i	−0.295695	−	0.512159i
$536$	−5.78518	+	10.0202i	−0.249882	+	0.432808i
$537$	−9.59201	−	16.6139i	−0.413926	−	0.716941i
$538$	0.145931	−	0.252759i	0.00629152	−	0.0108972i
$539$	−51.9360			−2.23704
$540$	0.0917248			0.00394721
$541$	12.9374	−	22.4083i	0.556224	−	0.963409i	−0.441583	−	0.897220i	$-0.645583\pi$
$541$	12.9374	−	22.4083i	0.556224	−	0.963409i	0.997807	−	0.0661881i	$-0.0210837\pi$
$542$	5.11622	−	8.86155i	0.219760	−	0.380636i
$543$	3.22984			0.138606
$544$	2.96372			0.127069
$545$	4.48337	−	7.76542i	0.192046	−	0.332634i
$546$	19.1725	+	33.2077i	0.820506	+	1.42116i
$547$	−3.20287	+	5.54753i	−0.136945	+	0.237195i	−0.926339	−	0.376692i	$-0.877062\pi$
$547$	−3.20287	+	5.54753i	−0.136945	+	0.237195i	0.789394	+	0.613887i	$0.210395\pi$
$548$	0.720793	+	1.24845i	0.0307907	+	0.0533311i
$549$	6.01053	+	10.4105i	0.256523	+	0.444311i
$550$	−5.96248			−0.254241
$551$	15.0940	−	3.47595i	0.643028	−	0.148080i
$552$	−1.67406			−0.0712528
$553$	24.7291	+	42.8320i	1.05159	+	1.82140i
$554$	20.0765	+	34.7736i	0.852970	+	1.47739i
$555$	−3.27305	+	5.66908i	−0.138933	+	0.240639i
$556$	0.300557	+	0.520580i	0.0127464	+	0.0220775i
$557$	1.76281	−	3.05327i	0.0746925	−	0.129371i	−0.826260	−	0.563289i	$-0.809536\pi$
$557$	1.76281	−	3.05327i	0.0746925	−	0.129371i	0.900953	+	0.433918i	$0.142869\pi$
$558$	1.63482			0.0692075
$559$	40.4832			1.71226
$560$	−8.30677	+	14.3878i	−0.351025	+	0.607993i
$561$	−12.3367	+	21.3678i	−0.520857	+	0.902151i
$562$	15.8529			0.668713
$563$	−30.7179			−1.29461			−0.647303	−	0.762232i	$-0.724103\pi$
$563$	−30.7179			−1.29461			−0.647303	+	0.762232i	$0.724103\pi$
$564$	0.125325	−	0.217070i	0.00527715	−	0.00914029i
$565$	−3.21476	−	5.56813i	−0.135246	−	0.234253i
$566$	18.8786	−	32.6986i	0.793525	−	1.37443i
$567$	2.18132	+	3.77816i	0.0916069	+	0.158668i
$568$	4.44849	+	7.70501i	0.186654	+	0.323295i
$569$	9.17896			0.384802			0.192401	−	0.981316i	$-0.438373\pi$
$569$	9.17896			0.384802			0.192401	+	0.981316i	$0.438373\pi$
$570$	−4.10415	−	4.40604i	−0.171904	−	0.184549i
$571$	−7.49001			−0.313447			−0.156724	−	0.987643i	$-0.550093\pi$
$571$	−7.49001			−0.313447			−0.156724	+	0.987643i	$0.550093\pi$
$572$	1.25951	+	2.18153i	0.0526627	+	0.0912145i
$573$	13.7755	+	23.8598i	0.575478	+	0.996758i
$574$	−2.29855	+	3.98121i	−0.0959398	+	0.166173i
$575$	0.289678	+	0.501738i	0.0120804	+	0.0209239i
$576$	−4.16624	+	7.21613i	−0.173593	+	0.300672i
$577$	32.6093			1.35754			0.678771	−	0.734350i	$-0.262513\pi$
$577$	32.6093			1.35754			0.678771	+	0.734350i	$0.262513\pi$
$578$	21.6568			0.900803
$579$	11.1233	−	19.2662i	0.462270	−	0.800674i
$580$	−0.162969	+	0.282271i	−0.00676694	+	0.0117207i
$581$	−33.5003			−1.38983
$582$	−2.76281			−0.114522
$583$	11.0864	−	19.2022i	0.459152	−	0.795275i
$584$	11.6829	+	20.2354i	0.483442	+	0.837346i
$585$	3.18132	−	5.51021i	0.131531	−	0.227819i
$586$	−8.99367	−	15.5775i	−0.371525	−	0.643500i
$587$	9.19474	+	15.9258i	0.379508	+	0.657326i	0.990991	−	0.133931i	$-0.0427601\pi$
$587$	9.19474	+	15.9258i	0.379508	+	0.657326i	−0.611483	+	0.791258i	$0.709427\pi$
$588$	1.10369			0.0455156
$589$	3.51603	+	3.77466i	0.144875	+	0.155532i
$590$	5.29033			0.217800
$591$	6.33133	+	10.9662i	0.260436	+	0.451089i
$592$	−12.4642	−	21.5886i	−0.512276	−	0.887288i
$593$	−0.208669	+	0.361425i	−0.00856900	+	0.0148419i	−0.870278	−	0.492561i	$-0.836061\pi$
$593$	−0.208669	+	0.361425i	−0.00856900	+	0.0148419i	0.861709	+	0.507403i	$0.169394\pi$
$594$	−2.98124	−	5.16366i	−0.122322	−	0.211868i
$595$	12.4693	−	21.5975i	0.511193	−	0.885412i
$596$	−0.527528			−0.0216084
$597$	8.76955			0.358914
$598$	−2.54609	+	4.40996i	−0.104118	+	0.180337i
$599$	19.4828	−	33.7452i	0.796045	−	1.37879i	−0.126129	−	0.992014i	$-0.540255\pi$
$599$	19.4828	−	33.7452i	0.796045	−	1.37879i	0.922174	−	0.386776i	$-0.126411\pi$
$600$	2.88952			0.117964
$601$	10.0358			0.409367			0.204683	−	0.978828i	$-0.434383\pi$
$601$	10.0358			0.409367			0.204683	+	0.978828i	$0.434383\pi$
$602$	−19.1725	+	33.2077i	−0.781411	+	1.35344i
$603$	2.00213	+	3.46779i	0.0815329	+	0.141219i
$604$	−0.580953	+	1.00624i	−0.0236386	+	0.0409433i
$605$	−3.81500	−	6.60778i	−0.155102	−	0.268644i
$606$	−3.10795	−	5.38313i	−0.126252	−	0.218675i
$607$	−6.25423			−0.253851			−0.126926	−	0.991912i	$-0.540511\pi$
$607$	−6.25423			−0.253851			−0.126926	+	0.991912i	$0.540511\pi$
$608$	−2.20227	+	0.507152i	−0.0893137	+	0.0205677i
$609$	−15.5024			−0.628189
$610$	8.30296	+	14.3812i	0.336177	+	0.582276i
$611$	−8.69340	−	15.0574i	−0.351697	−	0.609157i
$612$	0.262168	−	0.454089i	0.0105975	−	0.0183555i
$613$	−14.9371	−	25.8719i	−0.603306	−	1.04496i	−0.992317	−	0.123723i	$-0.960517\pi$
$613$	−14.9371	−	25.8719i	−0.603306	−	1.04496i	0.389011	−	0.921233i	$-0.372817\pi$
$614$	−2.78031	+	4.81563i	−0.112204	+	0.194343i
$615$	0.762807			0.0307593
$616$	−54.4103			−2.19225
$617$	15.3197	−	26.5346i	0.616749	−	1.06824i	−0.373326	−	0.927700i	$-0.621783\pi$
$617$	15.3197	−	26.5346i	0.616749	−	1.06824i	0.990075	−	0.140540i	$-0.0448840\pi$
$618$	−11.1008	+	19.2271i	−0.446538	+	0.773426i
$619$	21.1480			0.850011			0.425006	−	0.905191i	$-0.360272\pi$
$619$	21.1480			0.850011			0.425006	+	0.905191i	$0.360272\pi$
$620$	−0.108552			−0.00435954
$621$	−0.289678	+	0.501738i	−0.0116244	+	0.0201340i
$622$	−10.6076	−	18.3730i	−0.425328	−	0.736690i
$623$	21.4683	−	37.1841i	0.860108	−	1.48975i
$624$	12.1149	+	20.9836i	0.484985	+	0.840018i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	30.3356			1.21245
$627$	5.51065	−	17.9890i	0.220074	−	0.718410i
$628$	−0.126476			−0.00504696
$629$	18.7101	+	32.4068i	0.746020	+	1.29214i
$630$	3.01329	+	5.21916i	0.120052	+	0.207936i
$631$	13.0124	−	22.5381i	0.518014	−	0.897227i	−0.481767	−	0.876299i	$-0.660005\pi$
$631$	13.0124	−	22.5381i	0.518014	−	0.897227i	0.999781	−	0.0209274i	$-0.00666189\pi$
$632$	16.3788	+	28.3690i	0.651515	+	1.12846i
$633$	3.93389	−	6.81369i	0.156358	−	0.270820i
$634$	−33.3304			−1.32372
$635$	−6.18345			−0.245383
$636$	−0.235598	+	0.408067i	−0.00934206	+	0.0161809i
$637$	38.2798	−	66.3025i	1.51670	−	2.62700i
$638$	21.1873			0.838815
$639$	3.07906			0.121806
$640$	−5.23680	+	9.07040i	−0.207003	+	0.358539i
$641$	9.59982	+	16.6274i	0.379170	+	0.656742i	0.990942	−	0.134292i	$-0.0428761\pi$
$641$	9.59982	+	16.6274i	0.379170	+	0.656742i	−0.611771	+	0.791035i	$0.709543\pi$
$642$	9.44803	−	16.3645i	0.372884	−	0.645854i
$643$	−4.27305	−	7.40113i	−0.168513	−	0.291872i	0.769385	−	0.638786i	$-0.220563\pi$
$643$	−4.27305	−	7.40113i	−0.168513	−	0.291872i	−0.937897	+	0.346914i	$0.887230\pi$
$644$	0.115919	+	0.200777i	0.00456783	+	0.00791172i
$645$	6.36264			0.250529
$646$	−33.5429	+	7.72446i	−1.31973	+	0.303915i
$647$	−21.6966			−0.852983			−0.426492	−	0.904492i	$-0.640251\pi$
$647$	−21.6966			−0.852983			−0.426492	+	0.904492i	$0.640251\pi$
$648$	1.44476	+	2.50239i	0.0567554	+	0.0983033i
$649$	8.26493	+	14.3153i	0.324427	+	0.561924i
$650$	4.39469	−	7.61182i	0.172374	−	0.298560i
$651$	−2.58148	−	4.47126i	−0.101176	−	0.175243i
$652$	−0.532555	+	0.922413i	−0.0208565	+	0.0361245i
$653$	−4.39011			−0.171798			−0.0858991	−	0.996304i	$-0.527376\pi$
$653$	−4.39011			−0.171798			−0.0858991	+	0.996304i	$0.527376\pi$
$654$	12.3867			0.484358
$655$	−8.69872	+	15.0666i	−0.339887	+	0.588702i
$656$	−1.45244	+	2.51569i	−0.0567081	+	0.0982213i
$657$	8.08640			0.315481
$658$	16.4684			0.642006
$659$	7.57327	−	13.1173i	0.295013	−	0.510977i	−0.679975	−	0.733235i	$-0.738009\pi$
$659$	7.57327	−	13.1173i	0.295013	−	0.510977i	0.974988	+	0.222258i	$0.0713428\pi$
$660$	0.197954	+	0.342866i	0.00770534	+	0.0133460i
$661$	−3.65794	+	6.33574i	−0.142277	+	0.246432i	−0.928354	−	0.371698i	$-0.878776\pi$
$661$	−3.65794	+	6.33574i	−0.142277	+	0.246432i	0.786076	+	0.618129i	$0.212109\pi$
$662$	17.1582	+	29.7188i	0.666871	+	1.15505i
$663$	−18.1857	−	31.4986i	−0.706276	−	1.22331i
$664$	−22.1883			−0.861072
$665$	−5.56988	+	18.1823i	−0.215991	+	0.705080i
$666$	−9.04280			−0.350401
$667$	−1.02936	−	1.78290i	−0.0398568	−	0.0690340i
$668$	−0.931530	−	1.61346i	−0.0360420	−	0.0624265i
$669$	−13.6768	+	23.6889i	−0.528774	+	0.915864i
$670$	2.76575	+	4.79041i	0.106850	+	0.185070i
$671$	−25.9429	+	44.9345i	−1.00152	+	1.73468i
$672$	2.26185			0.0872527
$673$	39.7027			1.53043			0.765213	−	0.643777i	$-0.222634\pi$
$673$	39.7027			1.53043			0.765213	+	0.643777i	$0.222634\pi$
$674$	−0.393218	+	0.681074i	−0.0151462	+	0.0262340i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−2.52090			−0.0969575
$677$	−9.45197			−0.363269			−0.181634	−	0.983366i	$-0.558139\pi$
$677$	−9.45197			−0.363269			−0.181634	+	0.983366i	$0.558139\pi$
$678$	4.44088	−	7.69183i	0.170551	−	0.295403i
$679$	4.36264	+	7.55632i	0.167423	+	0.289985i
$680$	8.25883	−	14.3047i	0.316712	−	0.548561i
$681$	−12.5461	−	21.7305i	−0.480767	−	0.832713i
$682$	3.52815	+	6.11093i	0.135100	+	0.234000i
$683$	−6.27600			−0.240145			−0.120072	−	0.992765i	$-0.538313\pi$
$683$	−6.27600			−0.240145			−0.120072	+	0.992765i	$0.538313\pi$
$684$	−0.117107	+	0.382284i	−0.00447770	+	0.0146170i
$685$	15.7164			0.600493
$686$	15.1648	+	26.2663i	0.578996	+	1.00285i
$687$	2.49265	+	4.31740i	0.0951006	+	0.164719i
$688$	−12.1149	+	20.9836i	−0.461877	+	0.799994i
$689$	16.3426	+	28.3063i	0.622604	+	1.07838i
$690$	−0.400163	+	0.693102i	−0.0152339	+	0.0263860i
$691$	−33.8913			−1.28929			−0.644643	−	0.764483i	$-0.722994\pi$
$691$	−33.8913			−1.28929			−0.644643	+	0.764483i	$0.722994\pi$
$692$	1.12371			0.0427171
$693$	−9.41513	+	16.3075i	−0.357651	+	0.619470i
$694$	−6.47439	+	11.2140i	−0.245765	+	0.425677i
$695$	6.55344			0.248586
$696$	−10.2677			−0.389197
$697$	2.18026	−	3.77632i	0.0825832	−	0.143038i
$698$	−10.2429	−	17.7412i	−0.387699	−	0.671514i
$699$	6.39821	−	11.0820i	0.242002	−	0.419161i
$700$	−0.200081	−	0.346551i	−0.00756237	−	0.0130984i
$701$	−20.1520	−	34.9043i	−0.761131	−	1.31832i	−0.942268	−	0.334860i	$-0.891311\pi$
$701$	−20.1520	−	34.9043i	−0.761131	−	1.31832i	0.181136	−	0.983458i	$-0.442022\pi$
$702$	8.78938			0.331734
$703$	−19.4484	−	20.8790i	−0.733512	−	0.787467i
$704$	−35.9650			−1.35548
$705$	−1.36632	−	2.36653i	−0.0514585	−	0.0891288i
$706$	−21.5948	−	37.4033i	−0.812730	−	1.40769i
$707$	−9.81529	+	17.0006i	−0.369142	+	0.639373i
$708$	−0.175638	−	0.304215i	−0.00660090	−	0.0114331i
$709$	2.63706	−	4.56751i	0.0990367	−	0.171537i	−0.812249	−	0.583310i	$-0.801757\pi$
$709$	2.63706	−	4.56751i	0.0990367	−	0.171537i	0.911286	+	0.411774i	$0.135091\pi$
$710$	4.25342			0.159628
$711$	11.3367			0.425161
$712$	14.2191	−	24.6282i	0.532884	−	0.922981i
$713$	0.342820	−	0.593782i	0.0128387	−	0.0222373i
$714$	34.4504			1.28927
$715$	27.4628			1.02705
$716$	−0.879826	+	1.52390i	−0.0328806	+	0.0569509i
$717$	6.40247	+	11.0894i	0.239105	+	0.414142i
$718$	−7.50877	+	13.0056i	−0.280225	+	0.485364i
$719$	−11.8834	−	20.5827i	−0.443176	−	0.767604i	0.554747	−	0.832019i	$-0.312815\pi$
$719$	−11.8834	−	20.5827i	−0.443176	−	0.767604i	−0.997923	+	0.0644151i	$0.979482\pi$
$720$	1.90407	+	3.29794i	0.0709604	+	0.122907i
$721$	70.1151			2.61122
$722$	23.6030	−	11.4797i	0.878414	−	0.427231i
$723$	1.09279			0.0406413
$724$	−0.148128	−	0.256566i	−0.00550515	−	0.00953520i
$725$	1.77672	+	3.07737i	0.0659858	+	0.114291i
$726$	5.27006	−	9.12801i	0.195590	−	0.338772i
$727$	16.9225	+	29.3106i	0.627620	+	1.08707i	0.988028	+	0.154275i	$0.0493040\pi$
$727$	16.9225	+	29.3106i	0.627620	+	1.08707i	−0.360408	+	0.932795i	$0.617363\pi$
$728$	40.1035	−	69.4613i	1.48634	−	2.57441i
$729$	1.00000			0.0370370
$730$	11.1706			0.413442
$731$	18.1857	−	31.4986i	0.672624	−	1.16502i
$732$	0.551315	−	0.954905i	0.0203772	−	0.0352943i
$733$	24.6249			0.909542			0.454771	−	0.890608i	$-0.349721\pi$
$733$	24.6249			0.909542			0.454771	+	0.890608i	$0.349721\pi$
$734$	−25.8731			−0.954992
$735$	6.01633	−	10.4206i	0.221916	−	0.384369i
$736$	0.150186	+	0.260130i	0.00553594	+	0.00958853i
$737$	−8.64168	+	14.9678i	−0.318320	+	0.551347i
$738$	0.526872	+	0.912569i	0.0193944	+	0.0335921i
$739$	−9.22966	−	15.9862i	−0.339518	−	0.588063i	0.644824	−	0.764331i	$-0.276931\pi$
$739$	−9.22966	−	15.9862i	−0.339518	−	0.588063i	−0.984342	+	0.176268i	$0.943597\pi$
$740$	0.600439			0.0220726
$741$	18.9034	+	20.2939i	0.694434	+	0.745515i
$742$	−30.9588			−1.13653
$743$	4.47864	+	7.75723i	0.164305	+	0.284585i	0.936408	−	0.350912i	$-0.114128\pi$
$743$	4.47864	+	7.75723i	0.164305	+	0.284585i	−0.772103	+	0.635497i	$0.780795\pi$
$744$	−1.70980	−	2.96146i	−0.0626842	−	0.108572i
$745$	−2.87560	+	4.98069i	−0.105354	+	0.182478i
$746$	−20.2565	−	35.0853i	−0.741644	−	1.28457i
$747$	−3.83945	+	6.65012i	−0.140478	+	0.243315i
$748$	2.26317			0.0827497
$749$	−59.6761			−2.18052
$750$	0.690702	−	1.19633i	0.0252209	−	0.0436838i
$751$	14.6128	−	25.3101i	0.533228	−	0.923578i	−0.466019	−	0.884775i	$-0.654312\pi$
$751$	14.6128	−	25.3101i	0.533228	−	0.923578i	0.999247	−	0.0388032i	$-0.0123545\pi$
$752$	10.4063			0.379477
$753$	−6.09528			−0.222124
$754$	−15.6163	+	27.0482i	−0.568711	+	0.985037i
$755$	6.33364	+	10.9702i	0.230505	+	0.399246i
$756$	0.200081	−	0.346551i	0.00727689	−	0.0126039i
$757$	−9.33886	−	16.1754i	−0.339427	−	0.587904i	0.644898	−	0.764268i	$-0.276900\pi$
$757$	−9.33886	−	16.1754i	−0.339427	−	0.587904i	−0.984325	+	0.176364i	$0.943566\pi$
$758$	7.35499	+	12.7392i	0.267145	+	0.462709i
$759$	−2.50065			−0.0907678
$760$	−3.68911	+	12.0427i	−0.133818	+	0.436836i
$761$	41.5952			1.50782			0.753912	−	0.656975i	$-0.228164\pi$
$761$	41.5952			1.50782			0.753912	+	0.656975i	$0.228164\pi$
$762$	−4.27092	−	7.39745i	−0.154719	−	0.267981i
$763$	−19.5593	−	33.8778i	−0.708096	−	1.22646i
$764$	1.26355	−	2.18854i	0.0457137	−	0.0791785i
$765$	−2.85821	−	4.95056i	−0.103339	−	0.178988i
$766$	−6.40940	+	11.1014i	−0.231581	+	0.401110i
$767$	−24.3669			−0.879838
$768$	2.19670			0.0792664
$769$	−17.6255	+	30.5282i	−0.635590	+	1.10087i	0.350800	+	0.936450i	$0.385910\pi$
$769$	−17.6255	+	30.5282i	−0.635590	+	1.10087i	−0.986390	+	0.164424i	$0.947424\pi$
$770$	−13.0061	+	22.5272i	−0.468707	+	0.811824i
$771$	−4.62032			−0.166397
$772$	−2.04057			−0.0734417
$773$	−23.9762	+	41.5280i	−0.862364	+	1.49366i	0.00727780	+	0.999974i	$0.497683\pi$
$773$	−23.9762	+	41.5280i	−0.862364	+	1.49366i	−0.869641	+	0.493684i	$0.835650\pi$
$774$	4.39469	+	7.61182i	0.157964	+	0.273601i
$775$	−0.591725	+	1.02490i	−0.0212554	+	0.0368154i
$776$	2.88952	+	5.00479i	0.103728	+	0.179661i
$777$	14.2791	+	24.7322i	0.512261	+	0.887262i
$778$	1.84068			0.0659917
$779$	−0.973891	+	3.17917i	−0.0348933	+	0.113906i
$780$	−0.583613			−0.0208967
$781$	6.64499	+	11.5095i	0.237776	+	0.411841i
$782$	2.28750	+	3.96206i	0.0818007	+	0.141683i
$783$	−1.77672	+	3.07737i	−0.0634948	+	0.109976i
$784$	22.9110	+	39.6830i	0.818250	+	1.41725i
$785$	−0.689434	+	1.19414i	−0.0246070	+	0.0426205i
$786$	−24.0329			−0.857224
$787$	−5.26074			−0.187525			−0.0937626	−	0.995595i	$-0.529889\pi$
$787$	−5.26074			−0.187525			−0.0937626	+	0.995595i	$0.529889\pi$
$788$	0.580741	−	1.00587i	0.0206880	−	0.0358327i
$789$	−15.0247	+	26.0236i	−0.534895	+	0.926465i
$790$	15.6606			0.557179
$791$	−28.0497			−0.997333
$792$	−6.23593	+	10.8010i	−0.221584	+	0.383795i
$793$	−38.2429	−	66.2386i	−1.35804	−	2.35220i
$794$	21.8709	−	37.8815i	0.776170	−	1.34437i
$795$	2.56853	+	4.44882i	0.0910963	+	0.157783i
$796$	−0.402193	−	0.696619i	−0.0142554	−	0.0246910i
$797$	−21.0174			−0.744474			−0.372237	−	0.928138i	$-0.621409\pi$
$797$	−21.0174			−0.744474			−0.372237	+	0.928138i	$0.621409\pi$
$798$	−25.5992	+	5.89515i	−0.906202	+	0.208686i
$799$	−15.6209			−0.552627
$800$	−0.259229	−	0.448998i	−0.00916514	−	0.0158745i
$801$	−4.92093	−	8.52330i	−0.173873	−	0.301156i
$802$	3.37649	−	5.84825i	0.119228	−	0.206509i
$803$	17.4515	+	30.2268i	0.615849	+	1.06668i
$804$	0.183645	−	0.318082i	0.00647665	−	0.0112179i
$805$	2.52753			0.0890837
$806$	−10.4018			−0.366387
$807$	−0.105639	+	0.182973i	−0.00371869	+	0.00644095i
$808$	−6.50098	+	11.2600i	−0.228704	+	0.396126i
$809$	35.3856			1.24409			0.622046	−	0.782981i	$-0.286302\pi$
$809$	35.3856			1.24409			0.622046	+	0.782981i	$0.286302\pi$
$810$	1.38140			0.0485376
$811$	−2.67523	+	4.63364i	−0.0939401	+	0.162709i	−0.909166	−	0.416434i	$-0.863280\pi$
$811$	−2.67523	+	4.63364i	−0.0939401	+	0.162709i	0.815226	+	0.579143i	$0.196613\pi$
$812$	0.710978	+	1.23145i	0.0249504	+	0.0432154i
$813$	−3.70364	+	6.41489i	−0.129892	+	0.224980i
$814$	−19.5155	−	33.8018i	−0.684017	−	1.18475i
$815$	5.80601	+	10.0563i	0.203376	+	0.352257i
$816$	21.7689			0.762063
$817$	−8.12332	+	26.5178i	−0.284199	+	0.927740i
$818$	−31.4796			−1.10066
$819$	−13.8790	−	24.0391i	−0.484971	−	0.839994i
$820$	−0.0349842	−	0.0605943i	−0.00122170	−	0.00211605i
$821$	−3.81886	+	6.61446i	−0.133279	+	0.230846i	−0.924939	−	0.380116i	$-0.875884\pi$
$821$	−3.81886	+	6.61446i	−0.133279	+	0.230846i	0.791660	+	0.610962i	$0.209217\pi$
$822$	10.8554	+	18.8020i	0.378624	+	0.655796i
$823$	−13.7866	+	23.8791i	−0.480570	+	0.832372i	−0.999752	−	0.0222919i	$-0.992904\pi$
$823$	−13.7866	+	23.8791i	−0.480570	+	0.832372i	0.519181	+	0.854664i	$0.326237\pi$
$824$	46.4394			1.61779
$825$	4.31625			0.150273
$826$	11.5399	−	19.9877i	0.401525	−	0.695462i
$827$	9.51585	−	16.4819i	0.330898	−	0.573133i	−0.651790	−	0.758400i	$-0.725982\pi$
$827$	9.51585	−	16.4819i	0.330898	−	0.573133i	0.982688	+	0.185267i	$0.0593149\pi$
$828$	0.0531414			0.00184679
$829$	−13.7455			−0.477402			−0.238701	−	0.971093i	$-0.576722\pi$
$829$	−13.7455			−0.477402			−0.238701	+	0.971093i	$0.576722\pi$
$830$	−5.30382	+	9.18649i	−0.184098	+	0.318868i
$831$	−14.5334	−	25.1726i	−0.504159	−	0.873229i
$832$	26.5083	−	45.9137i	0.919009	−	1.59177i
$833$	−34.3918	−	59.5684i	−1.19161	−	2.06392i
$834$	4.52647	+	7.84008i	0.156739	+	0.271480i
$835$	−20.3114			−0.702905
$836$	−1.68170	+	0.387274i	−0.0581629	+	0.0133941i
$837$	−1.18345			−0.0409060
$838$	−21.3295	−	36.9438i	−0.736815	−	1.27620i
$839$	−17.1800	−	29.7566i	−0.593118	−	1.02731i	−0.993809	−	0.111098i	$-0.964563\pi$
$839$	−17.1800	−	29.7566i	−0.593118	−	1.02731i	0.400691	−	0.916213i	$-0.368770\pi$
$840$	6.30296	−	10.9171i	0.217473	−	0.376674i
$841$	8.18652	+	14.1795i	0.282294	+	0.488947i
$842$	−18.3576	+	31.7963i	−0.632644	+	1.09577i
$843$	−11.4759			−0.395251
$844$	−0.721671			−0.0248409
$845$	−13.7416	+	23.8012i	−0.472726	+	0.818786i
$846$	1.88744	−	3.26914i	0.0648914	−	0.112395i
$847$	−33.2870			−1.14375
$848$	−19.5626			−0.671783
$849$	−13.6662	+	23.6706i	−0.469024	+	0.812373i
$850$	−3.94834	−	6.83872i	−0.135427	−	0.234566i
$851$	−1.89626	+	3.28442i	−0.0650030	+	0.112589i
$852$	−0.141213	−	0.244588i	−0.00483788	−	0.00837945i
$853$	−22.7147	−	39.3431i	−0.777738	−	1.34708i	−0.933243	−	0.359247i	$-0.883034\pi$
$853$	−22.7147	−	39.3431i	−0.777738	−	1.34708i	0.155505	−	0.987835i	$-0.450300\pi$
$854$	72.4457			2.47904
$855$	2.97100	+	3.18954i	0.101606	+	0.109080i
$856$	−39.5254			−1.35095
$857$	−6.94674	−	12.0321i	−0.237296	−	0.411009i	0.722641	−	0.691223i	$-0.242928\pi$
$857$	−6.94674	−	12.0321i	−0.237296	−	0.411009i	−0.959937	+	0.280214i	$0.909594\pi$
$858$	18.9686	+	32.8545i	0.647576	+	1.12164i
$859$	1.60333	−	2.77705i	0.0547049	−	0.0947517i	−0.837376	−	0.546627i	$-0.815912\pi$
$859$	1.60333	−	2.77705i	0.0547049	−	0.0947517i	0.892081	+	0.451875i	$0.149245\pi$
$860$	−0.291806	−	0.505423i	−0.00995051	−	0.0172348i
$861$	1.66393	−	2.88201i	0.0567065	−	0.0982185i
$862$	22.7577			0.775132
$863$	51.7277			1.76083			0.880416	−	0.474201i	$-0.157263\pi$
$863$	51.7277			1.76083			0.880416	+	0.474201i	$0.157263\pi$
$864$	0.259229	−	0.448998i	0.00881916	−	0.0152752i
$865$	6.12545	−	10.6096i	0.208272	−	0.360737i
$866$	−50.8413			−1.72766
$867$	−15.6774			−0.532431
$868$	−0.236786	+	0.410126i	−0.00803705	+	0.0139206i
$869$	24.4661	+	42.3765i	0.829955	+	1.43752i
$870$	−2.45437	+	4.25109i	−0.0832109	+	0.144125i
$871$	−12.7388	−	22.0643i	−0.431639	−	0.747620i
$872$	−12.9548	−	22.4383i	−0.438704	−	0.759857i
$873$	2.00000			0.0676897
$874$	−2.37777	−	2.55267i	−0.0804292	−	0.0863453i
$875$	−4.36264			−0.147484
$876$	−0.370862	−	0.642352i	−0.0125303	−	0.0217031i
$877$	−8.51355	−	14.7459i	−0.287482	−	0.497933i	0.685726	−	0.727860i	$-0.259485\pi$
$877$	−8.51355	−	14.7459i	−0.287482	−	0.497933i	−0.973208	+	0.229926i	$0.926151\pi$
$878$	−6.61885	+	11.4642i	−0.223376	+	0.386898i
$879$	6.51053	+	11.2766i	0.219595	+	0.380349i
$880$	−8.21843	+	14.2347i	−0.277043	+	0.479853i
$881$	12.9112			0.434990			0.217495	−	0.976061i	$-0.430211\pi$
$881$	12.9112			0.434990			0.217495	+	0.976061i	$0.430211\pi$
$882$	16.6220			0.559690
$883$	−12.5102	+	21.6684i	−0.421003	+	0.729199i	−0.996038	−	0.0889302i	$-0.971655\pi$
$883$	−12.5102	+	21.6684i	−0.421003	+	0.729199i	0.575035	+	0.818129i	$0.304989\pi$
$884$	−1.66808	+	2.88921i	−0.0561038	+	0.0971746i
$885$	−3.82968			−0.128733
$886$	−30.7273			−1.03230
$887$	−5.03634	+	8.72319i	−0.169104	+	0.292896i	−0.938105	−	0.346351i	$-0.887421\pi$
$887$	−5.03634	+	8.72319i	−0.169104	+	0.292896i	0.769001	+	0.639247i	$0.220754\pi$
$888$	9.45752	+	16.3809i	0.317374	+	0.549707i
$889$	−13.4881	+	23.3621i	−0.452376	+	0.783539i
$890$	−6.79779	−	11.7741i	−0.227862	−	0.394669i
$891$	2.15812	+	3.73798i	0.0722999	+	0.125227i
$892$	2.50900			0.0840075
$893$	11.6075	−	2.67304i	0.388430	−	0.0894500i
$894$	−7.94473			−0.265712
$895$	9.59201	+	16.6139i	0.320626	+	0.555340i
$896$	22.8463	+	39.5709i	0.763240	+	1.32197i
$897$	1.84312	−	3.19238i	0.0615400	−	0.106590i
$898$	0.339264	+	0.587623i	0.0113214	+	0.0196092i
$899$	2.10266	−	3.64191i	0.0701276	−	0.121465i
$900$	−0.0917248			−0.00305749
$901$	29.3655			0.978307
$902$	−2.27411	+	3.93887i	−0.0757196	+	0.131150i
$903$	13.8790	−	24.0391i	0.461863	−	0.799971i
$904$	−18.5782			−0.617902
$905$	−3.22984			−0.107364
$906$	−8.74932	+	15.1543i	−0.290677	+	0.503467i
$907$	3.93231	+	6.81096i	0.130570	+	0.226154i	0.923897	−	0.382642i	$-0.124986\pi$
$907$	3.93231	+	6.81096i	0.130570	+	0.226154i	−0.793326	+	0.608797i	$0.791653\pi$
$908$	−1.15079	+	1.99322i	−0.0381903	+	0.0661475i
$909$	2.24985	+	3.89685i	0.0746228	+	0.129250i
$910$	−19.1725	−	33.2077i	−0.635561	−	1.10082i
$911$	−52.2665			−1.73167			−0.865833	−	0.500333i	$-0.833211\pi$
$911$	−52.2665			−1.73167			−0.865833	+	0.500333i	$0.833211\pi$
$912$	−16.1759	+	3.72509i	−0.535638	+	0.123350i
$913$	−33.1440			−1.09691
$914$	−9.15922	−	15.8642i	−0.302960	−	0.524742i
$915$	−6.01053	−	10.4105i	−0.198702	−	0.344162i
$916$	0.228638	−	0.396013i	0.00755441	−	0.0130846i
$917$	37.9494	+	65.7303i	1.25320	+	2.17061i
$918$	3.94834	−	6.83872i	0.130314	−	0.225711i
$919$	24.2225			0.799026			0.399513	−	0.916728i	$-0.369179\pi$
$919$	24.2225			0.799026			0.399513	+	0.916728i	$0.369179\pi$
$920$	1.67406			0.0551922
$921$	2.01267	−	3.48604i	0.0663197	−	0.114869i
$922$	−16.1441	+	27.9623i	−0.531677	+	0.920891i
$923$	−19.5909			−0.644844
$924$	1.72720			0.0568208
$925$	3.27305	−	5.66908i	0.107617	−	0.186398i
$926$	0.678026	+	1.17438i	0.0222813	+	0.0385924i
$927$	8.03585	−	13.9185i	0.263932	−	0.457144i
$928$	0.921156	+	1.59549i	0.0302384	+	0.0523745i
$929$	21.3993	+	37.0647i	0.702089	+	1.21605i	0.967732	+	0.251983i	$0.0810827\pi$
$929$	21.3993	+	37.0647i	0.702089	+	1.21605i	−0.265642	+	0.964072i	$0.585584\pi$
$930$	−1.63482			−0.0536079
$931$	35.7490	+	38.3786i	1.17163	+	1.25781i
$932$	−1.17375			−0.0384474
$933$	7.67889	+	13.3002i	0.251396	+	0.435430i
$934$	13.0196	+	22.5506i	0.426014	+	0.737877i
$935$	12.3367	−	21.3678i	0.403454	−	0.698803i
$936$	−9.19248	−	15.9218i	−0.300466	−	0.520422i
$937$	−5.67783	+	9.83429i	−0.185487	+	0.321272i	−0.943740	−	0.330687i	$-0.892719\pi$
$937$	−5.67783	+	9.83429i	−0.185487	+	0.321272i	0.758254	+	0.651960i	$0.226053\pi$
$938$	24.1319			0.787935
$939$	−21.9600			−0.716636
$940$	−0.125325	+	0.217070i	−0.00408766	+	0.00708004i
$941$	−22.0711	+	38.2283i	−0.719498	+	1.24621i	0.241701	+	0.970351i	$0.422295\pi$
$941$	−22.0711	+	38.2283i	−0.719498	+	1.24621i	−0.961199	+	0.275856i	$0.911039\pi$
$942$	−1.90477			−0.0620609
$943$	0.441937			0.0143915
$944$	7.29198	−	12.6301i	0.237334	−	0.411074i
$945$	−2.18132	−	3.77816i	−0.0709584	−	0.122904i
$946$	−18.9686	+	32.8545i	−0.616721	+	1.06819i
$947$	18.6191	+	32.2492i	0.605038	+	1.04796i	0.992045	+	0.125880i	$0.0401755\pi$
$947$	18.6191	+	32.2492i	0.605038	+	1.04796i	−0.387007	+	0.922077i	$0.626491\pi$
$948$	−0.519930	−	0.900545i	−0.0168865	−	0.0292483i
$949$	−51.4509			−1.67017
$950$	4.10415	+	4.40604i	0.133156	+	0.142951i
$951$	24.1279			0.782402
$952$	−36.0303	−	62.4064i	−1.16775	−	2.02260i
$953$	19.6433	+	34.0232i	0.636310	+	1.10212i	0.986236	+	0.165344i	$0.0528733\pi$
$953$	19.6433	+	34.0232i	0.636310	+	1.10212i	−0.349926	+	0.936777i	$0.613793\pi$
$954$	−3.54817	+	6.14561i	−0.114876	+	0.198972i
$955$	−13.7755	−	23.8598i	−0.445764	−	0.772085i
$956$	0.587266	−	1.01717i	0.0189935	−	0.0328978i
$957$	−15.3375			−0.495792
$958$	27.8478			0.899721
$959$	34.2826	−	59.3791i	1.10704	−	1.91745i
$960$	4.16624	−	7.21613i	0.134465	−	0.232900i
$961$	−29.5994			−0.954821
$962$	57.5361			1.85504
$963$	−6.83945	+	11.8463i	−0.220398	+	0.381741i
$964$	−0.0501180	−	0.0868069i	−0.00161419	−	0.00279586i
$965$	−11.1233	+	19.2662i	−0.358072	+	0.620200i
$966$	1.74577	+	3.02376i	0.0561692	+	0.0972878i
$967$	−10.5429	−	18.2608i	−0.339037	−	0.587229i	0.645215	−	0.764001i	$-0.276768\pi$
$967$	−10.5429	−	18.2608i	−0.339037	−	0.587229i	−0.984252	+	0.176772i	$0.943434\pi$
$968$	−22.0470			−0.708618
$969$	24.2817	−	5.59175i	0.780041	−	0.179633i
$970$	2.76281			0.0887084
$971$	12.1226	+	20.9969i	0.389031	+	0.673822i	0.992319	−	0.123701i	$-0.0394765\pi$
$971$	12.1226	+	20.9969i	0.389031	+	0.673822i	−0.603288	+	0.797523i	$0.706143\pi$
$972$	−0.0458624	−	0.0794360i	−0.00147104	−	0.00254791i
$973$	14.2952	−	24.7600i	0.458282	−	0.793768i
$974$	−1.92815	−	3.33966i	−0.0617820	−	0.107010i
$975$	−3.18132	+	5.51021i	−0.101884	+	0.176468i
$976$	45.7778			1.46531
$977$	−51.4540			−1.64616			−0.823080	−	0.567926i	$-0.807746\pi$
$977$	−51.4540			−1.64616			−0.823080	+	0.567926i	$0.807746\pi$
$978$	−8.02044	+	13.8918i	−0.256465	+	0.444211i
$979$	21.2400	−	36.7887i	0.678832	−	1.17577i
$980$	−1.10369			−0.0352562
$981$	−8.96674			−0.286286
$982$	−3.99093	+	6.91249i	−0.127356	+	0.220587i
$983$	−4.56746	−	7.91108i	−0.145679	−	0.252324i	0.783947	−	0.620828i	$-0.213203\pi$
$983$	−4.56746	−	7.91108i	−0.145679	−	0.252324i	−0.929626	+	0.368504i	$0.879870\pi$
$984$	1.10207	−	1.90884i	0.0351327	−	0.0608517i
$985$	−6.33133	−	10.9662i	−0.201733	−	0.349412i
$986$	14.0302	+	24.3010i	0.446812	+	0.773901i
$987$	−11.9215			−0.379466
$988$	0.745111	−	2.43234i	0.0237051	−	0.0773830i
$989$	3.68624			0.117216
$990$	2.98124	+	5.16366i	0.0947500	+	0.164112i
$991$	8.87713	+	15.3756i	0.281991	+	0.488424i	0.971875	−	0.235497i	$-0.0756717\pi$
$991$	8.87713	+	15.3756i	0.281991	+	0.488424i	−0.689884	+	0.723920i	$0.742338\pi$
$992$	−0.306785	+	0.531367i	−0.00974042	+	0.0168709i
$993$	−12.4208	−	21.5135i	−0.394163	−	0.682710i
$994$	9.27807	−	16.0701i	0.294283	−	0.509712i
$995$	−8.76955			−0.278014
$996$	0.704345			0.0223180
$997$	28.1217	−	48.7081i	0.890622	−	1.54260i	0.0514903	−	0.998673i	$-0.483603\pi$
$997$	28.1217	−	48.7081i	0.890622	−	1.54260i	0.839131	−	0.543929i	$-0.183064\pi$
$998$	−8.83810	+	15.3080i	−0.279765	+	0.484568i
$999$	6.54609			0.207109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.i.f.121.2	yes	10
3.2	odd	2		855.2.k.i.406.4		10
19.7	even	3		5415.2.a.y.1.4		5
19.11	even	3	inner	285.2.i.f.106.2	✓	10
19.12	odd	6		5415.2.a.z.1.2		5
57.11	odd	6		855.2.k.i.676.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.2	✓	10	19.11	even	3	inner
285.2.i.f.121.2	yes	10	1.1	even	1	trivial
855.2.k.i.406.4		10	3.2	odd	2
855.2.k.i.676.4		10	57.11	odd	6
5415.2.a.y.1.4		5	19.7	even	3
5415.2.a.z.1.2		5	19.12	odd	6

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.690702 - 1.19633i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.0458624 - 0.0794360i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.690702 - 1.19633i) q^{6} -4.36264 q^{7} -2.88952 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.690702 + 1.19633i) q^{10} -4.31625 q^{11} +0.0917248 q^{12} +(3.18132 - 5.51021i) q^{13} +(3.01329 + 5.21916i) q^{14} +(0.500000 - 0.866025i) q^{15} +(1.90407 + 3.29794i) q^{16} +(-2.85821 - 4.95056i) q^{17} +1.38140 q^{18} +(2.97100 + 3.18954i) q^{19} -0.0917248 q^{20} +(-2.18132 - 3.77816i) q^{21} +(2.98124 + 5.16366i) q^{22} +(0.289678 - 0.501738i) q^{23} +(-1.44476 - 2.50239i) q^{24} +(-0.500000 + 0.866025i) q^{25} -8.78938 q^{26} -1.00000 q^{27} +(-0.200081 + 0.346551i) q^{28} +(1.77672 - 3.07737i) q^{29} -1.38140 q^{30} +1.18345 q^{31} +(-0.259229 + 0.448998i) q^{32} +(-2.15812 - 3.73798i) q^{33} +(-3.94834 + 6.83872i) q^{34} +(2.18132 + 3.77816i) q^{35} +(0.0458624 + 0.0794360i) q^{36} -6.54609 q^{37} +(1.76367 - 5.75732i) q^{38} +6.36264 q^{39} +(1.44476 + 2.50239i) q^{40} +(0.381403 + 0.660610i) q^{41} +(-3.01329 + 5.21916i) q^{42} +(3.18132 + 5.51021i) q^{43} +(-0.197954 + 0.342866i) q^{44} +1.00000 q^{45} -0.800326 q^{46} +(1.36632 - 2.36653i) q^{47} +(-1.90407 + 3.29794i) q^{48} +12.0327 q^{49} +1.38140 q^{50} +(2.85821 - 4.95056i) q^{51} +(-0.291806 - 0.505423i) q^{52} +(-2.56853 + 4.44882i) q^{53} +(0.690702 + 1.19633i) q^{54} +(2.15812 + 3.73798i) q^{55} +12.6059 q^{56} +(-1.27672 + 4.16773i) q^{57} -4.90874 q^{58} +(-1.91484 - 3.31660i) q^{59} +(-0.0458624 - 0.0794360i) q^{60} +(6.01053 - 10.4105i) q^{61} +(-0.817411 - 1.41580i) q^{62} +(2.18132 - 3.77816i) q^{63} +8.33247 q^{64} -6.36264 q^{65} +(-2.98124 + 5.16366i) q^{66} +(2.00213 - 3.46779i) q^{67} -0.524337 q^{68} +0.579357 q^{69} +(3.01329 - 5.21916i) q^{70} +(-1.53953 - 2.66654i) q^{71} +(1.44476 - 2.50239i) q^{72} +(-4.04320 - 7.00303i) q^{73} +(4.52140 + 7.83129i) q^{74} -1.00000 q^{75} +(0.389622 - 0.0897246i) q^{76} +18.8303 q^{77} +(-4.39469 - 7.61182i) q^{78} +(-5.66836 - 9.81790i) q^{79} +(1.90407 - 3.29794i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.526872 - 0.912569i) q^{82} +7.67889 q^{83} -0.400163 q^{84} +(-2.85821 + 4.95056i) q^{85} +(4.39469 - 7.61182i) q^{86} +3.55344 q^{87} +12.4719 q^{88} +(-4.92093 + 8.52330i) q^{89} +(-0.690702 - 1.19633i) q^{90} +(-13.8790 + 24.0391i) q^{91} +(-0.0265707 - 0.0460218i) q^{92} +(0.591725 + 1.02490i) q^{93} -3.77487 q^{94} +(1.27672 - 4.16773i) q^{95} -0.518458 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-8.31098 - 14.3950i) q^{98} +(2.15812 - 3.73798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 5 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 4 q^{7} - 12 q^{8} - 5 q^{9} + q^{10} + 10 q^{11} - 14 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 7 q^{16} - 10 q^{17} - 2 q^{18} + 5 q^{19} + 14 q^{20}+ \cdots - 5 q^{99}+O(q^{100}) \) 10 * q + q^2 + 5 * q^3 - 7 * q^4 - 5 * q^5 - q^6 + 4 * q^7 - 12 * q^8 - 5 * q^9 + q^10 + 10 * q^11 - 14 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 7 * q^16 - 10 * q^17 - 2 * q^18 + 5 * q^19 + 14 * q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 - 4 * q^26 - 10 * q^27 - 10 * q^28 + 7 * q^29 + 2 * q^30 - 18 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 - 2 * q^35 - 7 * q^36 + 12 * q^37 - 37 * q^38 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 4 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 40 * q^46 - 6 * q^47 + 7 * q^48 + 30 * q^49 - 2 * q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 - q^54 - 5 * q^55 + 72 * q^56 - 2 * q^57 + 76 * q^58 + q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 2 * q^63 + 28 * q^64 - 16 * q^65 + 2 * q^66 + 14 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 - 26 * q^73 + 18 * q^74 - 10 * q^75 - 56 * q^76 + 28 * q^77 - 2 * q^78 - 23 * q^79 - 7 * q^80 - 5 * q^81 + 36 * q^82 - 24 * q^83 - 20 * q^84 - 10 * q^85 + 2 * q^86 + 14 * q^87 + 9 * q^89 + q^90 - 46 * q^91 + 52 * q^92 - 9 * q^93 + 90 * q^94 + 2 * q^95 + 46 * q^96 - 10 * q^97 - 21 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more