LMFDB - Embedded newform 755.2.e.d.636.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(571,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.571"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} + 2x^{5} + 55x^{4} - 18x^{3} + 78x^{2} + 36x + 36 $ x^8 - 2x^7 + 11x^6 + 2x^5 + 55x^4 - 18x^3 + 78x^2 + 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			636.4
Root			$-1.04092 - 1.80292i$ of defining polynomial
Character	$\chi$	$=$	755.636
Dual form			755.2.e.d.571.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +2.08183 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.04092 + 1.80292i) q^{6} +(0.716433 + 1.24090i) q^{7} +3.00000 q^{8} +1.33402 q^{9} +(0.500000 - 0.866025i) q^{10} +(1.46527 + 2.53793i) q^{11} +(1.04092 - 1.80292i) q^{12} +(-0.883443 + 1.53017i) q^{13} +(-0.716433 + 1.24090i) q^{14} +(-1.04092 - 1.80292i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.36540 - 4.09699i) q^{17} +(0.667010 + 1.15530i) q^{18} +6.28158 q^{19} -1.00000 q^{20} +(1.49149 + 2.58334i) q^{21} +(-1.46527 + 2.53793i) q^{22} +(0.400124 + 0.693034i) q^{23} +6.24549 q^{24} +(-0.500000 + 0.866025i) q^{25} -1.76689 q^{26} -3.46829 q^{27} +1.43287 q^{28} -3.98299 q^{29} +(1.04092 - 1.80292i) q^{30} +(-4.17320 - 7.22819i) q^{31} +(2.50000 - 4.33013i) q^{32} +(3.05045 + 5.28354i) q^{33} +(2.36540 - 4.09699i) q^{34} +(0.716433 - 1.24090i) q^{35} +(0.667010 - 1.15530i) q^{36} +(4.79826 + 8.31084i) q^{37} +(3.14079 + 5.44001i) q^{38} +(-1.83918 + 3.18555i) q^{39} +(-1.50000 - 2.59808i) q^{40} -2.51470 q^{41} +(-1.49149 + 2.58334i) q^{42} +(-2.52424 + 4.37210i) q^{43} +2.93055 q^{44} +(-0.667010 - 1.15530i) q^{45} +(-0.400124 + 0.693034i) q^{46} +(5.04711 - 8.74184i) q^{47} +(1.04092 + 1.80292i) q^{48} +(2.47345 - 4.28414i) q^{49} -1.00000 q^{50} +(-4.92436 - 8.52924i) q^{51} +(0.883443 + 1.53017i) q^{52} +11.4452 q^{53} +(-1.73414 - 3.00363i) q^{54} +(1.46527 - 2.53793i) q^{55} +(2.14930 + 3.72270i) q^{56} +13.0772 q^{57} +(-1.99149 - 3.44937i) q^{58} -12.9620 q^{59} -2.08183 q^{60} +(-6.56482 + 11.3706i) q^{61} +(4.17320 - 7.22819i) q^{62} +(0.955736 + 1.65538i) q^{63} +7.00000 q^{64} +1.76689 q^{65} +(-3.05045 + 5.28354i) q^{66} -10.4977 q^{67} -4.73080 q^{68} +(0.832990 + 1.44278i) q^{69} +1.43287 q^{70} +(-2.38344 + 4.12824i) q^{71} +4.00206 q^{72} -10.8441 q^{73} +(-4.79826 + 8.31084i) q^{74} +(-1.04092 + 1.80292i) q^{75} +(3.14079 - 5.44001i) q^{76} +(-2.09954 + 3.63651i) q^{77} -3.67836 q^{78} -8.89719 q^{79} +(0.500000 - 0.866025i) q^{80} -11.2225 q^{81} +(-1.25735 - 2.17779i) q^{82} -1.25013 q^{83} +2.98299 q^{84} +(-2.36540 + 4.09699i) q^{85} -5.04847 q^{86} -8.29190 q^{87} +(4.39582 + 7.61379i) q^{88} +(3.76354 - 6.51864i) q^{89} +(0.667010 - 1.15530i) q^{90} -2.53171 q^{91} +0.800247 q^{92} +(-8.68790 - 15.0479i) q^{93} +10.0942 q^{94} +(-3.14079 - 5.44001i) q^{95} +(5.20458 - 9.01459i) q^{96} +(-2.55896 - 4.43225i) q^{97} +4.94689 q^{98} +(1.95471 + 3.38565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 3 q^{7} + 24 q^{8} + 12 q^{9} + 4 q^{10} - 11 q^{11} - 2 q^{12} - 5 q^{13} - 3 q^{14} + 2 q^{15} + 4 q^{16} - q^{17} + 6 q^{18} + 20 q^{19} - 8 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 3 * q^7 + 24 * q^8 + 12 * q^9 + 4 * q^10 - 11 * q^11 - 2 * q^12 - 5 * q^13 - 3 * q^14 + 2 * q^15 + 4 * q^16 - q^17 + 6 * q^18 + 20 * q^19 - 8 * q^20 + 5 * q^21 + 11 * q^22 + 8 * q^23 - 12 * q^24 - 4 * q^25 - 10 * q^26 - 40 * q^27 + 6 * q^28 - 18 * q^29 - 2 * q^30 - q^31 + 20 * q^32 + 23 * q^33 + q^34 + 3 * q^35 + 6 * q^36 + 15 * q^37 + 10 * q^38 + 19 * q^39 - 12 * q^40 + 6 * q^41 - 5 * q^42 - 3 * q^43 - 22 * q^44 - 6 * q^45 - 8 * q^46 - 3 * q^47 - 2 * q^48 - 3 * q^49 - 8 * q^50 - 27 * q^51 + 5 * q^52 + 20 * q^53 - 20 * q^54 - 11 * q^55 + 9 * q^56 + 4 * q^57 - 9 * q^58 - 10 * q^59 + 4 * q^60 - 18 * q^61 + q^62 - 24 * q^63 + 56 * q^64 + 10 * q^65 - 23 * q^66 - 44 * q^67 - 2 * q^68 + 6 * q^69 + 6 * q^70 - 17 * q^71 + 36 * q^72 + 18 * q^73 - 15 * q^74 + 2 * q^75 + 10 * q^76 - 5 * q^77 + 38 * q^78 - 12 * q^79 + 4 * q^80 + 56 * q^81 + 3 * q^82 - 28 * q^83 + 10 * q^84 - q^85 - 6 * q^86 + 34 * q^87 - 33 * q^88 - 16 * q^89 + 6 * q^90 - 8 * q^91 + 16 * q^92 - 11 * q^93 - 6 * q^94 - 10 * q^95 - 10 * q^96 - 26 * q^97 - 6 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	2.08183			1.20195			0.600973	−	0.799269i	$-0.294780\pi$
$3$	2.08183			1.20195			0.600973	+	0.799269i	$0.294780\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.04092	+	1.80292i	0.424952	+	0.736038i
$7$	0.716433	+	1.24090i	0.270786	+	0.469016i	0.969063	−	0.246812i	$-0.0793830\pi$
$7$	0.716433	+	1.24090i	0.270786	+	0.469016i	−0.698277	+	0.715828i	$0.746050\pi$
$8$	3.00000			1.06066
$9$	1.33402			0.444673
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.46527	+	2.53793i	0.441797	+	0.765215i	0.997823	−	0.0659503i	$-0.0210079\pi$
$11$	1.46527	+	2.53793i	0.441797	+	0.765215i	−0.556026	+	0.831165i	$0.687675\pi$
$12$	1.04092	−	1.80292i	0.300486	−	0.520458i
$13$	−0.883443	+	1.53017i	−0.245023	+	0.424392i	−0.962138	−	0.272562i	$-0.912129\pi$
$13$	−0.883443	+	1.53017i	−0.245023	+	0.424392i	0.717115	+	0.696955i	$0.245462\pi$
$14$	−0.716433	+	1.24090i	−0.191475	+	0.331644i
$15$	−1.04092	−	1.80292i	−0.268763	−	0.465512i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.36540	−	4.09699i	−0.573693	−	0.993666i	−0.996182	−	0.0872978i	$-0.972177\pi$
$17$	−2.36540	−	4.09699i	−0.573693	−	0.993666i	0.422489	−	0.906368i	$-0.361157\pi$
$18$	0.667010	+	1.15530i	0.157216	+	0.272306i
$19$	6.28158			1.44109			0.720547	−	0.693406i	$-0.243891\pi$
$19$	6.28158			1.44109			0.720547	+	0.693406i	$0.243891\pi$
$20$	−1.00000			−0.223607
$21$	1.49149	+	2.58334i	0.325470	+	0.563731i
$22$	−1.46527	+	2.53793i	−0.312398	+	0.541088i
$23$	0.400124	+	0.693034i	0.0834315	+	0.144508i	0.904722	−	0.426003i	$-0.140079\pi$
$23$	0.400124	+	0.693034i	0.0834315	+	0.144508i	−0.821290	+	0.570511i	$0.806745\pi$
$24$	6.24549			1.27486
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.76689			−0.346515
$27$	−3.46829			−0.667472
$28$	1.43287			0.270786
$29$	−3.98299			−0.739622			−0.369811	−	0.929107i	$-0.620578\pi$
$29$	−3.98299			−0.739622			−0.369811	+	0.929107i	$0.620578\pi$
$30$	1.04092	−	1.80292i	0.190044	−	0.329166i
$31$	−4.17320	−	7.22819i	−0.749529	−	1.29822i	−0.948049	−	0.318125i	$-0.896947\pi$
$31$	−4.17320	−	7.22819i	−0.749529	−	1.29822i	0.198520	−	0.980097i	$-0.436387\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	3.05045	+	5.28354i	0.531016	+	0.919746i
$34$	2.36540	−	4.09699i	0.405662	−	0.702628i
$35$	0.716433	−	1.24090i	0.121099	−	0.209750i
$36$	0.667010	−	1.15530i	0.111168	−	0.192549i
$37$	4.79826	+	8.31084i	0.788830	+	1.36629i	0.926684	+	0.375841i	$0.122646\pi$
$37$	4.79826	+	8.31084i	0.788830	+	1.36629i	−0.137855	+	0.990452i	$0.544021\pi$
$38$	3.14079	+	5.44001i	0.509504	+	0.882486i
$39$	−1.83918	+	3.18555i	−0.294504	+	0.510097i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−2.51470			−0.392730			−0.196365	−	0.980531i	$-0.562914\pi$
$41$	−2.51470			−0.392730			−0.196365	+	0.980531i	$0.562914\pi$
$42$	−1.49149	+	2.58334i	−0.230142	+	0.398618i
$43$	−2.52424	+	4.37210i	−0.384942	+	0.666740i	−0.991761	−	0.128101i	$-0.959112\pi$
$43$	−2.52424	+	4.37210i	−0.384942	+	0.666740i	0.606819	+	0.794840i	$0.292445\pi$
$44$	2.93055			0.441797
$45$	−0.667010	−	1.15530i	−0.0994320	−	0.172221i
$46$	−0.400124	+	0.693034i	−0.0589950	+	0.102182i
$47$	5.04711	−	8.74184i	0.736196	−	1.27513i	−0.218001	−	0.975949i	$-0.569953\pi$
$47$	5.04711	−	8.74184i	0.736196	−	1.27513i	0.954197	−	0.299180i	$-0.0967132\pi$
$48$	1.04092	+	1.80292i	0.150243	+	0.260229i
$49$	2.47345	−	4.28414i	0.353350	−	0.612019i
$50$	−1.00000			−0.141421
$51$	−4.92436	−	8.52924i	−0.689548	−	1.19433i
$52$	0.883443	+	1.53017i	0.122512	+	0.212196i
$53$	11.4452			1.57213			0.786063	−	0.618147i	$-0.212116\pi$
$53$	11.4452			1.57213			0.786063	+	0.618147i	$0.212116\pi$
$54$	−1.73414	−	3.00363i	−0.235987	−	0.408742i
$55$	1.46527	−	2.53793i	0.197578	−	0.342214i
$56$	2.14930	+	3.72270i	0.287212	+	0.497466i
$57$	13.0772			1.73212
$58$	−1.99149	−	3.44937i	−0.261496	−	0.452924i
$59$	−12.9620			−1.68751			−0.843755	−	0.536729i	$-0.819660\pi$
$59$	−12.9620			−1.68751			−0.843755	+	0.536729i	$0.819660\pi$
$60$	−2.08183			−0.268763
$61$	−6.56482	+	11.3706i	−0.840539	+	1.45586i	0.0489014	+	0.998804i	$0.484428\pi$
$61$	−6.56482	+	11.3706i	−0.840539	+	1.45586i	−0.889440	+	0.457052i	$0.848905\pi$
$62$	4.17320	−	7.22819i	0.529997	−	0.917982i
$63$	0.955736	+	1.65538i	0.120411	+	0.208559i
$64$	7.00000			0.875000
$65$	1.76689			0.219155
$66$	−3.05045	+	5.28354i	−0.375485	+	0.650359i
$67$	−10.4977			−1.28250			−0.641248	−	0.767334i	$-0.721583\pi$
$67$	−10.4977			−1.28250			−0.641248	+	0.767334i	$0.721583\pi$
$68$	−4.73080			−0.573693
$69$	0.832990	+	1.44278i	0.100280	+	0.173690i
$70$	1.43287			0.171260
$71$	−2.38344	+	4.12824i	−0.282863	+	0.489933i	−0.972089	−	0.234614i	$-0.924617\pi$
$71$	−2.38344	+	4.12824i	−0.282863	+	0.489933i	0.689226	+	0.724546i	$0.257951\pi$
$72$	4.00206			0.471647
$73$	−10.8441			−1.26920			−0.634602	−	0.772839i	$-0.718836\pi$
$73$	−10.8441			−1.26920			−0.634602	+	0.772839i	$0.718836\pi$
$74$	−4.79826	+	8.31084i	−0.557787	+	0.966115i
$75$	−1.04092	+	1.80292i	−0.120195	+	0.208183i
$76$	3.14079	−	5.44001i	0.360274	−	0.624012i
$77$	−2.09954	+	3.63651i	−0.239265	+	0.414419i
$78$	−3.67836			−0.416492
$79$	−8.89719			−1.00101			−0.500506	−	0.865733i	$-0.666853\pi$
$79$	−8.89719			−1.00101			−0.500506	+	0.865733i	$0.666853\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−11.2225			−1.24694
$82$	−1.25735	−	2.17779i	−0.138851	−	0.240497i
$83$	−1.25013			−0.137219			−0.0686097	−	0.997644i	$-0.521856\pi$
$83$	−1.25013			−0.137219			−0.0686097	+	0.997644i	$0.521856\pi$
$84$	2.98299			0.325470
$85$	−2.36540	+	4.09699i	−0.256563	+	0.444381i
$86$	−5.04847			−0.544391
$87$	−8.29190			−0.888985
$88$	4.39582	+	7.61379i	0.468596	+	0.811633i
$89$	3.76354	−	6.51864i	0.398934	−	0.690974i	−0.594660	−	0.803977i	$-0.702713\pi$
$89$	3.76354	−	6.51864i	0.398934	−	0.690974i	0.993595	+	0.113003i	$0.0360468\pi$
$90$	0.667010	−	1.15530i	0.0703090	−	0.121779i
$91$	−2.53171			−0.265396
$92$	0.800247			0.0834315
$93$	−8.68790	−	15.0479i	−0.900893	−	1.56039i
$94$	10.0942			1.04114
$95$	−3.14079	−	5.44001i	−0.322238	−	0.558133i
$96$	5.20458	−	9.01459i	0.531190	−	0.920048i
$97$	−2.55896	−	4.43225i	−0.259823	−	0.450027i	0.706371	−	0.707842i	$-0.250331\pi$
$97$	−2.55896	−	4.43225i	−0.259823	−	0.450027i	−0.966194	+	0.257815i	$0.916998\pi$
$98$	4.94689			0.499712
$99$	1.95471	+	3.38565i	0.196455	+	0.340271i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	5.98299			0.595329			0.297665	−	0.954670i	$-0.403792\pi$
$101$	5.98299			0.595329			0.297665	+	0.954670i	$0.403792\pi$
$102$	4.92436	−	8.52924i	0.487584	−	0.844521i
$103$	6.48814	+	11.2378i	0.639296	+	1.10729i	0.985588	+	0.169166i	$0.0541074\pi$
$103$	6.48814	+	11.2378i	0.639296	+	1.10729i	−0.346292	+	0.938127i	$0.612559\pi$
$104$	−2.65033	+	4.59051i	−0.259886	+	0.450136i
$105$	1.49149	−	2.58334i	0.145555	−	0.252108i
$106$	5.72262	+	9.91187i	0.555830	+	0.962726i
$107$	−9.69471			−0.937223			−0.468611	−	0.883404i	$-0.655245\pi$
$107$	−9.69471			−0.937223			−0.468611	+	0.883404i	$0.655245\pi$
$108$	−1.73414	+	3.00363i	−0.166868	+	0.289024i
$109$	−6.34769	+	10.9945i	−0.607998	+	1.05308i	0.383572	+	0.923511i	$0.374694\pi$
$109$	−6.34769	+	10.9945i	−0.607998	+	1.05308i	−0.991570	+	0.129573i	$0.958639\pi$
$110$	2.93055			0.279417
$111$	9.98918	+	17.3018i	0.948131	+	1.64221i
$112$	−0.716433	+	1.24090i	−0.0676966	+	0.117254i
$113$	4.18137	+	7.24235i	0.393350	+	0.681303i	0.992889	−	0.119043i	$-0.0379826\pi$
$113$	4.18137	+	7.24235i	0.393350	+	0.681303i	−0.599539	+	0.800346i	$0.704649\pi$
$114$	6.53860	+	11.3252i	0.612396	+	1.06070i
$115$	0.400124	−	0.693034i	0.0373117	−	0.0646258i
$116$	−1.99149	+	3.44937i	−0.184905	+	0.320266i
$117$	−1.17853	+	2.04128i	−0.108955	+	0.188716i
$118$	−6.48100	−	11.2254i	−0.596625	−	1.03338i
$119$	3.38930	−	5.87044i	0.310696	−	0.538142i
$120$	−3.12275	−	5.40876i	−0.285066	−	0.493750i
$121$	1.20594	−	2.08875i	0.109631	−	0.189887i
$122$	−13.1296			−1.18870
$123$	−5.23517			−0.472040
$124$	−8.34640			−0.749529
$125$	1.00000			0.0894427
$126$	−0.955736	+	1.65538i	−0.0851438	+	0.147473i
$127$	22.4570			1.99273			0.996366	−	0.0851712i	$-0.0271437\pi$
$127$	22.4570			1.99273			0.996366	+	0.0851712i	$0.0271437\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−5.25503	+	9.10198i	−0.462680	+	0.801385i
$130$	0.883443	+	1.53017i	0.0774831	+	0.134205i
$131$	−10.3607			−0.905217			−0.452609	−	0.891709i	$-0.649507\pi$
$131$	−10.3607			−0.905217			−0.452609	+	0.891709i	$0.649507\pi$
$132$	6.10091			0.531016
$133$	4.50033	+	7.79481i	0.390228	+	0.675896i
$134$	−5.24884	−	9.09126i	−0.453431	−	0.785365i
$135$	1.73414	+	3.00363i	0.149251	+	0.258511i
$136$	−7.09619	−	12.2910i	−0.608494	−	1.05394i
$137$	1.05793	−	1.83239i	0.0903851	−	0.156552i	−0.817288	−	0.576229i	$-0.804524\pi$
$137$	1.05793	−	1.83239i	0.0903851	−	0.156552i	0.907673	+	0.419678i	$0.137857\pi$
$138$	−0.832990	+	1.44278i	−0.0709088	+	0.122818i
$139$	−10.4020	+	18.0168i	−0.882287	+	1.52817i	−0.0334955	+	0.999439i	$0.510664\pi$
$139$	−10.4020	+	18.0168i	−0.882287	+	1.52817i	−0.848792	+	0.528727i	$0.822669\pi$
$140$	−0.716433	−	1.24090i	−0.0605496	−	0.104875i
$141$	10.5072	−	18.1990i	0.884868	−	1.53264i
$142$	−4.76689			−0.400028
$143$	−5.17795			−0.433002
$144$	0.667010	+	1.15530i	0.0555842	+	0.0962746i
$145$	1.99149	+	3.44937i	0.165384	+	0.286454i
$146$	−5.42204	−	9.39125i	−0.448731	−	0.777225i
$147$	5.14930	−	8.91885i	0.424707	−	0.735614i
$148$	9.59653			0.788830
$149$	−0.759666	−	1.31578i	−0.0622343	−	0.107793i	0.833230	−	0.552927i	$-0.186489\pi$
$149$	−0.759666	−	1.31578i	−0.0622343	−	0.107793i	−0.895464	+	0.445134i	$0.853156\pi$
$150$	−2.08183			−0.169981
$151$	12.1112	−	2.07803i	0.985598	−	0.169108i
$151$	12.1112	−	2.07803i	0.985598	−	0.169108i
$152$	18.8448			1.52851
$153$	−3.15549	−	5.46547i	−0.255106	−	0.441857i
$154$	−4.19908			−0.338372
$155$	−4.17320	+	7.22819i	−0.335199	+	0.580583i
$156$	1.83918	+	3.18555i	0.147252	+	0.255048i
$157$	−5.64278	−	9.77357i	−0.450342	−	0.780016i	0.548065	−	0.836436i	$-0.315365\pi$
$157$	−5.64278	−	9.77357i	−0.450342	−	0.780016i	−0.998407	+	0.0564199i	$0.982031\pi$
$158$	−4.44859	−	7.70519i	−0.353911	−	0.612992i
$159$	23.8271			1.88961
$160$	−5.00000			−0.395285
$161$	−0.573324	+	0.993026i	−0.0451842	+	0.0782614i
$162$	−5.61123	−	9.71893i	−0.440860	−	0.763591i
$163$	2.24748	−	3.89274i	0.176036	−	0.304903i	−0.764483	−	0.644643i	$-0.777006\pi$
$163$	2.24748	−	3.89274i	0.176036	−	0.304903i	0.940519	+	0.339740i	$0.110339\pi$
$164$	−1.25735	+	2.17779i	−0.0981824	+	0.170057i
$165$	3.05045	−	5.28354i	0.237477	−	0.411323i
$166$	−0.625064	−	1.08264i	−0.0485144	−	0.0840294i
$167$	−8.81598	−	15.2697i	−0.682201	−	1.18161i	−0.974308	−	0.225221i	$-0.927690\pi$
$167$	−8.81598	−	15.2697i	−0.682201	−	1.18161i	0.292107	−	0.956386i	$-0.405644\pi$
$168$	4.47448	+	7.75002i	0.345213	+	0.597927i
$169$	4.93906	+	8.55470i	0.379927	+	0.658054i
$170$	−4.73080			−0.362835
$171$	8.37976			0.640816
$172$	2.52424	+	4.37210i	0.192471	+	0.333370i
$173$	−0.901154	+	1.56084i	−0.0685135	+	0.118669i	−0.898247	−	0.439491i	$-0.855159\pi$
$173$	−0.901154	+	1.56084i	−0.0685135	+	0.118669i	0.829734	+	0.558160i	$0.188492\pi$
$174$	−4.14595	−	7.18100i	−0.314304	−	0.544390i
$175$	−1.43287			−0.108315
$176$	−1.46527	+	2.53793i	−0.110449	+	0.191304i
$177$	−26.9847			−2.02829
$178$	7.52708			0.564178
$179$	−4.96391			−0.371020			−0.185510	−	0.982642i	$-0.559394\pi$
$179$	−4.96391			−0.371020			−0.185510	+	0.982642i	$0.559394\pi$
$180$	−1.33402			−0.0994320
$181$	5.40400	−	9.36000i	0.401676	−	0.695723i	−0.592252	−	0.805752i	$-0.701761\pi$
$181$	5.40400	−	9.36000i	0.401676	−	0.695723i	0.993928	+	0.110029i	$0.0350945\pi$
$182$	−1.26586	−	2.19253i	−0.0938315	−	0.162521i
$183$	−13.6668	+	23.6717i	−1.01028	+	1.74986i
$184$	1.20037	+	2.07910i	0.0884925	+	0.153274i
$185$	4.79826	−	8.31084i	0.352775	−	0.611025i
$186$	8.68790	−	15.0479i	0.637028	−	1.10336i
$187$	6.93191	−	12.0064i	0.506912	−	0.877997i
$188$	−5.04711	−	8.74184i	−0.368098	−	0.637564i
$189$	−2.48480	−	4.30379i	−0.180742	−	0.313055i
$190$	3.14079	−	5.44001i	0.227857	−	0.394660i
$191$	−11.0543	−	19.1467i	−0.799863	−	1.38540i	−0.919705	−	0.392610i	$-0.871572\pi$
$191$	−11.0543	−	19.1467i	−0.799863	−	1.38540i	0.119842	−	0.992793i	$-0.461761\pi$
$192$	14.5728			1.05170
$193$	4.62378	−	8.00862i	0.332827	−	0.576473i	−0.650238	−	0.759730i	$-0.725331\pi$
$193$	4.62378	−	8.00862i	0.332827	−	0.576473i	0.983065	+	0.183258i	$0.0586642\pi$
$194$	2.55896	−	4.43225i	0.183723	−	0.318217i
$195$	3.67836			0.263413
$196$	−2.47345	−	4.28414i	−0.176675	−	0.306010i
$197$	−6.32113	+	10.9485i	−0.450362	+	0.780050i	−0.998408	−	0.0563979i	$-0.982038\pi$
$197$	−6.32113	+	10.9485i	−0.450362	+	0.780050i	0.548046	+	0.836448i	$0.315372\pi$
$198$	−1.95471	+	3.38565i	−0.138915	+	0.240608i
$199$	−3.99905	−	6.92655i	−0.283485	−	0.491010i	0.688756	−	0.724994i	$-0.258157\pi$
$199$	−3.99905	−	6.92655i	−0.283485	−	0.491010i	−0.972241	+	0.233983i	$0.924824\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$	−21.8544			−1.54149
$202$	2.99149	+	5.18142i	0.210481	+	0.364563i
$203$	−2.85354	−	4.94248i	−0.200279	−	0.346894i
$204$	−9.84872			−0.689548
$205$	1.25735	+	2.17779i	0.0878170	+	0.152104i
$206$	−6.48814	+	11.2378i	−0.452050	+	0.782974i
$207$	0.533773	+	0.924522i	0.0370998	+	0.0642587i
$208$	−1.76689			−0.122512
$209$	9.20424	+	15.9422i	0.636671	+	1.10275i
$210$	2.98299			0.205846
$211$	8.34573			0.574544			0.287272	−	0.957849i	$-0.407252\pi$
$211$	8.34573			0.574544			0.287272	+	0.957849i	$0.407252\pi$
$212$	5.72262	−	9.91187i	0.393031	−	0.680750i
$213$	−4.96193	+	8.59431i	−0.339986	+	0.588872i
$214$	−4.84735	−	8.39586i	−0.331358	−	0.573929i
$215$	5.04847			0.344303
$216$	−10.4049			−0.707961
$217$	5.97964	−	10.3570i	0.405924	−	0.703081i
$218$	−12.6954			−0.859839
$219$	−22.5755			−1.52551
$220$	−1.46527	−	2.53793i	−0.0987888	−	0.171107i
$221$	8.35878			0.562272
$222$	−9.98918	+	17.3018i	−0.670430	+	1.16122i
$223$	4.23038			0.283287			0.141644	−	0.989918i	$-0.454761\pi$
$223$	4.23038			0.283287			0.141644	+	0.989918i	$0.454761\pi$
$224$	7.16433			0.478687
$225$	−0.667010	+	1.15530i	−0.0444673	+	0.0770197i
$226$	−4.18137	+	7.24235i	−0.278141	+	0.481754i
$227$	11.1447	−	19.3031i	0.739697	−	1.28119i	−0.212934	−	0.977067i	$-0.568302\pi$
$227$	11.1447	−	19.3031i	0.739697	−	1.28119i	0.952632	−	0.304127i	$-0.0983647\pi$
$228$	6.53860	−	11.3252i	0.433029	−	0.750029i
$229$	21.7413			1.43670			0.718352	−	0.695680i	$-0.244897\pi$
$229$	21.7413			1.43670			0.718352	+	0.695680i	$0.244897\pi$
$230$	0.800247			0.0527667
$231$	−4.37089	+	7.57061i	−0.287584	+	0.498109i
$232$	−11.9490			−0.784487
$233$	3.25503	+	5.63788i	0.213244	+	0.369350i	0.952728	−	0.303825i	$-0.0982637\pi$
$233$	3.25503	+	5.63788i	0.213244	+	0.369350i	−0.739484	+	0.673174i	$0.764930\pi$
$234$	−2.35706			−0.154086
$235$	−10.0942			−0.658474
$236$	−6.48100	+	11.2254i	−0.421877	+	0.730713i
$237$	−18.5224			−1.20316
$238$	6.77860			0.439391
$239$	−0.0327425	−	0.0567117i	−0.00211794	−	0.00366838i	0.864964	−	0.501833i	$-0.167341\pi$
$239$	−0.0327425	−	0.0567117i	−0.00211794	−	0.00366838i	−0.867082	+	0.498165i	$0.834007\pi$
$240$	1.04092	−	1.80292i	0.0671908	−	0.116378i
$241$	−4.50490	+	7.80272i	−0.290186	+	0.502617i	−0.973854	−	0.227176i	$-0.927051\pi$
$241$	−4.50490	+	7.80272i	−0.290186	+	0.502617i	0.683667	+	0.729794i	$0.260384\pi$
$242$	2.41189			0.155042
$243$	−12.9584			−0.831281
$244$	6.56482	+	11.3706i	0.420269	+	0.727928i
$245$	−4.94689			−0.316045
$246$	−2.61759	−	4.53379i	−0.166891	−	0.289064i
$247$	−5.54942	+	9.61188i	−0.353101	+	0.611589i
$248$	−12.5196	−	21.6846i	−0.794995	−	1.37697i
$249$	−2.60256			−0.164930
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	7.90400	+	13.6901i	0.498896	+	0.864113i	0.999999	−	0.00127456i	$-0.000405704\pi$
$251$	7.90400	+	13.6901i	0.498896	+	0.864113i	−0.501103	+	0.865387i	$0.667072\pi$
$252$	1.91147			0.120411
$253$	−1.17258	+	2.03097i	−0.0737196	+	0.127686i
$254$	11.2285	+	19.4483i	0.704537	+	1.22029i
$255$	−4.92436	+	8.52924i	−0.308375	+	0.534122i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−9.78744	−	16.9523i	−0.610524	−	1.05746i	−0.991152	−	0.132730i	$-0.957626\pi$
$257$	−9.78744	−	16.9523i	−0.610524	−	1.05746i	0.380629	−	0.924728i	$-0.375708\pi$
$258$	−10.5101			−0.654328
$259$	−6.87527	+	11.9083i	−0.427209	+	0.739947i
$260$	0.883443	−	1.53017i	0.0547888	−	0.0948970i
$261$	−5.31338			−0.328890
$262$	−5.18034	−	8.97262i	−0.320043	−	0.554330i
$263$	10.1624	−	17.6017i	0.626639	−	1.08537i	−0.361583	−	0.932340i	$-0.617763\pi$
$263$	10.1624	−	17.6017i	0.626639	−	1.08537i	0.988221	−	0.153030i	$-0.0489032\pi$
$264$	9.15136	+	15.8506i	0.563227	+	0.975538i
$265$	−5.72262	−	9.91187i	−0.351538	−	0.608882i
$266$	−4.50033	+	7.79481i	−0.275933	+	0.477930i
$267$	7.83505	−	13.5707i	0.479497	−	0.830514i
$268$	−5.24884	+	9.09126i	−0.320624	+	0.555337i
$269$	−2.86676	−	4.96538i	−0.174790	−	0.302745i	0.765299	−	0.643675i	$-0.222591\pi$
$269$	−2.86676	−	4.96538i	−0.174790	−	0.302745i	−0.940088	+	0.340931i	$0.889258\pi$
$270$	−1.73414	+	3.00363i	−0.105537	+	0.182795i
$271$	16.3168	+	28.2616i	0.991177	+	1.71677i	0.610375	+	0.792112i	$0.291019\pi$
$271$	16.3168	+	28.2616i	0.991177	+	1.71677i	0.380802	+	0.924657i	$0.375648\pi$
$272$	2.36540	−	4.09699i	0.143423	−	0.248416i
$273$	−5.27060			−0.318991
$274$	2.11586			0.127824
$275$	−2.93055			−0.176719
$276$	1.66598			0.100280
$277$	−4.90665	+	8.49856i	−0.294812	+	0.510629i	−0.974941	−	0.222463i	$-0.928590\pi$
$277$	−4.90665	+	8.49856i	−0.294812	+	0.510629i	0.680129	+	0.733092i	$0.261924\pi$
$278$	−20.8040			−1.24774
$279$	−5.56713	−	9.64256i	−0.333296	−	0.577285i
$280$	2.14930	−	3.72270i	0.128445	−	0.222474i
$281$	−7.43055	−	12.8701i	−0.443269	−	0.767765i	0.554660	−	0.832077i	$-0.312848\pi$
$281$	−7.43055	−	12.8701i	−0.443269	−	0.767765i	−0.997930	+	0.0643117i	$0.979515\pi$
$282$	21.0144			1.25139
$283$	20.7105			1.23111			0.615555	−	0.788094i	$-0.288932\pi$
$283$	20.7105			1.23111			0.615555	+	0.788094i	$0.288932\pi$
$284$	2.38344	+	4.12824i	0.141431	+	0.244966i
$285$	−6.53860	−	11.3252i	−0.387313	−	0.670846i
$286$	−2.58897	−	4.48423i	−0.153089	−	0.265158i
$287$	−1.80161	−	3.12048i	−0.106346	−	0.184196i
$288$	3.33505	−	5.77648i	0.196520	−	0.340382i
$289$	−2.69021	+	4.65959i	−0.158248	+	0.274093i
$290$	−1.99149	+	3.44937i	−0.116944	+	0.202554i
$291$	−5.32732	−	9.22720i	−0.312293	−	0.540908i
$292$	−5.42204	+	9.39125i	−0.317301	+	0.549581i
$293$	24.2797			1.41843			0.709217	−	0.704990i	$-0.249049\pi$
$293$	24.2797			1.41843			0.709217	+	0.704990i	$0.249049\pi$
$294$	10.2986			0.600626
$295$	6.48100	+	11.2254i	0.377339	+	0.653570i
$296$	14.3948	+	24.9325i	0.836680	+	1.44917i
$297$	−5.08199	−	8.80227i	−0.294887	−	0.510760i
$298$	0.759666	−	1.31578i	0.0440063	−	0.0762211i
$299$	−1.41395			−0.0817706
$300$	1.04092	+	1.80292i	0.0600973	+	0.104092i
$301$	−7.23378			−0.416948
$302$	7.85524	+	9.44961i	0.452018	+	0.543764i
$303$	12.4556			0.715553
$304$	3.14079	+	5.44001i	0.180137	+	0.312006i
$305$	13.1296			0.751801
$306$	3.15549	−	5.46547i	0.180387	−	0.312440i
$307$	−1.03344	−	1.78997i	−0.0589815	−	0.102159i	0.835027	−	0.550209i	$-0.185452\pi$
$307$	−1.03344	−	1.78997i	−0.0589815	−	0.102159i	−0.894008	+	0.448050i	$0.852119\pi$
$308$	2.09954	+	3.63651i	0.119633	+	0.207210i
$309$	13.5072	+	23.3952i	0.768399	+	1.33091i
$310$	−8.34640			−0.474044
$311$	27.4066			1.55408			0.777042	−	0.629448i	$-0.216719\pi$
$311$	27.4066			1.55408			0.777042	+	0.629448i	$0.216719\pi$
$312$	−5.51754	+	9.55666i	−0.312369	+	0.541039i
$313$	2.16701	+	3.75337i	0.122487	+	0.212153i	0.920748	−	0.390159i	$-0.127580\pi$
$313$	2.16701	+	3.75337i	0.122487	+	0.212153i	−0.798261	+	0.602312i	$0.794246\pi$
$314$	5.64278	−	9.77357i	0.318440	−	0.551555i
$315$	0.955736	−	1.65538i	0.0538496	−	0.0932703i
$316$	−4.44859	+	7.70519i	−0.250253	+	0.433451i
$317$	−1.64149	−	2.84314i	−0.0921952	−	0.159687i	0.816239	−	0.577714i	$-0.196055\pi$
$317$	−1.64149	−	2.84314i	−0.0921952	−	0.159687i	−0.908435	+	0.418027i	$0.862722\pi$
$318$	11.9135	+	20.6348i	0.668078	+	1.15714i
$319$	−5.83617	−	10.1085i	−0.326763	−	0.565969i
$320$	−3.50000	−	6.06218i	−0.195656	−	0.338886i
$321$	−20.1827			−1.12649
$322$	−1.14665			−0.0639002
$323$	−14.8584	−	25.7356i	−0.826746	−	1.43197i
$324$	−5.61123	+	9.71893i	−0.311735	+	0.539940i
$325$	−0.883443	−	1.53017i	−0.0490046	−	0.0848785i
$326$	4.49495			0.248952
$327$	−13.2148	+	22.8887i	−0.730781	+	1.26575i
$328$	−7.54409			−0.416553
$329$	14.4637			0.797407
$330$	6.10091			0.335844
$331$	1.64122			0.0902096			0.0451048	−	0.998982i	$-0.485638\pi$
$331$	1.64122			0.0902096			0.0451048	+	0.998982i	$0.485638\pi$
$332$	−0.625064	+	1.08264i	−0.0343048	+	0.0594177i
$333$	6.40098	+	11.0868i	0.350772	+	0.607554i
$334$	8.81598	−	15.2697i	0.482389	−	0.835522i
$335$	5.24884	+	9.09126i	0.286775	+	0.496709i
$336$	−1.49149	+	2.58334i	−0.0813676	+	0.140933i
$337$	5.12146	−	8.87063i	0.278984	−	0.483214i	−0.692149	−	0.721755i	$-0.743336\pi$
$337$	5.12146	−	8.87063i	0.278984	−	0.483214i	0.971132	+	0.238541i	$0.0766691\pi$
$338$	−4.93906	+	8.55470i	−0.268649	+	0.465314i
$339$	8.70491	+	15.0773i	0.472786	+	0.818889i
$340$	2.36540	+	4.09699i	0.128282	+	0.222190i
$341$	12.2298	−	21.1826i	0.662279	−	1.14710i
$342$	4.18988	+	7.25709i	0.226563	+	0.392418i
$343$	17.1183			0.924301
$344$	−7.57271	+	13.1163i	−0.408293	+	0.707184i
$345$	0.832990	−	1.44278i	0.0448467	−	0.0776767i
$346$	−1.80231			−0.0968927
$347$	−6.61354	−	11.4550i	−0.355034	−	0.614936i	0.632090	−	0.774895i	$-0.282197\pi$
$347$	−6.61354	−	11.4550i	−0.355034	−	0.614936i	−0.987124	+	0.159959i	$0.948864\pi$
$348$	−4.14595	+	7.18100i	−0.222246	+	0.384942i
$349$	0.593687	−	1.02830i	0.0317793	−	0.0550434i	−0.849698	−	0.527269i	$-0.823216\pi$
$349$	0.593687	−	1.02830i	0.0317793	−	0.0550434i	0.881478	+	0.472226i	$0.156549\pi$
$350$	−0.716433	−	1.24090i	−0.0382950	−	0.0663288i
$351$	3.06404	−	5.30707i	0.163546	−	0.283270i
$352$	14.6527			0.780994
$353$	6.54280	+	11.3325i	0.348238	+	0.603167i	0.985937	−	0.167120i	$-0.0534467\pi$
$353$	6.54280	+	11.3325i	0.348238	+	0.603167i	−0.637698	+	0.770286i	$0.720113\pi$
$354$	−13.4924	−	23.3694i	−0.717110	−	1.24207i
$355$	4.76689			0.253000
$356$	−3.76354	−	6.51864i	−0.199467	−	0.345487i
$357$	7.05595	−	12.2213i	0.373440	−	0.646818i
$358$	−2.48195	−	4.29887i	−0.131175	−	0.227202i
$359$	−31.8716			−1.68212			−0.841059	−	0.540944i	$-0.818067\pi$
$359$	−31.8716			−1.68212			−0.841059	+	0.540944i	$0.818067\pi$
$360$	−2.00103	−	3.46589i	−0.105464	−	0.182668i
$361$	20.4583			1.07675
$362$	10.8080			0.568055
$363$	2.51057	−	4.34843i	0.131771	−	0.228234i
$364$	−1.26586	+	2.19253i	−0.0663489	+	0.114920i
$365$	5.42204	+	9.39125i	0.283803	+	0.491561i
$366$	−27.3337			−1.42875
$367$	0.134936			0.00704363			0.00352181	−	0.999994i	$-0.498879\pi$
$367$	0.134936			0.00704363			0.00352181	+	0.999994i	$0.498879\pi$
$368$	−0.400124	+	0.693034i	−0.0208579	+	0.0361269i
$369$	−3.35466			−0.174636
$370$	9.59653			0.498900
$371$	8.19975	+	14.2024i	0.425710	+	0.737351i
$372$	−17.3758			−0.900893
$373$	−14.0690	+	24.3683i	−0.728466	+	1.26174i	0.229065	+	0.973411i	$0.426433\pi$
$373$	−14.0690	+	24.3683i	−0.728466	+	1.26174i	−0.957531	+	0.288330i	$0.906900\pi$
$374$	13.8638			0.716881
$375$	2.08183			0.107505
$376$	15.1413	−	26.2255i	0.780854	−	1.35248i
$377$	3.51874	−	6.09464i	0.181224	−	0.313890i
$378$	2.48480	−	4.30379i	0.127804	−	0.221363i
$379$	−16.2118	+	28.0797i	−0.832744	+	1.44236i	0.0631099	+	0.998007i	$0.479898\pi$
$379$	−16.2118	+	28.0797i	−0.832744	+	1.44236i	−0.895854	+	0.444349i	$0.853435\pi$
$380$	−6.28158			−0.322238
$381$	46.7516			2.39516
$382$	11.0543	−	19.1467i	0.565589	−	0.979628i
$383$	34.1951			1.74729			0.873644	−	0.486565i	$-0.161750\pi$
$383$	34.1951			1.74729			0.873644	+	0.486565i	$0.161750\pi$
$384$	−3.12275	−	5.40876i	−0.159357	−	0.276014i
$385$	4.19908			0.214005
$386$	9.24755			0.470688
$387$	−3.36738	+	5.83248i	−0.171174	+	0.296481i
$388$	−5.11792			−0.259823
$389$	1.99536			0.101169			0.0505845	−	0.998720i	$-0.483892\pi$
$389$	1.99536			0.101169			0.0505845	+	0.998720i	$0.483892\pi$
$390$	1.83918	+	3.18555i	0.0931305	+	0.161307i
$391$	1.89290	−	3.27860i	0.0957282	−	0.165806i
$392$	7.42034	−	12.8524i	0.374784	−	0.649145i
$393$	−21.5692			−1.08802
$394$	−12.6423			−0.636908
$395$	4.44859	+	7.70519i	0.223833	+	0.387690i
$396$	3.90941			0.196455
$397$	−1.83572	−	3.17956i	−0.0921321	−	0.159578i	0.816276	−	0.577662i	$-0.196035\pi$
$397$	−1.83572	−	3.17956i	−0.0921321	−	0.159578i	−0.908408	+	0.418085i	$0.862702\pi$
$398$	3.99905	−	6.92655i	0.200454	−	0.347197i
$399$	9.36894	+	16.2275i	0.469033	+	0.812390i
$400$	−1.00000			−0.0500000
$401$	5.51635	+	9.55459i	0.275473	+	0.477134i	0.970254	−	0.242088i	$-0.0778321\pi$
$401$	5.51635	+	9.55459i	0.275473	+	0.477134i	−0.694781	+	0.719221i	$0.744499\pi$
$402$	−10.9272	−	18.9265i	−0.544999	−	0.943966i
$403$	14.7471			0.734607
$404$	2.99149	−	5.18142i	0.148832	−	0.257785i
$405$	5.61123	+	9.71893i	0.278824	+	0.482937i
$406$	2.85354	−	4.94248i	0.141619	−	0.245291i
$407$	−14.0615	+	24.3553i	−0.697005	+	1.20725i
$408$	−14.7731	−	25.5877i	−0.731376	−	1.26678i
$409$	1.85904			0.0919234			0.0459617	−	0.998943i	$-0.485365\pi$
$409$	1.85904			0.0919234			0.0459617	+	0.998943i	$0.485365\pi$
$410$	−1.25735	+	2.17779i	−0.0620960	+	0.107553i
$411$	2.20243	−	3.81472i	0.108638	−	0.188166i
$412$	12.9763			0.639296
$413$	−9.28641	−	16.0845i	−0.456954	−	0.791468i
$414$	−0.533773	+	0.924522i	−0.0262335	+	0.0454378i
$415$	0.625064	+	1.08264i	0.0306832	+	0.0531448i
$416$	4.41722	+	7.65084i	0.216572	+	0.375113i
$417$	−21.6552	+	37.5080i	−1.06046	+	1.83677i
$418$	−9.20424	+	15.9422i	−0.450194	+	0.779759i
$419$	2.60607	−	4.51384i	0.127315	−	0.220515i	−0.795321	−	0.606189i	$-0.792698\pi$
$419$	2.60607	−	4.51384i	0.127315	−	0.220515i	0.922635	+	0.385673i	$0.126031\pi$
$420$	−1.49149	−	2.58334i	−0.0727774	−	0.126054i
$421$	−9.71146	+	16.8207i	−0.473308	+	0.819793i	−0.999533	−	0.0305520i	$-0.990273\pi$
$421$	−9.71146	+	16.8207i	−0.473308	+	0.819793i	0.526225	+	0.850345i	$0.323607\pi$
$422$	4.17287	+	7.22762i	0.203132	+	0.351835i
$423$	6.73294	−	11.6618i	0.327367	−	0.567016i
$424$	34.3357			1.66749
$425$	4.73080			0.229477
$426$	−9.92385			−0.480812
$427$	−18.8130			−0.910425
$428$	−4.84735	+	8.39586i	−0.234306	+	0.405829i
$429$	−10.7796			−0.520444
$430$	2.52424	+	4.37210i	0.121729	+	0.210842i
$431$	−13.2050	+	22.8717i	−0.636062	+	1.10169i	0.350227	+	0.936665i	$0.386104\pi$
$431$	−13.2050	+	22.8717i	−0.636062	+	1.10169i	−0.986289	+	0.165027i	$0.947229\pi$
$432$	−1.73414	−	3.00363i	−0.0834340	−	0.144512i
$433$	11.8391			0.568949			0.284475	−	0.958684i	$-0.408181\pi$
$433$	11.8391			0.568949			0.284475	+	0.958684i	$0.408181\pi$
$434$	11.9593			0.574064
$435$	4.14595	+	7.18100i	0.198783	+	0.344302i
$436$	6.34769	+	10.9945i	0.303999	+	0.526542i
$437$	2.51341	+	4.35335i	0.120233	+	0.208249i
$438$	−11.2878	−	19.5510i	−0.539351	−	0.934183i
$439$	−13.2050	+	22.8717i	−0.630240	+	1.09161i	0.357263	+	0.934004i	$0.383710\pi$
$439$	−13.2050	+	22.8717i	−0.630240	+	1.09161i	−0.987502	+	0.157603i	$0.949623\pi$
$440$	4.39582	−	7.61379i	0.209563	−	0.362973i
$441$	3.29963	−	5.71513i	0.157125	−	0.272149i
$442$	4.17939	+	7.23892i	0.198793	+	0.344320i
$443$	9.94001	−	17.2166i	0.472264	−	0.817985i	−0.527232	−	0.849721i	$-0.676770\pi$
$443$	9.94001	−	17.2166i	0.472264	−	0.817985i	0.999496	+	0.0317359i	$0.0101035\pi$
$444$	19.9784			0.948131
$445$	−7.52708			−0.356818
$446$	2.11519	+	3.66362i	0.100157	+	0.173477i
$447$	−1.58150	−	2.73923i	−0.0748022	−	0.129561i
$448$	5.01503	+	8.68629i	0.236938	+	0.410389i
$449$	−0.0405811	+	0.0702885i	−0.00191514	+	0.00331712i	−0.866981	−	0.498341i	$-0.833943\pi$
$449$	−0.0405811	+	0.0702885i	−0.00191514	+	0.00331712i	0.865066	+	0.501658i	$0.167276\pi$
$450$	−1.33402			−0.0628863
$451$	−3.68472	−	6.38212i	−0.173507	−	0.300522i
$452$	8.36275			0.393350
$453$	25.2135	−	4.32611i	1.18463	−	0.203259i
$454$	22.2893			1.04609
$455$	1.26586	+	2.19253i	0.0593442	+	0.102787i
$456$	39.2316			1.83719
$457$	5.62378	−	9.74067i	0.263069	−	0.455649i	−0.703987	−	0.710213i	$-0.748599\pi$
$457$	5.62378	−	9.74067i	0.263069	−	0.455649i	0.967056	+	0.254564i	$0.0819319\pi$
$458$	10.8706	+	18.8285i	0.507951	+	0.879798i
$459$	8.20388	+	14.2095i	0.382924	+	0.663244i
$460$	−0.400124	−	0.693034i	−0.0186559	−	0.0323129i
$461$	−5.63525			−0.262460			−0.131230	−	0.991352i	$-0.541893\pi$
$461$	−5.63525			−0.262460			−0.131230	+	0.991352i	$0.541893\pi$
$462$	−8.74178			−0.406705
$463$	5.80644	−	10.0570i	0.269848	−	0.467390i	−0.698974	−	0.715147i	$-0.746360\pi$
$463$	5.80644	−	10.0570i	0.269848	−	0.467390i	0.968822	+	0.247756i	$0.0796932\pi$
$464$	−1.99149	−	3.44937i	−0.0924527	−	0.160133i
$465$	−8.68790	+	15.0479i	−0.402892	+	0.697829i
$466$	−3.25503	+	5.63788i	−0.150786	+	0.261170i
$467$	−2.83634	+	4.91268i	−0.131250	+	0.227332i	−0.924159	−	0.382009i	$-0.875232\pi$
$467$	−2.83634	+	4.91268i	−0.131250	+	0.227332i	0.792909	+	0.609341i	$0.208566\pi$
$468$	1.17853	+	2.04128i	0.0544776	+	0.0943580i
$469$	−7.52089	−	13.0266i	−0.347282	−	0.601511i
$470$	−5.04711	−	8.74184i	−0.232806	−	0.403231i
$471$	−11.7473	−	20.3469i	−0.541287	−	0.937537i
$472$	−38.8860			−1.78987
$473$	−14.7948			−0.680265
$474$	−9.26122	−	16.0409i	−0.425382	−	0.736783i
$475$	−3.14079	+	5.44001i	−0.144109	+	0.249605i
$476$	−3.38930	−	5.87044i	−0.155348	−	0.269071i
$477$	15.2682			0.699082
$478$	0.0327425	−	0.0567117i	0.00149761	−	0.00259393i
$479$	−12.9496			−0.591683			−0.295842	−	0.955237i	$-0.595600\pi$
$479$	−12.9496			−0.591683			−0.295842	+	0.955237i	$0.595600\pi$
$480$	−10.4092			−0.475111
$481$	−16.9560			−0.773126
$482$	−9.00981			−0.410385
$483$	−1.19356	+	2.06731i	−0.0543090	+	0.0940659i
$484$	−1.20594	−	2.08875i	−0.0548156	−	0.0949434i
$485$	−2.55896	+	4.43225i	−0.116196	+	0.201258i
$486$	−6.47919	−	11.2223i	−0.293902	−	0.509053i
$487$	20.0110	−	34.6601i	0.906786	−	1.57060i	0.0882834	−	0.996095i	$-0.471862\pi$
$487$	20.0110	−	34.6601i	0.906786	−	1.57060i	0.818502	−	0.574503i	$-0.194805\pi$
$488$	−19.6944	+	34.1118i	−0.891526	+	1.54417i
$489$	4.67887	−	8.10403i	0.211586	−	0.366477i
$490$	−2.47345	−	4.28414i	−0.111739	−	0.193538i
$491$	19.4715	+	33.7256i	0.878735	+	1.52201i	0.852730	+	0.522352i	$0.174945\pi$
$491$	19.4715	+	33.7256i	0.878735	+	1.52201i	0.0260047	+	0.999662i	$0.491722\pi$
$492$	−2.61759	+	4.53379i	−0.118010	+	0.204399i
$493$	9.42135	+	16.3182i	0.424316	+	0.734937i
$494$	−11.0988			−0.499361
$495$	1.95471	−	3.38565i	0.0878575	−	0.152174i
$496$	4.17320	−	7.22819i	0.187382	−	0.324556i
$497$	−6.83031			−0.306381
$498$	−1.30128	−	2.25388i	−0.0583117	−	0.100999i
$499$	−4.76165	+	8.24742i	−0.213161	+	0.369205i	−0.952702	−	0.303906i	$-0.901709\pi$
$499$	−4.76165	+	8.24742i	−0.213161	+	0.369205i	0.739541	+	0.673111i	$0.235042\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−18.3534	−	31.7890i	−0.819968	−	1.42023i
$502$	−7.90400	+	13.6901i	−0.352773	+	0.611020i
$503$	3.43979			0.153372			0.0766862	−	0.997055i	$-0.475566\pi$
$503$	3.43979			0.153372			0.0766862	+	0.997055i	$0.475566\pi$
$504$	2.86721	+	4.96615i	0.127716	+	0.221210i
$505$	−2.99149	−	5.18142i	−0.133120	−	0.230570i
$506$	−2.34516			−0.104255
$507$	10.2823	+	17.8094i	0.456652	+	0.790945i
$508$	11.2285	−	19.4483i	0.498183	−	0.862879i
$509$	−15.4960	−	26.8399i	−0.686850	−	1.18966i	−0.972852	−	0.231429i	$-0.925660\pi$
$509$	−15.4960	−	26.8399i	−0.686850	−	1.18966i	0.286002	−	0.958229i	$-0.407674\pi$
$510$	−9.84872			−0.436109
$511$	−7.76906	−	13.4564i	−0.343683	−	0.595276i
$512$	11.0000			0.486136
$513$	−21.7863			−0.961890
$514$	9.78744	−	16.9523i	0.431705	−	0.747736i
$515$	6.48814	−	11.2378i	0.285902	−	0.495196i
$516$	5.25503	+	9.10198i	0.231340	+	0.400692i
$517$	29.5816			1.30100
$518$	−13.7505			−0.604164
$519$	−1.87605	+	3.24942i	−0.0823495	+	0.142634i
$520$	5.30066			0.232449
$521$	−8.88709			−0.389351			−0.194675	−	0.980868i	$-0.562365\pi$
$521$	−8.88709			−0.389351			−0.194675	+	0.980868i	$0.562365\pi$
$522$	−2.65669	−	4.60153i	−0.116280	−	0.201403i
$523$	36.9711			1.61663			0.808316	−	0.588748i	$-0.200379\pi$
$523$	36.9711			1.61663			0.808316	+	0.588748i	$0.200379\pi$
$524$	−5.18034	+	8.97262i	−0.226304	+	0.391971i
$525$	−2.98299			−0.130188
$526$	20.3248			0.886201
$527$	−19.7426	+	34.1951i	−0.859999	+	1.48956i
$528$	−3.05045	+	5.28354i	−0.132754	+	0.229937i
$529$	11.1798	−	19.3640i	0.486078	−	0.841912i
$530$	5.72262	−	9.91187i	0.248575	−	0.430544i
$531$	−17.2916			−0.750391
$532$	9.00067			0.390228
$533$	2.22159	−	3.84791i	0.0962278	−	0.166672i
$534$	15.6701			0.678112
$535$	4.84735	+	8.39586i	0.209569	+	0.362985i
$536$	−31.4930			−1.36029
$537$	−10.3340			−0.445946
$538$	2.86676	−	4.96538i	0.123595	−	0.214073i
$539$	14.4971			0.624435
$540$	3.46829			0.149251
$541$	16.6460	+	28.8318i	0.715669	+	1.23957i	0.962701	+	0.270567i	$0.0872113\pi$
$541$	16.6460	+	28.8318i	0.715669	+	1.23957i	−0.247032	+	0.969007i	$0.579455\pi$
$542$	−16.3168	+	28.2616i	−0.700868	+	1.21394i
$543$	11.2502	−	19.4859i	0.482793	−	0.836221i
$544$	−23.6540			−1.01416
$545$	12.6954			0.543810
$546$	−2.63530	−	4.56447i	−0.112780	−	0.195341i
$547$	31.1850			1.33338			0.666688	−	0.745337i	$-0.267712\pi$
$547$	31.1850			1.33338			0.666688	+	0.745337i	$0.267712\pi$
$548$	−1.05793	−	1.83239i	−0.0451925	−	0.0782758i
$549$	−8.75760	+	15.1686i	−0.373765	+	0.647380i
$550$	−1.46527	−	2.53793i	−0.0624795	−	0.108218i
$551$	−25.0195			−1.06586
$552$	2.49897	+	4.32834i	0.106363	+	0.184226i
$553$	−6.37424	−	11.0405i	−0.271060	−	0.469490i
$554$	−9.81330			−0.416927
$555$	9.98918	−	17.3018i	0.424017	−	0.734419i
$556$	10.4020	+	18.0168i	0.441144	+	0.764083i
$557$	12.7452	−	22.0754i	0.540033	−	0.935365i	−0.458868	−	0.888504i	$-0.651745\pi$
$557$	12.7452	−	22.0754i	0.540033	−	0.935365i	0.998901	−	0.0468604i	$-0.0149216\pi$
$558$	5.56713	−	9.64256i	0.235676	−	0.408202i
$559$	−4.46004	−	7.72501i	−0.188639	−	0.326733i
$560$	1.43287			0.0605496
$561$	14.4311	−	24.9954i	0.609280	−	1.05530i
$562$	7.43055	−	12.8701i	0.313439	−	0.542892i
$563$	−5.24086			−0.220876			−0.110438	−	0.993883i	$-0.535225\pi$
$563$	−5.24086			−0.220876			−0.110438	+	0.993883i	$0.535225\pi$
$564$	−10.5072	−	18.1990i	−0.442434	−	0.766318i
$565$	4.18137	−	7.24235i	0.175912	−	0.304688i
$566$	10.3552	+	17.9358i	0.435263	+	0.753898i
$567$	−8.04014	−	13.9259i	−0.337654	−	0.584834i
$568$	−7.15033	+	12.3847i	−0.300021	+	0.519652i
$569$	−4.20259	+	7.27911i	−0.176182	+	0.305156i	−0.940570	−	0.339601i	$-0.889708\pi$
$569$	−4.20259	+	7.27911i	−0.176182	+	0.305156i	0.764388	+	0.644757i	$0.223041\pi$
$570$	6.53860	−	11.3252i	0.273872	−	0.474360i
$571$	2.80610	+	4.86031i	0.117432	+	0.203398i	0.918749	−	0.394842i	$-0.129201\pi$
$571$	2.80610	+	4.86031i	0.117432	+	0.203398i	−0.801317	+	0.598239i	$0.795867\pi$
$572$	−2.58897	+	4.48423i	−0.108250	+	0.187495i
$573$	−23.0132	−	39.8601i	−0.961392	−	1.66518i
$574$	1.80161	−	3.12048i	0.0751978	−	0.130246i
$575$	−0.800247			−0.0333726
$576$	9.33814			0.389089
$577$	−38.2146			−1.59089			−0.795447	−	0.606024i	$-0.792764\pi$
$577$	−38.2146			−1.59089			−0.795447	+	0.606024i	$0.792764\pi$
$578$	−5.38043			−0.223796
$579$	9.62592	−	16.6726i	0.400040	−	0.692889i
$580$	3.98299			0.165384
$581$	−0.895633	−	1.55128i	−0.0371571	−	0.0643580i
$582$	5.32732	−	9.22720i	0.220825	−	0.382480i
$583$	16.7704	+	29.0472i	0.694560	+	1.20301i
$584$	−32.5322			−1.34619
$585$	2.35706			0.0974525
$586$	12.1398	+	21.0268i	0.501492	+	0.868610i
$587$	18.0732	+	31.3038i	0.745962	+	1.29204i	0.949744	+	0.313028i	$0.101343\pi$
$587$	18.0732	+	31.3038i	0.745962	+	1.29204i	−0.203782	+	0.979016i	$0.565323\pi$
$588$	−5.14930	−	8.91885i	−0.212354	−	0.367807i
$589$	−26.2143	−	45.4045i	−1.08014	−	1.87086i
$590$	−6.48100	+	11.2254i	−0.266819	+	0.462143i
$591$	−13.1595	+	22.7930i	−0.541311	+	0.937578i
$592$	−4.79826	+	8.31084i	−0.197207	+	0.341573i
$593$	−16.5319	−	28.6341i	−0.678884	−	1.17586i	−0.975317	−	0.220808i	$-0.929131\pi$
$593$	−16.5319	−	28.6341i	−0.678884	−	1.17586i	0.296434	−	0.955053i	$-0.404203\pi$
$594$	5.08199	−	8.80227i	0.208517	−	0.361162i
$595$	−6.77860			−0.277895
$596$	−1.51933			−0.0622343
$597$	−8.32534	−	14.4199i	−0.340734	−	0.590168i
$598$	−0.706973	−	1.22451i	−0.0289103	−	0.0500741i
$599$	−3.72031	−	6.44376i	−0.152008	−	0.263285i	0.779958	−	0.625832i	$-0.215240\pi$
$599$	−3.72031	−	6.44376i	−0.152008	−	0.263285i	−0.931965	+	0.362547i	$0.881907\pi$
$600$	−3.12275	+	5.40876i	−0.127486	+	0.220812i
$601$	−10.6366			−0.433875			−0.216938	−	0.976185i	$-0.569607\pi$
$601$	−10.6366			−0.433875			−0.216938	+	0.976185i	$0.569607\pi$
$602$	−3.61689	−	6.26464i	−0.147413	−	0.255328i
$603$	−14.0041			−0.570292
$604$	4.25598	−	11.5276i	0.173174	−	0.469053i
$605$	−2.41189			−0.0980571
$606$	6.22778	+	10.7868i	0.252986	+	0.438185i
$607$	−28.7719			−1.16782			−0.583908	−	0.811820i	$-0.698477\pi$
$607$	−28.7719			−1.16782			−0.583908	+	0.811820i	$0.698477\pi$
$608$	15.7040	−	27.2001i	0.636880	−	1.10311i
$609$	−5.94059	−	10.2894i	−0.240725	−	0.416948i
$610$	6.56482	+	11.3706i	0.265802	+	0.460382i
$611$	8.91766	+	15.4458i	0.360770	+	0.624872i
$612$	−6.31098			−0.255106
$613$	42.7897			1.72826			0.864131	−	0.503268i	$-0.167869\pi$
$613$	42.7897			1.72826			0.864131	+	0.503268i	$0.167869\pi$
$614$	1.03344	−	1.78997i	0.0417062	−	0.0722372i
$615$	2.61759	+	4.53379i	0.105551	+	0.182820i
$616$	−6.29863	+	10.9095i	−0.253779	+	0.439558i
$617$	−3.64543	+	6.31406i	−0.146759	+	0.254195i	−0.930028	−	0.367489i	$-0.880218\pi$
$617$	−3.64543	+	6.31406i	−0.146759	+	0.254195i	0.783269	+	0.621683i	$0.213551\pi$
$618$	−13.5072	+	23.3952i	−0.543340	+	0.941093i
$619$	−20.0805	−	34.7805i	−0.807105	−	1.39795i	−0.914861	−	0.403770i	$-0.867700\pi$
$619$	−20.0805	−	34.7805i	−0.807105	−	1.39795i	0.107755	−	0.994177i	$-0.465634\pi$
$620$	4.17320	+	7.22819i	0.167600	+	0.290291i
$621$	−1.38774	−	2.40364i	−0.0556883	−	0.0964549i
$622$	13.7033	+	23.7348i	0.549452	+	0.951679i
$623$	10.7853			0.432104
$624$	−3.67836			−0.147252
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.16701	+	3.75337i	−0.0866111	+	0.150015i
$627$	19.1617	+	33.1890i	0.765244	+	1.32544i
$628$	−11.2856			−0.450342
$629$	22.6996	−	39.3169i	0.905093	−	1.56767i
$630$	1.91147			0.0761549
$631$	27.7228			1.10363			0.551813	−	0.833968i	$-0.313936\pi$
$631$	27.7228			1.10363			0.551813	+	0.833968i	$0.313936\pi$
$632$	−26.6916			−1.06173
$633$	17.3744			0.690570
$634$	1.64149	−	2.84314i	0.0651918	−	0.112916i
$635$	−11.2285	−	19.4483i	−0.445589	−	0.771782i
$636$	11.9135	−	20.6348i	0.472402	−	0.818225i
$637$	4.37030	+	7.56958i	0.173158	+	0.299918i
$638$	5.83617	−	10.1085i	0.231056	−	0.400201i
$639$	−3.17956	+	5.50716i	−0.125782	+	0.217860i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−3.80350	−	6.58786i	−0.150229	−	0.260205i	0.781082	−	0.624428i	$-0.214668\pi$
$641$	−3.80350	−	6.58786i	−0.150229	−	0.260205i	−0.931312	+	0.364223i	$0.881335\pi$
$642$	−10.0914	−	17.4788i	−0.398275	−	0.689832i
$643$	−25.0290	+	43.3514i	−0.987046	+	1.70961i	−0.354580	+	0.935026i	$0.615376\pi$
$643$	−25.0290	+	43.3514i	−0.987046	+	1.70961i	−0.632466	+	0.774588i	$0.717957\pi$
$644$	0.573324	+	0.993026i	0.0225921	+	0.0391307i
$645$	10.5101			0.413833
$646$	14.8584	−	25.7356i	0.584598	−	1.01255i
$647$	−16.0192	+	27.7460i	−0.629779	+	1.09081i	0.357817	+	0.933792i	$0.383521\pi$
$647$	−16.0192	+	27.7460i	−0.629779	+	1.09081i	−0.987596	+	0.157018i	$0.949812\pi$
$648$	−33.6674			−1.32258
$649$	−18.9929	−	32.8967i	−0.745536	−	1.29131i
$650$	0.883443	−	1.53017i	0.0346515	−	0.0600182i
$651$	12.4486	−	21.5616i	0.487899	−	0.845066i
$652$	−2.24748	−	3.89274i	−0.0880180	−	0.152452i
$653$	−10.2946	+	17.8307i	−0.402858	+	0.697771i	−0.994070	−	0.108746i	$-0.965317\pi$
$653$	−10.2946	+	17.8307i	−0.402858	+	0.697771i	0.591211	+	0.806517i	$0.298650\pi$
$654$	−26.4296			−1.03348
$655$	5.18034	+	8.97262i	0.202413	+	0.350589i
$656$	−1.25735	−	2.17779i	−0.0490912	−	0.0850285i
$657$	−14.4662			−0.564381
$658$	7.23183	+	12.5259i	0.281926	+	0.488310i
$659$	0.893505	−	1.54760i	0.0348060	−	0.0602858i	−0.848098	−	0.529840i	$-0.822252\pi$
$659$	0.893505	−	1.54760i	0.0348060	−	0.0602858i	0.882904	+	0.469554i	$0.155585\pi$
$660$	−3.05045	−	5.28354i	−0.118739	−	0.205662i
$661$	2.97763			0.115816			0.0579081	−	0.998322i	$-0.481557\pi$
$661$	2.97763			0.115816			0.0579081	+	0.998322i	$0.481557\pi$
$662$	0.820610	+	1.42134i	0.0318939	+	0.0552419i
$663$	17.4016			0.675821
$664$	−3.75038			−0.145543
$665$	4.50033	−	7.79481i	0.174515	−	0.302270i
$666$	−6.40098	+	11.0868i	−0.248033	+	0.429606i
$667$	−1.59369	−	2.76035i	−0.0617078	−	0.106881i
$668$	−17.6320			−0.682201
$669$	8.80694			0.340496
$670$	−5.24884	+	9.09126i	−0.202780	+	0.351226i
$671$	−38.4770			−1.48539
$672$	14.9149			0.575356
$673$	−4.51470	−	7.81968i	−0.174029	−	0.301427i	0.765796	−	0.643084i	$-0.222345\pi$
$673$	−4.51470	−	7.81968i	−0.174029	−	0.301427i	−0.939825	+	0.341657i	$0.889012\pi$
$674$	10.2429			0.394542
$675$	1.73414	−	3.00363i	0.0667472	−	0.115610i
$676$	9.87811			0.379927
$677$	11.5324			0.443228			0.221614	−	0.975135i	$-0.428868\pi$
$677$	11.5324			0.443228			0.221614	+	0.975135i	$0.428868\pi$
$678$	−8.70491	+	15.0773i	−0.334310	+	0.579042i
$679$	3.66665	−	6.35082i	0.140713	−	0.243722i
$680$	−7.09619	+	12.2910i	−0.272127	+	0.471337i
$681$	23.2013	−	40.1858i	0.889076	−	1.53992i
$682$	24.4595			0.936604
$683$	−2.28637			−0.0874857			−0.0437429	−	0.999043i	$-0.513928\pi$
$683$	−2.28637			−0.0874857			−0.0437429	+	0.999043i	$0.513928\pi$
$684$	4.18988	−	7.25709i	0.160204	−	0.277482i
$685$	−2.11586			−0.0808429
$686$	8.55915	+	14.8249i	0.326790	+	0.566017i
$687$	45.2617			1.72684
$688$	−5.04847			−0.192471
$689$	−10.1112	+	17.5132i	−0.385207	+	0.667198i
$690$	1.66598			0.0634228
$691$	−39.8185			−1.51477			−0.757383	−	0.652971i	$-0.773522\pi$
$691$	−39.8185			−1.51477			−0.757383	+	0.652971i	$0.773522\pi$
$692$	0.901154	+	1.56084i	0.0342567	+	0.0593344i
$693$	−2.80083	+	4.85118i	−0.106395	+	0.184281i
$694$	6.61354	−	11.4550i	0.251047	−	0.434826i
$695$	20.8040			0.789142
$696$	−24.8757			−0.942911
$697$	5.94826	+	10.3027i	0.225306	+	0.390242i
$698$	1.18737			0.0449427
$699$	6.77642	+	11.7371i	0.256308	+	0.443938i
$700$	−0.716433	+	1.24090i	−0.0270786	+	0.0469016i
$701$	−1.68341	−	2.91575i	−0.0635814	−	0.110126i	0.832482	−	0.554051i	$-0.186919\pi$
$701$	−1.68341	−	2.91575i	−0.0635814	−	0.110126i	−0.896064	+	0.443925i	$0.853586\pi$
$702$	6.12807			0.231289
$703$	30.1407	+	52.2052i	1.13678	+	1.96896i
$704$	10.2569	+	17.7655i	0.386572	+	0.669563i
$705$	−21.0144			−0.791450
$706$	−6.54280	+	11.3325i	−0.246242	+	0.426503i
$707$	4.28641	+	7.42428i	0.161207	+	0.279219i
$708$	−13.4924	+	23.3694i	−0.507074	+	0.878277i
$709$	18.2030	−	31.5285i	0.683628	−	1.18408i	−0.290238	−	0.956955i	$-0.593734\pi$
$709$	18.2030	−	31.5285i	0.683628	−	1.18408i	0.973866	−	0.227124i	$-0.0729324\pi$
$710$	2.38344	+	4.12824i	0.0894490	+	0.154930i
$711$	−11.8690			−0.445123
$712$	11.2906	−	19.5559i	0.423134	−	0.732889i
$713$	3.33959	−	5.78434i	0.125069	−	0.216625i
$714$	14.1119			0.528124
$715$	2.58897	+	4.48423i	0.0968221	+	0.167701i
$716$	−2.48195	+	4.29887i	−0.0927550	+	0.160656i
$717$	−0.0681644	−	0.118064i	−0.00254565	−	0.00440919i
$718$	−15.9358	−	27.6016i	−0.594718	−	1.03008i
$719$	10.4054	−	18.0226i	0.388054	−	0.672130i	−0.604133	−	0.796883i	$-0.706481\pi$
$719$	10.4054	−	18.0226i	0.388054	−	0.672130i	0.992188	+	0.124753i	$0.0398139\pi$
$720$	0.667010	−	1.15530i	0.0248580	−	0.0430553i
$721$	−9.29664	+	16.1023i	−0.346225	+	0.599679i
$722$	10.2291	+	17.7174i	0.380689	+	0.659373i
$723$	−9.37845	+	16.2439i	−0.348788	+	0.604119i
$724$	−5.40400	−	9.36000i	−0.200838	−	0.347861i
$725$	1.99149	−	3.44937i	0.0739622	−	0.128106i
$726$	5.02114			0.186352
$727$	24.7884			0.919351			0.459675	−	0.888087i	$-0.347966\pi$
$727$	24.7884			0.919351			0.459675	+	0.888087i	$0.347966\pi$
$728$	−7.59514			−0.281494
$729$	6.69019			0.247785
$730$	−5.42204	+	9.39125i	−0.200679	+	0.347586i
$731$	23.8833			0.883355
$732$	13.6668	+	23.6717i	0.505141	+	0.874930i
$733$	4.63806	−	8.03336i	0.171311	−	0.296719i	−0.767568	−	0.640968i	$-0.778533\pi$
$733$	4.63806	−	8.03336i	0.171311	−	0.296719i	0.938878	+	0.344249i	$0.111866\pi$
$734$	0.0674682	+	0.116858i	0.00249030	+	0.00431332i
$735$	−10.2986			−0.379870
$736$	4.00124			0.147488
$737$	−15.3820	−	26.6424i	−0.566603	−	0.981385i
$738$	−1.67733	−	2.90522i	−0.0617433	−	0.106943i
$739$	−8.74925	−	15.1542i	−0.321846	−	0.557454i	0.659023	−	0.752123i	$-0.270970\pi$
$739$	−8.74925	−	15.1542i	−0.321846	−	0.557454i	−0.980869	+	0.194669i	$0.937637\pi$
$740$	−4.79826	−	8.31084i	−0.176388	−	0.305512i
$741$	−11.5530	+	20.0103i	−0.424409	+	0.735097i
$742$	−8.19975	+	14.2024i	−0.301022	+	0.521386i
$743$	3.50170	−	6.06512i	0.128465	−	0.222508i	−0.794617	−	0.607111i	$-0.792328\pi$
$743$	3.50170	−	6.06512i	0.128465	−	0.222508i	0.923082	+	0.384603i	$0.125662\pi$
$744$	−26.0637	−	45.1436i	−0.955541	−	1.65505i
$745$	−0.759666	+	1.31578i	−0.0278320	+	0.0482065i
$746$	−28.1380			−1.03021
$747$	−1.66770			−0.0610178
$748$	−6.93191	−	12.0064i	−0.253456	−	0.438998i
$749$	−6.94561	−	12.0301i	−0.253787	−	0.439572i
$750$	1.04092	+	1.80292i	0.0380089	+	0.0658333i
$751$	−16.1994	+	28.0582i	−0.591125	+	1.02386i	0.402956	+	0.915219i	$0.367983\pi$
$751$	−16.1994	+	28.0582i	−0.591125	+	1.02386i	−0.994081	+	0.108639i	$0.965351\pi$
$752$	10.0942			0.368098
$753$	16.4548	+	28.5005i	0.599646	+	1.03862i
$754$	7.03748			0.256290
$755$	−7.85524	−	9.44961i	−0.285882	−	0.343907i
$756$	−4.96959			−0.180742
$757$	−10.5707	−	18.3089i	−0.384198	−	0.665450i	0.607460	−	0.794350i	$-0.292189\pi$
$757$	−10.5707	−	18.3089i	−0.384198	−	0.665450i	−0.991658	+	0.128901i	$0.958855\pi$
$758$	−32.4236			−1.17768
$759$	−2.44112	+	4.22814i	−0.0886069	+	0.153472i
$760$	−9.42238	−	16.3200i	−0.341785	−	0.591990i
$761$	2.45153	+	4.24617i	0.0888679	+	0.153924i	0.907033	−	0.421060i	$-0.138342\pi$
$761$	2.45153	+	4.24617i	0.0888679	+	0.153924i	−0.818165	+	0.574984i	$0.805008\pi$
$762$	23.3758	+	40.4881i	0.846816	+	1.46673i
$763$	−18.1908			−0.658550
$764$	−22.1087			−0.799863
$765$	−3.15549	+	5.46547i	−0.114087	+	0.197604i
$766$	17.0976	+	29.6138i	0.617760	+	1.06999i
$767$	11.4512	−	19.8341i	0.413479	−	0.716166i
$768$	17.6956	−	30.6496i	0.638534	−	1.10597i
$769$	12.5874	−	21.8020i	0.453913	−	0.786201i	−0.544712	−	0.838623i	$-0.683361\pi$
$769$	12.5874	−	21.8020i	0.453913	−	0.786201i	0.998625	+	0.0524224i	$0.0166942\pi$
$770$	2.09954	+	3.63651i	0.0756622	+	0.131051i
$771$	−20.3758	−	35.2919i	−0.733816	−	1.27101i
$772$	−4.62378	−	8.00862i	−0.166413	−	0.288236i
$773$	−9.97283	−	17.2734i	−0.358698	−	0.621283i	0.629046	−	0.777368i	$-0.283446\pi$
$773$	−9.97283	−	17.2734i	−0.358698	−	0.621283i	−0.987744	+	0.156086i	$0.950112\pi$
$774$	−6.73476			−0.242076
$775$	8.34640			0.299812
$776$	−7.67688	−	13.2968i	−0.275584	−	0.477326i
$777$	−14.3132	+	24.7911i	−0.513481	+	0.889376i
$778$	0.997682	+	1.72804i	0.0357686	+	0.0619531i
$779$	−15.7963			−0.565960
$780$	1.83918	−	3.18555i	0.0658532	−	0.114061i
$781$	−13.9696			−0.499871
$782$	3.78581			0.135380
$783$	13.8141			0.493677
$784$	4.94689			0.176675
$785$	−5.64278	+	9.77357i	−0.201399	+	0.348834i
$786$	−10.7846	−	18.6795i	−0.384674	−	0.666275i
$787$	0.441708	−	0.765061i	0.0157452	−	0.0272715i	−0.858045	−	0.513574i	$-0.828321\pi$
$787$	0.441708	−	0.765061i	0.0157452	−	0.0272715i	0.873791	+	0.486302i	$0.161655\pi$
$788$	6.32113	+	10.9485i	0.225181	+	0.390025i
$789$	21.1563	−	36.6439i	0.753186	−	1.30456i
$790$	−4.44859	+	7.70519i	−0.158274	+	0.274138i
$791$	−5.99135	+	10.3773i	−0.213028	+	0.368975i
$792$	5.86412	+	10.1569i	0.208372	+	0.360911i
$793$	−11.5993	−	20.0906i	−0.411903	−	0.713436i
$794$	1.83572	−	3.17956i	0.0651473	−	0.112838i
$795$	−11.9135	−	20.6348i	−0.422530	−	0.731843i
$796$	−7.99809			−0.283485
$797$	−17.9463	+	31.0839i	−0.635690	+	1.10105i	0.350679	+	0.936496i	$0.385951\pi$
$797$	−17.9463	+	31.0839i	−0.635690	+	1.10105i	−0.986369	+	0.164551i	$0.947382\pi$
$798$	−9.36894	+	16.2275i	−0.331657	+	0.574446i
$799$	−47.7536			−1.68940
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	5.02064	−	8.69600i	0.177395	−	0.307258i
$802$	−5.51635	+	9.55459i	−0.194789	+	0.337384i
$803$	−15.8896	−	27.5215i	−0.560730	−	0.971213i
$804$	−10.9272	+	18.9265i	−0.385373	+	0.667485i
$805$	1.14665			0.0404140
$806$	7.37357	+	12.7714i	0.259723	+	0.449853i
$807$	−5.96812	−	10.3371i	−0.210088	−	0.363882i
$808$	17.9490			0.631442
$809$	11.5913	+	20.0767i	0.407528	+	0.705858i	0.994612	−	0.103667i	$-0.0330577\pi$
$809$	11.5913	+	20.0767i	0.407528	+	0.705858i	−0.587085	+	0.809526i	$0.699724\pi$
$810$	−5.61123	+	9.71893i	−0.197158	+	0.341488i
$811$	−20.9671	−	36.3161i	−0.736254	−	1.27523i	−0.954171	−	0.299262i	$-0.903260\pi$
$811$	−20.9671	−	36.3161i	−0.736254	−	1.27523i	0.217917	−	0.975967i	$-0.430074\pi$
$812$	−5.70708			−0.200279
$813$	33.9689	+	58.8358i	1.19134	+	2.06346i
$814$	−28.1231			−0.985714
$815$	−4.49495			−0.157451
$816$	4.92436	−	8.52924i	0.172387	−	0.298583i
$817$	−15.8562	+	27.4637i	−0.554738	+	0.960834i
$818$	0.929518	+	1.60997i	0.0324998	+	0.0562914i
$819$	−3.37736			−0.118014
$820$	2.51470			0.0878170
$821$	−2.61725	+	4.53321i	−0.0913428	+	0.158210i	−0.908076	−	0.418805i	$-0.862449\pi$
$821$	−2.61725	+	4.53321i	−0.0913428	+	0.158210i	0.816734	+	0.577015i	$0.195783\pi$
$822$	4.40486			0.153637
$823$	40.8812			1.42503			0.712515	−	0.701657i	$-0.247556\pi$
$823$	40.8812			1.42503			0.712515	+	0.701657i	$0.247556\pi$
$824$	19.4644	+	33.7134i	0.678076	+	1.17446i
$825$	−6.10091			−0.212406
$826$	9.28641	−	16.0845i	0.323115	−	0.559652i
$827$	−15.9895			−0.556009			−0.278005	−	0.960580i	$-0.589673\pi$
$827$	−15.9895			−0.556009			−0.278005	+	0.960580i	$0.589673\pi$
$828$	1.06755			0.0370998
$829$	15.4626	−	26.7820i	0.537039	−	0.930179i	−0.462023	−	0.886868i	$-0.652876\pi$
$829$	15.4626	−	26.7820i	0.537039	−	0.930179i	0.999062	−	0.0433108i	$-0.0137906\pi$
$830$	−0.625064	+	1.08264i	−0.0216963	+	0.0375791i
$831$	−10.2148	+	17.6926i	−0.354348	+	0.613749i
$832$	−6.18410	+	10.7112i	−0.214395	+	0.371343i
$833$	−23.4027			−0.810857
$834$	−43.3105			−1.49972
$835$	−8.81598	+	15.2697i	−0.305089	+	0.528430i
$836$	18.4085			0.636671
$837$	14.4739	+	25.0695i	0.500290	+	0.866527i
$838$	5.21213			0.180050
$839$	15.4107			0.532037			0.266018	−	0.963968i	$-0.414292\pi$
$839$	15.4107			0.532037			0.266018	+	0.963968i	$0.414292\pi$
$840$	4.47448	−	7.75002i	0.154384	−	0.267401i
$841$	−13.1358			−0.452960
$842$	−19.4229			−0.669358
$843$	−15.4691	−	26.7933i	−0.532786	−	0.922812i
$844$	4.17287	−	7.22762i	0.143636	−	0.248785i
$845$	4.93906	−	8.55470i	0.169909	−	0.294290i
$846$	13.4659			0.462967
$847$	3.45591			0.118746
$848$	5.72262	+	9.91187i	0.196516	+	0.340375i
$849$	43.1157			1.47973
$850$	2.36540	+	4.09699i	0.0811325	+	0.140526i
$851$	−3.83980	+	6.65072i	−0.131627	+	0.227984i
$852$	4.96193	+	8.59431i	0.169993	+	0.294436i
$853$	−11.2830			−0.386322			−0.193161	−	0.981167i	$-0.561874\pi$
$853$	−11.2830			−0.386322			−0.193161	+	0.981167i	$0.561874\pi$
$854$	−9.40650	−	16.2925i	−0.321884	−	0.557519i
$855$	−4.18988	−	7.25709i	−0.143291	−	0.248187i
$856$	−29.0841			−0.994075
$857$	14.4508	−	25.0295i	0.493631	−	0.854993i	−0.506343	−	0.862332i	$-0.669003\pi$
$857$	14.4508	−	25.0295i	0.493631	−	0.854993i	0.999973	+	0.00733930i	$0.00233619\pi$
$858$	−5.38981	−	9.33542i	−0.184005	−	0.318706i
$859$	−25.0087	+	43.3163i	−0.853286	+	1.47793i	0.0249406	+	0.999689i	$0.492060\pi$
$859$	−25.0087	+	43.3163i	−0.853286	+	1.47793i	−0.878226	+	0.478245i	$0.841273\pi$
$860$	2.52424	−	4.37210i	0.0860757	−	0.149087i
$861$	−3.75065	−	6.49632i	−0.127822	−	0.221394i
$862$	−26.4100			−0.899527
$863$	−21.5135	+	37.2625i	−0.732329	+	1.26843i	0.223557	+	0.974691i	$0.428233\pi$
$863$	−21.5135	+	37.2625i	−0.732329	+	1.26843i	−0.955885	+	0.293740i	$0.905100\pi$
$864$	−8.67072	+	15.0181i	−0.294984	+	0.510927i
$865$	1.80231			0.0612803
$866$	5.91953	+	10.2529i	0.201154	+	0.348409i
$867$	−5.60057	+	9.70048i	−0.190205	+	0.329445i
$868$	−5.97964	−	10.3570i	−0.202962	−	0.351541i
$869$	−13.0368	−	22.5804i	−0.442244	−	0.765989i
$870$	−4.14595	+	7.18100i	−0.140561	+	0.243459i
$871$	9.27411	−	16.0632i	0.314241	−	0.544282i
$872$	−19.0431	+	32.9835i	−0.644879	+	1.11696i
$873$	−3.41371	−	5.91271i	−0.115536	−	0.200115i
$874$	−2.51341	+	4.35335i	−0.0850174	+	0.147254i
$875$	0.716433	+	1.24090i	0.0242199	+	0.0419500i
$876$	−11.2878	+	19.5510i	−0.381379	+	0.660567i
$877$	50.0114			1.68876			0.844382	−	0.535742i	$-0.179968\pi$
$877$	50.0114			1.68876			0.844382	+	0.535742i	$0.179968\pi$
$878$	−26.4100			−0.891294
$879$	50.5462			1.70488
$880$	2.93055			0.0987888
$881$	28.2226	−	48.8829i	0.950842	−	1.64691i	0.207234	−	0.978291i	$-0.433554\pi$
$881$	28.2226	−	48.8829i	0.950842	−	1.64691i	0.743608	−	0.668615i	$-0.233113\pi$
$882$	6.59926			0.222209
$883$	−10.3900	−	17.9960i	−0.349650	−	0.605612i	0.636537	−	0.771246i	$-0.280366\pi$
$883$	−10.3900	−	17.9960i	−0.349650	−	0.605612i	−0.986187	+	0.165634i	$0.947033\pi$
$884$	4.17939	−	7.23892i	0.140568	−	0.243471i
$885$	13.4924	+	23.3694i	0.453540	+	0.785555i
$886$	19.8800			0.667882
$887$	54.3838			1.82603			0.913014	−	0.407928i	$-0.133749\pi$
$887$	54.3838			1.82603			0.913014	+	0.407928i	$0.133749\pi$
$888$	29.9675	+	51.9053i	1.00564	+	1.74183i
$889$	16.0889	+	27.8668i	0.539605	+	0.934623i
$890$	−3.76354	−	6.51864i	−0.126154	−	0.218505i
$891$	−16.4440	−	28.4818i	−0.550894	−	0.954176i
$892$	2.11519	−	3.66362i	0.0708219	−	0.122667i
$893$	31.7038	−	54.9126i	1.06093	−	1.83758i
$894$	1.58150	−	2.73923i	0.0528932	−	0.0916136i
$895$	2.48195	+	4.29887i	0.0829626	+	0.143695i
$896$	2.14930	−	3.72270i	0.0718030	−	0.124367i
$897$	−2.94360			−0.0982838
$898$	−0.0811622			−0.00270842
$899$	16.6218	+	28.7898i	0.554368	+	0.960193i
$900$	0.667010	+	1.15530i	0.0222337	+	0.0385099i
$901$	−27.0726	−	46.8911i	−0.901918	−	1.56217i
$902$	3.68472	−	6.38212i	0.122688	−	0.212501i
$903$	−15.0595			−0.501149
$904$	12.5441	+	21.7271i	0.417211	+	0.722631i
$905$	−10.8080			−0.359270
$906$	16.3533	+	19.6725i	0.543302	+	0.653575i
$907$	−24.4819			−0.812907			−0.406454	−	0.913671i	$-0.633235\pi$
$907$	−24.4819			−0.812907			−0.406454	+	0.913671i	$0.633235\pi$
$908$	−11.1447	−	19.3031i	−0.369849	−	0.640597i
$909$	7.98142			0.264727
$910$	−1.26586	+	2.19253i	−0.0419627	+	0.0726816i
$911$	−10.3286	−	17.8897i	−0.342202	−	0.592712i	0.642639	−	0.766169i	$-0.277839\pi$
$911$	−10.3286	−	17.8897i	−0.342202	−	0.592712i	−0.984841	+	0.173457i	$0.944506\pi$
$912$	6.53860	+	11.3252i	0.216515	+	0.375014i
$913$	−1.83178	−	3.17274i	−0.0606231	−	0.105002i
$914$	11.2476			0.372036
$915$	27.3337			0.903623
$916$	10.8706	−	18.8285i	0.359176	−	0.622111i
$917$	−7.42274	−	12.8566i	−0.245120	−	0.424561i
$918$	−8.20388	+	14.2095i	−0.270768	+	0.468985i
$919$	−11.9469	+	20.6926i	−0.394092	+	0.682587i	−0.992985	−	0.118242i	$-0.962274\pi$
$919$	−11.9469	+	20.6926i	−0.394092	+	0.682587i	0.598893	+	0.800829i	$0.295607\pi$
$920$	1.20037	−	2.07910i	0.0395751	−	0.0685460i
$921$	−2.15144	−	3.72641i	−0.0708925	−	0.122789i
$922$	−2.81762	−	4.88027i	−0.0927935	−	0.160723i
$923$	−4.21127	−	7.29414i	−0.138616	−	0.240090i
$924$	4.37089	+	7.57061i	0.143792	+	0.249055i
$925$	−9.59653			−0.315532
$926$	11.6129			0.381623
$927$	8.65532	+	14.9914i	0.284278	+	0.492384i
$928$	−9.95746	+	17.2468i	−0.326870	+	0.566155i
$929$	9.27659	+	16.0675i	0.304355	+	0.527158i	0.977117	−	0.212700i	$-0.0682258\pi$
$929$	9.27659	+	16.0675i	0.304355	+	0.527158i	−0.672763	+	0.739858i	$0.734892\pi$
$930$	−17.3758			−0.569775
$931$	15.5372	−	26.9112i	0.509210	−	0.881978i
$932$	6.51006			0.213244
$933$	57.0559			1.86793
$934$	−5.67268			−0.185616
$935$	−13.8638			−0.453396
$936$	−3.53559	+	6.12383i	−0.115565	+	0.200164i
$937$	5.60349	+	9.70553i	0.183058	+	0.317066i	0.942920	−	0.333018i	$-0.108067\pi$
$937$	5.60349	+	9.70553i	0.183058	+	0.317066i	−0.759862	+	0.650084i	$0.774734\pi$
$938$	7.52089	−	13.0266i	0.245566	−	0.425332i
$939$	4.51135	+	7.81389i	0.147222	+	0.254997i
$940$	−5.04711	+	8.74184i	−0.164618	+	0.285127i
$941$	5.49598	−	9.51932i	0.179164	−	0.310321i	−0.762430	−	0.647070i	$-0.775994\pi$
$941$	5.49598	−	9.51932i	0.179164	−	0.310321i	0.941594	+	0.336749i	$0.109327\pi$
$942$	11.7473	−	20.3469i	0.382748	−	0.662939i
$943$	−1.00619	−	1.74277i	−0.0327660	−	0.0567525i
$944$	−6.48100	−	11.2254i	−0.210939	−	0.365356i
$945$	−2.48480	+	4.30379i	−0.0808304	+	0.140002i
$946$	−7.39739	−	12.8127i	−0.240510	−	0.416576i
$947$	−43.3254			−1.40789			−0.703943	−	0.710256i	$-0.748579\pi$
$947$	−43.3254			−1.40789			−0.703943	+	0.710256i	$0.748579\pi$
$948$	−9.26122	+	16.0409i	−0.300790	+	0.520984i
$949$	9.58013	−	16.5933i	0.310984	−	0.538640i
$950$	−6.28158			−0.203801
$951$	−3.41730	−	5.91894i	−0.110814	−	0.191935i
$952$	10.1679	−	17.6113i	0.329543	−	0.570786i
$953$	6.44575	−	11.1644i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$953$	6.44575	−	11.1644i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997114\pi$
$954$	7.63410	+	13.2226i	0.247163	+	0.428099i
$955$	−11.0543	+	19.1467i	−0.357710	+	0.619571i
$956$	−0.0654850			−0.00211794
$957$	−12.1499	−	21.0443i	−0.392751	−	0.680264i
$958$	−6.47481	−	11.2147i	−0.209192	−	0.362331i
$959$	3.03175			0.0979002
$960$	−7.28641	−	12.6204i	−0.235168	−	0.407323i
$961$	−19.3312	+	33.4826i	−0.623587	+	1.08008i
$962$	−8.47799	−	14.6843i	−0.273341	−	0.473441i
$963$	−12.9329			−0.416758
$964$	4.50490	+	7.80272i	0.145093	+	0.251309i
$965$	−9.24755			−0.297689
$966$	−2.38713			−0.0768045
$967$	−19.1555	+	33.1783i	−0.615999	+	1.06694i	0.374209	+	0.927344i	$0.377914\pi$
$967$	−19.1555	+	33.1783i	−0.615999	+	1.06694i	−0.990208	+	0.139597i	$0.955419\pi$
$968$	3.61783	−	6.26626i	0.116281	−	0.201405i
$969$	−30.9328	−	53.5771i	−0.993704	−	1.72115i
$970$	−5.11792			−0.164327
$971$	−13.8913			−0.445795			−0.222897	−	0.974842i	$-0.571551\pi$
$971$	−13.8913			−0.445795			−0.222897	+	0.974842i	$0.571551\pi$
$972$	−6.47919	+	11.2223i	−0.207820	+	0.359955i
$973$	−29.8094			−0.955645
$974$	40.0220			1.28239
$975$	−1.83918	−	3.18555i	−0.0589009	−	0.102019i
$976$	−13.1296			−0.420269
$977$	3.88476	−	6.72860i	0.124284	−	0.215267i	−0.797169	−	0.603757i	$-0.793670\pi$
$977$	3.88476	−	6.72860i	0.124284	−	0.215267i	0.921453	+	0.388490i	$0.127003\pi$
$978$	9.35773			0.299227
$979$	22.0585			0.704992
$980$	−2.47345	+	4.28414i	−0.0790114	+	0.136852i
$981$	−8.46794	+	14.6669i	−0.270361	+	0.468278i
$982$	−19.4715	+	33.7256i	−0.621359	+	1.07623i
$983$	11.1508	−	19.3137i	0.355655	−	0.616012i	−0.631575	−	0.775315i	$-0.717591\pi$
$983$	11.1508	−	19.3137i	0.355655	−	0.616012i	0.987230	+	0.159303i	$0.0509246\pi$
$984$	−15.7055			−0.500674
$985$	12.6423			0.402816
$986$	−9.42135	+	16.3182i	−0.300037	+	0.519679i
$987$	30.1109			0.958440
$988$	5.54942	+	9.61188i	0.176551	+	0.305795i
$989$	−4.04002			−0.128465
$990$	3.90941			0.124249
$991$	7.83885	−	13.5773i	0.249009	−	0.431296i	−0.714242	−	0.699899i	$-0.753228\pi$
$991$	7.83885	−	13.5773i	0.249009	−	0.431296i	0.963251	+	0.268602i	$0.0865617\pi$
$992$	−41.7320			−1.32499
$993$	3.41674			0.108427
$994$	−3.41516	−	5.91522i	−0.108322	−	0.187619i
$995$	−3.99905	+	6.92655i	−0.126778	+	0.219587i
$996$	−1.30128	+	2.25388i	−0.0412326	+	0.0714169i
$997$	−22.9749			−0.727622			−0.363811	−	0.931473i	$-0.618525\pi$
$997$	−22.9749			−0.727622			−0.363811	+	0.931473i	$0.618525\pi$
$998$	−9.52330			−0.301455
$999$	−16.6418	−	28.8244i	−0.526522	−	0.911963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.e.d.636.4	yes	8
151.118	even	3	inner	755.2.e.d.571.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.e.d.571.4	✓	8	151.118	even	3	inner
755.2.e.d.636.4	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +2.08183 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.04092 + 1.80292i) q^{6} +(0.716433 + 1.24090i) q^{7} +3.00000 q^{8} +1.33402 q^{9} +(0.500000 - 0.866025i) q^{10} +(1.46527 + 2.53793i) q^{11} +(1.04092 - 1.80292i) q^{12} +(-0.883443 + 1.53017i) q^{13} +(-0.716433 + 1.24090i) q^{14} +(-1.04092 - 1.80292i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.36540 - 4.09699i) q^{17} +(0.667010 + 1.15530i) q^{18} +6.28158 q^{19} -1.00000 q^{20} +(1.49149 + 2.58334i) q^{21} +(-1.46527 + 2.53793i) q^{22} +(0.400124 + 0.693034i) q^{23} +6.24549 q^{24} +(-0.500000 + 0.866025i) q^{25} -1.76689 q^{26} -3.46829 q^{27} +1.43287 q^{28} -3.98299 q^{29} +(1.04092 - 1.80292i) q^{30} +(-4.17320 - 7.22819i) q^{31} +(2.50000 - 4.33013i) q^{32} +(3.05045 + 5.28354i) q^{33} +(2.36540 - 4.09699i) q^{34} +(0.716433 - 1.24090i) q^{35} +(0.667010 - 1.15530i) q^{36} +(4.79826 + 8.31084i) q^{37} +(3.14079 + 5.44001i) q^{38} +(-1.83918 + 3.18555i) q^{39} +(-1.50000 - 2.59808i) q^{40} -2.51470 q^{41} +(-1.49149 + 2.58334i) q^{42} +(-2.52424 + 4.37210i) q^{43} +2.93055 q^{44} +(-0.667010 - 1.15530i) q^{45} +(-0.400124 + 0.693034i) q^{46} +(5.04711 - 8.74184i) q^{47} +(1.04092 + 1.80292i) q^{48} +(2.47345 - 4.28414i) q^{49} -1.00000 q^{50} +(-4.92436 - 8.52924i) q^{51} +(0.883443 + 1.53017i) q^{52} +11.4452 q^{53} +(-1.73414 - 3.00363i) q^{54} +(1.46527 - 2.53793i) q^{55} +(2.14930 + 3.72270i) q^{56} +13.0772 q^{57} +(-1.99149 - 3.44937i) q^{58} -12.9620 q^{59} -2.08183 q^{60} +(-6.56482 + 11.3706i) q^{61} +(4.17320 - 7.22819i) q^{62} +(0.955736 + 1.65538i) q^{63} +7.00000 q^{64} +1.76689 q^{65} +(-3.05045 + 5.28354i) q^{66} -10.4977 q^{67} -4.73080 q^{68} +(0.832990 + 1.44278i) q^{69} +1.43287 q^{70} +(-2.38344 + 4.12824i) q^{71} +4.00206 q^{72} -10.8441 q^{73} +(-4.79826 + 8.31084i) q^{74} +(-1.04092 + 1.80292i) q^{75} +(3.14079 - 5.44001i) q^{76} +(-2.09954 + 3.63651i) q^{77} -3.67836 q^{78} -8.89719 q^{79} +(0.500000 - 0.866025i) q^{80} -11.2225 q^{81} +(-1.25735 - 2.17779i) q^{82} -1.25013 q^{83} +2.98299 q^{84} +(-2.36540 + 4.09699i) q^{85} -5.04847 q^{86} -8.29190 q^{87} +(4.39582 + 7.61379i) q^{88} +(3.76354 - 6.51864i) q^{89} +(0.667010 - 1.15530i) q^{90} -2.53171 q^{91} +0.800247 q^{92} +(-8.68790 - 15.0479i) q^{93} +10.0942 q^{94} +(-3.14079 - 5.44001i) q^{95} +(5.20458 - 9.01459i) q^{96} +(-2.55896 - 4.43225i) q^{97} +4.94689 q^{98} +(1.95471 + 3.38565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 2 q^{6} + 3 q^{7} + 24 q^{8} + 12 q^{9} + 4 q^{10} - 11 q^{11} - 2 q^{12} - 5 q^{13} - 3 q^{14} + 2 q^{15} + 4 q^{16} - q^{17} + 6 q^{18} + 20 q^{19} - 8 q^{20}+ \cdots - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 2 * q^6 + 3 * q^7 + 24 * q^8 + 12 * q^9 + 4 * q^10 - 11 * q^11 - 2 * q^12 - 5 * q^13 - 3 * q^14 + 2 * q^15 + 4 * q^16 - q^17 + 6 * q^18 + 20 * q^19 - 8 * q^20 + 5 * q^21 + 11 * q^22 + 8 * q^23 - 12 * q^24 - 4 * q^25 - 10 * q^26 - 40 * q^27 + 6 * q^28 - 18 * q^29 - 2 * q^30 - q^31 + 20 * q^32 + 23 * q^33 + q^34 + 3 * q^35 + 6 * q^36 + 15 * q^37 + 10 * q^38 + 19 * q^39 - 12 * q^40 + 6 * q^41 - 5 * q^42 - 3 * q^43 - 22 * q^44 - 6 * q^45 - 8 * q^46 - 3 * q^47 - 2 * q^48 - 3 * q^49 - 8 * q^50 - 27 * q^51 + 5 * q^52 + 20 * q^53 - 20 * q^54 - 11 * q^55 + 9 * q^56 + 4 * q^57 - 9 * q^58 - 10 * q^59 + 4 * q^60 - 18 * q^61 + q^62 - 24 * q^63 + 56 * q^64 + 10 * q^65 - 23 * q^66 - 44 * q^67 - 2 * q^68 + 6 * q^69 + 6 * q^70 - 17 * q^71 + 36 * q^72 + 18 * q^73 - 15 * q^74 + 2 * q^75 + 10 * q^76 - 5 * q^77 + 38 * q^78 - 12 * q^79 + 4 * q^80 + 56 * q^81 + 3 * q^82 - 28 * q^83 + 10 * q^84 - q^85 - 6 * q^86 + 34 * q^87 - 33 * q^88 - 16 * q^89 + 6 * q^90 - 8 * q^91 + 16 * q^92 - 11 * q^93 - 6 * q^94 - 10 * q^95 - 10 * q^96 - 26 * q^97 - 6 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more