LMFDB - Embedded newform 690.3.k.b.277.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.21
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.88214 + 1.07919i) q^{5} -2.44949 q^{6} +(6.40599 + 6.40599i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.88214 + 1.07919i) q^{5} -2.44949 q^{6} +(6.40599 + 6.40599i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-3.80295 - 5.96134i) q^{10} -0.735686 q^{11} +(2.44949 + 2.44949i) q^{12} +(6.53963 - 6.53963i) q^{13} -12.8120i q^{14} +(7.30112 - 4.65764i) q^{15} -4.00000 q^{16} +(-3.30976 - 3.30976i) q^{17} +(-3.00000 + 3.00000i) q^{18} -3.16515i q^{19} +(-2.15839 + 9.76429i) q^{20} +15.6914 q^{21} +(0.735686 + 0.735686i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.6707 + 10.5376i) q^{25} -13.0793 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-12.8120 + 12.8120i) q^{28} +0.982060i q^{29} +(-11.9588 - 2.64348i) q^{30} +29.3527 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.901028 + 0.901028i) q^{33} +6.61951i q^{34} +(24.3617 + 38.1883i) q^{35} +6.00000 q^{36} +(39.1330 + 39.1330i) q^{37} +(-3.16515 + 3.16515i) q^{38} -16.0187i q^{39} +(11.9227 - 7.60590i) q^{40} -2.92501 q^{41} +(-15.6914 - 15.6914i) q^{42} +(-29.2114 + 29.2114i) q^{43} -1.47137i q^{44} +(3.23758 - 14.6464i) q^{45} +6.78233 q^{46} +(18.9761 + 18.9761i) q^{47} +(-4.89898 + 4.89898i) q^{48} +33.0734i q^{49} +(-12.1331 - 33.2082i) q^{50} -8.10721 q^{51} +(13.0793 + 13.0793i) q^{52} +(-2.56764 + 2.56764i) q^{53} +7.34847i q^{54} +(-3.59173 - 0.793948i) q^{55} +25.6240 q^{56} +(-3.87651 - 3.87651i) q^{57} +(0.982060 - 0.982060i) q^{58} -52.3879i q^{59} +(9.31529 + 14.6022i) q^{60} +49.2869 q^{61} +(-29.3527 - 29.3527i) q^{62} +(19.2180 - 19.2180i) q^{63} -8.00000i q^{64} +(38.9849 - 24.8699i) q^{65} +1.80206 q^{66} +(-28.7370 - 28.7370i) q^{67} +(6.61951 - 6.61951i) q^{68} +8.30662i q^{69} +(13.8266 - 62.5500i) q^{70} -15.3321 q^{71} +(-6.00000 - 6.00000i) q^{72} +(22.2205 - 22.2205i) q^{73} -78.2661i q^{74} +(40.6716 - 14.8600i) q^{75} +6.33031 q^{76} +(-4.71280 - 4.71280i) q^{77} +(-16.0187 + 16.0187i) q^{78} +103.302i q^{79} +(-19.5286 - 4.31678i) q^{80} -9.00000 q^{81} +(2.92501 + 2.92501i) q^{82} +(37.5180 - 37.5180i) q^{83} +31.3828i q^{84} +(-12.5868 - 19.7306i) q^{85} +58.4228 q^{86} +(1.20277 + 1.20277i) q^{87} +(-1.47137 + 1.47137i) q^{88} -21.4071i q^{89} +(-17.8840 + 11.4089i) q^{90} +83.7856 q^{91} +(-6.78233 - 6.78233i) q^{92} +(35.9496 - 35.9496i) q^{93} -37.9522i q^{94} +(3.41582 - 15.4527i) q^{95} +9.79796 q^{96} +(-85.8950 - 85.8950i) q^{97} +(33.0734 - 33.0734i) q^{98} +2.20706i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	4.88214	+	1.07919i	0.976429	+	0.215839i
$5$	4.88214	+	1.07919i	0.976429	+	0.215839i
$6$	−2.44949			−0.408248
$7$	6.40599	+	6.40599i	0.915142	+	0.915142i	0.996671	−	0.0815294i	$-0.0259804\pi$
$7$	6.40599	+	6.40599i	0.915142	+	0.915142i	−0.0815294	+	0.996671i	$0.525980\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−3.80295	−	5.96134i	−0.380295	−	0.596134i
$11$	−0.735686			−0.0668806			−0.0334403	−	0.999441i	$-0.510646\pi$
$11$	−0.735686			−0.0668806			−0.0334403	+	0.999441i	$0.510646\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	6.53963	−	6.53963i	0.503048	−	0.503048i	−0.409336	−	0.912384i	$-0.634240\pi$
$13$	6.53963	−	6.53963i	0.503048	−	0.503048i	0.912384	+	0.409336i	$0.134240\pi$
$14$		−	12.8120i		−	0.915142i
$15$	7.30112	−	4.65764i	0.486741	−	0.310510i
$16$	−4.00000			−0.250000
$17$	−3.30976	−	3.30976i	−0.194692	−	0.194692i	0.603028	−	0.797720i	$-0.293961\pi$
$17$	−3.30976	−	3.30976i	−0.194692	−	0.194692i	−0.797720	+	0.603028i	$0.793961\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	3.16515i		−	0.166587i	−0.996525	−	0.0832935i	$-0.973456\pi$
$19$		−	3.16515i		−	0.166587i	0.996525	−	0.0832935i	$-0.0265439\pi$
$20$	−2.15839	+	9.76429i	−0.107919	+	0.488214i
$21$	15.6914			0.747210
$22$	0.735686	+	0.735686i	0.0334403	+	0.0334403i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	22.6707	+	10.5376i	0.906827	+	0.421503i
$26$	−13.0793			−0.503048
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−12.8120	+	12.8120i	−0.457571	+	0.457571i
$29$			0.982060i			0.0338642i	0.999857	+	0.0169321i	$0.00538990\pi$
$29$			0.982060i			0.0338642i	−0.999857	+	0.0169321i	$0.994610\pi$
$30$	−11.9588	−	2.64348i	−0.398625	−	0.0881159i
$31$	29.3527			0.946863			0.473431	−	0.880831i	$-0.343015\pi$
$31$	29.3527			0.946863			0.473431	+	0.880831i	$0.343015\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	−0.901028	+	0.901028i	−0.0273039	+	0.0273039i
$34$			6.61951i			0.194692i
$35$	24.3617	+	38.1883i	0.696048	+	1.09109i
$36$	6.00000			0.166667
$37$	39.1330	+	39.1330i	1.05765	+	1.05765i	0.998233	+	0.0594162i	$0.0189239\pi$
$37$	39.1330	+	39.1330i	1.05765	+	1.05765i	0.0594162	+	0.998233i	$0.481076\pi$
$38$	−3.16515	+	3.16515i	−0.0832935	+	0.0832935i
$39$		−	16.0187i		−	0.410737i
$40$	11.9227	−	7.60590i	0.298067	−	0.190148i
$41$	−2.92501			−0.0713417			−0.0356708	−	0.999364i	$-0.511357\pi$
$41$	−2.92501			−0.0713417			−0.0356708	+	0.999364i	$0.511357\pi$
$42$	−15.6914	−	15.6914i	−0.373605	−	0.373605i
$43$	−29.2114	+	29.2114i	−0.679334	+	0.679334i	−0.959850	−	0.280515i	$-0.909495\pi$
$43$	−29.2114	+	29.2114i	−0.679334	+	0.679334i	0.280515	+	0.959850i	$0.409495\pi$
$44$		−	1.47137i		−	0.0334403i
$45$	3.23758	−	14.6464i	0.0719463	−	0.325476i
$46$	6.78233			0.147442
$47$	18.9761	+	18.9761i	0.403747	+	0.403747i	0.879551	−	0.475804i	$-0.157843\pi$
$47$	18.9761	+	18.9761i	0.403747	+	0.403747i	−0.475804	+	0.879551i	$0.657843\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			33.0734i			0.674968i
$50$	−12.1331	−	33.2082i	−0.242662	−	0.664165i
$51$	−8.10721			−0.158965
$52$	13.0793	+	13.0793i	0.251524	+	0.251524i
$53$	−2.56764	+	2.56764i	−0.0484460	+	0.0484460i	−0.730915	−	0.682469i	$-0.760906\pi$
$53$	−2.56764	+	2.56764i	−0.0484460	+	0.0484460i	0.682469	+	0.730915i	$0.260906\pi$
$54$			7.34847i			0.136083i
$55$	−3.59173	−	0.793948i	−0.0653041	−	0.0144354i
$56$	25.6240			0.457571
$57$	−3.87651	−	3.87651i	−0.0680089	−	0.0680089i
$58$	0.982060	−	0.982060i	0.0169321	−	0.0169321i
$59$		−	52.3879i		−	0.887930i	−0.896044	−	0.443965i	$-0.853572\pi$
$59$		−	52.3879i		−	0.887930i	0.896044	−	0.443965i	$-0.146428\pi$
$60$	9.31529	+	14.6022i	0.155255	+	0.243371i
$61$	49.2869			0.807981			0.403991	−	0.914763i	$-0.367623\pi$
$61$	49.2869			0.807981			0.403991	+	0.914763i	$0.367623\pi$
$62$	−29.3527	−	29.3527i	−0.473431	−	0.473431i
$63$	19.2180	−	19.2180i	0.305047	−	0.305047i
$64$		−	8.00000i		−	0.125000i
$65$	38.9849	−	24.8699i	0.599768	−	0.382613i
$66$	1.80206			0.0273039
$67$	−28.7370	−	28.7370i	−0.428910	−	0.428910i	0.459347	−	0.888257i	$-0.348083\pi$
$67$	−28.7370	−	28.7370i	−0.428910	−	0.428910i	−0.888257	+	0.459347i	$0.848083\pi$
$68$	6.61951	−	6.61951i	0.0973458	−	0.0973458i
$69$			8.30662i			0.120386i
$70$	13.8266	−	62.5500i	0.197523	−	0.893571i
$71$	−15.3321			−0.215945			−0.107972	−	0.994154i	$-0.534436\pi$
$71$	−15.3321			−0.215945			−0.107972	+	0.994154i	$0.534436\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	22.2205	−	22.2205i	0.304390	−	0.304390i	−0.538339	−	0.842729i	$-0.680948\pi$
$73$	22.2205	−	22.2205i	0.304390	−	0.304390i	0.842729	+	0.538339i	$0.180948\pi$
$74$		−	78.2661i		−	1.05765i
$75$	40.6716	−	14.8600i	0.542288	−	0.198133i
$76$	6.33031			0.0832935
$77$	−4.71280	−	4.71280i	−0.0612052	−	0.0612052i
$78$	−16.0187	+	16.0187i	−0.205369	+	0.205369i
$79$			103.302i			1.30762i	0.756658	+	0.653811i	$0.226831\pi$
$79$			103.302i			1.30762i	−0.756658	+	0.653811i	$0.773169\pi$
$80$	−19.5286	−	4.31678i	−0.244107	−	0.0539597i
$81$	−9.00000			−0.111111
$82$	2.92501	+	2.92501i	0.0356708	+	0.0356708i
$83$	37.5180	−	37.5180i	0.452025	−	0.452025i	−0.444001	−	0.896026i	$-0.646441\pi$
$83$	37.5180	−	37.5180i	0.452025	−	0.452025i	0.896026	+	0.444001i	$0.146441\pi$
$84$			31.3828i			0.373605i
$85$	−12.5868	−	19.7306i	−0.148080	−	0.232124i
$86$	58.4228			0.679334
$87$	1.20277	+	1.20277i	0.0138250	+	0.0138250i
$88$	−1.47137	+	1.47137i	−0.0167201	+	0.0167201i
$89$		−	21.4071i		−	0.240529i	−0.992742	−	0.120265i	$-0.961626\pi$
$89$		−	21.4071i		−	0.240529i	0.992742	−	0.120265i	$-0.0383743\pi$
$90$	−17.8840	+	11.4089i	−0.198711	+	0.126765i
$91$	83.7856			0.920721
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	35.9496	−	35.9496i	0.386555	−	0.386555i
$94$		−	37.9522i		−	0.403747i
$95$	3.41582	−	15.4527i	0.0359560	−	0.162660i
$96$	9.79796			0.102062
$97$	−85.8950	−	85.8950i	−0.885515	−	0.885515i	0.108573	−	0.994088i	$-0.465372\pi$
$97$	−85.8950	−	85.8950i	−0.885515	−	0.885515i	−0.994088	+	0.108573i	$0.965372\pi$
$98$	33.0734	−	33.0734i	0.337484	−	0.337484i
$99$			2.20706i			0.0222935i
$100$	−21.0751	+	45.3414i	−0.210751	+	0.453414i
$101$	74.5816			0.738432			0.369216	−	0.929344i	$-0.379626\pi$
$101$	74.5816			0.738432			0.369216	+	0.929344i	$0.379626\pi$
$102$	8.10721	+	8.10721i	0.0794825	+	0.0794825i
$103$	54.5451	−	54.5451i	0.529564	−	0.529564i	−0.390879	−	0.920442i	$-0.627829\pi$
$103$	54.5451	−	54.5451i	0.529564	−	0.529564i	0.920442	+	0.390879i	$0.127829\pi$
$104$		−	26.1585i		−	0.251524i
$105$	76.6077	+	16.9341i	0.729597	+	0.161277i
$106$	5.13527			0.0484460
$107$	−140.187	−	140.187i	−1.31016	−	1.31016i	−0.921292	−	0.388871i	$-0.872865\pi$
$107$	−140.187	−	140.187i	−1.31016	−	1.31016i	−0.388871	−	0.921292i	$-0.627135\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			104.417i			0.957953i	0.877828	+	0.478977i	$0.158992\pi$
$109$			104.417i			0.957953i	−0.877828	+	0.478977i	$0.841008\pi$
$110$	2.79778	+	4.38568i	0.0254343	+	0.0398698i
$111$	95.8560			0.863567
$112$	−25.6240	−	25.6240i	−0.228785	−	0.228785i
$113$	97.4786	−	97.4786i	0.862643	−	0.862643i	−0.129002	−	0.991644i	$-0.541177\pi$
$113$	97.4786	−	97.4786i	0.862643	−	0.862643i	0.991644	+	0.129002i	$0.0411773\pi$
$114$			7.75301i			0.0680089i
$115$	−20.2159	+	12.8964i	−0.175790	+	0.112143i
$116$	−1.96412			−0.0169321
$117$	−19.6189	−	19.6189i	−0.167683	−	0.167683i
$118$	−52.3879	+	52.3879i	−0.443965	+	0.443965i
$119$		−	42.4045i		−	0.356341i
$120$	5.28695	−	23.9175i	0.0440579	−	0.199313i
$121$	−120.459			−0.995527
$122$	−49.2869	−	49.2869i	−0.403991	−	0.403991i
$123$	−3.58239	+	3.58239i	−0.0291251	+	0.0291251i
$124$			58.7055i			0.473431i
$125$	99.3095	+	75.9120i	0.794476	+	0.607296i
$126$	−38.4359			−0.305047
$127$	12.0704	+	12.0704i	0.0950426	+	0.0950426i	0.753029	−	0.657987i	$-0.228592\pi$
$127$	12.0704	+	12.0704i	0.0950426	+	0.0950426i	−0.657987	+	0.753029i	$0.728592\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			71.5530i			0.554674i
$130$	−63.8548	−	14.1151i	−0.491191	−	0.108577i
$131$	−34.8277			−0.265860			−0.132930	−	0.991125i	$-0.542439\pi$
$131$	−34.8277			−0.265860			−0.132930	+	0.991125i	$0.542439\pi$
$132$	−1.80206	−	1.80206i	−0.0136519	−	0.0136519i
$133$	20.2759	−	20.2759i	0.152451	−	0.152451i
$134$			57.4739i			0.428910i
$135$	−13.9729	−	21.9034i	−0.103503	−	0.162247i
$136$	−13.2390			−0.0973458
$137$	−61.0427	−	61.0427i	−0.445567	−	0.445567i	0.448311	−	0.893878i	$-0.352026\pi$
$137$	−61.0427	−	61.0427i	−0.445567	−	0.445567i	−0.893878	+	0.448311i	$0.852026\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			253.335i			1.82255i	0.411796	+	0.911276i	$0.364902\pi$
$139$			253.335i			1.82255i	−0.411796	+	0.911276i	$0.635098\pi$
$140$	−76.3766	+	48.7233i	−0.545547	+	0.348024i
$141$	46.4818			0.329658
$142$	15.3321	+	15.3321i	0.107972	+	0.107972i
$143$	−4.81111	+	4.81111i	−0.0336441	+	0.0336441i
$144$			12.0000i			0.0833333i
$145$	−1.05983	+	4.79456i	−0.00730920	+	0.0330659i
$146$	−44.4409			−0.304390
$147$	40.5065	+	40.5065i	0.275555	+	0.275555i
$148$	−78.2661	+	78.2661i	−0.528825	+	0.528825i
$149$		−	223.610i		−	1.50074i	−0.661020	−	0.750368i	$-0.729876\pi$
$149$		−	223.610i		−	1.50074i	0.661020	−	0.750368i	$-0.270124\pi$
$150$	−55.5316	−	25.8117i	−0.370211	−	0.172078i
$151$	227.599			1.50728			0.753641	−	0.657287i	$-0.228296\pi$
$151$	227.599			1.50728			0.753641	+	0.657287i	$0.228296\pi$
$152$	−6.33031	−	6.33031i	−0.0416468	−	0.0416468i
$153$	−9.92927	+	9.92927i	−0.0648972	+	0.0648972i
$154$			9.42560i			0.0612052i
$155$	143.304	+	31.6773i	0.924544	+	0.204370i
$156$	32.0375			0.205369
$157$	−112.274	−	112.274i	−0.715119	−	0.715119i	0.252482	−	0.967601i	$-0.418753\pi$
$157$	−112.274	−	112.274i	−0.715119	−	0.715119i	−0.967601	+	0.252482i	$0.918753\pi$
$158$	103.302	−	103.302i	0.653811	−	0.653811i
$159$			6.28940i			0.0395560i
$160$	15.2118	+	23.8454i	0.0950738	+	0.149033i
$161$	−43.4475			−0.269861
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−72.1767	+	72.1767i	−0.442802	+	0.442802i	−0.892953	−	0.450151i	$-0.851370\pi$
$163$	−72.1767	+	72.1767i	−0.442802	+	0.442802i	0.450151	+	0.892953i	$0.351370\pi$
$164$		−	5.85002i		−	0.0356708i
$165$	−5.37133	+	3.42656i	−0.0325535	+	0.0207671i
$166$	−75.0361			−0.452025
$167$	32.2083	+	32.2083i	0.192864	+	0.192864i	0.796933	−	0.604068i	$-0.206455\pi$
$167$	32.2083	+	32.2083i	0.192864	+	0.192864i	−0.604068	+	0.796933i	$0.706455\pi$
$168$	31.3828	−	31.3828i	0.186802	−	0.186802i
$169$			83.4666i			0.493885i
$170$	−7.14374	+	32.3174i	−0.0420220	+	0.190102i
$171$	−9.49546			−0.0555290
$172$	−58.4228	−	58.4228i	−0.339667	−	0.339667i
$173$	194.416	−	194.416i	1.12379	−	1.12379i	0.132629	−	0.991166i	$-0.457658\pi$
$173$	194.416	−	194.416i	1.12379	−	1.12379i	0.991166	−	0.132629i	$-0.0423418\pi$
$174$		−	2.40555i		−	0.0138250i
$175$	77.7246	+	212.732i	0.444141	+	1.21561i
$176$	2.94274			0.0167201
$177$	−64.1618	−	64.1618i	−0.362496	−	0.362496i
$178$	−21.4071	+	21.4071i	−0.120265	+	0.120265i
$179$			178.214i			0.995610i	0.867289	+	0.497805i	$0.165861\pi$
$179$			178.214i			0.995610i	−0.867289	+	0.497805i	$0.834139\pi$
$180$	29.2929	+	6.47517i	0.162738	+	0.0359731i
$181$	−27.8673			−0.153963			−0.0769814	−	0.997033i	$-0.524528\pi$
$181$	−27.8673			−0.153963			−0.0769814	+	0.997033i	$0.524528\pi$
$182$	−83.7856	−	83.7856i	−0.460360	−	0.460360i
$183$	60.3638	−	60.3638i	0.329857	−	0.329857i
$184$			13.5647i			0.0737210i
$185$	148.821	+	233.285i	0.804438	+	1.26100i
$186$	−71.8992			−0.386555
$187$	2.43494	+	2.43494i	0.0130211	+	0.0130211i
$188$	−37.9522	+	37.9522i	−0.201873	+	0.201873i
$189$		−	47.0742i		−	0.249070i
$190$	−18.8686	+	12.0369i	−0.0993082	+	0.0633522i
$191$	−184.071			−0.963721			−0.481861	−	0.876248i	$-0.660039\pi$
$191$	−184.071			−0.963721			−0.481861	+	0.876248i	$0.660039\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−162.465	+	162.465i	−0.841790	+	0.841790i	−0.989092	−	0.147302i	$-0.952941\pi$
$193$	−162.465	+	162.465i	−0.841790	+	0.841790i	0.147302	+	0.989092i	$0.452941\pi$
$194$			171.790i			0.885515i
$195$	17.2873	−	78.2058i	0.0886530	−	0.401056i
$196$	−66.1469			−0.337484
$197$	−236.239	−	236.239i	−1.19918	−	1.19918i	−0.974412	−	0.224769i	$-0.927837\pi$
$197$	−236.239	−	236.239i	−1.19918	−	1.19918i	−0.224769	−	0.974412i	$-0.572163\pi$
$198$	2.20706	−	2.20706i	0.0111468	−	0.0111468i
$199$			67.2029i			0.337703i	0.985641	+	0.168852i	$0.0540059\pi$
$199$			67.2029i			0.337703i	−0.985641	+	0.168852i	$0.945994\pi$
$200$	66.4165	−	24.2662i	0.332082	−	0.121331i
$201$	−70.3909			−0.350203
$202$	−74.5816	−	74.5816i	−0.369216	−	0.369216i
$203$	−6.29107	+	6.29107i	−0.0309905	+	0.0309905i
$204$		−	16.2144i		−	0.0794825i
$205$	−14.2803	−	3.15665i	−0.0696601	−	0.0153983i
$206$	−109.090			−0.529564
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−26.1585	+	26.1585i	−0.125762	+	0.125762i
$209$			2.32856i			0.0111414i
$210$	−59.6737	−	93.5418i	−0.284160	−	0.445437i
$211$	29.6438			0.140492			0.0702459	−	0.997530i	$-0.477622\pi$
$211$	29.6438			0.140492			0.0702459	+	0.997530i	$0.477622\pi$
$212$	−5.13527	−	5.13527i	−0.0242230	−	0.0242230i
$213$	−18.7779	+	18.7779i	−0.0881591	+	0.0881591i
$214$			280.375i			1.31016i
$215$	−174.139	+	111.089i	−0.809948	+	0.516695i
$216$	−14.6969			−0.0680414
$217$	188.033	+	188.033i	0.866513	+	0.866513i
$218$	104.417	−	104.417i	0.478977	−	0.478977i
$219$		−	54.4288i		−	0.248533i
$220$	1.58790	−	7.18345i	0.00721771	−	0.0326521i
$221$	−43.2891			−0.195878
$222$	−95.8560	−	95.8560i	−0.431784	−	0.431784i
$223$	−133.660	+	133.660i	−0.599374	+	0.599374i	−0.940146	−	0.340772i	$-0.889312\pi$
$223$	−133.660	+	133.660i	−0.599374	+	0.599374i	0.340772	+	0.940146i	$0.389312\pi$
$224$			51.2479i			0.228785i
$225$	31.6127	−	68.0120i	0.140501	−	0.302276i
$226$	−194.957			−0.862643
$227$	−211.462	−	211.462i	−0.931552	−	0.931552i	0.0662509	−	0.997803i	$-0.478896\pi$
$227$	−211.462	−	211.462i	−0.931552	−	0.931552i	−0.997803	+	0.0662509i	$0.978896\pi$
$228$	7.75301	−	7.75301i	0.0340044	−	0.0340044i
$229$		−	78.1379i		−	0.341213i	−0.985339	−	0.170607i	$-0.945427\pi$
$229$		−	78.1379i		−	0.341213i	0.985339	−	0.170607i	$-0.0545728\pi$
$230$	33.1123	+	7.31945i	0.143967	+	0.0318237i
$231$	−11.5440			−0.0499738
$232$	1.96412	+	1.96412i	0.00846604	+	0.00846604i
$233$	−253.848	+	253.848i	−1.08947	+	1.08947i	−0.0938922	+	0.995582i	$0.529931\pi$
$233$	−253.848	+	253.848i	−1.08947	+	1.08947i	−0.995582	+	0.0938922i	$0.970069\pi$
$234$			39.2378i			0.167683i
$235$	72.1652	+	113.123i	0.307086	+	0.481374i
$236$	104.776			0.443965
$237$	126.519	+	126.519i	0.533835	+	0.533835i
$238$	−42.4045	+	42.4045i	−0.178170	+	0.178170i
$239$			395.126i			1.65325i	0.562756	+	0.826623i	$0.309741\pi$
$239$			395.126i			1.65325i	−0.562756	+	0.826623i	$0.690259\pi$
$240$	−29.2045	+	18.6306i	−0.121685	+	0.0776274i
$241$	−285.834			−1.18603			−0.593016	−	0.805190i	$-0.702063\pi$
$241$	−285.834			−1.18603			−0.593016	+	0.805190i	$0.702063\pi$
$242$	120.459	+	120.459i	0.497763	+	0.497763i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			98.5737i			0.403991i
$245$	−35.6927	+	161.469i	−0.145684	+	0.659059i
$246$	7.16478			0.0291251
$247$	−20.6989	−	20.6989i	−0.0838013	−	0.0838013i
$248$	58.7055	−	58.7055i	0.236716	−	0.236716i
$249$		−	91.9001i		−	0.369077i
$250$	−23.3975	−	175.221i	−0.0935898	−	0.700886i
$251$	−117.352			−0.467536			−0.233768	−	0.972292i	$-0.575106\pi$
$251$	−117.352			−0.467536			−0.233768	+	0.972292i	$0.575106\pi$
$252$	38.4359	+	38.4359i	0.152524	+	0.152524i
$253$	2.49483	−	2.49483i	0.00986100	−	0.00986100i
$254$		−	24.1408i		−	0.0950426i
$255$	−39.5806	−	8.74926i	−0.155218	−	0.0343108i
$256$	16.0000			0.0625000
$257$	−61.0672	−	61.0672i	−0.237616	−	0.237616i	0.578246	−	0.815862i	$-0.303737\pi$
$257$	−61.0672	−	61.0672i	−0.237616	−	0.237616i	−0.815862	+	0.578246i	$0.803737\pi$
$258$	71.5530	−	71.5530i	0.277337	−	0.277337i
$259$			501.372i			1.93580i
$260$	49.7398	+	77.9699i	0.191307	+	0.299884i
$261$	2.94618			0.0112881
$262$	34.8277	+	34.8277i	0.132930	+	0.132930i
$263$	−73.8626	+	73.8626i	−0.280847	+	0.280847i	−0.833447	−	0.552600i	$-0.813636\pi$
$263$	−73.8626	+	73.8626i	−0.280847	+	0.280847i	0.552600	+	0.833447i	$0.313636\pi$
$264$			3.60411i			0.0136519i
$265$	−15.3066	+	9.76460i	−0.0577606	+	0.0368475i
$266$	−40.5519			−0.152451
$267$	−26.2182	−	26.2182i	−0.0981957	−	0.0981957i
$268$	57.4739	−	57.4739i	0.214455	−	0.214455i
$269$			29.3391i			0.109067i	0.998512	+	0.0545336i	$0.0173672\pi$
$269$			29.3391i			0.109067i	−0.998512	+	0.0545336i	$0.982633\pi$
$270$	−7.93043	+	35.8763i	−0.0293720	+	0.132875i
$271$	250.398			0.923979			0.461989	−	0.886885i	$-0.347136\pi$
$271$	250.398			0.923979			0.461989	+	0.886885i	$0.347136\pi$
$272$	13.2390	+	13.2390i	0.0486729	+	0.0486729i
$273$	102.616	−	102.616i	0.375883	−	0.375883i
$274$			122.085i			0.445567i
$275$	−16.6785	−	7.75234i	−0.0606491	−	0.0281903i
$276$	−16.6132			−0.0601929
$277$	−4.63185	−	4.63185i	−0.0167215	−	0.0167215i	0.698697	−	0.715418i	$-0.253764\pi$
$277$	−4.63185	−	4.63185i	−0.0167215	−	0.0167215i	−0.715418	+	0.698697i	$0.753764\pi$
$278$	253.335	−	253.335i	0.911276	−	0.911276i
$279$		−	88.0582i		−	0.315621i
$280$	125.100	+	27.6532i	0.446785	+	0.0987616i
$281$	−430.368			−1.53156			−0.765779	−	0.643104i	$-0.777646\pi$
$281$	−430.368			−1.53156			−0.765779	+	0.643104i	$0.777646\pi$
$282$	−46.4818	−	46.4818i	−0.164829	−	0.164829i
$283$	−83.9684	+	83.9684i	−0.296708	+	0.296708i	−0.839723	−	0.543015i	$-0.817283\pi$
$283$	−83.9684	+	83.9684i	−0.296708	+	0.296708i	0.543015	+	0.839723i	$0.317283\pi$
$284$		−	30.6642i		−	0.107972i
$285$	−14.7422	−	23.1092i	−0.0517269	−	0.0810848i
$286$	9.62223			0.0336441
$287$	−18.7376	−	18.7376i	−0.0652877	−	0.0652877i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	267.091i		−	0.924190i
$290$	5.85440	−	3.73473i	0.0201876	−	0.0128784i
$291$	−210.399			−0.723020
$292$	44.4409	+	44.4409i	0.152195	+	0.152195i
$293$	34.6749	−	34.6749i	0.118344	−	0.118344i	−0.645454	−	0.763799i	$-0.723332\pi$
$293$	34.6749	−	34.6749i	0.118344	−	0.118344i	0.763799	+	0.645454i	$0.223332\pi$
$294$		−	81.0131i		−	0.275555i
$295$	56.5367	−	255.765i	0.191650	−	0.867000i
$296$	156.532			0.528825
$297$	2.70308	+	2.70308i	0.00910129	+	0.00910129i
$298$	−223.610	+	223.610i	−0.750368	+	0.750368i
$299$			44.3539i			0.148341i
$300$	29.7199	+	81.3433i	0.0990664	+	0.271144i
$301$	−374.256			−1.24337
$302$	−227.599	−	227.599i	−0.753641	−	0.753641i
$303$	91.3435	−	91.3435i	0.301464	−	0.301464i
$304$			12.6606i			0.0416468i
$305$	240.626	+	53.1901i	0.788936	+	0.174394i
$306$	19.8585			0.0648972
$307$	−163.732	−	163.732i	−0.533328	−	0.533328i	0.388233	−	0.921561i	$-0.373085\pi$
$307$	−163.732	−	163.732i	−0.533328	−	0.533328i	−0.921561	+	0.388233i	$0.873085\pi$
$308$	9.42560	−	9.42560i	0.0306026	−	0.0306026i
$309$		−	133.608i		−	0.432387i
$310$	−111.627	−	174.982i	−0.360087	−	0.564457i
$311$	57.2138			0.183967			0.0919836	−	0.995761i	$-0.470679\pi$
$311$	57.2138			0.183967			0.0919836	+	0.995761i	$0.470679\pi$
$312$	−32.0375	−	32.0375i	−0.102684	−	0.102684i
$313$	193.211	−	193.211i	0.617287	−	0.617287i	−0.327547	−	0.944835i	$-0.606222\pi$
$313$	193.211	−	193.211i	0.617287	−	0.617287i	0.944835	+	0.327547i	$0.106222\pi$
$314$			224.547i			0.715119i
$315$	114.565	−	73.0850i	0.363698	−	0.232016i
$316$	−206.604			−0.653811
$317$	231.594	+	231.594i	0.730579	+	0.730579i	0.970734	−	0.240155i	$-0.0771984\pi$
$317$	231.594	+	231.594i	0.730579	+	0.730579i	−0.240155	+	0.970734i	$0.577198\pi$
$318$	6.28940	−	6.28940i	0.0197780	−	0.0197780i
$319$		−	0.722488i		−	0.00226485i
$320$	8.63356	−	39.0572i	0.0269799	−	0.122054i
$321$	−343.388			−1.06974
$322$	43.4475	+	43.4475i	0.134930	+	0.134930i
$323$	−10.4759	+	10.4759i	−0.0324331	+	0.0324331i
$324$		−	18.0000i		−	0.0555556i
$325$	217.170	−	79.3460i	0.668214	−	0.244142i
$326$	144.353			0.442802
$327$	127.884	+	127.884i	0.391083	+	0.391083i
$328$	−5.85002	+	5.85002i	−0.0178354	+	0.0178354i
$329$			243.121i			0.738971i
$330$	8.79790	+	1.94477i	0.0266603	+	0.00589324i
$331$	−191.879			−0.579694			−0.289847	−	0.957073i	$-0.593604\pi$
$331$	−191.879			−0.579694			−0.289847	+	0.957073i	$0.593604\pi$
$332$	75.0361	+	75.0361i	0.226012	+	0.226012i
$333$	117.399	−	117.399i	0.352550	−	0.352550i
$334$		−	64.4167i		−	0.192864i
$335$	−109.285	−	171.311i	−0.326225	−	0.511375i
$336$	−62.7656			−0.186802
$337$	−285.102	−	285.102i	−0.846001	−	0.846001i	0.143631	−	0.989631i	$-0.454122\pi$
$337$	−285.102	−	285.102i	−0.846001	−	0.846001i	−0.989631	+	0.143631i	$0.954122\pi$
$338$	83.4666	−	83.4666i	0.246943	−	0.246943i
$339$		−	238.773i		−	0.704345i
$340$	39.4612	−	25.1737i	0.116062	−	0.0740402i
$341$	−21.5944			−0.0633267
$342$	9.49546	+	9.49546i	0.0277645	+	0.0277645i
$343$	102.025	−	102.025i	0.297450	−	0.297450i
$344$			116.846i			0.339667i
$345$	−8.96446	+	40.5541i	−0.0259839	+	0.117548i
$346$	−388.833			−1.12379
$347$	102.065	+	102.065i	0.294136	+	0.294136i	0.838712	−	0.544576i	$-0.183309\pi$
$347$	102.065	+	102.065i	0.294136	+	0.294136i	−0.544576	+	0.838712i	$0.683309\pi$
$348$	−2.40555	+	2.40555i	−0.00691249	+	0.00691249i
$349$		−	385.605i		−	1.10488i	−0.833551	−	0.552442i	$-0.813696\pi$
$349$		−	385.605i		−	1.10488i	0.833551	−	0.552442i	$-0.186304\pi$
$350$	135.007	−	290.456i	0.385735	−	0.829875i
$351$	−48.0562			−0.136912
$352$	−2.94274	−	2.94274i	−0.00836007	−	0.00836007i
$353$	−123.125	+	123.125i	−0.348795	+	0.348795i	−0.859661	−	0.510865i	$-0.829325\pi$
$353$	−123.125	+	123.125i	−0.348795	+	0.348795i	0.510865	+	0.859661i	$0.329325\pi$
$354$			128.324i			0.362496i
$355$	−74.8534	−	16.5463i	−0.210855	−	0.0466093i
$356$	42.8142			0.120265
$357$	−51.9347	−	51.9347i	−0.145475	−	0.145475i
$358$	178.214	−	178.214i	0.497805	−	0.497805i
$359$			236.238i			0.658044i	0.944322	+	0.329022i	$0.106719\pi$
$359$			236.238i			0.658044i	−0.944322	+	0.329022i	$0.893281\pi$
$360$	−22.8177	−	35.7680i	−0.0633825	−	0.0993557i
$361$	350.982			0.972249
$362$	27.8673	+	27.8673i	0.0769814	+	0.0769814i
$363$	−147.531	+	147.531i	−0.406422	+	0.406422i
$364$			167.571i			0.460360i
$365$	132.464	−	84.5033i	0.362914	−	0.231516i
$366$	−120.728			−0.329857
$367$	−301.289	−	301.289i	−0.820952	−	0.820952i	0.165293	−	0.986245i	$-0.447143\pi$
$367$	−301.289	−	301.289i	−0.820952	−	0.820952i	−0.986245	+	0.165293i	$0.947143\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			8.77503i			0.0237806i
$370$	84.4643	−	382.106i	0.228282	−	1.03272i
$371$	−32.8965			−0.0886699
$372$	71.8992	+	71.8992i	0.193278	+	0.193278i
$373$	−135.527	+	135.527i	−0.363343	+	0.363343i	−0.865042	−	0.501699i	$-0.832709\pi$
$373$	−135.527	+	135.527i	−0.363343	+	0.363343i	0.501699	+	0.865042i	$0.332709\pi$
$374$		−	4.86988i		−	0.0130211i
$375$	214.602	−	28.6559i	0.572271	−	0.0764158i
$376$	75.9044			0.201873
$377$	6.42231	+	6.42231i	0.0170353	+	0.0170353i
$378$	−47.0742	+	47.0742i	−0.124535	+	0.124535i
$379$		−	195.582i		−	0.516046i	−0.966139	−	0.258023i	$-0.916929\pi$
$379$		−	195.582i		−	0.516046i	0.966139	−	0.258023i	$-0.0830711\pi$
$380$	30.9055	+	6.83163i	0.0813302	+	0.0179780i
$381$	29.5664			0.0776020
$382$	184.071	+	184.071i	0.481861	+	0.481861i
$383$	−274.665	+	274.665i	−0.717142	+	0.717142i	−0.968019	−	0.250877i	$-0.919281\pi$
$383$	−274.665	+	274.665i	−0.717142	+	0.717142i	0.250877	+	0.968019i	$0.419281\pi$
$384$			19.5959i			0.0510310i
$385$	−17.9225	−	28.0946i	−0.0465521	−	0.0729730i
$386$	324.931			0.841790
$387$	87.6341	+	87.6341i	0.226445	+	0.226445i
$388$	171.790	−	171.790i	0.442758	−	0.442758i
$389$		−	25.3609i		−	0.0651952i	−0.999469	−	0.0325976i	$-0.989622\pi$
$389$		−	25.3609i		−	0.0651952i	0.999469	−	0.0325976i	$-0.0103780\pi$
$390$	−95.4932	+	60.9185i	−0.244854	+	0.156201i
$391$	22.4479			0.0574114
$392$	66.1469	+	66.1469i	0.168742	+	0.168742i
$393$	−42.6550	+	42.6550i	−0.108537	+	0.108537i
$394$			472.477i			1.19918i
$395$	−111.483	+	504.336i	−0.282236	+	1.27680i
$396$	−4.41412			−0.0111468
$397$	250.977	+	250.977i	0.632183	+	0.632183i	0.948615	−	0.316432i	$-0.102485\pi$
$397$	250.977	+	250.977i	0.632183	+	0.632183i	−0.316432	+	0.948615i	$0.602485\pi$
$398$	67.2029	−	67.2029i	0.168852	−	0.168852i
$399$		−	49.6657i		−	0.124475i
$400$	−90.6827	−	42.1503i	−0.226707	−	0.105376i
$401$	118.805			0.296272			0.148136	−	0.988967i	$-0.452673\pi$
$401$	118.805			0.296272			0.148136	+	0.988967i	$0.452673\pi$
$402$	70.3909	+	70.3909i	0.175102	+	0.175102i
$403$	191.956	−	191.956i	0.476318	−	0.476318i
$404$			149.163i			0.369216i
$405$	−43.9393	−	9.71275i	−0.108492	−	0.0239821i
$406$	12.5821			0.0309905
$407$	−28.7896	−	28.7896i	−0.0707362	−	0.0707362i
$408$	−16.2144	+	16.2144i	−0.0397412	+	0.0397412i
$409$		−	314.345i		−	0.768569i	−0.923215	−	0.384284i	$-0.874448\pi$
$409$		−	314.345i		−	0.768569i	0.923215	−	0.384284i	$-0.125552\pi$
$410$	11.1237	+	17.4370i	0.0271309	+	0.0425292i
$411$	−149.524			−0.363804
$412$	109.090	+	109.090i	0.264782	+	0.264782i
$413$	335.596	−	335.596i	0.812581	−	0.812581i
$414$		−	20.3470i		−	0.0491473i
$415$	223.658	−	142.679i	0.538934	−	0.343805i
$416$	52.3170			0.125762
$417$	310.270	+	310.270i	0.744054	+	0.744054i
$418$	2.32856	−	2.32856i	0.00557072	−	0.00557072i
$419$			114.465i			0.273187i	0.990627	+	0.136594i	$0.0436155\pi$
$419$			114.465i			0.273187i	−0.990627	+	0.136594i	$0.956385\pi$
$420$	−33.8682	+	153.215i	−0.0806385	+	0.364799i
$421$	260.815			0.619512			0.309756	−	0.950816i	$-0.399753\pi$
$421$	260.815			0.619512			0.309756	+	0.950816i	$0.399753\pi$
$422$	−29.6438	−	29.6438i	−0.0702459	−	0.0702459i
$423$	56.9283	−	56.9283i	0.134582	−	0.134582i
$424$			10.2705i			0.0242230i
$425$	−40.1576	−	109.911i	−0.0944886	−	0.258615i
$426$	37.5558			0.0881591
$427$	315.731	+	315.731i	0.739417	+	0.739417i
$428$	280.375	−	280.375i	0.655082	−	0.655082i
$429$			11.7848i			0.0274703i
$430$	285.228	+	63.0495i	0.663322	+	0.146627i
$431$	113.472			0.263275			0.131638	−	0.991298i	$-0.457976\pi$
$431$	113.472			0.263275			0.131638	+	0.991298i	$0.457976\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	500.488	−	500.488i	1.15586	−	1.15586i	0.170505	−	0.985357i	$-0.445460\pi$
$433$	500.488	−	500.488i	1.15586	−	1.15586i	0.985357	−	0.170505i	$-0.0545399\pi$
$434$		−	376.067i		−	0.866513i
$435$	4.57409	+	7.17014i	0.0105151	+	0.0164831i
$436$	−208.834			−0.478977
$437$	10.7336	+	10.7336i	0.0245619	+	0.0245619i
$438$	−54.4288	+	54.4288i	−0.124267	+	0.124267i
$439$			275.486i			0.627530i	0.949501	+	0.313765i	$0.101590\pi$
$439$			275.486i			0.627530i	−0.949501	+	0.313765i	$0.898410\pi$
$440$	−8.77135	+	5.59556i	−0.0199349	+	0.0127172i
$441$	99.2203			0.224989
$442$	43.2891	+	43.2891i	0.0979392	+	0.0979392i
$443$	−108.041	+	108.041i	−0.243885	+	0.243885i	−0.818455	−	0.574570i	$-0.805169\pi$
$443$	−108.041	+	108.041i	−0.243885	+	0.243885i	0.574570	+	0.818455i	$0.305169\pi$
$444$			191.712i			0.431784i
$445$	23.1024	−	104.513i	0.0519156	−	0.234860i
$446$	267.321			0.599374
$447$	−273.865	−	273.865i	−0.612673	−	0.612673i
$448$	51.2479	−	51.2479i	0.114393	−	0.114393i
$449$		−	288.810i		−	0.643230i	−0.946870	−	0.321615i	$-0.895774\pi$
$449$		−	288.810i		−	0.643230i	0.946870	−	0.321615i	$-0.104226\pi$
$450$	−99.6247	+	36.3993i	−0.221388	+	0.0808874i
$451$	2.15189			0.00477137
$452$	194.957	+	194.957i	0.431321	+	0.431321i
$453$	278.751	−	278.751i	0.615345	−	0.615345i
$454$			422.925i			0.931552i
$455$	409.053	+	90.4209i	0.899018	+	0.198727i
$456$	−15.5060			−0.0340044
$457$	−153.083	−	153.083i	−0.334974	−	0.334974i	0.519498	−	0.854472i	$-0.326119\pi$
$457$	−153.083	−	153.083i	−0.334974	−	0.334974i	−0.854472	+	0.519498i	$0.826119\pi$
$458$	−78.1379	+	78.1379i	−0.170607	+	0.170607i
$459$			24.3216i			0.0529883i
$460$	−25.7929	−	40.4318i	−0.0560714	−	0.0878952i
$461$	−296.499			−0.643165			−0.321583	−	0.946882i	$-0.604215\pi$
$461$	−296.499			−0.643165			−0.321583	+	0.946882i	$0.604215\pi$
$462$	11.5440	+	11.5440i	0.0249869	+	0.0249869i
$463$	−396.313	+	396.313i	−0.855968	+	0.855968i	−0.990860	−	0.134893i	$-0.956931\pi$
$463$	−396.313	+	396.313i	−0.855968	+	0.855968i	0.134893	+	0.990860i	$0.456931\pi$
$464$		−	3.92824i		−	0.00846604i
$465$	214.308	−	136.715i	0.460877	−	0.294010i
$466$	507.695			1.08947
$467$	−438.477	−	438.477i	−0.938923	−	0.938923i	0.0593166	−	0.998239i	$-0.481108\pi$
$467$	−438.477	−	438.477i	−0.938923	−	0.938923i	−0.998239	+	0.0593166i	$0.981108\pi$
$468$	39.2378	−	39.2378i	0.0838414	−	0.0838414i
$469$		−	368.177i		−	0.785026i
$470$	40.9578	−	185.288i	0.0871443	−	0.394230i
$471$	−275.013			−0.583892
$472$	−104.776	−	104.776i	−0.221982	−	0.221982i
$473$	21.4904	−	21.4904i	0.0454343	−	0.0454343i
$474$		−	253.038i		−	0.533835i
$475$	33.3530	−	71.7562i	0.0702169	−	0.151066i
$476$	84.8091			0.178170
$477$	7.70291	+	7.70291i	0.0161487	+	0.0161487i
$478$	395.126	−	395.126i	0.826623	−	0.826623i
$479$		−	425.424i		−	0.888151i	−0.895989	−	0.444075i	$-0.853532\pi$
$479$		−	425.424i		−	0.888151i	0.895989	−	0.444075i	$-0.146468\pi$
$480$	47.8351	+	10.5739i	0.0996564	+	0.0220290i
$481$	511.831			1.06410
$482$	285.834	+	285.834i	0.593016	+	0.593016i
$483$	−53.2122	+	53.2122i	−0.110170	+	0.110170i
$484$		−	240.918i		−	0.497763i
$485$	−326.654	−	512.049i	−0.673514	−	1.05577i
$486$	22.0454			0.0453609
$487$	282.758	+	282.758i	0.580611	+	0.580611i	0.935071	−	0.354460i	$-0.115335\pi$
$487$	282.758	+	282.758i	0.580611	+	0.580611i	−0.354460	+	0.935071i	$0.615335\pi$
$488$	98.5737	−	98.5737i	0.201995	−	0.201995i
$489$			176.796i			0.361546i
$490$	197.162	−	125.777i	0.402371	−	0.256687i
$491$	49.8564			0.101541			0.0507703	−	0.998710i	$-0.483832\pi$
$491$	49.8564			0.101541			0.0507703	+	0.998710i	$0.483832\pi$
$492$	−7.16478	−	7.16478i	−0.0145626	−	0.0145626i
$493$	3.25038	−	3.25038i	0.00659306	−	0.00659306i
$494$			41.3978i			0.0838013i
$495$	−2.38185	+	10.7752i	−0.00481181	+	0.0217680i
$496$	−117.411			−0.236716
$497$	−98.2172	−	98.2172i	−0.197620	−	0.197620i
$498$	−91.9001	+	91.9001i	−0.184538	+	0.184538i
$499$			79.5355i			0.159390i	0.996819	+	0.0796949i	$0.0253946\pi$
$499$			79.5355i			0.159390i	−0.996819	+	0.0796949i	$0.974605\pi$
$500$	−151.824	+	198.619i	−0.303648	+	0.397238i
$501$	78.8940			0.157473
$502$	117.352	+	117.352i	0.233768	+	0.233768i
$503$	−17.2200	+	17.2200i	−0.0342345	+	0.0342345i	−0.724017	−	0.689782i	$-0.757706\pi$
$503$	−17.2200	+	17.2200i	−0.0342345	+	0.0342345i	0.689782	+	0.724017i	$0.257706\pi$
$504$		−	76.8719i		−	0.152524i
$505$	364.118	+	80.4881i	0.721026	+	0.159382i
$506$	−4.98967			−0.00986100
$507$	102.225	+	102.225i	0.201628	+	0.201628i
$508$	−24.1408	+	24.1408i	−0.0475213	+	0.0475213i
$509$		−	107.324i		−	0.210853i	−0.994427	−	0.105426i	$-0.966379\pi$
$509$		−	107.324i		−	0.210853i	0.994427	−	0.105426i	$-0.0336207\pi$
$510$	30.8313	+	48.3299i	0.0604536	+	0.0947644i
$511$	284.688			0.557120
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−11.6295	+	11.6295i	−0.0226696	+	0.0226696i
$514$			122.134i			0.237616i
$515$	325.162	−	207.432i	0.631382	−	0.402781i
$516$	−143.106			−0.277337
$517$	−13.9605	−	13.9605i	−0.0270028	−	0.0270028i
$518$	501.372	−	501.372i	0.967899	−	0.967899i
$519$		−	476.221i		−	0.917574i
$520$	28.2301	−	127.710i	0.0542887	−	0.245595i
$521$	401.266			0.770185			0.385093	−	0.922878i	$-0.374170\pi$
$521$	401.266			0.770185			0.385093	+	0.922878i	$0.374170\pi$
$522$	−2.94618	−	2.94618i	−0.00564403	−	0.00564403i
$523$	252.282	−	252.282i	0.482374	−	0.482374i	−0.423515	−	0.905889i	$-0.639204\pi$
$523$	252.282	−	252.282i	0.482374	−	0.482374i	0.905889	+	0.423515i	$0.139204\pi$
$524$		−	69.6554i		−	0.132930i
$525$	355.735	+	165.349i	0.677590	+	0.314951i
$526$	147.725			0.280847
$527$	−97.1504	−	97.1504i	−0.184346	−	0.184346i
$528$	3.60411	−	3.60411i	0.00682597	−	0.00682597i
$529$		−	23.0000i		−	0.0434783i
$530$	25.0712	+	5.54196i	0.0473041	+	0.0104565i
$531$	−157.164			−0.295977
$532$	40.5519	+	40.5519i	0.0762254	+	0.0762254i
$533$	−19.1285	+	19.1285i	−0.0358883	+	0.0358883i
$534$			52.4365i			0.0981957i
$535$	−533.126	−	835.705i	−0.996497	−	1.56207i
$536$	−114.948			−0.214455
$537$	218.267	+	218.267i	0.406456	+	0.406456i
$538$	29.3391	−	29.3391i	0.0545336	−	0.0545336i
$539$		−	24.3317i		−	0.0451423i
$540$	43.8067	−	27.9459i	0.0811236	−	0.0517516i
$541$	−616.279			−1.13915			−0.569574	−	0.821940i	$-0.692892\pi$
$541$	−616.279			−1.13915			−0.569574	+	0.821940i	$0.692892\pi$
$542$	−250.398	−	250.398i	−0.461989	−	0.461989i
$543$	−34.1303	+	34.1303i	−0.0628550	+	0.0628550i
$544$		−	26.4781i		−	0.0486729i
$545$	−112.686	+	509.778i	−0.206764	+	0.935373i
$546$	−205.232			−0.375883
$547$	17.2149	+	17.2149i	0.0314715	+	0.0314715i	0.722667	−	0.691196i	$-0.242916\pi$
$547$	17.2149	+	17.2149i	0.0314715	+	0.0314715i	−0.691196	+	0.722667i	$0.742916\pi$
$548$	122.085	−	122.085i	0.222784	−	0.222784i
$549$		−	147.861i		−	0.269327i
$550$	8.92616	+	24.4308i	0.0162294	+	0.0444197i
$551$	3.10837			0.00564133
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	−661.753	+	661.753i	−1.19666	+	1.19666i
$554$			9.26370i			0.0167215i
$555$	467.983	+	103.447i	0.843212	+	0.186391i
$556$	−506.670			−0.911276
$557$	−494.208	−	494.208i	−0.887267	−	0.887267i	0.106992	−	0.994260i	$-0.465878\pi$
$557$	−494.208	−	494.208i	−0.887267	−	0.887267i	−0.994260	+	0.106992i	$0.965878\pi$
$558$	−88.0582	+	88.0582i	−0.157810	+	0.157810i
$559$			382.063i			0.683476i
$560$	−97.4467	−	152.753i	−0.174012	−	0.272773i
$561$	5.96437			0.0106317
$562$	430.368	+	430.368i	0.765779	+	0.765779i
$563$	−372.518	+	372.518i	−0.661666	+	0.661666i	−0.955773	−	0.294106i	$-0.904978\pi$
$563$	−372.518	+	372.518i	−0.661666	+	0.661666i	0.294106	+	0.955773i	$0.404978\pi$
$564$			92.9635i			0.164829i
$565$	581.103	−	370.706i	1.02850	−	0.656117i
$566$	167.937			0.296708
$567$	−57.6539	−	57.6539i	−0.101682	−	0.101682i
$568$	−30.6642	+	30.6642i	−0.0539862	+	0.0539862i
$569$			583.724i			1.02588i	0.858425	+	0.512939i	$0.171443\pi$
$569$			583.724i			1.02588i	−0.858425	+	0.512939i	$0.828557\pi$
$570$	−8.36701	+	37.8513i	−0.0146790	+	0.0664058i
$571$	−210.937			−0.369417			−0.184708	−	0.982793i	$-0.559134\pi$
$571$	−210.937			−0.369417			−0.184708	+	0.982793i	$0.559134\pi$
$572$	−9.62223	−	9.62223i	−0.0168221	−	0.0168221i
$573$	−225.440	+	225.440i	−0.393438	+	0.393438i
$574$			37.4752i			0.0652877i
$575$	−112.615	+	41.1454i	−0.195852	+	0.0715572i
$576$	−24.0000			−0.0416667
$577$	−331.826	−	331.826i	−0.575089	−	0.575089i	0.358457	−	0.933546i	$-0.383303\pi$
$577$	−331.826	−	331.826i	−0.575089	−	0.575089i	−0.933546	+	0.358457i	$0.883303\pi$
$578$	−267.091	+	267.091i	−0.462095	+	0.462095i
$579$			397.957i			0.687318i
$580$	−9.58912	−	2.11967i	−0.0165330	−	0.00365460i
$581$	480.681			0.827333
$582$	210.399	+	210.399i	0.361510	+	0.361510i
$583$	1.88898	−	1.88898i	0.00324009	−	0.00324009i
$584$		−	88.8819i		−	0.152195i
$585$	−74.6096	−	116.955i	−0.127538	−	0.199923i
$586$	−69.3498			−0.118344
$587$	−561.771	−	561.771i	−0.957021	−	0.957021i	0.0420931	−	0.999114i	$-0.486597\pi$
$587$	−561.771	−	561.771i	−0.957021	−	0.957021i	−0.999114	+	0.0420931i	$0.986597\pi$
$588$	−81.0131	+	81.0131i	−0.137777	+	0.137777i
$589$		−	92.9059i		−	0.157735i
$590$	−312.302	+	199.228i	−0.529325	+	0.337675i
$591$	−578.664			−0.979127
$592$	−156.532	−	156.532i	−0.264412	−	0.264412i
$593$	105.552	−	105.552i	0.177997	−	0.177997i	−0.612485	−	0.790482i	$-0.709830\pi$
$593$	105.552	−	105.552i	0.177997	−	0.177997i	0.790482	+	0.612485i	$0.209830\pi$
$594$		−	5.40617i		−	0.00910129i
$595$	45.7627	−	207.025i	0.0769122	−	0.347941i
$596$	447.219			0.750368
$597$	82.3065	+	82.3065i	0.137867	+	0.137867i
$598$	44.3539	−	44.3539i	0.0741704	−	0.0741704i
$599$			1010.12i			1.68634i	0.537647	+	0.843170i	$0.319313\pi$
$599$			1010.12i			1.68634i	−0.537647	+	0.843170i	$0.680687\pi$
$600$	51.6233	−	111.063i	0.0860389	−	0.185105i
$601$	778.285			1.29498			0.647492	−	0.762073i	$-0.275818\pi$
$601$	778.285			1.29498			0.647492	+	0.762073i	$0.275818\pi$
$602$	374.256	+	374.256i	0.621687	+	0.621687i
$603$	−86.2109	+	86.2109i	−0.142970	+	0.142970i
$604$			455.199i			0.753641i
$605$	−588.097	−	129.998i	−0.972061	−	0.214873i
$606$	−182.687			−0.301464
$607$	−766.399	−	766.399i	−1.26260	−	1.26260i	−0.949828	−	0.312773i	$-0.898742\pi$
$607$	−766.399	−	766.399i	−1.26260	−	1.26260i	−0.312773	−	0.949828i	$-0.601258\pi$
$608$	12.6606	−	12.6606i	0.0208234	−	0.0208234i
$609$			15.4099i			0.0253036i
$610$	−187.436	−	293.816i	−0.307271	−	0.481665i
$611$	248.193			0.406208
$612$	−19.8585	−	19.8585i	−0.0324486	−	0.0324486i
$613$	−419.276	+	419.276i	−0.683974	+	0.683974i	−0.960893	−	0.276919i	$-0.910687\pi$
$613$	−419.276	+	419.276i	−0.683974	+	0.683974i	0.276919	+	0.960893i	$0.410687\pi$
$614$			327.463i			0.533328i
$615$	−21.3558	+	13.6237i	−0.0347249	+	0.0221523i
$616$	−18.8512			−0.0306026
$617$	−629.156	−	629.156i	−1.01970	−	1.01970i	−0.999802	−	0.0199000i	$-0.993665\pi$
$617$	−629.156	−	629.156i	−1.01970	−	1.01970i	−0.0199000	−	0.999802i	$-0.506335\pi$
$618$	−133.608	+	133.608i	−0.216193	+	0.216193i
$619$			767.208i			1.23943i	0.784827	+	0.619715i	$0.212752\pi$
$619$			767.208i			1.23943i	−0.784827	+	0.619715i	$0.787248\pi$
$620$	−63.3546	+	286.609i	−0.102185	+	0.462272i
$621$	24.9199			0.0401286
$622$	−57.2138	−	57.2138i	−0.0919836	−	0.0919836i
$623$	137.134	−	137.134i	0.220118	−	0.220118i
$624$			64.0750i			0.102684i
$625$	402.919	+	477.788i	0.644671	+	0.764460i
$626$	−386.422			−0.617287
$627$	2.85189	+	2.85189i	0.00454847	+	0.00454847i
$628$	224.547	−	224.547i	0.357560	−	0.357560i
$629$		−	259.042i		−	0.411831i
$630$	−187.650	−	41.4799i	−0.297857	−	0.0658410i
$631$	−668.072			−1.05875			−0.529376	−	0.848388i	$-0.677574\pi$
$631$	−668.072			−1.05875			−0.529376	+	0.848388i	$0.677574\pi$
$632$	206.604	+	206.604i	0.326906	+	0.326906i
$633$	36.3060	−	36.3060i	0.0573555	−	0.0573555i
$634$		−	463.187i		−	0.730579i
$635$	45.9032	+	71.9558i	0.0722885	+	0.113316i
$636$	−12.5788			−0.0197780
$637$	216.288	+	216.288i	0.339542	+	0.339542i
$638$	−0.722488	+	0.722488i	−0.00113243	+	0.00113243i
$639$			45.9962i			0.0719816i
$640$	−47.6907	+	30.4236i	−0.0745167	+	0.0475369i
$641$	−337.574			−0.526637			−0.263318	−	0.964709i	$-0.584817\pi$
$641$	−337.574			−0.526637			−0.263318	+	0.964709i	$0.584817\pi$
$642$	343.388	+	343.388i	0.534872	+	0.534872i
$643$	95.9880	−	95.9880i	0.149282	−	0.149282i	−0.628515	−	0.777797i	$-0.716337\pi$
$643$	95.9880	−	95.9880i	0.149282	−	0.149282i	0.777797	+	0.628515i	$0.216337\pi$
$644$		−	86.8951i		−	0.134930i
$645$	−77.2196	+	349.332i	−0.119720	+	0.541600i
$646$	20.9518			0.0324331
$647$	−94.6732	−	94.6732i	−0.146326	−	0.146326i	0.630148	−	0.776475i	$-0.282994\pi$
$647$	−94.6732	−	94.6732i	−0.146326	−	0.146326i	−0.776475	+	0.630148i	$0.782994\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			38.5410i			0.0593852i
$650$	−296.516	−	137.824i	−0.456178	−	0.212036i
$651$	460.586			0.707505
$652$	−144.353	−	144.353i	−0.221401	−	0.221401i
$653$	169.998	−	169.998i	0.260335	−	0.260335i	−0.564855	−	0.825190i	$-0.691068\pi$
$653$	169.998	−	169.998i	0.260335	−	0.260335i	0.825190	+	0.564855i	$0.191068\pi$
$654$		−	255.768i		−	0.391083i
$655$	−170.034	−	37.5859i	−0.259594	−	0.0573830i
$656$	11.7000			0.0178354
$657$	−66.6614	−	66.6614i	−0.101463	−	0.101463i
$658$	243.121	−	243.121i	0.369485	−	0.369485i
$659$			380.928i			0.578039i	0.957323	+	0.289020i	$0.0933293\pi$
$659$			380.928i			0.578039i	−0.957323	+	0.289020i	$0.906671\pi$
$660$	−6.85313	−	10.7427i	−0.0103835	−	0.0162768i
$661$	353.883			0.535376			0.267688	−	0.963506i	$-0.413740\pi$
$661$	353.883			0.535376			0.267688	+	0.963506i	$0.413740\pi$
$662$	191.879	+	191.879i	0.289847	+	0.289847i
$663$	−53.0182	+	53.0182i	−0.0799671	+	0.0799671i
$664$		−	150.072i		−	0.226012i
$665$	120.872	−	77.1084i	0.181762	−	0.115952i
$666$	−234.798			−0.352550
$667$	−3.33033	−	3.33033i	−0.00499300	−	0.00499300i
$668$	−64.4167	+	64.4167i	−0.0964321	+	0.0964321i
$669$			327.400i			0.489387i
$670$	−62.0255	+	280.596i	−0.0925754	+	0.418800i
$671$	−36.2597			−0.0540383
$672$	62.7656	+	62.7656i	0.0934012	+	0.0934012i
$673$	−567.893	+	567.893i	−0.843824	+	0.843824i	−0.989354	−	0.145530i	$-0.953511\pi$
$673$	−567.893	+	567.893i	−0.843824	+	0.843824i	0.145530	+	0.989354i	$0.453511\pi$
$674$			570.204i			0.846001i
$675$	−44.5799	−	122.015i	−0.0660443	−	0.180763i
$676$	−166.933			−0.246943
$677$	−337.349	−	337.349i	−0.498299	−	0.498299i	0.412609	−	0.910908i	$-0.364618\pi$
$677$	−337.349	−	337.349i	−0.498299	−	0.498299i	−0.910908	+	0.412609i	$0.864618\pi$
$678$	−238.773	+	238.773i	−0.352172	+	0.352172i
$679$		−	1100.49i		−	1.62074i
$680$	−64.6348	−	14.2875i	−0.0950512	−	0.0210110i
$681$	−517.975			−0.760609
$682$	21.5944	+	21.5944i	0.0316634	+	0.0316634i
$683$	49.1392	−	49.1392i	0.0719462	−	0.0719462i	−0.670218	−	0.742164i	$-0.733799\pi$
$683$	49.1392	−	49.1392i	0.0719462	−	0.0719462i	0.742164	+	0.670218i	$0.233799\pi$
$684$		−	18.9909i		−	0.0277645i
$685$	−232.142	−	363.896i	−0.338894	−	0.531236i
$686$	−204.051			−0.297450
$687$	−95.6990	−	95.6990i	−0.139300	−	0.139300i
$688$	116.846	−	116.846i	0.169834	−	0.169834i
$689$			33.5828i			0.0487413i
$690$	49.5186	−	31.5897i	0.0717661	−	0.0457821i
$691$	−890.511			−1.28873			−0.644364	−	0.764719i	$-0.722878\pi$
$691$	−890.511			−1.28873			−0.644364	+	0.764719i	$0.722878\pi$
$692$	388.833	+	388.833i	0.561897	+	0.561897i
$693$	−14.1384	+	14.1384i	−0.0204017	+	0.0204017i
$694$		−	204.130i		−	0.294136i
$695$	−273.398	+	1236.82i	−0.393378	+	1.77959i
$696$	4.81109			0.00691249
$697$	9.68107	+	9.68107i	0.0138896	+	0.0138896i
$698$	−385.605	+	385.605i	−0.552442	+	0.552442i
$699$			621.797i			0.889552i
$700$	−425.463	+	155.449i	−0.607805	+	0.222070i
$701$	735.307			1.04894			0.524470	−	0.851429i	$-0.324264\pi$
$701$	735.307			1.04894			0.524470	+	0.851429i	$0.324264\pi$
$702$	48.0562	+	48.0562i	0.0684562	+	0.0684562i
$703$	123.862	−	123.862i	0.176191	−	0.176191i
$704$			5.88549i			0.00836007i
$705$	226.931	+	50.1629i	0.321888	+	0.0711530i
$706$	246.249			0.348795
$707$	477.769	+	477.769i	0.675770	+	0.675770i
$708$	128.324	−	128.324i	0.181248	−	0.181248i
$709$		−	1352.58i		−	1.90773i	−0.300244	−	0.953863i	$-0.597068\pi$
$709$		−	1352.58i		−	1.90773i	0.300244	−	0.953863i	$-0.402932\pi$
$710$	58.3071	+	91.3997i	0.0821227	+	0.128732i
$711$	309.907			0.435874
$712$	−42.8142	−	42.8142i	−0.0601323	−	0.0601323i
$713$	−99.5400	+	99.5400i	−0.139607	+	0.139607i
$714$			103.869i			0.145475i
$715$	−28.6807	+	18.2964i	−0.0401128	+	0.0255894i
$716$	−356.429			−0.497805
$717$	483.928	+	483.928i	0.674935	+	0.674935i
$718$	236.238	−	236.238i	0.329022	−	0.329022i
$719$			1401.76i			1.94960i	0.223086	+	0.974799i	$0.428387\pi$
$719$			1401.76i			1.94960i	−0.223086	+	0.974799i	$0.571613\pi$
$720$	−12.9503	+	58.5857i	−0.0179866	+	0.0813691i
$721$	698.830			0.969251
$722$	−350.982	−	350.982i	−0.486124	−	0.486124i
$723$	−350.074	+	350.074i	−0.484196	+	0.484196i
$724$		−	55.7345i		−	0.0769814i
$725$	−10.3485	+	22.2640i	−0.0142738	+	0.0307089i
$726$	295.063			0.406422
$727$	558.895	+	558.895i	0.768768	+	0.768768i	0.977890	−	0.209121i	$-0.0670604\pi$
$727$	558.895	+	558.895i	0.768768	+	0.768768i	−0.209121	+	0.977890i	$0.567060\pi$
$728$	167.571	−	167.571i	0.230180	−	0.230180i
$729$			27.0000i			0.0370370i
$730$	−216.967	−	47.9604i	−0.297215	−	0.0656992i
$731$	193.365			0.264521
$732$	120.728	+	120.728i	0.164929	+	0.164929i
$733$	−73.0059	+	73.0059i	−0.0995988	+	0.0995988i	−0.755150	−	0.655552i	$-0.772436\pi$
$733$	−73.0059	+	73.0059i	−0.0995988	+	0.0995988i	0.655552	+	0.755150i	$0.272436\pi$
$734$			602.579i			0.820952i
$735$	154.044	+	241.473i	0.209584	+	0.328535i
$736$	−27.1293			−0.0368605
$737$	21.1414	+	21.1414i	0.0286857	+	0.0286857i
$738$	8.77503	−	8.77503i	0.0118903	−	0.0118903i
$739$		−	552.827i		−	0.748074i	−0.927414	−	0.374037i	$-0.877973\pi$
$739$		−	552.827i		−	0.748074i	0.927414	−	0.374037i	$-0.122027\pi$
$740$	−466.571	+	297.642i	−0.630501	+	0.402219i
$741$	−50.7018			−0.0684235
$742$	32.8965	+	32.8965i	0.0443349	+	0.0443349i
$743$	−928.252	+	928.252i	−1.24933	+	1.24933i	−0.293313	+	0.956016i	$0.594758\pi$
$743$	−928.252	+	928.252i	−1.24933	+	1.24933i	−0.956016	+	0.293313i	$0.905242\pi$
$744$		−	143.798i		−	0.193278i
$745$	241.318	−	1091.69i	0.323917	−	1.46536i
$746$	271.054			0.363343
$747$	−112.554	−	112.554i	−0.150675	−	0.150675i
$748$	−4.86988	+	4.86988i	−0.00651054	+	0.00651054i
$749$		−	1796.08i		−	2.39797i
$750$	−243.257	−	185.946i	−0.324343	−	0.247928i
$751$	−392.174			−0.522202			−0.261101	−	0.965312i	$-0.584086\pi$
$751$	−392.174			−0.522202			−0.261101	+	0.965312i	$0.584086\pi$
$752$	−75.9044	−	75.9044i	−0.100937	−	0.100937i
$753$	−143.726	+	143.726i	−0.190871	+	0.190871i
$754$		−	12.8446i		−	0.0170353i
$755$	1111.17	+	245.624i	1.47175	+	0.325330i
$756$	94.1485			0.124535
$757$	675.475	+	675.475i	0.892306	+	0.892306i	0.994740	−	0.102434i	$-0.0326631\pi$
$757$	675.475	+	675.475i	0.892306	+	0.892306i	−0.102434	+	0.994740i	$0.532663\pi$
$758$	−195.582	+	195.582i	−0.258023	+	0.258023i
$759$		−	6.11107i		−	0.00805147i
$760$	−24.0738	−	37.7371i	−0.0316761	−	0.0496541i
$761$	−33.6363			−0.0442002			−0.0221001	−	0.999756i	$-0.507035\pi$
$761$	−33.6363			−0.0442002			−0.0221001	+	0.999756i	$0.507035\pi$
$762$	−29.5664	−	29.5664i	−0.0388010	−	0.0388010i
$763$	−668.894	+	668.894i	−0.876663	+	0.876663i
$764$		−	368.141i		−	0.481861i
$765$	−59.1917	+	37.7605i	−0.0773748	+	0.0493602i
$766$	549.331			0.717142
$767$	−342.597	−	342.597i	−0.446671	−	0.446671i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	703.948i		−	0.915407i	−0.889105	−	0.457703i	$-0.848672\pi$
$769$		−	703.948i		−	0.915407i	0.889105	−	0.457703i	$-0.151328\pi$
$770$	−10.1721	+	46.0171i	−0.0132105	+	0.0597625i
$771$	−149.584			−0.194012
$772$	−324.931	−	324.931i	−0.420895	−	0.420895i
$773$	82.2891	−	82.2891i	0.106454	−	0.106454i	−0.651874	−	0.758328i	$-0.726017\pi$
$773$	82.2891	−	82.2891i	0.106454	−	0.106454i	0.758328	+	0.651874i	$0.226017\pi$
$774$		−	175.268i		−	0.226445i
$775$	665.447	+	309.306i	0.858641	+	0.399105i
$776$	−343.580			−0.442758
$777$	614.052	+	614.052i	0.790286	+	0.790286i
$778$	−25.3609	+	25.3609i	−0.0325976	+	0.0325976i
$779$			9.25810i			0.0118846i
$780$	156.412	+	34.5747i	0.200528	+	0.0443265i
$781$	11.2796			0.0144425
$782$	−22.4479	−	22.4479i	−0.0287057	−	0.0287057i
$783$	3.60832	−	3.60832i	0.00460833	−	0.00460833i
$784$		−	132.294i		−	0.168742i
$785$	−426.971	−	669.302i	−0.543912	−	0.852613i
$786$	85.3101			0.108537
$787$	171.662	+	171.662i	0.218122	+	0.218122i	0.807707	−	0.589585i	$-0.200709\pi$
$787$	171.662	+	171.662i	0.218122	+	0.218122i	−0.589585	+	0.807707i	$0.700709\pi$
$788$	472.477	−	472.477i	0.599591	−	0.599591i
$789$			180.926i			0.229310i
$790$	615.819	−	392.853i	0.779518	−	0.497282i
$791$	1248.89			1.57888
$792$	4.41412	+	4.41412i	0.00557338	+	0.00557338i
$793$	322.318	−	322.318i	0.406454	−	0.406454i
$794$		−	501.953i		−	0.632183i
$795$	−6.78749	+	30.7058i	−0.00853772	+	0.0386236i
$796$	−134.406			−0.168852
$797$	−395.242	−	395.242i	−0.495912	−	0.495912i	0.414251	−	0.910163i	$-0.364044\pi$
$797$	−395.242	−	395.242i	−0.495912	−	0.495912i	−0.910163	+	0.414251i	$0.864044\pi$
$798$	−49.6657	+	49.6657i	−0.0622377	+	0.0622377i
$799$		−	125.613i		−	0.157212i
$800$	48.5324	+	132.833i	0.0606656	+	0.166041i
$801$	−64.2213			−0.0801764
$802$	−118.805	−	118.805i	−0.148136	−	0.148136i
$803$	−16.3473	+	16.3473i	−0.0203578	+	0.0203578i
$804$		−	140.782i		−	0.175102i
$805$	−212.117	−	46.8883i	−0.263500	−	0.0582464i
$806$	−383.912			−0.476318
$807$	35.9329	+	35.9329i	0.0445265	+	0.0445265i
$808$	149.163	−	149.163i	0.184608	−	0.184608i
$809$		−	56.2964i		−	0.0695876i	−0.999395	−	0.0347938i	$-0.988923\pi$
$809$		−	56.2964i		−	0.0695876i	0.999395	−	0.0347938i	$-0.0110774\pi$
$810$	34.2266	+	53.6521i	0.0422550	+	0.0662371i
$811$	915.333			1.12865			0.564324	−	0.825554i	$-0.309137\pi$
$811$	915.333			1.12865			0.564324	+	0.825554i	$0.309137\pi$
$812$	−12.5821	−	12.5821i	−0.0154952	−	0.0154952i
$813$	306.674	−	306.674i	0.377213	−	0.377213i
$814$			57.5793i			0.0707362i
$815$	−430.270	+	274.484i	−0.527938	+	0.336791i
$816$	32.4289			0.0397412
$817$	92.4585	+	92.4585i	0.113168	+	0.113168i
$818$	−314.345	+	314.345i	−0.384284	+	0.384284i
$819$		−	251.357i		−	0.306907i
$820$	6.31331	−	28.5606i	0.00769916	−	0.0348300i
$821$	−1316.60			−1.60365			−0.801827	−	0.597556i	$-0.796138\pi$
$821$	−1316.60			−1.60365			−0.801827	+	0.597556i	$0.796138\pi$
$822$	149.524	+	149.524i	0.181902	+	0.181902i
$823$	−746.812	+	746.812i	−0.907426	+	0.907426i	−0.996064	−	0.0886379i	$-0.971749\pi$
$823$	−746.812	+	746.812i	−0.907426	+	0.907426i	0.0886379	+	0.996064i	$0.471749\pi$
$824$		−	218.180i		−	0.264782i
$825$	−29.9216	+	10.9323i	−0.0362686	+	0.0132512i
$826$	−671.192			−0.812581
$827$	876.942	+	876.942i	1.06039	+	1.06039i	0.998055	+	0.0623337i	$0.0198543\pi$
$827$	876.942	+	876.942i	1.06039	+	1.06039i	0.0623337	+	0.998055i	$0.480146\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	1121.54i		−	1.35288i	−0.736498	−	0.676439i	$-0.763522\pi$
$829$		−	1121.54i		−	1.35288i	0.736498	−	0.676439i	$-0.236478\pi$
$830$	−366.337	−	80.9785i	−0.441370	−	0.0975645i
$831$	−11.3457			−0.0136530
$832$	−52.3170	−	52.3170i	−0.0628810	−	0.0628810i
$833$	109.465	−	109.465i	0.131411	−	0.131411i
$834$		−	620.541i		−	0.744054i
$835$	122.487	+	192.005i	0.146691	+	0.229946i
$836$	−4.65712			−0.00557072
$837$	−107.849	−	107.849i	−0.128852	−	0.128852i
$838$	114.465	−	114.465i	0.136594	−	0.136594i
$839$			1496.53i			1.78371i	0.452320	+	0.891856i	$0.350597\pi$
$839$			1496.53i			1.78371i	−0.452320	+	0.891856i	$0.649403\pi$
$840$	187.084	−	119.347i	0.222719	−	0.142080i
$841$	840.036			0.998853
$842$	−260.815	−	260.815i	−0.309756	−	0.309756i
$843$	−527.091	+	527.091i	−0.625256	+	0.625256i
$844$			59.2875i			0.0702459i
$845$	−90.0767	+	407.496i	−0.106600	+	0.482244i
$846$	−113.857			−0.134582
$847$	−771.658	−	771.658i	−0.911048	−	0.911048i
$848$	10.2705	−	10.2705i	0.0121115	−	0.0121115i
$849$			205.680i			0.242261i
$850$	−69.7536	+	150.069i	−0.0820630	+	0.176552i
$851$	−265.413			−0.311884
$852$	−37.5558	−	37.5558i	−0.0440795	−	0.0440795i
$853$	−1023.72	+	1023.72i	−1.20014	+	1.20014i	−0.226023	+	0.974122i	$0.572572\pi$
$853$	−1023.72	+	1023.72i	−1.20014	+	1.20014i	−0.974122	+	0.226023i	$0.927428\pi$
$854$		−	631.462i		−	0.739417i
$855$	−46.3582	−	10.2474i	−0.0542201	−	0.0119853i
$856$	−560.750			−0.655082
$857$	222.920	+	222.920i	0.260117	+	0.260117i	0.825101	−	0.564985i	$-0.191118\pi$
$857$	222.920	+	222.920i	0.260117	+	0.260117i	−0.564985	+	0.825101i	$0.691118\pi$
$858$	11.7848	−	11.7848i	0.0137352	−	0.0137352i
$859$		−	1224.20i		−	1.42514i	−0.701600	−	0.712571i	$-0.747531\pi$
$859$		−	1224.20i		−	1.42514i	0.701600	−	0.712571i	$-0.252469\pi$
$860$	−222.179	−	348.278i	−0.258347	−	0.404974i
$861$	−45.8975			−0.0533072
$862$	−113.472	−	113.472i	−0.131638	−	0.131638i
$863$	544.641	−	544.641i	0.631102	−	0.631102i	−0.317242	−	0.948345i	$-0.602757\pi$
$863$	544.641	−	544.641i	0.631102	−	0.631102i	0.948345	+	0.317242i	$0.102757\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	1158.98	−	739.356i	1.33986	−	0.854747i
$866$	−1000.98			−1.15586
$867$	−327.118	−	327.118i	−0.377299	−	0.377299i
$868$	−376.067	+	376.067i	−0.433257	+	0.433257i
$869$		−	75.9980i		−	0.0874545i
$870$	2.59605	−	11.7442i	0.00298397	−	0.0134991i
$871$	−375.858			−0.431525
$872$	208.834	+	208.834i	0.239488	+	0.239488i
$873$	−257.685	+	257.685i	−0.295172	+	0.295172i
$874$		−	21.4671i		−	0.0245619i
$875$	149.884	+	1122.47i	0.171296	+	1.28282i
$876$	108.858			0.124267
$877$	337.281	+	337.281i	0.384584	+	0.384584i	0.872751	−	0.488166i	$-0.162334\pi$
$877$	337.281	+	337.281i	0.384584	+	0.384584i	−0.488166	+	0.872751i	$0.662334\pi$
$878$	275.486	−	275.486i	0.313765	−	0.313765i
$879$		−	84.9358i		−	0.0966277i
$880$	14.3669	+	3.17579i	0.0163260	+	0.00360886i
$881$	−406.144			−0.461003			−0.230502	−	0.973072i	$-0.574037\pi$
$881$	−406.144			−0.461003			−0.230502	+	0.973072i	$0.574037\pi$
$882$	−99.2203	−	99.2203i	−0.112495	−	0.112495i
$883$	342.111	−	342.111i	0.387442	−	0.387442i	−0.486332	−	0.873774i	$-0.661665\pi$
$883$	342.111	−	342.111i	0.387442	−	0.387442i	0.873774	+	0.486332i	$0.161665\pi$
$884$		−	86.5783i		−	0.0979392i
$885$	−244.004	−	382.490i	−0.275711	−	0.432192i
$886$	216.082			0.243885
$887$	−664.342	−	664.342i	−0.748976	−	0.748976i	0.225311	−	0.974287i	$-0.427660\pi$
$887$	−664.342	−	664.342i	−0.748976	−	0.748976i	−0.974287	+	0.225311i	$0.927660\pi$
$888$	191.712	−	191.712i	0.215892	−	0.215892i
$889$			154.646i			0.173955i
$890$	−127.615	+	81.4102i	−0.143388	+	0.0914721i
$891$	6.62118			0.00743117
$892$	−267.321	−	267.321i	−0.299687	−	0.299687i
$893$	60.0623	−	60.0623i	0.0672590	−	0.0672590i
$894$			547.730i			0.612673i
$895$	−192.328	+	870.068i	−0.214891	+	0.972143i
$896$	−102.496			−0.114393
$897$	54.3222	+	54.3222i	0.0605599	+	0.0605599i
$898$	−288.810	+	288.810i	−0.321615	+	0.321615i
$899$			28.8262i			0.0320647i
$900$	136.024	+	63.2254i	0.151138	+	0.0702504i
$901$	16.9965			0.0188640
$902$	−2.15189	−	2.15189i	−0.00238569	−	0.00238569i
$903$	−458.368	+	458.368i	−0.507605	+	0.507605i
$904$		−	389.914i		−	0.431321i
$905$	−136.052	−	30.0742i	−0.150334	−	0.0332312i
$906$	−557.503			−0.615345
$907$	−94.3600	−	94.3600i	−0.104035	−	0.104035i	0.653173	−	0.757209i	$-0.273437\pi$
$907$	−94.3600	−	94.3600i	−0.104035	−	0.104035i	−0.757209	+	0.653173i	$0.773437\pi$
$908$	422.925	−	422.925i	0.465776	−	0.465776i
$909$		−	223.745i		−	0.246144i
$910$	−318.632	−	499.474i	−0.350145	−	0.548873i
$911$	−303.778			−0.333455			−0.166728	−	0.986003i	$-0.553320\pi$
$911$	−303.778			−0.333455			−0.166728	+	0.986003i	$0.553320\pi$
$912$	15.5060	+	15.5060i	0.0170022	+	0.0170022i
$913$	−27.6015	+	27.6015i	−0.0302317	+	0.0302317i
$914$			306.166i			0.334974i
$915$	359.849	−	229.561i	0.393278	−	0.250886i
$916$	156.276			0.170607
$917$	−223.106	−	223.106i	−0.243300	−	0.243300i
$918$	24.3216	−	24.3216i	0.0264942	−	0.0264942i
$919$			1128.39i			1.22784i	0.789367	+	0.613922i	$0.210409\pi$
$919$			1128.39i			1.22784i	−0.789367	+	0.613922i	$0.789591\pi$
$920$	−14.6389	+	66.2246i	−0.0159119	+	0.0719833i
$921$	−401.059			−0.435460
$922$	296.499	+	296.499i	0.321583	+	0.321583i
$923$	−100.266	+	100.266i	−0.108631	+	0.108631i
$924$		−	23.0879i		−	0.0249869i
$925$	474.805	+	1299.54i	0.513303	+	1.40491i
$926$	792.626			0.855968
$927$	−163.635	−	163.635i	−0.176521	−	0.176521i
$928$	−3.92824	+	3.92824i	−0.00423302	+	0.00423302i
$929$		−	697.117i		−	0.750395i	−0.926945	−	0.375197i	$-0.877575\pi$
$929$		−	697.117i		−	0.750395i	0.926945	−	0.375197i	$-0.122425\pi$
$930$	−351.023	−	77.5933i	−0.377444	−	0.0834336i
$931$	104.683			0.112441
$932$	−507.695	−	507.695i	−0.544737	−	0.544737i
$933$	70.0723	−	70.0723i	0.0751043	−	0.0751043i
$934$			876.954i			0.938923i
$935$	9.25996	+	14.5155i	0.00990371	+	0.0155246i
$936$	−78.4755			−0.0838414
$937$	1039.23	+	1039.23i	1.10911	+	1.10911i	0.993268	+	0.115841i	$0.0369563\pi$
$937$	1039.23	+	1039.23i	1.10911	+	1.10911i	0.115841	+	0.993268i	$0.463044\pi$
$938$	−368.177	+	368.177i	−0.392513	+	0.392513i
$939$		−	473.268i		−	0.504013i
$940$	−226.246	+	144.330i	−0.240687	+	0.153543i
$941$	−912.139			−0.969329			−0.484665	−	0.874700i	$-0.661058\pi$
$941$	−912.139			−0.969329			−0.484665	+	0.874700i	$0.661058\pi$
$942$	275.013	+	275.013i	0.291946	+	0.291946i
$943$	9.91919	−	9.91919i	0.0105188	−	0.0105188i
$944$			209.551i			0.221982i
$945$	50.8022	−	229.823i	0.0537590	−	0.243199i
$946$	−42.9808			−0.0454343
$947$	215.503	+	215.503i	0.227564	+	0.227564i	0.811674	−	0.584111i	$-0.198557\pi$
$947$	215.503	+	215.503i	0.227564	+	0.227564i	−0.584111	+	0.811674i	$0.698557\pi$
$948$	−253.038	+	253.038i	−0.266917	+	0.266917i
$949$		−	290.627i		−	0.306246i
$950$	−105.109	+	38.4032i	−0.110641	+	0.0404244i
$951$	567.286			0.596515
$952$	−84.8091	−	84.8091i	−0.0890852	−	0.0890852i
$953$	1046.66	−	1046.66i	1.09828	−	1.09828i	0.103668	−	0.994612i	$-0.466942\pi$
$953$	1046.66	−	1046.66i	1.09828	−	1.09828i	0.994612	−	0.103668i	$-0.0330580\pi$
$954$		−	15.4058i		−	0.0161487i
$955$	−898.660	−	198.648i	−0.941005	−	0.208008i
$956$	−790.252			−0.826623
$957$	−0.884864	−	0.884864i	−0.000924623	−	0.000924623i
$958$	−425.424	+	425.424i	−0.444075	+	0.444075i
$959$		−	782.078i		−	0.815514i
$960$	−37.2612	−	58.4090i	−0.0388137	−	0.0608427i
$961$	−99.4166			−0.103451
$962$	−511.831	−	511.831i	−0.532049	−	0.532049i
$963$	−420.562	+	420.562i	−0.436721	+	0.436721i
$964$		−	571.668i		−	0.593016i
$965$	−968.512	+	617.848i	−1.00364	+	0.640257i
$966$	106.424			0.110170
$967$	680.034	+	680.034i	0.703241	+	0.703241i	0.965105	−	0.261864i	$-0.0843371\pi$
$967$	680.034	+	680.034i	0.703241	+	0.703241i	−0.261864	+	0.965105i	$0.584337\pi$
$968$	−240.918	+	240.918i	−0.248882	+	0.248882i
$969$			25.6606i			0.0264815i
$970$	−185.395	+	838.704i	−0.191129	+	0.864643i
$971$	318.463			0.327974			0.163987	−	0.986462i	$-0.447564\pi$
$971$	318.463			0.327974			0.163987	+	0.986462i	$0.447564\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	−1622.86	+	1622.86i	−1.66789	+	1.66789i
$974$		−	565.515i		−	0.580611i
$975$	168.799	−	363.156i	0.173127	−	0.372468i
$976$	−197.147			−0.201995
$977$	658.914	+	658.914i	0.674426	+	0.674426i	0.958733	−	0.284307i	$-0.0917636\pi$
$977$	658.914	+	658.914i	0.674426	+	0.674426i	−0.284307	+	0.958733i	$0.591764\pi$
$978$	176.796	−	176.796i	0.180773	−	0.180773i
$979$			15.7489i			0.0160867i
$980$	−322.939	−	71.3853i	−0.329529	−	0.0728422i
$981$	313.251			0.319318
$982$	−49.8564	−	49.8564i	−0.0507703	−	0.0507703i
$983$	−271.184	+	271.184i	−0.275874	+	0.275874i	−0.831459	−	0.555586i	$-0.812494\pi$
$983$	−271.184	+	271.184i	−0.275874	+	0.275874i	0.555586	+	0.831459i	$0.312494\pi$
$984$			14.3296i			0.0145626i
$985$	−898.404	−	1408.30i	−0.912085	−	1.42975i
$986$	−6.50076			−0.00659306
$987$	297.762	+	297.762i	0.301684	+	0.301684i
$988$	41.3978	−	41.3978i	0.0419006	−	0.0419006i
$989$		−	198.121i		−	0.200325i
$990$	13.1570	−	8.39333i	0.0132899	−	0.00847812i
$991$	821.565			0.829027			0.414513	−	0.910043i	$-0.363952\pi$
$991$	821.565			0.829027			0.414513	+	0.910043i	$0.363952\pi$
$992$	117.411	+	117.411i	0.118358	+	0.118358i
$993$	−235.002	+	235.002i	−0.236659	+	0.236659i
$994$			196.434i			0.197620i
$995$	−72.5250	+	328.095i	−0.0728895	+	0.329743i
$996$	183.800			0.184538
$997$	−555.308	−	555.308i	−0.556979	−	0.556979i	0.371467	−	0.928446i	$-0.378855\pi$
$997$	−555.308	−	555.308i	−0.556979	−	0.556979i	−0.928446	+	0.371467i	$0.878855\pi$
$998$	79.5355	−	79.5355i	0.0796949	−	0.0796949i
$999$		−	287.568i		−	0.287856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.21	✓	48
5.3	odd	4	inner	690.3.k.b.553.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.21	✓	48	1.1	even	1	trivial
690.3.k.b.553.21	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.88214 + 1.07919i) q^{5} -2.44949 q^{6} +(6.40599 + 6.40599i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.88214 + 1.07919i) q^{5} -2.44949 q^{6} +(6.40599 + 6.40599i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-3.80295 - 5.96134i) q^{10} -0.735686 q^{11} +(2.44949 + 2.44949i) q^{12} +(6.53963 - 6.53963i) q^{13} -12.8120i q^{14} +(7.30112 - 4.65764i) q^{15} -4.00000 q^{16} +(-3.30976 - 3.30976i) q^{17} +(-3.00000 + 3.00000i) q^{18} -3.16515i q^{19} +(-2.15839 + 9.76429i) q^{20} +15.6914 q^{21} +(0.735686 + 0.735686i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(22.6707 + 10.5376i) q^{25} -13.0793 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-12.8120 + 12.8120i) q^{28} +0.982060i q^{29} +(-11.9588 - 2.64348i) q^{30} +29.3527 q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.901028 + 0.901028i) q^{33} +6.61951i q^{34} +(24.3617 + 38.1883i) q^{35} +6.00000 q^{36} +(39.1330 + 39.1330i) q^{37} +(-3.16515 + 3.16515i) q^{38} -16.0187i q^{39} +(11.9227 - 7.60590i) q^{40} -2.92501 q^{41} +(-15.6914 - 15.6914i) q^{42} +(-29.2114 + 29.2114i) q^{43} -1.47137i q^{44} +(3.23758 - 14.6464i) q^{45} +6.78233 q^{46} +(18.9761 + 18.9761i) q^{47} +(-4.89898 + 4.89898i) q^{48} +33.0734i q^{49} +(-12.1331 - 33.2082i) q^{50} -8.10721 q^{51} +(13.0793 + 13.0793i) q^{52} +(-2.56764 + 2.56764i) q^{53} +7.34847i q^{54} +(-3.59173 - 0.793948i) q^{55} +25.6240 q^{56} +(-3.87651 - 3.87651i) q^{57} +(0.982060 - 0.982060i) q^{58} -52.3879i q^{59} +(9.31529 + 14.6022i) q^{60} +49.2869 q^{61} +(-29.3527 - 29.3527i) q^{62} +(19.2180 - 19.2180i) q^{63} -8.00000i q^{64} +(38.9849 - 24.8699i) q^{65} +1.80206 q^{66} +(-28.7370 - 28.7370i) q^{67} +(6.61951 - 6.61951i) q^{68} +8.30662i q^{69} +(13.8266 - 62.5500i) q^{70} -15.3321 q^{71} +(-6.00000 - 6.00000i) q^{72} +(22.2205 - 22.2205i) q^{73} -78.2661i q^{74} +(40.6716 - 14.8600i) q^{75} +6.33031 q^{76} +(-4.71280 - 4.71280i) q^{77} +(-16.0187 + 16.0187i) q^{78} +103.302i q^{79} +(-19.5286 - 4.31678i) q^{80} -9.00000 q^{81} +(2.92501 + 2.92501i) q^{82} +(37.5180 - 37.5180i) q^{83} +31.3828i q^{84} +(-12.5868 - 19.7306i) q^{85} +58.4228 q^{86} +(1.20277 + 1.20277i) q^{87} +(-1.47137 + 1.47137i) q^{88} -21.4071i q^{89} +(-17.8840 + 11.4089i) q^{90} +83.7856 q^{91} +(-6.78233 - 6.78233i) q^{92} +(35.9496 - 35.9496i) q^{93} -37.9522i q^{94} +(3.41582 - 15.4527i) q^{95} +9.79796 q^{96} +(-85.8950 - 85.8950i) q^{97} +(33.0734 - 33.0734i) q^{98} +2.20706i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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