LMFDB - Embedded newform 690.3.k.a.553.18

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.18
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.41665 + 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 - 0.381912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.41665 + 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 - 0.381912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(1.96054 + 6.79384i) q^{10} +6.70911 q^{11} +(2.44949 - 2.44949i) q^{12} +(3.27903 + 3.27903i) q^{13} -0.763823i q^{14} +(-8.32072 + 2.40116i) q^{15} -4.00000 q^{16} +(-12.9760 + 12.9760i) q^{17} +(3.00000 + 3.00000i) q^{18} +18.6900i q^{19} +(8.75438 + 4.83330i) q^{20} +0.935489 q^{21} +(6.70911 - 6.70911i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-13.3196 - 21.1563i) q^{25} +6.55805 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.763823 - 0.763823i) q^{28} +43.2683i q^{29} +(-5.91956 + 10.7219i) q^{30} +14.8962 q^{31} +(-4.00000 + 4.00000i) q^{32} +(8.21695 + 8.21695i) q^{33} +25.9520i q^{34} +(0.748754 + 2.59465i) q^{35} +6.00000 q^{36} +(-7.77957 + 7.77957i) q^{37} +(18.6900 + 18.6900i) q^{38} +8.03194i q^{39} +(13.5877 - 3.92108i) q^{40} -19.9186 q^{41} +(0.935489 - 0.935489i) q^{42} +(41.2213 + 41.2213i) q^{43} -13.4182i q^{44} +(-13.1316 - 7.24995i) q^{45} -6.78233 q^{46} +(-31.7502 + 31.7502i) q^{47} +(-4.89898 - 4.89898i) q^{48} +48.7083i q^{49} +(-34.4759 - 7.83666i) q^{50} -31.7846 q^{51} +(6.55805 - 6.55805i) q^{52} +(13.9434 + 13.9434i) q^{53} +7.34847i q^{54} +(-16.2136 + 29.3671i) q^{55} -1.52765 q^{56} +(-22.8905 + 22.8905i) q^{57} +(43.2683 + 43.2683i) q^{58} +2.31643i q^{59} +(4.80233 + 16.6414i) q^{60} +22.8724 q^{61} +(14.8962 - 14.8962i) q^{62} +(1.14574 + 1.14574i) q^{63} +8.00000i q^{64} +(-22.2772 + 6.42867i) q^{65} +16.4339 q^{66} +(59.1642 - 59.1642i) q^{67} +(25.9520 + 25.9520i) q^{68} -8.30662i q^{69} +(3.34340 + 1.84589i) q^{70} +29.7588 q^{71} +(6.00000 - 6.00000i) q^{72} +(-73.2037 - 73.2037i) q^{73} +15.5591i q^{74} +(9.59791 - 42.2242i) q^{75} +37.3801 q^{76} +(2.56229 - 2.56229i) q^{77} +(8.03194 + 8.03194i) q^{78} -12.0428i q^{79} +(9.66660 - 17.5088i) q^{80} -9.00000 q^{81} +(-19.9186 + 19.9186i) q^{82} +(-12.8507 - 12.8507i) q^{83} -1.87098i q^{84} +(-25.4400 - 88.1569i) q^{85} +82.4425 q^{86} +(-52.9926 + 52.9926i) q^{87} +(-13.4182 - 13.4182i) q^{88} +42.0148i q^{89} +(-20.3815 + 5.88163i) q^{90} +2.50460 q^{91} +(-6.78233 + 6.78233i) q^{92} +(18.2441 + 18.2441i) q^{93} +63.5004i q^{94} +(-81.8099 - 45.1673i) q^{95} -9.79796 q^{96} +(8.47487 - 8.47487i) q^{97} +(48.7083 + 48.7083i) q^{98} +20.1273i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$5$	−2.41665	+	4.37719i	−0.483330	+	0.875438i
$5$	−2.41665	+	4.37719i	−0.483330	+	0.875438i
$6$	2.44949			0.408248
$7$	0.381912	−	0.381912i	0.0545588	−	0.0545588i	−0.679301	−	0.733860i	$-0.737717\pi$
$7$	0.381912	−	0.381912i	0.0545588	−	0.0545588i	0.733860	+	0.679301i	$0.237717\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	1.96054	+	6.79384i	0.196054	+	0.679384i
$11$	6.70911			0.609919			0.304960	−	0.952365i	$-0.401357\pi$
$11$	6.70911			0.609919			0.304960	+	0.952365i	$0.401357\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	3.27903	+	3.27903i	0.252233	+	0.252233i	0.821885	−	0.569653i	$-0.192922\pi$
$13$	3.27903	+	3.27903i	0.252233	+	0.252233i	−0.569653	+	0.821885i	$0.692922\pi$
$14$		−	0.763823i		−	0.0545588i
$15$	−8.32072	+	2.40116i	−0.554715	+	0.160078i
$16$	−4.00000			−0.250000
$17$	−12.9760	+	12.9760i	−0.763294	+	0.763294i	−0.976916	−	0.213622i	$-0.931474\pi$
$17$	−12.9760	+	12.9760i	−0.763294	+	0.763294i	0.213622	+	0.976916i	$0.431474\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			18.6900i			0.983686i	0.870684	+	0.491843i	$0.163677\pi$
$19$			18.6900i			0.983686i	−0.870684	+	0.491843i	$0.836323\pi$
$20$	8.75438	+	4.83330i	0.437719	+	0.241665i
$21$	0.935489			0.0445471
$22$	6.70911	−	6.70911i	0.304960	−	0.304960i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−13.3196	−	21.1563i	−0.532785	−	0.846251i
$26$	6.55805			0.252233
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−0.763823	−	0.763823i	−0.0272794	−	0.0272794i
$29$			43.2683i			1.49201i	0.665941	+	0.746004i	$0.268030\pi$
$29$			43.2683i			1.49201i	−0.665941	+	0.746004i	$0.731970\pi$
$30$	−5.91956	+	10.7219i	−0.197319	+	0.357396i
$31$	14.8962			0.480523			0.240262	−	0.970708i	$-0.422767\pi$
$31$	14.8962			0.480523			0.240262	+	0.970708i	$0.422767\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	8.21695	+	8.21695i	0.248998	+	0.248998i
$34$			25.9520i			0.763294i
$35$	0.748754	+	2.59465i	0.0213930	+	0.0741328i
$36$	6.00000			0.166667
$37$	−7.77957	+	7.77957i	−0.210259	+	0.210259i	−0.804377	−	0.594119i	$-0.797501\pi$
$37$	−7.77957	+	7.77957i	−0.210259	+	0.210259i	0.594119	+	0.804377i	$0.297501\pi$
$38$	18.6900	+	18.6900i	0.491843	+	0.491843i
$39$			8.03194i			0.205947i
$40$	13.5877	−	3.92108i	0.339692	−	0.0980271i
$41$	−19.9186			−0.485819			−0.242910	−	0.970049i	$-0.578102\pi$
$41$	−19.9186			−0.485819			−0.242910	+	0.970049i	$0.578102\pi$
$42$	0.935489	−	0.935489i	0.0222735	−	0.0222735i
$43$	41.2213	+	41.2213i	0.958634	+	0.958634i	0.999178	−	0.0405438i	$-0.0129090\pi$
$43$	41.2213	+	41.2213i	0.958634	+	0.958634i	−0.0405438	+	0.999178i	$0.512909\pi$
$44$		−	13.4182i		−	0.304960i
$45$	−13.1316	−	7.24995i	−0.291813	−	0.161110i
$46$	−6.78233			−0.147442
$47$	−31.7502	+	31.7502i	−0.675536	+	0.675536i	−0.958987	−	0.283450i	$-0.908521\pi$
$47$	−31.7502	+	31.7502i	−0.675536	+	0.675536i	0.283450	+	0.958987i	$0.408521\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			48.7083i			0.994047i
$50$	−34.4759	−	7.83666i	−0.689518	−	0.156733i
$51$	−31.7846			−0.623227
$52$	6.55805	−	6.55805i	0.126116	−	0.126116i
$53$	13.9434	+	13.9434i	0.263083	+	0.263083i	0.826305	−	0.563223i	$-0.190439\pi$
$53$	13.9434	+	13.9434i	0.263083	+	0.263083i	−0.563223	+	0.826305i	$0.690439\pi$
$54$			7.34847i			0.136083i
$55$	−16.2136	+	29.3671i	−0.294792	+	0.533947i
$56$	−1.52765			−0.0272794
$57$	−22.8905	+	22.8905i	−0.401588	+	0.401588i
$58$	43.2683	+	43.2683i	0.746004	+	0.746004i
$59$			2.31643i			0.0392616i	0.999807	+	0.0196308i	$0.00624908\pi$
$59$			2.31643i			0.0392616i	−0.999807	+	0.0196308i	$0.993751\pi$
$60$	4.80233	+	16.6414i	0.0800388	+	0.277357i
$61$	22.8724			0.374957			0.187479	−	0.982269i	$-0.439968\pi$
$61$	22.8724			0.374957			0.187479	+	0.982269i	$0.439968\pi$
$62$	14.8962	−	14.8962i	0.240262	−	0.240262i
$63$	1.14574	+	1.14574i	0.0181863	+	0.0181863i
$64$			8.00000i			0.125000i
$65$	−22.2772	+	6.42867i	−0.342726	+	0.0989026i
$66$	16.4339			0.248998
$67$	59.1642	−	59.1642i	0.883047	−	0.883047i	−0.110796	−	0.993843i	$-0.535340\pi$
$67$	59.1642	−	59.1642i	0.883047	−	0.883047i	0.993843	+	0.110796i	$0.0353400\pi$
$68$	25.9520	+	25.9520i	0.381647	+	0.381647i
$69$		−	8.30662i		−	0.120386i
$70$	3.34340	+	1.84589i	0.0477629	+	0.0263699i
$71$	29.7588			0.419138			0.209569	−	0.977794i	$-0.432794\pi$
$71$	29.7588			0.419138			0.209569	+	0.977794i	$0.432794\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−73.2037	−	73.2037i	−1.00279	−	1.00279i	−0.999996	−	0.00279431i	$-0.999111\pi$
$73$	−73.2037	−	73.2037i	−1.00279	−	1.00279i	−0.00279431	−	0.999996i	$-0.500889\pi$
$74$			15.5591i			0.210259i
$75$	9.59791	−	42.2242i	0.127972	−	0.562989i
$76$	37.3801			0.491843
$77$	2.56229	−	2.56229i	0.0332765	−	0.0332765i
$78$	8.03194	+	8.03194i	0.102974	+	0.102974i
$79$		−	12.0428i		−	0.152440i	−0.997091	−	0.0762202i	$-0.975715\pi$
$79$		−	12.0428i		−	0.152440i	0.997091	−	0.0762202i	$-0.0242852\pi$
$80$	9.66660	−	17.5088i	0.120832	−	0.218860i
$81$	−9.00000			−0.111111
$82$	−19.9186	+	19.9186i	−0.242910	+	0.242910i
$83$	−12.8507	−	12.8507i	−0.154827	−	0.154827i	0.625443	−	0.780270i	$-0.284918\pi$
$83$	−12.8507	−	12.8507i	−0.154827	−	0.154827i	−0.780270	+	0.625443i	$0.784918\pi$
$84$		−	1.87098i		−	0.0222735i
$85$	−25.4400	−	88.1569i	−0.299294	−	1.03714i
$86$	82.4425			0.958634
$87$	−52.9926	+	52.9926i	−0.609110	+	0.609110i
$88$	−13.4182	−	13.4182i	−0.152480	−	0.152480i
$89$			42.0148i			0.472076i	0.971744	+	0.236038i	$0.0758490\pi$
$89$			42.0148i			0.472076i	−0.971744	+	0.236038i	$0.924151\pi$
$90$	−20.3815	+	5.88163i	−0.226461	+	0.0653514i
$91$	2.50460			0.0275230
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	18.2441	+	18.2441i	0.196173	+	0.196173i
$94$			63.5004i			0.675536i
$95$	−81.8099	−	45.1673i	−0.861157	−	0.475445i
$96$	−9.79796			−0.102062
$97$	8.47487	−	8.47487i	0.0873698	−	0.0873698i	−0.662071	−	0.749441i	$-0.730322\pi$
$97$	8.47487	−	8.47487i	0.0873698	−	0.0873698i	0.749441	+	0.662071i	$0.230322\pi$
$98$	48.7083	+	48.7083i	0.497023	+	0.497023i
$99$			20.1273i			0.203306i
$100$	−42.3125	+	26.6392i	−0.423125	+	0.266392i
$101$	−36.8005			−0.364361			−0.182180	−	0.983265i	$-0.558316\pi$
$101$	−36.8005			−0.364361			−0.182180	+	0.983265i	$0.558316\pi$
$102$	−31.7846	+	31.7846i	−0.311614	+	0.311614i
$103$	30.2577	+	30.2577i	0.293764	+	0.293764i	0.838565	−	0.544801i	$-0.183395\pi$
$103$	30.2577	+	30.2577i	0.293764	+	0.293764i	−0.544801	+	0.838565i	$0.683395\pi$
$104$		−	13.1161i		−	0.126116i
$105$	−2.26075	+	4.09481i	−0.0215309	+	0.0389982i
$106$	27.8867			0.263083
$107$	58.5497	−	58.5497i	0.547193	−	0.547193i	−0.378435	−	0.925628i	$-0.623538\pi$
$107$	58.5497	−	58.5497i	0.547193	−	0.547193i	0.925628	+	0.378435i	$0.123538\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$		−	156.152i		−	1.43258i	−0.697801	−	0.716291i	$-0.745838\pi$
$109$		−	156.152i		−	1.43258i	0.697801	−	0.716291i	$-0.254162\pi$
$110$	13.1535	+	45.5806i	0.119577	+	0.414369i
$111$	−19.0560			−0.171675
$112$	−1.52765	+	1.52765i	−0.0136397	+	0.0136397i
$113$	79.0970	+	79.0970i	0.699973	+	0.699973i	0.964405	−	0.264431i	$-0.0851842\pi$
$113$	79.0970	+	79.0970i	0.699973	+	0.699973i	−0.264431	+	0.964405i	$0.585184\pi$
$114$			45.7811i			0.401588i
$115$	23.0390	−	6.64852i	0.200339	−	0.0578132i
$116$	86.5365			0.746004
$117$	−9.83708	+	9.83708i	−0.0840776	+	0.0840776i
$118$	2.31643	+	2.31643i	0.0196308	+	0.0196308i
$119$			9.91138i			0.0832889i
$120$	21.4438	+	11.8391i	0.178698	+	0.0986593i
$121$	−75.9878			−0.627999
$122$	22.8724	−	22.8724i	0.187479	−	0.187479i
$123$	−24.3952	−	24.3952i	−0.198335	−	0.198335i
$124$		−	29.7924i		−	0.240262i
$125$	124.794	−	7.17521i	0.998351	−	0.0574016i
$126$	2.29147			0.0181863
$127$	132.249	−	132.249i	1.04133	−	1.04133i	0.0422197	−	0.999108i	$-0.486557\pi$
$127$	132.249	−	132.249i	1.04133	−	1.04133i	0.999108	−	0.0422197i	$-0.0134429\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$			100.971i			0.782721i
$130$	−15.8485	+	28.7059i	−0.121912	+	0.220814i
$131$	45.0132			0.343612			0.171806	−	0.985131i	$-0.445040\pi$
$131$	45.0132			0.343612			0.171806	+	0.985131i	$0.445040\pi$
$132$	16.4339	−	16.4339i	0.124499	−	0.124499i
$133$	7.13794	+	7.13794i	0.0536688	+	0.0536688i
$134$		−	118.328i		−	0.883047i
$135$	−7.20349	−	24.9622i	−0.0533592	−	0.184905i
$136$	51.9040			0.381647
$137$	48.0021	−	48.0021i	0.350380	−	0.350380i	−0.509871	−	0.860251i	$-0.670307\pi$
$137$	48.0021	−	48.0021i	0.350380	−	0.350380i	0.860251	+	0.509871i	$0.170307\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$		−	64.5350i		−	0.464281i	−0.972682	−	0.232140i	$-0.925427\pi$
$139$		−	64.5350i		−	0.464281i	0.972682	−	0.232140i	$-0.0745729\pi$
$140$	5.18929	−	1.49751i	0.0370664	−	0.0106965i
$141$	−77.7718			−0.551573
$142$	29.7588	−	29.7588i	0.209569	−	0.209569i
$143$	21.9994	+	21.9994i	0.153842	+	0.153842i
$144$		−	12.0000i		−	0.0833333i
$145$	−189.393	−	104.564i	−1.30616	−	0.721132i
$146$	−146.407			−1.00279
$147$	−59.6552	+	59.6552i	−0.405818	+	0.405818i
$148$	15.5591	+	15.5591i	0.105129	+	0.105129i
$149$		−	68.2371i		−	0.457967i	−0.973430	−	0.228984i	$-0.926460\pi$
$149$		−	68.2371i		−	0.457967i	0.973430	−	0.228984i	$-0.0735402\pi$
$150$	−32.6263	−	51.8221i	−0.217508	−	0.345481i
$151$	24.9568			0.165277			0.0826386	−	0.996580i	$-0.473665\pi$
$151$	24.9568			0.165277			0.0826386	+	0.996580i	$0.473665\pi$
$152$	37.3801	−	37.3801i	0.245922	−	0.245922i
$153$	−38.9280	−	38.9280i	−0.254431	−	0.254431i
$154$		−	5.12458i		−	0.0332765i
$155$	−35.9989	+	65.2036i	−0.232251	+	0.420668i
$156$	16.0639			0.102974
$157$	−74.5026	+	74.5026i	−0.474539	+	0.474539i	−0.903380	−	0.428841i	$-0.858922\pi$
$157$	−74.5026	+	74.5026i	−0.474539	+	0.474539i	0.428841	+	0.903380i	$0.358922\pi$
$158$	−12.0428	−	12.0428i	−0.0762202	−	0.0762202i
$159$			34.1541i			0.214806i
$160$	−7.84217	−	27.1754i	−0.0490136	−	0.169846i
$161$	−2.59025			−0.0160885
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−188.851	−	188.851i	−1.15859	−	1.15859i	−0.984778	−	0.173816i	$-0.944390\pi$
$163$	−188.851	−	188.851i	−1.15859	−	1.15859i	−0.173816	−	0.984778i	$-0.555610\pi$
$164$			39.8372i			0.242910i
$165$	−55.8246	+	16.1097i	−0.338331	+	0.0976344i
$166$	−25.7014			−0.154827
$167$	−48.1591	+	48.1591i	−0.288378	+	0.288378i	−0.836439	−	0.548061i	$-0.815366\pi$
$167$	−48.1591	+	48.1591i	−0.288378	+	0.288378i	0.548061	+	0.836439i	$0.315366\pi$
$168$	−1.87098	−	1.87098i	−0.0111368	−	0.0111368i
$169$		−	147.496i		−	0.872757i
$170$	−113.597	−	62.7169i	−0.668217	−	0.368923i
$171$	−56.0701			−0.327895
$172$	82.4425	−	82.4425i	0.479317	−	0.479317i
$173$	189.177	+	189.177i	1.09351	+	1.09351i	0.995151	+	0.0983603i	$0.0313598\pi$
$173$	189.177	+	189.177i	1.09351	+	1.09351i	0.0983603	+	0.995151i	$0.468640\pi$
$174$			105.985i			0.609110i
$175$	−13.1667	−	2.99291i	−0.0752385	−	0.0171024i
$176$	−26.8364			−0.152480
$177$	−2.83704	+	2.83704i	−0.0160285	+	0.0160285i
$178$	42.0148	+	42.0148i	0.236038	+	0.236038i
$179$			229.026i			1.27947i	0.768594	+	0.639737i	$0.220957\pi$
$179$			229.026i			1.27947i	−0.768594	+	0.639737i	$0.779043\pi$
$180$	−14.4999	+	26.2631i	−0.0805550	+	0.145906i
$181$	200.947			1.11020			0.555102	−	0.831782i	$-0.312679\pi$
$181$	200.947			1.11020			0.555102	+	0.831782i	$0.312679\pi$
$182$	2.50460	−	2.50460i	0.0137615	−	0.0137615i
$183$	28.0128	+	28.0128i	0.153076	+	0.153076i
$184$			13.5647i			0.0737210i
$185$	−15.2522	−	52.8532i	−0.0824442	−	0.285693i
$186$	36.4881			0.196173
$187$	−87.0575	+	87.0575i	−0.465548	+	0.465548i
$188$	63.5004	+	63.5004i	0.337768	+	0.337768i
$189$			2.80647i			0.0148490i
$190$	−126.977	+	36.6426i	−0.668301	+	0.192856i
$191$	−57.4984			−0.301039			−0.150519	−	0.988607i	$-0.548095\pi$
$191$	−57.4984			−0.301039			−0.150519	+	0.988607i	$0.548095\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−72.1304	−	72.1304i	−0.373733	−	0.373733i	0.495102	−	0.868835i	$-0.335131\pi$
$193$	−72.1304	−	72.1304i	−0.373733	−	0.373733i	−0.868835	+	0.495102i	$0.835131\pi$
$194$		−	16.9497i		−	0.0873698i
$195$	−35.1573	−	19.4104i	−0.180294	−	0.0995404i
$196$	97.4166			0.497023
$197$	167.259	−	167.259i	0.849032	−	0.849032i	−0.140980	−	0.990012i	$-0.545025\pi$
$197$	167.259	−	167.259i	0.849032	−	0.849032i	0.990012	+	0.140980i	$0.0450254\pi$
$198$	20.1273	+	20.1273i	0.101653	+	0.101653i
$199$		−	146.363i		−	0.735493i	−0.929926	−	0.367747i	$-0.880129\pi$
$199$		−	146.363i		−	0.735493i	0.929926	−	0.367747i	$-0.119871\pi$
$200$	−15.6733	+	68.9518i	−0.0783666	+	0.344759i
$201$	144.922			0.721005
$202$	−36.8005	+	36.8005i	−0.182180	+	0.182180i
$203$	16.5247	+	16.5247i	0.0814022	+	0.0814022i
$204$			63.5692i			0.311614i
$205$	48.1362	−	87.1875i	0.234811	−	0.425305i
$206$	60.5153			0.293764
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	−13.1161	−	13.1161i	−0.0630582	−	0.0630582i
$209$			125.394i			0.599969i
$210$	1.83407	+	6.35556i	0.00873364	+	0.0302646i
$211$	237.399			1.12511			0.562556	−	0.826759i	$-0.309818\pi$
$211$	237.399			1.12511			0.562556	+	0.826759i	$0.309818\pi$
$212$	27.8867	−	27.8867i	0.131541	−	0.131541i
$213$	36.4469	+	36.4469i	0.171112	+	0.171112i
$214$		−	117.099i		−	0.547193i
$215$	−280.051	+	80.8160i	−1.30256	+	0.375888i
$216$	14.6969			0.0680414
$217$	5.68904	−	5.68904i	0.0262168	−	0.0262168i
$218$	−156.152	−	156.152i	−0.716291	−	0.716291i
$219$		−	179.312i		−	0.818775i
$220$	58.7341	+	32.4271i	0.266973	+	0.147396i
$221$	−85.0973			−0.385056
$222$	−19.0560	+	19.0560i	−0.0858377	+	0.0858377i
$223$	−259.517	−	259.517i	−1.16375	−	1.16375i	−0.983648	−	0.180104i	$-0.942356\pi$
$223$	−259.517	−	259.517i	−1.16375	−	1.16375i	−0.180104	−	0.983648i	$-0.557644\pi$
$224$			3.05529i			0.0136397i
$225$	63.4688	−	39.9588i	0.282084	−	0.177595i
$226$	158.194			0.699973
$227$	−5.33385	+	5.33385i	−0.0234971	+	0.0234971i	−0.718758	−	0.695261i	$-0.755289\pi$
$227$	−5.33385	+	5.33385i	−0.0234971	+	0.0234971i	0.695261	+	0.718758i	$0.255289\pi$
$228$	45.7811	+	45.7811i	0.200794	+	0.200794i
$229$			129.029i			0.563447i	0.959496	+	0.281724i	$0.0909061\pi$
$229$			129.029i			0.563447i	−0.959496	+	0.281724i	$0.909094\pi$
$230$	16.3905	−	29.6876i	0.0712631	−	0.129076i
$231$	6.27630			0.0271701
$232$	86.5365	−	86.5365i	0.373002	−	0.373002i
$233$	−228.635	−	228.635i	−0.981267	−	0.981267i	0.0185604	−	0.999828i	$-0.494092\pi$
$233$	−228.635	−	228.635i	−0.981267	−	0.981267i	−0.999828	+	0.0185604i	$0.994092\pi$
$234$			19.6742i			0.0840776i
$235$	−62.2476	−	215.706i	−0.264884	−	0.917897i
$236$	4.63287			0.0196308
$237$	14.7494	−	14.7494i	0.0622336	−	0.0622336i
$238$	9.91138	+	9.91138i	0.0416444	+	0.0416444i
$239$			354.637i			1.48384i	0.670489	+	0.741919i	$0.266084\pi$
$239$			354.637i			1.48384i	−0.670489	+	0.741919i	$0.733916\pi$
$240$	33.2829	−	9.60466i	0.138679	−	0.0400194i
$241$	338.822			1.40590			0.702951	−	0.711238i	$-0.251865\pi$
$241$	338.822			1.40590			0.702951	+	0.711238i	$0.251865\pi$
$242$	−75.9878	+	75.9878i	−0.313999	+	0.313999i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	45.7448i		−	0.187479i
$245$	−213.206	−	117.711i	−0.870227	−	0.480452i
$246$	−48.7904			−0.198335
$247$	−61.2851	+	61.2851i	−0.248118	+	0.248118i
$248$	−29.7924	−	29.7924i	−0.120131	−	0.120131i
$249$		−	31.4776i		−	0.126416i
$250$	117.619	−	131.969i	0.470475	−	0.527876i
$251$	−288.350			−1.14880			−0.574402	−	0.818573i	$-0.694765\pi$
$251$	−288.350			−1.14880			−0.574402	+	0.818573i	$0.694765\pi$
$252$	2.29147	−	2.29147i	0.00909314	−	0.00909314i
$253$	−22.7517	−	22.7517i	−0.0899277	−	0.0899277i
$254$		−	264.497i		−	1.04133i
$255$	76.8122	−	139.127i	0.301224	−	0.545597i
$256$	16.0000			0.0625000
$257$	31.1551	−	31.1551i	0.121226	−	0.121226i	−0.643891	−	0.765117i	$-0.722681\pi$
$257$	31.1551	−	31.1551i	0.121226	−	0.121226i	0.765117	+	0.643891i	$0.222681\pi$
$258$	100.971	+	100.971i	0.391361	+	0.391361i
$259$			5.94222i			0.0229429i
$260$	12.8573	+	44.5544i	0.0494513	+	0.171363i
$261$	−129.805			−0.497336
$262$	45.0132	−	45.0132i	0.171806	−	0.171806i
$263$	−147.593	−	147.593i	−0.561190	−	0.561190i	0.368455	−	0.929645i	$-0.379887\pi$
$263$	−147.593	−	147.593i	−0.561190	−	0.561190i	−0.929645	+	0.368455i	$0.879887\pi$
$264$		−	32.8678i		−	0.124499i
$265$	−94.7291	+	27.3366i	−0.357468	+	0.103157i
$266$	14.2759			0.0536688
$267$	−51.4574	+	51.4574i	−0.192724	+	0.192724i
$268$	−118.328	−	118.328i	−0.441524	−	0.441524i
$269$			172.598i			0.641627i	0.947142	+	0.320813i	$0.103956\pi$
$269$			172.598i			0.641627i	−0.947142	+	0.320813i	$0.896044\pi$
$270$	−32.1657	−	17.7587i	−0.119132	−	0.0657729i
$271$	381.051			1.40609			0.703046	−	0.711144i	$-0.251823\pi$
$271$	381.051			1.40609			0.703046	+	0.711144i	$0.251823\pi$
$272$	51.9040	−	51.9040i	0.190824	−	0.190824i
$273$	3.06749	+	3.06749i	0.0112362	+	0.0112362i
$274$		−	96.0042i		−	0.350380i
$275$	−89.3628	−	141.940i	−0.324956	−	0.516145i
$276$	−16.6132			−0.0601929
$277$	156.346	−	156.346i	0.564426	−	0.564426i	−0.366136	−	0.930561i	$-0.619319\pi$
$277$	156.346	−	156.346i	0.564426	−	0.564426i	0.930561	+	0.366136i	$0.119319\pi$
$278$	−64.5350	−	64.5350i	−0.232140	−	0.232140i
$279$			44.6886i			0.160174i
$280$	3.69179	−	6.68680i	0.0131850	−	0.0238814i
$281$	−29.4130			−0.104673			−0.0523363	−	0.998630i	$-0.516667\pi$
$281$	−29.4130			−0.104673			−0.0523363	+	0.998630i	$0.516667\pi$
$282$	−77.7718	+	77.7718i	−0.275787	+	0.275787i
$283$	147.441	+	147.441i	0.520995	+	0.520995i	0.917872	−	0.396877i	$-0.129906\pi$
$283$	147.441	+	147.441i	0.520995	+	0.520995i	−0.396877	+	0.917872i	$0.629906\pi$
$284$		−	59.5176i		−	0.209569i
$285$	−44.8779	−	155.515i	−0.157466	−	0.545665i
$286$	43.9987			0.153842
$287$	−7.60714	+	7.60714i	−0.0265057	+	0.0265057i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	47.7533i		−	0.165236i
$290$	−293.958	+	84.8293i	−1.01365	+	0.292515i
$291$	20.7591			0.0713371
$292$	−146.407	+	146.407i	−0.501395	+	0.501395i
$293$	7.83296	+	7.83296i	0.0267336	+	0.0267336i	0.720347	−	0.693614i	$-0.243982\pi$
$293$	7.83296	+	7.83296i	0.0267336	+	0.0267336i	−0.693614	+	0.720347i	$0.743982\pi$
$294$			119.310i			0.405818i
$295$	−10.1395	−	5.59801i	−0.0343711	−	0.0189763i
$296$	31.1183			0.105129
$297$	−24.6508	+	24.6508i	−0.0829995	+	0.0829995i
$298$	−68.2371	−	68.2371i	−0.228984	−	0.228984i
$299$		−	22.2394i		−	0.0743794i
$300$	−84.4483	−	19.1958i	−0.281494	−	0.0639861i
$301$	31.4858			0.104604
$302$	24.9568	−	24.9568i	0.0826386	−	0.0826386i
$303$	−45.0712	−	45.0712i	−0.148750	−	0.148750i
$304$		−	74.7602i		−	0.245922i
$305$	−55.2745	+	100.117i	−0.181228	+	0.328252i
$306$	−77.8560			−0.254431
$307$	−336.989	+	336.989i	−1.09768	+	1.09768i	−0.103002	+	0.994681i	$0.532845\pi$
$307$	−336.989	+	336.989i	−1.09768	+	1.09768i	−0.994681	+	0.103002i	$0.967155\pi$
$308$	−5.12458	−	5.12458i	−0.0166382	−	0.0166382i
$309$			74.1158i			0.239857i
$310$	29.2047	+	101.203i	0.0942086	+	0.326460i
$311$	17.7007			0.0569155			0.0284578	−	0.999595i	$-0.490940\pi$
$311$	17.7007			0.0569155			0.0284578	+	0.999595i	$0.490940\pi$
$312$	16.0639	−	16.0639i	0.0514868	−	0.0514868i
$313$	−386.409	−	386.409i	−1.23453	−	1.23453i	−0.962204	−	0.272331i	$-0.912206\pi$
$313$	−386.409	−	386.409i	−1.23453	−	1.23453i	−0.272331	−	0.962204i	$-0.587794\pi$
$314$			149.005i			0.474539i
$315$	−7.78394	+	2.24626i	−0.0247109	+	0.00713099i
$316$	−24.0856			−0.0762202
$317$	103.379	−	103.379i	0.326118	−	0.326118i	−0.524990	−	0.851108i	$-0.675931\pi$
$317$	103.379	−	103.379i	0.326118	−	0.326118i	0.851108	+	0.524990i	$0.175931\pi$
$318$	34.1541	+	34.1541i	0.107403	+	0.107403i
$319$			290.292i			0.910005i
$320$	−35.0175	−	19.3332i	−0.109430	−	0.0604162i
$321$	143.417			0.446781
$322$	−2.59025	+	2.59025i	−0.00804426	+	0.00804426i
$323$	−242.522	−	242.522i	−0.750842	−	0.750842i
$324$			18.0000i			0.0555556i
$325$	25.6966	−	113.047i	0.0790665	−	0.347838i
$326$	−377.702			−1.15859
$327$	191.246	−	191.246i	0.584849	−	0.584849i
$328$	39.8372	+	39.8372i	0.121455	+	0.121455i
$329$			24.2516i			0.0737129i
$330$	−39.7150	+	71.9343i	−0.120348	+	0.217983i
$331$	−148.156			−0.447602			−0.223801	−	0.974635i	$-0.571847\pi$
$331$	−148.156			−0.447602			−0.223801	+	0.974635i	$0.571847\pi$
$332$	−25.7014	+	25.7014i	−0.0774137	+	0.0774137i
$333$	−23.3387	−	23.3387i	−0.0700862	−	0.0700862i
$334$			96.3182i			0.288378i
$335$	115.994	+	401.952i	0.346250	+	1.19986i
$336$	−3.74196			−0.0111368
$337$	342.881	−	342.881i	1.01745	−	1.01745i	0.0176066	−	0.999845i	$-0.494395\pi$
$337$	342.881	−	342.881i	1.01745	−	1.01745i	0.999845	−	0.0176066i	$-0.00560466\pi$
$338$	−147.496	−	147.496i	−0.436379	−	0.436379i
$339$			193.747i			0.571526i
$340$	−176.314	+	50.8800i	−0.518570	+	0.149647i
$341$	99.9404			0.293080
$342$	−56.0701	+	56.0701i	−0.163948	+	0.163948i
$343$	37.3159	+	37.3159i	0.108793	+	0.108793i
$344$		−	164.885i		−	0.479317i
$345$	36.3597	+	20.0742i	0.105390	+	0.0581861i
$346$	378.355			1.09351
$347$	−160.663	+	160.663i	−0.463005	+	0.463005i	−0.899639	−	0.436634i	$-0.856170\pi$
$347$	−160.663	+	160.663i	−0.463005	+	0.463005i	0.436634	+	0.899639i	$0.356170\pi$
$348$	105.985	+	105.985i	0.304555	+	0.304555i
$349$			20.4812i			0.0586855i	0.999569	+	0.0293427i	$0.00934142\pi$
$349$			20.4812i			0.0586855i	−0.999569	+	0.0293427i	$0.990659\pi$
$350$	−16.1597	+	10.1738i	−0.0461704	+	0.0290681i
$351$	−24.0958			−0.0686491
$352$	−26.8364	+	26.8364i	−0.0762399	+	0.0762399i
$353$	−260.115	−	260.115i	−0.736869	−	0.736869i	0.235102	−	0.971971i	$-0.424458\pi$
$353$	−260.115	−	260.115i	−0.736869	−	0.736869i	−0.971971	+	0.235102i	$0.924458\pi$
$354$			5.67408i			0.0160285i
$355$	−71.9166	+	130.260i	−0.202582	+	0.366930i
$356$	84.0295			0.236038
$357$	−12.1389	+	12.1389i	−0.0340025	+	0.0340025i
$358$	229.026	+	229.026i	0.639737	+	0.639737i
$359$			549.920i			1.53181i	0.642953	+	0.765905i	$0.277709\pi$
$359$			549.920i			1.53181i	−0.642953	+	0.765905i	$0.722291\pi$
$360$	11.7633	+	40.7630i	0.0326757	+	0.113231i
$361$	11.6825			0.0323614
$362$	200.947	−	200.947i	0.555102	−	0.555102i
$363$	−93.0657	−	93.0657i	−0.256379	−	0.256379i
$364$		−	5.00919i		−	0.0137615i
$365$	497.334	−	143.519i	1.36256	−	0.393203i
$366$	56.0257			0.153076
$367$	73.6271	−	73.6271i	0.200619	−	0.200619i	−0.599646	−	0.800265i	$-0.704692\pi$
$367$	73.6271	−	73.6271i	0.200619	−	0.200619i	0.800265	+	0.599646i	$0.204692\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	59.7558i		−	0.161940i
$370$	−68.1053	−	37.6010i	−0.184068	−	0.101624i
$371$	10.6503			0.0287069
$372$	36.4881	−	36.4881i	0.0980864	−	0.0980864i
$373$	−151.835	−	151.835i	−0.407063	−	0.407063i	0.473650	−	0.880713i	$-0.342936\pi$
$373$	−151.835	−	151.835i	−0.407063	−	0.407063i	−0.880713	+	0.473650i	$0.842936\pi$
$374$			174.115i			0.465548i
$375$	161.628	+	144.053i	0.431009	+	0.384141i
$376$	127.001			0.337768
$377$	−141.878	+	141.878i	−0.376334	+	0.376334i
$378$	2.80647	+	2.80647i	0.00742451	+	0.00742451i
$379$			0.463933i			0.00122410i	1.00000		0.000612049i	$0.000194821\pi$
$379$			0.463933i			0.00122410i	−1.00000		0.000612049i	$0.999805\pi$
$380$	−90.3345	+	163.620i	−0.237722	+	0.430578i
$381$	323.942			0.850241
$382$	−57.4984	+	57.4984i	−0.150519	+	0.150519i
$383$	148.165	+	148.165i	0.386853	+	0.386853i	0.873563	−	0.486710i	$-0.161803\pi$
$383$	148.165	+	148.165i	0.386853	+	0.386853i	−0.486710	+	0.873563i	$0.661803\pi$
$384$			19.5959i			0.0510310i
$385$	5.02347	+	17.4078i	0.0130480	+	0.0452150i
$386$	−144.261			−0.373733
$387$	−123.664	+	123.664i	−0.319545	+	0.319545i
$388$	−16.9497	−	16.9497i	−0.0436849	−	0.0436849i
$389$			512.669i			1.31791i	0.752180	+	0.658957i	$0.229002\pi$
$389$			512.669i			1.31791i	−0.752180	+	0.658957i	$0.770998\pi$
$390$	−54.5677	+	15.7470i	−0.139917	+	0.0403768i
$391$	88.0075			0.225083
$392$	97.4166	−	97.4166i	0.248512	−	0.248512i
$393$	55.1296	+	55.1296i	0.140279	+	0.140279i
$394$		−	334.519i		−	0.849032i
$395$	52.7136	+	29.1032i	0.133452	+	0.0736790i
$396$	40.2547			0.101653
$397$	190.235	−	190.235i	0.479181	−	0.479181i	−0.425688	−	0.904870i	$-0.639968\pi$
$397$	190.235	−	190.235i	0.479181	−	0.479181i	0.904870	+	0.425688i	$0.139968\pi$
$398$	−146.363	−	146.363i	−0.367747	−	0.367747i
$399$			17.4843i			0.0438204i
$400$	53.2785	+	84.6251i	0.133196	+	0.211563i
$401$	351.265			0.875972			0.437986	−	0.898982i	$-0.355692\pi$
$401$	351.265			0.875972			0.437986	+	0.898982i	$0.355692\pi$
$402$	144.922	−	144.922i	0.360503	−	0.360503i
$403$	48.8451	+	48.8451i	0.121204	+	0.121204i
$404$			73.6009i			0.182180i
$405$	21.7498	−	39.3947i	0.0537033	−	0.0972709i
$406$	33.0493			0.0814022
$407$	−52.1940	+	52.1940i	−0.128241	+	0.128241i
$408$	63.5692	+	63.5692i	0.155807	+	0.155807i
$409$			648.532i			1.58565i	0.609447	+	0.792827i	$0.291392\pi$
$409$			648.532i			1.58565i	−0.609447	+	0.792827i	$0.708608\pi$
$410$	−39.0512	−	135.324i	−0.0952469	−	0.330058i
$411$	117.581			0.286084
$412$	60.5153	−	60.5153i	0.146882	−	0.146882i
$413$	0.884673	+	0.884673i	0.00214207	+	0.00214207i
$414$		−	20.3470i		−	0.0491473i
$415$	87.3055	−	25.1943i	0.210375	−	0.0607092i
$416$	−26.2322			−0.0630582
$417$	79.0390	−	79.0390i	0.189542	−	0.189542i
$418$	125.394	+	125.394i	0.299985	+	0.299985i
$419$		−	331.895i		−	0.792113i	−0.918226	−	0.396056i	$-0.870378\pi$
$419$		−	331.895i		−	0.792113i	0.918226	−	0.396056i	$-0.129622\pi$
$420$	8.18963	+	4.52150i	0.0194991	+	0.0107655i
$421$	695.014			1.65086			0.825432	−	0.564501i	$-0.190931\pi$
$421$	695.014			1.65086			0.825432	+	0.564501i	$0.190931\pi$
$422$	237.399	−	237.399i	0.562556	−	0.562556i
$423$	−95.2506	−	95.2506i	−0.225179	−	0.225179i
$424$		−	55.7735i		−	0.131541i
$425$	447.359	+	101.689i	1.05261	+	0.239267i
$426$	72.8939			0.171112
$427$	8.73523	−	8.73523i	0.0204572	−	0.0204572i
$428$	−117.099	−	117.099i	−0.273597	−	0.273597i
$429$			53.8872i			0.125611i
$430$	−199.235	+	360.867i	−0.463336	+	0.839225i
$431$	196.821			0.456660			0.228330	−	0.973584i	$-0.426673\pi$
$431$	196.821			0.456660			0.228330	+	0.973584i	$0.426673\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	314.673	+	314.673i	0.726727	+	0.726727i	0.969966	−	0.243240i	$-0.0782102\pi$
$433$	314.673	+	314.673i	0.726727	+	0.726727i	−0.243240	+	0.969966i	$0.578210\pi$
$434$		−	11.3781i		−	0.0262168i
$435$	−103.894	−	360.023i	−0.238837	−	0.827639i
$436$	−312.303			−0.716291
$437$	63.3810	−	63.3810i	0.145037	−	0.145037i
$438$	−179.312	−	179.312i	−0.409387	−	0.409387i
$439$			383.648i			0.873914i	0.899482	+	0.436957i	$0.143944\pi$
$439$			383.648i			0.873914i	−0.899482	+	0.436957i	$0.856056\pi$
$440$	91.1613	−	26.3070i	0.207185	−	0.0597886i
$441$	−146.125			−0.331349
$442$	−85.0973	+	85.0973i	−0.192528	+	0.192528i
$443$	−14.3200	−	14.3200i	−0.0323251	−	0.0323251i	0.690759	−	0.723085i	$-0.257276\pi$
$443$	−14.3200	−	14.3200i	−0.0323251	−	0.0323251i	−0.723085	+	0.690759i	$0.757276\pi$
$444$			38.1120i			0.0858377i
$445$	−183.907	−	101.535i	−0.413273	−	0.228168i
$446$	−519.033			−1.16375
$447$	83.5731	−	83.5731i	0.186964	−	0.186964i
$448$	3.05529	+	3.05529i	0.00681985	+	0.00681985i
$449$			383.606i			0.854355i	0.904168	+	0.427178i	$0.140492\pi$
$449$			383.606i			0.854355i	−0.904168	+	0.427178i	$0.859508\pi$
$450$	23.5100	−	103.428i	0.0522444	−	0.229839i
$451$	−133.636			−0.296310
$452$	158.194	−	158.194i	0.349987	−	0.349987i
$453$	30.5658	+	30.5658i	0.0674741	+	0.0674741i
$454$			10.6677i			0.0234971i
$455$	−6.05273	+	10.9631i	−0.0133027	+	0.0240947i
$456$	91.5621			0.200794
$457$	512.331	−	512.331i	1.12107	−	1.12107i	0.129494	−	0.991580i	$-0.458665\pi$
$457$	512.331	−	512.331i	1.12107	−	1.12107i	0.991580	−	0.129494i	$-0.0413352\pi$
$458$	129.029	+	129.029i	0.281724	+	0.281724i
$459$		−	95.3538i		−	0.207742i
$460$	−13.2970	−	46.0781i	−0.0289066	−	0.100170i
$461$	327.942			0.711370			0.355685	−	0.934606i	$-0.384248\pi$
$461$	327.942			0.711370			0.355685	+	0.934606i	$0.384248\pi$
$462$	6.27630	−	6.27630i	0.0135851	−	0.0135851i
$463$	575.851	+	575.851i	1.24374	+	1.24374i	0.958438	+	0.285300i	$0.0920931\pi$
$463$	575.851	+	575.851i	1.24374	+	1.24374i	0.285300	+	0.958438i	$0.407907\pi$
$464$		−	173.073i		−	0.373002i
$465$	−123.947	+	35.7683i	−0.266553	+	0.0769210i
$466$	−457.271			−0.981267
$467$	359.804	−	359.804i	0.770459	−	0.770459i	−0.207728	−	0.978187i	$-0.566607\pi$
$467$	359.804	−	359.804i	0.770459	−	0.770459i	0.978187	+	0.207728i	$0.0666068\pi$
$468$	19.6742	+	19.6742i	0.0420388	+	0.0420388i
$469$		−	45.1910i		−	0.0963560i
$470$	−277.954	−	153.458i	−0.591391	−	0.326507i
$471$	−182.493			−0.387460
$472$	4.63287	−	4.63287i	0.00981540	−	0.00981540i
$473$	276.558	+	276.558i	0.584689	+	0.584689i
$474$		−	29.4987i		−	0.0622336i
$475$	395.412	−	248.944i	0.832445	−	0.524093i
$476$	19.8228			0.0416444
$477$	−41.8301	+	41.8301i	−0.0876942	+	0.0876942i
$478$	354.637	+	354.637i	0.741919	+	0.741919i
$479$			880.306i			1.83780i	0.394490	+	0.918900i	$0.370921\pi$
$479$			880.306i			1.83780i	−0.394490	+	0.918900i	$0.629079\pi$
$480$	23.6782	−	42.8875i	0.0493296	−	0.0893490i
$481$	−51.0188			−0.106068
$482$	338.822	−	338.822i	0.702951	−	0.702951i
$483$	−3.17240	−	3.17240i	−0.00656811	−	0.00656811i
$484$			151.976i			0.313999i
$485$	16.6153	+	57.5769i	0.0342584	+	0.118715i
$486$	−22.0454			−0.0453609
$487$	−500.051	+	500.051i	−1.02680	+	1.02680i	−0.0271685	+	0.999631i	$0.508649\pi$
$487$	−500.051	+	500.051i	−1.02680	+	1.02680i	−0.999631	+	0.0271685i	$0.991351\pi$
$488$	−45.7448	−	45.7448i	−0.0937393	−	0.0937393i
$489$		−	462.588i		−	0.945988i
$490$	−330.916	+	95.4947i	−0.675339	+	0.194887i
$491$	−224.036			−0.456286			−0.228143	−	0.973628i	$-0.573265\pi$
$491$	−224.036			−0.456286			−0.228143	+	0.973628i	$0.573265\pi$
$492$	−48.7904	+	48.7904i	−0.0991674	+	0.0991674i
$493$	−561.449	−	561.449i	−1.13884	−	1.13884i
$494$			122.570i			0.248118i
$495$	−88.1012	−	48.6407i	−0.177982	−	0.0982641i
$496$	−59.5849			−0.120131
$497$	11.3652	−	11.3652i	0.0228677	−	0.0228677i
$498$	−31.4776	−	31.4776i	−0.0632081	−	0.0632081i
$499$			74.3281i			0.148954i	0.997223	+	0.0744771i	$0.0237288\pi$
$499$			74.3281i			0.148954i	−0.997223	+	0.0744771i	$0.976271\pi$
$500$	−14.3504	−	249.588i	−0.0287008	−	0.499176i
$501$	−117.965			−0.235460
$502$	−288.350	+	288.350i	−0.574402	+	0.574402i
$503$	433.764	+	433.764i	0.862354	+	0.862354i	0.991611	−	0.129257i	$-0.0412592\pi$
$503$	433.764	+	433.764i	0.862354	+	0.862354i	−0.129257	+	0.991611i	$0.541259\pi$
$504$		−	4.58294i		−	0.00909314i
$505$	88.9338	−	161.083i	0.176107	−	0.318976i
$506$	−45.5034			−0.0899277
$507$	180.645	−	180.645i	0.356302	−	0.356302i
$508$	−264.497	−	264.497i	−0.520664	−	0.520664i
$509$			439.146i			0.862763i	0.902170	+	0.431381i	$0.141974\pi$
$509$			439.146i			0.862763i	−0.902170	+	0.431381i	$0.858026\pi$
$510$	−62.3150	−	215.939i	−0.122186	−	0.423411i
$511$	−55.9147			−0.109422
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−68.6716	−	68.6716i	−0.133863	−	0.133863i
$514$		−	62.3103i		−	0.121226i
$515$	−205.566	+	59.3214i	−0.399157	+	0.115187i
$516$	201.942			0.391361
$517$	−213.016	+	213.016i	−0.412023	+	0.412023i
$518$	5.94222	+	5.94222i	0.0114715	+	0.0114715i
$519$			463.388i			0.892848i
$520$	57.4117	+	31.6970i	0.110407	+	0.0609558i
$521$	564.612			1.08371			0.541855	−	0.840472i	$-0.317722\pi$
$521$	564.612			1.08371			0.541855	+	0.840472i	$0.317722\pi$
$522$	−129.805	+	129.805i	−0.248668	+	0.248668i
$523$	−178.399	−	178.399i	−0.341107	−	0.341107i	0.515676	−	0.856783i	$-0.327541\pi$
$523$	−178.399	−	178.399i	−0.341107	−	0.341107i	−0.856783	+	0.515676i	$0.827541\pi$
$524$		−	90.0263i		−	0.171806i
$525$	−12.4603	−	19.7915i	−0.0237340	−	0.0376980i
$526$	−295.186			−0.561190
$527$	−193.293	+	193.293i	−0.366781	+	0.366781i
$528$	−32.8678	−	32.8678i	−0.0622496	−	0.0622496i
$529$			23.0000i			0.0434783i
$530$	−67.3925	+	122.066i	−0.127156	+	0.230313i
$531$	−6.94930			−0.0130872
$532$	14.2759	−	14.2759i	0.0268344	−	0.0268344i
$533$	−65.3136	−	65.3136i	−0.122540	−	0.122540i
$534$			102.915i			0.192724i
$535$	114.789	+	397.777i	0.214559	+	0.743509i
$536$	−236.657			−0.441524
$537$	−280.498	+	280.498i	−0.522343	+	0.522343i
$538$	172.598	+	172.598i	0.320813	+	0.320813i
$539$			326.789i			0.606288i
$540$	−49.9243	+	14.4070i	−0.0924525	+	0.0266796i
$541$	671.336			1.24092			0.620459	−	0.784239i	$-0.286946\pi$
$541$	671.336			1.24092			0.620459	+	0.784239i	$0.286946\pi$
$542$	381.051	−	381.051i	0.703046	−	0.703046i
$543$	246.109	+	246.109i	0.453239	+	0.453239i
$544$		−	103.808i		−	0.190824i
$545$	683.505	+	377.363i	1.25414	+	0.692410i
$546$	6.13498			0.0112362
$547$	−364.741	+	364.741i	−0.666803	+	0.666803i	−0.956975	−	0.290172i	$-0.906288\pi$
$547$	−364.741	+	364.741i	−0.666803	+	0.666803i	0.290172	+	0.956975i	$0.406288\pi$
$548$	−96.0042	−	96.0042i	−0.175190	−	0.175190i
$549$			68.6172i			0.124986i
$550$	−231.303	−	52.5770i	−0.420550	−	0.0955946i
$551$	−808.685			−1.46767
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	−4.59929	−	4.59929i	−0.00831697	−	0.00831697i
$554$		−	312.692i		−	0.564426i
$555$	46.0516	−	83.4117i	0.0829759	−	0.150291i
$556$	−129.070			−0.232140
$557$	475.919	−	475.919i	0.854433	−	0.854433i	−0.136243	−	0.990675i	$-0.543503\pi$
$557$	475.919	−	475.919i	0.854433	−	0.854433i	0.990675	+	0.136243i	$0.0435028\pi$
$558$	44.6886	+	44.6886i	0.0800872	+	0.0800872i
$559$			270.331i			0.483598i
$560$	−2.99502	−	10.3786i	−0.00534824	−	0.0185332i
$561$	−213.246			−0.380118
$562$	−29.4130	+	29.4130i	−0.0523363	+	0.0523363i
$563$	145.318	+	145.318i	0.258114	+	0.258114i	0.824287	−	0.566172i	$-0.191576\pi$
$563$	145.318	+	145.318i	0.258114	+	0.258114i	−0.566172	+	0.824287i	$0.691576\pi$
$564$			155.544i			0.275787i
$565$	−537.372	+	155.073i	−0.951102	+	0.274466i
$566$	294.883			0.520995
$567$	−3.43721	+	3.43721i	−0.00606209	+	0.00606209i
$568$	−59.5176	−	59.5176i	−0.104785	−	0.104785i
$569$		−	265.620i		−	0.466820i	−0.972378	−	0.233410i	$-0.925012\pi$
$569$		−	265.620i		−	0.466820i	0.972378	−	0.233410i	$-0.0749884\pi$
$570$	−200.392	−	110.637i	−0.351566	−	0.194100i
$571$	624.384			1.09349			0.546746	−	0.837298i	$-0.315866\pi$
$571$	624.384			1.09349			0.546746	+	0.837298i	$0.315866\pi$
$572$	43.9987	−	43.9987i	0.0769208	−	0.0769208i
$573$	−70.4209	−	70.4209i	−0.122899	−	0.122899i
$574$			15.2143i			0.0265057i
$575$	−26.5754	+	116.913i	−0.0462181	+	0.203328i
$576$	−24.0000			−0.0416667
$577$	−281.919	+	281.919i	−0.488595	+	0.488595i	−0.907863	−	0.419268i	$-0.862287\pi$
$577$	−281.919	+	281.919i	−0.488595	+	0.488595i	0.419268	+	0.907863i	$0.362287\pi$
$578$	−47.7533	−	47.7533i	−0.0826182	−	0.0826182i
$579$		−	176.683i		−	0.305151i
$580$	−209.128	+	378.787i	−0.360566	+	0.653081i
$581$	−9.81565			−0.0168944
$582$	20.7591	−	20.7591i	0.0356686	−	0.0356686i
$583$	93.5476	+	93.5476i	0.160459	+	0.160459i
$584$			292.815i			0.501395i
$585$	−19.2860	−	66.8315i	−0.0329675	−	0.114242i
$586$	15.6659			0.0267336
$587$	−5.58217	+	5.58217i	−0.00950967	+	0.00950967i	−0.711846	−	0.702336i	$-0.752140\pi$
$587$	−5.58217	+	5.58217i	−0.00950967	+	0.00950967i	0.702336	+	0.711846i	$0.252140\pi$
$588$	119.310	+	119.310i	0.202909	+	0.202909i
$589$			278.411i			0.472684i
$590$	−15.7375	+	4.54147i	−0.0266737	+	0.00769740i
$591$	409.700			0.693232
$592$	31.1183	−	31.1183i	0.0525647	−	0.0525647i
$593$	−494.483	−	494.483i	−0.833866	−	0.833866i	0.154177	−	0.988043i	$-0.450727\pi$
$593$	−494.483	−	494.483i	−0.833866	−	0.833866i	−0.988043	+	0.154177i	$0.950727\pi$
$594$			49.3017i			0.0829995i
$595$	−43.3840	−	23.9523i	−0.0729143	−	0.0402560i
$596$	−136.474			−0.228984
$597$	179.258	−	179.258i	0.300264	−	0.300264i
$598$	−22.2394	−	22.2394i	−0.0371897	−	0.0371897i
$599$		−	79.8683i		−	0.133336i	−0.997775	−	0.0666680i	$-0.978763\pi$
$599$		−	79.8683i		−	0.133336i	0.997775	−	0.0666680i	$-0.0212368\pi$
$600$	−103.644	+	65.2525i	−0.172740	+	0.108754i
$601$	−676.719			−1.12599			−0.562995	−	0.826461i	$-0.690351\pi$
$601$	−676.719			−1.12599			−0.562995	+	0.826461i	$0.690351\pi$
$602$	31.4858	−	31.4858i	0.0523019	−	0.0523019i
$603$	177.493	+	177.493i	0.294349	+	0.294349i
$604$		−	49.9137i		−	0.0826386i
$605$	183.636	−	332.613i	0.303530	−	0.549774i
$606$	−90.1423			−0.148750
$607$	−641.010	+	641.010i	−1.05603	+	1.05603i	−0.0576959	+	0.998334i	$0.518375\pi$
$607$	−641.010	+	641.010i	−1.05603	+	1.05603i	−0.998334	+	0.0576959i	$0.981625\pi$
$608$	−74.7602	−	74.7602i	−0.122961	−	0.122961i
$609$			40.4770i			0.0664647i
$610$	44.8423	+	155.391i	0.0735119	+	0.254740i
$611$	−208.220			−0.340785
$612$	−77.8560	+	77.8560i	−0.127216	+	0.127216i
$613$	−781.053	−	781.053i	−1.27415	−	1.27415i	−0.943891	−	0.330257i	$-0.892864\pi$
$613$	−781.053	−	781.053i	−1.27415	−	1.27415i	−0.330257	−	0.943891i	$-0.607136\pi$
$614$			673.978i			1.09768i
$615$	165.737	−	47.8278i	0.269491	−	0.0777688i
$616$	−10.2492			−0.0166382
$617$	181.860	−	181.860i	0.294749	−	0.294749i	−0.544204	−	0.838953i	$-0.683168\pi$
$617$	181.860	−	181.860i	0.294749	−	0.294749i	0.838953	+	0.544204i	$0.183168\pi$
$618$	74.1158	+	74.1158i	0.119928	+	0.119928i
$619$			907.156i			1.46552i	0.680488	+	0.732759i	$0.261768\pi$
$619$			907.156i			1.46552i	−0.680488	+	0.732759i	$0.738232\pi$
$620$	130.407	+	71.9979i	0.210334	+	0.116126i
$621$	24.9199			0.0401286
$622$	17.7007	−	17.7007i	0.0284578	−	0.0284578i
$623$	16.0459	+	16.0459i	0.0257559	+	0.0257559i
$624$		−	32.1278i		−	0.0514868i
$625$	−270.176	+	563.587i	−0.432281	+	0.901739i
$626$	−772.819			−1.23453
$627$	−153.575	+	153.575i	−0.244936	+	0.244936i
$628$	149.005	+	149.005i	0.237270	+	0.237270i
$629$		−	201.895i		−	0.320978i
$630$	−5.53768	+	10.0302i	−0.00878997	+	0.0159210i
$631$	−362.814			−0.574983			−0.287492	−	0.957783i	$-0.592821\pi$
$631$	−362.814			−0.574983			−0.287492	+	0.957783i	$0.592821\pi$
$632$	−24.0856	+	24.0856i	−0.0381101	+	0.0381101i
$633$	290.753	+	290.753i	0.459325	+	0.459325i
$634$		−	206.759i		−	0.326118i
$635$	259.279	+	898.476i	0.408314	+	1.41492i
$636$	68.3083			0.107403
$637$	−159.716	+	159.716i	−0.250731	+	0.250731i
$638$	290.292	+	290.292i	0.455002	+	0.455002i
$639$			89.2764i			0.139713i
$640$	−54.3507	+	15.6843i	−0.0849230	+	0.0245068i
$641$	−479.570			−0.748158			−0.374079	−	0.927397i	$-0.622041\pi$
$641$	−479.570			−0.748158			−0.374079	+	0.927397i	$0.622041\pi$
$642$	143.417	−	143.417i	0.223391	−	0.223391i
$643$	−131.420	−	131.420i	−0.204386	−	0.204386i	0.597490	−	0.801876i	$-0.296165\pi$
$643$	−131.420	−	131.420i	−0.204386	−	0.204386i	−0.801876	+	0.597490i	$0.796165\pi$
$644$			5.18050i			0.00804426i
$645$	−441.970	−	244.012i	−0.685224	−	0.378313i
$646$	−485.044			−0.750842
$647$	508.219	−	508.219i	0.785500	−	0.785500i	−0.195253	−	0.980753i	$-0.562553\pi$
$647$	508.219	−	508.219i	0.785500	−	0.785500i	0.980753	+	0.195253i	$0.0625526\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			15.5412i			0.0239464i
$650$	−87.3507	−	138.744i	−0.134386	−	0.213452i
$651$	13.9352			0.0214059
$652$	−377.702	+	377.702i	−0.579297	+	0.579297i
$653$	−390.519	−	390.519i	−0.598039	−	0.598039i	0.341752	−	0.939790i	$-0.388980\pi$
$653$	−390.519	−	390.519i	−0.598039	−	0.598039i	−0.939790	+	0.341752i	$0.888980\pi$
$654$		−	382.492i		−	0.584849i
$655$	−108.781	+	197.031i	−0.166078	+	0.300811i
$656$	79.6743			0.121455
$657$	219.611	−	219.611i	0.334263	−	0.334263i
$658$	24.2516	+	24.2516i	0.0368565	+	0.0368565i
$659$		−	958.180i		−	1.45399i	−0.686643	−	0.726995i	$-0.740916\pi$
$659$		−	958.180i		−	1.45399i	0.686643	−	0.726995i	$-0.259084\pi$
$660$	32.2194	+	111.649i	0.0488172	+	0.169166i
$661$	337.049			0.509908			0.254954	−	0.966953i	$-0.417940\pi$
$661$	337.049			0.509908			0.254954	+	0.966953i	$0.417940\pi$
$662$	−148.156	+	148.156i	−0.223801	+	0.223801i
$663$	−104.222	−	104.222i	−0.157198	−	0.157198i
$664$			51.4027i			0.0774137i
$665$	−48.4941	+	13.9942i	−0.0729234	+	0.0210440i
$666$	−46.6774			−0.0700862
$667$	146.730	−	146.730i	0.219985	−	0.219985i
$668$	96.3182	+	96.3182i	0.144189	+	0.144189i
$669$		−	635.683i		−	0.950199i
$670$	517.946	+	285.958i	0.773054	+	0.426803i
$671$	153.453			0.228694
$672$	−3.74196	+	3.74196i	−0.00556839	+	0.00556839i
$673$	−268.654	−	268.654i	−0.399188	−	0.399188i	0.478758	−	0.877947i	$-0.341087\pi$
$673$	−268.654	−	268.654i	−0.399188	−	0.399188i	−0.877947	+	0.478758i	$0.841087\pi$
$674$		−	685.762i		−	1.01745i
$675$	126.672	+	28.7937i	0.187663	+	0.0426574i
$676$	−294.992			−0.436379
$677$	252.012	−	252.012i	0.372248	−	0.372248i	−0.496048	−	0.868295i	$-0.665216\pi$
$677$	252.012	−	252.012i	0.372248	−	0.372248i	0.868295	+	0.496048i	$0.165216\pi$
$678$	193.747	+	193.747i	0.285763	+	0.285763i
$679$		−	6.47330i		−	0.00953358i
$680$	−125.434	+	227.194i	−0.184461	+	0.334109i
$681$	−13.0652			−0.0191853
$682$	99.9404	−	99.9404i	0.146540	−	0.146540i
$683$	−22.9869	−	22.9869i	−0.0336558	−	0.0336558i	0.690079	−	0.723734i	$-0.257576\pi$
$683$	−22.9869	−	22.9869i	−0.0336558	−	0.0336558i	−0.723734	+	0.690079i	$0.757576\pi$
$684$			112.140i			0.163948i
$685$	94.1101	+	326.119i	0.137387	+	0.476085i
$686$	74.6319			0.108793
$687$	−158.028	+	158.028i	−0.230026	+	0.230026i
$688$	−164.885	−	164.885i	−0.239658	−	0.239658i
$689$			91.4414i			0.132716i
$690$	56.4339	−	16.2855i	0.0817882	−	0.0236022i
$691$	−387.581			−0.560898			−0.280449	−	0.959869i	$-0.590483\pi$
$691$	−387.581			−0.560898			−0.280449	+	0.959869i	$0.590483\pi$
$692$	378.355	−	378.355i	0.546756	−	0.546756i
$693$	7.68686	+	7.68686i	0.0110922	+	0.0110922i
$694$			321.326i			0.463005i
$695$	282.482	+	155.959i	0.406449	+	0.224401i
$696$	211.970			0.304555
$697$	258.464	−	258.464i	0.370823	−	0.370823i
$698$	20.4812	+	20.4812i	0.0293427	+	0.0293427i
$699$		−	560.040i		−	0.801201i
$700$	−5.98582	+	26.3335i	−0.00855118	+	0.0376193i
$701$	−151.713			−0.216424			−0.108212	−	0.994128i	$-0.534513\pi$
$701$	−151.713			−0.216424			−0.108212	+	0.994128i	$0.534513\pi$
$702$	−24.0958	+	24.0958i	−0.0343245	+	0.0343245i
$703$	−145.400	−	145.400i	−0.206829	−	0.206829i
$704$			53.6729i			0.0762399i
$705$	187.947	−	340.422i	0.266592	−	0.482868i
$706$	−520.230			−0.736869
$707$	−14.0545	+	14.0545i	−0.0198791	+	0.0198791i
$708$	5.67408	+	5.67408i	0.00801424	+	0.00801424i
$709$			522.875i			0.737482i	0.929532	+	0.368741i	$0.120211\pi$
$709$			522.875i			0.737482i	−0.929532	+	0.368741i	$0.879789\pi$
$710$	58.3434	+	202.177i	0.0821738	+	0.284756i
$711$	36.1284			0.0508135
$712$	84.0295	−	84.0295i	0.118019	−	0.118019i
$713$	−50.5155	−	50.5155i	−0.0708493	−	0.0708493i
$714$			24.2778i			0.0340025i
$715$	−149.460	+	43.1307i	−0.209035	+	0.0603226i
$716$	458.052			0.639737
$717$	−434.340	+	434.340i	−0.605775	+	0.605775i
$718$	549.920	+	549.920i	0.765905	+	0.765905i
$719$			201.802i			0.280670i	0.990104	+	0.140335i	$0.0448180\pi$
$719$			201.802i			0.280670i	−0.990104	+	0.140335i	$0.955182\pi$
$720$	52.5263	+	28.9998i	0.0729532	+	0.0402775i
$721$	23.1115			0.0320548
$722$	11.6825	−	11.6825i	0.0161807	−	0.0161807i
$723$	414.971	+	414.971i	0.573957	+	0.573957i
$724$		−	401.894i		−	0.555102i
$725$	915.395	−	576.316i	1.26261	−	0.794919i
$726$	−186.131			−0.256379
$727$	23.7355	−	23.7355i	0.0326486	−	0.0326486i	−0.690594	−	0.723243i	$-0.742651\pi$
$727$	23.7355	−	23.7355i	0.0326486	−	0.0326486i	0.723243	+	0.690594i	$0.242651\pi$
$728$	−5.00919	−	5.00919i	−0.00688076	−	0.00688076i
$729$		−	27.0000i		−	0.0370370i
$730$	353.815	−	640.853i	0.484679	−	0.877881i
$731$	−1069.77			−1.46344
$732$	56.0257	−	56.0257i	0.0765378	−	0.0765378i
$733$	−593.329	−	593.329i	−0.809453	−	0.809453i	0.175098	−	0.984551i	$-0.443976\pi$
$733$	−593.329	−	593.329i	−0.809453	−	0.809453i	−0.984551	+	0.175098i	$0.943976\pi$
$734$		−	147.254i		−	0.200619i
$735$	−116.957	−	405.288i	−0.159125	−	0.551412i
$736$	27.1293			0.0368605
$737$	396.939	−	396.939i	0.538588	−	0.538588i
$738$	−59.7558	−	59.7558i	−0.0809699	−	0.0809699i
$739$		−	1294.17i		−	1.75125i	−0.482992	−	0.875625i	$-0.660450\pi$
$739$		−	1294.17i		−	1.75125i	0.482992	−	0.875625i	$-0.339550\pi$
$740$	−105.706	+	30.5044i	−0.142846	+	0.0412221i
$741$	−150.117			−0.202587
$742$	10.6503	−	10.6503i	0.0143535	−	0.0143535i
$743$	−114.912	−	114.912i	−0.154660	−	0.154660i	0.625536	−	0.780196i	$-0.284881\pi$
$743$	−114.912	−	114.912i	−0.154660	−	0.154660i	−0.780196	+	0.625536i	$0.784881\pi$
$744$		−	72.9762i		−	0.0980864i
$745$	298.687	+	164.905i	0.400922	+	0.221349i
$746$	−303.669			−0.407063
$747$	38.5520	−	38.5520i	0.0516092	−	0.0516092i
$748$	174.115	+	174.115i	0.232774	+	0.232774i
$749$		−	44.7216i		−	0.0597084i
$750$	305.681	−	17.5756i	0.407575	−	0.0234341i
$751$	1130.53			1.50537			0.752684	−	0.658382i	$-0.228759\pi$
$751$	1130.53			1.50537			0.752684	+	0.658382i	$0.228759\pi$
$752$	127.001	−	127.001i	0.168884	−	0.168884i
$753$	−353.155	−	353.155i	−0.468997	−	0.468997i
$754$			283.756i			0.376334i
$755$	−60.3119	+	109.241i	−0.0798834	+	0.144690i
$756$	5.61293			0.00742451
$757$	99.9974	−	99.9974i	0.132097	−	0.132097i	−0.637967	−	0.770064i	$-0.720224\pi$
$757$	99.9974	−	99.9974i	0.132097	−	0.132097i	0.770064	+	0.637967i	$0.220224\pi$
$758$	0.463933	+	0.463933i	0.000612049	+	0.000612049i
$759$		−	55.7301i		−	0.0734256i
$760$	73.2852	+	253.954i	0.0964279	+	0.334150i
$761$	29.0412			0.0381619			0.0190809	−	0.999818i	$-0.493926\pi$
$761$	29.0412			0.0381619			0.0190809	+	0.999818i	$0.493926\pi$
$762$	323.942	−	323.942i	0.425120	−	0.425120i
$763$	−59.6361	−	59.6361i	−0.0781600	−	0.0781600i
$764$			114.997i			0.150519i
$765$	264.471	−	76.3200i	0.345713	−	0.0997647i
$766$	296.330			0.386853
$767$	−7.59565	+	7.59565i	−0.00990306	+	0.00990306i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	406.341i		−	0.528402i	−0.964468	−	0.264201i	$-0.914892\pi$
$769$		−	406.341i		−	0.528402i	0.964468	−	0.264201i	$-0.0851082\pi$
$770$	22.4313	+	12.3843i	0.0291315	+	0.0160835i
$771$	76.3142			0.0989808
$772$	−144.261	+	144.261i	−0.186866	+	0.186866i
$773$	243.088	+	243.088i	0.314473	+	0.314473i	0.846640	−	0.532166i	$-0.178622\pi$
$773$	243.088	+	243.088i	0.314473	+	0.314473i	−0.532166	+	0.846640i	$0.678622\pi$
$774$			247.328i			0.319545i
$775$	−198.412	−	315.148i	−0.256015	−	0.406643i
$776$	−33.8995			−0.0436849
$777$	−7.27770	+	7.27770i	−0.00936641	+	0.00936641i
$778$	512.669	+	512.669i	0.658957	+	0.658957i
$779$		−	372.279i		−	0.477894i
$780$	−38.8208	+	70.3147i	−0.0497702	+	0.0901470i
$781$	199.655			0.255640
$782$	88.0075	−	88.0075i	0.112542	−	0.112542i
$783$	−158.978	−	158.978i	−0.203037	−	0.203037i
$784$		−	194.833i		−	0.248512i
$785$	−146.066	−	506.159i	−0.186071	−	0.644789i
$786$	110.259			0.140279
$787$	−136.789	+	136.789i	−0.173810	+	0.173810i	−0.788651	−	0.614841i	$-0.789220\pi$
$787$	−136.789	+	136.789i	−0.173810	+	0.173810i	0.614841	+	0.788651i	$0.289220\pi$
$788$	−334.519	−	334.519i	−0.424516	−	0.424516i
$789$		−	361.528i		−	0.458210i
$790$	81.8168	−	23.6104i	0.103566	−	0.0298866i
$791$	60.4161			0.0763794
$792$	40.2547	−	40.2547i	0.0508266	−	0.0508266i
$793$	74.9991	+	74.9991i	0.0945765	+	0.0945765i
$794$		−	380.470i		−	0.479181i
$795$	−149.499	−	82.5386i	−0.188049	−	0.103822i
$796$	−292.726			−0.367747
$797$	1097.41	−	1097.41i	1.37693	−	1.37693i	0.527159	−	0.849767i	$-0.323257\pi$
$797$	1097.41	−	1097.41i	1.37693	−	1.37693i	0.849767	−	0.527159i	$-0.176743\pi$
$798$	17.4843	+	17.4843i	0.0219102	+	0.0219102i
$799$		−	823.982i		−	1.03127i
$800$	137.904	+	31.3466i	0.172379	+	0.0391833i
$801$	−126.044			−0.157359
$802$	351.265	−	351.265i	0.437986	−	0.437986i
$803$	−491.132	−	491.132i	−0.611621	−	0.611621i
$804$		−	289.844i		−	0.360503i
$805$	6.25973	−	11.3380i	0.00777606	−	0.0140845i
$806$	97.6902			0.121204
$807$	−211.388	+	211.388i	−0.261943	+	0.261943i
$808$	73.6009	+	73.6009i	0.0910902	+	0.0910902i
$809$		−	602.804i		−	0.745123i	−0.928008	−	0.372561i	$-0.878480\pi$
$809$		−	602.804i		−	0.745123i	0.928008	−	0.372561i	$-0.121520\pi$
$810$	−17.6449	−	61.1446i	−0.0217838	−	0.0754871i
$811$	391.224			0.482397			0.241199	−	0.970476i	$-0.422459\pi$
$811$	391.224			0.482397			0.241199	+	0.970476i	$0.422459\pi$
$812$	33.0493	−	33.0493i	0.0407011	−	0.0407011i
$813$	466.690	+	466.690i	0.574035	+	0.574035i
$814$			104.388i			0.128241i
$815$	1283.02	−	370.250i	1.57426	−	0.454295i
$816$	127.138			0.155807
$817$	−770.427	+	770.427i	−0.942995	+	0.942995i
$818$	648.532	+	648.532i	0.792827	+	0.792827i
$819$			7.51379i			0.00917435i
$820$	−174.375	−	96.2725i	−0.212652	−	0.117405i
$821$	−1083.57			−1.31981			−0.659906	−	0.751348i	$-0.729404\pi$
$821$	−1083.57			−1.31981			−0.659906	+	0.751348i	$0.729404\pi$
$822$	117.581	−	117.581i	0.143042	−	0.143042i
$823$	600.222	+	600.222i	0.729309	+	0.729309i	0.970482	−	0.241173i	$-0.0775320\pi$
$823$	600.222	+	600.222i	0.729309	+	0.729309i	−0.241173	+	0.970482i	$0.577532\pi$
$824$		−	121.031i		−	0.146882i
$825$	64.3934	−	283.287i	0.0780527	−	0.343378i
$826$	1.76935			0.00214207
$827$	−947.486	+	947.486i	−1.14569	+	1.14569i	−0.158299	+	0.987391i	$0.550601\pi$
$827$	−947.486	+	947.486i	−1.14569	+	1.14569i	−0.987391	+	0.158299i	$0.949399\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$		−	1022.25i		−	1.23311i	−0.787310	−	0.616557i	$-0.788527\pi$
$829$		−	1022.25i		−	1.23311i	0.787310	−	0.616557i	$-0.211473\pi$
$830$	62.1112	−	112.500i	0.0748327	−	0.135542i
$831$	382.968			0.460852
$832$	−26.2322	+	26.2322i	−0.0315291	+	0.0315291i
$833$	−632.039	−	632.039i	−0.758750	−	0.758750i
$834$		−	158.078i		−	0.189542i
$835$	−94.4180	−	327.185i	−0.113075	−	0.391839i
$836$	250.787			0.299985
$837$	−54.7322	+	54.7322i	−0.0653909	+	0.0653909i
$838$	−331.895	−	331.895i	−0.396056	−	0.396056i
$839$		−	683.287i		−	0.814406i	−0.913338	−	0.407203i	$-0.866504\pi$
$839$		−	683.287i		−	0.814406i	0.913338	−	0.407203i	$-0.133496\pi$
$840$	12.7111	−	3.66813i	0.0151323	−	0.00436682i
$841$	−1031.14			−1.22609
$842$	695.014	−	695.014i	0.825432	−	0.825432i
$843$	−36.0234	−	36.0234i	−0.0427324	−	0.0427324i
$844$		−	474.797i		−	0.562556i
$845$	645.618	+	356.446i	0.764045	+	0.421830i
$846$	−190.501			−0.225179
$847$	−29.0206	+	29.0206i	−0.0342629	+	0.0342629i
$848$	−55.7735	−	55.7735i	−0.0657706	−	0.0657706i
$849$			361.156i			0.425390i
$850$	549.048	−	345.671i	0.645939	−	0.406671i
$851$	52.7636			0.0620019
$852$	72.8939	−	72.8939i	0.0855562	−	0.0855562i
$853$	833.645	+	833.645i	0.977309	+	0.977309i	0.999748	−	0.0224387i	$-0.00714307\pi$
$853$	833.645	+	833.645i	0.977309	+	0.977309i	−0.0224387	+	0.999748i	$0.507143\pi$
$854$		−	17.4705i		−	0.0204572i
$855$	135.502	−	245.430i	0.158482	−	0.287052i
$856$	−234.199			−0.273597
$857$	789.695	−	789.695i	0.921465	−	0.921465i	−0.0756685	−	0.997133i	$-0.524109\pi$
$857$	789.695	−	789.695i	0.921465	−	0.921465i	0.997133	+	0.0756685i	$0.0241091\pi$
$858$	53.8872	+	53.8872i	0.0628056	+	0.0628056i
$859$			1020.26i			1.18773i	0.804565	+	0.593864i	$0.202398\pi$
$859$			1020.26i			1.18773i	−0.804565	+	0.593864i	$0.797602\pi$
$860$	161.632	+	560.101i	0.187944	+	0.651281i
$861$	−18.6336			−0.0216418
$862$	196.821	−	196.821i	0.228330	−	0.228330i
$863$	−746.400	−	746.400i	−0.864890	−	0.864890i	0.127011	−	0.991901i	$-0.459462\pi$
$863$	−746.400	−	746.400i	−0.864890	−	0.864890i	−0.991901	+	0.127011i	$0.959462\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−1285.24	+	370.890i	−1.48583	+	0.428775i
$866$	629.345			0.726727
$867$	58.4856	−	58.4856i	0.0674575	−	0.0674575i
$868$	−11.3781	−	11.3781i	−0.0131084	−	0.0131084i
$869$		−	80.7965i		−	0.0929764i
$870$	−463.917	−	256.129i	−0.533238	−	0.294401i
$871$	388.002			0.445467
$872$	−312.303	+	312.303i	−0.358146	+	0.358146i
$873$	25.4246	+	25.4246i	0.0291233	+	0.0291233i
$874$		−	126.762i		−	0.145037i
$875$	44.9200	−	50.4005i	0.0513371	−	0.0576006i
$876$	−358.623			−0.409387
$877$	356.244	−	356.244i	0.406207	−	0.406207i	−0.474206	−	0.880414i	$-0.657265\pi$
$877$	356.244	−	356.244i	0.406207	−	0.406207i	0.880414	+	0.474206i	$0.157265\pi$
$878$	383.648	+	383.648i	0.436957	+	0.436957i
$879$			19.1868i			0.0218279i
$880$	64.8543	−	117.468i	0.0736980	−	0.133487i
$881$	61.1191			0.0693747			0.0346874	−	0.999398i	$-0.488956\pi$
$881$	61.1191			0.0693747			0.0346874	+	0.999398i	$0.488956\pi$
$882$	−146.125	+	146.125i	−0.165674	+	0.165674i
$883$	−113.408	−	113.408i	−0.128435	−	0.128435i	0.639967	−	0.768402i	$-0.278948\pi$
$883$	−113.408	−	113.408i	−0.128435	−	0.128435i	−0.768402	+	0.639967i	$0.778948\pi$
$884$			170.195i			0.192528i
$885$	−5.56214	−	19.2744i	−0.00628490	−	0.0217790i
$886$	−28.6401			−0.0323251
$887$	−914.200	+	914.200i	−1.03067	+	1.03067i	−0.0311508	+	0.999515i	$0.509917\pi$
$887$	−914.200	+	914.200i	−1.03067	+	1.03067i	−0.999515	+	0.0311508i	$0.990083\pi$
$888$	38.1120	+	38.1120i	0.0429189	+	0.0429189i
$889$		−	101.015i		−	0.113627i
$890$	−285.442	+	82.3717i	−0.320721	+	0.0925525i
$891$	−60.3820			−0.0677688
$892$	−519.033	+	519.033i	−0.581876	+	0.581876i
$893$	−593.413	−	593.413i	−0.664516	−	0.664516i
$894$		−	167.146i		−	0.186964i
$895$	−1002.49	−	553.475i	−1.12010	−	0.618408i
$896$	6.11059			0.00681985
$897$	27.2376	−	27.2376i	0.0303653	−	0.0303653i
$898$	383.606	+	383.606i	0.427178	+	0.427178i
$899$			644.533i			0.716945i
$900$	−79.9177	−	126.938i	−0.0887974	−	0.141042i
$901$	−361.859			−0.401619
$902$	−133.636	+	133.636i	−0.148155	+	0.148155i
$903$	38.5620	+	38.5620i	0.0427043	+	0.0427043i
$904$		−	316.388i		−	0.349987i
$905$	−485.618	+	879.583i	−0.536595	+	0.971915i
$906$	61.1315			0.0674741
$907$	−576.492	+	576.492i	−0.635603	+	0.635603i	−0.949468	−	0.313865i	$-0.898376\pi$
$907$	−576.492	+	576.492i	−0.635603	+	0.635603i	0.313865	+	0.949468i	$0.398376\pi$
$908$	10.6677	+	10.6677i	0.0117486	+	0.0117486i
$909$		−	110.401i		−	0.121454i
$910$	4.91037	+	17.0158i	0.00539601	+	0.0186987i
$911$	275.968			0.302929			0.151464	−	0.988463i	$-0.451601\pi$
$911$	275.968			0.302929			0.151464	+	0.988463i	$0.451601\pi$
$912$	91.5621	−	91.5621i	0.100397	−	0.100397i
$913$	−86.2167	−	86.2167i	−0.0944323	−	0.0944323i
$914$		−	1024.66i		−	1.12107i
$915$	−190.315	+	54.9203i	−0.207994	+	0.0600222i
$916$	258.059			0.281724
$917$	17.1911	−	17.1911i	0.0187471	−	0.0187471i
$918$	−95.3538	−	95.3538i	−0.103871	−	0.103871i
$919$		−	425.975i		−	0.463520i	−0.972773	−	0.231760i	$-0.925552\pi$
$919$		−	425.975i		−	0.463520i	0.972773	−	0.231760i	$-0.0744484\pi$
$920$	−59.3751	−	32.7810i	−0.0645382	−	0.0356315i
$921$	−825.451			−0.896255
$922$	327.942	−	327.942i	0.355685	−	0.355685i
$923$	97.5799	+	97.5799i	0.105720	+	0.105720i
$924$		−	12.5526i		−	0.0135851i
$925$	268.208	+	60.9658i	0.289954	+	0.0659090i
$926$	1151.70			1.24374
$927$	−90.7730	+	90.7730i	−0.0979212	+	0.0979212i
$928$	−173.073	−	173.073i	−0.186501	−	0.186501i
$929$		−	91.2635i		−	0.0982384i	−0.998793	−	0.0491192i	$-0.984359\pi$
$929$		−	91.2635i		−	0.0982384i	0.998793	−	0.0491192i	$-0.0156414\pi$
$930$	−88.1790	+	159.716i	−0.0948161	+	0.171737i
$931$	−910.360			−0.977830
$932$	−457.271	+	457.271i	−0.490634	+	0.490634i
$933$	21.6789	+	21.6789i	0.0232357	+	0.0232357i
$934$		−	719.609i		−	0.770459i
$935$	−170.680	−	591.454i	−0.182545	−	0.632572i
$936$	39.3483			0.0420388
$937$	−644.076	+	644.076i	−0.687381	+	0.687381i	−0.961652	−	0.274271i	$-0.911563\pi$
$937$	−644.076	+	644.076i	−0.687381	+	0.687381i	0.274271	+	0.961652i	$0.411563\pi$
$938$	−45.1910	−	45.1910i	−0.0481780	−	0.0481780i
$939$		−	946.506i		−	1.00799i
$940$	−431.412	+	124.495i	−0.458949	+	0.132442i
$941$	−1283.19			−1.36365			−0.681824	−	0.731517i	$-0.738813\pi$
$941$	−1283.19			−1.36365			−0.681824	+	0.731517i	$0.738813\pi$
$942$	−182.493	+	182.493i	−0.193730	+	0.193730i
$943$	67.5472	+	67.5472i	0.0716301	+	0.0716301i
$944$		−	9.26573i		−	0.00981540i
$945$	−12.2844	−	6.78224i	−0.0129994	−	0.00717698i
$946$	553.116			0.584689
$947$	−628.854	+	628.854i	−0.664049	+	0.664049i	−0.956332	−	0.292283i	$-0.905585\pi$
$947$	−628.854	+	628.854i	−0.664049	+	0.664049i	0.292283	+	0.956332i	$0.405585\pi$
$948$	−29.4987	−	29.4987i	−0.0311168	−	0.0311168i
$949$		−	480.074i		−	0.505873i
$950$	146.467	−	644.356i	0.154176	−	0.678269i
$951$	253.227			0.266274
$952$	19.8228	−	19.8228i	0.0208222	−	0.0208222i
$953$	521.165	+	521.165i	0.546868	+	0.546868i	0.925533	−	0.378666i	$-0.123617\pi$
$953$	521.165	+	521.165i	0.546868	+	0.546868i	−0.378666	+	0.925533i	$0.623617\pi$
$954$			83.6602i			0.0876942i
$955$	138.954	−	251.682i	0.145501	−	0.263541i
$956$	709.275			0.741919
$957$	−355.533	+	355.533i	−0.371508	+	0.371508i
$958$	880.306	+	880.306i	0.918900	+	0.918900i
$959$		−	36.6651i		−	0.0382327i
$960$	−19.2093	−	66.5658i	−0.0200097	−	0.0693393i
$961$	−739.103			−0.769098
$962$	−51.0188	+	51.0188i	−0.0530341	+	0.0530341i
$963$	175.649	+	175.649i	0.182398	+	0.182398i
$964$		−	677.645i		−	0.702951i
$965$	490.042	−	141.415i	0.507816	−	0.146544i
$966$	−6.34479			−0.00656811
$967$	240.110	−	240.110i	0.248304	−	0.248304i	−0.571970	−	0.820274i	$-0.693821\pi$
$967$	240.110	−	240.110i	0.248304	−	0.248304i	0.820274	+	0.571970i	$0.193821\pi$
$968$	151.976	+	151.976i	0.157000	+	0.157000i
$969$		−	594.055i		−	0.613060i
$970$	74.1922	+	40.9616i	0.0764868	+	0.0422284i
$971$	−787.644			−0.811168			−0.405584	−	0.914058i	$-0.632932\pi$
$971$	−787.644			−0.811168			−0.405584	+	0.914058i	$0.632932\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−24.6467	−	24.6467i	−0.0253306	−	0.0253306i
$974$			1000.10i			1.02680i
$975$	169.926	−	106.982i	0.174283	−	0.109725i
$976$	−91.4895			−0.0937393
$977$	787.744	−	787.744i	0.806289	−	0.806289i	−0.177781	−	0.984070i	$-0.556892\pi$
$977$	787.744	−	787.744i	0.806289	−	0.806289i	0.984070	+	0.177781i	$0.0568920\pi$
$978$	−462.588	−	462.588i	−0.472994	−	0.472994i
$979$			281.882i			0.287928i
$980$	−235.422	+	426.411i	−0.240226	+	0.435113i
$981$	468.455			0.477528
$982$	−224.036	+	224.036i	−0.228143	+	0.228143i
$983$	−470.832	−	470.832i	−0.478975	−	0.478975i	0.425829	−	0.904804i	$-0.359983\pi$
$983$	−470.832	−	470.832i	−0.478975	−	0.478975i	−0.904804	+	0.425829i	$0.859983\pi$
$984$			97.5807i			0.0991674i
$985$	327.919	+	1136.33i	0.332913	+	1.15364i
$986$	−1122.90			−1.13884
$987$	−29.7020	+	29.7020i	−0.0300932	+	0.0300932i
$988$	122.570	+	122.570i	0.124059	+	0.124059i
$989$		−	279.576i		−	0.282686i
$990$	−136.742	+	39.4605i	−0.138123	+	0.0398591i
$991$	1781.55			1.79773			0.898863	−	0.438229i	$-0.144394\pi$
$991$	1781.55			1.79773			0.898863	+	0.438229i	$0.144394\pi$
$992$	−59.5849	+	59.5849i	−0.0600654	+	0.0600654i
$993$	−181.454	−	181.454i	−0.182733	−	0.182733i
$994$		−	22.7305i		−	0.0228677i
$995$	640.660	+	353.709i	0.643879	+	0.355486i
$996$	−62.9552			−0.0632081
$997$	−722.167	+	722.167i	−0.724340	+	0.724340i	−0.969486	−	0.245146i	$-0.921164\pi$
$997$	−722.167	+	722.167i	−0.724340	+	0.724340i	0.245146	+	0.969486i	$0.421164\pi$
$998$	74.3281	+	74.3281i	0.0744771	+	0.0744771i
$999$		−	57.1679i		−	0.0572252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.18	yes	40
5.2	odd	4	inner	690.3.k.a.277.18	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.18	✓	40	5.2	odd	4	inner
690.3.k.a.553.18	yes	40	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.41665 + 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 - 0.381912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-2.41665 + 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 - 0.381912i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(1.96054 + 6.79384i) q^{10} +6.70911 q^{11} +(2.44949 - 2.44949i) q^{12} +(3.27903 + 3.27903i) q^{13} -0.763823i q^{14} +(-8.32072 + 2.40116i) q^{15} -4.00000 q^{16} +(-12.9760 + 12.9760i) q^{17} +(3.00000 + 3.00000i) q^{18} +18.6900i q^{19} +(8.75438 + 4.83330i) q^{20} +0.935489 q^{21} +(6.70911 - 6.70911i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-13.3196 - 21.1563i) q^{25} +6.55805 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.763823 - 0.763823i) q^{28} +43.2683i q^{29} +(-5.91956 + 10.7219i) q^{30} +14.8962 q^{31} +(-4.00000 + 4.00000i) q^{32} +(8.21695 + 8.21695i) q^{33} +25.9520i q^{34} +(0.748754 + 2.59465i) q^{35} +6.00000 q^{36} +(-7.77957 + 7.77957i) q^{37} +(18.6900 + 18.6900i) q^{38} +8.03194i q^{39} +(13.5877 - 3.92108i) q^{40} -19.9186 q^{41} +(0.935489 - 0.935489i) q^{42} +(41.2213 + 41.2213i) q^{43} -13.4182i q^{44} +(-13.1316 - 7.24995i) q^{45} -6.78233 q^{46} +(-31.7502 + 31.7502i) q^{47} +(-4.89898 - 4.89898i) q^{48} +48.7083i q^{49} +(-34.4759 - 7.83666i) q^{50} -31.7846 q^{51} +(6.55805 - 6.55805i) q^{52} +(13.9434 + 13.9434i) q^{53} +7.34847i q^{54} +(-16.2136 + 29.3671i) q^{55} -1.52765 q^{56} +(-22.8905 + 22.8905i) q^{57} +(43.2683 + 43.2683i) q^{58} +2.31643i q^{59} +(4.80233 + 16.6414i) q^{60} +22.8724 q^{61} +(14.8962 - 14.8962i) q^{62} +(1.14574 + 1.14574i) q^{63} +8.00000i q^{64} +(-22.2772 + 6.42867i) q^{65} +16.4339 q^{66} +(59.1642 - 59.1642i) q^{67} +(25.9520 + 25.9520i) q^{68} -8.30662i q^{69} +(3.34340 + 1.84589i) q^{70} +29.7588 q^{71} +(6.00000 - 6.00000i) q^{72} +(-73.2037 - 73.2037i) q^{73} +15.5591i q^{74} +(9.59791 - 42.2242i) q^{75} +37.3801 q^{76} +(2.56229 - 2.56229i) q^{77} +(8.03194 + 8.03194i) q^{78} -12.0428i q^{79} +(9.66660 - 17.5088i) q^{80} -9.00000 q^{81} +(-19.9186 + 19.9186i) q^{82} +(-12.8507 - 12.8507i) q^{83} -1.87098i q^{84} +(-25.4400 - 88.1569i) q^{85} +82.4425 q^{86} +(-52.9926 + 52.9926i) q^{87} +(-13.4182 - 13.4182i) q^{88} +42.0148i q^{89} +(-20.3815 + 5.88163i) q^{90} +2.50460 q^{91} +(-6.78233 + 6.78233i) q^{92} +(18.2441 + 18.2441i) q^{93} +63.5004i q^{94} +(-81.8099 - 45.1673i) q^{95} -9.79796 q^{96} +(8.47487 - 8.47487i) q^{97} +(48.7083 + 48.7083i) q^{98} +20.1273i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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