LMFDB - Embedded newform 690.3.k.a.277.18

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			277.18
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.18

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	−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	0.733860	−	0.679301i	$-0.237717\pi$
$7$	0.381912	+	0.381912i	0.0545588	+	0.0545588i	−0.679301	+	0.733860i	$0.737717\pi$
$8$	−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	−0.569653	−	0.821885i	$-0.692922\pi$
$13$	3.27903	−	3.27903i	0.252233	−	0.252233i	0.821885	+	0.569653i	$0.192922\pi$
$14$			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	0.213622	−	0.976916i	$-0.431474\pi$
$17$	−12.9760	−	12.9760i	−0.763294	−	0.763294i	−0.976916	+	0.213622i	$0.931474\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	18.6900i		−	0.983686i	−0.870684	−	0.491843i	$-0.836323\pi$
$19$		−	18.6900i		−	0.983686i	0.870684	−	0.491843i	$-0.163677\pi$
$20$	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	$-0.731970\pi$
$29$		−	43.2683i		−	1.49201i	0.665941	−	0.746004i	$-0.268030\pi$
$30$	−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	0.594119	−	0.804377i	$-0.297501\pi$
$37$	−7.77957	−	7.77957i	−0.210259	−	0.210259i	−0.804377	+	0.594119i	$0.797501\pi$
$38$	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	−0.0405438	−	0.999178i	$-0.512909\pi$
$43$	41.2213	−	41.2213i	0.958634	−	0.958634i	0.999178	+	0.0405438i	$0.0129090\pi$
$44$			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	0.283450	−	0.958987i	$-0.408521\pi$
$47$	−31.7502	−	31.7502i	−0.675536	−	0.675536i	−0.958987	+	0.283450i	$0.908521\pi$
$48$	−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	−0.563223	−	0.826305i	$-0.690439\pi$
$53$	13.9434	−	13.9434i	0.263083	−	0.263083i	0.826305	+	0.563223i	$0.190439\pi$
$54$		−	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	$-0.993751\pi$
$59$		−	2.31643i		−	0.0392616i	0.999807	−	0.0196308i	$-0.00624908\pi$
$60$	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	0.993843	−	0.110796i	$-0.0353400\pi$
$67$	59.1642	+	59.1642i	0.883047	+	0.883047i	−0.110796	+	0.993843i	$0.535340\pi$
$68$	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	−0.00279431	+	0.999996i	$0.500889\pi$
$73$	−73.2037	+	73.2037i	−1.00279	+	1.00279i	−0.999996	+	0.00279431i	$0.999111\pi$
$74$		−	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	$0.0242852\pi$
$79$			12.0428i			0.152440i	−0.997091	+	0.0762202i	$0.975715\pi$
$80$	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	−0.780270	−	0.625443i	$-0.784918\pi$
$83$	−12.8507	+	12.8507i	−0.154827	+	0.154827i	0.625443	+	0.780270i	$0.284918\pi$
$84$			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	$-0.924151\pi$
$89$		−	42.0148i		−	0.472076i	0.971744	−	0.236038i	$-0.0758490\pi$
$90$	−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	0.749441	−	0.662071i	$-0.230322\pi$
$97$	8.47487	+	8.47487i	0.0873698	+	0.0873698i	−0.662071	+	0.749441i	$0.730322\pi$
$98$	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	−0.544801	−	0.838565i	$-0.683395\pi$
$103$	30.2577	−	30.2577i	0.293764	−	0.293764i	0.838565	+	0.544801i	$0.183395\pi$
$104$			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	0.925628	−	0.378435i	$-0.123538\pi$
$107$	58.5497	+	58.5497i	0.547193	+	0.547193i	−0.378435	+	0.925628i	$0.623538\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			156.152i			1.43258i	0.697801	+	0.716291i	$0.254162\pi$
$109$			156.152i			1.43258i	−0.697801	+	0.716291i	$0.745838\pi$
$110$	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	−0.264431	−	0.964405i	$-0.585184\pi$
$113$	79.0970	−	79.0970i	0.699973	−	0.699973i	0.964405	+	0.264431i	$0.0851842\pi$
$114$		−	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	0.999108	+	0.0422197i	$0.0134429\pi$
$127$	132.249	+	132.249i	1.04133	+	1.04133i	0.0422197	+	0.999108i	$0.486557\pi$
$128$	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	0.860251	−	0.509871i	$-0.170307\pi$
$137$	48.0021	+	48.0021i	0.350380	+	0.350380i	−0.509871	+	0.860251i	$0.670307\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$			64.5350i			0.464281i	0.972682	+	0.232140i	$0.0745729\pi$
$139$			64.5350i			0.464281i	−0.972682	+	0.232140i	$0.925427\pi$
$140$	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	$0.0735402\pi$
$149$			68.2371i			0.457967i	−0.973430	+	0.228984i	$0.926460\pi$
$150$	−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	0.428841	−	0.903380i	$-0.358922\pi$
$157$	−74.5026	−	74.5026i	−0.474539	−	0.474539i	−0.903380	+	0.428841i	$0.858922\pi$
$158$	−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	−0.173816	+	0.984778i	$0.555610\pi$
$163$	−188.851	+	188.851i	−1.15859	+	1.15859i	−0.984778	+	0.173816i	$0.944390\pi$
$164$		−	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	0.548061	−	0.836439i	$-0.315366\pi$
$167$	−48.1591	−	48.1591i	−0.288378	−	0.288378i	−0.836439	+	0.548061i	$0.815366\pi$
$168$	−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	0.0983603	−	0.995151i	$-0.468640\pi$
$173$	189.177	−	189.177i	1.09351	−	1.09351i	0.995151	−	0.0983603i	$-0.0313598\pi$
$174$		−	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	$-0.779043\pi$
$179$		−	229.026i		−	1.27947i	0.768594	−	0.639737i	$-0.220957\pi$
$180$	−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	−0.868835	−	0.495102i	$-0.835131\pi$
$193$	−72.1304	+	72.1304i	−0.373733	+	0.373733i	0.495102	+	0.868835i	$0.335131\pi$
$194$			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	0.990012	−	0.140980i	$-0.0450254\pi$
$197$	167.259	+	167.259i	0.849032	+	0.849032i	−0.140980	+	0.990012i	$0.545025\pi$
$198$	20.1273	−	20.1273i	0.101653	−	0.101653i
$199$			146.363i			0.735493i	0.929926	+	0.367747i	$0.119871\pi$
$199$			146.363i			0.735493i	−0.929926	+	0.367747i	$0.880129\pi$
$200$	−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	−0.180104	+	0.983648i	$0.557644\pi$
$223$	−259.517	+	259.517i	−1.16375	+	1.16375i	−0.983648	+	0.180104i	$0.942356\pi$
$224$		−	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	0.695261	−	0.718758i	$-0.255289\pi$
$227$	−5.33385	−	5.33385i	−0.0234971	−	0.0234971i	−0.718758	+	0.695261i	$0.755289\pi$
$228$	45.7811	−	45.7811i	0.200794	−	0.200794i
$229$		−	129.029i		−	0.563447i	−0.959496	−	0.281724i	$-0.909094\pi$
$229$		−	129.029i		−	0.563447i	0.959496	−	0.281724i	$-0.0909061\pi$
$230$	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	−0.999828	−	0.0185604i	$-0.994092\pi$
$233$	−228.635	+	228.635i	−0.981267	+	0.981267i	0.0185604	+	0.999828i	$0.494092\pi$
$234$		−	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	$-0.733916\pi$
$239$		−	354.637i		−	1.48384i	0.670489	−	0.741919i	$-0.266084\pi$
$240$	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	0.765117	−	0.643891i	$-0.222681\pi$
$257$	31.1551	+	31.1551i	0.121226	+	0.121226i	−0.643891	+	0.765117i	$0.722681\pi$
$258$	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	−0.929645	−	0.368455i	$-0.879887\pi$
$263$	−147.593	+	147.593i	−0.561190	+	0.561190i	0.368455	+	0.929645i	$0.379887\pi$
$264$			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	$-0.896044\pi$
$269$		−	172.598i		−	0.641627i	0.947142	−	0.320813i	$-0.103956\pi$
$270$	−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	0.930561	−	0.366136i	$-0.119319\pi$
$277$	156.346	+	156.346i	0.564426	+	0.564426i	−0.366136	+	0.930561i	$0.619319\pi$
$278$	−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	−0.396877	−	0.917872i	$-0.629906\pi$
$283$	147.441	−	147.441i	0.520995	−	0.520995i	0.917872	+	0.396877i	$0.129906\pi$
$284$			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	−0.693614	−	0.720347i	$-0.743982\pi$
$293$	7.83296	−	7.83296i	0.0267336	−	0.0267336i	0.720347	+	0.693614i	$0.243982\pi$
$294$		−	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	−0.994681	−	0.103002i	$-0.967155\pi$
$307$	−336.989	−	336.989i	−1.09768	−	1.09768i	−0.103002	−	0.994681i	$-0.532845\pi$
$308$	−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	−0.272331	+	0.962204i	$0.587794\pi$
$313$	−386.409	+	386.409i	−1.23453	+	1.23453i	−0.962204	+	0.272331i	$0.912206\pi$
$314$		−	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	0.851108	−	0.524990i	$-0.175931\pi$
$317$	103.379	+	103.379i	0.326118	+	0.326118i	−0.524990	+	0.851108i	$0.675931\pi$
$318$	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	0.999845	+	0.0176066i	$0.00560466\pi$
$337$	342.881	+	342.881i	1.01745	+	1.01745i	0.0176066	+	0.999845i	$0.494395\pi$
$338$	−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	0.436634	−	0.899639i	$-0.356170\pi$
$347$	−160.663	−	160.663i	−0.463005	−	0.463005i	−0.899639	+	0.436634i	$0.856170\pi$
$348$	105.985	−	105.985i	0.304555	−	0.304555i
$349$		−	20.4812i		−	0.0586855i	−0.999569	−	0.0293427i	$-0.990659\pi$
$349$		−	20.4812i		−	0.0586855i	0.999569	−	0.0293427i	$-0.00934142\pi$
$350$	−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	−0.971971	−	0.235102i	$-0.924458\pi$
$353$	−260.115	+	260.115i	−0.736869	+	0.736869i	0.235102	+	0.971971i	$0.424458\pi$
$354$		−	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	$-0.722291\pi$
$359$		−	549.920i		−	1.53181i	0.642953	−	0.765905i	$-0.277709\pi$
$360$	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	0.800265	−	0.599646i	$-0.204692\pi$
$367$	73.6271	+	73.6271i	0.200619	+	0.200619i	−0.599646	+	0.800265i	$0.704692\pi$
$368$	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	−0.880713	−	0.473650i	$-0.842936\pi$
$373$	−151.835	+	151.835i	−0.407063	+	0.407063i	0.473650	+	0.880713i	$0.342936\pi$
$374$		−	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	$-0.999805\pi$
$379$		−	0.463933i		−	0.00122410i	1.00000		0.000612049i	$-0.000194821\pi$
$380$	−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	−0.486710	−	0.873563i	$-0.661803\pi$
$383$	148.165	−	148.165i	0.386853	−	0.386853i	0.873563	+	0.486710i	$0.161803\pi$
$384$		−	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	$-0.770998\pi$
$389$		−	512.669i		−	1.31791i	0.752180	−	0.658957i	$-0.229002\pi$
$390$	−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	0.904870	−	0.425688i	$-0.139968\pi$
$397$	190.235	+	190.235i	0.479181	+	0.479181i	−0.425688	+	0.904870i	$0.639968\pi$
$398$	−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	$-0.708608\pi$
$409$		−	648.532i		−	1.58565i	0.609447	−	0.792827i	$-0.291392\pi$
$410$	−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	$0.129622\pi$
$419$			331.895i			0.792113i	−0.918226	+	0.396056i	$0.870378\pi$
$420$	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	−0.243240	−	0.969966i	$-0.578210\pi$
$433$	314.673	−	314.673i	0.726727	−	0.726727i	0.969966	+	0.243240i	$0.0782102\pi$
$434$			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	$-0.856056\pi$
$439$		−	383.648i		−	0.873914i	0.899482	−	0.436957i	$-0.143944\pi$
$440$	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	−0.723085	−	0.690759i	$-0.757276\pi$
$443$	−14.3200	+	14.3200i	−0.0323251	+	0.0323251i	0.690759	+	0.723085i	$0.257276\pi$
$444$		−	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	$-0.859508\pi$
$449$		−	383.606i		−	0.854355i	0.904168	−	0.427178i	$-0.140492\pi$
$450$	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	0.991580	+	0.129494i	$0.0413352\pi$
$457$	512.331	+	512.331i	1.12107	+	1.12107i	0.129494	+	0.991580i	$0.458665\pi$
$458$	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	0.285300	−	0.958438i	$-0.407907\pi$
$463$	575.851	−	575.851i	1.24374	−	1.24374i	0.958438	−	0.285300i	$-0.0920931\pi$
$464$			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	0.978187	−	0.207728i	$-0.0666068\pi$
$467$	359.804	+	359.804i	0.770459	+	0.770459i	−0.207728	+	0.978187i	$0.566607\pi$
$468$	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	$-0.629079\pi$
$479$		−	880.306i		−	1.83780i	0.394490	−	0.918900i	$-0.370921\pi$
$480$	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	−0.999631	−	0.0271685i	$-0.991351\pi$
$487$	−500.051	−	500.051i	−1.02680	−	1.02680i	−0.0271685	−	0.999631i	$-0.508649\pi$
$488$	−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	$-0.976271\pi$
$499$		−	74.3281i		−	0.148954i	0.997223	−	0.0744771i	$-0.0237288\pi$
$500$	−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	−0.129257	−	0.991611i	$-0.541259\pi$
$503$	433.764	−	433.764i	0.862354	−	0.862354i	0.991611	+	0.129257i	$0.0412592\pi$
$504$			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	$-0.858026\pi$
$509$		−	439.146i		−	0.862763i	0.902170	−	0.431381i	$-0.141974\pi$
$510$	−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	−0.856783	−	0.515676i	$-0.827541\pi$
$523$	−178.399	+	178.399i	−0.341107	+	0.341107i	0.515676	+	0.856783i	$0.327541\pi$
$524$			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	0.290172	−	0.956975i	$-0.406288\pi$
$547$	−364.741	−	364.741i	−0.666803	−	0.666803i	−0.956975	+	0.290172i	$0.906288\pi$
$548$	−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	0.990675	−	0.136243i	$-0.0435028\pi$
$557$	475.919	+	475.919i	0.854433	+	0.854433i	−0.136243	+	0.990675i	$0.543503\pi$
$558$	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	−0.566172	−	0.824287i	$-0.691576\pi$
$563$	145.318	−	145.318i	0.258114	−	0.258114i	0.824287	+	0.566172i	$0.191576\pi$
$564$		−	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	$0.0749884\pi$
$569$			265.620i			0.466820i	−0.972378	+	0.233410i	$0.925012\pi$
$570$	−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	0.419268	−	0.907863i	$-0.362287\pi$
$577$	−281.919	−	281.919i	−0.488595	−	0.488595i	−0.907863	+	0.419268i	$0.862287\pi$
$578$	−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	0.702336	−	0.711846i	$-0.252140\pi$
$587$	−5.58217	−	5.58217i	−0.00950967	−	0.00950967i	−0.711846	+	0.702336i	$0.752140\pi$
$588$	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	−0.988043	−	0.154177i	$-0.950727\pi$
$593$	−494.483	+	494.483i	−0.833866	+	0.833866i	0.154177	+	0.988043i	$0.450727\pi$
$594$		−	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	$0.0212368\pi$
$599$			79.8683i			0.133336i	−0.997775	+	0.0666680i	$0.978763\pi$
$600$	−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	−0.998334	−	0.0576959i	$-0.981625\pi$
$607$	−641.010	−	641.010i	−1.05603	−	1.05603i	−0.0576959	−	0.998334i	$-0.518375\pi$
$608$	−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	−0.330257	+	0.943891i	$0.607136\pi$
$613$	−781.053	+	781.053i	−1.27415	+	1.27415i	−0.943891	+	0.330257i	$0.892864\pi$
$614$		−	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	0.838953	−	0.544204i	$-0.183168\pi$
$617$	181.860	+	181.860i	0.294749	+	0.294749i	−0.544204	+	0.838953i	$0.683168\pi$
$618$	74.1158	−	74.1158i	0.119928	−	0.119928i
$619$		−	907.156i		−	1.46552i	−0.680488	−	0.732759i	$-0.738232\pi$
$619$		−	907.156i		−	1.46552i	0.680488	−	0.732759i	$-0.261768\pi$
$620$	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	−0.801876	−	0.597490i	$-0.796165\pi$
$643$	−131.420	+	131.420i	−0.204386	+	0.204386i	0.597490	+	0.801876i	$0.296165\pi$
$644$		−	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	0.980753	−	0.195253i	$-0.0625526\pi$
$647$	508.219	+	508.219i	0.785500	+	0.785500i	−0.195253	+	0.980753i	$0.562553\pi$
$648$	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	−0.939790	−	0.341752i	$-0.888980\pi$
$653$	−390.519	+	390.519i	−0.598039	+	0.598039i	0.341752	+	0.939790i	$0.388980\pi$
$654$			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	$0.259084\pi$
$659$			958.180i			1.45399i	−0.686643	+	0.726995i	$0.740916\pi$
$660$	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	−0.877947	−	0.478758i	$-0.841087\pi$
$673$	−268.654	+	268.654i	−0.399188	+	0.399188i	0.478758	+	0.877947i	$0.341087\pi$
$674$			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	0.868295	−	0.496048i	$-0.165216\pi$
$677$	252.012	+	252.012i	0.372248	+	0.372248i	−0.496048	+	0.868295i	$0.665216\pi$
$678$	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	−0.723734	−	0.690079i	$-0.757576\pi$
$683$	−22.9869	+	22.9869i	−0.0336558	+	0.0336558i	0.690079	+	0.723734i	$0.257576\pi$
$684$		−	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	$-0.879789\pi$
$709$		−	522.875i		−	0.737482i	0.929532	−	0.368741i	$-0.120211\pi$
$710$	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	$-0.955182\pi$
$719$		−	201.802i		−	0.280670i	0.990104	−	0.140335i	$-0.0448180\pi$
$720$	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	0.723243	−	0.690594i	$-0.242651\pi$
$727$	23.7355	+	23.7355i	0.0326486	+	0.0326486i	−0.690594	+	0.723243i	$0.742651\pi$
$728$	−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	−0.984551	−	0.175098i	$-0.943976\pi$
$733$	−593.329	+	593.329i	−0.809453	+	0.809453i	0.175098	+	0.984551i	$0.443976\pi$
$734$			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	$0.339550\pi$
$739$			1294.17i			1.75125i	−0.482992	+	0.875625i	$0.660450\pi$
$740$	−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	−0.780196	−	0.625536i	$-0.784881\pi$
$743$	−114.912	+	114.912i	−0.154660	+	0.154660i	0.625536	+	0.780196i	$0.284881\pi$
$744$			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	0.770064	−	0.637967i	$-0.220224\pi$
$757$	99.9974	+	99.9974i	0.132097	+	0.132097i	−0.637967	+	0.770064i	$0.720224\pi$
$758$	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	$0.0851082\pi$
$769$			406.341i			0.528402i	−0.964468	+	0.264201i	$0.914892\pi$
$770$	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	−0.532166	−	0.846640i	$-0.678622\pi$
$773$	243.088	−	243.088i	0.314473	−	0.314473i	0.846640	+	0.532166i	$0.178622\pi$
$774$		−	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	0.614841	−	0.788651i	$-0.289220\pi$
$787$	−136.789	−	136.789i	−0.173810	−	0.173810i	−0.788651	+	0.614841i	$0.789220\pi$
$788$	−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	0.849767	+	0.527159i	$0.176743\pi$
$797$	1097.41	+	1097.41i	1.37693	+	1.37693i	0.527159	+	0.849767i	$0.323257\pi$
$798$	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	$0.121520\pi$
$809$			602.804i			0.745123i	−0.928008	+	0.372561i	$0.878480\pi$
$810$	−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	−0.241173	−	0.970482i	$-0.577532\pi$
$823$	600.222	−	600.222i	0.729309	−	0.729309i	0.970482	+	0.241173i	$0.0775320\pi$
$824$			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	−0.987391	−	0.158299i	$-0.949399\pi$
$827$	−947.486	−	947.486i	−1.14569	−	1.14569i	−0.158299	−	0.987391i	$-0.550601\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			1022.25i			1.23311i	0.787310	+	0.616557i	$0.211473\pi$
$829$			1022.25i			1.23311i	−0.787310	+	0.616557i	$0.788527\pi$
$830$	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	$0.133496\pi$
$839$			683.287i			0.814406i	−0.913338	+	0.407203i	$0.866504\pi$
$840$	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	−0.0224387	−	0.999748i	$-0.507143\pi$
$853$	833.645	−	833.645i	0.977309	−	0.977309i	0.999748	+	0.0224387i	$0.00714307\pi$
$854$			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	0.997133	−	0.0756685i	$-0.0241091\pi$
$857$	789.695	+	789.695i	0.921465	+	0.921465i	−0.0756685	+	0.997133i	$0.524109\pi$
$858$	53.8872	−	53.8872i	0.0628056	−	0.0628056i
$859$		−	1020.26i		−	1.18773i	−0.804565	−	0.593864i	$-0.797602\pi$
$859$		−	1020.26i		−	1.18773i	0.804565	−	0.593864i	$-0.202398\pi$
$860$	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	−0.991901	−	0.127011i	$-0.959462\pi$
$863$	−746.400	+	746.400i	−0.864890	+	0.864890i	0.127011	+	0.991901i	$0.459462\pi$
$864$			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	0.880414	−	0.474206i	$-0.157265\pi$
$877$	356.244	+	356.244i	0.406207	+	0.406207i	−0.474206	+	0.880414i	$0.657265\pi$
$878$	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	−0.768402	−	0.639967i	$-0.778948\pi$
$883$	−113.408	+	113.408i	−0.128435	+	0.128435i	0.639967	+	0.768402i	$0.278948\pi$
$884$		−	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	−0.999515	−	0.0311508i	$-0.990083\pi$
$887$	−914.200	−	914.200i	−1.03067	−	1.03067i	−0.0311508	−	0.999515i	$-0.509917\pi$
$888$	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	0.313865	−	0.949468i	$-0.398376\pi$
$907$	−576.492	−	576.492i	−0.635603	−	0.635603i	−0.949468	+	0.313865i	$0.898376\pi$
$908$	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	$0.0744484\pi$
$919$			425.975i			0.463520i	−0.972773	+	0.231760i	$0.925552\pi$
$920$	−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	$0.0156414\pi$
$929$			91.2635i			0.0982384i	−0.998793	+	0.0491192i	$0.984359\pi$
$930$	−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	0.274271	−	0.961652i	$-0.411563\pi$
$937$	−644.076	−	644.076i	−0.687381	−	0.687381i	−0.961652	+	0.274271i	$0.911563\pi$
$938$	−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	0.292283	−	0.956332i	$-0.405585\pi$
$947$	−628.854	−	628.854i	−0.664049	−	0.664049i	−0.956332	+	0.292283i	$0.905585\pi$
$948$	−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	−0.378666	−	0.925533i	$-0.623617\pi$
$953$	521.165	−	521.165i	0.546868	−	0.546868i	0.925533	+	0.378666i	$0.123617\pi$
$954$		−	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	0.820274	−	0.571970i	$-0.193821\pi$
$967$	240.110	+	240.110i	0.248304	+	0.248304i	−0.571970	+	0.820274i	$0.693821\pi$
$968$	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	0.984070	−	0.177781i	$-0.0568920\pi$
$977$	787.744	+	787.744i	0.806289	+	0.806289i	−0.177781	+	0.984070i	$0.556892\pi$
$978$	−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	−0.904804	−	0.425829i	$-0.859983\pi$
$983$	−470.832	+	470.832i	−0.478975	+	0.478975i	0.425829	+	0.904804i	$0.359983\pi$
$984$		−	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	0.245146	−	0.969486i	$-0.421164\pi$
$997$	−722.167	−	722.167i	−0.724340	−	0.724340i	−0.969486	+	0.245146i	$0.921164\pi$
$998$	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.277.18	✓	40
5.3	odd	4	inner	690.3.k.a.553.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.18	✓	40	1.1	even	1	trivial
690.3.k.a.553.18	yes	40	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.41665 - 4.37719i) q^{5} +2.44949 q^{6} +(0.381912 + 0.381912i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(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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