LMFDB - Embedded newform 690.3.k.b.277.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			277.17
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.62723 + 2.46574i) q^{10} +6.56968 q^{11} +(2.44949 + 2.44949i) q^{12} +(16.0299 - 16.0299i) q^{13} +2.91676i q^{14} +(-3.01990 - 8.11666i) q^{15} -4.00000 q^{16} +(10.8651 + 10.8651i) q^{17} +(-3.00000 + 3.00000i) q^{18} +8.18603i q^{19} +(9.09297 + 4.16148i) q^{20} -3.57228 q^{21} +(-6.56968 - 6.56968i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-16.3410 - 18.9201i) q^{25} -32.0598 q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.91676 - 2.91676i) q^{28} -6.33745i q^{29} +(-5.09676 + 11.1366i) q^{30} +27.7263 q^{31} +(4.00000 + 4.00000i) q^{32} +(8.04619 - 8.04619i) q^{33} -21.7301i q^{34} +(-9.66500 + 3.59598i) q^{35} +6.00000 q^{36} +(-14.1170 - 14.1170i) q^{37} +(8.18603 - 8.18603i) q^{38} -39.2651i q^{39} +(-4.93148 - 13.2545i) q^{40} -69.6643 q^{41} +(3.57228 + 3.57228i) q^{42} +(17.6100 - 17.6100i) q^{43} +13.1394i q^{44} +(-13.6395 - 6.24223i) q^{45} -6.78233 q^{46} +(22.1675 + 22.1675i) q^{47} +(-4.89898 + 4.89898i) q^{48} -44.7463i q^{49} +(-2.57909 + 35.2611i) q^{50} +26.6138 q^{51} +(32.0598 + 32.0598i) q^{52} +(-1.75313 + 1.75313i) q^{53} +7.34847i q^{54} +(13.6698 - 29.8690i) q^{55} -5.83351 q^{56} +(10.0258 + 10.0258i) q^{57} +(-6.33745 + 6.33745i) q^{58} +84.6547i q^{59} +(16.2333 - 6.03981i) q^{60} +30.9806 q^{61} +(-27.7263 - 27.7263i) q^{62} +(-4.37513 + 4.37513i) q^{63} -8.00000i q^{64} +(-39.5256 - 106.234i) q^{65} -16.0924 q^{66} +(-30.7488 - 30.7488i) q^{67} +(-21.7301 + 21.7301i) q^{68} -8.30662i q^{69} +(13.2610 + 6.06902i) q^{70} -41.0485 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-37.1267 + 37.1267i) q^{73} +28.2340i q^{74} +(-43.1859 - 3.15873i) q^{75} -16.3721 q^{76} +(-9.58108 - 9.58108i) q^{77} +(-39.2651 + 39.2651i) q^{78} -95.7052i q^{79} +(-8.32297 + 18.1859i) q^{80} -9.00000 q^{81} +(69.6643 + 69.6643i) q^{82} +(44.3961 - 44.3961i) q^{83} -7.14456i q^{84} +(72.0051 - 26.7904i) q^{85} -35.2200 q^{86} +(-7.76176 - 7.76176i) q^{87} +(13.1394 - 13.1394i) q^{88} -142.109i q^{89} +(7.39723 + 19.8817i) q^{90} -46.7554 q^{91} +(6.78233 + 6.78233i) q^{92} +(33.9576 - 33.9576i) q^{93} -44.3349i q^{94} +(37.2176 + 17.0330i) q^{95} +9.79796 q^{96} +(99.3088 + 99.3088i) q^{97} +(-44.7463 + 44.7463i) q^{98} -19.7090i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	2.08074	−	4.54648i	0.416148	−	0.909297i
$5$	2.08074	−	4.54648i	0.416148	−	0.909297i
$6$	−2.44949			−0.408248
$7$	−1.45838	−	1.45838i	−0.208340	−	0.208340i	0.595222	−	0.803561i	$-0.297064\pi$
$7$	−1.45838	−	1.45838i	−0.208340	−	0.208340i	−0.803561	+	0.595222i	$0.797064\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−6.62723	+	2.46574i	−0.662723	+	0.246574i
$11$	6.56968			0.597244			0.298622	−	0.954371i	$-0.403473\pi$
$11$	6.56968			0.597244			0.298622	+	0.954371i	$0.403473\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	16.0299	−	16.0299i	1.23307	−	1.23307i	0.270292	−	0.962778i	$-0.412880\pi$
$13$	16.0299	−	16.0299i	1.23307	−	1.23307i	0.962778	−	0.270292i	$-0.0871204\pi$
$14$			2.91676i			0.208340i
$15$	−3.01990	−	8.11666i	−0.201327	−	0.541111i
$16$	−4.00000			−0.250000
$17$	10.8651	+	10.8651i	0.639121	+	0.639121i	0.950339	−	0.311218i	$-0.100737\pi$
$17$	10.8651	+	10.8651i	0.639121	+	0.639121i	−0.311218	+	0.950339i	$0.600737\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			8.18603i			0.430844i	0.976521	+	0.215422i	$0.0691126\pi$
$19$			8.18603i			0.430844i	−0.976521	+	0.215422i	$0.930887\pi$
$20$	9.09297	+	4.16148i	0.454648	+	0.208074i
$21$	−3.57228			−0.170109
$22$	−6.56968	−	6.56968i	−0.298622	−	0.298622i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−16.3410	−	18.9201i	−0.653641	−	0.756805i
$26$	−32.0598			−1.23307
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	2.91676	−	2.91676i	0.104170	−	0.104170i
$29$		−	6.33745i		−	0.218533i	−0.994012	−	0.109266i	$-0.965150\pi$
$29$		−	6.33745i		−	0.218533i	0.994012	−	0.109266i	$-0.0348502\pi$
$30$	−5.09676	+	11.1366i	−0.169892	+	0.371219i
$31$	27.7263			0.894397			0.447198	−	0.894435i	$-0.352422\pi$
$31$	27.7263			0.894397			0.447198	+	0.894435i	$0.352422\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	8.04619	−	8.04619i	0.243824	−	0.243824i
$34$		−	21.7301i		−	0.639121i
$35$	−9.66500	+	3.59598i	−0.276143	+	0.102742i
$36$	6.00000			0.166667
$37$	−14.1170	−	14.1170i	−0.381541	−	0.381541i	0.490116	−	0.871657i	$-0.336954\pi$
$37$	−14.1170	−	14.1170i	−0.381541	−	0.381541i	−0.871657	+	0.490116i	$0.836954\pi$
$38$	8.18603	−	8.18603i	0.215422	−	0.215422i
$39$		−	39.2651i		−	1.00680i
$40$	−4.93148	−	13.2545i	−0.123287	−	0.331361i
$41$	−69.6643			−1.69913			−0.849564	−	0.527485i	$-0.823135\pi$
$41$	−69.6643			−1.69913			−0.849564	+	0.527485i	$0.823135\pi$
$42$	3.57228	+	3.57228i	0.0850543	+	0.0850543i
$43$	17.6100	−	17.6100i	0.409535	−	0.409535i	−0.472042	−	0.881576i	$-0.656483\pi$
$43$	17.6100	−	17.6100i	0.409535	−	0.409535i	0.881576	+	0.472042i	$0.156483\pi$
$44$			13.1394i			0.298622i
$45$	−13.6395	−	6.24223i	−0.303099	−	0.138716i
$46$	−6.78233			−0.147442
$47$	22.1675	+	22.1675i	0.471648	+	0.471648i	0.902448	−	0.430800i	$-0.141768\pi$
$47$	22.1675	+	22.1675i	0.471648	+	0.471648i	−0.430800	+	0.902448i	$0.641768\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	44.7463i		−	0.913189i
$50$	−2.57909	+	35.2611i	−0.0515818	+	0.705223i
$51$	26.6138			0.521840
$52$	32.0598	+	32.0598i	0.616535	+	0.616535i
$53$	−1.75313	+	1.75313i	−0.0330779	+	0.0330779i	−0.723452	−	0.690374i	$-0.757446\pi$
$53$	−1.75313	+	1.75313i	−0.0330779	+	0.0330779i	0.690374	+	0.723452i	$0.257446\pi$
$54$			7.34847i			0.136083i
$55$	13.6698	−	29.8690i	0.248542	−	0.543072i
$56$	−5.83351			−0.104170
$57$	10.0258	+	10.0258i	0.175891	+	0.175891i
$58$	−6.33745	+	6.33745i	−0.109266	+	0.109266i
$59$			84.6547i			1.43483i	0.696649	+	0.717413i	$0.254674\pi$
$59$			84.6547i			1.43483i	−0.696649	+	0.717413i	$0.745326\pi$
$60$	16.2333	−	6.03981i	0.270555	−	0.100663i
$61$	30.9806			0.507879			0.253939	−	0.967220i	$-0.418274\pi$
$61$	30.9806			0.507879			0.253939	+	0.967220i	$0.418274\pi$
$62$	−27.7263	−	27.7263i	−0.447198	−	0.447198i
$63$	−4.37513	+	4.37513i	−0.0694466	+	0.0694466i
$64$		−	8.00000i		−	0.125000i
$65$	−39.5256	−	106.234i	−0.608087	−	1.63437i
$66$	−16.0924			−0.243824
$67$	−30.7488	−	30.7488i	−0.458937	−	0.458937i	0.439369	−	0.898307i	$-0.355202\pi$
$67$	−30.7488	−	30.7488i	−0.458937	−	0.458937i	−0.898307	+	0.439369i	$0.855202\pi$
$68$	−21.7301	+	21.7301i	−0.319560	+	0.319560i
$69$		−	8.30662i		−	0.120386i
$70$	13.2610	+	6.06902i	0.189443	+	0.0867002i
$71$	−41.0485			−0.578148			−0.289074	−	0.957307i	$-0.593347\pi$
$71$	−41.0485			−0.578148			−0.289074	+	0.957307i	$0.593347\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−37.1267	+	37.1267i	−0.508584	+	0.508584i	−0.914092	−	0.405507i	$-0.867095\pi$
$73$	−37.1267	+	37.1267i	−0.508584	+	0.508584i	0.405507	+	0.914092i	$0.367095\pi$
$74$			28.2340i			0.381541i
$75$	−43.1859	−	3.15873i	−0.575812	−	0.0421164i
$76$	−16.3721			−0.215422
$77$	−9.58108	−	9.58108i	−0.124430	−	0.124430i
$78$	−39.2651	+	39.2651i	−0.503399	+	0.503399i
$79$		−	95.7052i		−	1.21146i	−0.795671	−	0.605729i	$-0.792881\pi$
$79$		−	95.7052i		−	1.21146i	0.795671	−	0.605729i	$-0.207119\pi$
$80$	−8.32297	+	18.1859i	−0.104037	+	0.227324i
$81$	−9.00000			−0.111111
$82$	69.6643	+	69.6643i	0.849564	+	0.849564i
$83$	44.3961	−	44.3961i	0.534893	−	0.534893i	−0.387132	−	0.922024i	$-0.626534\pi$
$83$	44.3961	−	44.3961i	0.534893	−	0.534893i	0.922024	+	0.387132i	$0.126534\pi$
$84$		−	7.14456i		−	0.0850543i
$85$	72.0051	−	26.7904i	0.847119	−	0.315181i
$86$	−35.2200			−0.409535
$87$	−7.76176	−	7.76176i	−0.0892157	−	0.0892157i
$88$	13.1394	−	13.1394i	0.149311	−	0.149311i
$89$		−	142.109i		−	1.59673i	−0.602173	−	0.798366i	$-0.705698\pi$
$89$		−	142.109i		−	1.59673i	0.602173	−	0.798366i	$-0.294302\pi$
$90$	7.39723	+	19.8817i	0.0821914	+	0.220908i
$91$	−46.7554			−0.513795
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	33.9576	−	33.9576i	0.365136	−	0.365136i
$94$		−	44.3349i		−	0.471648i
$95$	37.2176	+	17.0330i	0.391765	+	0.179295i
$96$	9.79796			0.102062
$97$	99.3088	+	99.3088i	1.02380	+	1.02380i	0.999710	+	0.0240920i	$0.00766948\pi$
$97$	99.3088	+	99.3088i	1.02380	+	1.02380i	0.0240920	+	0.999710i	$0.492331\pi$
$98$	−44.7463	+	44.7463i	−0.456595	+	0.456595i
$99$		−	19.7090i		−	0.199081i
$100$	37.8402	−	32.6821i	0.378402	−	0.326821i
$101$	−120.819			−1.19623			−0.598114	−	0.801411i	$-0.704083\pi$
$101$	−120.819			−1.19623			−0.598114	+	0.801411i	$0.704083\pi$
$102$	−26.6138	−	26.6138i	−0.260920	−	0.260920i
$103$	−31.7941	+	31.7941i	−0.308681	+	0.308681i	−0.844398	−	0.535717i	$-0.820041\pi$
$103$	−31.7941	+	31.7941i	−0.308681	+	0.308681i	0.535717	+	0.844398i	$0.320041\pi$
$104$		−	64.1197i		−	0.616535i
$105$	−7.43300	+	16.2413i	−0.0707904	+	0.154679i
$106$	3.50625			0.0330779
$107$	−118.422	−	118.422i	−1.10675	−	1.10675i	−0.993575	−	0.113174i	$-0.963898\pi$
$107$	−118.422	−	118.422i	−1.10675	−	1.10675i	−0.113174	−	0.993575i	$-0.536102\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	21.5303i		−	0.197526i	−0.995111	−	0.0987628i	$-0.968511\pi$
$109$		−	21.5303i		−	0.197526i	0.995111	−	0.0987628i	$-0.0314885\pi$
$110$	−43.5388	+	16.1991i	−0.395807	+	0.147265i
$111$	−34.5795			−0.311527
$112$	5.83351	+	5.83351i	0.0520849	+	0.0520849i
$113$	−72.3235	+	72.3235i	−0.640031	+	0.640031i	−0.950563	−	0.310532i	$-0.899493\pi$
$113$	−72.3235	+	72.3235i	−0.640031	+	0.640031i	0.310532	+	0.950563i	$0.399493\pi$
$114$		−	20.0516i		−	0.175891i
$115$	−8.36174	−	22.4740i	−0.0727108	−	0.195426i
$116$	12.6749			0.109266
$117$	−48.0898	−	48.0898i	−0.411024	−	0.411024i
$118$	84.6547	−	84.6547i	0.717413	−	0.717413i
$119$		−	31.6907i		−	0.266308i
$120$	−22.2731	−	10.1935i	−0.185609	−	0.0849459i
$121$	−77.8393			−0.643300
$122$	−30.9806	−	30.9806i	−0.253939	−	0.253939i
$123$	−85.3210	+	85.3210i	−0.693667	+	0.693667i
$124$			55.4526i			0.447198i
$125$	−120.021	+	34.9263i	−0.960172	+	0.279411i
$126$	8.75027			0.0694466
$127$	74.6311	+	74.6311i	0.587646	+	0.587646i	0.936993	−	0.349347i	$-0.113597\pi$
$127$	74.6311	+	74.6311i	0.587646	+	0.587646i	−0.349347	+	0.936993i	$0.613597\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	43.1355i		−	0.334384i
$130$	−66.7082	+	145.760i	−0.513140	+	1.12123i
$131$	−159.638			−1.21861			−0.609304	−	0.792936i	$-0.708551\pi$
$131$	−159.638			−1.21861			−0.609304	+	0.792936i	$0.708551\pi$
$132$	16.0924	+	16.0924i	0.121912	+	0.121912i
$133$	11.9383	−	11.9383i	0.0897618	−	0.0897618i
$134$			61.4976i			0.458937i
$135$	−24.3500	+	9.05971i	−0.180370	+	0.0671090i
$136$	43.4602			0.319560
$137$	46.5130	+	46.5130i	0.339511	+	0.339511i	0.856183	−	0.516672i	$-0.172829\pi$
$137$	46.5130	+	46.5130i	0.339511	+	0.339511i	−0.516672	+	0.856183i	$0.672829\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$			128.651i			0.925547i	0.886477	+	0.462774i	$0.153146\pi$
$139$			128.651i			0.925547i	−0.886477	+	0.462774i	$0.846854\pi$
$140$	−7.19197	−	19.3300i	−0.0513712	−	0.138071i
$141$	54.2990			0.385099
$142$	41.0485	+	41.0485i	0.289074	+	0.289074i
$143$	105.311	−	105.311i	0.736444	−	0.736444i
$144$			12.0000i			0.0833333i
$145$	−28.8131	−	13.1866i	−0.198711	−	0.0909421i
$146$	74.2533			0.508584
$147$	−54.8028	−	54.8028i	−0.372808	−	0.372808i
$148$	28.2340	−	28.2340i	0.190770	−	0.190770i
$149$			93.9923i			0.630821i	0.948955	+	0.315410i	$0.102142\pi$
$149$			93.9923i			0.630821i	−0.948955	+	0.315410i	$0.897858\pi$
$150$	40.0272	+	46.3446i	0.266848	+	0.308964i
$151$	170.451			1.12881			0.564406	−	0.825497i	$-0.309105\pi$
$151$	170.451			1.12881			0.564406	+	0.825497i	$0.309105\pi$
$152$	16.3721	+	16.3721i	0.107711	+	0.107711i
$153$	32.5952	−	32.5952i	0.213040	−	0.213040i
$154$			19.1622i			0.124430i
$155$	57.6913	−	126.057i	0.372202	−	0.813272i
$156$	78.5302			0.503399
$157$	58.3661	+	58.3661i	0.371758	+	0.371758i	0.868117	−	0.496359i	$-0.165330\pi$
$157$	58.3661	+	58.3661i	0.371758	+	0.371758i	−0.496359	+	0.868117i	$0.665330\pi$
$158$	−95.7052	+	95.7052i	−0.605729	+	0.605729i
$159$			4.29427i			0.0270080i
$160$	26.5089	−	9.86297i	0.165681	−	0.0616435i
$161$	−9.89120			−0.0614360
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	24.0343	−	24.0343i	0.147450	−	0.147450i	−0.629528	−	0.776978i	$-0.716752\pi$
$163$	24.0343	−	24.0343i	0.147450	−	0.147450i	0.776978	+	0.629528i	$0.216752\pi$
$164$		−	139.329i		−	0.849564i
$165$	−19.8398	−	53.3239i	−0.120241	−	0.323175i
$166$	−88.7922			−0.534893
$167$	128.995	+	128.995i	0.772426	+	0.772426i	0.978530	−	0.206104i	$-0.0660785\pi$
$167$	128.995	+	128.995i	0.772426	+	0.772426i	−0.206104	+	0.978530i	$0.566078\pi$
$168$	−7.14456	+	7.14456i	−0.0425272	+	0.0425272i
$169$		−	344.917i		−	2.04093i
$170$	−98.7956	−	45.2147i	−0.581150	−	0.265969i
$171$	24.5581			0.143615
$172$	35.2200	+	35.2200i	0.204767	+	0.204767i
$173$	−14.8434	+	14.8434i	−0.0858000	+	0.0858000i	−0.748704	−	0.662904i	$-0.769324\pi$
$173$	−14.8434	+	14.8434i	−0.0858000	+	0.0858000i	0.662904	+	0.748704i	$0.269324\pi$
$174$			15.5235i			0.0892157i
$175$	−3.76129	+	51.4241i	−0.0214931	+	0.293852i
$176$	−26.2787			−0.149311
$177$	103.680	+	103.680i	0.585765	+	0.585765i
$178$	−142.109	+	142.109i	−0.798366	+	0.798366i
$179$			10.8323i			0.0605158i	0.999542	+	0.0302579i	$0.00963286\pi$
$179$			10.8323i			0.0605158i	−0.999542	+	0.0302579i	$0.990367\pi$
$180$	12.4845	−	27.2789i	0.0693581	−	0.151549i
$181$	−2.96458			−0.0163789			−0.00818944	−	0.999966i	$-0.502607\pi$
$181$	−2.96458			−0.0163789			−0.00818944	+	0.999966i	$0.502607\pi$
$182$	46.7554	+	46.7554i	0.256898	+	0.256898i
$183$	37.9433	−	37.9433i	0.207341	−	0.207341i
$184$		−	13.5647i		−	0.0737210i
$185$	−93.5566	+	34.8089i	−0.505711	+	0.188156i
$186$	−67.9153			−0.365136
$187$	71.3799	+	71.3799i	0.381711	+	0.381711i
$188$	−44.3349	+	44.3349i	−0.235824	+	0.235824i
$189$			10.7168i			0.0567029i
$190$	−20.1846	−	54.2507i	−0.106235	−	0.285530i
$191$	225.451			1.18037			0.590186	−	0.807267i	$-0.299054\pi$
$191$	225.451			1.18037			0.590186	+	0.807267i	$0.299054\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	231.799	−	231.799i	1.20103	−	1.20103i	0.227175	−	0.973854i	$-0.427051\pi$
$193$	231.799	−	231.799i	1.20103	−	1.20103i	0.973854	−	0.227175i	$-0.0729490\pi$
$194$		−	198.618i		−	1.02380i
$195$	−178.518	−	81.7006i	−0.915478	−	0.418977i
$196$	89.4925			0.456595
$197$	240.985	+	240.985i	1.22327	+	1.22327i	0.966462	+	0.256811i	$0.0826717\pi$
$197$	240.985	+	240.985i	1.22327	+	1.22327i	0.256811	+	0.966462i	$0.417328\pi$
$198$	−19.7090	+	19.7090i	−0.0995407	+	0.0995407i
$199$		−	87.8703i		−	0.441559i	−0.975324	−	0.220780i	$-0.929140\pi$
$199$		−	87.8703i		−	0.441559i	0.975324	−	0.220780i	$-0.0708602\pi$
$200$	−70.5223	−	5.15818i	−0.352611	−	0.0257909i
$201$	−75.3189			−0.374721
$202$	120.819	+	120.819i	0.598114	+	0.598114i
$203$	−9.24240	+	9.24240i	−0.0455291	+	0.0455291i
$204$			53.2277i			0.260920i
$205$	−144.953	+	316.728i	−0.707090	+	1.54501i
$206$	63.5882			0.308681
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	−64.1197	+	64.1197i	−0.308268	+	0.308268i
$209$			53.7796i			0.257319i
$210$	23.6743	−	8.80832i	0.112735	−	0.0419444i
$211$	275.082			1.30371			0.651854	−	0.758345i	$-0.273992\pi$
$211$	275.082			1.30371			0.651854	+	0.758345i	$0.273992\pi$
$212$	−3.50625	−	3.50625i	−0.0165389	−	0.0165389i
$213$	−50.2739	+	50.2739i	−0.236028	+	0.236028i
$214$			236.844i			1.10675i
$215$	−43.4217	−	116.705i	−0.201961	−	0.542816i
$216$	−14.6969			−0.0680414
$217$	−40.4354	−	40.4354i	−0.186338	−	0.186338i
$218$	−21.5303	+	21.5303i	−0.0987628	+	0.0987628i
$219$			90.9414i			0.415257i
$220$	59.7379	+	27.3396i	0.271536	+	0.124271i
$221$	348.332			1.57616
$222$	34.5795	+	34.5795i	0.155763	+	0.155763i
$223$	75.3025	−	75.3025i	0.337679	−	0.337679i	−0.517814	−	0.855493i	$-0.673254\pi$
$223$	75.3025	−	75.3025i	0.337679	−	0.337679i	0.855493	+	0.517814i	$0.173254\pi$
$224$		−	11.6670i		−	0.0520849i
$225$	−56.7604	+	49.0231i	−0.252268	+	0.217880i
$226$	144.647			0.640031
$227$	314.742	+	314.742i	1.38653	+	1.38653i	0.832491	+	0.554038i	$0.186914\pi$
$227$	314.742	+	314.742i	1.38653	+	1.38653i	0.554038	+	0.832491i	$0.313086\pi$
$228$	−20.0516	+	20.0516i	−0.0879456	+	0.0879456i
$229$			101.559i			0.443490i	0.975105	+	0.221745i	$0.0711752\pi$
$229$			101.559i			0.443490i	−0.975105	+	0.221745i	$0.928825\pi$
$230$	−14.1123	+	30.8358i	−0.0613577	+	0.134068i
$231$	−23.4688			−0.101596
$232$	−12.6749	−	12.6749i	−0.0546332	−	0.0546332i
$233$	−195.602	+	195.602i	−0.839494	+	0.839494i	−0.988792	−	0.149298i	$-0.952299\pi$
$233$	−195.602	+	195.602i	−0.839494	+	0.839494i	0.149298	+	0.988792i	$0.452299\pi$
$234$			96.1795i			0.411024i
$235$	146.909	−	54.6592i	0.625144	−	0.232592i
$236$	−169.309			−0.717413
$237$	−117.215	−	117.215i	−0.494576	−	0.494576i
$238$	−31.6907	+	31.6907i	−0.133154	+	0.133154i
$239$		−	262.676i		−	1.09906i	−0.835473	−	0.549531i	$-0.814806\pi$
$239$		−	262.676i		−	1.09906i	0.835473	−	0.549531i	$-0.185194\pi$
$240$	12.0796	+	32.4666i	0.0503317	+	0.135278i
$241$	290.284			1.20450			0.602249	−	0.798308i	$-0.294271\pi$
$241$	290.284			1.20450			0.602249	+	0.798308i	$0.294271\pi$
$242$	77.8393	+	77.8393i	0.321650	+	0.321650i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			61.9612i			0.253939i
$245$	−203.438	−	93.1054i	−0.830360	−	0.380022i
$246$	170.642			0.693667
$247$	131.221	+	131.221i	0.531261	+	0.531261i
$248$	55.4526	−	55.4526i	0.223599	−	0.223599i
$249$		−	108.748i		−	0.436738i
$250$	154.948	+	85.0951i	0.619791	+	0.340381i
$251$	77.4485			0.308560			0.154280	−	0.988027i	$-0.450694\pi$
$251$	77.4485			0.308560			0.154280	+	0.988027i	$0.450694\pi$
$252$	−8.75027	−	8.75027i	−0.0347233	−	0.0347233i
$253$	22.2789	−	22.2789i	0.0880588	−	0.0880588i
$254$		−	149.262i		−	0.587646i
$255$	55.3765	−	120.999i	0.217163	−	0.474507i
$256$	16.0000			0.0625000
$257$	214.236	+	214.236i	0.833602	+	0.833602i	0.988008	−	0.154406i	$-0.0493463\pi$
$257$	214.236	+	214.236i	0.833602	+	0.833602i	−0.154406	+	0.988008i	$0.549346\pi$
$258$	−43.1355	+	43.1355i	−0.167192	+	0.167192i
$259$			41.1758i			0.158980i
$260$	212.468	−	79.0513i	0.817184	−	0.304043i
$261$	−19.0124			−0.0728443
$262$	159.638	+	159.638i	0.609304	+	0.609304i
$263$	−208.462	+	208.462i	−0.792632	+	0.792632i	−0.981921	−	0.189289i	$-0.939382\pi$
$263$	−208.462	+	208.462i	−0.792632	+	0.792632i	0.189289	+	0.981921i	$0.439382\pi$
$264$		−	32.1847i		−	0.121912i
$265$	4.32276	+	11.6184i	0.0163123	+	0.0438429i
$266$	−23.8766			−0.0897618
$267$	−174.047	−	174.047i	−0.651863	−	0.651863i
$268$	61.4976	−	61.4976i	0.229469	−	0.229469i
$269$			177.937i			0.661474i	0.943723	+	0.330737i	$0.107297\pi$
$269$			177.937i			0.661474i	−0.943723	+	0.330737i	$0.892703\pi$
$270$	33.4097	+	15.2903i	0.123740	+	0.0566306i
$271$	196.940			0.726717			0.363359	−	0.931649i	$-0.381630\pi$
$271$	196.940			0.726717			0.363359	+	0.931649i	$0.381630\pi$
$272$	−43.4602	−	43.4602i	−0.159780	−	0.159780i
$273$	−57.2634	+	57.2634i	−0.209756	+	0.209756i
$274$		−	93.0261i		−	0.339511i
$275$	−107.355	−	124.299i	−0.390383	−	0.451997i
$276$	16.6132			0.0601929
$277$	35.9249	+	35.9249i	0.129693	+	0.129693i	0.768973	−	0.639281i	$-0.220768\pi$
$277$	35.9249	+	35.9249i	0.129693	+	0.129693i	−0.639281	+	0.768973i	$0.720768\pi$
$278$	128.651	−	128.651i	0.462774	−	0.462774i
$279$		−	83.1789i		−	0.298132i
$280$	−12.1380	+	26.5220i	−0.0433501	+	0.0947213i
$281$	−308.880			−1.09922			−0.549609	−	0.835422i	$-0.685223\pi$
$281$	−308.880			−1.09922			−0.549609	+	0.835422i	$0.685223\pi$
$282$	−54.2990	−	54.2990i	−0.192549	−	0.192549i
$283$	−145.332	+	145.332i	−0.513541	+	0.513541i	−0.915610	−	0.402068i	$-0.868291\pi$
$283$	−145.332	+	145.332i	−0.513541	+	0.513541i	0.402068	+	0.915610i	$0.368291\pi$
$284$		−	82.0970i		−	0.289074i
$285$	66.4432	−	24.7210i	0.233134	−	0.0867404i
$286$	−210.623			−0.736444
$287$	101.597	+	101.597i	0.353996	+	0.353996i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	52.9013i		−	0.183050i
$290$	15.6265	+	41.9997i	0.0538846	+	0.144827i
$291$	243.256			0.835931
$292$	−74.2533	−	74.2533i	−0.254292	−	0.254292i
$293$	−241.012	+	241.012i	−0.822568	+	0.822568i	−0.986476	−	0.163908i	$-0.947590\pi$
$293$	−241.012	+	241.012i	−0.822568	+	0.822568i	0.163908	+	0.986476i	$0.447590\pi$
$294$			109.606i			0.372808i
$295$	384.881	+	176.145i	1.30468	+	0.597100i
$296$	−56.4680			−0.190770
$297$	−24.1386	−	24.1386i	−0.0812746	−	0.0812746i
$298$	93.9923	−	93.9923i	0.315410	−	0.315410i
$299$		−	108.720i		−	0.363613i
$300$	6.31746	−	86.3718i	0.0210582	−	0.287906i
$301$	−51.3640			−0.170645
$302$	−170.451	−	170.451i	−0.564406	−	0.564406i
$303$	−147.973	+	147.973i	−0.488358	+	0.488358i
$304$		−	32.7441i		−	0.107711i
$305$	64.4626	−	140.853i	0.211353	−	0.461812i
$306$	−65.1903			−0.213040
$307$	68.9379	+	68.9379i	0.224553	+	0.224553i	0.810413	−	0.585859i	$-0.199243\pi$
$307$	68.9379	+	68.9379i	0.224553	+	0.224553i	−0.585859	+	0.810413i	$0.699243\pi$
$308$	19.1622	−	19.1622i	0.0622148	−	0.0622148i
$309$			77.8793i			0.252037i
$310$	−183.748	+	68.3659i	−0.592737	+	0.220535i
$311$	516.333			1.66024			0.830118	−	0.557588i	$-0.188273\pi$
$311$	516.333			1.66024			0.830118	+	0.557588i	$0.188273\pi$
$312$	−78.5302	−	78.5302i	−0.251700	−	0.251700i
$313$	−41.6424	+	41.6424i	−0.133043	+	0.133043i	−0.770492	−	0.637449i	$-0.779989\pi$
$313$	−41.6424	+	41.6424i	−0.133043	+	0.133043i	0.637449	+	0.770492i	$0.279989\pi$
$314$		−	116.732i		−	0.371758i
$315$	10.7879	+	28.9950i	0.0342475	+	0.0920476i
$316$	191.410			0.605729
$317$	132.540	+	132.540i	0.418106	+	0.418106i	0.884551	−	0.466444i	$-0.154465\pi$
$317$	132.540	+	132.540i	0.418106	+	0.418106i	−0.466444	+	0.884551i	$0.654465\pi$
$318$	4.29427	−	4.29427i	0.0135040	−	0.0135040i
$319$		−	41.6351i		−	0.130517i
$320$	−36.3719	−	16.6459i	−0.113662	−	0.0520185i
$321$	−290.074			−0.903657
$322$	9.89120	+	9.89120i	0.0307180	+	0.0307180i
$323$	−88.9416	+	88.9416i	−0.275361	+	0.275361i
$324$		−	18.0000i		−	0.0555556i
$325$	−565.233	−	41.3426i	−1.73918	−	0.127208i
$326$	−48.0687			−0.147450
$327$	−26.3691	−	26.3691i	−0.0806395	−	0.0806395i
$328$	−139.329	+	139.329i	−0.424782	+	0.424782i
$329$		−	64.6570i		−	0.196526i
$330$	−33.4841	+	73.1637i	−0.101467	+	0.221708i
$331$	−345.899			−1.04501			−0.522506	−	0.852635i	$-0.675003\pi$
$331$	−345.899			−1.04501			−0.522506	+	0.852635i	$0.675003\pi$
$332$	88.7922	+	88.7922i	0.267446	+	0.267446i
$333$	−42.3510	+	42.3510i	−0.127180	+	0.127180i
$334$		−	257.990i		−	0.772426i
$335$	−203.779	+	75.8186i	−0.608296	+	0.226324i
$336$	14.2891			0.0425272
$337$	−257.263	−	257.263i	−0.763393	−	0.763393i	0.213541	−	0.976934i	$-0.431500\pi$
$337$	−257.263	−	257.263i	−0.763393	−	0.763393i	−0.976934	+	0.213541i	$0.931500\pi$
$338$	−344.917	+	344.917i	−1.02046	+	1.02046i
$339$			177.156i			0.522583i
$340$	53.5808	+	144.010i	0.157591	+	0.423560i
$341$	182.153			0.534173
$342$	−24.5581	−	24.5581i	−0.0718073	−	0.0718073i
$343$	−136.717	+	136.717i	−0.398593	+	0.398593i
$344$		−	70.4399i		−	0.204767i
$345$	−37.7659	−	17.2839i	−0.109466	−	0.0500984i
$346$	29.6868			0.0858000
$347$	212.920	+	212.920i	0.613601	+	0.613601i	0.943883	−	0.330281i	$-0.107144\pi$
$347$	212.920	+	212.920i	0.613601	+	0.613601i	−0.330281	+	0.943883i	$0.607144\pi$
$348$	15.5235	−	15.5235i	0.0446078	−	0.0446078i
$349$		−	377.789i		−	1.08249i	−0.840865	−	0.541244i	$-0.817953\pi$
$349$		−	377.789i		−	1.08249i	0.840865	−	0.541244i	$-0.182047\pi$
$350$	55.1854	−	47.6628i	0.157672	−	0.136179i
$351$	−117.795			−0.335599
$352$	26.2787	+	26.2787i	0.0746555	+	0.0746555i
$353$	96.2068	−	96.2068i	0.272541	−	0.272541i	−0.557582	−	0.830122i	$-0.688271\pi$
$353$	96.2068	−	96.2068i	0.272541	−	0.272541i	0.830122	+	0.557582i	$0.188271\pi$
$354$		−	207.361i		−	0.585765i
$355$	−85.4113	+	186.626i	−0.240595	+	0.525708i
$356$	284.218			0.798366
$357$	−38.8130	−	38.8130i	−0.108720	−	0.108720i
$358$	10.8323	−	10.8323i	0.0302579	−	0.0302579i
$359$			181.790i			0.506380i	0.967417	+	0.253190i	$0.0814798\pi$
$359$			181.790i			0.506380i	−0.967417	+	0.253190i	$0.918520\pi$
$360$	−39.7634	+	14.7945i	−0.110454	+	0.0410957i
$361$	293.989			0.814374
$362$	2.96458	+	2.96458i	0.00818944	+	0.00818944i
$363$	−95.3332	+	95.3332i	−0.262626	+	0.262626i
$364$		−	93.5107i		−	0.256898i
$365$	91.5447	+	246.047i	0.250808	+	0.674101i
$366$	−75.8867			−0.207341
$367$	28.4702	+	28.4702i	0.0775756	+	0.0775756i	0.744830	−	0.667254i	$-0.232531\pi$
$367$	28.4702	+	28.4702i	0.0775756	+	0.0775756i	−0.667254	+	0.744830i	$0.732531\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			208.993i			0.566376i
$370$	128.365	+	58.7477i	0.346934	+	0.158778i
$371$	5.11344			0.0137829
$372$	67.9153	+	67.9153i	0.182568	+	0.182568i
$373$	−94.2294	+	94.2294i	−0.252626	+	0.252626i	−0.822046	−	0.569421i	$-0.807168\pi$
$373$	−94.2294	+	94.2294i	−0.252626	+	0.252626i	0.569421	+	0.822046i	$0.307168\pi$
$374$		−	142.760i		−	0.381711i
$375$	−104.220	+	189.772i	−0.277920	+	0.506057i
$376$	88.6698			0.235824
$377$	−101.589	−	101.589i	−0.269466	−	0.269466i
$378$	10.7168	−	10.7168i	0.0283514	−	0.0283514i
$379$		−	139.587i		−	0.368302i	−0.982898	−	0.184151i	$-0.941046\pi$
$379$		−	139.587i		−	0.368302i	0.982898	−	0.184151i	$-0.0589536\pi$
$380$	−34.0660	+	74.4353i	−0.0896474	+	0.195882i
$381$	182.808			0.479811
$382$	−225.451	−	225.451i	−0.590186	−	0.590186i
$383$	115.635	−	115.635i	0.301920	−	0.301920i	−0.539845	−	0.841764i	$-0.681517\pi$
$383$	115.635	−	115.635i	0.301920	−	0.301920i	0.841764	+	0.539845i	$0.181517\pi$
$384$			19.5959i			0.0510310i
$385$	−63.4960	+	23.6245i	−0.164925	+	0.0613623i
$386$	−463.597			−1.20103
$387$	−52.8300	−	52.8300i	−0.136512	−	0.136512i
$388$	−198.618	+	198.618i	−0.511901	+	0.511901i
$389$			443.439i			1.13995i	0.821663	+	0.569974i	$0.193047\pi$
$389$			443.439i			1.13995i	−0.821663	+	0.569974i	$0.806953\pi$
$390$	96.8177	+	260.219i	0.248250	+	0.667228i
$391$	73.6904			0.188466
$392$	−89.4925	−	89.4925i	−0.228297	−	0.228297i
$393$	−195.515	+	195.515i	−0.497495	+	0.497495i
$394$		−	481.969i		−	1.22327i
$395$	−435.122	−	199.138i	−1.10158	−	0.504147i
$396$	39.4181			0.0995407
$397$	−471.063	−	471.063i	−1.18656	−	1.18656i	−0.978013	−	0.208544i	$-0.933128\pi$
$397$	−471.063	−	471.063i	−1.18656	−	1.18656i	−0.208544	−	0.978013i	$-0.566872\pi$
$398$	−87.8703	+	87.8703i	−0.220780	+	0.220780i
$399$		−	29.2428i		−	0.0732902i
$400$	65.3641	+	75.6805i	0.163410	+	0.189201i
$401$	736.854			1.83754			0.918771	−	0.394791i	$-0.129183\pi$
$401$	736.854			1.83754			0.918771	+	0.394791i	$0.129183\pi$
$402$	75.3189	+	75.3189i	0.187360	+	0.187360i
$403$	444.450	−	444.450i	1.10285	−	1.10285i
$404$		−	241.638i		−	0.598114i
$405$	−18.7267	+	40.9184i	−0.0462387	+	0.101033i
$406$	18.4848			0.0455291
$407$	−92.7442	−	92.7442i	−0.227873	−	0.227873i
$408$	53.2277	−	53.2277i	0.130460	−	0.130460i
$409$			593.667i			1.45151i	0.687954	+	0.725754i	$0.258509\pi$
$409$			593.667i			1.45151i	−0.687954	+	0.725754i	$0.741491\pi$
$410$	461.681	−	171.774i	1.12605	−	0.418961i
$411$	113.933			0.277210
$412$	−63.5882	−	63.5882i	−0.154340	−	0.154340i
$413$	123.459	−	123.459i	0.298931	−	0.298931i
$414$			20.3470i			0.0491473i
$415$	−109.469	−	294.223i	−0.263781	−	0.708971i
$416$	128.239			0.308268
$417$	157.565	+	157.565i	0.377853	+	0.377853i
$418$	53.7796	−	53.7796i	0.128659	−	0.128659i
$419$		−	450.030i		−	1.07406i	−0.843564	−	0.537028i	$-0.819547\pi$
$419$		−	450.030i		−	1.07406i	0.843564	−	0.537028i	$-0.180453\pi$
$420$	−32.4826	−	14.8660i	−0.0773396	−	0.0353952i
$421$	−715.043			−1.69844			−0.849220	−	0.528039i	$-0.822928\pi$
$421$	−715.043			−1.69844			−0.849220	+	0.528039i	$0.822928\pi$
$422$	−275.082	−	275.082i	−0.651854	−	0.651854i
$423$	66.5024	−	66.5024i	0.157216	−	0.157216i
$424$			7.01251i			0.0165389i
$425$	28.0220	−	383.114i	0.0659340	−	0.901445i
$426$	100.548			0.236028
$427$	−45.1814	−	45.1814i	−0.105811	−	0.105811i
$428$	236.844	−	236.844i	0.553374	−	0.553374i
$429$		−	257.959i		−	0.601304i
$430$	−73.2837	+	160.127i	−0.170427	+	0.372388i
$431$	−643.338			−1.49266			−0.746332	−	0.665574i	$-0.768187\pi$
$431$	−643.338			−1.49266			−0.746332	+	0.665574i	$0.768187\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	198.297	−	198.297i	0.457961	−	0.457961i	−0.440025	−	0.897986i	$-0.645030\pi$
$433$	198.297	−	198.297i	0.457961	−	0.457961i	0.897986	+	0.440025i	$0.145030\pi$
$434$			80.8708i			0.186338i
$435$	−51.4390	+	19.1385i	−0.118250	+	0.0439966i
$436$	43.0606			0.0987628
$437$	27.7602	+	27.7602i	0.0635244	+	0.0635244i
$438$	90.9414	−	90.9414i	0.207629	−	0.207629i
$439$		−	337.344i		−	0.768438i	−0.923242	−	0.384219i	$-0.874471\pi$
$439$		−	337.344i		−	0.768438i	0.923242	−	0.384219i	$-0.125529\pi$
$440$	−32.3983	−	87.0775i	−0.0736325	−	0.197904i
$441$	−134.239			−0.304396
$442$	−348.332	−	348.332i	−0.788081	−	0.788081i
$443$	109.373	−	109.373i	0.246892	−	0.246892i	−0.572802	−	0.819694i	$-0.694143\pi$
$443$	109.373	−	109.373i	0.246892	−	0.246892i	0.819694	+	0.572802i	$0.194143\pi$
$444$		−	69.1589i		−	0.155763i
$445$	−646.097	−	295.692i	−1.45190	−	0.664477i
$446$	−150.605			−0.337679
$447$	115.117	+	115.117i	0.257531	+	0.257531i
$448$	−11.6670	+	11.6670i	−0.0260425	+	0.0260425i
$449$		−	372.277i		−	0.829124i	−0.910021	−	0.414562i	$-0.863935\pi$
$449$		−	372.277i		−	0.829124i	0.910021	−	0.414562i	$-0.136065\pi$
$450$	105.783	+	7.73727i	0.235074	+	0.0171939i
$451$	−457.672			−1.01479
$452$	−144.647	−	144.647i	−0.320016	−	0.320016i
$453$	208.758	−	208.758i	0.460835	−	0.460835i
$454$		−	629.484i		−	1.38653i
$455$	−97.2858	+	212.572i	−0.213815	+	0.467192i
$456$	40.1032			0.0879456
$457$	10.4967	+	10.4967i	0.0229688	+	0.0229688i	0.718498	−	0.695529i	$-0.244830\pi$
$457$	10.4967	+	10.4967i	0.0229688	+	0.0229688i	−0.695529	+	0.718498i	$0.744830\pi$
$458$	101.559	−	101.559i	0.221745	−	0.221745i
$459$		−	79.8415i		−	0.173947i
$460$	44.9480	−	16.7235i	0.0977131	−	0.0363554i
$461$	−833.333			−1.80766			−0.903832	−	0.427887i	$-0.859258\pi$
$461$	−833.333			−1.80766			−0.903832	+	0.427887i	$0.859258\pi$
$462$	23.4688	+	23.4688i	0.0507982	+	0.0507982i
$463$	52.1194	−	52.1194i	0.112569	−	0.112569i	−0.648579	−	0.761148i	$-0.724636\pi$
$463$	52.1194	−	52.1194i	0.112569	−	0.112569i	0.761148	+	0.648579i	$0.224636\pi$
$464$			25.3498i			0.0546332i
$465$	−83.7308	−	225.045i	−0.180066	−	0.483968i
$466$	391.204			0.839494
$467$	−185.727	−	185.727i	−0.397703	−	0.397703i	0.479719	−	0.877422i	$-0.340738\pi$
$467$	−185.727	−	185.727i	−0.397703	−	0.397703i	−0.877422	+	0.479719i	$0.840738\pi$
$468$	96.1795	−	96.1795i	0.205512	−	0.205512i
$469$			89.6867i			0.191230i
$470$	−201.568	−	92.2495i	−0.428868	−	0.196276i
$471$	142.967			0.303539
$472$	169.309	+	169.309i	0.358706	+	0.358706i
$473$	115.692	−	115.692i	0.244592	−	0.244592i
$474$			234.429i			0.494576i
$475$	154.881	−	133.768i	0.326064	−	0.281617i
$476$	63.3814			0.133154
$477$	5.25938	+	5.25938i	0.0110260	+	0.0110260i
$478$	−262.676	+	262.676i	−0.549531	+	0.549531i
$479$			384.415i			0.802536i	0.915961	+	0.401268i	$0.131430\pi$
$479$			384.415i			0.802536i	−0.915961	+	0.401268i	$0.868570\pi$
$480$	20.3870	−	44.5463i	0.0424730	−	0.0928047i
$481$	−452.589			−0.940933
$482$	−290.284	−	290.284i	−0.602249	−	0.602249i
$483$	−12.1142	+	12.1142i	−0.0250811	+	0.0250811i
$484$		−	155.679i		−	0.321650i
$485$	658.142	−	244.870i	1.35699	−	0.504886i
$486$	22.0454			0.0453609
$487$	176.011	+	176.011i	0.361420	+	0.361420i	0.864335	−	0.502916i	$-0.167739\pi$
$487$	176.011	+	176.011i	0.361420	+	0.361420i	−0.502916	+	0.864335i	$0.667739\pi$
$488$	61.9612	−	61.9612i	0.126970	−	0.126970i
$489$		−	58.8719i		−	0.120392i
$490$	110.333	+	296.544i	0.225169	+	0.605191i
$491$	565.321			1.15137			0.575683	−	0.817673i	$-0.304736\pi$
$491$	565.321			1.15137			0.575683	+	0.817673i	$0.304736\pi$
$492$	−170.642	−	170.642i	−0.346833	−	0.346833i
$493$	68.8568	−	68.8568i	0.139669	−	0.139669i
$494$		−	262.443i		−	0.531261i
$495$	−89.6069	−	41.0094i	−0.181024	−	0.0828474i
$496$	−110.905			−0.223599
$497$	59.8642	+	59.8642i	0.120451	+	0.120451i
$498$	−108.748	+	108.748i	−0.218369	+	0.218369i
$499$			876.225i			1.75596i	0.478696	+	0.877981i	$0.341110\pi$
$499$			876.225i			1.75596i	−0.478696	+	0.877981i	$0.658890\pi$
$500$	−69.8527	−	240.043i	−0.139705	−	0.480086i
$501$	315.972			0.630683
$502$	−77.4485	−	77.4485i	−0.154280	−	0.154280i
$503$	617.070	−	617.070i	1.22678	−	1.22678i	0.261605	−	0.965175i	$-0.415748\pi$
$503$	617.070	−	617.070i	1.22678	−	1.22678i	0.965175	−	0.261605i	$-0.0842516\pi$
$504$			17.5005i			0.0347233i
$505$	−251.393	+	549.302i	−0.497809	+	1.08773i
$506$	−44.5578			−0.0880588
$507$	−422.435	−	422.435i	−0.833205	−	0.833205i
$508$	−149.262	+	149.262i	−0.293823	+	0.293823i
$509$		−	466.623i		−	0.916744i	−0.888760	−	0.458372i	$-0.848433\pi$
$509$		−	466.623i		−	0.916744i	0.888760	−	0.458372i	$-0.151567\pi$
$510$	−176.376	+	65.6228i	−0.345835	+	0.128672i
$511$	108.289			0.211917
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	30.0774	−	30.0774i	0.0586304	−	0.0586304i
$514$		−	428.471i		−	0.833602i
$515$	78.3961	+	210.707i	0.152225	+	0.409139i
$516$	86.2710			0.167192
$517$	145.633	+	145.633i	0.281689	+	0.281689i
$518$	41.1758	−	41.1758i	0.0794900	−	0.0794900i
$519$			36.3587i			0.0700554i
$520$	−291.519	−	133.416i	−0.560614	−	0.256570i
$521$	−562.863			−1.08035			−0.540176	−	0.841552i	$-0.681642\pi$
$521$	−562.863			−1.08035			−0.540176	+	0.841552i	$0.681642\pi$
$522$	19.0124	+	19.0124i	0.0364221	+	0.0364221i
$523$	205.814	−	205.814i	0.393526	−	0.393526i	−0.482416	−	0.875942i	$-0.660241\pi$
$523$	205.814	−	205.814i	0.393526	−	0.393526i	0.875942	+	0.482416i	$0.160241\pi$
$524$		−	319.275i		−	0.609304i
$525$	58.3747	+	67.5880i	0.111190	+	0.128739i
$526$	416.924			0.792632
$527$	301.248	+	301.248i	0.571627	+	0.571627i
$528$	−32.1847	+	32.1847i	−0.0609560	+	0.0609560i
$529$		−	23.0000i		−	0.0434783i
$530$	7.29561	−	15.9411i	0.0137653	−	0.0300776i
$531$	253.964			0.478275
$532$	23.8766	+	23.8766i	0.0448809	+	0.0448809i
$533$	−1116.71	+	1116.71i	−2.09515	+	2.09515i
$534$			348.095i			0.651863i
$535$	−784.810	+	291.998i	−1.46693	+	0.545791i
$536$	−122.995			−0.229469
$537$	13.2668	+	13.2668i	0.0247055	+	0.0247055i
$538$	177.937	−	177.937i	0.330737	−	0.330737i
$539$		−	293.969i		−	0.545397i
$540$	−18.1194	−	48.7000i	−0.0335545	−	0.0901851i
$541$	−152.262			−0.281445			−0.140723	−	0.990049i	$-0.544943\pi$
$541$	−152.262			−0.281445			−0.140723	+	0.990049i	$0.544943\pi$
$542$	−196.940	−	196.940i	−0.363359	−	0.363359i
$543$	−3.63085	+	3.63085i	−0.00668665	+	0.00668665i
$544$			86.9204i			0.159780i
$545$	−97.8871	−	44.7990i	−0.179609	−	0.0822000i
$546$	114.527			0.209756
$547$	486.325	+	486.325i	0.889076	+	0.889076i	0.994434	−	0.105358i	$-0.0335989\pi$
$547$	486.325	+	486.325i	0.889076	+	0.889076i	−0.105358	+	0.994434i	$0.533599\pi$
$548$	−93.0261	+	93.0261i	−0.169756	+	0.169756i
$549$		−	92.9418i		−	0.169293i
$550$	−16.9438	+	231.655i	−0.0308069	+	0.421190i
$551$	51.8786			0.0941535
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	−139.574	+	139.574i	−0.252395	+	0.252395i
$554$		−	71.8498i		−	0.129693i
$555$	−71.9509	+	157.215i	−0.129641	+	0.283270i
$556$	−257.302			−0.462774
$557$	−93.7887	−	93.7887i	−0.168382	−	0.168382i	0.617886	−	0.786268i	$-0.287989\pi$
$557$	−93.7887	−	93.7887i	−0.168382	−	0.168382i	−0.786268	+	0.617886i	$0.787989\pi$
$558$	−83.1789	+	83.1789i	−0.149066	+	0.149066i
$559$		−	564.573i		−	1.00997i
$560$	38.6600	−	14.3839i	0.0690357	−	0.0256856i
$561$	174.844			0.311666
$562$	308.880	+	308.880i	0.549609	+	0.549609i
$563$	−4.76825	+	4.76825i	−0.00846936	+	0.00846936i	−0.711329	−	0.702859i	$-0.751906\pi$
$563$	−4.76825	+	4.76825i	−0.00846936	+	0.00846936i	0.702859	+	0.711329i	$0.251906\pi$
$564$			108.598i			0.192549i
$565$	178.331	+	479.304i	0.315630	+	0.848326i
$566$	290.664			0.513541
$567$	13.1254	+	13.1254i	0.0231489	+	0.0231489i
$568$	−82.0970	+	82.0970i	−0.144537	+	0.144537i
$569$			993.556i			1.74614i	0.487591	+	0.873072i	$0.337876\pi$
$569$			993.556i			1.74614i	−0.487591	+	0.873072i	$0.662124\pi$
$570$	−91.1642	−	41.7222i	−0.159937	−	0.0731968i
$571$	524.502			0.918567			0.459284	−	0.888290i	$-0.348106\pi$
$571$	524.502			0.918567			0.459284	+	0.888290i	$0.348106\pi$
$572$	210.623	+	210.623i	0.368222	+	0.368222i
$573$	276.120	−	276.120i	0.481885	−	0.481885i
$574$		−	203.194i		−	0.353996i
$575$	−119.576	−	8.74612i	−0.207959	−	0.0152107i
$576$	−24.0000			−0.0416667
$577$	−441.957	−	441.957i	−0.765956	−	0.765956i	0.211435	−	0.977392i	$-0.432186\pi$
$577$	−441.957	−	441.957i	−0.765956	−	0.765956i	−0.977392	+	0.211435i	$0.932186\pi$
$578$	−52.9013	+	52.9013i	−0.0915248	+	0.0915248i
$579$		−	567.788i		−	0.980636i
$580$	26.3732	−	57.6263i	0.0454710	−	0.0993556i
$581$	−129.493			−0.222879
$582$	−243.256	−	243.256i	−0.417965	−	0.417965i
$583$	−11.5175	+	11.5175i	−0.0197556	+	0.0197556i
$584$			148.507i			0.254292i
$585$	−318.702	+	118.577i	−0.544789	+	0.202696i
$586$	482.025			0.822568
$587$	659.069	+	659.069i	1.12278	+	1.12278i	0.991322	+	0.131453i	$0.0419644\pi$
$587$	659.069	+	659.069i	1.12278	+	1.12278i	0.131453	+	0.991322i	$0.458036\pi$
$588$	109.606	−	109.606i	0.186404	−	0.186404i
$589$			226.968i			0.385345i
$590$	−208.737	−	561.026i	−0.353791	−	0.950891i
$591$	590.290			0.998798
$592$	56.4680	+	56.4680i	0.0953852	+	0.0953852i
$593$	−224.731	+	224.731i	−0.378973	+	0.378973i	−0.870732	−	0.491758i	$-0.836354\pi$
$593$	−224.731	+	224.731i	−0.378973	+	0.378973i	0.491758	+	0.870732i	$0.336354\pi$
$594$			48.2771i			0.0812746i
$595$	−144.081	−	65.9402i	−0.242153	−	0.110824i
$596$	−187.985			−0.315410
$597$	−107.619	−	107.619i	−0.180266	−	0.180266i
$598$	−108.720	+	108.720i	−0.181806	+	0.181806i
$599$			104.512i			0.174477i	0.996187	+	0.0872386i	$0.0278043\pi$
$599$			104.512i			0.174477i	−0.996187	+	0.0872386i	$0.972196\pi$
$600$	−92.6893	+	80.0544i	−0.154482	+	0.133424i
$601$	−368.220			−0.612679			−0.306340	−	0.951922i	$-0.599104\pi$
$601$	−368.220			−0.612679			−0.306340	+	0.951922i	$0.599104\pi$
$602$	51.3640	+	51.3640i	0.0853223	+	0.0853223i
$603$	−92.2464	+	92.2464i	−0.152979	+	0.152979i
$604$			340.901i			0.564406i
$605$	−161.963	+	353.895i	−0.267708	+	0.584950i
$606$	295.945			0.488358
$607$	697.004	+	697.004i	1.14828	+	1.14828i	0.986891	+	0.161385i	$0.0515962\pi$
$607$	697.004	+	697.004i	1.14828	+	1.14828i	0.161385	+	0.986891i	$0.448404\pi$
$608$	−32.7441	+	32.7441i	−0.0538554	+	0.0538554i
$609$			22.6392i			0.0371743i
$610$	−205.315	+	76.3902i	−0.336583	+	0.125230i
$611$	710.685			1.16315
$612$	65.1903	+	65.1903i	0.106520	+	0.106520i
$613$	314.788	−	314.788i	0.513520	−	0.513520i	−0.402083	−	0.915603i	$-0.631714\pi$
$613$	314.788	−	314.788i	0.513520	−	0.513520i	0.915603	+	0.402083i	$0.131714\pi$
$614$		−	137.876i		−	0.224553i
$615$	210.379	+	565.441i	0.342080	+	0.919417i
$616$	−38.3243			−0.0622148
$617$	−371.648	−	371.648i	−0.602346	−	0.602346i	0.338588	−	0.940935i	$-0.390051\pi$
$617$	−371.648	−	371.648i	−0.602346	−	0.602346i	−0.940935	+	0.338588i	$0.890051\pi$
$618$	77.8793	−	77.8793i	0.126018	−	0.126018i
$619$		−	522.132i		−	0.843509i	−0.906710	−	0.421755i	$-0.861414\pi$
$619$		−	522.132i		−	0.843509i	0.906710	−	0.421755i	$-0.138586\pi$
$620$	252.114	+	115.383i	0.406636	+	0.186101i
$621$	−24.9199			−0.0401286
$622$	−516.333	−	516.333i	−0.830118	−	0.830118i
$623$	−207.249	+	207.249i	−0.332663	+	0.332663i
$624$			157.060i			0.251700i
$625$	−90.9417	+	618.348i	−0.145507	+	0.989357i
$626$	83.2848			0.133043
$627$	65.8663	+	65.8663i	0.105050	+	0.105050i
$628$	−116.732	+	116.732i	−0.185879	+	0.185879i
$629$		−	306.764i		−	0.487701i
$630$	18.2070	−	39.7829i	0.0289001	−	0.0631475i
$631$	−1205.43			−1.91034			−0.955171	−	0.296056i	$-0.904329\pi$
$631$	−1205.43			−1.91034			−0.955171	+	0.296056i	$0.904329\pi$
$632$	−191.410	−	191.410i	−0.302865	−	0.302865i
$633$	336.905	−	336.905i	0.532236	−	0.532236i
$634$		−	265.079i		−	0.418106i
$635$	494.597	−	184.021i	0.778893	−	0.289797i
$636$	−8.58853			−0.0135040
$637$	−717.279	−	717.279i	−1.12603	−	1.12603i
$638$	−41.6351	+	41.6351i	−0.0652587	+	0.0652587i
$639$			123.145i			0.192716i
$640$	19.7259	+	53.0178i	0.0308218	+	0.0828403i
$641$	274.948			0.428936			0.214468	−	0.976731i	$-0.431198\pi$
$641$	274.948			0.428936			0.214468	+	0.976731i	$0.431198\pi$
$642$	290.074	+	290.074i	0.451828	+	0.451828i
$643$	−253.931	+	253.931i	−0.394916	+	0.394916i	−0.876435	−	0.481520i	$-0.840085\pi$
$643$	−253.931	+	253.931i	−0.394916	+	0.394916i	0.481520	+	0.876435i	$0.340085\pi$
$644$		−	19.7824i		−	0.0307180i
$645$	−196.115	−	89.7538i	−0.304054	−	0.139153i
$646$	177.883			0.275361
$647$	486.345	+	486.345i	0.751693	+	0.751693i	0.974795	−	0.223102i	$-0.0716184\pi$
$647$	486.345	+	486.345i	0.751693	+	0.751693i	−0.223102	+	0.974795i	$0.571618\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$			556.154i			0.856941i
$650$	523.891	+	606.576i	0.805986	+	0.933194i
$651$	−99.0461			−0.152145
$652$	48.0687	+	48.0687i	0.0737250	+	0.0737250i
$653$	85.6860	−	85.6860i	0.131219	−	0.131219i	−0.638447	−	0.769666i	$-0.720423\pi$
$653$	85.6860	−	85.6860i	0.131219	−	0.131219i	0.769666	+	0.638447i	$0.220423\pi$
$654$			52.7382i			0.0806395i
$655$	−332.165	+	725.790i	−0.507122	+	1.10808i
$656$	278.657			0.424782
$657$	111.380	+	111.380i	0.169528	+	0.169528i
$658$	−64.6570	+	64.6570i	−0.0982630	+	0.0982630i
$659$			329.137i			0.499450i	0.968317	+	0.249725i	$0.0803402\pi$
$659$			329.137i			0.499450i	−0.968317	+	0.249725i	$0.919660\pi$
$660$	106.648	−	39.6796i	0.161588	−	0.0601207i
$661$	−845.705			−1.27943			−0.639717	−	0.768611i	$-0.720948\pi$
$661$	−845.705			−1.27943			−0.639717	+	0.768611i	$0.720948\pi$
$662$	345.899	+	345.899i	0.522506	+	0.522506i
$663$	426.618	−	426.618i	0.643465	−	0.643465i
$664$		−	177.584i		−	0.267446i
$665$	−29.4368	−	79.1179i	−0.0442659	−	0.118974i
$666$	84.7020			0.127180
$667$	−21.4913	−	21.4913i	−0.0322209	−	0.0322209i
$668$	−257.990	+	257.990i	−0.386213	+	0.386213i
$669$		−	184.453i		−	0.275714i
$670$	279.598	+	127.961i	0.417310	+	0.190986i
$671$	203.533			0.303328
$672$	−14.2891	−	14.2891i	−0.0212636	−	0.0212636i
$673$	462.307	−	462.307i	0.686935	−	0.686935i	−0.274619	−	0.961553i	$-0.588552\pi$
$673$	462.307	−	462.307i	0.686935	−	0.686935i	0.961553	+	0.274619i	$0.0885516\pi$
$674$			514.527i			0.763393i
$675$	−9.47619	+	129.558i	−0.0140388	+	0.191937i
$676$	689.833			1.02046
$677$	−324.228	−	324.228i	−0.478919	−	0.478919i	0.425867	−	0.904786i	$-0.359969\pi$
$677$	−324.228	−	324.228i	−0.478919	−	0.478919i	−0.904786	+	0.425867i	$0.859969\pi$
$678$	177.156	−	177.156i	0.261292	−	0.261292i
$679$		−	289.659i		−	0.426597i
$680$	90.4295	−	197.591i	0.132985	−	0.290575i
$681$	770.958			1.13210
$682$	−182.153	−	182.153i	−0.267086	−	0.267086i
$683$	448.652	−	448.652i	0.656884	−	0.656884i	−0.297757	−	0.954642i	$-0.596239\pi$
$683$	448.652	−	448.652i	0.656884	−	0.656884i	0.954642	+	0.297757i	$0.0962386\pi$
$684$			49.1162i			0.0718073i
$685$	308.252	−	114.689i	0.450004	−	0.167429i
$686$	273.435			0.398593
$687$	124.384	+	124.384i	0.181054	+	0.181054i
$688$	−70.4399	+	70.4399i	−0.102384	+	0.102384i
$689$			56.2050i			0.0815747i
$690$	20.4820	+	55.0499i	0.0296840	+	0.0797824i
$691$	−570.580			−0.825731			−0.412866	−	0.910792i	$-0.635472\pi$
$691$	−570.580			−0.825731			−0.412866	+	0.910792i	$0.635472\pi$
$692$	−29.6868	−	29.6868i	−0.0429000	−	0.0429000i
$693$	−28.7432	+	28.7432i	−0.0414765	+	0.0414765i
$694$		−	425.839i		−	0.613601i
$695$	584.910	+	267.690i	0.841597	+	0.385165i
$696$	−31.0471			−0.0446078
$697$	−756.906	−	756.906i	−1.08595	−	1.08595i
$698$	−377.789	+	377.789i	−0.541244	+	0.541244i
$699$			479.125i			0.685444i
$700$	−102.848	−	7.52258i	−0.146926	−	0.0107465i
$701$	−250.724			−0.357666			−0.178833	−	0.983879i	$-0.557232\pi$
$701$	−250.724			−0.357666			−0.178833	+	0.983879i	$0.557232\pi$
$702$	117.795	+	117.795i	0.167800	+	0.167800i
$703$	115.562	−	115.562i	0.164384	−	0.164384i
$704$		−	52.5575i		−	0.0746555i
$705$	112.982	−	246.869i	0.160258	−	0.350169i
$706$	−192.414			−0.272541
$707$	176.200	+	176.200i	0.249222	+	0.249222i
$708$	−207.361	+	207.361i	−0.292882	+	0.292882i
$709$			1105.31i			1.55898i	0.626417	+	0.779488i	$0.284521\pi$
$709$			1105.31i			1.55898i	−0.626417	+	0.779488i	$0.715479\pi$
$710$	272.038	−	101.215i	0.383152	−	0.142556i
$711$	−287.116			−0.403820
$712$	−284.218	−	284.218i	−0.399183	−	0.399183i
$713$	94.0244	−	94.0244i	0.131872	−	0.131872i
$714$			77.6260i			0.108720i
$715$	−259.671	−	697.923i	−0.363176	−	0.976116i
$716$	−21.6647			−0.0302579
$717$	−321.711	−	321.711i	−0.448690	−	0.448690i
$718$	181.790	−	181.790i	0.253190	−	0.253190i
$719$			693.532i			0.964579i	0.876012	+	0.482289i	$0.160195\pi$
$719$			693.532i			0.964579i	−0.876012	+	0.482289i	$0.839805\pi$
$720$	54.5578	+	24.9689i	0.0757747	+	0.0346790i
$721$	92.7356			0.128621
$722$	−293.989	−	293.989i	−0.407187	−	0.407187i
$723$	355.524	−	355.524i	0.491735	−	0.491735i
$724$		−	5.92916i		−	0.00818944i
$725$	−119.905	+	103.560i	−0.165387	+	0.142842i
$726$	190.666			0.262626
$727$	508.634	+	508.634i	0.699634	+	0.699634i	0.964332	−	0.264697i	$-0.0852721\pi$
$727$	508.634	+	508.634i	0.699634	+	0.699634i	−0.264697	+	0.964332i	$0.585272\pi$
$728$	−93.5107	+	93.5107i	−0.128449	+	0.128449i
$729$			27.0000i			0.0370370i
$730$	154.502	−	337.591i	0.211647	−	0.462454i
$731$	382.667			0.523484
$732$	75.8867	+	75.8867i	0.103670	+	0.103670i
$733$	685.681	−	685.681i	0.935445	−	0.935445i	−0.0625940	−	0.998039i	$-0.519937\pi$
$733$	685.681	−	685.681i	0.935445	−	0.935445i	0.998039	+	0.0625940i	$0.0199373\pi$
$734$		−	56.9405i		−	0.0775756i
$735$	−363.190	+	135.129i	−0.494136	+	0.183850i
$736$	27.1293			0.0368605
$737$	−202.010	−	202.010i	−0.274098	−	0.274098i
$738$	208.993	−	208.993i	0.283188	−	0.283188i
$739$			60.5009i			0.0818686i	0.999162	+	0.0409343i	$0.0130334\pi$
$739$			60.5009i			0.0818686i	−0.999162	+	0.0409343i	$0.986967\pi$
$740$	−69.6178	−	187.113i	−0.0940781	−	0.252856i
$741$	321.425			0.433772
$742$	−5.11344	−	5.11344i	−0.00689143	−	0.00689143i
$743$	−323.462	+	323.462i	−0.435346	+	0.435346i	−0.890442	−	0.455096i	$-0.849605\pi$
$743$	−323.462	+	323.462i	−0.435346	+	0.435346i	0.455096	+	0.890442i	$0.349605\pi$
$744$		−	135.831i		−	0.182568i
$745$	427.334	+	195.574i	0.573603	+	0.262515i
$746$	188.459			0.252626
$747$	−133.188	−	133.188i	−0.178298	−	0.178298i
$748$	−142.760	+	142.760i	−0.190855	+	0.190855i
$749$			345.408i			0.461159i
$750$	293.991	−	85.5517i	0.391988	−	0.114069i
$751$	−20.9996			−0.0279622			−0.0139811	−	0.999902i	$-0.504450\pi$
$751$	−20.9996			−0.0279622			−0.0139811	+	0.999902i	$0.504450\pi$
$752$	−88.6698	−	88.6698i	−0.117912	−	0.117912i
$753$	94.8546	−	94.8546i	0.125969	−	0.125969i
$754$			203.178i			0.269466i
$755$	354.664	−	774.951i	0.469753	−	1.02642i
$756$	−21.4337			−0.0283514
$757$	−315.246	−	315.246i	−0.416441	−	0.416441i	0.467534	−	0.883975i	$-0.345143\pi$
$757$	−315.246	−	315.246i	−0.416441	−	0.416441i	−0.883975	+	0.467534i	$0.845143\pi$
$758$	−139.587	+	139.587i	−0.184151	+	0.184151i
$759$		−	54.5719i		−	0.0718997i
$760$	108.501	−	40.3693i	0.142765	−	0.0531174i
$761$	−828.712			−1.08898			−0.544489	−	0.838768i	$-0.683276\pi$
$761$	−828.712			−1.08898			−0.544489	+	0.838768i	$0.683276\pi$
$762$	−182.808	−	182.808i	−0.239906	−	0.239906i
$763$	−31.3993	+	31.3993i	−0.0411524	+	0.0411524i
$764$			450.902i			0.590186i
$765$	−80.3712	−	216.015i	−0.105060	−	0.282373i
$766$	−231.270			−0.301920
$767$	1357.01	+	1357.01i	1.76924	+	1.76924i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	968.106i		−	1.25892i	−0.777035	−	0.629458i	$-0.783277\pi$
$769$		−	968.106i		−	1.25892i	0.777035	−	0.629458i	$-0.216723\pi$
$770$	87.1204	+	39.8715i	0.113143	+	0.0517812i
$771$	524.768			0.680633
$772$	463.597	+	463.597i	0.600515	+	0.600515i
$773$	−74.5415	+	74.5415i	−0.0964314	+	0.0964314i	−0.753677	−	0.657245i	$-0.771722\pi$
$773$	−74.5415	+	74.5415i	−0.0964314	+	0.0964314i	0.657245	+	0.753677i	$0.271722\pi$
$774$			105.660i			0.136512i
$775$	−453.076	−	524.585i	−0.584614	−	0.676884i
$776$	397.235			0.511901
$777$	50.4299	+	50.4299i	0.0649033	+	0.0649033i
$778$	443.439	−	443.439i	0.569974	−	0.569974i
$779$		−	570.274i		−	0.732059i
$780$	163.401	−	357.036i	0.209489	−	0.457739i
$781$	−269.676			−0.345295
$782$	−73.6904	−	73.6904i	−0.0942332	−	0.0942332i
$783$	−23.2853	+	23.2853i	−0.0297386	+	0.0297386i
$784$			178.985i			0.228297i
$785$	386.805	−	143.916i	0.492745	−	0.183332i
$786$	391.031			0.497495
$787$	−669.944	−	669.944i	−0.851263	−	0.851263i	0.139026	−	0.990289i	$-0.455603\pi$
$787$	−669.944	−	669.944i	−0.851263	−	0.851263i	−0.990289	+	0.139026i	$0.955603\pi$
$788$	−481.969	+	481.969i	−0.611636	+	0.611636i
$789$			510.626i			0.647181i
$790$	235.984	+	634.260i	0.298714	+	0.802861i
$791$	210.950			0.266688
$792$	−39.4181	−	39.4181i	−0.0497703	−	0.0497703i
$793$	496.617	−	496.617i	0.626250	−	0.626250i
$794$			942.126i			1.18656i
$795$	19.5238	+	8.93526i	0.0245582	+	0.0112393i
$796$	175.741			0.220780
$797$	852.114	+	852.114i	1.06915	+	1.06915i	0.997424	+	0.0717269i	$0.0228510\pi$
$797$	852.114	+	852.114i	1.06915	+	1.06915i	0.0717269	+	0.997424i	$0.477149\pi$
$798$	−29.2428	+	29.2428i	−0.0366451	+	0.0366451i
$799$			481.701i			0.602880i
$800$	10.3164	−	141.045i	0.0128955	−	0.176306i
$801$	−426.327			−0.532244
$802$	−736.854	−	736.854i	−0.918771	−	0.918771i
$803$	−243.910	+	243.910i	−0.303749	+	0.303749i
$804$		−	150.638i		−	0.187360i
$805$	−20.5810	+	44.9702i	−0.0255665	+	0.0558636i
$806$	−888.901			−1.10285
$807$	217.927	+	217.927i	0.270046	+	0.270046i
$808$	−241.638	+	241.638i	−0.299057	+	0.299057i
$809$		−	119.855i		−	0.148152i	−0.997253	−	0.0740761i	$-0.976399\pi$
$809$		−	119.855i		−	0.148152i	0.997253	−	0.0740761i	$-0.0236008\pi$
$810$	59.6450	−	22.1917i	0.0736358	−	0.0273971i
$811$	865.405			1.06708			0.533542	−	0.845773i	$-0.320861\pi$
$811$	865.405			1.06708			0.533542	+	0.845773i	$0.320861\pi$
$812$	−18.4848	−	18.4848i	−0.0227645	−	0.0227645i
$813$	241.202	−	241.202i	0.296681	−	0.296681i
$814$			185.488i			0.227873i
$815$	−59.2625	−	159.281i	−0.0727147	−	0.195437i
$816$	−106.455			−0.130460
$817$	144.156	+	144.156i	0.176445	+	0.176445i
$818$	593.667	−	593.667i	0.725754	−	0.725754i
$819$			140.266i			0.171265i
$820$	−633.455	−	289.907i	−0.772506	−	0.353545i
$821$	−45.9137			−0.0559241			−0.0279620	−	0.999609i	$-0.508902\pi$
$821$	−45.9137			−0.0559241			−0.0279620	+	0.999609i	$0.508902\pi$
$822$	−113.933	−	113.933i	−0.138605	−	0.138605i
$823$	442.133	−	442.133i	0.537221	−	0.537221i	−0.385491	−	0.922712i	$-0.625968\pi$
$823$	442.133	−	442.133i	0.537221	−	0.537221i	0.922712	+	0.385491i	$0.125968\pi$
$824$			127.176i			0.154340i
$825$	−283.718	−	20.7518i	−0.343900	−	0.0251538i
$826$	−246.917			−0.298931
$827$	−21.4492	−	21.4492i	−0.0259361	−	0.0259361i	0.694020	−	0.719956i	$-0.255838\pi$
$827$	−21.4492	−	21.4492i	−0.0259361	−	0.0259361i	−0.719956	+	0.694020i	$0.755838\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$			671.387i			0.809876i	0.914344	+	0.404938i	$0.132707\pi$
$829$			671.387i			0.809876i	−0.914344	+	0.404938i	$0.867293\pi$
$830$	−184.754	+	403.692i	−0.222595	+	0.486376i
$831$	87.9976			0.105894
$832$	−128.239	−	128.239i	−0.154134	−	0.154134i
$833$	486.171	−	486.171i	0.583638	−	0.583638i
$834$		−	315.129i		−	0.377853i
$835$	854.880	−	318.069i	1.02381	−	0.380921i
$836$	−107.559			−0.128659
$837$	−101.873	−	101.873i	−0.121712	−	0.121712i
$838$	−450.030	+	450.030i	−0.537028	+	0.537028i
$839$		−	1314.79i		−	1.56709i	−0.621332	−	0.783547i	$-0.713408\pi$
$839$		−	1314.79i		−	1.56709i	0.621332	−	0.783547i	$-0.286592\pi$
$840$	17.6166	+	47.3486i	0.0209722	+	0.0563674i
$841$	800.837			0.952243
$842$	715.043	+	715.043i	0.849220	+	0.849220i
$843$	−378.299	+	378.299i	−0.448754	+	0.448754i
$844$			550.164i			0.651854i
$845$	−1568.16	−	717.682i	−1.85581	−	0.849328i
$846$	−133.005			−0.157216
$847$	113.519	+	113.519i	0.134025	+	0.134025i
$848$	7.01251	−	7.01251i	0.00826947	−	0.00826947i
$849$			355.990i			0.419305i
$850$	−411.136	+	355.092i	−0.483690	+	0.417756i
$851$	−95.7462			−0.112510
$852$	−100.548	−	100.548i	−0.118014	−	0.118014i
$853$	1140.91	−	1140.91i	1.33753	−	1.33753i	0.439081	−	0.898447i	$-0.355304\pi$
$853$	1140.91	−	1140.91i	1.33753	−	1.33753i	0.898447	−	0.439081i	$-0.144696\pi$
$854$			90.3628i			0.105811i
$855$	51.0990	−	111.653i	0.0597650	−	0.130588i
$856$	−473.689			−0.553374
$857$	238.411	+	238.411i	0.278192	+	0.278192i	0.832387	−	0.554195i	$-0.186974\pi$
$857$	238.411	+	238.411i	0.278192	+	0.278192i	−0.554195	+	0.832387i	$0.686974\pi$
$858$	−257.959	+	257.959i	−0.300652	+	0.300652i
$859$			1134.94i			1.32124i	0.750721	+	0.660619i	$0.229706\pi$
$859$			1134.94i			1.32124i	−0.750721	+	0.660619i	$0.770294\pi$
$860$	233.411	−	86.8434i	0.271408	−	0.100981i
$861$	248.860			0.289037
$862$	643.338	+	643.338i	0.746332	+	0.746332i
$863$	308.927	−	308.927i	0.357968	−	0.357968i	−0.505095	−	0.863064i	$-0.668543\pi$
$863$	308.927	−	308.927i	0.357968	−	0.357968i	0.863064	+	0.505095i	$0.168543\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	36.6000	+	98.3705i	0.0423121	+	0.113723i
$866$	−396.594			−0.457961
$867$	−64.7906	−	64.7906i	−0.0747297	−	0.0747297i
$868$	80.8708	−	80.8708i	0.0931692	−	0.0931692i
$869$		−	628.753i		−	0.723536i
$870$	70.5775	+	32.3005i	0.0811235	+	0.0371270i
$871$	−985.802			−1.13180
$872$	−43.0606	−	43.0606i	−0.0493814	−	0.0493814i
$873$	297.926	−	297.926i	0.341267	−	0.341267i
$874$		−	55.5203i		−	0.0635244i
$875$	225.972	+	124.101i	0.258254	+	0.141830i
$876$	−181.883			−0.207629
$877$	52.6873	+	52.6873i	0.0600767	+	0.0600767i	0.736507	−	0.676430i	$-0.236474\pi$
$877$	52.6873	+	52.6873i	0.0600767	+	0.0600767i	−0.676430	+	0.736507i	$0.736474\pi$
$878$	−337.344	+	337.344i	−0.384219	+	0.384219i
$879$			590.358i			0.671624i
$880$	−54.6793	+	119.476i	−0.0621355	+	0.135768i
$881$	−1442.03			−1.63681			−0.818404	−	0.574644i	$-0.805141\pi$
$881$	−1442.03			−1.63681			−0.818404	+	0.574644i	$0.805141\pi$
$882$	134.239	+	134.239i	0.152198	+	0.152198i
$883$	−517.014	+	517.014i	−0.585520	+	0.585520i	−0.936415	−	0.350895i	$-0.885877\pi$
$883$	−517.014	+	517.014i	−0.585520	+	0.585520i	0.350895	+	0.936415i	$0.385877\pi$
$884$			696.664i			0.788081i
$885$	687.113	−	255.649i	0.776399	−	0.288869i
$886$	−218.747			−0.246892
$887$	645.843	+	645.843i	0.728121	+	0.728121i	0.970245	−	0.242124i	$-0.0778442\pi$
$887$	645.843	+	645.843i	0.728121	+	0.728121i	−0.242124	+	0.970245i	$0.577844\pi$
$888$	−69.1589	+	69.1589i	−0.0778817	+	0.0778817i
$889$		−	217.681i		−	0.244860i
$890$	350.404	+	941.789i	0.393713	+	1.05819i
$891$	−59.1271			−0.0663604
$892$	150.605	+	150.605i	0.168840	+	0.168840i
$893$	−181.463	+	181.463i	−0.203207	+	0.203207i
$894$		−	230.233i		−	0.257531i
$895$	49.2490	+	22.5393i	0.0550268	+	0.0251836i
$896$	23.3340			0.0260425
$897$	−133.155	−	133.155i	−0.148444	−	0.148444i
$898$	−372.277	+	372.277i	−0.414562	+	0.414562i
$899$		−	175.714i		−	0.195455i
$900$	−98.0462	−	113.521i	−0.108940	−	0.126134i
$901$	−38.0956			−0.0422815
$902$	457.672	+	457.672i	0.507397	+	0.507397i
$903$	−62.9078	+	62.9078i	−0.0696654	+	0.0696654i
$904$			289.294i			0.320016i
$905$	−6.16852	+	13.4784i	−0.00681605	+	0.0148933i
$906$	−417.517			−0.460835
$907$	−258.058	−	258.058i	−0.284518	−	0.284518i	0.550390	−	0.834908i	$-0.314479\pi$
$907$	−258.058	−	258.058i	−0.284518	−	0.284518i	−0.834908	+	0.550390i	$0.814479\pi$
$908$	−629.484	+	629.484i	−0.693265	+	0.693265i
$909$			362.457i			0.398743i
$910$	309.858	−	115.287i	0.340504	−	0.126689i
$911$	−1486.36			−1.63157			−0.815784	−	0.578357i	$-0.803694\pi$
$911$	−1486.36			−1.63157			−0.815784	+	0.578357i	$0.803694\pi$
$912$	−40.1032	−	40.1032i	−0.0439728	−	0.0439728i
$913$	291.668	−	291.668i	0.319461	−	0.319461i
$914$		−	20.9935i		−	0.0229688i
$915$	−93.5585	−	251.459i	−0.102250	−	0.274819i
$916$	−203.118			−0.221745
$917$	232.812	+	232.812i	0.253885	+	0.253885i
$918$	−79.8415	+	79.8415i	−0.0869733	+	0.0869733i
$919$			1545.07i			1.68125i	0.541614	+	0.840627i	$0.317813\pi$
$919$			1545.07i			1.68125i	−0.541614	+	0.840627i	$0.682187\pi$
$920$	−61.6715	−	28.2246i	−0.0670342	−	0.0306789i
$921$	168.863			0.183347
$922$	833.333	+	833.333i	0.903832	+	0.903832i
$923$	−658.004	+	658.004i	−0.712897	+	0.712897i
$924$		−	46.9375i		−	0.0507982i
$925$	−36.4090	+	497.782i	−0.0393611	+	0.538142i
$926$	−104.239			−0.112569
$927$	95.3823	+	95.3823i	0.102894	+	0.102894i
$928$	25.3498	−	25.3498i	0.0273166	−	0.0273166i
$929$			1408.56i			1.51621i	0.652130	+	0.758107i	$0.273876\pi$
$929$			1408.56i			1.51621i	−0.652130	+	0.758107i	$0.726124\pi$
$930$	−141.314	+	308.776i	−0.151951	+	0.332017i
$931$	366.294			0.393442
$932$	−391.204	−	391.204i	−0.419747	−	0.419747i
$933$	632.377	−	632.377i	0.677789	−	0.677789i
$934$			371.454i			0.397703i
$935$	473.051	−	176.005i	0.505937	−	0.188240i
$936$	−192.359			−0.205512
$937$	−1156.07	−	1156.07i	−1.23380	−	1.23380i	−0.962493	−	0.271306i	$-0.912544\pi$
$937$	−1156.07	−	1156.07i	−1.23380	−	1.23380i	−0.271306	−	0.962493i	$-0.587456\pi$
$938$	89.6867	−	89.6867i	0.0956149	−	0.0956149i
$939$			102.003i			0.108629i
$940$	109.318	+	293.817i	0.116296	+	0.312572i
$941$	−539.273			−0.573085			−0.286543	−	0.958068i	$-0.592506\pi$
$941$	−539.273			−0.573085			−0.286543	+	0.958068i	$0.592506\pi$
$942$	−142.967	−	142.967i	−0.151770	−	0.151770i
$943$	−236.243	+	236.243i	−0.250523	+	0.250523i
$944$		−	338.619i		−	0.358706i
$945$	48.7240	+	22.2990i	0.0515597	+	0.0235968i
$946$	−231.384			−0.244592
$947$	60.4452	+	60.4452i	0.0638281	+	0.0638281i	0.738300	−	0.674472i	$-0.235629\pi$
$947$	60.4452	+	60.4452i	0.0638281	+	0.0638281i	−0.674472	+	0.738300i	$0.735629\pi$
$948$	234.429	−	234.429i	0.247288	−	0.247288i
$949$			1190.27i			1.25424i
$950$	−288.649	−	21.1125i	−0.303841	−	0.0222237i
$951$	324.655			0.341382
$952$	−63.3814	−	63.3814i	−0.0665771	−	0.0665771i
$953$	397.881	−	397.881i	0.417503	−	0.417503i	−0.466839	−	0.884342i	$-0.654607\pi$
$953$	397.881	−	397.881i	0.417503	−	0.417503i	0.884342	+	0.466839i	$0.154607\pi$
$954$		−	10.5188i		−	0.0110260i
$955$	469.106	−	1025.01i	0.491210	−	1.07331i
$956$	525.351			0.549531
$957$	−50.9923	−	50.9923i	−0.0532835	−	0.0532835i
$958$	384.415	−	384.415i	0.401268	−	0.401268i
$959$		−	135.667i		−	0.141467i
$960$	−64.9333	+	24.1592i	−0.0676388	+	0.0251659i
$961$	−192.252			−0.200055
$962$	452.589	+	452.589i	0.470467	+	0.470467i
$963$	−355.266	+	355.266i	−0.368916	+	0.368916i
$964$			580.568i			0.602249i
$965$	−571.555	−	1536.18i	−0.592285	−	1.59190i
$966$	24.2284			0.0250811
$967$	627.872	+	627.872i	0.649299	+	0.649299i	0.952823	−	0.303525i	$-0.0981636\pi$
$967$	627.872	+	627.872i	0.649299	+	0.649299i	−0.303525	+	0.952823i	$0.598164\pi$
$968$	−155.679	+	155.679i	−0.160825	+	0.160825i
$969$			217.862i			0.224831i
$970$	−903.011	−	413.272i	−0.930940	−	0.426053i
$971$	−191.624			−0.197347			−0.0986735	−	0.995120i	$-0.531460\pi$
$971$	−191.624			−0.197347			−0.0986735	+	0.995120i	$0.531460\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	187.622	−	187.622i	0.192828	−	0.192828i
$974$		−	352.023i		−	0.361420i
$975$	−742.901	+	641.632i	−0.761949	+	0.658085i
$976$	−123.922			−0.126970
$977$	−1008.83	−	1008.83i	−1.03258	−	1.03258i	−0.999451	−	0.0331267i	$-0.989454\pi$
$977$	−1008.83	−	1008.83i	−1.03258	−	1.03258i	−0.0331267	−	0.999451i	$-0.510546\pi$
$978$	−58.8719	+	58.8719i	−0.0601962	+	0.0601962i
$979$		−	933.612i		−	0.953638i
$980$	186.211	−	406.876i	0.190011	−	0.415180i
$981$	−64.5909			−0.0658419
$982$	−565.321	−	565.321i	−0.575683	−	0.575683i
$983$	308.876	−	308.876i	0.314218	−	0.314218i	−0.532323	−	0.846541i	$-0.678681\pi$
$983$	308.876	−	308.876i	0.314218	−	0.314218i	0.846541	+	0.532323i	$0.178681\pi$
$984$			341.284i			0.346833i
$985$	1597.06	−	594.206i	1.62138	−	0.603255i
$986$	−137.714			−0.139669
$987$	−79.1884	−	79.1884i	−0.0802314	−	0.0802314i
$988$	−262.443	+	262.443i	−0.265630	+	0.265630i
$989$		−	119.437i		−	0.120765i
$990$	48.5974	+	130.616i	0.0490883	+	0.131936i
$991$	−273.887			−0.276374			−0.138187	−	0.990406i	$-0.544128\pi$
$991$	−273.887			−0.276374			−0.138187	+	0.990406i	$0.544128\pi$
$992$	110.905	+	110.905i	0.111800	+	0.111800i
$993$	−423.638	+	423.638i	−0.426625	+	0.426625i
$994$		−	119.728i		−	0.120451i
$995$	−399.501	−	182.835i	−0.401509	−	0.183754i
$996$	217.495			0.218369
$997$	276.311	+	276.311i	0.277142	+	0.277142i	0.831967	−	0.554825i	$-0.187215\pi$
$997$	276.311	+	276.311i	0.277142	+	0.277142i	−0.554825	+	0.831967i	$0.687215\pi$
$998$	876.225	−	876.225i	0.877981	−	0.877981i
$999$			103.738i			0.103842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.17	✓	48
5.3	odd	4	inner	690.3.k.b.553.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.17	✓	48	1.1	even	1	trivial
690.3.k.b.553.17	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(2.08074 - 4.54648i) q^{5} -2.44949 q^{6} +(-1.45838 - 1.45838i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.62723 + 2.46574i) q^{10} +6.56968 q^{11} +(2.44949 + 2.44949i) q^{12} +(16.0299 - 16.0299i) q^{13} +2.91676i q^{14} +(-3.01990 - 8.11666i) q^{15} -4.00000 q^{16} +(10.8651 + 10.8651i) q^{17} +(-3.00000 + 3.00000i) q^{18} +8.18603i q^{19} +(9.09297 + 4.16148i) q^{20} -3.57228 q^{21} +(-6.56968 - 6.56968i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-16.3410 - 18.9201i) q^{25} -32.0598 q^{26} +(-3.67423 - 3.67423i) q^{27} +(2.91676 - 2.91676i) q^{28} -6.33745i q^{29} +(-5.09676 + 11.1366i) q^{30} +27.7263 q^{31} +(4.00000 + 4.00000i) q^{32} +(8.04619 - 8.04619i) q^{33} -21.7301i q^{34} +(-9.66500 + 3.59598i) q^{35} +6.00000 q^{36} +(-14.1170 - 14.1170i) q^{37} +(8.18603 - 8.18603i) q^{38} -39.2651i q^{39} +(-4.93148 - 13.2545i) q^{40} -69.6643 q^{41} +(3.57228 + 3.57228i) q^{42} +(17.6100 - 17.6100i) q^{43} +13.1394i q^{44} +(-13.6395 - 6.24223i) q^{45} -6.78233 q^{46} +(22.1675 + 22.1675i) q^{47} +(-4.89898 + 4.89898i) q^{48} -44.7463i q^{49} +(-2.57909 + 35.2611i) q^{50} +26.6138 q^{51} +(32.0598 + 32.0598i) q^{52} +(-1.75313 + 1.75313i) q^{53} +7.34847i q^{54} +(13.6698 - 29.8690i) q^{55} -5.83351 q^{56} +(10.0258 + 10.0258i) q^{57} +(-6.33745 + 6.33745i) q^{58} +84.6547i q^{59} +(16.2333 - 6.03981i) q^{60} +30.9806 q^{61} +(-27.7263 - 27.7263i) q^{62} +(-4.37513 + 4.37513i) q^{63} -8.00000i q^{64} +(-39.5256 - 106.234i) q^{65} -16.0924 q^{66} +(-30.7488 - 30.7488i) q^{67} +(-21.7301 + 21.7301i) q^{68} -8.30662i q^{69} +(13.2610 + 6.06902i) q^{70} -41.0485 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-37.1267 + 37.1267i) q^{73} +28.2340i q^{74} +(-43.1859 - 3.15873i) q^{75} -16.3721 q^{76} +(-9.58108 - 9.58108i) q^{77} +(-39.2651 + 39.2651i) q^{78} -95.7052i q^{79} +(-8.32297 + 18.1859i) q^{80} -9.00000 q^{81} +(69.6643 + 69.6643i) q^{82} +(44.3961 - 44.3961i) q^{83} -7.14456i q^{84} +(72.0051 - 26.7904i) q^{85} -35.2200 q^{86} +(-7.76176 - 7.76176i) q^{87} +(13.1394 - 13.1394i) q^{88} -142.109i q^{89} +(7.39723 + 19.8817i) q^{90} -46.7554 q^{91} +(6.78233 + 6.78233i) q^{92} +(33.9576 - 33.9576i) q^{93} -44.3349i q^{94} +(37.2176 + 17.0330i) q^{95} +9.79796 q^{96} +(99.3088 + 99.3088i) q^{97} +(-44.7463 + 44.7463i) q^{98} -19.7090i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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