LMFDB - Embedded newform 690.3.k.b.277.9

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			277.9
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-1.01004 - 6.99856i) q^{10} -0.959032 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.15802 + 7.15802i) q^{13} +9.31993i q^{14} +(-8.57145 + 1.23704i) q^{15} -4.00000 q^{16} +(17.8295 + 17.8295i) q^{17} +(-3.00000 + 3.00000i) q^{18} -11.9544i q^{19} +(-5.98852 + 8.00860i) q^{20} +11.4145 q^{21} +(0.959032 + 0.959032i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(7.06884 + 23.9798i) q^{25} +14.3160 q^{26} +(3.67423 + 3.67423i) q^{27} +(9.31993 - 9.31993i) q^{28} -10.1798i q^{29} +(9.80849 + 7.33440i) q^{30} -17.8199 q^{31} +(4.00000 + 4.00000i) q^{32} +(1.17457 - 1.17457i) q^{33} -35.6590i q^{34} +(-4.70676 - 32.6130i) q^{35} +6.00000 q^{36} +(35.6436 + 35.6436i) q^{37} +(-11.9544 + 11.9544i) q^{38} -17.5335i q^{39} +(13.9971 - 2.02008i) q^{40} -70.4086 q^{41} +(-11.4145 - 11.4145i) q^{42} +(-32.3834 + 32.3834i) q^{43} -1.91806i q^{44} +(8.98277 - 12.0129i) q^{45} +6.78233 q^{46} +(-36.1043 - 36.1043i) q^{47} +(4.89898 - 4.89898i) q^{48} -5.56950i q^{49} +(16.9110 - 31.0487i) q^{50} -43.6732 q^{51} +(-14.3160 - 14.3160i) q^{52} +(-22.0370 + 22.0370i) q^{53} -7.34847i q^{54} +(-3.84025 - 2.87159i) q^{55} -18.6399 q^{56} +(14.6411 + 14.6411i) q^{57} +(-10.1798 + 10.1798i) q^{58} +7.49744i q^{59} +(-2.47409 - 17.1429i) q^{60} -83.1331 q^{61} +(17.8199 + 17.8199i) q^{62} +(-13.9799 + 13.9799i) q^{63} -8.00000i q^{64} +(-50.0958 + 7.22990i) q^{65} -2.34914 q^{66} +(36.1206 + 36.1206i) q^{67} +(-35.6590 + 35.6590i) q^{68} -8.30662i q^{69} +(-27.9063 + 37.3198i) q^{70} -19.9996 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-39.5875 + 39.5875i) q^{73} -71.2871i q^{74} +(-38.0267 - 20.7116i) q^{75} +23.9088 q^{76} +(4.46905 + 4.46905i) q^{77} +(-17.5335 + 17.5335i) q^{78} +26.1612i q^{79} +(-16.0172 - 11.9770i) q^{80} -9.00000 q^{81} +(70.4086 + 70.4086i) q^{82} +(-38.2400 + 38.2400i) q^{83} +22.8291i q^{84} +(18.0085 + 124.781i) q^{85} +64.7668 q^{86} +(12.4677 + 12.4677i) q^{87} +(-1.91806 + 1.91806i) q^{88} +67.4462i q^{89} +(-20.9957 + 3.03013i) q^{90} +66.7122 q^{91} +(-6.78233 - 6.78233i) q^{92} +(21.8248 - 21.8248i) q^{93} +72.2086i q^{94} +(35.7946 - 47.8690i) q^{95} -9.79796 q^{96} +(90.5751 + 90.5751i) q^{97} +(-5.56950 + 5.56950i) q^{98} +2.87709i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	4.00430	+	2.99426i	0.800860	+	0.598852i
$5$	4.00430	+	2.99426i	0.800860	+	0.598852i
$6$	2.44949			0.408248
$7$	−4.65996	−	4.65996i	−0.665709	−	0.665709i	0.291011	−	0.956720i	$-0.406008\pi$
$7$	−4.65996	−	4.65996i	−0.665709	−	0.665709i	−0.956720	+	0.291011i	$0.906008\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−1.01004	−	6.99856i	−0.101004	−	0.699856i
$11$	−0.959032			−0.0871847			−0.0435923	−	0.999049i	$-0.513880\pi$
$11$	−0.959032			−0.0871847			−0.0435923	+	0.999049i	$0.513880\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−7.15802	+	7.15802i	−0.550617	+	0.550617i	−0.926619	−	0.376002i	$-0.877299\pi$
$13$	−7.15802	+	7.15802i	−0.550617	+	0.550617i	0.376002	+	0.926619i	$0.377299\pi$
$14$			9.31993i			0.665709i
$15$	−8.57145	+	1.23704i	−0.571430	+	0.0824696i
$16$	−4.00000			−0.250000
$17$	17.8295	+	17.8295i	1.04879	+	1.04879i	0.998747	+	0.0500472i	$0.0159372\pi$
$17$	17.8295	+	17.8295i	1.04879	+	1.04879i	0.0500472	+	0.998747i	$0.484063\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	11.9544i		−	0.629180i	−0.949228	−	0.314590i	$-0.898133\pi$
$19$		−	11.9544i		−	0.629180i	0.949228	−	0.314590i	$-0.101867\pi$
$20$	−5.98852	+	8.00860i	−0.299426	+	0.400430i
$21$	11.4145			0.543549
$22$	0.959032	+	0.959032i	0.0435923	+	0.0435923i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	7.06884	+	23.9798i	0.282754	+	0.959193i
$26$	14.3160			0.550617
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	9.31993	−	9.31993i	0.332854	−	0.332854i
$29$		−	10.1798i		−	0.351028i	−0.984477	−	0.175514i	$-0.943841\pi$
$29$		−	10.1798i		−	0.351028i	0.984477	−	0.175514i	$-0.0561587\pi$
$30$	9.80849	+	7.33440i	0.326950	+	0.244480i
$31$	−17.8199			−0.574835			−0.287417	−	0.957805i	$-0.592797\pi$
$31$	−17.8199			−0.574835			−0.287417	+	0.957805i	$0.592797\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	1.17457	−	1.17457i	0.0355930	−	0.0355930i
$34$		−	35.6590i		−	1.04879i
$35$	−4.70676	−	32.6130i	−0.134479	−	0.931801i
$36$	6.00000			0.166667
$37$	35.6436	+	35.6436i	0.963340	+	0.963340i	0.999351	−	0.0360119i	$-0.0114654\pi$
$37$	35.6436	+	35.6436i	0.963340	+	0.963340i	−0.0360119	+	0.999351i	$0.511465\pi$
$38$	−11.9544	+	11.9544i	−0.314590	+	0.314590i
$39$		−	17.5335i		−	0.449577i
$40$	13.9971	−	2.02008i	0.349928	−	0.0505021i
$41$	−70.4086			−1.71728			−0.858642	−	0.512576i	$-0.828691\pi$
$41$	−70.4086			−1.71728			−0.858642	+	0.512576i	$0.828691\pi$
$42$	−11.4145	−	11.4145i	−0.271775	−	0.271775i
$43$	−32.3834	+	32.3834i	−0.753103	+	0.753103i	−0.975057	−	0.221954i	$-0.928756\pi$
$43$	−32.3834	+	32.3834i	−0.753103	+	0.753103i	0.221954	+	0.975057i	$0.428756\pi$
$44$		−	1.91806i		−	0.0435923i
$45$	8.98277	−	12.0129i	0.199617	−	0.266953i
$46$	6.78233			0.147442
$47$	−36.1043	−	36.1043i	−0.768176	−	0.768176i	0.209609	−	0.977785i	$-0.432781\pi$
$47$	−36.1043	−	36.1043i	−0.768176	−	0.768176i	−0.977785	+	0.209609i	$0.932781\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	5.56950i		−	0.113663i
$50$	16.9110	−	31.0487i	0.338220	−	0.620973i
$51$	−43.6732			−0.856337
$52$	−14.3160	−	14.3160i	−0.275309	−	0.275309i
$53$	−22.0370	+	22.0370i	−0.415793	+	0.415793i	−0.883751	−	0.467958i	$-0.844990\pi$
$53$	−22.0370	+	22.0370i	−0.415793	+	0.415793i	0.467958	+	0.883751i	$0.344990\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−3.84025	−	2.87159i	−0.0698227	−	0.0522107i
$56$	−18.6399			−0.332854
$57$	14.6411	+	14.6411i	0.256861	+	0.256861i
$58$	−10.1798	+	10.1798i	−0.175514	+	0.175514i
$59$			7.49744i			0.127075i	0.997979	+	0.0635376i	$0.0202383\pi$
$59$			7.49744i			0.127075i	−0.997979	+	0.0635376i	$0.979762\pi$
$60$	−2.47409	−	17.1429i	−0.0412348	−	0.285715i
$61$	−83.1331			−1.36284			−0.681419	−	0.731893i	$-0.738637\pi$
$61$	−83.1331			−1.36284			−0.681419	+	0.731893i	$0.738637\pi$
$62$	17.8199	+	17.8199i	0.287417	+	0.287417i
$63$	−13.9799	+	13.9799i	−0.221903	+	0.221903i
$64$		−	8.00000i		−	0.125000i
$65$	−50.0958	+	7.22990i	−0.770705	+	0.111229i
$66$	−2.34914			−0.0355930
$67$	36.1206	+	36.1206i	0.539114	+	0.539114i	0.923269	−	0.384155i	$-0.125507\pi$
$67$	36.1206	+	36.1206i	0.539114	+	0.539114i	−0.384155	+	0.923269i	$0.625507\pi$
$68$	−35.6590	+	35.6590i	−0.524397	+	0.524397i
$69$		−	8.30662i		−	0.120386i
$70$	−27.9063	+	37.3198i	−0.398661	+	0.533140i
$71$	−19.9996			−0.281684			−0.140842	−	0.990032i	$-0.544981\pi$
$71$	−19.9996			−0.281684			−0.140842	+	0.990032i	$0.544981\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−39.5875	+	39.5875i	−0.542295	+	0.542295i	−0.924201	−	0.381906i	$-0.875268\pi$
$73$	−39.5875	+	39.5875i	−0.542295	+	0.542295i	0.381906	+	0.924201i	$0.375268\pi$
$74$		−	71.2871i		−	0.963340i
$75$	−38.0267	−	20.7116i	−0.507022	−	0.276155i
$76$	23.9088			0.314590
$77$	4.46905	+	4.46905i	0.0580396	+	0.0580396i
$78$	−17.5335	+	17.5335i	−0.224788	+	0.224788i
$79$			26.1612i			0.331154i	0.986197	+	0.165577i	$0.0529487\pi$
$79$			26.1612i			0.331154i	−0.986197	+	0.165577i	$0.947051\pi$
$80$	−16.0172	−	11.9770i	−0.200215	−	0.149713i
$81$	−9.00000			−0.111111
$82$	70.4086	+	70.4086i	0.858642	+	0.858642i
$83$	−38.2400	+	38.2400i	−0.460723	+	0.460723i	−0.898892	−	0.438170i	$-0.855627\pi$
$83$	−38.2400	+	38.2400i	−0.460723	+	0.460723i	0.438170	+	0.898892i	$0.355627\pi$
$84$			22.8291i			0.271775i
$85$	18.0085	+	124.781i	0.211865	+	1.46801i
$86$	64.7668			0.753103
$87$	12.4677	+	12.4677i	0.143306	+	0.143306i
$88$	−1.91806	+	1.91806i	−0.0217962	+	0.0217962i
$89$			67.4462i			0.757822i	0.925433	+	0.378911i	$0.123701\pi$
$89$			67.4462i			0.757822i	−0.925433	+	0.378911i	$0.876299\pi$
$90$	−20.9957	+	3.03013i	−0.233285	+	0.0336681i
$91$	66.7122			0.733101
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	21.8248	−	21.8248i	0.234675	−	0.234675i
$94$			72.2086i			0.768176i
$95$	35.7946	−	47.8690i	0.376785	−	0.503885i
$96$	−9.79796			−0.102062
$97$	90.5751	+	90.5751i	0.933764	+	0.933764i	0.997939	−	0.0641750i	$-0.0204416\pi$
$97$	90.5751	+	90.5751i	0.933764	+	0.933764i	−0.0641750	+	0.997939i	$0.520442\pi$
$98$	−5.56950	+	5.56950i	−0.0568316	+	0.0568316i
$99$			2.87709i			0.0290616i
$100$	−47.9596	+	14.1377i	−0.479596	+	0.141377i
$101$	−8.25159			−0.0816989			−0.0408495	−	0.999165i	$-0.513006\pi$
$101$	−8.25159			−0.0816989			−0.0408495	+	0.999165i	$0.513006\pi$
$102$	43.6732	+	43.6732i	0.428168	+	0.428168i
$103$	−82.0811	+	82.0811i	−0.796904	+	0.796904i	−0.982606	−	0.185702i	$-0.940544\pi$
$103$	−82.0811	+	82.0811i	−0.796904	+	0.796904i	0.185702	+	0.982606i	$0.440544\pi$
$104$			28.6321i			0.275309i
$105$	45.7072	+	34.1780i	0.435307	+	0.325505i
$106$	44.0740			0.415793
$107$	−92.7956	−	92.7956i	−0.867249	−	0.867249i	0.124918	−	0.992167i	$-0.460133\pi$
$107$	−92.7956	−	92.7956i	−0.867249	−	0.867249i	−0.992167	+	0.124918i	$0.960133\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	11.0337i		−	0.101227i	−0.998718	−	0.0506134i	$-0.983882\pi$
$109$		−	11.0337i		−	0.101227i	0.998718	−	0.0506134i	$-0.0161176\pi$
$110$	0.968662	+	6.71184i	0.00880602	+	0.0610167i
$111$	−87.3085			−0.786563
$112$	18.6399	+	18.6399i	0.166427	+	0.166427i
$113$	−63.3403	+	63.3403i	−0.560534	+	0.560534i	−0.929459	−	0.368925i	$-0.879726\pi$
$113$	−63.3403	+	63.3403i	−0.560534	+	0.560534i	0.368925	+	0.929459i	$0.379726\pi$
$114$		−	29.2822i		−	0.256861i
$115$	−23.7333	+	3.42522i	−0.206376	+	0.0297845i
$116$	20.3596			0.175514
$117$	21.4741	+	21.4741i	0.183539	+	0.183539i
$118$	7.49744	−	7.49744i	0.0635376	−	0.0635376i
$119$		−	166.170i		−	1.39638i
$120$	−14.6688	+	19.6170i	−0.122240	+	0.163475i
$121$	−120.080			−0.992399
$122$	83.1331	+	83.1331i	0.681419	+	0.681419i
$123$	86.2326	−	86.2326i	0.701078	−	0.701078i
$124$		−	35.6398i		−	0.287417i
$125$	−43.4960	+	117.188i	−0.347968	+	0.937506i
$126$	27.9598			0.221903
$127$	115.171	+	115.171i	0.906861	+	0.906861i	0.996018	−	0.0891566i	$-0.0284172\pi$
$127$	115.171	+	115.171i	0.906861	+	0.906861i	−0.0891566	+	0.996018i	$0.528417\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	79.3229i		−	0.614906i
$130$	57.3257	+	42.8659i	0.440967	+	0.329738i
$131$	−59.8637			−0.456974			−0.228487	−	0.973547i	$-0.573378\pi$
$131$	−59.8637			−0.456974			−0.228487	+	0.973547i	$0.573378\pi$
$132$	2.34914	+	2.34914i	0.0177965	+	0.0177965i
$133$	−55.7071	+	55.7071i	−0.418850	+	0.418850i
$134$		−	72.2412i		−	0.539114i
$135$	3.71113	+	25.7143i	0.0274899	+	0.190477i
$136$	71.3180			0.524397
$137$	−184.443	−	184.443i	−1.34630	−	1.34630i	−0.889642	−	0.456660i	$-0.849046\pi$
$137$	−184.443	−	184.443i	−1.34630	−	1.34630i	−0.456660	−	0.889642i	$-0.650954\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$			18.2325i			0.131169i	0.997847	+	0.0655844i	$0.0208912\pi$
$139$			18.2325i			0.131169i	−0.997847	+	0.0655844i	$0.979109\pi$
$140$	65.2260	−	9.41352i	0.465900	−	0.0672394i
$141$	88.4371			0.627213
$142$	19.9996	+	19.9996i	0.140842	+	0.140842i
$143$	6.86477	−	6.86477i	0.0480054	−	0.0480054i
$144$			12.0000i			0.0833333i
$145$	30.4810	−	40.7630i	0.210213	−	0.281124i
$146$	79.1751			0.542295
$147$	6.82121	+	6.82121i	0.0464028	+	0.0464028i
$148$	−71.2871	+	71.2871i	−0.481670	+	0.481670i
$149$			43.1692i			0.289726i	0.989452	+	0.144863i	$0.0462742\pi$
$149$			43.1692i			0.289726i	−0.989452	+	0.144863i	$0.953726\pi$
$150$	17.3150	+	58.7383i	0.115434	+	0.391589i
$151$	182.218			1.20674			0.603372	−	0.797460i	$-0.293824\pi$
$151$	182.218			1.20674			0.603372	+	0.797460i	$0.293824\pi$
$152$	−23.9088	−	23.9088i	−0.157295	−	0.157295i
$153$	53.4885	−	53.4885i	0.349598	−	0.349598i
$154$		−	8.93810i		−	0.0580396i
$155$	−71.3561	−	53.3573i	−0.460362	−	0.344241i
$156$	35.0670			0.224788
$157$	24.5503	+	24.5503i	0.156371	+	0.156371i	0.780957	−	0.624585i	$-0.214732\pi$
$157$	24.5503	+	24.5503i	0.156371	+	0.156371i	−0.624585	+	0.780957i	$0.714732\pi$
$158$	26.1612	−	26.1612i	0.165577	−	0.165577i
$159$		−	53.9794i		−	0.339493i
$160$	4.04017	+	27.9942i	0.0252511	+	0.174964i
$161$	31.6054			0.196307
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−55.8359	+	55.8359i	−0.342552	+	0.342552i	−0.857326	−	0.514774i	$-0.827876\pi$
$163$	−55.8359	+	55.8359i	−0.342552	+	0.342552i	0.514774	+	0.857326i	$0.327876\pi$
$164$		−	140.817i		−	0.858642i
$165$	8.22029	−	1.18636i	0.0498199	−	0.00719009i
$166$	76.4800			0.460723
$167$	−157.546	−	157.546i	−0.943389	−	0.943389i	0.0550920	−	0.998481i	$-0.482455\pi$
$167$	−157.546	−	157.546i	−0.943389	−	0.943389i	−0.998481	+	0.0550920i	$0.982455\pi$
$168$	22.8291	−	22.8291i	0.135887	−	0.135887i
$169$			66.5254i			0.393642i
$170$	106.772	−	142.789i	0.628072	−	0.839937i
$171$	−35.8632			−0.209727
$172$	−64.7668	−	64.7668i	−0.376551	−	0.376551i
$173$	167.938	−	167.938i	0.970741	−	0.970741i	−0.0288432	−	0.999584i	$-0.509182\pi$
$173$	167.938	−	167.938i	0.970741	−	0.970741i	0.999584	+	0.0288432i	$0.00918235\pi$
$174$		−	24.9353i		−	0.143306i
$175$	78.8045	−	144.686i	0.450312	−	0.826775i
$176$	3.83613			0.0217962
$177$	−9.18245	−	9.18245i	−0.0518783	−	0.0518783i
$178$	67.4462	−	67.4462i	0.378911	−	0.378911i
$179$		−	237.552i		−	1.32711i	−0.748128	−	0.663554i	$-0.769047\pi$
$179$		−	237.552i		−	1.32711i	0.748128	−	0.663554i	$-0.230953\pi$
$180$	24.0258	+	17.9655i	0.133477	+	0.0998086i
$181$	74.4891			0.411542			0.205771	−	0.978600i	$-0.434030\pi$
$181$	74.4891			0.411542			0.205771	+	0.978600i	$0.434030\pi$
$182$	−66.7122	−	66.7122i	−0.366551	−	0.366551i
$183$	101.817	−	101.817i	0.556376	−	0.556376i
$184$			13.5647i			0.0737210i
$185$	36.0015	+	249.454i	0.194603	+	1.34840i
$186$	−43.6496			−0.234675
$187$	−17.0991	−	17.0991i	−0.0914388	−	0.0914388i
$188$	72.2086	−	72.2086i	0.384088	−	0.384088i
$189$		−	34.2436i		−	0.181183i
$190$	−83.6636	+	12.0745i	−0.440335	+	0.0635498i
$191$	241.019			1.26188			0.630940	−	0.775832i	$-0.282670\pi$
$191$	241.019			1.26188			0.630940	+	0.775832i	$0.282670\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−157.235	+	157.235i	−0.814687	+	0.814687i	−0.985332	−	0.170646i	$-0.945415\pi$
$193$	−157.235	+	157.235i	−0.814687	+	0.814687i	0.170646	+	0.985332i	$0.445415\pi$
$194$		−	181.150i		−	0.933764i
$195$	52.4998	−	70.2094i	0.269230	−	0.360048i
$196$	11.1390			0.0568316
$197$	155.381	+	155.381i	0.788736	+	0.788736i	0.981287	−	0.192551i	$-0.0616760\pi$
$197$	155.381	+	155.381i	0.788736	+	0.788736i	−0.192551	+	0.981287i	$0.561676\pi$
$198$	2.87709	−	2.87709i	0.0145308	−	0.0145308i
$199$		−	168.224i		−	0.845344i	−0.906283	−	0.422672i	$-0.861092\pi$
$199$		−	168.224i		−	0.845344i	0.906283	−	0.422672i	$-0.138908\pi$
$200$	62.0973	+	33.8220i	0.310487	+	0.169110i
$201$	−88.4771			−0.440185
$202$	8.25159	+	8.25159i	0.0408495	+	0.0408495i
$203$	−47.4375	+	47.4375i	−0.233682	+	0.233682i
$204$		−	87.3463i		−	0.428168i
$205$	−281.937	−	210.822i	−1.37530	−	1.02840i
$206$	164.162			0.796904
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	28.6321	−	28.6321i	0.137654	−	0.137654i
$209$			11.4647i			0.0548548i
$210$	−11.5292	−	79.8853i	−0.0549008	−	0.380406i
$211$	−389.389			−1.84545			−0.922723	−	0.385463i	$-0.874042\pi$
$211$	−389.389			−1.84545			−0.922723	+	0.385463i	$0.874042\pi$
$212$	−44.0740	−	44.0740i	−0.207896	−	0.207896i
$213$	24.4944	−	24.4944i	0.114997	−	0.114997i
$214$			185.591i			0.867249i
$215$	−226.637	+	32.7086i	−1.05413	+	0.152133i
$216$	14.6969			0.0680414
$217$	83.0400	+	83.0400i	0.382673	+	0.382673i
$218$	−11.0337	+	11.0337i	−0.0506134	+	0.0506134i
$219$		−	96.9693i		−	0.442782i
$220$	5.74318	−	7.68050i	0.0261053	−	0.0349114i
$221$	−255.248			−1.15497
$222$	87.3085	+	87.3085i	0.393282	+	0.393282i
$223$	54.1820	−	54.1820i	0.242969	−	0.242969i	−0.575109	−	0.818077i	$-0.695040\pi$
$223$	54.1820	−	54.1820i	0.242969	−	0.242969i	0.818077	+	0.575109i	$0.195040\pi$
$224$		−	37.2797i		−	0.166427i
$225$	71.9394	−	21.2065i	0.319731	−	0.0942512i
$226$	126.681			0.560534
$227$	180.088	+	180.088i	0.793339	+	0.793339i	0.982035	−	0.188697i	$-0.0604263\pi$
$227$	180.088	+	180.088i	0.793339	+	0.793339i	−0.188697	+	0.982035i	$0.560426\pi$
$228$	−29.2822	+	29.2822i	−0.128431	+	0.128431i
$229$		−	23.3678i		−	0.102043i	−0.998698	−	0.0510213i	$-0.983752\pi$
$229$		−	23.3678i		−	0.102043i	0.998698	−	0.0510213i	$-0.0162477\pi$
$230$	27.1585	+	20.3080i	0.118080	+	0.0882958i
$231$	−10.9469			−0.0473892
$232$	−20.3596	−	20.3596i	−0.0877569	−	0.0877569i
$233$	97.9581	−	97.9581i	0.420421	−	0.420421i	−0.464928	−	0.885349i	$-0.653920\pi$
$233$	97.9581	−	97.9581i	0.420421	−	0.420421i	0.885349	+	0.464928i	$0.153920\pi$
$234$		−	42.9481i		−	0.183539i
$235$	−36.4669	−	252.678i	−0.155178	−	1.07523i
$236$	−14.9949			−0.0635376
$237$	−32.0408	−	32.0408i	−0.135193	−	0.135193i
$238$	−166.170	+	166.170i	−0.698192	+	0.698192i
$239$			138.405i			0.579100i	0.957163	+	0.289550i	$0.0935056\pi$
$239$			138.405i			0.579100i	−0.957163	+	0.289550i	$0.906494\pi$
$240$	34.2858	−	4.94818i	0.142857	−	0.0206174i
$241$	179.237			0.743723			0.371861	−	0.928288i	$-0.378720\pi$
$241$	179.237			0.743723			0.371861	+	0.928288i	$0.378720\pi$
$242$	120.080	+	120.080i	0.496199	+	0.496199i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$		−	166.266i		−	0.681419i
$245$	16.6765	−	22.3019i	0.0680674	−	0.0910283i
$246$	−172.465			−0.701078
$247$	85.5699	+	85.5699i	0.346437	+	0.346437i
$248$	−35.6398	+	35.6398i	−0.143709	+	0.143709i
$249$		−	93.6685i		−	0.376179i
$250$	160.684	−	73.6923i	0.642737	−	0.294769i
$251$	310.376			1.23656			0.618279	−	0.785958i	$-0.287830\pi$
$251$	310.376			1.23656			0.618279	+	0.785958i	$0.287830\pi$
$252$	−27.9598	−	27.9598i	−0.110951	−	0.110951i
$253$	3.25223	−	3.25223i	0.0128547	−	0.0128547i
$254$		−	230.343i		−	0.906861i
$255$	−174.880	−	130.769i	−0.685806	−	0.512819i
$256$	16.0000			0.0625000
$257$	219.443	+	219.443i	0.853863	+	0.853863i	0.990606	−	0.136744i	$-0.0436636\pi$
$257$	219.443	+	219.443i	0.853863	+	0.853863i	−0.136744	+	0.990606i	$0.543664\pi$
$258$	−79.3229	+	79.3229i	−0.307453	+	0.307453i
$259$		−	332.195i		−	1.28261i
$260$	−14.4598	−	100.192i	−0.0556146	−	0.385353i
$261$	−30.5394			−0.117009
$262$	59.8637	+	59.8637i	0.228487	+	0.228487i
$263$	−303.730	+	303.730i	−1.15487	+	1.15487i	−0.169303	+	0.985564i	$0.554152\pi$
$263$	−303.730	+	303.730i	−1.15487	+	1.15487i	−0.985564	+	0.169303i	$0.945848\pi$
$264$		−	4.69828i		−	0.0177965i
$265$	−154.227	+	22.2583i	−0.581990	+	0.0839936i
$266$	111.414			0.418850
$267$	−82.6044	−	82.6044i	−0.309380	−	0.309380i
$268$	−72.2412	+	72.2412i	−0.269557	+	0.269557i
$269$		−	472.776i		−	1.75753i	−0.477254	−	0.878765i	$-0.658368\pi$
$269$		−	472.776i		−	1.75753i	0.477254	−	0.878765i	$-0.341632\pi$
$270$	22.0032	−	29.4255i	0.0814934	−	0.108983i
$271$	64.8046			0.239131			0.119566	−	0.992826i	$-0.461850\pi$
$271$	64.8046			0.239131			0.119566	+	0.992826i	$0.461850\pi$
$272$	−71.3180	−	71.3180i	−0.262199	−	0.262199i
$273$	−81.7055	+	81.7055i	−0.299287	+	0.299287i
$274$			368.887i			1.34630i
$275$	−6.77924	−	22.9974i	−0.0246518	−	0.0836269i
$276$	16.6132			0.0601929
$277$	160.806	+	160.806i	0.580526	+	0.580526i	0.935048	−	0.354522i	$-0.115356\pi$
$277$	160.806	+	160.806i	0.580526	+	0.580526i	−0.354522	+	0.935048i	$0.615356\pi$
$278$	18.2325	−	18.2325i	0.0655844	−	0.0655844i
$279$			53.4596i			0.191612i
$280$	−74.6396	−	55.8125i	−0.266570	−	0.199330i
$281$	−163.698			−0.582554			−0.291277	−	0.956639i	$-0.594080\pi$
$281$	−163.698			−0.582554			−0.291277	+	0.956639i	$0.594080\pi$
$282$	−88.4371	−	88.4371i	−0.313607	−	0.313607i
$283$	353.193	−	353.193i	1.24803	−	1.24803i	0.291445	−	0.956588i	$-0.405864\pi$
$283$	353.193	−	353.193i	1.24803	−	1.24803i	0.956588	−	0.291445i	$-0.0941360\pi$
$284$		−	39.9992i		−	0.140842i
$285$	14.7881	+	102.467i	0.0518882	+	0.359532i
$286$	−13.7295			−0.0480054
$287$	328.102	+	328.102i	1.14321	+	1.14321i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$			346.782i			1.19994i
$290$	−71.2439	+	10.2820i	−0.245669	+	0.0354553i
$291$	−221.863			−0.762415
$292$	−79.1751	−	79.1751i	−0.271148	−	0.271148i
$293$	−93.8150	+	93.8150i	−0.320188	+	0.320188i	−0.848839	−	0.528651i	$-0.822698\pi$
$293$	−93.8150	+	93.8150i	−0.320188	+	0.320188i	0.528651	+	0.848839i	$0.322698\pi$
$294$		−	13.6424i		−	0.0464028i
$295$	−22.4493	+	30.0220i	−0.0760992	+	0.101770i
$296$	142.574			0.481670
$297$	−3.52371	−	3.52371i	−0.0118643	−	0.0118643i
$298$	43.1692	−	43.1692i	0.144863	−	0.144863i
$299$		−	48.5481i		−	0.162368i
$300$	41.4233	−	76.0534i	0.138078	−	0.253511i
$301$	301.811			1.00269
$302$	−182.218	−	182.218i	−0.603372	−	0.603372i
$303$	10.1061	−	10.1061i	0.0333535	−	0.0333535i
$304$			47.8176i			0.157295i
$305$	−332.890	−	248.922i	−1.09144	−	0.816138i
$306$	−106.977			−0.349598
$307$	20.7338	+	20.7338i	0.0675367	+	0.0675367i	0.740068	−	0.672532i	$-0.234793\pi$
$307$	20.7338	+	20.7338i	0.0675367	+	0.0675367i	−0.672532	+	0.740068i	$0.734793\pi$
$308$	−8.93810	+	8.93810i	−0.0290198	+	0.0290198i
$309$		−	201.057i		−	0.650670i
$310$	17.9988	+	124.713i	0.0580607	+	0.402301i
$311$	530.664			1.70632			0.853158	−	0.521652i	$-0.174684\pi$
$311$	530.664			1.70632			0.853158	+	0.521652i	$0.174684\pi$
$312$	−35.0670	−	35.0670i	−0.112394	−	0.112394i
$313$	264.744	−	264.744i	0.845826	−	0.845826i	−0.143783	−	0.989609i	$-0.545927\pi$
$313$	264.744	−	264.744i	0.845826	−	0.845826i	0.989609	+	0.143783i	$0.0459267\pi$
$314$		−	49.1005i		−	0.156371i
$315$	−97.8391	+	14.1203i	−0.310600	+	0.0448263i
$316$	−52.3224			−0.165577
$317$	−74.8843	−	74.8843i	−0.236228	−	0.236228i	0.579058	−	0.815286i	$-0.303420\pi$
$317$	−74.8843	−	74.8843i	−0.236228	−	0.236228i	−0.815286	+	0.579058i	$0.803420\pi$
$318$	−53.9794	+	53.9794i	−0.169747	+	0.169747i
$319$			9.76275i			0.0306042i
$320$	23.9541	−	32.0344i	0.0748564	−	0.100108i
$321$	227.302			0.708106
$322$	−31.6054	−	31.6054i	−0.0981534	−	0.0981534i
$323$	213.141	−	213.141i	0.659880	−	0.659880i
$324$		−	18.0000i		−	0.0555556i
$325$	−222.247	−	121.049i	−0.683837	−	0.372459i
$326$	111.672			0.342552
$327$	13.5135	+	13.5135i	0.0413256	+	0.0413256i
$328$	−140.817	+	140.817i	−0.429321	+	0.429321i
$329$			336.489i			1.02276i
$330$	−9.40665	−	7.03392i	−0.0285050	−	0.0213149i
$331$	512.969			1.54975			0.774877	−	0.632112i	$-0.217812\pi$
$331$	512.969			1.54975			0.774877	+	0.632112i	$0.217812\pi$
$332$	−76.4800	−	76.4800i	−0.230361	−	0.230361i
$333$	106.931	−	106.931i	0.321113	−	0.321113i
$334$			315.092i			0.943389i
$335$	36.4834	+	252.792i	0.108906	+	0.754604i
$336$	−45.6581			−0.135887
$337$	50.5137	+	50.5137i	0.149892	+	0.149892i	0.778070	−	0.628178i	$-0.216199\pi$
$337$	50.5137	+	50.5137i	0.149892	+	0.149892i	−0.628178	+	0.778070i	$0.716199\pi$
$338$	66.5254	−	66.5254i	0.196821	−	0.196821i
$339$		−	155.152i		−	0.457674i
$340$	−249.562	+	36.0171i	−0.734005	+	0.105933i
$341$	17.0898			0.0501168
$342$	35.8632	+	35.8632i	0.104863	+	0.104863i
$343$	−254.292	+	254.292i	−0.741376	+	0.741376i
$344$			129.534i			0.376551i
$345$	24.8722	−	33.2622i	0.0720933	−	0.0964122i
$346$	−335.876			−0.970741
$347$	74.2970	+	74.2970i	0.214112	+	0.214112i	0.806012	−	0.591899i	$-0.201622\pi$
$347$	74.2970	+	74.2970i	0.214112	+	0.214112i	−0.591899	+	0.806012i	$0.701622\pi$
$348$	−24.9353	+	24.9353i	−0.0716532	+	0.0716532i
$349$		−	597.945i		−	1.71331i	−0.515891	−	0.856654i	$-0.672539\pi$
$349$		−	597.945i		−	1.71331i	0.515891	−	0.856654i	$-0.327461\pi$
$350$	−223.490	+	65.8810i	−0.638543	+	0.188232i
$351$	−52.6005			−0.149859
$352$	−3.83613	−	3.83613i	−0.0108981	−	0.0108981i
$353$	−5.18580	+	5.18580i	−0.0146907	+	0.0146907i	−0.714414	−	0.699723i	$-0.753307\pi$
$353$	−5.18580	+	5.18580i	−0.0146907	+	0.0146907i	0.699723	+	0.714414i	$0.253307\pi$
$354$			18.3649i			0.0518783i
$355$	−80.0844	−	59.8839i	−0.225590	−	0.168687i
$356$	−134.892			−0.378911
$357$	203.515	+	203.515i	0.570071	+	0.570071i
$358$	−237.552	+	237.552i	−0.663554	+	0.663554i
$359$		−	173.219i		−	0.482503i	−0.970463	−	0.241251i	$-0.922442\pi$
$359$		−	173.219i		−	0.482503i	0.970463	−	0.241251i	$-0.0775578\pi$
$360$	−6.06025	−	41.9913i	−0.0168340	−	0.116643i
$361$	218.092			0.604133
$362$	−74.4891	−	74.4891i	−0.205771	−	0.205771i
$363$	147.068	−	147.068i	0.405145	−	0.405145i
$364$			133.424i			0.366551i
$365$	−277.056	+	39.9851i	−0.759057	+	0.109548i
$366$	−203.634			−0.556376
$367$	134.667	+	134.667i	0.366941	+	0.366941i	0.866360	−	0.499419i	$-0.166453\pi$
$367$	134.667	+	134.667i	0.366941	+	0.366941i	−0.499419	+	0.866360i	$0.666453\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$			211.226i			0.572428i
$370$	213.452	−	285.455i	0.576897	−	0.771500i
$371$	205.383			0.553594
$372$	43.6496	+	43.6496i	0.117338	+	0.117338i
$373$	−119.301	+	119.301i	−0.319841	+	0.319841i	−0.848706	−	0.528865i	$-0.822618\pi$
$373$	−119.301	+	119.301i	−0.319841	+	0.319841i	0.528865	+	0.848706i	$0.322618\pi$
$374$			34.1981i			0.0914388i
$375$	−90.2543	−	196.797i	−0.240678	−	0.524793i
$376$	−144.417			−0.384088
$377$	72.8673	+	72.8673i	0.193282	+	0.193282i
$378$	−34.2436	+	34.2436i	−0.0905915	+	0.0905915i
$379$		−	180.139i		−	0.475301i	−0.971351	−	0.237650i	$-0.923623\pi$
$379$		−	180.139i		−	0.475301i	0.971351	−	0.237650i	$-0.0763773\pi$
$380$	95.7381	+	71.5892i	0.251942	+	0.188393i
$381$	−282.111			−0.740449
$382$	−241.019	−	241.019i	−0.630940	−	0.630940i
$383$	203.565	−	203.565i	0.531502	−	0.531502i	−0.389517	−	0.921019i	$-0.627358\pi$
$383$	203.565	−	203.565i	0.531502	−	0.531502i	0.921019	+	0.389517i	$0.127358\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	4.51393	+	31.2769i	0.0117245	+	0.0812387i
$386$	314.469			0.814687
$387$	97.1503	+	97.1503i	0.251034	+	0.251034i
$388$	−181.150	+	181.150i	−0.466882	+	0.466882i
$389$			155.622i			0.400056i	0.979790	+	0.200028i	$0.0641032\pi$
$389$			155.622i			0.400056i	−0.979790	+	0.200028i	$0.935897\pi$
$390$	−122.709	+	17.7096i	−0.314639	+	0.0454092i
$391$	−120.926			−0.309272
$392$	−11.1390	−	11.1390i	−0.0284158	−	0.0284158i
$393$	73.3177	−	73.3177i	0.186559	−	0.186559i
$394$		−	310.762i		−	0.788736i
$395$	−78.3334	+	104.757i	−0.198312	+	0.265208i
$396$	−5.75419			−0.0145308
$397$	253.869	+	253.869i	0.639469	+	0.639469i	0.950425	−	0.310955i	$-0.100649\pi$
$397$	253.869	+	253.869i	0.639469	+	0.639469i	−0.310955	+	0.950425i	$0.600649\pi$
$398$	−168.224	+	168.224i	−0.422672	+	0.422672i
$399$		−	136.454i		−	0.341990i
$400$	−28.2754	−	95.9193i	−0.0706884	−	0.239798i
$401$	−85.8020			−0.213970			−0.106985	−	0.994261i	$-0.534120\pi$
$401$	−85.8020			−0.213970			−0.106985	+	0.994261i	$0.534120\pi$
$402$	88.4771	+	88.4771i	0.220092	+	0.220092i
$403$	127.555	−	127.555i	0.316514	−	0.316514i
$404$		−	16.5032i		−	0.0408495i
$405$	−36.0387	−	26.9483i	−0.0889844	−	0.0665391i
$406$	94.8750			0.233682
$407$	−34.1833	−	34.1833i	−0.0839885	−	0.0839885i
$408$	−87.3463	+	87.3463i	−0.214084	+	0.214084i
$409$			483.568i			1.18232i	0.806555	+	0.591158i	$0.201329\pi$
$409$			483.568i			1.18232i	−0.806555	+	0.591158i	$0.798671\pi$
$410$	71.1157	+	492.759i	0.173453	+	1.20185i
$411$	451.792			1.09925
$412$	−164.162	−	164.162i	−0.398452	−	0.398452i
$413$	34.9378	−	34.9378i	0.0845952	−	0.0845952i
$414$		−	20.3470i		−	0.0491473i
$415$	−267.625	+	38.6240i	−0.644879	+	0.0930699i
$416$	−57.2642			−0.137654
$417$	−22.3301	−	22.3301i	−0.0535494	−	0.0535494i
$418$	11.4647	−	11.4647i	0.0274274	−	0.0274274i
$419$			519.575i			1.24004i	0.784588	+	0.620018i	$0.212875\pi$
$419$			519.575i			1.24004i	−0.784588	+	0.620018i	$0.787125\pi$
$420$	−68.3561	+	91.4144i	−0.162753	+	0.217653i
$421$	−137.505			−0.326616			−0.163308	−	0.986575i	$-0.552216\pi$
$421$	−137.505			−0.326616			−0.163308	+	0.986575i	$0.552216\pi$
$422$	389.389	+	389.389i	0.922723	+	0.922723i
$423$	−108.313	+	108.313i	−0.256059	+	0.256059i
$424$			88.1480i			0.207896i
$425$	−301.514	+	553.582i	−0.709445	+	1.30255i
$426$	−48.9888			−0.114997
$427$	387.397	+	387.397i	0.907254	+	0.907254i
$428$	185.591	−	185.591i	0.433624	−	0.433624i
$429$			16.8152i			0.0391962i
$430$	259.346	+	193.929i	0.603130	+	0.450997i
$431$	−555.836			−1.28964			−0.644822	−	0.764333i	$-0.723068\pi$
$431$	−555.836			−1.28964			−0.644822	+	0.764333i	$0.723068\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−153.478	+	153.478i	−0.354452	+	0.354452i	−0.861763	−	0.507311i	$-0.830639\pi$
$433$	−153.478	+	153.478i	−0.354452	+	0.354452i	0.507311	+	0.861763i	$0.330639\pi$
$434$		−	166.080i		−	0.382673i
$435$	12.5929	+	87.2557i	0.0289491	+	0.200588i
$436$	22.0674			0.0506134
$437$	40.5394	+	40.5394i	0.0927675	+	0.0927675i
$438$	−96.9693	+	96.9693i	−0.221391	+	0.221391i
$439$			399.370i			0.909727i	0.890561	+	0.454864i	$0.150312\pi$
$439$			399.370i			0.909727i	−0.890561	+	0.454864i	$0.849688\pi$
$440$	−13.4237	+	1.93732i	−0.0305084	+	0.00440301i
$441$	−16.7085			−0.0378877
$442$	255.248	+	255.248i	0.577484	+	0.577484i
$443$	99.1260	−	99.1260i	0.223761	−	0.223761i	−0.586319	−	0.810080i	$-0.699424\pi$
$443$	99.1260	−	99.1260i	0.223761	−	0.223761i	0.810080	+	0.586319i	$0.199424\pi$
$444$		−	174.617i		−	0.393282i
$445$	−201.951	+	270.075i	−0.453823	+	0.606909i
$446$	−108.364			−0.242969
$447$	−52.8713	−	52.8713i	−0.118280	−	0.118280i
$448$	−37.2797	+	37.2797i	−0.0832136	+	0.0832136i
$449$			88.4775i			0.197055i	0.995134	+	0.0985273i	$0.0314132\pi$
$449$			88.4775i			0.197055i	−0.995134	+	0.0985273i	$0.968587\pi$
$450$	−93.1460	−	50.7329i	−0.206991	−	0.112740i
$451$	67.5241			0.149721
$452$	−126.681	−	126.681i	−0.280267	−	0.280267i
$453$	−223.171	+	223.171i	−0.492651	+	0.492651i
$454$		−	360.176i		−	0.793339i
$455$	267.136	+	199.754i	0.587112	+	0.439019i
$456$	58.5644			0.128431
$457$	349.592	+	349.592i	0.764972	+	0.764972i	0.977217	−	0.212245i	$-0.0680774\pi$
$457$	349.592	+	349.592i	0.764972	+	0.764972i	−0.212245	+	0.977217i	$0.568077\pi$
$458$	−23.3678	+	23.3678i	−0.0510213	+	0.0510213i
$459$			131.020i			0.285446i
$460$	−6.85044	−	47.4665i	−0.0148923	−	0.103188i
$461$	−353.666			−0.767171			−0.383585	−	0.923505i	$-0.625311\pi$
$461$	−353.666			−0.767171			−0.383585	+	0.923505i	$0.625311\pi$
$462$	10.9469	+	10.9469i	0.0236946	+	0.0236946i
$463$	−466.196	+	466.196i	−1.00690	+	1.00690i	−0.00692730	+	0.999976i	$0.502205\pi$
$463$	−466.196	+	466.196i	−1.00690	+	1.00690i	−0.999976	+	0.00692730i	$0.997795\pi$
$464$			40.7192i			0.0877569i
$465$	152.742	−	22.0440i	0.328478	−	0.0474064i
$466$	−195.916			−0.420421
$467$	−259.814	−	259.814i	−0.556346	−	0.556346i	0.371919	−	0.928265i	$-0.378700\pi$
$467$	−259.814	−	259.814i	−0.556346	−	0.556346i	−0.928265	+	0.371919i	$0.878700\pi$
$468$	−42.9481	+	42.9481i	−0.0917695	+	0.0917695i
$469$		−	336.641i		−	0.717786i
$470$	−216.211	+	289.145i	−0.460024	+	0.615202i
$471$	−60.1356			−0.127677
$472$	14.9949	+	14.9949i	0.0317688	+	0.0317688i
$473$	31.0567	−	31.0567i	0.0656590	−	0.0656590i
$474$			64.0816i			0.135193i
$475$	286.665	−	84.5038i	0.603504	−	0.177903i
$476$	332.339			0.698192
$477$	66.1110	+	66.1110i	0.138598	+	0.138598i
$478$	138.405	−	138.405i	0.289550	−	0.289550i
$479$			397.780i			0.830439i	0.909721	+	0.415220i	$0.136295\pi$
$479$			397.780i			0.830439i	−0.909721	+	0.415220i	$0.863705\pi$
$480$	−39.2340	−	29.3376i	−0.0817374	−	0.0611200i
$481$	−510.275			−1.06086
$482$	−179.237	−	179.237i	−0.371861	−	0.371861i
$483$	−38.7086	+	38.7086i	−0.0801419	+	0.0801419i
$484$		−	240.161i		−	0.496199i
$485$	91.4847	+	633.895i	0.188628	+	1.30700i
$486$	−22.0454			−0.0453609
$487$	−297.105	−	297.105i	−0.610073	−	0.610073i	0.332892	−	0.942965i	$-0.391975\pi$
$487$	−297.105	−	297.105i	−0.610073	−	0.610073i	−0.942965	+	0.332892i	$0.891975\pi$
$488$	−166.266	+	166.266i	−0.340710	+	0.340710i
$489$		−	136.770i		−	0.279692i
$490$	−38.9785	+	5.62543i	−0.0795479	+	0.0114805i
$491$	−670.158			−1.36488			−0.682442	−	0.730940i	$-0.739082\pi$
$491$	−670.158			−1.36488			−0.682442	+	0.730940i	$0.739082\pi$
$492$	172.465	+	172.465i	0.350539	+	0.350539i
$493$	181.501	−	181.501i	0.368156	−	0.368156i
$494$		−	171.140i		−	0.346437i
$495$	−8.61476	+	11.5208i	−0.0174036	+	0.0232742i
$496$	71.2795			0.143709
$497$	93.1973	+	93.1973i	0.187520	+	0.187520i
$498$	−93.6685	+	93.6685i	−0.188089	+	0.188089i
$499$		−	76.3365i		−	0.152979i	−0.997070	−	0.0764895i	$-0.975629\pi$
$499$		−	76.3365i		−	0.152979i	0.997070	−	0.0764895i	$-0.0243712\pi$
$500$	−234.377	−	86.9920i	−0.468753	−	0.173984i
$501$	385.907			0.770274
$502$	−310.376	−	310.376i	−0.618279	−	0.618279i
$503$	−0.276837	+	0.276837i	−0.000550372	+	0.000550372i	−0.707382	−	0.706832i	$-0.750124\pi$
$503$	−0.276837	+	0.276837i	−0.000550372	+	0.000550372i	0.706832	+	0.707382i	$0.250124\pi$
$504$			55.9196i			0.110951i
$505$	−33.0419	−	24.7074i	−0.0654294	−	0.0489255i
$506$	−6.50447			−0.0128547
$507$	−81.4767	−	81.4767i	−0.160704	−	0.160704i
$508$	−230.343	+	230.343i	−0.453431	+	0.453431i
$509$			33.4655i			0.0657476i	0.999460	+	0.0328738i	$0.0104659\pi$
$509$			33.4655i			0.0657476i	−0.999460	+	0.0328738i	$0.989534\pi$
$510$	44.1117	+	305.649i	0.0864936	+	0.599312i
$511$	368.953			0.722021
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	43.9233	−	43.9233i	0.0856205	−	0.0856205i
$514$		−	438.886i		−	0.853863i
$515$	−574.450	+	82.9054i	−1.11544	+	0.160981i
$516$	158.646			0.307453
$517$	34.6252	+	34.6252i	0.0669732	+	0.0669732i
$518$	−332.195	+	332.195i	−0.641304	+	0.641304i
$519$			411.363i			0.792606i
$520$	−85.7319	+	114.651i	−0.164869	+	0.220484i
$521$	355.266			0.681892			0.340946	−	0.940083i	$-0.389253\pi$
$521$	355.266			0.681892			0.340946	+	0.940083i	$0.389253\pi$
$522$	30.5394	+	30.5394i	0.0585046	+	0.0585046i
$523$	313.483	−	313.483i	0.599394	−	0.599394i	−0.340757	−	0.940151i	$-0.610684\pi$
$523$	313.483	−	313.483i	0.599394	−	0.599394i	0.940151	+	0.340757i	$0.110684\pi$
$524$		−	119.727i		−	0.228487i
$525$	80.6875	+	273.718i	0.153690	+	0.521368i
$526$	607.460			1.15487
$527$	−317.719	−	317.719i	−0.602883	−	0.602883i
$528$	−4.69828	+	4.69828i	−0.00889825	+	0.00889825i
$529$		−	23.0000i		−	0.0434783i
$530$	176.486	+	131.969i	0.332992	+	0.248998i
$531$	22.4923			0.0423584
$532$	−111.414	−	111.414i	−0.209425	−	0.209425i
$533$	503.987	−	503.987i	0.945566	−	0.945566i
$534$			165.209i			0.309380i
$535$	−93.7275	−	649.436i	−0.175192	−	1.21390i
$536$	144.482			0.269557
$537$	290.941	+	290.941i	0.541790	+	0.541790i
$538$	−472.776	+	472.776i	−0.878765	+	0.878765i
$539$			5.34132i			0.00990969i
$540$	−51.4287	+	7.42226i	−0.0952383	+	0.0137449i
$541$	112.026			0.207071			0.103536	−	0.994626i	$-0.466984\pi$
$541$	112.026			0.207071			0.103536	+	0.994626i	$0.466984\pi$
$542$	−64.8046	−	64.8046i	−0.119566	−	0.119566i
$543$	−91.2302	+	91.2302i	−0.168011	+	0.168011i
$544$			142.636i			0.262199i
$545$	33.0378	−	44.1823i	0.0606198	−	0.0810684i
$546$	163.411			0.299287
$547$	−479.090	−	479.090i	−0.875850	−	0.875850i	0.117252	−	0.993102i	$-0.462591\pi$
$547$	−479.090	−	479.090i	−0.875850	−	0.875850i	−0.993102	+	0.117252i	$0.962591\pi$
$548$	368.887	−	368.887i	0.673151	−	0.673151i
$549$			249.399i			0.454279i
$550$	−16.2182	+	29.7766i	−0.0294876	+	0.0541393i
$551$	−121.694			−0.220859
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	121.910	−	121.910i	0.220452	−	0.220452i
$554$		−	321.611i		−	0.580526i
$555$	−349.610	−	261.424i	−0.629927	−	0.471035i
$556$	−36.4649			−0.0655844
$557$	41.0617	+	41.0617i	0.0737195	+	0.0737195i	0.743005	−	0.669286i	$-0.233400\pi$
$557$	41.0617	+	41.0617i	0.0737195	+	0.0737195i	−0.669286	+	0.743005i	$0.733400\pi$
$558$	53.4596	−	53.4596i	0.0958058	−	0.0958058i
$559$		−	463.603i		−	0.829343i
$560$	18.8270	+	130.452i	0.0336197	+	0.232950i
$561$	41.8840			0.0746595
$562$	163.698	+	163.698i	0.291277	+	0.291277i
$563$	302.703	−	302.703i	0.537661	−	0.537661i	−0.385180	−	0.922841i	$-0.625861\pi$
$563$	302.703	−	302.703i	0.537661	−	0.537661i	0.922841	+	0.385180i	$0.125861\pi$
$564$			176.874i			0.313607i
$565$	−443.291	+	63.9764i	−0.784586	+	0.113233i
$566$	−706.386			−1.24803
$567$	41.9397	+	41.9397i	0.0739677	+	0.0739677i
$568$	−39.9992	+	39.9992i	−0.0704211	+	0.0704211i
$569$		−	126.060i		−	0.221547i	−0.993846	−	0.110774i	$-0.964667\pi$
$569$		−	126.060i		−	0.221547i	0.993846	−	0.110774i	$-0.0353329\pi$
$570$	87.6785	−	117.255i	0.153822	−	0.205710i
$571$	−997.870			−1.74758			−0.873791	−	0.486301i	$-0.838346\pi$
$571$	−997.870			−1.74758			−0.873791	+	0.486301i	$0.838346\pi$
$572$	13.7295	+	13.7295i	0.0240027	+	0.0240027i
$573$	−295.187	+	295.187i	−0.515160	+	0.515160i
$574$		−	656.203i		−	1.14321i
$575$	−105.291	−	57.3479i	−0.183115	−	0.0997355i
$576$	−24.0000			−0.0416667
$577$	−97.7737	−	97.7737i	−0.169452	−	0.169452i	0.617287	−	0.786738i	$-0.288232\pi$
$577$	−97.7737	−	97.7737i	−0.169452	−	0.169452i	−0.786738	+	0.617287i	$0.788232\pi$
$578$	346.782	−	346.782i	0.599969	−	0.599969i
$579$		−	385.144i		−	0.665189i
$580$	81.5260	+	60.9619i	0.140562	+	0.105107i
$581$	356.394			0.613414
$582$	221.863	+	221.863i	0.381207	+	0.381207i
$583$	21.1342	−	21.1342i	0.0362507	−	0.0362507i
$584$			158.350i			0.271148i
$585$	21.6897	+	150.287i	0.0370764	+	0.256902i
$586$	187.630			0.320188
$587$	−222.168	−	222.168i	−0.378480	−	0.378480i	0.492074	−	0.870553i	$-0.336239\pi$
$587$	−222.168	−	222.168i	−0.378480	−	0.378480i	−0.870553	+	0.492074i	$0.836239\pi$
$588$	−13.6424	+	13.6424i	−0.0232014	+	0.0232014i
$589$			213.026i			0.361674i
$590$	52.4713	−	7.57273i	0.0889344	−	0.0128351i
$591$	−380.604			−0.644000
$592$	−142.574	−	142.574i	−0.240835	−	0.240835i
$593$	−724.293	+	724.293i	−1.22141	+	1.22141i	−0.254273	+	0.967133i	$0.581836\pi$
$593$	−724.293	+	724.293i	−1.22141	+	1.22141i	−0.967133	+	0.254273i	$0.918164\pi$
$594$			7.04741i			0.0118643i
$595$	497.555	−	665.393i	0.836226	−	1.11831i
$596$	−86.3384			−0.144863
$597$	206.031	+	206.031i	0.345110	+	0.345110i
$598$	−48.5481	+	48.5481i	−0.0811841	+	0.0811841i
$599$		−	511.979i		−	0.854723i	−0.904081	−	0.427361i	$-0.859443\pi$
$599$		−	511.979i		−	0.854723i	0.904081	−	0.427361i	$-0.140557\pi$
$600$	−117.477	+	34.6301i	−0.195794	+	0.0577168i
$601$	1102.28			1.83408			0.917039	−	0.398797i	$-0.130572\pi$
$601$	1102.28			1.83408			0.917039	+	0.398797i	$0.130572\pi$
$602$	−301.811	−	301.811i	−0.501347	−	0.501347i
$603$	108.362	−	108.362i	0.179705	−	0.179705i
$604$			364.437i			0.603372i
$605$	−480.837	−	359.551i	−0.794773	−	0.594300i
$606$	−20.2122			−0.0333535
$607$	−616.238	−	616.238i	−1.01522	−	1.01522i	−0.999882	−	0.0153372i	$-0.995118\pi$
$607$	−616.238	−	616.238i	−1.01522	−	1.01522i	−0.0153372	−	0.999882i	$-0.504882\pi$
$608$	47.8176	−	47.8176i	0.0786474	−	0.0786474i
$609$		−	116.198i		−	0.190801i
$610$	83.9680	+	581.812i	0.137652	+	0.953790i
$611$	516.871			0.845942
$612$	106.977	+	106.977i	0.174799	+	0.174799i
$613$	−373.603	+	373.603i	−0.609467	+	0.609467i	−0.942807	−	0.333340i	$-0.891824\pi$
$613$	−373.603	+	373.603i	−0.609467	+	0.609467i	0.333340	+	0.942807i	$0.391824\pi$
$614$		−	41.4675i		−	0.0675367i
$615$	603.504	−	87.0986i	0.981307	−	0.141624i
$616$	17.8762			0.0290198
$617$	460.974	+	460.974i	0.747121	+	0.747121i	0.973938	−	0.226816i	$-0.0728317\pi$
$617$	460.974	+	460.974i	0.747121	+	0.747121i	−0.226816	+	0.973938i	$0.572832\pi$
$618$	−201.057	+	201.057i	−0.325335	+	0.325335i
$619$			447.560i			0.723037i	0.932365	+	0.361518i	$0.117742\pi$
$619$			447.560i			0.723037i	−0.932365	+	0.361518i	$0.882258\pi$
$620$	106.715	−	142.712i	0.172120	−	0.230181i
$621$	−24.9199			−0.0401286
$622$	−530.664	−	530.664i	−0.853158	−	0.853158i
$623$	314.297	−	314.297i	0.504489	−	0.504489i
$624$			70.1340i			0.112394i
$625$	−525.063	+	339.019i	−0.840101	+	0.542430i
$626$	−529.487			−0.845826
$627$	−14.0413	−	14.0413i	−0.0223944	−	0.0223944i
$628$	−49.1005	+	49.1005i	−0.0781856	+	0.0781856i
$629$			1271.01i			2.02069i
$630$	111.959	+	83.7188i	0.177713	+	0.132887i
$631$	382.818			0.606685			0.303342	−	0.952882i	$-0.401897\pi$
$631$	382.818			0.606685			0.303342	+	0.952882i	$0.401897\pi$
$632$	52.3224	+	52.3224i	0.0827886	+	0.0827886i
$633$	476.902	−	476.902i	0.753400	−	0.753400i
$634$			149.769i			0.236228i
$635$	116.328	+	806.033i	0.183194	+	1.26934i
$636$	107.959			0.169747
$637$	39.8666	+	39.8666i	0.0625849	+	0.0625849i
$638$	9.76275	−	9.76275i	0.0153021	−	0.0153021i
$639$			59.9988i			0.0938948i
$640$	−55.9885	+	8.08034i	−0.0874820	+	0.0126255i
$641$	120.162			0.187460			0.0937302	−	0.995598i	$-0.470121\pi$
$641$	120.162			0.187460			0.0937302	+	0.995598i	$0.470121\pi$
$642$	−227.302	−	227.302i	−0.354053	−	0.354053i
$643$	211.922	−	211.922i	0.329583	−	0.329583i	−0.522845	−	0.852428i	$-0.675129\pi$
$643$	211.922	−	211.922i	0.329583	−	0.329583i	0.852428	+	0.522845i	$0.175129\pi$
$644$			63.2108i			0.0981534i
$645$	237.513	−	317.633i	0.368237	−	0.492454i
$646$	−426.282			−0.659880
$647$	−292.174	−	292.174i	−0.451583	−	0.451583i	0.444297	−	0.895880i	$-0.353454\pi$
$647$	−292.174	−	292.174i	−0.451583	−	0.451583i	−0.895880	+	0.444297i	$0.853454\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	7.19028i		−	0.0110790i
$650$	101.198	+	343.296i	0.155689	+	0.528148i
$651$	−203.406			−0.312451
$652$	−111.672	−	111.672i	−0.171276	−	0.171276i
$653$	537.675	−	537.675i	0.823391	−	0.823391i	−0.163201	−	0.986593i	$-0.552182\pi$
$653$	537.675	−	537.675i	0.823391	−	0.823391i	0.986593	+	0.163201i	$0.0521820\pi$
$654$		−	27.0270i		−	0.0413256i
$655$	−239.712	−	179.247i	−0.365973	−	0.273660i
$656$	281.635			0.429321
$657$	118.763	+	118.763i	0.180765	+	0.180765i
$658$	336.489	−	336.489i	0.511382	−	0.511382i
$659$			783.117i			1.18834i	0.804339	+	0.594170i	$0.202520\pi$
$659$			783.117i			1.18834i	−0.804339	+	0.594170i	$0.797480\pi$
$660$	2.37273	+	16.4406i	0.00359504	+	0.0249100i
$661$	752.684			1.13870			0.569352	−	0.822094i	$-0.307194\pi$
$661$	752.684			1.13870			0.569352	+	0.822094i	$0.307194\pi$
$662$	−512.969	−	512.969i	−0.774877	−	0.774877i
$663$	312.614	−	312.614i	0.471514	−	0.471514i
$664$			152.960i			0.230361i
$665$	−389.869	+	56.2665i	−0.586270	+	0.0846113i
$666$	−213.861			−0.321113
$667$	34.5214	+	34.5214i	0.0517562	+	0.0517562i
$668$	315.092	−	315.092i	0.471695	−	0.471695i
$669$			132.718i			0.198383i
$670$	216.309	−	289.276i	0.322849	−	0.431755i
$671$	79.7273			0.118819
$672$	45.6581	+	45.6581i	0.0679436	+	0.0679436i
$673$	652.940	−	652.940i	0.970193	−	0.970193i	−0.0293759	−	0.999568i	$-0.509352\pi$
$673$	652.940	−	652.940i	0.970193	−	0.970193i	0.999568	+	0.0293759i	$0.00935199\pi$
$674$		−	101.027i		−	0.149892i
$675$	−62.1349	+	114.080i	−0.0920517	+	0.169007i
$676$	−133.051			−0.196821
$677$	−824.188	−	824.188i	−1.21741	−	1.21741i	−0.968535	−	0.248876i	$-0.919939\pi$
$677$	−824.188	−	824.188i	−1.21741	−	1.21741i	−0.248876	−	0.968535i	$-0.580061\pi$
$678$	−155.152	+	155.152i	−0.228837	+	0.228837i
$679$		−	844.153i		−	1.24323i
$680$	285.579	+	213.544i	0.419969	+	0.314036i
$681$	−441.123			−0.647758
$682$	−17.0898	−	17.0898i	−0.0250584	−	0.0250584i
$683$	−335.080	+	335.080i	−0.490601	+	0.490601i	−0.908495	−	0.417895i	$-0.862768\pi$
$683$	−335.080	+	335.080i	−0.490601	+	0.490601i	0.417895	+	0.908495i	$0.362768\pi$
$684$		−	71.7265i		−	0.104863i
$685$	−186.295	−	1290.84i	−0.271964	−	1.88443i
$686$	508.584			0.741376
$687$	28.6196	+	28.6196i	0.0416588	+	0.0416588i
$688$	129.534	−	129.534i	0.188276	−	0.188276i
$689$		−	315.483i		−	0.457885i
$690$	−58.1344	+	8.39004i	−0.0842527	+	0.0121595i
$691$	−1243.37			−1.79938			−0.899690	−	0.436528i	$-0.856208\pi$
$691$	−1243.37			−1.79938			−0.899690	+	0.436528i	$0.856208\pi$
$692$	335.876	+	335.876i	0.485370	+	0.485370i
$693$	13.4072	−	13.4072i	0.0193465	−	0.0193465i
$694$		−	148.594i		−	0.214112i
$695$	−54.5927	+	73.0082i	−0.0785506	+	0.105048i
$696$	49.8706			0.0716532
$697$	−1255.35	−	1255.35i	−1.80108	−	1.80108i
$698$	−597.945	+	597.945i	−0.856654	+	0.856654i
$699$			239.947i			0.343272i
$700$	289.371	+	157.609i	0.413387	+	0.225156i
$701$	1034.82			1.47621			0.738103	−	0.674688i	$-0.235722\pi$
$701$	1034.82			1.47621			0.738103	+	0.674688i	$0.235722\pi$
$702$	52.6005	+	52.6005i	0.0749295	+	0.0749295i
$703$	426.098	−	426.098i	0.606113	−	0.606113i
$704$			7.67225i			0.0108981i
$705$	354.129	+	264.803i	0.502310	+	0.375608i
$706$	10.3716			0.0146907
$707$	38.4521	+	38.4521i	0.0543877	+	0.0543877i
$708$	18.3649	−	18.3649i	0.0259391	−	0.0259391i
$709$			1255.04i			1.77015i	0.465444	+	0.885077i	$0.345895\pi$
$709$			1255.04i			1.77015i	−0.465444	+	0.885077i	$0.654105\pi$
$710$	20.2004	+	139.968i	0.0284513	+	0.197138i
$711$	78.4836			0.110385
$712$	134.892	+	134.892i	0.189456	+	0.189456i
$713$	60.4301	−	60.4301i	0.0847548	−	0.0847548i
$714$		−	407.031i		−	0.570071i
$715$	48.0435	−	6.93371i	0.0671937	−	0.00969749i
$716$	475.105			0.663554
$717$	−169.511	−	169.511i	−0.236417	−	0.236417i
$718$	−173.219	+	173.219i	−0.241251	+	0.241251i
$719$		−	621.764i		−	0.864762i	−0.901691	−	0.432381i	$-0.857674\pi$
$719$		−	621.764i		−	0.864762i	0.901691	−	0.432381i	$-0.142326\pi$
$720$	−35.9311	+	48.0516i	−0.0499043	+	0.0667383i
$721$	764.990			1.06101
$722$	−218.092	−	218.092i	−0.302067	−	0.302067i
$723$	−219.520	+	219.520i	−0.303624	+	0.303624i
$724$			148.978i			0.205771i
$725$	244.110	−	71.9594i	0.336703	−	0.0992543i
$726$	−294.135			−0.405145
$727$	908.910	+	908.910i	1.25022	+	1.25022i	0.955621	+	0.294600i	$0.0951863\pi$
$727$	908.910	+	908.910i	1.25022	+	1.25022i	0.294600	+	0.955621i	$0.404814\pi$
$728$	133.424	−	133.424i	0.183275	−	0.183275i
$729$			27.0000i			0.0370370i
$730$	317.041	+	237.071i	0.434302	+	0.324754i
$731$	−1154.76			−1.57970
$732$	203.634	+	203.634i	0.278188	+	0.278188i
$733$	−425.796	+	425.796i	−0.580895	+	0.580895i	−0.935149	−	0.354254i	$-0.884735\pi$
$733$	−425.796	+	425.796i	−0.580895	+	0.580895i	0.354254	+	0.935149i	$0.384735\pi$
$734$		−	269.335i		−	0.366941i
$735$	6.88971	+	47.7387i	0.00937376	+	0.0649506i
$736$	−27.1293			−0.0368605
$737$	−34.6408	−	34.6408i	−0.0470025	−	0.0470025i
$738$	211.226	−	211.226i	0.286214	−	0.286214i
$739$		−	390.351i		−	0.528215i	−0.964493	−	0.264108i	$-0.914923\pi$
$739$		−	390.351i		−	0.528215i	0.964493	−	0.264108i	$-0.0850774\pi$
$740$	−498.907	+	72.0030i	−0.674199	+	0.0973014i
$741$	−209.603			−0.282865
$742$	−205.383	−	205.383i	−0.276797	−	0.276797i
$743$	935.528	−	935.528i	1.25912	−	1.25912i	0.307611	−	0.951512i	$-0.400471\pi$
$743$	935.528	−	935.528i	1.25912	−	1.25912i	0.951512	−	0.307611i	$-0.0995294\pi$
$744$		−	87.2992i		−	0.117338i
$745$	−129.260	+	172.863i	−0.173503	+	0.232030i
$746$	238.602			0.319841
$747$	114.720	+	114.720i	0.153574	+	0.153574i
$748$	34.1981	−	34.1981i	0.0457194	−	0.0457194i
$749$			864.848i			1.15467i
$750$	−106.543	+	287.052i	−0.142057	+	0.382735i
$751$	1021.05			1.35958			0.679791	−	0.733406i	$-0.262071\pi$
$751$	1021.05			1.35958			0.679791	+	0.733406i	$0.262071\pi$
$752$	144.417	+	144.417i	0.192044	+	0.192044i
$753$	−380.132	+	380.132i	−0.504823	+	0.504823i
$754$		−	145.735i		−	0.193282i
$755$	729.657	+	545.609i	0.966433	+	0.722660i
$756$	68.4872			0.0905915
$757$	262.137	+	262.137i	0.346284	+	0.346284i	0.858724	−	0.512439i	$-0.171258\pi$
$757$	262.137	+	262.137i	0.346284	+	0.346284i	−0.512439	+	0.858724i	$0.671258\pi$
$758$	−180.139	+	180.139i	−0.237650	+	0.237650i
$759$			7.96631i			0.0104958i
$760$	−24.1489	−	167.327i	−0.0317749	−	0.220167i
$761$	441.996			0.580809			0.290405	−	0.956904i	$-0.406210\pi$
$761$	441.996			0.580809			0.290405	+	0.956904i	$0.406210\pi$
$762$	282.111	+	282.111i	0.370224	+	0.370224i
$763$	−51.4167	+	51.4167i	−0.0673875	+	0.0673875i
$764$			482.038i			0.630940i
$765$	374.342	−	54.0256i	0.489336	−	0.0706217i
$766$	−407.130			−0.531502
$767$	−53.6669	−	53.6669i	−0.0699698	−	0.0699698i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			657.250i			0.854682i	0.904091	+	0.427341i	$0.140550\pi$
$769$			657.250i			0.854682i	−0.904091	+	0.427341i	$0.859450\pi$
$770$	26.7630	−	35.7908i	0.0347571	−	0.0464816i
$771$	−537.523			−0.697176
$772$	−314.469	−	314.469i	−0.407343	−	0.407343i
$773$	994.081	−	994.081i	1.28600	−	1.28600i	0.348810	−	0.937193i	$-0.386586\pi$
$773$	994.081	−	994.081i	1.28600	−	1.28600i	0.937193	−	0.348810i	$-0.113414\pi$
$774$		−	194.301i		−	0.251034i
$775$	−125.966	−	427.317i	−0.162537	−	0.551377i
$776$	362.300			0.466882
$777$	406.855	+	406.855i	0.523622	+	0.523622i
$778$	155.622	−	155.622i	0.200028	−	0.200028i
$779$			841.694i			1.08048i
$780$	140.419	+	105.000i	0.180024	+	0.134615i
$781$	19.1802			0.0245586
$782$	120.926	+	120.926i	0.154636	+	0.154636i
$783$	37.4030	−	37.4030i	0.0477688	−	0.0477688i
$784$			22.2780i			0.0284158i
$785$	24.7968	+	171.817i	0.0315883	+	0.218875i
$786$	−146.635			−0.186559
$787$	−54.9601	−	54.9601i	−0.0698350	−	0.0698350i	0.671327	−	0.741162i	$-0.265725\pi$
$787$	−54.9601	−	54.9601i	−0.0698350	−	0.0698350i	−0.741162	+	0.671327i	$0.765725\pi$
$788$	−310.762	+	310.762i	−0.394368	+	0.394368i
$789$		−	743.984i		−	0.942945i
$790$	183.091	−	26.4239i	0.231760	−	0.0334480i
$791$	590.327			0.746305
$792$	5.75419	+	5.75419i	0.00726539	+	0.00726539i
$793$	595.069	−	595.069i	0.750402	−	0.750402i
$794$		−	507.739i		−	0.639469i
$795$	161.628	−	216.150i	0.203306	−	0.271887i
$796$	336.447			0.422672
$797$	−929.747	−	929.747i	−1.16656	−	1.16656i	−0.983011	−	0.183548i	$-0.941242\pi$
$797$	−929.747	−	929.747i	−1.16656	−	1.16656i	−0.183548	−	0.983011i	$-0.558758\pi$
$798$	−136.454	+	136.454i	−0.170995	+	0.170995i
$799$		−	1287.44i		−	1.61132i
$800$	−67.6439	+	124.195i	−0.0845549	+	0.155243i
$801$	202.339			0.252607
$802$	85.8020	+	85.8020i	0.106985	+	0.106985i
$803$	37.9657	−	37.9657i	0.0472798	−	0.0472798i
$804$		−	176.954i		−	0.220092i
$805$	126.558	+	94.6347i	0.157214	+	0.117559i
$806$	−255.110			−0.316514
$807$	579.030	+	579.030i	0.717509	+	0.717509i
$808$	−16.5032	+	16.5032i	−0.0204247	+	0.0204247i
$809$		−	631.381i		−	0.780446i	−0.920720	−	0.390223i	$-0.872398\pi$
$809$		−	631.381i		−	0.780446i	0.920720	−	0.390223i	$-0.127602\pi$
$810$	9.09038	+	62.9870i	0.0112227	+	0.0777618i
$811$	−196.801			−0.242665			−0.121332	−	0.992612i	$-0.538717\pi$
$811$	−196.801			−0.242665			−0.121332	+	0.992612i	$0.538717\pi$
$812$	−94.8750	−	94.8750i	−0.116841	−	0.116841i
$813$	−79.3691	+	79.3691i	−0.0976250	+	0.0976250i
$814$			68.3666i			0.0839885i
$815$	−390.771	+	56.3967i	−0.479474	+	0.0691984i
$816$	174.693			0.214084
$817$	387.125	+	387.125i	0.473837	+	0.473837i
$818$	483.568	−	483.568i	0.591158	−	0.591158i
$819$		−	200.137i		−	0.244367i
$820$	421.643	−	563.875i	0.514199	−	0.687652i
$821$	−758.711			−0.924130			−0.462065	−	0.886846i	$-0.652891\pi$
$821$	−758.711			−0.924130			−0.462065	+	0.886846i	$0.652891\pi$
$822$	−451.792	−	451.792i	−0.549625	−	0.549625i
$823$	−459.985	+	459.985i	−0.558913	+	0.558913i	−0.928998	−	0.370085i	$-0.879329\pi$
$823$	−459.985	+	459.985i	−0.558913	+	0.558913i	0.370085	+	0.928998i	$0.379329\pi$
$824$			328.325i			0.398452i
$825$	36.4688	+	19.8631i	0.0442046	+	0.0240765i
$826$	−69.8756			−0.0845952
$827$	−992.512	−	992.512i	−1.20014	−	1.20014i	−0.974125	−	0.226010i	$-0.927432\pi$
$827$	−992.512	−	992.512i	−1.20014	−	1.20014i	−0.226010	−	0.974125i	$-0.572568\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$		−	923.007i		−	1.11340i	−0.830714	−	0.556699i	$-0.812068\pi$
$829$		−	923.007i		−	1.11340i	0.830714	−	0.556699i	$-0.187932\pi$
$830$	306.249	+	229.001i	0.368974	+	0.275905i
$831$	−393.892			−0.473998
$832$	57.2642	+	57.2642i	0.0688271	+	0.0688271i
$833$	99.3014	−	99.3014i	0.119209	−	0.119209i
$834$			44.6602i			0.0535494i
$835$	−159.128	−	1102.59i	−0.190573	−	1.32047i
$836$	−22.9293			−0.0274274
$837$	−65.4744	−	65.4744i	−0.0782251	−	0.0782251i
$838$	519.575	−	519.575i	0.620018	−	0.620018i
$839$			936.669i			1.11641i	0.829703	+	0.558206i	$0.188510\pi$
$839$			936.669i			1.11641i	−0.829703	+	0.558206i	$0.811490\pi$
$840$	159.771	−	23.0583i	0.190203	−	0.0274504i
$841$	737.372			0.876780
$842$	137.505	+	137.505i	0.163308	+	0.163308i
$843$	200.488	−	200.488i	0.237827	−	0.237827i
$844$		−	778.778i		−	0.922723i
$845$	−199.194	+	266.388i	−0.235733	+	0.315252i
$846$	216.626			0.256059
$847$	559.570	+	559.570i	0.660649	+	0.660649i
$848$	88.1480	−	88.1480i	0.103948	−	0.103948i
$849$			865.143i			1.01901i
$850$	855.096	−	252.068i	1.00600	−	0.296550i
$851$	−241.746			−0.284073
$852$	48.9888	+	48.9888i	0.0574986	+	0.0574986i
$853$	−430.920	+	430.920i	−0.505182	+	0.505182i	−0.913044	−	0.407862i	$-0.866275\pi$
$853$	−430.920	+	430.920i	−0.505182	+	0.505182i	0.407862	+	0.913044i	$0.366275\pi$
$854$		−	774.795i		−	0.907254i
$855$	−143.607	−	107.384i	−0.167962	−	0.125595i
$856$	−371.183			−0.433624
$857$	−45.4819	−	45.4819i	−0.0530710	−	0.0530710i	0.680073	−	0.733144i	$-0.261948\pi$
$857$	−45.4819	−	45.4819i	−0.0530710	−	0.0530710i	−0.733144	+	0.680073i	$0.761948\pi$
$858$	16.8152	−	16.8152i	0.0195981	−	0.0195981i
$859$			565.015i			0.657759i	0.944372	+	0.328880i	$0.106671\pi$
$859$			565.015i			0.657759i	−0.944372	+	0.328880i	$0.893329\pi$
$860$	−65.4173	−	453.275i	−0.0760666	−	0.527063i
$861$	−803.682			−0.933428
$862$	555.836	+	555.836i	0.644822	+	0.644822i
$863$	−397.354	+	397.354i	−0.460434	+	0.460434i	−0.898798	−	0.438364i	$-0.855558\pi$
$863$	−397.354	+	397.354i	−0.460434	+	0.460434i	0.438364	+	0.898798i	$0.355558\pi$
$864$			29.3939i			0.0340207i
$865$	1175.32	−	169.625i	1.35876	−	0.196098i
$866$	306.955			0.354452
$867$	−424.720	−	424.720i	−0.489873	−	0.489873i
$868$	−166.080	+	166.080i	−0.191336	+	0.191336i
$869$		−	25.0894i		−	0.0288716i
$870$	74.6628	−	99.8485i	0.0858193	−	0.114768i
$871$	−517.104			−0.593690
$872$	−22.0674	−	22.0674i	−0.0253067	−	0.0253067i
$873$	271.725	−	271.725i	0.311255	−	0.311255i
$874$		−	81.0788i		−	0.0927675i
$875$	748.783	−	343.403i	0.855752	−	0.392461i
$876$	193.939			0.221391
$877$	1177.94	+	1177.94i	1.34314	+	1.34314i	0.892910	+	0.450234i	$0.148660\pi$
$877$	1177.94	+	1177.94i	1.34314	+	1.34314i	0.450234	+	0.892910i	$0.351340\pi$
$878$	399.370	−	399.370i	0.454864	−	0.454864i
$879$		−	229.799i		−	0.261432i
$880$	15.3610	+	11.4864i	0.0174557	+	0.0130527i
$881$	−85.2417			−0.0967556			−0.0483778	−	0.998829i	$-0.515405\pi$
$881$	−85.2417			−0.0967556			−0.0483778	+	0.998829i	$0.515405\pi$
$882$	16.7085	+	16.7085i	0.0189439	+	0.0189439i
$883$	−897.394	+	897.394i	−1.01630	+	1.01630i	−0.0164359	+	0.999865i	$0.505232\pi$
$883$	−897.394	+	897.394i	−1.01630	+	1.01630i	−0.999865	+	0.0164359i	$0.994768\pi$
$884$		−	510.496i		−	0.577484i
$885$	−9.27467	−	64.2639i	−0.0104798	−	0.0726146i
$886$	−198.252			−0.223761
$887$	620.021	+	620.021i	0.699009	+	0.699009i	0.964197	−	0.265188i	$-0.0854339\pi$
$887$	620.021	+	620.021i	0.699009	+	0.699009i	−0.265188	+	0.964197i	$0.585434\pi$
$888$	−174.617	+	174.617i	−0.196641	+	0.196641i
$889$		−	1073.39i		−	1.20741i
$890$	472.026	−	68.1235i	0.530366	−	0.0765432i
$891$	8.63128			0.00968719
$892$	108.364	+	108.364i	0.121484	+	0.121484i
$893$	−431.606	+	431.606i	−0.483321	+	0.483321i
$894$			105.743i			0.118280i
$895$	711.293	−	951.231i	0.794741	−	1.06283i
$896$	74.5594			0.0832136
$897$	59.4590	+	59.4590i	0.0662865	+	0.0662865i
$898$	88.4775	−	88.4775i	0.0985273	−	0.0985273i
$899$			181.403i			0.201783i
$900$	42.4130	+	143.879i	0.0471256	+	0.159865i
$901$	−785.818			−0.872162
$902$	−67.5241	−	67.5241i	−0.0748604	−	0.0748604i
$903$	−369.642	+	369.642i	−0.409348	+	0.409348i
$904$			253.361i			0.280267i
$905$	298.277	+	223.040i	0.329588	+	0.246453i
$906$	446.342			0.492651
$907$	−254.687	−	254.687i	−0.280801	−	0.280801i	0.552627	−	0.833428i	$-0.313625\pi$
$907$	−254.687	−	254.687i	−0.280801	−	0.280801i	−0.833428	+	0.552627i	$0.813625\pi$
$908$	−360.176	+	360.176i	−0.396669	+	0.396669i
$909$			24.7548i			0.0272330i
$910$	−67.3822	−	466.889i	−0.0740463	−	0.513065i
$911$	−1570.85			−1.72431			−0.862157	−	0.506641i	$-0.830887\pi$
$911$	−1570.85			−1.72431			−0.862157	+	0.506641i	$0.830887\pi$
$912$	−58.5644	−	58.5644i	−0.0642154	−	0.0642154i
$913$	36.6734	−	36.6734i	0.0401680	−	0.0401680i
$914$		−	699.184i		−	0.764972i
$915$	712.571	−	102.839i	0.778767	−	0.112393i
$916$	46.7356			0.0510213
$917$	278.962	+	278.962i	0.304212	+	0.304212i
$918$	131.020	−	131.020i	0.142723	−	0.142723i
$919$			214.680i			0.233602i	0.993155	+	0.116801i	$0.0372639\pi$
$919$			214.680i			0.233602i	−0.993155	+	0.116801i	$0.962736\pi$
$920$	−40.6161	+	54.3170i	−0.0441479	+	0.0590402i
$921$	−50.7871			−0.0551434
$922$	353.666	+	353.666i	0.383585	+	0.383585i
$923$	143.157	−	143.157i	0.155100	−	0.155100i
$924$		−	21.8938i		−	0.0236946i
$925$	−602.767	+	1106.68i	−0.651640	+	1.19642i
$926$	932.392			1.00690
$927$	246.243	+	246.243i	0.265635	+	0.265635i
$928$	40.7192	−	40.7192i	0.0438785	−	0.0438785i
$929$			1273.76i			1.37110i	0.728024	+	0.685552i	$0.240439\pi$
$929$			1273.76i			1.37110i	−0.728024	+	0.685552i	$0.759561\pi$
$930$	−174.786	−	130.698i	−0.187942	−	0.140536i
$931$	−66.5801			−0.0715146
$932$	195.916	+	195.916i	0.210210	+	0.210210i
$933$	−649.929	+	649.929i	−0.696601	+	0.696601i
$934$			519.627i			0.556346i
$935$	−17.2708	−	119.669i	−0.0184714	−	0.127988i
$936$	85.8963			0.0917695
$937$	−1117.11	−	1117.11i	−1.19222	−	1.19222i	−0.976442	−	0.215781i	$-0.930770\pi$
$937$	−1117.11	−	1117.11i	−1.19222	−	1.19222i	−0.215781	−	0.976442i	$-0.569230\pi$
$938$	−336.641	+	336.641i	−0.358893	+	0.358893i
$939$			648.487i			0.690614i
$940$	505.356	−	72.9337i	0.537613	−	0.0775891i
$941$	354.052			0.376251			0.188126	−	0.982145i	$-0.439759\pi$
$941$	354.052			0.376251			0.188126	+	0.982145i	$0.439759\pi$
$942$	60.1356	+	60.1356i	0.0638383	+	0.0638383i
$943$	238.767	−	238.767i	0.253200	−	0.253200i
$944$		−	29.9898i		−	0.0317688i
$945$	102.534	−	137.122i	0.108502	−	0.145102i
$946$	−62.1135			−0.0656590
$947$	455.752	+	455.752i	0.481259	+	0.481259i	0.905533	−	0.424275i	$-0.139471\pi$
$947$	455.752	+	455.752i	0.481259	+	0.481259i	−0.424275	+	0.905533i	$0.639471\pi$
$948$	64.0816	−	64.0816i	0.0675966	−	0.0675966i
$949$		−	566.737i		−	0.597194i
$950$	−371.168	−	202.161i	−0.390704	−	0.212801i
$951$	183.428			0.192879
$952$	−332.339	−	332.339i	−0.349096	−	0.349096i
$953$	−1174.02	+	1174.02i	−1.23192	+	1.23192i	−0.268697	+	0.963225i	$0.586593\pi$
$953$	−1174.02	+	1174.02i	−1.23192	+	1.23192i	−0.963225	+	0.268697i	$0.913407\pi$
$954$		−	132.222i		−	0.138598i
$955$	965.112	+	721.673i	1.01059	+	0.755678i
$956$	−276.810			−0.289550
$957$	−11.9569	−	11.9569i	−0.0124941	−	0.0124941i
$958$	397.780	−	397.780i	0.415220	−	0.415220i
$959$			1719.00i			1.79249i
$960$	9.89635	+	68.5716i	0.0103087	+	0.0714287i
$961$	−643.452			−0.669565
$962$	510.275	+	510.275i	0.530431	+	0.530431i
$963$	−278.387	+	278.387i	−0.289083	+	0.289083i
$964$			358.474i			0.371861i
$965$	−1100.41	+	158.814i	−1.14033	+	0.164574i
$966$	77.4171			0.0801419
$967$	−963.133	−	963.133i	−0.996001	−	0.996001i	0.00399096	−	0.999992i	$-0.498730\pi$
$967$	−963.133	−	963.133i	−0.996001	−	0.996001i	−0.999992	+	0.00399096i	$0.998730\pi$
$968$	−240.161	+	240.161i	−0.248100	+	0.248100i
$969$			522.087i			0.538790i
$970$	542.410	−	725.380i	0.559186	−	0.747814i
$971$	607.964			0.626122			0.313061	−	0.949733i	$-0.398646\pi$
$971$	607.964			0.626122			0.313061	+	0.949733i	$0.398646\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	84.9626	−	84.9626i	0.0873202	−	0.0873202i
$974$			594.211i			0.610073i
$975$	420.450	−	123.941i	0.431231	−	0.127119i
$976$	332.533			0.340710
$977$	−473.021	−	473.021i	−0.484156	−	0.484156i	0.422300	−	0.906456i	$-0.361223\pi$
$977$	−473.021	−	473.021i	−0.484156	−	0.484156i	−0.906456	+	0.422300i	$0.861223\pi$
$978$	−136.770	+	136.770i	−0.139846	+	0.139846i
$979$		−	64.6830i		−	0.0660705i
$980$	44.6039	+	33.3530i	0.0455142	+	0.0340337i
$981$	−33.1011			−0.0337422
$982$	670.158	+	670.158i	0.682442	+	0.682442i
$983$	1085.16	−	1085.16i	1.10393	−	1.10393i	0.110000	−	0.993932i	$-0.464915\pi$
$983$	1085.16	−	1085.16i	1.10393	−	1.10393i	0.993932	−	0.110000i	$-0.0350850\pi$
$984$		−	344.931i		−	0.350539i
$985$	156.941	+	1087.44i	0.159331	+	1.10400i
$986$	−363.002			−0.368156
$987$	−412.114	−	412.114i	−0.417542	−	0.417542i
$988$	−171.140	+	171.140i	−0.173218	+	0.173218i
$989$		−	219.635i		−	0.222078i
$990$	20.1355	−	2.90599i	0.0203389	−	0.00293534i
$991$	−927.344			−0.935766			−0.467883	−	0.883790i	$-0.654983\pi$
$991$	−927.344			−0.935766			−0.467883	+	0.883790i	$0.654983\pi$
$992$	−71.2795	−	71.2795i	−0.0718543	−	0.0718543i
$993$	−628.256	+	628.256i	−0.632685	+	0.632685i
$994$		−	186.395i		−	0.187520i
$995$	503.705	−	673.618i	0.506236	−	0.677003i
$996$	187.337			0.188089
$997$	843.561	+	843.561i	0.846099	+	0.846099i	0.989644	−	0.143545i	$-0.0458501\pi$
$997$	843.561	+	843.561i	0.846099	+	0.846099i	−0.143545	+	0.989644i	$0.545850\pi$
$998$	−76.3365	+	76.3365i	−0.0764895	+	0.0764895i
$999$			261.926i			0.262188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.9	✓	48
5.3	odd	4	inner	690.3.k.b.553.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.9	✓	48	1.1	even	1	trivial
690.3.k.b.553.9	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.00430 + 2.99426i) q^{5} +2.44949 q^{6} +(-4.65996 - 4.65996i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-1.01004 - 6.99856i) q^{10} -0.959032 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.15802 + 7.15802i) q^{13} +9.31993i q^{14} +(-8.57145 + 1.23704i) q^{15} -4.00000 q^{16} +(17.8295 + 17.8295i) q^{17} +(-3.00000 + 3.00000i) q^{18} -11.9544i q^{19} +(-5.98852 + 8.00860i) q^{20} +11.4145 q^{21} +(0.959032 + 0.959032i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(7.06884 + 23.9798i) q^{25} +14.3160 q^{26} +(3.67423 + 3.67423i) q^{27} +(9.31993 - 9.31993i) q^{28} -10.1798i q^{29} +(9.80849 + 7.33440i) q^{30} -17.8199 q^{31} +(4.00000 + 4.00000i) q^{32} +(1.17457 - 1.17457i) q^{33} -35.6590i q^{34} +(-4.70676 - 32.6130i) q^{35} +6.00000 q^{36} +(35.6436 + 35.6436i) q^{37} +(-11.9544 + 11.9544i) q^{38} -17.5335i q^{39} +(13.9971 - 2.02008i) q^{40} -70.4086 q^{41} +(-11.4145 - 11.4145i) q^{42} +(-32.3834 + 32.3834i) q^{43} -1.91806i q^{44} +(8.98277 - 12.0129i) q^{45} +6.78233 q^{46} +(-36.1043 - 36.1043i) q^{47} +(4.89898 - 4.89898i) q^{48} -5.56950i q^{49} +(16.9110 - 31.0487i) q^{50} -43.6732 q^{51} +(-14.3160 - 14.3160i) q^{52} +(-22.0370 + 22.0370i) q^{53} -7.34847i q^{54} +(-3.84025 - 2.87159i) q^{55} -18.6399 q^{56} +(14.6411 + 14.6411i) q^{57} +(-10.1798 + 10.1798i) q^{58} +7.49744i q^{59} +(-2.47409 - 17.1429i) q^{60} -83.1331 q^{61} +(17.8199 + 17.8199i) q^{62} +(-13.9799 + 13.9799i) q^{63} -8.00000i q^{64} +(-50.0958 + 7.22990i) q^{65} -2.34914 q^{66} +(36.1206 + 36.1206i) q^{67} +(-35.6590 + 35.6590i) q^{68} -8.30662i q^{69} +(-27.9063 + 37.3198i) q^{70} -19.9996 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-39.5875 + 39.5875i) q^{73} -71.2871i q^{74} +(-38.0267 - 20.7116i) q^{75} +23.9088 q^{76} +(4.46905 + 4.46905i) q^{77} +(-17.5335 + 17.5335i) q^{78} +26.1612i q^{79} +(-16.0172 - 11.9770i) q^{80} -9.00000 q^{81} +(70.4086 + 70.4086i) q^{82} +(-38.2400 + 38.2400i) q^{83} +22.8291i q^{84} +(18.0085 + 124.781i) q^{85} +64.7668 q^{86} +(12.4677 + 12.4677i) q^{87} +(-1.91806 + 1.91806i) q^{88} +67.4462i q^{89} +(-20.9957 + 3.03013i) q^{90} +66.7122 q^{91} +(-6.78233 - 6.78233i) q^{92} +(21.8248 - 21.8248i) q^{93} +72.2086i q^{94} +(35.7946 - 47.8690i) q^{95} -9.79796 q^{96} +(90.5751 + 90.5751i) q^{97} +(-5.56950 + 5.56950i) q^{98} +2.87709i 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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