LMFDB - Embedded newform 23.3.d.a.15.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,3,Mod(5,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, 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:	$0.626704608029$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			15.3
Character	$\chi$	$=$	23.15
Dual form			23.3.d.a.20.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.496456 - 3.45293i) q^{2} +(1.53764 + 3.36695i) q^{3} +(-7.83827 - 2.30152i) q^{4} +(-4.84192 + 4.19555i) q^{5} +(12.3892 - 3.63780i) q^{6} +(3.55260 - 5.52795i) q^{7} +(-6.04175 + 13.2296i) q^{8} +(-3.07830 + 3.55255i) q^{9} +O(q^{10})$	\(q+(0.496456 - 3.45293i) q^{2} +(1.53764 + 3.36695i) q^{3} +(-7.83827 - 2.30152i) q^{4} +(-4.84192 + 4.19555i) q^{5} +(12.3892 - 3.63780i) q^{6} +(3.55260 - 5.52795i) q^{7} +(-6.04175 + 13.2296i) q^{8} +(-3.07830 + 3.55255i) q^{9} +(12.0831 + 18.8017i) q^{10} +(-7.17202 + 1.03118i) q^{11} +(-4.30328 - 29.9300i) q^{12} +(9.96529 - 6.40430i) q^{13} +(-17.3239 - 15.0112i) q^{14} +(-21.5713 - 9.85130i) q^{15} +(15.1920 + 9.76328i) q^{16} +(1.04520 + 3.55963i) q^{17} +(10.7384 + 12.3928i) q^{18} +(-3.34899 + 11.4056i) q^{19} +(47.6084 - 21.7420i) q^{20} +(24.0749 + 3.46145i) q^{21} +25.2764i q^{22} +(-21.0132 + 9.35129i) q^{23} -53.8334 q^{24} +(2.28371 - 15.8835i) q^{25} +(-17.1663 - 37.5889i) q^{26} +(15.2690 + 4.48339i) q^{27} +(-40.5689 + 35.1532i) q^{28} +(44.1267 - 12.9568i) q^{29} +(-44.7250 + 69.5935i) q^{30} +(11.7785 - 25.7914i) q^{31} +(3.15715 - 3.64354i) q^{32} +(-14.4999 - 22.5623i) q^{33} +(12.8100 - 1.84181i) q^{34} +(5.99139 + 41.6710i) q^{35} +(32.3048 - 20.7610i) q^{36} +(1.87208 + 1.62217i) q^{37} +(37.7202 + 17.2262i) q^{38} +(36.8860 + 23.7052i) q^{39} +(-26.2517 - 89.4052i) q^{40} +(-26.9760 - 31.1319i) q^{41} +(23.9043 - 81.4106i) q^{42} +(-44.3056 + 20.2337i) q^{43} +(58.5895 + 8.42389i) q^{44} -30.1163i q^{45} +(21.8572 + 77.1995i) q^{46} -36.5497 q^{47} +(-9.51280 + 66.1630i) q^{48} +(2.41806 + 5.29481i) q^{49} +(-53.7109 - 15.7710i) q^{50} +(-10.3780 + 8.99256i) q^{51} +(-92.8503 + 27.2633i) q^{52} +(3.67297 - 5.71526i) q^{53} +(23.0612 - 50.4971i) q^{54} +(30.4000 - 35.0835i) q^{55} +(51.6686 + 80.3979i) q^{56} +(-43.5517 + 6.26179i) q^{57} +(-22.8318 - 158.799i) q^{58} +(-42.6033 + 27.3795i) q^{59} +(146.409 + 126.864i) q^{60} +(88.9981 + 40.6441i) q^{61} +(-83.2084 - 53.4748i) q^{62} +(8.70234 + 29.6374i) q^{63} +(36.2903 + 41.8812i) q^{64} +(-21.3816 + 72.8190i) q^{65} +(-85.1044 + 38.8659i) q^{66} +(-28.0411 - 4.03170i) q^{67} -30.3069i q^{68} +(-63.7959 - 56.3715i) q^{69} +146.861 q^{70} +(4.93922 - 34.3530i) q^{71} +(-28.4004 - 62.1882i) q^{72} +(-7.15116 - 2.09977i) q^{73} +(6.53063 - 5.65882i) q^{74} +(56.9906 - 16.7340i) q^{75} +(52.5006 - 81.6925i) q^{76} +(-19.7790 + 43.3099i) q^{77} +(100.165 - 115.596i) q^{78} +(-71.3186 - 110.974i) q^{79} +(-114.521 + 16.4656i) q^{80} +(14.4036 + 100.180i) q^{81} +(-120.889 + 77.6904i) q^{82} +(16.5296 + 14.3229i) q^{83} +(-180.739 - 82.5408i) q^{84} +(-19.9954 - 12.8503i) q^{85} +(47.8697 + 163.029i) q^{86} +(111.476 + 128.650i) q^{87} +(29.6895 - 101.113i) q^{88} +(145.339 - 66.3743i) q^{89} +(-103.989 - 14.9514i) q^{90} -77.8395i q^{91} +(186.229 - 24.9356i) q^{92} +104.950 q^{93} +(-18.1453 + 126.203i) q^{94} +(-31.6373 - 69.2760i) q^{95} +(17.1222 + 5.02752i) q^{96} +(-81.7615 + 70.8467i) q^{97} +(19.4830 - 5.72074i) q^{98} +(18.4143 - 28.6532i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) $ 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{17}{22}\right)$

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 $

$2$	0.496456	−	3.45293i	0.248228	−	1.72646i	−0.360218	−	0.932868i	$-0.617298\pi$
$2$	0.496456	−	3.45293i	0.248228	−	1.72646i	0.608446	−	0.793595i	$-0.291793\pi$
$3$	1.53764	+	3.36695i	0.512545	+	1.12232i	0.972185	+	0.234212i	$0.0752511\pi$
$3$	1.53764	+	3.36695i	0.512545	+	1.12232i	−0.459640	+	0.888105i	$0.652022\pi$
$4$	−7.83827	−	2.30152i	−1.95957	−	0.575381i
$5$	−4.84192	+	4.19555i	−0.968385	+	0.839110i	−0.987001	−	0.160717i	$-0.948620\pi$
$5$	−4.84192	+	4.19555i	−0.968385	+	0.839110i	0.0186158	+	0.999827i	$0.494074\pi$
$6$	12.3892	−	3.63780i	2.06487	−	0.606300i
$7$	3.55260	−	5.52795i	0.507514	−	0.789707i	−0.489074	−	0.872242i	$-0.662665\pi$
$7$	3.55260	−	5.52795i	0.507514	−	0.789707i	0.996588	+	0.0825351i	$0.0263016\pi$
$8$	−6.04175	+	13.2296i	−0.755219	+	1.65370i
$9$	−3.07830	+	3.55255i	−0.342033	+	0.394727i
$10$	12.0831	+	18.8017i	1.20831	+	1.88017i
$11$	−7.17202	+	1.03118i	−0.652002	+	0.0937437i	−0.460375	−	0.887724i	$-0.652285\pi$
$11$	−7.17202	+	1.03118i	−0.652002	+	0.0937437i	−0.191626	+	0.981468i	$0.561376\pi$
$12$	−4.30328	−	29.9300i	−0.358607	−	2.49416i
$13$	9.96529	−	6.40430i	0.766561	−	0.492639i	−0.0979879	−	0.995188i	$-0.531241\pi$
$13$	9.96529	−	6.40430i	0.766561	−	0.492639i	0.864549	+	0.502549i	$0.167604\pi$
$14$	−17.3239	−	15.0112i	−1.23742	−	1.07223i
$15$	−21.5713	−	9.85130i	−1.43809	−	0.656753i
$16$	15.1920	+	9.76328i	0.949498	+	0.610205i
$17$	1.04520	+	3.55963i	0.0614825	+	0.209390i	0.984505	−	0.175355i	$-0.0561074\pi$
$17$	1.04520	+	3.55963i	0.0614825	+	0.209390i	−0.923023	+	0.384745i	$0.874289\pi$
$18$	10.7384	+	12.3928i	0.596580	+	0.688490i
$19$	−3.34899	+	11.4056i	−0.176263	+	0.600296i	0.823207	+	0.567741i	$0.192183\pi$
$19$	−3.34899	+	11.4056i	−0.176263	+	0.600296i	−0.999470	+	0.0325549i	$0.989636\pi$
$20$	47.6084	−	21.7420i	2.38042	−	1.08710i
$21$	24.0749	+	3.46145i	1.14643	+	0.164831i
$22$			25.2764i			1.14893i
$23$	−21.0132	+	9.35129i	−0.913616	+	0.406578i
$23$	−21.0132	+	9.35129i	−0.913616	+	0.406578i
$24$	−53.8334			−2.24306
$25$	2.28371	−	15.8835i	0.0913483	−	0.635342i
$26$	−17.1663	−	37.5889i	−0.660241	−	1.44573i
$27$	15.2690	+	4.48339i	0.565520	+	0.166052i
$28$	−40.5689	+	35.1532i	−1.44889	+	1.25547i
$29$	44.1267	−	12.9568i	1.52161	−	0.446785i	0.589140	−	0.808031i	$-0.299466\pi$
$29$	44.1267	−	12.9568i	1.52161	−	0.446785i	0.932471	+	0.361245i	$0.117648\pi$
$30$	−44.7250	+	69.5935i	−1.49083	+	2.31978i
$31$	11.7785	−	25.7914i	0.379953	−	0.831981i	−0.618962	−	0.785421i	$-0.712447\pi$
$31$	11.7785	−	25.7914i	0.379953	−	0.831981i	0.998915	−	0.0465606i	$-0.0148261\pi$
$32$	3.15715	−	3.64354i	0.0986608	−	0.113861i
$33$	−14.4999	−	22.5623i	−0.439390	−	0.683705i
$34$	12.8100	−	1.84181i	0.376766	−	0.0541708i
$35$	5.99139	+	41.6710i	0.171183	+	1.19060i
$36$	32.3048	−	20.7610i	0.897355	−	0.576695i
$37$	1.87208	+	1.62217i	0.0505968	+	0.0438424i	0.679792	−	0.733405i	$-0.262070\pi$
$37$	1.87208	+	1.62217i	0.0505968	+	0.0438424i	−0.629195	+	0.777247i	$0.716615\pi$
$38$	37.7202	+	17.2262i	0.992636	+	0.453322i
$39$	36.8860	+	23.7052i	0.945794	+	0.607825i
$40$	−26.2517	−	89.4052i	−0.656293	−	2.23513i
$41$	−26.9760	−	31.1319i	−0.657951	−	0.759316i	0.324490	−	0.945889i	$-0.394807\pi$
$41$	−26.9760	−	31.1319i	−0.657951	−	0.759316i	−0.982441	+	0.186573i	$0.940262\pi$
$42$	23.9043	−	81.4106i	0.569150	−	1.93835i
$43$	−44.3056	+	20.2337i	−1.03036	+	0.470551i	−0.857548	−	0.514404i	$-0.828013\pi$
$43$	−44.3056	+	20.2337i	−1.03036	+	0.470551i	−0.172814	+	0.984954i	$0.555286\pi$
$44$	58.5895	+	8.42389i	1.33158	+	0.191452i
$45$		−	30.1163i		−	0.669251i
$46$	21.8572	+	77.1995i	0.475156	+	1.67825i
$47$	−36.5497			−0.777653			−0.388826	−	0.921311i	$-0.627119\pi$
$47$	−36.5497			−0.777653			−0.388826	+	0.921311i	$0.627119\pi$
$48$	−9.51280	+	66.1630i	−0.198183	+	1.37840i
$49$	2.41806	+	5.29481i	0.0493481	+	0.108057i
$50$	−53.7109	−	15.7710i	−1.07422	−	0.315419i
$51$	−10.3780	+	8.99256i	−0.203490	+	0.176325i
$52$	−92.8503	+	27.2633i	−1.78558	+	0.524294i
$53$	3.67297	−	5.71526i	0.0693014	−	0.107835i	−0.804873	−	0.593447i	$-0.797767\pi$
$53$	3.67297	−	5.71526i	0.0693014	−	0.107835i	0.874175	+	0.485612i	$0.161403\pi$
$54$	23.0612	−	50.4971i	0.427060	−	0.935131i
$55$	30.4000	−	35.0835i	0.552727	−	0.637881i
$56$	51.6686	+	80.3979i	0.922654	+	1.43568i
$57$	−43.5517	+	6.26179i	−0.764065	+	0.109856i
$58$	−22.8318	−	158.799i	−0.393652	−	2.73791i
$59$	−42.6033	+	27.3795i	−0.722091	+	0.464059i	−0.849364	−	0.527808i	$-0.823014\pi$
$59$	−42.6033	+	27.3795i	−0.722091	+	0.464059i	0.127273	+	0.991868i	$0.459378\pi$
$60$	146.409	+	126.864i	2.44015	+	2.11440i
$61$	88.9981	+	40.6441i	1.45898	+	0.666296i	0.977650	−	0.210241i	$-0.0674247\pi$
$61$	88.9981	+	40.6441i	1.45898	+	0.666296i	0.481335	+	0.876537i	$0.340152\pi$
$62$	−83.2084	−	53.4748i	−1.34207	−	0.862496i
$63$	8.70234	+	29.6374i	0.138132	+	0.470436i
$64$	36.2903	+	41.8812i	0.567036	+	0.654394i
$65$	−21.3816	+	72.8190i	−0.328948	+	1.12029i
$66$	−85.1044	+	38.8659i	−1.28946	+	0.588877i
$67$	−28.0411	−	4.03170i	−0.418524	−	0.0601747i	−0.0701639	−	0.997535i	$-0.522352\pi$
$67$	−28.0411	−	4.03170i	−0.418524	−	0.0601747i	−0.348360	+	0.937361i	$0.613261\pi$
$68$		−	30.3069i		−	0.445690i
$69$	−63.7959	−	56.3715i	−0.924579	−	0.816978i
$70$	146.861			2.09802
$71$	4.93922	−	34.3530i	0.0695664	−	0.483845i	−0.925019	−	0.379921i	$-0.875951\pi$
$71$	4.93922	−	34.3530i	0.0695664	−	0.483845i	0.994585	−	0.103924i	$-0.0331398\pi$
$72$	−28.4004	−	62.1882i	−0.394450	−	0.863725i
$73$	−7.15116	−	2.09977i	−0.0979611	−	0.0287640i	0.232385	−	0.972624i	$-0.425347\pi$
$73$	−7.15116	−	2.09977i	−0.0979611	−	0.0287640i	−0.330346	+	0.943860i	$0.607165\pi$
$74$	6.53063	−	5.65882i	0.0882518	−	0.0764706i
$75$	56.9906	−	16.7340i	0.759875	−	0.223119i
$76$	52.5006	−	81.6925i	0.690797	−	1.07490i
$77$	−19.7790	+	43.3099i	−0.256870	+	0.562467i
$78$	100.165	−	115.596i	1.28416	−	1.48200i
$79$	−71.3186	−	110.974i	−0.902768	−	1.40473i	−0.914405	−	0.404802i	$-0.867341\pi$
$79$	−71.3186	−	110.974i	−0.902768	−	1.40473i	0.0116368	−	0.999932i	$-0.496296\pi$
$80$	−114.521	+	16.4656i	−1.43151	+	0.205820i
$81$	14.4036	+	100.180i	0.177823	+	1.23678i
$82$	−120.889	+	77.6904i	−1.47425	+	0.947444i
$83$	16.5296	+	14.3229i	0.199151	+	0.172566i	0.748727	−	0.662878i	$-0.230665\pi$
$83$	16.5296	+	14.3229i	0.199151	+	0.172566i	−0.549576	+	0.835444i	$0.685211\pi$
$84$	−180.739	−	82.5408i	−2.15166	−	0.982629i
$85$	−19.9954	−	12.8503i	−0.235240	−	0.151180i
$86$	47.8697	+	163.029i	0.556624	+	1.89569i
$87$	111.476	+	128.650i	1.28133	+	1.47873i
$88$	29.6895	−	101.113i	0.337380	−	1.14901i
$89$	145.339	−	66.3743i	1.63303	−	0.745778i	0.633419	−	0.773809i	$-0.281651\pi$
$89$	145.339	−	66.3743i	1.63303	−	0.745778i	0.999607	+	0.0280305i	$0.00892355\pi$
$90$	−103.989	−	14.9514i	−1.15544	−	0.166127i
$91$		−	77.8395i		−	0.855380i
$92$	186.229	−	24.9356i	2.02423	−	0.271039i
$93$	104.950			1.12849
$94$	−18.1453	+	126.203i	−0.193035	+	1.34259i
$95$	−31.6373	−	69.2760i	−0.333024	−	0.729221i
$96$	17.1222	+	5.02752i	0.178356	+	0.0523700i
$97$	−81.7615	+	70.8467i	−0.842902	+	0.730378i	−0.965031	−	0.262136i	$-0.915573\pi$
$97$	−81.7615	+	70.8467i	−0.842902	+	0.730378i	0.122129	+	0.992514i	$0.461028\pi$
$98$	19.4830	−	5.72074i	0.198807	−	0.0583749i
$99$	18.4143	−	28.6532i	0.186003	−	0.289426i
$100$	−54.4566	+	119.243i	−0.544566	+	1.19243i
$101$	−33.9396	+	39.1684i	−0.336036	+	0.387806i	−0.898469	−	0.439036i	$-0.855320\pi$
$101$	−33.9396	+	39.1684i	−0.336036	+	0.387806i	0.562433	+	0.826843i	$0.309865\pi$
$102$	25.8985	+	40.2988i	0.253906	+	0.395086i
$103$	25.2972	−	3.63718i	0.245604	−	0.0353125i	−0.0184135	−	0.999830i	$-0.505862\pi$
$103$	25.2972	−	3.63718i	0.245604	−	0.0353125i	0.264017	+	0.964518i	$0.414952\pi$
$104$	24.5185	+	170.530i	0.235755	+	1.63971i
$105$	−131.092	+	84.2476i	−1.24849	+	0.802358i
$106$	−17.9109	−	15.5199i	−0.168971	−	0.146414i
$107$	−20.7936	−	9.49610i	−0.194332	−	0.0887486i	0.315872	−	0.948802i	$-0.397703\pi$
$107$	−20.7936	−	9.49610i	−0.194332	−	0.0887486i	−0.510204	+	0.860053i	$0.670430\pi$
$108$	−109.364	−	70.2841i	−1.01263	−	0.650778i
$109$	−42.3006	−	144.062i	−0.388078	−	1.32167i	−0.889684	−	0.456577i	$-0.849075\pi$
$109$	−42.3006	−	144.062i	−0.388078	−	1.32167i	0.501605	−	0.865097i	$-0.332743\pi$
$110$	−106.048	−	122.386i	−0.964076	−	1.11260i
$111$	−2.58318	+	8.79751i	−0.0232719	+	0.0792568i
$112$	107.942	−	49.2954i	0.963767	−	0.440138i
$113$	36.1891	+	5.20321i	0.320258	+	0.0460461i	0.300569	−	0.953760i	$-0.402823\pi$
$113$	36.1891	+	5.20321i	0.320258	+	0.0460461i	0.0196886	+	0.999806i	$0.493733\pi$
$114$			153.490i			1.34640i
$115$	62.5104	−	133.440i	0.543569	−	1.16035i
$116$	−375.697			−3.23877
$117$	−7.92456	+	55.1165i	−0.0677313	+	0.471081i
$118$	73.3888	+	160.699i	0.621939	+	1.36186i
$119$	23.3906	+	6.86811i	0.196560	+	0.0577152i
$120$	260.657	−	225.861i	2.17214	−	1.88217i
$121$	−65.7241	+	19.2983i	−0.543175	+	0.159490i
$122$	184.525	−	287.126i	1.51250	−	2.35349i
$123$	63.3405	−	138.696i	0.514964	−	1.12761i
$124$	−151.683	+	175.051i	−1.22325	+	1.41171i
$125$	−31.0116	−	48.2549i	−0.248092	−	0.386039i
$126$	106.656	−	15.3349i	0.846478	−	0.121705i
$127$	14.9631	+	104.071i	0.117820	+	0.819453i	0.959948	+	0.280177i	$0.0903931\pi$
$127$	14.9631	+	104.071i	0.117820	+	0.819453i	−0.842129	+	0.539276i	$0.818698\pi$
$128$	178.852	−	114.941i	1.39728	−	0.897980i
$129$	−136.252	−	118.063i	−1.05621	−	0.915215i
$130$	240.824	+	109.981i	1.85249	+	0.846004i
$131$	159.497	+	102.503i	1.21754	+	0.782463i	0.981904	−	0.189379i	$-0.0606476\pi$
$131$	159.497	+	102.503i	1.21754	+	0.782463i	0.235632	+	0.971842i	$0.424284\pi$
$132$	61.7264	+	210.221i	0.467624	+	1.59258i
$133$	51.1521	+	59.0327i	0.384602	+	0.443855i
$134$	−27.8423	+	94.8223i	−0.207779	+	0.707629i
$135$	−92.7418	+	42.3538i	−0.686976	+	0.313732i
$136$	−53.4073	−	7.67881i	−0.392701	−	0.0564619i
$137$		−	187.566i		−	1.36910i	−0.728968	−	0.684548i	$-0.760000\pi$
$137$		−	187.566i		−	1.36910i	0.728968	−	0.684548i	$-0.240000\pi$
$138$	−226.319	+	192.297i	−1.63999	+	1.39345i
$139$	6.61672			0.0476023			0.0238012	−	0.999717i	$-0.492423\pi$
$139$	6.61672			0.0476023			0.0238012	+	0.999717i	$0.492423\pi$
$140$	48.9447	−	340.418i	0.349605	−	2.43156i
$141$	−56.2001	−	123.061i	−0.398582	−	0.872773i
$142$	−116.166	−	34.1095i	−0.818073	−	0.240208i
$143$	−64.8673	+	56.2078i	−0.453617	+	0.393062i
$144$	−81.4499	+	23.9159i	−0.565624	+	0.166082i
$145$	−159.297	+	247.872i	−1.09860	+	1.70946i
$146$	−10.8006	+	23.6500i	−0.0739766	+	0.161986i
$147$	−14.1093	+	16.2830i	−0.0959814	+	0.110768i
$148$	−10.9404	−	17.0236i	−0.0739217	−	0.115024i
$149$	183.434	−	26.3738i	1.23110	−	0.177005i	0.504100	−	0.863645i	$-0.331824\pi$
$149$	183.434	−	26.3738i	1.23110	−	0.177005i	0.726998	+	0.686640i	$0.240915\pi$
$150$	−29.4878	−	205.092i	−0.196585	−	1.36728i
$151$	120.747	−	77.5995i	0.799651	−	0.513904i	−0.0758512	−	0.997119i	$-0.524167\pi$
$151$	120.747	−	77.5995i	0.799651	−	0.513904i	0.875502	+	0.483215i	$0.160531\pi$
$152$	−130.658	−	113.216i	−0.859592	−	0.744841i
$153$	−15.8632	−	7.24448i	−0.103681	−	0.0473495i
$154$	139.727	+	89.7968i	0.907316	+	0.583096i
$155$	51.1784	+	174.298i	0.330183	+	1.12450i
$156$	−234.564	−	270.701i	−1.50362	−	1.73527i
$157$	−46.2159	+	157.397i	−0.294369	+	1.00253i	0.670960	+	0.741493i	$0.265882\pi$
$157$	−46.2159	+	157.397i	−0.294369	+	1.00253i	−0.965329	+	0.261035i	$0.915936\pi$
$158$	−418.592	+	191.164i	−2.64931	+	1.20990i
$159$	24.8907	+	3.57874i	0.156545	+	0.0225078i
$160$			30.8877i			0.193048i
$161$	−22.9579	+	149.381i	−0.142596	+	0.927833i
$162$	353.063			2.17940
$163$	−12.1270	+	84.3451i	−0.0743987	+	0.517455i	0.918210	+	0.396094i	$0.129635\pi$
$163$	−12.1270	+	84.3451i	−0.0743987	+	0.517455i	−0.992609	+	0.121360i	$0.961274\pi$
$164$	139.794	+	306.106i	0.852403	+	1.86650i
$165$	164.868	+	48.4097i	0.999203	+	0.293392i
$166$	57.6623	−	49.9647i	0.347363	−	0.300992i
$167$	141.642	−	41.5899i	0.848156	−	0.249041i	0.171357	−	0.985209i	$-0.445185\pi$
$167$	141.642	−	41.5899i	0.848156	−	0.249041i	0.676799	+	0.736168i	$0.263367\pi$
$168$	−191.248	+	297.588i	−1.13838	+	1.77136i
$169$	−11.9132	+	26.0863i	−0.0704924	+	0.154357i
$170$	−54.2979	+	62.6631i	−0.319399	+	0.368606i
$171$	−30.2098	−	47.0074i	−0.176666	−	0.274897i
$172$	393.847	−	56.6267i	2.28981	−	0.329225i
$173$	−8.50160	−	59.1300i	−0.0491422	−	0.341792i	−0.999528	−	0.0307182i	$-0.990221\pi$
$173$	−8.50160	−	59.1300i	−0.0491422	−	0.341792i	0.950386	−	0.311073i	$-0.100689\pi$
$174$	499.561	−	321.048i	2.87104	−	1.84511i
$175$	−79.6903	−	69.0520i	−0.455373	−	0.394583i
$176$	−119.025	−	54.3568i	−0.676277	−	0.308845i
$177$	−157.694	−	101.344i	−0.890926	−	0.572563i
$178$	−157.031	−	534.798i	−0.882196	−	3.00448i
$179$	−139.755	−	161.286i	−0.780753	−	0.901037i	0.216411	−	0.976302i	$-0.430565\pi$
$179$	−139.755	−	161.286i	−0.780753	−	0.901037i	−0.997164	+	0.0752656i	$0.976020\pi$
$180$	−69.3134	+	236.060i	−0.385074	+	1.31144i
$181$	190.628	−	87.0570i	1.05319	−	0.480978i	0.187872	−	0.982194i	$-0.439841\pi$
$181$	190.628	−	87.0570i	1.05319	−	0.480978i	0.865322	+	0.501216i	$0.167114\pi$
$182$	−268.774	−	38.6439i	−1.47678	−	0.212329i
$183$			362.148i			1.97895i
$184$	3.24270	−	334.494i	0.0176234	−	1.81790i
$185$	−15.8704			−0.0857857
$186$	52.1029	−	362.383i	0.280123	−	1.94830i
$187$	−11.1668	−	24.4519i	−0.0597157	−	0.130759i
$188$	286.486	+	84.1199i	1.52386	+	0.447446i
$189$	79.0287	−	68.4788i	0.418141	−	0.362322i
$190$	−254.912	+	74.8488i	−1.34164	+	0.393941i
$191$	−104.881	+	163.198i	−0.549114	+	0.854437i	−0.999258	−	0.0385184i	$-0.987736\pi$
$191$	−104.881	+	163.198i	−0.549114	+	0.854437i	0.450144	+	0.892956i	$0.351373\pi$
$192$	−85.2109	+	186.586i	−0.443807	+	0.971801i
$193$	−23.0726	+	26.6272i	−0.119547	+	0.137965i	−0.812368	−	0.583145i	$-0.801822\pi$
$193$	−23.0726	+	26.6272i	−0.119547	+	0.137965i	0.692821	+	0.721109i	$0.256367\pi$
$194$	204.038	+	317.489i	1.05174	+	1.63654i
$195$	−278.055	+	39.9783i	−1.42592	+	0.205017i
$196$	−6.76726	−	47.0673i	−0.0345268	−	0.240139i
$197$	−187.891	+	120.750i	−0.953761	+	0.612945i	−0.922265	−	0.386559i	$-0.873664\pi$
$197$	−187.891	+	120.750i	−0.953761	+	0.612945i	−0.0314960	+	0.999504i	$0.510027\pi$
$198$	−89.7955	−	77.8083i	−0.453513	−	0.392971i
$199$	−239.223	−	109.250i	−1.20213	−	0.548993i	−0.289260	−	0.957251i	$-0.593409\pi$
$199$	−239.223	−	109.250i	−1.20213	−	0.548993i	−0.912867	+	0.408258i	$0.866136\pi$
$200$	196.335	+	126.177i	0.981676	+	0.630885i
$201$	−29.5425	−	100.612i	−0.146977	−	0.500559i
$202$	118.396	+	136.637i	0.586120	+	0.676418i
$203$	85.1401	−	289.961i	0.419409	−	1.42838i
$204$	102.042	−	46.6010i	0.500205	−	0.228436i
$205$	261.231	+	37.5594i	1.27430	+	0.183216i
$206$		−	89.1550i		−	0.432791i
$207$	31.4639	−	103.436i	0.152000	−	0.499692i
$208$	213.919			1.02846
$209$	12.2578	−	85.2548i	0.0586497	−	0.407918i
$210$	225.819	+	494.475i	1.07533	+	2.35465i
$211$	−80.0740	−	23.5118i	−0.379497	−	0.111431i	0.0864198	−	0.996259i	$-0.472457\pi$
$211$	−80.0740	−	23.5118i	−0.379497	−	0.111431i	−0.465917	+	0.884828i	$0.654276\pi$
$212$	−41.9435	+	36.3443i	−0.197847	+	0.171435i
$213$	123.260	−	36.1923i	0.578684	−	0.169917i
$214$	−43.1124	+	67.0843i	−0.201460	+	0.313478i
$215$	129.633	−	283.856i	0.602943	−	1.32026i
$216$	−151.565	+	174.916i	−0.701691	+	0.809794i
$217$	−100.729	−	156.738i	−0.464190	−	0.722294i
$218$	−518.438	+	74.5401i	−2.37815	+	0.341927i
$219$	−3.92605	−	27.3063i	−0.0179272	−	0.124686i
$220$	−319.029	+	205.027i	−1.45013	+	0.931942i
$221$	33.2127	+	28.7790i	0.150284	+	0.130222i
$222$	29.0947	+	13.2871i	0.131057	+	0.0598519i
$223$	219.110	+	140.813i	0.982554	+	0.631449i	0.930151	−	0.367177i	$-0.119676\pi$
$223$	219.110	+	140.813i	0.982554	+	0.631449i	0.0524029	+	0.998626i	$0.483312\pi$
$224$	−8.92524	−	30.3966i	−0.0398448	−	0.135699i
$225$	49.3971	+	57.0072i	0.219543	+	0.253366i
$226$	35.9326	−	122.375i	0.158994	−	0.541483i
$227$	84.8462	−	38.7480i	0.373772	−	0.170696i	−0.219667	−	0.975575i	$-0.570497\pi$
$227$	84.8462	−	38.7480i	0.373772	−	0.170696i	0.593439	+	0.804879i	$0.297770\pi$
$228$	355.782	+	51.1537i	1.56045	+	0.224358i
$229$			409.074i			1.78635i	0.449711	+	0.893174i	$0.351527\pi$
$229$			409.074i			1.78635i	−0.449711	+	0.893174i	$0.648473\pi$
$230$	−429.725	−	282.091i	−1.86837	−	1.22648i
$231$	−176.235			−0.762923
$232$	−95.1899	+	662.060i	−0.410301	+	2.85371i
$233$	56.9265	+	124.652i	0.244320	+	0.534986i	0.991572	−	0.129554i	$-0.0413547\pi$
$233$	56.9265	+	124.652i	0.244320	+	0.534986i	−0.747252	+	0.664540i	$0.768627\pi$
$234$	186.379	+	54.7258i	0.796492	+	0.233871i
$235$	176.971	−	153.346i	0.753067	−	0.652536i
$236$	396.951	−	116.555i	1.68200	−	0.493878i
$237$	263.982	−	410.764i	1.11385	−	1.73318i
$238$	35.3275	−	77.3565i	0.148435	−	0.325027i
$239$	−153.270	+	176.883i	−0.641296	+	0.740095i	−0.979603	−	0.200941i	$-0.935600\pi$
$239$	−153.270	+	176.883i	−0.641296	+	0.740095i	0.338307	+	0.941036i	$0.390146\pi$
$240$	−231.530	−	360.268i	−0.964708	−	1.50112i
$241$	60.8442	−	8.74808i	0.252466	−	0.0362991i	−0.0149199	−	0.999889i	$-0.504749\pi$
$241$	60.8442	−	8.74808i	0.252466	−	0.0362991i	0.267386	+	0.963590i	$0.413840\pi$
$242$	34.0067	+	236.521i	0.140523	+	0.977361i
$243$	−194.665	+	125.104i	−0.801093	+	0.514831i
$244$	−604.047	−	523.410i	−2.47560	−	2.14512i
$245$	−33.9227	−	15.4920i	−0.138460	−	0.0632325i
$246$	−447.463	−	287.567i	−1.81895	−	1.16897i
$247$	39.6714	+	135.108i	0.160613	+	0.546997i
$248$	270.047	+	311.651i	1.08890	+	1.25666i
$249$	−22.8082	+	77.6777i	−0.0915993	+	0.311959i
$250$	−182.017	+	83.1242i	−0.728067	+	0.332497i
$251$	−18.4454	−	2.65204i	−0.0734875	−	0.0105659i	0.105473	−	0.994422i	$-0.466364\pi$
$251$	−18.4454	−	2.65204i	−0.0734875	−	0.0105659i	−0.178961	+	0.983856i	$0.557273\pi$
$252$		−	252.335i		−	1.00133i
$253$	141.064	−	88.7360i	0.557565	−	0.350735i
$254$	366.777			1.44400
$255$	12.5206	−	87.0826i	0.0491003	−	0.341500i
$256$	−216.008	−	472.992i	−0.843783	−	1.84763i
$257$	9.83039	+	2.88646i	0.0382505	+	0.0112314i	0.300802	−	0.953687i	$-0.402746\pi$
$257$	9.83039	+	2.88646i	0.0382505	+	0.0112314i	−0.262551	+	0.964918i	$0.584564\pi$
$258$	−475.305	+	411.854i	−1.84227	+	1.59633i
$259$	15.6180	−	4.58586i	0.0603012	−	0.0177060i
$260$	335.189	−	521.565i	1.28919	−	2.00602i
$261$	−89.8057	+	196.647i	−0.344083	+	0.753437i
$262$	433.118	−	499.844i	1.65312	−	1.90780i
$263$	39.6976	+	61.7706i	0.150941	+	0.234869i	0.908487	−	0.417913i	$-0.137238\pi$
$263$	39.6976	+	61.7706i	0.150941	+	0.234869i	−0.757546	+	0.652782i	$0.773602\pi$
$264$	386.094	−	55.5120i	1.46248	−	0.210273i
$265$	6.19440	+	43.0830i	0.0233751	+	0.162577i
$266$	229.230	−	147.317i	0.861768	−	0.553825i
$267$	446.958	+	387.291i	1.67400	+	1.45053i
$268$	210.515	+	96.1388i	0.785502	+	0.358727i
$269$	−221.236	−	142.180i	−0.822438	−	0.528549i	0.0604285	−	0.998173i	$-0.480753\pi$
$269$	−221.236	−	142.180i	−0.822438	−	0.528549i	−0.882867	+	0.469624i	$0.844390\pi$
$270$	100.202	+	341.258i	0.371119	+	1.26392i
$271$	−55.3534	−	63.8813i	−0.204256	−	0.235724i	0.644374	−	0.764710i	$-0.277118\pi$
$271$	−55.3534	−	63.8813i	−0.204256	−	0.235724i	−0.848631	+	0.528986i	$0.822572\pi$
$272$	−18.8750	+	64.2824i	−0.0693934	+	0.236332i
$273$	262.082	−	119.689i	0.960007	−	0.438421i
$274$	−647.652	−	93.1184i	−2.36370	−	0.339848i
$275$			116.272i			0.422807i
$276$	370.309	+	588.683i	1.34170	+	2.13291i
$277$	−240.484			−0.868174			−0.434087	−	0.900871i	$-0.642929\pi$
$277$	−240.484			−0.868174			−0.434087	+	0.900871i	$0.642929\pi$
$278$	3.28491	−	22.8471i	0.0118162	−	0.0821837i
$279$	55.3673	+	121.238i	0.198449	+	0.434543i
$280$	−587.489	−	172.502i	−2.09818	−	0.616080i
$281$	269.677	−	233.676i	0.959703	−	0.831588i	−0.0260714	−	0.999660i	$-0.508300\pi$
$281$	269.677	−	233.676i	0.959703	−	0.831588i	0.985775	+	0.168072i	$0.0537543\pi$
$282$	−452.822	+	132.960i	−1.60575	+	0.471491i
$283$	−62.9396	+	97.9360i	−0.222402	+	0.346064i	−0.934467	−	0.356049i	$-0.884123\pi$
$283$	−62.9396	+	97.9360i	−0.222402	+	0.346064i	0.712066	+	0.702113i	$0.247760\pi$
$284$	−117.779	+	257.900i	−0.414715	+	0.908100i
$285$	184.602	−	213.043i	0.647728	−	0.747518i
$286$	161.878	+	251.887i	0.566006	+	0.880722i
$287$	−267.931	+	38.5226i	−0.933556	+	0.134225i
$288$	3.22521	+	22.4318i	0.0111986	+	0.0778883i
$289$	231.544	−	148.804i	0.801189	−	0.514893i
$290$	776.799	+	673.100i	2.67862	+	2.32103i
$291$	−364.257	−	166.351i	−1.25174	−	0.571651i
$292$	51.2200	+	32.9171i	0.175411	+	0.112730i
$293$	−96.0233	−	327.025i	−0.327725	−	1.11613i	−0.944370	−	0.328886i	$-0.893327\pi$
$293$	−96.0233	−	327.025i	−0.327725	−	1.11613i	0.616645	−	0.787241i	$-0.288491\pi$
$294$	49.2193	+	56.8021i	0.167412	+	0.193204i
$295$	91.4100	−	311.314i	0.309865	−	1.05530i
$296$	−32.7713	+	14.9661i	−0.110714	+	0.0505613i
$297$	−114.133	−	16.4098i	−0.384286	−	0.0552520i
$298$		−	646.476i		−	2.16938i
$299$	−149.514	+	227.763i	−0.500047	+	0.761749i
$300$	−485.221			−1.61740
$301$	−45.5491	+	316.801i	−0.151326	+	1.05250i
$302$	−208.000	−	455.456i	−0.688741	−	1.50813i
$303$	−184.065	−	54.0464i	−0.607475	−	0.178371i
$304$	−162.234	+	140.577i	−0.533665	+	0.462423i
$305$	−601.446	+	176.601i	−1.97195	+	0.579018i
$306$	−32.8900	+	51.1779i	−0.107484	+	0.167248i
$307$	−84.5985	+	185.245i	−0.275565	+	0.603404i	−0.995924	−	0.0901982i	$-0.971250\pi$
$307$	−84.5985	+	185.245i	−0.275565	+	0.603404i	0.720359	+	0.693602i	$0.243977\pi$
$308$	254.712	−	293.953i	0.826986	−	0.954393i
$309$	51.1441	+	79.5817i	0.165515	+	0.257546i
$310$	627.245	−	90.1842i	2.02337	−	0.290917i
$311$	27.6915	+	192.599i	0.0890403	+	0.619289i	0.984662	+	0.174473i	$0.0558220\pi$
$311$	27.6915	+	192.599i	0.0890403	+	0.619289i	−0.895622	+	0.444816i	$0.853269\pi$
$312$	−536.466	+	344.766i	−1.71944	+	1.10502i
$313$	34.0669	+	29.5191i	0.108840	+	0.0943104i	0.707581	−	0.706632i	$-0.249787\pi$
$313$	34.0669	+	29.5191i	0.108840	+	0.0943104i	−0.598741	+	0.800943i	$0.704332\pi$
$314$	520.536	+	237.721i	1.65776	+	0.757073i
$315$	−166.481	−	106.991i	−0.528513	−	0.339654i
$316$	303.605	+	1033.99i	0.960777	+	3.27210i
$317$	−192.408	−	222.050i	−0.606965	−	0.700475i	0.366213	−	0.930531i	$-0.380654\pi$
$317$	−192.408	−	222.050i	−0.606965	−	0.700475i	−0.973177	+	0.230057i	$0.926109\pi$
$318$	24.7143	−	84.1691i	0.0777178	−	0.264683i
$319$	−303.117	+	138.429i	−0.950210	+	0.433946i
$320$	−351.430	−	50.5280i	−1.09822	−	0.157900i
$321$		−	84.6125i		−	0.263590i
$322$	504.405	+	153.433i	1.56647	+	0.476501i
$323$	−44.1002			−0.136533
$324$	117.666	−	818.384i	0.363166	−	2.52588i
$325$	−78.9652	−	172.910i	−0.242970	−	0.532030i
$326$	285.217	+	83.7473i	0.874899	+	0.256893i
$327$	420.009	−	363.939i	1.28443	−	1.11296i
$328$	574.845	−	168.790i	1.75258	−	0.514603i
$329$	−129.846	+	202.045i	−0.394670	+	0.614118i
$330$	249.005	−	545.245i	0.754561	−	1.65226i
$331$	−239.310	+	276.179i	−0.722991	+	0.834376i	−0.991663	−	0.128855i	$-0.958870\pi$
$331$	−239.310	+	276.179i	−0.722991	+	0.834376i	0.268672	+	0.963232i	$0.413415\pi$
$332$	−96.5985	−	150.310i	−0.290959	−	0.452742i
$333$	−11.5256	+	1.65714i	−0.0346115	+	0.00497639i
$334$	−73.2877	−	509.727i	−0.219424	−	1.52613i
$335$	152.688	−	98.1267i	0.455785	−	0.292915i
$336$	331.951	+	287.637i	0.987948	+	0.856062i
$337$	407.361	+	186.035i	1.20879	+	0.552034i	0.914851	−	0.403792i	$-0.132308\pi$
$337$	407.361	+	186.035i	1.20879	+	0.552034i	0.293934	+	0.955826i	$0.405035\pi$
$338$	84.1597	+	54.0862i	0.248993	+	0.160018i
$339$	38.1267	+	129.848i	0.112468	+	0.383031i
$340$	127.154	+	146.744i	0.373983	+	0.431599i
$341$	−57.8803	+	197.122i	−0.169737	+	0.578071i
$342$	−177.311	+	80.9752i	−0.518453	+	0.236769i
$343$	356.566	+	51.2664i	1.03955	+	0.149465i
$344$		−	708.392i		−	2.05928i
$345$	545.404	+	5.28734i	1.58088	+	0.0153256i
$346$	−208.392			−0.602289
$347$	−77.1632	+	536.682i	−0.222372	+	1.54663i	0.506655	+	0.862149i	$0.330882\pi$
$347$	−77.1632	+	536.682i	−0.222372	+	1.54663i	−0.729027	+	0.684485i	$0.760027\pi$
$348$	−577.686	−	1264.96i	−1.66002	−	3.63493i
$349$	−142.584	−	41.8664i	−0.408550	−	0.119961i	0.0709988	−	0.997476i	$-0.477381\pi$
$349$	−142.584	−	41.8664i	−0.408550	−	0.119961i	−0.479548	+	0.877515i	$0.659200\pi$
$350$	−277.994	+	240.884i	−0.794270	+	0.688239i
$351$	180.873	−	53.1092i	0.515309	−	0.151308i
$352$	−18.8860	+	29.3871i	−0.0536533	+	0.0834862i
$353$	79.5426	−	174.174i	0.225333	−	0.493411i	−0.762872	−	0.646550i	$-0.776211\pi$
$353$	79.5426	−	174.174i	0.225333	−	0.493411i	0.988205	+	0.153140i	$0.0489384\pi$
$354$	−428.221	+	494.193i	−1.20966	+	1.39603i
$355$	120.214	+	187.057i	0.338632	+	0.526922i
$356$	−1291.97	+	185.757i	−3.62913	+	0.521790i
$357$	12.8417	+	89.3158i	0.0359711	+	0.250184i
$358$	−626.290	+	402.492i	−1.74941	+	1.12428i
$359$	−173.079	−	149.974i	−0.482115	−	0.417755i	0.379598	−	0.925152i	$-0.376062\pi$
$359$	−173.079	−	149.974i	−0.482115	−	0.417755i	−0.861713	+	0.507397i	$0.830608\pi$
$360$	398.427	+	181.955i	1.10674	+	0.505431i
$361$	184.820	+	118.777i	0.511967	+	0.329021i
$362$	−205.963	−	701.445i	−0.568958	−	1.93769i
$363$	−166.036	−	191.616i	−0.457401	−	0.527868i
$364$	−179.149	+	610.127i	−0.492169	+	1.67617i
$365$	43.4350	−	19.8361i	0.119000	−	0.0543455i
$366$	1250.47	+	179.791i	3.41659	+	0.491231i
$367$		−	577.034i		−	1.57230i	−0.618035	−	0.786150i	$-0.712071\pi$
$367$		−	577.034i		−	1.57230i	0.618035	−	0.786150i	$-0.287929\pi$
$368$	−410.531	−	63.0932i	−1.11557	−	0.171449i
$369$	193.638			0.524763
$370$	−7.87893	+	54.7992i	−0.0212944	+	0.148106i
$371$	−18.5451	−	40.6080i	−0.0499867	−	0.109456i
$372$	−822.623	−	241.544i	−2.21135	−	0.649311i
$373$	−382.796	+	331.694i	−1.02626	+	0.889261i	−0.993908	−	0.110215i	$-0.964846\pi$
$373$	−382.796	+	331.694i	−1.02626	+	0.889261i	−0.0323544	+	0.999476i	$0.510301\pi$
$374$	−89.9746	+	26.4189i	−0.240574	+	0.0706389i
$375$	114.788	−	178.613i	0.306100	−	0.476301i
$376$	220.824	−	483.537i	0.587298	−	1.28600i
$377$	356.757	−	411.719i	0.946304	−	1.09209i
$378$	−197.218	−	306.877i	−0.521741	−	0.811844i
$379$	357.918	−	51.4608i	0.944373	−	0.135780i	0.347109	−	0.937825i	$-0.387163\pi$
$379$	357.918	−	51.4608i	0.944373	−	0.135780i	0.597264	+	0.802044i	$0.296254\pi$
$380$	88.5413	+	615.818i	0.233003	+	1.62057i
$381$	−327.393	+	210.403i	−0.859299	+	0.552238i
$382$	511.441	+	443.166i	1.33885	+	1.16012i
$383$	−155.246	−	70.8986i	−0.405343	−	0.185114i	0.202301	−	0.979323i	$-0.435158\pi$
$383$	−155.246	−	70.8986i	−0.405343	−	0.185114i	−0.607644	+	0.794210i	$0.707885\pi$
$384$	662.012	+	425.450i	1.72399	+	1.10794i
$385$	−85.9407	−	292.687i	−0.223223	−	0.760226i
$386$	80.4871	+	92.8871i	0.208516	+	0.240640i
$387$	64.5047	−	219.683i	0.166679	−	0.567656i
$388$	803.923	−	367.140i	2.07197	−	0.946236i
$389$	48.4762	+	6.96982i	0.124617	+	0.0179173i	0.204341	−	0.978900i	$-0.434495\pi$
$389$	48.4762	+	6.96982i	0.124617	+	0.0179173i	−0.0797239	+	0.996817i	$0.525404\pi$
$390$			979.952i			2.51270i
$391$	−55.2501	−	65.0252i	−0.141305	−	0.166305i
$392$	−84.6574			−0.215963
$393$	−99.8729	+	694.631i	−0.254130	+	1.76751i
$394$	323.662	+	708.721i	0.821477	+	1.79878i
$395$	810.916	+	238.107i	2.05295	+	0.602801i
$396$	−210.282	+	182.211i	−0.531016	+	0.460128i
$397$	−557.473	+	163.689i	−1.40421	+	0.412314i	−0.894129	−	0.447810i	$-0.852204\pi$
$397$	−557.473	+	163.689i	−1.40421	+	0.412314i	−0.510084	+	0.860124i	$0.670386\pi$
$398$	−495.995	+	771.783i	−1.24622	+	1.93915i
$399$	−120.107	+	262.997i	−0.301020	+	0.659141i
$400$	189.770	−	219.006i	0.474424	−	0.547514i
$401$	101.141	+	157.378i	0.252221	+	0.392463i	0.944157	−	0.329495i	$-0.106879\pi$
$401$	101.141	+	157.378i	0.252221	+	0.392463i	−0.691937	+	0.721958i	$0.743242\pi$
$402$	−362.074	+	52.0583i	−0.900681	+	0.129498i
$403$	−47.7994	−	332.452i	−0.118609	−	0.824944i
$404$	356.175	−	228.900i	0.881621	−	0.566584i
$405$	−490.050	−	424.631i	−1.21000	−	1.04847i
$406$	−958.944	−	437.935i	−2.36193	−	1.07866i
$407$	−15.0993	−	9.70376i	−0.0370991	−	0.0238422i
$408$	−56.2668	−	191.627i	−0.137909	−	0.469674i
$409$	−47.2593	−	54.5401i	−0.115548	−	0.133350i	0.695028	−	0.718982i	$-0.255392\pi$
$409$	−47.2593	−	54.5401i	−0.115548	−	0.133350i	−0.810577	+	0.585632i	$0.800846\pi$
$410$	259.380	−	883.366i	0.632633	−	2.15455i
$411$	631.526	−	288.408i	1.53656	−	0.701724i
$412$	−206.657	−	29.7128i	−0.501595	−	0.0721184i
$413$			332.778i			0.805757i
$414$	−341.538	−	159.994i	−0.824970	−	0.386460i
$415$	−140.128			−0.337657
$416$	8.12754	−	56.5283i	0.0195374	−	0.135885i
$417$	10.1741	+	22.2782i	0.0243983	+	0.0534249i
$418$	−288.293	−	84.6505i	−0.689696	−	0.202513i
$419$	117.767	−	102.045i	0.281066	−	0.243545i	−0.502906	−	0.864341i	$-0.667736\pi$
$419$	117.767	−	102.045i	0.281066	−	0.243545i	0.783972	+	0.620796i	$0.213190\pi$
$420$	1221.43	−	358.644i	2.90817	−	0.853915i
$421$	106.742	−	166.094i	0.253545	−	0.394523i	−0.691027	−	0.722829i	$-0.742841\pi$
$421$	106.742	−	166.094i	0.253545	−	0.394523i	0.944571	+	0.328306i	$0.106478\pi$
$422$	−120.938	+	264.817i	−0.286583	+	0.627528i
$423$	112.511	−	129.844i	0.265983	−	0.306961i
$424$	53.4193	+	83.1221i	0.125989	+	0.196043i
$425$	58.9265	−	8.47235i	0.138651	−	0.0199349i
$426$	−63.7764	−	443.574i	−0.149710	−	1.04125i
$427$	540.853	−	347.585i	1.26663	−	0.814016i
$428$	141.130	+	122.290i	0.329743	+	0.285724i
$429$	−288.991	−	131.978i	−0.673639	−	0.307641i
$430$	−915.778	−	588.535i	−2.12972	−	1.36869i
$431$	−153.825	−	523.879i	−0.356902	−	1.21550i	−0.920926	−	0.389738i	$-0.872566\pi$
$431$	−153.825	−	523.879i	−0.356902	−	1.21550i	0.564024	−	0.825758i	$-0.309252\pi$
$432$	188.194	+	217.188i	0.435634	+	0.502749i
$433$	−21.5686	+	73.4558i	−0.0498119	+	0.169644i	−0.980642	−	0.195808i	$-0.937267\pi$
$433$	−21.5686	+	73.4558i	−0.0498119	+	0.169644i	0.930830	+	0.365451i	$0.119085\pi$
$434$	−591.212	+	269.997i	−1.36224	+	0.622114i
$435$	−1079.51	−	155.211i	−2.48164	−	0.356806i
$436$			1226.56i			2.81320i
$437$	−36.2843	−	270.986i	−0.0830304	−	0.620105i
$438$	−96.2357			−0.219716
$439$	80.6869	−	561.190i	0.183797	−	1.27834i	−0.663886	−	0.747834i	$-0.731094\pi$
$439$	80.6869	−	561.190i	0.183797	−	1.27834i	0.847683	−	0.530503i	$-0.177997\pi$
$440$	280.471	+	614.145i	0.637433	+	1.39578i
$441$	−26.2535	−	7.70873i	−0.0595318	−	0.0174801i
$442$	115.860	−	100.394i	0.262127	−	0.227135i
$443$	150.565	−	44.2098i	0.339876	−	0.0997965i	−0.107341	−	0.994222i	$-0.534234\pi$
$443$	150.565	−	44.2098i	0.339876	−	0.0997965i	0.447216	+	0.894426i	$0.352415\pi$
$444$	40.4953	−	63.0120i	0.0912057	−	0.141919i
$445$	−425.246	+	931.158i	−0.955608	+	2.09249i
$446$	594.996	−	686.662i	1.33407	−	1.53960i
$447$	370.853	+	577.059i	0.829649	+	1.29096i
$448$	360.442	−	51.8238i	0.804558	−	0.115678i
$449$	−82.0122	−	570.407i	−0.182655	−	1.27039i	−0.850453	−	0.526051i	$-0.823672\pi$
$449$	−82.0122	−	570.407i	−0.182655	−	1.27039i	0.667798	−	0.744343i	$-0.267237\pi$
$450$	221.365	−	142.263i	0.491923	−	0.316140i
$451$	225.575	+	195.462i	0.500166	+	0.433396i
$452$	−271.685	−	124.074i	−0.601072	−	0.274500i
$453$	446.939	+	287.230i	0.986621	+	0.634063i
$454$	−91.6715	−	312.205i	−0.201920	−	0.687675i
$455$	326.580	+	376.893i	0.717758	+	0.828337i
$456$	180.288	−	614.004i	0.395368	−	1.34650i
$457$	−269.969	+	123.291i	−0.590742	+	0.269783i	−0.688276	−	0.725449i	$-0.741632\pi$
$457$	−269.969	+	123.291i	−0.590742	+	0.269783i	0.0975335	+	0.995232i	$0.468905\pi$
$458$	1412.50	+	203.087i	3.08406	+	0.443422i
$459$			59.0382i			0.128624i
$460$	−797.088	+	902.070i	−1.73280	+	1.96102i
$461$	190.925			0.414153			0.207076	−	0.978325i	$-0.433605\pi$
$461$	190.925			0.414153			0.207076	+	0.978325i	$0.433605\pi$
$462$	−87.4931	+	608.528i	−0.189379	+	1.31716i
$463$	−53.1267	−	116.331i	−0.114745	−	0.251255i	0.843543	−	0.537062i	$-0.180466\pi$
$463$	−53.1267	−	116.331i	−0.114745	−	0.251255i	−0.958287	+	0.285806i	$0.907739\pi$
$464$	796.872	+	233.983i	1.71740	+	0.504273i
$465$	−508.158	+	440.321i	−1.09281	+	0.946928i
$466$	458.675	−	134.679i	0.984281	−	0.289011i
$467$	48.3389	−	75.2168i	0.103509	−	0.161064i	−0.785635	−	0.618690i	$-0.787664\pi$
$467$	48.3389	−	75.2168i	0.103509	−	0.161064i	0.889145	+	0.457626i	$0.151300\pi$
$468$	188.967	−	413.779i	0.403775	−	0.884144i
$469$	−121.906	+	140.687i	−0.259927	+	0.299972i
$470$	−441.635	−	687.197i	−0.939648	−	1.46212i
$471$	−601.011	+	86.4124i	−1.27603	+	0.183466i
$472$	−104.821	−	729.045i	−0.222078	−	1.54459i
$473$	296.896	−	190.803i	0.627687	−	0.403390i
$474$	−1287.28	−	1115.44i	−2.71579	−	2.35324i
$475$	173.514	+	79.2410i	0.365292	+	0.166823i
$476$	−167.535	−	107.668i	−0.351964	−	0.226194i
$477$	8.99721	+	30.6417i	0.0188621	+	0.0642383i
$478$	534.671	+	617.044i	1.11856	+	1.29089i
$479$	−128.675	+	438.226i	−0.268632	+	0.914876i	0.709116	+	0.705092i	$0.249094\pi$
$479$	−128.675	+	438.226i	−0.268632	+	0.914876i	−0.977748	+	0.209784i	$0.932724\pi$
$480$	−103.997	+	47.4941i	−0.216661	+	0.0989460i
$481$	29.0447	+	4.17599i	0.0603840	+	0.00868190i
$482$		−	214.434i		−	0.444883i
$483$	−538.260	+	152.396i	−1.11441	+	0.315519i
$484$	559.579			1.15615
$485$	98.6418	−	686.069i	0.203385	−	1.41457i
$486$	335.332	+	734.274i	0.689983	+	1.51085i
$487$	209.336	+	61.4667i	0.429849	+	0.126215i	0.489498	−	0.872004i	$-0.337180\pi$
$487$	209.336	+	61.4667i	0.429849	+	0.126215i	−0.0596492	+	0.998219i	$0.518998\pi$
$488$	−1075.41	+	931.847i	−2.20371	+	1.90952i
$489$	−302.633	+	88.8610i	−0.618881	+	0.181720i
$490$	−70.3337	+	109.441i	−0.143538	+	0.223350i
$491$	163.271	−	357.513i	0.332527	−	0.728133i	−0.667335	−	0.744758i	$-0.732565\pi$
$491$	163.271	−	357.513i	0.332527	−	0.728133i	0.999862	+	0.0166253i	$0.00529225\pi$
$492$	−815.693	+	941.360i	−1.65791	+	1.91333i
$493$	92.2427	+	143.532i	0.187105	+	0.291141i
$494$	486.214	−	69.9071i	0.984240	−	0.141512i
$495$	31.0554	+	215.995i	0.0627381	+	0.436353i
$496$	430.748	−	276.825i	0.868444	−	0.558115i
$497$	−172.355	−	149.346i	−0.346790	−	0.300495i
$498$	256.892	+	117.319i	0.515848	+	0.235580i
$499$	−536.678	−	344.902i	−1.07551	−	0.691186i	−0.121991	−	0.992531i	$-0.538928\pi$
$499$	−536.678	−	344.902i	−1.07551	−	0.691186i	−0.953515	+	0.301345i	$0.902564\pi$
$500$	132.017	+	449.609i	0.264034	+	0.899218i
$501$	357.825	+	412.952i	0.714221	+	0.824255i
$502$	−18.3146	+	62.3739i	−0.0364833	+	0.124251i
$503$	−195.386	+	89.2297i	−0.388441	+	0.177395i	−0.600056	−	0.799958i	$-0.704855\pi$
$503$	−195.386	+	89.2297i	−0.388441	+	0.177395i	0.211615	+	0.977353i	$0.432128\pi$
$504$	−444.669	−	63.9337i	−0.882279	−	0.126853i
$505$		−	332.046i		−	0.657517i
$506$	−236.367	−	531.137i	−0.467128	−	1.04968i
$507$	−106.149			−0.209368
$508$	122.236	−	850.171i	0.240622	−	1.67356i
$509$	297.839	+	652.177i	0.585146	+	1.28129i	0.938331	+	0.345738i	$0.112371\pi$
$509$	297.839	+	652.177i	0.585146	+	1.28129i	−0.353185	+	0.935553i	$0.614901\pi$
$510$	−294.474	−	86.4654i	−0.577400	−	0.169540i
$511$	−37.0126	+	32.0716i	−0.0724317	+	0.0627624i
$512$	−924.485	+	271.453i	−1.80563	+	0.530182i
$513$	−102.272	+	159.138i	−0.199360	+	0.310211i
$514$	14.8471	−	32.5106i	0.0288854	−	0.0632502i
$515$	−107.227	+	123.747i	−0.208208	+	0.240285i
$516$	796.253	+	1238.99i	1.54313	+	2.40115i
$517$	262.135	−	37.6893i	0.507031	−	0.0729000i
$518$	−8.08099	−	56.2045i	−0.0156004	−	0.108503i
$519$	186.015	−	119.545i	0.358411	−	0.230337i
$520$	−834.184	−	722.824i	−1.60420	−	1.39005i
$521$	635.652	+	290.293i	1.22006	+	0.557183i	0.918181	−	0.396162i	$-0.129658\pi$
$521$	635.652	+	290.293i	1.22006	+	0.557183i	0.301881	+	0.953346i	$0.402386\pi$
$522$	634.423	+	407.719i	1.21537	+	0.781071i
$523$	194.561	+	662.614i	0.372009	+	1.26695i	0.906655	+	0.421872i	$0.138627\pi$
$523$	194.561	+	662.614i	0.372009	+	1.26695i	−0.534646	+	0.845076i	$0.679555\pi$
$524$	−1014.27	−	1170.53i	−1.93563	−	2.23384i
$525$	109.960	−	374.490i	0.209448	−	0.713315i
$526$	232.998	−	106.406i	0.442961	−	0.202294i
$527$	104.119	+	14.9700i	0.197569	+	0.0284061i
$528$		−	484.332i		−	0.917295i
$529$	354.107	−	393.000i	0.669389	−	0.742912i
$530$	151.838			0.286486
$531$	33.8789	−	235.633i	0.0638020	−	0.443753i
$532$	−265.079	−	580.441i	−0.498268	−	1.09106i
$533$	−468.202	−	137.476i	−0.878427	−	0.257930i
$534$	1559.18	−	1351.04i	2.91982	−	2.53004i
$535$	140.522	−	41.2611i	0.262658	−	0.0771235i
$536$	222.755	−	346.614i	0.415588	−	0.646668i
$537$	328.149	−	718.546i	0.611078	−	1.33807i
$538$	−600.770	+	693.326i	−1.11667	+	1.28871i
$539$	−22.8022	−	35.4810i	−0.0423047	−	0.0658274i
$540$	824.413	−	118.533i	1.52669	−	0.219505i
$541$	−45.9379	−	319.505i	−0.0849130	−	0.590583i	−0.987205	−	0.159457i	$-0.949026\pi$
$541$	−45.9379	−	319.505i	−0.0849130	−	0.590583i	0.902292	−	0.431126i	$-0.141883\pi$
$542$	−248.058	+	159.417i	−0.457671	+	0.294128i
$543$	586.233	+	507.974i	1.07962	+	0.935496i
$544$	16.2695	+	7.43004i	0.0299072	+	0.0136582i
$545$	809.237	+	520.065i	1.48484	+	0.954248i
$546$	−283.165	−	964.370i	−0.518617	−	1.76625i
$547$	−497.001	−	573.569i	−0.908594	−	1.04857i	−0.998614	−	0.0526331i	$-0.983239\pi$
$547$	−497.001	−	573.569i	−0.908594	−	1.04857i	0.0900202	−	0.995940i	$-0.471307\pi$
$548$	−431.688	+	1470.19i	−0.787752	+	2.68284i
$549$	−418.352	+	191.055i	−0.762026	+	0.348006i
$550$	401.479	+	57.7239i	0.729961	+	0.104953i
$551$			546.685i			0.992169i
$552$	1131.21	−	503.412i	2.04930	−	0.911978i
$553$	−866.825			−1.56750
$554$	−119.390	+	830.375i	−0.215505	+	1.49887i
$555$	−24.4028	−	53.4347i	−0.0439691	−	0.0962788i
$556$	−51.8636	−	15.2285i	−0.0932799	−	0.0273895i
$557$	−441.583	+	382.634i	−0.792789	+	0.686956i	−0.953948	−	0.299973i	$-0.903022\pi$
$557$	−441.583	+	382.634i	−0.792789	+	0.686956i	0.161159	+	0.986928i	$0.448477\pi$
$558$	446.112	−	130.990i	0.799483	−	0.234750i
$559$	−311.935	+	485.381i	−0.558024	+	0.868302i
$560$	−315.825	+	691.560i	−0.563973	+	1.23493i
$561$	65.1580	−	75.1964i	0.116146	−	0.134040i
$562$	−672.984	−	1047.18i	−1.19748	−	1.86332i
$563$	−302.985	+	43.5627i	−0.538162	+	0.0773760i	−0.406036	−	0.913857i	$-0.633089\pi$
$563$	−302.985	+	43.5627i	−0.538162	+	0.0773760i	−0.132126	+	0.991233i	$0.542180\pi$
$564$	157.284	+	1093.93i	0.278872	+	1.93959i
$565$	−197.055	+	126.640i	−0.348770	+	0.224141i
$566$	306.919	+	265.947i	0.542260	+	0.469871i
$567$	604.958	+	276.275i	1.06695	+	0.487258i
$568$	424.635	+	272.896i	0.747596	+	0.480451i
$569$	−5.93871	−	20.2254i	−0.0104371	−	0.0355455i	0.954110	−	0.299457i	$-0.0968055\pi$
$569$	−5.93871	−	20.2254i	−0.0104371	−	0.0355455i	−0.964547	+	0.263911i	$0.914987\pi$
$570$	−643.974	−	743.185i	−1.12978	−	1.30383i
$571$	190.281	−	648.037i	0.333241	−	1.13492i	−0.607084	−	0.794638i	$-0.707661\pi$
$571$	190.281	−	648.037i	0.333241	−	1.13492i	0.940325	−	0.340278i	$-0.110521\pi$
$572$	637.810	−	291.278i	1.11505	−	0.509228i
$573$	−710.747	−	102.190i	−1.24040	−	0.178342i
$574$			944.270i			1.64507i
$575$	100.544	+	355.119i	0.174858	+	0.617599i
$576$	−260.497			−0.452252
$577$	93.4193	−	649.746i	0.161905	−	1.12608i	−0.733133	−	0.680086i	$-0.761943\pi$
$577$	93.4193	−	649.746i	0.161905	−	1.12608i	0.895038	−	0.445990i	$-0.147148\pi$
$578$	−398.859	−	873.378i	−0.690067	−	1.51104i
$579$	−125.130	−	36.7414i	−0.216113	−	0.0634566i
$580$	1819.10	−	1576.26i	3.13638	−	2.71769i
$581$	137.899	−	40.4909i	0.237348	−	0.0696918i
$582$	−755.234	+	1175.17i	−1.29765	+	2.01919i
$583$	−20.4492	+	44.7774i	−0.0350758	+	0.0768052i
$584$	70.9846	−	81.9206i	0.121549	−	0.140275i
$585$	−192.874	−	300.118i	−0.329699	−	0.513022i
$586$	−1176.87	+	169.208i	−2.00830	+	0.288751i
$587$	86.7885	+	603.627i	0.147851	+	1.02833i	0.919729	+	0.392555i	$0.128409\pi$
$587$	86.7885	+	603.627i	0.147851	+	1.02833i	−0.771878	+	0.635771i	$0.780682\pi$
$588$	148.068	−	95.1574i	0.251816	−	0.161832i
$589$	254.721	+	220.717i	0.432463	+	0.374732i
$590$	−1029.56	−	470.186i	−1.74502	−	0.796925i
$591$	−695.468	−	446.950i	−1.17676	−	0.756260i
$592$	12.6029	+	42.9216i	0.0212887	+	0.0725026i
$593$	−284.726	−	328.591i	−0.480145	−	0.554117i	0.463060	−	0.886327i	$-0.346751\pi$
$593$	−284.726	−	328.591i	−0.480145	−	0.554117i	−0.943206	+	0.332210i	$0.892206\pi$
$594$	−113.324	+	385.946i	−0.190781	+	0.649741i
$595$	−142.071	+	64.8818i	−0.238775	+	0.109045i
$596$	−1498.50	−	215.452i	−2.51426	−	0.361497i
$597$		−	973.439i		−	1.63055i
$598$	712.222	+	629.335i	1.19101	+	1.05240i
$599$	164.249			0.274205			0.137102	−	0.990557i	$-0.456221\pi$
$599$	164.249			0.274205			0.137102	+	0.990557i	$0.456221\pi$
$600$	−122.940	+	855.065i	−0.204900	+	1.42511i
$601$	−9.97992	−	21.8530i	−0.0166055	−	0.0363610i	0.901148	−	0.433513i	$-0.142726\pi$
$601$	−9.97992	−	21.8530i	−0.0166055	−	0.0363610i	−0.917753	+	0.397152i	$0.869999\pi$
$602$	1071.28	+	314.556i	1.77953	+	0.522518i
$603$	100.642	−	87.2065i	0.166902	−	0.144621i
$604$	−1125.05	+	330.343i	−1.86266	+	0.546926i
$605$	237.264	−	369.190i	0.392172	−	0.610232i
$606$	−277.998	+	608.732i	−0.458743	+	1.00451i
$607$	119.627	−	138.057i	0.197079	−	0.227442i	−0.648605	−	0.761125i	$-0.724647\pi$
$607$	119.627	−	138.057i	0.197079	−	0.227442i	0.845684	+	0.533684i	$0.179193\pi$
$608$	30.9836	+	48.2114i	0.0509599	+	0.0792951i
$609$	1107.20	−	159.191i	1.81806	−	0.261397i
$610$	311.197	+	2164.42i	0.510159	+	3.54824i
$611$	−364.228	+	234.075i	−0.596118	+	0.383102i
$612$	107.667	+	93.2937i	0.175926	+	0.152441i
$613$	−732.277	−	334.420i	−1.19458	−	0.545546i	−0.283978	−	0.958831i	$-0.591654\pi$
$613$	−732.277	−	334.420i	−1.19458	−	0.545546i	−0.910602	+	0.413285i	$0.864381\pi$
$614$	597.638	+	384.078i	0.973351	+	0.625535i
$615$	275.218	+	937.306i	0.447509	+	1.52407i
$616$	−453.473	−	523.336i	−0.736157	−	0.849571i
$617$	−296.832	+	1010.92i	−0.481089	+	1.63844i	0.258961	+	0.965888i	$0.416620\pi$
$617$	−296.832	+	1010.92i	−0.481089	+	1.63844i	−0.740050	+	0.672551i	$0.765198\pi$
$618$	300.181	−	137.088i	0.485729	−	0.221825i
$619$	1157.56	+	166.432i	1.87005	+	0.268873i	0.981720	−	0.190331i	$-0.0609561\pi$
$619$	1157.56	+	166.432i	1.87005	+	0.268873i	0.888331	+	0.459204i	$0.151865\pi$
$620$		−	1483.98i		−	2.39351i
$621$	−362.776	+	48.5748i	−0.584181	+	0.0782203i
$622$	678.778			1.09128
$623$	149.419	−	1039.23i	0.239837	−	1.66811i
$624$	328.930	+	720.256i	0.527132	+	1.15426i
$625$	737.533	+	216.559i	1.18005	+	0.346495i
$626$	118.840	−	102.976i	0.189841	−	0.164498i
$627$	305.897	−	89.8194i	0.487874	−	0.143253i
$628$	724.505	−	1127.35i	1.15367	−	1.79515i
$629$	−3.81761	+	8.35941i	−0.00606934	+	0.0132900i
$630$	−452.083	+	521.732i	−0.717593	+	0.828146i
$631$	−412.278	−	641.517i	−0.653372	−	1.01667i	−0.996988	−	0.0775565i	$-0.975288\pi$
$631$	−412.278	−	641.517i	−0.653372	−	1.01667i	0.343616	−	0.939110i	$-0.388348\pi$
$632$	1899.03	−	273.039i	3.00479	−	0.432024i
$633$	−43.9613	−	305.758i	−0.0694492	−	0.483030i
$634$	−862.246	+	554.132i	−1.36001	+	0.874025i
$635$	−509.083	−	441.123i	−0.801706	−	0.694682i
$636$	−186.863	−	85.3376i	−0.293810	−	0.134179i
$637$	58.0062	+	37.2783i	0.0910615	+	0.0585217i
$638$	327.501	+	1115.36i	0.513324	+	1.74822i
$639$	106.836	+	123.296i	0.167193	+	0.192951i
$640$	−383.747	+	1306.92i	−0.599605	+	2.04207i
$641$	−469.026	+	214.197i	−0.731709	+	0.334160i	−0.746188	−	0.665735i	$-0.768118\pi$
$641$	−469.026	+	214.197i	−0.731709	+	0.334160i	0.0144792	+	0.999895i	$0.495391\pi$
$642$	−292.161	−	42.0064i	−0.455079	−	0.0654305i
$643$		−	509.523i		−	0.792416i	−0.918161	−	0.396208i	$-0.870326\pi$
$643$		−	509.523i		−	0.792416i	0.918161	−	0.396208i	$-0.129674\pi$
$644$	523.754	−	1118.05i	0.813283	−	1.73610i
$645$	1155.06			1.79079
$646$	−21.8938	+	152.275i	−0.0338913	+	0.235719i
$647$	−92.3050	−	202.120i	−0.142666	−	0.312395i	0.824788	−	0.565442i	$-0.191295\pi$
$647$	−92.3050	−	202.120i	−0.142666	−	0.312395i	−0.967454	+	0.253047i	$0.918567\pi$
$648$	−1412.36	−	414.706i	−2.17956	−	0.639978i
$649$	277.319	−	240.298i	0.427302	−	0.370259i
$650$	−636.247	+	186.819i	−0.978842	+	0.287414i
$651$	372.844	−	580.156i	0.572725	−	0.891177i
$652$	289.177	−	633.209i	0.443523	−	0.971179i
$653$	454.058	−	524.011i	0.695342	−	0.802468i	−0.292773	−	0.956182i	$-0.594578\pi$
$653$	454.058	−	524.011i	0.695342	−	0.802468i	0.988115	+	0.153714i	$0.0491235\pi$
$654$	−1048.14	−	1630.94i	−1.60266	−	2.49379i
$655$	−1202.33	+	172.869i	−1.83562	+	0.263922i
$656$	−105.868	−	736.329i	−0.161384	−	1.12245i
$657$	29.4729	−	18.9411i	0.0448598	−	0.0288297i
$658$	633.183	+	548.656i	0.962284	+	0.833824i
$659$	339.155	+	154.887i	0.514651	+	0.235033i	0.655772	−	0.754959i	$-0.272343\pi$
$659$	339.155	+	154.887i	0.514651	+	0.235033i	−0.141121	+	0.989992i	$0.545071\pi$
$660$	−1180.87	−	758.897i	−1.78919	−	1.14984i
$661$	70.1909	+	239.048i	0.106189	+	0.361646i	0.995395	−	0.0958612i	$-0.0305605\pi$
$661$	70.1909	+	239.048i	0.106189	+	0.361646i	−0.889206	+	0.457507i	$0.848742\pi$
$662$	834.818	+	963.431i	1.26105	+	1.45533i
$663$	−45.8284	+	156.077i	−0.0691228	+	0.235411i
$664$	−289.354	+	132.144i	−0.435775	+	0.199012i
$665$	−495.349	−	71.2204i	−0.744886	−	0.107098i
$666$			40.6199i			0.0609909i
$667$	−806.080	+	684.905i	−1.20852	+	1.02684i
$668$	−1205.95			−1.80531
$669$	−137.201	+	954.251i	−0.205083	+	1.42638i
$670$	−263.021	−	575.937i	−0.392569	−	0.859607i
$671$	−680.207	−	199.727i	−1.01372	−	0.297655i
$672$	88.6201	−	76.7897i	0.131875	−	0.114270i
$673$	1000.73	−	293.841i	1.48697	−	0.436614i	0.565397	−	0.824819i	$-0.308723\pi$
$673$	1000.73	−	293.841i	1.48697	−	0.436614i	0.921573	+	0.388205i	$0.126905\pi$
$674$	844.603	−	1314.23i	1.25312	−	1.94989i
$675$	106.082	−	232.288i	0.157159	−	0.344130i
$676$	153.417	−	177.053i	0.226948	−	0.261912i
$677$	508.378	+	791.051i	0.750927	+	1.16847i	0.980757	+	0.195235i	$0.0625469\pi$
$677$	508.378	+	791.051i	0.750927	+	1.16847i	−0.229829	+	0.973231i	$0.573817\pi$
$678$	467.283	−	67.1851i	0.689207	−	0.0990931i
$679$	101.171	+	703.663i	0.149001	+	1.03632i
$680$	290.811	−	186.893i	0.427663	−	0.274843i
$681$	260.925	+	226.093i	0.383150	+	0.332001i
$682$	651.914	+	297.719i	0.955886	+	0.436538i
$683$	−1032.34	−	663.442i	−1.51147	−	0.971365i	−0.993234	−	0.116129i	$-0.962951\pi$
$683$	−1032.34	−	663.442i	−1.51147	−	0.971365i	−0.518239	−	0.855236i	$-0.673412\pi$
$684$	128.604	+	437.985i	0.188017	+	0.640329i
$685$	786.944	+	908.181i	1.14882	+	1.32581i
$686$	354.038	−	1205.74i	0.516091	−	1.75764i
$687$	−1377.33	+	629.006i	−2.00485	+	0.915584i
$688$	−870.636	−	125.179i	−1.26546	−	0.181946i
$689$		−	80.4771i		−	0.116803i
$690$	289.026	−	1880.62i	0.418878	−	2.72553i
$691$	874.871			1.26609			0.633047	−	0.774114i	$-0.281804\pi$
$691$	874.871			1.26609			0.633047	+	0.774114i	$0.281804\pi$
$692$	−69.4511	+	483.043i	−0.100363	+	0.698039i
$693$	−92.9749	−	203.587i	−0.134163	−	0.293776i
$694$	1814.82	+	532.878i	2.61501	+	0.767836i
$695$	−32.0377	+	27.7608i	−0.0460974	+	0.0399436i
$696$	−2375.49	+	697.508i	−3.41306	+	1.00217i
$697$	82.6229	−	128.564i	0.118541	−	0.184453i
$698$	−215.348	+	471.547i	−0.308522	+	0.675569i
$699$	−332.164	+	383.338i	−0.475199	+	0.548409i
$700$	465.709	+	724.657i	0.665299	+	1.03522i
$701$	247.920	−	35.6455i	0.353666	−	0.0508495i	0.0368076	−	0.999322i	$-0.488281\pi$
$701$	247.920	−	35.6455i	0.353666	−	0.0508495i	0.316858	+	0.948473i	$0.397372\pi$
$702$	−93.5866	−	650.909i	−0.133314	−	0.927221i
$703$	−24.7714	+	15.9196i	−0.0352367	+	0.0226453i
$704$	−303.462	−	262.951i	−0.431054	−	0.373510i
$705$	788.425	+	360.062i	1.11833	+	0.510726i
$706$	−561.921	−	361.124i	−0.795921	−	0.511508i
$707$	95.9472	+	326.766i	0.135710	+	0.462187i
$708$	1002.80	+	1157.30i	1.41639	+	1.63460i
$709$	302.852	−	1031.42i	0.427154	−	1.45475i	−0.412162	−	0.911111i	$-0.635226\pi$
$709$	302.852	−	1031.42i	0.427154	−	1.45475i	0.839316	−	0.543643i	$-0.182956\pi$
$710$	705.577	−	322.226i	0.993770	−	0.453840i
$711$	613.780	+	88.2483i	0.863263	+	0.124119i
$712$			2323.80i			3.26376i
$713$	−6.32172	+	652.104i	−0.00886637	+	0.914592i
$714$	314.776			0.440863
$715$	78.2596	−	544.308i	0.109454	−	0.761270i
$716$	724.233	+	1585.85i	1.01150	+	2.21487i
$717$	−831.229	−	244.071i	−1.15931	−	0.340406i
$718$	−603.776	+	523.175i	−0.840913	+	0.728655i
$719$	140.968	−	41.3918i	0.196061	−	0.0575686i	−0.182228	−	0.983256i	$-0.558331\pi$
$719$	140.968	−	41.3918i	0.196061	−	0.0575686i	0.378289	+	0.925688i	$0.376513\pi$
$720$	294.034	−	457.526i	0.408381	−	0.635453i
$721$	69.7645	−	152.763i	0.0967608	−	0.211876i
$722$	501.882	−	579.203i	0.695127	−	0.802220i
$723$	123.011	+	191.408i	0.170139	+	0.264742i
$724$	−1694.56	+	243.641i	−2.34055	+	0.336520i
$725$	−105.027	−	730.478i	−0.144865	−	1.00756i
$726$	−744.067	+	478.183i	−1.02489	+	0.658654i
$727$	1.63150	+	1.41370i	0.00224416	+	0.00194457i	0.655982	−	0.754776i	$-0.272255\pi$
$727$	1.63150	+	1.41370i	0.00224416	+	0.00194457i	−0.653738	+	0.756721i	$0.726800\pi$
$728$	1029.79	+	470.287i	1.41454	+	0.645999i
$729$	45.7438	+	29.3978i	0.0627487	+	0.0403262i
$730$	−46.9291	−	159.826i	−0.0642864	−	0.218939i
$731$	−118.333	−	136.563i	−0.161878	−	0.186817i
$732$	833.492	−	2838.61i	1.13865	−	3.87789i
$733$	163.194	−	74.5284i	0.222639	−	0.101676i	−0.300973	−	0.953633i	$-0.597311\pi$
$733$	163.194	−	74.5284i	0.222639	−	0.101676i	0.523612	+	0.851957i	$0.324584\pi$
$734$	−1992.46	−	286.472i	−2.71452	−	0.390289i
$735$		−	138.037i		−	0.187805i
$736$	−32.2699	+	106.086i	−0.0438449	+	0.144138i
$737$	205.269			0.278519
$738$	96.1326	−	668.617i	0.130261	−	0.905985i
$739$	550.372	+	1205.15i	0.744753	+	1.63078i	0.775575	+	0.631256i	$0.217460\pi$
$739$	550.372	+	1205.15i	0.744753	+	1.63078i	−0.0308219	+	0.999525i	$0.509812\pi$
$740$	124.396	+	36.5260i	0.168103	+	0.0493594i
$741$	−393.903	+	341.319i	−0.531583	+	0.460620i
$742$	−149.423	+	43.8747i	−0.201379	+	0.0591303i
$743$	669.940	−	1042.45i	0.901669	−	1.40302i	−0.0134803	−	0.999909i	$-0.504291\pi$
$743$	669.940	−	1042.45i	0.901669	−	1.40302i	0.915149	−	0.403115i	$-0.132073\pi$
$744$	−634.079	+	1388.44i	−0.852257	+	1.86618i
$745$	−777.519	+	897.305i	−1.04365	+	1.20444i
$746$	955.275	+	1486.44i	1.28053	+	1.99254i
$747$	−101.766	+	14.6317i	−0.136233	+	0.0195873i
$748$	31.2519	+	217.362i	0.0417806	+	0.290590i
$749$	−126.365	+	81.2100i	−0.168712	+	0.108425i
$750$	−559.751	−	485.027i	−0.746334	−	0.646702i
$751$	−1016.60	−	464.265i	−1.35366	−	0.618196i	−0.399290	−	0.916825i	$-0.630743\pi$
$751$	−1016.60	−	464.265i	−1.35366	−	0.618196i	−0.954369	+	0.298629i	$0.903471\pi$
$752$	−555.262	−	356.845i	−0.738380	−	0.474528i
$753$	−19.4330	−	66.1826i	−0.0258074	−	0.0878919i
$754$	−1244.52	−	1436.25i	−1.65056	−	1.90485i
$755$	−259.076	+	882.332i	−0.343147	+	1.16865i
$756$	−777.054	+	354.868i	−1.02785	+	0.469403i
$757$	−560.345	−	80.5654i	−0.740218	−	0.106427i	−0.238117	−	0.971236i	$-0.576530\pi$
$757$	−560.345	−	80.5654i	−0.740218	−	0.106427i	−0.502101	+	0.864809i	$0.667439\pi$
$758$		−	1261.41i		−	1.66413i
$759$	515.675	+	338.512i	0.679413	+	0.445998i
$760$	1107.64			1.45742
$761$	−175.061	+	1217.57i	−0.230040	+	1.59997i	0.467882	+	0.883791i	$0.345017\pi$
$761$	−175.061	+	1217.57i	−0.230040	+	1.59997i	−0.697922	+	0.716174i	$0.745892\pi$
$762$	563.969	+	1234.92i	0.740116	+	1.62063i
$763$	−946.647	−	277.961i	−1.24069	−	0.364300i
$764$	1197.69	−	1037.80i	1.56765	−	1.35838i
$765$	107.203	−	31.4776i	0.140135	−	0.0411472i
$766$	−321.881	+	500.856i	−0.420210	+	0.653859i
$767$	−249.208	+	545.690i	−0.324913	+	0.711460i
$768$	1260.40	−	1454.58i	1.64115	−	1.89398i
$769$	−824.361	−	1282.73i	−1.07199	−	1.66805i	−0.646037	−	0.763306i	$-0.723575\pi$
$769$	−824.361	−	1282.73i	−1.07199	−	1.66805i	−0.425954	−	0.904745i	$-0.640061\pi$
$770$	−1053.29	+	151.441i	−1.36791	+	0.196676i
$771$	5.39697	+	37.5368i	0.00699997	+	0.0486858i
$772$	242.132	−	155.609i	0.313642	−	0.201566i
$773$	−675.776	−	585.563i	−0.874225	−	0.757520i	0.0971007	−	0.995275i	$-0.469043\pi$
$773$	−675.776	−	585.563i	−0.874225	−	0.757520i	−0.971325	+	0.237755i	$0.923589\pi$
$774$	−726.525	−	331.793i	−0.938663	−	0.428673i
$775$	−382.760	−	245.985i	−0.493884	−	0.317400i
$776$	−443.291	−	1509.71i	−0.571251	−	1.94550i
$777$	39.4552	+	45.5337i	0.0507789	+	0.0586019i
$778$	48.1326	−	163.924i	0.0618671	−	0.210700i
$779$	445.422	−	203.417i	0.571786	−	0.261126i
$780$	2271.48	+	326.590i	2.91216	+	0.418705i
$781$			251.474i			0.321989i
$782$	−251.956	+	158.493i	−0.322195	+	0.202676i
$783$	731.863			0.934691
$784$	−14.9597	+	104.047i	−0.0190812	+	0.132713i
$785$	−436.593	−	956.005i	−0.556170	−	1.21784i
$786$	2348.93	+	689.708i	2.98846	+	0.877491i
$787$	−650.309	+	563.496i	−0.826314	+	0.716005i	−0.961497	−	0.274816i	$-0.911383\pi$
$787$	−650.309	+	563.496i	−0.826314	+	0.716005i	0.135183	+	0.990821i	$0.456838\pi$
$788$	1750.65	−	514.037i	2.22163	−	0.652331i
$789$	−146.938	+	228.641i	−0.186234	+	0.289785i
$790$	1224.75	−	2681.83i	1.55032	−	3.39472i
$791$	157.328	−	181.567i	0.198898	−	0.229541i
$792$	267.816	+	416.729i	0.338151	+	0.526173i
$793$	1147.19	−	164.941i	1.44664	−	0.207996i
$794$	288.445	+	2006.18i	0.363280	+	2.52667i
$795$	−135.534	+	87.1022i	−0.170483	+	0.109563i
$796$	1623.65	+	1406.90i	2.03977	+	1.76747i
$797$	−92.9024	−	42.4271i	−0.116565	−	0.0532335i	0.356279	−	0.934380i	$-0.384045\pi$
$797$	−92.9024	−	42.4271i	−0.116565	−	0.0532335i	−0.472844	+	0.881146i	$0.656773\pi$
$798$	848.483	+	545.287i	1.06326	+	0.683317i
$799$	−38.2018	−	130.103i	−0.0478120	−	0.162833i
$800$	−50.6623	−	58.4675i	−0.0633279	−	0.0730843i
$801$	−211.600	+	720.644i	−0.264170	+	0.899681i
$802$	593.626	−	271.100i	0.740182	−	0.338030i
$803$	53.4535	+	7.68545i	0.0665672	+	0.00957092i
$804$			856.619i			1.06545i
$805$	−515.576	−	819.613i	−0.640467	−	1.01815i
$806$	−1171.66			−1.45368
$807$	138.532	−	963.511i	0.171663	−	1.19394i
$808$	−313.127	−	685.654i	−0.387534	−	0.848581i
$809$	−1372.26	−	402.930i	−1.69624	−	0.498060i	−0.716371	−	0.697720i	$-0.754198\pi$
$809$	−1372.26	−	402.930i	−1.69624	−	0.498060i	−0.979865	+	0.199660i	$0.936016\pi$
$810$	−1709.51	+	1481.30i	−2.11050	+	1.82876i
$811$	624.033	−	183.233i	0.769461	−	0.225934i	0.126638	−	0.991949i	$-0.459581\pi$
$811$	624.033	−	183.233i	0.769461	−	0.225934i	0.642823	+	0.766015i	$0.277763\pi$
$812$	−1334.70	+	2076.84i	−1.64372	+	2.55768i
$813$	129.972	−	284.598i	0.159867	−	0.350060i
$814$	−41.0025	+	47.3194i	−0.0503717	+	0.0581320i
$815$	−295.156	−	459.272i	−0.362155	−	0.563524i
$816$	−245.459	+	35.2916i	−0.300807	+	0.0432495i
$817$	−82.3987	−	573.095i	−0.100855	−	0.701463i
$818$	−211.785	+	136.106i	−0.258906	+	0.166389i
$819$	276.529	+	239.613i	0.337642	+	0.292568i
$820$	−1961.16	−	895.630i	−2.39165	−	1.09223i
$821$	607.072	+	390.142i	0.739430	+	0.475203i	0.855347	−	0.518056i	$-0.173344\pi$
$821$	607.072	+	390.142i	0.739430	+	0.475203i	−0.115916	+	0.993259i	$0.536980\pi$
$822$	−682.328	−	2323.80i	−0.830083	−	2.82700i
$823$	833.492	+	961.901i	1.01275	+	1.16877i	0.985592	+	0.169143i	$0.0540999\pi$
$823$	833.492	+	961.901i	1.01275	+	1.16877i	0.0271569	+	0.999631i	$0.491355\pi$
$824$	−104.721	+	356.646i	−0.127088	+	0.432823i
$825$	−391.482	+	178.784i	−0.474524	+	0.216708i
$826$	1149.06	+	165.209i	1.39111	+	0.200011i
$827$			809.088i			0.978341i	0.872188	+	0.489170i	$0.162700\pi$
$827$			809.088i			0.978341i	−0.872188	+	0.489170i	$0.837300\pi$
$828$	−484.684	+	738.346i	−0.585367	+	0.891723i
$829$	263.288			0.317597			0.158798	−	0.987311i	$-0.449238\pi$
$829$	263.288			0.317597			0.158798	+	0.987311i	$0.449238\pi$
$830$	−69.5672	+	483.850i	−0.0838159	+	0.582952i
$831$	−369.777	−	809.699i	−0.444978	−	0.974367i
$832$	629.864	+	184.945i	0.757048	+	0.222289i
$833$	−16.3202	+	14.1415i	−0.0195921	+	0.0169766i
$834$	81.9760	−	24.0703i	0.0982925	−	0.0288613i
$835$	−511.328	+	795.641i	−0.612368	+	0.952864i
$836$	−292.296	+	640.038i	−0.349636	+	0.765596i
$837$	295.480	−	341.002i	0.353023	−	0.407410i
$838$	−293.889	−	457.300i	−0.350703	−	0.545705i
$839$	1259.55	−	181.096i	1.50125	−	0.215848i	0.657859	−	0.753141i	$-0.271462\pi$
$839$	1259.55	−	181.096i	1.50125	−	0.215848i	0.843396	+	0.537293i	$0.180553\pi$
$840$	−322.537	−	2243.29i	−0.383972	−	2.67059i
$841$	1071.80	−	688.801i	1.27443	−	0.819027i
$842$	−520.518	−	451.032i	−0.618193	−	0.535667i
$843$	1201.44	+	548.680i	1.42520	+	0.650866i
$844$	573.528	+	368.584i	0.679536	+	0.436711i
$845$	−51.7635	−	176.290i	−0.0612586	−	0.208628i
$846$	−392.487	−	452.954i	−0.463932	−	0.535406i
$847$	−126.811	+	431.879i	−0.149718	+	0.509893i
$848$	111.599	−	50.9657i	0.131603	−	0.0601011i
$849$	−426.524	−	61.3249i	−0.502384	−	0.0722319i
$850$		−	207.675i		−	0.244324i
$851$	−54.5077	−	16.5805i	−0.0640514	−	0.0194836i
$852$	−1049.44			−1.23174
$853$	−83.9227	+	583.695i	−0.0983854	+	0.684285i	0.879616	+	0.475685i	$0.157800\pi$
$853$	−83.9227	+	583.695i	−0.0983854	+	0.684285i	−0.978001	+	0.208600i	$0.933109\pi$
$854$	−931.676	−	2040.09i	−1.09096	−	2.38886i
$855$	343.495	+	100.859i	0.401749	+	0.117964i
$856$	251.259	−	217.717i	0.293527	−	0.254343i
$857$	−294.600	+	86.5024i	−0.343757	+	0.100936i	−0.449054	−	0.893505i	$-0.648239\pi$
$857$	−294.600	+	86.5024i	−0.343757	+	0.100936i	0.105297	+	0.994441i	$0.466421\pi$
$858$	−599.181	+	932.344i	−0.698347	+	1.08665i
$859$	227.792	−	498.794i	0.265183	−	0.580669i	−0.729462	−	0.684021i	$-0.760230\pi$
$859$	227.792	−	498.794i	0.265183	−	0.580669i	0.994645	+	0.103352i	$0.0329569\pi$
$860$	−1669.40	+	1926.59i	−1.94116	+	2.24022i
$861$	−541.683	−	842.876i	−0.629133	−	0.978950i
$862$	−1885.28	+	271.063i	−2.18710	+	0.314458i
$863$	−49.1174	−	341.619i	−0.0569147	−	0.395851i	−0.998288	−	0.0584847i	$-0.981373\pi$
$863$	−49.1174	−	341.619i	−0.0569147	−	0.395851i	0.941374	−	0.337366i	$-0.109536\pi$
$864$	64.5420	−	41.4786i	0.0747014	−	0.0480077i
$865$	289.247	+	250.634i	0.334389	+	0.289750i
$866$	242.930	+	110.942i	0.280519	+	0.128109i
$867$	857.046	+	550.790i	0.988519	+	0.635283i
$868$	428.807	+	1460.38i	0.494017	+	1.68247i
$869$	625.933	+	722.365i	0.720291	+	0.831260i
$870$	−1071.86	+	3650.43i	−1.23203	+	4.19589i
$871$	−305.258	+	139.407i	−0.350468	+	0.160054i
$872$	2161.46	+	310.771i	2.47874	+	0.356388i
$873$		−	508.549i		−	0.582530i
$874$	−953.708	−	9.24557i	−1.09120	−	0.0105785i
$875$	−376.922			−0.430768
$876$	−32.0726	+	223.070i	−0.0366126	+	0.254646i
$877$	590.036	+	1292.00i	0.672789	+	1.47320i	0.870107	+	0.492864i	$0.164050\pi$
$877$	590.036	+	1292.00i	0.672789	+	1.47320i	−0.197317	+	0.980340i	$0.563223\pi$
$878$	−1897.69	−	557.212i	−2.16138	−	0.634638i
$879$	953.430	−	826.152i	1.08468	−	0.939877i
$880$	804.365	−	236.183i	0.914052	−	0.268390i
$881$	−915.522	+	1424.58i	−1.03919	+	1.61700i	−0.287145	+	0.957887i	$0.592706\pi$
$881$	−915.522	+	1424.58i	−1.03919	+	1.61700i	−0.752040	+	0.659117i	$0.770930\pi$
$882$	−39.6514	+	86.8245i	−0.0449563	+	0.0984405i
$883$	−99.0523	+	114.312i	−0.112177	+	0.129459i	−0.809061	−	0.587725i	$-0.800024\pi$
$883$	−99.0523	+	114.312i	−0.112177	+	0.129459i	0.696884	+	0.717184i	$0.254569\pi$
$884$	−194.095	−	302.017i	−0.219564	−	0.341648i
$885$	1188.73	−	170.914i	1.34320	−	0.193123i
$886$	−77.9045	−	541.838i	−0.0879284	−	0.611555i
$887$	231.878	−	149.019i	0.261418	−	0.168003i	−0.403366	−	0.915039i	$-0.632160\pi$
$887$	231.878	−	149.019i	0.261418	−	0.168003i	0.664784	+	0.747036i	$0.268524\pi$
$888$	−100.781	−	87.3268i	−0.113492	−	0.0983410i
$889$	628.455	+	287.006i	0.706923	+	0.322841i
$890$	3004.10	+	1930.62i	3.37540	+	2.16924i
$891$	−206.606	−	703.637i	−0.231881	−	0.789716i
$892$	−1393.35	−	1608.02i	−1.56206	−	1.80271i
$893$	122.405	−	416.872i	0.137071	−	0.466822i
$894$	2176.66	−	994.045i	2.43474	−	1.11191i
$895$	1353.36	+	194.584i	1.51214	+	0.217413i
$896$		−	1397.03i		−	1.55918i
$897$	−996.765	−	153.190i	−1.11122	−	0.170780i
$898$	−2010.29			−2.23863
$899$	185.575	−	1290.70i	0.206424	−	1.43571i
$900$	−255.984	−	560.526i	−0.284427	−	0.622807i
$901$	24.1832	+	7.10083i	0.0268404	+	0.00788106i
$902$	786.903	−	681.855i	0.872398	−	0.755937i
$903$	−1136.69	+	333.763i	−1.25880	+	0.369616i
$904$	−287.482	+	447.331i	−0.318011	+	0.494835i
$905$	−557.755	+	1221.31i	−0.616304	+	1.34952i
$906$	1213.67	−	1400.65i	1.33959	−	1.54597i
$907$	745.194	+	1159.54i	0.821603	+	1.27844i	0.957707	+	0.287745i	$0.0929055\pi$
$907$	745.194	+	1159.54i	0.821603	+	1.27844i	−0.136104	+	0.990695i	$0.543458\pi$
$908$	−754.227	+	108.441i	−0.830646	+	0.119429i
$909$	−34.6713	−	241.144i	−0.0381423	−	0.265285i
$910$	1463.52	−	940.545i	1.60826	−	1.03357i
$911$	−198.816	−	172.275i	−0.218239	−	0.189105i	0.538879	−	0.842383i	$-0.318848\pi$
$911$	−198.816	−	172.275i	−0.218239	−	0.189105i	−0.757118	+	0.653278i	$0.773393\pi$
$912$	−722.772	−	330.079i	−0.792513	−	0.361929i
$913$	−133.320	−	85.6795i	−0.146024	−	0.0938439i
$914$	291.686	+	993.392i	0.319132	+	1.08686i
$915$	−1519.41	−	1753.49i	−1.66056	−	1.91639i
$916$	941.492	−	3206.43i	1.02783	−	3.50047i
$917$	1133.26	−	517.542i	1.23583	−	0.564386i
$918$	203.855	+	29.3099i	0.222064	+	0.0319280i
$919$		−	200.414i		−	0.218078i	−0.994037	−	0.109039i	$-0.965223\pi$
$919$		−	200.414i		−	0.218078i	0.994037	−	0.109039i	$-0.0347774\pi$
$920$	1387.69	+	1633.20i	1.50835	+	1.77522i
$921$	−753.793			−0.818450
$922$	94.7856	−	659.248i	0.102804	−	0.715020i
$923$	−170.786	−	373.970i	−0.185034	−	0.405168i
$924$	1381.38	+	405.610i	1.49500	+	0.438971i
$925$	30.0410	−	26.0307i	0.0324768	−	0.0281413i
$926$	−428.059	+	125.689i	−0.462266	+	0.135734i
$927$	−64.9510	+	101.066i	−0.0700658	+	0.109024i
$928$	92.1060	−	201.684i	0.0992522	−	0.217332i
$929$	−233.876	+	269.908i	−0.251751	+	0.290536i	−0.867532	−	0.497381i	$-0.834295\pi$
$929$	−233.876	+	269.908i	−0.251751	+	0.290536i	0.615781	+	0.787917i	$0.288840\pi$
$930$	1268.12	+	1973.23i	1.36357	+	2.12176i
$931$	−68.4886	+	9.84718i	−0.0735646	+	0.0105770i
$932$	−159.317	−	1108.07i	−0.170941	−	1.18892i
$933$	−605.892	+	389.383i	−0.649402	+	0.417345i
$934$	−235.720	−	204.253i	−0.252377	−	0.218686i
$935$	156.658	+	71.5435i	0.167549	+	0.0765171i
$936$	−681.291	−	437.839i	−0.727875	−	0.467777i
$937$	−91.7114	−	312.340i	−0.0978777	−	0.333341i	0.895967	−	0.444120i	$-0.146484\pi$
$937$	−91.7114	−	312.340i	−0.0978777	−	0.333341i	−0.993845	+	0.110779i	$0.964665\pi$
$938$	425.260	+	490.777i	0.453369	+	0.523216i
$939$	−47.0071	+	160.091i	−0.0500608	+	0.170491i
$940$	−1740.07	+	794.665i	−1.85114	+	0.845388i
$941$	−286.157	−	41.1432i	−0.304099	−	0.0437228i	−0.0114237	−	0.999935i	$-0.503636\pi$
$941$	−286.157	−	41.1432i	−0.304099	−	0.0437228i	−0.292675	+	0.956212i	$0.594545\pi$
$942$			2118.15i			2.24857i
$943$	857.974	+	401.921i	0.909835	+	0.426215i
$944$	−914.543			−0.968795
$945$	−95.3449	+	663.138i	−0.100894	+	0.701733i
$946$	−511.434	−	1119.89i	−0.540628	−	1.18381i
$947$	868.305	+	254.957i	0.916900	+	0.269226i	0.705943	−	0.708269i	$-0.250524\pi$
$947$	868.305	+	254.957i	0.916900	+	0.269226i	0.210958	+	0.977495i	$0.432342\pi$
$948$	−3014.54	+	2612.12i	−3.17990	+	2.75540i
$949$	−84.7109	+	24.8734i	−0.0892634	+	0.0262101i
$950$	359.755	−	559.790i	0.378690	−	0.589253i
$951$	451.780	−	989.261i	0.475058	−	1.04023i
$952$	−232.183	+	267.953i	−0.243890	+	0.281464i
$953$	373.898	+	581.796i	0.392338	+	0.610489i	0.980091	−	0.198551i	$-0.0636236\pi$
$953$	373.898	+	581.796i	0.392338	+	0.610489i	−0.587753	+	0.809041i	$0.699987\pi$
$954$	110.270	−	15.8545i	0.115587	−	0.0166189i
$955$	−176.879	−	1230.22i	−0.185214	−	1.28819i
$956$	1608.47	−	1033.70i	1.68250	−	1.08128i
$957$	−932.167	−	807.727i	−0.974051	−	0.844020i
$958$	1449.28	+	661.864i	1.51282	+	0.690881i
$959$	−1036.86	−	666.347i	−1.08119	−	0.694836i
$960$	−370.246	−	1260.94i	−0.385672	−	1.31348i
$961$	102.858	+	118.704i	0.107032	+	0.123522i
$962$	28.8388	−	98.2160i	0.0299780	−	0.102096i
$963$	97.7441	−	44.6383i	0.101500	−	0.0463533i
$964$	−497.047	−	71.4646i	−0.515609	−	0.0741334i
$965$		−	225.729i		−	0.233916i
$966$	258.988	+	1934.23i	0.268104	+	2.00231i
$967$	−1508.98			−1.56047			−0.780236	−	0.625486i	$-0.784901\pi$
$967$	−1508.98			−1.56047			−0.780236	+	0.625486i	$0.784901\pi$
$968$	141.780	−	986.099i	0.146467	−	1.01870i
$969$	−67.8100	−	148.483i	−0.0699794	−	0.153233i
$970$	−2319.97	−	681.206i	−2.39173	−	0.702274i
$971$	−853.328	+	739.413i	−0.878814	+	0.761496i	−0.972205	−	0.234133i	$-0.924775\pi$
$971$	−853.328	+	739.413i	−0.878814	+	0.761496i	0.0933908	+	0.995630i	$0.470229\pi$
$972$	1813.77	−	532.571i	1.86602	−	0.547912i
$973$	23.5066	−	36.5769i	0.0241588	−	0.0375919i
$974$	316.166	−	692.308i	0.324606	−	0.710788i
$975$	460.759	−	531.744i	0.472573	−	0.545379i
$976$	955.236	+	1486.38i	0.978726	+	1.52293i
$977$	275.261	−	39.5766i	0.281741	−	0.0405083i	4.56174e−6	−	1.00000i	$-0.499999\pi$
$977$	275.261	−	39.5766i	0.281741	−	0.0405083i	0.281737	+	0.959492i	$0.409089\pi$
$978$	156.587	+	1089.08i	0.160109	+	1.11358i
$979$	−973.933	+	625.908i	−0.994824	+	0.639335i
$980$	230.240	+	199.504i	0.234939	+	0.203575i
$981$	642.002	+	293.193i	0.654436	+	0.298871i
$982$	−1153.41	−	741.252i	−1.17455	−	0.754839i
$983$	5.01355	+	17.0746i	0.00510026	+	0.0173699i	0.962004	−	0.273036i	$-0.0880278\pi$
$983$	5.01355	+	17.0746i	0.00510026	+	0.0173699i	−0.956904	+	0.290406i	$0.906210\pi$
$984$	1452.21	+	1675.94i	1.47582	+	1.70319i
$985$	403.140	−	1372.97i	0.409279	−	1.39388i
$986$	541.402	−	247.250i	0.549089	−	0.250760i
$987$	−879.932	−	126.515i	−0.891521	−	0.128181i
$988$		−	1150.32i		−	1.16429i
$989$	741.790	−	839.488i	0.750040	−	0.848825i
$990$	761.232			0.768921
$991$	122.938	−	855.049i	0.124054	−	0.862814i	−0.828835	−	0.559494i	$-0.810996\pi$
$991$	122.938	−	855.049i	0.124054	−	0.862814i	0.952889	−	0.303321i	$-0.0980953\pi$
$992$	−56.7855	−	124.343i	−0.0572435	−	0.125346i
$993$	−1297.85	−	381.084i	−1.30700	−	0.383770i
$994$	−601.248	+	520.984i	−0.604877	+	0.524129i
$995$	1616.66	−	474.695i	1.62479	−	0.477080i
$996$	357.554	−	556.365i	0.358990	−	0.558599i
$997$	−681.813	+	1492.96i	−0.683864	+	1.49745i	0.174632	+	0.984634i	$0.444126\pi$
$997$	−681.813	+	1492.96i	−0.683864	+	1.49745i	−0.858496	+	0.512820i	$0.828601\pi$
$998$	−1457.36	+	1681.88i	−1.46028	+	1.68525i
$999$	21.3121	+	33.1622i	0.0213334	+	0.0331954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.15.3	✓	30
3.2	odd	2		207.3.j.a.199.1		30
4.3	odd	2		368.3.p.a.337.1		30
23.7	odd	22		529.3.b.b.528.4		30
23.16	even	11		529.3.b.b.528.3		30
23.20	odd	22	inner	23.3.d.a.20.3	yes	30
69.20	even	22		207.3.j.a.181.1		30
92.43	even	22		368.3.p.a.273.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.15.3	✓	30	1.1	even	1	trivial
23.3.d.a.20.3	yes	30	23.20	odd	22	inner
207.3.j.a.181.1		30	69.20	even	22
207.3.j.a.199.1		30	3.2	odd	2
368.3.p.a.273.1		30	92.43	even	22
368.3.p.a.337.1		30	4.3	odd	2
529.3.b.b.528.3		30	23.16	even	11
529.3.b.b.528.4		30	23.7	odd	22

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.496456 - 3.45293i) q^{2} +(1.53764 + 3.36695i) q^{3} +(-7.83827 - 2.30152i) q^{4} +(-4.84192 + 4.19555i) q^{5} +(12.3892 - 3.63780i) q^{6} +(3.55260 - 5.52795i) q^{7} +(-6.04175 + 13.2296i) q^{8} +(-3.07830 + 3.55255i) q^{9} +O(q^{10})\)	\(q+(0.496456 - 3.45293i) q^{2} +(1.53764 + 3.36695i) q^{3} +(-7.83827 - 2.30152i) q^{4} +(-4.84192 + 4.19555i) q^{5} +(12.3892 - 3.63780i) q^{6} +(3.55260 - 5.52795i) q^{7} +(-6.04175 + 13.2296i) q^{8} +(-3.07830 + 3.55255i) q^{9} +(12.0831 + 18.8017i) q^{10} +(-7.17202 + 1.03118i) q^{11} +(-4.30328 - 29.9300i) q^{12} +(9.96529 - 6.40430i) q^{13} +(-17.3239 - 15.0112i) q^{14} +(-21.5713 - 9.85130i) q^{15} +(15.1920 + 9.76328i) q^{16} +(1.04520 + 3.55963i) q^{17} +(10.7384 + 12.3928i) q^{18} +(-3.34899 + 11.4056i) q^{19} +(47.6084 - 21.7420i) q^{20} +(24.0749 + 3.46145i) q^{21} +25.2764i q^{22} +(-21.0132 + 9.35129i) q^{23} -53.8334 q^{24} +(2.28371 - 15.8835i) q^{25} +(-17.1663 - 37.5889i) q^{26} +(15.2690 + 4.48339i) q^{27} +(-40.5689 + 35.1532i) q^{28} +(44.1267 - 12.9568i) q^{29} +(-44.7250 + 69.5935i) q^{30} +(11.7785 - 25.7914i) q^{31} +(3.15715 - 3.64354i) q^{32} +(-14.4999 - 22.5623i) q^{33} +(12.8100 - 1.84181i) q^{34} +(5.99139 + 41.6710i) q^{35} +(32.3048 - 20.7610i) q^{36} +(1.87208 + 1.62217i) q^{37} +(37.7202 + 17.2262i) q^{38} +(36.8860 + 23.7052i) q^{39} +(-26.2517 - 89.4052i) q^{40} +(-26.9760 - 31.1319i) q^{41} +(23.9043 - 81.4106i) q^{42} +(-44.3056 + 20.2337i) q^{43} +(58.5895 + 8.42389i) q^{44} -30.1163i q^{45} +(21.8572 + 77.1995i) q^{46} -36.5497 q^{47} +(-9.51280 + 66.1630i) q^{48} +(2.41806 + 5.29481i) q^{49} +(-53.7109 - 15.7710i) q^{50} +(-10.3780 + 8.99256i) q^{51} +(-92.8503 + 27.2633i) q^{52} +(3.67297 - 5.71526i) q^{53} +(23.0612 - 50.4971i) q^{54} +(30.4000 - 35.0835i) q^{55} +(51.6686 + 80.3979i) q^{56} +(-43.5517 + 6.26179i) q^{57} +(-22.8318 - 158.799i) q^{58} +(-42.6033 + 27.3795i) q^{59} +(146.409 + 126.864i) q^{60} +(88.9981 + 40.6441i) q^{61} +(-83.2084 - 53.4748i) q^{62} +(8.70234 + 29.6374i) q^{63} +(36.2903 + 41.8812i) q^{64} +(-21.3816 + 72.8190i) q^{65} +(-85.1044 + 38.8659i) q^{66} +(-28.0411 - 4.03170i) q^{67} -30.3069i q^{68} +(-63.7959 - 56.3715i) q^{69} +146.861 q^{70} +(4.93922 - 34.3530i) q^{71} +(-28.4004 - 62.1882i) q^{72} +(-7.15116 - 2.09977i) q^{73} +(6.53063 - 5.65882i) q^{74} +(56.9906 - 16.7340i) q^{75} +(52.5006 - 81.6925i) q^{76} +(-19.7790 + 43.3099i) q^{77} +(100.165 - 115.596i) q^{78} +(-71.3186 - 110.974i) q^{79} +(-114.521 + 16.4656i) q^{80} +(14.4036 + 100.180i) q^{81} +(-120.889 + 77.6904i) q^{82} +(16.5296 + 14.3229i) q^{83} +(-180.739 - 82.5408i) q^{84} +(-19.9954 - 12.8503i) q^{85} +(47.8697 + 163.029i) q^{86} +(111.476 + 128.650i) q^{87} +(29.6895 - 101.113i) q^{88} +(145.339 - 66.3743i) q^{89} +(-103.989 - 14.9514i) q^{90} -77.8395i q^{91} +(186.229 - 24.9356i) q^{92} +104.950 q^{93} +(-18.1453 + 126.203i) q^{94} +(-31.6373 - 69.2760i) q^{95} +(17.1222 + 5.02752i) q^{96} +(-81.7615 + 70.8467i) q^{97} +(19.4830 - 5.72074i) q^{98} +(18.4143 - 28.6532i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9}+O(q^{10}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9	\( 30 q - 11 q^{2} - 11 q^{3} - 23 q^{4} - 11 q^{5} + 22 q^{6} - 11 q^{7} + 10 q^{8} - 38 q^{9} - 11 q^{10} - 11 q^{11} - 14 q^{12} - 11 q^{13} - 11 q^{14} + 66 q^{15} + 73 q^{16} + 44 q^{17} + 126 q^{18} + 22 q^{19} + 77 q^{20} + 22 q^{21} + 36 q^{23} - 22 q^{24} - 152 q^{25} - 186 q^{26} - 62 q^{27} - 275 q^{28} - 88 q^{29} - 363 q^{30} - 110 q^{31} - 147 q^{32} - 132 q^{33} + 231 q^{34} + 209 q^{35} + 229 q^{36} + 341 q^{37} + 374 q^{38} + 295 q^{39} + 429 q^{40} + 77 q^{41} + 319 q^{42} + 77 q^{43} + 110 q^{44} - 99 q^{46} - 110 q^{47} - 550 q^{48} - 422 q^{49} - 396 q^{50} - 275 q^{51} - 472 q^{52} - 187 q^{53} - 198 q^{54} - 165 q^{55} + 176 q^{56} - 176 q^{57} - 13 q^{58} - q^{59} + 539 q^{60} + 297 q^{61} + 82 q^{62} + 264 q^{63} + 386 q^{64} + 220 q^{65} + 264 q^{66} + 11 q^{67} - 66 q^{69} - 198 q^{70} - 176 q^{71} - 605 q^{72} - 121 q^{73} - 352 q^{74} + 154 q^{75} + 110 q^{76} + 110 q^{77} + 360 q^{78} + 33 q^{79} - 242 q^{80} + 494 q^{81} + 96 q^{82} - 154 q^{83} + 11 q^{84} + 275 q^{85} + 143 q^{86} + 271 q^{87} + 429 q^{88} + 121 q^{89} + 242 q^{90} + 166 q^{92} + 260 q^{93} - 295 q^{94} - 154 q^{95} - 419 q^{96} + 154 q^{97} + 77 q^{98} - 242 q^{99}+O(q^{100}) \) 30 * q - 11 * q^2 - 11 * q^3 - 23 * q^4 - 11 * q^5 + 22 * q^6 - 11 * q^7 + 10 * q^8 - 38 * q^9 - 11 * q^10 - 11 * q^11 - 14 * q^12 - 11 * q^13 - 11 * q^14 + 66 * q^15 + 73 * q^16 + 44 * q^17 + 126 * q^18 + 22 * q^19 + 77 * q^20 + 22 * q^21 + 36 * q^23 - 22 * q^24 - 152 * q^25 - 186 * q^26 - 62 * q^27 - 275 * q^28 - 88 * q^29 - 363 * q^30 - 110 * q^31 - 147 * q^32 - 132 * q^33 + 231 * q^34 + 209 * q^35 + 229 * q^36 + 341 * q^37 + 374 * q^38 + 295 * q^39 + 429 * q^40 + 77 * q^41 + 319 * q^42 + 77 * q^43 + 110 * q^44 - 99 * q^46 - 110 * q^47 - 550 * q^48 - 422 * q^49 - 396 * q^50 - 275 * q^51 - 472 * q^52 - 187 * q^53 - 198 * q^54 - 165 * q^55 + 176 * q^56 - 176 * q^57 - 13 * q^58 - q^59 + 539 * q^60 + 297 * q^61 + 82 * q^62 + 264 * q^63 + 386 * q^64 + 220 * q^65 + 264 * q^66 + 11 * q^67 - 66 * q^69 - 198 * q^70 - 176 * q^71 - 605 * q^72 - 121 * q^73 - 352 * q^74 + 154 * q^75 + 110 * q^76 + 110 * q^77 + 360 * q^78 + 33 * q^79 - 242 * q^80 + 494 * q^81 + 96 * q^82 - 154 * q^83 + 11 * q^84 + 275 * q^85 + 143 * q^86 + 271 * q^87 + 429 * q^88 + 121 * q^89 + 242 * q^90 + 166 * q^92 + 260 * q^93 - 295 * q^94 - 154 * q^95 - 419 * q^96 + 154 * q^97 + 77 * q^98 - 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more