LMFDB - Embedded newform 23.3.d.a.7.3

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			7.3
Character	$\chi$	$=$	23.7
Dual form			23.3.d.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59301 - 1.83844i) q^{2} +(-1.87410 + 1.20441i) q^{3} +(-0.272894 - 1.89802i) q^{4} +(-2.69128 + 1.22907i) q^{5} +(-0.771235 + 5.36406i) q^{6} +(-1.33225 - 4.53722i) q^{7} +(4.26162 + 2.73877i) q^{8} +(-1.67709 + 3.67232i) q^{9} +O(q^{10})$	\(q+(1.59301 - 1.83844i) q^{2} +(-1.87410 + 1.20441i) q^{3} +(-0.272894 - 1.89802i) q^{4} +(-2.69128 + 1.22907i) q^{5} +(-0.771235 + 5.36406i) q^{6} +(-1.33225 - 4.53722i) q^{7} +(4.26162 + 2.73877i) q^{8} +(-1.67709 + 3.67232i) q^{9} +(-2.02769 + 6.90566i) q^{10} +(11.0247 - 9.55293i) q^{11} +(2.79743 + 3.22841i) q^{12} +(-22.7531 - 6.68090i) q^{13} +(-10.4637 - 4.77860i) q^{14} +(3.56342 - 5.54480i) q^{15} +(19.1833 - 5.63274i) q^{16} +(12.1869 + 1.75221i) q^{17} +(4.07969 + 8.93327i) q^{18} +(5.54565 - 0.797344i) q^{19} +(3.06723 + 4.77270i) q^{20} +(7.96145 + 6.89863i) q^{21} -35.4861i q^{22} +(5.15862 + 22.4140i) q^{23} -11.2853 q^{24} +(-10.6391 + 12.2782i) q^{25} +(-48.5283 + 31.1873i) q^{26} +(-4.13331 - 28.7478i) q^{27} +(-8.24818 + 3.76682i) q^{28} +(-3.08261 + 21.4400i) q^{29} +(-4.51717 - 15.3841i) q^{30} +(-0.0511435 - 0.0328679i) q^{31} +(11.7863 - 25.8083i) q^{32} +(-9.15568 + 31.1814i) q^{33} +(22.6352 - 19.6135i) q^{34} +(9.16200 + 10.5735i) q^{35} +(7.42780 + 2.18100i) q^{36} +(13.3445 + 6.09421i) q^{37} +(7.36843 - 11.4655i) q^{38} +(50.6880 - 14.8834i) q^{39} +(-14.8353 - 2.13300i) q^{40} +(4.95227 + 10.8440i) q^{41} +(25.3654 - 3.64699i) q^{42} +(-27.4308 - 42.6832i) q^{43} +(-21.1402 - 18.3181i) q^{44} -11.9445i q^{45} +(49.4245 + 26.2221i) q^{46} -23.0534 q^{47} +(-29.1674 + 33.6609i) q^{48} +(22.4099 - 14.4020i) q^{49} +(5.62443 + 39.1188i) q^{50} +(-24.9499 + 11.3942i) q^{51} +(-6.47131 + 45.0090i) q^{52} +(-28.2602 - 96.2454i) q^{53} +(-59.4355 - 38.1969i) q^{54} +(-17.9293 + 39.2596i) q^{55} +(6.74889 - 22.9846i) q^{56} +(-9.43277 + 8.17354i) q^{57} +(34.5055 + 39.8214i) q^{58} +(34.0311 + 9.99245i) q^{59} +(-11.4966 - 5.25031i) q^{60} +(-49.9475 + 77.7198i) q^{61} +(-0.141898 + 0.0416649i) q^{62} +(18.8964 + 2.71689i) q^{63} +(4.55063 + 9.96449i) q^{64} +(69.4461 - 9.98484i) q^{65} +(42.7398 + 66.5045i) q^{66} +(-72.5767 - 62.8880i) q^{67} -23.6092i q^{68} +(-36.6635 - 35.7930i) q^{69} +34.0339 q^{70} +(35.6457 - 41.1374i) q^{71} +(-17.2048 + 11.0568i) q^{72} +(6.81309 + 47.3861i) q^{73} +(32.4617 - 14.8248i) q^{74} +(5.15079 - 35.8245i) q^{75} +(-3.02675 - 10.3082i) q^{76} +(-58.0313 - 37.2945i) q^{77} +(53.3847 - 116.896i) q^{78} +(-10.2622 + 34.9499i) q^{79} +(-44.7047 + 38.7368i) q^{80} +(18.5765 + 21.4385i) q^{81} +(27.8249 + 8.17014i) q^{82} +(95.0493 + 43.4076i) q^{83} +(10.9211 - 16.9936i) q^{84} +(-34.9519 + 10.2628i) q^{85} +(-122.168 - 17.5651i) q^{86} +(-20.0455 - 43.8935i) q^{87} +(73.1462 - 10.5168i) q^{88} +(-2.45164 - 3.81483i) q^{89} +(-21.9592 - 19.0277i) q^{90} +112.136i q^{91} +(41.1346 - 15.9078i) q^{92} +0.135434 q^{93} +(-36.7244 + 42.3822i) q^{94} +(-13.9449 + 8.96184i) q^{95} +(8.99519 + 62.5629i) q^{96} +(119.559 - 54.6009i) q^{97} +(9.22220 - 64.1418i) q^{98} +(16.5920 + 56.5072i) 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 $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	1.59301	−	1.83844i	0.796507	−	0.919218i	−0.201677	−	0.979452i	$-0.564639\pi$
$2$	1.59301	−	1.83844i	0.796507	−	0.919218i	0.998184	+	0.0602341i	$0.0191847\pi$
$3$	−1.87410	+	1.20441i	−0.624700	+	0.401470i	−0.814344	−	0.580383i	$-0.802903\pi$
$3$	−1.87410	+	1.20441i	−0.624700	+	0.401470i	0.189644	+	0.981853i	$0.439267\pi$
$4$	−0.272894	−	1.89802i	−0.0682236	−	0.474505i
$5$	−2.69128	+	1.22907i	−0.538256	+	0.245813i	−0.665945	−	0.746001i	$-0.731971\pi$
$5$	−2.69128	+	1.22907i	−0.538256	+	0.245813i	0.127689	+	0.991814i	$0.459244\pi$
$6$	−0.771235	+	5.36406i	−0.128539	+	0.894009i
$7$	−1.33225	−	4.53722i	−0.190321	−	0.648175i	−0.998263	−	0.0589124i	$-0.981237\pi$
$7$	−1.33225	−	4.53722i	−0.190321	−	0.648175i	0.807942	−	0.589262i	$-0.200581\pi$
$8$	4.26162	+	2.73877i	0.532702	+	0.342347i
$9$	−1.67709	+	3.67232i	−0.186343	+	0.408035i
$10$	−2.02769	+	6.90566i	−0.202769	+	0.690566i
$11$	11.0247	−	9.55293i	1.00224	−	0.868448i	0.0109252	−	0.999940i	$-0.496522\pi$
$11$	11.0247	−	9.55293i	1.00224	−	0.868448i	0.991317	+	0.131492i	$0.0419769\pi$
$12$	2.79743	+	3.22841i	0.233119	+	0.269034i
$13$	−22.7531	−	6.68090i	−1.75024	−	0.513915i	−0.759593	−	0.650399i	$-0.774602\pi$
$13$	−22.7531	−	6.68090i	−1.75024	−	0.513915i	−0.990642	+	0.136484i	$0.956420\pi$
$14$	−10.4637	−	4.77860i	−0.747406	−	0.341329i
$15$	3.56342	−	5.54480i	0.237562	−	0.369653i
$16$	19.1833	−	5.63274i	1.19896	−	0.352046i
$17$	12.1869	+	1.75221i	0.716877	+	0.103071i	0.491094	−	0.871106i	$-0.336597\pi$
$17$	12.1869	+	1.75221i	0.716877	+	0.103071i	0.225783	+	0.974178i	$0.427506\pi$
$18$	4.07969	+	8.93327i	0.226649	+	0.496293i
$19$	5.54565	−	0.797344i	0.291876	−	0.0419655i	0.00517865	−	0.999987i	$-0.498352\pi$
$19$	5.54565	−	0.797344i	0.291876	−	0.0419655i	0.286698	+	0.958021i	$0.407442\pi$
$20$	3.06723	+	4.77270i	0.153361	+	0.238635i
$21$	7.96145	+	6.89863i	0.379116	+	0.328506i
$22$		−	35.4861i		−	1.61300i
$23$	5.15862	+	22.4140i	0.224288	+	0.974523i
$23$	5.15862	+	22.4140i	0.224288	+	0.974523i
$24$	−11.2853			−0.470221
$25$	−10.6391	+	12.2782i	−0.425566	+	0.491129i
$26$	−48.5283	+	31.1873i	−1.86647	+	1.19951i
$27$	−4.13331	−	28.7478i	−0.153086	−	1.06473i
$28$	−8.24818	+	3.76682i	−0.294578	+	0.134529i
$29$	−3.08261	+	21.4400i	−0.106297	+	0.739311i	0.865057	+	0.501674i	$0.167282\pi$
$29$	−3.08261	+	21.4400i	−0.106297	+	0.739311i	−0.971354	+	0.237637i	$0.923627\pi$
$30$	−4.51717	−	15.3841i	−0.150572	−	0.512802i
$31$	−0.0511435	−	0.0328679i	−0.00164979	−	0.00106025i	0.539816	−	0.841783i	$-0.318494\pi$
$31$	−0.0511435	−	0.0328679i	−0.00164979	−	0.00106025i	−0.541465	+	0.840723i	$0.682130\pi$
$32$	11.7863	−	25.8083i	0.368321	−	0.806510i
$33$	−9.15568	+	31.1814i	−0.277445	+	0.944890i
$34$	22.6352	−	19.6135i	0.665742	−	0.576869i
$35$	9.16200	+	10.5735i	0.261771	+	0.302100i
$36$	7.42780	+	2.18100i	0.206328	+	0.0605833i
$37$	13.3445	+	6.09421i	0.360661	+	0.164708i	0.587500	−	0.809224i	$-0.300112\pi$
$37$	13.3445	+	6.09421i	0.360661	+	0.164708i	−0.226840	+	0.973932i	$0.572839\pi$
$38$	7.36843	−	11.4655i	0.193906	−	0.301724i
$39$	50.6880	−	14.8834i	1.29969	−	0.381624i
$40$	−14.8353	−	2.13300i	−0.370883	−	0.0533250i
$41$	4.95227	+	10.8440i	0.120787	+	0.264487i	0.960361	−	0.278758i	$-0.0899228\pi$
$41$	4.95227	+	10.8440i	0.120787	+	0.264487i	−0.839574	+	0.543245i	$0.817196\pi$
$42$	25.3654	−	3.64699i	0.603938	−	0.0868331i
$43$	−27.4308	−	42.6832i	−0.637927	−	0.992633i	−0.998211	−	0.0597907i	$-0.980957\pi$
$43$	−27.4308	−	42.6832i	−0.637927	−	0.992633i	0.360284	−	0.932843i	$-0.382680\pi$
$44$	−21.1402	−	18.3181i	−0.480460	−	0.416321i
$45$		−	11.9445i		−	0.265433i
$46$	49.4245	+	26.2221i	1.07445	+	0.570045i
$47$	−23.0534			−0.490498			−0.245249	−	0.969460i	$-0.578870\pi$
$47$	−23.0534			−0.490498			−0.245249	+	0.969460i	$0.578870\pi$
$48$	−29.1674	+	33.6609i	−0.607653	+	0.701269i
$49$	22.4099	−	14.4020i	0.457345	−	0.293918i
$50$	5.62443	+	39.1188i	0.112489	+	0.782375i
$51$	−24.9499	+	11.3942i	−0.489213	+	0.223416i
$52$	−6.47131	+	45.0090i	−0.124448	+	0.865557i
$53$	−28.2602	−	96.2454i	−0.533211	−	1.81595i	−0.576779	−	0.816900i	$-0.695691\pi$
$53$	−28.2602	−	96.2454i	−0.533211	−	1.81595i	0.0435676	−	0.999050i	$-0.486128\pi$
$54$	−59.4355	−	38.1969i	−1.10066	−	0.707349i
$55$	−17.9293	+	39.2596i	−0.325987	+	0.713811i
$56$	6.74889	−	22.9846i	0.120516	−	0.410440i
$57$	−9.43277	+	8.17354i	−0.165487	+	0.143395i
$58$	34.5055	+	39.8214i	0.594922	+	0.686576i
$59$	34.0311	+	9.99245i	0.576799	+	0.169363i	0.557104	−	0.830443i	$-0.311912\pi$
$59$	34.0311	+	9.99245i	0.576799	+	0.169363i	0.0196948	+	0.999806i	$0.493731\pi$
$60$	−11.4966	−	5.25031i	−0.191610	−	0.0875052i
$61$	−49.9475	+	77.7198i	−0.818811	+	1.27409i	0.140029	+	0.990147i	$0.455280\pi$
$61$	−49.9475	+	77.7198i	−0.818811	+	1.27409i	−0.958840	+	0.283947i	$0.908356\pi$
$62$	−0.141898	+	0.0416649i	−0.00228867	+	0.000672015i
$63$	18.8964	+	2.71689i	0.299943	+	0.0431253i
$64$	4.55063	+	9.96449i	0.0711036	+	0.155695i
$65$	69.4461	−	9.98484i	1.06840	−	0.153613i
$66$	42.7398	+	66.5045i	0.647573	+	1.00764i
$67$	−72.5767	−	62.8880i	−1.08323	−	0.938628i	−0.0849036	−	0.996389i	$-0.527058\pi$
$67$	−72.5767	−	62.8880i	−1.08323	−	0.938628i	−0.998330	+	0.0577616i	$0.981604\pi$
$68$		−	23.6092i		−	0.347194i
$69$	−36.6635	−	35.7930i	−0.531355	−	0.518739i
$70$	34.0339			0.486199
$71$	35.6457	−	41.1374i	0.502053	−	0.579400i	−0.446993	−	0.894537i	$-0.647505\pi$
$71$	35.6457	−	41.1374i	0.502053	−	0.579400i	0.949046	+	0.315138i	$0.102051\pi$
$72$	−17.2048	+	11.0568i	−0.238955	+	0.153567i
$73$	6.81309	+	47.3861i	0.0933300	+	0.649124i	0.981762	+	0.190116i	$0.0608863\pi$
$73$	6.81309	+	47.3861i	0.0933300	+	0.649124i	−0.888432	+	0.459009i	$0.848205\pi$
$74$	32.4617	−	14.8248i	0.438672	−	0.200335i
$75$	5.15079	−	35.8245i	0.0686772	−	0.477660i
$76$	−3.02675	−	10.3082i	−0.0398257	−	0.135634i
$77$	−58.0313	−	37.2945i	−0.753654	−	0.484344i
$78$	53.3847	−	116.896i	0.684419	−	1.49867i
$79$	−10.2622	+	34.9499i	−0.129901	+	0.442404i	−0.998598	−	0.0529417i	$-0.983140\pi$
$79$	−10.2622	+	34.9499i	−0.129901	+	0.442404i	0.868696	+	0.495345i	$0.164958\pi$
$80$	−44.7047	+	38.7368i	−0.558809	+	0.484211i
$81$	18.5765	+	21.4385i	0.229340	+	0.264673i
$82$	27.8249	+	8.17014i	0.339329	+	0.0996359i
$83$	95.0493	+	43.4076i	1.14517	+	0.522983i	0.895374	−	0.445315i	$-0.146908\pi$
$83$	95.0493	+	43.4076i	1.14517	+	0.522983i	0.249798	+	0.968298i	$0.419636\pi$
$84$	10.9211	−	16.9936i	0.130013	−	0.202305i
$85$	−34.9519	+	10.2628i	−0.411199	+	0.120739i
$86$	−122.168	−	17.5651i	−1.42056	−	0.204246i
$87$	−20.0455	−	43.8935i	−0.230408	−	0.504523i
$88$	73.1462	−	10.5168i	0.831207	−	0.119509i
$89$	−2.45164	−	3.81483i	−0.0275466	−	0.0428633i	0.827207	−	0.561897i	$-0.189928\pi$
$89$	−2.45164	−	3.81483i	−0.0275466	−	0.0428633i	−0.854754	+	0.519034i	$0.826292\pi$
$90$	−21.9592	−	19.0277i	−0.243991	−	0.211419i
$91$			112.136i			1.23227i
$92$	41.1346	−	15.9078i	0.447115	−	0.172911i
$93$	0.135434			0.00145628
$94$	−36.7244	+	42.3822i	−0.390685	+	0.450874i
$95$	−13.9449	+	8.96184i	−0.146788	+	0.0943352i
$96$	8.99519	+	62.5629i	0.0936999	+	0.651697i
$97$	119.559	−	54.6009i	1.23257	−	0.562896i	0.310741	−	0.950495i	$-0.399423\pi$
$97$	119.559	−	54.6009i	1.23257	−	0.562896i	0.921828	+	0.387599i	$0.126695\pi$
$98$	9.22220	−	64.1418i	0.0941040	−	0.654508i
$99$	16.5920	+	56.5072i	0.167596	+	0.570780i
$100$	26.2077	+	16.8427i	0.262077	+	0.168427i
$101$	−22.6013	+	49.4900i	−0.223775	+	0.490000i	−0.987904	−	0.155064i	$-0.950442\pi$
$101$	−22.6013	+	49.4900i	−0.223775	+	0.490000i	0.764129	+	0.645063i	$0.223169\pi$
$102$	−18.7979	+	64.0199i	−0.184293	+	0.627646i
$103$	14.9023	−	12.9129i	0.144682	−	0.125368i	−0.579513	−	0.814963i	$-0.696757\pi$
$103$	14.9023	−	12.9129i	0.144682	−	0.125368i	0.724195	+	0.689595i	$0.242212\pi$
$104$	−78.6673	−	90.7869i	−0.756416	−	0.872951i
$105$	−29.9053	−	8.78100i	−0.284813	−	0.0836286i
$106$	−221.960	−	101.366i	−2.09396	−	0.956280i
$107$	−79.7149	+	124.039i	−0.744999	+	1.15924i	0.237211	+	0.971458i	$0.423767\pi$
$107$	−79.7149	+	124.039i	−0.744999	+	1.15924i	−0.982210	+	0.187784i	$0.939870\pi$
$108$	−53.4361	+	15.6902i	−0.494778	+	0.145280i
$109$	67.5885	+	9.71775i	0.620078	+	0.0891537i	0.445192	−	0.895435i	$-0.353135\pi$
$109$	67.5885	+	9.71775i	0.620078	+	0.0891537i	0.174886	+	0.984589i	$0.444044\pi$
$110$	43.6147	+	95.5029i	0.396498	+	0.868209i
$111$	−32.3488	+	4.65105i	−0.291430	+	0.0419013i
$112$	−51.1139	−	79.5348i	−0.456374	−	0.710132i
$113$	19.2502	+	16.6804i	0.170356	+	0.147614i	0.735866	−	0.677127i	$-0.236775\pi$
$113$	19.2502	+	16.6804i	0.170356	+	0.147614i	−0.565510	+	0.824741i	$0.691321\pi$
$114$			30.3621i			0.266334i
$115$	−41.4316	−	53.9821i	−0.360275	−	0.469410i
$116$	41.5348			0.358059
$117$	62.6933	−	72.3519i	0.535840	−	0.618393i
$118$	72.5826	−	46.6460i	0.615106	−	0.395305i
$119$	−8.28581	−	57.6291i	−0.0696287	−	0.484278i
$120$	30.3719	−	13.8704i	0.253099	−	0.115586i
$121$	13.0647	−	90.8673i	0.107973	−	0.750969i
$122$	63.3158	+	215.634i	0.518982	+	1.76749i
$123$	−22.3416	−	14.3581i	−0.181639	−	0.116732i
$124$	−0.0484272	+	0.106041i	−0.000390542	+	0.000855168i
$125$	34.3808	−	117.090i	0.275047	−	0.936722i
$126$	35.0971	−	30.4118i	0.278548	−	0.241363i
$127$	34.7125	+	40.0603i	0.273327	+	0.315436i	0.875773	−	0.482724i	$-0.160353\pi$
$127$	34.7125	+	40.0603i	0.273327	+	0.315436i	−0.602446	+	0.798160i	$0.705807\pi$
$128$	134.460	+	39.4811i	1.05047	+	0.308446i
$129$	102.816	+	46.9546i	0.797026	+	0.363989i
$130$	92.2721	−	143.578i	0.709785	−	1.10445i
$131$	80.0128	−	23.4939i	0.610784	−	0.179343i	0.0383112	−	0.999266i	$-0.487802\pi$
$131$	80.0128	−	23.4939i	0.610784	−	0.179343i	0.572473	+	0.819923i	$0.305984\pi$
$132$	61.6814	+	8.86845i	0.467284	+	0.0671852i
$133$	−11.0059	−	24.0996i	−0.0827512	−	0.181200i
$134$	−231.231	+	33.2460i	−1.72561	+	0.248105i
$135$	46.4569	+	72.2883i	0.344125	+	0.535469i
$136$	47.1370	+	40.8444i	0.346596	+	0.300327i
$137$		−	22.0385i		−	0.160865i	−0.996760	−	0.0804325i	$-0.974370\pi$
$137$		−	22.0385i		−	0.160865i	0.996760	−	0.0804325i	$-0.0256301\pi$
$138$	−124.209	+	10.3847i	−0.900062	+	0.0752511i
$139$	20.4932			0.147433			0.0737164	−	0.997279i	$-0.476514\pi$
$139$	20.4932			0.147433			0.0737164	+	0.997279i	$0.476514\pi$
$140$	17.5685	−	20.2751i	0.125489	−	0.144822i
$141$	43.2043	−	27.7657i	0.306414	−	0.196920i
$142$	−18.8443	−	131.065i	−0.132706	−	0.922992i
$143$	−314.667	+	143.704i	−2.20047	+	1.00492i
$144$	−11.4870	+	79.8939i	−0.0797709	+	0.554819i
$145$	−18.0550	−	61.4898i	−0.124517	−	0.424068i
$146$	97.9696	+	62.9612i	0.671025	+	0.431241i
$147$	−24.6525	+	53.9815i	−0.167704	+	0.367221i
$148$	7.92531	−	26.9911i	0.0535494	−	0.182373i
$149$	−19.5347	+	16.9270i	−0.131106	+	0.113604i	−0.717945	−	0.696099i	$-0.754917\pi$
$149$	−19.5347	+	16.9270i	−0.131106	+	0.113604i	0.586840	+	0.809703i	$0.300372\pi$
$150$	−57.6558	−	66.5383i	−0.384372	−	0.443589i
$151$	−214.839	−	63.0824i	−1.42277	−	0.417764i	−0.522333	−	0.852742i	$-0.674938\pi$
$151$	−214.839	−	63.0824i	−1.42277	−	0.417764i	−0.900441	+	0.434977i	$0.856756\pi$
$152$	25.8172	+	11.7903i	0.169850	+	0.0775678i
$153$	−26.8732	+	41.8156i	−0.175642	+	0.273304i
$154$	−161.008	+	47.2763i	−1.04551	+	0.306989i
$155$	0.178038	+	0.0255980i	0.00114863	+	0.000165148i
$156$	−42.0814	−	92.1454i	−0.269753	−	0.590676i
$157$	−224.842	+	32.3273i	−1.43211	+	0.205907i	−0.814311	−	0.580428i	$-0.802885\pi$
$157$	−224.842	+	32.3273i	−1.43211	+	0.205907i	−0.617800	+	0.786335i	$0.711976\pi$
$158$	47.9053	+	74.5421i	0.303198	+	0.471785i
$159$	168.881	+	146.337i	1.06215	+	0.920356i
$160$			83.9435i			0.524647i
$161$	94.8248	−	53.2669i	0.588974	−	0.330850i
$162$	69.0059			0.425963
$163$	−5.43908	+	6.27703i	−0.0333686	+	0.0385094i	−0.772189	−	0.635393i	$-0.780838\pi$
$163$	−5.43908	+	6.27703i	−0.0333686	+	0.0385094i	0.738820	+	0.673903i	$0.235383\pi$
$164$	19.2306	−	12.3588i	0.117260	−	0.0753583i
$165$	−13.6835	−	95.1707i	−0.0829302	−	0.576792i
$166$	231.217	−	105.593i	1.39287	−	0.636104i
$167$	4.46258	−	31.0379i	0.0267220	−	0.185856i	−0.972089	−	0.234614i	$-0.924617\pi$
$167$	4.46258	−	31.0379i	0.0267220	−	0.185856i	0.998811	+	0.0487583i	$0.0155264\pi$
$168$	15.0348	+	51.2039i	0.0894930	+	0.304785i
$169$	330.895	+	212.653i	1.95796	+	1.25830i
$170$	−36.8114	+	80.6057i	−0.216538	+	0.474151i
$171$	−6.37246	+	21.7026i	−0.0372658	+	0.126916i
$172$	−73.5280	+	63.7124i	−0.427488	+	0.370421i
$173$	−37.7366	−	43.5504i	−0.218131	−	0.251736i	0.636129	−	0.771583i	$-0.280535\pi$
$173$	−37.7366	−	43.5504i	−0.218131	−	0.251736i	−0.854260	+	0.519846i	$0.825989\pi$
$174$	−112.628	−	33.0706i	−0.647288	−	0.190061i
$175$	69.8830	+	31.9145i	0.399331	+	0.182369i
$176$	157.681	−	245.356i	0.895913	−	1.39407i
$177$	−75.8128	+	22.2606i	−0.428321	+	0.125766i
$178$	−10.9188	−	1.56989i	−0.0613417	−	0.00881961i
$179$	−78.0138	−	170.826i	−0.435831	−	0.954338i	−0.992345	−	0.123499i	$-0.960588\pi$
$179$	−78.0138	−	170.826i	−0.435831	−	0.954338i	0.556513	−	0.830839i	$-0.312139\pi$
$180$	−22.6709	+	3.25958i	−0.125949	+	0.0181088i
$181$	−135.371	−	210.641i	−0.747905	−	1.16376i	−0.981506	−	0.191430i	$-0.938688\pi$
$181$	−135.371	−	210.641i	−0.747905	−	1.16376i	0.233602	−	0.972332i	$-0.424949\pi$
$182$	206.155	+	178.635i	1.13272	+	0.981509i
$183$		−	205.812i		−	1.12466i
$184$	−39.4029	+	109.648i	−0.214146	+	0.595914i
$185$	−43.4038			−0.234615
$186$	0.215749	−	0.248987i	0.00115994	−	0.00133864i
$187$	151.095	−	97.1031i	0.807996	−	0.519268i
$188$	6.29114	+	43.7558i	0.0334635	+	0.232744i
$189$	−124.929	+	57.0530i	−0.660998	+	0.301868i
$190$	−5.73864	+	39.9131i	−0.0302034	+	0.210069i
$191$	−10.9255	−	37.2087i	−0.0572014	−	0.194810i	0.925935	−	0.377682i	$-0.123279\pi$
$191$	−10.9255	−	37.2087i	−0.0572014	−	0.194810i	−0.983137	+	0.182872i	$0.941461\pi$
$192$	−20.5297	−	13.1936i	−0.106925	−	0.0687168i
$193$	−121.051	+	265.066i	−0.627210	+	1.37340i	0.282948	+	0.959135i	$0.408688\pi$
$193$	−121.051	+	265.066i	−0.627210	+	1.37340i	−0.910158	+	0.414262i	$0.864040\pi$
$194$	90.0793	−	306.782i	0.464326	−	1.58135i
$195$	−118.123	+	102.354i	−0.605759	+	0.524893i
$196$	−33.4508	−	38.6043i	−0.170667	−	0.196961i
$197$	18.2288	+	5.35246i	0.0925320	+	0.0271698i	0.327671	−	0.944792i	$-0.393736\pi$
$197$	18.2288	+	5.35246i	0.0925320	+	0.0271698i	−0.235139	+	0.971962i	$0.575554\pi$
$198$	130.316	+	59.5134i	0.658162	+	0.300573i
$199$	183.112	−	284.928i	0.920160	−	1.43180i	0.0182695	−	0.999833i	$-0.494184\pi$
$199$	183.112	−	284.928i	0.920160	−	1.43180i	0.901891	−	0.431964i	$-0.142179\pi$
$200$	−78.9672	+	23.1869i	−0.394836	+	0.115934i
$201$	211.759	+	30.4463i	1.05353	+	0.151474i
$202$	54.9800	+	120.389i	0.272178	+	0.595987i
$203$	101.385	−	14.5770i	0.499433	−	0.0718076i
$204$	28.4352	+	44.2460i	0.139388	+	0.216892i
$205$	−26.6559	−	23.0974i	−0.130029	−	0.112670i
$206$		−	47.9673i		−	0.232851i
$207$	−90.9629	−	18.6463i	−0.439434	−	0.0900786i
$208$	−474.111			−2.27938
$209$	53.5220	−	61.7676i	0.256086	−	0.295539i
$210$	−63.7829	+	40.9908i	−0.303728	+	0.195194i
$211$	7.00938	+	48.7513i	0.0332198	+	0.231049i	0.999667	−	0.0258178i	$-0.00821898\pi$
$211$	7.00938	+	48.7513i	0.0332198	+	0.231049i	−0.966447	+	0.256867i	$0.917310\pi$
$212$	−174.964	+	79.9033i	−0.825301	+	0.376902i
$213$	−17.2574	+	120.028i	−0.0810206	+	0.563510i
$214$	101.051	+	344.146i	0.472199	+	1.60816i
$215$	126.285	+	81.1582i	0.587370	+	0.377480i
$216$	61.1192	−	133.832i	0.282959	−	0.619595i
$217$	−0.0809932	+	0.275837i	−0.000373240	+	0.00127114i
$218$	125.535	−	108.777i	0.575848	−	0.498975i
$219$	−69.8407	−	80.6005i	−0.318907	−	0.368039i
$220$	79.4084	+	23.3164i	0.360947	+	0.105984i
$221$	−265.583	−	121.288i	−1.20173	−	0.548813i
$222$	−42.9814	+	66.8803i	−0.193610	+	0.301263i
$223$	15.9060	−	4.67044i	0.0713275	−	0.0209437i	−0.245874	−	0.969302i	$-0.579075\pi$
$223$	15.9060	−	4.67044i	0.0713275	−	0.0209437i	0.317202	+	0.948358i	$0.397257\pi$
$224$	−132.800	−	19.0938i	−0.592859	−	0.0852402i
$225$	−27.2467	−	59.6620i	−0.121096	−	0.265164i
$226$	61.3317	−	8.81816i	0.271379	−	0.0390184i
$227$	222.274	+	345.865i	0.979181	+	1.52364i	0.846439	+	0.532485i	$0.178742\pi$
$227$	222.274	+	345.865i	0.979181	+	1.52364i	0.132742	+	0.991151i	$0.457622\pi$
$228$	18.0877	+	15.6731i	0.0793321	+	0.0687416i
$229$			259.654i			1.13386i	0.823767	+	0.566929i	$0.191869\pi$
$229$			259.654i			1.13386i	−0.823767	+	0.566929i	$0.808131\pi$
$230$	−165.244	−	9.82489i	−0.718451	−	0.0427169i
$231$	153.674			0.665257
$232$	−71.8563	+	82.9265i	−0.309725	+	0.357442i
$233$	−137.080	+	88.0962i	−0.588328	+	0.378095i	−0.800675	−	0.599099i	$-0.795526\pi$
$233$	−137.080	+	88.0962i	−0.588328	+	0.378095i	0.212347	+	0.977194i	$0.431889\pi$
$234$	−33.1431	−	230.515i	−0.141637	−	0.985108i
$235$	62.0431	−	28.3341i	0.264013	−	0.120571i
$236$	9.67897	−	67.3187i	0.0410126	−	0.285249i
$237$	−22.8616	−	77.8595i	−0.0964625	−	0.328521i
$238$	−119.147	−	76.5710i	−0.500617	−	0.321727i
$239$	15.9676	−	34.9641i	0.0668099	−	0.146293i	−0.873281	−	0.487216i	$-0.838012\pi$
$239$	15.9676	−	34.9641i	0.0668099	−	0.146293i	0.940091	+	0.340923i	$0.110740\pi$
$240$	37.1260	−	126.440i	0.154692	−	0.526831i
$241$	85.3703	−	73.9738i	0.354234	−	0.306945i	−0.459506	−	0.888175i	$-0.651974\pi$
$241$	85.3703	−	73.9738i	0.354234	−	0.306945i	0.813740	+	0.581229i	$0.197428\pi$
$242$	−146.241	−	168.772i	−0.604303	−	0.697403i
$243$	190.168	+	55.8383i	0.782584	+	0.229787i
$244$	161.144	+	73.5921i	0.660427	+	0.301607i
$245$	−42.6104	+	66.3030i	−0.173920	+	0.270625i
$246$	−61.9869	+	18.2010i	−0.251979	+	0.0739878i
$247$	−131.507	−	18.9079i	−0.532419	−	0.0765503i
$248$	−0.127936	−	0.280141i	−0.000515871	−	0.00112960i
$249$	−230.412	+	33.1283i	−0.925351	+	0.133045i
$250$	−160.494	−	249.733i	−0.641976	−	0.998934i
$251$	−108.593	−	94.0959i	−0.432639	−	0.374884i	0.411142	−	0.911571i	$-0.365130\pi$
$251$	−108.593	−	94.0959i	−0.432639	−	0.374884i	−0.843781	+	0.536687i	$0.819676\pi$
$252$		−	36.6072i		−	0.145267i
$253$	270.992	+	197.827i	1.07111	+	0.781926i
$254$	128.946			0.507661
$255$	53.1428	−	61.3300i	0.208403	−	0.240510i
$256$	249.919	−	160.613i	0.976245	−	0.627395i
$257$	57.7915	+	401.949i	0.224870	+	1.56400i	0.719246	+	0.694755i	$0.244487\pi$
$257$	57.7915	+	401.949i	0.224870	+	1.56400i	−0.494376	+	0.869248i	$0.664603\pi$
$258$	250.111	−	114.222i	0.969422	−	0.442720i
$259$	9.87264	−	68.6657i	0.0381183	−	0.265119i
$260$	−37.9029	−	129.085i	−0.145780	−	0.496482i
$261$	−73.5647	−	47.2772i	−0.281857	−	0.181139i
$262$	84.2695	−	184.524i	0.321639	−	0.704292i
$263$	25.8190	−	87.9315i	0.0981712	−	0.334340i	−0.895732	−	0.444594i	$-0.853348\pi$
$263$	25.8190	−	87.9315i	0.0981712	−	0.334340i	0.993904	+	0.110253i	$0.0351662\pi$
$264$	−124.417	+	107.808i	−0.471275	+	0.408362i
$265$	194.348	+	224.290i	0.733389	+	0.846376i
$266$	−61.8381	−	18.1573i	−0.232474	−	0.0682605i
$267$	9.18925	+	4.19659i	0.0344167	+	0.0157176i
$268$	−99.5571	+	154.914i	−0.371482	+	0.578037i
$269$	38.2022	−	11.2172i	0.142016	−	0.0416996i	−0.209952	−	0.977712i	$-0.567331\pi$
$269$	38.2022	−	11.2172i	0.142016	−	0.0416996i	0.351968	+	0.936012i	$0.385513\pi$
$270$	206.904	+	29.7483i	0.766311	+	0.110179i
$271$	−54.5020	−	119.343i	−0.201114	−	0.440379i	0.782023	−	0.623250i	$-0.214188\pi$
$271$	−54.5020	−	119.343i	−0.201114	−	0.440379i	−0.983137	+	0.182871i	$0.941461\pi$
$272$	243.655	−	35.0323i	0.895791	−	0.128795i
$273$	−135.058	−	210.155i	−0.494718	−	0.769797i
$274$	−40.5164	−	35.1076i	−0.147870	−	0.128130i
$275$			236.998i			0.861812i
$276$	−57.9307	+	79.3558i	−0.209894	+	0.287521i
$277$	382.249			1.37996			0.689981	−	0.723828i	$-0.257619\pi$
$277$	382.249			1.37996			0.689981	+	0.723828i	$0.257619\pi$
$278$	32.6459	−	37.6754i	0.117431	−	0.135523i
$279$	0.206474	−	0.132692i	0.000740048	−	0.000475600i
$280$	10.0865	+	70.1529i	0.0360231	+	0.250546i
$281$	−43.7143	+	19.9636i	−0.155567	+	0.0710450i	−0.491677	−	0.870778i	$-0.663616\pi$
$281$	−43.7143	+	19.9636i	−0.155567	+	0.0710450i	0.336110	+	0.941823i	$0.390889\pi$
$282$	17.7796	−	123.660i	0.0630481	−	0.438509i
$283$	−91.7065	−	312.324i	−0.324051	−	1.10362i	−0.946968	−	0.321329i	$-0.895870\pi$
$283$	−91.7065	−	312.324i	−0.324051	−	1.10362i	0.622916	−	0.782289i	$-0.285948\pi$
$284$	−87.8072	−	56.4302i	−0.309180	−	0.198698i
$285$	15.3404	−	33.5908i	0.0538259	−	0.117862i
$286$	−237.079	+	807.417i	−0.828948	+	2.82314i
$287$	42.6038	−	36.9164i	0.148445	−	0.128629i
$288$	75.0097	+	86.5658i	0.260450	+	0.300576i
$289$	−131.843	−	38.7126i	−0.456204	−	0.133954i
$290$	−141.807	−	64.7611i	−0.488990	−	0.223314i
$291$	−158.304	+	246.326i	−0.544000	+	0.846481i
$292$	88.0806	−	25.8628i	0.301646	−	0.0885712i
$293$	−189.510	−	27.2474i	−0.646792	−	0.0929946i	−0.188891	−	0.981998i	$-0.560489\pi$
$293$	−189.510	−	27.2474i	−0.646792	−	0.0929946i	−0.457901	+	0.889003i	$0.651398\pi$
$294$	59.9697	+	131.315i	0.203979	+	0.446651i
$295$	−103.869	+	14.9341i	−0.352097	+	0.0506239i
$296$	40.1783	+	62.5186i	0.135737	+	0.211211i
$297$	−320.194	−	277.450i	−1.07810	−	0.934175i
$298$			62.8782i			0.211001i
$299$	32.3715	−	544.452i	0.108266	−	1.82091i
$300$	−69.4013			−0.231338
$301$	−157.119	+	181.325i	−0.521989	+	0.602407i
$302$	−458.214	+	294.476i	−1.51727	+	0.975088i
$303$	−17.2491	−	119.970i	−0.0569279	−	0.395942i
$304$	101.893	−	46.5329i	0.335174	−	0.153069i
$305$	38.8998	−	270.554i	0.127540	−	0.887063i
$306$	34.0658	+	116.017i	0.111326	+	0.379142i
$307$	−402.942	−	258.955i	−1.31252	−	0.843502i	−0.318000	−	0.948091i	$-0.603011\pi$
$307$	−402.942	−	258.955i	−1.31252	−	0.843502i	−0.994516	+	0.104588i	$0.966648\pi$
$308$	−54.9493	+	120.322i	−0.178407	+	0.390657i
$309$	−12.3759	+	42.1485i	−0.0400515	+	0.136403i
$310$	0.330677	−	0.286534i	0.00106670	−	0.000924302i
$311$	256.570	+	296.097i	0.824983	+	0.952081i	0.999469	−	0.0325782i	$-0.0103718\pi$
$311$	256.570	+	296.097i	0.824983	+	0.952081i	−0.174486	+	0.984660i	$0.555826\pi$
$312$	256.775	+	75.3960i	0.822997	+	0.241654i
$313$	−106.020	−	48.4179i	−0.338723	−	0.154690i	0.238789	−	0.971071i	$-0.423249\pi$
$313$	−106.020	−	48.4179i	−0.338723	−	0.154690i	−0.577513	+	0.816382i	$0.695977\pi$
$314$	−298.744	+	464.855i	−0.951414	+	1.48043i
$315$	−54.1947	+	15.9130i	−0.172047	+	0.0505175i
$316$	69.1361	+	9.94027i	0.218785	+	0.0314566i
$317$	96.9005	+	212.182i	0.305680	+	0.669345i	0.998668	−	0.0516040i	$-0.0164334\pi$
$317$	96.9005	+	212.182i	0.305680	+	0.669345i	−0.692988	+	0.720949i	$0.743706\pi$
$318$	538.061	−	77.3615i	1.69202	−	0.243275i
$319$	170.830	+	265.817i	0.535518	+	0.833282i
$320$	−24.4940	−	21.2242i	−0.0765438	−	0.0663256i
$321$		−	328.471i		−	1.02327i
$322$	53.1296	−	259.184i	0.164999	−	0.804920i
$323$	68.9814			0.213565
$324$	35.6213	−	41.1091i	0.109942	−	0.126880i
$325$	324.103	−	208.288i	0.997239	−	0.640886i
$326$	2.87539	+	19.9988i	0.00882022	+	0.0613460i
$327$	−138.372	+	63.1922i	−0.423155	+	0.193248i
$328$	−8.59448	+	59.7759i	−0.0262027	+	0.182244i
$329$	30.7128	+	104.598i	0.0933521	+	0.317928i
$330$	−196.763	−	126.452i	−0.596252	−	0.383188i
$331$	168.068	−	368.018i	0.507759	−	1.11184i	−0.466111	−	0.884726i	$-0.654345\pi$
$331$	168.068	−	368.018i	0.507759	−	1.11184i	0.973869	−	0.227110i	$-0.0729276\pi$
$332$	56.4501	−	192.251i	0.170030	−	0.579070i
$333$	−44.7597	+	38.7845i	−0.134414	+	0.116470i
$334$	−49.9523	−	57.6480i	−0.149558	−	0.172599i
$335$	272.618	+	80.0477i	0.813784	+	0.238949i
$336$	191.585	+	87.4940i	0.570194	+	0.260399i
$337$	−35.7004	+	55.5509i	−0.105936	+	0.164839i	−0.890174	−	0.455620i	$-0.849418\pi$
$337$	−35.7004	+	55.5509i	−0.105936	+	0.164839i	0.784238	+	0.620460i	$0.213054\pi$
$338$	918.070	−	269.570i	2.71618	−	0.797544i
$339$	−56.1668	−	8.07557i	−0.165684	−	0.0238218i
$340$	29.0172	+	63.5389i	0.0853448	+	0.186879i
$341$	−0.877824	+	0.126212i	−0.00257426	+	0.000370123i
$342$	29.7474	+	46.2879i	0.0869808	+	0.135345i
$343$	−270.315	−	234.229i	−0.788091	−	0.682885i
$344$		−	257.026i		−	0.747170i
$345$	142.664	+	51.2672i	0.413518	+	0.148601i
$346$	−140.180			−0.405143
$347$	133.229	−	153.754i	0.383945	−	0.443096i	−0.530575	−	0.847638i	$-0.678024\pi$
$347$	133.229	−	153.754i	0.383945	−	0.443096i	0.914519	+	0.404543i	$0.132569\pi$
$348$	−77.8405	+	50.0250i	−0.223679	+	0.143750i
$349$	26.9375	+	187.355i	0.0771849	+	0.536832i	0.991325	+	0.131434i	$0.0419581\pi$
$349$	26.9375	+	187.355i	0.0771849	+	0.536832i	−0.914140	+	0.405398i	$0.867133\pi$
$350$	169.997	−	77.6352i	0.485707	−	0.221815i
$351$	−98.0159	+	681.715i	−0.279247	+	1.94221i
$352$	−116.605	−	397.122i	−0.331265	−	1.12819i
$353$	−79.9722	−	51.3950i	−0.226550	−	0.145595i	0.422442	−	0.906390i	$-0.361173\pi$
$353$	−79.9722	−	51.3950i	−0.226550	−	0.145595i	−0.648992	+	0.760795i	$0.724809\pi$
$354$	−79.8460	+	174.838i	−0.225554	+	0.493894i
$355$	−45.3721	+	154.523i	−0.127809	+	0.435276i
$356$	−6.57160	+	5.69432i	−0.0184595	+	0.0159953i
$357$	84.9375	+	98.0231i	0.237920	+	0.274575i
$358$	−438.331	−	128.705i	−1.22439	−	0.359512i
$359$	−117.941	−	53.8617i	−0.328526	−	0.150033i	0.244323	−	0.969694i	$-0.421434\pi$
$359$	−117.941	−	53.8617i	−0.328526	−	0.150033i	−0.572848	+	0.819661i	$0.694162\pi$
$360$	32.7132	−	50.9028i	0.0908701	−	0.141397i
$361$	−316.258	+	92.8619i	−0.876062	+	0.257235i
$362$	−602.897	−	86.6836i	−1.66546	−	0.239457i
$363$	84.9569	+	186.030i	0.234041	+	0.512478i
$364$	212.837	−	30.6014i	0.584717	−	0.0840696i
$365$	−76.5765	−	119.155i	−0.209799	−	0.326453i
$366$	−378.372	−	327.861i	−1.03380	−	0.895796i
$367$		−	167.326i		−	0.455928i	−0.973670	−	0.227964i	$-0.926793\pi$
$367$		−	167.326i		−	0.455928i	0.973670	−	0.227964i	$-0.0732069\pi$
$368$	225.212	+	400.919i	0.611989	+	1.08945i
$369$	−48.1278			−0.130428
$370$	−69.1429	+	79.7951i	−0.186873	+	0.215663i
$371$	−399.037	+	256.446i	−1.07557	+	0.691228i
$372$	−0.0369593	−	0.257057i	−9.93529e−5	−	0.000691015i
$373$	415.141	−	189.588i	1.11298	−	0.508280i	0.227882	−	0.973689i	$-0.426820\pi$
$373$	415.141	−	189.588i	1.11298	−	0.508280i	0.885096	+	0.465409i	$0.154093\pi$
$374$	62.1792	−	432.466i	0.166254	−	1.15633i
$375$	76.5918	+	260.848i	0.204245	+	0.695593i
$376$	−98.2447	−	63.1380i	−0.261289	−	0.167920i
$377$	213.377	−	467.231i	0.565988	−	1.23934i
$378$	−94.1248	+	320.560i	−0.249007	+	0.848041i
$379$	93.1043	−	80.6753i	0.245658	−	0.212864i	−0.523325	−	0.852133i	$-0.675309\pi$
$379$	93.1043	−	80.6753i	0.245658	−	0.212864i	0.768983	+	0.639270i	$0.220763\pi$
$380$	20.8153	+	24.0221i	0.0547770	+	0.0632160i
$381$	−113.304	−	33.2690i	−0.297385	−	0.0873202i
$382$	−85.8103	−	39.1882i	−0.224634	−	0.102587i
$383$	−93.3055	+	145.186i	−0.243618	+	0.379076i	−0.941432	−	0.337202i	$-0.890519\pi$
$383$	−93.3055	+	145.186i	−0.243618	+	0.379076i	0.697815	+	0.716278i	$0.254156\pi$
$384$	−299.543	+	87.9539i	−0.780061	+	0.229047i
$385$	202.016	+	29.0455i	0.524717	+	0.0754429i
$386$	294.470	+	644.799i	0.762875	+	1.67046i
$387$	202.750	−	29.1511i	0.523903	−	0.0753258i
$388$	−136.261	−	212.026i	−0.351187	−	0.546458i
$389$	373.082	+	323.277i	0.959079	+	0.831047i	0.985685	−	0.168599i	$-0.0539244\pi$
$389$	373.082	+	323.277i	0.959079	+	0.831047i	−0.0266058	+	0.999646i	$0.508470\pi$
$390$			380.213i			0.974906i
$391$	23.5935	+	282.197i	0.0603414	+	0.721731i
$392$	134.946			0.344251
$393$	−121.656	+	140.398i	−0.309556	+	0.357247i
$394$	38.8789	−	24.9859i	0.0986773	−	0.0634161i
$395$	−15.3372	−	106.673i	−0.0388284	−	0.270058i
$396$	102.724	−	46.9125i	0.259404	−	0.118466i
$397$	−55.4477	+	385.648i	−0.139667	+	0.971404i	0.792628	+	0.609705i	$0.208712\pi$
$397$	−55.4477	+	385.648i	−0.139667	+	0.971404i	−0.932295	+	0.361699i	$0.882197\pi$
$398$	−232.121	−	790.533i	−0.583220	−	1.98626i
$399$	49.6520	+	31.9094i	0.124441	+	0.0799734i
$400$	−134.934	+	295.465i	−0.337336	+	0.738662i
$401$	−52.2370	+	177.903i	−0.130267	+	0.443648i	−0.998633	−	0.0522762i	$-0.983352\pi$
$401$	−52.2370	+	177.903i	−0.130267	+	0.443648i	0.868366	+	0.495924i	$0.165171\pi$
$402$	393.309	−	340.804i	0.978380	−	0.847771i
$403$	0.944083	+	1.08953i	0.00234264	+	0.00270355i
$404$	100.101	+	29.3923i	0.247774	+	0.0727531i
$405$	−76.3439	−	34.8651i	−0.188504	−	0.0860867i
$406$	134.709	−	209.611i	0.331795	−	0.516283i
$407$	205.336	−	60.2920i	0.504510	−	0.148138i
$408$	−137.533	−	19.7742i	−0.337090	−	0.0484663i
$409$	−164.700	−	360.642i	−0.402689	−	0.881765i	−0.996991	−	0.0775233i	$-0.975299\pi$
$409$	−164.700	−	360.642i	−0.402689	−	0.881765i	0.594302	−	0.804242i	$-0.297428\pi$
$410$	−84.9263	+	12.2106i	−0.207137	+	0.0297819i
$411$	26.5434	+	41.3024i	0.0645825	+	0.100492i
$412$	−28.5757	−	24.7610i	−0.0693585	−	0.0600995i
$413$		−	167.719i		−	0.406100i
$414$	−179.185	+	137.526i	−0.432814	+	0.332188i
$415$	−309.155			−0.744952
$416$	−440.597	+	508.476i	−1.05913	+	1.22230i
$417$	−38.4062	+	24.6822i	−0.0921012	+	0.0591899i
$418$	−28.2946	−	196.793i	−0.0676905	−	0.470798i
$419$	−512.018	+	233.831i	−1.22200	+	0.558069i	−0.918749	−	0.394842i	$-0.870799\pi$
$419$	−512.018	+	233.831i	−1.22200	+	0.558069i	−0.303251	+	0.952911i	$0.598072\pi$
$420$	−8.50553	+	59.1573i	−0.0202513	+	0.140851i
$421$	−91.1004	−	310.259i	−0.216390	−	0.736958i	−0.994113	−	0.108350i	$-0.965443\pi$
$421$	−91.1004	−	310.259i	−0.216390	−	0.736958i	0.777722	−	0.628608i	$-0.216375\pi$
$422$	100.792	+	64.7752i	0.238844	+	0.153496i
$423$	38.6626	−	84.6593i	0.0914010	−	0.200140i
$424$	143.160	−	487.559i	0.337642	−	1.14990i
$425$	−151.172	+	130.992i	−0.355699	+	0.308215i
$426$	193.172	+	222.932i	0.453455	+	0.523315i
$427$	419.174	+	123.081i	0.981673	+	0.288245i
$428$	257.182	+	117.451i	0.600893	+	0.274419i
$429$	416.639	−	648.303i	0.971187	−	1.51120i
$430$	350.377	−	102.880i	0.814830	−	0.239256i
$431$	38.1700	+	5.48802i	0.0885615	+	0.0127332i	0.186453	−	0.982464i	$-0.440301\pi$
$431$	38.1700	+	5.48802i	0.0885615	+	0.0127332i	−0.0978916	+	0.995197i	$0.531210\pi$
$432$	−241.220	−	528.197i	−0.558379	−	1.22268i
$433$	480.792	−	69.1274i	1.11037	−	0.159648i	0.437366	−	0.899283i	$-0.355911\pi$
$433$	480.792	−	69.1274i	1.11037	−	0.159648i	0.673007	+	0.739636i	$0.265002\pi$
$434$	0.378086	+	0.588314i	0.000871166	+	0.00135556i
$435$	107.896	+	93.4923i	0.248037	+	0.214925i
$436$		−	130.936i		−	0.300313i
$437$	46.4796	+	120.187i	0.106361	+	0.275028i
$438$	−259.436			−0.592320
$439$	200.231	−	231.079i	0.456107	−	0.526376i	−0.480388	−	0.877056i	$-0.659504\pi$
$439$	200.231	−	231.079i	0.456107	−	0.526376i	0.936495	+	0.350680i	$0.114050\pi$
$440$	−183.931	+	118.205i	−0.418025	+	0.268648i
$441$	15.3052	+	106.450i	0.0347056	+	0.241383i
$442$	−646.057	+	295.044i	−1.46167	+	0.667521i
$443$	−22.3348	+	155.342i	−0.0504172	+	0.350659i	0.948961	+	0.315394i	$0.102137\pi$
$443$	−22.3348	+	155.342i	−0.0504172	+	0.350659i	−0.999378	+	0.0352652i	$0.988772\pi$
$444$	17.6556	+	60.1294i	0.0397648	+	0.135427i
$445$	11.2867	+	7.25355i	0.0253635	+	0.0163001i
$446$	16.7522	−	36.6823i	0.0375611	−	0.0822473i
$447$	16.2231	−	55.2506i	0.0362932	−	0.123603i
$448$	39.1485	−	33.9224i	0.0873851	−	0.0757196i
$449$	−343.647	−	396.590i	−0.765361	−	0.883274i	0.230601	−	0.973048i	$-0.425931\pi$
$449$	−343.647	−	396.590i	−0.765361	−	0.883274i	−0.995962	+	0.0897744i	$0.971385\pi$
$450$	−153.089	−	44.9510i	−0.340198	−	0.0998911i
$451$	158.189	+	72.2423i	0.350751	+	0.160183i
$452$	26.4065	−	41.0893i	0.0584214	−	0.0909055i
$453$	478.607	−	140.532i	1.05653	−	0.310224i
$454$	989.937	+	142.331i	2.18048	+	0.313505i
$455$	−137.823	−	301.790i	−0.302907	−	0.663275i
$456$	−62.5843	+	8.99827i	−0.137246	+	0.0197330i
$457$	108.003	+	168.056i	0.236330	+	0.367736i	0.939079	−	0.343701i	$-0.111681\pi$
$457$	108.003	+	168.056i	0.236330	+	0.367736i	−0.702749	+	0.711438i	$0.748044\pi$
$458$	477.356	+	413.632i	1.04226	+	0.903126i
$459$		−	357.590i		−	0.779062i
$460$	−91.1528	+	93.3695i	−0.198158	+	0.202977i
$461$	225.708			0.489606			0.244803	−	0.969573i	$-0.421277\pi$
$461$	225.708			0.489606			0.244803	+	0.969573i	$0.421277\pi$
$462$	244.805	−	282.521i	0.529882	−	0.611516i
$463$	−669.595	+	430.322i	−1.44621	+	0.929422i	−0.446815	+	0.894627i	$0.647442\pi$
$463$	−669.595	+	430.322i	−1.44621	+	0.929422i	−0.999394	+	0.0347955i	$0.988922\pi$
$464$	61.6312	+	428.655i	0.132826	+	0.923825i
$465$	−0.364492	+	0.166458i	−0.000783853	+	0.000357974i
$466$	−56.4117	+	392.352i	−0.121055	+	0.841957i
$467$	92.6078	+	315.393i	0.198304	+	0.675360i	0.997260	+	0.0739717i	$0.0235675\pi$
$467$	92.6078	+	315.393i	0.198304	+	0.675360i	−0.798957	+	0.601389i	$0.794614\pi$
$468$	−154.434	−	99.2488i	−0.329988	−	0.212070i
$469$	−188.647	+	413.079i	−0.402232	+	0.880765i
$470$	46.7450	−	159.199i	0.0994575	−	0.338721i
$471$	382.440	−	331.386i	0.811975	−	0.703580i
$472$	117.661	+	135.788i	0.249281	+	0.287686i
$473$	−710.166	−	208.523i	−1.50141	−	0.440853i
$474$	−179.559	−	82.0016i	−0.378815	−	0.172999i
$475$	−49.2110	+	76.5738i	−0.103602	+	0.161208i
$476$	−107.120	+	31.4533i	−0.225042	+	0.0660784i
$477$	400.838	+	57.6319i	0.840332	+	0.120822i
$478$	−38.8427	−	85.0536i	−0.0812609	−	0.177936i
$479$	−566.531	+	81.4549i	−1.18274	+	0.170052i	−0.705492	−	0.708718i	$-0.749274\pi$
$479$	−566.531	+	81.4549i	−1.18274	+	0.170052i	−0.477245	+	0.878770i	$0.658365\pi$
$480$	−101.102	−	157.319i	−0.210630	−	0.327747i
$481$	−262.912	−	227.815i	−0.546595	−	0.473627i
$482$		−	274.789i		−	0.570102i
$483$	−113.556	+	214.035i	−0.235106	+	0.443138i
$484$	−176.033			−0.363705
$485$	−254.659	+	293.892i	−0.525070	+	0.605964i
$486$	405.595	−	260.660i	0.834558	−	0.536338i
$487$	−59.8978	−	416.598i	−0.122993	−	0.855438i	−0.954135	−	0.299377i	$-0.903221\pi$
$487$	−59.8978	−	416.598i	−0.122993	−	0.855438i	0.831141	−	0.556061i	$-0.187688\pi$
$488$	−425.714	+	194.417i	−0.872364	+	0.398395i
$489$	2.63325	−	18.3147i	0.00538497	−	0.0374533i
$490$	54.0150	+	183.958i	0.110235	+	0.375425i
$491$	483.980	+	311.035i	0.985703	+	0.633473i	0.930996	−	0.365030i	$-0.118941\pi$
$491$	483.980	+	311.035i	0.985703	+	0.633473i	0.0547070	+	0.998502i	$0.482578\pi$
$492$	−21.1551	+	46.3231i	−0.0429981	+	0.0941527i
$493$	−75.1349	+	255.886i	−0.152404	+	0.519039i
$494$	−244.254	+	211.647i	−0.494442	+	0.428436i
$495$	−114.105	−	131.684i	−0.230515	−	0.266028i
$496$	−1.16624	−	0.342438i	−0.00235129	−	0.000690400i
$497$	−234.138	−	106.927i	−0.471103	−	0.215146i
$498$	−306.146	+	476.372i	−0.614751	+	0.956571i
$499$	−480.442	+	141.070i	−0.962809	+	0.282706i	−0.725110	−	0.688633i	$-0.758211\pi$
$499$	−480.442	+	141.070i	−0.962809	+	0.282706i	−0.237699	+	0.971339i	$0.576393\pi$
$500$	−231.622	−	33.3023i	−0.463245	−	0.0666045i
$501$	29.0191	+	63.5430i	0.0579224	+	0.126832i
$502$	−345.979	+	49.7442i	−0.689201	+	0.0990921i
$503$	79.0421	+	122.992i	0.157141	+	0.244517i	0.910893	−	0.412643i	$-0.135394\pi$
$503$	79.0421	+	122.992i	0.157141	+	0.244517i	−0.753752	+	0.657159i	$0.771758\pi$
$504$	73.0883	+	63.3314i	0.145016	+	0.125657i
$505$		−	160.970i		−	0.318752i
$506$	795.386	−	183.059i	1.57191	−	0.361777i
$507$	−876.253			−1.72831
$508$	66.5625	−	76.8173i	0.131029	−	0.151215i
$509$	562.571	−	361.542i	1.10525	−	0.710299i	0.144995	−	0.989432i	$-0.453684\pi$
$509$	562.571	−	361.542i	1.10525	−	0.710299i	0.960252	+	0.279133i	$0.0900471\pi$
$510$	−28.0942	−	195.399i	−0.0550866	−	0.383136i
$511$	205.924	−	94.0425i	0.402983	−	0.184036i
$512$	23.0731	−	160.477i	0.0450646	−	0.313431i
$513$	−45.8438	−	156.130i	−0.0893642	−	0.304347i
$514$	831.020	+	534.064i	1.61677	+	1.03904i
$515$	−24.2354	+	53.0681i	−0.0470590	+	0.103045i
$516$	61.0629	−	207.961i	0.118339	−	0.403026i
$517$	−254.156	+	220.227i	−0.491597	+	0.425972i
$518$	−110.510	−	127.536i	−0.213340	−	0.246208i
$519$	123.175	+	36.1674i	0.237331	+	0.0696867i
$520$	323.299	+	147.646i	0.621728	+	0.283934i
$521$	521.133	−	810.899i	1.00026	−	1.55643i	0.180612	−	0.983554i	$-0.442192\pi$
$521$	521.133	−	810.899i	1.00026	−	1.55643i	0.819644	−	0.572874i	$-0.194171\pi$
$522$	−204.106	+	59.9308i	−0.391007	+	0.114810i
$523$	191.414	+	27.5212i	0.365992	+	0.0526217i	0.322858	−	0.946448i	$-0.395357\pi$
$523$	191.414	+	27.5212i	0.365992	+	0.0526217i	0.0431345	+	0.999069i	$0.486266\pi$
$524$	−66.4269	−	145.455i	−0.126769	−	0.277585i
$525$	−169.406	+	24.3569i	−0.322678	+	0.0463941i
$526$	−120.526	−	187.543i	−0.229138	−	0.356545i
$527$	−0.565689	−	0.490172i	−0.00107341	−	0.000930118i
$528$			649.734i			1.23056i
$529$	−475.777	+	231.251i	−0.899390	+	0.437147i
$530$	721.941			1.36215
$531$	−93.7687	+	108.215i	−0.176589	+	0.203794i
$532$	−42.7381	+	27.4661i	−0.0803347	+	0.0516280i
$533$	−40.2319	−	279.819i	−0.0754819	−	0.524988i
$534$	22.3538	−	10.2086i	0.0418610	−	0.0191173i
$535$	62.0832	−	431.798i	0.116043	−	0.807099i
$536$	−137.058	−	466.776i	−0.255705	−	0.870850i
$537$	351.951	+	226.185i	0.655402	+	0.421201i
$538$	40.2346	−	88.1015i	0.0747855	−	0.163757i
$539$	109.481	−	372.858i	0.203118	−	0.691758i
$540$	124.527	−	107.903i	0.230606	−	0.199821i
$541$	363.384	+	419.368i	0.671690	+	0.775172i	0.984640	−	0.174598i	$-0.0558626\pi$
$541$	363.384	+	419.368i	0.671690	+	0.775172i	−0.312950	+	0.949770i	$0.601317\pi$
$542$	−306.226	−	89.9162i	−0.564993	−	0.165897i
$543$	507.397	+	231.720i	0.934432	+	0.426741i
$544$	188.860	−	293.872i	0.347169	−	0.540205i
$545$	−193.843	+	56.9175i	−0.355675	+	0.104436i
$546$	−601.505	−	86.4834i	−1.10166	−	0.158394i
$547$	149.989	+	328.431i	0.274204	+	0.600422i	0.995766	−	0.0919276i	$-0.0293028\pi$
$547$	149.989	+	328.431i	0.274204	+	0.600422i	−0.721562	+	0.692350i	$0.756576\pi$
$548$	−41.8296	+	6.01418i	−0.0763313	+	0.0109748i
$549$	−201.645	−	313.766i	−0.367295	−	0.571523i
$550$	435.706	+	377.541i	0.792193	+	0.686439i
$551$			121.357i			0.220248i
$552$	−58.2166	−	252.949i	−0.105465	−	0.458241i
$553$	172.247			0.311478
$554$	608.929	−	702.741i	1.09915	−	1.26849i
$555$	81.3431	−	52.2760i	0.146564	−	0.0941910i
$556$	−5.59247	−	38.8965i	−0.0100584	−	0.0699577i
$557$	724.858	−	331.032i	1.30136	−	0.594312i	0.360391	−	0.932801i	$-0.382643\pi$
$557$	724.858	−	331.032i	1.30136	−	0.594312i	0.940970	+	0.338490i	$0.109916\pi$
$558$	0.0849686	−	0.590969i	0.000152273	−	0.00105908i
$559$	338.973	+	1154.44i	0.606392	+	2.06518i
$560$	235.315	+	151.228i	0.420206	+	0.270050i
$561$	−166.216	+	363.962i	−0.296285	+	0.648773i
$562$	−32.9356	+	112.168i	−0.0586042	+	0.199588i
$563$	109.347	−	94.7494i	0.194221	−	0.168294i	−0.552321	−	0.833631i	$-0.686258\pi$
$563$	109.347	−	94.7494i	0.194221	−	0.168294i	0.746543	+	0.665338i	$0.231712\pi$
$564$	−64.4902	−	74.4257i	−0.114344	−	0.131960i
$565$	−72.3090	−	21.2318i	−0.127980	−	0.0375785i
$566$	−720.277	−	328.939i	−1.27257	−	0.581165i
$567$	72.5225	−	112.847i	0.127906	−	0.199025i
$568$	264.574	−	77.6861i	0.465800	−	0.136771i
$569$	−870.145	−	125.108i	−1.52925	−	0.219873i	−0.674253	−	0.738501i	$-0.735534\pi$
$569$	−870.145	−	125.108i	−1.52925	−	0.219873i	−0.855000	+	0.518627i	$0.826443\pi$
$570$	−37.3170	−	81.7129i	−0.0654685	−	0.143356i
$571$	−144.773	+	20.8153i	−0.253544	+	0.0364541i	−0.267915	−	0.963443i	$-0.586335\pi$
$571$	−144.773	+	20.8153i	−0.253544	+	0.0364541i	0.0143709	+	0.999897i	$0.495425\pi$
$572$	358.623	+	558.029i	0.626964	+	0.975575i
$573$	65.2900	+	56.5741i	0.113944	+	0.0987332i
$574$		−	137.133i		−	0.238907i
$575$	−330.088	−	175.127i	−0.574066	−	0.304569i
$576$	−44.2246			−0.0767788
$577$	−170.570	+	196.848i	−0.295615	+	0.341158i	−0.884055	−	0.467383i	$-0.845197\pi$
$577$	−170.570	+	196.848i	−0.295615	+	0.341158i	0.588440	+	0.808541i	$0.299742\pi$
$578$	−281.198	+	180.715i	−0.486502	+	0.312656i
$579$	−92.3855	−	642.555i	−0.159560	−	1.10977i
$580$	−111.782	+	51.0491i	−0.192727	+	0.0880156i
$581$	70.3204	−	489.089i	0.121033	−	0.841806i
$582$	200.674	+	683.432i	0.344800	+	1.17428i
$583$	−1230.98	−	791.106i	−2.11147	−	1.35696i
$584$	−100.745	+	220.601i	−0.172509	+	0.377741i
$585$	−79.7999	+	271.773i	−0.136410	+	0.464570i
$586$	−351.985	+	304.996i	−0.600656	+	0.520472i
$587$	−483.827	−	558.366i	−0.824236	−	0.951219i	0.175209	−	0.984531i	$-0.443940\pi$
$587$	−483.827	−	558.366i	−0.824236	−	0.951219i	−0.999445	+	0.0333121i	$0.989394\pi$
$588$	109.186	+	32.0598i	0.185690	+	0.0545235i
$589$	−0.309831	−	0.141495i	−0.000526028	−	0.000240229i
$590$	−138.009	+	214.746i	−0.233913	+	0.363976i
$591$	−40.6091	+	11.9239i	−0.0687126	+	0.0201758i
$592$	290.318	+	41.7414i	0.490402	+	0.0705092i
$593$	376.127	+	823.604i	0.634279	+	1.38888i	0.904664	+	0.426125i	$0.140121\pi$
$593$	376.127	+	823.604i	0.634279	+	1.38888i	−0.270386	+	0.962752i	$0.587151\pi$
$594$	−1020.15	+	146.675i	−1.71742	+	0.246928i
$595$	93.1294	+	144.912i	0.156520	+	0.243550i
$596$	37.4586	+	32.4581i	0.0628501	+	0.0544599i
$597$			754.525i			1.26386i
$598$	−949.372	−	926.832i	−1.58758	−	1.54989i
$599$	398.189			0.664757			0.332378	−	0.943146i	$-0.392149\pi$
$599$	398.189			0.664757			0.332378	+	0.943146i	$0.392149\pi$
$600$	120.066	−	138.563i	0.200110	−	0.230939i
$601$	320.527	−	205.990i	0.533324	−	0.342746i	−0.246099	−	0.969245i	$-0.579149\pi$
$601$	320.527	−	205.990i	0.533324	−	0.342746i	0.779423	+	0.626498i	$0.215513\pi$
$602$	83.0614	+	577.705i	0.137976	+	0.959643i
$603$	352.662	−	161.056i	0.584846	−	0.267090i
$604$	−61.1034	+	424.984i	−0.101165	+	0.703615i
$605$	76.5210	+	260.607i	0.126481	+	0.430755i
$606$	−248.036	−	159.403i	−0.409300	−	0.263041i
$607$	211.791	−	463.758i	0.348914	−	0.764016i	−0.651073	−	0.759015i	$-0.725681\pi$
$607$	211.791	−	463.758i	0.348914	−	0.764016i	0.999987	−	0.00500079i	$-0.00159181\pi$
$608$	44.7844	−	152.522i	0.0736586	−	0.250858i
$609$	−172.449	+	149.428i	−0.283167	+	0.245366i
$610$	−435.429	−	502.512i	−0.713818	−	0.823789i
$611$	524.535	+	154.017i	0.858486	+	0.252074i
$612$	86.7004	+	39.5947i	0.141667	+	0.0646973i
$613$	−539.765	+	839.890i	−0.880530	+	1.37013i	0.0479896	+	0.998848i	$0.484719\pi$
$613$	−539.765	+	839.890i	−0.880530	+	1.37013i	−0.928520	+	0.371283i	$0.878918\pi$
$614$	−1117.97	+	328.264i	−1.82079	+	0.534632i
$615$	77.7746	+	11.1823i	0.126463	+	0.0181826i
$616$	−145.166	−	317.869i	−0.235659	−	0.516022i
$617$	704.493	−	101.291i	1.14180	−	0.164167i	0.454644	−	0.890673i	$-0.349766\pi$
$617$	704.493	−	101.291i	1.14180	−	0.164167i	0.687160	+	0.726507i	$0.258857\pi$
$618$	57.7723	+	89.8955i	0.0934827	+	0.145462i
$619$	781.408	+	677.094i	1.26237	+	1.09385i	0.991345	+	0.131280i	$0.0419086\pi$
$619$	781.408	+	677.094i	1.26237	+	1.09385i	0.271027	+	0.962572i	$0.412637\pi$
$620$		−	0.344906i		−	0.000556300i
$621$	623.033	−	240.943i	1.00327	−	0.387993i
$622$	953.075			1.53228
$623$	−14.0425	+	16.2060i	−0.0225402	+	0.0260128i
$624$	888.532	−	571.025i	1.42393	−	0.915104i
$625$	−6.41932	−	44.6474i	−0.0102709	−	0.0714358i
$626$	−257.905	+	117.781i	−0.411989	+	0.188149i
$627$	−25.9119	+	180.221i	−0.0413268	+	0.287434i
$628$	122.716	+	417.932i	0.195408	+	0.665497i
$629$	151.949	+	97.6518i	0.241573	+	0.155249i
$630$	−57.0779	+	124.983i	−0.0905999	+	0.198386i
$631$	233.923	−	796.670i	0.370719	−	1.26255i	−0.537218	−	0.843444i	$-0.680525\pi$
$631$	233.923	−	796.670i	0.370719	−	1.26255i	0.907936	−	0.419108i	$-0.137657\pi$
$632$	−139.453	+	120.837i	−0.220654	+	0.191198i
$633$	−71.8529	−	82.9226i	−0.113512	−	0.130999i
$634$	544.448	+	159.864i	0.858750	+	0.252152i
$635$	−142.658	−	65.1496i	−0.224658	−	0.102598i
$636$	231.663	−	360.475i	0.364250	−	0.566785i
$637$	−606.113	+	177.971i	−0.951511	+	0.279389i
$638$	760.822	+	109.390i	1.19251	+	0.171457i
$639$	91.2883	+	199.894i	0.142861	+	0.312822i
$640$	−410.395	+	59.0059i	−0.641242	+	0.0921967i
$641$	−282.476	−	439.541i	−0.440680	−	0.685712i	0.547877	−	0.836559i	$-0.315436\pi$
$641$	−282.476	−	439.541i	−0.440680	−	0.685712i	−0.988557	+	0.150847i	$0.951800\pi$
$642$	−603.872	−	523.258i	−0.940611	−	0.815044i
$643$		−	397.331i		−	0.617934i	−0.951073	−	0.308967i	$-0.900017\pi$
$643$		−	397.331i		−	0.617934i	0.951073	−	0.308967i	$-0.0999832\pi$
$644$	−126.979	−	165.443i	−0.197172	−	0.256900i
$645$	−334.418			−0.518477
$646$	109.888	−	126.818i	0.170106	−	0.196313i
$647$	277.675	−	178.451i	0.429173	−	0.275812i	−0.308170	−	0.951331i	$-0.599717\pi$
$647$	277.675	−	178.451i	0.429173	−	0.275812i	0.737343	+	0.675519i	$0.236080\pi$
$648$	20.4510	+	142.239i	0.0315601	+	0.219505i
$649$	470.639	−	214.934i	0.725176	−	0.331177i
$650$	133.376	−	927.647i	0.205193	−	1.42715i
$651$	−0.180432	−	0.614496i	−0.000277162	−	0.000943926i
$652$	13.3982	+	8.61052i	0.0205494	+	0.0132063i
$653$	−109.216	+	239.149i	−0.167252	+	0.366232i	−0.974636	−	0.223795i	$-0.928155\pi$
$653$	−109.216	+	239.149i	−0.167252	+	0.366232i	0.807384	+	0.590027i	$0.200883\pi$
$654$	−104.253	+	355.054i	−0.159408	+	0.542895i
$655$	−186.461	+	161.569i	−0.284673	+	0.246671i
$656$	156.082	+	180.128i	0.237930	+	0.274586i
$657$	−185.443	−	54.4509i	−0.282257	−	0.0828781i
$658$	241.223	+	110.163i	0.366601	+	0.167421i
$659$	−180.425	+	280.746i	−0.273786	+	0.426019i	−0.950732	−	0.310013i	$-0.899666\pi$
$659$	−180.425	+	280.746i	−0.273786	+	0.426019i	0.676947	+	0.736032i	$0.263303\pi$
$660$	−176.902	+	51.9431i	−0.268033	+	0.0787016i
$661$	−897.351	−	129.020i	−1.35757	−	0.195188i	−0.575203	−	0.818011i	$-0.695077\pi$
$661$	−897.351	−	129.020i	−1.35757	−	0.195188i	−0.782363	+	0.622822i	$0.785986\pi$
$662$	−408.842	−	895.240i	−0.617587	−	1.35233i
$663$	643.809	−	92.5658i	0.971055	−	0.139617i
$664$	286.180	+	445.305i	0.430994	+	0.670640i
$665$	59.2399	+	51.3317i	0.0890826	+	0.0771905i
$666$			144.072i			0.216324i
$667$	−496.459	+	41.5073i	−0.744317	+	0.0622298i
$668$	−60.1285			−0.0900127
$669$	−24.1844	+	27.9103i	−0.0361501	+	0.0417194i
$670$	581.446	−	373.673i	0.867830	−	0.557721i
$671$	191.797	+	1333.98i	0.285838	+	1.98805i
$672$	271.878	−	124.162i	0.404580	−	0.184766i
$673$	137.056	−	953.247i	0.203650	−	1.41641i	−0.589687	−	0.807632i	$-0.700749\pi$
$673$	137.056	−	953.247i	0.203650	−	1.41641i	0.793337	−	0.608783i	$-0.208342\pi$
$674$	45.2556	+	154.126i	0.0671447	+	0.228674i
$675$	396.947	+	255.103i	0.588070	+	0.377930i
$676$	313.321	−	686.078i	0.463493	−	1.01491i
$677$	−70.7306	+	240.886i	−0.104477	+	0.355814i	−0.995093	−	0.0989400i	$-0.968455\pi$
$677$	−70.7306	+	240.886i	−0.104477	+	0.355814i	0.890617	+	0.454754i	$0.150273\pi$
$678$	−104.321	+	90.3947i	−0.153866	+	0.133325i
$679$	−407.019	−	469.725i	−0.599439	−	0.691789i
$680$	−177.059	−	51.9893i	−0.260381	−	0.0764548i
$681$	−833.128	−	380.477i	−1.22339	−	0.558703i
$682$	−1.16635	+	1.81488i	−0.00171020	+	0.00266112i
$683$	802.242	−	235.560i	1.17459	−	0.344889i	0.364501	−	0.931203i	$-0.381239\pi$
$683$	802.242	−	235.560i	1.17459	−	0.344889i	0.810084	+	0.586313i	$0.199421\pi$
$684$	42.9310	+	6.17255i	0.0627646	+	0.00902419i
$685$	27.0868	+	59.3117i	0.0395427	+	0.0865865i
$686$	−861.231	+	123.826i	−1.25544	+	0.180505i
$687$	−312.729	−	486.617i	−0.455210	−	0.708321i
$688$	−766.638	−	664.296i	−1.11430	−	0.965547i
$689$			2378.68i			3.45237i
$690$	321.517	−	180.609i	0.465966	−	0.261751i
$691$	278.397			0.402890			0.201445	−	0.979500i	$-0.435436\pi$
$691$	278.397			0.402890			0.201445	+	0.979500i	$0.435436\pi$
$692$	−72.3615	+	83.5096i	−0.104569	+	0.120679i
$693$	234.281	−	150.563i	0.338068	−	0.217263i
$694$	−70.4320	−	489.865i	−0.101487	−	0.705858i
$695$	−55.1528	+	25.1874i	−0.0793565	+	0.0362409i
$696$	34.7882	−	241.957i	0.0499830	−	0.347639i
$697$	41.3519	+	140.832i	0.0593284	+	0.202054i
$698$	387.351	+	248.935i	0.554944	+	0.356641i
$699$	150.798	−	330.202i	0.215734	−	0.472392i
$700$	41.5037	−	141.349i	0.0592910	−	0.201927i
$701$	−356.382	+	308.807i	−0.508391	+	0.440523i	−0.870902	−	0.491456i	$-0.836465\pi$
$701$	−356.382	+	308.807i	−0.508391	+	0.440523i	0.362511	+	0.931979i	$0.381919\pi$
$702$	1097.15	+	1266.18i	1.56289	+	1.80367i
$703$	78.8628	+	23.1562i	0.112180	+	0.0329391i
$704$	145.359	+	66.3833i	0.206476	+	0.0942945i
$705$	−82.1490	+	127.826i	−0.116523	+	0.181314i
$706$	−221.883	+	65.1508i	−0.314282	+	0.0922816i
$707$	254.658	+	36.6142i	0.360195	+	0.0517882i
$708$	62.9401	+	137.819i	0.0888984	+	0.194660i
$709$	−142.896	+	20.5453i	−0.201546	+	0.0289779i	−0.242348	−	0.970189i	$-0.577918\pi$
$709$	−142.896	+	20.5453i	−0.201546	+	0.0289779i	0.0408025	+	0.999167i	$0.487009\pi$
$710$	211.803	+	329.571i	0.298313	+	0.464185i
$711$	−111.136	−	96.3002i	−0.156310	−	0.135443i
$712$		−	22.9719i		−	0.0322638i
$713$	0.472872	−	1.31588i	0.000663215	−	0.00184556i
$714$	315.516			0.441899
$715$	670.235	−	773.493i	0.937392	−	1.08181i
$716$	−302.943	+	194.689i	−0.423104	+	0.271913i
$717$	12.1863	+	84.7577i	0.0169963	+	0.118212i
$718$	−286.902	+	131.024i	−0.399586	+	0.182485i
$719$	95.7063	−	665.652i	0.133110	−	0.925802i	−0.808356	−	0.588694i	$-0.799642\pi$
$719$	95.7063	−	665.652i	0.133110	−	0.925802i	0.941466	−	0.337108i	$-0.109449\pi$
$720$	−67.2801	−	229.135i	−0.0934446	−	0.318243i
$721$	−78.4422	−	50.4117i	−0.108796	−	0.0699192i
$722$	−333.084	+	729.351i	−0.461335	+	1.01018i
$723$	−70.8977	+	241.455i	−0.0980604	+	0.333963i
$724$	−362.859	+	314.419i	−0.501187	+	0.434281i
$725$	−230.449	−	265.952i	−0.317861	−	0.366831i
$726$	477.341	+	140.160i	0.657495	+	0.193058i
$727$	952.866	+	435.159i	1.31068	+	0.598568i	0.943436	−	0.331555i	$-0.107573\pi$
$727$	952.866	+	435.159i	1.31068	+	0.598568i	0.367246	+	0.930124i	$0.380301\pi$
$728$	−307.116	+	477.882i	−0.421862	+	0.656431i
$729$	−668.609	+	196.321i	−0.917159	+	0.269302i
$730$	−341.047	−	49.0352i	−0.467188	−	0.0671715i
$731$	−259.507	−	568.241i	−0.355003	−	0.777348i
$732$	−390.635	+	56.1649i	−0.533655	+	0.0767280i
$733$	−113.289	−	176.281i	−0.154555	−	0.240492i	0.755338	−	0.655336i	$-0.227473\pi$
$733$	−113.289	−	176.281i	−0.154555	−	0.240492i	−0.909893	+	0.414843i	$0.863836\pi$
$734$	−307.618	−	266.552i	−0.419098	−	0.363150i
$735$		−	175.579i		−	0.238883i
$736$	639.270	+	131.042i	0.868573	+	0.178047i
$737$	−1400.90			−1.90081
$738$	−76.6683	+	88.4799i	−0.103887	+	0.119892i
$739$	−689.858	+	443.345i	−0.933502	+	0.599926i	−0.916545	−	0.399931i	$-0.869034\pi$
$739$	−689.858	+	443.345i	−0.933502	+	0.599926i	−0.0169570	+	0.999856i	$0.505398\pi$
$740$	11.8447	+	82.3814i	0.0160063	+	0.111326i
$741$	269.231	−	122.954i	0.363335	−	0.165929i
$742$	−164.213	+	1142.13i	−0.221311	+	1.53925i
$743$	−181.837	−	619.280i	−0.244734	−	0.833486i	−0.986631	−	0.162972i	$-0.947892\pi$
$743$	−181.837	−	619.280i	−0.244734	−	0.833486i	0.741897	−	0.670514i	$-0.233926\pi$
$744$	0.577169	+	0.370924i	0.000775765	+	0.000498554i
$745$	31.7691	−	69.5646i	0.0426431	−	0.0933753i
$746$	312.779	−	1065.23i	0.419274	−	1.42792i
$747$	−318.813	+	276.253i	−0.426791	+	0.369816i
$748$	−225.537	−	260.283i	−0.301520	−	0.347972i
$749$	668.992	+	196.434i	0.893180	+	0.262261i
$750$	601.563	+	274.725i	0.802084	+	0.366300i
$751$	−257.803	+	401.149i	−0.343279	+	0.534153i	−0.969372	−	0.245595i	$-0.921017\pi$
$751$	−257.803	+	401.149i	−0.343279	+	0.534153i	0.626093	+	0.779748i	$0.284653\pi$
$752$	−442.241	+	129.854i	−0.588086	+	0.172678i
$753$	316.843	+	45.5552i	0.420775	+	0.0604983i
$754$	−519.062	−	1136.59i	−0.688411	−	1.50741i
$755$	655.724	−	94.2788i	0.868508	−	0.124873i
$756$	142.380	+	221.548i	0.188334	+	0.293053i
$757$	17.1887	+	14.8941i	0.0227063	+	0.0196751i	0.666140	−	0.745827i	$-0.267945\pi$
$757$	17.1887	+	14.8941i	0.0227063	+	0.0196751i	−0.643434	+	0.765502i	$0.722491\pi$
$758$		−	299.683i		−	0.395360i
$759$	−746.131	−	44.3627i	−0.983044	−	0.0584489i
$760$	−83.9723			−0.110490
$761$	−502.035	+	579.379i	−0.659704	+	0.761339i	−0.982729	−	0.185052i	$-0.940755\pi$
$761$	−502.035	+	579.379i	−0.659704	+	0.761339i	0.323025	+	0.946390i	$0.395300\pi$
$762$	−241.657	+	155.304i	−0.317136	+	0.203811i
$763$	−45.9530	−	319.610i	−0.0602268	−	0.418886i
$764$	−67.6415	+	30.8908i	−0.0885360	+	0.0404330i
$765$	20.9293	−	145.566i	0.0273585	−	0.190283i
$766$	118.279	+	402.820i	0.154411	+	0.525875i
$767$	−707.554	−	454.717i	−0.922495	−	0.592852i
$768$	−274.929	+	602.010i	−0.357980	+	0.783867i
$769$	185.155	−	630.579i	0.240773	−	0.819998i	−0.747097	−	0.664715i	$-0.768553\pi$
$769$	185.155	−	630.579i	0.240773	−	0.819998i	0.987870	−	0.155283i	$-0.0496289\pi$
$770$	375.212	−	325.123i	0.487289	−	0.422238i
$771$	−592.419	−	683.688i	−0.768377	−	0.886754i
$772$	536.135	+	157.423i	0.694475	+	0.203916i
$773$	403.094	+	184.087i	0.521467	+	0.238146i	0.658717	−	0.752390i	$-0.271099\pi$
$773$	403.094	+	184.087i	0.521467	+	0.238146i	−0.137250	+	0.990536i	$0.543827\pi$
$774$	269.392	−	419.182i	0.348051	−	0.541578i
$775$	0.947682	−	0.278265i	0.00122282	−	0.000359051i
$776$	659.055	+	94.7578i	0.849298	+	0.122111i
$777$	64.1994	+	140.577i	0.0826247	+	0.180923i
$778$	1188.65	−	170.902i	1.52783	−	0.219668i
$779$	36.1099	+	56.1881i	0.0463542	+	0.0721285i
$780$	226.506	+	196.268i	0.290392	+	0.251626i
$781$		−	794.047i		−	1.01671i
$782$	556.385	+	406.168i	0.711490	+	0.519396i
$783$	629.096			0.803443
$784$	348.775	−	402.507i	0.444866	−	0.513402i
$785$	565.379	−	363.347i	0.720228	−	0.462862i
$786$	64.3138	+	447.312i	0.0818242	+	0.569100i
$787$	−655.680	+	299.439i	−0.833139	+	0.380482i	−0.785863	−	0.618400i	$-0.787781\pi$
$787$	−655.680	+	299.439i	−0.833139	+	0.380482i	−0.0472755	+	0.998882i	$0.515054\pi$
$788$	5.18455	−	36.0593i	0.00657937	−	0.0457605i
$789$	57.5182	+	195.889i	0.0729002	+	0.248275i
$790$	−220.544	−	141.735i	−0.279169	−	0.179411i
$791$	50.0366	−	109.565i	0.0632574	−	0.138514i
$792$	−84.0516	+	286.254i	−0.106126	+	0.361431i
$793$	1655.70	−	1434.67i	2.08789	−	1.80917i
$794$	620.659	+	716.279i	0.781687	+	0.902115i
$795$	−634.364	−	186.266i	−0.797942	−	0.234297i
$796$	−590.769	−	269.795i	−0.742172	−	0.338939i
$797$	647.193	−	1007.05i	0.812037	−	1.26355i	−0.149468	−	0.988767i	$-0.547756\pi$
$797$	647.193	−	1007.05i	0.812037	−	1.26355i	0.961505	−	0.274787i	$-0.0886074\pi$
$798$	137.760	−	40.4499i	0.172631	−	0.0506891i
$799$	−280.949	−	40.3944i	−0.351626	−	0.0505562i
$800$	191.485	+	419.293i	0.239356	+	0.524116i
$801$	18.1209	−	2.60539i	0.0226228	−	0.00325267i
$802$	243.849	+	379.436i	0.304051	+	0.473112i
$803$	527.788	+	457.331i	0.657270	+	0.569528i
$804$		−	410.232i		−	0.510239i
$805$	−189.732	+	259.902i	−0.235691	+	0.322860i
$806$	3.50697			0.00435108
$807$	−58.0847	+	67.0333i	−0.0719761	+	0.0830648i
$808$	−231.860	+	149.007i	−0.286955	+	0.184415i
$809$	62.2875	+	433.219i	0.0769932	+	0.535500i	0.991417	+	0.130741i	$0.0417355\pi$
$809$	62.2875	+	433.219i	0.0769932	+	0.535500i	−0.914423	+	0.404759i	$0.867355\pi$
$810$	−185.714	+	84.8128i	−0.229277	+	0.104707i
$811$	−171.109	+	1190.09i	−0.210985	+	1.46743i	0.558894	+	0.829239i	$0.311226\pi$
$811$	−171.109	+	1190.09i	−0.210985	+	1.46743i	−0.769878	+	0.638191i	$0.779683\pi$
$812$	−55.3347	−	188.453i	−0.0681462	−	0.232085i
$813$	245.880	+	158.017i	0.302435	+	0.194363i
$814$	216.260	−	473.542i	0.265675	−	0.581747i
$815$	6.92319	−	23.5782i	0.00849471	−	0.0289303i
$816$	−414.441	+	359.115i	−0.507893	+	0.440092i
$817$	−186.155	−	214.834i	−0.227852	−	0.262955i
$818$	−925.386	−	271.718i	−1.13128	−	0.332173i
$819$	−411.800	−	188.063i	−0.502808	−	0.229625i
$820$	−36.5652	+	56.8966i	−0.0445917	+	0.0693861i
$821$	1451.03	−	426.060i	1.76739	−	0.518953i	0.773945	−	0.633253i	$-0.218281\pi$
$821$	1451.03	−	426.060i	1.76739	−	0.518953i	0.993446	+	0.114300i	$0.0364626\pi$
$822$	118.216	+	16.9969i	0.143815	+	0.0206774i
$823$	599.968	+	1313.75i	0.729001	+	1.59629i	0.800843	+	0.598875i	$0.204385\pi$
$823$	599.968	+	1313.75i	0.729001	+	1.59629i	−0.0718414	+	0.997416i	$0.522888\pi$
$824$	98.8732	−	14.2158i	0.119992	−	0.0172522i
$825$	−285.443	−	444.158i	−0.345992	−	0.538374i
$826$	−308.341	−	267.179i	−0.373294	−	0.323461i
$827$		−	1296.29i		−	1.56746i	−0.621103	−	0.783729i	$-0.713315\pi$
$827$		−	1296.29i		−	1.56746i	0.621103	−	0.783729i	$-0.286685\pi$
$828$	−10.5678	+	177.738i	−0.0127630	+	0.214659i
$829$	−633.394			−0.764046			−0.382023	−	0.924153i	$-0.624773\pi$
$829$	−633.394			−0.764046			−0.382023	+	0.924153i	$0.624773\pi$
$830$	−492.488	+	568.361i	−0.593359	+	0.684773i
$831$	−716.374	+	460.385i	−0.862062	+	0.554014i
$832$	−36.9690	−	257.125i	−0.0444339	−	0.309044i
$833$	298.343	−	136.249i	0.358155	−	0.163564i
$834$	−15.8050	+	109.926i	−0.0189509	+	0.131806i
$835$	26.1376	+	89.0165i	0.0313025	+	0.106607i
$836$	−131.842	−	84.7298i	−0.157706	−	0.101351i
$837$	−0.733489	+	1.60612i	−0.000876331	+	0.00191890i
$838$	−385.769	+	1313.81i	−0.460345	+	1.56779i
$839$	−621.738	+	538.739i	−0.741047	+	0.642121i	−0.941280	−	0.337628i	$-0.890376\pi$
$839$	−621.738	+	538.739i	−0.741047	+	0.642121i	0.200233	+	0.979748i	$0.435830\pi$
$840$	−103.396	−	119.325i	−0.123090	−	0.142054i
$841$	356.762	+	104.755i	0.424211	+	0.124560i
$842$	−715.516	−	326.765i	−0.849782	−	0.388082i
$843$	57.8805	−	90.0638i	0.0686601	−	0.106837i
$844$	90.6182	−	26.6079i	0.107368	−	0.0315260i
$845$	−1151.90	−	165.618i	−1.36319	−	0.195997i
$846$	−94.0506	−	205.942i	−0.111171	−	0.243430i
$847$	−429.690	+	61.7802i	−0.507309	+	0.0729400i
$848$	−1084.25	−	1687.13i	−1.27860	−	1.98953i
$849$	548.033	+	474.874i	0.645504	+	0.559333i
$850$			486.592i			0.572461i
$851$	−67.7567	+	330.541i	−0.0796201	+	0.388414i
$852$	232.525			0.272916
$853$	−776.489	+	896.116i	−0.910304	+	1.05055i	0.0882129	+	0.996102i	$0.471884\pi$
$853$	−776.489	+	896.116i	−0.910304	+	1.05055i	−0.998517	+	0.0544450i	$0.982661\pi$
$854$	894.026	−	574.556i	1.04687	−	0.672782i
$855$	−9.52386	−	66.2399i	−0.0111390	−	0.0774736i
$856$	−679.429	+	310.285i	−0.793725	+	0.362482i
$857$	−87.8641	+	611.108i	−0.102525	+	0.713078i	0.872115	+	0.489301i	$0.162748\pi$
$857$	−87.8641	+	611.108i	−0.102525	+	0.713078i	−0.974640	+	0.223777i	$0.928161\pi$
$858$	−528.152	−	1798.72i	−0.615562	−	2.09641i
$859$	−85.4117	−	54.8908i	−0.0994315	−	0.0639008i	0.489980	−	0.871734i	$-0.337004\pi$
$859$	−85.4117	−	54.8908i	−0.0994315	−	0.0639008i	−0.589412	+	0.807833i	$0.700640\pi$
$860$	119.578	−	261.838i	0.139044	−	0.304463i
$861$	−35.3812	+	120.497i	−0.0410932	+	0.139951i
$862$	70.8947	−	61.4306i	0.0822444	−	0.0712652i
$863$	454.801	+	524.868i	0.527000	+	0.608190i	0.955370	−	0.295413i	$-0.0954574\pi$
$863$	454.801	+	524.868i	0.527000	+	0.608190i	−0.428370	+	0.903604i	$0.640912\pi$
$864$	−790.650	−	232.156i	−0.915104	−	0.268699i
$865$	155.086	+	70.8254i	0.179290	+	0.0818791i
$866$	638.822	−	994.026i	0.737669	−	1.14784i
$867$	293.713	−	86.2419i	0.338769	−	0.0994716i
$868$	0.545648	+	0.0784523i	0.000628627	+	9.03829e-5i
$869$	220.736	+	483.345i	0.254012	+	0.556208i
$870$	343.759	−	49.4251i	0.395126	−	0.0568105i
$871$	1231.19	+	1915.77i	1.41354	+	2.19951i
$872$	261.421	+	226.523i	0.299795	+	0.259774i
$873$			530.630i			0.607823i
$874$	294.999	+	106.010i	0.337527	+	0.121293i
$875$	−577.068			−0.659507
$876$	−133.922	+	154.555i	−0.152879	+	0.176432i
$877$	−743.587	+	477.874i	−0.847876	+	0.544897i	−0.890911	−	0.454177i	$-0.849933\pi$
$877$	−743.587	+	477.874i	−0.847876	+	0.544897i	0.0430359	+	0.999074i	$0.486297\pi$
$878$	−105.853	−	736.224i	−0.120562	−	0.838524i
$879$	387.978	−	177.184i	0.441385	−	0.201574i
$880$	−122.804	+	854.121i	−0.139550	+	0.970593i
$881$	−351.982	−	1198.74i	−0.399526	−	1.36066i	−0.876355	−	0.481665i	$-0.840032\pi$
$881$	−351.982	−	1198.74i	−0.399526	−	1.36066i	0.476829	−	0.878996i	$-0.341786\pi$
$882$	220.082	+	141.438i	0.249527	+	0.160361i
$883$	−325.693	+	713.168i	−0.368848	+	0.807664i	0.630653	+	0.776065i	$0.282787\pi$
$883$	−325.693	+	713.168i	−0.368848	+	0.807664i	−0.999501	+	0.0315992i	$0.989940\pi$
$884$	−157.731	+	537.181i	−0.178428	+	0.607671i
$885$	176.673	−	153.088i	0.199631	−	0.172981i
$886$	250.007	+	288.523i	0.282175	+	0.325647i
$887$	93.3165	+	27.4002i	0.105205	+	0.0308909i	0.333911	−	0.942605i	$-0.391631\pi$
$887$	93.3165	+	27.4002i	0.105205	+	0.0308909i	−0.228707	+	0.973495i	$0.573450\pi$
$888$	−150.596	−	68.7750i	−0.169590	−	0.0774493i
$889$	135.517	−	210.869i	0.152438	−	0.237197i
$890$	31.3151	−	9.19495i	0.0351855	−	0.0103314i
$891$	409.600	+	58.8916i	0.459709	+	0.0660961i
$892$	−13.2053	−	28.9155i	−0.0148041	−	0.0324165i
$893$	−127.846	+	18.3815i	−0.143165	+	0.0205840i
$894$	−75.7312	−	117.840i	−0.0847105	−	0.131812i
$895$	419.914	+	363.857i	0.469177	+	0.406545i
$896$		−	662.675i		−	0.739592i
$897$	595.076	+	1059.35i	0.663407	+	1.18099i
$898$	−1276.54			−1.42154
$899$	0.862344	−	0.995198i	0.000959226	−	0.00110701i
$900$	−105.804	+	67.9963i	−0.117560	+	0.0755514i
$901$	−175.762	−	1222.45i	−0.195074	−	1.35677i
$902$	384.810	−	175.737i	0.426618	−	0.194830i
$903$	76.0667	−	529.056i	0.0842378	−	0.585887i
$904$	36.3531	+	123.807i	0.0402136	+	0.136955i
$905$	623.212	+	400.514i	0.688632	+	0.442557i
$906$	504.069	−	1103.76i	0.556367	−	1.21827i
$907$	196.944	−	670.728i	0.217137	−	0.739502i	−0.776819	−	0.629724i	$-0.783168\pi$
$907$	196.944	−	670.728i	0.217137	−	0.739502i	0.993956	−	0.109778i	$-0.0350139\pi$
$908$	595.802	−	516.266i	0.656170	−	0.568575i
$909$	−143.838	−	165.998i	−0.158238	−	0.182616i
$910$	−774.375	−	227.377i	−0.850962	−	0.249865i
$911$	200.329	+	91.4870i	0.219900	+	0.100425i	0.522319	−	0.852750i	$-0.325067\pi$
$911$	200.329	+	91.4870i	0.219900	+	0.100425i	−0.302419	+	0.953175i	$0.597794\pi$
$912$	−134.913	+	209.928i	−0.147931	+	0.230184i
$913$	1462.56	−	429.445i	1.60192	−	0.470367i
$914$	481.009	+	69.1587i	0.526268	+	0.0756660i
$915$	252.956	+	553.897i	0.276455	+	0.605352i
$916$	492.828	−	70.8580i	0.538022	−	0.0773559i
$917$	−213.194	−	331.736i	−0.232490	−	0.361762i
$918$	−657.406	−	569.645i	−0.716128	−	0.620529i
$919$		−	903.734i		−	0.983388i	−0.870768	−	0.491694i	$-0.836378\pi$
$919$		−	903.734i		−	0.983388i	0.870768	−	0.491694i	$-0.163622\pi$
$920$	−28.7208	−	343.523i	−0.0312182	−	0.373394i
$921$	1067.04			1.15857
$922$	359.556	−	414.950i	0.389974	−	0.450054i
$923$	−1085.88	+	697.856i	−1.17647	+	0.756073i
$924$	−41.9369	−	291.677i	−0.0453862	−	0.315668i
$925$	−216.800	+	99.0090i	−0.234378	+	0.107037i
$926$	−275.553	+	1916.52i	−0.297574	+	2.06967i
$927$	22.4278	+	76.3819i	0.0241939	+	0.0823969i
$928$	516.999	+	332.255i	0.557111	+	0.358033i
$929$	43.6565	−	95.5945i	0.0469930	−	0.102900i	−0.884679	−	0.466200i	$-0.845623\pi$
$929$	43.6565	−	95.5945i	0.0469930	−	0.102900i	0.931672	+	0.363300i	$0.118350\pi$
$930$	−0.274618	+	0.935264i	−0.000295289	+	0.00100566i
$931$	112.794	−	97.7368i	0.121154	−	0.104980i
$932$	204.617	+	236.141i	0.219546	+	0.253370i
$933$	−837.460	−	245.901i	−0.897599	−	0.263559i
$934$	727.356	+	332.172i	0.778754	+	0.355645i
$935$	−287.294	+	447.038i	−0.307266	+	0.478115i
$936$	465.330	−	136.633i	0.497148	−	0.145976i
$937$	756.387	+	108.752i	0.807244	+	0.116064i	0.533567	−	0.845758i	$-0.320851\pi$
$937$	756.387	+	108.752i	0.807244	+	0.116064i	0.273676	+	0.961822i	$0.411760\pi$
$938$	458.902	+	1004.86i	0.489235	+	1.07127i
$939$	257.008	−	36.9522i	0.273704	−	0.0393527i
$940$	−70.7100	−	110.027i	−0.0752234	−	0.117050i
$941$	−402.904	−	349.118i	−0.428166	−	0.371008i	0.413954	−	0.910298i	$-0.364147\pi$
$941$	−402.904	−	349.118i	−0.428166	−	0.371008i	−0.842120	+	0.539290i	$0.818693\pi$
$942$		−	1230.99i		−	1.30679i
$943$	−217.510	+	166.940i	−0.230657	+	0.177031i
$944$	709.116			0.751182
$945$	266.096	−	307.091i	0.281583	−	0.324964i
$946$	−1514.66	+	973.413i	−1.60112	+	1.02898i
$947$	−192.662	−	1340.00i	−0.203445	−	1.41499i	−0.793963	−	0.607966i	$-0.791986\pi$
$947$	−192.662	−	1340.00i	−0.203445	−	1.41499i	0.590518	−	0.807024i	$-0.298923\pi$
$948$	−141.540	+	64.6392i	−0.149304	+	0.0681848i
$949$	161.563	−	1123.70i	0.170246	−	1.18408i
$950$	62.3822	+	212.454i	0.0656655	+	0.223636i
$951$	−437.156	−	280.943i	−0.459680	−	0.295419i
$952$	122.522	−	268.286i	0.128700	−	0.281813i
$953$	−301.407	+	1026.50i	−0.316272	+	1.07712i	0.635954	+	0.771727i	$0.280607\pi$
$953$	−301.407	+	1026.50i	−0.316272	+	1.07712i	−0.952226	+	0.305395i	$0.901211\pi$
$954$	744.494	−	645.107i	0.780392	−	0.676213i
$955$	75.1355	+	86.7109i	0.0786759	+	0.0907968i
$956$	−70.7201	−	20.7653i	−0.0739750	−	0.0217210i
$957$	−640.306	−	292.418i	−0.669076	−	0.305557i
$958$	−752.742	+	1171.29i	−0.785744	+	1.22264i
$959$	−99.9936	+	29.3608i	−0.104269	+	0.0306160i
$960$	71.4669	+	10.2754i	0.0744447	+	0.0107035i
$961$	−399.212	−	874.153i	−0.415413	−	0.909628i
$962$	−837.646	+	120.435i	−0.870734	+	0.125193i
$963$	−321.821	−	500.763i	−0.334186	−	0.520003i
$964$	−163.701	−	141.848i	−0.169814	−	0.147145i
$965$		−	862.146i		−	0.893415i
$966$	212.594	+	549.727i	0.220077	+	0.569076i
$967$	1065.62			1.10198			0.550992	−	0.834510i	$-0.314249\pi$
$967$	1065.62			1.10198			0.550992	+	0.834510i	$0.314249\pi$
$968$	304.542	−	351.460i	0.314609	−	0.363079i
$969$	−129.278	+	83.0820i	−0.133414	+	0.0857399i
$970$	134.627	+	936.349i	0.138790	+	0.965308i
$971$	−1177.36	+	537.681i	−1.21252	+	0.553739i	−0.915958	−	0.401274i	$-0.868567\pi$
$971$	−1177.36	+	537.681i	−1.21252	+	0.553739i	−0.296562	+	0.955014i	$0.595840\pi$
$972$	54.0866	−	376.181i	0.0556447	−	0.387017i
$973$	−27.3020	−	92.9820i	−0.0280596	−	0.0955622i
$974$	−861.307	−	553.529i	−0.884299	−	0.568305i
$975$	−356.536	+	780.705i	−0.365678	+	0.800723i
$976$	−520.384	+	1772.27i	−0.533180	+	1.81585i
$977$	550.287	−	476.826i	0.563241	−	0.488051i	−0.326075	−	0.945344i	$-0.605726\pi$
$977$	550.287	−	476.826i	0.563241	−	0.488051i	0.889316	+	0.457293i	$0.151181\pi$
$978$	−29.4755	−	34.0166i	−0.0301386	−	0.0347818i
$979$	−63.4714	−	18.6369i	−0.0648329	−	0.0190367i
$980$	137.473	+	62.7817i	0.140278	+	0.0640630i
$981$	−149.039	+	231.909i	−0.151925	+	0.236400i
$982$	1342.81	−	394.283i	1.36742	−	0.401510i
$983$	−1113.86	−	160.148i	−1.13312	−	0.162918i	−0.449864	−	0.893097i	$-0.648528\pi$
$983$	−1113.86	−	160.148i	−1.13312	−	0.162918i	−0.683256	+	0.730179i	$0.739437\pi$
$984$	−55.8878	−	122.377i	−0.0567966	−	0.124367i
$985$	−55.6373	+	7.99943i	−0.0564846	+	0.00812125i
$986$	350.739	+	545.761i	0.355719	+	0.553510i
$987$	−183.538	−	159.037i	−0.185956	−	0.161132i
$988$			254.764i			0.257858i
$989$	815.198	−	835.022i	0.824265	−	0.844310i
$990$	−423.863			−0.428144
$991$	677.972	−	782.421i	0.684129	−	0.789527i	−0.302388	−	0.953185i	$-0.597784\pi$
$991$	677.972	−	782.421i	0.684129	−	0.789527i	0.986517	+	0.163658i	$0.0523294\pi$
$992$	−1.45106	+	0.932537i	−0.00146276	+	0.000940058i
$993$	128.268	+	892.125i	0.129172	+	0.898414i
$994$	−569.565	+	260.112i	−0.573003	+	0.261682i
$995$	−142.610	+	991.876i	−0.143327	+	0.996861i
$996$	125.756	+	428.287i	0.126262	+	0.430007i
$997$	−189.092	−	121.522i	−0.189661	−	0.121888i	0.442364	−	0.896836i	$-0.354140\pi$
$997$	−189.092	−	121.522i	−0.189661	−	0.121888i	−0.632026	+	0.774948i	$0.717776\pi$
$998$	−506.001	+	1107.99i	−0.507015	+	1.11021i
$999$	120.038	−	408.813i	0.120159	−	0.409223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.3.d.a.7.3	✓	30
3.2	odd	2		207.3.j.a.145.1		30
4.3	odd	2		368.3.p.a.145.2		30
23.6	even	11		529.3.b.b.528.6		30
23.10	odd	22	inner	23.3.d.a.10.3	yes	30
23.17	odd	22		529.3.b.b.528.5		30
69.56	even	22		207.3.j.a.10.1		30
92.79	even	22		368.3.p.a.33.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.3.d.a.7.3	✓	30	1.1	even	1	trivial
23.3.d.a.10.3	yes	30	23.10	odd	22	inner
207.3.j.a.10.1		30	69.56	even	22
207.3.j.a.145.1		30	3.2	odd	2
368.3.p.a.33.2		30	92.79	even	22
368.3.p.a.145.2		30	4.3	odd	2
529.3.b.b.528.5		30	23.17	odd	22
529.3.b.b.528.6		30	23.6	even	11

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)

\(f(q)\)	\(=\)	\(q+(1.59301 - 1.83844i) q^{2} +(-1.87410 + 1.20441i) q^{3} +(-0.272894 - 1.89802i) q^{4} +(-2.69128 + 1.22907i) q^{5} +(-0.771235 + 5.36406i) q^{6} +(-1.33225 - 4.53722i) q^{7} +(4.26162 + 2.73877i) q^{8} +(-1.67709 + 3.67232i) q^{9} +O(q^{10})\)	\(q+(1.59301 - 1.83844i) q^{2} +(-1.87410 + 1.20441i) q^{3} +(-0.272894 - 1.89802i) q^{4} +(-2.69128 + 1.22907i) q^{5} +(-0.771235 + 5.36406i) q^{6} +(-1.33225 - 4.53722i) q^{7} +(4.26162 + 2.73877i) q^{8} +(-1.67709 + 3.67232i) q^{9} +(-2.02769 + 6.90566i) q^{10} +(11.0247 - 9.55293i) q^{11} +(2.79743 + 3.22841i) q^{12} +(-22.7531 - 6.68090i) q^{13} +(-10.4637 - 4.77860i) q^{14} +(3.56342 - 5.54480i) q^{15} +(19.1833 - 5.63274i) q^{16} +(12.1869 + 1.75221i) q^{17} +(4.07969 + 8.93327i) q^{18} +(5.54565 - 0.797344i) q^{19} +(3.06723 + 4.77270i) q^{20} +(7.96145 + 6.89863i) q^{21} -35.4861i q^{22} +(5.15862 + 22.4140i) q^{23} -11.2853 q^{24} +(-10.6391 + 12.2782i) q^{25} +(-48.5283 + 31.1873i) q^{26} +(-4.13331 - 28.7478i) q^{27} +(-8.24818 + 3.76682i) q^{28} +(-3.08261 + 21.4400i) q^{29} +(-4.51717 - 15.3841i) q^{30} +(-0.0511435 - 0.0328679i) q^{31} +(11.7863 - 25.8083i) q^{32} +(-9.15568 + 31.1814i) q^{33} +(22.6352 - 19.6135i) q^{34} +(9.16200 + 10.5735i) q^{35} +(7.42780 + 2.18100i) q^{36} +(13.3445 + 6.09421i) q^{37} +(7.36843 - 11.4655i) q^{38} +(50.6880 - 14.8834i) q^{39} +(-14.8353 - 2.13300i) q^{40} +(4.95227 + 10.8440i) q^{41} +(25.3654 - 3.64699i) q^{42} +(-27.4308 - 42.6832i) q^{43} +(-21.1402 - 18.3181i) q^{44} -11.9445i q^{45} +(49.4245 + 26.2221i) q^{46} -23.0534 q^{47} +(-29.1674 + 33.6609i) q^{48} +(22.4099 - 14.4020i) q^{49} +(5.62443 + 39.1188i) q^{50} +(-24.9499 + 11.3942i) q^{51} +(-6.47131 + 45.0090i) q^{52} +(-28.2602 - 96.2454i) q^{53} +(-59.4355 - 38.1969i) q^{54} +(-17.9293 + 39.2596i) q^{55} +(6.74889 - 22.9846i) q^{56} +(-9.43277 + 8.17354i) q^{57} +(34.5055 + 39.8214i) q^{58} +(34.0311 + 9.99245i) q^{59} +(-11.4966 - 5.25031i) q^{60} +(-49.9475 + 77.7198i) q^{61} +(-0.141898 + 0.0416649i) q^{62} +(18.8964 + 2.71689i) q^{63} +(4.55063 + 9.96449i) q^{64} +(69.4461 - 9.98484i) q^{65} +(42.7398 + 66.5045i) q^{66} +(-72.5767 - 62.8880i) q^{67} -23.6092i q^{68} +(-36.6635 - 35.7930i) q^{69} +34.0339 q^{70} +(35.6457 - 41.1374i) q^{71} +(-17.2048 + 11.0568i) q^{72} +(6.81309 + 47.3861i) q^{73} +(32.4617 - 14.8248i) q^{74} +(5.15079 - 35.8245i) q^{75} +(-3.02675 - 10.3082i) q^{76} +(-58.0313 - 37.2945i) q^{77} +(53.3847 - 116.896i) q^{78} +(-10.2622 + 34.9499i) q^{79} +(-44.7047 + 38.7368i) q^{80} +(18.5765 + 21.4385i) q^{81} +(27.8249 + 8.17014i) q^{82} +(95.0493 + 43.4076i) q^{83} +(10.9211 - 16.9936i) q^{84} +(-34.9519 + 10.2628i) q^{85} +(-122.168 - 17.5651i) q^{86} +(-20.0455 - 43.8935i) q^{87} +(73.1462 - 10.5168i) q^{88} +(-2.45164 - 3.81483i) q^{89} +(-21.9592 - 19.0277i) q^{90} +112.136i q^{91} +(41.1346 - 15.9078i) q^{92} +0.135434 q^{93} +(-36.7244 + 42.3822i) q^{94} +(-13.9449 + 8.96184i) q^{95} +(8.99519 + 62.5629i) q^{96} +(119.559 - 54.6009i) q^{97} +(9.22220 - 64.1418i) q^{98} +(16.5920 + 56.5072i) 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

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