LMFDB - Embedded newform 572.2.bm.a.35.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(35,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 3, 20]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("572.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bm (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			35.4
Character	$\chi$	$=$	572.35
Dual form			572.2.bm.a.523.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40108 - 0.192317i) q^{2} +(1.35212 - 0.142114i) q^{3} +(1.92603 + 0.538900i) q^{4} +(-0.229666 - 0.706840i) q^{5} +(-1.92176 - 0.0609233i) q^{6} +(-0.0980876 + 0.933242i) q^{7} +(-2.59487 - 1.12545i) q^{8} +(-1.12640 + 0.239425i) q^{9} +O(q^{10})$	\(q+(-1.40108 - 0.192317i) q^{2} +(1.35212 - 0.142114i) q^{3} +(1.92603 + 0.538900i) q^{4} +(-0.229666 - 0.706840i) q^{5} +(-1.92176 - 0.0609233i) q^{6} +(-0.0980876 + 0.933242i) q^{7} +(-2.59487 - 1.12545i) q^{8} +(-1.12640 + 0.239425i) q^{9} +(0.185843 + 1.03451i) q^{10} +(-1.61037 + 2.89943i) q^{11} +(2.68081 + 0.454944i) q^{12} +(2.11313 + 2.92142i) q^{13} +(0.316906 - 1.28868i) q^{14} +(-0.410989 - 0.923096i) q^{15} +(3.41917 + 2.07588i) q^{16} +(5.83948 + 5.25789i) q^{17} +(1.62422 - 0.118826i) q^{18} +(1.43269 + 0.637874i) q^{19} +(-0.0614274 - 1.48516i) q^{20} +1.27580i q^{21} +(2.81386 - 3.75262i) q^{22} +(-0.0346633 - 0.0200129i) q^{23} +(-3.66853 - 1.15298i) q^{24} +(3.59821 - 2.61425i) q^{25} +(-2.39881 - 4.49952i) q^{26} +(-5.36810 + 1.74420i) q^{27} +(-0.691844 + 1.74459i) q^{28} +(0.599320 + 1.34610i) q^{29} +(0.398300 + 1.37237i) q^{30} +(3.00995 + 0.977992i) q^{31} +(-4.39130 - 3.56602i) q^{32} +(-1.76537 + 4.14924i) q^{33} +(-7.17038 - 8.48973i) q^{34} +(0.682180 - 0.145002i) q^{35} +(-2.29851 - 0.145881i) q^{36} +(5.97130 - 2.65859i) q^{37} +(-1.88463 - 1.16924i) q^{38} +(3.27238 + 3.64981i) q^{39} +(-0.199557 + 2.09264i) q^{40} +(-6.07618 + 0.638633i) q^{41} +(0.245357 - 1.78749i) q^{42} +(-1.24871 - 2.16283i) q^{43} +(-4.66413 + 4.71656i) q^{44} +(0.427932 + 0.741200i) q^{45} +(0.0447171 + 0.0347059i) q^{46} +(-2.54702 - 3.50568i) q^{47} +(4.91815 + 2.32093i) q^{48} +(5.98571 + 1.27230i) q^{49} +(-5.54413 + 2.97077i) q^{50} +(8.64291 + 6.27944i) q^{51} +(2.49559 + 6.76550i) q^{52} +(2.04851 - 6.30466i) q^{53} +(7.85655 - 1.41138i) q^{54} +(2.41928 + 0.472373i) q^{55} +(1.30484 - 2.31125i) q^{56} +(2.02782 + 0.658879i) q^{57} +(-0.580817 - 2.00124i) q^{58} +(-10.0789 - 1.05933i) q^{59} +(-0.294119 - 1.99939i) q^{60} +(6.44842 + 5.80618i) q^{61} +(-4.02909 - 1.94911i) q^{62} +(-0.112955 - 1.07469i) q^{63} +(5.46673 + 5.84079i) q^{64} +(1.57966 - 2.16459i) q^{65} +(3.27139 - 5.47389i) q^{66} +(-2.16894 - 1.25224i) q^{67} +(8.41353 + 13.2737i) q^{68} +(-0.0497132 - 0.0221337i) q^{69} +(-0.983673 + 0.0719641i) q^{70} +(0.376938 + 0.339396i) q^{71} +(3.19234 + 0.646433i) q^{72} +(-3.69943 + 5.09183i) q^{73} +(-8.87753 + 2.57651i) q^{74} +(4.49370 - 4.04614i) q^{75} +(2.41565 + 2.00064i) q^{76} +(-2.54791 - 1.78726i) q^{77} +(-3.88293 - 5.74300i) q^{78} +(-1.30624 + 4.02020i) q^{79} +(0.682043 - 2.89357i) q^{80} +(-3.85442 + 1.71610i) q^{81} +(8.63601 + 0.273778i) q^{82} +(4.60598 + 14.1758i) q^{83} +(-0.687527 + 2.45722i) q^{84} +(2.37536 - 5.33514i) q^{85} +(1.33359 + 3.27044i) q^{86} +(1.00165 + 1.73491i) q^{87} +(7.44187 - 5.71127i) q^{88} +(7.80883 - 13.5253i) q^{89} +(-0.457020 - 1.12078i) q^{90} +(-2.93366 + 1.68550i) q^{91} +(-0.0559776 - 0.0572255i) q^{92} +(4.20881 + 0.894610i) q^{93} +(2.89438 + 5.40156i) q^{94} +(0.121835 - 1.15918i) q^{95} +(-6.44435 - 4.19764i) q^{96} +(-13.4449 + 2.85781i) q^{97} +(-8.14176 - 2.93375i) q^{98} +(1.11973 - 3.65149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9}+O(q^{10}) $ 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9	$ 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9} - 36 q^{12} - 20 q^{13} - 28 q^{14} - 11 q^{16} - 10 q^{17} - 20 q^{18} - 29 q^{20} + 25 q^{22} - 65 q^{24} - 152 q^{25} + 40 q^{26} - 5 q^{28} - 10 q^{29} + 5 q^{30} + 4 q^{33} - 132 q^{34} - 24 q^{36} - 6 q^{37} - 10 q^{38} - 20 q^{40} - 50 q^{41} - 49 q^{42} - 4 q^{44} + 28 q^{45} - 25 q^{46} + 35 q^{48} + 62 q^{49} + 20 q^{50} + 15 q^{52} - 8 q^{53} - 2 q^{56} - 40 q^{57} + 41 q^{58} - 68 q^{60} - 10 q^{61} - 5 q^{62} - 36 q^{64} - 66 q^{66} + 60 q^{68} - 58 q^{69} + 118 q^{70} - 5 q^{72} - 40 q^{73} + 45 q^{74} - 76 q^{77} + 12 q^{78} - 41 q^{80} + 30 q^{81} - 37 q^{82} + 50 q^{84} - 10 q^{85} - 120 q^{86} + 89 q^{88} - 40 q^{89} - 250 q^{90} - 46 q^{92} - 2 q^{93} - 5 q^{94} + 110 q^{96} - 10 q^{97}+O(q^{100}) $ 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9 - 36 * q^12 - 20 * q^13 - 28 * q^14 - 11 * q^16 - 10 * q^17 - 20 * q^18 - 29 * q^20 + 25 * q^22 - 65 * q^24 - 152 * q^25 + 40 * q^26 - 5 * q^28 - 10 * q^29 + 5 * q^30 + 4 * q^33 - 132 * q^34 - 24 * q^36 - 6 * q^37 - 10 * q^38 - 20 * q^40 - 50 * q^41 - 49 * q^42 - 4 * q^44 + 28 * q^45 - 25 * q^46 + 35 * q^48 + 62 * q^49 + 20 * q^50 + 15 * q^52 - 8 * q^53 - 2 * q^56 - 40 * q^57 + 41 * q^58 - 68 * q^60 - 10 * q^61 - 5 * q^62 - 36 * q^64 - 66 * q^66 + 60 * q^68 - 58 * q^69 + 118 * q^70 - 5 * q^72 - 40 * q^73 + 45 * q^74 - 76 * q^77 + 12 * q^78 - 41 * q^80 + 30 * q^81 - 37 * q^82 + 50 * q^84 - 10 * q^85 - 120 * q^86 + 89 * q^88 - 40 * q^89 - 250 * q^90 - 46 * q^92 - 2 * q^93 - 5 * q^94 + 110 * q^96 - 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.40108	−	0.192317i	−0.990710	−	0.135988i
$2$	−1.40108	−	0.192317i	−0.990710	−	0.135988i
$3$	1.35212	−	0.142114i	0.780648	−	0.0820494i	0.294183	−	0.955749i	$-0.404953\pi$
$3$	1.35212	−	0.142114i	0.780648	−	0.0820494i	0.486466	+	0.873700i	$0.338286\pi$
$4$	1.92603	+	0.538900i	0.963014	+	0.269450i
$5$	−0.229666	−	0.706840i	−0.102710	−	0.316109i	0.886476	−	0.462774i	$-0.153146\pi$
$5$	−0.229666	−	0.706840i	−0.102710	−	0.316109i	−0.989186	+	0.146666i	$0.953146\pi$
$6$	−1.92176	−	0.0609233i	−0.784554	−	0.0248719i
$7$	−0.0980876	+	0.933242i	−0.0370736	+	0.352732i	0.960222	+	0.279238i	$0.0900818\pi$
$7$	−0.0980876	+	0.933242i	−0.0370736	+	0.352732i	−0.997296	+	0.0734944i	$0.976585\pi$
$8$	−2.59487	−	1.12545i	−0.917426	−	0.397906i
$9$	−1.12640	+	0.239425i	−0.375468	+	0.0798082i
$10$	0.185843	+	1.03451i	0.0587687	+	0.327139i
$11$	−1.61037	+	2.89943i	−0.485545	+	0.874212i
$11$	−1.61037	+	2.89943i	−0.485545	+	0.874212i
$12$	2.68081	+	0.454944i	0.773884	+	0.131331i
$13$	2.11313	+	2.92142i	0.586076	+	0.810256i
$13$	2.11313	+	2.92142i	0.586076	+	0.810256i
$14$	0.316906	−	1.28868i	0.0846967	−	0.344414i
$15$	−0.410989	−	0.923096i	−0.106117	−	0.238342i
$16$	3.41917	+	2.07588i	0.854793	+	0.518969i
$17$	5.83948	+	5.25789i	1.41628	+	1.27523i	0.911083	+	0.412223i	$0.135247\pi$
$17$	5.83948	+	5.25789i	1.41628	+	1.27523i	0.505199	+	0.863003i	$0.331419\pi$
$18$	1.62422	−	0.118826i	0.382833	−	0.0280075i
$19$	1.43269	+	0.637874i	0.328681	+	0.146338i	0.564442	−	0.825473i	$-0.309091\pi$
$19$	1.43269	+	0.637874i	0.328681	+	0.146338i	−0.235761	+	0.971811i	$0.575758\pi$
$20$	−0.0614274	−	1.48516i	−0.0137356	−	0.332092i
$21$			1.27580i			0.278402i
$22$	2.81386	−	3.75262i	0.599917	−	0.800062i
$23$	−0.0346633	−	0.0200129i	−0.00722780	−	0.00417297i	0.496382	−	0.868104i	$-0.334662\pi$
$23$	−0.0346633	−	0.0200129i	−0.00722780	−	0.00417297i	−0.503610	+	0.863931i	$0.667995\pi$
$24$	−3.66853	−	1.15298i	−0.748835	−	0.235350i
$25$	3.59821	−	2.61425i	0.719642	−	0.522850i
$26$	−2.39881	−	4.49952i	−0.470446	−	0.882429i
$27$	−5.36810	+	1.74420i	−1.03309	+	0.335671i
$28$	−0.691844	+	1.74459i	−0.130746	+	0.329697i
$29$	0.599320	+	1.34610i	0.111291	+	0.249964i	0.960601	−	0.277930i	$-0.0896485\pi$
$29$	0.599320	+	1.34610i	0.111291	+	0.249964i	−0.849310	+	0.527894i	$0.822982\pi$
$30$	0.398300	+	1.37237i	0.0727193	+	0.250559i
$31$	3.00995	+	0.977992i	0.540603	+	0.175653i	0.566575	−	0.824010i	$-0.308268\pi$
$31$	3.00995	+	0.977992i	0.540603	+	0.175653i	−0.0259720	+	0.999663i	$0.508268\pi$
$32$	−4.39130	−	3.56602i	−0.776279	−	0.630390i
$33$	−1.76537	+	4.14924i	−0.307311	+	0.722290i
$34$	−7.17038	−	8.48973i	−1.22971	−	1.45598i
$35$	0.682180	−	0.145002i	0.115309	−	0.0245098i
$36$	−2.29851	−	0.145881i	−0.383085	−	0.0243135i
$37$	5.97130	−	2.65859i	0.981675	−	0.437070i	0.147796	−	0.989018i	$-0.452782\pi$
$37$	5.97130	−	2.65859i	0.981675	−	0.437070i	0.833879	+	0.551948i	$0.186115\pi$
$38$	−1.88463	−	1.16924i	−0.305728	−	0.189676i
$39$	3.27238	+	3.64981i	0.524000	+	0.584438i
$40$	−0.199557	+	2.09264i	−0.0315527	+	0.330875i
$41$	−6.07618	+	0.638633i	−0.948940	+	0.0997376i	−0.566336	−	0.824175i	$-0.691639\pi$
$41$	−6.07618	+	0.638633i	−0.948940	+	0.0997376i	−0.382604	+	0.923912i	$0.624973\pi$
$42$	0.245357	−	1.78749i	0.0378594	−	0.275815i
$43$	−1.24871	−	2.16283i	−0.190427	−	0.329829i	0.754965	−	0.655765i	$-0.227654\pi$
$43$	−1.24871	−	2.16283i	−0.190427	−	0.329829i	−0.945392	+	0.325936i	$0.894320\pi$
$44$	−4.66413	+	4.71656i	−0.703143	+	0.711048i
$45$	0.427932	+	0.741200i	0.0637923	+	0.110492i
$46$	0.0447171	+	0.0347059i	0.00659318	+	0.00511711i
$47$	−2.54702	−	3.50568i	−0.371522	−	0.511356i	0.581792	−	0.813338i	$-0.302352\pi$
$47$	−2.54702	−	3.50568i	−0.371522	−	0.511356i	−0.953314	+	0.301982i	$0.902352\pi$
$48$	4.91815	+	2.32093i	0.709874	+	0.334997i
$49$	5.98571	+	1.27230i	0.855102	+	0.181758i
$50$	−5.54413	+	2.97077i	−0.784058	+	0.420130i
$51$	8.64291	+	6.27944i	1.21025	+	0.879298i
$52$	2.49559	+	6.76550i	0.346076	+	0.938207i
$53$	2.04851	−	6.30466i	0.281384	−	0.866011i	−0.706075	−	0.708137i	$-0.749536\pi$
$53$	2.04851	−	6.30466i	0.281384	−	0.866011i	0.987459	−	0.157874i	$-0.0504641\pi$
$54$	7.85655	−	1.41138i	1.06914	−	0.192065i
$55$	2.41928	+	0.472373i	0.326216	+	0.0636948i
$56$	1.30484	−	2.31125i	0.174367	−	0.308854i
$57$	2.02782	+	0.658879i	0.268591	+	0.0872706i
$58$	−0.580817	−	2.00124i	−0.0762650	−	0.262776i
$59$	−10.0789	−	1.05933i	−1.31216	−	0.137913i	−0.577521	−	0.816376i	$-0.695980\pi$
$59$	−10.0789	−	1.05933i	−1.31216	−	0.137913i	−0.734635	+	0.678462i	$0.762647\pi$
$60$	−0.294119	−	1.99939i	−0.0379706	−	0.258120i
$61$	6.44842	+	5.80618i	0.825636	+	0.743406i	0.969210	−	0.246234i	$-0.0791931\pi$
$61$	6.44842	+	5.80618i	0.825636	+	0.743406i	−0.143575	+	0.989639i	$0.545860\pi$
$62$	−4.02909	−	1.94911i	−0.511694	−	0.247537i
$63$	−0.112955	−	1.07469i	−0.0142310	−	0.135398i
$64$	5.46673	+	5.84079i	0.683342	+	0.730099i
$65$	1.57966	−	2.16459i	0.195933	−	0.268485i
$66$	3.27139	−	5.47389i	0.402680	−	0.673790i
$67$	−2.16894	−	1.25224i	−0.264978	−	0.152985i	0.361625	−	0.932324i	$-0.382222\pi$
$67$	−2.16894	−	1.25224i	−0.264978	−	0.152985i	−0.626603	+	0.779338i	$0.715555\pi$
$68$	8.41353	+	13.2737i	1.02029	+	1.60968i
$69$	−0.0497132	−	0.0221337i	−0.00598476	−	0.00266459i
$70$	−0.983673	+	0.0719641i	−0.117571	+	0.00860135i
$71$	0.376938	+	0.339396i	0.0447343	+	0.0402789i	0.691195	−	0.722669i	$-0.257085\pi$
$71$	0.376938	+	0.339396i	0.0447343	+	0.0402789i	−0.646460	+	0.762948i	$0.723751\pi$
$72$	3.19234	+	0.646433i	0.376220	+	0.0761828i
$73$	−3.69943	+	5.09183i	−0.432985	+	0.595953i	−0.968635	−	0.248487i	$-0.920067\pi$
$73$	−3.69943	+	5.09183i	−0.432985	+	0.595953i	0.535650	+	0.844440i	$0.320067\pi$
$74$	−8.87753	+	2.57651i	−1.03199	+	0.299513i
$75$	4.49370	−	4.04614i	0.518887	−	0.467208i
$76$	2.41565	+	2.00064i	0.277094	+	0.229489i
$77$	−2.54791	−	1.78726i	−0.290362	−	0.203678i
$78$	−3.88293	−	5.74300i	−0.439656	−	0.650267i
$79$	−1.30624	+	4.02020i	−0.146964	+	0.452308i	−0.997258	−	0.0739990i	$-0.976424\pi$
$79$	−1.30624	+	4.02020i	−0.146964	+	0.452308i	0.850294	+	0.526307i	$0.176424\pi$
$80$	0.682043	−	2.89357i	0.0762548	−	0.323511i
$81$	−3.85442	+	1.71610i	−0.428268	+	0.190677i
$82$	8.63601	+	0.273778i	0.953688	+	0.0302337i
$83$	4.60598	+	14.1758i	0.505572	+	1.55599i	0.799806	+	0.600258i	$0.204936\pi$
$83$	4.60598	+	14.1758i	0.505572	+	1.55599i	−0.294234	+	0.955733i	$0.595064\pi$
$84$	−0.687527	+	2.45722i	−0.0750154	+	0.268105i
$85$	2.37536	−	5.33514i	0.257644	−	0.578677i
$86$	1.33359	+	3.27044i	0.143805	+	0.352660i
$87$	1.00165	+	1.73491i	0.107389	+	0.186002i
$88$	7.44187	−	5.71127i	0.793306	−	0.608823i
$89$	7.80883	−	13.5253i	0.827734	−	1.43368i	−0.0720771	−	0.997399i	$-0.522963\pi$
$89$	7.80883	−	13.5253i	0.827734	−	1.43368i	0.899811	−	0.436279i	$-0.143704\pi$
$90$	−0.457020	−	1.12078i	−0.0481742	−	0.118140i
$91$	−2.93366	+	1.68550i	−0.307531	+	0.176689i
$92$	−0.0559776	−	0.0572255i	−0.00583607	−	0.00596617i
$93$	4.20881	+	0.894610i	0.436433	+	0.0927667i
$94$	2.89438	+	5.40156i	0.298532	+	0.557128i
$95$	0.121835	−	1.15918i	0.0125000	−	0.118929i
$96$	−6.44435	−	4.19764i	−0.657724	−	0.428419i
$97$	−13.4449	+	2.85781i	−1.36512	+	0.290166i	−0.831486	−	0.555546i	$-0.812509\pi$
$97$	−13.4449	+	2.85781i	−1.36512	+	0.290166i	−0.533639	+	0.845712i	$0.679176\pi$
$98$	−8.14176	−	2.93375i	−0.822442	−	0.296353i
$99$	1.11973	−	3.65149i	0.112537	−	0.366989i
$100$	8.33907	−	3.09605i	0.833907	−	0.309605i
$101$	6.99018	−	6.29398i	0.695548	−	0.626275i	−0.243564	−	0.969885i	$-0.578317\pi$
$101$	6.99018	−	6.29398i	0.695548	−	0.626275i	0.939112	+	0.343610i	$0.111650\pi$
$102$	−10.9017	−	10.4602i	−1.07943	−	1.03571i
$103$	−1.72248	+	2.37079i	−0.169721	+	0.233601i	−0.885402	−	0.464827i	$-0.846117\pi$
$103$	−1.72248	+	2.37079i	−0.169721	+	0.233601i	0.715681	+	0.698428i	$0.246117\pi$
$104$	−2.19539	−	9.95893i	−0.215276	−	0.976553i
$105$	0.901784	−	0.293007i	0.0880051	−	0.0285946i
$106$	−4.08260	+	8.43934i	−0.396538	+	0.819701i
$107$	0.872377	+	8.30011i	0.0843358	+	0.802402i	0.952174	+	0.305555i	$0.0988421\pi$
$107$	0.872377	+	8.30011i	0.0843358	+	0.802402i	−0.867838	+	0.496846i	$0.834491\pi$
$108$	−11.2791	+	0.466510i	−1.08533	+	0.0448900i
$109$			6.04090i			0.578613i	0.957236	+	0.289307i	$0.0934248\pi$
$109$			6.04090i			0.578613i	−0.957236	+	0.289307i	$0.906575\pi$
$110$	−3.29875	−	1.12710i	−0.314524	−	0.107465i
$111$	7.69610	−	4.44334i	0.730481	−	0.421744i
$112$	−2.27267	+	2.98730i	−0.214747	+	0.282273i
$113$	−2.53545	−	1.12886i	−0.238515	−	0.106194i	0.283998	−	0.958825i	$-0.408339\pi$
$113$	−2.53545	−	1.12886i	−0.238515	−	0.106194i	−0.522514	+	0.852631i	$0.675006\pi$
$114$	−2.71442	−	1.31312i	−0.254228	−	0.122985i
$115$	−0.00618491	+	0.0290977i	−0.000576746	+	0.00271338i
$116$	0.428897	+	2.91559i	0.0398221	+	0.270706i
$117$	−3.07969	−	2.78477i	−0.284718	−	0.257452i
$118$	13.9175	+	3.42254i	1.28121	+	0.315070i
$119$	−5.47966	+	4.93391i	−0.502320	+	0.452291i
$120$	0.0275675	+	2.85786i	0.00251656	+	0.260886i
$121$	−5.81341	−	9.33832i	−0.528492	−	0.848938i
$122$	−7.91810	−	9.37504i	−0.716871	−	0.848777i
$123$	−8.12498	+	1.72702i	−0.732605	+	0.155720i
$124$	5.27021	+	3.50571i	0.473279	+	0.314822i
$125$	−5.68062	−	4.12721i	−0.508090	−	0.369149i
$126$	−0.0484230	+	1.52745i	−0.00431386	+	0.136076i
$127$	−17.1064	−	3.63608i	−1.51795	−	0.322650i	−0.627820	−	0.778359i	$-0.716053\pi$
$127$	−17.1064	−	3.63608i	−1.51795	−	0.322650i	−0.890129	+	0.455709i	$0.849386\pi$
$128$	−6.53603	−	9.23473i	−0.577709	−	0.816243i
$129$	−1.99578	−	2.74695i	−0.175718	−	0.241856i
$130$	−2.62952	+	2.72897i	−0.230624	+	0.239346i
$131$	−15.3173			−1.33827			−0.669137	−	0.743139i	$-0.733336\pi$
$131$	−15.3173			−1.33827			−0.669137	+	0.743139i	$0.733336\pi$
$132$	−5.63618	+	7.04020i	−0.490567	+	0.612771i
$133$	−0.735819	+	1.27448i	−0.0638036	+	0.110511i
$134$	2.79802	+	2.17160i	0.241712	+	0.187598i
$135$	2.46574	+	3.39380i	0.212217	+	0.292092i
$136$	−9.23523	−	20.2156i	−0.791914	−	1.73347i
$137$	1.56399	−	1.73698i	0.133620	−	0.148401i	−0.672621	−	0.739987i	$-0.734832\pi$
$137$	1.56399	−	1.73698i	0.133620	−	0.148401i	0.806241	+	0.591587i	$0.201498\pi$
$138$	0.0653952	+	0.0405717i	0.00556681	+	0.00345369i
$139$	1.88368	−	17.9220i	0.159772	−	1.52013i	−0.561501	−	0.827476i	$-0.689776\pi$
$139$	1.88368	−	17.9220i	0.159772	−	1.52013i	0.721273	−	0.692651i	$-0.243557\pi$
$140$	1.39204	+	0.0883494i	0.117649	+	0.00746689i
$141$	−3.94209	−	4.37814i	−0.331984	−	0.368706i
$142$	−0.462847	−	0.548011i	−0.0388412	−	0.0459881i
$143$	−11.8734	+	1.42229i	−0.992902	+	0.118938i
$144$	−4.34839	−	1.51964i	−0.362366	−	0.126637i
$145$	0.813831	−	0.732777i	0.0675850	−	0.0608538i
$146$	6.16242	−	6.42257i	0.510006	−	0.531536i
$147$	8.27423	+	0.869657i	0.682447	+	0.0717281i
$148$	12.9336	−	1.90259i	1.06314	−	0.156392i
$149$	5.63946	+	5.07780i	0.462003	+	0.415989i	0.866984	−	0.498336i	$-0.166055\pi$
$149$	5.63946	+	5.07780i	0.462003	+	0.415989i	−0.404981	+	0.914325i	$0.632722\pi$
$150$	−7.07415	+	4.80474i	−0.577602	+	0.392306i
$151$	19.8568	−	14.4268i	1.61593	−	1.17404i	0.777965	−	0.628307i	$-0.216252\pi$
$151$	19.8568	−	14.4268i	1.61593	−	1.17404i	0.837960	−	0.545731i	$-0.183748\pi$
$152$	−2.99975	−	3.26762i	−0.243312	−	0.265039i
$153$	−7.83648	−	4.52440i	−0.633542	−	0.365776i
$154$	3.22610	+	2.99410i	0.259966	+	0.241271i
$155$		−	2.35217i		−	0.188931i
$156$	4.33581	+	8.79313i	0.347143	+	0.704014i
$157$	−14.4992	+	10.5343i	−1.15716	+	0.840726i	−0.989416	−	0.145105i	$-0.953648\pi$
$157$	−14.4992	+	10.5343i	−1.15716	+	0.840726i	−0.167744	+	0.985831i	$0.553648\pi$
$158$	2.60330	−	5.38140i	0.207107	−	0.428121i
$159$	1.87385	−	8.81579i	0.148606	−	0.699138i
$160$	−1.51208	+	3.92294i	−0.119540	+	0.310136i
$161$	0.0220769	−	0.0303862i	0.00173990	−	0.00239477i
$162$	5.73036	−	1.66311i	0.450220	−	0.130667i
$163$	1.37957	+	6.49039i	0.108057	+	0.508366i	0.998572	+	0.0534142i	$0.0170103\pi$
$163$	1.37957	+	6.49039i	0.108057	+	0.508366i	−0.890516	+	0.454952i	$0.849656\pi$
$164$	−12.0471	−	2.04443i	−0.940717	−	0.159643i
$165$	3.33830	+	0.294893i	0.259886	+	0.0229574i
$166$	−3.72710	−	20.7471i	−0.289279	−	1.61029i
$167$	−13.6370	−	15.1455i	−1.05527	−	1.17199i	−0.984659	−	0.174488i	$-0.944173\pi$
$167$	−13.6370	−	15.1455i	−1.05527	−	1.17199i	−0.0706068	−	0.997504i	$-0.522494\pi$
$168$	1.43584	−	3.31053i	0.110778	−	0.255413i
$169$	−4.06940	+	12.3467i	−0.313030	+	0.949743i
$170$	−4.35409	+	7.01812i	−0.333944	+	0.538265i
$171$	−1.76651	−	0.375483i	−0.135088	−	0.0287139i
$172$	−1.23950	−	4.83860i	−0.0945112	−	0.368940i
$173$	6.82894	−	15.3380i	0.519195	−	1.16613i	−0.443681	−	0.896185i	$-0.646328\pi$
$173$	6.82894	−	15.3380i	0.519195	−	1.16613i	0.962876	−	0.269945i	$-0.0870057\pi$
$174$	−1.06974	−	2.62338i	−0.0810968	−	0.198878i
$175$	2.08679	+	3.61442i	0.157746	+	0.273225i
$176$	−11.5250	+	6.57073i	−0.868729	+	0.495287i
$177$	−13.7784			−1.03565
$178$	−13.5419	+	17.4482i	−1.01501	+	1.30780i
$179$	−0.923854	+	0.0971010i	−0.0690521	+	0.00725767i	−0.138991	−	0.990294i	$-0.544386\pi$
$179$	−0.923854	+	0.0971010i	−0.0690521	+	0.00725767i	0.0699394	+	0.997551i	$0.477719\pi$
$180$	0.424776	+	1.65819i	0.0316610	+	0.123594i
$181$	2.31815	+	7.13452i	0.172306	+	0.530305i	0.999500	−	0.0316120i	$-0.0100641\pi$
$181$	2.31815	+	7.13452i	0.172306	+	0.530305i	−0.827194	+	0.561917i	$0.810064\pi$
$182$	4.43443	−	1.79732i	0.328702	−	0.133227i
$183$	9.54419	+	6.93426i	0.705527	+	0.512595i
$184$	0.0674235	+	0.0909426i	0.00497052	+	0.00670438i
$185$	−3.25060	−	3.61016i	−0.238989	−	0.265424i
$186$	−5.72481	−	2.06284i	−0.419764	−	0.151255i
$187$	−24.6486	+	8.46402i	−1.80249	+	0.618950i
$188$	−3.01643	−	8.12463i	−0.219996	−	0.592550i
$189$	−1.10122	−	5.18081i	−0.0801017	−	0.376849i
$190$	−0.393629	+	1.60067i	−0.0285569	+	0.116125i
$191$	25.1951	+	2.64811i	1.82305	+	0.191610i	0.953329	−	0.301934i	$-0.0976321\pi$
$191$	25.1951	+	2.64811i	1.82305	+	0.191610i	0.869721	+	0.493544i	$0.164299\pi$
$192$	8.22175	+	7.12056i	0.593354	+	0.513882i
$193$	2.06568	−	9.71827i	0.148691	−	0.699536i	−0.839129	−	0.543933i	$-0.816935\pi$
$193$	2.06568	−	9.71827i	0.148691	−	0.699536i	0.987820	−	0.155603i	$-0.0497321\pi$
$194$	19.3870	−	1.41832i	1.39190	−	0.101830i
$195$	1.82828	−	3.15129i	0.130926	−	0.225668i
$196$	10.8430	+	5.67620i	0.774501	+	0.405443i
$197$	−10.1676	−	5.87025i	−0.724410	−	0.418238i	0.0919638	−	0.995762i	$-0.470686\pi$
$197$	−10.1676	−	5.87025i	−0.724410	−	0.418238i	−0.816374	+	0.577524i	$0.804019\pi$
$198$	−2.27108	+	4.90068i	−0.161398	+	0.348276i
$199$	13.1433	−	7.58828i	0.931703	−	0.537919i	0.0443534	−	0.999016i	$-0.485877\pi$
$199$	13.1433	−	7.58828i	0.931703	−	0.537919i	0.887350	+	0.461097i	$0.152544\pi$
$200$	−12.2791	+	2.73406i	−0.868263	+	0.193327i
$201$	−3.11063	−	1.38494i	−0.219407	−	0.0976863i
$202$	−11.0042	+	7.47402i	−0.774253	+	0.525870i
$203$	−1.31502	+	0.427275i	−0.0922962	+	0.0299889i
$204$	13.2625	+	16.7521i	0.928561	+	1.17288i
$205$	1.84691	+	4.14822i	0.128993	+	0.289724i
$206$	2.86927	−	2.99040i	0.199911	−	0.208351i
$207$	0.0438365	+	0.0142433i	0.00304685	+	0.000989980i
$208$	1.16064	+	14.3754i	0.0804758	+	0.996757i
$209$	−4.15663	+	3.12677i	−0.287520	+	0.216283i
$210$	−1.31982	+	0.237098i	−0.0910761	+	0.0163613i
$211$	−7.88525	−	8.75746i	−0.542843	−	0.602889i	0.407839	−	0.913054i	$-0.366282\pi$
$211$	−7.88525	−	8.75746i	−0.542843	−	0.602889i	−0.950683	+	0.310165i	$0.899616\pi$
$212$	7.34307	−	11.0390i	0.504324	−	0.758162i
$213$	0.557899	+	0.405337i	0.0382266	+	0.0277732i
$214$	0.373983	−	11.7969i	0.0255649	−	0.806417i
$215$	−1.24199	+	1.37937i	−0.0847029	+	0.0940721i
$216$	15.8925	+	1.51553i	1.08135	+	0.103119i
$217$	−1.20794	+	2.71308i	−0.0820005	+	0.184176i
$218$	1.16177	−	8.46376i	0.0786847	−	0.573238i
$219$	−4.27846	+	7.41051i	−0.289112	+	0.500756i
$220$	4.40505	+	2.21356i	0.296988	+	0.149238i
$221$	−3.02095	+	28.1702i	−0.203211	+	1.89493i
$222$	−11.6373	+	4.74538i	−0.781048	+	0.318489i
$223$	24.3875	−	2.56323i	1.63311	−	0.171647i	0.756885	−	0.653548i	$-0.226720\pi$
$223$	24.3875	−	2.56323i	1.63311	−	0.171647i	0.876226	+	0.481901i	$0.160054\pi$
$224$	3.75869	−	3.74836i	0.251138	−	0.250448i
$225$	−3.42712	+	3.80620i	−0.228475	+	0.253747i
$226$	3.33526	+	2.06922i	0.221858	+	0.137643i
$227$	−1.67148	+	15.9030i	−0.110940	+	1.05552i	0.787467	+	0.616357i	$0.211392\pi$
$227$	−1.67148	+	15.9030i	−0.110940	+	1.05552i	−0.898407	+	0.439165i	$0.855274\pi$
$228$	3.55057	+	2.36181i	0.235142	+	0.156415i
$229$	3.50103	−	10.7751i	0.231355	−	0.712037i	−0.766229	−	0.642567i	$-0.777869\pi$
$229$	3.50103	−	10.7751i	0.231355	−	0.712037i	0.997584	−	0.0694694i	$-0.0221306\pi$
$230$	0.0142615	−	0.0395786i	0.000940376	−	0.00260974i
$231$	−3.69908	−	2.05451i	−0.243382	−	0.135177i
$232$	−0.0402001	−	4.16745i	−0.00263927	−	0.273607i
$233$	9.98760	+	3.24517i	0.654309	+	0.212598i	0.617313	−	0.786717i	$-0.288221\pi$
$233$	9.98760	+	3.24517i	0.654309	+	0.212598i	0.0369960	+	0.999315i	$0.488221\pi$
$234$	3.77933	+	4.49395i	0.247062	+	0.293778i
$235$	−1.89299	+	2.60548i	−0.123485	+	0.169963i
$236$	−18.8413	−	7.47181i	−1.22646	−	0.486373i
$237$	−1.19487	+	5.62144i	−0.0776154	+	0.365152i
$238$	8.62630	−	5.85895i	0.559160	−	0.379780i
$239$	16.4666	−	11.9637i	1.06514	−	0.773869i	0.0901068	−	0.995932i	$-0.471279\pi$
$239$	16.4666	−	11.9637i	1.06514	−	0.773869i	0.975032	+	0.222063i	$0.0712792\pi$
$240$	0.510990	−	4.00938i	0.0329843	−	0.258805i
$241$	5.31860	−	3.07069i	0.342601	−	0.197801i	−0.318821	−	0.947815i	$-0.603287\pi$
$241$	5.31860	−	3.07069i	0.342601	−	0.197801i	0.661422	+	0.750014i	$0.269953\pi$
$242$	6.34911	+	14.2017i	0.408137	+	0.912921i
$243$	9.69669	−	5.59839i	0.622043	−	0.359137i
$244$	9.29089	+	14.6579i	0.594788	+	0.938378i
$245$	−0.475402	−	4.52315i	−0.0303723	−	0.288973i
$246$	11.7159	−	0.857115i	0.746976	−	0.0546477i
$247$	1.16395	+	5.53339i	0.0740605	+	0.352081i
$248$	−6.70976	−	5.92531i	−0.426070	−	0.376257i
$249$	8.24242	+	18.5128i	0.522342	+	1.17320i
$250$	7.16524	+	6.87501i	0.453170	+	0.434814i
$251$	0.607759	+	2.85928i	0.0383614	+	0.180476i	0.993157	−	0.116787i	$-0.0372594\pi$
$251$	0.607759	+	2.85928i	0.0383614	+	0.180476i	−0.954796	+	0.297263i	$0.903926\pi$
$252$	0.361598	−	2.13076i	0.0227785	−	0.134225i
$253$	0.113847	−	0.0682758i	0.00715749	−	0.00429246i
$254$	23.2681	+	8.38427i	1.45997	+	0.526076i
$255$	2.45358	−	7.55133i	0.153649	−	0.472883i
$256$	7.38148	+	14.1956i	0.461343	+	0.887222i
$257$	−6.00822	+	2.67503i	−0.374783	+	0.166864i	−0.585479	−	0.810688i	$-0.699094\pi$
$257$	−6.00822	+	2.67503i	−0.374783	+	0.166864i	0.210696	+	0.977552i	$0.432427\pi$
$258$	2.26795	+	4.23251i	0.141197	+	0.263505i
$259$	1.89540	+	5.83344i	0.117774	+	0.362472i
$260$	4.20898	−	3.31779i	0.261030	−	0.205761i
$261$	−0.997366	−	1.37276i	−0.0617354	−	0.0849715i
$262$	21.4606	+	2.94576i	1.32584	+	0.181990i
$263$	7.88154	−	13.6512i	0.485997	−	0.841771i	−0.513874	−	0.857866i	$-0.671790\pi$
$263$	7.88154	−	13.6512i	0.485997	−	0.841771i	0.999870	+	0.0160949i	$0.00512340\pi$
$264$	9.25067	−	8.77993i	0.569339	−	0.540367i
$265$	−4.92686			−0.302654
$266$	1.27604	−	1.64413i	0.0782391	−	0.100808i
$267$	8.63636	−	19.3976i	0.528537	−	1.18711i
$268$	−3.50261	−	3.58069i	−0.213956	−	0.218725i
$269$	8.66757	−	9.62631i	0.528471	−	0.586927i	−0.418511	−	0.908212i	$-0.637448\pi$
$269$	8.66757	−	9.62631i	0.528471	−	0.586927i	0.946983	+	0.321285i	$0.104115\pi$
$270$	−2.80201	−	5.22918i	−0.170525	−	0.318238i
$271$	12.2611	−	5.45900i	0.744809	−	0.331610i	0.000997319	−	1.00000i	$-0.499683\pi$
$271$	12.2611	−	5.45900i	0.744809	−	0.331610i	0.743812	+	0.668389i	$0.233016\pi$
$272$	9.05146	+	30.0997i	0.548826	+	1.82506i
$273$	−3.72714	+	2.69592i	−0.225577	+	0.163164i
$274$	−2.52532	+	2.13287i	−0.152560	+	0.128851i
$275$	1.78539	+	14.6427i	0.107663	+	0.882987i
$276$	−0.0838211	−	0.0694206i	−0.00504544	−	0.00417863i
$277$	−2.33364	−	10.9789i	−0.140215	−	0.659658i	−0.990969	−	0.134094i	$-0.957188\pi$
$277$	−2.33364	−	10.9789i	−0.140215	−	0.659658i	0.850754	−	0.525564i	$-0.176146\pi$
$278$	−6.08589	+	24.7479i	−0.365007	+	1.48428i
$279$	−3.62458	−	0.380958i	−0.216998	−	0.0228074i
$280$	−1.93336	−	0.391497i	−0.115541	−	0.0233964i
$281$	−21.7825	+	7.07758i	−1.29944	+	0.422213i	−0.875386	−	0.483425i	$-0.839393\pi$
$281$	−21.7825	+	7.07758i	−1.29944	+	0.422213i	−0.424052	+	0.905638i	$0.639393\pi$
$282$	4.68119	+	6.89224i	0.278761	+	0.410427i
$283$	−2.15564	−	20.5095i	−0.128139	−	1.21916i	−0.849871	−	0.526991i	$-0.823320\pi$
$283$	−2.15564	−	20.5095i	−0.128139	−	1.21916i	0.721731	−	0.692173i	$-0.243347\pi$
$284$	0.543092	+	0.856818i	0.0322266	+	0.0508428i
$285$		−	1.58467i		−	0.0938676i
$286$	16.9090	+	0.290706i	0.999852	+	0.0171898i
$287$		−	5.73319i		−	0.338419i
$288$	5.80017	+	2.96540i	0.341778	+	0.174738i
$289$	4.67712	+	44.4998i	0.275125	+	2.61764i
$290$	−1.28116	+	0.870163i	−0.0752325	+	0.0510977i
$291$	−17.7730	+	5.77481i	−1.04187	+	0.338525i
$292$	−9.86919	+	7.81338i	−0.577551	+	0.457243i
$293$	1.26768	+	0.133239i	0.0740587	+	0.00778389i	0.141485	−	0.989940i	$-0.454812\pi$
$293$	1.26768	+	0.133239i	0.0740587	+	0.00778389i	−0.0674266	+	0.997724i	$0.521479\pi$
$294$	−11.4256	−	2.80973i	−0.666353	−	0.163867i
$295$	1.56600	+	7.36744i	0.0911759	+	0.428949i
$296$	−18.4869	+	0.178328i	−1.07453	+	0.0103651i
$297$	3.58744	−	18.3732i	0.208164	−	1.06612i
$298$	−6.92477	−	8.19894i	−0.401141	−	0.474952i
$299$	−0.0147819	−	0.143556i	−0.000854862	−	0.00830205i
$300$	10.8355	−	5.37133i	0.625585	−	0.310114i
$301$	2.14093	−	0.953202i	0.123401	−	0.0549416i
$302$	−30.5954	+	16.3943i	−1.76057	+	0.943385i
$303$	8.55711	−	9.50363i	0.491593	−	0.545970i
$304$	3.57446	+	5.15508i	0.205009	+	0.295664i
$305$	2.62306	−	5.89149i	0.150196	−	0.337346i
$306$	10.1094	+	7.84611i	0.577916	+	0.448532i
$307$	−22.4408			−1.28076			−0.640382	−	0.768057i	$-0.721224\pi$
$307$	−22.4408			−1.28076			−0.640382	+	0.768057i	$0.721224\pi$
$308$	−3.94420	−	4.81539i	−0.224741	−	0.274382i
$309$	−1.99208	+	3.45039i	−0.113326	+	0.196286i
$310$	−0.452361	+	3.29556i	−0.0256924	+	0.187175i
$311$	−8.26384	−	11.3742i	−0.468600	−	0.644972i	0.507665	−	0.861555i	$-0.330509\pi$
$311$	−8.26384	−	11.3742i	−0.468600	−	0.644972i	−0.976264	+	0.216583i	$0.930509\pi$
$312$	−4.38373	−	13.1537i	−0.248180	−	0.744681i
$313$	−1.85408	−	5.70629i	−0.104799	−	0.322538i	0.884884	−	0.465811i	$-0.154237\pi$
$313$	−1.85408	−	5.70629i	−0.104799	−	0.322538i	−0.989683	+	0.143273i	$0.954237\pi$
$314$	22.3404	−	11.9709i	1.26074	−	0.675556i
$315$	−0.733694	+	0.326661i	−0.0413390	+	0.0184053i
$316$	−4.68235	+	7.03909i	−0.263403	+	0.395980i
$317$	1.77341	−	5.45799i	0.0996046	−	0.306552i	−0.888822	−	0.458253i	$-0.848475\pi$
$317$	1.77341	−	5.45799i	0.0996046	−	0.306552i	0.988426	+	0.151702i	$0.0484753\pi$
$318$	−4.32083	+	11.9912i	−0.242300	+	0.672434i
$319$	−4.86804	−	0.430025i	−0.272558	−	0.0240768i
$320$	2.87298	−	5.20554i	0.160604	−	0.290999i
$321$	2.35912	+	11.0988i	0.131673	+	0.619474i
$322$	−0.0367752	+	0.0383277i	−0.00204940	+	0.00213592i
$323$	5.01228	+	11.2578i	0.278891	+	0.626399i
$324$	−8.34852	+	1.22810i	−0.463807	+	0.0682280i
$325$	15.2408	+	4.98764i	0.845407	+	0.276664i
$326$	−0.684680	−	9.35884i	−0.0379209	−	0.518338i
$327$	0.858495	+	8.16804i	0.0474749	+	0.451694i
$328$	16.4857	+	5.18126i	0.910269	+	0.286087i
$329$	3.52148	−	2.03313i	0.194145	−	0.112090i
$330$	−4.62050	−	1.05518i	−0.254350	−	0.0580856i
$331$	6.02410	−	3.47802i	0.331114	−	0.191169i	−0.325221	−	0.945638i	$-0.605439\pi$
$331$	6.02410	−	3.47802i	0.331114	−	0.191169i	0.656336	+	0.754469i	$0.272105\pi$
$332$	1.23193	+	29.7851i	0.0676111	+	1.63467i
$333$	−6.08956	+	4.42432i	−0.333706	+	0.242451i
$334$	16.1938	+	23.8426i	0.886086	+	1.30461i
$335$	−0.387000	+	1.82069i	−0.0211440	+	0.0994749i
$336$	−2.64839	+	4.36217i	−0.144482	+	0.237976i
$337$	1.54141	−	2.12157i	0.0839662	−	0.115570i	−0.764968	−	0.644069i	$-0.777245\pi$
$337$	1.54141	−	2.12157i	0.0839662	−	0.115570i	0.848934	+	0.528499i	$0.177245\pi$
$338$	8.07600	−	16.5160i	0.439277	−	0.898352i
$339$	−3.58867	−	1.16603i	−0.194910	−	0.0633300i
$340$	7.45011	−	8.99555i	0.404039	−	0.487852i
$341$	−7.68276	+	7.15222i	−0.416045	+	0.387314i
$342$	2.40280	+	0.865809i	0.129929	+	0.0468176i
$343$	−3.80432	+	11.7085i	−0.205414	+	0.632200i
$344$	0.806093	+	7.01763i	0.0434616	+	0.378365i
$345$	−0.00422757	+	0.0402226i	−0.000227605	+	0.00216551i
$346$	−12.5176	+	20.1765i	−0.672952	+	1.08469i
$347$	−9.82451	+	10.9112i	−0.527407	+	0.585745i	−0.946704	−	0.322104i	$-0.895610\pi$
$347$	−9.82451	+	10.9112i	−0.527407	+	0.585745i	0.419297	+	0.907849i	$0.362277\pi$
$348$	0.994267	+	3.88129i	0.0532983	+	0.208059i
$349$	26.6198	−	2.79785i	1.42492	−	0.149765i	0.639532	−	0.768765i	$-0.279128\pi$
$349$	26.6198	−	2.79785i	1.42492	−	0.149765i	0.785391	+	0.618999i	$0.212462\pi$
$350$	−2.22864	−	5.46541i	−0.119126	−	0.292138i
$351$	−16.4390	−	11.9967i	−0.877449	−	0.640339i
$352$	17.4111	−	6.98964i	0.928012	−	0.372549i
$353$	5.08081	−	8.80021i	0.270424	−	0.468388i	−0.698546	−	0.715565i	$-0.746169\pi$
$353$	5.08081	−	8.80021i	0.270424	−	0.468388i	0.968970	+	0.247177i	$0.0795028\pi$
$354$	19.3046	+	2.64982i	1.02603	+	0.140836i
$355$	0.153329	−	0.344382i	0.00813786	−	0.0182779i
$356$	22.3288	−	21.8419i	1.18342	−	1.15762i
$357$	−6.70800	+	7.44999i	−0.355025	+	0.394295i
$358$	1.31306	+	0.0416266i	0.0693976	+	0.00220004i
$359$	11.8616	+	8.61799i	0.626033	+	0.454840i	0.855024	−	0.518589i	$-0.173542\pi$
$359$	11.8616	+	8.61799i	0.626033	+	0.454840i	−0.228990	+	0.973429i	$0.573542\pi$
$360$	−0.276247	−	2.40494i	−0.0145595	−	0.126751i
$361$	−11.0678	−	12.2920i	−0.582514	−	0.646948i
$362$	−1.87581	−	10.4418i	−0.0985905	−	0.548810i
$363$	−9.18755	−	11.8004i	−0.482221	−	0.619360i
$364$	−6.55864	+	1.66537i	−0.343766	+	0.0872893i
$365$	4.44874	+	1.44548i	0.232858	+	0.0756601i
$366$	−12.0386	−	11.5509i	−0.629266	−	0.603777i
$367$	−13.6384	−	30.6323i	−0.711919	−	1.59900i	−0.797965	−	0.602704i	$-0.794090\pi$
$367$	−13.6384	−	30.6323i	−0.711919	−	1.59900i	0.0860463	−	0.996291i	$-0.472577\pi$
$368$	−0.0769756	−	0.140384i	−0.00401263	−	0.00731803i
$369$	6.69133	−	2.17415i	0.348337	−	0.113182i
$370$	3.86005	+	5.68326i	0.200674	+	0.295459i
$371$	5.68284	+	2.53016i	0.295038	+	0.131359i
$372$	7.62418	+	3.99117i	0.395295	+	0.206933i
$373$	−17.5831	+	10.1516i	−0.910419	+	0.525630i	−0.880566	−	0.473924i	$-0.842837\pi$
$373$	−17.5831	+	10.1516i	−0.910419	+	0.525630i	−0.0298527	+	0.999554i	$0.509504\pi$
$374$	36.1624	−	7.11839i	1.86991	−	0.368083i
$375$	−8.26742	−	4.77320i	−0.426928	−	0.246487i
$376$	2.66375	+	11.9633i	0.137372	+	0.616962i
$377$	−2.66607	+	4.59534i	−0.137310	+	0.236672i
$378$	0.546531	+	7.47050i	0.0281105	+	0.384241i
$379$	4.38705	−	20.6394i	0.225347	−	1.06018i	−0.709384	−	0.704822i	$-0.751027\pi$
$379$	4.38705	−	20.6394i	0.225347	−	1.06018i	0.934732	−	0.355354i	$-0.115640\pi$
$380$	0.859339	−	2.16696i	0.0440832	−	0.111163i
$381$	−23.6467	−	2.48537i	−1.21146	−	0.127329i
$382$	−34.7909	−	8.55563i	−1.78006	−	0.437744i
$383$	3.17139	+	14.9202i	0.162050	+	0.762387i	0.981838	+	0.189720i	$0.0607579\pi$
$383$	3.17139	+	14.9202i	0.162050	+	0.762387i	−0.819788	+	0.572667i	$0.805909\pi$
$384$	−10.1499	−	11.5576i	−0.517960	−	0.589798i
$385$	−0.678140	+	2.21144i	−0.0345612	+	0.112705i
$386$	−4.76316	+	13.2188i	−0.242439	+	0.672818i
$387$	1.92439	+	2.13725i	0.0978221	+	0.108642i
$388$	−27.4354	−	1.74126i	−1.39282	−	0.0883989i
$389$	−14.6982	−	10.6789i	−0.745230	−	0.541441i	0.149115	−	0.988820i	$-0.452358\pi$
$389$	−14.6982	−	10.6789i	−0.745230	−	0.541441i	−0.894345	+	0.447379i	$0.852358\pi$
$390$	−3.16760	+	4.06359i	−0.160398	+	0.205768i
$391$	−0.0971902	−	0.299121i	−0.00491512	−	0.0151272i
$392$	−14.1003	−	10.0381i	−0.712171	−	0.506999i
$393$	−20.7108	+	2.17679i	−1.04472	+	0.109805i
$394$	13.1166	+	10.1801i	0.660805	+	0.512864i
$395$	3.14164			0.158073
$396$	4.12443	−	6.42946i	0.207260	−	0.323092i
$397$	−2.91339	−	5.04614i	−0.146219	−	0.253258i	0.783608	−	0.621255i	$-0.213377\pi$
$397$	−2.91339	−	5.04614i	−0.146219	−	0.253258i	−0.929827	+	0.367997i	$0.880044\pi$
$398$	−19.8741	+	8.10409i	−0.996199	+	0.406221i
$399$	−0.813797	+	1.82782i	−0.0407408	+	0.0915054i
$400$	17.7298	−	1.46915i	0.886488	−	0.0734573i
$401$	23.2072	+	4.93284i	1.15891	+	0.246334i	0.746958	−	0.664871i	$-0.231513\pi$
$401$	23.2072	+	4.93284i	1.15891	+	0.246334i	0.411953	+	0.911205i	$0.364847\pi$
$402$	4.09188	+	2.53864i	0.204085	+	0.126616i
$403$	3.50328	+	10.8600i	0.174511	+	0.540973i
$404$	16.8551	−	8.35538i	0.838573	−	0.415696i
$405$	2.09824	+	2.33033i	0.104262	+	0.115795i
$406$	1.92461	−	0.345745i	0.0955169	−	0.0171591i
$407$	−1.90760	+	21.5947i	−0.0945560	+	1.07041i
$408$	−15.3601	−	26.0215i	−0.760437	−	1.28826i
$409$	−0.191806	−	0.902377i	−0.00948420	−	0.0446196i	0.973151	−	0.230167i	$-0.0739274\pi$
$409$	−0.191806	−	0.902377i	−0.00948420	−	0.0446196i	−0.982635	+	0.185548i	$0.940594\pi$
$410$	−1.78988	−	6.16716i	−0.0883961	−	0.304574i
$411$	1.86785	−	2.57088i	0.0921344	−	0.126812i
$412$	−4.59516	+	3.63796i	−0.226387	+	0.179230i
$413$	1.97722	−	9.30211i	0.0972929	−	0.457727i
$414$	−0.0586790	−	0.0283865i	−0.00288392	−	0.00139512i
$415$	8.96216	−	6.51139i	0.439935	−	0.319632i
$416$	1.13849	−	20.3643i	0.0558191	−	0.998441i
$417$		−	24.5005i		−	1.19979i
$418$	6.42509	−	3.58145i	0.314261	−	0.175174i
$419$	−21.9133	−	12.6517i	−1.07054	−	0.618074i	−0.142208	−	0.989837i	$-0.545420\pi$
$419$	−21.9133	−	12.6517i	−1.07054	−	0.618074i	−0.928328	+	0.371762i	$0.878754\pi$
$420$	1.89476	−	0.0783689i	0.0924550	−	0.00382401i
$421$	1.67592	−	1.21763i	0.0816795	−	0.0593436i	−0.546196	−	0.837657i	$-0.683925\pi$
$421$	1.67592	−	1.21763i	0.0816795	−	0.0593436i	0.627876	+	0.778314i	$0.283925\pi$
$422$	9.36364	+	13.7863i	0.455815	+	0.671108i
$423$	3.70833	+	3.33899i	0.180305	+	0.162347i
$424$	−12.4112	+	14.0543i	−0.602740	+	0.682537i
$425$	34.7571	+	3.65312i	1.68597	+	0.177202i
$426$	−0.703705	−	0.675201i	−0.0340946	−	0.0327136i
$427$	−6.05108	+	5.44842i	−0.292832	+	0.263667i
$428$	−2.79271	+	16.4564i	−0.134991	+	0.795449i
$429$	−15.8521	+	3.61049i	−0.765348	+	0.174316i
$430$	2.00540	−	1.69374i	0.0967088	−	0.0816796i
$431$	−12.2794	−	13.6377i	−0.591479	−	0.656904i	0.370882	−	0.928680i	$-0.379056\pi$
$431$	−12.2794	−	13.6377i	−0.591479	−	0.656904i	−0.962360	+	0.271776i	$0.912389\pi$
$432$	−21.9752	−	5.17978i	−1.05728	−	0.249212i
$433$	−0.421512	+	4.01042i	−0.0202566	+	0.192729i	−0.999971	−	0.00767231i	$-0.997558\pi$
$433$	−0.421512	+	4.01042i	−0.0202566	+	0.192729i	0.979714	+	0.200401i	$0.0642245\pi$
$434$	2.21419	−	3.56893i	0.106285	−	0.171314i
$435$	0.996261	−	1.10646i	0.0477671	−	0.0530507i
$436$	−3.25544	+	11.6349i	−0.155908	+	0.557213i
$437$	−0.0368960	−	0.0507830i	−0.00176498	−	0.00242928i
$438$	7.41961	−	9.55987i	0.354523	−	0.456788i
$439$	−17.3106	+	29.9829i	−0.826191	+	1.43101i	0.0748139	+	0.997198i	$0.476164\pi$
$439$	−17.3106	+	29.9829i	−0.826191	+	1.43101i	−0.901005	+	0.433808i	$0.857170\pi$
$440$	−5.74610	−	3.94853i	−0.273935	−	0.188239i
$441$	−7.04695			−0.335569
$442$	9.65018	−	38.8876i	0.459012	−	1.84969i
$443$	19.4379	+	26.7540i	0.923524	+	1.27112i	0.962333	+	0.271875i	$0.0876437\pi$
$443$	19.4379	+	26.7540i	0.923524	+	1.27112i	−0.0388088	+	0.999247i	$0.512356\pi$
$444$	17.2174	−	4.41058i	0.817103	−	0.209317i
$445$	−11.3536	−	2.41329i	−0.538214	−	0.114401i
$446$	−34.6618	−	1.09884i	−1.64128	−	0.0520317i
$447$	8.34687	+	6.06436i	0.394793	+	0.286834i
$448$	−5.98709	+	4.52887i	−0.282863	+	0.213969i
$449$	31.0627	−	6.60258i	1.46594	−	0.311595i	0.595295	−	0.803507i	$-0.297035\pi$
$449$	31.0627	−	6.60258i	1.46594	−	0.311595i	0.870645	+	0.491912i	$0.163702\pi$
$450$	5.53365	−	4.67369i	0.260859	−	0.220320i
$451$	7.93324	−	18.6459i	0.373562	−	0.878002i
$452$	−4.27501	−	3.54057i	−0.201080	−	0.166534i
$453$	24.7986	−	22.3288i	1.16514	−	1.04910i
$454$	5.40029	−	21.9599i	0.253448	−	1.03063i
$455$	1.86514	+	1.68653i	0.0874393	+	0.0790656i
$456$	−4.52040	−	3.99191i	−0.211687	−	0.186938i
$457$	8.74233	−	41.1294i	0.408949	−	1.92395i	0.0273490	−	0.999626i	$-0.491293\pi$
$457$	8.74233	−	41.1294i	0.408949	−	1.92395i	0.381600	−	0.924328i	$-0.375373\pi$
$458$	−6.97744	+	14.4234i	−0.326034	+	0.673961i
$459$	−40.5177	−	18.0396i	−1.89120	−	0.842018i
$460$	−0.0275931	+	0.0527100i	−0.00128653	+	0.00245762i
$461$	−6.71493	+	3.87687i	−0.312745	+	0.180564i	−0.648154	−	0.761509i	$-0.724459\pi$
$461$	−6.71493	+	3.87687i	−0.312745	+	0.180564i	0.335409	+	0.942073i	$0.391126\pi$
$462$	4.78758	+	3.58991i	0.222739	+	0.167018i
$463$			9.97317i			0.463492i	0.972776	+	0.231746i	$0.0744439\pi$
$463$			9.97317i			0.463492i	−0.972776	+	0.231746i	$0.925556\pi$
$464$	−0.745147	+	5.84665i	−0.0345926	+	0.271424i
$465$	−0.334275	−	3.18042i	−0.0155016	−	0.147488i
$466$	−13.3693	−	6.46751i	−0.619320	−	0.299602i
$467$	−10.7782	+	3.50205i	−0.498756	+	0.162056i	−0.547583	−	0.836752i	$-0.684452\pi$
$467$	−10.7782	+	3.50205i	−0.498756	+	0.162056i	0.0488266	+	0.998807i	$0.484452\pi$
$468$	−4.43087	−	7.02319i	−0.204817	−	0.324647i
$469$	1.38139	−	1.90132i	0.0637865	−	0.0877946i
$470$	3.15330	−	3.28642i	0.145451	−	0.151591i
$471$	−18.1076	+	16.3042i	−0.834354	+	0.751256i
$472$	24.9612	+	14.0921i	1.14893	+	0.648640i
$473$	8.28187	−	0.137592i	0.380801	−	0.00632648i
$474$	2.75521	−	7.64627i	0.126551	−	0.351205i
$475$	6.82267	−	1.45020i	0.313046	−	0.0665399i
$476$	−13.2129	+	6.54986i	−0.605611	+	0.300212i
$477$	−0.797957	+	7.59206i	−0.0365360	+	0.347616i
$478$	−25.3719	+	13.5953i	−1.16048	+	0.621833i
$479$	31.6135	+	6.71966i	1.44446	+	0.307029i	0.862445	−	0.506150i	$-0.168932\pi$
$479$	31.6135	+	6.71966i	1.44446	+	0.307029i	0.582013	+	0.813179i	$0.302265\pi$
$480$	−1.48701	+	5.51918i	−0.0678723	+	0.251915i
$481$	20.3850	+	11.8267i	0.929474	+	0.539252i
$482$	−8.04231	+	3.27942i	−0.366317	+	0.149374i
$483$	0.0255324	−	0.0442233i	0.00116176	−	0.00201223i
$484$	−6.16437	−	21.1187i	−0.280198	−	0.959942i
$485$	5.10786	+	8.84707i	0.231936	+	0.401725i
$486$	−14.6625	+	5.97893i	−0.665103	+	0.271210i
$487$	7.85082	−	17.6332i	0.355755	−	0.799038i	−0.643676	−	0.765298i	$-0.722592\pi$
$487$	7.85082	−	17.6332i	0.355755	−	0.799038i	0.999431	−	0.0337399i	$-0.0107418\pi$
$488$	−10.1983	−	22.3237i	−0.461654	−	1.01055i
$489$	2.78773	+	8.57974i	0.126065	+	0.387989i
$490$	−0.203802	+	6.42870i	−0.00920684	+	0.290419i
$491$	10.6744	−	4.75256i	0.481730	−	0.214480i	−0.151479	−	0.988460i	$-0.548404\pi$
$491$	10.6744	−	4.75256i	0.481730	−	0.214480i	0.633210	+	0.773980i	$0.281737\pi$
$492$	−16.5796	−	1.05227i	−0.747468	−	0.0474400i
$493$	−3.57791	+	11.0117i	−0.161141	+	0.495940i
$494$	−0.566623	−	7.97655i	−0.0254936	−	0.358882i
$495$	−2.83819	+	0.0471526i	−0.127567	+	0.00211935i
$496$	8.26135	+	9.59221i	0.370946	+	0.430703i
$497$	−0.353711	+	0.318483i	−0.0158661	+	0.0142859i
$498$	−7.98795	−	27.5230i	−0.357948	−	1.23333i
$499$	−7.01575	+	9.65636i	−0.314068	+	0.432278i	−0.936645	−	0.350281i	$-0.886086\pi$
$499$	−7.01575	+	9.65636i	−0.314068	+	0.432278i	0.622576	+	0.782559i	$0.286086\pi$
$500$	−8.71687	−	11.0104i	−0.389830	−	0.492400i
$501$	−20.5913	−	18.5405i	−0.919953	−	0.828329i
$502$	−0.301630	−	4.12296i	−0.0134624	−	0.184017i
$503$	21.5211	+	9.58179i	0.959576	+	0.427231i	0.825914	−	0.563796i	$-0.190660\pi$
$503$	21.5211	+	9.58179i	0.959576	+	0.427231i	0.133662	+	0.991027i	$0.457326\pi$
$504$	−0.916407	+	2.91581i	−0.0408200	+	0.129881i
$505$	−6.05425	−	3.49542i	−0.269410	−	0.155544i
$506$	−0.172639	+	0.0737649i	−0.00767472	+	0.00327925i
$507$	−3.74769	+	17.2725i	−0.166441	+	0.767099i
$508$	−30.9880	−	16.2218i	−1.37487	−	0.719728i
$509$	1.79461	+	17.0746i	0.0795447	+	0.756817i	0.959490	+	0.281742i	$0.0909123\pi$
$509$	1.79461	+	17.0746i	0.0795447	+	0.756817i	−0.879945	+	0.475075i	$0.842421\pi$
$510$	−4.88989	+	10.1081i	−0.216528	+	0.447595i
$511$	−4.38904	−	3.95191i	−0.194159	−	0.174822i
$512$	−7.61198	−	21.3086i	−0.336405	−	0.941717i
$513$	−8.80338	−	0.925273i	−0.388679	−	0.0408518i
$514$	8.93243	−	2.59244i	0.393993	−	0.114348i
$515$	2.07136	+	0.673027i	0.0912752	+	0.0296571i
$516$	−2.36359	−	6.36623i	−0.104051	−	0.280258i
$517$	14.2661	−	1.73948i	0.627424	−	0.0765023i
$518$	−1.53373	−	8.53760i	−0.0673883	−	0.375121i
$519$	7.05381	−	21.7094i	0.309628	−	0.952937i
$520$	−6.53516	+	3.83902i	−0.286586	+	0.168352i
$521$	23.5611	+	17.1182i	1.03223	+	0.749960i	0.968754	−	0.248023i	$-0.0797808\pi$
$521$	23.5611	+	17.1182i	1.03223	+	0.749960i	0.0634778	+	0.997983i	$0.479781\pi$
$522$	1.13338	+	2.11515i	0.0496068	+	0.0925774i
$523$	−8.10491	−	1.72275i	−0.354403	−	0.0753307i	0.0272700	−	0.999628i	$-0.491319\pi$
$523$	−8.10491	−	1.72275i	−0.354403	−	0.0753307i	−0.381673	+	0.924297i	$0.624652\pi$
$524$	−29.5015	−	8.25447i	−1.28878	−	0.360598i
$525$	3.33525	+	4.59058i	0.145562	+	0.200349i
$526$	−13.6680	+	17.6107i	−0.595953	+	0.767861i
$527$	12.4344	+	21.5370i	0.541650	+	0.938165i
$528$	−14.6494	+	10.5223i	−0.637534	+	0.457924i
$529$	−11.4992	−	19.9172i	−0.499965	−	0.865965i
$530$	6.90290	+	0.947517i	0.299843	+	0.0411575i
$531$	11.6065	−	1.21989i	0.503680	−	0.0529389i
$532$	−2.10402	+	2.05814i	−0.0912210	+	0.0892319i
$533$	−14.7055	−	16.4016i	−0.636964	−	0.710431i
$534$	−15.8307	+	25.5166i	−0.685061	+	1.10421i
$535$	5.66650	−	2.52289i	0.244984	−	0.109074i
$536$	4.21879	+	5.69043i	0.182224	+	0.245789i
$537$	−1.23536	+	0.262585i	−0.0533099	+	0.0113314i
$538$	−13.9952	+	11.8203i	−0.603377	+	0.509608i
$539$	−13.3282	+	15.3063i	−0.574085	+	0.659289i
$540$	2.92017	+	7.86535i	0.125664	+	0.338471i
$541$	−21.9260	−	7.12418i	−0.942672	−	0.306293i	−0.202937	−	0.979192i	$-0.565049\pi$
$541$	−21.9260	−	7.12418i	−0.942672	−	0.306293i	−0.739734	+	0.672899i	$0.765049\pi$
$542$	−18.2286	+	5.29045i	−0.782985	+	0.227244i
$543$	4.14833	+	9.31731i	0.178022	+	0.399844i
$544$	−6.89312	−	43.9127i	−0.295540	−	1.88274i
$545$	4.26995	−	1.38739i	0.182905	−	0.0594293i
$546$	5.74047	−	3.06040i	0.245670	−	0.130973i
$547$	−9.94390	+	7.22467i	−0.425170	+	0.308904i	−0.779715	−	0.626135i	$-0.784636\pi$
$547$	−9.94390	+	7.22467i	−0.425170	+	0.308904i	0.354544	+	0.935039i	$0.384636\pi$
$548$	3.94834	−	2.50265i	0.168665	−	0.106908i
$549$	−8.65367	−	4.99620i	−0.369330	−	0.213233i
$550$	0.314559	−	20.8589i	0.0134128	−	0.889425i
$551$			2.31083i			0.0984445i
$552$	0.104089	+	0.113384i	0.00443032	+	0.00482593i
$553$	−3.62370	−	1.61337i	−0.154095	−	0.0686076i
$554$	1.15818	+	15.8311i	0.0492063	+	0.672598i
$555$	−4.90827	−	4.41943i	−0.208344	−	0.187594i
$556$	13.2862	−	33.5032i	0.563461	−	1.42085i
$557$	−1.44435	−	3.24407i	−0.0611992	−	0.137456i	0.880357	−	0.474312i	$-0.157303\pi$
$557$	−1.44435	−	3.24407i	−0.0611992	−	0.137456i	−0.941556	+	0.336856i	$0.890636\pi$
$558$	5.00504	+	1.23082i	0.211880	+	0.0521047i
$559$	3.67985	−	8.21834i	0.155641	−	0.347599i
$560$	2.63350	+	0.920334i	0.111286	+	0.0388912i
$561$	−32.1251	+	14.9473i	−1.35632	+	0.631075i
$562$	31.8801	−	5.72708i	1.34478	−	0.241582i
$563$	−18.4883	+	3.92980i	−0.779187	+	0.165621i	−0.580302	−	0.814401i	$-0.697065\pi$
$563$	−18.4883	+	3.92980i	−0.779187	+	0.165621i	−0.198885	+	0.980023i	$0.563732\pi$
$564$	−5.23321	−	10.5568i	−0.220358	−	0.444522i
$565$	−0.215613	+	2.05142i	−0.00907090	+	0.0863039i
$566$	−0.924109	+	29.1500i	−0.0388432	+	1.22526i
$567$	−1.22346	−	3.76543i	−0.0513806	−	0.158133i
$568$	−0.596133	−	1.30491i	−0.0250132	−	0.0547530i
$569$	2.52042	−	0.264906i	0.105661	−	0.0111055i	−0.0515502	−	0.998670i	$-0.516416\pi$
$569$	2.52042	−	0.264906i	0.105661	−	0.0111055i	0.157212	+	0.987565i	$0.449750\pi$
$570$	−0.304758	+	2.22024i	−0.0127649	+	0.0929956i
$571$	−8.42191			−0.352446			−0.176223	−	0.984350i	$-0.556388\pi$
$571$	−8.42191			−0.352446			−0.176223	+	0.984350i	$0.556388\pi$
$572$	−23.6349	−	3.65919i	−0.988226	−	0.152998i
$573$	34.4431			1.43888
$574$	−1.10259	+	8.03263i	−0.0460211	+	0.335276i
$575$	−0.177045	+	0.0186081i	−0.00738327	+	0.000776013i
$576$	−7.55618	−	5.27022i	−0.314841	−	0.219592i
$577$	9.74706	+	29.9984i	0.405775	+	1.24885i	0.920246	+	0.391340i	$0.127988\pi$
$577$	9.74706	+	29.9984i	0.405775	+	1.24885i	−0.514471	+	0.857508i	$0.672012\pi$
$578$	2.00505	−	63.2471i	0.0833992	−	2.63073i
$579$	1.41195	−	13.4338i	0.0586788	−	0.558292i
$580$	1.96236	−	0.972775i	0.0814824	−	0.0403923i
$581$	−13.6812	+	2.90803i	−0.567592	+	0.120645i
$582$	26.0120	−	4.67290i	1.07823	−	0.193698i
$583$	14.9811	+	16.0923i	0.620452	+	0.666477i
$584$	15.3301	−	9.04913i	0.634365	−	0.374456i
$585$	−1.26108	+	2.81642i	−0.0521393	+	0.116445i
$586$	−1.75049	−	0.430474i	−0.0723122	−	0.0177827i
$587$	14.5488	+	32.6770i	0.600491	+	1.34873i	0.916525	+	0.399977i	$0.130982\pi$
$587$	14.5488	+	32.6770i	0.600491	+	1.34873i	−0.316034	+	0.948748i	$0.602351\pi$
$588$	15.4677	+	6.13397i	0.637879	+	0.252961i
$589$	3.68848	+	3.32113i	0.151981	+	0.136845i
$590$	−0.777201	−	10.6235i	−0.0319969	−	0.437363i
$591$	−14.5821	−	6.49235i	−0.599825	−	0.267059i
$592$	25.9358	+	3.30548i	1.06595	+	0.135854i
$593$		−	7.00942i		−	0.287842i	−0.989589	−	0.143921i	$-0.954029\pi$
$593$		−	7.00942i		−	0.287842i	0.989589	−	0.143921i	$-0.0459712\pi$
$594$	−8.55975	+	25.0524i	−0.351211	+	1.02791i
$595$	4.74598	+	2.74009i	0.194566	+	0.112333i
$596$	8.12534	+	12.8191i	0.332827	+	0.525090i
$597$	16.6929	−	12.1281i	0.683197	−	0.496371i
$598$	−0.00689755	+	0.203976i	−0.000282062	+	0.00834118i
$599$	21.5580	−	7.00463i	0.880837	−	0.286201i	0.166532	−	0.986036i	$-0.446743\pi$
$599$	21.5580	−	7.00463i	0.880837	−	0.286201i	0.714305	+	0.699835i	$0.246743\pi$
$600$	−16.2143	+	5.44181i	−0.661946	+	0.222161i
$601$	10.2023	+	22.9147i	0.416159	+	0.934708i	0.993029	+	0.117872i	$0.0376073\pi$
$601$	10.2023	+	22.9147i	0.416159	+	0.934708i	−0.576870	+	0.816836i	$0.695726\pi$
$602$	−3.18292	+	0.923773i	−0.129726	+	0.0376502i
$603$	2.74292	+	0.891228i	0.111700	+	0.0362936i
$604$	46.0194	−	17.0856i	1.87250	−	0.695205i
$605$	−5.26556	+	6.25385i	−0.214075	+	0.254255i
$606$	−13.8169	+	11.6696i	−0.561272	+	0.474047i
$607$	−13.7522	+	2.92312i	−0.558184	+	0.118646i	−0.478361	−	0.878163i	$-0.658769\pi$
$607$	−13.7522	+	2.92312i	−0.558184	+	0.118646i	−0.0798233	+	0.996809i	$0.525436\pi$
$608$	−4.01668	−	7.91009i	−0.162898	−	0.320797i
$609$	−1.71734	+	0.764611i	−0.0695903	+	0.0309836i
$610$	−4.80814	+	7.74996i	−0.194676	+	0.313787i
$611$	4.85938	−	14.8489i	0.196589	−	0.600721i
$612$	−12.6551	−	12.9372i	−0.511552	−	0.522955i
$613$	−21.2881	+	2.23747i	−0.859820	+	0.0903707i	−0.524168	−	0.851615i	$-0.675623\pi$
$613$	−21.2881	+	2.23747i	−0.859820	+	0.0903707i	−0.335652	+	0.941986i	$0.608957\pi$
$614$	31.4413	+	4.31574i	1.26887	+	0.174169i
$615$	3.08676	+	5.34643i	0.124470	+	0.215589i
$616$	4.60004	+	7.50527i	0.185341	+	0.302396i
$617$	5.81794	+	10.0770i	0.234221	+	0.405683i	0.959046	−	0.283250i	$-0.0914126\pi$
$617$	5.81794	+	10.0770i	0.234221	+	0.405683i	−0.724825	+	0.688933i	$0.758079\pi$
$618$	3.45462	−	4.45114i	0.138965	−	0.179051i
$619$	14.9857	+	20.6260i	0.602324	+	0.829028i	0.995919	−	0.0902560i	$-0.0287685\pi$
$619$	14.9857	+	20.6260i	0.602324	+	0.829028i	−0.393594	+	0.919284i	$0.628769\pi$
$620$	1.26758	−	4.53034i	0.0509074	−	0.181943i
$621$	0.220982	+	0.0469713i	0.00886772	+	0.00188489i
$622$	9.39082	+	17.5254i	0.376538	+	0.702705i
$623$	11.8564	+	8.61419i	0.475017	+	0.345120i
$624$	3.61227	+	19.2724i	0.144607	+	0.771513i
$625$	5.25934	−	16.1866i	0.210373	−	0.647463i
$626$	1.50030	+	8.35151i	0.0599641	+	0.333794i
$627$	−5.17592	+	4.81849i	−0.206706	+	0.192432i
$628$	−33.6027	+	12.4757i	−1.34090	+	0.497834i
$629$	48.8478	+	15.8716i	1.94769	+	0.632843i
$630$	1.09078	−	0.316576i	0.0434578	−	0.0126127i
$631$	26.6270	+	2.79861i	1.06000	+	0.111411i	0.618450	−	0.785824i	$-0.287761\pi$
$631$	26.6270	+	2.79861i	1.06000	+	0.111411i	0.441554	+	0.897235i	$0.354427\pi$
$632$	7.91407	−	8.96181i	0.314805	−	0.356482i
$633$	−11.9064	−	10.7206i	−0.473236	−	0.426104i
$634$	−3.53435	+	7.30601i	−0.140367	+	0.290159i
$635$	1.35864	+	12.9266i	0.0539159	+	0.512976i
$636$	8.35993	−	15.9696i	0.331493	−	0.633237i
$637$	8.93164	+	20.1753i	0.353884	+	0.799375i
$638$	6.73780	+	1.53870i	0.266752	+	0.0609178i
$639$	−0.505844	−	0.292049i	−0.0200109	−	0.0115533i
$640$	−5.02637	+	6.74084i	−0.198685	+	0.266455i
$641$	−15.7955	−	7.03261i	−0.623885	−	0.277772i	0.0703471	−	0.997523i	$-0.477589\pi$
$641$	−15.7955	−	7.03261i	−0.623885	−	0.277772i	−0.694232	+	0.719751i	$0.744256\pi$
$642$	−1.17083	−	16.0039i	−0.0462088	−	0.631625i
$643$	−0.505888	−	0.455504i	−0.0199503	−	0.0179633i	0.659095	−	0.752060i	$-0.270939\pi$
$643$	−0.505888	−	0.455504i	−0.0199503	−	0.0179633i	−0.679045	+	0.734096i	$0.737606\pi$
$644$	0.0588959	−	0.0466275i	0.00232082	−	0.00183738i
$645$	−1.48329	+	2.04158i	−0.0584046	+	0.0803871i
$646$	−4.85753	−	16.7369i	−0.191117	−	0.658506i
$647$	23.6856	−	21.3266i	0.931176	−	0.838434i	−0.0559414	−	0.998434i	$-0.517816\pi$
$647$	23.6856	−	21.3266i	0.931176	−	0.838434i	0.987117	+	0.160000i	$0.0511493\pi$
$648$	11.9331	−	0.115109i	0.468776	−	0.00452191i
$649$	19.3022	−	27.5171i	0.757677	−	1.08014i
$650$	−20.3943	−	9.91912i	−0.799931	−	0.389060i
$651$	−1.24772	+	3.84008i	−0.0489020	+	0.150505i
$652$	−0.840573	+	13.2441i	−0.0329194	+	0.518680i
$653$	−3.55910	+	1.58462i	−0.139279	+	0.0620108i	−0.475192	−	0.879882i	$-0.657622\pi$
$653$	−3.55910	+	1.58462i	−0.139279	+	0.0620108i	0.335914	+	0.941893i	$0.390955\pi$
$654$	0.368032	−	11.6091i	0.0143912	−	0.453954i
$655$	3.51786	+	10.8268i	0.137454	+	0.423040i
$656$	−22.1012	−	10.4298i	−0.862908	−	0.407215i
$657$	2.94794	−	6.62119i	0.115010	−	0.258317i
$658$	−5.32486	+	2.17133i	−0.207585	+	0.0846471i
$659$	7.00215	+	12.1281i	0.272765	+	0.472443i	0.969569	−	0.244819i	$-0.0787285\pi$
$659$	7.00215	+	12.1281i	0.272765	+	0.472443i	−0.696804	+	0.717262i	$0.745395\pi$
$660$	6.27074	+	2.36698i	0.244088	+	0.0921347i
$661$	−7.35464	+	12.7386i	−0.286062	+	0.495475i	−0.972866	−	0.231368i	$-0.925680\pi$
$661$	−7.35464	+	12.7386i	−0.286062	+	0.495475i	0.686804	+	0.726843i	$0.259013\pi$
$662$	−9.10910	+	3.71443i	−0.354035	+	0.144365i
$663$	−0.0813301	+	38.5188i	−0.00315860	+	1.49595i
$664$	4.00213	−	41.9681i	0.155313	−	1.62868i
$665$	1.06984	+	0.227402i	0.0414868	+	0.00881829i
$666$	9.38281	−	5.02769i	0.363576	−	0.194819i
$667$	0.00616481	−	0.0586543i	0.000238703	−	0.00227110i
$668$	−18.1034	−	36.5196i	−0.700443	−	1.41299i
$669$	32.6107	−	6.93161i	1.26080	−	0.267992i
$670$	0.892365	−	2.47650i	0.0344751	−	0.0956755i
$671$	−27.2190	+	9.34664i	−1.05078	+	0.360823i
$672$	4.54952	−	5.60240i	0.175502	−	0.216117i
$673$	9.45824	−	8.51624i	0.364588	−	0.328277i	−0.466392	−	0.884578i	$-0.654447\pi$
$673$	9.45824	−	8.51624i	0.364588	−	0.328277i	0.830981	+	0.556301i	$0.187780\pi$
$674$	−2.56765	+	2.67605i	−0.0989023	+	0.103078i
$675$	−14.7557	+	20.3095i	−0.567949	+	0.781715i
$676$	−14.4914	+	21.5870i	−0.557361	+	0.830270i
$677$	−47.4379	+	15.4135i	−1.82319	+	0.592389i	−0.823501	+	0.567315i	$0.807982\pi$
$677$	−47.4379	+	15.4135i	−1.82319	+	0.592389i	−0.999686	+	0.0250737i	$0.992018\pi$
$678$	4.80375	+	2.32386i	0.184487	+	0.0892471i
$679$	−1.34824	−	12.8277i	−0.0517408	−	0.492281i
$680$	−12.1682	+	11.1707i	−0.466628	+	0.428376i
$681$			21.7404i			0.833094i
$682$	12.1396	−	8.54328i	0.464850	−	0.327139i
$683$	19.2950	−	11.1400i	0.738304	−	0.426260i	−0.0831486	−	0.996537i	$-0.526498\pi$
$683$	19.2950	−	11.1400i	0.738304	−	0.426260i	0.821452	+	0.570277i	$0.193164\pi$
$684$	−3.20000	−	1.67516i	−0.122355	−	0.0640515i
$685$	−1.58696	−	0.706562i	−0.0606348	−	0.0269964i
$686$	7.58189	−	15.6729i	0.289478	−	0.598393i
$687$	3.20254	−	15.0668i	0.122184	−	0.574833i
$688$	0.220209	−	9.98726i	0.00839537	−	0.380761i
$689$	22.7473	−	7.33798i	0.866603	−	0.279555i
$690$	0.0136586	−	0.0555419i	0.000519975	−	0.00211445i
$691$	−13.7097	+	12.3442i	−0.521540	+	0.469597i	−0.887352	−	0.461092i	$-0.847458\pi$
$691$	−13.7097	+	12.3442i	−0.521540	+	0.469597i	0.365812	+	0.930689i	$0.380791\pi$
$692$	21.4184	−	25.8614i	0.814206	−	0.983103i
$693$	3.29789	+	1.40315i	0.125277	+	0.0533012i
$694$	15.8633	−	13.3980i	0.602162	−	0.508583i
$695$	−13.1006	+	2.78462i	−0.496935	+	0.105627i
$696$	−0.646608	−	5.62919i	−0.0245096	−	0.213374i
$697$	−38.8396	−	28.2186i	−1.47115	−	1.06886i
$698$	−37.8344	−	1.19942i	−1.43205	−	0.0453988i
$699$	13.9656	+	2.96849i	0.528229	+	0.112279i
$700$	2.07140	+	8.08605i	0.0782916	+	0.305624i
$701$	22.4897	+	30.9545i	0.849426	+	1.16913i	0.983989	+	0.178230i	$0.0570370\pi$
$701$	22.4897	+	30.9545i	0.849426	+	1.16913i	−0.134563	+	0.990905i	$0.542963\pi$
$702$	20.7251	+	19.9699i	0.782219	+	0.753713i
$703$	10.2508			0.386618
$704$	−25.7384	+	6.44459i	−0.970054	+	0.242889i
$705$	−2.18928	+	3.79194i	−0.0824530	+	0.142813i
$706$	−8.81102	+	11.3526i	−0.331607	+	0.427262i
$707$	5.18816	+	7.14088i	0.195121	+	0.268561i
$708$	−26.5376	−	7.42519i	−0.997344	−	0.279056i
$709$	−29.2504	+	32.4859i	−1.09852	+	1.22003i	−0.124828	+	0.992178i	$0.539838\pi$
$709$	−29.2504	+	32.4859i	−1.09852	+	1.22003i	−0.973695	+	0.227855i	$0.926829\pi$
$710$	−0.281056	+	0.453018i	−0.0105478	+	0.0170015i
$711$	0.508822	−	4.84112i	0.0190823	−	0.181556i
$712$	−35.4849	+	26.3080i	−1.32985	+	0.985933i
$713$	−0.0847625	−	0.0941382i	−0.00317438	−	0.00352550i
$714$	10.8312	−	9.14794i	0.405346	−	0.342353i
$715$	3.73225	+	8.06593i	0.139578	+	0.301649i
$716$	−1.83170	−	0.310846i	−0.0684537	−	0.0116169i
$717$	20.5647	−	18.5166i	0.768003	−	0.691513i
$718$	−14.9617	−	14.3556i	−0.558365	−	0.535748i
$719$	3.92353	+	0.412380i	0.146323	+	0.0153792i	0.177407	−	0.984138i	$-0.443229\pi$
$719$	3.92353	+	0.412380i	0.146323	+	0.0153792i	−0.0310837	+	0.999517i	$0.509896\pi$
$720$	−0.0754653	+	3.42262i	−0.00281242	+	0.127554i
$721$	−2.04357	−	1.84003i	−0.0761064	−	0.0685265i
$722$	13.1428	+	19.3505i	0.489126	+	0.720153i
$723$	6.75501	−	4.90780i	0.251221	−	0.182523i
$724$	0.620020	+	14.9905i	0.0230429	+	0.557119i
$725$	5.67551	+	3.27676i	0.210783	+	0.121696i
$726$	10.6030	+	18.3002i	0.393516	+	0.679183i
$727$		−	18.8782i		−	0.700154i	−0.936721	−	0.350077i	$-0.886155\pi$
$727$		−	18.8782i		−	0.700154i	0.936721	−	0.350077i	$-0.113845\pi$
$728$	9.50943	−	1.07198i	0.352443	−	0.0397302i
$729$	22.5557	−	16.3877i	0.835395	−	0.606950i
$730$	−5.95503	−	2.88080i	−0.220406	−	0.106623i
$731$	4.08011	−	19.1954i	0.150908	−	0.709967i
$732$	14.6455	+	18.4990i	0.541314	+	0.683741i
$733$	18.1753	−	25.0162i	0.671320	−	0.923993i	−0.328469	−	0.944515i	$-0.606533\pi$
$733$	18.1753	−	25.0162i	0.671320	−	0.923993i	0.999789	+	0.0205214i	$0.00653263\pi$
$734$	13.2173	+	45.5411i	0.487860	+	1.68095i
$735$	−1.28560	−	6.04829i	−0.0474202	−	0.223095i
$736$	0.0808505	+	0.211493i	0.00298019	+	0.00779572i
$737$	7.12357	−	4.27212i	0.262400	−	0.157366i
$738$	−9.79319	+	1.75929i	−0.360492	+	0.0647603i
$739$	8.52753	+	9.47078i	0.313690	+	0.348388i	0.879286	−	0.476294i	$-0.158020\pi$
$739$	8.52753	+	9.47078i	0.313690	+	0.348388i	−0.565596	+	0.824683i	$0.691354\pi$
$740$	−4.31524	−	8.70503i	−0.158631	−	0.320003i
$741$	2.36018	+	7.31641i	0.0867033	+	0.268775i
$742$	−7.47549	−	4.63785i	−0.274434	−	0.170261i
$743$	−47.4167	−	10.0787i	−1.73955	−	0.369753i	−0.774655	−	0.632384i	$-0.782077\pi$
$743$	−47.4167	−	10.0787i	−1.73955	−	0.369753i	−0.964896	+	0.262631i	$0.915410\pi$
$744$	−9.91449	−	7.05819i	−0.363483	−	0.258766i
$745$	2.29400	−	5.15240i	0.0840455	−	0.188769i
$746$	26.5876	−	10.8417i	0.973441	−	0.396941i
$747$	−8.58223	−	14.8649i	−0.314007	−	0.543876i
$748$	−52.0352	+	3.01878i	−1.90260	+	0.110378i
$749$	−7.83158			−0.286160
$750$	10.6653	+	8.27758i	0.389442	+	0.302254i
$751$	−16.4315	+	1.72702i	−0.599592	+	0.0630197i	−0.399462	−	0.916750i	$-0.630803\pi$
$751$	−16.4315	+	1.72702i	−0.599592	+	0.0630197i	−0.200130	+	0.979769i	$0.564136\pi$
$752$	−1.43137	−	17.2738i	−0.0521965	−	0.629912i
$753$	1.22811	+	3.77973i	0.0447548	+	0.137741i
$754$	4.61913	−	5.92569i	0.168219	−	0.215801i
$755$	−14.7579	−	10.7222i	−0.537095	−	0.390222i
$756$	0.670969	−	10.5718i	0.0244029	−	0.384494i
$757$	−15.0822	−	16.7505i	−0.548172	−	0.608807i	0.403854	−	0.914823i	$-0.367670\pi$
$757$	−15.0822	−	16.7505i	−0.548172	−	0.608807i	−0.952026	+	0.306017i	$0.901004\pi$
$758$	−10.1159	+	28.0737i	−0.367426	+	1.01968i
$759$	0.144232	−	0.108496i	0.00523528	−	0.00393817i
$760$	−1.62074	+	2.87081i	−0.0587905	+	0.104135i
$761$	−7.03328	−	33.0890i	−0.254956	−	1.19947i	−0.900193	−	0.435491i	$-0.856575\pi$
$761$	−7.03328	−	33.0890i	−0.254956	−	1.19947i	0.645237	−	0.763983i	$-0.276759\pi$
$762$	32.6529	+	8.02984i	1.18289	+	0.290891i
$763$	−5.63762	−	0.592538i	−0.204096	−	0.0214513i
$764$	47.0993	+	18.6780i	1.70399	+	0.675745i
$765$	−1.39825	+	6.57824i	−0.0505538	+	0.237837i
$766$	−1.57395	−	21.5143i	−0.0568692	−	0.777342i
$767$	−18.2032	−	31.6831i	−0.657278	−	1.14401i
$768$	11.9981	+	18.1451i	0.432942	+	0.654755i
$769$	−2.11613	−	1.22175i	−0.0763094	−	0.0440573i	0.461360	−	0.887213i	$-0.347362\pi$
$769$	−2.11613	−	1.22175i	−0.0763094	−	0.0440573i	−0.537669	+	0.843156i	$0.680695\pi$
$770$	1.37542	−	2.96798i	0.0495668	−	0.106959i
$771$	−7.74369	+	4.47082i	−0.278882	+	0.161013i
$772$	9.21574	−	17.6045i	0.331682	−	0.633599i
$773$	33.7817	+	15.0406i	1.21504	+	0.540973i	0.911285	−	0.411776i	$-0.135091\pi$
$773$	33.7817	+	15.0406i	1.21504	+	0.540973i	0.303759	+	0.952749i	$0.401758\pi$
$774$	−2.28519	−	3.36454i	−0.0821393	−	0.120936i
$775$	13.3871	−	4.34975i	0.480881	−	0.156248i
$776$	38.1042	+	7.71591i	1.36786	+	0.276985i
$777$	3.39182	+	7.61816i	0.121681	+	0.273300i
$778$	18.5396	+	17.7886i	0.664677	+	0.637754i
$779$	−9.11264	−	2.96088i	−0.326494	−	0.106084i
$780$	5.21955	−	5.08421i	0.186890	−	0.182044i
$781$	−1.59107	+	0.546351i	−0.0569328	+	0.0195500i
$782$	0.0786450	+	0.437782i	0.00281234	+	0.0156551i
$783$	−5.56507	−	6.18064i	−0.198879	−	0.220878i
$784$	17.8250	+	16.7758i	0.636609	+	0.599136i
$785$	10.7760	+	7.82923i	0.384612	+	0.279437i
$786$	29.4360	+	0.933178i	1.04995	+	0.0332854i
$787$	−11.7837	+	13.0872i	−0.420045	+	0.466507i	−0.915612	−	0.402062i	$-0.868293\pi$
$787$	−11.7837	+	13.0872i	−0.420045	+	0.466507i	0.495567	+	0.868569i	$0.334960\pi$
$788$	−16.4196	−	16.7856i	−0.584923	−	0.597962i
$789$	8.71678	−	19.5782i	0.310326	−	0.697003i
$790$	−4.40168	−	0.604190i	−0.156605	−	0.0214961i
$791$	1.30219	−	2.25546i	0.0463006	−	0.0801950i
$792$	−7.01513	+	8.21496i	−0.249272	+	0.291906i
$793$	−3.33598	+	31.1077i	−0.118464	+	1.10467i
$794$	3.11142	+	7.63032i	0.110420	+	0.270790i
$795$	−6.66172	+	0.700174i	−0.236267	+	0.0248326i
$796$	29.4037	−	7.53233i	1.04219	−	0.266976i
$797$	4.64761	−	5.16169i	0.164627	−	0.182836i	−0.655187	−	0.755467i	$-0.727410\pi$
$797$	4.64761	−	5.16169i	0.164627	−	0.182836i	0.819814	+	0.572630i	$0.194077\pi$
$798$	1.49171	−	2.40441i	0.0528060	−	0.0851150i
$799$	3.55918	−	33.8633i	0.125915	−	1.19800i
$800$	−25.1233	−	1.35134i	−0.888242	−	0.0477772i
$801$	−5.55761	+	17.1046i	−0.196369	+	0.604360i
$802$	−31.5664	−	11.3744i	−1.11465	−	0.401644i
$803$	−8.80595	−	18.9260i	−0.310755	−	0.667883i
$804$	−5.24482	−	4.34376i	−0.184971	−	0.153193i
$805$	−0.0265485	−	0.00862614i	−0.000935713	−	0.000304032i
$806$	−2.81981	−	15.8894i	−0.0993236	−	0.559679i
$807$	10.3516	−	14.2477i	0.364393	−	0.501544i
$808$	−25.2222	+	8.46501i	−0.887313	+	0.297798i
$809$	−3.00184	+	14.1226i	−0.105539	+	0.496523i	0.893348	+	0.449365i	$0.148350\pi$
$809$	−3.00184	+	14.1226i	−0.105539	+	0.496523i	−0.998887	+	0.0471577i	$0.984984\pi$
$810$	−2.49163	−	3.66849i	−0.0875468	−	0.128898i
$811$	−37.5622	+	27.2905i	−1.31899	+	0.958300i	−0.319043	+	0.947740i	$0.603361\pi$
$811$	−37.5622	+	27.2905i	−1.31899	+	0.958300i	−0.999944	+	0.0105596i	$0.996639\pi$
$812$	−2.76302	+	0.114281i	−0.0969631	+	0.00401047i
$813$	15.8027	−	9.12370i	0.554225	−	0.319982i
$814$	6.82570	−	29.8889i	0.239241	−	1.04761i
$815$	4.27083	−	2.46576i	0.149600	−	0.0863719i
$816$	16.5163	+	39.4121i	0.578185	+	1.37970i
$817$	−0.409400	−	3.89518i	−0.0143231	−	0.136275i
$818$	0.0951929	+	1.30119i	0.00332834	+	0.0454949i
$819$	2.90094	−	2.60095i	0.101367	−	0.0908845i
$820$	1.32172	+	8.98488i	0.0461563	+	0.313766i
$821$	7.08603	+	15.9155i	0.247304	+	0.555454i	0.993958	−	0.109758i	$-0.0350077\pi$
$821$	7.08603	+	15.9155i	0.247304	+	0.555454i	−0.746654	+	0.665212i	$0.768341\pi$
$822$	−3.11143	+	3.24278i	−0.108523	+	0.113105i
$823$	1.06104	+	4.99181i	0.0369856	+	0.174003i	0.992764	−	0.120086i	$-0.0383170\pi$
$823$	1.06104	+	4.99181i	0.0369856	+	0.174003i	−0.955778	+	0.294089i	$0.904984\pi$
$824$	7.13782	−	4.21334i	0.248658	−	0.146779i
$825$	4.49500	+	19.5450i	0.156496	+	0.680468i
$826$	−4.55919	+	12.6527i	−0.158635	+	0.440244i
$827$	8.57516	−	26.3916i	0.298187	−	0.917727i	−0.683945	−	0.729534i	$-0.739737\pi$
$827$	8.57516	−	26.3916i	0.298187	−	0.917727i	0.982132	−	0.188193i	$-0.0602630\pi$
$828$	0.0767546	+	0.0510566i	0.00266741	+	0.00177434i
$829$	−40.1700	+	17.8848i	−1.39516	+	0.621166i	−0.960208	−	0.279287i	$-0.909902\pi$
$829$	−40.1700	+	17.8848i	−1.39516	+	0.621166i	−0.434954	+	0.900453i	$0.643235\pi$
$830$	−13.8089	+	7.39938i	−0.479314	+	0.256836i
$831$	−4.71562	−	14.5132i	−0.163583	−	0.503456i
$832$	−5.51150	+	28.3130i	−0.191077	+	0.981575i
$833$	28.2638	+	38.9018i	0.979284	+	1.34787i
$834$	−4.71185	+	34.3270i	−0.163158	+	1.18865i
$835$	−7.57346	+	13.1176i	−0.262090	+	0.453954i
$836$	−9.69081	+	3.78223i	−0.335164	+	0.130811i
$837$	−17.8635			−0.617453
$838$	28.2691	+	21.9402i	0.976540	+	0.757913i
$839$	−2.83858	+	6.37556i	−0.0979987	+	0.220109i	−0.955891	−	0.293720i	$-0.905107\pi$
$839$	−2.83858	+	6.37556i	−0.0979987	+	0.220109i	0.857893	+	0.513829i	$0.171773\pi$
$840$	−2.66978	−	0.254594i	−0.0921162	−	0.00878432i
$841$	17.9520	−	19.9377i	0.619034	−	0.687507i
$842$	−2.58227	+	1.38368i	−0.0889908	+	0.0476849i
$843$	−28.4468	+	12.6653i	−0.979761	+	0.436218i
$844$	−10.4678	−	21.1165i	−0.360317	−	0.726860i
$845$	9.66172	+	0.0408004i	0.332373	+	0.00140358i
$846$	−4.55350	−	5.39135i	−0.156553	−	0.185359i
$847$	9.28514	−	4.50934i	0.319041	−	0.154943i
$848$	20.0919	−	17.3043i	0.689958	−	0.594231i
$849$	−5.82937	−	27.4250i	−0.200064	−	0.941225i
$850$	−47.9948	−	11.8027i	−1.64621	−	0.404828i
$851$	−0.260191	−	0.0273472i	−0.00891923	−	0.000937449i
$852$	0.856092	+	1.08134i	0.0293292	+	0.0370462i
$853$	11.8069	−	3.83629i	0.404260	−	0.131352i	−0.0998273	−	0.995005i	$-0.531829\pi$
$853$	11.8069	−	3.83629i	0.404260	−	0.131352i	0.504087	+	0.863653i	$0.331829\pi$
$854$	9.52585	−	6.46993i	0.325968	−	0.221396i
$855$	0.140301	+	1.33487i	0.00479819	+	0.0456518i
$856$	7.07763	−	22.5195i	0.241909	−	0.769702i
$857$		−	1.01320i		−	0.0346102i	−0.999850	−	0.0173051i	$-0.994491\pi$
$857$		−	1.01320i		−	0.0346102i	0.999850	−	0.0173051i	$-0.00550866\pi$
$858$	22.9044	−	2.00994i	0.781943	−	0.0686181i
$859$			9.85923i			0.336393i	0.985754	+	0.168196i	$0.0537942\pi$
$859$			9.85923i			0.336393i	−0.985754	+	0.168196i	$0.946206\pi$
$860$	−3.13545	+	1.98739i	−0.106918	+	0.0677696i
$861$	−0.814765	−	7.75197i	−0.0277671	−	0.264187i
$862$	14.5816	+	21.4690i	0.496653	+	0.731236i
$863$	−4.14517	+	1.34685i	−0.141103	+	0.0458472i	−0.378717	−	0.925512i	$-0.623635\pi$
$863$	−4.14517	+	1.34685i	−0.141103	+	0.0458472i	0.237614	+	0.971360i	$0.423635\pi$
$864$	29.7928	+	11.4835i	1.01357	+	0.390675i
$865$	−12.4099	−	1.30434i	−0.421950	−	0.0443487i
$866$	1.36184	−	5.53784i	0.0462773	−	0.188184i
$867$	12.6481	+	59.5045i	0.429551	+	2.02088i
$868$	−3.78861	+	4.57451i	−0.128594	+	0.155269i
$869$	−9.55277	−	10.2614i	−0.324056	−	0.348094i
$870$	−1.60863	+	1.35864i	−0.0545376	+	0.0460621i
$871$	−0.924930	−	8.98252i	−0.0313400	−	0.304361i
$872$	6.79872	−	15.6754i	0.230234	−	0.530835i
$873$	14.4602	−	6.43809i	0.489403	−	0.217896i
$874$	0.0419277	+	0.0782466i	0.00141823	+	0.00264673i
$875$	4.40888	−	4.89656i	0.149047	−	0.165534i
$876$	−12.2340	+	11.9672i	−0.413347	+	0.404334i
$877$	−14.2566	+	32.0208i	−0.481410	+	1.08126i	0.495693	+	0.868498i	$0.334914\pi$
$877$	−14.2566	+	32.0208i	−0.481410	+	1.08126i	−0.977103	+	0.212767i	$0.931752\pi$
$878$	30.0197	−	38.6792i	1.01312	−	1.30536i
$879$	1.73299			0.0584525
$880$	7.29136	+	6.63726i	0.245792	+	0.223742i
$881$	−5.42592	+	9.39796i	−0.182804	+	0.316625i	−0.942834	−	0.333262i	$-0.891851\pi$
$881$	−5.42592	+	9.39796i	−0.182804	+	0.316625i	0.760030	+	0.649887i	$0.225184\pi$
$882$	9.87332	+	1.35525i	0.332452	+	0.0456335i
$883$	4.58445	+	6.30995i	0.154279	+	0.212347i	0.879159	−	0.476528i	$-0.158105\pi$
$883$	4.58445	+	6.30995i	0.154279	+	0.212347i	−0.724880	+	0.688875i	$0.758105\pi$
$884$	−20.9994	+	52.6285i	−0.706285	+	1.77009i
$885$	3.16444	+	9.73913i	0.106371	+	0.327377i
$886$	−22.0888	−	41.2226i	−0.742087	−	1.38490i
$887$	−3.29584	+	1.46740i	−0.110664	+	0.0492706i	−0.461322	−	0.887233i	$-0.652625\pi$
$887$	−3.29584	+	1.46740i	−0.110664	+	0.0492706i	0.350658	+	0.936504i	$0.385958\pi$
$888$	−24.9712	+	2.86836i	−0.837977	+	0.0962558i
$889$	5.07127	−	15.6078i	0.170085	−	0.523468i
$890$	15.4432	+	5.56470i	0.517657	+	0.186529i
$891$	1.23134	−	13.9392i	0.0412513	−	0.466980i
$892$	48.3524	+	8.20559i	1.61896	+	0.274744i
$893$	−1.41291	−	6.64722i	−0.0472813	−	0.222441i
$894$	−10.5283	−	10.1019i	−0.352120	−	0.337857i
$895$	0.280813	+	0.630716i	0.00938654	+	0.0210825i
$896$	9.25934	−	5.19388i	0.309333	−	0.173515i
$897$	−0.0403883	−	0.192004i	−0.00134852	−	0.00641084i
$898$	−44.7910	+	3.27685i	−1.49470	+	0.109350i
$899$	0.487454	+	4.63781i	0.0162575	+	0.154680i
$900$	−8.65190	+	5.48398i	−0.288397	+	0.182799i
$901$	45.1114	−	26.0451i	1.50288	−	0.867688i
$902$	−14.7010	+	24.5986i	−0.489489	+	0.819045i
$903$	2.75933	−	1.59310i	0.0918248	−	0.0530151i
$904$	5.30871	+	5.78276i	0.176565	+	0.192332i
$905$	4.51057	−	3.27712i	0.149936	−	0.108935i
$906$	−39.0389	+	26.5151i	−1.29698	+	0.880906i
$907$	−0.336595	+	1.58356i	−0.0111765	+	0.0525811i	−0.983382	−	0.181546i	$-0.941890\pi$
$907$	−0.336595	+	1.58356i	−0.0111765	+	0.0525811i	0.972206	+	0.234127i	$0.0752232\pi$
$908$	−11.7895	+	29.7290i	−0.391247	+	0.986590i
$909$	−6.36683	+	8.76319i	−0.211174	+	0.290657i
$910$	−2.28886	−	2.72165i	−0.0758750	−	0.0902219i
$911$	−50.3067	−	16.3456i	−1.66673	−	0.541555i	−0.684467	−	0.729044i	$-0.739965\pi$
$911$	−50.3067	−	16.3456i	−1.66673	−	0.541555i	−0.982267	+	0.187489i	$0.939965\pi$
$912$	5.56572	+	6.46232i	0.184299	+	0.213989i
$913$	−48.5190	−	9.47350i	−1.60574	−	0.313527i
$914$	−20.1585	+	55.9442i	−0.666785	+	1.85047i
$915$	2.70944	−	8.33879i	0.0895712	−	0.275672i
$916$	12.5498	−	18.8664i	0.414656	−	0.623363i
$917$	1.50243	−	14.2947i	0.0496147	−	0.472052i
$918$	53.2991	+	33.0671i	1.75913	+	1.09138i
$919$	37.0604	−	41.1597i	1.22251	−	1.35773i	0.308925	−	0.951086i	$-0.400031\pi$
$919$	37.0604	−	41.1597i	1.22251	−	1.35773i	0.913585	−	0.406648i	$-0.133302\pi$
$920$	0.0487970	−	0.0685441i	0.00160879	−	0.00225983i
$921$	−30.3427	+	3.18915i	−0.999826	+	0.105086i
$922$	10.1537	−	4.14039i	0.334395	−	0.136357i
$923$	−0.195002	+	1.81838i	−0.00641857	+	0.0598527i
$924$	−6.01737	−	5.95048i	−0.197957	−	0.195756i
$925$	14.5357	−	25.1766i	0.477932	−	0.827803i
$926$	1.91801	−	13.9732i	0.0630296	−	0.459187i
$927$	1.37258	−	3.08287i	0.0450815	−	0.101255i
$928$	2.16841	−	8.04830i	0.0711817	−	0.264198i
$929$	22.8472	−	25.3744i	0.749592	−	0.832506i	−0.240832	−	0.970567i	$-0.577420\pi$
$929$	22.8472	−	25.3744i	0.749592	−	0.832506i	0.990424	+	0.138061i	$0.0440869\pi$
$930$	−0.143302	+	4.52029i	−0.00469905	+	0.148226i
$931$	7.76409	+	5.64094i	0.254458	+	0.184874i
$932$	17.4876	+	11.6326i	0.572825	+	0.381039i
$933$	−12.7902	−	14.2049i	−0.418731	−	0.465048i
$934$	15.7746	−	2.83381i	0.516160	−	0.0927252i
$935$	11.6437	+	15.4787i	0.380789	+	0.506209i
$936$	4.85731	+	10.6922i	0.158766	+	0.349484i
$937$	15.1373	+	4.91842i	0.494515	+	0.160678i	0.545649	−	0.838014i	$-0.316283\pi$
$937$	15.1373	+	4.91842i	0.494515	+	0.160678i	−0.0511334	+	0.998692i	$0.516283\pi$
$938$	−2.30108	+	2.39822i	−0.0751330	+	0.0783048i
$939$	−3.31789	−	7.45211i	−0.108275	−	0.243190i
$940$	−5.05004	+	3.99809i	−0.164714	+	0.130403i
$941$	16.2165	−	5.26906i	0.528642	−	0.171766i	−0.0325215	−	0.999471i	$-0.510354\pi$
$941$	16.2165	−	5.26906i	0.528642	−	0.171766i	0.561164	+	0.827705i	$0.310354\pi$
$942$	28.5057	−	19.3610i	0.928765	−	0.630814i
$943$	0.223402	+	0.0994648i	0.00727496	+	0.00323902i
$944$	−32.2623	−	24.5445i	−1.05005	−	0.798856i
$945$	−3.40910	+	1.96824i	−0.110898	+	0.0640269i
$946$	−11.6300	−	1.39996i	−0.378124	−	0.0455168i
$947$	29.6800	+	17.1358i	0.964471	+	0.556838i	0.897546	−	0.440920i	$-0.145348\pi$
$947$	29.6800	+	17.1358i	0.964471	+	0.556838i	0.0669248	+	0.997758i	$0.478681\pi$
$948$	−5.33076	+	10.1831i	−0.173135	+	0.330733i
$949$	−22.6927	−	0.0479143i	−0.736637	−	0.00155536i
$950$	−9.83798	+	0.719733i	−0.319186	+	0.0233512i
$951$	1.62221	−	7.63190i	0.0526038	−	0.247481i
$952$	19.7719	−	6.63580i	0.640811	−	0.215067i
$953$	−44.2260	−	4.64834i	−1.43262	−	0.150575i	−0.643799	−	0.765195i	$-0.722643\pi$
$953$	−44.2260	−	4.64834i	−1.43262	−	0.150575i	−0.788823	+	0.614620i	$0.789309\pi$
$954$	2.57808	−	10.4836i	0.0834683	−	0.339419i
$955$	−3.91467	−	18.4171i	−0.126676	−	0.595962i
$956$	38.1625	−	14.1686i	1.23426	−	0.458245i
$957$	−6.64330	+	0.110369i	−0.214747	+	0.00356773i
$958$	−43.0006	−	15.4946i	−1.38929	−	0.500607i
$959$	1.46762	+	1.62995i	0.0473918	+	0.0526340i
$960$	3.14484	−	7.44682i	0.101499	−	0.240345i
$961$	−16.9762	−	12.3339i	−0.547619	−	0.397869i
$962$	−26.2864	−	20.4905i	−0.847508	−	0.660640i
$963$	−2.96990	−	9.14041i	−0.0957037	−	0.294546i
$964$	11.8986	−	3.04805i	0.383227	−	0.0981711i
$965$	−7.34368	+	0.771852i	−0.236401	+	0.0248468i
$966$	−0.0442777	+	0.0570500i	−0.00142461	+	0.00183555i
$967$	9.00883			0.289704			0.144852	−	0.989453i	$-0.453729\pi$
$967$	9.00883			0.289704			0.144852	+	0.989453i	$0.453729\pi$
$968$	4.57527	+	30.7745i	0.147055	+	0.989128i
$969$	8.37710	+	14.5096i	0.269111	+	0.466114i
$970$	−5.45506	−	13.3777i	−0.175151	−	0.429533i
$971$	14.8922	−	33.4485i	0.477915	−	1.07341i	−0.500307	−	0.865848i	$-0.666779\pi$
$971$	14.8922	−	33.4485i	0.477915	−	1.07341i	0.978221	−	0.207565i	$-0.0665540\pi$
$972$	21.6931	−	5.55710i	0.695806	−	0.178244i
$973$	16.5408	+	3.51586i	0.530274	+	0.112713i
$974$	−14.3908	+	23.1957i	−0.461110	+	0.743237i
$975$	21.3162	+	4.57797i	0.682666	+	0.146612i
$976$	9.99535	+	33.2385i	0.319943	+	1.06394i
$977$	23.9185	+	26.5641i	0.765219	+	0.849862i	0.992280	−	0.124019i	$-0.0395783\pi$
$977$	23.9185	+	26.5641i	0.765219	+	0.849862i	−0.227061	+	0.973881i	$0.572912\pi$
$978$	−2.25579	−	12.5570i	−0.0721322	−	0.401529i
$979$	26.6405	+	44.4219i	0.851435	+	1.41973i
$980$	1.52189	−	8.96791i	0.0486150	−	0.286469i
$981$	−1.44634	−	6.80450i	−0.0461781	−	0.217251i
$982$	−15.8697	+	4.60583i	−0.506422	+	0.146978i
$983$	−14.3783	+	19.7900i	−0.458596	+	0.631203i	−0.974217	−	0.225614i	$-0.927561\pi$
$983$	−14.3783	+	19.7900i	−0.458596	+	0.631203i	0.515621	+	0.856817i	$0.327561\pi$
$984$	23.0270	+	4.66285i	0.734073	+	0.148646i
$985$	−1.81418	+	8.53505i	−0.0578046	+	0.271949i
$986$	7.13064	−	14.7401i	0.227086	−	0.469420i
$987$	4.47253	−	3.24949i	0.142362	−	0.103432i
$988$	−0.740140	+	11.2847i	−0.0235470	+	0.359015i
$989$			0.0999612i			0.00317858i
$990$	3.98559	+	0.479766i	0.126670	+	0.0152480i
$991$	22.6081	+	13.0528i	0.718171	+	0.414636i	0.814079	−	0.580754i	$-0.197242\pi$
$991$	22.6081	+	13.0528i	0.718171	+	0.414636i	−0.0959084	+	0.995390i	$0.530576\pi$
$992$	−9.73004	−	15.0282i	−0.308929	−	0.477146i
$993$	7.65105	−	5.55881i	0.242799	−	0.176403i
$994$	0.556826	−	0.378195i	0.0176615	−	0.0119956i
$995$	−8.38228	−	7.54743i	−0.265736	−	0.239270i
$996$	5.89860	+	40.0980i	0.186904	+	1.27055i
$997$	−9.94777	−	1.04555i	−0.315049	−	0.0331130i	−0.0543156	−	0.998524i	$-0.517298\pi$
$997$	−9.94777	−	1.04555i	−0.315049	−	0.0331130i	−0.260733	+	0.965411i	$0.583964\pi$
$998$	11.6867	−	12.1800i	0.369936	−	0.385553i
$999$	−27.4174	+	24.6867i	−0.867447	+	0.781053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bm.a.35.4	✓	640
4.3	odd	2	inner	572.2.bm.a.35.41	yes	640
11.6	odd	10	inner	572.2.bm.a.347.13	yes	640
13.3	even	3	inner	572.2.bm.a.211.57	yes	640
44.39	even	10	inner	572.2.bm.a.347.57	yes	640
52.3	odd	6	inner	572.2.bm.a.211.13	yes	640
143.94	odd	30	inner	572.2.bm.a.523.41	yes	640
572.523	even	30	inner	572.2.bm.a.523.4	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bm.a.35.4	✓	640	1.1	even	1	trivial
572.2.bm.a.35.41	yes	640	4.3	odd	2	inner
572.2.bm.a.211.13	yes	640	52.3	odd	6	inner
572.2.bm.a.211.57	yes	640	13.3	even	3	inner
572.2.bm.a.347.13	yes	640	11.6	odd	10	inner
572.2.bm.a.347.57	yes	640	44.39	even	10	inner
572.2.bm.a.523.4	yes	640	572.523	even	30	inner
572.2.bm.a.523.41	yes	640	143.94	odd	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40108 - 0.192317i) q^{2} +(1.35212 - 0.142114i) q^{3} +(1.92603 + 0.538900i) q^{4} +(-0.229666 - 0.706840i) q^{5} +(-1.92176 - 0.0609233i) q^{6} +(-0.0980876 + 0.933242i) q^{7} +(-2.59487 - 1.12545i) q^{8} +(-1.12640 + 0.239425i) q^{9} +O(q^{10})\)	\(q+(-1.40108 - 0.192317i) q^{2} +(1.35212 - 0.142114i) q^{3} +(1.92603 + 0.538900i) q^{4} +(-0.229666 - 0.706840i) q^{5} +(-1.92176 - 0.0609233i) q^{6} +(-0.0980876 + 0.933242i) q^{7} +(-2.59487 - 1.12545i) q^{8} +(-1.12640 + 0.239425i) q^{9} +(0.185843 + 1.03451i) q^{10} +(-1.61037 + 2.89943i) q^{11} +(2.68081 + 0.454944i) q^{12} +(2.11313 + 2.92142i) q^{13} +(0.316906 - 1.28868i) q^{14} +(-0.410989 - 0.923096i) q^{15} +(3.41917 + 2.07588i) q^{16} +(5.83948 + 5.25789i) q^{17} +(1.62422 - 0.118826i) q^{18} +(1.43269 + 0.637874i) q^{19} +(-0.0614274 - 1.48516i) q^{20} +1.27580i q^{21} +(2.81386 - 3.75262i) q^{22} +(-0.0346633 - 0.0200129i) q^{23} +(-3.66853 - 1.15298i) q^{24} +(3.59821 - 2.61425i) q^{25} +(-2.39881 - 4.49952i) q^{26} +(-5.36810 + 1.74420i) q^{27} +(-0.691844 + 1.74459i) q^{28} +(0.599320 + 1.34610i) q^{29} +(0.398300 + 1.37237i) q^{30} +(3.00995 + 0.977992i) q^{31} +(-4.39130 - 3.56602i) q^{32} +(-1.76537 + 4.14924i) q^{33} +(-7.17038 - 8.48973i) q^{34} +(0.682180 - 0.145002i) q^{35} +(-2.29851 - 0.145881i) q^{36} +(5.97130 - 2.65859i) q^{37} +(-1.88463 - 1.16924i) q^{38} +(3.27238 + 3.64981i) q^{39} +(-0.199557 + 2.09264i) q^{40} +(-6.07618 + 0.638633i) q^{41} +(0.245357 - 1.78749i) q^{42} +(-1.24871 - 2.16283i) q^{43} +(-4.66413 + 4.71656i) q^{44} +(0.427932 + 0.741200i) q^{45} +(0.0447171 + 0.0347059i) q^{46} +(-2.54702 - 3.50568i) q^{47} +(4.91815 + 2.32093i) q^{48} +(5.98571 + 1.27230i) q^{49} +(-5.54413 + 2.97077i) q^{50} +(8.64291 + 6.27944i) q^{51} +(2.49559 + 6.76550i) q^{52} +(2.04851 - 6.30466i) q^{53} +(7.85655 - 1.41138i) q^{54} +(2.41928 + 0.472373i) q^{55} +(1.30484 - 2.31125i) q^{56} +(2.02782 + 0.658879i) q^{57} +(-0.580817 - 2.00124i) q^{58} +(-10.0789 - 1.05933i) q^{59} +(-0.294119 - 1.99939i) q^{60} +(6.44842 + 5.80618i) q^{61} +(-4.02909 - 1.94911i) q^{62} +(-0.112955 - 1.07469i) q^{63} +(5.46673 + 5.84079i) q^{64} +(1.57966 - 2.16459i) q^{65} +(3.27139 - 5.47389i) q^{66} +(-2.16894 - 1.25224i) q^{67} +(8.41353 + 13.2737i) q^{68} +(-0.0497132 - 0.0221337i) q^{69} +(-0.983673 + 0.0719641i) q^{70} +(0.376938 + 0.339396i) q^{71} +(3.19234 + 0.646433i) q^{72} +(-3.69943 + 5.09183i) q^{73} +(-8.87753 + 2.57651i) q^{74} +(4.49370 - 4.04614i) q^{75} +(2.41565 + 2.00064i) q^{76} +(-2.54791 - 1.78726i) q^{77} +(-3.88293 - 5.74300i) q^{78} +(-1.30624 + 4.02020i) q^{79} +(0.682043 - 2.89357i) q^{80} +(-3.85442 + 1.71610i) q^{81} +(8.63601 + 0.273778i) q^{82} +(4.60598 + 14.1758i) q^{83} +(-0.687527 + 2.45722i) q^{84} +(2.37536 - 5.33514i) q^{85} +(1.33359 + 3.27044i) q^{86} +(1.00165 + 1.73491i) q^{87} +(7.44187 - 5.71127i) q^{88} +(7.80883 - 13.5253i) q^{89} +(-0.457020 - 1.12078i) q^{90} +(-2.93366 + 1.68550i) q^{91} +(-0.0559776 - 0.0572255i) q^{92} +(4.20881 + 0.894610i) q^{93} +(2.89438 + 5.40156i) q^{94} +(0.121835 - 1.15918i) q^{95} +(-6.44435 - 4.19764i) q^{96} +(-13.4449 + 2.85781i) q^{97} +(-8.14176 - 2.93375i) q^{98} +(1.11973 - 3.65149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9}+O(q^{10}) \) 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9	\( 640 q - 5 q^{2} - 3 q^{4} - 24 q^{5} - 5 q^{6} - 20 q^{8} - 78 q^{9} - 36 q^{12} - 20 q^{13} - 28 q^{14} - 11 q^{16} - 10 q^{17} - 20 q^{18} - 29 q^{20} + 25 q^{22} - 65 q^{24} - 152 q^{25} + 40 q^{26} - 5 q^{28} - 10 q^{29} + 5 q^{30} + 4 q^{33} - 132 q^{34} - 24 q^{36} - 6 q^{37} - 10 q^{38} - 20 q^{40} - 50 q^{41} - 49 q^{42} - 4 q^{44} + 28 q^{45} - 25 q^{46} + 35 q^{48} + 62 q^{49} + 20 q^{50} + 15 q^{52} - 8 q^{53} - 2 q^{56} - 40 q^{57} + 41 q^{58} - 68 q^{60} - 10 q^{61} - 5 q^{62} - 36 q^{64} - 66 q^{66} + 60 q^{68} - 58 q^{69} + 118 q^{70} - 5 q^{72} - 40 q^{73} + 45 q^{74} - 76 q^{77} + 12 q^{78} - 41 q^{80} + 30 q^{81} - 37 q^{82} + 50 q^{84} - 10 q^{85} - 120 q^{86} + 89 q^{88} - 40 q^{89} - 250 q^{90} - 46 q^{92} - 2 q^{93} - 5 q^{94} + 110 q^{96} - 10 q^{97}+O(q^{100}) \) 640 * q - 5 * q^2 - 3 * q^4 - 24 * q^5 - 5 * q^6 - 20 * q^8 - 78 * q^9 - 36 * q^12 - 20 * q^13 - 28 * q^14 - 11 * q^16 - 10 * q^17 - 20 * q^18 - 29 * q^20 + 25 * q^22 - 65 * q^24 - 152 * q^25 + 40 * q^26 - 5 * q^28 - 10 * q^29 + 5 * q^30 + 4 * q^33 - 132 * q^34 - 24 * q^36 - 6 * q^37 - 10 * q^38 - 20 * q^40 - 50 * q^41 - 49 * q^42 - 4 * q^44 + 28 * q^45 - 25 * q^46 + 35 * q^48 + 62 * q^49 + 20 * q^50 + 15 * q^52 - 8 * q^53 - 2 * q^56 - 40 * q^57 + 41 * q^58 - 68 * q^60 - 10 * q^61 - 5 * q^62 - 36 * q^64 - 66 * q^66 + 60 * q^68 - 58 * q^69 + 118 * q^70 - 5 * q^72 - 40 * q^73 + 45 * q^74 - 76 * q^77 + 12 * q^78 - 41 * q^80 + 30 * q^81 - 37 * q^82 + 50 * q^84 - 10 * q^85 - 120 * q^86 + 89 * q^88 - 40 * q^89 - 250 * q^90 - 46 * q^92 - 2 * q^93 - 5 * q^94 + 110 * q^96 - 10 * q^97

Introduction

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