LMFDB - Embedded newform 637.2.bl.a.625.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.1
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27310 + 1.54978i) q^{2} +(2.32870 - 2.16072i) q^{3} +(2.03451 - 5.18386i) q^{4} +(1.52353 + 0.469945i) q^{5} +(-1.94475 + 8.52050i) q^{6} +(-2.61577 + 0.397162i) q^{7} +(2.18478 + 9.57215i) q^{8} +(0.529951 - 7.07171i) q^{9} +O(q^{10})$	\(q+(-2.27310 + 1.54978i) q^{2} +(2.32870 - 2.16072i) q^{3} +(2.03451 - 5.18386i) q^{4} +(1.52353 + 0.469945i) q^{5} +(-1.94475 + 8.52050i) q^{6} +(-2.61577 + 0.397162i) q^{7} +(2.18478 + 9.57215i) q^{8} +(0.529951 - 7.07171i) q^{9} +(-4.19144 + 1.29289i) q^{10} +(-0.368753 - 4.92067i) q^{11} +(-6.46308 - 16.4677i) q^{12} +(0.900969 + 0.433884i) q^{13} +(5.33041 - 4.95665i) q^{14} +(4.56325 - 2.19755i) q^{15} +(-11.6365 - 10.7971i) q^{16} +(0.173824 + 0.0261997i) q^{17} +(9.75493 + 16.8960i) q^{18} +(-0.907059 + 1.57107i) q^{19} +(5.53576 - 6.94163i) q^{20} +(-5.23319 + 6.57681i) q^{21} +(8.46415 + 10.6137i) q^{22} +(3.03055 - 0.456783i) q^{23} +(25.7704 + 17.5700i) q^{24} +(-2.03091 - 1.38465i) q^{25} +(-2.72042 + 0.410037i) q^{26} +(-8.10390 - 10.1620i) q^{27} +(-3.26299 + 14.3678i) q^{28} +(2.94080 - 3.68765i) q^{29} +(-6.96704 + 12.0673i) q^{30} +(1.41446 + 2.44991i) q^{31} +(23.7666 + 3.58225i) q^{32} +(-11.4909 - 10.6620i) q^{33} +(-0.435723 + 0.209833i) q^{34} +(-4.17184 - 0.624183i) q^{35} +(-35.5805 - 17.1347i) q^{36} +(-0.572623 - 1.45902i) q^{37} +(-0.372971 - 4.97695i) q^{38} +(3.03558 - 0.936354i) q^{39} +(-1.16982 + 15.6101i) q^{40} +(-2.68182 - 11.7498i) q^{41} +(1.70300 - 23.0601i) q^{42} +(-2.07203 + 9.07814i) q^{43} +(-26.2583 - 8.09961i) q^{44} +(4.13071 - 10.5249i) q^{45} +(-6.18086 + 5.73500i) q^{46} +(1.58712 - 1.08208i) q^{47} -50.4272 q^{48} +(6.68452 - 2.07777i) q^{49} +6.76238 q^{50} +(0.461393 - 0.314572i) q^{51} +(4.08223 - 3.78775i) q^{52} +(-1.61718 + 4.12052i) q^{53} +(34.1698 + 10.5400i) q^{54} +(1.75064 - 7.67006i) q^{55} +(-9.51658 - 24.1708i) q^{56} +(1.28237 + 5.61845i) q^{57} +(-0.969718 + 12.9400i) q^{58} +(-8.14491 + 2.51237i) q^{59} +(-2.10777 - 28.1262i) q^{60} +(-0.0565384 - 0.144057i) q^{61} +(-7.01202 - 3.37681i) q^{62} +(1.42238 + 18.7084i) q^{63} +(-30.9718 + 14.9152i) q^{64} +(1.16875 + 1.08444i) q^{65} +(42.6437 + 6.42750i) q^{66} +(-1.89705 - 3.28579i) q^{67} +(0.489462 - 0.847773i) q^{68} +(6.07027 - 7.61188i) q^{69} +(10.4504 - 5.04658i) q^{70} +(5.83006 + 7.31067i) q^{71} +(68.8492 - 10.3774i) q^{72} +(0.801637 + 0.546547i) q^{73} +(3.56279 + 2.42907i) q^{74} +(-7.72123 + 1.16379i) q^{75} +(6.29879 + 7.89843i) q^{76} +(2.91888 + 12.7249i) q^{77} +(-5.44906 + 6.83291i) q^{78} +(1.33260 - 2.30814i) q^{79} +(-12.6544 - 21.9181i) q^{80} +(-19.7917 - 2.98312i) q^{81} +(24.3057 + 22.5524i) q^{82} +(11.0922 - 5.34173i) q^{83} +(23.4463 + 40.5087i) q^{84} +(0.252512 + 0.121603i) q^{85} +(-9.35916 - 23.8467i) q^{86} +(-1.11972 - 14.9417i) q^{87} +(46.2958 - 14.2803i) q^{88} +(0.386015 - 5.15102i) q^{89} +(6.92167 + 30.3258i) q^{90} +(-2.52905 - 0.777110i) q^{91} +(3.79781 - 16.6393i) q^{92} +(8.58741 + 2.64887i) q^{93} +(-1.93070 + 4.91935i) q^{94} +(-2.12025 + 1.96730i) q^{95} +(63.0856 - 43.0110i) q^{96} -5.09347 q^{97} +(-11.9745 + 15.0825i) q^{98} -34.9930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−2.27310	+	1.54978i	−1.60733	+	1.09586i	−0.672882	+	0.739749i	$0.734944\pi$
$2$	−2.27310	+	1.54978i	−1.60733	+	1.09586i	−0.934445	+	0.356108i	$0.884104\pi$
$3$	2.32870	−	2.16072i	1.34447	−	1.24749i	0.400987	−	0.916084i	$-0.368667\pi$
$3$	2.32870	−	2.16072i	1.34447	−	1.24749i	0.943488	−	0.331407i	$-0.107523\pi$
$4$	2.03451	−	5.18386i	1.01726	−	2.59193i
$5$	1.52353	+	0.469945i	0.681341	+	0.210166i	0.616058	−	0.787701i	$-0.288729\pi$
$5$	1.52353	+	0.469945i	0.681341	+	0.210166i	0.0652833	+	0.997867i	$0.479205\pi$
$6$	−1.94475	+	8.52050i	−0.793940	+	3.47848i
$7$	−2.61577	+	0.397162i	−0.988669	+	0.150113i
$7$	−2.61577	+	0.397162i	−0.988669	+	0.150113i
$8$	2.18478	+	9.57215i	0.772437	+	3.38427i
$9$	0.529951	−	7.07171i	0.176650	−	2.35724i
$10$	−4.19144	+	1.29289i	−1.32545	+	0.408847i
$11$	−0.368753	−	4.92067i	−0.111183	−	1.48364i	−0.722015	−	0.691878i	$-0.756784\pi$
$11$	−0.368753	−	4.92067i	−0.111183	−	1.48364i	0.610831	−	0.791761i	$-0.290835\pi$
$12$	−6.46308	−	16.4677i	−1.86573	−	4.75380i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$13$	0.900969	+	0.433884i	0.249884	+	0.120338i
$14$	5.33041	−	4.95665i	1.42461	−	1.32472i
$15$	4.56325	−	2.19755i	1.17823	−	0.567404i
$16$	−11.6365	−	10.7971i	−2.90912	−	2.69927i
$17$	0.173824	+	0.0261997i	0.0421584	+	0.00635436i	0.170088	−	0.985429i	$-0.445595\pi$
$17$	0.173824	+	0.0261997i	0.0421584	+	0.00635436i	−0.127929	+	0.991783i	$0.540833\pi$
$18$	9.75493	+	16.8960i	2.29926	+	3.98243i
$19$	−0.907059	+	1.57107i	−0.208094	+	0.360429i	−0.951114	−	0.308840i	$-0.900059\pi$
$19$	−0.907059	+	1.57107i	−0.208094	+	0.360429i	0.743020	+	0.669269i	$0.233393\pi$
$20$	5.53576	−	6.94163i	1.23783	−	1.55219i
$21$	−5.23319	+	6.57681i	−1.14198	+	1.43518i
$22$	8.46415	+	10.6137i	1.80456	+	2.26285i
$23$	3.03055	−	0.456783i	0.631914	−	0.0952458i	0.174728	−	0.984617i	$-0.444095\pi$
$23$	3.03055	−	0.456783i	0.631914	−	0.0952458i	0.457186	+	0.889371i	$0.348857\pi$
$24$	25.7704	+	17.5700i	5.26036	+	3.58645i
$25$	−2.03091	−	1.38465i	−0.406183	−	0.276931i
$26$	−2.72042	+	0.410037i	−0.533518	+	0.0804149i
$27$	−8.10390	−	10.1620i	−1.55960	−	1.95567i
$28$	−3.26299	+	14.3678i	−0.616648	+	2.71526i
$29$	2.94080	−	3.68765i	0.546093	−	0.684779i	−0.429826	−	0.902912i	$-0.641425\pi$
$29$	2.94080	−	3.68765i	0.546093	−	0.684779i	0.975919	+	0.218133i	$0.0699966\pi$
$30$	−6.96704	+	12.0673i	−1.27200	+	2.20317i
$31$	1.41446	+	2.44991i	0.254044	+	0.440017i	0.964635	−	0.263588i	$-0.0849058\pi$
$31$	1.41446	+	2.44991i	0.254044	+	0.440017i	−0.710591	+	0.703605i	$0.751573\pi$
$32$	23.7666	+	3.58225i	4.20139	+	0.633257i
$33$	−11.4909	−	10.6620i	−2.00031	−	1.85601i
$34$	−0.435723	+	0.209833i	−0.0747258	+	0.0359861i
$35$	−4.17184	−	0.624183i	−0.705169	−	0.105506i
$36$	−35.5805	−	17.1347i	−5.93009	−	2.85578i
$37$	−0.572623	−	1.45902i	−0.0941387	−	0.239861i	0.876046	−	0.482227i	$-0.160172\pi$
$37$	−0.572623	−	1.45902i	−0.0941387	−	0.239861i	−0.970185	+	0.242366i	$0.922077\pi$
$38$	−0.372971	−	4.97695i	−0.0605039	−	0.807368i
$39$	3.03558	−	0.936354i	0.486083	−	0.149937i
$40$	−1.16982	+	15.6101i	−0.184964	+	2.46818i
$41$	−2.68182	−	11.7498i	−0.418830	−	1.83502i	−0.539057	−	0.842269i	$-0.681219\pi$
$41$	−2.68182	−	11.7498i	−0.418830	−	1.83502i	0.120227	−	0.992746i	$-0.461638\pi$
$42$	1.70300	−	23.0601i	0.262778	−	3.55824i
$43$	−2.07203	+	9.07814i	−0.315981	+	1.38440i	0.528552	+	0.848901i	$0.322735\pi$
$43$	−2.07203	+	9.07814i	−0.315981	+	1.38440i	−0.844533	+	0.535503i	$0.820122\pi$
$44$	−26.2583	−	8.09961i	−3.95859	−	1.22106i
$45$	4.13071	−	10.5249i	0.615770	−	1.56896i
$46$	−6.18086	+	5.73500i	−0.911317	+	0.845579i
$47$	1.58712	−	1.08208i	0.231505	−	0.157837i	−0.442012	−	0.897009i	$-0.645735\pi$
$47$	1.58712	−	1.08208i	0.231505	−	0.157837i	0.673517	+	0.739172i	$0.264783\pi$
$48$	−50.4272			−7.27855
$49$	6.68452	−	2.07777i	0.954932	−	0.296824i
$50$	6.76238			0.956345
$51$	0.461393	−	0.314572i	0.0646079	−	0.0440489i
$52$	4.08223	−	3.78775i	0.566103	−	0.525267i
$53$	−1.61718	+	4.12052i	−0.222137	+	0.565997i	−0.997882	−	0.0650503i	$-0.979279\pi$
$53$	−1.61718	+	4.12052i	−0.222137	+	0.565997i	0.775745	+	0.631047i	$0.217374\pi$
$54$	34.1698	+	10.5400i	4.64992	+	1.43431i
$55$	1.75064	−	7.67006i	0.236056	−	1.03423i
$56$	−9.51658	−	24.1708i	−1.27171	−	3.22997i
$57$	1.28237	+	5.61845i	0.169855	+	0.744182i
$58$	−0.969718	+	12.9400i	−0.127330	+	1.69910i
$59$	−8.14491	+	2.51237i	−1.06038	+	0.327083i	−0.775413	−	0.631455i	$-0.782458\pi$
$59$	−8.14491	+	2.51237i	−1.06038	+	0.327083i	−0.284965	+	0.958538i	$0.591982\pi$
$60$	−2.10777	−	28.1262i	−0.272111	−	3.63107i
$61$	−0.0565384	−	0.144057i	−0.00723900	−	0.0184447i	0.927209	−	0.374545i	$-0.122201\pi$
$61$	−0.0565384	−	0.144057i	−0.00723900	−	0.0184447i	−0.934448	+	0.356101i	$0.884106\pi$
$62$	−7.01202	−	3.37681i	−0.890528	−	0.428856i
$63$	1.42238	+	18.7084i	0.179203	+	2.35704i
$64$	−30.9718	+	14.9152i	−3.87147	+	1.86440i
$65$	1.16875	+	1.08444i	0.144965	+	0.134508i
$66$	42.6437	+	6.42750i	5.24908	+	0.791171i
$67$	−1.89705	−	3.28579i	−0.231762	−	0.401423i	0.726565	−	0.687098i	$-0.241116\pi$
$67$	−1.89705	−	3.28579i	−0.231762	−	0.401423i	−0.958327	+	0.285675i	$0.907782\pi$
$68$	0.489462	−	0.847773i	0.0593560	−	0.102808i
$69$	6.07027	−	7.61188i	0.730775	−	0.916363i
$70$	10.4504	−	5.04658i	1.24906	−	0.603182i
$71$	5.83006	+	7.31067i	0.691901	+	0.867617i	0.996390	−	0.0848994i	$-0.0270569\pi$
$71$	5.83006	+	7.31067i	0.691901	+	0.867617i	−0.304488	+	0.952516i	$0.598485\pi$
$72$	68.8492	−	10.3774i	8.11396	−	1.22298i
$73$	0.801637	+	0.546547i	0.0938245	+	0.0639684i	0.609324	−	0.792922i	$-0.291441\pi$
$73$	0.801637	+	0.546547i	0.0938245	+	0.0639684i	−0.515499	+	0.856890i	$0.672393\pi$
$74$	3.56279	+	2.42907i	0.414165	+	0.282373i
$75$	−7.72123	+	1.16379i	−0.891571	+	0.134383i
$76$	6.29879	+	7.89843i	0.722521	+	0.906012i
$77$	2.91888	+	12.7249i	0.332637	+	1.45014i
$78$	−5.44906	+	6.83291i	−0.616985	+	0.773674i
$79$	1.33260	−	2.30814i	0.149929	−	0.259686i	−0.781272	−	0.624191i	$-0.785429\pi$
$79$	1.33260	−	2.30814i	0.149929	−	0.259686i	0.931201	+	0.364506i	$0.118762\pi$
$80$	−12.6544	−	21.9181i	−1.41481	−	2.45052i
$81$	−19.7917	−	2.98312i	−2.19908	−	0.331458i
$82$	24.3057	+	22.5524i	2.68411	+	2.49049i
$83$	11.0922	−	5.34173i	1.21753	−	0.586331i	0.288906	−	0.957357i	$-0.406708\pi$
$83$	11.0922	−	5.34173i	1.21753	−	0.586331i	0.928622	+	0.371027i	$0.120994\pi$
$84$	23.4463	+	40.5087i	2.55820	+	4.41986i
$85$	0.252512	+	0.121603i	0.0273888	+	0.0131897i
$86$	−9.35916	−	23.8467i	−1.00922	−	2.57146i
$87$	−1.11972	−	14.9417i	−0.120047	−	1.60191i
$88$	46.2958	−	14.2803i	4.93514	−	1.52229i
$89$	0.386015	−	5.15102i	0.0409176	−	0.546007i	−0.938647	−	0.344879i	$-0.887920\pi$
$89$	0.386015	−	5.15102i	0.0409176	−	0.546007i	0.979565	−	0.201128i	$-0.0644608\pi$
$90$	6.92167	+	30.3258i	0.729608	+	3.19662i
$91$	−2.52905	−	0.777110i	−0.265117	−	0.0814633i
$92$	3.79781	−	16.6393i	0.395949	−	1.73477i
$93$	8.58741	+	2.64887i	0.890473	+	0.274675i
$94$	−1.93070	+	4.91935i	−0.199137	+	0.507393i
$95$	−2.12025	+	1.96730i	−0.217533	+	0.201841i
$96$	63.0856	−	43.0110i	6.43864	−	4.38979i
$97$	−5.09347			−0.517164			−0.258582	−	0.965989i	$-0.583255\pi$
$97$	−5.09347			−0.517164			−0.258582	+	0.965989i	$0.583255\pi$
$98$	−11.9745	+	15.0825i	−1.20961	+	1.52356i
$99$	−34.9930			−3.51692
$100$	−11.3098	+	7.71087i	−1.13098	+	0.771087i
$101$	1.71767	−	1.59377i	0.170915	−	0.158586i	−0.590078	−	0.807346i	$-0.700903\pi$
$101$	1.71767	−	1.59377i	0.170915	−	0.158586i	0.760992	+	0.648761i	$0.224712\pi$
$102$	−0.561277	+	1.43011i	−0.0555747	+	0.141602i
$103$	2.96975	+	0.916046i	0.292618	+	0.0902606i	0.437589	−	0.899175i	$-0.355833\pi$
$103$	2.96975	+	0.916046i	0.292618	+	0.0902606i	−0.144971	+	0.989436i	$0.546309\pi$
$104$	−2.18478	+	9.57215i	−0.214235	+	0.938626i
$105$	−11.0636	+	7.56063i	−1.07970	+	0.737842i
$106$	−2.70985	−	11.8726i	−0.263204	−	1.15317i
$107$	−0.986625	+	13.1656i	−0.0953806	+	1.27277i	0.720055	+	0.693917i	$0.244117\pi$
$107$	−0.986625	+	13.1656i	−0.0953806	+	1.27277i	−0.815435	+	0.578848i	$0.803502\pi$
$108$	−69.1657	+	21.3348i	−6.65547	+	2.05294i
$109$	0.453817	+	6.05577i	0.0434678	+	0.580037i	0.975833	+	0.218519i	$0.0701225\pi$
$109$	0.453817	+	6.05577i	0.0434678	+	0.580037i	−0.932365	+	0.361519i	$0.882258\pi$
$110$	7.90749	+	20.1479i	0.753949	+	1.92103i
$111$	−4.48600	−	2.16034i	−0.425792	−	0.205051i
$112$	34.7265	+	23.6211i	3.28135	+	2.23198i
$113$	17.5072	−	8.43102i	1.64694	−	0.793124i	0.647418	−	0.762135i	$-0.275849\pi$
$113$	17.5072	−	8.43102i	1.64694	−	0.793124i	0.999520	−	0.0309889i	$-0.00986567\pi$
$114$	−11.6223	−	10.7839i	−1.08853	−	1.01001i
$115$	4.83179	+	0.728275i	0.450567	+	0.0679120i
$116$	−13.1331	−	22.7473i	−1.21938	−	2.11203i
$117$	3.54577	−	6.14145i	0.327806	−	0.567777i
$118$	14.6206	−	18.3337i	1.34594	−	1.68775i
$119$	−0.465088		0.000503745i	−0.0426346		4.61783e-5i
$120$	31.0049	+	38.8790i	2.83035	+	3.54915i
$121$	−13.1999	+	1.98956i	−1.19999	+	0.180869i
$122$	0.351774	+	0.239836i	0.0318482	+	0.0217137i
$123$	−31.6332	−	21.5672i	−2.85227	−	1.94465i
$124$	15.5777	−	2.34796i	1.39892	−	0.210853i
$125$	−7.41377	−	9.29657i	−0.663107	−	0.831510i
$126$	−32.2271	−	40.3219i	−2.87102	−	3.59216i
$127$	8.11865	−	10.1805i	0.720414	−	0.903370i	−0.277948	−	0.960596i	$-0.589654\pi$
$127$	8.11865	−	10.1805i	0.720414	−	0.903370i	0.998361	+	0.0572260i	$0.0182256\pi$
$128$	23.2517	−	40.2731i	2.05518	−	3.55967i
$129$	14.7902	+	25.6173i	1.30220	+	2.25548i
$130$	−4.33732	−	0.653746i	−0.380408	−	0.0573373i
$131$	7.75152	+	7.19236i	0.677253	+	0.628399i	0.941879	−	0.335952i	$-0.109058\pi$
$131$	7.75152	+	7.19236i	0.677253	+	0.628399i	−0.264626	+	0.964351i	$0.585249\pi$
$132$	−78.6486	+	37.8752i	−6.84548	+	3.29661i
$133$	1.74869	−	4.46982i	0.151631	−	0.387582i
$134$	9.40443	+	4.52893i	0.812419	+	0.391240i
$135$	−7.57093	−	19.2904i	−0.651602	−	1.66025i
$136$	0.128979	+	1.72111i	0.0110599	+	0.147584i
$137$	3.97814	−	1.22709i	0.339875	−	0.104838i	−0.120119	−	0.992759i	$-0.538328\pi$
$137$	3.97814	−	1.22709i	0.339875	−	0.104838i	0.459994	+	0.887922i	$0.347851\pi$
$138$	−2.00165	+	26.7102i	−0.170392	+	2.27372i
$139$	3.99923	+	17.5218i	0.339210	+	1.48618i	0.800719	+	0.599041i	$0.204451\pi$
$139$	3.99923	+	17.5218i	0.339210	+	1.48618i	−0.461509	+	0.887136i	$0.652692\pi$
$140$	−11.7233	+	20.3563i	−0.990803	+	1.72042i
$141$	1.35785	−	5.94915i	0.114352	−	0.501009i
$142$	−24.5822	−	7.58262i	−2.06290	−	0.636319i
$143$	1.80276	−	4.59337i	0.150755	−	0.384117i
$144$	−82.5204	+	76.5678i	−6.87670	+	6.38065i
$145$	6.21338	−	4.23621i	0.515993	−	0.351798i
$146$	−2.66923			−0.220907
$147$	11.0768	−	19.2819i	0.913596	−	1.59034i
$148$	−8.72836			−0.717467
$149$	18.5026	−	12.6149i	1.51579	−	1.03345i	0.533563	−	0.845760i	$-0.320853\pi$
$149$	18.5026	−	12.6149i	1.51579	−	1.03345i	0.982228	−	0.187689i	$-0.0600998\pi$
$150$	15.7475	−	14.6116i	1.28578	−	1.19303i
$151$	−3.20483	+	8.16578i	−0.260805	+	0.664521i	−0.999959	−	0.00901511i	$-0.997130\pi$
$151$	−3.20483	+	8.16578i	−0.260805	+	0.664521i	0.739154	+	0.673537i	$0.235226\pi$
$152$	−17.0203	−	5.25006i	−1.38053	−	0.425836i
$153$	0.277395	−	1.21534i	0.0224260	−	0.0982548i
$154$	−26.3557	−	24.4014i	−2.12380	−	1.96632i
$155$	1.00364	+	4.39722i	0.0806141	+	0.353193i
$156$	1.32202	−	17.6411i	0.105846	−	1.41242i
$157$	4.47682	−	1.38091i	0.357289	−	0.110209i	−0.110914	−	0.993830i	$-0.535378\pi$
$157$	4.47682	−	1.38091i	0.357289	−	0.110209i	0.468203	+	0.883621i	$0.344902\pi$
$158$	0.547949	+	7.31187i	0.0435925	+	0.581701i
$159$	5.13734	+	13.0897i	0.407417	+	1.03808i
$160$	34.5256	+	16.6267i	2.72949	+	1.31445i
$161$	−7.74582	+	2.39846i	−0.610456	+	0.189025i
$162$	49.6118	−	23.8918i	3.89787	−	1.87711i
$163$	9.05091	+	8.39802i	0.708922	+	0.657783i	0.949831	−	0.312764i	$-0.101255\pi$
$163$	9.05091	+	8.39802i	0.708922	+	0.657783i	−0.240909	+	0.970548i	$0.577446\pi$
$164$	−66.3657	−	10.0030i	−5.18229	−	0.781104i
$165$	−12.4961	−	21.6439i	−0.972821	−	1.68498i
$166$	−16.9353	+	29.3327i	−1.31443	+	2.27666i
$167$	−6.23824	+	7.82251i	−0.482730	+	0.605324i	−0.962237	−	0.272214i	$-0.912244\pi$
$167$	−6.23824	+	7.82251i	−0.482730	+	0.605324i	0.479507	+	0.877538i	$0.340816\pi$
$168$	−74.3876	−	35.7240i	−5.73913	−	2.75616i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−0.762445	+	0.114920i	−0.0584768	+	0.00881397i
$171$	10.6295	+	7.24705i	0.812855	+	0.554195i
$172$	42.8442	+	29.2107i	3.26684	+	2.22730i
$173$	−21.2725	+	3.20632i	−1.61732	+	0.243772i	−0.894435	−	0.447197i	$-0.852422\pi$
$173$	−21.2725	+	3.20632i	−1.61732	+	0.243772i	−0.722884	+	0.690969i	$0.757184\pi$
$174$	25.7015	+	32.2286i	1.94842	+	2.44325i
$175$	5.86234	+	2.81534i	0.443151	+	0.212819i
$176$	−48.8378	+	61.2407i	−3.68129	+	4.61619i
$177$	−13.5385	+	23.4494i	−1.01762	+	1.76257i
$178$	7.10547	+	12.3070i	0.532578	+	0.922452i
$179$	5.77441	+	0.870353i	0.431600	+	0.0650532i	0.361250	−	0.932469i	$-0.382350\pi$
$179$	5.77441	+	0.870353i	0.431600	+	0.0650532i	0.0703502	+	0.997522i	$0.477588\pi$
$180$	−46.1555	−	42.8260i	−3.44022	−	3.19206i
$181$	−13.5556	+	6.52802i	−1.00758	+	0.485224i	−0.863503	−	0.504343i	$-0.831735\pi$
$181$	−13.5556	+	6.52802i	−1.00758	+	0.485224i	−0.144074	+	0.989567i	$0.546020\pi$
$182$	6.95314	−	2.15301i	0.515401	−	0.159592i
$183$	−0.442928	−	0.213303i	−0.0327422	−	0.0157678i
$184$	10.9935	+	28.0110i	0.810451	+	2.06499i
$185$	−0.186746	−	2.49196i	−0.0137299	−	0.183212i
$186$	−23.6252	+	7.28742i	−1.73229	+	0.534339i
$187$	0.0648220	−	0.864990i	0.00474026	−	0.0632543i
$188$	−2.38033	−	10.4289i	−0.173603	−	0.760605i
$189$	25.2339	+	23.3628i	1.83550	+	1.69940i
$190$	1.77066	−	7.75778i	0.128457	−	0.562809i
$191$	14.0483	+	4.33334i	1.01650	+	0.313550i	0.757856	−	0.652422i	$-0.226247\pi$
$191$	14.0483	+	4.33334i	1.01650	+	0.313550i	0.258647	+	0.965972i	$0.416723\pi$
$192$	−39.8963	+	101.654i	−2.87927	+	7.33626i
$193$	−2.50574	+	2.32499i	−0.180367	+	0.167356i	−0.765190	−	0.643805i	$-0.777355\pi$
$193$	−2.50574	+	2.32499i	−0.180367	+	0.167356i	0.584822	+	0.811162i	$0.301164\pi$
$194$	11.5780	−	7.89375i	0.831252	−	0.566738i
$195$	5.06483			0.362700
$196$	2.82889	−	38.8789i	0.202063	−	2.77706i
$197$	1.90458			0.135696			0.0678480	−	0.997696i	$-0.478387\pi$
$197$	1.90458			0.135696			0.0678480	+	0.997696i	$0.478387\pi$
$198$	79.5426	−	54.2313i	5.65285	−	3.85405i
$199$	8.97062	−	8.32352i	0.635911	−	0.590039i	−0.294906	−	0.955526i	$-0.595288\pi$
$199$	8.97062	−	8.32352i	0.635911	−	0.590039i	0.930816	+	0.365488i	$0.119098\pi$
$200$	8.81701	−	22.4654i	0.623457	−	1.58854i
$201$	−11.5173	−	3.55262i	−0.812369	−	0.250583i
$202$	−1.43446	+	6.28480i	−0.100929	+	0.442197i
$203$	−6.22787	+	10.8140i	−0.437111	+	0.758995i
$204$	−0.691988	−	3.03180i	−0.0484488	−	0.212268i
$205$	1.43595	−	19.1615i	0.100291	−	1.33830i
$206$	−8.17021	+	2.52018i	−0.569245	+	0.175589i
$207$	−1.62419	−	21.6733i	−0.112889	−	1.50640i
$208$	−5.79943	−	14.7767i	−0.402118	−	1.02458i
$209$	8.06521	+	3.88400i	0.557882	+	0.268662i
$210$	13.4315	−	34.3323i	0.926863	−	2.36915i
$211$	−6.71534	+	3.23394i	−0.462303	+	0.222633i	−0.650512	−	0.759496i	$-0.725446\pi$
$211$	−6.71534	+	3.23394i	−0.462303	+	0.222633i	0.188210	+	0.982129i	$0.439732\pi$
$212$	18.0700	+	16.7665i	1.24105	+	1.15153i
$213$	29.3727	+	4.42723i	2.01259	+	0.303349i
$214$	−18.1610	−	31.4558i	−1.24146	−	2.15027i
$215$	−7.42302	+	12.8570i	−0.506245	+	0.876843i
$216$	79.5667	−	99.7734i	5.41383	−	6.78872i
$217$	−4.67291	−	5.84664i	−0.317218	−	0.396896i
$218$	−10.4167	−	13.0621i	−0.705505	−	0.884676i
$219$	3.04770	−	0.459367i	0.205945	−	0.0310412i
$220$	−36.1988	−	24.6799i	−2.44052	−	1.66392i
$221$	0.145242	+	0.0990243i	0.00977004	+	0.00666110i
$222$	13.5452	−	2.04161i	0.909093	−	0.137024i
$223$	13.8122	+	17.3199i	0.924932	+	1.15983i	0.986832	+	0.161746i	$0.0517125\pi$
$223$	13.8122	+	17.3199i	0.924932	+	1.15983i	−0.0619003	+	0.998082i	$0.519716\pi$
$224$	−63.5909	+	0.0688764i	−4.24884	+	0.00460200i
$225$	−10.8681	+	13.6282i	−0.724543	+	0.908548i
$226$	−26.7295	+	46.2968i	−1.77802	+	3.07962i
$227$	9.04241	+	15.6619i	0.600166	+	1.03952i	0.992795	+	0.119821i	$0.0382322\pi$
$227$	9.04241	+	15.6619i	0.600166	+	1.03952i	−0.392629	+	0.919697i	$0.628435\pi$
$228$	31.7343	+	4.78317i	2.10165	+	0.316773i
$229$	−5.63421	−	5.22778i	−0.372319	−	0.345461i	0.471715	−	0.881751i	$-0.343635\pi$
$229$	−5.63421	−	5.22778i	−0.372319	−	0.345461i	−0.844034	+	0.536290i	$0.819826\pi$
$230$	−12.1118	+	5.83275i	−0.798630	+	0.384600i
$231$	34.2921	+	23.3256i	2.25625	+	1.53471i
$232$	41.7237	+	20.0931i	2.73930	+	1.31918i
$233$	−8.69410	−	22.1522i	−0.569569	−	1.45124i	−0.867882	−	0.496771i	$-0.834519\pi$
$233$	−8.69410	−	22.1522i	−0.569569	−	1.45124i	0.298313	−	0.954468i	$-0.403576\pi$
$234$	1.45797	+	19.4553i	0.0953107	+	1.27183i
$235$	2.92653	−	0.902715i	0.190906	−	0.0588867i
$236$	−3.54716	+	47.3335i	−0.230900	+	3.08115i
$237$	−1.88400	−	8.25433i	−0.122379	−	0.536176i
$238$	1.05641	−	0.721928i	0.0684771	−	0.0467956i
$239$	0.466980	−	2.04597i	0.0302064	−	0.132343i	−0.957576	−	0.288179i	$-0.906950\pi$
$239$	0.466980	−	2.04597i	0.0302064	−	0.132343i	0.987783	+	0.155836i	$0.0498072\pi$
$240$	−76.8272	−	23.6980i	−4.95917	−	1.52970i
$241$	−1.24256	+	3.16598i	−0.0800401	+	0.203939i	−0.965292	−	0.261173i	$-0.915891\pi$
$241$	−1.24256	+	3.16598i	−0.0800401	+	0.203939i	0.885252	+	0.465112i	$0.153986\pi$
$242$	26.9213	−	24.9794i	1.73057	−	1.60573i
$243$	−20.3171	+	13.8520i	−1.30334	+	0.888604i
$244$	−0.861802			−0.0551712
$245$	11.1605	−	0.0241763i	0.713017	−	0.00154456i
$246$	105.330			6.71559
$247$	−1.49889	+	1.02193i	−0.0953724	+	0.0650238i
$248$	−20.3606	+	18.8919i	−1.29290	+	1.19964i
$249$	14.2885	−	36.4064i	0.905494	−	2.30716i
$250$	31.2599	+	9.64239i	1.97705	+	0.609838i
$251$	−1.51184	+	6.62381i	−0.0954266	+	0.418091i	−0.999966	−	0.00829975i	$-0.997358\pi$
$251$	−1.51184	+	6.62381i	−0.0954266	+	0.418091i	0.904539	+	0.426391i	$0.140215\pi$
$252$	99.8758	+	30.6892i	6.29158	+	1.93324i
$253$	−3.36520	−	14.7439i	−0.211569	−	0.926942i
$254$	−2.67709	+	35.7233i	−0.167976	+	2.24148i
$255$	0.850776	−	0.262430i	0.0532776	−	0.0164340i
$256$	4.42294	+	59.0200i	0.276434	+	3.68875i
$257$	2.38357	+	6.07323i	0.148683	+	0.378838i	0.985739	−	0.168279i	$-0.0538208\pi$
$257$	2.38357	+	6.07323i	0.148683	+	0.378838i	−0.837057	+	0.547116i	$0.815726\pi$
$258$	−73.3207	−	35.3094i	−4.56475	−	2.19827i
$259$	2.07732	+	3.58904i	0.129078	+	0.223012i
$260$	7.99941	−	3.85231i	0.496102	−	0.238910i
$261$	−24.5195	−	22.7508i	−1.51772	−	1.40824i
$262$	−28.7665	−	4.33586i	−1.77720	−	0.267870i
$263$	11.8685	+	20.5569i	0.731843	+	1.26759i	0.956095	+	0.293058i	$0.0946731\pi$
$263$	11.8685	+	20.5569i	0.731843	+	1.26759i	−0.224251	+	0.974531i	$0.571994\pi$
$264$	76.9531	−	133.287i	4.73613	−	8.20323i
$265$	−4.40024	+	5.51772i	−0.270304	+	0.338951i
$266$	2.95226	+	12.8704i	0.181015	+	0.789137i
$267$	−10.2310	−	12.8292i	−0.626126	−	0.785137i
$268$	−20.8926	+	3.14906i	−1.27622	+	0.192359i
$269$	16.0682	+	10.9551i	0.979698	+	0.667947i	0.943491	−	0.331398i	$-0.107520\pi$
$269$	16.0682	+	10.9551i	0.979698	+	0.667947i	0.0362068	+	0.999344i	$0.488473\pi$
$270$	47.1053	+	32.1159i	2.86674	+	1.95451i
$271$	−9.15415	+	1.37977i	−0.556075	+	0.0838149i	−0.421067	−	0.907030i	$-0.638344\pi$
$271$	−9.15415	+	1.37977i	−0.556075	+	0.0838149i	−0.135008	+	0.990844i	$0.543106\pi$
$272$	−1.73981	−	2.18166i	−0.105492	−	0.132282i
$273$	−7.56851	+	3.65491i	−0.458067	+	0.221205i
$274$	−7.14100	+	8.95453i	−0.431403	+	0.540963i
$275$	−6.06452	+	10.5041i	−0.365704	+	0.633418i
$276$	−27.1088	−	46.9539i	−1.63176	−	2.82629i
$277$	−10.4511	−	1.57526i	−0.627948	−	0.0946479i	−0.172644	−	0.984984i	$-0.555231\pi$
$277$	−10.4511	−	1.57526i	−0.627948	−	0.0946479i	−0.455304	+	0.890336i	$0.650469\pi$
$278$	−36.2455	−	33.6309i	−2.17386	−	2.01705i
$279$	18.0747	−	8.70429i	1.08210	−	0.521112i
$280$	−3.13978	−	41.2972i	−0.187638	−	2.46798i
$281$	8.69983	+	4.18962i	0.518988	+	0.249932i	0.674992	−	0.737825i	$-0.264147\pi$
$281$	8.69983	+	4.18962i	0.518988	+	0.249932i	−0.156004	+	0.987756i	$0.549861\pi$
$282$	6.13330	+	15.6274i	0.365233	+	0.930598i
$283$	−1.18027	−	15.7496i	−0.0701597	−	0.936216i	−0.915585	−	0.402123i	$-0.868272\pi$
$283$	−1.18027	−	15.7496i	−0.0701597	−	0.936216i	0.845426	−	0.534093i	$-0.179347\pi$
$284$	49.7588	−	15.3486i	2.95264	−	0.910769i
$285$	−0.686634	+	9.16250i	−0.0406727	+	0.542740i
$286$	3.02082	+	13.2351i	0.178625	+	0.782607i
$287$	11.6816	+	29.6698i	0.689545	+	1.75135i
$288$	37.9277	−	166.172i	2.23491	−	9.79180i
$289$	−16.2152	−	5.00173i	−0.953836	−	0.294219i
$290$	−7.55848	+	19.2587i	−0.443849	+	1.13091i
$291$	−11.8612	+	11.0056i	−0.695314	+	0.645157i
$292$	4.46416	−	3.04361i	0.261245	−	0.178114i
$293$	4.09534			0.239252			0.119626	−	0.992819i	$-0.461830\pi$
$293$	4.09534			0.239252			0.119626	+	0.992819i	$0.461830\pi$
$294$	4.70393	+	60.9962i	0.274339	+	3.55737i
$295$	−13.5897			−0.791220
$296$	12.7149	−	8.66887i	0.739039	−	0.503868i
$297$	−47.0154	+	43.6239i	−2.72811	+	2.53132i
$298$	−22.5081	+	57.3498i	−1.30386	+	3.32218i
$299$	2.92863	+	0.903361i	0.169367	+	0.0522427i
$300$	−9.67604	+	42.3935i	−0.558646	+	2.44759i
$301$	1.81445	−	24.5693i	0.104583	−	1.41615i
$302$	−5.37021	−	23.5284i	−0.309021	−	1.35391i
$303$	0.556262	−	7.42280i	0.0319564	−	0.426429i
$304$	27.5179	−	8.48816i	1.57826	−	0.486829i
$305$	−0.0184385	−	0.246045i	−0.00105579	−	0.0140885i
$306$	1.25297	+	3.19250i	0.0716273	+	0.182503i
$307$	−0.798423	−	0.384500i	−0.0455684	−	0.0219446i	0.410961	−	0.911653i	$-0.365193\pi$
$307$	−0.798423	−	0.384500i	−0.0455684	−	0.0219446i	−0.456529	+	0.889708i	$0.650908\pi$
$308$	71.9026	+	10.7579i	4.09703	+	0.612990i
$309$	8.89496	−	4.28359i	0.506017	−	0.243685i
$310$	−9.09608	−	8.43993i	−0.516623	−	0.479356i
$311$	−26.9992	−	4.06947i	−1.53098	−	0.230759i	−0.671146	−	0.741326i	$-0.734197\pi$
$311$	−26.9992	−	4.06947i	−1.53098	−	0.230759i	−0.859838	+	0.510567i	$0.829436\pi$
$312$	15.5950	+	27.0113i	0.882893	+	1.52922i
$313$	−8.20227	+	14.2067i	−0.463619	+	0.803012i	−0.999138	−	0.0415110i	$-0.986783\pi$
$313$	−8.20227	+	14.2067i	−0.463619	+	0.803012i	0.535519	+	0.844523i	$0.320116\pi$
$314$	−8.03616	+	10.0770i	−0.453507	+	0.568679i
$315$	−6.62491	+	29.1712i	−0.373271	+	1.64361i
$316$	−9.25385	−	11.6040i	−0.520569	−	0.652773i
$317$	−19.6379	+	2.95993i	−1.10297	+	0.166246i	−0.675196	−	0.737639i	$-0.735941\pi$
$317$	−19.6379	+	2.95993i	−1.10297	+	0.166246i	−0.427776	+	0.903885i	$0.640703\pi$
$318$	−31.9638	−	21.7926i	−1.79244	−	1.22207i
$319$	−19.2301	−	13.1109i	−1.07668	−	0.734069i
$320$	−54.1956	+	8.16867i	−3.02963	+	0.456643i
$321$	26.1496	+	32.7905i	1.45953	+	1.83019i
$322$	13.8900	−	17.4562i	0.774059	−	0.972798i
$323$	−0.198830	+	0.249325i	−0.0110632	+	0.0138728i
$324$	−55.7306	+	96.5282i	−3.09614	+	5.36268i
$325$	−1.22901	−	2.12871i	−0.0681733	−	0.118080i
$326$	−33.5887	−	5.06268i	−1.86031	−	0.280396i
$327$	14.1416	+	13.1215i	0.782033	+	0.725620i
$328$	106.612	−	51.3416i	5.88666	−	2.83487i
$329$	−3.72178	+	3.46081i	−0.205188	+	0.190801i
$330$	61.9482	+	29.8327i	3.41013	+	1.64223i
$331$	7.73167	+	19.7000i	0.424971	+	1.08281i	0.969722	+	0.244211i	$0.0785289\pi$
$331$	7.73167	+	19.7000i	0.424971	+	1.08281i	−0.544751	+	0.838598i	$0.683376\pi$
$332$	−5.12349	−	68.3682i	−0.281188	−	3.75220i
$333$	−10.6212	+	3.27621i	−0.582039	+	0.179535i
$334$	2.05704	−	27.4493i	0.112556	−	1.50196i
$335$	−1.34606	−	5.89749i	−0.0735433	−	0.322214i
$336$	131.906	−	20.0278i	7.19607	−	1.09261i
$337$	−1.42983	+	6.26451i	−0.0778880	+	0.341250i	−0.998825	−	0.0484617i	$-0.984568\pi$
$337$	−1.42983	+	6.26451i	−0.0778880	+	0.341250i	0.920937	+	0.389711i	$0.127425\pi$
$338$	−2.62892	−	0.810915i	−0.142994	−	0.0441079i
$339$	22.5519	−	57.4614i	1.22485	−	3.12087i
$340$	1.14411	−	1.06158i	0.0620483	−	0.0575724i
$341$	11.5336	−	7.86349i	0.624581	−	0.425832i
$342$	−35.3932			−1.91384
$343$	−16.6600	+	8.08982i	−0.899554	+	0.436809i
$344$	−91.4243			−4.92927
$345$	12.8254	−	8.74419i	0.690495	−	0.470772i
$346$	43.3856	−	40.2559i	2.33242	−	2.16417i
$347$	0.928472	−	2.36571i	0.0498430	−	0.126998i	−0.903784	−	0.427989i	$-0.859222\pi$
$347$	0.928472	−	2.36571i	0.0498430	−	0.126998i	0.953627	+	0.300991i	$0.0973175\pi$
$348$	−79.7335	−	24.5945i	−4.27417	−	1.31841i
$349$	−1.06595	+	4.67021i	−0.0570587	+	0.249991i	−0.995411	−	0.0956892i	$-0.969495\pi$
$349$	−1.06595	+	4.67021i	−0.0570587	+	0.249991i	0.938353	+	0.345680i	$0.112352\pi$
$350$	−17.6888	+	2.68576i	−0.945508	+	0.143560i
$351$	−2.89225	−	12.6718i	−0.154377	−	0.676369i
$352$	8.86302	−	118.269i	0.472401	−	6.30375i
$353$	14.8405	−	4.57769i	0.789880	−	0.243646i	0.126538	−	0.991962i	$-0.459613\pi$
$353$	14.8405	−	4.57769i	0.789880	−	0.243646i	0.663342	+	0.748316i	$0.269137\pi$
$354$	−5.56686	−	74.2846i	−0.295875	−	3.94818i
$355$	5.44663	+	13.8778i	0.289077	+	0.736557i
$356$	−25.9168	−	12.4809i	−1.37359	−	0.661485i
$357$	−1.08196	+	1.00610i	−0.0572635	+	0.0532483i
$358$	−14.4747	+	6.97064i	−0.765011	+	0.368410i
$359$	18.5797	+	17.2394i	0.980598	+	0.909862i	0.995940	−	0.0900204i	$-0.0286932\pi$
$359$	18.5797	+	17.2394i	0.980598	+	0.909862i	−0.0153420	+	0.999882i	$0.504884\pi$
$360$	109.770	+	16.5452i	5.78541	+	0.872010i
$361$	7.85449	+	13.6044i	0.413394	+	0.716020i
$362$	20.6962	−	35.8470i	1.08777	−	1.88407i
$363$	−26.4397	+	33.1543i	−1.38772	+	1.74015i
$364$	−9.17382	+	11.5292i	−0.480839	+	0.604294i
$365$	0.964467	+	1.20940i	0.0504825	+	0.0633030i
$366$	1.33739	−	0.201580i	0.0699067	−	0.0105367i
$367$	20.6998	+	14.1129i	1.08052	+	0.736686i	0.966468	−	0.256788i	$-0.0826643\pi$
$367$	20.6998	+	14.1129i	1.08052	+	0.736686i	0.114053	+	0.993475i	$0.463617\pi$
$368$	−40.1969	−	27.4058i	−2.09541	−	1.42862i
$369$	−84.5126	+	12.7382i	−4.39955	+	0.663125i
$370$	4.28647	+	5.37506i	0.222843	+	0.279436i
$371$	2.59367	−	11.4206i	0.134657	−	0.592929i
$372$	31.2026	−	39.1268i	1.61778	−	2.02863i
$373$	10.1677	−	17.6110i	0.526465	−	0.911865i	−0.473059	−	0.881031i	$-0.656850\pi$
$373$	10.1677	−	17.6110i	0.526465	−	0.911865i	0.999525	−	0.0308340i	$-0.00981632\pi$
$374$	1.19319	+	2.06667i	0.0616986	+	0.106865i
$375$	−37.3517	−	5.62986i	−1.92883	−	0.290725i
$376$	13.8253	+	12.8280i	0.712987	+	0.661555i
$377$	4.24958	−	2.04649i	0.218865	−	0.105400i
$378$	−93.5665	−	13.9992i	−4.81254	−	0.720044i
$379$	−9.29295	−	4.47525i	−0.477347	−	0.229878i	0.179709	−	0.983720i	$-0.442484\pi$
$379$	−9.29295	−	4.47525i	−0.477347	−	0.229878i	−0.657056	+	0.753842i	$0.728199\pi$
$380$	5.88453	+	14.9935i	0.301870	+	0.769153i
$381$	−3.09121	−	41.2493i	−0.158368	−	2.11327i
$382$	−38.6491	+	11.9217i	−1.97746	+	0.609965i
$383$	2.70725	−	36.1257i	0.138334	−	1.84594i	−0.308385	−	0.951262i	$-0.599788\pi$
$383$	2.70725	−	36.1257i	0.138334	−	1.84594i	0.446719	−	0.894675i	$-0.352593\pi$
$384$	−32.8726	−	144.024i	−1.67752	−	7.34971i
$385$	−1.53302	+	20.7584i	−0.0781299	+	1.05795i
$386$	2.09260	−	9.16829i	0.106511	−	0.466653i
$387$	63.0999	+	19.4637i	3.20755	+	0.989397i
$388$	−10.3627	+	26.4038i	−0.526089	+	1.34045i
$389$	28.1934	−	26.1596i	1.42946	−	1.32635i	0.563614	−	0.826038i	$-0.309410\pi$
$389$	28.1934	−	26.1596i	1.42946	−	1.32635i	0.865847	−	0.500308i	$-0.166780\pi$
$390$	−11.5129	+	7.84935i	−0.582977	+	0.397467i
$391$	0.538750			0.0272457
$392$	34.4930	+	59.4458i	1.74216	+	3.00247i
$393$	33.5916			1.69447
$394$	−4.32932	+	2.95168i	−0.218108	+	0.148703i
$395$	3.11495	−	2.89025i	0.156730	−	0.145424i
$396$	−71.1937	+	181.399i	−3.57762	+	9.11562i
$397$	33.5584	+	10.3514i	1.68425	+	0.519521i	0.981425	−	0.191845i	$-0.0614472\pi$
$397$	33.5584	+	10.3514i	1.68425	+	0.519521i	0.702821	+	0.711367i	$0.251923\pi$
$398$	−7.49156	+	32.8227i	−0.375518	+	1.64525i
$399$	−5.58584	−	14.1873i	−0.279642	−	0.710252i
$400$	8.68247	+	38.0404i	0.434124	+	1.90202i
$401$	−2.30616	+	30.7736i	−0.115164	+	1.53676i	0.578034	+	0.816013i	$0.303820\pi$
$401$	−2.30616	+	30.7736i	−0.115164	+	1.53676i	−0.693198	+	0.720747i	$0.743799\pi$
$402$	31.6858	−	9.77378i	1.58035	−	0.487472i
$403$	0.211405	+	2.82100i	0.0105308	+	0.140524i
$404$	−4.76723	−	12.1467i	−0.237178	−	0.604321i
$405$	−28.7513	−	13.8459i	−1.42866	−	0.688007i
$406$	−2.60271	−	34.2332i	−0.129170	−	1.69897i
$407$	−6.96820	+	3.35571i	−0.345401	+	0.166336i
$408$	4.01918	+	3.72925i	0.198979	+	0.184625i
$409$	−32.2611	−	4.86258i	−1.59521	−	0.240439i	−0.709509	−	0.704697i	$-0.751083\pi$
$409$	−32.2611	−	4.86258i	−1.59521	−	0.240439i	−0.885700	+	0.464258i	$0.846321\pi$
$410$	26.4319	+	45.7814i	1.30538	+	2.26098i
$411$	6.61248	−	11.4532i	0.326170	−	0.564942i
$412$	10.7906	−	13.5310i	0.531617	−	0.666626i
$413$	20.3074	−	9.80665i	0.999263	−	0.482554i
$414$	37.2806	+	46.7485i	1.83224	+	2.29756i
$415$	19.4096	−	2.92552i	0.952779	−	0.143608i
$416$	19.8587	+	13.5395i	0.973654	+	0.663826i
$417$	47.1726	+	32.1617i	2.31005	+	1.57497i
$418$	−24.3524	+	3.67053i	−1.19111	+	0.179532i
$419$	4.17159	+	5.23101i	0.203796	+	0.255552i	0.873217	−	0.487331i	$-0.162029\pi$
$419$	4.17159	+	5.23101i	0.203796	+	0.255552i	−0.669422	+	0.742883i	$0.733458\pi$
$420$	16.6841	+	72.7345i	0.814100	+	3.54908i
$421$	−11.6074	+	14.5552i	−0.565711	+	0.709379i	−0.979602	−	0.200947i	$-0.935598\pi$
$421$	−11.6074	+	14.5552i	−0.565711	+	0.709379i	0.413891	+	0.910326i	$0.364169\pi$
$422$	10.2528	−	17.7583i	0.499098	−	0.864462i
$423$	−6.81105	−	11.7971i	−0.331164	−	0.573594i
$424$	−42.9754	−	6.47750i	−2.08707	−	0.314575i
$425$	−0.316743	−	0.293895i	−0.0153643	−	0.0142560i
$426$	−73.6285	+	35.4576i	−3.56731	+	1.71793i
$427$	0.205106	+	0.354367i	0.00992576	+	0.0171490i
$428$	66.2412	+	31.9001i	3.20189	+	1.54195i
$429$	−5.72687	−	14.5918i	−0.276496	−	0.704500i
$430$	−3.05225	−	40.7294i	−0.147192	−	1.96415i
$431$	−21.8730	+	6.74693i	−1.05359	+	0.324988i	−0.772712	−	0.634757i	$-0.781100\pi$
$431$	−21.8730	+	6.74693i	−1.05359	+	0.324988i	−0.280874	+	0.959745i	$0.590624\pi$
$432$	−15.4187	+	205.748i	−0.741831	+	9.89905i
$433$	5.23206	+	22.9232i	0.251437	+	1.10162i	0.930140	+	0.367204i	$0.119685\pi$
$433$	5.23206	+	22.9232i	0.251437	+	1.10162i	−0.678703	+	0.734412i	$0.737458\pi$
$434$	19.6830	+	6.04806i	0.944814	+	0.290316i
$435$	5.31584	−	23.2902i	0.254875	−	1.11668i
$436$	32.3155	+	9.96802i	1.54763	+	0.477382i
$437$	−2.03125	+	5.17555i	−0.0971680	+	0.247580i
$438$	−6.21583	+	5.76745i	−0.297004	+	0.275579i
$439$	0.994978	−	0.678364i	0.0474877	−	0.0323766i	−0.539344	−	0.842086i	$-0.681328\pi$
$439$	0.994978	−	0.678364i	0.0474877	−	0.0323766i	0.586831	+	0.809709i	$0.300375\pi$
$440$	77.2437			3.68245
$441$	−11.1509	−	48.3721i	−0.530996	−	2.30343i
$442$	−0.483616			−0.0230033
$443$	3.69885	−	2.52183i	0.175738	−	0.119816i	−0.472257	−	0.881461i	$-0.656560\pi$
$443$	3.69885	−	2.52183i	0.175738	−	0.119816i	0.647994	+	0.761645i	$0.275608\pi$
$444$	−20.3257	+	18.8595i	−0.964616	+	0.895033i
$445$	3.00880	−	7.66630i	0.142631	−	0.363418i
$446$	−58.2385	−	17.9642i	−2.75767	−	0.850630i
$447$	15.8298	−	69.3551i	0.748726	−	3.28038i
$448$	75.0913	−	51.3156i	3.54773	−	2.42443i
$449$	2.07232	+	9.07942i	0.0977988	+	0.428485i	0.999996	−	0.00283933i	$-0.000903788\pi$
$449$	2.07232	+	9.07942i	0.0977988	+	0.428485i	−0.902197	+	0.431324i	$0.858047\pi$
$450$	3.58373	−	47.8216i	0.168939	−	2.25433i
$451$	−56.8281	+	17.5292i	−2.67593	+	0.825416i
$452$	−8.08657	−	107.908i	−0.380360	−	5.07556i
$453$	10.1808	+	25.9404i	0.478338	+	1.21878i
$454$	−44.8268	−	21.5875i	−2.10383	−	1.01315i
$455$	−3.48787	−	2.37246i	−0.163514	−	0.111223i
$456$	−50.9790	+	24.5502i	−2.38731	+	1.14967i
$457$	4.69402	+	4.35542i	0.219577	+	0.203738i	0.782290	−	0.622915i	$-0.214052\pi$
$457$	4.69402	+	4.35542i	0.219577	+	0.203738i	−0.562713	+	0.826653i	$0.690242\pi$
$458$	20.9090	+	3.15153i	0.977015	+	0.147261i
$459$	−1.14241	−	1.97871i	−0.0533231	−	0.0923583i
$460$	13.6056	−	23.5656i	0.634365	−	1.09875i
$461$	−7.80556	+	9.78786i	−0.363541	+	0.455866i	−0.929639	−	0.368472i	$-0.879881\pi$
$461$	−7.80556	+	9.78786i	−0.363541	+	0.455866i	0.566098	+	0.824338i	$0.308453\pi$
$462$	−114.099	+	0.123583i	−5.30836	+	0.00574958i
$463$	−2.28300	−	2.86279i	−0.106100	−	0.133045i	0.725946	−	0.687751i	$-0.241402\pi$
$463$	−2.28300	−	2.86279i	−0.106100	−	0.133045i	−0.832046	+	0.554706i	$0.812831\pi$
$464$	−74.0363	+	11.1592i	−3.43705	+	0.518052i
$465$	11.8383	+	8.07123i	0.548989	+	0.374294i
$466$	54.0935	+	36.8803i	2.50583	+	1.70845i
$467$	18.6298	−	2.80800i	0.862086	−	0.129939i	0.296907	−	0.954907i	$-0.404045\pi$
$467$	18.6298	−	2.80800i	0.862086	−	0.129939i	0.565179	+	0.824968i	$0.308807\pi$
$468$	−24.6225	−	30.8756i	−1.13817	−	1.42723i
$469$	6.26724	+	7.84143i	0.289394	+	0.362084i
$470$	−5.25330	+	6.58743i	−0.242317	+	0.303856i
$471$	7.44139	−	12.8889i	0.342881	−	0.593887i
$472$	−41.8437	−	72.4753i	−1.92601	−	3.33595i
$473$	45.4346	+	6.84817i	2.08909	+	0.314879i
$474$	17.0749	+	15.8432i	0.784275	+	0.727701i
$475$	4.01755	−	1.93475i	0.184338	−	0.0887724i
$476$	−0.943618	+	2.41198i	−0.0432506	+	0.110553i
$477$	28.2821	+	13.6199i	1.29495	+	0.623613i
$478$	2.10931	+	5.37442i	0.0964774	+	0.245820i
$479$	−0.818249	−	10.9188i	−0.0373867	−	0.498891i	−0.984194	−	0.177091i	$-0.943331\pi$
$479$	−0.818249	−	10.9188i	−0.0373867	−	0.498891i	0.946808	−	0.321800i	$-0.104288\pi$
$480$	116.325	−	35.8816i	5.30950	−	1.63776i
$481$	0.117129	−	1.56298i	0.00534064	−	0.0712659i
$482$	−2.08210	−	9.12229i	−0.0948372	−	0.415509i
$483$	−12.8553	+	22.3218i	−0.584936	+	1.01568i
$484$	−16.5417	+	72.4741i	−0.751898	+	3.29428i
$485$	−7.76004	−	2.39365i	−0.352365	−	0.108690i
$486$	24.7154	−	62.9739i	1.12112	−	2.85656i
$487$	−4.33623	+	4.02343i	−0.196493	+	0.182319i	−0.772283	−	0.635279i	$-0.780885\pi$
$487$	−4.33623	+	4.02343i	−0.196493	+	0.182319i	0.575790	+	0.817598i	$0.304695\pi$
$488$	1.25542	−	0.855928i	0.0568300	−	0.0387460i
$489$	39.2226			1.77371
$490$	−25.3315	+	17.3512i	−1.14436	+	0.783847i
$491$	−0.780851			−0.0352393			−0.0176197	−	0.999845i	$-0.505609\pi$
$491$	−0.780851			−0.0352393			−0.0176197	+	0.999845i	$0.505609\pi$
$492$	−176.159	+	120.103i	−7.94187	+	5.41468i
$493$	0.607796	−	0.563952i	0.0273738	−	0.0253991i
$494$	1.82338	−	4.64590i	0.0820378	−	0.209029i
$495$	−53.3127	−	16.4448i	−2.39623	−	0.739138i
$496$	9.99257	−	43.7803i	0.448680	−	1.96579i
$497$	−18.1536	−	16.8076i	−0.814302	−	0.753922i
$498$	23.9426	+	104.899i	1.07289	+	4.70066i
$499$	2.71838	−	36.2743i	0.121692	−	1.62386i	−0.518105	−	0.855317i	$-0.673362\pi$
$499$	2.71838	−	36.2743i	0.121692	−	1.62386i	0.639797	−	0.768544i	$-0.279019\pi$
$500$	−63.2755	+	19.5179i	−2.82977	+	0.872867i
$501$	2.37524	+	31.6954i	0.106118	+	1.41604i
$502$	−6.82885	−	17.3996i	−0.304787	−	0.776583i
$503$	11.6386	+	5.60488i	0.518941	+	0.249909i	0.674972	−	0.737843i	$-0.264156\pi$
$503$	11.6386	+	5.60488i	0.518941	+	0.249909i	−0.156031	+	0.987752i	$0.549870\pi$
$504$	−175.972	+	54.4891i	−7.83843	+	2.42714i
$505$	3.36590	−	1.62093i	0.149780	−	0.0721305i
$506$	30.4992	+	28.2992i	1.35586	+	1.25805i
$507$	3.14124	+	0.473465i	0.139507	+	0.0210273i
$508$	−36.2566	−	62.7982i	−1.60863	−	2.78622i
$509$	16.5012	−	28.5810i	0.731405	−	1.26683i	−0.224878	−	0.974387i	$-0.572198\pi$
$509$	16.5012	−	28.5810i	0.731405	−	1.26683i	0.956283	−	0.292443i	$-0.0944683\pi$
$510$	−1.52719	+	1.91504i	−0.0676253	+	0.0847995i
$511$	−2.31397	−	1.11126i	−0.102364	−	0.0491593i
$512$	−43.5329	−	54.5885i	−1.92390	−	2.41249i
$513$	23.3159	−	3.51431i	1.02942	−	0.155160i
$514$	−14.8302	−	10.1111i	−0.654134	−	0.445981i
$515$	4.09399	+	2.79124i	0.180403	+	0.122997i
$516$	162.887	−	24.5513i	7.17072	−	1.08081i
$517$	−5.90981	−	7.41066i	−0.259913	−	0.325921i
$518$	−10.2842	−	4.93888i	−0.451860	−	0.217002i
$519$	−42.6093	+	53.4304i	−1.87034	+	2.34534i
$520$	−7.82695	+	13.5567i	−0.343235	+	0.594500i
$521$	−4.87265	−	8.43967i	−0.213475	−	0.369749i	0.739325	−	0.673349i	$-0.235145\pi$
$521$	−4.87265	−	8.43967i	−0.213475	−	0.369749i	−0.952800	+	0.303600i	$0.901811\pi$
$522$	90.9939	+	13.7151i	3.98269	+	0.600295i
$523$	−12.8643	−	11.9363i	−0.562518	−	0.521940i	0.346857	−	0.937918i	$-0.387249\pi$
$523$	−12.8643	−	11.9363i	−0.562518	−	0.521940i	−0.909375	+	0.415978i	$0.863439\pi$
$524$	53.0547	−	25.5498i	2.31771	−	1.11615i
$525$	19.7348	−	6.11078i	0.861296	−	0.266696i
$526$	−58.8369	−	28.3343i	−2.56541	−	1.23544i
$527$	0.181679	+	0.462911i	0.00791407	+	0.0201647i
$528$	18.5952	+	248.136i	0.809253	+	10.7987i
$529$	−13.0026	+	4.01076i	−0.565329	+	0.174381i
$530$	1.45096	−	19.3617i	0.0630258	−	0.841020i
$531$	13.4504	+	58.9299i	0.583696	+	2.55734i
$532$	−19.6132	−	18.1589i	−0.850338	−	0.787286i
$533$	2.68182	−	11.7498i	0.116163	−	0.508942i
$534$	43.1385	+	13.3065i	1.86679	+	0.575827i
$535$	−7.69026	+	19.5945i	−0.332479	+	0.847142i
$536$	27.3074	−	25.3376i	1.17950	−	1.09442i
$537$	15.3275	−	10.4501i	0.661428	−	0.450954i
$538$	−53.5028			−2.30667
$539$	−12.6890	−	32.1262i	−0.546553	−	1.38377i
$540$	−115.402			−4.96611
$541$	−0.416625	+	0.284050i	−0.0179121	+	0.0122123i	−0.572243	−	0.820084i	$-0.693927\pi$
$541$	−0.416625	+	0.284050i	−0.0179121	+	0.0122123i	0.554331	+	0.832296i	$0.312974\pi$
$542$	18.6700	−	17.3232i	0.801946	−	0.744097i
$543$	−17.4616	+	44.4915i	−0.749350	+	1.90931i
$544$	4.03735	+	1.24536i	0.173100	+	0.0533943i
$545$	−2.15448	+	9.43939i	−0.0922877	+	0.404339i
$546$	11.5397	−	20.0375i	0.493855	−	0.857525i
$547$	1.92894	+	8.45124i	0.0824755	+	0.361349i	0.999278	−	0.0379920i	$-0.0120961\pi$
$547$	1.92894	+	8.45124i	0.0824755	+	0.361349i	−0.916803	+	0.399341i	$0.869239\pi$
$548$	1.73250	−	23.1186i	0.0740088	−	0.987579i
$549$	−1.04869	+	0.323479i	−0.0447572	+	0.0138058i
$550$	−2.49365	−	33.2755i	−0.106330	−	1.41887i
$551$	3.12608	+	7.96513i	0.133176	+	0.339326i
$552$	86.1243	+	41.4753i	3.66569	+	1.76530i
$553$	−2.56908	+	6.56681i	−0.109248	+	0.279249i
$554$	26.1978	−	12.6162i	1.11304	−	0.536011i
$555$	−5.81928	−	5.39951i	−0.247015	−	0.229196i
$556$	98.9668	+	14.9168i	4.19713	+	0.632615i
$557$	−1.62814	−	2.82001i	−0.0689863	−	0.119488i	0.829469	−	0.558553i	$-0.188643\pi$
$557$	−1.62814	−	2.82001i	−0.0689863	−	0.119488i	−0.898455	+	0.439065i	$0.855310\pi$
$558$	−27.5959	+	47.7974i	−1.16823	+	2.02343i
$559$	−5.80569	+	7.28011i	−0.245555	+	0.307916i
$560$	41.8061	+	52.3069i	1.76663	+	2.21037i
$561$	−1.71805	−	2.15436i	−0.0725360	−	0.0909573i
$562$	−26.2686	+	3.95935i	−1.10807	+	0.167015i
$563$	−9.70997	−	6.62014i	−0.409226	−	0.279006i	0.341160	−	0.940005i	$-0.389180\pi$
$563$	−9.70997	−	6.62014i	−0.409226	−	0.279006i	−0.750386	+	0.660999i	$0.770133\pi$
$564$	−28.0770	−	19.1425i	−1.18225	−	0.806046i
$565$	30.6348	−	4.61745i	1.28881	−	0.194258i
$566$	27.0912	+	33.9713i	1.13873	+	1.42792i
$567$	52.9554	−	0.0573569i	2.22392	−	0.00240876i
$568$	−57.2414	+	71.7784i	−2.40180	+	3.01176i
$569$	2.47652	−	4.28945i	0.103821	−	0.179823i	−0.809435	−	0.587210i	$-0.800226\pi$
$569$	2.47652	−	4.28945i	0.103821	−	0.179823i	0.913256	+	0.407386i	$0.133560\pi$
$570$	−12.6390	−	21.8914i	−0.529391	−	0.916932i
$571$	−30.8711	−	4.65306i	−1.29191	−	0.194725i	−0.533111	−	0.846045i	$-0.678977\pi$
$571$	−30.8711	−	4.65306i	−1.29191	−	0.194725i	−0.758803	+	0.651321i	$0.774215\pi$
$572$	−20.1436	−	18.6905i	−0.842247	−	0.781491i
$573$	42.0775	−	20.2634i	1.75781	−	0.846518i
$574$	−72.5350	−	49.3386i	−3.02755	−	2.05935i
$575$	−6.78728	−	3.26858i	−0.283049	−	0.136309i
$576$	89.0625	+	226.927i	3.71094	+	9.45531i
$577$	−0.382173	−	5.09974i	−0.0159101	−	0.212305i	−0.999493	−	0.0318471i	$-0.989861\pi$
$577$	−0.382173	−	5.09974i	−0.0159101	−	0.212305i	0.983583	−	0.180458i	$-0.0577580\pi$
$578$	44.6104	−	13.7605i	1.85555	−	0.572361i
$579$	−0.811477	+	10.8284i	−0.0337238	+	0.450013i
$580$	−9.31870	−	40.8279i	−0.386938	−	1.69529i
$581$	−26.8932	+	18.3781i	−1.11572	+	0.762454i
$582$	9.90552	−	43.3989i	0.410597	−	1.79894i
$583$	20.8721	+	6.43818i	0.864432	+	0.266642i
$584$	−3.48023	+	8.86747i	−0.144013	+	0.366939i
$585$	8.28821	−	7.69034i	0.342675	−	0.317956i
$586$	−9.30913	+	6.34686i	−0.384557	+	0.262186i
$587$	−16.3460			−0.674673			−0.337337	−	0.941384i	$-0.609526\pi$
$587$	−16.3460			−0.674673			−0.337337	+	0.941384i	$0.609526\pi$
$588$	−77.4186	−	96.6496i	−3.19269	−	3.98576i
$589$	−5.13199			−0.211460
$590$	30.8907	−	21.0609i	1.27175	−	0.867065i
$591$	4.43520	−	4.11526i	0.182440	−	0.169279i
$592$	−9.08982	+	23.1605i	−0.373589	+	0.951890i
$593$	−17.0994	−	5.27447i	−0.702189	−	0.216597i	−0.0769555	−	0.997035i	$-0.524520\pi$
$593$	−17.0994	−	5.27447i	−0.702189	−	0.216597i	−0.625233	+	0.780438i	$0.714996\pi$
$594$	39.2636	−	172.025i	1.61100	−	7.05827i
$595$	−0.708811	−	0.217799i	−0.0290584	−	0.00892887i
$596$	−27.7498	−	121.580i	−1.13668	−	4.98011i
$597$	2.90511	−	38.7659i	0.118898	−	1.58658i
$598$	−8.05708	+	2.48528i	−0.329478	+	0.101631i
$599$	1.81497	+	24.2190i	0.0741575	+	0.989563i	0.902877	+	0.429899i	$0.141451\pi$
$599$	1.81497	+	24.2190i	0.0741575	+	0.989563i	−0.828719	+	0.559664i	$0.810930\pi$
$600$	−28.0091	−	71.3661i	−1.14347	−	2.91351i
$601$	−17.9537	−	8.64604i	−0.732346	−	0.352679i	0.0302603	−	0.999542i	$-0.490366\pi$
$601$	−17.9537	−	8.64604i	−0.732346	−	0.352679i	−0.762606	+	0.646863i	$0.776081\pi$
$602$	33.9524	+	58.6605i	1.38380	+	2.39082i
$603$	−24.2415	+	11.6741i	−0.987189	+	0.475405i
$604$	35.8099	+	33.2268i	1.45709	+	1.35198i
$605$	−21.0453	−	3.17208i	−0.855615	−	0.128963i
$606$	10.2392	+	17.7349i	0.415941	+	0.720430i
$607$	−7.16262	+	12.4060i	−0.290722	+	0.503545i	−0.973981	−	0.226631i	$-0.927229\pi$
$607$	−7.16262	+	12.4060i	−0.290722	+	0.503545i	0.683259	+	0.730176i	$0.260562\pi$
$608$	−27.1857	+	34.0898i	−1.10253	+	1.38252i
$609$	8.86320	+	38.6393i	0.359155	+	1.56574i
$610$	0.423228	+	0.530711i	0.0171360	+	0.0214878i
$611$	1.89944	−	0.286295i	0.0768431	−	0.0115822i
$612$	−5.73581	−	3.91061i	−0.231856	−	0.158077i
$613$	−22.2495	−	15.1694i	−0.898649	−	0.612688i	0.0234153	−	0.999726i	$-0.492546\pi$
$613$	−22.2495	−	15.1694i	−0.898649	−	0.612688i	−0.922064	+	0.387038i	$0.873498\pi$
$614$	2.41079	−	0.363368i	0.0972914	−	0.0146643i
$615$	−38.0586	−	47.7240i	−1.53467	−	1.92442i
$616$	−115.428	+	55.7411i	−4.65071	+	2.24587i
$617$	13.0182	−	16.3243i	0.524093	−	0.657192i	−0.447379	−	0.894344i	$-0.647643\pi$
$617$	13.0182	−	16.3243i	0.524093	−	0.657192i	0.971472	+	0.237152i	$0.0762141\pi$
$618$	−13.5806	+	23.5222i	−0.546291	+	0.946203i
$619$	−15.6087	−	27.0350i	−0.627365	−	1.08663i	−0.988078	−	0.153951i	$-0.950800\pi$
$619$	−15.6087	−	27.0350i	−0.627365	−	1.08663i	0.360714	−	0.932677i	$-0.382533\pi$
$620$	24.8365	+	3.74350i	0.997457	+	0.150342i
$621$	−29.2011	−	27.0947i	−1.17180	−	1.08727i
$622$	67.6787	−	32.5924i	2.71367	−	1.30683i
$623$	1.03606	+	13.6272i	0.0415089	+	0.545962i
$624$	−45.4334	−	21.8796i	−1.81879	−	0.875883i
$625$	−2.43610	−	6.20708i	−0.0974440	−	0.248283i
$626$	−3.37266	−	45.0051i	−0.134799	−	1.79876i
$627$	27.1737	−	8.38197i	1.08521	−	0.334744i
$628$	1.94968	−	26.0167i	0.0778007	−	1.03818i
$629$	−0.0613095	−	0.268615i	−0.00244457	−	0.0107104i
$630$	−30.1498	−	76.5764i	−1.20120	−	3.05088i
$631$	6.00948	−	26.3292i	0.239234	−	1.04815i	−0.702472	−	0.711712i	$-0.747920\pi$
$631$	6.00948	−	26.3292i	0.239234	−	1.04815i	0.941705	−	0.336439i	$-0.109223\pi$
$632$	25.0053	+	7.71310i	0.994656	+	0.306811i
$633$	−8.65038	+	22.0408i	−0.343822	+	0.876043i
$634$	40.0517	−	37.1625i	1.59065	−	1.47591i
$635$	17.1532	−	11.6949i	0.680705	−	0.464097i
$636$	78.3072			3.10508
$637$	6.92406	+	1.02830i	0.274341	+	0.0407427i
$638$	64.0310			2.53501
$639$	54.7885	−	37.3542i	2.16740	−	1.47771i
$640$	54.3507	−	50.4301i	2.14840	−	1.99342i
$641$	17.9670	−	45.7792i	0.709655	−	1.80817i	0.133117	−	0.991100i	$-0.457502\pi$
$641$	17.9670	−	45.7792i	0.709655	−	1.80817i	0.576538	−	0.817070i	$-0.304403\pi$
$642$	−110.259	−	34.0103i	−4.35156	−	1.34228i
$643$	5.96194	−	26.1210i	0.235116	−	1.03011i	−0.710212	−	0.703988i	$-0.751401\pi$
$643$	5.96194	−	26.1210i	0.235116	−	1.03011i	0.945328	−	0.326122i	$-0.105742\pi$
$644$	−3.32571	+	45.0329i	−0.131051	+	1.77455i
$645$	10.4945	+	45.9792i	0.413219	+	1.81043i
$646$	0.0655634	−	0.874883i	0.00257956	−	0.0344218i
$647$	−29.5428	+	9.11276i	−1.16145	+	0.358260i	−0.814804	−	0.579737i	$-0.803155\pi$
$647$	−29.5428	+	9.11276i	−1.16145	+	0.358260i	−0.346645	+	0.937996i	$0.612679\pi$
$648$	−14.6857	−	195.967i	−0.576908	−	7.69830i
$649$	15.3660	+	39.1520i	0.603169	+	1.53685i
$650$	6.09269	+	2.93409i	0.238975	+	0.115084i
$651$	−23.5147	−	3.51823i	−0.921615	−	0.137890i
$652$	61.9483	−	29.8327i	2.42608	−	1.16834i
$653$	5.36673	+	4.97959i	0.210016	+	0.194867i	0.778166	−	0.628059i	$-0.216150\pi$
$653$	5.36673	+	4.97959i	0.210016	+	0.194867i	−0.568150	+	0.822925i	$0.692341\pi$
$654$	−52.4807	−	7.91019i	−2.05216	−	0.309313i
$655$	8.42962	+	14.6005i	0.329372	+	0.570490i
$656$	−95.6568	+	165.682i	−3.73477	+	6.46881i
$657$	4.28984	−	5.37930i	0.167363	−	0.209866i
$658$	3.09650	−	13.6347i	0.120714	−	0.531536i
$659$	−27.4887	−	34.4697i	−1.07081	−	1.34275i	−0.936049	−	0.351871i	$-0.885546\pi$
$659$	−27.4887	−	34.4697i	−1.07081	−	1.34275i	−0.134758	−	0.990879i	$-0.543026\pi$
$660$	−137.622	+	20.7432i	−5.35695	+	0.807430i
$661$	−12.2086	−	8.32371i	−0.474861	−	0.323755i	0.302130	−	0.953267i	$-0.402302\pi$
$661$	−12.2086	−	8.32371i	−0.474861	−	0.323755i	−0.776991	+	0.629512i	$0.783255\pi$
$662$	−48.1055	−	32.7977i	−1.86967	−	1.27472i
$663$	0.552189	−	0.0832290i	0.0214452	−	0.00323235i
$664$	75.3658	+	94.5058i	2.92476	+	3.66754i
$665$	4.76474	−	5.98809i	0.184769	−	0.232208i
$666$	19.0657	−	23.9077i	0.738783	−	0.926404i
$667$	7.22780	−	12.5189i	0.279862	−	0.484735i
$668$	27.8590	+	48.2532i	1.07790	+	1.86697i
$669$	69.5879	+	10.4887i	2.69042	+	0.405516i
$670$	12.1995	+	11.3195i	0.471309	+	0.437311i
$671$	−0.688011	+	0.331329i	−0.0265604	+	0.0127908i
$672$	−147.935	+	137.562i	−5.70672	+	5.30658i
$673$	−0.820023	−	0.394902i	−0.0316096	−	0.0152224i	0.418012	−	0.908441i	$-0.362727\pi$
$673$	−0.820023	−	0.394902i	−0.0316096	−	0.0152224i	−0.449622	+	0.893219i	$0.648441\pi$
$674$	−6.45843	−	16.4558i	−0.248769	−	0.633854i
$675$	2.38752	+	31.8592i	0.0918955	+	1.22626i
$676$	5.32140	−	1.64144i	0.204669	−	0.0631321i
$677$	−2.23806	+	29.8648i	−0.0860154	+	1.14780i	0.772502	+	0.635012i	$0.219005\pi$
$677$	−2.23806	+	29.8648i	−0.0860154	+	1.14780i	−0.858518	+	0.512784i	$0.828614\pi$
$678$	37.7894	+	165.566i	1.45129	+	6.35853i
$679$	13.3234	−	2.02294i	0.511304	−	0.0776331i
$680$	−0.612323	+	2.68276i	−0.0234815	+	0.102879i
$681$	54.8980	+	16.9338i	2.10370	+	0.648905i
$682$	−14.0305	+	35.7491i	−0.537255	+	1.36890i
$683$	−4.38330	+	4.06711i	−0.167722	+	0.155624i	−0.759568	−	0.650427i	$-0.774590\pi$
$683$	−4.38330	+	4.06711i	−0.167722	+	0.155624i	0.591846	+	0.806051i	$0.298399\pi$
$684$	59.1934	−	40.3574i	2.26332	−	1.54310i
$685$	6.63746			0.253604
$686$	25.3325	−	44.2082i	0.967198	−	1.68788i
$687$	−24.4161			−0.931533
$688$	122.128	−	83.2657i	4.65610	−	3.17448i
$689$	−3.24486	+	3.01079i	−0.123619	+	0.114702i
$690$	−15.6019	+	39.7529i	−0.593953	+	1.51337i
$691$	28.2027	+	8.69939i	1.07288	+	0.330940i	0.780368	−	0.625321i	$-0.215032\pi$
$691$	28.2027	+	8.69939i	1.07288	+	0.330940i	0.292514	+	0.956261i	$0.405508\pi$
$692$	−26.6582	+	116.797i	−1.01339	+	4.43996i
$693$	91.5336	−	13.8979i	3.47707	−	0.527937i
$694$	1.55580	+	6.81642i	0.0590575	+	0.258748i
$695$	−2.14134	+	28.5743i	−0.0812258	+	1.08388i
$696$	140.577	−	43.3624i	5.32857	−	1.64365i
$697$	−0.158322	−	2.11266i	−0.00599688	−	0.0800227i
$698$	−4.81478	−	12.2679i	−0.182242	−	0.464345i
$699$	−68.1106	−	32.8003i	−2.57618	−	1.24062i
$700$	26.5213	−	24.6617i	1.00241	−	0.932124i
$701$	6.36680	−	3.06609i	0.240471	−	0.115805i	−0.309767	−	0.950812i	$-0.600251\pi$
$701$	6.36680	−	3.06609i	0.240471	−	0.115805i	0.550238	+	0.835008i	$0.314537\pi$
$702$	26.2128	+	24.3219i	0.989338	+	0.917972i
$703$	2.81163	+	0.423785i	0.106043	+	0.0159833i
$704$	84.8138	+	146.902i	3.19654	+	5.53657i
$705$	4.86450	−	8.42556i	0.183208	−	0.317325i
$706$	−26.6396	+	33.4050i	−1.00260	+	1.25721i
$707$	−3.86005	+	4.85112i	−0.145172	+	0.182445i
$708$	94.0141	+	117.890i	3.53327	+	4.43057i
$709$	47.8927	−	7.21867i	1.79865	−	0.271103i	0.837362	−	0.546649i	$-0.184097\pi$
$709$	47.8927	−	7.21867i	1.79865	−	0.271103i	0.961288	+	0.275546i	$0.0888587\pi$
$710$	−33.8882	−	23.1046i	−1.27180	−	0.867101i
$711$	−15.6162	−	10.6470i	−0.585655	−	0.399293i
$712$	50.1497	−	7.55885i	1.87944	−	0.283280i
$713$	5.40567	+	6.77849i	0.202444	+	0.253857i
$714$	0.900187	−	3.96376i	0.0336887	−	0.148340i
$715$	4.90519	−	6.15091i	0.183444	−	0.230031i
$716$	16.2599	−	28.1630i	0.607661	−	1.05250i
$717$	−3.33331	−	5.77346i	−0.124485	−	0.215614i
$718$	−68.9508	−	10.3927i	−2.57322	−	0.387851i
$719$	−12.1896	−	11.3103i	−0.454596	−	0.421803i	0.419352	−	0.907824i	$-0.362257\pi$
$719$	−12.1896	−	11.3103i	−0.454596	−	0.421803i	−0.873947	+	0.486021i	$0.838448\pi$
$720$	−161.705	+	77.8729i	−6.02638	+	2.90215i
$721$	−8.13200	−	1.21669i	−0.302851	−	0.0453121i
$722$	−38.9378	−	18.7515i	−1.44911	−	0.697857i
$723$	3.94725	+	10.0574i	0.146800	+	0.374040i
$724$	6.26132	+	83.5515i	0.232700	+	3.10517i
$725$	−11.0786	+	3.41730i	−0.411450	+	0.126915i
$726$	8.71839	−	116.339i	0.323570	−	4.31774i
$727$	−2.33566	−	10.2332i	−0.0866249	−	0.379529i	0.912969	−	0.408029i	$-0.133784\pi$
$727$	−2.33566	−	10.2332i	−0.0866249	−	0.379529i	−0.999594	+	0.0285007i	$0.990927\pi$
$728$	1.91319	−	25.9063i	0.0709076	−	0.960150i
$729$	−4.02080	+	17.6163i	−0.148919	+	0.652455i
$730$	−4.06664	−	1.25439i	−0.150513	−	0.0464271i
$731$	−0.598012	+	1.52371i	−0.0221183	+	0.0563564i
$732$	−2.00688	+	1.86211i	−0.0741763	+	0.0688255i
$733$	8.19451	−	5.58692i	0.302671	−	0.206358i	−0.402455	−	0.915440i	$-0.631843\pi$
$733$	8.19451	−	5.58692i	0.302671	−	0.206358i	0.705126	+	0.709082i	$0.250891\pi$
$734$	−68.9246			−2.54405
$735$	25.9372	−	24.1709i	0.956706	−	0.891558i
$736$	73.6624			2.71523
$737$	−15.4687	+	10.5464i	−0.569798	+	0.388482i
$738$	172.365	−	159.931i	6.34483	−	5.88714i
$739$	14.8358	−	37.8010i	0.545744	−	1.39053i	−0.346103	−	0.938196i	$-0.612495\pi$
$739$	14.8358	−	37.8010i	0.545744	−	1.39053i	0.891847	−	0.452337i	$-0.149409\pi$
$740$	−13.2979	−	4.10185i	−0.488840	−	0.150787i
$741$	−1.28237	+	5.61845i	−0.0471092	+	0.206399i
$742$	11.8037	+	29.9799i	0.433328	+	1.10060i
$743$	−0.282613	−	1.23821i	−0.0103681	−	0.0454255i	0.969479	−	0.245173i	$-0.0788449\pi$
$743$	−0.282613	−	1.23821i	−0.0103681	−	0.0454255i	−0.979847	+	0.199748i	$0.935988\pi$
$744$	−6.59373	+	87.9872i	−0.241738	+	3.22577i
$745$	34.1175	−	10.5238i	1.24997	−	0.385564i
$746$	4.18084	+	55.7894i	0.153071	+	2.04260i
$747$	−31.8968	−	81.2717i	−1.16704	−	2.97358i
$748$	−4.35210	−	2.09586i	−0.159129	−	0.0766323i
$749$	−2.64809	−	34.8300i	−0.0967591	−	1.27266i
$750$	93.6293	−	45.0895i	3.41886	−	1.64644i
$751$	−39.6440	−	36.7843i	−1.44663	−	1.34228i	−0.833806	−	0.552057i	$-0.813843\pi$
$751$	−39.6440	−	36.7843i	−1.44663	−	1.34228i	−0.612824	−	0.790219i	$-0.709967\pi$
$752$	−30.1517	−	4.54464i	−1.09952	−	0.165726i
$753$	10.7916	+	18.6915i	0.393266	+	0.681157i
$754$	−6.48814	+	11.2378i	−0.236284	+	0.409256i
$755$	−8.72011	+	10.9347i	−0.317357	+	0.397953i
$756$	172.448	−	83.2770i	6.27189	−	3.02875i
$757$	−8.75573	−	10.9793i	−0.318232	−	0.399051i	0.596827	−	0.802370i	$-0.296428\pi$
$757$	−8.75573	−	10.9793i	−0.318232	−	0.399051i	−0.915059	+	0.403319i	$0.867856\pi$
$758$	28.0595	−	4.22928i	1.01917	−	0.153615i
$759$	−39.6940	−	27.0629i	−1.44080	−	0.982321i
$760$	−23.4636	−	15.9972i	−0.851113	−	0.580279i
$761$	−22.4238	+	3.37984i	−0.812861	+	0.122519i	−0.542301	−	0.840184i	$-0.682447\pi$
$761$	−22.4238	+	3.37984i	−0.812861	+	0.122519i	−0.270560	+	0.962703i	$0.587209\pi$
$762$	70.9539	+	88.9734i	2.57039	+	3.22316i
$763$	−3.59220	−	15.6603i	−0.130047	−	0.566940i
$764$	51.0450	−	64.0084i	1.84674	−	2.31574i
$765$	0.993763	−	1.72125i	0.0359296	−	0.0622319i
$766$	49.8329	+	86.3131i	1.80053	+	3.11862i
$767$	−8.42839	−	1.27038i	−0.304332	−	0.0458706i
$768$	137.825	+	127.883i	4.97334	+	4.61459i
$769$	−41.0103	+	19.7495i	−1.47887	+	0.712186i	−0.987332	−	0.158669i	$-0.949280\pi$
$769$	−41.0103	+	19.7495i	−1.47887	+	0.712186i	−0.491539	+	0.870856i	$0.663565\pi$
$770$	−28.6862	−	49.5619i	−1.03378	−	1.78609i
$771$	18.6731	+	8.99251i	0.672497	+	0.323857i
$772$	6.95445	+	17.7196i	0.250296	+	0.637744i
$773$	2.85653	+	38.1177i	0.102742	+	1.37100i	0.775599	+	0.631226i	$0.217448\pi$
$773$	2.85653	+	38.1177i	0.102742	+	1.37100i	−0.672857	+	0.739773i	$0.734933\pi$
$774$	−173.597	+	53.5476i	−6.23982	+	1.92473i
$775$	0.519638	−	6.93409i	0.0186660	−	0.249080i
$776$	−11.1281	−	48.7555i	−0.399476	−	1.75022i
$777$	12.5923	+	3.86929i	0.451748	+	0.138810i
$778$	−23.5449	+	103.157i	−0.844126	+	3.69836i
$779$	20.8924	+	6.44445i	0.748548	+	0.230897i
$780$	10.3045	−	26.2553i	0.368959	−	0.940092i
$781$	33.8235	−	31.3837i	1.21030	−	1.12300i
$782$	−1.22463	+	0.834941i	−0.0437928	+	0.0298574i
$783$	−61.3057			−2.19089
$784$	−100.218	−	47.9953i	−3.57922	−	1.71412i
$785$	7.46949			0.266598
$786$	−76.3572	+	52.0594i	−2.72357	+	1.85690i
$787$	8.39014	−	7.78491i	0.299076	−	0.277502i	−0.516332	−	0.856388i	$-0.672703\pi$
$787$	8.39014	−	7.78491i	0.299076	−	0.277502i	0.815408	+	0.578886i	$0.196512\pi$
$788$	3.87490	−	9.87309i	0.138038	−	0.351714i
$789$	72.0557	+	22.2262i	2.56525	+	0.791275i
$790$	−2.60136	+	11.3973i	−0.0925524	+	0.405498i
$791$	−42.4463	+	29.0068i	−1.50922	+	1.03136i
$792$	−76.4519	−	334.958i	−2.71660	−	11.9022i
$793$	0.0115649	−	0.154322i	0.000410680	−	0.00548015i
$794$	−92.3240	+	28.4782i	−3.27646	+	1.01065i
$795$	1.67541	+	22.3568i	0.0594206	+	0.792913i
$796$	−24.8971	−	63.4367i	−0.882454	−	2.24846i
$797$	−17.0824	−	8.22643i	−0.605088	−	0.291395i	0.106146	−	0.994351i	$-0.466149\pi$
$797$	−17.0824	−	8.22643i	−0.605088	−	0.291395i	−0.711234	+	0.702956i	$0.751863\pi$
$798$	34.6843	+	23.5924i	1.22781	+	0.835160i
$799$	0.304229	−	0.146509i	0.0107628	−	0.00518311i
$800$	−43.3078	−	40.1838i	−1.53116	−	1.42071i
$801$	−36.2219	−	5.45958i	−1.27984	−	0.192905i
$802$	−42.4500	−	73.5256i	−1.49896	−	2.59628i
$803$	2.39377	−	4.14613i	0.0844743	−	0.146314i
$804$	−41.8484	+	52.4763i	−1.47588	+	1.85070i
$805$	−12.9281	+	0.0140027i	−0.455656	+	0.000493529i
$806$	−4.85247	−	6.08481i	−0.170921	−	0.214328i
$807$	61.0891	−	9.20769i	2.15044	−	0.324126i
$808$	19.0085	+	12.9598i	0.668717	+	0.455923i
$809$	−24.9160	−	16.9874i	−0.875999	−	0.597246i	0.0396553	−	0.999213i	$-0.487374\pi$
$809$	−24.9160	−	16.9874i	−0.875999	−	0.597246i	−0.915654	+	0.401968i	$0.868326\pi$
$810$	86.8126	−	13.0849i	3.05028	−	0.459756i
$811$	19.8296	+	24.8655i	0.696311	+	0.873146i	0.996742	−	0.0806574i	$-0.0257020\pi$
$811$	19.8296	+	24.8655i	0.696311	+	0.873146i	−0.300431	+	0.953804i	$0.597131\pi$
$812$	43.3877	+	54.2857i	1.52261	+	1.90505i
$813$	−18.3360	+	22.9926i	−0.643071	+	0.806386i
$814$	10.6388	−	18.4270i	0.372891	−	0.645867i
$815$	9.84268	+	17.0480i	0.344774	+	0.597166i
$816$	−8.76545	−	1.32118i	−0.306852	−	0.0462505i
$817$	−12.3830	−	11.4897i	−0.433225	−	0.401974i
$818$	80.8687	−	38.9443i	2.82751	−	1.36166i
$819$	−6.83577	+	17.4729i	−0.238861	+	0.610552i
$820$	−96.4089	−	46.4281i	−3.36674	−	1.62134i
$821$	−18.9405	−	48.2597i	−0.661030	−	1.68428i	−0.727163	−	0.686465i	$-0.759161\pi$
$821$	−18.9405	−	48.2597i	−0.661030	−	1.68428i	0.0661329	−	0.997811i	$-0.478934\pi$
$822$	2.71897	+	36.2821i	0.0948348	+	1.26548i
$823$	14.6160	−	4.50845i	0.509483	−	0.157155i	−0.0293471	−	0.999569i	$-0.509343\pi$
$823$	14.6160	−	4.50845i	0.509483	−	0.157155i	0.538830	+	0.842415i	$0.318867\pi$
$824$	−2.28028	+	30.4282i	−0.0794373	+	1.06002i
$825$	8.57385	+	37.5645i	0.298503	+	1.30783i
$826$	−30.9628	+	53.7635i	−1.07733	+	1.87067i
$827$	5.21779	−	22.8606i	0.181440	−	0.794941i	−0.799505	−	0.600659i	$-0.794905\pi$
$827$	5.21779	−	22.8606i	0.181440	−	0.794941i	0.980946	−	0.194283i	$-0.0622379\pi$
$828$	−115.656	−	35.6750i	−4.01931	−	1.23979i
$829$	−9.31534	+	23.7351i	−0.323535	+	0.824354i	0.672880	+	0.739752i	$0.265057\pi$
$829$	−9.31534	+	23.7351i	−0.323535	+	0.824354i	−0.996415	+	0.0846023i	$0.973038\pi$
$830$	−39.5861	+	36.7305i	−1.37405	+	1.27494i
$831$	−27.7412	+	18.9137i	−0.962333	+	0.656107i
$832$	−34.3761			−1.19178
$833$	1.21637	−	0.186033i	0.0421446	−	0.00644567i
$834$	−157.072			−5.43894
$835$	−13.1803	+	8.98616i	−0.456122	+	0.310979i
$836$	36.5429	−	33.9069i	1.26386	−	1.17269i
$837$	13.4333	−	34.2275i	0.464323	−	1.18308i
$838$	−17.5894	−	5.42560i	−0.607614	−	0.187424i
$839$	3.78770	−	16.5950i	0.130766	−	0.572923i	−0.866510	−	0.499160i	$-0.833642\pi$
$839$	3.78770	−	16.5950i	0.130766	−	0.572923i	0.997276	−	0.0737630i	$-0.0235008\pi$
$840$	−96.5431	−	89.3845i	−3.33105	−	3.08406i
$841$	1.50267	+	6.58363i	0.0518162	+	0.227022i
$842$	3.82750	−	51.0745i	0.131904	−	1.76014i
$843$	29.3119	−	9.04151i	1.00955	−	0.311406i
$844$	3.10181	+	41.3908i	0.106769	+	1.42473i
$845$	0.582484	+	1.48415i	0.0200381	+	0.0510562i
$846$	33.7650	+	16.2604i	1.16087	+	0.559044i
$847$	33.7377	−	10.4467i	1.15924	−	0.358954i
$848$	63.3078	−	30.4874i	2.17400	−	1.04694i
$849$	−36.7789	−	34.1258i	−1.26225	−	1.17120i
$850$	1.17546	+	0.177172i	0.0403180	+	0.00607696i
$851$	−2.40182	−	4.16008i	−0.0823333	−	0.142606i
$852$	82.7094	−	143.257i	2.83358	−	4.90790i
$853$	−22.5873	+	28.3236i	−0.773376	+	0.969783i	−0.999991	−	0.00420164i	$-0.998663\pi$
$853$	−22.5873	+	28.3236i	−0.773376	+	0.969783i	0.226615	+	0.973984i	$0.427234\pi$
$854$	−1.01542	−	0.487644i	−0.0347468	−	0.0166868i
$855$	12.7885	+	16.0363i	0.437359	+	0.548431i
$856$	−128.179	+	19.3198i	−4.38105	+	0.660338i
$857$	27.1951	+	18.5413i	0.928968	+	0.633360i	0.930363	−	0.366639i	$-0.119492\pi$
$857$	27.1951	+	18.5413i	0.928968	+	0.633360i	−0.00139482	+	0.999999i	$0.500444\pi$
$858$	35.6318	+	24.2934i	1.21645	+	0.829362i
$859$	−15.7282	+	2.37064i	−0.536638	+	0.0808852i	−0.411770	−	0.911288i	$-0.635089\pi$
$859$	−15.7282	+	2.37064i	−0.536638	+	0.0808852i	−0.124869	+	0.992173i	$0.539851\pi$
$860$	51.5468	+	64.6377i	1.75773	+	2.20413i
$861$	91.3109	+	43.8513i	3.11187	+	1.49445i
$862$	39.2634	−	49.2347i	1.33732	−	1.67694i
$863$	−20.1314	+	34.8685i	−0.685280	+	1.18694i	0.288069	+	0.957610i	$0.406987\pi$
$863$	−20.1314	+	34.8685i	−0.685280	+	1.18694i	−0.973349	+	0.229329i	$0.926347\pi$
$864$	−156.200	−	270.546i	−5.31403	−	9.20417i
$865$	−33.9160	−	5.11202i	−1.15318	−	0.173814i
$866$	−47.4188	−	43.9982i	−1.61136	−	1.49512i
$867$	−48.5677	+	23.3890i	−1.64944	+	0.794330i
$868$	−39.8153	+	12.3286i	−1.35142	+	0.418461i
$869$	−11.8490	−	5.70617i	−0.401949	−	0.193568i
$870$	24.0111	+	61.1794i	0.814054	+	2.07418i
$871$	−0.283534	−	3.78349i	−0.00960717	−	0.128199i
$872$	−56.9752	+	17.5745i	−1.92942	+	0.595149i
$873$	−2.69929	+	36.0196i	−0.0913572	+	1.21908i
$874$	−3.40369	−	14.9125i	−0.115132	−	0.504425i
$875$	23.0850	+	21.3732i	0.780414	+	0.722547i
$876$	3.81930	−	16.7334i	0.129042	−	0.565371i
$877$	45.6721	+	14.0880i	1.54224	+	0.475717i	0.945199	−	0.326496i	$-0.105868\pi$
$877$	45.6721	+	14.0880i	1.54224	+	0.475717i	0.597038	+	0.802213i	$0.296344\pi$
$878$	−1.21037	+	3.08398i	−0.0408482	+	0.104079i
$879$	9.53681	−	8.84887i	0.321669	−	0.298465i
$880$	−103.185	+	70.3507i	−3.47838	+	2.37152i
$881$	22.8118			0.768548			0.384274	−	0.923219i	$-0.374452\pi$
$881$	22.8118			0.768548			0.384274	+	0.923219i	$0.374452\pi$
$882$	100.313	+	92.6734i	3.37772	+	3.12048i
$883$	−44.0449			−1.48223			−0.741114	−	0.671379i	$-0.765702\pi$
$883$	−44.0449			−1.48223			−0.741114	+	0.671379i	$0.765702\pi$
$884$	0.808825	−	0.551448i	0.0272037	−	0.0185472i
$885$	−31.6462	+	29.3634i	−1.06378	+	0.987040i
$886$	−4.49959	+	11.4648i	−0.151167	+	0.385167i
$887$	−27.2405	−	8.40259i	−0.914648	−	0.282131i	−0.198517	−	0.980097i	$-0.563612\pi$
$887$	−27.2405	−	8.40259i	−0.914648	−	0.282131i	−0.716131	+	0.697966i	$0.754089\pi$
$888$	10.8782	−	47.6605i	0.365048	−	1.59938i
$889$	−17.1932	+	29.8542i	−0.576643	+	1.00128i
$890$	5.04173	+	22.0893i	0.168999	+	0.740434i
$891$	−7.38069	+	98.4885i	−0.247263	+	3.29949i
$892$	117.885	−	36.3627i	3.94709	−	1.21751i
$893$	0.260414	+	3.47499i	0.00871443	+	0.116286i
$894$	71.5020	+	182.184i	2.39138	+	6.09315i
$895$	8.38844	+	4.03966i	0.280395	+	0.135031i
$896$	−44.8262	+	114.580i	−1.49754	+	3.82785i
$897$	8.77180	−	4.22427i	0.292882	−	0.141044i
$898$	−18.7817	−	17.4268i	−0.626753	−	0.581541i
$899$	13.1941	+	1.98868i	0.440046	+	0.0663263i
$900$	48.5354	+	84.0657i	1.61785	+	2.80219i
$901$	−0.389061	+	0.673873i	−0.0129615	+	0.0224500i
$902$	102.010	−	127.916i	3.39656	−	4.25915i
$903$	−48.8619	−	61.1350i	−1.62602	−	2.03444i
$904$	118.952	+	149.162i	3.95630	+	4.96104i
$905$	−23.7201	+	3.57522i	−0.788481	+	0.118844i
$906$	−63.3439	−	43.1871i	−2.10446	−	1.43480i
$907$	−16.2328	−	11.0673i	−0.539002	−	0.367485i	0.263010	−	0.964793i	$-0.415285\pi$
$907$	−16.2328	−	11.0673i	−0.539002	−	0.367485i	−0.802012	+	0.597308i	$0.796237\pi$
$908$	99.5861	−	15.0102i	3.30488	−	0.498130i
$909$	−10.3604	−	12.9915i	−0.343631	−	0.430900i
$910$	11.6051	−	0.0125697i	0.384705	−	0.000416681i
$911$	−15.2170	+	19.0815i	−0.504160	+	0.632197i	−0.967162	−	0.254161i	$-0.918201\pi$
$911$	−15.2170	+	19.0815i	−0.504160	+	0.632197i	0.463002	+	0.886357i	$0.346772\pi$
$912$	45.7405	−	79.2248i	1.51462	−	2.62340i
$913$	−30.3752	−	52.6113i	−1.00527	−	1.74118i
$914$	−17.4199	−	2.62563i	−0.576200	−	0.0868481i
$915$	−0.574572	−	0.533125i	−0.0189948	−	0.0176246i
$916$	−38.5629	+	18.5709i	−1.27416	+	0.613601i
$917$	−23.1327	−	15.7350i	−0.763910	−	0.519614i
$918$	5.66337	+	2.72734i	0.186919	+	0.0900155i
$919$	4.62897	+	11.7944i	0.152696	+	0.389062i	0.986668	−	0.162743i	$-0.0520343\pi$
$919$	4.62897	+	11.7944i	0.152696	+	0.389062i	−0.833973	+	0.551806i	$0.813939\pi$
$920$	3.58524	+	47.8417i	0.118202	+	1.57730i
$921$	−2.69008	+	0.829780i	−0.0886412	+	0.0273422i
$922$	2.57386	−	34.3457i	0.0847654	−	1.13112i
$923$	2.08073	+	9.11625i	0.0684879	+	0.300065i
$924$	190.684	−	130.309i	6.27305	−	4.28685i
$925$	−0.857289	+	3.75603i	−0.0281875	+	0.123497i
$926$	9.62617	+	2.96928i	0.316335	+	0.0975766i
$927$	8.05182	−	20.5157i	0.264457	−	0.673824i
$928$	83.1030	−	77.1083i	2.72799	−	2.53121i
$929$	13.7590	−	9.38075i	0.451419	−	0.307772i	−0.316184	−	0.948698i	$-0.602402\pi$
$929$	13.7590	−	9.38075i	0.451419	−	0.307772i	0.767603	+	0.640926i	$0.221449\pi$
$930$	−39.4183			−1.29258
$931$	−2.79893	+	12.3865i	−0.0917312	+	0.405952i
$932$	−132.522			−4.34091
$933$	−71.6660	+	48.8610i	−2.34624	+	1.59964i
$934$	−37.9958	+	35.2549i	−1.24326	+	1.15358i
$935$	0.505256	−	1.28737i	0.0165236	−	0.0421015i
$936$	66.5336	+	20.5229i	2.17472	+	0.670812i
$937$	−5.47562	+	23.9903i	−0.178881	+	0.783728i	0.803267	+	0.595619i	$0.203093\pi$
$937$	−5.47562	+	23.9903i	−0.178881	+	0.783728i	−0.982148	+	0.188109i	$0.939764\pi$
$938$	−26.3986	−	8.11158i	−0.861944	−	0.264852i
$939$	11.5961	+	50.8060i	0.378426	+	1.65799i
$940$	1.27452	−	17.0073i	0.0415703	−	0.554717i
$941$	30.1179	−	9.29013i	0.981814	−	0.302850i	0.238021	−	0.971260i	$-0.423501\pi$
$941$	30.1179	−	9.29013i	0.981814	−	0.302850i	0.743793	+	0.668410i	$0.233025\pi$
$942$	3.05980	+	40.8302i	0.0996937	+	1.33032i
$943$	−13.4945	−	34.3835i	−0.439442	−	1.11968i
$944$	121.904	+	58.7060i	3.96765	+	1.91072i
$945$	27.4652	+	47.4524i	0.893444	+	1.54363i
$946$	−113.891	+	54.8469i	−3.70291	+	1.78323i
$947$	23.3298	+	21.6469i	0.758118	+	0.703431i	0.961237	−	0.275723i	$-0.0889173\pi$
$947$	23.3298	+	21.6469i	0.758118	+	0.703431i	−0.203119	+	0.979154i	$0.565108\pi$
$948$	−46.6223	−	7.02718i	−1.51422	−	0.228232i
$949$	0.485112	+	0.840239i	0.0157474	+	0.0272753i
$950$	−6.13388	+	10.6242i	−0.199009	+	0.344694i
$951$	−39.3351	+	49.3246i	−1.27553	+	1.59946i
$952$	−1.02094	−	4.45080i	−0.0330888	−	0.144251i
$953$	−13.9634	−	17.5096i	−0.452319	−	0.567190i	0.502424	−	0.864621i	$-0.332442\pi$
$953$	−13.9634	−	17.5096i	−0.452319	−	0.567190i	−0.954743	+	0.297431i	$0.903870\pi$
$954$	−85.3959	+	12.8714i	−2.76479	+	0.416726i
$955$	19.3666	+	13.2039i	0.626688	+	0.427268i
$956$	−9.65595	−	6.58332i	−0.312296	−	0.212920i
$957$	−73.1101	+	11.0196i	−2.36331	+	0.356212i
$958$	18.7816	+	23.5514i	0.606806	+	0.760911i
$959$	−9.91854	+	4.78976i	−0.320286	+	0.154669i
$960$	−108.555	+	136.124i	−3.50360	+	4.39337i
$961$	11.4986	−	19.9162i	0.370923	−	0.642458i
$962$	2.15603	+	3.73435i	0.0695131	+	0.120400i
$963$	92.5803	+	13.9542i	2.98336	+	0.449669i
$964$	13.8840	+	12.8825i	0.447173	+	0.414916i
$965$	−4.91018	+	2.36462i	−0.158064	+	0.0761198i
$966$	−5.37241	−	70.6626i	−0.172854	−	2.27353i
$967$	−19.9473	−	9.60612i	−0.641462	−	0.308912i	0.0847296	−	0.996404i	$-0.472997\pi$
$967$	−19.9473	−	9.60612i	−0.641462	−	0.308912i	−0.726192	+	0.687492i	$0.758712\pi$
$968$	−47.8833	−	122.005i	−1.53903	−	3.92137i
$969$	0.0757053	+	1.01022i	0.00243201	+	0.0324529i
$970$	21.3490	−	6.58529i	0.685475	−	0.211441i
$971$	−4.31996	+	57.6459i	−0.138634	+	1.84995i	0.303296	+	0.952896i	$0.401913\pi$
$971$	−4.31996	+	57.6459i	−0.138634	+	1.84995i	−0.441930	+	0.897049i	$0.645706\pi$
$972$	30.4712	+	133.503i	0.977364	+	4.28211i
$973$	−17.4200	−	44.2446i	−0.558461	−	1.41842i
$974$	3.62128	−	15.8659i	0.116033	−	0.508375i
$975$	−7.46154	−	2.30158i	−0.238960	−	0.0737095i
$976$	−0.897491	+	2.28677i	−0.0287280	+	0.0731977i
$977$	−18.3042	+	16.9838i	−0.585603	+	0.543360i	−0.916360	−	0.400356i	$-0.868887\pi$
$977$	−18.3042	+	16.9838i	−0.585603	+	0.543360i	0.330757	+	0.943716i	$0.392696\pi$
$978$	−89.1570	+	60.7862i	−2.85093	+	1.94373i
$979$	−25.4888			−0.814626
$980$	22.5808	−	57.9035i	0.721318	−	1.84966i
$981$	43.0651			1.37496
$982$	1.77496	−	1.21014i	0.0566411	−	0.0386173i
$983$	4.17813	−	3.87673i	0.133262	−	0.123649i	−0.610726	−	0.791842i	$-0.709122\pi$
$983$	4.17813	−	3.87673i	0.133262	−	0.123649i	0.743988	+	0.668193i	$0.232932\pi$
$984$	137.332	−	349.917i	4.37800	−	11.1550i
$985$	2.90168	+	0.895050i	0.0924552	+	0.0285187i
$986$	−0.507584	+	2.22387i	−0.0161648	+	0.0708224i
$987$	−1.18906	+	16.1009i	−0.0378482	+	0.512497i
$988$	2.24801	+	9.84919i	0.0715188	+	0.313344i
$989$	−2.13265	+	28.4583i	−0.0678144	+	0.904920i
$990$	146.671	−	45.2420i	4.66151	−	1.43788i
$991$	0.579212	+	7.72905i	0.0183993	+	0.245521i	0.998818	+	0.0485990i	$0.0154756\pi$
$991$	0.579212	+	7.72905i	0.0183993	+	0.245521i	−0.980419	+	0.196922i	$0.936905\pi$
$992$	24.8407	+	63.2931i	0.788694	+	2.00956i
$993$	60.5708	+	29.1694i	1.92216	+	0.925662i
$994$	67.3131	+	10.0713i	2.13504	+	0.319441i
$995$	17.5786	−	8.46539i	0.557278	−	0.268371i
$996$	−159.655	−	148.139i	−5.05888	−	4.69395i
$997$	35.1275	+	5.29462i	1.11250	+	0.167682i	0.679474	−	0.733700i	$-0.262208\pi$
$997$	35.1275	+	5.29462i	1.11250	+	0.167682i	0.433025	+	0.901382i	$0.357446\pi$
$998$	50.0379	+	86.6682i	1.58392	+	2.74343i
$999$	−10.1860	+	17.6427i	−0.322272	+	0.558191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.625.1	yes	324
49.4	even	21	inner	637.2.bl.a.53.1	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.1	✓	324	49.4	even	21	inner
637.2.bl.a.625.1	yes	324	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27310 + 1.54978i) q^{2} +(2.32870 - 2.16072i) q^{3} +(2.03451 - 5.18386i) q^{4} +(1.52353 + 0.469945i) q^{5} +(-1.94475 + 8.52050i) q^{6} +(-2.61577 + 0.397162i) q^{7} +(2.18478 + 9.57215i) q^{8} +(0.529951 - 7.07171i) q^{9} +O(q^{10})\)	\(q+(-2.27310 + 1.54978i) q^{2} +(2.32870 - 2.16072i) q^{3} +(2.03451 - 5.18386i) q^{4} +(1.52353 + 0.469945i) q^{5} +(-1.94475 + 8.52050i) q^{6} +(-2.61577 + 0.397162i) q^{7} +(2.18478 + 9.57215i) q^{8} +(0.529951 - 7.07171i) q^{9} +(-4.19144 + 1.29289i) q^{10} +(-0.368753 - 4.92067i) q^{11} +(-6.46308 - 16.4677i) q^{12} +(0.900969 + 0.433884i) q^{13} +(5.33041 - 4.95665i) q^{14} +(4.56325 - 2.19755i) q^{15} +(-11.6365 - 10.7971i) q^{16} +(0.173824 + 0.0261997i) q^{17} +(9.75493 + 16.8960i) q^{18} +(-0.907059 + 1.57107i) q^{19} +(5.53576 - 6.94163i) q^{20} +(-5.23319 + 6.57681i) q^{21} +(8.46415 + 10.6137i) q^{22} +(3.03055 - 0.456783i) q^{23} +(25.7704 + 17.5700i) q^{24} +(-2.03091 - 1.38465i) q^{25} +(-2.72042 + 0.410037i) q^{26} +(-8.10390 - 10.1620i) q^{27} +(-3.26299 + 14.3678i) q^{28} +(2.94080 - 3.68765i) q^{29} +(-6.96704 + 12.0673i) q^{30} +(1.41446 + 2.44991i) q^{31} +(23.7666 + 3.58225i) q^{32} +(-11.4909 - 10.6620i) q^{33} +(-0.435723 + 0.209833i) q^{34} +(-4.17184 - 0.624183i) q^{35} +(-35.5805 - 17.1347i) q^{36} +(-0.572623 - 1.45902i) q^{37} +(-0.372971 - 4.97695i) q^{38} +(3.03558 - 0.936354i) q^{39} +(-1.16982 + 15.6101i) q^{40} +(-2.68182 - 11.7498i) q^{41} +(1.70300 - 23.0601i) q^{42} +(-2.07203 + 9.07814i) q^{43} +(-26.2583 - 8.09961i) q^{44} +(4.13071 - 10.5249i) q^{45} +(-6.18086 + 5.73500i) q^{46} +(1.58712 - 1.08208i) q^{47} -50.4272 q^{48} +(6.68452 - 2.07777i) q^{49} +6.76238 q^{50} +(0.461393 - 0.314572i) q^{51} +(4.08223 - 3.78775i) q^{52} +(-1.61718 + 4.12052i) q^{53} +(34.1698 + 10.5400i) q^{54} +(1.75064 - 7.67006i) q^{55} +(-9.51658 - 24.1708i) q^{56} +(1.28237 + 5.61845i) q^{57} +(-0.969718 + 12.9400i) q^{58} +(-8.14491 + 2.51237i) q^{59} +(-2.10777 - 28.1262i) q^{60} +(-0.0565384 - 0.144057i) q^{61} +(-7.01202 - 3.37681i) q^{62} +(1.42238 + 18.7084i) q^{63} +(-30.9718 + 14.9152i) q^{64} +(1.16875 + 1.08444i) q^{65} +(42.6437 + 6.42750i) q^{66} +(-1.89705 - 3.28579i) q^{67} +(0.489462 - 0.847773i) q^{68} +(6.07027 - 7.61188i) q^{69} +(10.4504 - 5.04658i) q^{70} +(5.83006 + 7.31067i) q^{71} +(68.8492 - 10.3774i) q^{72} +(0.801637 + 0.546547i) q^{73} +(3.56279 + 2.42907i) q^{74} +(-7.72123 + 1.16379i) q^{75} +(6.29879 + 7.89843i) q^{76} +(2.91888 + 12.7249i) q^{77} +(-5.44906 + 6.83291i) q^{78} +(1.33260 - 2.30814i) q^{79} +(-12.6544 - 21.9181i) q^{80} +(-19.7917 - 2.98312i) q^{81} +(24.3057 + 22.5524i) q^{82} +(11.0922 - 5.34173i) q^{83} +(23.4463 + 40.5087i) q^{84} +(0.252512 + 0.121603i) q^{85} +(-9.35916 - 23.8467i) q^{86} +(-1.11972 - 14.9417i) q^{87} +(46.2958 - 14.2803i) q^{88} +(0.386015 - 5.15102i) q^{89} +(6.92167 + 30.3258i) q^{90} +(-2.52905 - 0.777110i) q^{91} +(3.79781 - 16.6393i) q^{92} +(8.58741 + 2.64887i) q^{93} +(-1.93070 + 4.91935i) q^{94} +(-2.12025 + 1.96730i) q^{95} +(63.0856 - 43.0110i) q^{96} -5.09347 q^{97} +(-11.9745 + 15.0825i) q^{98} -34.9930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

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