LMFDB - Embedded newform 430.2.q.d.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			111.1
Character	$\chi$	$=$	430.111
Dual form			430.2.q.d.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 + 0.433884i) q^{2} +(-2.40821 - 1.64189i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(-1.45733 - 2.52418i) q^{6} +(0.522354 - 0.904743i) q^{7} +(0.222521 + 0.974928i) q^{8} +(2.00766 + 5.11543i) q^{9} +O(q^{10})$	\(q+(0.900969 + 0.433884i) q^{2} +(-2.40821 - 1.64189i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(-1.45733 - 2.52418i) q^{6} +(0.522354 - 0.904743i) q^{7} +(0.222521 + 0.974928i) q^{8} +(2.00766 + 5.11543i) q^{9} +(0.955573 - 0.294755i) q^{10} +(2.20440 - 2.76423i) q^{11} +(-0.217814 - 2.90652i) q^{12} +(-5.22187 - 1.61073i) q^{13} +(0.863178 - 0.588505i) q^{14} +(-2.88212 + 0.434409i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-2.57679 - 2.39091i) q^{17} +(-0.410664 + 5.47993i) q^{18} +(2.60916 - 6.64804i) q^{19} +(0.988831 + 0.149042i) q^{20} +(-2.74343 + 1.32117i) q^{21} +(3.18545 - 1.53403i) q^{22} +(-3.93952 - 0.593787i) q^{23} +(1.06485 - 2.71319i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-4.00587 - 3.71691i) q^{26} +(1.61839 - 7.09063i) q^{27} +(1.03304 - 0.155706i) q^{28} +(0.787579 - 0.536962i) q^{29} +(-2.78518 - 0.859114i) q^{30} +(-0.296574 - 3.95750i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(-9.84723 + 3.03747i) q^{33} +(-1.28423 - 3.27216i) q^{34} +(-0.232469 - 1.01851i) q^{35} +(-2.74765 + 4.75907i) q^{36} +(2.42401 + 4.19850i) q^{37} +(5.23525 - 4.85760i) q^{38} +(9.93073 + 12.4527i) q^{39} +(0.826239 + 0.563320i) q^{40} +(-5.47980 - 2.63893i) q^{41} -3.04498 q^{42} +(6.28197 - 1.88066i) q^{43} +3.53558 q^{44} +(4.95109 + 2.38432i) q^{45} +(-3.29175 - 2.24428i) q^{46} +(3.84478 + 4.82120i) q^{47} +(2.13660 - 1.98248i) q^{48} +(2.95429 + 5.11699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(2.27984 + 9.98864i) q^{51} +(-1.99646 - 5.08690i) q^{52} +(9.18936 - 2.83454i) q^{53} +(4.53463 - 5.68624i) q^{54} +(-0.264214 - 3.52569i) q^{55} +(0.998294 + 0.307933i) q^{56} +(-17.1988 + 11.7259i) q^{57} +(0.942564 - 0.142069i) q^{58} +(1.18177 - 5.17767i) q^{59} +(-2.13660 - 1.98248i) q^{60} +(-0.892678 + 11.9120i) q^{61} +(1.44989 - 3.69426i) q^{62} +(5.67686 + 0.855649i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-4.92348 + 2.37102i) q^{65} +(-10.1900 - 1.53589i) q^{66} +(-0.504308 + 1.28495i) q^{67} +(0.262688 - 3.50533i) q^{68} +(8.51226 + 7.89822i) q^{69} +(0.232469 - 1.01851i) q^{70} +(3.18215 - 0.479632i) q^{71} +(-4.54043 + 3.09561i) q^{72} +(-15.8333 - 4.88393i) q^{73} +(0.362292 + 4.83446i) q^{74} +(-1.81727 + 2.27878i) q^{75} +(6.82443 - 2.10506i) q^{76} +(-1.34944 - 3.43832i) q^{77} +(3.54424 + 15.5283i) q^{78} +(-1.86047 + 3.22242i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.45445 + 3.20526i) q^{81} +(-3.79214 - 4.75519i) q^{82} +(6.79027 + 4.62953i) q^{83} +(-2.74343 - 1.32117i) q^{84} -3.51515 q^{85} +(6.47584 + 1.03123i) q^{86} -2.77829 q^{87} +(3.18545 + 1.53403i) q^{88} +(12.6282 + 8.60978i) q^{89} +(3.42626 + 4.29640i) q^{90} +(-4.18497 + 3.88308i) q^{91} +(-1.99201 - 3.45026i) q^{92} +(-5.78358 + 10.0174i) q^{93} +(1.37218 + 6.01194i) q^{94} +(-2.60916 - 6.64804i) q^{95} +(2.78518 - 0.859114i) q^{96} +(1.84086 - 2.30837i) q^{97} +(0.441549 + 5.89206i) q^{98} +(18.5659 + 5.72682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$2$	0.900969	+	0.433884i	0.637081	+	0.306802i
$3$	−2.40821	−	1.64189i	−1.39038	−	0.947947i	−0.999623	−	0.0274539i	$-0.991260\pi$
$3$	−2.40821	−	1.64189i	−1.39038	−	0.947947i	−0.390759	−	0.920493i	$-0.627788\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	0.733052	−	0.680173i	0.327831	−	0.304182i
$5$	0.733052	−	0.680173i	0.327831	−	0.304182i
$6$	−1.45733	−	2.52418i	−0.594954	−	1.03049i
$7$	0.522354	−	0.904743i	0.197431	−	0.341961i	−0.750264	−	0.661139i	$-0.770073\pi$
$7$	0.522354	−	0.904743i	0.197431	−	0.341961i	0.947695	+	0.319178i	$0.103407\pi$
$8$	0.222521	+	0.974928i	0.0786730	+	0.344689i
$9$	2.00766	+	5.11543i	0.669219	+	1.70514i
$10$	0.955573	−	0.294755i	0.302179	−	0.0932098i
$11$	2.20440	−	2.76423i	0.664651	−	0.833446i	−0.329190	−	0.944264i	$-0.606776\pi$
$11$	2.20440	−	2.76423i	0.664651	−	0.833446i	0.993841	+	0.110818i	$0.0353469\pi$
$12$	−0.217814	−	2.90652i	−0.0628774	−	0.839040i
$13$	−5.22187	−	1.61073i	−1.44829	−	0.446737i	−0.531823	−	0.846855i	$-0.678493\pi$
$13$	−5.22187	−	1.61073i	−1.44829	−	0.446737i	−0.916464	+	0.400118i	$0.868969\pi$
$14$	0.863178	−	0.588505i	0.230694	−	0.157285i
$15$	−2.88212	+	0.434409i	−0.744159	+	0.112164i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−2.57679	−	2.39091i	−0.624963	−	0.579881i	0.302798	−	0.953055i	$-0.402079\pi$
$17$	−2.57679	−	2.39091i	−0.624963	−	0.579881i	−0.927762	+	0.373173i	$0.878270\pi$
$18$	−0.410664	+	5.47993i	−0.0967945	+	1.29163i
$19$	2.60916	−	6.64804i	0.598583	−	1.52516i	−0.234558	−	0.972102i	$-0.575364\pi$
$19$	2.60916	−	6.64804i	0.598583	−	1.52516i	0.833140	−	0.553062i	$-0.186541\pi$
$20$	0.988831	+	0.149042i	0.221109	+	0.0333269i
$21$	−2.74343	+	1.32117i	−0.598666	+	0.288302i
$22$	3.18545	−	1.53403i	0.679140	−	0.327057i
$23$	−3.93952	−	0.593787i	−0.821446	−	0.123813i	−0.275146	−	0.961403i	$-0.588726\pi$
$23$	−3.93952	−	0.593787i	−0.821446	−	0.123813i	−0.546300	+	0.837589i	$0.683964\pi$
$24$	1.06485	−	2.71319i	0.217361	−	0.553827i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	−4.00587	−	3.71691i	−0.785617	−	0.728946i
$27$	1.61839	−	7.09063i	0.311459	−	1.36459i
$28$	1.03304	−	0.155706i	0.195226	−	0.0294256i
$29$	0.787579	−	0.536962i	0.146250	−	0.0997114i	−0.487985	−	0.872852i	$-0.662268\pi$
$29$	0.787579	−	0.536962i	0.146250	−	0.0997114i	0.634234	+	0.773141i	$0.281315\pi$
$30$	−2.78518	−	0.859114i	−0.508502	−	0.156852i
$31$	−0.296574	−	3.95750i	−0.0532662	−	0.710788i	−0.958358	−	0.285571i	$-0.907817\pi$
$31$	−0.296574	−	3.95750i	−0.0532662	−	0.710788i	0.905091	−	0.425217i	$-0.139802\pi$
$32$	−0.623490	+	0.781831i	−0.110218	+	0.138210i
$33$	−9.84723	+	3.03747i	−1.71418	+	0.528755i
$34$	−1.28423	−	3.27216i	−0.220244	−	0.561172i
$35$	−0.232469	−	1.01851i	−0.0392945	−	0.172160i
$36$	−2.74765	+	4.75907i	−0.457942	+	0.793178i
$37$	2.42401	+	4.19850i	0.398504	+	0.690230i	0.993542	−	0.113468i	$-0.0361961\pi$
$37$	2.42401	+	4.19850i	0.398504	+	0.690230i	−0.595037	+	0.803698i	$0.702863\pi$
$38$	5.23525	−	4.85760i	0.849269	−	0.788007i
$39$	9.93073	+	12.4527i	1.59019	+	1.99403i
$40$	0.826239	+	0.563320i	0.130640	+	0.0890687i
$41$	−5.47980	−	2.63893i	−0.855801	−	0.412132i	−0.0460734	−	0.998938i	$-0.514671\pi$
$41$	−5.47980	−	2.63893i	−0.855801	−	0.412132i	−0.809728	+	0.586806i	$0.800385\pi$
$42$	−3.04498			−0.469850
$43$	6.28197	−	1.88066i	0.957991	−	0.286797i
$43$	6.28197	−	1.88066i	0.957991	−	0.286797i
$44$	3.53558			0.533009
$45$	4.95109	+	2.38432i	0.738065	+	0.355434i
$46$	−3.29175	−	2.24428i	−0.485342	−	0.330900i
$47$	3.84478	+	4.82120i	0.560818	+	0.703244i	0.978709	−	0.205253i	$-0.0658019\pi$
$47$	3.84478	+	4.82120i	0.560818	+	0.703244i	−0.417891	+	0.908497i	$0.637230\pi$
$48$	2.13660	−	1.98248i	0.308392	−	0.286146i
$49$	2.95429	+	5.11699i	0.422042	+	0.730998i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	2.27984	+	9.98864i	0.319242	+	1.39869i
$52$	−1.99646	−	5.08690i	−0.276859	−	0.705426i
$53$	9.18936	−	2.83454i	1.26226	−	0.389354i	0.409810	−	0.912171i	$-0.365595\pi$
$53$	9.18936	−	2.83454i	1.26226	−	0.389354i	0.852445	+	0.522817i	$0.175119\pi$
$54$	4.53463	−	5.68624i	0.617084	−	0.773799i
$55$	−0.264214	−	3.52569i	−0.0356266	−	0.475405i
$56$	0.998294	+	0.307933i	0.133403	+	0.0411493i
$57$	−17.1988	+	11.7259i	−2.27803	+	1.55314i
$58$	0.942564	−	0.142069i	0.123765	−	0.0186545i
$59$	1.18177	−	5.17767i	0.153853	−	0.674075i	−0.837890	−	0.545838i	$-0.816211\pi$
$59$	1.18177	−	5.17767i	0.153853	−	0.674075i	0.991744	−	0.128236i	$-0.0409316\pi$
$60$	−2.13660	−	1.98248i	−0.275834	−	0.255937i
$61$	−0.892678	+	11.9120i	−0.114296	+	1.52517i	0.585409	+	0.810738i	$0.300934\pi$
$61$	−0.892678	+	11.9120i	−0.114296	+	1.52517i	−0.699705	+	0.714432i	$0.746685\pi$
$62$	1.44989	−	3.69426i	0.184136	−	0.469172i
$63$	5.67686	+	0.855649i	0.715217	+	0.107802i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	−4.92348	+	2.37102i	−0.610683	+	0.294089i
$66$	−10.1900	−	1.53589i	−1.25430	−	0.189055i
$67$	−0.504308	+	1.28495i	−0.0616110	+	0.156982i	−0.958364	−	0.285549i	$-0.907824\pi$
$67$	−0.504308	+	1.28495i	−0.0616110	+	0.156982i	0.896753	+	0.442531i	$0.145919\pi$
$68$	0.262688	−	3.50533i	0.0318556	−	0.425083i
$69$	8.51226	+	7.89822i	1.02476	+	0.950835i
$70$	0.232469	−	1.01851i	0.0277854	−	0.121736i
$71$	3.18215	−	0.479632i	0.377652	−	0.0569218i	0.0425263	−	0.999095i	$-0.486459\pi$
$71$	3.18215	−	0.479632i	0.377652	−	0.0569218i	0.335125	+	0.942174i	$0.391221\pi$
$72$	−4.54043	+	3.09561i	−0.535095	+	0.364821i
$73$	−15.8333	−	4.88393i	−1.85315	−	0.571621i	−0.998637	−	0.0521903i	$-0.983380\pi$
$73$	−15.8333	−	4.88393i	−1.85315	−	0.571621i	−0.854513	−	0.519431i	$-0.826144\pi$
$74$	0.362292	+	4.83446i	0.0421156	+	0.561994i
$75$	−1.81727	+	2.27878i	−0.209840	+	0.263131i
$76$	6.82443	−	2.10506i	0.782816	−	0.241467i
$77$	−1.34944	−	3.43832i	−0.153783	−	0.391833i
$78$	3.54424	+	15.5283i	0.401306	+	1.75824i
$79$	−1.86047	+	3.22242i	−0.209319	+	0.362551i	−0.951500	−	0.307648i	$-0.900458\pi$
$79$	−1.86047	+	3.22242i	−0.209319	+	0.362551i	0.742181	+	0.670199i	$0.233791\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.45445	+	3.20526i	−0.383827	+	0.356140i
$82$	−3.79214	−	4.75519i	−0.418772	−	0.525123i
$83$	6.79027	+	4.62953i	0.745329	+	0.508157i	0.875431	−	0.483344i	$-0.160578\pi$
$83$	6.79027	+	4.62953i	0.745329	+	0.508157i	−0.130101	+	0.991501i	$0.541530\pi$
$84$	−2.74343	−	1.32117i	−0.299333	−	0.144151i
$85$	−3.51515			−0.381272
$86$	6.47584	+	1.03123i	0.698308	+	0.111201i
$87$	−2.77829			−0.297864
$88$	3.18545	+	1.53403i	0.339570	+	0.163528i
$89$	12.6282	+	8.60978i	1.33859	+	0.912635i	0.999604	−	0.0281563i	$-0.00896361\pi$
$89$	12.6282	+	8.60978i	1.33859	+	0.912635i	0.338986	+	0.940791i	$0.389916\pi$
$90$	3.42626	+	4.29640i	0.361160	+	0.452880i
$91$	−4.18497	+	3.88308i	−0.438704	+	0.407058i
$92$	−1.99201	−	3.45026i	−0.207681	−	0.359714i
$93$	−5.78358	+	10.0174i	−0.599729	+	1.03876i
$94$	1.37218	+	6.01194i	0.141530	+	0.620084i
$95$	−2.60916	−	6.64804i	−0.267694	−	0.682074i
$96$	2.78518	−	0.859114i	0.284261	−	0.0876830i
$97$	1.84086	−	2.30837i	0.186911	−	0.234380i	−0.679543	−	0.733636i	$-0.737822\pi$
$97$	1.84086	−	2.30837i	0.186911	−	0.234380i	0.866454	+	0.499256i	$0.166393\pi$
$98$	0.441549	+	5.89206i	0.0446032	+	0.595188i
$99$	18.5659	+	5.72682i	1.86594	+	0.575567i
$100$	0.826239	−	0.563320i	0.0826239	−	0.0563320i
$101$	1.62166	−	0.244426i	0.161361	−	0.0243213i	−0.0678647	−	0.997695i	$-0.521619\pi$
$101$	1.62166	−	0.244426i	0.161361	−	0.0243213i	0.229226	+	0.973373i	$0.426381\pi$
$102$	−2.27984	+	9.98864i	−0.225738	+	0.989022i
$103$	5.17532	+	4.80200i	0.509940	+	0.473155i	0.892674	−	0.450704i	$-0.148827\pi$
$103$	5.17532	+	4.80200i	0.509940	+	0.473155i	−0.382734	+	0.923859i	$0.625017\pi$
$104$	0.408374	−	5.44937i	0.0400444	−	0.534355i
$105$	−1.11246	+	2.83449i	−0.108565	+	0.276618i
$106$	9.50919	+	1.43328i	0.923614	+	0.139212i
$107$	9.71324	−	4.67765i	0.939015	−	0.452206i	0.0991932	−	0.995068i	$-0.468374\pi$
$107$	9.71324	−	4.67765i	0.939015	−	0.452206i	0.839822	+	0.542863i	$0.182660\pi$
$108$	6.55272	−	3.15563i	0.630536	−	0.303650i
$109$	3.83575	+	0.578146i	0.367398	+	0.0553763i	0.330147	−	0.943930i	$-0.392902\pi$
$109$	3.83575	+	0.578146i	0.367398	+	0.0553763i	0.0372512	+	0.999306i	$0.488140\pi$
$110$	1.29169	−	3.29118i	0.123158	−	0.313802i
$111$	1.05596	−	14.0908i	0.100228	−	1.33744i
$112$	0.765825	+	0.710582i	0.0723636	+	0.0671437i
$113$	3.13999	−	13.7572i	0.295386	−	1.29417i	−0.581530	−	0.813525i	$-0.697546\pi$
$113$	3.13999	−	13.7572i	0.295386	−	1.29417i	0.876916	−	0.480644i	$-0.159597\pi$
$114$	−20.5832	+	3.10243i	−1.92780	+	0.290569i
$115$	−3.29175	+	2.24428i	−0.306957	+	0.209280i
$116$	0.910862	+	0.280964i	0.0845714	+	0.0260868i
$117$	−2.24414	−	29.9459i	−0.207471	−	2.76850i
$118$	3.31124	−	4.15217i	0.304825	−	0.382238i
$119$	−3.50916	+	1.08243i	−0.321684	+	0.0992264i
$120$	−1.06485	−	2.71319i	−0.0972069	−	0.247679i
$121$	−0.333855	−	1.46272i	−0.0303505	−	0.132974i
$122$	−5.97268	+	10.3450i	−0.540741	+	0.936591i
$123$	8.86368	+	15.3524i	0.799211	+	1.38427i
$124$	2.90919	−	2.69933i	0.261253	−	0.242407i
$125$	−0.623490	−	0.781831i	−0.0557666	−	0.0699291i
$126$	4.74342	+	3.23401i	0.422578	+	0.288108i
$127$	−13.4844	−	6.49373i	−1.19654	−	0.576225i	−0.273855	−	0.961771i	$-0.588299\pi$
$127$	−13.4844	−	6.49373i	−1.19654	−	0.576225i	−0.922689	+	0.385546i	$0.874013\pi$
$128$	−1.00000			−0.0883883
$129$	−18.2162	−	5.78529i	−1.60384	−	0.509367i
$130$	−5.46465			−0.479282
$131$	0.714967	+	0.344310i	0.0624670	+	0.0300825i	0.464856	−	0.885386i	$-0.346106\pi$
$131$	0.714967	+	0.344310i	0.0624670	+	0.0300825i	−0.402389	+	0.915469i	$0.631820\pi$
$132$	−8.51443	−	5.80504i	−0.741086	−	0.505264i
$133$	−4.65186	−	5.83325i	−0.403367	−	0.505807i
$134$	−1.01189	+	0.938893i	−0.0874137	+	0.0811080i
$135$	−3.63649	−	6.29858i	−0.312979	−	0.542095i
$136$	1.75758	−	3.04421i	0.150711	−	0.261039i
$137$	4.93052	+	21.6020i	0.421243	+	1.84558i	0.525167	+	0.850999i	$0.324003\pi$
$137$	4.93052	+	21.6020i	0.421243	+	1.84558i	−0.103925	+	0.994585i	$0.533140\pi$
$138$	4.24237	+	10.8094i	0.361135	+	0.920156i
$139$	−9.34236	+	2.88174i	−0.792408	+	0.244426i	−0.664429	−	0.747351i	$-0.731325\pi$
$139$	−9.34236	+	2.88174i	−0.792408	+	0.244426i	−0.127979	+	0.991777i	$0.540849\pi$
$140$	0.651365	−	0.816785i	0.0550504	−	0.0690310i
$141$	−1.34316	−	17.9232i	−0.113114	−	1.50940i
$142$	3.07512	+	0.948550i	0.258059	+	0.0796005i
$143$	−15.9635	+	10.8838i	−1.33494	+	0.910145i
$144$	−5.43392	+	0.819032i	−0.452827	+	0.0682527i
$145$	0.212109	−	0.929311i	0.0176147	−	0.0771751i
$146$	−12.1463	−	11.2701i	−1.00523	−	0.932719i
$147$	1.28697	−	17.1734i	0.106148	−	1.41644i
$148$	−1.77118	+	4.51289i	−0.145590	+	0.370957i
$149$	−15.9913	−	2.41030i	−1.31006	−	0.197459i	−0.543376	−	0.839489i	$-0.682854\pi$
$149$	−15.9913	−	2.41030i	−1.31006	−	0.197459i	−0.766679	+	0.642030i	$0.778092\pi$
$150$	−2.62603	+	1.26463i	−0.214414	+	0.103256i
$151$	−5.92587	+	2.85375i	−0.482240	+	0.232235i	−0.659177	−	0.751987i	$-0.729095\pi$
$151$	−5.92587	+	2.85375i	−0.482240	+	0.232235i	0.176937	+	0.984222i	$0.443381\pi$
$152$	7.06195	+	1.06442i	0.572800	+	0.0863357i
$153$	7.05723	−	17.9815i	0.570543	−	1.45372i
$154$	0.276027	−	3.68332i	0.0222429	−	0.296810i
$155$	−2.90919	−	2.69933i	−0.233672	−	0.216816i
$156$	−3.54424	+	15.5283i	−0.283766	+	1.24326i
$157$	8.09301	−	1.21983i	0.645893	−	0.0973526i	0.182077	−	0.983284i	$-0.441718\pi$
$157$	8.09301	−	1.21983i	0.645893	−	0.0973526i	0.463816	+	0.885932i	$0.346480\pi$
$158$	−3.07438	+	2.09608i	−0.244585	+	0.166755i
$159$	−26.7839	−	8.26175i	−2.12410	−	0.655199i
$160$	0.0747301	+	0.997204i	0.00590793	+	0.0788359i
$161$	−2.59505	+	3.25408i	−0.204518	+	0.256458i
$162$	−4.50306	+	1.38901i	−0.353794	+	0.109131i
$163$	−7.12856	−	18.1633i	−0.558352	−	1.42266i	−0.879623	−	0.475671i	$-0.842205\pi$
$163$	−7.12856	−	18.1633i	−0.558352	−	1.42266i	0.321271	−	0.946987i	$-0.395890\pi$
$164$	−1.35340	−	5.92963i	−0.105683	−	0.463026i
$165$	−5.15253	+	8.92444i	−0.401124	+	0.694766i
$166$	4.10915	+	7.11725i	0.318932	+	0.552406i
$167$	8.91583	−	8.27268i	0.689928	−	0.640159i	−0.255189	−	0.966891i	$-0.582138\pi$
$167$	8.91583	−	8.27268i	0.689928	−	0.640159i	0.945117	+	0.326732i	$0.105947\pi$
$168$	−1.89851	−	2.38066i	−0.146473	−	0.183672i
$169$	13.9324	+	9.49894i	1.07172	+	0.730688i
$170$	−3.16704	−	1.52517i	−0.242901	−	0.116975i
$171$	39.2459			3.00121
$172$	5.38710	+	3.73887i	0.410763	+	0.285086i
$173$	24.0797			1.83074			0.915372	−	0.402609i	$-0.131896\pi$
$173$	24.0797			1.83074			0.915372	+	0.402609i	$0.131896\pi$
$174$	−2.50316	−	1.20546i	−0.189764	−	0.0913854i
$175$	−0.863178	−	0.588505i	−0.0652501	−	0.0444868i
$176$	2.20440	+	2.76423i	0.166163	+	0.208362i
$177$	−11.3471	+	10.5286i	−0.852902	+	0.791377i
$178$	7.64200	+	13.2363i	0.572792	+	0.992105i
$179$	0.0112812	−	0.0195397i	0.000843199	−	0.00146046i	−0.865603	−	0.500730i	$-0.833065\pi$
$179$	0.0112812	−	0.0195397i	0.000843199	−	0.00146046i	0.866447	+	0.499270i	$0.166398\pi$
$180$	1.22282	+	5.35752i	0.0911436	+	0.399326i
$181$	4.16052	+	10.6008i	0.309249	+	0.787954i	0.998015	+	0.0629703i	$0.0200573\pi$
$181$	4.16052	+	10.6008i	0.309249	+	0.787954i	−0.688766	+	0.724983i	$0.741847\pi$
$182$	−5.45533	+	1.68275i	−0.404376	+	0.124733i
$183$	21.7079	−	27.2209i	1.60469	−	2.01222i
$184$	−0.297726	−	3.97287i	−0.0219486	−	0.292884i
$185$	4.63263	+	1.42898i	0.340598	+	0.105060i
$186$	−9.55723	+	6.51601i	−0.700770	+	0.477777i
$187$	−12.2893	+	1.85231i	−0.898683	+	0.135455i
$188$	−1.37218	+	6.01194i	−0.100077	+	0.438465i
$189$	−5.56982	−	5.16804i	−0.405145	−	0.375920i
$190$	0.533701	−	7.12175i	0.0387187	−	0.516666i
$191$	3.98263	−	10.1476i	0.288173	−	0.734252i	−0.711334	−	0.702854i	$-0.751909\pi$
$191$	3.98263	−	10.1476i	0.288173	−	0.734252i	0.999507	−	0.0313984i	$-0.00999607\pi$
$192$	2.88212	+	0.434409i	0.207999	+	0.0313508i
$193$	14.8770	−	7.16436i	1.07087	−	0.515702i	0.186481	−	0.982459i	$-0.440292\pi$
$193$	14.8770	−	7.16436i	1.07087	−	0.515702i	0.884386	+	0.466756i	$0.154578\pi$
$194$	2.66013	−	1.28105i	0.190986	−	0.0919740i
$195$	15.7498	+	2.37389i	1.12786	+	0.169998i
$196$	−2.15865	+	5.50015i	−0.154189	+	0.392868i
$197$	−0.205316	+	2.73975i	−0.0146281	+	0.195199i	0.985102	+	0.171971i	$0.0550135\pi$
$197$	−0.205316	+	2.73975i	−0.0146281	+	0.195199i	−0.999730	+	0.0232282i	$0.992606\pi$
$198$	14.2425	+	13.2151i	1.01217	+	0.939158i
$199$	−4.31813	+	18.9190i	−0.306104	+	1.34113i	0.554640	+	0.832091i	$0.312856\pi$
$199$	−4.31813	+	18.9190i	−0.306104	+	1.34113i	−0.860744	+	0.509039i	$0.830001\pi$
$200$	0.988831	−	0.149042i	0.0699209	−	0.0105389i
$201$	3.32424	−	2.26643i	0.234474	−	0.159861i
$202$	1.56712	+	0.483392i	0.110262	+	0.0340113i
$203$	−0.0744182	−	0.993041i	−0.00522313	−	0.0696978i
$204$	−6.38797	+	8.01027i	−0.447248	+	0.560831i
$205$	−5.81191	+	1.79274i	−0.405921	+	0.125210i
$206$	2.57930	+	6.57194i	0.179708	+	0.457889i
$207$	−4.87173	−	21.3444i	−0.338609	−	1.48354i
$208$	2.73233	−	4.73253i	0.189453	−	0.328142i
$209$	−12.6251	−	21.8672i	−0.873293	−	1.51259i
$210$	−2.23213	+	2.07111i	−0.154031	+	0.142920i
$211$	−9.58525	−	12.0195i	−0.659876	−	0.827458i	0.333454	−	0.942766i	$-0.391786\pi$
$211$	−9.58525	−	12.0195i	−0.659876	−	0.827458i	−0.993330	+	0.115309i	$0.963214\pi$
$212$	7.94560	+	5.41722i	0.545706	+	0.372056i
$213$	−8.45080	−	4.06969i	−0.579039	−	0.278851i
$214$	10.7809			0.736966
$215$	3.32584	−	5.65144i	0.226820	−	0.385425i
$216$	7.27297			0.494863
$217$	−3.73544	−	1.79889i	−0.253578	−	0.122117i
$218$	3.20504	+	2.18516i	0.217073	+	0.147998i
$219$	30.1111	+	37.7581i	2.03472	+	2.55146i
$220$	2.59176	−	2.40481i	0.174737	−	0.162132i
$221$	9.60455	+	16.6356i	0.646072	+	1.11903i
$222$	7.06518	−	12.2372i	0.474184	−	0.821310i
$223$	−1.72043	−	7.53771i	−0.115209	−	0.504763i	−0.999299	−	0.0374458i	$-0.988078\pi$
$223$	−1.72043	−	7.53771i	−0.115209	−	0.504763i	0.884090	−	0.467317i	$-0.154779\pi$
$224$	0.381675	+	0.972491i	0.0255017	+	0.0649773i
$225$	5.25116	−	1.61977i	0.350077	−	0.107985i
$226$	8.79806	−	11.0324i	0.585238	−	0.733866i
$227$	0.810597	+	10.8167i	0.0538012	+	0.717927i	0.957256	+	0.289243i	$0.0934036\pi$
$227$	0.810597	+	10.8167i	0.0538012	+	0.717927i	−0.903454	+	0.428684i	$0.858977\pi$
$228$	−19.8910	−	6.13555i	−1.31731	−	0.406337i
$229$	−9.36135	+	6.38246i	−0.618616	+	0.421765i	−0.831666	−	0.555276i	$-0.812613\pi$
$229$	−9.36135	+	6.38246i	−0.618616	+	0.421765i	0.213050	+	0.977041i	$0.431660\pi$
$230$	−3.93952	+	0.593787i	−0.259764	+	0.0391531i
$231$	−2.39561	+	10.4958i	−0.157619	+	0.690576i
$232$	0.698753	+	0.648348i	0.0458754	+	0.0425661i
$233$	−2.26972	+	30.2873i	−0.148694	+	1.98419i	0.0264645	+	0.999650i	$0.491575\pi$
$233$	−2.26972	+	30.2873i	−0.148694	+	1.98419i	−0.175159	+	0.984540i	$0.556044\pi$
$234$	10.9712	−	27.9540i	0.717207	−	1.82741i
$235$	6.09767	+	0.919076i	0.397768	+	0.0599539i
$236$	4.78488	−	2.30428i	0.311469	−	0.149996i
$237$	9.77128	−	4.70560i	0.634713	−	0.305661i
$238$	−3.63129	−	0.547329i	−0.235382	−	0.0354781i
$239$	−3.72569	+	9.49289i	−0.240995	+	0.614044i	−0.999282	−	0.0378757i	$-0.987941\pi$
$239$	−3.72569	+	9.49289i	−0.240995	+	0.614044i	0.758288	+	0.651920i	$0.226036\pi$
$240$	0.217814	−	2.90652i	0.0140598	−	0.187615i
$241$	−21.7166	−	20.1501i	−1.39889	−	1.29798i	−0.903028	−	0.429581i	$-0.858661\pi$
$241$	−21.7166	−	20.1501i	−1.39889	−	1.29798i	−0.495863	−	0.868401i	$-0.665148\pi$
$242$	0.333855	−	1.46272i	0.0214610	−	0.0940269i
$243$	−7.99349	+	1.20482i	−0.512783	+	0.0772895i
$244$	−9.86972	+	6.72906i	−0.631844	+	0.430784i
$245$	5.64608	+	1.74159i	0.360715	+	0.111266i
$246$	1.32477	+	17.6778i	0.0844641	+	1.12710i
$247$	−24.3329	+	30.5125i	−1.54827	+	1.94147i
$248$	3.79228	−	1.16976i	0.240810	−	0.0742801i
$249$	−8.75124	−	22.2978i	−0.554587	−	1.41306i
$250$	−0.222521	−	0.974928i	−0.0140735	−	0.0616599i
$251$	12.9366	−	22.4069i	0.816552	−	1.41431i	−0.0916566	−	0.995791i	$-0.529216\pi$
$251$	12.9366	−	22.4069i	0.816552	−	1.41431i	0.908208	−	0.418518i	$-0.137450\pi$
$252$	2.87049	+	4.97184i	0.180824	+	0.313196i
$253$	−10.3256	+	9.58078i	−0.649167	+	0.602339i
$254$	−9.33147	−	11.7013i	−0.585508	−	0.734204i
$255$	8.46524	+	5.77150i	0.530114	+	0.361426i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$	25.3097			1.57878			0.789388	−	0.613894i	$-0.210398\pi$
$257$	25.3097			1.57878			0.789388	+	0.613894i	$0.210398\pi$
$258$	−13.9020	−	13.1161i	−0.865503	−	0.816570i
$259$	5.06476			0.314709
$260$	−4.92348	−	2.37102i	−0.305341	−	0.147045i
$261$	4.32798	+	2.95077i	0.267895	+	0.182648i
$262$	0.494773	+	0.620425i	0.0305672	+	0.0383300i
$263$	−12.9973	+	12.0597i	−0.801447	+	0.743634i	−0.970273	−	0.242012i	$-0.922193\pi$
$263$	−12.9973	+	12.0597i	−0.801447	+	0.743634i	0.168826	+	0.985646i	$0.446002\pi$
$264$	−5.15253	−	8.92444i	−0.317116	−	0.549261i
$265$	4.80830	−	8.32822i	0.295371	−	0.511598i
$266$	−1.66023	−	7.27394i	−0.101795	−	0.445994i
$267$	−16.2751	−	41.4684i	−0.996022	−	2.53782i
$268$	−1.31905	+	0.406873i	−0.0805737	+	0.0248537i
$269$	13.1127	−	16.4428i	0.799496	−	1.00254i	−0.200245	−	0.979746i	$-0.564174\pi$
$269$	13.1127	−	16.4428i	0.799496	−	1.00254i	0.999740	−	0.0227899i	$-0.00725488\pi$
$270$	−0.543510	−	7.25264i	−0.0330770	−	0.441381i
$271$	−11.3166	−	3.49070i	−0.687434	−	0.212045i	−0.0686899	−	0.997638i	$-0.521882\pi$
$271$	−11.3166	−	3.49070i	−0.687434	−	0.212045i	−0.618744	+	0.785593i	$0.712358\pi$
$272$	2.90436	−	1.98016i	0.176102	−	0.120065i
$273$	16.4539	−	2.48003i	0.995835	−	0.150098i
$274$	−4.93052	+	21.6020i	−0.297863	+	1.30503i
$275$	−2.59176	−	2.40481i	−0.156289	−	0.145015i
$276$	−0.867772	+	11.5796i	−0.0522338	+	0.697011i
$277$	−10.1602	+	25.8877i	−0.610465	+	1.55544i	0.206311	+	0.978486i	$0.433854\pi$
$277$	−10.1602	+	25.8877i	−0.610465	+	1.55544i	−0.816776	+	0.576954i	$0.804241\pi$
$278$	−9.66751	−	1.45714i	−0.579819	−	0.0873936i
$279$	19.6489	−	9.46241i	1.17635	−	0.566500i
$280$	0.941249	−	0.453282i	0.0562504	−	0.0270888i
$281$	15.0697	+	2.27140i	0.898986	+	0.135500i	0.582247	−	0.813012i	$-0.302174\pi$
$281$	15.0697	+	2.27140i	0.898986	+	0.135500i	0.316739	+	0.948513i	$0.397412\pi$
$282$	6.56643	−	16.7310i	0.391025	−	0.996317i
$283$	−0.147218	+	1.96449i	−0.00875122	+	0.116777i	−0.999869	−	0.0162134i	$-0.994839\pi$
$283$	−0.147218	+	1.96449i	−0.00875122	+	0.116777i	0.991117	+	0.132990i	$0.0424579\pi$
$284$	2.35903	+	2.18886i	0.139983	+	0.129885i
$285$	−4.63194	+	20.2938i	−0.274372	+	1.20210i
$286$	−19.1049	+	2.87960i	−1.12970	+	0.170275i
$287$	−5.24995	+	3.57936i	−0.309895	+	0.211283i
$288$	−5.25116	−	1.61977i	−0.309427	−	0.0954457i
$289$	−0.347023	−	4.63071i	−0.0204131	−	0.272394i
$290$	0.594317	−	0.745250i	0.0348995	−	0.0437626i
$291$	−8.22329	+	2.53655i	−0.482058	+	0.148695i
$292$	−6.05350	−	15.4241i	−0.354254	−	0.902625i
$293$	−5.97061	−	26.1590i	−0.348807	−	1.52822i	−0.779894	−	0.625912i	$-0.784727\pi$
$293$	−5.97061	−	26.1590i	−0.348807	−	1.52822i	0.431087	−	0.902311i	$-0.358130\pi$
$294$	8.61079	−	14.9143i	0.502191	−	0.869821i
$295$	−2.65541	−	4.59930i	−0.154604	−	0.267782i
$296$	−3.55385	+	3.29749i	−0.206563	+	0.191663i
$297$	−16.0325	−	20.1042i	−0.930302	−	1.16656i
$298$	−13.3618	−	9.10995i	−0.774031	−	0.527725i
$299$	19.6152	+	9.44619i	1.13438	+	0.546288i
$300$	−2.91467			−0.168279
$301$	1.57990	−	6.66594i	0.0910639	−	0.384218i
$302$	−6.57722			−0.378476
$303$	−4.30662	−	2.07396i	−0.247409	−	0.119146i
$304$	5.90076	+	4.02307i	0.338432	+	0.230739i
$305$	7.44781	+	9.33926i	0.426460	+	0.534764i
$306$	14.1602	−	13.1388i	0.809487	−	0.751094i
$307$	14.0948	+	24.4129i	0.804432	+	1.39332i	0.916674	+	0.399636i	$0.130864\pi$
$307$	14.0948	+	24.4129i	0.804432	+	1.39332i	−0.112242	+	0.993681i	$0.535803\pi$
$308$	1.84682	−	3.19879i	0.105233	−	0.182268i
$309$	−4.57892	−	20.0616i	−0.260486	−	1.14126i
$310$	−1.44989	−	3.69426i	−0.0823483	−	0.209820i
$311$	6.90658	−	2.13040i	0.391636	−	0.120804i	−0.0926819	−	0.995696i	$-0.529544\pi$
$311$	6.90658	−	2.13040i	0.391636	−	0.120804i	0.484318	+	0.874892i	$0.339068\pi$
$312$	−9.93073	+	12.4527i	−0.562217	+	0.704998i
$313$	−1.00493	−	13.4099i	−0.0568022	−	0.757973i	−0.950781	−	0.309864i	$-0.899717\pi$
$313$	−1.00493	−	13.4099i	−0.0568022	−	0.757973i	0.893979	−	0.448109i	$-0.147902\pi$
$314$	7.82081	+	2.41240i	0.441354	+	0.136140i
$315$	4.74342	−	3.23401i	0.267262	−	0.182216i
$316$	−3.67938	+	0.554577i	−0.206981	+	0.0311974i
$317$	5.20313	−	22.7964i	0.292237	−	1.28037i	−0.589167	−	0.808011i	$-0.700544\pi$
$317$	5.20313	−	22.7964i	0.292237	−	1.28037i	0.881404	−	0.472363i	$-0.156599\pi$
$318$	−20.5469	−	19.0647i	−1.15221	−	1.06910i
$319$	0.251852	−	3.36073i	0.0141010	−	0.188165i
$320$	−0.365341	+	0.930874i	−0.0204232	+	0.0520374i
$321$	−31.0718	−	4.68331i	−1.73426	−	0.261397i
$322$	−3.74995	+	1.80588i	−0.208977	+	0.100638i
$323$	−22.6181	+	10.8923i	−1.25851	+	0.606065i
$324$	−4.65978	−	0.702350i	−0.258877	−	0.0390194i
$325$	−1.99646	+	5.08690i	−0.110744	+	0.282171i
$326$	1.45814	−	19.4575i	0.0807589	−	1.07765i
$327$	−8.28804	−	7.69018i	−0.458330	−	0.425268i
$328$	1.35340	−	5.92963i	0.0747289	−	0.327409i
$329$	6.37028	−	0.960165i	0.351205	−	0.0529356i
$330$	−8.51443	+	5.80504i	−0.468704	+	0.319557i
$331$	12.0767	+	3.72516i	0.663794	+	0.204753i	0.608302	−	0.793706i	$-0.291851\pi$
$331$	12.0767	+	3.72516i	0.663794	+	0.204753i	0.0554920	+	0.998459i	$0.482327\pi$
$332$	0.614154	+	8.19531i	0.0337061	+	0.449776i
$333$	−16.6106	+	20.8290i	−0.910254	+	1.14142i
$334$	11.6223	−	3.58500i	0.635942	−	0.196162i
$335$	0.504308	+	1.28495i	0.0275533	+	0.0702046i
$336$	−0.677571	−	2.96863i	−0.0369645	−	0.161952i
$337$	−6.99346	+	12.1130i	−0.380958	+	0.659838i	−0.991199	−	0.132377i	$-0.957739\pi$
$337$	−6.99346	+	12.1130i	−0.380958	+	0.659838i	0.610242	+	0.792215i	$0.291072\pi$
$338$	8.43121	+	14.6033i	0.458598	+	0.794314i
$339$	−30.1496	+	27.9747i	−1.63750	+	1.51938i
$340$	−2.19166	−	2.74826i	−0.118860	−	0.149045i
$341$	−11.5932	−	7.90411i	−0.627807	−	0.428032i
$342$	35.3593	+	17.0281i	1.91201	+	0.920777i
$343$	13.4857			0.728159
$344$	3.23137	+	5.70598i	0.174224	+	0.307646i
$345$	11.6121			0.625174
$346$	21.6950	+	10.4478i	1.16633	+	0.561676i
$347$	−12.8211	−	8.74127i	−0.688272	−	0.469256i	0.167996	−	0.985788i	$-0.446270\pi$
$347$	−12.8211	−	8.74127i	−0.688272	−	0.469256i	−0.856268	+	0.516532i	$0.827223\pi$
$348$	−1.73224	−	2.17216i	−0.0928577	−	0.116440i
$349$	−8.63276	+	8.01003i	−0.462101	+	0.428767i	−0.876554	−	0.481304i	$-0.840163\pi$
$349$	−8.63276	+	8.01003i	−0.462101	+	0.428767i	0.414453	+	0.910071i	$0.363973\pi$
$350$	−0.522354	−	0.904743i	−0.0279210	−	0.0483606i
$351$	−19.8721	+	34.4196i	−1.06070	+	1.83718i
$352$	0.786741	+	3.44694i	0.0419334	+	0.183722i
$353$	4.17197	+	10.6300i	0.222051	+	0.565778i	0.997874	−	0.0651735i	$-0.0207601\pi$
$353$	4.17197	+	10.6300i	0.222051	+	0.565778i	−0.775823	+	0.630951i	$0.782665\pi$
$354$	−14.7916	+	4.56260i	−0.786164	+	0.242499i
$355$	2.00645	−	2.51601i	0.106491	−	0.133536i
$356$	1.14217	+	15.2413i	0.0605351	+	0.807785i
$357$	10.2280	+	3.15493i	0.541325	+	0.166977i
$358$	0.0186420	−	0.0127099i	0.000985260	−	0.000671739i
$359$	12.6771	−	1.91076i	0.669071	−	0.100846i	0.194282	−	0.980946i	$-0.437762\pi$
$359$	12.6771	−	1.91076i	0.669071	−	0.100846i	0.474789	+	0.880100i	$0.342524\pi$
$360$	−1.22282	+	5.35752i	−0.0644482	+	0.282366i
$361$	−23.4607	−	21.7683i	−1.23477	−	1.14570i
$362$	−0.851030	+	11.3562i	−0.0447291	+	0.596869i
$363$	−1.59763	+	4.07069i	−0.0838536	+	0.213656i
$364$	−5.64520	−	0.850877i	−0.295889	−	0.0445981i
$365$	−14.9286	+	7.18922i	−0.781397	+	0.376301i
$366$	31.3688	−	15.1064i	1.63968	−	0.789626i
$367$	−2.18658	−	0.329574i	−0.114138	−	0.0172036i	0.0917246	−	0.995784i	$-0.470762\pi$
$367$	−2.18658	−	0.329574i	−0.114138	−	0.0172036i	−0.205863	+	0.978581i	$0.566000\pi$
$368$	1.45552	−	3.70861i	0.0758744	−	0.193325i
$369$	2.49771	−	33.3296i	0.130026	−	1.73507i
$370$	3.55385	+	3.29749i	0.184756	+	0.171428i
$371$	2.23556	−	9.79464i	0.116065	−	0.508512i
$372$	−11.4380	+	1.72399i	−0.593030	+	0.0893850i
$373$	8.02244	−	5.46961i	0.415386	−	0.283205i	−0.337539	−	0.941311i	$-0.609595\pi$
$373$	8.02244	−	5.46961i	0.415386	−	0.283205i	0.752925	+	0.658106i	$0.228642\pi$
$374$	−11.8760	−	3.66325i	−0.614092	−	0.189422i
$375$	0.217814	+	2.90652i	0.0112478	+	0.150092i
$376$	−3.84478	+	4.82120i	−0.198279	+	0.248634i
$377$	−4.97754	+	1.53537i	−0.256357	+	0.0790755i
$378$	−2.77591	−	7.07290i	−0.142777	−	0.363791i
$379$	0.352532	+	1.54454i	0.0181083	+	0.0793378i	0.983175	−	0.182668i	$-0.0584733\pi$
$379$	0.352532	+	1.54454i	0.0181083	+	0.0793378i	−0.965066	+	0.262006i	$0.915616\pi$
$380$	3.57086	−	6.18491i	0.183181	−	0.317279i
$381$	21.8112	+	37.7781i	1.11742	+	1.93543i
$382$	7.99109	−	7.41465i	0.408860	−	0.379366i
$383$	2.87855	+	3.60958i	0.147087	+	0.184441i	0.849917	−	0.526917i	$-0.176652\pi$
$383$	2.87855	+	3.60958i	0.147087	+	0.184441i	−0.702830	+	0.711358i	$0.748081\pi$
$384$	2.40821	+	1.64189i	0.122894	+	0.0837874i
$385$	−3.32786	−	1.60261i	−0.169604	−	0.0816768i
$386$	16.5122			0.840448
$387$	22.2324	+	28.3593i	1.13014	+	1.44158i
$388$	2.95252			0.149891
$389$	−3.96900	−	1.91137i	−0.201237	−	0.0969104i	0.330551	−	0.943788i	$-0.392765\pi$
$389$	−3.96900	−	1.91137i	−0.201237	−	0.0969104i	−0.531788	+	0.846878i	$0.678480\pi$
$390$	13.1600	+	8.97237i	0.666385	+	0.454334i
$391$	8.73162	+	10.9491i	0.441577	+	0.553720i
$392$	−4.33130	+	4.01886i	−0.218764	+	0.202983i
$393$	−1.15647	−	2.00307i	−0.0583364	−	0.101042i
$394$	−1.37372	+	2.37935i	−0.0692068	+	0.119870i
$395$	0.827986	+	3.62764i	0.0416605	+	0.182527i
$396$	7.09824	+	18.0860i	0.356700	+	0.908857i
$397$	4.74789	−	1.46453i	0.238290	−	0.0735026i	−0.173310	−	0.984867i	$-0.555446\pi$
$397$	4.74789	−	1.46453i	0.238290	−	0.0735026i	0.411600	+	0.911365i	$0.364970\pi$
$398$	−12.0991	+	15.1718i	−0.606475	+	0.760495i
$399$	1.62511	+	21.6856i	0.0813572	+	1.08564i
$400$	0.955573	+	0.294755i	0.0477786	+	0.0147378i
$401$	−4.92038	+	3.35466i	−0.245712	+	0.167524i	−0.679914	−	0.733292i	$-0.737983\pi$
$401$	−4.92038	+	3.35466i	−0.245712	+	0.167524i	0.434202	+	0.900816i	$0.357030\pi$
$402$	3.97840	−	0.599647i	0.198425	−	0.0299077i
$403$	−4.82581	+	21.1433i	−0.240391	+	1.05322i
$404$	1.20219	+	1.11547i	0.0598111	+	0.0554966i
$405$	−0.352159	+	4.69924i	−0.0174989	+	0.233507i
$406$	0.363816	−	0.926988i	0.0180559	−	0.0460057i
$407$	16.9491	+	2.55467i	0.840136	+	0.126630i
$408$	−9.23089	+	4.44536i	−0.456997	+	0.220078i
$409$	4.55685	−	2.19446i	0.225322	−	0.108509i	−0.317817	−	0.948152i	$-0.602950\pi$
$409$	4.55685	−	2.19446i	0.225322	−	0.108509i	0.543139	+	0.839643i	$0.317236\pi$
$410$	−6.01419	−	0.906493i	−0.297020	−	0.0447685i
$411$	23.5944	−	60.1176i	1.16383	−	2.96538i
$412$	−0.527592	+	7.04023i	−0.0259926	+	0.346847i
$413$	−4.06716	−	3.77377i	−0.200132	−	0.185695i
$414$	4.87173	−	21.3444i	0.239432	−	1.04902i
$415$	8.12650	−	1.22487i	0.398914	−	0.0601266i
$416$	4.51511	−	3.07835i	0.221371	−	0.150928i
$417$	27.2299	+	8.39931i	1.33345	+	0.411316i
$418$	−1.88694	−	25.1795i	−0.0922934	−	1.23157i
$419$	2.88861	−	3.62221i	0.141118	−	0.176956i	−0.706250	−	0.707963i	$-0.749614\pi$
$419$	2.88861	−	3.62221i	0.141118	−	0.176956i	0.847368	+	0.531006i	$0.178186\pi$
$420$	−2.90970	+	0.897523i	−0.141979	+	0.0437946i
$421$	6.31792	+	16.0978i	0.307916	+	0.784558i	0.998140	+	0.0609622i	$0.0194169\pi$
$421$	6.31792	+	16.0978i	0.307916	+	0.784558i	−0.690224	+	0.723596i	$0.742488\pi$
$422$	−3.42093	−	14.9881i	−0.166528	−	0.729609i
$423$	−16.9435	+	29.3470i	−0.823821	+	1.42690i
$424$	4.80830	+	8.32822i	0.233512	+	0.404454i
$425$	−2.57679	+	2.39091i	−0.124993	+	0.115976i
$426$	−5.84813	−	7.33333i	−0.283343	−	0.355301i
$427$	10.3110	+	7.02990i	0.498983	+	0.340201i
$428$	9.71324	+	4.67765i	0.469507	+	0.226103i
$429$	56.3135			2.71884
$430$	5.44855	−	3.64875i	0.262752	−	0.175958i
$431$	−34.7885			−1.67570			−0.837852	−	0.545897i	$-0.816189\pi$
$431$	−34.7885			−1.67570			−0.837852	+	0.545897i	$0.816189\pi$
$432$	6.55272	+	3.15563i	0.315268	+	0.151825i
$433$	−21.6051	−	14.7301i	−1.03828	−	0.707884i	−0.0808978	−	0.996722i	$-0.525779\pi$
$433$	−21.6051	−	14.7301i	−1.03828	−	0.707884i	−0.957378	+	0.288838i	$0.906731\pi$
$434$	−2.58500	−	3.24149i	−0.124084	−	0.155597i
$435$	−2.03663	+	1.88972i	−0.0976491	+	0.0906051i
$436$	1.93954	+	3.35938i	0.0928870	+	0.160885i
$437$	−14.2263	+	24.6408i	−0.680539	+	1.17873i
$438$	10.7465	+	47.0836i	0.513489	+	2.24974i
$439$	1.73964	+	4.43253i	0.0830284	+	0.211553i	0.966359	−	0.257198i	$-0.0827993\pi$
$439$	1.73964	+	4.43253i	0.0830284	+	0.211553i	−0.883330	+	0.468751i	$0.844704\pi$
$440$	3.37850	−	1.04213i	0.161064	−	0.0496816i
$441$	−20.2444	+	25.3856i	−0.964018	+	1.20884i
$442$	1.43550	+	19.1554i	0.0682797	+	0.911129i
$443$	−22.0575	−	6.80383i	−1.04798	−	0.323260i	−0.277503	−	0.960725i	$-0.589507\pi$
$443$	−22.0575	−	6.80383i	−1.04798	−	0.323260i	−0.770480	+	0.637465i	$0.779983\pi$
$444$	11.6750	−	7.95991i	0.554073	−	0.377761i
$445$	15.1133	−	2.27796i	0.716439	−	0.107986i
$446$	1.72043	−	7.53771i	0.0814649	−	0.356921i
$447$	34.5529	+	32.0604i	1.63430	+	1.51641i
$448$	−0.0780711	+	1.04179i	−0.00368851	+	0.0492198i
$449$	13.4891	−	34.3698i	0.636592	−	1.62201i	−0.138648	−	0.990342i	$-0.544276\pi$
$449$	13.4891	−	34.3698i	0.636592	−	1.62201i	0.775239	−	0.631668i	$-0.217629\pi$
$450$	5.43392	+	0.819032i	0.256158	+	0.0386095i
$451$	−19.3743	+	9.33016i	−0.912299	+	0.439340i
$452$	12.7136	−	6.12253i	0.597996	−	0.287980i
$453$	18.9563	+	2.85720i	0.890645	+	0.134243i
$454$	−3.96285	+	10.0972i	−0.185986	+	0.473884i
$455$	−0.426631	+	5.69300i	−0.0200008	+	0.266892i
$456$	−15.2590	−	14.1583i	−0.714569	−	0.663023i
$457$	−5.87163	+	25.7253i	−0.274663	+	1.20338i	0.629776	+	0.776776i	$0.283147\pi$
$457$	−5.87163	+	25.7253i	−0.274663	+	1.20338i	−0.904440	+	0.426602i	$0.859711\pi$
$458$	−11.2035	+	1.68866i	−0.523507	+	0.0789060i
$459$	−21.1233	+	14.4016i	−0.985952	+	0.672211i
$460$	−3.80702	−	1.17431i	−0.177503	−	0.0547524i
$461$	0.941185	+	12.5592i	0.0438353	+	0.584942i	0.975268	+	0.221027i	$0.0709410\pi$
$461$	0.941185	+	12.5592i	0.0438353	+	0.584942i	−0.931432	+	0.363915i	$0.881440\pi$
$462$	−6.71234	+	8.41701i	−0.312287	+	0.391595i
$463$	31.0754	−	9.58550i	1.44420	−	0.445476i	0.529048	−	0.848592i	$-0.322549\pi$
$463$	31.0754	−	9.58550i	1.44420	−	0.445476i	0.915149	+	0.403116i	$0.132073\pi$
$464$	0.348247	+	0.887318i	0.0161670	+	0.0411927i
$465$	2.57393	+	11.2771i	0.119363	+	0.522965i
$466$	−15.1861	+	26.3032i	−0.703484	+	1.21847i
$467$	−3.56188	−	6.16936i	−0.164824	−	0.285484i	0.771769	−	0.635904i	$-0.219372\pi$
$467$	−3.56188	−	6.16936i	−0.164824	−	0.285484i	−0.936593	+	0.350419i	$0.886039\pi$
$468$	22.0135	−	20.4255i	1.01757	−	0.944170i
$469$	0.899127	+	1.12747i	0.0415178	+	0.0520617i
$470$	5.09504	+	3.47374i	0.235017	+	0.160232i
$471$	−21.4925	−	10.3502i	−0.990323	−	0.476914i
$472$	5.31082			0.244450
$473$	8.64940	−	21.5105i	0.397700	−	0.989054i
$474$	10.8453			0.498141
$475$	−6.43446	−	3.09867i	−0.295233	−	0.142177i
$476$	−3.03420	−	2.06868i	−0.139072	−	0.0948180i
$477$	32.9490	+	41.3167i	1.50863	+	1.89176i
$478$	−7.47554	+	6.93629i	−0.341923	+	0.317258i
$479$	−2.48108	−	4.29736i	−0.113363	−	0.196351i	0.803761	−	0.594952i	$-0.202829\pi$
$479$	−2.48108	−	4.29736i	−0.113363	−	0.196351i	−0.917124	+	0.398601i	$0.869496\pi$
$480$	1.45733	−	2.52418i	0.0665179	−	0.115212i
$481$	−5.89518	−	25.8285i	−0.268797	−	1.17768i
$482$	−10.8232	−	27.5771i	−0.492984	−	1.25610i
$483$	11.5923	−	3.57574i	0.527467	−	0.162702i
$484$	0.935442	−	1.17301i	0.0425201	−	0.0533185i
$485$	−0.220642	−	2.94426i	−0.0100188	−	0.133692i
$486$	−7.72464	−	2.38274i	−0.350397	−	0.108083i
$487$	0.747752	−	0.509808i	0.0338839	−	0.0231016i	−0.546260	−	0.837616i	$-0.683949\pi$
$487$	0.747752	−	0.509808i	0.0338839	−	0.0231016i	0.580144	+	0.814514i	$0.302996\pi$
$488$	−11.8119	+	1.78036i	−0.534702	+	0.0805933i
$489$	−12.6550	+	55.4454i	−0.572281	+	2.50733i
$490$	4.33130	+	4.01886i	0.195668	+	0.181554i
$491$	0.940416	−	12.5490i	0.0424404	−	0.566327i	−0.934936	−	0.354818i	$-0.884543\pi$
$491$	0.940416	−	12.5490i	0.0424404	−	0.566327i	0.977376	−	0.211510i	$-0.0678380\pi$
$492$	−6.47653	+	16.5019i	−0.291985	+	0.743965i
$493$	−3.31326	−	0.499393i	−0.149222	−	0.0224915i
$494$	−35.1621	+	16.9332i	−1.58202	+	0.761860i
$495$	17.5050	−	8.42996i	0.786791	−	0.378899i
$496$	3.92427	+	0.591489i	0.176205	+	0.0265586i
$497$	1.22826	−	3.12957i	0.0550952	−	0.140380i
$498$	1.79006	−	23.8866i	0.0802143	−	1.07039i
$499$	26.8679	+	24.9297i	1.20277	+	1.11601i	0.990315	+	0.138837i	$0.0443365\pi$
$499$	26.8679	+	24.9297i	1.20277	+	1.11601i	0.212455	+	0.977171i	$0.431854\pi$
$500$	0.222521	−	0.974928i	0.00995144	−	0.0436001i
$501$	−35.0541	+	5.28355i	−1.56610	+	0.236052i
$502$	21.3775	−	14.5749i	0.954123	−	0.650510i
$503$	9.97257	+	3.07613i	0.444655	+	0.137158i	0.508994	−	0.860770i	$-0.330018\pi$
$503$	9.97257	+	3.07613i	0.444655	+	0.137158i	−0.0643387	+	0.997928i	$0.520494\pi$
$504$	0.429024	+	5.72493i	0.0191103	+	0.255009i
$505$	1.02251	−	1.28219i	0.0455011	−	0.0570565i
$506$	−13.4600	+	4.15186i	−0.598371	+	0.184573i
$507$	−17.9559	−	45.7510i	−0.797451	−	2.03187i
$508$	−3.33036	−	14.5913i	−0.147761	−	0.647383i
$509$	14.0102	−	24.2664i	0.620992	−	1.07559i	−0.368310	−	0.929703i	$-0.620063\pi$
$509$	14.0102	−	24.2664i	0.620992	−	1.07559i	0.989301	−	0.145886i	$-0.0466033\pi$
$510$	5.12276	+	8.87288i	0.226839	+	0.392898i
$511$	−12.6893	+	11.7739i	−0.561342	+	0.520849i
$512$	−0.623490	−	0.781831i	−0.0275546	−	0.0345524i
$513$	−42.9161	−	29.2597i	−1.89479	−	1.29185i
$514$	22.8033	+	10.9815i	1.00581	+	0.484372i
$515$	7.05997			0.311099
$516$	−6.83446	−	17.8490i	−0.300870	−	0.785760i
$517$	21.8023			0.958865
$518$	4.56319	+	2.19752i	0.200495	+	0.0965533i
$519$	−57.9890	−	39.5362i	−2.54544	−	1.73545i
$520$	−3.40716	−	4.27244i	−0.149414	−	0.187359i
$521$	−20.1682	+	18.7133i	−0.883583	+	0.819845i	−0.984561	−	0.175044i	$-0.943993\pi$
$521$	−20.1682	+	18.7133i	−0.883583	+	0.819845i	0.100978	+	0.994889i	$0.467803\pi$
$522$	2.61909	+	4.53639i	0.114634	+	0.198553i
$523$	−12.4932	+	21.6388i	−0.546289	+	0.946200i	0.452236	+	0.891898i	$0.350627\pi$
$523$	−12.4932	+	21.6388i	−0.546289	+	0.946200i	−0.998525	+	0.0543017i	$0.982707\pi$
$524$	0.176582	+	0.773658i	0.00771404	+	0.0337974i
$525$	1.11246	+	2.83449i	0.0485515	+	0.123707i
$526$	−16.9427	+	5.22612i	−0.738735	+	0.227870i
$527$	−8.69783	+	10.9067i	−0.378883	+	0.475105i
$528$	−0.770097	−	10.2762i	−0.0335142	−	0.447216i
$529$	−6.81097	−	2.10091i	−0.296129	−	0.0913437i
$530$	7.94560	−	5.41722i	0.345135	−	0.235309i
$531$	28.8586	−	4.34973i	1.25236	−	0.188762i
$532$	1.66023	−	7.27394i	0.0719801	−	0.315365i
$533$	24.3642	+	22.6067i	1.05533	+	0.979204i
$534$	3.32906	−	44.4232i	0.144063	−	1.92238i
$535$	3.93870	−	10.0356i	0.170285	−	0.433879i
$536$	−1.36496	−	0.205734i	−0.0589572	−	0.00888636i
$537$	−0.0592497	+	0.0285331i	−0.00255681	+	0.00123130i
$538$	18.9484	−	9.12507i	0.816924	−	0.393410i
$539$	20.6570	+	3.11354i	0.889758	+	0.134109i
$540$	2.65712	−	6.77022i	0.114344	−	0.291344i
$541$	−1.42562	+	19.0235i	−0.0612920	+	0.817885i	0.878849	+	0.477100i	$0.158312\pi$
$541$	−1.42562	+	19.0235i	−0.0612920	+	0.817885i	−0.940141	+	0.340785i	$0.889307\pi$
$542$	−8.68133	−	8.05510i	−0.372895	−	0.345996i
$543$	7.38600	−	32.3602i	0.316964	−	1.38871i
$544$	3.47589	−	0.523907i	0.149028	−	0.0224623i
$545$	3.20504	−	2.18516i	0.137289	−	0.0936020i
$546$	15.9005	+	4.90465i	0.680478	+	0.209900i
$547$	−3.11588	−	41.5785i	−0.133225	−	1.77777i	−0.518610	−	0.855011i	$-0.673550\pi$
$547$	−3.11588	−	41.5785i	−0.133225	−	1.77777i	0.385385	−	0.922756i	$-0.374069\pi$
$548$	−13.8150	+	17.3235i	−0.590148	+	0.740022i
$549$	−62.7270	+	19.3487i	−2.67712	+	0.825783i
$550$	−1.29169	−	3.29118i	−0.0550780	−	0.140336i
$551$	−1.51482	−	6.63688i	−0.0645337	−	0.282740i
$552$	−5.80604	+	10.0564i	−0.247122	+	0.428027i
$553$	1.94364	+	3.36649i	0.0826522	+	0.143158i
$554$	−20.3862	+	18.9157i	−0.866129	+	0.803650i
$555$	−8.81013	−	11.0476i	−0.373969	−	0.468943i
$556$	−8.07790	−	5.50742i	−0.342579	−	0.233567i
$557$	34.7080	+	16.7145i	1.47062	+	0.708215i	0.986037	−	0.166528i	$-0.0532557\pi$
$557$	34.7080	+	16.7145i	1.47062	+	0.708215i	0.484587	+	0.874743i	$0.338970\pi$
$558$	21.8086			0.923233
$559$	−35.8329	−	0.298036i	−1.51557	−	0.0126056i
$560$	1.04471			0.0441470
$561$	32.6366	+	15.7169i	1.37792	+	0.663570i
$562$	12.5919	+	8.58498i	0.531155	+	0.362136i
$563$	−9.55331	−	11.9795i	−0.402624	−	0.504874i	0.538645	−	0.842533i	$-0.318936\pi$
$563$	−9.55331	−	11.9795i	−0.402624	−	0.504874i	−0.941269	+	0.337659i	$0.890365\pi$
$564$	13.1755	−	12.2250i	0.554787	−	0.514767i
$565$	−7.05550	−	12.2205i	−0.296827	−	0.514119i
$566$	−0.985001	+	1.70607i	−0.0414027	+	0.0717115i
$567$	1.09549	+	4.79967i	0.0460064	+	0.201567i
$568$	1.17570	+	2.99564i	0.0493313	+	0.125694i
$569$	6.91276	−	2.13230i	0.289798	−	0.0893908i	−0.146448	−	0.989218i	$-0.546784\pi$
$569$	6.91276	−	2.13230i	0.289798	−	0.0893908i	0.436246	+	0.899828i	$0.356308\pi$
$570$	−12.9784	+	16.2744i	−0.543605	+	0.681660i
$571$	−1.30890	−	17.4661i	−0.0547758	−	0.730933i	−0.955208	−	0.295936i	$-0.904369\pi$
$571$	−1.30890	−	17.4661i	−0.0547758	−	0.730933i	0.900432	−	0.434997i	$-0.143250\pi$
$572$	−18.4624	−	5.69488i	−0.771950	−	0.238115i
$573$	−26.2522	+	17.8985i	−1.09670	+	0.747719i
$574$	−6.28307	+	0.947020i	−0.262250	+	0.0395278i
$575$	−0.886527	+	3.88413i	−0.0369707	+	0.161979i
$576$	−4.02834	−	3.73775i	−0.167847	−	0.155740i
$577$	−1.10725	+	14.7753i	−0.0460955	+	0.615102i	0.925545	+	0.378638i	$0.123608\pi$
$577$	−1.10725	+	14.7753i	−0.0460955	+	0.615102i	−0.971640	+	0.236464i	$0.924011\pi$
$578$	1.69653	−	4.32269i	0.0705664	−	0.179800i
$579$	−47.5900	−	7.17304i	−1.97777	−	0.298101i
$580$	0.858813	−	0.413582i	0.0356603	−	0.0171731i
$581$	7.73546	−	3.72520i	0.320921	−	0.154547i
$582$	−8.50950	−	1.28260i	−0.352730	−	0.0531655i
$583$	12.4217	−	31.6499i	0.514454	−	1.31081i
$584$	1.23824	−	16.5231i	0.0512386	−	0.683732i
$585$	−22.0135	−	20.4255i	−0.910145	−	0.844491i
$586$	5.97061	−	26.1590i	0.246644	−	1.08062i
$587$	19.8435	−	2.99093i	0.819030	−	0.123449i	0.273855	−	0.961771i	$-0.411701\pi$
$587$	19.8435	−	2.99093i	0.819030	−	0.123449i	0.545175	+	0.838322i	$0.316463\pi$
$588$	14.2291	−	9.70126i	0.586800	−	0.400073i
$589$	−27.0834	−	8.35413i	−1.11595	−	0.344226i
$590$	−0.396878	−	5.29597i	−0.0163392	−	0.218032i
$591$	4.99282	−	6.26079i	0.205377	−	0.257535i
$592$	−4.63263	+	1.42898i	−0.190400	+	0.0587306i
$593$	11.4543	+	29.1852i	0.470374	+	1.19849i	0.947528	+	0.319673i	$0.103573\pi$
$593$	11.4543	+	29.1852i	0.470374	+	1.19849i	−0.477154	+	0.878820i	$0.658332\pi$
$594$	−5.72195	−	25.0695i	−0.234774	−	1.02861i
$595$	−1.83615	+	3.18031i	−0.0752750	+	0.130380i
$596$	−8.08595	−	14.0053i	−0.331213	−	0.573678i
$597$	41.4619	−	38.4710i	1.69692	−	1.57451i
$598$	13.5742	+	17.0215i	0.555089	+	0.696059i
$599$	−14.7726	−	10.0718i	−0.603591	−	0.411521i	0.222601	−	0.974910i	$-0.428545\pi$
$599$	−14.7726	−	10.0718i	−0.603591	−	0.411521i	−0.826192	+	0.563388i	$0.809498\pi$
$600$	−2.62603	−	1.26463i	−0.107207	−	0.0516282i
$601$	22.5941			0.921633			0.460816	−	0.887496i	$-0.347557\pi$
$601$	22.5941			0.921633			0.460816	+	0.887496i	$0.347557\pi$
$602$	4.31568	−	5.32031i	0.175894	−	0.216840i
$603$	−7.58557			−0.308908
$604$	−5.92587	−	2.85375i	−0.241120	−	0.116117i
$605$	−1.23963	−	0.845167i	−0.0503982	−	0.0343609i
$606$	−2.98028	−	3.73715i	−0.121065	−	0.151811i
$607$	−15.8736	+	14.7285i	−0.644288	+	0.597812i	−0.933119	−	0.359569i	$-0.882924\pi$
$607$	−15.8736	+	14.7285i	−0.644288	+	0.597812i	0.288831	+	0.957380i	$0.406733\pi$
$608$	3.57086	+	6.18491i	0.144817	+	0.250831i
$609$	−1.45125	+	2.51364i	−0.0588077	+	0.101858i
$610$	2.65809	+	11.6459i	0.107623	+	0.471527i
$611$	−12.3113	−	31.3686i	−0.498061	−	1.26904i
$612$	18.4586	−	5.69373i	0.746146	−	0.230156i
$613$	27.7573	−	34.8066i	1.12111	−	1.40582i	0.218245	−	0.975894i	$-0.429967\pi$
$613$	27.7573	−	34.8066i	1.12111	−	1.40582i	0.902862	−	0.429930i	$-0.141462\pi$
$614$	2.10661	+	28.1108i	0.0850159	+	1.13446i
$615$	16.9398	+	5.22523i	0.683078	+	0.210702i
$616$	3.05184	−	2.08071i	0.122962	−	0.0838340i
$617$	−5.35465	+	0.807084i	−0.215570	+	0.0324920i	−0.255939	−	0.966693i	$-0.582385\pi$
$617$	−5.35465	+	0.807084i	−0.215570	+	0.0324920i	0.0403691	+	0.999185i	$0.487147\pi$
$618$	4.57892	−	20.0616i	0.184191	−	0.806994i
$619$	−9.66611	−	8.96884i	−0.388514	−	0.360488i	0.461599	−	0.887089i	$-0.347276\pi$
$619$	−9.66611	−	8.96884i	−0.388514	−	0.360488i	−0.850113	+	0.526601i	$0.823466\pi$
$620$	0.296574	−	3.95750i	0.0119107	−	0.158937i
$621$	−10.5860	+	26.9727i	−0.424801	+	1.08238i
$622$	7.14696	+	1.07723i	0.286567	+	0.0431930i
$623$	14.3860	−	6.92796i	0.576365	−	0.277563i
$624$	−14.3503	+	6.91075i	−0.574473	+	0.276651i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	4.91293	−	12.5179i	0.196360	−	0.500317i
$627$	−5.49982	+	73.3900i	−0.219642	+	2.93091i
$628$	5.99961	+	5.56682i	0.239410	+	0.222140i
$629$	3.79209	−	16.6142i	0.151201	−	0.662453i
$630$	5.67686	−	0.855649i	0.226171	−	0.0340899i
$631$	10.3836	−	7.07945i	0.413366	−	0.281828i	−0.338727	−	0.940885i	$-0.609996\pi$
$631$	10.3836	−	7.07945i	0.413366	−	0.281828i	0.752094	+	0.659056i	$0.229044\pi$
$632$	−3.55563	−	1.09677i	−0.141435	−	0.0436270i
$633$	3.34857	+	44.6835i	0.133094	+	1.77601i
$634$	14.5788	−	18.2813i	0.579000	−	0.726043i
$635$	−14.3016	+	4.41146i	−0.567541	+	0.175063i
$636$	−10.2402	−	26.0916i	−0.406051	−	1.03460i
$637$	−7.18484	−	31.4788i	−0.284674	−	1.24724i
$638$	1.68508	−	2.91864i	0.0667128	−	0.115550i
$639$	8.84219	+	15.3151i	0.349792	+	0.605857i
$640$	−0.733052	+	0.680173i	−0.0289764	+	0.0268862i
$641$	−9.29436	−	11.6548i	−0.367105	−	0.460336i	0.563631	−	0.826027i	$-0.309404\pi$
$641$	−9.29436	−	11.6548i	−0.367105	−	0.460336i	−0.930736	+	0.365691i	$0.880833\pi$
$642$	−25.9627	−	17.7011i	−1.02467	−	0.698605i
$643$	−21.0464	−	10.1354i	−0.829990	−	0.399702i	−0.0298788	−	0.999554i	$-0.509512\pi$
$643$	−21.0464	−	10.1354i	−0.829990	−	0.399702i	−0.800112	+	0.599851i	$0.795226\pi$
$644$	−4.16213			−0.164011
$645$	−17.2884	+	8.14921i	−0.680729	+	0.320875i
$646$	−25.1042			−0.987713
$647$	−11.5669	−	5.57034i	−0.454743	−	0.218993i	0.192469	−	0.981303i	$-0.438351\pi$
$647$	−11.5669	−	5.57034i	−0.454743	−	0.218993i	−0.647211	+	0.762311i	$0.724065\pi$
$648$	−3.89358	−	2.65460i	−0.152954	−	0.104283i
$649$	−11.7072	−	14.6803i	−0.459546	−	0.576253i
$650$	−4.00587	+	3.71691i	−0.157123	+	0.145789i
$651$	6.04215	+	10.4653i	0.236810	+	0.410168i
$652$	9.75604	−	16.8980i	0.382076	−	0.661775i
$653$	1.82557	+	7.99835i	0.0714401	+	0.313000i	0.998005	−	0.0631354i	$-0.0201100\pi$
$653$	1.82557	+	7.99835i	0.0714401	+	0.313000i	−0.926565	+	0.376135i	$0.877253\pi$
$654$	−4.13063	−	10.5247i	−0.161520	−	0.411547i
$655$	0.758298	−	0.233904i	0.0296292	−	0.00913939i
$656$	3.79214	−	4.75519i	0.148058	−	0.185659i
$657$	−6.80448	−	90.7995i	−0.265468	−	3.54243i
$658$	6.15602	+	1.89888i	0.239987	+	0.0740261i
$659$	16.3242	−	11.1296i	0.635899	−	0.433549i	−0.201991	−	0.979387i	$-0.564741\pi$
$659$	16.3242	−	11.1296i	0.635899	−	0.433549i	0.837890	+	0.545839i	$0.183789\pi$
$660$	−10.1900	+	1.53589i	−0.396643	+	0.0597844i
$661$	−5.73945	+	25.1462i	−0.223239	+	0.978072i	0.731783	+	0.681537i	$0.238688\pi$
$661$	−5.73945	+	25.1462i	−0.223239	+	0.978072i	−0.955022	+	0.296535i	$0.904169\pi$
$662$	9.26442	+	8.59612i	0.360072	+	0.334098i
$663$	4.18400	−	55.8316i	0.162493	−	2.16832i
$664$	−3.00248	+	7.65019i	−0.116519	+	0.296885i
$665$	−7.37767	−	1.11201i	−0.286094	−	0.0431217i
$666$	−24.0030	+	11.5592i	−0.930096	+	0.447911i
$667$	−3.42152	+	1.64772i	−0.132482	+	0.0637999i
$668$	12.0268	+	1.81274i	0.465330	+	0.0701372i
$669$	−8.23294	+	20.9772i	−0.318304	+	0.811025i
$670$	−0.103156	+	1.37652i	−0.00398525	+	0.0531794i
$671$	30.9596	+	28.7263i	1.19518	+	1.10897i
$672$	0.677571	−	2.96863i	0.0261379	−	0.114518i
$673$	−31.6781	+	4.77470i	−1.22110	+	0.184051i	−0.727789	−	0.685802i	$-0.759452\pi$
$673$	−31.6781	+	4.77470i	−1.22110	+	0.184051i	−0.493311	+	0.869853i	$0.664214\pi$
$674$	−11.5565	+	7.87911i	−0.445141	+	0.303492i
$675$	−6.94986	−	2.14375i	−0.267500	−	0.0825128i
$676$	1.26013	+	16.8153i	0.0484666	+	0.646741i
$677$	12.0112	−	15.0615i	0.461626	−	0.578861i	−0.495472	−	0.868624i	$-0.665005\pi$
$677$	12.0112	−	15.0615i	0.461626	−	0.578861i	0.957099	+	0.289763i	$0.0935764\pi$
$678$	−39.3016	+	12.1230i	−1.50937	+	0.465579i
$679$	−1.12690	−	2.87130i	−0.0432465	−	0.110190i
$680$	−0.782195	−	3.42702i	−0.0299958	−	0.131420i
$681$	15.8077	−	27.3797i	0.605752	−	1.04919i
$682$	−7.01565	−	12.1515i	−0.268643	−	0.465304i
$683$	16.0564	−	14.8982i	0.614383	−	0.570064i	−0.310378	−	0.950613i	$-0.600456\pi$
$683$	16.0564	−	14.8982i	0.614383	−	0.570064i	0.924761	+	0.380549i	$0.124265\pi$
$684$	24.4694	+	30.6837i	0.935611	+	1.17322i
$685$	18.3074	+	12.4818i	0.699491	+	0.476905i
$686$	12.1502	+	5.85123i	0.463897	+	0.223401i
$687$	33.0235			1.25992
$688$	0.435635	+	6.54295i	0.0166084	+	0.249448i
$689$	−52.5514			−2.00205
$690$	10.4621	+	5.03830i	0.398286	+	0.191805i
$691$	8.50714	+	5.80007i	0.323627	+	0.220645i	0.714225	−	0.699916i	$-0.246779\pi$
$691$	8.50714	+	5.80007i	0.323627	+	0.220645i	−0.390598	+	0.920561i	$0.627732\pi$
$692$	15.0134	+	18.8263i	0.570725	+	0.715667i
$693$	14.8793	−	13.8059i	0.565217	−	0.524444i
$694$	−7.75871	−	13.4385i	−0.294516	−	0.510117i
$695$	−4.88836	+	8.46688i	−0.185426	+	0.321167i
$696$	−0.618228	−	2.70864i	−0.0234339	−	0.102671i
$697$	7.81084	+	19.9017i	0.295857	+	0.753830i
$698$	−11.2533	+	3.47118i	−0.425943	+	0.131386i
$699$	55.1945	−	69.2117i	2.08765	−	2.61783i
$700$	−0.0780711	−	1.04179i	−0.00295081	−	0.0393758i
$701$	28.0123	+	8.64064i	1.05801	+	0.326352i	0.774471	−	0.632609i	$-0.218016\pi$
$701$	28.0123	+	8.64064i	1.05801	+	0.326352i	0.283537	+	0.958961i	$0.408492\pi$
$702$	−32.8383	+	22.3887i	−1.23940	+	0.845009i
$703$	34.2364	−	5.16031i	1.29125	−	0.194625i
$704$	−0.786741	+	3.44694i	−0.0296514	+	0.129911i
$705$	−13.1755	−	12.2250i	−0.496217	−	0.460422i
$706$	−0.853371	+	11.3874i	−0.0321170	+	0.428572i
$707$	0.625938	−	1.59486i	0.0235408	−	0.0599810i
$708$	−15.3064	−	2.30707i	−0.575250	−	0.0867049i
$709$	−5.74558	+	2.76693i	−0.215780	+	0.103914i	−0.538652	−	0.842529i	$-0.681066\pi$
$709$	−5.74558	+	2.76693i	−0.215780	+	0.103914i	0.322872	+	0.946443i	$0.395352\pi$
$710$	2.89940	−	1.39628i	0.108813	−	0.0524014i
$711$	−20.2193	−	3.04757i	−0.758282	−	0.114293i
$712$	−5.58387	+	14.2275i	−0.209264	+	0.533197i
$713$	−1.18155	+	15.7667i	−0.0442495	+	0.590469i
$714$	7.84627	+	7.28027i	0.293639	+	0.272457i
$715$	−4.29927	+	18.8363i	−0.160783	+	0.704438i
$716$	0.0223105	−	0.00336276i	0.000833781	−	0.000125672i
$717$	24.5586	−	16.7437i	0.917156	−	0.625306i
$718$	12.2507	+	3.77884i	0.457192	+	0.141025i
$719$	−0.779901	−	10.4071i	−0.0290854	−	0.388118i	−0.992682	−	0.120757i	$-0.961468\pi$
$719$	−0.779901	−	10.4071i	−0.0290854	−	0.388118i	0.963597	−	0.267360i	$-0.0861514\pi$
$720$	−3.42626	+	4.29640i	−0.127689	+	0.160117i
$721$	7.04792	−	2.17400i	0.262478	−	0.0809639i
$722$	−11.6924	−	29.7918i	−0.435146	−	1.10874i
$723$	19.2140	+	84.1821i	0.714577	+	3.13077i
$724$	−5.69402	+	9.86234i	−0.211617	+	0.366531i
$725$	−0.476605	−	0.825504i	−0.0177007	−	0.0306585i
$726$	−3.20562	+	2.97438i	−0.118972	+	0.110389i
$727$	17.9549	+	22.5148i	0.665912	+	0.835027i	0.993973	−	0.109630i	$-0.0349664\pi$
$727$	17.9549	+	22.5148i	0.665912	+	0.835027i	−0.328061	+	0.944657i	$0.606395\pi$
$728$	−4.71697	−	3.21597i	−0.174822	−	0.119192i
$729$	33.9654	+	16.3569i	1.25798	+	0.605811i
$730$	−16.5695			−0.613263
$731$	−20.6838	−	10.1736i	−0.765018	−	0.376283i
$732$	34.8168			1.28687
$733$	22.9606	+	11.0573i	0.848070	+	0.408409i	0.806861	−	0.590741i	$-0.201165\pi$
$733$	22.9606	+	11.0573i	0.848070	+	0.408409i	0.0412093	+	0.999151i	$0.486879\pi$
$734$	−1.82704	−	1.24566i	−0.0674373	−	0.0459780i
$735$	−10.7375	−	13.4644i	−0.396058	−	0.496641i
$736$	2.92049	−	2.70982i	0.107651	−	0.0998852i
$737$	2.44021	+	4.22657i	0.0898864	+	0.155688i
$738$	16.7115	−	28.9452i	0.615160	−	1.06549i
$739$	−7.00838	−	30.7057i	−0.257807	−	1.12953i	−0.923590	−	0.383382i	$-0.874759\pi$
$739$	−7.00838	−	30.7057i	−0.257807	−	1.12953i	0.665783	−	0.746146i	$-0.268098\pi$
$740$	1.77118	+	4.51289i	0.0651098	+	0.165897i
$741$	108.697	−	33.5286i	3.99309	−	1.23171i
$742$	6.26391	−	7.85469i	0.229955	−	0.288355i
$743$	2.60652	+	34.7816i	0.0956240	+	1.27601i	0.814208	+	0.580573i	$0.197171\pi$
$743$	2.60652	+	34.7816i	0.0956240	+	1.27601i	−0.718584	+	0.695440i	$0.755209\pi$
$744$	−11.0533	−	3.40948i	−0.405232	−	0.124998i
$745$	−13.3618	+	9.10995i	−0.489540	+	0.333763i
$746$	9.60114	−	1.44714i	0.351523	−	0.0529835i
$747$	−10.0495	+	44.0297i	−0.367691	+	1.61096i
$748$	−9.11045	−	8.45326i	−0.333111	−	0.309082i
$749$	0.841676	−	11.2314i	0.0307542	−	0.410386i
$750$	−1.06485	+	2.71319i	−0.0388828	+	0.0990717i
$751$	40.5758	+	6.11581i	1.48063	+	0.223169i	0.839121	−	0.543945i	$-0.183070\pi$
$751$	40.5758	+	6.11581i	1.48063	+	0.223169i	0.641510	+	0.767115i	$0.278308\pi$
$752$	−5.55586	+	2.67556i	−0.202601	+	0.0975677i
$753$	−67.9438	+	32.7200i	−2.47601	+	1.19238i
$754$	−5.15078	−	0.776356i	−0.187580	−	0.0282732i
$755$	−2.40293	+	6.12256i	−0.0874515	+	0.222823i
$756$	0.567809	−	7.57689i	0.0206510	−	0.275569i
$757$	−13.7341	−	12.7434i	−0.499174	−	0.463166i	0.389947	−	0.920837i	$-0.372493\pi$
$757$	−13.7341	−	12.7434i	−0.499174	−	0.463166i	−0.889122	+	0.457671i	$0.848684\pi$
$758$	−0.352532	+	1.54454i	−0.0128045	+	0.0561003i
$759$	40.5969	−	6.11900i	1.47357	−	0.222106i
$760$	5.90076	−	4.02307i	0.214043	−	0.145932i
$761$	11.1967	+	3.45373i	0.405880	+	0.125197i	0.490971	−	0.871176i	$-0.336642\pi$
$761$	11.1967	+	3.45373i	0.405880	+	0.125197i	−0.0850911	+	0.996373i	$0.527118\pi$
$762$	3.25991	+	43.5005i	0.118094	+	1.57586i
$763$	2.52669	−	3.16837i	0.0914723	−	0.114703i
$764$	10.4168	−	3.21316i	0.376867	−	0.116248i
$765$	−7.05723	−	17.9815i	−0.255155	−	0.650123i
$766$	1.02734	+	4.50108i	0.0371193	+	0.162630i
$767$	−14.5109	+	25.1336i	−0.523958	+	0.907522i
$768$	1.45733	+	2.52418i	0.0525870	+	0.0910834i
$769$	−4.88858	+	4.53594i	−0.176287	+	0.163570i	−0.763381	−	0.645948i	$-0.776462\pi$
$769$	−4.88858	+	4.53594i	−0.176287	+	0.163570i	0.587094	+	0.809518i	$0.300272\pi$
$770$	−2.30295	−	2.88781i	−0.0829926	−	0.104069i
$771$	−60.9512	−	41.5558i	−2.19510	−	1.49660i
$772$	14.8770	+	7.16436i	0.535433	+	0.257851i
$773$	14.7905			0.531978			0.265989	−	0.963976i	$-0.414301\pi$
$773$	14.7905			0.531978			0.265989	+	0.963976i	$0.414301\pi$
$774$	7.72609	+	35.1971i	0.277709	+	1.26513i
$775$	−3.96860			−0.142556
$776$	2.66013	+	1.28105i	0.0954930	+	0.0459870i
$777$	−12.1970	−	8.31578i	−0.437565	−	0.298327i
$778$	−2.74664	−	3.44417i	−0.0984717	−	0.123480i
$779$	−31.8414	+	29.5445i	−1.14084	+	1.05854i
$780$	7.96383	+	13.7938i	0.285151	+	0.493896i
$781$	5.68892	−	9.85349i	0.203565	−	0.352586i
$782$	3.11628	+	13.6533i	0.111438	+	0.488241i
$783$	−2.53279	−	6.45344i	−0.0905145	−	0.230627i
$784$	−5.64608	+	1.74159i	−0.201646	+	0.0621995i
$785$	5.10290	−	6.39884i	0.182130	−	0.228384i
$786$	−0.172847	−	2.30648i	−0.00616524	−	0.0822694i
$787$	14.5922	+	4.50109i	0.520154	+	0.160446i	0.543705	−	0.839276i	$-0.317021\pi$
$787$	14.5922	+	4.50109i	0.520154	+	0.160446i	−0.0235509	+	0.999723i	$0.507497\pi$
$788$	−2.27003	+	1.54768i	−0.0808666	+	0.0551339i
$789$	51.1010	−	7.70224i	1.81924	−	0.274207i
$790$	−0.827986	+	3.62764i	−0.0294584	+	0.129066i
$791$	−10.8065	−	10.0270i	−0.384237	−	0.356520i
$792$	−1.45194	+	19.3747i	−0.0515923	+	0.688452i
$793$	23.8485	−	60.7649i	0.846884	−	2.15782i
$794$	4.91313	+	0.740536i	0.174361	+	0.0262806i
$795$	−25.2534	+	12.1614i	−0.895647	+	0.431321i
$796$	−17.4837	+	8.41973i	−0.619695	+	0.298429i
$797$	−30.1577	−	4.54555i	−1.06824	−	0.161011i	−0.408692	−	0.912672i	$-0.634015\pi$
$797$	−30.1577	−	4.54555i	−1.06824	−	0.161011i	−0.659550	+	0.751661i	$0.729253\pi$
$798$	−7.94484	+	20.2431i	−0.281244	+	0.716599i
$799$	1.61988	−	21.6157i	0.0573071	−	0.764710i
$800$	0.733052	+	0.680173i	0.0259173	+	0.0240477i
$801$	−18.6896	+	81.8843i	−0.660363	+	2.89324i
$802$	−5.88864	+	0.887570i	−0.207935	+	0.0313412i
$803$	−48.4032	+	33.0008i	−1.70811	+	1.16457i
$804$	3.84459	+	1.18590i	0.135588	+	0.0418234i
$805$	0.311036	+	4.15049i	0.0109626	+	0.146286i
$806$	−13.5216	+	16.9556i	−0.476279	+	0.597235i
$807$	−58.5755	+	18.0681i	−2.06196	+	0.636029i
$808$	0.599151	+	1.52661i	0.0210781	+	0.0537060i
$809$	1.48029	+	6.48557i	0.0520442	+	0.228021i	0.994261	−	0.106984i	$-0.0341193\pi$
$809$	1.48029	+	6.48557i	0.0520442	+	0.228021i	−0.942217	+	0.335004i	$0.891262\pi$
$810$	−2.35621	+	4.08107i	−0.0827888	+	0.143394i
$811$	21.6988	+	37.5834i	0.761947	+	1.31973i	0.941846	+	0.336046i	$0.109090\pi$
$811$	21.6988	+	37.5834i	0.761947	+	1.31973i	−0.179898	+	0.983685i	$0.557577\pi$
$812$	0.729992	−	0.677334i	0.0256177	−	0.0237698i
$813$	21.5214	+	26.9870i	0.754788	+	0.946474i
$814$	14.1622	+	9.65561i	0.496384	+	0.338429i
$815$	−17.5798	−	8.46597i	−0.615793	−	0.296550i
$816$	−10.2455			−0.358665
$817$	3.88800	−	46.6697i	0.136024	−	1.63277i
$818$	5.05772			0.176839
$819$	−28.2656	−	13.6120i	−0.987681	−	0.475642i
$820$	−5.02528	−	3.42618i	−0.175490	−	0.119647i
$821$	−14.9258	−	18.7163i	−0.520913	−	0.653204i	0.449890	−	0.893084i	$-0.351463\pi$
$821$	−14.9258	−	18.7163i	−0.520913	−	0.653204i	−0.970802	+	0.239880i	$0.922892\pi$
$822$	47.3419	−	43.9269i	1.65124	−	1.53213i
$823$	−14.3083	−	24.7827i	−0.498755	−	0.863870i	0.501244	−	0.865306i	$-0.332876\pi$
$823$	−14.3083	−	24.7827i	−0.498755	−	0.863870i	−0.999999	+	0.00143651i	$0.999543\pi$
$824$	−3.52998	+	6.11411i	−0.122973	+	0.212995i
$825$	2.29309	+	10.0467i	0.0798351	+	0.349781i
$826$	−2.02700	−	5.16472i	−0.0705285	−	0.179704i
$827$	−37.3384	+	11.5174i	−1.29838	+	0.400499i	−0.865481	−	0.500942i	$-0.832987\pi$
$827$	−37.3384	+	11.5174i	−1.29838	+	0.400499i	−0.432903	+	0.901440i	$0.642511\pi$
$828$	13.6503	−	17.1169i	0.474380	−	0.594854i
$829$	−3.17471	−	42.3636i	−0.110262	−	1.47135i	−0.728331	−	0.685225i	$-0.759704\pi$
$829$	−3.17471	−	42.3636i	−0.110262	−	1.47135i	0.618069	−	0.786124i	$-0.287915\pi$
$830$	7.85318	+	2.42238i	0.272588	+	0.0840822i
$831$	66.9726	−	45.6612i	2.32326	−	1.58397i
$832$	5.40362	−	0.814464i	0.187337	−	0.0282365i
$833$	4.62167	−	20.2489i	0.160131	−	0.701581i
$834$	20.8890	+	19.3821i	0.723325	+	0.671148i
$835$	0.908914	−	12.1286i	0.0314543	−	0.419728i
$836$	9.22490	−	23.5047i	0.319050	−	0.812926i
$837$	−28.5411	−	4.30188i	−0.986526	−	0.148695i
$838$	4.17417	−	2.01017i	0.144194	−	0.0694403i
$839$	15.7170	−	7.56892i	0.542612	−	0.261308i	−0.142439	−	0.989804i	$-0.545494\pi$
$839$	15.7170	−	7.56892i	0.542612	−	0.261308i	0.685051	+	0.728495i	$0.259780\pi$
$840$	−3.01097	−	0.453830i	−0.103888	−	0.0156586i
$841$	−10.2629	+	26.1495i	−0.353894	+	0.901708i
$842$	−1.29232	+	17.2448i	−0.0445364	+	0.594297i
$843$	−32.5618	−	30.2129i	−1.12149	−	1.04059i
$844$	3.42093	−	14.9881i	0.117753	−	0.515911i
$845$	16.6741	−	2.51321i	0.573606	−	0.0864572i
$846$	−27.9988	+	19.0892i	−0.962617	+	0.656301i
$847$	−1.49777	−	0.462002i	−0.0514641	−	0.0158746i
$848$	0.718649	+	9.58970i	0.0246785	+	0.329312i
$849$	3.58002	−	4.48920i	0.122866	−	0.154069i
$850$	−3.35899	+	1.03611i	−0.115212	+	0.0355383i
$851$	−7.05640	−	17.9794i	−0.241890	−	0.616326i
$852$	−2.08718	−	9.14451i	−0.0715054	−	0.313286i
$853$	21.7487	−	37.6698i	0.744660	−	1.28979i	−0.205694	−	0.978616i	$-0.565945\pi$
$853$	21.7487	−	37.6698i	0.744660	−	1.28979i	0.950354	−	0.311172i	$-0.100722\pi$
$854$	6.23971	+	10.8075i	0.213518	+	0.369825i
$855$	28.7693	−	26.6940i	0.983888	−	0.912914i
$856$	6.72177	+	8.42884i	0.229745	+	0.288092i
$857$	−3.25619	−	2.22003i	−0.111229	−	0.0758349i	0.506428	−	0.862282i	$-0.330966\pi$
$857$	−3.25619	−	2.22003i	−0.111229	−	0.0758349i	−0.617657	+	0.786447i	$0.711918\pi$
$858$	50.7367	+	24.4335i	1.73212	+	0.834147i
$859$	−36.3572			−1.24049			−0.620246	−	0.784407i	$-0.712967\pi$
$859$	−36.3572			−1.24049			−0.620246	+	0.784407i	$0.712967\pi$
$860$	6.49210	−	0.923372i	0.221379	−	0.0314867i
$861$	18.5199			0.631157
$862$	−31.3434	−	15.0942i	−1.06756	−	0.514110i
$863$	−38.5729	−	26.2985i	−1.31304	−	0.895212i	−0.314497	−	0.949259i	$-0.601836\pi$
$863$	−38.5729	−	26.2985i	−1.31304	−	0.895212i	−0.998538	+	0.0540463i	$0.982788\pi$
$864$	4.53463	+	5.68624i	0.154271	+	0.193450i
$865$	17.6517	−	16.3783i	0.600174	−	0.556880i
$866$	−13.0744	−	22.6455i	−0.444286	−	0.769525i
$867$	−6.76741	+	11.7215i	−0.229833	+	0.398083i
$868$	−0.922577	−	4.04208i	−0.0313143	−	0.137197i
$869$	4.80631	+	12.2463i	0.163043	+	0.415426i
$870$	−2.65486	+	0.818916i	−0.0900082	+	0.0277639i
$871$	4.70315	−	5.89757i	0.159360	−	0.199831i
$872$	0.289884	+	3.86823i	0.00981669	+	0.130995i
$873$	15.5041	+	4.78239i	0.524736	+	0.161859i
$874$	−23.5087	+	16.0280i	−0.795194	+	0.542154i
$875$	−1.03304	+	0.155706i	−0.0349231	+	0.00526381i
$876$	−10.7465	+	47.0836i	−0.363092	+	1.59081i
$877$	5.10812	+	4.73964i	0.172489	+	0.160046i	0.761693	−	0.647938i	$-0.224368\pi$
$877$	5.10812	+	4.73964i	0.172489	+	0.160046i	−0.589205	+	0.807984i	$0.700559\pi$
$878$	−0.355841	+	4.74837i	−0.0120091	+	0.160250i
$879$	−28.5717	+	72.7995i	−0.963699	+	2.45546i
$880$	3.49609	+	0.526951i	0.117853	+	0.0177635i
$881$	−8.65446	+	4.16777i	−0.291576	+	0.140416i	−0.573954	−	0.818888i	$-0.694591\pi$
$881$	−8.65446	+	4.16777i	−0.291576	+	0.140416i	0.282378	+	0.959303i	$0.408877\pi$
$882$	−29.2540	+	14.0880i	−0.985032	+	0.474367i
$883$	−25.0579	−	3.77686i	−0.843264	−	0.127102i	−0.286818	−	0.957985i	$-0.592597\pi$
$883$	−25.0579	−	3.77686i	−0.843264	−	0.127102i	−0.556446	+	0.830884i	$0.687836\pi$
$884$	−7.01787	+	17.8812i	−0.236037	+	0.601411i
$885$	−1.15677	+	15.4360i	−0.0388843	+	0.518876i
$886$	−16.9210	−	15.7004i	−0.568473	−	0.527466i
$887$	−4.66837	+	20.4535i	−0.156748	+	0.686760i	0.834081	+	0.551642i	$0.185999\pi$
$887$	−4.66837	+	20.4535i	−0.156748	+	0.686760i	−0.990830	+	0.135118i	$0.956859\pi$
$888$	13.9725	−	2.10602i	0.468888	−	0.0706734i
$889$	−12.9188	+	8.80786i	−0.433281	+	0.295406i
$890$	14.6050	+	4.50504i	0.489560	+	0.151009i
$891$	1.24509	+	16.6145i	0.0417120	+	0.556608i
$892$	4.82055	−	6.04478i	0.161404	−	0.202394i
$893$	42.0831	−	12.9809i	1.40826	−	0.434390i
$894$	17.2206	+	43.8774i	0.575943	+	1.46748i
$895$	−0.00502062	−	0.0219968i	−0.000167821	−	0.000735271i
$896$	−0.522354	+	0.904743i	−0.0174506	+	0.0302254i
$897$	−31.7280	−	54.9545i	−1.05937	−	1.83488i
$898$	27.0658	−	25.1134i	0.903197	−	0.838044i
$899$	−2.35860	−	2.95760i	−0.0786639	−	0.0986414i
$900$	4.54043	+	3.09561i	0.151348	+	0.103187i
$901$	−30.4562	−	14.6669i	−1.01464	−	0.488626i
$902$	−21.5038			−0.715999
$903$	−14.7495	+	13.4590i	−0.490832	+	0.447887i
$904$	14.1110			0.469325
$905$	10.2603	+	4.94109i	0.341063	+	0.164247i
$906$	15.8393	+	10.7991i	0.526227	+	0.358775i
$907$	3.86622	+	4.84809i	0.128376	+	0.160978i	0.841865	−	0.539688i	$-0.181458\pi$
$907$	3.86622	+	4.84809i	0.128376	+	0.160978i	−0.713489	+	0.700666i	$0.752886\pi$
$908$	−7.95141	+	7.37783i	−0.263877	+	0.244842i
$909$	4.50608	+	7.80476i	0.149457	+	0.258868i
$910$	−2.85448	+	4.94411i	−0.0946252	+	0.163896i
$911$	10.5043	+	46.0221i	0.348022	+	1.52478i	0.781666	+	0.623698i	$0.214370\pi$
$911$	10.5043	+	46.0221i	0.348022	+	1.52478i	−0.433644	+	0.901084i	$0.642773\pi$
$912$	−7.60484	−	19.3768i	−0.251822	−	0.641631i
$913$	27.7655	−	8.56454i	0.918905	−	0.283445i
$914$	−16.4519	+	20.6301i	−0.544182	+	0.682382i
$915$	−2.60186	−	34.7194i	−0.0860149	−	1.14779i
$916$	−10.8267	−	3.33960i	−0.357725	−	0.110344i
$917$	0.684978	−	0.467010i	0.0226200	−	0.0154220i
$918$	−25.2801	+	3.81036i	−0.834367	+	0.125761i
$919$	10.3841	−	45.4955i	0.342538	−	1.50076i	−0.451157	−	0.892444i	$-0.648989\pi$
$919$	10.3841	−	45.4955i	0.342538	−	1.50076i	0.793696	−	0.608315i	$-0.208154\pi$
$920$	−2.92049	−	2.70982i	−0.0962857	−	0.0893401i
$921$	6.14007	−	81.9336i	0.202322	−	2.69980i
$922$	−4.60127	+	11.7238i	−0.151535	+	0.386104i
$923$	−17.3893	−	2.62102i	−0.572377	−	0.0862720i
$924$	−9.69962	+	4.67109i	−0.319094	+	0.153668i
$925$	4.36791	−	2.10347i	0.143616	−	0.0691618i
$926$	32.1570	+	4.84688i	1.05674	+	0.159279i
$927$	−14.1740	+	36.1148i	−0.465535	+	1.18616i
$928$	−0.0712335	+	0.950545i	−0.00233835	+	0.0312032i
$929$	−15.4329	−	14.3197i	−0.506338	−	0.469813i	0.385152	−	0.922853i	$-0.374149\pi$
$929$	−15.4329	−	14.3197i	−0.506338	−	0.469813i	−0.891490	+	0.453040i	$0.850339\pi$
$930$	−2.57393	+	11.2771i	−0.0844026	+	0.369792i
$931$	41.7261	−	6.28920i	1.36752	−	0.206120i
$932$	−25.0947	+	17.1093i	−0.822006	+	0.560434i
$933$	−20.1304	−	6.20940i	−0.659040	−	0.203287i
$934$	−0.532360	−	7.10385i	−0.0174193	−	0.232445i
$935$	−7.74880	+	9.71669i	−0.253413	+	0.317770i
$936$	28.6958	−	8.85147i	0.937950	−	0.289319i
$937$	−12.4207	−	31.6475i	−0.405768	−	1.03388i	−0.977028	−	0.213111i	$-0.931640\pi$
$937$	−12.4207	−	31.6475i	−0.405768	−	1.03388i	0.571260	−	0.820769i	$-0.306455\pi$
$938$	0.320895	+	1.40593i	0.0104776	+	0.0459053i
$939$	−19.5975	+	33.9439i	−0.639541	+	1.10772i
$940$	3.08327	+	5.34038i	0.100565	+	0.174184i
$941$	−24.2973	+	22.5446i	−0.792070	+	0.734934i	−0.968401	−	0.249397i	$-0.919768\pi$
$941$	−24.2973	+	22.5446i	−0.792070	+	0.734934i	0.176331	+	0.984331i	$0.443577\pi$
$942$	−14.8733	−	18.6505i	−0.484598	−	0.607666i
$943$	20.0208	+	13.6499i	0.651967	+	0.444504i
$944$	4.78488	+	2.30428i	0.155735	+	0.0749979i
$945$	−7.59813			−0.247167
$946$	17.1259	−	15.6275i	0.556811	−	0.508093i
$947$	45.3865			1.47486			0.737432	−	0.675422i	$-0.236038\pi$
$947$	45.3865			1.47486			0.737432	+	0.675422i	$0.236038\pi$
$948$	9.77128	+	4.70560i	0.317356	+	0.152831i
$949$	74.8129	+	51.0065i	2.42853	+	1.65574i
$950$	−4.45279	−	5.58362i	−0.144467	−	0.181156i
$951$	−49.9595	+	46.3556i	−1.62005	+	1.50318i
$952$	−1.83615	−	3.18031i	−0.0595101	−	0.103075i
$953$	−18.2282	+	31.5721i	−0.590469	+	1.02272i	0.403701	+	0.914891i	$0.367724\pi$
$953$	−18.2282	+	31.5721i	−0.590469	+	1.02272i	−0.994169	+	0.107830i	$0.965610\pi$
$954$	11.7594	+	51.5211i	0.380723	+	1.66806i
$955$	−3.98263	−	10.1476i	−0.128875	−	0.328368i
$956$	−9.74477	+	3.00586i	−0.315168	+	0.0972166i
$957$	−6.12447	+	7.67984i	−0.197976	+	0.248254i
$958$	−0.370823	−	4.94828i	−0.0119807	−	0.159872i
$959$	22.1197	+	6.82304i	0.714284	+	0.220327i
$960$	2.40821	−	1.64189i	0.0777247	−	0.0529918i
$961$	15.0799	−	2.27293i	0.486448	−	0.0733203i
$962$	5.89518	−	25.8285i	0.190068	−	0.832744i
$963$	43.4291	+	40.2963i	1.39948	+	1.29853i
$964$	2.21388	−	29.5421i	0.0713042	−	0.951488i
$965$	6.03258	−	15.3708i	0.194195	−	0.494802i
$966$	11.9957	+	1.80807i	0.385957	+	0.0581736i
$967$	−19.1937	+	9.24318i	−0.617226	+	0.297241i	−0.716249	−	0.697845i	$-0.754143\pi$
$967$	−19.1937	+	9.24318i	−0.617226	+	0.297241i	0.0990228	+	0.995085i	$0.468428\pi$
$968$	1.35175	−	0.650970i	0.0434470	−	0.0209230i
$969$	72.3533	+	10.9055i	2.32432	+	0.350335i
$970$	1.07868	−	2.74842i	0.0346342	−	0.0882465i
$971$	−1.30482	+	17.4116i	−0.0418738	+	0.558766i	0.936330	+	0.351120i	$0.114199\pi$
$971$	−1.30482	+	17.4116i	−0.0418738	+	0.558766i	−0.978204	+	0.207646i	$0.933420\pi$
$972$	−5.92583	−	5.49837i	−0.190071	−	0.176360i
$973$	−2.27279	+	9.95772i	−0.0728621	+	0.319230i
$974$	0.894898	−	0.134884i	0.0286744	−	0.00432197i
$975$	13.1600	−	8.97237i	0.421459	−	0.287346i
$976$	−11.4147	−	3.52096i	−0.365374	−	0.112703i
$977$	2.34768	+	31.3276i	0.0751088	+	1.00226i	0.899694	+	0.436520i	$0.143789\pi$
$977$	2.34768	+	31.3276i	0.0751088	+	1.00226i	−0.824586	+	0.565737i	$0.808592\pi$
$978$	−35.4586	+	44.4637i	−1.13384	+	1.42179i
$979$	51.6371	−	15.9279i	1.65033	−	0.509059i
$980$	2.15865	+	5.50015i	0.0689555	+	0.175696i
$981$	4.74341	+	20.7822i	0.151445	+	0.663525i
$982$	6.29208	−	10.8982i	0.200788	−	0.347776i
$983$	12.3330	+	21.3614i	0.393362	+	0.681323i	0.992891	−	0.119030i	$-0.0379786\pi$
$983$	12.3330	+	21.3614i	0.393362	+	0.681323i	−0.599529	+	0.800353i	$0.704645\pi$
$984$	−12.9951	+	12.0577i	−0.414268	+	0.384385i
$985$	1.71300	+	2.14803i	0.0545806	+	0.0684419i
$986$	−2.76846	−	1.88751i	−0.0881658	−	0.0601104i
$987$	−16.9175	−	8.14703i	−0.538489	−	0.259323i
$988$	−39.0270			−1.24161
$989$	−25.8646	+	3.67873i	−0.822447	+	0.116977i
$990$	19.4291			0.617497
$991$	38.2704	+	18.4300i	1.21570	+	0.585449i	0.928110	−	0.372305i	$-0.121432\pi$
$991$	38.2704	+	18.4300i	1.21570	+	0.585449i	0.287588	+	0.957754i	$0.407147\pi$
$992$	3.27901	+	2.23559i	0.104109	+	0.0709801i
$993$	−22.9669	−	28.7996i	−0.728832	−	0.913926i
$994$	2.46450	−	2.28672i	0.0781691	−	0.0725303i
$995$	9.70275	+	16.8057i	0.307598	+	0.532775i
$996$	11.9768	−	20.7444i	0.379500	−	0.657313i
$997$	4.77297	+	20.9117i	0.151161	+	0.662282i	0.992549	+	0.121849i	$0.0388823\pi$
$997$	4.77297	+	20.9117i	0.151161	+	0.662282i	−0.841387	+	0.540433i	$0.818261\pi$
$998$	13.3905	+	34.1184i	0.423869	+	1.08000i
$999$	33.6930	−	10.3929i	1.06600	−	0.328817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.111.1	yes	60
43.31	even	21	inner	430.2.q.d.31.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.31.1	✓	60	43.31	even	21	inner
430.2.q.d.111.1	yes	60	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 + 0.433884i) q^{2} +(-2.40821 - 1.64189i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(-1.45733 - 2.52418i) q^{6} +(0.522354 - 0.904743i) q^{7} +(0.222521 + 0.974928i) q^{8} +(2.00766 + 5.11543i) q^{9} +O(q^{10})\)	\(q+(0.900969 + 0.433884i) q^{2} +(-2.40821 - 1.64189i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.733052 - 0.680173i) q^{5} +(-1.45733 - 2.52418i) q^{6} +(0.522354 - 0.904743i) q^{7} +(0.222521 + 0.974928i) q^{8} +(2.00766 + 5.11543i) q^{9} +(0.955573 - 0.294755i) q^{10} +(2.20440 - 2.76423i) q^{11} +(-0.217814 - 2.90652i) q^{12} +(-5.22187 - 1.61073i) q^{13} +(0.863178 - 0.588505i) q^{14} +(-2.88212 + 0.434409i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-2.57679 - 2.39091i) q^{17} +(-0.410664 + 5.47993i) q^{18} +(2.60916 - 6.64804i) q^{19} +(0.988831 + 0.149042i) q^{20} +(-2.74343 + 1.32117i) q^{21} +(3.18545 - 1.53403i) q^{22} +(-3.93952 - 0.593787i) q^{23} +(1.06485 - 2.71319i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(-4.00587 - 3.71691i) q^{26} +(1.61839 - 7.09063i) q^{27} +(1.03304 - 0.155706i) q^{28} +(0.787579 - 0.536962i) q^{29} +(-2.78518 - 0.859114i) q^{30} +(-0.296574 - 3.95750i) q^{31} +(-0.623490 + 0.781831i) q^{32} +(-9.84723 + 3.03747i) q^{33} +(-1.28423 - 3.27216i) q^{34} +(-0.232469 - 1.01851i) q^{35} +(-2.74765 + 4.75907i) q^{36} +(2.42401 + 4.19850i) q^{37} +(5.23525 - 4.85760i) q^{38} +(9.93073 + 12.4527i) q^{39} +(0.826239 + 0.563320i) q^{40} +(-5.47980 - 2.63893i) q^{41} -3.04498 q^{42} +(6.28197 - 1.88066i) q^{43} +3.53558 q^{44} +(4.95109 + 2.38432i) q^{45} +(-3.29175 - 2.24428i) q^{46} +(3.84478 + 4.82120i) q^{47} +(2.13660 - 1.98248i) q^{48} +(2.95429 + 5.11699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(2.27984 + 9.98864i) q^{51} +(-1.99646 - 5.08690i) q^{52} +(9.18936 - 2.83454i) q^{53} +(4.53463 - 5.68624i) q^{54} +(-0.264214 - 3.52569i) q^{55} +(0.998294 + 0.307933i) q^{56} +(-17.1988 + 11.7259i) q^{57} +(0.942564 - 0.142069i) q^{58} +(1.18177 - 5.17767i) q^{59} +(-2.13660 - 1.98248i) q^{60} +(-0.892678 + 11.9120i) q^{61} +(1.44989 - 3.69426i) q^{62} +(5.67686 + 0.855649i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-4.92348 + 2.37102i) q^{65} +(-10.1900 - 1.53589i) q^{66} +(-0.504308 + 1.28495i) q^{67} +(0.262688 - 3.50533i) q^{68} +(8.51226 + 7.89822i) q^{69} +(0.232469 - 1.01851i) q^{70} +(3.18215 - 0.479632i) q^{71} +(-4.54043 + 3.09561i) q^{72} +(-15.8333 - 4.88393i) q^{73} +(0.362292 + 4.83446i) q^{74} +(-1.81727 + 2.27878i) q^{75} +(6.82443 - 2.10506i) q^{76} +(-1.34944 - 3.43832i) q^{77} +(3.54424 + 15.5283i) q^{78} +(-1.86047 + 3.22242i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.45445 + 3.20526i) q^{81} +(-3.79214 - 4.75519i) q^{82} +(6.79027 + 4.62953i) q^{83} +(-2.74343 - 1.32117i) q^{84} -3.51515 q^{85} +(6.47584 + 1.03123i) q^{86} -2.77829 q^{87} +(3.18545 + 1.53403i) q^{88} +(12.6282 + 8.60978i) q^{89} +(3.42626 + 4.29640i) q^{90} +(-4.18497 + 3.88308i) q^{91} +(-1.99201 - 3.45026i) q^{92} +(-5.78358 + 10.0174i) q^{93} +(1.37218 + 6.01194i) q^{94} +(-2.60916 - 6.64804i) q^{95} +(2.78518 - 0.859114i) q^{96} +(1.84086 - 2.30837i) q^{97} +(0.441549 + 5.89206i) q^{98} +(18.5659 + 5.72682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

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