LMFDB - Embedded newform 805.2.bs.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(37,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(132))

chi = DirichletCharacter(H, H._module([33, 44, 126]))

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

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

chi := DirichletCharacter("805.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.bs (of order $132$, degree $40$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$3680$
Relative dimension:	$92$ over $\Q(\zeta_{132})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{132}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	805.37
Dual form			805.2.bs.a.718.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52376 + 0.928783i) q^{2} +(-0.164334 - 0.338297i) q^{3} +(0.542767 - 1.05282i) q^{4} +(-2.23602 - 0.0147772i) q^{5} +(0.564611 + 0.362854i) q^{6} +(1.55128 + 2.14325i) q^{7} +(-0.103819 - 1.45157i) q^{8} +(1.76704 - 2.24697i) q^{9} +O(q^{10})$	\(q+(-1.52376 + 0.928783i) q^{2} +(-0.164334 - 0.338297i) q^{3} +(0.542767 - 1.05282i) q^{4} +(-2.23602 - 0.0147772i) q^{5} +(0.564611 + 0.362854i) q^{6} +(1.55128 + 2.14325i) q^{7} +(-0.103819 - 1.45157i) q^{8} +(1.76704 - 2.24697i) q^{9} +(3.42089 - 2.05426i) q^{10} +(-5.54191 + 1.34445i) q^{11} +(-0.445361 - 0.0106016i) q^{12} +(-0.204639 - 0.0763262i) q^{13} +(-4.35440 - 1.82500i) q^{14} +(0.362456 + 0.758867i) q^{15} +(2.88054 + 4.04515i) q^{16} +(2.47386 + 2.72133i) q^{17} +(-0.605601 + 5.06505i) q^{18} +(-0.278759 - 5.85187i) q^{19} +(-1.22919 + 2.34611i) q^{20} +(0.470125 - 0.877004i) q^{21} +(7.19586 - 7.19586i) q^{22} +(-1.90238 - 4.40238i) q^{23} +(-0.474002 + 0.273665i) q^{24} +(4.99956 + 0.0660843i) q^{25} +(0.382711 - 0.0737616i) q^{26} +(-2.15304 - 0.468365i) q^{27} +(3.09844 - 0.469939i) q^{28} +(-1.82982 + 2.84725i) q^{29} +(-1.25712 - 0.819691i) q^{30} +(2.31401 + 0.445989i) q^{31} +(-5.47077 - 2.34272i) q^{32} +(1.36555 + 1.65387i) q^{33} +(-6.29710 - 1.84900i) q^{34} +(-3.43703 - 4.81527i) q^{35} +(-1.40657 - 3.07996i) q^{36} +(7.78993 - 0.931400i) q^{37} +(5.85988 + 8.65797i) q^{38} +(0.00780824 + 0.0817716i) q^{39} +(0.210690 + 3.24728i) q^{40} +(-0.100317 - 0.697718i) q^{41} +(0.0981865 + 1.77299i) q^{42} +(0.311526 - 4.35570i) q^{43} +(-1.59250 + 6.56436i) q^{44} +(-3.98433 + 4.99816i) q^{45} +(6.98764 + 4.94129i) q^{46} +(7.96163 - 2.13331i) q^{47} +(0.895091 - 1.63924i) q^{48} +(-2.18704 + 6.64958i) q^{49} +(-7.67953 + 4.54281i) q^{50} +(0.514079 - 1.28411i) q^{51} +(-0.191429 + 0.174020i) q^{52} +(9.15145 + 7.55608i) q^{53} +(3.71574 - 1.28603i) q^{54} +(12.4117 - 2.92433i) q^{55} +(2.95003 - 2.47431i) q^{56} +(-1.93386 + 1.05597i) q^{57} +(0.143732 - 6.03804i) q^{58} +(6.00444 + 4.27574i) q^{59} +(0.995680 + 0.0302865i) q^{60} +(-10.5272 + 3.64349i) q^{61} +(-3.94023 + 1.46963i) q^{62} +(7.55700 + 0.301513i) q^{63} +(0.681202 - 0.0979421i) q^{64} +(0.456448 + 0.173691i) q^{65} +(-3.61687 - 1.25181i) q^{66} +(13.6179 - 0.324166i) q^{67} +(4.20780 - 1.12748i) q^{68} +(-1.17668 + 1.36703i) q^{69} +(9.70956 + 4.14508i) q^{70} +(0.691782 - 0.203126i) q^{71} +(-3.44510 - 2.33171i) q^{72} +(6.30635 - 2.01592i) q^{73} +(-11.0049 + 8.65438i) q^{74} +(-0.799245 - 1.70220i) q^{75} +(-6.31227 - 2.88272i) q^{76} +(-11.4786 - 9.79207i) q^{77} +(-0.0878460 - 0.117348i) q^{78} +(5.29134 + 0.505262i) q^{79} +(-6.38117 - 9.08761i) q^{80} +(-1.82641 - 7.52858i) q^{81} +(0.800888 + 0.969986i) q^{82} +(6.18779 - 4.63212i) q^{83} +(-0.668160 - 0.970966i) q^{84} +(-5.49138 - 6.12151i) q^{85} +(3.57080 + 6.92640i) q^{86} +(1.26392 + 0.151120i) q^{87} +(2.52693 + 7.90492i) q^{88} +(8.95842 - 1.72659i) q^{89} +(1.42898 - 11.3166i) q^{90} +(-0.153866 - 0.556995i) q^{91} +(-5.66747 - 0.386596i) q^{92} +(-0.229395 - 0.856114i) q^{93} +(-10.1503 + 10.6453i) q^{94} +(0.536836 + 13.0890i) q^{95} +(0.106501 + 2.23573i) q^{96} +(8.97107 + 6.71566i) q^{97} +(-2.84348 - 12.1637i) q^{98} +(-6.77182 + 14.8282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	$ 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) $ 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.52376	+	0.928783i	−1.07746	+	0.656749i	−0.942535	−	0.334107i	$-0.891565\pi$
$2$	−1.52376	+	0.928783i	−1.07746	+	0.656749i	−0.134929	+	0.990855i	$0.543081\pi$
$3$	−0.164334	−	0.338297i	−0.0948786	−	0.195316i	0.846732	−	0.532020i	$-0.178567\pi$
$3$	−0.164334	−	0.338297i	−0.0948786	−	0.195316i	−0.941611	+	0.336704i	$0.890688\pi$
$4$	0.542767	−	1.05282i	0.271383	−	0.526410i
$5$	−2.23602	−	0.0147772i	−0.999978	−	0.00660857i
$5$	−2.23602	−	0.0147772i	−0.999978	−	0.00660857i
$6$	0.564611	+	0.362854i	0.230502	+	0.148134i
$7$	1.55128	+	2.14325i	0.586330	+	0.810072i
$7$	1.55128	+	2.14325i	0.586330	+	0.810072i
$8$	−0.103819	−	1.45157i	−0.0367054	−	0.513209i
$9$	1.76704	−	2.24697i	0.589013	−	0.748991i
$10$	3.42089	−	2.05426i	1.08178	−	0.649614i
$11$	−5.54191	+	1.34445i	−1.67095	+	0.405368i	−0.955897	−	0.293703i	$-0.905112\pi$
$11$	−5.54191	+	1.34445i	−1.67095	+	0.405368i	−0.715053	+	0.699071i	$0.753597\pi$
$12$	−0.445361	−	0.0106016i	−0.128565	−	0.00306041i
$13$	−0.204639	−	0.0763262i	−0.0567565	−	0.0211691i	0.320926	−	0.947104i	$-0.396006\pi$
$13$	−0.204639	−	0.0763262i	−0.0567565	−	0.0211691i	−0.377682	+	0.925935i	$0.623279\pi$
$14$	−4.35440	−	1.82500i	−1.16376	−	0.487752i
$15$	0.362456	+	0.758867i	0.0935857	+	0.195939i
$16$	2.88054	+	4.04515i	0.720135	+	1.01129i
$17$	2.47386	+	2.72133i	0.599998	+	0.660020i	0.962284	−	0.272047i	$-0.0877005\pi$
$17$	2.47386	+	2.72133i	0.599998	+	0.660020i	−0.362286	+	0.932067i	$0.618004\pi$
$18$	−0.605601	+	5.06505i	−0.142741	+	1.19384i
$19$	−0.278759	−	5.85187i	−0.0639517	−	1.34251i	−0.771673	−	0.636020i	$-0.780580\pi$
$19$	−0.278759	−	5.85187i	−0.0639517	−	1.34251i	0.707721	−	0.706492i	$-0.249723\pi$
$20$	−1.22919	+	2.34611i	−0.274856	+	0.524605i
$21$	0.470125	−	0.877004i	0.102590	−	0.191378i
$22$	7.19586	−	7.19586i	1.53416	−	1.53416i
$23$	−1.90238	−	4.40238i	−0.396674	−	0.917959i
$23$	−1.90238	−	4.40238i	−0.396674	−	0.917959i
$24$	−0.474002	+	0.273665i	−0.0967553	+	0.0558617i
$25$	4.99956	+	0.0660843i	0.999913	+	0.0132169i
$26$	0.382711	−	0.0737616i	0.0750559	−	0.0144658i
$27$	−2.15304	−	0.468365i	−0.414353	−	0.0901370i
$28$	3.09844	−	0.469939i	0.585551	−	0.0888101i
$29$	−1.82982	+	2.84725i	−0.339788	+	0.528721i	−0.968531	−	0.248892i	$-0.919933\pi$
$29$	−1.82982	+	2.84725i	−0.339788	+	0.528721i	0.628743	+	0.777613i	$0.283570\pi$
$30$	−1.25712	−	0.819691i	−0.229518	−	0.149654i
$31$	2.31401	+	0.445989i	0.415608	+	0.0801020i	0.392769	−	0.919637i	$-0.371517\pi$
$31$	2.31401	+	0.445989i	0.415608	+	0.0801020i	0.0228395	+	0.999739i	$0.492729\pi$
$32$	−5.47077	−	2.34272i	−0.967104	−	0.414138i
$33$	1.36555	+	1.65387i	0.237712	+	0.287902i
$34$	−6.29710	−	1.84900i	−1.07994	−	0.317100i
$35$	−3.43703	−	4.81527i	−0.580964	−	0.813929i
$36$	−1.40657	−	3.07996i	−0.234428	−	0.513326i
$37$	7.78993	−	0.931400i	1.28066	−	0.153121i	0.549594	−	0.835432i	$-0.314782\pi$
$37$	7.78993	−	0.931400i	1.28066	−	0.153121i	0.731062	+	0.682311i	$0.239025\pi$
$38$	5.85988	+	8.65797i	0.950598	+	1.40451i
$39$	0.00780824	+	0.0817716i	0.00125032	+	0.0130939i
$40$	0.210690	+	3.24728i	0.0333131	+	0.513440i
$41$	−0.100317	−	0.697718i	−0.0156668	−	0.108965i	0.980487	−	0.196582i	$-0.0629841\pi$
$41$	−0.100317	−	0.697718i	−0.0156668	−	0.108965i	−0.996154	+	0.0876164i	$0.972075\pi$
$42$	0.0981865	+	1.77299i	0.0151505	+	0.273579i
$43$	0.311526	−	4.35570i	0.0475072	−	0.664238i	−0.916782	−	0.399387i	$-0.869223\pi$
$43$	0.311526	−	4.35570i	0.0475072	−	0.664238i	0.964290	−	0.264850i	$-0.0853226\pi$
$44$	−1.59250	+	6.56436i	−0.240078	+	0.989615i
$45$	−3.98433	+	4.99816i	−0.593950	+	0.745082i
$46$	6.98764	+	4.94129i	1.03027	+	0.728553i
$47$	7.96163	−	2.13331i	1.16132	−	0.311176i	0.373829	−	0.927498i	$-0.378045\pi$
$47$	7.96163	−	2.13331i	1.16132	−	0.311176i	0.787494	+	0.616322i	$0.211378\pi$
$48$	0.895091	−	1.63924i	0.129195	−	0.236603i
$49$	−2.18704	+	6.64958i	−0.312434	+	0.949940i
$50$	−7.67953	+	4.54281i	−1.08605	+	0.642450i
$51$	0.514079	−	1.28411i	0.0719854	−	0.179811i
$52$	−0.191429	+	0.174020i	−0.0265464	+	0.0241323i
$53$	9.15145	+	7.55608i	1.25705	+	1.03791i	0.997390	+	0.0722066i	$0.0230041\pi$
$53$	9.15145	+	7.55608i	1.25705	+	1.03791i	0.259659	+	0.965700i	$0.416390\pi$
$54$	3.71574	−	1.28603i	0.505648	−	0.175006i
$55$	12.4117	−	2.92433i	1.67359	−	0.394317i
$56$	2.95003	−	2.47431i	0.394215	−	0.330644i
$57$	−1.93386	+	1.05597i	−0.256146	+	0.139866i
$58$	0.143732	−	6.03804i	0.0188729	−	0.792833i
$59$	6.00444	+	4.27574i	0.781711	+	0.556654i	0.899776	−	0.436352i	$-0.143730\pi$
$59$	6.00444	+	4.27574i	0.781711	+	0.556654i	−0.118065	+	0.993006i	$0.537669\pi$
$60$	0.995680	+	0.0302865i	0.128542	+	0.00390997i
$61$	−10.5272	+	3.64349i	−1.34787	+	0.466501i	−0.903210	−	0.429200i	$-0.858796\pi$
$61$	−10.5272	+	3.64349i	−1.34787	+	0.466501i	−0.444657	+	0.895701i	$0.646674\pi$
$62$	−3.94023	+	1.46963i	−0.500410	+	0.186643i
$63$	7.55700	+	0.301513i	0.952092	+	0.0379870i
$64$	0.681202	−	0.0979421i	0.0851503	−	0.0122428i
$65$	0.456448	+	0.173691i	0.0566154	+	0.0215437i
$66$	−3.61687	−	1.25181i	−0.445205	−	0.154087i
$67$	13.6179	−	0.324166i	1.66369	−	0.0396032i	0.818645	−	0.574300i	$-0.194726\pi$
$67$	13.6179	−	0.324166i	1.66369	−	0.0396032i	0.845044	+	0.534697i	$0.179574\pi$
$68$	4.20780	−	1.12748i	0.510271	−	0.136727i
$69$	−1.17668	+	1.36703i	−0.141656	+	0.164571i
$70$	9.70956	+	4.14508i	1.16051	+	0.495432i
$71$	0.691782	−	0.203126i	0.0820994	−	0.0241066i	−0.240425	−	0.970668i	$-0.577287\pi$
$71$	0.691782	−	0.203126i	0.0820994	−	0.0241066i	0.322524	+	0.946561i	$0.395469\pi$
$72$	−3.44510	−	2.33171i	−0.406009	−	0.274795i
$73$	6.30635	−	2.01592i	0.738102	−	0.235946i	0.0883475	−	0.996090i	$-0.471841\pi$
$73$	6.30635	−	2.01592i	0.738102	−	0.235946i	0.649754	+	0.760144i	$0.274872\pi$
$74$	−11.0049	+	8.65438i	−1.27930	+	1.00605i
$75$	−0.799245	−	1.70220i	−0.0922888	−	0.196553i
$76$	−6.31227	−	2.88272i	−0.724067	−	0.330671i
$77$	−11.4786	−	9.79207i	−1.30811	−	1.11591i
$78$	−0.0878460	−	0.117348i	−0.00994660	−	0.0132871i
$79$	5.29134	+	0.505262i	0.595323	+	0.0568464i	0.388368	−	0.921504i	$-0.373039\pi$
$79$	5.29134	+	0.505262i	0.595323	+	0.0568464i	0.206954	+	0.978351i	$0.433645\pi$
$80$	−6.38117	−	9.08761i	−0.713436	−	1.01603i
$81$	−1.82641	−	7.52858i	−0.202935	−	0.836509i
$82$	0.800888	+	0.969986i	0.0884433	+	0.107117i
$83$	6.18779	−	4.63212i	0.679199	−	0.508442i	−0.203084	−	0.979161i	$-0.565097\pi$
$83$	6.18779	−	4.63212i	0.679199	−	0.508442i	0.882283	+	0.470720i	$0.156006\pi$
$84$	−0.668160	−	0.970966i	−0.0729022	−	0.105941i
$85$	−5.49138	−	6.12151i	−0.595623	−	0.663971i
$86$	3.57080	+	6.92640i	0.385050	+	0.746892i
$87$	1.26392	+	0.151120i	0.135506	+	0.0162017i
$88$	2.52693	+	7.90492i	0.269371	+	0.842667i
$89$	8.95842	−	1.72659i	0.949591	−	0.183019i	0.309139	−	0.951017i	$-0.399959\pi$
$89$	8.95842	−	1.72659i	0.949591	−	0.183019i	0.640452	+	0.767998i	$0.278747\pi$
$90$	1.42898	−	11.3166i	0.150628	−	1.19287i
$91$	−0.153866	−	0.556995i	−0.0161296	−	0.0583889i
$92$	−5.66747	−	0.386596i	−0.590874	−	0.0403055i
$93$	−0.229395	−	0.856114i	−0.0237871	−	0.0887748i
$94$	−10.1503	+	10.6453i	−1.04692	+	1.09798i
$95$	0.536836	+	13.0890i	0.0550782	+	1.34291i
$96$	0.106501	+	2.23573i	0.0108697	+	0.228183i
$97$	8.97107	+	6.71566i	0.910874	+	0.681872i	0.948282	−	0.317428i	$-0.102819\pi$
$97$	8.97107	+	6.71566i	0.910874	+	0.681872i	−0.0374084	+	0.999300i	$0.511910\pi$
$98$	−2.84348	−	12.1637i	−0.287235	−	1.22872i
$99$	−6.77182	+	14.8282i	−0.680594	+	1.49029i
$100$	2.78317	−	5.22777i	0.278317	−	0.522777i
$101$	−3.52563	+	1.41145i	−0.350813	+	0.140444i	−0.540375	−	0.841424i	$-0.681718\pi$
$101$	−3.52563	+	1.41145i	−0.350813	+	0.140444i	0.189562	+	0.981869i	$0.439293\pi$
$102$	0.409321	+	2.43414i	0.0405289	+	0.241016i
$103$	−13.0437	−	0.310498i	−1.28524	−	0.0305943i	−0.624388	−	0.781114i	$-0.714652\pi$
$103$	−13.0437	−	0.310498i	−1.28524	−	0.0305943i	−0.660848	+	0.750520i	$0.729803\pi$
$104$	−0.0895479	+	0.304972i	−0.00878089	+	0.0299050i
$105$	−1.06417	+	1.95405i	−0.103852	+	0.190696i
$106$	−20.9626	−	3.01397i	−2.03607	−	0.292742i
$107$	16.0942	+	7.81808i	1.55589	+	0.755803i	0.997285	−	0.0736340i	$-0.0234597\pi$
$107$	16.0942	+	7.81808i	1.55589	+	0.755803i	0.558601	+	0.829437i	$0.311338\pi$
$108$	−1.66170	+	2.01255i	−0.159898	+	0.193658i
$109$	−0.0144369	+	0.303069i	−0.00138281	+	0.0290287i	−0.999453	−	0.0330625i	$-0.989474\pi$
$109$	−0.0144369	+	0.303069i	−0.00138281	+	0.0290287i	0.998070	+	0.0620913i	$0.0197770\pi$
$110$	−16.1964	+	15.9838i	−1.54427	+	1.52399i
$111$	−1.59524	−	2.48225i	−0.151414	−	0.235604i
$112$	−4.20124	+	12.4489i	−0.396980	+	1.17631i
$113$	−2.03327	−	1.11025i	−0.191274	−	0.104444i	0.380758	−	0.924675i	$-0.375663\pi$
$113$	−2.03327	−	1.11025i	−0.191274	−	0.104444i	−0.572032	+	0.820231i	$0.693845\pi$
$114$	1.96598	−	3.40518i	0.184131	−	0.318925i
$115$	4.18871	+	9.87191i	0.390599	+	0.920561i
$116$	2.00448	+	3.47186i	0.186111	+	0.322354i
$117$	−0.533107	+	0.324946i	−0.0492857	+	0.0300412i
$118$	−13.1206	−	0.938402i	−1.20785	−	0.0863869i
$119$	−1.99484	+	9.52365i	−0.182867	+	0.873032i
$120$	1.06392	−	0.604916i	0.0971223	−	0.0552210i
$121$	19.1280	−	9.86119i	1.73891	−	0.896472i
$122$	12.6569	−	15.3293i	1.14590	−	1.38785i
$123$	−0.219550	+	0.148596i	−0.0197962	+	0.0133985i
$124$	1.72551	−	2.19417i	0.154956	−	0.197042i
$125$	−11.1781	−	0.221645i	−0.999803	−	0.0198246i
$126$	−11.7951	+	6.55938i	−1.05079	+	0.584356i
$127$	5.81352	+	10.6467i	0.515867	+	0.944739i	0.997654	+	0.0684512i	$0.0218057\pi$
$127$	5.81352	+	10.6467i	0.515867	+	0.944739i	−0.481788	+	0.876288i	$0.660012\pi$
$128$	8.23126	−	6.79630i	0.727547	−	0.600714i
$129$	−1.52471	+	0.610403i	−0.134244	+	0.0537430i
$130$	−0.856840	+	0.159277i	−0.0751498	+	0.0139695i
$131$	−8.60657	−	12.0862i	−0.751960	−	1.05598i	−0.996271	−	0.0862825i	$-0.972501\pi$
$131$	−8.60657	−	12.0862i	−0.751960	−	1.05598i	0.244311	−	0.969697i	$-0.421438\pi$
$132$	2.48241	−	0.540014i	0.216066	−	0.0470022i
$133$	12.1096	−	9.67537i	1.05003	−	0.838961i
$134$	−20.4494	+	13.1420i	−1.76656	+	1.13530i
$135$	4.80732	+	1.07909i	0.413748	+	0.0928733i
$136$	3.69339	−	3.87351i	0.316705	−	0.332151i
$137$	−1.07952	−	0.289257i	−0.0922299	−	0.0247129i	0.212409	−	0.977181i	$-0.431869\pi$
$137$	−1.07952	−	0.289257i	−0.0922299	−	0.0247129i	−0.304639	+	0.952468i	$0.598536\pi$
$138$	0.523312	−	3.17592i	0.0445473	−	0.270352i
$139$		−	1.72374i		−	0.146206i	−0.997324	−	0.0731030i	$-0.976710\pi$
$139$		−	1.72374i		−	0.146206i	0.997324	−	0.0731030i	$-0.0232902\pi$
$140$	−6.93512	+	1.00501i	−0.586125	+	0.0849385i
$141$	−2.03006	−	2.34282i	−0.170962	−	0.197301i
$142$	−0.865453	+	0.952031i	−0.0726272	+	0.0798927i
$143$	1.23671	+	0.147866i	0.103419	+	0.0123652i
$144$	14.1794	+	0.675447i	1.18161	+	0.0562872i
$145$	4.13358	−	6.33946i	0.343275	−	0.526464i
$146$	−7.73703	+	8.92901i	−0.640321	+	0.738970i
$147$	2.60894	−	0.352887i	0.215181	−	0.0291056i
$148$	3.24752	−	8.70693i	0.266944	−	0.715705i
$149$	2.07740	−	1.98080i	0.170188	−	0.162273i	−0.600199	−	0.799851i	$-0.704912\pi$
$149$	2.07740	−	1.98080i	0.170188	−	0.162273i	0.770386	+	0.637577i	$0.220063\pi$
$150$	2.79883	+	1.85142i	0.228524	+	0.151168i
$151$	11.5001	−	16.1496i	0.935865	−	1.31424i	−0.0134488	−	0.999910i	$-0.504281\pi$
$151$	11.5001	−	16.1496i	0.935865	−	1.31424i	0.949314	−	0.314329i	$-0.101780\pi$
$152$	−8.46549	+	1.01217i	−0.686642	+	0.0820981i
$153$	10.4862	−	0.749985i	0.847756	−	0.0606327i
$154$	26.5854	+	4.25970i	2.14231	+	0.343257i
$155$	−5.16758	−	1.03143i	−0.415070	−	0.0828468i
$156$	0.0903289	+	0.0361622i	0.00723210	+	0.00289530i
$157$	−20.2768	+	6.48178i	−1.61826	+	0.517303i	−0.969791	−	0.243936i	$-0.921561\pi$
$157$	−20.2768	+	6.48178i	−1.61826	+	0.517303i	−0.648472	+	0.761238i	$0.724592\pi$
$158$	−8.53204	+	4.14461i	−0.678773	+	0.329727i
$159$	1.05230	−	4.33763i	0.0834527	−	0.343997i
$160$	12.1981	+	5.31921i	0.964346	+	0.420520i
$161$	6.48426	−	10.9066i	0.511031	−	0.859562i
$162$	9.77544	+	9.77544i	0.768031	+	0.768031i
$163$	0.309036	+	0.507006i	0.0242056	+	0.0397118i	0.865753	−	0.500471i	$-0.166840\pi$
$163$	0.309036	+	0.507006i	0.0242056	+	0.0397118i	−0.841548	+	0.540183i	$0.818355\pi$
$164$	−0.789021	−	0.273083i	−0.0616122	−	0.0213242i
$165$	−3.02896	−	3.71827i	−0.235804	−	0.289467i
$166$	−5.12650	+	12.8054i	−0.397894	+	0.993890i
$167$	−5.24109	−	24.0929i	−0.405568	−	1.86437i	−0.495788	−	0.868443i	$-0.665121\pi$
$167$	−5.24109	−	24.0929i	−0.405568	−	1.86437i	0.0902204	−	0.995922i	$-0.471243\pi$
$168$	−1.32184	−	0.591372i	−0.101983	−	0.0456254i
$169$	−9.78869	−	8.48195i	−0.752976	−	0.652458i
$170$	14.0531	+	4.22744i	1.07782	+	0.324230i
$171$	−13.6416	−	9.71412i	−1.04320	−	0.742857i
$172$	−4.41668	−	2.69211i	−0.336769	−	0.205271i
$173$	−0.295616	+	12.4185i	−0.0224752	+	0.944162i	0.869996	+	0.493058i	$0.164121\pi$
$173$	−0.295616	+	12.4185i	−0.0224752	+	0.944162i	−0.892472	+	0.451104i	$0.851031\pi$
$174$	−2.06627	+	0.943633i	−0.156643	+	0.0715367i
$175$	7.61411	+	10.8178i	0.575572	+	0.817751i
$176$	−21.4022	−	18.5451i	−1.61325	−	1.39789i
$177$	0.459734	−	2.73393i	0.0345557	−	0.205495i
$178$	−12.0469	+	10.9513i	−0.902952	+	0.820838i
$179$	−14.4385	−	18.3601i	−1.07918	−	1.37229i	−0.923104	−	0.384551i	$-0.874356\pi$
$179$	−14.4385	−	18.3601i	−1.07918	−	1.37229i	−0.156081	−	0.987744i	$-0.549886\pi$
$180$	3.09960	+	6.90762i	0.231031	+	0.514864i
$181$	−5.94883	+	5.15469i	−0.442173	+	0.383145i	−0.847299	−	0.531116i	$-0.821773\pi$
$181$	−5.94883	+	5.15469i	−0.442173	+	0.383145i	0.405126	+	0.914261i	$0.367227\pi$
$182$	0.751783	+	0.705821i	0.0557259	+	0.0523189i
$183$	2.96256	+	2.96256i	0.218999	+	0.218999i
$184$	−6.19288	+	3.21850i	−0.456545	+	0.237271i
$185$	−17.4322	+	1.96751i	−1.28164	+	0.144655i
$186$	1.14469	+	1.09146i	0.0839325	+	0.0800295i
$187$	−17.3686	−	11.7554i	−1.27012	−	0.859641i
$188$	2.07531	−	9.54006i	0.151358	−	0.695780i
$189$	−2.33615	−	5.34107i	−0.169930	−	0.388506i
$190$	−12.9749	−	19.4460i	−0.941296	−	1.41076i
$191$	2.94559	−	2.09754i	0.213135	−	0.151773i	−0.468504	−	0.883461i	$-0.655207\pi$
$191$	2.94559	−	2.09754i	0.213135	−	0.151773i	0.681639	+	0.731689i	$0.261267\pi$
$192$	−0.145079	−	0.214353i	−0.0104701	−	0.0154696i
$193$	−1.72124	+	4.01949i	−0.123898	+	0.289329i	−0.969755	−	0.244081i	$-0.921514\pi$
$193$	−1.72124	+	4.01949i	−0.123898	+	0.289329i	0.845857	+	0.533410i	$0.179090\pi$
$194$	−19.9072	−	1.90090i	−1.42925	−	0.136477i
$195$	−0.0162510	−	0.182958i	−0.00116376	−	0.0131019i
$196$	5.81376	+	5.91173i	0.415269	+	0.422266i
$197$	5.96343	−	15.9886i	0.424877	−	1.13914i	−0.531514	−	0.847049i	$-0.678377\pi$
$197$	5.96343	−	15.9886i	0.424877	−	1.13914i	0.956391	−	0.292089i	$-0.0943505\pi$
$198$	−3.45354	−	28.8843i	−0.245432	−	2.05271i
$199$	10.0783	+	1.94244i	0.714433	+	0.137696i	0.533500	−	0.845800i	$-0.320876\pi$
$199$	10.0783	+	1.94244i	0.714433	+	0.137696i	0.180932	+	0.983496i	$0.442088\pi$
$200$	−0.423122	−	7.26410i	−0.0299192	−	0.513649i
$201$	−2.34755	−	4.55362i	−0.165584	−	0.321187i
$202$	4.06130	−	5.42526i	0.285752	−	0.381720i
$203$	−8.94093	+	0.495139i	−0.627530	+	0.0347520i
$204$	−1.07291	−	1.23820i	−0.0751187	−	0.0866916i
$205$	0.214000	+	1.56159i	0.0149464	+	0.109066i
$206$	20.1639	−	11.6417i	1.40489	−	0.811112i
$207$	−13.2536	−	3.50457i	−0.921189	−	0.243584i
$208$	−0.280718	−	1.04765i	−0.0194643	−	0.0726418i
$209$	9.41243	+	32.0558i	0.651071	+	2.21735i
$210$	−0.193347	−	3.96589i	−0.0133422	−	0.273673i
$211$	16.5988	−	10.6674i	1.14271	−	0.734376i	0.174537	−	0.984651i	$-0.444157\pi$
$211$	16.5988	−	10.6674i	1.14271	−	0.734376i	0.968175	+	0.250274i	$0.0805208\pi$
$212$	12.9223	−	5.53365i	0.887507	−	0.380053i
$213$	−0.182400	−	0.200647i	−0.0124979	−	0.0137481i
$214$	−31.7851	+	3.03511i	−2.17278	+	0.207476i
$215$	−0.760942	+	9.73482i	−0.0518958	+	0.663909i
$216$	−0.456341	+	3.17392i	−0.0310501	+	0.215958i
$217$	2.63382	+	5.65136i	0.178795	+	0.383639i
$218$	−0.259487	−	0.475214i	−0.0175746	−	0.0321856i
$219$	−1.71833	−	1.80213i	−0.116114	−	0.121777i
$220$	3.65786	−	14.6545i	0.246613	−	0.988007i
$221$	−0.298537	−	0.745710i	−0.0200818	−	0.0501619i
$222$	4.73624	+	2.30072i	0.317876	+	0.154415i
$223$	−4.85875	−	13.0268i	−0.325366	−	0.872340i	−0.991918	−	0.126881i	$-0.959503\pi$
$223$	−4.85875	−	13.0268i	−0.325366	−	0.872340i	0.666552	−	0.745459i	$-0.267769\pi$
$224$	−3.46568	−	15.3594i	−0.231561	−	1.02625i
$225$	8.98291	−	11.1171i	0.598861	−	0.741140i
$226$	4.12941	−	0.196708i	0.274685	−	0.0130848i
$227$	−9.45676	−	19.4676i	−0.627667	−	1.29211i	−0.939688	−	0.342033i	$-0.888885\pi$
$227$	−9.45676	−	19.4676i	−0.627667	−	1.29211i	0.312021	−	0.950075i	$-0.398994\pi$
$228$	0.0621094	+	2.60915i	0.00411330	+	0.172795i
$229$	−2.31334	+	4.00683i	−0.152870	+	0.264779i	−0.932281	−	0.361734i	$-0.882185\pi$
$229$	−2.31334	+	4.00683i	−0.152870	+	0.264779i	0.779411	+	0.626512i	$0.215518\pi$
$230$	−15.5515	−	11.1521i	−1.02543	−	0.735346i
$231$	−1.42630	+	5.49234i	−0.0938437	+	0.361370i
$232$	4.32296	+	2.36052i	0.283816	+	0.154975i
$233$	12.7053	−	18.7721i	0.832354	−	1.22980i	−0.138556	−	0.990355i	$-0.544246\pi$
$233$	12.7053	−	18.7721i	0.832354	−	1.22980i	0.970909	−	0.239447i	$-0.0769662\pi$
$234$	0.510525	−	0.990281i	0.0333741	−	0.0647367i
$235$	−17.8339	+	4.65248i	−1.16335	+	0.303494i
$236$	7.76060	−	4.00087i	0.505172	−	0.260434i
$237$	−0.698622	−	1.87308i	−0.0453804	−	0.121669i
$238$	−5.80573	−	16.3646i	−0.376330	−	1.06076i
$239$	11.0401	+	1.58732i	0.714123	+	0.102675i	0.489794	−	0.871838i	$-0.337072\pi$
$239$	11.0401	+	1.58732i	0.714123	+	0.102675i	0.224329	+	0.974514i	$0.427981\pi$
$240$	−2.02566	+	3.65214i	−0.130756	+	0.235744i
$241$	−11.1523	+	2.70552i	−0.718383	+	0.174278i	−0.578255	−	0.815856i	$-0.696266\pi$
$241$	−11.1523	+	2.70552i	−0.718383	+	0.174278i	−0.140127	+	0.990134i	$0.544751\pi$
$242$	−19.9877	+	32.7919i	−1.28486	+	2.10795i
$243$	−7.34400	+	6.06372i	−0.471118	+	0.388988i
$244$	−1.87786	+	13.0608i	−0.120218	+	0.836132i
$245$	4.98852	−	14.8363i	0.318705	−	0.947854i
$246$	0.196530	−	0.430340i	0.0125303	−	0.0274375i
$247$	−0.389607	+	1.21880i	−0.0247901	+	0.0775501i
$248$	0.407149	−	3.40526i	0.0258540	−	0.216234i
$249$	−2.58390	−	1.33209i	−0.163748	−	0.0844180i
$250$	17.2387	−	10.0443i	1.09027	−	0.635259i
$251$	2.92541	+	9.96304i	0.184650	+	0.628862i	0.998835	+	0.0482555i	$0.0153662\pi$
$251$	2.92541	+	9.96304i	0.184650	+	0.628862i	−0.814185	+	0.580606i	$0.802816\pi$
$252$	4.41913	−	7.79251i	0.278379	−	0.490882i
$253$	16.4616	+	21.8399i	1.03493	+	1.37306i
$254$	−18.7469	−	10.8235i	−1.17628	−	0.679128i
$255$	−1.16847	+	2.86369i	−0.0731722	+	0.179331i
$256$	−6.68039	+	19.3017i	−0.417524	+	1.20636i
$257$	−11.3858	+	12.5247i	−0.710224	+	0.781272i	−0.983547	−	0.180650i	$-0.942180\pi$
$257$	−11.3858	+	12.5247i	−0.710224	+	0.781272i	0.273324	+	0.961922i	$0.411877\pi$
$258$	1.75637	−	2.34624i	0.109347	−	0.146070i
$259$	14.0806	+	15.2509i	0.874927	+	0.947644i
$260$	0.430610	−	0.386284i	0.0267053	−	0.0239563i
$261$	3.16433	+	9.14274i	0.195867	+	0.565921i
$262$	24.3399	+	10.4229i	1.50372	+	0.643931i
$263$	4.84197	−	0.814217i	0.298569	−	0.0502068i	−0.0146346	−	0.999893i	$-0.504659\pi$
$263$	4.84197	−	0.814217i	0.298569	−	0.0502068i	0.313203	+	0.949686i	$0.398598\pi$
$264$	2.25895	−	2.15390i	0.139029	−	0.132564i
$265$	−20.3512	−	17.0308i	−1.25016	−	1.04619i
$266$	−9.46585	+	25.9902i	−0.580388	+	1.59356i
$267$	−2.05628	−	2.74687i	−0.125842	−	0.168106i
$268$	7.05005	−	14.5131i	0.430650	−	0.886531i
$269$	0.327182	+	3.42641i	0.0199486	+	0.208912i	0.999951	+	0.00992455i	$0.00315913\pi$
$269$	0.327182	+	3.42641i	0.0199486	+	0.208912i	−0.980002	+	0.198987i	$0.936235\pi$
$270$	−8.32746	+	2.82068i	−0.506793	+	0.171661i
$271$	28.3697	+	11.3575i	1.72333	+	0.689919i	1.00000		0.000579669i	$-0.000184514\pi$
$271$	28.3697	+	11.3575i	1.72333	+	0.689919i	0.723334	+	0.690498i	$0.242609\pi$
$272$	−3.88217	+	17.8460i	−0.235391	+	1.08208i
$273$	−0.163144	+	0.143586i	−0.00987393	+	0.00869022i
$274$	1.91360	−	0.561883i	0.115605	−	0.0339446i
$275$	−27.7960	+	6.35545i	−1.67616	+	0.383248i
$276$	0.800576	+	1.98082i	0.0481890	+	0.119231i
$277$	1.72366	−	6.43279i	0.103565	−	0.386509i	−0.894614	−	0.446840i	$-0.852549\pi$
$277$	1.72366	−	6.43279i	0.103565	−	0.386509i	0.998178	+	0.0603317i	$0.0192158\pi$
$278$	1.60098	+	2.62658i	0.0960206	+	0.157532i
$279$	5.09107	−	4.41143i	0.304794	−	0.264106i
$280$	−6.63290	+	5.48902i	−0.396391	+	0.328032i
$281$	−3.88373	+	0.558396i	−0.231684	+	0.0333111i	−0.257179	−	0.966364i	$-0.582793\pi$
$281$	−3.88373	+	0.558396i	−0.231684	+	0.0333111i	0.0254948	+	0.999675i	$0.491884\pi$
$282$	5.26931	+	1.68441i	0.313783	+	0.100305i
$283$	−11.6124	−	9.58799i	−0.690285	−	0.569947i	0.224212	−	0.974540i	$-0.428019\pi$
$283$	−11.6124	−	9.58799i	−0.690285	−	0.569947i	−0.914497	+	0.404593i	$0.867413\pi$
$284$	0.161622	−	0.838572i	0.00959048	−	0.0497601i
$285$	4.33975	−	2.33259i	0.257065	−	0.138171i
$286$	−2.02178	+	0.923318i	−0.119551	+	0.0545969i
$287$	1.33977	−	1.29736i	0.0790838	−	0.0765809i
$288$	−14.9311	+	8.15298i	−0.879822	+	0.480419i
$289$	0.330260	−	3.45864i	0.0194271	−	0.203449i
$290$	−0.410613	+	13.4990i	−0.0241120	+	0.792691i
$291$	0.797630	−	4.13850i	0.0467579	−	0.242603i
$292$	1.30047	−	7.73362i	0.0761044	−	0.452576i
$293$	1.71211	+	7.87043i	0.100022	+	0.459795i	0.999729	+	0.0232993i	$0.00741708\pi$
$293$	1.71211	+	7.87043i	0.100022	+	0.459795i	−0.899706	+	0.436496i	$0.856219\pi$
$294$	−3.64765	+	2.96085i	−0.212735	+	0.172680i
$295$	−13.3629	−	9.64937i	−0.778015	−	0.561808i
$296$	−2.16074	−	11.2110i	−0.125590	−	0.651624i
$297$	12.5617	−	0.299023i	0.728902	−	0.0173511i
$298$	−1.32574	+	4.94773i	−0.0767980	+	0.286614i
$299$	0.0532840	+	1.04610i	0.00308149	+	0.0604974i
$300$	−2.22591	−	0.0824346i	−0.128513	−	0.00475937i
$301$	9.81861	−	6.08925i	0.565935	−	0.350978i
$302$	−2.52394	+	35.2893i	−0.145237	+	2.03067i
$303$	1.05687	+	0.960760i	0.0607157	+	0.0551942i
$304$	22.8687	−	17.9842i	1.31161	−	1.03146i
$305$	23.5928	−	7.99135i	1.35092	−	0.457584i
$306$	−15.2819	+	10.8822i	−0.873606	+	0.622092i
$307$	−9.43783	+	0.675007i	−0.538645	+	0.0385247i	−0.338012	−	0.941142i	$-0.609754\pi$
$307$	−9.43783	+	0.675007i	−0.538645	+	0.0385247i	−0.200633	+	0.979666i	$0.564300\pi$
$308$	−16.5395	+	6.77007i	−0.942425	+	0.385761i
$309$	2.03849	+	4.46367i	0.115966	+	0.253930i
$310$	8.83215	−	3.22790i	0.501632	−	0.183332i
$311$	6.18762	+	25.5057i	0.350868	+	1.44630i	0.824644	+	0.565652i	$0.191375\pi$
$311$	6.18762	+	25.5057i	0.350868	+	1.44630i	−0.473776	+	0.880645i	$0.657109\pi$
$312$	0.117887	−	0.0198237i	0.00667403	−	0.00112229i
$313$	2.63414	+	22.0311i	0.148890	+	1.24527i	0.847899	+	0.530157i	$0.177867\pi$
$313$	2.63414	+	22.0311i	0.148890	+	1.24527i	−0.699009	+	0.715113i	$0.746375\pi$
$314$	24.8769	−	28.7094i	1.40388	−	1.62017i
$315$	−16.8931	−	0.785859i	−0.951820	−	0.0442782i
$316$	3.40392	−	5.29660i	0.191485	−	0.297957i
$317$	6.06136	+	14.1546i	0.340440	+	0.795002i	0.999094	+	0.0425565i	$0.0135502\pi$
$317$	6.06136	+	14.1546i	0.340440	+	0.795002i	−0.658654	+	0.752446i	$0.728874\pi$
$318$	2.42526	+	7.58688i	0.136002	+	0.425451i
$319$	6.31268	−	18.2393i	0.353442	−	1.02120i
$320$	−1.52463	+	0.208934i	−0.0852293	+	0.0116798i
$321$		−	6.72940i		−	0.375599i
$322$	0.249399	+	22.6416i	0.0138985	+	1.26177i
$323$	15.2353	−	15.2353i	0.847714	−	0.847714i
$324$	−8.91756	−	2.16338i	−0.495420	−	0.120188i
$325$	−1.01806	−	0.395121i	−0.0564718	−	0.0219174i
$326$	−0.941797	−	0.485530i	−0.0521613	−	0.0268910i
$327$	0.104900	−	0.0449207i	0.00580097	−	0.00248412i
$328$	−1.00238	+	0.218053i	−0.0553469	+	0.0120400i
$329$	16.9230	+	13.7544i	0.932993	+	0.758304i
$330$	8.06888	+	2.85252i	0.444177	+	0.157026i
$331$	−12.4206	−	9.76765i	−0.682697	−	0.536879i	0.215483	−	0.976508i	$-0.430868\pi$
$331$	−12.4206	−	9.76765i	−0.682697	−	0.536879i	−0.898179	+	0.439629i	$0.855110\pi$
$332$	−1.51827	−	9.02880i	−0.0833257	−	0.495520i
$333$	11.6723	−	19.1496i	0.639636	−	1.04939i
$334$	30.3633	+	31.8441i	1.66140	+	1.74243i
$335$	−30.4546	+	0.523607i	−1.66391	+	0.0286077i
$336$	4.90183	−	0.624518i	0.267417	−	0.0340702i
$337$	−0.323619	−	4.52479i	−0.0176287	−	0.246481i	−0.998624	−	0.0524479i	$-0.983298\pi$
$337$	−0.323619	−	4.52479i	−0.0176287	−	0.246481i	0.980995	−	0.194033i	$-0.0621569\pi$
$338$	22.7935	+	3.83292i	1.23981	+	0.208484i
$339$	−0.0414577	+	0.870303i	−0.00225167	+	0.0472684i
$340$	−9.42539	+	2.45888i	−0.511164	+	0.133352i
$341$	−13.4236	+	0.639447i	−0.726931	+	0.0346280i
$342$	29.8088	+	2.13197i	1.61188	+	0.115284i
$343$	−17.6444	+	5.62802i	−0.952709	+	0.303884i
$344$	−6.35496			−0.342637
$345$	2.65129	−	3.03932i	0.142741	−	0.163632i
$346$	−11.0836	−	19.1974i	−0.595861	−	1.03206i
$347$	0.172293	+	7.23784i	0.00924916	+	0.388548i	0.985283	+	0.170930i	$0.0546772\pi$
$347$	0.172293	+	7.23784i	0.00924916	+	0.388548i	−0.976034	+	0.217618i	$0.930171\pi$
$348$	0.845114	−	1.24866i	0.0453029	−	0.0669349i
$349$	−13.6621	−	21.2587i	−0.731316	−	1.13795i	−0.985315	−	0.170745i	$-0.945383\pi$
$349$	−13.6621	−	21.2587i	−0.731316	−	1.13795i	0.254000	−	0.967204i	$-0.418254\pi$
$350$	−21.6495	−	9.41197i	−1.15722	−	0.503091i
$351$	0.404847	+	0.260179i	0.0216091	+	0.0138873i
$352$	33.4682	+	5.62795i	1.78386	+	0.299971i
$353$	9.84930	−	6.66620i	0.524225	−	0.354806i	−0.269580	−	0.962978i	$-0.586885\pi$
$353$	9.84930	−	6.66620i	0.524225	−	0.354806i	0.793805	+	0.608172i	$0.208097\pi$
$354$	1.83870	+	4.59286i	0.0977261	+	0.244108i
$355$	−1.54984	+	0.443970i	−0.0822570	+	0.0235635i
$356$	3.04454	−	10.3687i	0.161360	−	0.549542i
$357$	3.54964	−	0.890215i	0.187867	−	0.0471152i
$358$	39.0534	+	14.5662i	2.06404	+	0.769845i
$359$	14.3704	+	11.3010i	0.758439	+	0.596443i	0.920685	−	0.390308i	$-0.127631\pi$
$359$	14.3704	+	11.3010i	0.758439	+	0.596443i	−0.162246	+	0.986750i	$0.551874\pi$
$360$	7.66885	+	5.26466i	0.404184	+	0.277472i
$361$	−15.2527	+	1.45646i	−0.802776	+	0.0766558i
$362$	4.27702	−	13.3797i	0.224795	−	0.703221i
$363$	−6.47941	−	4.85042i	−0.340081	−	0.254581i
$364$	−0.669929	−	0.140325i	−0.0351138	−	0.00735502i
$365$	−14.1309	+	4.41444i	−0.739645	+	0.231063i
$366$	−7.26582	−	1.76267i	−0.379790	−	0.0921361i
$367$	24.5735	+	6.58445i	1.28273	+	0.343705i	0.834893	−	0.550412i	$-0.185529\pi$
$367$	24.5735	+	6.58445i	1.28273	+	0.343705i	0.447833	+	0.894117i	$0.352196\pi$
$368$	12.3284	−	20.3767i	0.642662	−	1.06221i
$369$	−1.74502	−	1.00749i	−0.0908420	−	0.0524476i
$370$	24.7352	−	19.1887i	1.28592	−	0.997575i
$371$	−1.99806	+	31.3355i	−0.103734	+	1.62686i
$372$	−1.02584	−	0.223158i	−0.0531874	−	0.0115702i
$373$	11.6510	+	27.2078i	0.603268	+	1.40877i	0.892299	+	0.451445i	$0.149091\pi$
$373$	11.6510	+	27.2078i	0.603268	+	1.40877i	−0.289031	+	0.957320i	$0.593333\pi$
$374$	37.3839	+	1.78081i	1.93307	+	0.0920837i
$375$	1.76197	+	3.81795i	0.0909879	+	0.197158i
$376$	−3.92323	−	11.3354i	−0.202325	−	0.584580i
$377$	0.591770	−	0.442994i	0.0304777	−	0.0228153i
$378$	8.52044	+	5.96875i	0.438244	+	0.307000i
$379$	−3.46898	−	1.01858i	−0.178190	−	0.0523212i	0.191421	−	0.981508i	$-0.438691\pi$
$379$	−3.46898	−	1.01858i	−0.178190	−	0.0523212i	−0.369610	+	0.929187i	$0.620509\pi$
$380$	14.0718	+	6.53909i	0.721866	+	0.335448i
$381$	2.64637	−	3.71631i	0.135578	−	0.190392i
$382$	−2.54022	+	5.93197i	−0.129969	+	0.303506i
$383$	−2.03314	+	4.18540i	−0.103889	+	0.213864i	−0.945054	−	0.326914i	$-0.893991\pi$
$383$	−2.03314	+	4.18540i	−0.103889	+	0.213864i	0.841165	+	0.540778i	$0.181870\pi$
$384$	−3.65185	−	1.66774i	−0.186358	−	0.0851066i
$385$	25.5216	+	22.0649i	1.30070	+	1.12453i
$386$	−1.11046	−	7.72341i	−0.0565209	−	0.393111i
$387$	−9.23665	−	8.39667i	−0.469525	−	0.426827i
$388$	11.9396	−	5.79989i	0.606140	−	0.294445i
$389$	23.4968	+	22.4042i	1.19134	+	1.13594i	0.987613	+	0.156907i	$0.0501524\pi$
$389$	23.4968	+	22.4042i	1.19134	+	1.13594i	0.203722	+	0.979029i	$0.434696\pi$
$390$	0.194691	+	0.263692i	0.00985857	+	0.0133525i
$391$	7.27412	−	16.0679i	0.367868	−	0.812587i
$392$	9.87941	+	2.48430i	0.498986	+	0.125476i
$393$	−2.67438	+	4.89776i	−0.134905	+	0.247059i
$394$	5.76305	+	29.9015i	0.290338	+	1.50642i
$395$	−11.8241	−	1.20797i	−0.594934	−	0.0607794i
$396$	11.9359	+	15.1778i	0.599803	+	0.762712i
$397$	−2.61794	−	0.836863i	−0.131390	−	0.0420010i	0.238066	−	0.971249i	$-0.423486\pi$
$397$	−2.61794	−	0.836863i	−0.131390	−	0.0420010i	−0.369457	+	0.929248i	$0.620456\pi$
$398$	−17.1611	+	6.40075i	−0.860207	+	0.320840i
$399$	−5.26317	−	2.50664i	−0.263488	−	0.125489i
$400$	14.1341	+	20.4144i	0.706706	+	1.02072i
$401$	−1.80812	+	18.9355i	−0.0902930	+	0.945591i	0.830884	+	0.556446i	$0.187836\pi$
$401$	−1.80812	+	18.9355i	−0.0902930	+	0.945591i	−0.921177	+	0.389145i	$0.872771\pi$
$402$	7.80644	+	4.75827i	0.389350	+	0.237321i
$403$	−0.439495	−	0.267886i	−0.0218928	−	0.0133444i
$404$	−0.427592	+	4.47794i	−0.0212735	+	0.222786i
$405$	3.97264	+	16.8610i	0.197402	+	0.837832i
$406$	13.1640	−	9.05865i	0.653318	−	0.449573i
$407$	−41.9189	+	15.6349i	−2.07784	+	0.774995i
$408$	−1.91735	−	0.612910i	−0.0949229	−	0.0303435i
$409$	−2.07222	−	2.63504i	−0.102464	−	0.130294i	0.732117	−	0.681179i	$-0.238533\pi$
$409$	−2.07222	−	2.63504i	−0.102464	−	0.130294i	−0.834581	+	0.550885i	$0.814290\pi$
$410$	−1.77647	−	2.18074i	−0.0877335	−	0.107699i
$411$	0.0795480	+	0.412734i	0.00392382	+	0.0203587i
$412$	−7.40659	+	13.5642i	−0.364897	+	0.668258i
$413$	0.150608	+	19.5019i	0.00741094	+	0.959625i
$414$	23.4503	−	6.96958i	1.15252	−	0.342536i
$415$	−13.9045	+	10.2661i	−0.682544	+	0.503942i
$416$	0.940719	+	0.896973i	0.0461225	+	0.0439777i
$417$	−0.583137	+	0.283271i	−0.0285563	+	0.0138718i
$418$	−44.1152	−	40.1034i	−2.15774	−	1.96152i
$419$	−0.313988	−	2.18384i	−0.0153393	−	0.106687i	0.980713	−	0.195452i	$-0.0626173\pi$
$419$	−0.313988	−	2.18384i	−0.0153393	−	0.106687i	−0.996053	+	0.0887643i	$0.971708\pi$
$420$	1.47967	+	2.18097i	0.0722005	+	0.106421i
$421$	−0.171436	−	0.0782923i	−0.00835529	−	0.00381573i	0.411233	−	0.911530i	$-0.365098\pi$
$421$	−0.171436	−	0.0782923i	−0.00835529	−	0.00381573i	−0.419588	+	0.907715i	$0.637826\pi$
$422$	−15.3850	+	31.6714i	−0.748930	+	1.54174i
$423$	9.27501	−	21.6592i	0.450966	−	1.05311i
$424$	10.0181	−	14.0685i	0.486523	−	0.683226i
$425$	12.1884	+	13.7690i	0.591223	+	0.667893i
$426$	0.464293	+	0.136329i	0.0224951	+	0.00660515i
$427$	−24.1396	−	16.9103i	−1.16819	−	0.818346i
$428$	16.9664	−	12.7009i	0.820104	−	0.613922i
$429$	−0.153211	−	0.442673i	−0.00739708	−	0.0213725i
$430$	−7.88204	−	15.5403i	−0.380105	−	0.749421i
$431$	16.4813	+	0.785102i	0.793877	+	0.0378170i	0.440602	−	0.897703i	$-0.354765\pi$
$431$	16.4813	+	0.785102i	0.793877	+	0.0378170i	0.353275	+	0.935520i	$0.385068\pi$
$432$	−4.30731	−	10.0585i	−0.207236	−	0.483941i
$433$	−8.21695	−	1.78749i	−0.394881	−	0.0859012i	0.0107401	−	0.999942i	$-0.496581\pi$
$433$	−8.21695	−	1.78749i	−0.394881	−	0.0859012i	−0.405621	+	0.914041i	$0.632945\pi$
$434$	−9.26220	−	6.16509i	−0.444600	−	0.295934i
$435$	−2.82391	−	0.356584i	−0.135396	−	0.0170969i
$436$	0.311241	+	0.179695i	0.0149057	+	0.00860584i
$437$	−25.2319	+	12.3597i	−1.20700	+	0.591245i
$438$	4.29212	+	1.15007i	0.205085	+	0.0549524i
$439$	−22.5050	−	5.45964i	−1.07410	−	0.260575i	−0.340564	−	0.940221i	$-0.610618\pi$
$439$	−22.5050	−	5.45964i	−1.07410	−	0.260575i	−0.733539	+	0.679647i	$0.762133\pi$
$440$	−5.53345	−	17.7129i	−0.263797	−	0.844429i
$441$	11.0768	+	16.6643i	0.527468	+	0.793536i
$442$	1.14750	+	0.859010i	0.0545811	+	0.0408589i
$443$	3.09351	−	9.67733i	0.146977	−	0.459784i	−0.850869	−	0.525377i	$-0.823924\pi$
$443$	3.09351	−	9.67733i	0.146977	−	0.459784i	0.997846	+	0.0655931i	$0.0208939\pi$
$444$	−3.47921	+	0.332224i	−0.165116	+	0.0157666i
$445$	−20.0567	+	3.72832i	−0.950779	+	0.176739i
$446$	19.5027	+	15.3371i	0.923478	+	0.726231i
$447$	−1.01149	−	0.377265i	−0.0478417	−	0.0178440i
$448$	1.26665	+	1.30805i	0.0598437	+	0.0617996i
$449$	−2.39876	+	8.16942i	−0.113204	+	0.385539i	−0.996531	−	0.0832188i	$-0.973480\pi$
$449$	−2.39876	+	8.16942i	−0.113204	+	0.385539i	0.883327	+	0.468757i	$0.155298\pi$
$450$	−3.36246	+	25.2830i	−0.158508	+	1.19185i
$451$	1.49400	+	3.73182i	0.0703496	+	0.175725i
$452$	−2.27249	+	1.53807i	−0.106889	+	0.0723445i
$453$	−7.35324	−	1.23651i	−0.345485	−	0.0580962i
$454$	32.4910	+	20.8807i	1.52488	+	0.979980i
$455$	0.335817	+	1.24773i	0.0157434	+	0.0584943i
$456$	1.73359	+	2.69751i	0.0811826	+	0.126323i
$457$	6.70730	−	9.91003i	0.313754	−	0.463571i	−0.638174	−	0.769892i	$-0.720310\pi$
$457$	6.70730	−	9.91003i	0.313754	−	0.463571i	0.951928	+	0.306321i	$0.0990979\pi$
$458$	−0.196483	−	8.25405i	−0.00918105	−	0.385686i
$459$	−4.05174	−	7.01781i	−0.189119	−	0.327563i
$460$	12.6668	+	0.948186i	0.590595	+	0.0442094i
$461$	−23.4204			−1.09079			−0.545397	−	0.838178i	$-0.683621\pi$
$461$	−23.4204			−1.09079			−0.545397	+	0.838178i	$0.683621\pi$
$462$	−2.92785	−	9.69376i	−0.136216	−	0.450994i
$463$	7.21831	+	0.516264i	0.335463	+	0.0239928i	0.238055	−	0.971252i	$-0.423490\pi$
$463$	7.21831	+	0.516264i	0.335463	+	0.0239928i	0.0974084	+	0.995244i	$0.468945\pi$
$464$	−16.7884	+	0.799731i	−0.779383	+	0.0371266i
$465$	0.500280	+	1.91768i	0.0232000	+	0.0889301i
$466$	−1.92472	+	40.4048i	−0.0891607	+	1.87171i
$467$	−14.7240	−	2.47596i	−0.681346	−	0.114574i	−0.185052	−	0.982729i	$-0.559245\pi$
$467$	−14.7240	−	2.47596i	−0.681346	−	0.114574i	−0.496293	+	0.868155i	$0.665306\pi$
$468$	0.0527567	+	0.737636i	0.00243868	+	0.0340972i
$469$	21.8200	+	28.6836i	1.00755	+	1.32449i
$470$	22.8535	−	23.6531i	1.05415	−	1.09104i
$471$	5.52494	+	5.79439i	0.254576	+	0.266992i
$472$	5.58318	−	9.15979i	0.256987	−	0.421613i
$473$	4.12958	+	24.5577i	0.189878	+	1.12917i
$474$	2.80422	+	2.20526i	0.128802	+	0.101291i
$475$	−1.00696	−	29.2752i	−0.0462023	−	1.34324i
$476$	8.94396	+	7.26934i	0.409946	+	0.333189i
$477$	33.1493	−	7.21118i	1.51780	−	0.330177i
$478$	−18.2967	+	7.83512i	−0.836874	+	0.358370i
$479$	2.79854	+	1.44275i	0.127868	+	0.0659208i	0.520974	−	0.853573i	$-0.325569\pi$
$479$	2.79854	+	1.44275i	0.127868	+	0.0659208i	−0.393105	+	0.919493i	$0.628599\pi$
$480$	−0.205101	−	5.00071i	−0.00936151	−	0.228250i
$481$	−1.66521	−	0.403975i	−0.0759270	−	0.0184197i
$482$	14.4806	−	14.4806i	0.659575	−	0.659575i
$483$	−4.75526	−	0.401271i	−0.216372	−	0.0182585i
$484$		−	25.4907i		−	1.15867i
$485$	−19.9602	−	15.1489i	−0.906348	−	0.687876i
$486$	5.55865	−	16.0607i	0.252145	−	0.728526i
$487$	−2.25848	−	7.06513i	−0.102341	−	0.320152i	0.887799	−	0.460232i	$-0.152234\pi$
$487$	−2.25848	−	7.06513i	−0.102341	−	0.320152i	−0.990140	+	0.140080i	$0.955264\pi$
$488$	6.38172	+	14.9027i	0.288887	+	0.674614i
$489$	0.120733	−	0.187865i	0.00545974	−	0.00849553i
$490$	6.17834	+	27.2402i	0.279109	+	1.23059i
$491$	−4.29237	+	4.95366i	−0.193712	+	0.223556i	−0.844294	−	0.535881i	$-0.819980\pi$
$491$	−4.29237	+	4.95366i	−0.193712	+	0.223556i	0.650582	+	0.759436i	$0.274525\pi$
$492$	0.0372803	+	0.311800i	0.00168073	+	0.0140570i
$493$	−12.2750	+	2.06415i	−0.552839	+	0.0929644i
$494$	−0.538328	−	2.21902i	−0.0242205	−	0.0998383i
$495$	15.3610	−	33.0561i	0.690427	−	1.48576i
$496$	4.86151	+	10.6452i	0.218288	+	0.477984i
$497$	1.50850	+	1.16756i	0.0676654	+	0.0523721i
$498$	5.17448	−	0.370086i	0.231874	−	0.0165840i
$499$	25.9337	−	18.4673i	1.16095	−	0.826710i	0.173531	−	0.984828i	$-0.444482\pi$
$499$	25.9337	−	18.4673i	1.16095	−	0.826710i	0.987420	+	0.158119i	$0.0505429\pi$
$500$	−6.30048	+	11.6483i	−0.281766	+	0.520927i
$501$	−7.28926	+	5.73234i	−0.325660	+	0.256102i
$502$	−13.7111	−	12.4643i	−0.611958	−	0.556307i
$503$	−2.93443	+	41.0287i	−0.130840	+	1.82938i	0.332392	+	0.943141i	$0.392144\pi$
$503$	−2.93443	+	41.0287i	−0.130840	+	1.82938i	−0.463232	+	0.886237i	$0.653310\pi$
$504$	−0.346889	−	11.0008i	−0.0154517	−	0.490017i
$505$	7.90423	−	3.10393i	0.351734	−	0.138123i
$506$	−45.3682	−	17.9896i	−2.01686	−	0.799736i
$507$	−1.26080	+	4.70536i	−0.0559940	+	0.208972i
$508$	14.3644	−	0.341937i	0.637318	−	0.0151710i
$509$	−7.61621	−	39.5167i	−0.337583	−	1.75154i	−0.612871	−	0.790183i	$-0.709985\pi$
$509$	−7.61621	−	39.5167i	−0.337583	−	1.75154i	0.275288	−	0.961362i	$-0.411227\pi$
$510$	−0.879281	−	5.44884i	−0.0389352	−	0.241279i
$511$	14.1036	+	10.3888i	0.623904	+	0.459574i
$512$	−3.20974	−	14.7549i	−0.141852	−	0.652083i
$513$	−2.14064	+	12.7299i	−0.0945114	+	0.562038i
$514$	5.71643	−	29.6596i	0.252141	−	1.30823i
$515$	29.1614	+	0.887030i	1.28501	+	0.0390872i
$516$	−0.184919	+	1.93656i	−0.00814059	+	0.0852521i
$517$	−41.2545	+	22.5267i	−1.81437	+	0.990722i
$518$	−35.6203	−	10.1609i	−1.56507	−	0.446446i
$519$	4.24972	−	1.94078i	0.186542	−	0.0851909i
$520$	0.204737	−	0.680600i	0.00897833	−	0.0298463i
$521$	1.31313	−	6.81318i	0.0575294	−	0.298491i	−0.941756	−	0.336298i	$-0.890825\pi$
$521$	1.31313	−	6.81318i	0.0575294	−	0.298491i	0.999285	+	0.0378070i	$0.0120372\pi$
$522$	−13.3133	−	10.9924i	−0.582708	−	0.481124i
$523$	−13.2863	−	4.24716i	−0.580969	−	0.185716i	−0.000502568	−	1.00000i	$-0.500160\pi$
$523$	−13.2863	−	4.24716i	−0.580969	−	0.185716i	−0.580466	+	0.814284i	$0.697130\pi$
$524$	−17.3960	+	2.50117i	−0.759948	+	0.109264i
$525$	2.40838	−	4.35357i	0.105110	−	0.190005i
$526$	−6.62179	+	5.73781i	−0.288724	+	0.250180i
$527$	4.51084	+	7.40051i	0.196495	+	0.322371i
$528$	−2.75664	+	10.2879i	−0.119967	+	0.447724i
$529$	−15.7619	+	16.7500i	−0.685299	+	0.728262i
$530$	46.8283	+	7.04906i	2.03409	+	0.306192i
$531$	20.2175	−	5.93640i	0.877366	−	0.257618i
$532$	−3.61374	−	18.0007i	−0.156676	−	0.780429i
$533$	−0.0327255	+	0.150437i	−0.00141750	+	0.00651614i
$534$	5.68453	+	2.27574i	0.245993	+	0.0984809i
$535$	−35.8714	−	17.7192i	−1.55086	−	0.766068i
$536$	−1.88434	−	19.7337i	−0.0813912	−	0.852367i
$537$	−3.83840	+	7.90169i	−0.165639	+	0.340983i
$538$	−3.68094	−	4.91715i	−0.158696	−	0.211994i
$539$	3.18032	−	39.7917i	0.136986	−	1.71395i
$540$	3.74534	−	4.47555i	0.161174	−	0.192597i
$541$	−2.47888	+	2.36361i	−0.106575	+	0.101619i	−0.741494	−	0.670960i	$-0.765882\pi$
$541$	−2.47888	+	2.36361i	−0.106575	+	0.101619i	0.634918	+	0.772579i	$0.281034\pi$
$542$	−53.7773	+	9.04310i	−2.30993	+	0.388434i
$543$	2.72141	+	1.16538i	0.116787	+	0.0500111i
$544$	−7.15857	−	20.6833i	−0.306921	−	0.886791i
$545$	0.0367598	−	0.677454i	0.00157462	−	0.0290190i
$546$	0.115233	−	0.370317i	0.00493152	−	0.0158481i
$547$	−12.3443	+	16.4901i	−0.527806	+	0.705066i	−0.982643	−	0.185509i	$-0.940607\pi$
$547$	−12.3443	+	16.4901i	−0.527806	+	0.705066i	0.454837	+	0.890575i	$0.349698\pi$
$548$	−0.890466	+	0.979545i	−0.0380388	+	0.0418441i
$549$	−10.4151	+	30.0925i	−0.444506	+	1.28431i
$550$	36.4517	−	35.5006i	1.55431	−	1.51375i
$551$	17.1718	+	9.91415i	0.731544	+	0.422357i
$552$	2.10651	+	1.56612i	0.0896591	+	0.0666585i
$553$	7.12547	+	12.1245i	0.303006	+	0.515585i
$554$	3.34821	+	11.4030i	0.142252	+	0.484465i
$555$	3.53031	+	5.57393i	0.149853	+	0.236600i
$556$	−1.81479	−	0.935591i	−0.0769644	−	0.0396779i
$557$	1.71376	−	14.3333i	0.0726142	−	0.607322i	−0.909048	−	0.416692i	$-0.863189\pi$
$557$	1.71376	−	14.3333i	0.0726142	−	0.607322i	0.981662	−	0.190630i	$-0.0610530\pi$
$558$	−3.66032	+	11.4505i	−0.154954	+	0.484737i
$559$	−0.396204	+	0.867566i	−0.0167576	+	0.0366941i
$560$	9.57801	−	27.7739i	0.404745	−	1.17366i
$561$	−1.12256	+	7.80756i	−0.0473944	+	0.329636i
$562$	5.39926	−	4.45801i	0.227754	−	0.188050i
$563$	18.3281	−	30.0692i	0.772439	−	1.26727i	−0.186163	−	0.982519i	$-0.559605\pi$
$563$	18.3281	−	30.0692i	0.772439	−	1.26727i	0.958603	−	0.284748i	$-0.0919098\pi$
$564$	−3.56842	+	0.865689i	−0.150257	+	0.0364521i
$565$	4.53003	+	2.51259i	0.190580	+	0.105705i
$566$	26.5997	+	3.82446i	1.11807	+	0.160754i
$567$	13.3023	−	15.5934i	0.558646	−	0.654862i
$568$	−0.366672	−	0.983085i	−0.0153852	−	0.0412493i
$569$	11.9347	−	6.15274i	0.500327	−	0.257936i	−0.189540	−	0.981873i	$-0.560700\pi$
$569$	11.9347	−	6.15274i	0.500327	−	0.257936i	0.689866	+	0.723937i	$0.257669\pi$
$570$	−4.44629	+	7.58500i	−0.186235	+	0.317701i
$571$	−4.27033	+	8.28329i	−0.178708	+	0.346645i	−0.961127	−	0.276108i	$-0.910955\pi$
$571$	−4.27033	+	8.28329i	−0.178708	+	0.346645i	0.782419	+	0.622753i	$0.213986\pi$
$572$	0.826919	−	1.22177i	0.0345752	−	0.0510849i
$573$	−1.19365	−	0.651784i	−0.0498656	−	0.0272287i
$574$	−0.836517	+	3.22123i	−0.0349156	+	0.134451i
$575$	−9.22016	−	22.1357i	−0.384507	−	0.923122i
$576$	0.983637	−	1.70371i	0.0409849	−	0.0709879i
$577$	0.357109	+	15.0018i	0.0148666	+	0.624532i	0.957130	+	0.289659i	$0.0935418\pi$
$577$	0.357109	+	15.0018i	0.0148666	+	0.624532i	−0.942263	+	0.334873i	$0.891307\pi$
$578$	2.70909	+	5.57689i	0.112683	+	0.231968i
$579$	1.64264	−	0.0782486i	0.0682658	−	0.00325190i
$580$	−4.43075	−	7.79276i	−0.183977	−	0.323577i
$581$	19.5268	+	6.07625i	0.810109	+	0.252085i
$582$	2.62837	+	7.04692i	0.108949	+	0.292104i
$583$	−60.8753	−	29.5714i	−2.52120	−	1.22472i
$584$	−3.58097	−	8.94484i	−0.148182	−	0.370140i
$585$	1.19684	−	0.718707i	0.0494832	−	0.0297149i
$586$	−9.91877	−	10.4025i	−0.409740	−	0.429723i
$587$	7.05419	+	12.9188i	0.291157	+	0.533215i	0.981785	−	0.189996i	$-0.0608474\pi$
$587$	7.05419	+	12.9188i	0.291157	+	0.533215i	−0.690628	+	0.723211i	$0.742666\pi$
$588$	1.04452	−	2.93828i	0.0430752	−	0.121173i
$589$	1.96482	−	13.6656i	0.0809589	−	0.563082i
$590$	29.3240	+	2.29217i	1.20725	+	0.0943672i
$591$	−6.38888	+	0.610064i	−0.262804	+	0.0250947i
$592$	26.2069	+	28.8285i	1.07710	+	1.18484i
$593$	12.0141	−	5.14474i	0.493360	−	0.211269i	−0.132532	−	0.991179i	$-0.542311\pi$
$593$	12.0141	−	5.14474i	0.493360	−	0.211269i	0.625892	+	0.779910i	$0.284735\pi$
$594$	−18.8633	+	12.1227i	−0.773970	+	0.497400i
$595$	4.60124	−	21.2656i	0.188633	−	0.871804i
$596$	−0.957882	−	3.26225i	−0.0392364	−	0.133627i
$597$	−0.999094	−	3.72867i	−0.0408902	−	0.152604i
$598$	−1.05279	−	1.54452i	−0.0430518	−	0.0631600i
$599$	13.4182	−	7.74701i	0.548254	−	0.316534i	−0.200164	−	0.979762i	$-0.564147\pi$
$599$	13.4182	−	7.74701i	0.548254	−	0.316534i	0.748417	+	0.663228i	$0.230814\pi$
$600$	−2.38789	+	1.33688i	−0.0974851	+	0.0545780i
$601$	−11.6730	−	13.4713i	−0.476150	−	0.549506i	0.465962	−	0.884805i	$-0.345708\pi$
$601$	−11.6730	−	13.4713i	−0.476150	−	0.549506i	−0.942112	+	0.335299i	$0.891163\pi$
$602$	−9.30566	+	18.3979i	−0.379270	+	0.749844i
$603$	23.3349	−	31.1718i	0.950272	−	1.26941i
$604$	−10.7608	−	20.8730i	−0.437851	−	0.849312i
$605$	−42.9164	+	21.7672i	−1.74480	+	0.884961i
$606$	−2.50276	−	0.482367i	−0.101668	−	0.0195948i
$607$	−0.0848481	−	0.709642i	−0.00344388	−	0.0288035i	0.991101	−	0.133108i	$-0.0424958\pi$
$607$	−0.0848481	−	0.709642i	−0.00344388	−	0.0288035i	−0.994545	+	0.104305i	$0.966738\pi$
$608$	−12.1843	+	32.6673i	−0.494137	+	1.32483i
$609$	1.63681	+	2.94332i	0.0663268	+	0.119269i
$610$	−28.5276	+	34.0895i	−1.15505	+	1.38024i
$611$	−1.79208	−	0.171123i	−0.0724999	−	0.00692291i
$612$	4.90194	−	11.4471i	0.198149	−	0.462722i
$613$	−1.03199	−	1.52476i	−0.0416815	−	0.0615844i	0.806736	−	0.590912i	$-0.201232\pi$
$613$	−1.03199	−	1.52476i	−0.0416815	−	0.0615844i	−0.848417	+	0.529328i	$0.822444\pi$
$614$	13.7541	−	9.79424i	0.555070	−	0.395263i
$615$	0.493115	−	0.329019i	0.0198843	−	0.0132673i
$616$	−13.0222	+	17.6786i	−0.524681	+	0.712291i
$617$	−6.23102	+	28.6436i	−0.250852	+	1.15315i	0.663485	+	0.748190i	$0.269077\pi$
$617$	−6.23102	+	28.6436i	−0.250852	+	1.15315i	−0.914336	+	0.404956i	$0.867287\pi$
$618$	−7.25196	−	4.90827i	−0.291717	−	0.197440i
$619$	19.8274	+	18.9054i	0.796932	+	0.759873i	0.974537	−	0.224229i	$-0.0719862\pi$
$619$	19.8274	+	18.9054i	0.796932	+	0.759873i	−0.177604	+	0.984102i	$0.556835\pi$
$620$	−3.89071	+	4.88071i	−0.156254	+	0.196014i
$621$	2.03399	+	10.3695i	0.0816211	+	0.416114i
$622$	−33.1178	−	33.1178i	−1.32790	−	1.32790i
$623$	17.5976	+	16.5217i	0.705032	+	0.661928i
$624$	−0.308287	+	0.267132i	−0.0123413	+	0.0106938i
$625$	24.9913	+	0.660785i	0.999651	+	0.0264314i
$626$	−24.4759	−	31.1236i	−0.978253	−	1.24395i
$627$	9.29759	−	8.45207i	0.371310	−	0.337543i
$628$	−4.18141	+	24.8659i	−0.166856	+	0.992258i
$629$	21.8058	+	18.8948i	0.869455	+	0.753387i
$630$	26.4710	−	14.4926i	1.05463	−	0.577399i
$631$	−14.4558	+	6.60176i	−0.575478	+	0.262812i	−0.681823	−	0.731517i	$-0.738812\pi$
$631$	−14.4558	+	6.60176i	−0.575478	+	0.262812i	0.106345	+	0.994329i	$0.466085\pi$
$632$	0.184085	−	7.73324i	0.00732252	−	0.307612i
$633$	−6.33652	−	3.86231i	−0.251854	−	0.153513i
$634$	−22.3826	−	15.9386i	−0.888928	−	0.633003i
$635$	−12.8418	−	23.8921i	−0.509612	−	0.948128i
$636$	−3.99560	−	3.46220i	−0.158436	−	0.137285i
$637$	0.955089	−	1.19383i	0.0378420	−	0.0473013i
$638$	7.32131	+	33.6555i	0.289853	+	1.33243i
$639$	0.765988	−	1.91335i	0.0303020	−	0.0756908i
$640$	−18.5057	+	15.0750i	−0.731501	+	0.595893i
$641$	6.63727	+	2.29718i	0.262156	+	0.0907332i	0.454985	−	0.890499i	$-0.349645\pi$
$641$	6.63727	+	2.29718i	0.262156	+	0.0907332i	−0.192828	+	0.981233i	$0.561766\pi$
$642$	6.25015	+	10.2540i	0.246674	+	0.404694i
$643$	0.0476897	+	0.0476897i	0.00188070	+	0.00188070i	0.708047	−	0.706166i	$-0.249577\pi$
$643$	0.0476897	+	0.0476897i	0.00188070	+	0.00188070i	−0.706166	+	0.708047i	$0.749577\pi$
$644$	−7.96327	−	12.7465i	−0.313797	−	0.502283i
$645$	3.41831	−	1.34234i	0.134596	−	0.0528547i
$646$	−9.06472	+	37.3653i	−0.356646	+	1.47012i
$647$	18.3641	−	8.92072i	0.721966	−	0.350710i	−0.0392307	−	0.999230i	$-0.512491\pi$
$647$	18.3641	−	8.92072i	0.721966	−	0.350710i	0.761197	+	0.648521i	$0.224612\pi$
$648$	−10.7387	+	3.43278i	−0.421855	+	0.134852i
$649$	−39.0246	−	15.6231i	−1.53185	−	0.613260i
$650$	1.91826	−	0.343484i	0.0752405	−	0.0134726i
$651$	1.47901	−	1.81973i	0.0579669	−	0.0713207i
$652$	0.701521	−	0.0501738i	0.0274737	−	0.00196496i
$653$	15.8684	−	1.89730i	0.620978	−	0.0742470i	0.197723	−	0.980258i	$-0.436645\pi$
$653$	15.8684	−	1.89730i	0.620978	−	0.0742470i	0.423254	+	0.906011i	$0.360888\pi$
$654$	−0.118121	+	0.165878i	−0.00461889	+	0.00648633i
$655$	19.0659	+	27.1522i	0.744965	+	1.06093i
$656$	2.53341	−	2.41560i	0.0989131	−	0.0943135i
$657$	6.61384	−	17.7324i	0.258030	−	0.691806i
$658$	−38.5614	−	5.24068i	−1.50328	−	0.204303i
$659$	7.56226	−	8.72731i	0.294584	−	0.339968i	−0.589093	−	0.808065i	$-0.700515\pi$
$659$	7.56226	−	8.72731i	0.294584	−	0.339968i	0.883677	+	0.468097i	$0.155060\pi$
$660$	−5.55869	+	1.17080i	−0.216372	+	0.0455733i
$661$	21.9442	+	1.04533i	0.853530	+	0.0406587i	0.469786	−	0.882781i	$-0.344331\pi$
$661$	21.9442	+	1.04533i	0.853530	+	0.0406587i	0.383745	+	0.923439i	$0.374634\pi$
$662$	27.9981	+	3.34758i	1.08818	+	0.130107i
$663$	−0.203211	+	0.223540i	−0.00789208	+	0.00868158i
$664$	−7.36628	−	8.50114i	−0.285867	−	0.329908i
$665$	−27.2202	+	21.4554i	−1.05556	+	0.832003i
$666$			40.0204i			1.55076i
$667$	16.0157	+	2.63898i	0.620129	+	0.102182i
$668$	−28.2102	−	7.55890i	−1.09149	−	0.292463i
$669$	−3.60847	+	3.78445i	−0.139511	+	0.146315i
$670$	45.9194	−	29.0836i	1.77402	−	1.12360i
$671$	53.4422	−	34.3452i	2.06311	−	1.32588i
$672$	−4.62652	+	3.69651i	−0.178472	+	0.142596i
$673$	21.9104	−	4.76631i	0.844582	−	0.183728i	0.230601	−	0.973048i	$-0.425931\pi$
$673$	21.9104	−	4.76631i	0.844582	−	0.183728i	0.613981	+	0.789321i	$0.289567\pi$
$674$	4.69566	+	6.59414i	0.180870	+	0.253997i
$675$	−10.7333	−	2.48390i	−0.413125	−	0.0956055i
$676$	−14.2429	+	5.70202i	−0.547806	+	0.219308i
$677$	28.9377	−	23.8929i	1.11216	−	0.918281i	0.114987	−	0.993367i	$-0.463317\pi$
$677$	28.9377	−	23.8929i	1.11216	−	0.918281i	0.997177	+	0.0750864i	$0.0239233\pi$
$678$	−0.745151	−	1.36464i	−0.0286173	−	0.0524088i
$679$	−0.476656	+	29.6451i	−0.0182924	+	1.13768i
$680$	−8.31572	+	8.60667i	−0.318893	+	0.330051i
$681$	−5.03175	+	6.39838i	−0.192817	+	0.245187i
$682$	19.8606	−	13.4420i	0.760500	−	0.514722i
$683$	−28.9772	+	35.0954i	−1.10878	+	1.34289i	−0.175199	+	0.984533i	$0.556057\pi$
$683$	−28.9772	+	35.0954i	−1.10878	+	1.34289i	−0.933585	+	0.358357i	$0.883337\pi$
$684$	−17.6314	+	9.08963i	−0.674154	+	0.347551i
$685$	2.40956	+	0.662738i	0.0920646	+	0.0253219i
$686$	21.6587	−	24.9636i	0.826934	−	0.953115i
$687$	1.73566	+	0.124137i	0.0662195	+	0.00473611i
$688$	18.5168	−	11.2866i	0.705947	−	0.430297i
$689$	−1.29601	−	2.24476i	−0.0493742	−	0.0855185i
$690$	−1.21707	+	7.09368i	−0.0463329	+	0.270052i
$691$	17.6463	−	30.5642i	0.671295	−	1.16272i	−0.306242	−	0.951954i	$-0.599072\pi$
$691$	17.6463	−	30.5642i	0.671295	−	1.16272i	0.977537	−	0.210764i	$-0.0675950\pi$
$692$	12.9140	+	7.05158i	0.490917	+	0.268061i
$693$	−42.2856	+	8.48908i	−1.60630	+	0.322473i
$694$	−6.98492	−	10.8687i	−0.265144	−	0.412572i
$695$	−0.0254721	+	3.85432i	−0.000966213	+	0.146203i
$696$	0.0881434	−	1.85036i	0.00334107	−	0.0701377i
$697$	1.65056	−	1.99905i	0.0625193	−	0.0757195i
$698$	40.5625	+	19.7040i	1.53531	+	0.745809i
$699$	−8.43847	−	1.21327i	−0.319172	−	0.0458900i
$700$	15.5219	−	2.14473i	0.586673	−	0.0810632i
$701$	6.92584	−	23.5872i	0.261585	−	0.890877i	−0.719037	−	0.694971i	$-0.755417\pi$
$701$	6.92584	−	23.5872i	0.261585	−	0.890877i	0.980623	−	0.195906i	$-0.0627648\pi$
$702$	−0.858541	−	0.0204371i	−0.0324035	−	0.000771348i
$703$	−7.62195	−	45.3260i	−0.287467	−	1.70950i
$704$	−3.64348	+	1.45863i	−0.137319	+	0.0549742i
$705$	4.50464	+	5.26858i	0.169655	+	0.198426i
$706$	−8.81656	+	19.3056i	−0.331816	+	0.726575i
$707$	−8.49434	−	5.36675i	−0.319463	−	0.201837i
$708$	−2.62881	−	1.96791i	−0.0987969	−	0.0739584i
$709$	0.350394	+	7.35568i	0.0131593	+	0.276248i	0.995851	+	0.0909994i	$0.0290061\pi$
$709$	0.350394	+	7.35568i	0.0131593	+	0.276248i	−0.982692	+	0.185249i	$0.940691\pi$
$710$	1.94924	−	2.11597i	0.0731536	−	0.0794109i
$711$	10.4853	−	10.9967i	0.393230	−	0.412408i
$712$	−3.43633	−	12.8246i	−0.128782	−	0.480621i
$713$	−2.43872	−	11.0356i	−0.0913308	−	0.413286i
$714$	−4.58200	+	4.65333i	−0.171477	+	0.174146i
$715$	−2.76311	−	0.348907i	−0.103335	−	0.0130484i
$716$	−27.1666	+	5.23593i	−1.01526	+	0.195676i
$717$	−1.27728	−	3.99567i	−0.0477008	−	0.149221i
$718$	−32.3932	−	3.87308i	−1.20890	−	0.144542i
$719$	−21.9280	−	42.5345i	−0.817778	−	1.58627i	−0.810096	−	0.586297i	$-0.800585\pi$
$719$	−21.9280	−	42.5345i	−0.817778	−	1.58627i	−0.00768166	−	0.999970i	$-0.502445\pi$
$720$	−31.6954	−	1.71984i	−1.18122	−	0.0640948i
$721$	−19.5690	−	28.4376i	−0.728789	−	1.05907i
$722$	21.8889	−	16.3858i	0.814619	−	0.609816i
$723$	2.74798	+	3.32818i	0.102198	+	0.123776i
$724$	2.19814	+	9.06084i	0.0816931	+	0.336743i
$725$	−9.33644	+	14.1141i	−0.346747	+	0.524184i
$726$	14.3781	+	1.37294i	0.533621	+	0.0509546i
$727$	−22.3640	−	29.8749i	−0.829437	−	1.10800i	−0.992604	−	0.121399i	$-0.961262\pi$
$727$	−22.3640	−	29.8749i	−0.829437	−	1.10800i	0.163167	−	0.986598i	$-0.447829\pi$
$728$	−0.792546	+	0.281175i	−0.0293737	+	0.0104210i
$729$	−17.8824	−	8.16663i	−0.662312	−	0.302468i
$730$	17.4321	−	19.8511i	0.645191	−	0.734722i
$731$	12.6240	−	9.92761i	0.466915	−	0.367186i
$732$	4.72702	−	1.51107i	0.174716	−	0.0558506i
$733$	23.1278	+	15.6533i	0.854244	+	0.578169i	0.907329	−	0.420421i	$-0.138118\pi$
$733$	23.1278	+	15.6533i	0.854244	+	0.578169i	−0.0530853	+	0.998590i	$0.516906\pi$
$734$	−43.5597	+	12.7903i	−1.60782	+	0.472098i
$735$	−5.83885	+	0.750509i	−0.215369	+	0.0276829i
$736$	0.0939596	+	28.5411i	0.00346340	+	1.05204i
$737$	−75.0333	+	20.1051i	−2.76389	+	0.740581i
$738$	3.59473	−	0.0855705i	0.132324	−	0.00314990i
$739$	−37.7899	−	13.0792i	−1.39012	−	0.481126i	−0.473470	−	0.880810i	$-0.656999\pi$
$739$	−37.7899	−	13.0792i	−1.39012	−	0.481126i	−0.916653	+	0.399684i	$0.869120\pi$
$740$	−7.39017	+	19.4209i	−0.271668	+	0.713925i
$741$	0.476340	−	0.0684874i	0.0174988	−	0.00251595i
$742$	−26.0593	−	49.6036i	−0.956666	−	1.82101i
$743$	16.3972	−	6.11583i	0.601554	−	0.224368i	−0.0301914	−	0.999544i	$-0.509612\pi$
$743$	16.3972	−	6.11583i	0.601554	−	0.224368i	0.631745	+	0.775176i	$0.282339\pi$
$744$	−1.21890	+	0.421864i	−0.0446869	+	0.0154663i
$745$	−4.67438	+	4.39841i	−0.171256	+	0.161145i
$746$	−43.0236	−	30.6369i	−1.57520	−	1.12170i
$747$	0.525815	−	22.0889i	0.0192386	−	0.808192i
$748$	−21.8034	+	11.9056i	−0.797213	+	0.435311i
$749$	8.21058	+	46.6220i	0.300008	+	1.70353i
$750$	−6.23088	−	4.18117i	−0.227520	−	0.152675i
$751$	−34.0534	+	11.7860i	−1.24263	+	0.430077i	−0.867751	−	0.496999i	$-0.834435\pi$
$751$	−34.0534	+	11.7860i	−1.24263	+	0.430077i	−0.374874	+	0.927076i	$0.622314\pi$
$752$	31.5634	+	26.0609i	1.15100	+	0.950344i
$753$	2.88972	−	2.62693i	0.105307	−	0.0957306i
$754$	−0.490274	+	1.22464i	−0.0178547	+	0.0445989i
$755$	−25.9531	+	35.9410i	−0.944530	+	1.30803i
$756$	−6.89118	−	0.439405i	−0.250630	−	0.0159810i
$757$	−4.88899	+	8.95351i	−0.177693	+	0.325421i	−0.951312	−	0.308231i	$-0.900263\pi$
$757$	−4.88899	+	8.95351i	−0.177693	+	0.325421i	0.773618	+	0.633652i	$0.218445\pi$
$758$	6.23195	−	1.66985i	0.226355	−	0.0606515i
$759$	4.68317	−	9.15797i	0.169988	−	0.332413i
$760$	18.9440	−	2.13814i	0.687169	−	0.0775586i
$761$	−2.31833	+	9.55628i	−0.0840393	+	0.346415i	−0.998271	−	0.0587767i	$-0.981280\pi$
$761$	−2.31833	+	9.55628i	−0.0840393	+	0.346415i	0.914232	+	0.405191i	$0.132795\pi$
$762$	−0.580803	+	8.12069i	−0.0210403	+	0.294181i
$763$	−0.671948	+	0.439204i	−0.0243261	+	0.0159002i
$764$	−0.609570	−	4.23965i	−0.0220535	−	0.153385i
$765$	−23.4583	+	1.52202i	−0.848138	+	0.0550289i
$766$	−0.789300	−	8.26592i	−0.0285186	−	0.298660i
$767$	−0.902388	−	1.33328i	−0.0325833	−	0.0481418i
$768$	7.62753	−	0.911983i	0.275235	−	0.0329084i
$769$	−9.28081	−	20.3221i	−0.334675	−	0.732835i	0.665230	−	0.746638i	$-0.268333\pi$
$769$	−9.28081	−	20.3221i	−0.334675	−	0.732835i	−0.999905	+	0.0138032i	$0.995606\pi$
$770$	−59.3824	−	9.91764i	−2.13999	−	0.357407i
$771$	6.10815	+	1.79352i	0.219980	+	0.0645919i
$772$	3.29756	+	3.99381i	0.118682	+	0.143740i
$773$	0.959387	+	0.410833i	0.0345067	+	0.0147766i	0.410834	−	0.911710i	$-0.365237\pi$
$773$	0.959387	+	0.410833i	0.0345067	+	0.0147766i	−0.376328	+	0.926487i	$0.622813\pi$
$774$	21.8732	+	4.21571i	0.786215	+	0.151530i
$775$	11.5396	+	2.38267i	0.414513	+	0.0855880i
$776$	8.81691	−	13.7194i	0.316509	−	0.492497i
$777$	2.84540	−	7.26967i	0.102078	−	0.260798i
$778$	−56.6122	−	12.3152i	−2.02965	−	0.441522i
$779$	−4.05500	+	0.781536i	−0.145285	+	0.0280014i
$780$	−0.201443	−	0.0821942i	−0.00721281	−	0.00294303i
$781$	−3.56070	+	2.05577i	−0.127412	+	0.0735613i
$782$	3.83952	+	31.2397i	0.137301	+	1.11713i
$783$	5.27322	−	5.27322i	0.188450	−	0.188450i
$784$	−33.1984	+	10.3075i	−1.18566	+	0.368124i
$785$	45.4351	−	14.1938i	1.62165	−	0.506597i
$786$	−0.473832	−	9.94695i	−0.0169010	−	0.354796i
$787$	−0.0316096	+	0.264372i	−0.00112676	+	0.00942386i	−0.993480	−	0.114006i	$-0.963632\pi$
$787$	−0.0316096	+	0.264372i	−0.00112676	+	0.00942386i	0.992353	+	0.123430i	$0.0393893\pi$
$788$	−13.5963	−	14.9565i	−0.484350	−	0.532803i
$789$	−1.07115	−	1.50422i	−0.0381339	−	0.0535516i
$790$	19.1390	−	9.14134i	0.680937	−	0.325234i
$791$	−0.774639	−	6.08013i	−0.0275430	−	0.216185i
$792$	22.2273	+	8.29036i	0.789813	+	0.294585i
$793$	2.43236	+	0.0579010i	0.0863756	+	0.00205612i
$794$	4.76638	−	1.15631i	0.169153	−	0.0410360i
$795$	−2.41706	+	9.68348i	−0.0857242	+	0.343438i
$796$	7.51521	−	9.55636i	0.266369	−	0.338716i
$797$	0.956147	+	13.3687i	0.0338685	+	0.473543i	0.985877	+	0.167471i	$0.0535601\pi$
$797$	0.956147	+	13.3687i	0.0338685	+	0.473543i	−0.952009	+	0.306072i	$0.900985\pi$
$798$	10.3480	−	1.06881i	0.366314	−	0.0378355i
$799$	25.5014	+	16.3887i	0.902174	+	0.579792i
$800$	−27.1966	−	12.0741i	−0.961546	−	0.426884i
$801$	11.9503	−	23.1803i	0.422242	−	0.819035i
$802$	−14.8318	−	30.5325i	−0.523728	−	1.07814i
$803$	−32.2389	+	19.6506i	−1.13769	+	0.693456i
$804$	−6.06831			−0.214013
$805$	−14.6601	+	24.2916i	−0.516701	+	0.856166i
$806$	0.918494			0.0323526
$807$	1.10538	−	0.673761i	0.0389111	−	0.0237175i
$808$	2.41485	+	4.97118i	0.0849541	+	0.174885i
$809$	−7.66618	+	14.8703i	−0.269528	+	0.522812i	−0.984291	−	0.176555i	$-0.943505\pi$
$809$	−7.66618	+	14.8703i	−0.269528	+	0.522812i	0.714762	+	0.699367i	$0.246535\pi$
$810$	−21.7136	−	22.0025i	−0.762938	−	0.773090i
$811$	−0.112321	−	0.0721844i	−0.00394413	−	0.00253474i	0.538667	−	0.842519i	$-0.318928\pi$
$811$	−0.112321	−	0.0721844i	−0.00394413	−	0.00253474i	−0.542611	+	0.839984i	$0.682564\pi$
$812$	−4.33154	+	9.68194i	−0.152007	+	0.339769i
$813$	−0.819907	−	11.4638i	−0.0287554	−	0.402053i
$814$	49.3530	−	62.7575i	1.72982	−	2.19965i
$815$	−0.683519	−	1.13824i	−0.0239426	−	0.0398709i
$816$	6.67523	−	1.61939i	0.233680	−	0.0566901i
$817$	−25.5758	−	0.608818i	−0.894785	−	0.0212999i
$818$	5.60495	+	2.09054i	0.195972	+	0.0730939i
$819$	−1.52344	−	0.638498i	−0.0532333	−	0.0223109i
$820$	1.76023	+	0.622278i	0.0614699	+	0.0217309i
$821$	−14.2474	−	20.0077i	−0.497238	−	0.698274i	0.487341	−	0.873212i	$-0.337967\pi$
$821$	−14.2474	−	20.0077i	−0.497238	−	0.698274i	−0.984579	+	0.174938i	$0.944027\pi$
$822$	−0.504553	−	0.555027i	−0.0175983	−	0.0193588i
$823$	−2.00269	+	16.7499i	−0.0698095	+	0.583864i	0.914138	+	0.405404i	$0.132869\pi$
$823$	−2.00269	+	16.7499i	−0.0698095	+	0.583864i	−0.983947	+	0.178460i	$0.942888\pi$
$824$	0.903470	+	18.9662i	0.0314739	+	0.660718i
$825$	6.71787	+	8.35888i	0.233886	+	0.291019i
$826$	−18.3425	−	29.5764i	−0.638218	−	1.02909i
$827$	8.08134	−	8.08134i	0.281016	−	0.281016i	−0.552498	−	0.833514i	$-0.686325\pi$
$827$	8.08134	−	8.08134i	0.281016	−	0.281016i	0.833514	+	0.552498i	$0.186325\pi$
$828$	−10.8833	+	12.0515i	−0.378221	+	0.418819i
$829$	12.6519	−	7.30457i	0.439418	−	0.253698i	−0.263933	−	0.964541i	$-0.585020\pi$
$829$	12.6519	−	7.30457i	0.439418	−	0.253698i	0.703351	+	0.710843i	$0.251686\pi$
$830$	11.6522	−	28.5573i	0.404453	−	0.991239i
$831$	−2.45945	+	0.474020i	−0.0853173	+	0.0164436i
$832$	−0.146876	−	0.0319509i	−0.00509200	−	0.00110770i
$833$	−23.5061	+	10.4984i	−0.814439	+	0.363749i
$834$	0.625467	−	0.973245i	0.0216581	−	0.0337007i
$835$	11.3632	+	53.9497i	0.393238	+	1.86700i
$836$	38.8577	+	7.48922i	1.34392	+	0.259020i
$837$	−4.77327	−	2.04403i	−0.164988	−	0.0706522i
$838$	2.50675	+	3.03602i	0.0865943	+	0.104878i
$839$	16.3917	+	4.81302i	0.565903	+	0.166164i	0.552155	−	0.833741i	$-0.313806\pi$
$839$	16.3917	+	4.81302i	0.565903	+	0.166164i	0.0137478	+	0.999905i	$0.495624\pi$
$840$	2.94693	+	1.34185i	0.101679	+	0.0462983i
$841$	7.28844	+	15.9594i	0.251325	+	0.550326i
$842$	0.333945	−	0.0399280i	0.0115085	−	0.00137601i
$843$	0.827135	+	1.22209i	0.0284880	+	0.0420910i
$844$	−2.22159	−	23.2655i	−0.0764703	−	0.800833i
$845$	21.7624	+	19.1105i	0.748648	+	0.657420i
$846$	5.98376	+	41.6180i	0.205726	+	1.43086i
$847$	50.8080	+	25.6987i	1.74578	+	0.883017i
$848$	−4.20436	+	58.7846i	−0.144378	+	2.01867i
$849$	−1.33527	+	5.50407i	−0.0458265	+	0.188899i
$850$	−31.3606	−	9.66031i	−1.07566	−	0.331346i
$851$	−18.9198	−	32.5223i	−0.648563	−	1.11485i
$852$	−0.310246	+	0.0831303i	−0.0106289	+	0.00284800i
$853$	−14.3261	+	26.2362i	−0.490515	+	0.898311i	0.508785	+	0.860894i	$0.330095\pi$
$853$	−14.3261	+	26.2362i	−0.490515	+	0.898311i	−0.999300	+	0.0374176i	$0.988087\pi$
$854$	52.4890	+	3.34688i	1.79614	+	0.114528i
$855$	30.3593	+	21.9225i	1.03826	+	0.749735i
$856$	9.67765	−	24.1736i	0.330775	−	0.826237i
$857$	4.95585	−	4.50516i	0.169289	−	0.153893i	−0.583601	−	0.812041i	$-0.698357\pi$
$857$	4.95585	−	4.50516i	0.169289	−	0.153893i	0.752889	+	0.658147i	$0.228660\pi$
$858$	0.644604	+	0.532230i	0.0220064	+	0.0181700i
$859$	−30.8634	+	10.6819i	−1.05305	+	0.364463i	−0.798121	−	0.602498i	$-0.794172\pi$
$859$	−30.8634	+	10.6819i	−1.05305	+	0.364463i	−0.254926	+	0.966961i	$0.582051\pi$
$860$	9.83600	+	6.08487i	0.335405	+	0.207492i
$861$	−0.659064	−	0.240037i	−0.0224608	−	0.00818043i
$862$	−25.8428	+	14.1112i	−0.880210	+	0.480631i
$863$	0.0286269	−	1.20259i	0.000974472	−	0.0409366i	−0.999020	−	0.0442610i	$-0.985907\pi$
$863$	0.0286269	−	1.20259i	0.000974472	−	0.0409366i	0.999994	+	0.00332442i	$0.00105820\pi$
$864$	10.6815	+	7.60629i	0.363393	+	0.258771i
$865$	0.844513	−	27.7637i	0.0287143	−	0.943993i
$866$	14.1809	−	4.90805i	0.481886	−	0.166782i
$867$	−1.22432	+	0.456648i	−0.0415801	+	0.0155086i
$868$	7.37941	+	0.294427i	0.250474	+	0.00999351i
$869$	−30.0035	+	4.31385i	−1.01780	+	0.146337i
$870$	4.63416	−	2.07945i	0.157113	−	0.0704999i
$871$	−2.81149	−	0.973065i	−0.0952636	−	0.0329710i
$872$	0.441426	−	0.0105079i	0.0149486	−	0.000355842i
$873$	30.9421	−	8.29091i	1.04723	−	0.280605i
$874$	26.9679	−	42.2682i	0.912203	−	1.42974i
$875$	−16.8654	−	24.3014i	−0.570156	−	0.821537i
$876$	−2.82997	+	0.830955i	−0.0956159	+	0.0280754i
$877$	46.5954	+	31.5367i	1.57341	+	1.06492i	0.961797	+	0.273763i	$0.0882683\pi$
$877$	46.5954	+	31.5367i	1.57341	+	1.06492i	0.611616	+	0.791154i	$0.290520\pi$
$878$	39.3631	−	12.5830i	1.32844	−	0.424656i
$879$	2.38118	−	1.87258i	0.0803153	−	0.0631607i
$880$	47.5817	+	41.7835i	1.60398	+	1.40852i
$881$	43.9544	+	20.0733i	1.48086	+	0.676286i	0.981737	−	0.190244i	$-0.0609280\pi$
$881$	43.9544	+	20.0733i	1.48086	+	0.676286i	0.499124	+	0.866531i	$0.333655\pi$
$882$	−32.3560	−	15.1044i	−1.08948	−	0.508593i
$883$	−4.86747	−	6.50218i	−0.163804	−	0.218816i	0.711128	−	0.703063i	$-0.248185\pi$
$883$	−4.86747	−	6.50218i	−0.163804	−	0.218816i	−0.874932	+	0.484247i	$0.839094\pi$
$884$	−0.947135	−	0.0904404i	−0.0318556	−	0.00304184i
$885$	−1.06837	+	6.10634i	−0.0359130	+	0.205262i
$886$	4.27436	+	17.6192i	0.143600	+	0.591928i
$887$	−23.0322	−	27.8952i	−0.773345	−	0.936628i	0.225951	−	0.974139i	$-0.427451\pi$
$887$	−23.0322	−	27.8952i	−0.773345	−	0.936628i	−0.999296	+	0.0375109i	$0.988057\pi$
$888$	−3.43755	+	2.57332i	−0.115357	+	0.0863549i
$889$	−13.8000	+	28.9758i	−0.462839	+	0.971818i
$890$	27.0989	−	24.3094i	0.908357	−	0.814853i
$891$	20.2436	+	39.2672i	0.678188	+	1.31550i
$892$	−16.3521	−	1.95513i	−0.547508	−	0.0654625i
$893$	−14.7032	−	45.9958i	−0.492025	−	1.53919i
$894$	1.89167	−	0.364589i	0.0632668	−	0.0121937i
$895$	32.0135	+	41.2668i	1.07009	+	1.37940i
$896$	27.3352	+	7.09865i	0.913204	+	0.237149i
$897$	0.345135	−	0.189936i	0.0115237	−	0.00634177i
$898$	−3.93247	−	14.6762i	−0.131228	−	0.489751i
$899$	−5.50405	+	5.77248i	−0.183570	+	0.192523i
$900$	−6.82869	−	15.4914i	−0.227623	−	0.516379i
$901$	2.07677	+	43.5968i	0.0691873	+	1.45242i
$902$	−5.74255	−	4.29882i	−0.191206	−	0.143135i
$903$	−3.67351	−	2.32093i	−0.122247	−	0.0772358i
$904$	−1.40052	+	3.06671i	−0.0465807	+	0.101997i
$905$	13.3779	−	11.4381i	0.444695	−	0.380214i
$906$	12.3530	−	4.94541i	0.410402	−	0.164300i
$907$	−2.23430	−	13.2869i	−0.0741886	−	0.441183i	−0.998260	−	0.0589635i	$-0.981220\pi$
$907$	−2.23430	−	13.2869i	−0.0741886	−	0.441183i	0.924072	−	0.382219i	$-0.124840\pi$
$908$	−25.6287	−	0.610076i	−0.850517	−	0.0202461i
$909$	−3.05844	+	10.4161i	−0.101442	+	0.345479i
$910$	−1.67057	−	1.58934i	−0.0553789	−	0.0526860i
$911$	−36.0235	−	5.17940i	−1.19351	−	0.171601i	−0.483215	−	0.875502i	$-0.660531\pi$
$911$	−36.0235	−	5.17940i	−1.19351	−	0.171601i	−0.710298	+	0.703901i	$0.751440\pi$
$912$	−9.84212	−	4.78100i	−0.325905	−	0.158315i
$913$	−28.0645	+	33.9900i	−0.928801	+	1.12491i
$914$	−1.01608	+	21.3302i	−0.0336090	+	0.705539i
$915$	−6.58056	−	6.66812i	−0.217547	−	0.220441i
$916$	2.96286	+	4.61031i	0.0978958	+	0.152329i
$917$	12.5526	−	37.1952i	0.414523	−	1.22829i
$918$	12.6919	+	6.93031i	0.418896	+	0.228734i
$919$	−8.86796	+	15.3598i	−0.292527	+	0.506671i	−0.974407	−	0.224793i	$-0.927829\pi$
$919$	−8.86796	+	15.3598i	−0.292527	+	0.506671i	0.681880	+	0.731464i	$0.261163\pi$
$920$	13.8950	−	7.10511i	0.458103	−	0.234249i
$921$	1.77931	+	3.08186i	0.0586304	+	0.101551i
$922$	35.6871	−	21.7524i	1.17529	−	0.716378i
$923$	−0.157069	−	0.0112338i	−0.00516999	−	0.000369765i
$924$	5.00830	+	4.48270i	0.164761	+	0.147470i
$925$	39.0078	−	4.14180i	1.28257	−	0.136182i
$926$	−11.4785	+	5.91758i	−0.377207	+	0.194464i
$927$	−23.7464	+	28.7602i	−0.779935	+	0.944609i
$928$	16.6808	−	11.2899i	0.547574	−	0.370609i
$929$	−3.40486	+	4.32963i	−0.111710	+	0.142051i	−0.838693	−	0.544605i	$-0.816680\pi$
$929$	−3.40486	+	4.32963i	−0.111710	+	0.142051i	0.726983	+	0.686656i	$0.240922\pi$
$930$	−2.54341	−	2.45743i	−0.0834018	−	0.0805824i
$931$	39.5221	+	10.9446i	1.29529	+	0.358696i
$932$	−12.8676	−	23.5653i	−0.421493	−	0.771907i
$933$	7.61167	−	6.28472i	0.249195	−	0.205753i
$934$	24.7355	−	9.90262i	0.809372	−	0.324023i
$935$	38.6628	+	26.5420i	1.26441	+	0.868016i
$936$	0.527029	+	0.740109i	0.0172265	+	0.0241912i
$937$	−51.6651	+	11.2391i	−1.68783	+	0.367164i	−0.951065	−	0.308990i	$-0.900009\pi$
$937$	−51.6651	+	11.2391i	−1.68783	+	0.367164i	−0.736760	+	0.676154i	$0.763645\pi$
$938$	−59.8894	−	23.4411i	−1.95546	−	0.765379i
$939$	7.02017	−	4.51159i	0.229094	−	0.147230i
$940$	−4.78141	+	21.3011i	−0.155953	+	0.694765i
$941$	11.0263	−	11.5641i	0.359448	−	0.376978i	−0.519034	−	0.854754i	$-0.673708\pi$
$941$	11.0263	−	11.5641i	0.359448	−	0.376978i	0.878482	+	0.477775i	$0.158557\pi$
$942$	−13.8004	−	3.69782i	−0.449643	−	0.120481i
$943$	−2.88078	+	1.76896i	−0.0938111	+	0.0576053i
$944$			36.6053i			1.19140i
$945$	5.14476	+	11.9773i	0.167359	+	0.389620i
$946$	−29.1013	−	33.5847i	−0.946165	−	1.09193i
$947$	0.876896	−	0.964618i	0.0284953	−	0.0313459i	−0.725538	−	0.688182i	$-0.758409\pi$
$947$	0.876896	−	0.964618i	0.0284953	−	0.0313459i	0.754033	+	0.656837i	$0.228106\pi$
$948$	−2.35120	−	0.281121i	−0.0763635	−	0.00913038i
$949$	−1.44439	−	0.0688047i	−0.0468868	−	0.00223350i
$950$	28.7247	+	43.6733i	0.931952	+	1.41695i
$951$	3.79237	−	4.37663i	0.122976	−	0.141922i
$952$	14.0314	+	1.90693i	0.454760	+	0.0618040i
$953$	5.48285	−	14.7001i	0.177607	−	0.476183i	−0.817390	−	0.576084i	$-0.804580\pi$
$953$	5.48285	−	14.7001i	0.177607	−	0.476183i	0.994997	+	0.0999015i	$0.0318528\pi$
$954$	−43.8140	+	41.7766i	−1.41853	+	1.35257i
$955$	−6.61738	+	4.64662i	−0.214134	+	0.150361i
$956$	7.66335	−	10.7617i	0.247850	−	0.348057i
$957$	−7.20769	+	0.861785i	−0.232992	+	0.0278576i
$958$	−5.60431	+	0.400828i	−0.181067	+	0.0129502i
$959$	−1.05470	−	2.76241i	−0.0340579	−	0.0892028i
$960$	0.321231	+	0.481442i	0.0103677	+	0.0155385i
$961$	−23.6237	−	9.45749i	−0.762054	−	0.305080i
$962$	2.91259	−	0.931055i	0.0939057	−	0.0300184i
$963$	46.0061	−	22.3484i	1.48253	−	0.720167i
$964$	−3.20467	+	13.2098i	−0.103216	+	0.425460i
$965$	3.90813	−	8.96222i	0.125807	−	0.288504i
$966$	7.61859	−	3.80516i	0.245124	−	0.122429i
$967$	22.9430	+	22.9430i	0.737797	+	0.737797i	0.972151	−	0.234354i	$-0.0752975\pi$
$967$	22.9430	+	22.9430i	0.737797	+	0.737797i	−0.234354	+	0.972151i	$0.575298\pi$
$968$	−16.3001	−	26.7420i	−0.523905	−	0.859521i
$969$	−7.65774	−	2.65037i	−0.246002	−	0.0851421i
$970$	44.4847	+	4.54463i	1.42832	+	0.145919i
$971$	11.6590	−	29.1227i	0.374155	−	0.934593i	−0.615108	−	0.788443i	$-0.710888\pi$
$971$	11.6590	−	29.1227i	0.374155	−	0.934593i	0.989262	−	0.146150i	$-0.0466883\pi$
$972$	2.39793	+	11.0231i	0.0769136	+	0.353566i
$973$	3.69441	−	2.67402i	0.118437	−	0.0857250i
$974$	10.0034	+	8.66796i	0.320528	+	0.277739i
$975$	0.0336340	+	0.409338i	0.00107715	+	0.0131093i
$976$	−45.0624	−	32.0888i	−1.44241	−	1.02714i
$977$	−4.54409	−	2.76977i	−0.145378	−	0.0886127i	0.445889	−	0.895088i	$-0.352887\pi$
$977$	−4.54409	−	2.76977i	−0.145378	−	0.0886127i	−0.591268	+	0.806475i	$0.701372\pi$
$978$	−0.00948360	+	0.398396i	−0.000303252	+	0.0127393i
$979$	−47.3255	+	21.6128i	−1.51253	+	0.690748i
$980$	−12.9123	−	13.3046i	−0.412469	−	0.425001i
$981$	0.655476	+	0.567973i	0.0209277	+	0.0181340i
$982$	1.93969	−	11.5349i	0.0618979	−	0.368093i
$983$	−31.7651	+	28.8764i	−1.01315	+	0.921014i	−0.996886	−	0.0788539i	$-0.974874\pi$
$983$	−31.7651	+	28.8764i	−1.01315	+	0.921014i	−0.0162633	+	0.999868i	$0.505177\pi$
$984$	0.238492	+	0.303267i	0.00760284	+	0.00966779i
$985$	−13.5706	+	35.6626i	−0.432396	+	1.13631i
$986$	16.7871	−	14.5461i	0.534610	−	0.463242i
$987$	1.87204	−	7.98531i	0.0595877	−	0.254175i
$988$	1.07171	+	1.07171i	0.0340955	+	0.0340955i
$989$	−19.7681	+	6.91475i	−0.628588	+	0.219876i
$990$	7.29534	+	64.6368i	0.231861	+	2.05429i
$991$	14.3648	+	13.6968i	0.456312	+	0.435093i	0.883047	−	0.469284i	$-0.155488\pi$
$991$	14.3648	+	13.6968i	0.456312	+	0.435093i	−0.426735	+	0.904377i	$0.640336\pi$
$992$	−11.6146	−	7.86097i	−0.368763	−	0.249586i
$993$	−1.26324	+	5.80701i	−0.0400876	+	0.184280i
$994$	−3.38300	−	0.378013i	−0.107302	−	0.0119898i
$995$	−22.5066	−	4.49225i	−0.713507	−	0.142414i
$996$	−2.80491	+	1.99737i	−0.0888770	+	0.0632890i
$997$	3.68290	+	5.44148i	0.116639	+	0.172333i	0.881974	−	0.471299i	$-0.156215\pi$
$997$	3.68290	+	5.44148i	0.116639	+	0.172333i	−0.765335	+	0.643632i	$0.777427\pi$
$998$	−22.3647	+	52.2266i	−0.707943	+	1.65320i
$999$	−17.2083	−	1.64319i	−0.544446	−	0.0519883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.bs.a.37.19	✓	3680
5.3	odd	4	inner	805.2.bs.a.198.74	yes	3680
7.4	even	3	inner	805.2.bs.a.382.19	yes	3680
23.5	odd	22	inner	805.2.bs.a.212.19	yes	3680
35.18	odd	12	inner	805.2.bs.a.543.19	yes	3680
115.28	even	44	inner	805.2.bs.a.373.19	yes	3680
161.74	odd	66	inner	805.2.bs.a.557.74	yes	3680
805.718	even	132	inner	805.2.bs.a.718.19	yes	3680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.bs.a.37.19	✓	3680	1.1	even	1	trivial
805.2.bs.a.198.74	yes	3680	5.3	odd	4	inner
805.2.bs.a.212.19	yes	3680	23.5	odd	22	inner
805.2.bs.a.373.19	yes	3680	115.28	even	44	inner
805.2.bs.a.382.19	yes	3680	7.4	even	3	inner
805.2.bs.a.543.19	yes	3680	35.18	odd	12	inner
805.2.bs.a.557.74	yes	3680	161.74	odd	66	inner
805.2.bs.a.718.19	yes	3680	805.718	even	132	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.bs (of order \(132\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52376 + 0.928783i) q^{2} +(-0.164334 - 0.338297i) q^{3} +(0.542767 - 1.05282i) q^{4} +(-2.23602 - 0.0147772i) q^{5} +(0.564611 + 0.362854i) q^{6} +(1.55128 + 2.14325i) q^{7} +(-0.103819 - 1.45157i) q^{8} +(1.76704 - 2.24697i) q^{9} +O(q^{10})\)	\(q+(-1.52376 + 0.928783i) q^{2} +(-0.164334 - 0.338297i) q^{3} +(0.542767 - 1.05282i) q^{4} +(-2.23602 - 0.0147772i) q^{5} +(0.564611 + 0.362854i) q^{6} +(1.55128 + 2.14325i) q^{7} +(-0.103819 - 1.45157i) q^{8} +(1.76704 - 2.24697i) q^{9} +(3.42089 - 2.05426i) q^{10} +(-5.54191 + 1.34445i) q^{11} +(-0.445361 - 0.0106016i) q^{12} +(-0.204639 - 0.0763262i) q^{13} +(-4.35440 - 1.82500i) q^{14} +(0.362456 + 0.758867i) q^{15} +(2.88054 + 4.04515i) q^{16} +(2.47386 + 2.72133i) q^{17} +(-0.605601 + 5.06505i) q^{18} +(-0.278759 - 5.85187i) q^{19} +(-1.22919 + 2.34611i) q^{20} +(0.470125 - 0.877004i) q^{21} +(7.19586 - 7.19586i) q^{22} +(-1.90238 - 4.40238i) q^{23} +(-0.474002 + 0.273665i) q^{24} +(4.99956 + 0.0660843i) q^{25} +(0.382711 - 0.0737616i) q^{26} +(-2.15304 - 0.468365i) q^{27} +(3.09844 - 0.469939i) q^{28} +(-1.82982 + 2.84725i) q^{29} +(-1.25712 - 0.819691i) q^{30} +(2.31401 + 0.445989i) q^{31} +(-5.47077 - 2.34272i) q^{32} +(1.36555 + 1.65387i) q^{33} +(-6.29710 - 1.84900i) q^{34} +(-3.43703 - 4.81527i) q^{35} +(-1.40657 - 3.07996i) q^{36} +(7.78993 - 0.931400i) q^{37} +(5.85988 + 8.65797i) q^{38} +(0.00780824 + 0.0817716i) q^{39} +(0.210690 + 3.24728i) q^{40} +(-0.100317 - 0.697718i) q^{41} +(0.0981865 + 1.77299i) q^{42} +(0.311526 - 4.35570i) q^{43} +(-1.59250 + 6.56436i) q^{44} +(-3.98433 + 4.99816i) q^{45} +(6.98764 + 4.94129i) q^{46} +(7.96163 - 2.13331i) q^{47} +(0.895091 - 1.63924i) q^{48} +(-2.18704 + 6.64958i) q^{49} +(-7.67953 + 4.54281i) q^{50} +(0.514079 - 1.28411i) q^{51} +(-0.191429 + 0.174020i) q^{52} +(9.15145 + 7.55608i) q^{53} +(3.71574 - 1.28603i) q^{54} +(12.4117 - 2.92433i) q^{55} +(2.95003 - 2.47431i) q^{56} +(-1.93386 + 1.05597i) q^{57} +(0.143732 - 6.03804i) q^{58} +(6.00444 + 4.27574i) q^{59} +(0.995680 + 0.0302865i) q^{60} +(-10.5272 + 3.64349i) q^{61} +(-3.94023 + 1.46963i) q^{62} +(7.55700 + 0.301513i) q^{63} +(0.681202 - 0.0979421i) q^{64} +(0.456448 + 0.173691i) q^{65} +(-3.61687 - 1.25181i) q^{66} +(13.6179 - 0.324166i) q^{67} +(4.20780 - 1.12748i) q^{68} +(-1.17668 + 1.36703i) q^{69} +(9.70956 + 4.14508i) q^{70} +(0.691782 - 0.203126i) q^{71} +(-3.44510 - 2.33171i) q^{72} +(6.30635 - 2.01592i) q^{73} +(-11.0049 + 8.65438i) q^{74} +(-0.799245 - 1.70220i) q^{75} +(-6.31227 - 2.88272i) q^{76} +(-11.4786 - 9.79207i) q^{77} +(-0.0878460 - 0.117348i) q^{78} +(5.29134 + 0.505262i) q^{79} +(-6.38117 - 9.08761i) q^{80} +(-1.82641 - 7.52858i) q^{81} +(0.800888 + 0.969986i) q^{82} +(6.18779 - 4.63212i) q^{83} +(-0.668160 - 0.970966i) q^{84} +(-5.49138 - 6.12151i) q^{85} +(3.57080 + 6.92640i) q^{86} +(1.26392 + 0.151120i) q^{87} +(2.52693 + 7.90492i) q^{88} +(8.95842 - 1.72659i) q^{89} +(1.42898 - 11.3166i) q^{90} +(-0.153866 - 0.556995i) q^{91} +(-5.66747 - 0.386596i) q^{92} +(-0.229395 - 0.856114i) q^{93} +(-10.1503 + 10.6453i) q^{94} +(0.536836 + 13.0890i) q^{95} +(0.106501 + 2.23573i) q^{96} +(8.97107 + 6.71566i) q^{97} +(-2.84348 - 12.1637i) q^{98} +(-6.77182 + 14.8282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8}+O(q^{10}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8	\( 3680 q - 18 q^{2} - 18 q^{3} - 22 q^{5} - 160 q^{6} - 44 q^{7} - 56 q^{8} - 22 q^{10} - 44 q^{11} + 14 q^{12} - 72 q^{13} - 88 q^{15} - 196 q^{16} - 22 q^{17} - 62 q^{18} - 88 q^{20} - 88 q^{21} - 44 q^{23} - 30 q^{25} - 28 q^{26} - 48 q^{27} + 132 q^{28} - 22 q^{30} - 40 q^{31} - 50 q^{32} - 22 q^{33} - 40 q^{35} - 416 q^{36} - 110 q^{37} - 22 q^{38} - 22 q^{40} - 192 q^{41} - 264 q^{42} - 88 q^{43} - 44 q^{47} + 24 q^{48} - 44 q^{51} - 374 q^{52} - 22 q^{53} - 32 q^{55} - 220 q^{56} + 88 q^{57} - 58 q^{58} - 22 q^{60} - 220 q^{61} + 8 q^{62} - 44 q^{63} - 22 q^{65} - 44 q^{66} - 22 q^{67} - 96 q^{70} - 136 q^{71} - 46 q^{72} + 18 q^{73} - 34 q^{75} - 176 q^{76} - 116 q^{77} + 80 q^{78} + 176 q^{80} - 236 q^{81} - 2 q^{82} - 88 q^{83} - 448 q^{85} - 86 q^{87} - 110 q^{88} - 88 q^{90} - 228 q^{92} + 4 q^{93} - 236 q^{95} - 332 q^{96} - 88 q^{97} + 84 q^{98}+O(q^{100}) \) 3680 * q - 18 * q^2 - 18 * q^3 - 22 * q^5 - 160 * q^6 - 44 * q^7 - 56 * q^8 - 22 * q^10 - 44 * q^11 + 14 * q^12 - 72 * q^13 - 88 * q^15 - 196 * q^16 - 22 * q^17 - 62 * q^18 - 88 * q^20 - 88 * q^21 - 44 * q^23 - 30 * q^25 - 28 * q^26 - 48 * q^27 + 132 * q^28 - 22 * q^30 - 40 * q^31 - 50 * q^32 - 22 * q^33 - 40 * q^35 - 416 * q^36 - 110 * q^37 - 22 * q^38 - 22 * q^40 - 192 * q^41 - 264 * q^42 - 88 * q^43 - 44 * q^47 + 24 * q^48 - 44 * q^51 - 374 * q^52 - 22 * q^53 - 32 * q^55 - 220 * q^56 + 88 * q^57 - 58 * q^58 - 22 * q^60 - 220 * q^61 + 8 * q^62 - 44 * q^63 - 22 * q^65 - 44 * q^66 - 22 * q^67 - 96 * q^70 - 136 * q^71 - 46 * q^72 + 18 * q^73 - 34 * q^75 - 176 * q^76 - 116 * q^77 + 80 * q^78 + 176 * q^80 - 236 * q^81 - 2 * q^82 - 88 * q^83 - 448 * q^85 - 86 * q^87 - 110 * q^88 - 88 * q^90 - 228 * q^92 + 4 * q^93 - 236 * q^95 - 332 * q^96 - 88 * q^97 + 84 * q^98

Introduction

L-functions

Modular forms

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