LMFDB - Embedded newform 429.2.bv.a.20.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(20,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 36, 55]))

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

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

chi := DirichletCharacter("429.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bv (of order $60$, degree $16$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$52$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			20.12
Character	$\chi$	$=$	429.20
Dual form			429.2.bv.a.236.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53416 - 0.0804022i) q^{2} +(1.22300 + 1.22648i) q^{3} +(0.358152 + 0.0376433i) q^{4} +(3.02311 + 1.54035i) q^{5} +(-1.77768 - 1.97996i) q^{6} +(2.44154 + 3.01505i) q^{7} +(2.48827 + 0.394104i) q^{8} +(-0.00852784 + 2.99999i) q^{9} +O(q^{10})$	\(q+(-1.53416 - 0.0804022i) q^{2} +(1.22300 + 1.22648i) q^{3} +(0.358152 + 0.0376433i) q^{4} +(3.02311 + 1.54035i) q^{5} +(-1.77768 - 1.97996i) q^{6} +(2.44154 + 3.01505i) q^{7} +(2.48827 + 0.394104i) q^{8} +(-0.00852784 + 2.99999i) q^{9} +(-4.51410 - 2.60622i) q^{10} +(2.15733 - 2.51911i) q^{11} +(0.391853 + 0.485306i) q^{12} +(-3.59575 + 0.265624i) q^{13} +(-3.50331 - 4.82189i) q^{14} +(1.80805 + 5.59165i) q^{15} +(-4.49025 - 0.954431i) q^{16} +(1.67992 - 1.86574i) q^{17} +(0.254289 - 4.60179i) q^{18} +(-1.96327 - 5.11450i) q^{19} +(1.02475 + 0.665480i) q^{20} +(-0.711903 + 6.68193i) q^{21} +(-3.51224 + 3.69128i) q^{22} +(0.800366 - 1.38628i) q^{23} +(2.55980 + 3.53382i) q^{24} +(3.82758 + 5.26821i) q^{25} +(5.53783 - 0.118405i) q^{26} +(-3.68987 + 3.65853i) q^{27} +(0.760947 + 1.17176i) q^{28} +(-2.40533 - 5.40245i) q^{29} +(-2.32427 - 8.72388i) q^{30} +(3.68069 - 1.87540i) q^{31} +(1.94514 + 0.521199i) q^{32} +(5.72807 - 0.434955i) q^{33} +(-2.72728 + 2.72728i) q^{34} +(2.73681 + 12.8757i) q^{35} +(-0.115984 + 1.07413i) q^{36} +(-2.51732 + 6.55784i) q^{37} +(2.60077 + 8.00434i) q^{38} +(-4.72340 - 4.08528i) q^{39} +(6.91526 + 5.02423i) q^{40} +(-6.77669 - 5.48766i) q^{41} +(1.62942 - 10.1939i) q^{42} +(-3.53712 + 2.04216i) q^{43} +(0.867480 - 0.821018i) q^{44} +(-4.64681 + 9.05615i) q^{45} +(-1.33935 + 2.06242i) q^{46} +(-1.97109 - 0.312189i) q^{47} +(-4.32099 - 6.67449i) q^{48} +(-1.67404 + 7.87572i) q^{49} +(-5.44856 - 8.39004i) q^{50} +(4.34285 - 0.221410i) q^{51} +(-1.29783 - 0.0402222i) q^{52} +(10.6807 + 3.47038i) q^{53} +(5.95502 - 5.31612i) q^{54} +(10.4022 - 4.29251i) q^{55} +(4.88698 + 8.46450i) q^{56} +(3.87177 - 8.66297i) q^{57} +(3.25580 + 8.48164i) q^{58} +(-6.14572 + 4.97670i) q^{59} +(0.437071 + 2.07072i) q^{60} +(8.02107 - 8.90830i) q^{61} +(-5.79757 + 2.58124i) q^{62} +(-9.06594 + 7.29888i) q^{63} +(5.78950 + 1.88112i) q^{64} +(-11.2795 - 4.73571i) q^{65} +(-8.82278 + 0.206743i) q^{66} +(-5.08077 + 1.36139i) q^{67} +(0.671900 - 0.604982i) q^{68} +(2.67910 - 0.713782i) q^{69} +(-3.16348 - 19.9734i) q^{70} +(-0.435630 - 8.31232i) q^{71} +(-1.20353 + 7.46143i) q^{72} +(-3.75049 + 0.594019i) q^{73} +(4.38924 - 9.85840i) q^{74} +(-1.78024 + 11.1375i) q^{75} +(-0.510624 - 1.90568i) q^{76} +(12.8625 + 0.353936i) q^{77} +(6.91801 + 6.64726i) q^{78} +(-1.94477 + 5.98538i) q^{79} +(-12.1043 - 9.80190i) q^{80} +(-8.99985 - 0.0511669i) q^{81} +(9.95534 + 8.96383i) q^{82} +(5.43789 + 2.77074i) q^{83} +(-0.506500 + 2.36635i) q^{84} +(7.95247 - 3.05267i) q^{85} +(5.59072 - 2.84861i) q^{86} +(3.68430 - 9.55731i) q^{87} +(6.36081 - 5.41803i) q^{88} +(1.58195 - 0.423881i) q^{89} +(7.85711 - 13.5200i) q^{90} +(-9.58005 - 10.1929i) q^{91} +(0.338837 - 0.466370i) q^{92} +(6.80165 + 2.22068i) q^{93} +(2.99887 + 0.637430i) q^{94} +(1.94294 - 18.4858i) q^{95} +(1.73967 + 3.02311i) q^{96} +(-7.52653 - 4.88779i) q^{97} +(3.20147 - 11.9480i) q^{98} +(7.53891 + 6.49344i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	$ 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) $ 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−1.53416	−	0.0804022i	−1.08482	−	0.0568529i	−0.498466	−	0.866909i	$-0.666103\pi$
$2$	−1.53416	−	0.0804022i	−1.08482	−	0.0568529i	−0.586352	+	0.810056i	$0.699436\pi$
$3$	1.22300	+	1.22648i	0.706101	+	0.708111i
$3$	1.22300	+	1.22648i	0.706101	+	0.708111i
$4$	0.358152	+	0.0376433i	0.179076	+	0.0188217i
$5$	3.02311	+	1.54035i	1.35198	+	0.688866i	0.971747	−	0.236027i	$-0.0758453\pi$
$5$	3.02311	+	1.54035i	1.35198	+	0.688866i	0.380229	+	0.924893i	$0.375845\pi$
$6$	−1.77768	−	1.97996i	−0.725733	−	0.808316i
$7$	2.44154	+	3.01505i	0.922816	+	1.13958i	0.989890	+	0.141835i	$0.0453001\pi$
$7$	2.44154	+	3.01505i	0.922816	+	1.13958i	−0.0670745	+	0.997748i	$0.521367\pi$
$8$	2.48827	+	0.394104i	0.879738	+	0.139337i
$9$	−0.00852784	+	2.99999i	−0.00284261	+	0.999996i
$10$	−4.51410	−	2.60622i	−1.42748	−	0.824158i
$11$	2.15733	−	2.51911i	0.650459	−	0.759541i
$11$	2.15733	−	2.51911i	0.650459	−	0.759541i
$12$	0.391853	+	0.485306i	0.113118	+	0.140096i
$13$	−3.59575	+	0.265624i	−0.997283	+	0.0736709i
$13$	−3.59575	+	0.265624i	−0.997283	+	0.0736709i
$14$	−3.50331	−	4.82189i	−0.936299	−	1.28870i
$15$	1.80805	+	5.59165i	0.466838	+	1.44376i
$16$	−4.49025	−	0.954431i	−1.12256	−	0.238608i
$17$	1.67992	−	1.86574i	0.407440	−	0.452508i	−0.504145	−	0.863619i	$-0.668192\pi$
$17$	1.67992	−	1.86574i	0.407440	−	0.452508i	0.911585	+	0.411111i	$0.134859\pi$
$18$	0.254289	−	4.60179i	0.0599364	−	1.08465i
$19$	−1.96327	−	5.11450i	−0.450406	−	1.17335i	−0.951417	−	0.307906i	$-0.900372\pi$
$19$	−1.96327	−	5.11450i	−0.450406	−	1.17335i	0.501011	−	0.865441i	$-0.332962\pi$
$20$	1.02475	+	0.665480i	0.229141	+	0.148806i
$21$	−0.711903	+	6.68193i	−0.155350	+	1.45812i
$22$	−3.51224	+	3.69128i	−0.748812	+	0.786984i
$23$	0.800366	−	1.38628i	0.166888	−	0.289058i	−0.770436	−	0.637517i	$-0.779962\pi$
$23$	0.800366	−	1.38628i	0.166888	−	0.289058i	0.937324	+	0.348459i	$0.113295\pi$
$24$	2.55980	+	3.53382i	0.522518	+	0.721338i
$25$	3.82758	+	5.26821i	0.765516	+	1.05364i
$26$	5.53783	−	0.118405i	1.08606	−	0.0232211i
$27$	−3.68987	+	3.65853i	−0.710115	+	0.704085i
$28$	0.760947	+	1.17176i	0.143806	+	0.221441i
$29$	−2.40533	−	5.40245i	−0.446658	−	1.00321i	−0.986846	−	0.161666i	$-0.948313\pi$
$29$	−2.40533	−	5.40245i	−0.446658	−	1.00321i	0.540188	−	0.841545i	$-0.318353\pi$
$30$	−2.32427	−	8.72388i	−0.424352	−	1.59276i
$31$	3.68069	−	1.87540i	0.661071	−	0.336833i	−0.0910605	−	0.995845i	$-0.529026\pi$
$31$	3.68069	−	1.87540i	0.661071	−	0.336833i	0.752132	+	0.659013i	$0.229026\pi$
$32$	1.94514	+	0.521199i	0.343856	+	0.0921359i
$33$	5.72807	−	0.434955i	0.997129	−	0.0757159i
$34$	−2.72728	+	2.72728i	−0.467725	+	0.467725i
$35$	2.73681	+	12.8757i	0.462605	+	2.17638i
$36$	−0.115984	+	1.07413i	−0.0193306	+	0.179022i
$37$	−2.51732	+	6.55784i	−0.413844	+	1.07810i	0.555309	+	0.831644i	$0.312600\pi$
$37$	−2.51732	+	6.55784i	−0.413844	+	1.07810i	−0.969154	+	0.246458i	$0.920733\pi$
$38$	2.60077	+	8.00434i	0.421900	+	1.29847i
$39$	−4.72340	−	4.08528i	−0.756349	−	0.654168i
$40$	6.91526	+	5.02423i	1.09340	+	0.794401i
$41$	−6.77669	−	5.48766i	−1.05834	−	0.857028i	−0.0682807	−	0.997666i	$-0.521751\pi$
$41$	−6.77669	−	5.48766i	−1.05834	−	0.857028i	−0.990061	+	0.140638i	$0.955085\pi$
$42$	1.62942	−	10.1939i	0.251425	−	1.57296i
$43$	−3.53712	+	2.04216i	−0.539406	+	0.311426i	−0.744838	−	0.667245i	$-0.767473\pi$
$43$	−3.53712	+	2.04216i	−0.539406	+	0.311426i	0.205432	+	0.978671i	$0.434140\pi$
$44$	0.867480	−	0.821018i	0.130778	−	0.123773i
$45$	−4.64681	+	9.05615i	−0.692706	+	1.35001i
$46$	−1.33935	+	2.06242i	−0.197477	+	0.304088i
$47$	−1.97109	−	0.312189i	−0.287513	−	0.0455375i	0.0110124	−	0.999939i	$-0.496495\pi$
$47$	−1.97109	−	0.312189i	−0.287513	−	0.0455375i	−0.298525	+	0.954402i	$0.596495\pi$
$48$	−4.32099	−	6.67449i	−0.623681	−	0.963379i
$49$	−1.67404	+	7.87572i	−0.239148	+	1.12510i
$50$	−5.44856	−	8.39004i	−0.770543	−	1.18653i
$51$	4.34285	−	0.221410i	0.608120	−	0.0310036i
$52$	−1.29783	−	0.0402222i	−0.179976	−	0.00557782i
$53$	10.6807	+	3.47038i	1.46711	+	0.476694i	0.930234	−	0.366966i	$-0.119603\pi$
$53$	10.6807	+	3.47038i	1.46711	+	0.476694i	0.536878	+	0.843660i	$0.319603\pi$
$54$	5.95502	−	5.31612i	0.810375	−	0.723432i
$55$	10.4022	−	4.29251i	1.40263	−	0.578802i
$56$	4.88698	+	8.46450i	0.653050	+	1.13112i
$57$	3.87177	−	8.66297i	0.512828	−	1.14744i
$58$	3.25580	+	8.48164i	0.427507	+	1.11369i
$59$	−6.14572	+	4.97670i	−0.800104	+	0.647911i	−0.939586	−	0.342313i	$-0.888790\pi$
$59$	−6.14572	+	4.97670i	−0.800104	+	0.647911i	0.139482	+	0.990225i	$0.455456\pi$
$60$	0.437071	+	2.07072i	0.0564256	+	0.267329i
$61$	8.02107	−	8.90830i	1.02699	−	1.14059i	0.0370224	−	0.999314i	$-0.488213\pi$
$61$	8.02107	−	8.90830i	1.02699	−	1.14059i	0.989970	−	0.141276i	$-0.0451206\pi$
$62$	−5.79757	+	2.58124i	−0.736292	+	0.327818i
$63$	−9.06594	+	7.29888i	−1.14220	+	0.919573i
$64$	5.78950	+	1.88112i	0.723688	+	0.235140i
$65$	−11.2795	−	4.73571i	−1.39905	−	0.587393i
$66$	−8.82278	+	0.206743i	−1.08601	+	0.0254483i
$67$	−5.08077	+	1.36139i	−0.620715	+	0.166320i	−0.555453	−	0.831548i	$-0.687455\pi$
$67$	−5.08077	+	1.36139i	−0.620715	+	0.166320i	−0.0652624	+	0.997868i	$0.520788\pi$
$68$	0.671900	−	0.604982i	0.0814798	−	0.0733648i
$69$	2.67910	−	0.713782i	0.322525	−	0.0859292i
$70$	−3.16348	−	19.9734i	−0.378108	−	2.38728i
$71$	−0.435630	−	8.31232i	−0.0516998	−	0.986490i	−0.894164	−	0.447739i	$-0.852229\pi$
$71$	−0.435630	−	8.31232i	−0.0516998	−	0.986490i	0.842465	−	0.538752i	$-0.181104\pi$
$72$	−1.20353	+	7.46143i	−0.141837	+	0.879338i
$73$	−3.75049	+	0.594019i	−0.438962	+	0.0695247i	−0.372004	−	0.928231i	$-0.621329\pi$
$73$	−3.75049	+	0.594019i	−0.438962	+	0.0695247i	−0.0669576	+	0.997756i	$0.521329\pi$
$74$	4.38924	−	9.85840i	0.510239	−	1.14602i
$75$	−1.78024	+	11.1375i	−0.205564	+	1.28605i
$76$	−0.510624	−	1.90568i	−0.0585726	−	0.218596i
$77$	12.8625	+	0.353936i	1.46581	+	0.0403347i
$78$	6.91801	+	6.64726i	0.783310	+	0.752654i
$79$	−1.94477	+	5.98538i	−0.218803	+	0.673408i	0.780058	+	0.625707i	$0.215189\pi$
$79$	−1.94477	+	5.98538i	−0.218803	+	0.673408i	−0.998862	+	0.0477009i	$0.984811\pi$
$80$	−12.1043	−	9.80190i	−1.35331	−	1.09589i
$81$	−8.99985	−	0.0511669i	−0.999984	−	0.00568521i
$82$	9.95534	+	8.96383i	1.09938	+	0.989890i
$83$	5.43789	+	2.77074i	0.596886	+	0.304128i	0.726209	−	0.687474i	$-0.241281\pi$
$83$	5.43789	+	2.77074i	0.596886	+	0.304128i	−0.129323	+	0.991602i	$0.541281\pi$
$84$	−0.506500	+	2.36635i	−0.0552637	+	0.258190i
$85$	7.95247	−	3.05267i	0.862567	−	0.331108i
$86$	5.59072	−	2.84861i	0.602863	−	0.307174i
$87$	3.68430	−	9.55731i	0.394999	−	1.02465i
$88$	6.36081	−	5.41803i	0.678065	−	0.577564i
$89$	1.58195	−	0.423881i	0.167686	−	0.0449313i	−0.173999	−	0.984746i	$-0.555669\pi$
$89$	1.58195	−	0.423881i	0.167686	−	0.0449313i	0.341685	+	0.939814i	$0.389002\pi$
$90$	7.85711	−	13.5200i	0.828212	−	1.42513i
$91$	−9.58005	−	10.1929i	−1.00426	−	1.06850i
$92$	0.338837	−	0.466370i	0.0353262	−	0.0486224i
$93$	6.80165	+	2.22068i	0.705298	+	0.230274i
$94$	2.99887	+	0.637430i	0.309310	+	0.0657458i
$95$	1.94294	−	18.4858i	0.199341	−	1.89660i
$96$	1.73967	+	3.02311i	0.177555	+	0.308545i
$97$	−7.52653	−	4.88779i	−0.764203	−	0.496279i	0.102727	−	0.994710i	$-0.467243\pi$
$97$	−7.52653	−	4.88779i	−0.764203	−	0.496279i	−0.866930	+	0.498430i	$0.833910\pi$
$98$	3.20147	−	11.9480i	0.323397	−	1.20694i
$99$	7.53891	+	6.49344i	0.757689	+	0.652615i
$100$	1.17254	+	2.03090i	0.117254	+	0.203090i
$101$	−5.51449	−	6.12446i	−0.548713	−	0.609407i	0.403449	−	0.915002i	$-0.367811\pi$
$101$	−5.51449	−	6.12446i	−0.548713	−	0.609407i	−0.952162	+	0.305595i	$0.901145\pi$
$102$	−6.68044	−	0.00949498i	−0.661463	−	0.000940143i
$103$	−6.26746	+	8.62641i	−0.617551	+	0.849986i	−0.997172	−	0.0751563i	$-0.976054\pi$
$103$	−6.26746	+	8.62641i	−0.617551	+	0.849986i	0.379621	+	0.925142i	$0.376054\pi$
$104$	−9.05190	−	0.756155i	−0.887612	−	0.0741471i
$105$	−12.4447	+	19.1036i	−1.21448	+	1.86432i
$106$	−16.1070	−	6.18289i	−1.56445	−	0.600536i
$107$	−0.0515309	+	0.00541611i	−0.00498168	+	0.000523595i	−0.107019	−	0.994257i	$-0.534131\pi$
$107$	−0.0515309	+	0.00541611i	−0.00498168	+	0.000523595i	0.102037	+	0.994781i	$0.467464\pi$
$108$	−1.45925	+	1.17141i	−0.140417	+	0.112719i
$109$	−8.47093	−	8.47093i	−0.811368	−	0.811368i	0.173471	−	0.984839i	$-0.444502\pi$
$109$	−8.47093	−	8.47093i	−0.811368	−	0.811368i	−0.984839	+	0.173471i	$0.944502\pi$
$110$	−16.3037	+	5.74907i	−1.55450	+	0.548152i
$111$	−11.1218	+	4.93280i	−1.05563	+	0.468201i
$112$	−8.08546	−	15.8686i	−0.764004	−	1.49944i
$113$	4.90380	−	11.0141i	0.461311	−	1.03612i	−0.521793	−	0.853072i	$-0.674737\pi$
$113$	4.90380	−	11.0141i	0.461311	−	1.03612i	0.983104	−	0.183049i	$-0.0585967\pi$
$114$	−6.63645	+	12.9791i	−0.621560	+	1.21561i
$115$	4.55494	−	2.95802i	0.424751	−	0.275836i
$116$	−0.658107	−	2.02545i	−0.0611037	−	0.188058i
$117$	−0.766205	−	10.7895i	−0.0708357	−	0.997488i
$118$	9.82868	−	7.14095i	0.904803	−	0.657378i
$119$	9.72690	+	0.509765i	0.891663	+	0.0467301i
$120$	2.29524	+	14.6261i	0.209526	+	1.33518i
$121$	−1.69187	−	10.8691i	−0.153807	−	0.988101i
$122$	−13.0219	+	13.0219i	−1.17895	+	1.17895i
$123$	−1.55739	−	15.0229i	−0.140425	−	1.35457i
$124$	1.38884	−	0.533127i	0.124722	−	0.0478763i
$125$	0.802450	+	5.06647i	0.0717733	+	0.453159i
$126$	14.4955	−	10.4688i	1.29136	−	0.932632i
$127$	0.937468	−	4.41044i	0.0831868	−	0.391363i	−0.916781	−	0.399390i	$-0.869222\pi$
$127$	0.937468	−	4.41044i	0.0831868	−	0.391363i	0.999968	+	0.00802720i	$0.00255517\pi$
$128$	−12.4908	−	4.79477i	−1.10404	−	0.423802i
$129$	−6.83058	−	1.84066i	−0.601399	−	0.162061i
$130$	16.9239	+	8.17226i	1.48432	+	0.716754i
$131$			10.6859i			0.933633i	0.884354	+	0.466817i	$0.154599\pi$
$131$			10.6859i			0.933633i	−0.884354	+	0.466817i	$0.845401\pi$
$132$	2.06790	+	0.0598437i	0.179987	+	0.00520872i
$133$	10.6271	−	18.4066i	0.921484	−	1.59606i
$134$	7.90420	−	1.68009i	0.682819	−	0.145138i
$135$	−16.7903	+	5.37646i	−1.44508	+	0.462732i
$136$	4.91539	−	3.98041i	0.421492	−	0.341317i
$137$	7.46275	−	0.391106i	0.637585	−	0.0334144i	0.269195	−	0.963086i	$-0.413242\pi$
$137$	7.46275	−	0.391106i	0.637585	−	0.0334144i	0.368390	+	0.929671i	$0.379909\pi$
$138$	−4.16756	+	0.879654i	−0.354767	+	0.0748811i
$139$	−2.41922	+	23.0174i	−0.205196	+	1.95231i	0.0876553	+	0.996151i	$0.472063\pi$
$139$	−2.41922	+	23.0174i	−0.205196	+	1.95231i	−0.292851	+	0.956158i	$0.594604\pi$
$140$	0.495511	+	4.71447i	0.0418783	+	0.398446i
$141$	−2.02775	−	2.79932i	−0.170767	−	0.235745i
$142$			12.7875i			1.07310i
$143$	−7.08808	+	9.63115i	−0.592735	+	0.805397i
$144$	2.90157	−	13.4625i	0.241798	−	1.12188i
$145$	1.05011	−	20.0372i	0.0872067	−	1.66400i
$146$	5.80163	−	0.609776i	0.480146	−	0.0504654i
$147$	−11.7068	+	7.57885i	−0.965560	+	0.625093i
$148$	−1.14844	+	2.25395i	−0.0944014	+	0.185273i
$149$	0.396329	+	7.56241i	0.0324686	+	0.619537i	0.965605	+	0.260014i	$0.0837272\pi$
$149$	0.396329	+	7.56241i	0.0324686	+	0.619537i	−0.933136	+	0.359523i	$0.882939\pi$
$150$	3.62666	−	16.9436i	0.296115	−	1.38344i
$151$	1.37433	−	8.67717i	0.111841	−	0.706138i	−0.866506	−	0.499167i	$-0.833639\pi$
$151$	1.37433	−	8.67717i	0.111841	−	0.706138i	0.978347	−	0.206971i	$-0.0663606\pi$
$152$	−2.86952	−	13.5000i	−0.232748	−	1.09500i
$153$	5.58287	+	5.05565i	0.451348	+	0.408725i
$154$	−19.7047	−	1.57717i	−1.58785	−	0.127092i
$155$	14.0159			1.12578
$156$	−1.53791	−	1.64096i	−0.123132	−	0.131382i
$157$	−4.28224	+	3.11123i	−0.341760	+	0.248303i	−0.745404	−	0.666613i	$-0.767743\pi$
$157$	−4.28224	+	3.11123i	−0.341760	+	0.248303i	0.403644	+	0.914916i	$0.367743\pi$
$158$	3.46483	−	9.02619i	0.275647	−	0.718085i
$159$	8.80621	+	17.3441i	0.698378	+	1.37547i
$160$	5.07755	+	4.57184i	0.401415	+	0.361436i
$161$	6.13382	−	0.971502i	0.483413	−	0.0765651i
$162$	13.8031	+	0.802106i	1.08448	+	0.0630194i
$163$	3.75017	−	5.77476i	0.293736	−	0.452314i	−0.660734	−	0.750620i	$-0.729755\pi$
$163$	3.75017	−	5.77476i	0.293736	−	0.452314i	0.954470	+	0.298306i	$0.0964216\pi$
$164$	−2.22052	−	2.22052i	−0.173393	−	0.173393i
$165$	17.9866	+	7.50832i	1.40025	+	0.584522i
$166$	−8.11984	−	4.68799i	−0.630222	−	0.363859i
$167$	−0.687974	+	13.1273i	−0.0532371	+	1.01582i	0.833199	+	0.552973i	$0.186507\pi$
$167$	−0.687974	+	13.1273i	−0.0532371	+	1.01582i	−0.886436	+	0.462851i	$0.846827\pi$
$168$	−4.40478	+	16.3459i	−0.339836	+	1.26111i
$169$	12.8589	−	1.91024i	0.989145	−	0.146941i
$170$	−12.4458	+	4.04390i	−0.954552	+	0.310153i
$171$	15.3602	−	5.84618i	1.17462	−	0.447068i
$172$	−1.34370	+	0.598255i	−0.102456	+	0.0456165i
$173$	16.0872	+	7.16250i	1.22309	+	0.544555i	0.913704	−	0.406381i	$-0.133210\pi$
$173$	16.0872	+	7.16250i	1.22309	+	0.544555i	0.309387	+	0.950936i	$0.399876\pi$
$174$	−6.42075	+	14.3663i	−0.486756	+	1.08910i
$175$	−6.53874	+	24.4029i	−0.494282	+	1.84469i
$176$	−12.0913	+	9.25242i	−0.911413	+	0.697427i
$177$	−13.6201	−	1.45110i	−1.02375	−	0.109072i
$178$	−2.46105	+	0.523111i	−0.184463	+	0.0392089i
$179$	−0.192807	−	1.83444i	−0.0144111	−	0.137112i	0.984951	−	0.172836i	$-0.0552931\pi$
$179$	−0.192807	−	1.83444i	−0.0144111	−	0.137112i	−0.999362	+	0.0357236i	$0.988626\pi$
$180$	−2.00517	+	3.06856i	−0.149457	+	0.228717i
$181$	15.0408	−	4.88706i	1.11798	−	0.363252i	0.308981	−	0.951068i	$-0.400012\pi$
$181$	15.0408	−	4.88706i	1.11798	−	0.363252i	0.808995	+	0.587816i	$0.200012\pi$
$182$	13.8778	+	16.4078i	1.02869	+	1.21622i
$183$	20.7357	−	1.05716i	1.53283	−	0.0781475i
$184$	2.53787	−	3.13401i	0.187094	−	0.231042i
$185$	−17.7115	+	15.9475i	−1.30217	+	1.17248i
$186$	−10.2563	−	3.95376i	−0.752028	−	0.289904i
$187$	−1.07587	−	8.25692i	−0.0786757	−	0.603806i
$188$	−0.694198	−	0.186010i	−0.0506296	−	0.0135662i
$189$	−20.0396	−	2.19268i	−1.45767	−	0.159494i
$190$	−4.46709	+	28.2041i	−0.324076	+	2.04614i
$191$	3.52842	+	0.370852i	0.255307	+	0.0268339i	0.231318	−	0.972878i	$-0.425696\pi$
$191$	3.52842	+	0.370852i	0.255307	+	0.0268339i	0.0239899	+	0.999712i	$0.492363\pi$
$192$	4.77341	+	9.40135i	0.344491	+	0.678484i
$193$	−10.6014	+	6.88461i	−0.763103	+	0.495565i	−0.866562	−	0.499069i	$-0.833676\pi$
$193$	−10.6014	+	6.88461i	−0.763103	+	0.495565i	0.103459	+	0.994634i	$0.467009\pi$
$194$	11.1539	+	8.10382i	0.800807	+	0.581820i
$195$	−7.98659	−	19.6259i	−0.571932	−	1.40544i
$196$	−0.896028	+	2.75769i	−0.0640020	+	0.196978i
$197$	1.88471	+	7.03385i	0.134280	+	0.501141i	1.00000		0.000611397i	$0.000194614\pi$
$197$	1.88471	+	7.03385i	0.134280	+	0.501141i	−0.865720	+	0.500529i	$0.833139\pi$
$198$	−11.0438	−	10.5682i	−0.784852	−	0.751046i
$199$	−13.5359	+	7.81496i	−0.959535	+	0.553988i	−0.896030	−	0.443994i	$-0.853561\pi$
$199$	−13.5359	+	7.81496i	−0.959535	+	0.553988i	−0.0635053	+	0.997982i	$0.520228\pi$
$200$	7.44784	+	14.6172i	0.526642	+	1.03359i
$201$	−7.88352	−	4.56651i	−0.556061	−	0.322097i
$202$	7.96772	+	9.83931i	0.560607	+	0.692292i
$203$	10.4160	−	20.4425i	0.731058	−	1.43478i
$204$	1.56374	+	0.0841808i	0.109483	+	0.00589383i
$205$	−12.0338	−	27.0283i	−0.840474	−	1.88774i
$206$	10.3089	−	12.7304i	0.718255	−	0.886970i
$207$	4.15198	+	2.41291i	0.288583	+	0.167709i
$208$	16.3993	+	2.23918i	1.13709	+	0.155259i
$209$	−17.1194	−	6.08795i	−1.18418	−	0.421112i
$210$	20.6281	−	28.3075i	1.42348	−	1.95340i
$211$	14.5865	+	16.1999i	1.00417	+	1.11525i	0.993330	+	0.115306i	$0.0367850\pi$
$211$	14.5865	+	16.1999i	1.00417	+	1.11525i	0.0108434	+	0.999941i	$0.496548\pi$
$212$	3.69470	+	1.64499i	0.253753	+	0.112978i
$213$	9.66215	−	10.7003i	0.662040	−	0.733171i
$214$	0.0794923	−	0.00416601i	0.00543398	−	0.000284783i
$215$	−13.8387	+	0.725257i	−0.943794	+	0.0494621i
$216$	−10.6232	+	7.64924i	−0.722820	+	0.520465i
$217$	14.6410	+	6.51859i	0.993896	+	0.442511i
$218$	12.3147	+	13.6769i	0.834058	+	0.926315i
$219$	−5.31541	−	3.87343i	−0.359182	−	0.261742i
$220$	3.88714	−	1.14580i	0.262071	−	0.0772500i
$221$	−5.54499	+	7.15497i	−0.372996	+	0.481295i
$222$	17.4592	−	6.67352i	1.17179	−	0.447897i
$223$	3.37682	−	4.17003i	0.226129	−	0.279246i	−0.651436	−	0.758703i	$-0.725833\pi$
$223$	3.37682	−	4.17003i	0.226129	−	0.279246i	0.877565	+	0.479457i	$0.159167\pi$
$224$	3.17770	+	7.13723i	0.212319	+	0.476877i
$225$	−15.8372	+	11.4378i	−1.05581	+	0.762517i
$226$	−8.40880	+	16.5032i	−0.559345	+	1.09778i
$227$	−8.91587	−	11.0102i	−0.591767	−	0.730771i	0.390009	−	0.920811i	$-0.372472\pi$
$227$	−8.91587	−	11.0102i	−0.591767	−	0.730771i	−0.981776	+	0.190040i	$0.939138\pi$
$228$	1.71279	−	2.95692i	0.113432	−	0.195827i
$229$	6.20095	+	12.1700i	0.409770	+	0.804219i	0.999995	−	0.00301920i	$-0.000961043\pi$
$229$	6.20095	+	12.1700i	0.409770	+	0.804219i	−0.590225	+	0.807239i	$0.700961\pi$
$230$	−7.22587	+	4.17186i	−0.476459	+	0.275084i
$231$	15.2967	+	16.2085i	1.00645	+	1.06644i
$232$	−3.85598	−	14.3907i	−0.253158	−	0.944798i
$233$	4.73713	−	14.5794i	0.310339	−	0.955127i	−0.667291	−	0.744797i	$-0.732546\pi$
$233$	4.73713	−	14.5794i	0.310339	−	0.955127i	0.977631	−	0.210330i	$-0.0674537\pi$
$234$	0.307987	+	16.6144i	0.0201338	+	1.08612i
$235$	−5.47793	−	3.97995i	−0.357341	−	0.259623i
$236$	−2.38844	+	1.55107i	−0.155474	+	0.100966i
$237$	−9.71943	+	4.93491i	−0.631345	+	0.320557i
$238$	−14.8817	−	1.56413i	−0.964636	−	0.101387i
$239$	−1.32902	+	8.39112i	−0.0859674	+	0.542777i	0.906688	+	0.421802i	$0.138602\pi$
$239$	−1.32902	+	8.39112i	−0.0859674	+	0.542777i	−0.992656	+	0.120975i	$0.961398\pi$
$240$	−2.78176	−	26.8335i	−0.179562	−	1.73210i
$241$	7.79150	+	2.08773i	0.501894	+	0.134482i	0.500879	−	0.865517i	$-0.333010\pi$
$241$	7.79150	+	2.08773i	0.501894	+	0.134482i	0.00101534	+	0.999999i	$0.499677\pi$
$242$	1.72171	+	16.8110i	0.110676	+	1.08065i
$243$	−10.9441	−	11.1008i	−0.702064	−	0.712114i
$244$	3.20810	−	2.88859i	0.205378	−	0.184923i
$245$	−17.1922	+	21.2305i	−1.09837	+	1.35637i
$246$	1.18141	+	23.1729i	0.0753242	+	1.47745i
$247$	8.41798	+	17.8690i	0.535623	+	1.13698i
$248$	9.89767	−	3.21595i	0.628502	−	0.204213i
$249$	3.25228	+	10.0581i	0.206105	+	0.637407i
$250$	−0.823735	−	7.83732i	−0.0520976	−	0.495676i
$251$	5.37925	−	1.14339i	0.339535	−	0.0721704i	−0.0349887	−	0.999388i	$-0.511140\pi$
$251$	5.37925	−	1.14339i	0.339535	−	0.0721704i	0.374524	+	0.927217i	$0.377806\pi$
$252$	−3.52174	+	2.27284i	−0.221849	+	0.143175i
$253$	−1.76553	−	5.00687i	−0.110998	−	0.314779i
$254$	−1.79284	+	6.69096i	−0.112493	+	0.419828i
$255$	13.4699	+	6.02016i	0.843521	+	0.376997i
$256$	7.65514	+	3.40829i	0.478446	+	0.213018i
$257$	13.2695	−	5.90798i	0.827731	−	0.368530i	0.0512623	−	0.998685i	$-0.483676\pi$
$257$	13.2695	−	5.90798i	0.827731	−	0.368530i	0.776469	+	0.630156i	$0.217009\pi$
$258$	10.3312	+	3.37307i	0.643195	+	0.209998i
$259$	−25.9184	+	8.42138i	−1.61049	+	0.523279i
$260$	−3.86152	−	2.12070i	−0.239481	−	0.131521i
$261$	16.2278	−	7.16988i	1.00448	−	0.443804i
$262$	0.859171	−	16.3940i	0.0530798	−	1.01282i
$263$	−6.66349	−	3.84717i	−0.410888	−	0.237226i	0.280283	−	0.959917i	$-0.409572\pi$
$263$	−6.66349	−	3.84717i	−0.410888	−	0.237226i	−0.691171	+	0.722691i	$0.742905\pi$
$264$	14.4244	+	1.17517i	0.887762	+	0.0723266i
$265$	26.9434	+	26.9434i	1.65512	+	1.65512i
$266$	−17.7836	+	27.3844i	−1.09038	+	1.67904i
$267$	2.45461	+	1.42182i	0.150220	+	0.0870142i
$268$	−1.87094	+	0.296328i	−0.114286	+	0.0181011i
$269$	−18.0359	−	16.2396i	−1.09967	−	0.990144i	−0.0996786	−	0.995020i	$-0.531781\pi$
$269$	−18.0359	−	16.2396i	−1.09967	−	0.990144i	−0.999988	+	0.00487536i	$0.998448\pi$
$270$	26.1914	−	6.89839i	1.59396	−	0.419823i
$271$	5.80382	−	15.1195i	0.352557	−	0.918442i	−0.636549	−	0.771236i	$-0.719639\pi$
$271$	5.80382	−	15.1195i	0.352557	−	0.918442i	0.989106	−	0.147206i	$-0.0470279\pi$
$272$	−9.32397	+	6.77426i	−0.565349	+	0.410750i
$273$	0.784944	−	24.2157i	0.0475070	−	1.46560i
$274$	−11.4805			−0.693564
$275$	21.5286	+	1.72315i	1.29822	+	0.103910i
$276$	0.986394	−	0.154793i	0.0593739	−	0.00931742i
$277$	4.48743	+	21.1117i	0.269623	+	1.26848i	0.879468	+	0.475957i	$0.157898\pi$
$277$	4.48743	+	21.1117i	0.269623	+	1.26848i	−0.609845	+	0.792521i	$0.708768\pi$
$278$	5.56214	−	35.1179i	0.333595	−	2.10623i
$279$	5.59480	+	11.0580i	0.334952	+	0.662026i
$280$	1.73558	+	33.1167i	0.103720	+	1.97910i
$281$	−3.99766	+	7.84584i	−0.238480	+	0.468044i	−0.978965	−	0.204030i	$-0.934596\pi$
$281$	−3.99766	+	7.84584i	−0.238480	+	0.468044i	0.740484	+	0.672073i	$0.234596\pi$
$282$	2.88583	+	4.45765i	0.171849	+	0.265449i
$283$	−24.7968	+	2.60625i	−1.47402	+	0.154925i	−0.807192	−	0.590289i	$-0.799014\pi$
$283$	−24.7968	+	2.60625i	−1.47402	+	0.154925i	−0.666825	+	0.745214i	$0.732347\pi$
$284$	0.156881	−	2.99347i	0.00930920	−	0.177630i
$285$	25.0488	−	20.2252i	1.48376	−	1.19804i
$286$	11.6486	−	14.2059i	0.688799	−	0.840011i
$287$		−	33.8304i		−	1.99695i
$288$	−1.58018	+	5.83096i	−0.0931130	+	0.343593i
$289$	1.11813	+	10.6383i	0.0657723	+	0.625782i
$290$	−3.22208	+	30.6560i	−0.189207	+	1.80018i
$291$	−3.21018	−	15.2089i	−0.188184	−	0.891564i
$292$	−1.36561	+	0.0715685i	−0.0799162	+	0.00418823i
$293$	6.88907	−	5.57866i	0.402464	−	0.325909i	−0.406625	−	0.913595i	$-0.633294\pi$
$293$	6.88907	−	5.57866i	0.402464	−	0.325909i	0.809089	+	0.587686i	$0.199961\pi$
$294$	18.5695	−	10.6859i	1.08300	−	0.623217i
$295$	−26.2450	+	5.57855i	−1.52804	+	0.324796i
$296$	−8.84824	+	15.3256i	−0.514294	+	0.890783i
$297$	1.25601	+	17.1879i	0.0728812	+	0.997341i
$298$		−	11.6339i		−	0.673931i
$299$	−2.50969	+	5.19730i	−0.145139	+	0.300568i
$300$	−1.05685	+	3.92191i	−0.0610172	+	0.226432i
$301$	−14.7932	−	5.67859i	−0.852668	−	0.327308i
$302$	−2.80611	+	13.2017i	−0.161473	+	0.759673i
$303$	0.767320	−	14.2537i	0.0440814	−	0.818852i
$304$	3.93414	+	24.8392i	0.225638	+	1.42462i
$305$	37.9705	−	14.5755i	2.17418	−	0.834590i
$306$	−8.15856	−	8.20507i	−0.466394	−	0.469053i
$307$	10.4132	−	10.4132i	0.594314	−	0.594314i	−0.344480	−	0.938794i	$-0.611945\pi$
$307$	10.4132	−	10.4132i	0.594314	−	0.594314i	0.938794	+	0.344480i	$0.111945\pi$
$308$	4.59340	+	0.610949i	0.261733	+	0.0348121i
$309$	−18.2453	+	2.86319i	−1.03794	+	0.162881i
$310$	−21.5027	−	1.12691i	−1.22127	−	0.0640041i
$311$	7.99344	−	5.80758i	0.453267	−	0.329317i	−0.337618	−	0.941283i	$-0.609621\pi$
$311$	7.99344	−	5.80758i	0.453267	−	0.329317i	0.790884	+	0.611966i	$0.209621\pi$
$312$	−10.1431	−	12.0268i	−0.574239	−	0.680883i
$313$	−3.32136	−	10.2221i	−0.187734	−	0.577787i	0.812250	−	0.583309i	$-0.198242\pi$
$313$	−3.32136	−	10.2221i	−0.187734	−	0.577787i	−0.999985	+	0.00552194i	$0.998242\pi$
$314$	6.81980	−	4.42883i	0.384864	−	0.249933i
$315$	−38.6502	+	8.10058i	−2.17769	+	0.456416i
$316$	−0.921833	+	2.07047i	−0.0518572	+	0.116473i
$317$	−10.3076	−	20.2299i	−0.578934	−	1.13622i	−0.975865	−	0.218374i	$-0.929925\pi$
$317$	−10.3076	−	20.2299i	−0.578934	−	1.13622i	0.396931	−	0.917848i	$-0.370075\pi$
$318$	−12.1157	−	27.3167i	−0.679413	−	1.53184i
$319$	−18.7985	−	5.59557i	−1.05251	−	0.313292i
$320$	14.6047	+	14.6047i	0.816428	+	0.816428i
$321$	−0.0696652	−	0.0565779i	−0.00388833	−	0.00315787i
$322$	−9.48840	+	0.997271i	−0.528768	+	0.0555757i
$323$	−12.8405	−	4.92899i	−0.714463	−	0.274257i
$324$	−3.22139	−	0.357110i	−0.178966	−	0.0198395i
$325$	−15.1624	−	17.9265i	−0.841058	−	0.994382i
$326$	−6.21768	+	8.55791i	−0.344366	+	0.473979i
$327$	0.0294914	−	20.7494i	0.00163088	−	1.14745i
$328$	−14.6996	−	16.3255i	−0.811647	−	0.901426i
$329$	−3.87122	−	6.70515i	−0.213427	−	0.369667i
$330$	−26.9907	−	12.9652i	−1.48579	−	0.713709i
$331$	−6.59130	+	24.5991i	−0.362291	+	1.35209i	0.508766	+	0.860905i	$0.330102\pi$
$331$	−6.59130	+	24.5991i	−0.362291	+	1.35209i	−0.871057	+	0.491182i	$0.836565\pi$
$332$	1.84329	+	1.19705i	0.101164	+	0.0656965i
$333$	−19.6520	−	7.60785i	−1.07692	−	0.416907i
$334$	2.11093	−	20.0842i	0.115505	−	1.09896i
$335$	−17.4567	−	3.71055i	−0.953764	−	0.202729i
$336$	9.57406	−	29.3240i	0.522308	−	1.59976i
$337$	9.22883	−	12.7024i	0.502726	−	0.691943i	−0.479945	−	0.877298i	$-0.659343\pi$
$337$	9.22883	−	12.7024i	0.502726	−	0.691943i	0.982672	+	0.185355i	$0.0593435\pi$
$338$	−19.8812	+	1.89674i	−1.08140	+	0.103169i
$339$	19.5060	−	7.45586i	1.05942	−	0.404947i
$340$	2.96311	−	0.793963i	0.160697	−	0.0430587i
$341$	3.21609	−	13.3179i	0.174161	−	0.721207i
$342$	−24.0351	+	7.73401i	−1.29967	+	0.418207i
$343$	−3.63538	+	1.85232i	−0.196292	+	0.100016i
$344$	−9.60614	+	3.68745i	−0.517929	+	0.198814i
$345$	9.19867	+	1.96891i	0.495240	+	0.106002i
$346$	−24.1046	−	12.2819i	−1.29587	−	0.660279i
$347$	3.43718	+	3.09485i	0.184518	+	0.166140i	0.756213	−	0.654326i	$-0.227047\pi$
$347$	3.43718	+	3.09485i	0.184518	+	0.166140i	−0.571695	+	0.820466i	$0.693714\pi$
$348$	1.67931	−	3.28429i	0.0900205	−	0.176056i
$349$	15.0880	+	12.2180i	0.807643	+	0.654016i	0.941511	−	0.336983i	$-0.109406\pi$
$349$	15.0880	+	12.2180i	0.807643	+	0.654016i	−0.133868	+	0.990999i	$0.542740\pi$
$350$	11.9935	−	36.9123i	0.641082	−	1.97305i
$351$	12.2961	−	14.1353i	0.656315	−	0.754487i
$352$	5.50927	−	3.77564i	0.293645	−	0.201242i
$353$	−8.00814	−	29.8868i	−0.426230	−	1.59071i	−0.761222	−	0.648492i	$-0.775400\pi$
$353$	−8.00814	−	29.8868i	−0.426230	−	1.59071i	0.334991	−	0.942221i	$-0.391267\pi$
$354$	20.7788	+	3.32131i	1.10438	+	0.176526i
$355$	11.4869	−	25.8001i	0.609663	−	1.36932i
$356$	0.582534	−	0.0922643i	0.0308742	−	0.00489000i
$357$	11.2708	+	12.5533i	0.596514	+	0.664393i
$358$	0.148305	+	2.82983i	0.00783817	+	0.149561i
$359$	2.10115	+	13.2661i	0.110894	+	0.700159i	0.979012	+	0.203801i	$0.0653295\pi$
$359$	2.10115	+	13.2661i	0.110894	+	0.700159i	−0.868118	+	0.496358i	$0.834670\pi$
$360$	−15.1316	+	20.7029i	−0.797506	+	1.09114i
$361$	−8.18392	+	7.36884i	−0.430733	+	0.387833i
$362$	−23.4680	+	6.28824i	−1.23345	+	0.330502i
$363$	11.2616	−	15.3680i	0.591082	−	0.806611i
$364$	−3.04743	−	4.01122i	−0.159729	−	0.210245i
$365$	−12.2531	−	3.98128i	−0.641358	−	0.208390i
$366$	−31.8969	−	0.0453354i	−1.66728	−	0.00236972i
$367$	32.9296	−	14.6612i	1.71891	−	0.765309i	0.721578	−	0.692334i	$-0.243417\pi$
$367$	32.9296	−	14.6612i	1.71891	−	0.765309i	0.997334	−	0.0729751i	$-0.0232494\pi$
$368$	−4.91695	+	5.46082i	−0.256314	+	0.284665i
$369$	16.5207	−	20.2832i	0.860033	−	1.05590i
$370$	28.4546	−	23.0420i	1.47928	−	1.19790i
$371$	15.6141	+	40.6761i	0.810643	+	2.11180i
$372$	2.35243	+	1.05138i	0.121968	+	0.0545115i
$373$	8.45782	+	14.6494i	0.437930	+	0.758516i	0.997530	−	0.0702465i	$-0.0223786\pi$
$373$	8.45782	+	14.6494i	0.437930	+	0.758516i	−0.559600	+	0.828763i	$0.689045\pi$
$374$	0.986693	+	12.7540i	0.0510207	+	0.659493i
$375$	−5.23255	+	7.18050i	−0.270208	+	0.370799i
$376$	−4.78157	−	1.55363i	−0.246591	−	0.0801221i
$377$	10.0840	+	18.7870i	0.519352	+	0.967578i
$378$	30.5678	+	4.97516i	1.57224	+	0.255895i
$379$	−0.668399	−	1.02924i	−0.0343334	−	0.0528688i	0.821087	−	0.570803i	$-0.193368\pi$
$379$	−0.668399	−	1.02924i	−0.0343334	−	0.0528688i	−0.855421	+	0.517934i	$0.826701\pi$
$380$	1.39174	−	6.54760i	0.0713945	−	0.335885i
$381$	6.55586	−	4.24419i	0.335867	−	0.217436i
$382$	−5.38336	−	0.852640i	−0.275437	−	0.0436249i
$383$	−8.30072	+	12.7820i	−0.424147	+	0.653129i	−0.984553	−	0.175089i	$-0.943979\pi$
$383$	−8.30072	+	12.7820i	−0.424147	+	0.653129i	0.560406	+	0.828218i	$0.310645\pi$
$384$	−9.39559	−	21.1838i	−0.479467	−	1.08103i
$385$	38.3394	+	20.8827i	1.95396	+	1.06428i
$386$	16.8178	−	9.70975i	0.856002	−	0.494213i
$387$	−6.09628	−	10.6287i	−0.309891	−	0.540289i
$388$	−2.51165	−	2.03390i	−0.127510	−	0.103255i
$389$	−24.3868	−	17.7180i	−1.23646	−	0.898339i	−0.239100	−	0.970995i	$-0.576853\pi$
$389$	−24.3868	−	17.7180i	−1.23646	−	0.898339i	−0.997357	+	0.0726558i	$0.976853\pi$
$390$	10.6748	+	30.7515i	0.540539	+	1.55716i
$391$	−1.24188	−	3.82211i	−0.0628045	−	0.193292i
$392$	−7.26931	+	18.9372i	−0.367155	+	0.956473i
$393$	−13.1061	+	13.0689i	−0.661116	+	0.659239i
$394$	−2.32592	−	10.9426i	−0.117178	−	0.551281i
$395$	−15.0988	+	15.0988i	−0.759705	+	0.759705i
$396$	2.45565	+	2.60943i	0.123401	+	0.131129i
$397$	−21.6934	−	5.81273i	−1.08876	−	0.291733i	−0.330581	−	0.943778i	$-0.607245\pi$
$397$	−21.6934	−	5.81273i	−1.08876	−	0.291733i	−0.758180	+	0.652045i	$0.773911\pi$
$398$	21.3947	−	10.9011i	1.07242	−	0.546424i
$399$	35.5724	−	9.47742i	1.78085	−	0.474465i
$400$	−12.1586	−	27.3087i	−0.607931	−	1.36544i
$401$	2.57960	+	3.97223i	0.128819	+	0.198364i	0.897195	−	0.441635i	$-0.145601\pi$
$401$	2.57960	+	3.97223i	0.128819	+	0.198364i	−0.768376	+	0.639999i	$0.778935\pi$
$402$	11.7275	+	7.63962i	0.584913	+	0.381030i
$403$	−12.7367	+	7.72117i	−0.634460	+	0.384619i
$404$	−1.74448	−	2.40108i	−0.0867913	−	0.119458i
$405$	−27.1287	−	14.0176i	−1.34804	−	0.696541i
$406$	−17.6234	+	30.5247i	−0.874636	+	1.51491i
$407$	11.0893	+	20.4888i	0.549674	+	1.01559i
$408$	10.8935	+	1.16060i	0.539306	+	0.0574585i
$409$	−33.3426	−	21.6530i	−1.64869	−	1.07067i	−0.924585	−	0.380977i	$-0.875588\pi$
$409$	−33.3426	−	21.6530i	−1.64869	−	1.07067i	−0.724102	−	0.689693i	$-0.757746\pi$
$410$	16.2886	+	42.4334i	0.804439	+	2.09563i
$411$	9.60665	+	8.67462i	0.473861	+	0.427887i
$412$	−2.56943	+	2.85364i	−0.126587	+	0.140589i
$413$	−30.0100	−	6.37883i	−1.47670	−	0.313882i
$414$	−6.17582	−	4.03563i	−0.303525	−	0.198340i
$415$	12.1714	+	16.7525i	0.597471	+	0.822348i
$416$	−7.13269	−	1.35743i	−0.349709	−	0.0665534i
$417$	−31.1892	+	25.1832i	−1.52734	+	1.23323i
$418$	25.7745	+	10.7164i	1.26067	+	0.524154i
$419$	19.8035	+	11.4335i	0.967462	+	0.558565i	0.898462	−	0.439052i	$-0.144686\pi$
$419$	19.8035	+	11.4335i	0.967462	+	0.558565i	0.0690007	+	0.997617i	$0.478019\pi$
$420$	−5.17621	+	6.37355i	−0.252573	+	0.310997i
$421$	4.05331	+	0.641981i	0.197546	+	0.0312883i	0.254423	−	0.967093i	$-0.418114\pi$
$421$	4.05331	+	0.641981i	0.197546	+	0.0312883i	−0.0568771	+	0.998381i	$0.518114\pi$
$422$	−21.0755	−	26.0261i	−1.02594	−	1.26693i
$423$	0.953374	−	5.91057i	0.0463546	−	0.287382i
$424$	25.2089	+	12.8446i	1.22425	+	0.623788i
$425$	16.2591	+	1.70890i	0.788684	+	0.0828940i
$426$	−15.6837	+	15.6391i	−0.759875	+	0.757718i
$427$	46.4428	+	2.43396i	2.24752	+	0.117788i
$428$	−0.0186598			−0.000901955
$429$	−20.4812	+	3.08550i	−0.988842	+	0.148970i
$430$	21.2892			1.02666
$431$	−20.7164	−	1.08570i	−0.997874	−	0.0522964i	−0.453601	−	0.891205i	$-0.649861\pi$
$431$	−20.7164	−	1.08570i	−0.997874	−	0.0522964i	−0.544273	+	0.838908i	$0.683194\pi$
$432$	20.0602	−	12.9060i	0.965148	−	0.620940i
$433$	29.8197	+	3.13418i	1.43305	+	0.150619i	0.789012	−	0.614378i	$-0.210593\pi$
$433$	29.8197	+	3.13418i	1.43305	+	0.150619i	0.644033	+	0.764997i	$0.277260\pi$
$434$	−21.9376	−	11.1778i	−1.05304	−	0.536550i
$435$	25.8597	−	23.2177i	1.23988	−	1.11320i
$436$	−2.71501	−	3.35276i	−0.130025	−	0.160568i
$437$	−8.66144	−	1.37184i	−0.414333	−	0.0656239i
$438$	7.84329	+	6.36985i	0.374767	+	0.304363i
$439$	3.70519	+	2.13919i	0.176839	+	0.102098i	0.585807	−	0.810451i	$-0.300778\pi$
$439$	3.70519	+	2.13919i	0.176839	+	0.102098i	−0.408968	+	0.912549i	$0.634111\pi$
$440$	27.5751	−	6.58142i	1.31459	−	0.313757i
$441$	−23.6128	−	5.08925i	−1.12442	−	0.242345i
$442$	9.08220	−	10.5311i	0.431996	−	0.500912i
$443$	−3.89259	−	5.35769i	−0.184942	−	0.254551i	0.706471	−	0.707742i	$-0.250286\pi$
$443$	−3.89259	−	5.35769i	−0.184942	−	0.254551i	−0.891414	+	0.453190i	$0.850286\pi$
$444$	−4.16898	+	1.34803i	−0.197851	+	0.0639749i
$445$	5.43532	+	1.15531i	0.257659	+	0.0547671i
$446$	−5.51588	+	6.12601i	−0.261185	+	0.290075i
$447$	−8.79047	+	9.73494i	−0.415775	+	0.460447i
$448$	8.46362	+	22.0485i	0.399869	+	1.04169i
$449$	−4.73125	−	3.07251i	−0.223282	−	0.145001i	0.428151	−	0.903707i	$-0.359165\pi$
$449$	−4.73125	−	3.07251i	−0.223282	−	0.145001i	−0.651433	+	0.758706i	$0.725832\pi$
$450$	25.2165	−	16.2741i	1.18872	−	0.767167i
$451$	−28.4436	+	5.23259i	−1.33936	+	0.246393i
$452$	2.17092	−	3.76014i	0.102111	−	0.176862i
$453$	12.3232	−	8.92661i	0.578996	−	0.419409i
$454$	12.7932	+	17.6083i	0.600413	+	0.826398i
$455$	−13.2610	−	45.5707i	−0.621684	−	2.13639i
$456$	13.0481	−	20.0300i	0.611034	−	0.937989i
$457$	8.87651	+	13.6686i	0.415226	+	0.639391i	0.982960	−	0.183820i	$-0.0588465\pi$
$457$	8.87651	+	13.6686i	0.415226	+	0.639391i	−0.567734	+	0.823212i	$0.692180\pi$
$458$	−8.53478	−	19.1694i	−0.398804	−	0.895728i
$459$	0.627192	+	13.0304i	0.0292748	+	0.608206i
$460$	1.74271	−	0.887957i	0.0812545	−	0.0414012i
$461$	4.57204	+	1.22508i	0.212941	+	0.0570574i	0.363713	−	0.931511i	$-0.381509\pi$
$461$	4.57204	+	1.22508i	0.212941	+	0.0570574i	−0.150771	+	0.988569i	$0.548176\pi$
$462$	−22.1645	−	26.0964i	−1.03119	−	1.21411i
$463$	0.435884	−	0.435884i	0.0202572	−	0.0202572i	−0.696906	−	0.717163i	$-0.745440\pi$
$463$	0.435884	−	0.435884i	0.0202572	−	0.0202572i	0.717163	+	0.696906i	$0.245440\pi$
$464$	5.64424	+	26.5541i	0.262027	+	1.23274i
$465$	17.1415	+	17.1903i	0.794918	+	0.797180i
$466$	−8.43974	+	21.9863i	−0.390964	+	1.01850i
$467$	9.40923	+	28.9586i	0.435407	+	1.34005i	0.892669	+	0.450713i	$0.148830\pi$
$467$	9.40923	+	28.9586i	0.435407	+	1.34005i	−0.457262	+	0.889332i	$0.651170\pi$
$468$	0.131734	−	3.89312i	0.00608940	−	0.179960i
$469$	−16.5096	−	11.9949i	−0.762342	−	0.553874i
$470$	8.08404	+	6.54633i	0.372889	+	0.301960i
$471$	−9.05306	−	1.44706i	−0.417143	−	0.0666768i
$472$	−17.2536	+	9.96135i	−0.794159	+	0.458508i
$473$	−2.48630	+	13.3160i	−0.114320	+	0.612271i
$474$	15.3080	−	6.78950i	0.703119	−	0.311852i
$475$	19.4297	−	29.9191i	0.891495	−	1.37278i
$476$	3.46452	+	0.548726i	0.158796	+	0.0251508i
$477$	−10.5022	+	32.0125i	−0.480862	+	1.46575i
$478$	2.71360	−	12.7665i	0.124117	−	0.583926i
$479$	13.7379	+	21.1545i	0.627700	+	0.966574i	0.999271	+	0.0381691i	$0.0121525\pi$
$479$	13.7379	+	21.1545i	0.627700	+	0.966574i	−0.371571	+	0.928405i	$0.621181\pi$
$480$	0.602559	+	11.8189i	0.0275030	+	0.539457i
$481$	7.30973	−	24.2490i	0.333295	−	1.10566i
$482$	−11.7856	−	3.82937i	−0.536818	−	0.174423i
$483$	8.69321	+	6.33489i	0.395555	+	0.288247i
$484$	−0.196798	−	3.95649i	−0.00894538	−	0.179840i
$485$	−15.2246	−	26.3698i	−0.691314	−	1.19739i
$486$	15.8975	+	17.9103i	0.721126	+	0.812429i
$487$	4.73745	+	12.3415i	0.214675	+	0.559246i	0.998058	−	0.0622925i	$-0.0198412\pi$
$487$	4.73745	+	12.3415i	0.214675	+	0.559246i	−0.783383	+	0.621539i	$0.786508\pi$
$488$	23.4694	−	19.0052i	1.06241	−	0.860323i
$489$	11.6691	−	2.46302i	0.527696	−	0.111382i
$490$	28.0826	−	31.1889i	1.26864	−	1.40897i
$491$	9.01630	−	4.01431i	0.406900	−	0.181163i	−0.193072	−	0.981185i	$-0.561845\pi$
$491$	9.01630	−	4.01431i	0.406900	−	0.181163i	0.599972	+	0.800021i	$0.295178\pi$
$492$	0.00773068	−	5.43913i	0.000348526	−	0.245215i
$493$	−14.1203	−	4.58797i	−0.635947	−	0.206632i
$494$	−11.4779	−	28.0908i	−0.516413	−	1.26386i
$495$	12.7888	+	31.2429i	0.574813	+	1.40427i
$496$	−18.3171	+	4.90806i	−0.822464	+	0.220379i
$497$	23.9985	−	21.6083i	1.07648	−	0.969265i
$498$	−4.18084	−	15.6923i	−0.187348	−	0.703188i
$499$	1.87196	+	11.8191i	0.0838003	+	0.529094i	0.993500	+	0.113828i	$0.0363114\pi$
$499$	1.87196	+	11.8191i	0.0838003	+	0.529094i	−0.909700	+	0.415266i	$0.863689\pi$
$500$	0.0966806	+	1.84478i	0.00432369	+	0.0825009i
$501$	−16.9419	+	15.2110i	−0.756907	+	0.679576i
$502$	−8.34458	+	1.32165i	−0.372437	+	0.0589882i
$503$	5.92322	−	13.3038i	0.264103	−	0.593186i	−0.732007	−	0.681297i	$-0.761416\pi$
$503$	5.92322	−	13.3038i	0.264103	−	0.593186i	0.996111	+	0.0881107i	$0.0280829\pi$
$504$	−25.4351	+	14.5887i	−1.13297	+	0.649832i
$505$	−7.23709	−	27.0092i	−0.322046	−	1.20189i
$506$	2.30606	+	7.82331i	0.102517	+	0.347788i
$507$	18.0693	+	13.4350i	0.802487	+	0.596669i
$508$	0.501780	−	1.54432i	0.0222629	−	0.0685181i
$509$	−5.92635	−	4.79907i	−0.262681	−	0.212715i	0.488927	−	0.872324i	$-0.337388\pi$
$509$	−5.92635	−	4.79907i	−0.262681	−	0.212715i	−0.751608	+	0.659610i	$0.770722\pi$
$510$	−20.1811	−	10.3189i	−0.893633	−	0.456930i
$511$	−10.9480	−	9.85760i	−0.484310	−	0.436075i
$512$	12.3722	+	6.30394i	0.546778	+	0.278597i
$513$	25.9558	+	11.6891i	1.14598	+	0.516088i
$514$	−20.8327	+	7.99691i	−0.918890	+	0.352729i
$515$	−32.2349	+	16.4245i	−1.42044	+	0.723750i
$516$	−2.37710	−	0.916362i	−0.104646	−	0.0403406i
$517$	−5.03872	+	4.29190i	−0.221603	+	0.188757i
$518$	40.4401	−	10.8359i	1.77684	−	0.476102i
$519$	10.8900	+	28.4905i	0.478020	+	1.25059i
$520$	−26.2001	−	16.2290i	−1.14895	−	0.711691i
$521$	−7.02657	+	9.67124i	−0.307840	+	0.423705i	−0.934706	−	0.355422i	$-0.884337\pi$
$521$	−7.02657	+	9.67124i	−0.307840	+	0.423705i	0.626866	+	0.779127i	$0.284337\pi$
$522$	−25.4726	+	9.69503i	−1.11491	+	0.424340i
$523$	−4.62679	−	0.983455i	−0.202315	−	0.0430035i	0.105639	−	0.994405i	$-0.466311\pi$
$523$	−4.62679	−	0.983455i	−0.202315	−	0.0430035i	−0.307955	+	0.951401i	$0.599644\pi$
$524$	−0.402254	+	3.82719i	−0.0175725	+	0.167192i
$525$	−37.9267	+	21.8252i	−1.65526	+	0.952528i
$526$	9.91357	+	6.43795i	0.432252	+	0.280708i
$527$	2.68424	−	10.0177i	0.116928	−	0.436379i
$528$	−26.1356	−	3.51400i	−1.13741	−	0.152927i
$529$	10.2188	+	17.6995i	0.444297	+	0.769545i
$530$	−39.1693	−	43.5020i	−1.70141	−	1.88960i
$531$	−14.8776	−	18.4795i	−0.645634	−	0.801943i
$532$	4.49900	−	6.19234i	0.195056	−	0.268472i
$533$	25.8250	+	17.9322i	1.11860	+	0.776730i
$534$	−3.65145	−	2.37867i	−0.158014	−	0.102935i
$535$	−0.164126	−	0.0630021i	−0.00709579	−	0.00272382i
$536$	−13.1789	+	1.38516i	−0.569241	+	0.0598296i
$537$	2.01411	−	2.48000i	0.0869151	−	0.107020i
$538$	26.3643	+	26.3643i	1.13665	+	1.13665i
$539$	16.2284	+	21.2076i	0.699006	+	0.913475i
$540$	−6.21587	+	1.29355i	−0.267489	+	0.0556655i
$541$	−13.0070	−	25.5277i	−0.559216	−	1.09752i	−0.981572	−	0.191093i	$-0.938797\pi$
$541$	−13.0070	−	25.5277i	−0.559216	−	1.09752i	0.422356	−	0.906430i	$-0.361203\pi$
$542$	−10.1196	+	22.7291i	−0.434676	+	0.976298i
$543$	24.3889	+	12.4704i	1.04663	+	0.535158i
$544$	4.24010	−	2.75356i	0.181793	−	0.118058i
$545$	−12.5603	−	38.6567i	−0.538026	−	1.65587i
$546$	−3.15123	+	37.0877i	−0.134860	+	1.58721i
$547$	−37.3958	+	27.1696i	−1.59893	+	1.16169i	−0.709403	+	0.704803i	$0.751035\pi$
$547$	−37.3958	+	27.1696i	−1.59893	+	1.16169i	−0.889525	+	0.456887i	$0.848965\pi$
$548$	2.68752	+	0.140847i	0.114805	+	0.00601669i
$549$	26.6564	+	24.1391i	1.13767	+	1.03023i
$550$	−32.8898	−	4.37454i	−1.40243	−	0.186531i
$551$	−22.9085	+	22.9085i	−0.975936	+	0.975936i
$552$	6.94763	−	0.720243i	0.295711	−	0.0306556i
$553$	−22.7945	+	8.74998i	−0.969319	+	0.372087i
$554$	−5.18702	−	32.7496i	−0.220376	−	1.39140i
$555$	−41.2206	−	2.21903i	−1.74972	−	0.0941926i
$556$	−1.73290	+	8.15266i	−0.0734914	+	0.345750i
$557$	−23.8100	−	9.13979i	−1.00886	−	0.387265i	−0.202878	−	0.979204i	$-0.565029\pi$
$557$	−23.8100	−	9.13979i	−1.00886	−	0.387265i	−0.805983	+	0.591939i	$0.798363\pi$
$558$	−7.69426	−	17.4146i	−0.325724	−	0.737221i
$559$	12.1762	−	8.28264i	0.514997	−	0.350318i
$560$		−	60.4270i		−	2.55351i
$561$	8.81119	−	11.4178i	0.372009	−	0.482059i
$562$	6.76389	−	11.7154i	0.285317	−	0.494184i
$563$	0.345462	−	0.0734303i	0.0145595	−	0.00309472i	−0.200626	−	0.979668i	$-0.564298\pi$
$563$	0.345462	−	0.0734303i	0.0145595	−	0.00309472i	0.215186	+	0.976573i	$0.430964\pi$
$564$	−0.620868	−	1.07891i	−0.0261432	−	0.0454304i
$565$	31.7903	−	25.7433i	1.33743	−	1.08303i
$566$	38.2519	−	2.00470i	1.60785	−	0.0842638i
$567$	−21.8192	−	27.2600i	−0.916322	−	1.14481i
$568$	2.19195	−	20.8550i	0.0919721	−	0.875056i
$569$	−1.73593	−	16.5163i	−0.0727740	−	0.692398i	−0.968707	−	0.248208i	$-0.920158\pi$
$569$	−1.73593	−	16.5163i	−0.0727740	−	0.692398i	0.895933	−	0.444190i	$-0.146508\pi$
$570$	−40.0551	+	29.0148i	−1.67772	+	1.21530i
$571$			38.7909i			1.62335i	0.584109	+	0.811675i	$0.301444\pi$
$571$			38.7909i			1.62335i	−0.584109	+	0.811675i	$0.698556\pi$
$572$	−2.90116	+	3.18260i	−0.121304	+	0.133071i
$573$	3.86042	+	4.78110i	0.161271	+	0.199733i
$574$	−2.72004	+	51.9014i	−0.113532	+	2.16632i
$575$	10.3667	−	1.08958i	0.432319	−	0.0454386i
$576$	−5.69272	+	17.3524i	−0.237197	+	0.723016i
$577$	−1.03524	+	2.03177i	−0.0430976	+	0.0845839i	−0.911551	−	0.411187i	$-0.865114\pi$
$577$	−1.03524	+	2.03177i	−0.0430976	+	0.0845839i	0.868453	+	0.495771i	$0.165114\pi$
$578$	−0.860053	−	16.4108i	−0.0357735	−	0.682599i
$579$	−21.4094	−	4.58252i	−0.889743	−	0.190443i
$580$	1.13037	−	7.13686i	0.0469360	−	0.296342i
$581$	4.92289	+	23.1604i	0.204236	+	0.960855i
$582$	3.70210	+	23.5911i	0.153457	+	0.977884i
$583$	31.7842	−	19.4193i	1.31637	−	0.804263i
$584$	−9.56635			−0.395858
$585$	14.3033	−	33.7980i	0.591367	−	1.39738i
$586$	−11.0175	+	8.00469i	−0.455129	+	0.330671i
$587$	−12.6199	+	32.8760i	−0.520879	+	1.35694i	0.380851	+	0.924637i	$0.375631\pi$
$587$	−12.6199	+	32.8760i	−0.520879	+	1.35694i	−0.901730	+	0.432300i	$0.857702\pi$
$588$	−4.47811	+	2.27370i	−0.184674	+	0.0937658i
$589$	−16.8180	−	15.1430i	−0.692972	−	0.623955i
$590$	40.7127	−	6.44826i	1.67612	−	0.265471i
$591$	−6.32189	+	10.9140i	−0.260048	+	0.448941i
$592$	17.5624	−	27.0437i	0.721809	−	1.11149i
$593$	5.40959	+	5.40959i	0.222145	+	0.222145i	0.809401	−	0.587256i	$-0.199792\pi$
$593$	5.40959	+	5.40959i	0.222145	+	0.222145i	−0.587256	+	0.809401i	$0.699792\pi$
$594$	−0.544987	−	26.4700i	−0.0223611	−	1.08608i
$595$	28.6202	+	16.5239i	1.17332	+	0.677414i
$596$	−0.142728	+	2.72342i	−0.00584637	+	0.111555i
$597$	−26.1394	−	7.04386i	−1.06981	−	0.288286i
$598$	4.26816	−	7.77173i	0.174538	−	0.317810i
$599$	−42.1563	+	13.6974i	−1.72246	+	0.559662i	−0.992327	−	0.123642i	$-0.960543\pi$
$599$	−42.1563	+	13.6974i	−1.72246	+	0.559662i	−0.730134	+	0.683304i	$0.760543\pi$
$600$	−8.81905	+	27.0115i	−0.360036	+	1.10274i
$601$	−19.5025	+	8.68306i	−0.795522	+	0.354189i	−0.763920	−	0.645311i	$-0.776728\pi$
$601$	−19.5025	+	8.68306i	−0.795522	+	0.354189i	−0.0316025	+	0.999501i	$0.510061\pi$
$602$	22.2387	+	9.90130i	0.906381	+	0.403547i
$603$	−4.04082	−	15.2539i	−0.164555	−	0.621186i
$604$	0.818857	−	3.05602i	0.0333188	−	0.124348i
$605$	11.6275	−	35.4646i	0.472726	−	1.44184i
$606$	−2.32322	+	21.8058i	−0.0943744	+	0.885800i
$607$	−22.8310	+	4.85289i	−0.926683	+	0.196973i	−0.646447	−	0.762959i	$-0.723746\pi$
$607$	−22.8310	+	4.85289i	−0.926683	+	0.196973i	−0.280236	+	0.959931i	$0.590413\pi$
$608$	−1.15317	−	10.9717i	−0.0467672	−	0.444961i
$609$	37.8112	−	12.2262i	1.53219	−	0.495431i
$610$	−59.4248	+	19.3083i	−2.40604	+	0.781770i
$611$	7.17047	+	0.598988i	0.290086	+	0.0242325i
$612$	1.80921	+	2.02085i	0.0731329	+	0.0816881i
$613$	17.7930	−	21.9726i	0.718653	−	0.887463i	−0.278684	−	0.960383i	$-0.589898\pi$
$613$	17.7930	−	21.9726i	0.718653	−	0.887463i	0.997338	+	0.0729197i	$0.0232317\pi$
$614$	−16.8128	+	15.1383i	−0.678511	+	0.610934i
$615$	18.4324	−	47.8149i	0.743267	−	1.92808i
$616$	31.8658	+	5.94984i	1.28391	+	0.239726i
$617$	15.6000	+	4.18000i	0.628031	+	0.168280i	0.558776	−	0.829319i	$-0.311271\pi$
$617$	15.6000	+	4.18000i	0.628031	+	0.168280i	0.0692547	+	0.997599i	$0.477938\pi$
$618$	28.2215	−	2.92565i	1.13523	−	0.117687i
$619$	3.06564	−	19.3557i	0.123219	−	0.777971i	−0.846255	−	0.532777i	$-0.821148\pi$
$619$	3.06564	−	19.3557i	0.123219	−	0.777971i	0.969474	−	0.245194i	$-0.0788517\pi$
$620$	5.01983	+	0.527605i	0.201601	+	0.0211891i
$621$	2.11849	+	8.04334i	0.0850121	+	0.322768i
$622$	−12.7302	+	8.26709i	−0.510434	+	0.331480i
$623$	5.14041	+	3.73473i	0.205946	+	0.149629i
$624$	17.3101	+	22.8521i	0.692959	+	0.914814i
$625$	4.68314	−	14.4132i	0.187325	−	0.576528i
$626$	4.27363	+	15.9494i	0.170809	+	0.637467i
$627$	−13.4703	−	28.4423i	−0.537954	−	1.13588i
$628$	−1.65081	+	0.953096i	−0.0658745	+	0.0380327i
$629$	8.00633	+	15.7133i	0.319233	+	0.626530i
$630$	59.9470	−	9.32007i	2.38835	−	0.371321i
$631$	−14.5507	−	17.9687i	−0.579256	−	0.715321i	0.400325	−	0.916373i	$-0.368897\pi$
$631$	−14.5507	−	17.9687i	−0.579256	−	0.715321i	−0.979581	+	0.201052i	$0.935564\pi$
$632$	−7.19798	+	14.1268i	−0.286320	+	0.561935i
$633$	−2.02965	+	37.7026i	−0.0806713	+	1.49854i
$634$	14.1871	+	31.8647i	0.563441	+	1.26551i
$635$	9.62769	−	11.8892i	0.382063	−	0.471809i
$636$	2.50108	+	6.54331i	0.0991741	+	0.259459i
$637$	3.92744	−	28.7638i	0.155611	−	1.13966i
$638$	28.3901	+	10.0960i	1.12397	+	0.399703i
$639$	24.9406	−	1.23600i	0.986633	−	0.0488953i
$640$	−30.3755	−	33.7354i	−1.20070	−	1.33351i
$641$	24.7100	+	11.0016i	0.975985	+	0.434537i	0.831837	−	0.555019i	$-0.187289\pi$
$641$	24.7100	+	11.0016i	0.975985	+	0.434537i	0.144148	+	0.989556i	$0.453956\pi$
$642$	0.102329	+	0.0924010i	0.00403860	+	0.00364678i
$643$	12.1070	−	0.634499i	0.477452	−	0.0250222i	0.187907	−	0.982187i	$-0.439830\pi$
$643$	12.1070	−	0.634499i	0.477452	−	0.0250222i	0.289544	+	0.957165i	$0.406496\pi$
$644$	2.23341	−	0.117048i	0.0880088	−	0.00461235i
$645$	−17.8143	−	16.0860i	−0.701438	−	0.633386i
$646$	19.3031	+	8.59429i	0.759470	+	0.338138i
$647$	3.06399	+	3.40291i	0.120458	+	0.133782i	0.800357	−	0.599523i	$-0.204643\pi$
$647$	3.06399	+	3.40291i	0.120458	+	0.133782i	−0.679899	+	0.733305i	$0.737977\pi$
$648$	−22.3739	−	3.67419i	−0.878931	−	0.144336i
$649$	−0.721443	+	26.2181i	−0.0283191	+	1.02915i
$650$	21.8203	+	28.7213i	0.855861	+	1.12654i
$651$	9.91103	+	25.9292i	0.388444	+	1.01625i
$652$	1.56051	−	1.92708i	0.0611145	−	0.0754701i
$653$	13.5418	+	30.4153i	0.529930	+	1.19024i	0.958071	+	0.286530i	$0.0925018\pi$
$653$	13.5418	+	30.4153i	0.529930	+	1.19024i	−0.428142	+	0.903712i	$0.640832\pi$
$654$	−1.71354	+	31.8307i	−0.0670049	+	1.24468i
$655$	−16.4601	+	32.3047i	−0.643148	+	1.26225i
$656$	25.1914	+	31.1088i	0.983560	+	1.21460i
$657$	−1.75007	−	11.2565i	−0.0682766	−	0.439157i
$658$	5.39998	+	10.5981i	0.210513	+	0.413155i
$659$	17.1375	−	9.89435i	0.667583	−	0.385429i	−0.127577	−	0.991829i	$-0.540720\pi$
$659$	17.1375	−	9.89435i	0.667583	−	0.385429i	0.795160	+	0.606399i	$0.207387\pi$
$660$	6.15929	+	3.36620i	0.239750	+	0.131029i
$661$	−5.85921	−	21.8669i	−0.227897	−	0.850523i	−0.981223	−	0.192876i	$-0.938218\pi$
$661$	−5.85921	−	21.8669i	−0.227897	−	0.850523i	0.753326	−	0.657647i	$-0.228448\pi$
$662$	12.0900	−	37.2091i	0.469890	−	1.44617i
$663$	−15.5570	+	1.94970i	−0.604184	+	0.0757201i
$664$	12.4390	+	9.03745i	0.482726	+	0.350721i
$665$	60.4795	−	39.2758i	2.34529	−	1.52305i
$666$	29.5377	+	13.2517i	1.14456	+	0.513495i
$667$	−9.41443	−	0.989496i	−0.364528	−	0.0383135i
$668$	−0.740556	+	4.67569i	−0.0286530	+	0.180908i
$669$	9.24434	−	0.958337i	0.357407	−	0.0370515i
$670$	26.4832	+	7.09615i	1.02313	+	0.274148i
$671$	−5.13695	−	39.4241i	−0.198310	−	1.52195i
$672$	−4.86737	+	12.6263i	−0.187763	+	0.487069i
$673$	−27.1121	+	24.4119i	−1.04510	+	0.941008i	−0.998323	−	0.0578978i	$-0.981560\pi$
$673$	−27.1121	+	24.4119i	−1.04510	+	0.941008i	−0.0467725	+	0.998906i	$0.514894\pi$
$674$	−15.1798	+	18.7455i	−0.584706	+	0.722051i
$675$	−33.3972	−	5.43567i	−1.28546	−	0.209219i
$676$	4.67735	−	0.200105i	0.179898	−	0.00769634i
$677$	12.8296	−	4.16859i	0.493082	−	0.160212i	−0.0519127	−	0.998652i	$-0.516532\pi$
$677$	12.8296	−	4.16859i	0.493082	−	0.160212i	0.544994	+	0.838440i	$0.316532\pi$
$678$	−30.5249	+	9.87020i	−1.17230	+	0.379063i
$679$	−3.63940	−	34.6266i	−0.139667	−	1.32885i
$680$	20.9910	−	4.46177i	0.804968	−	0.171101i
$681$	2.59968	−	24.4007i	0.0996200	−	0.935035i
$682$	−6.00481	+	20.1733i	−0.229936	+	0.772477i
$683$	−3.79471	+	14.1621i	−0.145201	+	0.541896i	0.854546	+	0.519376i	$0.173836\pi$
$683$	−3.79471	+	14.1621i	−0.145201	+	0.541896i	−0.999746	+	0.0225201i	$0.992831\pi$
$684$	5.72136	−	1.51561i	0.218762	−	0.0579510i
$685$	23.1631	+	10.3129i	0.885018	+	0.394035i
$686$	5.72621	−	2.54947i	0.218628	−	0.0973393i
$687$	−7.34260	+	22.4894i	−0.280137	+	0.858023i
$688$	17.8316	−	5.79385i	0.679825	−	0.220888i
$689$	−39.3271	−	9.64158i	−1.49824	−	0.367315i
$690$	−13.9540	−	3.76022i	−0.531219	−	0.143149i
$691$	−2.44039	+	46.5654i	−0.0928367	+	1.77143i	0.414851	+	0.909889i	$0.363834\pi$
$691$	−2.44039	+	46.5654i	−0.0928367	+	1.77143i	−0.507688	+	0.861541i	$0.669500\pi$
$692$	5.49206	+	3.17084i	0.208777	+	0.120537i
$693$	−1.17149	+	38.5842i	−0.0445013	+	1.46569i
$694$	−5.02437	−	5.02437i	−0.190723	−	0.190723i
$695$	−42.7684	+	65.8576i	−1.62230	+	2.49812i
$696$	12.9341	−	22.3292i	0.490267	−	0.846386i
$697$	−21.6228	+	3.42472i	−0.819024	+	0.129721i
$698$	−22.1651	−	19.9576i	−0.838963	−	0.755406i
$699$	23.6749	−	12.0206i	0.895467	−	0.454661i
$700$	−3.26047	+	8.49382i	−0.123234	+	0.321036i
$701$	30.3893	−	22.0791i	1.14779	−	0.833916i	0.159602	−	0.987181i	$-0.448979\pi$
$701$	30.3893	−	22.0791i	1.14779	−	0.833916i	0.988185	+	0.153266i	$0.0489790\pi$
$702$	−20.0007	+	20.6973i	−0.754877	+	0.781168i
$703$	38.4822			1.45139
$704$	17.2286	−	10.5262i	0.649328	−	0.396722i
$705$	−1.81818	−	11.5861i	−0.0684765	−	0.436357i
$706$	9.88284	+	46.4951i	0.371946	+	1.74987i
$707$	5.00172	−	31.5796i	0.188109	−	1.18767i
$708$	−4.82344	−	1.03242i	−0.181276	−	0.0388008i
$709$	−1.17426	−	22.4061i	−0.0441001	−	0.841480i	−0.927720	−	0.373276i	$-0.878234\pi$
$709$	−1.17426	−	22.4061i	−0.0441001	−	0.841480i	0.883620	−	0.468204i	$-0.155099\pi$
$710$	−19.6972	+	38.6580i	−0.739223	+	1.45081i
$711$	−17.9395	−	5.88532i	−0.672783	−	0.220717i
$712$	4.10337	−	0.431281i	0.153780	−	0.0161629i
$713$	0.346073	−	6.60346i	0.0129605	−	0.247302i
$714$	−16.2820	−	20.1651i	−0.609337	−	0.754659i
$715$	−36.2634	+	18.1979i	−1.35617	+	0.680562i
$716$		−	0.664267i		−	0.0248248i
$717$	−11.9170	+	8.63234i	−0.445048	+	0.322381i
$718$	−2.15688	−	20.5213i	−0.0804940	−	0.765849i
$719$	1.12223	−	10.6773i	0.0418520	−	0.398195i	−0.953463	−	0.301510i	$-0.902509\pi$
$719$	1.12223	−	10.6773i	0.0418520	−	0.398195i	0.995315	−	0.0966851i	$-0.0308240\pi$
$720$	29.5088	−	36.2293i	1.09973	−	1.35019i
$721$	−41.3113	+	2.16504i	−1.53851	+	0.0806301i
$722$	13.1480	−	10.6470i	0.489316	−	0.396240i
$723$	6.96846	+	12.1094i	0.259160	+	0.450355i
$724$	5.57087	−	1.18413i	0.207040	−	0.0440077i
$725$	19.2547	−	33.3501i	0.715101	−	1.23859i
$726$	−18.5128	+	22.6716i	−0.687075	+	0.841422i
$727$		−	46.3786i		−	1.72009i	−0.510221	−	0.860043i	$-0.670436\pi$
$727$		−	46.3786i		−	1.72009i	0.510221	−	0.860043i	$-0.329564\pi$
$728$	−19.8207	−	29.1381i	−0.734606	−	1.07993i
$729$	0.230249	−	26.9990i	0.00852775	−	0.999964i
$730$	18.4782	+	7.09312i	0.683910	+	0.262528i
$731$	−2.13194	+	10.0300i	−0.0788528	+	0.370973i
$732$	7.46633	+	0.401936i	0.275964	+	0.0148560i
$733$	0.697032	+	4.40089i	0.0257455	+	0.162550i	0.997211	−	0.0746287i	$-0.0237772\pi$
$733$	0.697032	+	4.40089i	0.0257455	+	0.162550i	−0.971466	+	0.237179i	$0.923777\pi$
$734$	−51.6982	+	19.8451i	−1.90822	+	0.732496i
$735$	−47.0650	+	4.87911i	−1.73602	+	0.179969i
$736$	2.27935	−	2.27935i	0.0840180	−	0.0840180i
$737$	−7.53140	+	15.7360i	−0.277423	+	0.579643i
$738$	−26.9763	+	29.7895i	−0.993011	+	1.09657i
$739$	−8.00986	−	0.419779i	−0.294647	−	0.0154418i	−0.0955604	−	0.995424i	$-0.530464\pi$
$739$	−8.00986	−	0.419779i	−0.294647	−	0.0154418i	−0.199087	+	0.979982i	$0.563798\pi$
$740$	−6.94373	+	5.04492i	−0.255257	+	0.185455i
$741$	−11.6208	+	32.1783i	−0.426902	+	1.18210i
$742$	−20.6841	−	63.6592i	−0.759338	−	2.33700i
$743$	−10.7938	+	7.00959i	−0.395987	+	0.257157i	−0.727237	−	0.686386i	$-0.759196\pi$
$743$	−10.7938	+	7.00959i	−0.395987	+	0.257157i	0.331251	+	0.943543i	$0.392529\pi$
$744$	16.0492	+	8.20622i	0.588392	+	0.300855i
$745$	−10.4506	+	23.4725i	−0.382881	+	0.859965i
$746$	−11.7979	−	23.1546i	−0.431950	−	0.847750i
$747$	−8.35856	+	16.2900i	−0.305824	+	0.596019i
$748$	−0.0745087	−	2.99774i	−0.00272431	−	0.109608i
$749$	−0.142145	−	0.142145i	−0.00519385	−	0.00519385i
$750$	8.60492	−	10.5954i	0.314207	−	0.386888i
$751$	−6.40341	+	0.673026i	−0.233664	+	0.0245591i	−0.220637	−	0.975356i	$-0.570813\pi$
$751$	−6.40341	+	0.673026i	−0.233664	+	0.0245591i	−0.0130272	+	0.999915i	$0.504147\pi$
$752$	8.55270	+	3.28307i	0.311885	+	0.119721i
$753$	7.98119	+	5.19919i	0.290851	+	0.189469i
$754$	−13.9600	−	29.6331i	−0.508392	−	1.07917i
$755$	17.5206	−	24.1151i	0.637641	−	0.877638i
$756$	−7.09471	−	1.53967i	−0.258032	−	0.0559974i
$757$	32.4741	+	36.0662i	1.18029	+	1.31085i	0.940409	+	0.340045i	$0.110442\pi$
$757$	32.4741	+	36.0662i	1.18029	+	1.31085i	0.239883	+	0.970802i	$0.422891\pi$
$758$	0.942681	+	1.63277i	0.0342397	+	0.0593049i
$759$	3.98159	−	8.28881i	0.144523	−	0.300865i
$760$	12.1199	−	45.2321i	0.439635	−	1.64074i
$761$	0.641577	+	0.416645i	0.0232571	+	0.0151034i	0.556215	−	0.831038i	$-0.312253\pi$
$761$	0.641577	+	0.416645i	0.0232571	+	0.0151034i	−0.532958	+	0.846142i	$0.678920\pi$
$762$	−10.3990	+	5.98418i	−0.376716	+	0.216784i
$763$	4.85817	−	46.2224i	0.175878	−	1.67336i
$764$	1.24975	+	0.265643i	0.0452144	+	0.00961062i
$765$	9.09015	+	23.8834i	0.328655	+	0.863504i
$766$	13.7624	−	18.9423i	0.497255	−	0.684412i
$767$	20.7765	−	19.5274i	0.750198	−	0.705095i
$768$	5.18205	+	13.5573i	0.186991	+	0.489206i
$769$	−21.3580	+	5.72286i	−0.770189	+	0.206372i	−0.622455	−	0.782656i	$-0.713865\pi$
$769$	−21.3580	+	5.72286i	−0.770189	+	0.206372i	−0.147734	+	0.989027i	$0.547198\pi$
$770$	−57.1400	−	35.1201i	−2.05918	−	1.26564i
$771$	23.4747	+	9.04941i	0.845422	+	0.325906i
$772$	−4.05607	+	2.06667i	−0.145981	+	0.0743810i
$773$	−50.0867	+	19.2265i	−1.80149	+	0.691528i	−0.806541	+	0.591179i	$0.798663\pi$
$773$	−50.0867	+	19.2265i	−1.80149	+	0.691528i	−0.994952	+	0.100350i	$0.968004\pi$
$774$	8.49813	+	16.7964i	0.305459	+	0.603733i
$775$	23.9681	+	12.2124i	0.860961	+	0.438682i
$776$	−16.8018	−	15.1284i	−0.603148	−	0.543077i
$777$	−42.0269	−	21.4891i	−1.50771	−	0.770917i
$778$	35.9887	+	29.1431i	1.29026	+	1.04483i
$779$	−14.7621	+	45.4332i	−0.528908	+	1.62781i
$780$	−2.12163	−	7.32972i	−0.0759666	−	0.262446i
$781$	−21.8795	−	16.8350i	−0.782909	−	0.602403i
$782$	1.59794	+	5.96359i	0.0571422	+	0.213258i
$783$	28.6404	+	11.1344i	1.02352	+	0.397910i
$784$	15.0337	−	33.7661i	0.536916	−	1.20593i
$785$	−17.7380	+	2.80943i	−0.633098	+	0.100273i
$786$	21.1577	−	18.9961i	0.754670	−	0.677569i
$787$	1.11009	+	21.1819i	0.0395706	+	0.755052i	0.944304	+	0.329074i	$0.106737\pi$
$787$	1.11009	+	21.1819i	0.0395706	+	0.755052i	−0.904734	+	0.425978i	$0.859930\pi$
$788$	0.410237	+	2.59014i	0.0146141	+	0.0922698i
$789$	−3.43098	−	12.8778i	−0.122146	−	0.458460i
$790$	24.3781	−	21.9501i	0.867333	−	0.780950i
$791$	45.1810	−	12.1062i	1.60645	−	0.430447i
$792$	16.1998	+	19.1286i	0.575635	+	0.679704i
$793$	−26.4755	+	34.1626i	−0.940174	+	1.21315i
$794$	32.8139	+	10.6619i	1.16452	+	0.378376i
$795$	−0.0938030	+	65.9976i	−0.00332685	+	2.34069i
$796$	−5.14210	+	2.28941i	−0.182257	+	0.0811460i
$797$	35.3718	−	39.2843i	1.25293	−	1.39152i	0.365352	−	0.930869i	$-0.380948\pi$
$797$	35.3718	−	39.2843i	1.25293	−	1.39152i	0.887580	−	0.460653i	$-0.152385\pi$
$798$	−55.3359	+	11.6798i	−1.95887	+	0.413462i
$799$	−3.89373	+	3.15308i	−0.137750	+	0.111548i
$800$	4.69940	+	12.2423i	0.166149	+	0.432832i
$801$	1.25815	+	4.74943i	0.0444544	+	0.167813i
$802$	−3.63815	−	6.30146i	−0.128467	−	0.222512i
$803$	−6.59463	+	10.7294i	−0.232720	+	0.378632i
$804$	−2.65160	−	1.93227i	−0.0935149	−	0.0681458i
$805$	20.0397	+	6.51128i	0.706305	+	0.229492i
$806$	20.1610	−	10.8215i	0.710141	−	0.381171i
$807$	−2.14034	−	41.9818i	−0.0753436	−	1.47783i
$808$	−11.3079	−	17.4126i	−0.397810	−	0.612574i
$809$	−1.25243	+	5.89223i	−0.0440332	+	0.207160i	−0.994664	−	0.103163i	$-0.967104\pi$
$809$	−1.25243	+	5.89223i	−0.0440332	+	0.207160i	0.950631	+	0.310323i	$0.100437\pi$
$810$	40.4929	+	23.6865i	1.42277	+	0.832260i
$811$	−22.8803	−	3.62389i	−0.803436	−	0.127252i	−0.258807	−	0.965929i	$-0.583330\pi$
$811$	−22.8803	−	3.62389i	−0.803436	−	0.127252i	−0.544629	+	0.838677i	$0.683330\pi$
$812$	4.50003	−	6.92944i	0.157920	−	0.243176i
$813$	25.6419	−	11.3729i	0.899299	−	0.398863i
$814$	−15.3654	−	32.3248i	−0.538557	−	1.13298i
$815$	20.2323	−	11.6811i	0.708708	−	0.409173i
$816$	−19.7118	−	3.15076i	−0.690050	−	0.110299i
$817$	17.3889	+	14.0813i	0.608362	+	0.492642i
$818$	49.4121	+	35.9000i	1.72765	+	1.25521i
$819$	30.6601	−	28.6531i	1.07135	−	1.00122i
$820$	−3.29249	−	10.1332i	−0.114979	−	0.353868i
$821$	−5.87578	+	15.3069i	−0.205066	+	0.534216i	−0.997087	−	0.0762789i	$-0.975696\pi$
$821$	−5.87578	+	15.3069i	−0.205066	+	0.534216i	0.792020	+	0.610495i	$0.209029\pi$
$822$	−14.0407	−	14.0807i	−0.489726	−	0.491120i
$823$	5.01631	+	23.5999i	0.174858	+	0.822641i	0.974891	+	0.222685i	$0.0714820\pi$
$823$	5.01631	+	23.5999i	0.174858	+	0.822641i	−0.800033	+	0.599956i	$0.795185\pi$
$824$	−18.9948	+	18.9948i	−0.661717	+	0.661717i
$825$	24.2161	+	28.5119i	0.843096	+	0.992655i
$826$	45.5275	+	12.1990i	1.58410	+	0.424459i
$827$	1.18267	−	0.602598i	0.0411253	−	0.0209544i	−0.433307	−	0.901246i	$-0.642653\pi$
$827$	1.18267	−	0.602598i	0.0411253	−	0.0209544i	0.474432	+	0.880292i	$0.342653\pi$
$828$	1.39621	+	1.02048i	0.0485218	+	0.0354643i
$829$	7.11247	+	15.9749i	0.247026	+	0.554830i	0.993919	−	0.110114i	$-0.0351217\pi$
$829$	7.11247	+	15.9749i	0.247026	+	0.554830i	−0.746892	+	0.664945i	$0.768455\pi$
$830$	−17.3260	−	26.6797i	−0.601394	−	0.926066i
$831$	−20.4050	+	31.3234i	−0.707842	+	1.08660i
$832$	−21.3173	−	5.22622i	−0.739044	−	0.181187i
$833$	11.8818	+	16.3539i	0.411680	+	0.566628i
$834$	49.8741	−	36.1275i	1.72700	−	1.25099i
$835$	−22.3005	+	38.6256i	−0.771741	+	1.33670i
$836$	−5.90220	−	2.82485i	−0.204132	−	0.0976993i
$837$	−6.72002	+	20.3859i	−0.232278	+	0.704641i
$838$	−29.4625	−	19.1332i	−1.01776	−	0.660944i
$839$	−2.32662	−	6.06104i	−0.0803237	−	0.209250i	0.887537	−	0.460736i	$-0.152414\pi$
$839$	−2.32662	−	6.06104i	−0.0803237	−	0.209250i	−0.967861	+	0.251485i	$0.919081\pi$
$840$	−38.4946	+	42.6305i	−1.32819	+	1.47089i
$841$	−3.99611	+	4.43813i	−0.137797	+	0.153039i
$842$	−6.16683	−	1.31080i	−0.212523	−	0.0451732i
$843$	−14.5120	+	4.69243i	−0.499818	+	0.161616i
$844$	4.61436	+	6.35112i	0.158833	+	0.218615i
$845$	41.8162	+	14.0323i	1.43852	+	0.482727i
$846$	−1.93785	+	8.99114i	−0.0666248	+	0.309122i
$847$	28.6402	−	31.6385i	0.984088	−	1.08711i
$848$	−44.6469	−	25.7769i	−1.53318	−	0.885183i
$849$	−33.5231	−	27.2254i	−1.15051	−	0.934375i
$850$	−24.8068	−	3.92901i	−0.850866	−	0.134764i
$851$	7.07619	+	8.73837i	0.242569	+	0.299547i
$852$	3.86332	−	3.46862i	0.132355	−	0.118833i
$853$	−5.78051	−	2.94532i	−0.197921	−	0.100846i	0.352221	−	0.935917i	$-0.385426\pi$
$853$	−5.78051	−	2.94532i	−0.197921	−	0.100846i	−0.550142	+	0.835071i	$0.685426\pi$
$854$	−71.0551	−	7.46820i	−2.43146	−	0.255556i
$855$	55.4407	+	5.98643i	1.89603	+	0.204732i
$856$	−0.130357	−	0.00683174i	−0.00445552	−	0.000233504i
$857$	−16.9132			−0.577743			−0.288872	−	0.957368i	$-0.593280\pi$
$857$	−16.9132			−0.577743			−0.288872	+	0.957368i	$0.593280\pi$
$858$	31.6696	−	3.08694i	1.08118	−	0.105386i
$859$	5.38216			0.183637			0.0918184	−	0.995776i	$-0.470732\pi$
$859$	5.38216			0.183637			0.0918184	+	0.995776i	$0.470732\pi$
$860$	−4.98368	−	0.261183i	−0.169942	−	0.00890628i
$861$	41.4925	−	41.3747i	1.41406	−	1.41005i
$862$	31.6951	+	3.33129i	1.07954	+	0.113464i
$863$	−2.31414	−	1.17912i	−0.0787744	−	0.0401376i	0.414160	−	0.910204i	$-0.364076\pi$
$863$	−2.31414	−	1.17912i	−0.0787744	−	0.0401376i	−0.492934	+	0.870067i	$0.664076\pi$
$864$	−9.08414	+	5.19321i	−0.309049	+	0.176677i
$865$	37.6007	+	46.4330i	1.27846	+	1.57877i
$866$	−45.4964	−	7.20592i	−1.54603	−	0.244867i
$867$	−11.6802	+	14.3820i	−0.396681	+	0.488439i
$868$	4.99833	+	2.88579i	0.169654	+	0.0979500i
$869$	10.8824	+	17.8115i	0.369159	+	0.604214i
$870$	−41.5397	+	33.5406i	−1.40833	+	1.13713i
$871$	17.9076	−	6.24480i	0.606776	−	0.211597i
$872$	−17.7396	−	24.4164i	−0.600737	−	0.826844i
$873$	14.7275	−	22.5378i	0.498450	−	0.762790i
$874$	13.1778	+	2.80102i	0.445745	+	0.0947460i
$875$	−13.3165	+	14.7894i	−0.450178	+	0.499974i
$876$	−1.75792	−	1.58737i	−0.0593946	−	0.0536322i
$877$	−1.69465	−	4.41472i	−0.0572244	−	0.149075i	0.901988	−	0.431761i	$-0.142108\pi$
$877$	−1.69465	−	4.41472i	−0.0572244	−	0.149075i	−0.959212	+	0.282687i	$0.908774\pi$
$878$	−5.51238	−	3.57978i	−0.186034	−	0.120812i
$879$	15.2675	+	1.62662i	0.514960	+	0.0548646i
$880$	−50.8051	+	9.34630i	−1.71264	+	0.315064i
$881$	17.0452	−	29.5231i	0.574267	−	0.994660i	−0.421854	−	0.906664i	$-0.638620\pi$
$881$	17.0452	−	29.5231i	0.574267	−	0.994660i	0.996121	−	0.0879958i	$-0.0280462\pi$
$882$	35.8167	+	9.70626i	1.20601	+	0.326827i
$883$	−16.4334	−	22.6186i	−0.553028	−	0.761178i	0.437391	−	0.899271i	$-0.355903\pi$
$883$	−16.4334	−	22.6186i	−0.553028	−	0.761178i	−0.990419	+	0.138093i	$0.955903\pi$
$884$	−2.25529	+	2.35384i	−0.0758536	+	0.0791681i
$885$	−38.9398	−	25.3665i	−1.30895	−	0.852687i
$886$	5.54110	+	8.53254i	0.186157	+	0.286656i
$887$	13.3760	+	30.0431i	0.449123	+	1.00875i	0.986252	+	0.165247i	$0.0528423\pi$
$887$	13.3760	+	30.0431i	0.449123	+	1.00875i	−0.537129	+	0.843500i	$0.680491\pi$
$888$	−29.6180	+	7.89103i	−0.993917	+	0.264806i
$889$	15.5866	−	7.94175i	0.522757	−	0.266358i
$890$	−8.24578	−	2.20945i	−0.276399	−	0.0740610i
$891$	−19.5445	+	22.5613i	−0.654766	+	0.755831i
$892$	1.36639	−	1.36639i	0.0457502	−	0.0457502i
$893$	2.27309	+	10.6940i	0.0760660	+	0.357862i
$894$	14.2687	−	14.2282i	0.477218	−	0.475863i
$895$	2.24280	−	5.84270i	0.0749686	−	0.195300i
$896$	−16.0403	−	49.3671i	−0.535870	−	1.64924i
$897$	−9.44377	+	3.27822i	−0.315318	+	0.109456i
$898$	7.01148	+	5.09414i	0.233976	+	0.169994i
$899$	−18.9850	−	15.3738i	−0.633187	−	0.512744i
$900$	−6.10269	+	3.50030i	−0.203423	+	0.116677i
$901$	24.4176	−	14.0975i	0.813469	−	0.469656i
$902$	44.0579	−	5.74072i	1.46697	−	0.191145i
$903$	−11.1275	−	25.0886i	−0.370299	−	0.834896i
$904$	16.5427	−	25.4735i	0.550202	−	0.847237i
$905$	52.9978	+	8.39403i	1.76171	+	0.279027i
$906$	−19.6236	+	12.7041i	−0.651950	+	0.422065i
$907$	4.07313	−	19.1626i	0.135246	−	0.636283i	−0.857341	−	0.514749i	$-0.827885\pi$
$907$	4.07313	−	19.1626i	0.135246	−	0.636283i	0.992587	−	0.121535i	$-0.0387815\pi$
$908$	−2.77878	−	4.27895i	−0.0922171	−	0.142002i
$909$	18.4203	−	16.4912i	0.610964	−	0.546978i
$910$	16.6805	+	70.9792i	0.552954	+	2.35294i
$911$	26.5451	+	8.62503i	0.879479	+	0.285760i	0.713741	−	0.700410i	$-0.246999\pi$
$911$	26.5451	+	8.62503i	0.879479	+	0.285760i	0.165738	+	0.986170i	$0.446999\pi$
$912$	−25.6534	+	35.2035i	−0.849469	+	1.16571i
$913$	18.7111	−	7.72126i	0.619248	−	0.255536i
$914$	−12.5190	−	21.6836i	−0.414093	−	0.717230i
$915$	64.3146	+	28.7443i	2.12618	+	0.950257i
$916$	1.76276	+	4.59216i	0.0582434	+	0.151729i
$917$	−32.2186	+	26.0901i	−1.06395	+	0.861572i
$918$	0.0854546	−	20.0412i	0.00282042	−	0.661457i
$919$	20.5927	−	22.8706i	0.679292	−	0.754430i	−0.300645	−	0.953736i	$-0.597202\pi$
$919$	20.5927	−	22.8706i	0.679292	−	0.754430i	0.979937	+	0.199306i	$0.0638687\pi$
$920$	12.4997	−	5.56523i	0.412103	−	0.183480i
$921$	25.5070	+	0.0362534i	0.840485	+	0.00119459i
$922$	−6.91577	−	2.24707i	−0.227759	−	0.0740033i
$923$	3.77437	+	29.7733i	0.124235	+	0.980001i
$924$	4.86842	+	6.38093i	0.160159	+	0.209917i
$925$	−44.1833	+	11.8389i	−1.45274	+	0.389260i
$926$	−0.703763	+	0.633671i	−0.0231271	+	0.0208237i
$927$	−25.8257	−	18.8759i	−0.848227	−	0.619965i
$928$	−1.86295	−	11.7622i	−0.0611543	−	0.386113i
$929$	−0.739033	−	14.1016i	−0.0242469	−	0.462658i	−0.983590	−	0.180417i	$-0.942255\pi$
$929$	−0.739033	−	14.1016i	−0.0242469	−	0.462658i	0.959343	−	0.282241i	$-0.0910779\pi$
$930$	−24.9157	−	27.7509i	−0.817019	−	0.909989i
$931$	43.5669	−	6.90033i	1.42785	−	0.226149i
$932$	2.24543	−	5.04332i	0.0735515	−	0.165199i
$933$	16.8989	+	2.70115i	0.553245	+	0.0884317i
$934$	−12.1070	−	45.1838i	−0.396152	−	1.47846i
$935$	9.46607	−	26.6188i	0.309574	−	0.870528i
$936$	2.34565	−	27.1491i	0.0766699	−	0.887398i
$937$	−13.0285	+	40.0975i	−0.425621	+	1.30993i	0.476777	+	0.879025i	$0.341805\pi$
$937$	−13.0285	+	40.0975i	−0.425621	+	1.30993i	−0.902398	+	0.430904i	$0.858195\pi$
$938$	24.3640	+	19.7296i	0.795513	+	0.644193i
$939$	8.47521	−	16.5752i	0.276578	−	0.540913i
$940$	−1.81211	−	1.63164i	−0.0591047	−	0.0532181i
$941$	−31.7516	−	16.1782i	−1.03507	−	0.527395i	−0.147980	−	0.988990i	$-0.547277\pi$
$941$	−31.7516	−	16.1782i	−1.03507	−	0.527395i	−0.887091	+	0.461595i	$0.847277\pi$
$942$	13.7725	+	2.94791i	0.448733	+	0.0960480i
$943$	−13.0312	+	5.00223i	−0.424356	+	0.162895i
$944$	32.3457	−	16.4810i	1.05276	−	0.536409i
$945$	−57.2045	−	37.4968i	−1.86086	−	1.21977i
$946$	4.88503	−	20.2290i	0.158826	−	0.657703i
$947$	−36.3910	+	9.75095i	−1.18255	+	0.316863i	−0.795937	−	0.605379i	$-0.793021\pi$
$947$	−36.3910	+	9.75095i	−1.18255	+	0.316863i	−0.386612	+	0.922242i	$0.626355\pi$
$948$	−3.66681	+	1.40158i	−0.119092	+	0.0455211i
$949$	13.3281	−	3.13217i	0.432647	−	0.101674i
$950$	−32.2139	+	44.3386i	−1.04516	+	1.43853i
$951$	12.2053	−	37.3833i	0.395786	−	1.21224i
$952$	24.0023	+	5.10184i	0.777918	+	0.165352i
$953$	−6.05572	+	57.6164i	−0.196164	+	1.86638i	0.245769	+	0.969329i	$0.420960\pi$
$953$	−6.05572	+	57.6164i	−0.196164	+	1.86638i	−0.441933	+	0.897048i	$0.645707\pi$
$954$	18.6860	−	48.2680i	0.604980	−	1.56274i
$955$	10.0955	+	6.55613i	0.326684	+	0.212151i
$956$	−0.791863	+	2.95527i	−0.0256107	+	0.0955803i
$957$	−16.1277	−	29.8994i	−0.521335	−	0.966511i
$958$	−19.3753	−	33.5590i	−0.625988	−	1.08424i
$959$	19.3998	+	21.5457i	0.626452	+	0.695746i
$960$	−0.0508460	+	35.7740i	−0.00164105	+	1.15460i
$961$	−8.19101	+	11.2740i	−0.264226	+	0.363676i
$962$	−13.1640	+	36.6143i	−0.424425	+	1.18049i
$963$	−0.0158088	−	0.154638i	−0.000509432	−	0.00498314i
$964$	2.71195	+	1.04102i	0.0873462	+	0.0335291i
$965$	−42.6538	+	4.48309i	−1.37307	+	0.144316i
$966$	−12.8275	−	10.4177i	−0.412717	−	0.335184i
$967$	−10.5090	−	10.5090i	−0.337947	−	0.337947i	0.517647	−	0.855594i	$-0.326808\pi$
$967$	−10.5090	−	10.5090i	−0.337947	−	0.337947i	−0.855594	+	0.517647i	$0.826808\pi$
$968$	0.0737178	−	27.7121i	0.00236938	−	0.890700i
$969$	−9.65859	−	21.7768i	−0.310279	−	0.699572i
$970$	21.2369	+	41.6797i	0.681875	+	1.33825i
$971$	9.92575	−	22.2936i	0.318533	−	0.715436i	−0.681331	−	0.731976i	$-0.738598\pi$
$971$	9.92575	−	22.2936i	0.318533	−	0.715436i	0.999863	+	0.0165399i	$0.00526506\pi$
$972$	−3.50178	−	4.38774i	−0.112320	−	0.140737i
$973$	−75.3052	+	48.9038i	−2.41418	+	1.56778i
$974$	−6.27575	−	19.3148i	−0.201088	−	0.618885i
$975$	3.44291	−	40.5206i	0.110261	−	1.29770i
$976$	−44.5189	+	32.3449i	−1.42502	+	1.03533i
$977$	−49.2755	−	2.58242i	−1.57646	−	0.0826189i	−0.756098	−	0.654459i	$-0.772897\pi$
$977$	−49.2755	−	2.58242i	−1.57646	−	0.0826189i	−0.820365	+	0.571840i	$0.806230\pi$
$978$	−18.1004	+	2.84045i	−0.578787	+	0.0908277i
$979$	2.34497	−	4.89955i	0.0749456	−	0.156590i
$980$	−6.95660	+	6.95660i	−0.222220	+	0.222220i
$981$	25.4849	−	25.3404i	0.813671	−	0.809058i
$982$	−14.1552	+	5.43369i	−0.451712	+	0.173396i
$983$	−8.47238	−	53.4925i	−0.270227	−	1.70615i	−0.632904	−	0.774230i	$-0.718137\pi$
$983$	−8.47238	−	53.4925i	−0.270227	−	1.70615i	0.362677	−	0.931915i	$-0.381863\pi$
$984$	2.04539	−	37.9949i	0.0652045	−	1.21123i
$985$	−5.13690	+	24.1672i	−0.163675	+	0.770031i
$986$	21.2940	+	8.17401i	0.678140	+	0.260313i
$987$	3.48925	−	12.9484i	0.111064	−	0.412153i
$988$	2.34227	+	6.71670i	0.0745176	+	0.213687i
$989$			6.53790i			0.207893i
$990$	−17.1081	−	48.9601i	−0.543731	−	1.55605i
$991$	−9.74270	+	16.8749i	−0.309487	+	0.536047i	−0.978250	−	0.207428i	$-0.933491\pi$
$991$	−9.74270	+	16.8749i	−0.309487	+	0.536047i	0.668763	+	0.743475i	$0.266824\pi$
$992$	8.13692	−	1.72956i	0.258348	−	0.0549135i
$993$	−38.2316	+	22.0006i	−1.21324	+	0.698168i
$994$	−38.5549	+	31.2212i	−1.22289	+	0.990275i
$995$	−52.9583	+	2.77543i	−1.67889	+	0.0879870i
$996$	0.786191	+	3.72476i	0.0249114	+	0.118024i
$997$	−1.47633	+	14.0463i	−0.0467558	+	0.444852i	0.945952	+	0.324306i	$0.105131\pi$
$997$	−1.47633	+	14.0463i	−0.0467558	+	0.444852i	−0.992708	+	0.120545i	$0.961536\pi$
$998$	−1.92161	−	18.2829i	−0.0608275	−	0.578735i
$999$	−14.7035	−	33.4072i	−0.465198	−	1.05696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bv.a.20.12	✓	832
3.2	odd	2	inner	429.2.bv.a.20.41	yes	832
11.5	even	5	inner	429.2.bv.a.137.41	yes	832
13.2	odd	12	inner	429.2.bv.a.119.12	yes	832
33.5	odd	10	inner	429.2.bv.a.137.12	yes	832
39.2	even	12	inner	429.2.bv.a.119.41	yes	832
143.93	odd	60	inner	429.2.bv.a.236.41	yes	832
429.236	even	60	inner	429.2.bv.a.236.12	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bv.a.20.12	✓	832	1.1	even	1	trivial
429.2.bv.a.20.41	yes	832	3.2	odd	2	inner
429.2.bv.a.119.12	yes	832	13.2	odd	12	inner
429.2.bv.a.119.41	yes	832	39.2	even	12	inner
429.2.bv.a.137.12	yes	832	33.5	odd	10	inner
429.2.bv.a.137.41	yes	832	11.5	even	5	inner
429.2.bv.a.236.12	yes	832	429.236	even	60	inner
429.2.bv.a.236.41	yes	832	143.93	odd	60	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53416 - 0.0804022i) q^{2} +(1.22300 + 1.22648i) q^{3} +(0.358152 + 0.0376433i) q^{4} +(3.02311 + 1.54035i) q^{5} +(-1.77768 - 1.97996i) q^{6} +(2.44154 + 3.01505i) q^{7} +(2.48827 + 0.394104i) q^{8} +(-0.00852784 + 2.99999i) q^{9} +O(q^{10})\)	\(q+(-1.53416 - 0.0804022i) q^{2} +(1.22300 + 1.22648i) q^{3} +(0.358152 + 0.0376433i) q^{4} +(3.02311 + 1.54035i) q^{5} +(-1.77768 - 1.97996i) q^{6} +(2.44154 + 3.01505i) q^{7} +(2.48827 + 0.394104i) q^{8} +(-0.00852784 + 2.99999i) q^{9} +(-4.51410 - 2.60622i) q^{10} +(2.15733 - 2.51911i) q^{11} +(0.391853 + 0.485306i) q^{12} +(-3.59575 + 0.265624i) q^{13} +(-3.50331 - 4.82189i) q^{14} +(1.80805 + 5.59165i) q^{15} +(-4.49025 - 0.954431i) q^{16} +(1.67992 - 1.86574i) q^{17} +(0.254289 - 4.60179i) q^{18} +(-1.96327 - 5.11450i) q^{19} +(1.02475 + 0.665480i) q^{20} +(-0.711903 + 6.68193i) q^{21} +(-3.51224 + 3.69128i) q^{22} +(0.800366 - 1.38628i) q^{23} +(2.55980 + 3.53382i) q^{24} +(3.82758 + 5.26821i) q^{25} +(5.53783 - 0.118405i) q^{26} +(-3.68987 + 3.65853i) q^{27} +(0.760947 + 1.17176i) q^{28} +(-2.40533 - 5.40245i) q^{29} +(-2.32427 - 8.72388i) q^{30} +(3.68069 - 1.87540i) q^{31} +(1.94514 + 0.521199i) q^{32} +(5.72807 - 0.434955i) q^{33} +(-2.72728 + 2.72728i) q^{34} +(2.73681 + 12.8757i) q^{35} +(-0.115984 + 1.07413i) q^{36} +(-2.51732 + 6.55784i) q^{37} +(2.60077 + 8.00434i) q^{38} +(-4.72340 - 4.08528i) q^{39} +(6.91526 + 5.02423i) q^{40} +(-6.77669 - 5.48766i) q^{41} +(1.62942 - 10.1939i) q^{42} +(-3.53712 + 2.04216i) q^{43} +(0.867480 - 0.821018i) q^{44} +(-4.64681 + 9.05615i) q^{45} +(-1.33935 + 2.06242i) q^{46} +(-1.97109 - 0.312189i) q^{47} +(-4.32099 - 6.67449i) q^{48} +(-1.67404 + 7.87572i) q^{49} +(-5.44856 - 8.39004i) q^{50} +(4.34285 - 0.221410i) q^{51} +(-1.29783 - 0.0402222i) q^{52} +(10.6807 + 3.47038i) q^{53} +(5.95502 - 5.31612i) q^{54} +(10.4022 - 4.29251i) q^{55} +(4.88698 + 8.46450i) q^{56} +(3.87177 - 8.66297i) q^{57} +(3.25580 + 8.48164i) q^{58} +(-6.14572 + 4.97670i) q^{59} +(0.437071 + 2.07072i) q^{60} +(8.02107 - 8.90830i) q^{61} +(-5.79757 + 2.58124i) q^{62} +(-9.06594 + 7.29888i) q^{63} +(5.78950 + 1.88112i) q^{64} +(-11.2795 - 4.73571i) q^{65} +(-8.82278 + 0.206743i) q^{66} +(-5.08077 + 1.36139i) q^{67} +(0.671900 - 0.604982i) q^{68} +(2.67910 - 0.713782i) q^{69} +(-3.16348 - 19.9734i) q^{70} +(-0.435630 - 8.31232i) q^{71} +(-1.20353 + 7.46143i) q^{72} +(-3.75049 + 0.594019i) q^{73} +(4.38924 - 9.85840i) q^{74} +(-1.78024 + 11.1375i) q^{75} +(-0.510624 - 1.90568i) q^{76} +(12.8625 + 0.353936i) q^{77} +(6.91801 + 6.64726i) q^{78} +(-1.94477 + 5.98538i) q^{79} +(-12.1043 - 9.80190i) q^{80} +(-8.99985 - 0.0511669i) q^{81} +(9.95534 + 8.96383i) q^{82} +(5.43789 + 2.77074i) q^{83} +(-0.506500 + 2.36635i) q^{84} +(7.95247 - 3.05267i) q^{85} +(5.59072 - 2.84861i) q^{86} +(3.68430 - 9.55731i) q^{87} +(6.36081 - 5.41803i) q^{88} +(1.58195 - 0.423881i) q^{89} +(7.85711 - 13.5200i) q^{90} +(-9.58005 - 10.1929i) q^{91} +(0.338837 - 0.466370i) q^{92} +(6.80165 + 2.22068i) q^{93} +(2.99887 + 0.637430i) q^{94} +(1.94294 - 18.4858i) q^{95} +(1.73967 + 3.02311i) q^{96} +(-7.52653 - 4.88779i) q^{97} +(3.20147 - 11.9480i) q^{98} +(7.53891 + 6.49344i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9	\( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) 832 * q - 6 * q^3 - 36 * q^4 - 4 * q^6 - 24 * q^7 - 6 * q^9 - 96 * q^10 - 40 * q^13 + 12 * q^15 - 68 * q^16 - 20 * q^18 - 32 * q^19 - 84 * q^21 - 24 * q^22 - 72 * q^24 - 114 * q^30 - 8 * q^31 + 14 * q^33 - 24 * q^34 + 78 * q^36 - 24 * q^37 - 72 * q^39 - 112 * q^40 + 2 * q^42 - 96 * q^43 + 4 * q^45 - 16 * q^46 + 14 * q^48 - 36 * q^49 + 8 * q^52 + 32 * q^54 - 24 * q^55 - 12 * q^57 + 112 * q^58 - 120 * q^60 + 12 * q^61 + 28 * q^63 - 300 * q^66 - 32 * q^67 - 18 * q^69 - 140 * q^70 + 204 * q^72 - 24 * q^73 + 66 * q^75 + 176 * q^76 - 28 * q^78 - 224 * q^79 - 58 * q^81 - 264 * q^82 + 20 * q^84 - 168 * q^85 + 72 * q^87 - 120 * q^88 - 146 * q^93 - 4 * q^94 - 10 * q^96 - 88 * q^97 + 40 * q^99

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