LMFDB - Embedded newform 273.2.t.c.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$0.655911 - 1.25291i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.c.205.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50582i q^{2} +(-0.500000 - 0.866025i) q^{3} -4.27912 q^{4} +(2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-2.46263 - 0.967177i) q^{7} +5.71107i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.50582i q^{2} +(-0.500000 - 0.866025i) q^{3} -4.27912 q^{4} +(2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-2.46263 - 0.967177i) q^{7} +5.71107i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.77981 - 6.54683i) q^{10} +(-1.34340 + 0.775614i) q^{11} +(2.13956 + 3.70583i) q^{12} +(-0.822385 - 3.51051i) q^{13} +(-2.42357 + 6.17091i) q^{14} +(-2.61265 - 1.50841i) q^{15} +5.75266 q^{16} -1.51419 q^{17} +(2.17010 + 1.25291i) q^{18} +(7.11603 + 4.10844i) q^{19} +(-11.1799 + 6.45469i) q^{20} +(0.393717 + 2.61629i) q^{21} +(1.94355 + 3.36632i) q^{22} +3.64614 q^{23} +(4.94593 - 2.85554i) q^{24} +(2.05063 - 3.55179i) q^{25} +(-8.79670 + 2.06075i) q^{26} +1.00000 q^{27} +(10.5379 + 4.13867i) q^{28} +(2.75027 - 4.76361i) q^{29} +(-3.77981 + 6.54683i) q^{30} +(-4.47820 - 2.58549i) q^{31} -2.99297i q^{32} +(1.34340 + 0.775614i) q^{33} +3.79429i q^{34} +(-7.89291 + 1.18778i) q^{35} +(2.13956 - 3.70583i) q^{36} -9.20056i q^{37} +(10.2950 - 17.8315i) q^{38} +(-2.62900 + 2.46746i) q^{39} +(8.61466 + 14.9210i) q^{40} +(2.85275 + 1.64704i) q^{41} +(6.55595 - 0.986584i) q^{42} +(-1.97898 - 3.42770i) q^{43} +(5.74858 - 3.31895i) q^{44} +3.01683i q^{45} -9.13658i q^{46} +(-8.00565 + 4.62206i) q^{47} +(-2.87633 - 4.98195i) q^{48} +(5.12914 + 4.76361i) q^{49} +(-8.90014 - 5.13850i) q^{50} +(0.757096 + 1.31133i) q^{51} +(3.51909 + 15.0219i) q^{52} +(3.90722 - 6.76751i) q^{53} -2.50582i q^{54} +(-2.33989 + 4.05281i) q^{55} +(5.52362 - 14.0643i) q^{56} -8.21689i q^{57} +(-11.9367 - 6.89168i) q^{58} +10.0204i q^{59} +(11.1799 + 6.45469i) q^{60} +(5.23565 - 9.06841i) q^{61} +(-6.47877 + 11.2216i) q^{62} +(2.06892 - 1.64912i) q^{63} +4.00548 q^{64} +(-7.44391 - 7.93124i) q^{65} +(1.94355 - 3.36632i) q^{66} +(2.52349 - 1.45694i) q^{67} +6.47941 q^{68} +(-1.82307 - 3.15765i) q^{69} +(2.97635 + 19.7782i) q^{70} +(-1.11232 + 0.642201i) q^{71} +(-4.94593 - 2.85554i) q^{72} +(-2.27528 - 1.31363i) q^{73} -23.0549 q^{74} -4.10125 q^{75} +(-30.4504 - 17.5805i) q^{76} +(4.05846 - 0.610745i) q^{77} +(6.18301 + 6.58779i) q^{78} +(-3.28050 - 5.68199i) q^{79} +(15.0297 - 8.67739i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.12718 - 7.14848i) q^{82} -5.49127i q^{83} +(-1.68476 - 11.1954i) q^{84} +(-3.95605 + 2.28403i) q^{85} +(-8.58919 + 4.95897i) q^{86} -5.50054 q^{87} +(-4.42958 - 7.67226i) q^{88} +9.76396i q^{89} +7.55962 q^{90} +(-1.37005 + 9.44050i) q^{91} -15.6023 q^{92} +5.17098i q^{93} +(11.5821 + 20.0607i) q^{94} +24.7889 q^{95} +(-2.59199 + 1.49648i) q^{96} +(10.8340 - 6.25500i) q^{97} +(11.9367 - 12.8527i) q^{98} -1.55123i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	2.50582i		−	1.77188i	−0.463799	−	0.885940i	$-0.653514\pi$
$2$		−	2.50582i		−	1.77188i	0.463799	−	0.885940i	$-0.346486\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−4.27912			−2.13956
$5$	2.61265	−	1.50841i	1.16841	−	0.674583i	0.215107	−	0.976591i	$-0.430990\pi$
$5$	2.61265	−	1.50841i	1.16841	−	0.674583i	0.953306	+	0.302007i	$0.0976567\pi$
$6$	−2.17010	+	1.25291i	−0.885940	+	0.511498i
$7$	−2.46263	−	0.967177i	−0.930788	−	0.365559i
$7$	−2.46263	−	0.967177i	−0.930788	−	0.365559i
$8$			5.71107i			2.01917i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.77981	−	6.54683i	−1.19528	−	2.07029i
$11$	−1.34340	+	0.775614i	−0.405051	+	0.233856i	−0.688661	−	0.725083i	$-0.741801\pi$
$11$	−1.34340	+	0.775614i	−0.405051	+	0.233856i	0.283610	+	0.958940i	$0.408468\pi$
$12$	2.13956	+	3.70583i	0.617638	+	1.06978i
$13$	−0.822385	−	3.51051i	−0.228089	−	0.973640i
$13$	−0.822385	−	3.51051i	−0.228089	−	0.973640i
$14$	−2.42357	+	6.17091i	−0.647726	+	1.64925i
$15$	−2.61265	−	1.50841i	−0.674583	−	0.389471i
$16$	5.75266			1.43816
$17$	−1.51419			−0.367245			−0.183623	−	0.982997i	$-0.558782\pi$
$17$	−1.51419			−0.367245			−0.183623	+	0.982997i	$0.558782\pi$
$18$	2.17010	+	1.25291i	0.511498	+	0.295313i
$19$	7.11603	+	4.10844i	1.63253	+	0.942542i	0.983309	+	0.181942i	$0.0582383\pi$
$19$	7.11603	+	4.10844i	1.63253	+	0.942542i	0.649221	+	0.760600i	$0.275095\pi$
$20$	−11.1799	+	6.45469i	−2.49989	+	1.44331i
$21$	0.393717	+	2.61629i	0.0859161	+	0.570922i
$22$	1.94355	+	3.36632i	0.414365	+	0.717702i
$23$	3.64614			0.760274			0.380137	−	0.924930i	$-0.375877\pi$
$23$	3.64614			0.760274			0.380137	+	0.924930i	$0.375877\pi$
$24$	4.94593	−	2.85554i	1.00958	−	0.582884i
$25$	2.05063	−	3.55179i	0.410125	−	0.710358i
$26$	−8.79670	+	2.06075i	−1.72517	+	0.404146i
$27$	1.00000			0.192450
$28$	10.5379	+	4.13867i	1.99148	+	0.782135i
$29$	2.75027	−	4.76361i	0.510712	−	0.884580i	−0.489211	−	0.872166i	$-0.662715\pi$
$29$	2.75027	−	4.76361i	0.510712	−	0.884580i	0.999923	−	0.0124140i	$-0.00395161\pi$
$30$	−3.77981	+	6.54683i	−0.690096	+	1.19528i
$31$	−4.47820	−	2.58549i	−0.804308	−	0.464368i	0.0406670	−	0.999173i	$-0.487052\pi$
$31$	−4.47820	−	2.58549i	−0.804308	−	0.464368i	−0.844975	+	0.534805i	$0.820385\pi$
$32$		−	2.99297i		−	0.529087i
$33$	1.34340	+	0.775614i	0.233856	+	0.135017i
$34$			3.79429i			0.650715i
$35$	−7.89291	+	1.18778i	−1.33414	+	0.200771i
$36$	2.13956	−	3.70583i	0.356594	−	0.617638i
$37$		−	9.20056i		−	1.51256i	−0.654246	−	0.756281i	$-0.727014\pi$
$37$		−	9.20056i		−	1.51256i	0.654246	−	0.756281i	$-0.272986\pi$
$38$	10.2950	−	17.8315i	1.67007	−	2.89265i
$39$	−2.62900	+	2.46746i	−0.420977	+	0.395110i
$40$	8.61466	+	14.9210i	1.36210	+	2.35922i
$41$	2.85275	+	1.64704i	0.445525	+	0.257224i	0.705938	−	0.708273i	$-0.250526\pi$
$41$	2.85275	+	1.64704i	0.445525	+	0.257224i	−0.260413	+	0.965497i	$0.583859\pi$
$42$	6.55595	−	0.986584i	1.01161	−	0.152233i
$43$	−1.97898	−	3.42770i	−0.301792	−	0.522719i	0.674750	−	0.738046i	$-0.264252\pi$
$43$	−1.97898	−	3.42770i	−0.301792	−	0.522719i	−0.976542	+	0.215327i	$0.930918\pi$
$44$	5.74858	−	3.31895i	0.866632	−	0.500350i
$45$			3.01683i			0.449722i
$46$		−	9.13658i		−	1.34711i
$47$	−8.00565	+	4.62206i	−1.16774	+	0.674197i	−0.953148	−	0.302505i	$-0.902177\pi$
$47$	−8.00565	+	4.62206i	−1.16774	+	0.674197i	−0.214597	+	0.976703i	$0.568844\pi$
$48$	−2.87633	−	4.98195i	−0.415162	−	0.719082i
$49$	5.12914	+	4.76361i	0.732734	+	0.680515i
$50$	−8.90014	−	5.13850i	−1.25867	−	0.726693i
$51$	0.757096	+	1.31133i	0.106015	+	0.183623i
$52$	3.51909	+	15.0219i	0.488010	+	2.08316i
$53$	3.90722	−	6.76751i	0.536698	−	0.929588i	−0.462381	−	0.886681i	$-0.653005\pi$
$53$	3.90722	−	6.76751i	0.536698	−	0.929588i	0.999079	−	0.0429071i	$-0.0136619\pi$
$54$		−	2.50582i		−	0.340999i
$55$	−2.33989	+	4.05281i	−0.315511	+	0.546481i
$56$	5.52362	−	14.0643i	0.738124	−	1.87942i
$57$		−	8.21689i		−	1.08835i
$58$	−11.9367	−	6.89168i	−1.56737	−	0.904921i
$59$			10.0204i			1.30455i	0.757982	+	0.652275i	$0.226185\pi$
$59$			10.0204i			1.30455i	−0.757982	+	0.652275i	$0.773815\pi$
$60$	11.1799	+	6.45469i	1.44331	+	0.833297i
$61$	5.23565	−	9.06841i	0.670356	−	1.16109i	−0.307447	−	0.951565i	$-0.599475\pi$
$61$	5.23565	−	9.06841i	0.670356	−	1.16109i	0.977803	−	0.209526i	$-0.0671920\pi$
$62$	−6.47877	+	11.2216i	−0.822804	+	1.42514i
$63$	2.06892	−	1.64912i	0.260659	−	0.207769i
$64$	4.00548			0.500685
$65$	−7.44391	−	7.93124i	−0.923303	−	0.983749i
$66$	1.94355	−	3.36632i	0.239234	−	0.414365i
$67$	2.52349	−	1.45694i	0.308294	−	0.177994i	−0.337869	−	0.941193i	$-0.609706\pi$
$67$	2.52349	−	1.45694i	0.308294	−	0.177994i	0.646163	+	0.763200i	$0.276373\pi$
$68$	6.47941			0.785744
$69$	−1.82307	−	3.15765i	−0.219472	−	0.380137i
$70$	2.97635	+	19.7782i	0.355742	+	2.36395i
$71$	−1.11232	+	0.642201i	−0.132009	+	0.0762152i	−0.564550	−	0.825399i	$-0.690950\pi$
$71$	−1.11232	+	0.642201i	−0.132009	+	0.0762152i	0.432541	+	0.901614i	$0.357617\pi$
$72$	−4.94593	−	2.85554i	−0.582884	−	0.336528i
$73$	−2.27528	−	1.31363i	−0.266301	−	0.153749i	0.360905	−	0.932603i	$-0.382468\pi$
$73$	−2.27528	−	1.31363i	−0.266301	−	0.153749i	−0.627205	+	0.778854i	$0.715801\pi$
$74$	−23.0549			−2.68008
$75$	−4.10125			−0.473572
$76$	−30.4504	−	17.5805i	−3.49290	−	2.01663i
$77$	4.05846	−	0.610745i	0.462505	−	0.0696008i
$78$	6.18301	+	6.58779i	0.700088	+	0.745921i
$79$	−3.28050	−	5.68199i	−0.369085	−	0.639274i	0.620338	−	0.784335i	$-0.286996\pi$
$79$	−3.28050	−	5.68199i	−0.369085	−	0.639274i	−0.989423	+	0.145061i	$0.953662\pi$
$80$	15.0297	−	8.67739i	1.68037	−	0.970161i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.12718	−	7.14848i	0.455770	−	0.789417i
$83$		−	5.49127i		−	0.602746i	−0.953506	−	0.301373i	$-0.902555\pi$
$83$		−	5.49127i		−	0.602746i	0.953506	−	0.301373i	$-0.0974449\pi$
$84$	−1.68476	−	11.1954i	−0.183823	−	1.22152i
$85$	−3.95605	+	2.28403i	−0.429094	+	0.247738i
$86$	−8.58919	+	4.95897i	−0.926196	+	0.534740i
$87$	−5.50054			−0.589720
$88$	−4.42958	−	7.67226i	−0.472195	−	0.817866i
$89$			9.76396i			1.03498i	0.855690	+	0.517489i	$0.173133\pi$
$89$			9.76396i			1.03498i	−0.855690	+	0.517489i	$0.826867\pi$
$90$	7.55962			0.796854
$91$	−1.37005	+	9.44050i	−0.143620	+	0.989633i
$92$	−15.6023			−1.62665
$93$			5.17098i			0.536206i
$94$	11.5821	+	20.0607i	1.19460	+	2.06910i
$95$	24.7889			2.54329
$96$	−2.59199	+	1.49648i	−0.264544	+	0.152734i
$97$	10.8340	−	6.25500i	1.10002	−	0.635099i	0.163796	−	0.986494i	$-0.447626\pi$
$97$	10.8340	−	6.25500i	1.10002	−	0.635099i	0.936227	+	0.351395i	$0.114293\pi$
$98$	11.9367	−	12.8527i	1.20579	−	1.29832i
$99$		−	1.55123i		−	0.155904i
$100$	−8.77489	+	15.1985i	−0.877489	+	1.51985i
$101$	5.79380	+	10.0352i	0.576505	+	0.998536i	0.995876	+	0.0907209i	$0.0289171\pi$
$101$	5.79380	+	10.0352i	0.576505	+	0.998536i	−0.419372	+	0.907815i	$0.637750\pi$
$102$	3.28595	−	1.89714i	0.325358	−	0.187845i
$103$	−0.750179	−	1.29935i	−0.0739174	−	0.128029i	0.826698	−	0.562647i	$-0.190217\pi$
$103$	−0.750179	−	1.29935i	−0.0739174	−	0.128029i	−0.900615	+	0.434618i	$0.856883\pi$
$104$	20.0488	−	4.69670i	1.96594	−	0.460549i
$105$	4.97510	+	6.24157i	0.485520	+	0.609115i
$106$	−16.9581	−	9.79079i	−1.64712	−	0.950965i
$107$	20.2334			1.95604			0.978018	−	0.208522i	$-0.0668654\pi$
$107$	20.2334			1.95604			0.978018	+	0.208522i	$0.0668654\pi$
$108$	−4.27912			−0.411759
$109$	1.55541	+	0.898018i	0.148982	+	0.0860145i	0.572638	−	0.819809i	$-0.305920\pi$
$109$	1.55541	+	0.898018i	0.148982	+	0.0860145i	−0.423656	+	0.905823i	$0.639254\pi$
$110$	10.1556	+	5.86335i	0.968300	+	0.559048i
$111$	−7.96792	+	4.60028i	−0.756281	+	0.436639i
$112$	−14.1667	−	5.56384i	−1.33863	−	0.525733i
$113$	8.44912	+	14.6343i	0.794826	+	1.37668i	0.922950	+	0.384921i	$0.125771\pi$
$113$	8.44912	+	14.6343i	0.794826	+	1.37668i	−0.128124	+	0.991758i	$0.540895\pi$
$114$	−20.5900			−1.92843
$115$	9.52610	−	5.49990i	0.888313	−	0.512868i
$116$	−11.7687	+	20.3841i	−1.09270	+	1.89261i
$117$	3.45138	+	1.04305i	0.319081	+	0.0964299i
$118$	25.1094			2.31151
$119$	3.72890	+	1.46449i	0.341828	+	0.134250i
$120$	8.61466	−	14.9210i	0.786407	−	1.36210i
$121$	−4.29685	+	7.44236i	−0.390622	+	0.676578i
$122$	−22.7238	−	13.1196i	−2.05732	−	1.18779i
$123$		−	3.29407i		−	0.297017i
$124$	19.1628	+	11.0636i	1.72087	+	0.993544i
$125$			2.71137i			0.242512i
$126$	−4.13238	−	5.18433i	−0.368142	−	0.461857i
$127$	−5.34134	+	9.25146i	−0.473967	+	0.820935i	−0.999556	−	0.0298040i	$-0.990512\pi$
$127$	−5.34134	+	9.25146i	−0.473967	+	0.820935i	0.525589	+	0.850739i	$0.323845\pi$
$128$		−	16.0229i		−	1.41624i
$129$	−1.97898	+	3.42770i	−0.174240	+	0.301792i
$130$	−19.8742	+	18.6531i	−1.74309	+	1.63598i
$131$	−0.296957	−	0.514345i	−0.0259453	−	0.0449386i	0.852761	−	0.522301i	$-0.174926\pi$
$131$	−0.296957	−	0.514345i	−0.0259453	−	0.0449386i	−0.878707	+	0.477362i	$0.841593\pi$
$132$	−5.74858	−	3.31895i	−0.500350	−	0.288877i
$133$	−13.5506	−	17.0001i	−1.17499	−	1.47409i
$134$	−3.65083	−	6.32342i	−0.315383	−	0.546260i
$135$	2.61265	−	1.50841i	0.224861	−	0.129824i
$136$		−	8.64765i		−	0.741530i
$137$		−	5.01081i		−	0.428102i	−0.976822	−	0.214051i	$-0.931334\pi$
$137$		−	5.01081i		−	0.428102i	0.976822	−	0.214051i	$-0.0686659\pi$
$138$	−7.91251	+	4.56829i	−0.673557	+	0.388878i
$139$	8.33459	+	14.4359i	0.706930	+	1.22444i	0.965990	+	0.258578i	$0.0832539\pi$
$139$	8.33459	+	14.4359i	0.706930	+	1.22444i	−0.259060	+	0.965861i	$0.583413\pi$
$140$	33.7747	−	5.08265i	2.85449	−	0.429562i
$141$	8.00565	+	4.62206i	0.674197	+	0.389248i
$142$	1.60924	+	2.78728i	0.135044	+	0.233903i
$143$	3.82759	+	4.07817i	0.320079	+	0.341034i
$144$	−2.87633	+	4.98195i	−0.239694	+	0.415162i
$145$		−	16.5942i		−	1.37807i
$146$	−3.29172	+	5.70143i	−0.272425	+	0.471853i
$147$	1.56084	−	6.82377i	0.128736	−	0.562815i
$148$			39.3703i			3.23622i
$149$	1.75459	+	1.01301i	0.143742	+	0.0829892i	0.570146	−	0.821543i	$-0.306887\pi$
$149$	1.75459	+	1.01301i	0.143742	+	0.0829892i	−0.426404	+	0.904533i	$0.640220\pi$
$150$			10.2770i			0.839113i
$151$	−8.08579	−	4.66833i	−0.658012	−	0.379904i	0.133507	−	0.991048i	$-0.457376\pi$
$151$	−8.08579	−	4.66833i	−0.658012	−	0.379904i	−0.791519	+	0.611144i	$0.790710\pi$
$152$	−23.4636	+	40.6402i	−1.90315	+	3.29635i
$153$	0.757096	−	1.31133i	0.0612076	−	0.106015i
$154$	−1.53042	−	10.1698i	−0.123324	−	0.819504i
$155$	−15.6000			−1.25302
$156$	11.2498	−	10.5586i	0.900706	−	0.845363i
$157$	−5.90209	+	10.2227i	−0.471038	+	0.815862i	−0.999451	−	0.0331251i	$-0.989454\pi$
$157$	−5.90209	+	10.2227i	−0.471038	+	0.815862i	0.528413	+	0.848988i	$0.322787\pi$
$158$	−14.2380	+	8.22033i	−1.13272	+	0.653975i
$159$	−7.81444			−0.619726
$160$	−4.51464	−	7.81958i	−0.356913	−	0.618192i
$161$	−8.97912	−	3.52647i	−0.707654	−	0.277925i
$162$	−2.17010	+	1.25291i	−0.170499	+	0.0984378i
$163$	0.513048	+	0.296209i	0.0401850	+	0.0232008i	0.519958	−	0.854192i	$-0.325948\pi$
$163$	0.513048	+	0.296209i	0.0401850	+	0.0232008i	−0.479773	+	0.877393i	$0.659281\pi$
$164$	−12.2073	−	7.04788i	−0.953228	−	0.550347i
$165$	4.67979			0.364321
$166$	−13.7601			−1.06799
$167$	7.52026	+	4.34182i	0.581935	+	0.335980i	0.761902	−	0.647692i	$-0.224266\pi$
$167$	7.52026	+	4.34182i	0.581935	+	0.335980i	−0.179967	+	0.983673i	$0.557599\pi$
$168$	−14.9418	+	2.24855i	−1.15279	+	0.173479i
$169$	−11.6474	+	5.77398i	−0.895951	+	0.444153i
$170$	5.72336	+	9.91315i	0.438962	+	0.760304i
$171$	−7.11603	+	4.10844i	−0.544177	+	0.314181i
$172$	8.46831	+	14.6676i	0.645703	+	1.11839i
$173$	−6.87952	+	11.9157i	−0.523041	+	0.905933i	0.476600	+	0.879120i	$0.341869\pi$
$173$	−6.87952	+	11.9157i	−0.523041	+	0.905933i	−0.999640	+	0.0268126i	$0.991464\pi$
$174$			13.7834i			1.04491i
$175$	−8.48515	+	6.76344i	−0.641417	+	0.511268i
$176$	−7.72813	+	4.46184i	−0.582530	+	0.336324i
$177$	8.67795	−	5.01022i	0.652275	−	0.376591i
$178$	24.4667			1.83386
$179$	−0.535312	−	0.927188i	−0.0400111	−	0.0693013i	0.845326	−	0.534250i	$-0.179406\pi$
$179$	−0.535312	−	0.927188i	−0.0400111	−	0.0693013i	−0.885337	+	0.464949i	$0.846073\pi$
$180$		−	12.9094i		−	0.962209i
$181$	9.60905			0.714235			0.357117	−	0.934059i	$-0.383760\pi$
$181$	9.60905			0.714235			0.357117	+	0.934059i	$0.383760\pi$
$182$	23.6562	+	3.43310i	1.75351	+	0.254478i
$183$	−10.4713			−0.774061
$184$			20.8234i			1.53512i
$185$	−13.8783	−	24.0378i	−1.02035	−	1.76730i
$186$	12.9575			0.950093
$187$	2.03417	−	1.17443i	0.148753	−	0.0858826i
$188$	34.2572	−	19.7784i	2.49846	−	1.44249i
$189$	−2.46263	−	0.967177i	−0.179130	−	0.0703518i
$190$		−	62.1166i		−	4.50641i
$191$	10.5179	−	18.2176i	0.761051	−	1.31818i	−0.181258	−	0.983436i	$-0.558017\pi$
$191$	10.5179	−	18.2176i	0.761051	−	1.31818i	0.942309	−	0.334744i	$-0.108650\pi$
$192$	−2.00274	−	3.46885i	−0.144535	−	0.250342i
$193$	6.81659	−	3.93556i	0.490669	−	0.283288i	−0.234183	−	0.972193i	$-0.575241\pi$
$193$	6.81659	−	3.93556i	0.490669	−	0.283288i	0.724852	+	0.688905i	$0.241908\pi$
$194$	−15.6739	−	27.1480i	−1.12532	−	1.94911i
$195$	−3.14670	+	10.4122i	−0.225340	+	0.745635i
$196$	−21.9482	−	20.3841i	−1.56773	−	1.45600i
$197$	0.193007	+	0.111433i	0.0137512	+	0.00793924i	0.506860	−	0.862028i	$-0.330806\pi$
$197$	0.193007	+	0.111433i	0.0137512	+	0.00793924i	−0.493109	+	0.869968i	$0.664140\pi$
$198$	−3.88709			−0.276244
$199$	−11.6258			−0.824133			−0.412067	−	0.911154i	$-0.635193\pi$
$199$	−11.6258			−0.824133			−0.412067	+	0.911154i	$0.635193\pi$
$200$	20.2845	+	11.7113i	1.43433	+	0.828112i
$201$	−2.52349	−	1.45694i	−0.177994	−	0.102765i
$202$	25.1463	−	14.5182i	1.76929	−	1.02150i
$203$	−11.3802	+	9.07103i	−0.798731	+	0.636661i
$204$	−3.23971	−	5.61134i	−0.226825	−	0.392872i
$205$	9.93766			0.694076
$206$	−3.25593	+	1.87981i	−0.226852	+	0.130973i
$207$	−1.82307	+	3.15765i	−0.126712	+	0.219472i
$208$	−4.73090	−	20.1948i	−0.328029	−	1.40025i
$209$	−12.7463			−0.881677
$210$	15.6402	−	12.4667i	1.07928	−	0.860283i
$211$	8.79477	−	15.2330i	0.605457	−	1.04868i	−0.386522	−	0.922280i	$-0.626324\pi$
$211$	8.79477	−	15.2330i	0.605457	−	1.04868i	0.991979	−	0.126402i	$-0.0403430\pi$
$212$	−16.7195	+	28.9590i	−1.14830	+	1.98891i
$213$	1.11232	+	0.642201i	0.0762152	+	0.0440029i
$214$		−	50.7012i		−	3.46586i
$215$	−10.3408	−	5.97025i	−0.705235	−	0.407168i
$216$			5.71107i			0.388589i
$217$	8.52754	+	10.6983i	0.578887	+	0.726250i
$218$	2.25027	−	3.89758i	0.152408	−	0.263978i
$219$			2.62726i			0.177534i
$220$	10.0127	−	17.3425i	0.675056	−	1.16923i
$221$	1.24525	+	5.31558i	0.0837645	+	0.357565i
$222$	11.5275	+	19.9662i	0.773673	+	1.34004i
$223$	−15.7545	−	9.09585i	−1.05500	−	0.609103i	−0.130953	−	0.991389i	$-0.541804\pi$
$223$	−15.7545	−	9.09585i	−1.05500	−	0.609103i	−0.924044	+	0.382285i	$0.875137\pi$
$224$	−2.89473	+	7.37059i	−0.193412	+	0.492468i
$225$	2.05063	+	3.55179i	0.136708	+	0.236786i
$226$	36.6709	−	21.1719i	2.43931	−	1.40834i
$227$			20.6069i			1.36773i	0.729610	+	0.683863i	$0.239701\pi$
$227$			20.6069i			1.36773i	−0.729610	+	0.683863i	$0.760299\pi$
$228$			35.1611i			2.32860i
$229$	−6.95359	+	4.01466i	−0.459506	+	0.265296i	−0.711837	−	0.702345i	$-0.752136\pi$
$229$	−6.95359	+	4.01466i	−0.459506	+	0.265296i	0.252330	+	0.967641i	$0.418803\pi$
$230$	−13.7817	−	23.8707i	−0.908741	−	1.57399i
$231$	−2.55815	−	3.20936i	−0.168314	−	0.211160i
$232$	27.2053	+	15.7070i	1.78612	+	1.03121i
$233$	7.15034	+	12.3848i	0.468434	+	0.811352i	0.999349	−	0.0360731i	$-0.0114849\pi$
$233$	7.15034	+	12.3848i	0.468434	+	0.811352i	−0.530915	+	0.847425i	$0.678152\pi$
$234$	2.61369	−	8.64854i	0.170862	−	0.565373i
$235$	−13.9440	+	24.1517i	−0.909605	+	1.57548i
$236$		−	42.8787i		−	2.79117i
$237$	−3.28050	+	5.68199i	−0.213091	+	0.369085i
$238$	3.66975	−	9.34394i	0.237874	−	0.605678i
$239$			4.31863i			0.279349i	0.990197	+	0.139674i	$0.0446056\pi$
$239$			4.31863i			0.279349i	−0.990197	+	0.139674i	$0.955394\pi$
$240$	−15.0297	−	8.67739i	−0.970161	−	0.560123i
$241$		−	1.32960i		−	0.0856468i	−0.999083	−	0.0428234i	$-0.986365\pi$
$241$		−	1.32960i		−	0.0856468i	0.999083	−	0.0428234i	$-0.0136353\pi$
$242$	18.6492	+	10.7671i	1.19882	+	0.692137i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−22.4040	+	38.8049i	−1.43427	+	2.48423i
$245$	20.5861	+	4.70878i	1.31520	+	0.300833i
$246$	−8.25435			−0.526278
$247$	8.57062	−	28.3596i	0.545335	−	1.80448i
$248$	14.7659	−	25.5753i	0.937637	−	1.62403i
$249$	−4.75558	+	2.74564i	−0.301373	+	0.173998i
$250$	6.79419			0.429702
$251$	1.13399	+	1.96413i	0.0715769	+	0.123975i	0.899593	−	0.436730i	$-0.143864\pi$
$251$	1.13399	+	1.96413i	0.0715769	+	0.123975i	−0.828016	+	0.560705i	$0.810530\pi$
$252$	−8.85315	+	7.05677i	−0.557696	+	0.444535i
$253$	−4.89824	+	2.82800i	−0.307950	+	0.177795i
$254$	23.1825	+	13.3844i	1.45460	+	0.839813i
$255$	3.95605	+	2.28403i	0.247738	+	0.143031i
$256$	−32.1396			−2.00873
$257$	−11.8482			−0.739073			−0.369537	−	0.929216i	$-0.620484\pi$
$257$	−11.8482			−0.739073			−0.369537	+	0.929216i	$0.620484\pi$
$258$	8.58919	+	4.95897i	0.534740	+	0.308732i
$259$	−8.89857	+	22.6576i	−0.552930	+	1.40788i
$260$	31.8534	+	33.9388i	1.97546	+	2.10479i
$261$	2.75027	+	4.76361i	0.170237	+	0.294860i
$262$	−1.28886	+	0.744121i	−0.0796258	+	0.0459720i
$263$	10.4383	+	18.0797i	0.643655	+	1.11484i	0.984610	+	0.174764i	$0.0559161\pi$
$263$	10.4383	+	18.0797i	0.643655	+	1.11484i	−0.340955	+	0.940079i	$0.610751\pi$
$264$	−4.42958	+	7.67226i	−0.272622	+	0.472195i
$265$		−	23.5748i		−	1.44819i
$266$	−42.5991	+	33.9553i	−2.61192	+	2.08194i
$267$	8.45584	−	4.88198i	0.517489	−	0.298772i
$268$	−10.7983	+	6.23443i	−0.659614	+	0.380828i
$269$	−12.3198			−0.751149			−0.375574	−	0.926792i	$-0.622555\pi$
$269$	−12.3198			−0.751149			−0.375574	+	0.926792i	$0.622555\pi$
$270$	−3.77981	−	6.54683i	−0.230032	−	0.398427i
$271$			20.6751i			1.25592i	0.778245	+	0.627960i	$0.216110\pi$
$271$			20.6751i			1.25592i	−0.778245	+	0.627960i	$0.783890\pi$
$272$	−8.71062			−0.528159
$273$	8.86073	−	3.53375i	0.536276	−	0.213872i
$274$	−12.5562			−0.758546
$275$			6.36197i			0.383642i
$276$	7.80115	+	13.5120i	0.469574	+	0.813326i
$277$	−7.10329			−0.426796			−0.213398	−	0.976965i	$-0.568453\pi$
$277$	−7.10329			−0.426796			−0.213398	+	0.976965i	$0.568453\pi$
$278$	36.1738	−	20.8850i	2.16956	−	1.25260i
$279$	4.47820	−	2.58549i	0.268103	−	0.154789i
$280$	−6.78348	−	45.0769i	−0.405390	−	2.69386i
$281$		−	25.8932i		−	1.54466i	−0.635223	−	0.772329i	$-0.719092\pi$
$281$		−	25.8932i		−	1.54466i	0.635223	−	0.772329i	$-0.280908\pi$
$282$	11.5821	−	20.0607i	0.689701	−	1.19460i
$283$	−13.0984	−	22.6872i	−0.778621	−	1.34861i	−0.932737	−	0.360559i	$-0.882586\pi$
$283$	−13.0984	−	22.6872i	−0.778621	−	1.34861i	0.154115	−	0.988053i	$-0.450747\pi$
$284$	4.75977	−	2.74806i	0.282441	−	0.163067i
$285$	−12.3945	−	21.4679i	−0.734185	−	1.27165i
$286$	10.2192	−	9.59125i	0.604272	−	0.567143i
$287$	−5.43231	−	6.81517i	−0.320659	−	0.402287i
$288$	2.59199	+	1.49648i	0.152734	+	0.0881812i
$289$	−14.7072			−0.865131
$290$	−41.5820			−2.44178
$291$	−10.8340	−	6.25500i	−0.635099	−	0.366674i
$292$	9.73619	+	5.62119i	0.569767	+	0.328955i
$293$	7.57306	−	4.37231i	0.442423	−	0.255433i	−0.262202	−	0.965013i	$-0.584449\pi$
$293$	7.57306	−	4.37231i	0.442423	−	0.255433i	0.704625	+	0.709580i	$0.251115\pi$
$294$	−17.0991	−	3.91117i	−0.997241	−	0.228104i
$295$	15.1150	+	26.1799i	0.880028	+	1.52425i
$296$	52.5451			3.05412
$297$	−1.34340	+	0.775614i	−0.0779521	+	0.0450057i
$298$	2.53843	−	4.39668i	0.147047	−	0.254693i
$299$	−2.99853	−	12.7998i	−0.173410	−	0.740233i
$300$	17.5498			1.01324
$301$	1.55832	+	10.3552i	0.0898200	+	0.596864i
$302$	−11.6980	+	20.2615i	−0.673144	+	1.16592i
$303$	5.79380	−	10.0352i	0.332845	−	0.576505i
$304$	40.9361	+	23.6345i	2.34785	+	1.35553i
$305$		−	31.5901i		−	1.80884i
$306$	−3.28595	−	1.89714i	−0.187845	−	0.108453i
$307$		−	1.43567i		−	0.0819379i	−0.999160	−	0.0409689i	$-0.986956\pi$
$307$		−	1.43567i		−	0.0819379i	0.999160	−	0.0409689i	$-0.0130445\pi$
$308$	−17.3667	+	2.61345i	−0.989558	+	0.148915i
$309$	−0.750179	+	1.29935i	−0.0426762	+	0.0739174i
$310$			39.0907i			2.22020i
$311$	11.8624	−	20.5463i	0.672655	−	1.16507i	−0.304494	−	0.952514i	$-0.598487\pi$
$311$	11.8624	−	20.5463i	0.672655	−	1.16507i	0.977148	−	0.212558i	$-0.0681794\pi$
$312$	−14.0918	−	15.0144i	−0.797794	−	0.850023i
$313$	10.9459	+	18.9588i	0.618697	+	1.07161i	0.989724	+	0.142993i	$0.0456725\pi$
$313$	10.9459	+	18.9588i	0.618697	+	1.07161i	−0.371027	+	0.928622i	$0.620994\pi$
$314$	25.6163	+	14.7896i	1.44561	+	0.834624i
$315$	2.91781	−	7.42935i	0.164400	−	0.418596i
$316$	14.0377	+	24.3139i	0.789680	+	1.36777i
$317$	−25.9713	+	14.9946i	−1.45869	+	0.842178i	−0.998947	−	0.0458717i	$-0.985393\pi$
$317$	−25.9713	+	14.9946i	−1.45869	+	0.842178i	−0.459748	+	0.888050i	$0.652060\pi$
$318$			19.5816i			1.09808i
$319$			8.53259i			0.477733i
$320$	10.4649	−	6.04192i	0.585006	−	0.337754i
$321$	−10.1167	−	17.5226i	−0.564659	−	0.978018i
$322$	−8.83669	+	22.5000i	−0.492449	+	1.25388i
$323$	−10.7750	−	6.22097i	−0.599539	−	0.346144i
$324$	2.13956	+	3.70583i	0.118865	+	0.205879i
$325$	−14.1550	−	4.27781i	−0.785178	−	0.237290i
$326$	0.742245	−	1.28561i	0.0411091	−	0.0712031i
$327$		−	1.79604i		−	0.0993210i
$328$	−9.40635	+	16.2923i	−0.519379	+	0.899590i
$329$	24.1853	−	3.63957i	1.33338	−	0.200656i
$330$		−	11.7267i		−	0.645533i
$331$	−14.1672	−	8.17942i	−0.778698	−	0.449581i	0.0572707	−	0.998359i	$-0.481760\pi$
$331$	−14.1672	−	8.17942i	−0.778698	−	0.449581i	−0.835969	+	0.548777i	$0.815094\pi$
$332$			23.4978i			1.28961i
$333$	7.96792	+	4.60028i	0.436639	+	0.252094i
$334$	10.8798	−	18.8444i	0.595317	−	1.03112i
$335$	4.39534	−	7.61295i	0.240143	−	0.415940i
$336$	2.26492	+	15.0506i	0.123562	+	0.821079i
$337$	30.4117			1.65663			0.828316	−	0.560261i	$-0.189299\pi$
$337$	30.4117			1.65663			0.828316	+	0.560261i	$0.189299\pi$
$338$	14.4686	+	29.1862i	0.786985	+	1.58752i
$339$	8.44912	−	14.6343i	0.458893	−	0.794826i
$340$	16.9284	−	9.77364i	0.918073	−	0.530050i
$341$	8.02136			0.434381
$342$	10.2950	+	17.8315i	0.556691	+	0.964216i
$343$	−8.02394	−	16.6918i	−0.433252	−	0.901273i
$344$	19.5758	−	11.3021i	1.05546	−	0.609369i
$345$	−9.52610	−	5.49990i	−0.512868	−	0.296104i
$346$	29.8585	+	17.2388i	1.60521	+	0.926766i
$347$	15.3067			0.821707			0.410854	−	0.911701i	$-0.365231\pi$
$347$	15.3067			0.821707			0.410854	+	0.911701i	$0.365231\pi$
$348$	23.5375			1.26174
$349$	8.28543	+	4.78359i	0.443509	+	0.256060i	0.705085	−	0.709123i	$-0.250909\pi$
$349$	8.28543	+	4.78359i	0.443509	+	0.256060i	−0.261576	+	0.965183i	$0.584242\pi$
$350$	16.9479	+	21.2623i	0.905906	+	1.13652i
$351$	−0.822385	−	3.51051i	−0.0438957	−	0.187377i
$352$	2.32139	+	4.02076i	0.123730	+	0.214307i
$353$	−10.8166	+	6.24499i	−0.575711	+	0.332387i	−0.759427	−	0.650592i	$-0.774521\pi$
$353$	−10.8166	+	6.24499i	−0.575711	+	0.332387i	0.183716	+	0.982979i	$0.441187\pi$
$354$	−12.5547	−	21.7454i	−0.667275	−	1.15575i
$355$	−1.93741	+	3.35569i	−0.102827	+	0.178102i
$356$		−	41.7812i		−	2.21440i
$357$	−0.596163	−	3.96157i	−0.0315523	−	0.209668i
$358$	−2.32337	+	1.34140i	−0.122794	+	0.0708950i
$359$	−9.56860	+	5.52443i	−0.505012	+	0.291569i	−0.730781	−	0.682612i	$-0.760844\pi$
$359$	−9.56860	+	5.52443i	−0.505012	+	0.291569i	0.225769	+	0.974181i	$0.427510\pi$
$360$	−17.2293			−0.908065
$361$	24.2586	+	42.0172i	1.27677	+	2.21143i
$362$		−	24.0785i		−	1.26554i
$363$	8.59369			0.451052
$364$	5.86262	−	40.3971i	0.307285	−	2.11738i
$365$	−7.92600			−0.414866
$366$			26.2392i			1.37154i
$367$	6.46083	+	11.1905i	0.337253	+	0.584139i	0.983915	−	0.178638i	$-0.0571690\pi$
$367$	6.46083	+	11.1905i	0.337253	+	0.584139i	−0.646662	+	0.762776i	$0.723836\pi$
$368$	20.9750			1.09340
$369$	−2.85275	+	1.64704i	−0.148508	+	0.0857413i
$370$	−60.2345	+	34.7764i	−3.13144	+	1.80794i
$371$	−16.1674	+	12.8869i	−0.839371	+	0.669055i
$372$		−	22.1273i		−	1.14725i
$373$	4.51383	−	7.81818i	0.233717	−	0.404810i	−0.725182	−	0.688557i	$-0.758244\pi$
$373$	4.51383	−	7.81818i	0.233717	−	0.404810i	0.958899	+	0.283747i	$0.0915777\pi$
$374$	−2.94290	−	5.09725i	−0.152174	−	0.263573i
$375$	2.34811	−	1.35568i	0.121256	−	0.0700071i
$376$	−26.3969	−	45.7208i	−1.36132	−	2.35787i
$377$	−18.9845	−	5.73733i	−0.977750	−	0.295488i
$378$	−2.42357	+	6.17091i	−0.124655	+	0.317398i
$379$	−14.6856	−	8.47871i	−0.754346	−	0.435522i	0.0729159	−	0.997338i	$-0.476770\pi$
$379$	−14.6856	−	8.47871i	−0.754346	−	0.435522i	−0.827262	+	0.561816i	$0.810103\pi$
$380$	−106.075			−5.44153
$381$	10.6827			0.547290
$382$	−45.6500	−	26.3560i	−2.33566	−	1.34849i
$383$	1.77758	+	1.02629i	0.0908303	+	0.0524409i	0.544727	−	0.838613i	$-0.316633\pi$
$383$	1.77758	+	1.02629i	0.0908303	+	0.0524409i	−0.453897	+	0.891054i	$0.649967\pi$
$384$	−13.8763	+	8.01147i	−0.708120	+	0.408834i
$385$	9.68209	−	7.71751i	0.493445	−	0.393321i
$386$	−9.86180	−	17.0811i	−0.501953	−	0.869407i
$387$	3.95797			0.201195
$388$	−46.3599	+	26.7659i	−2.35357	+	1.35883i
$389$	15.7463	−	27.2733i	0.798367	−	1.38281i	−0.122312	−	0.992492i	$-0.539031\pi$
$389$	15.7463	−	27.2733i	0.798367	−	1.38281i	0.920679	−	0.390321i	$-0.127636\pi$
$390$	26.0912	+	7.88506i	1.32118	+	0.399275i
$391$	−5.52096			−0.279207
$392$	−27.2053	+	29.2929i	−1.37408	+	1.47951i
$393$	−0.296957	+	0.514345i	−0.0149795	+	0.0259453i
$394$	0.279230	−	0.483640i	0.0140674	−	0.0243654i
$395$	−17.1416	−	9.89670i	−0.862487	−	0.497957i
$396$			6.63789i			0.333567i
$397$	−10.0156	−	5.78251i	−0.502668	−	0.290216i	0.227147	−	0.973861i	$-0.427060\pi$
$397$	−10.0156	−	5.78251i	−0.502668	−	0.290216i	−0.729815	+	0.683645i	$0.760394\pi$
$398$			29.1322i			1.46027i
$399$	−7.94719	+	20.2352i	−0.397857	+	1.01303i
$400$	11.7965	−	20.4322i	0.589827	−	1.02161i
$401$			4.25609i			0.212539i	0.994337	+	0.106270i	$0.0338906\pi$
$401$			4.25609i			0.212539i	−0.994337	+	0.106270i	$0.966109\pi$
$402$	−3.65083	+	6.32342i	−0.182087	+	0.315383i
$403$	−5.39358	+	17.8470i	−0.268674	+	0.889024i
$404$	−24.7924	−	42.9417i	−1.23347	−	2.13643i
$405$	−2.61265	−	1.50841i	−0.129824	−	0.0749537i
$406$	22.7303	+	28.5166i	1.12809	+	1.41526i
$407$	7.13608	+	12.3601i	0.353722	+	0.612665i
$408$	−7.48909	+	4.32383i	−0.370765	+	0.214061i
$409$			11.0739i			0.547570i	0.961791	+	0.273785i	$0.0882756\pi$
$409$			11.0739i			0.547570i	−0.961791	+	0.273785i	$0.911724\pi$
$410$		−	24.9020i		−	1.22982i
$411$	−4.33949	+	2.50540i	−0.214051	+	0.123582i
$412$	3.21011	+	5.56008i	0.158151	+	0.273925i
$413$	9.69154	−	24.6767i	0.476889	−	1.21426i
$414$	7.91251	+	4.56829i	0.388878	+	0.224519i
$415$	−8.28311	−	14.3468i	−0.406602	−	0.704255i
$416$	−10.5068	+	2.46137i	−0.515140	+	0.120679i
$417$	8.33459	−	14.4359i	0.408146	−	0.706930i
$418$			31.9398i			1.56223i
$419$	−1.10511	+	1.91411i	−0.0539884	+	0.0935106i	−0.891757	−	0.452515i	$-0.850527\pi$
$419$	−1.10511	+	1.91411i	−0.0539884	+	0.0935106i	0.837768	+	0.546026i	$0.183860\pi$
$420$	−21.2891	−	26.7084i	−1.03880	−	1.30324i
$421$			15.9741i			0.778532i	0.921125	+	0.389266i	$0.127271\pi$
$421$			15.9741i			0.778532i	−0.921125	+	0.389266i	$0.872729\pi$
$422$	−38.1711	−	22.0381i	−1.85814	−	1.07280i
$423$		−	9.24413i		−	0.449465i
$424$	38.6497	+	22.3144i	1.87700	+	1.08368i
$425$	−3.10504	+	5.37809i	−0.150617	+	0.260876i
$426$	1.60924	−	2.78728i	0.0779678	−	0.135044i
$427$	−21.6642	+	17.2684i	−1.04841	+	0.835675i
$428$	−86.5812			−4.18506
$429$	1.61801	−	5.35388i	0.0781180	−	0.258488i
$430$	−14.9604	+	25.9121i	−0.721453	+	1.24959i
$431$	−20.4558	+	11.8102i	−0.985322	+	0.568876i	−0.903873	−	0.427802i	$-0.859288\pi$
$431$	−20.4558	+	11.8102i	−0.985322	+	0.568876i	−0.0814494	+	0.996677i	$0.525955\pi$
$432$	5.75266			0.276775
$433$	0.771302	+	1.33593i	0.0370664	+	0.0642009i	0.883963	−	0.467556i	$-0.154865\pi$
$433$	0.771302	+	1.33593i	0.0370664	+	0.0642009i	−0.846897	+	0.531757i	$0.821532\pi$
$434$	26.8081	−	21.3685i	1.28683	−	1.02572i
$435$	−14.3710	+	8.29709i	−0.689036	+	0.397815i
$436$	−6.65581	−	3.84273i	−0.318755	−	0.184033i
$437$	25.9461	+	14.9800i	1.24117	+	0.716590i
$438$	6.58344			0.314569
$439$	31.7140			1.51363			0.756813	−	0.653631i	$-0.226755\pi$
$439$	31.7140			1.51363			0.756813	+	0.653631i	$0.226755\pi$
$440$	−23.1459	−	13.3633i	−1.10344	−	0.637070i
$441$	−6.68997	+	2.06016i	−0.318570	+	0.0981028i
$442$	13.3199	−	3.12037i	0.633562	−	0.148421i
$443$	−3.37631	−	5.84795i	−0.160414	−	0.277844i	0.774604	−	0.632447i	$-0.217949\pi$
$443$	−3.37631	−	5.84795i	−0.160414	−	0.277844i	−0.935017	+	0.354603i	$0.884616\pi$
$444$	34.0957	−	19.6852i	1.61811	−	0.934217i
$445$	14.7281	+	25.5098i	0.698179	+	1.20928i
$446$	−22.7925	+	39.4778i	−1.07926	+	1.86933i
$447$		−	2.02603i		−	0.0958277i
$448$	−9.86403	−	3.87401i	−0.466032	−	0.183030i
$449$	−2.75752	+	1.59206i	−0.130136	+	0.0751338i	−0.563655	−	0.826011i	$-0.690605\pi$
$449$	−2.75752	+	1.59206i	−0.130136	+	0.0751338i	0.433519	+	0.901144i	$0.357272\pi$
$450$	8.90014	−	5.13850i	0.419557	−	0.242231i
$451$	−5.10986			−0.240614
$452$	−36.1548	−	62.6220i	−1.70058	−	2.94549i
$453$			9.33667i			0.438675i
$454$	51.6371			2.42345
$455$	10.6607	+	26.7313i	0.499782	+	1.25318i
$456$	46.9272			2.19757
$457$		−	27.2645i		−	1.27538i	−0.770293	−	0.637690i	$-0.779890\pi$
$457$		−	27.2645i		−	1.27538i	0.770293	−	0.637690i	$-0.220110\pi$
$458$	10.0600	+	17.4244i	0.470073	+	0.814190i
$459$	−1.51419			−0.0706764
$460$	−40.7634	+	23.5347i	−1.90060	+	1.09731i
$461$	−0.946746	+	0.546604i	−0.0440943	+	0.0254579i	−0.521885	−	0.853016i	$-0.674771\pi$
$461$	−0.946746	+	0.546604i	−0.0440943	+	0.0254579i	0.477791	+	0.878474i	$0.341438\pi$
$462$	−8.04207	+	6.41026i	−0.374151	+	0.298233i
$463$		−	4.50452i		−	0.209343i	−0.994507	−	0.104671i	$-0.966621\pi$
$463$		−	4.50452i		−	0.209343i	0.994507	−	0.104671i	$-0.0333791\pi$
$464$	15.8214	−	27.4034i	0.734488	−	1.27217i
$465$	7.79998	+	13.5100i	0.361715	+	0.626509i
$466$	31.0339	−	17.9175i	1.43762	−	0.830010i
$467$	5.98771	+	10.3710i	0.277078	+	0.479913i	0.970657	−	0.240467i	$-0.0773006\pi$
$467$	5.98771	+	10.3710i	0.277078	+	0.479913i	−0.693579	+	0.720380i	$0.743967\pi$
$468$	−14.7689	−	4.46334i	−0.682693	−	0.206318i
$469$	−7.62356	+	1.14724i	−0.352023	+	0.0529748i
$470$	60.5197	+	34.9411i	2.79157	+	1.61171i
$471$	11.8042			0.543908
$472$	−57.2274			−2.63411
$473$	5.31714	+	3.06985i	0.244482	+	0.141152i
$474$	14.2380	+	8.22033i	0.653975	+	0.377572i
$475$	29.1847	−	16.8498i	1.33908	−	0.773121i
$476$	−15.9564	−	6.26674i	−0.731362	−	0.287236i
$477$	3.90722	+	6.76751i	0.178899	+	0.309863i
$478$	10.8217			0.494973
$479$	−1.54966	+	0.894696i	−0.0708057	+	0.0408797i	−0.534985	−	0.844862i	$-0.679683\pi$
$479$	−1.54966	+	0.894696i	−0.0708057	+	0.0408797i	0.464179	+	0.885741i	$0.346349\pi$
$480$	−4.51464	+	7.81958i	−0.206064	+	0.356913i
$481$	−32.2987	+	7.56640i	−1.47269	+	0.344998i
$482$	−3.33173			−0.151756
$483$	1.43555	+	9.53938i	0.0653198	+	0.434057i
$484$	18.3867	−	31.8468i	0.835761	−	1.44758i
$485$	18.8703	−	32.6842i	0.856854	−	1.48411i
$486$	2.17010	+	1.25291i	0.0984378	+	0.0568331i
$487$		−	5.31496i		−	0.240844i	−0.992723	−	0.120422i	$-0.961575\pi$
$487$		−	5.31496i		−	0.240844i	0.992723	−	0.120422i	$-0.0384248\pi$
$488$	51.7903	+	29.9012i	2.34444	+	1.35356i
$489$		−	0.592417i		−	0.0267900i
$490$	11.7993	−	51.5851i	0.533040	−	2.33038i
$491$	9.96478	−	17.2595i	0.449704	−	0.778910i	−0.548662	−	0.836044i	$-0.684863\pi$
$491$	9.96478	−	17.2595i	0.449704	−	0.778910i	0.998367	+	0.0571337i	$0.0181961\pi$
$492$			14.0958i			0.635486i
$493$	−4.16444	+	7.21301i	−0.187557	+	0.324858i
$494$	−71.0641	−	21.4764i	−3.19732	−	0.966269i
$495$	−2.33989	−	4.05281i	−0.105170	−	0.182160i
$496$	−25.7615	−	14.8734i	−1.15673	−	0.667837i
$497$	3.36037	−	0.505691i	0.150733	−	0.0226833i
$498$	6.88007	+	11.9166i	0.308303	+	0.533997i
$499$	−27.9202	+	16.1198i	−1.24988	+	0.721620i	−0.971086	−	0.238731i	$-0.923269\pi$
$499$	−27.9202	+	16.1198i	−1.24988	+	0.721620i	−0.278796	+	0.960350i	$0.589935\pi$
$500$		−	11.6023i		−	0.518869i
$501$		−	8.68365i		−	0.387957i
$502$	4.92175	−	2.84158i	0.219669	−	0.126826i
$503$	−4.27646	−	7.40705i	−0.190678	−	0.330264i	0.754797	−	0.655958i	$-0.227735\pi$
$503$	−4.27646	−	7.40705i	−0.190678	−	0.330264i	−0.945475	+	0.325694i	$0.894402\pi$
$504$	9.41821	+	11.8157i	0.419521	+	0.526315i
$505$	30.2744	+	17.4789i	1.34719	+	0.777801i
$506$	7.08645	+	12.2741i	0.315031	+	0.545650i
$507$	10.8241	+	7.19992i	0.480715	+	0.319760i
$508$	22.8562	−	39.5882i	1.01408	−	1.75644i
$509$			13.4877i			0.597831i	0.954280	+	0.298915i	$0.0966248\pi$
$509$			13.4877i			0.597831i	−0.954280	+	0.298915i	$0.903375\pi$
$510$	5.72336	−	9.91315i	0.253435	−	0.438962i
$511$	4.33266	+	5.43559i	0.191666	+	0.240456i
$512$			48.4901i			2.14298i
$513$	7.11603	+	4.10844i	0.314181	+	0.181392i
$514$			29.6896i			1.30955i
$515$	−3.91991	−	2.26316i	−0.172732	−	0.0997269i
$516$	8.46831	−	14.6676i	0.372797	−	0.645703i
$517$	7.16987	−	12.4186i	0.315331	−	0.546169i
$518$	56.7759	+	22.2982i	2.49459	+	0.979727i
$519$	13.7590			0.603955
$520$	45.2959	−	42.5127i	1.98635	−	1.86430i
$521$	0.258151	−	0.447130i	0.0113098	−	0.0195891i	−0.860315	−	0.509763i	$-0.829733\pi$
$521$	0.258151	−	0.447130i	0.0113098	−	0.0195891i	0.871625	+	0.490173i	$0.163067\pi$
$522$	11.9367	−	6.89168i	0.522457	−	0.301640i
$523$	−38.3714			−1.67786			−0.838932	−	0.544236i	$-0.816820\pi$
$523$	−38.3714			−1.67786			−0.838932	+	0.544236i	$0.816820\pi$
$524$	1.27072	+	2.20095i	0.0555116	+	0.0961489i
$525$	10.0999	+	3.96664i	0.440795	+	0.173118i
$526$	45.3045	−	26.1566i	1.97537	−	1.14048i
$527$	6.78085	+	3.91493i	0.295379	+	0.170537i
$528$	7.72813	+	4.46184i	0.336324	+	0.194177i
$529$	−9.70563			−0.421984
$530$	−59.0742			−2.56602
$531$	−8.67795	−	5.01022i	−0.376591	−	0.217425i
$532$	57.9847	+	72.7454i	2.51396	+	3.15391i
$533$	3.43588	−	11.3691i	0.148824	−	0.492451i
$534$	−12.2334	−	21.1888i	−0.529389	−	0.916929i
$535$	52.8628	−	30.5203i	2.28546	−	1.31951i
$536$	8.32069	+	14.4119i	0.359399	+	0.622497i
$537$	−0.535312	+	0.927188i	−0.0231004	+	0.0400111i
$538$			30.8711i			1.33095i
$539$	−10.5852	−	2.42121i	−0.455937	−	0.104289i
$540$	−11.1799	+	6.45469i	−0.481104	+	0.277766i
$541$	−21.9830	+	12.6919i	−0.945121	+	0.545666i	−0.891562	−	0.452899i	$-0.850390\pi$
$541$	−21.9830	+	12.6919i	−0.945121	+	0.545666i	−0.0535592	+	0.998565i	$0.517057\pi$
$542$	51.8079			2.22534
$543$	−4.80452	−	8.32168i	−0.206182	−	0.357117i
$544$			4.53193i			0.194305i
$545$	5.41833			0.232096
$546$	−8.85493	−	22.2034i	−0.378956	−	0.950217i
$547$	−17.9501			−0.767491			−0.383746	−	0.923439i	$-0.625366\pi$
$547$	−17.9501			−0.767491			−0.383746	+	0.923439i	$0.625366\pi$
$548$			21.4419i			0.915951i
$549$	5.23565	+	9.06841i	0.223452	+	0.387030i
$550$	15.9420			0.679767
$551$	39.1420	−	22.5987i	1.66751	−	0.962735i
$552$	18.0336	−	10.4117i	0.767560	−	0.443151i
$553$	2.58318	+	17.1655i	0.109848	+	0.729951i
$554$			17.7996i			0.756231i
$555$	−13.8783	+	24.0378i	−0.589099	+	1.02035i
$556$	−35.6647	−	61.7731i	−1.51252	−	2.61976i
$557$	2.70158	−	1.55976i	0.114470	−	0.0660890i	−0.441672	−	0.897177i	$-0.645615\pi$
$557$	2.70158	−	1.55976i	0.114470	−	0.0660890i	0.556142	+	0.831088i	$0.312281\pi$
$558$	−6.47877	−	11.2216i	−0.274268	−	0.475046i
$559$	−10.4055	+	9.76613i	−0.440105	+	0.413063i
$560$	−45.4052	+	6.83287i	−1.91872	+	0.288742i
$561$	−2.03417	−	1.17443i	−0.0858826	−	0.0495844i
$562$	−64.8836			−2.73695
$563$	15.9165			0.670802			0.335401	−	0.942076i	$-0.391128\pi$
$563$	15.9165			0.670802			0.335401	+	0.942076i	$0.391128\pi$
$564$	−34.2572	−	19.7784i	−1.44249	−	0.832820i
$565$	44.1492	+	25.4895i	1.85737	+	1.07235i
$566$	−56.8499	+	32.8223i	−2.38958	+	1.37962i
$567$	0.393717	+	2.61629i	0.0165346	+	0.109874i
$568$	−3.66765	−	6.35256i	−0.153891	−	0.266548i
$569$	2.00211			0.0839328			0.0419664	−	0.999119i	$-0.486638\pi$
$569$	2.00211			0.0839328			0.0419664	+	0.999119i	$0.486638\pi$
$570$	−53.7945	+	31.0583i	−2.25321	+	1.30089i
$571$	15.4415	−	26.7455i	0.646208	−	1.11927i	−0.337813	−	0.941213i	$-0.609687\pi$
$571$	15.4415	−	26.7455i	0.646208	−	1.11927i	0.984021	−	0.178052i	$-0.0569797\pi$
$572$	−16.3787	−	17.4510i	−0.684830	−	0.729663i
$573$	−21.0359			−0.878786
$574$	−17.0776	+	13.6124i	−0.712804	+	0.568170i
$575$	7.47688	−	12.9503i	0.311807	−	0.540066i
$576$	−2.00274	+	3.46885i	−0.0834475	+	0.144535i
$577$	17.4279	+	10.0620i	0.725533	+	0.418887i	0.816786	−	0.576941i	$-0.195754\pi$
$577$	17.4279	+	10.0620i	0.725533	+	0.418887i	−0.0912526	+	0.995828i	$0.529087\pi$
$578$			36.8536i			1.53291i
$579$	−6.81659	−	3.93556i	−0.283288	−	0.163556i
$580$			71.0086i			2.94847i
$581$	−5.31103	+	13.5230i	−0.220339	+	0.561029i
$582$	−15.6739	+	27.1480i	−0.649704	+	1.12532i
$583$			12.1220i			0.502041i
$584$	7.50224	−	12.9943i	0.310445	−	0.537706i
$585$	10.5906	−	2.48099i	0.437868	−	0.102577i
$586$	−10.9562	−	18.9767i	−0.452597	−	0.783921i
$587$	1.07751	+	0.622102i	0.0444737	+	0.0256769i	0.522072	−	0.852901i	$-0.325159\pi$
$587$	1.07751	+	0.622102i	0.0444737	+	0.0256769i	−0.477598	+	0.878578i	$0.658493\pi$
$588$	−6.67901	+	29.1997i	−0.275438	+	1.20418i
$589$	−21.2447	−	36.7969i	−0.875372	−	1.51619i
$590$	65.6021	−	37.8754i	2.70079	−	1.55930i
$591$		−	0.222865i		−	0.00916745i
$592$		−	52.9277i		−	2.17531i
$593$	24.2540	−	14.0031i	0.995994	−	0.575037i	0.0889335	−	0.996038i	$-0.471654\pi$
$593$	24.2540	−	14.0031i	0.995994	−	0.575037i	0.907061	+	0.421000i	$0.138321\pi$
$594$	1.94355	+	3.36632i	0.0797447	+	0.138122i
$595$	11.9514	−	1.79852i	0.489958	−	0.0737322i
$596$	−7.50811	−	4.33481i	−0.307544	−	0.177561i
$597$	5.81292	+	10.0683i	0.237907	+	0.412067i
$598$	−32.0740	+	7.51378i	−1.31161	+	0.307261i
$599$	1.33444	−	2.31132i	0.0545238	−	0.0944380i	−0.837475	−	0.546475i	$-0.815969\pi$
$599$	1.33444	−	2.31132i	0.0545238	−	0.0944380i	0.891999	+	0.452037i	$0.149303\pi$
$600$		−	23.4225i		−	0.956221i
$601$	20.5235	−	35.5478i	0.837172	−	1.45003i	−0.0550770	−	0.998482i	$-0.517540\pi$
$601$	20.5235	−	35.5478i	0.837172	−	1.45003i	0.892249	−	0.451543i	$-0.149126\pi$
$602$	25.9482	−	3.90487i	1.05757	−	0.159150i
$603$			2.91388i			0.118662i
$604$	34.6001	+	19.9764i	1.40786	+	0.812828i
$605$			25.9257i			1.05403i
$606$	−25.1463	−	14.5182i	−1.02150	−	0.589762i
$607$	18.7628	−	32.4982i	0.761560	−	1.31906i	−0.180487	−	0.983577i	$-0.557767\pi$
$607$	18.7628	−	32.4982i	0.761560	−	1.31906i	0.942046	−	0.335482i	$-0.108899\pi$
$608$	12.2964	−	21.2981i	0.498687	−	0.863751i
$609$	13.5458	+	5.32000i	0.548904	+	0.215577i
$610$	−79.1591			−3.20506
$611$	22.8095	+	24.3028i	0.922775	+	0.983186i
$612$	−3.23971	+	5.61134i	−0.130957	+	0.226825i
$613$	2.82741	−	1.63241i	0.114198	−	0.0659324i	−0.441813	−	0.897107i	$-0.645665\pi$
$613$	2.82741	−	1.63241i	0.114198	−	0.0659324i	0.556011	+	0.831175i	$0.312331\pi$
$614$	−3.59752			−0.145184
$615$	−4.96883	−	8.60626i	−0.200362	−	0.347038i
$616$	3.48801	+	23.1782i	0.140536	+	0.933875i
$617$	−30.8621	+	17.8182i	−1.24246	+	0.717334i	−0.969594	−	0.244718i	$-0.921305\pi$
$617$	−30.8621	+	17.8182i	−1.24246	+	0.717334i	−0.272865	+	0.962052i	$0.587971\pi$
$618$	3.25593	+	1.87981i	0.130973	+	0.0756172i
$619$	−13.6521	−	7.88206i	−0.548725	−	0.316807i	0.199882	−	0.979820i	$-0.435944\pi$
$619$	−13.6521	−	7.88206i	−0.548725	−	0.316807i	−0.748608	+	0.663013i	$0.769277\pi$
$620$	66.7542			2.68091
$621$	3.64614			0.146315
$622$	−51.4852	−	29.7250i	−2.06437	−	1.19186i
$623$	9.44348	−	24.0451i	0.378345	−	0.963345i
$624$	−15.1237	+	14.1945i	−0.605434	+	0.568233i
$625$	14.3430	+	24.8428i	0.573720	+	0.993712i
$626$	47.5073	−	27.4284i	1.89877	−	1.09626i
$627$	6.37313	+	11.0386i	0.254518	+	0.440839i
$628$	25.2558	−	43.7443i	1.00782	−	1.74559i
$629$			13.9314i			0.555482i
$630$	−18.6166	−	7.31149i	−0.741703	−	0.291297i
$631$	34.9566	−	20.1822i	1.39160	−	0.803441i	0.398109	−	0.917338i	$-0.369667\pi$
$631$	34.9566	−	20.1822i	1.39160	−	0.803441i	0.993493	+	0.113897i	$0.0363333\pi$
$632$	32.4502	−	18.7352i	1.29080	−	0.745245i
$633$	−17.5895			−0.699122
$634$	37.5736	+	65.0794i	1.49224	+	2.58463i
$635$			32.2278i			1.27892i
$636$	33.4390			1.32594
$637$	12.5046	−	21.9234i	0.495449	−	0.868637i
$638$	21.3811			0.846486
$639$		−	1.28440i		−	0.0508101i
$640$	−24.1692	−	41.8623i	−0.955373	−	1.65475i
$641$	−31.2513			−1.23435			−0.617176	−	0.786825i	$-0.711723\pi$
$641$	−31.2513			−1.23435			−0.617176	+	0.786825i	$0.711723\pi$
$642$	−43.9085	+	25.3506i	−1.73293	+	1.00051i
$643$	−27.5603	+	15.9120i	−1.08687	+	0.627507i	−0.932742	−	0.360544i	$-0.882591\pi$
$643$	−27.5603	+	15.9120i	−1.08687	+	0.627507i	−0.154131	+	0.988050i	$0.549258\pi$
$644$	38.4228	+	15.0902i	1.51407	+	0.594637i
$645$			11.9405i			0.470157i
$646$	−15.5886	+	27.0003i	−0.613326	+	1.06231i
$647$	−7.50299	−	12.9956i	−0.294973	−	0.510908i	0.680006	−	0.733207i	$-0.261977\pi$
$647$	−7.50299	−	12.9956i	−0.294973	−	0.510908i	−0.974979	+	0.222299i	$0.928644\pi$
$648$	4.94593	−	2.85554i	0.194295	−	0.112176i
$649$	−7.77199	−	13.4615i	−0.305077	−	0.528409i
$650$	−10.7194	+	35.4699i	−0.420450	+	1.39124i
$651$	5.00125	−	12.7342i	0.196015	−	0.499094i
$652$	−2.19540	−	1.26751i	−0.0859784	−	0.0496396i
$653$	−42.9725			−1.68164			−0.840822	−	0.541311i	$-0.817928\pi$
$653$	−42.9725			−1.68164			−0.840822	+	0.541311i	$0.817928\pi$
$654$	−4.50054			−0.175985
$655$	−1.55169	−	0.895870i	−0.0606296	−	0.0350045i
$656$	16.4109	+	9.47484i	0.640738	+	0.369930i
$657$	2.27528	−	1.31363i	0.0887670	−	0.0512496i
$658$	−9.12011	−	60.6041i	−0.355539	−	2.36259i
$659$	23.8419	+	41.2953i	0.928747	+	1.60864i	0.785421	+	0.618962i	$0.212446\pi$
$659$	23.8419	+	41.2953i	0.928747	+	1.60864i	0.143326	+	0.989676i	$0.454220\pi$
$660$	−20.0254			−0.779487
$661$	15.5907	−	9.00132i	0.606410	−	0.350111i	−0.165149	−	0.986269i	$-0.552811\pi$
$661$	15.5907	−	9.00132i	0.606410	−	0.350111i	0.771559	+	0.636158i	$0.219477\pi$
$662$	−20.4961	+	35.5003i	−0.796605	+	1.37976i
$663$	3.98081	−	3.73621i	0.154602	−	0.145102i
$664$	31.3611			1.21704
$665$	−61.0461	−	23.9753i	−2.36727	−	0.929722i
$666$	11.5275	−	19.9662i	0.446680	−	0.773673i
$667$	10.0279	−	17.3688i	0.388281	−	0.672523i
$668$	−32.1801	−	18.5792i	−1.24509	−	0.718851i
$669$			18.1917i			0.703332i
$670$	−19.0767	−	11.0139i	−0.736996	−	0.425505i
$671$			16.2434i			0.627068i
$672$	7.83048	−	1.17838i	0.302067	−	0.0454571i
$673$	−5.90181	+	10.2222i	−0.227498	+	0.394038i	−0.957066	−	0.289870i	$-0.906388\pi$
$673$	−5.90181	+	10.2222i	−0.227498	+	0.394038i	0.729568	+	0.683908i	$0.239721\pi$
$674$		−	76.2062i		−	2.93535i
$675$	2.05063	−	3.55179i	0.0789287	−	0.136708i
$676$	49.8405	−	24.7076i	1.91694	−	0.950292i
$677$	5.84113	+	10.1171i	0.224493	+	0.388833i	0.956167	−	0.292821i	$-0.0945941\pi$
$677$	5.84113	+	10.1171i	0.224493	+	0.388833i	−0.731674	+	0.681654i	$0.761261\pi$
$678$	−36.6709	−	21.1719i	−1.40834	−	0.813104i
$679$	−32.7298	+	4.92540i	−1.25605	+	0.189020i
$680$	−13.0442	−	22.5933i	−0.500224	−	0.866413i
$681$	17.8461	−	10.3034i	0.683863	−	0.394829i
$682$		−	20.1001i		−	0.769672i
$683$			1.99904i			0.0764911i	0.999268	+	0.0382456i	$0.0121769\pi$
$683$			1.99904i			0.0764911i	−0.999268	+	0.0382456i	$0.987823\pi$
$684$	30.4504	−	17.5805i	1.16430	−	0.672209i
$685$	−7.55837	−	13.0915i	−0.288791	−	0.500200i
$686$	−41.8266	+	20.1065i	−1.59695	+	0.767671i
$687$	6.95359	+	4.01466i	0.265296	+	0.153169i
$688$	−11.3844	−	19.7184i	−0.434027	−	0.751756i
$689$	−26.9706	−	8.15085i	−1.02750	−	0.310522i
$690$	−13.7817	+	23.8707i	−0.524662	+	0.908741i
$691$			18.1824i			0.691693i	0.938291	+	0.345846i	$0.112408\pi$
$691$			18.1824i			0.691693i	−0.938291	+	0.345846i	$0.887592\pi$
$692$	29.4383	−	50.9887i	1.11908	−	1.93830i
$693$	−1.50031	+	3.82011i	−0.0569921	+	0.145114i
$694$		−	38.3558i		−	1.45597i
$695$	43.5507	+	25.1440i	1.65197	+	0.953767i
$696$		−	31.4140i		−	1.19074i
$697$	−4.31961	−	2.49393i	−0.163617	−	0.0944643i
$698$	11.9868	−	20.7618i	0.453708	−	0.785845i
$699$	7.15034	−	12.3848i	0.270451	−	0.468434i
$700$	36.3090	−	28.9416i	1.37235	−	1.09389i
$701$	−22.5231			−0.850684			−0.425342	−	0.905033i	$-0.639846\pi$
$701$	−22.5231			−0.850684			−0.425342	+	0.905033i	$0.639846\pi$
$702$	−8.79670	+	2.06075i	−0.332010	+	0.0777779i
$703$	37.8000	−	65.4715i	1.42565	−	2.46930i
$704$	−5.38097	+	3.10670i	−0.202803	+	0.117088i
$705$	27.8880			1.05032
$706$	15.6488	+	27.1045i	0.588950	+	1.02009i
$707$	−4.56224	−	30.3166i	−0.171581	−	1.14017i
$708$	−37.1340	+	21.4393i	−1.39558	+	0.805740i
$709$	−6.19497	−	3.57667i	−0.232657	−	0.134324i	0.379140	−	0.925339i	$-0.376220\pi$
$709$	−6.19497	−	3.57667i	−0.232657	−	0.134324i	−0.611797	+	0.791015i	$0.709553\pi$
$710$	8.40875	+	4.85479i	0.315575	+	0.182197i
$711$	6.56100			0.246057
$712$	−55.7627			−2.08979
$713$	−16.3282	−	9.42707i	−0.611495	−	0.353047i
$714$	−9.92697	+	1.49388i	−0.371507	+	0.0559069i
$715$	16.1517	+	4.88124i	0.604041	+	0.182548i
$716$	2.29067	+	3.96755i	0.0856063	+	0.148274i
$717$	3.74004	−	2.15931i	0.139674	−	0.0806410i
$718$	13.8432	+	23.9772i	0.516625	+	0.894820i
$719$	−3.94008	+	6.82441i	−0.146940	+	0.254508i	−0.930095	−	0.367319i	$-0.880276\pi$
$719$	−3.94008	+	6.82441i	−0.146940	+	0.254508i	0.783155	+	0.621827i	$0.213609\pi$
$720$			17.3548i			0.646774i
$721$	0.590717	+	3.92538i	0.0219995	+	0.146189i
$722$	105.287	−	60.7877i	3.91839	−	2.26228i
$723$	−1.15146	+	0.664798i	−0.0428234	+	0.0247241i
$724$	−41.1183			−1.52815
$725$	−11.2796	−	19.5368i	−0.418912	−	0.725577i
$726$		−	21.5342i		−	0.799210i
$727$	−18.8301			−0.698371			−0.349185	−	0.937054i	$-0.613542\pi$
$727$	−18.8301			−0.698371			−0.349185	+	0.937054i	$0.613542\pi$
$728$	−53.9153	−	7.82446i	−1.99824	−	0.289994i
$729$	1.00000			0.0370370
$730$			19.8611i			0.735093i
$731$	2.99656	+	5.19019i	0.110832	+	0.191966i
$732$	44.8080			1.65615
$733$	−24.7277	+	14.2766i	−0.913339	+	0.527317i	−0.881504	−	0.472177i	$-0.843468\pi$
$733$	−24.7277	+	14.2766i	−0.913339	+	0.527317i	−0.0318352	+	0.999493i	$0.510135\pi$
$734$	28.0413	−	16.1897i	1.03502	−	0.597571i
$735$	−6.21515	−	20.1825i	−0.229249	−	0.744443i
$736$		−	10.9128i		−	0.402251i
$737$	−2.26004	+	3.91451i	−0.0832498	+	0.144193i
$738$	4.12718	+	7.14848i	0.151923	+	0.263139i
$739$	6.59865	−	3.80973i	0.242735	−	0.140143i	−0.373698	−	0.927550i	$-0.621910\pi$
$739$	6.59865	−	3.80973i	0.242735	−	0.140143i	0.616433	+	0.787407i	$0.288577\pi$
$740$	59.3868	+	102.861i	2.18310	+	3.78124i
$741$	−28.8455	+	6.75745i	−1.05966	+	0.248241i
$742$	32.2923	+	40.5127i	1.18549	+	1.48727i
$743$	−42.4488	−	24.5078i	−1.55730	−	0.899105i	−0.997514	−	0.0704641i	$-0.977552\pi$
$743$	−42.4488	−	24.5078i	−1.55730	−	0.899105i	−0.559781	−	0.828641i	$-0.689115\pi$
$744$	−29.5318			−1.08269
$745$	6.11217			0.223933
$746$	−19.5909	−	11.3108i	−0.717275	−	0.414119i
$747$	4.75558	+	2.74564i	0.173998	+	0.100458i
$748$	−8.70446	+	5.02552i	−0.318266	+	0.183751i
$749$	−49.8274	−	19.5693i	−1.82065	−	0.715046i
$750$	−3.39709	−	5.88394i	−0.124044	−	0.214851i
$751$	23.6811			0.864134			0.432067	−	0.901841i	$-0.357784\pi$
$751$	23.6811			0.864134			0.432067	+	0.901841i	$0.357784\pi$
$752$	−46.0538	+	26.5891i	−1.67941	+	0.969607i
$753$	1.13399	−	1.96413i	0.0413249	−	0.0715769i
$754$	−14.3767	+	47.5716i	−0.523569	+	1.73246i
$755$	−28.1671			−1.02511
$756$	10.5379	+	4.13867i	0.383260	+	0.150522i
$757$	16.7491	−	29.0103i	0.608756	−	1.05440i	−0.382689	−	0.923877i	$-0.625002\pi$
$757$	16.7491	−	29.0103i	0.608756	−	1.05440i	0.991446	−	0.130520i	$-0.0416646\pi$
$758$	−21.2461	+	36.7993i	−0.771693	+	1.33661i
$759$	4.89824	+	2.82800i	0.177795	+	0.102650i
$760$			141.571i			5.13533i
$761$	−43.7204	−	25.2420i	−1.58486	−	0.915021i	−0.994135	−	0.108150i	$-0.965507\pi$
$761$	−43.7204	−	25.2420i	−1.58486	−	0.915021i	−0.590728	−	0.806871i	$-0.701160\pi$
$762$		−	26.7688i		−	0.969732i
$763$	−2.96187	−	3.71585i	−0.107227	−	0.134523i
$764$	−45.0076	+	77.9554i	−1.62832	+	2.82033i
$765$		−	4.56806i		−	0.165158i
$766$	2.57169	−	4.45430i	0.0929190	−	0.160940i
$767$	35.1769	−	8.24066i	1.27016	−	0.297553i
$768$	16.0698	+	27.8337i	0.579869	+	1.00436i
$769$	32.2438	+	18.6160i	1.16274	+	0.671309i	0.951959	−	0.306224i	$-0.0990657\pi$
$769$	32.2438	+	18.6160i	1.16274	+	0.671309i	0.210782	+	0.977533i	$0.432399\pi$
$770$	−19.3387	−	24.2616i	−0.696917	−	0.874326i
$771$	5.92412	+	10.2609i	0.213352	+	0.369537i
$772$	−29.1691	+	16.8408i	−1.04982	+	0.606112i
$773$			16.8715i			0.606827i	0.952859	+	0.303414i	$0.0981264\pi$
$773$			16.8715i			0.606827i	−0.952859	+	0.303414i	$0.901874\pi$
$774$		−	9.91794i		−	0.356493i
$775$	−18.3662	+	10.6037i	−0.659735	+	0.380898i
$776$	35.7227	+	61.8736i	1.28237	+	2.22113i
$777$	24.0714	−	3.62242i	0.863555	−	0.129954i
$778$	−68.3420	−	39.4573i	−2.45018	−	1.41461i
$779$	13.5335	+	23.4407i	0.484889	+	0.839852i
$780$	13.4651	−	44.5552i	0.482129	−	1.59533i
$781$	0.996199	−	1.72547i	0.0356468	−	0.0617421i
$782$			13.8345i			0.494722i
$783$	2.75027	−	4.76361i	0.0982866	−	0.170237i
$784$	29.5062	+	27.4034i	1.05379	+	0.978693i
$785$			35.6112i			1.27102i
$786$	1.28886	+	0.744121i	0.0459720	+	0.0265419i
$787$			34.4000i			1.22623i	0.789995	+	0.613113i	$0.210083\pi$
$787$			34.4000i			1.22623i	−0.789995	+	0.613113i	$0.789917\pi$
$788$	−0.825901	−	0.476834i	−0.0294215	−	0.0169865i
$789$	10.4383	−	18.0797i	0.371614	−	0.643655i
$790$	−24.7993	+	42.9537i	−0.882321	+	1.52822i
$791$	−6.65313	−	44.2107i	−0.236558	−	1.57195i
$792$	8.85917			0.314797
$793$	−36.1405	−	10.9221i	−1.28339	−	0.387854i
$794$	−14.4899	+	25.0973i	−0.514228	+	0.890668i
$795$	−20.4164	+	11.7874i	−0.724095	+	0.418057i
$796$	49.7484			1.76328
$797$	2.27035	+	3.93236i	0.0804200	+	0.139291i	0.903430	−	0.428735i	$-0.141041\pi$
$797$	2.27035	+	3.93236i	0.0804200	+	0.139291i	−0.823010	+	0.568026i	$0.807707\pi$
$798$	50.7057	+	19.9142i	1.79496	+	0.704955i
$799$	12.1221	−	6.99869i	0.428849	−	0.247596i
$800$	−10.6304	−	6.13746i	−0.375841	−	0.216992i
$801$	−8.45584	−	4.88198i	−0.298772	−	0.172496i
$802$	10.6650			0.376594
$803$	4.07548			0.143821
$804$	10.7983	+	6.23443i	0.380828	+	0.219871i
$805$	−28.7787	+	4.33081i	−1.01431	+	0.152641i
$806$	44.7214	+	13.5153i	1.57525	+	0.476058i
$807$	6.15988	+	10.6692i	0.216838	+	0.375574i
$808$	−57.3115	+	33.0888i	−2.01621	+	1.16406i
$809$	−2.91983	−	5.05729i	−0.102656	−	0.177805i	0.810122	−	0.586261i	$-0.199401\pi$
$809$	−2.91983	−	5.05729i	−0.102656	−	0.177805i	−0.912778	+	0.408456i	$0.866067\pi$
$810$	−3.77981	+	6.54683i	−0.132809	+	0.230032i
$811$			4.79606i			0.168412i	0.996448	+	0.0842061i	$0.0268354\pi$
$811$			4.79606i			0.168412i	−0.996448	+	0.0842061i	$0.973165\pi$
$812$	48.6971	−	38.8160i	1.70893	−	1.36218i
$813$	17.9051	−	10.3375i	0.627960	−	0.362553i
$814$	30.9720	−	17.8817i	1.08557	−	0.626754i
$815$	1.78722			0.0626036
$816$	4.35531	+	7.54362i	0.152466	+	0.264080i
$817$		−	32.5222i		−	1.13781i
$818$	27.7492			0.970229
$819$	−7.49068	−	5.90675i	−0.261746	−	0.206398i
$820$	−42.5245			−1.48502
$821$			18.7979i			0.656053i	0.944669	+	0.328026i	$0.106383\pi$
$821$			18.7979i			0.656053i	−0.944669	+	0.328026i	$0.893617\pi$
$822$	6.27808	+	10.8740i	0.218973	+	0.379273i
$823$	−17.8174			−0.621076			−0.310538	−	0.950561i	$-0.600509\pi$
$823$	−17.8174			−0.621076			−0.310538	+	0.950561i	$0.600509\pi$
$824$	7.42067	−	4.28433i	0.258511	−	0.149252i
$825$	5.50963	−	3.18099i	0.191821	−	0.110748i
$826$	−61.8353	−	24.2852i	−2.15152	−	0.844991i
$827$		−	32.3754i		−	1.12580i	−0.826524	−	0.562902i	$-0.809685\pi$
$827$		−	32.3754i		−	1.12580i	0.826524	−	0.562902i	$-0.190315\pi$
$828$	7.80115	−	13.5120i	0.271109	−	0.469574i
$829$	15.9881	+	27.6923i	0.555291	+	0.961793i	0.997881	+	0.0650684i	$0.0207265\pi$
$829$	15.9881	+	27.6923i	0.555291	+	0.961793i	−0.442590	+	0.896724i	$0.645940\pi$
$830$	−35.9504	+	20.7560i	−1.24786	+	0.720451i
$831$	3.55165	+	6.15163i	0.123205	+	0.213398i
$832$	−3.29405	−	14.0613i	−0.114200	−	0.487487i
$833$	−7.76649	−	7.21301i	−0.269093	−	0.249916i
$834$	−36.1738	−	20.8850i	−1.25260	−	0.723187i
$835$	26.1971			0.906587
$836$	54.5428			1.88640
$837$	−4.47820	−	2.58549i	−0.154789	−	0.0893676i
$838$	4.79642	+	2.76922i	0.165690	+	0.0956610i
$839$	0.0485960	−	0.0280569i	0.00167772	−	0.000968633i	−0.499161	−	0.866509i	$-0.666358\pi$
$839$	0.0485960	−	0.0280569i	0.00167772	−	0.000968633i	0.500839	+	0.865541i	$0.333025\pi$
$840$	−35.6460	+	28.4131i	−1.22991	+	0.980346i
$841$	−0.627971	−	1.08768i	−0.0216542	−	0.0375061i
$842$	40.0283			1.37947
$843$	−22.4241	+	12.9466i	−0.772329	+	0.445904i
$844$	−37.6339	+	65.1839i	−1.29541	+	2.24372i
$845$	−21.7209	+	32.6544i	−0.747223	+	1.12335i
$846$	−23.1641			−0.796398
$847$	17.7796	−	14.1720i	0.610916	−	0.486955i
$848$	22.4769	−	38.9311i	0.771860	−	1.33690i
$849$	−13.0984	+	22.6872i	−0.449537	+	0.778621i
$850$	13.4765	+	7.78067i	0.462241	+	0.266875i
$851$		−	33.5466i		−	1.14996i
$852$	−4.75977	−	2.74806i	−0.163067	−	0.0941469i
$853$		−	21.8470i		−	0.748028i	−0.927423	−	0.374014i	$-0.877981\pi$
$853$		−	21.8470i		−	0.748028i	0.927423	−	0.374014i	$-0.122019\pi$
$854$	43.2714	+	54.2867i	1.48072	+	1.85765i
$855$	−12.3945	+	21.4679i	−0.423882	+	0.734185i
$856$			115.554i			3.94956i
$857$	−4.56160	+	7.90092i	−0.155821	+	0.269890i	−0.933358	−	0.358947i	$-0.883136\pi$
$857$	−4.56160	+	7.90092i	−0.155821	+	0.269890i	0.777536	+	0.628838i	$0.216469\pi$
$858$	−13.4158	−	4.05443i	−0.458010	−	0.138416i
$859$	−10.4710	−	18.1363i	−0.357266	−	0.618803i	0.630237	−	0.776403i	$-0.282958\pi$
$859$	−10.4710	−	18.1363i	−0.357266	−	0.618803i	−0.987503	+	0.157600i	$0.949624\pi$
$860$	44.2495	+	25.5475i	1.50889	+	0.871161i
$861$	−3.18595	+	8.11210i	−0.108577	+	0.276460i
$862$	29.5941	+	51.2586i	1.00798	+	1.74587i
$863$	−5.75442	+	3.32232i	−0.195883	+	0.113093i	−0.594734	−	0.803923i	$-0.702742\pi$
$863$	−5.75442	+	3.32232i	−0.195883	+	0.113093i	0.398851	+	0.917016i	$0.369409\pi$
$864$		−	2.99297i		−	0.101823i
$865$			41.5087i			1.41134i
$866$	3.34761	−	1.93274i	0.113756	−	0.0656772i
$867$	7.35361	+	12.7368i	0.249742	+	0.432565i
$868$	−36.4904	−	45.7795i	−1.23857	−	1.55386i
$869$	8.81406	+	5.08880i	0.298996	+	0.172626i
$870$	20.7910	+	36.0111i	0.704881	+	1.22089i
$871$	−7.18989	−	7.66059i	−0.243620	−	0.259569i
$872$	−5.12865	+	8.88307i	−0.173678	+	0.300819i
$873$			12.5100i			0.423399i
$874$	37.5371	−	65.0162i	1.26971	−	2.19921i
$875$	2.62237	−	6.67710i	0.0886523	−	0.225727i
$876$		−	11.2424i		−	0.379845i
$877$	−28.3374	−	16.3606i	−0.956885	−	0.552458i	−0.0616724	−	0.998096i	$-0.519643\pi$
$877$	−28.3374	−	16.3606i	−0.956885	−	0.552458i	−0.895213	+	0.445638i	$0.852977\pi$
$878$		−	79.4695i		−	2.68197i
$879$	−7.57306	−	4.37231i	−0.255433	−	0.147474i
$880$	−13.4606	+	23.3144i	−0.453757	+	0.785930i
$881$	15.0565	−	26.0786i	0.507267	−	0.878612i	−0.492698	−	0.870201i	$-0.663989\pi$
$881$	15.0565	−	26.0786i	0.507267	−	0.878612i	0.999965	−	0.00841150i	$-0.00267750\pi$
$882$	5.16238	+	16.7639i	0.173826	+	0.564468i
$883$	−17.3595			−0.584194			−0.292097	−	0.956389i	$-0.594353\pi$
$883$	−17.3595			−0.584194			−0.292097	+	0.956389i	$0.594353\pi$
$884$	−5.32857	−	22.7460i	−0.179219	−	0.765032i
$885$	15.1150	−	26.1799i	0.508084	−	0.880028i
$886$	−14.6539	+	8.46043i	−0.492307	+	0.284234i
$887$	43.5680			1.46287			0.731434	−	0.681912i	$-0.238851\pi$
$887$	43.5680			1.46287			0.731434	+	0.681912i	$0.238851\pi$
$888$	−26.2725	−	45.5054i	−0.881648	−	1.52706i
$889$	22.1016	−	17.6170i	0.741263	−	0.590854i
$890$	63.9229	−	36.9059i	2.14270	−	1.23709i
$891$	1.34340	+	0.775614i	0.0450057	+	0.0259840i
$892$	67.4153	+	38.9223i	2.25723	+	1.30321i
$893$	−75.9580			−2.54184
$894$	−5.07685			−0.169795
$895$	−2.79717	−	1.61495i	−0.0934990	−	0.0539817i
$896$	−15.4970	+	39.4586i	−0.517719	+	1.31822i
$897$	−9.58571	+	8.99672i	−0.320058	+	0.300392i
$898$	3.98941	+	6.90985i	0.133128	+	0.230585i
$899$	−24.6325	+	14.2216i	−0.821541	+	0.474317i
$900$	−8.77489	−	15.1985i	−0.292496	−	0.506618i
$901$	−5.91628	+	10.2473i	−0.197100	+	0.341387i
$902$			12.8044i			0.426339i
$903$	8.18870	−	6.52714i	0.272503	−	0.217210i
$904$	−83.5775	+	48.2535i	−2.77975	+	1.60489i
$905$	25.1051	−	14.4944i	0.834521	−	0.481811i
$906$	23.3960			0.777280
$907$	−7.15731	−	12.3968i	−0.237655	−	0.411630i	0.722386	−	0.691490i	$-0.243045\pi$
$907$	−7.15731	−	12.3968i	−0.237655	−	0.411630i	−0.960041	+	0.279860i	$0.909712\pi$
$908$		−	88.1794i		−	2.92634i
$909$	−11.5876			−0.384337
$910$	66.9838	−	26.7138i	2.22049	−	0.885554i
$911$	29.9541			0.992422			0.496211	−	0.868202i	$-0.334724\pi$
$911$	29.9541			0.992422			0.496211	+	0.868202i	$0.334724\pi$
$912$		−	47.2689i		−	1.56523i
$913$	4.25911	+	7.37699i	0.140956	+	0.244143i
$914$	−68.3199			−2.25982
$915$	−27.3578	+	15.7951i	−0.904422	+	0.522168i
$916$	29.7553	−	17.1792i	0.983142	−	0.567617i
$917$	0.233835	+	1.55386i	0.00772190	+	0.0513128i
$918$			3.79429i			0.125230i
$919$	−7.67389	+	13.2916i	−0.253138	+	0.438448i	−0.964388	−	0.264491i	$-0.914796\pi$
$919$	−7.67389	+	13.2916i	−0.253138	+	0.438448i	0.711250	+	0.702939i	$0.248129\pi$
$920$	31.4103	+	54.4042i	1.03557	+	1.79365i
$921$	−1.24332	+	0.717834i	−0.0409689	+	0.0236534i
$922$	1.36969	+	2.37237i	0.0451083	+	0.0781299i
$923$	3.16921	+	3.37669i	0.104316	+	0.111145i
$924$	10.9467	+	13.7333i	0.360118	+	0.451791i
$925$	−32.6785	−	18.8669i	−1.07446	−	0.620340i
$926$	−11.2875			−0.370930
$927$	1.50036			0.0492782
$928$	−14.2573	−	8.23147i	−0.468020	−	0.270211i
$929$	−5.25138	−	3.03189i	−0.172292	−	0.0994729i	0.411374	−	0.911467i	$-0.365049\pi$
$929$	−5.25138	−	3.03189i	−0.172292	−	0.0994729i	−0.583666	+	0.811994i	$0.698382\pi$
$930$	33.8535	−	19.5453i	1.11010	−	0.640917i
$931$	16.9281	+	54.9708i	0.554796	+	1.80159i
$932$	−30.5972	−	52.9959i	−1.00224	−	1.73594i
$933$	−23.7248			−0.776715
$934$	25.9879	−	15.0041i	0.850349	−	0.490949i
$935$	3.54305	−	6.13673i	0.115870	−	0.200693i
$936$	−5.95693	+	19.7111i	−0.194708	+	0.644277i
$937$	17.7949			0.581333			0.290666	−	0.956824i	$-0.406123\pi$
$937$	17.7949			0.581333			0.290666	+	0.956824i	$0.406123\pi$
$938$	2.87479	+	19.1033i	0.0938651	+	0.623743i
$939$	10.9459	−	18.9588i	0.357205	−	0.618697i
$940$	59.6680	−	103.348i	1.94616	−	3.37084i
$941$	37.1431	+	21.4446i	1.21083	+	0.699074i	0.962941	−	0.269714i	$-0.0869291\pi$
$941$	37.1431	+	21.4446i	1.21083	+	0.699074i	0.247891	+	0.968788i	$0.420262\pi$
$942$		−	29.5792i		−	0.963741i
$943$	10.4015	+	6.00534i	0.338721	+	0.195561i
$944$			57.6441i			1.87616i
$945$	−7.89291	+	1.18778i	−0.256756	+	0.0386384i
$946$	7.69249	−	13.3238i	0.250104	−	0.433194i
$947$			43.3496i			1.40867i	0.709867	+	0.704336i	$0.248755\pi$
$947$			43.3496i			1.40867i	−0.709867	+	0.704336i	$0.751245\pi$
$948$	14.0377	−	24.3139i	0.455922	−	0.789680i
$949$	−2.74036	+	9.06769i	−0.0889559	+	0.294350i
$950$	−42.2225	−	73.1314i	−1.36988	−	2.37270i
$951$	25.9713	+	14.9946i	0.842178	+	0.486232i
$952$	−8.36381	+	21.2960i	−0.271073	+	0.690208i
$953$	−11.7522	−	20.3554i	−0.380692	−	0.659378i	0.610469	−	0.792040i	$-0.290981\pi$
$953$	−11.7522	−	20.3554i	−0.380692	−	0.659378i	−0.991161	+	0.132662i	$0.957647\pi$
$954$	16.9581	−	9.79079i	0.549040	−	0.316988i
$955$		−	63.4616i		−	2.05357i
$956$		−	18.4799i		−	0.597684i
$957$	7.38944	−	4.26629i	0.238867	−	0.137910i
$958$	2.24194	+	3.88316i	0.0724339	+	0.125459i
$959$	−4.84634	+	12.3398i	−0.156496	+	0.398472i
$960$	−10.4649	−	6.04192i	−0.337754	−	0.195002i
$961$	−2.13048	−	3.69010i	−0.0687252	−	0.119036i
$962$	18.9600	+	80.9346i	0.611296	+	2.60944i
$963$	−10.1167	+	17.5226i	−0.326006	+	0.564659i
$964$			5.68951i			0.183247i
$965$	11.8729	−	20.5645i	0.382203	−	0.661994i
$966$	23.9040	−	3.59723i	0.769097	−	0.115739i
$967$		−	25.9127i		−	0.833296i	−0.909068	−	0.416648i	$-0.863205\pi$
$967$		−	25.9127i		−	0.833296i	0.909068	−	0.416648i	$-0.136795\pi$
$968$	−42.5038	−	24.5396i	−1.36612	−	0.788733i
$969$			12.4419i			0.399693i
$970$	−81.9008	−	47.2854i	−2.62968	−	1.51824i
$971$	−14.1176	+	24.4524i	−0.453056	+	0.784716i	−0.998574	−	0.0533832i	$-0.983000\pi$
$971$	−14.1176	+	24.4524i	−0.453056	+	0.784716i	0.545518	+	0.838099i	$0.316333\pi$
$972$	2.13956	−	3.70583i	0.0686265	−	0.118865i
$973$	−6.56294	−	43.6114i	−0.210398	−	1.39812i
$974$	−13.3183			−0.426747
$975$	3.37281	+	14.3975i	0.108016	+	0.461089i
$976$	30.1189	−	52.1674i	0.964082	−	1.66984i
$977$	22.5114	−	12.9970i	0.720203	−	0.415809i	−0.0946243	−	0.995513i	$-0.530165\pi$
$977$	22.5114	−	12.9970i	0.720203	−	0.415809i	0.814827	+	0.579704i	$0.196832\pi$
$978$	−1.48449			−0.0474687
$979$	−7.57306	−	13.1169i	−0.242036	−	0.419219i
$980$	−88.0906	−	20.1494i	−2.81395	−	0.643650i
$981$	−1.55541	+	0.898018i	−0.0496605	+	0.0286715i
$982$	−43.2492	−	24.9699i	−1.38014	−	0.796822i
$983$	14.9096	+	8.60807i	0.475543	+	0.274555i	0.718557	−	0.695468i	$-0.244803\pi$
$983$	14.9096	+	8.60807i	0.475543	+	0.274555i	−0.243014	+	0.970023i	$0.578136\pi$
$984$	18.8127			0.599727
$985$	0.672346			0.0214227
$986$	18.0745	+	10.4353i	0.575609	+	0.332328i
$987$	−15.2446	−	19.1253i	−0.485242	−	0.608766i
$988$	−36.6747	+	121.354i	−1.16678	+	3.86080i
$989$	−7.21566	−	12.4979i	−0.229445	−	0.397410i
$990$	−10.1556	+	5.86335i	−0.322767	+	0.186349i
$991$	−7.82485	−	13.5530i	−0.248565	−	0.430527i	0.714563	−	0.699571i	$-0.246626\pi$
$991$	−7.82485	−	13.5530i	−0.248565	−	0.430527i	−0.963128	+	0.269044i	$0.913292\pi$
$992$	−7.73829	+	13.4031i	−0.245691	+	0.425549i
$993$			16.3588i			0.519132i
$994$	−1.26717	−	8.42047i	−0.0401922	−	0.267081i
$995$	−30.3742	+	17.5366i	−0.962928	+	0.555947i
$996$	20.3497	−	11.7489i	0.644806	−	0.372279i
$997$	44.0274			1.39436			0.697181	−	0.716896i	$-0.254438\pi$
$997$	44.0274			1.39436			0.697181	+	0.716896i	$0.254438\pi$
$998$	40.3932	+	69.9631i	1.27862	+	2.21464i
$999$		−	9.20056i		−	0.291093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.4.1	✓	12
3.2	odd	2		819.2.bm.e.550.6		12
7.2	even	3		273.2.bl.c.121.1	yes	12
13.10	even	6		273.2.bl.c.88.1	yes	12
21.2	odd	6		819.2.do.f.667.6		12
39.23	odd	6		819.2.do.f.361.6		12
91.23	even	6	inner	273.2.t.c.205.6	yes	12
273.23	odd	6		819.2.bm.e.478.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.1	✓	12	1.1	even	1	trivial
273.2.t.c.205.6	yes	12	91.23	even	6	inner
273.2.bl.c.88.1	yes	12	13.10	even	6
273.2.bl.c.121.1	yes	12	7.2	even	3
819.2.bm.e.478.1		12	273.23	odd	6
819.2.bm.e.550.6		12	3.2	odd	2
819.2.do.f.361.6		12	39.23	odd	6
819.2.do.f.667.6		12	21.2	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.50582i q^{2} +(-0.500000 - 0.866025i) q^{3} -4.27912 q^{4} +(2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-2.46263 - 0.967177i) q^{7} +5.71107i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.50582i q^{2} +(-0.500000 - 0.866025i) q^{3} -4.27912 q^{4} +(2.61265 - 1.50841i) q^{5} +(-2.17010 + 1.25291i) q^{6} +(-2.46263 - 0.967177i) q^{7} +5.71107i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.77981 - 6.54683i) q^{10} +(-1.34340 + 0.775614i) q^{11} +(2.13956 + 3.70583i) q^{12} +(-0.822385 - 3.51051i) q^{13} +(-2.42357 + 6.17091i) q^{14} +(-2.61265 - 1.50841i) q^{15} +5.75266 q^{16} -1.51419 q^{17} +(2.17010 + 1.25291i) q^{18} +(7.11603 + 4.10844i) q^{19} +(-11.1799 + 6.45469i) q^{20} +(0.393717 + 2.61629i) q^{21} +(1.94355 + 3.36632i) q^{22} +3.64614 q^{23} +(4.94593 - 2.85554i) q^{24} +(2.05063 - 3.55179i) q^{25} +(-8.79670 + 2.06075i) q^{26} +1.00000 q^{27} +(10.5379 + 4.13867i) q^{28} +(2.75027 - 4.76361i) q^{29} +(-3.77981 + 6.54683i) q^{30} +(-4.47820 - 2.58549i) q^{31} -2.99297i q^{32} +(1.34340 + 0.775614i) q^{33} +3.79429i q^{34} +(-7.89291 + 1.18778i) q^{35} +(2.13956 - 3.70583i) q^{36} -9.20056i q^{37} +(10.2950 - 17.8315i) q^{38} +(-2.62900 + 2.46746i) q^{39} +(8.61466 + 14.9210i) q^{40} +(2.85275 + 1.64704i) q^{41} +(6.55595 - 0.986584i) q^{42} +(-1.97898 - 3.42770i) q^{43} +(5.74858 - 3.31895i) q^{44} +3.01683i q^{45} -9.13658i q^{46} +(-8.00565 + 4.62206i) q^{47} +(-2.87633 - 4.98195i) q^{48} +(5.12914 + 4.76361i) q^{49} +(-8.90014 - 5.13850i) q^{50} +(0.757096 + 1.31133i) q^{51} +(3.51909 + 15.0219i) q^{52} +(3.90722 - 6.76751i) q^{53} -2.50582i q^{54} +(-2.33989 + 4.05281i) q^{55} +(5.52362 - 14.0643i) q^{56} -8.21689i q^{57} +(-11.9367 - 6.89168i) q^{58} +10.0204i q^{59} +(11.1799 + 6.45469i) q^{60} +(5.23565 - 9.06841i) q^{61} +(-6.47877 + 11.2216i) q^{62} +(2.06892 - 1.64912i) q^{63} +4.00548 q^{64} +(-7.44391 - 7.93124i) q^{65} +(1.94355 - 3.36632i) q^{66} +(2.52349 - 1.45694i) q^{67} +6.47941 q^{68} +(-1.82307 - 3.15765i) q^{69} +(2.97635 + 19.7782i) q^{70} +(-1.11232 + 0.642201i) q^{71} +(-4.94593 - 2.85554i) q^{72} +(-2.27528 - 1.31363i) q^{73} -23.0549 q^{74} -4.10125 q^{75} +(-30.4504 - 17.5805i) q^{76} +(4.05846 - 0.610745i) q^{77} +(6.18301 + 6.58779i) q^{78} +(-3.28050 - 5.68199i) q^{79} +(15.0297 - 8.67739i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.12718 - 7.14848i) q^{82} -5.49127i q^{83} +(-1.68476 - 11.1954i) q^{84} +(-3.95605 + 2.28403i) q^{85} +(-8.58919 + 4.95897i) q^{86} -5.50054 q^{87} +(-4.42958 - 7.67226i) q^{88} +9.76396i q^{89} +7.55962 q^{90} +(-1.37005 + 9.44050i) q^{91} -15.6023 q^{92} +5.17098i q^{93} +(11.5821 + 20.0607i) q^{94} +24.7889 q^{95} +(-2.59199 + 1.49648i) q^{96} +(10.8340 - 6.25500i) q^{97} +(11.9367 - 12.8527i) q^{98} -1.55123i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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