LMFDB - Embedded newform 546.2.by.b.397.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.6
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.620250 - 2.31481i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.53665 - 0.751945i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.620250 - 2.31481i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.53665 - 0.751945i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -2.39646 q^{10} +(-2.37595 + 2.37595i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.14551 + 2.89772i) q^{13} +(-1.38286 + 2.25560i) q^{14} +(2.31481 - 0.620250i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.18530 + 5.51710i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(4.51024 - 4.51024i) q^{19} +(-0.620250 + 2.31481i) q^{20} +(0.751945 - 2.53665i) q^{21} +(1.68005 + 2.90993i) q^{22} +(-5.63845 + 3.25536i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-0.643487 + 0.371517i) q^{25} +(2.24368 + 2.82239i) q^{26} -1.00000i q^{27} +(1.82083 + 1.91953i) q^{28} +(1.87496 - 3.24753i) q^{29} -2.39646i q^{30} +(-5.84629 - 1.56651i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.37595 - 2.37595i) q^{33} +(4.50469 + 4.50469i) q^{34} +(-0.167251 + 6.33824i) q^{35} +(0.866025 + 0.500000i) q^{36} +(3.05363 + 0.818218i) q^{37} +(-3.18922 - 5.52389i) q^{38} +(-2.89772 - 2.14551i) q^{39} +(2.07540 + 1.19823i) q^{40} +(-2.36414 - 8.82310i) q^{41} +(-2.25560 - 1.38286i) q^{42} +(-7.35081 + 4.24399i) q^{43} +(3.24561 - 0.869658i) q^{44} +(0.620250 + 2.31481i) q^{45} +(1.68510 + 6.28888i) q^{46} +(-8.00816 + 2.14578i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(5.86916 + 3.81484i) q^{49} +(0.192312 + 0.717716i) q^{50} +(-5.51710 - 3.18530i) q^{51} +(3.30693 - 1.43674i) q^{52} +(-4.65896 - 8.06956i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(6.97354 + 4.02618i) q^{55} +(2.32539 - 1.26197i) q^{56} +(4.51024 + 4.51024i) q^{57} +(-2.65160 - 2.65160i) q^{58} +(-2.37113 + 0.635342i) q^{59} +(-2.31481 - 0.620250i) q^{60} -7.54245i q^{61} +(-3.02626 + 5.24164i) q^{62} +(2.53665 + 0.751945i) q^{63} -1.00000i q^{64} +(8.03841 + 3.16913i) q^{65} +(-2.90993 + 1.68005i) q^{66} +(5.28059 + 5.28059i) q^{67} +(5.51710 - 3.18530i) q^{68} +(-3.25536 - 5.63845i) q^{69} +(6.07898 + 1.80201i) q^{70} +(0.165170 - 0.616423i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.86646 - 10.6978i) q^{73} +(1.58068 - 2.73781i) q^{74} +(-0.371517 - 0.643487i) q^{75} +(-6.16110 + 1.65086i) q^{76} +(7.81353 - 4.24036i) q^{77} +(-2.82239 + 2.24368i) q^{78} +(-2.75688 + 4.77505i) q^{79} +(1.69456 - 1.69456i) q^{80} +1.00000 q^{81} -9.13435 q^{82} +(-0.287435 + 0.287435i) q^{83} +(-1.91953 + 1.82083i) q^{84} +(14.7467 + 3.95136i) q^{85} +(2.19685 + 8.19877i) q^{86} +(3.24753 + 1.87496i) q^{87} -3.36010i q^{88} +(0.715092 - 2.66876i) q^{89} +2.39646 q^{90} +(7.62133 - 5.73719i) q^{91} +6.51073 q^{92} +(1.56651 - 5.84629i) q^{93} +8.29066i q^{94} +(-13.2378 - 7.64285i) q^{95} +(0.258819 + 0.965926i) q^{96} +(3.55971 + 0.953822i) q^{97} +(5.20390 - 4.68182i) q^{98} +(2.37595 - 2.37595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.620250	−	2.31481i	−0.277384	−	1.03521i	−0.954227	−	0.299084i	$-0.903319\pi$
$5$	−0.620250	−	2.31481i	−0.277384	−	1.03521i	0.676842	−	0.736128i	$-0.263348\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−2.53665	−	0.751945i	−0.958762	−	0.284209i
$7$	−2.53665	−	0.751945i	−0.958762	−	0.284209i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−2.39646			−0.757828
$11$	−2.37595	+	2.37595i	−0.716376	+	0.716376i	−0.967861	−	0.251485i	$-0.919081\pi$
$11$	−2.37595	+	2.37595i	−0.716376	+	0.716376i	0.251485	+	0.967861i	$0.419081\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.14551	+	2.89772i	−0.595058	+	0.803683i
$13$	−2.14551	+	2.89772i	−0.595058	+	0.803683i
$14$	−1.38286	+	2.25560i	−0.369584	+	0.602833i
$15$	2.31481	−	0.620250i	0.597680	−	0.160148i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.18530	+	5.51710i	−0.772548	+	1.33809i	0.163614	+	0.986524i	$0.447685\pi$
$17$	−3.18530	+	5.51710i	−0.772548	+	1.33809i	−0.936162	+	0.351568i	$0.885649\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	4.51024	−	4.51024i	1.03472	−	1.03472i	0.0353450	−	0.999375i	$-0.488747\pi$
$19$	4.51024	−	4.51024i	1.03472	−	1.03472i	0.999375	−	0.0353450i	$-0.0112530\pi$
$20$	−0.620250	+	2.31481i	−0.138692	+	0.517606i
$21$	0.751945	−	2.53665i	0.164088	−	0.553542i
$22$	1.68005	+	2.90993i	0.358188	+	0.620400i
$23$	−5.63845	+	3.25536i	−1.17570	+	0.678790i	−0.955016	−	0.296555i	$-0.904162\pi$
$23$	−5.63845	+	3.25536i	−1.17570	+	0.678790i	−0.220683	+	0.975346i	$0.570829\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−0.643487	+	0.371517i	−0.128697	+	0.0743035i
$26$	2.24368	+	2.82239i	0.440023	+	0.553516i
$27$		−	1.00000i		−	0.192450i
$28$	1.82083	+	1.91953i	0.344104	+	0.362757i
$29$	1.87496	−	3.24753i	0.348172	−	0.603052i	−0.637753	−	0.770241i	$-0.720136\pi$
$29$	1.87496	−	3.24753i	0.348172	−	0.603052i	0.985925	+	0.167189i	$0.0534691\pi$
$30$		−	2.39646i		−	0.437532i
$31$	−5.84629	−	1.56651i	−1.05002	−	0.281353i	−0.307762	−	0.951463i	$-0.599580\pi$
$31$	−5.84629	−	1.56651i	−1.05002	−	0.281353i	−0.742262	+	0.670110i	$0.766247\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−2.37595	−	2.37595i	−0.413600	−	0.413600i
$34$	4.50469	+	4.50469i	0.772548	+	0.772548i
$35$	−0.167251	+	6.33824i	−0.0282705	+	1.07136i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	3.05363	+	0.818218i	0.502014	+	0.134514i	0.500935	−	0.865485i	$-0.332990\pi$
$37$	3.05363	+	0.818218i	0.502014	+	0.134514i	0.00107953	+	0.999999i	$0.499656\pi$
$38$	−3.18922	−	5.52389i	−0.517360	−	0.896094i
$39$	−2.89772	−	2.14551i	−0.464007	−	0.343557i
$40$	2.07540	+	1.19823i	0.328149	+	0.189457i
$41$	−2.36414	−	8.82310i	−0.369217	−	1.37794i	−0.861613	−	0.507566i	$-0.830545\pi$
$41$	−2.36414	−	8.82310i	−0.369217	−	1.37794i	0.492396	−	0.870371i	$-0.336121\pi$
$42$	−2.25560	−	1.38286i	−0.348046	−	0.213379i
$43$	−7.35081	+	4.24399i	−1.12099	+	0.647203i	−0.941653	−	0.336585i	$-0.890728\pi$
$43$	−7.35081	+	4.24399i	−1.12099	+	0.647203i	−0.179335	+	0.983788i	$0.557395\pi$
$44$	3.24561	−	0.869658i	0.489294	−	0.131106i
$45$	0.620250	+	2.31481i	0.0924614	+	0.345071i
$46$	1.68510	+	6.28888i	0.248454	+	0.927245i
$47$	−8.00816	+	2.14578i	−1.16811	+	0.312994i	−0.790201	−	0.612848i	$-0.790024\pi$
$47$	−8.00816	+	2.14578i	−1.16811	+	0.312994i	−0.377910	+	0.925842i	$0.623357\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	5.86916	+	3.81484i	0.838451	+	0.544977i
$50$	0.192312	+	0.717716i	0.0271970	+	0.101500i
$51$	−5.51710	−	3.18530i	−0.772548	−	0.446031i
$52$	3.30693	−	1.43674i	0.458588	−	0.199241i
$53$	−4.65896	−	8.06956i	−0.639958	−	1.10844i	−0.985442	−	0.170015i	$-0.945618\pi$
$53$	−4.65896	−	8.06956i	−0.639958	−	1.10844i	0.345484	−	0.938425i	$-0.387715\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	6.97354	+	4.02618i	0.940312	+	0.542890i
$56$	2.32539	−	1.26197i	0.310743	−	0.168638i
$57$	4.51024	+	4.51024i	0.597396	+	0.597396i
$58$	−2.65160	−	2.65160i	−0.348172	−	0.348172i
$59$	−2.37113	+	0.635342i	−0.308695	+	0.0827145i	−0.409841	−	0.912157i	$-0.634416\pi$
$59$	−2.37113	+	0.635342i	−0.308695	+	0.0827145i	0.101146	+	0.994872i	$0.467749\pi$
$60$	−2.31481	−	0.620250i	−0.298840	−	0.0800740i
$61$		−	7.54245i		−	0.965712i	−0.875700	−	0.482856i	$-0.839600\pi$
$61$		−	7.54245i		−	0.965712i	0.875700	−	0.482856i	$-0.160400\pi$
$62$	−3.02626	+	5.24164i	−0.384335	+	0.665689i
$63$	2.53665	+	0.751945i	0.319587	+	0.0947362i
$64$		−	1.00000i		−	0.125000i
$65$	8.03841	+	3.16913i	0.997042	+	0.393082i
$66$	−2.90993	+	1.68005i	−0.358188	+	0.206800i
$67$	5.28059	+	5.28059i	0.645126	+	0.645126i	0.951811	−	0.306685i	$-0.0992197\pi$
$67$	5.28059	+	5.28059i	0.645126	+	0.645126i	−0.306685	+	0.951811i	$0.599220\pi$
$68$	5.51710	−	3.18530i	0.669046	−	0.386274i
$69$	−3.25536	−	5.63845i	−0.391900	−	0.678790i
$70$	6.07898	+	1.80201i	0.726577	+	0.215381i
$71$	0.165170	−	0.616423i	0.0196021	−	0.0731559i	−0.955432	−	0.295211i	$-0.904610\pi$
$71$	0.165170	−	0.616423i	0.0196021	−	0.0731559i	0.975034	+	0.222055i	$0.0712766\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	2.86646	−	10.6978i	0.335493	−	1.25208i	−0.567840	−	0.823139i	$-0.692221\pi$
$73$	2.86646	−	10.6978i	0.335493	−	1.25208i	0.903333	−	0.428939i	$-0.141113\pi$
$74$	1.58068	−	2.73781i	0.183750	−	0.318264i
$75$	−0.371517	−	0.643487i	−0.0428991	−	0.0743035i
$76$	−6.16110	+	1.65086i	−0.706727	+	0.189367i
$77$	7.81353	−	4.24036i	0.890434	−	0.483234i
$78$	−2.82239	+	2.24368i	−0.319573	+	0.254047i
$79$	−2.75688	+	4.77505i	−0.310173	+	0.537235i	−0.978400	−	0.206722i	$-0.933720\pi$
$79$	−2.75688	+	4.77505i	−0.310173	+	0.537235i	0.668227	+	0.743958i	$0.267054\pi$
$80$	1.69456	−	1.69456i	0.189457	−	0.189457i
$81$	1.00000			0.111111
$82$	−9.13435			−1.00872
$83$	−0.287435	+	0.287435i	−0.0315501	+	0.0315501i	−0.722706	−	0.691156i	$-0.757102\pi$
$83$	−0.287435	+	0.287435i	−0.0315501	+	0.0315501i	0.691156	+	0.722706i	$0.257102\pi$
$84$	−1.91953	+	1.82083i	−0.209438	+	0.198669i
$85$	14.7467	+	3.95136i	1.59950	+	0.428586i
$86$	2.19685	+	8.19877i	0.236893	+	0.884096i
$87$	3.24753	+	1.87496i	0.348172	+	0.201017i
$88$		−	3.36010i		−	0.358188i
$89$	0.715092	−	2.66876i	0.0757996	−	0.282888i	−0.917614	−	0.397473i	$-0.869887\pi$
$89$	0.715092	−	2.66876i	0.0757996	−	0.282888i	0.993413	+	0.114585i	$0.0365539\pi$
$90$	2.39646			0.252609
$91$	7.62133	−	5.73719i	0.798933	−	0.601421i
$92$	6.51073			0.678790
$93$	1.56651	−	5.84629i	0.162439	−	0.606232i
$94$			8.29066i			0.855116i
$95$	−13.2378	−	7.64285i	−1.35817	−	0.784140i
$96$	0.258819	+	0.965926i	0.0264156	+	0.0985844i
$97$	3.55971	+	0.953822i	0.361434	+	0.0968460i	0.434966	−	0.900447i	$-0.356760\pi$
$97$	3.55971	+	0.953822i	0.361434	+	0.0968460i	−0.0735319	+	0.997293i	$0.523427\pi$
$98$	5.20390	−	4.68182i	0.525673	−	0.472935i
$99$	2.37595	−	2.37595i	0.238792	−	0.238792i
$100$	0.743035			0.0743035
$101$	−4.84536			−0.482131			−0.241066	−	0.970509i	$-0.577497\pi$
$101$	−4.84536			−0.482131			−0.241066	+	0.970509i	$0.577497\pi$
$102$	−4.50469	+	4.50469i	−0.446031	+	0.446031i
$103$	8.89257	−	15.4024i	0.876211	−	1.51764i	0.0207442	−	0.999785i	$-0.493396\pi$
$103$	8.89257	−	15.4024i	0.876211	−	1.51764i	0.855467	−	0.517857i	$-0.173270\pi$
$104$	−0.531892	−	3.56610i	−0.0521563	−	0.349685i
$105$	−6.33824	−	0.167251i	−0.618549	−	0.0163220i
$106$	−9.00043	+	2.41166i	−0.874199	+	0.234241i
$107$	6.68786	+	11.5837i	0.646540	+	1.11984i	0.983944	+	0.178480i	$0.0571178\pi$
$107$	6.68786	+	11.5837i	0.646540	+	1.11984i	−0.337404	+	0.941360i	$0.609549\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−2.65649	+	9.91417i	−0.254446	+	0.949605i	0.713952	+	0.700195i	$0.246904\pi$
$109$	−2.65649	+	9.91417i	−0.254446	+	0.949605i	−0.968398	+	0.249411i	$0.919763\pi$
$110$	5.69387	−	5.69387i	0.542890	−	0.542890i
$111$	−0.818218	+	3.05363i	−0.0776619	+	0.289838i
$112$	−0.617120	−	2.57277i	−0.0583124	−	0.243104i
$113$	6.08846	+	10.5455i	0.572754	+	0.992040i	0.996282	+	0.0861564i	$0.0274585\pi$
$113$	6.08846	+	10.5455i	0.572754	+	0.992040i	−0.423527	+	0.905883i	$0.639208\pi$
$114$	5.52389	−	3.18922i	0.517360	−	0.298698i
$115$	11.0328	+	11.0328i	1.02881	+	1.02881i
$116$	−3.24753	+	1.87496i	−0.301526	+	0.174086i
$117$	2.14551	−	2.89772i	0.198353	−	0.267894i
$118$			2.45477i			0.225980i
$119$	12.2285	−	11.5998i	1.12099	−	1.06335i
$120$	−1.19823	+	2.07540i	−0.109383	+	0.189457i
$121$		−	0.290272i		−	0.0263883i
$122$	−7.28545	−	1.95213i	−0.659593	−	0.176737i
$123$	8.82310	−	2.36414i	0.795552	−	0.213168i
$124$	4.27978	+	4.27978i	0.384335	+	0.384335i
$125$	−7.21366	−	7.21366i	−0.645210	−	0.645210i
$126$	1.38286	−	2.25560i	0.123195	−	0.200944i
$127$	3.36327	+	1.94179i	0.298442	+	0.172306i	0.641743	−	0.766920i	$-0.278212\pi$
$127$	3.36327	+	1.94179i	0.298442	+	0.172306i	−0.343301	+	0.939226i	$0.611545\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−4.24399	−	7.35081i	−0.373663	−	0.647203i
$130$	5.14164	−	6.94428i	0.450951	−	0.609054i
$131$	−14.6139	−	8.43733i	−1.27682	−	0.737173i	−0.300559	−	0.953763i	$-0.597173\pi$
$131$	−14.6139	−	8.43733i	−1.27682	−	0.737173i	−0.976263	+	0.216590i	$0.930507\pi$
$132$	0.869658	+	3.24561i	0.0756940	+	0.282494i
$133$	−14.8323	+	8.04944i	−1.28613	+	0.697975i
$134$	6.46737	−	3.73394i	0.558696	−	0.322563i
$135$	−2.31481	+	0.620250i	−0.199227	+	0.0533826i
$136$	−1.64883	−	6.15352i	−0.141386	−	0.527660i
$137$	0.0755407	+	0.281922i	0.00645388	+	0.0240862i	0.969078	−	0.246756i	$-0.0793646\pi$
$137$	0.0755407	+	0.281922i	0.00645388	+	0.0240862i	−0.962624	+	0.270842i	$0.912698\pi$
$138$	−6.28888	+	1.68510i	−0.535345	+	0.143445i
$139$	−7.59129	+	4.38283i	−0.643884	+	0.371747i	−0.786109	−	0.618088i	$-0.787908\pi$
$139$	−7.59129	+	4.38283i	−0.643884	+	0.371747i	0.142225	+	0.989834i	$0.454574\pi$
$140$	3.31396	−	5.40545i	0.280081	−	0.456844i
$141$	−2.14578	−	8.00816i	−0.180707	−	0.674409i
$142$	−0.552669	−	0.319084i	−0.0463790	−	0.0267769i
$143$	−1.78721	−	11.9825i	−0.149454	−	1.00202i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−8.68036	−	2.32589i	−0.720864	−	0.193155i
$146$	−9.59135	−	5.53757i	−0.793786	−	0.458292i
$147$	−3.81484	+	5.86916i	−0.314643	+	0.484080i
$148$	−2.23541	−	2.23541i	−0.183750	−	0.183750i
$149$	−2.93611	−	2.93611i	−0.240535	−	0.240535i	0.576536	−	0.817072i	$-0.304404\pi$
$149$	−2.93611	−	2.93611i	−0.240535	−	0.240535i	−0.817072	+	0.576536i	$0.804404\pi$
$150$	−0.717716	+	0.192312i	−0.0586013	+	0.0157022i
$151$	12.5283	+	3.35695i	1.01954	+	0.273185i	0.729610	−	0.683864i	$-0.239702\pi$
$151$	12.5283	+	3.35695i	1.01954	+	0.273185i	0.289929	+	0.957048i	$0.406368\pi$
$152$			6.37844i			0.517360i
$153$	3.18530	−	5.51710i	0.257516	−	0.446031i
$154$	−2.07358	−	8.64478i	−0.167094	−	0.696616i
$155$			14.5046i			1.16504i
$156$	1.43674	+	3.30693i	0.115032	+	0.264766i
$157$	−7.83081	+	4.52112i	−0.624966	+	0.360825i	−0.778800	−	0.627272i	$-0.784171\pi$
$157$	−7.83081	+	4.52112i	−0.624966	+	0.360825i	0.153834	+	0.988097i	$0.450838\pi$
$158$	3.89881	+	3.89881i	0.310173	+	0.310173i
$159$	8.06956	−	4.65896i	0.639958	−	0.369480i
$160$	−1.19823	−	2.07540i	−0.0947285	−	0.164075i
$161$	16.7506	−	4.01790i	1.32013	−	0.316655i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	7.06636	−	7.06636i	0.553480	−	0.553480i	−0.373964	−	0.927443i	$-0.622001\pi$
$163$	7.06636	−	7.06636i	0.553480	−	0.553480i	0.927443	+	0.373964i	$0.122001\pi$
$164$	−2.36414	+	8.82310i	−0.184609	+	0.688968i
$165$	−4.02618	+	6.97354i	−0.313437	+	0.542890i
$166$	0.203247	+	0.352035i	0.0157750	+	0.0273232i
$167$	−9.35729	+	2.50728i	−0.724089	+	0.194019i	−0.601995	−	0.798500i	$-0.705627\pi$
$167$	−9.35729	+	2.50728i	−0.724089	+	0.194019i	−0.122093	+	0.992519i	$0.538961\pi$
$168$	1.26197	+	2.32539i	0.0973635	+	0.179407i
$169$	−3.79356	−	12.4342i	−0.291813	−	0.956475i
$170$	7.63345	−	13.2215i	0.585459	−	1.01404i
$171$	−4.51024	+	4.51024i	−0.344907	+	0.344907i
$172$	8.48799			0.647203
$173$	−8.79475			−0.668653			−0.334326	−	0.942457i	$-0.608509\pi$
$173$	−8.79475			−0.668653			−0.334326	+	0.942457i	$0.608509\pi$
$174$	2.65160	−	2.65160i	0.201017	−	0.201017i
$175$	1.91166	−	0.458542i	0.144508	−	0.0346625i
$176$	−3.24561	−	0.869658i	−0.244647	−	0.0655529i
$177$	−0.635342	−	2.37113i	−0.0477552	−	0.178225i
$178$	−2.39274	−	1.38145i	−0.179344	−	0.103544i
$179$			13.1864i			0.985600i	0.870143	+	0.492800i	$0.164027\pi$
$179$			13.1864i			0.985600i	−0.870143	+	0.492800i	$0.835973\pi$
$180$	0.620250	−	2.31481i	0.0462307	−	0.172535i
$181$	1.53653			0.114209			0.0571046	−	0.998368i	$-0.481813\pi$
$181$	1.53653			0.114209			0.0571046	+	0.998368i	$0.481813\pi$
$182$	−3.56915	−	8.84653i	−0.264563	−	0.655749i
$183$	7.54245			0.557554
$184$	1.68510	−	6.28888i	0.124227	−	0.463622i
$185$		−	7.57607i		−	0.557003i
$186$	−5.24164	−	3.02626i	−0.384335	−	0.221896i
$187$	−5.54024	−	20.6765i	−0.405142	−	1.51201i
$188$	8.00816	+	2.14578i	0.584055	+	0.156497i
$189$	−0.751945	+	2.53665i	−0.0546960	+	0.184514i
$190$	−10.8086	+	10.8086i	−0.784140	+	0.784140i
$191$	−27.2183			−1.96944			−0.984722	−	0.174133i	$-0.944288\pi$
$191$	−27.2183			−1.96944			−0.984722	+	0.174133i	$0.944288\pi$
$192$	1.00000			0.0721688
$193$	1.51835	−	1.51835i	0.109293	−	0.109293i	−0.650346	−	0.759639i	$-0.725376\pi$
$193$	1.51835	−	1.51835i	0.109293	−	0.109293i	0.759639	+	0.650346i	$0.225376\pi$
$194$	1.84264	−	3.19155i	0.132294	−	0.229140i
$195$	−3.16913	+	8.03841i	−0.226946	+	0.575643i
$196$	−3.17542	−	6.23833i	−0.226816	−	0.445595i
$197$	21.2058	−	5.68207i	1.51085	−	0.404831i	0.594132	−	0.804368i	$-0.297496\pi$
$197$	21.2058	−	5.68207i	1.51085	−	0.404831i	0.916717	+	0.399537i	$0.130829\pi$
$198$	−1.68005	−	2.90993i	−0.119396	−	0.206800i
$199$	12.5189	−	21.6834i	0.887443	−	1.53710i	0.0445561	−	0.999007i	$-0.485813\pi$
$199$	12.5189	−	21.6834i	0.887443	−	1.53710i	0.842887	−	0.538090i	$-0.180854\pi$
$200$	0.192312	−	0.717716i	0.0135985	−	0.0507502i
$201$	−5.28059	+	5.28059i	−0.372464	+	0.372464i
$202$	−1.25407	+	4.68026i	−0.0882361	+	0.329302i
$203$	−7.19809	+	6.82798i	−0.505207	+	0.479230i
$204$	3.18530	+	5.51710i	0.223015	+	0.386274i
$205$	−18.9574	+	10.9451i	−1.32404	+	0.764436i
$206$	−12.5760	−	12.5760i	−0.876211	−	0.876211i
$207$	5.63845	−	3.25536i	0.391900	−	0.226263i
$208$	−3.58225	−	0.409207i	−0.248385	−	0.0283734i
$209$			21.4322i			1.48250i
$210$	−1.80201	+	6.07898i	−0.124350	+	0.419490i
$211$	−11.9314	+	20.6658i	−0.821392	+	1.42269i	0.0832538	+	0.996528i	$0.473469\pi$
$211$	−11.9314	+	20.6658i	−0.821392	+	1.42269i	−0.904646	+	0.426164i	$0.859865\pi$
$212$			9.31793i			0.639958i
$213$	0.616423	+	0.165170i	0.0422366	+	0.0113173i
$214$	12.9199	−	3.46189i	0.883190	−	0.236650i
$215$	14.3834	+	14.3834i	0.980937	+	0.980937i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	13.6520	+	8.36976i	0.926761	+	0.568177i
$218$	8.88880	+	5.13195i	0.602026	+	0.347580i
$219$	10.6978	+	2.86646i	0.722888	+	0.193697i
$220$	−4.02618	−	6.97354i	−0.271445	−	0.470156i
$221$	−9.15291	−	21.0671i	−0.615692	−	1.41713i
$222$	2.73781	+	1.58068i	0.183750	+	0.106088i
$223$	3.96426	+	14.7948i	0.265467	+	0.990735i	0.961964	+	0.273176i	$0.0880740\pi$
$223$	3.96426	+	14.7948i	0.265467	+	0.990735i	−0.696498	+	0.717559i	$0.745259\pi$
$224$	−2.64483	−	0.0697906i	−0.176715	−	0.00466308i
$225$	0.643487	−	0.371517i	0.0428991	−	0.0247678i
$226$	11.7620	−	3.15162i	0.782397	−	0.209643i
$227$	2.68985	+	10.0387i	0.178532	+	0.666290i	0.995923	+	0.0902070i	$0.0287529\pi$
$227$	2.68985	+	10.0387i	0.178532	+	0.666290i	−0.817391	+	0.576083i	$0.804580\pi$
$228$	−1.65086	−	6.16110i	−0.109331	−	0.408029i
$229$	−14.8969	+	3.99160i	−0.984413	+	0.263773i	−0.714902	−	0.699225i	$-0.753529\pi$
$229$	−14.8969	+	3.99160i	−0.984413	+	0.263773i	−0.269511	+	0.962997i	$0.586862\pi$
$230$	13.5123	−	7.80136i	0.890978	−	0.514406i
$231$	4.24036	+	7.81353i	0.278995	+	0.514092i
$232$	0.970553	+	3.62215i	0.0637199	+	0.237806i
$233$	−3.08882	−	1.78333i	−0.202355	−	0.116830i	0.395398	−	0.918510i	$-0.370607\pi$
$233$	−3.08882	−	1.78333i	−0.202355	−	0.116830i	−0.597754	+	0.801680i	$0.703940\pi$
$234$	−2.24368	−	2.82239i	−0.146674	−	0.184505i
$235$	9.93413	+	17.2064i	0.648031	+	1.12242i
$236$	2.37113	+	0.635342i	0.154347	+	0.0413573i
$237$	−4.77505	−	2.75688i	−0.310173	−	0.179078i
$238$	−8.03953	−	14.8141i	−0.521125	−	0.960255i
$239$	−13.8603	−	13.8603i	−0.896550	−	0.896550i	0.0985792	−	0.995129i	$-0.468570\pi$
$239$	−13.8603	−	13.8603i	−0.896550	−	0.896550i	−0.995129	+	0.0985792i	$0.968570\pi$
$240$	1.69456	+	1.69456i	0.109383	+	0.109383i
$241$	26.8046	−	7.18226i	1.72663	−	0.462650i	0.747230	−	0.664565i	$-0.231383\pi$
$241$	26.8046	−	7.18226i	1.72663	−	0.462650i	0.979403	+	0.201915i	$0.0647165\pi$
$242$	−0.280381	−	0.0751278i	−0.0180236	−	0.00482940i
$243$			1.00000i			0.0641500i
$244$	−3.77122	+	6.53195i	−0.241428	+	0.418165i
$245$	5.19026	−	15.9521i	0.331594	−	1.01914i
$246$		−	9.13435i		−	0.582385i
$247$	3.39264	+	22.7462i	0.215869	+	1.44731i
$248$	5.24164	−	3.02626i	0.332844	−	0.192168i
$249$	−0.287435	−	0.287435i	−0.0182155	−	0.0182155i
$250$	−8.83490	+	5.10083i	−0.558768	+	0.322605i
$251$	10.3080	+	17.8540i	0.650637	+	1.12694i	0.982969	+	0.183774i	$0.0588314\pi$
$251$	10.3080	+	17.8540i	0.650637	+	1.12694i	−0.332332	+	0.943163i	$0.607835\pi$
$252$	−1.82083	−	1.91953i	−0.114701	−	0.120919i
$253$	5.66210	−	21.1313i	0.355973	−	1.32851i
$254$	2.74610	−	2.74610i	0.172306	−	0.172306i
$255$	−3.95136	+	14.7467i	−0.247444	+	0.923473i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.5038	+	19.9251i	0.717586	+	1.24289i	0.961954	+	0.273212i	$0.0880862\pi$
$257$	11.5038	+	19.9251i	0.717586	+	1.24289i	−0.244368	+	0.969683i	$0.578581\pi$
$258$	−8.19877	+	2.19685i	−0.510433	+	0.136770i
$259$	−7.13073	−	4.37170i	−0.443082	−	0.271644i
$260$	−5.37690	−	6.76375i	−0.333461	−	0.419470i
$261$	−1.87496	+	3.24753i	−0.116057	+	0.201017i
$262$	−11.9322	+	11.9322i	−0.737173	+	0.737173i
$263$	10.8423			0.668568			0.334284	−	0.942472i	$-0.391506\pi$
$263$	10.8423			0.668568			0.334284	+	0.942472i	$0.391506\pi$
$264$	3.36010			0.206800
$265$	−15.7897	+	15.7897i	−0.969956	+	0.969956i
$266$	3.93627	+	16.4103i	0.241348	+	1.00618i
$267$	2.66876	+	0.715092i	0.163325	+	0.0437629i
$268$	−1.93283	−	7.21342i	−0.118066	−	0.440630i
$269$	18.5510	+	10.7104i	1.13108	+	0.653027i	0.944205	−	0.329358i	$-0.106832\pi$
$269$	18.5510	+	10.7104i	1.13108	+	0.653027i	0.186870	+	0.982385i	$0.440166\pi$
$270$			2.39646i			0.145844i
$271$	−8.49687	+	31.7107i	−0.516148	+	1.92629i	−0.184835	+	0.982770i	$0.559175\pi$
$271$	−8.49687	+	31.7107i	−0.516148	+	1.92629i	−0.331313	+	0.943521i	$0.607492\pi$
$272$	−6.37060			−0.386274
$273$	5.73719	+	7.62133i	0.347230	+	0.461264i
$274$	0.291867			0.0176323
$275$	0.646186	−	2.41160i	0.0389665	−	0.145425i
$276$			6.51073i			0.391900i
$277$	−15.5130	−	8.95644i	−0.932086	−	0.538140i	−0.0446154	−	0.999004i	$-0.514206\pi$
$277$	−15.5130	−	8.95644i	−0.932086	−	0.538140i	−0.887471	+	0.460864i	$0.847540\pi$
$278$	2.26872	+	8.46698i	0.136069	+	0.507816i
$279$	5.84629	+	1.56651i	0.350008	+	0.0937844i
$280$	−4.36355	−	4.60008i	−0.260772	−	0.274907i
$281$	−7.49939	+	7.49939i	−0.447376	+	0.447376i	−0.894481	−	0.447105i	$-0.852455\pi$
$281$	−7.49939	+	7.49939i	−0.447376	+	0.447376i	0.447105	+	0.894481i	$0.352455\pi$
$282$	−8.29066			−0.493702
$283$	−21.7378			−1.29218			−0.646088	−	0.763263i	$-0.723596\pi$
$283$	−21.7378			−1.29218			−0.646088	+	0.763263i	$0.723596\pi$
$284$	−0.451253	+	0.451253i	−0.0267769	+	0.0267769i
$285$	7.64285	−	13.2378i	0.452723	−	0.784140i
$286$	−12.0367	−	1.37498i	−0.711747	−	0.0813040i
$287$	−0.637491	+	24.1588i	−0.0376299	+	1.42605i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	−11.7922	−	20.4248i	−0.693661	−	1.20146i
$290$	−4.49328	+	7.78260i	−0.263855	+	0.457010i
$291$	−0.953822	+	3.55971i	−0.0559141	+	0.208674i
$292$	−7.83130	+	7.83130i	−0.458292	+	0.458292i
$293$	−0.450034	+	1.67955i	−0.0262913	+	0.0981203i	−0.977825	−	0.209425i	$-0.932841\pi$
$293$	−0.450034	+	1.67955i	−0.0262913	+	0.0981203i	0.951533	+	0.307545i	$0.0995075\pi$
$294$	4.68182	+	5.20390i	0.273049	+	0.303498i
$295$	2.94139	+	5.09463i	0.171254	+	0.296621i
$296$	−2.73781	+	1.58068i	−0.159132	+	0.0918750i
$297$	2.37595	+	2.37595i	0.137867	+	0.137867i
$298$	−3.59598	+	2.07614i	−0.208310	+	0.120268i
$299$	2.66423	−	23.3231i	0.154077	−	1.34881i
$300$			0.743035i			0.0428991i
$301$	21.8377	−	5.23811i	1.25870	−	0.301919i
$302$	6.48513	−	11.2326i	0.373177	−	0.646362i
$303$		−	4.84536i		−	0.278359i
$304$	6.16110	+	1.65086i	0.353363	+	0.0946835i
$305$	−17.4593	+	4.67821i	−0.999717	+	0.267873i
$306$	−4.50469	−	4.50469i	−0.257516	−	0.257516i
$307$	−10.5367	−	10.5367i	−0.601358	−	0.601358i	0.339315	−	0.940673i	$-0.389805\pi$
$307$	−10.5367	−	10.5367i	−0.601358	−	0.601358i	−0.940673	+	0.339315i	$0.889805\pi$
$308$	−8.88690	−	0.234503i	−0.506378	−	0.0133621i
$309$	15.4024	+	8.89257i	0.876211	+	0.505881i
$310$	14.0104	+	3.75408i	0.795738	+	0.213217i
$311$	−0.0418085	−	0.0724144i	−0.00237074	−	0.00410624i	0.864838	−	0.502052i	$-0.167421\pi$
$311$	−0.0418085	−	0.0724144i	−0.00237074	−	0.00410624i	−0.867208	+	0.497945i	$0.834088\pi$
$312$	3.56610	−	0.531892i	0.201891	−	0.0301125i
$313$	−21.7563	−	12.5610i	−1.22974	−	0.709991i	−0.262765	−	0.964860i	$-0.584634\pi$
$313$	−21.7563	−	12.5610i	−1.22974	−	0.709991i	−0.966976	+	0.254869i	$0.917968\pi$
$314$	2.34030	+	8.73413i	0.132071	+	0.492895i
$315$	0.167251	−	6.33824i	0.00942350	−	0.357119i
$316$	4.77505	−	2.75688i	0.268618	−	0.155086i
$317$	−19.3195	+	5.17664i	−1.08509	+	0.290749i	−0.756680	−	0.653786i	$-0.773180\pi$
$317$	−19.3195	+	5.17664i	−1.08509	+	0.290749i	−0.328411	+	0.944535i	$0.606513\pi$
$318$	−2.41166	−	9.00043i	−0.135239	−	0.504719i
$319$	3.26116	+	12.1708i	0.182590	+	0.681434i
$320$	−2.31481	+	0.620250i	−0.129402	+	0.0346730i
$321$	−11.5837	+	6.68786i	−0.646540	+	0.373280i
$322$	0.454387	−	17.2198i	0.0253220	−	0.959620i
$323$	10.5170	+	39.2499i	0.585180	+	2.18392i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	0.304055	−	2.66174i	0.0168659	−	0.147647i
$326$	−4.99667	−	8.65449i	−0.276740	−	0.479328i
$327$	−9.91417	−	2.65649i	−0.548255	−	0.146904i
$328$	7.91058	+	4.56717i	0.436788	+	0.252180i
$329$	21.9274	+	0.578610i	1.20890	+	0.0318998i
$330$	5.69387	+	5.69387i	0.313437	+	0.313437i
$331$	8.07828	+	8.07828i	0.444022	+	0.444022i	0.893361	−	0.449339i	$-0.148341\pi$
$331$	8.07828	+	8.07828i	0.444022	+	0.444022i	−0.449339	+	0.893361i	$0.648341\pi$
$332$	0.392643	−	0.105209i	0.0215491	−	0.00577407i
$333$	−3.05363	−	0.818218i	−0.167338	−	0.0448381i
$334$			9.68738i			0.530070i
$335$	8.94825	−	15.4988i	0.488895	−	0.846791i
$336$	2.57277	−	0.617120i	0.140356	−	0.0336667i
$337$		−	0.594432i		−	0.0323808i	−0.999869	−	0.0161904i	$-0.994846\pi$
$337$		−	0.594432i		−	0.0323808i	0.999869	−	0.0161904i	$-0.00515378\pi$
$338$	−12.9923	+	0.446099i	−0.706690	+	0.0242646i
$339$	−10.5455	+	6.08846i	−0.572754	+	0.330680i
$340$	−10.7953	−	10.7953i	−0.585459	−	0.585459i
$341$	17.6124	−	10.1685i	0.953766	−	0.550657i
$342$	3.18922	+	5.52389i	0.172453	+	0.298698i
$343$	−12.0194	−	14.0902i	−0.648988	−	0.760798i
$344$	2.19685	−	8.19877i	0.118446	−	0.442048i
$345$	−11.0328	+	11.0328i	−0.593985	+	0.593985i
$346$	−2.27625	+	8.49508i	−0.122372	+	0.456698i
$347$	13.5542	−	23.4766i	0.727629	−	1.26029i	−0.230254	−	0.973131i	$-0.573956\pi$
$347$	13.5542	−	23.4766i	0.727629	−	1.26029i	0.957883	−	0.287160i	$-0.0927111\pi$
$348$	−1.87496	−	3.24753i	−0.100509	−	0.174086i
$349$	3.89257	−	1.04301i	0.208365	−	0.0558311i	−0.153127	−	0.988207i	$-0.548934\pi$
$349$	3.89257	−	1.04301i	0.208365	−	0.0558311i	0.361491	+	0.932375i	$0.382268\pi$
$350$	0.0518568	−	1.96520i	0.00277186	−	0.105044i
$351$	2.89772	+	2.14551i	0.154669	+	0.114519i
$352$	−1.68005	+	2.90993i	−0.0895470	+	0.155100i
$353$	−13.3776	+	13.3776i	−0.712016	+	0.712016i	−0.966957	−	0.254941i	$-0.917944\pi$
$353$	−13.3776	+	13.3776i	−0.712016	+	0.712016i	0.254941	+	0.966957i	$0.417944\pi$
$354$	−2.45477			−0.130470
$355$	−1.52935			−0.0811692
$356$	−1.95367	+	1.95367i	−0.103544	+	0.103544i
$357$	11.5998	+	12.2285i	0.613924	+	0.647202i
$358$	12.7371	+	3.41290i	0.673177	+	0.180377i
$359$	−1.93271	−	7.21299i	−0.102005	−	0.380687i	0.895983	−	0.444088i	$-0.146472\pi$
$359$	−1.93271	−	7.21299i	−0.102005	−	0.380687i	−0.997988	+	0.0634006i	$0.979805\pi$
$360$	−2.07540	−	1.19823i	−0.109383	−	0.0631523i
$361$		−	21.6845i		−	1.14129i
$362$	0.397682	−	1.48417i	0.0209017	−	0.0780063i
$363$	0.290272			0.0152353
$364$	−9.46886	+	1.15788i	−0.496303	+	0.0606896i
$365$	−26.5412			−1.38923
$366$	1.95213	−	7.28545i	0.102039	−	0.380816i
$367$		−	36.4451i		−	1.90242i	−0.308546	−	0.951209i	$-0.599843\pi$
$367$		−	36.4451i		−	1.90242i	0.308546	−	0.951209i	$-0.400157\pi$
$368$	−5.63845	−	3.25536i	−0.293925	−	0.169698i
$369$	2.36414	+	8.82310i	0.123072	+	0.459312i
$370$	−7.31792	−	1.96083i	−0.380440	−	0.101939i
$371$	5.75028	+	23.9729i	0.298540	+	1.24461i
$372$	−4.27978	+	4.27978i	−0.221896	+	0.221896i
$373$	−12.7227			−0.658758			−0.329379	−	0.944198i	$-0.606839\pi$
$373$	−12.7227			−0.658758			−0.329379	+	0.944198i	$0.606839\pi$
$374$	−21.4058			−1.10687
$375$	7.21366	−	7.21366i	0.372512	−	0.372512i
$376$	4.14533	−	7.17992i	0.213779	−	0.370276i
$377$	5.38769	+	12.4007i	0.277480	+	0.638671i
$378$	2.25560	+	1.38286i	0.116015	+	0.0711264i
$379$	−5.32301	+	1.42630i	−0.273425	+	0.0732640i	−0.392926	−	0.919570i	$-0.628537\pi$
$379$	−5.32301	+	1.42630i	−0.273425	+	0.0732640i	0.119501	+	0.992834i	$0.461870\pi$
$380$	7.64285	+	13.2378i	0.392070	+	0.679085i
$381$	−1.94179	+	3.36327i	−0.0994807	+	0.172306i
$382$	−7.04460	+	26.2908i	−0.360433	+	1.34516i
$383$	4.74343	−	4.74343i	0.242378	−	0.242378i	−0.575455	−	0.817833i	$-0.695175\pi$
$383$	4.74343	−	4.74343i	0.242378	−	0.242378i	0.817833	+	0.575455i	$0.195175\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	−14.6620	−	15.4567i	−0.747242	−	0.787747i
$386$	−1.07363	−	1.85959i	−0.0546465	−	0.0946505i
$387$	7.35081	−	4.24399i	0.373663	−	0.215734i
$388$	−2.60589	−	2.60589i	−0.132294	−	0.132294i
$389$	21.4686	−	12.3949i	1.08850	−	0.628446i	0.155324	−	0.987864i	$-0.450358\pi$
$389$	21.4686	−	12.3949i	1.08850	−	0.628446i	0.933177	+	0.359417i	$0.117025\pi$
$390$	6.94428	+	5.14164i	0.351637	+	0.260357i
$391$		−	41.4772i		−	2.09759i
$392$	−6.84762	+	1.45262i	−0.345857	+	0.0733685i
$393$	8.43733	−	14.6139i	0.425607	−	0.737173i
$394$		−	21.9538i		−	1.10602i
$395$	12.7633	+	3.41991i	0.642190	+	0.172074i
$396$	−3.24561	+	0.869658i	−0.163098	+	0.0437020i
$397$	−10.8637	−	10.8637i	−0.545235	−	0.545235i	0.379824	−	0.925059i	$-0.375985\pi$
$397$	−10.8637	−	10.8637i	−0.545235	−	0.545235i	−0.925059	+	0.379824i	$0.875985\pi$
$398$	−17.7044	−	17.7044i	−0.887443	−	0.887443i
$399$	−8.04944	−	14.8323i	−0.402976	−	0.742546i
$400$	−0.643487	−	0.371517i	−0.0321743	−	0.0185759i
$401$	−16.8846	−	4.52422i	−0.843178	−	0.225929i	−0.188723	−	0.982030i	$-0.560435\pi$
$401$	−16.8846	−	4.52422i	−0.843178	−	0.225929i	−0.654454	+	0.756102i	$0.727102\pi$
$402$	3.73394	+	6.46737i	0.186232	+	0.322563i
$403$	17.0826	−	13.5799i	0.850944	−	0.676465i
$404$	4.19620	+	2.42268i	0.208769	+	0.120533i
$405$	−0.620250	−	2.31481i	−0.0308205	−	0.115024i
$406$	4.73232	+	8.72003i	0.234861	+	0.432768i
$407$	−9.19932	+	5.31123i	−0.455994	+	0.263268i
$408$	6.15352	−	1.64883i	0.304645	−	0.0816293i
$409$	−7.21837	−	26.9393i	−0.356926	−	1.33206i	−0.878044	−	0.478580i	$-0.841152\pi$
$409$	−7.21837	−	26.9393i	−0.356926	−	1.33206i	0.521118	−	0.853484i	$-0.325515\pi$
$410$	5.66558	+	21.1442i	0.279803	+	1.04424i
$411$	−0.281922	+	0.0755407i	−0.0139062	+	0.00372615i
$412$	−15.4024	+	8.89257i	−0.758821	+	0.438106i
$413$	6.49246	+	0.171320i	0.319473	+	0.00843011i
$414$	−1.68510	−	6.28888i	−0.0828181	−	0.309082i
$415$	0.843638	+	0.487074i	0.0414125	+	0.0239095i
$416$	−1.32242	+	3.35428i	−0.0648369	+	0.164457i
$417$	−4.38283	−	7.59129i	−0.214628	−	0.371747i
$418$	20.7019	+	5.54706i	1.01256	+	0.271316i
$419$	−13.7060	−	7.91317i	−0.669583	−	0.386584i	0.126336	−	0.991988i	$-0.459678\pi$
$419$	−13.7060	−	7.91317i	−0.669583	−	0.386584i	−0.795919	+	0.605404i	$0.793012\pi$
$420$	5.40545	+	3.31396i	0.263759	+	0.161705i
$421$	13.1569	+	13.1569i	0.641228	+	0.641228i	0.950857	−	0.309629i	$-0.100205\pi$
$421$	13.1569	+	13.1569i	0.641228	+	0.641228i	−0.309629	+	0.950857i	$0.600205\pi$
$422$	16.8736	+	16.8736i	0.821392	+	0.821392i
$423$	8.00816	−	2.14578i	0.389370	−	0.104331i
$424$	9.00043	+	2.41166i	0.437099	+	0.117120i
$425$		−	4.73357i		−	0.229612i
$426$	0.319084	−	0.552669i	0.0154597	−	0.0267769i
$427$	−5.67151	+	19.1325i	−0.274463	+	0.925888i
$428$		−	13.3757i		−	0.646540i
$429$	11.9825	−	1.78721i	0.578519	−	0.0862874i
$430$	17.6159	−	10.1706i	0.849516	−	0.490469i
$431$	−4.12267	−	4.12267i	−0.198582	−	0.198582i	0.600810	−	0.799392i	$-0.294845\pi$
$431$	−4.12267	−	4.12267i	−0.198582	−	0.198582i	−0.799392	+	0.600810i	$0.794845\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	15.2205	+	26.3626i	0.731449	+	1.26691i	0.956264	+	0.292506i	$0.0944891\pi$
$433$	15.2205	+	26.3626i	0.731449	+	1.26691i	−0.224814	+	0.974402i	$0.572178\pi$
$434$	11.6180	−	11.0206i	0.557681	−	0.529006i
$435$	2.32589	−	8.68036i	0.111518	−	0.416191i
$436$	7.25768	−	7.25768i	0.347580	−	0.347580i
$437$	−10.7483	+	40.1133i	−0.514162	+	1.91888i
$438$	5.53757	−	9.59135i	0.264595	−	0.458292i
$439$	0.203070	+	0.351727i	0.00969198	+	0.0167870i	0.870831	−	0.491583i	$-0.163582\pi$
$439$	0.203070	+	0.351727i	0.00969198	+	0.0167870i	−0.861139	+	0.508370i	$0.830248\pi$
$440$	−7.77798	+	2.08410i	−0.370801	+	0.0993557i
$441$	−5.86916	−	3.81484i	−0.279484	−	0.181659i
$442$	−22.7182	+	3.38847i	−1.08059	+	0.161173i
$443$	−9.26476	+	16.0470i	−0.440182	+	0.762418i	−0.997703	−	0.0677454i	$-0.978419\pi$
$443$	−9.26476	+	16.0470i	−0.440182	+	0.762418i	0.557521	+	0.830163i	$0.311753\pi$
$444$	2.23541	−	2.23541i	0.106088	−	0.106088i
$445$	−6.62120			−0.313875
$446$	15.3167			0.725268
$447$	2.93611	−	2.93611i	0.138873	−	0.138873i
$448$	−0.751945	+	2.53665i	−0.0355261	+	0.119845i
$449$	−3.33970	−	0.894870i	−0.157610	−	0.0422315i	0.179151	−	0.983822i	$-0.442665\pi$
$449$	−3.33970	−	0.894870i	−0.157610	−	0.0422315i	−0.336761	+	0.941590i	$0.609332\pi$
$450$	−0.192312	−	0.717716i	−0.00906565	−	0.0338335i
$451$	26.5803	+	15.3462i	1.25162	+	0.722622i
$452$		−	12.1769i		−	0.572754i
$453$	−3.35695	+	12.5283i	−0.157723	+	0.588631i
$454$	10.3928			0.487758
$455$	−18.0076	−	14.0834i	−0.844210	−	0.660240i
$456$	−6.37844			−0.298698
$457$	0.700798	−	2.61542i	0.0327820	−	0.122344i	−0.947596	−	0.319471i	$-0.896495\pi$
$457$	0.700798	−	2.61542i	0.0327820	−	0.122344i	0.980378	+	0.197128i	$0.0631613\pi$
$458$			15.4224i			0.720640i
$459$	5.51710	+	3.18530i	0.257516	+	0.148677i
$460$	−4.03828	−	15.0711i	−0.188286	−	0.702692i
$461$	5.81853	+	1.55907i	0.270996	+	0.0726132i	0.391758	−	0.920068i	$-0.371867\pi$
$461$	5.81853	+	1.55907i	0.270996	+	0.0726132i	−0.120762	+	0.992682i	$0.538534\pi$
$462$	8.64478	−	2.07358i	0.402191	−	0.0964719i
$463$	7.99091	−	7.99091i	0.371369	−	0.371369i	−0.496607	−	0.867976i	$-0.665421\pi$
$463$	7.99091	−	7.99091i	0.371369	−	0.371369i	0.867976	+	0.496607i	$0.165421\pi$
$464$	3.74993			0.174086
$465$	−14.5046			−0.672637
$466$	−2.52201	+	2.52201i	−0.116830	+	0.116830i
$467$	−6.03438	+	10.4519i	−0.279238	+	0.483654i	−0.971196	−	0.238284i	$-0.923415\pi$
$467$	−6.03438	+	10.4519i	−0.279238	+	0.483654i	0.691958	+	0.721938i	$0.256749\pi$
$468$	−3.30693	+	1.43674i	−0.152863	+	0.0664135i
$469$	−9.42428	−	17.3657i	−0.435173	−	0.801873i
$470$	19.1913	−	5.14228i	0.885227	−	0.237196i
$471$	−4.52112	−	7.83081i	−0.208322	−	0.360825i
$472$	1.22739	−	2.12590i	0.0564951	−	0.0978523i
$473$	7.38164	−	27.5487i	0.339408	−	1.26669i
$474$	−3.89881	+	3.89881i	−0.179078	+	0.179078i
$475$	−1.22665	+	4.57791i	−0.0562825	+	0.210049i
$476$	−16.3901	+	3.93142i	−0.751239	+	0.180196i
$477$	4.65896	+	8.06956i	0.213319	+	0.369480i
$478$	−16.9754	+	9.80073i	−0.776435	+	0.448275i
$479$	0.207535	+	0.207535i	0.00948254	+	0.00948254i	0.711832	−	0.702350i	$-0.247866\pi$
$479$	0.207535	+	0.207535i	0.00948254	+	0.00948254i	−0.702350	+	0.711832i	$0.747866\pi$
$480$	2.07540	−	1.19823i	0.0947285	−	0.0546915i
$481$	−8.92257	+	7.09308i	−0.406834	+	0.323416i
$482$		−	27.7501i		−	1.26398i
$483$	4.01790	+	16.7506i	0.182821	+	0.762180i
$484$	−0.145136	+	0.251383i	−0.00659708	+	0.0114265i
$485$		−	8.83165i		−	0.401025i
$486$	0.965926	+	0.258819i	0.0438153	+	0.0117403i
$487$	−1.06982	+	0.286659i	−0.0484784	+	0.0129897i	−0.282977	−	0.959127i	$-0.591322\pi$
$487$	−1.06982	+	0.286659i	−0.0484784	+	0.0129897i	0.234498	+	0.972117i	$0.424655\pi$
$488$	5.33332	+	5.33332i	0.241428	+	0.241428i
$489$	7.06636	+	7.06636i	0.319552	+	0.319552i
$490$	−14.0652	−	9.14212i	−0.635402	−	0.412999i
$491$	−7.42479	−	4.28670i	−0.335076	−	0.193456i	0.323017	−	0.946393i	$-0.395303\pi$
$491$	−7.42479	−	4.28670i	−0.335076	−	0.193456i	−0.658092	+	0.752937i	$0.728636\pi$
$492$	−8.82310	−	2.36414i	−0.397776	−	0.106584i
$493$	11.9446	+	20.6887i	0.537960	+	0.931773i
$494$	22.8492	+	2.61010i	1.02803	+	0.117434i
$495$	−6.97354	−	4.02618i	−0.313437	−	0.180963i
$496$	−1.56651	−	5.84629i	−0.0703383	−	0.262506i
$497$	−0.882494	+	1.43945i	−0.0395853	+	0.0645681i
$498$	−0.352035	+	0.203247i	−0.0157750	+	0.00910773i
$499$	−12.0684	+	3.23373i	−0.540258	+	0.144762i	−0.518621	−	0.855004i	$-0.673554\pi$
$499$	−12.0684	+	3.23373i	−0.540258	+	0.144762i	−0.0216369	+	0.999766i	$0.506888\pi$
$500$	2.64038	+	9.85405i	0.118082	+	0.440686i
$501$	−2.50728	−	9.35729i	−0.112017	−	0.418053i
$502$	19.9136	−	5.33583i	0.888787	−	0.238150i
$503$	−9.79693	+	5.65626i	−0.436823	+	0.252200i	−0.702249	−	0.711931i	$-0.747821\pi$
$503$	−9.79693	+	5.65626i	−0.436823	+	0.252200i	0.265426	+	0.964131i	$0.414487\pi$
$504$	−2.32539	+	1.26197i	−0.103581	+	0.0562128i
$505$	3.00533	+	11.2161i	0.133736	+	0.499108i
$506$	−18.9458	−	10.9383i	−0.842242	−	0.486269i
$507$	12.4342	−	3.79356i	0.552221	−	0.168478i
$508$	−1.94179	−	3.36327i	−0.0861528	−	0.149221i
$509$	6.40990	+	1.71753i	0.284114	+	0.0761281i	0.398062	−	0.917359i	$-0.369683\pi$
$509$	6.40990	+	1.71753i	0.284114	+	0.0761281i	−0.113948	+	0.993487i	$0.536350\pi$
$510$	13.2215	+	7.63345i	0.585459	+	0.338015i
$511$	−15.3153	+	24.9810i	−0.677510	+	1.10510i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.51024	−	4.51024i	−0.199132	−	0.199132i
$514$	22.2236	−	5.95479i	0.980240	−	0.262655i
$515$	−41.1691	−	11.0312i	−1.81413	−	0.486095i
$516$			8.48799i			0.373663i
$517$	13.9287	−	24.1253i	0.612585	−	1.06103i
$518$	−6.06830	+	5.75628i	−0.266626	+	0.252916i
$519$		−	8.79475i		−	0.386047i
$520$	−7.92493	+	3.44310i	−0.347531	+	0.150990i
$521$	−6.78078	+	3.91489i	−0.297071	+	0.171514i	−0.641127	−	0.767435i	$-0.721533\pi$
$521$	−6.78078	+	3.91489i	−0.297071	+	0.171514i	0.344055	+	0.938949i	$0.388199\pi$
$522$	2.65160	+	2.65160i	0.116057	+	0.116057i
$523$	−15.4478	+	8.91880i	−0.675486	+	0.389992i	−0.798152	−	0.602456i	$-0.794189\pi$
$523$	−15.4478	+	8.91880i	−0.675486	+	0.389992i	0.122666	+	0.992448i	$0.460856\pi$
$524$	8.43733	+	14.6139i	0.368587	+	0.638411i
$525$	0.458542	+	1.91166i	0.0200124	+	0.0834317i
$526$	2.80620	−	10.4729i	0.122356	−	0.456640i
$527$	27.2647	−	27.2647i	1.18767	−	1.18767i
$528$	0.869658	−	3.24561i	0.0378470	−	0.141247i
$529$	9.69478	−	16.7918i	0.421512	−	0.730080i
$530$	11.1650	+	19.3384i	0.484978	+	0.840007i
$531$	2.37113	−	0.635342i	0.102898	−	0.0275715i
$532$	16.8699	+	0.445155i	0.731403	+	0.0192999i
$533$	30.6392	+	12.0794i	1.32713	+	0.523218i
$534$	1.38145	−	2.39274i	0.0597813	−	0.103544i
$535$	22.6659	−	22.6659i	0.979932	−	0.979932i
$536$	−7.46788			−0.322563
$537$	−13.1864			−0.569036
$538$	15.1468	−	15.1468i	0.653027	−	0.653027i
$539$	−23.0087	+	4.88096i	−0.991054	+	0.210238i
$540$	2.31481	+	0.620250i	0.0996134	+	0.0266913i
$541$	−2.49436	−	9.30908i	−0.107241	−	0.400229i	0.891349	−	0.453318i	$-0.149760\pi$
$541$	−2.49436	−	9.30908i	−0.107241	−	0.400229i	−0.998590	+	0.0530895i	$0.983093\pi$
$542$	28.4311	+	16.4147i	1.22122	+	0.705071i
$543$			1.53653i			0.0659387i
$544$	−1.64883	+	6.15352i	−0.0706931	+	0.263830i
$545$	24.5971			1.05362
$546$	8.84653	−	3.56915i	0.378597	−	0.152746i
$547$	−1.49793			−0.0640470			−0.0320235	−	0.999487i	$-0.510195\pi$
$547$	−1.49793			−0.0640470			−0.0320235	+	0.999487i	$0.510195\pi$
$548$	0.0755407	−	0.281922i	0.00322694	−	0.0120431i
$549$			7.54245i			0.321904i
$550$	−2.16218	−	1.24834i	−0.0921957	−	0.0532292i
$551$	−6.19062	−	23.1037i	−0.263729	−	0.984251i
$552$	6.28888	+	1.68510i	0.267672	+	0.0717226i
$553$	10.5838	−	10.0396i	0.450069	−	0.426927i
$554$	−12.6663	+	12.6663i	−0.538140	+	0.538140i
$555$	7.57607			0.321586
$556$	8.76566			0.371747
$557$	−11.3265	+	11.3265i	−0.479920	+	0.479920i	−0.905106	−	0.425186i	$-0.860209\pi$
$557$	−11.3265	+	11.3265i	−0.479920	+	0.479920i	0.425186	+	0.905106i	$0.360209\pi$
$558$	3.02626	−	5.24164i	0.128112	−	0.221896i
$559$	3.47334	−	30.4061i	0.146907	−	1.28604i
$560$	−5.57270	+	3.02428i	−0.235490	+	0.127799i
$561$	20.6765	−	5.54024i	0.872960	−	0.233909i
$562$	5.30287	+	9.18484i	0.223688	+	0.387439i
$563$	7.75164	−	13.4262i	0.326692	−	0.565848i	−0.655161	−	0.755489i	$-0.727399\pi$
$563$	7.75164	−	13.4262i	0.326692	−	0.565848i	0.981853	+	0.189641i	$0.0607325\pi$
$564$	−2.14578	+	8.00816i	−0.0903537	+	0.337204i
$565$	20.6345	−	20.6345i	0.868099	−	0.868099i
$566$	−5.62615	+	20.9971i	−0.236485	+	0.882573i
$567$	−2.53665	−	0.751945i	−0.106529	−	0.0315787i
$568$	0.319084	+	0.552669i	0.0133885	+	0.0231895i
$569$	30.4784	−	17.5967i	1.27772	−	0.737694i	0.301294	−	0.953531i	$-0.402582\pi$
$569$	30.4784	−	17.5967i	1.27772	−	0.737694i	0.976429	+	0.215838i	$0.0692482\pi$
$570$	−10.8086	−	10.8086i	−0.452723	−	0.452723i
$571$	0.873557	−	0.504348i	0.0365572	−	0.0211063i	−0.481610	−	0.876386i	$-0.659948\pi$
$571$	0.873557	−	0.504348i	0.0365572	−	0.0211063i	0.518167	+	0.855279i	$0.326614\pi$
$572$	−4.44346	+	11.2707i	−0.185790	+	0.471253i
$573$		−	27.2183i		−	1.13706i
$574$	23.1706	+	6.86853i	0.967123	+	0.286687i
$575$	2.41885	−	4.18957i	0.100873	−	0.174717i
$576$			1.00000i			0.0416667i
$577$	24.8465	+	6.65759i	1.03437	+	0.277159i	0.735779	−	0.677222i	$-0.236816\pi$
$577$	24.8465	+	6.65759i	1.03437	+	0.277159i	0.298592	+	0.954381i	$0.403483\pi$
$578$	−22.7809	+	6.10411i	−0.947559	+	0.253898i
$579$	1.51835	+	1.51835i	0.0631004	+	0.0631004i
$580$	6.35446	+	6.35446i	0.263855	+	0.263855i
$581$	0.945256	−	0.512986i	0.0392158	−	0.0212822i
$582$	3.19155	+	1.84264i	0.132294	+	0.0763800i
$583$	30.2423	+	8.10341i	1.25251	+	0.335609i
$584$	5.53757	+	9.59135i	0.229146	+	0.396893i
$585$	−8.03841	−	3.16913i	−0.332347	−	0.131027i
$586$	1.50584	+	0.869398i	0.0622058	+	0.0359145i
$587$	−3.90487	−	14.5732i	−0.161171	−	0.601499i	−0.998498	−	0.0547955i	$-0.982549\pi$
$587$	−3.90487	−	14.5732i	−0.161171	−	0.601499i	0.837327	−	0.546703i	$-0.184117\pi$
$588$	6.23833	−	3.17542i	0.257264	−	0.130952i
$589$	−33.4335	+	19.3028i	−1.37760	+	0.795359i
$590$	5.68232	−	1.52257i	0.233938	−	0.0626834i
$591$	5.68207	+	21.2058i	0.233729	+	0.872289i
$592$	0.818218	+	3.05363i	0.0336286	+	0.125504i
$593$	28.4048	−	7.61104i	1.16644	−	0.312548i	0.376908	−	0.926251i	$-0.376987\pi$
$593$	28.4048	−	7.61104i	1.16644	−	0.312548i	0.789537	+	0.613703i	$0.210321\pi$
$594$	2.90993	−	1.68005i	0.119396	−	0.0689333i
$595$	−34.4359	−	21.1119i	−1.41174	−	0.865504i
$596$	1.07469	+	4.01080i	0.0440210	+	0.164289i
$597$	21.6834	+	12.5189i	0.887443	+	0.512366i
$598$	−21.8388	−	8.60991i	−0.893055	−	0.352085i
$599$	12.3677	+	21.4216i	0.505332	+	0.875261i	0.999981	+	0.00616822i	$0.00196342\pi$
$599$	12.3677	+	21.4216i	0.505332	+	0.875261i	−0.494649	+	0.869093i	$0.664703\pi$
$600$	0.717716	+	0.192312i	0.0293006	+	0.00785109i
$601$	−7.62030	−	4.39958i	−0.310838	−	0.179463i	0.336463	−	0.941697i	$-0.390769\pi$
$601$	−7.62030	−	4.39958i	−0.310838	−	0.179463i	−0.647302	+	0.762234i	$0.724103\pi$
$602$	0.592381	−	22.4493i	0.0241437	−	0.914965i
$603$	−5.28059	−	5.28059i	−0.215042	−	0.215042i
$604$	−9.17136	−	9.17136i	−0.373177	−	0.373177i
$605$	−0.671923	+	0.180041i	−0.0273175	+	0.00731971i
$606$	−4.68026	−	1.25407i	−0.190122	−	0.0509432i
$607$			22.6359i			0.918763i	0.888239	+	0.459382i	$0.151929\pi$
$607$			22.6359i			0.918763i	−0.888239	+	0.459382i	$0.848071\pi$
$608$	3.18922	−	5.52389i	0.129340	−	0.224023i
$609$	−6.82798	−	7.19809i	−0.276684	−	0.291681i
$610$			18.0752i			0.731843i
$611$	10.9637	−	27.8092i	0.443545	−	1.12504i
$612$	−5.51710	+	3.18530i	−0.223015	+	0.128758i
$613$	24.9589	+	24.9589i	1.00808	+	1.00808i	0.999967	+	0.00811456i	$0.00258297\pi$
$613$	24.9589	+	24.9589i	1.00808	+	1.00808i	0.00811456	+	0.999967i	$0.497417\pi$
$614$	−12.9047	+	7.45054i	−0.520792	+	0.300679i
$615$	−10.9451	−	18.9574i	−0.441347	−	0.764436i
$616$	−2.52661	+	8.52339i	−0.101800	+	0.343417i
$617$	9.32719	−	34.8095i	0.375498	−	1.40138i	−0.477117	−	0.878840i	$-0.658318\pi$
$617$	9.32719	−	34.8095i	0.375498	−	1.40138i	0.852615	−	0.522539i	$-0.175015\pi$
$618$	12.5760	−	12.5760i	0.505881	−	0.505881i
$619$	4.95915	−	18.5078i	0.199325	−	0.743892i	−0.791779	−	0.610807i	$-0.790845\pi$
$619$	4.95915	−	18.5078i	0.199325	−	0.743892i	0.991105	−	0.133085i	$-0.0424882\pi$
$620$	7.25232	−	12.5614i	0.291260	−	0.504478i
$621$	3.25536	+	5.63845i	0.130633	+	0.226263i
$622$	−0.0807678	+	0.0216417i	−0.00323849	+	0.000867752i
$623$	−3.82070	+	6.23199i	−0.153073	+	0.249680i
$624$	0.409207	−	3.58225i	0.0163814	−	0.143405i
$625$	−14.0815	+	24.3899i	−0.563261	+	0.975597i
$626$	−17.7640	+	17.7640i	−0.709991	+	0.709991i
$627$	−21.4322			−0.855920
$628$	9.04224			0.360825
$629$	−14.2409	+	14.2409i	−0.567823	+	0.567823i
$630$	−6.07898	−	1.80201i	−0.242192	−	0.0717937i
$631$	−22.0223	−	5.90086i	−0.876694	−	0.234910i	−0.207714	−	0.978190i	$-0.566602\pi$
$631$	−22.0223	−	5.90086i	−0.876694	−	0.234910i	−0.668980	+	0.743280i	$0.733269\pi$
$632$	−1.42707	−	5.32588i	−0.0567656	−	0.211852i
$633$	−20.6658	−	11.9314i	−0.821392	−	0.474231i
$634$			20.0010i			0.794341i
$635$	2.40879	−	8.98971i	0.0955898	−	0.356746i
$636$	−9.31793			−0.369480
$637$	−23.6467	+	8.82240i	−0.936915	+	0.349556i
$638$	12.6001			0.498844
$639$	−0.165170	+	0.616423i	−0.00653402	+	0.0243853i
$640$			2.39646i			0.0947285i
$641$	−8.69994	−	5.02291i	−0.343627	−	0.198393i	0.318248	−	0.948008i	$-0.396906\pi$
$641$	−8.69994	−	5.02291i	−0.343627	−	0.198393i	−0.661875	+	0.749614i	$0.730239\pi$
$642$	3.46189	+	12.9199i	0.136630	+	0.509910i
$643$	−19.2831	−	5.16690i	−0.760452	−	0.203763i	−0.142303	−	0.989823i	$-0.545451\pi$
$643$	−19.2831	−	5.16690i	−0.760452	−	0.203763i	−0.618149	+	0.786061i	$0.712117\pi$
$644$	−16.5154	−	4.89571i	−0.650799	−	0.192918i
$645$	−14.3834	+	14.3834i	−0.566344	+	0.566344i
$646$	40.6345			1.59874
$647$	5.92105			0.232780			0.116390	−	0.993204i	$-0.462868\pi$
$647$	5.92105			0.232780			0.116390	+	0.993204i	$0.462868\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	4.12414	−	7.14323i	0.161887	−	0.280396i
$650$	−2.49235	−	0.982603i	−0.0977579	−	0.0385409i
$651$	−8.36976	+	13.6520i	−0.328037	+	0.535066i
$652$	−9.65282	+	2.58647i	−0.378034	+	0.101294i
$653$	10.6174	+	18.3898i	0.415490	+	0.719649i	0.995480	−	0.0949745i	$-0.0302770\pi$
$653$	10.6174	+	18.3898i	0.415490	+	0.719649i	−0.579990	+	0.814623i	$0.696944\pi$
$654$	−5.13195	+	8.88880i	−0.200675	+	0.347580i
$655$	−10.4665	+	39.0616i	−0.408961	+	1.52626i
$656$	6.45896	−	6.45896i	0.252180	−	0.252180i
$657$	−2.86646	+	10.6978i	−0.111831	+	0.417359i
$658$	6.23412	−	21.0305i	0.243031	−	0.819853i
$659$	−18.8111	−	32.5818i	−0.732776	−	1.26920i	−0.955692	−	0.294367i	$-0.904891\pi$
$659$	−18.8111	−	32.5818i	−0.732776	−	1.26920i	0.222917	−	0.974838i	$-0.428442\pi$
$660$	6.97354	−	4.02618i	0.271445	−	0.156719i
$661$	17.3759	+	17.3759i	0.675846	+	0.675846i	0.959057	−	0.283212i	$-0.0913999\pi$
$661$	17.3759	+	17.3759i	0.675846	+	0.675846i	−0.283212	+	0.959057i	$0.591400\pi$
$662$	9.89383	−	5.71220i	0.384534	−	0.222011i
$663$	21.0671	−	9.15291i	0.818178	−	0.355470i
$664$		−	0.406494i		−	0.0157750i
$665$	27.8326	+	29.3413i	1.07930	+	1.13781i
$666$	−1.58068	+	2.73781i	−0.0612500	+	0.106088i
$667$			24.4148i			0.945343i
$668$	9.35729	+	2.50728i	0.362044	+	0.0970095i
$669$	−14.7948	+	3.96426i	−0.572001	+	0.153267i
$670$	−12.6547	−	12.6547i	−0.488895	−	0.488895i
$671$	17.9205	+	17.9205i	0.691812	+	0.691812i
$672$	0.0697906	−	2.64483i	0.00269223	−	0.102027i
$673$	−19.5012	−	11.2590i	−0.751715	−	0.434003i	0.0745983	−	0.997214i	$-0.476233\pi$
$673$	−19.5012	−	11.2590i	−0.751715	−	0.434003i	−0.826313	+	0.563211i	$0.809566\pi$
$674$	−0.574177	−	0.153850i	−0.0221165	−	0.00592609i
$675$	0.371517	+	0.643487i	0.0142997	+	0.0247678i
$676$	−2.93177	+	12.6651i	−0.112760	+	0.487119i
$677$	−32.8385	−	18.9593i	−1.26209	−	0.728666i	−0.288609	−	0.957447i	$-0.593193\pi$
$677$	−32.8385	−	18.9593i	−1.26209	−	0.728666i	−0.973478	+	0.228781i	$0.926526\pi$
$678$	3.15162	+	11.7620i	0.121037	+	0.451717i
$679$	−8.31251	−	5.09622i	−0.319005	−	0.195575i
$680$	−13.2215	+	7.63345i	−0.507022	+	0.292729i
$681$	−10.0387	+	2.68985i	−0.384683	+	0.103075i
$682$	−5.26362	−	19.6441i	−0.201555	−	0.752212i
$683$	3.26576	+	12.1880i	0.124961	+	0.466360i	0.999838	−	0.0179841i	$-0.00572483\pi$
$683$	3.26576	+	12.1880i	0.124961	+	0.466360i	−0.874877	+	0.484344i	$0.839058\pi$
$684$	6.16110	−	1.65086i	0.235576	−	0.0631223i
$685$	0.605740	−	0.349724i	0.0231441	−	0.0133623i
$686$	−16.7209	+	7.96307i	−0.638408	+	0.304031i
$687$	−3.99160	−	14.8969i	−0.152289	−	0.568351i
$688$	−7.35081	−	4.24399i	−0.280247	−	0.161801i
$689$	33.3792	+	3.81296i	1.27165	+	0.145262i
$690$	7.80136	+	13.5123i	0.296993	+	0.514406i
$691$	−4.41138	−	1.18203i	−0.167817	−	0.0449664i	0.173932	−	0.984758i	$-0.444353\pi$
$691$	−4.41138	−	1.18203i	−0.167817	−	0.0449664i	−0.341749	+	0.939791i	$0.611019\pi$
$692$	7.61648	+	4.39738i	0.289535	+	0.167163i
$693$	−7.81353	+	4.24036i	−0.296811	+	0.161078i
$694$	−19.1686	−	19.1686i	−0.727629	−	0.727629i
$695$	14.8539	+	14.8539i	0.563440	+	0.563440i
$696$	−3.62215	+	0.970553i	−0.137297	+	0.0367887i
$697$	56.2084	+	15.0610i	2.12905	+	0.570476i
$698$		−	4.02989i		−	0.152533i
$699$	1.78333	−	3.08882i	0.0674518	−	0.116830i
$700$	−1.88482	−	0.558721i	−0.0712394	−	0.0211177i
$701$		−	35.0204i		−	1.32270i	−0.750077	−	0.661350i	$-0.769984\pi$
$701$		−	35.0204i		−	1.32270i	0.750077	−	0.661350i	$-0.230016\pi$
$702$	2.82239	−	2.24368i	0.106524	−	0.0846824i
$703$	17.4630	−	10.0823i	0.658629	−	0.380260i
$704$	2.37595	+	2.37595i	0.0895470	+	0.0895470i
$705$	−17.2064	+	9.93413i	−0.648031	+	0.374141i
$706$	9.45936	+	16.3841i	0.356008	+	0.616624i
$707$	12.2910	+	3.64344i	0.462249	+	0.137026i
$708$	−0.635342	+	2.37113i	−0.0238776	+	0.0891125i
$709$	−34.8402	+	34.8402i	−1.30845	+	1.30845i	−0.385917	+	0.922533i	$0.626115\pi$
$709$	−34.8402	+	34.8402i	−1.30845	+	1.30845i	−0.922533	+	0.385917i	$0.873885\pi$
$710$	−0.395824	+	1.47723i	−0.0148550	+	0.0554396i
$711$	2.75688	−	4.77505i	0.103391	−	0.179078i
$712$	1.38145	+	2.39274i	0.0517721	+	0.0896719i
$713$	38.0636	−	10.1991i	1.42549	−	0.381959i
$714$	14.8141	−	8.03953i	0.554403	−	0.300872i
$715$	−26.6286	+	11.5692i	−0.995851	+	0.432662i
$716$	6.59322	−	11.4198i	0.246400	−	0.426777i
$717$	13.8603	−	13.8603i	0.517623	−	0.517623i
$718$	−7.46744			−0.278682
$719$	32.1531			1.19911			0.599554	−	0.800334i	$-0.295345\pi$
$719$	32.1531			1.19911			0.599554	+	0.800334i	$0.295345\pi$
$720$	−1.69456	+	1.69456i	−0.0631523	+	0.0631523i
$721$	−34.1391	+	32.3837i	−1.27141	+	1.20603i
$722$	−20.9457	−	5.61237i	−0.779517	−	0.208871i
$723$	7.18226	+	26.8046i	0.267111	+	0.996872i
$724$	−1.33067	−	0.768263i	−0.0494540	−	0.0285523i
$725$			2.78633i			0.103482i
$726$	0.0751278	−	0.280381i	0.00278826	−	0.0104059i
$727$	19.7580			0.732783			0.366392	−	0.930461i	$-0.380593\pi$
$727$	19.7580			0.732783			0.366392	+	0.930461i	$0.380593\pi$
$728$	−1.33229	+	9.44590i	−0.0493780	+	0.350088i
$729$	−1.00000			−0.0370370
$730$	−6.86936	+	25.6368i	−0.254246	+	0.948860i
$731$		−	54.0735i		−	1.99998i
$732$	−6.53195	−	3.77122i	−0.241428	−	0.139388i
$733$	−0.232738	−	0.868590i	−0.00859637	−	0.0320821i	0.961494	−	0.274824i	$-0.0886197\pi$
$733$	−0.232738	−	0.868590i	−0.00859637	−	0.0320821i	−0.970091	+	0.242742i	$0.921953\pi$
$734$	−35.2033	−	9.43268i	−1.29938	−	0.348167i
$735$	15.9521	+	5.19026i	0.588403	+	0.191446i
$736$	−4.60378	+	4.60378i	−0.169698	+	0.169698i
$737$	−25.0928			−0.924306
$738$	9.13435			0.336240
$739$	−6.39478	+	6.39478i	−0.235236	+	0.235236i	−0.814874	−	0.579638i	$-0.803194\pi$
$739$	−6.39478	+	6.39478i	−0.235236	+	0.235236i	0.579638	+	0.814874i	$0.303194\pi$
$740$	−3.78803	+	6.56107i	−0.139251	+	0.241190i
$741$	−22.7462	+	3.39264i	−0.835602	+	0.124632i
$742$	24.6443	+	0.650303i	0.904722	+	0.0238734i
$743$	−10.6974	+	2.86636i	−0.392450	+	0.105157i	−0.449647	−	0.893206i	$-0.648450\pi$
$743$	−10.6974	+	2.86636i	−0.392450	+	0.105157i	0.0571974	+	0.998363i	$0.481784\pi$
$744$	3.02626	+	5.24164i	0.110948	+	0.192168i
$745$	−4.97539	+	8.61764i	−0.182284	+	0.315726i
$746$	−3.29288	+	12.2892i	−0.120561	+	0.449940i
$747$	0.287435	−	0.287435i	0.0105167	−	0.0105167i
$748$	−5.54024	+	20.6765i	−0.202571	+	0.756006i
$749$	−8.25442	−	34.4127i	−0.301610	−	1.25741i
$750$	−5.10083	−	8.83490i	−0.186256	−	0.322605i
$751$	4.25678	−	2.45765i	0.155332	−	0.0896810i	−0.420319	−	0.907376i	$-0.638082\pi$
$751$	4.25678	−	2.45765i	0.155332	−	0.0896810i	0.575651	+	0.817695i	$0.304749\pi$
$752$	−5.86238	−	5.86238i	−0.213779	−	0.213779i
$753$	−17.8540	+	10.3080i	−0.650637	+	0.375645i
$754$	13.3726	−	1.99456i	0.487003	−	0.0726375i
$755$		−	31.0827i		−	1.13122i
$756$	1.91953	−	1.82083i	0.0698125	−	0.0662229i
$757$	−13.0641	+	22.6277i	−0.474822	+	0.822416i	−0.999584	−	0.0288326i	$-0.990821\pi$
$757$	−13.0641	+	22.6277i	−0.474822	+	0.822416i	0.524762	+	0.851249i	$0.324154\pi$
$758$			5.51079i			0.200161i
$759$	21.1313	+	5.66210i	0.767016	+	0.205521i
$760$	14.7649	−	3.95623i	0.535578	−	0.143508i
$761$	−8.80800	−	8.80800i	−0.319290	−	0.319290i	0.529205	−	0.848494i	$-0.322490\pi$
$761$	−8.80800	−	8.80800i	−0.319290	−	0.319290i	−0.848494	+	0.529205i	$0.822490\pi$
$762$	2.74610	+	2.74610i	0.0994807	+	0.0994807i
$763$	14.1935	−	23.1512i	0.513839	−	0.838130i
$764$	23.5717	+	13.6091i	0.852794	+	0.492361i
$765$	−14.7467	−	3.95136i	−0.533168	−	0.142862i
$766$	−3.35411	−	5.80950i	−0.121189	−	0.209906i
$767$	3.24624	−	8.23400i	0.117215	−	0.297313i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−9.34074	−	34.8601i	−0.336836	−	1.25709i	−0.901865	−	0.432017i	$-0.857802\pi$
$769$	−9.34074	−	34.8601i	−0.336836	−	1.25709i	0.565030	−	0.825070i	$-0.308865\pi$
$770$	−18.7248	+	10.1619i	−0.674796	+	0.366208i
$771$	−19.9251	+	11.5038i	−0.717586	+	0.414298i
$772$	−2.07410	+	0.555754i	−0.0746485	+	0.0200020i
$773$	−6.65737	−	24.8456i	−0.239449	−	0.893635i	−0.976093	−	0.217354i	$-0.930257\pi$
$773$	−6.65737	−	24.8456i	−0.239449	−	0.893635i	0.736644	−	0.676281i	$-0.236409\pi$
$774$	−2.19685	−	8.19877i	−0.0789642	−	0.294699i
$775$	4.34399	−	1.16397i	0.156041	−	0.0418110i
$776$	−3.19155	+	1.84264i	−0.114570	+	0.0661470i
$777$	4.37170	−	7.13073i	0.156834	−	0.255814i
$778$	−6.41607	−	23.9451i	−0.230027	−	0.858474i
$779$	−50.4572	−	29.1315i	−1.80782	−	1.04374i
$780$	6.76375	−	5.37690i	0.242181	−	0.192524i
$781$	1.07215	+	1.85702i	0.0383647	+	0.0664496i
$782$	−40.0639	−	10.7351i	−1.43268	−	0.383886i
$783$	−3.24753	−	1.87496i	−0.116057	−	0.0670058i
$784$	−0.369168	+	6.99026i	−0.0131846	+	0.249652i
$785$	15.3226	+	15.3226i	0.546886	+	0.546886i
$786$	−11.9322	−	11.9322i	−0.425607	−	0.425607i
$787$	−18.7148	+	5.01460i	−0.667109	+	0.178751i	−0.576452	−	0.817131i	$-0.695563\pi$
$787$	−18.7148	+	5.01460i	−0.667109	+	0.178751i	−0.0906568	+	0.995882i	$0.528897\pi$
$788$	−21.2058	−	5.68207i	−0.755424	−	0.202415i
$789$			10.8423i			0.385998i
$790$	6.60676	−	11.4432i	0.235058	−	0.407132i
$791$	−7.51463	−	31.3285i	−0.267189	−	1.11391i
$792$			3.36010i			0.119396i
$793$	21.8559	+	16.1824i	0.776126	+	0.574654i
$794$	−13.3053	+	7.68182i	−0.472187	+	0.272617i
$795$	−15.7897	−	15.7897i	−0.560004	−	0.560004i
$796$	−21.6834	+	12.5189i	−0.768549	+	0.443722i
$797$	26.4379	+	45.7917i	0.936477	+	1.62203i	0.771978	+	0.635649i	$0.219267\pi$
$797$	26.4379	+	45.7917i	0.936477	+	1.62203i	0.164499	+	0.986377i	$0.447399\pi$
$798$	−16.4103	+	3.93627i	−0.580918	+	0.139342i
$799$	13.6699	−	51.0168i	0.483606	−	1.80484i
$800$	−0.525405	+	0.525405i	−0.0185759	+	0.0185759i
$801$	−0.715092	+	2.66876i	−0.0252665	+	0.0942960i
$802$	−8.74012	+	15.1383i	−0.308624	+	0.534553i
$803$	18.6068	+	32.2279i	0.656619	+	1.13730i
$804$	7.21342	−	1.93283i	0.254398	−	0.0681656i
$805$	−19.6902	−	36.2823i	−0.693990	−	1.27878i
$806$	−8.69592	−	20.0152i	−0.306301	−	0.705007i
$807$	−10.7104	+	18.5510i	−0.377025	+	0.653027i
$808$	3.42619	−	3.42619i	0.120533	−	0.120533i
$809$	37.6487			1.32366			0.661830	−	0.749654i	$-0.269780\pi$
$809$	37.6487			1.32366			0.661830	+	0.749654i	$0.269780\pi$
$810$	−2.39646			−0.0842031
$811$	−9.93129	+	9.93129i	−0.348735	+	0.348735i	−0.859638	−	0.510903i	$-0.829311\pi$
$811$	−9.93129	+	9.93129i	−0.348735	+	0.348735i	0.510903	+	0.859638i	$0.329311\pi$
$812$	9.64772	−	2.31416i	0.338569	−	0.0812110i
$813$	−31.7107	−	8.49687i	−1.11214	−	0.297998i
$814$	2.74930	+	10.2605i	0.0963628	+	0.359631i
$815$	−20.7402	−	11.9743i	−0.726496	−	0.419443i
$816$		−	6.37060i		−	0.223015i
$817$	−14.0125	+	52.2954i	−0.490235	+	1.82958i
$818$	−27.8897			−0.975139
$819$	−7.62133	+	5.73719i	−0.266311	+	0.200474i
$820$	21.8901			0.764436
$821$	−6.02169	+	22.4732i	−0.210158	+	0.784322i	0.777657	+	0.628689i	$0.216408\pi$
$821$	−6.02169	+	22.4732i	−0.210158	+	0.784322i	−0.987815	+	0.155633i	$0.950258\pi$
$822$			0.291867i			0.0101800i
$823$	1.80907	+	1.04447i	0.0630604	+	0.0364079i	0.531199	−	0.847247i	$-0.321742\pi$
$823$	1.80907	+	1.04447i	0.0630604	+	0.0364079i	−0.468138	+	0.883655i	$0.655075\pi$
$824$	4.60313	+	17.1791i	0.160358	+	0.598463i
$825$	2.41160	+	0.646186i	0.0839611	+	0.0224973i
$826$	1.84586	−	6.22690i	0.0642255	−	0.216661i
$827$	−28.8903	+	28.8903i	−1.00461	+	1.00461i	−0.00462441	+	0.999989i	$0.501472\pi$
$827$	−28.8903	+	28.8903i	−1.00461	+	1.00461i	−0.999989	+	0.00462441i	$0.998528\pi$
$828$	−6.51073			−0.226263
$829$	−56.0638			−1.94717			−0.973587	−	0.228315i	$-0.926678\pi$
$829$	−56.0638			−1.94717			−0.973587	+	0.228315i	$0.926678\pi$
$830$	0.688827	−	0.688827i	0.0239095	−	0.0239095i
$831$	8.95644	−	15.5130i	0.310695	−	0.538140i
$832$	2.89772	+	2.14551i	0.100460	+	0.0743822i
$833$	−39.7418	+	20.2293i	−1.37697	+	0.700904i
$834$	−8.46698	+	2.26872i	−0.293187	+	0.0785594i
$835$	11.6077	+	20.1052i	0.401702	+	0.695768i
$836$	10.7161	−	18.5608i	0.370624	−	0.641940i
$837$	−1.56651	+	5.84629i	−0.0541464	+	0.202077i
$838$	−11.1909	+	11.1909i	−0.386584	+	0.386584i
$839$	7.10574	−	26.5190i	0.245317	−	0.915537i	−0.727906	−	0.685677i	$-0.759506\pi$
$839$	7.10574	−	26.5190i	0.245317	−	0.915537i	0.973224	−	0.229860i	$-0.0738269\pi$
$840$	4.60008	−	4.36355i	0.158718	−	0.150557i
$841$	7.46902	+	12.9367i	0.257552	+	0.446094i
$842$	16.1138	−	9.30334i	0.555320	−	0.320614i
$843$	−7.49939	−	7.49939i	−0.258293	−	0.258293i
$844$	20.6658	−	11.9314i	0.711346	−	0.410696i
$845$	−26.4298	+	16.4937i	−0.909211	+	0.567399i
$846$		−	8.29066i		−	0.285039i
$847$	−0.218268	+	0.736317i	−0.00749979	+	0.0253001i
$848$	4.65896	−	8.06956i	0.159989	−	0.277110i
$849$		−	21.7378i		−	0.746038i
$850$	−4.57228	−	1.22514i	−0.156828	−	0.0420219i
$851$	−19.8814	+	5.32720i	−0.681524	+	0.182614i
$852$	−0.451253	−	0.451253i	−0.0154597	−	0.0154597i
$853$	−2.37750	−	2.37750i	−0.0814041	−	0.0814041i	0.665232	−	0.746636i	$-0.268332\pi$
$853$	−2.37750	−	2.37750i	−0.0814041	−	0.0814041i	−0.746636	+	0.665232i	$0.768332\pi$
$854$	17.0127	+	10.4301i	0.582163	+	0.356911i
$855$	13.2378	+	7.64285i	0.452723	+	0.261380i
$856$	−12.9199	−	3.46189i	−0.441595	−	0.118325i
$857$	0.305713	+	0.529511i	0.0104430	+	0.0180878i	0.871200	−	0.490929i	$-0.163343\pi$
$857$	0.305713	+	0.529511i	0.0104430	+	0.0180878i	−0.860757	+	0.509017i	$0.830009\pi$
$858$	1.37498	−	12.0367i	0.0469409	−	0.410927i
$859$	36.0041	+	20.7870i	1.22844	+	0.709243i	0.966704	−	0.255896i	$-0.0823704\pi$
$859$	36.0041	+	20.7870i	1.22844	+	0.709243i	0.261740	+	0.965138i	$0.415704\pi$
$860$	−5.26468	−	19.6480i	−0.179524	−	0.669992i
$861$	−24.1588	−	0.637491i	−0.823330	−	0.0217256i
$862$	−5.04922	+	2.91517i	−0.171977	+	0.0992911i
$863$	19.6584	−	5.26746i	0.669180	−	0.179306i	0.0917948	−	0.995778i	$-0.470740\pi$
$863$	19.6584	−	5.26746i	0.669180	−	0.179306i	0.577386	+	0.816472i	$0.304073\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	5.45495	+	20.3581i	0.185474	+	0.692198i
$866$	29.4037	−	7.87870i	0.999179	−	0.267729i
$867$	20.4248	−	11.7922i	0.693661	−	0.400486i
$868$	−7.63813	−	14.0744i	−0.259255	−	0.477718i
$869$	−4.79508	−	17.8955i	−0.162662	−	0.607063i
$870$	−7.78260	−	4.49328i	−0.263855	−	0.152337i
$871$	−26.6312	+	3.97211i	−0.902365	+	0.134590i
$872$	−5.13195	−	8.88880i	−0.173790	−	0.301013i
$873$	−3.55971	−	0.953822i	−0.120478	−	0.0322820i
$874$	35.9646	+	20.7641i	1.21652	+	0.702358i
$875$	12.8742	+	23.7228i	0.435229	+	0.801977i
$876$	−7.83130	−	7.83130i	−0.264595	−	0.264595i
$877$	26.3374	+	26.3374i	0.889351	+	0.889351i	0.994461	−	0.105110i	$-0.0335195\pi$
$877$	26.3374	+	26.3374i	0.889351	+	0.889351i	−0.105110	+	0.994461i	$0.533519\pi$
$878$	0.392300	−	0.105117i	0.0132395	−	0.00354751i
$879$	−1.67955	−	0.450034i	−0.0566498	−	0.0151793i
$880$			8.05236i			0.271445i
$881$	20.6694	−	35.8005i	0.696371	−	1.20615i	−0.273346	−	0.961916i	$-0.588130\pi$
$881$	20.6694	−	35.8005i	0.696371	−	1.20615i	0.969716	−	0.244233i	$-0.0785363\pi$
$882$	−5.20390	+	4.68182i	−0.175224	+	0.157645i
$883$			5.80574i			0.195379i	0.995217	+	0.0976894i	$0.0311452\pi$
$883$			5.80574i			0.195379i	−0.995217	+	0.0976894i	$0.968855\pi$
$884$	−2.60689	+	22.8211i	−0.0876793	+	0.767557i
$885$	−5.09463	+	2.94139i	−0.171254	+	0.0988737i
$886$	13.1024	+	13.1024i	0.440182	+	0.440182i
$887$	−19.1259	+	11.0424i	−0.642186	+	0.370766i	−0.785456	−	0.618918i	$-0.787571\pi$
$887$	−19.1259	+	11.0424i	−0.642186	+	0.370766i	0.143270	+	0.989684i	$0.454238\pi$
$888$	−1.58068	−	2.73781i	−0.0530440	−	0.0918750i
$889$	−7.07132	−	7.45462i	−0.237164	−	0.250020i
$890$	−1.71369	+	6.39559i	−0.0574431	+	0.214380i
$891$	−2.37595	+	2.37595i	−0.0795973	+	0.0795973i
$892$	3.96426	−	14.7948i	0.132733	−	0.495367i
$893$	−26.4408	+	45.7967i	−0.884806	+	1.53253i
$894$	−2.07614	−	3.59598i	−0.0694365	−	0.120268i
$895$	30.5240	−	8.17889i	1.02031	−	0.273390i
$896$	2.25560	+	1.38286i	0.0753541	+	0.0461980i
$897$	23.3231	+	2.66423i	0.778735	+	0.0889562i
$898$	−1.72876	+	2.99429i	−0.0576893	+	0.0999208i
$899$	−16.0489	+	16.0489i	−0.535260	+	0.535260i
$900$	−0.743035			−0.0247678
$901$	59.3607			1.97759
$902$	21.7027	−	21.7027i	0.722622	−	0.722622i
$903$	5.23811	+	21.8377i	0.174313	+	0.726712i
$904$	−11.7620	−	3.15162i	−0.391199	−	0.104821i
$905$	−0.953031	−	3.55676i	−0.0316798	−	0.118231i
$906$	11.2326	+	6.48513i	0.373177	+	0.215454i
$907$			9.58261i			0.318185i	0.987264	+	0.159093i	$0.0508569\pi$
$907$			9.58261i			0.318185i	−0.987264	+	0.159093i	$0.949143\pi$
$908$	2.68985	−	10.0387i	0.0892660	−	0.333145i
$909$	4.84536			0.160710
$910$	−18.2642	+	13.7490i	−0.605454	+	0.455773i
$911$	34.0329			1.12756			0.563780	−	0.825925i	$-0.309347\pi$
$911$	34.0329			1.12756			0.563780	+	0.825925i	$0.309347\pi$
$912$	−1.65086	+	6.16110i	−0.0546655	+	0.204015i
$913$		−	1.36586i		−	0.0452034i
$914$	−2.34492	−	1.35384i	−0.0775630	−	0.0447810i
$915$	−4.67821	−	17.4593i	−0.154657	−	0.577187i
$916$	14.8969	+	3.99160i	0.492206	+	0.131886i
$917$	30.7259	+	32.3914i	1.01466	+	1.06966i
$918$	4.50469	−	4.50469i	0.148677	−	0.148677i
$919$	−37.4935			−1.23680			−0.618398	−	0.785865i	$-0.712218\pi$
$919$	−37.4935			−1.23680			−0.618398	+	0.785865i	$0.712218\pi$
$920$	−15.6027			−0.514406
$921$	10.5367	−	10.5367i	0.347194	−	0.347194i
$922$	3.01189	−	5.21675i	0.0991914	−	0.171805i
$923$	1.43185	+	1.80116i	0.0471298	+	0.0592858i
$924$	0.234503	−	8.88690i	0.00771459	−	0.292357i
$925$	−2.26896	+	0.607965i	−0.0746028	+	0.0199898i
$926$	−5.65043	−	9.78683i	−0.185685	−	0.321615i
$927$	−8.89257	+	15.4024i	−0.292070	+	0.505881i
$928$	0.970553	−	3.62215i	0.0318600	−	0.118903i
$929$	−25.5287	+	25.5287i	−0.837570	+	0.837570i	−0.988539	−	0.150969i	$-0.951761\pi$
$929$	−25.5287	+	25.5287i	−0.837570	+	0.837570i	0.150969	+	0.988539i	$0.451761\pi$
$930$	−3.75408	+	14.0104i	−0.123101	+	0.459419i
$931$	43.6772	−	9.26547i	1.43146	−	0.303664i
$932$	1.78333	+	3.08882i	0.0584149	+	0.101178i
$933$	0.0724144	−	0.0418085i	0.00237074	−	0.00136875i
$934$	8.53391	+	8.53391i	0.279238	+	0.279238i
$935$	−44.4256	+	25.6491i	−1.45287	+	0.838817i
$936$	0.531892	+	3.56610i	0.0173854	+	0.116562i
$937$			40.1007i			1.31003i	0.755615	+	0.655016i	$0.227338\pi$
$937$			40.1007i			1.31003i	−0.755615	+	0.655016i	$0.772662\pi$
$938$	−19.2132	+	4.60858i	−0.627332	+	0.150475i
$939$	12.5610	−	21.7563i	0.409914	−	0.709991i
$940$		−	19.8683i		−	0.648031i
$941$	−13.9577	−	3.73995i	−0.455007	−	0.121919i	0.0240342	−	0.999711i	$-0.492349\pi$
$941$	−13.9577	−	3.73995i	−0.455007	−	0.121919i	−0.479041	+	0.877792i	$0.659016\pi$
$942$	−8.73413	+	2.34030i	−0.284573	+	0.0762512i
$943$	42.0525	+	42.0525i	1.36942	+	1.36942i
$944$	−1.73579	−	1.73579i	−0.0564951	−	0.0564951i
$945$	6.33824	+	0.167251i	0.206183	+	0.00544066i
$946$	−24.6995	−	14.2602i	−0.803049	−	0.463640i
$947$	2.49756	+	0.669218i	0.0811596	+	0.0217467i	0.299170	−	0.954200i	$-0.403290\pi$
$947$	2.49756	+	0.669218i	0.0811596	+	0.0217467i	−0.218011	+	0.975946i	$0.569957\pi$
$948$	2.75688	+	4.77505i	0.0895392	+	0.155086i
$949$	24.8491	+	31.2583i	0.806636	+	1.01469i
$950$	4.10444	+	2.36970i	0.133166	+	0.0768833i
$951$	−5.17664	−	19.3195i	−0.167864	−	0.626477i
$952$	−0.444607	+	16.8491i	−0.0144098	+	0.546084i
$953$	−10.9952	+	6.34808i	−0.356169	+	0.205634i	−0.667399	−	0.744700i	$-0.732592\pi$
$953$	−10.9952	+	6.34808i	−0.356169	+	0.205634i	0.311230	+	0.950335i	$0.399259\pi$
$954$	9.00043	−	2.41166i	0.291400	−	0.0780803i
$955$	16.8821	+	63.0050i	0.546293	+	2.03879i
$956$	5.07323	+	18.9336i	0.164080	+	0.612355i
$957$	−12.1708	+	3.26116i	−0.393426	+	0.105418i
$958$	0.254178	−	0.146750i	0.00821212	−	0.00474127i
$959$	0.0203695	−	0.771938i	0.000657767	−	0.0249272i
$960$	−0.620250	−	2.31481i	−0.0200185	−	0.0747100i
$961$	4.87833	+	2.81650i	0.157365	+	0.0908550i
$962$	4.54205	+	10.4544i	0.146442	+	0.337062i
$963$	−6.68786	−	11.5837i	−0.215513	−	0.373280i
$964$	−26.8046	−	7.18226i	−0.863317	−	0.231325i
$965$	−4.45643	−	2.57292i	−0.143458	−	0.0828253i
$966$	17.2198	+	0.454387i	0.554037	+	0.0146197i
$967$	−32.9354	−	32.9354i	−1.05913	−	1.05913i	−0.998138	−	0.0609945i	$-0.980573\pi$
$967$	−32.9354	−	32.9354i	−1.05913	−	1.05913i	−0.0609945	−	0.998138i	$-0.519427\pi$
$968$	0.205253	+	0.205253i	0.00659708	+	0.00659708i
$969$	−39.2499	+	10.5170i	−1.26089	+	0.337854i
$970$	−8.53072	−	2.28580i	−0.273905	−	0.0733926i
$971$			31.7302i			1.01827i	0.860687	+	0.509135i	$0.170035\pi$
$971$			31.7302i			1.01827i	−0.860687	+	0.509135i	$0.829965\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	22.5521	−	5.40947i	0.722986	−	0.173419i
$974$			1.10756i			0.0354886i
$975$	2.66174	+	0.304055i	0.0852439	+	0.00973755i
$976$	6.53195	−	3.77122i	0.209083	−	0.120714i
$977$	−40.6831	−	40.6831i	−1.30157	−	1.30157i	−0.927334	−	0.374235i	$-0.877905\pi$
$977$	−40.6831	−	40.6831i	−1.30157	−	1.30157i	−0.374235	−	0.927334i	$-0.622095\pi$
$978$	8.65449	−	4.99667i	0.276740	−	0.159776i
$979$	4.64182	+	8.03986i	0.148353	+	0.256955i
$980$	−12.4710	+	11.2198i	−0.398370	+	0.358403i
$981$	2.65649	−	9.91417i	0.0848153	−	0.316535i
$982$	−6.06231	+	6.06231i	−0.193456	+	0.193456i
$983$	7.62627	−	28.4616i	0.243240	−	0.907785i	−0.731019	−	0.682357i	$-0.760955\pi$
$983$	7.62627	−	28.4616i	0.243240	−	0.907785i	0.974260	−	0.225429i	$-0.0723782\pi$
$984$	−4.56717	+	7.91058i	−0.145596	+	0.252180i
$985$	−26.3058	−	45.5629i	−0.838172	−	1.45176i
$986$	23.0753	−	6.18300i	0.734866	−	0.196907i
$987$	−0.578610	+	21.9274i	−0.0184174	+	0.697957i
$988$	8.43498	−	21.3951i	0.268352	−	0.680669i
$989$	27.6315	−	47.8591i	0.878630	−	1.52183i
$990$	−5.69387	+	5.69387i	−0.180963	+	0.180963i
$991$	48.6140			1.54427			0.772137	−	0.635457i	$-0.219188\pi$
$991$	48.6140			1.54427			0.772137	+	0.635457i	$0.219188\pi$
$992$	−6.05252			−0.192168
$993$	−8.07828	+	8.07828i	−0.256356	+	0.256356i
$994$	1.16199	+	1.22498i	0.0368562	+	0.0388540i
$995$	−57.9578	−	15.5297i	−1.83738	−	0.492326i
$996$	0.105209	+	0.392643i	0.00333366	+	0.0124414i
$997$	−9.34113	−	5.39310i	−0.295837	−	0.170801i	0.344734	−	0.938700i	$-0.387969\pi$
$997$	−9.34113	−	5.39310i	−0.295837	−	0.170801i	−0.640571	+	0.767899i	$0.721302\pi$
$998$			12.4942i			0.395496i
$999$	0.818218	−	3.05363i	0.0258873	−	0.0966127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.6	✓	40
7.3	odd	6		546.2.cg.b.241.6	yes	40
13.2	odd	12		546.2.cg.b.145.6	yes	40
91.80	even	12	inner	546.2.by.b.535.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.6	✓	40	1.1	even	1	trivial
546.2.by.b.535.6	yes	40	91.80	even	12	inner
546.2.cg.b.145.6	yes	40	13.2	odd	12
546.2.cg.b.241.6	yes	40	7.3	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.620250 - 2.31481i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.53665 - 0.751945i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.620250 - 2.31481i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-2.53665 - 0.751945i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -2.39646 q^{10} +(-2.37595 + 2.37595i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.14551 + 2.89772i) q^{13} +(-1.38286 + 2.25560i) q^{14} +(2.31481 - 0.620250i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.18530 + 5.51710i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(4.51024 - 4.51024i) q^{19} +(-0.620250 + 2.31481i) q^{20} +(0.751945 - 2.53665i) q^{21} +(1.68005 + 2.90993i) q^{22} +(-5.63845 + 3.25536i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-0.643487 + 0.371517i) q^{25} +(2.24368 + 2.82239i) q^{26} -1.00000i q^{27} +(1.82083 + 1.91953i) q^{28} +(1.87496 - 3.24753i) q^{29} -2.39646i q^{30} +(-5.84629 - 1.56651i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-2.37595 - 2.37595i) q^{33} +(4.50469 + 4.50469i) q^{34} +(-0.167251 + 6.33824i) q^{35} +(0.866025 + 0.500000i) q^{36} +(3.05363 + 0.818218i) q^{37} +(-3.18922 - 5.52389i) q^{38} +(-2.89772 - 2.14551i) q^{39} +(2.07540 + 1.19823i) q^{40} +(-2.36414 - 8.82310i) q^{41} +(-2.25560 - 1.38286i) q^{42} +(-7.35081 + 4.24399i) q^{43} +(3.24561 - 0.869658i) q^{44} +(0.620250 + 2.31481i) q^{45} +(1.68510 + 6.28888i) q^{46} +(-8.00816 + 2.14578i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(5.86916 + 3.81484i) q^{49} +(0.192312 + 0.717716i) q^{50} +(-5.51710 - 3.18530i) q^{51} +(3.30693 - 1.43674i) q^{52} +(-4.65896 - 8.06956i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(6.97354 + 4.02618i) q^{55} +(2.32539 - 1.26197i) q^{56} +(4.51024 + 4.51024i) q^{57} +(-2.65160 - 2.65160i) q^{58} +(-2.37113 + 0.635342i) q^{59} +(-2.31481 - 0.620250i) q^{60} -7.54245i q^{61} +(-3.02626 + 5.24164i) q^{62} +(2.53665 + 0.751945i) q^{63} -1.00000i q^{64} +(8.03841 + 3.16913i) q^{65} +(-2.90993 + 1.68005i) q^{66} +(5.28059 + 5.28059i) q^{67} +(5.51710 - 3.18530i) q^{68} +(-3.25536 - 5.63845i) q^{69} +(6.07898 + 1.80201i) q^{70} +(0.165170 - 0.616423i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.86646 - 10.6978i) q^{73} +(1.58068 - 2.73781i) q^{74} +(-0.371517 - 0.643487i) q^{75} +(-6.16110 + 1.65086i) q^{76} +(7.81353 - 4.24036i) q^{77} +(-2.82239 + 2.24368i) q^{78} +(-2.75688 + 4.77505i) q^{79} +(1.69456 - 1.69456i) q^{80} +1.00000 q^{81} -9.13435 q^{82} +(-0.287435 + 0.287435i) q^{83} +(-1.91953 + 1.82083i) q^{84} +(14.7467 + 3.95136i) q^{85} +(2.19685 + 8.19877i) q^{86} +(3.24753 + 1.87496i) q^{87} -3.36010i q^{88} +(0.715092 - 2.66876i) q^{89} +2.39646 q^{90} +(7.62133 - 5.73719i) q^{91} +6.51073 q^{92} +(1.56651 - 5.84629i) q^{93} +8.29066i q^{94} +(-13.2378 - 7.64285i) q^{95} +(0.258819 + 0.965926i) q^{96} +(3.55971 + 0.953822i) q^{97} +(5.20390 - 4.68182i) q^{98} +(2.37595 - 2.37595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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