LMFDB - Embedded newform 560.2.bd.a.141.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.19
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20137 - 0.746130i) q^{2} +(2.18833 + 2.18833i) q^{3} +(0.886580 - 1.79276i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.26177 + 0.996215i) q^{6} -1.00000i q^{7} +(-0.272519 - 2.81527i) q^{8} +6.57756i q^{9} +O(q^{10})$	\(q+(1.20137 - 0.746130i) q^{2} +(2.18833 + 2.18833i) q^{3} +(0.886580 - 1.79276i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.26177 + 0.996215i) q^{6} -1.00000i q^{7} +(-0.272519 - 2.81527i) q^{8} +6.57756i q^{9} +(-0.321903 + 1.37709i) q^{10} +(0.847972 - 0.847972i) q^{11} +(5.86327 - 1.98301i) q^{12} +(3.07718 + 3.07718i) q^{13} +(-0.746130 - 1.20137i) q^{14} -3.09476 q^{15} +(-2.42795 - 3.17884i) q^{16} -5.75841 q^{17} +(4.90772 + 7.90209i) q^{18} +(3.49935 + 3.49935i) q^{19} +(0.640764 + 1.89458i) q^{20} +(2.18833 - 2.18833i) q^{21} +(0.386031 - 1.65143i) q^{22} -8.84350i q^{23} +(5.56437 - 6.75709i) q^{24} -1.00000i q^{25} +(5.99280 + 1.40085i) q^{26} +(-7.82888 + 7.82888i) q^{27} +(-1.79276 - 0.886580i) q^{28} +(-2.20718 - 2.20718i) q^{29} +(-3.71796 + 2.30910i) q^{30} -5.44796 q^{31} +(-5.28870 - 2.00740i) q^{32} +3.71128 q^{33} +(-6.91798 + 4.29652i) q^{34} +(0.707107 + 0.707107i) q^{35} +(11.7920 + 5.83153i) q^{36} +(4.16747 - 4.16747i) q^{37} +(6.81499 + 1.59305i) q^{38} +13.4677i q^{39} +(2.18340 + 1.79800i) q^{40} -4.94926i q^{41} +(0.996215 - 4.26177i) q^{42} +(-7.34128 + 7.34128i) q^{43} +(-0.768413 - 2.27200i) q^{44} +(-4.65104 - 4.65104i) q^{45} +(-6.59840 - 10.6243i) q^{46} +5.42928 q^{47} +(1.64320 - 12.2695i) q^{48} -1.00000 q^{49} +(-0.746130 - 1.20137i) q^{50} +(-12.6013 - 12.6013i) q^{51} +(8.24479 - 2.78847i) q^{52} +(-2.14124 + 2.14124i) q^{53} +(-3.56402 + 15.2467i) q^{54} +1.19921i q^{55} +(-2.81527 + 0.272519i) q^{56} +15.3155i q^{57} +(-4.29848 - 1.00480i) q^{58} +(-3.49480 + 3.49480i) q^{59} +(-2.74376 + 5.54816i) q^{60} +(-3.45415 - 3.45415i) q^{61} +(-6.54501 + 4.06488i) q^{62} +6.57756 q^{63} +(-7.85147 + 1.53443i) q^{64} -4.35179 q^{65} +(4.45862 - 2.76910i) q^{66} +(3.12477 + 3.12477i) q^{67} +(-5.10529 + 10.3234i) q^{68} +(19.3525 - 19.3525i) q^{69} +(1.37709 + 0.321903i) q^{70} -0.245356i q^{71} +(18.5176 - 1.79251i) q^{72} -0.160291i q^{73} +(1.89720 - 8.11615i) q^{74} +(2.18833 - 2.18833i) q^{75} +(9.37594 - 3.17103i) q^{76} +(-0.847972 - 0.847972i) q^{77} +(10.0487 + 16.1797i) q^{78} -9.95271 q^{79} +(3.96460 + 0.530961i) q^{80} -14.5316 q^{81} +(-3.69279 - 5.94589i) q^{82} +(6.68896 + 6.68896i) q^{83} +(-1.98301 - 5.86327i) q^{84} +(4.07181 - 4.07181i) q^{85} +(-3.34205 + 14.2972i) q^{86} -9.66007i q^{87} +(-2.61836 - 2.15618i) q^{88} -6.01478i q^{89} +(-9.05790 - 2.11734i) q^{90} +(3.07718 - 3.07718i) q^{91} +(-15.8542 - 7.84047i) q^{92} +(-11.9219 - 11.9219i) q^{93} +(6.52257 - 4.05095i) q^{94} -4.94883 q^{95} +(-7.18056 - 15.9663i) q^{96} -14.8733 q^{97} +(-1.20137 + 0.746130i) q^{98} +(5.57759 + 5.57759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.20137	−	0.746130i	0.849497	−	0.527594i
$2$	1.20137	−	0.746130i	0.849497	−	0.527594i
$3$	2.18833	+	2.18833i	1.26343	+	1.26343i	0.949419	+	0.314013i	$0.101674\pi$
$3$	2.18833	+	2.18833i	1.26343	+	1.26343i	0.314013	+	0.949419i	$0.398326\pi$
$4$	0.886580	−	1.79276i	0.443290	−	0.896378i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	4.26177	+	0.996215i	1.73986	+	0.406703i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.272519	−	2.81527i	−0.0963500	−	0.995348i
$9$			6.57756i			2.19252i
$10$	−0.321903	+	1.37709i	−0.101795	+	0.435474i
$11$	0.847972	−	0.847972i	0.255673	−	0.255673i	−0.567618	−	0.823292i	$-0.692135\pi$
$11$	0.847972	−	0.847972i	0.255673	−	0.255673i	0.823292	+	0.567618i	$0.192135\pi$
$12$	5.86327	−	1.98301i	1.69258	−	0.572446i
$13$	3.07718	+	3.07718i	0.853455	+	0.853455i	0.990557	−	0.137102i	$-0.0437787\pi$
$13$	3.07718	+	3.07718i	0.853455	+	0.853455i	−0.137102	+	0.990557i	$0.543779\pi$
$14$	−0.746130	−	1.20137i	−0.199412	−	0.321080i
$15$	−3.09476			−0.799065
$16$	−2.42795	−	3.17884i	−0.606988	−	0.794711i
$17$	−5.75841			−1.39662			−0.698310	−	0.715796i	$-0.746064\pi$
$17$	−5.75841			−1.39662			−0.698310	+	0.715796i	$0.746064\pi$
$18$	4.90772	+	7.90209i	1.15676	+	1.86254i
$19$	3.49935	+	3.49935i	0.802806	+	0.802806i	0.983533	−	0.180727i	$-0.0578450\pi$
$19$	3.49935	+	3.49935i	0.802806	+	0.802806i	−0.180727	+	0.983533i	$0.557845\pi$
$20$	0.640764	+	1.89458i	0.143279	+	0.423640i
$21$	2.18833	−	2.18833i	0.477532	−	0.477532i
$22$	0.386031	−	1.65143i	0.0823021	−	0.352085i
$23$		−	8.84350i		−	1.84400i	−0.387193	−	0.921999i	$-0.626555\pi$
$23$		−	8.84350i		−	1.84400i	0.387193	−	0.921999i	$-0.373445\pi$
$24$	5.56437	−	6.75709i	1.13582	−	1.37929i
$25$		−	1.00000i		−	0.200000i
$26$	5.99280	+	1.40085i	1.17529	+	0.274730i
$27$	−7.82888	+	7.82888i	−1.50667	+	1.50667i
$28$	−1.79276	−	0.886580i	−0.338799	−	0.167548i
$29$	−2.20718	−	2.20718i	−0.409863	−	0.409863i	0.471828	−	0.881691i	$-0.343594\pi$
$29$	−2.20718	−	2.20718i	−0.409863	−	0.409863i	−0.881691	+	0.471828i	$0.843594\pi$
$30$	−3.71796	+	2.30910i	−0.678803	+	0.421581i
$31$	−5.44796			−0.978482			−0.489241	−	0.872149i	$-0.662726\pi$
$31$	−5.44796			−0.978482			−0.489241	+	0.872149i	$0.662726\pi$
$32$	−5.28870	−	2.00740i	−0.934919	−	0.354862i
$33$	3.71128			0.646051
$34$	−6.91798	+	4.29652i	−1.18642	+	0.736848i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	11.7920	+	5.83153i	1.96533	+	0.971922i
$37$	4.16747	−	4.16747i	0.685128	−	0.685128i	−0.276023	−	0.961151i	$-0.589017\pi$
$37$	4.16747	−	4.16747i	0.685128	−	0.685128i	0.961151	+	0.276023i	$0.0890165\pi$
$38$	6.81499	+	1.59305i	1.10554	+	0.258426i
$39$			13.4677i			2.15657i
$40$	2.18340	+	1.79800i	0.345225	+	0.284288i
$41$		−	4.94926i		−	0.772944i	−0.922301	−	0.386472i	$-0.873694\pi$
$41$		−	4.94926i		−	0.772944i	0.922301	−	0.386472i	$-0.126306\pi$
$42$	0.996215	−	4.26177i	0.153719	−	0.657605i
$43$	−7.34128	+	7.34128i	−1.11954	+	1.11954i	−0.127726	+	0.991810i	$0.540768\pi$
$43$	−7.34128	+	7.34128i	−1.11954	+	1.11954i	−0.991810	+	0.127726i	$0.959232\pi$
$44$	−0.768413	−	2.27200i	−0.115843	−	0.342517i
$45$	−4.65104	−	4.65104i	−0.693336	−	0.693336i
$46$	−6.59840	−	10.6243i	−0.972881	−	1.56647i
$47$	5.42928			0.791942			0.395971	−	0.918263i	$-0.370408\pi$
$47$	5.42928			0.791942			0.395971	+	0.918263i	$0.370408\pi$
$48$	1.64320	−	12.2695i	0.237175	−	1.77095i
$49$	−1.00000			−0.142857
$50$	−0.746130	−	1.20137i	−0.105519	−	0.169899i
$51$	−12.6013	−	12.6013i	−1.76453	−	1.76453i
$52$	8.24479	−	2.78847i	1.14335	−	0.386691i
$53$	−2.14124	+	2.14124i	−0.294122	+	0.294122i	−0.838706	−	0.544584i	$-0.816688\pi$
$53$	−2.14124	+	2.14124i	−0.294122	+	0.294122i	0.544584	+	0.838706i	$0.316688\pi$
$54$	−3.56402	+	15.2467i	−0.485002	+	2.07482i
$55$			1.19921i			0.161702i
$56$	−2.81527	+	0.272519i	−0.376206	+	0.0364169i
$57$			15.3155i			2.02858i
$58$	−4.29848	−	1.00480i	−0.564419	−	0.131936i
$59$	−3.49480	+	3.49480i	−0.454984	+	0.454984i	−0.897005	−	0.442021i	$-0.854262\pi$
$59$	−3.49480	+	3.49480i	−0.454984	+	0.454984i	0.442021	+	0.897005i	$0.354262\pi$
$60$	−2.74376	+	5.54816i	−0.354217	+	0.716264i
$61$	−3.45415	−	3.45415i	−0.442258	−	0.442258i	0.450512	−	0.892770i	$-0.351241\pi$
$61$	−3.45415	−	3.45415i	−0.442258	−	0.442258i	−0.892770	+	0.450512i	$0.851241\pi$
$62$	−6.54501	+	4.06488i	−0.831217	+	0.516241i
$63$	6.57756			0.828695
$64$	−7.85147	+	1.53443i	−0.981433	+	0.191803i
$65$	−4.35179			−0.539773
$66$	4.45862	−	2.76910i	0.548819	−	0.340853i
$67$	3.12477	+	3.12477i	0.381751	+	0.381751i	0.871733	−	0.489981i	$-0.162996\pi$
$67$	3.12477	+	3.12477i	0.381751	+	0.381751i	−0.489981	+	0.871733i	$0.662996\pi$
$68$	−5.10529	+	10.3234i	−0.619107	+	1.25190i
$69$	19.3525	−	19.3525i	2.32977	−	2.32977i
$70$	1.37709	+	0.321903i	0.164594	+	0.0384748i
$71$		−	0.245356i		−	0.0291184i	−0.999894	−	0.0145592i	$-0.995366\pi$
$71$		−	0.245356i		−	0.0291184i	0.999894	−	0.0145592i	$-0.00463449\pi$
$72$	18.5176	−	1.79251i	2.18232	−	0.211249i
$73$		−	0.160291i		−	0.0187606i	−0.999956	−	0.00938030i	$-0.997014\pi$
$73$		−	0.160291i		−	0.0187606i	0.999956	−	0.00938030i	$-0.00298589\pi$
$74$	1.89720	−	8.11615i	0.220545	−	0.943484i
$75$	2.18833	−	2.18833i	0.252686	−	0.252686i
$76$	9.37594	−	3.17103i	1.07549	−	0.363742i
$77$	−0.847972	−	0.847972i	−0.0966354	−	0.0966354i
$78$	10.0487	+	16.1797i	1.13779	+	1.83200i
$79$	−9.95271			−1.11977			−0.559883	−	0.828571i	$-0.689154\pi$
$79$	−9.95271			−1.11977			−0.559883	+	0.828571i	$0.689154\pi$
$80$	3.96460	+	0.530961i	0.443256	+	0.0593632i
$81$	−14.5316			−1.61463
$82$	−3.69279	−	5.94589i	−0.407800	−	0.656614i
$83$	6.68896	+	6.68896i	0.734209	+	0.734209i	0.971451	−	0.237242i	$-0.0762434\pi$
$83$	6.68896	+	6.68896i	0.734209	+	0.734209i	−0.237242	+	0.971451i	$0.576243\pi$
$84$	−1.98301	−	5.86327i	−0.216364	−	0.639735i
$85$	4.07181	−	4.07181i	0.441650	−	0.441650i
$86$	−3.34205	+	14.2972i	−0.360382	+	1.54170i
$87$		−	9.66007i		−	1.03567i
$88$	−2.61836	−	2.15618i	−0.279118	−	0.229850i
$89$		−	6.01478i		−	0.637565i	−0.947828	−	0.318783i	$-0.896726\pi$
$89$		−	6.01478i		−	0.637565i	0.947828	−	0.318783i	$-0.103274\pi$
$90$	−9.05790	−	2.11734i	−0.954786	−	0.223187i
$91$	3.07718	−	3.07718i	0.322576	−	0.322576i
$92$	−15.8542	−	7.84047i	−1.65292	−	0.817425i
$93$	−11.9219	−	11.9219i	−1.23625	−	1.23625i
$94$	6.52257	−	4.05095i	0.672752	−	0.417823i
$95$	−4.94883			−0.507739
$96$	−7.18056	−	15.9663i	−0.732863	−	1.62955i
$97$	−14.8733			−1.51015			−0.755076	−	0.655637i	$-0.772400\pi$
$97$	−14.8733			−1.51015			−0.755076	+	0.655637i	$0.772400\pi$
$98$	−1.20137	+	0.746130i	−0.121357	+	0.0753705i
$99$	5.57759	+	5.57759i	0.560569	+	0.560569i
$100$	−1.79276	−	0.886580i	−0.179276	−	0.0886580i
$101$	13.6445	−	13.6445i	1.35768	−	1.35768i	0.480913	−	0.876769i	$-0.340305\pi$
$101$	13.6445	−	13.6445i	1.35768	−	1.35768i	0.876769	−	0.480913i	$-0.159695\pi$
$102$	−24.5410	−	5.73661i	−2.42992	−	0.568009i
$103$			1.46938i			0.144782i	0.997376	+	0.0723911i	$0.0230630\pi$
$103$			1.46938i			0.144782i	−0.997376	+	0.0723911i	$0.976937\pi$
$104$	7.82449	−	9.50167i	0.767254	−	0.931715i
$105$			3.09476i			0.302018i
$106$	−0.974780	+	4.17007i	−0.0946790	+	0.405033i
$107$	11.8430	−	11.8430i	1.14490	−	1.14490i	0.157362	−	0.987541i	$-0.449701\pi$
$107$	11.8430	−	11.8430i	1.14490	−	1.14490i	0.987541	−	0.157362i	$-0.0502989\pi$
$108$	7.09435	+	20.9762i	0.682654	+	2.01844i
$109$	−9.31425	−	9.31425i	−0.892144	−	0.892144i	0.102581	−	0.994725i	$-0.467290\pi$
$109$	−9.31425	−	9.31425i	−0.892144	−	0.892144i	−0.994725	+	0.102581i	$0.967290\pi$
$110$	0.894769	+	1.44070i	0.0853129	+	0.137365i
$111$	18.2396			1.73123
$112$	−3.17884	+	2.42795i	−0.300373	+	0.229420i
$113$	5.90655			0.555641			0.277821	−	0.960633i	$-0.410388\pi$
$113$	5.90655			0.555641			0.277821	+	0.960633i	$0.410388\pi$
$114$	11.4273	+	18.3995i	1.07027	+	1.72327i
$115$	6.25330	+	6.25330i	0.583123	+	0.583123i
$116$	−5.91378	+	2.00010i	−0.549081	+	0.185704i
$117$	−20.2403	+	20.2403i	−1.87122	+	1.87122i
$118$	−1.59097	+	6.80612i	−0.146461	+	0.626554i
$119$			5.75841i			0.527873i
$120$	0.843382	+	8.71259i	0.0769899	+	0.795347i
$121$			9.56189i			0.869262i
$122$	−6.72695	−	1.57247i	−0.609030	−	0.142364i
$123$	10.8306	−	10.8306i	0.976562	−	0.976562i
$124$	−4.83005	+	9.76686i	−0.433751	+	0.877090i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	7.90209	−	4.90772i	0.703974	−	0.437214i
$127$	20.4712			1.81653			0.908265	−	0.418396i	$-0.137408\pi$
$127$	20.4712			1.81653			0.908265	+	0.418396i	$0.137408\pi$
$128$	−8.28763	+	7.70163i	−0.732530	+	0.680734i
$129$	−32.1303			−2.82891
$130$	−5.22811	+	3.24700i	−0.458535	+	0.284781i
$131$	−0.656784	−	0.656784i	−0.0573835	−	0.0573835i	0.677833	−	0.735216i	$-0.262919\pi$
$131$	−0.656784	−	0.656784i	−0.0573835	−	0.0573835i	−0.735216	+	0.677833i	$0.762919\pi$
$132$	3.29035	−	6.65343i	0.286388	−	0.579106i
$133$	3.49935	−	3.49935i	0.303432	−	0.303432i
$134$	6.08549	+	1.42252i	0.525706	+	0.122887i
$135$		−	11.0717i		−	0.952901i
$136$	1.56928	+	16.2115i	0.134564	+	1.39012i
$137$			16.6901i			1.42593i	0.701201	+	0.712964i	$0.252648\pi$
$137$			16.6901i			1.42593i	−0.701201	+	0.712964i	$0.747352\pi$
$138$	8.81002	−	37.6890i	0.749959	−	3.20830i
$139$	−3.42603	+	3.42603i	−0.290592	+	0.290592i	−0.837314	−	0.546722i	$-0.815875\pi$
$139$	−3.42603	+	3.42603i	−0.290592	+	0.290592i	0.546722	+	0.837314i	$0.315875\pi$
$140$	1.89458	−	0.640764i	0.160121	−	0.0541544i
$141$	11.8810	+	11.8810i	1.00056	+	1.00056i
$142$	−0.183067	−	0.294763i	−0.0153627	−	0.0247359i
$143$	5.21872			0.436411
$144$	20.9090	−	15.9700i	1.74242	−	1.33083i
$145$	3.12142			0.259220
$146$	−0.119598	−	0.192568i	−0.00989797	−	0.0159371i
$147$	−2.18833	−	2.18833i	−0.180490	−	0.180490i
$148$	−3.77647	−	11.1661i	−0.310424	−	0.917845i
$149$	−5.45946	+	5.45946i	−0.447256	+	0.447256i	−0.894441	−	0.447185i	$-0.852426\pi$
$149$	−5.45946	+	5.45946i	−0.447256	+	0.447256i	0.447185	+	0.894441i	$0.352426\pi$
$150$	0.996215	−	4.26177i	0.0813406	−	0.347972i
$151$			18.7152i			1.52302i	0.648154	+	0.761509i	$0.275541\pi$
$151$			18.7152i			1.52302i	−0.648154	+	0.761509i	$0.724459\pi$
$152$	8.89797	−	10.8053i	0.721721	−	0.876422i
$153$		−	37.8763i		−	3.06212i
$154$	−1.65143	−	0.386031i	−0.133076	−	0.0311073i
$155$	3.85229	−	3.85229i	0.309423	−	0.309423i
$156$	24.1444	+	11.9402i	1.93310	+	0.955984i
$157$	−2.00348	−	2.00348i	−0.159895	−	0.159895i	0.622625	−	0.782520i	$-0.286066\pi$
$157$	−2.00348	−	2.00348i	−0.159895	−	0.159895i	−0.782520	+	0.622625i	$0.786066\pi$
$158$	−11.9569	+	7.42601i	−0.951238	+	0.590782i
$159$	−9.37149			−0.743207
$160$	5.15912	−	2.32023i	0.407864	−	0.183430i
$161$	−8.84350			−0.696965
$162$	−17.4579	+	10.8425i	−1.37162	+	0.851866i
$163$	−6.13696	−	6.13696i	−0.480684	−	0.480684i	0.424666	−	0.905350i	$-0.360391\pi$
$163$	−6.13696	−	6.13696i	−0.480684	−	0.480684i	−0.905350	+	0.424666i	$0.860391\pi$
$164$	−8.87281	−	4.38791i	−0.692850	−	0.342638i
$165$	−2.62427	+	2.62427i	−0.204299	+	0.204299i
$166$	13.0267	+	3.04508i	1.01107	+	0.236344i
$167$			6.50930i			0.503705i	0.967766	+	0.251852i	$0.0810398\pi$
$167$			6.50930i			0.503705i	−0.967766	+	0.251852i	$0.918960\pi$
$168$	−6.75709	−	5.56437i	−0.521321	−	0.429300i
$169$			5.93804i			0.456772i
$170$	1.85365	−	7.92985i	0.142169	−	0.608192i
$171$	−23.0172	+	23.0172i	−1.76017	+	1.76017i
$172$	6.65250	+	19.6698i	0.507248	+	1.49981i
$173$	6.01341	+	6.01341i	0.457191	+	0.457191i	0.897732	−	0.440541i	$-0.145213\pi$
$173$	6.01341	+	6.01341i	0.457191	+	0.457191i	−0.440541	+	0.897732i	$0.645213\pi$
$174$	−7.20767	−	11.6053i	−0.546412	−	0.879797i
$175$	−1.00000			−0.0755929
$176$	−4.75441	−	0.636735i	−0.358377	−	0.0479957i
$177$	−15.2955			−1.14968
$178$	−4.48781	−	7.22598i	−0.336375	−	0.541610i
$179$	4.11690	+	4.11690i	0.307711	+	0.307711i	0.844021	−	0.536310i	$-0.180182\pi$
$179$	4.11690	+	4.11690i	0.307711	+	0.307711i	−0.536310	+	0.844021i	$0.680182\pi$
$180$	−12.4617	+	4.21466i	−0.928840	+	0.314142i
$181$	−11.5047	+	11.5047i	−0.855138	+	0.855138i	−0.990761	−	0.135623i	$-0.956696\pi$
$181$	−11.5047	+	11.5047i	−0.855138	+	0.855138i	0.135623	+	0.990761i	$0.456696\pi$
$182$	1.40085	−	5.99280i	0.103838	−	0.444216i
$183$		−	15.1176i		−	1.11753i
$184$	−24.8968	+	2.41002i	−1.83542	+	0.177669i
$185$			5.89370i			0.433313i
$186$	−23.2179	−	5.42733i	−1.70242	−	0.397951i
$187$	−4.88297	+	4.88297i	−0.357078	+	0.357078i
$188$	4.81349	−	9.73338i	0.351060	−	0.709879i
$189$	7.82888	+	7.82888i	0.569467	+	0.569467i
$190$	−5.94538	+	3.69247i	−0.431323	+	0.267880i
$191$	3.24138			0.234538			0.117269	−	0.993100i	$-0.462586\pi$
$191$	3.24138			0.234538			0.117269	+	0.993100i	$0.462586\pi$
$192$	−20.5394	−	13.8238i	−1.48230	−	0.997644i
$193$	23.1345			1.66526			0.832629	−	0.553831i	$-0.186835\pi$
$193$	23.1345			1.66526			0.832629	+	0.553831i	$0.186835\pi$
$194$	−17.8683	+	11.0974i	−1.28287	+	0.796747i
$195$	−9.52314	−	9.52314i	−0.681966	−	0.681966i
$196$	−0.886580	+	1.79276i	−0.0633271	+	0.128054i
$197$	−5.22988	+	5.22988i	−0.372614	+	0.372614i	−0.868428	−	0.495815i	$-0.834870\pi$
$197$	−5.22988	+	5.22988i	−0.372614	+	0.372614i	0.495815	+	0.868428i	$0.334870\pi$
$198$	10.8624	+	2.53914i	0.771954	+	0.180449i
$199$			22.2685i			1.57857i	0.614027	+	0.789285i	$0.289549\pi$
$199$			22.2685i			1.57857i	−0.614027	+	0.789285i	$0.710451\pi$
$200$	−2.81527	+	0.272519i	−0.199070	+	0.0192700i
$201$			13.6760i			0.964634i
$202$	6.21153	−	26.5727i	0.437042	−	1.86965i
$203$	−2.20718	+	2.20718i	−0.154914	+	0.154914i
$204$	−33.7631	+	11.4190i	−2.36389	+	0.799490i
$205$	3.49965	+	3.49965i	0.244426	+	0.244426i
$206$	1.09635	+	1.76527i	0.0763862	+	0.122992i
$207$	58.1687			4.04300
$208$	2.31063	−	17.2531i	0.160213	−	1.19629i
$209$	5.93471			0.410512
$210$	2.30910	+	3.71796i	0.159343	+	0.256563i
$211$	14.9441	+	14.9441i	1.02879	+	1.02879i	0.999573	+	0.0292204i	$0.00930246\pi$
$211$	14.9441	+	14.9441i	1.02879	+	1.02879i	0.0292204	+	0.999573i	$0.490698\pi$
$212$	1.94034	+	5.73711i	0.133263	+	0.394026i
$213$	0.536919	−	0.536919i	0.0367891	−	0.0367891i
$214$	5.39139	−	23.0642i	0.368548	−	1.57664i
$215$		−	10.3821i		−	0.708056i
$216$	24.1739	+	19.9069i	1.64483	+	1.35449i
$217$			5.44796i			0.369831i
$218$	−18.1395	−	4.24022i	−1.22856	−	0.287184i
$219$	0.350768	−	0.350768i	0.0237027	−	0.0237027i
$220$	2.14990	+	1.06320i	0.144946	+	0.0716809i
$221$	−17.7196	−	17.7196i	−1.19195	−	1.19195i
$222$	21.9125	−	13.6091i	1.47067	−	0.913384i
$223$	5.67149			0.379791			0.189896	−	0.981804i	$-0.439185\pi$
$223$	5.67149			0.379791			0.189896	+	0.981804i	$0.439185\pi$
$224$	−2.00740	+	5.28870i	−0.134125	+	0.353366i
$225$	6.57756			0.438504
$226$	7.09595	−	4.40705i	0.472016	−	0.293153i
$227$	−5.17740	−	5.17740i	−0.343636	−	0.343636i	0.514096	−	0.857732i	$-0.328127\pi$
$227$	−5.17740	−	5.17740i	−0.343636	−	0.343636i	−0.857732	+	0.514096i	$0.828127\pi$
$228$	27.4569	+	13.5784i	1.81838	+	0.899250i
$229$	2.04579	−	2.04579i	0.135190	−	0.135190i	−0.636274	−	0.771463i	$-0.719525\pi$
$229$	2.04579	−	2.04579i	0.135190	−	0.135190i	0.771463	+	0.636274i	$0.219525\pi$
$230$	12.1783	+	2.84675i	0.803013	+	0.187709i
$231$		−	3.71128i		−	0.244184i
$232$	−5.61231	+	6.81530i	−0.368466	+	0.447447i
$233$		−	21.5432i		−	1.41135i	−0.708538	−	0.705673i	$-0.750645\pi$
$233$		−	21.5432i		−	1.41135i	0.708538	−	0.705673i	$-0.249355\pi$
$234$	−9.21421	+	39.4180i	−0.602351	+	2.57684i
$235$	−3.83908	+	3.83908i	−0.250434	+	0.250434i
$236$	3.16690	+	9.36374i	0.206148	+	0.609528i
$237$	−21.7798	−	21.7798i	−1.41475	−	1.41475i
$238$	4.29652	+	6.91798i	0.278502	+	0.448426i
$239$	−23.1375			−1.49664			−0.748319	−	0.663339i	$-0.769139\pi$
$239$	−23.1375			−1.49664			−0.748319	+	0.663339i	$0.769139\pi$
$240$	7.51394	+	9.83777i	0.485023	+	0.635025i
$241$	29.3260			1.88906			0.944528	−	0.328432i	$-0.106520\pi$
$241$	29.3260			1.88906			0.944528	+	0.328432i	$0.106520\pi$
$242$	7.13441	+	11.4874i	0.458617	+	0.738436i
$243$	−8.31335	−	8.31335i	−0.533301	−	0.533301i
$244$	−9.25482	+	3.13007i	−0.592479	+	0.200382i
$245$	0.707107	−	0.707107i	0.0451754	−	0.0451754i
$246$	4.93052	−	21.0926i	0.314359	−	1.34481i
$247$			21.5363i			1.37032i
$248$	1.48467	+	15.3375i	0.0942767	+	0.973929i
$249$			29.2753i			1.85525i
$250$	1.37709	+	0.321903i	0.0870949	+	0.0203590i
$251$	−10.8792	+	10.8792i	−0.686691	+	0.686691i	−0.961499	−	0.274808i	$-0.911386\pi$
$251$	−10.8792	+	10.8792i	−0.686691	+	0.686691i	0.274808	+	0.961499i	$0.411386\pi$
$252$	5.83153	−	11.7920i	0.367352	−	0.742824i
$253$	−7.49904	−	7.49904i	−0.471461	−	0.471461i
$254$	24.5935	−	15.2742i	1.54314	−	0.958389i
$255$	17.8209			1.11599
$256$	−4.21010	+	15.4362i	−0.263131	+	0.964760i
$257$	14.3719			0.896498			0.448249	−	0.893909i	$-0.352048\pi$
$257$	14.3719			0.896498			0.448249	+	0.893909i	$0.352048\pi$
$258$	−38.6004	+	23.9734i	−2.40315	+	1.49252i
$259$	−4.16747	−	4.16747i	−0.258954	−	0.258954i
$260$	−3.85821	+	7.80169i	−0.239276	+	0.483840i
$261$	14.5179	−	14.5179i	0.898633	−	0.898633i
$262$	−1.27909	−	0.298994i	−0.0790223	−	0.0184719i
$263$			19.7079i			1.21524i	0.794227	+	0.607621i	$0.207876\pi$
$263$			19.7079i			1.21524i	−0.794227	+	0.607621i	$0.792124\pi$
$264$	−1.01139	−	10.4483i	−0.0622471	−	0.643046i
$265$		−	3.02818i		−	0.186019i
$266$	1.59305	−	6.81499i	0.0976759	−	0.417854i
$267$	13.1623	−	13.1623i	0.805521	−	0.805521i
$268$	8.37231	−	2.83159i	0.511420	−	0.172967i
$269$	−8.14780	−	8.14780i	−0.496780	−	0.496780i	0.413654	−	0.910434i	$-0.364252\pi$
$269$	−8.14780	−	8.14780i	−0.496780	−	0.496780i	−0.910434	+	0.413654i	$0.864252\pi$
$270$	−8.26093	−	13.3012i	−0.502744	−	0.809486i
$271$	−4.96255			−0.301453			−0.150727	−	0.988575i	$-0.548161\pi$
$271$	−4.96255			−0.301453			−0.150727	+	0.988575i	$0.548161\pi$
$272$	13.9811	+	18.3051i	0.847731	+	1.10991i
$273$	13.4677			0.815105
$274$	12.4529	+	20.0509i	0.752310	+	1.21132i
$275$	−0.847972	−	0.847972i	−0.0511346	−	0.0511346i
$276$	−17.5368	−	51.8518i	−1.05559	−	3.12111i
$277$	6.05851	−	6.05851i	0.364021	−	0.364021i	−0.501270	−	0.865291i	$-0.667134\pi$
$277$	6.05851	−	6.05851i	0.364021	−	0.364021i	0.865291	+	0.501270i	$0.167134\pi$
$278$	−1.55967	+	6.67220i	−0.0935426	+	0.400172i
$279$		−	35.8343i		−	2.14534i
$280$	1.79800	−	2.18340i	0.107451	−	0.130483i
$281$		−	5.84556i		−	0.348717i	−0.984682	−	0.174358i	$-0.944215\pi$
$281$		−	5.84556i		−	0.348717i	0.984682	−	0.174358i	$-0.0557851\pi$
$282$	23.1383	+	5.40873i	1.37787	+	0.322085i
$283$	6.37132	−	6.37132i	0.378735	−	0.378735i	−0.491910	−	0.870646i	$-0.663701\pi$
$283$	6.37132	−	6.37132i	0.378735	−	0.378735i	0.870646	+	0.491910i	$0.163701\pi$
$284$	−0.439863	−	0.217527i	−0.0261011	−	0.0129079i
$285$	−10.8297	−	10.8297i	−0.641494	−	0.641494i
$286$	6.26962	−	3.89384i	0.370730	−	0.230248i
$287$	−4.94926			−0.292145
$288$	13.2038	−	34.7867i	0.778041	−	2.04983i
$289$	16.1593			0.950546
$290$	3.74999	−	2.32899i	0.220207	−	0.136763i
$291$	−32.5476	−	32.5476i	−1.90797	−	1.90797i
$292$	−0.287362	−	0.142110i	−0.0168166	−	0.00831638i
$293$	8.51162	−	8.51162i	0.497254	−	0.497254i	−0.413328	−	0.910582i	$-0.635634\pi$
$293$	8.51162	−	8.51162i	0.497254	−	0.497254i	0.910582	+	0.413328i	$0.135634\pi$
$294$	−4.26177	−	0.996215i	−0.248551	−	0.0581004i
$295$		−	4.94239i		−	0.287757i
$296$	−12.8683	−	10.5968i	−0.747953	−	0.615929i
$297$			13.2773i			0.770430i
$298$	−2.48536	+	10.6323i	−0.143973	+	0.615912i
$299$	27.2130	−	27.2130i	1.57377	−	1.57377i
$300$	−1.98301	−	5.86327i	−0.114489	−	0.338516i
$301$	7.34128	+	7.34128i	0.423145	+	0.423145i
$302$	13.9639	+	22.4838i	0.803535	+	1.29380i
$303$	59.7174			3.43068
$304$	2.62764	−	19.6202i	0.150705	−	1.12529i
$305$	4.88490			0.279709
$306$	−28.2606	−	45.5034i	−1.61555	−	2.60126i
$307$	19.6732	+	19.6732i	1.12281	+	1.12281i	0.991317	+	0.131494i	$0.0419775\pi$
$307$	19.6732	+	19.6732i	1.12281	+	1.12281i	0.131494	+	0.991317i	$0.458022\pi$
$308$	−2.27200	+	0.768413i	−0.129459	+	0.0437844i
$309$	−3.21548	+	3.21548i	−0.182923	+	0.182923i
$310$	1.75371	−	7.50233i	0.0996043	−	0.426104i
$311$			11.3513i			0.643674i	0.946795	+	0.321837i	$0.104300\pi$
$311$			11.3513i			0.643674i	−0.946795	+	0.321837i	$0.895700\pi$
$312$	37.9153	−	3.67022i	2.14653	−	0.207785i
$313$		−	23.1011i		−	1.30575i	−0.757466	−	0.652875i	$-0.773563\pi$
$313$		−	23.1011i		−	1.30575i	0.757466	−	0.652875i	$-0.226437\pi$
$314$	−3.90178	−	0.912066i	−0.220190	−	0.0514709i
$315$	−4.65104	+	4.65104i	−0.262056	+	0.262056i
$316$	−8.82387	+	17.8428i	−0.496381	+	1.00373i
$317$	−4.08023	−	4.08023i	−0.229169	−	0.229169i	0.583177	−	0.812345i	$-0.301810\pi$
$317$	−4.08023	−	4.08023i	−0.229169	−	0.229169i	−0.812345	+	0.583177i	$0.801810\pi$
$318$	−11.2586	+	6.99235i	−0.631352	+	0.392111i
$319$	−3.74326			−0.209582
$320$	4.46682	−	6.63683i	0.249703	−	0.371010i
$321$	51.8326			2.89301
$322$	−10.6243	+	6.59840i	−0.592070	+	0.367715i
$323$	−20.1507	−	20.1507i	−1.12122	−	1.12122i
$324$	−12.8835	+	26.0517i	−0.715747	+	1.44732i
$325$	3.07718	−	3.07718i	0.170691	−	0.170691i
$326$	−11.9517	−	2.79379i	−0.661945	−	0.154734i
$327$		−	40.7653i		−	2.25433i
$328$	−13.9335	+	1.34877i	−0.769348	+	0.0744732i
$329$		−	5.42928i		−	0.299326i
$330$	−1.19467	+	5.11077i	−0.0657647	+	0.281339i
$331$	9.07863	−	9.07863i	0.499007	−	0.499007i	−0.412122	−	0.911129i	$-0.635212\pi$
$331$	9.07863	−	9.07863i	0.499007	−	0.499007i	0.911129	+	0.412122i	$0.135212\pi$
$332$	17.9220	−	6.06138i	0.983596	−	0.332661i
$333$	27.4118	+	27.4118i	1.50216	+	1.50216i
$334$	4.85679	+	7.82008i	0.265751	+	0.427896i
$335$	−4.41909			−0.241441
$336$	−12.2695	−	1.64320i	−0.669357	−	0.0896438i
$337$	15.6429			0.852123			0.426062	−	0.904694i	$-0.359901\pi$
$337$	15.6429			0.852123			0.426062	+	0.904694i	$0.359901\pi$
$338$	4.43055	+	7.13378i	0.240990	+	0.388027i
$339$	12.9255	+	12.9255i	0.702015	+	0.702015i
$340$	−3.68978	−	10.9098i	−0.200106	−	0.591664i
$341$	−4.61972	+	4.61972i	−0.250172	+	0.250172i
$342$	−10.4784	+	44.8260i	−0.566604	+	2.42391i
$343$			1.00000i			0.0539949i
$344$	22.6683	+	18.6670i	1.22219	+	1.00646i
$345$			27.3685i			1.47347i
$346$	11.7111	+	2.73755i	0.629594	+	0.147171i
$347$	−7.96501	+	7.96501i	−0.427584	+	0.427584i	−0.887805	−	0.460220i	$-0.847770\pi$
$347$	−7.96501	+	7.96501i	−0.427584	+	0.427584i	0.460220	+	0.887805i	$0.347770\pi$
$348$	−17.3182	−	8.56443i	−0.928351	−	0.459101i
$349$	−3.54063	−	3.54063i	−0.189525	−	0.189525i	0.605965	−	0.795491i	$-0.292787\pi$
$349$	−3.54063	−	3.54063i	−0.189525	−	0.189525i	−0.795491	+	0.605965i	$0.792787\pi$
$350$	−1.20137	+	0.746130i	−0.0642159	+	0.0398823i
$351$	−48.1817			−2.57175
$352$	−6.18689	+	2.78245i	−0.329762	+	0.148305i
$353$	−22.2929			−1.18653			−0.593266	−	0.805007i	$-0.702162\pi$
$353$	−22.2929			−1.18653			−0.593266	+	0.805007i	$0.702162\pi$
$354$	−18.3756	+	11.4125i	−0.976652	+	0.606565i
$355$	0.173493	+	0.173493i	0.00920803	+	0.00920803i
$356$	−10.7830	−	5.33258i	−0.571500	−	0.282626i
$357$	−12.6013	+	12.6013i	−0.666931	+	0.666931i
$358$	8.01766	+	1.87418i	0.423746	+	0.0990533i
$359$		−	12.8441i		−	0.677883i	−0.940807	−	0.338942i	$-0.889931\pi$
$359$		−	12.8441i		−	0.677883i	0.940807	−	0.338942i	$-0.110069\pi$
$360$	−11.8264	+	14.3614i	−0.623307	+	0.756913i
$361$			5.49093i			0.288996i
$362$	−5.23740	+	22.4054i	−0.275272	+	1.17760i
$363$	−20.9245	+	20.9245i	−1.09825	+	1.09825i
$364$	−2.78847	−	8.24479i	−0.146155	−	0.432145i
$365$	0.113343	+	0.113343i	0.00593262	+	0.00593262i
$366$	−11.2797	−	18.1619i	−0.589600	−	0.949335i
$367$	−13.6296			−0.711458			−0.355729	−	0.934589i	$-0.615767\pi$
$367$	−13.6296			−0.711458			−0.355729	+	0.934589i	$0.615767\pi$
$368$	−28.1121	+	21.4716i	−1.46544	+	1.11928i
$369$	32.5540			1.69470
$370$	4.39746	+	7.08051i	0.228613	+	0.368098i
$371$	2.14124	+	2.14124i	0.111168	+	0.111168i
$372$	−31.9428	+	10.8034i	−1.65616	+	0.560128i
$373$	6.73500	−	6.73500i	0.348725	−	0.348725i	−0.510910	−	0.859634i	$-0.670691\pi$
$373$	6.73500	−	6.73500i	0.348725	−	0.348725i	0.859634	+	0.510910i	$0.170691\pi$
$374$	−2.22292	+	9.50959i	−0.114945	+	0.491729i
$375$			3.09476i			0.159813i
$376$	−1.47958	−	15.2849i	−0.0763036	−	0.788257i
$377$		−	13.5838i		−	0.699600i
$378$	15.2467	+	3.56402i	0.784208	+	0.183313i
$379$	−13.0373	+	13.0373i	−0.669679	+	0.669679i	−0.957642	−	0.287963i	$-0.907022\pi$
$379$	−13.0373	+	13.0373i	−0.669679	+	0.669679i	0.287963	+	0.957642i	$0.407022\pi$
$380$	−4.38753	+	8.87205i	−0.225076	+	0.455127i
$381$	44.7978	+	44.7978i	2.29506	+	2.29506i
$382$	3.89410	−	2.41849i	0.199239	−	0.123741i
$383$	9.00155			0.459958			0.229979	−	0.973196i	$-0.426134\pi$
$383$	9.00155			0.459958			0.229979	+	0.973196i	$0.426134\pi$
$384$	−34.9898	−	1.28237i	−1.78556	−	0.0654406i
$385$	1.19921			0.0611176
$386$	27.7931	−	17.2613i	1.41463	−	0.878579i
$387$	−48.2877	−	48.2877i	−2.45460	−	2.45460i
$388$	−13.1863	+	26.6642i	−0.669435	+	1.35367i
$389$	9.98081	−	9.98081i	0.506047	−	0.506047i	−0.407264	−	0.913311i	$-0.633517\pi$
$389$	9.98081	−	9.98081i	0.506047	−	0.506047i	0.913311	+	0.407264i	$0.133517\pi$
$390$	−18.5463	−	4.33531i	−0.939129	−	0.219527i
$391$			50.9245i			2.57536i
$392$	0.272519	+	2.81527i	0.0137643	+	0.142193i
$393$		−	2.87452i		−	0.145000i
$394$	−2.38085	+	10.1852i	−0.119946	+	0.513123i
$395$	7.03763	−	7.03763i	0.354101	−	0.354101i
$396$	14.9442	−	5.05428i	0.750976	−	0.253987i
$397$	6.78250	+	6.78250i	0.340404	+	0.340404i	0.856519	−	0.516115i	$-0.172622\pi$
$397$	6.78250	+	6.78250i	0.340404	+	0.340404i	−0.516115	+	0.856519i	$0.672622\pi$
$398$	16.6152	+	26.7527i	0.832843	+	1.34099i
$399$	15.3155			0.766732
$400$	−3.17884	+	2.42795i	−0.158942	+	0.121398i
$401$	−12.1728			−0.607883			−0.303942	−	0.952691i	$-0.598303\pi$
$401$	−12.1728			−0.607883			−0.303942	+	0.952691i	$0.598303\pi$
$402$	10.2041	+	16.4300i	0.508935	+	0.819454i
$403$	−16.7643	−	16.7643i	−0.835091	−	0.835091i
$404$	−12.3644	−	36.5583i	−0.615149	−	1.81884i
$405$	10.2754	−	10.2754i	0.510590	−	0.510590i
$406$	−1.00480	+	4.29848i	−0.0498672	+	0.213330i
$407$		−	7.06780i		−	0.350338i
$408$	−32.0419	+	38.9101i	−1.58631	+	1.92634i
$409$			13.9406i			0.689319i	0.938728	+	0.344660i	$0.112006\pi$
$409$			13.9406i			0.689319i	−0.938728	+	0.344660i	$0.887994\pi$
$410$	6.81558	+	1.59318i	0.336597	+	0.0786817i
$411$	−36.5233	+	36.5233i	−1.80156	+	1.80156i
$412$	2.63424	+	1.30272i	0.129780	+	0.0641805i
$413$	3.49480	+	3.49480i	0.171968	+	0.171968i
$414$	69.8821	−	43.4014i	3.43452	−	2.13306i
$415$	−9.45962			−0.464354
$416$	−10.0971	−	22.4514i	−0.495053	−	1.10077i
$417$	−14.9946			−0.734287
$418$	7.12978	−	4.42806i	0.348729	−	0.216584i
$419$	0.656515	+	0.656515i	0.0320729	+	0.0320729i	0.722961	−	0.690888i	$-0.242780\pi$
$419$	0.656515	+	0.656515i	0.0320729	+	0.0320729i	−0.690888	+	0.722961i	$0.742780\pi$
$420$	5.54816	+	2.74376i	0.270722	+	0.133882i
$421$	−20.5128	+	20.5128i	−0.999731	+	0.999731i	−1.00000		0.000268850i	$-0.999914\pi$
$421$	−20.5128	+	20.5128i	−0.999731	+	0.999731i	0.000268850		1.00000i	$0.499914\pi$
$422$	29.1036	+	6.80315i	1.41674	+	0.331172i
$423$			35.7114i			1.73635i
$424$	6.61170	+	5.44464i	0.321093	+	0.264415i
$425$			5.75841i			0.279324i
$426$	0.244427	−	1.04565i	0.0118425	−	0.0506619i
$427$	−3.45415	+	3.45415i	−0.167158	+	0.167158i
$428$	−10.7318	−	31.7313i	−0.518742	−	1.53379i
$429$	11.4203	+	11.4203i	0.551376	+	0.551376i
$430$	−7.74643	−	12.4728i	−0.373566	−	0.601492i
$431$	24.0169			1.15685			0.578427	−	0.815734i	$-0.303667\pi$
$431$	24.0169			1.15685			0.578427	+	0.815734i	$0.303667\pi$
$432$	43.8949	+	5.87864i	2.11190	+	0.282836i
$433$	−23.5582			−1.13213			−0.566067	−	0.824359i	$-0.691536\pi$
$433$	−23.5582			−1.13213			−0.566067	+	0.824359i	$0.691536\pi$
$434$	4.06488	+	6.54501i	0.195121	+	0.314171i
$435$	6.83070	+	6.83070i	0.327507	+	0.327507i
$436$	−24.9560	+	8.44036i	−1.19518	+	0.404220i
$437$	30.9465	−	30.9465i	1.48037	−	1.48037i
$438$	0.159684	−	0.683122i	0.00762999	−	0.0326408i
$439$			2.63689i			0.125852i	0.998018	+	0.0629259i	$0.0200432\pi$
$439$			2.63689i			0.125852i	−0.998018	+	0.0629259i	$0.979957\pi$
$440$	3.37611	−	0.326808i	0.160950	−	0.0155800i
$441$		−	6.57756i		−	0.313217i
$442$	−34.5090	−	8.06669i	−1.64143	−	0.383693i
$443$	5.38859	−	5.38859i	0.256020	−	0.256020i	−0.567413	−	0.823433i	$-0.692056\pi$
$443$	5.38859	−	5.38859i	0.256020	−	0.256020i	0.823433	+	0.567413i	$0.192056\pi$
$444$	16.1709	−	32.6992i	0.767435	−	1.55183i
$445$	4.25309	+	4.25309i	0.201616	+	0.201616i
$446$	6.81356	−	4.23167i	0.322631	−	0.200375i
$447$	−23.8942			−1.13016
$448$	1.53443	+	7.85147i	0.0724949	+	0.370947i
$449$	−20.9830			−0.990248			−0.495124	−	0.868822i	$-0.664877\pi$
$449$	−20.9830			−0.990248			−0.495124	+	0.868822i	$0.664877\pi$
$450$	7.90209	−	4.90772i	0.372508	−	0.231352i
$451$	−4.19683	−	4.19683i	−0.197621	−	0.197621i
$452$	5.23663	−	10.5890i	0.246310	−	0.498065i
$453$	−40.9549	+	40.9549i	−1.92423	+	1.92423i
$454$	−10.0830	−	2.35696i	−0.473218	−	0.110618i
$455$			4.35179i			0.204015i
$456$	43.1171	−	4.17375i	2.01914	−	0.195454i
$457$		−	19.5052i		−	0.912415i	−0.889873	−	0.456208i	$-0.849207\pi$
$457$		−	19.5052i		−	0.912415i	0.889873	−	0.456208i	$-0.150793\pi$
$458$	0.931325	−	3.98418i	0.0435180	−	0.186168i
$459$	45.0819	−	45.0819i	2.10424	−	2.10424i
$460$	16.7547	−	5.66659i	0.781192	−	0.264206i
$461$	−14.8818	−	14.8818i	−0.693116	−	0.693116i	0.269800	−	0.962916i	$-0.413042\pi$
$461$	−14.8818	−	14.8818i	−0.693116	−	0.693116i	−0.962916	+	0.269800i	$0.913042\pi$
$462$	−2.76910	−	4.45862i	−0.128830	−	0.207434i
$463$	−19.3913			−0.901191			−0.450595	−	0.892728i	$-0.648788\pi$
$463$	−19.3913			−0.901191			−0.450595	+	0.892728i	$0.648788\pi$
$464$	−1.65735	+	12.3752i	−0.0769407	+	0.574505i
$465$	16.8601			0.781870
$466$	−16.0741	−	25.8814i	−0.744617	−	1.19893i
$467$	10.8576	+	10.8576i	0.502430	+	0.502430i	0.912192	−	0.409763i	$-0.134388\pi$
$467$	10.8576	+	10.8576i	0.502430	+	0.502430i	−0.409763	+	0.912192i	$0.634388\pi$
$468$	18.3413	+	54.2306i	0.847827	+	2.50681i
$469$	3.12477	−	3.12477i	0.144288	−	0.144288i
$470$	−1.74770	+	7.47661i	−0.0806155	+	0.344870i
$471$		−	8.76856i		−	0.404034i
$472$	10.7912	+	8.88640i	0.496705	+	0.409029i
$473$			12.4504i			0.572470i
$474$	−42.4161	−	9.91503i	−1.94824	−	0.455412i
$475$	3.49935	−	3.49935i	0.160561	−	0.160561i
$476$	10.3234	+	5.10529i	0.473173	+	0.234001i
$477$	−14.0842	−	14.0842i	−0.644869	−	0.644869i
$478$	−27.7966	+	17.2635i	−1.27139	+	0.789616i
$479$	−28.6762			−1.31025			−0.655125	−	0.755520i	$-0.727384\pi$
$479$	−28.6762			−1.31025			−0.655125	+	0.755520i	$0.727384\pi$
$480$	16.3673	+	6.21243i	0.747061	+	0.283557i
$481$	25.6481			1.16945
$482$	35.2314	−	21.8810i	1.60475	−	0.996653i
$483$	−19.3525	−	19.3525i	−0.880568	−	0.880568i
$484$	17.1421	+	8.47738i	0.779188	+	0.385335i
$485$	10.5170	−	10.5170i	0.477552	−	0.477552i
$486$	−16.1902	−	3.78457i	−0.734404	−	0.171671i
$487$		−	21.4381i		−	0.971453i	−0.874111	−	0.485726i	$-0.838555\pi$
$487$		−	21.4381i		−	0.971453i	0.874111	−	0.485726i	$-0.161445\pi$
$488$	−8.78303	+	10.6657i	−0.397589	+	0.482812i
$489$		−	26.8594i		−	1.21462i
$490$	0.321903	−	1.37709i	0.0145421	−	0.0622106i
$491$	13.4057	−	13.4057i	0.604991	−	0.604991i	−0.336642	−	0.941633i	$-0.609291\pi$
$491$	13.4057	−	13.4057i	0.604991	−	0.604991i	0.941633	+	0.336642i	$0.109291\pi$
$492$	−9.81444	−	29.0188i	−0.442469	−	1.30827i
$493$	12.7099	+	12.7099i	0.572423	+	0.572423i
$494$	16.0688	+	25.8730i	0.722972	+	1.16408i
$495$	−7.88790			−0.354535
$496$	13.2274	+	17.3182i	0.593927	+	0.777610i
$497$	−0.245356			−0.0110057
$498$	21.8432	+	35.1704i	0.978816	+	1.57603i
$499$	−25.8696	−	25.8696i	−1.15808	−	1.15808i	−0.984887	−	0.173196i	$-0.944591\pi$
$499$	−25.8696	−	25.8696i	−1.15808	−	1.15808i	−0.173196	−	0.984887i	$-0.555409\pi$
$500$	1.89458	−	0.640764i	0.0847281	−	0.0286558i
$501$	−14.2445	+	14.2445i	−0.636397	+	0.636397i
$502$	−4.95266	+	21.1873i	−0.221048	+	0.945635i
$503$			21.5963i			0.962930i	0.876465	+	0.481465i	$0.159895\pi$
$503$			21.5963i			0.962930i	−0.876465	+	0.481465i	$0.840105\pi$
$504$	−1.79251	−	18.5176i	−0.0798447	−	0.824839i
$505$			19.2963i			0.858673i
$506$	−14.6044	−	3.41386i	−0.649244	−	0.151765i
$507$	−12.9944	+	12.9944i	−0.577101	+	0.577101i
$508$	18.1494	−	36.7000i	0.805249	−	1.62830i
$509$	−2.49795	−	2.49795i	−0.110720	−	0.110720i	0.649577	−	0.760296i	$-0.274946\pi$
$509$	−2.49795	−	2.49795i	−0.110720	−	0.110720i	−0.760296	+	0.649577i	$0.774946\pi$
$510$	21.4095	−	13.2967i	0.948029	−	0.588789i
$511$	−0.160291			−0.00709084
$512$	6.45950	+	21.6858i	0.285472	+	0.958387i
$513$	−54.7920			−2.41913
$514$	17.2660	−	10.7233i	0.761572	−	0.472986i
$515$	−1.03901	−	1.03901i	−0.0457842	−	0.0457842i
$516$	−28.4861	+	57.6018i	−1.25403	+	2.53578i
$517$	4.60388	−	4.60388i	0.202478	−	0.202478i
$518$	−8.11615	−	1.89720i	−0.356603	−	0.0833582i
$519$			26.3186i			1.15526i
$520$	1.18594	+	12.2514i	0.0520071	+	0.537261i
$521$			3.85387i			0.168841i	0.996430	+	0.0844206i	$0.0269039\pi$
$521$			3.85387i			0.168841i	−0.996430	+	0.0844206i	$0.973096\pi$
$522$	6.60911	−	28.2735i	0.289273	−	1.23750i
$523$	21.5930	−	21.5930i	0.944197	−	0.944197i	−0.0543258	−	0.998523i	$-0.517301\pi$
$523$	21.5930	−	21.5930i	0.944197	−	0.944197i	0.998523	+	0.0543258i	$0.0173010\pi$
$524$	−1.75975	+	0.595162i	−0.0768748	+	0.0259998i
$525$	−2.18833	−	2.18833i	−0.0955065	−	0.0955065i
$526$	14.7047	+	23.6765i	0.641154	+	1.03234i
$527$	31.3716			1.36657
$528$	−9.01082	−	11.7976i	−0.392145	−	0.513424i
$529$	−55.2075			−2.40033
$530$	−2.25941	−	3.63796i	−0.0981426	−	0.158023i
$531$	−22.9873	−	22.9873i	−0.997562	−	0.997562i
$532$	−3.17103	−	9.37594i	−0.137482	−	0.406499i
$533$	15.2297	−	15.2297i	0.659673	−	0.659673i
$534$	5.99201	−	25.6336i	0.259300	−	1.10927i
$535$			16.7485i			0.724100i
$536$	7.94551	−	9.64862i	0.343194	−	0.416757i
$537$			18.0182i			0.777545i
$538$	−15.8678	−	3.70921i	−0.684111	−	0.159915i
$539$	−0.847972	+	0.847972i	−0.0365247	+	0.0365247i
$540$	−19.8489	−	9.81595i	−0.854160	−	0.422411i
$541$	−5.17070	−	5.17070i	−0.222306	−	0.222306i	0.587163	−	0.809469i	$-0.300245\pi$
$541$	−5.17070	−	5.17070i	−0.222306	−	0.222306i	−0.809469	+	0.587163i	$0.800245\pi$
$542$	−5.96186	+	3.70271i	−0.256084	+	0.159045i
$543$	−50.3521			−2.16082
$544$	30.4545	+	11.5594i	1.30573	+	0.495607i
$545$	13.1723			0.564241
$546$	16.1797	−	10.0487i	0.692429	−	0.430044i
$547$	11.2461	+	11.2461i	0.480847	+	0.480847i	0.905402	−	0.424555i	$-0.139569\pi$
$547$	11.2461	+	11.2461i	0.480847	+	0.480847i	−0.424555	+	0.905402i	$0.639569\pi$
$548$	29.9212	+	14.7971i	1.27817	+	0.632099i
$549$	22.7199	−	22.7199i	0.969660	−	0.969660i
$550$	−1.65143	−	0.386031i	−0.0704170	−	0.0164604i
$551$		−	15.4474i		−	0.658082i
$552$	−59.7563	−	49.2085i	−2.54340	−	2.09445i
$553$			9.95271i			0.423232i
$554$	2.75808	−	11.7989i	0.117179	−	0.501289i
$555$	−12.8973	+	12.8973i	−0.547462	+	0.547462i
$556$	3.10459	+	9.17949i	0.131664	+	0.389297i
$557$	−5.10566	−	5.10566i	−0.216334	−	0.216334i	0.590618	−	0.806951i	$-0.298884\pi$
$557$	−5.10566	−	5.10566i	−0.216334	−	0.216334i	−0.806951	+	0.590618i	$0.798884\pi$
$558$	−26.7370	−	43.0502i	−1.13187	−	1.82246i
$559$	−45.1809			−1.91095
$560$	0.530961	−	3.96460i	0.0224372	−	0.167535i
$561$	−21.3711			−0.902288
$562$	−4.36154	−	7.02268i	−0.183981	−	0.296234i
$563$	−29.5241	−	29.5241i	−1.24429	−	1.24429i	−0.958203	−	0.286090i	$-0.907644\pi$
$563$	−29.5241	−	29.5241i	−1.24429	−	1.24429i	−0.286090	−	0.958203i	$-0.592356\pi$
$564$	31.8333	−	10.7663i	1.34042	−	0.453344i
$565$	−4.17656	+	4.17656i	−0.175709	+	0.175709i
$566$	2.90048	−	12.4081i	0.121916	−	0.521553i
$567$			14.5316i			0.610271i
$568$	−0.690742	+	0.0668640i	−0.0289829	+	0.00280555i
$569$			11.7289i			0.491702i	0.969308	+	0.245851i	$0.0790674\pi$
$569$			11.7289i			0.491702i	−0.969308	+	0.245851i	$0.920933\pi$
$570$	−21.0908	−	4.93010i	−0.883396	−	0.206499i
$571$	−21.3982	+	21.3982i	−0.895488	+	0.895488i	−0.995033	−	0.0995448i	$-0.968261\pi$
$571$	−21.3982	+	21.3982i	−0.895488	+	0.895488i	0.0995448	+	0.995033i	$0.468261\pi$
$572$	4.62681	−	9.35590i	0.193457	−	0.391190i
$573$	7.09321	+	7.09321i	0.296323	+	0.296323i
$574$	−5.94589	+	3.69279i	−0.248177	+	0.154134i
$575$	−8.84350			−0.368799
$576$	−10.0928	−	51.6435i	−0.420533	−	2.15181i
$577$	39.3729			1.63912			0.819558	−	0.572997i	$-0.194219\pi$
$577$	39.3729			1.63912			0.819558	+	0.572997i	$0.194219\pi$
$578$	19.4133	−	12.0569i	0.807486	−	0.501502i
$579$	50.6259	+	50.6259i	2.10394	+	2.10394i
$580$	2.76739	−	5.59595i	0.114910	−	0.232359i
$581$	6.68896	−	6.68896i	0.277505	−	0.277505i
$582$	−63.3865	−	14.8170i	−2.62745	−	0.614183i
$583$			3.63143i			0.150398i
$584$	−0.451261	+	0.0436822i	−0.0186733	+	0.00180758i
$585$		−	28.6241i		−	1.18346i
$586$	3.87483	−	16.5764i	0.160068	−	0.684764i
$587$	−12.3201	+	12.3201i	−0.508506	+	0.508506i	−0.914068	−	0.405562i	$-0.867076\pi$
$587$	−12.3201	+	12.3201i	−0.508506	+	0.508506i	0.405562	+	0.914068i	$0.367076\pi$
$588$	−5.86327	+	1.98301i	−0.241797	+	0.0817780i
$589$	−19.0643	−	19.0643i	−0.785532	−	0.785532i
$590$	−3.68767	−	5.93764i	−0.151819	−	0.244449i
$591$	−22.8894			−0.941544
$592$	−23.3662	−	3.12932i	−0.960344	−	0.128614i
$593$	9.77506			0.401414			0.200707	−	0.979651i	$-0.435676\pi$
$593$	9.77506			0.401414			0.200707	+	0.979651i	$0.435676\pi$
$594$	9.90663	+	15.9510i	0.406474	+	0.654478i
$595$	−4.07181	−	4.07181i	−0.166928	−	0.166928i
$596$	4.94723	+	14.6277i	0.202647	+	0.599175i
$597$	−48.7307	+	48.7307i	−1.99442	+	1.99442i
$598$	12.3885	−	52.9974i	0.506602	−	2.16722i
$599$		−	23.5391i		−	0.961783i	−0.876780	−	0.480892i	$-0.840313\pi$
$599$		−	23.5391i		−	0.961783i	0.876780	−	0.480892i	$-0.159687\pi$
$600$	−6.75709	−	5.56437i	−0.275857	−	0.227164i
$601$		−	42.6943i		−	1.74154i	−0.491692	−	0.870769i	$-0.663621\pi$
$601$		−	42.6943i		−	1.74154i	0.491692	−	0.870769i	$-0.336379\pi$
$602$	14.2972	+	3.34205i	0.582708	+	0.136212i
$603$	−20.5534	+	20.5534i	−0.836998	+	0.836998i
$604$	33.5517	+	16.5925i	1.36520	+	0.675139i
$605$	−6.76127	−	6.76127i	−0.274885	−	0.274885i
$606$	71.7427	−	44.5570i	2.91435	−	1.81000i
$607$	11.7930			0.478663			0.239331	−	0.970938i	$-0.423072\pi$
$607$	11.7930			0.478663			0.239331	+	0.970938i	$0.423072\pi$
$608$	−11.4824	−	25.5316i	−0.465674	−	1.03544i
$609$	−9.66007			−0.391446
$610$	5.86857	−	3.64477i	0.237612	−	0.147572i
$611$	16.7069	+	16.7069i	0.675887	+	0.675887i
$612$	−67.9030	−	33.5804i	−2.74482	−	1.35741i
$613$	−3.78380	+	3.78380i	−0.152826	+	0.152826i	−0.779379	−	0.626553i	$-0.784465\pi$
$613$	−3.78380	+	3.78380i	−0.152826	+	0.152826i	0.626553	+	0.779379i	$0.284465\pi$
$614$	38.3136	+	8.95605i	1.54621	+	0.361437i
$615$			15.3168i			0.617632i
$616$	−2.15618	+	2.61836i	−0.0868750	+	0.105497i
$617$		−	8.12770i		−	0.327209i	−0.986526	−	0.163604i	$-0.947688\pi$
$617$		−	8.12770i		−	0.327209i	0.986526	−	0.163604i	$-0.0523121\pi$
$618$	−1.46382	+	6.26216i	−0.0588834	+	0.251901i
$619$	−3.29631	+	3.29631i	−0.132490	+	0.132490i	−0.770242	−	0.637752i	$-0.779864\pi$
$619$	−3.29631	+	3.29631i	−0.132490	+	0.132490i	0.637752	+	0.770242i	$0.279864\pi$
$620$	−3.49085	−	10.3216i	−0.140196	−	0.414524i
$621$	69.2347	+	69.2347i	2.77829	+	2.77829i
$622$	8.46956	+	13.6371i	0.339598	+	0.546799i
$623$	−6.01478			−0.240977
$624$	42.8119	−	32.6990i	1.71385	−	1.30901i
$625$	−1.00000			−0.0400000
$626$	−17.2364	−	27.7529i	−0.688905	−	1.10923i
$627$	12.9871	+	12.9871i	0.518654	+	0.518654i
$628$	−5.36801	+	1.81551i	−0.214207	+	0.0724467i
$629$	−23.9980	+	23.9980i	−0.956863	+	0.956863i
$630$	−2.11734	+	9.05790i	−0.0843568	+	0.360875i
$631$		−	43.1144i		−	1.71636i	−0.513353	−	0.858178i	$-0.671597\pi$
$631$		−	43.1144i		−	1.71636i	0.513353	−	0.858178i	$-0.328403\pi$
$632$	2.71230	+	28.0195i	0.107890	+	1.11456i
$633$			65.4051i			2.59962i
$634$	−7.94625	−	1.85748i	−0.315586	−	0.0737701i
$635$	−14.4754	+	14.4754i	−0.574437	+	0.574437i
$636$	−8.30857	+	16.8008i	−0.329456	+	0.666195i
$637$	−3.07718	−	3.07718i	−0.121922	−	0.121922i
$638$	−4.49703	+	2.79296i	−0.178039	+	0.110574i
$639$	1.61384			0.0638426
$640$	0.414367	−	11.3061i	0.0163793	−	0.446914i
$641$	−22.9054			−0.904707			−0.452354	−	0.891839i	$-0.649415\pi$
$641$	−22.9054			−0.904707			−0.452354	+	0.891839i	$0.649415\pi$
$642$	62.2701	−	38.6739i	2.45761	−	1.52634i
$643$	−16.6642	−	16.6642i	−0.657172	−	0.657172i	0.297538	−	0.954710i	$-0.403834\pi$
$643$	−16.6642	−	16.6642i	−0.657172	−	0.657172i	−0.954710	+	0.297538i	$0.903834\pi$
$644$	−7.84047	+	15.8542i	−0.308958	+	0.624745i
$645$	22.7195	−	22.7195i	0.894581	−	0.894581i
$646$	−39.2435	−	9.17341i	−1.54401	−	0.360923i
$647$			1.66057i			0.0652837i	0.999467	+	0.0326419i	$0.0103921\pi$
$647$			1.66057i			0.0652837i	−0.999467	+	0.0326419i	$0.989608\pi$
$648$	3.96015	+	40.9104i	0.155569	+	1.60711i
$649$			5.92698i			0.232654i
$650$	1.40085	−	5.99280i	0.0549460	−	0.235057i
$651$	−11.9219	+	11.9219i	−0.467257	+	0.467257i
$652$	−16.4430	+	5.56117i	−0.643957	+	0.217792i
$653$	17.3717	+	17.3717i	0.679807	+	0.679807i	0.959956	−	0.280150i	$-0.0903841\pi$
$653$	17.3717	+	17.3717i	0.679807	+	0.679807i	−0.280150	+	0.959956i	$0.590384\pi$
$654$	−30.4162	−	48.9742i	−1.18937	−	1.91504i
$655$	0.928833			0.0362925
$656$	−15.7329	+	12.0166i	−0.614267	+	0.469168i
$657$	1.05432			0.0411330
$658$	−4.05095	−	6.52257i	−0.157922	−	0.254276i
$659$	0.126108	+	0.126108i	0.00491247	+	0.00491247i	0.709559	−	0.704646i	$-0.248894\pi$
$659$	0.126108	+	0.126108i	0.00491247	+	0.00491247i	−0.704646	+	0.709559i	$0.748894\pi$
$660$	2.37806	+	7.03131i	0.0925657	+	0.273693i
$661$	−9.17026	+	9.17026i	−0.356682	+	0.356682i	−0.862588	−	0.505906i	$-0.831158\pi$
$661$	−9.17026	+	9.17026i	−0.356682	+	0.356682i	0.505906	+	0.862588i	$0.331158\pi$
$662$	4.13296	−	17.6806i	0.160632	−	0.687177i
$663$		−	77.5528i		−	3.01190i
$664$	17.0083	−	20.6541i	0.660052	−	0.801534i
$665$			4.94883i			0.191907i
$666$	53.3845	+	12.4790i	2.06861	+	0.483550i
$667$	−19.5192	+	19.5192i	−0.755787	+	0.755787i
$668$	11.6696	+	5.77102i	0.451510	+	0.223287i
$669$	12.4111	+	12.4111i	0.479840	+	0.479840i
$670$	−5.30897	+	3.29722i	−0.205103	+	0.127383i
$671$	−5.85804			−0.226147
$672$	−15.9663	+	7.18056i	−0.615912	+	0.276996i
$673$	12.9697			0.499943			0.249972	−	0.968253i	$-0.419579\pi$
$673$	12.9697			0.499943			0.249972	+	0.968253i	$0.419579\pi$
$674$	18.7929	−	11.6716i	0.723876	−	0.449575i
$675$	7.82888	+	7.82888i	0.301334	+	0.301334i
$676$	10.6455	+	5.26455i	0.409441	+	0.202483i
$677$	−36.0230	+	36.0230i	−1.38448	+	1.38448i	−0.547998	+	0.836479i	$0.684610\pi$
$677$	−36.0230	+	36.0230i	−1.38448	+	1.38448i	−0.836479	+	0.547998i	$0.815390\pi$
$678$	25.1724	+	5.88419i	0.966738	+	0.225981i
$679$			14.8733i			0.570784i
$680$	−12.5729	−	10.3536i	−0.482148	−	0.397042i
$681$		−	22.6597i		−	0.868322i
$682$	−2.10308	+	8.99690i	−0.0805311	+	0.344509i
$683$	27.7472	−	27.7472i	1.06172	−	1.06172i	0.0637518	−	0.997966i	$-0.479693\pi$
$683$	27.7472	−	27.7472i	1.06172	−	1.06172i	0.997966	−	0.0637518i	$-0.0203066\pi$
$684$	20.8577	+	61.6708i	0.797512	+	2.35804i
$685$	−11.8016	−	11.8016i	−0.450918	−	0.450918i
$686$	0.746130	+	1.20137i	0.0284874	+	0.0458685i
$687$	8.95372			0.341606
$688$	41.1611	+	5.51251i	1.56925	+	0.210162i
$689$	−13.1780			−0.502041
$690$	20.4205	+	32.8797i	0.777395	+	1.25171i
$691$	28.3182	+	28.3182i	1.07728	+	1.07728i	0.996753	+	0.0805238i	$0.0256593\pi$
$691$	28.3182	+	28.3182i	1.07728	+	1.07728i	0.0805238	+	0.996753i	$0.474341\pi$
$692$	16.1120	−	5.44921i	0.612485	−	0.207148i
$693$	5.57759	−	5.57759i	0.211875	−	0.211875i
$694$	−3.62599	+	15.5119i	−0.137641	+	0.588822i
$695$		−	4.84514i		−	0.183787i
$696$	−27.1957	+	2.63255i	−1.03085	+	0.0997866i
$697$			28.4999i			1.07951i
$698$	−6.89537	−	1.61184i	−0.260994	−	0.0610089i
$699$	47.1437	−	47.1437i	1.78314	−	1.78314i
$700$	−0.886580	+	1.79276i	−0.0335096	+	0.0677598i
$701$	−22.2724	−	22.2724i	−0.841215	−	0.841215i	0.147802	−	0.989017i	$-0.452780\pi$
$701$	−22.2724	−	22.2724i	−0.841215	−	0.841215i	−0.989017	+	0.147802i	$0.952780\pi$
$702$	−57.8841	+	35.9498i	−2.18469	+	1.35684i
$703$	29.1669			1.10005
$704$	−5.35667	+	7.95898i	−0.201887	+	0.299965i
$705$	−16.8023			−0.632813
$706$	−26.7820	+	16.6334i	−1.00795	+	0.626006i
$707$	−13.6445	−	13.6445i	−0.513155	−	0.513155i
$708$	−13.5607	+	27.4212i	−0.509643	+	1.03055i
$709$	24.1894	−	24.1894i	0.908452	−	0.908452i	−0.0876953	−	0.996147i	$-0.527950\pi$
$709$	24.1894	−	24.1894i	0.908452	−	0.908452i	0.996147	+	0.0876953i	$0.0279502\pi$
$710$	0.337877	+	0.0789808i	0.0126803	+	0.00296410i
$711$		−	65.4645i		−	2.45511i
$712$	−16.9332	+	1.63914i	−0.634599	+	0.0614294i
$713$			48.1790i			1.80432i
$714$	−5.73661	+	24.5410i	−0.214687	+	0.918424i
$715$	−3.69019	+	3.69019i	−0.138005	+	0.138005i
$716$	11.0306	−	3.73064i	0.412231	−	0.139420i
$717$	−50.6323	−	50.6323i	−1.89090	−	1.89090i
$718$	−9.58333	−	15.4305i	−0.357647	−	0.575860i
$719$	35.6643			1.33006			0.665028	−	0.746819i	$-0.268420\pi$
$719$	35.6643			1.33006			0.665028	+	0.746819i	$0.268420\pi$
$720$	−3.49243	+	26.0774i	−0.130155	+	0.971848i
$721$	1.46938			0.0547225
$722$	4.09695	+	6.59664i	0.152473	+	0.245502i
$723$	64.1750	+	64.1750i	2.38669	+	2.38669i
$724$	10.4253	+	30.8250i	0.387453	+	1.14560i
$725$	−2.20718	+	2.20718i	−0.0819726	+	0.0819726i
$726$	−9.52569	+	40.7506i	−0.353532	+	1.51240i
$727$		−	16.4452i		−	0.609918i	−0.952366	−	0.304959i	$-0.901357\pi$
$727$		−	16.4452i		−	0.609918i	0.952366	−	0.304959i	$-0.0986427\pi$
$728$	−9.50167	−	7.82449i	−0.352155	−	0.289995i
$729$			7.21024i			0.267046i
$730$	0.220735	+	0.0515981i	0.00816976	+	0.00190973i
$731$	42.2741	−	42.2741i	1.56356	−	1.56356i
$732$	−27.1022	−	13.4030i	−1.00173	−	0.495388i
$733$	−10.2414	−	10.2414i	−0.378273	−	0.378273i	0.492206	−	0.870479i	$-0.336191\pi$
$733$	−10.2414	−	10.2414i	−0.378273	−	0.378273i	−0.870479	+	0.492206i	$0.836191\pi$
$734$	−16.3742	+	10.1694i	−0.604381	+	0.375361i
$735$	3.09476			0.114152
$736$	−17.7524	+	46.7706i	−0.654364	+	1.72399i
$737$	5.29944			0.195207
$738$	39.1095	−	24.2896i	1.43964	−	0.894111i
$739$	26.3254	+	26.3254i	0.968394	+	0.968394i	0.999516	−	0.0311219i	$-0.00990802\pi$
$739$	26.3254	+	26.3254i	0.968394	+	0.968394i	−0.0311219	+	0.999516i	$0.509908\pi$
$740$	10.5660	+	5.22523i	0.388412	+	0.192083i
$741$	−47.1284	+	47.1284i	−1.73130	+	1.73130i
$742$	4.17007	+	0.974780i	0.153088	+	0.0357853i
$743$			3.64694i			0.133793i	0.997760	+	0.0668966i	$0.0213098\pi$
$743$			3.64694i			0.133793i	−0.997760	+	0.0668966i	$0.978690\pi$
$744$	−30.3144	+	36.8123i	−1.11138	+	1.34961i
$745$		−	7.72084i		−	0.282870i
$746$	3.06604	−	13.1164i	0.112256	−	0.480226i
$747$	−43.9970	+	43.9970i	−1.60977	+	1.60977i
$748$	4.42483	+	13.0831i	0.161788	+	0.478366i
$749$	−11.8430	−	11.8430i	−0.432733	−	0.432733i
$750$	2.30910	+	3.71796i	0.0843163	+	0.135761i
$751$	−48.6372			−1.77480			−0.887398	−	0.461004i	$-0.847489\pi$
$751$	−48.6372			−1.77480			−0.887398	+	0.461004i	$0.847489\pi$
$752$	−13.1820	−	17.2588i	−0.480699	−	0.629365i
$753$	−47.6146			−1.73517
$754$	−10.1353	−	16.3191i	−0.369104	−	0.594308i
$755$	−13.2336	−	13.2336i	−0.481621	−	0.481621i
$756$	20.9762	−	7.09435i	0.762897	−	0.258019i
$757$	27.3450	−	27.3450i	0.993870	−	0.993870i	−0.00611134	−	0.999981i	$-0.501945\pi$
$757$	27.3450	−	27.3450i	0.993870	−	0.993870i	0.999981	+	0.00611134i	$0.00194531\pi$
$758$	−5.93508	+	25.3901i	−0.215572	+	0.922208i
$759$		−	32.8207i		−	1.19132i
$760$	1.34865	+	13.9323i	0.0489207	+	0.505377i
$761$		−	6.63482i		−	0.240512i	−0.992743	−	0.120256i	$-0.961628\pi$
$761$		−	6.63482i		−	0.240512i	0.992743	−	0.120256i	$-0.0383715\pi$
$762$	87.2437	+	20.3938i	3.16051	+	0.738788i
$763$	−9.31425	+	9.31425i	−0.337199	+	0.337199i
$764$	2.87374	−	5.81101i	0.103968	−	0.210235i
$765$	26.7826	+	26.7826i	0.968326	+	0.968326i
$766$	10.8142	−	6.71632i	0.390732	−	0.242671i
$767$	−21.5082			−0.776617
$768$	−42.9925	+	24.5663i	−1.55136	+	0.886460i
$769$	9.61482			0.346719			0.173360	−	0.984859i	$-0.444538\pi$
$769$	9.61482			0.346719			0.173360	+	0.984859i	$0.444538\pi$
$770$	1.44070	−	0.894769i	0.0519192	−	0.0322453i
$771$	31.4505	+	31.4505i	1.13266	+	1.13266i
$772$	20.5106	−	41.4745i	0.738192	−	1.49270i
$773$	−7.09164	+	7.09164i	−0.255069	+	0.255069i	−0.823045	−	0.567976i	$-0.807727\pi$
$773$	−7.09164	+	7.09164i	−0.255069	+	0.255069i	0.567976	+	0.823045i	$0.307727\pi$
$774$	−94.0404	−	21.9825i	−3.38021	−	0.790145i
$775$			5.44796i			0.195696i
$776$	4.05325	+	41.8723i	0.145503	+	1.50313i
$777$		−	18.2396i		−	0.654342i
$778$	4.54366	−	19.4376i	0.162898	−	0.696873i
$779$	17.3192	−	17.3192i	0.620525	−	0.620525i
$780$	−25.5157	+	8.62964i	−0.913608	+	0.308991i
$781$	−0.208055	−	0.208055i	−0.00744478	−	0.00744478i
$782$	37.9963	+	61.1792i	1.35874	+	2.18776i
$783$	34.5595			1.23506
$784$	2.42795	+	3.17884i	0.0867126	+	0.113530i
$785$	2.83335			0.101127
$786$	−2.14476	−	3.45336i	−0.0765012	−	0.123177i
$787$	32.5040	+	32.5040i	1.15864	+	1.15864i	0.984768	+	0.173873i	$0.0556284\pi$
$787$	32.5040	+	32.5040i	1.15864	+	1.15864i	0.173873	+	0.984768i	$0.444372\pi$
$788$	4.73920	+	14.0126i	0.168827	+	0.499179i
$789$	−43.1274	+	43.1274i	−1.53538	+	1.53538i
$790$	3.20381	−	13.7058i	0.113986	−	0.487630i
$791$		−	5.90655i		−	0.210013i
$792$	14.1824	−	17.2224i	0.503950	−	0.611972i
$793$		−	21.2580i		−	0.754895i
$794$	13.2089	+	3.08766i	0.468767	+	0.109577i
$795$	6.62664	−	6.62664i	0.235023	−	0.235023i
$796$	39.9219	+	19.7428i	1.41500	+	0.699764i
$797$	−5.69973	−	5.69973i	−0.201895	−	0.201895i	0.598917	−	0.800811i	$-0.295598\pi$
$797$	−5.69973	−	5.69973i	−0.201895	−	0.201895i	−0.800811	+	0.598917i	$0.795598\pi$
$798$	18.3995	−	11.4273i	0.651337	−	0.404523i
$799$	−31.2640			−1.10604
$800$	−2.00740	+	5.28870i	−0.0709723	+	0.186984i
$801$	39.5626			1.39788
$802$	−14.6241	+	9.08253i	−0.516395	+	0.320715i
$803$	−0.135922	−	0.135922i	−0.00479658	−	0.00479658i
$804$	24.5178	+	12.1249i	0.864677	+	0.427613i
$805$	6.25330	−	6.25330i	0.220400	−	0.220400i
$806$	−32.6485	−	7.63179i	−1.15000	−	0.268818i
$807$		−	35.6601i		−	1.25530i
$808$	−42.1314	−	34.6946i	−1.48218	−	1.22055i
$809$		−	16.5904i		−	0.583288i	−0.956527	−	0.291644i	$-0.905798\pi$
$809$		−	16.5904i		−	0.583288i	0.956527	−	0.291644i	$-0.0942022\pi$
$810$	4.67778	−	20.0114i	0.164360	−	0.703128i
$811$	2.28734	−	2.28734i	0.0803195	−	0.0803195i	−0.665806	−	0.746125i	$-0.731912\pi$
$811$	2.28734	−	2.28734i	0.0803195	−	0.0803195i	0.746125	+	0.665806i	$0.231912\pi$
$812$	2.00010	+	5.91378i	0.0701896	+	0.207533i
$813$	−10.8597	−	10.8597i	−0.380866	−	0.380866i
$814$	−5.27350	−	8.49104i	−0.184836	−	0.297611i
$815$	8.67897			0.304011
$816$	−9.46221	+	70.6529i	−0.331244	+	2.47335i
$817$	−51.3795			−1.79754
$818$	10.4015	+	16.7478i	0.363680	+	0.585574i
$819$	20.2403	+	20.2403i	0.707254	+	0.707254i
$820$	9.37675	−	3.17130i	0.327450	−	0.110747i
$821$	37.2996	−	37.2996i	1.30176	−	1.30176i	0.374563	−	0.927201i	$-0.377793\pi$
$821$	37.2996	−	37.2996i	1.30176	−	1.30176i	0.927201	−	0.374563i	$-0.122207\pi$
$822$	−16.6269	+	71.1291i	−0.579929	+	2.48091i
$823$		−	3.52918i		−	0.123020i	−0.998106	−	0.0615098i	$-0.980408\pi$
$823$		−	3.52918i		−	0.123020i	0.998106	−	0.0615098i	$-0.0195915\pi$
$824$	4.13670	−	0.400434i	0.144109	−	0.0139498i
$825$		−	3.71128i		−	0.129210i
$826$	6.80612	+	1.59097i	0.236815	+	0.0553570i
$827$	32.9003	−	32.9003i	1.14406	−	1.14406i	0.156355	−	0.987701i	$-0.450026\pi$
$827$	32.9003	−	32.9003i	1.14406	−	1.14406i	0.987701	−	0.156355i	$-0.0499744\pi$
$828$	51.5712	−	104.282i	1.79222	−	3.62406i
$829$	−6.40321	−	6.40321i	−0.222393	−	0.222393i	0.587113	−	0.809505i	$-0.300265\pi$
$829$	−6.40321	−	6.40321i	−0.222393	−	0.222393i	−0.809505	+	0.587113i	$0.800265\pi$
$830$	−11.3645	+	7.05810i	−0.394468	+	0.244990i
$831$	26.5160			0.919831
$832$	−28.8821	−	19.4386i	−1.00131	−	0.673914i
$833$	5.75841			0.199517
$834$	−18.0140	+	11.1879i	−0.623774	+	0.387405i
$835$	−4.60277	−	4.60277i	−0.159285	−	0.159285i
$836$	5.26159	−	10.6395i	0.181976	−	0.367974i
$837$	42.6514	−	42.6514i	1.47425	−	1.47425i
$838$	1.27856	+	0.298872i	0.0441672	+	0.0103244i
$839$			0.558194i			0.0192710i	0.999954	+	0.00963550i	$0.00306712\pi$
$839$			0.558194i			0.0192710i	−0.999954	+	0.00963550i	$0.996933\pi$
$840$	8.71259	−	0.843382i	0.300613	−	0.0290994i
$841$		−	19.2567i		−	0.664024i
$842$	−9.33823	+	39.9486i	−0.321817	+	1.37672i
$843$	12.7920	−	12.7920i	0.440580	−	0.440580i
$844$	40.0402	−	13.5420i	1.37824	−	0.466134i
$845$	−4.19883	−	4.19883i	−0.144444	−	0.144444i
$846$	26.6454	+	42.9026i	0.916087	+	1.47502i
$847$	9.56189			0.328550
$848$	12.0055	+	1.60784i	0.412271	+	0.0552135i
$849$	27.8851			0.957013
$850$	4.29652	+	6.91798i	0.147370	+	0.237285i
$851$	−36.8550	−	36.8550i	−1.26337	−	1.26337i
$852$	−0.486543	−	1.43859i	−0.0166687	−	0.0492851i
$853$	−0.0903143	+	0.0903143i	−0.00309230	+	0.00309230i	−0.708651	−	0.705559i	$-0.750696\pi$
$853$	−0.0903143	+	0.0903143i	−0.00309230	+	0.00309230i	0.705559	+	0.708651i	$0.250696\pi$
$854$	−1.57247	+	6.72695i	−0.0538087	+	0.230192i
$855$		−	32.5512i		−	1.11323i
$856$	−36.5686	−	30.1137i	−1.24989	−	1.02926i
$857$			1.11983i			0.0382526i	0.999817	+	0.0191263i	$0.00608846\pi$
$857$			1.11983i			0.0382526i	−0.999817	+	0.0191263i	$0.993912\pi$
$858$	22.2410	+	5.19897i	0.759295	+	0.177490i
$859$	−1.38287	+	1.38287i	−0.0471828	+	0.0471828i	−0.730305	−	0.683122i	$-0.760622\pi$
$859$	−1.38287	+	1.38287i	−0.0471828	+	0.0471828i	0.683122	+	0.730305i	$0.260622\pi$
$860$	−18.6127	−	9.20460i	−0.634686	−	0.313874i
$861$	−10.8306	−	10.8306i	−0.369106	−	0.369106i
$862$	28.8532	−	17.9197i	0.982744	−	0.610349i
$863$	−31.4276			−1.06981			−0.534904	−	0.844913i	$-0.679652\pi$
$863$	−31.4276			−1.06981			−0.534904	+	0.844913i	$0.679652\pi$
$864$	57.1203	−	25.6889i	1.94327	−	0.873954i
$865$	−8.50425			−0.289153
$866$	−28.3021	+	17.5775i	−0.961745	+	0.597307i
$867$	35.3618	+	35.3618i	1.20095	+	1.20095i
$868$	9.76686	+	4.83005i	0.331509	+	0.163943i
$869$	−8.43962	+	8.43962i	−0.286294	+	0.286294i
$870$	13.3028	+	3.10961i	0.451007	+	0.105426i
$871$			19.2309i			0.651616i
$872$	−23.6838	+	28.7604i	−0.802035	+	0.973951i
$873$		−	97.8299i		−	3.31104i
$874$	14.0881	−	60.2684i	0.476537	−	2.03861i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−0.317858	−	0.939827i	−0.0107394	−	0.0317538i
$877$	−25.6685	−	25.6685i	−0.866764	−	0.866764i	0.125349	−	0.992113i	$-0.459995\pi$
$877$	−25.6685	−	25.6685i	−0.866764	−	0.866764i	−0.992113	+	0.125349i	$0.959995\pi$
$878$	1.96746	+	3.16788i	0.0663986	+	0.106911i
$879$	37.2524			1.25649
$880$	3.81211	−	2.91163i	0.128506	−	0.0981511i
$881$	1.58788			0.0534972			0.0267486	−	0.999642i	$-0.491485\pi$
$881$	1.58788			0.0534972			0.0267486	+	0.999642i	$0.491485\pi$
$882$	−4.90772	−	7.90209i	−0.165251	−	0.266077i
$883$	23.4314	+	23.4314i	0.788529	+	0.788529i	0.981253	−	0.192724i	$-0.0617321\pi$
$883$	23.4314	+	23.4314i	0.788529	+	0.788529i	−0.192724	+	0.981253i	$0.561732\pi$
$884$	−47.4769	+	16.0571i	−1.59682	+	0.540060i
$885$	10.8156	−	10.8156i	0.363562	−	0.363562i
$886$	2.45310	−	10.4943i	0.0824135	−	0.352562i
$887$			57.9216i			1.94482i	0.233284	+	0.972409i	$0.425053\pi$
$887$			57.9216i			1.94482i	−0.233284	+	0.972409i	$0.574947\pi$
$888$	−4.97064	−	51.3493i	−0.166804	−	1.72317i
$889$		−	20.4712i		−	0.686584i
$890$	8.28290	+	1.93618i	0.277643	+	0.0649008i
$891$	−12.3224	+	12.3224i	−0.412817	+	0.412817i
$892$	5.02823	−	10.1676i	0.168358	−	0.340437i
$893$	18.9990	+	18.9990i	0.635776	+	0.635776i
$894$	−28.7057	+	17.8282i	−0.960063	+	0.596263i
$895$	−5.82217			−0.194614
$896$	7.70163	+	8.28763i	0.257293	+	0.276870i
$897$	119.102			3.97670
$898$	−25.2083	+	15.6560i	−0.841212	+	0.522448i
$899$	12.0246	+	12.0246i	0.401044	+	0.401044i
$900$	5.83153	−	11.7920i	0.194384	−	0.393066i
$901$	12.3302	−	12.3302i	0.410777	−	0.410777i
$902$	−8.17333	−	1.91057i	−0.272142	−	0.0636149i
$903$			32.1303i			1.06923i
$904$	−1.60965	−	16.6285i	−0.0535360	−	0.553056i
$905$		−	16.2701i		−	0.540837i
$906$	−18.6443	+	79.7597i	−0.619416	+	2.64984i
$907$	−16.8139	+	16.8139i	−0.558297	+	0.558297i	−0.928822	−	0.370525i	$-0.879178\pi$
$907$	−16.8139	+	16.8139i	−0.558297	+	0.558297i	0.370525	+	0.928822i	$0.379178\pi$
$908$	−13.8720	+	4.69164i	−0.460358	+	0.155698i
$909$	89.7477	+	89.7477i	2.97674	+	2.97674i
$910$	3.24700	+	5.22811i	0.107637	+	0.173310i
$911$	−44.6449			−1.47915			−0.739576	−	0.673073i	$-0.764974\pi$
$911$	−44.6449			−1.47915			−0.739576	+	0.673073i	$0.764974\pi$
$912$	48.6855	−	37.1852i	1.61214	−	1.23133i
$913$	11.3441			0.375435
$914$	−14.5534	−	23.4330i	−0.481384	−	0.775094i
$915$	10.6898	+	10.6898i	0.353393	+	0.353393i
$916$	−1.85385	−	5.48136i	−0.0612528	−	0.181109i
$917$	−0.656784	+	0.656784i	−0.0216889	+	0.0216889i
$918$	20.5231	−	87.7970i	0.677363	−	2.89773i
$919$		−	10.1210i		−	0.333862i	−0.985969	−	0.166931i	$-0.946614\pi$
$919$		−	10.1210i		−	0.333862i	0.985969	−	0.166931i	$-0.0533858\pi$
$920$	15.9006	−	19.3089i	0.524226	−	0.636594i
$921$			86.1030i			2.83719i
$922$	−28.9824	−	6.77481i	−0.954484	−	0.223116i
$923$	0.755003	−	0.755003i	0.0248512	−	0.0248512i
$924$	−6.65343	−	3.29035i	−0.218882	−	0.108245i
$925$	−4.16747	−	4.16747i	−0.137026	−	0.137026i
$926$	−23.2961	+	14.4684i	−0.765559	+	0.475462i
$927$	−9.66493			−0.317438
$928$	7.24242	+	16.1038i	0.237744	+	0.528633i
$929$	−36.1823			−1.18710			−0.593551	−	0.804796i	$-0.702274\pi$
$929$	−36.1823			−1.18710			−0.593551	+	0.804796i	$0.702274\pi$
$930$	20.2553	−	12.5799i	0.664196	−	0.412510i
$931$	−3.49935	−	3.49935i	−0.114687	−	0.114687i
$932$	−38.6218	−	19.0998i	−1.26510	−	0.625635i
$933$	−24.8404	+	24.8404i	−0.813239	+	0.813239i
$934$	21.1452	+	4.94281i	0.691891	+	0.161734i
$935$		−	6.90556i		−	0.225836i
$936$	62.4978	+	51.4661i	2.04280	+	1.68222i
$937$			51.9642i			1.69760i	0.528718	+	0.848798i	$0.322673\pi$
$937$			51.9642i			1.69760i	−0.528718	+	0.848798i	$0.677327\pi$
$938$	1.42252	−	6.08549i	0.0464469	−	0.198698i
$939$	50.5527	−	50.5527i	1.64973	−	1.64973i
$940$	3.47888	+	10.2862i	0.113469	+	0.335498i
$941$	11.7290	+	11.7290i	0.382356	+	0.382356i	0.871950	−	0.489594i	$-0.162855\pi$
$941$	11.7290	+	11.7290i	0.382356	+	0.382356i	−0.489594	+	0.871950i	$0.662855\pi$
$942$	−6.54249	−	10.5343i	−0.213166	−	0.343226i
$943$	−43.7688			−1.42531
$944$	19.5946	+	2.62422i	0.637751	+	0.0854110i
$945$	−11.0717			−0.360163
$946$	9.28962	+	14.9575i	0.302032	+	0.486312i
$947$	−8.81428	−	8.81428i	−0.286426	−	0.286426i	0.549239	−	0.835665i	$-0.314918\pi$
$947$	−8.81428	−	8.81428i	−0.286426	−	0.286426i	−0.835665	+	0.549239i	$0.814918\pi$
$948$	−58.3554	+	19.7363i	−1.89529	+	0.641006i
$949$	0.493243	−	0.493243i	0.0160113	−	0.0160113i
$950$	1.59305	−	6.81499i	0.0516852	−	0.221107i
$951$		−	17.8578i		−	0.579078i
$952$	16.2115	−	1.56928i	0.525417	−	0.0508605i
$953$		−	32.4726i		−	1.05189i	−0.850519	−	0.525945i	$-0.823712\pi$
$953$		−	32.4726i		−	1.05189i	0.850519	−	0.525945i	$-0.176288\pi$
$954$	−27.4289	−	6.41167i	−0.888044	−	0.207586i
$955$	−2.29200	+	2.29200i	−0.0741675	+	0.0741675i
$956$	−20.5132	+	41.4798i	−0.663444	+	1.34155i
$957$	−8.19147	−	8.19147i	−0.264793	−	0.264793i
$958$	−34.4508	+	21.3962i	−1.11305	+	0.691280i
$959$	16.6901			0.538950
$960$	24.2984	−	4.74869i	0.784229	−	0.153263i
$961$	−1.31977			−0.0425734
$962$	30.8129	−	19.1368i	0.993447	−	0.616996i
$963$	77.8979	+	77.8979i	2.51022	+	2.51022i
$964$	25.9999	−	52.5744i	0.837399	−	1.69331i
$965$	−16.3586	+	16.3586i	−0.526601	+	0.526601i
$966$	−37.6890	−	8.81002i	−1.21262	−	0.283458i
$967$			5.87401i			0.188895i	0.995530	+	0.0944477i	$0.0301085\pi$
$967$			5.87401i			0.188895i	−0.995530	+	0.0944477i	$0.969891\pi$
$968$	26.9193	−	2.60580i	0.865218	−	0.0837534i
$969$		−	88.1927i		−	2.83316i
$970$	4.78776	−	20.4818i	0.153726	−	0.657633i
$971$	26.6323	−	26.6323i	0.854670	−	0.854670i	−0.136034	−	0.990704i	$-0.543436\pi$
$971$	26.6323	−	26.6323i	0.854670	−	0.854670i	0.990704	+	0.136034i	$0.0434357\pi$
$972$	−22.2743	+	7.53336i	−0.714447	+	0.241633i
$973$	3.42603	+	3.42603i	0.109834	+	0.109834i
$974$	−15.9956	−	25.7551i	−0.512532	−	0.825246i
$975$	13.4677			0.431313
$976$	−2.59369	+	19.3667i	−0.0830220	+	0.619913i
$977$	−37.4838			−1.19921			−0.599607	−	0.800294i	$-0.704677\pi$
$977$	−37.4838			−1.19921			−0.599607	+	0.800294i	$0.704677\pi$
$978$	−20.0406	−	32.2680i	−0.640827	−	1.03182i
$979$	−5.10037	−	5.10037i	−0.163008	−	0.163008i
$980$	−0.640764	−	1.89458i	−0.0204684	−	0.0605200i
$981$	61.2651	−	61.2651i	1.95604	−	1.95604i
$982$	6.10281	−	26.1076i	0.194749	−	0.833127i
$983$		−	6.16848i		−	0.196744i	−0.995150	−	0.0983719i	$-0.968637\pi$
$983$		−	6.16848i		−	0.196744i	0.995150	−	0.0983719i	$-0.0313635\pi$
$984$	−33.4426	−	27.5395i	−1.06611	−	0.877927i
$985$		−	7.39617i		−	0.235662i
$986$	24.7524	+	5.78603i	0.788278	+	0.184265i
$987$	11.8810	−	11.8810i	0.378178	−	0.378178i
$988$	38.6093	+	19.0936i	1.22832	+	0.607449i
$989$	64.9226	+	64.9226i	2.06442	+	2.06442i
$990$	−9.47629	+	5.88540i	−0.301176	+	0.187050i
$991$	8.10013			0.257309			0.128655	−	0.991689i	$-0.458934\pi$
$991$	8.10013			0.257309			0.128655	+	0.991689i	$0.458934\pi$
$992$	28.8126	+	10.9362i	0.914801	+	0.347226i
$993$	39.7341			1.26092
$994$	−0.294763	+	0.183067i	−0.00934931	+	0.00580654i
$995$	−15.7462	−	15.7462i	−0.499188	−	0.499188i
$996$	52.4834	+	25.9549i	1.66300	+	0.822412i
$997$	9.76260	−	9.76260i	0.309185	−	0.309185i	−0.535409	−	0.844593i	$-0.679842\pi$
$997$	9.76260	−	9.76260i	0.309185	−	0.309185i	0.844593	+	0.535409i	$0.179842\pi$
$998$	−50.3811	−	11.7769i	−1.59479	−	0.372791i
$999$			65.2533i			2.06452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.19	✓	44
4.3	odd	2		2240.2.bd.a.1681.2		44
16.5	even	4	inner	560.2.bd.a.421.19	yes	44
16.11	odd	4		2240.2.bd.a.561.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.19	✓	44	1.1	even	1	trivial
560.2.bd.a.421.19	yes	44	16.5	even	4	inner
2240.2.bd.a.561.2		44	16.11	odd	4
2240.2.bd.a.1681.2		44	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20137 - 0.746130i) q^{2} +(2.18833 + 2.18833i) q^{3} +(0.886580 - 1.79276i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.26177 + 0.996215i) q^{6} -1.00000i q^{7} +(-0.272519 - 2.81527i) q^{8} +6.57756i q^{9} +O(q^{10})\)	\(q+(1.20137 - 0.746130i) q^{2} +(2.18833 + 2.18833i) q^{3} +(0.886580 - 1.79276i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(4.26177 + 0.996215i) q^{6} -1.00000i q^{7} +(-0.272519 - 2.81527i) q^{8} +6.57756i q^{9} +(-0.321903 + 1.37709i) q^{10} +(0.847972 - 0.847972i) q^{11} +(5.86327 - 1.98301i) q^{12} +(3.07718 + 3.07718i) q^{13} +(-0.746130 - 1.20137i) q^{14} -3.09476 q^{15} +(-2.42795 - 3.17884i) q^{16} -5.75841 q^{17} +(4.90772 + 7.90209i) q^{18} +(3.49935 + 3.49935i) q^{19} +(0.640764 + 1.89458i) q^{20} +(2.18833 - 2.18833i) q^{21} +(0.386031 - 1.65143i) q^{22} -8.84350i q^{23} +(5.56437 - 6.75709i) q^{24} -1.00000i q^{25} +(5.99280 + 1.40085i) q^{26} +(-7.82888 + 7.82888i) q^{27} +(-1.79276 - 0.886580i) q^{28} +(-2.20718 - 2.20718i) q^{29} +(-3.71796 + 2.30910i) q^{30} -5.44796 q^{31} +(-5.28870 - 2.00740i) q^{32} +3.71128 q^{33} +(-6.91798 + 4.29652i) q^{34} +(0.707107 + 0.707107i) q^{35} +(11.7920 + 5.83153i) q^{36} +(4.16747 - 4.16747i) q^{37} +(6.81499 + 1.59305i) q^{38} +13.4677i q^{39} +(2.18340 + 1.79800i) q^{40} -4.94926i q^{41} +(0.996215 - 4.26177i) q^{42} +(-7.34128 + 7.34128i) q^{43} +(-0.768413 - 2.27200i) q^{44} +(-4.65104 - 4.65104i) q^{45} +(-6.59840 - 10.6243i) q^{46} +5.42928 q^{47} +(1.64320 - 12.2695i) q^{48} -1.00000 q^{49} +(-0.746130 - 1.20137i) q^{50} +(-12.6013 - 12.6013i) q^{51} +(8.24479 - 2.78847i) q^{52} +(-2.14124 + 2.14124i) q^{53} +(-3.56402 + 15.2467i) q^{54} +1.19921i q^{55} +(-2.81527 + 0.272519i) q^{56} +15.3155i q^{57} +(-4.29848 - 1.00480i) q^{58} +(-3.49480 + 3.49480i) q^{59} +(-2.74376 + 5.54816i) q^{60} +(-3.45415 - 3.45415i) q^{61} +(-6.54501 + 4.06488i) q^{62} +6.57756 q^{63} +(-7.85147 + 1.53443i) q^{64} -4.35179 q^{65} +(4.45862 - 2.76910i) q^{66} +(3.12477 + 3.12477i) q^{67} +(-5.10529 + 10.3234i) q^{68} +(19.3525 - 19.3525i) q^{69} +(1.37709 + 0.321903i) q^{70} -0.245356i q^{71} +(18.5176 - 1.79251i) q^{72} -0.160291i q^{73} +(1.89720 - 8.11615i) q^{74} +(2.18833 - 2.18833i) q^{75} +(9.37594 - 3.17103i) q^{76} +(-0.847972 - 0.847972i) q^{77} +(10.0487 + 16.1797i) q^{78} -9.95271 q^{79} +(3.96460 + 0.530961i) q^{80} -14.5316 q^{81} +(-3.69279 - 5.94589i) q^{82} +(6.68896 + 6.68896i) q^{83} +(-1.98301 - 5.86327i) q^{84} +(4.07181 - 4.07181i) q^{85} +(-3.34205 + 14.2972i) q^{86} -9.66007i q^{87} +(-2.61836 - 2.15618i) q^{88} -6.01478i q^{89} +(-9.05790 - 2.11734i) q^{90} +(3.07718 - 3.07718i) q^{91} +(-15.8542 - 7.84047i) q^{92} +(-11.9219 - 11.9219i) q^{93} +(6.52257 - 4.05095i) q^{94} -4.94883 q^{95} +(-7.18056 - 15.9663i) q^{96} -14.8733 q^{97} +(-1.20137 + 0.746130i) q^{98} +(5.57759 + 5.57759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

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