LMFDB - Embedded newform 240.2.s.c.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, 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("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			181.2
Root			$-1.13207 - 0.847599i$ of defining polynomial
Character	$\chi$	$=$	240.181
Dual form			240.2.s.c.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13207 - 0.847599i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.563151 + 1.91908i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.39984 + 0.201149i) q^{6} +4.27253i q^{7} +(0.989085 - 2.64985i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.13207 - 0.847599i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.563151 + 1.91908i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.39984 + 0.201149i) q^{6} +4.27253i q^{7} +(0.989085 - 2.64985i) q^{8} -1.00000i q^{9} +(-0.201149 - 1.39984i) q^{10} +(2.94281 + 2.94281i) q^{11} +(1.75520 + 0.958786i) q^{12} +(-4.05962 + 4.05962i) q^{13} +(3.62140 - 4.83679i) q^{14} +1.00000 q^{15} +(-3.36572 + 2.16146i) q^{16} +0.160060 q^{17} +(-0.847599 + 1.13207i) q^{18} +(4.32576 - 4.32576i) q^{19} +(-0.958786 + 1.75520i) q^{20} +(3.02114 + 3.02114i) q^{21} +(-0.837134 - 5.82579i) q^{22} -8.40564i q^{23} +(-1.17434 - 2.57312i) q^{24} +1.00000i q^{25} +(8.03670 - 1.15483i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-8.19933 + 2.40608i) q^{28} +(-1.78072 + 1.78072i) q^{29} +(-1.13207 - 0.847599i) q^{30} +7.17282 q^{31} +(5.64228 + 0.405867i) q^{32} +4.16177 q^{33} +(-0.181198 - 0.135667i) q^{34} +(-3.02114 + 3.02114i) q^{35} +(1.91908 - 0.563151i) q^{36} +(-0.669226 - 0.669226i) q^{37} +(-8.56355 + 1.23054i) q^{38} +5.74117i q^{39} +(2.57312 - 1.17434i) q^{40} -3.96632i q^{41} +(-0.859415 - 5.98084i) q^{42} +(-0.255733 - 0.255733i) q^{43} +(-3.99024 + 7.30473i) q^{44} +(0.707107 - 0.707107i) q^{45} +(-7.12462 + 9.51575i) q^{46} +0.0752658 q^{47} +(-0.851542 + 3.90831i) q^{48} -11.2545 q^{49} +(0.847599 - 1.13207i) q^{50} +(0.113179 - 0.113179i) q^{51} +(-10.0769 - 5.50456i) q^{52} +(-2.88214 - 2.88214i) q^{53} +(0.201149 + 1.39984i) q^{54} +4.16177i q^{55} +(11.3216 + 4.22590i) q^{56} -6.11754i q^{57} +(3.52522 - 0.506556i) q^{58} +(-5.63594 - 5.63594i) q^{59} +(0.563151 + 1.91908i) q^{60} +(-4.48857 + 4.48857i) q^{61} +(-8.12011 - 6.07968i) q^{62} +4.27253 q^{63} +(-6.04342 - 5.24186i) q^{64} -5.74117 q^{65} +(-4.71140 - 3.52751i) q^{66} +(-0.131176 + 0.131176i) q^{67} +(0.0901377 + 0.307167i) q^{68} +(-5.94369 - 5.94369i) q^{69} +(5.98084 - 0.859415i) q^{70} +12.1137i q^{71} +(-2.64985 - 0.989085i) q^{72} +0.382876i q^{73} +(0.190373 + 1.32484i) q^{74} +(0.707107 + 0.707107i) q^{75} +(10.7375 + 5.86541i) q^{76} +(-12.5733 + 12.5733i) q^{77} +(4.86622 - 6.49939i) q^{78} +15.3239 q^{79} +(-3.90831 - 0.851542i) q^{80} -1.00000 q^{81} +(-3.36185 + 4.49014i) q^{82} +(-5.54562 + 5.54562i) q^{83} +(-4.09644 + 7.49916i) q^{84} +(0.113179 + 0.113179i) q^{85} +(0.0727477 + 0.506266i) q^{86} +2.51831i q^{87} +(10.7087 - 4.88732i) q^{88} -13.8991i q^{89} +(-1.39984 + 0.201149i) q^{90} +(-17.3449 - 17.3449i) q^{91} +(16.1311 - 4.73364i) q^{92} +(5.07195 - 5.07195i) q^{93} +(-0.0852060 - 0.0637953i) q^{94} +6.11754 q^{95} +(4.27668 - 3.70270i) q^{96} +10.8999 q^{97} +(12.7409 + 9.53935i) q^{98} +(2.94281 - 2.94281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.13207	−	0.847599i	−0.800492	−	0.599343i
$2$	−1.13207	−	0.847599i	−0.800492	−	0.599343i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	0.563151	+	1.91908i	0.281575	+	0.959539i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	−1.39984	+	0.201149i	−0.571480	+	0.0821187i
$7$			4.27253i			1.61487i	0.589959	+	0.807433i	$0.299144\pi$
$7$			4.27253i			1.61487i	−0.589959	+	0.807433i	$0.700856\pi$
$8$	0.989085	−	2.64985i	0.349695	−	0.936864i
$9$		−	1.00000i		−	0.333333i
$10$	−0.201149	−	1.39984i	−0.0636089	−	0.442667i
$11$	2.94281	+	2.94281i	0.887291	+	0.887291i	0.994262	−	0.106971i	$-0.0341151\pi$
$11$	2.94281	+	2.94281i	0.887291	+	0.887291i	−0.106971	+	0.994262i	$0.534115\pi$
$12$	1.75520	+	0.958786i	0.506683	+	0.276778i
$13$	−4.05962	+	4.05962i	−1.12594	+	1.12594i	−0.135106	+	0.990831i	$0.543137\pi$
$13$	−4.05962	+	4.05962i	−1.12594	+	1.12594i	−0.990831	+	0.135106i	$0.956863\pi$
$14$	3.62140	−	4.83679i	0.967859	−	1.29269i
$15$	1.00000			0.258199
$16$	−3.36572	+	2.16146i	−0.841431	+	0.540365i
$17$	0.160060			0.0388202			0.0194101	−	0.999812i	$-0.493821\pi$
$17$	0.160060			0.0388202			0.0194101	+	0.999812i	$0.493821\pi$
$18$	−0.847599	+	1.13207i	−0.199781	+	0.266831i
$19$	4.32576	−	4.32576i	0.992396	−	0.992396i	−0.00757497	−	0.999971i	$-0.502411\pi$
$19$	4.32576	−	4.32576i	0.992396	−	0.992396i	0.999971	+	0.00757497i	$0.00241121\pi$
$20$	−0.958786	+	1.75520i	−0.214391	+	0.392475i
$21$	3.02114	+	3.02114i	0.659266	+	0.659266i
$22$	−0.837134	−	5.82579i	−0.178478	−	1.24206i
$23$		−	8.40564i		−	1.75270i	−0.481677	−	0.876349i	$-0.659972\pi$
$23$		−	8.40564i		−	1.75270i	0.481677	−	0.876349i	$-0.340028\pi$
$24$	−1.17434	−	2.57312i	−0.239711	−	0.525235i
$25$			1.00000i			0.200000i
$26$	8.03670	−	1.15483i	1.57613	−	0.226481i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−8.19933	+	2.40608i	−1.54953	+	0.454706i
$29$	−1.78072	+	1.78072i	−0.330671	+	0.330671i	−0.852841	−	0.522171i	$-0.825122\pi$
$29$	−1.78072	+	1.78072i	−0.330671	+	0.330671i	0.522171	+	0.852841i	$0.325122\pi$
$30$	−1.13207	−	0.847599i	−0.206686	−	0.154750i
$31$	7.17282			1.28828			0.644138	−	0.764909i	$-0.277216\pi$
$31$	7.17282			1.28828			0.644138	+	0.764909i	$0.277216\pi$
$32$	5.64228	+	0.405867i	0.997423	+	0.0717479i
$33$	4.16177			0.724470
$34$	−0.181198	−	0.135667i	−0.0310752	−	0.0232666i
$35$	−3.02114	+	3.02114i	−0.510666	+	0.510666i
$36$	1.91908	−	0.563151i	0.319846	−	0.0938584i
$37$	−0.669226	−	0.669226i	−0.110020	−	0.110020i	0.649954	−	0.759974i	$-0.274788\pi$
$37$	−0.669226	−	0.669226i	−0.110020	−	0.110020i	−0.759974	+	0.649954i	$0.774788\pi$
$38$	−8.56355	+	1.23054i	−1.38919	+	0.199619i
$39$			5.74117i			0.919324i
$40$	2.57312	−	1.17434i	0.406845	−	0.185679i
$41$		−	3.96632i		−	0.619435i	−0.950829	−	0.309717i	$-0.899766\pi$
$41$		−	3.96632i		−	0.619435i	0.950829	−	0.309717i	$-0.100234\pi$
$42$	−0.859415	−	5.98084i	−0.132611	−	0.922864i
$43$	−0.255733	−	0.255733i	−0.0389989	−	0.0389989i	0.687338	−	0.726337i	$-0.258779\pi$
$43$	−0.255733	−	0.255733i	−0.0389989	−	0.0389989i	−0.726337	+	0.687338i	$0.758779\pi$
$44$	−3.99024	+	7.30473i	−0.601551	+	1.10123i
$45$	0.707107	−	0.707107i	0.105409	−	0.105409i
$46$	−7.12462	+	9.51575i	−1.05047	+	1.40302i
$47$	0.0752658			0.0109787			0.00548933	−	0.999985i	$-0.498253\pi$
$47$	0.0752658			0.0109787			0.00548933	+	0.999985i	$0.498253\pi$
$48$	−0.851542	+	3.90831i	−0.122910	+	0.564116i
$49$	−11.2545			−1.60779
$50$	0.847599	−	1.13207i	0.119869	−	0.160098i
$51$	0.113179	−	0.113179i	0.0158483	−	0.0158483i
$52$	−10.0769	−	5.50456i	−1.39742	−	0.763345i
$53$	−2.88214	−	2.88214i	−0.395892	−	0.395892i	0.480889	−	0.876781i	$-0.340314\pi$
$53$	−2.88214	−	2.88214i	−0.395892	−	0.395892i	−0.876781	+	0.480889i	$0.840314\pi$
$54$	0.201149	+	1.39984i	0.0273729	+	0.190493i
$55$			4.16177i			0.561172i
$56$	11.3216	+	4.22590i	1.51291	+	0.564710i
$57$		−	6.11754i		−	0.810288i
$58$	3.52522	−	0.506556i	0.462884	−	0.0665140i
$59$	−5.63594	−	5.63594i	−0.733737	−	0.733737i	0.237621	−	0.971358i	$-0.423632\pi$
$59$	−5.63594	−	5.63594i	−0.733737	−	0.733737i	−0.971358	+	0.237621i	$0.923632\pi$
$60$	0.563151	+	1.91908i	0.0727024	+	0.247752i
$61$	−4.48857	+	4.48857i	−0.574703	+	0.574703i	−0.933439	−	0.358736i	$-0.883208\pi$
$61$	−4.48857	+	4.48857i	−0.574703	+	0.574703i	0.358736	+	0.933439i	$0.383208\pi$
$62$	−8.12011	−	6.07968i	−1.03126	−	0.772120i
$63$	4.27253			0.538289
$64$	−6.04342	−	5.24186i	−0.755428	−	0.655232i
$65$	−5.74117			−0.712105
$66$	−4.71140	−	3.52751i	−0.579933	−	0.434206i
$67$	−0.131176	+	0.131176i	−0.0160257	+	0.0160257i	−0.715074	−	0.699049i	$-0.753607\pi$
$67$	−0.131176	+	0.131176i	−0.0160257	+	0.0160257i	0.699049	+	0.715074i	$0.253607\pi$
$68$	0.0901377	+	0.307167i	0.0109308	+	0.0372495i
$69$	−5.94369	−	5.94369i	−0.715536	−	0.715536i
$70$	5.98084	−	0.859415i	0.714848	−	0.102720i
$71$			12.1137i			1.43764i	0.695199	+	0.718818i	$0.255316\pi$
$71$			12.1137i			1.43764i	−0.695199	+	0.718818i	$0.744684\pi$
$72$	−2.64985	−	0.989085i	−0.312288	−	0.116565i
$73$			0.382876i			0.0448123i	0.999749	+	0.0224061i	$0.00713269\pi$
$73$			0.382876i			0.0448123i	−0.999749	+	0.0224061i	$0.992867\pi$
$74$	0.190373	+	1.32484i	0.0221304	+	0.154010i
$75$	0.707107	+	0.707107i	0.0816497	+	0.0816497i
$76$	10.7375	+	5.86541i	1.23168	+	0.672809i
$77$	−12.5733	+	12.5733i	−1.43286	+	1.43286i
$78$	4.86622	−	6.49939i	0.550990	−	0.735911i
$79$	15.3239			1.72408			0.862039	−	0.506841i	$-0.169187\pi$
$79$	15.3239			1.72408			0.862039	+	0.506841i	$0.169187\pi$
$80$	−3.90831	−	0.851542i	−0.436962	−	0.0952053i
$81$	−1.00000			−0.111111
$82$	−3.36185	+	4.49014i	−0.371254	+	0.495853i
$83$	−5.54562	+	5.54562i	−0.608710	+	0.608710i	−0.942609	−	0.333899i	$-0.891636\pi$
$83$	−5.54562	+	5.54562i	−0.608710	+	0.608710i	0.333899	+	0.942609i	$0.391636\pi$
$84$	−4.09644	+	7.49916i	−0.446959	+	0.818225i
$85$	0.113179	+	0.113179i	0.0122760	+	0.0122760i
$86$	0.0727477	+	0.506266i	0.00784459	+	0.0545921i
$87$			2.51831i			0.269991i
$88$	10.7087	−	4.88732i	1.14155	−	0.520990i
$89$		−	13.8991i		−	1.47330i	−0.676275	−	0.736649i	$-0.736407\pi$
$89$		−	13.8991i		−	1.47330i	0.676275	−	0.736649i	$-0.263593\pi$
$90$	−1.39984	+	0.201149i	−0.147556	+	0.0212030i
$91$	−17.3449	−	17.3449i	−1.81824	−	1.81824i
$92$	16.1311	−	4.73364i	1.68178	−	0.493516i
$93$	5.07195	−	5.07195i	0.525937	−	0.525937i
$94$	−0.0852060	−	0.0637953i	−0.00878832	−	0.00657998i
$95$	6.11754			0.627647
$96$	4.27668	−	3.70270i	0.436487	−	0.377905i
$97$	10.8999			1.10672			0.553358	−	0.832944i	$-0.313346\pi$
$97$	10.8999			1.10672			0.553358	+	0.832944i	$0.313346\pi$
$98$	12.7409	+	9.53935i	1.28703	+	0.963620i
$99$	2.94281	−	2.94281i	0.295764	−	0.295764i
$100$	−1.91908	+	0.563151i	−0.191908	+	0.0563151i
$101$	−2.98972	−	2.98972i	−0.297489	−	0.297489i	0.542541	−	0.840029i	$-0.317462\pi$
$101$	−2.98972	−	2.98972i	−0.297489	−	0.297489i	−0.840029	+	0.542541i	$0.817462\pi$
$102$	−0.224057	+	0.0321958i	−0.0221850	+	0.00318786i
$103$		−	16.8190i		−	1.65723i	−0.559820	−	0.828615i	$-0.689130\pi$
$103$		−	16.8190i		−	1.65723i	0.559820	−	0.828615i	$-0.310870\pi$
$104$	6.74208	+	14.7727i	0.661116	+	1.44858i
$105$			4.27253i			0.416957i
$106$	0.819874	+	5.70567i	0.0796332	+	0.554184i
$107$	1.64447	+	1.64447i	0.158977	+	0.158977i	0.782113	−	0.623136i	$-0.214142\pi$
$107$	1.64447	+	1.64447i	0.158977	+	0.158977i	−0.623136	+	0.782113i	$0.714142\pi$
$108$	0.958786	−	1.75520i	0.0922592	−	0.168894i
$109$	4.67023	−	4.67023i	0.447327	−	0.447327i	−0.447138	−	0.894465i	$-0.647557\pi$
$109$	4.67023	−	4.67023i	0.447327	−	0.447327i	0.894465	+	0.447138i	$0.147557\pi$
$110$	3.52751	−	4.71140i	0.336335	−	0.449214i
$111$	−0.946429			−0.0898311
$112$	−9.23491	−	14.3802i	−0.872617	−	1.35880i
$113$	5.00533			0.470862			0.235431	−	0.971891i	$-0.424350\pi$
$113$	5.00533			0.470862			0.235431	+	0.971891i	$0.424350\pi$
$114$	−5.18522	+	6.92547i	−0.485641	+	0.648629i
$115$	5.94369	−	5.94369i	0.554252	−	0.554252i
$116$	−4.42014	−	2.41452i	−0.410400	−	0.224183i
$117$	4.05962	+	4.05962i	0.375312	+	0.375312i
$118$	1.60324	+	11.1573i	0.147590	+	1.02711i
$119$			0.683861i			0.0626894i
$120$	0.989085	−	2.64985i	0.0902907	−	0.241897i
$121$			6.32029i			0.574572i
$122$	8.88588	−	1.27685i	0.804489	−	0.115601i
$123$	−2.80461	−	2.80461i	−0.252883	−	0.252883i
$124$	4.03938	+	13.7652i	0.362747	+	1.23615i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−4.83679	−	3.62140i	−0.430896	−	0.322620i
$127$	1.96679			0.174525			0.0872623	−	0.996185i	$-0.472188\pi$
$127$	1.96679			0.174525			0.0872623	+	0.996185i	$0.472188\pi$
$128$	2.39856	+	11.0565i	0.212005	+	0.977269i
$129$	−0.361661			−0.0318425
$130$	6.49939	+	4.86622i	0.570035	+	0.426795i
$131$	−0.852904	+	0.852904i	−0.0745186	+	0.0745186i	−0.743384	−	0.668865i	$-0.766780\pi$
$131$	−0.852904	+	0.852904i	−0.0745186	+	0.0745186i	0.668865	+	0.743384i	$0.266780\pi$
$132$	2.34370	+	7.98675i	0.203993	+	0.695158i
$133$	18.4819	+	18.4819i	1.60259	+	1.60259i
$134$	0.259686	−	0.0373154i	0.0224334	−	0.00322356i
$135$		−	1.00000i		−	0.0860663i
$136$	0.158313	−	0.424134i	0.0135752	−	0.0363692i
$137$		−	4.12023i		−	0.352015i	−0.984389	−	0.176007i	$-0.943682\pi$
$137$		−	4.12023i		−	0.352015i	0.984389	−	0.176007i	$-0.0563183\pi$
$138$	1.69079	+	11.7665i	0.143929	+	1.00163i
$139$	5.73895	+	5.73895i	0.486771	+	0.486771i	0.907286	−	0.420514i	$-0.138150\pi$
$139$	5.73895	+	5.73895i	0.486771	+	0.486771i	−0.420514	+	0.907286i	$0.638150\pi$
$140$	−7.49916	−	4.09644i	−0.633794	−	0.346213i
$141$	0.0532210	−	0.0532210i	0.00448202	−	0.00448202i
$142$	10.2676	−	13.7136i	0.861637	−	1.15082i
$143$	−23.8934			−1.99807
$144$	2.16146	+	3.36572i	0.180122	+	0.280477i
$145$	−2.51831			−0.209134
$146$	0.324525	−	0.433441i	0.0268579	−	0.0358719i
$147$	−7.95817	+	7.95817i	−0.656379	+	0.656379i
$148$	0.907422	−	1.66117i	0.0745897	−	0.136548i
$149$	−9.96311	−	9.96311i	−0.816210	−	0.816210i	0.169346	−	0.985557i	$-0.445834\pi$
$149$	−9.96311	−	9.96311i	−0.816210	−	0.816210i	−0.985557	+	0.169346i	$0.945834\pi$
$150$	−0.201149	−	1.39984i	−0.0164237	−	0.114296i
$151$		−	4.01882i		−	0.327047i	−0.986539	−	0.163524i	$-0.947714\pi$
$151$		−	4.01882i		−	0.327047i	0.986539	−	0.163524i	$-0.0522860\pi$
$152$	−7.18407	−	15.7411i	−0.582705	−	1.27678i
$153$		−	0.160060i		−	0.0129401i
$154$	24.8909	−	3.57669i	2.00576	−	0.288218i
$155$	5.07195	+	5.07195i	0.407389	+	0.407389i
$156$	−11.0178	+	3.23315i	−0.882127	+	0.258859i
$157$	−9.14459	+	9.14459i	−0.729818	+	0.729818i	−0.970583	−	0.240766i	$-0.922601\pi$
$157$	−9.14459	+	9.14459i	−0.729818	+	0.729818i	0.240766	+	0.970583i	$0.422601\pi$
$158$	−17.3477	−	12.9886i	−1.38011	−	1.03332i
$159$	−4.07596			−0.323244
$160$	3.70270	+	4.27668i	0.292724	+	0.338101i
$161$	35.9134			2.83037
$162$	1.13207	+	0.847599i	0.0889436	+	0.0665937i
$163$	−0.346095	+	0.346095i	−0.0271082	+	0.0271082i	−0.720531	−	0.693423i	$-0.756102\pi$
$163$	−0.346095	+	0.346095i	−0.0271082	+	0.0271082i	0.693423	+	0.720531i	$0.256102\pi$
$164$	7.61168	−	2.23363i	0.594372	−	0.174418i
$165$	2.94281	+	2.94281i	0.229098	+	0.229098i
$166$	10.9785	−	1.57755i	0.852094	−	0.122441i
$167$		−	10.9882i		−	0.850296i	−0.905124	−	0.425148i	$-0.860222\pi$
$167$		−	10.9882i		−	0.850296i	0.905124	−	0.425148i	$-0.139778\pi$
$168$	10.9937	−	5.01740i	0.848185	−	0.387101i
$169$		−	19.9611i		−	1.53547i
$170$	−0.0321958	−	0.224057i	−0.00246931	−	0.0171844i
$171$	−4.32576	−	4.32576i	−0.330799	−	0.330799i
$172$	0.346755	−	0.634788i	0.0264398	−	0.0484021i
$173$	2.70605	−	2.70605i	0.205737	−	0.205737i	−0.596716	−	0.802453i	$-0.703528\pi$
$173$	2.70605	−	2.70605i	0.205737	−	0.205737i	0.802453	+	0.596716i	$0.203528\pi$
$174$	2.13452	−	2.85090i	0.161818	−	0.216126i
$175$	−4.27253			−0.322973
$176$	−16.2655	−	3.54392i	−1.22606	−	0.267133i
$177$	−7.97042			−0.599093
$178$	−11.7808	+	15.7347i	−0.883012	+	1.17936i
$179$	−10.4088	+	10.4088i	−0.777990	+	0.777990i	−0.979489	−	0.201499i	$-0.935419\pi$
$179$	−10.4088	+	10.4088i	−0.777990	+	0.777990i	0.201499	+	0.979489i	$0.435419\pi$
$180$	1.75520	+	0.958786i	0.130825	+	0.0714637i
$181$	−15.4792	−	15.4792i	−1.15056	−	1.15056i	−0.986441	−	0.164119i	$-0.947522\pi$
$181$	−15.4792	−	15.4792i	−1.15056	−	1.15056i	−0.164119	−	0.986441i	$-0.552478\pi$
$182$	4.93405	+	34.3371i	0.365736	+	2.54523i
$183$			6.34780i			0.469243i
$184$	−22.2737	−	8.31390i	−1.64204	−	0.612909i
$185$		−	0.946429i		−	0.0695828i
$186$	−10.0408	+	1.44280i	−0.736225	+	0.105792i
$187$	0.471026	+	0.471026i	0.0344448	+	0.0344448i
$188$	0.0423860	+	0.144441i	0.00309132	+	0.0105344i
$189$	3.02114	−	3.02114i	0.219755	−	0.219755i
$190$	−6.92547	−	5.18522i	−0.502426	−	0.376176i
$191$	4.75146			0.343803			0.171902	−	0.985114i	$-0.445009\pi$
$191$	4.75146			0.343803			0.171902	+	0.985114i	$0.445009\pi$
$192$	−7.97990	+	0.566790i	−0.575899	+	0.0409046i
$193$	−11.7915			−0.848772			−0.424386	−	0.905481i	$-0.639510\pi$
$193$	−11.7915			−0.848772			−0.424386	+	0.905481i	$0.639510\pi$
$194$	−12.3394	−	9.23873i	−0.885917	−	0.663302i
$195$	−4.05962	+	4.05962i	−0.290716	+	0.290716i
$196$	−6.33801	−	21.5984i	−0.452715	−	1.54274i
$197$	4.56244	+	4.56244i	0.325060	+	0.325060i	0.850705	−	0.525644i	$-0.176176\pi$
$197$	4.56244	+	4.56244i	0.325060	+	0.325060i	−0.525644	+	0.850705i	$0.676176\pi$
$198$	−5.82579	+	0.837134i	−0.414021	+	0.0594926i
$199$			3.60262i			0.255383i	0.991814	+	0.127691i	$0.0407567\pi$
$199$			3.60262i			0.255383i	−0.991814	+	0.127691i	$0.959243\pi$
$200$	2.64985	+	0.989085i	0.187373	+	0.0699389i
$201$			0.185511i			0.0130850i
$202$	0.850479	+	5.91865i	0.0598395	+	0.416435i
$203$	−7.60817	−	7.60817i	−0.533989	−	0.533989i
$204$	0.280937	+	0.153463i	0.0196695	+	0.0107446i
$205$	2.80461	−	2.80461i	0.195883	−	0.195883i
$206$	−14.2558	+	19.0403i	−0.993249	+	1.32660i
$207$	−8.40564			−0.584233
$208$	4.88885	−	22.4383i	0.338981	−	1.55582i
$209$	25.4598			1.76109
$210$	3.62140	−	4.83679i	0.249900	−	0.333771i
$211$	−0.975389	+	0.975389i	−0.0671486	+	0.0671486i	−0.739884	−	0.672735i	$-0.765119\pi$
$211$	−0.975389	+	0.975389i	−0.0671486	+	0.0671486i	0.672735	+	0.739884i	$0.265119\pi$
$212$	3.90797	−	7.15412i	0.268400	−	0.491347i
$213$	8.56570	+	8.56570i	0.586912	+	0.586912i
$214$	−0.467799	−	3.25551i	−0.0319781	−	0.222542i
$215$		−	0.361661i		−	0.0246651i
$216$	−2.57312	+	1.17434i	−0.175078	+	0.0799036i
$217$			30.6461i			2.08039i
$218$	−9.24550	+	1.32853i	−0.626184	+	0.0899793i
$219$	0.270734	+	0.270734i	0.0182945	+	0.0182945i
$220$	−7.98675	+	2.34370i	−0.538467	+	0.158012i
$221$	−0.649782	+	0.649782i	−0.0437091	+	0.0437091i
$222$	1.07142	+	0.802193i	0.0719091	+	0.0538396i
$223$	4.66343			0.312286			0.156143	−	0.987734i	$-0.450094\pi$
$223$	4.66343			0.312286			0.156143	+	0.987734i	$0.450094\pi$
$224$	−1.73408	+	24.1068i	−0.115863	+	1.61070i
$225$	1.00000			0.0666667
$226$	−5.66637	−	4.24251i	−0.376921	−	0.282208i
$227$	−1.61701	+	1.61701i	−0.107325	+	0.107325i	−0.758730	−	0.651405i	$-0.774180\pi$
$227$	−1.61701	+	1.61701i	−0.107325	+	0.107325i	0.651405	+	0.758730i	$0.274180\pi$
$228$	11.7400	−	3.44510i	0.777503	−	0.228157i
$229$	9.14882	+	9.14882i	0.604571	+	0.604571i	0.941522	−	0.336951i	$-0.109396\pi$
$229$	9.14882	+	9.14882i	0.604571	+	0.604571i	−0.336951	+	0.941522i	$0.609396\pi$
$230$	−11.7665	+	1.69079i	−0.775861	+	0.111487i
$231$			17.7813i			1.16992i
$232$	2.95735	+	6.47991i	0.194160	+	0.425427i
$233$			10.3002i			0.674789i	0.941363	+	0.337394i	$0.109546\pi$
$233$			10.3002i			0.674789i	−0.941363	+	0.337394i	$0.890454\pi$
$234$	−1.15483	−	8.03670i	−0.0754937	−	0.525376i
$235$	0.0532210	+	0.0532210i	0.00347175	+	0.00347175i
$236$	7.64192	−	13.9897i	0.497447	−	0.910651i
$237$	10.8357	−	10.8357i	0.703852	−	0.703852i
$238$	0.579640	−	0.774176i	0.0375725	−	0.0501824i
$239$	3.73825			0.241807			0.120904	−	0.992664i	$-0.461421\pi$
$239$	3.73825			0.241807			0.120904	+	0.992664i	$0.461421\pi$
$240$	−3.36572	+	2.16146i	−0.217256	+	0.139522i
$241$	−9.34283			−0.601824			−0.300912	−	0.953652i	$-0.597291\pi$
$241$	−9.34283			−0.601824			−0.300912	+	0.953652i	$0.597291\pi$
$242$	5.35707	−	7.15499i	0.344366	−	0.459940i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−11.1417	−	6.08618i	−0.713272	−	0.389628i
$245$	−7.95817	−	7.95817i	−0.508429	−	0.508429i
$246$	0.797821	+	5.55219i	0.0508672	+	0.353995i
$247$			35.1219i			2.23475i
$248$	7.09453	−	19.0069i	0.450503	−	1.20694i
$249$			7.84269i			0.497010i
$250$	1.39984	−	0.201149i	0.0885334	−	0.0127218i
$251$	−9.31174	−	9.31174i	−0.587752	−	0.587752i	0.349270	−	0.937022i	$-0.386429\pi$
$251$	−9.31174	−	9.31174i	−0.587752	−	0.587752i	−0.937022	+	0.349270i	$0.886429\pi$
$252$	2.40608	+	8.19933i	0.151569	+	0.516509i
$253$	24.7362	−	24.7362i	1.55515	−	1.55515i
$254$	−2.22654	−	1.66705i	−0.139706	−	0.104600i
$255$	0.160060			0.0100233
$256$	6.65618	−	14.5498i	0.416011	−	0.909359i
$257$	8.68522			0.541769			0.270885	−	0.962612i	$-0.412684\pi$
$257$	8.68522			0.541769			0.270885	+	0.962612i	$0.412684\pi$
$258$	0.409424	+	0.306544i	0.0254897	+	0.0190846i
$259$	2.85929	−	2.85929i	0.177668	−	0.177668i
$260$	−3.23315	−	11.0178i	−0.200511	−	0.683293i
$261$	1.78072	+	1.78072i	0.110224	+	0.110224i
$262$	1.68847	−	0.242624i	0.104314	−	0.0149893i
$263$		−	5.18971i		−	0.320011i	−0.987116	−	0.160006i	$-0.948849\pi$
$263$		−	5.18971i		−	0.320011i	0.987116	−	0.160006i	$-0.0511513\pi$
$264$	4.11634	−	11.0281i	0.253343	−	0.678730i
$265$		−	4.07596i		−	0.250384i
$266$	−5.25751	−	36.5881i	−0.322359	−	2.24336i
$267$	−9.82813	−	9.82813i	−0.601472	−	0.601472i
$268$	−0.325610	−	0.177866i	−0.0198898	−	0.0108649i
$269$	−7.99426	+	7.99426i	−0.487418	+	0.487418i	−0.907491	−	0.420072i	$-0.862005\pi$
$269$	−7.99426	+	7.99426i	−0.487418	+	0.487418i	0.420072	+	0.907491i	$0.362005\pi$
$270$	−0.847599	+	1.13207i	−0.0515833	+	0.0688954i
$271$	−18.8342			−1.14410			−0.572048	−	0.820220i	$-0.693851\pi$
$271$	−18.8342			−1.14410			−0.572048	+	0.820220i	$0.693851\pi$
$272$	−0.538717	+	0.345963i	−0.0326645	+	0.0209771i
$273$	−24.5294			−1.48458
$274$	−3.49230	+	4.66437i	−0.210978	+	0.281785i
$275$	−2.94281	+	2.94281i	−0.177458	+	0.177458i
$276$	8.05921	−	14.7536i	0.485107	−	0.888062i
$277$	3.71919	+	3.71919i	0.223465	+	0.223465i	0.809956	−	0.586491i	$-0.199491\pi$
$277$	3.71919	+	3.71919i	0.223465	+	0.223465i	−0.586491	+	0.809956i	$0.699491\pi$
$278$	−1.63254	−	11.3612i	−0.0979135	−	0.681400i
$279$		−	7.17282i		−	0.429425i
$280$	5.01740	+	10.9937i	0.299847	+	0.657001i
$281$			11.0223i			0.657538i	0.944410	+	0.328769i	$0.106634\pi$
$281$			11.0223i			0.657538i	−0.944410	+	0.328769i	$0.893366\pi$
$282$	−0.105360	+	0.0151396i	−0.00627408	+	0.000901552i
$283$	10.5210	+	10.5210i	0.625411	+	0.625411i	0.946910	−	0.321499i	$-0.104187\pi$
$283$	10.5210	+	10.5210i	0.625411	+	0.625411i	−0.321499	+	0.946910i	$0.604187\pi$
$284$	−23.2472	+	6.82186i	−1.37947	+	0.404803i
$285$	4.32576	−	4.32576i	0.256236	−	0.256236i
$286$	27.0490	+	20.2521i	1.59944	+	1.19753i
$287$	16.9462			1.00030
$288$	0.405867	−	5.64228i	0.0239160	−	0.332474i
$289$	−16.9744			−0.998493
$290$	2.85090	+	2.13452i	0.167410	+	0.125343i
$291$	7.70738	−	7.70738i	0.451815	−	0.451815i
$292$	−0.734769	+	0.215617i	−0.0429991	+	0.0126180i
$293$	15.5643	+	15.5643i	0.909274	+	0.909274i	0.996214	−	0.0869399i	$-0.0277088\pi$
$293$	15.5643	+	15.5643i	0.909274	+	0.909274i	−0.0869399	+	0.996214i	$0.527709\pi$
$294$	15.7545	−	2.26384i	0.918822	−	0.132030i
$295$		−	7.97042i		−	0.464056i
$296$	−2.43527	+	1.11143i	−0.141547	+	0.0646004i
$297$		−	4.16177i		−	0.241490i
$298$	2.83418	+	19.7236i	0.164180	+	1.14256i
$299$	34.1237	+	34.1237i	1.97343	+	1.97343i
$300$	−0.958786	+	1.75520i	−0.0553555	+	0.101337i
$301$	1.09263	−	1.09263i	0.0629780	−	0.0629780i
$302$	−3.40635	+	4.54958i	−0.196014	+	0.261799i
$303$	−4.22811			−0.242898
$304$	−5.20935	+	23.9092i	−0.298776	+	1.37129i
$305$	−6.34780			−0.363474
$306$	−0.135667	+	0.181198i	−0.00775554	+	0.0103584i
$307$	19.6795	−	19.6795i	1.12317	−	1.12317i	0.131908	−	0.991262i	$-0.457890\pi$
$307$	19.6795	−	19.6795i	1.12317	−	1.12317i	0.991262	−	0.131908i	$-0.0421104\pi$
$308$	−31.2097	−	17.0484i	−1.77834	−	0.971425i
$309$	−11.8929	−	11.8929i	−0.676561	−	0.676561i
$310$	−1.44280	−	10.0408i	−0.0819458	−	0.570277i
$311$		−	11.8922i		−	0.674344i	−0.941443	−	0.337172i	$-0.890530\pi$
$311$		−	11.8922i		−	0.674344i	0.941443	−	0.337172i	$-0.109470\pi$
$312$	15.2133	+	5.67851i	0.861281	+	0.321482i
$313$			9.61193i			0.543298i	0.962396	+	0.271649i	$0.0875690\pi$
$313$			9.61193i			0.543298i	−0.962396	+	0.271649i	$0.912431\pi$
$314$	18.1032	−	2.60134i	1.02162	−	0.146802i
$315$	3.02114	+	3.02114i	0.170222	+	0.170222i
$316$	8.62969	+	29.4079i	0.485458	+	1.65432i
$317$	8.10049	−	8.10049i	0.454969	−	0.454969i	−0.442031	−	0.897000i	$-0.645742\pi$
$317$	8.10049	−	8.10049i	0.454969	−	0.454969i	0.897000	+	0.442031i	$0.145742\pi$
$318$	4.61426	+	3.45478i	0.258755	+	0.193734i
$319$	−10.4806			−0.586802
$320$	−0.566790	−	7.97990i	−0.0316845	−	0.446090i
$321$	2.32563			0.129804
$322$	−40.6564	−	30.4402i	−2.26569	−	1.69636i
$323$	0.692379	−	0.692379i	0.0385250	−	0.0385250i
$324$	−0.563151	−	1.91908i	−0.0312861	−	0.106615i
$325$	−4.05962	−	4.05962i	−0.225187	−	0.225187i
$326$	0.685152	−	0.0984526i	0.0379470	−	0.00545279i
$327$		−	6.60470i		−	0.365241i
$328$	−10.5102	−	3.92303i	−0.580326	−	0.216613i
$329$			0.321576i			0.0177291i
$330$	−0.837134	−	5.82579i	−0.0460827	−	0.320699i
$331$	−13.3267	−	13.3267i	−0.732501	−	0.732501i	0.238613	−	0.971115i	$-0.423307\pi$
$331$	−13.3267	−	13.3267i	−0.732501	−	0.732501i	−0.971115	+	0.238613i	$0.923307\pi$
$332$	−13.7655	−	7.51945i	−0.755479	−	0.412684i
$333$	−0.669226	+	0.669226i	−0.0366734	+	0.0366734i
$334$	−9.31363	+	12.4394i	−0.509619	+	0.680655i
$335$	−0.185511			−0.0101356
$336$	−16.6984	−	3.63824i	−0.910971	−	0.198482i
$337$	32.6763			1.77999			0.889996	−	0.455967i	$-0.150707\pi$
$337$	32.6763			1.77999			0.889996	+	0.455967i	$0.150707\pi$
$338$	−16.9190	+	22.5973i	−0.920273	+	1.22913i
$339$	3.53930	−	3.53930i	0.192229	−	0.192229i
$340$	−0.153463	+	0.280937i	−0.00832270	+	0.0152359i
$341$	21.1083	+	21.1083i	1.14308	+	1.14308i
$342$	1.23054	+	8.56355i	0.0665398	+	0.463064i
$343$		−	18.1777i		−	0.981504i
$344$	−0.930596	+	0.424712i	−0.0501744	+	0.0228990i
$345$		−	8.40564i		−	0.452545i
$346$	−5.35708	+	0.769784i	−0.287998	+	0.0413838i
$347$	22.4898	+	22.4898i	1.20732	+	1.20732i	0.971893	+	0.235423i	$0.0756477\pi$
$347$	22.4898	+	22.4898i	1.20732	+	1.20732i	0.235423	+	0.971893i	$0.424352\pi$
$348$	−4.83284	+	1.41819i	−0.259067	+	0.0760229i
$349$	−22.6617	+	22.6617i	−1.21305	+	1.21305i	−0.243032	+	0.970018i	$0.578142\pi$
$349$	−22.6617	+	22.6617i	−1.21305	+	1.21305i	−0.970018	+	0.243032i	$0.921858\pi$
$350$	4.83679	+	3.62140i	0.258538	+	0.193572i
$351$	5.74117			0.306441
$352$	15.4098	+	17.7985i	0.821343	+	0.948666i
$353$	−10.6347			−0.566026			−0.283013	−	0.959116i	$-0.591334\pi$
$353$	−10.6347			−0.566026			−0.283013	+	0.959116i	$0.591334\pi$
$354$	9.02305	+	6.75572i	0.479570	+	0.359063i
$355$	−8.56570	+	8.56570i	−0.454620	+	0.454620i
$356$	26.6734	−	7.82727i	1.41369	−	0.414845i
$357$	0.483562	+	0.483562i	0.0255928	+	0.0255928i
$358$	20.6059	−	2.96096i	1.08906	−	0.156492i
$359$		−	17.0191i		−	0.898235i	−0.893473	−	0.449118i	$-0.851738\pi$
$359$		−	17.0191i		−	0.898235i	0.893473	−	0.449118i	$-0.148262\pi$
$360$	−1.17434	−	2.57312i	−0.0618931	−	0.135615i
$361$		−	18.4243i		−	0.969701i
$362$	4.40333	+	30.6436i	0.231434	+	1.61059i
$363$	4.46912	+	4.46912i	0.234568	+	0.234568i
$364$	23.5184	−	43.0540i	1.23270	−	2.25664i
$365$	−0.270734	+	0.270734i	−0.0141709	+	0.0141709i
$366$	5.38039	−	7.18613i	0.281238	−	0.375625i
$367$	−25.7040			−1.34174			−0.670868	−	0.741577i	$-0.734078\pi$
$367$	−25.7040			−1.34174			−0.670868	+	0.741577i	$0.734078\pi$
$368$	18.1685	+	28.2911i	0.947097	+	1.47477i
$369$	−3.96632			−0.206478
$370$	−0.802193	+	1.07142i	−0.0417040	+	0.0557005i
$371$	12.3140	−	12.3140i	0.639313	−	0.639313i
$372$	12.5897	+	6.87720i	0.652747	+	0.356566i
$373$	−14.7290	−	14.7290i	−0.762641	−	0.762641i	0.214158	−	0.976799i	$-0.431299\pi$
$373$	−14.7290	−	14.7290i	−0.762641	−	0.762641i	−0.976799	+	0.214158i	$0.931299\pi$
$374$	−0.133991	−	0.932474i	−0.00692853	−	0.0482171i
$375$			1.00000i			0.0516398i
$376$	0.0744443	−	0.199443i	0.00383917	−	0.0102855i
$377$		−	14.4581i		−	0.744628i
$378$	−5.98084	+	0.859415i	−0.307621	+	0.0442036i
$379$	10.0142	+	10.0142i	0.514395	+	0.514395i	0.915870	−	0.401475i	$-0.131502\pi$
$379$	10.0142	+	10.0142i	0.514395	+	0.514395i	−0.401475	+	0.915870i	$0.631502\pi$
$380$	3.44510	+	11.7400i	0.176730	+	0.602251i
$381$	1.39073	−	1.39073i	0.0712494	−	0.0712494i
$382$	−5.37897	−	4.02733i	−0.275212	−	0.206056i
$383$	−28.1834			−1.44010			−0.720052	−	0.693920i	$-0.755882\pi$
$383$	−28.1834			−1.44010			−0.720052	+	0.693920i	$0.755882\pi$
$384$	9.51419	+	6.12211i	0.485519	+	0.312418i
$385$	−17.7813			−0.906218
$386$	13.3488	+	9.99448i	0.679435	+	0.508706i
$387$	−0.255733	+	0.255733i	−0.0129996	+	0.0129996i
$388$	6.13828	+	20.9177i	0.311624	+	1.06194i
$389$	−11.1551	−	11.1551i	−0.565586	−	0.565586i	0.365303	−	0.930889i	$-0.380965\pi$
$389$	−11.1551	−	11.1551i	−0.565586	−	0.565586i	−0.930889	+	0.365303i	$0.880965\pi$
$390$	8.03670	−	1.15483i	0.406954	−	0.0584771i
$391$		−	1.34540i		−	0.0680400i
$392$	−11.1317	+	29.8229i	−0.562236	+	1.50628i
$393$			1.20619i			0.0608442i
$394$	−1.29787	−	9.03211i	−0.0653855	−	0.455031i
$395$	10.8357	+	10.8357i	0.545202	+	0.545202i
$396$	7.30473	+	3.99024i	0.367077	+	0.200517i
$397$	2.98216	−	2.98216i	0.149670	−	0.149670i	−0.628300	−	0.777971i	$-0.716249\pi$
$397$	2.98216	−	2.98216i	0.149670	−	0.149670i	0.777971	+	0.628300i	$0.216249\pi$
$398$	3.05358	−	4.07841i	0.153062	−	0.204432i
$399$	26.1374			1.30851
$400$	−2.16146	−	3.36572i	−0.108073	−	0.168286i
$401$	−15.9896			−0.798485			−0.399242	−	0.916845i	$-0.630727\pi$
$401$	−15.9896			−0.798485			−0.399242	+	0.916845i	$0.630727\pi$
$402$	0.157239	−	0.210011i	0.00784239	−	0.0104744i
$403$	−29.1189	+	29.1189i	−1.45052	+	1.45052i
$404$	4.05385	−	7.42118i	0.201687	−	0.369217i
$405$	−0.707107	−	0.707107i	−0.0351364	−	0.0351364i
$406$	2.16428	+	15.0616i	0.107411	+	0.747496i
$407$		−	3.93881i		−	0.195240i
$408$	−0.187964	−	0.411852i	−0.00930562	−	0.0203897i
$409$			27.5110i			1.36033i	0.733059	+	0.680165i	$0.238092\pi$
$409$			27.5110i			1.36033i	−0.733059	+	0.680165i	$0.761908\pi$
$410$	−5.55219	+	0.797821i	−0.274203	+	0.0394015i
$411$	−2.91344	−	2.91344i	−0.143709	−	0.143709i
$412$	32.2770	−	9.47165i	1.59018	−	0.466635i
$413$	24.0797	−	24.0797i	1.18489	−	1.18489i
$414$	9.51575	+	7.12462i	0.467674	+	0.350156i
$415$	−7.84269			−0.384982
$416$	−24.5532	+	21.2578i	−1.20382	+	1.04225i
$417$	8.11610			0.397447
$418$	−28.8222	−	21.5797i	−1.40974	−	1.05550i
$419$	1.95916	−	1.95916i	0.0957114	−	0.0957114i	−0.657630	−	0.753341i	$-0.728441\pi$
$419$	1.95916	−	1.95916i	0.0957114	−	0.0957114i	0.753341	+	0.657630i	$0.228441\pi$
$420$	−8.19933	+	2.40608i	−0.400086	+	0.117405i
$421$	6.23743	+	6.23743i	0.303994	+	0.303994i	0.842574	−	0.538580i	$-0.181039\pi$
$421$	6.23743	+	6.23743i	0.303994	+	0.303994i	−0.538580	+	0.842574i	$0.681039\pi$
$422$	1.93095	−	0.277467i	0.0939970	−	0.0135069i
$423$		−	0.0752658i		−	0.00365955i
$424$	−10.4879	+	4.78655i	−0.509338	+	0.232456i
$425$			0.160060i			0.00776404i
$426$	−2.43666	−	16.9572i	−0.118057	−	0.821581i
$427$	−19.1776	−	19.1776i	−0.928068	−	0.928068i
$428$	−2.22978	+	4.08196i	−0.107781	+	0.197309i
$429$	−16.8952	+	16.8952i	−0.815708	+	0.815708i
$430$	−0.306544	+	0.409424i	−0.0147828	+	0.0197442i
$431$	5.88180			0.283317			0.141658	−	0.989916i	$-0.454757\pi$
$431$	5.88180			0.283317			0.141658	+	0.989916i	$0.454757\pi$
$432$	3.90831	+	0.851542i	0.188039	+	0.0409698i
$433$	−6.37830			−0.306522			−0.153261	−	0.988186i	$-0.548977\pi$
$433$	−6.37830			−0.306522			−0.153261	+	0.988186i	$0.548977\pi$
$434$	25.9756	−	34.6934i	1.24687	−	1.66534i
$435$	−1.78072	+	1.78072i	−0.0853788	+	0.0853788i
$436$	11.5926	+	6.33250i	0.555184	+	0.303272i
$437$	−36.3608	−	36.3608i	−1.73937	−	1.73937i
$438$	−0.0770151	−	0.535963i	−0.00367992	−	0.0256093i
$439$			37.2899i			1.77975i	0.456206	+	0.889874i	$0.349208\pi$
$439$			37.2899i			1.77975i	−0.456206	+	0.889874i	$0.650792\pi$
$440$	11.0281	+	4.11634i	0.525742	+	0.196239i
$441$			11.2545i			0.535931i
$442$	1.28635	−	0.184842i	0.0611855	−	0.00879203i
$443$	28.4238	+	28.4238i	1.35046	+	1.35046i	0.885149	+	0.465308i	$0.154056\pi$
$443$	28.4238	+	28.4238i	1.35046	+	1.35046i	0.465308	+	0.885149i	$0.345944\pi$
$444$	−0.532982	−	1.81627i	−0.0252942	−	0.0861964i
$445$	9.82813	−	9.82813i	0.465898	−	0.465898i
$446$	−5.27931	−	3.95272i	−0.249983	−	0.187167i
$447$	−14.0900			−0.666433
$448$	22.3960	−	25.8207i	1.05811	−	1.21991i
$449$	11.9658			0.564701			0.282350	−	0.959311i	$-0.408886\pi$
$449$	11.9658			0.564701			0.282350	+	0.959311i	$0.408886\pi$
$450$	−1.13207	−	0.847599i	−0.0533661	−	0.0399562i
$451$	11.6721	−	11.6721i	0.549619	−	0.549619i
$452$	2.81875	+	9.60562i	0.132583	+	0.451810i
$453$	−2.84174	−	2.84174i	−0.133516	−	0.133516i
$454$	3.20114	−	0.459986i	0.150237	−	0.0215882i
$455$		−	24.5294i		−	1.14995i
$456$	−16.2106	−	6.05077i	−0.759130	−	0.283353i
$457$		−	33.0504i		−	1.54603i	−0.634385	−	0.773017i	$-0.718747\pi$
$457$		−	33.0504i		−	1.54603i	0.634385	−	0.773017i	$-0.281253\pi$
$458$	−2.60254	−	18.1116i	−0.121609	−	0.846300i
$459$	−0.113179	−	0.113179i	−0.00528276	−	0.00528276i
$460$	14.7536	+	8.05921i	0.687890	+	0.375763i
$461$	−20.7242	+	20.7242i	−0.965221	+	0.965221i	−0.999415	−	0.0341939i	$-0.989114\pi$
$461$	−20.7242	+	20.7242i	−0.965221	+	0.965221i	0.0341939	+	0.999415i	$0.489114\pi$
$462$	15.0714	−	20.1296i	0.701185	−	0.936514i
$463$	14.2359			0.661599			0.330800	−	0.943701i	$-0.392682\pi$
$463$	14.2359			0.661599			0.330800	+	0.943701i	$0.392682\pi$
$464$	2.14445	−	9.84234i	0.0995536	−	0.456919i
$465$	7.17282			0.332632
$466$	8.73045	−	11.6605i	0.404430	−	0.540163i
$467$	18.7991	−	18.7991i	0.869918	−	0.869918i	−0.122545	−	0.992463i	$-0.539106\pi$
$467$	18.7991	−	18.7991i	0.869918	−	0.869918i	0.992463	+	0.122545i	$0.0391056\pi$
$468$	−5.50456	+	10.0769i	−0.254448	+	0.465806i
$469$	−0.560456	−	0.560456i	−0.0258794	−	0.0258794i
$470$	−0.0151396	−	0.105360i	−0.000698339	−	0.00485988i
$471$			12.9324i			0.595894i
$472$	−20.5088	+	9.35997i	−0.943995	+	0.430828i
$473$		−	1.50515i		−	0.0692068i
$474$	−21.4510	+	3.08239i	−0.985277	+	0.141579i
$475$	4.32576	+	4.32576i	0.198479	+	0.198479i
$476$	−1.31238	+	0.385117i	−0.0601529	+	0.0176518i
$477$	−2.88214	+	2.88214i	−0.131964	+	0.131964i
$478$	−4.23195	−	3.16854i	−0.193565	−	0.144926i
$479$	−26.7178			−1.22077			−0.610384	−	0.792106i	$-0.708985\pi$
$479$	−26.7178			−1.22077			−0.610384	+	0.792106i	$0.708985\pi$
$480$	5.64228	+	0.405867i	0.257533	+	0.0185252i
$481$	5.43361			0.247751
$482$	10.5767	+	7.91897i	0.481756	+	0.360699i
$483$	25.3946	−	25.3946i	1.15549	−	1.15549i
$484$	−12.1291	+	3.55928i	−0.551324	+	0.161785i
$485$	7.70738	+	7.70738i	0.349974	+	0.349974i
$486$	1.39984	−	0.201149i	0.0634978	−	0.00912430i
$487$		−	27.0801i		−	1.22712i	−0.789650	−	0.613558i	$-0.789738\pi$
$487$		−	27.0801i		−	1.22712i	0.789650	−	0.613558i	$-0.210262\pi$
$488$	7.45447	+	16.3336i	0.337448	+	0.739389i
$489$			0.489452i			0.0221338i
$490$	2.26384	+	15.7545i	0.102270	+	0.711717i
$491$	1.51536	+	1.51536i	0.0683872	+	0.0683872i	0.740473	−	0.672086i	$-0.234601\pi$
$491$	1.51536	+	1.51536i	0.0683872	+	0.0683872i	−0.672086	+	0.740473i	$0.734601\pi$
$492$	3.80285	−	6.96169i	0.171446	−	0.313857i
$493$	−0.285021	+	0.285021i	−0.0128367	+	0.0128367i
$494$	29.7693	−	39.7603i	1.33938	−	1.78890i
$495$	4.16177			0.187057
$496$	−24.1417	+	15.5038i	−1.08400	+	0.696139i
$497$	−51.7563			−2.32159
$498$	6.64746	−	8.87844i	0.297880	−	0.397853i
$499$	7.31012	−	7.31012i	0.327246	−	0.327246i	−0.524292	−	0.851538i	$-0.675670\pi$
$499$	7.31012	−	7.31012i	0.327246	−	0.327246i	0.851538	+	0.524292i	$0.175670\pi$
$500$	−1.75520	−	0.958786i	−0.0784950	−	0.0428782i
$501$	−7.76986	−	7.76986i	−0.347132	−	0.347132i
$502$	2.64889	+	18.4341i	0.118226	+	0.822756i
$503$		−	37.4924i		−	1.67170i	−0.548954	−	0.835852i	$-0.684974\pi$
$503$		−	37.4924i		−	1.67170i	0.548954	−	0.835852i	$-0.315026\pi$
$504$	4.22590	−	11.3216i	0.188237	−	0.504303i
$505$		−	4.22811i		−	0.188148i
$506$	−48.9695	+	7.03665i	−2.17696	+	0.312817i
$507$	−14.1146	−	14.1146i	−0.626852	−	0.626852i
$508$	1.10760	+	3.77443i	0.0491418	+	0.167463i
$509$	27.7592	−	27.7592i	1.23040	−	1.23040i	0.266595	−	0.963809i	$-0.414101\pi$
$509$	27.7592	−	27.7592i	1.23040	−	1.23040i	0.963809	−	0.266595i	$-0.0858987\pi$
$510$	−0.181198	−	0.135667i	−0.00802359	−	0.00600741i
$511$	−1.63585			−0.0723658
$512$	−19.8676	+	10.8295i	−0.878032	+	0.478602i
$513$	−6.11754			−0.270096
$514$	−9.83225	−	7.36159i	−0.433682	−	0.324706i
$515$	11.8929	−	11.8929i	0.524062	−	0.524062i
$516$	−0.203670	−	0.694056i	−0.00896605	−	0.0305541i
$517$	0.221493	+	0.221493i	0.00974126	+	0.00974126i
$518$	−5.66044	+	0.813376i	−0.248706	+	0.0357377i
$519$		−	3.82694i		−	0.167984i
$520$	−5.67851	+	15.2133i	−0.249019	+	0.667145i
$521$			10.0782i			0.441533i	0.975327	+	0.220767i	$0.0708559\pi$
$521$			10.0782i			0.441533i	−0.975327	+	0.220767i	$0.929144\pi$
$522$	−0.506556	−	3.52522i	−0.0221713	−	0.154295i
$523$	8.16934	+	8.16934i	0.357220	+	0.357220i	0.862787	−	0.505567i	$-0.168717\pi$
$523$	8.16934	+	8.16934i	0.357220	+	0.357220i	−0.505567	+	0.862787i	$0.668717\pi$
$524$	−2.11710	−	1.15648i	−0.0924861	−	0.0505209i
$525$	−3.02114	+	3.02114i	−0.131853	+	0.131853i
$526$	−4.39880	+	5.87510i	−0.191797	+	0.256167i
$527$	1.14808			0.0500111
$528$	−14.0073	+	8.99549i	−0.609592	+	0.391478i
$529$	−47.6548			−2.07195
$530$	−3.45478	+	4.61426i	−0.150066	+	0.200430i
$531$	−5.63594	+	5.63594i	−0.244579	+	0.244579i
$532$	−25.0602	+	45.8764i	−1.08650	+	1.98899i
$533$	16.1018	+	16.1018i	0.697445	+	0.697445i
$534$	2.79578	+	19.4564i	0.120985	+	0.841961i
$535$			2.32563i			0.100546i
$536$	0.217853	+	0.477343i	0.00940983	+	0.0206181i
$537$			14.7203i			0.635226i
$538$	15.8260	−	2.27411i	0.682306	−	0.0980437i
$539$	−33.1200	−	33.1200i	−1.42658	−	1.42658i
$540$	1.91908	−	0.563151i	0.0825840	−	0.0242341i
$541$	1.98301	−	1.98301i	0.0852564	−	0.0852564i	−0.663192	−	0.748449i	$-0.730799\pi$
$541$	1.98301	−	1.98301i	0.0852564	−	0.0852564i	0.748449	+	0.663192i	$0.230799\pi$
$542$	21.3216	+	15.9639i	0.915840	+	0.685707i
$543$	−21.8909			−0.939428
$544$	0.903101	+	0.0649630i	0.0387201	+	0.00278526i
$545$	6.60470			0.282914
$546$	27.7689	+	20.7911i	1.18840	+	0.889776i
$547$	−14.5464	+	14.5464i	−0.621959	+	0.621959i	−0.946032	−	0.324073i	$-0.894948\pi$
$547$	−14.5464	+	14.5464i	−0.621959	+	0.621959i	0.324073	+	0.946032i	$0.394948\pi$
$548$	7.90704	−	2.32031i	0.337772	−	0.0991187i
$549$	4.48857	+	4.48857i	0.191568	+	0.191568i
$550$	5.82579	−	0.837134i	0.248412	−	0.0356955i
$551$			15.4059i			0.656313i
$552$	−21.6287	+	9.87107i	−0.920579	+	0.420141i
$553$			65.4721i			2.78416i
$554$	−1.05799	−	7.36276i	−0.0449496	−	0.312814i
$555$	−0.669226	−	0.669226i	−0.0284071	−	0.0284071i
$556$	−7.78160	+	14.2454i	−0.330013	+	0.604139i
$557$	−25.6935	+	25.6935i	−1.08867	+	1.08867i	−0.0930007	+	0.995666i	$0.529646\pi$
$557$	−25.6935	+	25.6935i	−1.08867	+	1.08867i	−0.995666	+	0.0930007i	$0.970354\pi$
$558$	−6.07968	+	8.12011i	−0.257373	+	0.343752i
$559$	2.07636			0.0878206
$560$	3.63824	−	16.6984i	0.153744	−	0.705635i
$561$	0.666131			0.0281241
$562$	9.34253	−	12.4780i	0.394091	−	0.526354i
$563$	−15.8673	+	15.8673i	−0.668729	+	0.668729i	−0.957422	−	0.288693i	$-0.906779\pi$
$563$	−15.8673	+	15.8673i	−0.668729	+	0.668729i	0.288693	+	0.957422i	$0.406779\pi$
$564$	0.132107	+	0.0721638i	0.00556269	+	0.00303864i
$565$	3.53930	+	3.53930i	0.148900	+	0.148900i
$566$	−2.99289	−	20.8281i	−0.125801	−	0.875472i
$567$		−	4.27253i		−	0.179430i
$568$	32.0996	+	11.9815i	1.34687	+	0.502733i
$569$			45.0379i			1.88809i	0.329819	+	0.944044i	$0.393012\pi$
$569$			45.0379i			1.88809i	−0.329819	+	0.944044i	$0.606988\pi$
$570$	−8.56355	+	1.23054i	−0.358688	+	0.0515415i
$571$	23.0995	+	23.0995i	0.966684	+	0.966684i	0.999463	−	0.0327783i	$-0.0104355\pi$
$571$	23.0995	+	23.0995i	0.966684	+	0.966684i	−0.0327783	+	0.999463i	$0.510436\pi$
$572$	−13.4556	−	45.8533i	−0.562607	−	1.91722i
$573$	3.35979	−	3.35979i	0.140357	−	0.140357i
$574$	−19.1843	−	14.3636i	−0.800736	−	0.599526i
$575$	8.40564			0.350540
$576$	−5.24186	+	6.04342i	−0.218411	+	0.251809i
$577$	−10.3572			−0.431178			−0.215589	−	0.976484i	$-0.569167\pi$
$577$	−10.3572			−0.431178			−0.215589	+	0.976484i	$0.569167\pi$
$578$	19.2161	+	14.3875i	0.799286	+	0.598440i
$579$	−8.33786	+	8.33786i	−0.346510	+	0.346510i
$580$	−1.41819	−	4.83284i	−0.0588871	−	0.200673i
$581$	−23.6938	−	23.6938i	−0.982986	−	0.982986i
$582$	−15.2580	+	2.19250i	−0.632466	+	0.0908820i
$583$		−	16.9632i		−	0.702543i
$584$	1.01456	+	0.378697i	0.0419830	+	0.0156706i
$585$			5.74117i			0.237368i
$586$	−4.42753	−	30.8120i	−0.182899	−	1.27283i
$587$	−23.6336	−	23.6336i	−0.975462	−	0.975462i	0.0242436	−	0.999706i	$-0.492282\pi$
$587$	−23.6336	−	23.6336i	−0.975462	−	0.975462i	−0.999706	+	0.0242436i	$0.992282\pi$
$588$	−19.7540	−	10.7907i	−0.814641	−	0.445001i
$589$	31.0279	−	31.0279i	1.27848	−	1.27848i
$590$	−6.75572	+	9.02305i	−0.278129	+	0.371473i
$591$	6.45226			0.265411
$592$	3.69894	+	0.805924i	0.152025	+	0.0331233i
$593$	−30.5649			−1.25515			−0.627575	−	0.778556i	$-0.715952\pi$
$593$	−30.5649			−1.25515			−0.627575	+	0.778556i	$0.715952\pi$
$594$	−3.52751	+	4.71140i	−0.144735	+	0.193311i
$595$	−0.483562	+	0.483562i	−0.0198241	+	0.0198241i
$596$	13.5093	−	24.7307i	0.553361	−	1.01301i
$597$	2.54744	+	2.54744i	0.104260	+	0.104260i
$598$	−9.70710	−	67.5536i	−0.396953	−	2.76247i
$599$			10.2816i			0.420096i	0.977691	+	0.210048i	$0.0673620\pi$
$599$			10.2816i			0.420096i	−0.977691	+	0.210048i	$0.932638\pi$
$600$	2.57312	−	1.17434i	0.105047	−	0.0479422i
$601$		−	22.9223i		−	0.935021i	−0.883987	−	0.467511i	$-0.845151\pi$
$601$		−	22.9223i		−	0.935021i	0.883987	−	0.467511i	$-0.154849\pi$
$602$	−2.16304	+	0.310817i	−0.0881589	+	0.0126680i
$603$	0.131176	+	0.131176i	0.00534192	+	0.00534192i
$604$	7.71244	−	2.26320i	0.313815	−	0.0920884i
$605$	−4.46912	+	4.46912i	−0.181696	+	0.181696i
$606$	4.78650	+	3.58374i	0.194438	+	0.145580i
$607$	39.7832			1.61475			0.807374	−	0.590040i	$-0.200888\pi$
$607$	39.7832			1.61475			0.807374	+	0.590040i	$0.200888\pi$
$608$	26.1628	−	22.6514i	1.06104	−	0.918636i
$609$	−10.7596			−0.436000
$610$	7.18613	+	5.38039i	0.290958	+	0.217846i
$611$	−0.305551	+	0.305551i	−0.0123613	+	0.0123613i
$612$	0.307167	−	0.0901377i	0.0124165	−	0.00364360i
$613$	−26.9534	−	26.9534i	−1.08864	−	1.08864i	−0.995669	−	0.0929665i	$-0.970365\pi$
$613$	−26.9534	−	26.9534i	−1.08864	−	1.08864i	−0.0929665	−	0.995669i	$-0.529635\pi$
$614$	−38.9589	+	5.59819i	−1.57225	+	0.225924i
$615$		−	3.96632i		−	0.159937i
$616$	20.8812	+	45.7533i	0.841330	+	1.84345i
$617$			12.2306i			0.492385i	0.969221	+	0.246193i	$0.0791795\pi$
$617$			12.2306i			0.492385i	−0.969221	+	0.246193i	$0.920820\pi$
$618$	3.38313	+	23.5439i	0.136089	+	0.947074i
$619$	−4.13984	−	4.13984i	−0.166394	−	0.166394i	0.618998	−	0.785392i	$-0.287539\pi$
$619$	−4.13984	−	4.13984i	−0.166394	−	0.166394i	−0.785392	+	0.618998i	$0.787539\pi$
$620$	−6.87720	+	12.5897i	−0.276195	+	0.505616i
$621$	−5.94369	+	5.94369i	−0.238512	+	0.238512i
$622$	−10.0798	+	13.4628i	−0.404164	+	0.539807i
$623$	59.3843			2.37918
$624$	−12.4093	−	19.3232i	−0.496770	−	0.773547i
$625$	−1.00000			−0.0400000
$626$	8.14706	−	10.8813i	0.325622	−	0.434906i
$627$	18.0028	−	18.0028i	0.718962	−	0.718962i
$628$	−22.6990	−	12.3994i	−0.905787	−	0.494790i
$629$	−0.107116	−	0.107116i	−0.00427100	−	0.00427100i
$630$	−0.859415	−	5.98084i	−0.0342399	−	0.238283i
$631$			25.3923i			1.01085i	0.862870	+	0.505426i	$0.168664\pi$
$631$			25.3923i			1.01085i	−0.862870	+	0.505426i	$0.831336\pi$
$632$	15.1567	−	40.6062i	0.602901	−	1.61523i
$633$			1.37941i			0.0548266i
$634$	−16.0363	+	2.30433i	−0.636881	+	0.0915164i
$635$	1.39073	+	1.39073i	0.0551895	+	0.0551895i
$636$	−2.29538	−	7.82208i	−0.0910176	−	0.310166i
$637$	45.6892	−	45.6892i	1.81027	−	1.81027i
$638$	11.8648	+	8.88337i	0.469731	+	0.351696i
$639$	12.1137			0.479212
$640$	−6.12211	+	9.51419i	−0.241998	+	0.376081i
$641$	42.0683			1.66160			0.830799	−	0.556572i	$-0.187884\pi$
$641$	42.0683			1.66160			0.830799	+	0.556572i	$0.187884\pi$
$642$	−2.63277	−	1.97121i	−0.103907	−	0.0777973i
$643$	−8.73724	+	8.73724i	−0.344563	+	0.344563i	−0.858080	−	0.513517i	$-0.828343\pi$
$643$	−8.73724	+	8.73724i	−0.344563	+	0.344563i	0.513517	+	0.858080i	$0.328343\pi$
$644$	20.2247	+	68.9206i	0.796963	+	2.71585i
$645$	−0.255733	−	0.255733i	−0.0100695	−	0.0100695i
$646$	−1.37068	+	0.196959i	−0.0539287	+	0.00774926i
$647$			4.04843i			0.159160i	0.996828	+	0.0795802i	$0.0253580\pi$
$647$			4.04843i			0.159160i	−0.996828	+	0.0795802i	$0.974642\pi$
$648$	−0.989085	+	2.64985i	−0.0388549	+	0.104096i
$649$		−	33.1710i		−	1.30208i
$650$	1.15483	+	8.03670i	0.0452962	+	0.315225i
$651$	21.6701	+	21.6701i	0.849317	+	0.849317i
$652$	−0.859086	−	0.469279i	−0.0336444	−	0.0183784i
$653$	−12.8095	+	12.8095i	−0.501275	+	0.501275i	−0.911834	−	0.410559i	$-0.865334\pi$
$653$	−12.8095	+	12.8095i	−0.501275	+	0.501275i	0.410559	+	0.911834i	$0.365334\pi$
$654$	−5.59814	+	7.47697i	−0.218905	+	0.292373i
$655$	−1.20619			−0.0471297
$656$	8.57304	+	13.3495i	0.334721	+	0.521212i
$657$	0.382876			0.0149374
$658$	0.272568	−	0.364045i	0.0106258	−	0.0141920i
$659$	−29.8196	+	29.8196i	−1.16161	+	1.16161i	−0.177481	+	0.984124i	$0.556795\pi$
$659$	−29.8196	+	29.8196i	−1.16161	+	1.16161i	−0.984124	+	0.177481i	$0.943205\pi$
$660$	−3.99024	+	7.30473i	−0.155320	+	0.284336i
$661$	−30.2458	−	30.2458i	−1.17642	−	1.17642i	−0.980649	−	0.195775i	$-0.937278\pi$
$661$	−30.2458	−	30.2458i	−1.17642	−	1.17642i	−0.195775	−	0.980649i	$-0.562722\pi$
$662$	3.79101	+	26.3824i	0.147342	+	1.02538i
$663$			0.918931i			0.0356883i
$664$	9.20997	+	20.1801i	0.357416	+	0.783141i
$665$			26.1374i			1.01357i
$666$	1.32484	−	0.190373i	0.0513367	−	0.00737681i
$667$	14.9681	+	14.9681i	0.579566	+	0.579566i
$668$	21.0873	−	6.18804i	0.815892	−	0.239422i
$669$	3.29754	−	3.29754i	0.127490	−	0.127490i
$670$	0.210011	+	0.157239i	0.00811345	+	0.00607469i
$671$	−26.4181			−1.01986
$672$	15.8199	+	18.2723i	0.610266	+	0.704868i
$673$	38.3587			1.47862			0.739309	−	0.673366i	$-0.235152\pi$
$673$	38.3587			1.47862			0.739309	+	0.673366i	$0.235152\pi$
$674$	−36.9918	−	27.6964i	−1.42487	−	1.06683i
$675$	0.707107	−	0.707107i	0.0272166	−	0.0272166i
$676$	38.3069	−	11.2411i	1.47334	−	0.432350i
$677$	−19.3263	−	19.3263i	−0.742772	−	0.742772i	0.230339	−	0.973111i	$-0.426017\pi$
$677$	−19.3263	−	19.3263i	−0.742772	−	0.742772i	−0.973111	+	0.230339i	$0.926017\pi$
$678$	−7.00664	+	1.00682i	−0.269088	+	0.0386665i
$679$			46.5701i			1.78720i
$680$	0.411852	−	0.187964i	0.0157938	−	0.00720810i
$681$			2.28680i			0.0876302i
$682$	−6.00461	−	41.7873i	−0.229929	−	1.60012i
$683$	21.3741	+	21.3741i	0.817856	+	0.817856i	0.985797	−	0.167941i	$-0.0537119\pi$
$683$	21.3741	+	21.3741i	0.817856	+	0.817856i	−0.167941	+	0.985797i	$0.553712\pi$
$684$	5.86541	−	10.7375i	0.224270	−	0.410559i
$685$	2.91344	−	2.91344i	0.111317	−	0.111317i
$686$	−15.4074	+	20.5784i	−0.588258	+	0.785686i
$687$	12.9384			0.493630
$688$	1.41348	+	0.307970i	0.0538885	+	0.0117412i
$689$	23.4008			0.891499
$690$	−7.12462	+	9.51575i	−0.271230	+	0.362258i
$691$	3.96331	−	3.96331i	0.150771	−	0.150771i	−0.627691	−	0.778462i	$-0.716000\pi$
$691$	3.96331	−	3.96331i	0.150771	−	0.150771i	0.778462	+	0.627691i	$0.216000\pi$
$692$	6.71704	+	3.66921i	0.255344	+	0.139482i
$693$	12.5733	+	12.5733i	0.477619	+	0.477619i
$694$	−6.39762	−	44.5223i	−0.242850	−	1.69004i
$695$			8.11610i			0.307861i
$696$	6.67315	+	2.49083i	0.252945	+	0.0944145i
$697$		−	0.634848i		−	0.0240466i
$698$	44.8625	−	6.44650i	1.69807	−	0.244004i
$699$	7.28334	+	7.28334i	0.275481	+	0.275481i
$700$	−2.40608	−	8.19933i	−0.0909413	−	0.309905i
$701$	−27.4177	+	27.4177i	−1.03555	+	1.03555i	−0.0362086	+	0.999344i	$0.511528\pi$
$701$	−27.4177	+	27.4177i	−1.03555	+	1.03555i	−0.999344	+	0.0362086i	$0.988472\pi$
$702$	−6.49939	−	4.86622i	−0.245304	−	0.183663i
$703$	−5.78982			−0.218367
$704$	−2.35885	−	33.2105i	−0.0889024	−	1.25167i
$705$	0.0752658			0.00283468
$706$	12.0391	+	9.01393i	0.453099	+	0.339244i
$707$	12.7737	−	12.7737i	0.480404	−	0.480404i
$708$	−4.48855	−	15.2959i	−0.168690	−	0.574854i
$709$	36.8453	+	36.8453i	1.38376	+	1.38376i	0.837840	+	0.545915i	$0.183818\pi$
$709$	36.8453	+	36.8453i	1.38376	+	1.38376i	0.545915	+	0.837840i	$0.316182\pi$
$710$	16.9572	−	2.43666i	0.636394	−	0.0914464i
$711$		−	15.3239i		−	0.574693i
$712$	−36.8305	−	13.7474i	−1.38028	−	0.515204i
$713$		−	60.2922i		−	2.25796i
$714$	−0.137558	−	0.957292i	−0.00514797	−	0.0358258i
$715$	−16.8952	−	16.8952i	−0.631845	−	0.631845i
$716$	−25.8370	−	14.1136i	−0.965575	−	0.527449i
$717$	2.64334	−	2.64334i	0.0987175	−	0.0987175i
$718$	−14.4254	+	19.2668i	−0.538351	+	0.719030i
$719$	−26.8739			−1.00223			−0.501114	−	0.865382i	$-0.667076\pi$
$719$	−26.8739			−1.00223			−0.501114	+	0.865382i	$0.667076\pi$
$720$	−0.851542	+	3.90831i	−0.0317351	+	0.145654i
$721$	71.8599			2.67620
$722$	−15.6164	+	20.8576i	−0.581184	+	0.776238i
$723$	−6.60638	+	6.60638i	−0.245694	+	0.245694i
$724$	20.9887	−	38.4229i	0.780038	−	1.42798i
$725$	−1.78072	−	1.78072i	−0.0661341	−	0.0661341i
$726$	−1.27132	−	8.84737i	−0.0471831	−	0.328357i
$727$		−	9.81023i		−	0.363841i	−0.983313	−	0.181921i	$-0.941769\pi$
$727$		−	9.81023i		−	0.363841i	0.983313	−	0.181921i	$-0.0582314\pi$
$728$	−63.1169	+	28.8058i	−2.33927	+	1.06761i
$729$			1.00000i			0.0370370i
$730$	0.535963	−	0.0770151i	0.0198369	−	0.00285046i
$731$	−0.0409325	−	0.0409325i	−0.00151394	−	0.00151394i
$732$	−12.1819	+	3.57477i	−0.450257	+	0.132127i
$733$	−1.66941	+	1.66941i	−0.0616610	+	0.0616610i	−0.737265	−	0.675604i	$-0.763883\pi$
$733$	−1.66941	+	1.66941i	−0.0616610	+	0.0616610i	0.675604	+	0.737265i	$0.263883\pi$
$734$	29.0986	+	21.7867i	1.07405	+	0.804160i
$735$	−11.2545			−0.415130
$736$	3.41157	−	47.4270i	0.125752	−	1.74818i
$737$	−0.772055			−0.0284390
$738$	4.49014	+	3.36185i	0.165284	+	0.123751i
$739$	36.2208	−	36.2208i	1.33240	−	1.33240i	0.429191	−	0.903214i	$-0.358799\pi$
$739$	36.2208	−	36.2208i	1.33240	−	1.33240i	0.903214	−	0.429191i	$-0.141201\pi$
$740$	1.81627	−	0.532982i	0.0667675	−	0.0195928i
$741$	24.8349	+	24.8349i	0.912334	+	0.912334i
$742$	−24.3777	+	3.50294i	−0.894932	+	0.128597i
$743$			32.7601i			1.20185i	0.799305	+	0.600926i	$0.205201\pi$
$743$			32.7601i			1.20185i	−0.799305	+	0.600926i	$0.794799\pi$
$744$	−8.42332	−	18.4565i	−0.308814	−	0.676648i
$745$		−	14.0900i		−	0.516217i
$746$	4.18993	+	29.1586i	0.153404	+	1.06757i
$747$	5.54562	+	5.54562i	0.202903	+	0.202903i
$748$	−0.638677	+	1.16919i	−0.0233523	+	0.0427500i
$749$	−7.02606	+	7.02606i	−0.256727	+	0.256727i
$750$	0.847599	−	1.13207i	0.0309500	−	0.0413372i
$751$	8.98910			0.328017			0.164008	−	0.986459i	$-0.447558\pi$
$751$	8.98910			0.328017			0.164008	+	0.986459i	$0.447558\pi$
$752$	−0.253324	+	0.162684i	−0.00923777	+	0.00593248i
$753$	−13.1688			−0.479897
$754$	−12.2547	+	16.3675i	−0.446288	+	0.596069i
$755$	2.84174	−	2.84174i	0.103421	−	0.103421i
$756$	7.49916	+	4.09644i	0.272742	+	0.148986i
$757$	27.4805	+	27.4805i	0.998796	+	0.998796i	0.999999	−	0.00120342i	$-0.000383062\pi$
$757$	27.4805	+	27.4805i	0.998796	+	0.998796i	−0.00120342	+	0.999999i	$0.500383\pi$
$758$	−2.84871	−	19.8248i	−0.103470	−	0.720068i
$759$		−	34.9823i		−	1.26978i
$760$	6.05077	−	16.2106i	0.219485	−	0.588019i
$761$		−	1.80961i		−	0.0655984i	−0.999462	−	0.0327992i	$-0.989558\pi$
$761$		−	1.80961i		−	0.0655984i	0.999462	−	0.0327992i	$-0.0104422\pi$
$762$	−2.75319	+	0.395618i	−0.0997374	+	0.0143317i
$763$	19.9537	+	19.9537i	0.722373	+	0.722373i
$764$	2.67579	+	9.11842i	0.0968065	+	0.329893i
$765$	0.113179	−	0.113179i	0.00409201	−	0.00409201i
$766$	31.9055	+	23.8882i	1.15279	+	0.863117i
$767$	45.7596			1.65228
$768$	−5.58160	−	14.9949i	−0.201409	−	0.541080i
$769$	41.3952			1.49275			0.746374	−	0.665527i	$-0.231793\pi$
$769$	41.3952			1.49275			0.746374	+	0.665527i	$0.231793\pi$
$770$	20.1296	+	15.0714i	0.725421	+	0.543136i
$771$	6.14138	−	6.14138i	0.221176	−	0.221176i
$772$	−6.64040	−	22.6288i	−0.238993	−	0.814430i
$773$	20.2439	+	20.2439i	0.728122	+	0.728122i	0.970246	−	0.242123i	$-0.0778438\pi$
$773$	20.2439	+	20.2439i	0.728122	+	0.728122i	−0.242123	+	0.970246i	$0.577844\pi$
$774$	0.506266	−	0.0727477i	0.0181974	−	0.00261486i
$775$			7.17282i			0.257655i
$776$	10.7809	−	28.8831i	0.387012	−	1.03684i
$777$		−	4.04365i		−	0.145065i
$778$	3.17326	+	22.0834i	0.113767	+	0.791727i
$779$	−17.1573	−	17.1573i	−0.614725	−	0.614725i
$780$	−10.0769	−	5.50456i	−0.360811	−	0.197095i
$781$	−35.6484	+	35.6484i	−1.27560	+	1.27560i
$782$	−1.14036	+	1.52309i	−0.0407793	+	0.0544655i
$783$	2.51831			0.0899971
$784$	37.8797	−	24.3263i	1.35285	−	0.868795i
$785$	−12.9324			−0.461577
$786$	1.02236	−	1.36549i	0.0364665	−	0.0487053i
$787$	−36.5446	+	36.5446i	−1.30267	+	1.30267i	−0.376091	+	0.926583i	$0.622732\pi$
$787$	−36.5446	+	36.5446i	−1.30267	+	1.30267i	−0.926583	+	0.376091i	$0.877268\pi$
$788$	−6.18634	+	11.3250i	−0.220379	+	0.403437i
$789$	−3.66968	−	3.66968i	−0.130644	−	0.130644i
$790$	−3.08239	−	21.4510i	−0.109667	−	0.763193i
$791$			21.3854i			0.760379i
$792$	−4.88732	−	10.7087i	−0.173663	−	0.380517i
$793$		−	36.4438i		−	1.29416i
$794$	−5.90368	+	0.848328i	−0.209514	+	0.0301060i
$795$	−2.88214	−	2.88214i	−0.102219	−	0.102219i
$796$	−6.91371	+	2.02882i	−0.245050	+	0.0719095i
$797$	−12.7215	+	12.7215i	−0.450619	+	0.450619i	−0.895560	−	0.444941i	$-0.853225\pi$
$797$	−12.7215	+	12.7215i	−0.450619	+	0.450619i	0.444941	+	0.895560i	$0.353225\pi$
$798$	−29.5893	−	22.1541i	−1.04745	−	0.784245i
$799$	0.0120470			0.000426193
$800$	−0.405867	+	5.64228i	−0.0143496	+	0.199485i
$801$	−13.8991			−0.491100
$802$	18.1013	+	13.5528i	0.639181	+	0.478566i
$803$	−1.12673	+	1.12673i	−0.0397615	+	0.0397615i
$804$	−0.356011	+	0.104471i	−0.0125555	+	0.00368440i
$805$	25.3946	+	25.3946i	0.895042	+	0.895042i
$806$	57.6458	−	8.28339i	2.03049	−	0.291770i
$807$			11.3056i			0.397975i
$808$	−10.8794	+	4.96523i	−0.382736	+	0.174676i
$809$		−	5.24547i		−	0.184421i	−0.995740	−	0.0922105i	$-0.970607\pi$
$809$		−	5.24547i		−	0.184421i	0.995740	−	0.0922105i	$-0.0293933\pi$
$810$	0.201149	+	1.39984i	0.00706765	+	0.0491852i
$811$	−2.66407	−	2.66407i	−0.0935481	−	0.0935481i	0.658784	−	0.752332i	$-0.271071\pi$
$811$	−2.66407	−	2.66407i	−0.0935481	−	0.0935481i	−0.752332	+	0.658784i	$0.771071\pi$
$812$	10.3161	−	18.8852i	0.362025	−	0.662741i
$813$	−13.3178	+	13.3178i	−0.467075	+	0.467075i
$814$	−3.33854	+	4.45900i	−0.117016	+	0.156288i
$815$	−0.489452			−0.0171447
$816$	−0.136298	+	0.625563i	−0.00477137	+	0.0218991i
$817$	−2.21248			−0.0774047
$818$	23.3183	−	31.1443i	0.815305	−	1.08893i
$819$	−17.3449	+	17.3449i	−0.606079	+	0.606079i
$820$	6.96169	+	3.80285i	0.243113	+	0.132801i
$821$	1.11276	+	1.11276i	0.0388357	+	0.0388357i	0.726258	−	0.687422i	$-0.241258\pi$
$821$	1.11276	+	1.11276i	0.0388357	+	0.0388357i	−0.687422	+	0.726258i	$0.741258\pi$
$822$	0.828779	+	5.76764i	0.0289070	+	0.201170i
$823$		−	11.7558i		−	0.409781i	−0.978785	−	0.204891i	$-0.934316\pi$
$823$		−	11.7558i		−	0.409781i	0.978785	−	0.204891i	$-0.0656838\pi$
$824$	−44.5679	−	16.6355i	−1.55260	−	0.579524i
$825$			4.16177i			0.144894i
$826$	−47.6698	+	6.84990i	−1.65865	+	0.238339i
$827$	−30.1964	−	30.1964i	−1.05003	−	1.05003i	−0.998681	−	0.0513511i	$-0.983647\pi$
$827$	−30.1964	−	30.1964i	−1.05003	−	1.05003i	−0.0513511	−	0.998681i	$-0.516353\pi$
$828$	−4.73364	−	16.1311i	−0.164505	−	0.560594i
$829$	0.0724462	−	0.0724462i	0.00251616	−	0.00251616i	−0.705848	−	0.708364i	$-0.749434\pi$
$829$	0.0724462	−	0.0724462i	0.00251616	−	0.00251616i	0.708364	+	0.705848i	$0.249434\pi$
$830$	8.87844	+	6.64746i	0.308175	+	0.230737i
$831$	5.25973			0.182458
$832$	45.8140	−	3.25404i	1.58831	−	0.112814i
$833$	−1.80140			−0.0624148
$834$	−9.18797	−	6.87920i	−0.318153	−	0.238207i
$835$	7.76986	−	7.76986i	0.268887	−	0.268887i
$836$	14.3377	+	48.8593i	0.495879	+	1.68983i
$837$	−5.07195	−	5.07195i	−0.175312	−	0.175312i
$838$	−3.87849	+	0.557318i	−0.133980	+	0.0192522i
$839$			7.91971i			0.273419i	0.990611	+	0.136709i	$0.0436527\pi$
$839$			7.91971i			0.273419i	−0.990611	+	0.136709i	$0.956347\pi$
$840$	11.3216	+	4.22590i	0.390632	+	0.145807i
$841$			22.6581i			0.781314i
$842$	−1.77435	−	12.3480i	−0.0611480	−	0.425541i
$843$	7.79397	+	7.79397i	0.268439	+	0.268439i
$844$	−2.42114	−	1.32256i	−0.0833391	−	0.0455243i
$845$	14.1146	−	14.1146i	0.485558	−	0.485558i
$846$	−0.0637953	+	0.0852060i	−0.00219333	+	0.00292944i
$847$	−27.0037			−0.927857
$848$	15.9301	+	3.47085i	0.547042	+	0.119189i
$849$	14.8790			0.510646
$850$	0.135667	−	0.181198i	0.00465332	−	0.00621505i
$851$	−5.62528	+	5.62528i	−0.192832	+	0.192832i
$852$	−11.6145	+	21.2620i	−0.397905	+	0.728425i
$853$	−14.1305	−	14.1305i	−0.483817	−	0.483817i	0.422531	−	0.906348i	$-0.361142\pi$
$853$	−14.1305	−	14.1305i	−0.483817	−	0.483817i	−0.906348	+	0.422531i	$0.861142\pi$
$854$	5.45540	+	37.9652i	0.186680	+	1.29914i
$855$		−	6.11754i		−	0.209216i
$856$	5.98413	−	2.73108i	0.204533	−	0.0933465i
$857$		−	4.80762i		−	0.164225i	−0.996623	−	0.0821126i	$-0.973833\pi$
$857$		−	4.80762i		−	0.164225i	0.996623	−	0.0821126i	$-0.0261667\pi$
$858$	33.4469	−	4.80613i	1.14186	−	0.164079i
$859$	−34.8123	−	34.8123i	−1.18778	−	1.18778i	−0.977680	−	0.210101i	$-0.932621\pi$
$859$	−34.8123	−	34.8123i	−1.18778	−	1.18778i	−0.210101	−	0.977680i	$-0.567379\pi$
$860$	0.694056	−	0.203670i	0.0236671	−	0.00694508i
$861$	11.9828	−	11.9828i	0.408373	−	0.408373i
$862$	−6.65859	−	4.98541i	−0.226793	−	0.169804i
$863$	−51.5605			−1.75514			−0.877570	−	0.479449i	$-0.840837\pi$
$863$	−51.5605			−1.75514			−0.877570	+	0.479449i	$0.840837\pi$
$864$	−3.70270	−	4.27668i	−0.125968	−	0.145496i
$865$	3.82694			0.130120
$866$	7.22066	+	5.40624i	0.245368	+	0.183712i
$867$	−12.0027	+	12.0027i	−0.407633	+	0.407633i
$868$	−58.8123	+	17.2584i	−1.99622	+	0.585788i
$869$	45.0955	+	45.0955i	1.52976	+	1.52976i
$870$	3.52522	−	0.506556i	0.119516	−	0.0171738i
$871$		−	1.06505i		−	0.0360880i
$872$	−7.75616	−	16.9947i	−0.262657	−	0.575512i
$873$		−	10.8999i		−	0.368905i
$874$	10.3435	+	71.9822i	0.349872	+	2.43483i
$875$	−3.02114	−	3.02114i	−0.102133	−	0.102133i
$876$	−0.367096	+	0.672024i	−0.0124030	+	0.0227056i
$877$	−12.4082	+	12.4082i	−0.418994	+	0.418994i	−0.884857	−	0.465863i	$-0.845744\pi$
$877$	−12.4082	+	12.4082i	−0.418994	+	0.418994i	0.465863	+	0.884857i	$0.345744\pi$
$878$	31.6069	−	42.2146i	1.06668	−	1.42467i
$879$	22.0112			0.742419
$880$	−8.99549	−	14.0073i	−0.303238	−	0.472188i
$881$	−45.7147			−1.54017			−0.770084	−	0.637942i	$-0.779786\pi$
$881$	−45.7147			−1.54017			−0.770084	+	0.637942i	$0.779786\pi$
$882$	9.53935	−	12.7409i	0.321207	−	0.429009i
$883$	−8.68322	+	8.68322i	−0.292213	+	0.292213i	−0.837954	−	0.545741i	$-0.816248\pi$
$883$	−8.68322	+	8.68322i	−0.292213	+	0.292213i	0.545741	+	0.837954i	$0.316248\pi$
$884$	−1.61291	−	0.881058i	−0.0542480	−	0.0296332i
$885$	−5.63594	−	5.63594i	−0.189450	−	0.189450i
$886$	−8.08565	−	56.2697i	−0.271643	−	1.89042i
$887$			5.87579i			0.197290i	0.995123	+	0.0986449i	$0.0314508\pi$
$887$			5.87579i			0.197290i	−0.995123	+	0.0986449i	$0.968549\pi$
$888$	−0.936099	+	2.50790i	−0.0314134	+	0.0841595i
$889$			8.40319i			0.281834i
$890$	−19.4564	+	2.79578i	−0.652180	+	0.0937148i
$891$	−2.94281	−	2.94281i	−0.0985879	−	0.0985879i
$892$	2.62621	+	8.94948i	0.0879321	+	0.299651i
$893$	0.325582	−	0.325582i	0.0108952	−	0.0108952i
$894$	15.9508	+	11.9427i	0.533474	+	0.399422i
$895$	−14.7203			−0.492044
$896$	−47.2394	+	10.2479i	−1.57816	+	0.342359i
$897$	48.2583			1.61130
$898$	−13.5461	−	10.1422i	−0.452039	−	0.338450i
$899$	−12.7727	+	12.7727i	−0.425995	+	0.425995i
$900$	0.563151	+	1.91908i	0.0187717	+	0.0639693i
$901$	−0.461314	−	0.461314i	−0.0153686	−	0.0153686i
$902$	−23.1069	+	3.32034i	−0.769377	+	0.110555i
$903$		−	1.54521i		−	0.0514213i
$904$	4.95070	−	13.2634i	0.164658	−	0.441133i
$905$		−	21.8909i		−	0.727678i
$906$	0.808382	+	5.62569i	0.0268567	+	0.186901i
$907$	0.656960	+	0.656960i	0.0218140	+	0.0218140i	0.717930	−	0.696116i	$-0.245090\pi$
$907$	0.656960	+	0.656960i	0.0218140	+	0.0218140i	−0.696116	+	0.717930i	$0.745090\pi$
$908$	−4.01379	−	2.19255i	−0.133202	−	0.0727622i
$909$	−2.98972	+	2.98972i	−0.0991629	+	0.0991629i
$910$	−20.7911	+	27.7689i	−0.689217	+	0.920530i
$911$	−3.71828			−0.123192			−0.0615960	−	0.998101i	$-0.519619\pi$
$911$	−3.71828			−0.123192			−0.0615960	+	0.998101i	$0.519619\pi$
$912$	13.2228	+	20.5900i	0.437851	+	0.681801i
$913$	−32.6394			−1.08021
$914$	−28.0135	+	37.4153i	−0.926605	+	1.23759i
$915$	−4.48857	+	4.48857i	−0.148388	+	0.148388i
$916$	−12.4051	+	22.7095i	−0.409877	+	0.750341i
$917$	−3.64406	−	3.64406i	−0.120338	−	0.120338i
$918$	0.0321958	+	0.224057i	0.00106262	+	0.00739499i
$919$		−	33.0548i		−	1.09038i	−0.838313	−	0.545189i	$-0.816458\pi$
$919$		−	33.0548i		−	1.09038i	0.838313	−	0.545189i	$-0.183542\pi$
$920$	−9.87107	−	21.6287i	−0.325440	−	0.713077i
$921$		−	27.8311i		−	0.917064i
$922$	41.0270	−	5.89535i	1.35115	−	0.194153i
$923$	−49.1772	−	49.1772i	−1.61869	−	1.61869i
$924$	−34.1237	+	10.0135i	−1.12259	+	0.329421i
$925$	0.669226	−	0.669226i	0.0220040	−	0.0220040i
$926$	−16.1160	−	12.0664i	−0.529605	−	0.396525i
$927$	−16.8190			−0.552410
$928$	−10.7700	+	9.32455i	−0.353543	+	0.306093i
$929$	−17.6732			−0.579839			−0.289919	−	0.957051i	$-0.593629\pi$
$929$	−17.6732			−0.579839			−0.289919	+	0.957051i	$0.593629\pi$
$930$	−8.12011	−	6.07968i	−0.266269	−	0.199360i
$931$	−48.6844	+	48.6844i	−1.59557	+	1.59557i
$932$	−19.7669	+	5.80057i	−0.647486	+	0.190004i
$933$	−8.40905	−	8.40905i	−0.275300	−	0.275300i
$934$	−37.2159	+	5.34773i	−1.21774	+	0.174983i
$935$			0.666131i			0.0217848i
$936$	14.7727	−	6.74208i	0.482861	−	0.220372i
$937$		−	25.9902i		−	0.849061i	−0.905414	−	0.424531i	$-0.860439\pi$
$937$		−	25.9902i		−	0.849061i	0.905414	−	0.424531i	$-0.139561\pi$
$938$	0.159431	+	1.10952i	0.00520562	+	0.0362270i
$939$	6.79666	+	6.79666i	0.221801	+	0.221801i
$940$	−0.0721638	+	0.132107i	−0.00235372	+	0.00430884i
$941$	29.0860	−	29.0860i	0.948176	−	0.948176i	−0.0505455	−	0.998722i	$-0.516096\pi$
$941$	29.0860	−	29.0860i	0.948176	−	0.948176i	0.998722	+	0.0505455i	$0.0160960\pi$
$942$	10.9615	−	14.6403i	0.357145	−	0.477008i
$943$	−33.3395			−1.08568
$944$	31.1509	+	6.78715i	1.01387	+	0.220903i
$945$	4.27253			0.138986
$946$	−1.27576	+	1.70393i	−0.0414786	+	0.0553995i
$947$	30.8896	−	30.8896i	1.00378	−	1.00378i	0.00378509	−	0.999993i	$-0.498795\pi$
$947$	30.8896	−	30.8896i	1.00378	−	1.00378i	0.999993	−	0.00378509i	$-0.00120483\pi$
$948$	26.8966	+	14.6924i	0.873561	+	0.477186i
$949$	−1.55433	−	1.55433i	−0.0504558	−	0.0504558i
$950$	−1.23054	−	8.56355i	−0.0399239	−	0.277838i
$951$		−	11.4558i		−	0.371480i
$952$	1.81213	+	0.676397i	0.0587314	+	0.0219221i
$953$			51.5794i			1.67082i	0.549626	+	0.835411i	$0.314770\pi$
$953$			51.5794i			1.67082i	−0.549626	+	0.835411i	$0.685230\pi$
$954$	5.70567	−	0.819874i	0.184728	−	0.0265444i
$955$	3.35979	+	3.35979i	0.108720	+	0.108720i
$956$	2.10520	+	7.17400i	0.0680870	+	0.232024i
$957$	−7.41092	+	7.41092i	−0.239561	+	0.239561i
$958$	30.2463	+	22.6460i	0.977215	+	0.731659i
$959$	17.6038			0.568457
$960$	−6.04342	−	5.24186i	−0.195051	−	0.169180i
$961$	20.4493			0.659656
$962$	−6.15121	−	4.60553i	−0.198323	−	0.148488i
$963$	1.64447	−	1.64447i	0.0529924	−	0.0529924i
$964$	−5.26142	−	17.9296i	−0.169459	−	0.577474i
$965$	−8.33786	−	8.33786i	−0.268405	−	0.268405i
$966$	−50.2728	+	7.22394i	−1.61750	+	0.232426i
$967$			5.55245i			0.178555i	0.996007	+	0.0892774i	$0.0284558\pi$
$967$			5.55245i			0.178555i	−0.996007	+	0.0892774i	$0.971544\pi$
$968$	16.7478	+	6.25131i	0.538296	+	0.200925i
$969$		−	0.979172i		−	0.0314555i
$970$	−2.19250	−	15.2580i	−0.0703969	−	0.489906i
$971$	−30.5095	−	30.5095i	−0.979098	−	0.979098i	0.0206884	−	0.999786i	$-0.493414\pi$
$971$	−30.5095	−	30.5095i	−0.979098	−	0.979098i	−0.999786	+	0.0206884i	$0.993414\pi$
$972$	−1.75520	−	0.958786i	−0.0562981	−	0.0307531i
$973$	−24.5199	+	24.5199i	−0.786071	+	0.786071i
$974$	−22.9531	+	30.6564i	−0.735463	+	0.982296i
$975$	−5.74117			−0.183865
$976$	5.40542	−	24.8092i	0.173023	−	0.794122i
$977$	31.8649			1.01945			0.509723	−	0.860338i	$-0.329748\pi$
$977$	31.8649			1.01945			0.509723	+	0.860338i	$0.329748\pi$
$978$	0.414859	−	0.554092i	0.0132657	−	0.0177179i
$979$	40.9024	−	40.9024i	1.30725	−	1.30725i
$980$	10.7907	−	19.7540i	0.344696	−	0.631018i
$981$	−4.67023	−	4.67023i	−0.149109	−	0.149109i
$982$	−0.431070	−	2.99990i	−0.0137560	−	0.0957308i
$983$			24.2289i			0.772782i	0.922335	+	0.386391i	$0.126279\pi$
$983$			24.2289i			0.772782i	−0.922335	+	0.386391i	$0.873721\pi$
$984$	−10.2058	+	4.65780i	−0.325349	+	0.148485i
$985$			6.45226i			0.205586i
$986$	0.564246	−	0.0810791i	0.0179693	−	0.00258209i
$987$	0.227388	+	0.227388i	0.00723786	+	0.00723786i
$988$	−67.4016	+	19.7789i	−2.14433	+	0.629251i
$989$	−2.14960	+	2.14960i	−0.0683533	+	0.0683533i
$990$	−4.71140	−	3.52751i	−0.149738	−	0.112112i
$991$	38.9268			1.23655			0.618276	−	0.785961i	$-0.287832\pi$
$991$	38.9268			1.23655			0.618276	+	0.785961i	$0.287832\pi$
$992$	40.4710	+	2.91121i	1.28496	+	0.0924311i
$993$	−18.8468			−0.598085
$994$	58.5916	+	43.8686i	1.85841	+	1.39143i
$995$	−2.54744	+	2.54744i	−0.0807592	+	0.0807592i
$996$	−15.0507	+	4.41661i	−0.476901	+	0.139946i
$997$	−8.00046	−	8.00046i	−0.253377	−	0.253377i	0.568977	−	0.822354i	$-0.307340\pi$
$997$	−8.00046	−	8.00046i	−0.253377	−	0.253377i	−0.822354	+	0.568977i	$0.807340\pi$
$998$	−14.4716	+	2.07949i	−0.458090	+	0.0658251i
$999$			0.946429i			0.0299437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.181.2	yes	20
3.2	odd	2		720.2.t.d.181.9		20
4.3	odd	2		960.2.s.c.241.1		20
8.3	odd	2		1920.2.s.f.481.6		20
8.5	even	2		1920.2.s.e.481.5		20
12.11	even	2		2880.2.t.d.2161.1		20
16.3	odd	4		960.2.s.c.721.5		20
16.5	even	4		1920.2.s.e.1441.1		20
16.11	odd	4		1920.2.s.f.1441.10		20
16.13	even	4	inner	240.2.s.c.61.2	✓	20
48.29	odd	4		720.2.t.d.541.9		20
48.35	even	4		2880.2.t.d.721.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.2	✓	20	16.13	even	4	inner
240.2.s.c.181.2	yes	20	1.1	even	1	trivial
720.2.t.d.181.9		20	3.2	odd	2
720.2.t.d.541.9		20	48.29	odd	4
960.2.s.c.241.1		20	4.3	odd	2
960.2.s.c.721.5		20	16.3	odd	4
1920.2.s.e.481.5		20	8.5	even	2
1920.2.s.e.1441.1		20	16.5	even	4
1920.2.s.f.481.6		20	8.3	odd	2
1920.2.s.f.1441.10		20	16.11	odd	4
2880.2.t.d.721.5		20	48.35	even	4
2880.2.t.d.2161.1		20	12.11	even	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13207 - 0.847599i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.563151 + 1.91908i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.39984 + 0.201149i) q^{6} +4.27253i q^{7} +(0.989085 - 2.64985i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.13207 - 0.847599i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.563151 + 1.91908i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.39984 + 0.201149i) q^{6} +4.27253i q^{7} +(0.989085 - 2.64985i) q^{8} -1.00000i q^{9} +(-0.201149 - 1.39984i) q^{10} +(2.94281 + 2.94281i) q^{11} +(1.75520 + 0.958786i) q^{12} +(-4.05962 + 4.05962i) q^{13} +(3.62140 - 4.83679i) q^{14} +1.00000 q^{15} +(-3.36572 + 2.16146i) q^{16} +0.160060 q^{17} +(-0.847599 + 1.13207i) q^{18} +(4.32576 - 4.32576i) q^{19} +(-0.958786 + 1.75520i) q^{20} +(3.02114 + 3.02114i) q^{21} +(-0.837134 - 5.82579i) q^{22} -8.40564i q^{23} +(-1.17434 - 2.57312i) q^{24} +1.00000i q^{25} +(8.03670 - 1.15483i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-8.19933 + 2.40608i) q^{28} +(-1.78072 + 1.78072i) q^{29} +(-1.13207 - 0.847599i) q^{30} +7.17282 q^{31} +(5.64228 + 0.405867i) q^{32} +4.16177 q^{33} +(-0.181198 - 0.135667i) q^{34} +(-3.02114 + 3.02114i) q^{35} +(1.91908 - 0.563151i) q^{36} +(-0.669226 - 0.669226i) q^{37} +(-8.56355 + 1.23054i) q^{38} +5.74117i q^{39} +(2.57312 - 1.17434i) q^{40} -3.96632i q^{41} +(-0.859415 - 5.98084i) q^{42} +(-0.255733 - 0.255733i) q^{43} +(-3.99024 + 7.30473i) q^{44} +(0.707107 - 0.707107i) q^{45} +(-7.12462 + 9.51575i) q^{46} +0.0752658 q^{47} +(-0.851542 + 3.90831i) q^{48} -11.2545 q^{49} +(0.847599 - 1.13207i) q^{50} +(0.113179 - 0.113179i) q^{51} +(-10.0769 - 5.50456i) q^{52} +(-2.88214 - 2.88214i) q^{53} +(0.201149 + 1.39984i) q^{54} +4.16177i q^{55} +(11.3216 + 4.22590i) q^{56} -6.11754i q^{57} +(3.52522 - 0.506556i) q^{58} +(-5.63594 - 5.63594i) q^{59} +(0.563151 + 1.91908i) q^{60} +(-4.48857 + 4.48857i) q^{61} +(-8.12011 - 6.07968i) q^{62} +4.27253 q^{63} +(-6.04342 - 5.24186i) q^{64} -5.74117 q^{65} +(-4.71140 - 3.52751i) q^{66} +(-0.131176 + 0.131176i) q^{67} +(0.0901377 + 0.307167i) q^{68} +(-5.94369 - 5.94369i) q^{69} +(5.98084 - 0.859415i) q^{70} +12.1137i q^{71} +(-2.64985 - 0.989085i) q^{72} +0.382876i q^{73} +(0.190373 + 1.32484i) q^{74} +(0.707107 + 0.707107i) q^{75} +(10.7375 + 5.86541i) q^{76} +(-12.5733 + 12.5733i) q^{77} +(4.86622 - 6.49939i) q^{78} +15.3239 q^{79} +(-3.90831 - 0.851542i) q^{80} -1.00000 q^{81} +(-3.36185 + 4.49014i) q^{82} +(-5.54562 + 5.54562i) q^{83} +(-4.09644 + 7.49916i) q^{84} +(0.113179 + 0.113179i) q^{85} +(0.0727477 + 0.506266i) q^{86} +2.51831i q^{87} +(10.7087 - 4.88732i) q^{88} -13.8991i q^{89} +(-1.39984 + 0.201149i) q^{90} +(-17.3449 - 17.3449i) q^{91} +(16.1311 - 4.73364i) q^{92} +(5.07195 - 5.07195i) q^{93} +(-0.0852060 - 0.0637953i) q^{94} +6.11754 q^{95} +(4.27668 - 3.70270i) q^{96} +10.8999 q^{97} +(12.7409 + 9.53935i) q^{98} +(2.94281 - 2.94281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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