LMFDB - Embedded newform 845.2.m.c.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.316
Dual form			845.2.m.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-4.09808 + 2.36603i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.73205i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-4.09808 + 2.36603i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.73205i q^{8} +(-2.23205 - 3.86603i) q^{9} +(0.866025 - 1.50000i) q^{10} +(-4.09808 - 2.36603i) q^{11} -2.73205 q^{12} -3.46410 q^{14} +(2.36603 + 1.36603i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-1.73205 - 3.00000i) q^{17} -7.73205i q^{18} +(-5.36603 + 3.09808i) q^{19} +(0.866025 - 0.500000i) q^{20} -5.46410i q^{21} +(-4.09808 - 7.09808i) q^{22} +(0.633975 - 1.09808i) q^{23} +(4.09808 + 2.36603i) q^{24} -1.00000 q^{25} +4.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(1.26795 - 2.19615i) q^{29} +(2.36603 + 4.09808i) q^{30} +10.1962i q^{31} +(4.50000 - 2.59808i) q^{32} +(11.1962 - 6.46410i) q^{33} -6.00000i q^{34} +(1.00000 + 1.73205i) q^{35} +(2.23205 - 3.86603i) q^{36} +(-3.46410 - 2.00000i) q^{37} -10.7321 q^{38} -1.73205 q^{40} +(-3.00000 - 1.73205i) q^{41} +(4.73205 - 8.19615i) q^{42} +(-0.0980762 - 0.169873i) q^{43} -4.73205i q^{44} +(-3.86603 + 2.23205i) q^{45} +(1.90192 - 1.09808i) q^{46} -6.00000i q^{47} +(6.83013 + 11.8301i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(-1.50000 - 0.866025i) q^{50} +9.46410 q^{51} +10.3923 q^{53} +(6.00000 + 3.46410i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(1.73205 + 3.00000i) q^{56} -16.9282i q^{57} +(3.80385 - 2.19615i) q^{58} +(-7.90192 + 4.56218i) q^{59} +2.73205i q^{60} +(4.19615 + 7.26795i) q^{61} +(-8.83013 + 15.2942i) q^{62} +(7.73205 + 4.46410i) q^{63} -1.00000 q^{64} +22.3923 q^{66} +(-5.53590 - 3.19615i) q^{67} +(1.73205 - 3.00000i) q^{68} +(1.73205 + 3.00000i) q^{69} +3.46410i q^{70} +(4.09808 - 2.36603i) q^{71} +(-6.69615 + 3.86603i) q^{72} +4.00000i q^{73} +(-3.46410 - 6.00000i) q^{74} +(1.36603 - 2.36603i) q^{75} +(-5.36603 - 3.09808i) q^{76} +9.46410 q^{77} -8.39230 q^{79} +(-4.33013 - 2.50000i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-3.00000 - 5.19615i) q^{82} -6.00000i q^{83} +(4.73205 - 2.73205i) q^{84} +(-3.00000 + 1.73205i) q^{85} -0.339746i q^{86} +(3.46410 + 6.00000i) q^{87} +(-4.09808 + 7.09808i) q^{88} +(-11.1962 - 6.46410i) q^{89} -7.73205 q^{90} +1.26795 q^{92} +(-24.1244 - 13.9282i) q^{93} +(5.19615 - 9.00000i) q^{94} +(3.09808 + 5.36603i) q^{95} +14.1962i q^{96} +(1.73205 - 1.00000i) q^{97} +(-4.50000 + 2.59808i) q^{98} +21.1244i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	$ 4 q + 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 6 q^{15} + 10 q^{16} - 18 q^{19} - 6 q^{22} + 6 q^{23} + 6 q^{24} - 4 q^{25} + 16 q^{27} + 12 q^{29} + 6 q^{30} + 18 q^{32} + 24 q^{33} + 4 q^{35} + 2 q^{36} - 36 q^{38} - 12 q^{41} + 12 q^{42} + 10 q^{43} - 12 q^{45} + 18 q^{46} + 10 q^{48} - 6 q^{49} - 6 q^{50} + 24 q^{51} + 24 q^{54} - 6 q^{55} + 36 q^{58} - 42 q^{59} - 4 q^{61} - 18 q^{62} + 24 q^{63} - 4 q^{64} + 48 q^{66} - 36 q^{67} + 6 q^{71} - 6 q^{72} + 2 q^{75} - 18 q^{76} + 24 q^{77} + 8 q^{79} - 2 q^{81} - 12 q^{82} + 12 q^{84} - 12 q^{85} - 6 q^{88} - 24 q^{89} - 24 q^{90} + 12 q^{92} - 48 q^{93} + 2 q^{95} - 18 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 6 * q^15 + 10 * q^16 - 18 * q^19 - 6 * q^22 + 6 * q^23 + 6 * q^24 - 4 * q^25 + 16 * q^27 + 12 * q^29 + 6 * q^30 + 18 * q^32 + 24 * q^33 + 4 * q^35 + 2 * q^36 - 36 * q^38 - 12 * q^41 + 12 * q^42 + 10 * q^43 - 12 * q^45 + 18 * q^46 + 10 * q^48 - 6 * q^49 - 6 * q^50 + 24 * q^51 + 24 * q^54 - 6 * q^55 + 36 * q^58 - 42 * q^59 - 4 * q^61 - 18 * q^62 + 24 * q^63 - 4 * q^64 + 48 * q^66 - 36 * q^67 + 6 * q^71 - 6 * q^72 + 2 * q^75 - 18 * q^76 + 24 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^82 + 12 * q^84 - 12 * q^85 - 6 * q^88 - 24 * q^89 - 24 * q^90 + 12 * q^92 - 48 * q^93 + 2 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	0.138104	+	0.990418i	$0.455899\pi$
$3$	−1.36603	+	2.36603i	−0.788675	+	1.36603i	−0.926779	+	0.375608i	$0.877434\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−4.09808	+	2.36603i	−1.67303	+	0.965926i
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−2.23205	−	3.86603i	−0.744017	−	1.28868i
$10$	0.866025	−	1.50000i	0.273861	−	0.474342i
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.267421	−	0.963580i	$-0.586172\pi$
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.968195	+	0.250196i	$0.919505\pi$
$12$	−2.73205			−0.788675
$13$		0			0
$13$		0			0
$14$	−3.46410			−0.925820
$15$	2.36603	+	1.36603i	0.610905	+	0.352706i
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	0.575863	−	0.817546i	$-0.304666\pi$
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	−0.995947	+	0.0899392i	$0.971333\pi$
$18$		−	7.73205i		−	1.82246i
$19$	−5.36603	+	3.09808i	−1.23105	+	0.710747i	−0.967249	−	0.253830i	$-0.918310\pi$
$19$	−5.36603	+	3.09808i	−1.23105	+	0.710747i	−0.263802	+	0.964577i	$0.584976\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		−	5.46410i		−	1.19236i
$22$	−4.09808	−	7.09808i	−0.873713	−	1.51331i
$23$	0.633975	−	1.09808i	0.132193	−	0.228965i	−0.792329	−	0.610094i	$-0.791132\pi$
$23$	0.633975	−	1.09808i	0.132193	−	0.228965i	0.924522	+	0.381130i	$0.124465\pi$
$24$	4.09808	+	2.36603i	0.836516	+	0.482963i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$	−1.73205	−	1.00000i	−0.327327	−	0.188982i
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	−0.723952	−	0.689851i	$-0.757676\pi$
$29$	1.26795	−	2.19615i	0.235452	−	0.407815i	0.959404	+	0.282035i	$0.0910095\pi$
$30$	2.36603	+	4.09808i	0.431975	+	0.748203i
$31$			10.1962i			1.83128i	0.401996	+	0.915642i	$0.368317\pi$
$31$			10.1962i			1.83128i	−0.401996	+	0.915642i	$0.631683\pi$
$32$	4.50000	−	2.59808i	0.795495	−	0.459279i
$33$	11.1962	−	6.46410i	1.94900	−	1.12526i
$34$		−	6.00000i		−	1.02899i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	2.23205	−	3.86603i	0.372008	−	0.644338i
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	0.187453	−	0.982274i	$-0.439977\pi$
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	−0.756948	+	0.653476i	$0.773310\pi$
$38$	−10.7321			−1.74097
$39$		0			0
$40$	−1.73205			−0.273861
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	0.247099	−	0.968990i	$-0.420523\pi$
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	−0.715621	+	0.698489i	$0.753856\pi$
$42$	4.73205	−	8.19615i	0.730171	−	1.26469i
$43$	−0.0980762	−	0.169873i	−0.0149565	−	0.0259054i	0.858450	−	0.512897i	$-0.171428\pi$
$43$	−0.0980762	−	0.169873i	−0.0149565	−	0.0259054i	−0.873407	+	0.486991i	$0.838094\pi$
$44$		−	4.73205i		−	0.713384i
$45$	−3.86603	+	2.23205i	−0.576313	+	0.332734i
$46$	1.90192	−	1.09808i	0.280423	−	0.161903i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	6.83013	+	11.8301i	0.985844	+	1.70753i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	−1.50000	−	0.866025i	−0.212132	−	0.122474i
$51$	9.46410			1.32524
$52$		0			0
$53$	10.3923			1.42749			0.713746	−	0.700404i	$-0.246997\pi$
$53$	10.3923			1.42749			0.713746	+	0.700404i	$0.246997\pi$
$54$	6.00000	+	3.46410i	0.816497	+	0.471405i
$55$	−2.36603	+	4.09808i	−0.319035	+	0.552584i
$56$	1.73205	+	3.00000i	0.231455	+	0.400892i
$57$		−	16.9282i		−	2.24220i
$58$	3.80385	−	2.19615i	0.499470	−	0.288369i
$59$	−7.90192	+	4.56218i	−1.02874	+	0.593945i	−0.916624	−	0.399750i	$-0.869097\pi$
$59$	−7.90192	+	4.56218i	−1.02874	+	0.593945i	−0.112119	+	0.993695i	$0.535764\pi$
$60$			2.73205i			0.352706i
$61$	4.19615	+	7.26795i	0.537262	+	0.930566i	0.999050	+	0.0435752i	$0.0138748\pi$
$61$	4.19615	+	7.26795i	0.537262	+	0.930566i	−0.461788	+	0.886990i	$0.652792\pi$
$62$	−8.83013	+	15.2942i	−1.12143	+	1.94237i
$63$	7.73205	+	4.46410i	0.974147	+	0.562424i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	22.3923			2.75630
$67$	−5.53590	−	3.19615i	−0.676318	−	0.390472i	0.122149	−	0.992512i	$-0.461022\pi$
$67$	−5.53590	−	3.19615i	−0.676318	−	0.390472i	−0.798466	+	0.602040i	$0.794355\pi$
$68$	1.73205	−	3.00000i	0.210042	−	0.363803i
$69$	1.73205	+	3.00000i	0.208514	+	0.361158i
$70$			3.46410i			0.414039i
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	−0.236708	−	0.971581i	$-0.576068\pi$
$71$	4.09808	−	2.36603i	0.486352	−	0.280796i	0.723060	+	0.690785i	$0.242735\pi$
$72$	−6.69615	+	3.86603i	−0.789149	+	0.455615i
$73$			4.00000i			0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$			4.00000i			0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	−3.46410	−	6.00000i	−0.402694	−	0.697486i
$75$	1.36603	−	2.36603i	0.157735	−	0.273205i
$76$	−5.36603	−	3.09808i	−0.615525	−	0.355374i
$77$	9.46410			1.07853
$78$		0			0
$79$	−8.39230			−0.944208			−0.472104	−	0.881543i	$-0.656505\pi$
$79$	−8.39230			−0.944208			−0.472104	+	0.881543i	$0.656505\pi$
$80$	−4.33013	−	2.50000i	−0.484123	−	0.279508i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	4.73205	−	2.73205i	0.516309	−	0.298091i
$85$	−3.00000	+	1.73205i	−0.325396	+	0.187867i
$86$		−	0.339746i		−	0.0366357i
$87$	3.46410	+	6.00000i	0.371391	+	0.643268i
$88$	−4.09808	+	7.09808i	−0.436856	+	0.756657i
$89$	−11.1962	−	6.46410i	−1.18679	−	0.685193i	−0.229214	−	0.973376i	$-0.573616\pi$
$89$	−11.1962	−	6.46410i	−1.18679	−	0.685193i	−0.957575	+	0.288183i	$0.906949\pi$
$90$	−7.73205			−0.815030
$91$		0			0
$92$	1.26795			0.132193
$93$	−24.1244	−	13.9282i	−2.50158	−	1.44429i
$94$	5.19615	−	9.00000i	0.535942	−	0.928279i
$95$	3.09808	+	5.36603i	0.317856	+	0.550543i
$96$			14.1962i			1.44889i
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$	−4.50000	+	2.59808i	−0.454569	+	0.262445i
$99$			21.1244i			2.12308i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−0.464102	+	0.803848i	−0.0461798	+	0.0799858i	−0.888191	−	0.459474i	$-0.848038\pi$
$101$	−0.464102	+	0.803848i	−0.0461798	+	0.0799858i	0.842012	+	0.539459i	$0.181371\pi$
$102$	14.1962	+	8.19615i	1.40563	+	0.811540i
$103$	0.196152			0.0193275			0.00966374	−	0.999953i	$-0.496924\pi$
$103$	0.196152			0.0193275			0.00966374	+	0.999953i	$0.496924\pi$
$104$		0			0
$105$	−5.46410			−0.533242
$106$	15.5885	+	9.00000i	1.51408	+	0.874157i
$107$	−8.83013	+	15.2942i	−0.853641	+	1.47855i	0.0242598	+	0.999706i	$0.492277\pi$
$107$	−8.83013	+	15.2942i	−0.853641	+	1.47855i	−0.877900	+	0.478843i	$0.841056\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	−7.09808	+	4.09808i	−0.676775	+	0.390736i
$111$	9.46410	−	5.46410i	0.898293	−	0.518630i
$112$			10.0000i			0.944911i
$113$	−4.26795	−	7.39230i	−0.401495	−	0.695410i	0.592412	−	0.805635i	$-0.298176\pi$
$113$	−4.26795	−	7.39230i	−0.401495	−	0.695410i	−0.993907	+	0.110226i	$0.964843\pi$
$114$	14.6603	−	25.3923i	1.37306	−	2.37821i
$115$	−1.09808	−	0.633975i	−0.102396	−	0.0591184i
$116$	2.53590			0.235452
$117$		0			0
$118$	−15.8038			−1.45486
$119$	6.00000	+	3.46410i	0.550019	+	0.317554i
$120$	2.36603	−	4.09808i	0.215988	−	0.374101i
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$			14.5359i			1.31602i
$123$	8.19615	−	4.73205i	0.739022	−	0.426675i
$124$	−8.83013	+	5.09808i	−0.792969	+	0.457821i
$125$			1.00000i			0.0894427i
$126$	7.73205	+	13.3923i	0.688826	+	1.19308i
$127$	8.09808	−	14.0263i	0.718588	−	1.24463i	−0.242971	−	0.970034i	$-0.578122\pi$
$127$	8.09808	−	14.0263i	0.718588	−	1.24463i	0.961559	−	0.274598i	$-0.0885446\pi$
$128$	−10.5000	−	6.06218i	−0.928078	−	0.535826i
$129$	0.535898			0.0471832
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	11.1962	+	6.46410i	0.974500	+	0.562628i
$133$	6.19615	−	10.7321i	0.537275	−	0.930587i
$134$	−5.53590	−	9.58846i	−0.478229	−	0.828317i
$135$		−	4.00000i		−	0.344265i
$136$	−5.19615	+	3.00000i	−0.445566	+	0.257248i
$137$	−0.803848	+	0.464102i	−0.0686773	+	0.0396509i	−0.533945	−	0.845519i	$-0.679291\pi$
$137$	−0.803848	+	0.464102i	−0.0686773	+	0.0396509i	0.465268	+	0.885170i	$0.345958\pi$
$138$			6.00000i			0.510754i
$139$	−6.19615	−	10.7321i	−0.525551	−	0.910281i	−0.999557	−	0.0297592i	$-0.990526\pi$
$139$	−6.19615	−	10.7321i	−0.525551	−	0.910281i	0.474006	−	0.880521i	$-0.342807\pi$
$140$	−1.00000	+	1.73205i	−0.0845154	+	0.146385i
$141$	14.1962	+	8.19615i	1.19553	+	0.690241i
$142$	8.19615			0.687806
$143$		0			0
$144$	−22.3205			−1.86004
$145$	−2.19615	−	1.26795i	−0.182381	−	0.105297i
$146$	−3.46410	+	6.00000i	−0.286691	+	0.496564i
$147$	−4.09808	−	7.09808i	−0.338004	−	0.585439i
$148$		−	4.00000i		−	0.328798i
$149$	−6.80385	+	3.92820i	−0.557393	+	0.321811i	−0.752098	−	0.659051i	$-0.770958\pi$
$149$	−6.80385	+	3.92820i	−0.557393	+	0.321811i	0.194706	+	0.980862i	$0.437625\pi$
$150$	4.09808	−	2.36603i	0.334607	−	0.193185i
$151$			1.80385i			0.146795i	0.997303	+	0.0733975i	$0.0233842\pi$
$151$			1.80385i			0.146795i	−0.997303	+	0.0733975i	$0.976616\pi$
$152$	5.36603	+	9.29423i	0.435242	+	0.753861i
$153$	−7.73205	+	13.3923i	−0.625099	+	1.08270i
$154$	14.1962	+	8.19615i	1.14396	+	0.660465i
$155$	10.1962			0.818975
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−12.5885	−	7.26795i	−1.00148	−	0.578207i
$159$	−14.1962	+	24.5885i	−1.12583	+	1.94999i
$160$	−2.59808	−	4.50000i	−0.205396	−	0.355756i
$161$			2.53590i			0.199857i
$162$	3.69615	−	2.13397i	0.290397	−	0.167661i
$163$	12.4641	−	7.19615i	0.976264	−	0.563646i	0.0751237	−	0.997174i	$-0.476065\pi$
$163$	12.4641	−	7.19615i	0.976264	−	0.563646i	0.901140	+	0.433528i	$0.142731\pi$
$164$		−	3.46410i		−	0.270501i
$165$	−6.46410	−	11.1962i	−0.503230	−	0.871619i
$166$	5.19615	−	9.00000i	0.403300	−	0.698535i
$167$	−0.803848	−	0.464102i	−0.0622036	−	0.0359133i	0.468576	−	0.883423i	$-0.344767\pi$
$167$	−0.803848	−	0.464102i	−0.0622036	−	0.0359133i	−0.530779	+	0.847510i	$0.678101\pi$
$168$	−9.46410			−0.730171
$169$		0			0
$170$	−6.00000			−0.460179
$171$	23.9545	+	13.8301i	1.83185	+	1.05762i
$172$	0.0980762	−	0.169873i	0.00747824	−	0.0129527i
$173$	4.26795	+	7.39230i	0.324486	+	0.562027i	0.981408	−	0.191932i	$-0.0614753\pi$
$173$	4.26795	+	7.39230i	0.324486	+	0.562027i	−0.656922	+	0.753958i	$0.728142\pi$
$174$			12.0000i			0.909718i
$175$	1.73205	−	1.00000i	0.130931	−	0.0755929i
$176$	−20.4904	+	11.8301i	−1.54452	+	0.891729i
$177$		−	24.9282i		−	1.87372i
$178$	−11.1962	−	19.3923i	−0.839187	−	1.45351i
$179$	−9.46410	+	16.3923i	−0.707380	+	1.22522i	0.258446	+	0.966026i	$0.416790\pi$
$179$	−9.46410	+	16.3923i	−0.707380	+	1.22522i	−0.965826	+	0.259193i	$0.916544\pi$
$180$	−3.86603	−	2.23205i	−0.288157	−	0.166367i
$181$	−0.392305			−0.0291598			−0.0145799	−	0.999894i	$-0.504641\pi$
$181$	−0.392305			−0.0291598			−0.0145799	+	0.999894i	$0.504641\pi$
$182$		0			0
$183$	−22.9282			−1.69490
$184$	−1.90192	−	1.09808i	−0.140212	−	0.0809513i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	−24.1244	−	41.7846i	−1.76888	−	3.06380i
$187$			16.3923i			1.19872i
$188$	5.19615	−	3.00000i	0.378968	−	0.218797i
$189$	−6.92820	+	4.00000i	−0.503953	+	0.290957i
$190$			10.7321i			0.778585i
$191$	2.53590	+	4.39230i	0.183491	+	0.317816i	0.943067	−	0.332603i	$-0.107927\pi$
$191$	2.53590	+	4.39230i	0.183491	+	0.317816i	−0.759576	+	0.650419i	$0.774593\pi$
$192$	1.36603	−	2.36603i	0.0985844	−	0.170753i
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	0.154805	−	0.987945i	$-0.450525\pi$
$193$	−8.66025	−	5.00000i	−0.623379	−	0.359908i	−0.778183	+	0.628037i	$0.783859\pi$
$194$	3.46410			0.248708
$195$		0			0
$196$	−3.00000			−0.214286
$197$	11.1962	+	6.46410i	0.797693	+	0.460548i	0.842664	−	0.538440i	$-0.180986\pi$
$197$	11.1962	+	6.46410i	0.797693	+	0.460548i	−0.0449709	+	0.998988i	$0.514320\pi$
$198$	−18.2942	+	31.6865i	−1.30011	+	2.25186i
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$			1.73205i			0.122474i
$201$	15.1244	−	8.73205i	1.06679	−	0.615911i
$202$	−1.39230	+	0.803848i	−0.0979622	+	0.0565585i
$203$			5.07180i			0.355970i
$204$	4.73205	+	8.19615i	0.331310	+	0.573845i
$205$	−1.73205	+	3.00000i	−0.120972	+	0.209529i
$206$	0.294229	+	0.169873i	0.0204999	+	0.0118356i
$207$	−5.66025			−0.393415
$208$		0			0
$209$	29.3205			2.02814
$210$	−8.19615	−	4.73205i	−0.565588	−	0.326543i
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	5.19615	+	9.00000i	0.356873	+	0.618123i
$213$			12.9282i			0.885826i
$214$	−26.4904	+	15.2942i	−1.81085	+	1.04549i
$215$	−0.169873	+	0.0980762i	−0.0115852	+	0.00668874i
$216$		−	6.92820i		−	0.471405i
$217$	−10.1962	−	17.6603i	−0.692160	−	1.19886i
$218$	−1.73205	+	3.00000i	−0.117309	+	0.203186i
$219$	−9.46410	−	5.46410i	−0.639525	−	0.369230i
$220$	−4.73205			−0.319035
$221$		0			0
$222$	18.9282			1.27038
$223$	−1.73205	−	1.00000i	−0.115987	−	0.0669650i	0.440884	−	0.897564i	$-0.354665\pi$
$223$	−1.73205	−	1.00000i	−0.115987	−	0.0669650i	−0.556871	+	0.830599i	$0.687998\pi$
$224$	−5.19615	+	9.00000i	−0.347183	+	0.601338i
$225$	2.23205	+	3.86603i	0.148803	+	0.257735i
$226$		−	14.7846i		−	0.983458i
$227$	−3.00000	+	1.73205i	−0.199117	+	0.114960i	−0.596244	−	0.802804i	$-0.703341\pi$
$227$	−3.00000	+	1.73205i	−0.199117	+	0.114960i	0.397127	+	0.917764i	$0.370007\pi$
$228$	14.6603	−	8.46410i	0.970899	−	0.560549i
$229$		−	6.39230i		−	0.422415i	−0.977441	−	0.211208i	$-0.932260\pi$
$229$		−	6.39230i		−	0.422415i	0.977441	−	0.211208i	$-0.0677396\pi$
$230$	−1.09808	−	1.90192i	−0.0724050	−	0.125409i
$231$	−12.9282	+	22.3923i	−0.850613	+	1.47331i
$232$	−3.80385	−	2.19615i	−0.249735	−	0.144184i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	−7.90192	−	4.56218i	−0.514371	−	0.296972i
$237$	11.4641	−	19.8564i	0.744673	−	1.28981i
$238$	6.00000	+	10.3923i	0.388922	+	0.673633i
$239$		−	14.1962i		−	0.918273i	−0.888366	−	0.459136i	$-0.848159\pi$
$239$		−	14.1962i		−	0.918273i	0.888366	−	0.459136i	$-0.151841\pi$
$240$	11.8301	−	6.83013i	0.763631	−	0.440883i
$241$	2.07180	−	1.19615i	0.133456	−	0.0770510i	−0.431785	−	0.901976i	$-0.642116\pi$
$241$	2.07180	−	1.19615i	0.133456	−	0.0770510i	0.565242	+	0.824925i	$0.308783\pi$
$242$			19.7321i			1.26842i
$243$	9.36603	+	16.2224i	0.600831	+	1.04067i
$244$	−4.19615	+	7.26795i	−0.268631	+	0.465283i
$245$	2.59808	+	1.50000i	0.165985	+	0.0958315i
$246$	16.3923			1.04514
$247$		0			0
$248$	17.6603			1.12143
$249$	14.1962	+	8.19615i	0.899645	+	0.519410i
$250$	−0.866025	+	1.50000i	−0.0547723	+	0.0948683i
$251$	−10.7321	−	18.5885i	−0.677401	−	1.17329i	−0.975761	−	0.218840i	$-0.929773\pi$
$251$	−10.7321	−	18.5885i	−0.677401	−	1.17329i	0.298360	−	0.954453i	$-0.403560\pi$
$252$			8.92820i			0.562424i
$253$	−5.19615	+	3.00000i	−0.326679	+	0.188608i
$254$	24.2942	−	14.0263i	1.52436	−	0.880087i
$255$		−	9.46410i		−	0.592665i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	9.92820	−	17.1962i	0.619304	−	1.07267i	−0.370309	−	0.928909i	$-0.620748\pi$
$257$	9.92820	−	17.1962i	0.619304	−	1.07267i	0.989613	−	0.143758i	$-0.0459186\pi$
$258$	0.803848	+	0.464102i	0.0500454	+	0.0288937i
$259$	8.00000			0.497096
$260$		0			0
$261$	−11.3205			−0.700722
$262$		0			0
$263$	−0.633975	+	1.09808i	−0.0390925	+	0.0677103i	−0.884910	−	0.465763i	$-0.845780\pi$
$263$	−0.633975	+	1.09808i	−0.0390925	+	0.0677103i	0.845817	+	0.533473i	$0.179113\pi$
$264$	−11.1962	−	19.3923i	−0.689076	−	1.19351i
$265$		−	10.3923i		−	0.638394i
$266$	18.5885	−	10.7321i	1.13973	−	0.658024i
$267$	30.5885	−	17.6603i	1.87198	−	1.08079i
$268$		−	6.39230i		−	0.390472i
$269$	9.92820	+	17.1962i	0.605333	+	1.04847i	0.991999	+	0.126248i	$0.0402935\pi$
$269$	9.92820	+	17.1962i	0.605333	+	1.04847i	−0.386665	+	0.922220i	$0.626373\pi$
$270$	3.46410	−	6.00000i	0.210819	−	0.365148i
$271$	26.8301	+	15.4904i	1.62981	+	0.940974i	0.984147	+	0.177355i	$0.0567540\pi$
$271$	26.8301	+	15.4904i	1.62981	+	0.940974i	0.645667	+	0.763619i	$0.276579\pi$
$272$	−17.3205			−1.05021
$273$		0			0
$274$	−1.60770			−0.0971244
$275$	4.09808	+	2.36603i	0.247123	+	0.142677i
$276$	−1.73205	+	3.00000i	−0.104257	+	0.180579i
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	−0.924177	−	0.381965i	$-0.875247\pi$
$277$	−13.1962	−	22.8564i	−0.792880	−	1.37331i	0.131297	−	0.991343i	$-0.458086\pi$
$278$		−	21.4641i		−	1.28733i
$279$	39.4186	−	22.7583i	2.35993	−	1.36251i
$280$	3.00000	−	1.73205i	0.179284	−	0.103510i
$281$		−	22.3923i		−	1.33581i	−0.744245	−	0.667906i	$-0.767191\pi$
$281$		−	22.3923i		−	1.33581i	0.744245	−	0.667906i	$-0.232809\pi$
$282$	14.1962	+	24.5885i	0.845369	+	1.46422i
$283$	16.2942	−	28.2224i	0.968591	−	1.67765i	0.268952	−	0.963154i	$-0.413323\pi$
$283$	16.2942	−	28.2224i	0.968591	−	1.67765i	0.699640	−	0.714496i	$-0.253344\pi$
$284$	4.09808	+	2.36603i	0.243176	+	0.140398i
$285$	−16.9282			−1.00274
$286$		0			0
$287$	6.92820			0.408959
$288$	−20.0885	−	11.5981i	−1.18372	−	0.683423i
$289$	2.50000	−	4.33013i	0.147059	−	0.254713i
$290$	−2.19615	−	3.80385i	−0.128963	−	0.223370i
$291$			5.46410i			0.320311i
$292$	−3.46410	+	2.00000i	−0.202721	+	0.117041i
$293$	4.39230	−	2.53590i	0.256601	−	0.148149i	−0.366182	−	0.930543i	$-0.619335\pi$
$293$	4.39230	−	2.53590i	0.256601	−	0.148149i	0.622783	+	0.782395i	$0.286002\pi$
$294$		−	14.1962i		−	0.827936i
$295$	4.56218	+	7.90192i	0.265620	+	0.460068i
$296$	−3.46410	+	6.00000i	−0.201347	+	0.348743i
$297$	−16.3923	−	9.46410i	−0.951178	−	0.549163i
$298$	−13.6077			−0.788273
$299$		0			0
$300$	2.73205			0.157735
$301$	0.339746	+	0.196152i	0.0195826	+	0.0113060i
$302$	−1.56218	+	2.70577i	−0.0898932	+	0.155700i
$303$	−1.26795	−	2.19615i	−0.0728418	−	0.126166i
$304$			30.9808i			1.77687i
$305$	7.26795	−	4.19615i	0.416162	−	0.240271i
$306$	−23.1962	+	13.3923i	−1.32604	+	0.765587i
$307$			18.7846i			1.07209i	0.844188	+	0.536047i	$0.180083\pi$
$307$			18.7846i			1.07209i	−0.844188	+	0.536047i	$0.819917\pi$
$308$	4.73205	+	8.19615i	0.269634	+	0.467019i
$309$	−0.267949	+	0.464102i	−0.0152431	+	0.0264018i
$310$	15.2942	+	8.83013i	0.868654	+	0.501518i
$311$	16.3923			0.929522			0.464761	−	0.885436i	$-0.346140\pi$
$311$	16.3923			0.929522			0.464761	+	0.885436i	$0.346140\pi$
$312$		0			0
$313$	−14.3923			−0.813501			−0.406751	−	0.913539i	$-0.633338\pi$
$313$	−14.3923			−0.813501			−0.406751	+	0.913539i	$0.633338\pi$
$314$	−15.0000	−	8.66025i	−0.846499	−	0.488726i
$315$	4.46410	−	7.73205i	0.251524	−	0.435652i
$316$	−4.19615	−	7.26795i	−0.236052	−	0.408854i
$317$			24.0000i			1.34797i	0.738743	+	0.673987i	$0.235420\pi$
$317$			24.0000i			1.34797i	−0.738743	+	0.673987i	$0.764580\pi$
$318$	−42.5885	+	24.5885i	−2.38824	+	1.37885i
$319$	−10.3923	+	6.00000i	−0.581857	+	0.335936i
$320$			1.00000i			0.0559017i
$321$	−24.1244	−	41.7846i	−1.34649	−	2.33219i
$322$	−2.19615	+	3.80385i	−0.122387	+	0.211980i
$323$	18.5885	+	10.7321i	1.03429	+	0.597147i
$324$	2.46410			0.136895
$325$		0			0
$326$	24.9282			1.38065
$327$	−4.73205	−	2.73205i	−0.261683	−	0.151083i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		−	22.3923i		−	1.23266i
$331$	2.24167	−	1.29423i	0.123213	−	0.0711372i	−0.437127	−	0.899400i	$-0.644004\pi$
$331$	2.24167	−	1.29423i	0.123213	−	0.0711372i	0.560340	+	0.828263i	$0.310671\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$			17.8564i			0.978525i
$334$	−0.803848	−	1.39230i	−0.0439846	−	0.0761835i
$335$	−3.19615	+	5.53590i	−0.174624	+	0.302458i
$336$	−23.6603	−	13.6603i	−1.29077	−	0.745228i
$337$	26.3923			1.43768			0.718840	−	0.695175i	$-0.244673\pi$
$337$	26.3923			1.43768			0.718840	+	0.695175i	$0.244673\pi$
$338$		0			0
$339$	23.3205			1.26660
$340$	−3.00000	−	1.73205i	−0.162698	−	0.0939336i
$341$	24.1244	−	41.7846i	1.30641	−	2.26276i
$342$	23.9545	+	41.4904i	1.29531	+	2.24354i
$343$		−	20.0000i		−	1.07990i
$344$	−0.294229	+	0.169873i	−0.0158637	+	0.00915894i
$345$	3.00000	−	1.73205i	0.161515	−	0.0932505i
$346$			14.7846i			0.794826i
$347$	2.83013	+	4.90192i	0.151929	+	0.263149i	0.931937	−	0.362621i	$-0.118118\pi$
$347$	2.83013	+	4.90192i	0.151929	+	0.263149i	−0.780007	+	0.625770i	$0.784785\pi$
$348$	−3.46410	+	6.00000i	−0.185695	+	0.321634i
$349$	−12.4641	−	7.19615i	−0.667188	−	0.385201i	0.127822	−	0.991797i	$-0.459201\pi$
$349$	−12.4641	−	7.19615i	−0.667188	−	0.385201i	−0.795010	+	0.606596i	$0.792535\pi$
$350$	3.46410			0.185164
$351$		0			0
$352$	−24.5885			−1.31057
$353$	24.0000	+	13.8564i	1.27739	+	0.737502i	0.976368	−	0.216115i	$-0.0693385\pi$
$353$	24.0000	+	13.8564i	1.27739	+	0.737502i	0.301023	+	0.953617i	$0.402672\pi$
$354$	21.5885	−	37.3923i	1.14741	−	1.98738i
$355$	−2.36603	−	4.09808i	−0.125576	−	0.217503i
$356$		−	12.9282i		−	0.685193i
$357$	−16.3923	+	9.46410i	−0.867573	+	0.500893i
$358$	−28.3923	+	16.3923i	−1.50058	+	0.866360i
$359$			2.19615i			0.115908i	0.998319	+	0.0579542i	$0.0184578\pi$
$359$			2.19615i			0.115908i	−0.998319	+	0.0579542i	$0.981542\pi$
$360$	3.86603	+	6.69615i	0.203757	+	0.352918i
$361$	9.69615	−	16.7942i	0.510324	−	0.883907i
$362$	−0.588457	−	0.339746i	−0.0309286	−	0.0178567i
$363$	−31.1244			−1.63361
$364$		0			0
$365$	4.00000			0.209370
$366$	−34.3923	−	19.8564i	−1.79771	−	1.03791i
$367$	−5.90192	+	10.2224i	−0.308078	+	0.533607i	−0.977942	−	0.208877i	$-0.933019\pi$
$367$	−5.90192	+	10.2224i	−0.308078	+	0.533607i	0.669864	+	0.742484i	$0.266352\pi$
$368$	−3.16987	−	5.49038i	−0.165241	−	0.286206i
$369$			15.4641i			0.805029i
$370$	−6.00000	+	3.46410i	−0.311925	+	0.180090i
$371$	−18.0000	+	10.3923i	−0.934513	+	0.539542i
$372$		−	27.8564i		−	1.44429i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	−14.1962	+	24.5885i	−0.734066	+	1.27144i
$375$	−2.36603	−	1.36603i	−0.122181	−	0.0705412i
$376$	−10.3923			−0.535942
$377$		0			0
$378$	−13.8564			−0.712697
$379$	−16.4378	−	9.49038i	−0.844354	−	0.487488i	0.0143877	−	0.999896i	$-0.495420\pi$
$379$	−16.4378	−	9.49038i	−0.844354	−	0.487488i	−0.858742	+	0.512408i	$0.828753\pi$
$380$	−3.09808	+	5.36603i	−0.158928	+	0.275271i
$381$	22.1244	+	38.3205i	1.13347	+	1.96322i
$382$			8.78461i			0.449460i
$383$	11.1962	−	6.46410i	0.572097	−	0.330300i	−0.185890	−	0.982571i	$-0.559517\pi$
$383$	11.1962	−	6.46410i	0.572097	−	0.330300i	0.757986	+	0.652270i	$0.226183\pi$
$384$	28.6865	−	16.5622i	1.46390	−	0.845185i
$385$		−	9.46410i		−	0.482335i
$386$	−8.66025	−	15.0000i	−0.440795	−	0.763480i
$387$	−0.437822	+	0.758330i	−0.0222558	+	0.0385481i
$388$	1.73205	+	1.00000i	0.0879316	+	0.0507673i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−4.39230			−0.222128
$392$	4.50000	+	2.59808i	0.227284	+	0.131223i
$393$		0			0
$394$	11.1962	+	19.3923i	0.564054	+	0.976970i
$395$			8.39230i			0.422263i
$396$	−18.2942	+	10.5622i	−0.919320	+	0.530769i
$397$	−24.9282	+	14.3923i	−1.25111	+	0.722329i	−0.971330	−	0.237735i	$-0.923595\pi$
$397$	−24.9282	+	14.3923i	−1.25111	+	0.722329i	−0.279781	+	0.960064i	$0.590262\pi$
$398$			34.6410i			1.73640i
$399$	16.9282	+	29.3205i	0.847470	+	1.46786i
$400$	−2.50000	+	4.33013i	−0.125000	+	0.216506i
$401$	−31.9808	−	18.4641i	−1.59704	−	0.922053i	−0.992053	−	0.125820i	$-0.959844\pi$
$401$	−31.9808	−	18.4641i	−1.59704	−	0.922053i	−0.604990	−	0.796233i	$-0.706823\pi$
$402$	30.2487			1.50867
$403$		0			0
$404$	−0.928203			−0.0461798
$405$	−2.13397	−	1.23205i	−0.106038	−	0.0612211i
$406$	−4.39230	+	7.60770i	−0.217986	+	0.377564i
$407$	9.46410	+	16.3923i	0.469118	+	0.812536i
$408$		−	16.3923i		−	0.811540i
$409$	−15.2487	+	8.80385i	−0.754000	+	0.435322i	−0.827137	−	0.562000i	$-0.810032\pi$
$409$	−15.2487	+	8.80385i	−0.754000	+	0.435322i	0.0731372	+	0.997322i	$0.476699\pi$
$410$	−5.19615	+	3.00000i	−0.256620	+	0.148159i
$411$		−	2.53590i		−	0.125087i
$412$	0.0980762	+	0.169873i	0.00483187	+	0.00836904i
$413$	9.12436	−	15.8038i	0.448980	−	0.777657i
$414$	−8.49038	−	4.90192i	−0.417279	−	0.240916i
$415$	−6.00000			−0.294528
$416$		0			0
$417$	33.8564			1.65796
$418$	43.9808	+	25.3923i	2.15117	+	1.24198i
$419$	1.26795	−	2.19615i	0.0619434	−	0.107289i	−0.833391	−	0.552684i	$-0.813604\pi$
$419$	1.26795	−	2.19615i	0.0619434	−	0.107289i	0.895334	+	0.445395i	$0.146937\pi$
$420$	−2.73205	−	4.73205i	−0.133310	−	0.230900i
$421$		−	30.7846i		−	1.50035i	−0.661239	−	0.750175i	$-0.729969\pi$
$421$		−	30.7846i		−	1.50035i	0.661239	−	0.750175i	$-0.270031\pi$
$422$	−12.0000	+	6.92820i	−0.584151	+	0.337260i
$423$	−23.1962	+	13.3923i	−1.12784	+	0.651156i
$424$		−	18.0000i		−	0.874157i
$425$	1.73205	+	3.00000i	0.0840168	+	0.145521i
$426$	−11.1962	+	19.3923i	−0.542455	+	0.939560i
$427$	−14.5359	−	8.39230i	−0.703441	−	0.406132i
$428$	−17.6603			−0.853641
$429$		0			0
$430$	−0.339746			−0.0163840
$431$	22.0981	+	12.7583i	1.06443	+	0.614547i	0.926653	−	0.375917i	$-0.122672\pi$
$431$	22.0981	+	12.7583i	1.06443	+	0.614547i	0.137773	+	0.990464i	$0.456005\pi$
$432$	10.0000	−	17.3205i	0.481125	−	0.833333i
$433$	17.3923	+	30.1244i	0.835821	+	1.44768i	0.893360	+	0.449341i	$0.148341\pi$
$433$	17.3923	+	30.1244i	0.835821	+	1.44768i	−0.0575395	+	0.998343i	$0.518326\pi$
$434$		−	35.3205i		−	1.69544i
$435$	6.00000	−	3.46410i	0.287678	−	0.166091i
$436$	−1.73205	+	1.00000i	−0.0829502	+	0.0478913i
$437$			7.85641i			0.375823i
$438$	−9.46410	−	16.3923i	−0.452212	−	0.783255i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	7.09808	+	4.09808i	0.338388	+	0.195368i
$441$	13.3923			0.637729
$442$		0			0
$443$	−16.9808			−0.806780			−0.403390	−	0.915028i	$-0.632168\pi$
$443$	−16.9808			−0.806780			−0.403390	+	0.915028i	$0.632168\pi$
$444$	9.46410	+	5.46410i	0.449146	+	0.259315i
$445$	−6.46410	+	11.1962i	−0.306428	+	0.530749i
$446$	−1.73205	−	3.00000i	−0.0820150	−	0.142054i
$447$		−	21.4641i		−	1.01522i
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	−17.7846	+	10.2679i	−0.839308	+	0.484574i	−0.857029	−	0.515268i	$-0.827692\pi$
$449$	−17.7846	+	10.2679i	−0.839308	+	0.484574i	0.0177212	+	0.999843i	$0.494359\pi$
$450$			7.73205i			0.364492i
$451$	8.19615	+	14.1962i	0.385942	+	0.668471i
$452$	4.26795	−	7.39230i	0.200747	−	0.347705i
$453$	−4.26795	−	2.46410i	−0.200526	−	0.115774i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	−29.3205			−1.37306
$457$	−9.33975	−	5.39230i	−0.436895	−	0.252241i	0.265385	−	0.964143i	$-0.414501\pi$
$457$	−9.33975	−	5.39230i	−0.436895	−	0.252241i	−0.702280	+	0.711901i	$0.747834\pi$
$458$	5.53590	−	9.58846i	0.258676	−	0.448039i
$459$	−6.92820	−	12.0000i	−0.323381	−	0.560112i
$460$		−	1.26795i		−	0.0591184i
$461$	−3.00000	+	1.73205i	−0.139724	+	0.0806696i	−0.568232	−	0.822868i	$-0.692373\pi$
$461$	−3.00000	+	1.73205i	−0.139724	+	0.0806696i	0.428508	+	0.903538i	$0.359039\pi$
$462$	−38.7846	+	22.3923i	−1.80442	+	1.04178i
$463$			2.39230i			0.111180i	0.998454	+	0.0555899i	$0.0177039\pi$
$463$			2.39230i			0.111180i	−0.998454	+	0.0555899i	$0.982296\pi$
$464$	−6.33975	−	10.9808i	−0.294315	−	0.509769i
$465$	−13.9282	+	24.1244i	−0.645905	+	1.11874i
$466$	9.00000	+	5.19615i	0.416917	+	0.240707i
$467$	−27.8038			−1.28661			−0.643304	−	0.765611i	$-0.722437\pi$
$467$	−27.8038			−1.28661			−0.643304	+	0.765611i	$0.722437\pi$
$468$		0			0
$469$	12.7846			0.590338
$470$	−9.00000	−	5.19615i	−0.415139	−	0.239681i
$471$	13.6603	−	23.6603i	0.629431	−	1.09021i
$472$	7.90192	+	13.6865i	0.363716	+	0.629974i
$473$			0.928203i			0.0426788i
$474$	34.3923	−	19.8564i	1.57969	−	0.912035i
$475$	5.36603	−	3.09808i	0.246210	−	0.142149i
$476$			6.92820i			0.317554i
$477$	−23.1962	−	40.1769i	−1.06208	−	1.83957i
$478$	12.2942	−	21.2942i	0.562325	−	0.973975i
$479$	30.8827	+	17.8301i	1.41107	+	0.814679i	0.995489	−	0.0948787i	$-0.0302463\pi$
$479$	30.8827	+	17.8301i	1.41107	+	0.814679i	0.415577	+	0.909558i	$0.363580\pi$
$480$	14.1962			0.647963
$481$		0			0
$482$	4.14359			0.188736
$483$	−6.00000	−	3.46410i	−0.273009	−	0.157622i
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$			32.4449i			1.47173i
$487$	−22.8564	+	13.1962i	−1.03572	+	0.597975i	−0.918619	−	0.395145i	$-0.870694\pi$
$487$	−22.8564	+	13.1962i	−1.03572	+	0.597975i	−0.117104	+	0.993120i	$0.537361\pi$
$488$	12.5885	−	7.26795i	0.569853	−	0.329005i
$489$			39.3205i			1.77813i
$490$	2.59808	+	4.50000i	0.117369	+	0.203289i
$491$	−1.26795	+	2.19615i	−0.0572217	+	0.0991110i	−0.893217	−	0.449625i	$-0.851558\pi$
$491$	−1.26795	+	2.19615i	−0.0572217	+	0.0991110i	0.835996	+	0.548736i	$0.184891\pi$
$492$	8.19615	+	4.73205i	0.369511	+	0.213337i
$493$	−8.78461			−0.395639
$494$		0			0
$495$	21.1244			0.949469
$496$	44.1506	+	25.4904i	1.98242	+	1.14455i
$497$	−4.73205	+	8.19615i	−0.212261	+	0.367648i
$498$	14.1962	+	24.5885i	0.636145	+	1.10184i
$499$		−	38.9808i		−	1.74502i	−0.488598	−	0.872509i	$-0.662491\pi$
$499$		−	38.9808i		−	1.74502i	0.488598	−	0.872509i	$-0.337509\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	2.19615	−	1.26795i	0.0981169	−	0.0566478i
$502$		−	37.1769i		−	1.65929i
$503$	−9.75833	−	16.9019i	−0.435102	−	0.753620i	0.562202	−	0.827000i	$-0.309955\pi$
$503$	−9.75833	−	16.9019i	−0.435102	−	0.753620i	−0.997304	+	0.0733807i	$0.976621\pi$
$504$	7.73205	−	13.3923i	0.344413	−	0.596541i
$505$	0.803848	+	0.464102i	0.0357707	+	0.0206523i
$506$	−10.3923			−0.461994
$507$		0			0
$508$	16.1962			0.718588
$509$	−34.1769	−	19.7321i	−1.51487	−	0.874608i	−0.999848	−	0.0174278i	$-0.994452\pi$
$509$	−34.1769	−	19.7321i	−1.51487	−	0.874608i	−0.515017	−	0.857180i	$-0.672214\pi$
$510$	8.19615	−	14.1962i	0.362932	−	0.628616i
$511$	−4.00000	−	6.92820i	−0.176950	−	0.306486i
$512$		−	8.66025i		−	0.382733i
$513$	−21.4641	+	12.3923i	−0.947663	+	0.547134i
$514$	29.7846	−	17.1962i	1.31374	−	0.758490i
$515$		−	0.196152i		−	0.00864351i
$516$	0.267949	+	0.464102i	0.0117958	+	0.0204309i
$517$	−14.1962	+	24.5885i	−0.624346	+	1.08140i
$518$	12.0000	+	6.92820i	0.527250	+	0.304408i
$519$	−23.3205			−1.02366
$520$		0			0
$521$	−28.3923			−1.24389			−0.621945	−	0.783061i	$-0.713657\pi$
$521$	−28.3923			−1.24389			−0.621945	+	0.783061i	$0.713657\pi$
$522$	−16.9808	−	9.80385i	−0.743228	−	0.429103i
$523$	12.0981	−	20.9545i	0.529012	−	0.916276i	−0.470416	−	0.882445i	$-0.655896\pi$
$523$	12.0981	−	20.9545i	0.529012	−	0.916276i	0.999428	−	0.0338306i	$-0.0107707\pi$
$524$		0			0
$525$			5.46410i			0.238473i
$526$	−1.90192	+	1.09808i	−0.0829278	+	0.0478784i
$527$	30.5885	−	17.6603i	1.33245	−	0.769293i
$528$		−	64.6410i		−	2.81314i
$529$	10.6962	+	18.5263i	0.465050	+	0.805490i
$530$	9.00000	−	15.5885i	0.390935	−	0.677119i
$531$	35.2750	+	20.3660i	1.53080	+	0.883810i
$532$	12.3923			0.537275
$533$		0			0
$534$	61.1769			2.64738
$535$	15.2942	+	8.83013i	0.661227	+	0.381760i
$536$	−5.53590	+	9.58846i	−0.239114	+	0.414158i
$537$	−25.8564	−	44.7846i	−1.11579	−	1.93260i
$538$			34.3923i			1.48276i
$539$	12.2942	−	7.09808i	0.529550	−	0.305736i
$540$	3.46410	−	2.00000i	0.149071	−	0.0860663i
$541$			26.3923i			1.13469i	0.823479	+	0.567347i	$0.192030\pi$
$541$			26.3923i			1.13469i	−0.823479	+	0.567347i	$0.807970\pi$
$542$	26.8301	+	46.4711i	1.15245	+	1.99611i
$543$	0.535898	−	0.928203i	0.0229976	−	0.0398330i
$544$	−15.5885	−	9.00000i	−0.668350	−	0.385872i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−12.1962			−0.521470			−0.260735	−	0.965410i	$-0.583965\pi$
$547$	−12.1962			−0.521470			−0.260735	+	0.965410i	$0.583965\pi$
$548$	−0.803848	−	0.464102i	−0.0343387	−	0.0198254i
$549$	18.7321	−	32.4449i	0.799464	−	1.38471i
$550$	4.09808	+	7.09808i	0.174743	+	0.302663i
$551$			15.7128i			0.669388i
$552$	5.19615	−	3.00000i	0.221163	−	0.127688i
$553$	14.5359	−	8.39230i	0.618129	−	0.356877i
$554$		−	45.7128i		−	1.94215i
$555$	−5.46410	−	9.46410i	−0.231938	−	0.401729i
$556$	6.19615	−	10.7321i	0.262775	−	0.455140i
$557$	1.60770	+	0.928203i	0.0681202	+	0.0393292i	0.533673	−	0.845691i	$-0.320811\pi$
$557$	1.60770	+	0.928203i	0.0681202	+	0.0393292i	−0.465553	+	0.885020i	$0.654145\pi$
$558$	78.8372			3.33744
$559$		0			0
$560$	10.0000			0.422577
$561$	−38.7846	−	22.3923i	−1.63749	−	0.945404i
$562$	19.3923	−	33.5885i	0.818015	−	1.41684i
$563$	−11.0263	−	19.0981i	−0.464702	−	0.804888i	0.534486	−	0.845177i	$-0.320505\pi$
$563$	−11.0263	−	19.0981i	−0.464702	−	0.804888i	−0.999188	+	0.0402895i	$0.987172\pi$
$564$			16.3923i			0.690241i
$565$	−7.39230	+	4.26795i	−0.310997	+	0.179554i
$566$	48.8827	−	28.2224i	2.05469	−	1.18628i
$567$			4.92820i			0.206965i
$568$	−4.09808	−	7.09808i	−0.171951	−	0.297829i
$569$	−1.26795	+	2.19615i	−0.0531552	+	0.0920675i	−0.891379	−	0.453259i	$-0.850261\pi$
$569$	−1.26795	+	2.19615i	−0.0531552	+	0.0920675i	0.838223	+	0.545327i	$0.183594\pi$
$570$	−25.3923	−	14.6603i	−1.06357	−	0.614050i
$571$	−36.3923			−1.52297			−0.761485	−	0.648182i	$-0.775530\pi$
$571$	−36.3923			−1.52297			−0.761485	+	0.648182i	$0.775530\pi$
$572$		0			0
$573$	−13.8564			−0.578860
$574$	10.3923	+	6.00000i	0.433766	+	0.250435i
$575$	−0.633975	+	1.09808i	−0.0264386	+	0.0457929i
$576$	2.23205	+	3.86603i	0.0930021	+	0.161084i
$577$		−	4.00000i		−	0.166522i	−0.996528	−	0.0832611i	$-0.973466\pi$
$577$		−	4.00000i		−	0.166522i	0.996528	−	0.0832611i	$-0.0265335\pi$
$578$	7.50000	−	4.33013i	0.311959	−	0.180110i
$579$	23.6603	−	13.6603i	0.983287	−	0.567701i
$580$		−	2.53590i		−	0.105297i
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−4.73205	+	8.19615i	−0.196150	+	0.339741i
$583$	−42.5885	−	24.5885i	−1.76383	−	1.01835i
$584$	6.92820			0.286691
$585$		0			0
$586$	8.78461			0.362889
$587$	7.39230	+	4.26795i	0.305113	+	0.176157i	0.644738	−	0.764404i	$-0.276967\pi$
$587$	7.39230	+	4.26795i	0.305113	+	0.176157i	−0.339624	+	0.940561i	$0.610300\pi$
$588$	4.09808	−	7.09808i	0.169002	−	0.292720i
$589$	−31.5885	−	54.7128i	−1.30158	−	2.25440i
$590$			15.8038i			0.650634i
$591$	−30.5885	+	17.6603i	−1.25824	+	0.726446i
$592$	−17.3205	+	10.0000i	−0.711868	+	0.410997i
$593$		−	26.7846i		−	1.09991i	−0.835194	−	0.549956i	$-0.814644\pi$
$593$		−	26.7846i		−	1.09991i	0.835194	−	0.549956i	$-0.185356\pi$
$594$	−16.3923	−	28.3923i	−0.672584	−	1.16495i
$595$	3.46410	−	6.00000i	0.142014	−	0.245976i
$596$	−6.80385	−	3.92820i	−0.278696	−	0.160905i
$597$	−54.6410			−2.23631
$598$		0			0
$599$	−7.60770			−0.310842			−0.155421	−	0.987848i	$-0.549673\pi$
$599$	−7.60770			−0.310842			−0.155421	+	0.987848i	$0.549673\pi$
$600$	−4.09808	−	2.36603i	−0.167303	−	0.0965926i
$601$	−21.7846	+	37.7321i	−0.888613	+	1.53912i	−0.0470967	+	0.998890i	$0.514997\pi$
$601$	−21.7846	+	37.7321i	−0.888613	+	1.53912i	−0.841516	+	0.540232i	$0.818336\pi$
$602$	0.339746	+	0.588457i	0.0138470	+	0.0239837i
$603$			28.5359i			1.16207i
$604$	−1.56218	+	0.901924i	−0.0635641	+	0.0366988i
$605$	9.86603	−	5.69615i	0.401111	−	0.231582i
$606$		−	4.39230i		−	0.178425i
$607$	−12.4904	−	21.6340i	−0.506969	−	0.878096i	−0.999967	−	0.00806581i	$-0.997433\pi$
$607$	−12.4904	−	21.6340i	−0.506969	−	0.878096i	0.492999	−	0.870030i	$-0.335901\pi$
$608$	−16.0981	+	27.8827i	−0.652863	+	1.13079i
$609$	−12.0000	−	6.92820i	−0.486265	−	0.280745i
$610$	14.5359			0.588541
$611$		0			0
$612$	−15.4641			−0.625099
$613$	−22.5167	−	13.0000i	−0.909439	−	0.525065i	−0.0291886	−	0.999574i	$-0.509292\pi$
$613$	−22.5167	−	13.0000i	−0.909439	−	0.525065i	−0.880251	+	0.474509i	$0.842626\pi$
$614$	−16.2679	+	28.1769i	−0.656521	+	1.13713i
$615$	−4.73205	−	8.19615i	−0.190815	−	0.330501i
$616$		−	16.3923i		−	0.660465i
$617$	29.1962	−	16.8564i	1.17539	−	0.678613i	0.220449	−	0.975399i	$-0.429248\pi$
$617$	29.1962	−	16.8564i	1.17539	−	0.678613i	0.954944	+	0.296785i	$0.0959145\pi$
$618$	−0.803848	+	0.464102i	−0.0323355	+	0.0186689i
$619$		−	6.98076i		−	0.280581i	−0.990110	−	0.140290i	$-0.955196\pi$
$619$		−	6.98076i		−	0.280581i	0.990110	−	0.140290i	$-0.0448036\pi$
$620$	5.09808	+	8.83013i	0.204744	+	0.354626i
$621$	2.53590	−	4.39230i	0.101762	−	0.176257i
$622$	24.5885	+	14.1962i	0.985907	+	0.569214i
$623$	25.8564			1.03592
$624$		0			0
$625$	1.00000			0.0400000
$626$	−21.5885	−	12.4641i	−0.862848	−	0.498166i
$627$	−40.0526	+	69.3731i	−1.59955	+	2.77049i
$628$	−5.00000	−	8.66025i	−0.199522	−	0.345582i
$629$			13.8564i			0.552491i
$630$	13.3923	−	7.73205i	0.533562	−	0.308052i
$631$	−5.02628	+	2.90192i	−0.200093	+	0.115524i	−0.596699	−	0.802465i	$-0.703521\pi$
$631$	−5.02628	+	2.90192i	−0.200093	+	0.115524i	0.396606	+	0.917989i	$0.370188\pi$
$632$			14.5359i			0.578207i
$633$	−10.9282	−	18.9282i	−0.434357	−	0.752329i
$634$	−20.7846	+	36.0000i	−0.825462	+	1.42974i
$635$	−14.0263	−	8.09808i	−0.556616	−	0.321362i
$636$	−28.3923			−1.12583
$637$		0			0
$638$	−20.7846			−0.822871
$639$	−18.2942	−	10.5622i	−0.723708	−	0.417833i
$640$	−6.06218	+	10.5000i	−0.239629	+	0.415049i
$641$	6.46410	+	11.1962i	0.255317	+	0.442221i	0.964981	−	0.262318i	$-0.0844869\pi$
$641$	6.46410	+	11.1962i	0.255317	+	0.442221i	−0.709665	+	0.704539i	$0.751154\pi$
$642$		−	83.5692i		−	3.29821i
$643$	−5.87564	+	3.39230i	−0.231713	+	0.133779i	−0.611362	−	0.791351i	$-0.709378\pi$
$643$	−5.87564	+	3.39230i	−0.231713	+	0.133779i	0.379649	+	0.925131i	$0.376045\pi$
$644$	−2.19615	+	1.26795i	−0.0865405	+	0.0499642i
$645$		−	0.535898i		−	0.0211010i
$646$	18.5885	+	32.1962i	0.731353	+	1.26674i
$647$	11.0263	−	19.0981i	0.433488	−	0.750823i	−0.563683	−	0.825991i	$-0.690616\pi$
$647$	11.0263	−	19.0981i	0.433488	−	0.750823i	0.997171	+	0.0751683i	$0.0239494\pi$
$648$	−3.69615	−	2.13397i	−0.145199	−	0.0838304i
$649$	43.1769			1.69484
$650$		0			0
$651$	55.7128			2.18356
$652$	12.4641	+	7.19615i	0.488132	+	0.281823i
$653$	−3.92820	+	6.80385i	−0.153722	+	0.266255i	−0.932593	−	0.360929i	$-0.882460\pi$
$653$	−3.92820	+	6.80385i	−0.153722	+	0.266255i	0.778871	+	0.627185i	$0.215793\pi$
$654$	−4.73205	−	8.19615i	−0.185038	−	0.320495i
$655$		0			0
$656$	−15.0000	+	8.66025i	−0.585652	+	0.338126i
$657$	15.4641	−	8.92820i	0.603312	−	0.348322i
$658$			20.7846i			0.810268i
$659$	10.7321	+	18.5885i	0.418061	+	0.724103i	0.995744	−	0.0921577i	$-0.0293764\pi$
$659$	10.7321	+	18.5885i	0.418061	+	0.724103i	−0.577683	+	0.816261i	$0.696043\pi$
$660$	6.46410	−	11.1962i	0.251615	−	0.435810i
$661$	9.33975	+	5.39230i	0.363274	+	0.209736i	0.670516	−	0.741895i	$-0.266073\pi$
$661$	9.33975	+	5.39230i	0.363274	+	0.209736i	−0.307242	+	0.951631i	$0.599406\pi$
$662$	4.48334			0.174250
$663$		0			0
$664$	−10.3923			−0.403300
$665$	−10.7321	−	6.19615i	−0.416171	−	0.240276i
$666$	−15.4641	+	26.7846i	−0.599222	+	1.03788i
$667$	−1.60770	−	2.78461i	−0.0622502	−	0.107821i
$668$		−	0.928203i		−	0.0359133i
$669$	4.73205	−	2.73205i	0.182952	−	0.105627i
$670$	−9.58846	+	5.53590i	−0.370434	+	0.213870i
$671$		−	39.7128i		−	1.53310i
$672$	−14.1962	−	24.5885i	−0.547628	−	0.948520i
$673$	−7.19615	+	12.4641i	−0.277391	+	0.480456i	−0.970736	−	0.240151i	$-0.922803\pi$
$673$	−7.19615	+	12.4641i	−0.277391	+	0.480456i	0.693344	+	0.720606i	$0.256137\pi$
$674$	39.5885	+	22.8564i	1.52489	+	0.880396i
$675$	−4.00000			−0.153960
$676$		0			0
$677$	10.3923			0.399409			0.199704	−	0.979856i	$-0.436002\pi$
$677$	10.3923			0.399409			0.199704	+	0.979856i	$0.436002\pi$
$678$	34.9808	+	20.1962i	1.34343	+	0.775629i
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$		−	9.46410i		−	0.362665i
$682$	72.3731	−	41.7846i	2.77131	−	1.60002i
$683$	−28.1769	+	16.2679i	−1.07816	+	0.622476i	−0.930399	−	0.366547i	$-0.880540\pi$
$683$	−28.1769	+	16.2679i	−1.07816	+	0.622476i	−0.147760	+	0.989023i	$0.547206\pi$
$684$			27.6603i			1.05762i
$685$	0.464102	+	0.803848i	0.0177324	+	0.0307134i
$686$	17.3205	−	30.0000i	0.661300	−	1.14541i
$687$	15.1244	+	8.73205i	0.577030	+	0.333149i
$688$	−0.980762			−0.0373912
$689$		0			0
$690$	6.00000			0.228416
$691$	41.3660	+	23.8827i	1.57364	+	0.908540i	0.995718	+	0.0924469i	$0.0294688\pi$
$691$	41.3660	+	23.8827i	1.57364	+	0.908540i	0.577920	+	0.816093i	$0.303865\pi$
$692$	−4.26795	+	7.39230i	−0.162243	+	0.281013i
$693$	−21.1244	−	36.5885i	−0.802448	−	1.38988i
$694$			9.80385i			0.372149i
$695$	−10.7321	+	6.19615i	−0.407090	+	0.235033i
$696$	10.3923	−	6.00000i	0.393919	−	0.227429i
$697$			12.0000i			0.454532i
$698$	−12.4641	−	21.5885i	−0.471773	−	0.817135i
$699$	−8.19615	+	14.1962i	−0.310007	+	0.536948i
$700$	1.73205	+	1.00000i	0.0654654	+	0.0377964i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	24.7846			0.934769
$704$	4.09808	+	2.36603i	0.154452	+	0.0891729i
$705$	8.19615	−	14.1962i	0.308685	−	0.534658i
$706$	24.0000	+	41.5692i	0.903252	+	1.56448i
$707$		−	1.85641i		−	0.0698174i
$708$	21.5885	−	12.4641i	0.811344	−	0.468430i
$709$	−26.3205	+	15.1962i	−0.988487	+	0.570703i	−0.904822	−	0.425790i	$-0.859996\pi$
$709$	−26.3205	+	15.1962i	−0.988487	+	0.570703i	−0.0836656	+	0.996494i	$0.526663\pi$
$710$		−	8.19615i		−	0.307596i
$711$	18.7321	+	32.4449i	0.702507	+	1.21678i
$712$	−11.1962	+	19.3923i	−0.419594	+	0.726757i
$713$	11.1962	+	6.46410i	0.419299	+	0.242083i
$714$	−32.7846			−1.22693
$715$		0			0
$716$	−18.9282			−0.707380
$717$	33.5885	+	19.3923i	1.25438	+	0.724219i
$718$	−1.90192	+	3.29423i	−0.0709792	+	0.122940i
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	0.517649	−	0.855593i	$-0.326807\pi$
$719$	−12.9282	−	22.3923i	−0.482141	−	0.835092i	−0.999790	+	0.0205009i	$0.993474\pi$
$720$			22.3205i			0.831836i
$721$	−0.339746	+	0.196152i	−0.0126528	+	0.00730510i
$722$	29.0885	−	16.7942i	1.08256	−	0.625016i
$723$			6.53590i			0.243073i
$724$	−0.196152	−	0.339746i	−0.00728995	−	0.0126266i
$725$	−1.26795	+	2.19615i	−0.0470905	+	0.0815631i
$726$	−46.6865	−	26.9545i	−1.73270	−	1.00037i
$727$	−44.5885			−1.65369			−0.826847	−	0.562427i	$-0.809868\pi$
$727$	−44.5885			−1.65369			−0.826847	+	0.562427i	$0.809868\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	6.00000	+	3.46410i	0.222070	+	0.128212i
$731$	−0.339746	+	0.588457i	−0.0125660	+	0.0217649i
$732$	−11.4641	−	19.8564i	−0.423725	−	0.733914i
$733$			38.0000i			1.40356i	0.712393	+	0.701781i	$0.247612\pi$
$733$			38.0000i			1.40356i	−0.712393	+	0.701781i	$0.752388\pi$
$734$	−17.7058	+	10.2224i	−0.653532	+	0.377317i
$735$	−7.09808	+	4.09808i	−0.261816	+	0.151160i
$736$		−	6.58846i		−	0.242854i
$737$	15.1244	+	26.1962i	0.557113	+	0.964948i
$738$	−13.3923	+	23.1962i	−0.492978	+	0.853862i
$739$	−15.7583	−	9.09808i	−0.579680	−	0.334678i	0.181326	−	0.983423i	$-0.441961\pi$
$739$	−15.7583	−	9.09808i	−0.579680	−	0.334678i	−0.761006	+	0.648745i	$0.775294\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	−36.0000			−1.32160
$743$	13.9808	+	8.07180i	0.512904	+	0.296126i	0.734027	−	0.679121i	$-0.237639\pi$
$743$	13.9808	+	8.07180i	0.512904	+	0.296126i	−0.221122	+	0.975246i	$0.570972\pi$
$744$	−24.1244	+	41.7846i	−0.884442	+	1.53190i
$745$	3.92820	+	6.80385i	0.143918	+	0.249274i
$746$			17.3205i			0.634149i
$747$	−23.1962	+	13.3923i	−0.848703	+	0.489999i
$748$	−14.1962	+	8.19615i	−0.519063	+	0.299681i
$749$		−	35.3205i		−	1.29058i
$750$	−2.36603	−	4.09808i	−0.0863950	−	0.149641i
$751$	18.1962	−	31.5167i	0.663987	−	1.15006i	−0.315572	−	0.948902i	$-0.602196\pi$
$751$	18.1962	−	31.5167i	0.663987	−	1.15006i	0.979559	−	0.201158i	$-0.0644703\pi$
$752$	−25.9808	−	15.0000i	−0.947421	−	0.546994i
$753$	58.6410			2.13700
$754$		0			0
$755$	1.80385			0.0656487
$756$	−6.92820	−	4.00000i	−0.251976	−	0.145479i
$757$	1.19615	−	2.07180i	0.0434749	−	0.0753007i	−0.843469	−	0.537178i	$-0.819490\pi$
$757$	1.19615	−	2.07180i	0.0434749	−	0.0753007i	0.886944	+	0.461877i	$0.152824\pi$
$758$	−16.4378	−	28.4711i	−0.597049	−	1.03412i
$759$		−	16.3923i		−	0.595003i
$760$	9.29423	−	5.36603i	0.337137	−	0.194646i
$761$	17.1962	−	9.92820i	0.623360	−	0.359897i	−0.154816	−	0.987943i	$-0.549478\pi$
$761$	17.1962	−	9.92820i	0.623360	−	0.359897i	0.778176	+	0.628046i	$0.216145\pi$
$762$			76.6410i			2.77641i
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−2.53590	+	4.39230i	−0.0917456	+	0.158908i
$765$	13.3923	+	7.73205i	0.484200	+	0.279553i
$766$	22.3923			0.809067
$767$		0			0
$768$	51.9090			1.87310
$769$	−30.1244	−	17.3923i	−1.08631	−	0.627183i	−0.153720	−	0.988114i	$-0.549125\pi$
$769$	−30.1244	−	17.3923i	−1.08631	−	0.627183i	−0.932592	+	0.360932i	$0.882459\pi$
$770$	8.19615	−	14.1962i	0.295369	−	0.511594i
$771$	27.1244	+	46.9808i	0.976860	+	1.69197i
$772$		−	10.0000i		−	0.359908i
$773$	6.00000	−	3.46410i	0.215805	−	0.124595i	−0.388201	−	0.921575i	$-0.626903\pi$
$773$	6.00000	−	3.46410i	0.215805	−	0.124595i	0.604006	+	0.796980i	$0.293570\pi$
$774$	−1.31347	+	0.758330i	−0.0472116	+	0.0272576i
$775$		−	10.1962i		−	0.366257i
$776$	−1.73205	−	3.00000i	−0.0621770	−	0.107694i
$777$	−10.9282	+	18.9282i	−0.392047	+	0.679046i
$778$	−9.00000	−	5.19615i	−0.322666	−	0.186291i
$779$	21.4641			0.769031
$780$		0			0
$781$	−22.3923			−0.801260
$782$	−6.58846	−	3.80385i	−0.235603	−	0.136025i
$783$	5.07180	−	8.78461i	0.181251	−	0.313936i
$784$	7.50000	+	12.9904i	0.267857	+	0.463942i
$785$			10.0000i			0.356915i
$786$		0			0
$787$	−27.3397	+	15.7846i	−0.974557	+	0.562661i	−0.900622	−	0.434603i	$-0.856889\pi$
$787$	−27.3397	+	15.7846i	−0.974557	+	0.562661i	−0.0739343	+	0.997263i	$0.523556\pi$
$788$			12.9282i			0.460548i
$789$	−1.73205	−	3.00000i	−0.0616626	−	0.106803i
$790$	−7.26795	+	12.5885i	−0.258582	+	0.447877i
$791$	14.7846	+	8.53590i	0.525680	+	0.303502i
$792$	36.5885			1.30011
$793$		0			0
$794$	−49.8564			−1.76934
$795$	24.5885	+	14.1962i	0.872063	+	0.503486i
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−20.3205	−	35.1962i	−0.719789	−	1.24671i	−0.961083	−	0.276260i	$-0.910905\pi$
$797$	−20.3205	−	35.1962i	−0.719789	−	1.24671i	0.241294	−	0.970452i	$-0.422428\pi$
$798$			58.6410i			2.07587i
$799$	−18.0000	+	10.3923i	−0.636794	+	0.367653i
$800$	−4.50000	+	2.59808i	−0.159099	+	0.0918559i
$801$			57.7128i			2.03918i
$802$	−31.9808	−	55.3923i	−1.12928	−	1.95597i
$803$	9.46410	−	16.3923i	0.333981	−	0.578472i
$804$	15.1244	+	8.73205i	0.533395	+	0.307956i
$805$	2.53590			0.0893787
$806$		0			0
$807$	−54.2487			−1.90965
$808$	1.39230	+	0.803848i	0.0489811	+	0.0282793i
$809$	1.26795	−	2.19615i	0.0445787	−	0.0772126i	−0.842875	−	0.538109i	$-0.819139\pi$
$809$	1.26795	−	2.19615i	0.0445787	−	0.0772126i	0.887454	+	0.460897i	$0.152472\pi$
$810$	−2.13397	−	3.69615i	−0.0749802	−	0.129870i
$811$			17.8038i			0.625178i	0.949889	+	0.312589i	$0.101196\pi$
$811$			17.8038i			0.625178i	−0.949889	+	0.312589i	$0.898804\pi$
$812$	−4.39230	+	2.53590i	−0.154140	+	0.0889926i
$813$	−73.3013	+	42.3205i	−2.57079	+	1.48425i
$814$			32.7846i			1.14910i
$815$	−7.19615	−	12.4641i	−0.252070	−	0.436598i
$816$	23.6603	−	40.9808i	0.828275	−	1.43461i
$817$	1.05256	+	0.607695i	0.0368244	+	0.0212606i
$818$	−30.4974			−1.06632
$819$		0			0
$820$	−3.46410			−0.120972
$821$	−24.8038	−	14.3205i	−0.865660	−	0.499789i	0.000243419	−	1.00000i	$-0.499923\pi$
$821$	−24.8038	−	14.3205i	−0.865660	−	0.499789i	−0.865904	+	0.500211i	$0.833256\pi$
$822$	2.19615	−	3.80385i	0.0765996	−	0.132674i
$823$	−7.70577	−	13.3468i	−0.268606	−	0.465240i	0.699896	−	0.714245i	$-0.253230\pi$
$823$	−7.70577	−	13.3468i	−0.268606	−	0.465240i	−0.968502	+	0.249005i	$0.919896\pi$
$824$		−	0.339746i		−	0.0118356i
$825$	−11.1962	+	6.46410i	−0.389800	+	0.225051i
$826$	27.3731	−	15.8038i	0.952431	−	0.549886i
$827$		−	18.0000i		−	0.625921i	−0.949766	−	0.312961i	$-0.898679\pi$
$827$		−	18.0000i		−	0.625921i	0.949766	−	0.312961i	$-0.101321\pi$
$828$	−2.83013	−	4.90192i	−0.0983537	−	0.170354i
$829$	0.196152	−	0.339746i	0.00681266	−	0.0117999i	−0.862599	−	0.505888i	$-0.831165\pi$
$829$	0.196152	−	0.339746i	0.00681266	−	0.0117999i	0.869412	+	0.494088i	$0.164498\pi$
$830$	−9.00000	−	5.19615i	−0.312395	−	0.180361i
$831$	72.1051			2.50130
$832$		0			0
$833$	10.3923			0.360072
$834$	50.7846	+	29.3205i	1.75853	+	1.01529i
$835$	−0.464102	+	0.803848i	−0.0160609	+	0.0278183i
$836$	14.6603	+	25.3923i	0.507035	+	0.878211i
$837$			40.7846i			1.40972i
$838$	3.80385	−	2.19615i	0.131402	−	0.0758648i
$839$	−0.294229	+	0.169873i	−0.0101579	+	0.00586467i	−0.505070	−	0.863078i	$-0.668533\pi$
$839$	−0.294229	+	0.169873i	−0.0101579	+	0.00586467i	0.494912	+	0.868943i	$0.335200\pi$
$840$			9.46410i			0.326543i
$841$	11.2846	+	19.5455i	0.389124	+	0.673983i
$842$	26.6603	−	46.1769i	0.918773	−	1.59136i
$843$	52.9808	+	30.5885i	1.82475	+	1.05352i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	−46.3923			−1.59500
$847$	−19.7321	−	11.3923i	−0.678001	−	0.391444i
$848$	25.9808	−	45.0000i	0.892183	−	1.54531i
$849$	44.5167	+	77.1051i	1.52781	+	2.64624i
$850$			6.00000i			0.205798i
$851$	−4.39230	+	2.53590i	−0.150566	+	0.0869295i
$852$	−11.1962	+	6.46410i	−0.383574	+	0.221456i
$853$		−	8.00000i		−	0.273915i	−0.990577	−	0.136957i	$-0.956268\pi$
$853$		−	8.00000i		−	0.273915i	0.990577	−	0.136957i	$-0.0437323\pi$
$854$	−14.5359	−	25.1769i	−0.497408	−	0.861536i
$855$	13.8301	−	23.9545i	0.472980	−	0.819226i
$856$	26.4904	+	15.2942i	0.905423	+	0.522746i
$857$	35.5692			1.21502			0.607511	−	0.794311i	$-0.292168\pi$
$857$	35.5692			1.21502			0.607511	+	0.794311i	$0.292168\pi$
$858$		0			0
$859$	−17.1769			−0.586069			−0.293034	−	0.956102i	$-0.594665\pi$
$859$	−17.1769			−0.586069			−0.293034	+	0.956102i	$0.594665\pi$
$860$	−0.169873	−	0.0980762i	−0.00579262	−	0.00334437i
$861$	−9.46410	+	16.3923i	−0.322536	+	0.558648i
$862$	22.0981	+	38.2750i	0.752663	+	1.30365i
$863$		−	38.7846i		−	1.32024i	−0.751159	−	0.660122i	$-0.770505\pi$
$863$		−	38.7846i		−	1.32024i	0.751159	−	0.660122i	$-0.229495\pi$
$864$	18.0000	−	10.3923i	0.612372	−	0.353553i
$865$	7.39230	−	4.26795i	0.251346	−	0.145115i
$866$			60.2487i			2.04733i
$867$	6.83013	+	11.8301i	0.231963	+	0.401772i
$868$	10.1962	−	17.6603i	0.346080	−	0.599428i
$869$	34.3923	+	19.8564i	1.16668	+	0.673582i
$870$	12.0000			0.406838
$871$		0			0
$872$	3.46410			0.117309
$873$	−7.73205	−	4.46410i	−0.261690	−	0.151087i
$874$	−6.80385	+	11.7846i	−0.230144	+	0.398620i
$875$	−1.00000	−	1.73205i	−0.0338062	−	0.0585540i
$876$		−	10.9282i		−	0.369230i
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	−0.470471	−	0.882415i	$-0.655916\pi$
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	0.528958	+	0.848648i	$0.322583\pi$
$878$	48.0000	−	27.7128i	1.61992	−	0.935262i
$879$			13.8564i			0.467365i
$880$	11.8301	+	20.4904i	0.398794	+	0.690731i
$881$	−23.6603	+	40.9808i	−0.797134	+	1.38068i	0.124341	+	0.992240i	$0.460318\pi$
$881$	−23.6603	+	40.9808i	−0.797134	+	1.38068i	−0.921475	+	0.388437i	$0.873015\pi$
$882$	20.0885	+	11.5981i	0.676414	+	0.390528i
$883$	−23.8038			−0.801063			−0.400532	−	0.916283i	$-0.631175\pi$
$883$	−23.8038			−0.801063			−0.400532	+	0.916283i	$0.631175\pi$
$884$		0			0
$885$	−24.9282			−0.837952
$886$	−25.4711	−	14.7058i	−0.855720	−	0.494050i
$887$	23.9545	−	41.4904i	0.804313	−	1.39311i	−0.112441	−	0.993658i	$-0.535867\pi$
$887$	23.9545	−	41.4904i	0.804313	−	1.39311i	0.916754	−	0.399452i	$-0.130800\pi$
$888$	−9.46410	−	16.3923i	−0.317594	−	0.550090i
$889$			32.3923i			1.08640i
$890$	−19.3923	+	11.1962i	−0.650032	+	0.375296i
$891$	−10.0981	+	5.83013i	−0.338298	+	0.195317i
$892$		−	2.00000i		−	0.0669650i
$893$	18.5885	+	32.1962i	0.622039	+	1.07740i
$894$	18.5885	−	32.1962i	0.621691	−	1.07680i
$895$	16.3923	+	9.46410i	0.547934	+	0.316350i
$896$	24.2487			0.810093
$897$		0			0
$898$	−35.5692			−1.18696
$899$	22.3923	+	12.9282i	0.746825	+	0.431180i
$900$	−2.23205	+	3.86603i	−0.0744017	+	0.128868i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$			28.3923i			0.945360i
$903$	−0.928203	+	0.535898i	−0.0308887	+	0.0178336i
$904$	−12.8038	+	7.39230i	−0.425850	+	0.245864i
$905$			0.392305i			0.0130407i
$906$	−4.26795	−	7.39230i	−0.141793	−	0.245593i
$907$	−26.8827	+	46.5622i	−0.892625	+	1.54607i	−0.0559081	+	0.998436i	$0.517805\pi$
$907$	−26.8827	+	46.5622i	−0.892625	+	1.54607i	−0.836717	+	0.547636i	$0.815528\pi$
$908$	−3.00000	−	1.73205i	−0.0995585	−	0.0574801i
$909$	4.14359			0.137434
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−73.3013	−	42.3205i	−2.42725	−	1.40137i
$913$	−14.1962	+	24.5885i	−0.469824	+	0.813759i
$914$	−9.33975	−	16.1769i	−0.308931	−	0.535085i
$915$			22.9282i			0.757983i
$916$	5.53590	−	3.19615i	0.182911	−	0.105604i
$917$		0			0
$918$		−	24.0000i		−	0.792118i
$919$	−4.58846	−	7.94744i	−0.151359	−	0.262162i	0.780368	−	0.625320i	$-0.215032\pi$
$919$	−4.58846	−	7.94744i	−0.151359	−	0.262162i	−0.931727	+	0.363158i	$0.881698\pi$
$920$	−1.09808	+	1.90192i	−0.0362025	+	0.0627046i
$921$	−44.4449	−	25.6603i	−1.46451	−	0.845534i
$922$	−6.00000			−0.197599
$923$		0			0
$924$	−25.8564			−0.850613
$925$	3.46410	+	2.00000i	0.113899	+	0.0657596i
$926$	−2.07180	+	3.58846i	−0.0680835	+	0.117924i
$927$	−0.437822	−	0.758330i	−0.0143800	−	0.0249068i
$928$		−	13.1769i		−	0.432553i
$929$	38.5692	−	22.2679i	1.26542	−	0.730588i	0.291298	−	0.956632i	$-0.405913\pi$
$929$	38.5692	−	22.2679i	1.26542	−	0.730588i	0.974117	+	0.226045i	$0.0725795\pi$
$930$	−41.7846	+	24.1244i	−1.37017	+	0.791069i
$931$		−	18.5885i		−	0.609212i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	−22.3923	+	38.7846i	−0.733091	+	1.26975i
$934$	−41.7058	−	24.0788i	−1.36465	−	0.787884i
$935$	16.3923			0.536086
$936$		0			0
$937$	34.7846			1.13636			0.568182	−	0.822903i	$-0.307647\pi$
$937$	34.7846			1.13636			0.568182	+	0.822903i	$0.307647\pi$
$938$	19.1769	+	11.0718i	0.626148	+	0.361507i
$939$	19.6603	−	34.0526i	0.641588	−	1.11126i
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$			31.1769i			1.01634i	0.861257	+	0.508169i	$0.169678\pi$
$941$			31.1769i			1.01634i	−0.861257	+	0.508169i	$0.830322\pi$
$942$	40.9808	−	23.6603i	1.33523	−	0.770893i
$943$	−3.80385	+	2.19615i	−0.123870	+	0.0715166i
$944$			45.6218i			1.48486i
$945$	4.00000	+	6.92820i	0.130120	+	0.225374i
$946$	−0.803848	+	1.39230i	−0.0261353	+	0.0452677i
$947$	35.1962	+	20.3205i	1.14372	+	0.660328i	0.947349	−	0.320202i	$-0.103751\pi$
$947$	35.1962	+	20.3205i	1.14372	+	0.660328i	0.196372	+	0.980529i	$0.437084\pi$
$948$	22.9282			0.744673
$949$		0			0
$950$	10.7321			0.348194
$951$	−56.7846	−	32.7846i	−1.84137	−	1.06311i
$952$	6.00000	−	10.3923i	0.194461	−	0.336817i
$953$	0.464102	+	0.803848i	0.0150337	+	0.0260392i	0.873444	−	0.486924i	$-0.161881\pi$
$953$	0.464102	+	0.803848i	0.0150337	+	0.0260392i	−0.858411	+	0.512963i	$0.828548\pi$
$954$		−	80.3538i		−	2.60155i
$955$	4.39230	−	2.53590i	0.142132	−	0.0820597i
$956$	12.2942	−	7.09808i	0.397624	−	0.229568i
$957$		−	32.7846i		−	1.05978i
$958$	30.8827	+	53.4904i	0.997774	+	1.72820i
$959$	0.928203	−	1.60770i	0.0299732	−	0.0519152i
$960$	−2.36603	−	1.36603i	−0.0763631	−	0.0440883i
$961$	−72.9615			−2.35360
$962$		0			0
$963$	78.8372			2.54049
$964$	2.07180	+	1.19615i	0.0667281	+	0.0385255i
$965$	−5.00000	+	8.66025i	−0.160956	+	0.278783i
$966$	−6.00000	−	10.3923i	−0.193047	−	0.334367i
$967$		−	50.3923i		−	1.62051i	−0.586079	−	0.810254i	$-0.699329\pi$
$967$		−	50.3923i		−	1.62051i	0.586079	−	0.810254i	$-0.300671\pi$
$968$	17.0885	−	9.86603i	0.549244	−	0.317106i
$969$	−50.7846	+	29.3205i	−1.63144	+	0.941910i
$970$		−	3.46410i		−	0.111226i
$971$	−9.46410	−	16.3923i	−0.303717	−	0.526054i	0.673257	−	0.739408i	$-0.264895\pi$
$971$	−9.46410	−	16.3923i	−0.303717	−	0.526054i	−0.976975	+	0.213354i	$0.931561\pi$
$972$	−9.36603	+	16.2224i	−0.300415	+	0.520335i
$973$	21.4641	+	12.3923i	0.688108	+	0.397279i
$974$	−45.7128			−1.46473
$975$		0			0
$976$	41.9615			1.34316
$977$	13.6077	+	7.85641i	0.435349	+	0.251349i	0.701623	−	0.712549i	$-0.252459\pi$
$977$	13.6077	+	7.85641i	0.435349	+	0.251349i	−0.266274	+	0.963897i	$0.585793\pi$
$978$	−34.0526	+	58.9808i	−1.08888	+	1.88600i
$979$	30.5885	+	52.9808i	0.977611	+	1.69327i
$980$			3.00000i			0.0958315i
$981$	7.73205	−	4.46410i	0.246865	−	0.142528i
$982$	−3.80385	+	2.19615i	−0.121386	+	0.0700820i
$983$			34.3923i			1.09694i	0.836169	+	0.548472i	$0.184790\pi$
$983$			34.3923i			1.09694i	−0.836169	+	0.548472i	$0.815210\pi$
$984$	−8.19615	−	14.1962i	−0.261284	−	0.452557i
$985$	6.46410	−	11.1962i	0.205963	−	0.356739i
$986$	−13.1769	−	7.60770i	−0.419638	−	0.242278i
$987$	−32.7846			−1.04355
$988$		0			0
$989$	−0.248711			−0.00790856
$990$	31.6865	+	18.2942i	1.00706	+	0.581429i
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	−0.922538	−	0.385906i	$-0.873889\pi$
$991$	−4.00000	+	6.92820i	−0.127064	+	0.220082i	0.795474	+	0.605988i	$0.207222\pi$
$992$	26.4904	+	45.8827i	0.841070	+	1.45678i
$993$			7.07180i			0.224417i
$994$	−14.1962	+	8.19615i	−0.450275	+	0.259966i
$995$	17.3205	−	10.0000i	0.549097	−	0.317021i
$996$			16.3923i			0.519410i
$997$	−16.8038	−	29.1051i	−0.532183	−	0.921768i	−0.999294	−	0.0375696i	$-0.988038\pi$
$997$	−16.8038	−	29.1051i	−0.532183	−	0.921768i	0.467111	−	0.884199i	$-0.345295\pi$
$998$	33.7583	−	58.4711i	1.06860	−	1.85087i
$999$	−13.8564	−	8.00000i	−0.438397	−	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.c.316.1		4
13.2	odd	12		845.2.e.e.146.2		4
13.3	even	3		845.2.m.a.361.1		4
13.4	even	6		845.2.c.e.506.4		4
13.5	odd	4		845.2.e.e.191.2		4
13.6	odd	12		65.2.a.c.1.1	✓	2
13.7	odd	12		845.2.a.d.1.2		2
13.8	odd	4		845.2.e.f.191.1		4
13.9	even	3		845.2.c.e.506.2		4
13.10	even	6	inner	845.2.m.c.361.1		4
13.11	odd	12		845.2.e.f.146.1		4
13.12	even	2		845.2.m.a.316.1		4
39.20	even	12		7605.2.a.be.1.1		2
39.32	even	12		585.2.a.k.1.2		2
52.19	even	12		1040.2.a.h.1.1		2
65.19	odd	12		325.2.a.g.1.2		2
65.32	even	12		325.2.b.e.274.1		4
65.58	even	12		325.2.b.e.274.4		4
65.59	odd	12		4225.2.a.w.1.1		2
91.6	even	12		3185.2.a.k.1.1		2
104.19	even	12		4160.2.a.bj.1.2		2
104.45	odd	12		4160.2.a.y.1.1		2
143.32	even	12		7865.2.a.h.1.2		2
156.71	odd	12		9360.2.a.cm.1.1		2
195.32	odd	12		2925.2.c.v.2224.4		4
195.149	even	12		2925.2.a.z.1.1		2
195.188	odd	12		2925.2.c.v.2224.1		4
260.19	even	12		5200.2.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.c.1.1	✓	2	13.6	odd	12
325.2.a.g.1.2		2	65.19	odd	12
325.2.b.e.274.1		4	65.32	even	12
325.2.b.e.274.4		4	65.58	even	12
585.2.a.k.1.2		2	39.32	even	12
845.2.a.d.1.2		2	13.7	odd	12
845.2.c.e.506.2		4	13.9	even	3
845.2.c.e.506.4		4	13.4	even	6
845.2.e.e.146.2		4	13.2	odd	12
845.2.e.e.191.2		4	13.5	odd	4
845.2.e.f.146.1		4	13.11	odd	12
845.2.e.f.191.1		4	13.8	odd	4
845.2.m.a.316.1		4	13.12	even	2
845.2.m.a.361.1		4	13.3	even	3
845.2.m.c.316.1		4	1.1	even	1	trivial
845.2.m.c.361.1		4	13.10	even	6	inner
1040.2.a.h.1.1		2	52.19	even	12
2925.2.a.z.1.1		2	195.149	even	12
2925.2.c.v.2224.1		4	195.188	odd	12
2925.2.c.v.2224.4		4	195.32	odd	12
3185.2.a.k.1.1		2	91.6	even	12
4160.2.a.y.1.1		2	104.45	odd	12
4160.2.a.bj.1.2		2	104.19	even	12
4225.2.a.w.1.1		2	65.59	odd	12
5200.2.a.ca.1.2		2	260.19	even	12
7605.2.a.be.1.1		2	39.20	even	12
7865.2.a.h.1.2		2	143.32	even	12
9360.2.a.cm.1.1		2	156.71	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-4.09808 + 2.36603i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.73205i q^{8} +(-2.23205 - 3.86603i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{2} +(-1.36603 + 2.36603i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-4.09808 + 2.36603i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.73205i q^{8} +(-2.23205 - 3.86603i) q^{9} +(0.866025 - 1.50000i) q^{10} +(-4.09808 - 2.36603i) q^{11} -2.73205 q^{12} -3.46410 q^{14} +(2.36603 + 1.36603i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-1.73205 - 3.00000i) q^{17} -7.73205i q^{18} +(-5.36603 + 3.09808i) q^{19} +(0.866025 - 0.500000i) q^{20} -5.46410i q^{21} +(-4.09808 - 7.09808i) q^{22} +(0.633975 - 1.09808i) q^{23} +(4.09808 + 2.36603i) q^{24} -1.00000 q^{25} +4.00000 q^{27} +(-1.73205 - 1.00000i) q^{28} +(1.26795 - 2.19615i) q^{29} +(2.36603 + 4.09808i) q^{30} +10.1962i q^{31} +(4.50000 - 2.59808i) q^{32} +(11.1962 - 6.46410i) q^{33} -6.00000i q^{34} +(1.00000 + 1.73205i) q^{35} +(2.23205 - 3.86603i) q^{36} +(-3.46410 - 2.00000i) q^{37} -10.7321 q^{38} -1.73205 q^{40} +(-3.00000 - 1.73205i) q^{41} +(4.73205 - 8.19615i) q^{42} +(-0.0980762 - 0.169873i) q^{43} -4.73205i q^{44} +(-3.86603 + 2.23205i) q^{45} +(1.90192 - 1.09808i) q^{46} -6.00000i q^{47} +(6.83013 + 11.8301i) q^{48} +(-1.50000 + 2.59808i) q^{49} +(-1.50000 - 0.866025i) q^{50} +9.46410 q^{51} +10.3923 q^{53} +(6.00000 + 3.46410i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(1.73205 + 3.00000i) q^{56} -16.9282i q^{57} +(3.80385 - 2.19615i) q^{58} +(-7.90192 + 4.56218i) q^{59} +2.73205i q^{60} +(4.19615 + 7.26795i) q^{61} +(-8.83013 + 15.2942i) q^{62} +(7.73205 + 4.46410i) q^{63} -1.00000 q^{64} +22.3923 q^{66} +(-5.53590 - 3.19615i) q^{67} +(1.73205 - 3.00000i) q^{68} +(1.73205 + 3.00000i) q^{69} +3.46410i q^{70} +(4.09808 - 2.36603i) q^{71} +(-6.69615 + 3.86603i) q^{72} +4.00000i q^{73} +(-3.46410 - 6.00000i) q^{74} +(1.36603 - 2.36603i) q^{75} +(-5.36603 - 3.09808i) q^{76} +9.46410 q^{77} -8.39230 q^{79} +(-4.33013 - 2.50000i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-3.00000 - 5.19615i) q^{82} -6.00000i q^{83} +(4.73205 - 2.73205i) q^{84} +(-3.00000 + 1.73205i) q^{85} -0.339746i q^{86} +(3.46410 + 6.00000i) q^{87} +(-4.09808 + 7.09808i) q^{88} +(-11.1962 - 6.46410i) q^{89} -7.73205 q^{90} +1.26795 q^{92} +(-24.1244 - 13.9282i) q^{93} +(5.19615 - 9.00000i) q^{94} +(3.09808 + 5.36603i) q^{95} +14.1962i q^{96} +(1.73205 - 1.00000i) q^{97} +(-4.50000 + 2.59808i) q^{98} +21.1244i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	\( 4 q + 6 q^{2} - 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 6 q^{15} + 10 q^{16} - 18 q^{19} - 6 q^{22} + 6 q^{23} + 6 q^{24} - 4 q^{25} + 16 q^{27} + 12 q^{29} + 6 q^{30} + 18 q^{32} + 24 q^{33} + 4 q^{35} + 2 q^{36} - 36 q^{38} - 12 q^{41} + 12 q^{42} + 10 q^{43} - 12 q^{45} + 18 q^{46} + 10 q^{48} - 6 q^{49} - 6 q^{50} + 24 q^{51} + 24 q^{54} - 6 q^{55} + 36 q^{58} - 42 q^{59} - 4 q^{61} - 18 q^{62} + 24 q^{63} - 4 q^{64} + 48 q^{66} - 36 q^{67} + 6 q^{71} - 6 q^{72} + 2 q^{75} - 18 q^{76} + 24 q^{77} + 8 q^{79} - 2 q^{81} - 12 q^{82} + 12 q^{84} - 12 q^{85} - 6 q^{88} - 24 q^{89} - 24 q^{90} + 12 q^{92} - 48 q^{93} + 2 q^{95} - 18 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 - 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 6 * q^15 + 10 * q^16 - 18 * q^19 - 6 * q^22 + 6 * q^23 + 6 * q^24 - 4 * q^25 + 16 * q^27 + 12 * q^29 + 6 * q^30 + 18 * q^32 + 24 * q^33 + 4 * q^35 + 2 * q^36 - 36 * q^38 - 12 * q^41 + 12 * q^42 + 10 * q^43 - 12 * q^45 + 18 * q^46 + 10 * q^48 - 6 * q^49 - 6 * q^50 + 24 * q^51 + 24 * q^54 - 6 * q^55 + 36 * q^58 - 42 * q^59 - 4 * q^61 - 18 * q^62 + 24 * q^63 - 4 * q^64 + 48 * q^66 - 36 * q^67 + 6 * q^71 - 6 * q^72 + 2 * q^75 - 18 * q^76 + 24 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^82 + 12 * q^84 - 12 * q^85 - 6 * q^88 - 24 * q^89 - 24 * q^90 + 12 * q^92 - 48 * q^93 + 2 * q^95 - 18 * q^98

Introduction

L-functions

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