LMFDB - Embedded newform 676.2.f.i.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(99,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("676.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.f (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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.102930383934669717504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 2 x^{13} + 5 x^{12} - 8 x^{11} - 12 x^{10} + 32 x^{9} - 36 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 5x^14 - 2x^13 + 5x^12 - 8x^11 - 12x^10 + 32x^9 - 36x^8 + 64x^7 - 48x^6 - 64x^5 + 80x^4 - 64x^3 + 320x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.1
Root			$1.31256 + 0.526485i$ of defining polynomial
Character	$\chi$	$=$	676.239
Dual form			676.2.f.i.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39995 - 0.200331i) q^{2} +2.50548i q^{3} +(1.91973 + 0.560908i) q^{4} +(2.19962 - 2.19962i) q^{5} +(0.501925 - 3.50755i) q^{6} +(0.416921 - 0.416921i) q^{7} +(-2.57517 - 1.16983i) q^{8} -3.27743 q^{9} +O(q^{10})$	\(q+(-1.39995 - 0.200331i) q^{2} +2.50548i q^{3} +(1.91973 + 0.560908i) q^{4} +(2.19962 - 2.19962i) q^{5} +(0.501925 - 3.50755i) q^{6} +(0.416921 - 0.416921i) q^{7} +(-2.57517 - 1.16983i) q^{8} -3.27743 q^{9} +(-3.52002 + 2.63871i) q^{10} +(-2.08856 + 2.08856i) q^{11} +(-1.40534 + 4.80986i) q^{12} +(-0.667192 + 0.500148i) q^{14} +(5.51111 + 5.51111i) q^{15} +(3.37076 + 2.15359i) q^{16} +2.66719i q^{17} +(4.58824 + 0.656570i) q^{18} +(2.28350 + 2.28350i) q^{19} +(5.45648 - 2.98891i) q^{20} +(1.04459 + 1.04459i) q^{21} +(3.34229 - 2.50548i) q^{22} +2.06152 q^{23} +(2.93098 - 6.45204i) q^{24} -4.67667i q^{25} -0.695088i q^{27} +(1.03423 - 0.566524i) q^{28} +1.24363 q^{29} +(-6.61124 - 8.81933i) q^{30} +(6.34495 + 6.34495i) q^{31} +(-4.28748 - 3.69019i) q^{32} +(-5.23284 - 5.23284i) q^{33} +(0.534321 - 3.73394i) q^{34} -1.83414i q^{35} +(-6.29179 - 1.83834i) q^{36} +(0.366025 + 0.366025i) q^{37} +(-2.73933 - 3.65425i) q^{38} +(-8.23758 + 3.09122i) q^{40} +(4.09808 - 4.09808i) q^{41} +(-1.25311 - 1.67164i) q^{42} +7.21518 q^{43} +(-5.18097 + 2.83799i) q^{44} +(-7.20910 + 7.20910i) q^{45} +(-2.88603 - 0.412986i) q^{46} +(-3.16813 + 3.16813i) q^{47} +(-5.39577 + 8.44538i) q^{48} +6.65235i q^{49} +(-0.936882 + 6.54712i) q^{50} -6.68260 q^{51} +3.67667 q^{53} +(-0.139248 + 0.973090i) q^{54} +9.18808i q^{55} +(-1.56137 + 0.585918i) q^{56} +(-5.72126 + 5.72126i) q^{57} +(-1.74103 - 0.249138i) q^{58} +(-4.98392 + 4.98392i) q^{59} +(7.48864 + 13.6711i) q^{60} +7.95410 q^{61} +(-7.61154 - 10.1537i) q^{62} +(-1.36643 + 1.36643i) q^{63} +(5.26301 + 6.02501i) q^{64} +(6.27743 + 8.37403i) q^{66} +(-5.25669 - 5.25669i) q^{67} +(-1.49605 + 5.12030i) q^{68} +5.16509i q^{69} +(-0.367435 + 2.56771i) q^{70} +(1.44966 + 1.44966i) q^{71} +(8.43993 + 3.83402i) q^{72} +(-0.0440105 - 0.0440105i) q^{73} +(-0.439092 - 0.585744i) q^{74} +11.7173 q^{75} +(3.10288 + 5.66454i) q^{76} +1.74153i q^{77} -2.73286i q^{79} +(12.1515 - 2.67732i) q^{80} -8.09075 q^{81} +(-6.55808 + 4.91614i) q^{82} +(-10.1844 - 10.1844i) q^{83} +(1.41941 + 2.59125i) q^{84} +(5.86681 + 5.86681i) q^{85} +(-10.1009 - 1.44543i) q^{86} +3.11589i q^{87} +(7.82165 - 2.93514i) q^{88} +(-5.86739 - 5.86739i) q^{89} +(11.5366 - 8.64819i) q^{90} +(3.95757 + 1.15632i) q^{92} +(-15.8971 + 15.8971i) q^{93} +(5.06990 - 3.80056i) q^{94} +10.0457 q^{95} +(9.24570 - 10.7422i) q^{96} +(3.35308 - 3.35308i) q^{97} +(1.33267 - 9.31298i) q^{98} +(6.84510 - 6.84510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9	$ 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} + 6 q^{18} + 22 q^{20} + 28 q^{21} - 4 q^{24} + 36 q^{28} + 16 q^{29} + 2 q^{32} - 28 q^{33} - 14 q^{34} - 8 q^{37} - 40 q^{40} + 24 q^{41} + 56 q^{42} + 8 q^{44} - 20 q^{45} - 56 q^{46} + 20 q^{48} + 32 q^{50} - 32 q^{53} - 44 q^{54} - 12 q^{57} - 30 q^{58} + 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} - 28 q^{70} + 46 q^{72} - 20 q^{73} - 8 q^{74} + 8 q^{76} + 22 q^{80} - 96 q^{81} + 48 q^{84} + 52 q^{85} - 16 q^{86} - 44 q^{89} - 12 q^{92} - 112 q^{93} + 76 q^{94} + 72 q^{96} + 52 q^{97} - 70 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 + 6 * q^18 + 22 * q^20 + 28 * q^21 - 4 * q^24 + 36 * q^28 + 16 * q^29 + 2 * q^32 - 28 * q^33 - 14 * q^34 - 8 * q^37 - 40 * q^40 + 24 * q^41 + 56 * q^42 + 8 * q^44 - 20 * q^45 - 56 * q^46 + 20 * q^48 + 32 * q^50 - 32 * q^53 - 44 * q^54 - 12 * q^57 - 30 * q^58 + 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 - 28 * q^70 + 46 * q^72 - 20 * q^73 - 8 * q^74 + 8 * q^76 + 22 * q^80 - 96 * q^81 + 48 * q^84 + 52 * q^85 - 16 * q^86 - 44 * q^89 - 12 * q^92 - 112 * q^93 + 76 * q^94 + 72 * q^96 + 52 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.39995	−	0.200331i	−0.989916	−	0.141655i
$2$	−1.39995	−	0.200331i	−0.989916	−	0.141655i
$3$			2.50548i			1.44654i	0.690566	+	0.723270i	$0.257362\pi$
$3$			2.50548i			1.44654i	−0.690566	+	0.723270i	$0.742638\pi$
$4$	1.91973	+	0.560908i	0.959867	+	0.280454i
$5$	2.19962	−	2.19962i	0.983701	−	0.983701i	−0.0161686	−	0.999869i	$-0.505147\pi$
$5$	2.19962	−	2.19962i	0.983701	−	0.983701i	0.999869	+	0.0161686i	$0.00514685\pi$
$6$	0.501925	−	3.50755i	0.204910	−	1.43195i
$7$	0.416921	−	0.416921i	0.157581	−	0.157581i	−0.623913	−	0.781494i	$-0.714458\pi$
$7$	0.416921	−	0.416921i	0.157581	−	0.157581i	0.781494	+	0.623913i	$0.214458\pi$
$8$	−2.57517	−	1.16983i	−0.910460	−	0.413596i
$9$	−3.27743			−1.09248
$10$	−3.52002	+	2.63871i	−1.11313	+	0.834435i
$11$	−2.08856	+	2.08856i	−0.629724	+	0.629724i	−0.947999	−	0.318275i	$-0.896897\pi$
$11$	−2.08856	+	2.08856i	−0.629724	+	0.629724i	0.318275	+	0.947999i	$0.396897\pi$
$12$	−1.40534	+	4.80986i	−0.405688	+	1.38849i
$13$		0			0
$13$		0			0
$14$	−0.667192	+	0.500148i	−0.178315	+	0.133670i
$15$	5.51111	+	5.51111i	1.42296	+	1.42296i
$16$	3.37076	+	2.15359i	0.842691	+	0.538397i
$17$			2.66719i			0.646889i	0.946247	+	0.323445i	$0.104841\pi$
$17$			2.66719i			0.646889i	−0.946247	+	0.323445i	$0.895159\pi$
$18$	4.58824	+	0.656570i	1.08146	+	0.154755i
$19$	2.28350	+	2.28350i	0.523870	+	0.523870i	0.918738	−	0.394868i	$-0.129210\pi$
$19$	2.28350	+	2.28350i	0.523870	+	0.523870i	−0.394868	+	0.918738i	$0.629210\pi$
$20$	5.45648	−	2.98891i	1.22011	−	0.668339i
$21$	1.04459	+	1.04459i	0.227948	+	0.227948i
$22$	3.34229	−	2.50548i	0.712578	−	0.534170i
$23$	2.06152			0.429856			0.214928	−	0.976630i	$-0.431048\pi$
$23$	2.06152			0.429856			0.214928	+	0.976630i	$0.431048\pi$
$24$	2.93098	−	6.45204i	0.598283	−	1.31702i
$25$		−	4.67667i		−	0.935334i
$26$		0			0
$27$		−	0.695088i		−	0.133770i
$28$	1.03423	−	0.566524i	0.195452	−	0.107063i
$29$	1.24363			0.230937			0.115468	−	0.993311i	$-0.463163\pi$
$29$	1.24363			0.230937			0.115468	+	0.993311i	$0.463163\pi$
$30$	−6.61124	−	8.81933i	−1.20704	−	1.61018i
$31$	6.34495	+	6.34495i	1.13959	+	1.13959i	0.988524	+	0.151062i	$0.0482694\pi$
$31$	6.34495	+	6.34495i	1.13959	+	1.13959i	0.151062	+	0.988524i	$0.451731\pi$
$32$	−4.28748	−	3.69019i	−0.757926	−	0.652340i
$33$	−5.23284	−	5.23284i	−0.910920	−	0.910920i
$34$	0.534321	−	3.73394i	0.0916354	−	0.640366i
$35$		−	1.83414i		−	0.310026i
$36$	−6.29179	−	1.83834i	−1.04863	−	0.306389i
$37$	0.366025	+	0.366025i	0.0601742	+	0.0601742i	0.736553	−	0.676379i	$-0.236452\pi$
$37$	0.366025	+	0.366025i	0.0601742	+	0.0601742i	−0.676379	+	0.736553i	$0.736452\pi$
$38$	−2.73933	−	3.65425i	−0.444379	−	0.592797i
$39$		0			0
$40$	−8.23758	+	3.09122i	−1.30248	+	0.488765i
$41$	4.09808	−	4.09808i	0.640012	−	0.640012i	−0.310546	−	0.950558i	$-0.600512\pi$
$41$	4.09808	−	4.09808i	0.640012	−	0.640012i	0.950558	+	0.310546i	$0.100512\pi$
$42$	−1.25311	−	1.67164i	−0.193359	−	0.257939i
$43$	7.21518			1.10030			0.550152	−	0.835064i	$-0.314570\pi$
$43$	7.21518			1.10030			0.550152	+	0.835064i	$0.314570\pi$
$44$	−5.18097	+	2.83799i	−0.781060	+	0.427843i
$45$	−7.20910	+	7.20910i	−1.07467	+	1.07467i
$46$	−2.88603	−	0.412986i	−0.425521	−	0.0608915i
$47$	−3.16813	+	3.16813i	−0.462119	+	0.462119i	−0.899350	−	0.437230i	$-0.855959\pi$
$47$	−3.16813	+	3.16813i	−0.462119	+	0.462119i	0.437230	+	0.899350i	$0.355959\pi$
$48$	−5.39577	+	8.44538i	−0.778813	+	1.21899i
$49$			6.65235i			0.950336i
$50$	−0.936882	+	6.54712i	−0.132495	+	0.925902i
$51$	−6.68260			−0.935751
$52$		0			0
$53$	3.67667			0.505030			0.252515	−	0.967593i	$-0.418742\pi$
$53$	3.67667			0.505030			0.252515	+	0.967593i	$0.418742\pi$
$54$	−0.139248	+	0.973090i	−0.0189492	+	0.132421i
$55$			9.18808i			1.23892i
$56$	−1.56137	+	0.585918i	−0.208647	+	0.0782965i
$57$	−5.72126	+	5.72126i	−0.757799	+	0.757799i
$58$	−1.74103	−	0.249138i	−0.228608	−	0.0327134i
$59$	−4.98392	+	4.98392i	−0.648851	+	0.648851i	−0.952715	−	0.303864i	$-0.901723\pi$
$59$	−4.98392	+	4.98392i	−0.648851	+	0.648851i	0.303864	+	0.952715i	$0.401723\pi$
$60$	7.48864	+	13.6711i	0.966779	+	1.76493i
$61$	7.95410			1.01842			0.509209	−	0.860643i	$-0.329938\pi$
$61$	7.95410			1.01842			0.509209	+	0.860643i	$0.329938\pi$
$62$	−7.61154	−	10.1537i	−0.966666	−	1.28952i
$63$	−1.36643	+	1.36643i	−0.172154	+	0.172154i
$64$	5.26301	+	6.02501i	0.657876	+	0.753126i
$65$		0			0
$66$	6.27743	+	8.37403i	0.772698	+	1.03077i
$67$	−5.25669	−	5.25669i	−0.642207	−	0.642207i	0.308891	−	0.951097i	$-0.400042\pi$
$67$	−5.25669	−	5.25669i	−0.642207	−	0.642207i	−0.951097	+	0.308891i	$0.900042\pi$
$68$	−1.49605	+	5.12030i	−0.181423	+	0.620928i
$69$			5.16509i			0.621804i
$70$	−0.367435	+	2.56771i	−0.0439169	+	0.306900i
$71$	1.44966	+	1.44966i	0.172042	+	0.172042i	0.787876	−	0.615834i	$-0.211181\pi$
$71$	1.44966	+	1.44966i	0.172042	+	0.172042i	−0.615834	+	0.787876i	$0.711181\pi$
$72$	8.43993	+	3.83402i	0.994656	+	0.451844i
$73$	−0.0440105	−	0.0440105i	−0.00515104	−	0.00515104i	0.704527	−	0.709678i	$-0.251159\pi$
$73$	−0.0440105	−	0.0440105i	−0.00515104	−	0.00515104i	−0.709678	+	0.704527i	$0.751159\pi$
$74$	−0.439092	−	0.585744i	−0.0510434	−	0.0680914i
$75$	11.7173			1.35300
$76$	3.10288	+	5.66454i	0.355925	+	0.649768i
$77$			1.74153i			0.198466i
$78$		0			0
$79$		−	2.73286i		−	0.307471i	−0.988112	−	0.153735i	$-0.950870\pi$
$79$		−	2.73286i		−	0.307471i	0.988112	−	0.153735i	$-0.0491303\pi$
$80$	12.1515	−	2.67732i	1.35858	−	0.299334i
$81$	−8.09075			−0.898973
$82$	−6.55808	+	4.91614i	−0.724219	+	0.542897i
$83$	−10.1844	−	10.1844i	−1.11789	−	1.11789i	−0.992051	−	0.125834i	$-0.959839\pi$
$83$	−10.1844	−	10.1844i	−1.11789	−	1.11789i	−0.125834	−	0.992051i	$-0.540161\pi$
$84$	1.41941	+	2.59125i	0.154871	+	0.282728i
$85$	5.86681	+	5.86681i	0.636345	+	0.636345i
$86$	−10.1009	−	1.44543i	−1.08921	−	0.155864i
$87$			3.11589i			0.334059i
$88$	7.82165	−	2.93514i	0.833790	−	0.312887i
$89$	−5.86739	−	5.86739i	−0.621942	−	0.621942i	0.324086	−	0.946028i	$-0.394943\pi$
$89$	−5.86739	−	5.86739i	−0.621942	−	0.621942i	−0.946028	+	0.324086i	$0.894943\pi$
$90$	11.5366	−	8.64819i	1.21606	−	0.911599i
$91$		0			0
$92$	3.95757	+	1.15632i	0.412605	+	0.120555i
$93$	−15.8971	+	15.8971i	−1.64846	+	1.64846i
$94$	5.06990	−	3.80056i	0.522921	−	0.391997i
$95$	10.0457			1.03066
$96$	9.24570	−	10.7422i	0.943635	−	1.09637i
$97$	3.35308	−	3.35308i	0.340454	−	0.340454i	−0.516084	−	0.856538i	$-0.672611\pi$
$97$	3.35308	−	3.35308i	0.340454	−	0.340454i	0.856538	+	0.516084i	$0.172611\pi$
$98$	1.33267	−	9.31298i	0.134620	−	0.940753i
$99$	6.84510	−	6.84510i	0.687958	−	0.687958i
$100$	2.62318	−	8.97797i	0.262318	−	0.897797i
$101$			8.97841i			0.893386i	0.894687	+	0.446693i	$0.147398\pi$
$101$			8.97841i			0.893386i	−0.894687	+	0.446693i	$0.852602\pi$
$102$	9.35532	+	1.33873i	0.926314	+	0.132554i
$103$	−9.60170			−0.946084			−0.473042	−	0.881040i	$-0.656844\pi$
$103$	−9.60170			−0.946084			−0.473042	+	0.881040i	$0.656844\pi$
$104$		0			0
$105$	4.59540			0.448465
$106$	−5.14716	−	0.736551i	−0.499937	−	0.0715402i
$107$		−	18.8637i		−	1.82362i	−0.410614	−	0.911809i	$-0.634686\pi$
$107$		−	18.8637i		−	1.82362i	0.410614	−	0.911809i	$-0.365314\pi$
$108$	0.389880	−	1.33438i	0.0375163	−	0.128401i
$109$	2.95252	−	2.95252i	0.282800	−	0.282800i	−0.551425	−	0.834225i	$-0.685916\pi$
$109$	2.95252	−	2.95252i	0.282800	−	0.282800i	0.834225	+	0.551425i	$0.185916\pi$
$110$	1.84066	−	12.8629i	0.175500	−	1.22643i
$111$	−0.917069	+	0.917069i	−0.0870443	+	0.0870443i
$112$	2.30322	−	0.507466i	0.217634	−	0.0479510i
$113$	5.64288			0.530837			0.265419	−	0.964133i	$-0.414490\pi$
$113$	5.64288			0.530837			0.265419	+	0.964133i	$0.414490\pi$
$114$	9.15564	−	6.86334i	0.857504	−	0.642811i
$115$	4.53456	−	4.53456i	0.422850	−	0.422850i
$116$	2.38744	+	0.697563i	0.221669	+	0.0647671i
$117$		0			0
$118$	7.97568	−	5.97882i	0.734221	−	0.550395i
$119$	1.11201	+	1.11201i	0.101938	+	0.101938i
$120$	−7.74500	−	20.6391i	−0.707018	−	1.88408i
$121$			2.27585i			0.206895i
$122$	−11.1354	−	1.59345i	−1.00815	−	0.144264i
$123$	10.2676	+	10.2676i	0.925802	+	0.925802i
$124$	8.62169	+	15.7396i	0.774250	+	1.41345i
$125$	0.711203	+	0.711203i	0.0636119	+	0.0636119i
$126$	2.18667	−	1.63920i	0.194804	−	0.146031i
$127$	−12.0834			−1.07223			−0.536116	−	0.844144i	$-0.680109\pi$
$127$	−12.0834			−1.07223			−0.536116	+	0.844144i	$0.680109\pi$
$128$	−6.16097	−	9.48907i	−0.544558	−	0.838723i
$129$			18.0775i			1.59163i
$130$		0			0
$131$		−	19.1689i		−	1.67479i	−0.546597	−	0.837396i	$-0.684077\pi$
$131$		−	19.1689i		−	1.67479i	0.546597	−	0.837396i	$-0.315923\pi$
$132$	−7.11052	−	12.9808i	−0.618892	−	1.12983i
$133$	1.90408			0.165105
$134$	6.30604	+	8.41219i	0.544758	+	0.726703i
$135$	−1.52893	−	1.52893i	−0.131589	−	0.131589i
$136$	3.12015	−	6.86848i	0.267551	−	0.588967i
$137$	−5.13187	−	5.13187i	−0.438445	−	0.438445i	0.453043	−	0.891489i	$-0.350338\pi$
$137$	−5.13187	−	5.13187i	−0.438445	−	0.438445i	−0.891489	+	0.453043i	$0.850338\pi$
$138$	1.03473	−	7.23088i	0.0880819	−	0.615533i
$139$			11.1069i			0.942074i	0.882114	+	0.471037i	$0.156120\pi$
$139$			11.1069i			0.942074i	−0.882114	+	0.471037i	$0.843880\pi$
$140$	1.02878	−	3.52106i	0.0869480	−	0.297584i
$141$	−7.93768	−	7.93768i	−0.668473	−	0.668473i
$142$	−1.73904	−	2.31986i	−0.145937	−	0.194678i
$143$		0			0
$144$	−11.0474	−	7.05823i	−0.920620	−	0.588186i
$145$	2.73552	−	2.73552i	0.227173	−	0.227173i
$146$	0.0527959	+	0.0704293i	0.00436942	+	0.00582877i
$147$	−16.6673			−1.37470
$148$	0.497365	+	0.907978i	0.0408832	+	0.0746354i
$149$	−3.67452	+	3.67452i	−0.301028	+	0.301028i	−0.841416	−	0.540388i	$-0.818277\pi$
$149$	−3.67452	+	3.67452i	−0.301028	+	0.301028i	0.540388	+	0.841416i	$0.318277\pi$
$150$	−16.4037	−	2.34734i	−1.33935	−	0.191659i
$151$	3.67697	−	3.67697i	0.299227	−	0.299227i	−0.541484	−	0.840711i	$-0.682137\pi$
$151$	3.67697	−	3.67697i	0.299227	−	0.299227i	0.840711	+	0.541484i	$0.182137\pi$
$152$	−3.20910	−	8.55170i	−0.260292	−	0.693634i
$153$		−	8.74153i		−	0.706711i
$154$	0.348882	−	2.43806i	0.0281137	−	0.196464i
$155$	27.9130			2.24202
$156$		0			0
$157$	−10.7605			−0.858780			−0.429390	−	0.903119i	$-0.641271\pi$
$157$	−10.7605			−0.858780			−0.429390	+	0.903119i	$0.641271\pi$
$158$	−0.547476	+	3.82587i	−0.0435549	+	0.304370i
$159$			9.21182i			0.730545i
$160$	−17.5479	+	1.31381i	−1.38728	+	0.103866i
$161$	0.859490	−	0.859490i	0.0677373	−	0.0677373i
$162$	11.3267	+	1.62083i	0.889907	+	0.127344i
$163$	−10.0490	+	10.0490i	−0.787095	+	0.787095i	−0.981017	−	0.193922i	$-0.937879\pi$
$163$	−10.0490	+	10.0490i	−0.787095	+	0.787095i	0.193922	+	0.981017i	$0.437879\pi$
$164$	10.1659	−	5.56858i	0.793821	−	0.434833i
$165$	−23.0205			−1.79215
$166$	12.2174	+	16.2980i	0.948258	+	1.26497i
$167$	−6.59068	+	6.59068i	−0.510002	+	0.510002i	−0.914527	−	0.404525i	$-0.867437\pi$
$167$	−6.59068	+	6.59068i	−0.510002	+	0.510002i	0.404525	+	0.914527i	$0.367437\pi$
$168$	−1.46800	−	3.91198i	−0.113259	−	0.301816i
$169$		0			0
$170$	−7.03796	−	9.38857i	−0.539787	−	0.720070i
$171$	−7.48400	−	7.48400i	−0.572316	−	0.572316i
$172$	13.8512	+	4.04705i	1.05615	+	0.308585i
$173$		−	22.8918i		−	1.74043i	−0.492672	−	0.870215i	$-0.663980\pi$
$173$		−	22.8918i		−	1.74043i	0.492672	−	0.870215i	$-0.336020\pi$
$174$	0.624210	−	4.36210i	0.0473213	−	0.330690i
$175$	−1.94980	−	1.94980i	−0.147391	−	0.147391i
$176$	−11.5379	+	2.54214i	−0.869704	+	0.191621i
$177$	−12.4871	−	12.4871i	−0.938588	−	0.938588i
$178$	7.03865	+	9.38949i	0.527569	+	0.703772i
$179$	13.2185			0.988000			0.494000	−	0.869462i	$-0.335534\pi$
$179$	13.2185			0.988000			0.494000	+	0.869462i	$0.335534\pi$
$180$	−17.8832	+	9.79592i	−1.33294	+	0.730145i
$181$		−	26.1208i		−	1.94154i	−0.240009	−	0.970771i	$-0.577151\pi$
$181$		−	26.1208i		−	1.94154i	0.240009	−	0.970771i	$-0.422849\pi$
$182$		0			0
$183$			19.9288i			1.47318i
$184$	−5.30876	−	2.41162i	−0.391367	−	0.177787i
$185$	1.61023			0.118387
$186$	25.4399	−	19.0706i	1.86535	−	1.39832i
$187$	−5.57059	−	5.57059i	−0.407362	−	0.407362i
$188$	−7.85900	+	4.30494i	−0.573176	+	0.313970i
$189$	−0.289797	−	0.289797i	−0.0210796	−	0.0210796i
$190$	−14.0635	−	2.01246i	−1.02027	−	0.145999i
$191$		−	14.1381i		−	1.02300i	−0.859284	−	0.511499i	$-0.829090\pi$
$191$		−	14.1381i		−	1.02300i	0.859284	−	0.511499i	$-0.170910\pi$
$192$	−15.0955	+	13.1864i	−1.08943	+	0.951644i
$193$	16.4039	+	16.4039i	1.18078	+	1.18078i	0.979542	+	0.201239i	$0.0644968\pi$
$193$	16.4039	+	16.4039i	1.18078	+	1.18078i	0.201239	+	0.979542i	$0.435503\pi$
$194$	−5.36588	+	4.02243i	−0.385247	+	0.288793i
$195$		0			0
$196$	−3.73136	+	12.7708i	−0.266526	+	0.912197i
$197$	4.38845	−	4.38845i	0.312664	−	0.312664i	−0.533277	−	0.845941i	$-0.679040\pi$
$197$	4.38845	−	4.38845i	0.312664	−	0.312664i	0.845941	+	0.533277i	$0.179040\pi$
$198$	−10.9541	+	8.21153i	−0.778474	+	0.583568i
$199$	−3.01432			−0.213679			−0.106840	−	0.994276i	$-0.534073\pi$
$199$	−3.01432			−0.213679			−0.106840	+	0.994276i	$0.534073\pi$
$200$	−5.47090	+	12.0432i	−0.386851	+	0.851585i
$201$	13.1705	−	13.1705i	0.928977	−	0.928977i
$202$	1.79866	−	12.5694i	0.126553	−	0.884377i
$203$	0.518497	−	0.518497i	0.0363913	−	0.0363913i
$204$	−12.8288	−	3.74832i	−0.898197	−	0.262435i
$205$		−	18.0284i		−	1.25916i
$206$	13.4419	+	1.92352i	0.936544	+	0.134018i
$207$	−6.75647			−0.469607
$208$		0			0
$209$	−9.53844			−0.659788
$210$	−6.43334	−	0.920601i	−0.443942	−	0.0635275i
$211$		−	18.2136i		−	1.25388i	−0.779068	−	0.626940i	$-0.784307\pi$
$211$		−	18.2136i		−	1.25388i	0.779068	−	0.626940i	$-0.215693\pi$
$212$	7.05823	+	2.06227i	0.484761	+	0.141638i
$213$	−3.63208	+	3.63208i	−0.248866	+	0.248866i
$214$	−3.77898	+	26.4082i	−0.258325	+	1.80523i
$215$	15.8707	−	15.8707i	1.08237	−	1.08237i
$216$	−0.813133	+	1.78997i	−0.0553267	+	0.121792i
$217$	5.29069			0.359155
$218$	−4.72487	+	3.54191i	−0.320009	+	0.239888i
$219$	0.110267	−	0.110267i	0.00745118	−	0.00745118i
$220$	−5.15367	+	17.6387i	−0.347460	+	1.18920i
$221$		0			0
$222$	1.46757	−	1.10014i	0.0984969	−	0.0738363i
$223$	−2.51088	−	2.51088i	−0.168141	−	0.168141i	0.618021	−	0.786162i	$-0.287935\pi$
$223$	−2.51088	−	2.51088i	−0.168141	−	0.168141i	−0.786162	+	0.618021i	$0.787935\pi$
$224$	−3.32606	+	0.249022i	−0.222232	+	0.0166385i
$225$			15.3274i			1.02183i
$226$	−7.89976	−	1.13044i	−0.525484	−	0.0751960i
$227$	−12.3292	−	12.3292i	−0.818315	−	0.818315i	0.167549	−	0.985864i	$-0.446415\pi$
$227$	−12.3292	−	12.3292i	−0.818315	−	0.818315i	−0.985864	+	0.167549i	$0.946415\pi$
$228$	−14.1924	+	7.77420i	−0.939915	+	0.514859i
$229$	14.2869	+	14.2869i	0.944105	+	0.944105i	0.998519	−	0.0544132i	$-0.0173288\pi$
$229$	14.2869	+	14.2869i	0.944105	+	0.944105i	−0.0544132	+	0.998519i	$0.517329\pi$
$230$	−7.25658	+	5.43975i	−0.478485	+	0.358687i
$231$	−4.36336			−0.287088
$232$	−3.20256	−	1.45483i	−0.210259	−	0.0955146i
$233$		−	13.3205i		−	0.872655i	−0.899788	−	0.436328i	$-0.856279\pi$
$233$		−	13.3205i		−	0.872655i	0.899788	−	0.436328i	$-0.143721\pi$
$234$		0			0
$235$			13.9374i			0.909174i
$236$	−12.3633	+	6.77228i	−0.804784	+	0.440838i
$237$	6.84712			0.444768
$238$	−1.33399	−	1.77953i	−0.0864698	−	0.115350i
$239$	10.2493	+	10.2493i	0.662972	+	0.662972i	0.956079	−	0.293108i	$-0.0946894\pi$
$239$	10.2493	+	10.2493i	0.662972	+	0.662972i	−0.293108	+	0.956079i	$0.594689\pi$
$240$	6.70798	+	30.4453i	0.432998	+	1.96524i
$241$	9.79370	+	9.79370i	0.630868	+	0.630868i	0.948286	−	0.317418i	$-0.102816\pi$
$241$	9.79370	+	9.79370i	0.630868	+	0.630868i	−0.317418	+	0.948286i	$0.602816\pi$
$242$	0.455923	−	3.18608i	0.0293079	−	0.204809i
$243$		−	22.3565i		−	1.43417i
$244$	15.2698	+	4.46152i	0.977546	+	0.285619i
$245$	14.6327	+	14.6327i	0.934846	+	0.934846i
$246$	−12.3173	−	16.4311i	−0.785322	−	1.04761i
$247$		0			0
$248$	−8.91683	−	23.7618i	−0.566219	−	1.50888i
$249$	25.5169	−	25.5169i	1.61706	−	1.61706i
$250$	−0.853174	−	1.13813i	−0.0539595	−	0.0719814i
$251$	−2.51628			−0.158826			−0.0794129	−	0.996842i	$-0.525305\pi$
$251$	−2.51628			−0.158826			−0.0794129	+	0.996842i	$0.525305\pi$
$252$	−3.38962	+	1.85674i	−0.213526	+	0.116964i
$253$	−4.30560	+	4.30560i	−0.270691	+	0.270691i
$254$	16.9162	+	2.42069i	1.06142	+	0.151887i
$255$	−14.6992	+	14.6992i	−0.920498	+	0.920498i
$256$	6.72411	+	14.5185i	0.420257	+	0.907405i
$257$			6.41347i			0.400061i	0.979790	+	0.200031i	$0.0641041\pi$
$257$			6.41347i			0.400061i	−0.979790	+	0.200031i	$0.935896\pi$
$258$	3.62148	−	25.3076i	0.225464	−	1.57558i
$259$	0.305208			0.0189647
$260$		0			0
$261$	−4.07591			−0.252293
$262$	−3.84012	+	26.8355i	−0.237243	+	1.65790i
$263$			5.30826i			0.327322i	0.986517	+	0.163661i	$0.0523302\pi$
$263$			5.30826i			0.327322i	−0.986517	+	0.163661i	$0.947670\pi$
$264$	7.35394	+	19.5970i	0.452604	+	1.20611i
$265$	8.08728	−	8.08728i	0.496798	−	0.496798i
$266$	−2.66562	−	0.381446i	−0.163440	−	0.0233880i
$267$	14.7006	−	14.7006i	0.899664	−	0.899664i
$268$	−7.14293	−	13.0400i	−0.436324	−	0.796543i
$269$	−10.0010			−0.609769			−0.304885	−	0.952389i	$-0.598618\pi$
$269$	−10.0010			−0.609769			−0.304885	+	0.952389i	$0.598618\pi$
$270$	1.83414	+	2.44672i	0.111622	+	0.148903i
$271$	18.0439	−	18.0439i	1.09609	−	1.09609i	0.101225	−	0.994864i	$-0.467724\pi$
$271$	18.0439	−	18.0439i	1.09609	−	1.09609i	0.994864	−	0.101225i	$-0.0322763\pi$
$272$	−5.74404	+	8.99048i	−0.348283	+	0.545128i
$273$		0			0
$274$	6.15630	+	8.21245i	0.371916	+	0.496132i
$275$	9.76750	+	9.76750i	0.589002	+	0.589002i
$276$	−2.89714	+	9.91560i	−0.174387	+	0.596849i
$277$		−	0.534321i		−	0.0321043i	−0.999871	−	0.0160521i	$-0.994890\pi$
$277$		−	0.534321i		−	0.0321043i	0.999871	−	0.0160521i	$-0.00510977\pi$
$278$	2.22505	−	15.5491i	0.133450	−	0.932574i
$279$	−20.7951	−	20.7951i	−1.24497	−	1.24497i
$280$	−2.14562	+	4.72322i	−0.128226	+	0.282266i
$281$	0.275535	+	0.275535i	0.0164370	+	0.0164370i	0.715278	−	0.698840i	$-0.246300\pi$
$281$	0.275535	+	0.275535i	0.0164370	+	0.0164370i	−0.698840	+	0.715278i	$0.746300\pi$
$282$	9.52221	+	12.7025i	0.567040	+	0.756425i
$283$	−16.0638			−0.954892			−0.477446	−	0.878661i	$-0.658437\pi$
$283$	−16.0638			−0.954892			−0.477446	+	0.878661i	$0.658437\pi$
$284$	1.96983	+	3.59608i	0.116888	+	0.213388i
$285$			25.1692i			1.49090i
$286$		0			0
$287$		−	3.41715i		−	0.201708i
$288$	14.0519	+	12.0943i	0.828016	+	0.712666i
$289$	9.88608			0.581534
$290$	−4.37761	+	3.28159i	−0.257062	+	0.192702i
$291$	8.40107	+	8.40107i	0.492479	+	0.492479i
$292$	−0.0598026	−	0.109174i	−0.00349968	−	0.00638894i
$293$	1.44888	+	1.44888i	0.0846443	+	0.0846443i	0.748161	−	0.663517i	$-0.230937\pi$
$293$	1.44888	+	1.44888i	0.0846443	+	0.0846443i	−0.663517	+	0.748161i	$0.730937\pi$
$294$	23.3335	+	3.33898i	1.36084	+	0.194734i
$295$			21.9255i			1.27655i
$296$	−0.514391	−	1.37076i	−0.0298984	−	0.0796741i
$297$	1.45173	+	1.45173i	0.0842380	+	0.0842380i
$298$	5.88027	−	4.40803i	0.340635	−	0.255350i
$299$		0			0
$300$	22.4941	+	6.57233i	1.29870	+	0.379454i
$301$	3.00816	−	3.00816i	0.173388	−	0.173388i
$302$	−5.88419	+	4.41097i	−0.338597	+	0.253823i
$303$	−22.4952			−1.29232
$304$	2.77942	+	12.6149i	0.159410	+	0.723511i
$305$	17.4960	−	17.4960i	1.00182	−	1.00182i
$306$	−1.75120	+	12.2377i	−0.100109	+	0.699584i
$307$	−11.4337	+	11.4337i	−0.652558	+	0.652558i	−0.953608	−	0.301050i	$-0.902663\pi$
$307$	−11.4337	+	11.4337i	−0.652558	+	0.652558i	0.301050	+	0.953608i	$0.402663\pi$
$308$	−0.976837	+	3.34327i	−0.0556605	+	0.190501i
$309$		−	24.0569i		−	1.36855i
$310$	−39.0768	−	5.59184i	−2.21942	−	0.317595i
$311$	24.0242			1.36229			0.681143	−	0.732151i	$-0.261483\pi$
$311$	24.0242			1.36229			0.681143	+	0.732151i	$0.261483\pi$
$312$		0			0
$313$	28.9008			1.63357			0.816786	−	0.576941i	$-0.195754\pi$
$313$	28.9008			1.63357			0.816786	+	0.576941i	$0.195754\pi$
$314$	15.0642	+	2.15566i	0.850120	+	0.121651i
$315$			6.01125i			0.338696i
$316$	1.53288	−	5.24636i	0.0862314	−	0.295131i
$317$	−0.0141017	+	0.0141017i	−0.000792031	+	0.000792031i	−0.707503	−	0.706711i	$-0.750178\pi$
$317$	−0.0141017	+	0.0141017i	−0.000792031	+	0.000792031i	0.706711	+	0.707503i	$0.250178\pi$
$318$	1.84541	−	12.8961i	0.103486	−	0.723178i
$319$	−2.59740	+	2.59740i	−0.145426	+	0.145426i
$320$	24.8294	+	1.67611i	1.38800	+	0.0936976i
$321$	47.2625			2.63794
$322$	−1.37543	+	1.03106i	−0.0766496	+	0.0574589i
$323$	−6.09053	+	6.09053i	−0.338886	+	0.338886i
$324$	−15.5321	−	4.53817i	−0.862894	−	0.252120i
$325$		0			0
$326$	16.0812	−	12.0549i	0.890654	−	0.667662i
$327$	7.39748	+	7.39748i	0.409082	+	0.409082i
$328$	−15.3473	+	5.75920i	−0.847412	+	0.317999i
$329$			2.64172i			0.145643i
$330$	32.2277	+	4.61173i	1.77407	+	0.253867i
$331$	−2.98728	−	2.98728i	−0.164196	−	0.164196i	0.620227	−	0.784423i	$-0.287041\pi$
$331$	−2.98728	−	2.98728i	−0.164196	−	0.164196i	−0.784423	+	0.620227i	$0.787041\pi$
$332$	−13.8389	−	25.2639i	−0.759506	−	1.38654i
$333$	−1.19962	−	1.19962i	−0.0657389	−	0.0657389i
$334$	10.5470	−	7.90632i	0.577104	−	0.432615i
$335$	−23.1254			−1.26348
$336$	1.27145	+	5.77067i	0.0693631	+	0.314816i
$337$			9.58550i			0.522155i	0.965318	+	0.261078i	$0.0840778\pi$
$337$			9.58550i			0.522155i	−0.965318	+	0.261078i	$0.915922\pi$
$338$		0			0
$339$			14.1381i			0.767877i
$340$	7.97198	+	14.5535i	0.432342	+	0.789273i
$341$	−26.5036			−1.43525
$342$	8.97797	+	11.9765i	0.485473	+	0.647616i
$343$	5.69196	+	5.69196i	0.307337	+	0.307337i
$344$	−18.5803	−	8.44052i	−1.00178	−	0.455082i
$345$	11.3612	+	11.3612i	0.611669	+	0.611669i
$346$	−4.58593	+	32.0474i	−0.246541	+	1.72288i
$347$			4.11619i			0.220969i	0.993878	+	0.110484i	$0.0352402\pi$
$347$			4.11619i			0.220969i	−0.993878	+	0.110484i	$0.964760\pi$
$348$	−1.74773	+	5.98169i	−0.0936882	+	0.320652i
$349$	−20.5439	−	20.5439i	−1.09969	−	1.09969i	−0.994447	−	0.105241i	$-0.966438\pi$
$349$	−20.5439	−	20.5439i	−1.09969	−	1.09969i	−0.105241	−	0.994447i	$-0.533562\pi$
$350$	2.33903	+	3.12024i	0.125026	+	0.166784i
$351$		0			0
$352$	16.6618	−	1.24747i	0.888079	−	0.0664904i
$353$	−18.6181	+	18.6181i	−0.990941	+	0.990941i	−0.999959	−	0.00901875i	$-0.997129\pi$
$353$	−18.6181	+	18.6181i	−0.990941	+	0.990941i	0.00901875	+	0.999959i	$0.497129\pi$
$354$	14.9798	+	19.9829i	0.796167	+	1.06208i
$355$	6.37739			0.338477
$356$	−7.97277	−	14.5549i	−0.422556	−	0.771408i
$357$	−2.78612	+	2.78612i	−0.147457	+	0.147457i
$358$	−18.5053	−	2.64808i	−0.978037	−	0.139956i
$359$	7.69873	−	7.69873i	0.406324	−	0.406324i	−0.474131	−	0.880454i	$-0.657238\pi$
$359$	7.69873	−	7.69873i	0.406324	−	0.406324i	0.880454	+	0.474131i	$0.157238\pi$
$360$	26.9981	−	10.1313i	1.42292	−	0.533964i
$361$		−	8.57127i		−	0.451120i
$362$	−5.23280	+	36.5678i	−0.275030	+	1.92196i
$363$	−5.70210			−0.299282
$364$		0			0
$365$	−0.193613			−0.0101342
$366$	3.99236	−	27.8994i	0.208684	−	1.45833i
$367$			2.09822i			0.109526i	0.998499	+	0.0547630i	$0.0174403\pi$
$367$			2.09822i			0.109526i	−0.998499	+	0.0547630i	$0.982560\pi$
$368$	6.94889	+	4.43966i	0.362236	+	0.231433i
$369$	−13.4311	+	13.4311i	−0.699198	+	0.699198i
$370$	−2.25425	−	0.322580i	−0.117193	−	0.0167701i
$371$	1.53288	−	1.53288i	0.0795833	−	0.0795833i
$372$	−39.4351	+	21.6015i	−2.04462	+	1.11998i
$373$	−28.3047			−1.46556			−0.732781	−	0.680464i	$-0.761778\pi$
$373$	−28.3047			−1.46556			−0.732781	+	0.680464i	$0.761778\pi$
$374$	6.68260	+	8.91452i	0.345549	+	0.460959i
$375$	−1.78190	+	1.78190i	−0.0920171	+	0.0920171i
$376$	11.8646	−	4.45231i	0.611872	−	0.229610i
$377$		0			0
$378$	0.347647	+	0.463757i	0.0178810	+	0.0238531i
$379$	−20.4431	−	20.4431i	−1.05009	−	1.05009i	−0.998678	−	0.0514122i	$-0.983628\pi$
$379$	−20.4431	−	20.4431i	−1.05009	−	1.05009i	−0.0514122	−	0.998678i	$-0.516372\pi$
$380$	19.2850	+	5.63469i	0.989300	+	0.289054i
$381$		−	30.2748i		−	1.55102i
$382$	−2.83230	+	19.7927i	−0.144913	+	1.01268i
$383$	−10.7029	−	10.7029i	−0.546893	−	0.546893i	0.378648	−	0.925541i	$-0.376389\pi$
$383$	−10.7029	−	10.7029i	−0.546893	−	0.546893i	−0.925541	+	0.378648i	$0.876389\pi$
$384$	23.7747	−	15.4362i	1.21325	−	0.787724i
$385$	3.83070	+	3.83070i	0.195231	+	0.195231i
$386$	−19.6785	−	26.2510i	−1.00161	−	1.33614i
$387$	−23.6472			−1.20206
$388$	8.31779	−	4.55625i	0.422272	−	0.231309i
$389$			30.3695i			1.53979i	0.638168	+	0.769897i	$0.279692\pi$
$389$			30.3695i			1.53979i	−0.638168	+	0.769897i	$0.720308\pi$
$390$		0			0
$391$			5.49846i			0.278069i
$392$	7.78210	−	17.1309i	0.393056	−	0.865243i
$393$	48.0272			2.42265
$394$	−7.02277	+	5.26448i	−0.353802	+	0.265221i
$395$	−6.01125	−	6.01125i	−0.302459	−	0.302459i
$396$	16.9802	−	9.30130i	0.853289	−	0.467408i
$397$	−11.3167	−	11.3167i	−0.567967	−	0.567967i	0.363592	−	0.931558i	$-0.381550\pi$
$397$	−11.3167	−	11.3167i	−0.567967	−	0.567967i	−0.931558	+	0.363592i	$0.881550\pi$
$398$	4.21990	+	0.603862i	0.211525	+	0.0302689i
$399$			4.77063i			0.238830i
$400$	10.0716	−	15.7640i	0.503581	−	0.788198i
$401$	−9.73578	−	9.73578i	−0.486182	−	0.486182i	0.420917	−	0.907099i	$-0.361708\pi$
$401$	−9.73578	−	9.73578i	−0.486182	−	0.486182i	−0.907099	+	0.420917i	$0.861708\pi$
$402$	−21.0766	+	15.7996i	−1.05120	+	0.788014i
$403$		0			0
$404$	−5.03606	+	17.2362i	−0.250554	+	0.857532i
$405$	−17.7966	+	17.7966i	−0.884320	+	0.884320i
$406$	−0.829742	+	0.622000i	−0.0411794	+	0.0308693i
$407$	−1.52893			−0.0757863
$408$	17.2088	+	7.81748i	0.851964	+	0.387023i
$409$	−0.413505	+	0.413505i	−0.0204465	+	0.0204465i	−0.717256	−	0.696810i	$-0.754602\pi$
$409$	−0.413505	+	0.413505i	−0.0204465	+	0.0204465i	0.696810	+	0.717256i	$0.254602\pi$
$410$	−3.61166	+	25.2390i	−0.178367	+	1.24646i
$411$	12.8578	−	12.8578i	0.634228	−	0.634228i
$412$	−18.4327	−	5.38567i	−0.908115	−	0.265333i
$413$			4.15580i			0.204494i
$414$	9.45874	+	1.35353i	0.464872	+	0.0665224i
$415$	−44.8037			−2.19933
$416$		0			0
$417$	−27.8281			−1.36275
$418$	13.3534	+	1.91085i	0.653134	+	0.0934625i
$419$			36.8974i			1.80256i	0.433240	+	0.901278i	$0.357370\pi$
$419$			36.8974i			1.80256i	−0.433240	+	0.901278i	$0.642630\pi$
$420$	8.82194	+	2.57759i	0.430467	+	0.125774i
$421$	22.1875	−	22.1875i	1.08135	−	1.08135i	0.0849697	−	0.996384i	$-0.472921\pi$
$421$	22.1875	−	22.1875i	1.08135	−	1.08135i	0.996384	−	0.0849697i	$-0.0270794\pi$
$422$	−3.64876	+	25.4982i	−0.177619	+	1.24124i
$423$	10.3833	−	10.3833i	0.504854	−	0.504854i
$424$	−9.46805	−	4.30107i	−0.459809	−	0.208878i
$425$	12.4736			0.605057
$426$	5.81236	−	4.35712i	0.281610	−	0.211103i
$427$	3.31623	−	3.31623i	0.160484	−	0.160484i
$428$	10.5808	−	36.2132i	0.511441	−	1.75043i
$429$		0			0
$430$	−25.3976	+	19.0388i	−1.22478	+	0.918132i
$431$	21.9936	+	21.9936i	1.05940	+	1.05940i	0.998121	+	0.0612754i	$0.0195168\pi$
$431$	21.9936	+	21.9936i	1.05940	+	1.05940i	0.0612754	+	0.998121i	$0.480483\pi$
$432$	1.49693	−	2.34298i	0.0720213	−	0.112727i
$433$		−	10.7931i		−	0.518684i	−0.965785	−	0.259342i	$-0.916494\pi$
$433$		−	10.7931i		−	0.518684i	0.965785	−	0.259342i	$-0.0835058\pi$
$434$	−7.40671	−	1.05989i	−0.355534	−	0.0508763i
$435$	6.85379	+	6.85379i	0.328614	+	0.328614i
$436$	7.32415	−	4.01196i	0.350763	−	0.192138i
$437$	4.70747	+	4.70747i	0.225189	+	0.225189i
$438$	−0.176459	+	0.132279i	−0.00843154	+	0.00632054i
$439$	−12.9663			−0.618848			−0.309424	−	0.950924i	$-0.600136\pi$
$439$	−12.9663			−0.618848			−0.309424	+	0.950924i	$0.600136\pi$
$440$	10.7485	−	23.6609i	0.512413	−	1.12799i
$441$		−	21.8026i		−	1.03822i
$442$		0			0
$443$			15.6512i			0.743611i	0.928311	+	0.371805i	$0.121261\pi$
$443$			15.6512i			0.743611i	−0.928311	+	0.371805i	$0.878739\pi$
$444$	−2.27492	+	1.24614i	−0.107963	+	0.0591391i
$445$	−25.8121			−1.22361
$446$	3.01210	+	4.01812i	0.142627	+	0.190263i
$447$	−9.20642	−	9.20642i	−0.435449	−	0.435449i
$448$	4.70622	+	0.317694i	0.222348	+	0.0150097i
$449$	7.92277	+	7.92277i	0.373899	+	0.373899i	0.868895	−	0.494996i	$-0.164831\pi$
$449$	7.92277	+	7.92277i	0.373899	+	0.373899i	−0.494996	+	0.868895i	$0.664831\pi$
$450$	3.07056	−	21.4577i	0.144748	−	1.01153i
$451$			17.1181i			0.806062i
$452$	10.8328	+	3.16513i	0.509533	+	0.148875i
$453$	9.21257	+	9.21257i	0.432844	+	0.432844i
$454$	14.7903	+	19.7302i	0.694145	+	0.925982i
$455$		0			0
$456$	21.4261	−	8.04033i	1.00337	−	0.376523i
$457$	13.5869	−	13.5869i	0.635569	−	0.635569i	−0.313890	−	0.949459i	$-0.601632\pi$
$457$	13.5869	−	13.5869i	0.635569	−	0.635569i	0.949459	+	0.313890i	$0.101632\pi$
$458$	−17.1389	−	22.8631i	−0.800847	−	1.06832i
$459$	1.85393			0.0865342
$460$	11.2486	−	6.16168i	0.524470	−	0.287290i
$461$	−17.3417	+	17.3417i	−0.807684	+	0.807684i	−0.984283	−	0.176599i	$-0.943490\pi$
$461$	−17.3417	+	17.3417i	−0.807684	+	0.807684i	0.176599	+	0.984283i	$0.443490\pi$
$462$	6.10850	+	0.874117i	0.284193	+	0.0406676i
$463$	13.2027	−	13.2027i	0.613581	−	0.613581i	−0.330296	−	0.943877i	$-0.607149\pi$
$463$	13.2027	−	13.2027i	0.613581	−	0.613581i	0.943877	+	0.330296i	$0.107149\pi$
$464$	4.19199	+	2.67827i	0.194608	+	0.124336i
$465$			69.9354i			3.24318i
$466$	−2.66851	+	18.6481i	−0.123616	+	0.863856i
$467$	−22.6548			−1.04834			−0.524171	−	0.851613i	$-0.675625\pi$
$467$	−22.6548			−1.04834			−0.524171	+	0.851613i	$0.675625\pi$
$468$		0			0
$469$	−4.38325			−0.202400
$470$	2.79209	−	19.5117i	0.128789	−	0.900006i
$471$		−	26.9602i		−	1.24226i
$472$	18.6648	−	7.00412i	0.859115	−	0.322391i
$473$	−15.0693	+	15.0693i	−0.692888	+	0.692888i
$474$	−9.58564	−	1.37169i	−0.440283	−	0.0630039i
$475$	10.6792	−	10.6792i	0.489994	−	0.489994i
$476$	1.51103	+	2.75850i	0.0692579	+	0.126436i
$477$	−12.0500			−0.551732
$478$	−12.2953	−	16.4018i	−0.562373	−	0.750200i
$479$	2.29645	−	2.29645i	0.104927	−	0.104927i	−0.652694	−	0.757622i	$-0.726361\pi$
$479$	2.29645	−	2.29645i	0.104927	−	0.104927i	0.757622	+	0.652694i	$0.226361\pi$
$480$	−3.29172	−	43.9658i	−0.150246	−	2.00676i
$481$		0			0
$482$	−11.7487	−	15.6727i	−0.535140	−	0.713872i
$483$	2.15344	+	2.15344i	0.0979847	+	0.0979847i
$484$	−1.27654	+	4.36903i	−0.0580247	+	0.198592i
$485$		−	14.7510i		−	0.669809i
$486$	−4.47870	+	31.2980i	−0.203158	+	1.41971i
$487$	30.3265	+	30.3265i	1.37423	+	1.37423i	0.854072	+	0.520154i	$0.174125\pi$
$487$	30.3265	+	30.3265i	1.37423	+	1.37423i	0.520154	+	0.854072i	$0.325875\pi$
$488$	−20.4832	−	9.30492i	−0.927229	−	0.421214i
$489$	−25.1775	−	25.1775i	−1.13856	−	1.13856i
$490$	−17.5537	−	23.4164i	−0.792993	−	1.05785i
$491$	1.59381			0.0719276			0.0359638	−	0.999353i	$-0.488550\pi$
$491$	1.59381			0.0719276			0.0359638	+	0.999353i	$0.488550\pi$
$492$	13.9520	+	25.4704i	0.629003	+	1.14829i
$493$			3.31701i			0.149390i
$494$		0			0
$495$		−	30.1132i		−	1.35349i
$496$	7.72291	+	35.0517i	0.346769	+	1.57387i
$497$	1.20878			0.0542214
$498$	−40.8342	+	30.6106i	−1.82982	+	1.37169i
$499$	2.89721	+	2.89721i	0.129697	+	0.129697i	0.768975	−	0.639278i	$-0.220767\pi$
$499$	2.89721	+	2.89721i	0.129697	+	0.129697i	−0.639278	+	0.768975i	$0.720767\pi$
$500$	0.966402	+	1.76424i	0.0432188	+	0.0788992i
$501$	−16.5128	−	16.5128i	−0.737738	−	0.737738i
$502$	3.52267	+	0.504088i	0.157224	+	0.0224986i
$503$		−	15.1255i		−	0.674411i	−0.941431	−	0.337205i	$-0.890518\pi$
$503$		−	15.1255i		−	0.674411i	0.941431	−	0.337205i	$-0.109482\pi$
$504$	5.11727	−	1.92030i	0.227942	−	0.0855371i
$505$	19.7491	+	19.7491i	0.878824	+	0.878824i
$506$	6.89018	−	5.16509i	0.306306	−	0.229616i
$507$		0			0
$508$	−23.1970	−	6.77770i	−1.02920	−	0.300712i
$509$	−17.6856	+	17.6856i	−0.783899	+	0.783899i	−0.980486	−	0.196587i	$-0.937014\pi$
$509$	−17.6856	+	17.6856i	−0.783899	+	0.783899i	0.196587	+	0.980486i	$0.437014\pi$
$510$	23.5229	−	17.6335i	1.04161	−	0.780823i
$511$	−0.0366978			−0.00162342
$512$	−6.50493	−	21.6722i	−0.287480	−	0.957787i
$513$	1.58723	−	1.58723i	0.0700780	−	0.0700780i
$514$	1.28482	−	8.97855i	0.0566708	−	0.396027i
$515$	−21.1201	+	21.1201i	−0.930663	+	0.930663i
$516$	−10.1398	+	34.7040i	−0.446380	+	1.52776i
$517$		−	13.2336i		−	0.582015i
$518$	−0.427276	−	0.0611426i	−0.0187734	−	0.00268645i
$519$	57.3549			2.51760
$520$		0			0
$521$	−41.1166			−1.80135			−0.900675	−	0.434494i	$-0.856927\pi$
$521$	−41.1166			−1.80135			−0.900675	+	0.434494i	$0.856927\pi$
$522$	5.70609	+	0.816532i	0.249749	+	0.0357386i
$523$		−	2.63080i		−	0.115037i	−0.998344	−	0.0575185i	$-0.981681\pi$
$523$		−	2.63080i		−	0.115037i	0.998344	−	0.0575185i	$-0.0183188\pi$
$524$	10.7520	−	36.7991i	0.469702	−	1.60758i
$525$	4.88519	−	4.88519i	0.213207	−	0.213207i
$526$	1.06341	−	7.43132i	0.0463669	−	0.324021i
$527$	−16.9232	+	16.9232i	−0.737186	+	0.737186i
$528$	−6.36928	−	28.9081i	−0.277187	−	1.25806i
$529$	−18.7501			−0.815224
$530$	−12.9419	+	9.70168i	−0.562162	+	0.421414i
$531$	16.3344	−	16.3344i	0.708854	−	0.708854i
$532$	3.65533	+	1.06801i	0.158478	+	0.0463042i
$533$		0			0
$534$	−23.5252	+	17.6352i	−1.01803	+	0.763149i
$535$	−41.4929	−	41.4929i	−1.79389	−	1.79389i
$536$	7.38745	+	19.6863i	0.319089	+	0.850318i
$537$			33.1188i			1.42918i
$538$	14.0009	+	2.00350i	0.603621	+	0.0863772i
$539$	−13.8938	−	13.8938i	−0.598449	−	0.598449i
$540$	−2.07755	−	3.79273i	−0.0894036	−	0.163213i
$541$	−14.2591	−	14.2591i	−0.613047	−	0.613047i	0.330692	−	0.943739i	$-0.392718\pi$
$541$	−14.2591	−	14.2591i	−0.613047	−	0.613047i	−0.943739	+	0.330692i	$0.892718\pi$
$542$	−28.8754	+	21.6459i	−1.24030	+	0.929769i
$543$	65.4450			2.80852
$544$	9.84245	−	11.4355i	0.421992	−	0.490294i
$545$		−	12.9889i		−	0.556381i
$546$		0			0
$547$		−	40.9532i		−	1.75103i	−0.483190	−	0.875515i	$-0.660522\pi$
$547$		−	40.9532i		−	1.75103i	0.483190	−	0.875515i	$-0.339478\pi$
$548$	−6.97332	−	12.7303i	−0.297886	−	0.543813i
$549$	−26.0690			−1.11260
$550$	−11.7173	−	15.6308i	−0.499627	−	0.666498i
$551$	2.83983	+	2.83983i	0.120981	+	0.120981i
$552$	6.04226	−	13.3010i	0.257176	−	0.566128i
$553$	−1.13939	−	1.13939i	−0.0484517	−	0.0484517i
$554$	−0.107041	+	0.748024i	−0.00454774	+	0.0317805i
$555$			4.03441i			0.171251i
$556$	−6.22994	+	21.3223i	−0.264208	+	0.904266i
$557$	−21.2821	−	21.2821i	−0.901752	−	0.901752i	0.0938353	−	0.995588i	$-0.470087\pi$
$557$	−21.2821	−	21.2821i	−0.901752	−	0.901752i	−0.995588	+	0.0938353i	$0.970087\pi$
$558$	24.9463	+	33.2781i	1.05606	+	1.40877i
$559$		0			0
$560$	3.94998	−	6.18245i	0.166917	−	0.261256i
$561$	13.9570	−	13.9570i	0.589265	−	0.589265i
$562$	−0.330538	−	0.440934i	−0.0139429	−	0.0185997i
$563$	15.8944			0.669870			0.334935	−	0.942241i	$-0.391286\pi$
$563$	15.8944			0.669870			0.334935	+	0.942241i	$0.391286\pi$
$564$	−10.7859	−	19.6906i	−0.454170	−	0.829122i
$565$	12.4122	−	12.4122i	0.522185	−	0.522185i
$566$	22.4885	+	3.21807i	0.945263	+	0.135266i
$567$	−3.37321	+	3.37321i	−0.141661	+	0.141661i
$568$	−2.03726	−	5.42896i	−0.0854817	−	0.227794i
$569$		−	22.5913i		−	0.947076i	−0.880773	−	0.473538i	$-0.842977\pi$
$569$		−	22.5913i		−	0.947076i	0.880773	−	0.473538i	$-0.157023\pi$
$570$	5.04217	−	35.2357i	0.211193	−	1.47586i
$571$	−2.17784			−0.0911398			−0.0455699	−	0.998961i	$-0.514510\pi$
$571$	−2.17784			−0.0911398			−0.0455699	+	0.998961i	$0.514510\pi$
$572$		0			0
$573$	35.4227			1.47981
$574$	−0.684561	+	4.78385i	−0.0285730	+	0.199674i
$575$		−	9.64104i		−	0.402059i
$576$	−17.2491	−	19.7465i	−0.718714	−	0.822772i
$577$	−15.8624	+	15.8624i	−0.660361	+	0.660361i	−0.955465	−	0.295104i	$-0.904646\pi$
$577$	−15.8624	+	15.8624i	−0.660361	+	0.660361i	0.295104	+	0.955465i	$0.404646\pi$
$578$	−13.8401	−	1.98049i	−0.575670	−	0.0823775i
$579$	−41.0997	+	41.0997i	−1.70805	+	1.70805i
$580$	6.78585	−	3.71710i	0.281767	−	0.154344i
$581$	−8.49220			−0.352316
$582$	−10.0781	−	13.4441i	−0.417751	−	0.557276i
$583$	−7.67894	+	7.67894i	−0.318029	+	0.318029i
$584$	0.0618498	+	0.164819i	0.00255936	+	0.00682027i
$585$		0			0
$586$	−1.73810	−	2.31861i	−0.0718004	−	0.0957811i
$587$	15.3387	+	15.3387i	0.633098	+	0.633098i	0.948844	−	0.315746i	$-0.102255\pi$
$587$	15.3387	+	15.3387i	0.633098	+	0.633098i	−0.315746	+	0.948844i	$0.602255\pi$
$588$	−31.9969	−	9.34884i	−1.31953	−	0.385540i
$589$			28.9774i			1.19399i
$590$	4.39235	−	30.6946i	0.180830	−	1.26368i
$591$	10.9952	+	10.9952i	0.452281	+	0.452281i
$592$	0.445517	+	2.02205i	0.0183106	+	0.0831059i
$593$	−0.858298	−	0.858298i	−0.0352461	−	0.0352461i	0.689264	−	0.724510i	$-0.257934\pi$
$593$	−0.858298	−	0.858298i	−0.0352461	−	0.0352461i	−0.724510	+	0.689264i	$0.757934\pi$
$594$	−1.74153	−	2.32318i	−0.0714558	−	0.0953213i
$595$	4.89200			0.200552
$596$	−9.11516	+	4.99303i	−0.373372	+	0.204523i
$597$		−	7.55231i		−	0.309096i
$598$		0			0
$599$			7.16374i			0.292702i	0.989233	+	0.146351i	$0.0467529\pi$
$599$			7.16374i			0.292702i	−0.989233	+	0.146351i	$0.953247\pi$
$600$	−30.1741	−	13.7072i	−1.23185	−	0.559595i
$601$	16.0510			0.654733			0.327367	−	0.944897i	$-0.393839\pi$
$601$	16.0510			0.654733			0.327367	+	0.944897i	$0.393839\pi$
$602$	−4.81391	+	3.60866i	−0.196201	+	0.147078i
$603$	17.2284	+	17.2284i	0.701595	+	0.701595i
$604$	9.12125	−	4.99636i	0.371138	−	0.203299i
$605$	5.00601	+	5.00601i	0.203523	+	0.203523i
$606$	31.4923	+	4.50649i	1.27929	+	0.183064i
$607$		−	35.0013i		−	1.42066i	−0.703869	−	0.710329i	$-0.748546\pi$
$607$		−	35.0013i		−	1.42066i	0.703869	−	0.710329i	$-0.251454\pi$
$608$	−1.36391	−	18.2170i	−0.0553137	−	0.738797i
$609$	1.29908	+	1.29908i	0.0526415	+	0.0526415i
$610$	−27.9986	+	20.9886i	−1.13363	+	0.849803i
$611$		0			0
$612$	4.90319	−	16.7814i	0.198200	−	0.678349i
$613$	14.5194	−	14.5194i	0.586434	−	0.586434i	−0.350230	−	0.936664i	$-0.613896\pi$
$613$	14.5194	−	14.5194i	0.586434	−	0.586434i	0.936664	+	0.350230i	$0.113896\pi$
$614$	18.2972	−	13.7162i	0.738416	−	0.553539i
$615$	45.1699			1.82142
$616$	2.03729	−	4.48473i	0.0820847	−	0.180695i
$617$	−13.3150	+	13.3150i	−0.536040	+	0.536040i	−0.922363	−	0.386323i	$-0.873745\pi$
$617$	−13.3150	+	13.3150i	−0.536040	+	0.536040i	0.386323	+	0.922363i	$0.373745\pi$
$618$	−4.81934	+	33.6785i	−0.193862	+	1.35475i
$619$	28.1707	−	28.1707i	1.13228	−	1.13228i	0.142478	−	0.989798i	$-0.454493\pi$
$619$	28.1707	−	28.1707i	1.13228	−	1.13228i	0.989798	−	0.142478i	$-0.0455069\pi$
$620$	53.5855	+	15.6566i	2.15205	+	0.628785i
$621$		−	1.43294i		−	0.0575017i
$622$	−33.6327	−	4.81279i	−1.34855	−	0.192975i
$623$	−4.89248			−0.196013
$624$		0			0
$625$	26.5121			1.06048
$626$	−40.4598	−	5.78973i	−1.61710	−	0.231404i
$627$		−	23.8984i		−	0.954409i
$628$	−20.6573	−	6.03564i	−0.824315	−	0.240848i
$629$	−0.976260	+	0.976260i	−0.0389260	+	0.0389260i
$630$	1.20424	−	8.41547i	0.0479781	−	0.335280i
$631$	−8.84898	+	8.84898i	−0.352272	+	0.352272i	−0.860954	−	0.508682i	$-0.830133\pi$
$631$	−8.84898	+	8.84898i	−0.352272	+	0.352272i	0.508682	+	0.860954i	$0.330133\pi$
$632$	−3.19697	+	7.03758i	−0.127169	+	0.279940i
$633$	45.6339			1.81379
$634$	0.0225667	−	0.0169167i	0.000896240	−	0.000671849i
$635$	−26.5790	+	26.5790i	−1.05475	+	1.05475i
$636$	−5.16698	+	17.6843i	−0.204884	+	0.701226i
$637$		0			0
$638$	4.15657	−	3.11589i	0.164560	−	0.123359i
$639$	−4.75114	−	4.75114i	−0.187952	−	0.187952i
$640$	−34.4242	−	7.32057i	−1.36073	−	0.289371i
$641$			26.2040i			1.03499i	0.855685	+	0.517497i	$0.173136\pi$
$641$			26.2040i			1.03499i	−0.855685	+	0.517497i	$0.826864\pi$
$642$	−66.1653	−	9.46815i	−2.61133	−	0.373678i
$643$	0.265216	+	0.265216i	0.0104591	+	0.0104591i	0.712317	−	0.701858i	$-0.247646\pi$
$643$	0.265216	+	0.265216i	0.0104591	+	0.0104591i	−0.701858	+	0.712317i	$0.747646\pi$
$644$	2.13209	−	1.16790i	0.0840161	−	0.0460217i
$645$	39.7636	+	39.7636i	1.56569	+	1.56569i
$646$	9.74658	−	7.30633i	0.383474	−	0.287464i
$647$	35.3054			1.38800			0.693999	−	0.719976i	$-0.255847\pi$
$647$	35.3054			1.38800			0.693999	+	0.719976i	$0.255847\pi$
$648$	20.8351	+	9.46478i	0.818479	+	0.371812i
$649$		−	20.8184i		−	0.817194i
$650$		0			0
$651$			13.2557i			0.519532i
$652$	−24.9279	+	13.6548i	−0.976251	+	0.534763i
$653$	32.1212			1.25700			0.628500	−	0.777810i	$-0.283669\pi$
$653$	32.1212			1.25700			0.628500	+	0.777810i	$0.283669\pi$
$654$	−8.87418	−	11.8381i	−0.347008	−	0.462905i
$655$	−42.1642	−	42.1642i	−1.64749	−	1.64749i
$656$	22.6392	−	4.98808i	0.883913	−	0.194752i
$657$	0.144241	+	0.144241i	0.00562738	+	0.00562738i
$658$	0.529219	−	3.69828i	0.0206311	−	0.144174i
$659$		−	10.6347i		−	0.414271i	−0.978312	−	0.207135i	$-0.933586\pi$
$659$		−	10.6347i		−	0.414271i	0.978312	−	0.207135i	$-0.0664141\pi$
$660$	−44.1933	−	12.9124i	−1.72022	−	0.502615i
$661$	−5.69463	−	5.69463i	−0.221495	−	0.221495i	0.587633	−	0.809128i	$-0.300060\pi$
$661$	−5.69463	−	5.69463i	−0.221495	−	0.221495i	−0.809128	+	0.587633i	$0.800060\pi$
$662$	3.58360	+	4.78049i	0.139281	+	0.185799i
$663$		0			0
$664$	14.3126	+	38.1406i	0.555437	+	1.48014i
$665$	4.18825	−	4.18825i	0.162413	−	0.162413i
$666$	1.43909	+	1.91973i	0.0557637	+	0.0743882i
$667$	2.56377			0.0992695
$668$	−16.3491	+	8.95559i	−0.632566	+	0.346502i
$669$	6.29095	−	6.29095i	0.243222	−	0.243222i
$670$	32.3745	+	4.63274i	1.25074	+	0.178979i
$671$	−16.6126	+	16.6126i	−0.641322	+	0.641322i
$672$	−0.623919	−	8.33338i	−0.0240682	−	0.321467i
$673$			1.32965i			0.0512544i	0.999672	+	0.0256272i	$0.00815828\pi$
$673$			1.32965i			0.0512544i	−0.999672	+	0.0256272i	$0.991842\pi$
$674$	1.92027	−	13.4192i	0.0739661	−	0.516890i
$675$	−3.25070			−0.125119
$676$		0			0
$677$	33.7816			1.29833			0.649167	−	0.760646i	$-0.275118\pi$
$677$	33.7816			1.29833			0.649167	+	0.760646i	$0.275118\pi$
$678$	2.83230	−	19.7927i	0.108774	−	0.760133i
$679$		−	2.79594i		−	0.107298i
$680$	−8.24489	−	21.9712i	−0.316177	−	0.842557i
$681$	30.8905	−	30.8905i	1.18373	−	1.18373i
$682$	37.1038	+	5.30949i	1.42078	+	0.203311i
$683$	31.2339	−	31.2339i	1.19513	−	1.19513i	0.219527	−	0.975606i	$-0.429548\pi$
$683$	31.2339	−	31.2339i	1.19513	−	1.19513i	0.975606	−	0.219527i	$-0.0704516\pi$
$684$	−10.1695	−	18.5651i	−0.388839	−	0.709856i
$685$	−22.5763			−0.862598
$686$	−6.82819	−	9.10875i	−0.260702	−	0.347774i
$687$	−35.7955	+	35.7955i	−1.36569	+	1.36569i
$688$	24.3207	+	15.5385i	0.927217	+	0.592401i
$689$		0			0
$690$	−13.6292	−	18.1812i	−0.518854	−	0.692147i
$691$	29.3872	+	29.3872i	1.11794	+	1.11794i	0.992043	+	0.125897i	$0.0401810\pi$
$691$	29.3872	+	29.3872i	1.11794	+	1.11794i	0.125897	+	0.992043i	$0.459819\pi$
$692$	12.8402	−	43.9461i	0.488110	−	1.67058i
$693$		−	5.70773i		−	0.216819i
$694$	0.824601	−	5.76247i	0.0313014	−	0.218740i
$695$	24.4309	+	24.4309i	0.926719	+	0.926719i
$696$	3.64506	−	8.02396i	0.138166	−	0.304147i
$697$	10.9304	+	10.9304i	0.414017	+	0.414017i
$698$	24.6449	+	32.8760i	0.932822	+	1.24438i
$699$	33.3743			1.26233
$700$	−2.64945	−	4.83677i	−0.100140	−	0.182813i
$701$		−	17.2912i		−	0.653080i	−0.945183	−	0.326540i	$-0.894117\pi$
$701$		−	17.2912i		−	0.653080i	0.945183	−	0.326540i	$-0.105883\pi$
$702$		0			0
$703$			1.67164i			0.0630470i
$704$	−23.5757	−	1.59148i	−0.888542	−	0.0599813i
$705$	−34.9198			−1.31516
$706$	29.7942	−	22.3347i	1.12132	−	0.840576i
$707$	3.74329	+	3.74329i	0.140781	+	0.140781i
$708$	−16.9678	−	30.9760i	−0.637689	−	1.16415i
$709$	−29.6113	−	29.6113i	−1.11208	−	1.11208i	−0.992869	−	0.119208i	$-0.961965\pi$
$709$	−29.6113	−	29.6113i	−1.11208	−	1.11208i	−0.119208	−	0.992869i	$-0.538035\pi$
$710$	−8.92804	−	1.27759i	−0.335063	−	0.0479471i
$711$			8.95674i			0.335904i
$712$	8.24570	+	21.9734i	0.309021	+	0.823487i
$713$	13.0802	+	13.0802i	0.489858	+	0.489858i
$714$	4.45858	−	3.34229i	0.166858	−	0.125082i
$715$		0			0
$716$	25.3761	+	7.41438i	0.948349	+	0.277088i
$717$	−25.6794	+	25.6794i	−0.959015	+	0.959015i
$718$	−12.3202	+	9.23557i	−0.459784	+	0.344668i
$719$	−34.5133			−1.28713			−0.643565	−	0.765392i	$-0.722545\pi$
$719$	−34.5133			−1.28713			−0.643565	+	0.765392i	$0.722545\pi$
$720$	−39.8256	+	8.77474i	−1.48421	+	0.327015i
$721$	−4.00315	+	4.00315i	−0.149085	+	0.149085i
$722$	−1.71709	+	11.9994i	−0.0639035	+	0.446570i
$723$	−24.5379	+	24.5379i	−0.912575	+	0.912575i
$724$	14.6513	−	50.1449i	0.544513	−	1.86362i
$725$		−	5.81606i		−	0.216003i
$726$	7.98266	+	1.14231i	0.296264	+	0.0423950i
$727$	3.77644			0.140060			0.0700302	−	0.997545i	$-0.477690\pi$
$727$	3.77644			0.140060			0.0700302	+	0.997545i	$0.477690\pi$
$728$		0			0
$729$	31.7414			1.17561
$730$	0.271049	+	0.0387867i	0.0100320	+	0.00143556i
$731$			19.2443i			0.711775i
$732$	−11.1782	+	38.2581i	−0.413160	+	1.41406i
$733$	−4.25026	+	4.25026i	−0.156987	+	0.156987i	−0.781230	−	0.624243i	$-0.785407\pi$
$733$	−4.25026	+	4.25026i	−0.156987	+	0.156987i	0.624243	+	0.781230i	$0.285407\pi$
$734$	0.420338	−	2.93740i	0.0155149	−	0.108421i
$735$	−36.6618	+	36.6618i	−1.35229	+	1.35229i
$736$	−8.83871	−	7.60739i	−0.325799	−	0.280412i
$737$	21.9578			0.808826
$738$	21.4936	−	16.1123i	0.791192	−	0.593102i
$739$	12.7605	−	12.7605i	0.469402	−	0.469402i	−0.432319	−	0.901721i	$-0.642305\pi$
$739$	12.7605	−	12.7605i	0.469402	−	0.469402i	0.901721	+	0.432319i	$0.142305\pi$
$740$	3.09122	+	0.903194i	0.113636	+	0.0332021i
$741$		0			0
$742$	−2.45305	+	1.83888i	−0.0900542	+	0.0675074i
$743$	−9.47524	−	9.47524i	−0.347613	−	0.347613i	0.511607	−	0.859220i	$-0.329050\pi$
$743$	−9.47524	−	9.47524i	−0.347613	−	0.347613i	−0.859220	+	0.511607i	$0.829050\pi$
$744$	59.5348	−	22.3409i	2.18265	−	0.819059i
$745$			16.1651i			0.592243i
$746$	39.6252	+	5.67031i	1.45078	+	0.207605i
$747$	33.3787	+	33.3787i	1.22126	+	1.22126i
$748$	−7.56946	−	13.8186i	−0.276767	−	0.505259i
$749$	−7.86466	−	7.86466i	−0.287368	−	0.287368i
$750$	2.85155	−	2.13761i	0.104124	−	0.0780545i
$751$	25.0205			0.913011			0.456506	−	0.889721i	$-0.349101\pi$
$751$	25.0205			0.913011			0.456506	+	0.889721i	$0.349101\pi$
$752$	−17.5019	+	3.85617i	−0.638227	+	0.140620i
$753$		−	6.30448i		−	0.229748i
$754$		0			0
$755$		−	16.1759i		−	0.588700i
$756$	−0.393784	−	0.718883i	−0.0143218	−	0.0261455i
$757$	−39.2246			−1.42564			−0.712821	−	0.701346i	$-0.752583\pi$
$757$	−39.2246			−1.42564			−0.712821	+	0.701346i	$0.752583\pi$
$758$	24.5239	+	32.7147i	0.890750	+	1.18825i
$759$	−10.7876	−	10.7876i	−0.391565	−	0.391565i
$760$	−25.8693	−	11.7517i	−0.938378	−	0.426279i
$761$	10.0714	+	10.0714i	0.365090	+	0.365090i	0.865683	−	0.500593i	$-0.166885\pi$
$761$	10.0714	+	10.0714i	0.365090	+	0.365090i	−0.500593	+	0.865683i	$0.666885\pi$
$762$	−6.06498	+	42.3833i	−0.219711	+	1.53538i
$763$		−	2.46194i		−	0.0891281i
$764$	7.93018	−	27.1414i	0.286904	−	0.981942i
$765$	−19.2281	−	19.2281i	−0.695192	−	0.695192i
$766$	12.8394	+	17.1277i	0.463908	+	0.618849i
$767$		0			0
$768$	−36.3758	+	16.8471i	−1.31260	+	0.607918i
$769$	14.1390	−	14.1390i	0.509867	−	0.509867i	−0.404619	−	0.914485i	$-0.632596\pi$
$769$	14.1390	−	14.1390i	0.509867	−	0.509867i	0.914485	+	0.404619i	$0.132596\pi$
$770$	−4.59540	−	6.13021i	−0.165607	−	0.220918i
$771$	−16.0688			−0.578704
$772$	22.2901	+	40.6923i	0.802239	+	1.46455i
$773$	−21.3872	+	21.3872i	−0.769244	+	0.769244i	−0.977973	−	0.208729i	$-0.933067\pi$
$773$	−21.3872	+	21.3872i	−0.769244	+	0.769244i	0.208729	+	0.977973i	$0.433067\pi$
$774$	33.1050	+	4.73728i	1.18993	+	0.170278i
$775$	29.6732	−	29.6732i	1.06589	−	1.06589i
$776$	−12.5573	+	4.71223i	−0.450780	+	0.169159i
$777$			0.764691i			0.0274331i
$778$	6.08395	−	42.5158i	0.218120	−	1.52427i
$779$	18.7159			0.670567
$780$		0			0
$781$	−6.05538			−0.216679
$782$	1.10151	−	7.69759i	0.0393900	−	0.275265i
$783$		−	0.864434i		−	0.0308923i
$784$	−14.3264	+	22.4235i	−0.511658	+	0.800840i
$785$	−23.6690	+	23.6690i	−0.844783	+	0.844783i
$786$	−67.2358	−	9.62134i	−2.39822	−	0.343182i
$787$	6.63607	−	6.63607i	0.236550	−	0.236550i	−0.578870	−	0.815420i	$-0.696506\pi$
$787$	6.63607	−	6.63607i	0.236550	−	0.236550i	0.815420	+	0.578870i	$0.196506\pi$
$788$	10.8862	−	5.96314i	0.387804	−	0.212428i
$789$	−13.2997			−0.473483
$790$	7.21123	+	9.61971i	0.256564	+	0.342254i
$791$	2.35263	−	2.35263i	0.0836501	−	0.0836501i
$792$	−25.6349	+	9.61971i	−0.910896	+	0.341822i
$793$		0			0
$794$	13.5757	+	18.1099i	0.481784	+	0.642695i
$795$	20.2625	+	20.2625i	0.718638	+	0.718638i
$796$	−5.78669	−	1.69076i	−0.205104	−	0.0599273i
$797$			11.6578i			0.412941i	0.978453	+	0.206471i	$0.0661978\pi$
$797$			11.6578i			0.412941i	−0.978453	+	0.206471i	$0.933802\pi$
$798$	0.955705	−	6.67865i	0.0338316	−	0.236422i
$799$	−8.45001	−	8.45001i	−0.298940	−	0.298940i
$800$	−17.2578	+	20.0511i	−0.610156	+	0.708914i
$801$	19.2299	+	19.2299i	0.679457	+	0.679457i
$802$	11.6793	+	15.5800i	0.412409	+	0.550149i
$803$	0.183837			0.00648746
$804$	32.6714	−	17.8965i	1.15223	−	0.631159i
$805$		−	3.78111i		−	0.133267i
$806$		0			0
$807$		−	25.0572i		−	0.882055i
$808$	10.5032	−	23.1210i	0.369501	−	0.813392i
$809$	−31.0859			−1.09292			−0.546461	−	0.837484i	$-0.684025\pi$
$809$	−31.0859			−1.09292			−0.546461	+	0.837484i	$0.684025\pi$
$810$	28.4796	−	21.3492i	1.00067	−	0.750134i
$811$	−0.110267	−	0.110267i	−0.00387201	−	0.00387201i	0.705168	−	0.709040i	$-0.250872\pi$
$811$	−0.110267	−	0.110267i	−0.00387201	−	0.00387201i	−0.709040	+	0.705168i	$0.750872\pi$
$812$	1.28621	−	0.704547i	0.0451370	−	0.0247248i
$813$	45.2086	+	45.2086i	1.58554	+	1.58554i
$814$	2.14043	+	0.306292i	0.0750221	+	0.0107355i
$815$			44.2078i			1.54853i
$816$	−22.5255	−	14.3916i	−0.788549	−	0.503806i
$817$	16.4759	+	16.4759i	0.576417	+	0.576417i
$818$	0.661725	−	0.496050i	0.0231367	−	0.0173440i
$819$		0			0
$820$	10.1123	−	34.6098i	0.353137	−	1.20863i
$821$	−12.7888	+	12.7888i	−0.446334	+	0.446334i	−0.894134	−	0.447800i	$-0.852208\pi$
$821$	−12.7888	+	12.7888i	−0.446334	+	0.446334i	0.447800	+	0.894134i	$0.352208\pi$
$822$	−20.5761	+	15.4245i	−0.717675	+	0.537991i
$823$	26.1938			0.913060			0.456530	−	0.889708i	$-0.349092\pi$
$823$	26.1938			0.913060			0.456530	+	0.889708i	$0.349092\pi$
$824$	24.7260	+	11.2323i	0.861372	+	0.391297i
$825$	−24.4723	+	24.4723i	−0.852015	+	0.852015i
$826$	0.832536	−	5.81793i	0.0289676	−	0.202432i
$827$	11.7822	−	11.7822i	0.409707	−	0.409707i	−0.471930	−	0.881636i	$-0.656442\pi$
$827$	11.7822	−	11.7822i	0.409707	−	0.409707i	0.881636	+	0.471930i	$0.156442\pi$
$828$	−12.9706	−	3.78976i	−0.450761	−	0.131703i
$829$		−	13.1050i		−	0.455155i	−0.973760	−	0.227577i	$-0.926920\pi$
$829$		−	13.1050i		−	0.455155i	0.973760	−	0.227577i	$-0.0730805\pi$
$830$	62.7231	+	8.97558i	2.17715	+	0.311547i
$831$	1.33873			0.0464401
$832$		0			0
$833$	−17.7431			−0.614762
$834$	38.9580	+	5.57483i	1.34900	+	0.193041i
$835$			28.9940i			1.00338i
$836$	−18.3113	−	5.35019i	−0.633309	−	0.185040i
$837$	4.41030	−	4.41030i	0.152442	−	0.152442i
$838$	7.39170	−	51.6546i	0.255342	−	1.78438i
$839$	−16.9239	+	16.9239i	−0.584276	+	0.584276i	−0.936076	−	0.351799i	$-0.885570\pi$
$839$	−16.9239	+	16.9239i	−0.584276	+	0.584276i	0.351799	+	0.936076i	$0.385570\pi$
$840$	−11.8339	−	5.37582i	−0.408309	−	0.185483i
$841$	−27.4534			−0.946668
$842$	−35.5063	+	26.6166i	−1.22363	+	0.917269i
$843$	−0.690348	+	0.690348i	−0.0237768	+	0.0237768i
$844$	10.2162	−	34.9654i	0.351655	−	1.20356i
$845$		0			0
$846$	−16.6162	+	12.4560i	−0.571278	+	0.428248i
$847$	0.948850	+	0.948850i	0.0326029	+	0.0326029i
$848$	12.3932	+	7.91804i	0.425584	+	0.271907i
$849$		−	40.2474i		−	1.38129i
$850$	−17.4624	−	2.49885i	−0.598956	−	0.0857097i
$851$	0.754568	+	0.754568i	0.0258662	+	0.0258662i
$852$	−9.00990	+	4.93537i	−0.308674	+	0.169083i
$853$	12.1913	+	12.1913i	0.417422	+	0.417422i	0.884314	−	0.466892i	$-0.154626\pi$
$853$	12.1913	+	12.1913i	0.417422	+	0.417422i	−0.466892	+	0.884314i	$0.654626\pi$
$854$	−5.30691	+	3.97822i	−0.181599	+	0.136132i
$855$	−32.9239			−1.12597
$856$	−22.0672	+	48.5771i	−0.754242	+	1.66033i
$857$			20.1694i			0.688974i	0.938791	+	0.344487i	$0.111947\pi$
$857$			20.1694i			0.688974i	−0.938791	+	0.344487i	$0.888053\pi$
$858$		0			0
$859$		−	10.5286i		−	0.359231i	−0.983737	−	0.179616i	$-0.942515\pi$
$859$		−	10.5286i		−	0.359231i	0.983737	−	0.179616i	$-0.0574854\pi$
$860$	39.3695	−	21.5655i	1.34249	−	0.735377i
$861$	8.56160			0.291779
$862$	−26.3840	−	35.1961i	−0.898644	−	1.19878i
$863$	−0.357134	−	0.357134i	−0.0121570	−	0.0121570i	0.701002	−	0.713159i	$-0.252736\pi$
$863$	−0.357134	−	0.357134i	−0.0121570	−	0.0121570i	−0.713159	+	0.701002i	$0.752736\pi$
$864$	−2.56501	+	2.98018i	−0.0872634	+	0.101388i
$865$	−50.3533	−	50.3533i	−1.71206	−	1.71206i
$866$	−2.16220	+	15.1099i	−0.0734745	+	0.513454i
$867$			24.7694i			0.841212i
$868$	10.1567	+	2.96759i	0.344742	+	0.100727i
$869$	5.70773	+	5.70773i	0.193622	+	0.193622i
$870$	−8.22195	−	10.9680i	−0.278750	−	0.371850i
$871$		0			0
$872$	−11.0572	+	4.14931i	−0.374443	+	0.140513i
$873$	−10.9895	+	10.9895i	−0.371937	+	0.371937i
$874$	−5.64718	−	7.53329i	−0.191019	−	0.254817i
$875$	0.593031			0.0200481
$876$	0.273534	−	0.149834i	0.00924186	−	0.00506243i
$877$	−22.5944	+	22.5944i	−0.762959	+	0.762959i	−0.976856	−	0.213898i	$-0.931384\pi$
$877$	−22.5944	+	22.5944i	−0.762959	+	0.762959i	0.213898	+	0.976856i	$0.431384\pi$
$878$	18.1522	+	2.59755i	0.612608	+	0.0876632i
$879$	−3.63013	+	3.63013i	−0.122441	+	0.122441i
$880$	−19.7873	+	30.9708i	−0.667031	+	1.04403i
$881$			30.5337i			1.02871i	0.857579	+	0.514353i	$0.171968\pi$
$881$			30.5337i			1.02871i	−0.857579	+	0.514353i	$0.828032\pi$
$882$	−4.36774	+	30.5226i	−0.147069	+	1.02775i
$883$	−49.7844			−1.67538			−0.837689	−	0.546148i	$-0.816094\pi$
$883$	−49.7844			−1.67538			−0.837689	+	0.546148i	$0.816094\pi$
$884$		0			0
$885$	−54.9338			−1.84658
$886$	3.13542	−	21.9109i	0.105337	−	0.736112i
$887$		−	25.0572i		−	0.841339i	−0.907214	−	0.420669i	$-0.861795\pi$
$887$		−	25.0572i		−	0.841339i	0.907214	−	0.420669i	$-0.138205\pi$
$888$	3.43442	−	1.28880i	0.115252	−	0.0432492i
$889$	−5.03784	+	5.03784i	−0.168964	+	0.168964i
$890$	36.1357	+	5.17096i	1.21127	+	0.173331i
$891$	16.8980	−	16.8980i	0.566105	−	0.566105i
$892$	−3.41185	−	6.22859i	−0.114237	−	0.208549i
$893$	−14.4688			−0.484181
$894$	11.0442	+	14.7329i	0.369374	+	0.492742i
$895$	29.0758	−	29.0758i	0.971896	−	0.971896i
$896$	−6.52483	−	1.38756i	−0.217979	−	0.0463551i
$897$		0			0
$898$	−9.50433	−	12.6787i	−0.317164	−	0.423093i
$899$	7.89078	+	7.89078i	0.263172	+	0.263172i
$900$	−8.59729	+	29.4246i	−0.286576	+	0.980821i
$901$			9.80639i			0.326698i
$902$	3.42930	−	23.9646i	0.114183	−	0.797933i
$903$	7.53689	+	7.53689i	0.250812	+	0.250812i
$904$	−14.5314	−	6.60119i	−0.483306	−	0.219552i
$905$	−57.4558	−	57.4558i	−1.90990	−	1.90990i
$906$	−11.0516	−	14.7427i	−0.367165	−	0.489794i
$907$	−50.3945			−1.67332			−0.836661	−	0.547721i	$-0.815496\pi$
$907$	−50.3945			−1.67332			−0.836661	+	0.547721i	$0.815496\pi$
$908$	−16.7532	−	30.5843i	−0.555974	−	1.01497i
$909$		−	29.4261i		−	0.976002i
$910$		0			0
$911$			7.50959i			0.248804i	0.992232	+	0.124402i	$0.0397012\pi$
$911$			7.50959i			0.248804i	−0.992232	+	0.124402i	$0.960299\pi$
$912$	−31.6063	+	6.96377i	−1.04659	+	0.230594i
$913$	42.5415			1.40792
$914$	−21.7429	+	16.2992i	−0.719192	+	0.539128i
$915$	43.8359	+	43.8359i	1.44917	+	1.44917i
$916$	19.4134	+	35.4407i	0.641438	+	1.17099i
$917$	−7.99191	−	7.99191i	−0.263916	−	0.263916i
$918$	−2.59542	−	0.371400i	−0.0856616	−	0.0122580i
$919$			28.1179i			0.927525i	0.885960	+	0.463762i	$0.153501\pi$
$919$			28.1179i			0.927525i	−0.885960	+	0.463762i	$0.846499\pi$
$920$	−16.9819	+	6.37261i	−0.559877	+	0.210099i
$921$	−28.6470	−	28.6470i	−0.943950	−	0.943950i
$922$	27.7517	−	20.8035i	0.913952	−	0.685126i
$923$		0			0
$924$	−8.37650	−	2.44745i	−0.275567	−	0.0805151i
$925$	1.71178	−	1.71178i	0.0562830	−	0.0562830i
$926$	−21.1280	+	15.8382i	−0.694311	+	0.520477i
$927$	31.4689			1.03357
$928$	−5.33205	−	4.58924i	−0.175033	−	0.150649i
$929$	30.3326	−	30.3326i	0.995179	−	0.995179i	−0.00480932	−	0.999988i	$-0.501531\pi$
$929$	30.3326	−	30.3326i	0.995179	−	0.995179i	0.999988	+	0.00480932i	$0.00153086\pi$
$930$	14.0102	−	97.9062i	0.459414	−	3.21047i
$931$	−15.1906	+	15.1906i	−0.497853	+	0.497853i
$932$	7.47158	−	25.5718i	0.244740	−	0.837634i
$933$			60.1920i			1.97060i
$934$	31.7157	+	4.53847i	1.03777	+	0.148503i
$935$	−24.5064			−0.801444
$936$		0			0
$937$	−0.397858			−0.0129975			−0.00649873	−	0.999979i	$-0.502069\pi$
$937$	−0.397858			−0.0129975			−0.00649873	+	0.999979i	$0.502069\pi$
$938$	6.13634	+	0.878101i	0.200359	+	0.0286710i
$939$			72.4104i			2.36303i
$940$	−7.81758	+	26.7561i	−0.254981	+	0.872686i
$941$	4.33123	−	4.33123i	0.141194	−	0.141194i	−0.632977	−	0.774171i	$-0.718167\pi$
$941$	4.33123	−	4.33123i	0.141194	−	0.141194i	0.774171	+	0.632977i	$0.218167\pi$
$942$	−5.40096	+	37.7430i	−0.175973	+	1.22973i
$943$	8.44825	−	8.44825i	0.275113	−	0.275113i
$944$	−27.5329	+	6.06630i	−0.896120	+	0.197441i
$945$	−1.27489			−0.0414721
$946$	24.1152	−	18.0775i	0.784053	−	0.587750i
$947$	−5.47327	+	5.47327i	−0.177857	+	0.177857i	−0.790421	−	0.612564i	$-0.790138\pi$
$947$	−5.47327	+	5.47327i	−0.177857	+	0.177857i	0.612564	+	0.790421i	$0.290138\pi$
$948$	13.1447	+	3.84060i	0.426919	+	0.124737i
$949$		0			0
$950$	−17.0897	+	12.8110i	−0.554463	+	0.415642i
$951$	−0.0353315	−	0.0353315i	−0.00114570	−	0.00114570i
$952$	−1.56276	−	4.16447i	−0.0506492	−	0.134971i
$953$			14.6102i			0.473272i	0.971598	+	0.236636i	$0.0760449\pi$
$953$			14.6102i			0.473272i	−0.971598	+	0.236636i	$0.923955\pi$
$954$	16.8695	+	2.41399i	0.546169	+	0.0781559i
$955$	−31.0985	−	31.0985i	−1.00632	−	1.00632i
$956$	13.9270	+	25.4248i	0.450432	+	0.822298i
$957$	−6.50773	−	6.50773i	−0.210365	−	0.210365i
$958$	−3.67497	+	2.75487i	−0.118733	+	0.0890058i
$959$	−4.27917			−0.138182
$960$	−4.19947	+	62.2095i	−0.135537	+	2.00780i
$961$			49.5168i			1.59731i
$962$		0			0
$963$			61.8243i			1.99226i
$964$	13.3079	+	24.2947i	0.428620	+	0.782479i
$965$	72.1649			2.32307
$966$	−2.58331	−	3.44611i	−0.0831166	−	0.110877i
$967$	6.52725	+	6.52725i	0.209902	+	0.209902i	0.804226	−	0.594324i	$-0.202580\pi$
$967$	6.52725	+	6.52725i	0.209902	+	0.209902i	−0.594324	+	0.804226i	$0.702580\pi$
$968$	2.66235	−	5.86070i	0.0855712	−	0.188370i
$969$	−15.2597	−	15.2597i	−0.490212	−	0.490212i
$970$	−2.95508	+	20.6507i	−0.0948821	+	0.663054i
$971$		−	39.2145i		−	1.25845i	−0.777222	−	0.629226i	$-0.783372\pi$
$971$		−	39.2145i		−	1.25845i	0.777222	−	0.629226i	$-0.216628\pi$
$972$	12.5399	−	42.9185i	0.402218	−	1.37661i
$973$	4.63070	+	4.63070i	0.148453	+	0.148453i
$974$	−36.3804	−	48.5311i	−1.16570	−	1.55504i
$975$		0			0
$976$	26.8114	+	17.1299i	0.858212	+	0.548313i
$977$	8.30811	−	8.30811i	0.265800	−	0.265800i	−0.561605	−	0.827405i	$-0.689816\pi$
$977$	8.30811	−	8.30811i	0.265800	−	0.265800i	0.827405	+	0.561605i	$0.189816\pi$
$978$	30.2034	+	40.2911i	0.965799	+	1.28837i
$979$	24.5088			0.783304
$980$	19.8833	+	36.2984i	0.635147	+	1.15951i
$981$	−9.67667	+	9.67667i	−0.308952	+	0.308952i
$982$	−2.23126	−	0.319289i	−0.0712022	−	0.0101889i
$983$	17.0818	−	17.0818i	0.544823	−	0.544823i	−0.380116	−	0.924939i	$-0.624116\pi$
$983$	17.0818	−	17.0818i	0.544823	−	0.544823i	0.924939	+	0.380116i	$0.124116\pi$
$984$	−14.4296	−	38.4523i	−0.459998	−	1.22581i
$985$		−	19.3059i		−	0.615136i
$986$	0.664499	−	4.64365i	0.0211620	−	0.147884i
$987$	−6.61878			−0.210678
$988$		0			0
$989$	14.8742			0.472973
$990$	−6.03262	+	42.1571i	−0.191729	+	1.33984i
$991$		−	28.8027i		−	0.914948i	−0.889223	−	0.457474i	$-0.848754\pi$
$991$		−	28.8027i		−	0.914948i	0.889223	−	0.457474i	$-0.151246\pi$
$992$	−3.78976	−	50.6179i	−0.120325	−	1.60712i
$993$	7.48456	−	7.48456i	0.237515	−	0.237515i
$994$	−1.69224	−	0.242157i	−0.0536746	−	0.00768076i
$995$	−6.63036	+	6.63036i	−0.210197	+	0.210197i
$996$	63.2982	−	34.6730i	2.00568	−	1.09866i
$997$	53.9318			1.70804			0.854019	−	0.520242i	$-0.174158\pi$
$997$	53.9318			1.70804			0.854019	+	0.520242i	$0.174158\pi$
$998$	−3.47555	−	4.63635i	−0.110017	−	0.146761i
$999$	0.254420	−	0.254420i	0.00804949	−	0.00804949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.f.i.239.1		16
4.3	odd	2	inner	676.2.f.i.239.4		16
13.2	odd	12		52.2.l.b.7.1	✓	16
13.3	even	3		676.2.l.i.19.3		16
13.4	even	6		52.2.l.b.15.2	yes	16
13.5	odd	4		676.2.f.h.99.5		16
13.6	odd	12		676.2.l.m.427.4		16
13.7	odd	12		676.2.l.i.427.1		16
13.8	odd	4	inner	676.2.f.i.99.4		16
13.9	even	3		676.2.l.k.587.3		16
13.10	even	6		676.2.l.m.19.2		16
13.11	odd	12		676.2.l.k.319.4		16
13.12	even	2		676.2.f.h.239.8		16
39.2	even	12		468.2.cb.f.163.4		16
39.17	odd	6		468.2.cb.f.379.3		16
52.3	odd	6		676.2.l.i.19.1		16
52.7	even	12		676.2.l.i.427.3		16
52.11	even	12		676.2.l.k.319.3		16
52.15	even	12		52.2.l.b.7.2	yes	16
52.19	even	12		676.2.l.m.427.2		16
52.23	odd	6		676.2.l.m.19.4		16
52.31	even	4		676.2.f.h.99.8		16
52.35	odd	6		676.2.l.k.587.4		16
52.43	odd	6		52.2.l.b.15.1	yes	16
52.47	even	4	inner	676.2.f.i.99.1		16
52.51	odd	2		676.2.f.h.239.5		16
104.43	odd	6		832.2.bu.n.639.4		16
104.67	even	12		832.2.bu.n.319.1		16
104.69	even	6		832.2.bu.n.639.1		16
104.93	odd	12		832.2.bu.n.319.4		16
156.95	even	6		468.2.cb.f.379.4		16
156.119	odd	12		468.2.cb.f.163.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	13.2	odd	12
52.2.l.b.7.2	yes	16	52.15	even	12
52.2.l.b.15.1	yes	16	52.43	odd	6
52.2.l.b.15.2	yes	16	13.4	even	6
468.2.cb.f.163.3		16	156.119	odd	12
468.2.cb.f.163.4		16	39.2	even	12
468.2.cb.f.379.3		16	39.17	odd	6
468.2.cb.f.379.4		16	156.95	even	6
676.2.f.h.99.5		16	13.5	odd	4
676.2.f.h.99.8		16	52.31	even	4
676.2.f.h.239.5		16	52.51	odd	2
676.2.f.h.239.8		16	13.12	even	2
676.2.f.i.99.1		16	52.47	even	4	inner
676.2.f.i.99.4		16	13.8	odd	4	inner
676.2.f.i.239.1		16	1.1	even	1	trivial
676.2.f.i.239.4		16	4.3	odd	2	inner
676.2.l.i.19.1		16	52.3	odd	6
676.2.l.i.19.3		16	13.3	even	3
676.2.l.i.427.1		16	13.7	odd	12
676.2.l.i.427.3		16	52.7	even	12
676.2.l.k.319.3		16	52.11	even	12
676.2.l.k.319.4		16	13.11	odd	12
676.2.l.k.587.3		16	13.9	even	3
676.2.l.k.587.4		16	52.35	odd	6
676.2.l.m.19.2		16	13.10	even	6
676.2.l.m.19.4		16	52.23	odd	6
676.2.l.m.427.2		16	52.19	even	12
676.2.l.m.427.4		16	13.6	odd	12
832.2.bu.n.319.1		16	104.67	even	12
832.2.bu.n.319.4		16	104.93	odd	12
832.2.bu.n.639.1		16	104.69	even	6
832.2.bu.n.639.4		16	104.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39995 - 0.200331i) q^{2} +2.50548i q^{3} +(1.91973 + 0.560908i) q^{4} +(2.19962 - 2.19962i) q^{5} +(0.501925 - 3.50755i) q^{6} +(0.416921 - 0.416921i) q^{7} +(-2.57517 - 1.16983i) q^{8} -3.27743 q^{9} +O(q^{10})\)	\(q+(-1.39995 - 0.200331i) q^{2} +2.50548i q^{3} +(1.91973 + 0.560908i) q^{4} +(2.19962 - 2.19962i) q^{5} +(0.501925 - 3.50755i) q^{6} +(0.416921 - 0.416921i) q^{7} +(-2.57517 - 1.16983i) q^{8} -3.27743 q^{9} +(-3.52002 + 2.63871i) q^{10} +(-2.08856 + 2.08856i) q^{11} +(-1.40534 + 4.80986i) q^{12} +(-0.667192 + 0.500148i) q^{14} +(5.51111 + 5.51111i) q^{15} +(3.37076 + 2.15359i) q^{16} +2.66719i q^{17} +(4.58824 + 0.656570i) q^{18} +(2.28350 + 2.28350i) q^{19} +(5.45648 - 2.98891i) q^{20} +(1.04459 + 1.04459i) q^{21} +(3.34229 - 2.50548i) q^{22} +2.06152 q^{23} +(2.93098 - 6.45204i) q^{24} -4.67667i q^{25} -0.695088i q^{27} +(1.03423 - 0.566524i) q^{28} +1.24363 q^{29} +(-6.61124 - 8.81933i) q^{30} +(6.34495 + 6.34495i) q^{31} +(-4.28748 - 3.69019i) q^{32} +(-5.23284 - 5.23284i) q^{33} +(0.534321 - 3.73394i) q^{34} -1.83414i q^{35} +(-6.29179 - 1.83834i) q^{36} +(0.366025 + 0.366025i) q^{37} +(-2.73933 - 3.65425i) q^{38} +(-8.23758 + 3.09122i) q^{40} +(4.09808 - 4.09808i) q^{41} +(-1.25311 - 1.67164i) q^{42} +7.21518 q^{43} +(-5.18097 + 2.83799i) q^{44} +(-7.20910 + 7.20910i) q^{45} +(-2.88603 - 0.412986i) q^{46} +(-3.16813 + 3.16813i) q^{47} +(-5.39577 + 8.44538i) q^{48} +6.65235i q^{49} +(-0.936882 + 6.54712i) q^{50} -6.68260 q^{51} +3.67667 q^{53} +(-0.139248 + 0.973090i) q^{54} +9.18808i q^{55} +(-1.56137 + 0.585918i) q^{56} +(-5.72126 + 5.72126i) q^{57} +(-1.74103 - 0.249138i) q^{58} +(-4.98392 + 4.98392i) q^{59} +(7.48864 + 13.6711i) q^{60} +7.95410 q^{61} +(-7.61154 - 10.1537i) q^{62} +(-1.36643 + 1.36643i) q^{63} +(5.26301 + 6.02501i) q^{64} +(6.27743 + 8.37403i) q^{66} +(-5.25669 - 5.25669i) q^{67} +(-1.49605 + 5.12030i) q^{68} +5.16509i q^{69} +(-0.367435 + 2.56771i) q^{70} +(1.44966 + 1.44966i) q^{71} +(8.43993 + 3.83402i) q^{72} +(-0.0440105 - 0.0440105i) q^{73} +(-0.439092 - 0.585744i) q^{74} +11.7173 q^{75} +(3.10288 + 5.66454i) q^{76} +1.74153i q^{77} -2.73286i q^{79} +(12.1515 - 2.67732i) q^{80} -8.09075 q^{81} +(-6.55808 + 4.91614i) q^{82} +(-10.1844 - 10.1844i) q^{83} +(1.41941 + 2.59125i) q^{84} +(5.86681 + 5.86681i) q^{85} +(-10.1009 - 1.44543i) q^{86} +3.11589i q^{87} +(7.82165 - 2.93514i) q^{88} +(-5.86739 - 5.86739i) q^{89} +(11.5366 - 8.64819i) q^{90} +(3.95757 + 1.15632i) q^{92} +(-15.8971 + 15.8971i) q^{93} +(5.06990 - 3.80056i) q^{94} +10.0457 q^{95} +(9.24570 - 10.7422i) q^{96} +(3.35308 - 3.35308i) q^{97} +(1.33267 - 9.31298i) q^{98} +(6.84510 - 6.84510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9	\( 16 q + 2 q^{2} + 12 q^{5} - 4 q^{6} - 10 q^{8} - 8 q^{9} + 8 q^{14} + 4 q^{16} + 6 q^{18} + 22 q^{20} + 28 q^{21} - 4 q^{24} + 36 q^{28} + 16 q^{29} + 2 q^{32} - 28 q^{33} - 14 q^{34} - 8 q^{37} - 40 q^{40} + 24 q^{41} + 56 q^{42} + 8 q^{44} - 20 q^{45} - 56 q^{46} + 20 q^{48} + 32 q^{50} - 32 q^{53} - 44 q^{54} - 12 q^{57} - 30 q^{58} + 24 q^{60} - 8 q^{61} + 56 q^{66} - 32 q^{68} - 28 q^{70} + 46 q^{72} - 20 q^{73} - 8 q^{74} + 8 q^{76} + 22 q^{80} - 96 q^{81} + 48 q^{84} + 52 q^{85} - 16 q^{86} - 44 q^{89} - 12 q^{92} - 112 q^{93} + 76 q^{94} + 72 q^{96} + 52 q^{97} - 70 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 12 * q^5 - 4 * q^6 - 10 * q^8 - 8 * q^9 + 8 * q^14 + 4 * q^16 + 6 * q^18 + 22 * q^20 + 28 * q^21 - 4 * q^24 + 36 * q^28 + 16 * q^29 + 2 * q^32 - 28 * q^33 - 14 * q^34 - 8 * q^37 - 40 * q^40 + 24 * q^41 + 56 * q^42 + 8 * q^44 - 20 * q^45 - 56 * q^46 + 20 * q^48 + 32 * q^50 - 32 * q^53 - 44 * q^54 - 12 * q^57 - 30 * q^58 + 24 * q^60 - 8 * q^61 + 56 * q^66 - 32 * q^68 - 28 * q^70 + 46 * q^72 - 20 * q^73 - 8 * q^74 + 8 * q^76 + 22 * q^80 - 96 * q^81 + 48 * q^84 + 52 * q^85 - 16 * q^86 - 44 * q^89 - 12 * q^92 - 112 * q^93 + 76 * q^94 + 72 * q^96 + 52 * q^97 - 70 * q^98

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