LMFDB - Embedded newform 676.2.f.i.99.4

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			99.4
Root			$-0.873468 - 1.11223i$ of defining polynomial
Character	$\chi$	$=$	676.99
Dual form			676.2.f.i.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.200331 - 1.39995i) q^{2} +2.50548i q^{3} +(-1.91973 - 0.560908i) q^{4} +(2.19962 + 2.19962i) q^{5} +(3.50755 + 0.501925i) q^{6} +(-0.416921 - 0.416921i) q^{7} +(-1.16983 + 2.57517i) q^{8} -3.27743 q^{9} +O(q^{10})$	\(q+(0.200331 - 1.39995i) q^{2} +2.50548i q^{3} +(-1.91973 - 0.560908i) q^{4} +(2.19962 + 2.19962i) q^{5} +(3.50755 + 0.501925i) q^{6} +(-0.416921 - 0.416921i) q^{7} +(-1.16983 + 2.57517i) 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} +(-0.656570 + 4.58824i) q^{18} +(-2.28350 + 2.28350i) q^{19} +(-2.98891 - 5.45648i) q^{20} +(1.04459 - 1.04459i) q^{21} +(3.34229 - 2.50548i) q^{22} -2.06152 q^{23} +(-6.45204 - 2.93098i) q^{24} +4.67667i q^{25} -0.695088i q^{27} +(0.566524 + 1.03423i) q^{28} +1.24363 q^{29} +(6.61124 + 8.81933i) q^{30} +(-6.34495 + 6.34495i) q^{31} +(3.69019 - 4.28748i) q^{32} +(-5.23284 + 5.23284i) q^{33} +(-3.73394 - 0.534321i) 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} +(-2.83799 - 5.18097i) q^{44} +(-7.20910 - 7.20910i) q^{45} +(-0.412986 + 2.88603i) q^{46} +(3.16813 + 3.16813i) q^{47} +(-5.39577 + 8.44538i) q^{48} -6.65235i q^{49} +(6.54712 + 0.936882i) q^{50} +6.68260 q^{51} +3.67667 q^{53} +(-0.973090 - 0.139248i) q^{54} +9.18808i q^{55} +(1.56137 - 0.585918i) q^{56} +(-5.72126 - 5.72126i) q^{57} +(0.249138 - 1.74103i) q^{58} +(4.98392 + 4.98392i) q^{59} +(13.6711 - 7.48864i) 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} +(-2.56771 - 0.367435i) q^{70} +(-1.44966 + 1.44966i) q^{71} +(3.83402 - 8.43993i) q^{72} +(-0.0440105 + 0.0440105i) q^{73} +(-0.439092 - 0.585744i) q^{74} -11.7173 q^{75} +(5.66454 - 3.10288i) q^{76} -1.74153i q^{77} -2.73286i q^{79} +(2.67732 + 12.1515i) q^{80} -8.09075 q^{81} +(6.55808 - 4.91614i) q^{82} +(10.1844 - 10.1844i) q^{83} +(-2.59125 + 1.41941i) q^{84} +(5.86681 - 5.86681i) q^{85} +(-1.44543 + 10.1009i) 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} +(10.7422 + 9.24570i) q^{96} +(3.35308 + 3.35308i) q^{97} +(-9.31298 - 1.33267i) 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 $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.200331	−	1.39995i	0.141655	−	0.989916i
$2$	0.200331	−	1.39995i	0.141655	−	0.989916i
$3$			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	0.999869	−	0.0161686i	$-0.00514685\pi$
$5$	2.19962	+	2.19962i	0.983701	+	0.983701i	−0.0161686	+	0.999869i	$0.505147\pi$
$6$	3.50755	+	0.501925i	1.43195	+	0.204910i
$7$	−0.416921	−	0.416921i	−0.157581	−	0.157581i	0.623913	−	0.781494i	$-0.285542\pi$
$7$	−0.416921	−	0.416921i	−0.157581	−	0.157581i	−0.781494	+	0.623913i	$0.785542\pi$
$8$	−1.16983	+	2.57517i	−0.413596	+	0.910460i
$9$	−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	$-0.103103\pi$
$11$	2.08856	+	2.08856i	0.629724	+	0.629724i	−0.318275	+	0.947999i	$0.603103\pi$
$12$	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	$-0.895159\pi$
$17$		−	2.66719i		−	0.646889i	0.946247	−	0.323445i	$-0.104841\pi$
$18$	−0.656570	+	4.58824i	−0.154755	+	1.08146i
$19$	−2.28350	+	2.28350i	−0.523870	+	0.523870i	−0.918738	−	0.394868i	$-0.870790\pi$
$19$	−2.28350	+	2.28350i	−0.523870	+	0.523870i	0.394868	+	0.918738i	$0.370790\pi$
$20$	−2.98891	−	5.45648i	−0.668339	−	1.22011i
$21$	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	$-0.568952\pi$
$23$	−2.06152			−0.429856			−0.214928	+	0.976630i	$0.568952\pi$
$24$	−6.45204	−	2.93098i	−1.31702	−	0.598283i
$25$			4.67667i			0.935334i
$26$		0			0
$27$		−	0.695088i		−	0.133770i
$28$	0.566524	+	1.03423i	0.107063	+	0.195452i
$29$	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	−0.151062	+	0.988524i	$0.548269\pi$
$31$	−6.34495	+	6.34495i	−1.13959	+	1.13959i	−0.988524	+	0.151062i	$0.951731\pi$
$32$	3.69019	−	4.28748i	0.652340	−	0.757926i
$33$	−5.23284	+	5.23284i	−0.910920	+	0.910920i
$34$	−3.73394	−	0.534321i	−0.640366	−	0.0916354i
$35$		−	1.83414i		−	0.310026i
$36$	6.29179	+	1.83834i	1.04863	+	0.306389i
$37$	0.366025	−	0.366025i	0.0601742	−	0.0601742i	−0.676379	−	0.736553i	$-0.736452\pi$
$37$	0.366025	−	0.366025i	0.0601742	−	0.0601742i	0.736553	+	0.676379i	$0.236452\pi$
$38$	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	0.950558	−	0.310546i	$-0.100512\pi$
$41$	4.09808	+	4.09808i	0.640012	+	0.640012i	−0.310546	+	0.950558i	$0.600512\pi$
$42$	−1.25311	−	1.67164i	−0.193359	−	0.257939i
$43$	−7.21518			−1.10030			−0.550152	−	0.835064i	$-0.685430\pi$
$43$	−7.21518			−1.10030			−0.550152	+	0.835064i	$0.685430\pi$
$44$	−2.83799	−	5.18097i	−0.427843	−	0.781060i
$45$	−7.20910	−	7.20910i	−1.07467	−	1.07467i
$46$	−0.412986	+	2.88603i	−0.0608915	+	0.425521i
$47$	3.16813	+	3.16813i	0.462119	+	0.462119i	0.899350	−	0.437230i	$-0.144041\pi$
$47$	3.16813	+	3.16813i	0.462119	+	0.462119i	−0.437230	+	0.899350i	$0.644041\pi$
$48$	−5.39577	+	8.44538i	−0.778813	+	1.21899i
$49$		−	6.65235i		−	0.950336i
$50$	6.54712	+	0.936882i	0.925902	+	0.132495i
$51$	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	$0.418742\pi$
$54$	−0.973090	−	0.139248i	−0.132421	−	0.0189492i
$55$			9.18808i			1.23892i
$56$	1.56137	−	0.585918i	0.208647	−	0.0782965i
$57$	−5.72126	−	5.72126i	−0.757799	−	0.757799i
$58$	0.249138	−	1.74103i	0.0327134	−	0.228608i
$59$	4.98392	+	4.98392i	0.648851	+	0.648851i	0.952715	−	0.303864i	$-0.0982770\pi$
$59$	4.98392	+	4.98392i	0.648851	+	0.648851i	−0.303864	+	0.952715i	$0.598277\pi$
$60$	13.6711	−	7.48864i	1.76493	−	0.966779i
$61$	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	$-0.599958\pi$
$67$	5.25669	−	5.25669i	0.642207	−	0.642207i	0.951097	+	0.308891i	$0.0999578\pi$
$68$	−1.49605	+	5.12030i	−0.181423	+	0.620928i
$69$		−	5.16509i		−	0.621804i
$70$	−2.56771	−	0.367435i	−0.306900	−	0.0439169i
$71$	−1.44966	+	1.44966i	−0.172042	+	0.172042i	−0.787876	−	0.615834i	$-0.788819\pi$
$71$	−1.44966	+	1.44966i	−0.172042	+	0.172042i	0.615834	+	0.787876i	$0.288819\pi$
$72$	3.83402	−	8.43993i	0.451844	−	0.994656i
$73$	−0.0440105	+	0.0440105i	−0.00515104	+	0.00515104i	−0.709678	−	0.704527i	$-0.751159\pi$
$73$	−0.0440105	+	0.0440105i	−0.00515104	+	0.00515104i	0.704527	+	0.709678i	$0.251159\pi$
$74$	−0.439092	−	0.585744i	−0.0510434	−	0.0680914i
$75$	−11.7173			−1.35300
$76$	5.66454	−	3.10288i	0.649768	−	0.355925i
$77$		−	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	$-0.0491303\pi$
$80$	2.67732	+	12.1515i	0.299334	+	1.35858i
$81$	−8.09075			−0.898973
$82$	6.55808	−	4.91614i	0.724219	−	0.542897i
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.125834	−	0.992051i	$-0.459839\pi$
$83$	10.1844	−	10.1844i	1.11789	−	1.11789i	0.992051	−	0.125834i	$-0.0401606\pi$
$84$	−2.59125	+	1.41941i	−0.282728	+	0.154871i
$85$	5.86681	−	5.86681i	0.636345	−	0.636345i
$86$	−1.44543	+	10.1009i	−0.155864	+	1.08921i
$87$			3.11589i			0.334059i
$88$	−7.82165	+	2.93514i	−0.833790	+	0.312887i
$89$	−5.86739	+	5.86739i	−0.621942	+	0.621942i	−0.946028	−	0.324086i	$-0.894943\pi$
$89$	−5.86739	+	5.86739i	−0.621942	+	0.621942i	0.324086	+	0.946028i	$0.394943\pi$
$90$	−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
$96$	10.7422	+	9.24570i	1.09637	+	0.943635i
$97$	3.35308	+	3.35308i	0.340454	+	0.340454i	0.856538	−	0.516084i	$-0.172611\pi$
$97$	3.35308	+	3.35308i	0.340454	+	0.340454i	−0.516084	+	0.856538i	$0.672611\pi$
$98$	−9.31298	−	1.33267i	−0.940753	−	0.134620i
$99$	−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	$-0.852602\pi$
$101$		−	8.97841i		−	0.893386i	0.894687	−	0.446693i	$-0.147398\pi$
$102$	1.33873	−	9.35532i	0.132554	−	0.926314i
$103$	9.60170			0.946084			0.473042	−	0.881040i	$-0.343156\pi$
$103$	9.60170			0.946084			0.473042	+	0.881040i	$0.343156\pi$
$104$		0			0
$105$	4.59540			0.448465
$106$	0.736551	−	5.14716i	0.0715402	−	0.499937i
$107$		−	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	0.834225	−	0.551425i	$-0.185916\pi$
$109$	2.95252	+	2.95252i	0.282800	+	0.282800i	−0.551425	+	0.834225i	$0.685916\pi$
$110$	12.8629	+	1.84066i	1.22643	+	0.175500i
$111$	0.917069	+	0.917069i	0.0870443	+	0.0870443i
$112$	−0.507466	−	2.30322i	−0.0479510	−	0.217634i
$113$	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
$122$	1.59345	−	11.1354i	0.144264	−	1.00815i
$123$	−10.2676	+	10.2676i	−0.925802	+	0.925802i
$124$	15.7396	−	8.62169i	1.41345	−	0.774250i
$125$	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	$-0.319891\pi$
$127$	12.0834			1.07223			0.536116	+	0.844144i	$0.319891\pi$
$128$	−9.48907	+	6.16097i	−0.838723	+	0.544558i
$129$		−	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	$-0.315923\pi$
$132$	12.9808	−	7.11052i	1.12983	−	0.618892i
$133$	1.90408			0.165105
$134$	−6.30604	−	8.41219i	−0.544758	−	0.726703i
$135$	1.52893	−	1.52893i	0.131589	−	0.131589i
$136$	6.86848	+	3.12015i	0.588967	+	0.267551i
$137$	−5.13187	+	5.13187i	−0.438445	+	0.438445i	−0.891489	−	0.453043i	$-0.850338\pi$
$137$	−5.13187	+	5.13187i	−0.438445	+	0.438445i	0.453043	+	0.891489i	$0.350338\pi$
$138$	−7.23088	−	1.03473i	−0.615533	−	0.0880819i
$139$			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
$148$	−0.907978	+	0.497365i	−0.0746354	+	0.0408832i
$149$	−3.67452	−	3.67452i	−0.301028	−	0.301028i	0.540388	−	0.841416i	$-0.318277\pi$
$149$	−3.67452	−	3.67452i	−0.301028	−	0.301028i	−0.841416	+	0.540388i	$0.818277\pi$
$150$	−2.34734	+	16.4037i	−0.191659	+	1.33935i
$151$	−3.67697	−	3.67697i	−0.299227	−	0.299227i	0.541484	−	0.840711i	$-0.317863\pi$
$151$	−3.67697	−	3.67697i	−0.299227	−	0.299227i	−0.840711	+	0.541484i	$0.817863\pi$
$152$	−3.20910	−	8.55170i	−0.260292	−	0.693634i
$153$			8.74153i			0.706711i
$154$	−2.43806	−	0.348882i	−0.196464	−	0.0281137i
$155$	−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	$0.641271\pi$
$158$	−3.82587	−	0.547476i	−0.304370	−	0.0435549i
$159$			9.21182i			0.730545i
$160$	17.5479	−	1.31381i	1.38728	−	0.103866i
$161$	0.859490	+	0.859490i	0.0677373	+	0.0677373i
$162$	−1.62083	+	11.3267i	−0.127344	+	0.889907i
$163$	10.0490	+	10.0490i	0.787095	+	0.787095i	0.981017	−	0.193922i	$-0.0621208\pi$
$163$	10.0490	+	10.0490i	0.787095	+	0.787095i	−0.193922	+	0.981017i	$0.562121\pi$
$164$	−5.56858	−	10.1659i	−0.434833	−	0.793821i
$165$	−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	$-0.132563\pi$
$167$	6.59068	+	6.59068i	0.510002	+	0.510002i	−0.404525	+	0.914527i	$0.632563\pi$
$168$	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	$0.336020\pi$
$173$			22.8918i			1.74043i	−0.492672	+	0.870215i	$0.663980\pi$
$174$	4.36210	+	0.624210i	0.330690	+	0.0473213i
$175$	1.94980	−	1.94980i	0.147391	−	0.147391i
$176$	2.54214	+	11.5379i	0.191621	+	0.869704i
$177$	−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	$-0.664466\pi$
$179$	−13.2185			−0.988000			−0.494000	+	0.869462i	$0.664466\pi$
$180$	9.79592	+	17.8832i	0.730145	+	1.33294i
$181$			26.1208i			1.94154i	0.240009	+	0.970771i	$0.422849\pi$
$181$			26.1208i			1.94154i	−0.240009	+	0.970771i	$0.577151\pi$
$182$		0			0
$183$			19.9288i			1.47318i
$184$	2.41162	−	5.30876i	0.177787	−	0.391367i
$185$	1.61023			0.118387
$186$	−25.4399	+	19.0706i	−1.86535	+	1.39832i
$187$	5.57059	−	5.57059i	0.407362	−	0.407362i
$188$	−4.30494	−	7.85900i	−0.313970	−	0.573176i
$189$	−0.289797	+	0.289797i	−0.0210796	+	0.0210796i
$190$	−2.01246	+	14.0635i	−0.145999	+	1.02027i
$191$		−	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	0.201239	−	0.979542i	$-0.435503\pi$
$193$	16.4039	−	16.4039i	1.18078	−	1.18078i	0.979542	−	0.201239i	$-0.0644968\pi$
$194$	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	0.845941	−	0.533277i	$-0.179040\pi$
$197$	4.38845	+	4.38845i	0.312664	+	0.312664i	−0.533277	+	0.845941i	$0.679040\pi$
$198$	−10.9541	+	8.21153i	−0.778474	+	0.583568i
$199$	3.01432			0.213679			0.106840	−	0.994276i	$-0.465927\pi$
$199$	3.01432			0.213679			0.106840	+	0.994276i	$0.465927\pi$
$200$	−12.0432	−	5.47090i	−0.851585	−	0.386851i
$201$	13.1705	+	13.1705i	0.928977	+	0.928977i
$202$	−12.5694	−	1.79866i	−0.884377	−	0.126553i
$203$	−0.518497	−	0.518497i	−0.0363913	−	0.0363913i
$204$	−12.8288	−	3.74832i	−0.898197	−	0.262435i
$205$			18.0284i			1.25916i
$206$	1.92352	−	13.4419i	0.134018	−	0.936544i
$207$	6.75647			0.469607
$208$		0			0
$209$	−9.53844			−0.659788
$210$	0.920601	−	6.43334i	0.0635275	−	0.443942i
$211$		−	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
$214$	−26.4082	−	3.77898i	−1.80523	−	0.258325i
$215$	−15.8707	−	15.8707i	−1.08237	−	1.08237i
$216$	1.78997	+	0.813133i	0.121792	+	0.0553267i
$217$	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	$-0.712065\pi$
$223$	2.51088	−	2.51088i	0.168141	−	0.168141i	0.786162	+	0.618021i	$0.212065\pi$
$224$	−3.32606	+	0.249022i	−0.222232	+	0.0166385i
$225$		−	15.3274i		−	1.02183i
$226$	1.13044	−	7.89976i	0.0751960	−	0.525484i
$227$	12.3292	−	12.3292i	0.818315	−	0.818315i	−0.167549	−	0.985864i	$-0.553585\pi$
$227$	12.3292	−	12.3292i	0.818315	−	0.818315i	0.985864	+	0.167549i	$0.0535851\pi$
$228$	7.77420	+	14.1924i	0.514859	+	0.939915i
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	−0.0544132	−	0.998519i	$-0.517329\pi$
$229$	14.2869	−	14.2869i	0.944105	−	0.944105i	0.998519	+	0.0544132i	$0.0173288\pi$
$230$	−7.25658	+	5.43975i	−0.478485	+	0.358687i
$231$	4.36336			0.287088
$232$	−1.45483	+	3.20256i	−0.0955146	+	0.210259i
$233$			13.3205i			0.872655i	0.899788	+	0.436328i	$0.143721\pi$
$233$			13.3205i			0.872655i	−0.899788	+	0.436328i	$0.856279\pi$
$234$		0			0
$235$			13.9374i			0.909174i
$236$	−6.77228	−	12.3633i	−0.440838	−	0.804784i
$237$	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	$-0.905311\pi$
$239$	−10.2493	+	10.2493i	−0.662972	+	0.662972i	0.293108	+	0.956079i	$0.405311\pi$
$240$	−30.4453	+	6.70798i	−1.96524	+	0.432998i
$241$	9.79370	−	9.79370i	0.630868	−	0.630868i	−0.317418	−	0.948286i	$-0.602816\pi$
$241$	9.79370	−	9.79370i	0.630868	−	0.630868i	0.948286	+	0.317418i	$0.102816\pi$
$242$	−3.18608	−	0.455923i	−0.204809	−	0.0293079i
$243$		−	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	$-0.474695\pi$
$251$	2.51628			0.158826			0.0794129	+	0.996842i	$0.474695\pi$
$252$	−1.85674	−	3.38962i	−0.116964	−	0.213526i
$253$	−4.30560	−	4.30560i	−0.270691	−	0.270691i
$254$	2.42069	−	16.9162i	0.151887	−	1.06142i
$255$	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	$-0.935896\pi$
$257$		−	6.41347i		−	0.400061i	0.979790	−	0.200031i	$-0.0641041\pi$
$258$	−25.3076	−	3.62148i	−1.57558	−	0.225464i
$259$	−0.305208			−0.0189647
$260$		0			0
$261$	−4.07591			−0.252293
$262$	−26.8355	−	3.84012i	−1.65790	−	0.237243i
$263$			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
$266$	0.381446	−	2.66562i	0.0233880	−	0.163440i
$267$	−14.7006	−	14.7006i	−0.899664	−	0.899664i
$268$	−13.0400	+	7.14293i	−0.796543	+	0.436324i
$269$	−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	−0.994864	−	0.101225i	$-0.967724\pi$
$271$	−18.0439	−	18.0439i	−1.09609	−	1.09609i	−0.101225	−	0.994864i	$-0.532276\pi$
$272$	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	$0.00510977\pi$
$277$			0.534321i			0.0321043i	−0.999871	+	0.0160521i	$0.994890\pi$
$278$	15.5491	+	2.22505i	0.932574	+	0.133450i
$279$	20.7951	−	20.7951i	1.24497	−	1.24497i
$280$	4.72322	+	2.14562i	0.282266	+	0.128226i
$281$	0.275535	−	0.275535i	0.0164370	−	0.0164370i	−0.698840	−	0.715278i	$-0.746300\pi$
$281$	0.275535	−	0.275535i	0.0164370	−	0.0164370i	0.715278	+	0.698840i	$0.246300\pi$
$282$	9.52221	+	12.7025i	0.567040	+	0.756425i
$283$	16.0638			0.954892			0.477446	−	0.878661i	$-0.341563\pi$
$283$	16.0638			0.954892			0.477446	+	0.878661i	$0.341563\pi$
$284$	3.59608	−	1.96983i	0.213388	−	0.116888i
$285$		−	25.1692i		−	1.49090i
$286$		0			0
$287$		−	3.41715i		−	0.201708i
$288$	−12.0943	+	14.0519i	−0.712666	+	0.828016i
$289$	9.88608			0.581534
$290$	4.37761	−	3.28159i	0.257062	−	0.192702i
$291$	−8.40107	+	8.40107i	−0.492479	+	0.492479i
$292$	0.109174	−	0.0598026i	0.00638894	−	0.00349968i
$293$	1.44888	−	1.44888i	0.0846443	−	0.0846443i	−0.663517	−	0.748161i	$-0.730937\pi$
$293$	1.44888	−	1.44888i	0.0846443	−	0.0846443i	0.748161	+	0.663517i	$0.230937\pi$
$294$	3.33898	−	23.3335i	0.194734	−	1.36084i
$295$			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
$304$	−12.6149	+	2.77942i	−0.723511	+	0.159410i
$305$	17.4960	+	17.4960i	1.00182	+	1.00182i
$306$	12.2377	+	1.75120i	0.699584	+	0.100109i
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	0.953608	−	0.301050i	$-0.0973372\pi$
$307$	11.4337	+	11.4337i	0.652558	+	0.652558i	−0.301050	+	0.953608i	$0.597337\pi$
$308$	−0.976837	+	3.34327i	−0.0556605	+	0.190501i
$309$			24.0569i			1.36855i
$310$	−5.59184	+	39.0768i	−0.317595	+	2.21942i
$311$	−24.0242			−1.36229			−0.681143	−	0.732151i	$-0.738517\pi$
$311$	−24.0242			−1.36229			−0.681143	+	0.732151i	$0.738517\pi$
$312$		0			0
$313$	28.9008			1.63357			0.816786	−	0.576941i	$-0.195754\pi$
$313$	28.9008			1.63357			0.816786	+	0.576941i	$0.195754\pi$
$314$	−2.15566	+	15.0642i	−0.121651	+	0.850120i
$315$			6.01125i			0.338696i
$316$	−1.53288	+	5.24636i	−0.0862314	+	0.295131i
$317$	−0.0141017	−	0.0141017i	−0.000792031	−	0.000792031i	0.706711	−	0.707503i	$-0.250178\pi$
$317$	−0.0141017	−	0.0141017i	−0.000792031	−	0.000792031i	−0.707503	+	0.706711i	$0.750178\pi$
$318$	12.8961	+	1.84541i	0.723178	+	0.103486i
$319$	2.59740	+	2.59740i	0.145426	+	0.145426i
$320$	1.67611	−	24.8294i	0.0936976	−	1.38800i
$321$	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
$330$	−4.61173	+	32.2277i	−0.253867	+	1.77407i
$331$	2.98728	−	2.98728i	0.164196	−	0.164196i	−0.620227	−	0.784423i	$-0.712959\pi$
$331$	2.98728	−	2.98728i	0.164196	−	0.164196i	0.784423	+	0.620227i	$0.212959\pi$
$332$	−25.2639	+	13.8389i	−1.38654	+	0.759506i
$333$	−1.19962	+	1.19962i	−0.0657389	+	0.0657389i
$334$	10.5470	−	7.90632i	0.577104	−	0.432615i
$335$	23.1254			1.26348
$336$	5.77067	−	1.27145i	0.314816	−	0.0693631i
$337$		−	9.58550i		−	0.522155i	−0.965318	−	0.261078i	$-0.915922\pi$
$337$		−	9.58550i		−	0.522155i	0.965318	−	0.261078i	$-0.0840778\pi$
$338$		0			0
$339$			14.1381i			0.767877i
$340$	−14.5535	+	7.97198i	−0.789273	+	0.432342i
$341$	−26.5036			−1.43525
$342$	−8.97797	−	11.9765i	−0.485473	−	0.647616i
$343$	−5.69196	+	5.69196i	−0.307337	+	0.307337i
$344$	8.44052	−	18.5803i	0.455082	−	1.00178i
$345$	11.3612	−	11.3612i	0.611669	−	0.611669i
$346$	32.0474	+	4.58593i	1.72288	+	0.246541i
$347$			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	−0.105241	+	0.994447i	$0.533562\pi$
$349$	−20.5439	+	20.5439i	−1.09969	+	1.09969i	−0.994447	+	0.105241i	$0.966438\pi$
$350$	−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	0.00901875	−	0.999959i	$-0.497129\pi$
$353$	−18.6181	−	18.6181i	−0.990941	−	0.990941i	−0.999959	+	0.00901875i	$0.997129\pi$
$354$	14.9798	+	19.9829i	0.796167	+	1.06208i
$355$	−6.37739			−0.338477
$356$	14.5549	−	7.97277i	0.771408	−	0.422556i
$357$	−2.78612	−	2.78612i	−0.147457	−	0.147457i
$358$	−2.64808	+	18.5053i	−0.139956	+	0.978037i
$359$	−7.69873	−	7.69873i	−0.406324	−	0.406324i	0.474131	−	0.880454i	$-0.342762\pi$
$359$	−7.69873	−	7.69873i	−0.406324	−	0.406324i	−0.880454	+	0.474131i	$0.842762\pi$
$360$	26.9981	−	10.1313i	1.42292	−	0.533964i
$361$			8.57127i			0.451120i
$362$	36.5678	+	5.23280i	1.92196	+	0.275030i
$363$	5.70210			0.299282
$364$		0			0
$365$	−0.193613			−0.0101342
$366$	27.8994	+	3.99236i	1.45833	+	0.208684i
$367$			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
$370$	0.322580	−	2.25425i	0.0167701	−	0.117193i
$371$	−1.53288	−	1.53288i	−0.0795833	−	0.0795833i
$372$	21.6015	+	39.4351i	1.11998	+	2.04462i
$373$	−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	0.0514122	−	0.998678i	$-0.483628\pi$
$379$	20.4431	−	20.4431i	1.05009	−	1.05009i	0.998678	−	0.0514122i	$-0.0163722\pi$
$380$	19.2850	+	5.63469i	0.989300	+	0.289054i
$381$			30.2748i			1.55102i
$382$	−19.7927	−	2.83230i	−1.01268	−	0.144913i
$383$	10.7029	−	10.7029i	0.546893	−	0.546893i	−0.378648	−	0.925541i	$-0.623611\pi$
$383$	10.7029	−	10.7029i	0.546893	−	0.546893i	0.925541	+	0.378648i	$0.123611\pi$
$384$	−15.4362	−	23.7747i	−0.787724	−	1.21325i
$385$	3.83070	−	3.83070i	0.195231	−	0.195231i
$386$	−19.6785	−	26.2510i	−1.00161	−	1.33614i
$387$	23.6472			1.20206
$388$	−4.55625	−	8.31779i	−0.231309	−	0.422272i
$389$		−	30.3695i		−	1.53979i	−0.638168	−	0.769897i	$-0.720308\pi$
$389$		−	30.3695i		−	1.53979i	0.638168	−	0.769897i	$-0.279692\pi$
$390$		0			0
$391$			5.49846i			0.278069i
$392$	17.1309	+	7.78210i	0.865243	+	0.393056i
$393$	48.0272			2.42265
$394$	7.02277	−	5.26448i	0.353802	−	0.265221i
$395$	6.01125	−	6.01125i	0.302459	−	0.302459i
$396$	9.30130	+	16.9802i	0.467408	+	0.853289i
$397$	−11.3167	+	11.3167i	−0.567967	+	0.567967i	−0.931558	−	0.363592i	$-0.881550\pi$
$397$	−11.3167	+	11.3167i	−0.567967	+	0.567967i	0.363592	+	0.931558i	$0.381550\pi$
$398$	0.603862	−	4.21990i	0.0302689	−	0.211525i
$399$			4.77063i			0.238830i
$400$	−10.0716	+	15.7640i	−0.503581	+	0.788198i
$401$	−9.73578	+	9.73578i	−0.486182	+	0.486182i	−0.907099	−	0.420917i	$-0.861708\pi$
$401$	−9.73578	+	9.73578i	−0.486182	+	0.486182i	0.420917	+	0.907099i	$0.361708\pi$
$402$	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
$408$	−7.81748	+	17.2088i	−0.387023	+	0.851964i
$409$	−0.413505	−	0.413505i	−0.0204465	−	0.0204465i	0.696810	−	0.717256i	$-0.254602\pi$
$409$	−0.413505	−	0.413505i	−0.0204465	−	0.0204465i	−0.717256	+	0.696810i	$0.754602\pi$
$410$	25.2390	+	3.61166i	1.24646	+	0.178367i
$411$	−12.8578	−	12.8578i	−0.634228	−	0.634228i
$412$	−18.4327	−	5.38567i	−0.908115	−	0.265333i
$413$		−	4.15580i		−	0.204494i
$414$	1.35353	−	9.45874i	0.0665224	−	0.464872i
$415$	44.8037			2.19933
$416$		0			0
$417$	−27.8281			−1.36275
$418$	−1.91085	+	13.3534i	−0.0934625	+	0.653134i
$419$			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	0.996384	+	0.0849697i	$0.0270794\pi$
$421$	22.1875	+	22.1875i	1.08135	+	1.08135i	0.0849697	+	0.996384i	$0.472921\pi$
$422$	−25.4982	−	3.64876i	−1.24124	−	0.177619i
$423$	−10.3833	−	10.3833i	−0.504854	−	0.504854i
$424$	−4.30107	+	9.46805i	−0.208878	+	0.459809i
$425$	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	−0.0612754	+	0.998121i	$0.519517\pi$
$431$	−21.9936	+	21.9936i	−1.05940	+	1.05940i	−0.998121	+	0.0612754i	$0.980483\pi$
$432$	1.49693	−	2.34298i	0.0720213	−	0.112727i
$433$			10.7931i			0.518684i	0.965785	+	0.259342i	$0.0835058\pi$
$433$			10.7931i			0.518684i	−0.965785	+	0.259342i	$0.916494\pi$
$434$	1.05989	−	7.40671i	0.0508763	−	0.355534i
$435$	−6.85379	+	6.85379i	−0.328614	+	0.328614i
$436$	−4.01196	−	7.32415i	−0.192138	−	0.350763i
$437$	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	$-0.399864\pi$
$439$	12.9663			0.618848			0.309424	+	0.950924i	$0.399864\pi$
$440$	−23.6609	−	10.7485i	−1.12799	−	0.512413i
$441$			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	$0.878739\pi$
$444$	−1.24614	−	2.27492i	−0.0591391	−	0.107963i
$445$	−25.8121			−1.22361
$446$	−3.01210	−	4.01812i	−0.142627	−	0.190263i
$447$	9.20642	−	9.20642i	0.435449	−	0.435449i
$448$	−0.317694	+	4.70622i	−0.0150097	+	0.222348i
$449$	7.92277	−	7.92277i	0.373899	−	0.373899i	−0.494996	−	0.868895i	$-0.664831\pi$
$449$	7.92277	−	7.92277i	0.373899	−	0.373899i	0.868895	+	0.494996i	$0.164831\pi$
$450$	−21.4577	−	3.07056i	−1.01153	−	0.144748i
$451$			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	0.949459	−	0.313890i	$-0.101632\pi$
$457$	13.5869	+	13.5869i	0.635569	+	0.635569i	−0.313890	+	0.949459i	$0.601632\pi$
$458$	−17.1389	−	22.8631i	−0.800847	−	1.06832i
$459$	−1.85393			−0.0865342
$460$	6.16168	+	11.2486i	0.287290	+	0.524470i
$461$	−17.3417	−	17.3417i	−0.807684	−	0.807684i	0.176599	−	0.984283i	$-0.443490\pi$
$461$	−17.3417	−	17.3417i	−0.807684	−	0.807684i	−0.984283	+	0.176599i	$0.943490\pi$
$462$	0.874117	−	6.10850i	0.0406676	−	0.284193i
$463$	−13.2027	−	13.2027i	−0.613581	−	0.613581i	0.330296	−	0.943877i	$-0.392851\pi$
$463$	−13.2027	−	13.2027i	−0.613581	−	0.613581i	−0.943877	+	0.330296i	$0.892851\pi$
$464$	4.19199	+	2.67827i	0.194608	+	0.124336i
$465$		−	69.9354i		−	3.24318i
$466$	18.6481	+	2.66851i	0.863856	+	0.123616i
$467$	22.6548			1.04834			0.524171	−	0.851613i	$-0.324375\pi$
$467$	22.6548			1.04834			0.524171	+	0.851613i	$0.324375\pi$
$468$		0			0
$469$	−4.38325			−0.202400
$470$	19.5117	+	2.79209i	0.900006	+	0.128789i
$471$		−	26.9602i		−	1.24226i
$472$	−18.6648	+	7.00412i	−0.859115	+	0.322391i
$473$	−15.0693	−	15.0693i	−0.692888	−	0.692888i
$474$	1.37169	−	9.58564i	0.0630039	−	0.440283i
$475$	−10.6792	−	10.6792i	−0.489994	−	0.489994i
$476$	2.75850	−	1.51103i	0.126436	−	0.0692579i
$477$	−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	$-0.273639\pi$
$479$	−2.29645	−	2.29645i	−0.104927	−	0.104927i	−0.757622	+	0.652694i	$0.773639\pi$
$480$	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
$486$	−31.2980	−	4.47870i	−1.41971	−	0.203158i
$487$	−30.3265	+	30.3265i	−1.37423	+	1.37423i	−0.520154	+	0.854072i	$0.674125\pi$
$487$	−30.3265	+	30.3265i	−1.37423	+	1.37423i	−0.854072	+	0.520154i	$0.825875\pi$
$488$	−9.30492	+	20.4832i	−0.421214	+	0.927229i
$489$	−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	$-0.511450\pi$
$491$	−1.59381			−0.0719276			−0.0359638	+	0.999353i	$0.511450\pi$
$492$	25.4704	−	13.9520i	1.14829	−	0.629003i
$493$		−	3.31701i		−	0.149390i
$494$		0			0
$495$		−	30.1132i		−	1.35349i
$496$	−35.0517	+	7.72291i	−1.57387	+	0.346769i
$497$	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	$-0.779233\pi$
$499$	−2.89721	+	2.89721i	−0.129697	+	0.129697i	0.639278	+	0.768975i	$0.279233\pi$
$500$	−1.76424	+	0.966402i	−0.0788992	+	0.0432188i
$501$	−16.5128	+	16.5128i	−0.737738	+	0.737738i
$502$	0.504088	−	3.52267i	0.0224986	−	0.157224i
$503$		−	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	0.196587	−	0.980486i	$-0.437014\pi$
$509$	−17.6856	−	17.6856i	−0.783899	−	0.783899i	−0.980486	+	0.196587i	$0.937014\pi$
$510$	23.5229	−	17.6335i	1.04161	−	0.780823i
$511$	0.0366978			0.00162342
$512$	21.6722	−	6.50493i	0.957787	−	0.287480i
$513$	1.58723	+	1.58723i	0.0700780	+	0.0700780i
$514$	−8.97855	−	1.28482i	−0.396027	−	0.0566708i
$515$	21.1201	+	21.1201i	0.930663	+	0.930663i
$516$	−10.1398	+	34.7040i	−0.446380	+	1.52776i
$517$			13.2336i			0.582015i
$518$	−0.0611426	+	0.427276i	−0.00268645	+	0.0187734i
$519$	−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	$0.856927\pi$
$522$	−0.816532	+	5.70609i	−0.0357386	+	0.249749i
$523$		−	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
$526$	7.43132	+	1.06341i	0.324021	+	0.0463669i
$527$	16.9232	+	16.9232i	0.737186	+	0.737186i
$528$	−28.9081	+	6.36928i	−1.25806	+	0.277187i
$529$	−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
$538$	−2.00350	+	14.0009i	−0.0863772	+	0.603621i
$539$	13.8938	−	13.8938i	0.598449	−	0.598449i
$540$	−3.79273	+	2.07755i	−0.163213	+	0.0894036i
$541$	−14.2591	+	14.2591i	−0.613047	+	0.613047i	−0.943739	−	0.330692i	$-0.892718\pi$
$541$	−14.2591	+	14.2591i	−0.613047	+	0.613047i	0.330692	+	0.943739i	$0.392718\pi$
$542$	−28.8754	+	21.6459i	−1.24030	+	0.929769i
$543$	−65.4450			−2.80852
$544$	−11.4355	−	9.84245i	−0.490294	−	0.421992i
$545$			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	$-0.339478\pi$
$548$	12.7303	−	6.97332i	0.543813	−	0.297886i
$549$	−26.0690			−1.11260
$550$	11.7173	+	15.6308i	0.499627	+	0.666498i
$551$	−2.83983	+	2.83983i	−0.120981	+	0.120981i
$552$	13.3010	+	6.04226i	0.566128	+	0.257176i
$553$	−1.13939	+	1.13939i	−0.0484517	+	0.0484517i
$554$	0.748024	+	0.107041i	0.0317805	+	0.00454774i
$555$			4.03441i			0.171251i
$556$	6.22994	−	21.3223i	0.264208	−	0.904266i
$557$	−21.2821	+	21.2821i	−0.901752	+	0.901752i	−0.995588	−	0.0938353i	$-0.970087\pi$
$557$	−21.2821	+	21.2821i	−0.901752	+	0.901752i	0.0938353	+	0.995588i	$0.470087\pi$
$558$	−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	$-0.608714\pi$
$563$	−15.8944			−0.669870			−0.334935	+	0.942241i	$0.608714\pi$
$564$	19.6906	−	10.7859i	0.829122	−	0.454170i
$565$	12.4122	+	12.4122i	0.522185	+	0.522185i
$566$	3.21807	−	22.4885i	0.135266	−	0.945263i
$567$	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	$0.157023\pi$
$569$			22.5913i			0.947076i	−0.880773	+	0.473538i	$0.842977\pi$
$570$	−35.2357	−	5.04217i	−1.47586	−	0.211193i
$571$	2.17784			0.0911398			0.0455699	−	0.998961i	$-0.485490\pi$
$571$	2.17784			0.0911398			0.0455699	+	0.998961i	$0.485490\pi$
$572$		0			0
$573$	35.4227			1.47981
$574$	−4.78385	−	0.684561i	−0.199674	−	0.0285730i
$575$		−	9.64104i		−	0.402059i
$576$	17.2491	+	19.7465i	0.718714	+	0.822772i
$577$	−15.8624	−	15.8624i	−0.660361	−	0.660361i	0.295104	−	0.955465i	$-0.404646\pi$
$577$	−15.8624	−	15.8624i	−0.660361	−	0.660361i	−0.955465	+	0.295104i	$0.904646\pi$
$578$	1.98049	−	13.8401i	0.0823775	−	0.575670i
$579$	41.0997	+	41.0997i	1.70805	+	1.70805i
$580$	−3.71710	−	6.78585i	−0.154344	−	0.281767i
$581$	−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	$-0.897745\pi$
$587$	−15.3387	+	15.3387i	−0.633098	+	0.633098i	0.315746	+	0.948844i	$0.397745\pi$
$588$	−31.9969	−	9.34884i	−1.31953	−	0.385540i
$589$		−	28.9774i		−	1.19399i
$590$	30.6946	+	4.39235i	1.26368	+	0.180830i
$591$	−10.9952	+	10.9952i	−0.452281	+	0.452281i
$592$	2.02205	−	0.445517i	0.0831059	−	0.0183106i
$593$	−0.858298	+	0.858298i	−0.0352461	+	0.0352461i	−0.724510	−	0.689264i	$-0.757934\pi$
$593$	−0.858298	+	0.858298i	−0.0352461	+	0.0352461i	0.689264	+	0.724510i	$0.257934\pi$
$594$	−1.74153	−	2.32318i	−0.0714558	−	0.0953213i
$595$	−4.89200			−0.200552
$596$	4.99303	+	9.11516i	0.204523	+	0.373372i
$597$			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	$0.953247\pi$
$600$	13.7072	−	30.1741i	0.559595	−	1.23185i
$601$	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
$604$	4.99636	+	9.12125i	0.203299	+	0.371138i
$605$	5.00601	−	5.00601i	0.203523	−	0.203523i
$606$	4.50649	−	31.4923i	0.183064	−	1.27929i
$607$		−	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	0.936664	−	0.350230i	$-0.113896\pi$
$613$	14.5194	+	14.5194i	0.586434	+	0.586434i	−0.350230	+	0.936664i	$0.613896\pi$
$614$	18.2972	−	13.7162i	0.738416	−	0.553539i
$615$	−45.1699			−1.82142
$616$	4.48473	+	2.03729i	0.180695	+	0.0820847i
$617$	−13.3150	−	13.3150i	−0.536040	−	0.536040i	0.386323	−	0.922363i	$-0.373745\pi$
$617$	−13.3150	−	13.3150i	−0.536040	−	0.536040i	−0.922363	+	0.386323i	$0.873745\pi$
$618$	33.6785	+	4.81934i	1.35475	+	0.193862i
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.989798	−	0.142478i	$-0.954493\pi$
$619$	−28.1707	−	28.1707i	−1.13228	−	1.13228i	−0.142478	−	0.989798i	$-0.545507\pi$
$620$	53.5855	+	15.6566i	2.15205	+	0.628785i
$621$			1.43294i			0.0575017i
$622$	−4.81279	+	33.6327i	−0.192975	+	1.34855i
$623$	4.89248			0.196013
$624$		0			0
$625$	26.5121			1.06048
$626$	5.78973	−	40.4598i	0.231404	−	1.61710i
$627$		−	23.8984i		−	0.954409i
$628$	20.6573	+	6.03564i	0.824315	+	0.240848i
$629$	−0.976260	−	0.976260i	−0.0389260	−	0.0389260i
$630$	8.41547	+	1.20424i	0.335280	+	0.0479781i
$631$	8.84898	+	8.84898i	0.352272	+	0.352272i	0.860954	−	0.508682i	$-0.169867\pi$
$631$	8.84898	+	8.84898i	0.352272	+	0.352272i	−0.508682	+	0.860954i	$0.669867\pi$
$632$	7.03758	+	3.19697i	0.279940	+	0.127169i
$633$	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	$-0.826864\pi$
$641$		−	26.2040i		−	1.03499i	0.855685	−	0.517497i	$-0.173136\pi$
$642$	9.46815	−	66.1653i	0.373678	−	2.61133i
$643$	−0.265216	+	0.265216i	−0.0104591	+	0.0104591i	−0.712317	−	0.701858i	$-0.752354\pi$
$643$	−0.265216	+	0.265216i	−0.0104591	+	0.0104591i	0.701858	+	0.712317i	$0.252354\pi$
$644$	−1.16790	−	2.13209i	−0.0460217	−	0.0840161i
$645$	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	$-0.744153\pi$
$647$	−35.3054			−1.38800			−0.693999	+	0.719976i	$0.744153\pi$
$648$	9.46478	−	20.8351i	0.371812	−	0.818479i
$649$			20.8184i			0.817194i
$650$		0			0
$651$			13.2557i			0.519532i
$652$	−13.6548	−	24.9279i	−0.534763	−	0.976251i
$653$	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
$656$	4.98808	+	22.6392i	0.194752	+	0.883913i
$657$	0.144241	−	0.144241i	0.00562738	−	0.00562738i
$658$	−3.69828	−	0.529219i	−0.144174	−	0.0206311i
$659$		−	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	−0.809128	−	0.587633i	$-0.800060\pi$
$661$	−5.69463	+	5.69463i	−0.221495	+	0.221495i	0.587633	+	0.809128i	$0.300060\pi$
$662$	−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
$668$	−8.95559	−	16.3491i	−0.346502	−	0.632566i
$669$	6.29095	+	6.29095i	0.243222	+	0.243222i
$670$	4.63274	−	32.3745i	0.178979	−	1.25074i
$671$	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	$-0.991842\pi$
$673$		−	1.32965i		−	0.0512544i	0.999672	−	0.0256272i	$-0.00815828\pi$
$674$	−13.4192	−	1.92027i	−0.516890	−	0.0739661i
$675$	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	$0.275118\pi$
$678$	19.7927	+	2.83230i	0.760133	+	0.108774i
$679$		−	2.79594i		−	0.107298i
$680$	8.24489	+	21.9712i	0.316177	+	0.842557i
$681$	30.8905	+	30.8905i	1.18373	+	1.18373i
$682$	−5.30949	+	37.1038i	−0.203311	+	1.42078i
$683$	−31.2339	−	31.2339i	−1.19513	−	1.19513i	−0.975606	−	0.219527i	$-0.929548\pi$
$683$	−31.2339	−	31.2339i	−1.19513	−	1.19513i	−0.219527	−	0.975606i	$-0.570452\pi$
$684$	−18.5651	+	10.1695i	−0.709856	+	0.388839i
$685$	−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	−0.125897	+	0.992043i	$0.540181\pi$
$691$	−29.3872	+	29.3872i	−1.11794	+	1.11794i	−0.992043	+	0.125897i	$0.959819\pi$
$692$	12.8402	−	43.9461i	0.488110	−	1.67058i
$693$			5.70773i			0.216819i
$694$	5.76247	+	0.824601i	0.218740	+	0.0313014i
$695$	−24.4309	+	24.4309i	−0.926719	+	0.926719i
$696$	−8.02396	−	3.64506i	−0.304147	−	0.138166i
$697$	10.9304	−	10.9304i	0.414017	−	0.414017i
$698$	24.6449	+	32.8760i	0.932822	+	1.24438i
$699$	−33.3743			−1.26233
$700$	−4.83677	+	2.64945i	−0.182813	+	0.100140i
$701$			17.2912i			0.653080i	0.945183	+	0.326540i	$0.105883\pi$
$701$			17.2912i			0.653080i	−0.945183	+	0.326540i	$0.894117\pi$
$702$		0			0
$703$			1.67164i			0.0630470i
$704$	1.59148	−	23.5757i	0.0599813	−	0.888542i
$705$	−34.9198			−1.31516
$706$	−29.7942	+	22.3347i	−1.12132	+	0.840576i
$707$	−3.74329	+	3.74329i	−0.140781	+	0.140781i
$708$	30.9760	−	16.9678i	1.16415	−	0.637689i
$709$	−29.6113	+	29.6113i	−1.11208	+	1.11208i	−0.119208	+	0.992869i	$0.538035\pi$
$709$	−29.6113	+	29.6113i	−1.11208	+	1.11208i	−0.992869	+	0.119208i	$0.961965\pi$
$710$	−1.27759	+	8.92804i	−0.0479471	+	0.335063i
$711$			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	$-0.277455\pi$
$719$	34.5133			1.28713			0.643565	+	0.765392i	$0.277455\pi$
$720$	−8.77474	−	39.8256i	−0.327015	−	1.48421i
$721$	−4.00315	−	4.00315i	−0.149085	−	0.149085i
$722$	11.9994	+	1.71709i	0.446570	+	0.0639035i
$723$	24.5379	+	24.5379i	0.912575	+	0.912575i
$724$	14.6513	−	50.1449i	0.544513	−	1.86362i
$725$			5.81606i			0.216003i
$726$	1.14231	−	7.98266i	0.0423950	−	0.296264i
$727$	−3.77644			−0.140060			−0.0700302	−	0.997545i	$-0.522310\pi$
$727$	−3.77644			−0.140060			−0.0700302	+	0.997545i	$0.522310\pi$
$728$		0			0
$729$	31.7414			1.17561
$730$	−0.0387867	+	0.271049i	−0.00143556	+	0.0100320i
$731$			19.2443i			0.711775i
$732$	11.1782	−	38.2581i	0.413160	−	1.41406i
$733$	−4.25026	−	4.25026i	−0.156987	−	0.156987i	0.624243	−	0.781230i	$-0.285407\pi$
$733$	−4.25026	−	4.25026i	−0.156987	−	0.156987i	−0.781230	+	0.624243i	$0.785407\pi$
$734$	2.93740	+	0.420338i	0.108421	+	0.0155149i
$735$	36.6618	+	36.6618i	1.35229	+	1.35229i
$736$	−7.60739	+	8.83871i	−0.280412	+	0.325799i
$737$	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	$-0.357695\pi$
$739$	−12.7605	−	12.7605i	−0.469402	−	0.469402i	−0.901721	+	0.432319i	$0.857695\pi$
$740$	−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	$-0.670950\pi$
$743$	9.47524	−	9.47524i	0.347613	−	0.347613i	0.859220	+	0.511607i	$0.170950\pi$
$744$	59.5348	−	22.3409i	2.18265	−	0.819059i
$745$		−	16.1651i		−	0.592243i
$746$	−5.67031	+	39.6252i	−0.207605	+	1.45078i
$747$	−33.3787	+	33.3787i	−1.22126	+	1.22126i
$748$	−13.8186	+	7.56946i	−0.505259	+	0.276767i
$749$	−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	$-0.650899\pi$
$751$	−25.0205			−0.913011			−0.456506	+	0.889721i	$0.650899\pi$
$752$	3.85617	+	17.5019i	0.140620	+	0.638227i
$753$			6.30448i			0.229748i
$754$		0			0
$755$		−	16.1759i		−	0.588700i
$756$	0.718883	−	0.393784i	0.0261455	−	0.0143218i
$757$	−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
$760$	11.7517	−	25.8693i	0.426279	−	0.938378i
$761$	10.0714	−	10.0714i	0.365090	−	0.365090i	−0.500593	−	0.865683i	$-0.666885\pi$
$761$	10.0714	−	10.0714i	0.365090	−	0.365090i	0.865683	+	0.500593i	$0.166885\pi$
$762$	42.3833	+	6.06498i	1.53538	+	0.219711i
$763$		−	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	0.914485	−	0.404619i	$-0.132596\pi$
$769$	14.1390	+	14.1390i	0.509867	+	0.509867i	−0.404619	+	0.914485i	$0.632596\pi$
$770$	−4.59540	−	6.13021i	−0.165607	−	0.220918i
$771$	16.0688			0.578704
$772$	−40.6923	+	22.2901i	−1.46455	+	0.802239i
$773$	−21.3872	−	21.3872i	−0.769244	−	0.769244i	0.208729	−	0.977973i	$-0.433067\pi$
$773$	−21.3872	−	21.3872i	−0.769244	−	0.769244i	−0.977973	+	0.208729i	$0.933067\pi$
$774$	4.73728	−	33.1050i	0.170278	−	1.18993i
$775$	−29.6732	−	29.6732i	−1.06589	−	1.06589i
$776$	−12.5573	+	4.71223i	−0.450780	+	0.169159i
$777$		−	0.764691i		−	0.0274331i
$778$	−42.5158	−	6.08395i	−1.52427	−	0.218120i
$779$	−18.7159			−0.670567
$780$		0			0
$781$	−6.05538			−0.216679
$782$	7.69759	+	1.10151i	0.275265	+	0.0393900i
$783$		−	0.864434i		−	0.0308923i
$784$	14.3264	−	22.4235i	0.511658	−	0.800840i
$785$	−23.6690	−	23.6690i	−0.844783	−	0.844783i
$786$	9.62134	−	67.2358i	0.343182	−	2.39822i
$787$	−6.63607	−	6.63607i	−0.236550	−	0.236550i	0.578870	−	0.815420i	$-0.303494\pi$
$787$	−6.63607	−	6.63607i	−0.236550	−	0.236550i	−0.815420	+	0.578870i	$0.803494\pi$
$788$	−5.96314	−	10.8862i	−0.212428	−	0.387804i
$789$	−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	$-0.933802\pi$
$797$		−	11.6578i		−	0.412941i	0.978453	−	0.206471i	$-0.0661978\pi$
$798$	6.67865	+	0.955705i	0.236422	+	0.0338316i
$799$	8.45001	−	8.45001i	0.298940	−	0.298940i
$800$	20.0511	+	17.2578i	0.708914	+	0.610156i
$801$	19.2299	−	19.2299i	0.679457	−	0.679457i
$802$	11.6793	+	15.5800i	0.412409	+	0.550149i
$803$	−0.183837			−0.00648746
$804$	−17.8965	−	32.6714i	−0.631159	−	1.15223i
$805$			3.78111i			0.133267i
$806$		0			0
$807$		−	25.0572i		−	0.882055i
$808$	23.1210	+	10.5032i	0.813392	+	0.369501i
$809$	−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	$-0.749128\pi$
$811$	0.110267	−	0.110267i	0.00387201	−	0.00387201i	0.709040	+	0.705168i	$0.249128\pi$
$812$	0.704547	+	1.28621i	0.0247248	+	0.0451370i
$813$	45.2086	−	45.2086i	1.58554	−	1.58554i
$814$	0.306292	−	2.14043i	0.0107355	−	0.0750221i
$815$			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	0.447800	−	0.894134i	$-0.352208\pi$
$821$	−12.7888	−	12.7888i	−0.446334	−	0.446334i	−0.894134	+	0.447800i	$0.852208\pi$
$822$	−20.5761	+	15.4245i	−0.717675	+	0.537991i
$823$	−26.1938			−0.913060			−0.456530	−	0.889708i	$-0.650908\pi$
$823$	−26.1938			−0.913060			−0.456530	+	0.889708i	$0.650908\pi$
$824$	−11.2323	+	24.7260i	−0.391297	+	0.861372i
$825$	−24.4723	−	24.4723i	−0.852015	−	0.852015i
$826$	−5.81793	−	0.832536i	−0.202432	−	0.0289676i
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	0.471930	−	0.881636i	$-0.343558\pi$
$827$	−11.7822	−	11.7822i	−0.409707	−	0.409707i	−0.881636	+	0.471930i	$0.843558\pi$
$828$	−12.9706	−	3.78976i	−0.450761	−	0.131703i
$829$			13.1050i			0.455155i	0.973760	+	0.227577i	$0.0730805\pi$
$829$			13.1050i			0.455155i	−0.973760	+	0.227577i	$0.926920\pi$
$830$	8.97558	−	62.7231i	0.311547	−	2.17715i
$831$	−1.33873			−0.0464401
$832$		0			0
$833$	−17.7431			−0.614762
$834$	−5.57483	+	38.9580i	−0.193041	+	1.34900i
$835$			28.9940i			1.00338i
$836$	18.3113	+	5.35019i	0.633309	+	0.185040i
$837$	4.41030	+	4.41030i	0.152442	+	0.152442i
$838$	51.6546	+	7.39170i	1.78438	+	0.255342i
$839$	16.9239	+	16.9239i	0.584276	+	0.584276i	0.936076	−	0.351799i	$-0.114430\pi$
$839$	16.9239	+	16.9239i	0.584276	+	0.584276i	−0.351799	+	0.936076i	$0.614430\pi$
$840$	−5.37582	+	11.8339i	−0.185483	+	0.408309i
$841$	−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
$850$	2.49885	−	17.4624i	0.0857097	−	0.598956i
$851$	−0.754568	+	0.754568i	−0.0258662	+	0.0258662i
$852$	4.93537	+	9.00990i	0.169083	+	0.308674i
$853$	12.1913	−	12.1913i	0.417422	−	0.417422i	−0.466892	−	0.884314i	$-0.654626\pi$
$853$	12.1913	−	12.1913i	0.417422	−	0.417422i	0.884314	+	0.466892i	$0.154626\pi$
$854$	−5.30691	+	3.97822i	−0.181599	+	0.136132i
$855$	32.9239			1.12597
$856$	48.5771	+	22.0672i	1.66033	+	0.754242i
$857$		−	20.1694i		−	0.688974i	−0.938791	−	0.344487i	$-0.888053\pi$
$857$		−	20.1694i		−	0.688974i	0.938791	−	0.344487i	$-0.111947\pi$
$858$		0			0
$859$		−	10.5286i		−	0.359231i	−0.983737	−	0.179616i	$-0.942515\pi$
$859$		−	10.5286i		−	0.359231i	0.983737	−	0.179616i	$-0.0574854\pi$
$860$	21.5655	+	39.3695i	0.735377	+	1.34249i
$861$	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	$-0.747264\pi$
$863$	0.357134	−	0.357134i	0.0121570	−	0.0121570i	0.713159	+	0.701002i	$0.247264\pi$
$864$	−2.98018	−	2.56501i	−0.101388	−	0.0872634i
$865$	−50.3533	+	50.3533i	−1.71206	+	1.71206i
$866$	15.1099	+	2.16220i	0.513454	+	0.0734745i
$867$			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
$876$	0.149834	+	0.273534i	0.00506243	+	0.00924186i
$877$	−22.5944	−	22.5944i	−0.762959	−	0.762959i	0.213898	−	0.976856i	$-0.431384\pi$
$877$	−22.5944	−	22.5944i	−0.762959	−	0.762959i	−0.976856	+	0.213898i	$0.931384\pi$
$878$	2.59755	−	18.1522i	0.0876632	−	0.612608i
$879$	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	$-0.828032\pi$
$881$		−	30.5337i		−	1.02871i	0.857579	−	0.514353i	$-0.171968\pi$
$882$	30.5226	+	4.36774i	1.02775	+	0.147069i
$883$	49.7844			1.67538			0.837689	−	0.546148i	$-0.183906\pi$
$883$	49.7844			1.67538			0.837689	+	0.546148i	$0.183906\pi$
$884$		0			0
$885$	−54.9338			−1.84658
$886$	21.9109	+	3.13542i	0.736112	+	0.105337i
$887$		−	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
$890$	−5.17096	+	36.1357i	−0.173331	+	1.21127i
$891$	−16.8980	−	16.8980i	−0.566105	−	0.566105i
$892$	−6.22859	+	3.41185i	−0.208549	+	0.114237i
$893$	−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
$902$	23.9646	+	3.42930i	0.797933	+	0.114183i
$903$	−7.53689	+	7.53689i	−0.250812	+	0.250812i
$904$	−6.60119	+	14.5314i	−0.219552	+	0.483306i
$905$	−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	$-0.184504\pi$
$907$	50.3945			1.67332			0.836661	+	0.547721i	$0.184504\pi$
$908$	−30.5843	+	16.7532i	−1.01497	+	0.555974i
$909$			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	$0.960299\pi$
$912$	−6.96377	−	31.6063i	−0.230594	−	1.04659i
$913$	42.5415			1.40792
$914$	21.7429	−	16.2992i	0.719192	−	0.539128i
$915$	−43.8359	+	43.8359i	−1.44917	+	1.44917i
$916$	−35.4407	+	19.4134i	−1.17099	+	0.641438i
$917$	−7.99191	+	7.99191i	−0.263916	+	0.263916i
$918$	−0.371400	+	2.59542i	−0.0122580	+	0.0856616i
$919$			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
$928$	4.58924	−	5.33205i	0.150649	−	0.175033i
$929$	30.3326	+	30.3326i	0.995179	+	0.995179i	0.999988	−	0.00480932i	$-0.00153086\pi$
$929$	30.3326	+	30.3326i	0.995179	+	0.995179i	−0.00480932	+	0.999988i	$0.501531\pi$
$930$	−97.9062	−	14.0102i	−3.21047	−	0.459414i
$931$	15.1906	+	15.1906i	0.497853	+	0.497853i
$932$	7.47158	−	25.5718i	0.244740	−	0.837634i
$933$		−	60.1920i		−	1.97060i
$934$	4.53847	−	31.7157i	0.148503	−	1.03777i
$935$	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	$0.502069\pi$
$938$	−0.878101	+	6.13634i	−0.0286710	+	0.200359i
$939$			72.4104i			2.36303i
$940$	7.81758	−	26.7561i	0.254981	−	0.872686i
$941$	4.33123	+	4.33123i	0.141194	+	0.141194i	0.774171	−	0.632977i	$-0.218167\pi$
$941$	4.33123	+	4.33123i	0.141194	+	0.141194i	−0.632977	+	0.774171i	$0.718167\pi$
$942$	−37.7430	−	5.40096i	−1.22973	−	0.175973i
$943$	−8.44825	−	8.44825i	−0.275113	−	0.275113i
$944$	6.06630	+	27.5329i	0.197441	+	0.896120i
$945$	−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	$-0.209862\pi$
$947$	5.47327	+	5.47327i	0.177857	+	0.177857i	−0.612564	+	0.790421i	$0.709862\pi$
$948$	−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	$-0.923955\pi$
$953$		−	14.6102i		−	0.473272i	0.971598	−	0.236636i	$-0.0760449\pi$
$954$	−2.41399	+	16.8695i	−0.0781559	+	0.546169i
$955$	31.0985	−	31.0985i	1.00632	−	1.00632i
$956$	25.4248	−	13.9270i	0.822298	−	0.450432i
$957$	−6.50773	+	6.50773i	−0.210365	+	0.210365i
$958$	−3.67497	+	2.75487i	−0.118733	+	0.0890058i
$959$	4.27917			0.138182
$960$	62.2095	+	4.19947i	2.00780	+	0.135537i
$961$		−	49.5168i		−	1.59731i
$962$		0			0
$963$			61.8243i			1.99226i
$964$	−24.2947	+	13.3079i	−0.782479	+	0.428620i
$965$	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	$-0.797420\pi$
$967$	−6.52725	+	6.52725i	−0.209902	+	0.209902i	0.594324	+	0.804226i	$0.297420\pi$
$968$	5.86070	+	2.66235i	0.188370	+	0.0855712i
$969$	−15.2597	+	15.2597i	−0.490212	+	0.490212i
$970$	20.6507	+	2.95508i	0.663054	+	0.0948821i
$971$		−	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	0.827405	−	0.561605i	$-0.189816\pi$
$977$	8.30811	+	8.30811i	0.265800	+	0.265800i	−0.561605	+	0.827405i	$0.689816\pi$
$978$	30.2034	+	40.2911i	0.965799	+	1.28837i
$979$	−24.5088			−0.783304
$980$	−36.2984	+	19.8833i	−1.15951	+	0.635147i
$981$	−9.67667	−	9.67667i	−0.308952	−	0.308952i
$982$	−0.319289	+	2.23126i	−0.0101889	+	0.0712022i
$983$	−17.0818	−	17.0818i	−0.544823	−	0.544823i	0.380116	−	0.924939i	$-0.375884\pi$
$983$	−17.0818	−	17.0818i	−0.544823	−	0.544823i	−0.924939	+	0.380116i	$0.875884\pi$
$984$	−14.4296	−	38.4523i	−0.459998	−	1.22581i
$985$			19.3059i			0.615136i
$986$	−4.64365	−	0.664499i	−0.147884	−	0.0211620i
$987$	6.61878			0.210678
$988$		0			0
$989$	14.8742			0.472973
$990$	−42.1571	−	6.03262i	−1.33984	−	0.191729i
$991$		−	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
$994$	0.242157	−	1.69224i	0.00768076	−	0.0536746i
$995$	6.63036	+	6.63036i	0.210197	+	0.210197i
$996$	−34.6730	−	63.2982i	−1.09866	−	2.00568i
$997$	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.99.4		16
4.3	odd	2	inner	676.2.f.i.99.1		16
13.2	odd	12		676.2.l.i.19.3		16
13.3	even	3		676.2.l.k.319.4		16
13.4	even	6		676.2.l.m.427.4		16
13.5	odd	4	inner	676.2.f.i.239.1		16
13.6	odd	12		676.2.l.k.587.3		16
13.7	odd	12		52.2.l.b.15.2	yes	16
13.8	odd	4		676.2.f.h.239.8		16
13.9	even	3		676.2.l.i.427.1		16
13.10	even	6		52.2.l.b.7.1	✓	16
13.11	odd	12		676.2.l.m.19.2		16
13.12	even	2		676.2.f.h.99.5		16
39.20	even	12		468.2.cb.f.379.3		16
39.23	odd	6		468.2.cb.f.163.4		16
52.3	odd	6		676.2.l.k.319.3		16
52.7	even	12		52.2.l.b.15.1	yes	16
52.11	even	12		676.2.l.m.19.4		16
52.15	even	12		676.2.l.i.19.1		16
52.19	even	12		676.2.l.k.587.4		16
52.23	odd	6		52.2.l.b.7.2	yes	16
52.31	even	4	inner	676.2.f.i.239.4		16
52.35	odd	6		676.2.l.i.427.3		16
52.43	odd	6		676.2.l.m.427.2		16
52.47	even	4		676.2.f.h.239.5		16
52.51	odd	2		676.2.f.h.99.8		16
104.59	even	12		832.2.bu.n.639.4		16
104.75	odd	6		832.2.bu.n.319.1		16
104.85	odd	12		832.2.bu.n.639.1		16
104.101	even	6		832.2.bu.n.319.4		16
156.23	even	6		468.2.cb.f.163.3		16
156.59	odd	12		468.2.cb.f.379.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.l.b.7.1	✓	16	13.10	even	6
52.2.l.b.7.2	yes	16	52.23	odd	6
52.2.l.b.15.1	yes	16	52.7	even	12
52.2.l.b.15.2	yes	16	13.7	odd	12
468.2.cb.f.163.3		16	156.23	even	6
468.2.cb.f.163.4		16	39.23	odd	6
468.2.cb.f.379.3		16	39.20	even	12
468.2.cb.f.379.4		16	156.59	odd	12
676.2.f.h.99.5		16	13.12	even	2
676.2.f.h.99.8		16	52.51	odd	2
676.2.f.h.239.5		16	52.47	even	4
676.2.f.h.239.8		16	13.8	odd	4
676.2.f.i.99.1		16	4.3	odd	2	inner
676.2.f.i.99.4		16	1.1	even	1	trivial
676.2.f.i.239.1		16	13.5	odd	4	inner
676.2.f.i.239.4		16	52.31	even	4	inner
676.2.l.i.19.1		16	52.15	even	12
676.2.l.i.19.3		16	13.2	odd	12
676.2.l.i.427.1		16	13.9	even	3
676.2.l.i.427.3		16	52.35	odd	6
676.2.l.k.319.3		16	52.3	odd	6
676.2.l.k.319.4		16	13.3	even	3
676.2.l.k.587.3		16	13.6	odd	12
676.2.l.k.587.4		16	52.19	even	12
676.2.l.m.19.2		16	13.11	odd	12
676.2.l.m.19.4		16	52.11	even	12
676.2.l.m.427.2		16	52.43	odd	6
676.2.l.m.427.4		16	13.4	even	6
832.2.bu.n.319.1		16	104.75	odd	6
832.2.bu.n.319.4		16	104.101	even	6
832.2.bu.n.639.1		16	104.85	odd	12
832.2.bu.n.639.4		16	104.59	even	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:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.200331 - 1.39995i) q^{2} +2.50548i q^{3} +(-1.91973 - 0.560908i) q^{4} +(2.19962 + 2.19962i) q^{5} +(3.50755 + 0.501925i) q^{6} +(-0.416921 - 0.416921i) q^{7} +(-1.16983 + 2.57517i) q^{8} -3.27743 q^{9} +O(q^{10})\)	\(q+(0.200331 - 1.39995i) q^{2} +2.50548i q^{3} +(-1.91973 - 0.560908i) q^{4} +(2.19962 + 2.19962i) q^{5} +(3.50755 + 0.501925i) q^{6} +(-0.416921 - 0.416921i) q^{7} +(-1.16983 + 2.57517i) 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} +(-0.656570 + 4.58824i) q^{18} +(-2.28350 + 2.28350i) q^{19} +(-2.98891 - 5.45648i) q^{20} +(1.04459 - 1.04459i) q^{21} +(3.34229 - 2.50548i) q^{22} -2.06152 q^{23} +(-6.45204 - 2.93098i) q^{24} +4.67667i q^{25} -0.695088i q^{27} +(0.566524 + 1.03423i) q^{28} +1.24363 q^{29} +(6.61124 + 8.81933i) q^{30} +(-6.34495 + 6.34495i) q^{31} +(3.69019 - 4.28748i) q^{32} +(-5.23284 + 5.23284i) q^{33} +(-3.73394 - 0.534321i) 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} +(-2.83799 - 5.18097i) q^{44} +(-7.20910 - 7.20910i) q^{45} +(-0.412986 + 2.88603i) q^{46} +(3.16813 + 3.16813i) q^{47} +(-5.39577 + 8.44538i) q^{48} -6.65235i q^{49} +(6.54712 + 0.936882i) q^{50} +6.68260 q^{51} +3.67667 q^{53} +(-0.973090 - 0.139248i) q^{54} +9.18808i q^{55} +(1.56137 - 0.585918i) q^{56} +(-5.72126 - 5.72126i) q^{57} +(0.249138 - 1.74103i) q^{58} +(4.98392 + 4.98392i) q^{59} +(13.6711 - 7.48864i) 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} +(-2.56771 - 0.367435i) q^{70} +(-1.44966 + 1.44966i) q^{71} +(3.83402 - 8.43993i) q^{72} +(-0.0440105 + 0.0440105i) q^{73} +(-0.439092 - 0.585744i) q^{74} -11.7173 q^{75} +(5.66454 - 3.10288i) q^{76} -1.74153i q^{77} -2.73286i q^{79} +(2.67732 + 12.1515i) q^{80} -8.09075 q^{81} +(6.55808 - 4.91614i) q^{82} +(10.1844 - 10.1844i) q^{83} +(-2.59125 + 1.41941i) q^{84} +(5.86681 - 5.86681i) q^{85} +(-1.44543 + 10.1009i) 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} +(10.7422 + 9.24570i) q^{96} +(3.35308 + 3.35308i) q^{97} +(-9.31298 - 1.33267i) 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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