LMFDB - Embedded newform 260.2.o.a.27.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.25
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.867719 + 1.11672i) q^{2} +(-0.487193 - 0.487193i) q^{3} +(-0.494127 + 1.93800i) q^{4} +(2.20683 + 0.360390i) q^{5} +(0.121312 - 0.966804i) q^{6} +(3.04434 - 3.04434i) q^{7} +(-2.59297 + 1.12984i) q^{8} -2.52529i q^{9} +O(q^{10})$	\(q+(0.867719 + 1.11672i) q^{2} +(-0.487193 - 0.487193i) q^{3} +(-0.494127 + 1.93800i) q^{4} +(2.20683 + 0.360390i) q^{5} +(0.121312 - 0.966804i) q^{6} +(3.04434 - 3.04434i) q^{7} +(-2.59297 + 1.12984i) q^{8} -2.52529i q^{9} +(1.51246 + 2.77713i) q^{10} +6.32063i q^{11} +(1.18491 - 0.703444i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(6.04132 + 0.758045i) q^{14} +(-0.899574 - 1.25073i) q^{15} +(-3.51168 - 1.91524i) q^{16} +(0.541422 + 0.541422i) q^{17} +(2.82004 - 2.19124i) q^{18} -5.33011 q^{19} +(-1.78889 + 4.09876i) q^{20} -2.96637 q^{21} +(-7.05837 + 5.48453i) q^{22} +(1.30456 + 1.30456i) q^{23} +(1.81372 + 0.712826i) q^{24} +(4.74024 + 1.59064i) q^{25} +(-1.40321 - 0.176070i) q^{26} +(-2.69188 + 2.69188i) q^{27} +(4.39564 + 7.40423i) q^{28} -4.13546i q^{29} +(0.616141 - 2.08986i) q^{30} -8.12460i q^{31} +(-0.908365 - 5.58345i) q^{32} +(3.07936 - 3.07936i) q^{33} +(-0.134815 + 1.07442i) q^{34} +(7.81552 - 5.62121i) q^{35} +(4.89400 + 1.24781i) q^{36} +(-2.03359 - 2.03359i) q^{37} +(-4.62504 - 5.95225i) q^{38} +0.688995 q^{39} +(-6.12943 + 1.55888i) q^{40} -5.86321 q^{41} +(-2.57397 - 3.31260i) q^{42} +(1.47725 + 1.47725i) q^{43} +(-12.2494 - 3.12319i) q^{44} +(0.910088 - 5.57289i) q^{45} +(-0.324838 + 2.58883i) q^{46} +(-2.36824 + 2.36824i) q^{47} +(0.777774 + 2.64395i) q^{48} -11.5361i q^{49} +(2.33689 + 6.67375i) q^{50} -0.527554i q^{51} +(-1.02097 - 1.71977i) q^{52} +(1.38101 - 1.38101i) q^{53} +(-5.34187 - 0.670281i) q^{54} +(-2.27789 + 13.9486i) q^{55} +(-4.45427 + 11.3335i) q^{56} +(2.59679 + 2.59679i) q^{57} +(4.61815 - 3.58842i) q^{58} -6.39130 q^{59} +(2.86842 - 1.12535i) q^{60} -6.69722 q^{61} +(9.07290 - 7.04987i) q^{62} +(-7.68784 - 7.68784i) q^{63} +(5.44694 - 5.85925i) q^{64} +(-1.81530 + 1.30563i) q^{65} +(6.11081 + 0.766765i) q^{66} +(3.14304 - 3.14304i) q^{67} +(-1.31681 + 0.781744i) q^{68} -1.27115i q^{69} +(13.0590 + 3.85011i) q^{70} -1.54723i q^{71} +(2.85316 + 6.54798i) q^{72} +(-5.09934 + 5.09934i) q^{73} +(0.506366 - 4.03553i) q^{74} +(-1.53446 - 3.08436i) q^{75} +(2.63376 - 10.3298i) q^{76} +(19.2422 + 19.2422i) q^{77} +(0.597854 + 0.769414i) q^{78} +4.56373 q^{79} +(-7.05946 - 5.49218i) q^{80} -4.95293 q^{81} +(-5.08762 - 6.54757i) q^{82} +(6.37025 + 6.37025i) q^{83} +(1.46576 - 5.74881i) q^{84} +(0.999706 + 1.38995i) q^{85} +(-0.367837 + 2.93151i) q^{86} +(-2.01477 + 2.01477i) q^{87} +(-7.14127 - 16.3892i) q^{88} -3.46028i q^{89} +(7.01306 - 3.81939i) q^{90} +4.30535i q^{91} +(-3.17286 + 1.88362i) q^{92} +(-3.95825 + 3.95825i) q^{93} +(-4.69964 - 0.589695i) q^{94} +(-11.7627 - 1.92092i) q^{95} +(-2.27767 + 3.16276i) q^{96} +(1.56194 + 1.56194i) q^{97} +(12.8826 - 10.0101i) q^{98} +15.9614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.867719	+	1.11672i	0.613570	+	0.789640i
$2$	0.867719	+	1.11672i	0.613570	+	0.789640i
$3$	−0.487193	−	0.487193i	−0.281281	−	0.281281i	0.552339	−	0.833620i	$-0.313735\pi$
$3$	−0.487193	−	0.487193i	−0.281281	−	0.281281i	−0.833620	+	0.552339i	$0.813735\pi$
$4$	−0.494127	+	1.93800i	−0.247064	+	0.968999i
$5$	2.20683	+	0.360390i	0.986926	+	0.161171i
$5$	2.20683	+	0.360390i	0.986926	+	0.161171i
$6$	0.121312	−	0.966804i	0.0495252	−	0.394696i
$7$	3.04434	−	3.04434i	1.15065	−	1.15065i	0.164232	−	0.986422i	$-0.447485\pi$
$7$	3.04434	−	3.04434i	1.15065	−	1.15065i	0.986422	−	0.164232i	$-0.0525147\pi$
$8$	−2.59297	+	1.12984i	−0.916752	+	0.399457i
$9$		−	2.52529i		−	0.841762i
$10$	1.51246	+	2.77713i	0.478281	+	0.878207i
$11$			6.32063i			1.90574i	0.303378	+	0.952870i	$0.401885\pi$
$11$			6.32063i			1.90574i	−0.303378	+	0.952870i	$0.598115\pi$
$12$	1.18491	−	0.703444i	0.342055	−	0.203067i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	6.04132	+	0.758045i	1.61461	+	0.202596i
$15$	−0.899574	−	1.25073i	−0.232269	−	0.322938i
$16$	−3.51168	−	1.91524i	−0.877919	−	0.478809i
$17$	0.541422	+	0.541422i	0.131314	+	0.131314i	0.769709	−	0.638395i	$-0.220401\pi$
$17$	0.541422	+	0.541422i	0.131314	+	0.131314i	−0.638395	+	0.769709i	$0.720401\pi$
$18$	2.82004	−	2.19124i	0.664689	−	0.516480i
$19$	−5.33011			−1.22281			−0.611406	−	0.791317i	$-0.709396\pi$
$19$	−5.33011			−1.22281			−0.611406	+	0.791317i	$0.709396\pi$
$20$	−1.78889	+	4.09876i	−0.400009	+	0.916511i
$21$	−2.96637			−0.647314
$22$	−7.05837	+	5.48453i	−1.50485	+	1.16931i
$23$	1.30456	+	1.30456i	0.272020	+	0.272020i	0.829913	−	0.557893i	$-0.188390\pi$
$23$	1.30456	+	1.30456i	0.272020	+	0.272020i	−0.557893	+	0.829913i	$0.688390\pi$
$24$	1.81372	+	0.712826i	0.370224	+	0.145505i
$25$	4.74024	+	1.59064i	0.948048	+	0.318128i
$26$	−1.40321	−	0.176070i	−0.275192	−	0.0345302i
$27$	−2.69188	+	2.69188i	−0.518052	+	0.518052i
$28$	4.39564	+	7.40423i	0.830698	+	1.39927i
$29$		−	4.13546i		−	0.767936i	−0.923346	−	0.383968i	$-0.874557\pi$
$29$		−	4.13546i		−	0.767936i	0.923346	−	0.383968i	$-0.125443\pi$
$30$	0.616141	−	2.08986i	0.112491	−	0.381554i
$31$		−	8.12460i		−	1.45922i	−0.683863	−	0.729610i	$-0.739701\pi$
$31$		−	8.12460i		−	1.45922i	0.683863	−	0.729610i	$-0.260299\pi$
$32$	−0.908365	−	5.58345i	−0.160578	−	0.987023i
$33$	3.07936	−	3.07936i	0.536048	−	0.536048i
$34$	−0.134815	+	1.07442i	−0.0231205	+	0.184261i
$35$	7.81552	−	5.62121i	1.32106	−	0.950158i
$36$	4.89400	+	1.24781i	0.815667	+	0.207969i
$37$	−2.03359	−	2.03359i	−0.334320	−	0.334320i	0.519905	−	0.854224i	$-0.325968\pi$
$37$	−2.03359	−	2.03359i	−0.334320	−	0.334320i	−0.854224	+	0.519905i	$0.825968\pi$
$38$	−4.62504	−	5.95225i	−0.750281	−	0.965582i
$39$	0.688995			0.110327
$40$	−6.12943	+	1.55888i	−0.969148	+	0.246481i
$41$	−5.86321			−0.915680			−0.457840	−	0.889035i	$-0.651377\pi$
$41$	−5.86321			−0.915680			−0.457840	+	0.889035i	$0.651377\pi$
$42$	−2.57397	−	3.31260i	−0.397172	−	0.511145i
$43$	1.47725	+	1.47725i	0.225279	+	0.225279i	0.810717	−	0.585438i	$-0.199078\pi$
$43$	1.47725	+	1.47725i	0.225279	+	0.225279i	−0.585438	+	0.810717i	$0.699078\pi$
$44$	−12.2494	−	3.12319i	−1.84666	−	0.470839i
$45$	0.910088	−	5.57289i	0.135668	−	0.830757i
$46$	−0.324838	+	2.58883i	−0.0478947	+	0.381702i
$47$	−2.36824	+	2.36824i	−0.345444	+	0.345444i	−0.858409	−	0.512965i	$-0.828547\pi$
$47$	−2.36824	+	2.36824i	−0.345444	+	0.345444i	0.512965	+	0.858409i	$0.328547\pi$
$48$	0.777774	+	2.64395i	0.112262	+	0.381622i
$49$		−	11.5361i		−	1.64801i
$50$	2.33689	+	6.67375i	0.330487	+	0.943811i
$51$		−	0.527554i		−	0.0738723i
$52$	−1.02097	−	1.71977i	−0.141583	−	0.238490i
$53$	1.38101	−	1.38101i	0.189696	−	0.189696i	−0.605869	−	0.795565i	$-0.707174\pi$
$53$	1.38101	−	1.38101i	0.189696	−	0.189696i	0.795565	+	0.605869i	$0.207174\pi$
$54$	−5.34187	−	0.670281i	−0.726937	−	0.0912137i
$55$	−2.27789	+	13.9486i	−0.307151	+	1.88083i
$56$	−4.45427	+	11.3335i	−0.595227	+	1.51450i
$57$	2.59679	+	2.59679i	0.343954	+	0.343954i
$58$	4.61815	−	3.58842i	0.606393	−	0.471182i
$59$	−6.39130			−0.832076			−0.416038	−	0.909347i	$-0.636582\pi$
$59$	−6.39130			−0.832076			−0.416038	+	0.909347i	$0.636582\pi$
$60$	2.86842	−	1.12535i	0.370312	−	0.145282i
$61$	−6.69722			−0.857492			−0.428746	−	0.903425i	$-0.641044\pi$
$61$	−6.69722			−0.857492			−0.428746	+	0.903425i	$0.641044\pi$
$62$	9.07290	−	7.04987i	1.15226	−	0.895334i
$63$	−7.68784	−	7.68784i	−0.968577	−	0.968577i
$64$	5.44694	−	5.85925i	0.680868	−	0.732407i
$65$	−1.81530	+	1.30563i	−0.225160	+	0.161944i
$66$	6.11081	+	0.766765i	0.752189	+	0.0943822i
$67$	3.14304	−	3.14304i	0.383984	−	0.383984i	−0.488551	−	0.872535i	$-0.662475\pi$
$67$	3.14304	−	3.14304i	0.383984	−	0.383984i	0.872535	+	0.488551i	$0.162475\pi$
$68$	−1.31681	+	0.781744i	−0.159686	+	0.0948003i
$69$		−	1.27115i		−	0.153028i
$70$	13.0590	+	3.85011i	1.56085	+	0.460176i
$71$		−	1.54723i		−	0.183623i	−0.995776	−	0.0918114i	$-0.970734\pi$
$71$		−	1.54723i		−	0.183623i	0.995776	−	0.0918114i	$-0.0292657\pi$
$72$	2.85316	+	6.54798i	0.336248	+	0.771687i
$73$	−5.09934	+	5.09934i	−0.596832	+	0.596832i	−0.939468	−	0.342636i	$-0.888680\pi$
$73$	−5.09934	+	5.09934i	−0.596832	+	0.596832i	0.342636	+	0.939468i	$0.388680\pi$
$74$	0.506366	−	4.03553i	0.0588638	−	0.469121i
$75$	−1.53446	−	3.08436i	−0.177184	−	0.356151i
$76$	2.63376	−	10.3298i	0.302112	−	1.18490i
$77$	19.2422	+	19.2422i	2.19285	+	2.19285i
$78$	0.597854	+	0.769414i	0.0676936	+	0.0871190i
$79$	4.56373			0.513460			0.256730	−	0.966483i	$-0.417355\pi$
$79$	4.56373			0.513460			0.256730	+	0.966483i	$0.417355\pi$
$80$	−7.05946	−	5.49218i	−0.789271	−	0.614045i
$81$	−4.95293			−0.550326
$82$	−5.08762	−	6.54757i	−0.561834	−	0.723058i
$83$	6.37025	+	6.37025i	0.699226	+	0.699226i	0.964244	−	0.265018i	$-0.0853778\pi$
$83$	6.37025	+	6.37025i	0.699226	+	0.699226i	−0.265018	+	0.964244i	$0.585378\pi$
$84$	1.46576	−	5.74881i	0.159928	−	0.627247i
$85$	0.999706	+	1.38995i	0.108433	+	0.150761i
$86$	−0.367837	+	2.93151i	−0.0396649	+	0.316113i
$87$	−2.01477	+	2.01477i	−0.216006	+	0.216006i
$88$	−7.14127	−	16.3892i	−0.761262	−	1.74709i
$89$		−	3.46028i		−	0.366789i	−0.983039	−	0.183394i	$-0.941291\pi$
$89$		−	3.46028i		−	0.366789i	0.983039	−	0.183394i	$-0.0587085\pi$
$90$	7.01306	−	3.81939i	0.739241	−	0.402599i
$91$			4.30535i			0.451324i
$92$	−3.17286	+	1.88362i	−0.330794	+	0.196381i
$93$	−3.95825	+	3.95825i	−0.410451	+	0.410451i
$94$	−4.69964	−	0.589695i	−0.484731	−	0.0608224i
$95$	−11.7627	−	1.92092i	−1.20683	−	0.197082i
$96$	−2.27767	+	3.16276i	−0.232463	+	0.322798i
$97$	1.56194	+	1.56194i	0.158591	+	0.158591i	0.781942	−	0.623351i	$-0.214229\pi$
$97$	1.56194	+	1.56194i	0.158591	+	0.158591i	−0.623351	+	0.781942i	$0.714229\pi$
$98$	12.8826	−	10.0101i	1.30133	−	1.01117i
$99$	15.9614			1.60418
$100$	−5.42494	+	8.40059i	−0.542494	+	0.840059i
$101$	0.128809			0.0128170			0.00640850	−	0.999979i	$-0.497960\pi$
$101$	0.128809			0.0128170			0.00640850	+	0.999979i	$0.497960\pi$
$102$	0.589130	−	0.457769i	0.0583326	−	0.0453258i
$103$	4.99431	+	4.99431i	0.492104	+	0.492104i	0.908969	−	0.416864i	$-0.136871\pi$
$103$	4.99431	+	4.99431i	0.492104	+	0.492104i	−0.416864	+	0.908969i	$0.636871\pi$
$104$	1.03459	−	2.63242i	0.101450	−	0.258130i
$105$	−6.54628	−	1.06905i	−0.638851	−	0.104328i
$106$	2.74053	+	0.343873i	0.266184	+	0.0333999i
$107$	10.1696	−	10.1696i	0.983136	−	0.983136i	−0.0167246	−	0.999860i	$-0.505324\pi$
$107$	10.1696	−	10.1696i	0.983136	−	0.983136i	0.999860	+	0.0167246i	$0.00532385\pi$
$108$	−3.88673	−	6.54699i	−0.374000	−	0.629984i
$109$			16.5422i			1.58446i	0.610223	+	0.792230i	$0.291080\pi$
$109$			16.5422i			1.58446i	−0.610223	+	0.792230i	$0.708920\pi$
$110$	−17.5532	+	9.55968i	−1.67363	+	0.911480i
$111$			1.98150i			0.188076i
$112$	−16.5214	+	4.86011i	−1.56112	+	0.459237i
$113$	2.03455	−	2.03455i	0.191395	−	0.191395i	−0.604904	−	0.796298i	$-0.706788\pi$
$113$	2.03455	−	2.03455i	0.191395	−	0.191395i	0.796298	+	0.604904i	$0.206788\pi$
$114$	−0.646604	+	5.15318i	−0.0605600	+	0.482639i
$115$	2.40881	+	3.34911i	0.224622	+	0.312306i
$116$	8.01452	+	2.04344i	0.744129	+	0.189729i
$117$	1.78565	+	1.78565i	0.165083	+	0.165083i
$118$	−5.54585	−	7.13729i	−0.510537	−	0.657041i
$119$	3.29655			0.302194
$120$	3.74569	+	2.22674i	0.341933	+	0.203272i
$121$	−28.9503			−2.63185
$122$	−5.81131	−	7.47892i	−0.526131	−	0.677110i
$123$	2.85652	+	2.85652i	0.257563	+	0.257563i
$124$	15.7455	+	4.01459i	1.41398	+	0.360521i
$125$	9.88767	+	5.21862i	0.884380	+	0.466767i
$126$	1.91428	−	15.2561i	0.170538	−	1.35912i
$127$	−4.04376	+	4.04376i	−0.358826	+	0.358826i	−0.863380	−	0.504554i	$-0.831657\pi$
$127$	−4.04376	+	4.04376i	−0.358826	+	0.358826i	0.504554	+	0.863380i	$0.331657\pi$
$128$	11.2696	+	0.998523i	0.996098	+	0.0882578i
$129$		−	1.43941i		−	0.126733i
$130$	−3.03320	−	0.894261i	−0.266029	−	0.0784319i
$131$		−	12.4097i		−	1.08424i	−0.840301	−	0.542120i	$-0.817622\pi$
$131$		−	12.4097i		−	1.08424i	0.840301	−	0.542120i	$-0.182378\pi$
$132$	4.44620	+	7.48940i	0.386992	+	0.651869i
$133$	−16.2267	+	16.2267i	−1.40703	+	1.40703i
$134$	6.23717	+	0.782620i	0.538810	+	0.0676081i
$135$	−6.91066	+	4.97041i	−0.594775	+	0.427784i
$136$	−2.01561	−	0.792171i	−0.172837	−	0.0679281i
$137$	9.83725	+	9.83725i	0.840453	+	0.840453i	0.988918	−	0.148465i	$-0.0474331\pi$
$137$	9.83725	+	9.83725i	0.840453	+	0.840453i	−0.148465	+	0.988918i	$0.547433\pi$
$138$	1.41952	−	1.10300i	0.120837	−	0.0938936i
$139$	−15.9503			−1.35288			−0.676442	−	0.736496i	$-0.736479\pi$
$139$	−15.9503			−1.35288			−0.676442	+	0.736496i	$0.736479\pi$
$140$	7.03204	+	17.9241i	0.594316	+	1.51486i
$141$	2.30758			0.194334
$142$	1.72783	−	1.34256i	0.144996	−	0.112665i
$143$	−4.46936	−	4.46936i	−0.373746	−	0.373746i
$144$	−4.83652	+	8.86799i	−0.403043	+	0.738999i
$145$	1.49038	−	9.12628i	0.123769	−	0.757896i
$146$	−10.1193	−	1.26974i	−0.837481	−	0.105084i
$147$	−5.62029	+	5.62029i	−0.463553	+	0.463553i
$148$	4.94594	−	2.93624i	0.406554	−	0.241357i
$149$			14.5572i			1.19257i	0.802771	+	0.596287i	$0.203358\pi$
$149$			14.5572i			1.19257i	−0.802771	+	0.596287i	$0.796642\pi$
$150$	2.11289	−	4.38992i	0.172516	−	0.358435i
$151$			10.2236i			0.831983i	0.909369	+	0.415991i	$0.136565\pi$
$151$			10.2236i			0.831983i	−0.909369	+	0.415991i	$0.863435\pi$
$152$	13.8208	−	6.02216i	1.12102	−	0.488461i
$153$	1.36725	−	1.36725i	0.110535	−	0.110535i
$154$	−4.79132	+	38.1849i	−0.386095	+	3.07703i
$155$	2.92802	−	17.9296i	0.235185	−	1.44014i
$156$	−0.340451	+	1.33527i	−0.0272579	+	0.106907i
$157$	−8.74373	−	8.74373i	−0.697826	−	0.697826i	0.266116	−	0.963941i	$-0.414260\pi$
$157$	−8.74373	−	8.74373i	−0.697826	−	0.697826i	−0.963941	+	0.266116i	$0.914260\pi$
$158$	3.96004	+	5.09641i	0.315044	+	0.405449i
$159$	−1.34564			−0.106716
$160$	0.00760586	−	12.6491i	0.000601296	−	1.00000i
$161$	7.94309			0.626003
$162$	−4.29775	−	5.53104i	−0.337663	−	0.434559i
$163$	−5.49536	−	5.49536i	−0.430430	−	0.430430i	0.458345	−	0.888775i	$-0.348443\pi$
$163$	−5.49536	−	5.49536i	−0.430430	−	0.430430i	−0.888775	+	0.458345i	$0.848443\pi$
$164$	2.89717	−	11.3629i	0.226231	−	0.887293i
$165$	7.90542	−	5.68587i	0.615436	−	0.442645i
$166$	−1.58620	+	12.6414i	−0.123113	+	0.981161i
$167$	8.56252	−	8.56252i	0.662588	−	0.662588i	−0.293401	−	0.955989i	$-0.594787\pi$
$167$	8.56252	−	8.56252i	0.662588	−	0.662588i	0.955989	+	0.293401i	$0.0947873\pi$
$168$	7.69168	−	3.35151i	0.593426	−	0.258574i
$169$		−	1.00000i		−	0.0769231i
$170$	−0.684724	+	2.32248i	−0.0525159	+	0.178126i
$171$			13.4601i			1.02932i
$172$	−3.59286	+	2.13296i	−0.273953	+	0.162637i
$173$	7.58302	−	7.58302i	0.576526	−	0.576526i	−0.357418	−	0.933944i	$-0.616343\pi$
$173$	7.58302	−	7.58302i	0.576526	−	0.576526i	0.933944	+	0.357418i	$0.116343\pi$
$174$	−3.99818	−	0.501679i	−0.303101	−	0.0380322i
$175$	19.2734	−	9.58845i	1.45693	−	0.724819i
$176$	12.1055	−	22.1960i	0.912486	−	1.67309i
$177$	3.11379	+	3.11379i	0.234047	+	0.234047i
$178$	3.86416	−	3.00255i	0.289631	−	0.225051i
$179$	−7.06690			−0.528205			−0.264103	−	0.964495i	$-0.585076\pi$
$179$	−7.06690			−0.528205			−0.264103	+	0.964495i	$0.585076\pi$
$180$	10.3506	+	4.51747i	0.771485	+	0.336712i
$181$	16.0764			1.19495			0.597477	−	0.801886i	$-0.296170\pi$
$181$	16.0764			1.19495			0.597477	+	0.801886i	$0.296170\pi$
$182$	−4.80787	+	3.73584i	−0.356383	+	0.276919i
$183$	3.26284	+	3.26284i	0.241196	+	0.241196i
$184$	−4.85663	−	1.90875i	−0.358036	−	0.140715i
$185$	−3.75491	−	5.22068i	−0.276066	−	0.383832i
$186$	−7.85490	−	0.985607i	−0.575949	−	0.0722682i
$187$	−3.42213	+	3.42213i	−0.250251	+	0.250251i
$188$	−3.41944	−	5.75987i	−0.249388	−	0.420082i
$189$			16.3900i			1.19220i
$190$	−8.06157	−	14.8024i	−0.584848	−	1.07388i
$191$			22.1030i			1.59932i	0.600455	+	0.799658i	$0.294986\pi$
$191$			22.1030i			1.59932i	−0.600455	+	0.799658i	$0.705014\pi$
$192$	−5.50830	+	0.200875i	−0.397527	+	0.0144969i
$193$	6.79192	−	6.79192i	0.488893	−	0.488893i	−0.419064	−	0.907957i	$-0.637642\pi$
$193$	6.79192	−	6.79192i	0.488893	−	0.488893i	0.907957	+	0.419064i	$0.137642\pi$
$194$	−0.388924	+	3.09957i	−0.0279231	+	0.222536i
$195$	1.52050	+	0.248307i	0.108885	+	0.0177816i
$196$	22.3569	+	5.70029i	1.59692	+	0.407163i
$197$	16.5615	+	16.5615i	1.17996	+	1.17996i	0.979754	+	0.200205i	$0.0641609\pi$
$197$	16.5615	+	16.5615i	1.17996	+	1.17996i	0.200205	+	0.979754i	$0.435839\pi$
$198$	13.8500	+	17.8244i	0.984277	+	1.26673i
$199$	15.1829			1.07629			0.538144	−	0.842853i	$-0.319126\pi$
$199$	15.1829			1.07629			0.538144	+	0.842853i	$0.319126\pi$
$200$	−14.0884	+	1.23121i	−0.996203	+	0.0870598i
$201$	−3.06253			−0.216014
$202$	0.111770	+	0.143844i	0.00786413	+	0.0101208i
$203$	−12.5898	−	12.5898i	−0.883628	−	0.883628i
$204$	1.02240	+	0.260679i	0.0715822	+	0.0182512i
$205$	−12.9391	−	2.11304i	−0.903709	−	0.147581i
$206$	−1.24359	+	9.91091i	−0.0866450	+	0.690526i
$207$	3.29440	−	3.29440i	0.228977	−	0.228977i
$208$	3.83741	−	1.12885i	0.266076	−	0.0782719i
$209$		−	33.6897i		−	2.33036i
$210$	−4.48650	−	8.23799i	−0.309598	−	0.568475i
$211$		−	6.24339i		−	0.429813i	−0.976635	−	0.214906i	$-0.931055\pi$
$211$		−	6.24339i		−	0.429813i	0.976635	−	0.214906i	$-0.0689446\pi$
$212$	1.99400	+	3.35879i	0.136948	+	0.230683i
$213$	−0.753801	+	0.753801i	−0.0516496	+	0.0516496i
$214$	20.1810	+	2.53225i	1.37955	+	0.173101i
$215$	2.72766	+	3.79244i	0.186025	+	0.258642i
$216$	3.93857	−	10.0213i	0.267986	−	0.681865i
$217$	−24.7341	−	24.7341i	−1.67906	−	1.67906i
$218$	−18.4730	+	14.3540i	−1.25115	+	0.972177i
$219$	4.96872			0.335755
$220$	−25.9068	−	11.3069i	−1.74663	−	0.762313i
$221$	−0.765686			−0.0515056
$222$	−2.21278	+	1.71938i	−0.148512	+	0.115398i
$223$	−16.3948	−	16.3948i	−1.09788	−	1.09788i	−0.994659	−	0.103219i	$-0.967086\pi$
$223$	−16.3948	−	16.3948i	−1.09788	−	1.09788i	−0.103219	−	0.994659i	$-0.532914\pi$
$224$	−19.7633	−	14.2326i	−1.32049	−	0.950953i
$225$	4.01683	−	11.9705i	0.267788	−	0.798031i
$226$	4.03745	+	0.506606i	0.268567	+	0.0336989i
$227$	−9.51581	+	9.51581i	−0.631586	+	0.631586i	−0.948466	−	0.316880i	$-0.897365\pi$
$227$	−9.51581	+	9.51581i	−0.631586	+	0.631586i	0.316880	+	0.948466i	$0.397365\pi$
$228$	−6.31573	+	3.74943i	−0.418269	+	0.248312i
$229$			11.3862i			0.752419i	0.926535	+	0.376209i	$0.122773\pi$
$229$			11.3862i			0.752419i	−0.926535	+	0.376209i	$0.877227\pi$
$230$	−1.64985	+	5.59605i	−0.108788	+	0.368992i
$231$		−	18.7493i		−	1.23361i
$232$	4.67239	+	10.7231i	0.306758	+	0.704007i
$233$	−9.53117	+	9.53117i	−0.624408	+	0.624408i	−0.946655	−	0.322248i	$-0.895562\pi$
$233$	−9.53117	+	9.53117i	−0.624408	+	0.624408i	0.322248	+	0.946655i	$0.395562\pi$
$234$	−0.444628	+	3.54351i	−0.0290662	+	0.231646i
$235$	−6.07982	+	4.37283i	−0.396603	+	0.285252i
$236$	3.15812	−	12.3863i	0.205576	−	0.806281i
$237$	−2.22342	−	2.22342i	−0.144426	−	0.144426i
$238$	2.86048	+	3.68132i	0.185417	+	0.238625i
$239$	10.6020			0.685786			0.342893	−	0.939374i	$-0.388593\pi$
$239$	10.6020			0.685786			0.342893	+	0.939374i	$0.388593\pi$
$240$	0.763565	+	6.11507i	0.0492879	+	0.394726i
$241$	10.5504			0.679609			0.339804	−	0.940496i	$-0.389639\pi$
$241$	10.5504			0.679609			0.339804	+	0.940496i	$0.389639\pi$
$242$	−25.1207	−	32.3294i	−1.61482	−	2.07821i
$243$	10.4887	+	10.4887i	0.672849	+	0.672849i
$244$	3.30928	−	12.9792i	0.211855	−	0.830909i
$245$	4.15748	−	25.4582i	0.265612	−	1.62646i
$246$	−0.711275	+	5.66858i	−0.0453493	+	0.361416i
$247$	3.76896	−	3.76896i	0.239813	−	0.239813i
$248$	9.17947	+	21.0668i	0.582897	+	1.33774i
$249$		−	6.20708i		−	0.393358i
$250$	2.75198	+	15.5701i	0.174051	+	0.984737i
$251$		−	1.45377i		−	0.0917611i	−0.998947	−	0.0458806i	$-0.985391\pi$
$251$		−	1.45377i		−	0.0917611i	0.998947	−	0.0458806i	$-0.0146094\pi$
$252$	18.6978	−	11.1003i	1.17785	−	0.699250i
$253$	−8.24566	+	8.24566i	−0.518400	+	0.518400i
$254$	−8.02460	−	1.00690i	−0.503508	−	0.0631786i
$255$	0.190125	−	1.16422i	0.0119061	−	0.0729065i
$256$	8.66374	+	13.4514i	0.541484	+	0.840711i
$257$	6.25916	+	6.25916i	0.390436	+	0.390436i	0.874843	−	0.484407i	$-0.160965\pi$
$257$	6.25916	+	6.25916i	0.390436	+	0.390436i	−0.484407	+	0.874843i	$0.660965\pi$
$258$	1.60742	−	1.24901i	0.100074	−	0.0777597i
$259$	−12.3819			−0.769373
$260$	−1.63333	−	4.16320i	−0.101295	−	0.258191i
$261$	−10.4432			−0.646419
$262$	13.8582	−	10.7681i	0.856160	−	0.665258i
$263$	6.97831	+	6.97831i	0.430301	+	0.430301i	0.888731	−	0.458430i	$-0.151588\pi$
$263$	6.97831	+	6.97831i	0.430301	+	0.430301i	−0.458430	+	0.888731i	$0.651588\pi$
$264$	−4.50551	+	11.4639i	−0.277295	+	0.705552i
$265$	3.54536	−	2.54996i	0.217790	−	0.156643i
$266$	−32.2009	−	4.04047i	−1.97436	−	0.247737i
$267$	−1.68582	+	1.68582i	−0.103171	+	0.103171i
$268$	4.53815	+	7.64427i	0.277211	+	0.466948i
$269$		−	20.7480i		−	1.26503i	−0.774549	−	0.632514i	$-0.782023\pi$
$269$		−	20.7480i		−	1.26503i	0.774549	−	0.632514i	$-0.217977\pi$
$270$	−11.5471	−	3.40436i	−0.702732	−	0.207182i
$271$		−	2.82507i		−	0.171611i	−0.996312	−	0.0858053i	$-0.972654\pi$
$271$		−	2.82507i		−	0.171611i	0.996312	−	0.0858053i	$-0.0273463\pi$
$272$	−0.864348	−	2.93825i	−0.0524088	−	0.178158i
$273$	2.09754	−	2.09754i	0.126949	−	0.126949i
$274$	−2.44949	+	19.5214i	−0.147979	+	1.17933i
$275$	−10.0539	+	29.9613i	−0.606270	+	1.80673i
$276$	2.46348	+	0.628109i	0.148284	+	0.0378077i
$277$	−3.69919	−	3.69919i	−0.222263	−	0.222263i	0.587188	−	0.809451i	$-0.300235\pi$
$277$	−3.69919	−	3.69919i	−0.222263	−	0.222263i	−0.809451	+	0.587188i	$0.800235\pi$
$278$	−13.8404	−	17.8120i	−0.830089	−	1.06829i
$279$	−20.5169			−1.22832
$280$	−13.9143	+	23.4059i	−0.831539	+	1.39877i
$281$	16.4883			0.983607			0.491804	−	0.870706i	$-0.336338\pi$
$281$	16.4883			0.983607			0.491804	+	0.870706i	$0.336338\pi$
$282$	2.00233	+	2.57692i	0.119237	+	0.153454i
$283$	21.4886	+	21.4886i	1.27737	+	1.27737i	0.942136	+	0.335230i	$0.108814\pi$
$283$	21.4886	+	21.4886i	1.27737	+	1.27737i	0.335230	+	0.942136i	$0.391186\pi$
$284$	2.99854	+	0.764531i	0.177930	+	0.0453665i
$285$	4.79483	+	6.66655i	0.284021	+	0.394892i
$286$	1.11287	−	8.86917i	0.0658057	−	0.524445i
$287$	−17.8496	+	17.8496i	−1.05363	+	1.05363i
$288$	−14.0998	+	2.29388i	−0.830839	+	0.135168i
$289$		−	16.4137i		−	0.965513i
$290$	11.4847	−	6.25471i	0.674407	−	0.367289i
$291$		−	1.52193i		−	0.0892171i
$292$	−7.36279	−	12.4022i	−0.430874	−	0.725786i
$293$	7.36829	−	7.36829i	0.430460	−	0.430460i	−0.458325	−	0.888785i	$-0.651550\pi$
$293$	7.36829	−	7.36829i	0.430460	−	0.430460i	0.888785	+	0.458325i	$0.151550\pi$
$294$	−11.1531	−	1.39946i	−0.650463	−	0.0816180i
$295$	−14.1045	−	2.30336i	−0.821198	−	0.134107i
$296$	7.57065	+	2.97540i	0.440035	+	0.172942i
$297$	−17.0144	−	17.0144i	−0.987274	−	0.987274i
$298$	−16.2563	+	12.6316i	−0.941705	+	0.731728i
$299$	−1.84493			−0.106695
$300$	6.73570	−	1.44972i	0.388886	−	0.0836994i
$301$	8.99452			0.518436
$302$	−11.4169	+	8.87119i	−0.656967	+	0.510480i
$303$	−0.0627550	−	0.0627550i	−0.00360518	−	0.00360518i
$304$	18.7176	+	10.2084i	1.07353	+	0.585494i
$305$	−14.7797	−	2.41361i	−0.846281	−	0.138203i
$306$	2.71322	+	0.340446i	0.155104	+	0.0194620i
$307$	10.4721	−	10.4721i	0.597672	−	0.597672i	−0.342021	−	0.939692i	$-0.611111\pi$
$307$	10.4721	−	10.4721i	0.597672	−	0.597672i	0.939692	+	0.342021i	$0.111111\pi$
$308$	−46.7994	+	27.7832i	−2.66664	+	1.58309i
$309$		−	4.86639i		−	0.276839i
$310$	22.5631	−	12.2881i	1.28150	−	0.697918i
$311$		−	7.44464i		−	0.422147i	−0.977470	−	0.211073i	$-0.932304\pi$
$311$		−	7.44464i		−	0.422147i	0.977470	−	0.211073i	$-0.0676959\pi$
$312$	−1.78654	+	0.778451i	−0.101143	+	0.0440711i
$313$	13.5542	−	13.5542i	0.766130	−	0.766130i	−0.211293	−	0.977423i	$-0.567767\pi$
$313$	13.5542	−	13.5542i	0.766130	−	0.766130i	0.977423	+	0.211293i	$0.0677674\pi$
$314$	2.17720	−	17.3514i	0.122866	−	0.979196i
$315$	−14.1952	−	19.7364i	−0.799807	−	1.11202i
$316$	−2.25507	+	8.84451i	−0.126857	+	0.497542i
$317$	−6.80714	−	6.80714i	−0.382327	−	0.382327i	0.489613	−	0.871940i	$-0.337138\pi$
$317$	−6.80714	−	6.80714i	−0.382327	−	0.382327i	−0.871940	+	0.489613i	$0.837138\pi$
$318$	−1.16763	−	1.50270i	−0.0654777	−	0.0842672i
$319$	26.1387			1.46349
$320$	14.1321	−	10.9674i	0.790009	−	0.613095i
$321$	−9.90914			−0.553074
$322$	6.89237	+	8.87020i	0.384097	+	0.494317i
$323$	−2.88584	−	2.88584i	−0.160573	−	0.160573i
$324$	2.44738	−	9.59877i	0.135965	−	0.533265i
$325$	−4.47661	+	2.22710i	−0.248318	+	0.123537i
$326$	1.36835	−	10.9052i	0.0757860	−	0.603984i
$327$	8.05926	−	8.05926i	0.445678	−	0.445678i
$328$	15.2031	−	6.62447i	0.839451	−	0.365775i
$329$			14.4195i			0.794973i
$330$	13.2092	+	3.89440i	0.727143	+	0.214380i
$331$		−	1.37445i		−	0.0755466i	−0.999286	−	0.0377733i	$-0.987974\pi$
$331$		−	1.37445i		−	0.0755466i	0.999286	−	0.0377733i	$-0.0120265\pi$
$332$	−15.4933	+	9.19782i	−0.850303	+	0.504796i
$333$	−5.13539	+	5.13539i	−0.281418	+	0.281418i
$334$	16.9918	+	2.13208i	0.929750	+	0.116662i
$335$	8.06889	−	5.80345i	0.440851	−	0.317076i
$336$	10.4169	+	5.68129i	0.568289	+	0.309940i
$337$	−0.674535	−	0.674535i	−0.0367443	−	0.0367443i	0.688496	−	0.725240i	$-0.258271\pi$
$337$	−0.674535	−	0.674535i	−0.0367443	−	0.0367443i	−0.725240	+	0.688496i	$0.758271\pi$
$338$	1.11672	−	0.867719i	0.0607416	−	0.0471977i
$339$	−1.98244			−0.107671
$340$	−3.18771	+	1.25062i	−0.172878	+	0.0678241i
$341$	51.3526			2.78090
$342$	−15.0311	+	11.6796i	−0.812790	+	0.631558i
$343$	−13.8093	−	13.8093i	−0.745634	−	0.745634i
$344$	−5.49951	−	2.16141i	−0.296514	−	0.116535i
$345$	0.458109	−	2.80521i	0.0246638	−	0.151028i
$346$	15.0480	+	1.88818i	0.808987	+	0.101509i
$347$	8.96110	−	8.96110i	0.481057	−	0.481057i	−0.424412	−	0.905469i	$-0.639519\pi$
$347$	8.96110	−	8.96110i	0.481057	−	0.481057i	0.905469	+	0.424412i	$0.139519\pi$
$348$	−2.90906	−	4.90017i	−0.155942	−	0.262676i
$349$		−	7.49139i		−	0.401005i	−0.979693	−	0.200502i	$-0.935743\pi$
$349$		−	7.49139i		−	0.401005i	0.979693	−	0.200502i	$-0.0642574\pi$
$350$	27.4315	+	13.2029i	1.46628	+	0.705724i
$351$		−	3.80689i		−	0.203197i
$352$	35.2909	−	5.74144i	1.88101	−	0.306020i
$353$	2.31003	−	2.31003i	0.122951	−	0.122951i	−0.642954	−	0.765905i	$-0.722291\pi$
$353$	2.31003	−	2.31003i	0.122951	−	0.122951i	0.765905	+	0.642954i	$0.222291\pi$
$354$	−0.775338	+	6.17913i	−0.0412087	+	0.328417i
$355$	0.557608	−	3.41449i	0.0295947	−	0.181222i
$356$	6.70601	+	1.70982i	0.355418	+	0.0906202i
$357$	−1.60606	−	1.60606i	−0.0850015	−	0.0850015i
$358$	−6.13209	−	7.89175i	−0.324091	−	0.417092i
$359$	−14.4912			−0.764819			−0.382409	−	0.923993i	$-0.624906\pi$
$359$	−14.4912			−0.764819			−0.382409	+	0.923993i	$0.624906\pi$
$360$	3.93663	+	15.4786i	0.207478	+	0.815792i
$361$	9.41012			0.495269
$362$	13.9498	+	17.9529i	0.733187	+	0.943583i
$363$	14.1044	+	14.1044i	0.740288	+	0.740288i
$364$	−8.34377	−	2.12739i	−0.437332	−	0.111506i
$365$	−13.0911	+	9.41564i	−0.685222	+	0.492837i
$366$	−0.812450	+	6.47491i	−0.0424675	+	0.338449i
$367$	−13.0271	+	13.0271i	−0.680010	+	0.680010i	−0.960002	−	0.279992i	$-0.909668\pi$
$367$	−13.0271	+	13.0271i	−0.680010	+	0.680010i	0.279992	+	0.960002i	$0.409668\pi$
$368$	−2.08266	−	7.07976i	−0.108566	−	0.369058i
$369$			14.8063i			0.770785i
$370$	2.57183	−	8.72326i	0.133703	−	0.453501i
$371$		−	8.40854i		−	0.436550i
$372$	−5.71520	−	9.62695i	−0.296319	−	0.499134i
$373$	−17.7001	+	17.7001i	−0.916479	+	0.916479i	−0.996771	−	0.0802924i	$-0.974415\pi$
$373$	−17.7001	+	17.7001i	−0.916479	+	0.916479i	0.0802924	+	0.996771i	$0.474415\pi$
$374$	−6.79100	−	0.852113i	−0.351154	−	0.0440617i
$375$	−2.27473	−	7.35967i	−0.117466	−	0.380052i
$376$	3.46505	−	8.81650i	0.178696	−	0.454676i
$377$	2.92421	+	2.92421i	0.150605	+	0.150605i
$378$	−18.3031	+	14.2219i	−0.941408	+	0.731497i
$379$	6.17545			0.317211			0.158606	−	0.987342i	$-0.449300\pi$
$379$	6.17545			0.317211			0.158606	+	0.987342i	$0.449300\pi$
$380$	9.53500	−	21.8469i	0.489135	−	1.12072i
$381$	3.94019			0.201862
$382$	−24.6829	+	19.1792i	−1.26289	+	0.981293i
$383$	12.1391	+	12.1391i	0.620278	+	0.620278i	0.945602	−	0.325325i	$-0.105474\pi$
$383$	12.1391	+	12.1391i	0.620278	+	0.620278i	−0.325325	+	0.945602i	$0.605474\pi$
$384$	−5.00397	−	5.97692i	−0.255358	−	0.305008i
$385$	35.5296	+	49.3990i	1.81076	+	2.51760i
$386$	13.4782	+	1.69120i	0.686020	+	0.0860796i
$387$	3.73048	−	3.73048i	0.189631	−	0.189631i
$388$	−3.79883	+	2.25524i	−0.192856	+	0.114492i
$389$			21.7389i			1.10220i	0.834438	+	0.551102i	$0.185792\pi$
$389$			21.7389i			1.10220i	−0.834438	+	0.551102i	$0.814208\pi$
$390$	1.04208	+	1.91343i	0.0527675	+	0.0968903i
$391$			1.41264i			0.0714403i
$392$	13.0339	+	29.9126i	0.658309	+	1.51082i
$393$	−6.04592	+	6.04592i	−0.304976	+	0.304976i
$394$	−4.12383	+	32.8653i	−0.207756	+	1.65573i
$395$	10.0714	+	1.64472i	0.506747	+	0.0827550i
$396$	−7.88696	+	30.9332i	−0.396335	+	1.55445i
$397$	−5.15514	−	5.15514i	−0.258729	−	0.258729i	0.565808	−	0.824537i	$-0.308564\pi$
$397$	−5.15514	−	5.15514i	−0.258729	−	0.258729i	−0.824537	+	0.565808i	$0.808564\pi$
$398$	13.1745	+	16.9551i	0.660378	+	0.849880i
$399$	15.8111			0.791543
$400$	−13.5997	−	14.6645i	−0.679986	−	0.733225i
$401$	−16.8263			−0.840268			−0.420134	−	0.907462i	$-0.638017\pi$
$401$	−16.8263			−0.840268			−0.420134	+	0.907462i	$0.638017\pi$
$402$	−2.65742	−	3.41999i	−0.132540	−	0.170574i
$403$	5.74496	+	5.74496i	0.286177	+	0.286177i
$404$	−0.0636482	+	0.249632i	−0.00316662	+	0.0124197i
$405$	−10.9303	−	1.78499i	−0.543131	−	0.0886967i
$406$	3.13487	−	24.9836i	0.155581	−	1.23992i
$407$	12.8536	−	12.8536i	0.637127	−	0.637127i
$408$	0.596049	+	1.36793i	0.0295088	+	0.0677226i
$409$			33.9837i			1.68039i	0.542286	+	0.840194i	$0.317559\pi$
$409$			33.9837i			1.68039i	−0.542286	+	0.840194i	$0.682441\pi$
$410$	−8.86786	−	16.2829i	−0.437953	−	0.804157i
$411$		−	9.58528i		−	0.472807i
$412$	−12.1468	+	7.21114i	−0.598430	+	0.355268i
$413$	−19.4573	+	19.4573i	−0.957432	+	0.957432i
$414$	6.53753	+	0.820309i	0.321302	+	0.0403160i
$415$	11.7623	+	16.3539i	0.577389	+	0.802780i
$416$	4.59040	+	3.30578i	0.225063	+	0.162079i
$417$	7.77086	+	7.77086i	0.380541	+	0.380541i
$418$	37.6219	−	29.2332i	1.84015	−	1.42984i
$419$	12.5313			0.612192			0.306096	−	0.952001i	$-0.400977\pi$
$419$	12.5313			0.612192			0.306096	+	0.952001i	$0.400977\pi$
$420$	5.30651	−	12.1584i	0.258931	−	0.593271i
$421$	31.0380			1.51270			0.756351	−	0.654167i	$-0.226980\pi$
$421$	31.0380			1.51270			0.756351	+	0.654167i	$0.226980\pi$
$422$	6.97212	−	5.41751i	0.339397	−	0.263720i
$423$	5.98050	+	5.98050i	0.290782	+	0.290782i
$424$	−2.02060	+	5.14123i	−0.0981288	+	0.249680i
$425$	1.70526	+	3.42768i	0.0827173	+	0.166267i
$426$	−1.49587	−	0.187697i	−0.0724752	−	0.00909396i
$427$	−20.3887	+	20.3887i	−0.986676	+	0.986676i
$428$	14.6836	+	24.7338i	0.709760	+	1.19555i
$429$			4.35488i			0.210255i
$430$	−1.86824	+	6.33680i	−0.0900947	+	0.305588i
$431$		−	18.1942i		−	0.876383i	−0.898882	−	0.438191i	$-0.855619\pi$
$431$		−	18.1942i		−	0.876383i	0.898882	−	0.438191i	$-0.144381\pi$
$432$	14.6086	−	4.29742i	0.702856	−	0.206760i
$433$	11.7674	−	11.7674i	0.565506	−	0.565506i	−0.365360	−	0.930866i	$-0.619054\pi$
$433$	11.7674	−	11.7674i	0.565506	−	0.565506i	0.930866	+	0.365360i	$0.119054\pi$
$434$	6.15881	−	49.0833i	0.295632	−	2.35607i
$435$	−5.17236	+	3.72016i	−0.247996	+	0.178368i
$436$	−32.0588	−	8.17397i	−1.53534	−	0.391462i
$437$	−6.95348	−	6.95348i	−0.332630	−	0.332630i
$438$	4.31145	+	5.54867i	0.206009	+	0.265126i
$439$	−34.5531			−1.64913			−0.824564	−	0.565768i	$-0.808580\pi$
$439$	−34.5531			−1.64913			−0.824564	+	0.565768i	$0.808580\pi$
$440$	−9.85312	−	38.7418i	−0.469729	−	1.84694i
$441$	−29.1319			−1.38723
$442$	−0.664401	−	0.855057i	−0.0316023	−	0.0406709i
$443$	−15.6679	−	15.6679i	−0.744406	−	0.744406i	0.229016	−	0.973423i	$-0.426449\pi$
$443$	−15.6679	−	15.6679i	−0.744406	−	0.744406i	−0.973423	+	0.229016i	$0.926449\pi$
$444$	−3.84014	−	0.979113i	−0.182245	−	0.0464666i
$445$	1.24705	−	7.63626i	0.0591158	−	0.361993i
$446$	4.08232	−	32.5345i	0.193304	−	1.54055i
$447$	7.09217	−	7.09217i	0.335448	−	0.335448i
$448$	−1.25522	−	34.4199i	−0.0593036	−	1.62619i
$449$			13.9711i			0.659337i	0.944097	+	0.329669i	$0.106937\pi$
$449$			13.9711i			0.659337i	−0.944097	+	0.329669i	$0.893063\pi$
$450$	16.8531	−	5.90132i	0.794464	−	0.278191i
$451$		−	37.0592i		−	1.74505i
$452$	2.93763	+	4.94829i	0.138175	+	0.232748i
$453$	4.98085	−	4.98085i	0.234021	−	0.234021i
$454$	−18.8835	−	2.36945i	−0.886248	−	0.111204i
$455$	−1.55161	+	9.50120i	−0.0727404	+	0.445423i
$456$	−9.66735	−	3.79944i	−0.452715	−	0.177925i
$457$	−0.978870	−	0.978870i	−0.0457896	−	0.0457896i	0.683841	−	0.729631i	$-0.260308\pi$
$457$	−0.978870	−	0.978870i	−0.0457896	−	0.0457896i	−0.729631	+	0.683841i	$0.760308\pi$
$458$	−12.7152	+	9.87999i	−0.594140	+	0.461661i
$459$	−2.91489			−0.136055
$460$	−7.68083	+	3.01338i	−0.358120	+	0.140499i
$461$	8.67886			0.404215			0.202107	−	0.979363i	$-0.435221\pi$
$461$	8.67886			0.404215			0.202107	+	0.979363i	$0.435221\pi$
$462$	20.9377	−	16.2691i	0.974110	−	0.756908i
$463$	13.7918	+	13.7918i	0.640957	+	0.640957i	0.950791	−	0.309834i	$-0.100273\pi$
$463$	13.7918	+	13.7918i	0.640957	+	0.640957i	−0.309834	+	0.950791i	$0.600273\pi$
$464$	−7.92039	+	14.5224i	−0.367695	+	0.674186i
$465$	−10.1617	+	7.30868i	−0.471238	+	0.338932i
$466$	−18.9140	−	2.37327i	−0.876176	−	0.109940i
$467$	−14.3243	+	14.3243i	−0.662851	+	0.662851i	−0.956051	−	0.293200i	$-0.905280\pi$
$467$	−14.3243	+	14.3243i	−0.662851	+	0.662851i	0.293200	+	0.956051i	$0.405280\pi$
$468$	−4.34292	+	2.57824i	−0.200751	+	0.119179i
$469$		−	19.1370i		−	0.883664i
$470$	−10.1588	−	2.99506i	−0.468591	−	0.138152i
$471$			8.51976i			0.392570i
$472$	16.5724	−	7.22112i	0.762807	−	0.332379i
$473$	−9.33715	+	9.33715i	−0.429323	+	0.429323i
$474$	0.553633	−	4.41224i	0.0254292	−	0.202661i
$475$	−25.2660	−	8.47830i	−1.15928	−	0.389011i
$476$	−1.62892	+	6.38871i	−0.0746612	+	0.292826i
$477$	−3.48745	−	3.48745i	−0.159679	−	0.159679i
$478$	9.19955	+	11.8395i	0.420778	+	0.541524i
$479$	−12.7377			−0.582000			−0.291000	−	0.956723i	$-0.593988\pi$
$479$	−12.7377			−0.582000			−0.291000	+	0.956723i	$0.593988\pi$
$480$	−6.16626	+	6.15885i	−0.281450	+	0.281112i
$481$	2.87593			0.131131
$482$	9.15476	+	11.7818i	0.416988	+	0.536647i
$483$	−3.86981	−	3.86981i	−0.176083	−	0.176083i
$484$	14.3051	−	56.1057i	0.650234	−	2.55026i
$485$	2.88403	+	4.00985i	0.130957	+	0.182078i
$486$	−2.61169	+	20.8141i	−0.118469	+	0.944148i
$487$	−12.1189	+	12.1189i	−0.549158	+	0.549158i	−0.926197	−	0.377039i	$-0.876942\pi$
$487$	−12.1189	+	12.1189i	−0.549158	+	0.549158i	0.377039	+	0.926197i	$0.376942\pi$
$488$	17.3657	−	7.56677i	0.786107	−	0.342531i
$489$			5.35460i			0.242143i
$490$	32.0372	−	17.4478i	1.44729	−	0.788212i
$491$			35.3063i			1.59335i	0.604406	+	0.796676i	$0.293410\pi$
$491$			35.3063i			1.59335i	−0.604406	+	0.796676i	$0.706590\pi$
$492$	−6.94741	+	4.12444i	−0.313213	+	0.185944i
$493$	2.23903	−	2.23903i	0.100841	−	0.100841i
$494$	7.47927	+	0.938475i	0.336508	+	0.0422240i
$495$	35.2242	+	5.75233i	1.58321	+	0.258548i
$496$	−15.5605	+	28.5310i	−0.698688	+	1.28108i
$497$	−4.71031	−	4.71031i	−0.211286	−	0.211286i
$498$	6.93157	−	5.38600i	0.310611	−	0.241353i
$499$	−4.07422			−0.182387			−0.0911935	−	0.995833i	$-0.529068\pi$
$499$	−4.07422			−0.182387			−0.0911935	+	0.995833i	$0.529068\pi$
$500$	−14.9994	+	16.5836i	−0.670796	+	0.741642i
$501$	−8.34320			−0.372747
$502$	1.62345	−	1.26146i	0.0724583	−	0.0563019i
$503$	−17.4924	−	17.4924i	−0.779948	−	0.779948i	0.199873	−	0.979822i	$-0.435947\pi$
$503$	−17.4924	−	17.4924i	−0.779948	−	0.779948i	−0.979822	+	0.199873i	$0.935947\pi$
$504$	28.6203	+	11.2483i	1.27485	+	0.501039i
$505$	0.284261	+	0.0464216i	0.0126494	+	0.00206573i
$506$	−16.3630	−	2.05318i	−0.727425	−	0.0912749i
$507$	−0.487193	+	0.487193i	−0.0216370	+	0.0216370i
$508$	−5.83867	−	9.83494i	−0.259049	−	0.436355i
$509$			5.36481i			0.237791i	0.992907	+	0.118895i	$0.0379353\pi$
$509$			5.36481i			0.237791i	−0.992907	+	0.118895i	$0.962065\pi$
$510$	1.46509	−	0.797903i	0.0648752	−	0.0353317i
$511$			31.0483i			1.37349i
$512$	−7.50373	+	21.3470i	−0.331621	+	0.943413i
$513$	14.3480	−	14.3480i	0.633481	−	0.633481i
$514$	−1.55854	+	12.4209i	−0.0687442	+	0.547864i
$515$	9.22172	+	12.8215i	0.406358	+	0.564984i
$516$	2.78958	+	0.711253i	0.122804	+	0.0313112i
$517$	−14.9688	−	14.9688i	−0.658327	−	0.658327i
$518$	−10.7440	−	13.8271i	−0.472064	−	0.607528i
$519$	−7.38878			−0.324332
$520$	3.23186	−	5.43646i	0.141727	−	0.238404i
$521$	−42.8486			−1.87723			−0.938615	−	0.344966i	$-0.887890\pi$
$521$	−42.8486			−1.87723			−0.938615	+	0.344966i	$0.887890\pi$
$522$	−9.06178	−	11.6622i	−0.396624	−	0.510439i
$523$	−19.0978	−	19.0978i	−0.835087	−	0.835087i	0.153121	−	0.988208i	$-0.451068\pi$
$523$	−19.0978	−	19.0978i	−0.835087	−	0.835087i	−0.988208	+	0.153121i	$0.951068\pi$
$524$	24.0500	+	6.13197i	1.05063	+	0.267877i
$525$	−14.0613	−	4.71843i	−0.613684	−	0.205929i
$526$	−1.73761	+	13.8480i	−0.0757632	+	0.603803i
$527$	4.39884	−	4.39884i	0.191616	−	0.191616i
$528$	−16.7114	+	4.91602i	−0.727272	+	0.213942i
$529$		−	19.5962i		−	0.852010i
$530$	5.92397	+	1.74653i	0.257321	+	0.0758644i
$531$			16.1399i			0.700410i
$532$	−23.4293	−	39.4654i	−1.01579	−	1.71104i
$533$	4.14592	−	4.14592i	0.179580	−	0.179580i
$534$	−3.34541	−	0.419771i	−0.144770	−	0.0181653i
$535$	26.1077	−	18.7777i	1.12874	−	0.811829i
$536$	−4.59868	+	11.7009i	−0.198633	+	0.505403i
$537$	3.44294	+	3.44294i	0.148574	+	0.148574i
$538$	23.1697	−	18.0034i	0.998917	−	0.776183i
$539$	72.9151			3.14068
$540$	−6.21789	−	15.8489i	−0.267576	−	0.682026i
$541$	−33.1020			−1.42316			−0.711582	−	0.702603i	$-0.752021\pi$
$541$	−33.1020			−1.42316			−0.711582	+	0.702603i	$0.752021\pi$
$542$	3.15481	−	2.45137i	0.135511	−	0.105295i
$543$	−7.83233	−	7.83233i	−0.336117	−	0.336117i
$544$	2.53119	−	3.51481i	0.108524	−	0.150696i
$545$	−5.96166	+	36.5060i	−0.255369	+	1.56374i
$546$	4.16243	+	0.522289i	0.178136	+	0.0223519i
$547$	32.7366	−	32.7366i	1.39971	−	1.39971i	0.598864	−	0.800850i	$-0.295619\pi$
$547$	32.7366	−	32.7366i	1.39971	−	1.39971i	0.800850	−	0.598864i	$-0.204381\pi$
$548$	−23.9254	+	14.2037i	−1.02204	+	0.606753i
$549$			16.9124i			0.721804i
$550$	−42.1823	+	14.7706i	−1.79866	+	0.629822i
$551$			22.0425i			0.939041i
$552$	1.43619	+	3.29604i	0.0611283	+	0.140289i
$553$	13.8936	−	13.8936i	0.590815	−	0.590815i
$554$	0.921101	−	7.34081i	0.0391338	−	0.311881i
$555$	−0.714112	+	4.37284i	−0.0303124	+	0.185617i
$556$	7.88147	−	30.9116i	0.334249	−	1.31094i
$557$	−20.8822	−	20.8822i	−0.884809	−	0.884809i	0.109210	−	0.994019i	$-0.465168\pi$
$557$	−20.8822	−	20.8822i	−0.884809	−	0.884809i	−0.994019	+	0.109210i	$0.965168\pi$
$558$	−17.8029	−	22.9117i	−0.753658	−	0.969929i
$559$	−2.08915			−0.0883616
$560$	−38.2115	+	4.77132i	−1.61473	+	0.201625i
$561$	3.33447			0.140781
$562$	14.3072	+	18.4128i	0.603512	+	0.776696i
$563$	−5.63992	−	5.63992i	−0.237694	−	0.237694i	0.578200	−	0.815895i	$-0.303755\pi$
$563$	−5.63992	−	5.63992i	−0.237694	−	0.237694i	−0.815895	+	0.578200i	$0.803755\pi$
$564$	−1.14024	+	4.47209i	−0.0480128	+	0.188309i
$565$	5.22315	−	3.75669i	0.219740	−	0.158045i
$566$	−5.35069	+	42.6429i	−0.224906	+	1.79241i
$567$	−15.0784	+	15.0784i	−0.633234	+	0.633234i
$568$	1.74812	+	4.01192i	0.0733495	+	0.168337i
$569$		−	6.50119i		−	0.272544i	−0.990671	−	0.136272i	$-0.956488\pi$
$569$		−	6.50119i		−	0.272544i	0.990671	−	0.136272i	$-0.0435121\pi$
$570$	−3.28410	+	11.1392i	−0.137556	+	0.466569i
$571$		−	0.432691i		−	0.0181075i	−0.999959	−	0.00905377i	$-0.997118\pi$
$571$		−	0.432691i		−	0.0181075i	0.999959	−	0.00905377i	$-0.00288194\pi$
$572$	10.8700	−	6.45318i	0.454499	−	0.269821i
$573$	10.7684	−	10.7684i	0.449857	−	0.449857i
$574$	−35.4215	−	4.44458i	−1.47847	−	0.185513i
$575$	4.10885	+	8.25904i	0.171351	+	0.344426i
$576$	−14.7963	−	13.7551i	−0.616512	−	0.573129i
$577$	−8.05122	−	8.05122i	−0.335177	−	0.335177i	0.519372	−	0.854548i	$-0.326166\pi$
$577$	−8.05122	−	8.05122i	−0.335177	−	0.335177i	−0.854548	+	0.519372i	$0.826166\pi$
$578$	18.3295	−	14.2425i	0.762408	−	0.592410i
$579$	−6.61795			−0.275033
$580$	16.9503	+	7.39790i	0.703822	+	0.307181i
$581$	38.7865			1.60913
$582$	1.69957	−	1.32061i	0.0704495	−	0.0547410i
$583$	8.72885	+	8.72885i	0.361512	+	0.361512i
$584$	7.46099	−	18.9838i	0.308738	−	0.785556i
$585$	3.29710	+	4.58416i	0.136318	+	0.189532i
$586$	14.6219	+	1.83471i	0.604026	+	0.0757913i
$587$	21.4798	−	21.4798i	0.886565	−	0.886565i	−0.107626	−	0.994191i	$-0.534325\pi$
$587$	21.4798	−	21.4798i	0.886565	−	0.886565i	0.994191	+	0.107626i	$0.0343249\pi$
$588$	−8.11497	−	13.6692i	−0.334656	−	0.563710i
$589$			43.3050i			1.78435i
$590$	−9.66657	−	17.7495i	−0.397966	−	0.730735i
$591$		−	16.1373i		−	0.663800i
$592$	3.24650	+	11.0361i	0.133430	+	0.453581i
$593$	12.5840	−	12.5840i	0.516761	−	0.516761i	−0.399829	−	0.916590i	$-0.630930\pi$
$593$	12.5840	−	12.5840i	0.516761	−	0.516761i	0.916590	+	0.399829i	$0.130930\pi$
$594$	4.23659	−	33.7640i	0.173830	−	1.38535i
$595$	7.27494	+	1.18804i	0.298244	+	0.0487050i
$596$	−28.2119	−	7.19312i	−1.15560	−	0.294642i
$597$	−7.39700	−	7.39700i	−0.302739	−	0.302739i
$598$	−1.60088	−	2.06027i	−0.0654650	−	0.0842508i
$599$	−23.6821			−0.967624			−0.483812	−	0.875172i	$-0.660748\pi$
$599$	−23.6821			−0.967624			−0.483812	+	0.875172i	$0.660748\pi$
$600$	7.46362	+	6.26395i	0.304701	+	0.255725i
$601$	25.3948			1.03587			0.517937	−	0.855419i	$-0.326700\pi$
$601$	25.3948			1.03587			0.517937	+	0.855419i	$0.326700\pi$
$602$	7.80472	+	10.0444i	0.318097	+	0.409378i
$603$	−7.93708	−	7.93708i	−0.323223	−	0.323223i
$604$	−19.8133	−	5.05175i	−0.806190	−	0.205553i
$605$	−63.8886	−	10.4334i	−2.59744	−	0.424178i
$606$	0.0156261	−	0.124533i	0.000634765	−	0.00505883i
$607$	−11.0006	+	11.0006i	−0.446502	+	0.446502i	−0.894190	−	0.447688i	$-0.852248\pi$
$607$	−11.0006	+	11.0006i	−0.446502	+	0.446502i	0.447688	+	0.894190i	$0.352248\pi$
$608$	4.84169	+	29.7604i	0.196357	+	1.20694i
$609$			12.2673i			0.497096i
$610$	−10.1293	−	18.5991i	−0.410122	−	0.753055i
$611$		−	3.34920i		−	0.135494i
$612$	1.97413	+	3.32531i	0.0797993	+	0.134418i
$613$	28.0148	−	28.0148i	1.13151	−	1.13151i	0.141581	−	0.989927i	$-0.454782\pi$
$613$	28.0148	−	28.0148i	1.13151	−	1.13151i	0.989927	−	0.141581i	$-0.0452184\pi$
$614$	20.7811	+	2.60755i	0.838659	+	0.105232i
$615$	5.27440	+	7.33332i	0.212684	+	0.295708i
$616$	−71.6348	−	28.1538i	−2.88625	−	1.13435i
$617$	17.8181	+	17.8181i	0.717331	+	0.717331i	0.968058	−	0.250727i	$-0.0806696\pi$
$617$	17.8181	+	17.8181i	0.717331	+	0.717331i	−0.250727	+	0.968058i	$0.580670\pi$
$618$	5.43439	−	4.22266i	0.218603	−	0.169860i
$619$	−15.8677			−0.637778			−0.318889	−	0.947792i	$-0.603310\pi$
$619$	−15.8677			−0.637778			−0.318889	+	0.947792i	$0.603310\pi$
$620$	33.3008	+	14.5340i	1.33739	+	0.583701i
$621$	−7.02346			−0.281842
$622$	8.31358	−	6.45985i	0.333344	−	0.259017i
$623$	−10.5343	−	10.5343i	−0.422047	−	0.422047i
$624$	−2.41953	−	1.31959i	−0.0968586	−	0.0528258i
$625$	19.9397	+	15.0800i	0.797589	+	0.603202i
$626$	26.8975	+	3.37502i	1.07504	+	0.134893i
$627$	−16.4134	+	16.4134i	−0.655486	+	0.655486i
$628$	21.2658	−	12.6248i	0.848600	−	0.503785i
$629$		−	2.20206i		−	0.0878018i
$630$	9.72263	−	32.9777i	0.387359	−	1.31386i
$631$			24.6220i			0.980186i	0.871670	+	0.490093i	$0.163037\pi$
$631$			24.6220i			0.980186i	−0.871670	+	0.490093i	$0.836963\pi$
$632$	−11.8336	+	5.15627i	−0.470715	+	0.205105i
$633$	−3.04173	+	3.04173i	−0.120898	+	0.120898i
$634$	1.69498	−	13.5084i	0.0673164	−	0.536485i
$635$	−10.3813	+	7.46659i	−0.411967	+	0.296302i
$636$	0.664916	−	2.60784i	0.0263656	−	0.103408i
$637$	8.15723	+	8.15723i	0.323201	+	0.323201i
$638$	22.6811	+	29.1896i	0.897951	+	1.15563i
$639$	−3.90721			−0.154567
$640$	24.5102	+	6.26501i	0.968851	+	0.247646i
$641$	−21.9723			−0.867854			−0.433927	−	0.900948i	$-0.642872\pi$
$641$	−21.9723			−0.867854			−0.433927	+	0.900948i	$0.642872\pi$
$642$	−8.59835	−	11.0657i	−0.339350	−	0.436730i
$643$	−23.4378	−	23.4378i	−0.924297	−	0.924297i	0.0730326	−	0.997330i	$-0.476732\pi$
$643$	−23.4378	−	23.4378i	−0.924297	−	0.924297i	−0.997330	+	0.0730326i	$0.976732\pi$
$644$	−3.92490	+	15.3937i	−0.154663	+	0.606596i
$645$	0.518750	−	3.17654i	0.0204258	−	0.125076i
$646$	0.718578	−	5.72678i	0.0282721	−	0.225317i
$647$	10.1699	−	10.1699i	0.399821	−	0.399821i	−0.478349	−	0.878170i	$-0.658765\pi$
$647$	10.1699	−	10.1699i	0.399821	−	0.399821i	0.878170	+	0.478349i	$0.158765\pi$
$648$	12.8428	−	5.59600i	0.504512	−	0.219832i
$649$		−	40.3970i		−	1.58572i
$650$	−6.37149	−	3.06662i	−0.249910	−	0.120283i
$651$			24.1005i			0.944574i
$652$	13.3654	−	7.93460i	0.523430	−	0.310743i
$653$	−17.6134	+	17.6134i	−0.689264	+	0.689264i	−0.962069	−	0.272805i	$-0.912048\pi$
$653$	−17.6134	+	17.6134i	−0.689264	+	0.689264i	0.272805	+	0.962069i	$0.412048\pi$
$654$	15.9931	+	2.00676i	0.625380	+	0.0784707i
$655$	4.47233	−	27.3862i	0.174749	−	1.07007i
$656$	20.5897	+	11.2294i	0.803893	+	0.438436i
$657$	12.8773	+	12.8773i	0.502391	+	0.502391i
$658$	−16.1025	+	12.5121i	−0.627743	+	0.487772i
$659$	−32.0112			−1.24698			−0.623489	−	0.781832i	$-0.714285\pi$
$659$	−32.0112			−1.24698			−0.623489	+	0.781832i	$0.714285\pi$
$660$	7.11293	+	18.1302i	0.276871	+	0.705718i
$661$	−0.879296			−0.0342006			−0.0171003	−	0.999854i	$-0.505443\pi$
$661$	−0.879296			−0.0342006			−0.0171003	+	0.999854i	$0.505443\pi$
$662$	1.53488	−	1.19264i	0.0596547	−	0.0463531i
$663$	0.373037	+	0.373037i	0.0144876	+	0.0144876i
$664$	−23.7152	−	9.32050i	−0.920328	−	0.361706i
$665$	−41.6576	+	29.9617i	−1.61541	+	1.16187i
$666$	−10.1909	−	1.27872i	−0.394888	−	0.0495493i
$667$	5.39498	−	5.39498i	0.208894	−	0.208894i
$668$	12.3632	+	20.8251i	0.478346	+	0.805749i
$669$			15.9749i			0.617624i
$670$	13.4824	+	3.97493i	0.520869	+	0.153565i
$671$		−	42.3307i		−	1.63416i
$672$	2.69454	+	16.5625i	0.103944	+	0.638914i
$673$	29.3095	−	29.3095i	1.12980	−	1.12980i	0.139589	−	0.990209i	$-0.455422\pi$
$673$	29.3095	−	29.3095i	1.12980	−	1.12980i	0.990209	−	0.139589i	$-0.0445782\pi$
$674$	0.167960	−	1.33857i	0.00646958	−	0.0515600i
$675$	−17.0420	+	8.47833i	−0.655946	+	0.326331i
$676$	1.93800	+	0.494127i	0.0745384	+	0.0190049i
$677$	1.89034	+	1.89034i	0.0726515	+	0.0726515i	0.742499	−	0.669847i	$-0.233640\pi$
$677$	1.89034	+	1.89034i	0.0726515	+	0.0726515i	−0.669847	+	0.742499i	$0.733640\pi$
$678$	−1.72020	−	2.21383i	−0.0660639	−	0.0850216i
$679$	9.51016			0.364966
$680$	−4.16262	−	2.47459i	−0.159629	−	0.0948963i
$681$	9.27206			0.355306
$682$	44.5596	+	57.3464i	1.70627	+	2.19591i
$683$	18.2932	+	18.2932i	0.699968	+	0.699968i	0.964403	−	0.264435i	$-0.0851855\pi$
$683$	18.2932	+	18.2932i	0.699968	+	0.699968i	−0.264435	+	0.964403i	$0.585186\pi$
$684$	−26.0856	−	6.65099i	−0.997407	−	0.254307i
$685$	18.1639	+	25.2544i	0.694008	+	0.964922i
$686$	3.43854	−	27.4038i	0.131284	−	1.04628i
$687$	5.54725	−	5.54725i	0.211641	−	0.211641i
$688$	−2.35834	−	8.01691i	−0.0899110	−	0.305642i
$689$			1.95304i			0.0744050i
$690$	3.53015	−	1.92256i	0.134391	−	0.0731906i
$691$		−	8.36945i		−	0.318389i	−0.987247	−	0.159194i	$-0.949110\pi$
$691$		−	8.36945i		−	0.318389i	0.987247	−	0.159194i	$-0.0508897\pi$
$692$	10.9489	+	18.4429i	0.416215	+	0.701092i
$693$	48.5920	−	48.5920i	1.84586	−	1.84586i
$694$	17.7827	+	2.23132i	0.675024	+	0.0846998i
$695$	−35.1996	−	5.74832i	−1.33520	−	0.218046i
$696$	2.94786	−	7.50058i	0.111739	−	0.284309i
$697$	−3.17447	−	3.17447i	−0.120242	−	0.120242i
$698$	8.36578	−	6.50042i	0.316650	−	0.246044i
$699$	9.28704			0.351268
$700$	9.05890	+	42.0897i	0.342394	+	1.59084i
$701$	5.59262			0.211230			0.105615	−	0.994407i	$-0.466319\pi$
$701$	5.59262			0.211230			0.105615	+	0.994407i	$0.466319\pi$
$702$	4.25123	−	3.30331i	0.160452	−	0.124676i
$703$	10.8393	+	10.8393i	0.408810	+	0.408810i
$704$	37.0341	+	34.4281i	1.39578	+	1.29756i
$705$	5.09245	+	0.831630i	0.191793	+	0.0313210i
$706$	4.58412	+	0.575200i	0.172525	+	0.0216479i
$707$	0.392140	−	0.392140i	0.0147479	−	0.0147479i
$708$	−7.57314	+	4.49592i	−0.284616	+	0.168967i
$709$		−	19.2710i		−	0.723737i	−0.932229	−	0.361868i	$-0.882139\pi$
$709$		−	19.2710i		−	0.723737i	0.932229	−	0.361868i	$-0.117861\pi$
$710$	4.29687	−	2.34013i	0.161259	−	0.0878233i
$711$		−	11.5247i		−	0.432211i
$712$	3.90955	+	8.97238i	0.146516	+	0.336254i
$713$	10.5991	−	10.5991i	0.396938	−	0.396938i
$714$	0.399909	−	3.18712i	0.0149662	−	0.119275i
$715$	−8.25242	−	11.4738i	−0.308623	−	0.429097i
$716$	3.49195	−	13.6956i	0.130500	−	0.511830i
$717$	−5.16522	−	5.16522i	−0.192899	−	0.192899i
$718$	−12.5743	−	16.1827i	−0.469270	−	0.603932i
$719$	−34.2943			−1.27896			−0.639481	−	0.768807i	$-0.720851\pi$
$719$	−34.2943			−1.27896			−0.639481	+	0.768807i	$0.720851\pi$
$720$	−13.8693	+	17.8271i	−0.516880	+	0.664379i
$721$	30.4088			1.13248
$722$	8.16534	+	10.5085i	0.303882	+	0.391085i
$723$	−5.14006	−	5.14006i	−0.191161	−	0.191161i
$724$	−7.94381	+	31.1561i	−0.295230	+	1.15791i
$725$	6.57804	−	19.6031i	0.244302	−	0.728040i
$726$	−3.51201	+	27.9893i	−0.130343	+	1.03878i
$727$	16.1714	−	16.1714i	0.599765	−	0.599765i	−0.340485	−	0.940250i	$-0.610591\pi$
$727$	16.1714	−	16.1714i	0.599765	−	0.599765i	0.940250	+	0.340485i	$0.110591\pi$
$728$	−4.86434	−	11.1636i	−0.180285	−	0.413752i
$729$			4.63878i			0.171807i
$730$	−21.8741	−	6.44901i	−0.809596	−	0.238689i
$731$			1.59963i			0.0591646i
$732$	−7.93564	+	4.71112i	−0.293310	+	0.174128i
$733$	−29.5527	+	29.5527i	−1.09156	+	1.09156i	−0.0961930	+	0.995363i	$0.530667\pi$
$733$	−29.5527	+	29.5527i	−1.09156	+	1.09156i	−0.995363	+	0.0961930i	$0.969333\pi$
$734$	−25.8515	−	3.24377i	−0.954197	−	0.119730i
$735$	−14.4285	+	10.3775i	−0.532205	+	0.382782i
$736$	6.09894	−	8.46899i	0.224810	−	0.312171i
$737$	19.8660	+	19.8660i	0.731773	+	0.731773i
$738$	−16.5345	+	12.8477i	−0.608643	+	0.472931i
$739$	39.5202			1.45377			0.726886	−	0.686758i	$-0.240967\pi$
$739$	39.5202			1.45377			0.726886	+	0.686758i	$0.240967\pi$
$740$	11.9731	−	4.69733i	0.440139	−	0.172677i
$741$	−3.67242			−0.134910
$742$	9.38998	−	7.29625i	0.344717	−	0.267854i
$743$	36.7002	+	36.7002i	1.34640	+	1.34640i	0.889536	+	0.456865i	$0.151028\pi$
$743$	36.7002	+	36.7002i	1.34640	+	1.34640i	0.456865	+	0.889536i	$0.348972\pi$
$744$	5.79143	−	14.7358i	0.212324	−	0.540239i
$745$	−5.24628	+	32.1254i	−0.192209	+	1.17698i
$746$	−35.1249	−	4.40736i	−1.28601	−	0.161365i
$747$	16.0867	−	16.0867i	0.588582	−	0.588582i
$748$	−4.94111	−	8.32304i	−0.180665	−	0.304321i
$749$		−	61.9197i		−	2.26250i
$750$	6.24487	−	8.92636i	0.228030	−	0.325945i
$751$		−	6.73728i		−	0.245847i	−0.992416	−	0.122923i	$-0.960773\pi$
$751$		−	6.73728i		−	0.245847i	0.992416	−	0.122923i	$-0.0392269\pi$
$752$	12.8523	−	3.78076i	0.468674	−	0.137870i
$753$	−0.708266	+	0.708266i	−0.0258106	+	0.0258106i
$754$	−0.728132	+	5.80292i	−0.0265170	+	0.211330i
$755$	−3.68447	+	22.5617i	−0.134092	+	0.821106i
$756$	−31.7638	−	8.09876i	−1.15524	−	0.294549i
$757$	−26.3455	−	26.3455i	−0.957545	−	0.957545i	0.0415899	−	0.999135i	$-0.486758\pi$
$757$	−26.3455	−	26.3455i	−0.957545	−	0.957545i	−0.999135	+	0.0415899i	$0.986758\pi$
$758$	5.35855	+	6.89625i	0.194631	+	0.250483i
$759$	8.03446			0.291632
$760$	32.6705	−	8.30902i	1.18509	−	0.301400i
$761$	−38.3797			−1.39126			−0.695632	−	0.718398i	$-0.744876\pi$
$761$	−38.3797			−1.39126			−0.695632	+	0.718398i	$0.744876\pi$
$762$	3.41897	+	4.40008i	0.123856	+	0.159398i
$763$	50.3603	+	50.3603i	1.82316	+	1.82316i
$764$	−42.8356	−	10.9217i	−1.54974	−	0.395133i
$765$	3.51003	−	2.52454i	0.126905	−	0.0912751i
$766$	−3.02264	+	24.0892i	−0.109212	+	0.870380i
$767$	4.51933	−	4.51933i	0.163184	−	0.163184i
$768$	2.33250	−	10.7743i	0.0841670	−	0.388785i
$769$		−	16.1949i		−	0.584002i	−0.956418	−	0.292001i	$-0.905679\pi$
$769$		−	16.1949i		−	0.584002i	0.956418	−	0.292001i	$-0.0943211\pi$
$770$	−24.3351	+	82.5410i	−0.876976	+	2.97457i
$771$		−	6.09884i		−	0.219644i
$772$	9.80666	+	16.5188i	0.352950	+	0.594525i
$773$	11.2859	−	11.2859i	0.405925	−	0.405925i	−0.474390	−	0.880315i	$-0.657331\pi$
$773$	11.2859	−	11.2859i	0.405925	−	0.405925i	0.880315	+	0.474390i	$0.157331\pi$
$774$	7.40291	+	0.928894i	0.266092	+	0.0333884i
$775$	12.9233	−	38.5125i	0.464220	−	1.38341i
$776$	−5.81479	−	2.28532i	−0.208739	−	0.0820381i
$777$	6.03236	+	6.03236i	0.216410	+	0.216410i
$778$	−24.2762	+	18.8632i	−0.870345	+	0.676279i
$779$	31.2516			1.11970
$780$	−1.23254	+	2.82403i	−0.0441319	+	0.101116i
$781$	9.77949			0.349938
$782$	−1.57752	+	1.22577i	−0.0564121	+	0.0438336i
$783$	11.1322	+	11.1322i	0.397831	+	0.397831i
$784$	−22.0943	+	40.5109i	−0.789082	+	1.44682i
$785$	−16.1448	−	22.4471i	−0.576233	−	0.801172i
$786$	−11.9978	−	1.50544i	−0.427946	−	0.0536973i
$787$	6.97678	−	6.97678i	0.248695	−	0.248695i	−0.571740	−	0.820435i	$-0.693731\pi$
$787$	6.97678	−	6.97678i	0.248695	−	0.248695i	0.820435	+	0.571740i	$0.193731\pi$
$788$	−40.2797	+	23.9127i	−1.43490	+	0.851854i
$789$		−	6.79956i		−	0.242071i
$790$	6.90245	+	12.6741i	0.245578	+	0.450924i
$791$		−	12.3878i		−	0.440458i
$792$	−41.3873	+	18.0338i	−1.47064	+	0.640802i
$793$	4.73565	−	4.73565i	0.168168	−	0.168168i
$794$	1.28363	−	10.2301i	0.0455545	−	0.363051i
$795$	−2.96960	−	0.484954i	−0.105321	−	0.0171995i
$796$	−7.50229	+	29.4244i	−0.265912	+	1.04292i
$797$	12.0723	+	12.0723i	0.427621	+	0.427621i	0.887817	−	0.460196i	$-0.152221\pi$
$797$	12.0723	+	12.0723i	0.427621	+	0.427621i	−0.460196	+	0.887817i	$0.652221\pi$
$798$	13.7196	+	17.6565i	0.485667	+	0.625034i
$799$	−2.56444			−0.0907234
$800$	4.57540	−	27.9117i	0.161765	−	0.986829i
$801$	−8.73819			−0.308749
$802$	−14.6005	−	18.7903i	−0.515563	−	0.663509i
$803$	−32.2310	−	32.2310i	−1.13741	−	1.13741i
$804$	1.51328	−	5.93519i	0.0533693	−	0.209318i
$805$	17.5291	+	2.86261i	0.617819	+	0.100894i
$806$	−1.43050	+	11.4005i	−0.0503872	+	0.401566i
$807$	−10.1083	+	10.1083i	−0.355828	+	0.355828i
$808$	−0.333998	+	0.145533i	−0.0117500	+	0.00511985i
$809$			34.8121i			1.22393i	0.790885	+	0.611964i	$0.209620\pi$
$809$			34.8121i			1.22393i	−0.790885	+	0.611964i	$0.790380\pi$
$810$	−7.49110	−	13.7550i	−0.263210	−	0.483300i
$811$			34.5221i			1.21223i	0.795376	+	0.606117i	$0.207274\pi$
$811$			34.5221i			1.21223i	−0.795376	+	0.606117i	$0.792726\pi$
$812$	30.6199	−	18.1780i	1.07455	−	0.637923i
$813$	−1.37635	+	1.37635i	−0.0482708	+	0.0482708i
$814$	25.5071	+	3.20055i	0.894023	+	0.112179i
$815$	−10.1469	−	14.1078i	−0.355430	−	0.494176i
$816$	−1.01039	+	1.85260i	−0.0353707	+	0.0648539i
$817$	−7.87392	−	7.87392i	−0.275473	−	0.275473i
$818$	−37.9503	+	29.4883i	−1.32690	+	1.03104i
$819$	10.8722			0.379907
$820$	10.4887	−	24.0319i	0.366280	−	0.839231i
$821$	−19.2884			−0.673170			−0.336585	−	0.941653i	$-0.609272\pi$
$821$	−19.2884			−0.673170			−0.336585	+	0.941653i	$0.609272\pi$
$822$	10.7041	−	8.31733i	0.373347	−	0.290100i
$823$	−20.5632	−	20.5632i	−0.716789	−	0.716789i	0.251157	−	0.967946i	$-0.419189\pi$
$823$	−20.5632	−	20.5632i	−0.716789	−	0.716789i	−0.967946	+	0.251157i	$0.919189\pi$
$824$	−18.5928	−	7.30733i	−0.647712	−	0.254563i
$825$	19.4951	−	9.69875i	0.678732	−	0.337667i
$826$	−38.6118	−	4.84489i	−1.34348	−	0.168575i
$827$	−28.0616	+	28.0616i	−0.975798	+	0.975798i	−0.999714	−	0.0239161i	$-0.992387\pi$
$827$	−28.0616	+	28.0616i	−0.975798	+	0.975798i	0.0239161	+	0.999714i	$0.492387\pi$
$828$	4.75669	+	8.01239i	0.165306	+	0.278450i
$829$		−	33.3820i		−	1.15941i	−0.814828	−	0.579703i	$-0.803169\pi$
$829$		−	33.3820i		−	1.15941i	0.814828	−	0.579703i	$-0.196831\pi$
$830$	−8.05631	+	27.3258i	−0.279638	+	0.948492i
$831$			3.60443i			0.125036i
$832$	0.291549	+	7.99469i	0.0101076	+	0.277166i
$833$	6.24588	−	6.24588i	0.216407	−	0.216407i
$834$	−1.93495	+	15.4208i	−0.0670019	+	0.533978i
$835$	21.9819	−	15.8102i	0.760716	−	0.547135i
$836$	65.2905	+	16.6470i	2.25812	+	0.575748i
$837$	21.8704	+	21.8704i	0.755953	+	0.755953i
$838$	10.8736	+	13.9939i	0.375623	+	0.483412i
$839$	−6.15756			−0.212583			−0.106291	−	0.994335i	$-0.533898\pi$
$839$	−6.15756			−0.212583			−0.106291	+	0.994335i	$0.533898\pi$
$840$	18.1821	−	4.62422i	0.627343	−	0.159551i
$841$	11.8980			0.410274
$842$	26.9323	+	34.6608i	0.928148	+	1.19449i
$843$	−8.03296	−	8.03296i	−0.276670	−	0.276670i
$844$	12.0997	+	3.08503i	0.416488	+	0.106191i
$845$	0.360390	−	2.20683i	0.0123978	−	0.0759174i
$846$	−1.48915	+	11.8679i	−0.0511980	+	0.408028i
$847$	−88.1347	+	88.1347i	−3.02835	+	3.02835i
$848$	−7.49462	+	2.20470i	−0.257366	+	0.0757097i
$849$		−	20.9382i		−	0.718597i
$850$	−2.34807	+	4.87856i	−0.0805381	+	0.167333i
$851$		−	5.30589i		−	0.181884i
$852$	−1.08839	−	1.83334i	−0.0372877	−	0.0628092i
$853$	−30.6005	+	30.6005i	−1.04774	+	1.04774i	−0.0489409	+	0.998802i	$0.515585\pi$
$853$	−30.6005	+	30.6005i	−1.04774	+	1.04774i	−0.998802	+	0.0489409i	$0.984415\pi$
$854$	−40.4600	−	5.07680i	−1.38451	−	0.173724i
$855$	−4.85087	+	29.7041i	−0.165896	+	1.01586i
$856$	−14.8795	+	37.8595i	−0.508570	+	1.29401i
$857$	−34.2190	−	34.2190i	−1.16890	−	1.16890i	−0.982468	−	0.186433i	$-0.940307\pi$
$857$	−34.2190	−	34.2190i	−1.16890	−	1.16890i	−0.186433	−	0.982468i	$-0.559693\pi$
$858$	−4.86318	+	3.77881i	−0.166026	+	0.129006i
$859$	−6.49249			−0.221521			−0.110760	−	0.993847i	$-0.535329\pi$
$859$	−6.49249			−0.221521			−0.110760	+	0.993847i	$0.535329\pi$
$860$	−8.69755	+	3.41226i	−0.296584	+	0.116357i
$861$	17.3924			0.592733
$862$	20.3178	−	15.7874i	0.692027	−	0.537722i
$863$	9.27533	+	9.27533i	0.315736	+	0.315736i	0.847127	−	0.531391i	$-0.178330\pi$
$863$	9.27533	+	9.27533i	0.315736	+	0.315736i	−0.531391	+	0.847127i	$0.678330\pi$
$864$	17.4752	+	12.5848i	0.594518	+	0.428142i
$865$	19.4673	−	14.0016i	0.661908	−	0.476069i
$866$	23.3517	+	2.93010i	0.793524	+	0.0995689i
$867$	−7.99665	+	7.99665i	−0.271580	+	0.271580i
$868$	60.1564	−	35.7128i	2.04184	−	1.21217i
$869$			28.8456i			0.978521i
$870$	−8.64253	−	2.54803i	−0.293009	−	0.0863862i
$871$			4.44493i			0.150611i
$872$	−18.6900	−	42.8935i	−0.632924	−	1.45256i
$873$	3.94434	−	3.94434i	0.133496	−	0.133496i
$874$	1.73142	−	13.7988i	0.0585663	−	0.466750i
$875$	45.9887	−	14.2142i	1.55470	−	0.480528i
$876$	−2.45518	+	9.62937i	−0.0829529	+	0.325346i
$877$	−5.63902	−	5.63902i	−0.190416	−	0.190416i	0.605460	−	0.795876i	$-0.292989\pi$
$877$	−5.63902	−	5.63902i	−0.190416	−	0.190416i	−0.795876	+	0.605460i	$0.792989\pi$
$878$	−29.9824	−	38.5861i	−1.01186	−	1.30222i
$879$	−7.17956			−0.242161
$880$	34.7140	−	44.6202i	1.17021	−	1.50415i
$881$	30.8838			1.04050			0.520250	−	0.854014i	$-0.325839\pi$
$881$	30.8838			1.04050			0.520250	+	0.854014i	$0.325839\pi$
$882$	−25.2783	−	32.5321i	−0.851164	−	1.09541i
$883$	−36.0168	−	36.0168i	−1.21206	−	1.21206i	−0.970347	−	0.241715i	$-0.922290\pi$
$883$	−36.0168	−	36.0168i	−1.21206	−	1.21206i	−0.241715	−	0.970347i	$-0.577710\pi$
$884$	0.378347	−	1.48390i	0.0127252	−	0.0499089i
$885$	5.74945	+	7.99381i	0.193266	+	0.268709i
$886$	3.90133	−	31.0921i	0.131068	−	1.04456i
$887$	30.8430	−	30.8430i	1.03561	−	1.03561i	0.0362639	−	0.999342i	$-0.488454\pi$
$887$	30.8430	−	30.8430i	1.03561	−	1.03561i	0.999342	−	0.0362639i	$-0.0115457\pi$
$888$	−2.23877	−	5.13796i	−0.0751282	−	0.172419i
$889$			24.6212i			0.825769i
$890$	9.60965	−	5.23352i	0.322116	−	0.175428i
$891$		−	31.3056i		−	1.04878i
$892$	39.8742	−	23.6720i	1.33509	−	0.792597i
$893$	12.6230	−	12.6230i	0.422413	−	0.422413i
$894$	14.0740	+	1.76596i	0.470705	+	0.0590625i
$895$	−15.5955	−	2.54684i	−0.521300	−	0.0851315i
$896$	37.3483	−	31.2686i	1.24772	−	1.04461i
$897$	0.898838	+	0.898838i	0.0300113	+	0.0300113i
$898$	−15.6018	+	12.1230i	−0.520639	+	0.404549i
$899$	−33.5990			−1.12059
$900$	21.2139	+	13.6995i	0.707130	+	0.456651i
$901$	1.49542			0.0498196
$902$	41.3847	−	32.1570i	1.37796	−	1.07071i
$903$	−4.38207	−	4.38207i	−0.145826	−	0.145826i
$904$	−2.97681	+	7.57423i	−0.0990073	+	0.251915i
$905$	35.4781	+	5.79379i	1.17933	+	0.192592i
$906$	9.88419	+	1.24024i	0.328380	+	0.0412041i
$907$	13.9428	−	13.9428i	0.462962	−	0.462962i	−0.436663	−	0.899625i	$-0.643840\pi$
$907$	13.9428	−	13.9428i	0.462962	−	0.462962i	0.899625	+	0.436663i	$0.143840\pi$
$908$	−13.7396	−	23.1436i	−0.455965	−	0.768049i
$909$		−	0.325280i		−	0.0107889i
$910$	−11.9565	+	6.51166i	−0.396355	+	0.215860i
$911$		−	40.3602i		−	1.33719i	−0.743625	−	0.668597i	$-0.766895\pi$
$911$		−	40.3602i		−	1.33719i	0.743625	−	0.668597i	$-0.233105\pi$
$912$	−4.14562	−	14.0926i	−0.137275	−	0.466652i
$913$	−40.2640	+	40.2640i	−1.33254	+	1.33254i
$914$	0.243740	−	1.94251i	0.00806220	−	0.0642525i
$915$	6.02465	+	8.37644i	0.199169	+	0.276917i
$916$	−22.0664	−	5.62621i	−0.729093	−	0.185895i
$917$	−37.7794	−	37.7794i	−1.24759	−	1.24759i
$918$	−2.52930	−	3.25511i	−0.0834794	−	0.107435i
$919$	47.5003			1.56689			0.783445	−	0.621461i	$-0.213461\pi$
$919$	47.5003			1.56689			0.783445	+	0.621461i	$0.213461\pi$
$920$	−10.0299	−	5.96257i	−0.330676	−	0.196580i
$921$	−10.2038			−0.336227
$922$	7.53082	+	9.69186i	0.248014	+	0.319184i
$923$	1.09406	+	1.09406i	0.0360114	+	0.0360114i
$924$	36.3361	+	9.26454i	1.19537	+	0.304781i
$925$	−6.40498	−	12.8744i	−0.210594	−	0.423308i
$926$	−3.43416	+	27.3689i	−0.112854	+	0.899398i
$927$	12.6121	−	12.6121i	0.414235	−	0.414235i
$928$	−23.0901	+	3.75651i	−0.757971	+	0.123313i
$929$		−	16.2883i		−	0.534403i	−0.963641	−	0.267201i	$-0.913901\pi$
$929$		−	16.2883i		−	0.534403i	0.963641	−	0.267201i	$-0.0860989\pi$
$930$	−16.9793	−	5.00590i	−0.556772	−	0.164150i
$931$			61.4885i			2.01521i
$932$	−13.7618	−	23.1810i	−0.450782	−	0.759319i
$933$	−3.62697	+	3.62697i	−0.118742	+	0.118742i
$934$	−28.4258	−	3.56678i	−0.930120	−	0.116708i
$935$	−8.78537	+	6.31877i	−0.287312	+	0.206646i
$936$	−6.64761	−	2.61263i	−0.217284	−	0.0853966i
$937$	16.9391	+	16.9391i	0.553376	+	0.553376i	0.927414	−	0.374038i	$-0.122027\pi$
$937$	16.9391	+	16.9391i	0.553376	+	0.553376i	−0.374038	+	0.927414i	$0.622027\pi$
$938$	21.3707	−	16.6055i	0.697777	−	0.542190i
$939$	−13.2070			−0.430995
$940$	−5.47034	−	13.9434i	−0.178423	−	0.454784i
$941$	13.4762			0.439312			0.219656	−	0.975577i	$-0.429506\pi$
$941$	13.4762			0.439312			0.219656	+	0.975577i	$0.429506\pi$
$942$	−9.51419	+	7.39276i	−0.309989	+	0.240869i
$943$	−7.64894	−	7.64894i	−0.249084	−	0.249084i
$944$	22.4442	+	12.2408i	0.730495	+	0.398406i
$945$	−5.90680	+	36.1701i	−0.192148	+	1.17661i
$946$	−18.5290	−	2.32496i	−0.602430	−	0.0755910i
$947$	−11.5277	+	11.5277i	−0.374600	+	0.374600i	−0.869150	−	0.494549i	$-0.835333\pi$
$947$	−11.5277	+	11.5277i	−0.374600	+	0.374600i	0.494549	+	0.869150i	$0.335333\pi$
$948$	5.40763	−	3.21033i	0.175632	−	0.104267i
$949$		−	7.21155i		−	0.234097i
$950$	−12.4559	−	35.5718i	−0.404123	−	1.15410i
$951$			6.63278i			0.215083i
$952$	−8.54784	+	3.72456i	−0.277037	+	0.120714i
$953$	18.7484	−	18.7484i	0.607319	−	0.607319i	−0.334925	−	0.942245i	$-0.608711\pi$
$953$	18.7484	−	18.7484i	0.607319	−	0.607319i	0.942245	+	0.334925i	$0.108711\pi$
$954$	0.868377	−	6.92062i	0.0281148	−	0.224063i
$955$	−7.96570	+	48.7777i	−0.257764	+	1.57841i
$956$	−5.23874	+	20.5467i	−0.169433	+	0.664526i
$957$	−12.7346	−	12.7346i	−0.411651	−	0.411651i
$958$	−11.0527	−	14.2244i	−0.357098	−	0.459570i
$959$	59.8960			1.93414
$960$	−12.2283	−	1.54184i	−0.394666	−	0.0497625i
$961$	−35.0091			−1.12933
$962$	2.49550	+	3.21161i	0.0804581	+	0.103546i
$963$	−25.6812	−	25.6812i	−0.827566	−	0.827566i
$964$	−5.21323	+	20.4466i	−0.167907	+	0.658541i
$965$	17.4364	−	12.5409i	0.561297	−	0.403706i
$966$	0.963588	−	7.67941i	0.0310029	−	0.247081i
$967$	−6.21745	+	6.21745i	−0.199940	+	0.199940i	−0.799974	−	0.600034i	$-0.795154\pi$
$967$	−6.21745	+	6.21745i	−0.199940	+	0.199940i	0.600034	+	0.799974i	$0.295154\pi$
$968$	75.0672	−	32.7091i	2.41275	−	1.05131i
$969$			2.81192i			0.0903320i
$970$	−1.97535	+	6.70008i	−0.0634246	+	0.215127i
$971$			13.9613i			0.448039i	0.974585	+	0.224019i	$0.0719179\pi$
$971$			13.9613i			0.448039i	−0.974585	+	0.224019i	$0.928082\pi$
$972$	−25.5098	+	15.1443i	−0.818226	+	0.485753i
$973$	−48.5581	+	48.5581i	−1.55670	+	1.55670i
$974$	−24.0491	−	3.01761i	−0.770584	−	0.0966904i
$975$	3.26600	+	1.09594i	0.104596	+	0.0350983i
$976$	23.5185	+	12.8268i	0.752808	+	0.410575i
$977$	22.0756	+	22.0756i	0.706262	+	0.706262i	0.965747	−	0.259485i	$-0.0835528\pi$
$977$	22.0756	+	22.0756i	0.706262	+	0.706262i	−0.259485	+	0.965747i	$0.583553\pi$
$978$	−5.97959	+	4.64629i	−0.191206	+	0.148572i
$979$	21.8711			0.699004
$980$	47.2836	+	20.6368i	1.51042	+	0.659218i
$981$	41.7739			1.33374
$982$	−39.4273	+	30.6360i	−1.25818	+	0.977633i
$983$	32.7496	+	32.7496i	1.04455	+	1.04455i	0.998960	+	0.0455907i	$0.0145170\pi$
$983$	32.7496	+	32.7496i	1.04455	+	1.04455i	0.0455907	+	0.998960i	$0.485483\pi$
$984$	−10.6342	−	4.17945i	−0.339007	−	0.133236i
$985$	30.5799	+	42.5171i	0.974357	+	1.35471i
$986$	4.44322	+	0.557521i	0.141501	+	0.0177551i
$987$	7.02508	−	7.02508i	0.223611	−	0.223611i
$988$	5.44189	+	9.16658i	0.173130	+	0.291628i
$989$			3.85434i			0.122561i
$990$	24.1409	+	44.3269i	0.767249	+	1.40880i
$991$		−	58.6120i		−	1.86187i	−0.365182	−	0.930936i	$-0.618993\pi$
$991$		−	58.6120i		−	1.86187i	0.365182	−	0.930936i	$-0.381007\pi$
$992$	−45.3633	+	7.38010i	−1.44028	+	0.234319i
$993$	−0.669622	+	0.669622i	−0.0212498	+	0.0212498i
$994$	1.17287	−	9.34733i	0.0372013	−	0.296479i
$995$	33.5062	+	5.47177i	1.06222	+	0.173467i
$996$	12.0293	+	3.06709i	0.381163	+	0.0971844i
$997$	0.709943	+	0.709943i	0.0224841	+	0.0224841i	0.718259	−	0.695775i	$-0.244939\pi$
$997$	0.709943	+	0.709943i	0.0224841	+	0.0224841i	−0.695775	+	0.718259i	$0.744939\pi$
$998$	−3.53527	−	4.54976i	−0.111907	−	0.144020i
$999$	10.9483			0.346390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.25	✓	72
4.3	odd	2	inner	260.2.o.a.27.30	yes	72
5.3	odd	4	inner	260.2.o.a.183.30	yes	72
20.3	even	4	inner	260.2.o.a.183.25	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.25	✓	72	1.1	even	1	trivial
260.2.o.a.27.30	yes	72	4.3	odd	2	inner
260.2.o.a.183.25	yes	72	20.3	even	4	inner
260.2.o.a.183.30	yes	72	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.867719 + 1.11672i) q^{2} +(-0.487193 - 0.487193i) q^{3} +(-0.494127 + 1.93800i) q^{4} +(2.20683 + 0.360390i) q^{5} +(0.121312 - 0.966804i) q^{6} +(3.04434 - 3.04434i) q^{7} +(-2.59297 + 1.12984i) q^{8} -2.52529i q^{9} +O(q^{10})\)	\(q+(0.867719 + 1.11672i) q^{2} +(-0.487193 - 0.487193i) q^{3} +(-0.494127 + 1.93800i) q^{4} +(2.20683 + 0.360390i) q^{5} +(0.121312 - 0.966804i) q^{6} +(3.04434 - 3.04434i) q^{7} +(-2.59297 + 1.12984i) q^{8} -2.52529i q^{9} +(1.51246 + 2.77713i) q^{10} +6.32063i q^{11} +(1.18491 - 0.703444i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(6.04132 + 0.758045i) q^{14} +(-0.899574 - 1.25073i) q^{15} +(-3.51168 - 1.91524i) q^{16} +(0.541422 + 0.541422i) q^{17} +(2.82004 - 2.19124i) q^{18} -5.33011 q^{19} +(-1.78889 + 4.09876i) q^{20} -2.96637 q^{21} +(-7.05837 + 5.48453i) q^{22} +(1.30456 + 1.30456i) q^{23} +(1.81372 + 0.712826i) q^{24} +(4.74024 + 1.59064i) q^{25} +(-1.40321 - 0.176070i) q^{26} +(-2.69188 + 2.69188i) q^{27} +(4.39564 + 7.40423i) q^{28} -4.13546i q^{29} +(0.616141 - 2.08986i) q^{30} -8.12460i q^{31} +(-0.908365 - 5.58345i) q^{32} +(3.07936 - 3.07936i) q^{33} +(-0.134815 + 1.07442i) q^{34} +(7.81552 - 5.62121i) q^{35} +(4.89400 + 1.24781i) q^{36} +(-2.03359 - 2.03359i) q^{37} +(-4.62504 - 5.95225i) q^{38} +0.688995 q^{39} +(-6.12943 + 1.55888i) q^{40} -5.86321 q^{41} +(-2.57397 - 3.31260i) q^{42} +(1.47725 + 1.47725i) q^{43} +(-12.2494 - 3.12319i) q^{44} +(0.910088 - 5.57289i) q^{45} +(-0.324838 + 2.58883i) q^{46} +(-2.36824 + 2.36824i) q^{47} +(0.777774 + 2.64395i) q^{48} -11.5361i q^{49} +(2.33689 + 6.67375i) q^{50} -0.527554i q^{51} +(-1.02097 - 1.71977i) q^{52} +(1.38101 - 1.38101i) q^{53} +(-5.34187 - 0.670281i) q^{54} +(-2.27789 + 13.9486i) q^{55} +(-4.45427 + 11.3335i) q^{56} +(2.59679 + 2.59679i) q^{57} +(4.61815 - 3.58842i) q^{58} -6.39130 q^{59} +(2.86842 - 1.12535i) q^{60} -6.69722 q^{61} +(9.07290 - 7.04987i) q^{62} +(-7.68784 - 7.68784i) q^{63} +(5.44694 - 5.85925i) q^{64} +(-1.81530 + 1.30563i) q^{65} +(6.11081 + 0.766765i) q^{66} +(3.14304 - 3.14304i) q^{67} +(-1.31681 + 0.781744i) q^{68} -1.27115i q^{69} +(13.0590 + 3.85011i) q^{70} -1.54723i q^{71} +(2.85316 + 6.54798i) q^{72} +(-5.09934 + 5.09934i) q^{73} +(0.506366 - 4.03553i) q^{74} +(-1.53446 - 3.08436i) q^{75} +(2.63376 - 10.3298i) q^{76} +(19.2422 + 19.2422i) q^{77} +(0.597854 + 0.769414i) q^{78} +4.56373 q^{79} +(-7.05946 - 5.49218i) q^{80} -4.95293 q^{81} +(-5.08762 - 6.54757i) q^{82} +(6.37025 + 6.37025i) q^{83} +(1.46576 - 5.74881i) q^{84} +(0.999706 + 1.38995i) q^{85} +(-0.367837 + 2.93151i) q^{86} +(-2.01477 + 2.01477i) q^{87} +(-7.14127 - 16.3892i) q^{88} -3.46028i q^{89} +(7.01306 - 3.81939i) q^{90} +4.30535i q^{91} +(-3.17286 + 1.88362i) q^{92} +(-3.95825 + 3.95825i) q^{93} +(-4.69964 - 0.589695i) q^{94} +(-11.7627 - 1.92092i) q^{95} +(-2.27767 + 3.16276i) q^{96} +(1.56194 + 1.56194i) q^{97} +(12.8826 - 10.0101i) q^{98} +15.9614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

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