LMFDB - Embedded newform 273.2.n.c.8.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.n (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.6
Character	$\chi$	$=$	273.8
Dual form			273.2.n.c.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34745 + 1.34745i) q^{2} +(-0.469658 - 1.66716i) q^{3} -1.63125i q^{4} +(3.06725 - 3.06725i) q^{5} +(2.87926 + 1.61358i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.496878 - 0.496878i) q^{8} +(-2.55884 + 1.56599i) q^{9} +O(q^{10})$	\(q+(-1.34745 + 1.34745i) q^{2} +(-0.469658 - 1.66716i) q^{3} -1.63125i q^{4} +(3.06725 - 3.06725i) q^{5} +(2.87926 + 1.61358i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.496878 - 0.496878i) q^{8} +(-2.55884 + 1.56599i) q^{9} +8.26592i q^{10} +(-1.91411 - 1.91411i) q^{11} +(-2.71955 + 0.766127i) q^{12} +(-2.89062 - 2.15507i) q^{13} -1.90558i q^{14} +(-6.55414 - 3.67303i) q^{15} +4.60153 q^{16} -5.21403 q^{17} +(1.33782 - 5.55801i) q^{18} +(2.19814 + 2.19814i) q^{19} +(-5.00343 - 5.00343i) q^{20} +(1.51096 + 0.846762i) q^{21} +5.15835 q^{22} +1.85140 q^{23} +(-0.595013 + 1.06174i) q^{24} -13.8160i q^{25} +(6.79882 - 0.991111i) q^{26} +(3.81253 + 3.53052i) q^{27} +(1.15346 + 1.15346i) q^{28} -5.69557i q^{29} +(13.7806 - 3.88215i) q^{30} +(2.18591 + 2.18591i) q^{31} +(-5.20658 + 5.20658i) q^{32} +(-2.29216 + 4.09011i) q^{33} +(7.02565 - 7.02565i) q^{34} +4.33774i q^{35} +(2.55451 + 4.17410i) q^{36} +(1.32331 - 1.32331i) q^{37} -5.92376 q^{38} +(-2.23525 + 5.83127i) q^{39} -3.04810 q^{40} +(2.07049 - 2.07049i) q^{41} +(-3.17691 + 0.894971i) q^{42} -3.43302i q^{43} +(-3.12239 + 3.12239i) q^{44} +(-3.04533 + 12.6519i) q^{45} +(-2.49467 + 2.49467i) q^{46} +(-0.505559 - 0.505559i) q^{47} +(-2.16114 - 7.67148i) q^{48} -1.00000i q^{49} +(18.6164 + 18.6164i) q^{50} +(2.44881 + 8.69263i) q^{51} +(-3.51545 + 4.71531i) q^{52} -7.99109i q^{53} +(-9.89440 + 0.379994i) q^{54} -11.7421 q^{55} +0.702692 q^{56} +(2.63228 - 4.69702i) q^{57} +(7.67450 + 7.67450i) q^{58} +(2.49007 + 2.49007i) q^{59} +(-5.99162 + 10.6914i) q^{60} +3.37763 q^{61} -5.89082 q^{62} +(0.702055 - 2.91670i) q^{63} -4.82815i q^{64} +(-15.4764 + 2.25610i) q^{65} +(-2.42266 - 8.59979i) q^{66} +(8.77475 + 8.77475i) q^{67} +8.50537i q^{68} +(-0.869525 - 3.08659i) q^{69} +(-5.84489 - 5.84489i) q^{70} +(0.255545 - 0.255545i) q^{71} +(2.04954 + 0.493328i) q^{72} +(3.52217 - 3.52217i) q^{73} +3.56619i q^{74} +(-23.0335 + 6.48879i) q^{75} +(3.58570 - 3.58570i) q^{76} +2.70697 q^{77} +(-4.84545 - 10.8692i) q^{78} -7.05110 q^{79} +(14.1140 - 14.1140i) q^{80} +(4.09536 - 8.01424i) q^{81} +5.57977i q^{82} +(-4.05801 + 4.05801i) q^{83} +(1.38128 - 2.46474i) q^{84} +(-15.9927 + 15.9927i) q^{85} +(4.62582 + 4.62582i) q^{86} +(-9.49542 + 2.67497i) q^{87} +1.90216i q^{88} +(12.8887 + 12.8887i) q^{89} +(-12.9443 - 21.1512i) q^{90} +(3.56784 - 0.520109i) q^{91} -3.02009i q^{92} +(2.61763 - 4.67089i) q^{93} +1.36243 q^{94} +13.4845 q^{95} +(11.1255 + 6.23489i) q^{96} +(4.00954 + 4.00954i) q^{97} +(1.34745 + 1.34745i) q^{98} +(7.89540 + 1.90044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) $ 48 * q + 8 * q^3 + 4 * q^6	$ 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) $ 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.34745	+	1.34745i	−0.952791	+	0.952791i	−0.998935	−	0.0461434i	$-0.985307\pi$
$2$	−1.34745	+	1.34745i	−0.952791	+	0.952791i	0.0461434	+	0.998935i	$0.485307\pi$
$3$	−0.469658	−	1.66716i	−0.271157	−	0.962535i
$3$	−0.469658	−	1.66716i	−0.271157	−	0.962535i
$4$		−	1.63125i		−	0.815623i
$5$	3.06725	−	3.06725i	1.37171	−	1.37171i	0.513810	−	0.857904i	$-0.328234\pi$
$5$	3.06725	−	3.06725i	1.37171	−	1.37171i	0.857904	−	0.513810i	$-0.171766\pi$
$6$	2.87926	+	1.61358i	1.17545	+	0.658739i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.496878	−	0.496878i	−0.175673	−	0.175673i
$9$	−2.55884	+	1.56599i	−0.852948	+	0.521996i
$10$			8.26592i			2.61391i
$11$	−1.91411	−	1.91411i	−0.577127	−	0.577127i	0.356984	−	0.934111i	$-0.383805\pi$
$11$	−1.91411	−	1.91411i	−0.577127	−	0.577127i	−0.934111	+	0.356984i	$0.883805\pi$
$12$	−2.71955	+	0.766127i	−0.785066	+	0.221162i
$13$	−2.89062	−	2.15507i	−0.801713	−	0.597709i
$13$	−2.89062	−	2.15507i	−0.801713	−	0.597709i
$14$		−	1.90558i		−	0.509288i
$15$	−6.55414	−	3.67303i	−1.69227	−	0.948373i
$16$	4.60153			1.15038
$17$	−5.21403			−1.26459			−0.632294	−	0.774728i	$-0.717887\pi$
$17$	−5.21403			−1.26459			−0.632294	+	0.774728i	$0.717887\pi$
$18$	1.33782	−	5.55801i	0.315328	−	1.31003i
$19$	2.19814	+	2.19814i	0.504287	+	0.504287i	0.912767	−	0.408480i	$-0.133941\pi$
$19$	2.19814	+	2.19814i	0.504287	+	0.504287i	−0.408480	+	0.912767i	$0.633941\pi$
$20$	−5.00343	−	5.00343i	−1.11880	−	1.11880i
$21$	1.51096	+	0.846762i	0.329718	+	0.184779i
$22$	5.15835			1.09976
$23$	1.85140			0.386044			0.193022	−	0.981194i	$-0.438171\pi$
$23$	1.85140			0.386044			0.193022	+	0.981194i	$0.438171\pi$
$24$	−0.595013	+	1.06174i	−0.121456	+	0.216726i
$25$		−	13.8160i		−	2.76320i
$26$	6.79882	−	0.991111i	1.33336	−	0.194373i
$27$	3.81253	+	3.53052i	0.733722	+	0.679449i
$28$	1.15346	+	1.15346i	0.217984	+	0.217984i
$29$		−	5.69557i		−	1.05764i	−0.848734	−	0.528820i	$-0.822635\pi$
$29$		−	5.69557i		−	1.05764i	0.848734	−	0.528820i	$-0.177365\pi$
$30$	13.7806	−	3.88215i	2.51598	−	0.708781i
$31$	2.18591	+	2.18591i	0.392601	+	0.392601i	0.875614	−	0.483012i	$-0.160457\pi$
$31$	2.18591	+	2.18591i	0.392601	+	0.392601i	−0.483012	+	0.875614i	$0.660457\pi$
$32$	−5.20658	+	5.20658i	−0.920401	+	0.920401i
$33$	−2.29216	+	4.09011i	−0.399013	+	0.711997i
$34$	7.02565	−	7.02565i	1.20489	−	1.20489i
$35$			4.33774i			0.733212i
$36$	2.55451	+	4.17410i	0.425752	+	0.695684i
$37$	1.32331	−	1.32331i	0.217551	−	0.217551i	−0.589915	−	0.807466i	$-0.700839\pi$
$37$	1.32331	−	1.32331i	0.217551	−	0.217551i	0.807466	+	0.589915i	$0.200839\pi$
$38$	−5.92376			−0.960961
$39$	−2.23525	+	5.83127i	−0.357926	+	0.933750i
$40$	−3.04810			−0.481946
$41$	2.07049	−	2.07049i	0.323357	−	0.323357i	−0.526697	−	0.850053i	$-0.676570\pi$
$41$	2.07049	−	2.07049i	0.323357	−	0.323357i	0.850053	+	0.526697i	$0.176570\pi$
$42$	−3.17691	+	0.894971i	−0.490208	+	0.138097i
$43$		−	3.43302i		−	0.523531i	−0.965132	−	0.261765i	$-0.915695\pi$
$43$		−	3.43302i		−	0.523531i	0.965132	−	0.261765i	$-0.0843046\pi$
$44$	−3.12239	+	3.12239i	−0.470718	+	0.470718i
$45$	−3.04533	+	12.6519i	−0.453971	+	1.88603i
$46$	−2.49467	+	2.49467i	−0.367820	+	0.367820i
$47$	−0.505559	−	0.505559i	−0.0737433	−	0.0737433i	0.669273	−	0.743016i	$-0.266606\pi$
$47$	−0.505559	−	0.505559i	−0.0737433	−	0.0737433i	−0.743016	+	0.669273i	$0.766606\pi$
$48$	−2.16114	−	7.67148i	−0.311934	−	1.10728i
$49$		−	1.00000i		−	0.142857i
$50$	18.6164	+	18.6164i	2.63275	+	2.63275i
$51$	2.44881	+	8.69263i	0.342902	+	1.21721i
$52$	−3.51545	+	4.71531i	−0.487505	+	0.653895i
$53$		−	7.99109i		−	1.09766i	−0.835934	−	0.548830i	$-0.815073\pi$
$53$		−	7.99109i		−	1.09766i	0.835934	−	0.548830i	$-0.184927\pi$
$54$	−9.89440	+	0.379994i	−1.34646	+	0.0517106i
$55$	−11.7421			−1.58331
$56$	0.702692			0.0939012
$57$	2.63228	−	4.69702i	0.348653	−	0.622135i
$58$	7.67450	+	7.67450i	1.00771	+	1.00771i
$59$	2.49007	+	2.49007i	0.324180	+	0.324180i	0.850368	−	0.526188i	$-0.176379\pi$
$59$	2.49007	+	2.49007i	0.324180	+	0.324180i	−0.526188	+	0.850368i	$0.676379\pi$
$60$	−5.99162	+	10.6914i	−0.773515	+	1.38026i
$61$	3.37763			0.432461			0.216231	−	0.976342i	$-0.430624\pi$
$61$	3.37763			0.432461			0.216231	+	0.976342i	$0.430624\pi$
$62$	−5.89082			−0.748134
$63$	0.702055	−	2.91670i	0.0884506	−	0.367469i
$64$		−	4.82815i		−	0.603519i
$65$	−15.4764	+	2.25610i	−1.91961	+	0.279835i
$66$	−2.42266	−	8.59979i	−0.298208	−	1.05856i
$67$	8.77475	+	8.77475i	1.07201	+	1.07201i	0.997198	+	0.0748084i	$0.0238345\pi$
$67$	8.77475	+	8.77475i	1.07201	+	1.07201i	0.0748084	+	0.997198i	$0.476165\pi$
$68$			8.50537i			1.03143i
$69$	−0.869525	−	3.08659i	−0.104679	−	0.371581i
$70$	−5.84489	−	5.84489i	−0.698598	−	0.698598i
$71$	0.255545	−	0.255545i	0.0303276	−	0.0303276i	−0.691780	−	0.722108i	$-0.743173\pi$
$71$	0.255545	−	0.255545i	0.0303276	−	0.0303276i	0.722108	+	0.691780i	$0.243173\pi$
$72$	2.04954	+	0.493328i	0.241541	+	0.0581393i
$73$	3.52217	−	3.52217i	0.412238	−	0.412238i	−0.470279	−	0.882518i	$-0.655847\pi$
$73$	3.52217	−	3.52217i	0.412238	−	0.412238i	0.882518	+	0.470279i	$0.155847\pi$
$74$			3.56619i			0.414561i
$75$	−23.0335	+	6.48879i	−2.65968	+	0.749261i
$76$	3.58570	−	3.58570i	0.411308	−	0.411308i
$77$	2.70697			0.308487
$78$	−4.84545	−	10.8692i	−0.548640	−	1.23070i
$79$	−7.05110			−0.793311			−0.396655	−	0.917968i	$-0.629829\pi$
$79$	−7.05110			−0.793311			−0.396655	+	0.917968i	$0.629829\pi$
$80$	14.1140	−	14.1140i	1.57800	−	1.57800i
$81$	4.09536	−	8.01424i	0.455040	−	0.890471i
$82$			5.57977i			0.616183i
$83$	−4.05801	+	4.05801i	−0.445424	+	0.445424i	−0.893830	−	0.448406i	$-0.851992\pi$
$83$	−4.05801	+	4.05801i	−0.445424	+	0.445424i	0.448406	+	0.893830i	$0.351992\pi$
$84$	1.38128	−	2.46474i	0.150710	−	0.268926i
$85$	−15.9927	+	15.9927i	−1.73465	+	1.73465i
$86$	4.62582	+	4.62582i	0.498815	+	0.498815i
$87$	−9.49542	+	2.67497i	−1.01802	+	0.286786i
$88$			1.90216i			0.202771i
$89$	12.8887	+	12.8887i	1.36620	+	1.36620i	0.865782	+	0.500422i	$0.166822\pi$
$89$	12.8887	+	12.8887i	1.36620	+	1.36620i	0.500422	+	0.865782i	$0.333178\pi$
$90$	−12.9443	−	21.1512i	−1.36445	−	2.22953i
$91$	3.56784	−	0.520109i	0.374011	−	0.0545222i
$92$		−	3.02009i		−	0.314867i
$93$	2.61763	−	4.67089i	0.271436	−	0.484349i
$94$	1.36243			0.140524
$95$	13.4845			1.38348
$96$	11.1255	+	6.23489i	1.13549	+	0.636345i
$97$	4.00954	+	4.00954i	0.407107	+	0.407107i	0.880729	−	0.473621i	$-0.157053\pi$
$97$	4.00954	+	4.00954i	0.407107	+	0.407107i	−0.473621	+	0.880729i	$0.657053\pi$
$98$	1.34745	+	1.34745i	0.136113	+	0.136113i
$99$	7.89540	+	1.90044i	0.793517	+	0.191001i
$100$	−22.5373			−2.25373
$101$	8.50911			0.846688			0.423344	−	0.905969i	$-0.360856\pi$
$101$	8.50911			0.846688			0.423344	+	0.905969i	$0.360856\pi$
$102$	−15.0125	−	8.41323i	−1.48646	−	0.833034i
$103$		−	8.55361i		−	0.842812i	−0.906872	−	0.421406i	$-0.861537\pi$
$103$		−	8.55361i		−	0.842812i	0.906872	−	0.421406i	$-0.138463\pi$
$104$	0.365476	+	2.50709i	0.0358379	+	0.245841i
$105$	7.23171	−	2.03725i	0.705742	−	0.198815i
$106$	10.7676	+	10.7676i	1.04584	+	1.04584i
$107$			17.3338i			1.67572i	0.545887	+	0.837859i	$0.316193\pi$
$107$			17.3338i			1.67572i	−0.545887	+	0.837859i	$0.683807\pi$
$108$	5.75915	−	6.21918i	0.554175	−	0.598441i
$109$	8.29123	+	8.29123i	0.794156	+	0.794156i	0.982167	−	0.188011i	$-0.0602040\pi$
$109$	8.29123	+	8.29123i	0.794156	+	0.794156i	−0.188011	+	0.982167i	$0.560204\pi$
$110$	15.8219	−	15.8219i	1.50856	−	1.50856i
$111$	−2.82767	−	1.58467i	−0.268391	−	0.150410i
$112$	−3.25377	+	3.25377i	−0.307453	+	0.307453i
$113$		−	4.66364i		−	0.438719i	−0.975644	−	0.219359i	$-0.929603\pi$
$113$		−	4.66364i		−	0.438719i	0.975644	−	0.219359i	$-0.0703967\pi$
$114$	2.78214	+	9.87586i	0.260571	+	0.924959i
$115$	5.67871	−	5.67871i	0.529542	−	0.529542i
$116$	−9.29087			−0.862636
$117$	10.7715	+	0.987819i	0.995821	+	0.0913239i
$118$	−6.71050			−0.617751
$119$	3.68688	−	3.68688i	0.337976	−	0.337976i
$120$	1.43156	+	5.08166i	0.130683	+	0.463890i
$121$		−	3.67234i		−	0.333849i
$122$	−4.55119	+	4.55119i	−0.412045	+	0.412045i
$123$	−4.42426	−	2.47942i	−0.398922	−	0.223562i
$124$	3.56576	−	3.56576i	0.320215	−	0.320215i
$125$	−27.0408	−	27.0408i	−2.41861	−	2.41861i
$126$	2.98412	+	4.87609i	0.265847	+	0.434396i
$127$		−	17.5458i		−	1.55694i	−0.627684	−	0.778469i	$-0.715997\pi$
$127$		−	17.5458i		−	1.55694i	0.627684	−	0.778469i	$-0.284003\pi$
$128$	−3.90746	−	3.90746i	−0.345374	−	0.345374i
$129$	−5.72339	+	1.61234i	−0.503917	+	0.141959i
$130$	17.8137	−	23.8936i	1.56236	−	2.09561i
$131$			9.34758i			0.816702i	0.912825	+	0.408351i	$0.133896\pi$
$131$			9.34758i			0.816702i	−0.912825	+	0.408351i	$0.866104\pi$
$132$	6.67198	+	3.73907i	0.580721	+	0.325444i
$133$	−3.10864			−0.269553
$134$	−23.6471			−2.04280
$135$	22.5230	−	0.864993i	1.93847	−	0.0744467i
$136$	2.59074	+	2.59074i	0.222154	+	0.222154i
$137$	−14.4945	−	14.4945i	−1.23835	−	1.23835i	−0.960674	−	0.277677i	$-0.910435\pi$
$137$	−14.4945	−	14.4945i	−1.23835	−	1.23835i	−0.277677	−	0.960674i	$-0.589565\pi$
$138$	5.33066	+	2.98738i	0.453776	+	0.254303i
$139$	9.19282			0.779725			0.389863	−	0.920873i	$-0.372522\pi$
$139$	9.19282			0.779725			0.389863	+	0.920873i	$0.372522\pi$
$140$	7.07592			0.598024
$141$	−0.605408	+	1.08029i	−0.0509845	+	0.0909765i
$142$			0.688669i			0.0577918i
$143$	1.40792	+	9.65802i	0.117736	+	0.807644i
$144$	−11.7746	+	7.20594i	−0.981216	+	0.600495i
$145$	−17.4697	−	17.4697i	−1.45078	−	1.45078i
$146$			9.49189i			0.785554i
$147$	−1.66716	+	0.469658i	−0.137505	+	0.0387367i
$148$	−2.15864	−	2.15864i	−0.177439	−	0.177439i
$149$	1.59460	−	1.59460i	0.130635	−	0.130635i	−0.638766	−	0.769401i	$-0.720555\pi$
$149$	1.59460	−	1.59460i	0.130635	−	0.130635i	0.769401	+	0.638766i	$0.220555\pi$
$150$	22.2931	−	39.7798i	1.82023	−	3.24801i
$151$	5.71018	−	5.71018i	0.464688	−	0.464688i	−0.435501	−	0.900188i	$-0.643429\pi$
$151$	5.71018	−	5.71018i	0.464688	−	0.464688i	0.900188	+	0.435501i	$0.143429\pi$
$152$		−	2.18441i		−	0.177179i
$153$	13.3419	−	8.16511i	1.07863	−	0.660110i
$154$	−3.64750	+	3.64750i	−0.293924	+	0.293924i
$155$	13.4095			1.07707
$156$	9.51223	+	3.64624i	0.761588	+	0.291933i
$157$	1.63916			0.130819			0.0654096	−	0.997858i	$-0.479165\pi$
$157$	1.63916			0.130819			0.0654096	+	0.997858i	$0.479165\pi$
$158$	9.50101	−	9.50101i	0.755860	−	0.755860i
$159$	−13.3224	+	3.75307i	−1.05654	+	0.297638i
$160$			31.9397i			2.52505i
$161$	−1.30914	+	1.30914i	−0.103175	+	0.103175i
$162$	5.28049	+	16.3171i	0.414875	+	1.28199i
$163$	4.65678	−	4.65678i	0.364747	−	0.364747i	−0.500810	−	0.865557i	$-0.666964\pi$
$163$	4.65678	−	4.65678i	0.364747	−	0.364747i	0.865557	+	0.500810i	$0.166964\pi$
$164$	−3.37748	−	3.37748i	−0.263737	−	0.263737i
$165$	5.51477	+	19.5760i	0.429324	+	1.52399i
$166$		−	10.9359i		−	0.848793i
$167$	3.94937	+	3.94937i	0.305611	+	0.305611i	0.843204	−	0.537593i	$-0.180666\pi$
$167$	3.94937	+	3.94937i	0.305611	+	0.305611i	−0.537593	+	0.843204i	$0.680666\pi$
$168$	−0.330025	−	1.17150i	−0.0254619	−	0.0903832i
$169$	3.71133	+	12.4590i	0.285487	+	0.958383i
$170$		−	43.0988i		−	3.30553i
$171$	−9.06695	−	2.18243i	−0.693367	−	0.166895i
$172$	−5.60010			−0.427004
$173$	−10.8734			−0.826689			−0.413344	−	0.910575i	$-0.635639\pi$
$173$	−10.8734			−0.826689			−0.413344	+	0.910575i	$0.635639\pi$
$174$	9.19023	−	16.3990i	0.696709	−	1.24320i
$175$	9.76938	+	9.76938i	0.738496	+	0.738496i
$176$	−8.80785	−	8.80785i	−0.663917	−	0.663917i
$177$	2.98187	−	5.32083i	0.224131	−	0.399938i
$178$	−34.7339			−2.60341
$179$	11.7741			0.880037			0.440019	−	0.897989i	$-0.354972\pi$
$179$	11.7741			0.880037			0.440019	+	0.897989i	$0.354972\pi$
$180$	20.6383	+	4.96768i	1.53829	+	0.370269i
$181$			15.3551i			1.14134i	0.821180	+	0.570670i	$0.193316\pi$
$181$			15.3551i			1.14134i	−0.821180	+	0.570670i	$0.806684\pi$
$182$	−4.10667	+	5.50831i	−0.304406	+	0.408303i
$183$	−1.58633	−	5.63105i	−0.117265	−	0.416259i
$184$	−0.919922	−	0.919922i	−0.0678176	−	0.0678176i
$185$		−	8.11783i		−	0.596835i
$186$	2.76667	+	9.82093i	0.202862	+	0.720106i
$187$	9.98025	+	9.98025i	0.729828	+	0.729828i
$188$	−0.824690	+	0.824690i	−0.0601467	+	0.0601467i
$189$	−5.19232	+	0.199411i	−0.377686	+	0.0145050i
$190$	−18.1696	+	18.1696i	−1.31816	+	1.31816i
$191$			7.66383i			0.554536i	0.960793	+	0.277268i	$0.0894289\pi$
$191$			7.66383i			0.554536i	−0.960793	+	0.277268i	$0.910571\pi$
$192$	−8.04930	+	2.26758i	−0.580908	+	0.163648i
$193$	−6.46090	+	6.46090i	−0.465065	+	0.465065i	−0.900312	−	0.435246i	$-0.856661\pi$
$193$	−6.46090	+	6.46090i	−0.465065	+	0.465065i	0.435246	+	0.900312i	$0.356661\pi$
$194$	−10.8053			−0.775777
$195$	11.0299	+	24.7420i	0.789865	+	1.77181i
$196$	−1.63125			−0.116518
$197$	−9.90302	+	9.90302i	−0.705561	+	0.705561i	−0.965599	−	0.260037i	$-0.916265\pi$
$197$	−9.90302	+	9.90302i	−0.705561	+	0.705561i	0.260037	+	0.965599i	$0.416265\pi$
$198$	−13.1994	+	8.07791i	−0.938041	+	0.574072i
$199$		−	22.9534i		−	1.62712i	−0.581480	−	0.813560i	$-0.697526\pi$
$199$		−	22.9534i		−	1.62712i	0.581480	−	0.813560i	$-0.302474\pi$
$200$	−6.86487	+	6.86487i	−0.485419	+	0.485419i
$201$	10.5078	−	18.7500i	0.741162	−	1.32253i
$202$	−11.4656	+	11.4656i	−0.806717	+	0.806717i
$203$	4.02737	+	4.02737i	0.282666	+	0.282666i
$204$	14.1798	−	3.99461i	0.992785	−	0.279679i
$205$		−	12.7014i		−	0.887106i
$206$	11.5256	+	11.5256i	0.803024	+	0.803024i
$207$	−4.73745	+	2.89928i	−0.329276	+	0.201514i
$208$	−13.3013	−	9.91662i	−0.922276	−	0.687594i
$209$		−	8.41497i		−	0.582076i
$210$	−6.99927	+	12.4895i	−0.482996	+	0.861855i
$211$	−23.7363			−1.63408			−0.817038	−	0.576584i	$-0.804385\pi$
$211$	−23.7363			−1.63408			−0.817038	+	0.576584i	$0.804385\pi$
$212$	−13.0354			−0.895277
$213$	−0.546053	−	0.306016i	−0.0374149	−	0.0209679i
$214$	−23.3564	−	23.3564i	−1.59661	−	1.59661i
$215$	−10.5299	−	10.5299i	−0.718134	−	0.718134i
$216$	−0.140124	−	3.64860i	−0.00953426	−	0.248256i
$217$	−3.09135			−0.209854
$218$	−22.3441			−1.51333
$219$	−7.52623	−	4.21780i	−0.508575	−	0.285013i
$220$			19.1543i			1.29138i
$221$	15.0718	+	11.2366i	1.01384	+	0.755856i
$222$	5.94541	−	1.67489i	0.399030	−	0.112411i
$223$	7.40038	+	7.40038i	0.495566	+	0.495566i	0.910055	−	0.414489i	$-0.136040\pi$
$223$	7.40038	+	7.40038i	0.495566	+	0.495566i	−0.414489	+	0.910055i	$0.636040\pi$
$224$		−	7.36321i		−	0.491975i
$225$	21.6357	+	35.3530i	1.44238	+	2.35686i
$226$	6.28403	+	6.28403i	0.418007	+	0.418007i
$227$	0.593113	−	0.593113i	0.0393663	−	0.0393663i	−0.687150	−	0.726516i	$-0.741138\pi$
$227$	0.593113	−	0.593113i	0.0393663	−	0.0393663i	0.726516	+	0.687150i	$0.241138\pi$
$228$	−7.66199	−	4.29389i	−0.507428	−	0.284370i
$229$	−9.80717	+	9.80717i	−0.648076	+	0.648076i	−0.952528	−	0.304452i	$-0.901527\pi$
$229$	−9.80717	+	9.80717i	−0.648076	+	0.648076i	0.304452	+	0.952528i	$0.401527\pi$
$230$			15.3036i			1.00909i
$231$	−1.27135	−	4.51294i	−0.0836485	−	0.296930i
$232$	−2.83000	+	2.83000i	−0.185799	+	0.185799i
$233$	8.97337			0.587865			0.293932	−	0.955826i	$-0.405036\pi$
$233$	8.97337			0.587865			0.293932	+	0.955826i	$0.405036\pi$
$234$	−15.8450	+	13.1830i	−1.03582	+	0.861797i
$235$	−3.10134			−0.202309
$236$	4.06192	−	4.06192i	0.264408	−	0.264408i
$237$	3.31160	+	11.7553i	0.215112	+	0.763590i
$238$			9.93577i			0.644040i
$239$	14.9351	−	14.9351i	0.966068	−	0.966068i	−0.0333745	−	0.999443i	$-0.510625\pi$
$239$	14.9351	−	14.9351i	0.966068	−	0.966068i	0.999443	+	0.0333745i	$0.0106254\pi$
$240$	−30.1591	−	16.9016i	−1.94676	−	1.09099i
$241$	4.46955	−	4.46955i	0.287909	−	0.287909i	−0.548344	−	0.836253i	$-0.684741\pi$
$241$	4.46955	−	4.46955i	0.287909	−	0.287909i	0.836253	+	0.548344i	$0.184741\pi$
$242$	4.94829	+	4.94829i	0.318088	+	0.318088i
$243$	−15.2844	−	3.06368i	−0.980497	−	0.196535i
$244$		−	5.50974i		−	0.352725i
$245$	−3.06725	−	3.06725i	−0.195959	−	0.195959i
$246$	9.30237	−	2.62058i	0.593098	−	0.167082i
$247$	−1.61683	−	11.0911i	−0.102876	−	0.705711i
$248$		−	2.17226i		−	0.137939i
$249$	8.67123	+	4.85948i	0.549517	+	0.307957i
$250$	72.8724			4.60885
$251$	−9.06501			−0.572178			−0.286089	−	0.958203i	$-0.592355\pi$
$251$	−9.06501			−0.572178			−0.286089	+	0.958203i	$0.592355\pi$
$252$	−4.75785	−	1.14522i	−0.299716	−	0.0721423i
$253$	−3.54380	−	3.54380i	−0.222797	−	0.222797i
$254$	23.6421	+	23.6421i	1.48344	+	1.48344i
$255$	34.1735	+	19.1513i	2.14003	+	1.19930i
$256$	20.1865			1.26166
$257$	12.9051			0.805001			0.402501	−	0.915420i	$-0.368141\pi$
$257$	12.9051			0.805001			0.402501	+	0.915420i	$0.368141\pi$
$258$	5.53944	−	9.88454i	0.344870	−	0.615385i
$259$			1.87144i			0.116286i
$260$	3.68025	+	25.2458i	0.228239	+	1.56568i
$261$	8.91919	+	14.5741i	0.552084	+	0.902112i
$262$	−12.5954	−	12.5954i	−0.778146	−	0.778146i
$263$			16.3414i			1.00765i	0.863804	+	0.503827i	$0.168075\pi$
$263$			16.3414i			1.00765i	−0.863804	+	0.503827i	$0.831925\pi$
$264$	3.17121	−	0.893365i	0.195174	−	0.0549828i
$265$	−24.5106	−	24.5106i	−1.50568	−	1.50568i
$266$	4.18873	−	4.18873i	0.256828	−	0.256828i
$267$	15.4343	−	27.5409i	0.944564	−	1.68547i
$268$	14.3138	−	14.3138i	0.874353	−	0.874353i
$269$		−	15.8168i		−	0.964366i	−0.876070	−	0.482183i	$-0.839844\pi$
$269$		−	15.8168i		−	0.964366i	0.876070	−	0.482183i	$-0.160156\pi$
$270$	−29.1830	+	31.5141i	−1.77602	+	1.91789i
$271$	−17.0364	+	17.0364i	−1.03489	+	1.03489i	−0.0355174	+	0.999369i	$0.511308\pi$
$271$	−17.0364	+	17.0364i	−1.03489	+	1.03489i	−0.999369	+	0.0355174i	$0.988692\pi$
$272$	−23.9925			−1.45476
$273$	−2.54277	−	5.70389i	−0.153895	−	0.345215i
$274$	39.0613			2.35978
$275$	−26.4454	+	26.4454i	−1.59472	+	1.59472i
$276$	−5.03498	+	1.41841i	−0.303070	+	0.0853782i
$277$		−	13.6372i		−	0.819382i	−0.912224	−	0.409691i	$-0.865637\pi$
$277$		−	13.6372i		−	0.819382i	0.912224	−	0.409691i	$-0.134363\pi$
$278$	−12.3869	+	12.3869i	−0.742915	+	0.742915i
$279$	−9.01652	−	2.17029i	−0.539805	−	0.129932i
$280$	2.15533	−	2.15533i	0.128806	−	0.128806i
$281$	2.38232	+	2.38232i	0.142117	+	0.142117i	0.774586	−	0.632469i	$-0.217958\pi$
$281$	2.38232	+	2.38232i	0.142117	+	0.142117i	−0.632469	+	0.774586i	$0.717958\pi$
$282$	−0.639876	−	2.27139i	−0.0381040	−	0.135259i
$283$		−	8.78572i		−	0.522257i	−0.965304	−	0.261128i	$-0.915905\pi$
$283$		−	8.78572i		−	0.522257i	0.965304	−	0.261128i	$-0.0840946\pi$
$284$	−0.416857	−	0.416857i	−0.0247359	−	0.0247359i
$285$	−6.33308	−	22.4807i	−0.375139	−	1.33164i
$286$	−14.9108	−	11.1166i	−0.881694	−	0.657339i
$287$			2.92812i			0.172841i
$288$	5.16938	−	21.4763i	0.304608	−	1.26550i
$289$	10.1861			0.599185
$290$	47.0791			2.76458
$291$	4.80144	−	8.56766i	0.281465	−	0.502245i
$292$	−5.74552	−	5.74552i	−0.336231	−	0.336231i
$293$	18.7655	+	18.7655i	1.09629	+	1.09629i	0.994840	+	0.101453i	$0.0323491\pi$
$293$	18.7655	+	18.7655i	1.09629	+	1.09629i	0.101453	+	0.994840i	$0.467651\pi$
$294$	1.61358	−	2.87926i	0.0941056	−	0.167922i
$295$	15.2753			0.889364
$296$	−1.31505			−0.0764356
$297$	−0.539799	−	14.0554i	−0.0313223	−	0.815580i
$298$			4.29730i			0.248936i
$299$	−5.35170	−	3.98991i	−0.309497	−	0.230742i
$300$	10.5848	+	37.5733i	0.611114	+	2.16929i
$301$	2.42751	+	2.42751i	0.139919	+	0.139919i
$302$			15.3884i			0.885501i
$303$	−3.99637	−	14.1860i	−0.229585	−	0.814967i
$304$	10.1148	+	10.1148i	0.580123	+	0.580123i
$305$	10.3600	−	10.3600i	0.593213	−	0.593213i
$306$	−6.97546	+	28.9796i	−0.398760	+	1.65666i
$307$	2.44935	−	2.44935i	0.139792	−	0.139792i	−0.633748	−	0.773540i	$-0.718484\pi$
$307$	2.44935	−	2.44935i	0.139792	−	0.139792i	0.773540	+	0.633748i	$0.218484\pi$
$308$		−	4.41573i		−	0.251609i
$309$	−14.2602	+	4.01727i	−0.811236	+	0.228534i
$310$	−18.0686	+	18.0686i	−1.02623	+	1.02623i
$311$	−20.0398			−1.13635			−0.568176	−	0.822907i	$-0.692351\pi$
$311$	−20.0398			−1.13635			−0.568176	+	0.822907i	$0.692351\pi$
$312$	4.00808	−	1.78678i	0.226913	−	0.101157i
$313$	−0.485134			−0.0274214			−0.0137107	−	0.999906i	$-0.504364\pi$
$313$	−0.485134			−0.0274214			−0.0137107	+	0.999906i	$0.504364\pi$
$314$	−2.20869	+	2.20869i	−0.124643	+	0.124643i
$315$	−6.79285	−	11.0996i	−0.382734	−	0.625392i
$316$			11.5021i			0.647042i
$317$	10.8984	−	10.8984i	0.612114	−	0.612114i	−0.331383	−	0.943496i	$-0.607515\pi$
$317$	10.8984	−	10.8984i	0.612114	−	0.612114i	0.943496	+	0.331383i	$0.107515\pi$
$318$	12.8942	−	23.0084i	0.723072	−	1.29025i
$319$	−10.9020	+	10.9020i	−0.610393	+	0.610393i
$320$	−14.8091	−	14.8091i	−0.827855	−	0.827855i
$321$	28.8982	−	8.14093i	1.61294	−	0.454383i
$322$		−	3.52800i		−	0.196608i
$323$	−11.4612	−	11.4612i	−0.637716	−	0.637716i
$324$	−13.0732	−	6.68054i	−0.726288	−	0.371141i
$325$	−29.7745	+	39.9368i	−1.65159	+	2.21529i
$326$			12.5496i			0.695057i
$327$	9.92877	−	17.7169i	0.549062	−	0.979744i
$328$	−2.05757			−0.113610
$329$	0.714968			0.0394174
$330$	−33.8086	−	18.9468i	−1.86110	−	1.04299i
$331$	4.75702	+	4.75702i	0.261469	+	0.261469i	0.825651	−	0.564181i	$-0.190808\pi$
$331$	4.75702	+	4.75702i	0.261469	+	0.261469i	−0.564181	+	0.825651i	$0.690808\pi$
$332$	6.61961	+	6.61961i	0.363298	+	0.363298i
$333$	−1.31386	+	5.45843i	−0.0719988	+	0.299120i
$334$	−10.6432			−0.582368
$335$	53.8286			2.94097
$336$	6.95272	+	3.89640i	0.379302	+	0.212566i
$337$		−	1.96656i		−	0.107125i	−0.998564	−	0.0535627i	$-0.982942\pi$
$337$		−	1.96656i		−	0.107125i	0.998564	−	0.0535627i	$-0.0170577\pi$
$338$	−21.7887	−	11.7870i	−1.18515	−	0.641129i
$339$	−7.77504	+	2.19031i	−0.422282	+	0.118962i
$340$	26.0881	+	26.0881i	1.41482	+	1.41482i
$341$		−	8.36817i		−	0.453162i
$342$	15.1580	−	9.27654i	0.819650	−	0.501618i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−1.70579	+	1.70579i	−0.0919702	+	0.0919702i
$345$	−12.1344	−	6.80027i	−0.653292	−	0.366114i
$346$	14.6514	−	14.6514i	0.787662	−	0.787662i
$347$		−	26.5384i		−	1.42466i	−0.701846	−	0.712329i	$-0.747641\pi$
$347$		−	26.5384i		−	1.42466i	0.701846	−	0.712329i	$-0.252359\pi$
$348$	4.36353	+	15.4894i	0.233910	+	0.830317i
$349$	7.64767	−	7.64767i	0.409370	−	0.409370i	−0.472149	−	0.881519i	$-0.656521\pi$
$349$	7.64767	−	7.64767i	0.409370	−	0.409370i	0.881519	+	0.472149i	$0.156521\pi$
$350$	−26.3275			−1.40727
$351$	−3.41204	−	18.4217i	−0.182121	−	0.983276i
$352$	19.9320			1.06238
$353$	−1.82752	+	1.82752i	−0.0972692	+	0.0972692i	−0.754067	−	0.656798i	$-0.771911\pi$
$353$	−1.82752	+	1.82752i	−0.0972692	+	0.0972692i	0.656798	+	0.754067i	$0.271911\pi$
$354$	3.15164	+	11.1875i	0.167508	+	0.594607i
$355$		−	1.56764i		−	0.0832016i
$356$	21.0247	−	21.0247i	1.11431	−	1.11431i
$357$	−7.87818	−	4.41504i	−0.416958	−	0.233669i
$358$	−15.8650	+	15.8650i	−0.838492	+	0.838492i
$359$	−0.548224	−	0.548224i	−0.0289341	−	0.0289341i	0.692492	−	0.721426i	$-0.256513\pi$
$359$	−0.548224	−	0.548224i	−0.0289341	−	0.0289341i	−0.721426	+	0.692492i	$0.756513\pi$
$360$	7.79960	−	4.77328i	0.411075	−	0.251574i
$361$		−	9.33638i		−	0.491388i
$362$	−20.6903	−	20.6903i	−1.08746	−	1.08746i
$363$	−6.12237	+	1.72474i	−0.321341	+	0.0905254i
$364$	−0.848426	−	5.82002i	−0.0444696	−	0.305052i
$365$		−	21.6067i		−	1.13095i
$366$	9.72506	+	5.45006i	0.508337	+	0.284879i
$367$	−20.9512			−1.09364			−0.546821	−	0.837249i	$-0.684162\pi$
$367$	−20.9512			−1.09364			−0.546821	+	0.837249i	$0.684162\pi$
$368$	8.51929			0.444098
$369$	−2.05570	+	8.54043i	−0.107015	+	0.444597i
$370$	10.9384	+	10.9384i	0.568659	+	0.568659i
$371$	5.65055	+	5.65055i	0.293362	+	0.293362i
$372$	−7.61938	−	4.27000i	−0.395046	−	0.221389i
$373$	22.3102			1.15518			0.577589	−	0.816328i	$-0.303994\pi$
$373$	22.3102			1.15518			0.577589	+	0.816328i	$0.303994\pi$
$374$	−26.8958			−1.39075
$375$	−32.3815	+	57.7813i	−1.67217	+	2.98381i
$376$			0.502402i			0.0259094i
$377$	−12.2744	+	16.4637i	−0.632161	+	0.847924i
$378$	6.72770	−	7.26510i	0.346036	−	0.373676i
$379$	1.28402	+	1.28402i	0.0659556	+	0.0659556i	0.739315	−	0.673360i	$-0.235149\pi$
$379$	1.28402	+	1.28402i	0.0659556	+	0.0659556i	−0.673360	+	0.739315i	$0.735149\pi$
$380$		−	21.9965i		−	1.12839i
$381$	−29.2516	+	8.24051i	−1.49861	+	0.422174i
$382$	−10.3266	−	10.3266i	−0.528357	−	0.528357i
$383$	−12.8040	+	12.8040i	−0.654255	+	0.654255i	−0.954015	−	0.299760i	$-0.903094\pi$
$383$	−12.8040	+	12.8040i	−0.654255	+	0.654255i	0.299760	+	0.954015i	$0.403094\pi$
$384$	−4.67919	+	8.34953i	−0.238784	+	0.426085i
$385$	8.30293	−	8.30293i	0.423156	−	0.423156i
$386$		−	17.4115i		−	0.886221i
$387$	5.37607	+	8.78456i	0.273281	+	0.446544i
$388$	6.54055	−	6.54055i	0.332046	−	0.332046i
$389$	−13.7093			−0.695090			−0.347545	−	0.937663i	$-0.612985\pi$
$389$	−13.7093			−0.695090			−0.347545	+	0.937663i	$0.612985\pi$
$390$	−48.2008	−	18.4764i	−2.44074	−	0.935589i
$391$	−9.65328			−0.488187
$392$	−0.496878	+	0.496878i	−0.0250961	+	0.0250961i
$393$	15.5839	−	4.39016i	0.786104	−	0.221454i
$394$		−	26.6877i		−	1.34451i
$395$	−21.6275	+	21.6275i	−1.08820	+	1.08820i
$396$	3.10008	−	12.8793i	0.155785	−	0.647211i
$397$	18.3719	−	18.3719i	0.922062	−	0.922062i	−0.0751134	−	0.997175i	$-0.523932\pi$
$397$	18.3719	−	18.3719i	0.922062	−	0.922062i	0.997175	+	0.0751134i	$0.0239319\pi$
$398$	30.9285	+	30.9285i	1.55031	+	1.55031i
$399$	1.45999	+	5.18259i	0.0730911	+	0.259454i
$400$		−	63.5747i		−	3.17874i
$401$	7.97718	+	7.97718i	0.398361	+	0.398361i	0.877655	−	0.479294i	$-0.159107\pi$
$401$	7.97718	+	7.97718i	0.398361	+	0.398361i	−0.479294	+	0.877655i	$0.659107\pi$
$402$	11.1060	+	39.4235i	0.553918	+	1.96626i
$403$	−1.60784	−	11.0294i	−0.0800921	−	0.549415i
$404$		−	13.8804i		−	0.690578i
$405$	−12.0202	−	37.1431i	−0.597286	−	1.84566i
$406$	−10.8534			−0.538644
$407$	−5.06593			−0.251109
$408$	3.10242	−	5.53594i	0.153593	−	0.274070i
$409$	2.72430	+	2.72430i	0.134708	+	0.134708i	0.771246	−	0.636538i	$-0.219634\pi$
$409$	2.72430	+	2.72430i	0.134708	+	0.134708i	−0.636538	+	0.771246i	$0.719634\pi$
$410$	17.1145	+	17.1145i	0.845227	+	0.845227i
$411$	−17.3572	+	30.9722i	−0.856170	+	1.52774i
$412$	−13.9530			−0.687417
$413$	−3.52149			−0.173281
$414$	2.47685	−	10.2901i	0.121731	−	0.505731i
$415$			24.8938i			1.22199i
$416$	26.2708	−	3.82967i	1.28803	−	0.187765i
$417$	−4.31748	−	15.3259i	−0.211428	−	0.750513i
$418$	11.3388	+	11.3388i	0.554597	+	0.554597i
$419$		−	40.1007i		−	1.95905i	−0.201325	−	0.979525i	$-0.564525\pi$
$419$		−	40.1007i		−	1.95905i	0.201325	−	0.979525i	$-0.435475\pi$
$420$	−3.32326	−	11.7967i	−0.162158	−	0.575620i
$421$	3.47047	+	3.47047i	0.169141	+	0.169141i	0.786602	−	0.617461i	$-0.211839\pi$
$421$	3.47047	+	3.47047i	0.169141	+	0.169141i	−0.617461	+	0.786602i	$0.711839\pi$
$422$	31.9835	−	31.9835i	1.55693	−	1.55693i
$423$	2.08534	+	0.501947i	0.101393	+	0.0244055i
$424$	−3.97060	+	3.97060i	−0.192829	+	0.192829i
$425$			72.0371i			3.49431i
$426$	1.14812	−	0.323438i	0.0556266	−	0.0156706i
$427$	−2.38834	+	2.38834i	−0.115580	+	0.115580i
$428$	28.2756			1.36675
$429$	15.4402	−	6.88319i	0.745461	−	0.332323i
$430$	28.3771			1.36846
$431$	−5.62609	+	5.62609i	−0.270999	+	0.270999i	−0.829502	−	0.558503i	$-0.811376\pi$
$431$	−5.62609	+	5.62609i	−0.270999	+	0.270999i	0.558503	+	0.829502i	$0.311376\pi$
$432$	17.5435	+	16.2458i	0.844061	+	0.781627i
$433$			32.7812i			1.57537i	0.616081	+	0.787683i	$0.288719\pi$
$433$			32.7812i			1.57537i	−0.616081	+	0.787683i	$0.711281\pi$
$434$	4.16544	−	4.16544i	0.199947	−	0.199947i
$435$	−20.9200	+	37.3296i	−1.00304	+	1.78982i
$436$	13.5250	−	13.5250i	0.647732	−	0.647732i
$437$	4.06964	+	4.06964i	0.194677	+	0.194677i
$438$	15.8245	−	4.45794i	0.756124	−	0.213008i
$439$			27.9883i			1.33581i	0.744247	+	0.667905i	$0.232809\pi$
$439$			27.9883i			1.33581i	−0.744247	+	0.667905i	$0.767191\pi$
$440$	5.83440	+	5.83440i	0.278144	+	0.278144i
$441$	1.56599	+	2.55884i	0.0745709	+	0.121850i
$442$	−35.4492	+	5.16768i	−1.68615	+	0.245802i
$443$			15.3841i			0.730920i	0.930827	+	0.365460i	$0.119088\pi$
$443$			15.3841i			0.730920i	−0.930827	+	0.365460i	$0.880912\pi$
$444$	−2.58498	+	4.61263i	−0.122678	+	0.218906i
$445$	79.0659			3.74808
$446$	−19.9433			−0.944342
$447$	−3.40738	−	1.90954i	−0.161163	−	0.0903182i
$448$	3.41402	+	3.41402i	0.161297	+	0.161297i
$449$	−20.9622	−	20.9622i	−0.989267	−	0.989267i	0.0106762	−	0.999943i	$-0.496602\pi$
$449$	−20.9622	−	20.9622i	−0.989267	−	0.989267i	−0.999943	+	0.0106762i	$0.996602\pi$
$450$	−76.7894	−	18.4834i	−3.61989	−	0.871314i
$451$	−7.92632			−0.373236
$452$	−7.60755			−0.357829
$453$	−12.2016	−	6.83795i	−0.573282	−	0.321275i
$454$			1.59838i			0.0750157i
$455$	9.34814	−	12.5387i	0.438248	−	0.587826i
$456$	−3.64177	+	1.02593i	−0.170541	+	0.0480434i
$457$	−15.5233	−	15.5233i	−0.726149	−	0.726149i	0.243702	−	0.969850i	$-0.421638\pi$
$457$	−15.5233	−	15.5233i	−0.726149	−	0.726149i	−0.969850	+	0.243702i	$0.921638\pi$
$458$		−	26.4293i		−	1.23496i
$459$	−19.8787	−	18.4083i	−0.927857	−	0.859224i
$460$	−9.26337	−	9.26337i	−0.431907	−	0.431907i
$461$	1.34882	−	1.34882i	0.0628206	−	0.0628206i	−0.674998	−	0.737819i	$-0.735856\pi$
$461$	1.34882	−	1.34882i	0.0628206	−	0.0628206i	0.737819	+	0.674998i	$0.235856\pi$
$462$	7.79405	+	4.36789i	0.362612	+	0.203213i
$463$	13.9103	−	13.9103i	0.646467	−	0.646467i	−0.305671	−	0.952137i	$-0.598881\pi$
$463$	13.9103	−	13.9103i	0.646467	−	0.646467i	0.952137	+	0.305671i	$0.0988806\pi$
$464$		−	26.2083i		−	1.21669i
$465$	−6.29785	−	22.3557i	−0.292056	−	1.03672i
$466$	−12.0912	+	12.0912i	−0.560113	+	0.560113i
$467$	−4.70623			−0.217778			−0.108889	−	0.994054i	$-0.534729\pi$
$467$	−4.70623			−0.217778			−0.108889	+	0.994054i	$0.534729\pi$
$468$	1.61138	−	17.5709i	0.0744859	−	0.812215i
$469$	−12.4094			−0.573011
$470$	4.17891	−	4.17891i	0.192759	−	0.192759i
$471$	−0.769844	−	2.73274i	−0.0354725	−	0.125918i
$472$		−	2.47453i		−	0.113899i
$473$	−6.57119	+	6.57119i	−0.302144	+	0.302144i
$474$	−20.3019	−	11.3775i	−0.932498	−	0.522585i
$475$	30.3695	−	30.3695i	1.39345	−	1.39345i
$476$	−6.01420	−	6.01420i	−0.275661	−	0.275661i
$477$	12.5139	+	20.4479i	0.572974	+	0.936247i
$478$			40.2485i			1.84092i
$479$	−3.57878	−	3.57878i	−0.163518	−	0.163518i	0.620605	−	0.784123i	$-0.286887\pi$
$479$	−3.57878	−	3.57878i	−0.163518	−	0.163518i	−0.784123	+	0.620605i	$0.786887\pi$
$480$	53.2486	−	15.0007i	2.43045	−	0.684686i
$481$	−6.67701	+	0.973354i	−0.304445	+	0.0443811i
$482$			12.0450i			0.548635i
$483$	2.79739	+	1.56770i	0.127286	+	0.0713327i
$484$	−5.99048			−0.272295
$485$	24.5965			1.11687
$486$	24.7232	−	16.4669i	1.12147	−	0.746952i
$487$	−11.2967	−	11.2967i	−0.511904	−	0.511904i	0.403206	−	0.915109i	$-0.367896\pi$
$487$	−11.2967	−	11.2967i	−0.511904	−	0.511904i	−0.915109	+	0.403206i	$0.867896\pi$
$488$	−1.67827	−	1.67827i	−0.0759717	−	0.0759717i
$489$	−9.95070	−	5.57651i	−0.449986	−	0.252178i
$490$	8.26592			0.373416
$491$	12.3442			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$491$	12.3442			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$492$	−4.04454	+	7.21706i	−0.182342	+	0.325370i
$493$			29.6969i			1.33748i
$494$	17.1233	+	12.7661i	0.770415	+	0.574376i
$495$	30.0462	−	18.3880i	1.35048	−	0.826480i
$496$	10.0585	+	10.0585i	0.451642	+	0.451642i
$497$			0.361395i			0.0162108i
$498$	−18.2320	+	5.13614i	−0.816993	+	0.230156i
$499$	−3.74836	−	3.74836i	−0.167800	−	0.167800i	0.618212	−	0.786012i	$-0.287857\pi$
$499$	−3.74836	−	3.74836i	−0.167800	−	0.167800i	−0.786012	+	0.618212i	$0.787857\pi$
$500$	−44.1102	+	44.1102i	−1.97267	+	1.97267i
$501$	4.72938	−	8.43908i	0.211293	−	0.377030i
$502$	12.2146	−	12.2146i	0.545166	−	0.545166i
$503$			37.0026i			1.64986i	0.565233	+	0.824931i	$0.308786\pi$
$503$			37.0026i			1.64986i	−0.565233	+	0.824931i	$0.691214\pi$
$504$	−1.79808	+	1.10041i	−0.0800928	+	0.0490160i
$505$	26.0995	−	26.0995i	1.16141	−	1.16141i
$506$	9.55018			0.424557
$507$	19.0280	−	12.0388i	0.845065	−	0.534663i
$508$	−28.6215			−1.26987
$509$	14.3151	−	14.3151i	0.634505	−	0.634505i	−0.314690	−	0.949195i	$-0.601900\pi$
$509$	14.3151	−	14.3151i	0.634505	−	0.634505i	0.949195	+	0.314690i	$0.101900\pi$
$510$	−71.8526	+	20.2417i	−3.18169	+	0.896316i
$511$			4.98109i			0.220351i
$512$	−19.3854	+	19.3854i	−0.856722	+	0.856722i
$513$	0.619896	+	16.1410i	0.0273691	+	0.712645i
$514$	−17.3891	+	17.3891i	−0.766998	+	0.766998i
$515$	−26.2360	−	26.2360i	−1.15610	−	1.15610i
$516$	2.63013	+	9.33626i	0.115785	+	0.411006i
$517$			1.93539i			0.0851185i
$518$	−2.52168	−	2.52168i	−0.110796	−	0.110796i
$519$	5.10677	+	18.1277i	0.224162	+	0.795717i
$520$	8.81088	+	6.56886i	0.386383	+	0.288064i
$521$			25.6337i			1.12303i	0.827466	+	0.561516i	$0.189782\pi$
$521$			25.6337i			1.12303i	−0.827466	+	0.561516i	$0.810218\pi$
$522$	−31.6560	−	7.61966i	−1.38555	−	0.333504i
$523$	8.67706			0.379421			0.189711	−	0.981840i	$-0.439245\pi$
$523$	8.67706			0.379421			0.189711	+	0.981840i	$0.439245\pi$
$524$	15.2482			0.666120
$525$	11.6989	−	20.8754i	0.510580	−	0.911077i
$526$	−22.0192	−	22.0192i	−0.960084	−	0.960084i
$527$	−11.3974	−	11.3974i	−0.496479	−	0.496479i
$528$	−10.5474	+	18.8208i	−0.459018	+	0.819069i
$529$	−19.5723			−0.850970
$530$	66.0537			2.86919
$531$	−10.2711	−	2.47228i	−0.445729	−	0.107288i
$532$			5.07095i			0.219854i
$533$	−10.4471	+	1.52294i	−0.452512	+	0.0659659i
$534$	16.3130	+	57.9069i	0.705934	+	2.50588i
$535$	53.1669	+	53.1669i	2.29861	+	2.29861i
$536$		−	8.71997i		−	0.376645i
$537$	−5.52979	−	19.6293i	−0.238628	−	0.847067i
$538$	21.3123	+	21.3123i	0.918840	+	0.918840i
$539$	−1.91411	+	1.91411i	−0.0824467	+	0.0824467i
$540$	−1.41102	−	36.7405i	−0.0607205	−	1.58106i
$541$	15.1652	−	15.1652i	0.652001	−	0.652001i	−0.301473	−	0.953475i	$-0.597478\pi$
$541$	15.1652	−	15.1652i	0.652001	−	0.652001i	0.953475	+	0.301473i	$0.0974784\pi$
$542$		−	45.9114i		−	1.97206i
$543$	25.5995	−	7.21166i	1.09858	−	0.309482i
$544$	27.1473	−	27.1473i	1.16393	−	1.16393i
$545$	50.8625			2.17871
$546$	11.1120	+	4.25945i	0.475548	+	0.182288i
$547$	−16.1735			−0.691528			−0.345764	−	0.938321i	$-0.612380\pi$
$547$	−16.1735			−0.691528			−0.345764	+	0.938321i	$0.612380\pi$
$548$	−23.6441	+	23.6441i	−1.01003	+	1.01003i
$549$	−8.64282	+	5.28933i	−0.368867	+	0.225743i
$550$		−	71.2677i		−	3.03887i
$551$	12.5196	−	12.5196i	0.533355	−	0.533355i
$552$	−1.10161	+	1.96571i	−0.0468876	+	0.0836660i
$553$	4.98588	−	4.98588i	0.212021	−	0.212021i
$554$	18.3755	+	18.3755i	0.780700	+	0.780700i
$555$	−13.5337	+	3.81260i	−0.574475	+	0.161836i
$556$		−	14.9958i		−	0.635962i
$557$	18.0849	+	18.0849i	0.766283	+	0.766283i	0.977450	−	0.211167i	$-0.0677265\pi$
$557$	18.0849	+	18.0849i	0.766283	+	0.766283i	−0.211167	+	0.977450i	$0.567726\pi$
$558$	15.0737	−	9.22495i	0.638120	−	0.390523i
$559$	−7.39840	+	9.92355i	−0.312919	+	0.419721i
$560$			19.9602i			0.843474i
$561$	11.9514	−	21.3260i	0.504587	−	0.900383i
$562$	−6.42012			−0.270816
$563$	−36.8671			−1.55376			−0.776881	−	0.629647i	$-0.783199\pi$
$563$	−36.8671			−1.55376			−0.776881	+	0.629647i	$0.783199\pi$
$564$	1.76221	+	0.987568i	0.0742025	+	0.0415841i
$565$	−14.3045	−	14.3045i	−0.601796	−	0.601796i
$566$	11.8383	+	11.8383i	0.497602	+	0.497602i
$567$	2.77106	+	8.56278i	0.116374	+	0.359603i
$568$	−0.253950			−0.0106555
$569$	−36.1573			−1.51579			−0.757896	−	0.652376i	$-0.773772\pi$
$569$	−36.1573			−1.51579			−0.757896	+	0.652376i	$0.773772\pi$
$570$	38.8252	+	21.7582i	1.62621	+	0.911350i
$571$		−	26.0239i		−	1.08907i	−0.838739	−	0.544533i	$-0.816707\pi$
$571$		−	26.0239i		−	1.08907i	0.838739	−	0.544533i	$-0.183293\pi$
$572$	15.7546	−	2.29666i	0.658733	−	0.0960281i
$573$	12.7768	−	3.59938i	0.533760	−	0.150366i
$574$	−3.94549	−	3.94549i	−0.164682	−	0.164682i
$575$		−	25.5790i		−	1.06672i
$576$	7.56082	+	12.3545i	0.315034	+	0.514770i
$577$	−0.567454	−	0.567454i	−0.0236234	−	0.0236234i	0.695196	−	0.718820i	$-0.255317\pi$
$577$	−0.567454	−	0.567454i	−0.0236234	−	0.0236234i	−0.718820	+	0.695196i	$0.755317\pi$
$578$	−13.7253	+	13.7253i	−0.570898	+	0.570898i
$579$	13.8058	+	7.73694i	0.573748	+	0.321536i
$580$	−28.4974	+	28.4974i	−1.18329	+	1.18329i
$581$		−	5.73889i		−	0.238089i
$582$	5.07480	+	18.0142i	0.210357	+	0.746712i
$583$	−15.2959	+	15.2959i	−0.633489	+	0.633489i
$584$	−3.50018			−0.144838
$585$	36.0686	−	30.0088i	1.49125	−	1.24071i
$586$	−50.5712			−2.08908
$587$	−31.1600	+	31.1600i	−1.28611	+	1.28611i	−0.348983	+	0.937129i	$0.613473\pi$
$587$	−31.1600	+	31.1600i	−1.28611	+	1.28611i	−0.937129	+	0.348983i	$0.886527\pi$
$588$	0.766127	+	2.71955i	0.0315945	+	0.112152i
$589$			9.60987i			0.395968i
$590$	−20.5827	+	20.5827i	−0.847378	+	0.847378i
$591$	21.1610	+	11.8589i	0.870445	+	0.487810i
$592$	6.08925	−	6.08925i	0.250267	−	0.250267i
$593$	−5.43836	−	5.43836i	−0.223327	−	0.223327i	0.586571	−	0.809898i	$-0.300478\pi$
$593$	−5.43836	−	5.43836i	−0.223327	−	0.223327i	−0.809898	+	0.586571i	$0.800478\pi$
$594$	19.6664	+	18.2117i	0.806921	+	0.747234i
$595$		−	22.6171i		−	0.927212i
$596$	−2.60119	−	2.60119i	−0.106549	−	0.106549i
$597$	−38.2669	+	10.7802i	−1.56616	+	0.441205i
$598$	12.5873	−	1.83495i	0.514735	−	0.0750365i
$599$		−	5.52891i		−	0.225905i	−0.993600	−	0.112952i	$-0.963969\pi$
$599$		−	5.52891i		−	0.225905i	0.993600	−	0.112952i	$-0.0360308\pi$
$600$	14.6690	+	8.22070i	0.598858	+	0.335608i
$601$	5.76977			0.235354			0.117677	−	0.993052i	$-0.462455\pi$
$601$	5.76977			0.235354			0.117677	+	0.993052i	$0.462455\pi$
$602$	−6.54190			−0.266628
$603$	−36.1944	−	8.71206i	−1.47395	−	0.354782i
$604$	−9.31470	−	9.31470i	−0.379010	−	0.379010i
$605$	−11.2640	−	11.2640i	−0.457945	−	0.457945i
$606$	24.4999	+	13.7301i	0.995240	+	0.557747i
$607$	40.6265			1.64898			0.824490	−	0.565877i	$-0.191462\pi$
$607$	40.6265			1.64898			0.824490	+	0.565877i	$0.191462\pi$
$608$	−22.8895			−0.928294
$609$	4.82279	−	8.60576i	0.195429	−	0.348723i
$610$			27.9192i			1.13042i
$611$	0.371861	+	2.55089i	0.0150439	+	0.103198i
$612$	−13.3193	−	21.7639i	−0.538401	−	0.879754i
$613$	−4.36092	−	4.36092i	−0.176136	−	0.176136i	0.613533	−	0.789669i	$-0.289748\pi$
$613$	−4.36092	−	4.36092i	−0.176136	−	0.176136i	−0.789669	+	0.613533i	$0.789748\pi$
$614$			6.60074i			0.266384i
$615$	−21.1753	+	5.96532i	−0.853870	+	0.240545i
$616$	−1.34503	−	1.34503i	−0.0541929	−	0.0541929i
$617$	−18.7195	+	18.7195i	−0.753618	+	0.753618i	−0.975153	−	0.221534i	$-0.928894\pi$
$617$	−18.7195	+	18.7195i	−0.753618	+	0.753618i	0.221534	+	0.975153i	$0.428894\pi$
$618$	13.8019	−	24.6280i	0.555193	−	0.990684i
$619$	−11.3362	+	11.3362i	−0.455640	+	0.455640i	−0.897221	−	0.441581i	$-0.854418\pi$
$619$	−11.3362	+	11.3362i	−0.455640	+	0.455640i	0.441581	+	0.897221i	$0.354418\pi$
$620$		−	21.8741i		−	0.878486i
$621$	7.05854	+	6.53642i	0.283249	+	0.262298i
$622$	27.0026	−	27.0026i	1.08271	−	1.08271i
$623$	−18.2274			−0.730267
$624$	−10.2856	+	26.8327i	−0.411752	+	1.07417i
$625$	−96.8018			−3.87207
$626$	0.653694	−	0.653694i	0.0261269	−	0.0261269i
$627$	−14.0291	+	3.95215i	−0.560268	+	0.157834i
$628$		−	2.67387i		−	0.106699i
$629$	−6.89978	+	6.89978i	−0.275112	+	0.275112i
$630$	24.1092	+	5.80313i	0.960533	+	0.231202i
$631$	13.1506	−	13.1506i	0.523518	−	0.523518i	−0.395114	−	0.918632i	$-0.629295\pi$
$631$	13.1506	−	13.1506i	0.523518	−	0.523518i	0.918632	+	0.395114i	$0.129295\pi$
$632$	3.50354	+	3.50354i	0.139363	+	0.139363i
$633$	11.1479	+	39.5722i	0.443091	+	1.57286i
$634$			29.3701i			1.16643i
$635$	−53.8173	−	53.8173i	−2.13567	−	2.13567i
$636$	6.12219	+	21.7321i	0.242760	+	0.861735i
$637$	−2.15507	+	2.89062i	−0.0853870	+	0.114530i
$638$		−	29.3797i		−	1.16315i
$639$	−0.253719	+	1.05408i	−0.0100370	+	0.0416988i
$640$	−23.9703			−0.947509
$641$	−2.51172			−0.0992069			−0.0496035	−	0.998769i	$-0.515796\pi$
$641$	−2.51172			−0.0992069			−0.0496035	+	0.998769i	$0.515796\pi$
$642$	−27.9693	+	49.9083i	−1.10386	+	1.96972i
$643$	20.1416	+	20.1416i	0.794305	+	0.794305i	0.982191	−	0.187886i	$-0.0601634\pi$
$643$	20.1416	+	20.1416i	0.794305	+	0.794305i	−0.187886	+	0.982191i	$0.560163\pi$
$644$	2.13553	+	2.13553i	0.0841516	+	0.0841516i
$645$	−12.6096	+	22.5005i	−0.496503	+	0.885957i
$646$	30.8867			1.21522
$647$	19.8693			0.781143			0.390572	−	0.920572i	$-0.372277\pi$
$647$	19.8693			0.781143			0.390572	+	0.920572i	$0.372277\pi$
$648$	−6.01700	+	1.94720i	−0.236370	+	0.0764934i
$649$		−	9.53256i		−	0.374186i
$650$	−13.6932	−	93.9324i	−0.537091	−	3.68433i
$651$	1.45187	+	5.15377i	0.0569034	+	0.201992i
$652$	−7.59636	−	7.59636i	−0.297496	−	0.297496i
$653$			4.00796i			0.156844i	0.996920	+	0.0784219i	$0.0249881\pi$
$653$			4.00796i			0.156844i	−0.996920	+	0.0784219i	$0.975012\pi$
$654$	10.4941	+	37.2511i	0.410350	+	1.45663i
$655$	28.6713	+	28.6713i	1.12028	+	1.12028i
$656$	9.52743	−	9.52743i	0.371984	−	0.371984i
$657$	−3.49700	+	14.5283i	−0.136431	+	0.566805i
$658$	−0.963384	+	0.963384i	−0.0375566	+	0.0375566i
$659$			14.3364i			0.558466i	0.960223	+	0.279233i	$0.0900803\pi$
$659$			14.3364i			0.558466i	−0.960223	+	0.279233i	$0.909920\pi$
$660$	31.9332	−	8.99595i	1.24300	−	0.350167i
$661$	−14.5263	+	14.5263i	−0.565009	+	0.565009i	−0.930726	−	0.365717i	$-0.880824\pi$
$661$	−14.5263	+	14.5263i	−0.565009	+	0.565009i	0.365717	+	0.930726i	$0.380824\pi$
$662$	−12.8197			−0.498251
$663$	11.6547	−	30.4044i	0.452630	−	1.18081i
$664$	4.03267			0.156498
$665$	−9.53495	+	9.53495i	−0.369750	+	0.369750i
$666$	−5.58461	−	9.12532i	−0.216399	−	0.353599i
$667$		−	10.5448i		−	0.408296i
$668$	6.44239	−	6.44239i	0.249264	−	0.249264i
$669$	8.86197	−	15.8133i	0.342624	−	0.611376i
$670$	−72.5314	+	72.5314i	−2.80213	+	2.80213i
$671$	−6.46517	−	6.46517i	−0.249585	−	0.249585i
$672$	−12.2756	+	3.45819i	−0.473543	+	0.133402i
$673$			34.3678i			1.32478i	0.749158	+	0.662391i	$0.230458\pi$
$673$			34.3678i			1.32478i	−0.749158	+	0.662391i	$0.769542\pi$
$674$	2.64984	+	2.64984i	0.102068	+	0.102068i
$675$	48.7777	−	52.6739i	1.87745	−	2.02742i
$676$	20.3236	−	6.05409i	0.781679	−	0.232850i
$677$			37.1327i			1.42713i	0.700591	+	0.713563i	$0.252920\pi$
$677$			37.1327i			1.42713i	−0.700591	+	0.713563i	$0.747080\pi$
$678$	7.52514	−	13.4278i	0.289001	−	0.515692i
$679$	−5.67035			−0.217608
$680$	15.8929			0.609464
$681$	−1.26737	−	0.710254i	−0.0485659	−	0.0272170i
$682$	11.2757	+	11.2757i	0.431769	+	0.431769i
$683$	29.6505	+	29.6505i	1.13454	+	1.13454i	0.989412	+	0.145131i	$0.0463604\pi$
$683$	29.6505	+	29.6505i	1.13454	+	1.13454i	0.145131	+	0.989412i	$0.453640\pi$
$684$	−3.56008	+	14.7904i	−0.136123	+	0.565526i
$685$	−88.9166			−3.39733
$686$	−1.90558			−0.0727555
$687$	20.9561	+	11.7441i	0.799526	+	0.448066i
$688$		−	15.7971i		−	0.602260i
$689$	−17.2214	+	23.0992i	−0.656082	+	0.880008i
$690$	25.5135	−	7.18743i	0.971282	−	0.273621i
$691$	−26.1045	−	26.1045i	−0.993064	−	0.993064i	0.00691223	−	0.999976i	$-0.497800\pi$
$691$	−26.1045	−	26.1045i	−0.993064	−	0.993064i	−0.999976	+	0.00691223i	$0.997800\pi$
$692$			17.7372i			0.674266i
$693$	−6.92670	+	4.23908i	−0.263124	+	0.161029i
$694$	35.7592	+	35.7592i	1.35740	+	1.35740i
$695$	28.1967	−	28.1967i	1.06956	−	1.06956i
$696$	6.04720	+	3.38894i	0.229219	+	0.128457i
$697$	−10.7956	+	10.7956i	−0.408913	+	0.408913i
$698$			20.6097i			0.780089i
$699$	−4.21441	−	14.9600i	−0.159404	−	0.565841i
$700$	15.9363	−	15.9363i	0.602334	−	0.602334i
$701$	51.3273			1.93860			0.969302	−	0.245874i	$-0.0790749\pi$
$701$	51.3273			1.93860			0.969302	+	0.245874i	$0.0790749\pi$
$702$	29.4198	+	20.2247i	1.11038	+	0.763333i
$703$	5.81763			0.219416
$704$	−9.24163	+	9.24163i	−0.348307	+	0.348307i
$705$	1.45657	+	5.17044i	0.0548576	+	0.194730i
$706$		−	4.92499i		−	0.185355i
$707$	−6.01685	+	6.01685i	−0.226287	+	0.226287i
$708$	−8.67958	−	4.86416i	−0.326199	−	0.182806i
$709$	−33.7913	+	33.7913i	−1.26906	+	1.26906i	−0.322484	+	0.946575i	$0.604518\pi$
$709$	−33.7913	+	33.7913i	−1.26906	+	1.26906i	−0.946575	+	0.322484i	$0.895482\pi$
$710$	2.11232	+	2.11232i	0.0792738	+	0.0792738i
$711$	18.0427	−	11.0419i	0.676653	−	0.414105i
$712$		−	12.8083i		−	0.480010i
$713$	4.04700	+	4.04700i	0.151562	+	0.151562i
$714$	16.5645	−	4.66641i	0.619912	−	0.174636i
$715$	33.9420	+	25.3051i	1.26936	+	0.946357i
$716$		−	19.2064i		−	0.717778i
$717$	−31.9135	−	17.8848i	−1.19183	−	0.667919i
$718$	1.47741			0.0551364
$719$	10.5110			0.391995			0.195997	−	0.980604i	$-0.437206\pi$
$719$	10.5110			0.391995			0.195997	+	0.980604i	$0.437206\pi$
$720$	−14.0132	+	58.2180i	−0.522240	+	2.16966i
$721$	6.04831	+	6.04831i	0.225251	+	0.225251i
$722$	12.5803	+	12.5803i	0.468191	+	0.468191i
$723$	−9.55062	−	5.35230i	−0.355191	−	0.199054i
$724$	25.0480			0.930902
$725$	−78.6899			−2.92247
$726$	5.92559	−	10.5736i	0.219919	−	0.392423i
$727$		−	20.4732i		−	0.759310i	−0.925128	−	0.379655i	$-0.876043\pi$
$727$		−	20.4732i		−	0.759310i	0.925128	−	0.379655i	$-0.123957\pi$
$728$	−2.03121	−	1.51435i	−0.0752818	−	0.0561256i
$729$	2.07081	+	26.9205i	0.0766968	+	0.997054i
$730$	29.1140	+	29.1140i	1.07756	+	1.07756i
$731$			17.8999i			0.662051i
$732$	−9.18562	+	2.58769i	−0.339510	+	0.0956438i
$733$	30.2386	+	30.2386i	1.11689	+	1.11689i	0.992195	+	0.124693i	$0.0397946\pi$
$733$	30.2386	+	30.2386i	1.11689	+	1.11689i	0.124693	+	0.992195i	$0.460205\pi$
$734$	28.2307	−	28.2307i	1.04201	−	1.04201i
$735$	−3.67303	+	6.55414i	−0.135482	+	0.241753i
$736$	−9.63947	+	9.63947i	−0.355316	+	0.355316i
$737$		−	33.5917i		−	1.23737i
$738$	−8.73786	−	14.2778i	−0.321645	−	0.525572i
$739$	−18.1135	+	18.1135i	−0.666318	+	0.666318i	−0.956862	−	0.290544i	$-0.906164\pi$
$739$	−18.1135	+	18.1135i	−0.666318	+	0.666318i	0.290544	+	0.956862i	$0.406164\pi$
$740$	−13.2422			−0.486792
$741$	−17.7313	+	7.90454i	−0.651376	+	0.290381i
$742$	−15.2277			−0.559026
$743$	32.8599	−	32.8599i	1.20551	−	1.20551i	0.233047	−	0.972465i	$-0.425130\pi$
$743$	32.8599	−	32.8599i	1.20551	−	1.20551i	0.972465	−	0.233047i	$-0.0748697\pi$
$744$	−3.62151	+	1.02022i	−0.132771	+	0.0374031i
$745$		−	9.78208i		−	0.358388i
$746$	−30.0619	+	30.0619i	−1.10064	+	1.10064i
$747$	4.02902	−	16.7386i	0.147414	−	0.612434i
$748$	16.2802	−	16.2802i	0.595265	−	0.595265i
$749$	−12.2568	−	12.2568i	−0.447855	−	0.447855i
$750$	−34.2251	−	121.490i	−1.24972	−	4.43618i
$751$		−	11.9844i		−	0.437318i	−0.975801	−	0.218659i	$-0.929832\pi$
$751$		−	11.9844i		−	0.437318i	0.975801	−	0.218659i	$-0.0701682\pi$
$752$	−2.32634	−	2.32634i	−0.0848330	−	0.0848330i
$753$	4.25745	+	15.1128i	0.155150	+	0.550742i
$754$	−5.64494	−	38.7231i	−0.205577	−	1.41021i
$755$		−	35.0290i		−	1.27484i
$756$	0.325288	+	8.46996i	0.0118306	+	0.308049i
$757$	−14.5754			−0.529753			−0.264876	−	0.964282i	$-0.585331\pi$
$757$	−14.5754			−0.529753			−0.264876	+	0.964282i	$0.585331\pi$
$758$	−3.46030			−0.125684
$759$	−4.24370	+	7.57245i	−0.154037	+	0.274862i
$760$	−6.70014	−	6.70014i	−0.243039	−	0.243039i
$761$	−4.68784	−	4.68784i	−0.169934	−	0.169934i	0.617016	−	0.786950i	$-0.288341\pi$
$761$	−4.68784	−	4.68784i	−0.169934	−	0.169934i	−0.786950	+	0.617016i	$0.788341\pi$
$762$	28.3115	−	50.5188i	1.02562	−	1.83010i
$763$	−11.7256			−0.424494
$764$	12.5016			0.452292
$765$	15.8785	−	65.9673i	0.574087	−	2.38505i
$766$		−	34.5056i		−	1.24674i
$767$	−1.83156	−	12.5641i	−0.0661338	−	0.453664i
$768$	−9.48075	−	33.6541i	−0.342107	−	1.21439i
$769$	−5.52357	−	5.52357i	−0.199185	−	0.199185i	0.600466	−	0.799651i	$-0.294982\pi$
$769$	−5.52357	−	5.52357i	−0.199185	−	0.199185i	−0.799651	+	0.600466i	$0.794982\pi$
$770$			22.3756i			0.806360i
$771$	−6.06100	−	21.5149i	−0.218282	−	0.774842i
$772$	10.5393	+	10.5393i	0.379318	+	0.379318i
$773$	−5.14738	+	5.14738i	−0.185138	+	0.185138i	−0.793590	−	0.608452i	$-0.791791\pi$
$773$	−5.14738	+	5.14738i	−0.185138	+	0.185138i	0.608452	+	0.793590i	$0.291791\pi$
$774$	−19.0807	−	4.59277i	−0.685843	−	0.165084i
$775$	30.2006	−	30.2006i	1.08484	−	1.08484i
$776$		−	3.98451i		−	0.143036i
$777$	3.11999	−	0.878937i	0.111929	−	0.0315317i
$778$	18.4726	−	18.4726i	0.662276	−	0.662276i
$779$	9.10246			0.326129
$780$	40.3603	−	17.9924i	1.44513	−	0.644232i
$781$	−0.978285			−0.0350058
$782$	13.0073	−	13.0073i	0.465141	−	0.465141i
$783$	20.1083	−	21.7145i	0.718613	−	0.776014i
$784$		−	4.60153i		−	0.164340i
$785$	5.02771	−	5.02771i	0.179447	−	0.179447i
$786$	−15.0830	+	26.9141i	−0.537993	+	0.959993i
$787$	16.0048	−	16.0048i	0.570509	−	0.570509i	−0.361761	−	0.932271i	$-0.617824\pi$
$787$	16.0048	−	16.0048i	0.570509	−	0.570509i	0.932271	+	0.361761i	$0.117824\pi$
$788$	16.1543	+	16.1543i	0.575472	+	0.575472i
$789$	27.2437	−	7.67487i	0.969903	−	0.273232i
$790$		−	58.2839i		−	2.07365i
$791$	3.29769	+	3.29769i	0.117252	+	0.117252i
$792$	−2.97876	−	4.86734i	−0.105846	−	0.172953i
$793$	−9.76343	−	7.27903i	−0.346710	−	0.258486i
$794$			49.5106i			1.75706i
$795$	−29.3515	+	52.3747i	−1.04099	+	1.85754i
$796$	−37.4426			−1.32712
$797$	12.3383			0.437045			0.218523	−	0.975832i	$-0.429876\pi$
$797$	12.3383			0.437045			0.218523	+	0.975832i	$0.429876\pi$
$798$	−8.95056	−	5.01602i	−0.316846	−	0.177565i
$799$	2.63600	+	2.63600i	0.0932549	+	0.0932549i
$800$	71.9340	+	71.9340i	2.54325	+	2.54325i
$801$	−53.1639	−	12.7967i	−1.87845	−	0.452148i
$802$	−21.4977			−0.759110
$803$	−13.4837			−0.475828
$804$	−30.5859	−	17.1408i	−1.07868	−	0.604509i
$805$			8.03091i			0.283052i
$806$	17.0281	+	12.6951i	0.599789	+	0.447167i
$807$	−26.3691	+	7.42847i	−0.928236	+	0.261495i
$808$	−4.22799	−	4.22799i	−0.148740	−	0.148740i
$809$		−	43.3765i		−	1.52504i	−0.646966	−	0.762519i	$-0.723962\pi$
$809$		−	43.3765i		−	1.52504i	0.646966	−	0.762519i	$-0.276038\pi$
$810$	66.2451	+	33.8519i	2.32762	+	1.18944i
$811$	−31.4263	−	31.4263i	−1.10353	−	1.10353i	−0.993982	−	0.109546i	$-0.965060\pi$
$811$	−31.4263	−	31.4263i	−1.10353	−	1.10353i	−0.109546	−	0.993982i	$-0.534940\pi$
$812$	6.56964	−	6.56964i	0.230549	−	0.230549i
$813$	36.4036	+	20.4011i	1.27673	+	0.715498i
$814$	6.82609	−	6.82609i	0.239254	−	0.239254i
$815$		−	28.5670i		−	1.00066i
$816$	11.2683	+	39.9994i	0.394468	+	1.40026i
$817$	7.54625	−	7.54625i	0.264010	−	0.264010i
$818$	−7.34171			−0.256697
$819$	−8.31506	+	6.91807i	−0.290552	+	0.241737i
$820$	−20.7191			−0.723544
$821$	18.2813	−	18.2813i	0.638021	−	0.638021i	−0.312046	−	0.950067i	$-0.601014\pi$
$821$	18.2813	−	18.2813i	0.638021	−	0.638021i	0.950067	+	0.312046i	$0.101014\pi$
$822$	−18.3455	−	65.1215i	−0.639871	−	2.27137i
$823$			38.7437i			1.35052i	0.737580	+	0.675260i	$0.235969\pi$
$823$			38.7437i			1.35052i	−0.737580	+	0.675260i	$0.764031\pi$
$824$	−4.25010	+	4.25010i	−0.148059	+	0.148059i
$825$	56.5090	+	31.6684i	1.96739	+	1.10255i
$826$	4.74504	−	4.74504i	0.165101	−	0.165101i
$827$	8.34660	+	8.34660i	0.290240	+	0.290240i	0.837175	−	0.546935i	$-0.184206\pi$
$827$	8.34660	+	8.34660i	0.290240	+	0.290240i	−0.546935	+	0.837175i	$0.684206\pi$
$828$	4.72943	+	7.72795i	0.164359	+	0.268565i
$829$		−	51.8625i		−	1.80126i	−0.434587	−	0.900630i	$-0.643106\pi$
$829$		−	51.8625i		−	1.80126i	0.434587	−	0.900630i	$-0.356894\pi$
$830$	−33.5432	−	33.5432i	−1.16430	−	1.16430i
$831$	−22.7355	+	6.40483i	−0.788684	+	0.222181i
$832$	−10.4050	+	13.9563i	−0.360729	+	0.483849i
$833$			5.21403i			0.180656i
$834$	26.4685	+	14.8333i	0.916529	+	0.513636i
$835$	24.2274			0.838423
$836$	−13.7269			−0.474754
$837$	0.616448	+	16.0513i	0.0213076	+	0.554813i
$838$	54.0338	+	54.0338i	1.86656	+	1.86656i
$839$	−1.45922	−	1.45922i	−0.0503779	−	0.0503779i	0.681469	−	0.731847i	$-0.261341\pi$
$839$	−1.45922	−	1.45922i	−0.0503779	−	0.0503779i	−0.731847	+	0.681469i	$0.761341\pi$
$840$	−4.60554	−	2.58101i	−0.158906	−	0.0890534i
$841$	−3.43949			−0.118603
$842$	−9.35258			−0.322311
$843$	2.85283	−	5.09058i	0.0982568	−	0.175329i
$844$			38.7198i			1.33279i
$845$	49.5983	+	26.8312i	1.70623	+	0.923020i
$846$	−3.48625	+	2.13355i	−0.119860	+	0.0733530i
$847$	2.59673	+	2.59673i	0.0892248	+	0.0892248i
$848$		−	36.7712i		−	1.26273i
$849$	−14.6472	+	4.12628i	−0.502690	+	0.141614i
$850$	−97.0664	−	97.0664i	−3.32935	−	3.32935i
$851$	2.44998	−	2.44998i	0.0839842	−	0.0839842i
$852$	−0.499187	+	0.890747i	−0.0171019	+	0.0305165i
$853$	−17.3640	+	17.3640i	−0.594532	+	0.594532i	−0.938852	−	0.344320i	$-0.888109\pi$
$853$	−17.3640	+	17.3640i	−0.594532	+	0.594532i	0.344320	+	0.938852i	$0.388109\pi$
$854$		−	6.43635i		−	0.220247i
$855$	−34.5046	+	21.1165i	−1.18003	+	0.722169i
$856$	8.61277	−	8.61277i	0.294378	−	0.294378i
$857$	34.6091			1.18223			0.591113	−	0.806589i	$-0.298689\pi$
$857$	34.6091			1.18223			0.591113	+	0.806589i	$0.298689\pi$
$858$	−11.5302	+	30.0797i	−0.393634	+	1.02690i
$859$	34.9175			1.19137			0.595684	−	0.803219i	$-0.296881\pi$
$859$	34.9175			1.19137			0.595684	+	0.803219i	$0.296881\pi$
$860$	−17.1769	+	17.1769i	−0.585727	+	0.585727i
$861$	4.88164	−	1.37521i	0.166366	−	0.0468671i
$862$		−	15.1618i		−	0.516411i
$863$	5.65263	−	5.65263i	0.192418	−	0.192418i	−0.604322	−	0.796740i	$-0.706556\pi$
$863$	5.65263	−	5.65263i	0.192418	−	0.192418i	0.796740	+	0.604322i	$0.206556\pi$
$864$	−38.2322	+	1.46830i	−1.30069	+	0.0499527i
$865$	−33.3514	+	33.3514i	−1.13398	+	1.13398i
$866$	−44.1711	−	44.1711i	−1.50100	−	1.50100i
$867$	−4.78400	−	16.9819i	−0.162473	−	0.576736i
$868$			5.04274i			0.171162i
$869$	13.4966	+	13.4966i	0.457841	+	0.457841i
$870$	−22.1111	−	78.4884i	−0.749635	−	2.66101i
$871$	−6.45423	−	44.2747i	−0.218693	−	1.50019i
$872$		−	8.23947i		−	0.279024i
$873$	−16.5387	−	3.98090i	−0.559750	−	0.134733i
$874$	−10.9673			−0.370974
$875$	38.2415			1.29280
$876$	−6.88027	+	12.2771i	−0.232463	+	0.414806i
$877$	−3.76386	−	3.76386i	−0.127097	−	0.127097i	0.640697	−	0.767794i	$-0.278645\pi$
$877$	−3.76386	−	3.76386i	−0.127097	−	0.127097i	−0.767794	+	0.640697i	$0.778645\pi$
$878$	−37.7129	−	37.7129i	−1.27275	−	1.27275i
$879$	22.4717	−	40.0985i	0.757953	−	1.35249i
$880$	−54.0317			−1.82141
$881$	−31.7400			−1.06935			−0.534674	−	0.845058i	$-0.679566\pi$
$881$	−31.7400			−1.06935			−0.534674	+	0.845058i	$0.679566\pi$
$882$	−5.55801	−	1.33782i	−0.187148	−	0.0450469i
$883$			24.0484i			0.809294i	0.914473	+	0.404647i	$0.132606\pi$
$883$			24.0484i			0.809294i	−0.914473	+	0.404647i	$0.867394\pi$
$884$	18.3297	−	24.5858i	0.616494	−	0.826909i
$885$	−7.17417	−	25.4664i	−0.241157	−	0.856044i
$886$	−20.7293	−	20.7293i	−0.696414	−	0.696414i
$887$			5.73279i			0.192488i	0.995358	+	0.0962442i	$0.0306830\pi$
$887$			5.73279i			0.192488i	−0.995358	+	0.0962442i	$0.969317\pi$
$888$	0.617622	+	2.19239i	0.0207260	+	0.0735719i
$889$	12.4067	+	12.4067i	0.416109	+	0.416109i
$890$	−106.537	+	106.537i	−3.57114	+	3.57114i
$891$	−23.1792	+	7.50118i	−0.776531	+	0.251299i
$892$	12.0718	−	12.0718i	0.404195	−	0.404195i
$893$		−	2.22257i		−	0.0743756i
$894$	7.16428	−	2.01826i	0.239610	−	0.0675007i
$895$	36.1141	−	36.1141i	1.20716	−	1.20716i
$896$	5.52598			0.184610
$897$	−4.13835	+	10.7960i	−0.138175	+	0.360469i
$898$	56.4910			1.88513
$899$	12.4500	−	12.4500i	0.415231	−	0.415231i
$900$	57.6694	−	35.2931i	1.92231	−	1.17644i
$901$			41.6658i			1.38809i
$902$	10.6803	−	10.6803i	0.355616	−	0.355616i
$903$	2.90695	−	5.18715i	0.0967373	−	0.172618i
$904$	−2.31726	+	2.31726i	−0.0770710	+	0.0770710i
$905$	47.0980	+	47.0980i	1.56559	+	1.56559i
$906$	25.6549	−	7.22726i	0.852326	−	0.240110i
$907$			36.0684i			1.19763i	0.800887	+	0.598816i	$0.204362\pi$
$907$			36.0684i			1.19763i	−0.800887	+	0.598816i	$0.795638\pi$
$908$	−0.967513	−	0.967513i	−0.0321081	−	0.0321081i
$909$	−21.7735	+	13.3252i	−0.722181	+	0.441968i
$910$	4.29918	+	29.4915i	0.142516	+	0.977634i
$911$			45.8860i			1.52027i	0.649765	+	0.760135i	$0.274867\pi$
$911$			45.8860i			1.52027i	−0.649765	+	0.760135i	$0.725133\pi$
$912$	12.1125	−	21.6135i	0.401085	−	0.715694i
$913$	15.5350			0.514133
$914$	41.8337			1.38374
$915$	−22.1375	−	12.4061i	−0.731842	−	0.410135i
$916$	15.9979	+	15.9979i	0.528586	+	0.528586i
$917$	−6.60973	−	6.60973i	−0.218273	−	0.218273i
$918$	51.5897	−	1.98130i	1.70272	−	0.0653927i
$919$	−32.2433			−1.06361			−0.531804	−	0.846868i	$-0.678486\pi$
$919$	−32.2433			−1.06361			−0.531804	+	0.846868i	$0.678486\pi$
$920$	−5.64325			−0.186053
$921$	−5.23380	−	2.93310i	−0.172460	−	0.0966488i
$922$			3.63493i			0.119710i
$923$	−1.28940	+	0.187965i	−0.0424411	+	0.00618694i
$924$	−7.36172	+	2.07388i	−0.242183	+	0.0682256i
$925$	−18.2828	−	18.2828i	−0.601136	−	0.601136i
$926$			37.4869i			1.23190i
$927$	13.3948	+	21.8873i	0.439944	+	0.718875i
$928$	29.6544	+	29.6544i	0.973454	+	0.973454i
$929$	19.4935	−	19.4935i	0.639560	−	0.639560i	−0.310887	−	0.950447i	$-0.600626\pi$
$929$	19.4935	−	19.4935i	0.639560	−	0.639560i	0.950447	+	0.310887i	$0.100626\pi$
$930$	38.6093	+	21.6372i	1.26605	+	0.709511i
$931$	2.19814	−	2.19814i	0.0720411	−	0.0720411i
$932$		−	14.6378i		−	0.479476i
$933$	9.41184	+	33.4095i	0.308130	+	1.09378i
$934$	6.34141	−	6.34141i	0.207497	−	0.207497i
$935$	61.2238			2.00223
$936$	−4.86128	−	5.84293i	−0.158896	−	0.190982i
$937$	41.8804			1.36817			0.684086	−	0.729401i	$-0.260201\pi$
$937$	41.8804			1.36817			0.684086	+	0.729401i	$0.260201\pi$
$938$	16.7210	−	16.7210i	0.545960	−	0.545960i
$939$	0.227847	+	0.808796i	0.00743550	+	0.0263941i
$940$			5.05906i			0.165008i
$941$	37.1832	−	37.1832i	1.21214	−	1.21214i	0.241814	−	0.970323i	$-0.422257\pi$
$941$	37.1832	−	37.1832i	1.21214	−	1.21214i	0.970323	−	0.241814i	$-0.0777425\pi$
$942$	4.71956	+	2.64491i	0.153772	+	0.0861758i
$943$	3.83332	−	3.83332i	0.124830	−	0.124830i
$944$	11.4581	+	11.4581i	0.372931	+	0.372931i
$945$	−15.3145	+	16.5378i	−0.498181	+	0.537974i
$946$		−	17.7087i		−	0.575760i
$947$	−3.11531	−	3.11531i	−0.101234	−	0.101234i	0.654676	−	0.755910i	$-0.272805\pi$
$947$	−3.11531	−	3.11531i	−0.101234	−	0.101234i	−0.755910	+	0.654676i	$0.772805\pi$
$948$	19.1758	−	5.40204i	0.622801	−	0.175450i
$949$	−17.7718	+	2.59071i	−0.576896	+	0.0840981i
$950$			81.8427i			2.65533i
$951$	−23.2878	−	13.0508i	−0.755160	−	0.423202i
$952$	−3.66386			−0.118746
$953$	−30.3418			−0.982868			−0.491434	−	0.870915i	$-0.663527\pi$
$953$	−30.3418			−0.982868			−0.491434	+	0.870915i	$0.663527\pi$
$954$	−44.4145	−	10.6907i	−1.43797	−	0.346123i
$955$	23.5069	+	23.5069i	0.760664	+	0.760664i
$956$	−24.3627	−	24.3627i	−0.787947	−	0.787947i
$957$	23.2955	+	13.0551i	0.753037	+	0.422012i
$958$	9.64445			0.311598
$959$	20.4984			0.661927
$960$	−17.7340	+	31.6444i	−0.572361	+	1.02132i
$961$		−	21.4436i		−	0.691728i
$962$	7.68539	−	10.3085i	0.247787	−	0.332359i
$963$	−27.1445	−	44.3544i	−0.874718	−	1.42930i
$964$	−7.29094	−	7.29094i	−0.234825	−	0.234825i
$965$			39.6343i			1.27587i
$966$	−5.88174	+	1.65695i	−0.189242	+	0.0533116i
$967$	25.2582	+	25.2582i	0.812247	+	0.812247i	0.984970	−	0.172723i	$-0.0552566\pi$
$967$	25.2582	+	25.2582i	0.812247	+	0.812247i	−0.172723	+	0.984970i	$0.555257\pi$
$968$	−1.82470	+	1.82470i	−0.0586482	+	0.0586482i
$969$	−13.7248	+	24.4904i	−0.440903	+	0.786745i
$970$	−33.1426	+	33.1426i	−1.06414	+	1.06414i
$971$		−	6.75561i		−	0.216798i	−0.994107	−	0.108399i	$-0.965428\pi$
$971$		−	6.75561i		−	0.216798i	0.994107	−	0.108399i	$-0.0345724\pi$
$972$	−4.99761	+	24.9327i	−0.160298	+	0.799716i
$973$	−6.50031	+	6.50031i	−0.208390	+	0.208390i
$974$	30.4436			0.975475
$975$	80.5647	+	30.8822i	2.58014	+	0.989022i
$976$	15.5423			0.497495
$977$	4.21510	−	4.21510i	0.134853	−	0.134853i	−0.636458	−	0.771311i	$-0.719601\pi$
$977$	4.21510	−	4.21510i	0.134853	−	0.134853i	0.771311	+	0.636458i	$0.219601\pi$
$978$	20.9221	−	5.89400i	0.669016	−	0.188469i
$979$		−	49.3410i		−	1.57695i
$980$	−5.00343	+	5.00343i	−0.159829	+	0.159829i
$981$	−34.1999	−	8.23200i	−1.09192	−	0.262827i
$982$	−16.6332	+	16.6332i	−0.530787	+	0.530787i
$983$	19.1692	+	19.1692i	0.611402	+	0.611402i	0.943311	−	0.331909i	$-0.107693\pi$
$983$	19.1692	+	19.1692i	0.611402	+	0.611402i	−0.331909	+	0.943311i	$0.607693\pi$
$984$	0.966351	+	3.43029i	0.0308061	+	0.109354i
$985$			60.7500i			1.93566i
$986$	−40.0151	−	40.0151i	−1.27434	−	1.27434i
$987$	−0.335790	−	1.19197i	−0.0106883	−	0.0379407i
$988$	−18.0923	+	2.63745i	−0.575594	+	0.0839084i
$989$		−	6.35590i		−	0.202106i
$990$	−15.7089	+	65.2628i	−0.499261	+	2.07419i
$991$	36.0646			1.14563			0.572815	−	0.819685i	$-0.305851\pi$
$991$	36.0646			1.14563			0.572815	+	0.819685i	$0.305851\pi$
$992$	−22.7622			−0.722702
$993$	5.69654	−	10.1649i	0.180774	−	0.322573i
$994$	−0.486962	−	0.486962i	−0.0154455	−	0.0154455i
$995$	−70.4036	−	70.4036i	−2.23194	−	2.23194i
$996$	7.92700	−	14.1449i	0.251177	−	0.448198i
$997$	17.9793			0.569410			0.284705	−	0.958615i	$-0.408104\pi$
$997$	17.9793			0.569410			0.284705	+	0.958615i	$0.408104\pi$
$998$	10.1015			0.319756
$999$	9.71714	−	0.373186i	0.307437	−	0.0118071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.c.8.6	✓	48
3.2	odd	2	inner	273.2.n.c.8.19	yes	48
13.5	odd	4	inner	273.2.n.c.239.19	yes	48
39.5	even	4	inner	273.2.n.c.239.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.c.8.6	✓	48	1.1	even	1	trivial
273.2.n.c.8.19	yes	48	3.2	odd	2	inner
273.2.n.c.239.6	yes	48	39.5	even	4	inner
273.2.n.c.239.19	yes	48	13.5	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34745 + 1.34745i) q^{2} +(-0.469658 - 1.66716i) q^{3} -1.63125i q^{4} +(3.06725 - 3.06725i) q^{5} +(2.87926 + 1.61358i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.496878 - 0.496878i) q^{8} +(-2.55884 + 1.56599i) q^{9} +O(q^{10})\)	\(q+(-1.34745 + 1.34745i) q^{2} +(-0.469658 - 1.66716i) q^{3} -1.63125i q^{4} +(3.06725 - 3.06725i) q^{5} +(2.87926 + 1.61358i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.496878 - 0.496878i) q^{8} +(-2.55884 + 1.56599i) q^{9} +8.26592i q^{10} +(-1.91411 - 1.91411i) q^{11} +(-2.71955 + 0.766127i) q^{12} +(-2.89062 - 2.15507i) q^{13} -1.90558i q^{14} +(-6.55414 - 3.67303i) q^{15} +4.60153 q^{16} -5.21403 q^{17} +(1.33782 - 5.55801i) q^{18} +(2.19814 + 2.19814i) q^{19} +(-5.00343 - 5.00343i) q^{20} +(1.51096 + 0.846762i) q^{21} +5.15835 q^{22} +1.85140 q^{23} +(-0.595013 + 1.06174i) q^{24} -13.8160i q^{25} +(6.79882 - 0.991111i) q^{26} +(3.81253 + 3.53052i) q^{27} +(1.15346 + 1.15346i) q^{28} -5.69557i q^{29} +(13.7806 - 3.88215i) q^{30} +(2.18591 + 2.18591i) q^{31} +(-5.20658 + 5.20658i) q^{32} +(-2.29216 + 4.09011i) q^{33} +(7.02565 - 7.02565i) q^{34} +4.33774i q^{35} +(2.55451 + 4.17410i) q^{36} +(1.32331 - 1.32331i) q^{37} -5.92376 q^{38} +(-2.23525 + 5.83127i) q^{39} -3.04810 q^{40} +(2.07049 - 2.07049i) q^{41} +(-3.17691 + 0.894971i) q^{42} -3.43302i q^{43} +(-3.12239 + 3.12239i) q^{44} +(-3.04533 + 12.6519i) q^{45} +(-2.49467 + 2.49467i) q^{46} +(-0.505559 - 0.505559i) q^{47} +(-2.16114 - 7.67148i) q^{48} -1.00000i q^{49} +(18.6164 + 18.6164i) q^{50} +(2.44881 + 8.69263i) q^{51} +(-3.51545 + 4.71531i) q^{52} -7.99109i q^{53} +(-9.89440 + 0.379994i) q^{54} -11.7421 q^{55} +0.702692 q^{56} +(2.63228 - 4.69702i) q^{57} +(7.67450 + 7.67450i) q^{58} +(2.49007 + 2.49007i) q^{59} +(-5.99162 + 10.6914i) q^{60} +3.37763 q^{61} -5.89082 q^{62} +(0.702055 - 2.91670i) q^{63} -4.82815i q^{64} +(-15.4764 + 2.25610i) q^{65} +(-2.42266 - 8.59979i) q^{66} +(8.77475 + 8.77475i) q^{67} +8.50537i q^{68} +(-0.869525 - 3.08659i) q^{69} +(-5.84489 - 5.84489i) q^{70} +(0.255545 - 0.255545i) q^{71} +(2.04954 + 0.493328i) q^{72} +(3.52217 - 3.52217i) q^{73} +3.56619i q^{74} +(-23.0335 + 6.48879i) q^{75} +(3.58570 - 3.58570i) q^{76} +2.70697 q^{77} +(-4.84545 - 10.8692i) q^{78} -7.05110 q^{79} +(14.1140 - 14.1140i) q^{80} +(4.09536 - 8.01424i) q^{81} +5.57977i q^{82} +(-4.05801 + 4.05801i) q^{83} +(1.38128 - 2.46474i) q^{84} +(-15.9927 + 15.9927i) q^{85} +(4.62582 + 4.62582i) q^{86} +(-9.49542 + 2.67497i) q^{87} +1.90216i q^{88} +(12.8887 + 12.8887i) q^{89} +(-12.9443 - 21.1512i) q^{90} +(3.56784 - 0.520109i) q^{91} -3.02009i q^{92} +(2.61763 - 4.67089i) q^{93} +1.36243 q^{94} +13.4845 q^{95} +(11.1255 + 6.23489i) q^{96} +(4.00954 + 4.00954i) q^{97} +(1.34745 + 1.34745i) q^{98} +(7.89540 + 1.90044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{3} + 4 q^{6}+O(q^{10}) \) 48 * q + 8 * q^3 + 4 * q^6	\( 48 q + 8 q^{3} + 4 q^{6} + 8 q^{13} - 16 q^{15} - 72 q^{16} - 12 q^{18} + 40 q^{19} + 16 q^{22} + 8 q^{24} - 16 q^{27} + 44 q^{33} - 32 q^{34} - 8 q^{37} - 4 q^{39} - 48 q^{40} - 8 q^{42} + 44 q^{45} - 32 q^{46} + 80 q^{48} - 72 q^{52} + 44 q^{54} - 80 q^{55} - 52 q^{57} + 16 q^{58} + 44 q^{60} - 64 q^{61} + 24 q^{63} - 152 q^{66} + 56 q^{67} + 16 q^{70} + 16 q^{72} + 32 q^{73} + 104 q^{76} - 44 q^{78} + 8 q^{79} + 12 q^{84} - 96 q^{85} - 72 q^{87} - 8 q^{91} - 8 q^{93} + 160 q^{94} + 8 q^{96} - 32 q^{97} - 12 q^{99}+O(q^{100}) \) 48 * q + 8 * q^3 + 4 * q^6 + 8 * q^13 - 16 * q^15 - 72 * q^16 - 12 * q^18 + 40 * q^19 + 16 * q^22 + 8 * q^24 - 16 * q^27 + 44 * q^33 - 32 * q^34 - 8 * q^37 - 4 * q^39 - 48 * q^40 - 8 * q^42 + 44 * q^45 - 32 * q^46 + 80 * q^48 - 72 * q^52 + 44 * q^54 - 80 * q^55 - 52 * q^57 + 16 * q^58 + 44 * q^60 - 64 * q^61 + 24 * q^63 - 152 * q^66 + 56 * q^67 + 16 * q^70 + 16 * q^72 + 32 * q^73 + 104 * q^76 - 44 * q^78 + 8 * q^79 + 12 * q^84 - 96 * q^85 - 72 * q^87 - 8 * q^91 - 8 * q^93 + 160 * q^94 + 8 * q^96 - 32 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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