LMFDB - Embedded newform 224.2.u.c.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.631975 - 1.26515i) q^{2} +(2.91760 + 1.20851i) q^{3} +(-1.20122 - 1.59909i) q^{4} +(-0.629460 - 1.51965i) q^{5} +(3.37279 - 2.92745i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.78223 + 0.509137i) q^{8} +(4.93055 + 4.93055i) q^{9} +O(q^{10})$	\(q+(0.631975 - 1.26515i) q^{2} +(2.91760 + 1.20851i) q^{3} +(-1.20122 - 1.59909i) q^{4} +(-0.629460 - 1.51965i) q^{5} +(3.37279 - 2.92745i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.78223 + 0.509137i) q^{8} +(4.93055 + 4.93055i) q^{9} +(-2.32039 - 0.164019i) q^{10} +(-5.75610 + 2.38425i) q^{11} +(-1.57215 - 6.11717i) q^{12} +(0.0753604 - 0.181936i) q^{13} +(-0.447724 - 1.34147i) q^{14} -5.19444i q^{15} +(-1.11416 + 3.84170i) q^{16} +3.98721i q^{17} +(9.35388 - 3.12191i) q^{18} +(1.18647 - 2.86440i) q^{19} +(-1.67394 + 2.83199i) q^{20} +(2.91760 - 1.20851i) q^{21} +(-0.621266 + 8.78912i) q^{22} +(0.860956 + 0.860956i) q^{23} +(-8.73271 - 1.87688i) q^{24} +(1.62241 - 1.62241i) q^{25} +(-0.182551 - 0.210321i) q^{26} +(4.80123 + 11.5912i) q^{27} +(-1.98011 - 0.281338i) q^{28} +(5.85615 + 2.42570i) q^{29} +(-6.57175 - 3.28275i) q^{30} -5.52776 q^{31} +(4.15621 + 3.83744i) q^{32} -19.6754 q^{33} +(5.04443 + 2.51982i) q^{34} +(-1.51965 - 0.629460i) q^{35} +(1.96173 - 13.8070i) q^{36} +(-4.25158 - 10.2642i) q^{37} +(-2.87408 - 3.31130i) q^{38} +(0.439742 - 0.439742i) q^{39} +(2.52501 + 3.90753i) q^{40} +(-2.48800 - 2.48800i) q^{41} +(0.314901 - 4.45495i) q^{42} +(-1.99108 + 0.824733i) q^{43} +(10.7269 + 6.34050i) q^{44} +(4.38913 - 10.5963i) q^{45} +(1.63334 - 0.545137i) q^{46} +7.41348i q^{47} +(-7.89339 + 9.86205i) q^{48} -1.00000i q^{49} +(-1.02727 - 3.07792i) q^{50} +(-4.81857 + 11.6331i) q^{51} +(-0.381456 + 0.0980367i) q^{52} +(1.28857 - 0.533743i) q^{53} +(17.6989 + 1.25106i) q^{54} +(7.24647 + 7.24647i) q^{55} +(-1.60732 + 2.32735i) q^{56} +(6.92330 - 6.92330i) q^{57} +(6.76981 - 5.87594i) q^{58} +(0.0193914 + 0.0468150i) q^{59} +(-8.30636 + 6.23964i) q^{60} +(-11.0396 - 4.57274i) q^{61} +(-3.49340 + 6.99345i) q^{62} +6.97285 q^{63} +(7.48156 - 2.83307i) q^{64} -0.323916 q^{65} +(-12.4343 + 24.8923i) q^{66} +(3.63165 + 1.50428i) q^{67} +(6.37590 - 4.78950i) q^{68} +(1.47145 + 3.55239i) q^{69} +(-1.75674 + 1.52479i) q^{70} +(-0.181485 + 0.181485i) q^{71} +(-16.2282 - 11.2076i) q^{72} +(2.49063 + 2.49063i) q^{73} +(-15.6727 - 1.10784i) q^{74} +(6.69425 - 2.77285i) q^{75} +(-6.00564 + 1.54349i) q^{76} +(-2.38425 + 5.75610i) q^{77} +(-0.278435 - 0.834247i) q^{78} -4.65759i q^{79} +(6.53936 - 0.725061i) q^{80} +18.7021i q^{81} +(-4.72006 + 1.57535i) q^{82} +(2.03104 - 4.90335i) q^{83} +(-5.43717 - 3.21381i) q^{84} +(6.05917 - 2.50979i) q^{85} +(-0.214901 + 3.04023i) q^{86} +(14.1544 + 14.1544i) q^{87} +(14.8009 - 9.56418i) q^{88} +(5.52373 - 5.52373i) q^{89} +(-10.6321 - 12.2495i) q^{90} +(-0.0753604 - 0.181936i) q^{91} +(0.342550 - 2.41094i) q^{92} +(-16.1278 - 6.68033i) q^{93} +(9.37917 + 4.68513i) q^{94} -5.09973 q^{95} +(7.48856 + 16.2189i) q^{96} +14.4758 q^{97} +(-1.26515 - 0.631975i) q^{98} +(-40.1364 - 16.6251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.631975	−	1.26515i	0.446874	−	0.894597i
$2$	0.631975	−	1.26515i	0.446874	−	0.894597i
$3$	2.91760	+	1.20851i	1.68447	+	0.697732i	0.999524	−	0.0308571i	$-0.00982368\pi$
$3$	2.91760	+	1.20851i	1.68447	+	0.697732i	0.684951	+	0.728589i	$0.259824\pi$
$4$	−1.20122	−	1.59909i	−0.600608	−	0.799544i
$5$	−0.629460	−	1.51965i	−0.281503	−	0.679609i	0.718368	−	0.695663i	$-0.244889\pi$
$5$	−0.629460	−	1.51965i	−0.281503	−	0.679609i	−0.999871	+	0.0160546i	$0.994889\pi$
$6$	3.37279	−	2.92745i	1.37694	−	1.19513i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.78223	+	0.509137i	−0.983665	+	0.180007i
$9$	4.93055	+	4.93055i	1.64352	+	1.64352i
$10$	−2.32039	−	0.164019i	−0.733772	−	0.0518673i
$11$	−5.75610	+	2.38425i	−1.73553	+	0.718880i	−0.736426	+	0.676518i	$0.763488\pi$
$11$	−5.75610	+	2.38425i	−1.73553	+	0.718880i	−0.999102	+	0.0423620i	$0.986512\pi$
$12$	−1.57215	−	6.11717i	−0.453842	−	1.76587i
$13$	0.0753604	−	0.181936i	0.0209012	−	0.0504600i	−0.913084	−	0.407771i	$-0.866306\pi$
$13$	0.0753604	−	0.181936i	0.0209012	−	0.0504600i	0.933986	+	0.357311i	$0.116306\pi$
$14$	−0.447724	−	1.34147i	−0.119659	−	0.358523i
$15$		−	5.19444i		−	1.34120i
$16$	−1.11416	+	3.84170i	−0.278540	+	0.960425i
$17$			3.98721i			0.967041i	0.875333	+	0.483520i	$0.160642\pi$
$17$			3.98721i			0.967041i	−0.875333	+	0.483520i	$0.839358\pi$
$18$	9.35388	−	3.12191i	2.20473	−	0.735841i
$19$	1.18647	−	2.86440i	0.272196	−	0.657139i	−0.727381	−	0.686234i	$-0.759263\pi$
$19$	1.18647	−	2.86440i	0.272196	−	0.657139i	0.999577	+	0.0290951i	$0.00926257\pi$
$20$	−1.67394	+	2.83199i	−0.374304	+	0.633252i
$21$	2.91760	−	1.20851i	0.636672	−	0.263718i
$22$	−0.621266	+	8.78912i	−0.132454	+	1.87385i
$23$	0.860956	+	0.860956i	0.179522	+	0.179522i	0.791147	−	0.611626i	$-0.209484\pi$
$23$	0.860956	+	0.860956i	0.179522	+	0.179522i	−0.611626	+	0.791147i	$0.709484\pi$
$24$	−8.73271	−	1.87688i	−1.78256	−	0.383117i
$25$	1.62241	−	1.62241i	0.324483	−	0.324483i
$26$	−0.182551	−	0.210321i	−0.0358012	−	0.0412474i
$27$	4.80123	+	11.5912i	0.923996	+	2.23072i
$28$	−1.98011	−	0.281338i	−0.374206	−	0.0531678i
$29$	5.85615	+	2.42570i	1.08746	+	0.450441i	0.853120	−	0.521714i	$-0.174707\pi$
$29$	5.85615	+	2.42570i	1.08746	+	0.450441i	0.234340	+	0.972155i	$0.424707\pi$
$30$	−6.57175	−	3.28275i	−1.19983	−	0.599346i
$31$	−5.52776			−0.992814			−0.496407	−	0.868090i	$-0.665348\pi$
$31$	−5.52776			−0.992814			−0.496407	+	0.868090i	$0.665348\pi$
$32$	4.15621	+	3.83744i	0.734721	+	0.678370i
$33$	−19.6754			−3.42504
$34$	5.04443	+	2.51982i	0.865112	+	0.432145i
$35$	−1.51965	−	0.629460i	−0.256868	−	0.106398i
$36$	1.96173	−	13.8070i	0.326954	−	2.30117i
$37$	−4.25158	−	10.2642i	−0.698955	−	1.68743i	−0.725909	−	0.687790i	$-0.758581\pi$
$37$	−4.25158	−	10.2642i	−0.698955	−	1.68743i	0.0269541	−	0.999637i	$-0.491419\pi$
$38$	−2.87408	−	3.31130i	−0.466237	−	0.537164i
$39$	0.439742	−	0.439742i	0.0704152	−	0.0704152i
$40$	2.52501	+	3.90753i	0.399239	+	0.617835i
$41$	−2.48800	−	2.48800i	−0.388561	−	0.388561i	0.485613	−	0.874174i	$-0.338596\pi$
$41$	−2.48800	−	2.48800i	−0.388561	−	0.388561i	−0.874174	+	0.485613i	$0.838596\pi$
$42$	0.314901	−	4.45495i	0.0485904	−	0.687413i
$43$	−1.99108	+	0.824733i	−0.303637	+	0.125771i	−0.529300	−	0.848435i	$-0.677545\pi$
$43$	−1.99108	+	0.824733i	−0.303637	+	0.125771i	0.225663	+	0.974206i	$0.427545\pi$
$44$	10.7269	+	6.34050i	1.61715	+	0.955866i
$45$	4.38913	−	10.5963i	0.654293	−	1.57960i
$46$	1.63334	−	0.545137i	0.240823	−	0.0803761i
$47$			7.41348i			1.08137i	0.841226	+	0.540684i	$0.181834\pi$
$47$			7.41348i			1.08137i	−0.841226	+	0.540684i	$0.818166\pi$
$48$	−7.89339	+	9.86205i	−1.13931	+	1.42346i
$49$		−	1.00000i		−	0.142857i
$50$	−1.02727	−	3.07792i	−0.145279	−	0.435284i
$51$	−4.81857	+	11.6331i	−0.674735	+	1.62896i
$52$	−0.381456	+	0.0980367i	−0.0528984	+	0.0135952i
$53$	1.28857	−	0.533743i	0.176999	−	0.0733152i	−0.292424	−	0.956289i	$-0.594462\pi$
$53$	1.28857	−	0.533743i	0.176999	−	0.0733152i	0.469423	+	0.882973i	$0.344462\pi$
$54$	17.6989	+	1.25106i	2.40851	+	0.170247i
$55$	7.24647	+	7.24647i	0.977114	+	0.977114i
$56$	−1.60732	+	2.32735i	−0.214787	+	0.311005i
$57$	6.92330	−	6.92330i	0.917014	−	0.917014i
$58$	6.76981	−	5.87594i	0.888920	−	0.771549i
$59$	0.0193914	+	0.0468150i	0.00252455	+	0.00609480i	0.925137	−	0.379634i	$-0.123950\pi$
$59$	0.0193914	+	0.0468150i	0.00252455	+	0.00609480i	−0.922612	+	0.385729i	$0.873950\pi$
$60$	−8.30636	+	6.23964i	−1.07235	+	0.805534i
$61$	−11.0396	−	4.57274i	−1.41347	−	0.585479i	−0.460261	−	0.887784i	$-0.652244\pi$
$61$	−11.0396	−	4.57274i	−1.41347	−	0.585479i	−0.953211	+	0.302305i	$0.902244\pi$
$62$	−3.49340	+	6.99345i	−0.443662	+	0.888169i
$63$	6.97285			0.878497
$64$	7.48156	−	2.83307i	0.935195	−	0.354134i
$65$	−0.323916			−0.0401768
$66$	−12.4343	+	24.8923i	−1.53056	+	3.06403i
$67$	3.63165	+	1.50428i	0.443677	+	0.183777i	0.593326	−	0.804962i	$-0.297814\pi$
$67$	3.63165	+	1.50428i	0.443677	+	0.183777i	−0.149649	+	0.988739i	$0.547814\pi$
$68$	6.37590	−	4.78950i	0.773191	−	0.580812i
$69$	1.47145	+	3.55239i	0.177142	+	0.427658i
$70$	−1.75674	+	1.52479i	−0.209971	+	0.182247i
$71$	−0.181485	+	0.181485i	−0.0215383	+	0.0215383i	−0.717794	−	0.696256i	$-0.754848\pi$
$71$	−0.181485	+	0.181485i	−0.0215383	+	0.0215383i	0.696256	+	0.717794i	$0.254848\pi$
$72$	−16.2282	−	11.2076i	−1.91252	−	1.32083i
$73$	2.49063	+	2.49063i	0.291506	+	0.291506i	0.837675	−	0.546169i	$-0.183914\pi$
$73$	2.49063	+	2.49063i	0.291506	+	0.291506i	−0.546169	+	0.837675i	$0.683914\pi$
$74$	−15.6727	−	1.10784i	−1.82191	−	0.128783i
$75$	6.69425	−	2.77285i	0.772985	−	0.320181i
$76$	−6.00564	+	1.54349i	−0.688894	+	0.177050i
$77$	−2.38425	+	5.75610i	−0.271711	+	0.655968i
$78$	−0.278435	−	0.834247i	−0.0315265	−	0.0944599i
$79$		−	4.65759i		−	0.524020i	−0.965065	−	0.262010i	$-0.915615\pi$
$79$		−	4.65759i		−	0.524020i	0.965065	−	0.262010i	$-0.0843854\pi$
$80$	6.53936	−	0.725061i	0.731123	−	0.0810643i
$81$			18.7021i			2.07802i
$82$	−4.72006	+	1.57535i	−0.521243	+	0.173968i
$83$	2.03104	−	4.90335i	0.222935	−	0.538213i	−0.772351	−	0.635196i	$-0.780919\pi$
$83$	2.03104	−	4.90335i	0.222935	−	0.538213i	0.995286	+	0.0969831i	$0.0309193\pi$
$84$	−5.43717	−	3.21381i	−0.593244	−	0.350656i
$85$	6.05917	−	2.50979i	0.657209	−	0.272225i
$86$	−0.214901	+	3.04023i	−0.0231734	+	0.327836i
$87$	14.1544	+	14.1544i	1.51751	+	1.51751i
$88$	14.8009	−	9.56418i	1.57778	−	1.01954i
$89$	5.52373	−	5.52373i	0.585514	−	0.585514i	−0.350899	−	0.936413i	$-0.614124\pi$
$89$	5.52373	−	5.52373i	0.585514	−	0.585514i	0.936413	+	0.350899i	$0.114124\pi$
$90$	−10.6321	−	12.2495i	−1.12072	−	1.29121i
$91$	−0.0753604	−	0.181936i	−0.00789992	−	0.0190721i
$92$	0.342550	−	2.41094i	0.0357133	−	0.251358i
$93$	−16.1278	−	6.68033i	−1.67237	−	0.692718i
$94$	9.37917	+	4.68513i	0.967388	+	0.483234i
$95$	−5.09973			−0.523221
$96$	7.48856	+	16.2189i	0.764298	+	1.65533i
$97$	14.4758			1.46980			0.734898	−	0.678178i	$-0.237230\pi$
$97$	14.4758			1.46980			0.734898	+	0.678178i	$0.237230\pi$
$98$	−1.26515	−	0.631975i	−0.127800	−	0.0638391i
$99$	−40.1364	−	16.6251i	−4.03386	−	1.67088i
$100$	−4.54325	−	0.645512i	−0.454325	−	0.0645512i
$101$	−0.393131	−	0.949102i	−0.0391180	−	0.0944392i	0.903113	−	0.429403i	$-0.141276\pi$
$101$	−0.393131	−	0.949102i	−0.0391180	−	0.0944392i	−0.942231	+	0.334964i	$0.891276\pi$
$102$	11.6724	+	13.4480i	1.15574	+	1.33155i
$103$	−5.11797	+	5.11797i	−0.504288	+	0.504288i	−0.912768	−	0.408479i	$-0.866059\pi$
$103$	−5.11797	+	5.11797i	−0.504288	+	0.504288i	0.408479	+	0.912768i	$0.366059\pi$
$104$	−0.117039	+	0.544556i	−0.0114766	+	0.0533981i
$105$	−3.67302	−	3.67302i	−0.358450	−	0.358450i
$106$	0.139078	−	1.96755i	0.0135084	−	0.191105i
$107$	2.14692	−	0.889284i	0.207551	−	0.0859703i	−0.276486	−	0.961018i	$-0.589170\pi$
$107$	2.14692	−	0.889284i	0.207551	−	0.0859703i	0.484037	+	0.875048i	$0.339170\pi$
$108$	12.7680	−	21.6011i	1.22860	−	2.07857i
$109$	4.70861	−	11.3676i	0.451003	−	1.08882i	−0.520939	−	0.853594i	$-0.674418\pi$
$109$	4.70861	−	11.3676i	0.451003	−	1.08882i	0.971941	−	0.235223i	$-0.0755821\pi$
$110$	13.7475	−	4.58829i	1.31077	−	0.437477i
$111$		−	35.0849i		−	3.33011i
$112$	1.92866	+	3.50432i	0.182241	+	0.331127i
$113$			2.11397i			0.198865i	0.995044	+	0.0994327i	$0.0317028\pi$
$113$			2.11397i			0.198865i	−0.995044	+	0.0994327i	$0.968297\pi$
$114$	−4.38367	−	13.1344i	−0.410569	−	1.23015i
$115$	0.766415	−	1.85029i	0.0714686	−	0.172540i
$116$	−3.15560	−	12.2783i	−0.292990	−	1.14001i
$117$	1.26861	−	0.525477i	0.117283	−	0.0485804i
$118$	0.0714830	+	0.00505283i	0.00658054	+	0.000465151i
$119$	2.81938	+	2.81938i	0.258452	+	0.258452i
$120$	2.64468	+	14.4521i	0.241425	+	1.31929i
$121$	19.6698	−	19.6698i	1.78817	−	1.78817i
$122$	−12.7619	+	11.0769i	−1.15541	+	1.00285i
$123$	−4.25222	−	10.2658i	−0.383410	−	0.925633i
$124$	6.64003	+	8.83936i	0.596292	+	0.793798i
$125$	−11.0850	−	4.59156i	−0.991473	−	0.410682i
$126$	4.40667	−	8.82172i	0.392577	−	0.785901i
$127$	3.19723			0.283708			0.141854	−	0.989888i	$-0.454694\pi$
$127$	3.19723			0.283708			0.141854	+	0.989888i	$0.454694\pi$
$128$	1.14389	−	11.2557i	0.101107	−	0.994876i
$129$	−6.80587			−0.599223
$130$	−0.204707	+	0.409803i	−0.0179540	+	0.0359421i
$131$	−9.81263	−	4.06453i	−0.857334	−	0.355119i	−0.0896695	−	0.995972i	$-0.528581\pi$
$131$	−9.81263	−	4.06453i	−0.857334	−	0.355119i	−0.767664	+	0.640852i	$0.778581\pi$
$132$	23.6344	+	31.4626i	2.05711	+	2.73847i
$133$	−1.18647	−	2.86440i	−0.102880	−	0.248375i
$134$	4.19825	−	3.64392i	0.362674	−	0.314787i
$135$	14.5924	−	14.5924i	1.25591	−	1.25591i
$136$	−2.03004	−	11.0933i	−0.174074	−	0.951244i
$137$	3.70378	+	3.70378i	0.316436	+	0.316436i	0.847396	−	0.530961i	$-0.178169\pi$
$137$	3.70378	+	3.70378i	0.316436	+	0.316436i	−0.530961	+	0.847396i	$0.678169\pi$
$138$	5.42423	+	0.383416i	0.461741	+	0.0326386i
$139$	−16.6880	+	6.91241i	−1.41546	+	0.586303i	−0.953715	−	0.300711i	$-0.902776\pi$
$139$	−16.6880	+	6.91241i	−1.41546	+	0.586303i	−0.461744	+	0.887013i	$0.652776\pi$
$140$	0.818868	+	3.18617i	0.0692069	+	0.269281i
$141$	−8.95925	+	21.6295i	−0.754505	+	1.82154i
$142$	0.114912	+	0.344301i	0.00964322	+	0.0288931i
$143$			1.22692i			0.102600i
$144$	−24.4351	+	13.4483i	−2.03626	+	1.12069i
$145$		−	10.4262i		−	0.865848i
$146$	4.72503	−	1.57701i	0.391046	−	0.130514i
$147$	1.20851	−	2.91760i	0.0996760	−	0.240639i
$148$	−11.3063	+	19.1282i	−0.929374	+	1.57233i
$149$	−17.6053	+	7.29236i	−1.44228	+	0.597413i	−0.960351	−	0.278795i	$-0.910065\pi$
$149$	−17.6053	+	7.29236i	−1.44228	+	0.597413i	−0.481933	+	0.876208i	$0.660065\pi$
$150$	0.722523	−	10.2216i	0.0589937	−	0.834591i
$151$	5.85547	+	5.85547i	0.476512	+	0.476512i	0.904014	−	0.427502i	$-0.140606\pi$
$151$	5.85547	+	5.85547i	0.476512	+	0.476512i	−0.427502	+	0.904014i	$0.640606\pi$
$152$	−1.84267	+	8.57349i	−0.149460	+	0.695402i
$153$	−19.6592	+	19.6592i	−1.58935	+	1.58935i
$154$	5.77555	+	6.65415i	0.465407	+	0.536207i
$155$	3.47950	+	8.40026i	0.279480	+	0.674725i
$156$	−1.23141	−	0.174961i	−0.0985919	−	0.0140081i
$157$	10.2112	+	4.22962i	0.814943	+	0.337560i	0.750924	−	0.660388i	$-0.229608\pi$
$157$	10.2112	+	4.22962i	0.814943	+	0.337560i	0.0640187	+	0.997949i	$0.479608\pi$
$158$	−5.89256	−	2.94348i	−0.468787	−	0.234171i
$159$	4.40455			0.349304
$160$	3.21540	−	8.73150i	0.254200	−	0.690286i
$161$	1.21758			0.0959584
$162$	23.6610	+	11.8193i	1.85899	+	0.928610i
$163$	18.8888	+	7.82400i	1.47949	+	0.612823i	0.969000	−	0.247062i	$-0.0794653\pi$
$163$	18.8888	+	7.82400i	1.47949	+	0.612823i	0.510487	+	0.859886i	$0.329465\pi$
$164$	−0.989906	+	6.96717i	−0.0772986	+	0.544044i
$165$	12.3849	+	29.8997i	0.964159	+	2.32769i
$166$	−4.91992	−	5.66836i	−0.381860	−	0.439950i
$167$	−13.8476	+	13.8476i	−1.07156	+	1.07156i	−0.0743233	+	0.997234i	$0.523680\pi$
$167$	−13.8476	+	13.8476i	−1.07156	+	1.07156i	−0.997234	+	0.0743233i	$0.976320\pi$
$168$	−7.50211	+	4.84780i	−0.578801	+	0.374016i
$169$	9.16497	+	9.16497i	0.704997	+	0.704997i
$170$	0.653977	−	9.25189i	0.0501578	−	0.709588i
$171$	19.9731	−	8.27311i	1.52738	−	0.632661i
$172$	3.71054	+	2.19323i	0.282926	+	0.167232i
$173$	2.31711	−	5.59399i	0.176166	−	0.425303i	−0.810990	−	0.585060i	$-0.801071\pi$
$173$	2.31711	−	5.59399i	0.176166	−	0.425303i	0.987156	+	0.159757i	$0.0510710\pi$
$174$	26.8527	−	8.96224i	2.03570	−	0.679426i
$175$		−	2.29444i		−	0.173443i
$176$	−2.74637	−	24.7696i	−0.207015	−	1.86708i
$177$			0.160022i			0.0120280i
$178$	−3.49750	−	10.4792i	−0.262149	−	0.785450i
$179$	7.14012	−	17.2378i	0.533677	−	1.28841i	−0.395394	−	0.918511i	$-0.629392\pi$
$179$	7.14012	−	17.2378i	0.533677	−	1.28841i	0.929072	−	0.369900i	$-0.120608\pi$
$180$	−22.2167	+	5.70984i	−1.65594	+	0.425587i
$181$	1.10021	−	0.455724i	0.0817783	−	0.0338737i	−0.341419	−	0.939911i	$-0.610908\pi$
$181$	1.10021	−	0.455724i	0.0817783	−	0.0338737i	0.423198	+	0.906037i	$0.360908\pi$
$182$	−0.277803	−	0.0196367i	−0.0205921	−	0.00145557i
$183$	−26.6828	−	26.6828i	−1.97245	−	1.97245i
$184$	−2.83372	−	1.95703i	−0.208904	−	0.144274i
$185$	−12.9218	+	12.9218i	−0.950032	+	0.950032i
$186$	−18.6440	+	16.1822i	−1.36704	+	1.18654i
$187$	−9.50652	−	22.9508i	−0.695186	−	1.67833i
$188$	11.8548	−	8.90519i	0.864600	−	0.649478i
$189$	11.5912	+	4.80123i	0.843135	+	0.349238i
$190$	−3.22290	+	6.45193i	−0.233814	+	0.468072i
$191$	24.8929			1.80119			0.900594	−	0.434661i	$-0.143132\pi$
$191$	24.8929			1.80119			0.900594	+	0.434661i	$0.143132\pi$
$192$	25.2519	+	0.775769i	1.82240	+	0.0559863i
$193$	−0.323836			−0.0233102			−0.0116551	−	0.999932i	$-0.503710\pi$
$193$	−0.323836			−0.0233102			−0.0116551	+	0.999932i	$0.503710\pi$
$194$	9.14834	−	18.3141i	0.656813	−	1.31487i
$195$	−0.945056	−	0.391455i	−0.0676768	−	0.0280327i
$196$	−1.59909	+	1.20122i	−0.114221	+	0.0858011i
$197$	−0.677417	−	1.63543i	−0.0482639	−	0.116519i	0.897909	−	0.440182i	$-0.145086\pi$
$197$	−0.677417	−	1.63543i	−0.0482639	−	0.116519i	−0.946173	+	0.323662i	$0.895086\pi$
$198$	−46.3984	+	40.2721i	−3.29739	+	2.86201i
$199$	−8.39216	+	8.39216i	−0.594904	+	0.594904i	−0.938952	−	0.344048i	$-0.888202\pi$
$199$	−8.39216	+	8.39216i	−0.594904	+	0.594904i	0.344048	+	0.938952i	$0.388202\pi$
$200$	−3.68789	+	5.33995i	−0.260773	+	0.377592i
$201$	8.77776	+	8.77776i	0.619136	+	0.619136i
$202$	−1.44921	−	0.102438i	−0.101966	−	0.00720754i
$203$	5.85615	−	2.42570i	0.411021	−	0.170251i
$204$	24.3904	−	6.26851i	1.70767	−	0.438883i
$205$	−2.21480	+	5.34700i	−0.154688	+	0.373451i
$206$	3.24058	+	9.70943i	0.225782	+	0.676488i
$207$			8.48997i			0.590094i
$208$	0.614980	+	0.492218i	0.0426412	+	0.0341292i
$209$			19.3166i			1.33616i
$210$	−6.96818	+	2.32567i	−0.480850	+	0.160487i
$211$	−5.70616	+	13.7759i	−0.392828	+	0.948371i	0.596493	+	0.802618i	$0.296560\pi$
$211$	−5.70616	+	13.7759i	−0.392828	+	0.948371i	−0.989321	+	0.145753i	$0.953440\pi$
$212$	−2.40135	−	1.41939i	−0.164925	−	0.0974844i
$213$	−0.748827	+	0.310174i	−0.0513088	+	0.0212528i
$214$	0.231721	−	3.27819i	0.0158401	−	0.224092i
$215$	2.50661	+	2.50661i	0.170950	+	0.170950i
$216$	−19.2596	−	29.8048i	−1.31045	−	2.02796i
$217$	−3.90871	+	3.90871i	−0.265341	+	0.265341i
$218$	−11.4060	−	13.1411i	−0.772511	−	0.890030i
$219$	4.25670	+	10.2766i	0.287641	+	0.694427i
$220$	2.88316	−	20.2923i	0.194383	−	1.36811i
$221$	0.725418	+	0.300478i	0.0487969	+	0.0202123i
$222$	−44.3877	−	22.1728i	−2.97911	−	1.48814i
$223$	−0.469193			−0.0314195			−0.0157097	−	0.999877i	$-0.505001\pi$
$223$	−0.469193			−0.0314195			−0.0157097	+	0.999877i	$0.505001\pi$
$224$	5.65236	−	0.225405i	0.377664	−	0.0150605i
$225$	15.9988			1.06659
$226$	2.67449	+	1.33597i	0.177904	+	0.0888677i
$227$	−16.8893	−	6.99577i	−1.12098	−	0.464326i	−0.256275	−	0.966604i	$-0.582495\pi$
$227$	−16.8893	−	6.99577i	−1.12098	−	0.464326i	−0.864706	+	0.502278i	$0.832495\pi$
$228$	−19.3874	−	2.75458i	−1.28396	−	0.182427i
$229$	4.60075	+	11.1072i	0.304026	+	0.733984i	0.999875	+	0.0157961i	$0.00502825\pi$
$229$	4.60075	+	11.1072i	0.304026	+	0.733984i	−0.695849	+	0.718188i	$0.744972\pi$
$230$	−1.85654	−	2.13897i	−0.122417	−	0.141039i
$231$	−13.9126	+	13.9126i	−0.915380	+	0.915380i
$232$	−17.5281	−	3.76725i	−1.15078	−	0.247332i
$233$	6.25804	+	6.25804i	0.409978	+	0.409978i	0.881731	−	0.471753i	$-0.156379\pi$
$233$	6.25804	+	6.25804i	0.409978	+	0.409978i	−0.471753	+	0.881731i	$0.656379\pi$
$234$	0.136924	−	1.93708i	0.00895100	−	0.126631i
$235$	11.2659	−	4.66649i	0.734906	−	0.304408i
$236$	0.0515680	−	0.0872435i	0.00335679	−	0.00567907i
$237$	5.62874	−	13.5890i	0.365626	−	0.882699i
$238$	5.34873	−	1.78517i	0.346706	−	0.115715i
$239$			4.46457i			0.288789i	0.989520	+	0.144395i	$0.0461235\pi$
$239$			4.46457i			0.288789i	−0.989520	+	0.144395i	$0.953877\pi$
$240$	19.9555	+	5.78743i	1.28812	+	0.373577i
$241$		−	20.7152i		−	1.33438i	−0.744885	−	0.667192i	$-0.767496\pi$
$241$		−	20.7152i		−	1.33438i	0.744885	−	0.667192i	$-0.232504\pi$
$242$	−12.4545	−	37.3161i	−0.800604	−	2.39877i
$243$	−8.19800	+	19.7917i	−0.525902	+	1.26964i
$244$	5.94870	+	23.1461i	0.380826	+	1.48178i
$245$	−1.51965	+	0.629460i	−0.0970870	+	0.0402147i
$246$	−15.6750	−	1.10800i	−0.999404	−	0.0706437i
$247$	−0.431725	−	0.431725i	−0.0274700	−	0.0274700i
$248$	15.3795	−	2.81439i	0.976597	−	0.178714i
$249$	11.8515	−	11.8515i	0.751057	−	0.751057i
$250$	−12.8145	+	11.1225i	−0.810458	+	0.703446i
$251$	5.88475	+	14.2071i	0.371442	+	0.896741i	0.993507	+	0.113775i	$0.0362943\pi$
$251$	5.88475	+	14.2071i	0.371442	+	0.896741i	−0.622064	+	0.782966i	$0.713706\pi$
$252$	−8.37590	−	11.1502i	−0.527632	−	0.702397i
$253$	−7.00848	−	2.90301i	−0.440619	−	0.182511i
$254$	2.02057	−	4.04498i	0.126782	−	0.253805i
$255$	20.7113			1.29699
$256$	−13.5173	−	8.56054i	−0.844831	−	0.535034i
$257$	−16.7204			−1.04299			−0.521495	−	0.853254i	$-0.674626\pi$
$257$	−16.7204			−1.04299			−0.521495	+	0.853254i	$0.674626\pi$
$258$	−4.30114	+	8.61045i	−0.267777	+	0.536063i
$259$	−10.2642	−	4.25158i	−0.637788	−	0.264180i
$260$	0.389093	+	0.517970i	0.0241305	+	0.0321231i
$261$	16.9140	+	40.8341i	1.04695	+	2.52757i
$262$	−11.3436	+	9.84579i	−0.700808	+	0.608275i
$263$	1.06306	−	1.06306i	0.0655513	−	0.0655513i	−0.673571	−	0.739122i	$-0.735240\pi$
$263$	1.06306	−	1.06306i	0.0655513	−	0.0655513i	0.739122	+	0.673571i	$0.235240\pi$
$264$	54.7413	−	10.0175i	3.36909	−	0.616532i
$265$	−1.62221	−	1.62221i	−0.0996513	−	0.0996513i
$266$	−4.37372	−	0.309160i	−0.268170	−	0.0189558i
$267$	22.7915	−	9.44054i	1.39482	−	0.577752i
$268$	−1.95692	−	7.61430i	−0.119538	−	0.465117i
$269$	0.585066	−	1.41247i	0.0356721	−	0.0861200i	−0.905039	−	0.425328i	$-0.860159\pi$
$269$	0.585066	−	1.41247i	0.0356721	−	0.0861200i	0.940712	+	0.339208i	$0.110159\pi$
$270$	−9.23955	−	27.6836i	−0.562301	−	1.68477i
$271$			16.2629i			0.987900i	0.869490	+	0.493950i	$0.164447\pi$
$271$			16.2629i			0.987900i	−0.869490	+	0.493950i	$0.835553\pi$
$272$	−15.3177	−	4.44239i	−0.928770	−	0.269360i
$273$		−	0.621890i		−	0.0376385i
$274$	7.02655	−	2.34515i	0.424489	−	0.141676i
$275$	−5.47053	+	13.2070i	−0.329885	+	0.796413i
$276$	3.91306	−	6.62016i	0.235538	−	0.398487i
$277$	15.9466	−	6.60532i	0.958141	−	0.396875i	0.151856	−	0.988403i	$-0.451475\pi$
$277$	15.9466	−	6.60532i	0.958141	−	0.396875i	0.806285	+	0.591527i	$0.201475\pi$
$278$	−1.80117	+	25.4813i	−0.108027	+	1.52827i
$279$	−27.2549	−	27.2549i	−1.63171	−	1.63171i
$280$	4.54849	+	0.977589i	0.271825	+	0.0584221i
$281$	−3.53270	+	3.53270i	−0.210743	+	0.210743i	−0.804583	−	0.593840i	$-0.797611\pi$
$281$	−3.53270	+	3.53270i	−0.210743	+	0.210743i	0.593840	+	0.804583i	$0.297611\pi$
$282$	21.7026	+	25.0041i	1.29237	+	1.48897i
$283$	8.09216	+	19.5362i	0.481029	+	1.16131i	0.959121	+	0.282997i	$0.0913287\pi$
$283$	8.09216	+	19.5362i	0.481029	+	1.16131i	−0.478092	+	0.878310i	$0.658671\pi$
$284$	0.508214	+	0.0722078i	0.0301570	+	0.00428475i
$285$	−14.8790	−	6.16306i	−0.881353	−	0.365068i
$286$	1.55224	+	0.775383i	0.0917859	+	0.0458494i
$287$	−3.51857			−0.207695
$288$	1.57172	+	39.4131i	0.0926143	+	2.32244i
$289$	1.10215			0.0648323
$290$	−13.1907	−	6.58909i	−0.774585	−	0.386925i
$291$	42.2346	+	17.4941i	2.47583	+	1.02552i
$292$	0.990949	−	6.97451i	0.0579909	−	0.408152i
$293$	−10.6347	−	25.6745i	−0.621286	−	1.49992i	−0.850194	−	0.526470i	$-0.823515\pi$
$293$	−10.6347	−	25.6745i	−0.621286	−	1.49992i	0.228907	−	0.973448i	$-0.426485\pi$
$294$	−2.92745	−	3.37279i	−0.170733	−	0.196705i
$295$	0.0589364	−	0.0589364i	0.00343141	−	0.00343141i
$296$	17.0547	+	26.3927i	0.991287	+	1.53405i
$297$	−55.2726	−	55.2726i	−3.20724	−	3.20724i
$298$	−1.90017	+	26.8820i	−0.110074	+	1.55723i
$299$	0.221521	−	0.0917570i	0.0128109	−	0.00530644i
$300$	−12.4753	−	7.37390i	−0.720260	−	0.425732i
$301$	−0.824733	+	1.99108i	−0.0475368	+	0.114764i
$302$	11.1086	−	3.70755i	0.639227	−	0.213346i
$303$		−	3.24420i		−	0.186374i
$304$	9.68225	+	7.74948i	0.555315	+	0.444463i
$305$			19.6547i			1.12542i
$306$	12.4477	+	37.2959i	0.711589	+	2.13206i
$307$	−5.57127	+	13.4502i	−0.317969	+	0.767646i	0.681392	+	0.731918i	$0.261375\pi$
$307$	−5.57127	+	13.4502i	−0.317969	+	0.767646i	−0.999362	+	0.0357274i	$0.988625\pi$
$308$	12.0685	−	3.10169i	0.687667	−	0.176735i
$309$	−21.1173	+	8.74706i	−1.20132	+	0.497603i
$310$	12.8266	+	0.906656i	0.728500	+	0.0514946i
$311$	4.27224	+	4.27224i	0.242257	+	0.242257i	0.817783	−	0.575527i	$-0.195203\pi$
$311$	4.27224	+	4.27224i	0.242257	+	0.242257i	−0.575527	+	0.817783i	$0.695203\pi$
$312$	−0.999574	+	1.44735i	−0.0565897	+	0.0819402i
$313$	−11.3681	+	11.3681i	−0.642563	+	0.642563i	−0.951185	−	0.308622i	$-0.900132\pi$
$313$	−11.3681	+	11.3681i	−0.642563	+	0.642563i	0.308622	+	0.951185i	$0.400132\pi$
$314$	11.8043	−	10.2457i	0.666157	−	0.578199i
$315$	−4.38913	−	10.5963i	−0.247300	−	0.597034i
$316$	−7.44790	+	5.59477i	−0.418977	+	0.314731i
$317$	−8.38560	−	3.47343i	−0.470982	−	0.195087i	0.134552	−	0.990907i	$-0.457040\pi$
$317$	−8.38560	−	3.47343i	−0.470982	−	0.195087i	−0.605534	+	0.795819i	$0.707040\pi$
$318$	2.78357	−	5.57243i	0.156095	−	0.312486i
$319$	−39.4921			−2.21113
$320$	−9.01462	−	9.58605i	−0.503933	−	0.535877i
$321$	7.33856			0.409598
$322$	0.769477	−	1.54042i	0.0428813	−	0.0858441i
$323$	11.4210	+	4.73072i	0.635480	+	0.263224i
$324$	29.9064	−	22.4653i	1.66146	−	1.24807i
$325$	−0.172910	−	0.417442i	−0.00959132	−	0.0231555i
$326$	21.8358	−	18.9526i	1.20937	−	1.04969i
$327$	27.4756	−	27.4756i	1.51941	−	1.51941i
$328$	8.18892	+	5.65545i	0.452158	+	0.312270i
$329$	5.24212	+	5.24212i	0.289008	+	0.289008i
$330$	45.6545	+	3.22713i	2.51320	+	0.177648i
$331$	−15.5741	+	6.45099i	−0.856028	+	0.354579i	−0.767153	−	0.641464i	$-0.778327\pi$
$331$	−15.5741	+	6.45099i	−0.856028	+	0.354579i	−0.0888754	+	0.996043i	$0.528327\pi$
$332$	−10.2806	+	2.64218i	−0.564221	+	0.145009i
$333$	29.6456	−	71.5709i	1.62457	−	3.92206i
$334$	8.76796	+	26.2706i	0.479762	+	1.43746i
$335$		−	6.46573i		−	0.353261i
$336$	1.39205	+	12.5550i	0.0759427	+	0.684931i
$337$			18.7902i			1.02357i	0.859114	+	0.511784i	$0.171015\pi$
$337$			18.7902i			1.02357i	−0.859114	+	0.511784i	$0.828985\pi$
$338$	17.3871	−	5.80304i	0.945733	−	0.315644i
$339$	−2.55475	+	6.16770i	−0.138755	+	0.334984i
$340$	−11.2917	−	6.67434i	−0.612381	−	0.361967i
$341$	31.8183	−	13.1796i	1.72306	−	0.713714i
$342$	2.15573	−	30.4973i	0.116568	−	1.64911i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	5.11974	−	3.30833i	0.276038	−	0.178373i
$345$	4.47218	−	4.47218i	0.240774	−	0.240774i
$346$	−5.61289	−	6.46675i	−0.301751	−	0.347655i
$347$	−8.53942	−	20.6160i	−0.458420	−	1.10672i	−0.969037	−	0.246916i	$-0.920583\pi$
$347$	−8.53942	−	20.6160i	−0.458420	−	1.10672i	0.510617	−	0.859808i	$-0.329417\pi$
$348$	5.63163	−	39.6366i	0.301887	−	2.12475i
$349$	2.92644	+	1.21217i	0.156649	+	0.0648861i	0.459630	−	0.888110i	$-0.347982\pi$
$349$	2.92644	+	1.21217i	0.156649	+	0.0648861i	−0.302981	+	0.952997i	$0.597982\pi$
$350$	−2.90281	−	1.45003i	−0.155162	−	0.0775073i
$351$	2.47068			0.131875
$352$	−33.0730	−	12.1792i	−1.76280	−	0.649154i
$353$	−0.929161			−0.0494542			−0.0247271	−	0.999694i	$-0.507872\pi$
$353$	−0.929161			−0.0494542			−0.0247271	+	0.999694i	$0.507872\pi$
$354$	0.202452	+	0.101130i	0.0107602	+	0.00537499i
$355$	0.390032	+	0.161557i	0.0207008	+	0.00857454i
$356$	−15.4681	−	2.19773i	−0.819809	−	0.116480i
$357$	4.81857	+	11.6331i	0.255026	+	0.615687i
$358$	−17.2960	−	19.9272i	−0.914122	−	1.05318i
$359$	−17.9614	+	17.9614i	−0.947968	+	0.947968i	−0.998712	−	0.0507435i	$-0.983841\pi$
$359$	−17.9614	+	17.9614i	−0.947968	+	0.947968i	0.0507435	+	0.998712i	$0.483841\pi$
$360$	−6.81659	+	31.7160i	−0.359266	+	1.67158i
$361$	6.63795	+	6.63795i	0.349366	+	0.349366i
$362$	0.118748	−	1.67994i	0.00624127	−	0.0882959i
$363$	81.1597	−	33.6175i	4.25978	−	1.76446i
$364$	−0.200408	+	0.339053i	−0.0105042	+	0.0177712i
$365$	2.21713	−	5.35263i	0.116050	−	0.280170i
$366$	−50.6207	+	16.8949i	−2.64598	+	0.883112i
$367$		−	10.8302i		−	0.565330i	−0.959219	−	0.282665i	$-0.908782\pi$
$367$		−	10.8302i		−	0.565330i	0.959219	−	0.282665i	$-0.0912184\pi$
$368$	−4.26677	+	2.34829i	−0.222421	+	0.122413i
$369$		−	24.5345i		−	1.27721i
$370$	8.18180	+	24.5143i	0.425352	+	1.27444i
$371$	0.533743	−	1.28857i	0.0277105	−	0.0668992i
$372$	8.69048	+	33.8142i	0.450580	+	1.75319i
$373$	−7.44891	+	3.08544i	−0.385690	+	0.159758i	−0.567099	−	0.823650i	$-0.691934\pi$
$373$	−7.44891	+	3.08544i	−0.385690	+	0.159758i	0.181409	+	0.983408i	$0.441934\pi$
$374$	−35.0441	−	2.47712i	−1.81209	−	0.128089i
$375$	−26.7926	−	26.7926i	−1.38357	−	1.38357i
$376$	−3.77448	−	20.6260i	−0.194654	−	1.06370i
$377$	0.882644	−	0.882644i	0.0454585	−	0.0454585i
$378$	13.3996	−	11.6303i	0.689202	−	0.598201i
$379$	−3.80670	−	9.19018i	−0.195537	−	0.472068i	0.795451	−	0.606018i	$-0.207234\pi$
$379$	−3.80670	−	9.19018i	−0.195537	−	0.472068i	−0.990988	+	0.133950i	$0.957234\pi$
$380$	6.12588	+	8.15491i	0.314251	+	0.418338i
$381$	9.32823	+	3.86388i	0.477900	+	0.197953i
$382$	15.7317	−	31.4933i	0.804903	−	1.61134i
$383$	−11.7333			−0.599542			−0.299771	−	0.954011i	$-0.596910\pi$
$383$	−11.7333			−0.599542			−0.299771	+	0.954011i	$0.596910\pi$
$384$	16.9401	−	31.4573i	0.864469	−	1.60530i
$385$	10.2481			0.522289
$386$	−0.204656	+	0.409702i	−0.0104167	+	0.0208533i
$387$	−13.8835	−	5.75074i	−0.705739	−	0.292327i
$388$	−17.3886	−	23.1481i	−0.882771	−	1.17517i
$389$	13.5884	+	32.8053i	0.688960	+	1.66330i	0.746866	+	0.664974i	$0.231557\pi$
$389$	13.5884	+	32.8053i	0.688960	+	1.66330i	−0.0579065	+	0.998322i	$0.518443\pi$
$390$	−1.09250	+	0.948249i	−0.0553209	+	0.0480164i
$391$	−3.43281	+	3.43281i	−0.173605	+	0.173605i
$392$	0.509137	+	2.78223i	0.0257153	+	0.140524i
$393$	−23.7173	−	23.7173i	−1.19638	−	1.19638i
$394$	−2.49717	−	0.176515i	−0.125806	−	0.00889269i
$395$	−7.07792	+	2.93177i	−0.356129	+	0.147513i
$396$	21.6276	+	84.1519i	1.08683	+	4.22879i
$397$	−15.0713	+	36.3853i	−0.756406	+	1.82613i	−0.237244	+	0.971450i	$0.576244\pi$
$397$	−15.0713	+	36.3853i	−0.756406	+	1.82613i	−0.519162	+	0.854676i	$0.673756\pi$
$398$	5.31372	+	15.9210i	0.266353	+	0.798047i
$399$		−	9.79103i		−	0.490165i
$400$	4.42520	+	8.04046i	0.221260	+	0.402023i
$401$		−	20.5271i		−	1.02507i	−0.858665	−	0.512537i	$-0.828706\pi$
$401$		−	20.5271i		−	1.02507i	0.858665	−	0.512537i	$-0.171294\pi$
$402$	16.6525	−	5.55787i	0.830552	−	0.277202i
$403$	−0.416574	+	1.00570i	−0.0207510	+	0.0500974i
$404$	−1.04546	+	1.76873i	−0.0520137	+	0.0879975i
$405$	28.4207	−	11.7723i	1.41224	−	0.584968i
$406$	0.632065	−	8.94190i	0.0313689	−	0.443779i
$407$	48.9450	+	48.9450i	2.42611	+	2.42611i
$408$	7.48353	−	34.8191i	0.370490	−	1.72380i
$409$	11.0718	−	11.0718i	0.547467	−	0.547467i	−0.378240	−	0.925707i	$-0.623471\pi$
$409$	11.0718	−	11.0718i	0.547467	−	0.547467i	0.925707	+	0.378240i	$0.123471\pi$
$410$	5.36506	+	6.18122i	0.264962	+	0.305269i
$411$	6.33009	+	15.2822i	0.312241	+	0.753815i
$412$	14.3319	+	2.03629i	0.706080	+	0.100321i
$413$	0.0468150	+	0.0193914i	0.00230362	+	0.000954190i
$414$	10.7411	+	5.36545i	0.527896	+	0.263697i
$415$	−8.72984			−0.428531
$416$	1.01138	−	0.466974i	0.0495871	−	0.0228953i
$417$	−57.0426			−2.79339
$418$	24.4385	+	12.2076i	1.19532	+	0.597094i
$419$	−8.28075	−	3.43000i	−0.404541	−	0.167566i	0.171129	−	0.985249i	$-0.445259\pi$
$419$	−8.28075	−	3.43000i	−0.404541	−	0.167566i	−0.575670	+	0.817682i	$0.695259\pi$
$420$	−1.46139	+	10.2856i	−0.0713085	+	0.501884i
$421$	−2.04223	−	4.93038i	−0.0995323	−	0.240292i	0.866268	−	0.499580i	$-0.166512\pi$
$421$	−2.04223	−	4.93038i	−0.0995323	−	0.240292i	−0.965800	+	0.259288i	$0.916512\pi$
$422$	13.8224	+	15.9252i	0.672865	+	0.775225i
$423$	−36.5526	+	36.5526i	−1.77725	+	1.77725i
$424$	−3.31334	+	2.14105i	−0.160910	+	0.103979i
$425$	6.46891	+	6.46891i	0.313788	+	0.313788i
$426$	−0.0808223	+	1.14340i	−0.00391585	+	0.0553980i
$427$	−11.0396	+	4.57274i	−0.534242	+	0.221290i
$428$	−4.00096	−	2.36489i	−0.193394	−	0.114311i
$429$	−1.48274	+	3.57966i	−0.0715875	+	0.172828i
$430$	4.75536	−	1.58713i	0.229324	−	0.0765381i
$431$			5.26383i			0.253550i	0.991932	+	0.126775i	$0.0404625\pi$
$431$			5.26383i			0.253550i	−0.991932	+	0.126775i	$0.959537\pi$
$432$	−49.8792	+	5.53042i	−2.39981	+	0.266083i
$433$		−	27.8109i		−	1.33651i	−0.743933	−	0.668254i	$-0.767042\pi$
$433$		−	27.8109i		−	1.33651i	0.743933	−	0.668254i	$-0.232958\pi$
$434$	2.47491	+	7.41532i	0.118799	+	0.355947i
$435$	12.6001	−	30.4194i	0.604130	−	1.45850i
$436$	−23.8338	+	6.12545i	−1.14143	+	0.293356i
$437$	3.48763	−	1.44462i	0.166836	−	0.0691056i
$438$	15.6916	+	1.10917i	0.749771	+	0.0529982i
$439$	−8.37999	−	8.37999i	−0.399955	−	0.399955i	0.478262	−	0.878217i	$-0.341267\pi$
$439$	−8.37999	−	8.37999i	−0.399955	−	0.399955i	−0.878217	+	0.478262i	$0.841267\pi$
$440$	−23.8508	−	16.4719i	−1.13704	−	0.785265i
$441$	4.93055	−	4.93055i	0.234788	−	0.234788i
$442$	0.838596	−	0.727869i	0.0398879	−	0.0346212i
$443$	−9.51351	−	22.9676i	−0.452000	−	1.09123i	−0.971560	−	0.236792i	$-0.923904\pi$
$443$	−9.51351	−	22.9676i	−0.452000	−	1.09123i	0.519560	−	0.854434i	$-0.326096\pi$
$444$	−56.1038	+	42.1445i	−2.66257	+	2.00009i
$445$	−11.8711	−	4.91718i	−0.562745	−	0.233097i
$446$	−0.296518	+	0.593600i	−0.0140405	+	0.0281078i
$447$	−60.1780			−2.84632
$448$	3.28698	−	7.29354i	0.155295	−	0.344588i
$449$	−0.323826			−0.0152823			−0.00764115	−	0.999971i	$-0.502432\pi$
$449$	−0.323826			−0.0152823			−0.00764115	+	0.999971i	$0.502432\pi$
$450$	10.1108	−	20.2409i	0.476629	−	0.954165i
$451$	20.2532	+	8.38916i	0.953687	+	0.395030i
$452$	3.38042	−	2.53933i	0.159001	−	0.119440i
$453$	10.0075	+	24.1603i	0.470194	+	1.13515i
$454$	−19.5243	+	16.9464i	−0.916321	+	0.795332i
$455$	−0.229043	+	0.229043i	−0.0107377	+	0.0107377i
$456$	−15.7373	+	22.7871i	−0.736966	+	1.06710i
$457$	−24.7992	−	24.7992i	−1.16006	−	1.16006i	−0.984462	−	0.175595i	$-0.943815\pi$
$457$	−24.7992	−	24.7992i	−1.16006	−	1.16006i	−0.175595	−	0.984462i	$-0.556185\pi$
$458$	16.9598	+	1.19882i	0.792481	+	0.0560172i
$459$	−46.2165	+	19.1435i	−2.15720	+	0.893542i
$460$	−3.87940	+	0.997033i	−0.180878	+	0.0464869i
$461$	−15.3222	+	36.9910i	−0.713624	+	1.72284i	−0.0228829	+	0.999738i	$0.507284\pi$
$461$	−15.3222	+	36.9910i	−0.713624	+	1.72284i	−0.690741	+	0.723102i	$0.742716\pi$
$462$	8.80912	+	26.3939i	0.409837	+	1.22796i
$463$			5.19844i			0.241592i	0.992677	+	0.120796i	$0.0385447\pi$
$463$			5.19844i			0.241592i	−0.992677	+	0.120796i	$0.961455\pi$
$464$	−15.8435	+	19.7950i	−0.735516	+	0.918958i
$465$			28.7136i			1.33156i
$466$	11.8723	−	3.96245i	0.549974	−	0.183557i
$467$	8.05999	−	19.4585i	0.372972	−	0.900433i	−0.620272	−	0.784387i	$-0.712978\pi$
$467$	8.05999	−	19.4585i	0.372972	−	0.900433i	0.993244	−	0.116047i	$-0.0370222\pi$
$468$	−2.36416	−	1.39741i	−0.109284	−	0.0645955i
$469$	3.63165	−	1.50428i	0.167694	−	0.0694612i
$470$	1.21595	−	17.2022i	0.0560876	−	0.793477i
$471$	24.6806	+	24.6806i	1.13722	+	1.13722i
$472$	−0.0777866	−	0.120377i	−0.00358042	−	0.00554080i
$473$	9.49449	−	9.49449i	0.436557	−	0.436557i
$474$	−13.6349	−	15.7091i	−0.626271	−	0.721542i
$475$	−2.72229	−	6.57220i	−0.124907	−	0.301553i
$476$	1.12175	−	7.89513i	0.0514154	−	0.361873i
$477$	8.98500	+	3.72171i	0.411395	+	0.170405i
$478$	5.64836	+	2.82150i	0.258350	+	0.129052i
$479$	38.5055			1.75936			0.879681	−	0.475565i	$-0.157756\pi$
$479$	38.5055			1.75936			0.879681	+	0.475565i	$0.157756\pi$
$480$	19.9333	−	21.5892i	0.909827	−	0.985406i
$481$	−2.18783			−0.0997566
$482$	−26.2079	−	13.0915i	−1.19374	−	0.596301i
$483$	3.55239	+	1.47145i	0.161639	+	0.0669532i
$484$	−55.0815	−	7.82606i	−2.50370	−	0.355730i
$485$	−9.11194	−	21.9982i	−0.413752	−	0.998886i
$486$	19.8586	+	22.8796i	0.900804	+	1.03784i
$487$	19.8099	−	19.8099i	0.897674	−	0.897674i	−0.0975559	−	0.995230i	$-0.531102\pi$
$487$	19.8099	−	19.8099i	0.897674	−	0.897674i	0.995230	+	0.0975559i	$0.0311025\pi$
$488$	33.0427	+	7.10174i	1.49577	+	0.321480i
$489$	45.6546	+	45.6546i	2.06457	+	2.06457i
$490$	−0.164019	+	2.32039i	−0.00740961	+	0.104825i
$491$	−4.05018	+	1.67764i	−0.182782	+	0.0757108i	−0.472197	−	0.881493i	$-0.656539\pi$
$491$	−4.05018	+	1.67764i	−0.182782	+	0.0757108i	0.289416	+	0.957204i	$0.406539\pi$
$492$	−11.3080	+	19.1311i	−0.509805	+	0.862495i
$493$	−9.67177	+	23.3497i	−0.435595	+	1.05162i
$494$	−0.819037	+	0.273358i	−0.0368502	+	0.0122990i
$495$			71.4582i			3.21181i
$496$	6.15881	−	21.2360i	0.276539	−	0.953523i
$497$			0.256659i			0.0115127i
$498$	−7.50408	−	22.4838i	−0.336266	−	1.00752i
$499$	8.21812	−	19.8403i	0.367893	−	0.888173i	−0.626202	−	0.779661i	$-0.715391\pi$
$499$	8.21812	−	19.8403i	0.367893	−	0.888173i	0.994095	−	0.108512i	$-0.0346086\pi$
$500$	5.97318	+	23.2413i	0.267129	+	1.03938i
$501$	−57.1365	+	23.6667i	−2.55267	+	1.05735i
$502$	21.6931	+	1.53339i	0.968210	+	0.0684387i
$503$	−23.7800	−	23.7800i	−1.06030	−	1.06030i	−0.998062	−	0.0622340i	$-0.980177\pi$
$503$	−23.7800	−	23.7800i	−1.06030	−	1.06030i	−0.0622340	−	0.998062i	$-0.519823\pi$
$504$	−19.4001	+	3.55014i	−0.864147	+	0.158136i
$505$	−1.19484	+	1.19484i	−0.0531699	+	0.0531699i
$506$	−8.10193	+	7.03216i	−0.360175	+	0.312618i
$507$	15.6637	+	37.8156i	0.695651	+	1.67945i
$508$	−3.84057	−	5.11265i	−0.170398	−	0.226837i
$509$	7.80811	+	3.23423i	0.346089	+	0.143355i	0.548955	−	0.835852i	$-0.315026\pi$
$509$	7.80811	+	3.23423i	0.346089	+	0.143355i	−0.202867	+	0.979206i	$0.565026\pi$
$510$	13.0890	−	26.2029i	0.579592	−	1.16029i
$511$	3.52228			0.155816
$512$	−19.3730	+	11.6914i	−0.856172	+	0.516691i
$513$	38.8983			1.71740
$514$	−10.5669	+	21.1539i	−0.466085	+	0.933057i
$515$	10.9991	+	4.55597i	0.484677	+	0.200760i
$516$	8.17532	+	10.8832i	0.359898	+	0.479105i
$517$	−17.6756	−	42.6727i	−0.777373	−	1.87674i
$518$	−11.8656	+	10.2989i	−0.521345	+	0.452508i
$519$	13.5208	−	13.5208i	0.593495	−	0.593495i
$520$	0.901207	−	0.164918i	0.0395205	−	0.00723212i
$521$	14.9711	+	14.9711i	0.655895	+	0.655895i	0.954406	−	0.298511i	$-0.0964899\pi$
$521$	14.9711	+	14.9711i	0.655895	+	0.655895i	−0.298511	+	0.954406i	$0.596490\pi$
$522$	62.3506	+	4.40730i	2.72901	+	0.192902i
$523$	−22.9292	+	9.49757i	−1.00262	+	0.415300i	−0.822758	−	0.568392i	$-0.807566\pi$
$523$	−22.9292	+	9.49757i	−1.00262	+	0.415300i	−0.179864	+	0.983691i	$0.557566\pi$
$524$	5.28756	+	20.5736i	0.230988	+	0.898763i
$525$	2.77285	−	6.69425i	0.121017	−	0.292161i
$526$	−0.673107	−	2.01677i	−0.0293489	−	0.0879352i
$527$		−	22.0403i		−	0.960092i
$528$	21.9215	−	75.5868i	0.954011	−	3.28949i
$529$		−	21.5175i		−	0.935544i
$530$	−3.07753	+	1.02714i	−0.133679	+	0.0446162i
$531$	−0.135214	+	0.326434i	−0.00586777	+	0.0141660i
$532$	−3.15522	+	5.33804i	−0.136796	+	0.231433i
$533$	−0.640155	+	0.265161i	−0.0277282	+	0.0114854i
$534$	2.45993	−	34.8009i	0.106451	−	1.50598i
$535$	−2.70280	−	2.70280i	−0.116852	−	0.116852i
$536$	−10.8700	−	2.33624i	−0.469511	−	0.100910i
$537$	41.6639	−	41.6639i	1.79793	−	1.79793i
$538$	−1.41725	−	1.63284i	−0.0611018	−	0.0703969i
$539$	2.38425	+	5.75610i	0.102697	+	0.247933i
$540$	−40.8631	−	5.80589i	−1.75847	−	0.249846i
$541$	12.9919	+	5.38144i	0.558567	+	0.231366i	0.644063	−	0.764973i	$-0.277247\pi$
$541$	12.9919	+	5.38144i	0.558567	+	0.231366i	−0.0854960	+	0.996339i	$0.527247\pi$
$542$	20.5750	+	10.2777i	0.883773	+	0.441467i
$543$	3.76073			0.161388
$544$	−15.3007	+	16.5717i	−0.656011	+	0.710505i
$545$	−20.2386			−0.866928
$546$	−0.786785	−	0.393019i	−0.0336713	−	0.0168196i
$547$	4.33631	+	1.79616i	0.185407	+	0.0767983i	0.473456	−	0.880818i	$-0.343006\pi$
$547$	4.33631	+	1.79616i	0.185407	+	0.0767983i	−0.288048	+	0.957616i	$0.593006\pi$
$548$	1.47363	−	10.3717i	0.0629504	−	0.443058i
$549$	−31.8850	−	76.9773i	−1.36082	−	3.28531i
$550$	13.2516	+	15.2675i	0.565052	+	0.651010i
$551$	13.8963	−	13.8963i	0.592004	−	0.592004i
$552$	−5.90256	−	9.13439i	−0.251230	−	0.388785i
$553$	−3.29342	−	3.29342i	−0.140050	−	0.140050i
$554$	1.72115	−	24.3493i	0.0731247	−	1.03450i
$555$	−53.3168	+	22.0845i	−2.26317	+	0.937437i
$556$	31.0995	+	18.3823i	1.31891	+	0.779584i
$557$	−17.1893	+	41.4987i	−0.728334	+	1.75835i	−0.0802647	+	0.996774i	$0.525577\pi$
$557$	−17.1893	+	41.4987i	−0.728334	+	1.75835i	−0.648070	+	0.761581i	$0.724423\pi$
$558$	−51.7060	+	17.2572i	−2.18889	+	0.730554i
$559$			0.424402i			0.0179503i
$560$	4.11133	−	5.13672i	0.173735	−	0.217066i
$561$		−	78.4498i		−	3.31215i
$562$	2.23682	+	6.70197i	0.0943546	+	0.282706i
$563$	16.6307	−	40.1500i	0.700900	−	1.69212i	−0.0206760	−	0.999786i	$-0.506582\pi$
$563$	16.6307	−	40.1500i	0.700900	−	1.69212i	0.721576	−	0.692335i	$-0.243418\pi$
$564$	45.3495	−	11.6551i	1.90956	−	0.490769i
$565$	3.21249	−	1.33066i	0.135151	−	0.0559812i
$566$	29.8303	+	2.10858i	1.25386	+	0.0886302i
$567$	13.2244	+	13.2244i	0.555373	+	0.555373i
$568$	0.412532	−	0.597334i	0.0173095	−	0.0250636i
$569$	−10.1679	+	10.1679i	−0.426259	+	0.426259i	−0.887352	−	0.461093i	$-0.847458\pi$
$569$	−10.1679	+	10.1679i	−0.426259	+	0.426259i	0.461093	+	0.887352i	$0.347458\pi$
$570$	−17.2003	+	14.9292i	−0.720443	+	0.625316i
$571$	−9.05090	−	21.8508i	−0.378769	−	0.914428i	−0.992197	−	0.124678i	$-0.960210\pi$
$571$	−9.05090	−	21.8508i	−0.378769	−	0.914428i	0.613429	−	0.789750i	$-0.289790\pi$
$572$	1.96195	−	1.47380i	0.0820334	−	0.0616225i
$573$	72.6275	+	30.0833i	3.03406	+	1.25675i
$574$	−2.22365	+	4.45152i	−0.0928132	+	0.185803i
$575$	2.79365			0.116503
$576$	50.8568	+	22.9196i	2.11903	+	0.954984i
$577$	23.0941			0.961418			0.480709	−	0.876880i	$-0.340379\pi$
$577$	23.0941			0.961418			0.480709	+	0.876880i	$0.340379\pi$
$578$	0.696531	−	1.39439i	0.0289719	−	0.0579988i
$579$	−0.944823	−	0.391359i	−0.0392655	−	0.0162643i
$580$	−16.6724	+	12.5241i	−0.692283	+	0.520035i
$581$	−2.03104	−	4.90335i	−0.0842616	−	0.203425i
$582$	48.8239	−	42.3773i	2.02382	−	1.75659i
$583$	−6.14455	+	6.14455i	−0.254481	+	0.254481i
$584$	−8.19755	−	5.66141i	−0.339217	−	0.234271i
$585$	−1.59708	−	1.59708i	−0.0660313	−	0.0660313i
$586$	−39.2030	−	2.77109i	−1.61946	−	0.114473i
$587$	−19.9230	+	8.25238i	−0.822310	+	0.340612i	−0.753854	−	0.657042i	$-0.771807\pi$
$587$	−19.9230	+	8.25238i	−0.822310	+	0.340612i	−0.0684564	+	0.997654i	$0.521807\pi$
$588$	−6.11717	+	1.57215i	−0.252268	+	0.0648345i
$589$	−6.55854	+	15.8337i	−0.270240	+	0.652417i
$590$	−0.0373172	−	0.111810i	−0.00153632	−	0.00460314i
$591$		−	5.59018i		−	0.229949i
$592$	44.1690	−	4.89730i	1.81533	−	0.201278i
$593$		−	6.86424i		−	0.281880i	−0.990018	−	0.140940i	$-0.954987\pi$
$593$		−	6.86424i		−	0.281880i	0.990018	−	0.140940i	$-0.0450125\pi$
$594$	−104.859	+	34.9974i	−4.30242	+	1.43596i
$595$	2.50979	−	6.05917i	0.102891	−	0.248402i
$596$	32.8089	+	19.3927i	1.34390	+	0.794357i
$597$	−34.6269	+	14.3429i	−1.41719	+	0.587017i
$598$	0.0239092	−	0.338246i	0.000977718	−	0.0138319i
$599$	1.28148	+	1.28148i	0.0523600	+	0.0523600i	0.732802	−	0.680442i	$-0.238212\pi$
$599$	1.28148	+	1.28148i	0.0523600	+	0.0523600i	−0.680442	+	0.732802i	$0.738212\pi$
$600$	−17.2131	+	11.1230i	−0.702724	+	0.454094i
$601$	−7.61024	+	7.61024i	−0.310428	+	0.310428i	−0.845075	−	0.534647i	$-0.820445\pi$
$601$	−7.61024	+	7.61024i	−0.310428	+	0.310428i	0.534647	+	0.845075i	$0.320445\pi$
$602$	1.99781	+	2.30173i	0.0814246	+	0.0938113i
$603$	10.4891	+	25.3230i	0.427150	+	1.03123i
$604$	2.32973	−	16.3971i	0.0947952	−	0.667189i
$605$	−42.2726	−	17.5099i	−1.71863	−	0.711879i
$606$	−4.10440	−	2.05025i	−0.166730	−	0.0832857i
$607$	−22.7630			−0.923922			−0.461961	−	0.886900i	$-0.652854\pi$
$607$	−22.7630			−0.923922			−0.461961	+	0.886900i	$0.652854\pi$
$608$	15.9232	−	7.35203i	0.645771	−	0.298164i
$609$	20.0174			0.811144
$610$	24.8661	+	12.4212i	1.00680	+	0.502921i
$611$	1.34878	+	0.558683i	0.0545658	+	0.0226019i
$612$	55.0516	+	7.82181i	2.22533	+	0.316178i
$613$	−7.16049	−	17.2869i	−0.289209	−	0.698213i	0.710777	−	0.703417i	$-0.248343\pi$
$613$	−7.16049	−	17.2869i	−0.289209	−	0.698213i	−0.999986	+	0.00520419i	$0.998343\pi$
$614$	13.4957	+	15.5487i	0.544642	+	0.627495i
$615$	−12.9238	+	12.9238i	−0.521137	+	0.521137i
$616$	3.70289	−	17.2287i	0.149194	−	0.694163i
$617$	23.7607	+	23.7607i	0.956570	+	0.956570i	0.999095	−	0.0425258i	$-0.0135405\pi$
$617$	23.7607	+	23.7607i	0.956570	+	0.956570i	−0.0425258	+	0.999095i	$0.513540\pi$
$618$	−2.27923	+	32.2445i	−0.0916839	+	1.29706i
$619$	23.1416	−	9.58555i	0.930138	−	0.385276i	0.134407	−	0.990926i	$-0.457087\pi$
$619$	23.1416	−	9.58555i	0.930138	−	0.385276i	0.795731	+	0.605650i	$0.207087\pi$
$620$	9.25312	−	15.6546i	0.371614	−	0.628702i
$621$	−5.84585	+	14.1131i	−0.234586	+	0.566341i
$622$	8.10498	−	2.70508i	0.324980	−	0.108464i
$623$		−	7.81174i		−	0.312971i
$624$	1.19941	+	2.17930i	0.0480150	+	0.0872419i
$625$			8.26334i			0.330534i
$626$	7.19802	+	21.5667i	0.287691	+	0.861980i
$627$	−23.3443	+	56.3581i	−0.932282	+	2.25073i
$628$	−5.50233	−	21.4093i	−0.219567	−	0.854324i
$629$	40.9256	−	16.9519i	1.63181	−	0.675918i
$630$	−16.1798	−	1.14368i	−0.644617	−	0.0455653i
$631$	9.75860	+	9.75860i	0.388484	+	0.388484i	0.874146	−	0.485663i	$-0.161422\pi$
$631$	9.75860	+	9.75860i	0.388484	+	0.388484i	−0.485663	+	0.874146i	$0.661422\pi$
$632$	2.37135	+	12.9585i	0.0943274	+	0.515460i
$633$	−33.2965	+	33.2965i	−1.32342	+	1.32342i
$634$	−9.69390	+	8.41393i	−0.384994	+	0.334160i
$635$	−2.01253	−	4.85868i	−0.0798648	−	0.192811i
$636$	−5.29082	−	7.04327i	−0.209795	−	0.279284i
$637$	−0.181936	−	0.0753604i	−0.00720857	−	0.00298589i
$638$	−24.9580	+	49.9634i	−0.988096	+	1.97807i
$639$	−1.78965			−0.0707973
$640$	−17.8248	+	5.34672i	−0.704588	+	0.211347i
$641$	−16.9429			−0.669206			−0.334603	−	0.942359i	$-0.608602\pi$
$641$	−16.9429			−0.669206			−0.334603	+	0.942359i	$0.608602\pi$
$642$	4.63778	−	9.28438i	0.183039	−	0.366425i
$643$	1.94579	+	0.805973i	0.0767345	+	0.0317845i	0.420721	−	0.907190i	$-0.361777\pi$
$643$	1.94579	+	0.805973i	0.0767345	+	0.0317845i	−0.343986	+	0.938975i	$0.611777\pi$
$644$	−1.46257	−	1.94701i	−0.0576334	−	0.0767229i
$645$	4.28402	+	10.3425i	0.168683	+	0.407237i
$646$	13.2028	−	11.4596i	0.519459	−	0.450871i
$647$	17.8656	−	17.8656i	0.702368	−	0.702368i	−0.262550	−	0.964918i	$-0.584564\pi$
$647$	17.8656	−	17.8656i	0.702368	−	0.702368i	0.964918	+	0.262550i	$0.0845636\pi$
$648$	−9.52196	−	52.0336i	−0.374058	−	2.04407i
$649$	−0.223238	−	0.223238i	−0.00876285	−	0.00876285i
$650$	−0.637402	−	0.0450552i	−0.0250009	−	0.00176721i
$651$	−16.1278	+	6.68033i	−0.632097	+	0.261823i
$652$	−10.1783	−	39.6032i	−0.398612	−	1.55098i
$653$	17.2420	−	41.6258i	0.674730	−	1.62894i	−0.0987430	−	0.995113i	$-0.531482\pi$
$653$	17.2420	−	41.6258i	0.674730	−	1.62894i	0.773473	−	0.633829i	$-0.218518\pi$
$654$	−17.3969	−	52.1247i	−0.680274	−	2.03824i
$655$			17.4702i			0.682619i
$656$	12.3302	−	6.78613i	0.481413	−	0.264954i
$657$			24.5603i			0.958189i
$658$	9.94497	−	3.31919i	0.387695	−	0.129395i
$659$	−6.11881	+	14.7721i	−0.238355	+	0.575440i	−0.997113	−	0.0759327i	$-0.975807\pi$
$659$	−6.11881	+	14.7721i	−0.238355	+	0.575440i	0.758758	+	0.651373i	$0.225807\pi$
$660$	32.9353	−	55.7204i	1.28201	−	2.16891i
$661$	−16.1894	+	6.70585i	−0.629693	+	0.260828i	−0.674623	−	0.738163i	$-0.735694\pi$
$661$	−16.1894	+	6.70585i	−0.629693	+	0.260828i	0.0449295	+	0.998990i	$0.485694\pi$
$662$	−1.68094	+	23.7804i	−0.0653315	+	0.924252i
$663$	1.75335	+	1.75335i	0.0680943	+	0.0680943i
$664$	−3.15432	+	14.6763i	−0.122411	+	0.569551i
$665$	−3.60605	+	3.60605i	−0.139837	+	0.139837i
$666$	−71.8127	−	82.7372i	−2.78269	−	3.20600i
$667$	2.95347	+	7.13031i	0.114359	+	0.276087i
$668$	38.7774	+	5.50955i	1.50034	+	0.213171i
$669$	−1.36892	−	0.567023i	−0.0529253	−	0.0219224i
$670$	−8.18013	−	4.08618i	−0.316026	−	0.157863i
$671$	74.4474			2.87401
$672$	16.7637	+	6.17328i	0.646674	+	0.238140i
$673$	2.01887			0.0778215			0.0389108	−	0.999243i	$-0.487611\pi$
$673$	2.01887			0.0778215			0.0389108	+	0.999243i	$0.487611\pi$
$674$	23.7725	+	11.8749i	0.915681	+	0.457405i
$675$	26.5953	+	11.0161i	1.02365	+	0.424011i
$676$	3.64648	−	25.6647i	0.140249	−	0.987103i
$677$	−5.13139	−	12.3883i	−0.197215	−	0.476120i	0.794074	−	0.607821i	$-0.207956\pi$
$677$	−5.13139	−	12.3883i	−0.197215	−	0.476120i	−0.991289	+	0.131701i	$0.957956\pi$
$678$	6.18854	+	7.12997i	0.237669	+	0.273825i
$679$	10.2359	−	10.2359i	0.392819	−	0.392819i
$680$	−15.5801	+	10.0678i	−0.597471	+	0.386081i
$681$	−40.8217	−	40.8217i	−1.56429	−	1.56429i
$682$	3.43421	−	48.5841i	0.131503	−	1.86038i
$683$	−19.3002	+	7.99442i	−0.738503	+	0.305898i	−0.720041	−	0.693932i	$-0.755877\pi$
$683$	−19.3002	+	7.99442i	−0.738503	+	0.305898i	−0.0184619	+	0.999830i	$0.505877\pi$
$684$	−37.2214	−	22.0009i	−1.42320	−	0.841224i
$685$	3.29708	−	7.95985i	0.125975	−	0.304130i
$686$	−1.34147	+	0.447724i	−0.0512176	+	0.0170942i
$687$			37.9663i			1.44851i
$688$	−0.949991	−	8.56802i	−0.0362181	−	0.326653i
$689$		−	0.274660i		−	0.0104637i
$690$	−2.83168	−	8.48429i	−0.107800	−	0.322991i
$691$	7.63037	−	18.4213i	0.290273	−	0.700781i	−0.709720	−	0.704484i	$-0.751179\pi$
$691$	7.63037	−	18.4213i	0.290273	−	0.700781i	0.999993	+	0.00370270i	$0.00117861\pi$
$692$	−11.7286	+	3.01433i	−0.445855	+	0.114588i
$693$	−40.1364	+	16.6251i	−1.52466	+	0.631534i
$694$	−31.4790	−	2.22512i	−1.19493	−	0.0844645i
$695$	21.0089	+	21.0089i	0.796913	+	0.796913i
$696$	−46.5873	−	32.1742i	−1.76589	−	1.21956i
$697$	9.92020	−	9.92020i	0.375754	−	0.375754i
$698$	3.38302	−	2.93633i	0.128049	−	0.111142i
$699$	10.6955	+	25.8213i	0.404543	+	0.976652i
$700$	−3.66901	+	2.75612i	−0.138676	+	0.104171i
$701$	20.1097	+	8.32971i	0.759533	+	0.314609i	0.728625	−	0.684913i	$-0.240160\pi$
$701$	20.1097	+	8.32971i	0.759533	+	0.314609i	0.0309085	+	0.999522i	$0.490160\pi$
$702$	1.56141	−	3.12578i	0.0589315	−	0.117975i
$703$	−34.4452			−1.29913
$704$	−36.3098	+	34.1454i	−1.36848	+	1.28690i
$705$	38.5088			1.45033
$706$	−0.587206	+	1.17553i	−0.0220998	+	0.0442416i
$707$	−0.949102	−	0.393131i	−0.0356947	−	0.0147852i
$708$	0.255889	−	0.192221i	0.00961690	−	0.00722411i
$709$	6.82463	+	16.4761i	0.256304	+	0.618773i	0.998688	−	0.0512014i	$-0.0163050\pi$
$709$	6.82463	+	16.4761i	0.256304	+	0.618773i	−0.742384	+	0.669974i	$0.766305\pi$
$710$	0.450884	−	0.391350i	0.0169214	−	0.0146871i
$711$	22.9645	−	22.9645i	0.861236	−	0.861236i
$712$	−12.5559	+	18.1806i	−0.470553	+	0.681347i
$713$	−4.75915	−	4.75915i	−0.178232	−	0.178232i
$714$	17.7628	+	1.25558i	0.664756	+	0.0469888i
$715$	1.86449	−	0.772298i	0.0697280	−	0.0288823i
$716$	−36.1415	+	9.28861i	−1.35067	+	0.347132i
$717$	−5.39547	+	13.0258i	−0.201498	+	0.486458i
$718$	11.3728	+	34.0751i	0.424428	+	1.27167i
$719$		−	46.5403i		−	1.73566i	−0.496861	−	0.867830i	$-0.665514\pi$
$719$		−	46.5403i		−	1.73566i	0.496861	−	0.867830i	$-0.334486\pi$
$720$	35.8176	+	28.6677i	1.33484	+	1.06838i
$721$			7.23790i			0.269553i
$722$	12.5930	−	4.20299i	0.468664	−	0.156419i
$723$	25.0345	−	60.4386i	0.931043	−	2.24774i
$724$	−2.05034	−	1.21192i	−0.0762002	−	0.0450405i
$725$	13.4366	−	5.56562i	0.499022	−	0.206702i
$726$	8.75972	−	123.925i	0.325104	−	4.59928i
$727$	10.4198	+	10.4198i	0.386448	+	0.386448i	0.873418	−	0.486970i	$-0.161898\pi$
$727$	10.4198	+	10.4198i	0.386448	+	0.386448i	−0.486970	+	0.873418i	$0.661898\pi$
$728$	0.302300	+	0.467819i	0.0112040	+	0.0173385i
$729$	−8.16368	+	8.16368i	−0.302359	+	0.302359i
$730$	−5.37072	−	6.18774i	−0.198779	−	0.229018i
$731$	−3.28838	−	7.93886i	−0.121625	−	0.293629i
$732$	−10.6163	+	74.7200i	−0.392391	+	2.76173i
$733$	33.3482	+	13.8133i	1.23175	+	0.510206i	0.901126	−	0.433558i	$-0.142742\pi$
$733$	33.3482	+	13.8133i	1.23175	+	0.510206i	0.330620	+	0.943764i	$0.392742\pi$
$734$	−13.7018	−	6.84438i	−0.505742	−	0.252631i
$735$	−5.19444			−0.191600
$736$	0.274448	+	6.88217i	0.0101163	+	0.253680i
$737$	−24.4907			−0.902128
$738$	−31.0398	−	15.5052i	−1.14259	−	0.570753i
$739$	31.7629	+	13.1566i	1.16842	+	0.483974i	0.880669	−	0.473733i	$-0.157094\pi$
$739$	31.7629	+	13.1566i	1.16842	+	0.483974i	0.287747	+	0.957706i	$0.407094\pi$
$740$	36.1851	+	5.14123i	1.33019	+	0.188995i
$741$	−0.737856	−	1.78134i	−0.0271058	−	0.0654393i
$742$	−1.29292	−	1.48961i	−0.0474647	−	0.0546852i
$743$	9.90027	−	9.90027i	0.363206	−	0.363206i	−0.501786	−	0.864992i	$-0.667324\pi$
$743$	9.90027	−	9.90027i	0.363206	−	0.363206i	0.864992	+	0.501786i	$0.167324\pi$
$744$	48.2723	+	10.3750i	1.76975	+	0.380364i
$745$	22.1637	+	22.1637i	0.812015	+	0.812015i
$746$	−0.803975	+	11.3739i	−0.0294356	+	0.416429i
$747$	34.1904	−	14.1621i	1.25096	−	0.518165i
$748$	−25.2809	+	42.7706i	−0.924362	+	1.56385i
$749$	0.889284	−	2.14692i	0.0324937	−	0.0784468i
$750$	−50.8290	+	16.9645i	−1.85601	+	0.619455i
$751$			38.4024i			1.40132i	0.713493	+	0.700662i	$0.247112\pi$
$751$			38.4024i			1.40132i	−0.713493	+	0.700662i	$0.752888\pi$
$752$	−28.4804	−	8.25981i	−1.03857	−	0.301204i
$753$			48.5622i			1.76971i
$754$	−0.558870	−	1.67449i	−0.0203528	−	0.0609812i
$755$	5.21249	−	12.5841i	0.189702	−	0.457981i
$756$	−6.24594	−	24.3026i	−0.227162	−	0.883878i
$757$	5.15489	−	2.13523i	0.187358	−	0.0776061i	−0.287032	−	0.957921i	$-0.592669\pi$
$757$	5.15489	−	2.13523i	0.187358	−	0.0776061i	0.474390	+	0.880315i	$0.342669\pi$
$758$	−14.0327	−	0.991913i	−0.509691	−	0.0360279i
$759$	−16.9396	−	16.9396i	−0.614869	−	0.614869i
$760$	14.1886	−	2.59646i	0.514675	−	0.0941836i
$761$	−19.2892	+	19.2892i	−0.699232	+	0.699232i	−0.964245	−	0.265012i	$-0.914624\pi$
$761$	−19.2892	+	19.2892i	−0.699232	+	0.699232i	0.265012	+	0.964245i	$0.414624\pi$
$762$	10.7836	−	9.35975i	0.390648	−	0.339068i
$763$	−4.70861	−	11.3676i	−0.170463	−	0.411534i
$764$	−29.9018	−	39.8059i	−1.08181	−	1.44013i
$765$	42.2497	+	17.5004i	1.52754	+	0.632728i
$766$	−7.41513	+	14.8444i	−0.267920	+	0.536349i
$767$	0.00997869			0.000360310
$768$	−29.0925	−	41.3119i	−1.04979	−	1.49072i
$769$	−17.8703			−0.644420			−0.322210	−	0.946668i	$-0.604426\pi$
$769$	−17.8703			−0.644420			−0.322210	+	0.946668i	$0.604426\pi$
$770$	6.47651	−	12.9653i	0.233397	−	0.467238i
$771$	−48.7834	−	20.2067i	−1.75689	−	0.727728i
$772$	0.388997	+	0.517843i	0.0140003	+	0.0186376i
$773$	−7.59136	−	18.3272i	−0.273042	−	0.659182i	0.726568	−	0.687094i	$-0.241114\pi$
$773$	−7.59136	−	18.3272i	−0.273042	−	0.659182i	−0.999610	+	0.0279122i	$0.991114\pi$
$774$	−16.0496	+	13.9304i	−0.576891	+	0.500719i
$775$	−8.96831	+	8.96831i	−0.322151	+	0.322151i
$776$	−40.2750	+	7.37017i	−1.44579	+	0.264574i
$777$	−24.8088	−	24.8088i	−0.890010	−	0.890010i
$778$	50.0912	+	3.54074i	1.79586	+	0.126942i
$779$	−10.0786	+	4.17469i	−0.361103	+	0.149574i
$780$	0.509245	+	1.98145i	0.0182339	+	0.0709472i
$781$	0.611940	−	1.47735i	0.0218969	−	0.0528639i
$782$	2.17358	+	6.51248i	0.0777269	+	0.232886i
$783$			79.5261i			2.84203i
$784$	3.84170	+	1.11416i	0.137204	+	0.0397914i
$785$		−	18.1799i		−	0.648867i
$786$	−44.9947	+	15.0172i	−1.60491	+	0.535647i
$787$	−7.14714	+	17.2547i	−0.254768	+	0.615065i	−0.998577	−	0.0533275i	$-0.983017\pi$
$787$	−7.14714	+	17.2547i	−0.254768	+	0.615065i	0.743809	+	0.668392i	$0.233017\pi$
$788$	−1.80147	+	3.04775i	−0.0641747	+	0.108572i
$789$	4.38631	−	1.81687i	0.156157	−	0.0646823i
$790$	−0.763933	+	10.8074i	−0.0271795	+	0.384511i
$791$	1.49480	+	1.49480i	0.0531490	+	0.0531490i
$792$	120.133	+	25.8197i	4.26874	+	0.917463i
$793$	−1.66389	+	1.66389i	−0.0590866	+	0.0590866i
$794$	36.5082	+	42.0620i	1.29563	+	1.49273i
$795$	−2.77249	−	6.69339i	−0.0983302	−	0.237390i
$796$	23.5006	+	3.33900i	0.832956	+	0.118348i
$797$	−22.8308	−	9.45683i	−0.808709	−	0.334978i	−0.0602700	−	0.998182i	$-0.519196\pi$
$797$	−22.8308	−	9.45683i	−0.808709	−	0.334978i	−0.748439	+	0.663204i	$0.769196\pi$
$798$	−12.3871	−	6.18768i	−0.438500	−	0.219042i
$799$	−29.5591			−1.04573
$800$	12.9690	−	0.517179i	0.458524	−	0.0182850i
$801$	54.4701			1.92461
$802$	−25.9699	−	12.9726i	−0.917029	−	0.458079i
$803$	−20.2746	−	8.39800i	−0.715474	−	0.296359i
$804$	3.49242	−	24.5804i	0.123168	−	0.866884i
$805$	−0.766415	−	1.85029i	−0.0270126	−	0.0652141i
$806$	1.00910	+	1.16261i	0.0355439	+	0.0409510i
$807$	3.41397	−	3.41397i	0.120177	−	0.120177i
$808$	1.57700	+	2.44046i	0.0554787	+	0.0858550i
$809$	0.965769	+	0.965769i	0.0339546	+	0.0339546i	0.723880	−	0.689926i	$-0.242357\pi$
$809$	0.965769	+	0.965769i	0.0339546	+	0.0339546i	−0.689926	+	0.723880i	$0.742357\pi$
$810$	3.06750	−	43.3963i	0.107781	−	1.52479i
$811$	17.7733	−	7.36196i	0.624106	−	0.258513i	−0.0481404	−	0.998841i	$-0.515329\pi$
$811$	17.7733	−	7.36196i	0.624106	−	0.258513i	0.672247	+	0.740327i	$0.265329\pi$
$812$	−10.9134	−	6.45071i	−0.382985	−	0.226376i
$813$	−19.6538	+	47.4485i	−0.689290	+	1.66409i
$814$	92.8548	−	30.9908i	3.25456	−	1.08623i
$815$		−	33.6293i		−	1.17798i
$816$	−39.3221	−	31.4726i	−1.37655	−	1.10176i
$817$			6.68178i			0.233766i
$818$	−7.01043	−	21.0047i	−0.245114	−	0.734411i
$819$	0.525477	−	1.26861i	0.0183617	−	0.0443290i
$820$	11.2108	−	2.88124i	0.391497	−	0.100617i
$821$	25.6746	−	10.6347i	0.896048	−	0.371155i	0.113349	−	0.993555i	$-0.463842\pi$
$821$	25.6746	−	10.6347i	0.896048	−	0.371155i	0.782699	+	0.622400i	$0.213842\pi$
$822$	23.3348	+	1.64944i	0.813893	+	0.0575307i
$823$	−3.51294	−	3.51294i	−0.122454	−	0.122454i	0.643224	−	0.765678i	$-0.277596\pi$
$823$	−3.51294	−	3.51294i	−0.122454	−	0.122454i	−0.765678	+	0.643224i	$0.777596\pi$
$824$	11.6336	−	16.8451i	0.405275	−	0.586826i
$825$	−31.9216	+	31.9216i	−1.11137	+	1.11137i
$826$	0.0541190	−	0.0469732i	0.00188304	−	0.00163441i
$827$	−13.1301	−	31.6988i	−0.456578	−	1.10228i	−0.969774	−	0.244005i	$-0.921539\pi$
$827$	−13.1301	−	31.6988i	−0.456578	−	1.10228i	0.513196	−	0.858271i	$-0.328461\pi$
$828$	13.5762	−	10.1983i	0.471806	−	0.354415i
$829$	33.6094	+	13.9215i	1.16730	+	0.483513i	0.880301	−	0.474416i	$-0.157341\pi$
$829$	33.6094	+	13.9215i	1.16730	+	0.483513i	0.287004	+	0.957930i	$0.407341\pi$
$830$	−5.51704	+	11.0446i	−0.191499	+	0.383363i
$831$	54.5084			1.89088
$832$	0.0483756	−	1.57467i	0.00167712	−	0.0545918i
$833$	3.98721			0.138149
$834$	−36.0495	+	72.1675i	−1.24829	+	2.49896i
$835$	29.7600	+	12.3270i	1.02989	+	0.426593i
$836$	30.8890	−	23.2035i	1.06832	−	0.802508i
$837$	−26.5400	−	64.0732i	−0.917357	−	2.21469i
$838$	−9.57269	+	8.30873i	−0.330683	+	0.287020i
$839$	9.42342	−	9.42342i	0.325333	−	0.325333i	−0.525476	−	0.850809i	$-0.676113\pi$
$839$	9.42342	−	9.42342i	0.325333	−	0.325333i	0.850809	+	0.525476i	$0.176113\pi$
$840$	12.0892	+	8.34910i	0.417118	+	0.288071i
$841$	7.90441	+	7.90441i	0.272566	+	0.272566i
$842$	−7.52832	−	0.532145i	−0.259443	−	0.0183389i
$843$	−14.5763	+	6.03769i	−0.502033	+	0.207949i
$844$	28.8832	−	7.42317i	0.994200	−	0.255516i
$845$	8.15857	−	19.6965i	0.280663	−	0.677581i
$846$	23.1442	+	69.3448i	0.795715	+	2.38412i
$847$		−	27.8173i		−	0.955815i
$848$	0.614806	+	5.54497i	0.0211125	+	0.190415i
$849$			66.7782i			2.29182i
$850$	12.2723	−	4.09596i	0.420938	−	0.140490i
$851$	5.17662	−	12.4975i	0.177452	−	0.428407i
$852$	1.39550	+	0.824854i	0.0478090	+	0.0282590i
$853$	19.2625	−	7.97881i	0.659537	−	0.273189i	−0.0277067	−	0.999616i	$-0.508820\pi$
$853$	19.2625	−	7.97881i	0.659537	−	0.273189i	0.687244	+	0.726427i	$0.258820\pi$
$854$	−1.19152	+	16.8566i	−0.0407730	+	0.576820i
$855$	−25.1445	−	25.1445i	−0.859924	−	0.859924i
$856$	−5.52045	+	3.56727i	−0.188685	+	0.121927i
$857$	1.54602	−	1.54602i	0.0528110	−	0.0528110i	−0.680208	−	0.733019i	$-0.738111\pi$
$857$	1.54602	−	1.54602i	0.0528110	−	0.0528110i	0.733019	+	0.680208i	$0.238111\pi$
$858$	3.59175	+	4.13815i	0.122620	+	0.141274i
$859$	20.0607	+	48.4307i	0.684461	+	1.65243i	0.755653	+	0.654972i	$0.227320\pi$
$859$	20.0607	+	48.4307i	0.684461	+	1.65243i	−0.0711920	+	0.997463i	$0.522680\pi$
$860$	0.997309	−	7.01928i	0.0340080	−	0.239355i
$861$	−10.2658	−	4.25222i	−0.349856	−	0.144915i
$862$	6.65954	+	3.32660i	0.226825	+	0.113305i
$863$	−34.4444			−1.17250			−0.586251	−	0.810130i	$-0.699397\pi$
$863$	−34.4444			−1.17250			−0.586251	+	0.810130i	$0.699397\pi$
$864$	−24.5256	+	66.5998i	−0.834376	+	2.26577i
$865$	−9.95944			−0.338631
$866$	−35.1850	−	17.5758i	−1.19564	−	0.597250i
$867$	3.21563	+	1.33196i	0.109208	+	0.0452356i
$868$	10.9456	+	1.55517i	0.371517	+	0.0527857i
$869$	11.1049	+	26.8096i	0.376707	+	0.909452i
$870$	−30.5222	−	35.1654i	−1.03480	−	1.19222i
$871$	0.547366	−	0.547366i	0.0185468	−	0.0185468i
$872$	−7.31275	+	34.0245i	−0.247641	+	1.15222i
$873$	71.3737	+	71.3737i	2.41564	+	2.41564i
$874$	0.376426	−	5.32534i	0.0127328	−	0.180132i
$875$	−11.0850	+	4.59156i	−0.374742	+	0.155223i
$876$	11.3199	−	19.1512i	0.382465	−	0.647060i
$877$	−8.59005	+	20.7382i	−0.290065	+	0.700280i	−0.999992	−	0.00399584i	$-0.998728\pi$
$877$	−8.59005	+	20.7382i	−0.290065	+	0.700280i	0.709927	+	0.704276i	$0.248728\pi$
$878$	−15.8979	+	5.30601i	−0.536528	+	0.179069i
$879$		−	87.7598i		−	2.96007i
$880$	−35.9125	+	19.7650i	−1.21061	+	0.666279i
$881$			33.4900i			1.12831i	0.825670	+	0.564154i	$0.190798\pi$
$881$			33.4900i			1.12831i	−0.825670	+	0.564154i	$0.809202\pi$
$882$	−3.12191	−	9.35388i	−0.105120	−	0.314962i
$883$	1.74506	−	4.21294i	0.0587258	−	0.141777i	−0.891793	−	0.452444i	$-0.850552\pi$
$883$	1.74506	−	4.21294i	0.0587258	−	0.141777i	0.950519	+	0.310667i	$0.100552\pi$
$884$	−0.390893	−	1.52095i	−0.0131472	−	0.0511549i
$885$	0.243178	−	0.100727i	0.00817433	−	0.00338592i
$886$	−35.0698	−	2.47894i	−1.17819	−	0.0832816i
$887$	−24.8774	−	24.8774i	−0.835301	−	0.835301i	0.152935	−	0.988236i	$-0.451127\pi$
$887$	−24.8774	−	24.8774i	−0.835301	−	0.835301i	−0.988236	+	0.152935i	$0.951127\pi$
$888$	17.8630	+	97.6141i	0.599444	+	3.27572i
$889$	2.26078	−	2.26078i	0.0758243	−	0.0758243i
$890$	−13.7232	+	11.9112i	−0.460003	+	0.399265i
$891$	−44.5906	−	107.651i	−1.49384	−	3.60646i
$892$	0.563602	+	0.750281i	0.0188708	+	0.0251213i
$893$	21.2352	+	8.79590i	0.710608	+	0.294344i
$894$	−38.0310	+	76.1343i	−1.27195	+	2.54631i
$895$	−30.6898			−1.02585
$896$	−7.15015	−	8.76786i	−0.238870	−	0.292914i
$897$	0.757198			0.0252821
$898$	−0.204650	+	0.409689i	−0.00682926	+	0.0136715i
$899$	−32.3714	−	13.4087i	−1.07965	−	0.447204i
$900$	−19.2180	−	25.5835i	−0.640600	−	0.852782i
$901$	2.12814	+	5.13780i	0.0708988	+	0.171165i
$902$	23.4131	−	20.3217i	0.779571	−	0.676637i
$903$	−4.81247	+	4.81247i	−0.160149	+	0.160149i
$904$	−1.07630	−	5.88153i	−0.0357972	−	0.195617i
$905$	−1.38508	−	1.38508i	−0.0460417	−	0.0460417i
$906$	36.8909	+	2.60766i	1.22562	+	0.0866339i
$907$	−2.88600	+	1.19542i	−0.0958282	+	0.0396933i	−0.430083	−	0.902790i	$-0.641516\pi$
$907$	−2.88600	+	1.19542i	−0.0958282	+	0.0396933i	0.334254	+	0.942483i	$0.391516\pi$
$908$	9.10083	+	35.4109i	0.302022	+	1.17515i
$909$	2.74124	−	6.61795i	0.0909214	−	0.219504i
$910$	0.145025	+	0.434524i	0.00480752	+	0.0144043i
$911$		−	46.1043i		−	1.52750i	−0.645511	−	0.763751i	$-0.723355\pi$
$911$		−	46.1043i		−	1.52750i	0.645511	−	0.763751i	$-0.276645\pi$
$912$	18.8836	+	34.3109i	0.625298	+	1.13615i
$913$			33.0667i			1.09435i
$914$	−47.0472	+	15.7023i	−1.55618	+	0.519385i
$915$	−23.7528	+	57.3443i	−0.785243	+	1.89574i
$916$	12.2349	−	20.6991i	0.404252	−	0.683919i
$917$	−9.81263	+	4.06453i	−0.324042	+	0.134222i
$918$	−4.98823	+	70.5691i	−0.164636	+	2.32913i
$919$	−17.8289	−	17.8289i	−0.588121	−	0.588121i	0.349002	−	0.937122i	$-0.386521\pi$
$919$	−17.8289	−	17.8289i	−0.588121	−	0.588121i	−0.937122	+	0.349002i	$0.886521\pi$
$920$	−1.19029	+	5.53813i	−0.0392426	+	0.182587i
$921$	−32.5094	+	32.5094i	−1.07122	+	1.07122i
$922$	37.1159	+	42.7622i	1.22235	+	1.40830i
$923$	0.0193419	+	0.0466956i	0.000636647	+	0.00153700i
$924$	38.9594	+	5.53542i	1.28167	+	0.182102i
$925$	−23.5506	−	9.75499i	−0.774340	−	0.320742i
$926$	6.57681	+	3.28528i	0.216127	+	0.107961i
$927$	−50.4688			−1.65761
$928$	15.0309	+	32.5543i	0.493414	+	1.06865i
$929$	−40.3989			−1.32545			−0.662723	−	0.748865i	$-0.730599\pi$
$929$	−40.3989			−1.32545			−0.662723	+	0.748865i	$0.730599\pi$
$930$	36.3270	+	18.1462i	1.19121	+	0.595039i
$931$	−2.86440	−	1.18647i	−0.0938770	−	0.0388851i
$932$	2.48990	−	17.5244i	0.0815593	−	0.574031i
$933$	7.30164	+	17.6277i	0.239045	+	0.577105i
$934$	−19.5243	−	22.4944i	−0.638854	−	0.736039i
$935$	−28.8932	+	28.8932i	−0.944909	+	0.944909i
$936$	−3.26203	+	2.10790i	−0.106623	+	0.0688987i
$937$	−20.7984	−	20.7984i	−0.679455	−	0.679455i	0.280422	−	0.959877i	$-0.409526\pi$
$937$	−20.7984	−	20.7984i	−0.679455	−	0.679455i	−0.959877	+	0.280422i	$0.909526\pi$
$938$	0.391971	−	5.54526i	0.0127983	−	0.181059i
$939$	−46.9060	+	19.4291i	−1.53072	+	0.634044i
$940$	−20.9949	−	12.4097i	−0.684778	−	0.404760i
$941$	20.6472	−	49.8468i	0.673080	−	1.62496i	−0.103268	−	0.994654i	$-0.532930\pi$
$941$	20.6472	−	49.8468i	0.673080	−	1.62496i	0.776348	−	0.630305i	$-0.217070\pi$
$942$	46.8223	−	15.6272i	1.52555	−	0.509162i
$943$		−	4.28412i		−	0.139510i
$944$	−0.201454	+	0.0223365i	−0.00655678	+	0.000726992i
$945$		−	20.6367i		−	0.671313i
$946$	−6.01169	−	18.0122i	−0.195457	−	0.585628i
$947$	1.72478	−	4.16398i	0.0560477	−	0.135311i	−0.893375	−	0.449312i	$-0.851669\pi$
$947$	1.72478	−	4.16398i	0.0560477	−	0.135311i	0.949423	+	0.314000i	$0.101669\pi$
$948$	−28.4913	+	7.32245i	−0.925354	+	0.237822i
$949$	0.640829	−	0.265440i	0.0208022	−	0.00861656i
$950$	−10.0352	−	0.709350i	−0.325586	−	0.0230143i
$951$	−20.2681	−	20.2681i	−0.657239	−	0.657239i
$952$	−9.27962	−	6.40871i	−0.300754	−	0.207707i
$953$	−5.97020	+	5.97020i	−0.193394	+	0.193394i	−0.797161	−	0.603767i	$-0.793666\pi$
$953$	−5.97020	+	5.97020i	−0.193394	+	0.193394i	0.603767	+	0.797161i	$0.293666\pi$
$954$	10.3868	−	9.01536i	0.336286	−	0.291883i
$955$	−15.6691	−	37.8286i	−0.507040	−	1.22410i
$956$	7.13924	−	5.36292i	0.230900	−	0.173449i
$957$	−115.222	−	47.7265i	−3.72459	−	1.54278i
$958$	24.3345	−	48.7153i	0.786212	−	1.57392i
$959$	5.23794			0.169142
$960$	−14.7162	−	38.8625i	−0.474963	−	1.25428i
$961$	−0.443919			−0.0143200
$962$	−1.38266	+	2.76794i	−0.0445786	+	0.0892420i
$963$	14.9702	+	6.20085i	0.482407	+	0.199820i
$964$	−33.1255	+	24.8835i	−1.06690	+	0.801442i
$965$	0.203842	+	0.492118i	0.00656191	+	0.0158418i
$966$	4.10663	−	3.56439i	0.132129	−	0.114683i
$967$	20.7913	−	20.7913i	0.668603	−	0.668603i	−0.288789	−	0.957393i	$-0.593253\pi$
$967$	20.7913	−	20.7913i	0.668603	−	0.668603i	0.957393	+	0.288789i	$0.0932528\pi$
$968$	−44.7112	+	64.7405i	−1.43707	+	2.08084i
$969$	27.6047	+	27.6047i	0.886790	+	0.886790i
$970$	−33.5895	−	2.37430i	−1.07850	−	0.0762343i
$971$	34.3357	−	14.2223i	1.10189	−	0.456416i	0.243749	−	0.969838i	$-0.421623\pi$
$971$	34.3357	−	14.2223i	1.10189	−	0.456416i	0.858136	+	0.513422i	$0.171623\pi$
$972$	41.4963	−	10.6648i	1.33099	−	0.342074i
$973$	−6.91241	+	16.6880i	−0.221602	+	0.534993i
$974$	−12.5432	−	37.5820i	−0.401910	−	1.20420i
$975$		−	1.42689i		−	0.0456970i
$976$	29.8669	−	37.3159i	0.956017	−	1.19445i
$977$			9.84891i			0.315095i	0.987511	+	0.157547i	$0.0503587\pi$
$977$			9.84891i			0.315095i	−0.987511	+	0.157547i	$0.949641\pi$
$978$	86.6125	−	28.9074i	2.76956	−	0.924357i
$979$	−18.6252	+	44.9651i	−0.595263	+	1.43709i
$980$	2.83199	+	1.67394i	0.0904646	+	0.0534720i
$981$	79.2645	−	32.8324i	2.53072	−	1.04826i
$982$	−0.437143	+	6.18431i	−0.0139498	+	0.197349i
$983$	−22.7161	−	22.7161i	−0.724530	−	0.724530i	0.244994	−	0.969524i	$-0.421214\pi$
$983$	−22.7161	−	22.7161i	−0.724530	−	0.724530i	−0.969524	+	0.244994i	$0.921214\pi$
$984$	17.0573	+	26.3967i	0.543767	+	0.841496i
$985$	−2.05887	+	2.05887i	−0.0656012	+	0.0656012i
$986$	23.4286	+	26.9927i	0.746119	+	0.859622i
$987$	8.95925	+	21.6295i	0.285176	+	0.688476i
$988$	−0.171771	+	1.20896i	−0.00546477	+	0.0384622i
$989$	−2.42429	−	1.00417i	−0.0770880	−	0.0319309i
$990$	90.4054	+	45.1598i	2.87327	+	1.43527i
$991$	17.8682			0.567603			0.283801	−	0.958883i	$-0.408404\pi$
$991$	17.8682			0.567603			0.283801	+	0.958883i	$0.408404\pi$
$992$	−22.9745	−	21.2124i	−0.729441	−	0.673495i
$993$	−53.2349			−1.68936
$994$	0.324713	+	0.162202i	0.0102993	+	0.00514474i
$995$	18.0357	+	7.47063i	0.571770	+	0.236835i
$996$	−33.1877	−	4.71537i	−1.05159	−	0.149412i
$997$	4.49617	+	10.8547i	0.142395	+	0.343772i	0.978947	−	0.204116i	$-0.0654319\pi$
$997$	4.49617	+	10.8547i	0.142395	+	0.343772i	−0.836552	+	0.547888i	$0.815432\pi$
$998$	−19.9073	−	22.9357i	−0.630155	−	0.726018i
$999$	98.5617	−	98.5617i	3.11835	−	3.11835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.9	✓	52
4.3	odd	2		896.2.u.c.337.1		52
32.11	odd	8		896.2.u.c.561.1		52
32.21	even	8	inner	224.2.u.c.85.9	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.9	✓	52	1.1	even	1	trivial
224.2.u.c.85.9	yes	52	32.21	even	8	inner
896.2.u.c.337.1		52	4.3	odd	2
896.2.u.c.561.1		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.631975 - 1.26515i) q^{2} +(2.91760 + 1.20851i) q^{3} +(-1.20122 - 1.59909i) q^{4} +(-0.629460 - 1.51965i) q^{5} +(3.37279 - 2.92745i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.78223 + 0.509137i) q^{8} +(4.93055 + 4.93055i) q^{9} +O(q^{10})\)	\(q+(0.631975 - 1.26515i) q^{2} +(2.91760 + 1.20851i) q^{3} +(-1.20122 - 1.59909i) q^{4} +(-0.629460 - 1.51965i) q^{5} +(3.37279 - 2.92745i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.78223 + 0.509137i) q^{8} +(4.93055 + 4.93055i) q^{9} +(-2.32039 - 0.164019i) q^{10} +(-5.75610 + 2.38425i) q^{11} +(-1.57215 - 6.11717i) q^{12} +(0.0753604 - 0.181936i) q^{13} +(-0.447724 - 1.34147i) q^{14} -5.19444i q^{15} +(-1.11416 + 3.84170i) q^{16} +3.98721i q^{17} +(9.35388 - 3.12191i) q^{18} +(1.18647 - 2.86440i) q^{19} +(-1.67394 + 2.83199i) q^{20} +(2.91760 - 1.20851i) q^{21} +(-0.621266 + 8.78912i) q^{22} +(0.860956 + 0.860956i) q^{23} +(-8.73271 - 1.87688i) q^{24} +(1.62241 - 1.62241i) q^{25} +(-0.182551 - 0.210321i) q^{26} +(4.80123 + 11.5912i) q^{27} +(-1.98011 - 0.281338i) q^{28} +(5.85615 + 2.42570i) q^{29} +(-6.57175 - 3.28275i) q^{30} -5.52776 q^{31} +(4.15621 + 3.83744i) q^{32} -19.6754 q^{33} +(5.04443 + 2.51982i) q^{34} +(-1.51965 - 0.629460i) q^{35} +(1.96173 - 13.8070i) q^{36} +(-4.25158 - 10.2642i) q^{37} +(-2.87408 - 3.31130i) q^{38} +(0.439742 - 0.439742i) q^{39} +(2.52501 + 3.90753i) q^{40} +(-2.48800 - 2.48800i) q^{41} +(0.314901 - 4.45495i) q^{42} +(-1.99108 + 0.824733i) q^{43} +(10.7269 + 6.34050i) q^{44} +(4.38913 - 10.5963i) q^{45} +(1.63334 - 0.545137i) q^{46} +7.41348i q^{47} +(-7.89339 + 9.86205i) q^{48} -1.00000i q^{49} +(-1.02727 - 3.07792i) q^{50} +(-4.81857 + 11.6331i) q^{51} +(-0.381456 + 0.0980367i) q^{52} +(1.28857 - 0.533743i) q^{53} +(17.6989 + 1.25106i) q^{54} +(7.24647 + 7.24647i) q^{55} +(-1.60732 + 2.32735i) q^{56} +(6.92330 - 6.92330i) q^{57} +(6.76981 - 5.87594i) q^{58} +(0.0193914 + 0.0468150i) q^{59} +(-8.30636 + 6.23964i) q^{60} +(-11.0396 - 4.57274i) q^{61} +(-3.49340 + 6.99345i) q^{62} +6.97285 q^{63} +(7.48156 - 2.83307i) q^{64} -0.323916 q^{65} +(-12.4343 + 24.8923i) q^{66} +(3.63165 + 1.50428i) q^{67} +(6.37590 - 4.78950i) q^{68} +(1.47145 + 3.55239i) q^{69} +(-1.75674 + 1.52479i) q^{70} +(-0.181485 + 0.181485i) q^{71} +(-16.2282 - 11.2076i) q^{72} +(2.49063 + 2.49063i) q^{73} +(-15.6727 - 1.10784i) q^{74} +(6.69425 - 2.77285i) q^{75} +(-6.00564 + 1.54349i) q^{76} +(-2.38425 + 5.75610i) q^{77} +(-0.278435 - 0.834247i) q^{78} -4.65759i q^{79} +(6.53936 - 0.725061i) q^{80} +18.7021i q^{81} +(-4.72006 + 1.57535i) q^{82} +(2.03104 - 4.90335i) q^{83} +(-5.43717 - 3.21381i) q^{84} +(6.05917 - 2.50979i) q^{85} +(-0.214901 + 3.04023i) q^{86} +(14.1544 + 14.1544i) q^{87} +(14.8009 - 9.56418i) q^{88} +(5.52373 - 5.52373i) q^{89} +(-10.6321 - 12.2495i) q^{90} +(-0.0753604 - 0.181936i) q^{91} +(0.342550 - 2.41094i) q^{92} +(-16.1278 - 6.68033i) q^{93} +(9.37917 + 4.68513i) q^{94} -5.09973 q^{95} +(7.48856 + 16.2189i) q^{96} +14.4758 q^{97} +(-1.26515 - 0.631975i) q^{98} +(-40.1364 - 16.6251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more