LMFDB - Embedded newform 572.2.y.a.79.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(79,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 0]))

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

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

chi := DirichletCharacter("572.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.y (of order $10$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			79.16
Character	$\chi$	$=$	572.79
Dual form			572.2.y.a.391.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10068 + 0.887979i) q^{2} +(-0.684477 - 0.942102i) q^{3} +(0.422987 - 1.95476i) q^{4} +(-0.0530453 - 0.163257i) q^{5} +(1.58996 + 0.429150i) q^{6} +(0.351116 + 0.255100i) q^{7} +(1.27021 + 2.52717i) q^{8} +(0.508004 - 1.56347i) q^{9} +O(q^{10})$	\(q+(-1.10068 + 0.887979i) q^{2} +(-0.684477 - 0.942102i) q^{3} +(0.422987 - 1.95476i) q^{4} +(-0.0530453 - 0.163257i) q^{5} +(1.58996 + 0.429150i) q^{6} +(0.351116 + 0.255100i) q^{7} +(1.27021 + 2.52717i) q^{8} +(0.508004 - 1.56347i) q^{9} +(0.203354 + 0.132590i) q^{10} +(2.28237 + 2.40640i) q^{11} +(-2.13111 + 0.939491i) q^{12} +(-0.951057 - 0.309017i) q^{13} +(-0.612989 + 0.0309996i) q^{14} +(-0.117496 + 0.161720i) q^{15} +(-3.64216 - 1.65368i) q^{16} +(4.01222 - 1.30365i) q^{17} +(0.829184 + 2.17198i) q^{18} +(-4.72891 + 3.43575i) q^{19} +(-0.341565 + 0.0346353i) q^{20} -0.505397i q^{21} +(-4.64899 - 0.621978i) q^{22} -4.96983i q^{23} +(1.51142 - 2.92646i) q^{24} +(4.02125 - 2.92161i) q^{25} +(1.32121 - 0.504390i) q^{26} +(-5.14319 + 1.67112i) q^{27} +(0.647177 - 0.578442i) q^{28} +(4.82468 - 6.64060i) q^{29} +(-0.0142781 - 0.282336i) q^{30} +(1.44761 + 0.470356i) q^{31} +(5.47728 - 1.41400i) q^{32} +(0.704845 - 3.79736i) q^{33} +(-3.25855 + 4.99766i) q^{34} +(0.0230218 - 0.0708539i) q^{35} +(-2.84134 - 1.65435i) q^{36} +(-0.700727 - 0.509108i) q^{37} +(2.15413 - 7.98083i) q^{38} +(0.359851 + 1.10751i) q^{39} +(0.345198 - 0.341425i) q^{40} +(-2.36383 - 3.25353i) q^{41} +(0.448782 + 0.556280i) q^{42} +7.99574 q^{43} +(5.66935 - 3.44361i) q^{44} -0.282195 q^{45} +(4.41311 + 5.47019i) q^{46} +(-6.03303 - 8.30375i) q^{47} +(0.935046 + 4.56319i) q^{48} +(-2.10491 - 6.47826i) q^{49} +(-1.83178 + 6.78653i) q^{50} +(-3.97444 - 2.88760i) q^{51} +(-1.00634 + 1.72838i) q^{52} +(-0.399513 + 1.22957i) q^{53} +(4.17708 - 6.40642i) q^{54} +(0.271792 - 0.500261i) q^{55} +(-0.198690 + 1.21136i) q^{56} +(6.47366 + 2.10342i) q^{57} +(0.586291 + 11.5934i) q^{58} +(5.24591 - 7.22037i) q^{59} +(0.266424 + 0.298082i) q^{60} +(12.6514 - 4.11070i) q^{61} +(-2.01102 + 0.767733i) q^{62} +(0.577211 - 0.419368i) q^{63} +(-4.77313 + 6.42007i) q^{64} +0.171658i q^{65} +(2.59616 + 4.80556i) q^{66} +9.93440i q^{67} +(-0.851201 - 8.39434i) q^{68} +(-4.68209 + 3.40174i) q^{69} +(0.0375771 + 0.0984302i) q^{70} +(12.9798 - 4.21738i) q^{71} +(4.59643 - 0.702134i) q^{72} +(-9.25034 + 12.7320i) q^{73} +(1.22335 - 0.0618664i) q^{74} +(-5.50490 - 1.78865i) q^{75} +(4.71580 + 10.6971i) q^{76} +(0.187502 + 1.42716i) q^{77} +(-1.37952 - 0.899470i) q^{78} +(0.843069 - 2.59470i) q^{79} +(-0.0767740 + 0.682328i) q^{80} +(1.10485 + 0.802724i) q^{81} +(5.49088 + 1.48206i) q^{82} +(-1.31867 - 4.05846i) q^{83} +(-0.987929 - 0.213777i) q^{84} +(-0.425659 - 0.585869i) q^{85} +(-8.80074 + 7.10004i) q^{86} -9.55850 q^{87} +(-3.18228 + 8.82457i) q^{88} -6.84683 q^{89} +(0.310606 - 0.250583i) q^{90} +(-0.255100 - 0.351116i) q^{91} +(-9.71482 - 2.10218i) q^{92} +(-0.547731 - 1.68574i) q^{93} +(14.0140 + 3.78256i) q^{94} +(0.811756 + 0.589775i) q^{95} +(-5.08120 - 4.19231i) q^{96} +(2.90795 - 8.94976i) q^{97} +(8.06939 + 5.26136i) q^{98} +(4.92180 - 2.34597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) $ 288 * q - 4 * q^4 + 80 * q^9	$ 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) $ 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.10068	+	0.887979i	−0.778297	+	0.627896i
$2$	−1.10068	+	0.887979i	−0.778297	+	0.627896i
$3$	−0.684477	−	0.942102i	−0.395183	−	0.543923i	0.564344	−	0.825540i	$-0.309129\pi$
$3$	−0.684477	−	0.942102i	−0.395183	−	0.543923i	−0.959527	+	0.281617i	$0.909129\pi$
$4$	0.422987	−	1.95476i	0.211494	−	0.977379i
$5$	−0.0530453	−	0.163257i	−0.0237226	−	0.0730107i	0.938494	−	0.345295i	$-0.112221\pi$
$5$	−0.0530453	−	0.163257i	−0.0237226	−	0.0730107i	−0.962217	+	0.272284i	$0.912221\pi$
$6$	1.58996	+	0.429150i	0.649097	+	0.175200i
$7$	0.351116	+	0.255100i	0.132709	+	0.0964189i	0.652159	−	0.758082i	$-0.273863\pi$
$7$	0.351116	+	0.255100i	0.132709	+	0.0964189i	−0.519450	+	0.854501i	$0.673863\pi$
$8$	1.27021	+	2.52717i	0.449087	+	0.893488i
$9$	0.508004	−	1.56347i	0.169335	−	0.521158i
$10$	0.203354	+	0.132590i	0.0643063	+	0.0419287i
$11$	2.28237	+	2.40640i	0.688161	+	0.725558i
$11$	2.28237	+	2.40640i	0.688161	+	0.725558i
$12$	−2.13111	+	0.939491i	−0.615198	+	0.271208i
$13$	−0.951057	−	0.309017i	−0.263776	−	0.0857059i
$13$	−0.951057	−	0.309017i	−0.263776	−	0.0857059i
$14$	−0.612989	+	0.0309996i	−0.163828	+	0.00828499i
$15$	−0.117496	+	0.161720i	−0.0303374	+	0.0417558i
$16$	−3.64216	−	1.65368i	−0.910541	−	0.413419i
$17$	4.01222	−	1.30365i	0.973106	−	0.316181i	0.221037	−	0.975266i	$-0.429056\pi$
$17$	4.01222	−	1.30365i	0.973106	−	0.316181i	0.752069	+	0.659084i	$0.229056\pi$
$18$	0.829184	+	2.17198i	0.195440	+	0.511941i
$19$	−4.72891	+	3.43575i	−1.08489	+	0.788215i	−0.978528	−	0.206113i	$-0.933919\pi$
$19$	−4.72891	+	3.43575i	−1.08489	+	0.788215i	−0.106357	+	0.994328i	$0.533919\pi$
$20$	−0.341565	+	0.0346353i	−0.0763763	+	0.00774469i
$21$		−	0.505397i		−	0.110287i
$22$	−4.64899	−	0.621978i	−0.991169	−	0.132606i
$23$		−	4.96983i		−	1.03628i	−0.855295	−	0.518141i	$-0.826624\pi$
$23$		−	4.96983i		−	1.03628i	0.855295	−	0.518141i	$-0.173376\pi$
$24$	1.51142	−	2.92646i	0.308517	−	0.597360i
$25$	4.02125	−	2.92161i	0.804249	−	0.584321i
$26$	1.32121	−	0.504390i	0.259110	−	0.0989189i
$27$	−5.14319	+	1.67112i	−0.989808	+	0.321608i
$28$	0.647177	−	0.578442i	0.122305	−	0.109315i
$29$	4.82468	−	6.64060i	0.895920	−	1.23313i	−0.0758315	−	0.997121i	$-0.524161\pi$
$29$	4.82468	−	6.64060i	0.895920	−	1.23313i	0.971751	−	0.236007i	$-0.0758389\pi$
$30$	−0.0142781	−	0.282336i	−0.00260680	−	0.0515472i
$31$	1.44761	+	0.470356i	0.259998	+	0.0844784i	0.436115	−	0.899891i	$-0.356354\pi$
$31$	1.44761	+	0.470356i	0.259998	+	0.0844784i	−0.176118	+	0.984369i	$0.556354\pi$
$32$	5.47728	−	1.41400i	0.968256	−	0.249962i
$33$	0.704845	−	3.79736i	0.122698	−	0.661035i
$34$	−3.25855	+	4.99766i	−0.558837	+	0.857092i
$35$	0.0230218	−	0.0708539i	0.00389140	−	0.0119765i
$36$	−2.84134	−	1.65435i	−0.473556	−	0.275726i
$37$	−0.700727	−	0.509108i	−0.115199	−	0.0836968i	0.528694	−	0.848812i	$-0.322682\pi$
$37$	−0.700727	−	0.509108i	−0.115199	−	0.0836968i	−0.643893	+	0.765116i	$0.722682\pi$
$38$	2.15413	−	7.98083i	0.349446	−	1.29466i
$39$	0.359851	+	1.10751i	0.0576223	+	0.177343i
$40$	0.345198	−	0.341425i	0.0545806	−	0.0539840i
$41$	−2.36383	−	3.25353i	−0.369168	−	0.508116i	0.583506	−	0.812108i	$-0.301680\pi$
$41$	−2.36383	−	3.25353i	−0.369168	−	0.508116i	−0.952674	+	0.303992i	$0.901680\pi$
$42$	0.448782	+	0.556280i	0.0692485	+	0.0858358i
$43$	7.99574			1.21934			0.609669	−	0.792656i	$-0.291302\pi$
$43$	7.99574			1.21934			0.609669	+	0.792656i	$0.291302\pi$
$44$	5.66935	−	3.44361i	0.854687	−	0.519144i
$45$	−0.282195			−0.0420672
$46$	4.41311	+	5.47019i	0.650677	+	0.806535i
$47$	−6.03303	−	8.30375i	−0.880008	−	1.21123i	−0.976419	−	0.215885i	$-0.930736\pi$
$47$	−6.03303	−	8.30375i	−0.880008	−	1.21123i	0.0964107	−	0.995342i	$-0.469264\pi$
$48$	0.935046	+	4.56319i	0.134962	+	0.658640i
$49$	−2.10491	−	6.47826i	−0.300702	−	0.925465i
$50$	−1.83178	+	6.78653i	−0.259052	+	0.959760i
$51$	−3.97444	−	2.88760i	−0.556533	−	0.404345i
$52$	−1.00634	+	1.72838i	−0.139554	+	0.239683i
$53$	−0.399513	+	1.22957i	−0.0548773	+	0.168895i	−0.974739	−	0.223349i	$-0.928301\pi$
$53$	−0.399513	+	1.22957i	−0.0548773	+	0.168895i	0.919861	+	0.392244i	$0.128301\pi$
$54$	4.17708	−	6.40642i	0.568428	−	0.871803i
$55$	0.271792	−	0.500261i	0.0366485	−	0.0674552i
$56$	−0.198690	+	1.21136i	−0.0265510	+	0.161875i
$57$	6.47366	+	2.10342i	0.857457	+	0.278605i
$58$	0.586291	+	11.5934i	0.0769838	+	1.52228i
$59$	5.24591	−	7.22037i	0.682959	−	0.940013i	−0.317005	−	0.948424i	$-0.602677\pi$
$59$	5.24591	−	7.22037i	0.682959	−	0.940013i	0.999965	+	0.00841101i	$0.00267734\pi$
$60$	0.266424	+	0.298082i	0.0343951	+	0.0384822i
$61$	12.6514	−	4.11070i	1.61985	−	0.526321i	0.647942	−	0.761689i	$-0.275630\pi$
$61$	12.6514	−	4.11070i	1.61985	−	0.526321i	0.971906	+	0.235369i	$0.0756297\pi$
$62$	−2.01102	+	0.767733i	−0.255399	+	0.0975022i
$63$	0.577211	−	0.419368i	0.0727217	−	0.0528354i
$64$	−4.77313	+	6.42007i	−0.596641	+	0.802508i
$65$			0.171658i			0.0212916i
$66$	2.59616	+	4.80556i	0.319566	+	0.591523i
$67$			9.93440i			1.21368i	0.794824	+	0.606840i	$0.207563\pi$
$67$			9.93440i			1.21368i	−0.794824	+	0.606840i	$0.792437\pi$
$68$	−0.851201	−	8.39434i	−0.103223	−	1.01796i
$69$	−4.68209	+	3.40174i	−0.563657	+	0.409521i
$70$	0.0375771	+	0.0984302i	0.00449132	+	0.0117647i
$71$	12.9798	−	4.21738i	1.54041	−	0.500511i	0.588924	−	0.808189i	$-0.299552\pi$
$71$	12.9798	−	4.21738i	1.54041	−	0.500511i	0.951491	+	0.307678i	$0.0995519\pi$
$72$	4.59643	−	0.702134i	0.541695	−	0.0827473i
$73$	−9.25034	+	12.7320i	−1.08267	+	1.49017i	−0.226123	+	0.974099i	$0.572605\pi$
$73$	−9.25034	+	12.7320i	−1.08267	+	1.49017i	−0.856547	+	0.516069i	$0.827395\pi$
$74$	1.22335	−	0.0618664i	0.142212	−	0.00719182i
$75$	−5.50490	−	1.78865i	−0.635651	−	0.206536i
$76$	4.71580	+	10.6971i	0.540939	+	1.22705i
$77$	0.187502	+	1.42716i	0.0213679	+	0.162640i
$78$	−1.37952	−	0.899470i	−0.156200	−	0.101845i
$79$	0.843069	−	2.59470i	0.0948527	−	0.291927i	−0.892363	−	0.451319i	$-0.850954\pi$
$79$	0.843069	−	2.59470i	0.0948527	−	0.291927i	0.987215	+	0.159393i	$0.0509536\pi$
$80$	−0.0767740	+	0.682328i	−0.00858360	+	0.0762866i
$81$	1.10485	+	0.802724i	0.122762	+	0.0891915i
$82$	5.49088	+	1.48206i	0.606367	+	0.163666i
$83$	−1.31867	−	4.05846i	−0.144743	−	0.445473i	0.852235	−	0.523160i	$-0.175247\pi$
$83$	−1.31867	−	4.05846i	−0.144743	−	0.445473i	−0.996978	+	0.0776861i	$0.975247\pi$
$84$	−0.987929	−	0.213777i	−0.107792	−	0.0233249i
$85$	−0.425659	−	0.585869i	−0.0461692	−	0.0635464i
$86$	−8.80074	+	7.10004i	−0.949008	+	0.765617i
$87$	−9.55850			−1.02478
$88$	−3.18228	+	8.82457i	−0.339232	+	0.940703i
$89$	−6.84683			−0.725763			−0.362882	−	0.931835i	$-0.618207\pi$
$89$	−6.84683			−0.725763			−0.362882	+	0.931835i	$0.618207\pi$
$90$	0.310606	−	0.250583i	0.0327408	−	0.0264138i
$91$	−0.255100	−	0.351116i	−0.0267418	−	0.0368069i
$92$	−9.71482	−	2.10218i	−1.01284	−	0.219167i
$93$	−0.547731	−	1.68574i	−0.0567970	−	0.174803i
$94$	14.0140	+	3.78256i	1.44543	+	0.390142i
$95$	0.811756	+	0.589775i	0.0832844	+	0.0605097i
$96$	−5.08120	−	4.19231i	−0.518598	−	0.427876i
$97$	2.90795	−	8.94976i	0.295258	−	0.908710i	−0.687877	−	0.725827i	$-0.741457\pi$
$97$	2.90795	−	8.94976i	0.295258	−	0.908710i	0.983135	−	0.182883i	$-0.0585429\pi$
$98$	8.06939	+	5.26136i	0.815131	+	0.531478i
$99$	4.92180	−	2.34597i	0.494660	−	0.235779i
$100$	−4.01010	−	9.09637i	−0.401010	−	0.909637i
$101$	11.3812	+	3.69799i	1.13248	+	0.367964i	0.814516	−	0.580141i	$-0.197002\pi$
$101$	11.3812	+	3.69799i	1.13248	+	0.367964i	0.317960	+	0.948104i	$0.397002\pi$
$102$	6.93871	−	0.350899i	0.687035	−	0.0347442i
$103$	−4.40417	+	6.06182i	−0.433956	+	0.597289i	−0.968855	−	0.247627i	$-0.920349\pi$
$103$	−4.40417	+	6.06182i	−0.433956	+	0.597289i	0.534900	+	0.844915i	$0.320349\pi$
$104$	−0.427106	−	2.79599i	−0.0418812	−	0.274170i
$105$	−0.0825095	+	0.0268090i	−0.00805210	+	0.00261629i
$106$	−0.652101	−	1.70813i	−0.0633376	−	0.165908i
$107$	−8.97064	+	6.51755i	−0.867224	+	0.630075i	−0.929841	−	0.367962i	$-0.880056\pi$
$107$	−8.97064	+	6.51755i	−0.867224	+	0.630075i	0.0626163	+	0.998038i	$0.480056\pi$
$108$	1.09114	+	10.7606i	0.104995	+	1.03544i
$109$		−	3.66506i		−	0.351049i	−0.984475	−	0.175524i	$-0.943838\pi$
$109$		−	3.66506i		−	0.351049i	0.984475	−	0.175524i	$-0.0561621\pi$
$110$	0.145065	+	0.791973i	0.0138314	+	0.0755116i
$111$			1.00863i			0.0957348i
$112$	−0.856967	−	1.50975i	−0.0809757	−	0.142658i
$113$	−15.5007	+	11.2619i	−1.45819	+	1.05943i	−0.474355	+	0.880334i	$0.657319\pi$
$113$	−15.5007	+	11.2619i	−1.45819	+	1.05943i	−0.983831	+	0.179100i	$0.942681\pi$
$114$	−8.99321	+	3.43328i	−0.842291	+	0.321556i
$115$	−0.811359	+	0.263627i	−0.0756596	+	0.0245833i
$116$	−10.9400	−	12.2400i	−1.01575	−	1.13645i
$117$	−0.966281	+	1.32997i	−0.0893327	+	0.122956i
$118$	0.637479	+	12.6056i	0.0586847	+	1.16044i
$119$	1.74131	+	0.565787i	0.159626	+	0.0518656i
$120$	−0.557937	−	0.0915142i	−0.0509325	−	0.00835407i
$121$	−0.581552	+	10.9846i	−0.0528683	+	0.998601i
$122$	−10.2749	+	15.7588i	−0.930249	+	1.42673i
$123$	−1.44717	+	4.45394i	−0.130487	+	0.401598i
$124$	1.53175	−	2.63077i	0.137555	−	0.236250i
$125$	−1.38465	−	1.00601i	−0.123847	−	0.0899802i
$126$	−0.262934	+	0.974141i	−0.0234240	+	0.0867834i
$127$	−3.58436	−	11.0315i	−0.318060	−	0.978889i	−0.974476	−	0.224490i	$-0.927928\pi$
$127$	−3.58436	−	11.0315i	−0.318060	−	0.978889i	0.656416	−	0.754399i	$-0.272072\pi$
$128$	−0.447204	−	11.3049i	−0.0395276	−	0.999218i
$129$	−5.47290	−	7.53280i	−0.481862	−	0.663226i
$130$	−0.152429	−	0.188941i	−0.0133689	−	0.0165712i
$131$	11.0415			0.964699			0.482350	−	0.875979i	$-0.339784\pi$
$131$	11.0415			0.964699			0.482350	+	0.875979i	$0.339784\pi$
$132$	−7.12477	−	2.98404i	−0.620132	−	0.259727i
$133$	−2.53685			−0.219973
$134$	−8.82154	−	10.9346i	−0.762065	−	0.944604i
$135$	0.545645	+	0.751016i	0.0469616	+	0.0646371i
$136$	8.39090	+	8.48363i	0.719514	+	0.727465i
$137$	0.145442	+	0.447624i	0.0124259	+	0.0382431i	0.957077	−	0.289833i	$-0.0935998\pi$
$137$	0.145442	+	0.447624i	0.0124259	+	0.0382431i	−0.944651	+	0.328076i	$0.893600\pi$
$138$	2.13281	−	7.90182i	0.181557	−	0.672647i
$139$	−17.8411	−	12.9623i	−1.51326	−	1.09945i	−0.964705	−	0.263332i	$-0.915179\pi$
$139$	−17.8411	−	12.9623i	−1.51326	−	1.09945i	−0.548554	−	0.836115i	$-0.684821\pi$
$140$	−0.128764	−	0.0749724i	−0.0108826	−	0.00633632i
$141$	−3.69351	+	11.3675i	−0.311050	+	0.957313i
$142$	−10.5416	+	16.1677i	−0.884632	+	1.35677i
$143$	−1.42705	−	2.99392i	−0.119336	−	0.250364i
$144$	−4.43571	+	4.85436i	−0.369643	+	0.404530i
$145$	−1.34005	−	0.435408i	−0.111285	−	0.0361587i
$146$	−1.12409	−	22.2279i	−0.0930307	−	1.83960i
$147$	−4.66241	+	6.41726i	−0.384549	+	0.529287i
$148$	−1.29158	+	1.15441i	−0.106167	+	0.0948916i
$149$	11.5791	−	3.76227i	0.948595	−	0.308217i	0.206450	−	0.978457i	$-0.433809\pi$
$149$	11.5791	−	3.76227i	0.948595	−	0.308217i	0.742144	+	0.670240i	$0.233809\pi$
$150$	7.64741	−	2.91951i	0.624409	−	0.238377i
$151$	−10.7466	+	7.80786i	−0.874545	+	0.635394i	−0.931803	−	0.362965i	$-0.881764\pi$
$151$	−10.7466	+	7.80786i	−0.874545	+	0.635394i	0.0572575	+	0.998359i	$0.481764\pi$
$152$	−14.6894	−	7.58660i	−1.19147	−	0.615354i
$153$		−	6.93526i		−	0.560682i
$154$	−1.47367	−	1.40435i	−0.118751	−	0.113165i
$155$		−	0.261282i		−	0.0209867i
$156$	2.31712	−	0.234960i	0.185518	−	0.0188119i
$157$	−11.9270	+	8.66546i	−0.951877	+	0.691579i	−0.951250	−	0.308421i	$-0.900200\pi$
$157$	−11.9270	+	8.66546i	−0.951877	+	0.691579i	−0.000626978		1.00000i	$0.500200\pi$
$158$	1.37609	+	3.60456i	0.109476	+	0.286763i
$159$	1.43184	−	0.465234i	0.113553	−	0.0368954i
$160$	−0.521389	−	0.819197i	−0.0412194	−	0.0647632i
$161$	1.26781	−	1.74499i	0.0999171	−	0.137524i
$162$	−1.92889	+	0.0975464i	−0.151548	+	0.00766397i
$163$	0.501667	+	0.163001i	0.0392936	+	0.0127673i	0.328598	−	0.944470i	$-0.393424\pi$
$163$	0.501667	+	0.163001i	0.0392936	+	0.0127673i	−0.289304	+	0.957237i	$0.593424\pi$
$164$	−7.35974	+	3.24451i	−0.574699	+	0.253354i
$165$	−0.657333	+	0.0863613i	−0.0511733	+	0.00672322i
$166$	5.05526	+	3.29610i	0.392364	+	0.255827i
$167$	−0.295959	+	0.910869i	−0.0229020	+	0.0704852i	−0.961854	−	0.273562i	$-0.911798\pi$
$167$	−0.295959	+	0.910869i	−0.0229020	+	0.0704852i	0.938952	+	0.344047i	$0.111798\pi$
$168$	1.27722	−	0.641961i	0.0985398	−	0.0495284i
$169$	0.809017	+	0.587785i	0.0622321	+	0.0452143i
$170$	0.988753	+	0.266878i	0.0758339	+	0.0204686i
$171$	2.96941	+	9.13890i	0.227076	+	0.698869i
$172$	3.38209	−	15.6297i	0.257882	−	1.19176i
$173$	6.39045	+	8.79570i	0.485857	+	0.668725i	0.979617	−	0.200873i	$-0.0643780\pi$
$173$	6.39045	+	8.79570i	0.485857	+	0.668725i	−0.493760	+	0.869598i	$0.664378\pi$
$174$	10.5208	−	8.48775i	0.797583	−	0.643454i
$175$	2.15722			0.163071
$176$	−4.33336	−	12.5388i	−0.326639	−	0.945149i
$177$	−10.3930			−0.781188
$178$	7.53617	−	6.07984i	0.564859	−	0.455704i
$179$	3.66962	+	5.05079i	0.274280	+	0.377514i	0.923829	−	0.382806i	$-0.125042\pi$
$179$	3.66962	+	5.05079i	0.274280	+	0.377514i	−0.649549	+	0.760320i	$0.725042\pi$
$180$	−0.119365	+	0.551623i	−0.00889694	+	0.0411156i
$181$	6.68181	+	20.5645i	0.496655	+	1.52855i	0.814361	+	0.580358i	$0.197087\pi$
$181$	6.68181	+	20.5645i	0.496655	+	1.52855i	−0.317706	+	0.948189i	$0.602913\pi$
$182$	0.592567	+	0.159942i	0.0439240	+	0.0118557i
$183$	−12.5323	−	9.10525i	−0.926415	−	0.673080i
$184$	12.5596	−	6.31274i	0.925905	−	0.465381i
$185$	−0.0459450	+	0.141404i	−0.00337794	+	0.0103962i
$186$	2.09978	+	1.36909i	0.153963	+	0.100386i
$187$	12.2945	+	6.67960i	0.899061	+	0.488461i
$188$	−18.7837	+	8.28074i	−1.36994	+	0.603935i
$189$	−2.23216	−	0.725272i	−0.162366	−	0.0527558i
$190$	−1.41719	+	0.0716691i	−0.102814	+	0.00519942i
$191$	11.0158	−	15.1619i	0.797073	−	1.09708i	−0.196118	−	0.980580i	$-0.562833\pi$
$191$	11.0158	−	15.1619i	0.797073	−	1.09708i	0.993191	−	0.116497i	$-0.0371665\pi$
$192$	9.31546	+	0.102383i	0.672285	+	0.00738887i
$193$	22.4194	−	7.28451i	1.61379	−	0.524351i	0.643321	−	0.765596i	$-0.277556\pi$
$193$	22.4194	−	7.28451i	1.61379	−	0.524351i	0.970464	+	0.241246i	$0.0775560\pi$
$194$	4.74647	+	12.4330i	0.340777	+	0.892638i
$195$	0.161720	−	0.117496i	0.0115810	−	0.00841408i
$196$	−13.5538	+	1.37438i	−0.968127	+	0.0981698i
$197$			19.8986i			1.41772i	0.705351	+	0.708858i	$0.250789\pi$
$197$			19.8986i			1.41772i	−0.705351	+	0.708858i	$0.749211\pi$
$198$	−3.33415	+	6.95262i	−0.236948	+	0.494101i
$199$			6.99660i			0.495976i	0.968763	+	0.247988i	$0.0797694\pi$
$199$			6.99660i			0.495976i	−0.968763	+	0.247988i	$0.920231\pi$
$200$	12.4912	+	6.45130i	0.883262	+	0.456175i
$201$	9.35922	−	6.79987i	0.660148	−	0.479626i
$202$	−15.8108	+	6.03600i	−1.11245	+	0.424692i
$203$	3.38804	−	1.10084i	0.237794	−	0.0772638i
$204$	−7.32570	+	6.54765i	−0.512902	+	0.458428i
$205$	−0.405771	+	0.558496i	−0.0283403	+	0.0390070i
$206$	−0.535191	−	10.5829i	−0.0372885	−	0.737347i
$207$	−7.77021	−	2.52469i	−0.540067	−	0.175478i
$208$	2.95289	+	2.69823i	0.204746	+	0.187089i
$209$	−19.0609	−	3.53799i	−1.31847	−	0.244728i
$210$	0.0670107	−	0.102775i	0.00462418	−	0.00709213i
$211$	−6.15052	+	18.9293i	−0.423419	+	1.30315i	0.481081	+	0.876676i	$0.340244\pi$
$211$	−6.15052	+	18.9293i	−0.423419	+	1.30315i	−0.904500	+	0.426474i	$0.859756\pi$
$212$	2.23453	+	1.30105i	0.153468	+	0.0893562i
$213$	−12.8576	−	9.34156i	−0.880985	−	0.640073i
$214$	4.08634	−	15.1395i	0.279337	−	1.03491i
$215$	−0.424137	−	1.30536i	−0.0289259	−	0.0890247i
$216$	−10.7561	−	10.8750i	−0.731863	−	0.739951i
$217$	0.388289	+	0.534434i	0.0263588	+	0.0362798i
$218$	3.25449	+	4.03405i	0.220422	+	0.273220i
$219$	18.3265			1.23839
$220$	−0.862925	−	0.742893i	−0.0581784	−	0.0500858i
$221$	−4.21869			−0.283780
$222$	−0.895641	−	1.11018i	−0.0601115	−	0.0745101i
$223$	9.15773	+	12.6045i	0.613247	+	0.844062i	0.996840	−	0.0794403i	$-0.0253133\pi$
$223$	9.15773	+	12.6045i	0.613247	+	0.844062i	−0.383593	+	0.923502i	$0.625313\pi$
$224$	2.28387	+	0.900780i	0.152597	+	0.0601859i
$225$	−2.52505	−	7.77130i	−0.168337	−	0.518087i
$226$	7.06096	−	26.1601i	0.469688	−	1.74014i
$227$	6.10372	+	4.43461i	0.405118	+	0.294335i	0.771622	−	0.636081i	$-0.219446\pi$
$227$	6.10372	+	4.43461i	0.405118	+	0.294335i	−0.366504	+	0.930416i	$0.619446\pi$
$228$	6.84995	−	11.7647i	0.453649	−	0.779137i
$229$	−3.29696	+	10.1470i	−0.217869	+	0.670532i	0.781068	+	0.624445i	$0.214675\pi$
$229$	−3.29696	+	10.1470i	−0.217869	+	0.670532i	−0.998937	+	0.0460865i	$0.985325\pi$
$230$	0.658951	−	1.01064i	0.0434499	−	0.0666395i
$231$	1.21619	−	1.15350i	0.0800194	−	0.0758950i
$232$	22.9102	+	3.75779i	1.50413	+	0.246711i
$233$	9.10237	+	2.95754i	0.596316	+	0.193755i	0.591597	−	0.806234i	$-0.298498\pi$
$233$	9.10237	+	2.95754i	0.596316	+	0.193755i	0.00471949	+	0.999989i	$0.498498\pi$
$234$	−0.117422	−	2.32191i	−0.00767610	−	0.151788i
$235$	−1.03562	+	1.42541i	−0.0675564	+	0.0929834i
$236$	−11.8951	−	13.3086i	−0.774308	−	0.866317i
$237$	−3.02153	+	0.981756i	−0.196270	+	0.0637719i
$238$	−2.41903	+	0.923499i	−0.156803	+	0.0598616i
$239$	11.7841	−	8.56162i	0.762247	−	0.553805i	−0.137352	−	0.990522i	$-0.543859\pi$
$239$	11.7841	−	8.56162i	0.762247	−	0.553805i	0.899599	+	0.436717i	$0.143859\pi$
$240$	0.695372	−	0.394709i	0.0448861	−	0.0254783i
$241$		−	0.844506i		−	0.0543994i	−0.999630	−	0.0271997i	$-0.991341\pi$
$241$		−	0.844506i		−	0.0543994i	0.999630	−	0.0271997i	$-0.00865900\pi$
$242$	−9.11401	−	12.6069i	−0.585870	−	0.810405i
$243$			14.6333i			0.938726i
$244$	−2.68403	−	26.4693i	−0.171827	−	1.69452i
$245$	−0.945963	+	0.687283i	−0.0604354	+	0.0439089i
$246$	−2.36213	−	6.18741i	−0.150604	−	0.394495i
$247$	5.55916	−	1.80628i	0.353721	−	0.114931i
$248$	0.650099	+	4.25579i	0.0412813	+	0.270243i
$249$	−2.92088	+	4.02024i	−0.185103	+	0.254773i
$250$	2.41737	−	0.122249i	0.152888	−	0.00773174i
$251$	11.0858	+	3.60200i	0.699730	+	0.227356i	0.637213	−	0.770688i	$-0.280087\pi$
$251$	11.0858	+	3.60200i	0.699730	+	0.227356i	0.0625174	+	0.998044i	$0.480087\pi$
$252$	−0.575611	−	1.30570i	−0.0362601	−	0.0822511i
$253$	11.9594	−	11.3430i	0.751882	−	0.713129i
$254$	13.7410	+	8.95933i	0.862186	+	0.562158i
$255$	−0.260595	+	0.802028i	−0.0163191	+	0.0502250i
$256$	10.5307	+	12.0459i	0.658169	+	0.752870i
$257$	9.47120	+	6.88123i	0.590797	+	0.429239i	0.842600	−	0.538539i	$-0.181024\pi$
$257$	9.47120	+	6.88123i	0.590797	+	0.429239i	−0.251803	+	0.967778i	$0.581024\pi$
$258$	12.7129	+	3.43137i	0.791469	+	0.213628i
$259$	−0.116162	−	0.357511i	−0.00721798	−	0.0222147i
$260$	0.335551	+	0.0726093i	0.0208100	+	0.00450304i
$261$	−7.93145	−	10.9167i	−0.490945	−	0.675727i
$262$	−12.1531	+	9.80460i	−0.750823	+	0.605731i
$263$	28.0732			1.73107			0.865535	−	0.500849i	$-0.166979\pi$
$263$	28.0732			1.73107			0.865535	+	0.500849i	$0.166979\pi$
$264$	10.4918	−	3.04218i	0.645729	−	0.187233i
$265$	0.221929			0.0136330
$266$	2.79226	−	2.25267i	0.171204	−	0.138120i
$267$	4.68650	+	6.45042i	0.286809	+	0.394759i
$268$	19.4194	+	4.20213i	1.18623	+	0.256686i
$269$	−2.32433	−	7.15356i	−0.141717	−	0.436160i	0.854857	−	0.518863i	$-0.173645\pi$
$269$	−2.32433	−	7.15356i	−0.141717	−	0.436160i	−0.996574	+	0.0827031i	$0.973645\pi$
$270$	−1.26747	−	0.342106i	−0.0771355	−	0.0208199i
$271$	3.19198	+	2.31911i	0.193899	+	0.140876i	0.680499	−	0.732749i	$-0.261763\pi$
$271$	3.19198	+	2.31911i	0.193899	+	0.140876i	−0.486600	+	0.873625i	$0.661763\pi$
$272$	−16.7690	−	1.88681i	−1.01677	−	0.114405i
$273$	−0.156176	+	0.480661i	−0.00945222	+	0.0290909i
$274$	−0.557565	−	0.363541i	−0.0336837	−	0.0219623i
$275$	16.2085	+	3.00855i	0.977412	+	0.181422i
$276$	4.66911	+	10.5912i	0.281047	+	0.637518i
$277$	−4.69419	−	1.52523i	−0.282046	−	0.0916424i	0.164578	−	0.986364i	$-0.447374\pi$
$277$	−4.69419	−	1.52523i	−0.282046	−	0.0916424i	−0.446624	+	0.894722i	$0.647374\pi$
$278$	31.1475	−	1.57517i	1.86810	−	0.0944723i
$279$	1.47078	−	2.02435i	0.0880532	−	0.121195i
$280$	0.208302	−	0.0318195i	0.0124484	−	0.00190158i
$281$	−27.4909	+	8.93233i	−1.63997	+	0.532858i	−0.976532	−	0.215374i	$-0.930903\pi$
$281$	−27.4909	+	8.93233i	−1.63997	+	0.532858i	−0.663437	+	0.748232i	$0.730903\pi$
$282$	−6.02869	−	15.7917i	−0.359004	−	0.940381i
$283$	−16.4538	+	11.9544i	−0.978074	+	0.710613i	−0.957277	−	0.289171i	$-0.906620\pi$
$283$	−16.4538	+	11.9544i	−0.978074	+	0.710613i	−0.0207969	+	0.999784i	$0.506620\pi$
$284$	−2.75369	−	27.1562i	−0.163401	−	1.61142i
$285$		−	1.16844i		−	0.0692127i
$286$	4.22925	+	2.02815i	0.250081	+	0.119927i
$287$		−	1.74538i		−	0.103026i
$288$	0.571730	−	9.28191i	0.0336895	−	0.546942i
$289$	0.645096	−	0.468690i	0.0379468	−	0.0275700i
$290$	1.86160	−	0.710690i	0.109317	−	0.0417332i
$291$	−10.4220	+	3.38632i	−0.610949	+	0.198509i
$292$	20.9752	+	23.4677i	1.22748	+	1.37334i
$293$	−3.91871	+	5.39364i	−0.228933	+	0.315100i	−0.907995	−	0.418982i	$-0.862387\pi$
$293$	−3.91871	+	5.39364i	−0.228933	+	0.315100i	0.679061	+	0.734082i	$0.262387\pi$
$294$	−0.566573	−	11.2035i	−0.0330432	−	0.653400i
$295$	−1.45705	−	0.473423i	−0.0848325	−	0.0275638i
$296$	0.396528	−	2.41753i	0.0230477	−	0.140516i
$297$	−15.7601	−	8.56246i	−0.914493	−	0.496845i
$298$	−9.40402	+	14.4230i	−0.544760	+	0.835503i
$299$	−1.53576	+	4.72659i	−0.0888155	+	0.273346i
$300$	−5.82489	+	10.0042i	−0.336300	+	0.577592i
$301$	2.80743	+	2.03972i	0.161817	+	0.117567i
$302$	4.89533	−	18.1367i	0.281695	−	1.04365i
$303$	−4.30632	−	13.2535i	−0.247391	−	0.761393i
$304$	22.9051	−	4.69349i	1.31370	−	0.269190i
$305$	−1.34220	−	1.84738i	−0.0768540	−	0.105781i
$306$	6.15836	+	7.63349i	0.352050	+	0.436378i
$307$	−16.8801			−0.963400			−0.481700	−	0.876336i	$-0.659981\pi$
$307$	−16.8801			−0.963400			−0.481700	+	0.876336i	$0.659981\pi$
$308$	2.86906	+	0.237149i	0.163480	+	0.0135128i
$309$	8.72540			0.496371
$310$	0.232013	+	0.287587i	0.0131774	+	0.0163339i
$311$	−9.18371	−	12.6403i	−0.520761	−	0.716765i	0.464927	−	0.885349i	$-0.346081\pi$
$311$	−9.18371	−	12.6403i	−0.520761	−	0.716765i	−0.985687	+	0.168584i	$0.946081\pi$
$312$	−2.34177	+	2.31617i	−0.132576	+	0.131127i
$313$	7.00484	+	21.5587i	0.395937	+	1.21857i	0.928230	+	0.372008i	$0.121331\pi$
$313$	7.00484	+	21.5587i	0.395937	+	1.21857i	−0.532293	+	0.846560i	$0.678669\pi$
$314$	5.43303	−	20.1288i	0.306604	−	1.13593i
$315$	−0.0990831	−	0.0719881i	−0.00558270	−	0.00405607i
$316$	−4.71540	−	2.74552i	−0.265262	−	0.154448i
$317$	9.71993	−	29.9149i	0.545926	−	1.68019i	−0.172853	−	0.984948i	$-0.555299\pi$
$317$	9.71993	−	29.9149i	0.545926	−	1.68019i	0.718779	−	0.695239i	$-0.244701\pi$
$318$	−1.16288	+	1.78352i	−0.0652111	+	0.100015i
$319$	26.9917	−	3.54620i	1.51124	−	0.198549i
$320$	1.30131	+	0.438691i	0.0727455	+	0.0245236i
$321$	12.2804	+	3.99014i	0.685425	+	0.222708i
$322$	0.154063	+	3.04645i	0.00858559	+	0.169772i
$323$	−14.4944	+	19.9498i	−0.806489	+	1.11004i
$324$	2.03647	−	1.82018i	0.113137	−	0.101121i
$325$	−4.72726	+	1.53598i	−0.262221	+	0.0852008i
$326$	−0.696916	+	0.266057i	−0.0385986	+	0.0147356i
$327$	−3.45286	+	2.50865i	−0.190944	+	0.138729i
$328$	5.21965	−	10.1065i	0.288207	−	0.558036i
$329$		−	4.45461i		−	0.245590i
$330$	0.646825	−	0.678754i	0.0356066	−	0.0373642i
$331$		−	12.0510i		−	0.662385i	−0.943563	−	0.331192i	$-0.892549\pi$
$331$		−	12.0510i		−	0.662385i	0.943563	−	0.331192i	$-0.107451\pi$
$332$	−8.49108	+	0.861011i	−0.466009	+	0.0472541i
$333$	−1.15195	+	0.836940i	−0.0631264	+	0.0458640i
$334$	−0.483076	−	1.26538i	−0.0264328	−	0.0692385i
$335$	1.62186	−	0.526974i	0.0886116	−	0.0287916i
$336$	−0.835763	+	1.84074i	−0.0455946	+	0.100421i
$337$	1.85470	−	2.55277i	0.101032	−	0.139058i	−0.755508	−	0.655140i	$-0.772610\pi$
$337$	1.85470	−	2.55277i	0.101032	−	0.139058i	0.856540	+	0.516081i	$0.172610\pi$
$338$	−1.41241	+	0.0714272i	−0.0768249	+	0.00388513i
$339$	21.2198	+	6.89473i	1.15250	+	0.374470i
$340$	−1.32528	+	0.584245i	−0.0718735	+	0.0316851i
$341$	2.17211	+	4.55705i	0.117626	+	0.246778i
$342$	−11.3835	−	7.42222i	−0.615550	−	0.401348i
$343$	1.85234	−	5.70091i	0.100017	−	0.307820i
$344$	10.1563	+	20.2065i	0.547590	+	1.08946i
$345$	0.803720	+	0.583937i	0.0432708	+	0.0314381i
$346$	−14.8442	−	4.00666i	−0.798031	−	0.215399i
$347$	1.75907	+	5.41387i	0.0944319	+	0.290632i	0.987105	−	0.160073i	$-0.0511729\pi$
$347$	1.75907	+	5.41387i	0.0944319	+	0.290632i	−0.892673	+	0.450704i	$0.851173\pi$
$348$	−4.04312	+	18.6846i	−0.216734	+	1.00160i
$349$	−17.7481	−	24.4281i	−0.950032	−	1.30761i	−0.951513	−	0.307608i	$-0.900472\pi$
$349$	−17.7481	−	24.4281i	−0.950032	−	1.30761i	0.00148152	−	0.999999i	$-0.499528\pi$
$350$	−2.37441	+	1.91557i	−0.126918	+	0.102392i
$351$	5.40787			0.288651
$352$	15.9038	+	9.95328i	0.847678	+	0.530511i
$353$	1.34830			0.0717629			0.0358814	−	0.999356i	$-0.488576\pi$
$353$	1.34830			0.0717629			0.0358814	+	0.999356i	$0.488576\pi$
$354$	11.4394	−	9.22880i	0.607997	−	0.490505i
$355$	−1.37703	−	1.89532i	−0.0730853	−	0.100593i
$356$	−2.89612	+	13.3839i	−0.153494	+	0.709346i
$357$	−0.658860	−	2.02776i	−0.0348706	−	0.107321i
$358$	−8.52406	−	2.30076i	−0.450511	−	0.121599i
$359$	−6.93538	−	5.03885i	−0.366036	−	0.265940i	0.389530	−	0.921014i	$-0.372638\pi$
$359$	−6.93538	−	5.03885i	−0.366036	−	0.265940i	−0.755565	+	0.655074i	$0.772638\pi$
$360$	−0.358447	−	0.713154i	−0.0188918	−	0.0375865i
$361$	4.68684	−	14.4246i	0.246676	−	0.759190i
$362$	−25.6154	−	16.7016i	−1.34631	−	0.877817i
$363$	10.7467	−	6.97084i	0.564055	−	0.365874i
$364$	−0.794250	+	0.350142i	−0.0416300	+	0.0183524i
$365$	2.56927	+	0.834807i	0.134482	+	0.0436958i
$366$	21.8793	−	1.10646i	1.14365	−	0.0578358i
$367$	3.99038	−	5.49228i	0.208296	−	0.286695i	−0.692068	−	0.721832i	$-0.743300\pi$
$367$	3.99038	−	5.49228i	0.208296	−	0.286695i	0.900364	+	0.435137i	$0.143300\pi$
$368$	−8.21849	+	18.1009i	−0.428419	+	0.943577i
$369$	−6.28765	+	2.04298i	−0.327322	+	0.106353i
$370$	−0.0749932	−	0.196439i	−0.00389871	−	0.0102124i
$371$	−0.453940	+	0.329807i	−0.0235674	+	0.0171227i
$372$	−3.52690	+	0.357634i	−0.182861	+	0.0185425i
$373$			7.83074i			0.405460i	0.979235	+	0.202730i	$0.0649814\pi$
$373$			7.83074i			0.405460i	−0.979235	+	0.202730i	$0.935019\pi$
$374$	−19.4636	+	3.56514i	−1.00644	+	0.184349i
$375$			1.99307i			0.102922i
$376$	13.3217	−	25.7940i	0.687016	−	1.33022i
$377$	−6.64060	+	4.82468i	−0.342008	+	0.248483i
$378$	3.10092	−	1.18382i	0.159494	−	0.0608890i
$379$	−3.94969	+	1.28333i	−0.202882	+	0.0659203i	−0.408695	−	0.912671i	$-0.634016\pi$
$379$	−3.94969	+	1.28333i	−0.202882	+	0.0659203i	0.205813	+	0.978591i	$0.434016\pi$
$380$	1.49623	−	1.33732i	0.0767550	−	0.0686031i
$381$	−7.93941	+	10.9277i	−0.406748	+	0.559841i
$382$	1.33863	+	26.4702i	0.0684902	+	1.35433i
$383$	−26.3768	−	8.57034i	−1.34779	−	0.437924i	−0.455843	−	0.890060i	$-0.650662\pi$
$383$	−26.3768	−	8.57034i	−1.34779	−	0.437924i	−0.891949	+	0.452136i	$0.850662\pi$
$384$	−10.3442	+	8.15924i	−0.527877	+	0.416374i
$385$	0.223047	−	0.106315i	0.0113675	−	0.00541832i
$386$	−18.2081	+	27.9259i	−0.926767	+	1.42139i
$387$	4.06186	−	12.5011i	0.206476	−	0.635468i
$388$	−16.2646	−	9.46998i	−0.825709	−	0.480765i
$389$	1.20841	+	0.877965i	0.0612691	+	0.0445146i	0.617998	−	0.786179i	$-0.287944\pi$
$389$	1.20841	+	0.877965i	0.0612691	+	0.0445146i	−0.556729	+	0.830694i	$0.687944\pi$
$390$	−0.0736673	+	0.272929i	−0.00373029	+	0.0138203i
$391$	−6.47891	−	19.9400i	−0.327653	−	1.00841i
$392$	13.6979	−	13.5482i	0.691850	−	0.684288i
$393$	−7.55765	−	10.4022i	−0.381233	−	0.524722i
$394$	−17.6695	−	21.9020i	−0.890178	−	1.10340i
$395$	−0.468323			−0.0235639
$396$	−2.50394	−	10.6133i	−0.125828	−	0.533336i
$397$	−0.967496			−0.0485572			−0.0242786	−	0.999705i	$-0.507729\pi$
$397$	−0.967496			−0.0485572			−0.0242786	+	0.999705i	$0.507729\pi$
$398$	−6.21283	−	7.70101i	−0.311421	−	0.386017i
$399$	1.73642	+	2.38997i	0.0869297	+	0.119648i
$400$	−19.4774	+	3.99113i	−0.973871	+	0.199556i
$401$	6.21809	+	19.1373i	0.310516	+	0.955671i	0.977561	+	0.210653i	$0.0675591\pi$
$401$	6.21809	+	19.1373i	0.310516	+	0.955671i	−0.667044	+	0.745018i	$0.732441\pi$
$402$	−4.26335	+	15.7953i	−0.212637	+	0.787796i
$403$	−1.23141	−	0.894670i	−0.0613408	−	0.0445667i
$404$	12.0428	−	20.6834i	0.599152	−	1.02904i
$405$	0.0724427	−	0.222956i	0.00359971	−	0.0110788i
$406$	−2.75162	+	4.22018i	−0.136561	+	0.209444i
$407$	−0.374201	−	2.84820i	−0.0185485	−	0.141180i
$408$	2.24906	−	13.7119i	0.111345	−	0.678842i
$409$	35.1422	+	11.4184i	1.73767	+	0.564604i	0.994523	−	0.104523i	$-0.0333315\pi$
$409$	35.1422	+	11.4184i	1.73767	+	0.564604i	0.743149	+	0.669126i	$0.233331\pi$
$410$	−0.0493090	−	0.975040i	−0.00243520	−	0.0481538i
$411$	0.322156	−	0.443409i	0.0158908	−	0.0218718i
$412$	9.98648	+	11.1732i	0.491999	+	0.550462i
$413$	3.68384	−	1.19695i	0.181270	−	0.0588982i
$414$	10.7944	−	4.12090i	0.530515	−	0.202531i
$415$	−0.592621	+	0.430564i	−0.0290906	+	0.0211356i
$416$	−5.64615	−	0.347781i	−0.276825	−	0.0170514i
$417$			25.6805i			1.25758i
$418$	24.1216	−	13.0315i	1.17983	−	0.637392i
$419$			17.3404i			0.847133i	0.905865	+	0.423567i	$0.139222\pi$
$419$			17.3404i			0.847133i	−0.905865	+	0.423567i	$0.860778\pi$
$420$	0.0175046	+	0.172626i	0.000854136	+	0.00842329i
$421$	1.01143	−	0.734848i	0.0492942	−	0.0358143i	−0.562865	−	0.826549i	$-0.690301\pi$
$421$	1.01143	−	0.734848i	0.0492942	−	0.0358143i	0.612159	+	0.790734i	$0.290301\pi$
$422$	−10.0391	−	26.2967i	−0.488696	−	1.28010i
$423$	−16.0475	+	5.21415i	−0.780257	+	0.253521i
$424$	−3.61481	+	0.552184i	−0.175550	+	0.0268164i
$425$	12.3254	−	16.9644i	0.597868	−	0.822895i
$426$	22.4471	−	1.13518i	1.08757	−	0.0549996i
$427$	5.49075	+	1.78405i	0.265716	+	0.0863364i
$428$	8.94577	+	20.2923i	0.432410	+	0.980864i
$429$	−1.84380	+	3.39369i	−0.0890193	+	0.163849i
$430$	1.62597	+	1.06016i	0.0784112	+	0.0511252i
$431$	−6.00076	+	18.4685i	−0.289047	+	0.889594i	0.696110	+	0.717935i	$0.254913\pi$
$431$	−6.00076	+	18.4685i	−0.289047	+	0.889594i	−0.985156	+	0.171659i	$0.945087\pi$
$432$	21.4958	+	2.41867i	1.03422	+	0.116368i
$433$	−20.3354	−	14.7745i	−0.977255	−	0.710018i	−0.0201618	−	0.999797i	$-0.506418\pi$
$433$	−20.3354	−	14.7745i	−0.977255	−	0.710018i	−0.957094	+	0.289779i	$0.906418\pi$
$434$	−0.901948	−	0.243448i	−0.0432949	−	0.0116859i
$435$	0.507034	+	1.56049i	0.0243104	+	0.0748198i
$436$	−7.16430	−	1.55027i	−0.343108	−	0.0742446i
$437$	17.0751	+	23.5019i	0.816813	+	1.12425i
$438$	−20.1716	+	16.2735i	−0.963835	+	0.777580i
$439$	5.81152			0.277369			0.138684	−	0.990337i	$-0.455713\pi$
$439$	5.81152			0.277369			0.138684	+	0.990337i	$0.455713\pi$
$440$	1.60948	+	0.0514268i	0.0767288	+	0.00245167i
$441$	−11.1979			−0.533233
$442$	4.64343	−	3.74611i	0.220865	−	0.178184i
$443$	−21.4612	−	29.5388i	−1.01965	−	1.40343i	−0.912447	−	0.409194i	$-0.865810\pi$
$443$	−21.4612	−	29.5388i	−1.01965	−	1.40343i	−0.107205	−	0.994237i	$-0.534190\pi$
$444$	1.97163	+	0.426637i	0.0935692	+	0.0202473i
$445$	0.363193	+	1.11779i	0.0172170	+	0.0529884i
$446$	−21.2723	−	5.74167i	−1.00727	−	0.271876i
$447$	−11.4701	−	8.33348i	−0.542515	−	0.394160i
$448$	−3.31368	+	1.03656i	−0.156557	+	0.0489728i
$449$	−1.52777	+	4.70198i	−0.0720997	+	0.221900i	−0.980613	−	0.195957i	$-0.937219\pi$
$449$	−1.52777	+	4.70198i	−0.0720997	+	0.221900i	0.908513	+	0.417857i	$0.137219\pi$
$450$	9.68002	+	6.31152i	0.456321	+	0.297528i
$451$	2.43417	−	13.1141i	0.114621	−	0.617519i
$452$	15.4578	+	35.0638i	0.727072	+	1.64926i
$453$	14.7116	+	4.78009i	0.691211	+	0.224588i
$454$	−10.6561	+	0.538890i	−0.500114	+	0.0252914i
$455$	−0.0437901	+	0.0602719i	−0.00205291	+	0.00282559i
$456$	2.90723	+	19.0318i	0.136143	+	0.891245i
$457$	−27.6678	+	8.98980i	−1.29424	+	0.420525i	−0.873575	−	0.486689i	$-0.838204\pi$
$457$	−27.6678	+	8.98980i	−1.29424	+	0.420525i	−0.420669	+	0.907214i	$0.638204\pi$
$458$	−5.38142	−	14.0962i	−0.251457	−	0.658672i
$459$	−18.4570	+	13.4098i	−0.861501	+	0.625917i
$460$	0.172132	+	1.69752i	0.00802568	+	0.0791474i
$461$		−	23.2765i		−	1.08409i	−0.840349	−	0.542046i	$-0.817650\pi$
$461$		−	23.2765i		−	1.08409i	0.840349	−	0.542046i	$-0.182350\pi$
$462$	−0.314346	+	2.34959i	−0.0146247	+	0.109313i
$463$		−	16.0464i		−	0.745740i	−0.927884	−	0.372870i	$-0.878374\pi$
$463$		−	16.0464i		−	0.745740i	0.927884	−	0.372870i	$-0.121626\pi$
$464$	−28.5537	+	16.2077i	−1.32557	+	0.752423i
$465$	−0.246154	+	0.178841i	−0.0114151	+	0.00829357i
$466$	−12.6450	+	4.82741i	−0.585769	+	0.223626i
$467$	−15.4940	+	5.03432i	−0.716978	+	0.232960i	−0.644713	−	0.764425i	$-0.723023\pi$
$467$	−15.4940	+	5.03432i	−0.716978	+	0.232960i	−0.0722656	+	0.997385i	$0.523023\pi$
$468$	2.19105	+	2.45141i	0.101281	+	0.113316i
$469$	−2.53427	+	3.48812i	−0.117022	+	0.161067i
$470$	−0.125848	−	2.48853i	−0.00580493	−	0.114787i
$471$	16.3275	+	5.30513i	0.752331	+	0.244447i
$472$	24.9105	+	4.08588i	1.14660	+	0.188068i
$473$	18.2492	+	19.2410i	0.839101	+	0.884700i
$474$	2.45396	−	3.76366i	0.112714	−	0.172870i
$475$	−8.97818	+	27.6320i	−0.411947	+	1.26784i
$476$	1.84253	−	3.16453i	0.0844522	−	0.145046i
$477$	1.71946	+	1.24926i	0.0787284	+	0.0571996i
$478$	−5.36792	+	19.8876i	−0.245523	+	0.909637i
$479$	−1.39537	−	4.29450i	−0.0637559	−	0.196221i	0.914105	−	0.405479i	$-0.132895\pi$
$479$	−1.39537	−	4.29450i	−0.0637559	−	0.196221i	−0.977860	+	0.209258i	$0.932895\pi$
$480$	−0.414889	+	1.05192i	−0.0189370	+	0.0480135i
$481$	0.509108	+	0.700727i	0.0232133	+	0.0319504i
$482$	0.749903	+	0.929530i	0.0341572	+	0.0423389i
$483$	−2.51174			−0.114288
$484$	21.2263	+	5.78315i	0.964831	+	0.262870i
$485$	−1.61536			−0.0733498
$486$	−12.9940	−	16.1065i	−0.589422	−	0.730608i
$487$	−17.6392	−	24.2782i	−0.799307	−	1.10015i	−0.992886	−	0.119067i	$-0.962010\pi$
$487$	−17.6392	−	24.2782i	−0.799307	−	1.10015i	0.193579	−	0.981085i	$-0.437990\pi$
$488$	26.4584	+	26.7508i	1.19771	+	1.21095i
$489$	−0.189816	−	0.584192i	−0.00858375	−	0.0264181i
$490$	0.430909	−	1.59647i	0.0194665	−	0.0721213i
$491$	−3.18288	−	2.31250i	−0.143642	−	0.104362i	0.513644	−	0.858004i	$-0.328295\pi$
$491$	−3.18288	−	2.31250i	−0.143642	−	0.104362i	−0.657285	+	0.753642i	$0.728295\pi$
$492$	8.09423	+	4.71283i	0.364916	+	0.212471i
$493$	10.7006	−	32.9332i	0.481933	−	1.48324i
$494$	−4.51491	+	6.92455i	−0.203135	+	0.311550i
$495$	−0.644074	−	0.679075i	−0.0289490	−	0.0305222i
$496$	−4.49460	−	4.10699i	−0.201814	−	0.184409i
$497$	5.63325	+	1.83035i	0.252686	+	0.0821026i
$498$	−0.354943	−	7.01868i	−0.0159054	−	0.314514i
$499$	5.04697	−	6.94655i	0.225933	−	0.310970i	−0.680968	−	0.732313i	$-0.738441\pi$
$499$	5.04697	−	6.94655i	0.225933	−	0.310970i	0.906902	+	0.421342i	$0.138441\pi$
$500$	−2.55220	+	2.28113i	−0.114138	+	0.102015i
$501$	1.06071	−	0.344645i	0.0473890	−	0.0153976i
$502$	−15.4004	+	5.87932i	−0.687354	+	0.262407i
$503$	5.27922	−	3.83558i	0.235389	−	0.171020i	−0.463838	−	0.885920i	$-0.653528\pi$
$503$	5.27922	−	3.83558i	0.235389	−	0.171020i	0.699227	+	0.714900i	$0.253528\pi$
$504$	1.79299	+	0.926021i	0.0798662	+	0.0412483i
$505$		−	2.05423i		−	0.0914119i
$506$	−3.09113	+	23.1047i	−0.137417	+	1.02713i
$507$		−	1.16450i		−	0.0517174i
$508$	−23.0801	+	2.34036i	−1.02401	+	0.103837i
$509$	−24.6777	+	17.9294i	−1.09382	+	0.794707i	−0.980040	−	0.198799i	$-0.936296\pi$
$509$	−24.6777	+	17.9294i	−1.09382	+	0.794707i	−0.113780	+	0.993506i	$0.536296\pi$
$510$	−0.425353	−	1.11418i	−0.0188349	−	0.0493366i
$511$	−6.49588	+	2.11064i	−0.287361	+	0.0933691i
$512$	−22.2874	−	3.90764i	−0.984975	−	0.172695i
$513$	18.5801	−	25.5733i	0.820332	−	1.12909i
$514$	−16.5351	+	0.836202i	−0.729333	+	0.0368833i
$515$	1.22325	+	0.397459i	0.0539030	+	0.0175141i
$516$	−17.0398	+	7.51192i	−0.750134	+	0.330694i
$517$	6.21256	−	33.4702i	0.273228	−	1.47202i
$518$	0.445320	+	0.290355i	0.0195662	+	0.0127575i
$519$	3.91233	−	12.0409i	0.171732	−	0.528537i
$520$	−0.433809	+	0.218042i	−0.0190238	+	0.00956179i
$521$	6.87807	+	4.99721i	0.301334	+	0.218932i	0.728169	−	0.685398i	$-0.240372\pi$
$521$	6.87807	+	4.99721i	0.301334	+	0.218932i	−0.426835	+	0.904329i	$0.640372\pi$
$522$	18.4238	+	4.97283i	0.806387	+	0.217655i
$523$	7.10607	+	21.8702i	0.310727	+	0.956319i	0.977478	+	0.211038i	$0.0676845\pi$
$523$	7.10607	+	21.8702i	0.310727	+	0.956319i	−0.666751	+	0.745281i	$0.732316\pi$
$524$	4.67041	−	21.5834i	0.204028	−	0.942877i
$525$	−1.47657	−	2.03233i	−0.0644429	−	0.0886980i
$526$	−30.8996	+	24.9284i	−1.34729	+	1.08693i
$527$	6.42129			0.279716
$528$	−8.84676	+	12.6650i	−0.385006	+	0.551174i
$529$	−1.69924			−0.0738800
$530$	−0.244272	+	0.197068i	−0.0106105	+	0.00856009i
$531$	−8.62393	−	11.8698i	−0.374247	−	0.515106i
$532$	−1.07306	+	4.95894i	−0.0465229	+	0.214997i
$533$	1.24274	+	3.82476i	0.0538290	+	0.165669i
$534$	−10.8862	−	2.93832i	−0.471091	−	0.127154i
$535$	1.53989	+	1.11879i	0.0665750	+	0.0483696i
$536$	−25.1059	+	12.6188i	−1.08441	+	0.545049i
$537$	2.24659	−	6.91430i	0.0969477	−	0.298374i
$538$	8.91055	+	5.80981i	0.384161	+	0.250479i
$539$	10.7851	−	19.8511i	0.464547	−	0.855046i
$540$	1.69886	−	0.748934i	0.0731071	−	0.0322290i
$541$	−19.9476	−	6.48138i	−0.857616	−	0.278656i	−0.152983	−	0.988229i	$-0.548888\pi$
$541$	−19.9476	−	6.48138i	−0.857616	−	0.278656i	−0.704632	+	0.709573i	$0.748888\pi$
$542$	−5.57266	+	0.281816i	−0.239366	+	0.0121050i
$543$	14.8003	−	20.3709i	0.635142	−	0.874198i
$544$	20.1327	−	12.8137i	0.863182	−	0.549383i
$545$	−0.598346	+	0.194414i	−0.0256303	+	0.00832779i
$546$	−0.254917	−	0.667735i	−0.0109094	−	0.0285764i
$547$	−12.7302	+	9.24901i	−0.544303	+	0.395459i	−0.825680	−	0.564138i	$-0.809209\pi$
$547$	−12.7302	+	9.24901i	−0.544303	+	0.395459i	0.281378	+	0.959597i	$0.409209\pi$
$548$	0.936516	−	0.0949644i	0.0400060	−	0.00405668i
$549$		−	21.8684i		−	0.933322i
$550$	−20.5119	+	11.0814i	−0.874631	+	0.472513i
$551$			47.9791i			2.04398i
$552$	−14.5440	−	7.51149i	−0.619034	−	0.319710i
$553$	0.957924	−	0.695972i	0.0407351	−	0.0295957i
$554$	6.52117	−	2.48955i	0.277058	−	0.105771i
$555$	0.164665	−	0.0535031i	0.00698966	−	0.00227108i
$556$	−32.8847	+	29.3921i	−1.39462	+	1.24650i
$557$	−9.44447	+	12.9992i	−0.400175	+	0.550793i	−0.960788	−	0.277284i	$-0.910566\pi$
$557$	−9.44447	+	12.9992i	−0.400175	+	0.550793i	0.560613	+	0.828078i	$0.310566\pi$
$558$	0.178728	+	3.53418i	0.00756616	+	0.149614i
$559$	−7.60440	−	2.47082i	−0.321632	−	0.104504i
$560$	−0.201019	+	0.219991i	−0.00849459	+	0.00929631i
$561$	−2.12242	−	16.1547i	−0.0896088	−	0.682051i
$562$	22.3269	−	34.2429i	0.941804	−	1.44445i
$563$	−8.91962	+	27.4518i	−0.375917	+	1.15695i	0.566940	+	0.823759i	$0.308127\pi$
$563$	−8.91962	+	27.4518i	−0.375917	+	1.15695i	−0.942858	+	0.333196i	$0.891873\pi$
$564$	20.6583	+	12.0282i	0.869873	+	0.506479i
$565$	2.66083	+	1.93321i	0.111942	+	0.0813306i
$566$	7.49509	−	27.7685i	0.315042	−	1.16720i
$567$	0.183156	+	0.563698i	0.00769185	+	0.0236731i
$568$	27.1451	+	27.4450i	1.13898	+	1.15157i
$569$	18.5155	+	25.4844i	0.776209	+	1.06836i	0.995690	+	0.0927431i	$0.0295635\pi$
$569$	18.5155	+	25.4844i	0.776209	+	1.06836i	−0.219481	+	0.975617i	$0.570436\pi$
$570$	1.03755	+	1.28608i	0.0434584	+	0.0538681i
$571$	6.64600			0.278126			0.139063	−	0.990284i	$-0.455591\pi$
$571$	6.64600			0.278126			0.139063	+	0.990284i	$0.455591\pi$
$572$	−6.45601	+	1.52314i	−0.269939	+	0.0636857i
$573$	−21.8241			−0.911715
$574$	1.54986	+	1.92110i	0.0646899	+	0.0801852i
$575$	−14.5199	−	19.9849i	−0.605521	−	0.833429i
$576$	7.61285	+	10.7241i	0.317202	+	0.446837i
$577$	4.41598	+	13.5910i	0.183840	+	0.565801i	0.999926	−	0.0121289i	$-0.00386085\pi$
$577$	4.41598	+	13.5910i	0.183840	+	0.565801i	−0.816087	+	0.577930i	$0.803861\pi$
$578$	−0.293857	+	1.08871i	−0.0122228	+	0.0452843i
$579$	−22.2083	−	16.1353i	−0.922947	−	0.670560i
$580$	−1.41794	+	2.43530i	−0.0588768	+	0.101120i
$581$	0.572307	−	1.76138i	0.0237433	−	0.0730744i
$582$	8.46431	−	12.9818i	0.350857	−	0.538112i
$583$	−3.87069	+	1.84496i	−0.160308	+	0.0764104i
$584$	−43.9257	−	7.20481i	−1.81766	−	0.298137i
$585$	0.268383	+	0.0872031i	0.0110963	+	0.00360540i
$586$	−0.476199	−	9.41639i	−0.0196716	−	0.388988i
$587$	5.02759	−	6.91988i	0.207511	−	0.285614i	−0.692558	−	0.721362i	$-0.743516\pi$
$587$	5.02759	−	6.91988i	0.207511	−	0.285614i	0.900069	+	0.435748i	$0.143516\pi$
$588$	10.5721	+	11.8283i	0.435984	+	0.487791i
$589$	−8.46162	+	2.74935i	−0.348655	+	0.113285i
$590$	2.02413	−	0.772740i	0.0833321	−	0.0318132i
$591$	18.7465	−	13.6201i	0.771128	−	0.560257i
$592$	1.71026	+	3.01303i	0.0702913	+	0.123835i
$593$		−	4.79645i		−	0.196967i	−0.995139	−	0.0984833i	$-0.968601\pi$
$593$		−	4.79645i		−	0.196967i	0.995139	−	0.0984833i	$-0.0313991\pi$
$594$	24.9501	−	4.57009i	1.02371	−	0.187513i
$595$		−	0.314293i		−	0.0128848i
$596$	−2.45653	−	24.2257i	−0.100623	−	0.992323i
$597$	6.59151	−	4.78902i	0.269773	−	0.196001i
$598$	−2.50673	−	6.56618i	−0.102508	−	0.268511i
$599$	−3.59590	+	1.16838i	−0.146924	+	0.0477386i	−0.381556	−	0.924346i	$-0.624612\pi$
$599$	−3.59590	+	1.16838i	−0.146924	+	0.0477386i	0.234632	+	0.972084i	$0.424612\pi$
$600$	−2.47217	−	16.1838i	−0.100926	−	0.660699i
$601$	−11.2897	+	15.5389i	−0.460515	+	0.633844i	−0.974615	−	0.223886i	$-0.928126\pi$
$601$	−11.2897	+	15.5389i	−0.460515	+	0.633844i	0.514101	+	0.857730i	$0.328126\pi$
$602$	−4.90130	+	0.247865i	−0.199762	+	0.0101022i
$603$	15.5322	+	5.04671i	0.632519	+	0.205518i
$604$	10.7168	+	24.3096i	0.436061	+	0.989144i
$605$	1.82416	−	0.487741i	0.0741627	−	0.0198295i
$606$	16.5087	+	10.7639i	0.670619	+	0.437254i
$607$	−3.64649	+	11.2227i	−0.148007	+	0.455517i	−0.997385	−	0.0722664i	$-0.976977\pi$
$607$	−3.64649	+	11.2227i	−0.148007	+	0.455517i	0.849379	+	0.527784i	$0.176977\pi$
$608$	−21.0434	+	25.5052i	−0.853423	+	1.03437i
$609$	−3.35614	−	2.43838i	−0.135998	−	0.0988080i
$610$	3.11776	+	0.841525i	0.126234	+	0.0340724i
$611$	3.17175	+	9.76165i	0.128315	+	0.394914i
$612$	−13.5568	−	2.93353i	−0.547999	−	0.118581i
$613$	11.9670	+	16.4711i	0.483342	+	0.665263i	0.979143	−	0.203173i	$-0.0651254\pi$
$613$	11.9670	+	16.4711i	0.483342	+	0.665263i	−0.495801	+	0.868436i	$0.665125\pi$
$614$	18.5796	−	14.9892i	0.749812	−	0.604915i
$615$	0.803901			0.0324164
$616$	−3.36850	+	2.28664i	−0.135721	+	0.0921315i
$617$	32.1948			1.29612			0.648058	−	0.761591i	$-0.275581\pi$
$617$	32.1948			1.29612			0.648058	+	0.761591i	$0.275581\pi$
$618$	−9.60387	+	7.74797i	−0.386324	+	0.311669i
$619$	19.8646	+	27.3413i	0.798425	+	1.09894i	0.993007	+	0.118052i	$0.0376650\pi$
$619$	19.8646	+	27.3413i	0.798425	+	1.09894i	−0.194582	+	0.980886i	$0.562335\pi$
$620$	−0.510743	−	0.110519i	−0.0205119	−	0.00443855i
$621$	8.30521	+	25.5608i	0.333277	+	1.02572i
$622$	21.3326	+	5.75796i	0.855361	+	0.230873i
$623$	−2.40403	−	1.74663i	−0.0963154	−	0.0699773i
$624$	0.520823	−	4.62880i	0.0208496	−	0.185300i
$625$	7.58911	−	23.3569i	0.303564	−	0.934275i
$626$	−26.8537	−	17.5090i	−1.07329	−	0.699801i
$627$	9.71362	+	20.3790i	0.387925	+	0.813859i
$628$	11.8939	+	26.9798i	0.474619	+	1.07661i
$629$	−3.47516	−	1.12915i	−0.138564	−	0.0450221i
$630$	0.172983	−	0.00874794i	0.00689179	−	0.000348526i
$631$	−6.84360	+	9.41940i	−0.272439	+	0.374981i	−0.923211	−	0.384293i	$-0.874445\pi$
$631$	−6.84360	+	9.41940i	−0.272439	+	0.374981i	0.650772	+	0.759273i	$0.274445\pi$
$632$	7.62811	−	1.16524i	0.303430	−	0.0463508i
$633$	22.0433	−	7.16229i	0.876141	−	0.284675i
$634$	15.8652	+	41.5577i	0.630089	+	1.65047i
$635$	−1.61084	+	1.17034i	−0.0639241	+	0.0464436i
$636$	−0.303769	−	2.99570i	−0.0120452	−	0.118787i
$637$			6.81164i			0.269887i
$638$	−26.5602	+	27.8712i	−1.05153	+	1.10343i
$639$		−	22.4360i		−	0.887553i
$640$	−1.82187	+	0.672680i	−0.0720159	+	0.0265900i
$641$	5.48518	−	3.98522i	0.216652	−	0.157407i	−0.474166	−	0.880435i	$-0.657251\pi$
$641$	5.48518	−	3.98522i	0.216652	−	0.157407i	0.690818	+	0.723029i	$0.257251\pi$
$642$	−17.0599	+	6.51287i	−0.673302	+	0.257042i
$643$	−17.7905	+	5.78047i	−0.701588	+	0.227960i	−0.638022	−	0.770018i	$-0.720247\pi$
$643$	−17.7905	+	5.78047i	−0.701588	+	0.227960i	−0.0635654	+	0.997978i	$0.520247\pi$
$644$	−2.87476	−	3.21636i	−0.113281	−	0.126742i
$645$	−0.939469	+	1.29307i	−0.0369915	+	0.0509145i
$646$	−1.76135	−	34.8290i	−0.0692993	−	1.37033i
$647$	−1.69984	−	0.552312i	−0.0668277	−	0.0217136i	0.275412	−	0.961326i	$-0.411186\pi$
$647$	−1.69984	−	0.552312i	−0.0668277	−	0.0217136i	−0.342240	+	0.939613i	$0.611186\pi$
$648$	−0.625217	+	3.81178i	−0.0245608	+	0.149741i
$649$	29.3483	−	3.85581i	1.15202	−	0.151354i
$650$	3.83928	−	5.88832i	0.150589	−	0.230959i
$651$	0.237717	−	0.731616i	0.00931684	−	0.0286743i
$652$	0.530827	−	0.911690i	0.0207888	−	0.0357045i
$653$	−5.25386	−	3.81715i	−0.205599	−	0.149377i	0.480221	−	0.877148i	$-0.340556\pi$
$653$	−5.25386	−	3.81715i	−0.205599	−	0.149377i	−0.685820	+	0.727771i	$0.740556\pi$
$654$	1.57286	−	5.82728i	0.0615037	−	0.227865i
$655$	−0.585699	−	1.80260i	−0.0228852	−	0.0704333i
$656$	3.22916	+	15.7589i	0.126078	+	0.615282i
$657$	15.2070	+	20.9306i	0.593280	+	0.816579i
$658$	3.95560	+	4.90309i	0.154205	+	0.191142i
$659$	3.58539			0.139667			0.0698335	−	0.997559i	$-0.477753\pi$
$659$	3.58539			0.139667			0.0698335	+	0.997559i	$0.477753\pi$
$660$	−0.109228	+	1.32146i	−0.00425169	+	0.0514376i
$661$	−6.52961			−0.253972			−0.126986	−	0.991904i	$-0.540530\pi$
$661$	−6.52961			−0.253972			−0.126986	+	0.991904i	$0.540530\pi$
$662$	10.7011	+	13.2643i	0.415909	+	0.515532i
$663$	2.88760	+	3.97444i	0.112145	+	0.154354i
$664$	8.58140	−	8.48760i	0.333023	−	0.329383i
$665$	0.134568	+	0.414159i	0.00521833	+	0.0160604i
$666$	0.524741	−	1.94411i	0.0203333	−	0.0753327i
$667$	−33.0027	−	23.9778i	−1.27787	−	0.928425i
$668$	1.65534	+	0.963815i	0.0640471	+	0.0372911i
$669$	5.60650	−	17.2550i	0.216760	−	0.667118i
$670$	−1.31720	+	2.02020i	−0.0508880	+	0.0780473i
$671$	38.7673	+	21.0623i	1.49659	+	0.813100i
$672$	−0.714630	−	2.76820i	−0.0275675	−	0.106786i
$673$	−12.7625	−	4.14679i	−0.491958	−	0.159847i	0.0525234	−	0.998620i	$-0.483274\pi$
$673$	−12.7625	−	4.14679i	−0.491958	−	0.159847i	−0.544482	+	0.838773i	$0.683274\pi$
$674$	0.225381	+	4.45671i	0.00868136	+	0.171666i
$675$	−15.7997	+	21.7464i	−0.608130	+	0.837019i
$676$	1.49118	−	1.33281i	0.0573532	−	0.0512618i
$677$	14.1152	−	4.58630i	0.542491	−	0.176266i	−0.0249372	−	0.999689i	$-0.507939\pi$
$677$	14.1152	−	4.58630i	0.542491	−	0.176266i	0.567428	+	0.823423i	$0.307939\pi$
$678$	−29.4785	+	11.2538i	−1.13212	+	0.432201i
$679$	3.30411	−	2.40058i	0.126800	−	0.0921258i
$680$	0.939911	−	1.81989i	0.0360440	−	0.0697895i
$681$		−	8.78571i		−	0.336669i
$682$	−6.43736	−	3.08706i	−0.246499	−	0.118210i
$683$		−	38.4086i		−	1.46967i	−0.678248	−	0.734833i	$-0.737261\pi$
$683$		−	38.4086i		−	1.46967i	0.678248	−	0.734833i	$-0.262739\pi$
$684$	19.1204	−	1.93884i	0.731085	−	0.0741333i
$685$	0.0653626	−	0.0474887i	0.00249738	−	0.00181445i
$686$	3.02346	+	7.91970i	0.115436	+	0.302376i
$687$	11.8162	−	3.83931i	0.450816	−	0.146479i
$688$	−29.1218	−	13.2224i	−1.11026	−	0.504098i
$689$	0.759919	−	1.04594i	0.0289506	−	0.0398471i
$690$	−1.40316	+	0.0709595i	−0.0534174	+	0.00270138i
$691$	1.66393	+	0.540644i	0.0632989	+	0.0205670i	0.340495	−	0.940246i	$-0.389405\pi$
$691$	1.66393	+	0.540644i	0.0632989	+	0.0205670i	−0.277196	+	0.960813i	$0.589405\pi$
$692$	19.8966	−	8.77132i	0.756353	−	0.333436i
$693$	2.32658	+	0.431848i	0.0883795	+	0.0164045i
$694$	−6.74357	−	4.39691i	−0.255983	−	0.166904i
$695$	−1.16980	+	3.60026i	−0.0443729	+	0.136566i
$696$	−12.1413	−	24.1559i	−0.460215	−	0.915627i
$697$	−13.7257	−	9.97227i	−0.519896	−	0.377727i
$698$	41.2266	+	11.1276i	1.56045	+	0.421186i
$699$	−3.44406	−	10.5997i	−0.130266	−	0.400919i
$700$	0.912479	−	4.21685i	0.0344885	−	0.159382i
$701$	27.9028	+	38.4050i	1.05388	+	1.45054i	0.885400	+	0.464830i	$0.153884\pi$
$701$	27.9028	+	38.4050i	1.05388	+	1.45054i	0.168476	+	0.985706i	$0.446116\pi$
$702$	−5.95233	+	4.80208i	−0.224656	+	0.181243i
$703$	5.06284			0.190949
$704$	−26.3433	+	3.16692i	−0.992851	+	0.119358i
$705$	2.05174			0.0772730
$706$	−1.48405	+	1.19726i	−0.0558529	+	0.0450596i
$707$	3.05277	+	4.20178i	0.114811	+	0.158024i
$708$	−4.39612	+	20.3159i	−0.165216	+	0.763517i
$709$	−13.5306	−	41.6430i	−0.508153	−	1.56393i	−0.795404	−	0.606079i	$-0.792741\pi$
$709$	−13.5306	−	41.6430i	−0.508153	−	1.56393i	0.287251	−	0.957855i	$-0.407259\pi$
$710$	3.19868	+	0.863365i	0.120044	+	0.0324015i
$711$	−3.62847	−	2.63623i	−0.136078	−	0.0988665i
$712$	−8.69693	−	17.3031i	−0.325931	−	0.648460i
$713$	2.33759	−	7.19436i	0.0875435	−	0.269431i
$714$	2.52580	+	1.64686i	0.0945258	+	0.0616322i
$715$	−0.413079	+	0.391788i	−0.0154483	+	0.0146521i
$716$	11.4253	−	5.03679i	0.426983	−	0.188234i
$717$	−16.1318	−	5.24155i	−0.602454	−	0.195749i
$718$	12.1080	−	0.612317i	0.451867	−	0.0228515i
$719$	27.5329	−	37.8958i	1.02681	−	1.41328i	0.119485	−	0.992836i	$-0.461876\pi$
$719$	27.5329	−	37.8958i	1.02681	−	1.41328i	0.907320	−	0.420440i	$-0.138124\pi$
$720$	1.02780	+	0.466659i	0.0383039	+	0.0173914i
$721$	−3.09274	+	1.00489i	−0.115180	+	0.0374242i
$722$	7.65004	+	20.0387i	0.284705	+	0.745762i
$723$	−0.795611	+	0.578045i	−0.0295891	+	0.0214977i
$724$	43.0250	−	4.36281i	1.59901	−	0.162142i
$725$		−	40.7993i		−	1.51525i
$726$	−5.63869	+	17.2155i	−0.209272	+	0.638927i
$727$		−	29.3335i		−	1.08792i	−0.839111	−	0.543960i	$-0.816924\pi$
$727$		−	29.3335i		−	1.08792i	0.839111	−	0.543960i	$-0.183076\pi$
$728$	0.563296	−	1.09067i	0.0208771	−	0.0404230i
$729$	17.1006	−	12.4243i	0.633356	−	0.460160i
$730$	−3.56924	+	1.36261i	−0.132103	+	0.0504323i
$731$	32.0806	−	10.4236i	1.18654	−	0.385532i
$732$	−23.0996	+	20.6462i	−0.853785	+	0.763107i
$733$	16.0054	−	22.0296i	0.591173	−	0.813680i	−0.403691	−	0.914895i	$-0.632273\pi$
$733$	16.0054	−	22.0296i	0.591173	−	0.813680i	0.994865	+	0.101215i	$0.0322730\pi$
$734$	0.484908	+	9.58861i	0.0178983	+	0.353922i
$735$	1.29498	+	0.420765i	0.0477661	+	0.0155201i
$736$	−7.02733	−	27.2212i	−0.259031	−	1.00339i
$737$	−23.9062	+	22.6740i	−0.880595	+	0.835208i
$738$	5.10656	−	7.83196i	0.187975	−	0.288299i
$739$	−1.18590	+	3.64982i	−0.0436240	+	0.134261i	−0.970496	−	0.241116i	$-0.922487\pi$
$739$	−1.18590	+	3.64982i	−0.0436240	+	0.134261i	0.926872	+	0.375377i	$0.122487\pi$
$740$	0.256977	+	0.149624i	0.00944666	+	0.00550027i
$741$	−5.50682	−	4.00094i	−0.202298	−	0.146978i
$742$	0.206781	−	0.766101i	0.00759116	−	0.0281244i
$743$	−4.56212	−	14.0408i	−0.167368	−	0.515106i	0.831835	−	0.555023i	$-0.187291\pi$
$743$	−4.56212	−	14.0408i	−0.167368	−	0.515106i	−0.999203	+	0.0399171i	$0.987291\pi$
$744$	3.56441	−	3.52545i	0.130678	−	0.129249i
$745$	−1.22843	−	1.69079i	−0.0450063	−	0.0619458i
$746$	−6.95353	−	8.61913i	−0.254587	−	0.315569i
$747$	−7.01518			−0.256672
$748$	18.2574	−	21.2073i	0.667557	−	0.775417i
$749$	−4.81236			−0.175840
$750$	−1.76981	−	2.19374i	−0.0646243	−	0.0801039i
$751$	−12.3702	−	17.0261i	−0.451394	−	0.621291i	0.521302	−	0.853372i	$-0.325446\pi$
$751$	−12.3702	−	17.0261i	−0.451394	−	0.621291i	−0.972696	+	0.232081i	$0.925446\pi$
$752$	8.24156	+	40.2203i	0.300539	+	1.46668i
$753$	−4.19454	−	12.9095i	−0.152857	−	0.470447i
$754$	3.02495	−	11.2071i	0.110162	−	0.408140i
$755$	1.84474	+	1.34028i	0.0671370	+	0.0487779i
$756$	−2.36191	+	4.05655i	−0.0859017	+	0.147535i
$757$	−5.92940	+	18.2488i	−0.215508	+	0.663265i	0.783609	+	0.621254i	$0.213376\pi$
$757$	−5.92940	+	18.2488i	−0.215508	+	0.663265i	−0.999117	+	0.0420110i	$0.986624\pi$
$758$	3.20777	−	4.91977i	0.116511	−	0.178694i
$759$	−18.8722	−	3.50296i	−0.685018	−	0.127150i
$760$	−0.459358	+	2.80058i	−0.0166627	+	0.101588i
$761$	−6.57910	−	2.13768i	−0.238492	−	0.0774908i	0.187332	−	0.982297i	$-0.440016\pi$
$761$	−6.57910	−	2.13768i	−0.238492	−	0.0774908i	−0.425824	+	0.904806i	$0.640016\pi$
$762$	−0.964791	−	19.0779i	−0.0349507	−	0.691118i
$763$	0.934958	−	1.28686i	0.0338477	−	0.0465874i
$764$	−24.9783	−	27.9465i	−0.903685	−	1.01107i
$765$	−1.13223	+	0.367883i	−0.0409358	+	0.0133008i
$766$	36.6427	−	13.9888i	1.32395	−	0.505437i
$767$	−7.22037	+	5.24591i	−0.260713	+	0.189419i
$768$	4.14045	−	18.1662i	0.149406	−	0.655515i
$769$		−	17.8499i		−	0.643684i	−0.946793	−	0.321842i	$-0.895698\pi$
$769$		−	17.8499i		−	0.643684i	0.946793	−	0.321842i	$-0.104302\pi$
$770$	−0.151098	+	0.315080i	−0.00544519	+	0.0113547i
$771$		−	13.6329i		−	0.490976i
$772$	−4.75633	−	46.9058i	−0.171184	−	1.68818i
$773$	13.7565	−	9.99469i	0.494788	−	0.359484i	−0.312235	−	0.950005i	$-0.601078\pi$
$773$	13.7565	−	9.99469i	0.494788	−	0.359484i	0.807022	+	0.590521i	$0.201078\pi$
$774$	6.62993	+	17.3666i	0.238308	+	0.624229i
$775$	7.19538	−	2.33792i	0.258466	−	0.0839806i
$776$	26.3112	−	4.01921i	0.944518	−	0.144281i
$777$	−0.257302	+	0.354145i	−0.00923064	+	0.0127049i
$778$	−2.10969	+	0.106690i	−0.0756361	+	0.00382501i
$779$	22.3566	+	7.26411i	0.801010	+	0.260264i
$780$	−0.161271	−	0.365822i	−0.00577444	−	0.0130985i
$781$	39.7734	+	21.6089i	1.42320	+	0.773227i
$782$	24.8375	+	16.1944i	0.888189	+	0.579112i
$783$	−13.7170	+	42.2165i	−0.490205	+	1.50869i
$784$	−3.04650	+	27.0757i	−0.108804	+	0.966990i
$785$	2.04737	+	1.48750i	0.0730736	+	0.0530911i
$786$	17.5555	+	4.73846i	0.626183	+	0.169015i
$787$	4.48096	+	13.7910i	0.159729	+	0.491596i	0.998609	−	0.0527205i	$-0.0167892\pi$
$787$	4.48096	+	13.7910i	0.159729	+	0.491596i	−0.838880	+	0.544316i	$0.816789\pi$
$788$	38.8969	+	8.41685i	1.38565	+	0.299838i
$789$	−19.2155	−	26.4478i	−0.684089	−	0.941568i
$790$	0.515473	−	0.415861i	0.0183397	−	0.0147957i
$791$	−8.31547			−0.295664
$792$	12.1804	+	9.45833i	0.432811	+	0.336087i
$793$	−13.3025			−0.472385
$794$	1.06490	−	0.859116i	0.0377920	−	0.0304889i
$795$	−0.151905	−	0.209080i	−0.00538752	−	0.00741529i
$796$	13.6767	+	2.95947i	0.484757	+	0.104896i
$797$	14.8390	+	45.6698i	0.525625	+	1.61771i	0.763076	+	0.646309i	$0.223688\pi$
$797$	14.8390	+	45.6698i	0.525625	+	1.61771i	−0.237450	+	0.971400i	$0.576312\pi$
$798$	−4.03349	−	1.08869i	−0.142784	−	0.0385393i
$799$	−35.0310	−	25.4515i	−1.23931	−	0.900410i
$800$	17.8944	−	21.6885i	0.632661	−	0.766804i
$801$	−3.47822	+	10.7049i	−0.122897	+	0.378237i
$802$	−23.8376	−	15.5425i	−0.841736	−	0.548825i
$803$	−51.7510	+	6.79912i	−1.82625	+	0.239936i
$804$	−9.33328	−	21.1713i	−0.329159	−	0.746653i
$805$	−0.352132	−	0.114415i	−0.0124110	−	0.00403259i
$806$	2.14983	−	0.108720i	0.0757246	−	0.00382949i
$807$	−5.14843	+	7.08621i	−0.181233	+	0.249446i
$808$	5.11115	+	33.4595i	0.179810	+	1.17710i
$809$	−18.4831	+	6.00551i	−0.649830	+	0.211142i	−0.615339	−	0.788263i	$-0.710981\pi$
$809$	−18.4831	+	6.00551i	−0.649830	+	0.211142i	−0.0344906	+	0.999405i	$0.510981\pi$
$810$	0.118244	+	0.309730i	0.00415466	+	0.0108828i
$811$	−3.03704	+	2.20654i	−0.106645	+	0.0774820i	−0.639830	−	0.768517i	$-0.720995\pi$
$811$	−3.03704	+	2.20654i	−0.106645	+	0.0774820i	0.533185	+	0.845999i	$0.320995\pi$
$812$	−0.718780	−	7.08844i	−0.0252242	−	0.248755i
$813$		−	4.59454i		−	0.161138i
$814$	2.94102	+	2.80268i	0.103083	+	0.0982337i
$815$		−	0.0905470i		−	0.00317172i
$816$	9.70041	+	17.0896i	0.339582	+	0.598254i
$817$	−37.8111	+	27.4714i	−1.32284	+	0.961101i
$818$	−48.8196	+	18.6376i	−1.70694	+	0.651647i
$819$	−0.678552	+	0.220475i	−0.0237105	+	0.00770402i
$820$	0.920089	+	1.02942i	0.0321309	+	0.0359489i
$821$	−11.8703	+	16.3381i	−0.414277	+	0.570203i	−0.964255	−	0.264976i	$-0.914636\pi$
$821$	−11.8703	+	16.3381i	−0.414277	+	0.570203i	0.549978	+	0.835179i	$0.314636\pi$
$822$	0.0391481	+	0.774118i	0.00136545	+	0.0270005i
$823$	14.1703	+	4.60422i	0.493947	+	0.160493i	0.545389	−	0.838183i	$-0.316382\pi$
$823$	14.1703	+	4.60422i	0.493947	+	0.160493i	−0.0514425	+	0.998676i	$0.516382\pi$
$824$	−20.9134	−	3.43027i	−0.728554	−	0.119499i
$825$	−8.26002	−	17.3294i	−0.287577	−	0.603332i
$826$	−2.99186	+	4.58863i	−0.104100	+	0.159659i
$827$	2.11457	−	6.50798i	0.0735309	−	0.226305i	−0.907536	−	0.419974i	$-0.862039\pi$
$827$	2.11457	−	6.50798i	0.0735309	−	0.226305i	0.981067	+	0.193670i	$0.0620390\pi$
$828$	−8.22187	+	14.1210i	−0.285730	+	0.490738i
$829$	−17.8680	−	12.9819i	−0.620582	−	0.450879i	0.232543	−	0.972586i	$-0.425295\pi$
$829$	−17.8680	−	12.9819i	−0.620582	−	0.450879i	−0.853125	+	0.521707i	$0.825295\pi$
$830$	0.269953	−	1.00015i	0.00937022	−	0.0347156i
$831$	1.77614	+	5.46639i	0.0616135	+	0.189627i
$832$	6.52342	−	4.63087i	0.226159	−	0.160547i
$833$	−16.8907	−	23.2481i	−0.585229	−	0.805499i
$834$	−22.8037	−	28.2660i	−0.789629	−	0.978771i
$835$	0.164405			0.00568946
$836$	−14.9784	+	35.7630i	−0.518040	+	1.23689i
$837$	−8.23134			−0.284517
$838$	−15.3979	−	19.0862i	−0.531911	−	0.659322i
$839$	−23.3075	−	32.0801i	−0.804666	−	1.10753i	−0.992125	−	0.125255i	$-0.960025\pi$
$839$	−23.3075	−	32.0801i	−0.804666	−	1.10753i	0.187459	−	0.982272i	$-0.439975\pi$
$840$	−0.172555	−	0.174462i	−0.00595372	−	0.00601951i
$841$	−11.8585	−	36.4968i	−0.408915	−	1.25851i
$842$	−0.460732	+	1.70696i	−0.0158779	+	0.0588258i
$843$	27.2320	+	19.7852i	0.937921	+	0.681440i
$844$	34.4007	+	20.0296i	1.18412	+	0.689449i
$845$	0.0530453	−	0.163257i	0.00182482	−	0.00561620i
$846$	13.0331	−	19.9890i	0.448087	−	0.687235i
$847$	−3.00637	+	3.70852i	−0.103300	+	0.127426i
$848$	3.48841	−	3.81765i	0.119793	−	0.131099i
$849$	22.5244	+	7.31864i	0.773037	+	0.251175i
$850$	1.49777	+	29.6170i	0.0513731	+	1.01586i
$851$	−2.53018	+	3.48249i	−0.0867335	+	0.119378i
$852$	−23.6991	+	21.1821i	−0.811917	+	0.725685i
$853$	−23.4212	+	7.61002i	−0.801927	+	0.260562i	−0.681175	−	0.732121i	$-0.738531\pi$
$853$	−23.4212	+	7.61002i	−0.801927	+	0.260562i	−0.120752	+	0.992683i	$0.538531\pi$
$854$	−7.62775	+	2.91200i	−0.261016	+	0.0996466i
$855$	1.33447	−	0.969552i	0.0456380	−	0.0331580i
$856$	−27.8655	−	14.3916i	−0.952424	−	0.491895i
$857$			3.65070i			0.124706i	0.998054	+	0.0623528i	$0.0198604\pi$
$857$			3.65070i			0.124706i	−0.998054	+	0.0623528i	$0.980140\pi$
$858$	−0.984099	−	5.37261i	−0.0335966	−	0.183418i
$859$			18.7856i			0.640955i	0.947256	+	0.320478i	$0.103843\pi$
$859$			18.7856i			0.640955i	−0.947256	+	0.320478i	$0.896157\pi$
$860$	−2.73106	+	0.276935i	−0.0931285	+	0.00944340i
$861$	−1.64433	+	1.19467i	−0.0560384	+	0.0407143i
$862$	−9.79468	−	25.6564i	−0.333608	−	0.873860i
$863$	−16.4768	+	5.35362i	−0.560875	+	0.182239i	−0.575715	−	0.817650i	$-0.695276\pi$
$863$	−16.4768	+	5.35362i	−0.560875	+	0.182239i	0.0148396	+	0.999890i	$0.495276\pi$
$864$	−25.8077	+	16.4257i	−0.877997	+	0.558813i
$865$	1.09697	−	1.50986i	0.0372982	−	0.0513366i
$866$	35.5022	−	1.79539i	1.20641	−	0.0610097i
$867$	−0.883107	−	0.286939i	−0.0299919	−	0.00974496i
$868$	1.20893	−	0.532953i	0.0410338	−	0.0180896i
$869$	8.16809	−	3.89331i	0.277084	−	0.132071i
$870$	−1.94376	−	1.26736i	−0.0658998	−	0.0429676i
$871$	3.06990	−	9.44818i	0.104020	−	0.320139i
$872$	9.26221	−	4.65540i	0.313658	−	0.157652i
$873$	−12.5155	−	9.09302i	−0.423584	−	0.307752i
$874$	−39.6634	−	10.7057i	−1.34163	−	0.362125i
$875$	−0.229540	−	0.706451i	−0.00775986	−	0.0238824i
$876$	7.75187	−	35.8239i	0.261911	−	1.21038i
$877$	13.0400	+	17.9480i	0.440329	+	0.606061i	0.970285	−	0.241964i	$-0.0777916\pi$
$877$	13.0400	+	17.9480i	0.440329	+	0.606061i	−0.529956	+	0.848025i	$0.677792\pi$
$878$	−6.39662	+	5.16051i	−0.215875	+	0.174159i
$879$	7.76363			0.261861
$880$	−1.81718	+	1.37258i	−0.0612572	+	0.0462696i
$881$	45.5672			1.53520			0.767599	−	0.640931i	$-0.221451\pi$
$881$	45.5672			1.53520			0.767599	+	0.640931i	$0.221451\pi$
$882$	12.3253	−	9.94349i	0.415014	−	0.334815i
$883$	−25.0305	−	34.4515i	−0.842343	−	1.15939i	−0.985498	−	0.169685i	$-0.945725\pi$
$883$	−25.0305	−	34.4515i	−0.842343	−	1.15939i	0.143156	−	0.989700i	$-0.454275\pi$
$884$	−1.78445	+	8.24653i	−0.0600177	+	0.277361i
$885$	0.551302	+	1.69673i	0.0185318	+	0.0570351i
$886$	49.8517	+	13.4556i	1.67480	+	0.452051i
$887$	7.92847	+	5.76037i	0.266212	+	0.193414i	0.712881	−	0.701285i	$-0.247390\pi$
$887$	7.92847	+	5.76037i	0.266212	+	0.193414i	−0.446669	+	0.894699i	$0.647390\pi$
$888$	−2.54897	+	1.28117i	−0.0855379	+	0.0429933i
$889$	1.55562	−	4.78771i	0.0521739	−	0.160575i
$890$	−1.39233	−	0.907823i	−0.0466712	−	0.0304303i
$891$	0.590013	+	4.49084i	0.0197662	+	0.150449i
$892$	28.5124	−	12.5696i	0.954667	−	0.420861i
$893$	57.0593	+	18.5397i	1.90942	+	0.620407i
$894$	20.0248	−	1.01268i	0.669729	−	0.0338690i
$895$	0.629920	−	0.867011i	0.0210559	−	0.0289810i
$896$	2.72686	−	4.08340i	0.0910978	−	0.136417i
$897$	5.50413	−	1.78840i	0.183777	−	0.0597129i
$898$	−2.49368	−	6.53199i	−0.0832152	−	0.217975i
$899$	10.1077	−	7.34366i	0.337110	−	0.244925i
$900$	−16.2591	+	1.64870i	−0.541970	+	0.0549567i
$901$			5.45415i			0.181704i
$902$	8.96580	+	16.5959i	0.298528	+	0.552583i
$903$		−	4.04102i		−	0.134477i
$904$	−48.1500	−	24.8679i	−1.60144	−	0.827093i
$905$	3.00286	−	2.18170i	0.0998183	−	0.0725222i
$906$	−20.4374	+	7.80224i	−0.678986	+	0.259212i
$907$	26.6220	−	8.65001i	0.883969	−	0.287219i	0.168365	−	0.985725i	$-0.446151\pi$
$907$	26.6220	−	8.65001i	0.883969	−	0.287219i	0.715604	+	0.698506i	$0.246151\pi$
$908$	11.2504	−	10.0555i	0.373357	−	0.333704i
$909$	11.5634	−	15.9157i	0.383535	−	0.527890i
$910$	−0.00532134	−	0.105225i	−0.000176401	−	0.00348816i
$911$	18.5203	+	6.01760i	0.613604	+	0.199372i	0.599298	−	0.800526i	$-0.295446\pi$
$911$	18.5203	+	6.01760i	0.613604	+	0.199372i	0.0143053	+	0.999898i	$0.495446\pi$
$912$	−20.0997	−	18.3663i	−0.665569	−	0.608170i
$913$	6.75658	−	12.4362i	0.223610	−	0.411577i
$914$	22.4706	−	34.4633i	0.743260	−	1.13994i
$915$	−0.821714	+	2.52898i	−0.0271650	+	0.0836053i
$916$	18.4403	+	10.7368i	0.609286	+	0.354754i
$917$	3.87684	+	2.81669i	0.128024	+	0.0930152i
$918$	8.40763	−	31.1494i	0.277493	−	1.02808i
$919$	16.7062	+	51.4163i	0.551085	+	1.69607i	0.706064	+	0.708148i	$0.250469\pi$
$919$	16.7062	+	51.4163i	0.551085	+	1.69607i	−0.154978	+	0.987918i	$0.549531\pi$
$920$	−1.69682	−	1.71558i	−0.0559427	−	0.0565609i
$921$	11.5541	+	15.9028i	0.380719	+	0.524015i
$922$	20.6690	+	25.6199i	0.680697	+	0.843747i
$923$	−13.6477			−0.449220
$924$	−1.74039	−	2.86527i	−0.0572546	−	0.0942606i
$925$	−4.30521			−0.141554
$926$	14.2489	+	17.6620i	0.468247	+	0.580408i
$927$	7.24016	+	9.96523i	0.237798	+	0.327301i
$928$	17.0363	−	43.1945i	0.559245	−	1.41793i
$929$	−5.45685	−	16.7945i	−0.179034	−	0.551009i	0.820761	−	0.571272i	$-0.193550\pi$
$929$	−5.45685	−	16.7945i	−0.179034	−	0.551009i	−0.999795	+	0.0202629i	$0.993550\pi$
$930$	0.112129	−	0.415427i	0.00367686	−	0.0136224i
$931$	32.2116	+	23.4031i	1.05569	+	0.767006i
$932$	9.63147	−	16.5419i	0.315489	−	0.541849i
$933$	−5.62241	+	17.3040i	−0.184069	+	0.566507i
$934$	12.5836	−	19.2995i	0.411747	−	0.631500i
$935$	0.438325	−	2.36148i	0.0143348	−	0.0772286i
$936$	−4.58844	−	0.752606i	−0.149978	−	0.0245997i
$937$	−13.8735	−	4.50777i	−0.453227	−	0.147262i	0.0735031	−	0.997295i	$-0.476582\pi$
$937$	−13.8735	−	4.50777i	−0.453227	−	0.147262i	−0.526730	+	0.850033i	$0.676582\pi$
$938$	−0.307962	−	6.08968i	−0.0100553	−	0.198835i
$939$	15.5158	−	21.3557i	0.506340	−	0.696917i
$940$	2.34828	+	2.62732i	0.0765923	+	0.0856936i
$941$	−36.3056	+	11.7964i	−1.18353	+	0.384552i	−0.833676	−	0.552254i	$-0.813768\pi$
$941$	−36.3056	+	11.7964i	−1.18353	+	0.384552i	−0.349852	+	0.936805i	$0.613768\pi$
$942$	−22.6822	+	8.65923i	−0.739025	+	0.282133i
$943$	−16.1695	+	11.7478i	−0.526552	+	0.382562i
$944$	−31.0466	+	17.6227i	−1.01048	+	0.573572i
$945$			0.402887i			0.0131059i
$946$	−37.1721	−	4.97317i	−1.20857	−	0.161692i
$947$			37.8539i			1.23009i	0.788494	+	0.615043i	$0.210861\pi$
$947$			37.8539i			1.23009i	−0.788494	+	0.615043i	$0.789139\pi$
$948$	0.641025	+	6.32164i	0.0208195	+	0.205317i
$949$	12.7320	−	9.25034i	0.413298	−	0.300279i
$950$	−14.6545	−	38.3864i	−0.475456	−	1.24542i
$951$	−34.8359	+	11.3189i	−1.12963	+	0.367040i
$952$	0.781998	+	5.11925i	0.0253447	+	0.165916i
$953$	−12.8957	+	17.7494i	−0.417732	+	0.574959i	−0.965083	−	0.261944i	$-0.915636\pi$
$953$	−12.8957	+	17.7494i	−0.417732	+	0.574959i	0.547351	+	0.836903i	$0.315636\pi$
$954$	−3.00188	+	0.151809i	−0.0971895	+	0.00491499i
$955$	−3.05962	−	0.994131i	−0.0990070	−	0.0321693i
$956$	−11.7514	−	26.6564i	−0.380067	−	0.862131i
$957$	−21.8161	−	23.0016i	−0.705213	−	0.743536i
$958$	5.34927	+	3.48781i	0.172827	+	0.112686i
$959$	−0.0631221	+	0.194270i	−0.00203832	+	0.00627330i
$960$	−0.477427	−	1.52624i	−0.0154089	−	0.0492593i
$961$	−23.2052	−	16.8596i	−0.748555	−	0.543857i
$962$	−1.18259	−	0.319198i	−0.0381284	−	0.0102914i
$963$	5.63291	+	17.3363i	0.181518	+	0.558655i
$964$	−1.65081	−	0.357215i	−0.0531689	−	0.0115051i
$965$	−2.37849	−	3.27371i	−0.0765664	−	0.105385i
$966$	2.76462	−	2.23037i	0.0889501	−	0.0717610i
$967$	36.4297			1.17150			0.585750	−	0.810492i	$-0.300800\pi$
$967$	36.4297			1.17150			0.585750	+	0.810492i	$0.300800\pi$
$968$	−28.4986	+	12.4831i	−0.915981	+	0.401222i
$969$	28.7158			0.922485
$970$	1.77799	−	1.43441i	0.0570880	−	0.0460560i
$971$	6.65504	+	9.15987i	0.213570	+	0.293954i	0.902339	−	0.431027i	$-0.141849\pi$
$971$	6.65504	+	9.15987i	0.213570	+	0.293954i	−0.688769	+	0.724981i	$0.741849\pi$
$972$	28.6045	+	6.18969i	0.917491	+	0.198535i
$973$	−2.95759	−	9.10252i	−0.0948160	−	0.291814i
$974$	40.9736	+	11.0593i	1.31288	+	0.354364i
$975$	4.68275	+	3.40222i	0.149968	+	0.108958i
$976$	−52.8763	−	5.94953i	−1.69253	−	0.190440i
$977$	−1.62044	+	4.98721i	−0.0518426	+	0.159555i	−0.973626	−	0.228150i	$-0.926732\pi$
$977$	−1.62044	+	4.98721i	−0.0518426	+	0.159555i	0.921783	+	0.387705i	$0.126732\pi$
$978$	0.727676	+	0.474456i	0.0232685	+	0.0151714i
$979$	−15.6270	−	16.4762i	−0.499442	−	0.526583i
$980$	0.943341	+	2.13984i	0.0301339	+	0.0683548i
$981$	−5.73022	−	1.86186i	−0.182952	−	0.0594447i
$982$	5.55679	−	0.281013i	0.177324	−	0.00896750i
$983$	−7.27088	+	10.0075i	−0.231905	+	0.319190i	−0.909072	−	0.416640i	$-0.863208\pi$
$983$	−7.27088	+	10.0075i	−0.231905	+	0.319190i	0.677167	+	0.735830i	$0.263208\pi$
$984$	−13.0940	+	2.00020i	−0.417423	+	0.0637640i
$985$	3.24858	−	1.05553i	0.103508	−	0.0336319i
$986$	17.4660	+	45.7508i	0.556231	+	1.45700i
$987$	−4.19669	+	3.04908i	−0.133582	+	0.0970532i
$988$	−1.17939	−	11.6309i	−0.0375214	−	0.370027i
$989$		−	39.7375i		−	1.26358i
$990$	1.31192	+	0.175519i	0.0416957	+	0.00557837i
$991$		−	14.4724i		−	0.459731i	−0.973222	−	0.229866i	$-0.926171\pi$
$991$		−	14.4724i		−	0.459731i	0.973222	−	0.229866i	$-0.0738286\pi$
$992$	8.59403	+	0.529359i	0.272861	+	0.0168072i
$993$	−11.3533	+	8.24866i	−0.360286	+	0.261763i
$994$	−7.82571	+	2.98758i	−0.248217	+	0.0947601i
$995$	1.14224	−	0.371137i	0.0362115	−	0.0117658i
$996$	6.62311	+	7.41013i	0.209861	+	0.234799i
$997$	−19.3933	+	26.6925i	−0.614190	+	0.845361i	−0.996914	−	0.0785023i	$-0.974986\pi$
$997$	−19.3933	+	26.6925i	−0.614190	+	0.845361i	0.382723	+	0.923863i	$0.374986\pi$
$998$	0.613304	+	12.1275i	0.0194138	+	0.383890i
$999$	4.45475	+	1.44744i	0.140942	+	0.0457949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.y.a.79.16	✓	288
4.3	odd	2	inner	572.2.y.a.79.30	yes	288
11.6	odd	10	inner	572.2.y.a.391.30	yes	288
44.39	even	10	inner	572.2.y.a.391.16	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.y.a.79.16	✓	288	1.1	even	1	trivial
572.2.y.a.79.30	yes	288	4.3	odd	2	inner
572.2.y.a.391.16	yes	288	44.39	even	10	inner
572.2.y.a.391.30	yes	288	11.6	odd	10	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10068 + 0.887979i) q^{2} +(-0.684477 - 0.942102i) q^{3} +(0.422987 - 1.95476i) q^{4} +(-0.0530453 - 0.163257i) q^{5} +(1.58996 + 0.429150i) q^{6} +(0.351116 + 0.255100i) q^{7} +(1.27021 + 2.52717i) q^{8} +(0.508004 - 1.56347i) q^{9} +O(q^{10})\)	\(q+(-1.10068 + 0.887979i) q^{2} +(-0.684477 - 0.942102i) q^{3} +(0.422987 - 1.95476i) q^{4} +(-0.0530453 - 0.163257i) q^{5} +(1.58996 + 0.429150i) q^{6} +(0.351116 + 0.255100i) q^{7} +(1.27021 + 2.52717i) q^{8} +(0.508004 - 1.56347i) q^{9} +(0.203354 + 0.132590i) q^{10} +(2.28237 + 2.40640i) q^{11} +(-2.13111 + 0.939491i) q^{12} +(-0.951057 - 0.309017i) q^{13} +(-0.612989 + 0.0309996i) q^{14} +(-0.117496 + 0.161720i) q^{15} +(-3.64216 - 1.65368i) q^{16} +(4.01222 - 1.30365i) q^{17} +(0.829184 + 2.17198i) q^{18} +(-4.72891 + 3.43575i) q^{19} +(-0.341565 + 0.0346353i) q^{20} -0.505397i q^{21} +(-4.64899 - 0.621978i) q^{22} -4.96983i q^{23} +(1.51142 - 2.92646i) q^{24} +(4.02125 - 2.92161i) q^{25} +(1.32121 - 0.504390i) q^{26} +(-5.14319 + 1.67112i) q^{27} +(0.647177 - 0.578442i) q^{28} +(4.82468 - 6.64060i) q^{29} +(-0.0142781 - 0.282336i) q^{30} +(1.44761 + 0.470356i) q^{31} +(5.47728 - 1.41400i) q^{32} +(0.704845 - 3.79736i) q^{33} +(-3.25855 + 4.99766i) q^{34} +(0.0230218 - 0.0708539i) q^{35} +(-2.84134 - 1.65435i) q^{36} +(-0.700727 - 0.509108i) q^{37} +(2.15413 - 7.98083i) q^{38} +(0.359851 + 1.10751i) q^{39} +(0.345198 - 0.341425i) q^{40} +(-2.36383 - 3.25353i) q^{41} +(0.448782 + 0.556280i) q^{42} +7.99574 q^{43} +(5.66935 - 3.44361i) q^{44} -0.282195 q^{45} +(4.41311 + 5.47019i) q^{46} +(-6.03303 - 8.30375i) q^{47} +(0.935046 + 4.56319i) q^{48} +(-2.10491 - 6.47826i) q^{49} +(-1.83178 + 6.78653i) q^{50} +(-3.97444 - 2.88760i) q^{51} +(-1.00634 + 1.72838i) q^{52} +(-0.399513 + 1.22957i) q^{53} +(4.17708 - 6.40642i) q^{54} +(0.271792 - 0.500261i) q^{55} +(-0.198690 + 1.21136i) q^{56} +(6.47366 + 2.10342i) q^{57} +(0.586291 + 11.5934i) q^{58} +(5.24591 - 7.22037i) q^{59} +(0.266424 + 0.298082i) q^{60} +(12.6514 - 4.11070i) q^{61} +(-2.01102 + 0.767733i) q^{62} +(0.577211 - 0.419368i) q^{63} +(-4.77313 + 6.42007i) q^{64} +0.171658i q^{65} +(2.59616 + 4.80556i) q^{66} +9.93440i q^{67} +(-0.851201 - 8.39434i) q^{68} +(-4.68209 + 3.40174i) q^{69} +(0.0375771 + 0.0984302i) q^{70} +(12.9798 - 4.21738i) q^{71} +(4.59643 - 0.702134i) q^{72} +(-9.25034 + 12.7320i) q^{73} +(1.22335 - 0.0618664i) q^{74} +(-5.50490 - 1.78865i) q^{75} +(4.71580 + 10.6971i) q^{76} +(0.187502 + 1.42716i) q^{77} +(-1.37952 - 0.899470i) q^{78} +(0.843069 - 2.59470i) q^{79} +(-0.0767740 + 0.682328i) q^{80} +(1.10485 + 0.802724i) q^{81} +(5.49088 + 1.48206i) q^{82} +(-1.31867 - 4.05846i) q^{83} +(-0.987929 - 0.213777i) q^{84} +(-0.425659 - 0.585869i) q^{85} +(-8.80074 + 7.10004i) q^{86} -9.55850 q^{87} +(-3.18228 + 8.82457i) q^{88} -6.84683 q^{89} +(0.310606 - 0.250583i) q^{90} +(-0.255100 - 0.351116i) q^{91} +(-9.71482 - 2.10218i) q^{92} +(-0.547731 - 1.68574i) q^{93} +(14.0140 + 3.78256i) q^{94} +(0.811756 + 0.589775i) q^{95} +(-5.08120 - 4.19231i) q^{96} +(2.90795 - 8.94976i) q^{97} +(8.06939 + 5.26136i) q^{98} +(4.92180 - 2.34597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) \) 288 * q - 4 * q^4 + 80 * q^9	\( 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) \) 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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