LMFDB - Embedded newform 91.2.bc.a.6.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(6,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("91.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.bc (of order $12$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			6.6
Character	$\chi$	$=$	91.6
Dual form			91.2.bc.a.76.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.218036 + 0.813723i) q^{2} +(1.24122 + 0.716618i) q^{3} +(1.11745 - 0.645157i) q^{4} +(-1.01306 - 1.01306i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(-2.62506 - 0.330214i) q^{7} +(1.96000 + 1.96000i) q^{8} +(-0.472916 - 0.819114i) q^{9} +O(q^{10})$	\(q+(0.218036 + 0.813723i) q^{2} +(1.24122 + 0.716618i) q^{3} +(1.11745 - 0.645157i) q^{4} +(-1.01306 - 1.01306i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(-2.62506 - 0.330214i) q^{7} +(1.96000 + 1.96000i) q^{8} +(-0.472916 - 0.819114i) q^{9} +(0.603466 - 1.04523i) q^{10} +(-4.68859 + 1.25630i) q^{11} +1.84933 q^{12} +(1.04975 + 3.44935i) q^{13} +(-0.303657 - 2.20807i) q^{14} +(-0.531452 - 1.98341i) q^{15} +(0.122771 - 0.212645i) q^{16} +(1.49151 + 2.58338i) q^{17} +(0.563419 - 0.563419i) q^{18} +(1.62522 - 6.06542i) q^{19} +(-1.78562 - 0.478455i) q^{20} +(-3.02164 - 2.29104i) q^{21} +(-2.04457 - 3.54129i) q^{22} +(-1.02242 - 0.590296i) q^{23} +(1.02822 + 3.83736i) q^{24} -2.94742i q^{25} +(-2.57793 + 1.60629i) q^{26} -5.65531i q^{27} +(-3.14641 + 1.32458i) q^{28} +(-2.77911 + 4.81356i) q^{29} +(1.49807 - 0.864909i) q^{30} +(4.79337 + 4.79337i) q^{31} +(5.55461 + 1.48835i) q^{32} +(-6.71986 - 1.80058i) q^{33} +(-1.77695 + 1.77695i) q^{34} +(2.32482 + 2.99387i) q^{35} +(-1.05692 - 0.610210i) q^{36} +(5.40165 - 1.44737i) q^{37} +5.28993 q^{38} +(-1.16890 + 5.03367i) q^{39} -3.97118i q^{40} +(4.71621 - 1.26371i) q^{41} +(1.20544 - 2.95831i) q^{42} +(-2.90941 + 1.67975i) q^{43} +(-4.42873 + 4.42873i) q^{44} +(-0.350719 + 1.30890i) q^{45} +(0.257412 - 0.960674i) q^{46} +(-4.12822 + 4.12822i) q^{47} +(0.304771 - 0.175960i) q^{48} +(6.78192 + 1.73367i) q^{49} +(2.39839 - 0.642646i) q^{50} +4.27539i q^{51} +(3.39841 + 3.17721i) q^{52} +5.79315 q^{53} +(4.60186 - 1.23306i) q^{54} +(6.02252 + 3.47711i) q^{55} +(-4.49790 - 5.79233i) q^{56} +(6.36385 - 6.36385i) q^{57} +(-4.52285 - 1.21190i) q^{58} +(-10.7576 - 2.88250i) q^{59} +(-1.87348 - 1.87348i) q^{60} +(-7.95118 + 4.59062i) q^{61} +(-2.85534 + 4.94560i) q^{62} +(0.970951 + 2.30639i) q^{63} +4.35335i q^{64} +(2.43094 - 4.55785i) q^{65} -5.86070i q^{66} +(-0.508485 - 1.89769i) q^{67} +(3.33337 + 1.92452i) q^{68} +(-0.846033 - 1.46537i) q^{69} +(-1.92929 + 2.54453i) q^{70} +(-3.19094 - 0.855010i) q^{71} +(0.678548 - 2.53237i) q^{72} +(-0.353010 + 0.353010i) q^{73} +(2.35552 + 4.07987i) q^{74} +(2.11218 - 3.65840i) q^{75} +(-2.09705 - 7.82630i) q^{76} +(12.7227 - 1.74964i) q^{77} +(-4.35088 + 0.146360i) q^{78} -6.95423 q^{79} +(-0.339796 + 0.0910481i) q^{80} +(2.63395 - 4.56214i) q^{81} +(2.05661 + 3.56216i) q^{82} +(3.22886 + 3.22886i) q^{83} +(-4.85460 - 0.610674i) q^{84} +(1.10612 - 4.12811i) q^{85} +(-2.00121 - 2.00121i) q^{86} +(-6.89897 + 3.98312i) q^{87} +(-11.6520 - 6.72727i) q^{88} +(-0.0636346 - 0.237487i) q^{89} -1.14155 q^{90} +(-1.61663 - 9.40141i) q^{91} -1.52333 q^{92} +(2.51461 + 9.38464i) q^{93} +(-4.25933 - 2.45913i) q^{94} +(-7.79107 + 4.49818i) q^{95} +(5.82791 + 5.82791i) q^{96} +(2.43374 - 9.08284i) q^{97} +(0.0679801 + 5.89661i) q^{98} +(3.24636 + 3.24636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9	$ 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) $ 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9 - 4 * q^11 - 32 * q^14 - 8 * q^15 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^22 - 12 * q^23 + 24 * q^28 + 4 * q^29 + 12 * q^30 + 4 * q^32 - 20 * q^35 + 4 * q^37 - 36 * q^39 - 28 * q^42 - 48 * q^43 + 24 * q^44 + 84 * q^46 + 24 * q^49 - 44 * q^50 + 72 * q^53 + 60 * q^56 - 92 * q^57 - 16 * q^58 + 76 * q^60 + 48 * q^63 + 4 * q^65 - 56 * q^67 + 56 * q^70 + 84 * q^71 - 128 * q^72 - 24 * q^74 + 148 * q^78 - 80 * q^79 + 28 * q^81 - 64 * q^84 + 36 * q^85 - 48 * q^86 - 228 * q^88 - 48 * q^91 + 24 * q^92 + 108 * q^93 - 84 * q^95 - 32 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.218036	+	0.813723i	0.154175	+	0.575389i	0.999175	+	0.0406221i	$0.0129340\pi$
$2$	0.218036	+	0.813723i	0.154175	+	0.575389i	−0.845000	+	0.534767i	$0.820399\pi$
$3$	1.24122	+	0.716618i	0.716618	+	0.413740i	0.813507	−	0.581555i	$-0.197556\pi$
$3$	1.24122	+	0.716618i	0.716618	+	0.413740i	−0.0968883	+	0.995295i	$0.530889\pi$
$4$	1.11745	−	0.645157i	0.558723	−	0.322579i
$5$	−1.01306	−	1.01306i	−0.453054	−	0.453054i	0.443313	−	0.896367i	$-0.353803\pi$
$5$	−1.01306	−	1.01306i	−0.453054	−	0.453054i	−0.896367	+	0.443313i	$0.853803\pi$
$6$	−0.312498	+	1.16626i	−0.127577	+	0.476123i
$7$	−2.62506	−	0.330214i	−0.992181	−	0.124809i
$7$	−2.62506	−	0.330214i	−0.992181	−	0.124809i
$8$	1.96000	+	1.96000i	0.692963	+	0.692963i
$9$	−0.472916	−	0.819114i	−0.157639	−	0.273038i
$10$	0.603466	−	1.04523i	0.190833	−	0.330532i
$11$	−4.68859	+	1.25630i	−1.41366	+	0.378790i	−0.883231	−	0.468938i	$-0.844637\pi$
$11$	−4.68859	+	1.25630i	−1.41366	+	0.378790i	−0.530431	+	0.847728i	$0.677970\pi$
$12$	1.84933			0.533855
$13$	1.04975	+	3.44935i	0.291147	+	0.956678i
$13$	1.04975	+	3.44935i	0.291147	+	0.956678i
$14$	−0.303657	−	2.20807i	−0.0811556	−	0.590133i
$15$	−0.531452	−	1.98341i	−0.137220	−	0.512113i
$16$	0.122771	−	0.212645i	0.0306927	−	0.0531613i
$17$	1.49151	+	2.58338i	0.361745	+	0.626561i	0.988248	−	0.152858i	$-0.0488477\pi$
$17$	1.49151	+	2.58338i	0.361745	+	0.626561i	−0.626503	+	0.779419i	$0.715514\pi$
$18$	0.563419	−	0.563419i	0.132799	−	0.132799i
$19$	1.62522	−	6.06542i	0.372852	−	1.39150i	−0.483606	−	0.875286i	$-0.660673\pi$
$19$	1.62522	−	6.06542i	0.372852	−	1.39150i	0.856458	−	0.516217i	$-0.172660\pi$
$20$	−1.78562	−	0.478455i	−0.399277	−	0.106986i
$21$	−3.02164	−	2.29104i	−0.659377	−	0.499945i
$22$	−2.04457	−	3.54129i	−0.435903	−	0.755006i
$23$	−1.02242	−	0.590296i	−0.213190	−	0.123085i	0.389603	−	0.920983i	$-0.372612\pi$
$23$	−1.02242	−	0.590296i	−0.213190	−	0.123085i	−0.602793	+	0.797898i	$0.705945\pi$
$24$	1.02822	+	3.83736i	0.209884	+	0.783297i
$25$		−	2.94742i		−	0.589485i
$26$	−2.57793	+	1.60629i	−0.505575	+	0.315019i
$27$		−	5.65531i		−	1.08837i
$28$	−3.14641	+	1.32458i	−0.594615	+	0.250323i
$29$	−2.77911	+	4.81356i	−0.516068	+	0.893856i	0.483758	+	0.875202i	$0.339271\pi$
$29$	−2.77911	+	4.81356i	−0.516068	+	0.893856i	−0.999826	+	0.0186541i	$0.994062\pi$
$30$	1.49807	−	0.864909i	0.273508	−	0.157910i
$31$	4.79337	+	4.79337i	0.860914	+	0.860914i	0.991444	−	0.130530i	$-0.0416680\pi$
$31$	4.79337	+	4.79337i	0.860914	+	0.860914i	−0.130530	+	0.991444i	$0.541668\pi$
$32$	5.55461	+	1.48835i	0.981926	+	0.263106i
$33$	−6.71986	−	1.80058i	−1.16978	−	0.313441i
$34$	−1.77695	+	1.77695i	−0.304744	+	0.304744i
$35$	2.32482	+	2.99387i	0.392966	+	0.506056i
$36$	−1.05692	−	0.610210i	−0.176153	−	0.101702i
$37$	5.40165	−	1.44737i	0.888027	−	0.237946i	0.214160	−	0.976799i	$-0.431299\pi$
$37$	5.40165	−	1.44737i	0.888027	−	0.237946i	0.673867	+	0.738853i	$0.264632\pi$
$38$	5.28993			0.858140
$39$	−1.16890	+	5.03367i	−0.187174	+	0.806033i
$40$		−	3.97118i		−	0.627899i
$41$	4.71621	−	1.26371i	0.736549	−	0.197358i	0.129005	−	0.991644i	$-0.458822\pi$
$41$	4.71621	−	1.26371i	0.736549	−	0.197358i	0.607544	+	0.794286i	$0.292155\pi$
$42$	1.20544	−	2.95831i	0.186004	−	0.456477i
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	−0.705158	−	0.709050i	$-0.749124\pi$
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	0.261477	+	0.965210i	$0.415790\pi$
$44$	−4.42873	+	4.42873i	−0.667656	+	0.667656i
$45$	−0.350719	+	1.30890i	−0.0522822	+	0.195120i
$46$	0.257412	−	0.960674i	0.0379533	−	0.141644i
$47$	−4.12822	+	4.12822i	−0.602163	+	0.602163i	−0.940886	−	0.338723i	$-0.890005\pi$
$47$	−4.12822	+	4.12822i	−0.602163	+	0.602163i	0.338723	+	0.940886i	$0.390005\pi$
$48$	0.304771	−	0.175960i	0.0439899	−	0.0253976i
$49$	6.78192	+	1.73367i	0.968845	+	0.247667i
$50$	2.39839	−	0.642646i	0.339183	−	0.0908839i
$51$			4.27539i			0.598674i
$52$	3.39841	+	3.17721i	0.471275	+	0.440600i
$53$	5.79315			0.795751			0.397875	−	0.917439i	$-0.369748\pi$
$53$	5.79315			0.795751			0.397875	+	0.917439i	$0.369748\pi$
$54$	4.60186	−	1.23306i	0.626234	−	0.167799i
$55$	6.02252	+	3.47711i	0.812077	+	0.468853i
$56$	−4.49790	−	5.79233i	−0.601057	−	0.774033i
$57$	6.36385	−	6.36385i	0.842913	−	0.842913i
$58$	−4.52285	−	1.21190i	−0.593880	−	0.159130i
$59$	−10.7576	−	2.88250i	−1.40053	−	0.375270i	−0.521992	−	0.852950i	$-0.674811\pi$
$59$	−10.7576	−	2.88250i	−1.40053	−	0.375270i	−0.878534	+	0.477681i	$0.841478\pi$
$60$	−1.87348	−	1.87348i	−0.241865	−	0.241865i
$61$	−7.95118	+	4.59062i	−1.01804	+	0.587768i	−0.913537	−	0.406756i	$-0.866660\pi$
$61$	−7.95118	+	4.59062i	−1.01804	+	0.587768i	−0.104508	+	0.994524i	$0.533327\pi$
$62$	−2.85534	+	4.94560i	−0.362629	+	0.628092i
$63$	0.970951	+	2.30639i	0.122328	+	0.290578i
$64$			4.35335i			0.544169i
$65$	2.43094	−	4.55785i	0.301521	−	0.565332i
$66$		−	5.86070i		−	0.721402i
$67$	−0.508485	−	1.89769i	−0.0621214	−	0.231840i	0.927884	−	0.372869i	$-0.121626\pi$
$67$	−0.508485	−	1.89769i	−0.0621214	−	0.231840i	−0.990006	+	0.141028i	$0.954959\pi$
$68$	3.33337	+	1.92452i	0.404231	+	0.233383i
$69$	−0.846033	−	1.46537i	−0.101850	−	0.176410i
$70$	−1.92929	+	2.54453i	−0.230594	+	0.304130i
$71$	−3.19094	−	0.855010i	−0.378695	−	0.101471i	0.0644501	−	0.997921i	$-0.479471\pi$
$71$	−3.19094	−	0.855010i	−0.378695	−	0.101471i	−0.443145	+	0.896450i	$0.646137\pi$
$72$	0.678548	−	2.53237i	0.0799676	−	0.298443i
$73$	−0.353010	+	0.353010i	−0.0413167	+	0.0413167i	−0.727463	−	0.686147i	$-0.759301\pi$
$73$	−0.353010	+	0.353010i	−0.0413167	+	0.0413167i	0.686147	+	0.727463i	$0.259301\pi$
$74$	2.35552	+	4.07987i	0.273823	+	0.474275i
$75$	2.11218	−	3.65840i	0.243893	−	0.422436i
$76$	−2.09705	−	7.82630i	−0.240548	−	0.897738i
$77$	12.7227	−	1.74964i	1.44989	−	0.199390i
$78$	−4.35088	+	0.146360i	−0.492640	+	0.0165720i
$79$	−6.95423			−0.782412			−0.391206	−	0.920303i	$-0.627942\pi$
$79$	−6.95423			−0.782412			−0.391206	+	0.920303i	$0.627942\pi$
$80$	−0.339796	+	0.0910481i	−0.0379904	+	0.0101795i
$81$	2.63395	−	4.56214i	0.292662	−	0.506905i
$82$	2.05661	+	3.56216i	0.227115	+	0.393374i
$83$	3.22886	+	3.22886i	0.354413	+	0.354413i	0.861749	−	0.507335i	$-0.169369\pi$
$83$	3.22886	+	3.22886i	0.354413	+	0.354413i	−0.507335	+	0.861749i	$0.669369\pi$
$84$	−4.85460	−	0.610674i	−0.529680	−	0.0666300i
$85$	1.10612	−	4.12811i	0.119976	−	0.447756i
$86$	−2.00121	−	2.00121i	−0.215796	−	0.215796i
$87$	−6.89897	+	3.98312i	−0.739648	+	0.427036i
$88$	−11.6520	−	6.72727i	−1.24210	−	0.717129i
$89$	−0.0636346	−	0.237487i	−0.00674525	−	0.0251736i	0.962471	−	0.271384i	$-0.0874813\pi$
$89$	−0.0636346	−	0.237487i	−0.00674525	−	0.0251736i	−0.969216	+	0.246210i	$0.920815\pi$
$90$	−1.14155			−0.120330
$91$	−1.61663	−	9.40141i	−0.169468	−	0.985536i
$92$	−1.52333			−0.158819
$93$	2.51461	+	9.38464i	0.260752	+	0.973141i
$94$	−4.25933	−	2.45913i	−0.439316	−	0.253639i
$95$	−7.79107	+	4.49818i	−0.799347	+	0.461503i
$96$	5.82791	+	5.82791i	0.594809	+	0.594809i
$97$	2.43374	−	9.08284i	0.247109	−	0.922223i	−0.725203	−	0.688535i	$-0.758254\pi$
$97$	2.43374	−	9.08284i	0.247109	−	0.922223i	0.972312	−	0.233688i	$-0.0750793\pi$
$98$	0.0679801	+	5.89661i	0.00686703	+	0.595647i
$99$	3.24636	+	3.24636i	0.326272	+	0.326272i
$100$	−1.90155	−	3.29359i	−0.190155	−	0.329359i
$101$	7.14344	−	12.3728i	0.710799	−	1.23114i	−0.253759	−	0.967267i	$-0.581667\pi$
$101$	7.14344	−	12.3728i	0.710799	−	1.23114i	0.964558	−	0.263872i	$-0.0849996\pi$
$102$	−3.47898	+	0.932190i	−0.344470	+	0.0923006i
$103$	−7.45130			−0.734198			−0.367099	−	0.930182i	$-0.619649\pi$
$103$	−7.45130			−0.734198			−0.367099	+	0.930182i	$0.619649\pi$
$104$	−4.70322	+	8.81822i	−0.461189	+	0.864698i
$105$	0.740146	+	5.38206i	0.0722309	+	0.525235i
$106$	1.26312	+	4.71402i	0.122685	+	0.457866i
$107$	2.34132	−	4.05528i	0.226344	−	0.392039i	−0.730378	−	0.683043i	$-0.760656\pi$
$107$	2.34132	−	4.05528i	0.226344	−	0.392039i	0.956722	+	0.291004i	$0.0939894\pi$
$108$	−3.64857	−	6.31950i	−0.351083	−	0.608094i
$109$	−3.04192	+	3.04192i	−0.291363	+	0.291363i	−0.837619	−	0.546256i	$-0.816053\pi$
$109$	−3.04192	+	3.04192i	−0.291363	+	0.291363i	0.546256	+	0.837619i	$0.316053\pi$
$110$	−1.51627	+	5.65880i	−0.144571	+	0.539546i
$111$	7.74185	+	2.07442i	0.734824	+	0.196895i
$112$	−0.392500	+	0.517667i	−0.0370877	+	0.0489149i
$113$	2.02372	+	3.50518i	0.190375	+	0.329740i	0.945375	−	0.325986i	$-0.105696\pi$
$113$	2.02372	+	3.50518i	0.190375	+	0.329740i	−0.754999	+	0.655725i	$0.772363\pi$
$114$	6.56597	+	3.79086i	0.614959	+	0.355047i
$115$	0.437769	+	1.63378i	0.0408222	+	0.152351i
$116$			7.17186i			0.665890i
$117$	2.32897	−	2.49112i	0.215314	−	0.230304i
$118$		−	9.38223i		−	0.863705i
$119$	−3.06225	−	7.27405i	−0.280716	−	0.666811i
$120$	2.84582	−	4.92911i	0.259787	−	0.449964i
$121$	10.8783	−	6.28058i	0.988935	−	0.570962i
$122$	−5.46914	−	5.46914i	−0.495153	−	0.495153i
$123$	6.75945	+	1.81119i	0.609479	+	0.163309i
$124$	8.44880	+	2.26385i	0.758725	+	0.203300i
$125$	−8.05121	+	8.05121i	−0.720122	+	0.720122i
$126$	−1.66506	+	1.29296i	−0.148335	+	0.115186i
$127$	10.6871	+	6.17021i	0.948328	+	0.547518i	0.892561	−	0.450926i	$-0.148906\pi$
$127$	10.6871	+	6.17021i	0.948328	+	0.547518i	0.0557671	+	0.998444i	$0.482240\pi$
$128$	7.56681	−	2.02752i	0.668817	−	0.179209i
$129$	−4.81496			−0.423933
$130$	4.23886	+	0.984335i	0.371773	+	0.0863319i
$131$			6.71360i			0.586570i	0.956025	+	0.293285i	$0.0947485\pi$
$131$			6.71360i			0.586570i	−0.956025	+	0.293285i	$0.905251\pi$
$132$	−8.67073	+	2.32332i	−0.754690	+	0.202219i
$133$	−6.26921	+	15.3854i	−0.543609	+	1.33409i
$134$	1.43333	−	0.827533i	0.123821	−	0.0714879i
$135$	−5.72916	+	5.72916i	−0.493088	+	0.493088i
$136$	−2.14005	+	7.98678i	−0.183508	+	0.684860i
$137$	5.66652	−	21.1477i	0.484124	−	1.80677i	−0.0998520	−	0.995002i	$-0.531837\pi$
$137$	5.66652	−	21.1477i	0.484124	−	1.80677i	0.583976	−	0.811771i	$-0.301496\pi$
$138$	1.00794	−	1.00794i	0.0858017	−	0.0858017i
$139$	3.49682	−	2.01889i	0.296597	−	0.171240i	−0.344316	−	0.938854i	$-0.611889\pi$
$139$	3.49682	−	2.01889i	0.296597	−	0.171240i	0.640913	+	0.767614i	$0.278556\pi$
$140$	4.52937	+	1.84561i	0.382802	+	0.155983i
$141$	−8.08239	+	2.16567i	−0.680660	+	0.182382i
$142$		−	2.78296i		−	0.233541i
$143$	−9.25526	−	14.8538i	−0.773964	−	1.24214i
$144$	−0.232241			−0.0193534
$145$	7.69182	−	2.06102i	0.638771	−	0.171158i
$146$	−0.364221	−	0.210283i	−0.0301432	−	0.0174032i
$147$	7.17547	+	7.01191i	0.591823	+	0.578332i
$148$	5.10227	−	5.10227i	0.419404	−	0.419404i
$149$	−2.74006	−	0.734196i	−0.224474	−	0.0601477i	0.144829	−	0.989457i	$-0.453737\pi$
$149$	−2.74006	−	0.734196i	−0.224474	−	0.0601477i	−0.369303	+	0.929309i	$0.620404\pi$
$150$	3.43746	+	0.921064i	0.280667	+	0.0752045i
$151$	11.8387	+	11.8387i	0.963421	+	0.963421i	0.999354	−	0.0359335i	$-0.0114404\pi$
$151$	11.8387	+	11.8387i	0.963421	+	0.963421i	−0.0359335	+	0.999354i	$0.511440\pi$
$152$	15.0736	−	8.70277i	1.22263	−	0.705888i
$153$	1.41072	−	2.44344i	0.114050	−	0.197541i
$154$	4.19773	+	9.97126i	0.338263	+	0.803507i
$155$		−	9.71192i		−	0.780080i
$156$	1.94132	+	6.37898i	0.155430	+	0.510727i
$157$			2.86867i			0.228945i	0.993426	+	0.114472i	$0.0365177\pi$
$157$			2.86867i			0.228945i	−0.993426	+	0.114472i	$0.963482\pi$
$158$	−1.51628	−	5.65882i	−0.120628	−	0.450191i
$159$	7.19058	+	4.15148i	0.570250	+	0.329234i
$160$	−4.11936	−	7.13494i	−0.325664	−	0.564067i
$161$	2.48900	+	1.88718i	0.196161	+	0.148731i
$162$	4.28662	+	1.14860i	0.336789	+	0.0902422i
$163$	−6.23736	+	23.2781i	−0.488548	+	1.82328i	0.0749773	+	0.997185i	$0.476112\pi$
$163$	−6.23736	+	23.2781i	−0.488548	+	1.82328i	−0.563525	+	0.826099i	$0.690555\pi$
$164$	4.45482	−	4.45482i	0.347863	−	0.347863i
$165$	4.98352	+	8.63170i	0.387966	+	0.671977i
$166$	−1.92339	+	3.33141i	−0.149284	+	0.258567i
$167$	−2.53997	−	9.47931i	−0.196549	−	0.733531i	−0.991860	−	0.127330i	$-0.959359\pi$
$167$	−2.53997	−	9.47931i	−0.196549	−	0.733531i	0.795311	−	0.606201i	$-0.207307\pi$
$168$	−1.43198	−	10.4128i	−0.110480	−	0.803368i
$169$	−10.7961	+	7.24189i	−0.830466	+	0.557069i
$170$	3.60031			0.276131
$171$	−5.73687	+	1.53719i	−0.438709	+	0.117552i
$172$	−2.16740	+	3.75405i	−0.165263	+	0.286244i
$173$	2.61883	+	4.53595i	0.199106	+	0.344862i	0.948239	−	0.317558i	$-0.102863\pi$
$173$	2.61883	+	4.53595i	0.199106	+	0.344862i	−0.749133	+	0.662420i	$0.769529\pi$
$174$	−4.74539	−	4.74539i	−0.359747	−	0.359747i
$175$	−0.973282	+	7.73717i	−0.0735732	+	0.584875i
$176$	−0.308475	+	1.15124i	−0.0232522	+	0.0867783i
$177$	−11.2869	−	11.2869i	−0.848379	−	0.848379i
$178$	0.179374	−	0.103562i	0.0134447	−	0.00776229i
$179$	−19.5491	−	11.2867i	−1.46117	−	0.843605i	−0.462101	−	0.886827i	$-0.652904\pi$
$179$	−19.5491	−	11.2867i	−1.46117	−	0.843605i	−0.999065	+	0.0432226i	$0.986238\pi$
$180$	0.452538	+	1.68890i	0.0337302	+	0.125883i
$181$	−22.4803			−1.67095			−0.835474	−	0.549530i	$-0.814807\pi$
$181$	−22.4803			−1.67095			−0.835474	+	0.549530i	$0.814807\pi$
$182$	7.29766	−	3.36534i	0.540939	−	0.249455i
$183$	−13.1589			−0.972733
$184$	−0.846966	−	3.16092i	−0.0624392	−	0.233026i
$185$	−6.93846	−	4.00592i	−0.510126	−	0.294521i
$186$	−7.08822	+	4.09239i	−0.519733	+	0.300068i
$187$	−10.2386	−	10.2386i	−0.748721	−	0.748721i
$188$	−1.94971	+	7.27641i	−0.142197	+	0.530687i
$189$	−1.86746	+	14.8456i	−0.135838	+	1.07986i
$190$	−5.35901	−	5.35901i	−0.388783	−	0.388783i
$191$	−12.3354	−	21.3655i	−0.892557	−	1.54595i	−0.836800	−	0.547509i	$-0.815576\pi$
$191$	−12.3354	−	21.3655i	−0.892557	−	1.54595i	−0.0557571	−	0.998444i	$-0.517757\pi$
$192$	−3.11969	+	5.40346i	−0.225144	+	0.389961i
$193$	3.32194	−	0.890112i	0.239119	−	0.0640717i	−0.137269	−	0.990534i	$-0.543833\pi$
$193$	3.32194	−	0.890112i	0.239119	−	0.0640717i	0.376388	+	0.926462i	$0.377166\pi$
$194$	7.92156			0.568735
$195$	6.28357	−	3.91524i	0.449976	−	0.280376i
$196$	8.69691	−	2.43813i	0.621208	−	0.174152i
$197$	−1.03338	−	3.85664i	−0.0736255	−	0.274774i	0.919293	−	0.393575i	$-0.128762\pi$
$197$	−1.03338	−	3.85664i	−0.0736255	−	0.274774i	−0.992918	+	0.118801i	$0.962095\pi$
$198$	−1.93382	+	3.34947i	−0.137430	+	0.238036i
$199$	−0.511550	−	0.886031i	−0.0362628	−	0.0628091i	0.847324	−	0.531076i	$-0.178212\pi$
$199$	−0.511550	−	0.886031i	−0.0362628	−	0.0628091i	−0.883587	+	0.468267i	$0.844879\pi$
$200$	5.77694	−	5.77694i	0.408491	−	0.408491i
$201$	0.728780	−	2.71984i	0.0514042	−	0.191843i
$202$	11.6256	+	3.11506i	0.817972	+	0.219175i
$203$	8.88485	−	11.7182i	0.623594	−	0.822457i
$204$	2.75830	+	4.77751i	0.193119	+	0.334493i
$205$	−6.05801	−	3.49759i	−0.423110	−	0.244282i
$206$	−1.62465	−	6.06329i	−0.113195	−	0.422450i
$207$			1.11664i			0.0776119i
$208$	0.862367	+	0.200256i	0.0597944	+	0.0138853i
$209$			30.4800i			2.10835i
$210$	−4.21813	+	1.77576i	−0.291078	+	0.122539i
$211$	2.70061	−	4.67759i	0.185918	−	0.322019i	−0.757968	−	0.652292i	$-0.773808\pi$
$211$	2.70061	−	4.67759i	0.185918	−	0.322019i	0.943885	+	0.330273i	$0.107141\pi$
$212$	6.47353	−	3.73750i	0.444604	−	0.256692i
$213$	−3.34794	−	3.34794i	−0.229397	−	0.229397i
$214$	3.81037	+	1.02099i	0.260472	+	0.0697932i
$215$	4.64909	+	1.24572i	0.317065	+	0.0849573i
$216$	11.0844	−	11.0844i	0.754197	−	0.754197i
$217$	−11.0001	−	14.1657i	−0.746732	−	0.961632i
$218$	−3.13853	−	1.81203i	−0.212568	−	0.122726i
$219$	−0.691136	+	0.185189i	−0.0467026	+	0.0125139i
$220$	8.97312			0.604968
$221$	−7.34527	+	7.85665i	−0.494096	+	0.528496i
$222$			6.75202i			0.453166i
$223$	16.6138	−	4.45165i	1.11254	−	0.298105i	0.344680	−	0.938720i	$-0.387987\pi$
$223$	16.6138	−	4.45165i	1.11254	−	0.298105i	0.767862	+	0.640616i	$0.221321\pi$
$224$	−14.0897	−	5.74124i	−0.941410	−	0.383603i
$225$	−2.41428	+	1.39388i	−0.160952	+	0.0929256i
$226$	−2.41100	+	2.41100i	−0.160377	+	0.160377i
$227$	2.57850	−	9.62310i	0.171141	−	0.638707i	−0.826036	−	0.563618i	$-0.809409\pi$
$227$	2.57850	−	9.62310i	0.171141	−	0.638707i	0.997177	−	0.0750896i	$-0.0239243\pi$
$228$	3.00557	−	11.2169i	0.199049	−	0.742860i
$229$	2.94885	−	2.94885i	0.194865	−	0.194865i	−0.602929	−	0.797795i	$-0.706000\pi$
$229$	2.94885	−	2.94885i	0.194865	−	0.194865i	0.797795	+	0.602929i	$0.206000\pi$
$230$	−1.23399	+	0.712446i	−0.0813671	+	0.0469773i
$231$	17.0455	+	6.94563i	1.12151	+	0.456989i
$232$	−14.8816	+	3.98752i	−0.977026	+	0.261793i
$233$			6.32614i			0.414439i	0.978294	+	0.207220i	$0.0664414\pi$
$233$			6.32614i			0.414439i	−0.978294	+	0.207220i	$0.933559\pi$
$234$	2.53488	+	1.35198i	0.165710	+	0.0883820i
$235$	8.36426			0.545624
$236$	−13.8807	+	3.71933i	−0.903560	+	0.242108i
$237$	−8.63172	−	4.98353i	−0.560691	−	0.323715i
$238$	5.25138	−	4.07783i	0.340397	−	0.264327i
$239$	7.84175	−	7.84175i	0.507241	−	0.507241i	−0.406438	−	0.913679i	$-0.633229\pi$
$239$	7.84175	−	7.84175i	0.507241	−	0.507241i	0.913679	+	0.406438i	$0.133229\pi$
$240$	−0.487009	−	0.130494i	−0.0314363	−	0.00842332i
$241$	13.5060	+	3.61892i	0.869996	+	0.233115i	0.666086	−	0.745875i	$-0.267968\pi$
$241$	13.5060	+	3.61892i	0.869996	+	0.233115i	0.203910	+	0.978990i	$0.434635\pi$
$242$	7.48251	+	7.48251i	0.480994	+	0.480994i
$243$	−8.15430	+	4.70789i	−0.523099	+	0.302011i
$244$	−5.92334	+	10.2595i	−0.379203	+	0.656799i
$245$	−5.11417	−	8.62679i	−0.326733	−	0.551145i
$246$			5.89523i			0.375866i
$247$	22.6278	−	0.761183i	1.43978	−	0.0484329i
$248$			18.7900i			1.19316i
$249$	1.69386	+	6.32158i	0.107344	+	0.400614i
$250$	−8.30691	−	4.79600i	−0.525375	−	0.303325i
$251$	13.1784	+	22.8256i	0.831813	+	1.44074i	0.896599	+	0.442843i	$0.146030\pi$
$251$	13.1784	+	22.8256i	0.831813	+	1.44074i	−0.0647865	+	0.997899i	$0.520637\pi$
$252$	2.57297	+	1.95085i	0.162082	+	0.122892i
$253$	5.53531	+	1.48318i	0.348002	+	0.0932468i
$254$	−2.69066	+	10.0417i	−0.168827	+	0.630071i
$255$	4.33122	−	4.33122i	0.271231	−	0.271231i
$256$	7.65303	+	13.2554i	0.478314	+	0.828465i
$257$	−5.39025	+	9.33618i	−0.336234	+	0.582375i	−0.983721	−	0.179702i	$-0.942487\pi$
$257$	−5.39025	+	9.33618i	−0.336234	+	0.582375i	0.647487	+	0.762077i	$0.275820\pi$
$258$	−1.04984	−	3.91804i	−0.0653599	−	0.243927i
$259$	−14.6576	+	2.01573i	−0.910781	+	0.125251i
$260$	−0.224087	−	6.66149i	−0.0138973	−	0.413128i
$261$	5.25714			0.325409
$262$	−5.46301	+	1.46381i	−0.337506	+	0.0904345i
$263$	7.74562	−	13.4158i	0.477616	−	0.827254i	−0.522055	−	0.852912i	$-0.674835\pi$
$263$	7.74562	−	13.4158i	0.477616	−	0.827254i	0.999671	+	0.0256573i	$0.00816786\pi$
$264$	−9.64177	−	16.7000i	−0.593410	−	1.02782i
$265$	−5.86881	−	5.86881i	−0.360518	−	0.360518i
$266$	−13.8864	−	1.74681i	−0.851430	−	0.107104i
$267$	0.0912034	−	0.340376i	0.00558156	−	0.0208307i
$268$	−1.79252	−	1.79252i	−0.109495	−	0.109495i
$269$	22.6324	−	13.0668i	1.37992	−	0.796697i	0.387770	−	0.921756i	$-0.373246\pi$
$269$	22.6324	−	13.0668i	1.37992	−	0.796697i	0.992149	+	0.125060i	$0.0399122\pi$
$270$	−5.91112	−	3.41279i	−0.359739	−	0.207696i
$271$	−1.70363	−	6.35804i	−0.103488	−	0.386223i	0.894681	−	0.446706i	$-0.147403\pi$
$271$	−1.70363	−	6.35804i	−0.103488	−	0.386223i	−0.998169	+	0.0604821i	$0.980736\pi$
$272$	0.732458			0.0444118
$273$	4.73064	−	12.8277i	0.286311	−	0.776369i
$274$	18.4439			1.11424
$275$	3.70286	+	13.8193i	0.223291	+	0.833333i
$276$	−1.89079	−	1.09165i	−0.113812	−	0.0657096i
$277$	−25.2681	+	14.5885i	−1.51821	+	0.876540i	−0.518442	+	0.855113i	$0.673488\pi$
$277$	−25.2681	+	14.5885i	−1.51821	+	0.876540i	−0.999770	+	0.0214270i	$0.993179\pi$
$278$	2.40525	+	2.40525i	0.144258	+	0.144258i
$279$	1.65946	−	6.19317i	0.0993490	−	0.370776i
$280$	−1.31134	+	10.4246i	−0.0783677	+	0.622990i
$281$	8.85369	+	8.85369i	0.528167	+	0.528167i	0.920025	−	0.391859i	$-0.128168\pi$
$281$	8.85369	+	8.85369i	0.528167	+	0.528167i	−0.391859	+	0.920025i	$0.628168\pi$
$282$	−3.52451	−	6.10463i	−0.209882	−	0.363526i
$283$	−15.9706	+	27.6618i	−0.949351	+	1.64432i	−0.202556	+	0.979271i	$0.564925\pi$
$283$	−15.9706	+	27.6618i	−0.949351	+	1.64432i	−0.746795	+	0.665054i	$0.768409\pi$
$284$	−4.11732	+	1.10323i	−0.244318	+	0.0654648i
$285$	−12.8939			−0.763769
$286$	10.0689	−	10.7699i	0.595386	−	0.636837i
$287$	−12.7976	+	1.75995i	−0.755421	+	0.103886i
$288$	−1.40773	−	5.25373i	−0.0829514	−	0.309579i
$289$	4.05077	−	7.01614i	0.238281	−	0.412714i
$290$	3.35420	+	5.80964i	0.196965	+	0.341154i
$291$	9.52974	−	9.52974i	0.558643	−	0.558643i
$292$	−0.166722	+	0.622216i	−0.00975668	+	0.0364124i
$293$	−12.4822	−	3.34459i	−0.729218	−	0.195393i	−0.124937	−	0.992165i	$-0.539873\pi$
$293$	−12.4822	−	3.34459i	−0.729218	−	0.195393i	−0.604281	+	0.796771i	$0.706540\pi$
$294$	−4.14124	+	7.36770i	−0.241522	+	0.429693i
$295$	7.97798	+	13.8183i	0.464496	+	0.804531i
$296$	13.4241	+	7.75039i	0.780258	+	0.450482i
$297$	7.10479	+	26.5154i	0.412262	+	1.53858i
$298$		−	2.38973i		−	0.138433i
$299$	0.962853	−	4.14635i	0.0556832	−	0.239790i
$300$		−	5.45075i		−	0.314699i
$301$	8.19206	−	3.44872i	0.472183	−	0.198781i
$302$	−7.05216	+	12.2147i	−0.405806	+	0.702877i
$303$	17.7332	−	10.2382i	1.01874	−	0.588171i
$304$	−1.09025	−	1.09025i	−0.0625303	−	0.0625303i
$305$	12.7056	+	3.40445i	0.727520	+	0.194938i
$306$	2.29587	+	0.615177i	0.131246	+	0.0351674i
$307$	5.42520	−	5.42520i	0.309632	−	0.309632i	−0.535135	−	0.844767i	$-0.679739\pi$
$307$	5.42520	−	5.42520i	0.309632	−	0.309632i	0.844767	+	0.535135i	$0.179739\pi$
$308$	13.0881	−	10.1633i	0.745765	−	0.579106i
$309$	−9.24869	−	5.33974i	−0.526140	−	0.303767i
$310$	7.90282	−	2.11755i	0.448850	−	0.120269i
$311$	0.483376			0.0274097			0.0137049	−	0.999906i	$-0.495637\pi$
$311$	0.483376			0.0274097			0.0137049	+	0.999906i	$0.495637\pi$
$312$	−12.1570	+	7.57493i	−0.688256	+	0.428846i
$313$		−	0.445328i		−	0.0251715i	−0.999921	−	0.0125857i	$-0.995994\pi$
$313$		−	0.445328i		−	0.0251715i	0.999921	−	0.0125857i	$-0.00400627\pi$
$314$	−2.33430	+	0.625474i	−0.131732	+	0.0352976i
$315$	1.35288	−	3.32014i	0.0762261	−	0.187069i
$316$	−7.77097	+	4.48657i	−0.437151	+	0.252389i
$317$	−17.5588	+	17.5588i	−0.986201	+	0.986201i	−0.999906	−	0.0137052i	$-0.995637\pi$
$317$	−17.5588	+	17.5588i	−0.986201	+	0.986201i	0.0137052	+	0.999906i	$0.495637\pi$
$318$	−1.81035	+	6.75631i	−0.101519	+	0.378875i
$319$	6.98281	−	26.0602i	0.390962	−	1.45909i
$320$	4.41020	−	4.41020i	0.246538	−	0.246538i
$321$	5.81218	−	3.35567i	0.324404	−	0.187295i
$322$	−0.992951	+	2.43683i	−0.0553350	+	0.135799i
$323$	18.0933	−	4.84809i	1.00674	−	0.269755i
$324$		−	6.79726i		−	0.377625i
$325$	10.1667	−	3.09405i	0.563947	−	0.171627i
$326$	−20.3019			−1.12442
$327$	−5.95559	+	1.59579i	−0.329345	+	0.0882476i
$328$	11.7206	+	6.76690i	0.647163	+	0.373640i
$329$	12.2000	−	9.47364i	0.672610	−	0.522299i
$330$	−5.93723	+	5.93723i	−0.326834	+	0.326834i
$331$	−14.3822	−	3.85370i	−0.790518	−	0.211819i	−0.159101	−	0.987262i	$-0.550860\pi$
$331$	−14.3822	−	3.85370i	−0.790518	−	0.211819i	−0.631417	+	0.775444i	$0.717526\pi$
$332$	5.69120	+	1.52495i	0.312345	+	0.0836926i
$333$	−3.74009	−	3.74009i	−0.204956	−	0.204956i
$334$	7.15973	−	4.13367i	0.391763	−	0.226184i
$335$	−1.40735	+	2.43760i	−0.0768917	+	0.133180i
$336$	−0.858148	+	0.361266i	−0.0468158	+	0.0197087i
$337$		−	7.23643i		−	0.394194i	−0.980384	−	0.197097i	$-0.936849\pi$
$337$		−	7.23643i		−	0.394194i	0.980384	−	0.197097i	$-0.0631513\pi$
$338$	−8.24683	−	7.20601i	−0.448568	−	0.391955i
$339$			5.80093i			0.315063i
$340$	−1.42725	−	5.32656i	−0.0774033	−	0.288873i
$341$	−28.4960	−	16.4522i	−1.54315	−	0.890936i
$342$	−2.50169	−	4.33306i	−0.135276	−	0.234305i
$343$	−17.2305	−	6.79047i	−0.930359	−	0.366651i
$344$	−8.99474	−	2.41013i	−0.484964	−	0.129946i
$345$	−0.627427	+	2.34159i	−0.0337795	+	0.126067i
$346$	−3.12001	+	3.12001i	−0.167733	+	0.167733i
$347$	6.28405	+	10.8843i	0.337345	+	0.584299i	0.983933	−	0.178541i	$-0.0571376\pi$
$347$	6.28405	+	10.8843i	0.337345	+	0.584299i	−0.646587	+	0.762840i	$0.723804\pi$
$348$	−5.13948	+	8.90185i	−0.275505	+	0.477189i
$349$	4.81774	+	17.9800i	0.257888	+	0.962450i	0.966461	+	0.256813i	$0.0826723\pi$
$349$	4.81774	+	17.9800i	0.257888	+	0.962450i	−0.708574	+	0.705637i	$0.750661\pi$
$350$	−6.50813	+	0.895005i	−0.347874	+	0.0478400i
$351$	19.5072	−	5.93665i	1.04122	−	0.316875i
$352$	−27.9131			−1.48777
$353$	6.04570	−	1.61994i	0.321780	−	0.0862207i	−0.0943134	−	0.995543i	$-0.530066\pi$
$353$	6.04570	−	1.61994i	0.321780	−	0.0862207i	0.416093	+	0.909322i	$0.363399\pi$
$354$	6.72348	−	11.6454i	0.357349	−	0.618947i
$355$	2.36643	+	4.09878i	0.125597	+	0.217541i
$356$	−0.224325	−	0.224325i	−0.0118892	−	0.0118892i
$357$	1.41179	−	11.2232i	0.0747201	−	0.593993i
$358$	4.92181	−	18.3684i	0.260126	−	0.970802i
$359$	−1.66592	−	1.66592i	−0.0879237	−	0.0879237i	0.661777	−	0.749701i	$-0.269803\pi$
$359$	−1.66592	−	1.66592i	−0.0879237	−	0.0879237i	−0.749701	+	0.661777i	$0.769803\pi$
$360$	−3.25285	+	1.87804i	−0.171440	+	0.0989812i
$361$	−17.6935	−	10.2153i	−0.931236	−	0.537649i
$362$	−4.90153	−	18.2928i	−0.257619	−	0.961446i
$363$	18.0031			0.944918
$364$	−7.87188	−	9.46258i	−0.412599	−	0.495974i
$365$	0.715239			0.0374373
$366$	−2.86912	−	10.7077i	−0.149971	−	0.559700i
$367$	16.7399	+	9.66481i	0.873818	+	0.504499i	0.868615	−	0.495487i	$-0.165011\pi$
$367$	16.7399	+	9.66481i	0.873818	+	0.504499i	0.00520293	+	0.999986i	$0.498344\pi$
$368$	−0.251047	+	0.144942i	−0.0130867	+	0.00755563i
$369$	−3.26549	−	3.26549i	−0.169995	−	0.169995i
$370$	1.74687	−	6.51943i	0.0908157	−	0.338929i
$371$	−15.2074	−	1.91298i	−0.789529	−	0.0993171i
$372$	8.86450	+	8.86450i	0.459603	+	0.459603i
$373$	4.17375	+	7.22914i	0.216108	+	0.374311i	0.953615	−	0.301029i	$-0.0973302\pi$
$373$	4.17375	+	7.22914i	0.216108	+	0.374311i	−0.737507	+	0.675340i	$0.763997\pi$
$374$	6.09900	−	10.5638i	0.315372	−	0.546240i
$375$	−15.7630	+	4.22367i	−0.813996	+	0.218110i
$376$	−16.1826			−0.834554
$377$	−19.5210	−	4.53311i	−1.00538	−	0.233467i
$378$	−12.4873	+	1.71727i	−0.642280	+	0.0883270i
$379$	−4.99923	−	18.6574i	−0.256793	−	0.958365i	−0.967084	−	0.254457i	$-0.918103\pi$
$379$	−4.99923	−	18.6574i	−0.256793	−	0.958365i	0.710291	−	0.703908i	$-0.248563\pi$
$380$	−5.80407	+	10.0529i	−0.297742	+	0.515705i
$381$	8.84337	+	15.3172i	0.453060	+	0.784723i
$382$	14.6960	−	14.6960i	0.751915	−	0.751915i
$383$	−6.09034	+	22.7295i	−0.311202	+	1.16142i	0.616272	+	0.787533i	$0.288642\pi$
$383$	−6.09034	+	22.7295i	−0.311202	+	1.16142i	−0.927474	+	0.373888i	$0.878024\pi$
$384$	10.8450	+	2.90592i	0.553433	+	0.148292i
$385$	−14.6613	−	11.1163i	−0.747210	−	0.566542i
$386$	1.44861	+	2.50906i	0.0737323	+	0.127708i
$387$	2.75181	+	1.58876i	0.139882	+	0.0807612i
$388$	−3.14029	−	11.7197i	−0.159424	−	0.594979i
$389$			27.9585i			1.41755i	0.705434	+	0.708775i	$0.250752\pi$
$389$			27.9585i			1.41755i	−0.705434	+	0.708775i	$0.749248\pi$
$390$	4.55597	+	4.25942i	0.230700	+	0.215684i
$391$		−	3.52174i		−	0.178102i
$392$	9.89455	+	16.6905i	0.499750	+	0.842998i
$393$	−4.81109	+	8.33305i	−0.242687	+	0.420347i
$394$	2.91292	−	1.68177i	0.146751	−	0.0847266i
$395$	7.04504	+	7.04504i	0.354475	+	0.354475i
$396$	5.72205	+	1.53322i	0.287544	+	0.0770471i
$397$	11.5874	+	3.10484i	0.581556	+	0.155827i	0.537591	−	0.843206i	$-0.319334\pi$
$397$	11.5874	+	3.10484i	0.581556	+	0.155827i	0.0439649	+	0.999033i	$0.486001\pi$
$398$	0.609447	−	0.609447i	0.0305488	−	0.0305488i
$399$	−18.8070	+	14.6041i	−0.941525	+	0.731119i
$400$	−0.626756	−	0.361858i	−0.0313378	−	0.0180929i
$401$	19.1246	−	5.12441i	0.955035	−	0.255901i	0.252537	−	0.967587i	$-0.418735\pi$
$401$	19.1246	−	5.12441i	0.955035	−	0.255901i	0.702497	+	0.711686i	$0.252068\pi$
$402$	2.37210			0.118310
$403$	−11.5022	+	21.5658i	−0.572965	+	1.07427i
$404$		−	18.4346i		−	0.917154i
$405$	−7.29007	+	1.95337i	−0.362246	+	0.0970636i
$406$	11.4726	+	4.67481i	0.569375	+	0.232007i
$407$	−23.5078	+	13.5722i	−1.16524	+	0.672751i
$408$	−8.37974	+	8.37974i	−0.414859	+	0.414859i
$409$	4.60743	−	17.1952i	0.227823	−	0.850247i	−0.753431	−	0.657527i	$-0.771602\pi$
$409$	4.60743	−	17.1952i	0.227823	−	0.850247i	0.981254	−	0.192720i	$-0.0617308\pi$
$410$	1.52521	−	5.69214i	0.0753245	−	0.281115i
$411$	22.1883	−	22.1883i	1.09447	−	1.09447i
$412$	−8.32642	+	4.80726i	−0.410213	+	0.236837i
$413$	27.2877	+	11.1191i	1.34274	+	0.547134i
$414$	−0.908636	+	0.243468i	−0.0446570	+	0.0119658i
$415$		−	6.54205i		−	0.321137i
$416$	0.697079	+	20.7222i	0.0341771	+	1.01599i
$417$	5.78710			0.283396
$418$	−24.8023	+	6.64576i	−1.21312	+	0.325055i
$419$	−8.03474	−	4.63886i	−0.392523	−	0.226623i	0.290730	−	0.956805i	$-0.406102\pi$
$419$	−8.03474	−	4.63886i	−0.392523	−	0.226623i	−0.683253	+	0.730182i	$0.739435\pi$
$420$	4.29935	+	5.53664i	0.209787	+	0.270161i
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	−0.951617	−	0.307288i	$-0.900579\pi$
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	0.307288	+	0.951617i	$0.400579\pi$
$422$	4.39510	+	1.17766i	0.213950	+	0.0573277i
$423$	5.33379	+	1.42918i	0.259338	+	0.0694893i
$424$	11.3546	+	11.3546i	0.551426	+	0.551426i
$425$	7.61431	−	4.39612i	0.369348	−	0.213243i
$426$	1.99432	−	3.45427i	0.0966253	−	0.167360i
$427$	22.3883	−	9.42507i	1.08344	−	0.456111i
$428$		−	6.04208i		−	0.292055i
$429$	−0.843312	−	25.0693i	−0.0407155	−	1.21036i
$430$			4.05468i			0.195534i
$431$	1.53438	+	5.72637i	0.0739083	+	0.275830i	0.992984	−	0.118252i	$-0.0377292\pi$
$431$	1.53438	+	5.72637i	0.0739083	+	0.275830i	−0.919075	+	0.394082i	$0.871063\pi$
$432$	−1.20258	−	0.694307i	−0.0578589	−	0.0334049i
$433$	−6.32385	−	10.9532i	−0.303905	−	0.526379i	0.673112	−	0.739541i	$-0.264957\pi$
$433$	−6.32385	−	10.9532i	−0.303905	−	0.526379i	−0.977017	+	0.213162i	$0.931624\pi$
$434$	9.12857	−	12.0396i	0.438185	−	0.577921i
$435$	11.0242	+	2.95393i	0.528570	+	0.141630i
$436$	−1.43666	+	5.36170i	−0.0688036	+	0.256779i
$437$	−5.24205	+	5.24205i	−0.250761	+	0.250761i
$438$	−0.301386	−	0.522015i	−0.0144008	−	0.0249429i
$439$	12.8788	−	22.3067i	0.614670	−	1.06464i	−0.375772	−	0.926712i	$-0.622622\pi$
$439$	12.8788	−	22.3067i	0.614670	−	1.06464i	0.990442	−	0.137928i	$-0.0440442\pi$
$440$	4.98901	+	18.6192i	0.237842	+	0.887638i
$441$	−1.78720	−	6.37504i	−0.0851050	−	0.303574i
$442$	−7.99468	−	4.26398i	−0.380268	−	0.202817i
$443$	17.2441			0.819293			0.409647	−	0.912244i	$-0.365652\pi$
$443$	17.2441			0.819293			0.409647	+	0.912244i	$0.365652\pi$
$444$	9.98942	−	2.67666i	0.474077	−	0.127029i
$445$	−0.176123	+	0.305054i	−0.00834904	+	0.0144610i
$446$	7.24482	+	12.5484i	0.343052	+	0.594184i
$447$	−2.87487	−	2.87487i	−0.135977	−	0.135977i
$448$	1.43754	−	11.4278i	0.0679173	−	0.539914i
$449$	−1.50842	+	5.62952i	−0.0711870	+	0.265673i	−0.992342	−	0.123523i	$-0.960581\pi$
$449$	−1.50842	+	5.62952i	−0.0711870	+	0.265673i	0.921155	+	0.389197i	$0.127247\pi$
$450$	−1.66064	−	1.66064i	−0.0782831	−	0.0782831i
$451$	−20.5248	+	11.8500i	−0.966474	+	0.557994i
$452$	4.52278	+	2.61123i	0.212734	+	0.122822i
$453$	6.21060	+	23.1783i	0.291800	+	1.08901i
$454$	8.39274			0.393891
$455$	−7.88644	+	11.1619i	−0.369722	+	0.523279i
$456$	24.9463			1.16822
$457$	5.74697	+	21.4480i	0.268832	+	1.00329i	0.959863	+	0.280469i	$0.0904901\pi$
$457$	5.74697	+	21.4480i	0.268832	+	1.00329i	−0.691031	+	0.722825i	$0.742843\pi$
$458$	3.04250	+	1.75659i	0.142167	+	0.0820801i
$459$	14.6098	−	8.43498i	0.681928	−	0.393711i
$460$	1.54323	+	1.54323i	0.0719533	+	0.0719533i
$461$	−5.52093	+	20.6044i	−0.257135	+	0.959642i	0.709755	+	0.704449i	$0.248806\pi$
$461$	−5.52093	+	20.6044i	−0.257135	+	0.959642i	−0.966890	+	0.255193i	$0.917861\pi$
$462$	−1.93529	+	15.3847i	−0.0900376	+	0.715761i
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	0.577330	−	0.816511i	$-0.304095\pi$
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	−0.816511	+	0.577330i	$0.804095\pi$
$464$	0.682387	+	1.18193i	0.0316790	+	0.0548697i
$465$	6.95974	−	12.0546i	0.322750	−	0.559020i
$466$	−5.14772	+	1.37933i	−0.238464	+	0.0638962i
$467$	28.5108			1.31932			0.659661	−	0.751563i	$-0.270700\pi$
$467$	28.5108			1.31932			0.659661	+	0.751563i	$0.270700\pi$
$468$	0.995337	−	4.28624i	0.0460095	−	0.198131i
$469$	0.708161	+	5.14948i	0.0326998	+	0.237781i
$470$	1.82371	+	6.80619i	0.0841216	+	0.313946i
$471$	−2.05574	+	3.56065i	−0.0947235	+	0.164066i
$472$	−15.4352	−	26.7346i	−0.710465	−	1.23056i
$473$	11.5308	−	11.5308i	0.530184	−	0.530184i
$474$	2.17318	−	8.11042i	0.0998175	−	0.372524i
$475$	−17.8774	−	4.79022i	−0.820270	−	0.219791i
$476$	−8.11481	−	6.15272i	−0.371942	−	0.282010i
$477$	−2.73967	−	4.74526i	−0.125441	−	0.217270i
$478$	8.09080	+	4.67123i	0.370065	+	0.213657i
$479$	−8.52110	−	31.8012i	−0.389339	−	1.45303i	−0.831212	−	0.555955i	$-0.812352\pi$
$479$	−8.52110	−	31.8012i	−0.389339	−	1.45303i	0.441873	−	0.897078i	$-0.354314\pi$
$480$		−	11.8080i		−	0.538961i
$481$	10.6629	+	17.1128i	0.486184	+	0.780278i
$482$			11.7792i			0.536527i
$483$	1.73700	+	4.12607i	0.0790364	+	0.187743i
$484$	8.10392	−	14.0364i	0.368360	−	0.638018i
$485$	−11.6670	+	6.73593i	−0.529770	+	0.305863i
$486$	−5.60885	−	5.60885i	−0.254423	−	0.254423i
$487$	13.6913	+	3.66858i	0.620414	+	0.166239i	0.555316	−	0.831640i	$-0.312597\pi$
$487$	13.6913	+	3.66858i	0.620414	+	0.166239i	0.0650979	+	0.997879i	$0.479264\pi$
$488$	−24.5819	−	6.58670i	−1.11277	−	0.298166i
$489$	−24.4235	+	24.4235i	−1.10447	+	1.10447i
$490$	5.90474	−	6.04248i	0.266749	−	0.272971i
$491$	−25.7788	−	14.8834i	−1.16338	−	0.671678i	−0.211269	−	0.977428i	$-0.567759\pi$
$491$	−25.7788	−	14.8834i	−1.16338	−	0.671678i	−0.952112	+	0.305750i	$0.901093\pi$
$492$	8.72182	−	2.33700i	0.393210	−	0.105360i
$493$	−16.5803			−0.746741
$494$	5.55309	+	18.2468i	0.249845	+	0.820964i
$495$		−	6.57751i		−	0.295637i
$496$	1.60777	−	0.430801i	0.0721911	−	0.0193435i
$497$	8.09408	+	3.29815i	0.363069	+	0.147942i
$498$	−4.77470	+	2.75667i	−0.213959	+	0.123529i
$499$	13.0693	−	13.0693i	0.585064	−	0.585064i	−0.351226	−	0.936291i	$-0.614235\pi$
$499$	13.0693	−	13.0693i	0.585064	−	0.585064i	0.936291	+	0.351226i	$0.114235\pi$
$500$	−3.80249	+	14.1911i	−0.170052	+	0.634644i
$501$	3.64039	−	13.5861i	0.162640	−	0.606982i
$502$	−15.7004	+	15.7004i	−0.700743	+	0.700743i
$503$	5.05931	−	2.92099i	0.225583	−	0.130241i	−0.382949	−	0.923769i	$-0.625092\pi$
$503$	5.05931	−	2.92099i	0.225583	−	0.130241i	0.608533	+	0.793529i	$0.291758\pi$
$504$	−2.61746	+	6.42358i	−0.116591	+	0.286129i
$505$	−19.7711	+	5.29765i	−0.879802	+	0.235742i
$506$			4.82759i			0.214613i
$507$	−18.5900	+	1.25212i	−0.825609	+	0.0556086i
$508$	15.9230			0.706470
$509$	28.3274	−	7.59031i	1.25559	−	0.336435i	0.431097	−	0.902306i	$-0.358127\pi$
$509$	28.3274	−	7.59031i	1.25559	−	0.336435i	0.824494	+	0.565871i	$0.191460\pi$
$510$	4.46878	+	2.58005i	0.197881	+	0.114246i
$511$	1.04324	−	0.810104i	0.0461503	−	0.0358369i
$512$	1.96096	−	1.96096i	0.0866629	−	0.0866629i
$513$	−34.3018	−	9.19115i	−1.51446	−	0.405799i
$514$	−8.77234	−	2.35054i	−0.386931	−	0.103678i
$515$	7.54860	+	7.54860i	0.332631	+	0.332631i
$516$	−5.38045	+	3.10640i	−0.236861	+	0.136752i
$517$	14.1692	−	24.5418i	0.623162	−	1.07935i
$518$	−4.83614	−	11.4877i	−0.212488	−	0.504743i
$519$			7.50681i			0.329513i
$520$	13.6980	−	4.16874i	0.600698	−	0.182811i
$521$		−	41.0128i		−	1.79680i	−0.439173	−	0.898402i	$-0.644729\pi$
$521$		−	41.0128i		−	1.79680i	0.439173	−	0.898402i	$-0.355271\pi$
$522$	1.14625	+	4.27786i	0.0501699	+	0.187237i
$523$	38.4309	+	22.1881i	1.68047	+	0.970217i	0.961351	+	0.275325i	$0.0887854\pi$
$523$	38.4309	+	22.1881i	1.68047	+	0.970217i	0.719114	+	0.694892i	$0.244548\pi$
$524$	4.33133	+	7.50208i	0.189215	+	0.327730i
$525$	−6.75266	+	8.90606i	−0.294710	+	0.388692i
$526$	12.6056	+	3.37766i	0.549630	+	0.147273i
$527$	−5.23370	+	19.5325i	−0.227984	+	0.850847i
$528$	−1.20789	+	1.20789i	−0.0525666	+	0.0525666i
$529$	−10.8031	−	18.7115i	−0.469700	−	0.813544i
$530$	3.49597	−	6.05520i	0.151855	−	0.263021i
$531$	2.72636	+	10.1749i	0.118314	+	0.441554i
$532$	2.92054	+	21.2370i	0.126621	+	0.920741i
$533$	9.30979	+	14.9413i	0.403252	+	0.647180i
$534$	0.296857			0.0128463
$535$	−6.48014	+	1.73635i	−0.280161	+	0.0750688i
$536$	2.72284	−	4.71610i	0.117609	−	0.203705i
$537$	−16.1765	−	28.0185i	−0.698066	−	1.20909i
$538$	15.5674	+	15.5674i	0.671160	+	0.671160i
$539$	−33.9756	+	0.391695i	−1.46343	+	0.0168715i
$540$	−2.70581	+	10.0982i	−0.116440	+	0.434559i
$541$	−4.85001	−	4.85001i	−0.208518	−	0.208518i	0.595119	−	0.803637i	$-0.297105\pi$
$541$	−4.85001	−	4.85001i	−0.208518	−	0.208518i	−0.803637	+	0.595119i	$0.797105\pi$
$542$	4.80223	−	2.77257i	0.206273	−	0.119092i
$543$	−27.9030	−	16.1098i	−1.19743	−	0.691338i
$544$	4.43980	+	16.5696i	0.190355	+	0.710414i
$545$	6.16329			0.264006
$546$	11.4697	+	1.05252i	0.490856	+	0.0450436i
$547$	−16.7670			−0.716904			−0.358452	−	0.933548i	$-0.616695\pi$
$547$	−16.7670			−0.716904			−0.358452	+	0.933548i	$0.616695\pi$
$548$	−7.31159	−	27.2872i	−0.312336	−	1.16565i
$549$	7.52048	+	4.34195i	0.320966	+	0.185310i
$550$	−10.4377	+	6.02620i	−0.445065	+	0.256958i
$551$	24.6796	+	24.6796i	1.05139	+	1.05139i
$552$	1.21390	−	4.53035i	0.0516672	−	0.192824i
$553$	18.2553	+	2.29639i	0.776294	+	0.0976523i
$554$	−17.3804	−	17.3804i	−0.738422	−	0.738422i
$555$	−5.74144	−	9.94446i	−0.243710	−	0.422119i
$556$	2.60501	−	4.51200i	0.110477	−	0.191352i
$557$	−38.0545	+	10.1967i	−1.61242	+	0.432046i	−0.948762	−	0.315991i	$-0.897663\pi$
$557$	−38.0545	+	10.1967i	−1.61242	+	0.432046i	−0.663657	+	0.748037i	$0.730996\pi$
$558$	5.40135			0.228657
$559$	−8.84819	−	8.27227i	−0.374238	−	0.349880i
$560$	0.922052	−	0.126802i	0.0389638	−	0.00535834i
$561$	−5.37118	−	20.0455i	−0.226772	−	0.846323i
$562$	−5.27402	+	9.13488i	−0.222471	+	0.385332i
$563$	−1.05586	−	1.82880i	−0.0444991	−	0.0770748i	0.842918	−	0.538042i	$-0.180836\pi$
$563$	−1.05586	−	1.82880i	−0.0444991	−	0.0770748i	−0.887417	+	0.460967i	$0.847503\pi$
$564$	−7.63443	+	7.63443i	−0.321467	+	0.321467i
$565$	1.50081	−	5.60110i	0.0631395	−	0.235640i
$566$	−25.9912	−	6.96433i	−1.09249	−	0.292733i
$567$	−8.42078	+	11.1061i	−0.353640	+	0.466414i
$568$	−4.57841	−	7.93005i	−0.192106	−	0.332737i
$569$	31.5451	+	18.2126i	1.32244	+	0.763512i	0.984117	−	0.177518i	$-0.0568069\pi$
$569$	31.5451	+	18.2126i	1.32244	+	0.763512i	0.338323	+	0.941030i	$0.390140\pi$
$570$	−2.81134	−	10.4921i	−0.117754	−	0.439465i
$571$		−	15.2042i		−	0.636275i	−0.948045	−	0.318138i	$-0.896943\pi$
$571$		−	15.2042i		−	0.636275i	0.948045	−	0.318138i	$-0.103057\pi$
$572$	−19.9253	−	10.6272i	−0.833118	−	0.444346i
$573$		−	35.3590i		−	1.47715i
$574$	−4.22246	−	10.0300i	−0.176242	−	0.418645i
$575$	−1.73985	+	3.01351i	−0.0725568	+	0.125672i
$576$	3.56589	−	2.05877i	0.148579	−	0.0857820i
$577$	8.00711	+	8.00711i	0.333341	+	0.333341i	0.853854	−	0.520513i	$-0.174259\pi$
$577$	8.00711	+	8.00711i	0.333341	+	0.333341i	−0.520513	+	0.853854i	$0.674259\pi$
$578$	6.59241	+	1.76643i	0.274208	+	0.0734739i
$579$	4.76113	+	1.27574i	0.197866	+	0.0530180i
$580$	7.26551	−	7.26551i	0.301684	−	0.301684i
$581$	−7.40975	−	9.54218i	−0.307408	−	0.395876i
$582$	9.83240	+	5.67674i	0.407566	+	0.235308i
$583$	−27.1617	+	7.27796i	−1.12492	+	0.301422i
$584$	−1.38380			−0.0572619
$585$	−4.88303	+	0.164261i	−0.201889	+	0.00679137i
$586$		−	10.8863i		−	0.449709i
$587$	−3.32195	+	0.890113i	−0.137111	+	0.0367389i	−0.326722	−	0.945120i	$-0.605944\pi$
$587$	−3.32195	+	0.890113i	−0.137111	+	0.0367389i	0.189611	+	0.981859i	$0.439277\pi$
$588$	12.5420	+	3.20612i	0.517223	+	0.132218i
$589$	36.8641	−	21.2835i	1.51896	−	0.876971i
$590$	−9.50475	+	9.50475i	−0.391304	+	0.391304i
$591$	1.48108	−	5.52747i	0.0609236	−	0.227370i
$592$	0.355389	−	1.32633i	0.0146064	−	0.0545119i
$593$	−32.9017	+	32.9017i	−1.35111	+	1.35111i	−0.466687	+	0.884422i	$0.654553\pi$
$593$	−32.9017	+	32.9017i	−1.35111	+	1.35111i	−0.884422	+	0.466687i	$0.845447\pi$
$594$	−20.0271	+	11.5627i	−0.821722	+	0.474422i
$595$	−4.26680	+	10.4713i	−0.174922	+	0.429281i
$596$	−3.53554	+	0.947344i	−0.144821	+	0.0388047i
$597$		−	1.46635i		−	0.0600135i
$598$	3.58392	−	0.120560i	0.146557	−	0.00493008i
$599$	7.61769			0.311251			0.155625	−	0.987816i	$-0.450261\pi$
$599$	7.61769			0.311251			0.155625	+	0.987816i	$0.450261\pi$
$600$	11.3103	−	3.03059i	0.461742	−	0.123723i
$601$	−32.3774	−	18.6931i	−1.32070	−	0.762508i	−0.336863	−	0.941554i	$-0.609366\pi$
$601$	−32.3774	−	18.6931i	−1.32070	−	0.762508i	−0.983841	+	0.179045i	$0.942699\pi$
$602$	4.59247	+	5.91412i	0.187175	+	0.241042i
$603$	−1.31396	+	1.31396i	−0.0535085	+	0.0535085i
$604$	20.8669	+	5.59128i	0.849064	+	0.227506i
$605$	−17.3829	−	4.65774i	−0.706717	−	0.189364i
$606$	12.1976	+	12.1976i	0.495492	+	0.495492i
$607$	−16.4375	+	9.49020i	−0.667178	+	0.385195i	−0.795006	−	0.606601i	$-0.792533\pi$
$607$	−16.4375	+	9.49020i	−0.667178	+	0.385195i	0.127829	+	0.991796i	$0.459199\pi$
$608$	18.0550	−	31.2722i	0.732226	−	1.26825i
$609$	19.4255	−	8.17782i	0.787162	−	0.331382i
$610$			11.0811i			0.448661i
$611$	−18.5733	−	9.90610i	−0.751394	−	0.400758i
$612$		−	3.64055i		−	0.147160i
$613$	−1.13756	−	4.24543i	−0.0459456	−	0.171471i	0.939141	−	0.343533i	$-0.111624\pi$
$613$	−1.13756	−	4.24543i	−0.0459456	−	0.171471i	−0.985086	+	0.172062i	$0.944957\pi$
$614$	5.59750	+	3.23172i	0.225897	+	0.130421i
$615$	−5.01288	−	8.68256i	−0.202139	−	0.350115i
$616$	28.3657	+	21.5071i	1.14289	+	0.866548i
$617$	23.9468	+	6.41652i	0.964061	+	0.258319i	0.706318	−	0.707894i	$-0.250355\pi$
$617$	23.9468	+	6.41652i	0.964061	+	0.258319i	0.257743	+	0.966214i	$0.417021\pi$
$618$	2.32851	−	8.69013i	0.0936666	−	0.349568i
$619$	−17.2383	+	17.2383i	−0.692866	+	0.692866i	−0.962862	−	0.269995i	$-0.912978\pi$
$619$	−17.2383	+	17.2383i	−0.692866	+	0.692866i	0.269995	+	0.962862i	$0.412978\pi$
$620$	−6.26572	−	10.8525i	−0.251637	−	0.435849i
$621$	−3.33831	+	5.78211i	−0.133962	+	0.232028i
$622$	0.105394	+	0.393334i	0.00422590	+	0.0157713i
$623$	0.0886230	+	0.644433i	0.00355061	+	0.0258186i
$624$	0.926879	+	0.866550i	0.0371049	+	0.0346898i
$625$	1.57557			0.0630229
$626$	0.362374	−	0.0970978i	0.0144834	−	0.00388081i
$627$	−21.8426	+	37.8324i	−0.872307	+	1.51088i
$628$	1.85074	+	3.20558i	0.0738527	+	0.127917i
$629$	11.7957	+	11.7957i	0.470327	+	0.470327i
$630$	2.99665	+	0.376957i	0.119389	+	0.0150183i
$631$	0.701056	−	2.61638i	0.0279086	−	0.104156i	−0.950567	−	0.310521i	$-0.899497\pi$
$631$	0.701056	−	2.61638i	0.0279086	−	0.104156i	0.978475	+	0.206364i	$0.0661633\pi$
$632$	−13.6303	−	13.6303i	−0.542183	−	0.542183i
$633$	6.70410	−	3.87061i	0.266464	−	0.153843i
$634$	−18.1165	−	10.4595i	−0.719497	−	0.415402i
$635$	−4.57589	−	17.0775i	−0.181589	−	0.677698i
$636$	10.7134			0.424815
$637$	1.13927	+	25.2131i	0.0451394	+	0.998981i
$638$	22.7283			0.899822
$639$	0.808695	+	3.01809i	0.0319915	+	0.119394i
$640$	−9.71961	−	5.61162i	−0.384202	−	0.221819i
$641$	2.71103	−	1.56522i	0.107079	−	0.0618223i	−0.445504	−	0.895280i	$-0.646975\pi$
$641$	2.71103	−	1.56522i	0.107079	−	0.0618223i	0.552583	+	0.833458i	$0.313642\pi$
$642$	3.99785	+	3.99785i	0.157783	+	0.157783i
$643$	0.747638	−	2.79022i	0.0294840	−	0.110036i	−0.949616	−	0.313417i	$-0.898526\pi$
$643$	0.747638	−	2.79022i	0.0294840	−	0.110036i	0.979100	+	0.203381i	$0.0651930\pi$
$644$	3.99885	+	0.503027i	0.157577	+	0.0198220i
$645$	4.87783	+	4.87783i	0.192064	+	0.192064i
$646$	7.89001	+	13.6659i	0.310428	+	0.537677i
$647$	−8.86801	+	15.3598i	−0.348637	+	0.603857i	−0.986008	−	0.166700i	$-0.946689\pi$
$647$	−8.86801	+	15.3598i	−0.348637	+	0.603857i	0.637370	+	0.770558i	$0.280022\pi$
$648$	14.1043	−	3.77924i	0.554070	−	0.148463i
$649$	54.0594			2.12202
$650$	4.73441	+	7.59827i	0.185699	+	0.298029i
$651$	−3.50206	−	25.4656i	−0.137256	−	0.998076i
$652$	8.04815	+	30.0361i	0.315190	+	1.17631i
$653$	11.0978	−	19.2219i	0.434289	−	0.752211i	−0.562948	−	0.826492i	$-0.690333\pi$
$653$	11.0978	−	19.2219i	0.434289	−	0.752211i	0.997237	+	0.0742811i	$0.0236662\pi$
$654$	−2.59707	−	4.49826i	−0.101553	−	0.175896i
$655$	6.80127	−	6.80127i	0.265748	−	0.265748i
$656$	0.310292	−	1.15803i	0.0121149	−	0.0452133i
$657$	0.456099	+	0.122211i	0.0177941	+	0.00476792i
$658$	10.3690	+	7.86185i	0.404225	+	0.306487i
$659$	14.4500	+	25.0282i	0.562893	+	0.974960i	0.997242	+	0.0742153i	$0.0236452\pi$
$659$	14.4500	+	25.0282i	0.562893	+	0.974960i	−0.434349	+	0.900745i	$0.643021\pi$
$660$	11.1376	+	6.43031i	0.433531	+	0.250299i
$661$	−1.00395	−	3.74678i	−0.0390490	−	0.145733i	0.943649	−	0.330948i	$-0.107368\pi$
$661$	−1.00395	−	3.74678i	−0.0390490	−	0.145733i	−0.982698	+	0.185215i	$0.940702\pi$
$662$		−	12.5434i		−	0.487513i
$663$	−14.7473	+	4.48807i	−0.572738	+	0.174302i
$664$			12.6571i			0.491191i
$665$	21.9374	−	9.23528i	0.850697	−	0.358129i
$666$	2.22792	−	3.85887i	0.0863302	−	0.149528i
$667$	5.68285	−	3.28099i	0.220041	−	0.127041i
$668$	−8.95393	−	8.95393i	−0.346438	−	0.346438i
$669$	23.8115	+	6.38027i	0.920606	+	0.246676i
$670$	−2.29039	−	0.613707i	−0.0884853	−	0.0237096i
$671$	31.5126	−	31.5126i	1.21653	−	1.21653i
$672$	−13.3742	−	17.2231i	−0.515920	−	0.664396i
$673$	14.8015	+	8.54566i	0.570557	+	0.329411i	0.757372	−	0.652984i	$-0.226483\pi$
$673$	14.8015	+	8.54566i	0.570557	+	0.329411i	−0.186815	+	0.982395i	$0.559816\pi$
$674$	5.88845	−	1.57781i	0.226815	−	0.0607748i
$675$	−16.6686			−0.641575
$676$	−7.39185	+	15.0576i	−0.284302	+	0.579138i
$677$			30.5733i			1.17503i	0.809214	+	0.587514i	$0.199893\pi$
$677$			30.5733i			1.17503i	−0.809214	+	0.587514i	$0.800107\pi$
$678$	−4.72035	+	1.26481i	−0.181284	+	0.0485749i
$679$	−9.38801	+	23.0394i	−0.360279	+	0.884170i
$680$	10.2591	−	5.92308i	0.393417	−	0.227140i
$681$	10.0966	−	10.0966i	0.386902	−	0.386902i
$682$	7.17436	−	26.7751i	0.274720	−	1.02527i
$683$	1.64019	−	6.12129i	0.0627603	−	0.234224i	−0.927420	−	0.374022i	$-0.877978\pi$
$683$	1.64019	−	6.12129i	0.0627603	−	0.234224i	0.990180	+	0.139797i	$0.0446451\pi$
$684$	−5.41891	+	5.41891i	−0.207197	+	0.207197i
$685$	−27.1644	+	15.6834i	−1.03790	+	0.599231i
$686$	1.76869	−	15.5014i	0.0675289	−	0.591847i
$687$	5.77337	−	1.54697i	0.220268	−	0.0590206i
$688$			0.824896i			0.0314489i
$689$	6.08135	+	19.9826i	0.231681	+	0.761278i
$690$	−2.04221			−0.0777455
$691$	−4.60739	+	1.23455i	−0.175273	+	0.0469643i	−0.345388	−	0.938460i	$-0.612253\pi$
$691$	−4.60739	+	1.23455i	−0.175273	+	0.0469643i	0.170115	+	0.985424i	$0.445586\pi$
$692$	5.85280	+	3.37912i	0.222490	+	0.128455i
$693$	−7.44992	−	9.59391i	−0.282999	−	0.364442i
$694$	−7.48665	+	7.48665i	−0.284189	+	0.284189i
$695$	−5.58774	−	1.49723i	−0.211955	−	0.0567932i
$696$	−21.3289	−	5.71506i	−0.808469	−	0.216629i
$697$	10.2989	+	10.2989i	0.390100	+	0.390100i
$698$	−13.5803	+	7.84061i	−0.514023	+	0.296771i
$699$	−4.53343	+	7.85213i	−0.171470	+	0.296995i
$700$	3.90411	+	9.27379i	0.147561	+	0.350516i
$701$		−	29.4647i		−	1.11287i	−0.830892	−	0.556433i	$-0.812169\pi$
$701$		−	29.4647i		−	1.11287i	0.830892	−	0.556433i	$-0.187831\pi$
$702$	9.08406	+	14.5790i	0.342856	+	0.550250i
$703$		−	35.1156i		−	1.32441i
$704$	−5.46913	−	20.4111i	−0.206126	−	0.769271i
$705$	10.3819	+	5.99398i	0.391004	+	0.225746i
$706$	2.63637	+	4.56632i	0.0992209	+	0.171856i
$707$	−22.8377	+	30.1205i	−0.858898	+	1.13280i
$708$	−19.8944	−	5.33069i	−0.747677	−	0.200340i
$709$	−4.33842	+	16.1912i	−0.162933	+	0.608073i	0.835362	+	0.549700i	$0.185258\pi$
$709$	−4.33842	+	16.1912i	−0.162933	+	0.608073i	−0.998295	+	0.0583730i	$0.981409\pi$
$710$	−2.81931	+	2.81931i	−0.105807	+	0.105807i
$711$	3.28876	+	5.69631i	0.123338	+	0.213628i
$712$	0.340751	−	0.590198i	0.0127702	−	0.0221186i
$713$	−2.07134	−	7.73035i	−0.0775723	−	0.289504i
$714$	9.44037	−	1.29825i	0.353297	−	0.0485858i
$715$	−5.67164	+	24.4239i	−0.212107	+	0.913402i
$716$	−29.1267			−1.08852
$717$	15.3529	−	4.11379i	0.573364	−	0.153632i
$718$	0.992364	−	1.71882i	0.0370347	−	0.0641460i
$719$	8.96395	+	15.5260i	0.334299	+	0.579023i	0.983350	−	0.181722i	$-0.0581672\pi$
$719$	8.96395	+	15.5260i	0.334299	+	0.579023i	−0.649051	+	0.760745i	$0.724834\pi$
$720$	0.235274	+	0.235274i	0.00876814	+	0.00876814i
$721$	19.5601	+	2.46052i	0.728457	+	0.0916347i
$722$	4.45463	−	16.6249i	0.165784	−	0.618715i
$723$	14.1705	+	14.1705i	0.527007	+	0.527007i
$724$	−25.1205	+	14.5033i	−0.933597	+	0.539012i
$725$	14.1876	+	8.19122i	0.526914	+	0.304214i
$726$	3.92534	+	14.6496i	0.145683	+	0.543696i
$727$	32.6548			1.21110			0.605549	−	0.795808i	$-0.292954\pi$
$727$	32.6548			1.21110			0.605549	+	0.795808i	$0.292954\pi$
$728$	15.2582	−	21.5953i	0.565505	−	0.800376i
$729$	−29.2988			−1.08514
$730$	0.155948	+	0.582007i	0.00577190	+	0.0215410i
$731$	−8.67885	−	5.01074i	−0.320999	−	0.185329i
$732$	−14.7043	+	8.48955i	−0.543488	+	0.313783i
$733$	−25.0843	−	25.0843i	−0.926510	−	0.926510i	0.0709685	−	0.997479i	$-0.477391\pi$
$733$	−25.0843	−	25.0843i	−0.926510	−	0.926510i	−0.997479	+	0.0709685i	$0.977391\pi$
$734$	−4.21456	+	15.7290i	−0.155562	+	0.580567i
$735$	−0.165698	−	14.3726i	−0.00611186	−	0.530143i
$736$	−4.80059	−	4.80059i	−0.176952	−	0.176952i
$737$	4.76816	+	8.25869i	0.175637	+	0.304213i
$738$	1.94521	−	3.36920i	0.0716041	−	0.124022i
$739$	13.8732	−	3.71731i	0.510333	−	0.136743i	0.00554159	−	0.999985i	$-0.498236\pi$
$739$	13.8732	−	3.71731i	0.510333	−	0.136743i	0.504791	+	0.863241i	$0.331569\pi$
$740$	−10.3378			−0.380025
$741$	28.6316	+	15.2707i	1.05181	+	0.560984i
$742$	−1.75913	−	12.7917i	−0.0645797	−	0.469599i
$743$	6.76509	+	25.2477i	0.248187	+	0.926247i	0.971755	+	0.235993i	$0.0758344\pi$
$743$	6.76509	+	25.2477i	0.248187	+	0.926247i	−0.723568	+	0.690254i	$0.757499\pi$
$744$	−13.4652	+	23.3225i	−0.493659	+	0.855043i
$745$	2.03206	+	3.51962i	0.0744487	+	0.128949i
$746$	−4.97249	+	4.97249i	−0.182056	+	0.182056i
$747$	1.11783	−	4.17178i	0.0408991	−	0.152638i
$748$	−18.0466	−	4.83557i	−0.659849	−	0.176806i
$749$	−7.48523	+	9.87224i	−0.273504	+	0.360724i
$750$	−6.87380	−	11.9058i	−0.250996	−	0.434737i
$751$	10.2898	+	5.94079i	0.375479	+	0.216783i	0.675849	−	0.737040i	$-0.263777\pi$
$751$	10.2898	+	5.94079i	0.375479	+	0.216783i	−0.300371	+	0.953823i	$0.597110\pi$
$752$	0.371022	+	1.38467i	0.0135298	+	0.0504938i
$753$			37.7755i			1.37662i
$754$	−0.567598	−	16.8731i	−0.0206707	−	0.614482i
$755$		−	23.9866i		−	0.872963i
$756$	7.49093	+	17.7939i	0.272442	+	0.647158i
$757$	21.1088	−	36.5615i	0.767212	−	1.32885i	−0.171857	−	0.985122i	$-0.554977\pi$
$757$	21.1088	−	36.5615i	0.767212	−	1.32885i	0.939069	−	0.343729i	$-0.111690\pi$
$758$	14.0919	−	8.13598i	0.511842	−	0.295512i
$759$	5.80765	+	5.80765i	0.210805	+	0.210805i
$760$	−24.0869	−	6.45406i	−0.873723	−	0.234114i
$761$	−27.8046	−	7.45021i	−1.00792	−	0.270070i	−0.283157	−	0.959074i	$-0.591382\pi$
$761$	−27.8046	−	7.45021i	−1.00792	−	0.270070i	−0.724758	+	0.689003i	$0.758048\pi$
$762$	−10.5358	+	10.5358i	−0.381670	+	0.381670i
$763$	8.98972	−	6.98075i	0.325450	−	0.252720i
$764$	−27.5682	−	15.9165i	−0.997383	−	0.575840i
$765$	−3.90449	+	1.04621i	−0.141167	+	0.0378257i
$766$	−19.8234			−0.716249
$767$	−1.35004	−	40.1328i	−0.0487470	−	1.44911i
$768$			21.9372i			0.791591i
$769$	−33.9039	+	9.08451i	−1.22260	+	0.327596i	−0.811696	−	0.584081i	$-0.801455\pi$
$769$	−33.9039	+	9.08451i	−1.22260	+	0.327596i	−0.410909	+	0.911676i	$0.634789\pi$
$770$	5.84893	−	14.3540i	0.210781	−	0.517283i
$771$	−13.3810	+	7.72550i	−0.481903	+	0.278227i
$772$	3.13783	−	3.13783i	0.112933	−	0.112933i
$773$	−7.86544	+	29.3542i	−0.282900	+	1.05580i	0.667460	+	0.744646i	$0.267381\pi$
$773$	−7.86544	+	29.3542i	−0.282900	+	1.05580i	−0.950360	+	0.311152i	$0.899285\pi$
$774$	−0.692815	+	2.58562i	−0.0249027	+	0.0929382i
$775$	14.1281	−	14.1281i	0.507496	−	0.507496i
$776$	22.5725	−	13.0322i	0.810304	−	0.467829i
$777$	−19.6378	−	8.00196i	−0.704504	−	0.287069i
$778$	−22.7505	+	6.09597i	−0.815643	+	0.218551i
$779$		−	30.6596i		−	1.09849i
$780$	4.49561	−	8.42896i	0.160968	−	0.301805i
$781$	16.0352			0.573783
$782$	2.86572	−	0.767867i	0.102478	−	0.0274589i
$783$	27.2222	+	15.7167i	0.972842	+	0.561670i
$784$	1.20128	−	1.22930i	0.0429028	−	0.0439035i
$785$	2.90613	−	2.90613i	0.103724	−	0.103724i
$786$	−7.82979	−	2.09799i	−0.279279	−	0.0748327i
$787$	9.81284	+	2.62934i	0.349790	+	0.0937260i	0.429436	−	0.903097i	$-0.358712\pi$
$787$	9.81284	+	2.62934i	0.349790	+	0.0937260i	−0.0796460	+	0.996823i	$0.525379\pi$
$788$	−3.64289	−	3.64289i	−0.129772	−	0.129772i
$789$	19.2280	−	11.1013i	0.684536	−	0.395217i
$790$	−4.19664	+	7.26879i	−0.149310	+	0.258612i
$791$	−4.15492	−	9.86958i	−0.147732	−	0.350922i
$792$			12.7257i			0.452189i
$793$	−24.1814	−	22.6075i	−0.858706	−	0.802814i
$794$			10.1059i			0.358646i
$795$	−3.07878	−	11.4902i	−0.109193	−	0.407514i
$796$	−1.14326	−	0.660061i	−0.0405217	−	0.0233952i
$797$	−18.3972	−	31.8649i	−0.651662	−	1.12871i	−0.982719	−	0.185101i	$-0.940739\pi$
$797$	−18.3972	−	31.8649i	−0.651662	−	1.12871i	0.331057	−	0.943611i	$-0.392595\pi$
$798$	−15.9843	−	12.1194i	−0.565837	−	0.429023i
$799$	−16.8221	−	4.50746i	−0.595122	−	0.159462i
$800$	4.38681	−	16.3718i	0.155097	−	0.578831i
$801$	−0.164436	+	0.164436i	−0.00581004	+	0.00581004i
$802$	8.33970	+	14.4448i	0.294485	+	0.510063i
$803$	1.21163	−	2.09860i	0.0427575	−	0.0740582i
$804$	−0.940356	−	3.50946i	−0.0331638	−	0.123769i
$805$	−0.609676	−	4.43333i	−0.0214882	−	0.156254i
$806$	−20.0565	−	4.65746i	−0.706460	−	0.164052i
$807$	37.4556			1.31850
$808$	38.2518	−	10.2495i	1.34569	−	0.360577i
$809$	9.38058	−	16.2476i	0.329804	−	0.571237i	−0.652669	−	0.757643i	$-0.726351\pi$
$809$	9.38058	−	16.2476i	0.329804	−	0.571237i	0.982473	+	0.186407i	$0.0596841\pi$
$810$	−3.17900	−	5.50619i	−0.111699	−	0.193468i
$811$	3.85841	+	3.85841i	0.135487	+	0.135487i	0.771598	−	0.636111i	$-0.219458\pi$
$811$	3.85841	+	3.85841i	0.135487	+	0.135487i	−0.636111	+	0.771598i	$0.719458\pi$
$812$	2.36825	−	18.8266i	0.0831093	−	0.660683i
$813$	2.44171	−	9.11258i	0.0856344	−	0.319592i
$814$	−16.1696	−	16.1696i	−0.566744	−	0.566744i
$815$	29.9009	−	17.2633i	1.04738	−	0.604707i
$816$	0.909141	+	0.524893i	0.0318263	+	0.0183749i
$817$	5.45994	+	20.3768i	0.191019	+	0.712893i
$818$	14.9967			0.524347
$819$	−6.93630	+	5.77028i	−0.242374	+	0.201630i
$820$	−9.02599			−0.315201
$821$	−0.535196	−	1.99738i	−0.0186785	−	0.0697089i	0.955958	−	0.293505i	$-0.0948217\pi$
$821$	−0.535196	−	1.99738i	−0.0186785	−	0.0697089i	−0.974636	+	0.223796i	$0.928155\pi$
$822$	22.8929	+	13.2173i	0.798483	+	0.461005i
$823$	−23.4776	+	13.5548i	−0.818379	+	0.472491i	−0.849857	−	0.527013i	$-0.823312\pi$
$823$	−23.4776	+	13.5548i	−0.818379	+	0.472491i	0.0314782	+	0.999504i	$0.489979\pi$
$824$	−14.6045	−	14.6045i	−0.508772	−	0.508772i
$825$	−5.30707	+	19.8063i	−0.184769	+	0.689566i
$826$	−3.09815	+	24.6290i	−0.107798	+	0.856951i
$827$	−18.8233	−	18.8233i	−0.654550	−	0.654550i	0.299535	−	0.954085i	$-0.403168\pi$
$827$	−18.8233	−	18.8233i	−0.654550	−	0.654550i	−0.954085	+	0.299535i	$0.903168\pi$
$828$	0.720409	+	1.24778i	0.0250359	+	0.0433635i
$829$	2.50749	−	4.34310i	0.0870887	−	0.150842i	−0.819191	−	0.573521i	$-0.805577\pi$
$829$	2.50749	−	4.34310i	0.0870887	−	0.150842i	0.906279	+	0.422679i	$0.138910\pi$
$830$	5.32342	−	1.42641i	0.184778	−	0.0495112i
$831$	−41.8177			−1.45064
$832$	−15.0162	+	4.56991i	−0.520594	+	0.158433i
$833$	5.63661	+	20.1060i	0.195297	+	0.696633i
$834$	1.26180	+	4.70910i	0.0436925	+	0.163063i
$835$	−7.02996	+	12.1762i	−0.243282	+	0.421376i
$836$	19.6644	+	34.0598i	0.680108	+	1.17798i
$837$	27.1080	−	27.1080i	0.936989	−	0.936989i
$838$	2.02288	−	7.54949i	0.0698792	−	0.260793i
$839$	1.91166	+	0.512227i	0.0659978	+	0.0176840i	0.291667	−	0.956520i	$-0.405790\pi$
$839$	1.91166	+	0.512227i	0.0659978	+	0.0176840i	−0.225669	+	0.974204i	$0.572457\pi$
$840$	−9.09813	+	11.9995i	−0.313915	+	0.414022i
$841$	−0.946916	−	1.64011i	−0.0326523	−	0.0565554i
$842$	−13.6404	−	7.87529i	−0.470079	−	0.271400i
$843$	4.64466	+	17.3341i	0.159970	+	0.597018i
$844$		−	6.96927i		−	0.239892i
$845$	18.2735	+	3.60058i	0.628628	+	0.123864i
$846$			4.65184i			0.159934i
$847$	−30.6301	+	12.8948i	−1.05246	+	0.443069i
$848$	0.711230	−	1.23189i	0.0244238	−	0.0423032i
$849$	−39.6459	+	22.8896i	−1.36065	+	0.785569i
$850$	5.23743	+	5.23743i	0.179642	+	0.179642i
$851$	−6.37714	−	1.70875i	−0.218606	−	0.0585752i
$852$	−5.90109	−	1.58119i	−0.202168	−	0.0541708i
$853$	−0.494551	+	0.494551i	−0.0169331	+	0.0169331i	−0.715523	−	0.698590i	$-0.753811\pi$
$853$	−0.494551	+	0.494551i	−0.0169331	+	0.0169331i	0.698590	+	0.715523i	$0.253811\pi$
$854$	12.5509	+	16.1628i	0.429481	+	0.553081i
$855$	7.36904	+	4.25452i	0.252016	+	0.145502i
$856$	12.5373	−	3.35937i	0.428517	−	0.114821i
$857$	15.3761			0.525236			0.262618	−	0.964900i	$-0.415414\pi$
$857$	15.3761			0.525236			0.262618	+	0.964900i	$0.415414\pi$
$858$	20.2156	−	6.15225i	0.690149	−	0.210034i
$859$		−	33.1503i		−	1.13108i	−0.824723	−	0.565538i	$-0.808669\pi$
$859$		−	33.1503i		−	1.13108i	0.824723	−	0.565538i	$-0.191331\pi$
$860$	5.99879	−	1.60737i	0.204557	−	0.0548109i
$861$	−17.1459	−	6.98655i	−0.584331	−	0.238101i
$862$	−4.32513	+	2.49712i	−0.147315	+	0.0850521i
$863$	18.6818	−	18.6818i	0.635935	−	0.635935i	−0.313615	−	0.949550i	$-0.601540\pi$
$863$	18.6818	−	18.6818i	0.635935	−	0.635935i	0.949550	+	0.313615i	$0.101540\pi$
$864$	8.41711	−	31.4131i	0.286356	−	1.06869i
$865$	1.94215	−	7.24822i	0.0660352	−	0.246447i
$866$	7.53407	−	7.53407i	0.256018	−	0.256018i
$867$	10.0558	−	5.80571i	0.341513	−	0.197172i
$868$	−21.4311	−	8.73266i	−0.727418	−	0.296406i
$869$	32.6055	−	8.73662i	1.10607	−	0.296370i
$870$			9.61472i			0.325969i
$871$	6.01203	−	3.74604i	0.203710	−	0.126930i
$872$	−11.9243			−0.403808
$873$	−8.59084	+	2.30191i	−0.290756	+	0.0779078i
$874$	−5.40854	−	3.12262i	−0.182947	−	0.105624i
$875$	23.7936	−	18.4763i	0.804369	−	0.624613i
$876$	−0.652830	+	0.652830i	−0.0220571	+	0.0220571i
$877$	−13.9428	−	3.73595i	−0.470813	−	0.126154i	0.0156084	−	0.999878i	$-0.495031\pi$
$877$	−13.9428	−	3.73595i	−0.470813	−	0.126154i	−0.486422	+	0.873724i	$0.661698\pi$
$878$	20.9595	+	5.61608i	0.707349	+	0.189534i
$879$	−13.0964	−	13.0964i	−0.441729	−	0.441729i
$880$	1.47878	−	0.853774i	0.0498497	−	0.0287807i
$881$	−2.13690	+	3.70122i	−0.0719941	+	0.124697i	−0.899775	−	0.436354i	$-0.856270\pi$
$881$	−2.13690	+	3.70122i	−0.0719941	+	0.124697i	0.827781	+	0.561051i	$0.189603\pi$
$882$	4.79784	−	2.84428i	0.161552	−	0.0957719i
$883$			32.6002i			1.09708i	0.836123	+	0.548542i	$0.184817\pi$
$883$			32.6002i			1.09708i	−0.836123	+	0.548542i	$0.815183\pi$
$884$	−3.13916	+	13.5182i	−0.105581	+	0.454667i
$885$			22.8687i			0.768722i
$886$	3.75985	+	14.0319i	0.126315	+	0.471412i
$887$	−15.4078	−	8.89570i	−0.517343	−	0.298688i	0.218504	−	0.975836i	$-0.429882\pi$
$887$	−15.4078	−	8.89570i	−0.517343	−	0.298688i	−0.735847	+	0.677148i	$0.763216\pi$
$888$	11.1081	+	19.2399i	0.372765	+	0.645648i
$889$	−26.0169	−	19.7262i	−0.872578	−	0.661597i
$890$	−0.286631	−	0.0768025i	−0.00960789	−	0.00257443i
$891$	−6.61809	+	24.6990i	−0.221714	+	0.827449i
$892$	15.6930	−	15.6930i	0.525440	−	0.525440i
$893$	18.3301	+	31.7487i	0.613394	+	1.06243i
$894$	1.71252	−	2.96618i	0.0572754	−	0.0992039i
$895$	8.37031	+	31.2384i	0.279789	+	1.04418i
$896$	−20.5329	+	2.82370i	−0.685955	+	0.0943332i
$897$	4.16647	−	4.45654i	0.139114	−	0.148799i
$898$	−4.90976			−0.163841
$899$	−36.3945	+	9.75187i	−1.21382	+	0.325243i
$900$	−1.79855	+	3.11518i	−0.0599516	+	0.103839i
$901$	8.64057	+	14.9659i	0.287859	+	0.498587i
$902$	−14.1178	−	14.1178i	−0.470070	−	0.470070i
$903$	12.6396	+	1.58997i	0.420618	+	0.0529108i
$904$	−2.90366	+	10.8366i	−0.0965744	+	0.360421i
$905$	22.7739	+	22.7739i	0.757029	+	0.757029i
$906$	−17.5066	+	10.1074i	−0.581617	+	0.335797i
$907$	28.0724	+	16.2076i	0.932129	+	0.538165i	0.887484	−	0.460838i	$-0.152451\pi$
$907$	28.0724	+	16.2076i	0.932129	+	0.538165i	0.0446448	+	0.999003i	$0.485784\pi$
$908$	−3.32708	−	12.4168i	−0.110413	−	0.412067i
$909$	−13.5130			−0.448197
$910$	−10.8022	−	3.98368i	−0.358091	−	0.132058i
$911$	−15.2599			−0.505585			−0.252792	−	0.967521i	$-0.581349\pi$
$911$	−15.2599			−0.505585			−0.252792	+	0.967521i	$0.581349\pi$
$912$	−0.571948	−	2.13454i	−0.0189391	−	0.0706816i
$913$	−19.1952	−	11.0824i	−0.635269	−	0.366773i
$914$	−16.1997	+	9.35288i	−0.535838	+	0.309366i
$915$	13.3307	+	13.3307i	0.440700	+	0.440700i
$916$	1.39271	−	5.19765i	0.0460163	−	0.171735i
$917$	2.21693	−	17.6236i	0.0732094	−	0.581984i
$918$	10.0492	+	10.0492i	0.331673	+	0.331673i
$919$	−6.10555	−	10.5751i	−0.201404	−	0.348841i	0.747577	−	0.664175i	$-0.231217\pi$
$919$	−6.10555	−	10.5751i	−0.201404	−	0.348841i	−0.948981	+	0.315334i	$0.897884\pi$
$920$	−2.34417	+	4.06022i	−0.0772851	+	0.133862i
$921$	10.6217	−	2.84606i	0.349995	−	0.0937810i
$922$	−17.9700			−0.591811
$923$	−0.400449	−	11.9042i	−0.0131809	−	0.391832i
$924$	23.5284	−	3.23565i	0.774028	−	0.106445i
$925$	−4.26601	−	15.9210i	−0.140266	−	0.523478i
$926$	3.06574	−	5.31002i	0.100747	−	0.174498i
$927$	3.52384	+	6.10346i	0.115738	+	0.200464i
$928$	−22.6012	+	22.6012i	−0.741920	+	0.741920i
$929$	9.42897	−	35.1894i	0.309354	−	1.15453i	−0.619777	−	0.784778i	$-0.712777\pi$
$929$	9.42897	−	35.1894i	0.309354	−	1.15453i	0.929132	−	0.369749i	$-0.120556\pi$
$930$	11.3266	+	3.03496i	0.371414	+	0.0995201i
$931$	21.5376	−	38.3176i	0.705865	−	1.25581i
$932$	4.08135	+	7.06911i	0.133689	+	0.231556i
$933$	0.599976	+	0.346396i	0.0196423	+	0.0113405i
$934$	6.21639	+	23.1999i	0.203407	+	0.759124i
$935$			20.7446i			0.678421i
$936$	9.44736	−	0.317802i	0.308797	−	0.0103877i
$937$			37.8200i			1.23553i	0.786365	+	0.617763i	$0.211961\pi$
$937$			37.8200i			1.23553i	−0.786365	+	0.617763i	$0.788039\pi$
$938$	−4.03584	+	1.69902i	−0.131775	+	0.0554750i
$939$	0.319131	−	0.552750i	0.0104144	−	0.0180383i
$940$	9.34660	−	5.39626i	0.304853	−	0.176007i
$941$	17.5606	+	17.5606i	0.572458	+	0.572458i	0.932815	−	0.360357i	$-0.117345\pi$
$941$	17.5606	+	17.5606i	0.572458	+	0.572458i	−0.360357	+	0.932815i	$0.617345\pi$
$942$	−3.34561	−	0.896453i	−0.109006	−	0.0292080i
$943$	−5.56792	−	1.49192i	−0.181316	−	0.0485836i
$944$	−1.93368	+	1.93368i	−0.0629358	+	0.0629358i
$945$	16.9313	−	13.1476i	0.550774	−	0.427690i
$946$	11.8970	+	6.86871i	0.386804	+	0.223321i
$947$	−24.3265	+	6.51827i	−0.790505	+	0.211815i	−0.631411	−	0.775448i	$-0.717524\pi$
$947$	−24.3265	+	6.51827i	−0.790505	+	0.211815i	−0.159094	+	0.987263i	$0.550857\pi$
$948$	−12.8606			−0.417694
$949$	−1.58823	−	0.847084i	−0.0515560	−	0.0274975i
$950$		−	15.5917i		−	0.505860i
$951$	−34.3773	+	9.21137i	−1.11476	+	0.298699i
$952$	8.25512	−	20.2591i	0.267550	−	0.656602i
$953$	15.6650	−	9.04419i	0.507439	−	0.292970i	−0.224341	−	0.974511i	$-0.572023\pi$
$953$	15.6650	−	9.04419i	0.507439	−	0.292970i	0.731780	+	0.681541i	$0.238690\pi$
$954$	3.26398	−	3.26398i	0.105675	−	0.105675i
$955$	−9.14805	+	34.1410i	−0.296024	+	1.10478i
$956$	3.70357	−	13.8219i	0.119782	−	0.447032i
$957$	27.3424	−	27.3424i	0.883855	−	0.883855i
$958$	24.0194	−	13.8676i	0.776033	−	0.448043i
$959$	−21.8583	+	53.6430i	−0.705840	+	1.73222i
$960$	8.63446	−	2.31360i	0.278676	−	0.0746710i
$961$			14.9527i			0.482346i
$962$	−11.6002	+	12.4078i	−0.374006	+	0.400045i
$963$	−4.42899			−0.142722
$964$	17.4270	−	4.66954i	0.561285	−	0.150396i
$965$	−4.26706	−	2.46359i	−0.137361	−	0.0793057i
$966$	−2.97875	+	2.31307i	−0.0958396	+	0.0744219i
$967$	−2.32489	+	2.32489i	−0.0747635	+	0.0747635i	−0.743500	−	0.668736i	$-0.766836\pi$
$967$	−2.32489	+	2.32489i	−0.0747635	+	0.0747635i	0.668736	+	0.743500i	$0.266836\pi$
$968$	33.6313	+	9.01148i	1.08095	+	0.289640i
$969$	25.9320	+	6.94846i	0.833056	+	0.223217i
$970$	−8.02501	−	8.02501i	−0.257667	−	0.257667i
$971$	−12.8317	+	7.40841i	−0.411790	+	0.237747i	−0.691559	−	0.722320i	$-0.743076\pi$
$971$	−12.8317	+	7.40841i	−0.411790	+	0.237747i	0.279768	+	0.960068i	$0.409742\pi$
$972$	−6.07466	+	10.5216i	−0.194845	+	0.337481i
$973$	−9.84605	+	4.14502i	−0.315650	+	0.132883i
$974$			11.9408i			0.382609i
$975$	14.8364	+	3.44525i	0.475144	+	0.110336i
$976$			2.25438i			0.0721608i
$977$	−4.87838	−	18.2064i	−0.156073	−	0.582474i	−0.999011	−	0.0444625i	$-0.985842\pi$
$977$	−4.87838	−	18.2064i	−0.156073	−	0.582474i	0.842938	−	0.538011i	$-0.180824\pi$
$978$	−25.1992	−	14.5487i	−0.805780	−	0.465217i
$979$	0.596712	+	1.03354i	0.0190710	+	0.0330320i
$980$	−11.2804	−	6.34052i	−0.360341	−	0.202540i
$981$	3.93025	+	1.05311i	0.125483	+	0.0336231i
$982$	6.49024	−	24.2219i	0.207112	−	0.772952i
$983$	3.43860	−	3.43860i	0.109674	−	0.109674i	−0.650140	−	0.759814i	$-0.725290\pi$
$983$	3.43860	−	3.43860i	0.109674	−	0.109674i	0.759814	+	0.650140i	$0.225290\pi$
$984$	9.69857	+	16.7984i	0.309179	+	0.535514i
$985$	−2.86012	+	4.95388i	−0.0911311	+	0.157844i
$986$	−3.61512	−	13.4918i	−0.115129	−	0.429666i
$987$	21.9319	−	3.01610i	0.698101	−	0.0960035i
$988$	24.7943	−	15.4491i	0.788812	−	0.491501i
$989$	3.96619			0.126118
$990$	5.35228	−	1.43414i	0.170106	−	0.0455799i
$991$	8.04617	−	13.9364i	0.255595	−	0.442703i	−0.709462	−	0.704744i	$-0.751062\pi$
$991$	8.04617	−	13.9364i	0.255595	−	0.442703i	0.965057	+	0.262040i	$0.0843953\pi$
$992$	19.4911	+	33.7595i	0.618842	+	1.07187i
$993$	−15.0898	−	15.0898i	−0.478862	−	0.478862i
$994$	−0.918975	+	7.30546i	−0.0291481	+	0.231715i
$995$	−0.379371	+	1.41583i	−0.0120269	+	0.0448849i
$996$	5.97122	+	5.97122i	0.189205	+	0.189205i
$997$	22.1768	−	12.8038i	0.702346	−	0.405500i	−0.105875	−	0.994379i	$-0.533764\pi$
$997$	22.1768	−	12.8038i	0.702346	−	0.405500i	0.808221	+	0.588880i	$0.200431\pi$
$998$	13.4844	+	7.78523i	0.426842	+	0.246437i
$999$	−8.18532	−	30.5480i	−0.258972	−	0.966497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.bc.a.6.6	yes	32
3.2	odd	2		819.2.fm.g.370.4		32
7.2	even	3		637.2.bb.b.227.5		32
7.3	odd	6		637.2.x.b.19.4		32
7.4	even	3		637.2.x.b.19.3		32
7.5	odd	6		637.2.bb.b.227.6		32
7.6	odd	2	inner	91.2.bc.a.6.5	✓	32
13.11	odd	12	inner	91.2.bc.a.76.5	yes	32
21.20	even	2		819.2.fm.g.370.3		32
39.11	even	12		819.2.fm.g.622.3		32
91.11	odd	12		637.2.bb.b.362.6		32
91.24	even	12		637.2.bb.b.362.5		32
91.37	odd	12		637.2.x.b.570.3		32
91.76	even	12	inner	91.2.bc.a.76.6	yes	32
91.89	even	12		637.2.x.b.570.4		32
273.167	odd	12		819.2.fm.g.622.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.5	✓	32	7.6	odd	2	inner
91.2.bc.a.6.6	yes	32	1.1	even	1	trivial
91.2.bc.a.76.5	yes	32	13.11	odd	12	inner
91.2.bc.a.76.6	yes	32	91.76	even	12	inner
637.2.x.b.19.3		32	7.4	even	3
637.2.x.b.19.4		32	7.3	odd	6
637.2.x.b.570.3		32	91.37	odd	12
637.2.x.b.570.4		32	91.89	even	12
637.2.bb.b.227.5		32	7.2	even	3
637.2.bb.b.227.6		32	7.5	odd	6
637.2.bb.b.362.5		32	91.24	even	12
637.2.bb.b.362.6		32	91.11	odd	12
819.2.fm.g.370.3		32	21.20	even	2
819.2.fm.g.370.4		32	3.2	odd	2
819.2.fm.g.622.3		32	39.11	even	12
819.2.fm.g.622.4		32	273.167	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.218036 + 0.813723i) q^{2} +(1.24122 + 0.716618i) q^{3} +(1.11745 - 0.645157i) q^{4} +(-1.01306 - 1.01306i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(-2.62506 - 0.330214i) q^{7} +(1.96000 + 1.96000i) q^{8} +(-0.472916 - 0.819114i) q^{9} +O(q^{10})\)	\(q+(0.218036 + 0.813723i) q^{2} +(1.24122 + 0.716618i) q^{3} +(1.11745 - 0.645157i) q^{4} +(-1.01306 - 1.01306i) q^{5} +(-0.312498 + 1.16626i) q^{6} +(-2.62506 - 0.330214i) q^{7} +(1.96000 + 1.96000i) q^{8} +(-0.472916 - 0.819114i) q^{9} +(0.603466 - 1.04523i) q^{10} +(-4.68859 + 1.25630i) q^{11} +1.84933 q^{12} +(1.04975 + 3.44935i) q^{13} +(-0.303657 - 2.20807i) q^{14} +(-0.531452 - 1.98341i) q^{15} +(0.122771 - 0.212645i) q^{16} +(1.49151 + 2.58338i) q^{17} +(0.563419 - 0.563419i) q^{18} +(1.62522 - 6.06542i) q^{19} +(-1.78562 - 0.478455i) q^{20} +(-3.02164 - 2.29104i) q^{21} +(-2.04457 - 3.54129i) q^{22} +(-1.02242 - 0.590296i) q^{23} +(1.02822 + 3.83736i) q^{24} -2.94742i q^{25} +(-2.57793 + 1.60629i) q^{26} -5.65531i q^{27} +(-3.14641 + 1.32458i) q^{28} +(-2.77911 + 4.81356i) q^{29} +(1.49807 - 0.864909i) q^{30} +(4.79337 + 4.79337i) q^{31} +(5.55461 + 1.48835i) q^{32} +(-6.71986 - 1.80058i) q^{33} +(-1.77695 + 1.77695i) q^{34} +(2.32482 + 2.99387i) q^{35} +(-1.05692 - 0.610210i) q^{36} +(5.40165 - 1.44737i) q^{37} +5.28993 q^{38} +(-1.16890 + 5.03367i) q^{39} -3.97118i q^{40} +(4.71621 - 1.26371i) q^{41} +(1.20544 - 2.95831i) q^{42} +(-2.90941 + 1.67975i) q^{43} +(-4.42873 + 4.42873i) q^{44} +(-0.350719 + 1.30890i) q^{45} +(0.257412 - 0.960674i) q^{46} +(-4.12822 + 4.12822i) q^{47} +(0.304771 - 0.175960i) q^{48} +(6.78192 + 1.73367i) q^{49} +(2.39839 - 0.642646i) q^{50} +4.27539i q^{51} +(3.39841 + 3.17721i) q^{52} +5.79315 q^{53} +(4.60186 - 1.23306i) q^{54} +(6.02252 + 3.47711i) q^{55} +(-4.49790 - 5.79233i) q^{56} +(6.36385 - 6.36385i) q^{57} +(-4.52285 - 1.21190i) q^{58} +(-10.7576 - 2.88250i) q^{59} +(-1.87348 - 1.87348i) q^{60} +(-7.95118 + 4.59062i) q^{61} +(-2.85534 + 4.94560i) q^{62} +(0.970951 + 2.30639i) q^{63} +4.35335i q^{64} +(2.43094 - 4.55785i) q^{65} -5.86070i q^{66} +(-0.508485 - 1.89769i) q^{67} +(3.33337 + 1.92452i) q^{68} +(-0.846033 - 1.46537i) q^{69} +(-1.92929 + 2.54453i) q^{70} +(-3.19094 - 0.855010i) q^{71} +(0.678548 - 2.53237i) q^{72} +(-0.353010 + 0.353010i) q^{73} +(2.35552 + 4.07987i) q^{74} +(2.11218 - 3.65840i) q^{75} +(-2.09705 - 7.82630i) q^{76} +(12.7227 - 1.74964i) q^{77} +(-4.35088 + 0.146360i) q^{78} -6.95423 q^{79} +(-0.339796 + 0.0910481i) q^{80} +(2.63395 - 4.56214i) q^{81} +(2.05661 + 3.56216i) q^{82} +(3.22886 + 3.22886i) q^{83} +(-4.85460 - 0.610674i) q^{84} +(1.10612 - 4.12811i) q^{85} +(-2.00121 - 2.00121i) q^{86} +(-6.89897 + 3.98312i) q^{87} +(-11.6520 - 6.72727i) q^{88} +(-0.0636346 - 0.237487i) q^{89} -1.14155 q^{90} +(-1.61663 - 9.40141i) q^{91} -1.52333 q^{92} +(2.51461 + 9.38464i) q^{93} +(-4.25933 - 2.45913i) q^{94} +(-7.79107 + 4.49818i) q^{95} +(5.82791 + 5.82791i) q^{96} +(2.43374 - 9.08284i) q^{97} +(0.0679801 + 5.89661i) q^{98} +(3.24636 + 3.24636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9	\( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99}+O(q^{100}) \) 32 * q - 8 * q^2 - 12 * q^4 - 16 * q^8 + 8 * q^9 - 4 * q^11 - 32 * q^14 - 8 * q^15 + 12 * q^16 - 4 * q^18 + 16 * q^21 + 4 * q^22 - 12 * q^23 + 24 * q^28 + 4 * q^29 + 12 * q^30 + 4 * q^32 - 20 * q^35 + 4 * q^37 - 36 * q^39 - 28 * q^42 - 48 * q^43 + 24 * q^44 + 84 * q^46 + 24 * q^49 - 44 * q^50 + 72 * q^53 + 60 * q^56 - 92 * q^57 - 16 * q^58 + 76 * q^60 + 48 * q^63 + 4 * q^65 - 56 * q^67 + 56 * q^70 + 84 * q^71 - 128 * q^72 - 24 * q^74 + 148 * q^78 - 80 * q^79 + 28 * q^81 - 64 * q^84 + 36 * q^85 - 48 * q^86 - 228 * q^88 - 48 * q^91 + 24 * q^92 + 108 * q^93 - 84 * q^95 - 32 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more