LMFDB - Embedded newform 197.2.e.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,2,Mod(6,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("197.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	197.19
Dual form			197.2.e.b.83.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.63334 + 1.30255i) q^{2} +(-0.0124583 - 0.00993517i) q^{3} +(0.526135 - 2.30515i) q^{4} +(1.56168 - 0.356443i) q^{5} +0.0332897 q^{6} +(0.877717 - 1.10062i) q^{7} +(0.330331 + 0.685939i) q^{8} +(-0.667506 - 2.92454i) q^{9} +(-2.08647 + 2.61635i) q^{10} +(3.63490 - 2.89874i) q^{11} +(-0.0294568 + 0.0234910i) q^{12} +(-1.59469 + 3.31140i) q^{13} +2.94096i q^{14} +(-0.0229972 - 0.0110749i) q^{15} +(2.82754 + 1.36167i) q^{16} +(6.84584 - 1.56252i) q^{17} +(4.89961 + 3.90731i) q^{18} -5.94283 q^{19} -3.78744i q^{20} +(-0.0218697 + 0.00499163i) q^{21} +(-2.16130 + 9.46926i) q^{22} +(3.95465 + 4.95897i) q^{23} +(0.00269956 - 0.0118275i) q^{24} +(-2.19306 + 1.05612i) q^{25} +(-1.70859 - 7.48580i) q^{26} +(-0.0414813 + 0.0861368i) q^{27} +(-2.07530 - 2.60234i) q^{28} +(1.83588 + 2.30212i) q^{29} +(0.0519878 - 0.0118659i) q^{30} +(1.96070 - 1.56360i) q^{31} +(-7.87648 + 1.79775i) q^{32} -0.0740842 q^{33} +(-9.14634 + 11.4691i) q^{34} +(0.978403 - 2.03167i) q^{35} -7.09268 q^{36} +(5.49171 - 2.64467i) q^{37} +(9.70667 - 7.74081i) q^{38} +(0.0527665 - 0.0254110i) q^{39} +(0.760369 + 0.953473i) q^{40} +(-1.79941 - 7.88371i) q^{41} +(0.0292189 - 0.0366394i) q^{42} +(-7.64816 - 9.59049i) q^{43} +(-4.76957 - 9.90411i) q^{44} +(-2.08486 - 4.32926i) q^{45} +(-12.9186 - 2.94858i) q^{46} +(1.36779 - 0.658695i) q^{47} +(-0.0216980 - 0.0450563i) q^{48} +(1.11666 + 4.89243i) q^{49} +(2.20636 - 4.58156i) q^{50} +(-0.100812 - 0.0485483i) q^{51} +(6.79425 + 5.41823i) q^{52} +(-2.51994 + 11.0406i) q^{53} +(-0.0444440 - 0.194722i) q^{54} +(4.64332 - 5.82253i) q^{55} +(1.04490 + 0.238491i) q^{56} +(0.0740376 + 0.0590430i) q^{57} +(-5.99723 - 1.36883i) q^{58} +(-5.51197 - 6.91179i) q^{59} +(-0.0376288 + 0.0471851i) q^{60} +(1.18338 + 1.48392i) q^{61} +(-1.16582 + 5.10780i) q^{62} +(-3.80469 - 1.83224i) q^{63} +(6.60987 - 8.28852i) q^{64} +(-1.31006 + 5.73976i) q^{65} +(0.121005 - 0.0964981i) q^{66} +(3.34307 + 6.94196i) q^{67} -16.6028i q^{68} -0.101070i q^{69} +(1.04828 + 4.59283i) q^{70} +(-1.01294 + 0.231197i) q^{71} +(1.78556 - 1.42393i) q^{72} +(3.43651 + 7.13598i) q^{73} +(-5.52503 + 11.4728i) q^{74} +(0.0378145 + 0.00863091i) q^{75} +(-3.12673 + 13.6991i) q^{76} -6.54493i q^{77} +(-0.0530866 + 0.110236i) q^{78} +(-10.5179 - 2.40064i) q^{79} +(4.90107 + 1.11864i) q^{80} +(-8.10666 + 3.90396i) q^{81} +(13.2079 + 10.5330i) q^{82} -3.90127 q^{83} +0.0530392i q^{84} +(10.1341 - 4.88030i) q^{85} +(24.9841 + 5.70246i) q^{86} -0.0469203i q^{87} +(3.18908 + 1.53578i) q^{88} +(2.46367 + 1.96471i) q^{89} +(9.04435 + 4.35553i) q^{90} +(2.24492 + 4.66162i) q^{91} +(13.5118 - 6.50696i) q^{92} -0.0399617 q^{93} +(-1.37609 + 2.85749i) q^{94} +(-9.28079 + 2.11828i) q^{95} +(0.115989 + 0.0558572i) q^{96} +(3.75879 + 16.4683i) q^{97} +(-8.19650 - 6.53649i) q^{98} +(-10.9038 - 8.69548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 7 q^{2} + 25 q^{4} - 14 q^{5} - 18 q^{6} + 6 q^{7} - 28 q^{8} + 7 q^{9} + 10 q^{10} - 14 q^{11} - 21 q^{12} + 35 q^{15} - 5 q^{16} - 21 q^{18} - 20 q^{19} - 14 q^{21} + 10 q^{22} - 40 q^{23} - 26 q^{24}+ \cdots - 63 q^{99}+O(q^{100}) $ 90 * q - 7 * q^2 + 25 * q^4 - 14 * q^5 - 18 * q^6 + 6 * q^7 - 28 * q^8 + 7 * q^9 + 10 * q^10 - 14 * q^11 - 21 * q^12 + 35 * q^15 - 5 * q^16 - 21 * q^18 - 20 * q^19 - 14 * q^21 + 10 * q^22 - 40 * q^23 - 26 * q^24 - 5 * q^25 + 29 * q^26 - 42 * q^27 - 36 * q^28 - 5 * q^29 - 133 * q^30 + 28 * q^31 + 28 * q^32 + 6 * q^33 + 38 * q^34 - 28 * q^35 + 232 * q^36 - 55 * q^37 - 49 * q^38 + 15 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 35 * q^43 + 7 * q^44 + 14 * q^45 - 28 * q^46 + q^47 - 98 * q^48 + 17 * q^49 + 98 * q^50 - 26 * q^51 - 112 * q^52 - 24 * q^53 - 43 * q^54 - 8 * q^55 + 63 * q^56 + 42 * q^57 + 14 * q^58 + 22 * q^59 - 73 * q^60 - 46 * q^61 + 34 * q^62 + 5 * q^63 - 10 * q^64 + 13 * q^65 - 91 * q^66 + 98 * q^67 + 27 * q^70 + 63 * q^71 - 7 * q^72 + 42 * q^73 + 7 * q^74 + 49 * q^75 + 78 * q^76 - 147 * q^78 - 126 * q^79 + 21 * q^80 - 37 * q^81 - 42 * q^82 - 26 * q^83 + 130 * q^85 + 119 * q^86 + 20 * q^88 - 56 * q^89 - 119 * q^90 + 84 * q^91 + 71 * q^92 - 66 * q^93 + 147 * q^94 - 77 * q^95 + 53 * q^96 + 12 * q^97 - 35 * q^98 - 63 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{14}\right)$

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 $

$2$	−1.63334	+	1.30255i	−1.15495	+	0.921039i	−0.997784	−	0.0665337i	$-0.978806\pi$
$2$	−1.63334	+	1.30255i	−1.15495	+	0.921039i	−0.157162	+	0.987573i	$0.550235\pi$
$3$	−0.0124583	−	0.00993517i	−0.00719281	−	0.00573607i	0.619887	−	0.784691i	$-0.287179\pi$
$3$	−0.0124583	−	0.00993517i	−0.00719281	−	0.00573607i	−0.627080	+	0.778955i	$0.715750\pi$
$4$	0.526135	−	2.30515i	0.263067	−	1.15257i
$5$	1.56168	−	0.356443i	0.698404	−	0.159406i	0.141445	−	0.989946i	$-0.454825\pi$
$5$	1.56168	−	0.356443i	0.698404	−	0.159406i	0.556959	+	0.830540i	$0.311968\pi$
$6$	0.0332897			0.0135905
$7$	0.877717	−	1.10062i	0.331746	−	0.415996i	−0.587783	−	0.809019i	$-0.699999\pi$
$7$	0.877717	−	1.10062i	0.331746	−	0.415996i	0.919529	+	0.393023i	$0.128571\pi$
$8$	0.330331	+	0.685939i	0.116790	+	0.242516i
$9$	−0.667506	−	2.92454i	−0.222502	−	0.974845i
$10$	−2.08647	+	2.61635i	−0.659800	+	0.827363i
$11$	3.63490	−	2.89874i	1.09596	−	0.874003i	0.103270	−	0.994653i	$-0.467070\pi$
$11$	3.63490	−	2.89874i	1.09596	−	0.874003i	0.992695	+	0.120651i	$0.0384982\pi$
$12$	−0.0294568	+	0.0234910i	−0.00850344	+	0.00678127i
$13$	−1.59469	+	3.31140i	−0.442287	+	0.918418i	0.554016	+	0.832506i	$0.313095\pi$
$13$	−1.59469	+	3.31140i	−0.442287	+	0.918418i	−0.996303	+	0.0859118i	$0.972620\pi$
$14$			2.94096i			0.786004i
$15$	−0.0229972	−	0.0110749i	−0.00593785	−	0.00285952i
$16$	2.82754	+	1.36167i	0.706886	+	0.340418i
$17$	6.84584	−	1.56252i	1.66036	−	0.378966i	0.713511	−	0.700644i	$-0.247104\pi$
$17$	6.84584	−	1.56252i	1.66036	−	0.378966i	0.946849	+	0.321677i	$0.104247\pi$
$18$	4.89961	+	3.90731i	1.15485	+	0.920961i
$19$	−5.94283			−1.36338			−0.681689	−	0.731642i	$-0.738754\pi$
$19$	−5.94283			−1.36338			−0.681689	+	0.731642i	$0.738754\pi$
$20$		−	3.78744i		−	0.846896i
$21$	−0.0218697	+	0.00499163i	−0.00477237	+	0.00108926i
$22$	−2.16130	+	9.46926i	−0.460790	+	2.01885i
$23$	3.95465	+	4.95897i	0.824601	+	1.03402i	0.998784	+	0.0493034i	$0.0157001\pi$
$23$	3.95465	+	4.95897i	0.824601	+	1.03402i	−0.174183	+	0.984713i	$0.555728\pi$
$24$	0.00269956	−	0.0118275i	0.000551045	−	0.00241429i
$25$	−2.19306	+	1.05612i	−0.438611	+	0.211224i
$26$	−1.70859	−	7.48580i	−0.335081	−	1.46809i
$27$	−0.0414813	+	0.0861368i	−0.00798308	+	0.0165770i
$28$	−2.07530	−	2.60234i	−0.392195	−	0.491796i
$29$	1.83588	+	2.30212i	0.340914	+	0.427493i	0.922503	−	0.385990i	$-0.126140\pi$
$29$	1.83588	+	2.30212i	0.340914	+	0.427493i	−0.581589	+	0.813483i	$0.697569\pi$
$30$	0.0519878	−	0.0118659i	0.00949163	−	0.00216640i
$31$	1.96070	−	1.56360i	0.352152	−	0.280832i	−0.431397	−	0.902162i	$-0.641979\pi$
$31$	1.96070	−	1.56360i	0.352152	−	0.280832i	0.783548	+	0.621331i	$0.213408\pi$
$32$	−7.87648	+	1.79775i	−1.39238	+	0.317801i
$33$	−0.0740842			−0.0128964
$34$	−9.14634	+	11.4691i	−1.56858	+	1.96694i
$35$	0.978403	−	2.03167i	0.165380	−	0.343416i
$36$	−7.09268			−1.18211
$37$	5.49171	−	2.64467i	0.902831	−	0.434781i	0.0759206	−	0.997114i	$-0.475810\pi$
$37$	5.49171	−	2.64467i	0.902831	−	0.434781i	0.826911	+	0.562333i	$0.190096\pi$
$38$	9.70667	−	7.74081i	1.57463	−	1.25572i
$39$	0.0527665	−	0.0254110i	0.00844940	−	0.00406902i
$40$	0.760369	+	0.953473i	0.120225	+	0.150757i
$41$	−1.79941	−	7.88371i	−0.281020	−	1.23123i	−0.896488	−	0.443067i	$-0.853890\pi$
$41$	−1.79941	−	7.88371i	−0.281020	−	1.23123i	0.615468	−	0.788162i	$-0.288967\pi$
$42$	0.0292189	−	0.0366394i	0.00450858	−	0.00565358i
$43$	−7.64816	−	9.59049i	−1.16633	−	1.46254i	−0.859767	−	0.510686i	$-0.829391\pi$
$43$	−7.64816	−	9.59049i	−1.16633	−	1.46254i	−0.306566	−	0.951849i	$-0.599180\pi$
$44$	−4.76957	−	9.90411i	−0.719040	−	1.49310i
$45$	−2.08486	−	4.32926i	−0.310793	−	0.645368i
$46$	−12.9186	−	2.94858i	−1.90474	−	0.434744i
$47$	1.36779	−	0.658695i	0.199513	−	0.0960805i	−0.331459	−	0.943469i	$-0.607541\pi$
$47$	1.36779	−	0.658695i	0.199513	−	0.0960805i	0.530973	+	0.847389i	$0.321827\pi$
$48$	−0.0216980	−	0.0450563i	−0.00313183	−	0.00650331i
$49$	1.11666	+	4.89243i	0.159523	+	0.698918i
$50$	2.20636	−	4.58156i	0.312027	−	0.647930i
$51$	−0.100812	−	0.0485483i	−0.0141164	−	0.00679812i
$52$	6.79425	+	5.41823i	0.942193	+	0.751374i
$53$	−2.51994	+	11.0406i	−0.346140	+	1.51654i	0.439721	+	0.898134i	$0.355077\pi$
$53$	−2.51994	+	11.0406i	−0.346140	+	1.51654i	−0.785861	+	0.618403i	$0.787780\pi$
$54$	−0.0444440	−	0.194722i	−0.00604807	−	0.0264983i
$55$	4.64332	−	5.82253i	0.626105	−	0.785110i
$56$	1.04490	+	0.238491i	0.139630	+	0.0318697i
$57$	0.0740376	+	0.0590430i	0.00980652	+	0.00782044i
$58$	−5.99723	−	1.36883i	−0.787475	−	0.179736i
$59$	−5.51197	−	6.91179i	−0.717597	−	0.899838i	0.280602	−	0.959824i	$-0.409466\pi$
$59$	−5.51197	−	6.91179i	−0.717597	−	0.899838i	−0.998199	+	0.0599859i	$0.980894\pi$
$60$	−0.0376288	+	0.0471851i	−0.00485786	+	0.00609157i
$61$	1.18338	+	1.48392i	0.151517	+	0.189996i	0.851797	−	0.523872i	$-0.175513\pi$
$61$	1.18338	+	1.48392i	0.151517	+	0.189996i	−0.700280	+	0.713868i	$0.746942\pi$
$62$	−1.16582	+	5.10780i	−0.148060	+	0.648691i
$63$	−3.80469	−	1.83224i	−0.479346	−	0.230841i
$64$	6.60987	−	8.28852i	0.826234	−	1.03606i
$65$	−1.31006	+	5.73976i	−0.162493	+	0.711930i
$66$	0.121005	−	0.0964981i	0.0148947	−	0.0118781i
$67$	3.34307	+	6.94196i	0.408422	+	0.848096i	0.999150	+	0.0412255i	$0.0131262\pi$
$67$	3.34307	+	6.94196i	0.408422	+	0.848096i	−0.590728	+	0.806870i	$0.701160\pi$
$68$		−	16.6028i		−	2.01338i
$69$		−	0.101070i		−	0.0121675i
$70$	1.04828	+	4.59283i	0.125294	+	0.548948i
$71$	−1.01294	+	0.231197i	−0.120214	+	0.0274381i	−0.282205	−	0.959354i	$-0.591066\pi$
$71$	−1.01294	+	0.231197i	−0.120214	+	0.0274381i	0.161991	+	0.986792i	$0.448209\pi$
$72$	1.78556	−	1.42393i	0.210430	−	0.167812i
$73$	3.43651	+	7.13598i	0.402213	+	0.835204i	0.999451	+	0.0331394i	$0.0105505\pi$
$73$	3.43651	+	7.13598i	0.402213	+	0.835204i	−0.597238	+	0.802064i	$0.703735\pi$
$74$	−5.52503	+	11.4728i	−0.642272	+	1.33369i
$75$	0.0378145	+	0.00863091i	0.00436644	+	0.000996612i
$76$	−3.12673	+	13.6991i	−0.358660	+	1.57139i
$77$		−	6.54493i		−	0.745864i
$78$	−0.0530866	+	0.110236i	−0.00601088	+	0.0124817i
$79$	−10.5179	−	2.40064i	−1.18336	−	0.270093i	−0.414822	−	0.909902i	$-0.636156\pi$
$79$	−10.5179	−	2.40064i	−1.18336	−	0.270093i	−0.768534	+	0.639809i	$0.779013\pi$
$80$	4.90107	+	1.11864i	0.547956	+	0.125067i
$81$	−8.10666	+	3.90396i	−0.900740	+	0.433774i
$82$	13.2079	+	10.5330i	1.45857	+	1.16317i
$83$	−3.90127			−0.428220			−0.214110	−	0.976810i	$-0.568685\pi$
$83$	−3.90127			−0.428220			−0.214110	+	0.976810i	$0.568685\pi$
$84$			0.0530392i			0.00578706i
$85$	10.1341	−	4.88030i	1.09919	−	0.529343i
$86$	24.9841	+	5.70246i	2.69410	+	0.614912i
$87$		−	0.0469203i		−	0.00503039i
$88$	3.18908	+	1.53578i	0.339957	+	0.163715i
$89$	2.46367	+	1.96471i	0.261149	+	0.208259i	0.745307	−	0.666721i	$-0.232303\pi$
$89$	2.46367	+	1.96471i	0.261149	+	0.208259i	−0.484159	+	0.874980i	$0.660874\pi$
$90$	9.04435	+	4.35553i	0.953358	+	0.459113i
$91$	2.24492	+	4.66162i	0.235331	+	0.488671i
$92$	13.5118	−	6.50696i	1.40871	−	0.678397i
$93$	−0.0399617			−0.00414383
$94$	−1.37609	+	2.85749i	−0.141933	+	0.294727i
$95$	−9.28079	+	2.11828i	−0.952189	+	0.217331i
$96$	0.115989	+	0.0558572i	0.0118380	+	0.00570090i
$97$	3.75879	+	16.4683i	0.381647	+	1.67211i	0.692322	+	0.721589i	$0.256588\pi$
$97$	3.75879	+	16.4683i	0.381647	+	1.67211i	−0.310674	+	0.950516i	$0.600555\pi$
$98$	−8.19650	−	6.53649i	−0.827972	−	0.660286i
$99$	−10.9038	−	8.69548i	−1.09587	−	0.873929i
$100$	1.28067	+	5.61098i	0.128067	+	0.561098i
$101$	2.51222	+	1.20982i	0.249975	+	0.120382i	0.554676	−	0.832066i	$-0.312842\pi$
$101$	2.51222	+	1.20982i	0.249975	+	0.120382i	−0.304701	+	0.952448i	$0.598556\pi$
$102$	0.227896	−	0.0520158i	0.0225651	−	0.00515033i
$103$	3.94231	−	8.18629i	0.388447	−	0.806619i	−0.611435	−	0.791294i	$-0.709408\pi$
$103$	3.94231	−	8.18629i	0.388447	−	0.806619i	0.999883	−	0.0153245i	$-0.00487814\pi$
$104$	−2.79820			−0.274386
$105$	−0.0323743	+	0.0155906i	−0.00315941	+	0.00152149i
$106$	−10.2649	−	21.3153i	−0.997017	−	2.07033i
$107$	−1.06250	−	0.511673i	−0.102716	−	0.0494653i	0.381820	−	0.924237i	$-0.375297\pi$
$107$	−1.06250	−	0.511673i	−0.102716	−	0.0494653i	−0.484536	+	0.874771i	$0.661012\pi$
$108$	0.176733	+	0.140940i	0.0170062	+	0.0135620i
$109$	2.20610	+	1.06240i	0.211306	+	0.101760i	0.536543	−	0.843873i	$-0.319730\pi$
$109$	2.20610	+	1.06240i	0.211306	+	0.101760i	−0.325237	+	0.945633i	$0.605444\pi$
$110$			15.5583i			1.48343i
$111$	−0.0946926	−	0.0216130i	−0.00898783	−	0.00205141i
$112$	3.98047	−	1.91689i	0.376119	−	0.181129i
$113$		−	0.153586i		−	0.0144481i	−0.999974	−	0.00722406i	$-0.997700\pi$
$113$		−	0.153586i		−	0.0144481i	0.999974	−	0.00722406i	$-0.00229951\pi$
$114$	−0.197835			−0.0185289
$115$	7.94348	+	6.33471i	0.740733	+	0.590715i
$116$	6.27265	−	3.02075i	0.582401	−	0.280469i
$117$	10.7488	+	2.45334i	0.993725	+	0.226811i
$118$	18.0058	+	4.10972i	1.65757	+	0.378330i
$119$	4.28897	−	8.90613i	0.393169	−	0.816424i
$120$		−	0.0194331i		−	0.00177399i
$121$	2.36211	−	10.3491i	0.214737	−	0.940824i
$122$	−3.86574	−	0.882329i	−0.349987	−	0.0798823i
$123$	−0.0559085	+	0.116095i	−0.00504110	+	0.0104679i
$124$	−2.57275	−	5.34236i	−0.231040	−	0.479759i
$125$	−9.31025	+	7.42467i	−0.832734	+	0.664083i
$126$	8.60094	−	1.96311i	0.766232	−	0.174888i
$127$	3.72829	+	16.3347i	0.330832	+	1.44947i	0.817522	+	0.575897i	$0.195347\pi$
$127$	3.72829	+	16.3347i	0.330832	+	1.44947i	−0.486690	+	0.873575i	$0.661796\pi$
$128$			5.98957i			0.529408i
$129$			0.195467i			0.0172099i
$130$	−5.33652	−	11.0814i	−0.468044	−	0.971904i
$131$	−0.289961	+	0.231236i	−0.0253340	+	0.0202032i	−0.636075	−	0.771627i	$-0.719443\pi$
$131$	−0.289961	+	0.231236i	−0.0253340	+	0.0202032i	0.610741	+	0.791830i	$0.290872\pi$
$132$	−0.0389783	+	0.170775i	−0.00339262	+	0.0148641i
$133$	−5.21612	+	6.54081i	−0.452295	+	0.567160i
$134$	−14.5026	−	6.98409i	−1.25283	−	0.603333i
$135$	−0.0340776	+	0.149304i	−0.00293293	+	0.0128500i
$136$	3.33319	+	4.17968i	0.285818	+	0.358405i
$137$	−3.47410	+	4.35638i	−0.296812	+	0.372191i	−0.907767	−	0.419475i	$-0.862214\pi$
$137$	−3.47410	+	4.35638i	−0.296812	+	0.372191i	0.610955	+	0.791665i	$0.290786\pi$
$138$	0.131649	+	0.165083i	0.0112067	+	0.0140528i
$139$	−16.1579	−	3.68794i	−1.37050	−	0.312807i	−0.526965	−	0.849887i	$-0.676670\pi$
$139$	−16.1579	−	3.68794i	−1.37050	−	0.312807i	−0.843531	+	0.537080i	$0.819527\pi$
$140$	−4.16854	−	3.32430i	−0.352306	−	0.280954i
$141$	−0.0235847	−	0.00538304i	−0.00198619	−	0.000453334i
$142$	1.35333	−	1.69703i	0.113569	−	0.142411i
$143$	3.80236	+	16.6592i	0.317969	+	1.39311i
$144$	2.09486	−	9.17817i	0.174572	−	0.764848i
$145$	3.68763	+	2.94079i	0.306241	+	0.244219i
$146$	−14.9079	−	7.17928i	−1.23379	−	0.594162i
$147$	0.0346953	−	0.0720456i	0.00286162	−	0.00594222i
$148$	−3.20697	−	14.0506i	−0.263611	−	1.15496i
$149$	−1.35115	−	2.80570i	−0.110691	−	0.229852i	0.838263	−	0.545265i	$-0.183571\pi$
$149$	−1.35115	−	2.80570i	−0.110691	−	0.229852i	−0.948954	+	0.315413i	$0.897857\pi$
$150$	−0.0730061	+	0.0351579i	−0.00596093	+	0.00287063i
$151$	−12.9550	−	2.95690i	−1.05426	−	0.240629i	−0.339943	−	0.940446i	$-0.610408\pi$
$151$	−12.9550	−	2.95690i	−1.05426	−	0.240629i	−0.714322	+	0.699817i	$0.753265\pi$
$152$	−1.96310	−	4.07642i	−0.159228	−	0.330641i
$153$	−9.13928	−	18.9779i	−0.738867	−	1.53427i
$154$	8.52507	+	10.6901i	0.686970	+	0.861433i
$155$	2.50464	−	3.14072i	0.201178	−	0.252269i
$156$	−0.0308138	−	0.135004i	−0.00246708	−	0.0108090i
$157$	−11.7980	−	14.7942i	−0.941581	−	1.18071i	−0.983376	−	0.181579i	$-0.941879\pi$
$157$	−11.7980	−	14.7942i	−0.941581	−	1.18071i	0.0417952	−	0.999126i	$-0.486692\pi$
$158$	20.3063	−	9.77898i	1.61548	−	0.777974i
$159$	0.141084	−	0.112511i	0.0111887	−	0.00892268i
$160$	−11.6597	+	5.61503i	−0.921782	+	0.443907i
$161$	8.92901			0.703705
$162$	8.15585	−	16.9358i	0.640784	−	1.33060i
$163$	−2.80286	+	3.51468i	−0.219537	+	0.275291i	−0.879388	−	0.476106i	$-0.842048\pi$
$163$	−2.80286	+	3.51468i	−0.219537	+	0.275291i	0.659851	+	0.751396i	$0.270619\pi$
$164$	−19.1198			−1.49301
$165$	−0.115696	+	0.0264068i	−0.00900690	+	0.00205577i
$166$	6.37210	−	5.08158i	0.494571	−	0.394407i
$167$	−10.6333	+	2.42699i	−0.822832	+	0.187806i	−0.613153	−	0.789964i	$-0.710099\pi$
$167$	−10.6333	+	2.42699i	−0.822832	+	0.187806i	−0.209679	+	0.977770i	$0.567242\pi$
$168$	−0.0106482	−	0.0133524i	−0.000821527	−	0.00103016i
$169$	−0.316991	−	0.397494i	−0.0243839	−	0.0305765i
$170$	−10.1955	+	21.1713i	−0.781963	+	1.62376i
$171$	3.96688	+	17.3800i	0.303355	+	1.32908i
$172$	−26.1314	+	12.5842i	−1.99250	+	0.959539i
$173$	0.934894	−	4.09604i	0.0710787	−	0.311416i	−0.926874	−	0.375373i	$-0.877515\pi$
$173$	0.934894	−	4.09604i	0.0710787	−	0.311416i	0.997953	+	0.0639566i	$0.0203719\pi$
$174$	0.0611159	+	0.0766369i	0.00463318	+	0.00580983i
$175$	−0.762493	+	3.34070i	−0.0576391	+	0.252533i
$176$	14.2250	−	3.24676i	1.07225	−	0.244734i
$177$			0.140872i			0.0105886i
$178$	−6.58314			−0.493427
$179$	11.5970	+	9.24828i	0.866799	+	0.691249i	0.952324	−	0.305087i	$-0.0986856\pi$
$179$	11.5970	+	9.24828i	0.866799	+	0.691249i	−0.0855258	+	0.996336i	$0.527257\pi$
$180$	−11.0765	+	2.52814i	−0.825593	+	0.188436i
$181$	−3.15516	−	1.51944i	−0.234521	−	0.112939i	0.312933	−	0.949775i	$-0.398689\pi$
$181$	−3.15516	−	1.51944i	−0.234521	−	0.112939i	−0.547454	+	0.836836i	$0.684403\pi$
$182$	−9.73869	−	4.68991i	−0.721880	−	0.347639i
$183$		−	0.0302442i		−	0.00223572i
$184$	−2.09521	+	4.35075i	−0.154461	+	0.320741i
$185$	7.63361	−	6.08760i	0.561234	−	0.447569i
$186$	0.0652710	−	0.0520519i	0.00478590	−	0.00381663i
$187$	20.3546	−	25.5239i	1.48848	−	1.86649i
$188$	−0.798745	−	3.49953i	−0.0582544	−	0.255229i
$189$	0.0583952	+	0.121259i	0.00424763	+	0.00882029i
$190$	12.3995	−	15.5485i	0.899557	−	1.12801i
$191$	1.56379			0.113152			0.0565758	−	0.998398i	$-0.481982\pi$
$191$	1.56379			0.113152			0.0565758	+	0.998398i	$0.481982\pi$
$192$	−0.164696	+	0.0375907i	−0.0118859	+	0.00271288i
$193$	−1.85165	+	8.11259i	−0.133284	+	0.583957i	0.863537	+	0.504286i	$0.168244\pi$
$193$	−1.85165	+	8.11259i	−0.133284	+	0.583957i	−0.996821	+	0.0796712i	$0.974613\pi$
$194$	−27.5901	−	22.0024i	−1.98086	−	1.57968i
$195$	0.0733467	−	0.0584920i	0.00525247	−	0.00418870i
$196$	11.8653			0.847520
$197$	4.78662	+	13.1943i	0.341033	+	0.940051i
$197$	4.78662	+	13.1943i	0.341033	+	0.940051i
$198$	29.1359			2.07060
$199$	0.141647	−	0.112960i	0.0100411	−	0.00800752i	−0.618456	−	0.785819i	$-0.712242\pi$
$199$	0.141647	−	0.112960i	0.0100411	−	0.00800752i	0.628498	+	0.777812i	$0.283670\pi$
$200$	−1.44887	−	1.15543i	−0.102450	−	0.0817015i
$201$	0.0273206	−	0.119699i	0.00192704	−	0.00844293i
$202$	−5.67916	+	1.29623i	−0.399584	+	0.0912025i
$203$	4.14515			0.290932
$204$	−0.164951	+	0.206842i	−0.0115489	+	0.0144819i
$205$	−5.62019	−	11.6704i	−0.392531	−	0.815099i
$206$	4.22388	+	18.5060i	0.294292	+	1.28938i
$207$	11.8629	−	14.8756i	0.824531	−	1.03393i
$208$	−9.01809	+	7.19169i	−0.625292	+	0.498654i
$209$	−21.6016	+	17.2267i	−1.49421	+	1.19160i
$210$	0.0325707	−	0.0676338i	0.00224759	−	0.00466718i
$211$			26.5758i			1.82955i	0.403960	+	0.914777i	$0.367634\pi$
$211$			26.5758i			1.82955i	−0.403960	+	0.914777i	$0.632366\pi$
$212$	24.1243	+	11.6176i	1.65686	+	0.797903i
$213$	0.0149165	+	0.00718343i	0.00102206	+	0.000492200i
$214$	2.40190	−	0.548219i	0.164191	−	0.0374755i
$215$	−15.3624	−	12.2511i	−1.04771	−	0.835520i
$216$	−0.0727872			−0.00495254
$217$		−	3.53039i		−	0.239658i
$218$	−4.98715	+	1.13828i	−0.337772	+	0.0770943i
$219$	0.0280841	−	0.123045i	0.00189775	−	0.00831458i
$220$	−10.9788	−	13.7670i	−0.740190	−	0.928169i
$221$	−5.74285	+	25.1611i	−0.386306	+	1.69252i
$222$	0.182817	−	0.0880402i	0.0122699	−	0.00590887i
$223$	−2.94084	−	12.8847i	−0.196933	−	0.862821i	−0.972749	−	0.231861i	$-0.925518\pi$
$223$	−2.94084	−	12.8847i	−0.196933	−	0.862821i	0.775816	−	0.630960i	$-0.217339\pi$
$224$	−4.93467	+	10.2469i	−0.329711	+	0.684653i
$225$	4.55254	+	5.70870i	0.303503	+	0.380580i
$226$	0.200052	+	0.250858i	0.0133073	+	0.0166868i
$227$	3.58716	−	0.818746i	0.238088	−	0.0543421i	−0.101812	−	0.994804i	$-0.532464\pi$
$227$	3.58716	−	0.818746i	0.238088	−	0.0543421i	0.339900	+	0.940462i	$0.389607\pi$
$228$	0.175057	−	0.139603i	0.0115934	−	0.00924544i
$229$	14.5321	−	3.31685i	0.960306	−	0.219184i	0.286490	−	0.958083i	$-0.407511\pi$
$229$	14.5321	−	3.31685i	0.960306	−	0.219184i	0.673816	+	0.738900i	$0.264654\pi$
$230$	−21.2257			−1.39958
$231$	−0.0650250	+	0.0815387i	−0.00427833	+	0.00536486i
$232$	−0.972667	+	2.01976i	−0.0638587	+	0.132604i
$233$	24.4255			1.60017			0.800083	−	0.599890i	$-0.204789\pi$
$233$	24.4255			1.60017			0.800083	+	0.599890i	$0.204789\pi$
$234$	−20.7520	+	9.99364i	−1.35660	+	0.653305i
$235$	1.90127	−	1.51621i	0.124025	−	0.0989066i
$236$	−18.8327	+	9.06936i	−1.22591	+	0.590365i
$237$	0.107184	+	0.134405i	0.00696238	+	0.00873055i
$238$	4.59530	+	20.1333i	0.297869	+	1.30505i
$239$	4.08767	−	5.12578i	0.264409	−	0.331559i	−0.631849	−	0.775092i	$-0.717704\pi$
$239$	4.08767	−	5.12578i	0.264409	−	0.331559i	0.896258	+	0.443533i	$0.146275\pi$
$240$	−0.0499452	−	0.0626293i	−0.00322395	−	0.00404271i
$241$	7.24454	+	15.0434i	0.466662	+	0.969033i	0.992929	+	0.118714i	$0.0378770\pi$
$241$	7.24454	+	15.0434i	0.466662	+	0.969033i	−0.526267	+	0.850319i	$0.676409\pi$
$242$	9.62200	+	19.9803i	0.618526	+	1.28438i
$243$	0.419405	+	0.0957264i	0.0269048	+	0.00614085i
$244$	4.04326	−	1.94713i	0.258843	−	0.124652i
$245$	3.48774	+	7.24237i	0.222824	+	0.462698i
$246$	−0.0599017	−	0.262446i	−0.00381919	−	0.0167330i
$247$	9.47695	−	19.6791i	0.603004	−	1.25215i
$248$	1.72022	+	0.828413i	0.109234	+	0.0526043i
$249$	0.0486032	+	0.0387598i	0.00308011	+	0.00245630i
$250$	5.53583	−	24.2540i	0.350117	−	1.53396i
$251$	−1.83603	−	8.04419i	−0.115889	−	0.507745i	−0.999238	−	0.0390282i	$-0.987574\pi$
$251$	−1.83603	−	8.04419i	−0.115889	−	0.507745i	0.883349	−	0.468716i	$-0.155283\pi$
$252$	−6.22537	+	7.80637i	−0.392161	+	0.491755i
$253$	28.7495	+	6.56189i	1.80747	+	0.412542i
$254$	−27.3663	−	21.8239i	−1.71711	−	1.36935i
$255$	−0.174740	−	0.0398832i	−0.0109426	−	0.00249759i
$256$	5.41805	+	6.79403i	0.338628	+	0.424627i
$257$	−1.91825	+	2.40541i	−0.119657	+	0.150045i	−0.838052	−	0.545590i	$-0.816306\pi$
$257$	−1.91825	+	2.40541i	−0.119657	+	0.150045i	0.718395	+	0.695635i	$0.244877\pi$
$258$	−0.254605	−	0.319264i	−0.0158510	−	0.0198765i
$259$	1.90939	−	8.36557i	0.118643	−	0.519811i
$260$	12.5417	+	6.03978i	0.777805	+	0.374571i
$261$	5.50717	−	6.90578i	0.340885	−	0.427457i
$262$	0.172409	−	0.755375i	0.0106515	−	0.0466672i
$263$	−12.7114	+	10.1370i	−0.783819	+	0.625075i	−0.931409	−	0.363974i	$-0.881420\pi$
$263$	−12.7114	+	10.1370i	−0.783819	+	0.625075i	0.147590	+	0.989049i	$0.452848\pi$
$264$	−0.0244723	−	0.0508173i	−0.00150617	−	0.00312759i
$265$			18.1400i			1.11433i
$266$		−	17.4776i		−	1.07162i
$267$	−0.0111734	−	0.0489540i	−0.000683803	−	0.00299594i
$268$	17.7612	−	4.05387i	1.08494	−	0.247629i
$269$	−18.1446	+	14.4698i	−1.10629	+	0.882240i	−0.993775	−	0.111410i	$-0.964463\pi$
$269$	−18.1446	+	14.4698i	−1.10629	+	0.882240i	−0.112519	+	0.993650i	$0.535892\pi$
$270$	−0.138815	−	0.288251i	−0.00844799	−	0.0175424i
$271$	8.06685	−	16.7510i	0.490026	−	1.01755i	−0.498555	−	0.866858i	$-0.666136\pi$
$271$	8.06685	−	16.7510i	0.490026	−	1.01755i	0.988581	−	0.150691i	$-0.0481500\pi$
$272$	21.4845	+	4.90371i	1.30269	+	0.297331i
$273$	0.0183461	−	0.0803796i	0.00111036	−	0.00486479i
$274$		−	11.6406i		−	0.703236i
$275$	−4.91013	+	10.1960i	−0.296092	+	0.614841i
$276$	−0.232982	−	0.0531767i	−0.0140239	−	0.00320086i
$277$	−29.4813	−	6.72892i	−1.77136	−	0.404301i	−0.792671	−	0.609649i	$-0.791310\pi$
$277$	−29.4813	−	6.72892i	−1.77136	−	0.404301i	−0.978689	+	0.205348i	$0.934167\pi$
$278$	31.1951	−	15.0228i	1.87096	−	0.901006i
$279$	−5.88160	−	4.69042i	−0.352122	−	0.280808i
$280$	1.71680			0.102599
$281$		−	21.1843i		−	1.26375i	−0.775071	−	0.631874i	$-0.782286\pi$
$281$		−	21.1843i		−	1.26375i	0.775071	−	0.631874i	$-0.217714\pi$
$282$	0.0455334	−	0.0219277i	0.00271148	−	0.00130578i
$283$	−25.0452	−	5.71640i	−1.48878	−	0.339805i	−0.600694	−	0.799479i	$-0.705109\pi$
$283$	−25.0452	−	5.71640i	−1.48878	−	0.339805i	−0.888087	+	0.459675i	$0.847966\pi$
$284$			2.45662i			0.145774i
$285$	0.136668	+	0.0658160i	0.00809554	+	0.00389861i
$286$	−27.9099	−	22.2574i	−1.65035	−	1.31611i
$287$	−10.2564	−	4.93920i	−0.605414	−	0.291552i
$288$	10.5152	+	21.8350i	0.619614	+	1.28664i
$289$	29.1076	−	14.0175i	1.71221	−	0.824558i
$290$	−9.85366			−0.578627
$291$	0.116788	−	0.242512i	0.00684621	−	0.0142163i
$292$	18.2576	−	4.16717i	1.06844	−	0.243865i
$293$	21.1323	+	10.1768i	1.23456	+	0.594534i	0.933331	−	0.359016i	$-0.116888\pi$
$293$	21.1323	+	10.1768i	1.23456	+	0.594534i	0.301232	+	0.953551i	$0.402602\pi$
$294$	0.0371734	+	0.162867i	0.00216800	+	0.00949862i
$295$	−11.0716	−	8.82929i	−0.644612	−	0.514061i
$296$	3.62816	+	2.89336i	0.210883	+	0.168173i
$297$	0.0989076	+	0.433342i	0.00573920	+	0.0251451i
$298$	5.86145	+	2.82273i	0.339545	+	0.163516i
$299$	−22.7276	+	5.18742i	−1.31437	+	0.299996i
$300$	0.0397911	−	0.0826270i	0.00229734	−	0.00477047i
$301$	−17.2684			−0.995335
$302$	25.0115	−	12.0449i	1.43925	−	0.693105i
$303$	−0.0192782	−	0.0400317i	−0.00110751	−	0.00229976i
$304$	−16.8036	−	8.09219i	−0.963753	−	0.464119i
$305$	2.37700	+	1.89559i	0.136106	+	0.108541i
$306$	39.6472	+	19.0931i	2.26648	+	1.09148i
$307$			7.48489i			0.427185i	0.976923	+	0.213592i	$0.0685165\pi$
$307$			7.48489i			0.427185i	−0.976923	+	0.213592i	$0.931484\pi$
$308$	−15.0870	−	3.44351i	−0.859663	−	0.196212i
$309$	−0.130447	+	0.0628198i	−0.00742085	+	0.00357369i
$310$			8.39229i			0.476650i
$311$	25.7880			1.46231			0.731153	−	0.682214i	$-0.238983\pi$
$311$	25.7880			1.46231			0.731153	+	0.682214i	$0.238983\pi$
$312$	0.0348608	+	0.0278006i	0.00197360	+	0.00157390i
$313$	1.15973	−	0.558497i	0.0655519	−	0.0315681i	−0.400821	−	0.916157i	$-0.631275\pi$
$313$	1.15973	−	0.558497i	0.0655519	−	0.0315681i	0.466373	+	0.884588i	$0.345561\pi$
$314$	38.5402	+	8.79656i	2.17495	+	0.496418i
$315$	−6.59479	−	1.50522i	−0.371575	−	0.0848095i
$316$	−11.0677	+	22.9822i	−0.622605	+	1.29285i
$317$		−	5.02620i		−	0.282300i	−0.989988	−	0.141150i	$-0.954920\pi$
$317$		−	5.02620i		−	0.282300i	0.989988	−	0.141150i	$-0.0450800\pi$
$318$	−0.0838879	+	0.367537i	−0.00470420	+	0.0206104i
$319$	13.3465	+	3.04625i	0.747260	+	0.170557i
$320$	7.36811	−	15.3000i	0.411890	−	0.855298i
$321$	0.00815340	+	0.0169307i	0.000455079	+	0.000944981i
$322$	−14.5841	+	11.6304i	−0.812741	+	0.648140i
$323$	−40.6837	+	9.28578i	−2.26370	+	0.516675i
$324$	4.73401	+	20.7411i	0.263001	+	1.15228i
$325$		−	8.94627i		−	0.496250i
$326$		−	9.39152i		−	0.520148i
$327$	−0.0169292	−	0.0351538i	−0.000936185	−	0.00194401i
$328$	4.81335	−	3.83852i	0.265773	−	0.211947i
$329$	0.475562	−	2.08357i	0.0262186	−	0.114871i
$330$	0.154575	−	0.193830i	0.00850905	−	0.0106700i
$331$	−4.61820	−	2.22401i	−0.253839	−	0.122242i	0.302638	−	0.953106i	$-0.402133\pi$
$331$	−4.61820	−	2.22401i	−0.253839	−	0.122242i	−0.556477	+	0.830863i	$0.687847\pi$
$332$	−2.05259	+	8.99300i	−0.112651	+	0.493555i
$333$	−11.4002	−	14.2954i	−0.624726	−	0.783381i
$334$	14.2066	−	17.8145i	0.777350	−	0.974766i
$335$	7.69522	+	9.64950i	0.420435	+	0.527209i
$336$	−0.0686346	−	0.0156654i	−0.00374432	−	0.000854617i
$337$	7.21332	+	5.75243i	0.392935	+	0.313355i	0.799950	−	0.600066i	$-0.204859\pi$
$337$	7.21332	+	5.75243i	0.392935	+	0.313355i	−0.407016	+	0.913421i	$0.633431\pi$
$338$	1.03551	+	0.236348i	0.0563243	+	0.0128557i
$339$	−0.00152590	+	0.00191342i	−8.28755e−5	+	0.000103923i
$340$	−5.91794	−	25.9282i	−0.320945	−	1.40615i
$341$	2.59447	−	11.3671i	0.140498	−	0.615563i
$342$	−29.1175	−	23.2205i	−1.57450	−	1.25562i
$343$	15.2432	+	7.34073i	0.823055	+	0.396362i
$344$	4.05207	−	8.41421i	0.218473	−	0.453664i
$345$	−0.0360259	−	0.157840i	−0.00193957	−	0.00849780i
$346$	3.80828	+	7.90797i	0.204734	+	0.425135i
$347$	1.42500	−	0.686245i	0.0764981	−	0.0368396i	−0.395244	−	0.918576i	$-0.629340\pi$
$347$	1.42500	−	0.686245i	0.0764981	−	0.0368396i	0.471742	+	0.881737i	$0.343626\pi$
$348$	−0.108158	−	0.0246864i	−0.00579789	−	0.00132333i
$349$	7.24900	+	15.0527i	0.388030	+	0.805752i	0.999891	+	0.0147869i	$0.00470698\pi$
$349$	7.24900	+	15.0527i	0.388030	+	0.805752i	−0.611861	+	0.790965i	$0.709579\pi$
$350$	−3.10600	−	6.44968i	−0.166023	−	0.344750i
$351$	−0.219084	−	0.274723i	−0.0116938	−	0.0146636i
$352$	−23.4190	+	29.3665i	−1.24824	+	1.56524i
$353$	−6.55422	−	28.7159i	−0.348846	−	1.52839i	−0.779805	−	0.626023i	$-0.784682\pi$
$353$	−6.55422	−	28.7159i	−0.348846	−	1.52839i	0.430959	−	0.902372i	$-0.358175\pi$
$354$	−0.183492	−	0.230091i	−0.00975247	−	0.0122292i
$355$	−1.49948	+	0.722112i	−0.0795842	+	0.0383257i
$356$	5.82517	−	4.64542i	0.308734	−	0.246207i
$357$	−0.141917	+	0.0683438i	−0.00751106	+	0.00361714i
$358$	−30.9881			−1.63777
$359$	10.2351	−	21.2534i	0.540187	−	1.12171i	−0.435022	−	0.900420i	$-0.643259\pi$
$359$	10.2351	−	21.2534i	0.540187	−	1.12171i	0.975208	−	0.221289i	$-0.0710265\pi$
$360$	2.28091	−	2.86018i	0.120215	−	0.150744i
$361$	16.3172			0.858801
$362$	7.13260	−	1.62797i	0.374881	−	0.0855641i
$363$	−0.132248	+	0.105464i	−0.00694120	+	0.00553542i
$364$	11.9269	−	2.72223i	0.625137	−	0.142683i
$365$	7.91029	+	9.91919i	0.414044	+	0.519194i
$366$	0.0393945	+	0.0493991i	0.00205918	+	0.00258213i
$367$	0.212959	−	0.442214i	0.0111164	−	0.0230834i	−0.895337	−	0.445390i	$-0.853065\pi$
$367$	0.212959	−	0.442214i	0.0111164	−	0.0230834i	0.906453	+	0.422306i	$0.138779\pi$
$368$	4.42944	+	19.4066i	0.230900	+	1.01164i
$369$	−21.8551	+	10.5249i	−1.13773	+	0.547902i
$370$	−4.53891	+	19.8863i	−0.235967	+	1.03384i
$371$	9.93969	+	12.4640i	0.516043	+	0.647098i
$372$	−0.0210252	+	0.0921175i	−0.00109011	+	0.00477607i
$373$	−26.0951	+	5.95604i	−1.35115	+	0.308392i	−0.836011	−	0.548712i	$-0.815118\pi$
$373$	−26.0951	+	5.95604i	−1.35115	+	0.308392i	−0.515143	+	0.857104i	$0.672261\pi$
$374$			68.2021i			3.52665i
$375$	0.189755			0.00979893
$376$	0.903649	+	0.720636i	0.0466022	+	0.0371640i
$377$	−10.5509	+	2.40817i	−0.543399	+	0.124027i
$378$	−0.253325	−	0.121995i	−0.0130296	−	0.00627473i
$379$	16.1111	+	7.75871i	0.827572	+	0.398538i	0.799204	−	0.601060i	$-0.205255\pi$
$379$	16.1111	+	7.75871i	0.827572	+	0.398538i	0.0283683	+	0.999598i	$0.490969\pi$
$380$			22.5081i			1.15464i
$381$	0.115840	−	0.240544i	0.00593466	−	0.0123235i
$382$	−2.55419	+	2.03690i	−0.130684	+	0.104217i
$383$	12.4258	−	9.90924i	0.634928	−	0.506338i	−0.252312	−	0.967646i	$-0.581191\pi$
$383$	12.4258	−	9.90924i	0.634928	−	0.506338i	0.887240	+	0.461308i	$0.152620\pi$
$384$	0.0595074	−	0.0746199i	0.00303672	−	0.00380793i
$385$	−2.33289	−	10.2211i	−0.118895	−	0.520914i
$386$	−7.54265	−	15.6625i	−0.383911	−	0.797199i
$387$	−22.9425	+	28.7690i	−1.16623	+	1.46241i
$388$	39.9396			2.02762
$389$	15.6129	−	3.56354i	0.791605	−	0.180679i	0.192445	−	0.981308i	$-0.438358\pi$
$389$	15.6129	−	3.56354i	0.791605	−	0.180679i	0.599160	+	0.800629i	$0.295501\pi$
$390$	−0.0436116	+	0.191075i	−0.00220836	+	0.00967545i
$391$	34.8214	+	27.7691i	1.76099	+	1.40434i
$392$	−2.98704	+	2.38208i	−0.150868	+	0.120313i
$393$	0.00590980			0.000298110
$394$	−25.0043	−	15.3159i	−1.25970	−	0.771605i
$395$	−17.2813			−0.869515
$396$	−25.7812	+	20.5598i	−1.29556	+	1.03317i
$397$	8.60188	+	6.85977i	0.431716	+	0.344282i	0.815113	−	0.579302i	$-0.196675\pi$
$397$	8.60188	+	6.85977i	0.431716	+	0.344282i	−0.383397	+	0.923583i	$0.625246\pi$
$398$	−0.0842228	+	0.369004i	−0.00422171	+	0.0184965i
$399$	0.129968	−	0.0296644i	0.00650654	−	0.00148508i
$400$	−7.63905			−0.381952
$401$	16.7626	−	21.0196i	0.837083	−	1.04967i	−0.160950	−	0.986963i	$-0.551456\pi$
$401$	16.7626	−	21.0196i	0.837083	−	1.04967i	0.998032	−	0.0627056i	$-0.0199729\pi$
$402$	0.111290	+	0.231096i	0.00555064	+	0.0115260i
$403$	2.05102	+	8.98612i	0.102169	+	0.447631i
$404$	4.11058	−	5.15451i	0.204509	−	0.256446i
$405$	−11.2685	+	8.98630i	−0.559934	+	0.446533i
$406$	−6.77044	+	5.39924i	−0.336011	+	0.267960i
$407$	12.2956	−	25.5321i	0.609472	−	1.26558i
$408$		−	0.0851876i		−	0.00421741i
$409$	−11.6039	−	5.58814i	−0.573775	−	0.276316i	0.124412	−	0.992231i	$-0.460296\pi$
$409$	−11.6039	−	5.58814i	−0.573775	−	0.276316i	−0.698188	+	0.715915i	$0.746010\pi$
$410$	24.3810	+	11.7413i	1.20409	+	0.579859i
$411$	0.0865628	−	0.0197574i	0.00426983	−	0.000974560i
$412$	−16.7964	−	13.3947i	−0.827500	−	0.659909i
$413$	−12.4452			−0.612389
$414$			39.7490i			1.95356i
$415$	−6.09253	+	1.39058i	−0.299071	+	0.0682609i
$416$	6.60743	−	28.9490i	0.323956	−	1.41934i
$417$	0.164660	+	0.206477i	0.00806344	+	0.0101112i
$418$	12.8442	−	56.2742i	0.628231	−	2.75246i
$419$	−15.8969	+	7.65556i	−0.776616	+	0.373998i	−0.779826	−	0.625996i	$-0.784692\pi$
$419$	−15.8969	+	7.65556i	−0.776616	+	0.373998i	0.00321014	+	0.999995i	$0.498978\pi$
$420$	0.0189055	+	0.0828303i	0.000922492	+	0.00404170i
$421$	0.868857	−	1.80420i	0.0423455	−	0.0879314i	−0.878723	−	0.477333i	$-0.841604\pi$
$421$	0.868857	−	1.80420i	0.0423455	−	0.0879314i	0.921068	+	0.389401i	$0.127318\pi$
$422$	−34.6162	−	43.4073i	−1.68509	−	2.11304i
$423$	−2.83939	−	3.56048i	−0.138056	−	0.173116i
$424$	−8.40557	+	1.91852i	−0.408210	+	0.0931714i
$425$	−13.3631	+	10.6567i	−0.648206	+	0.516927i
$426$	−0.0337205	+	0.00769649i	−0.00163377	+	0.000372896i
$427$	2.67191			0.129303
$428$	−1.73850	+	2.18001i	−0.0840336	+	0.105375i
$429$	0.118141	−	0.245323i	0.00570391	−	0.0118443i
$430$	41.0497			1.97959
$431$	8.15135	−	3.92548i	0.392637	−	0.189084i	−0.227140	−	0.973862i	$-0.572937\pi$
$431$	8.15135	−	3.92548i	0.392637	−	0.189084i	0.619777	+	0.784778i	$0.287223\pi$
$432$	−0.234580	+	0.187071i	−0.0112862	+	0.00900048i
$433$	−0.929889	+	0.447811i	−0.0446876	+	0.0215204i	−0.456094	−	0.889932i	$-0.650752\pi$
$433$	−0.929889	+	0.447811i	−0.0446876	+	0.0215204i	0.411406	+	0.911452i	$0.365038\pi$
$434$	4.59850	+	5.76633i	0.220735	+	0.276793i
$435$	−0.0167244	−	0.0732744i	−0.000801874	−	0.00351324i
$436$	3.60970	−	4.52643i	0.172874	−	0.216777i
$437$	−23.5018	−	29.4703i	−1.12424	−	1.40976i
$438$	0.114400	+	0.237555i	0.00546626	+	0.0113508i
$439$	1.60324	+	3.32917i	0.0765187	+	0.158893i	0.935719	−	0.352747i	$-0.114752\pi$
$439$	1.60324	+	3.32917i	0.0765187	+	0.158893i	−0.859200	+	0.511640i	$0.829038\pi$
$440$	5.52774	+	1.26167i	0.263524	+	0.0601477i
$441$	13.5627	−	6.53145i	0.645843	−	0.311021i
$442$	−23.3934	−	48.5769i	−1.11271	−	2.31057i
$443$	7.48301	+	32.7852i	0.355528	+	1.55767i	0.764193	+	0.644987i	$0.223137\pi$
$443$	7.48301	+	32.7852i	0.355528	+	1.55767i	−0.408665	+	0.912684i	$0.634006\pi$
$444$	−0.0996422	+	0.206909i	−0.00472881	+	0.00981947i
$445$	4.54777	+	2.19009i	0.215585	+	0.103820i
$446$	21.5863	+	17.2145i	1.02214	+	0.815129i
$447$	−0.0110420	+	0.0483783i	−0.000522270	+	0.00228821i
$448$	−3.32093	−	14.5499i	−0.156899	−	0.687420i
$449$	16.4630	−	20.6440i	0.776939	−	0.974251i	−0.223061	−	0.974805i	$-0.571605\pi$
$449$	16.4630	−	20.6440i	0.776939	−	0.974251i	1.00000		0.000553862i	$0.000176300\pi$
$450$	−14.8717	−	3.39437i	−0.701059	−	0.160012i
$451$	−29.3935	−	23.4405i	−1.38409	−	1.10377i
$452$	−0.354038	−	0.0808068i	−0.0166525	−	0.00380083i
$453$	0.132020	+	0.165548i	0.00620286	+	0.00777814i
$454$	−4.79260	+	6.00974i	−0.224928	+	0.282051i
$455$	5.16744	+	6.47977i	0.242254	+	0.303776i
$456$	−0.0160430	+	0.0702890i	−0.000751283	+	0.00329159i
$457$	−34.8437	−	16.7798i	−1.62992	−	0.784928i	−0.999966	−	0.00829483i	$-0.997360\pi$
$457$	−34.8437	−	16.7798i	−1.62992	−	0.784928i	−0.629954	−	0.776633i	$-0.716926\pi$
$458$	−19.4155	+	24.3462i	−0.907225	+	1.13762i
$459$	−0.149384	+	0.654494i	−0.00697265	+	0.0305492i
$460$	18.7818	−	14.9780i	0.875705	−	0.698351i
$461$	−13.7870	−	28.6289i	−0.642122	−	1.33338i	−0.927088	−	0.374843i	$-0.877697\pi$
$461$	−13.7870	−	28.6289i	−0.642122	−	1.33338i	0.284966	−	0.958538i	$-0.408018\pi$
$462$		−	0.217879i		−	0.0101366i
$463$			2.70816i			0.125859i	0.998018	+	0.0629294i	$0.0200443\pi$
$463$			2.70816i			0.125859i	−0.998018	+	0.0629294i	$0.979956\pi$
$464$	2.05629	+	9.00921i	0.0954610	+	0.418242i
$465$	−0.0624073	+	0.0142441i	−0.00289407	+	0.000660552i
$466$	−39.8951	+	31.8153i	−1.84811	+	1.47381i
$467$	−18.3193	−	38.0404i	−0.847717	−	1.76030i	−0.616418	−	0.787419i	$-0.711417\pi$
$467$	−18.3193	−	38.0404i	−0.847717	−	1.76030i	−0.231299	−	0.972883i	$-0.574297\pi$
$468$	11.3106	−	23.4867i	0.522833	−	1.08567i
$469$	10.5748	+	2.41362i	0.488297	+	0.111451i
$470$	−1.13048	+	4.95298i	−0.0521454	+	0.228464i
$471$			0.301526i			0.0138936i
$472$	2.92029	−	6.06405i	0.134417	−	0.279121i
$473$	−55.6006	−	12.6905i	−2.55652	−	0.583509i
$474$	−0.350138	−	0.0799166i	−0.0160824	−	0.00367069i
$475$	13.0330	−	6.27634i	0.597993	−	0.287978i
$476$	−18.2734	−	14.5725i	−0.837559	−	0.667931i
$477$	33.9706			1.55541
$478$			13.6965i			0.626464i
$479$	37.4178	−	18.0195i	1.70966	−	0.823331i	0.717768	−	0.696283i	$-0.245164\pi$
$479$	37.4178	−	18.0195i	1.70966	−	0.823331i	0.991897	−	0.127048i	$-0.0405503\pi$
$480$	0.201047	+	0.0458876i	0.00917649	+	0.00209447i
$481$			22.4027i			1.02147i
$482$	−31.4276	−	15.1347i	−1.43149	−	0.689368i
$483$	−0.111240	−	0.0887113i	−0.00506161	−	0.00403650i
$484$	−22.6133	−	10.8900i	−1.02788	−	0.495000i
$485$	11.7400	+	24.3784i	0.533088	+	1.10697i
$486$	−0.809719	+	0.389940i	−0.0367296	+	0.0176880i
$487$	2.87897			0.130459			0.0652293	−	0.997870i	$-0.479222\pi$
$487$	2.87897			0.130459			0.0652293	+	0.997870i	$0.479222\pi$
$488$	−0.626968	+	1.30191i	−0.0283815	+	0.0589348i
$489$	0.0698378	−	0.0159400i	0.00315818	−	0.000720833i
$490$	−15.1302	−	7.28632i	−0.683512	−	0.329162i
$491$	4.38441	+	19.2093i	0.197865	+	0.866905i	0.972204	+	0.234134i	$0.0752255\pi$
$491$	4.38441	+	19.2093i	0.197865	+	0.866905i	−0.774339	+	0.632771i	$0.781917\pi$
$492$	0.238201	+	0.189959i	0.0107389	+	0.00856401i
$493$	16.1652	+	12.8914i	0.728046	+	0.580597i
$494$	10.1538	+	44.4868i	0.456842	+	2.00156i
$495$	−20.1277	−	9.69297i	−0.904671	−	0.435666i
$496$	7.67307	−	1.75133i	0.344531	−	0.0786370i
$497$	−0.634616	+	1.31779i	−0.0284664	+	0.0591111i
$498$	−0.129872			−0.00581971
$499$	9.56401	−	4.60579i	0.428144	−	0.206183i	−0.207386	−	0.978259i	$-0.566496\pi$
$499$	9.56401	−	4.60579i	0.428144	−	0.206183i	0.635530	+	0.772076i	$0.280781\pi$
$500$	12.2165	+	25.3679i	0.546339	+	1.13449i
$501$	0.156586	+	0.0754078i	0.00699574	+	0.00336897i
$502$	13.4768	+	10.7474i	0.601499	+	0.479679i
$503$	18.0931	+	8.71318i	0.806732	+	0.388502i	0.791337	−	0.611380i	$-0.209385\pi$
$503$	18.0931	+	8.71318i	0.806732	+	0.388502i	0.0153947	+	0.999881i	$0.495100\pi$
$504$		−	3.21503i		−	0.143209i
$505$	4.35451	+	0.993889i	0.193773	+	0.0442275i
$506$	−55.5049	+	26.7298i	−2.46749	+	1.18828i
$507$			0.00810147i			0.000359799i
$508$	39.6155			1.75765
$509$	−14.6151	−	11.6551i	−0.647801	−	0.516604i	0.243567	−	0.969884i	$-0.421682\pi$
$509$	−14.6151	−	11.6551i	−0.647801	−	0.516604i	−0.891368	+	0.453280i	$0.850254\pi$
$510$	0.337360	−	0.162464i	0.0149385	−	0.00719402i
$511$	10.8703	+	2.48108i	0.480874	+	0.109756i
$512$	−29.3779	−	6.70530i	−1.29833	−	0.296335i
$513$	0.246516	−	0.511896i	0.0108840	−	0.0226008i
$514$		−	6.42746i		−	0.283503i
$515$	3.23867	−	14.1896i	0.142713	−	0.625267i
$516$	0.450580	+	0.102842i	0.0198357	+	0.00452737i
$517$	3.06241	−	6.35917i	0.134685	−	0.279676i
$518$	7.77786	+	16.1509i	0.341739	+	0.709629i
$519$	−0.0523420	+	0.0417414i	−0.00229756	+	0.00183224i
$520$	−4.36988	+	0.997397i	−0.191632	+	0.0437388i
$521$	2.01808	+	8.84178i	0.0884136	+	0.387365i	0.999702	−	0.0244029i	$-0.00776845\pi$
$521$	2.01808	+	8.84178i	0.0884136	+	0.387365i	−0.911289	+	0.411768i	$0.864911\pi$
$522$			18.4528i			0.807659i
$523$		−	16.1512i		−	0.706243i	−0.935577	−	0.353122i	$-0.885120\pi$
$523$		−	16.1512i		−	0.706243i	0.935577	−	0.353122i	$-0.114880\pi$
$524$	0.380475	+	0.790064i	0.0166211	+	0.0345141i
$525$	0.0426898	−	0.0340440i	0.00186314	−	0.00148580i
$526$	7.55814	−	33.1144i	0.329551	−	1.44386i
$527$	10.9795	−	13.7678i	0.478273	−	0.599735i
$528$	−0.209476	−	0.100878i	−0.00911628	−	0.00439017i
$529$	−3.83417	+	16.7986i	−0.166703	+	0.730374i
$530$	−23.6282	−	29.6288i	−1.02634	−	1.28699i
$531$	−16.5345	+	20.7336i	−0.717536	+	0.899762i
$532$	12.3331	+	15.4653i	0.534710	+	0.670505i
$533$	28.9756	+	6.61350i	1.25507	+	0.286462i
$534$	0.0820148	+	0.0654047i	0.00354913	+	0.00283034i
$535$	−1.84167	−	0.420349i	−0.0796222	−	0.0181733i
$536$	−3.65745	+	4.58629i	−0.157978	+	0.198098i
$537$	−0.0525955	−	0.230436i	−0.00226966	−	0.00994404i
$538$	10.7887	−	47.2683i	0.465133	−	2.03788i
$539$	18.2408	+	14.5466i	0.785688	+	0.626565i
$540$	0.326238	+	0.157108i	0.0140390	+	0.00676084i
$541$	15.3323	−	31.8378i	0.659186	−	1.36881i	−0.256352	−	0.966584i	$-0.582520\pi$
$541$	15.3323	−	31.8378i	0.659186	−	1.36881i	0.915538	−	0.402231i	$-0.131765\pi$
$542$	8.64301	+	37.8675i	0.371249	+	1.62655i
$543$	0.0242120	+	0.0502768i	0.00103904	+	0.00215758i
$544$	−51.1121	+	24.6143i	−2.19141	+	1.05533i
$545$	3.82391	+	0.872783i	0.163798	+	0.0373859i
$546$	0.0747327	+	0.155184i	0.00319826	+	0.00664126i
$547$	−13.3329	−	27.6860i	−0.570073	−	1.18377i	−0.964314	−	0.264762i	$-0.914707\pi$
$547$	−13.3329	−	27.6860i	−0.570073	−	1.18377i	0.394241	−	0.919007i	$-0.371008\pi$
$548$	8.21426	+	10.3004i	0.350896	+	0.440009i
$549$	3.54985	−	4.45137i	0.151504	−	0.189980i
$550$	−5.26083	−	23.0492i	−0.224322	−	0.982821i
$551$	−10.9103	−	13.6811i	−0.464795	−	0.582835i
$552$	0.0693282	−	0.0333867i	0.00295080	−	0.00142103i
$553$	−11.8739	+	9.46915i	−0.504931	+	0.402669i
$554$	56.9178	−	27.4101i	2.41820	−	1.16455i
$555$	−0.155583			−0.00660414
$556$	−17.0025	+	35.3060i	−0.721066	+	1.49731i
$557$	4.66159	−	5.84544i	0.197518	−	0.247679i	−0.673202	−	0.739458i	$-0.735082\pi$
$557$	4.66159	−	5.84544i	0.197518	−	0.247679i	0.870720	+	0.491779i	$0.163653\pi$
$558$	15.7161			0.665317
$559$	43.9544	−	10.0323i	1.85907	−	0.424321i
$560$	5.53295	−	4.41238i	0.233810	−	0.186457i
$561$	−0.507169	+	0.115758i	−0.0214127	+	0.00488731i
$562$	27.5935	+	34.6011i	1.16396	+	1.45956i
$563$	−9.95430	−	12.4823i	−0.419524	−	0.526066i	0.526495	−	0.850178i	$-0.323506\pi$
$563$	−9.95430	−	12.4823i	−0.419524	−	0.526066i	−0.946019	+	0.324112i	$0.894934\pi$
$564$	−0.0248174	+	0.0515339i	−0.00104500	+	0.00216997i
$565$	−0.0547445	−	0.239852i	−0.00230312	−	0.0100906i
$566$	48.3532	−	23.2857i	2.03244	−	0.978769i
$567$	−2.81857	+	12.3489i	−0.118369	+	0.518607i
$568$	−0.493194	−	0.618445i	−0.0206939	−	0.0259494i
$569$	3.47380	−	15.2197i	0.145629	−	0.638044i	−0.848440	−	0.529292i	$-0.822458\pi$
$569$	3.47380	−	15.2197i	0.145629	−	0.638044i	0.994069	−	0.108752i	$-0.0346853\pi$
$570$	−0.308955	+	0.0705169i	−0.0129407	+	0.00295363i
$571$			28.6023i			1.19697i	0.801135	+	0.598484i	$0.204230\pi$
$571$			28.6023i			1.19697i	−0.801135	+	0.598484i	$0.795770\pi$
$572$	40.4025			1.68931
$573$	−0.0194821	−	0.0155365i	−0.000813877	−	0.000649046i
$574$	23.1857	−	5.29198i	0.967751	−	0.220883i
$575$	−13.9100	−	6.69872i	−0.580088	−	0.279356i
$576$	−28.6522	−	13.7982i	−1.19384	−	0.574924i
$577$			39.1763i			1.63093i	0.578805	+	0.815466i	$0.303519\pi$
$577$			39.1763i			1.63093i	−0.578805	+	0.815466i	$0.696481\pi$
$578$	−29.2842	+	60.8093i	−1.21806	+	2.52933i
$579$	0.103668	−	0.0826728i	0.00430831	−	0.00343576i
$580$	8.71913	−	6.95328i	0.362042	−	0.288719i
$581$	−3.42421	+	4.29382i	−0.142060	+	0.178138i
$582$	0.125129	+	0.548226i	0.00518676	+	0.0227247i
$583$	22.8440	+	47.4360i	0.946101	+	1.96460i
$584$	−3.75967	+	4.71447i	−0.155576	+	0.195086i
$585$	17.6606			0.730177
$586$	−47.7720	+	10.9037i	−1.97344	+	0.450426i
$587$	−2.94850	+	12.9182i	−0.121698	+	0.533193i	0.876920	+	0.480636i	$0.159594\pi$
$587$	−2.94850	+	12.9182i	−0.121698	+	0.533193i	−0.998618	+	0.0525568i	$0.983263\pi$
$588$	−0.147821	−	0.117884i	−0.00609605	−	0.00486144i
$589$	−11.6521	+	9.29223i	−0.480116	+	0.382880i
$590$	29.5842			1.21796
$591$	0.0714540	−	0.211934i	0.00293922	−	0.00871780i
$592$	19.1292			0.786206
$593$	−14.3081	+	11.4103i	−0.587564	+	0.468567i	−0.871580	−	0.490253i	$-0.836904\pi$
$593$	−14.3081	+	11.4103i	−0.587564	+	0.468567i	0.284016	+	0.958819i	$0.408333\pi$
$594$	−0.725998	−	0.578964i	−0.0297881	−	0.0237552i
$595$	3.52346	−	15.4373i	0.144448	−	0.632867i
$596$	−7.17844	+	1.63843i	−0.294041	+	0.0671128i
$597$	−0.00288696			−0.000118156
$598$	30.3650	−	38.0765i	1.24172	−	1.55706i
$599$	7.78402	+	16.1637i	0.318047	+	0.660430i	0.997297	−	0.0734761i	$-0.0234093\pi$
$599$	7.78402	+	16.1637i	0.318047	+	0.660430i	−0.679250	+	0.733907i	$0.737695\pi$
$600$	0.00657102	+	0.0287895i	0.000268261	+	0.00117533i
$601$	−14.5377	+	18.2297i	−0.593004	+	0.743603i	−0.984269	−	0.176675i	$-0.943466\pi$
$601$	−14.5377	+	18.2297i	−0.593004	+	0.743603i	0.391266	+	0.920278i	$0.372037\pi$
$602$	28.2052	−	22.4929i	1.14956	−	0.916743i
$603$	18.0705	−	14.4107i	0.735888	−	0.586851i
$604$	−13.6322	+	28.3075i	−0.554686	+	1.15182i
$605$		−	17.0039i		−	0.691305i
$606$	0.0836311	+	0.0402746i	0.00339728	+	0.00163604i
$607$	24.9868	+	12.0330i	1.01418	+	0.488404i	0.865728	−	0.500515i	$-0.166856\pi$
$607$	24.9868	+	12.0330i	1.01418	+	0.488404i	0.148454	+	0.988919i	$0.452570\pi$
$608$	46.8085	−	10.6837i	1.89834	−	0.433283i
$609$	−0.0516415	−	0.0411827i	−0.00209262	−	0.00166881i
$610$	−6.35154			−0.257166
$611$			5.57973i			0.225732i
$612$	−48.5554	+	11.0825i	−1.96274	+	0.447982i
$613$	0.291392	−	1.27667i	0.0117692	−	0.0515643i	−0.968702	−	0.248225i	$-0.920153\pi$
$613$	0.291392	−	1.27667i	0.0117692	−	0.0515643i	0.980472	+	0.196661i	$0.0630098\pi$
$614$	−9.74941	−	12.2254i	−0.393454	−	0.493376i
$615$	−0.0459298	+	0.201232i	−0.00185207	+	0.00811444i
$616$	4.48942	−	2.16199i	0.180884	−	0.0871091i
$617$	0.297724	+	1.30441i	0.0119859	+	0.0525137i	0.980567	−	0.196183i	$-0.0628548\pi$
$617$	0.297724	+	1.30441i	0.0119859	+	0.0525137i	−0.968581	+	0.248697i	$0.919998\pi$
$618$	0.131238	−	0.272519i	0.00527918	−	0.0109623i
$619$	2.69160	+	3.37516i	0.108185	+	0.135659i	0.832976	−	0.553309i	$-0.186635\pi$
$619$	2.69160	+	3.37516i	0.108185	+	0.135659i	−0.724791	+	0.688968i	$0.758064\pi$
$620$	−5.92205	−	7.42602i	−0.237835	−	0.298236i
$621$	−0.591194	+	0.134936i	−0.0237238	+	0.00541480i
$622$	−42.1207	+	33.5901i	−1.68888	+	1.34684i
$623$	4.32481	−	0.987110i	0.173270	−	0.0395477i
$624$	0.183801			0.00735792
$625$	−4.30493	+	5.39821i	−0.172197	+	0.215929i
$626$	−1.16677	+	2.42282i	−0.0466335	+	0.0968354i
$627$	0.440270			0.0175827
$628$	−40.3101	+	19.4123i	−1.60855	+	0.774636i
$629$	33.4630	−	26.6859i	1.33426	−	1.06404i
$630$	12.7322	−	6.13149i	0.507262	−	0.244284i
$631$	1.04195	+	1.30656i	0.0414792	+	0.0520133i	0.802138	−	0.597138i	$-0.203696\pi$
$631$	1.04195	+	1.30656i	0.0414792	+	0.0520133i	−0.760659	+	0.649151i	$0.775124\pi$
$632$	−1.82769	−	8.00765i	−0.0727017	−	0.318527i
$633$	0.264035	−	0.331090i	0.0104945	−	0.0131596i
$634$	6.54686	+	8.20951i	0.260009	+	0.326041i
$635$	11.6448	+	24.1806i	0.462109	+	0.959580i
$636$	−0.185125	−	0.384415i	−0.00734067	−	0.0152431i
$637$	−17.9815	−	4.10417i	−0.712454	−	0.162613i
$638$	−25.7672	+	12.4089i	−1.02014	+	0.491271i
$639$	1.35229	+	2.80806i	0.0534958	+	0.111085i
$640$	2.13494	+	9.35378i	0.0843909	+	0.369741i
$641$	11.7083	−	24.3126i	0.462452	−	0.960291i	−0.531142	−	0.847283i	$-0.678237\pi$
$641$	11.7083	−	24.3126i	0.462452	−	0.960291i	0.993594	−	0.113008i	$-0.0360486\pi$
$642$	−0.0353703	−	0.0170335i	−0.00139596	−	0.000672257i
$643$	0.125193	+	0.0998383i	0.00493714	+	0.00393724i	0.625955	−	0.779859i	$-0.284709\pi$
$643$	0.125193	+	0.0998383i	0.00493714	+	0.00393724i	−0.621018	+	0.783796i	$0.713281\pi$
$644$	4.69786	−	20.5827i	0.185122	−	0.811071i
$645$	0.0696729	+	0.305257i	0.00274337	+	0.0120195i
$646$	54.3551	−	68.1592i	2.13857	−	2.68169i
$647$	16.9358	+	3.86548i	0.665814	+	0.151968i	0.542053	−	0.840344i	$-0.317647\pi$
$647$	16.9358	+	3.86548i	0.665814	+	0.151968i	0.123761	+	0.992312i	$0.460504\pi$
$648$	−5.35576	−	4.27108i	−0.210394	−	0.167784i
$649$	−40.0709	−	9.14593i	−1.57292	−	0.359009i
$650$	11.6529	+	14.6123i	0.457065	+	0.573142i
$651$	−0.0350750	+	0.0439827i	−0.00137470	+	0.00172382i
$652$	6.62716	+	8.31020i	0.259540	+	0.325453i
$653$	−7.29814	+	31.9752i	−0.285598	+	1.25129i	0.604900	+	0.796301i	$0.293213\pi$
$653$	−7.29814	+	31.9752i	−0.285598	+	1.25129i	−0.890498	+	0.454986i	$0.849644\pi$
$654$	0.0734405	+	0.0353671i	0.00287175	+	0.00138296i
$655$	−0.370403	+	0.464471i	−0.0144729	+	0.0181484i
$656$	5.64714	−	24.7417i	0.220484	−	0.966002i
$657$	18.5755	−	14.8135i	0.724701	−	0.577930i
$658$	1.93719	+	4.02262i	0.0755197	+	0.156818i
$659$			22.7626i			0.886707i	0.896347	+	0.443353i	$0.146211\pi$
$659$			22.7626i			0.886707i	−0.896347	+	0.443353i	$0.853789\pi$
$660$			0.280589i			0.0109219i
$661$	−6.01254	−	26.3427i	−0.233861	−	1.02461i	−0.946405	−	0.322984i	$-0.895314\pi$
$661$	−6.01254	−	26.3427i	−0.233861	−	1.02461i	0.712544	−	0.701628i	$-0.247543\pi$
$662$	10.4400	−	2.38285i	0.405761	−	0.0926122i
$663$	0.321526	−	0.256408i	0.0124870	−	0.00995807i
$664$	−1.28871	−	2.67603i	−0.0500117	−	0.103850i
$665$	−5.81448	+	12.0739i	−0.225476	+	0.468205i
$666$	37.2407	+	8.49996i	1.44305	+	0.329367i
$667$	−4.15589	+	18.2081i	−0.160917	+	0.705022i
$668$			25.7883i			0.997780i
$669$	−0.0913735	+	0.189739i	−0.00353270	+	0.00733573i
$670$	−25.1378	−	5.73755i	−0.971160	−	0.221661i
$671$	8.60297	+	1.96357i	0.332114	+	0.0758028i
$672$	0.163283	−	0.0786328i	0.00629877	−	0.00303333i
$673$	−19.8613	−	15.8388i	−0.765595	−	0.610542i	0.160847	−	0.986979i	$-0.448578\pi$
$673$	−19.8613	−	15.8388i	−0.765595	−	0.610542i	−0.926442	+	0.376437i	$0.877149\pi$
$674$	−19.2746			−0.742431
$675$		−	0.232712i		−	0.00895709i
$676$	−1.08306	+	0.521576i	−0.0416563	+	0.0200606i
$677$	−20.0027	−	4.56549i	−0.768768	−	0.175466i	−0.179888	−	0.983687i	$-0.557574\pi$
$677$	−20.0027	−	4.56549i	−0.768768	−	0.175466i	−0.588880	+	0.808221i	$0.700431\pi$
$678$		−	0.00511282i		−	0.000196357i
$679$	21.4246	+	10.3175i	0.822199	+	0.395950i
$680$	6.69518	+	5.33923i	0.256749	+	0.204750i
$681$	−0.0528244	−	0.0254389i	−0.00202423	−	0.000974820i
$682$	10.5685	+	21.9458i	0.404690	+	0.840347i
$683$	1.13764	−	0.547861i	0.0435307	−	0.0209633i	−0.411992	−	0.911188i	$-0.635167\pi$
$683$	1.13764	−	0.547861i	0.0435307	−	0.0209633i	0.455522	+	0.890224i	$0.349452\pi$
$684$	42.1506			1.61167
$685$	−3.87262	+	8.04158i	−0.147965	+	0.307253i
$686$	−34.4590	+	7.86504i	−1.31565	+	0.300288i
$687$	−0.213998	−	0.103056i	−0.00816455	−	0.00393184i
$688$	−8.56639	−	37.5318i	−0.326590	−	1.43089i
$689$	−32.5412	−	25.9508i	−1.23972	−	0.988645i
$690$	0.264436	+	0.210881i	0.0100669	+	0.00802809i
$691$	2.48461	+	10.8858i	0.0945190	+	0.414115i	0.999946	−	0.0103872i	$-0.00330640\pi$
$691$	2.48461	+	10.8858i	0.0945190	+	0.414115i	−0.905427	+	0.424502i	$0.860449\pi$
$692$	−8.95009	−	4.31014i	−0.340231	−	0.163847i
$693$	−19.1409	+	4.36878i	−0.727102	+	0.165956i
$694$	−1.43365	+	2.97700i	−0.0544206	+	0.113006i
$695$	−26.5480			−1.00702
$696$	0.0321845	−	0.0154992i	0.00121995	−	0.000587497i
$697$	−24.6369	−	51.1590i	−0.933189	−	1.93779i
$698$	−31.4469	−	15.1440i	−1.19028	−	0.573210i
$699$	−0.304300	−	0.242671i	−0.0115097	−	0.00917867i
$700$	7.29963	+	3.51532i	0.275900	+	0.132867i
$701$			37.4505i			1.41449i	0.706970	+	0.707243i	$0.250061\pi$
$701$			37.4505i			1.41449i	−0.706970	+	0.707243i	$0.749939\pi$
$702$	0.715677	+	0.163349i	0.0270115	+	0.00616520i
$703$	−32.6363	+	15.7168i	−1.23090	+	0.592771i
$704$		−	49.2883i		−	1.85762i
$705$	−0.0387504			−0.00145942
$706$	48.1091	+	38.3657i	1.81061	+	1.44391i
$707$	3.53658	−	1.70312i	0.133007	−	0.0640526i
$708$	0.324730	+	0.0741174i	0.0122041	+	0.00278550i
$709$	−4.91286	−	1.12133i	−0.184507	−	0.0421124i	0.129269	−	0.991610i	$-0.458737\pi$
$709$	−4.91286	−	1.12133i	−0.184507	−	0.0421124i	−0.313776	+	0.949497i	$0.601594\pi$
$710$	1.50858	−	3.13260i	0.0566160	−	0.117564i
$711$			32.3624i			1.21369i
$712$	−0.533846	+	2.33893i	−0.0200067	+	0.0876553i
$713$	15.5077	+	3.53954i	0.580769	+	0.132557i
$714$	0.142778	−	0.296482i	0.00534335	−	0.0110956i
$715$	11.8761	+	24.6610i	0.444142	+	0.922269i
$716$	27.4202	−	21.8669i	1.02474	−	0.817204i
$717$	−0.101851	+	0.0232468i	−0.00380369	+	0.000868168i
$718$	10.9661	+	48.0456i	0.409251	+	1.79305i
$719$			27.6327i			1.03053i	0.857032	+	0.515263i	$0.172306\pi$
$719$			27.6327i			1.03053i	−0.857032	+	0.515263i	$0.827694\pi$
$720$		−	15.0801i		−	0.562001i
$721$	−5.54978	−	11.5242i	−0.206685	−	0.429185i
$722$	−26.6516	+	21.2539i	−0.991869	+	0.790989i
$723$	0.0592044	−	0.259392i	0.00220184	−	0.00964688i
$724$	−5.16258	+	6.47367i	−0.191866	+	0.240592i
$725$	−6.45750	−	3.10977i	−0.239826	−	0.115494i
$726$	0.0786338	−	0.344517i	0.00291837	−	0.0127862i
$727$	−21.6562	−	27.1560i	−0.803183	−	1.00716i	−0.999645	−	0.0266477i	$-0.991517\pi$
$727$	−21.6562	−	27.1560i	−0.803183	−	1.00716i	0.196462	−	0.980511i	$-0.437055\pi$
$728$	−2.45602	+	3.07976i	−0.0910263	+	0.114143i
$729$	16.8257	+	21.0987i	0.623173	+	0.781434i
$730$	−25.8404	−	5.89790i	−0.956396	−	0.218291i
$731$	−67.3434	−	53.7046i	−2.49079	−	1.98634i
$732$	−0.0697174	−	0.0159125i	−0.00257683	−	0.000588144i
$733$	17.8291	−	22.3570i	0.658532	−	0.825774i	−0.334650	−	0.942342i	$-0.608618\pi$
$733$	17.8291	−	22.3570i	0.658532	−	0.825774i	0.993183	+	0.116569i	$0.0371896\pi$
$734$	0.228169	+	0.999676i	0.00842189	+	0.0368987i
$735$	0.0285028	−	0.124879i	0.00105134	−	0.00460623i
$736$	−40.0637	−	31.9497i	−1.47677	−	1.17768i
$737$	32.2747	+	15.5427i	1.18885	+	0.572522i
$738$	21.9877	−	45.6579i	0.809378	−	1.68069i
$739$	0.113103	+	0.495536i	0.00416056	+	0.0182286i	0.976966	−	0.213397i	$-0.0684527\pi$
$739$	0.113103	+	0.495536i	0.00416056	+	0.0182286i	−0.972805	+	0.231626i	$0.925596\pi$
$740$	−10.0165	−	20.7995i	−0.368214	−	0.764605i
$741$	−0.313582	+	0.151013i	−0.0115197	+	0.00554761i
$742$	−32.4698	−	7.41102i	−1.19200	−	0.272067i
$743$	5.07360	+	10.5354i	0.186132	+	0.386507i	0.973065	−	0.230531i	$-0.0740464\pi$
$743$	5.07360	+	10.5354i	0.186132	+	0.386507i	−0.786933	+	0.617039i	$0.788332\pi$
$744$	−0.0132006	−	0.0274113i	−0.000483957	−	0.00100495i
$745$	−3.11014	−	3.89999i	−0.113947	−	0.142885i
$746$	34.8642	−	43.7183i	1.27647	−	1.60064i
$747$	2.60412	+	11.4094i	0.0952799	+	0.417448i
$748$	−48.1271	−	60.3495i	−1.75970	−	2.20659i
$749$	−1.49573	+	0.720308i	−0.0546529	+	0.0263195i
$750$	−0.309935	+	0.247165i	−0.0113172	+	0.00902519i
$751$	−2.80777	+	1.35215i	−0.102457	+	0.0493407i	−0.484410	−	0.874841i	$-0.660966\pi$
$751$	−2.80777	+	1.35215i	−0.102457	+	0.0493407i	0.381953	+	0.924182i	$0.375252\pi$
$752$	4.76442			0.173741
$753$	−0.0570465	+	0.118458i	−0.00207889	+	0.00431686i
$754$	14.0965	−	17.6764i	0.513363	−	0.643737i
$755$	−21.2856			−0.774661
$756$	0.310243	−	0.0708111i	0.0112834	−	0.00257537i
$757$	30.7495	−	24.5219i	1.11761	−	0.891264i	0.122741	−	0.992439i	$-0.460831\pi$
$757$	30.7495	−	24.5219i	1.11761	−	0.891264i	0.994869	+	0.101174i	$0.0322600\pi$
$758$	−36.4210	+	8.31286i	−1.32287	+	0.301937i
$759$	−0.292977	−	0.367381i	−0.0106344	−	0.0133351i
$760$	−4.51874	−	5.66632i	−0.163912	−	0.205539i
$761$	12.1321	−	25.1926i	0.439789	−	0.913231i	−0.556795	−	0.830650i	$-0.687969\pi$
$761$	12.1321	−	25.1926i	0.439789	−	0.913231i	0.996584	−	0.0825816i	$-0.0263165\pi$
$762$	0.124114	+	0.543778i	0.00449616	+	0.0196990i
$763$	3.10564	−	1.49560i	0.112432	−	0.0541443i
$764$	0.822762	−	3.60476i	0.0297665	−	0.130415i
$765$	−21.0372	−	26.3798i	−0.760601	−	0.953763i
$766$	−7.38831	+	32.3703i	−0.266951	+	1.16959i
$767$	31.6776	−	7.23020i	1.14381	−	0.261067i
$768$		−	0.138471i		−	0.00499666i
$769$	−13.0868			−0.471923			−0.235961	−	0.971762i	$-0.575824\pi$
$769$	−13.0868			−0.471923			−0.235961	+	0.971762i	$0.575824\pi$
$770$	17.1238	+	13.6558i	0.617100	+	0.492121i
$771$	0.0477963	−	0.0109092i	0.00172134	−	0.000392885i
$772$	17.7265	+	8.53663i	0.637991	+	0.307240i
$773$	−27.5640	−	13.2741i	−0.991407	−	0.477436i	−0.133393	−	0.991063i	$-0.542587\pi$
$773$	−27.5640	−	13.2741i	−0.991407	−	0.477436i	−0.858014	+	0.513627i	$0.828302\pi$
$774$		−	76.8733i		−	2.76315i
$775$	−2.64857	+	5.49980i	−0.0951393	+	0.197559i
$776$	−10.0546	+	8.01830i	−0.360940	+	0.287840i
$777$	−0.106901	+	0.0852508i	−0.00383505	+	0.00305835i
$778$	−20.8595	+	26.1570i	−0.747849	+	0.937773i
$779$	10.6936	+	46.8516i	0.383137	+	1.67863i
$780$	−0.0962425	−	0.199850i	−0.00344603	−	0.00715576i
$781$	−3.01177	+	3.77664i	−0.107769	+	0.135139i
$782$	−93.0457			−3.32731
$783$	−0.274452	+	0.0626419i	−0.00980811	+	0.00223864i
$784$	−3.50447	+	15.3541i	−0.125160	+	0.548360i
$785$	−23.6979	−	18.8985i	−0.845816	−	0.674515i
$786$	−0.00965271	+	0.00769778i	−0.000344301	+	0.000274571i
$787$	0.231569			0.00825454			0.00412727	−	0.999991i	$-0.498686\pi$
$787$	0.231569			0.00825454			0.00412727	+	0.999991i	$0.498686\pi$
$788$	32.9331	−	4.09191i	1.17319	−	0.145768i
$789$	0.259076			0.00922334
$790$	28.2262	−	22.5096i	1.00424	−	0.800857i
$791$	−0.169040	−	0.134805i	−0.00601037	−	0.00479311i
$792$	2.36271	−	10.3517i	0.0839553	−	0.367832i
$793$	−6.80097	+	1.55228i	−0.241510	+	0.0551230i
$794$	−22.9850			−0.815706
$795$	0.180224	−	0.225994i	0.00639189	−	0.00801518i
$796$	−0.185864	−	0.385950i	−0.00658777	−	0.0136796i
$797$	−5.59334	−	24.5060i	−0.198126	−	0.868047i	−0.972051	−	0.234770i	$-0.924566\pi$
$797$	−5.59334	−	24.5060i	−0.198126	−	0.868047i	0.773925	−	0.633277i	$-0.218291\pi$
$798$	−0.173643	+	0.217741i	−0.00614690	+	0.00770797i
$799$	8.33448	−	6.64652i	0.294853	−	0.235137i
$800$	15.3749	−	12.2611i	0.543585	−	0.433495i
$801$	4.10136	−	8.51655i	0.144914	−	0.300918i
$802$			56.1662i			1.98330i
$803$	33.1767	+	15.9771i	1.17078	+	0.563818i
$804$	−0.261550	−	0.125956i	−0.00922416	−	0.00444212i
$805$	13.9442	−	3.18268i	0.491470	−	0.112175i
$806$	−15.0549	−	12.0058i	−0.530285	−	0.422888i
$807$	0.369811			0.0130180
$808$			2.12287i			0.0746824i
$809$	−35.3265	+	8.06303i	−1.24201	+	0.283481i	−0.792544	−	0.609815i	$-0.791244\pi$
$809$	−35.3265	+	8.06303i	−1.24201	+	0.283481i	−0.449468	+	0.893296i	$0.648387\pi$
$810$	6.70017	−	29.3554i	0.235420	−	1.03144i
$811$	−32.6722	−	40.9696i	−1.14728	−	1.43864i	−0.879971	−	0.475027i	$-0.842438\pi$
$811$	−32.6722	−	40.9696i	−1.14728	−	1.43864i	−0.267305	−	0.963612i	$-0.586133\pi$
$812$	2.18091	−	9.55517i	0.0765348	−	0.335321i
$813$	−0.266923	+	0.128543i	−0.00936140	+	0.00450821i
$814$	13.1738	+	57.7183i	0.461742	+	2.02303i
$815$	−3.12439	+	6.48785i	−0.109442	+	0.227260i
$816$	−0.218942	−	0.274545i	−0.00766450	−	0.00961098i
$817$	45.4517	+	56.9946i	1.59015	+	1.99399i
$818$	26.2319	−	5.98726i	0.917178	−	0.209340i
$819$	12.1346	−	9.67701i	0.424017	−	0.338142i
$820$	−29.8591	+	6.81514i	−1.04272	+	0.237995i
$821$	5.65339			0.197305			0.0986523	−	0.995122i	$-0.468547\pi$
$821$	5.65339			0.197305			0.0986523	+	0.995122i	$0.468547\pi$
$822$	−0.115652	+	0.145023i	−0.00403381	+	0.00505824i
$823$	0.318077	−	0.660493i	0.0110875	−	0.0230233i	−0.895352	−	0.445360i	$-0.853076\pi$
$823$	0.318077	−	0.660493i	0.0110875	−	0.0230233i	0.906439	+	0.422337i	$0.138790\pi$
$824$	6.91756			0.240985
$825$	0.162471	−	0.0782418i	0.00565651	−	0.00272403i
$826$	20.3273	−	16.2105i	0.707276	−	0.564034i
$827$	−36.2154	+	17.4404i	−1.25933	+	0.606464i	−0.939999	−	0.341178i	$-0.889174\pi$
$827$	−36.2154	+	17.4404i	−1.25933	+	0.606464i	−0.319336	+	0.947642i	$0.603460\pi$
$828$	−28.0491	−	35.1724i	−0.974772	−	1.22233i
$829$	4.53758	+	19.8804i	0.157597	+	0.690477i	0.990552	+	0.137136i	$0.0437899\pi$
$829$	4.53758	+	19.8804i	0.157597	+	0.690477i	−0.832955	+	0.553340i	$0.813353\pi$
$830$	8.13988	−	10.2071i	0.282540	−	0.354293i
$831$	0.300434	+	0.376733i	0.0104220	+	0.0130687i
$832$	16.9059	+	35.1055i	0.586108	+	1.21707i
$833$	15.2890	+	31.7480i	0.529733	+	1.10000i
$834$	−0.537892	−	0.122770i	−0.0186257	−	0.00425119i
$835$	−15.7408	+	7.58035i	−0.544732	+	0.262329i
$836$	28.3447	+	58.8585i	0.980323	+	2.03566i
$837$	0.0533516	+	0.233749i	0.00184410	+	0.00807953i
$838$	15.9934	−	33.2106i	0.552482	−	1.14724i
$839$	−13.8965	−	6.69222i	−0.479762	−	0.231041i	0.178342	−	0.983969i	$-0.442927\pi$
$839$	−13.8965	−	6.69222i	−0.479762	−	0.231041i	−0.658104	+	0.752927i	$0.728641\pi$
$840$	−0.0213885	−	0.0170567i	−0.000737972	−	0.000588513i
$841$	4.52380	−	19.8201i	0.155993	−	0.683451i
$842$	0.930914	+	4.07860i	0.0320814	+	0.140558i
$843$	−0.210469	+	0.263920i	−0.00724895	+	0.00908990i
$844$	61.2611	+	13.9825i	2.10870	+	0.481296i
$845$	−0.636723	−	0.507769i	−0.0219039	−	0.0174678i
$846$	9.27538	+	2.11704i	0.318894	+	0.0727855i
$847$	−9.31715	−	11.6833i	−0.320141	−	0.401444i
$848$	−22.1589	+	27.7863i	−0.760938	+	0.954186i
$849$	0.255227	+	0.320045i	0.00875937	+	0.0109839i
$850$	7.94564	−	34.8121i	0.272533	−	1.19405i
$851$	34.8326	+	16.7745i	1.19405	+	0.575022i
$852$	0.0244070	−	0.0306054i	0.000836169	−	0.00104852i
$853$	−9.72240	+	42.5966i	−0.332889	+	1.45848i	0.480620	+	0.876929i	$0.340412\pi$
$853$	−9.72240	+	42.5966i	−0.332889	+	1.45848i	−0.813509	+	0.581552i	$0.802446\pi$
$854$	−4.36413	+	3.48028i	−0.149338	+	0.119093i
$855$	12.3900	+	25.7280i	0.423728	+	0.879880i
$856$		−	0.897833i		−	0.0306873i
$857$		−	14.9830i		−	0.511811i	−0.966702	−	0.255905i	$-0.917626\pi$
$857$		−	14.9830i		−	0.511811i	0.966702	−	0.255905i	$-0.0823735\pi$
$858$	0.126579	+	0.554580i	0.00432134	+	0.0189330i
$859$	−18.6587	+	4.25872i	−0.636626	+	0.145306i	−0.528639	−	0.848847i	$-0.677298\pi$
$859$	−18.6587	+	4.25872i	−0.636626	+	0.145306i	−0.107987	+	0.994152i	$0.534440\pi$
$860$	−36.3234	+	28.9669i	−1.23862	+	0.987763i
$861$	0.0787051	+	0.163433i	0.00268226	+	0.00556977i
$862$	−8.20081	+	17.0292i	−0.279321	+	0.580016i
$863$	−43.5262	−	9.93458i	−1.48165	−	0.338177i	−0.596172	−	0.802857i	$-0.703312\pi$
$863$	−43.5262	−	9.93458i	−1.48165	−	0.338177i	−0.885479	+	0.464680i	$0.846169\pi$
$864$	0.171874	−	0.753028i	0.00584726	−	0.0256185i
$865$		−	6.72993i		−	0.228824i
$866$	0.935531	−	1.94265i	0.0317906	−	0.0660140i
$867$	−0.501898	−	0.114555i	−0.0170453	−	0.00389049i
$868$	−8.13807	−	1.85746i	−0.276224	−	0.0630463i
$869$	−45.1904	+	21.7625i	−1.53298	+	0.738243i
$870$	0.122760	+	0.0978978i	0.00416195	+	0.00331905i
$871$	−28.3188			−0.959546
$872$			1.86420i			0.0631297i
$873$	45.6532	−	21.9854i	1.54513	−	0.744094i
$874$	76.7729	+	17.5229i	2.59688	+	0.592721i
$875$			16.7638i			0.566721i
$876$	−0.268860	−	0.129476i	−0.00908393	−	0.00437459i
$877$	−5.36910	−	4.28172i	−0.181302	−	0.144583i	0.528634	−	0.848850i	$-0.322705\pi$
$877$	−5.36910	−	4.28172i	−0.181302	−	0.144583i	−0.709935	+	0.704267i	$0.751276\pi$
$878$	−6.95504	−	3.34937i	−0.234721	−	0.113036i
$879$	−0.162165	−	0.336739i	−0.00546969	−	0.0113579i
$880$	21.0576	−	10.1408i	0.709850	−	0.341846i
$881$	−2.90036			−0.0977157			−0.0488578	−	0.998806i	$-0.515558\pi$
$881$	−2.90036			−0.0977157			−0.0488578	+	0.998806i	$0.515558\pi$
$882$	−13.6450	+	28.3341i	−0.459451	+	0.954059i
$883$	43.0413	−	9.82389i	1.44845	−	0.330600i	0.575260	−	0.817971i	$-0.304901\pi$
$883$	43.0413	−	9.82389i	1.44845	−	0.330600i	0.873195	+	0.487371i	$0.162044\pi$
$884$	54.9784	+	26.4762i	1.84913	+	0.890492i
$885$	0.0502127	+	0.219996i	0.00168788	+	0.00739509i
$886$	−54.9265	−	43.8024i	−1.84529	−	1.47157i
$887$	−34.1816	−	27.2589i	−1.14771	−	0.915265i	−0.150400	−	0.988625i	$-0.548056\pi$
$887$	−34.1816	−	27.2589i	−1.14771	−	0.915265i	−0.997306	+	0.0733603i	$0.976628\pi$
$888$	−0.0164547	−	0.0720928i	−0.000552184	−	0.00241928i
$889$	21.2507	+	10.2338i	0.712727	+	0.343231i
$890$	−10.2808	+	2.34651i	−0.344612	+	0.0786554i
$891$	−18.1504	+	37.6896i	−0.608060	+	1.26265i
$892$	−31.2483			−1.04627
$893$	−8.12857	+	3.91451i	−0.272012	+	0.130994i
$894$	−0.0449795	−	0.0934009i	−0.00150434	−	0.00312379i
$895$	21.4072	+	10.3092i	0.715565	+	0.344598i
$896$	6.59225	+	5.25715i	0.220232	+	0.175629i
$897$	0.334685	+	0.161176i	0.0111748	+	0.00538150i
$898$			55.1626i			1.84080i
$899$	7.19921	+	1.64317i	0.240107	+	0.0548029i
$900$	15.5547	−	7.49073i	0.518488	−	0.249691i
$901$			79.5194i			2.64917i
$902$	78.5419			2.61516
$903$	0.215135	+	0.171565i	0.00715926	+	0.00570932i
$904$	0.105350	−	0.0507341i	0.00350390	−	0.00168739i
$905$	−5.46894	−	1.24825i	−0.181794	−	0.0414932i
$906$	−0.431269	−	0.0984343i	−0.0143279	−	0.00327026i
$907$	1.52398	−	3.16457i	0.0506028	−	0.105078i	−0.874134	−	0.485684i	$-0.838570\pi$
$907$	1.52398	−	3.16457i	0.0506028	−	0.105078i	0.924737	+	0.380606i	$0.124285\pi$
$908$		−	8.69971i		−	0.288710i
$909$	1.86124	−	8.15464i	0.0617336	−	0.270472i
$910$	−16.8804	−	3.85284i	−0.559580	−	0.127720i
$911$	−11.3763	+	23.6231i	−0.376913	+	0.782667i	0.623087	+	0.782152i	$0.285878\pi$
$911$	−11.3763	+	23.6231i	−0.376913	+	0.782667i	−1.00000		0.000514741i	$0.999836\pi$
$912$	0.128947	+	0.267762i	0.00426987	+	0.00886647i
$913$	−14.1807	+	11.3088i	−0.469314	+	0.374265i
$914$	78.7681	−	17.9783i	2.60542	−	0.594670i
$915$	−0.0107803	−	0.0472317i	−0.000356387	−	0.00156143i
$916$		−	35.2437i		−	1.16448i
$917$			0.522097i			0.0172412i
$918$	−0.608514	−	1.26359i	−0.0200839	−	0.0417047i
$919$	12.3655	−	9.86113i	0.407899	−	0.325289i	−0.397953	−	0.917406i	$-0.630279\pi$
$919$	12.3655	−	9.86113i	0.407899	−	0.325289i	0.805852	+	0.592117i	$0.201708\pi$
$920$	−1.72125	+	7.54129i	−0.0567480	+	0.248629i
$921$	0.0743636	−	0.0932490i	0.00245036	−	0.00307266i
$922$	59.8092	+	28.8026i	1.96971	+	0.948564i
$923$	0.849738	−	3.72295i	0.0279695	−	0.122542i
$924$	0.153747	+	0.192793i	0.00505790	+	0.00634241i
$925$	−9.25054	+	11.5998i	−0.304156	+	0.381399i
$926$	−3.52750	−	4.42334i	−0.115921	−	0.145360i
$927$	−26.5726	−	6.06502i	−0.872759	−	0.199202i
$928$	−18.5989	−	14.8321i	−0.610539	−	0.486889i
$929$	−40.4012	−	9.22132i	−1.32552	−	0.302542i	−0.499566	−	0.866276i	$-0.666507\pi$
$929$	−40.4012	−	9.22132i	−1.32552	−	0.302542i	−0.825956	+	0.563734i	$0.809364\pi$
$930$	0.0833788	−	0.104554i	0.00273410	−	0.00342845i
$931$	−6.63614	−	29.0749i	−0.217491	−	0.952890i
$932$	12.8511	−	56.3043i	0.420951	−	1.84431i
$933$	−0.321275	−	0.256209i	−0.0105181	−	0.00838789i
$934$	79.4711	+	38.2713i	2.60037	+	1.25227i
$935$	22.6896	−	47.1154i	0.742029	−	1.54084i
$936$	1.86781	+	8.18342i	0.0610514	+	0.267484i
$937$	0.0577275	+	0.119872i	0.00188588	+	0.00391606i	0.901910	−	0.431925i	$-0.142165\pi$
$937$	0.0577275	+	0.119872i	0.00188588	+	0.00391606i	−0.900024	+	0.435841i	$0.856451\pi$
$938$	−20.4160	+	9.83184i	−0.666607	+	0.321021i
$939$	−0.0199971	−	0.00456420i	−0.000652580	−	0.000148947i
$940$	−2.49476	−	5.18043i	−0.0813703	−	0.168967i
$941$	18.3332	+	38.0693i	0.597645	+	1.24102i	0.952053	+	0.305932i	$0.0989681\pi$
$941$	18.3332	+	38.0693i	0.597645	+	1.24102i	−0.354408	+	0.935091i	$0.615318\pi$
$942$	−0.392751	−	0.492494i	−0.0127965	−	0.0160463i
$943$	31.9791	−	40.1005i	1.04138	−	1.30585i
$944$	−6.17373	−	27.0489i	−0.200938	−	0.880366i
$945$	0.134416	+	0.168553i	0.00437257	+	0.00548303i
$946$	107.345	−	51.6945i	3.49008	−	1.68073i
$947$	−14.7823	+	11.7885i	−0.480361	+	0.383075i	−0.833521	−	0.552488i	$-0.813679\pi$
$947$	−14.7823	+	11.7885i	−0.480361	+	0.383075i	0.353160	+	0.935563i	$0.385107\pi$
$948$	0.366217	−	0.176361i	0.0118942	−	0.00572793i
$949$	−29.1103			−0.944959
$950$	−13.1120	+	27.2274i	−0.425411	+	0.883374i
$951$	−0.0499362	+	0.0626180i	−0.00161929	+	0.00203053i
$952$	7.52585			0.243914
$953$	15.4740	−	3.53185i	0.501254	−	0.114408i	0.0355843	−	0.999367i	$-0.488671\pi$
$953$	15.4740	−	3.53185i	0.501254	−	0.114408i	0.465669	+	0.884959i	$0.345814\pi$
$954$	−55.4856	+	44.2483i	−1.79641	+	1.43259i
$955$	2.44213	−	0.557400i	0.0790255	−	0.0180370i
$956$	−9.66500	−	12.1195i	−0.312589	−	0.391974i
$957$	−0.136010	−	0.170551i	−0.00439657	−	0.00551312i
$958$	−37.6449	+	78.1704i	−1.21625	+	2.52557i
$959$	1.74545	+	7.64734i	0.0563637	+	0.246945i
$960$	−0.243803	+	0.117409i	−0.00786870	+	0.00378937i
$961$	−5.49867	+	24.0913i	−0.177376	+	0.777137i
$962$	−29.1805	−	36.5912i	−0.940818	−	1.17975i
$963$	−0.787182	+	3.44887i	−0.0253666	+	0.111138i
$964$	38.4889	−	8.78485i	1.23965	−	0.282941i
$965$			13.3293i			0.429084i
$966$	0.297244			0.00956367
$967$	47.6896	+	38.0312i	1.53360	+	1.22300i	0.888479	+	0.458917i	$0.151763\pi$
$967$	47.6896	+	38.0312i	1.53360	+	1.22300i	0.645116	+	0.764084i	$0.276809\pi$
$968$	7.87910	−	1.79835i	0.253244	−	0.0578013i
$969$	0.599106	+	0.288514i	0.0192460	+	0.00926841i
$970$	−50.9295	−	24.5264i	−1.63525	−	0.787494i
$971$			21.1420i			0.678478i	0.940700	+	0.339239i	$0.110169\pi$
$971$			21.1420i			0.678478i	−0.940700	+	0.339239i	$0.889831\pi$
$972$	0.441327	−	0.916425i	0.0141556	−	0.0293943i
$973$	−18.2411	+	14.5468i	−0.584783	+	0.466349i
$974$	−4.70234	+	3.74999i	−0.150673	+	0.120158i
$975$	−0.0888827	+	0.111455i	−0.00284653	+	0.00356943i
$976$	1.32546	+	5.80722i	0.0424269	+	0.185884i
$977$	−14.9317	−	31.0060i	−0.477707	−	0.991969i	−0.991013	−	0.133763i	$-0.957294\pi$
$977$	−14.9317	−	31.0060i	−0.477707	−	0.991969i	0.513306	−	0.858205i	$-0.328420\pi$
$978$	−0.0933063	+	0.117002i	−0.00298361	+	0.00374133i
$979$	14.6504			0.468229
$980$	18.5298	−	4.22929i	0.591911	−	0.135100i
$981$	1.63445	−	7.16099i	0.0521840	−	0.228633i
$982$	−32.1823	−	25.6645i	−1.02698	−	0.818987i
$983$	3.66398	−	2.92193i	0.116863	−	0.0931950i	−0.563315	−	0.826242i	$-0.690474\pi$
$983$	3.66398	−	2.92193i	0.116863	−	0.0931950i	0.680178	+	0.733047i	$0.261903\pi$
$984$	−0.0981025			−0.00312739
$985$	12.1782	+	18.8990i	0.388028	+	0.602173i
$986$	−43.1949			−1.37561
$987$	−0.0266253	+	0.0212330i	−0.000847494	+	0.000675854i
$988$	−40.3771	−	32.1996i	−1.28457	−	1.02441i
$989$	17.3132	−	75.8540i	0.550527	−	2.41202i
$990$	45.5009	−	10.3853i	1.44611	−	0.330066i
$991$	35.7916			1.13696			0.568479	−	0.822698i	$-0.307532\pi$
$991$	35.7916			1.13696			0.568479	+	0.822698i	$0.307532\pi$
$992$	−12.6324	+	15.8405i	−0.401080	+	0.502938i
$993$	0.0354391	+	0.0735899i	0.00112462	+	0.00233531i
$994$	−0.679942	−	2.97902i	−0.0215665	−	0.0944888i
$995$	0.180944	−	0.226896i	0.00573631	−	0.00719310i
$996$	0.114919	−	0.0916448i	0.00364134	−	0.00290388i
$997$	2.47015	−	1.96988i	0.0782304	−	0.0623867i	−0.583594	−	0.812046i	$-0.698354\pi$
$997$	2.47015	−	1.96988i	0.0782304	−	0.0623867i	0.661824	+	0.749659i	$0.269783\pi$
$998$	−9.62205	+	19.9804i	−0.304581	+	0.632468i
$999$			0.582742i			0.0184372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.e.b.19.3	✓	90
197.83	even	14	inner	197.2.e.b.83.3	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.e.b.19.3	✓	90	1.1	even	1	trivial
197.2.e.b.83.3	yes	90	197.83	even	14	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63334 + 1.30255i) q^{2} +(-0.0124583 - 0.00993517i) q^{3} +(0.526135 - 2.30515i) q^{4} +(1.56168 - 0.356443i) q^{5} +0.0332897 q^{6} +(0.877717 - 1.10062i) q^{7} +(0.330331 + 0.685939i) q^{8} +(-0.667506 - 2.92454i) q^{9} +(-2.08647 + 2.61635i) q^{10} +(3.63490 - 2.89874i) q^{11} +(-0.0294568 + 0.0234910i) q^{12} +(-1.59469 + 3.31140i) q^{13} +2.94096i q^{14} +(-0.0229972 - 0.0110749i) q^{15} +(2.82754 + 1.36167i) q^{16} +(6.84584 - 1.56252i) q^{17} +(4.89961 + 3.90731i) q^{18} -5.94283 q^{19} -3.78744i q^{20} +(-0.0218697 + 0.00499163i) q^{21} +(-2.16130 + 9.46926i) q^{22} +(3.95465 + 4.95897i) q^{23} +(0.00269956 - 0.0118275i) q^{24} +(-2.19306 + 1.05612i) q^{25} +(-1.70859 - 7.48580i) q^{26} +(-0.0414813 + 0.0861368i) q^{27} +(-2.07530 - 2.60234i) q^{28} +(1.83588 + 2.30212i) q^{29} +(0.0519878 - 0.0118659i) q^{30} +(1.96070 - 1.56360i) q^{31} +(-7.87648 + 1.79775i) q^{32} -0.0740842 q^{33} +(-9.14634 + 11.4691i) q^{34} +(0.978403 - 2.03167i) q^{35} -7.09268 q^{36} +(5.49171 - 2.64467i) q^{37} +(9.70667 - 7.74081i) q^{38} +(0.0527665 - 0.0254110i) q^{39} +(0.760369 + 0.953473i) q^{40} +(-1.79941 - 7.88371i) q^{41} +(0.0292189 - 0.0366394i) q^{42} +(-7.64816 - 9.59049i) q^{43} +(-4.76957 - 9.90411i) q^{44} +(-2.08486 - 4.32926i) q^{45} +(-12.9186 - 2.94858i) q^{46} +(1.36779 - 0.658695i) q^{47} +(-0.0216980 - 0.0450563i) q^{48} +(1.11666 + 4.89243i) q^{49} +(2.20636 - 4.58156i) q^{50} +(-0.100812 - 0.0485483i) q^{51} +(6.79425 + 5.41823i) q^{52} +(-2.51994 + 11.0406i) q^{53} +(-0.0444440 - 0.194722i) q^{54} +(4.64332 - 5.82253i) q^{55} +(1.04490 + 0.238491i) q^{56} +(0.0740376 + 0.0590430i) q^{57} +(-5.99723 - 1.36883i) q^{58} +(-5.51197 - 6.91179i) q^{59} +(-0.0376288 + 0.0471851i) q^{60} +(1.18338 + 1.48392i) q^{61} +(-1.16582 + 5.10780i) q^{62} +(-3.80469 - 1.83224i) q^{63} +(6.60987 - 8.28852i) q^{64} +(-1.31006 + 5.73976i) q^{65} +(0.121005 - 0.0964981i) q^{66} +(3.34307 + 6.94196i) q^{67} -16.6028i q^{68} -0.101070i q^{69} +(1.04828 + 4.59283i) q^{70} +(-1.01294 + 0.231197i) q^{71} +(1.78556 - 1.42393i) q^{72} +(3.43651 + 7.13598i) q^{73} +(-5.52503 + 11.4728i) q^{74} +(0.0378145 + 0.00863091i) q^{75} +(-3.12673 + 13.6991i) q^{76} -6.54493i q^{77} +(-0.0530866 + 0.110236i) q^{78} +(-10.5179 - 2.40064i) q^{79} +(4.90107 + 1.11864i) q^{80} +(-8.10666 + 3.90396i) q^{81} +(13.2079 + 10.5330i) q^{82} -3.90127 q^{83} +0.0530392i q^{84} +(10.1341 - 4.88030i) q^{85} +(24.9841 + 5.70246i) q^{86} -0.0469203i q^{87} +(3.18908 + 1.53578i) q^{88} +(2.46367 + 1.96471i) q^{89} +(9.04435 + 4.35553i) q^{90} +(2.24492 + 4.66162i) q^{91} +(13.5118 - 6.50696i) q^{92} -0.0399617 q^{93} +(-1.37609 + 2.85749i) q^{94} +(-9.28079 + 2.11828i) q^{95} +(0.115989 + 0.0558572i) q^{96} +(3.75879 + 16.4683i) q^{97} +(-8.19650 - 6.53649i) q^{98} +(-10.9038 - 8.69548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 7 q^{2} + 25 q^{4} - 14 q^{5} - 18 q^{6} + 6 q^{7} - 28 q^{8} + 7 q^{9} + 10 q^{10} - 14 q^{11} - 21 q^{12} + 35 q^{15} - 5 q^{16} - 21 q^{18} - 20 q^{19} - 14 q^{21} + 10 q^{22} - 40 q^{23} - 26 q^{24}+ \cdots - 63 q^{99}+O(q^{100}) \) 90 * q - 7 * q^2 + 25 * q^4 - 14 * q^5 - 18 * q^6 + 6 * q^7 - 28 * q^8 + 7 * q^9 + 10 * q^10 - 14 * q^11 - 21 * q^12 + 35 * q^15 - 5 * q^16 - 21 * q^18 - 20 * q^19 - 14 * q^21 + 10 * q^22 - 40 * q^23 - 26 * q^24 - 5 * q^25 + 29 * q^26 - 42 * q^27 - 36 * q^28 - 5 * q^29 - 133 * q^30 + 28 * q^31 + 28 * q^32 + 6 * q^33 + 38 * q^34 - 28 * q^35 + 232 * q^36 - 55 * q^37 - 49 * q^38 + 15 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 + 35 * q^43 + 7 * q^44 + 14 * q^45 - 28 * q^46 + q^47 - 98 * q^48 + 17 * q^49 + 98 * q^50 - 26 * q^51 - 112 * q^52 - 24 * q^53 - 43 * q^54 - 8 * q^55 + 63 * q^56 + 42 * q^57 + 14 * q^58 + 22 * q^59 - 73 * q^60 - 46 * q^61 + 34 * q^62 + 5 * q^63 - 10 * q^64 + 13 * q^65 - 91 * q^66 + 98 * q^67 + 27 * q^70 + 63 * q^71 - 7 * q^72 + 42 * q^73 + 7 * q^74 + 49 * q^75 + 78 * q^76 - 147 * q^78 - 126 * q^79 + 21 * q^80 - 37 * q^81 - 42 * q^82 - 26 * q^83 + 130 * q^85 + 119 * q^86 + 20 * q^88 - 56 * q^89 - 119 * q^90 + 84 * q^91 + 71 * q^92 - 66 * q^93 + 147 * q^94 - 77 * q^95 + 53 * q^96 + 12 * q^97 - 35 * q^98 - 63 * q^99

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