LMFDB - Embedded newform 930.2.be.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.11885 - 0.714484i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.511082 - 1.90738i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.11885 - 0.714484i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.511082 - 1.90738i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.00347 - 0.993035i) q^{10} +(-1.57425 - 0.908896i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-3.83611 + 1.02788i) q^{13} +(-1.71011 + 0.987335i) q^{14} +(-0.141741 - 2.23157i) q^{15} -1.00000 q^{16} +(-7.08570 - 1.89861i) q^{17} +(0.258819 + 0.965926i) q^{18} +(2.55715 - 1.47637i) q^{19} +(0.714484 + 2.11885i) q^{20} +(-1.71011 - 0.987335i) q^{21} +(0.470479 + 1.75585i) q^{22} +(-2.62160 - 2.62160i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.97903 - 3.02776i) q^{25} +(3.43936 + 1.98572i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.90738 + 0.511082i) q^{28} +6.71733 q^{29} +(-1.47773 + 1.67818i) q^{30} +(-5.31886 - 1.64612i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.28537 + 1.28537i) q^{33} +(3.66783 + 6.35286i) q^{34} +(-0.279891 - 4.40662i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.80448 + 1.01941i) q^{37} +(-2.85213 - 0.764225i) q^{38} +3.97144i q^{39} +(0.993035 - 2.00347i) q^{40} +(1.97145 - 3.41465i) q^{41} +(0.511082 + 1.90738i) q^{42} +(-0.271236 + 1.01227i) q^{43} +(0.908896 - 1.57425i) q^{44} +(-2.19222 - 0.440662i) q^{45} +3.70750i q^{46} +(-7.79399 - 7.79399i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(2.68527 + 1.55034i) q^{49} +(-4.95455 - 0.672643i) q^{50} +(-3.66783 + 6.35286i) q^{51} +(-1.02788 - 3.83611i) q^{52} +(3.83449 - 1.02745i) q^{53} +1.00000 q^{54} +(-3.98500 - 0.801033i) q^{55} +(-0.987335 - 1.71011i) q^{56} +(-0.764225 - 2.85213i) q^{57} +(-4.74987 - 4.74987i) q^{58} +(5.05014 - 2.91570i) q^{59} +(2.23157 - 0.141741i) q^{60} -1.54971i q^{61} +(2.59702 + 4.92498i) q^{62} +(-1.39630 + 1.39630i) q^{63} -1.00000i q^{64} +(-7.39373 + 4.91877i) q^{65} +1.81779 q^{66} +(-6.17346 + 1.65417i) q^{67} +(1.89861 - 7.08570i) q^{68} +(-3.21079 + 1.85375i) q^{69} +(-2.91803 + 3.31386i) q^{70} +(5.23799 - 9.07247i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-12.5490 + 3.36249i) q^{73} +(-1.96935 - 3.41101i) q^{74} +(-1.89475 - 4.62709i) q^{75} +(1.47637 + 2.55715i) q^{76} +(-2.53819 + 2.53819i) q^{77} +(2.80823 - 2.80823i) q^{78} +(8.71914 + 15.1020i) q^{79} +(-2.11885 + 0.714484i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-3.80855 + 1.02050i) q^{82} +(16.5034 - 4.42208i) q^{83} +(0.987335 - 1.71011i) q^{84} +(-16.3700 + 1.03976i) q^{85} +(0.907574 - 0.523988i) q^{86} +(1.73857 - 6.48844i) q^{87} +(-1.75585 + 0.470479i) q^{88} -17.9130 q^{89} +(1.23854 + 1.86173i) q^{90} +7.84227i q^{91} +(2.62160 - 2.62160i) q^{92} +(-2.96665 + 4.71158i) q^{93} +11.0224i q^{94} +(4.36336 - 4.95524i) q^{95} +(0.866025 - 0.500000i) q^{96} +(9.33706 + 9.33706i) q^{97} +(-0.802515 - 2.99503i) q^{98} +(0.908896 + 1.57425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	2.11885	−	0.714484i	0.947577	−	0.319527i
$5$	2.11885	−	0.714484i	0.947577	−	0.319527i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.511082	−	1.90738i	0.193171	−	0.720923i	−0.799562	−	0.600584i	$-0.794935\pi$
$7$	0.511082	−	1.90738i	0.193171	−	0.720923i	0.992733	−	0.120340i	$-0.0383984\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−2.00347	−	0.993035i	−0.633552	−	0.314025i
$11$	−1.57425	−	0.908896i	−0.474656	−	0.274043i	0.243531	−	0.969893i	$-0.421694\pi$
$11$	−1.57425	−	0.908896i	−0.474656	−	0.274043i	−0.718187	+	0.695851i	$0.755028\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−3.83611	+	1.02788i	−1.06395	+	0.285084i	−0.748004	−	0.663695i	$-0.768987\pi$
$13$	−3.83611	+	1.02788i	−1.06395	+	0.285084i	−0.315943	+	0.948778i	$0.602321\pi$
$14$	−1.71011	+	0.987335i	−0.457047	+	0.263876i
$15$	−0.141741	−	2.23157i	−0.0365972	−	0.576189i
$16$	−1.00000			−0.250000
$17$	−7.08570	−	1.89861i	−1.71853	−	0.460480i	−0.741044	−	0.671457i	$-0.765669\pi$
$17$	−7.08570	−	1.89861i	−1.71853	−	0.460480i	−0.977491	+	0.210977i	$0.932336\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	2.55715	−	1.47637i	0.586650	−	0.338702i	−0.177122	−	0.984189i	$-0.556679\pi$
$19$	2.55715	−	1.47637i	0.586650	−	0.338702i	0.763772	+	0.645487i	$0.223345\pi$
$20$	0.714484	+	2.11885i	0.159763	+	0.473789i
$21$	−1.71011	−	0.987335i	−0.373177	−	0.215454i
$22$	0.470479	+	1.75585i	0.100307	+	0.374349i
$23$	−2.62160	−	2.62160i	−0.546641	−	0.546641i	0.378827	−	0.925468i	$-0.376328\pi$
$23$	−2.62160	−	2.62160i	−0.546641	−	0.546641i	−0.925468	+	0.378827i	$0.876328\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	3.97903	−	3.02776i	0.795805	−	0.605553i
$26$	3.43936	+	1.98572i	0.674515	+	0.389431i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.90738	+	0.511082i	0.360462	+	0.0965854i
$29$	6.71733			1.24738			0.623689	−	0.781673i	$-0.285633\pi$
$29$	6.71733			1.24738			0.623689	+	0.781673i	$0.285633\pi$
$30$	−1.47773	+	1.67818i	−0.269796	+	0.306393i
$31$	−5.31886	−	1.64612i	−0.955296	−	0.295651i
$31$	−5.31886	−	1.64612i	−0.955296	−	0.295651i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.28537	+	1.28537i	−0.223755	+	0.223755i
$34$	3.66783	+	6.35286i	0.629027	+	1.08951i
$35$	−0.279891	−	4.40662i	−0.0473102	−	0.744854i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.80448	+	1.01941i	0.625453	+	0.167590i	0.557606	−	0.830106i	$-0.311720\pi$
$37$	3.80448	+	1.01941i	0.625453	+	0.167590i	0.0678476	+	0.997696i	$0.478387\pi$
$38$	−2.85213	−	0.764225i	−0.462676	−	0.123974i
$39$			3.97144i			0.635939i
$40$	0.993035	−	2.00347i	0.157013	−	0.316776i
$41$	1.97145	−	3.41465i	0.307888	−	0.533279i	−0.670012	−	0.742350i	$-0.733711\pi$
$41$	1.97145	−	3.41465i	0.307888	−	0.533279i	0.977900	+	0.209072i	$0.0670443\pi$
$42$	0.511082	+	1.90738i	0.0788617	+	0.294316i
$43$	−0.271236	+	1.01227i	−0.0413631	+	0.154369i	−0.983519	−	0.180807i	$-0.942129\pi$
$43$	−0.271236	+	1.01227i	−0.0413631	+	0.154369i	0.942156	+	0.335176i	$0.108796\pi$
$44$	0.908896	−	1.57425i	0.137021	−	0.237328i
$45$	−2.19222	−	0.440662i	−0.326796	−	0.0656901i
$46$			3.70750i			0.546641i
$47$	−7.79399	−	7.79399i	−1.13687	−	1.13687i	−0.989008	−	0.147862i	$-0.952761\pi$
$47$	−7.79399	−	7.79399i	−1.13687	−	1.13687i	−0.147862	−	0.989008i	$-0.547239\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	2.68527	+	1.55034i	0.383610	+	0.221477i
$50$	−4.95455	−	0.672643i	−0.700679	−	0.0951261i
$51$	−3.66783	+	6.35286i	−0.513599	+	0.889579i
$52$	−1.02788	−	3.83611i	−0.142542	−	0.531973i
$53$	3.83449	−	1.02745i	0.526708	−	0.141131i	0.0143404	−	0.999897i	$-0.495435\pi$
$53$	3.83449	−	1.02745i	0.526708	−	0.141131i	0.512368	+	0.858766i	$0.328768\pi$
$54$	1.00000			0.136083
$55$	−3.98500	−	0.801033i	−0.537337	−	0.108011i
$56$	−0.987335	−	1.71011i	−0.131938	−	0.228524i
$57$	−0.764225	−	2.85213i	−0.101224	−	0.377773i
$58$	−4.74987	−	4.74987i	−0.623689	−	0.623689i
$59$	5.05014	−	2.91570i	0.657472	−	0.379592i	−0.133841	−	0.991003i	$-0.542731\pi$
$59$	5.05014	−	2.91570i	0.657472	−	0.379592i	0.791313	+	0.611411i	$0.209398\pi$
$60$	2.23157	−	0.141741i	0.288095	−	0.0182986i
$61$		−	1.54971i		−	0.198420i	−0.995067	−	0.0992101i	$-0.968368\pi$
$61$		−	1.54971i		−	0.198420i	0.995067	−	0.0992101i	$-0.0316316\pi$
$62$	2.59702	+	4.92498i	0.329822	+	0.625474i
$63$	−1.39630	+	1.39630i	−0.175918	+	0.175918i
$64$		−	1.00000i		−	0.125000i
$65$	−7.39373	+	4.91877i	−0.917079	+	0.610098i
$66$	1.81779			0.223755
$67$	−6.17346	+	1.65417i	−0.754208	+	0.202090i	−0.615384	−	0.788227i	$-0.710999\pi$
$67$	−6.17346	+	1.65417i	−0.754208	+	0.202090i	−0.138824	+	0.990317i	$0.544332\pi$
$68$	1.89861	−	7.08570i	0.230240	−	0.859267i
$69$	−3.21079	+	1.85375i	−0.386534	+	0.223165i
$70$	−2.91803	+	3.31386i	−0.348772	+	0.396082i
$71$	5.23799	−	9.07247i	0.621635	−	1.07670i	−0.367546	−	0.930005i	$-0.619802\pi$
$71$	5.23799	−	9.07247i	0.621635	−	1.07670i	0.989181	−	0.146699i	$-0.0468648\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−12.5490	+	3.36249i	−1.46875	+	0.393550i	−0.902502	−	0.430686i	$-0.858272\pi$
$73$	−12.5490	+	3.36249i	−1.46875	+	0.393550i	−0.566247	+	0.824236i	$0.691605\pi$
$74$	−1.96935	−	3.41101i	−0.228932	−	0.396521i
$75$	−1.89475	−	4.62709i	−0.218787	−	0.534290i
$76$	1.47637	+	2.55715i	0.169351	+	0.293325i
$77$	−2.53819	+	2.53819i	−0.289253	+	0.289253i
$78$	2.80823	−	2.80823i	0.317969	−	0.317969i
$79$	8.71914	+	15.1020i	0.980980	+	1.69911i	0.658592	+	0.752500i	$0.271152\pi$
$79$	8.71914	+	15.1020i	0.980980	+	1.69911i	0.322389	+	0.946607i	$0.395514\pi$
$80$	−2.11885	+	0.714484i	−0.236894	+	0.0798817i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−3.80855	+	1.02050i	−0.420583	+	0.112695i
$83$	16.5034	−	4.42208i	1.81149	−	0.485386i	0.815813	−	0.578316i	$-0.196290\pi$
$83$	16.5034	−	4.42208i	1.81149	−	0.485386i	0.995673	+	0.0929296i	$0.0296231\pi$
$84$	0.987335	−	1.71011i	0.107727	−	0.186589i
$85$	−16.3700	+	1.03976i	−1.77558	+	0.112778i
$86$	0.907574	−	0.523988i	0.0978662	−	0.0565031i
$87$	1.73857	−	6.48844i	0.186395	−	0.695634i
$88$	−1.75585	+	0.470479i	−0.187175	+	0.0501533i
$89$	−17.9130			−1.89877			−0.949385	−	0.314115i	$-0.898292\pi$
$89$	−17.9130			−1.89877			−0.949385	+	0.314115i	$0.898292\pi$
$90$	1.23854	+	1.86173i	0.130553	+	0.196243i
$91$			7.84227i			0.822094i
$92$	2.62160	−	2.62160i	0.273321	−	0.273321i
$93$	−2.96665	+	4.71158i	−0.307627	+	0.488568i
$94$			11.0224i			1.13687i
$95$	4.36336	−	4.95524i	0.447671	−	0.508397i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	9.33706	+	9.33706i	0.948035	+	0.948035i	0.998715	−	0.0506799i	$-0.0161388\pi$
$97$	9.33706	+	9.33706i	0.948035	+	0.948035i	−0.0506799	+	0.998715i	$0.516139\pi$
$98$	−0.802515	−	2.99503i	−0.0810663	−	0.302544i
$99$	0.908896	+	1.57425i	0.0913475	+	0.158219i
$100$	3.02776	+	3.97903i	0.302776	+	0.397903i
$101$	−12.2173			−1.21567			−0.607836	−	0.794063i	$-0.707962\pi$
$101$	−12.2173			−1.21567			−0.607836	+	0.794063i	$0.707962\pi$
$102$	7.08570	−	1.89861i	0.701589	−	0.187990i
$103$	−2.51456	−	9.38448i	−0.247767	−	0.924681i	−0.971972	−	0.235096i	$-0.924460\pi$
$103$	−2.51456	−	9.38448i	−0.247767	−	0.924681i	0.724205	−	0.689585i	$-0.242207\pi$
$104$	−1.98572	+	3.43936i	−0.194716	+	0.337257i
$105$	−4.32890	−	0.870162i	−0.422458	−	0.0849191i
$106$	−3.43791	−	1.98488i	−0.333920	−	0.192789i
$107$	3.07554	−	11.4781i	0.297324	−	1.10963i	−0.642030	−	0.766679i	$-0.721908\pi$
$107$	3.07554	−	11.4781i	0.297324	−	1.10963i	0.939354	−	0.342949i	$-0.111426\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			16.6208i			1.59198i	0.605307	+	0.795992i	$0.293051\pi$
$109$			16.6208i			1.59198i	−0.605307	+	0.795992i	$0.706949\pi$
$110$	2.25140	+	3.38423i	0.214663	+	0.322674i
$111$	1.96935	−	3.41101i	0.186922	−	0.323758i
$112$	−0.511082	+	1.90738i	−0.0482927	+	0.180231i
$113$	−0.0366188	−	0.136663i	−0.00344481	−	0.0128562i	0.964182	−	0.265241i	$-0.0854517\pi$
$113$	−0.0366188	−	0.136663i	−0.00344481	−	0.0128562i	−0.967627	+	0.252385i	$0.918785\pi$
$114$	−1.47637	+	2.55715i	−0.138275	+	0.239499i
$115$	−7.42786	−	3.68168i	−0.692651	−	0.343318i
$116$			6.71733i			0.623689i
$117$	3.83611	+	1.02788i	0.354649	+	0.0950278i
$118$	−5.63270	−	1.50928i	−0.518532	−	0.138940i
$119$	−7.24275	+	12.5448i	−0.663942	+	1.14998i
$120$	−1.67818	−	1.47773i	−0.153197	−	0.134898i
$121$	−3.84782	−	6.66461i	−0.349801	−	0.605874i
$122$	−1.09581	+	1.09581i	−0.0992101	+	0.0992101i
$123$	−2.78805	−	2.78805i	−0.251390	−	0.251390i
$124$	1.64612	−	5.31886i	0.147826	−	0.477648i
$125$	6.26766	−	9.25832i	0.560596	−	0.828089i
$126$	1.97467			0.175918
$127$	4.52301	+	1.21194i	0.401352	+	0.107542i	0.453848	−	0.891079i	$-0.350051\pi$
$127$	4.52301	+	1.21194i	0.401352	+	0.107542i	−0.0524959	+	0.998621i	$0.516718\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.907574	+	0.523988i	0.0799074	+	0.0461346i
$130$	8.70625	+	1.75006i	0.763589	+	0.153491i
$131$	0.998124	+	1.72880i	0.0872065	+	0.151046i	0.906329	−	0.422572i	$-0.138873\pi$
$131$	0.998124	+	1.72880i	0.0872065	+	0.151046i	−0.819123	+	0.573618i	$0.805539\pi$
$132$	−1.28537	−	1.28537i	−0.111877	−	0.111877i
$133$	−1.50909	−	5.63201i	−0.130855	−	0.488357i
$134$	5.53497	+	3.19562i	0.478149	+	0.276059i
$135$	−0.993035	+	2.00347i	−0.0854668	+	0.172431i
$136$	−6.35286	+	3.66783i	−0.544754	+	0.314514i
$137$	2.51831	+	9.39845i	0.215154	+	0.802964i	0.986112	+	0.166079i	$0.0531107\pi$
$137$	2.51831	+	9.39845i	0.215154	+	0.802964i	−0.770959	+	0.636885i	$0.780223\pi$
$138$	3.58117	+	0.959572i	0.304849	+	0.0816842i
$139$	12.9208			1.09593			0.547963	−	0.836502i	$-0.315403\pi$
$139$	12.9208			1.09593			0.547963	+	0.836502i	$0.315403\pi$
$140$	4.40662	−	0.279891i	0.372427	−	0.0236551i
$141$	−9.54565	+	5.51118i	−0.803889	+	0.464125i
$142$	−10.1190	+	2.71138i	−0.849170	+	0.227534i
$143$	6.97326	+	1.86848i	0.583133	+	0.156250i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	14.2330	−	4.79943i	1.18199	−	0.398571i
$146$	11.2511	+	6.49584i	0.931149	+	0.537599i
$147$	2.19251	−	2.19251i	0.180835	−	0.180835i
$148$	−1.01941	+	3.80448i	−0.0837948	+	0.312727i
$149$	9.27954	−	5.35755i	0.760210	−	0.438907i	−0.0691613	−	0.997605i	$-0.522032\pi$
$149$	9.27954	−	5.35755i	0.760210	−	0.438907i	0.829371	+	0.558698i	$0.188699\pi$
$150$	−1.93205	+	4.61163i	−0.157752	+	0.376538i
$151$			5.50318i			0.447843i	0.974607	+	0.223921i	$0.0718859\pi$
$151$			5.50318i			0.447843i	−0.974607	+	0.223921i	$0.928114\pi$
$152$	0.764225	−	2.85213i	0.0619868	−	0.231338i
$153$	5.18709	+	5.18709i	0.419352	+	0.419352i
$154$	3.58954			0.289253
$155$	−12.4460	+	0.312372i	−0.999685	+	0.0250904i
$156$	−3.97144			−0.317969
$157$	−10.7195	−	10.7195i	−0.855507	−	0.855507i	0.135298	−	0.990805i	$-0.456801\pi$
$157$	−10.7195	−	10.7195i	−0.855507	−	0.855507i	−0.990805	+	0.135298i	$0.956801\pi$
$158$	4.51336	−	16.8441i	0.359064	−	1.34004i
$159$		−	3.96976i		−	0.314822i
$160$	2.00347	+	0.993035i	0.158388	+	0.0785063i
$161$	−6.34025	+	3.66054i	−0.499681	+	0.288491i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	16.3078	−	16.3078i	1.27733	−	1.27733i	0.335172	−	0.942157i	$-0.391206\pi$
$163$	16.3078	−	16.3078i	1.27733	−	1.27733i	0.942157	−	0.335172i	$-0.108794\pi$
$164$	3.41465	+	1.97145i	0.266639	+	0.153944i
$165$	−1.80513	+	3.64189i	−0.140529	+	0.283521i
$166$	−14.7966	−	8.54280i	−1.14844	−	0.663050i
$167$	13.0654	+	3.50087i	1.01103	+	0.270905i	0.726061	−	0.687630i	$-0.241349\pi$
$167$	13.0654	+	3.50087i	1.01103	+	0.270905i	0.284972	+	0.958536i	$0.408016\pi$
$168$	−1.90738	+	0.511082i	−0.147158	+	0.0394308i
$169$	2.40089	−	1.38615i	0.184684	−	0.106627i
$170$	12.3106	+	10.8401i	0.944179	+	0.831401i
$171$	−2.95274			−0.225802
$172$	−1.01227	−	0.271236i	−0.0771846	−	0.0206816i
$173$	−3.69357	−	13.7846i	−0.280817	−	1.04802i	−0.951842	−	0.306588i	$-0.900813\pi$
$173$	−3.69357	−	13.7846i	−0.280817	−	1.04802i	0.671026	−	0.741434i	$-0.265854\pi$
$174$	−5.81738	+	3.35867i	−0.441014	+	0.254620i
$175$	−3.74150	−	9.13697i	−0.282831	−	0.690690i
$176$	1.57425	+	0.908896i	0.118664	+	0.0685106i
$177$	−1.50928	−	5.63270i	−0.113444	−	0.423380i
$178$	12.6664	+	12.6664i	0.949385	+	0.949385i
$179$	3.41495	+	5.91486i	0.255245	+	0.442098i	0.964962	−	0.262389i	$-0.0845105\pi$
$179$	3.41495	+	5.91486i	0.255245	+	0.442098i	−0.709717	+	0.704487i	$0.751177\pi$
$180$	0.440662	−	2.19222i	0.0328450	−	0.163398i
$181$	2.89944	+	1.67399i	0.215514	+	0.124427i	0.603871	−	0.797082i	$-0.293624\pi$
$181$	2.89944	+	1.67399i	0.215514	+	0.124427i	−0.388358	+	0.921509i	$0.626957\pi$
$182$	5.54532	−	5.54532i	0.411047	−	0.411047i
$183$	−1.49691	−	0.401095i	−0.110654	−	0.0296498i
$184$	−3.70750			−0.273321
$185$	8.78947	−	0.558272i	0.646215	−	0.0410450i
$186$	5.42933	−	1.23385i	0.398098	−	0.0904705i
$187$	9.42906	+	9.42906i	0.689521	+	0.689521i
$188$	7.79399	−	7.79399i	0.568435	−	0.568435i
$189$	0.987335	+	1.71011i	0.0718180	+	0.124392i
$190$	−6.58924	+	0.418523i	−0.478034	+	0.0303628i
$191$	7.84799	−	13.5931i	0.567861	−	0.983564i	−0.428916	−	0.903344i	$-0.641105\pi$
$191$	7.84799	−	13.5931i	0.567861	−	0.983564i	0.996777	−	0.0802195i	$-0.0255621\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	11.1309	+	2.98252i	0.801221	+	0.214687i	0.636120	−	0.771590i	$-0.280538\pi$
$193$	11.1309	+	2.98252i	0.801221	+	0.214687i	0.165101	+	0.986277i	$0.447205\pi$
$194$		−	13.2046i		−	0.948035i
$195$	2.83753	+	8.41487i	0.203200	+	0.602601i
$196$	−1.55034	+	2.68527i	−0.110739	+	0.191805i
$197$	3.43305	+	12.8123i	0.244595	+	0.912840i	0.973587	+	0.228318i	$0.0733225\pi$
$197$	3.43305	+	12.8123i	0.244595	+	0.912840i	−0.728992	+	0.684522i	$0.760011\pi$
$198$	0.470479	−	1.75585i	0.0334355	−	0.124783i
$199$	2.88072	−	4.98956i	0.204209	−	0.353700i	−0.745671	−	0.666314i	$-0.767871\pi$
$199$	2.88072	−	4.98956i	0.204209	−	0.353700i	0.949880	+	0.312613i	$0.101204\pi$
$200$	0.672643	−	4.95455i	0.0475631	−	0.350339i
$201$			6.39124i			0.450803i
$202$	8.63897	+	8.63897i	0.607836	+	0.607836i
$203$	3.43311	−	12.8125i	0.240957	−	0.899263i
$204$	−6.35286	−	3.66783i	−0.444790	−	0.256799i
$205$	1.73749	−	8.64369i	0.121351	−	0.603701i
$206$	−4.85777	+	8.41390i	−0.338457	+	0.586224i
$207$	0.959572	+	3.58117i	0.0666948	+	0.248909i
$208$	3.83611	−	1.02788i	0.265987	−	0.0712709i
$209$	−5.36746			−0.371275
$210$	2.44570	+	3.67630i	0.168769	+	0.253688i
$211$	4.86256	+	8.42221i	0.334753	+	0.579809i	0.983437	−	0.181249i	$-0.0580139\pi$
$211$	4.86256	+	8.42221i	0.334753	+	0.579809i	−0.648685	+	0.761057i	$0.724681\pi$
$212$	1.02745	+	3.83449i	0.0705655	+	0.263354i
$213$	−7.40764	−	7.40764i	−0.507563	−	0.507563i
$214$	−10.2910	+	5.94149i	−0.703476	+	0.406152i
$215$	0.148541	+	2.33863i	0.0101304	+	0.159493i
$216$			1.00000i			0.0680414i
$217$	−5.85815	+	9.30381i	−0.397677	+	0.631584i
$218$	11.7527	−	11.7527i	0.795992	−	0.795992i
$219$			12.9917i			0.877896i
$220$	0.801033	−	3.98500i	0.0540056	−	0.268668i
$221$	29.1331			1.95970
$222$	−3.80448	+	1.01941i	−0.255340	+	0.0684182i
$223$	0.285720	−	1.06632i	0.0191332	−	0.0714063i	−0.955699	−	0.294345i	$-0.904898\pi$
$223$	0.285720	−	1.06632i	0.0191332	−	0.0714063i	0.974832	+	0.222939i	$0.0715651\pi$
$224$	1.71011	−	0.987335i	0.114262	−	0.0659691i
$225$	−4.95982	+	0.632608i	−0.330655	+	0.0421739i
$226$	−0.0707421	+	0.122529i	−0.00470570	+	0.00815050i
$227$	5.64627	−	1.51291i	0.374756	−	0.100416i	−0.0665243	−	0.997785i	$-0.521191\pi$
$227$	5.64627	−	1.51291i	0.374756	−	0.100416i	0.441281	+	0.897369i	$0.354524\pi$
$228$	2.85213	−	0.764225i	0.188887	−	0.0506120i
$229$	−2.89135	−	5.00797i	−0.191066	−	0.330936i	0.754538	−	0.656257i	$-0.227861\pi$
$229$	−2.89135	−	5.00797i	−0.191066	−	0.330936i	−0.945604	+	0.325321i	$0.894528\pi$
$230$	2.64895	+	7.85563i	0.174667	+	0.517985i
$231$	1.79477	+	3.10863i	0.118087	+	0.204533i
$232$	4.74987	−	4.74987i	0.311844	−	0.311844i
$233$	−16.6830	+	16.6830i	−1.09294	+	1.09294i	−0.0977242	+	0.995214i	$0.531156\pi$
$233$	−16.6830	+	16.6830i	−1.09294	+	1.09294i	−0.995214	+	0.0977242i	$0.968844\pi$
$234$	−1.98572	−	3.43936i	−0.129810	−	0.224838i
$235$	−22.0830	−	10.9456i	−1.44053	−	0.714012i
$236$	2.91570	+	5.05014i	0.189796	+	0.328736i
$237$	16.8441	−	4.51336i	1.09414	−	0.293174i
$238$	13.9919	−	3.74912i	0.906961	−	0.243020i
$239$	13.5695	−	23.5030i	0.877736	−	1.52028i	0.0239158	−	0.999714i	$-0.492387\pi$
$239$	13.5695	−	23.5030i	0.877736	−	1.52028i	0.853820	−	0.520569i	$-0.174280\pi$
$240$	0.141741	+	2.23157i	0.00914931	+	0.144047i
$241$	18.2829	−	10.5557i	1.17771	−	0.679950i	0.222225	−	0.974995i	$-0.428668\pi$
$241$	18.2829	−	10.5557i	1.17771	−	0.679950i	0.955483	+	0.295045i	$0.0953348\pi$
$242$	−1.99178	+	7.43341i	−0.128036	+	0.477838i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	1.54971			0.0992101
$245$	6.79737	+	1.36635i	0.434268	+	0.0872931i
$246$			3.94290i			0.251390i
$247$	−8.29197	+	8.29197i	−0.527605	+	0.527605i
$248$	−4.92498	+	2.59702i	−0.312737	+	0.164911i
$249$		−	17.0856i		−	1.08276i
$250$	−10.9785	+	2.11472i	−0.694343	+	0.133746i
$251$	−25.8353	+	14.9160i	−1.63071	+	0.941492i	−0.646839	+	0.762627i	$0.723909\pi$
$251$	−25.8353	+	14.9160i	−1.63071	+	0.941492i	−0.983874	+	0.178865i	$0.942757\pi$
$252$	−1.39630	−	1.39630i	−0.0879588	−	0.0879588i
$253$	1.74430	+	6.50982i	0.109663	+	0.409269i
$254$	−2.34128	−	4.05522i	−0.146905	−	0.254447i
$255$	−3.23255	+	16.0814i	−0.202430	+	1.00705i
$256$	1.00000			0.0625000
$257$	7.09180	−	1.90024i	0.442374	−	0.118534i	−0.0307548	−	0.999527i	$-0.509791\pi$
$257$	7.09180	−	1.90024i	0.442374	−	0.118534i	0.473129	+	0.880993i	$0.343124\pi$
$258$	−0.271236	−	1.01227i	−0.0168864	−	0.0630210i
$259$	3.88881	−	6.73561i	0.241639	−	0.418530i
$260$	−4.91877	−	7.39373i	−0.305049	−	0.458540i
$261$	−5.81738	−	3.35867i	−0.360087	−	0.207896i
$262$	0.516667	−	1.92823i	0.0319198	−	0.119126i
$263$	7.33685	+	7.33685i	0.452410	+	0.452410i	0.896154	−	0.443744i	$-0.146350\pi$
$263$	7.33685	+	7.33685i	0.452410	+	0.452410i	−0.443744	+	0.896154i	$0.646350\pi$
$264$			1.81779i			0.111877i
$265$	7.39061	−	4.91669i	0.454002	−	0.302030i
$266$	−2.91534	+	5.04952i	−0.178751	+	0.309606i
$267$	−4.63622	+	17.3026i	−0.283732	+	1.05890i
$268$	−1.65417	−	6.17346i	−0.101045	−	0.377104i
$269$	−2.76303	+	4.78571i	−0.168465	+	0.291790i	−0.937880	−	0.346959i	$-0.887214\pi$
$269$	−2.76303	+	4.78571i	−0.168465	+	0.291790i	0.769415	+	0.638749i	$0.220548\pi$
$270$	2.11885	−	0.714484i	0.128949	−	0.0434821i
$271$			16.0122i			0.972669i	0.873773	+	0.486334i	$0.161666\pi$
$271$			16.0122i			0.972669i	−0.873773	+	0.486334i	$0.838334\pi$
$272$	7.08570	+	1.89861i	0.429634	+	0.115120i
$273$	7.57505	+	2.02973i	0.458463	+	0.122845i
$274$	4.86500	−	8.42642i	0.293905	−	0.509059i
$275$	−9.01592	+	1.14995i	−0.543681	+	0.0693446i
$276$	−1.85375	−	3.21079i	−0.111583	−	0.193267i
$277$	2.18307	−	2.18307i	0.131168	−	0.131168i	−0.638475	−	0.769643i	$-0.720434\pi$
$277$	2.18307	−	2.18307i	0.131168	−	0.131168i	0.769643	+	0.638475i	$0.220434\pi$
$278$	−9.13638	−	9.13638i	−0.547963	−	0.547963i
$279$	3.78321	+	4.08501i	0.226495	+	0.244563i
$280$	−3.31386	−	2.91803i	−0.198041	−	0.174386i
$281$	1.86959			0.111530			0.0557651	−	0.998444i	$-0.482240\pi$
$281$	1.86959			0.111530			0.0557651	+	0.998444i	$0.482240\pi$
$282$	10.6468	+	2.85280i	0.634007	+	0.169882i
$283$	17.0366	−	17.0366i	1.01272	−	1.01272i	0.0128042	−	0.999918i	$-0.495924\pi$
$283$	17.0366	−	17.0366i	1.01272	−	1.01272i	0.999918	−	0.0128042i	$-0.00407581\pi$
$284$	9.07247	+	5.23799i	0.538352	+	0.310818i
$285$	−3.65707	−	5.49719i	−0.216626	−	0.325626i
$286$	−3.60962	−	6.25205i	−0.213442	−	0.369692i
$287$	−5.50547	−	5.50547i	−0.324978	−	0.324978i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	31.8800	+	18.4059i	1.87529	+	1.08270i
$290$	−13.4580	−	6.67054i	−0.790278	−	0.391708i
$291$	11.4355	−	6.60230i	0.670362	−	0.387034i
$292$	−3.36249	−	12.5490i	−0.196775	−	0.734374i
$293$	−1.25973	−	0.337544i	−0.0735944	−	0.0197196i	0.221834	−	0.975084i	$-0.428796\pi$
$293$	−1.25973	−	0.337544i	−0.0735944	−	0.0197196i	−0.295428	+	0.955365i	$0.595462\pi$
$294$	−3.10068			−0.180835
$295$	8.61725	−	9.78616i	0.501716	−	0.569772i
$296$	3.41101	−	1.96935i	0.198261	−	0.114466i
$297$	1.75585	−	0.470479i	0.101885	−	0.0273000i
$298$	−10.3500	−	2.77327i	−0.599559	−	0.160651i
$299$	12.7514	+	7.36205i	0.737435	+	0.425758i
$300$	4.62709	−	1.89475i	0.267145	−	0.109393i
$301$	1.79216	+	1.03470i	0.103298	+	0.0596393i
$302$	3.89134	−	3.89134i	0.223921	−	0.223921i
$303$	−3.16208	+	11.8011i	−0.181657	+	0.677953i
$304$	−2.55715	+	1.47637i	−0.146662	+	0.0846756i
$305$	−1.10724	−	3.28360i	−0.0634006	−	0.188018i
$306$		−	7.33566i		−	0.419352i
$307$	−0.787427	+	2.93872i	−0.0449408	+	0.167721i	−0.984749	−	0.173981i	$-0.944337\pi$
$307$	−0.787427	+	2.93872i	−0.0449408	+	0.167721i	0.939808	+	0.341702i	$0.111004\pi$
$308$	−2.53819	−	2.53819i	−0.144627	−	0.144627i
$309$	−9.71553			−0.552697
$310$	9.02152	+	8.57976i	0.512388	+	0.487297i
$311$	18.5313			1.05081			0.525407	−	0.850851i	$-0.323913\pi$
$311$	18.5313			1.05081			0.525407	+	0.850851i	$0.323913\pi$
$312$	2.80823	+	2.80823i	0.158985	+	0.158985i
$313$	−2.38217	+	8.89038i	−0.134648	+	0.502514i	0.865351	+	0.501166i	$0.167096\pi$
$313$	−2.38217	+	8.89038i	−0.134648	+	0.502514i	−0.999999	+	0.00134747i	$0.999571\pi$
$314$			15.1596i			0.855507i
$315$	−1.96092	+	3.95619i	−0.110485	+	0.222906i
$316$	−15.1020	+	8.71914i	−0.849554	+	0.490490i
$317$	−3.93089	+	14.6703i	−0.220781	+	0.823966i	0.763270	+	0.646079i	$0.223593\pi$
$317$	−3.93089	+	14.6703i	−0.220781	+	0.823966i	−0.984051	+	0.177886i	$0.943074\pi$
$318$	−2.80704	+	2.80704i	−0.157411	+	0.157411i
$319$	−10.5748	−	6.10536i	−0.592075	−	0.341834i
$320$	−0.714484	−	2.11885i	−0.0399409	−	0.118447i
$321$	−10.2910	−	5.94149i	−0.574386	−	0.331622i
$322$	7.07163	+	1.89484i	0.394086	+	0.105595i
$323$	−20.9222	+	5.60609i	−1.16414	+	0.311931i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−12.1518	+	15.7048i	−0.674061	+	0.871147i
$326$	−23.0628			−1.27733
$327$	16.0545	+	4.30178i	0.887814	+	0.237889i
$328$	−1.02050	−	3.80855i	−0.0563475	−	0.210292i
$329$	−18.8495	+	10.8828i	−1.03921	+	0.599986i
$330$	3.85162	−	1.29878i	0.212025	−	0.0714957i
$331$	−10.4948	−	6.05918i	−0.576847	−	0.333043i	0.183033	−	0.983107i	$-0.441409\pi$
$331$	−10.4948	−	6.05918i	−0.576847	−	0.333043i	−0.759879	+	0.650064i	$0.774742\pi$
$332$	4.42208	+	16.5034i	0.242693	+	0.905743i
$333$	−2.78507	−	2.78507i	−0.152621	−	0.152621i
$334$	−6.76316	−	11.7141i	−0.370064	−	0.640969i
$335$	−11.8987	+	7.91578i	−0.650098	+	0.432485i
$336$	1.71011	+	0.987335i	0.0932944	+	0.0538635i
$337$	13.1497	−	13.1497i	0.716311	−	0.716311i	−0.251537	−	0.967848i	$-0.580936\pi$
$337$	13.1497	−	13.1497i	0.716311	−	0.716311i	0.967848	+	0.251537i	$0.0809360\pi$
$338$	−2.67784	−	0.717525i	−0.145655	−	0.0390282i
$339$	−0.141484			−0.00768437
$340$	−1.03976	−	16.3700i	−0.0563889	−	0.887790i
$341$	6.87709	+	7.42570i	0.372416	+	0.402124i
$342$	2.08790	+	2.08790i	0.112901	+	0.112901i
$343$	14.1036	−	14.1036i	0.761523	−	0.761523i
$344$	0.523988	+	0.907574i	0.0282515	+	0.0489331i
$345$	−5.47870	+	6.22187i	−0.294963	+	0.334974i
$346$	−7.13542	+	12.3589i	−0.383603	+	0.664419i
$347$	−6.66349	−	1.78548i	−0.357715	−	0.0958494i	0.0754860	−	0.997147i	$-0.475949\pi$
$347$	−6.66349	−	1.78548i	−0.357715	−	0.0958494i	−0.433201	+	0.901298i	$0.642616\pi$
$348$	6.48844	+	1.73857i	0.347817	+	0.0931973i
$349$			2.47571i			0.132522i	0.997802	+	0.0662608i	$0.0211069\pi$
$349$			2.47571i			0.132522i	−0.997802	+	0.0662608i	$0.978893\pi$
$350$	−3.81517	+	9.10645i	−0.203929	+	0.486760i
$351$	1.98572	−	3.43936i	0.105990	−	0.183580i
$352$	−0.470479	−	1.75585i	−0.0250766	−	0.0935873i
$353$	1.21823	−	4.54651i	0.0648401	−	0.241987i	−0.925898	−	0.377774i	$-0.876690\pi$
$353$	1.21823	−	4.54651i	0.0648401	−	0.241987i	0.990738	+	0.135787i	$0.0433564\pi$
$354$	−2.91570	+	5.05014i	−0.154968	+	0.268412i
$355$	4.61637	−	22.9656i	0.245012	−	1.21889i
$356$		−	17.9130i		−	0.949385i
$357$	10.2428	+	10.2428i	0.542106	+	0.542106i
$358$	1.76771	−	6.59717i	0.0934262	−	0.348671i
$359$	−1.41775	−	0.818538i	−0.0748260	−	0.0432008i	0.462120	−	0.886817i	$-0.347089\pi$
$359$	−1.41775	−	0.818538i	−0.0748260	−	0.0432008i	−0.536946	+	0.843616i	$0.680422\pi$
$360$	−1.86173	+	1.23854i	−0.0981216	+	0.0652766i
$361$	−5.14067	+	8.90390i	−0.270562	+	0.468626i
$362$	−0.866522	−	3.23391i	−0.0455434	−	0.169970i
$363$	−7.43341	+	1.99178i	−0.390153	+	0.104541i
$364$	−7.84227			−0.411047
$365$	−24.1870	+	16.0907i	−1.26600	+	0.842224i
$366$	0.774856	+	1.34209i	0.0405023	+	0.0701521i
$367$	−1.39918	−	5.22181i	−0.0730366	−	0.272576i	0.919744	−	0.392518i	$-0.128396\pi$
$367$	−1.39918	−	5.22181i	−0.0730366	−	0.272576i	−0.992781	+	0.119942i	$0.961729\pi$
$368$	2.62160	+	2.62160i	0.136660	+	0.136660i
$369$	−3.41465	+	1.97145i	−0.177760	+	0.102629i
$370$	−6.60985	−	5.82033i	−0.343630	−	0.302585i
$371$		−	7.83896i		−	0.406979i
$372$	−4.71158	−	2.96665i	−0.244284	−	0.153814i
$373$	−15.3805	+	15.3805i	−0.796370	+	0.796370i	−0.982521	−	0.186151i	$-0.940399\pi$
$373$	−15.3805	+	15.3805i	−0.796370	+	0.796370i	0.186151	+	0.982521i	$0.440399\pi$
$374$		−	13.3347i		−	0.689521i
$375$	−7.32066	−	8.45032i	−0.378037	−	0.436373i
$376$	−11.0224			−0.568435
$377$	−25.7684	+	6.90463i	−1.32714	+	0.355607i
$378$	0.511082	−	1.90738i	0.0262872	−	0.0981053i
$379$	5.86875	−	3.38832i	0.301457	−	0.174047i	−0.341640	−	0.939831i	$-0.610982\pi$
$379$	5.86875	−	3.38832i	0.301457	−	0.174047i	0.643097	+	0.765784i	$0.277649\pi$
$380$	4.95524	+	4.36336i	0.254198	+	0.223836i
$381$	2.34128	−	4.05522i	0.119947	−	0.207755i
$382$	−15.1612	+	4.06242i	−0.775712	+	0.207851i
$383$	−10.3116	+	2.76298i	−0.526898	+	0.141182i	−0.512455	−	0.858714i	$-0.671264\pi$
$383$	−10.3116	+	2.76298i	−0.526898	+	0.141182i	−0.0144423	+	0.999896i	$0.504597\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−3.56454	+	7.19152i	−0.181666	+	0.366514i
$386$	−5.76179	−	9.97971i	−0.293267	−	0.507954i
$387$	0.741031	−	0.741031i	0.0376687	−	0.0376687i
$388$	−9.33706	+	9.33706i	−0.474018	+	0.474018i
$389$	−2.79900	−	4.84802i	−0.141915	−	0.245804i	0.786303	−	0.617842i	$-0.211993\pi$
$389$	−2.79900	−	4.84802i	−0.141915	−	0.245804i	−0.928218	+	0.372037i	$0.878659\pi$
$390$	3.94377	−	7.95664i	0.199701	−	0.402900i
$391$	13.5985	+	23.5532i	0.687704	+	1.19114i
$392$	2.99503	−	0.802515i	0.151272	−	0.0405331i
$393$	1.92823	−	0.516667i	0.0972662	−	0.0260624i
$394$	6.63215	−	11.4872i	0.334123	−	0.578717i
$395$	29.2647	+	25.7691i	1.47247	+	1.29659i
$396$	−1.57425	+	0.908896i	−0.0791093	+	0.0456738i
$397$	−0.00717538	+	0.0267789i	−0.000360122	+	0.00134399i	−0.966106	−	0.258147i	$-0.916888\pi$
$397$	−0.00717538	+	0.0267789i	−0.000360122	+	0.00134399i	0.965746	+	0.259491i	$0.0835548\pi$
$398$	−5.56513	+	1.49117i	−0.278955	+	0.0747457i
$399$	−5.83068			−0.291899
$400$	−3.97903	+	3.02776i	−0.198951	+	0.151388i
$401$		−	26.3395i		−	1.31533i	−0.753310	−	0.657666i	$-0.771544\pi$
$401$		−	26.3395i		−	1.31533i	0.753310	−	0.657666i	$-0.228456\pi$
$402$	4.51929	−	4.51929i	0.225402	−	0.225402i
$403$	22.0958	+	0.847519i	1.10067	+	0.0422179i
$404$		−	12.2173i		−	0.607836i
$405$	1.67818	+	1.47773i	0.0833897	+	0.0734292i
$406$	−11.4874	+	6.63225i	−0.570110	+	0.329153i
$407$	−5.06269	−	5.06269i	−0.250948	−	0.250948i
$408$	1.89861	+	7.08570i	0.0939951	+	0.350794i
$409$	14.7547	+	25.5559i	0.729573	+	1.26366i	0.957064	+	0.289877i	$0.0936144\pi$
$409$	14.7547	+	25.5559i	0.729573	+	1.26366i	−0.227491	+	0.973780i	$0.573052\pi$
$410$	−7.34060	+	4.88342i	−0.362526	+	0.241175i
$411$	9.72999			0.479945
$412$	9.38448	−	2.51456i	0.462340	−	0.123884i
$413$	−2.98032	−	11.1227i	−0.146652	−	0.547313i
$414$	1.85375	−	3.21079i	0.0911068	−	0.157802i
$415$	31.8087	−	21.1611i	1.56143	−	1.03876i
$416$	−3.43936	−	1.98572i	−0.168629	−	0.0973578i
$417$	3.34415	−	12.4805i	0.163764	−	0.611174i
$418$	3.79537	+	3.79537i	0.185638	+	0.185638i
$419$			21.7562i			1.06286i	0.847102	+	0.531430i	$0.178345\pi$
$419$			21.7562i			1.06286i	−0.847102	+	0.531430i	$0.821655\pi$
$420$	0.870162	−	4.32890i	0.0424596	−	0.211229i
$421$	7.48697	−	12.9678i	0.364892	−	0.632012i	−0.623866	−	0.781531i	$-0.714439\pi$
$421$	7.48697	−	12.9678i	0.364892	−	0.632012i	0.988759	+	0.149519i	$0.0477724\pi$
$422$	2.51705	−	9.39375i	0.122528	−	0.457281i
$423$	2.85280	+	10.6468i	0.138708	+	0.517664i
$424$	1.98488	−	3.43791i	0.0963943	−	0.166960i
$425$	−33.9427	+	13.8992i	−1.64646	+	0.674211i
$426$			10.4760i			0.507563i
$427$	−2.95589	−	0.792029i	−0.143046	−	0.0383290i
$428$	11.4781	+	3.07554i	0.554814	+	0.148662i
$429$	3.60962	−	6.25205i	0.174274	−	0.301852i
$430$	1.54863	−	1.75870i	0.0746815	−	0.0848119i
$431$	−5.51374	−	9.55008i	−0.265588	−	0.460011i	0.702130	−	0.712049i	$-0.252233\pi$
$431$	−5.51374	−	9.55008i	−0.265588	−	0.460011i	−0.967717	+	0.252038i	$0.918899\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−12.7502	−	12.7502i	−0.612734	−	0.612734i	0.330923	−	0.943658i	$-0.392640\pi$
$433$	−12.7502	−	12.7502i	−0.612734	−	0.612734i	−0.943658	+	0.330923i	$0.892640\pi$
$434$	10.7211	−	2.43645i	0.514631	−	0.116953i
$435$	−0.952118	−	14.9902i	−0.0456506	−	0.718725i
$436$	−16.6208			−0.795992
$437$	−10.5743	−	2.83336i	−0.505835	−	0.135538i
$438$	9.18650	−	9.18650i	0.438948	−	0.438948i
$439$	10.5810	+	6.10892i	0.505001	+	0.291563i	0.730777	−	0.682617i	$-0.239158\pi$
$439$	10.5810	+	6.10892i	0.505001	+	0.291563i	−0.225775	+	0.974179i	$0.572491\pi$
$440$	−3.38423	+	2.25140i	−0.161337	+	0.107331i
$441$	−1.55034	−	2.68527i	−0.0738257	−	0.127870i
$442$	−20.6002	−	20.6002i	−0.979852	−	0.979852i
$443$	−1.96421	−	7.33054i	−0.0933225	−	0.348284i	0.903437	−	0.428720i	$-0.141035\pi$
$443$	−1.96421	−	7.33054i	−0.0933225	−	0.348284i	−0.996760	+	0.0804360i	$0.974369\pi$
$444$	3.41101	+	1.96935i	0.161879	+	0.0934610i
$445$	−37.9548	+	12.7985i	−1.79923	+	0.606708i
$446$	−0.956039	+	0.551969i	−0.0452698	+	0.0261365i
$447$	−2.77327	−	10.3500i	−0.131171	−	0.489538i
$448$	−1.90738	−	0.511082i	−0.0901154	−	0.0241464i
$449$	16.6048			0.783631			0.391815	−	0.920044i	$-0.371847\pi$
$449$	16.6048			0.783631			0.391815	+	0.920044i	$0.371847\pi$
$450$	3.95444	+	3.05980i	0.186414	+	0.144240i
$451$	−6.20712	+	3.58368i	−0.292282	+	0.168749i
$452$	0.136663	−	0.0366188i	0.00642810	−	0.00172240i
$453$	5.31567	+	1.42433i	0.249752	+	0.0669208i
$454$	−5.06231	−	2.92273i	−0.237586	−	0.137170i
$455$	5.60318	+	16.6166i	0.262681	+	0.778997i
$456$	−2.55715	−	1.47637i	−0.119749	−	0.0691373i
$457$	7.90741	−	7.90741i	0.369893	−	0.369893i	−0.497545	−	0.867438i	$-0.665765\pi$
$457$	7.90741	−	7.90741i	0.369893	−	0.369893i	0.867438	+	0.497545i	$0.165765\pi$
$458$	−1.49667	+	5.58566i	−0.0699350	+	0.261001i
$459$	6.35286	−	3.66783i	0.296526	−	0.171200i
$460$	3.68168	−	7.42786i	0.171659	−	0.346326i
$461$			3.14285i			0.146377i	0.997318	+	0.0731886i	$0.0233175\pi$
$461$			3.14285i			0.146377i	−0.997318	+	0.0731886i	$0.976682\pi$
$462$	0.929041	−	3.46723i	0.0432229	−	0.161310i
$463$	0.788263	+	0.788263i	0.0366337	+	0.0366337i	0.725186	−	0.688553i	$-0.241754\pi$
$463$	0.788263	+	0.788263i	0.0366337	+	0.0366337i	−0.688553	+	0.725186i	$0.741754\pi$
$464$	−6.71733			−0.311844
$465$	−2.91953	+	12.1027i	−0.135390	+	0.561251i
$466$	23.5933			1.09294
$467$	5.21366	+	5.21366i	0.241259	+	0.241259i	0.817371	−	0.576112i	$-0.195431\pi$
$467$	5.21366	+	5.21366i	0.241259	+	0.241259i	−0.576112	+	0.817371i	$0.695431\pi$
$468$	−1.02788	+	3.83611i	−0.0475139	+	0.177324i
$469$			12.6206i			0.582764i
$470$	7.87530	+	23.3547i	0.363261	+	1.07727i
$471$	−13.1286	+	7.57981i	−0.604935	+	0.349259i
$472$	1.50928	−	5.63270i	0.0694701	−	0.259266i
$473$	1.34704	−	1.34704i	0.0619370	−	0.0619370i
$474$	−15.1020	−	8.71914i	−0.693658	−	0.400484i
$475$	5.70485	−	13.6169i	0.261757	−	0.624788i
$476$	−12.5448	−	7.24275i	−0.574990	−	0.331971i
$477$	−3.83449	−	1.02745i	−0.175569	−	0.0470437i
$478$	−26.2142	+	7.02407i	−1.19901	+	0.321274i
$479$	−28.0822	+	16.2133i	−1.28311	+	0.740802i	−0.977415	−	0.211328i	$-0.932221\pi$
$479$	−28.0822	+	16.2133i	−1.28311	+	0.740802i	−0.305692	+	0.952130i	$0.598888\pi$
$480$	1.47773	−	1.67818i	0.0674490	−	0.0765983i
$481$	−15.6423			−0.713226
$482$	−20.3920	−	5.46401i	−0.928829	−	0.248879i
$483$	1.89484	+	7.07163i	0.0862181	+	0.321770i
$484$	6.66461	−	3.84782i	0.302937	−	0.174901i
$485$	26.4550	+	13.1126i	1.20126	+	0.595414i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−2.58658	−	9.65323i	−0.117209	−	0.437430i	0.882234	−	0.470812i	$-0.156039\pi$
$487$	−2.58658	−	9.65323i	−0.117209	−	0.437430i	−0.999443	+	0.0333820i	$0.989372\pi$
$488$	−1.09581	−	1.09581i	−0.0496050	−	0.0496050i
$489$	−11.5314	−	19.9730i	−0.521467	−	0.903208i
$490$	−3.84031	−	5.77262i	−0.173487	−	0.260780i
$491$	−30.4886	−	17.6026i	−1.37593	−	0.794395i	−0.384266	−	0.923222i	$-0.625545\pi$
$491$	−30.4886	−	17.6026i	−1.37593	−	0.794395i	−0.991667	+	0.128827i	$0.958879\pi$
$492$	2.78805	−	2.78805i	0.125695	−	0.125695i
$493$	−47.5970	−	12.7536i	−2.14366	−	0.574392i
$494$	11.7266			0.527605
$495$	3.05059	+	2.68621i	0.137114	+	0.120736i
$496$	5.31886	+	1.64612i	0.238824	+	0.0739128i
$497$	−14.6276	−	14.6276i	−0.656139	−	0.656139i
$498$	−12.0813	+	12.0813i	−0.541378	+	0.541378i
$499$	−3.10888	−	5.38474i	−0.139173	−	0.241054i	0.788011	−	0.615661i	$-0.211111\pi$
$499$	−3.10888	−	5.38474i	−0.139173	−	0.241054i	−0.927184	+	0.374607i	$0.877778\pi$
$500$	9.25832	+	6.26766i	0.414045	+	0.280298i
$501$	6.76316	−	11.7141i	0.302156	−	0.523349i
$502$	28.8156	+	7.72111i	1.28610	+	0.344610i
$503$	19.0768	+	5.11161i	0.850591	+	0.227915i	0.657677	−	0.753300i	$-0.271539\pi$
$503$	19.0768	+	5.11161i	0.850591	+	0.227915i	0.192915	+	0.981216i	$0.438206\pi$
$504$			1.97467i			0.0879588i
$505$	−25.8867	+	8.72910i	−1.15194	+	0.388440i
$506$	3.36973	−	5.83655i	0.149803	−	0.259466i
$507$	−0.717525	−	2.67784i	−0.0318664	−	0.118927i
$508$	−1.21194	+	4.52301i	−0.0537710	+	0.200676i
$509$	−6.07906	+	10.5292i	−0.269450	+	0.466701i	−0.968720	−	0.248157i	$-0.920175\pi$
$509$	−6.07906	+	10.5292i	−0.269450	+	0.466701i	0.699270	+	0.714857i	$0.253508\pi$
$510$	13.6570	−	9.08548i	0.604742	−	0.402312i
$511$			25.6543i			1.13488i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.764225	+	2.85213i	−0.0337413	+	0.125924i
$514$	−6.35833	−	3.67098i	−0.280454	−	0.161920i
$515$	−12.0330	−	18.0877i	−0.530239	−	0.797038i
$516$	−0.523988	+	0.907574i	−0.0230673	+	0.0399537i
$517$	5.18579	+	19.3536i	0.228071	+	0.851173i
$518$	−7.51260	+	2.01299i	−0.330085	+	0.0884459i
$519$	−14.2708			−0.626420
$520$	−1.75006	+	8.70625i	−0.0767453	+	0.381794i
$521$	−15.1576	−	26.2538i	−0.664069	−	1.15020i	−0.979537	−	0.201264i	$-0.935495\pi$
$521$	−15.1576	−	26.2538i	−0.664069	−	1.15020i	0.315468	−	0.948936i	$-0.397838\pi$
$522$	1.73857	+	6.48844i	0.0760953	+	0.283992i
$523$	−25.5714	−	25.5714i	−1.11816	−	1.11816i	−0.992011	−	0.126149i	$-0.959738\pi$
$523$	−25.5714	−	25.5714i	−1.11816	−	1.11816i	−0.126149	−	0.992011i	$-0.540262\pi$
$524$	−1.72880	+	0.998124i	−0.0755230	+	0.0436032i
$525$	−9.79400	+	1.24919i	−0.427445	+	0.0545192i
$526$		−	10.3759i		−	0.452410i
$527$	34.5625	+	21.7623i	1.50557	+	0.947982i
$528$	1.28537	−	1.28537i	0.0559387	−	0.0559387i
$529$		−	9.25444i		−	0.402367i
$530$	−8.70258	−	1.74932i	−0.378016	−	0.0759858i
$531$	−5.83140			−0.253061
$532$	5.63201	−	1.50909i	0.244178	−	0.0654274i
$533$	−4.05284	+	15.1254i	−0.175548	+	0.655154i
$534$	15.5131	−	8.95648i	0.671317	−	0.387585i
$535$	−1.68430	−	26.5177i	−0.0728187	−	1.14646i
$536$	−3.19562	+	5.53497i	−0.138030	+	0.239075i
$537$	6.59717	−	1.76771i	0.284689	−	0.0762822i
$538$	5.33777	−	1.43025i	0.230128	−	0.0616625i
$539$	−2.81820	−	4.88126i	−0.121388	−	0.210251i
$540$	−2.00347	−	0.993035i	−0.0862155	−	0.0427334i
$541$	10.2862	+	17.8163i	0.442240	+	0.765982i	0.997855	−	0.0654573i	$-0.0208506\pi$
$541$	10.2862	+	17.8163i	0.442240	+	0.765982i	−0.555615	+	0.831439i	$0.687517\pi$
$542$	11.3223	−	11.3223i	0.486334	−	0.486334i
$543$	2.36738	−	2.36738i	0.101594	−	0.101594i
$544$	−3.66783	−	6.35286i	−0.157257	−	0.272377i
$545$	11.8753	+	35.2170i	0.508682	+	1.50853i
$546$	−3.92114	−	6.79161i	−0.167809	−	0.290654i
$547$	−16.8170	+	4.50610i	−0.719043	+	0.192667i	−0.599745	−	0.800192i	$-0.704731\pi$
$547$	−16.8170	+	4.50610i	−0.719043	+	0.192667i	−0.119298	+	0.992858i	$0.538064\pi$
$548$	−9.39845	+	2.51831i	−0.401482	+	0.107577i
$549$	−0.774856	+	1.34209i	−0.0330700	+	0.0572790i
$550$	7.18836	+	5.56208i	0.306513	+	0.237168i
$551$	17.1772	−	9.91726i	0.731773	−	0.422490i
$552$	−0.959572	+	3.58117i	−0.0408421	+	0.152425i
$553$	33.2615	−	8.91240i	1.41442	−	0.378994i
$554$	−3.08733			−0.131168
$555$	1.73563	−	8.63447i	0.0736735	−	0.366513i
$556$			12.9208i			0.547963i
$557$	17.4220	−	17.4220i	0.738196	−	0.738196i	−0.234033	−	0.972229i	$-0.575192\pi$
$557$	17.4220	−	17.4220i	0.738196	−	0.738196i	0.972229	+	0.234033i	$0.0751923\pi$
$558$	0.213404	−	5.56367i	0.00903410	−	0.235529i
$559$		−	4.16197i		−	0.176033i
$560$	0.279891	+	4.40662i	0.0118275	+	0.186213i
$561$	11.5482	−	6.66735i	0.487565	−	0.281496i
$562$	−1.32200	−	1.32200i	−0.0557651	−	0.0557651i
$563$	7.62002	+	28.4383i	0.321146	+	1.19853i	0.918130	+	0.396279i	$0.129699\pi$
$563$	7.62002	+	28.4383i	0.321146	+	1.19853i	−0.596985	+	0.802253i	$0.703635\pi$
$564$	−5.51118	−	9.54565i	−0.232063	−	0.401944i
$565$	−0.175233	−	0.263405i	−0.00737212	−	0.0110815i
$566$	−24.0934			−1.01272
$567$	1.90738	−	0.511082i	0.0801026	−	0.0214634i
$568$	−2.71138	−	10.1190i	−0.113767	−	0.424585i
$569$	9.10918	−	15.7776i	0.381877	−	0.661430i	−0.609454	−	0.792822i	$-0.708611\pi$
$569$	9.10918	−	15.7776i	0.381877	−	0.661430i	0.991331	+	0.131392i	$0.0419446\pi$
$570$	−1.30116	+	6.47304i	−0.0544996	+	0.271126i
$571$	−13.8454	−	7.99367i	−0.579414	−	0.334525i	0.181487	−	0.983393i	$-0.441909\pi$
$571$	−13.8454	−	7.99367i	−0.579414	−	0.334525i	−0.760900	+	0.648869i	$0.775242\pi$
$572$	−1.86848	+	6.97326i	−0.0781250	+	0.291567i
$573$	−11.0987	−	11.0987i	−0.463656	−	0.463656i
$574$			7.78592i			0.324978i
$575$	−18.3690	−	2.49382i	−0.766040	−	0.104000i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−6.85377	+	25.5786i	−0.285326	+	1.06485i	0.663274	+	0.748376i	$0.269166\pi$
$577$	−6.85377	+	25.5786i	−0.285326	+	1.06485i	−0.948601	+	0.316476i	$0.897500\pi$
$578$	−9.52761	−	35.5575i	−0.396296	−	1.47900i
$579$	5.76179	−	9.97971i	0.239452	−	0.414743i
$580$	4.79943	+	14.2330i	0.199285	+	0.590993i
$581$		−	33.7384i		−	1.39970i
$582$	−12.7547	−	3.41760i	−0.528698	−	0.141664i
$583$	−6.97031	−	1.86769i	−0.288681	−	0.0773518i
$584$	−6.49584	+	11.2511i	−0.268800	+	0.465575i
$585$	8.86254	−	0.562913i	0.366421	−	0.0232736i
$586$	0.652086	+	1.12945i	0.0269374	+	0.0466570i
$587$	−5.21314	+	5.21314i	−0.215169	+	0.215169i	−0.806459	−	0.591290i	$-0.798619\pi$
$587$	−5.21314	+	5.21314i	−0.215169	+	0.215169i	0.591290	+	0.806459i	$0.298619\pi$
$588$	2.19251	+	2.19251i	0.0904177	+	0.0904177i
$589$	−16.0314	+	3.64324i	−0.660562	+	0.150117i
$590$	−13.0132	+	0.826545i	−0.535744	+	0.0340283i
$591$	13.2643			0.545620
$592$	−3.80448	−	1.01941i	−0.156363	−	0.0418974i
$593$	−21.5420	+	21.5420i	−0.884626	+	0.884626i	−0.994001	−	0.109375i	$-0.965115\pi$
$593$	−21.5420	+	21.5420i	−0.884626	+	0.884626i	0.109375	+	0.994001i	$0.465115\pi$
$594$	−1.57425	−	0.908896i	−0.0645924	−	0.0372925i
$595$	−6.38321	+	31.7554i	−0.261686	+	1.30184i
$596$	5.35755	+	9.27954i	0.219454	+	0.380105i
$597$	−4.07396	−	4.07396i	−0.166736	−	0.166736i
$598$	−3.81088	−	14.2224i	−0.155838	−	0.581597i
$599$	−18.8961	−	10.9097i	−0.772074	−	0.445757i	0.0615402	−	0.998105i	$-0.480399\pi$
$599$	−18.8961	−	10.9097i	−0.772074	−	0.445757i	−0.833614	+	0.552348i	$0.813732\pi$
$600$	−4.61163	−	1.93205i	−0.188269	−	0.0788758i
$601$	31.2470	−	18.0405i	1.27459	−	0.735887i	0.298744	−	0.954333i	$-0.403432\pi$
$601$	31.2470	−	18.0405i	1.27459	−	0.735887i	0.975849	+	0.218446i	$0.0700989\pi$
$602$	−0.535602	−	1.99889i	−0.0218295	−	0.0814688i
$603$	6.17346	+	1.65417i	0.251403	+	0.0673632i
$604$	−5.50318			−0.223921
$605$	−12.9147	−	11.3721i	−0.525057	−	0.462341i
$606$	10.5805	−	6.10867i	0.429805	−	0.248148i
$607$	−1.01937	+	0.273141i	−0.0413751	+	0.0110864i	−0.279447	−	0.960161i	$-0.590151\pi$
$607$	−1.01937	+	0.273141i	−0.0413751	+	0.0110864i	0.238072	+	0.971247i	$0.423485\pi$
$608$	2.85213	+	0.764225i	0.115669	+	0.0309934i
$609$	−11.4874	−	6.63225i	−0.465493	−	0.268753i
$610$	−1.53892	+	3.10480i	−0.0623089	+	0.125710i
$611$	37.9099	+	21.8873i	1.53367	+	0.885466i
$612$	−5.18709	+	5.18709i	−0.209676	+	0.209676i
$613$	−8.69152	+	32.4372i	−0.351047	+	1.31013i	0.534339	+	0.845270i	$0.320560\pi$
$613$	−8.69152	+	32.4372i	−0.351047	+	1.31013i	−0.885386	+	0.464856i	$0.846106\pi$
$614$	2.63478	−	1.52119i	0.106331	−	0.0613903i
$615$	−7.89947	−	3.91543i	−0.318537	−	0.157885i
$616$			3.58954i			0.144627i
$617$	10.7419	−	40.0893i	0.432453	−	1.61394i	−0.314636	−	0.949212i	$-0.601883\pi$
$617$	10.7419	−	40.0893i	0.432453	−	1.61394i	0.747089	−	0.664724i	$-0.231451\pi$
$618$	6.86992	+	6.86992i	0.276349	+	0.276349i
$619$	−29.1468			−1.17151			−0.585754	−	0.810489i	$-0.699201\pi$
$619$	−29.1468			−1.17151			−0.585754	+	0.810489i	$0.699201\pi$
$620$	−0.312372	−	12.4460i	−0.0125452	−	0.499843i
$621$	3.70750			0.148777
$622$	−13.1036	−	13.1036i	−0.525407	−	0.525407i
$623$	−9.15499	+	34.1669i	−0.366787	+	1.36887i
$624$		−	3.97144i		−	0.158985i
$625$	6.66529	−	24.0951i	0.266611	−	0.963804i
$626$	7.97090	−	4.60200i	0.318581	−	0.183933i
$627$	−1.38920	+	5.18457i	−0.0554794	+	0.207052i
$628$	10.7195	−	10.7195i	0.427753	−	0.427753i
$629$	−25.0220	−	14.4464i	−0.997691	−	0.576017i
$630$	4.18402	−	1.41087i	0.166695	−	0.0562104i
$631$	−3.75303	−	2.16681i	−0.149406	−	0.0862594i	0.423433	−	0.905927i	$-0.360825\pi$
$631$	−3.75303	−	2.16681i	−0.149406	−	0.0862594i	−0.572839	+	0.819668i	$0.694158\pi$
$632$	16.8441	+	4.51336i	0.670022	+	0.179532i
$633$	9.39375	−	2.51705i	0.373368	−	0.100044i
$634$	13.1530	−	7.59390i	0.522373	−	0.301592i
$635$	10.4495	−	0.663708i	0.414674	−	0.0263385i
$636$	3.96976			0.157411
$637$	−11.8946	−	3.18714i	−0.471280	−	0.126279i
$638$	3.16037	+	11.7946i	0.125120	+	0.466954i
$639$	−9.07247	+	5.23799i	−0.358901	+	0.207212i
$640$	−0.993035	+	2.00347i	−0.0392531	+	0.0791940i
$641$	14.0724	+	8.12468i	0.555825	+	0.320906i	0.751468	−	0.659769i	$-0.229346\pi$
$641$	14.0724	+	8.12468i	0.555825	+	0.320906i	−0.195643	+	0.980675i	$0.562679\pi$
$642$	3.07554	+	11.4781i	0.121382	+	0.453004i
$643$	−7.54912	−	7.54912i	−0.297708	−	0.297708i	0.542407	−	0.840116i	$-0.317513\pi$
$643$	−7.54912	−	7.54912i	−0.297708	−	0.297708i	−0.840116	+	0.542407i	$0.817513\pi$
$644$	−3.66054	−	6.34025i	−0.144246	−	0.249841i
$645$	2.29739	+	0.461803i	0.0904597	+	0.0181835i
$646$	18.7583	+	10.8301i	0.738037	+	0.426106i
$647$	−16.8173	+	16.8173i	−0.661154	+	0.661154i	−0.955652	−	0.294498i	$-0.904848\pi$
$647$	−16.8173	+	16.8173i	−0.661154	+	0.661154i	0.294498	+	0.955652i	$0.404848\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−10.6003			−0.416097
$650$	19.6976	−	2.51236i	0.772604	−	0.0985430i
$651$	7.47059	+	8.06654i	0.292796	+	0.316153i
$652$	16.3078	+	16.3078i	0.638665	+	0.638665i
$653$	−18.8989	+	18.8989i	−0.739570	+	0.739570i	−0.972495	−	0.232925i	$-0.925170\pi$
$653$	−18.8989	+	18.8989i	−0.739570	+	0.739570i	0.232925	+	0.972495i	$0.425170\pi$
$654$	−8.31040	−	14.3940i	−0.324963	−	0.562852i
$655$	3.35007	+	2.94992i	0.130898	+	0.115263i
$656$	−1.97145	+	3.41465i	−0.0769721	+	0.133320i
$657$	12.5490	+	3.36249i	0.489583	+	0.131183i
$658$	21.0239	+	5.63333i	0.819596	+	0.219610i
$659$			0.721478i			0.0281048i	0.999901	+	0.0140524i	$0.00447316\pi$
$659$			0.721478i			0.0281048i	−0.999901	+	0.0140524i	$0.995527\pi$
$660$	−3.64189	−	1.80513i	−0.141760	−	0.0702646i
$661$	13.8021	−	23.9060i	0.536841	−	0.929836i	−0.462231	−	0.886760i	$-0.652951\pi$
$661$	13.8021	−	23.9060i	0.536841	−	0.929836i	0.999072	−	0.0430763i	$-0.0137158\pi$
$662$	3.13646	+	11.7054i	0.121902	+	0.454945i
$663$	7.54020	−	28.1404i	0.292837	−	1.09288i
$664$	8.54280	−	14.7966i	0.331525	−	0.574218i
$665$	−7.22151	−	10.8551i	−0.280038	−	0.420944i
$666$			3.93869i			0.152621i
$667$	−17.6101	−	17.6101i	−0.681868	−	0.681868i
$668$	−3.50087	+	13.0654i	−0.135453	+	0.505516i
$669$	−0.956039	−	0.551969i	−0.0369626	−	0.0213404i
$670$	14.0110	+	2.81638i	0.541292	+	0.108806i
$671$	−1.40853	+	2.43964i	−0.0543756	+	0.0941812i
$672$	−0.511082	−	1.90738i	−0.0197154	−	0.0735789i
$673$	16.2831	−	4.36305i	0.627668	−	0.168183i	0.0690567	−	0.997613i	$-0.478001\pi$
$673$	16.2831	−	4.36305i	0.627668	−	0.168183i	0.558611	+	0.829430i	$0.311334\pi$
$674$	−18.5965			−0.716311
$675$	−0.672643	+	4.95455i	−0.0258900	+	0.190701i
$676$	1.38615	+	2.40089i	0.0533136	+	0.0923418i
$677$	1.97897	+	7.38561i	0.0760579	+	0.283852i	0.993471	−	0.114084i	$-0.0363933\pi$
$677$	1.97897	+	7.38561i	0.0760579	+	0.283852i	−0.917413	+	0.397936i	$0.869727\pi$
$678$	0.100044	+	0.100044i	0.00384218	+	0.00384218i
$679$	22.5814	−	13.0374i	0.866593	−	0.500328i
$680$	−10.8401	+	12.3106i	−0.415701	+	0.472089i
$681$		−	5.84545i		−	0.223998i
$682$	0.387924	−	10.1136i	0.0148544	−	0.387270i
$683$	7.09870	−	7.09870i	0.271624	−	0.271624i	−0.558130	−	0.829754i	$-0.688481\pi$
$683$	7.09870	−	7.09870i	0.271624	−	0.271624i	0.829754	+	0.558130i	$0.188481\pi$
$684$		−	2.95274i		−	0.112901i
$685$	12.0509	+	18.1146i	0.460443	+	0.692123i
$686$	−19.9455			−0.761523
$687$	−5.58566	+	1.49667i	−0.213106	+	0.0571017i
$688$	0.271236	−	1.01227i	0.0103408	−	0.0385923i
$689$	−13.6535	+	7.88282i	−0.520155	+	0.300312i
$690$	8.27355	−	0.525503i	0.314969	−	0.0200056i
$691$	7.23910	−	12.5385i	0.275388	−	0.476987i	−0.694845	−	0.719160i	$-0.744527\pi$
$691$	7.23910	−	12.5385i	0.275388	−	0.476987i	0.970233	+	0.242173i	$0.0778602\pi$
$692$	13.7846	−	3.69357i	0.524011	−	0.140408i
$693$	3.46723	−	0.929041i	0.131709	−	0.0352914i
$694$	3.44927	+	5.97432i	0.130933	+	0.226782i
$695$	27.3772	−	9.23170i	1.03848	−	0.350178i
$696$	−3.35867	−	5.81738i	−0.127310	−	0.220507i
$697$	−20.4522	+	20.4522i	−0.774681	+	0.774681i
$698$	1.75059	−	1.75059i	0.0662608	−	0.0662608i
$699$	11.7966	+	20.4324i	0.446190	+	0.772824i
$700$	9.13697	−	3.74150i	0.345345	−	0.141415i
$701$	22.9935	+	39.8259i	0.868452	+	1.50420i	0.863578	+	0.504216i	$0.168218\pi$
$701$	22.9935	+	39.8259i	0.868452	+	1.50420i	0.00487469	+	0.999988i	$0.498448\pi$
$702$	−3.83611	+	1.02788i	−0.144785	+	0.0387950i
$703$	11.2336	−	3.01005i	0.423685	−	0.113526i
$704$	−0.908896	+	1.57425i	−0.0342553	+	0.0593319i
$705$	−16.2881	+	18.4976i	−0.613446	+	0.696659i
$706$	−4.07629	+	2.35345i	−0.153413	+	0.0885732i
$707$	−6.24407	+	23.3032i	−0.234832	+	0.876406i
$708$	5.63270	−	1.50928i	0.211690	−	0.0567221i
$709$	38.8668			1.45967			0.729836	−	0.683622i	$-0.239596\pi$
$709$	38.8668			1.45967			0.729836	+	0.683622i	$0.239596\pi$
$710$	−19.5034	+	12.9749i	−0.731951	+	0.486939i
$711$		−	17.4383i		−	0.653987i
$712$	−12.6664	+	12.6664i	−0.474693	+	0.474693i
$713$	9.62847	+	18.2594i	0.360589	+	0.683819i
$714$		−	14.4855i		−	0.542106i
$715$	16.1103	−	1.02326i	0.602490	−	0.0382677i
$716$	−5.91486	+	3.41495i	−0.221049	+	0.127623i
$717$	−19.1901	−	19.1901i	−0.716668	−	0.716668i
$718$	0.423707	+	1.58129i	0.0158126	+	0.0590134i
$719$	16.3356	+	28.2940i	0.609213	+	1.05519i	0.991370	+	0.131091i	$0.0418481\pi$
$719$	16.3356	+	28.2940i	0.609213	+	1.05519i	−0.382157	+	0.924097i	$0.624819\pi$
$720$	2.19222	+	0.440662i	0.0816991	+	0.0164225i
$721$	−19.1850			−0.714485
$722$	9.93101	−	2.66101i	0.369594	−	0.0990324i
$723$	−5.46401	−	20.3920i	−0.203209	−	0.758386i
$724$	−1.67399	+	2.89944i	−0.0622135	+	0.107757i
$725$	26.7284	−	20.3385i	0.992669	−	0.755353i
$726$	6.66461	+	3.84782i	0.247347	+	0.142806i
$727$	11.7955	−	44.0216i	0.437472	−	1.63267i	−0.297607	−	0.954688i	$-0.596189\pi$
$727$	11.7955	−	44.0216i	0.437472	−	1.63267i	0.735080	−	0.677981i	$-0.237145\pi$
$728$	5.54532	+	5.54532i	0.205523	+	0.205523i
$729$		−	1.00000i		−	0.0370370i
$730$	28.4806	+	5.72494i	1.05411	+	0.211890i
$731$	3.84380	−	6.65765i	0.142168	−	0.246242i
$732$	0.401095	−	1.49691i	0.0148249	−	0.0553272i
$733$	7.25163	+	27.0634i	0.267845	+	0.999611i	0.960486	+	0.278329i	$0.0897804\pi$
$733$	7.25163	+	27.0634i	0.267845	+	0.999611i	−0.692641	+	0.721283i	$0.743553\pi$
$734$	−2.70301	+	4.68174i	−0.0997698	+	0.172806i
$735$	3.07908	−	6.21211i	0.113574	−	0.229137i
$736$		−	3.70750i		−	0.136660i
$737$	11.2221	+	3.00695i	0.413370	+	0.110762i
$738$	3.80855	+	1.02050i	0.140194	+	0.0375650i
$739$	7.84846	−	13.5939i	0.288710	−	0.500061i	−0.684792	−	0.728739i	$-0.740107\pi$
$739$	7.84846	−	13.5939i	0.288710	−	0.500061i	0.973502	+	0.228678i	$0.0734402\pi$
$740$	0.558272	+	8.78947i	0.0205225	+	0.323107i
$741$	5.86331	+	10.1555i	0.215394	+	0.373073i
$742$	−5.54298	+	5.54298i	−0.203489	+	0.203489i
$743$	34.8279	+	34.8279i	1.27771	+	1.27771i	0.941945	+	0.335767i	$0.108995\pi$
$743$	34.8279	+	34.8279i	1.27771	+	1.27771i	0.335767	+	0.941945i	$0.391005\pi$
$744$	1.23385	+	5.42933i	0.0452352	+	0.199049i
$745$	15.8341	−	17.9819i	0.580115	−	0.658806i
$746$	21.7513			0.796370
$747$	−16.5034	−	4.42208i	−0.603829	−	0.161795i
$748$	−9.42906	+	9.42906i	−0.344760	+	0.344760i
$749$	−20.3213	−	11.7325i	−0.742523	−	0.428696i
$750$	−0.798791	+	11.1518i	−0.0291677	+	0.407205i
$751$	9.47115	+	16.4045i	0.345607	+	0.598609i	0.985464	−	0.169885i	$-0.0543397\pi$
$751$	9.47115	+	16.4045i	0.345607	+	0.598609i	−0.639857	+	0.768494i	$0.721006\pi$
$752$	7.79399	+	7.79399i	0.284218	+	0.284218i
$753$	7.72111	+	28.8156i	0.281373	+	1.05010i
$754$	23.1034	+	13.3387i	0.841375	+	0.485768i
$755$	3.93194	+	11.6604i	0.143098	+	0.424365i
$756$	−1.71011	+	0.987335i	−0.0621962	+	0.0359090i
$757$	2.43378	+	9.08298i	0.0884571	+	0.330126i	0.995946	−	0.0899488i	$-0.0286703\pi$
$757$	2.43378	+	9.08298i	0.0884571	+	0.330126i	−0.907489	+	0.420075i	$0.862004\pi$
$758$	−6.54574	−	1.75393i	−0.237752	−	0.0637054i
$759$	6.73947			0.244627
$760$	−0.418523	−	6.58924i	−0.0151814	−	0.239017i
$761$	35.8051	−	20.6721i	1.29794	−	0.749363i	0.317888	−	0.948128i	$-0.397026\pi$
$761$	35.8051	−	20.6721i	1.29794	−	0.749363i	0.980047	+	0.198765i	$0.0636931\pi$
$762$	−4.52301	+	1.21194i	−0.163851	+	0.0439038i
$763$	31.7023	+	8.49460i	1.14770	+	0.307525i
$764$	13.5931	+	7.84799i	0.491782	+	0.283930i
$765$	14.6967	+	7.28456i	0.531362	+	0.263374i
$766$	9.24512	+	5.33767i	0.334040	+	0.192858i
$767$	−16.3759	+	16.3759i	−0.591300	+	0.591300i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−23.5828	+	13.6155i	−0.850418	+	0.490989i	−0.860792	−	0.508957i	$-0.830031\pi$
$769$	−23.5828	+	13.6155i	−0.850418	+	0.490989i	0.0103740	+	0.999946i	$0.496698\pi$
$770$	7.60568	−	2.56467i	0.274090	−	0.0924242i
$771$		−	7.34197i		−	0.264415i
$772$	−2.98252	+	11.1309i	−0.107343	+	0.400611i
$773$	32.9588	+	32.9588i	1.18545	+	1.18545i	0.978313	+	0.207133i	$0.0664134\pi$
$773$	32.9588	+	32.9588i	1.18545	+	1.18545i	0.207133	+	0.978313i	$0.433587\pi$
$774$	−1.04798			−0.0376687
$775$	−26.1479	+	9.55432i	−0.939262	+	0.343201i
$776$	13.2046			0.474018
$777$	−5.49960	−	5.49960i	−0.197297	−	0.197297i
$778$	−1.44887	+	5.40726i	−0.0519446	+	0.193860i
$779$		−	11.6423i		−	0.417130i
$780$	−8.41487	+	2.83753i	−0.301301	+	0.101600i
$781$	−16.4919	+	9.52158i	−0.590125	+	0.340709i
$782$	7.03909	−	26.2702i	0.251717	−	0.939422i
$783$	−4.74987	+	4.74987i	−0.169747	+	0.169747i
$784$	−2.68527	−	1.55034i	−0.0959024	−	0.0553693i
$785$	−30.3718	−	15.0540i	−1.08402	−	0.537301i
$786$	−1.72880	−	0.998124i	−0.0616643	−	0.0356019i
$787$	−1.61878	−	0.433752i	−0.0577034	−	0.0154616i	0.229852	−	0.973226i	$-0.426176\pi$
$787$	−1.61878	−	0.433752i	−0.0577034	−	0.0154616i	−0.287555	+	0.957764i	$0.592843\pi$
$788$	−12.8123	+	3.43305i	−0.456420	+	0.122297i
$789$	8.98577	−	5.18794i	0.319902	−	0.184695i
$790$	−2.47171	−	38.9148i	−0.0879396	−	1.38453i
$791$	−0.279385			−0.00993377
$792$	1.75585	+	0.470479i	0.0623915	+	0.0167178i
$793$	1.59292	+	5.94487i	0.0565663	+	0.211108i
$794$	0.0240093	−	0.0138618i	0.000852058	−	0.000491936i
$795$	−2.83633	−	8.41131i	−0.100594	−	0.298319i
$796$	4.98956	+	2.88072i	0.176850	+	0.102104i
$797$	−4.75491	−	17.7456i	−0.168428	−	0.628581i	−0.997578	−	0.0695552i	$-0.977842\pi$
$797$	−4.75491	−	17.7456i	−0.168428	−	0.628581i	0.829150	−	0.559026i	$-0.188825\pi$
$798$	4.12291	+	4.12291i	0.145950	+	0.145950i
$799$	40.4281	+	70.0236i	1.43024	+	2.47726i
$800$	4.95455	+	0.672643i	0.175170	+	0.0237815i
$801$	15.5131	+	8.95648i	0.548128	+	0.316462i
$802$	−18.6248	+	18.6248i	−0.657666	+	0.657666i
$803$	22.8115	+	6.11231i	0.804999	+	0.215699i
$804$	−6.39124			−0.225402
$805$	−10.8186	+	12.2861i	−0.381306	+	0.433029i
$806$	−15.0248	−	16.2234i	−0.529225	−	0.571443i
$807$	3.90752	+	3.90752i	0.137551	+	0.137551i
$808$	−8.63897	+	8.63897i	−0.303918	+	0.303918i
$809$	−3.20019	−	5.54290i	−0.112513	−	0.194878i	0.804270	−	0.594264i	$-0.202557\pi$
$809$	−3.20019	−	5.54290i	−0.112513	−	0.194878i	−0.916783	+	0.399386i	$0.869223\pi$
$810$	−0.141741	−	2.23157i	−0.00498025	−	0.0784094i
$811$	0.491819	−	0.851856i	0.0172701	−	0.0299127i	−0.857261	−	0.514882i	$-0.827836\pi$
$811$	0.491819	−	0.851856i	0.0172701	−	0.0299127i	0.874531	+	0.484969i	$0.161169\pi$
$812$	12.8125	+	3.43311i	0.449632	+	0.120478i
$813$	15.4666	+	4.14425i	0.542436	+	0.145345i
$814$			7.15972i			0.250948i
$815$	22.9021	−	46.2055i	0.802227	−	1.61851i
$816$	3.66783	−	6.35286i	0.128400	−	0.222395i
$817$	0.800889	+	2.98896i	0.0280196	+	0.104570i
$818$	7.63759	−	28.5039i	0.267042	−	0.996615i
$819$	3.92114	−	6.79161i	0.137016	−	0.237318i
$820$	8.64369	+	1.73749i	0.301851	+	0.0606756i
$821$			28.0282i			0.978190i	0.872230	+	0.489095i	$0.162673\pi$
$821$			28.0282i			0.978190i	−0.872230	+	0.489095i	$0.837327\pi$
$822$	−6.88014	−	6.88014i	−0.239973	−	0.239973i
$823$	−2.06426	+	7.70393i	−0.0719556	+	0.268542i	−0.992526	−	0.122035i	$-0.961058\pi$
$823$	−2.06426	+	7.70393i	−0.0719556	+	0.268542i	0.920570	+	0.390577i	$0.127725\pi$
$824$	−8.41390	−	4.85777i	−0.293112	−	0.169228i
$825$	−1.22273	+	9.00634i	−0.0425698	+	0.313561i
$826$	−5.75754	+	9.97235i	−0.200330	+	0.346983i
$827$	−10.8942	−	40.6579i	−0.378830	−	1.41381i	−0.847667	−	0.530529i	$-0.821993\pi$
$827$	−10.8942	−	40.6579i	−0.378830	−	1.41381i	0.468837	−	0.883285i	$-0.344673\pi$
$828$	−3.58117	+	0.959572i	−0.124454	+	0.0333474i
$829$	−31.4312			−1.09165			−0.545825	−	0.837899i	$-0.683784\pi$
$829$	−31.4312			−1.09165			−0.545825	+	0.837899i	$0.683784\pi$
$830$	−37.4553	−	7.52898i	−1.30009	−	0.261335i
$831$	−1.54366	−	2.67370i	−0.0535491	−	0.0927497i
$832$	1.02788	+	3.83611i	0.0356354	+	0.132993i
$833$	−16.0835	−	16.0835i	−0.557261	−	0.557261i
$834$	−11.1897	+	6.46039i	−0.387469	+	0.223705i
$835$	30.1849	−	1.91723i	1.04459	−	0.0663484i
$836$		−	5.36746i		−	0.185638i
$837$	4.92498	−	2.59702i	0.170232	−	0.0897663i
$838$	15.3840	−	15.3840i	0.531430	−	0.531430i
$839$			0.601623i			0.0207703i	0.999946	+	0.0103852i	$0.00330576\pi$
$839$			0.601623i			0.0207703i	−0.999946	+	0.0103852i	$0.996694\pi$
$840$	−3.67630	+	2.44570i	−0.126844	+	0.0843847i
$841$	16.1226			0.555950
$842$	−14.4637	+	3.87554i	−0.498452	+	0.133560i
$843$	0.483885	−	1.80588i	0.0166659	−	0.0621979i
$844$	−8.42221	+	4.86256i	−0.289904	+	0.167376i
$845$	4.09673	−	4.65244i	0.140932	−	0.160049i
$846$	5.51118	−	9.54565i	0.189478	−	0.328186i
$847$	−14.6785	+	3.93310i	−0.504360	+	0.135143i
$848$	−3.83449	+	1.02745i	−0.131677	+	0.0352828i
$849$	−12.0467	−	20.8655i	−0.413442	−	0.716103i
$850$	33.8294	+	14.1729i	1.16034	+	0.486126i
$851$	−7.30135	−	12.6463i	−0.250287	−	0.433510i
$852$	7.40764	−	7.40764i	0.253782	−	0.253782i
$853$	18.4221	−	18.4221i	0.630761	−	0.630761i	−0.317498	−	0.948259i	$-0.602843\pi$
$853$	18.4221	−	18.4221i	0.630761	−	0.630761i	0.948259	+	0.317498i	$0.102843\pi$
$854$	1.53008	+	2.65018i	0.0523584	+	0.0906874i
$855$	−6.25640	+	2.10968i	−0.213964	+	0.0721497i
$856$	−5.94149	−	10.2910i	−0.203076	−	0.351738i
$857$	−33.2534	+	8.91021i	−1.13591	+	0.304367i	−0.777307	−	0.629122i	$-0.783415\pi$
$857$	−33.2534	+	8.91021i	−1.13591	+	0.304367i	−0.358606	+	0.933489i	$0.616748\pi$
$858$	−6.97326	+	1.86848i	−0.238063	+	0.0637888i
$859$	24.8540	−	43.0483i	0.848006	−	1.46879i	−0.0349779	−	0.999388i	$-0.511136\pi$
$859$	24.8540	−	43.0483i	0.848006	−	1.46879i	0.882984	−	0.469402i	$-0.155531\pi$
$860$	−2.33863	+	0.148541i	−0.0797467	+	0.00506519i
$861$	−6.74280	+	3.89296i	−0.229794	+	0.132672i
$862$	−2.85412	+	10.6517i	−0.0972118	+	0.362799i
$863$	−30.7289	+	8.23378i	−1.04602	+	0.280281i	−0.740608	−	0.671938i	$-0.765462\pi$
$863$	−30.7289	+	8.23378i	−1.04602	+	0.280281i	−0.305416	+	0.952219i	$0.598796\pi$
$864$	−1.00000			−0.0340207
$865$	−17.6750	−	26.5684i	−0.600966	−	0.903353i
$866$			18.0315i			0.612734i
$867$	26.0299	−	26.0299i	0.884022	−	0.884022i
$868$	−9.30381	−	5.85815i	−0.315792	−	0.198839i
$869$		−	31.6992i		−	1.07532i
$870$	−9.92643	+	11.2729i	−0.336537	+	0.382188i
$871$	21.9818	−	12.6912i	0.744825	−	0.430025i
$872$	11.7527	+	11.7527i	0.397996	+	0.397996i
$873$	−3.41760	−	12.7547i	−0.115668	−	0.431680i
$874$	5.47364	+	9.48062i	0.185149	+	0.320687i
$875$	−14.4559	−	16.6866i	−0.488698	−	0.564110i
$876$	−12.9917			−0.438948
$877$	18.9046	−	5.06547i	0.638363	−	0.171049i	0.0749010	−	0.997191i	$-0.476136\pi$
$877$	18.9046	−	5.06547i	0.638363	−	0.171049i	0.563462	+	0.826142i	$0.309469\pi$
$878$	−3.16221	−	11.8015i	−0.106719	−	0.398282i
$879$	−0.652086	+	1.12945i	−0.0219943	+	0.0380952i
$880$	3.98500	+	0.801033i	0.134334	+	0.0270028i
$881$	−11.8740	−	6.85548i	−0.400046	−	0.230967i	0.286458	−	0.958093i	$-0.407522\pi$
$881$	−11.8740	−	6.85548i	−0.400046	−	0.230967i	−0.686504	+	0.727126i	$0.740856\pi$
$882$	−0.802515	+	2.99503i	−0.0270221	+	0.100848i
$883$	−10.7765	−	10.7765i	−0.362658	−	0.362658i	0.502132	−	0.864791i	$-0.332549\pi$
$883$	−10.7765	−	10.7765i	−0.362658	−	0.362658i	−0.864791	+	0.502132i	$0.832549\pi$
$884$			29.1331i			0.979852i
$885$	−7.22240	−	10.8565i	−0.242778	−	0.364936i
$886$	−3.79457	+	6.57238i	−0.127481	+	0.220803i
$887$	−13.9007	+	51.8783i	−0.466741	+	1.74190i	0.184309	+	0.982868i	$0.440995\pi$
$887$	−13.9007	+	51.8783i	−0.466741	+	1.74190i	−0.651050	+	0.759035i	$0.725671\pi$
$888$	−1.01941	−	3.80448i	−0.0342091	−	0.127670i
$889$	4.62325	−	8.00771i	0.155059	−	0.268570i
$890$	35.8880	+	17.7882i	1.20297	+	0.596262i
$891$		−	1.81779i		−	0.0608983i
$892$	1.06632	+	0.285720i	0.0357031	+	0.00956662i
$893$	−31.4372	−	8.42356i	−1.05200	−	0.281884i
$894$	−5.35755	+	9.27954i	−0.179183	+	0.310354i
$895$	11.4618	+	10.0928i	0.383127	+	0.337364i
$896$	0.987335	+	1.71011i	0.0329845	+	0.0571309i
$897$	10.4115	−	10.4115i	0.347630	−	0.347630i
$898$	−11.7414	−	11.7414i	−0.391815	−	0.391815i
$899$	−35.7286	−	11.0575i	−1.19161	−	0.368789i
$900$	−0.632608	−	4.95982i	−0.0210869	−	0.165327i
$901$	−29.1208			−0.970154
$902$	6.92315	+	1.85505i	0.230516	+	0.0617664i
$903$	1.46329	−	1.46329i	0.0486953	−	0.0486953i
$904$	−0.122529	−	0.0707421i	−0.00407525	−	0.00235285i
$905$	7.33951	+	1.47533i	0.243974	+	0.0490417i
$906$	−2.75159	−	4.76590i	−0.0914155	−	0.158336i
$907$	−21.1299	−	21.1299i	−0.701607	−	0.701607i	0.263149	−	0.964755i	$-0.415239\pi$
$907$	−21.1299	−	21.1299i	−0.701607	−	0.701607i	−0.964755	+	0.263149i	$0.915239\pi$
$908$	1.51291	+	5.64627i	0.0502078	+	0.187378i
$909$	10.5805	+	6.10867i	0.350934	+	0.202612i
$910$	7.78765	−	15.7117i	0.258158	−	0.520839i
$911$	28.4663	−	16.4350i	0.943129	−	0.544516i	0.0521894	−	0.998637i	$-0.483380\pi$
$911$	28.4663	−	16.4350i	0.943129	−	0.544516i	0.890940	+	0.454121i	$0.150047\pi$
$912$	0.764225	+	2.85213i	0.0253060	+	0.0944433i
$913$	−29.9998	−	8.03842i	−0.992848	−	0.266033i
$914$	−11.1828			−0.369893
$915$	−3.45829	+	0.219657i	−0.114328	+	0.00726163i
$916$	5.00797	−	2.89135i	0.165468	−	0.0955330i
$917$	3.80761	−	1.02025i	0.125738	−	0.0336915i
$918$	−7.08570	−	1.89861i	−0.233863	−	0.0626634i
$919$	11.8109	+	6.81900i	0.389604	+	0.224938i	0.681989	−	0.731363i	$-0.261115\pi$
$919$	11.8109	+	6.81900i	0.389604	+	0.224938i	−0.292384	+	0.956301i	$0.594449\pi$
$920$	−7.85563	+	2.64895i	−0.258992	+	0.0873333i
$921$	2.63478	+	1.52119i	0.0868190	+	0.0501250i
$922$	2.22233	−	2.22233i	0.0731886	−	0.0731886i
$923$	−10.7681	+	40.1871i	−0.354436	+	1.32277i
$924$	−3.10863	+	1.79477i	−0.102266	+	0.0590436i
$925$	18.2247	−	7.46283i	0.599223	−	0.245376i
$926$		−	1.11477i		−	0.0366337i
$927$	−2.51456	+	9.38448i	−0.0825891	+	0.308227i
$928$	4.74987	+	4.74987i	0.155922	+	0.155922i
$929$	45.8368			1.50386			0.751928	−	0.659245i	$-0.229124\pi$
$929$	45.8368			1.50386			0.751928	+	0.659245i	$0.229124\pi$
$930$	10.6223	−	6.49351i	0.348321	−	0.212931i
$931$	9.15550			0.300059
$932$	−16.6830	−	16.6830i	−0.546469	−	0.546469i
$933$	4.79626	−	17.8999i	0.157022	−	0.586016i
$934$		−	7.37323i		−	0.241259i
$935$	26.7156	+	13.2418i	0.873695	+	0.433054i
$936$	3.43936	−	1.98572i	0.112419	−	0.0649052i
$937$	−6.31163	+	23.5553i	−0.206192	+	0.769519i	0.782891	+	0.622159i	$0.213744\pi$
$937$	−6.31163	+	23.5553i	−0.206192	+	0.769519i	−0.989083	+	0.147360i	$0.952922\pi$
$938$	8.92410	−	8.92410i	0.291382	−	0.291382i
$939$	7.97090	+	4.60200i	0.260120	+	0.150181i
$940$	10.9456	−	22.0830i	0.357006	−	0.720266i
$941$	−42.5582	−	24.5710i	−1.38736	−	0.800991i	−0.394340	−	0.918964i	$-0.629027\pi$
$941$	−42.5582	−	24.5710i	−1.38736	−	0.800991i	−0.993017	+	0.117973i	$0.962360\pi$
$942$	14.6431	+	3.92360i	0.477097	+	0.127838i
$943$	−14.1202	+	3.78349i	−0.459816	+	0.123207i
$944$	−5.05014	+	2.91570i	−0.164368	+	0.0948979i
$945$	3.31386	+	2.91803i	0.107800	+	0.0949237i
$946$	−1.90500			−0.0619370
$947$	−13.9461	−	3.73685i	−0.453187	−	0.121431i	0.0250031	−	0.999687i	$-0.492040\pi$
$947$	−13.9461	−	3.73685i	−0.453187	−	0.121431i	−0.478190	+	0.878256i	$0.658707\pi$
$948$	4.51336	+	16.8441i	0.146587	+	0.547071i
$949$	44.6831	−	25.7978i	1.45048	−	0.837432i
$950$	−13.6626	+	5.59469i	−0.443272	+	0.181516i
$951$	13.1530	+	7.59390i	0.426516	+	0.246249i
$952$	3.74912	+	13.9919i	0.121510	+	0.453481i
$953$	−12.0372	−	12.0372i	−0.389924	−	0.389924i	0.484736	−	0.874660i	$-0.338916\pi$
$953$	−12.0372	−	12.0372i	−0.389924	−	0.389924i	−0.874660	+	0.484736i	$0.838916\pi$
$954$	1.98488	+	3.43791i	0.0642629	+	0.111307i
$955$	6.91663	−	34.4090i	0.223817	−	1.11345i
$956$	23.5030	+	13.5695i	0.760141	+	0.438868i
$957$	−8.63428	+	8.63428i	−0.279107	+	0.279107i
$958$	31.3216	+	8.39260i	1.01195	+	0.271153i
$959$	19.2135			0.620437
$960$	−2.23157	+	0.141741i	−0.0720236	+	0.00457466i
$961$	25.5806	+	17.5109i	0.825181	+	0.564869i
$962$	11.0607	+	11.0607i	0.356613	+	0.356613i
$963$	−8.40254	+	8.40254i	−0.270768	+	0.270768i
$964$	10.5557	+	18.2829i	0.339975	+	0.588854i
$965$	25.7157	−	1.63336i	0.827817	−	0.0525796i
$966$	3.66054	−	6.34025i	0.117776	−	0.203994i
$967$	−47.2817	−	12.6691i	−1.52048	−	0.407410i	−0.600578	−	0.799566i	$-0.705063\pi$
$967$	−47.2817	−	12.6691i	−1.52048	−	0.407410i	−0.919899	+	0.392156i	$0.871729\pi$
$968$	−7.43341	−	1.99178i	−0.238919	−	0.0640181i
$969$			21.6603i			0.695828i
$970$	−9.43447	−	27.9785i	−0.302923	−	0.898336i
$971$	4.26461	−	7.38652i	0.136858	−	0.237045i	−0.789448	−	0.613818i	$-0.789633\pi$
$971$	4.26461	−	7.38652i	0.136858	−	0.237045i	0.926306	+	0.376773i	$0.122966\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	6.60358	−	24.6449i	0.211701	−	0.790079i
$974$	−4.99688	+	8.65485i	−0.160110	+	0.277319i
$975$	12.0246	+	15.8024i	0.385095	+	0.506083i
$976$			1.54971i			0.0496050i
$977$	−20.1240	−	20.1240i	−0.643822	−	0.643822i	0.307671	−	0.951493i	$-0.400451\pi$
$977$	−20.1240	−	20.1240i	−0.643822	−	0.643822i	−0.951493	+	0.307671i	$0.900451\pi$
$978$	−5.96909	+	22.2769i	−0.190870	+	0.712338i
$979$	28.1996	+	16.2810i	0.901262	+	0.520344i
$980$	−1.36635	+	6.79737i	−0.0436466	+	0.217134i
$981$	8.31040	−	14.3940i	0.265331	−	0.459566i
$982$	9.11179	+	34.0057i	0.290769	+	1.08516i
$983$	3.32780	−	0.891681i	0.106140	−	0.0284402i	−0.205358	−	0.978687i	$-0.565836\pi$
$983$	3.32780	−	0.891681i	0.106140	−	0.0284402i	0.311498	+	0.950247i	$0.399169\pi$
$984$	−3.94290			−0.125695
$985$	16.4283	+	24.6945i	0.523449	+	0.786832i
$986$	24.6380	+	42.6743i	0.784634	+	1.35903i
$987$	5.63333	+	21.0239i	0.179311	+	0.669198i
$988$	−8.29197	−	8.29197i	−0.263803	−	0.263803i
$989$	3.36483	−	1.94269i	0.106995	−	0.0617738i
$990$	−0.257655	−	4.05653i	−0.00818881	−	0.128925i
$991$		−	1.03254i		−	0.0327996i	−0.999866	−	0.0163998i	$-0.994780\pi$
$991$		−	1.03254i		−	0.0327996i	0.999866	−	0.0163998i	$-0.00522045\pi$
$992$	−2.59702	−	4.92498i	−0.0824556	−	0.156368i
$993$	−8.56897	+	8.56897i	−0.271928	+	0.271928i
$994$			20.6866i			0.656139i
$995$	2.53885	−	12.6303i	0.0804870	−	0.400409i
$996$	17.0856			0.541378
$997$	31.6325	−	8.47590i	1.00181	−	0.268434i	0.279607	−	0.960115i	$-0.409796\pi$
$997$	31.6325	−	8.47590i	1.00181	−	0.268434i	0.722204	+	0.691680i	$0.243129\pi$
$998$	−1.60928	+	6.00590i	−0.0509407	+	0.190113i
$999$	−3.41101	+	1.96935i	−0.107919	+	0.0623073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.8	yes	64
5.3	odd	4		930.2.be.a.223.3	✓	64
31.26	odd	6		930.2.be.a.367.3	yes	64
155.88	even	12	inner	930.2.be.b.553.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.3	✓	64	5.3	odd	4
930.2.be.a.367.3	yes	64	31.26	odd	6
930.2.be.b.37.8	yes	64	1.1	even	1	trivial
930.2.be.b.553.8	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.11885 - 0.714484i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.511082 - 1.90738i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.11885 - 0.714484i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.511082 - 1.90738i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.00347 - 0.993035i) q^{10} +(-1.57425 - 0.908896i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-3.83611 + 1.02788i) q^{13} +(-1.71011 + 0.987335i) q^{14} +(-0.141741 - 2.23157i) q^{15} -1.00000 q^{16} +(-7.08570 - 1.89861i) q^{17} +(0.258819 + 0.965926i) q^{18} +(2.55715 - 1.47637i) q^{19} +(0.714484 + 2.11885i) q^{20} +(-1.71011 - 0.987335i) q^{21} +(0.470479 + 1.75585i) q^{22} +(-2.62160 - 2.62160i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.97903 - 3.02776i) q^{25} +(3.43936 + 1.98572i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.90738 + 0.511082i) q^{28} +6.71733 q^{29} +(-1.47773 + 1.67818i) q^{30} +(-5.31886 - 1.64612i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.28537 + 1.28537i) q^{33} +(3.66783 + 6.35286i) q^{34} +(-0.279891 - 4.40662i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.80448 + 1.01941i) q^{37} +(-2.85213 - 0.764225i) q^{38} +3.97144i q^{39} +(0.993035 - 2.00347i) q^{40} +(1.97145 - 3.41465i) q^{41} +(0.511082 + 1.90738i) q^{42} +(-0.271236 + 1.01227i) q^{43} +(0.908896 - 1.57425i) q^{44} +(-2.19222 - 0.440662i) q^{45} +3.70750i q^{46} +(-7.79399 - 7.79399i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(2.68527 + 1.55034i) q^{49} +(-4.95455 - 0.672643i) q^{50} +(-3.66783 + 6.35286i) q^{51} +(-1.02788 - 3.83611i) q^{52} +(3.83449 - 1.02745i) q^{53} +1.00000 q^{54} +(-3.98500 - 0.801033i) q^{55} +(-0.987335 - 1.71011i) q^{56} +(-0.764225 - 2.85213i) q^{57} +(-4.74987 - 4.74987i) q^{58} +(5.05014 - 2.91570i) q^{59} +(2.23157 - 0.141741i) q^{60} -1.54971i q^{61} +(2.59702 + 4.92498i) q^{62} +(-1.39630 + 1.39630i) q^{63} -1.00000i q^{64} +(-7.39373 + 4.91877i) q^{65} +1.81779 q^{66} +(-6.17346 + 1.65417i) q^{67} +(1.89861 - 7.08570i) q^{68} +(-3.21079 + 1.85375i) q^{69} +(-2.91803 + 3.31386i) q^{70} +(5.23799 - 9.07247i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-12.5490 + 3.36249i) q^{73} +(-1.96935 - 3.41101i) q^{74} +(-1.89475 - 4.62709i) q^{75} +(1.47637 + 2.55715i) q^{76} +(-2.53819 + 2.53819i) q^{77} +(2.80823 - 2.80823i) q^{78} +(8.71914 + 15.1020i) q^{79} +(-2.11885 + 0.714484i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-3.80855 + 1.02050i) q^{82} +(16.5034 - 4.42208i) q^{83} +(0.987335 - 1.71011i) q^{84} +(-16.3700 + 1.03976i) q^{85} +(0.907574 - 0.523988i) q^{86} +(1.73857 - 6.48844i) q^{87} +(-1.75585 + 0.470479i) q^{88} -17.9130 q^{89} +(1.23854 + 1.86173i) q^{90} +7.84227i q^{91} +(2.62160 - 2.62160i) q^{92} +(-2.96665 + 4.71158i) q^{93} +11.0224i q^{94} +(4.36336 - 4.95524i) q^{95} +(0.866025 - 0.500000i) q^{96} +(9.33706 + 9.33706i) q^{97} +(-0.802515 - 2.99503i) q^{98} +(0.908896 + 1.57425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

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