LMFDB - Embedded newform 630.2.bk.b.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (of order $6$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	630.131
Dual form			630.2.bk.b.101.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.0386792 + 1.73162i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.73162 + 0.0386792i) q^{6} +(0.281867 + 2.63069i) q^{7} +1.00000i q^{8} +(-2.99701 - 0.133955i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.0386792 + 1.73162i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.73162 + 0.0386792i) q^{6} +(0.281867 + 2.63069i) q^{7} +1.00000i q^{8} +(-2.99701 - 0.133955i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(0.390121 + 0.225236i) q^{11} +(0.0386792 - 1.73162i) q^{12} +(-4.26160 - 2.46044i) q^{13} +(2.63069 - 0.281867i) q^{14} +(1.51897 - 0.832312i) q^{15} +1.00000 q^{16} +(3.93285 + 6.81190i) q^{17} +(-0.133955 + 2.99701i) q^{18} +(-4.75019 - 2.74252i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.56626 + 0.386332i) q^{21} +(0.225236 - 0.390121i) q^{22} +(-4.21087 + 2.43115i) q^{23} +(-1.73162 - 0.0386792i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.46044 + 4.26160i) q^{26} +(0.347881 - 5.18449i) q^{27} +(-0.281867 - 2.63069i) q^{28} +(-8.05558 + 4.65089i) q^{29} +(-0.832312 - 1.51897i) q^{30} -0.574100i q^{31} -1.00000i q^{32} +(-0.405113 + 0.666828i) q^{33} +(6.81190 - 3.93285i) q^{34} +(2.13731 - 1.55945i) q^{35} +(2.99701 + 0.133955i) q^{36} +(-0.721812 + 1.25022i) q^{37} +(-2.74252 + 4.75019i) q^{38} +(4.42538 - 7.28430i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-0.956724 + 1.65709i) q^{41} +(0.386332 + 4.56626i) q^{42} +(-0.459119 - 0.795218i) q^{43} +(-0.390121 - 0.225236i) q^{44} +(1.38250 + 2.66246i) q^{45} +(2.43115 + 4.21087i) q^{46} +7.42609 q^{47} +(-0.0386792 + 1.73162i) q^{48} +(-6.84110 + 1.48301i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-11.9477 + 6.54672i) q^{51} +(4.26160 + 2.46044i) q^{52} +(-8.30591 + 4.79542i) q^{53} +(-5.18449 - 0.347881i) q^{54} -0.450472i q^{55} +(-2.63069 + 0.281867i) q^{56} +(4.93274 - 8.11944i) q^{57} +(4.65089 + 8.05558i) q^{58} +8.86555 q^{59} +(-1.51897 + 0.832312i) q^{60} +9.86290i q^{61} -0.574100 q^{62} +(-0.492361 - 7.92197i) q^{63} -1.00000 q^{64} +4.92088i q^{65} +(0.666828 + 0.405113i) q^{66} -4.64204 q^{67} +(-3.93285 - 6.81190i) q^{68} +(-4.04694 - 7.38565i) q^{69} +(-1.55945 - 2.13731i) q^{70} -3.88571i q^{71} +(0.133955 - 2.99701i) q^{72} +(4.91339 - 2.83675i) q^{73} +(1.25022 + 0.721812i) q^{74} +(-1.48029 - 0.899307i) q^{75} +(4.75019 + 2.74252i) q^{76} +(-0.482566 + 1.08977i) q^{77} +(-7.28430 - 4.42538i) q^{78} -2.00640 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.96411 + 0.802930i) q^{81} +(1.65709 + 0.956724i) q^{82} +(4.76689 + 8.25650i) q^{83} +(4.56626 - 0.386332i) q^{84} +(3.93285 - 6.81190i) q^{85} +(-0.795218 + 0.459119i) q^{86} +(-7.74198 - 14.1291i) q^{87} +(-0.225236 + 0.390121i) q^{88} +(1.98445 - 3.43716i) q^{89} +(2.66246 - 1.38250i) q^{90} +(5.27146 - 11.9045i) q^{91} +(4.21087 - 2.43115i) q^{92} +(0.994122 + 0.0222057i) q^{93} -7.42609i q^{94} +5.48505i q^{95} +(1.73162 + 0.0386792i) q^{96} +(8.69468 - 5.01988i) q^{97} +(1.48301 + 6.84110i) q^{98} +(-1.13902 - 0.727293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	$ 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.0386792	+	1.73162i	−0.0223314	+	0.999751i
$3$	−0.0386792	+	1.73162i	−0.0223314	+	0.999751i
$4$	−1.00000			−0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.73162	+	0.0386792i	0.706930	+	0.0157907i
$7$	0.281867	+	2.63069i	0.106536	+	0.994309i
$7$	0.281867	+	2.63069i	0.106536	+	0.994309i
$8$			1.00000i			0.353553i
$9$	−2.99701	−	0.133955i	−0.999003	−	0.0446517i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	0.390121	+	0.225236i	0.117626	+	0.0679113i	0.557659	−	0.830070i	$-0.311700\pi$
$11$	0.390121	+	0.225236i	0.117626	+	0.0679113i	−0.440033	+	0.897982i	$0.645033\pi$
$12$	0.0386792	−	1.73162i	0.0111657	−	0.499875i
$13$	−4.26160	−	2.46044i	−1.18196	−	0.682403i	−0.225490	−	0.974246i	$-0.572398\pi$
$13$	−4.26160	−	2.46044i	−1.18196	−	0.682403i	−0.956466	+	0.291843i	$0.905732\pi$
$14$	2.63069	−	0.281867i	0.703083	−	0.0753320i
$15$	1.51897	−	0.832312i	0.392195	−	0.214902i
$16$	1.00000			0.250000
$17$	3.93285	+	6.81190i	0.953857	+	1.65213i	0.736963	+	0.675933i	$0.236259\pi$
$17$	3.93285	+	6.81190i	0.953857	+	1.65213i	0.216894	+	0.976195i	$0.430407\pi$
$18$	−0.133955	+	2.99701i	−0.0315736	+	0.706402i
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.156254	−	0.987717i	$-0.549942\pi$
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.933515	+	0.358539i	$0.883275\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−4.56626	+	0.386332i	−0.996440	+	0.0843046i
$22$	0.225236	−	0.390121i	0.0480205	−	0.0831740i
$23$	−4.21087	+	2.43115i	−0.878026	+	0.506929i	−0.870007	−	0.493039i	$-0.835886\pi$
$23$	−4.21087	+	2.43115i	−0.878026	+	0.506929i	−0.00801924	+	0.999968i	$0.502553\pi$
$24$	−1.73162	−	0.0386792i	−0.353465	−	0.00789536i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.46044	+	4.26160i	−0.482532	+	0.835769i
$27$	0.347881	−	5.18449i	0.0669498	−	0.997756i
$28$	−0.281867	−	2.63069i	−0.0532678	−	0.497154i
$29$	−8.05558	+	4.65089i	−1.49588	+	0.863648i	−0.999989	−	0.00473444i	$-0.998493\pi$
$29$	−8.05558	+	4.65089i	−1.49588	+	0.863648i	−0.495894	+	0.868383i	$0.665160\pi$
$30$	−0.832312	−	1.51897i	−0.151959	−	0.277324i
$31$		−	0.574100i		−	0.103111i	−0.998670	−	0.0515557i	$-0.983582\pi$
$31$		−	0.574100i		−	0.103111i	0.998670	−	0.0515557i	$-0.0164180\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.405113	+	0.666828i	−0.0705211	+	0.116080i
$34$	6.81190	−	3.93285i	1.16823	−	0.674479i
$35$	2.13731	−	1.55945i	0.361272	−	0.263595i
$36$	2.99701	+	0.133955i	0.499501	+	0.0223259i
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	−0.919239	−	0.393700i	$-0.871195\pi$
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	0.800574	+	0.599234i	$0.204528\pi$
$38$	−2.74252	+	4.75019i	−0.444896	+	0.770583i
$39$	4.42538	−	7.28430i	0.708627	−	1.16642i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	−0.956724	+	1.65709i	−0.149415	+	0.258795i	−0.931011	−	0.364990i	$-0.881072\pi$
$41$	−0.956724	+	1.65709i	−0.149415	+	0.258795i	0.781596	+	0.623785i	$0.214406\pi$
$42$	0.386332	+	4.56626i	0.0596124	+	0.704590i
$43$	−0.459119	−	0.795218i	−0.0700151	−	0.121270i	0.828893	−	0.559408i	$-0.188971\pi$
$43$	−0.459119	−	0.795218i	−0.0700151	−	0.121270i	−0.898908	+	0.438138i	$0.855638\pi$
$44$	−0.390121	−	0.225236i	−0.0588129	−	0.0339556i
$45$	1.38250	+	2.66246i	0.206090	+	0.396896i
$46$	2.43115	+	4.21087i	0.358453	+	0.620858i
$47$	7.42609			1.08321			0.541604	−	0.840634i	$-0.317817\pi$
$47$	7.42609			1.08321			0.541604	+	0.840634i	$0.317817\pi$
$48$	−0.0386792	+	1.73162i	−0.00558286	+	0.249938i
$49$	−6.84110	+	1.48301i	−0.977300	+	0.211858i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−11.9477	+	6.54672i	−1.67302	+	0.916724i
$52$	4.26160	+	2.46044i	0.590978	+	0.341201i
$53$	−8.30591	+	4.79542i	−1.14090	+	0.658701i	−0.946654	−	0.322251i	$-0.895561\pi$
$53$	−8.30591	+	4.79542i	−1.14090	+	0.658701i	−0.194250	+	0.980952i	$0.562227\pi$
$54$	−5.18449	−	0.347881i	−0.705520	−	0.0473406i
$55$		−	0.450472i		−	0.0607417i
$56$	−2.63069	+	0.281867i	−0.351541	+	0.0376660i
$57$	4.93274	−	8.11944i	0.653357	−	1.07545i
$58$	4.65089	+	8.05558i	0.610692	+	1.05775i
$59$	8.86555			1.15420			0.577098	−	0.816675i	$-0.304185\pi$
$59$	8.86555			1.15420			0.577098	+	0.816675i	$0.304185\pi$
$60$	−1.51897	+	0.832312i	−0.196098	+	0.107451i
$61$			9.86290i			1.26281i	0.775451	+	0.631407i	$0.217522\pi$
$61$			9.86290i			1.26281i	−0.775451	+	0.631407i	$0.782478\pi$
$62$	−0.574100			−0.0729107
$63$	−0.492361	−	7.92197i	−0.0620317	−	0.998074i
$64$	−1.00000			−0.125000
$65$			4.92088i			0.610359i
$66$	0.666828	+	0.405113i	0.0820809	+	0.0498659i
$67$	−4.64204			−0.567116			−0.283558	−	0.958955i	$-0.591515\pi$
$67$	−4.64204			−0.567116			−0.283558	+	0.958955i	$0.591515\pi$
$68$	−3.93285	−	6.81190i	−0.476928	−	0.826064i
$69$	−4.04694	−	7.38565i	−0.487195	−	0.889128i
$70$	−1.55945	−	2.13731i	−0.186390	−	0.255458i
$71$		−	3.88571i		−	0.461149i	−0.973055	−	0.230575i	$-0.925939\pi$
$71$		−	3.88571i		−	0.461149i	0.973055	−	0.230575i	$-0.0740606\pi$
$72$	0.133955	−	2.99701i	0.0157868	−	0.353201i
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	−0.184102	−	0.982907i	$-0.558938\pi$
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	0.759171	+	0.650891i	$0.225604\pi$
$74$	1.25022	+	0.721812i	0.145335	+	0.0839090i
$75$	−1.48029	−	0.899307i	−0.170929	−	0.103843i
$76$	4.75019	+	2.74252i	0.544884	+	0.314589i
$77$	−0.482566	+	1.08977i	−0.0549935	+	0.124191i
$78$	−7.28430	−	4.42538i	−0.824785	−	0.501075i
$79$	−2.00640			−0.225738			−0.112869	−	0.993610i	$-0.536004\pi$
$79$	−2.00640			−0.225738			−0.112869	+	0.993610i	$0.536004\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	8.96411	+	0.802930i	0.996012	+	0.0892144i
$82$	1.65709	+	0.956724i	0.182995	+	0.105652i
$83$	4.76689	+	8.25650i	0.523234	+	0.906268i	0.999634	+	0.0270398i	$0.00860808\pi$
$83$	4.76689	+	8.25650i	0.523234	+	0.906268i	−0.476400	+	0.879229i	$0.658059\pi$
$84$	4.56626	−	0.386332i	0.498220	−	0.0421523i
$85$	3.93285	−	6.81190i	0.426578	−	0.738854i
$86$	−0.795218	+	0.459119i	−0.0857506	+	0.0495081i
$87$	−7.74198	−	14.1291i	−0.830028	−	1.51480i
$88$	−0.225236	+	0.390121i	−0.0240103	+	0.0415870i
$89$	1.98445	−	3.43716i	0.210351	−	0.364339i	−0.741473	−	0.670982i	$-0.765873\pi$
$89$	1.98445	−	3.43716i	0.210351	−	0.364339i	0.951824	+	0.306644i	$0.0992060\pi$
$90$	2.66246	−	1.38250i	0.280648	−	0.145728i
$91$	5.27146	−	11.9045i	0.552599	−	1.24793i
$92$	4.21087	−	2.43115i	0.439013	−	0.253464i
$93$	0.994122	+	0.0222057i	0.103086	+	0.00230263i
$94$		−	7.42609i		−	0.765943i
$95$			5.48505i			0.562754i
$96$	1.73162	+	0.0386792i	0.176733	+	0.00394768i
$97$	8.69468	−	5.01988i	0.882811	−	0.509691i	0.0112270	−	0.999937i	$-0.496426\pi$
$97$	8.69468	−	5.01988i	0.882811	−	0.509691i	0.871584	+	0.490246i	$0.163093\pi$
$98$	1.48301	+	6.84110i	0.149807	+	0.691056i
$99$	−1.13902	−	0.727293i	−0.114476	−	0.0730957i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−2.74955	+	4.76235i	−0.273590	+	0.473872i	−0.969778	−	0.243987i	$-0.921545\pi$
$101$	−2.74955	+	4.76235i	−0.273590	+	0.473872i	0.696188	+	0.717859i	$0.254878\pi$
$102$	6.54672	+	11.9477i	0.648222	+	1.18300i
$103$	13.4299	−	7.75376i	1.32329	−	0.764000i	0.339036	−	0.940773i	$-0.389899\pi$
$103$	13.4299	−	7.75376i	1.32329	−	0.764000i	0.984252	+	0.176773i	$0.0565659\pi$
$104$	2.46044	−	4.26160i	0.241266	−	0.417885i
$105$	2.61770	+	3.76133i	0.255462	+	0.367068i
$106$	4.79542	+	8.30591i	0.465772	+	0.806741i
$107$	−8.60043	−	4.96546i	−0.831435	−	0.480029i	0.0229088	−	0.999738i	$-0.492707\pi$
$107$	−8.60043	−	4.96546i	−0.831435	−	0.480029i	−0.854344	+	0.519708i	$0.826041\pi$
$108$	−0.347881	+	5.18449i	−0.0334749	+	0.498878i
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	0.952784	−	0.303647i	$-0.0982045\pi$
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	−0.739359	+	0.673312i	$0.764871\pi$
$110$	−0.450472			−0.0429509
$111$	−2.13698	−	1.29826i	−0.202833	−	0.123225i
$112$	0.281867	+	2.63069i	0.0266339	+	0.248577i
$113$	17.4964	+	10.1015i	1.64592	+	0.950271i	0.978671	+	0.205435i	$0.0658610\pi$
$113$	17.4964	+	10.1015i	1.64592	+	0.950271i	0.667247	+	0.744836i	$0.267472\pi$
$114$	−8.11944	−	4.93274i	−0.760455	−	0.461993i
$115$	4.21087	+	2.43115i	0.392665	+	0.226705i
$116$	8.05558	−	4.65089i	0.747942	−	0.431824i
$117$	12.4425	+	7.94482i	1.15031	+	0.734498i
$118$		−	8.86555i		−	0.816140i
$119$	−16.8115	+	12.2662i	−1.54111	+	1.12444i
$120$	0.832312	+	1.51897i	0.0759794	+	0.138662i
$121$	−5.39854	−	9.35054i	−0.490776	−	0.850049i
$122$	9.86290			0.892945
$123$	−2.83245	−	1.72078i	−0.255393	−	0.155157i
$124$			0.574100i			0.0515557i
$125$	1.00000			0.0894427
$126$	−7.92197	+	0.492361i	−0.705745	+	0.0438630i
$127$	3.08808			0.274023			0.137012	−	0.990569i	$-0.456250\pi$
$127$	3.08808			0.274023			0.137012	+	0.990569i	$0.456250\pi$
$128$			1.00000i			0.0883883i
$129$	1.39477	−	0.764261i	0.122803	−	0.0672895i
$130$	4.92088			0.431589
$131$	−7.85422	−	13.6039i	−0.686227	−	1.18858i	−0.973050	−	0.230596i	$-0.925933\pi$
$131$	−7.85422	−	13.6039i	−0.686227	−	1.18858i	0.286823	−	0.957984i	$-0.407401\pi$
$132$	0.405113	−	0.666828i	0.0352605	−	0.0580399i
$133$	5.87582	−	13.2693i	0.509498	−	1.15060i
$134$			4.64204i			0.401012i
$135$	−4.66384	+	2.29097i	−0.401400	+	0.197176i
$136$	−6.81190	+	3.93285i	−0.584116	+	0.337239i
$137$	11.3130	+	6.53158i	0.966537	+	0.558030i	0.898179	−	0.439631i	$-0.144891\pi$
$137$	11.3130	+	6.53158i	0.966537	+	0.558030i	0.0683579	+	0.997661i	$0.478224\pi$
$138$	−7.38565	+	4.04694i	−0.628708	+	0.344499i
$139$	0.567606	+	0.327707i	0.0481437	+	0.0277958i	0.523879	−	0.851793i	$-0.324485\pi$
$139$	0.567606	+	0.327707i	0.0481437	+	0.0277958i	−0.475735	+	0.879589i	$0.657818\pi$
$140$	−2.13731	+	1.55945i	−0.180636	+	0.131798i
$141$	−0.287235	+	12.8592i	−0.0241896	+	1.08294i
$142$	−3.88571			−0.326082
$143$	−1.10836	−	1.91973i	−0.0926857	−	0.160536i
$144$	−2.99701	−	0.133955i	−0.249751	−	0.0111629i
$145$	8.05558	+	4.65089i	0.668979	+	0.386235i
$146$	−2.83675	−	4.91339i	−0.234771	−	0.406635i
$147$	−2.30340	−	11.9035i	−0.189981	−	0.981788i
$148$	0.721812	−	1.25022i	0.0593326	−	0.102767i
$149$	−4.00375	+	2.31156i	−0.328000	+	0.189371i	−0.654953	−	0.755670i	$-0.727311\pi$
$149$	−4.00375	+	2.31156i	−0.328000	+	0.189371i	0.326953	+	0.945041i	$0.393978\pi$
$150$	−0.899307	+	1.48029i	−0.0734281	+	0.120865i
$151$	−6.15097	+	10.6538i	−0.500559	+	0.866993i	0.499441	+	0.866348i	$0.333539\pi$
$151$	−6.15097	+	10.6538i	−0.500559	+	0.866993i	−1.00000		0.000645075i	$0.999795\pi$
$152$	2.74252	−	4.75019i	0.222448	−	0.385291i
$153$	−10.8743	−	20.9421i	−0.879135	−	1.69307i
$154$	1.08977	+	0.482566i	0.0878165	+	0.0388862i
$155$	−0.497185	+	0.287050i	−0.0399349	+	0.0230564i
$156$	−4.42538	+	7.28430i	−0.354314	+	0.583211i
$157$		−	19.2365i		−	1.53524i	−0.640905	−	0.767620i	$-0.721441\pi$
$157$		−	19.2365i		−	1.53524i	0.640905	−	0.767620i	$-0.278559\pi$
$158$			2.00640i			0.159621i
$159$	−7.98257	−	14.5682i	−0.633059	−	1.15533i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−7.58250	−	10.3922i	−0.597585	−	0.819024i
$162$	0.802930	−	8.96411i	0.0630841	−	0.704287i
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	−0.717879	−	0.696168i	$-0.754887\pi$
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	0.961839	+	0.273617i	$0.0882200\pi$
$164$	0.956724	−	1.65709i	0.0747076	−	0.129397i
$165$	0.780047	+	0.0174239i	0.0607265	+	0.00135645i
$166$	8.25650	−	4.76689i	0.640829	−	0.369983i
$167$	3.60660	−	6.24681i	0.279087	−	0.483393i	−0.692071	−	0.721829i	$-0.743302\pi$
$167$	3.60660	−	6.24681i	0.279087	−	0.483393i	0.971158	+	0.238437i	$0.0766349\pi$
$168$	−0.386332	−	4.56626i	−0.0298062	−	0.352295i
$169$	5.60751	+	9.71249i	0.431347	+	0.747114i
$170$	−6.81190	−	3.93285i	−0.522449	−	0.301636i
$171$	13.8690	+	8.85568i	1.06059	+	0.677211i
$172$	0.459119	+	0.795218i	0.0350075	+	0.0606348i
$173$	15.6000			1.18605			0.593024	−	0.805185i	$-0.297934\pi$
$173$	15.6000			1.18605			0.593024	+	0.805185i	$0.297934\pi$
$174$	−14.1291	+	7.74198i	−1.07112	+	0.586918i
$175$	−2.41918	−	1.07124i	−0.182873	−	0.0809784i
$176$	0.390121	+	0.225236i	0.0294064	+	0.0169778i
$177$	−0.342912	+	15.3518i	−0.0257749	+	1.15391i
$178$	−3.43716	−	1.98445i	−0.257626	−	0.148741i
$179$	3.30274	−	1.90684i	0.246858	−	0.142524i	−0.371466	−	0.928446i	$-0.621145\pi$
$179$	3.30274	−	1.90684i	0.246858	−	0.142524i	0.618325	+	0.785923i	$0.287812\pi$
$180$	−1.38250	−	2.66246i	−0.103045	−	0.198448i
$181$			4.59480i			0.341529i	0.985312	+	0.170764i	$0.0546237\pi$
$181$			4.59480i			0.341529i	−0.985312	+	0.170764i	$0.945376\pi$
$182$	−11.9045	−	5.27146i	−0.882419	−	0.390746i
$183$	−17.0788	−	0.381489i	−1.26250	−	0.0282005i
$184$	−2.43115	−	4.21087i	−0.179226	−	0.310429i
$185$	1.44362			0.106137
$186$	0.0222057	−	0.994122i	0.00162820	−	0.0728925i
$187$			3.54328i			0.259110i
$188$	−7.42609			−0.541604
$189$	13.7369	−	0.546166i	0.999211	−	0.0397277i
$190$	5.48505			0.397927
$191$			25.0936i			1.81571i	0.419285	+	0.907855i	$0.362281\pi$
$191$			25.0936i			1.81571i	−0.419285	+	0.907855i	$0.637719\pi$
$192$	0.0386792	−	1.73162i	0.00279143	−	0.124969i
$193$	−17.9048			−1.28882			−0.644408	−	0.764682i	$-0.722896\pi$
$193$	−17.9048			−1.28882			−0.644408	+	0.764682i	$0.722896\pi$
$194$	−5.01988	−	8.69468i	−0.360406	−	0.624242i
$195$	−8.52108	−	0.190335i	−0.610207	−	0.0136302i
$196$	6.84110	−	1.48301i	0.488650	−	0.105929i
$197$			12.6523i			0.901439i	0.892666	+	0.450720i	$0.148833\pi$
$197$			12.6523i			0.901439i	−0.892666	+	0.450720i	$0.851167\pi$
$198$	−0.727293	+	1.13902i	−0.0516865	+	0.0809468i
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.979832	−	0.199823i	$-0.935963\pi$
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.316865	+	0.948471i	$0.602630\pi$
$200$	−0.866025	−	0.500000i	−0.0612372	−	0.0353553i
$201$	0.179551	−	8.03825i	0.0126645	−	0.566975i
$202$	4.76235	+	2.74955i	0.335078	+	0.193457i
$203$	−14.5057	−	19.8808i	−1.01810	−	1.39536i
$204$	11.9477	−	6.54672i	0.836509	−	0.458362i
$205$	1.91345			0.133641
$206$	−7.75376	−	13.4299i	−0.540230	−	0.935705i
$207$	12.9457	−	6.72209i	0.899786	−	0.467218i
$208$	−4.26160	−	2.46044i	−0.295489	−	0.170601i
$209$	−1.23543	−	2.13983i	−0.0854566	−	0.148015i
$210$	3.76133	−	2.61770i	0.259557	−	0.180639i
$211$	10.0132	−	17.3434i	0.689338	−	1.19397i	−0.282714	−	0.959204i	$-0.591235\pi$
$211$	10.0132	−	17.3434i	0.689338	−	1.19397i	0.972052	−	0.234764i	$-0.0754318\pi$
$212$	8.30591	−	4.79542i	0.570452	−	0.329351i
$213$	6.72857	+	0.150296i	0.461034	+	0.0102981i
$214$	−4.96546	+	8.60043i	−0.339432	+	0.587913i
$215$	−0.459119	+	0.795218i	−0.0313117	+	0.0542334i
$216$	5.18449	+	0.347881i	0.352760	+	0.0236703i
$217$	1.51028	−	0.161819i	0.102525	−	0.0109850i
$218$	3.85941	−	2.22823i	0.261392	−	0.150915i
$219$	4.72212	+	8.61785i	0.319091	+	0.582340i
$220$			0.450472i			0.0303708i
$221$		−	38.7061i		−	2.60366i
$222$	−1.29826	+	2.13698i	−0.0871336	+	0.143425i
$223$	−2.43988	+	1.40867i	−0.163387	+	0.0943313i	−0.579464	−	0.814998i	$-0.696738\pi$
$223$	−2.43988	+	1.40867i	−0.163387	+	0.0943313i	0.416077	+	0.909329i	$0.363405\pi$
$224$	2.63069	−	0.281867i	0.175771	−	0.0188330i
$225$	1.61451	−	2.52851i	0.107634	−	0.168567i
$226$	10.1015	−	17.4964i	0.671943	−	1.16384i
$227$	−1.29508	+	2.24315i	−0.0859577	+	0.148883i	−0.905799	−	0.423708i	$-0.860728\pi$
$227$	−1.29508	+	2.24315i	−0.0859577	+	0.148883i	0.819841	+	0.572591i	$0.194062\pi$
$228$	−4.93274	+	8.11944i	−0.326679	+	0.537723i
$229$	−18.6354	+	10.7592i	−1.23146	+	0.710986i	−0.967335	−	0.253501i	$-0.918418\pi$
$229$	−18.6354	+	10.7592i	−1.23146	+	0.710986i	−0.264129	+	0.964487i	$0.585084\pi$
$230$	2.43115	−	4.21087i	0.160305	−	0.277656i
$231$	−1.86841	−	0.877771i	−0.122932	−	0.0577531i
$232$	−4.65089	−	8.05558i	−0.305346	−	0.528875i
$233$	2.79452	+	1.61342i	0.183075	+	0.105699i	0.588737	−	0.808325i	$-0.299625\pi$
$233$	2.79452	+	1.61342i	0.183075	+	0.105699i	−0.405661	+	0.914023i	$0.632959\pi$
$234$	7.94482	−	12.4425i	0.519369	−	0.813390i
$235$	−3.71305	−	6.43119i	−0.242212	−	0.419524i
$236$	−8.86555			−0.577098
$237$	0.0776060	−	3.47432i	0.00504105	−	0.225682i
$238$	12.2662	+	16.8115i	0.795098	+	1.08973i
$239$	13.9417	+	8.04923i	0.901812	+	0.520661i	0.877788	−	0.479050i	$-0.159019\pi$
$239$	13.9417	+	8.04923i	0.901812	+	0.520661i	0.0240242	+	0.999711i	$0.492352\pi$
$240$	1.51897	−	0.832312i	0.0980488	−	0.0537255i
$241$	−22.2029	−	12.8188i	−1.43021	−	0.825733i	−0.433075	−	0.901358i	$-0.642572\pi$
$241$	−22.2029	−	12.8188i	−1.43021	−	0.825733i	−0.997136	+	0.0756248i	$0.975905\pi$
$242$	−9.35054	+	5.39854i	−0.601076	+	0.347031i
$243$	−1.73709	+	15.4914i	−0.111435	+	0.993772i
$244$		−	9.86290i		−	0.631407i
$245$	4.70487	+	5.18306i	0.300583	+	0.331134i
$246$	−1.72078	+	2.83245i	−0.109713	+	0.180590i
$247$	13.4956	+	23.3751i	0.858706	+	1.48732i
$248$	0.574100			0.0364554
$249$	−14.4815	+	7.93508i	−0.917727	+	0.502866i
$250$		−	1.00000i		−	0.0632456i
$251$	−12.7547			−0.805068			−0.402534	−	0.915405i	$-0.631871\pi$
$251$	−12.7547			−0.805068			−0.402534	+	0.915405i	$0.631871\pi$
$252$	0.492361	+	7.92197i	0.0310158	+	0.499037i
$253$	−2.19033			−0.137705
$254$		−	3.08808i		−	0.193764i
$255$	11.6435	+	7.07368i	0.729144	+	0.442971i
$256$	1.00000			0.0625000
$257$	13.5388	+	23.4499i	0.844528	+	1.46276i	0.886031	+	0.463626i	$0.153452\pi$
$257$	13.5388	+	23.4499i	0.844528	+	1.46276i	−0.0415034	+	0.999138i	$0.513215\pi$
$258$	−0.764261	−	1.39477i	−0.0475808	−	0.0868348i
$259$	−3.49239	−	1.54647i	−0.217007	−	0.0960932i
$260$		−	4.92088i		−	0.305180i
$261$	24.7656	−	12.8597i	1.53295	−	0.795993i
$262$	−13.6039	+	7.85422i	−0.840453	+	0.485235i
$263$	−11.5471	−	6.66669i	−0.712022	−	0.411086i	0.0997875	−	0.995009i	$-0.468184\pi$
$263$	−11.5471	−	6.66669i	−0.712022	−	0.411086i	−0.811809	+	0.583923i	$0.801517\pi$
$264$	−0.666828	−	0.405113i	−0.0410404	−	0.0249330i
$265$	8.30591	+	4.79542i	0.510228	+	0.294580i
$266$	−13.2693	−	5.87582i	−0.813595	−	0.360270i
$267$	5.87510	+	3.56925i	0.359550	+	0.218435i
$268$	4.64204			0.283558
$269$	7.58415	+	13.1361i	0.462414	+	0.800924i	0.999081	−	0.0428702i	$-0.0136502\pi$
$269$	7.58415	+	13.1361i	0.462414	+	0.800924i	−0.536667	+	0.843794i	$0.680317\pi$
$270$	2.29097	+	4.66384i	0.139424	+	0.283833i
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.992542	−	0.121900i	$-0.0388986\pi$
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.390703	+	0.920517i	$0.372232\pi$
$272$	3.93285	+	6.81190i	0.238464	+	0.413032i
$273$	20.4101	+	9.58861i	1.23528	+	0.580329i
$274$	6.53158	−	11.3130i	0.394587	−	0.683445i
$275$	−0.390121	+	0.225236i	−0.0235252	+	0.0135823i
$276$	4.04694	+	7.38565i	0.243597	+	0.444564i
$277$	−11.6400	+	20.1611i	−0.699381	+	1.21136i	0.269301	+	0.963056i	$0.413207\pi$
$277$	−11.6400	+	20.1611i	−0.699381	+	1.21136i	−0.968681	+	0.248307i	$0.920126\pi$
$278$	0.327707	−	0.567606i	0.0196546	−	0.0340427i
$279$	−0.0769037	+	1.72058i	−0.00460410	+	0.103009i
$280$	1.55945	+	2.13731i	0.0931950	+	0.127729i
$281$	−3.40387	+	1.96523i	−0.203058	+	0.117236i	−0.598081	−	0.801436i	$-0.704070\pi$
$281$	−3.40387	+	1.96523i	−0.203058	+	0.117236i	0.395023	+	0.918671i	$0.370737\pi$
$282$	12.8592	+	0.287235i	0.765752	+	0.0171046i
$283$			28.8938i			1.71756i	0.512348	+	0.858778i	$0.328776\pi$
$283$			28.8938i			1.71756i	−0.512348	+	0.858778i	$0.671224\pi$
$284$			3.88571i			0.230575i
$285$	−9.49801	−	0.212157i	−0.562614	−	0.0125671i
$286$	−1.91973	+	1.10836i	−0.113516	+	0.0655387i
$287$	−4.62898	−	2.04977i	−0.273240	−	0.120994i
$288$	−0.133955	+	2.99701i	−0.00789339	+	0.176600i
$289$	−22.4347	+	38.8580i	−1.31969	+	2.28576i
$290$	4.65089	−	8.05558i	0.273110	−	0.473040i
$291$	8.35621	+	15.2500i	0.489850	+	0.893973i
$292$	−4.91339	+	2.83675i	−0.287535	+	0.166008i
$293$	−2.16359	+	3.74744i	−0.126398	+	0.218928i	−0.922279	−	0.386526i	$-0.873675\pi$
$293$	−2.16359	+	3.74744i	−0.126398	+	0.218928i	0.795880	+	0.605454i	$0.207008\pi$
$294$	−11.9035	+	2.30340i	−0.694229	+	0.134337i
$295$	−4.43278	−	7.67779i	−0.258086	−	0.447018i
$296$	−1.25022	−	0.721812i	−0.0726673	−	0.0419545i
$297$	1.30345	−	1.94422i	0.0756339	−	0.112815i
$298$	2.31156	+	4.00375i	0.133905	+	0.231931i
$299$	23.9267			1.38372
$300$	1.48029	+	0.899307i	0.0854644	+	0.0519215i
$301$	1.96257	−	1.43195i	0.113120	−	0.0825361i
$302$	10.6538	+	6.15097i	0.613057	+	0.353948i
$303$	−8.14023	−	4.94537i	−0.467644	−	0.284104i
$304$	−4.75019	−	2.74252i	−0.272442	−	0.157295i
$305$	8.54152	−	4.93145i	0.489086	−	0.282374i
$306$	−20.9421	+	10.8743i	−1.19718	+	0.621642i
$307$			0.419882i			0.0239639i	0.999928	+	0.0119820i	$0.00381407\pi$
$307$			0.419882i			0.0239639i	−0.999928	+	0.0119820i	$0.996186\pi$
$308$	0.482566	−	1.08977i	0.0274967	−	0.0620957i
$309$	12.9071	+	23.5554i	0.734259	+	1.34002i
$310$	0.287050	+	0.497185i	0.0163033	+	0.0282382i
$311$	−6.28435			−0.356353			−0.178177	−	0.983999i	$-0.557020\pi$
$311$	−6.28435			−0.356353			−0.178177	+	0.983999i	$0.557020\pi$
$312$	7.28430	+	4.42538i	0.412393	+	0.250538i
$313$		−	5.68411i		−	0.321285i	−0.987013	−	0.160642i	$-0.948643\pi$
$313$		−	5.68411i		−	0.321285i	0.987013	−	0.160642i	$-0.0513566\pi$
$314$	−19.2365			−1.08558
$315$	−6.61445	+	4.38738i	−0.372682	+	0.247201i
$316$	2.00640			0.112869
$317$			10.0314i			0.563419i	0.959500	+	0.281710i	$0.0909015\pi$
$317$			10.0314i			0.563419i	−0.959500	+	0.281710i	$0.909099\pi$
$318$	−14.5682	+	7.98257i	−0.816941	+	0.447640i
$319$	−4.19019			−0.234606
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	8.93094	−	14.7006i	0.498477	−	0.820508i
$322$	−10.3922	+	7.58250i	−0.579137	+	0.422556i
$323$		−	43.1438i		−	2.40058i
$324$	−8.96411	−	0.802930i	−0.498006	−	0.0446072i
$325$	4.26160	−	2.46044i	0.236391	−	0.136481i
$326$	−5.39478	−	3.11468i	−0.298789	−	0.172506i
$327$	−6.76922	+	3.70917i	−0.374338	+	0.205118i
$328$	−1.65709	−	0.956724i	−0.0914977	−	0.0528262i
$329$	2.09317	+	19.5358i	0.115400	+	1.07704i
$330$	0.0174239	−	0.780047i	0.000959155	−	0.0429401i
$331$	31.7032			1.74256			0.871282	−	0.490783i	$-0.163289\pi$
$331$	31.7032			1.74256			0.871282	+	0.490783i	$0.163289\pi$
$332$	−4.76689	−	8.25650i	−0.261617	−	0.453134i
$333$	2.33075	−	3.65022i	0.127724	−	0.200031i
$334$	−6.24681	−	3.60660i	−0.341810	−	0.197344i
$335$	2.32102	+	4.02013i	0.126811	+	0.219643i
$336$	−4.56626	+	0.386332i	−0.249110	+	0.0210762i
$337$	−7.09612	+	12.2908i	−0.386550	+	0.669525i	−0.991983	−	0.126372i	$-0.959667\pi$
$337$	−7.09612	+	12.2908i	−0.386550	+	0.669525i	0.605433	+	0.795897i	$0.293000\pi$
$338$	9.71249	−	5.60751i	0.528290	−	0.305008i
$339$	−18.1687	+	29.9063i	−0.986790	+	1.62429i
$340$	−3.93285	+	6.81190i	−0.213289	+	0.369427i
$341$	0.129308	−	0.223968i	0.00700242	−	0.0121286i
$342$	8.85568	−	13.8690i	0.478860	−	0.749949i
$343$	−5.82962	−	17.5788i	−0.314770	−	0.949168i
$344$	0.795218	−	0.459119i	0.0428753	−	0.0247541i
$345$	−4.37269	+	7.19758i	−0.235418	+	0.387505i
$346$		−	15.6000i		−	0.838663i
$347$			0.732838i			0.0393408i	0.999807	+	0.0196704i	$0.00626169\pi$
$347$			0.732838i			0.0393408i	−0.999807	+	0.0196704i	$0.993738\pi$
$348$	7.74198	+	14.1291i	0.415014	+	0.757398i
$349$	23.1243	−	13.3508i	1.23782	−	0.714653i	0.269169	−	0.963093i	$-0.413251\pi$
$349$	23.1243	−	13.3508i	1.23782	−	0.714653i	0.968647	+	0.248440i	$0.0799178\pi$
$350$	−1.07124	+	2.41918i	−0.0572604	+	0.129311i
$351$	−14.2387	+	21.2383i	−0.760003	+	1.13362i
$352$	0.225236	−	0.390121i	0.0120051	−	0.0207935i
$353$	3.00158	−	5.19889i	0.159758	−	0.276709i	−0.775023	−	0.631933i	$-0.782262\pi$
$353$	3.00158	−	5.19889i	0.159758	−	0.276709i	0.934781	+	0.355223i	$0.115595\pi$
$354$	15.3518	+	0.342912i	0.815937	+	0.0182256i
$355$	−3.36513	+	1.94286i	−0.178602	+	0.103116i
$356$	−1.98445	+	3.43716i	−0.105176	+	0.182169i
$357$	−20.5901	−	29.5855i	−1.08974	−	1.56583i
$358$	−1.90684	−	3.30274i	−0.100780	−	0.174555i
$359$	−25.3873	−	14.6574i	−1.33989	−	0.773587i	−0.353101	−	0.935585i	$-0.614873\pi$
$359$	−25.3873	−	14.6574i	−1.33989	−	0.773587i	−0.986791	+	0.161998i	$0.948206\pi$
$360$	−2.66246	+	1.38250i	−0.140324	+	0.0728639i
$361$	5.54288	+	9.60055i	0.291730	+	0.505292i
$362$	4.59480			0.241497
$363$	16.4004	−	8.98654i	0.860797	−	0.471671i
$364$	−5.27146	+	11.9045i	−0.276299	+	0.623965i
$365$	−4.91339	−	2.83675i	−0.257179	−	0.148482i
$366$	−0.381489	+	17.0788i	−0.0199407	+	0.892722i
$367$	−17.3499	−	10.0170i	−0.905658	−	0.522882i	−0.0266265	−	0.999645i	$-0.508476\pi$
$367$	−17.3499	−	10.0170i	−0.905658	−	0.522882i	−0.879032	+	0.476763i	$0.841810\pi$
$368$	−4.21087	+	2.43115i	−0.219507	+	0.126732i
$369$	3.08929	−	4.83817i	0.160822	−	0.251865i
$370$		−	1.44362i		−	0.0750505i
$371$	−14.9564	−	20.4986i	−0.776500	−	1.06424i
$372$	−0.994122	−	0.0222057i	−0.0515428	−	0.00115131i
$373$	3.43358	+	5.94714i	0.177784	+	0.307931i	0.941121	−	0.338069i	$-0.109774\pi$
$373$	3.43358	+	5.94714i	0.177784	+	0.307931i	−0.763337	+	0.646000i	$0.776440\pi$
$374$	3.54328			0.183219
$375$	−0.0386792	+	1.73162i	−0.00199738	+	0.0894204i
$376$			7.42609i			0.382972i
$377$	45.7729			2.35742
$378$	−0.546166	−	13.7369i	−0.0280918	−	0.706549i
$379$	0.682216			0.0350431			0.0175216	−	0.999846i	$-0.494422\pi$
$379$	0.682216			0.0350431			0.0175216	+	0.999846i	$0.494422\pi$
$380$		−	5.48505i		−	0.281377i
$381$	−0.119445	+	5.34739i	−0.00611933	+	0.273955i
$382$	25.0936			1.28390
$383$	15.8162	+	27.3944i	0.808168	+	1.39979i	0.914132	+	0.405417i	$0.132874\pi$
$383$	15.8162	+	27.3944i	0.808168	+	1.39979i	−0.105964	+	0.994370i	$0.533793\pi$
$384$	−1.73162	−	0.0386792i	−0.0883663	−	0.00197384i
$385$	1.18506	−	0.126973i	0.0603960	−	0.00647115i
$386$			17.9048i			0.911331i
$387$	1.26946	+	2.44478i	0.0645303	+	0.124275i
$388$	−8.69468	+	5.01988i	−0.441406	+	0.254846i
$389$	−24.2765	−	14.0160i	−1.23087	−	0.710641i	−0.263656	−	0.964617i	$-0.584929\pi$
$389$	−24.2765	−	14.0160i	−1.23087	−	0.710641i	−0.967211	+	0.253975i	$0.918262\pi$
$390$	−0.190335	+	8.52108i	−0.00963801	+	0.431482i
$391$	−33.1214	−	19.1227i	−1.67502	−	0.967075i
$392$	−1.48301	−	6.84110i	−0.0749033	−	0.345528i
$393$	23.8606	−	13.0743i	1.20361	−	0.659513i
$394$	12.6523			0.637414
$395$	1.00320	+	1.73760i	0.0504765	+	0.0874279i
$396$	1.13902	+	0.727293i	0.0572380	+	0.0365479i
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.295682	−	0.955286i	$-0.595547\pi$
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.975143	+	0.221575i	$0.928880\pi$
$398$	10.5610	+	18.2922i	0.529374	+	0.916903i
$399$	22.7501	+	10.6879i	1.13893	+	0.535066i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	10.0194	−	5.78471i	0.500346	−	0.288875i	−0.228510	−	0.973541i	$-0.573386\pi$
$401$	10.0194	−	5.78471i	0.500346	−	0.288875i	0.728856	+	0.684667i	$0.240052\pi$
$402$	−8.03825	−	0.179551i	−0.400912	−	0.00895517i
$403$	−1.41254	+	2.44658i	−0.0703635	+	0.121873i
$404$	2.74955	−	4.76235i	0.136795	−	0.236936i
$405$	−3.78670	−	8.16461i	−0.188163	−	0.405703i
$406$	−19.8808	+	14.5057i	−0.986669	+	0.719904i
$407$	−0.563188	+	0.325157i	−0.0279162	+	0.0161174i
$408$	−6.54672	−	11.9477i	−0.324111	−	0.591501i
$409$			2.07755i			0.102728i	0.998680	+	0.0513641i	$0.0163569\pi$
$409$			2.07755i			0.102728i	−0.998680	+	0.0513641i	$0.983643\pi$
$410$		−	1.91345i		−	0.0944984i
$411$	−11.7478	+	19.3372i	−0.579475	+	0.953834i
$412$	−13.4299	+	7.75376i	−0.661644	+	0.382000i
$413$	2.49890	+	23.3226i	0.122963	+	1.14763i
$414$	−6.72209	−	12.9457i	−0.330373	−	0.636245i
$415$	4.76689	−	8.25650i	0.233998	−	0.405296i
$416$	−2.46044	+	4.26160i	−0.120633	+	0.208942i
$417$	−0.589419	+	0.970201i	−0.0288640	+	0.0475110i
$418$	−2.13983	+	1.23543i	−0.104663	+	0.0604269i
$419$	3.15211	−	5.45962i	0.153991	−	0.266720i	−0.778700	−	0.627396i	$-0.784121\pi$
$419$	3.15211	−	5.45962i	0.153991	−	0.266720i	0.932691	+	0.360676i	$0.117454\pi$
$420$	−2.61770	−	3.76133i	−0.127731	−	0.183534i
$421$	−1.30121	−	2.25376i	−0.0634172	−	0.109842i	0.832574	−	0.553914i	$-0.186867\pi$
$421$	−1.30121	−	2.25376i	−0.0634172	−	0.109842i	−0.895991	+	0.444073i	$0.853533\pi$
$422$	−17.3434	−	10.0132i	−0.844263	−	0.487436i
$423$	−22.2561	−	0.994764i	−1.08213	−	0.0483671i
$424$	−4.79542	−	8.30591i	−0.232886	−	0.403371i
$425$	−7.86570			−0.381543
$426$	0.150296	−	6.72857i	0.00728187	−	0.326000i
$427$	−25.9463	+	2.78002i	−1.25563	+	0.134535i
$428$	8.60043	+	4.96546i	0.415717	+	0.240015i
$429$	3.36712	−	1.84500i	0.162566	−	0.0890775i
$430$	0.795218	+	0.459119i	0.0383488	+	0.0221407i
$431$	8.46126	−	4.88511i	0.407564	−	0.235307i	−0.282178	−	0.959362i	$-0.591057\pi$
$431$	8.46126	−	4.88511i	0.407564	−	0.235307i	0.689743	+	0.724055i	$0.257724\pi$
$432$	0.347881	−	5.18449i	0.0167374	−	0.249439i
$433$			34.4543i			1.65577i	0.560898	+	0.827885i	$0.310456\pi$
$433$			34.4543i			1.65577i	−0.560898	+	0.827885i	$0.689544\pi$
$434$	−0.161819	−	1.51028i	−0.00776758	−	0.0724958i
$435$	−8.36515	+	13.7693i	−0.401078	+	0.660187i
$436$	−2.22823	−	3.85941i	−0.106713	−	0.184832i
$437$	26.6699			1.27579
$438$	8.61785	−	4.72212i	0.411777	−	0.225632i
$439$		−	20.7278i		−	0.989284i	−0.869097	−	0.494642i	$-0.835299\pi$
$439$		−	20.7278i		−	0.989284i	0.869097	−	0.494642i	$-0.164701\pi$
$440$	0.450472			0.0214754
$441$	20.7015	−	3.52819i	0.985785	−	0.168009i
$442$	−38.7061			−1.84106
$443$		−	9.53617i		−	0.453077i	−0.974002	−	0.226538i	$-0.927259\pi$
$443$		−	9.53617i		−	0.453077i	0.974002	−	0.226538i	$-0.0727409\pi$
$444$	2.13698	+	1.29826i	0.101416	+	0.0616127i
$445$	−3.96890			−0.188144
$446$	1.40867	+	2.43988i	0.0667023	+	0.115532i
$447$	−3.84789	−	7.02237i	−0.181999	−	0.332147i
$448$	−0.281867	−	2.63069i	−0.0133169	−	0.124289i
$449$		−	2.23000i		−	0.105240i	−0.998615	−	0.0526200i	$-0.983243\pi$
$449$		−	2.23000i		−	0.105240i	0.998615	−	0.0526200i	$-0.0167572\pi$
$450$	−2.52851	−	1.61451i	−0.119195	−	0.0761089i
$451$	−0.746475	+	0.430978i	−0.0351501	+	0.0202939i
$452$	−17.4964	−	10.1015i	−0.822959	−	0.475136i
$453$	−18.2104	−	11.0632i	−0.855598	−	0.519795i
$454$	2.24315	+	1.29508i	0.105276	+	0.0607813i
$455$	−12.9453	+	1.38703i	−0.606886	+	0.0650250i
$456$	8.11944	+	4.93274i	0.380228	+	0.230997i
$457$	12.8764			0.602332			0.301166	−	0.953572i	$-0.402624\pi$
$457$	12.8764			0.602332			0.301166	+	0.953572i	$0.402624\pi$
$458$	10.7592	+	18.6354i	0.502743	+	0.870776i
$459$	36.6844	−	18.0201i	1.71228	−	0.841107i
$460$	−4.21087	−	2.43115i	−0.196333	−	0.113353i
$461$	−1.56738	−	2.71478i	−0.0730000	−	0.126440i	0.827215	−	0.561886i	$-0.189924\pi$
$461$	−1.56738	−	2.71478i	−0.0730000	−	0.126440i	−0.900215	+	0.435446i	$0.856591\pi$
$462$	−0.877771	+	1.86841i	−0.0408376	+	0.0869262i
$463$	−7.25355	+	12.5635i	−0.337101	+	0.583877i	−0.983886	−	0.178796i	$-0.942780\pi$
$463$	−7.25355	+	12.5635i	−0.337101	+	0.583877i	0.646785	+	0.762672i	$0.276113\pi$
$464$	−8.05558	+	4.65089i	−0.373971	+	0.215912i
$465$	−0.477830	−	0.872038i	−0.0221588	−	0.0404398i
$466$	1.61342	−	2.79452i	0.0747402	−	0.129454i
$467$	−4.83041	+	8.36651i	−0.223525	+	0.387156i	−0.955876	−	0.293771i	$-0.905090\pi$
$467$	−4.83041	+	8.36651i	−0.223525	+	0.387156i	0.732351	+	0.680927i	$0.238423\pi$
$468$	−12.4425	−	7.94482i	−0.575153	−	0.367249i
$469$	−1.30844	−	12.2118i	−0.0604180	−	0.563888i
$470$	−6.43119	+	3.71305i	−0.296648	+	0.171270i
$471$	33.3103	+	0.744053i	1.53486	+	0.0342841i
$472$			8.86555i			0.408070i
$473$		−	0.413641i		−	0.0190192i
$474$	−3.47432	−	0.0776060i	−0.159581	−	0.00356456i
$475$	4.75019	−	2.74252i	0.217954	−	0.125836i
$476$	16.8115	−	12.2662i	0.770553	−	0.562219i
$477$	25.5352	−	13.2593i	1.16918	−	0.607101i
$478$	8.04923	−	13.9417i	0.368163	−	0.637677i
$479$	17.8678	−	30.9480i	0.816402	−	1.41405i	−0.0919140	−	0.995767i	$-0.529298\pi$
$479$	17.8678	−	30.9480i	0.816402	−	1.41405i	0.908316	−	0.418284i	$-0.137368\pi$
$480$	−0.832312	−	1.51897i	−0.0379897	−	0.0693310i
$481$	6.15215	−	3.55195i	0.280514	−	0.161955i
$482$	−12.8188	+	22.2029i	−0.583881	+	1.01131i
$483$	18.2887	−	12.7280i	0.832164	−	0.579146i
$484$	5.39854	+	9.35054i	0.245388	+	0.425025i
$485$	−8.69468	−	5.01988i	−0.394805	−	0.227941i
$486$	15.4914	+	1.73709i	0.702703	+	0.0787961i
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	0.569707	−	0.821848i	$-0.307057\pi$
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	−0.996595	+	0.0824564i	$0.973723\pi$
$488$	−9.86290			−0.446472
$489$	9.22122	+	5.60210i	0.416998	+	0.253336i
$490$	5.18306	−	4.70487i	0.234147	−	0.212545i
$491$	−13.9486	−	8.05323i	−0.629492	−	0.363437i	0.151064	−	0.988524i	$-0.451730\pi$
$491$	−13.9486	−	8.05323i	−0.629492	−	0.363437i	−0.780555	+	0.625087i	$0.785064\pi$
$492$	2.83245	+	1.72078i	0.127697	+	0.0775786i
$493$	−63.3628	−	36.5825i	−2.85372	−	1.64759i
$494$	23.3751	−	13.4956i	1.05170	−	0.607197i
$495$	−0.0603431	+	1.35007i	−0.00271222	+	0.0606811i
$496$		−	0.574100i		−	0.0257778i
$497$	10.2221	−	1.09525i	0.458525	−	0.0491288i
$498$	7.93508	+	14.4815i	0.355580	+	0.648931i
$499$	−0.676312	−	1.17141i	−0.0302759	−	0.0524394i	0.850490	−	0.525990i	$-0.176305\pi$
$499$	−0.676312	−	1.17141i	−0.0302759	−	0.0524394i	−0.880766	+	0.473551i	$0.842972\pi$
$500$	−1.00000			−0.0447214
$501$	10.6776	+	6.48687i	0.477040	+	0.289812i
$502$			12.7547i			0.569269i
$503$	−39.9065			−1.77934			−0.889671	−	0.456603i	$-0.849066\pi$
$503$	−39.9065			−1.77934			−0.889671	+	0.456603i	$0.849066\pi$
$504$	7.92197	−	0.492361i	0.352873	−	0.0219315i
$505$	5.49909			0.244706
$506$			2.19033i			0.0973719i
$507$	−17.0352	+	9.33439i	−0.756561	+	0.414555i
$508$	−3.08808			−0.137012
$509$	−5.43992	−	9.42221i	−0.241120	−	0.417632i	0.719914	−	0.694064i	$-0.244181\pi$
$509$	−5.43992	−	9.42221i	−0.241120	−	0.417632i	−0.961034	+	0.276432i	$0.910848\pi$
$510$	7.07368	−	11.6435i	0.313228	−	0.515583i
$511$	8.84754	+	12.1260i	0.391392	+	0.536425i
$512$		−	1.00000i		−	0.0441942i
$513$	−15.8711	+	23.6733i	−0.700726	+	1.04520i
$514$	23.4499	−	13.5388i	1.03433	−	0.597171i
$515$	−13.4299	−	7.75376i	−0.591792	−	0.341671i
$516$	−1.39477	+	0.764261i	−0.0614015	+	0.0336447i
$517$	2.89707	+	1.67263i	0.127413	+	0.0735620i
$518$	−1.54647	+	3.49239i	−0.0679481	+	0.153447i
$519$	−0.603396	+	27.0133i	−0.0264862	+	1.18575i
$520$	−4.92088			−0.215795
$521$	−19.6042	−	33.9555i	−0.858877	−	1.48762i	−0.873001	−	0.487718i	$-0.837829\pi$
$521$	−19.6042	−	33.9555i	−0.858877	−	1.48762i	0.0141243	−	0.999900i	$-0.495504\pi$
$522$	−12.8597	−	24.7656i	−0.562852	−	1.08396i
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	0.769164	−	0.639052i	$-0.220673\pi$
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	−0.168853	+	0.985641i	$0.554006\pi$
$524$	7.85422	+	13.6039i	0.343113	+	0.594290i
$525$	1.94856	−	4.14766i	0.0850420	−	0.181019i
$526$	−6.66669	+	11.5471i	−0.290682	+	0.503475i
$527$	3.91071	−	2.25785i	0.170353	−	0.0983535i
$528$	−0.405113	+	0.666828i	−0.0176303	+	0.0290200i
$529$	0.320933	−	0.555872i	0.0139536	−	0.0241683i
$530$	4.79542	−	8.30591i	0.208300	−	0.360786i
$531$	−26.5701	−	1.18759i	−1.15305	−	0.0515369i
$532$	−5.87582	+	13.2693i	−0.254749	+	0.575298i
$533$	8.15435	−	4.70792i	0.353204	−	0.203923i
$534$	3.56925	−	5.87510i	0.154457	−	0.254241i
$535$			9.93092i			0.429351i
$536$		−	4.64204i		−	0.200506i
$537$	3.17417	+	5.79284i	0.136976	+	0.249980i
$538$	13.1361	−	7.58415i	0.566339	−	0.326976i
$539$	−3.00288	−	0.962312i	−0.129343	−	0.0414497i
$540$	4.66384	−	2.29097i	0.200700	−	0.0985878i
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	−0.988291	−	0.152580i	$-0.951242\pi$
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	0.626284	+	0.779595i	$0.284575\pi$
$542$	13.1469	−	22.7711i	0.564708	−	0.978102i
$543$	−7.95644	−	0.177723i	−0.341443	−	0.00762683i
$544$	6.81190	−	3.93285i	0.292058	−	0.168620i
$545$	2.22823	−	3.85941i	0.0954470	−	0.165319i
$546$	9.58861	−	20.4101i	0.410355	−	0.873473i
$547$	−13.5255	−	23.4268i	−0.578307	−	1.00166i	−0.995674	−	0.0929192i	$-0.970380\pi$
$547$	−13.5255	−	23.4268i	−0.578307	−	1.00166i	0.417366	−	0.908738i	$-0.362953\pi$
$548$	−11.3130	−	6.53158i	−0.483268	−	0.279015i
$549$	1.32119	−	29.5592i	0.0563869	−	1.26155i
$550$	0.225236	+	0.390121i	0.00960410	+	0.0166348i
$551$	51.0207			2.17356
$552$	7.38565	−	4.04694i	0.314354	−	0.172249i
$553$	−0.565538	−	5.27823i	−0.0240491	−	0.224453i
$554$	20.1611	+	11.6400i	0.856563	+	0.494537i
$555$	−0.0558382	+	2.49981i	−0.00237020	+	0.106111i
$556$	−0.567606	−	0.327707i	−0.0240718	−	0.0138979i
$557$	−31.3474	+	18.0984i	−1.32823	+	0.766854i	−0.985026	−	0.172406i	$-0.944846\pi$
$557$	−31.3474	+	18.0984i	−1.32823	+	0.766854i	−0.343205	+	0.939261i	$0.611513\pi$
$558$	1.72058	+	0.0769037i	0.0728380	+	0.00325559i
$559$			4.51854i			0.191114i
$560$	2.13731	−	1.55945i	0.0903180	−	0.0658988i
$561$	−6.13562	−	0.137051i	−0.259046	−	0.00578631i
$562$	1.96523	+	3.40387i	0.0828981	+	0.143584i
$563$	14.0186			0.590816			0.295408	−	0.955371i	$-0.404544\pi$
$563$	14.0186			0.590816			0.295408	+	0.955371i	$0.404544\pi$
$564$	0.287235	−	12.8592i	0.0120948	−	0.541468i
$565$		−	20.2030i		−	0.849948i
$566$	28.8938			1.21450
$567$	0.414421	+	23.8082i	0.0174040	+	0.999849i
$568$	3.88571			0.163041
$569$			25.6991i			1.07736i	0.842509	+	0.538682i	$0.181077\pi$
$569$			25.6991i			1.07736i	−0.842509	+	0.538682i	$0.818923\pi$
$570$	−0.212157	+	9.49801i	−0.00888629	+	0.397828i
$571$	15.6502			0.654941			0.327470	−	0.944861i	$-0.393804\pi$
$571$	15.6502			0.654941			0.327470	+	0.944861i	$0.393804\pi$
$572$	1.10836	+	1.91973i	0.0463428	+	0.0802681i
$573$	−43.4526	−	0.970600i	−1.81526	−	0.0405474i
$574$	−2.04977	+	4.62898i	−0.0855557	+	0.193210i
$575$		−	4.86229i		−	0.202772i
$576$	2.99701	+	0.133955i	0.124875	+	0.00558147i
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.941994	−	0.335629i	$-0.891051\pi$
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.180334	+	0.983605i	$0.557718\pi$
$578$	38.8580	+	22.4347i	1.61628	+	0.933158i
$579$	0.692544	−	31.0043i	0.0287811	−	1.28849i
$580$	−8.05558	−	4.65089i	−0.334490	−	0.193118i
$581$	−20.3767	+	14.8675i	−0.845368	+	0.616806i
$582$	15.2500	−	8.35621i	0.632135	−	0.346376i
$583$	−4.32041			−0.178933
$584$	2.83675	+	4.91339i	0.117385	+	0.203318i
$585$	0.659177	−	14.7479i	0.0272536	−	0.609751i
$586$	3.74744	+	2.16359i	0.154805	+	0.0893770i
$587$	2.19821	+	3.80741i	0.0907299	+	0.157149i	0.907818	−	0.419363i	$-0.137747\pi$
$587$	2.19821	+	3.80741i	0.0907299	+	0.157149i	−0.817089	+	0.576512i	$0.804413\pi$
$588$	2.30340	+	11.9035i	0.0949906	+	0.490894i
$589$	−1.57448	+	2.72708i	−0.0648754	+	0.112368i
$590$	−7.67779	+	4.43278i	−0.316090	+	0.182495i
$591$	−21.9090	−	0.489381i	−0.901215	−	0.0201304i
$592$	−0.721812	+	1.25022i	−0.0296663	+	0.0513835i
$593$	−8.99345	+	15.5771i	−0.369317	+	0.639675i	−0.989459	−	0.144814i	$-0.953742\pi$
$593$	−8.99345	+	15.5771i	−0.369317	+	0.639675i	0.620142	+	0.784489i	$0.287075\pi$
$594$	−1.94422	−	1.30345i	−0.0797724	−	0.0534813i
$595$	19.0286	+	8.42608i	0.780095	+	0.345436i
$596$	4.00375	−	2.31156i	0.164000	−	0.0946853i
$597$	−17.5801	−	32.0835i	−0.719504	−	1.31309i
$598$		−	23.9267i		−	0.978436i
$599$		−	1.37970i		−	0.0563732i	−0.999603	−	0.0281866i	$-0.991027\pi$
$599$		−	1.37970i		−	0.0563732i	0.999603	−	0.0281866i	$-0.00897326\pi$
$600$	0.899307	−	1.48029i	0.0367140	−	0.0604324i
$601$	40.5777	−	23.4275i	1.65520	−	0.955630i	0.680314	−	0.732921i	$-0.261843\pi$
$601$	40.5777	−	23.4275i	1.65520	−	0.955630i	0.974885	−	0.222709i	$-0.0714899\pi$
$602$	−1.43195	−	1.96257i	−0.0583618	−	0.0799882i
$603$	13.9122	+	0.621826i	0.566550	+	0.0253227i
$604$	6.15097	−	10.6538i	0.250279	−	0.433496i
$605$	−5.39854	+	9.35054i	−0.219482	+	0.380154i
$606$	−4.94537	+	8.14023i	−0.200892	+	0.330674i
$607$	−19.5682	+	11.2977i	−0.794250	+	0.458561i	−0.841457	−	0.540324i	$-0.818301\pi$
$607$	−19.5682	+	11.2977i	−0.794250	+	0.458561i	0.0472064	+	0.998885i	$0.484968\pi$
$608$	−2.74252	+	4.75019i	−0.111224	+	0.192646i
$609$	34.9871	−	24.3493i	1.41775	−	0.986684i
$610$	−4.93145	−	8.54152i	−0.199668	−	0.345836i
$611$	−31.6471	−	18.2714i	−1.28030	−	0.739183i
$612$	10.8743	+	20.9421i	0.439567	+	0.846536i
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	0.996162	−	0.0875282i	$-0.0278968\pi$
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	−0.573883	+	0.818938i	$0.694563\pi$
$614$	0.419882			0.0169451
$615$	−0.0740106	+	3.31336i	−0.00298440	+	0.133608i
$616$	−1.08977	−	0.482566i	−0.0439083	−	0.0194431i
$617$	−8.43544	−	4.87020i	−0.339598	−	0.196067i	0.320496	−	0.947250i	$-0.396150\pi$
$617$	−8.43544	−	4.87020i	−0.339598	−	0.196067i	−0.660094	+	0.751183i	$0.729484\pi$
$618$	23.5554	−	12.9071i	0.947536	−	0.519199i
$619$	−15.8305	−	9.13975i	−0.636282	−	0.367358i	0.146899	−	0.989152i	$-0.453071\pi$
$619$	−15.8305	−	9.13975i	−0.636282	−	0.367358i	−0.783181	+	0.621794i	$0.786404\pi$
$620$	0.497185	−	0.287050i	0.0199674	−	0.0115282i
$621$	11.1394	+	22.6770i	0.447008	+	0.909995i
$622$			6.28435i			0.251980i
$623$	9.60148	+	4.25165i	0.384675	+	0.170339i
$624$	4.42538	−	7.28430i	0.177157	−	0.291606i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.68411			−0.227183
$627$	3.75316	−	2.05653i	0.149887	−	0.0821299i
$628$			19.2365i			0.767620i
$629$	−11.3551			−0.452758
$630$	4.38738	+	6.61445i	0.174797	+	0.263526i
$631$	23.4168			0.932209			0.466104	−	0.884730i	$-0.345657\pi$
$631$	23.4168			0.932209			0.466104	+	0.884730i	$0.345657\pi$
$632$		−	2.00640i		−	0.0798104i
$633$	29.6448	+	18.0099i	1.17828	+	0.715829i
$634$	10.0314			0.398397
$635$	−1.54404	−	2.67436i	−0.0612735	−	0.106129i
$636$	7.98257	+	14.5682i	0.316530	+	0.577665i
$637$	32.8029	+	10.5121i	1.29970	+	0.416505i
$638$			4.19019i			0.165891i
$639$	−0.520511	+	11.6455i	−0.0205911	+	0.460689i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	3.46338	+	1.99958i	0.136795	+	0.0789788i	0.566836	−	0.823831i	$-0.308167\pi$
$641$	3.46338	+	1.99958i	0.136795	+	0.0789788i	−0.430041	+	0.902810i	$0.641501\pi$
$642$	−14.7006	−	8.93094i	−0.580187	−	0.352476i
$643$	14.6262	+	8.44444i	0.576801	+	0.333016i	0.759861	−	0.650085i	$-0.225267\pi$
$643$	14.6262	+	8.44444i	0.576801	+	0.333016i	−0.183060	+	0.983102i	$0.558600\pi$
$644$	7.58250	+	10.3922i	0.298792	+	0.409512i
$645$	−1.35926	−	0.825778i	−0.0535207	−	0.0325150i
$646$	−43.1438			−1.69747
$647$	14.0753	+	24.3792i	0.553358	+	0.958443i	0.998029	+	0.0627498i	$0.0199870\pi$
$647$	14.0753	+	24.3792i	0.553358	+	0.958443i	−0.444672	+	0.895694i	$0.646680\pi$
$648$	−0.802930	+	8.96411i	−0.0315421	+	0.352144i
$649$	3.45863	+	1.99684i	0.135763	+	0.0783830i
$650$	−2.46044	−	4.26160i	−0.0965063	−	0.167154i
$651$	0.221793	+	2.62149i	0.00869276	+	0.102744i
$652$	−3.11468	+	5.39478i	−0.121980	+	0.211276i
$653$	20.3091	−	11.7254i	0.794755	−	0.458852i	−0.0468790	−	0.998901i	$-0.514928\pi$
$653$	20.3091	−	11.7254i	0.794755	−	0.458852i	0.841634	+	0.540049i	$0.181594\pi$
$654$	3.70917	+	6.76922i	0.145040	+	0.264697i
$655$	−7.85422	+	13.6039i	−0.306890	+	0.531549i
$656$	−0.956724	+	1.65709i	−0.0373538	+	0.0646987i
$657$	−15.1055	+	7.84358i	−0.589321	+	0.306007i
$658$	19.5358	−	2.09317i	0.761584	−	0.0816002i
$659$	13.7094	−	7.91513i	0.534043	−	0.308330i	−0.208618	−	0.977997i	$-0.566897\pi$
$659$	13.7094	−	7.91513i	0.534043	−	0.308330i	0.742661	+	0.669667i	$0.233563\pi$
$660$	−0.780047	−	0.0174239i	−0.0303633	−	0.000678225i
$661$		−	11.8945i		−	0.462643i	−0.972877	−	0.231321i	$-0.925695\pi$
$661$		−	11.8945i		−	0.462643i	0.972877	−	0.231321i	$-0.0743049\pi$
$662$		−	31.7032i		−	1.23218i
$663$	67.0243	+	1.49712i	2.60301	+	0.0581434i
$664$	−8.25650	+	4.76689i	−0.320414	+	0.184991i
$665$	−14.4295	+	1.54605i	−0.559551	+	0.0599533i
$666$	−3.65022	−	2.33075i	−0.141443	−	0.0903147i
$667$	22.6140	−	39.1686i	0.875617	−	1.51661i
$668$	−3.60660	+	6.24681i	−0.139543	+	0.241696i
$669$	−2.34490	−	4.27943i	−0.0906591	−	0.165452i
$670$	4.02013	−	2.32102i	0.155311	−	0.0896689i
$671$	−2.22148	+	3.84772i	−0.0857593	+	0.148540i
$672$	0.386332	+	4.56626i	0.0149031	+	0.176147i
$673$	−2.58993	−	4.48588i	−0.0998343	−	0.172918i	0.811782	−	0.583961i	$-0.198498\pi$
$673$	−2.58993	−	4.48588i	−0.0998343	−	0.172918i	−0.911616	+	0.411043i	$0.865165\pi$
$674$	12.2908	+	7.09612i	0.473425	+	0.273332i
$675$	4.31596	+	2.89352i	0.166121	+	0.111372i
$676$	−5.60751	−	9.71249i	−0.215673	−	0.373557i
$677$	−11.1639			−0.429065			−0.214533	−	0.976717i	$-0.568823\pi$
$677$	−11.1639			−0.429065			−0.214533	+	0.976717i	$0.568823\pi$
$678$	29.9063	+	18.1687i	1.14854	+	0.697766i
$679$	15.6565	+	21.4581i	0.600841	+	0.823487i
$680$	6.81190	+	3.93285i	0.261224	+	0.150818i
$681$	−3.83419	−	2.32935i	−0.146926	−	0.0892610i
$682$	−0.223968	−	0.129308i	−0.00857618	−	0.00495146i
$683$	31.3199	−	18.0825i	1.19842	−	0.691909i	0.238219	−	0.971211i	$-0.423436\pi$
$683$	31.3199	−	18.0825i	1.19842	−	0.691909i	0.960203	+	0.279302i	$0.0901031\pi$
$684$	−13.8690	−	8.85568i	−0.530294	−	0.338605i
$685$		−	13.0632i		−	0.499117i
$686$	−17.5788	+	5.82962i	−0.671163	+	0.222576i
$687$	−17.9100	−	32.6856i	−0.683308	−	1.24703i
$688$	−0.459119	−	0.795218i	−0.0175038	−	0.0303174i
$689$	47.1953			1.79800
$690$	7.19758	+	4.37269i	0.274007	+	0.166465i
$691$			6.70563i			0.255094i	0.991833	+	0.127547i	$0.0407104\pi$
$691$			6.70563i			0.255094i	−0.991833	+	0.127547i	$0.959290\pi$
$692$	−15.6000			−0.593024
$693$	1.59223	−	3.20142i	0.0604840	−	0.121612i
$694$	0.732838			0.0278181
$695$		−	0.655415i		−	0.0248613i
$696$	14.1291	−	7.74198i	0.535561	−	0.293459i
$697$	−15.0506			−0.570083
$698$	−13.3508	−	23.1243i	−0.505336	−	0.875268i
$699$	−2.90192	+	4.77665i	−0.109761	+	0.180669i
$700$	2.41918	+	1.07124i	0.0914365	+	0.0404892i
$701$		−	1.39464i		−	0.0526749i	−0.999653	−	0.0263375i	$-0.991616\pi$
$701$		−	1.39464i		−	0.0526749i	0.999653	−	0.0263375i	$-0.00838445\pi$
$702$	21.2383	+	14.2387i	0.801589	+	0.537403i
$703$	6.85749	−	3.95918i	0.258635	−	0.149323i
$704$	−0.390121	−	0.225236i	−0.0147032	−	0.00848891i
$705$	11.2800	−	6.18083i	0.424829	−	0.232783i
$706$	−5.19889	−	3.00158i	−0.195663	−	0.112966i
$707$	−13.3033	−	5.89087i	−0.500322	−	0.221549i
$708$	0.342912	−	15.3518i	0.0128874	−	0.576954i
$709$	−49.6112			−1.86319			−0.931593	−	0.363503i	$-0.881581\pi$
$709$	−49.6112			−1.86319			−0.931593	+	0.363503i	$0.881581\pi$
$710$	1.94286	+	3.36513i	0.0729141	+	0.126291i
$711$	6.01320	+	0.268768i	0.225513	+	0.0100796i
$712$	3.43716	+	1.98445i	0.128813	+	0.0743703i
$713$	1.39572	+	2.41746i	0.0522701	+	0.0905345i
$714$	−29.5855	+	20.5901i	−1.10721	+	0.770565i
$715$	−1.10836	+	1.91973i	−0.0414503	+	0.0717940i
$716$	−3.30274	+	1.90684i	−0.123429	+	0.0712619i
$717$	−14.4774	+	23.8303i	−0.540670	+	0.889960i
$718$	−14.6574	+	25.3873i	−0.547009	+	0.947447i
$719$	10.4343	−	18.0727i	0.389133	−	0.673998i	−0.603200	−	0.797590i	$-0.706108\pi$
$719$	10.4343	−	18.0727i	0.389133	−	0.673998i	0.992333	+	0.123592i	$0.0394413\pi$
$720$	1.38250	+	2.66246i	0.0515226	+	0.0992241i
$721$	24.1832	+	33.1444i	0.900629	+	1.23436i
$722$	9.60055	−	5.54288i	0.357295	−	0.206285i
$723$	23.0561	−	37.9511i	0.857466	−	1.41142i
$724$		−	4.59480i		−	0.170764i
$725$		−	9.30178i		−	0.345459i
$726$	−8.98654	−	16.4004i	−0.333522	−	0.608675i
$727$	32.1908	−	18.5854i	1.19389	−	0.689293i	0.234704	−	0.972067i	$-0.424588\pi$
$727$	32.1908	−	18.5854i	1.19389	−	0.689293i	0.959187	+	0.282773i	$0.0912545\pi$
$728$	11.9045	+	5.27146i	0.441210	+	0.195373i
$729$	−26.7580	−	3.60718i	−0.991035	−	0.133599i
$730$	−2.83675	+	4.91339i	−0.104993	+	0.181853i
$731$	3.61130	−	6.25495i	0.133569	−	0.231348i
$732$	17.0788	+	0.381489i	0.631250	+	0.0141002i
$733$	10.3892	−	5.99818i	0.383732	−	0.221548i	−0.295709	−	0.955278i	$-0.595556\pi$
$733$	10.3892	−	5.99818i	0.383732	−	0.221548i	0.679441	+	0.733730i	$0.262222\pi$
$734$	−10.0170	+	17.3499i	−0.369733	+	0.640397i
$735$	−9.15707	+	7.94657i	−0.337764	+	0.293114i
$736$	2.43115	+	4.21087i	0.0896132	+	0.155215i
$737$	−1.81096	−	1.04556i	−0.0667075	−	0.0385136i
$738$	−4.83817	−	3.08929i	−0.178095	−	0.113718i
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	0.990507	+	0.137463i	$0.0438947\pi$
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	−0.376207	+	0.926535i	$0.622772\pi$
$740$	−1.44362			−0.0530687
$741$	−40.9988	+	22.4651i	−1.50613	+	0.825278i
$742$	−20.4986	+	14.9564i	−0.752529	+	0.549068i
$743$	−42.2679	−	24.4034i	−1.55066	−	0.895273i	−0.998088	−	0.0618062i	$-0.980314\pi$
$743$	−42.2679	−	24.4034i	−1.55066	−	0.895273i	−0.552570	−	0.833467i	$-0.686353\pi$
$744$	−0.0222057	+	0.994122i	−0.000814101	+	0.0364463i
$745$	4.00375	+	2.31156i	0.146686	+	0.0846891i
$746$	5.94714	−	3.43358i	0.217740	−	0.125712i
$747$	−13.1804	−	25.3833i	−0.482246	−	0.928728i
$748$		−	3.54328i		−	0.129555i
$749$	10.6384	−	24.0247i	0.388720	−	0.877843i
$750$	1.73162	+	0.0386792i	0.0632298	+	0.00141236i
$751$	−5.31095	−	9.19884i	−0.193799	−	0.335670i	0.752707	−	0.658356i	$-0.228748\pi$
$751$	−5.31095	−	9.19884i	−0.193799	−	0.335670i	−0.946506	+	0.322685i	$0.895414\pi$
$752$	7.42609			0.270802
$753$	0.493341	−	22.0862i	0.0179783	−	0.804868i
$754$		−	45.7729i		−	1.66695i
$755$	12.3019			0.447713
$756$	−13.7369	+	0.546166i	−0.499605	+	0.0198639i
$757$	−41.0132			−1.49065			−0.745326	−	0.666701i	$-0.767706\pi$
$757$	−41.0132			−1.49065			−0.745326	+	0.666701i	$0.767706\pi$
$758$		−	0.682216i		−	0.0247792i
$759$	0.0847201	−	3.79281i	0.00307514	−	0.137670i
$760$	−5.48505			−0.198964
$761$	0.811328	+	1.40526i	0.0294106	+	0.0509407i	0.880356	−	0.474313i	$-0.157304\pi$
$761$	0.811328	+	1.40526i	0.0294106	+	0.0509407i	−0.850945	+	0.525254i	$0.823970\pi$
$762$	5.34739	+	0.119445i	0.193715	+	0.00432702i
$763$	−9.52487	+	6.94964i	−0.344823	+	0.251594i
$764$		−	25.0936i		−	0.907855i
$765$	−12.6993	+	19.8885i	−0.459143	+	0.719070i
$766$	27.3944	−	15.8162i	0.989799	−	0.571461i
$767$	−37.7815	−	21.8131i	−1.36421	−	0.787627i
$768$	−0.0386792	+	1.73162i	−0.00139572	+	0.0624844i
$769$	15.4016	+	8.89210i	0.555395	+	0.320657i	0.751295	−	0.659966i	$-0.229430\pi$
$769$	15.4016	+	8.89210i	0.555395	+	0.320657i	−0.195900	+	0.980624i	$0.562763\pi$
$770$	−0.126973	−	1.18506i	−0.00457579	−	0.0427064i
$771$	−41.1300	+	22.5370i	−1.48126	+	0.811651i
$772$	17.9048			0.644408
$773$	13.0759	+	22.6481i	0.470307	+	0.814596i	0.999423	−	0.0339536i	$-0.0108099\pi$
$773$	13.0759	+	22.6481i	0.470307	+	0.814596i	−0.529116	+	0.848549i	$0.677477\pi$
$774$	2.44478	−	1.26946i	0.0878757	−	0.0456298i
$775$	0.497185	+	0.287050i	0.0178594	+	0.0103111i
$776$	5.01988	+	8.69468i	0.180203	+	0.312121i
$777$	2.81299	−	5.98767i	0.100915	−	0.214807i
$778$	−14.0160	+	24.2765i	−0.502499	+	0.870355i
$779$	9.08924	−	5.24768i	0.325656	−	0.188018i
$780$	8.52108	+	0.190335i	0.305104	+	0.00681510i
$781$	0.875203	−	1.51590i	0.0313172	−	0.0542430i
$782$	−19.1227	+	33.1214i	−0.683825	+	1.18442i
$783$	21.3101	+	43.3820i	0.761562	+	1.55035i
$784$	−6.84110	+	1.48301i	−0.244325	+	0.0529646i
$785$	−16.6593	+	9.61826i	−0.594596	+	0.343290i
$786$	−13.0743	−	23.8606i	−0.466346	−	0.851079i
$787$		−	22.8957i		−	0.816142i	−0.912950	−	0.408071i	$-0.866202\pi$
$787$		−	22.8957i		−	0.816142i	0.912950	−	0.408071i	$-0.133798\pi$
$788$		−	12.6523i		−	0.450720i
$789$	11.9908	−	19.7372i	0.426884	−	0.702664i
$790$	1.73760	−	1.00320i	0.0618209	−	0.0356923i
$791$	−21.6424	+	48.8748i	−0.769514	+	1.73779i
$792$	0.727293	−	1.13902i	0.0258432	−	0.0404734i
$793$	24.2670	−	42.0317i	0.861748	−	1.49259i
$794$	−14.6191	+	25.3210i	−0.518812	+	0.898609i
$795$	−8.62510	+	14.1972i	−0.305901	+	0.503522i
$796$	18.2922	−	10.5610i	0.648348	−	0.374324i
$797$	8.74751	−	15.1511i	0.309853	−	0.536681i	−0.668477	−	0.743733i	$-0.733054\pi$
$797$	8.74751	−	15.1511i	0.309853	−	0.536681i	0.978330	+	0.207052i	$0.0663869\pi$
$798$	10.6879	−	22.7501i	0.378349	−	0.805346i
$799$	29.2057	+	50.5858i	1.03322	+	1.78960i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	−6.40783	+	10.0354i	−0.226410	+	0.354583i
$802$	−5.78471	−	10.0194i	−0.204265	−	0.353798i
$803$	2.55575			0.0901906
$804$	−0.179551	+	8.03825i	−0.00633226	+	0.283487i
$805$	−5.20870	+	11.7628i	−0.183582	+	0.414583i
$806$	2.44658	+	1.41254i	0.0861773	+	0.0497545i
$807$	−23.0401	+	12.6248i	−0.811051	+	0.444413i
$808$	−4.76235	−	2.74955i	−0.167539	−	0.0967287i
$809$	3.79610	−	2.19168i	0.133464	−	0.0770553i	−0.431782	−	0.901978i	$-0.642115\pi$
$809$	3.79610	−	2.19168i	0.133464	−	0.0770553i	0.565245	+	0.824923i	$0.308782\pi$
$810$	−8.16461	+	3.78670i	−0.286875	+	0.133051i
$811$			55.5831i			1.95179i	0.218247	+	0.975893i	$0.429966\pi$
$811$			55.5831i			1.95179i	−0.218247	+	0.975893i	$0.570034\pi$
$812$	14.5057	+	19.8808i	0.509049	+	0.697680i
$813$	−23.6462	+	38.9223i	−0.829308	+	1.36507i
$814$	0.325157	+	0.563188i	0.0113967	+	0.0197397i
$815$	−6.22935			−0.218205
$816$	−11.9477	+	6.54672i	−0.418254	+	0.229181i
$817$			5.03658i			0.176208i
$818$	2.07755			0.0726398
$819$	−17.3933	+	34.9717i	−0.607770	+	1.22201i
$820$	−1.91345			−0.0668205
$821$			15.1341i			0.528185i	0.964497	+	0.264093i	$0.0850725\pi$
$821$			15.1341i			0.528185i	−0.964497	+	0.264093i	$0.914928\pi$
$822$	19.3372	+	11.7478i	0.674462	+	0.409751i
$823$	−36.2022			−1.26193			−0.630964	−	0.775812i	$-0.717341\pi$
$823$	−36.2022			−1.26193			−0.630964	+	0.775812i	$0.717341\pi$
$824$	7.75376	+	13.4299i	0.270115	+	0.467853i
$825$	−0.374934	−	0.684252i	−0.0130535	−	0.0238226i
$826$	23.3226	−	2.49890i	0.811496	−	0.0869479i
$827$			3.78131i			0.131489i	0.997836	+	0.0657446i	$0.0209422\pi$
$827$			3.78131i			0.131489i	−0.997836	+	0.0657446i	$0.979058\pi$
$828$	−12.9457	+	6.72209i	−0.449893	+	0.233609i
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	−0.00776491	−	0.999970i	$-0.502472\pi$
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	0.862117	+	0.506710i	$0.169138\pi$
$830$	−8.25650	−	4.76689i	−0.286587	−	0.165461i
$831$	−34.4611	−	20.9359i	−1.19544	−	0.726258i
$832$	4.26160	+	2.46044i	0.147745	+	0.0853003i
$833$	−37.0072	−	40.7684i	−1.28222	−	1.41254i
$834$	0.970201	+	0.589419i	0.0335953	+	0.0204099i
$835$	−7.21319			−0.249623
$836$	1.23543	+	2.13983i	0.0427283	+	0.0740076i
$837$	−2.97642	−	0.199719i	−0.102880	−	0.00690328i
$838$	−5.45962	−	3.15211i	−0.188600	−	0.108888i
$839$	−13.6621	−	23.6634i	−0.471667	−	0.816951i	0.527808	−	0.849364i	$-0.323014\pi$
$839$	−13.6621	−	23.6634i	−0.471667	−	0.816951i	−0.999475	+	0.0324131i	$0.989681\pi$
$840$	−3.76133	+	2.61770i	−0.129778	+	0.0903194i
$841$	28.7615	−	49.8165i	0.991777	−	1.71781i
$842$	−2.25376	+	1.30121i	−0.0776698	+	0.0448427i
$843$	−3.27136	−	5.97022i	−0.112672	−	0.205625i
$844$	−10.0132	+	17.3434i	−0.344669	+	0.596984i
$845$	5.60751	−	9.71249i	0.192904	−	0.334120i
$846$	−0.994764	+	22.2561i	−0.0342007	+	0.765179i
$847$	23.0767	−	16.8375i	0.792926	−	0.578544i
$848$	−8.30591	+	4.79542i	−0.285226	+	0.164675i
$849$	−50.0330	−	1.11759i	−1.71713	−	0.0383555i
$850$			7.86570i			0.269791i
$851$		−	7.01932i		−	0.240619i
$852$	−6.72857	−	0.150296i	−0.230517	−	0.00514906i
$853$	7.91557	−	4.57006i	0.271024	−	0.156476i	−0.358329	−	0.933595i	$-0.616653\pi$
$853$	7.91557	−	4.57006i	0.271024	−	0.156476i	0.629353	+	0.777120i	$0.283320\pi$
$854$	2.78002	+	25.9463i	0.0951303	+	0.887863i
$855$	0.734751	−	16.4387i	0.0251280	−	0.562193i
$856$	4.96546	−	8.60043i	0.169716	−	0.293957i
$857$	0.475999	−	0.824454i	0.0162598	−	0.0281628i	−0.857781	−	0.514015i	$-0.828157\pi$
$857$	0.475999	−	0.824454i	0.0162598	−	0.0281628i	0.874041	+	0.485853i	$0.161491\pi$
$858$	−1.84500	−	3.36712i	−0.0629873	−	0.114952i
$859$	30.6690	−	17.7068i	1.04641	−	0.604147i	0.124771	−	0.992186i	$-0.460180\pi$
$859$	30.6690	−	17.7068i	1.04641	−	0.604147i	0.921643	+	0.388038i	$0.126847\pi$
$860$	0.459119	−	0.795218i	0.0156558	−	0.0271167i
$861$	3.72846	−	7.93634i	0.127066	−	0.270470i
$862$	−4.88511	−	8.46126i	−0.166388	−	0.288192i
$863$	22.9444	+	13.2469i	0.781036	+	0.450931i	0.836797	−	0.547513i	$-0.184425\pi$
$863$	22.9444	+	13.2469i	0.781036	+	0.450931i	−0.0557615	+	0.998444i	$0.517759\pi$
$864$	−5.18449	−	0.347881i	−0.176380	−	0.0118352i
$865$	−7.80001	−	13.5100i	−0.265208	−	0.459354i
$866$	34.4543			1.17081
$867$	−66.4194	−	40.3513i	−2.25572	−	1.37040i
$868$	−1.51028	+	0.161819i	−0.0512623	+	0.00549251i
$869$	−0.782739	−	0.451915i	−0.0265526	−	0.0153301i
$870$	13.7693	+	8.36515i	0.466823	+	0.283605i
$871$	19.7826	+	11.4215i	0.670306	+	0.387001i
$872$	−3.85941	+	2.22823i	−0.130696	+	0.0754575i
$873$	−26.7305	+	13.8799i	−0.904689	+	0.469764i
$874$		−	26.6699i		−	0.902123i
$875$	0.281867	+	2.63069i	0.00952883	+	0.0889337i
$876$	−4.72212	−	8.61785i	−0.159546	−	0.291170i
$877$	−6.25891	−	10.8408i	−0.211349	−	0.366066i	0.740788	−	0.671739i	$-0.234452\pi$
$877$	−6.25891	−	10.8408i	−0.211349	−	0.366066i	−0.952137	+	0.305672i	$0.901119\pi$
$878$	−20.7278			−0.699529
$879$	−6.40546	−	3.89146i	−0.216051	−	0.131256i
$880$		−	0.450472i		−	0.0151854i
$881$	32.3516			1.08995			0.544977	−	0.838451i	$-0.316538\pi$
$881$	32.3516			1.08995			0.544977	+	0.838451i	$0.316538\pi$
$882$	−3.52819	−	20.7015i	−0.118800	−	0.697056i
$883$	24.9749			0.840473			0.420237	−	0.907415i	$-0.361947\pi$
$883$	24.9749			0.840473			0.420237	+	0.907415i	$0.361947\pi$
$884$			38.7061i			1.30183i
$885$	13.4665	−	7.37891i	0.452670	−	0.248039i
$886$	−9.53617			−0.320374
$887$	−0.205908	−	0.356642i	−0.00691370	−	0.0119749i	0.862548	−	0.505975i	$-0.168867\pi$
$887$	−0.205908	−	0.356642i	−0.00691370	−	0.0119749i	−0.869462	+	0.494001i	$0.835534\pi$
$888$	1.29826	−	2.13698i	0.0435668	−	0.0717123i
$889$	0.870428	+	8.12381i	0.0291932	+	0.272464i
$890$			3.96890i			0.133038i
$891$	3.31624	+	2.33228i	0.111098	+	0.0781344i
$892$	2.43988	−	1.40867i	0.0816933	−	0.0471657i
$893$	−35.2754	−	20.3662i	−1.18045	−	0.681530i
$894$	−7.02237	+	3.84789i	−0.234863	+	0.128693i
$895$	−3.30274	−	1.90684i	−0.110398	−	0.0637386i
$896$	−2.63069	+	0.281867i	−0.0878853	+	0.00941650i
$897$	−0.925466	+	41.4320i	−0.0309004	+	1.38337i
$898$	−2.23000			−0.0744159
$899$	2.67007	+	4.62470i	0.0890520	+	0.154243i
$900$	−1.61451	+	2.52851i	−0.0538171	+	0.0842836i
$901$	−65.3318	−	37.7193i	−2.17652	−	1.25661i
$902$	0.430978	+	0.746475i	0.0143500	+	0.0248549i
$903$	2.40368	+	3.45380i	0.0799894	+	0.114935i
$904$	−10.1015	+	17.4964i	−0.335972	+	0.581920i
$905$	3.97921	−	2.29740i	0.132273	−	0.0763681i
$906$	−11.0632	+	18.2104i	−0.367551	+	0.604999i
$907$	20.2158	−	35.0148i	0.671254	−	1.16265i	−0.306295	−	0.951937i	$-0.599089\pi$
$907$	20.2158	−	35.0148i	0.671254	−	1.16265i	0.977549	−	0.210709i	$-0.0675773\pi$
$908$	1.29508	−	2.24315i	0.0429789	−	0.0744416i
$909$	8.87836	−	13.9045i	0.294476	−	0.461183i
$910$	1.38703	+	12.9453i	0.0459796	+	0.429133i
$911$	−24.9849	+	14.4250i	−0.827786	+	0.477923i	−0.853094	−	0.521757i	$-0.825277\pi$
$911$	−24.9849	+	14.4250i	−0.827786	+	0.477923i	0.0253077	+	0.999680i	$0.491943\pi$
$912$	4.93274	−	8.11944i	0.163339	−	0.268862i
$913$			4.29471i			0.142134i
$914$		−	12.8764i		−	0.425913i
$915$	8.20901	+	14.9814i	0.271381	+	0.495270i
$916$	18.6354	−	10.7592i	0.615732	−	0.355493i
$917$	33.5739	−	24.4965i	1.10871	−	0.808947i
$918$	−18.0201	−	36.6844i	−0.594752	−	1.21077i
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	−0.831282	−	0.555850i	$-0.812393\pi$
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	0.897022	+	0.441986i	$0.145726\pi$
$920$	−2.43115	+	4.21087i	−0.0801525	+	0.138828i
$921$	−0.727076	−	0.0162407i	−0.0239580	−	0.000535149i
$922$	−2.71478	+	1.56738i	−0.0894064	+	0.0516188i
$923$	−9.56055	+	16.5594i	−0.314689	+	0.545058i
$924$	1.86841	+	0.877771i	0.0614661	+	0.0288766i
$925$	−0.721812	−	1.25022i	−0.0237330	−	0.0411068i
$926$	12.5635	+	7.25355i	0.412863	+	0.238367i
$927$	−41.2882	+	21.4391i	−1.35608	+	0.704151i
$928$	4.65089	+	8.05558i	0.152673	+	0.264437i
$929$	−42.1953			−1.38438			−0.692191	−	0.721714i	$-0.743354\pi$
$929$	−42.1953			−1.38438			−0.692191	+	0.721714i	$0.743354\pi$
$930$	−0.872038	+	0.477830i	−0.0285952	+	0.0156687i
$931$	36.5637	+	11.7173i	1.19833	+	0.384019i
$932$	−2.79452	−	1.61342i	−0.0915377	−	0.0528493i
$933$	0.243074	−	10.8821i	0.00795788	−	0.356264i
$934$	8.36651	+	4.83041i	0.273761	+	0.158056i
$935$	3.06857	−	1.77164i	0.100353	−	0.0579389i
$936$	−7.94482	+	12.4425i	−0.259684	+	0.406695i
$937$			41.8456i			1.36704i	0.729933	+	0.683519i	$0.239551\pi$
$937$			41.8456i			1.36704i	−0.729933	+	0.683519i	$0.760449\pi$
$938$	−12.2118	+	1.30844i	−0.398729	+	0.0427220i
$939$	9.84271	+	0.219857i	0.321205	+	0.00717476i
$940$	3.71305	+	6.43119i	0.121106	+	0.209762i
$941$	−34.3185			−1.11875			−0.559375	−	0.828915i	$-0.688959\pi$
$941$	−34.3185			−1.11875			−0.559375	+	0.828915i	$0.688959\pi$
$942$	0.744053	−	33.3103i	0.0242426	−	1.08531i
$943$		−	9.30374i		−	0.302971i
$944$	8.86555			0.288549
$945$	−7.34143	−	11.6234i	−0.238817	−	0.378109i
$946$	−0.413641			−0.0134486
$947$			24.3511i			0.791303i	0.918401	+	0.395652i	$0.129481\pi$
$947$			24.3511i			0.791303i	−0.918401	+	0.395652i	$0.870519\pi$
$948$	−0.0776060	+	3.47432i	−0.00252053	+	0.112841i
$949$	−27.9186			−0.906275
$950$	−2.74252	−	4.75019i	−0.0889792	−	0.154117i
$951$	−17.3705	−	0.388006i	−0.563279	−	0.0125820i
$952$	−12.2662	−	16.8115i	−0.397549	−	0.544863i
$953$			39.1967i			1.26970i	0.772634	+	0.634852i	$0.218939\pi$
$953$			39.1967i			1.26970i	−0.772634	+	0.634852i	$0.781061\pi$
$954$	−13.2593	−	25.5352i	−0.429285	−	0.826734i
$955$	21.7317	−	12.5468i	0.703221	−	0.406005i
$956$	−13.9417	−	8.04923i	−0.450906	−	0.260331i
$957$	0.162073	−	7.25582i	0.00523909	−	0.234547i
$958$	−30.9480	−	17.8678i	−0.999885	−	0.577284i
$959$	−13.9938	+	31.6021i	−0.451884	+	1.02049i
$960$	−1.51897	+	0.832312i	−0.0490244	+	0.0268628i
$961$	30.6704			0.989368
$962$	−3.55195	−	6.15215i	−0.114519	−	0.198353i
$963$	25.1104	+	16.0336i	0.809172	+	0.516675i
$964$	22.2029	+	12.8188i	0.715106	+	0.412867i
$965$	8.95240	+	15.5060i	0.288188	+	0.499156i
$966$	−12.7280	−	18.2887i	−0.409518	−	0.588429i
$967$	7.42308	−	12.8572i	0.238710	−	0.413458i	−0.721634	−	0.692275i	$-0.756609\pi$
$967$	7.42308	−	12.8572i	0.238710	−	0.413458i	0.960344	+	0.278816i	$0.0899421\pi$
$968$	9.35054	−	5.39854i	0.300538	−	0.173516i
$969$	74.7086	+	1.66877i	2.39998	+	0.0536085i
$970$	−5.01988	+	8.69468i	−0.161179	+	0.279169i
$971$	−21.8681	+	37.8766i	−0.701780	+	1.21552i	0.266061	+	0.963956i	$0.414278\pi$
$971$	−21.8681	+	37.8766i	−0.701780	+	1.21552i	−0.967841	+	0.251562i	$0.919056\pi$
$972$	1.73709	−	15.4914i	0.0557173	−	0.496886i
$973$	−0.702109	+	1.58557i	−0.0225086	+	0.0508309i
$974$	−16.3170	+	9.42060i	−0.522829	+	0.301855i
$975$	4.09570	+	7.47464i	0.131168	+	0.239380i
$976$			9.86290i			0.315704i
$977$			42.3878i			1.35610i	0.735014	+	0.678052i	$0.237176\pi$
$977$			42.3878i			1.35610i	−0.735014	+	0.678052i	$0.762824\pi$
$978$	5.60210	−	9.22122i	0.179135	−	0.294862i
$979$	1.54835	−	0.893939i	0.0494854	−	0.0285704i
$980$	−4.70487	−	5.18306i	−0.150292	−	0.165567i
$981$	−6.16104	−	11.8652i	−0.196707	−	0.378826i
$982$	−8.05323	+	13.9486i	−0.256989	+	0.445118i
$983$	28.6421	−	49.6095i	0.913540	−	1.58230i	0.104516	−	0.994523i	$-0.466671\pi$
$983$	28.6421	−	49.6095i	0.913540	−	1.58230i	0.809024	−	0.587775i	$-0.199996\pi$
$984$	1.72078	−	2.83245i	0.0548563	−	0.0902952i
$985$	10.9572	−	6.32615i	0.349126	−	0.201568i
$986$	−36.5825	+	63.3628i	−1.16502	+	2.01788i
$987$	−33.9095	+	2.86894i	−1.07935	+	0.0913194i
$988$	−13.4956	−	23.3751i	−0.429353	−	0.743661i
$989$	3.86658	+	2.23237i	0.122950	+	0.0709853i
$990$	1.35007	+	0.0603431i	0.0429080	+	0.00191783i
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	0.569154	−	0.822231i	$-0.307271\pi$
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	−0.996650	+	0.0817862i	$0.973938\pi$
$992$	−0.574100			−0.0182277
$993$	−1.22625	+	54.8978i	−0.0389140	+	1.74213i
$994$	−1.09525	−	10.2221i	−0.0347393	−	0.324226i
$995$	18.2922	+	10.5610i	0.579900	+	0.334806i
$996$	14.4815	−	7.93508i	0.458864	−	0.251433i
$997$	51.2194	+	29.5715i	1.62213	+	0.936540i	0.986348	+	0.164675i	$0.0526576\pi$
$997$	51.2194	+	29.5715i	1.62213	+	0.936540i	0.635787	+	0.771865i	$0.280676\pi$
$998$	−1.17141	+	0.676312i	−0.0370802	+	0.0214083i
$999$	6.23063	+	4.17716i	0.197128	+	0.132159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.b.131.3	yes	28
3.2	odd	2		1890.2.bk.b.341.9		28
7.3	odd	6		630.2.t.b.311.8	✓	28
9.2	odd	6		630.2.t.b.551.8	yes	28
9.7	even	3		1890.2.t.b.1601.5		28
21.17	even	6		1890.2.t.b.1151.5		28
63.38	even	6	inner	630.2.bk.b.101.10	yes	28
63.52	odd	6		1890.2.bk.b.521.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.8	✓	28	7.3	odd	6
630.2.t.b.551.8	yes	28	9.2	odd	6
630.2.bk.b.101.10	yes	28	63.38	even	6	inner
630.2.bk.b.131.3	yes	28	1.1	even	1	trivial
1890.2.t.b.1151.5		28	21.17	even	6
1890.2.t.b.1601.5		28	9.7	even	3
1890.2.bk.b.341.9		28	3.2	odd	2
1890.2.bk.b.521.9		28	63.52	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.0386792 + 1.73162i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.73162 + 0.0386792i) q^{6} +(0.281867 + 2.63069i) q^{7} +1.00000i q^{8} +(-2.99701 - 0.133955i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.0386792 + 1.73162i) q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.73162 + 0.0386792i) q^{6} +(0.281867 + 2.63069i) q^{7} +1.00000i q^{8} +(-2.99701 - 0.133955i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(0.390121 + 0.225236i) q^{11} +(0.0386792 - 1.73162i) q^{12} +(-4.26160 - 2.46044i) q^{13} +(2.63069 - 0.281867i) q^{14} +(1.51897 - 0.832312i) q^{15} +1.00000 q^{16} +(3.93285 + 6.81190i) q^{17} +(-0.133955 + 2.99701i) q^{18} +(-4.75019 - 2.74252i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.56626 + 0.386332i) q^{21} +(0.225236 - 0.390121i) q^{22} +(-4.21087 + 2.43115i) q^{23} +(-1.73162 - 0.0386792i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.46044 + 4.26160i) q^{26} +(0.347881 - 5.18449i) q^{27} +(-0.281867 - 2.63069i) q^{28} +(-8.05558 + 4.65089i) q^{29} +(-0.832312 - 1.51897i) q^{30} -0.574100i q^{31} -1.00000i q^{32} +(-0.405113 + 0.666828i) q^{33} +(6.81190 - 3.93285i) q^{34} +(2.13731 - 1.55945i) q^{35} +(2.99701 + 0.133955i) q^{36} +(-0.721812 + 1.25022i) q^{37} +(-2.74252 + 4.75019i) q^{38} +(4.42538 - 7.28430i) q^{39} +(0.866025 - 0.500000i) q^{40} +(-0.956724 + 1.65709i) q^{41} +(0.386332 + 4.56626i) q^{42} +(-0.459119 - 0.795218i) q^{43} +(-0.390121 - 0.225236i) q^{44} +(1.38250 + 2.66246i) q^{45} +(2.43115 + 4.21087i) q^{46} +7.42609 q^{47} +(-0.0386792 + 1.73162i) q^{48} +(-6.84110 + 1.48301i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-11.9477 + 6.54672i) q^{51} +(4.26160 + 2.46044i) q^{52} +(-8.30591 + 4.79542i) q^{53} +(-5.18449 - 0.347881i) q^{54} -0.450472i q^{55} +(-2.63069 + 0.281867i) q^{56} +(4.93274 - 8.11944i) q^{57} +(4.65089 + 8.05558i) q^{58} +8.86555 q^{59} +(-1.51897 + 0.832312i) q^{60} +9.86290i q^{61} -0.574100 q^{62} +(-0.492361 - 7.92197i) q^{63} -1.00000 q^{64} +4.92088i q^{65} +(0.666828 + 0.405113i) q^{66} -4.64204 q^{67} +(-3.93285 - 6.81190i) q^{68} +(-4.04694 - 7.38565i) q^{69} +(-1.55945 - 2.13731i) q^{70} -3.88571i q^{71} +(0.133955 - 2.99701i) q^{72} +(4.91339 - 2.83675i) q^{73} +(1.25022 + 0.721812i) q^{74} +(-1.48029 - 0.899307i) q^{75} +(4.75019 + 2.74252i) q^{76} +(-0.482566 + 1.08977i) q^{77} +(-7.28430 - 4.42538i) q^{78} -2.00640 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.96411 + 0.802930i) q^{81} +(1.65709 + 0.956724i) q^{82} +(4.76689 + 8.25650i) q^{83} +(4.56626 - 0.386332i) q^{84} +(3.93285 - 6.81190i) q^{85} +(-0.795218 + 0.459119i) q^{86} +(-7.74198 - 14.1291i) q^{87} +(-0.225236 + 0.390121i) q^{88} +(1.98445 - 3.43716i) q^{89} +(2.66246 - 1.38250i) q^{90} +(5.27146 - 11.9045i) q^{91} +(4.21087 - 2.43115i) q^{92} +(0.994122 + 0.0222057i) q^{93} -7.42609i q^{94} +5.48505i q^{95} +(1.73162 + 0.0386792i) q^{96} +(8.69468 - 5.01988i) q^{97} +(1.48301 + 6.84110i) q^{98} +(-1.13902 - 0.727293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9	\( 28 q + 2 q^{3} - 28 q^{4} - 14 q^{5} + 8 q^{6} + 8 q^{7} + 6 q^{9} - 2 q^{12} + 2 q^{15} + 28 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} + 14 q^{20} + 16 q^{21} - 6 q^{22} + 30 q^{23} - 8 q^{24} - 14 q^{25} - 12 q^{26} - 28 q^{27} - 8 q^{28} - 4 q^{30} - 20 q^{33} - 4 q^{35} - 6 q^{36} + 4 q^{37} - 6 q^{38} - 42 q^{39} - 18 q^{41} + 28 q^{43} - 12 q^{45} - 18 q^{46} + 60 q^{47} + 2 q^{48} - 20 q^{49} - 74 q^{51} + 42 q^{53} + 10 q^{54} - 30 q^{57} + 6 q^{58} - 48 q^{59} - 2 q^{60} + 12 q^{62} - 28 q^{63} - 28 q^{64} - 26 q^{66} + 80 q^{67} - 6 q^{68} - 8 q^{69} + 6 q^{70} - 8 q^{72} + 6 q^{73} - 4 q^{75} + 6 q^{76} - 18 q^{77} + 14 q^{78} - 4 q^{79} - 14 q^{80} + 38 q^{81} + 24 q^{82} + 18 q^{83} - 16 q^{84} + 6 q^{85} - 96 q^{86} + 52 q^{87} + 6 q^{88} - 6 q^{89} - 4 q^{90} + 66 q^{91} - 30 q^{92} + 22 q^{93} + 8 q^{96} + 72 q^{97} + 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q + 2 * q^3 - 28 * q^4 - 14 * q^5 + 8 * q^6 + 8 * q^7 + 6 * q^9 - 2 * q^12 + 2 * q^15 + 28 * q^16 + 6 * q^17 + 8 * q^18 - 6 * q^19 + 14 * q^20 + 16 * q^21 - 6 * q^22 + 30 * q^23 - 8 * q^24 - 14 * q^25 - 12 * q^26 - 28 * q^27 - 8 * q^28 - 4 * q^30 - 20 * q^33 - 4 * q^35 - 6 * q^36 + 4 * q^37 - 6 * q^38 - 42 * q^39 - 18 * q^41 + 28 * q^43 - 12 * q^45 - 18 * q^46 + 60 * q^47 + 2 * q^48 - 20 * q^49 - 74 * q^51 + 42 * q^53 + 10 * q^54 - 30 * q^57 + 6 * q^58 - 48 * q^59 - 2 * q^60 + 12 * q^62 - 28 * q^63 - 28 * q^64 - 26 * q^66 + 80 * q^67 - 6 * q^68 - 8 * q^69 + 6 * q^70 - 8 * q^72 + 6 * q^73 - 4 * q^75 + 6 * q^76 - 18 * q^77 + 14 * q^78 - 4 * q^79 - 14 * q^80 + 38 * q^81 + 24 * q^82 + 18 * q^83 - 16 * q^84 + 6 * q^85 - 96 * q^86 + 52 * q^87 + 6 * q^88 - 6 * q^89 - 4 * q^90 + 66 * q^91 - 30 * q^92 + 22 * q^93 + 8 * q^96 + 72 * q^97 + 24 * q^98 - 42 * q^99

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