LMFDB - Embedded newform 210.2.r.b.101.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(101,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("210.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.r (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.5
Root			$0.312065 - 1.70371i$ of defining polynomial
Character	$\chi$	$=$	210.101
Dual form			210.2.r.b.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(1.12211 + 1.31942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.63149 + 0.581597i) q^{6} +(1.26546 - 2.32349i) q^{7} -1.00000i q^{8} +(-0.481739 + 2.96107i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(1.12211 + 1.31942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.63149 + 0.581597i) q^{6} +(1.26546 - 2.32349i) q^{7} -1.00000i q^{8} +(-0.481739 + 2.96107i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.834397 + 0.481739i) q^{11} +(1.70371 - 0.312065i) q^{12} +1.98782i q^{13} +(-0.0658248 - 2.64493i) q^{14} +(0.581597 - 1.63149i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.31614 + 2.27961i) q^{17} +(1.06334 + 2.80523i) q^{18} +(-4.47548 + 2.58392i) q^{19} -1.00000 q^{20} +(4.48565 - 0.937538i) q^{21} +0.963479 q^{22} +(-2.33317 + 1.34706i) q^{23} +(1.31942 - 1.12211i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.993908 + 1.72150i) q^{26} +(-4.44746 + 2.68703i) q^{27} +(-1.37947 - 2.25767i) q^{28} -9.90498i q^{29} +(-0.312065 - 1.70371i) q^{30} +(-2.96312 - 1.71076i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.300668 + 1.64148i) q^{33} +2.63227i q^{34} +(-2.64493 + 0.0658248i) q^{35} +(2.32349 + 1.89773i) q^{36} +(-4.57302 - 7.92070i) q^{37} +(-2.58392 + 4.47548i) q^{38} +(-2.62276 + 2.23055i) q^{39} +(-0.866025 + 0.500000i) q^{40} +1.12202 q^{41} +(3.41591 - 3.05475i) q^{42} +1.54917 q^{43} +(0.834397 - 0.481739i) q^{44} +(2.80523 - 1.06334i) q^{45} +(-1.34706 + 2.33317i) q^{46} +(5.19438 + 8.99693i) q^{47} +(0.581597 - 1.63149i) q^{48} +(-3.79722 - 5.88057i) q^{49} +1.00000i q^{50} +(-4.48462 + 0.821441i) q^{51} +(1.72150 + 0.993908i) q^{52} +(11.4092 + 6.58709i) q^{53} +(-2.50810 + 4.55076i) q^{54} -0.963479i q^{55} +(-2.32349 - 1.26546i) q^{56} +(-8.43126 - 3.00560i) q^{57} +(-4.95249 - 8.57796i) q^{58} +(1.05123 - 1.82079i) q^{59} +(-1.12211 - 1.31942i) q^{60} +(-7.76184 + 4.48130i) q^{61} -3.42151 q^{62} +(6.27039 + 4.86643i) q^{63} -1.00000 q^{64} +(1.72150 - 0.993908i) q^{65} +(1.08113 + 1.27123i) q^{66} +(0.897733 - 1.55492i) q^{67} +(1.31614 + 2.27961i) q^{68} +(-4.39541 - 1.56689i) q^{69} +(-2.25767 + 1.37947i) q^{70} +11.1501i q^{71} +(2.96107 + 0.481739i) q^{72} +(10.1961 + 5.88674i) q^{73} +(-7.92070 - 4.57302i) q^{74} +(-1.70371 + 0.312065i) q^{75} +5.16784i q^{76} +(2.17521 - 1.32909i) q^{77} +(-1.15611 + 3.24309i) q^{78} +(0.204174 + 0.353640i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-8.53585 - 2.85293i) q^{81} +(0.971699 - 0.561011i) q^{82} +4.53092 q^{83} +(1.43089 - 4.35345i) q^{84} +2.63227 q^{85} +(1.34162 - 0.774585i) q^{86} +(13.0688 - 11.1145i) q^{87} +(0.481739 - 0.834397i) q^{88} +(-5.76070 - 9.97782i) q^{89} +(1.89773 - 2.32349i) q^{90} +(4.61867 + 2.51550i) q^{91} +2.69411i q^{92} +(-1.06774 - 5.82926i) q^{93} +(8.99693 + 5.19438i) q^{94} +(4.47548 + 2.58392i) q^{95} +(-0.312065 - 1.70371i) q^{96} +14.6992i q^{97} +(-6.22878 - 3.19411i) q^{98} +(-1.82842 + 2.23863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7}+O(q^{10}) $ 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7	$ 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{11} - 2 q^{12} - 12 q^{14} - 4 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 12 q^{20} + 4 q^{21} + 24 q^{23} - 2 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{30} + 12 q^{31} - 2 q^{33} - 4 q^{35} + 6 q^{36} - 8 q^{37} - 8 q^{38} - 42 q^{39} + 4 q^{41} + 24 q^{42} + 12 q^{44} + 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{51} - 12 q^{52} + 48 q^{53} - 32 q^{54} - 6 q^{56} - 36 q^{57} + 8 q^{58} - 12 q^{59} - 2 q^{60} - 30 q^{61} - 8 q^{62} + 20 q^{63} - 12 q^{64} - 12 q^{65} - 14 q^{66} - 4 q^{67} + 12 q^{68} - 50 q^{69} + 6 q^{70} + 4 q^{72} + 2 q^{75} - 20 q^{77} + 32 q^{78} - 4 q^{79} - 6 q^{80} - 40 q^{81} + 40 q^{83} + 20 q^{84} + 24 q^{85} + 54 q^{86} + 64 q^{87} - 26 q^{89} + 8 q^{90} + 28 q^{91} + 4 q^{93} + 24 q^{94} - 4 q^{96} - 16 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^11 - 2 * q^12 - 12 * q^14 - 4 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 12 * q^20 + 4 * q^21 + 24 * q^23 - 2 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^30 + 12 * q^31 - 2 * q^33 - 4 * q^35 + 6 * q^36 - 8 * q^37 - 8 * q^38 - 42 * q^39 + 4 * q^41 + 24 * q^42 + 12 * q^44 + 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^51 - 12 * q^52 + 48 * q^53 - 32 * q^54 - 6 * q^56 - 36 * q^57 + 8 * q^58 - 12 * q^59 - 2 * q^60 - 30 * q^61 - 8 * q^62 + 20 * q^63 - 12 * q^64 - 12 * q^65 - 14 * q^66 - 4 * q^67 + 12 * q^68 - 50 * q^69 + 6 * q^70 + 4 * q^72 + 2 * q^75 - 20 * q^77 + 32 * q^78 - 4 * q^79 - 6 * q^80 - 40 * q^81 + 40 * q^83 + 20 * q^84 + 24 * q^85 + 54 * q^86 + 64 * q^87 - 26 * q^89 + 8 * q^90 + 28 * q^91 + 4 * q^93 + 24 * q^94 - 4 * q^96 - 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.12211	+	1.31942i	0.647850	+	0.761768i
$3$	1.12211	+	1.31942i	0.647850	+	0.761768i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.63149	+	0.581597i	0.666051	+	0.237436i
$7$	1.26546	−	2.32349i	0.478299	−	0.878197i
$7$	1.26546	−	2.32349i	0.478299	−	0.878197i
$8$		−	1.00000i		−	0.353553i
$9$	−0.481739	+	2.96107i	−0.160580	+	0.987023i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	0.834397	+	0.481739i	0.251580	+	0.145250i	0.620488	−	0.784216i	$-0.286935\pi$
$11$	0.834397	+	0.481739i	0.251580	+	0.145250i	−0.368907	+	0.929466i	$0.620268\pi$
$12$	1.70371	−	0.312065i	0.491818	−	0.0900855i
$13$			1.98782i			0.551321i	0.961255	+	0.275660i	$0.0888966\pi$
$13$			1.98782i			0.551321i	−0.961255	+	0.275660i	$0.911103\pi$
$14$	−0.0658248	−	2.64493i	−0.0175924	−	0.706888i
$15$	0.581597	−	1.63149i	0.150168	−	0.421248i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.31614	+	2.27961i	−0.319210	+	0.552888i	−0.980323	−	0.197398i	$-0.936751\pi$
$17$	−1.31614	+	2.27961i	−0.319210	+	0.552888i	0.661113	+	0.750286i	$0.270084\pi$
$18$	1.06334	+	2.80523i	0.250631	+	0.661199i
$19$	−4.47548	+	2.58392i	−1.02675	+	0.592792i	−0.916051	−	0.401062i	$-0.868641\pi$
$19$	−4.47548	+	2.58392i	−1.02675	+	0.592792i	−0.110695	+	0.993854i	$0.535308\pi$
$20$	−1.00000			−0.223607
$21$	4.48565	−	0.937538i	0.978848	−	0.204588i
$22$	0.963479			0.205414
$23$	−2.33317	+	1.34706i	−0.486500	+	0.280881i	−0.723121	−	0.690721i	$-0.757293\pi$
$23$	−2.33317	+	1.34706i	−0.486500	+	0.280881i	0.236621	+	0.971602i	$0.423960\pi$
$24$	1.31942	−	1.12211i	0.269326	−	0.229050i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.993908	+	1.72150i	0.194921	+	0.337614i
$27$	−4.44746	+	2.68703i	−0.855914	+	0.517119i
$28$	−1.37947	−	2.25767i	−0.260696	−	0.426659i
$29$		−	9.90498i		−	1.83931i	−0.392730	−	0.919654i	$-0.628469\pi$
$29$		−	9.90498i		−	1.83931i	0.392730	−	0.919654i	$-0.371531\pi$
$30$	−0.312065	−	1.70371i	−0.0569751	−	0.311053i
$31$	−2.96312	−	1.71076i	−0.532192	−	0.307261i	0.209717	−	0.977762i	$-0.432746\pi$
$31$	−2.96312	−	1.71076i	−0.532192	−	0.307261i	−0.741909	+	0.670501i	$0.766079\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.300668	+	1.64148i	0.0523397	+	0.285746i
$34$			2.63227i			0.451431i
$35$	−2.64493	+	0.0658248i	−0.447075	+	0.0111264i
$36$	2.32349	+	1.89773i	0.387248	+	0.316289i
$37$	−4.57302	−	7.92070i	−0.751799	−	1.30215i	−0.946950	−	0.321381i	$-0.895853\pi$
$37$	−4.57302	−	7.92070i	−0.751799	−	1.30215i	0.195151	−	0.980773i	$-0.437480\pi$
$38$	−2.58392	+	4.47548i	−0.419167	+	0.726019i
$39$	−2.62276	+	2.23055i	−0.419978	+	0.357174i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	1.12202			0.175230			0.0876152	−	0.996154i	$-0.472075\pi$
$41$	1.12202			0.175230			0.0876152	+	0.996154i	$0.472075\pi$
$42$	3.41591	−	3.05475i	0.527087	−	0.471359i
$43$	1.54917			0.236246			0.118123	−	0.992999i	$-0.462312\pi$
$43$	1.54917			0.236246			0.118123	+	0.992999i	$0.462312\pi$
$44$	0.834397	−	0.481739i	0.125790	−	0.0726249i
$45$	2.80523	−	1.06334i	0.418179	−	0.158513i
$46$	−1.34706	+	2.33317i	−0.198613	+	0.344007i
$47$	5.19438	+	8.99693i	0.757679	+	1.31234i	0.944032	+	0.329855i	$0.107000\pi$
$47$	5.19438	+	8.99693i	0.757679	+	1.31234i	−0.186353	+	0.982483i	$0.559667\pi$
$48$	0.581597	−	1.63149i	0.0839462	−	0.235485i
$49$	−3.79722	−	5.88057i	−0.542460	−	0.840082i
$50$			1.00000i			0.141421i
$51$	−4.48462	+	0.821441i	−0.627972	+	0.115025i
$52$	1.72150	+	0.993908i	0.238729	+	0.137830i
$53$	11.4092	+	6.58709i	1.56717	+	0.904806i	0.996497	+	0.0836280i	$0.0266507\pi$
$53$	11.4092	+	6.58709i	1.56717	+	0.904806i	0.570672	+	0.821178i	$0.306683\pi$
$54$	−2.50810	+	4.55076i	−0.341309	+	0.619280i
$55$		−	0.963479i		−	0.129915i
$56$	−2.32349	−	1.26546i	−0.310490	−	0.169104i
$57$	−8.43126	−	3.00560i	−1.11675	−	0.398101i
$58$	−4.95249	−	8.57796i	−0.650293	−	1.12634i
$59$	1.05123	−	1.82079i	0.136859	−	0.237046i	−0.789447	−	0.613818i	$-0.789633\pi$
$59$	1.05123	−	1.82079i	0.136859	−	0.237046i	0.926306	+	0.376772i	$0.122966\pi$
$60$	−1.12211	−	1.31942i	−0.144864	−	0.170336i
$61$	−7.76184	+	4.48130i	−0.993802	+	0.573772i	−0.906408	−	0.422402i	$-0.861187\pi$
$61$	−7.76184	+	4.48130i	−0.993802	+	0.573772i	−0.0873932	+	0.996174i	$0.527854\pi$
$62$	−3.42151			−0.434533
$63$	6.27039	+	4.86643i	0.789995	+	0.613113i
$64$	−1.00000			−0.125000
$65$	1.72150	−	0.993908i	0.213526	−	0.123279i
$66$	1.08113	+	1.27123i	0.133078	+	0.156478i
$67$	0.897733	−	1.55492i	0.109676	−	0.189964i	−0.805963	−	0.591966i	$-0.798352\pi$
$67$	0.897733	−	1.55492i	0.109676	−	0.189964i	0.915639	+	0.402002i	$0.131685\pi$
$68$	1.31614	+	2.27961i	0.159605	+	0.276444i
$69$	−4.39541	−	1.56689i	−0.529145	−	0.188631i
$70$	−2.25767	+	1.37947i	−0.269843	+	0.164878i
$71$			11.1501i			1.32328i	0.749823	+	0.661639i	$0.230139\pi$
$71$			11.1501i			1.32328i	−0.749823	+	0.661639i	$0.769861\pi$
$72$	2.96107	+	0.481739i	0.348965	+	0.0567735i
$73$	10.1961	+	5.88674i	1.19337	+	0.688991i	0.959069	−	0.283174i	$-0.0913873\pi$
$73$	10.1961	+	5.88674i	1.19337	+	0.688991i	0.234299	+	0.972165i	$0.424721\pi$
$74$	−7.92070	−	4.57302i	−0.920762	−	0.531602i
$75$	−1.70371	+	0.312065i	−0.196727	+	0.0360342i
$76$			5.16784i			0.592792i
$77$	2.17521	−	1.32909i	0.247889	−	0.151464i
$78$	−1.15611	+	3.24309i	−0.130903	+	0.367208i
$79$	0.204174	+	0.353640i	0.0229714	+	0.0397876i	0.877283	−	0.479974i	$-0.159354\pi$
$79$	0.204174	+	0.353640i	0.0229714	+	0.0397876i	−0.854311	+	0.519762i	$0.826021\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−8.53585	−	2.85293i	−0.948428	−	0.316992i
$82$	0.971699	−	0.561011i	0.107306	−	0.0619533i
$83$	4.53092			0.497333			0.248667	−	0.968589i	$-0.420008\pi$
$83$	4.53092			0.497333			0.248667	+	0.968589i	$0.420008\pi$
$84$	1.43089	−	4.35345i	0.156123	−	0.475001i
$85$	2.63227			0.285510
$86$	1.34162	−	0.774585i	0.144671	−	0.0835257i
$87$	13.0688	−	11.1145i	1.40113	−	1.19160i
$88$	0.481739	−	0.834397i	0.0513536	−	0.0889470i
$89$	−5.76070	−	9.97782i	−0.610633	−	1.05765i	−0.991134	−	0.132867i	$-0.957582\pi$
$89$	−5.76070	−	9.97782i	−0.610633	−	1.05765i	0.380501	−	0.924781i	$-0.375752\pi$
$90$	1.89773	−	2.32349i	0.200039	−	0.244917i
$91$	4.61867	+	2.51550i	0.484168	+	0.263696i
$92$			2.69411i			0.280881i
$93$	−1.06774	−	5.82926i	−0.110719	−	0.604466i
$94$	8.99693	+	5.19438i	0.927963	+	0.535760i
$95$	4.47548	+	2.58392i	0.459175	+	0.265105i
$96$	−0.312065	−	1.70371i	−0.0318500	−	0.173884i
$97$			14.6992i			1.49248i	0.665679	+	0.746239i	$0.268142\pi$
$97$			14.6992i			1.49248i	−0.665679	+	0.746239i	$0.731858\pi$
$98$	−6.22878	−	3.19411i	−0.629201	−	0.322654i
$99$	−1.82842	+	2.23863i	−0.183764	+	0.224991i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	7.58148	−	13.1315i	0.754386	−	1.30663i	−0.191293	−	0.981533i	$-0.561268\pi$
$101$	7.58148	−	13.1315i	0.754386	−	1.30663i	0.945679	−	0.325102i	$-0.105399\pi$
$102$	−3.47307	+	2.95370i	−0.343886	+	0.292460i
$103$	7.85525	−	4.53523i	0.774001	−	0.446870i	−0.0602991	−	0.998180i	$-0.519205\pi$
$103$	7.85525	−	4.53523i	0.774001	−	0.446870i	0.834300	+	0.551311i	$0.185872\pi$
$104$	1.98782			0.194921
$105$	−3.05475	−	3.41591i	−0.298114	−	0.333359i
$106$	13.1742			1.27959
$107$	−12.0022	+	6.92949i	−1.16030	+	0.669899i	−0.951376	−	0.308033i	$-0.900329\pi$
$107$	−12.0022	+	6.92949i	−1.16030	+	0.669899i	−0.208924	+	0.977932i	$0.566996\pi$
$108$	0.103305	+	5.19513i	0.00994053	+	0.499901i
$109$	8.36670	−	14.4915i	0.801385	−	1.38804i	−0.117320	−	0.993094i	$-0.537430\pi$
$109$	8.36670	−	14.4915i	0.801385	−	1.38804i	0.918705	−	0.394945i	$-0.129236\pi$
$110$	−0.481739	−	0.834397i	−0.0459320	−	0.0795566i
$111$	5.31930	−	14.9216i	0.504886	−	1.41630i
$112$	−2.64493	+	0.0658248i	−0.249923	+	0.00621985i
$113$		−	13.9355i		−	1.31095i	−0.755219	−	0.655473i	$-0.772470\pi$
$113$		−	13.9355i		−	1.31095i	0.755219	−	0.655473i	$-0.227530\pi$
$114$	−8.80449	+	1.61271i	−0.824616	+	0.151044i
$115$	2.33317	+	1.34706i	0.217569	+	0.125614i
$116$	−8.57796	−	4.95249i	−0.796444	−	0.459827i
$117$	−5.88606	−	0.957609i	−0.544166	−	0.0885310i
$118$		−	2.10246i		−	0.193547i
$119$	3.63115	+	5.94279i	0.332867	+	0.544775i
$120$	−1.63149	−	0.581597i	−0.148934	−	0.0530923i
$121$	−5.03585	−	8.72236i	−0.457805	−	0.792941i
$122$	−4.48130	+	7.76184i	−0.405718	+	0.702724i
$123$	1.25903	+	1.48042i	0.113523	+	0.133485i
$124$	−2.96312	+	1.71076i	−0.266096	+	0.153631i
$125$	1.00000			0.0894427
$126$	7.86354	+	1.07926i	0.700540	+	0.0961478i
$127$	16.1937			1.43696			0.718479	−	0.695548i	$-0.244839\pi$
$127$	16.1937			1.43696			0.718479	+	0.695548i	$0.244839\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.73834	+	2.04401i	0.153052	+	0.179965i
$130$	0.993908	−	1.72150i	0.0871715	−	0.150985i
$131$	−2.96107	−	5.12872i	−0.258710	−	0.448098i	0.707187	−	0.707027i	$-0.249964\pi$
$131$	−2.96107	−	5.12872i	−0.258710	−	0.448098i	−0.965897	+	0.258928i	$0.916631\pi$
$132$	1.57190	+	0.560356i	0.136816	+	0.0487727i
$133$	0.340172	+	13.6686i	0.0294967	+	1.18522i
$134$		−	1.79547i		−	0.155105i
$135$	4.55076	+	2.50810i	0.391667	+	0.215863i
$136$	2.27961	+	1.31614i	0.195475	+	0.112858i
$137$	6.60004	+	3.81054i	0.563880	+	0.325556i	0.754701	−	0.656069i	$-0.227782\pi$
$137$	6.60004	+	3.81054i	0.563880	+	0.325556i	−0.190822	+	0.981625i	$0.561115\pi$
$138$	−4.58998	+	0.840740i	−0.390725	+	0.0715685i
$139$			7.13772i			0.605413i	0.953084	+	0.302707i	$0.0978902\pi$
$139$			7.13772i			0.605413i	−0.953084	+	0.302707i	$0.902110\pi$
$140$	−1.26546	+	2.32349i	−0.106951	+	0.196371i
$141$	−6.04207	+	16.9491i	−0.508834	+	1.42737i
$142$	5.57507	+	9.65630i	0.467849	+	0.810338i
$143$	−0.957609	+	1.65863i	−0.0800793	+	0.138701i
$144$	2.80523	−	1.06334i	0.233769	−	0.0886113i
$145$	−8.57796	+	4.95249i	−0.712361	+	0.411282i
$146$	11.7735			0.974380
$147$	3.49805	−	11.6088i	0.288514	−	0.957476i
$148$	−9.14603			−0.751799
$149$	10.3652	−	5.98436i	0.849151	−	0.490258i	−0.0112130	−	0.999937i	$-0.503569\pi$
$149$	10.3652	−	5.98436i	0.849151	−	0.490258i	0.860364	+	0.509679i	$0.170236\pi$
$150$	−1.31942	+	1.12211i	−0.107730	+	0.0916199i
$151$	−4.49850	+	7.79163i	−0.366083	+	0.634074i	−0.988949	−	0.148254i	$-0.952635\pi$
$151$	−4.49850	+	7.79163i	−0.366083	+	0.634074i	0.622867	+	0.782328i	$0.285968\pi$
$152$	2.58392	+	4.47548i	0.209584	+	0.363010i
$153$	−6.11606	−	4.99535i	−0.494454	−	0.403850i
$154$	1.21924	−	2.23863i	0.0982495	−	0.180394i
$155$			3.42151i			0.274823i
$156$	0.620329	+	3.38665i	0.0496661	+	0.271149i
$157$	−5.70434	−	3.29340i	−0.455256	−	0.262842i	0.254792	−	0.966996i	$-0.417993\pi$
$157$	−5.70434	−	3.29340i	−0.455256	−	0.262842i	−0.710047	+	0.704154i	$0.751326\pi$
$158$	0.353640	+	0.204174i	0.0281341	+	0.0162432i
$159$	4.11120	+	22.4449i	0.326040	+	1.78000i
$160$			1.00000i			0.0790569i
$161$	0.177339	+	7.12575i	0.0139763	+	0.561588i
$162$	−8.81873	+	1.79722i	−0.692865	+	0.141203i
$163$	−1.32525	−	2.29539i	−0.103801	−	0.179789i	0.809447	−	0.587194i	$-0.199767\pi$
$163$	−1.32525	−	2.29539i	−0.103801	−	0.179789i	−0.913248	+	0.407404i	$0.866434\pi$
$164$	0.561011	−	0.971699i	0.0438076	−	0.0758770i
$165$	1.27123	−	1.08113i	0.0989654	−	0.0841658i
$166$	3.92389	−	2.26546i	0.304553	−	0.175834i
$167$	−7.68946			−0.595029			−0.297514	−	0.954717i	$-0.596158\pi$
$167$	−7.68946			−0.595029			−0.297514	+	0.954717i	$0.596158\pi$
$168$	−0.937538	−	4.48565i	−0.0723326	−	0.346075i
$169$	9.04859			0.696045
$170$	2.27961	−	1.31614i	0.174838	−	0.100943i
$171$	−5.49515	−	14.4970i	−0.420225	−	1.10861i
$172$	0.774585	−	1.34162i	0.0590616	−	0.102298i
$173$	−10.6454	−	18.4384i	−0.809355	−	1.40184i	−0.913311	−	0.407262i	$-0.866484\pi$
$173$	−10.6454	−	18.4384i	−0.809355	−	1.40184i	0.103956	−	0.994582i	$-0.466850\pi$
$174$	5.76070	−	16.1598i	0.436717	−	1.22507i
$175$	1.37947	+	2.25767i	0.104278	+	0.170664i
$176$		−	0.963479i		−	0.0726249i
$177$	3.58198	−	0.656106i	0.269238	−	0.0493159i
$178$	−9.97782	−	5.76070i	−0.747870	−	0.431783i
$179$	1.14867	+	0.663182i	0.0858553	+	0.0495686i	0.542313	−	0.840177i	$-0.317549\pi$
$179$	1.14867	+	0.663182i	0.0858553	+	0.0495686i	−0.456458	+	0.889745i	$0.650882\pi$
$180$	0.481739	−	2.96107i	0.0359067	−	0.220705i
$181$			2.17439i			0.161621i	0.996729	+	0.0808107i	$0.0257509\pi$
$181$			2.17439i			0.161621i	−0.996729	+	0.0808107i	$0.974249\pi$
$182$	5.25764	−	0.130847i	0.389722	−	0.00969906i
$183$	−14.6224	−	5.21262i	−1.08092	−	0.385328i
$184$	1.34706	+	2.33317i	0.0993063	+	0.172004i
$185$	−4.57302	+	7.92070i	−0.336215	+	0.582341i
$186$	−3.83931	−	4.51441i	−0.281512	−	0.331013i
$187$	−2.19636	+	1.26807i	−0.160614	+	0.0927304i
$188$	10.3888			0.757679
$189$	0.615203	+	13.7340i	0.0447494	+	0.998998i
$190$	5.16784			0.374915
$191$	−14.7718	+	8.52848i	−1.06885	+	0.617099i	−0.927866	−	0.372913i	$-0.878359\pi$
$191$	−14.7718	+	8.52848i	−1.06885	+	0.617099i	−0.140981	+	0.990012i	$0.545026\pi$
$192$	−1.12211	−	1.31942i	−0.0809813	−	0.0952210i
$193$	−1.02534	+	1.77593i	−0.0738053	+	0.127835i	−0.900566	−	0.434719i	$-0.856848\pi$
$193$	−1.02534	+	1.77593i	−0.0738053	+	0.127835i	0.826761	+	0.562554i	$0.190181\pi$
$194$	7.34960	+	12.7299i	0.527670	+	0.913952i
$195$	3.24309	+	1.15611i	0.232243	+	0.0827905i
$196$	−6.99133	+	0.348204i	−0.499381	+	0.0248717i
$197$			12.9420i			0.922083i	0.887379	+	0.461041i	$0.152524\pi$
$197$			12.9420i			0.922083i	−0.887379	+	0.461041i	$0.847476\pi$
$198$	−0.464146	+	2.85293i	−0.0329854	+	0.202749i
$199$	−14.8843	−	8.59346i	−1.05512	−	0.609174i	−0.131042	−	0.991377i	$-0.541832\pi$
$199$	−14.8843	−	8.59346i	−1.05512	−	0.609174i	−0.924078	+	0.382203i	$0.875166\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	3.05895	−	0.560303i	0.215761	−	0.0395207i
$202$		−	15.1630i		−	1.06686i
$203$	−23.0141	−	12.5344i	−1.61527	−	0.879739i
$204$	−1.53092	+	4.29451i	−0.107186	+	0.300676i
$205$	−0.561011	−	0.971699i	−0.0391827	−	0.0678664i
$206$	4.53523	−	7.85525i	0.315985	−	0.547301i
$207$	−2.86475	−	7.55761i	−0.199114	−	0.525290i
$208$	1.72150	−	0.993908i	0.119364	−	0.0689151i
$209$	−4.97911			−0.344412
$210$	−4.35345	−	1.43089i	−0.300417	−	0.0987409i
$211$	2.19691			0.151242			0.0756208	−	0.997137i	$-0.475906\pi$
$211$	2.19691			0.151242			0.0756208	+	0.997137i	$0.475906\pi$
$212$	11.4092	−	6.58709i	0.783585	−	0.452403i
$213$	−14.7117	+	12.5117i	−1.00803	+	0.857286i
$214$	−6.92949	+	12.0022i	−0.473690	+	0.820456i
$215$	−0.774585	−	1.34162i	−0.0528263	−	0.0914978i
$216$	2.68703	+	4.44746i	0.182829	+	0.302611i
$217$	−7.72464	+	4.71988i	−0.524383	+	0.320407i
$218$		−	16.7334i		−	1.13333i
$219$	3.67410	+	20.0586i	0.248273	+	1.35543i
$220$	−0.834397	−	0.481739i	−0.0562550	−	0.0324789i
$221$	−4.53146	−	2.61624i	−0.304819	−	0.175987i
$222$	−2.85416	−	15.5822i	−0.191559	−	1.04581i
$223$			23.8443i			1.59673i	0.602173	+	0.798365i	$0.294302\pi$
$223$			23.8443i			1.59673i	−0.602173	+	0.798365i	$0.705698\pi$
$224$	−2.25767	+	1.37947i	−0.150847	+	0.0921699i
$225$	−2.32349	−	1.89773i	−0.154899	−	0.126516i
$226$	−6.96777	−	12.0685i	−0.463489	−	0.802787i
$227$	2.33586	−	4.04582i	0.155036	−	0.268531i	−0.778036	−	0.628220i	$-0.783784\pi$
$227$	2.33586	−	4.04582i	0.155036	−	0.268531i	0.933072	+	0.359689i	$0.117117\pi$
$228$	−6.81856	+	5.79889i	−0.451570	+	0.384041i
$229$	20.0497	−	11.5757i	1.32492	−	0.764944i	0.340413	−	0.940276i	$-0.389433\pi$
$229$	20.0497	−	11.5757i	1.32492	−	0.764944i	0.984509	+	0.175332i	$0.0560999\pi$
$230$	2.69411			0.177645
$231$	4.19446	+	1.37863i	0.275975	+	0.0907074i
$232$	−9.90498			−0.650293
$233$	11.4677	−	6.62090i	0.751276	−	0.433750i	−0.0748785	−	0.997193i	$-0.523857\pi$
$233$	11.4677	−	6.62090i	0.751276	−	0.433750i	0.826155	+	0.563443i	$0.190524\pi$
$234$	−5.57628	+	2.11372i	−0.364533	+	0.138178i
$235$	5.19438	−	8.99693i	0.338844	−	0.586895i
$236$	−1.05123	−	1.82079i	−0.0684293	−	0.118523i
$237$	−0.237494	+	0.666214i	−0.0154269	+	0.0432753i
$238$	6.11606	+	3.33104i	0.396445	+	0.215919i
$239$			14.7280i			0.952675i	0.879263	+	0.476337i	$0.158036\pi$
$239$			14.7280i			0.952675i	−0.879263	+	0.476337i	$0.841964\pi$
$240$	−1.70371	+	0.312065i	−0.109974	+	0.0201437i
$241$	−5.13289	−	2.96347i	−0.330638	−	0.190894i	0.325486	−	0.945547i	$-0.394472\pi$
$241$	−5.13289	−	2.96347i	−0.330638	−	0.190894i	−0.656124	+	0.754653i	$0.727805\pi$
$242$	−8.72236	−	5.03585i	−0.560694	−	0.323717i
$243$	−5.81396	−	14.4637i	−0.372966	−	0.927845i
$244$			8.96260i			0.573772i
$245$	−3.19411	+	6.22878i	−0.204064	+	0.397942i
$246$	1.83056	+	0.652564i	0.116712	+	0.0416059i
$247$	−5.13636	−	8.89644i	−0.326819	−	0.566067i
$248$	−1.71076	+	2.96312i	−0.108633	+	0.188158i
$249$	5.08419	+	5.97819i	0.322197	+	0.378852i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−19.4694			−1.22890			−0.614450	−	0.788956i	$-0.710622\pi$
$251$	−19.4694			−1.22890			−0.614450	+	0.788956i	$0.710622\pi$
$252$	7.34965	−	2.99710i	0.462984	−	0.188800i
$253$	−2.59572			−0.163192
$254$	14.0242	−	8.09685i	0.879954	−	0.508042i
$255$	2.95370	+	3.47307i	0.184968	+	0.217492i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.41896	−	2.45771i	−0.0885122	−	0.153308i	0.818370	−	0.574691i	$-0.194878\pi$
$257$	−1.41896	−	2.45771i	−0.0885122	−	0.153308i	−0.906882	+	0.421384i	$0.861545\pi$
$258$	2.52745	+	0.900992i	0.157352	+	0.0560933i
$259$	−24.1906	+	0.602035i	−1.50313	+	0.0374086i
$260$		−	1.98782i		−	0.123279i
$261$	29.3293	+	4.77162i	1.81544	+	0.295356i
$262$	−5.12872	−	2.96107i	−0.316853	−	0.182935i
$263$	15.6505	+	9.03582i	0.965052	+	0.557173i	0.897724	−	0.440558i	$-0.145219\pi$
$263$	15.6505	+	9.03582i	0.965052	+	0.557173i	0.0673275	+	0.997731i	$0.478553\pi$
$264$	1.64148	−	0.300668i	0.101026	−	0.0185049i
$265$		−	13.1742i		−	0.809283i
$266$	7.12890	+	11.6673i	0.437101	+	0.715366i
$267$	6.70081	−	18.7970i	0.410083	−	1.15036i
$268$	−0.897733	−	1.55492i	−0.0548378	−	0.0949818i
$269$	−8.57087	+	14.8452i	−0.522575	+	0.905127i	0.477080	+	0.878860i	$0.341695\pi$
$269$	−8.57087	+	14.8452i	−0.522575	+	0.905127i	−0.999655	+	0.0262671i	$0.991638\pi$
$270$	5.19513	−	0.103305i	0.316165	−	0.00628694i
$271$	17.6563	−	10.1939i	1.07254	−	0.619233i	0.143668	−	0.989626i	$-0.454110\pi$
$271$	17.6563	−	10.1939i	1.07254	−	0.619233i	0.928875	+	0.370393i	$0.120777\pi$
$272$	2.63227			0.159605
$273$	1.86365	+	8.91664i	0.112793	+	0.539660i
$274$	7.62107			0.460406
$275$	−0.834397	+	0.481739i	−0.0503160	+	0.0290500i
$276$	−3.55467	+	3.02309i	−0.213966	+	0.181969i
$277$	−3.81017	+	6.59942i	−0.228931	+	0.396521i	−0.957492	−	0.288461i	$-0.906856\pi$
$277$	−3.81017	+	6.59942i	−0.228931	+	0.396521i	0.728560	+	0.684982i	$0.240190\pi$
$278$	3.56886	+	6.18144i	0.214046	+	0.370738i
$279$	6.49312	−	7.94986i	0.388733	−	0.475946i
$280$	0.0658248	+	2.64493i	0.00393378	+	0.158065i
$281$			4.58608i			0.273583i	0.990600	+	0.136791i	$0.0436790\pi$
$281$			4.58608i			0.273583i	−0.990600	+	0.136791i	$0.956321\pi$
$282$	3.24197	+	17.6994i	0.193057	+	1.05398i
$283$	−13.8353	−	7.98782i	−0.822423	−	0.474826i	0.0288280	−	0.999584i	$-0.490822\pi$
$283$	−13.8353	−	7.98782i	−0.822423	−	0.474826i	−0.851251	+	0.524758i	$0.824156\pi$
$284$	9.65630	+	5.57507i	0.572996	+	0.330819i
$285$	1.61271	+	8.80449i	0.0955284	+	0.521533i
$286$			1.91522i			0.113249i
$287$	1.41987	−	2.60701i	0.0838125	−	0.153887i
$288$	1.89773	−	2.32349i	0.111825	−	0.136913i
$289$	5.03557	+	8.72186i	0.296210	+	0.513051i
$290$	−4.95249	+	8.57796i	−0.290820	+	0.503715i
$291$	−19.3944	+	16.4941i	−1.13692	+	0.966902i
$292$	10.1961	−	5.88674i	0.596684	−	0.344496i
$293$	−1.03780			−0.0606290			−0.0303145	−	0.999540i	$-0.509651\pi$
$293$	−1.03780			−0.0606290			−0.0303145	+	0.999540i	$0.509651\pi$
$294$	−2.77499	−	11.8025i	−0.161841	−	0.688337i
$295$	−2.10246			−0.122410
$296$	−7.92070	+	4.57302i	−0.460381	+	0.265801i
$297$	−5.00539	+	0.0995321i	−0.290442	+	0.00577544i
$298$	5.98436	−	10.3652i	0.346665	−	0.600441i
$299$	−2.67770	−	4.63791i	−0.154855	−	0.268218i
$300$	−0.581597	+	1.63149i	−0.0335785	+	0.0941939i
$301$	1.96041	−	3.59948i	0.112996	−	0.207471i
$302$			8.99700i			0.517719i
$303$	25.8332	−	4.73184i	1.48408	−	0.271837i
$304$	4.47548	+	2.58392i	0.256687	+	0.148198i
$305$	7.76184	+	4.48130i	0.444442	+	0.256598i
$306$	−7.79434	−	1.26807i	−0.445573	−	0.0724907i
$307$		−	3.19308i		−	0.182238i	−0.995840	−	0.0911192i	$-0.970956\pi$
$307$		−	3.19308i		−	0.182238i	0.995840	−	0.0911192i	$-0.0290444\pi$
$308$	−0.0634207	−	2.54834i	−0.00361373	−	0.145205i
$309$	14.7983	+	5.27535i	0.841848	+	0.300104i
$310$	1.71076	+	2.96312i	0.0971645	+	0.168294i
$311$	15.4907	−	26.8306i	0.878395	−	1.52143i	0.0252936	−	0.999680i	$-0.491948\pi$
$311$	15.4907	−	26.8306i	0.878395	−	1.52143i	0.853102	−	0.521745i	$-0.174719\pi$
$312$	2.23055	+	2.62276i	0.126280	+	0.148485i
$313$	8.53147	−	4.92565i	0.482227	−	0.278414i	−0.239117	−	0.970991i	$-0.576858\pi$
$313$	8.53147	−	4.92565i	0.482227	−	0.278414i	0.721344	+	0.692577i	$0.243525\pi$
$314$	−6.58680			−0.371715
$315$	1.07926	−	7.86354i	0.0608092	−	0.443060i
$316$	0.408348			0.0229714
$317$	−16.1373	+	9.31686i	−0.906360	+	0.523287i	−0.879258	−	0.476345i	$-0.841961\pi$
$317$	−16.1373	+	9.31686i	−0.906360	+	0.523287i	−0.0271018	+	0.999633i	$0.508628\pi$
$318$	14.7829	+	17.3823i	0.828982	+	0.974749i
$319$	4.77162	−	8.26468i	0.267159	−	0.462733i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−22.6107	−	8.06034i	−1.26201	−	0.449884i
$322$	3.71645	+	6.08241i	0.207110	+	0.338959i
$323$		−	13.6032i		−	0.756901i
$324$	−6.73863	+	5.96580i	−0.374369	+	0.331434i
$325$	−1.72150	−	0.993908i	−0.0954916	−	0.0551321i
$326$	−2.29539	−	1.32525i	−0.127130	−	0.0733986i
$327$	28.5088	−	5.22192i	1.57654	−	0.288773i
$328$		−	1.12202i		−	0.0619533i
$329$	27.4776	−	0.683838i	1.51489	−	0.0377012i
$330$	0.560356	−	1.57190i	0.0308466	−	0.0865303i
$331$	17.3391	+	30.0322i	0.953044	+	1.65072i	0.738782	+	0.673945i	$0.235401\pi$
$331$	17.3391	+	30.0322i	0.953044	+	1.65072i	0.214262	+	0.976776i	$0.431265\pi$
$332$	2.26546	−	3.92389i	0.124333	−	0.215352i
$333$	25.6567	−	9.72530i	1.40598	−	0.532943i
$334$	−6.65927	+	3.84473i	−0.364379	+	0.210374i
$335$	−1.79547			−0.0980968
$336$	−3.05475	−	3.41591i	−0.166651	−	0.186353i
$337$	15.1938			0.827657			0.413828	−	0.910355i	$-0.364191\pi$
$337$	15.1938			0.827657			0.413828	+	0.910355i	$0.364191\pi$
$338$	7.83631	−	4.52429i	0.426239	−	0.246089i
$339$	18.3868	−	15.6372i	0.998635	−	0.849296i
$340$	1.31614	−	2.27961i	0.0713775	−	0.123629i
$341$	−1.64828	−	2.85490i	−0.0892593	−	0.154602i
$342$	−12.0074	−	9.80719i	−0.649288	−	0.530312i
$343$	−18.4687	+	1.38118i	−0.997215	+	0.0745767i
$344$		−	1.54917i		−	0.0835257i
$345$	0.840740	+	4.58998i	0.0452639	+	0.247116i
$346$	−18.4384	−	10.6454i	−0.991253	−	0.572300i
$347$	−13.4180	−	7.74691i	−0.720318	−	0.415876i	0.0945516	−	0.995520i	$-0.469858\pi$
$347$	−13.4180	−	7.74691i	−0.720318	−	0.415876i	−0.814870	+	0.579644i	$0.803192\pi$
$348$	−3.09100	−	16.8752i	−0.165695	−	0.904604i
$349$			1.85927i			0.0995246i	0.998761	+	0.0497623i	$0.0158464\pi$
$349$			1.85927i			0.0995246i	−0.998761	+	0.0497623i	$0.984154\pi$
$350$	2.32349	+	1.26546i	0.124196	+	0.0676417i
$351$	−5.34132	−	8.84073i	−0.285098	−	0.471883i
$352$	−0.481739	−	0.834397i	−0.0256768	−	0.0444735i
$353$	−17.4553	+	30.2334i	−0.929050	+	1.60916i	−0.144134	+	0.989558i	$0.546040\pi$
$353$	−17.4553	+	30.2334i	−0.929050	+	1.60916i	−0.784916	+	0.619603i	$0.787294\pi$
$354$	2.77403	−	2.35919i	0.147438	−	0.125390i
$355$	9.65630	−	5.57507i	0.512503	−	0.295894i
$356$	−11.5214			−0.610633
$357$	−3.76650	+	11.4595i	−0.199344	+	0.606500i
$358$	1.32636			0.0701005
$359$	7.11602	−	4.10844i	0.375569	−	0.216835i	−0.300319	−	0.953839i	$-0.597093\pi$
$359$	7.11602	−	4.10844i	0.375569	−	0.216835i	0.675889	+	0.737004i	$0.263760\pi$
$360$	−1.06334	−	2.80523i	−0.0560427	−	0.147849i
$361$	3.85330	−	6.67411i	0.202805	−	0.351269i
$362$	1.08720	+	1.88308i	0.0571418	+	0.0989725i
$363$	5.85767	−	16.4318i	0.307448	−	0.862448i
$364$	4.48783	−	2.74214i	0.235226	−	0.143727i
$365$		−	11.7735i		−	0.616252i
$366$	−15.2696	+	2.79692i	−0.798157	+	0.146197i
$367$	−11.5792	−	6.68525i	−0.604429	−	0.348967i	0.166353	−	0.986066i	$-0.446801\pi$
$367$	−11.5792	−	6.68525i	−0.604429	−	0.348967i	−0.770782	+	0.637099i	$0.780134\pi$
$368$	2.33317	+	1.34706i	0.121625	+	0.0702202i
$369$	−0.540522	+	3.32238i	−0.0281384	+	0.172956i
$370$			9.14603i			0.475480i
$371$	29.7429	−	18.1734i	1.54417	−	0.943516i
$372$	−5.58215	−	1.98994i	−0.289421	−	0.103174i
$373$	−5.04285	−	8.73447i	−0.261109	−	0.452254i	0.705428	−	0.708782i	$-0.250755\pi$
$373$	−5.04285	−	8.73447i	−0.261109	−	0.452254i	−0.966537	+	0.256528i	$0.917421\pi$
$374$	−1.26807	+	2.19636i	−0.0655703	+	0.113571i
$375$	1.12211	+	1.31942i	0.0579455	+	0.0681346i
$376$	8.99693	−	5.19438i	0.463981	−	0.267880i
$377$	19.6893			1.01405
$378$	7.39976	+	11.5864i	0.380603	+	0.595938i
$379$	−22.9625			−1.17951			−0.589753	−	0.807583i	$-0.700775\pi$
$379$	−22.9625			−1.17951			−0.589753	+	0.807583i	$0.700775\pi$
$380$	4.47548	−	2.58392i	0.229587	−	0.132552i
$381$	18.1711	+	21.3663i	0.930934	+	1.09463i
$382$	−8.52848	+	14.7718i	−0.436355	+	0.755789i
$383$	8.44382	+	14.6251i	0.431459	+	0.747309i	0.996999	−	0.0774116i	$-0.0246656\pi$
$383$	8.44382	+	14.6251i	0.431459	+	0.747309i	−0.565540	+	0.824721i	$0.691332\pi$
$384$	−1.63149	−	0.581597i	−0.0832564	−	0.0296795i
$385$	−2.23863	−	1.21924i	−0.114091	−	0.0621384i
$386$			2.05067i			0.104376i
$387$	−0.746296	+	4.58720i	−0.0379364	+	0.233180i
$388$	12.7299	+	7.34960i	0.646262	+	0.373119i
$389$	−17.4724	−	10.0877i	−0.885888	−	0.511467i	−0.0132924	−	0.999912i	$-0.504231\pi$
$389$	−17.4724	−	10.0877i	−0.885888	−	0.511467i	−0.872595	+	0.488444i	$0.837565\pi$
$390$	3.38665	−	0.620329i	0.171490	−	0.0314116i
$391$		−	7.09164i		−	0.358640i
$392$	−5.88057	+	3.79722i	−0.297014	+	0.191789i
$393$	3.44429	−	9.66188i	0.173742	−	0.487377i
$394$	6.47102	+	11.2081i	0.326005	+	0.564658i
$395$	0.204174	−	0.353640i	0.0102731	−	0.0177936i
$396$	1.02450	+	2.70278i	0.0514831	+	0.135820i
$397$	−16.4730	+	9.51068i	−0.826755	+	0.477327i	−0.852740	−	0.522335i	$-0.825061\pi$
$397$	−16.4730	+	9.51068i	−0.826755	+	0.477327i	0.0259850	+	0.999662i	$0.491728\pi$
$398$	−17.1869			−0.861502
$399$	−17.6529	+	15.7865i	−0.883751	+	0.790313i
$400$	1.00000			0.0500000
$401$	−4.14687	+	2.39420i	−0.207085	+	0.119561i	−0.599956	−	0.800033i	$-0.704815\pi$
$401$	−4.14687	+	2.39420i	−0.207085	+	0.119561i	0.392871	+	0.919594i	$0.371482\pi$
$402$	2.36897	−	2.01471i	0.118154	−	0.100485i
$403$	3.40067	−	5.89013i	0.169399	−	0.293408i
$404$	−7.58148	−	13.1315i	−0.377193	−	0.653317i
$405$	1.79722	+	8.81873i	0.0893046	+	0.438206i
$406$	−26.1980	+	0.651993i	−1.30018	+	0.0323578i
$407$		−	8.81201i		−	0.436795i
$408$	0.821441	+	4.48462i	0.0406674	+	0.222022i
$409$	0.294070	+	0.169781i	0.0145408	+	0.00839514i	0.507253	−	0.861797i	$-0.330661\pi$
$409$	0.294070	+	0.169781i	0.0145408	+	0.00839514i	−0.492712	+	0.870192i	$0.663994\pi$
$410$	−0.971699	−	0.561011i	−0.0479888	−	0.0277063i
$411$	2.37827	+	12.9841i	0.117312	+	0.640457i
$412$		−	9.07046i		−	0.446870i
$413$	−2.90029	−	4.74666i	−0.142714	−	0.233568i
$414$	−6.25975	−	5.11271i	−0.307650	−	0.251276i
$415$	−2.26546	−	3.92389i	−0.111207	−	0.192616i
$416$	0.993908	−	1.72150i	0.0487304	−	0.0844034i
$417$	−9.41765	+	8.00930i	−0.461184	+	0.392217i
$418$	−4.31203	+	2.48955i	−0.210908	+	0.121768i
$419$	−15.1963			−0.742389			−0.371194	−	0.928555i	$-0.621052\pi$
$419$	−15.1963			−0.742389			−0.371194	+	0.928555i	$0.621052\pi$
$420$	−4.48565	+	0.937538i	−0.218877	+	0.0457472i
$421$	−19.5755			−0.954052			−0.477026	−	0.878889i	$-0.658285\pi$
$421$	−19.5755			−0.954052			−0.477026	+	0.878889i	$0.658285\pi$
$422$	1.90258	−	1.09846i	0.0926162	−	0.0534720i
$423$	−29.1429	+	11.0467i	−1.41698	+	0.537111i
$424$	6.58709	−	11.4092i	0.319897	−	0.554078i
$425$	−1.31614	−	2.27961i	−0.0638420	−	0.110578i
$426$	−6.48488	+	18.1913i	−0.314193	+	0.881370i
$427$	0.589961	+	23.7055i	0.0285502	+	1.14719i
$428$			13.8590i			0.669899i
$429$	−3.26297	+	0.597674i	−0.157538	+	0.0288559i
$430$	−1.34162	−	0.774585i	−0.0646987	−	0.0373538i
$431$	−1.03187	−	0.595751i	−0.0497035	−	0.0286963i	0.474942	−	0.880017i	$-0.342469\pi$
$431$	−1.03187	−	0.595751i	−0.0497035	−	0.0286963i	−0.524646	+	0.851321i	$0.675802\pi$
$432$	4.55076	+	2.50810i	0.218949	+	0.120671i
$433$		−	18.9398i		−	0.910188i	−0.890443	−	0.455094i	$-0.849606\pi$
$433$		−	18.9398i		−	0.910188i	0.890443	−	0.455094i	$-0.150394\pi$
$434$	−4.32979	+	7.94986i	−0.207837	+	0.381605i
$435$	−16.1598	−	5.76070i	−0.774804	−	0.276204i
$436$	−8.36670	−	14.4915i	−0.400692	−	0.694019i
$437$	6.96138	−	12.0575i	0.333008	−	0.576787i
$438$	13.2111	+	15.5342i	0.631253	+	0.742251i
$439$	−2.47354	+	1.42810i	−0.118056	+	0.0681594i	−0.557865	−	0.829932i	$-0.688379\pi$
$439$	−2.47354	+	1.42810i	−0.118056	+	0.0681594i	0.439809	+	0.898091i	$0.355046\pi$
$440$	−0.963479			−0.0459320
$441$	19.2420	−	8.41093i	0.916288	−	0.400520i
$442$	−5.23247			−0.248883
$443$	−30.2368	+	17.4572i	−1.43659	+	0.829417i	−0.997611	−	0.0690790i	$-0.977994\pi$
$443$	−30.2368	+	17.4572i	−1.43659	+	0.829417i	−0.438981	+	0.898496i	$0.644661\pi$
$444$	−10.2629	−	12.0675i	−0.487053	−	0.572696i
$445$	−5.76070	+	9.97782i	−0.273083	+	0.472994i
$446$	11.9221	+	20.6497i	0.564530	+	0.977794i
$447$	19.5268	+	6.96096i	0.923586	+	0.329242i
$448$	−1.26546	+	2.32349i	−0.0597874	+	0.109775i
$449$			20.6789i			0.975895i	0.872873	+	0.487948i	$0.162254\pi$
$449$			20.6789i			0.975895i	−0.872873	+	0.487948i	$0.837746\pi$
$450$	−2.96107	−	0.481739i	−0.139586	−	0.0227094i
$451$	0.936211	+	0.540522i	0.0440845	+	0.0254522i
$452$	−12.0685	−	6.96777i	−0.567656	−	0.327736i
$453$	−15.3282	+	2.80765i	−0.720184	+	0.131915i
$454$		−	4.67171i		−	0.219254i
$455$	−0.130847	−	5.25764i	−0.00613423	−	0.246482i
$456$	−3.00560	+	8.43126i	−0.140750	+	0.394830i
$457$	−2.17141	−	3.76098i	−0.101574	−	0.175931i	0.810759	−	0.585380i	$-0.199055\pi$
$457$	−2.17141	−	3.76098i	−0.101574	−	0.175931i	−0.912333	+	0.409448i	$0.865721\pi$
$458$	11.5757	−	20.0497i	0.540897	−	0.936861i
$459$	−0.271927	−	13.6750i	−0.0126925	−	0.638294i
$460$	2.33317	−	1.34706i	0.108785	−	0.0628068i
$461$	10.7827			0.502203			0.251101	−	0.967961i	$-0.419207\pi$
$461$	10.7827			0.502203			0.251101	+	0.967961i	$0.419207\pi$
$462$	4.32182	−	0.903298i	0.201069	−	0.0420252i
$463$	−18.5503			−0.862105			−0.431053	−	0.902327i	$-0.641858\pi$
$463$	−18.5503			−0.862105			−0.431053	+	0.902327i	$0.641858\pi$
$464$	−8.57796	+	4.95249i	−0.398222	+	0.229913i
$465$	−4.51441	+	3.83931i	−0.209351	+	0.178044i
$466$	6.62090	−	11.4677i	0.306707	−	0.531233i
$467$	−2.77666	−	4.80932i	−0.128489	−	0.222549i	0.794603	−	0.607130i	$-0.207679\pi$
$467$	−2.77666	−	4.80932i	−0.128489	−	0.222549i	−0.923091	+	0.384581i	$0.874346\pi$
$468$	−3.77234	+	4.61867i	−0.174377	+	0.213498i
$469$	−2.47679	−	4.05356i	−0.114368	−	0.187176i
$470$		−	10.3888i		−	0.479198i
$471$	−2.05551	−	11.2220i	−0.0947131	−	0.517081i
$472$	−1.82079	−	1.05123i	−0.0838084	−	0.0483868i
$473$	1.29262	+	0.746296i	0.0594349	+	0.0343147i
$474$	0.127431	+	0.695705i	0.00585312	+	0.0319548i
$475$		−	5.16784i		−	0.237117i
$476$	6.96218	−	0.173269i	0.319111	−	0.00794176i
$477$	−25.0011	+	30.6101i	−1.14472	+	1.40154i
$478$	7.36400	+	12.7548i	0.336821	+	0.583392i
$479$	−0.756678	+	1.31060i	−0.0345735	+	0.0598831i	−0.882794	−	0.469760i	$-0.844341\pi$
$479$	−0.756678	+	1.31060i	−0.0345735	+	0.0598831i	0.848221	+	0.529643i	$0.177674\pi$
$480$	−1.31942	+	1.12211i	−0.0602230	+	0.0512171i
$481$	15.7449	−	9.09031i	0.717905	−	0.414483i
$482$	−5.92695			−0.269965
$483$	−9.20286	+	8.22986i	−0.418745	+	0.374471i
$484$	−10.0717			−0.457805
$485$	12.7299	−	7.34960i	0.578034	−	0.333728i
$486$	−12.2669	−	9.61893i	−0.556437	−	0.436324i
$487$	5.30215	−	9.18360i	0.240264	−	0.416149i	−0.720526	−	0.693428i	$-0.756099\pi$
$487$	5.30215	−	9.18360i	0.240264	−	0.416149i	0.960789	+	0.277280i	$0.0894328\pi$
$488$	4.48130	+	7.76184i	0.202859	+	0.351362i
$489$	1.54152	−	4.32424i	0.0697098	−	0.195549i
$490$	0.348204	+	6.99133i	0.0157303	+	0.315836i
$491$			12.2648i			0.553504i	0.960941	+	0.276752i	$0.0892580\pi$
$491$			12.2648i			0.553504i	−0.960941	+	0.276752i	$0.910742\pi$
$492$	1.91160	−	0.350144i	0.0861814	−	0.0157857i
$493$	22.5795	+	13.0363i	1.01693	+	0.587125i
$494$	−8.89644	−	5.13636i	−0.400270	−	0.231096i
$495$	2.85293	+	0.464146i	0.128229	+	0.0208618i
$496$			3.42151i			0.153631i
$497$	25.9072	+	14.1100i	1.16210	+	0.632922i
$498$	7.39213	+	2.63517i	0.331249	+	0.118085i
$499$	−13.9143	−	24.1002i	−0.622889	−	1.07887i	−0.988945	−	0.148282i	$-0.952626\pi$
$499$	−13.9143	−	24.1002i	−0.622889	−	1.07887i	0.366057	−	0.930593i	$-0.380708\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−8.62842	−	10.1456i	−0.385489	−	0.453273i
$502$	−16.8610	+	9.73472i	−0.752545	+	0.434482i
$503$	31.7645			1.41631			0.708154	−	0.706058i	$-0.249528\pi$
$503$	31.7645			1.41631			0.708154	+	0.706058i	$0.249528\pi$
$504$	4.86643	−	6.27039i	0.216768	−	0.279306i
$505$	−15.1630			−0.674743
$506$	−2.24796	+	1.29786i	−0.0999340	+	0.0576969i
$507$	10.1535	+	11.9389i	0.450933	+	0.530225i
$508$	8.09685	−	14.0242i	0.359240	−	0.622221i
$509$	−19.6568	−	34.0465i	−0.871270	−	1.50908i	−0.860683	−	0.509141i	$-0.829963\pi$
$509$	−19.6568	−	34.0465i	−0.871270	−	1.50908i	−0.0105870	−	0.999944i	$-0.503370\pi$
$510$	4.29451	+	1.53092i	0.190164	+	0.0677903i
$511$	26.5806	−	16.2412i	1.17586	−	0.718468i
$512$			1.00000i			0.0441942i
$513$	12.9615	−	23.5176i	0.572262	−	1.03833i
$514$	−2.45771	−	1.41896i	−0.108405	−	0.0625876i
$515$	−7.85525	−	4.53523i	−0.346144	−	0.199846i
$516$	2.63933	−	0.483443i	0.116190	−	0.0212824i
$517$			10.0094i			0.440211i
$518$	−20.6487	+	12.6167i	−0.907251	+	0.554346i
$519$	12.3827	−	34.7356i	0.543538	−	1.52473i
$520$	−0.993908	−	1.72150i	−0.0435858	−	0.0754927i
$521$	−4.39885	+	7.61904i	−0.192717	+	0.333796i	−0.946150	−	0.323729i	$-0.895063\pi$
$521$	−4.39885	+	7.61904i	−0.192717	+	0.333796i	0.753433	+	0.657525i	$0.228397\pi$
$522$	27.7857	−	10.5323i	1.21615	−	0.460987i
$523$	−6.72353	+	3.88183i	−0.293999	+	0.169741i	−0.639744	−	0.768588i	$-0.720960\pi$
$523$	−6.72353	+	3.88183i	−0.293999	+	0.169741i	0.345745	+	0.938329i	$0.387626\pi$
$524$	−5.92214			−0.258710
$525$	−1.43089	+	4.35345i	−0.0624492	+	0.190000i
$526$	18.0716			0.787961
$527$	7.79973	−	4.50318i	0.339762	−	0.196162i
$528$	1.27123	−	1.08113i	0.0553233	−	0.0470501i
$529$	−7.87088	+	13.6328i	−0.342212	+	0.592729i
$530$	−6.58709	−	11.4092i	−0.286125	−	0.495583i
$531$	4.88505	+	3.98991i	0.211993	+	0.173147i
$532$	12.0074	+	6.53970i	0.520588	+	0.283532i
$533$			2.23037i			0.0966081i
$534$	−3.59543	−	19.6291i	−0.155590	−	0.849433i
$535$	12.0022	+	6.92949i	0.518902	+	0.299588i
$536$	−1.55492	−	0.897733i	−0.0671623	−	0.0387761i
$537$	0.413913	+	2.25974i	0.0178616	+	0.0975148i
$538$			17.1417i			0.739033i
$539$	−0.335487	−	6.73600i	−0.0144505	−	0.290140i
$540$	4.44746	−	2.68703i	0.191388	−	0.115631i
$541$	18.5800	+	32.1815i	0.798816	+	1.38359i	0.920388	+	0.391007i	$0.127873\pi$
$541$	18.5800	+	32.1815i	0.798816	+	1.38359i	−0.121572	+	0.992583i	$0.538793\pi$
$542$	10.1939	−	17.6563i	0.437864	−	0.758402i
$543$	−2.86894	+	2.43991i	−0.123118	+	0.104707i
$544$	2.27961	−	1.31614i	0.0977377	−	0.0564289i
$545$	−16.7334			−0.716780
$546$	6.07229	+	6.79021i	0.259870	+	0.290594i
$547$	35.9929			1.53895			0.769473	−	0.638679i	$-0.220519\pi$
$547$	35.9929			1.53895			0.769473	+	0.638679i	$0.220519\pi$
$548$	6.60004	−	3.81054i	0.281940	−	0.162778i
$549$	−9.53025	−	25.1422i	−0.406741	−	1.07304i
$550$	−0.481739	+	0.834397i	−0.0205414	+	0.0355788i
$551$	25.5937	+	44.3296i	1.09033	+	1.88850i
$552$	−1.56689	+	4.39541i	−0.0666911	+	0.187081i
$553$	1.08005	−	0.0268794i	0.0459285	−	0.00114303i
$554$			7.62035i			0.323758i
$555$	−15.5822	+	2.85416i	−0.661425	+	0.121152i
$556$	6.18144	+	3.56886i	0.262152	+	0.151353i
$557$	−27.9527	−	16.1385i	−1.18439	−	0.683810i	−0.227367	−	0.973809i	$-0.573012\pi$
$557$	−27.9527	−	16.1385i	−1.18439	−	0.683810i	−0.957027	+	0.289999i	$0.906345\pi$
$558$	1.64828	−	10.1313i	0.0697772	−	0.428894i
$559$			3.07947i			0.130248i
$560$	1.37947	+	2.25767i	0.0582933	+	0.0954038i
$561$	−4.13767	−	1.47501i	−0.174693	−	0.0622749i
$562$	2.29304	+	3.97166i	0.0967261	+	0.167534i
$563$	−0.232331	+	0.402409i	−0.00979159	+	0.0169595i	−0.870880	−	0.491496i	$-0.836450\pi$
$563$	−0.232331	+	0.402409i	−0.00979159	+	0.0169595i	0.861088	+	0.508456i	$0.169783\pi$
$564$	11.6573	+	13.7071i	0.490862	+	0.577175i
$565$	−12.0685	+	6.96777i	−0.507727	+	0.293136i
$566$	−15.9756			−0.671506
$567$	−17.4305	+	16.2227i	−0.732014	+	0.681290i
$568$	11.1501			0.467849
$569$	9.53755	−	5.50651i	0.399835	−	0.230845i	−0.286578	−	0.958057i	$-0.592518\pi$
$569$	9.53755	−	5.50651i	0.399835	−	0.230845i	0.686413	+	0.727212i	$0.259184\pi$
$570$	5.79889	+	6.81856i	0.242889	+	0.285598i
$571$	−5.54190	+	9.59885i	−0.231921	+	0.401699i	−0.958373	−	0.285518i	$-0.907834\pi$
$571$	−5.54190	+	9.59885i	−0.231921	+	0.401699i	0.726452	+	0.687217i	$0.241168\pi$
$572$	0.957609	+	1.65863i	0.0400396	+	0.0693507i
$573$	−27.8282	−	9.92027i	−1.16254	−	0.414425i
$574$	−0.0738568	−	2.96767i	−0.00308272	−	0.123868i
$575$		−	2.69411i		−	0.112352i
$576$	0.481739	−	2.96107i	0.0200725	−	0.123378i
$577$	8.76809	+	5.06226i	0.365020	+	0.210745i	0.671281	−	0.741203i	$-0.265745\pi$
$577$	8.76809	+	5.06226i	0.365020	+	0.210745i	−0.306260	+	0.951948i	$0.599078\pi$
$578$	8.72186	+	5.03557i	0.362782	+	0.209452i
$579$	−3.49374	+	0.639944i	−0.145195	+	0.0265952i
$580$			9.90498i			0.411282i
$581$	5.73370	−	10.5276i	0.237874	−	0.436756i
$582$	−8.54900	+	23.9815i	−0.354367	+	0.994066i
$583$	6.34652	+	10.9925i	0.262846	+	0.455262i
$584$	5.88674	−	10.1961i	0.243595	−	0.421919i
$585$	2.11372	+	5.57628i	0.0873914	+	0.230551i
$586$	−0.898762	+	0.518900i	−0.0371275	+	0.0214356i
$587$	36.0697			1.48876			0.744378	−	0.667759i	$-0.232746\pi$
$587$	36.0697			1.48876			0.744378	+	0.667759i	$0.232746\pi$
$588$	−8.30447	−	8.83378i	−0.342471	−	0.364299i
$589$	17.6818			0.728568
$590$	−1.82079	+	1.05123i	−0.0749605	+	0.0432785i
$591$	−17.0760	+	14.5224i	−0.702413	+	0.597372i
$592$	−4.57302	+	7.92070i	−0.187950	+	0.325539i
$593$	15.9238	+	27.5809i	0.653913	+	1.13261i	0.982165	+	0.188020i	$0.0602070\pi$
$593$	15.9238	+	27.5809i	0.653913	+	1.13261i	−0.328253	+	0.944590i	$0.606460\pi$
$594$	−4.28503	+	2.58889i	−0.175817	+	0.106224i
$595$	3.33104	−	6.11606i	0.136559	−	0.250734i
$596$		−	11.9687i		−	0.490258i
$597$	−5.36344	−	29.2815i	−0.219511	−	1.19841i
$598$	−4.63791	−	2.67770i	−0.189658	−	0.109499i
$599$	−11.7065	−	6.75877i	−0.478316	−	0.276156i	0.241398	−	0.970426i	$-0.422394\pi$
$599$	−11.7065	−	6.75877i	−0.478316	−	0.276156i	−0.719715	+	0.694270i	$0.755727\pi$
$600$	0.312065	+	1.70371i	0.0127400	+	0.0695535i
$601$			15.7057i			0.640650i	0.947308	+	0.320325i	$0.103792\pi$
$601$			15.7057i			0.640650i	−0.947308	+	0.320325i	$0.896208\pi$
$602$	−0.101974	−	4.09745i	−0.00415614	−	0.167000i
$603$	4.17175	+	3.40731i	0.169887	+	0.138757i
$604$	4.49850	+	7.79163i	0.183041	+	0.317037i
$605$	−5.03585	+	8.72236i	−0.204737	+	0.354614i
$606$	20.0063	−	17.0145i	0.812701	−	0.691167i
$607$	−0.912277	+	0.526704i	−0.0370282	+	0.0213782i	−0.518400	−	0.855138i	$-0.673472\pi$
$607$	−0.912277	+	0.526704i	−0.0370282	+	0.0213782i	0.481372	+	0.876517i	$0.340139\pi$
$608$	5.16784			0.209584
$609$	−9.28629	−	44.4302i	−0.376300	−	1.80040i
$610$	8.96260			0.362885
$611$	−17.8842	+	10.3255i	−0.723519	+	0.417724i
$612$	−7.38413	+	2.79899i	−0.298486	+	0.113142i
$613$	2.70320	−	4.68208i	0.109181	−	0.189107i	−0.806258	−	0.591565i	$-0.798510\pi$
$613$	2.70320	−	4.68208i	0.109181	−	0.189107i	0.915439	+	0.402457i	$0.131844\pi$
$614$	−1.59654	−	2.76528i	−0.0644310	−	0.111598i
$615$	0.652564	−	1.83056i	0.0263139	−	0.0738154i
$616$	−1.32909	−	2.17521i	−0.0535506	−	0.0876418i
$617$		−	3.10356i		−	0.124945i	−0.998047	−	0.0624723i	$-0.980101\pi$
$617$		−	3.10356i		−	0.124945i	0.998047	−	0.0624723i	$-0.0198985\pi$
$618$	15.4534	−	2.83058i	0.621627	−	0.113863i
$619$	15.9121	+	9.18688i	0.639563	+	0.369252i	0.784446	−	0.620197i	$-0.212947\pi$
$619$	15.9121	+	9.18688i	0.639563	+	0.369252i	−0.144883	+	0.989449i	$0.546281\pi$
$620$	2.96312	+	1.71076i	0.119002	+	0.0687057i
$621$	6.75710	−	12.2603i	0.271153	−	0.491988i
$622$		−	30.9813i		−	1.24224i
$623$	−30.4733	+	0.758393i	−1.22089	+	0.0303844i
$624$	3.24309	+	1.15611i	0.129828	+	0.0462813i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.92565	−	8.53147i	0.196868	−	0.340986i
$627$	−5.58710	−	6.56953i	−0.223127	−	0.262362i
$628$	−5.70434	+	3.29340i	−0.227628	+	0.131421i
$629$	24.0748			0.959927
$630$	−2.99710	−	7.34965i	−0.119408	−	0.292817i
$631$	3.40873			0.135699			0.0678496	−	0.997696i	$-0.478386\pi$
$631$	3.40873			0.135699			0.0678496	+	0.997696i	$0.478386\pi$
$632$	0.353640	−	0.204174i	0.0140670	−	0.00812161i
$633$	2.46518	+	2.89865i	0.0979819	+	0.115211i
$634$	−9.31686	+	16.1373i	−0.370020	+	0.640893i
$635$	−8.09685	−	14.0242i	−0.321314	−	0.556532i
$636$	21.4935	+	7.66205i	0.852272	+	0.303820i
$637$	11.6895	−	7.54818i	0.463155	−	0.299070i
$638$		−	9.54323i		−	0.377820i
$639$	−33.0163	−	5.37146i	−1.30610	−	0.212492i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−15.2832	−	8.82377i	−0.603651	−	0.348518i	0.166826	−	0.985986i	$-0.446648\pi$
$641$	−15.2832	−	8.82377i	−0.603651	−	0.348518i	−0.770476	+	0.637469i	$0.779982\pi$
$642$	−23.6116	+	4.32491i	−0.931877	+	0.170691i
$643$		−	7.27025i		−	0.286711i	−0.989671	−	0.143355i	$-0.954211\pi$
$643$		−	7.27025i		−	0.286711i	0.989671	−	0.143355i	$-0.0457892\pi$
$644$	6.25975	+	3.40929i	0.246669	+	0.134345i
$645$	0.900992	−	2.52745i	0.0354765	−	0.0995182i
$646$	−6.80159	−	11.7807i	−0.267605	−	0.463505i
$647$	5.75695	−	9.97133i	0.226329	−	0.392013i	−0.730388	−	0.683032i	$-0.760661\pi$
$647$	5.75695	−	9.97133i	0.226329	−	0.392013i	0.956717	+	0.291019i	$0.0939942\pi$
$648$	−2.85293	+	8.53585i	−0.112074	+	0.335320i
$649$	1.75429	−	1.01284i	0.0688618	−	0.0397574i
$650$	−1.98782			−0.0779686
$651$	−14.8954	−	4.89581i	−0.583797	−	0.191882i
$652$	−2.65049			−0.103801
$653$	−16.4747	+	9.51167i	−0.644705	+	0.372221i	−0.786425	−	0.617686i	$-0.788070\pi$
$653$	−16.4747	+	9.51167i	−0.644705	+	0.372221i	0.141720	+	0.989907i	$0.454737\pi$
$654$	22.0784	−	18.7767i	0.863333	−	0.734228i
$655$	−2.96107	+	5.12872i	−0.115699	+	0.200396i
$656$	−0.561011	−	0.971699i	−0.0219038	−	0.0379385i
$657$	−22.3429	+	27.3556i	−0.871681	+	1.06724i
$658$	23.4544	−	14.3310i	0.914346	−	0.558681i
$659$			14.0201i			0.546146i	0.961993	+	0.273073i	$0.0880401\pi$
$659$			14.0201i			0.546146i	−0.961993	+	0.273073i	$0.911960\pi$
$660$	−0.300668	−	1.64148i	−0.0117035	−	0.0638947i
$661$	9.45461	+	5.45862i	0.367742	+	0.212316i	0.672471	−	0.740123i	$-0.265233\pi$
$661$	9.45461	+	5.45862i	0.367742	+	0.212316i	−0.304730	+	0.952439i	$0.598566\pi$
$662$	30.0322	+	17.3391i	1.16724	+	0.673904i
$663$	−1.63287	−	8.91460i	−0.0634156	−	0.346214i
$664$		−	4.53092i		−	0.175834i
$665$	11.6673	−	7.12890i	0.452437	−	0.276447i
$666$	17.3567	−	21.2507i	0.672559	−	0.823449i
$667$	13.3426	+	23.1100i	0.516626	+	0.894823i
$668$	−3.84473	+	6.65927i	−0.148757	+	0.257655i
$669$	−31.4606	+	26.7559i	−1.21634	+	1.03444i
$670$	−1.55492	+	0.897733i	−0.0600718	+	0.0346824i
$671$	−8.63527			−0.333361
$672$	−4.35345	−	1.43089i	−0.167938	−	0.0551978i
$673$	13.4579			0.518765			0.259382	−	0.965775i	$-0.416481\pi$
$673$	13.4579			0.518765			0.259382	+	0.965775i	$0.416481\pi$
$674$	13.1582	−	7.59688i	0.506834	−	0.292621i
$675$	−0.103305	−	5.19513i	−0.00397621	−	0.199960i
$676$	4.52429	−	7.83631i	0.174011	−	0.301396i
$677$	−16.1391	−	27.9537i	−0.620274	−	1.07435i	−0.989434	−	0.144981i	$-0.953688\pi$
$677$	−16.1391	−	27.9537i	−0.620274	−	1.07435i	0.369160	−	0.929366i	$-0.379645\pi$
$678$	8.10486	−	22.7356i	0.311265	−	0.873157i
$679$	34.1534	+	18.6012i	1.31069	+	0.713850i
$680$		−	2.63227i		−	0.100943i
$681$	7.95923	−	1.45788i	0.304998	−	0.0558661i
$682$	−2.85490	−	1.64828i	−0.109320	−	0.0631158i
$683$	40.2694	+	23.2495i	1.54086	+	0.889619i	0.998784	+	0.0492920i	$0.0156965\pi$
$683$	40.2694	+	23.2495i	1.54086	+	0.889619i	0.542080	+	0.840327i	$0.317637\pi$
$684$	−15.3023	−	2.48955i	−0.585100	−	0.0951904i
$685$		−	7.62107i		−	0.291186i
$686$	−15.3038	+	10.4305i	−0.584300	+	0.398238i
$687$	37.7712	+	13.4648i	1.44106	+	0.513713i
$688$	−0.774585	−	1.34162i	−0.0295308	−	0.0511488i
$689$	−13.0939	+	22.6793i	−0.498838	+	0.864013i
$690$	3.02309	+	3.55467i	0.115087	+	0.135324i
$691$	−41.9807	+	24.2376i	−1.59702	+	0.922041i	−0.604965	+	0.796252i	$0.706813\pi$
$691$	−41.9807	+	24.2376i	−1.59702	+	0.922041i	−0.992057	+	0.125789i	$0.959854\pi$
$692$	−21.2908			−0.809355
$693$	2.88765	+	7.08123i	0.109693	+	0.268994i
$694$	−15.4938			−0.588137
$695$	6.18144	−	3.56886i	0.234475	−	0.135374i
$696$	−11.1145	−	13.0688i	−0.421293	−	0.495373i
$697$	−1.47673	+	2.55778i	−0.0559353	+	0.0968827i
$698$	0.929637	+	1.61018i	0.0351873	+	0.0609461i
$699$	21.6038	+	7.70139i	0.817131	+	0.291293i
$700$	2.64493	−	0.0658248i	0.0999690	−	0.00248794i
$701$			20.0722i			0.758118i	0.925372	+	0.379059i	$0.123752\pi$
$701$			20.0722i			0.758118i	−0.925372	+	0.379059i	$0.876248\pi$
$702$	−9.04608	−	4.98564i	−0.341422	−	0.188171i
$703$	40.9329	+	23.6326i	1.54381	+	0.891321i
$704$	−0.834397	−	0.481739i	−0.0314475	−	0.0181562i
$705$	17.6994	−	3.24197i	0.666598	−	0.122100i
$706$			34.9105i			1.31387i
$707$	−20.9169	−	34.2329i	−0.786661	−	1.28746i
$708$	1.22278	−	3.43014i	0.0459551	−	0.128912i
$709$	−11.3248	−	19.6151i	−0.425311	−	0.736661i	0.571138	−	0.820854i	$-0.306502\pi$
$709$	−11.3248	−	19.6151i	−0.425311	−	0.736661i	−0.996449	+	0.0841930i	$0.973169\pi$
$710$	5.57507	−	9.65630i	0.209228	−	0.362394i
$711$	−1.14551	+	0.434211i	−0.0429600	+	0.0162842i
$712$	−9.97782	+	5.76070i	−0.373935	+	0.215891i
$713$	9.21795			0.345215
$714$	2.46786	+	11.8074i	0.0923572	+	0.441882i
$715$	1.91522			0.0716251
$716$	1.14867	−	0.663182i	0.0429276	−	0.0247843i
$717$	−19.4324	+	16.5264i	−0.725717	+	0.617191i
$718$	4.10844	−	7.11602i	0.153326	−	0.265568i
$719$	0.612866	+	1.06152i	0.0228561	+	0.0395878i	0.877227	−	0.480075i	$-0.159391\pi$
$719$	0.612866	+	1.06152i	0.0228561	+	0.0395878i	−0.854371	+	0.519663i	$0.826057\pi$
$720$	−2.32349	−	1.89773i	−0.0865914	−	0.0707243i
$721$	−0.597061	−	23.9908i	−0.0222357	−	0.893463i
$722$		−	7.70660i		−	0.286810i
$723$	−1.84959	−	10.0978i	−0.0687872	−	0.375540i
$724$	1.88308	+	1.08720i	0.0699842	+	0.0404054i
$725$	8.57796	+	4.95249i	0.318577	+	0.183931i
$726$	−3.14303	−	17.1592i	−0.116649	−	0.636839i
$727$		−	33.9559i		−	1.25936i	−0.776856	−	0.629678i	$-0.783187\pi$
$727$		−	33.9559i		−	1.25936i	0.776856	−	0.629678i	$-0.216813\pi$
$728$	2.51550	−	4.61867i	0.0932307	−	0.171179i
$729$	12.5598	−	23.9009i	0.465177	−	0.885218i
$730$	−5.88674	−	10.1961i	−0.217878	−	0.377376i
$731$	−2.03892	+	3.53151i	−0.0754122	+	0.130618i
$732$	−11.8254	+	10.0570i	−0.437081	+	0.371718i
$733$	−18.0188	+	10.4032i	−0.665540	+	0.384250i	−0.794385	−	0.607415i	$-0.792207\pi$
$733$	−18.0188	+	10.4032i	−0.665540	+	0.384250i	0.128844	+	0.991665i	$0.458873\pi$
$734$	−13.3705			−0.493514
$735$	−11.8025	+	2.77499i	−0.435342	+	0.102357i
$736$	2.69411			0.0993063
$737$	1.49813	−	0.864946i	0.0551844	−	0.0318607i
$738$	1.19309	+	3.14753i	0.0439181	+	0.115862i
$739$	−4.93210	+	8.54265i	−0.181430	+	0.314247i	−0.942368	−	0.334579i	$-0.891406\pi$
$739$	−4.93210	+	8.54265i	−0.181430	+	0.314247i	0.760937	+	0.648825i	$0.224739\pi$
$740$	4.57302	+	7.92070i	0.168107	+	0.291171i
$741$	5.97458	−	16.7598i	0.219482	−	0.615687i
$742$	16.6714	−	30.6101i	0.612026	−	1.12373i
$743$			18.9248i			0.694283i	0.937813	+	0.347141i	$0.112848\pi$
$743$			18.9248i			0.694283i	−0.937813	+	0.347141i	$0.887152\pi$
$744$	−5.82926	+	1.06774i	−0.213711	+	0.0391451i
$745$	−10.3652	−	5.98436i	−0.379752	−	0.219250i
$746$	−8.73447	−	5.04285i	−0.319792	−	0.184632i
$747$	−2.18272	+	13.4164i	−0.0798616	+	0.490879i
$748$			2.53614i			0.0927304i
$749$	0.912264	+	36.6561i	0.0333334	+	1.33938i
$750$	1.63149	+	0.581597i	0.0595734	+	0.0212369i
$751$	−4.89044	−	8.47048i	−0.178455	−	0.309092i	0.762897	−	0.646520i	$-0.223776\pi$
$751$	−4.89044	−	8.47048i	−0.178455	−	0.309092i	−0.941351	+	0.337428i	$0.890443\pi$
$752$	5.19438	−	8.99693i	0.189420	−	0.328084i
$753$	−21.8469	−	25.6884i	−0.796144	−	0.936137i
$754$	17.0514	−	9.84463i	0.620976	−	0.358520i
$755$	8.99700			0.327434
$756$	12.2016	+	6.33420i	0.443766	+	0.230373i
$757$	25.5979			0.930373			0.465187	−	0.885213i	$-0.345987\pi$
$757$	25.5979			0.930373			0.465187	+	0.885213i	$0.345987\pi$
$758$	−19.8861	+	11.4813i	−0.722297	+	0.417019i
$759$	−2.91268	−	3.42485i	−0.105724	−	0.124314i
$760$	2.58392	−	4.47548i	0.0937287	−	0.162343i
$761$	0.751279	+	1.30125i	0.0272338	+	0.0471704i	0.879321	−	0.476229i	$-0.157997\pi$
$761$	0.751279	+	1.30125i	0.0272338	+	0.0471704i	−0.852087	+	0.523400i	$0.824663\pi$
$762$	26.4198	+	9.41820i	0.957088	+	0.341185i
$763$	−23.0833	−	37.7784i	−0.835670	−	1.36767i
$764$			17.0570i			0.617099i
$765$	−1.26807	+	7.79434i	−0.0458471	+	0.281805i
$766$	14.6251	+	8.44382i	0.528427	+	0.305088i
$767$	3.61939	+	2.08965i	0.130688	+	0.0754530i
$768$	−1.70371	+	0.312065i	−0.0614772	+	0.0112607i
$769$			34.5776i			1.24690i	0.781863	+	0.623451i	$0.214270\pi$
$769$			34.5776i			1.24690i	−0.781863	+	0.623451i	$0.785730\pi$
$770$	−2.54834	+	0.0634207i	−0.0918356	+	0.00228552i
$771$	1.65052	−	4.63002i	0.0594421	−	0.166746i
$772$	1.02534	+	1.77593i	0.0369027	+	0.0639173i
$773$	15.9427	−	27.6135i	0.573418	−	0.993190i	−0.422793	−	0.906226i	$-0.638950\pi$
$773$	15.9427	−	27.6135i	0.573418	−	0.993190i	0.996211	−	0.0869636i	$-0.0277164\pi$
$774$	1.64729	+	4.34578i	0.0592106	+	0.156206i
$775$	2.96312	−	1.71076i	0.106438	−	0.0614522i
$776$	14.6992			0.527670
$777$	−27.9389	−	31.2421i	−1.00230	−	1.12080i
$778$	−20.1754			−0.723324
$779$	−5.02159	+	2.89922i	−0.179917	+	0.103875i
$780$	2.62276	−	2.23055i	0.0939100	−	0.0798664i
$781$	−5.37146	+	9.30363i	−0.192206	+	0.332910i
$782$	−3.54582	−	6.14154i	−0.126798	−	0.219621i
$783$	26.6149	+	44.0520i	0.951140	+	1.57429i
$784$	−3.19411	+	6.22878i	−0.114075	+	0.222456i
$785$			6.58680i			0.235093i
$786$	−1.84809	−	10.0896i	−0.0659193	−	0.359883i
$787$	−31.9087	−	18.4225i	−1.13742	−	0.656692i	−0.191633	−	0.981467i	$-0.561378\pi$
$787$	−31.9087	−	18.4225i	−1.13742	−	0.656692i	−0.945791	+	0.324775i	$0.894712\pi$
$788$	11.2081	+	6.47102i	0.399274	+	0.230521i
$789$	5.63954	+	30.7888i	0.200773	+	1.09611i
$790$		−	0.408348i		−	0.0145284i
$791$	−32.3791	−	17.6349i	−1.15127	−	0.627024i
$792$	2.23863	+	1.82842i	0.0795464	+	0.0649703i
$793$	−8.90800	−	15.4291i	−0.316332	−	0.547904i
$794$	−9.51068	+	16.4730i	−0.337521	+	0.584604i
$795$	17.3823	−	14.7829i	0.616485	−	0.524294i
$796$	−14.8843	+	8.59346i	−0.527560	+	0.304587i
$797$	23.2407			0.823228			0.411614	−	0.911358i	$-0.364965\pi$
$797$	23.2407			0.823228			0.411614	+	0.911358i	$0.364965\pi$
$798$	−7.39462	+	22.4980i	−0.261767	+	0.796419i
$799$	−27.3461			−0.967434
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	32.3202	−	12.2511i	1.14198	−	0.432872i
$802$	−2.39420	+	4.14687i	−0.0845421	+	0.146431i
$803$	5.67175	+	9.82376i	0.200152	+	0.346673i
$804$	1.04424	−	2.92928i	0.0368274	−	0.103308i
$805$	6.08241	−	3.71645i	0.214377	−	0.130988i
$806$		−	6.80134i		−	0.239567i
$807$	−29.2045	+	5.34935i	−1.02805	+	0.188306i
$808$	−13.1315	−	7.58148i	−0.461965	−	0.266716i
$809$	25.6148	+	14.7887i	0.900569	+	0.519944i	0.877385	−	0.479787i	$-0.159286\pi$
$809$	25.6148	+	14.7887i	0.900569	+	0.519944i	0.0231843	+	0.999731i	$0.492620\pi$
$810$	5.96580	+	6.73863i	0.209617	+	0.236771i
$811$		−	23.3350i		−	0.819404i	−0.912219	−	0.409702i	$-0.865633\pi$
$811$		−	23.3350i		−	0.819404i	0.912219	−	0.409702i	$-0.134367\pi$
$812$	−22.3621	+	13.6636i	−0.784757	+	0.479500i
$813$	33.2623	+	11.8574i	1.16656	+	0.415858i
$814$	−4.40600	−	7.63142i	−0.154430	−	0.267481i
$815$	−1.32525	+	2.29539i	−0.0464213	+	0.0804041i
$816$	2.95370	+	3.47307i	0.103400	+	0.121582i
$817$	−6.93329	+	4.00294i	−0.242565	+	0.140045i
$818$	0.339562			0.0118725
$819$	−9.67357	+	12.4644i	−0.338022	+	0.435541i
$820$	−1.12202			−0.0391827
$821$	12.7019	−	7.33346i	0.443300	−	0.255939i	−0.261696	−	0.965150i	$-0.584282\pi$
$821$	12.7019	−	7.33346i	0.443300	−	0.255939i	0.704996	+	0.709211i	$0.250949\pi$
$822$	8.55168	+	10.0554i	0.298274	+	0.350722i
$823$	−25.9546	+	44.9548i	−0.904722	+	1.56702i	−0.0834324	+	0.996513i	$0.526588\pi$
$823$	−25.9546	+	44.9548i	−0.904722	+	1.56702i	−0.821290	+	0.570511i	$0.806745\pi$
$824$	−4.53523	−	7.85525i	−0.157992	−	0.273651i
$825$	−1.57190	−	0.560356i	−0.0547266	−	0.0195091i
$826$	−4.88505	−	2.66058i	−0.169973	−	0.0925735i
$827$			3.36232i			0.116919i	0.998290	+	0.0584596i	$0.0186189\pi$
$827$			3.36232i			0.116919i	−0.998290	+	0.0584596i	$0.981381\pi$
$828$	−7.97746	−	1.29786i	−0.277236	−	0.0451038i
$829$	−5.94150	−	3.43033i	−0.206357	−	0.119140i	0.393260	−	0.919427i	$-0.371347\pi$
$829$	−5.94150	−	3.43033i	−0.206357	−	0.119140i	−0.599617	+	0.800287i	$0.704680\pi$
$830$	−3.92389	−	2.26546i	−0.136200	−	0.0786353i
$831$	−12.9828	+	2.37805i	−0.450370	+	0.0824936i
$832$		−	1.98782i		−	0.0689151i
$833$	18.4031	−	0.916568i	0.637630	−	0.0317572i
$834$	−4.15127	+	11.6451i	−0.143747	+	0.403236i
$835$	3.84473	+	6.65927i	0.133052	+	0.230454i
$836$	−2.48955	+	4.31203i	−0.0861030	+	0.149135i
$837$	17.7752	−	0.353459i	0.614401	−	0.0122173i
$838$	−13.1604	+	7.59816i	−0.454619	+	0.262474i
$839$	8.29693			0.286442			0.143221	−	0.989691i	$-0.454254\pi$
$839$	8.29693			0.286442			0.143221	+	0.989691i	$0.454254\pi$
$840$	−3.41591	+	3.05475i	−0.117860	+	0.105399i
$841$	−69.1085			−2.38305
$842$	−16.9529	+	9.78775i	−0.584235	+	0.337308i
$843$	−6.05097	+	5.14609i	−0.208406	+	0.177241i
$844$	1.09846	−	1.90258i	0.0378104	−	0.0654895i
$845$	−4.52429	−	7.83631i	−0.155640	−	0.269577i
$846$	−19.7151	+	24.1382i	−0.677819	+	0.829888i
$847$	−26.6390	+	0.662968i	−0.915326	+	0.0227798i
$848$		−	13.1742i		−	0.452403i
$849$	−4.98544	−	27.2178i	−0.171100	−	0.934112i
$850$	−2.27961	−	1.31614i	−0.0781901	−	0.0451431i
$851$	21.3393	+	12.3202i	0.731500	+	0.422332i
$852$	3.47957	+	18.9965i	0.119208	+	0.650811i
$853$		−	50.8963i		−	1.74266i	−0.490700	−	0.871328i	$-0.663259\pi$
$853$		−	50.8963i		−	1.74266i	0.490700	−	0.871328i	$-0.336741\pi$
$854$	12.3637	+	20.2346i	0.423076	+	0.692412i
$855$	−9.80719	+	12.0074i	−0.335399	+	0.410646i
$856$	6.92949	+	12.0022i	0.236845	+	0.410228i
$857$	1.03706	−	1.79624i	0.0354252	−	0.0613583i	−0.847769	−	0.530365i	$-0.822055\pi$
$857$	1.03706	−	1.79624i	0.0354252	−	0.0613583i	0.883194	+	0.469007i	$0.155388\pi$
$858$	−2.52698	+	2.14909i	−0.0862696	+	0.0733686i
$859$	15.8664	−	9.16048i	0.541355	−	0.312552i	−0.204273	−	0.978914i	$-0.565483\pi$
$859$	15.8664	−	9.16048i	0.541355	−	0.312552i	0.745628	+	0.666362i	$0.232150\pi$
$860$	−1.54917			−0.0528263
$861$	5.03299	−	1.05194i	0.171524	−	0.0358499i
$862$	−1.19150			−0.0405827
$863$	21.1691	−	12.2220i	0.720606	−	0.416042i	−0.0943698	−	0.995537i	$-0.530084\pi$
$863$	21.1691	−	12.2220i	0.720606	−	0.416042i	0.814976	+	0.579495i	$0.196750\pi$
$864$	5.19513	−	0.103305i	0.176742	−	0.00351451i
$865$	−10.6454	+	18.4384i	−0.361955	+	0.626924i
$866$	−9.46989	−	16.4023i	−0.321800	−	0.557374i
$867$	−5.85734	+	16.4309i	−0.198926	+	0.558023i
$868$	0.225220	+	9.04967i	0.00764448	+	0.307166i
$869$			0.393435i			0.0133464i
$870$	−16.8752	+	3.09100i	−0.572122	+	0.104795i
$871$	3.09089	+	1.78453i	0.104731	+	0.0604664i
$872$	−14.4915	−	8.36670i	−0.490746	−	0.283332i
$873$	−43.5253	−	7.08118i	−1.47311	−	0.239662i
$874$		−	13.9228i		−	0.470944i
$875$	1.26546	−	2.32349i	0.0427804	−	0.0785483i
$876$	19.2083	+	6.84742i	0.648987	+	0.231353i
$877$	−15.2682	−	26.4453i	−0.515571	−	0.892995i	−0.999837	−	0.0180742i	$-0.994246\pi$
$877$	−15.2682	−	26.4453i	−0.515571	−	0.892995i	0.484266	−	0.874921i	$-0.339087\pi$
$878$	−1.42810	+	2.47354i	−0.0481960	+	0.0834779i
$879$	−1.16453	−	1.36930i	−0.0392785	−	0.0461852i
$880$	−0.834397	+	0.481739i	−0.0281275	+	0.0162394i
$881$	−12.8329			−0.432352			−0.216176	−	0.976354i	$-0.569358\pi$
$881$	−12.8329			−0.432352			−0.216176	+	0.976354i	$0.569358\pi$
$882$	12.4586	−	16.9051i	0.419504	−	0.569224i
$883$	12.8658			0.432970			0.216485	−	0.976286i	$-0.430541\pi$
$883$	12.8658			0.432970			0.216485	+	0.976286i	$0.430541\pi$
$884$	−4.53146	+	2.61624i	−0.152409	+	0.0879936i
$885$	−2.35919	−	2.77403i	−0.0793034	−	0.0932480i
$886$	−17.4572	+	30.2368i	−0.586486	+	1.01582i
$887$	5.49109	+	9.51084i	0.184373	+	0.319343i	0.943365	−	0.331757i	$-0.107641\pi$
$887$	5.49109	+	9.51084i	0.184373	+	0.319343i	−0.758992	+	0.651100i	$0.774308\pi$
$888$	−14.9216	−	5.31930i	−0.500737	−	0.178504i
$889$	20.4925	−	37.6259i	0.687296	−	1.26193i
$890$			11.5214i			0.386198i
$891$	−5.74792	−	6.49253i	−0.192563	−	0.217508i
$892$	20.6497	+	11.9221i	0.691405	+	0.399183i
$893$	−46.4947	−	26.8438i	−1.55589	−	0.898292i
$894$	20.3912	−	3.73502i	0.681983	−	0.124918i
$895$		−	1.32636i		−	0.0443355i
$896$	0.0658248	+	2.64493i	0.00219905	+	0.0883610i
$897$	3.11468	−	8.73726i	0.103996	−	0.291729i
$898$	10.3394	+	17.9084i	0.345031	+	0.597611i
$899$	−16.9450	+	29.3496i	−0.565148	+	0.978864i
$900$	−2.80523	+	1.06334i	−0.0935077	+	0.0354445i
$901$	−30.0320	+	17.3390i	−1.00051	+	0.577646i
$902$	1.08104			0.0359948
$903$	6.94903	−	1.45241i	0.231249	−	0.0483331i
$904$	−13.9355			−0.463489
$905$	1.88308	−	1.08720i	0.0625957	−	0.0361397i
$906$	−11.8708	+	10.0956i	−0.394382	+	0.335404i
$907$	14.3608	−	24.8737i	0.476844	−	0.825918i	−0.522804	−	0.852453i	$-0.675114\pi$
$907$	14.3608	−	24.8737i	0.476844	−	0.825918i	0.999648	+	0.0265347i	$0.00844726\pi$
$908$	−2.33586	−	4.04582i	−0.0775181	−	0.134265i
$909$	35.2310	+	28.7753i	1.16854	+	0.954415i
$910$	−2.74214	−	4.48783i	−0.0909009	−	0.148770i
$911$		−	41.5041i		−	1.37509i	−0.726141	−	0.687546i	$-0.758688\pi$
$911$		−	41.5041i		−	1.37509i	0.726141	−	0.687546i	$-0.241312\pi$
$912$	1.61271	+	8.80449i	0.0534020	+	0.291546i
$913$	3.78059	+	2.18272i	0.125119	+	0.0722376i
$914$	−3.76098	−	2.17141i	−0.124402	−	0.0718237i
$915$	2.79692	+	15.2696i	0.0924633	+	0.504799i
$916$		−	23.1514i		−	0.764944i
$917$	−15.6637	+	0.389823i	−0.517259	+	0.0128731i
$918$	−7.07299	−	11.7069i	−0.233443	−	0.386386i
$919$	−10.9171	−	18.9090i	−0.360122	−	0.623749i	0.627859	−	0.778327i	$-0.283932\pi$
$919$	−10.9171	−	18.9090i	−0.360122	−	0.623749i	−0.987981	+	0.154578i	$0.950598\pi$
$920$	1.34706	−	2.33317i	0.0444111	−	0.0769224i
$921$	4.21301	−	3.58298i	0.138823	−	0.118063i
$922$	9.33813	−	5.39137i	0.307535	−	0.177555i
$923$	−22.1644			−0.729550
$924$	3.29116	−	2.94319i	0.108271	−	0.0968239i
$925$	9.14603			0.300720
$926$	−16.0650	+	9.27515i	−0.527930	+	0.304800i
$927$	9.64495	+	25.4447i	0.316782	+	0.835715i
$928$	−4.95249	+	8.57796i	−0.162573	+	0.281585i
$929$	1.70838	+	2.95899i	0.0560500	+	0.0970814i	0.892689	−	0.450673i	$-0.148816\pi$
$929$	1.70838	+	2.95899i	0.0560500	+	0.0970814i	−0.836639	+	0.547755i	$0.815483\pi$
$930$	−1.98994	+	5.58215i	−0.0652527	+	0.183046i
$931$	32.1893	+	16.5067i	1.05496	+	0.540985i
$932$		−	13.2418i		−	0.433750i
$933$	52.7831	−	9.66820i	1.72804	−	0.316523i
$934$	−4.80932	−	2.77666i	−0.157366	−	0.0908551i
$935$	2.19636	+	1.26807i	0.0718287	+	0.0414703i
$936$	−0.957609	+	5.88606i	−0.0313004	+	0.192392i
$937$			3.57133i			0.116670i	0.998297	+	0.0583351i	$0.0185792\pi$
$937$			3.57133i			0.116670i	−0.998297	+	0.0583351i	$0.981421\pi$
$938$	−4.17175	−	2.27209i	−0.136212	−	0.0741864i
$939$	16.0722	+	5.72948i	0.524498	+	0.186974i
$940$	−5.19438	−	8.99693i	−0.169422	−	0.293448i
$941$	9.20901	−	15.9505i	0.300205	−	0.519971i	−0.675977	−	0.736923i	$-0.736278\pi$
$941$	9.20901	−	15.9505i	0.300205	−	0.519971i	0.976182	+	0.216952i	$0.0696115\pi$
$942$	−7.39111	−	8.69076i	−0.240816	−	0.283160i
$943$	−2.61787	+	1.51143i	−0.0852495	+	0.0492188i
$944$	−2.10246			−0.0684293
$945$	11.5864	−	7.39976i	0.376904	−	0.240714i
$946$	1.49259			0.0485284
$947$	18.0857	−	10.4418i	0.587706	−	0.339312i	−0.176484	−	0.984304i	$-0.556472\pi$
$947$	18.0857	−	10.4418i	0.587706	−	0.339312i	0.764190	+	0.644991i	$0.223139\pi$
$948$	0.458211	+	0.538783i	0.0148820	+	0.0174988i
$949$	−11.7018	+	20.2680i	−0.379855	+	0.657929i
$950$	−2.58392	−	4.47548i	−0.0838335	−	0.145204i
$951$	−30.4007	−	10.8373i	−0.985809	−	0.351424i
$952$	5.94279	−	3.63115i	0.192607	−	0.117686i
$953$		−	52.2153i		−	1.69142i	−0.533644	−	0.845709i	$-0.679178\pi$
$953$		−	52.2153i		−	1.69142i	0.533644	−	0.845709i	$-0.320822\pi$
$954$	−6.34652	+	39.0096i	−0.205476	+	1.26298i
$955$	14.7718	+	8.52848i	0.478003	+	0.275975i
$956$	12.7548	+	7.36400i	0.412520	+	0.238169i
$957$	16.2589	−	2.97811i	0.525574	−	0.0962687i
$958$			1.51336i			0.0488943i
$959$	17.2058	−	10.5131i	0.555605	−	0.339484i
$960$	−0.581597	+	1.63149i	−0.0187709	+	0.0526560i
$961$	−9.64662	−	16.7084i	−0.311181	−	0.538982i
$962$	9.09031	−	15.7449i	0.293083	−	0.507635i
$963$	−14.7368	−	38.8776i	−0.474885	−	1.25281i
$964$	−5.13289	+	2.96347i	−0.165319	+	0.0954470i
$965$	2.05067			0.0660135
$966$	−3.85498	+	11.7287i	−0.124032	+	0.377365i
$967$	−46.2991			−1.48888			−0.744440	−	0.667689i	$-0.767283\pi$
$967$	−46.2991			−1.48888			−0.744440	+	0.667689i	$0.767283\pi$
$968$	−8.72236	+	5.03585i	−0.280347	+	0.161858i
$969$	17.9483	−	15.2643i	0.576582	−	0.490358i
$970$	7.34960	−	12.7299i	0.235981	−	0.408732i
$971$	4.72817	+	8.18944i	0.151734	+	0.262812i	0.931865	−	0.362805i	$-0.118181\pi$
$971$	4.72817	+	8.18944i	0.151734	+	0.262812i	−0.780131	+	0.625616i	$0.784848\pi$
$972$	−15.4329	−	2.19680i	−0.495010	−	0.0704625i
$973$	16.5844	+	9.03250i	0.531672	+	0.289569i
$974$		−	10.6043i		−	0.339784i
$975$	−0.620329	−	3.38665i	−0.0198664	−	0.108460i
$976$	7.76184	+	4.48130i	0.248450	+	0.143443i
$977$	4.17619	+	2.41113i	0.133608	+	0.0771388i	0.565314	−	0.824876i	$-0.308755\pi$
$977$	4.17619	+	2.41113i	0.133608	+	0.0771388i	−0.431706	+	0.902014i	$0.642088\pi$
$978$	−0.827127	−	4.51566i	−0.0264486	−	0.144395i
$979$		−	11.1006i		−	0.354777i
$980$	3.79722	+	5.88057i	0.121298	+	0.187848i
$981$	38.8799	+	31.7555i	1.24134	+	1.01388i
$982$	6.13241	+	10.6216i	0.195693	+	0.338950i
$983$	22.3313	−	38.6789i	0.712258	−	1.23367i	−0.251750	−	0.967792i	$-0.581006\pi$
$983$	22.3313	−	38.6789i	0.712258	−	1.23367i	0.964008	−	0.265874i	$-0.0856607\pi$
$984$	1.48042	−	1.25903i	0.0471940	−	0.0401365i
$985$	11.2081	−	6.47102i	0.357121	−	0.206184i
$986$	26.0726			0.830321
$987$	31.7351	+	35.4871i	1.01014	+	1.12957i
$988$	−10.2727			−0.326819
$989$	−3.61448	+	2.08682i	−0.114934	+	0.0663570i
$990$	2.70278	−	1.02450i	0.0859000	−	0.0325608i
$991$	16.6566	−	28.8501i	0.529116	−	0.916455i	−0.470308	−	0.882502i	$-0.655857\pi$
$991$	16.6566	−	28.8501i	0.529116	−	0.916455i	0.999423	−	0.0339527i	$-0.0108096\pi$
$992$	1.71076	+	2.96312i	0.0543166	+	0.0940791i
$993$	−20.1687	+	56.5770i	−0.640036	+	1.79542i
$994$	29.4913	−	0.733955i	0.935409	−	0.0232796i
$995$			17.1869i			0.544862i
$996$	7.71936	−	1.41394i	0.244597	−	0.0448025i
$997$	14.7400	+	8.51013i	0.466820	+	0.269519i	0.714908	−	0.699219i	$-0.246469\pi$
$997$	14.7400	+	8.51013i	0.466820	+	0.269519i	−0.248088	+	0.968738i	$0.579802\pi$
$998$	−24.1002	−	13.9143i	−0.762880	−	0.440449i
$999$	41.6214	+	22.9391i	1.31684	+	0.725762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.r.b.101.5	yes	12
3.2	odd	2		210.2.r.a.101.3	✓	12
5.2	odd	4		1050.2.u.h.899.5		12
5.3	odd	4		1050.2.u.e.899.2		12
5.4	even	2		1050.2.s.f.101.2		12
7.3	odd	6		1470.2.b.b.881.8		12
7.4	even	3		1470.2.b.a.881.11		12
7.5	odd	6		210.2.r.a.131.3	yes	12
15.2	even	4		1050.2.u.f.899.4		12
15.8	even	4		1050.2.u.g.899.3		12
15.14	odd	2		1050.2.s.g.101.4		12
21.5	even	6	inner	210.2.r.b.131.5	yes	12
21.11	odd	6		1470.2.b.b.881.2		12
21.17	even	6		1470.2.b.a.881.5		12
35.12	even	12		1050.2.u.g.299.3		12
35.19	odd	6		1050.2.s.g.551.4		12
35.33	even	12		1050.2.u.f.299.4		12
105.47	odd	12		1050.2.u.e.299.2		12
105.68	odd	12		1050.2.u.h.299.5		12
105.89	even	6		1050.2.s.f.551.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.3	✓	12	3.2	odd	2
210.2.r.a.131.3	yes	12	7.5	odd	6
210.2.r.b.101.5	yes	12	1.1	even	1	trivial
210.2.r.b.131.5	yes	12	21.5	even	6	inner
1050.2.s.f.101.2		12	5.4	even	2
1050.2.s.f.551.2		12	105.89	even	6
1050.2.s.g.101.4		12	15.14	odd	2
1050.2.s.g.551.4		12	35.19	odd	6
1050.2.u.e.299.2		12	105.47	odd	12
1050.2.u.e.899.2		12	5.3	odd	4
1050.2.u.f.299.4		12	35.33	even	12
1050.2.u.f.899.4		12	15.2	even	4
1050.2.u.g.299.3		12	35.12	even	12
1050.2.u.g.899.3		12	15.8	even	4
1050.2.u.h.299.5		12	105.68	odd	12
1050.2.u.h.899.5		12	5.2	odd	4
1470.2.b.a.881.5		12	21.17	even	6
1470.2.b.a.881.11		12	7.4	even	3
1470.2.b.b.881.2		12	21.11	odd	6
1470.2.b.b.881.8		12	7.3	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.12211 + 1.31942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.63149 + 0.581597i) q^{6} +(1.26546 - 2.32349i) q^{7} -1.00000i q^{8} +(-0.481739 + 2.96107i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.12211 + 1.31942i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.63149 + 0.581597i) q^{6} +(1.26546 - 2.32349i) q^{7} -1.00000i q^{8} +(-0.481739 + 2.96107i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.834397 + 0.481739i) q^{11} +(1.70371 - 0.312065i) q^{12} +1.98782i q^{13} +(-0.0658248 - 2.64493i) q^{14} +(0.581597 - 1.63149i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.31614 + 2.27961i) q^{17} +(1.06334 + 2.80523i) q^{18} +(-4.47548 + 2.58392i) q^{19} -1.00000 q^{20} +(4.48565 - 0.937538i) q^{21} +0.963479 q^{22} +(-2.33317 + 1.34706i) q^{23} +(1.31942 - 1.12211i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.993908 + 1.72150i) q^{26} +(-4.44746 + 2.68703i) q^{27} +(-1.37947 - 2.25767i) q^{28} -9.90498i q^{29} +(-0.312065 - 1.70371i) q^{30} +(-2.96312 - 1.71076i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.300668 + 1.64148i) q^{33} +2.63227i q^{34} +(-2.64493 + 0.0658248i) q^{35} +(2.32349 + 1.89773i) q^{36} +(-4.57302 - 7.92070i) q^{37} +(-2.58392 + 4.47548i) q^{38} +(-2.62276 + 2.23055i) q^{39} +(-0.866025 + 0.500000i) q^{40} +1.12202 q^{41} +(3.41591 - 3.05475i) q^{42} +1.54917 q^{43} +(0.834397 - 0.481739i) q^{44} +(2.80523 - 1.06334i) q^{45} +(-1.34706 + 2.33317i) q^{46} +(5.19438 + 8.99693i) q^{47} +(0.581597 - 1.63149i) q^{48} +(-3.79722 - 5.88057i) q^{49} +1.00000i q^{50} +(-4.48462 + 0.821441i) q^{51} +(1.72150 + 0.993908i) q^{52} +(11.4092 + 6.58709i) q^{53} +(-2.50810 + 4.55076i) q^{54} -0.963479i q^{55} +(-2.32349 - 1.26546i) q^{56} +(-8.43126 - 3.00560i) q^{57} +(-4.95249 - 8.57796i) q^{58} +(1.05123 - 1.82079i) q^{59} +(-1.12211 - 1.31942i) q^{60} +(-7.76184 + 4.48130i) q^{61} -3.42151 q^{62} +(6.27039 + 4.86643i) q^{63} -1.00000 q^{64} +(1.72150 - 0.993908i) q^{65} +(1.08113 + 1.27123i) q^{66} +(0.897733 - 1.55492i) q^{67} +(1.31614 + 2.27961i) q^{68} +(-4.39541 - 1.56689i) q^{69} +(-2.25767 + 1.37947i) q^{70} +11.1501i q^{71} +(2.96107 + 0.481739i) q^{72} +(10.1961 + 5.88674i) q^{73} +(-7.92070 - 4.57302i) q^{74} +(-1.70371 + 0.312065i) q^{75} +5.16784i q^{76} +(2.17521 - 1.32909i) q^{77} +(-1.15611 + 3.24309i) q^{78} +(0.204174 + 0.353640i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-8.53585 - 2.85293i) q^{81} +(0.971699 - 0.561011i) q^{82} +4.53092 q^{83} +(1.43089 - 4.35345i) q^{84} +2.63227 q^{85} +(1.34162 - 0.774585i) q^{86} +(13.0688 - 11.1145i) q^{87} +(0.481739 - 0.834397i) q^{88} +(-5.76070 - 9.97782i) q^{89} +(1.89773 - 2.32349i) q^{90} +(4.61867 + 2.51550i) q^{91} +2.69411i q^{92} +(-1.06774 - 5.82926i) q^{93} +(8.99693 + 5.19438i) q^{94} +(4.47548 + 2.58392i) q^{95} +(-0.312065 - 1.70371i) q^{96} +14.6992i q^{97} +(-6.22878 - 3.19411i) q^{98} +(-1.82842 + 2.23863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} + 12 q^{11} - 2 q^{12} - 12 q^{14} - 4 q^{15} - 6 q^{16} - 12 q^{17} - 4 q^{18} - 12 q^{20} + 4 q^{21} + 24 q^{23} - 2 q^{24} - 6 q^{25} + 4 q^{26} + 8 q^{27} + 4 q^{28} - 4 q^{30} + 12 q^{31} - 2 q^{33} - 4 q^{35} + 6 q^{36} - 8 q^{37} - 8 q^{38} - 42 q^{39} + 4 q^{41} + 24 q^{42} + 12 q^{44} + 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 14 q^{49} - 8 q^{51} - 12 q^{52} + 48 q^{53} - 32 q^{54} - 6 q^{56} - 36 q^{57} + 8 q^{58} - 12 q^{59} - 2 q^{60} - 30 q^{61} - 8 q^{62} + 20 q^{63} - 12 q^{64} - 12 q^{65} - 14 q^{66} - 4 q^{67} + 12 q^{68} - 50 q^{69} + 6 q^{70} + 4 q^{72} + 2 q^{75} - 20 q^{77} + 32 q^{78} - 4 q^{79} - 6 q^{80} - 40 q^{81} + 40 q^{83} + 20 q^{84} + 24 q^{85} + 54 q^{86} + 64 q^{87} - 26 q^{89} + 8 q^{90} + 28 q^{91} + 4 q^{93} + 24 q^{94} - 4 q^{96} - 16 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 + 12 * q^11 - 2 * q^12 - 12 * q^14 - 4 * q^15 - 6 * q^16 - 12 * q^17 - 4 * q^18 - 12 * q^20 + 4 * q^21 + 24 * q^23 - 2 * q^24 - 6 * q^25 + 4 * q^26 + 8 * q^27 + 4 * q^28 - 4 * q^30 + 12 * q^31 - 2 * q^33 - 4 * q^35 + 6 * q^36 - 8 * q^37 - 8 * q^38 - 42 * q^39 + 4 * q^41 + 24 * q^42 + 12 * q^44 + 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 14 * q^49 - 8 * q^51 - 12 * q^52 + 48 * q^53 - 32 * q^54 - 6 * q^56 - 36 * q^57 + 8 * q^58 - 12 * q^59 - 2 * q^60 - 30 * q^61 - 8 * q^62 + 20 * q^63 - 12 * q^64 - 12 * q^65 - 14 * q^66 - 4 * q^67 + 12 * q^68 - 50 * q^69 + 6 * q^70 + 4 * q^72 + 2 * q^75 - 20 * q^77 + 32 * q^78 - 4 * q^79 - 6 * q^80 - 40 * q^81 + 40 * q^83 + 20 * q^84 + 24 * q^85 + 54 * q^86 + 64 * q^87 - 26 * q^89 + 8 * q^90 + 28 * q^91 + 4 * q^93 + 24 * q^94 - 4 * q^96 - 16 * q^98 + 48 * q^99

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