LMFDB - Embedded newform 370.2.g.e.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (of order $4$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$1.28931 - 1.28931i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.e.327.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.28931 + 1.28931i) q^{3} -1.00000 q^{4} +(1.45999 + 1.69364i) q^{5} +(-1.28931 - 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000i q^{8} -0.324646i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.28931 + 1.28931i) q^{3} -1.00000 q^{4} +(1.45999 + 1.69364i) q^{5} +(-1.28931 - 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000i q^{8} -0.324646i q^{9} +(-1.69364 + 1.45999i) q^{10} +3.64633i q^{11} +(1.28931 - 1.28931i) q^{12} +3.10704i q^{13} +(0.579841 + 0.579841i) q^{14} +(-4.06602 - 0.301249i) q^{15} +1.00000 q^{16} -8.09027 q^{17} +0.324646 q^{18} +(3.05234 - 3.05234i) q^{19} +(-1.45999 - 1.69364i) q^{20} +1.49519i q^{21} -3.64633 q^{22} -7.79067i q^{23} +(1.28931 + 1.28931i) q^{24} +(-0.736849 + 4.94541i) q^{25} -3.10704 q^{26} +(-3.44936 - 3.44936i) q^{27} +(-0.579841 + 0.579841i) q^{28} +(-1.37472 - 1.37472i) q^{29} +(0.301249 - 4.06602i) q^{30} +(3.23904 - 3.23904i) q^{31} +1.00000i q^{32} +(-4.70126 - 4.70126i) q^{33} -8.09027i q^{34} +(1.82861 + 0.135480i) q^{35} +0.324646i q^{36} +(3.63294 + 4.87870i) q^{37} +(3.05234 + 3.05234i) q^{38} +(-4.00594 - 4.00594i) q^{39} +(1.69364 - 1.45999i) q^{40} +9.31106i q^{41} -1.49519 q^{42} +10.9160i q^{43} -3.64633i q^{44} +(0.549834 - 0.473980i) q^{45} +7.79067 q^{46} +(-4.11794 + 4.11794i) q^{47} +(-1.28931 + 1.28931i) q^{48} +6.32757i q^{49} +(-4.94541 - 0.736849i) q^{50} +(10.4309 - 10.4309i) q^{51} -3.10704i q^{52} +(0.446555 + 0.446555i) q^{53} +(3.44936 - 3.44936i) q^{54} +(-6.17558 + 5.32361i) q^{55} +(-0.579841 - 0.579841i) q^{56} +7.87084i q^{57} +(1.37472 - 1.37472i) q^{58} +(6.16388 - 6.16388i) q^{59} +(4.06602 + 0.301249i) q^{60} +(8.71382 - 8.71382i) q^{61} +(3.23904 + 3.23904i) q^{62} +(-0.188243 - 0.188243i) q^{63} -1.00000 q^{64} +(-5.26221 + 4.53625i) q^{65} +(4.70126 - 4.70126i) q^{66} +(2.01024 + 2.01024i) q^{67} +8.09027 q^{68} +(10.0446 + 10.0446i) q^{69} +(-0.135480 + 1.82861i) q^{70} +0.00151598 q^{71} -0.324646 q^{72} +(9.32759 - 9.32759i) q^{73} +(-4.87870 + 3.63294i) q^{74} +(-5.42614 - 7.32620i) q^{75} +(-3.05234 + 3.05234i) q^{76} +(2.11429 + 2.11429i) q^{77} +(4.00594 - 4.00594i) q^{78} +(-0.760897 + 0.760897i) q^{79} +(1.45999 + 1.69364i) q^{80} +9.86854 q^{81} -9.31106 q^{82} +(3.16981 + 3.16981i) q^{83} -1.49519i q^{84} +(-11.8117 - 13.7020i) q^{85} -10.9160 q^{86} +3.54488 q^{87} +3.64633 q^{88} +(5.80016 + 5.80016i) q^{89} +(0.473980 + 0.549834i) q^{90} +(1.80159 + 1.80159i) q^{91} +7.79067i q^{92} +8.35226i q^{93} +(-4.11794 - 4.11794i) q^{94} +(9.62597 + 0.713182i) q^{95} +(-1.28931 - 1.28931i) q^{96} -14.6206 q^{97} -6.32757 q^{98} +1.18377 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.28931	+	1.28931i	−0.744384	+	0.744384i	−0.973418	−	0.229034i	$-0.926443\pi$
$3$	−1.28931	+	1.28931i	−0.744384	+	0.744384i	0.229034	+	0.973418i	$0.426443\pi$
$4$	−1.00000			−0.500000
$5$	1.45999	+	1.69364i	0.652928	+	0.757420i
$5$	1.45999	+	1.69364i	0.652928	+	0.757420i
$6$	−1.28931	−	1.28931i	−0.526359	−	0.526359i
$7$	0.579841	−	0.579841i	0.219159	−	0.219159i	−0.588985	−	0.808144i	$-0.700472\pi$
$7$	0.579841	−	0.579841i	0.219159	−	0.219159i	0.808144	+	0.588985i	$0.200472\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	0.324646i		−	0.108215i
$10$	−1.69364	+	1.45999i	−0.535577	+	0.461690i
$11$			3.64633i			1.09941i	0.835359	+	0.549705i	$0.185260\pi$
$11$			3.64633i			1.09941i	−0.835359	+	0.549705i	$0.814740\pi$
$12$	1.28931	−	1.28931i	0.372192	−	0.372192i
$13$			3.10704i			0.861737i	0.902415	+	0.430868i	$0.141793\pi$
$13$			3.10704i			0.861737i	−0.902415	+	0.430868i	$0.858207\pi$
$14$	0.579841	+	0.579841i	0.154969	+	0.154969i
$15$	−4.06602	−	0.301249i	−1.04984	−	0.0777820i
$16$	1.00000			0.250000
$17$	−8.09027			−1.96218			−0.981089	−	0.193558i	$-0.937997\pi$
$17$	−8.09027			−1.96218			−0.981089	+	0.193558i	$0.937997\pi$
$18$	0.324646			0.0765198
$19$	3.05234	−	3.05234i	0.700255	−	0.700255i	−0.264210	−	0.964465i	$-0.585111\pi$
$19$	3.05234	−	3.05234i	0.700255	−	0.700255i	0.964465	+	0.264210i	$0.0851112\pi$
$20$	−1.45999	−	1.69364i	−0.326464	−	0.378710i
$21$			1.49519i			0.326278i
$22$	−3.64633			−0.777401
$23$		−	7.79067i		−	1.62447i	−0.583333	−	0.812233i	$-0.698252\pi$
$23$		−	7.79067i		−	1.62447i	0.583333	−	0.812233i	$-0.301748\pi$
$24$	1.28931	+	1.28931i	0.263180	+	0.263180i
$25$	−0.736849	+	4.94541i	−0.147370	+	0.989081i
$26$	−3.10704			−0.609340
$27$	−3.44936	−	3.44936i	−0.663830	−	0.663830i
$28$	−0.579841	+	0.579841i	−0.109580	+	0.109580i
$29$	−1.37472	−	1.37472i	−0.255279	−	0.255279i	0.567852	−	0.823131i	$-0.307775\pi$
$29$	−1.37472	−	1.37472i	−0.255279	−	0.255279i	−0.823131	+	0.567852i	$0.807775\pi$
$30$	0.301249	−	4.06602i	0.0550002	−	0.742349i
$31$	3.23904	−	3.23904i	0.581749	−	0.581749i	−0.353635	−	0.935384i	$-0.615054\pi$
$31$	3.23904	−	3.23904i	0.581749	−	0.581749i	0.935384	+	0.353635i	$0.115054\pi$
$32$			1.00000i			0.176777i
$33$	−4.70126	−	4.70126i	−0.818384	−	0.818384i
$34$		−	8.09027i		−	1.38747i
$35$	1.82861	+	0.135480i	0.309091	+	0.0229004i
$36$			0.324646i			0.0541076i
$37$	3.63294	+	4.87870i	0.597252	+	0.802054i
$37$	3.63294	+	4.87870i	0.597252	+	0.802054i
$38$	3.05234	+	3.05234i	0.495155	+	0.495155i
$39$	−4.00594	−	4.00594i	−0.641463	−	0.641463i
$40$	1.69364	−	1.45999i	0.267788	−	0.230845i
$41$			9.31106i			1.45414i	0.686562	+	0.727072i	$0.259119\pi$
$41$			9.31106i			1.45414i	−0.686562	+	0.727072i	$0.740881\pi$
$42$	−1.49519			−0.230713
$43$			10.9160i			1.66467i	0.554275	+	0.832334i	$0.312996\pi$
$43$			10.9160i			1.66467i	−0.554275	+	0.832334i	$0.687004\pi$
$44$		−	3.64633i		−	0.549705i
$45$	0.549834	−	0.473980i	0.0819644	−	0.0706568i
$46$	7.79067			1.14867
$47$	−4.11794	+	4.11794i	−0.600663	+	0.600663i	−0.940489	−	0.339825i	$-0.889632\pi$
$47$	−4.11794	+	4.11794i	−0.600663	+	0.600663i	0.339825	+	0.940489i	$0.389632\pi$
$48$	−1.28931	+	1.28931i	−0.186096	+	0.186096i
$49$			6.32757i			0.903938i
$50$	−4.94541	−	0.736849i	−0.699386	−	0.104206i
$51$	10.4309	−	10.4309i	1.46061	−	1.46061i
$52$		−	3.10704i		−	0.430868i
$53$	0.446555	+	0.446555i	0.0613390	+	0.0613390i	0.737111	−	0.675772i	$-0.236190\pi$
$53$	0.446555	+	0.446555i	0.0613390	+	0.0613390i	−0.675772	+	0.737111i	$0.736190\pi$
$54$	3.44936	−	3.44936i	0.469399	−	0.469399i
$55$	−6.17558	+	5.32361i	−0.832715	+	0.717836i
$56$	−0.579841	−	0.579841i	−0.0774846	−	0.0774846i
$57$			7.87084i			1.04252i
$58$	1.37472	−	1.37472i	0.180509	−	0.180509i
$59$	6.16388	−	6.16388i	0.802468	−	0.802468i	−0.181012	−	0.983481i	$-0.557937\pi$
$59$	6.16388	−	6.16388i	0.802468	−	0.802468i	0.983481	+	0.181012i	$0.0579374\pi$
$60$	4.06602	+	0.301249i	0.524920	+	0.0388910i
$61$	8.71382	−	8.71382i	1.11569	−	1.11569i	0.123324	−	0.992366i	$-0.460644\pi$
$61$	8.71382	−	8.71382i	1.11569	−	1.11569i	0.992366	−	0.123324i	$-0.0393555\pi$
$62$	3.23904	+	3.23904i	0.411359	+	0.411359i
$63$	−0.188243	−	0.188243i	−0.0237164	−	0.0237164i
$64$	−1.00000			−0.125000
$65$	−5.26221	+	4.53625i	−0.652697	+	0.562652i
$66$	4.70126	−	4.70126i	0.578685	−	0.578685i
$67$	2.01024	+	2.01024i	0.245590	+	0.245590i	0.819158	−	0.573568i	$-0.194441\pi$
$67$	2.01024	+	2.01024i	0.245590	+	0.245590i	−0.573568	+	0.819158i	$0.694441\pi$
$68$	8.09027			0.981089
$69$	10.0446	+	10.0446i	1.20923	+	1.20923i
$70$	−0.135480	+	1.82861i	−0.0161930	+	0.218560i
$71$	0.00151598			0.000179913			8.99567e−5	−	1.00000i	$-0.499971\pi$
$71$	0.00151598			0.000179913			8.99567e−5		1.00000i	$0.499971\pi$
$72$	−0.324646			−0.0382599
$73$	9.32759	−	9.32759i	1.09171	−	1.09171i	0.0963663	−	0.995346i	$-0.469278\pi$
$73$	9.32759	−	9.32759i	1.09171	−	1.09171i	0.995346	−	0.0963663i	$-0.0307220\pi$
$74$	−4.87870	+	3.63294i	−0.567138	+	0.422321i
$75$	−5.42614	−	7.32620i	−0.626557	−	0.845956i
$76$	−3.05234	+	3.05234i	−0.350128	+	0.350128i
$77$	2.11429	+	2.11429i	0.240946	+	0.240946i
$78$	4.00594	−	4.00594i	0.453583	−	0.453583i
$79$	−0.760897	+	0.760897i	−0.0856076	+	0.0856076i	−0.748614	−	0.663006i	$-0.769280\pi$
$79$	−0.760897	+	0.760897i	−0.0856076	+	0.0856076i	0.663006	+	0.748614i	$0.269280\pi$
$80$	1.45999	+	1.69364i	0.163232	+	0.189355i
$81$	9.86854			1.09650
$82$	−9.31106			−1.02823
$83$	3.16981	+	3.16981i	0.347932	+	0.347932i	0.859339	−	0.511407i	$-0.170875\pi$
$83$	3.16981	+	3.16981i	0.347932	+	0.347932i	−0.511407	+	0.859339i	$0.670875\pi$
$84$		−	1.49519i		−	0.163139i
$85$	−11.8117	−	13.7020i	−1.28116	−	1.48619i
$86$	−10.9160			−1.17710
$87$	3.54488			0.380051
$88$	3.64633			0.388700
$89$	5.80016	+	5.80016i	0.614816	+	0.614816i	0.944197	−	0.329381i	$-0.106840\pi$
$89$	5.80016	+	5.80016i	0.614816	+	0.614816i	−0.329381	+	0.944197i	$0.606840\pi$
$90$	0.473980	+	0.549834i	0.0499619	+	0.0579576i
$91$	1.80159	+	1.80159i	0.188858	+	0.188858i
$92$			7.79067i			0.812233i
$93$			8.35226i			0.866089i
$94$	−4.11794	−	4.11794i	−0.424733	−	0.424733i
$95$	9.62597	+	0.713182i	0.987604	+	0.0731710i
$96$	−1.28931	−	1.28931i	−0.131590	−	0.131590i
$97$	−14.6206			−1.48449			−0.742246	−	0.670127i	$-0.766240\pi$
$97$	−14.6206			−1.48449			−0.742246	+	0.670127i	$0.766240\pi$
$98$	−6.32757			−0.639181
$99$	1.18377			0.118973
$100$	0.736849	−	4.94541i	0.0736849	−	0.494541i
$101$			3.68870i			0.367039i	0.983016	+	0.183520i	$0.0587491\pi$
$101$			3.68870i			0.367039i	−0.983016	+	0.183520i	$0.941251\pi$
$102$	10.4309	+	10.4309i	1.03281	+	1.03281i
$103$	11.1543			1.09907			0.549535	−	0.835471i	$-0.314805\pi$
$103$	11.1543			1.09907			0.549535	+	0.835471i	$0.314805\pi$
$104$	3.10704			0.304670
$105$	−2.53232	+	2.18297i	−0.247129	+	0.213036i
$106$	−0.446555	+	0.446555i	−0.0433732	+	0.0433732i
$107$	−3.88311	+	3.88311i	−0.375394	+	0.375394i	−0.869437	−	0.494043i	$-0.835519\pi$
$107$	−3.88311	+	3.88311i	−0.375394	+	0.375394i	0.494043	+	0.869437i	$0.335519\pi$
$108$	3.44936	+	3.44936i	0.331915	+	0.331915i
$109$	−2.01583	+	2.01583i	−0.193081	+	0.193081i	−0.797026	−	0.603945i	$-0.793595\pi$
$109$	−2.01583	+	2.01583i	−0.193081	+	0.193081i	0.603945	+	0.797026i	$0.293595\pi$
$110$	−5.32361	−	6.17558i	−0.507587	−	0.588819i
$111$	−10.9742	−	1.60617i	−1.04162	−	0.152451i
$112$	0.579841	−	0.579841i	0.0547899	−	0.0547899i
$113$	11.8892			1.11844			0.559220	−	0.829019i	$-0.311101\pi$
$113$	11.8892			1.11844			0.559220	+	0.829019i	$0.311101\pi$
$114$	−7.87084			−0.737171
$115$	13.1946	−	11.3743i	1.23040	−	1.06066i
$116$	1.37472	+	1.37472i	0.127639	+	0.127639i
$117$	1.00869			0.0932531
$118$	6.16388	+	6.16388i	0.567431	+	0.567431i
$119$	−4.69107	+	4.69107i	−0.430030	+	0.430030i
$120$	−0.301249	+	4.06602i	−0.0275001	+	0.371175i
$121$	−2.29574			−0.208704
$122$	8.71382	+	8.71382i	0.788912	+	0.788912i
$123$	−12.0049	−	12.0049i	−1.08244	−	1.08244i
$124$	−3.23904	+	3.23904i	−0.290875	+	0.290875i
$125$	−9.45154	+	5.97229i	−0.845372	+	0.534178i
$126$	0.188243	−	0.188243i	0.0167700	−	0.0167700i
$127$	13.9019	−	13.9019i	1.23359	−	1.23359i	0.271015	−	0.962575i	$-0.412641\pi$
$127$	13.9019	−	13.9019i	1.23359	−	1.23359i	0.962575	−	0.271015i	$-0.0873593\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−14.0741	−	14.0741i	−1.23915	−	1.23915i
$130$	−4.53625	−	5.26221i	−0.397855	−	0.461526i
$131$	2.71250	−	2.71250i	0.236992	−	0.236992i	−0.578611	−	0.815603i	$-0.696405\pi$
$131$	2.71250	−	2.71250i	0.236992	−	0.236992i	0.815603	+	0.578611i	$0.196405\pi$
$132$	4.70126	+	4.70126i	0.409192	+	0.409192i
$133$		−	3.53975i		−	0.306935i
$134$	−2.01024	+	2.01024i	−0.173658	+	0.173658i
$135$	0.805947	−	10.8780i	0.0693648	−	0.936232i
$136$			8.09027i			0.693735i
$137$	−11.4519	+	11.4519i	−0.978406	+	0.978406i	−0.999772	−	0.0213660i	$-0.993198\pi$
$137$	−11.4519	+	11.4519i	−0.978406	+	0.978406i	0.0213660	+	0.999772i	$0.493198\pi$
$138$	−10.0446	+	10.0446i	−0.855053	+	0.855053i
$139$	2.41427			0.204775			0.102388	−	0.994745i	$-0.467352\pi$
$139$	2.41427			0.204775			0.102388	+	0.994745i	$0.467352\pi$
$140$	−1.82861	−	0.135480i	−0.154546	−	0.0114502i
$141$		−	10.6186i		−	0.894248i
$142$			0.00151598i			0.000127218i
$143$	−11.3293			−0.947403
$144$		−	0.324646i		−	0.0270538i
$145$	0.321204	−	4.33536i	0.0266746	−	0.360032i
$146$	9.32759	+	9.32759i	0.771957	+	0.771957i
$147$	−8.15820	−	8.15820i	−0.672877	−	0.672877i
$148$	−3.63294	−	4.87870i	−0.298626	−	0.401027i
$149$		−	4.02923i		−	0.330088i	−0.986286	−	0.165044i	$-0.947223\pi$
$149$		−	4.02923i		−	0.330088i	0.986286	−	0.165044i	$-0.0527765\pi$
$150$	7.32620	−	5.42614i	0.598181	−	0.443043i
$151$			8.86568i			0.721479i	0.932667	+	0.360739i	$0.117476\pi$
$151$			8.86568i			0.721479i	−0.932667	+	0.360739i	$0.882524\pi$
$152$	−3.05234	−	3.05234i	−0.247578	−	0.247578i
$153$			2.62647i			0.212338i
$154$	−2.11429	+	2.11429i	−0.170375	+	0.170375i
$155$	10.2148	+	0.756805i	0.820469	+	0.0607880i
$156$	4.00594	+	4.00594i	0.320732	+	0.320732i
$157$	6.87897	−	6.87897i	0.549001	−	0.549001i	−0.377151	−	0.926152i	$-0.623096\pi$
$157$	6.87897	−	6.87897i	0.549001	−	0.549001i	0.926152	+	0.377151i	$0.123096\pi$
$158$	−0.760897	−	0.760897i	−0.0605337	−	0.0605337i
$159$	−1.15150			−0.0913196
$160$	−1.69364	+	1.45999i	−0.133894	+	0.115422i
$161$	−4.51735	−	4.51735i	−0.356017	−	0.356017i
$162$			9.86854i			0.775346i
$163$	−10.6733			−0.835995			−0.417997	−	0.908448i	$-0.637268\pi$
$163$	−10.6733			−0.835995			−0.417997	+	0.908448i	$0.637268\pi$
$164$		−	9.31106i		−	0.727072i
$165$	1.09845	−	14.8260i	0.0855144	−	1.15421i
$166$	−3.16981	+	3.16981i	−0.246025	+	0.246025i
$167$	−0.864796			−0.0669199			−0.0334600	−	0.999440i	$-0.510653\pi$
$167$	−0.864796			−0.0669199			−0.0334600	+	0.999440i	$0.510653\pi$
$168$	1.49519			0.115357
$169$	3.34633			0.257410
$170$	13.7020	−	11.8117i	1.05090	−	0.905918i
$171$	−0.990930	−	0.990930i	−0.0757783	−	0.0757783i
$172$		−	10.9160i		−	0.832334i
$173$	2.14973	−	2.14973i	0.163441	−	0.163441i	−0.620648	−	0.784089i	$-0.713130\pi$
$173$	2.14973	−	2.14973i	0.163441	−	0.163441i	0.784089	+	0.620648i	$0.213130\pi$
$174$			3.54488i			0.268737i
$175$	2.44030	+	3.29481i	0.184469	+	0.249064i
$176$			3.64633i			0.274853i
$177$			15.8943i			1.19469i
$178$	−5.80016	+	5.80016i	−0.434741	+	0.434741i
$179$	0.313292	+	0.313292i	0.0234165	+	0.0234165i	0.718718	−	0.695302i	$-0.244729\pi$
$179$	0.313292	+	0.313292i	0.0234165	+	0.0234165i	−0.695302	+	0.718718i	$0.744729\pi$
$180$	−0.549834	+	0.473980i	−0.0409822	+	0.0353284i
$181$	16.2161			1.20533			0.602667	−	0.797993i	$-0.294105\pi$
$181$	16.2161			1.20533			0.602667	+	0.797993i	$0.294105\pi$
$182$	−1.80159	+	1.80159i	−0.133543	+	0.133543i
$183$			22.4697i			1.66100i
$184$	−7.79067			−0.574336
$185$	−2.95871	+	13.2758i	−0.217529	+	0.976054i
$186$	−8.35226			−0.612418
$187$		−	29.4998i		−	2.15724i
$188$	4.11794	−	4.11794i	0.300332	−	0.300332i
$189$	−4.00017			−0.290969
$190$	−0.713182	+	9.62597i	−0.0517397	+	0.698341i
$191$	0.276686	+	0.276686i	0.0200203	+	0.0200203i	0.717046	−	0.697026i	$-0.245494\pi$
$191$	0.276686	+	0.276686i	0.0200203	+	0.0200203i	−0.697026	+	0.717046i	$0.745494\pi$
$192$	1.28931	−	1.28931i	0.0930480	−	0.0930480i
$193$			8.78779i			0.632559i	0.948666	+	0.316279i	$0.102434\pi$
$193$			8.78779i			0.632559i	−0.948666	+	0.316279i	$0.897566\pi$
$194$		−	14.6206i		−	1.04969i
$195$	0.935990	−	12.6333i	0.0670276	−	0.904686i
$196$		−	6.32757i		−	0.451969i
$197$	8.41487	−	8.41487i	0.599535	−	0.599535i	−0.340654	−	0.940189i	$-0.610649\pi$
$197$	8.41487	−	8.41487i	0.599535	−	0.599535i	0.940189	+	0.340654i	$0.110649\pi$
$198$			1.18377i			0.0841266i
$199$	−4.20114	−	4.20114i	−0.297811	−	0.297811i	0.542345	−	0.840156i	$-0.317537\pi$
$199$	−4.20114	−	4.20114i	−0.297811	−	0.297811i	−0.840156	+	0.542345i	$0.817537\pi$
$200$	4.94541	+	0.736849i	0.349693	+	0.0521031i
$201$	−5.18365			−0.365627
$202$	−3.68870			−0.259536
$203$	−1.59424			−0.111894
$204$	−10.4309	+	10.4309i	−0.730307	+	0.730307i
$205$	−15.7696	+	13.5941i	−1.10140	+	0.949451i
$206$			11.1543i			0.777160i
$207$	−2.52921			−0.175792
$208$			3.10704i			0.215434i
$209$	11.1299	+	11.1299i	0.769868	+	0.769868i
$210$	−2.18297	−	2.53232i	−0.150639	−	0.174747i
$211$	−27.4901			−1.89250			−0.946248	−	0.323442i	$-0.895160\pi$
$211$	−27.4901			−1.89250			−0.946248	+	0.323442i	$0.895160\pi$
$212$	−0.446555	−	0.446555i	−0.0306695	−	0.0306695i
$213$	−0.00195457	+	0.00195457i	−0.000133925	+	0.000133925i
$214$	−3.88311	−	3.88311i	−0.265444	−	0.265444i
$215$	−18.4877	+	15.9372i	−1.26085	+	1.08691i
$216$	−3.44936	+	3.44936i	−0.234699	+	0.234699i
$217$		−	3.75626i		−	0.254992i
$218$	−2.01583	−	2.01583i	−0.136529	−	0.136529i
$219$			24.0523i			1.62531i
$220$	6.17558	−	5.32361i	0.416358	−	0.358918i
$221$		−	25.1367i		−	1.69088i
$222$	1.60617	−	10.9742i	0.107799	−	0.736537i
$223$	−9.42660	−	9.42660i	−0.631252	−	0.631252i	0.317130	−	0.948382i	$-0.397281\pi$
$223$	−9.42660	−	9.42660i	−0.631252	−	0.631252i	−0.948382	+	0.317130i	$0.897281\pi$
$224$	0.579841	+	0.579841i	0.0387423	+	0.0387423i
$225$	1.60551	+	0.239215i	0.107034	+	0.0159477i
$226$			11.8892i			0.790856i
$227$	17.9587			1.19196			0.595981	−	0.802999i	$-0.296763\pi$
$227$	17.9587			1.19196			0.595981	+	0.802999i	$0.296763\pi$
$228$		−	7.87084i		−	0.521259i
$229$		−	18.1673i		−	1.20053i	−0.799802	−	0.600264i	$-0.795062\pi$
$229$		−	18.1673i		−	1.20053i	0.799802	−	0.600264i	$-0.204938\pi$
$230$	11.3743	+	13.1946i	0.750000	+	0.870027i
$231$	−5.45197			−0.358713
$232$	−1.37472	+	1.37472i	−0.0902547	+	0.0902547i
$233$	−2.23686	+	2.23686i	−0.146541	+	0.146541i	−0.776571	−	0.630030i	$-0.783043\pi$
$233$	−2.23686	+	2.23686i	−0.146541	+	0.146541i	0.630030	+	0.776571i	$0.283043\pi$
$234$			1.00869i			0.0659399i
$235$	−12.9865	−	0.962160i	−0.847144	−	0.0627644i
$236$	−6.16388	+	6.16388i	−0.401234	+	0.401234i
$237$		−	1.96207i		−	0.127450i
$238$	−4.69107	−	4.69107i	−0.304077	−	0.304077i
$239$	−4.53542	+	4.53542i	−0.293372	+	0.293372i	−0.838411	−	0.545039i	$-0.816515\pi$
$239$	−4.53542	+	4.53542i	−0.293372	+	0.293372i	0.545039	+	0.838411i	$0.316515\pi$
$240$	−4.06602	−	0.301249i	−0.262460	−	0.0194455i
$241$	2.95256	+	2.95256i	0.190191	+	0.190191i	0.795779	−	0.605587i	$-0.207062\pi$
$241$	2.95256	+	2.95256i	0.190191	+	0.190191i	−0.605587	+	0.795779i	$0.707062\pi$
$242$		−	2.29574i		−	0.147576i
$243$	−2.37553	+	2.37553i	−0.152390	+	0.152390i
$244$	−8.71382	+	8.71382i	−0.557845	+	0.557845i
$245$	−10.7166	+	9.23820i	−0.684661	+	0.590207i
$246$	12.0049	−	12.0049i	0.765402	−	0.765402i
$247$	9.48374	+	9.48374i	0.603436	+	0.603436i
$248$	−3.23904	−	3.23904i	−0.205679	−	0.205679i
$249$	−8.17374			−0.517990
$250$	−5.97229	−	9.45154i	−0.377721	−	0.597768i
$251$	−9.93109	+	9.93109i	−0.626845	+	0.626845i	−0.947273	−	0.320428i	$-0.896173\pi$
$251$	−9.93109	+	9.93109i	−0.626845	+	0.626845i	0.320428	+	0.947273i	$0.396173\pi$
$252$	0.188243	+	0.188243i	0.0118582	+	0.0118582i
$253$	28.4074			1.78596
$254$	13.9019	+	13.9019i	0.872280	+	0.872280i
$255$	32.8951	+	2.43718i	2.05997	+	0.152622i
$256$	1.00000			0.0625000
$257$	−15.1135			−0.942757			−0.471378	−	0.881931i	$-0.656243\pi$
$257$	−15.1135			−0.942757			−0.471378	+	0.881931i	$0.656243\pi$
$258$	14.0741	−	14.0741i	0.876213	−	0.876213i
$259$	4.93540	+	0.722344i	0.306671	+	0.0448842i
$260$	5.26221	−	4.53625i	0.326348	−	0.281326i
$261$	−0.446297	+	0.446297i	−0.0276251	+	0.0276251i
$262$	2.71250	+	2.71250i	0.167579	+	0.167579i
$263$	−9.74250	+	9.74250i	−0.600749	+	0.600749i	−0.940511	−	0.339763i	$-0.889653\pi$
$263$	−9.74250	+	9.74250i	−0.600749	+	0.600749i	0.339763	+	0.940511i	$0.389653\pi$
$264$	−4.70126	+	4.70126i	−0.289342	+	0.289342i
$265$	−0.104338	+	1.40827i	−0.00640942	+	0.0865094i
$266$	3.53975			0.217036
$267$	−14.9564			−0.915319
$268$	−2.01024	−	2.01024i	−0.122795	−	0.122795i
$269$		−	6.43418i		−	0.392299i	−0.980574	−	0.196150i	$-0.937156\pi$
$269$		−	6.43418i		−	0.392299i	0.980574	−	0.196150i	$-0.0628438\pi$
$270$	10.8780	+	0.805947i	0.662016	+	0.0490483i
$271$	−25.6662			−1.55911			−0.779556	−	0.626332i	$-0.784555\pi$
$271$	−25.6662			−1.55911			−0.779556	+	0.626332i	$0.784555\pi$
$272$	−8.09027			−0.490544
$273$	−4.64561			−0.281165
$274$	−11.4519	−	11.4519i	−0.691837	−	0.691837i
$275$	−18.0326	−	2.68680i	−1.08741	−	0.162020i
$276$	−10.0446	−	10.0446i	−0.604614	−	0.604614i
$277$			17.2625i			1.03720i	0.855016	+	0.518602i	$0.173548\pi$
$277$			17.2625i			1.03720i	−0.855016	+	0.518602i	$0.826452\pi$
$278$			2.41427i			0.144798i
$279$	−1.05154	−	1.05154i	−0.0629541	−	0.0629541i
$280$	0.135480	−	1.82861i	0.00809650	−	0.109280i
$281$	−3.84098	−	3.84098i	−0.229134	−	0.229134i	0.583197	−	0.812331i	$-0.301802\pi$
$281$	−3.84098	−	3.84098i	−0.229134	−	0.229134i	−0.812331	+	0.583197i	$0.801802\pi$
$282$	10.6186			0.632329
$283$	20.5564			1.22195			0.610975	−	0.791650i	$-0.290778\pi$
$283$	20.5564			1.22195			0.610975	+	0.791650i	$0.290778\pi$
$284$	−0.00151598			−8.99567e−5
$285$	−13.3304	+	11.4914i	−0.789624	+	0.680689i
$286$		−	11.3293i		−	0.669915i
$287$	5.39894	+	5.39894i	0.318689	+	0.318689i
$288$	0.324646			0.0191299
$289$	48.4524			2.85014
$290$	4.33536	+	0.321204i	0.254581	+	0.0188618i
$291$	18.8504	−	18.8504i	1.10503	−	1.10503i
$292$	−9.32759	+	9.32759i	−0.545856	+	0.545856i
$293$	−11.2671	−	11.2671i	−0.658232	−	0.658232i	0.296729	−	0.954962i	$-0.404104\pi$
$293$	−11.2671	−	11.2671i	−0.658232	−	0.658232i	−0.954962	+	0.296729i	$0.904104\pi$
$294$	8.15820	−	8.15820i	0.475796	−	0.475796i
$295$	19.4386	+	1.44019i	1.13176	+	0.0838514i
$296$	4.87870	−	3.63294i	0.283569	−	0.211160i
$297$	12.5775	−	12.5775i	0.729822	−	0.729822i
$298$	4.02923			0.233407
$299$	24.2059			1.39986
$300$	5.42614	+	7.32620i	0.313278	+	0.422978i
$301$	6.32952	+	6.32952i	0.364828	+	0.364828i
$302$	−8.86568			−0.510163
$303$	−4.75588	−	4.75588i	−0.273218	−	0.273218i
$304$	3.05234	−	3.05234i	0.175064	−	0.175064i
$305$	27.4802	+	2.03599i	1.57351	+	0.116581i
$306$	−2.62647			−0.150145
$307$	−9.43686	−	9.43686i	−0.538590	−	0.538590i	0.384525	−	0.923115i	$-0.374365\pi$
$307$	−9.43686	−	9.43686i	−0.538590	−	0.538590i	−0.923115	+	0.384525i	$0.874365\pi$
$308$	−2.11429	−	2.11429i	−0.120473	−	0.120473i
$309$	−14.3814	+	14.3814i	−0.818131	+	0.818131i
$310$	−0.756805	+	10.2148i	−0.0429836	+	0.580159i
$311$	6.70368	−	6.70368i	0.380131	−	0.380131i	−0.491019	−	0.871149i	$-0.663375\pi$
$311$	6.70368	−	6.70368i	0.380131	−	0.380131i	0.871149	+	0.491019i	$0.163375\pi$
$312$	−4.00594	+	4.00594i	−0.226791	+	0.226791i
$313$		−	23.2157i		−	1.31223i	−0.754662	−	0.656114i	$-0.772199\pi$
$313$		−	23.2157i		−	1.31223i	0.754662	−	0.656114i	$-0.227801\pi$
$314$	6.87897	+	6.87897i	0.388203	+	0.388203i
$315$	0.0439832	−	0.593650i	0.00247817	−	0.0334484i
$316$	0.760897	−	0.760897i	0.0428038	−	0.0428038i
$317$	15.3696	+	15.3696i	0.863245	+	0.863245i	0.991714	−	0.128469i	$-0.0410062\pi$
$317$	15.3696	+	15.3696i	0.863245	+	0.863245i	−0.128469	+	0.991714i	$0.541006\pi$
$318$		−	1.15150i		−	0.0645727i
$319$	5.01268	−	5.01268i	0.280656	−	0.280656i
$320$	−1.45999	−	1.69364i	−0.0816160	−	0.0946775i
$321$		−	10.0131i		−	0.558875i
$322$	4.51735	−	4.51735i	0.251742	−	0.251742i
$323$	−24.6943	+	24.6943i	−1.37403	+	1.37403i
$324$	−9.86854			−0.548252
$325$	−15.3656	−	2.28942i	−0.852328	−	0.126994i
$326$		−	10.6733i		−	0.591137i
$327$		−	5.19806i		−	0.287454i
$328$	9.31106			0.514117
$329$			4.77550i			0.263282i
$330$	14.8260	+	1.09845i	0.816147	+	0.0604678i
$331$	−5.72839	−	5.72839i	−0.314861	−	0.314861i	0.531929	−	0.846789i	$-0.321467\pi$
$331$	−5.72839	−	5.72839i	−0.314861	−	0.314861i	−0.846789	+	0.531929i	$0.821467\pi$
$332$	−3.16981	−	3.16981i	−0.173966	−	0.173966i
$333$	1.58385	−	1.17942i	0.0867945	−	0.0646318i
$334$		−	0.864796i		−	0.0473195i
$335$	−0.469695	+	6.33957i	−0.0256622	+	0.346368i
$336$			1.49519i			0.0815694i
$337$	−5.31333	−	5.31333i	−0.289436	−	0.289436i	0.547421	−	0.836857i	$-0.315609\pi$
$337$	−5.31333	−	5.31333i	−0.289436	−	0.289436i	−0.836857	+	0.547421i	$0.815609\pi$
$338$			3.34633i			0.182016i
$339$	−15.3288	+	15.3288i	−0.832549	+	0.832549i
$340$	11.8117	+	13.7020i	0.640580	+	0.743096i
$341$	11.8106	+	11.8106i	0.639581	+	0.639581i
$342$	0.990930	−	0.990930i	0.0535834	−	0.0535834i
$343$	7.72788	+	7.72788i	0.417266	+	0.417266i
$344$	10.9160			0.588549
$345$	−2.34693	+	31.6770i	−0.126354	+	1.70543i
$346$	2.14973	+	2.14973i	0.115570	+	0.115570i
$347$		−	32.7620i		−	1.75876i	−0.476123	−	0.879379i	$-0.657958\pi$
$347$		−	32.7620i		−	1.75876i	0.476123	−	0.879379i	$-0.342042\pi$
$348$	−3.54488			−0.190026
$349$			14.0604i			0.752637i	0.926490	+	0.376318i	$0.122810\pi$
$349$			14.0604i			0.752637i	−0.926490	+	0.376318i	$0.877190\pi$
$350$	−3.29481	+	2.44030i	−0.176115	+	0.130439i
$351$	10.7173	−	10.7173i	0.572047	−	0.572047i
$352$	−3.64633			−0.194350
$353$	6.79098			0.361447			0.180724	−	0.983534i	$-0.442156\pi$
$353$	6.79098			0.361447			0.180724	+	0.983534i	$0.442156\pi$
$354$	−15.8943			−0.844773
$355$	0.00221331	+	0.00256752i	0.000117471	+	0.000136270i
$356$	−5.80016	−	5.80016i	−0.307408	−	0.307408i
$357$		−	12.0965i		−	0.640215i
$358$	−0.313292	+	0.313292i	−0.0165580	+	0.0165580i
$359$		−	4.91904i		−	0.259617i	−0.991539	−	0.129808i	$-0.958564\pi$
$359$		−	4.91904i		−	0.259617i	0.991539	−	0.129808i	$-0.0414362\pi$
$360$	−0.473980	−	0.549834i	−0.0249810	−	0.0289788i
$361$			0.366413i			0.0192849i
$362$			16.2161i			0.852300i
$363$	2.95992	−	2.95992i	0.155356	−	0.155356i
$364$	−1.80159	−	1.80159i	−0.0944289	−	0.0944289i
$365$	29.4158	+	2.17940i	1.53969	+	0.114075i
$366$	−22.4697			−1.17451
$367$	21.4924	−	21.4924i	1.12189	−	1.12189i	0.130436	−	0.991457i	$-0.458362\pi$
$367$	21.4924	−	21.4924i	1.12189	−	1.12189i	0.991457	−	0.130436i	$-0.0416378\pi$
$368$		−	7.79067i		−	0.406117i
$369$	3.02280			0.157361
$370$	−13.2758	−	2.95871i	−0.690174	−	0.153816i
$371$	0.517862			0.0268860
$372$		−	8.35226i		−	0.433045i
$373$	−19.5734	+	19.5734i	−1.01347	+	1.01347i	−0.0135632	+	0.999908i	$0.504317\pi$
$373$	−19.5734	+	19.5734i	−1.01347	+	1.01347i	−0.999908	+	0.0135632i	$0.995683\pi$
$374$	29.4998			1.52540
$375$	4.48584	−	19.8861i	0.231648	−	1.02692i
$376$	4.11794	+	4.11794i	0.212367	+	0.212367i
$377$	4.27130	−	4.27130i	0.219983	−	0.219983i
$378$		−	4.00017i		−	0.205746i
$379$		−	1.90775i		−	0.0979943i	−0.998799	−	0.0489972i	$-0.984397\pi$
$379$		−	1.90775i		−	0.0979943i	0.998799	−	0.0489972i	$-0.0156025\pi$
$380$	−9.62597	−	0.713182i	−0.493802	−	0.0365855i
$381$			35.8476i			1.83653i
$382$	−0.276686	+	0.276686i	−0.0141565	+	0.0141565i
$383$			12.0669i			0.616591i	0.951291	+	0.308295i	$0.0997585\pi$
$383$			12.0669i			0.616591i	−0.951291	+	0.308295i	$0.900241\pi$
$384$	1.28931	+	1.28931i	0.0657949	+	0.0657949i
$385$	−0.494007	+	6.66771i	−0.0251769	+	0.339818i
$386$	−8.78779			−0.447287
$387$	3.54382			0.180142
$388$	14.6206			0.742246
$389$	16.8015	−	16.8015i	0.851868	−	0.851868i	−0.138495	−	0.990363i	$-0.544227\pi$
$389$	16.8015	−	16.8015i	0.851868	−	0.851868i	0.990363	+	0.138495i	$0.0442266\pi$
$390$	12.6333	+	0.935990i	0.639710	+	0.0473957i
$391$			63.0286i			3.18749i
$392$	6.32757			0.319590
$393$			6.99450i			0.352826i
$394$	8.41487	+	8.41487i	0.423935	+	0.423935i
$395$	−2.39959	−	0.177784i	−0.120737	−	0.00894529i
$396$	−1.18377			−0.0594865
$397$	6.99419	+	6.99419i	0.351028	+	0.351028i	0.860492	−	0.509464i	$-0.170156\pi$
$397$	6.99419	+	6.99419i	0.351028	+	0.351028i	−0.509464	+	0.860492i	$0.670156\pi$
$398$	4.20114	−	4.20114i	0.210584	−	0.210584i
$399$	4.56384	+	4.56384i	0.228478	+	0.228478i
$400$	−0.736849	+	4.94541i	−0.0368425	+	0.247270i
$401$	0.759591	−	0.759591i	0.0379322	−	0.0379322i	−0.687886	−	0.725818i	$-0.741461\pi$
$401$	0.759591	−	0.759591i	0.0379322	−	0.0379322i	0.725818	+	0.687886i	$0.241461\pi$
$402$		−	5.18365i		−	0.258537i
$403$	10.0638	+	10.0638i	0.501315	+	0.501315i
$404$		−	3.68870i		−	0.183520i
$405$	14.4080	+	16.7138i	0.715939	+	0.830515i
$406$		−	1.59424i		−	0.0791207i
$407$	−17.7894	+	13.2469i	−0.881786	+	0.656625i
$408$	−10.4309	−	10.4309i	−0.516405	−	0.516405i
$409$	−22.0320	−	22.0320i	−1.08941	−	1.08941i	−0.995589	−	0.0938237i	$-0.970091\pi$
$409$	−22.0320	−	22.0320i	−1.08941	−	1.08941i	−0.0938237	−	0.995589i	$-0.529909\pi$
$410$	−13.5941	−	15.7696i	−0.671363	−	0.778805i
$411$		−	29.5302i		−	1.45662i
$412$	−11.1543			−0.549535
$413$		−	7.14814i		−	0.351737i
$414$		−	2.52921i		−	0.124304i
$415$	−0.740629	+	9.99642i	−0.0363560	+	0.490705i
$416$	−3.10704			−0.152335
$417$	−3.11274	+	3.11274i	−0.152432	+	0.152432i
$418$	−11.1299	+	11.1299i	−0.544379	+	0.544379i
$419$		−	13.7527i		−	0.671863i	−0.941886	−	0.335931i	$-0.890949\pi$
$419$		−	13.7527i		−	0.671863i	0.941886	−	0.335931i	$-0.109051\pi$
$420$	2.53232	−	2.18297i	0.123565	−	0.106518i
$421$	4.62725	−	4.62725i	0.225519	−	0.225519i	−0.585299	−	0.810818i	$-0.699023\pi$
$421$	4.62725	−	4.62725i	0.225519	−	0.225519i	0.810818	+	0.585299i	$0.199023\pi$
$422$		−	27.4901i		−	1.33820i
$423$	1.33687	+	1.33687i	0.0650010	+	0.0650010i
$424$	0.446555	−	0.446555i	0.0216866	−	0.0216866i
$425$	5.96131	−	40.0097i	0.289166	−	1.94075i
$426$	−0.00195457	−	0.00195457i	−9.46990e−5	−	9.46990e-5i
$427$		−	10.1053i		−	0.489028i
$428$	3.88311	−	3.88311i	0.187697	−	0.187697i
$429$	14.6070	−	14.6070i	0.705231	−	0.705231i
$430$	−15.9372	−	18.4877i	−0.768560	−	0.891557i
$431$	2.01292	−	2.01292i	0.0969591	−	0.0969591i	−0.656963	−	0.753922i	$-0.728159\pi$
$431$	2.01292	−	2.01292i	0.0969591	−	0.0969591i	0.753922	+	0.656963i	$0.228159\pi$
$432$	−3.44936	−	3.44936i	−0.165958	−	0.165958i
$433$	−23.2986	−	23.2986i	−1.11966	−	1.11966i	−0.991791	−	0.127870i	$-0.959186\pi$
$433$	−23.2986	−	23.2986i	−1.11966	−	1.11966i	−0.127870	−	0.991791i	$-0.540814\pi$
$434$	3.75626			0.180306
$435$	5.17549	+	6.00376i	0.248146	+	0.287858i
$436$	2.01583	−	2.01583i	0.0965407	−	0.0965407i
$437$	−23.7798	−	23.7798i	−1.13754	−	1.13754i
$438$	−24.0523			−1.14927
$439$	6.59762	+	6.59762i	0.314887	+	0.314887i	0.846800	−	0.531912i	$-0.178526\pi$
$439$	6.59762	+	6.59762i	0.314887	+	0.314887i	−0.531912	+	0.846800i	$0.678526\pi$
$440$	5.32361	+	6.17558i	0.253793	+	0.294409i
$441$	2.05422			0.0978199
$442$	25.1367			1.19563
$443$	28.2758	−	28.2758i	1.34343	−	1.34343i	0.450801	−	0.892625i	$-0.351138\pi$
$443$	28.2758	−	28.2758i	1.34343	−	1.34343i	0.892625	−	0.450801i	$-0.148862\pi$
$444$	10.9742	+	1.60617i	0.520810	+	0.0762256i
$445$	−1.35521	+	18.2916i	−0.0642432	+	0.867105i
$446$	9.42660	−	9.42660i	0.446363	−	0.446363i
$447$	5.19493	+	5.19493i	0.245712	+	0.245712i
$448$	−0.579841	+	0.579841i	−0.0273949	+	0.0273949i
$449$	−11.7576	+	11.7576i	−0.554876	+	0.554876i	−0.927844	−	0.372968i	$-0.878340\pi$
$449$	−11.7576	+	11.7576i	−0.554876	+	0.554876i	0.372968	+	0.927844i	$0.378340\pi$
$450$	−0.239215	+	1.60551i	−0.0112767	+	0.0756843i
$451$	−33.9512			−1.59870
$452$	−11.8892			−0.559220
$453$	−11.4306	−	11.4306i	−0.537057	−	0.537057i
$454$			17.9587i			0.842844i
$455$	−0.420942	+	5.68155i	−0.0197341	+	0.266355i
$456$	7.87084			0.368586
$457$	31.9954			1.49668			0.748341	−	0.663314i	$-0.230851\pi$
$457$	31.9954			1.49668			0.748341	+	0.663314i	$0.230851\pi$
$458$	18.1673			0.848901
$459$	27.9063	+	27.9063i	1.30255	+	1.30255i
$460$	−13.1946	+	11.3743i	−0.615202	+	0.530330i
$461$	−17.2203	−	17.2203i	−0.802031	−	0.802031i	0.181382	−	0.983413i	$-0.441943\pi$
$461$	−17.2203	−	17.2203i	−0.802031	−	0.802031i	−0.983413	+	0.181382i	$0.941943\pi$
$462$		−	5.45197i		−	0.253648i
$463$		−	13.3316i		−	0.619570i	−0.950807	−	0.309785i	$-0.899743\pi$
$463$		−	13.3316i		−	0.619570i	0.950807	−	0.309785i	$-0.100257\pi$
$464$	−1.37472	−	1.37472i	−0.0638197	−	0.0638197i
$465$	−14.1457	+	12.1942i	−0.655993	+	0.565494i
$466$	−2.23686	−	2.23686i	−0.103620	−	0.103620i
$467$	32.1997			1.49003			0.745013	−	0.667050i	$-0.232443\pi$
$467$	32.1997			1.49003			0.745013	+	0.667050i	$0.232443\pi$
$468$	−1.00869			−0.0466265
$469$	2.33124			0.107647
$470$	0.962160	−	12.9865i	0.0443811	−	0.599022i
$471$			17.7383i			0.817336i
$472$	−6.16388	−	6.16388i	−0.283715	−	0.283715i
$473$	−39.8032			−1.83015
$474$	1.96207			0.0901207
$475$	12.8460	+	17.3442i	0.589413	+	0.795806i
$476$	4.69107	−	4.69107i	0.215015	−	0.215015i
$477$	0.144972	−	0.144972i	0.00663782	−	0.00663782i
$478$	−4.53542	−	4.53542i	−0.207445	−	0.207445i
$479$	−10.6512	+	10.6512i	−0.486664	+	0.486664i	−0.907252	−	0.420588i	$-0.861824\pi$
$479$	−10.6512	+	10.6512i	−0.486664	+	0.486664i	0.420588	+	0.907252i	$0.361824\pi$
$480$	0.301249	−	4.06602i	0.0137501	−	0.185587i
$481$	−15.1583	+	11.2877i	−0.691159	+	0.514674i
$482$	−2.95256	+	2.95256i	−0.134486	+	0.134486i
$483$	11.6485			0.530027
$484$	2.29574			0.104352
$485$	−21.3459	−	24.7620i	−0.969267	−	1.12438i
$486$	−2.37553	−	2.37553i	−0.107756	−	0.107756i
$487$	17.1695			0.778022			0.389011	−	0.921233i	$-0.372817\pi$
$487$	17.1695			0.778022			0.389011	+	0.921233i	$0.372817\pi$
$488$	−8.71382	−	8.71382i	−0.394456	−	0.394456i
$489$	13.7612	−	13.7612i	0.622301	−	0.622301i
$490$	−9.23820	−	10.7166i	−0.417339	−	0.484128i
$491$	−9.04897			−0.408374			−0.204187	−	0.978932i	$-0.565455\pi$
$491$	−9.04897			−0.408374			−0.204187	+	0.978932i	$0.565455\pi$
$492$	12.0049	+	12.0049i	0.541221	+	0.541221i
$493$	11.1218	+	11.1218i	0.500902	+	0.500902i
$494$	−9.48374	+	9.48374i	−0.426694	+	0.426694i
$495$	1.72829	+	2.00488i	0.0776808	+	0.0901125i
$496$	3.23904	−	3.23904i	0.145437	−	0.145437i
$497$	0.000879026	0	0.000879026i	3.94297e−5	0	3.94297e-5i
$498$		−	8.17374i		−	0.366274i
$499$	8.81194	+	8.81194i	0.394477	+	0.394477i	0.876280	−	0.481803i	$-0.160018\pi$
$499$	8.81194	+	8.81194i	0.394477	+	0.394477i	−0.481803	+	0.876280i	$0.660018\pi$
$500$	9.45154	−	5.97229i	0.422686	−	0.267089i
$501$	1.11499	−	1.11499i	0.0498141	−	0.0498141i
$502$	−9.93109	−	9.93109i	−0.443246	−	0.443246i
$503$			13.2027i			0.588678i	0.955701	+	0.294339i	$0.0950995\pi$
$503$			13.2027i			0.588678i	−0.955701	+	0.294339i	$0.904900\pi$
$504$	−0.188243	+	0.188243i	−0.00838501	+	0.00838501i
$505$	−6.24734	+	5.38547i	−0.278003	+	0.239650i
$506$			28.4074i			1.26286i
$507$	−4.31446	+	4.31446i	−0.191612	+	0.191612i
$508$	−13.9019	+	13.9019i	−0.616795	+	0.616795i
$509$	−25.2057			−1.11722			−0.558612	−	0.829429i	$-0.688666\pi$
$509$	−25.2057			−1.11722			−0.558612	+	0.829429i	$0.688666\pi$
$510$	−2.43718	+	32.8951i	−0.107920	+	1.45662i
$511$		−	10.8170i		−	0.478518i
$512$			1.00000i			0.0441942i
$513$	−21.0573			−0.929701
$514$		−	15.1135i		−	0.666630i
$515$	16.2853	+	18.8915i	0.717614	+	0.832458i
$516$	14.0741	+	14.0741i	0.619576	+	0.619576i
$517$	−15.0154	−	15.0154i	−0.660376	−	0.660376i
$518$	−0.722344	+	4.93540i	−0.0317380	+	0.216849i
$519$			5.54335i			0.243326i
$520$	4.53625	+	5.26221i	0.198928	+	0.230763i
$521$		−	8.65279i		−	0.379086i	−0.981872	−	0.189543i	$-0.939299\pi$
$521$		−	8.65279i		−	0.379086i	0.981872	−	0.189543i	$-0.0607006\pi$
$522$	−0.446297	−	0.446297i	−0.0195339	−	0.0195339i
$523$		−	28.4569i		−	1.24433i	−0.782884	−	0.622167i	$-0.786252\pi$
$523$		−	28.4569i		−	1.24433i	0.782884	−	0.622167i	$-0.213748\pi$
$524$	−2.71250	+	2.71250i	−0.118496	+	0.118496i
$525$	−7.39433	−	1.10173i	−0.322715	−	0.0480835i
$526$	−9.74250	−	9.74250i	−0.424793	−	0.424793i
$527$	−26.2047	+	26.2047i	−1.14149	+	1.14149i
$528$	−4.70126	−	4.70126i	−0.204596	−	0.204596i
$529$	−37.6945			−1.63889
$530$	−1.40827	−	0.104338i	−0.0611713	−	0.00453215i
$531$	−2.00108	−	2.00108i	−0.0868393	−	0.0868393i
$532$			3.53975i			0.153468i
$533$	−28.9298			−1.25309
$534$		−	14.9564i		−	0.647228i
$535$	−12.2459	−	0.907292i	−0.529437	−	0.0392256i
$536$	2.01024	−	2.01024i	0.0868292	−	0.0868292i
$537$	−0.807861			−0.0348618
$538$	6.43418			0.277397
$539$	−23.0724			−0.993799
$540$	−0.805947	+	10.8780i	−0.0346824	+	0.468116i
$541$	22.0757	+	22.0757i	0.949106	+	0.949106i	0.998766	−	0.0496598i	$-0.0158137\pi$
$541$	22.0757	+	22.0757i	0.949106	+	0.949106i	−0.0496598	+	0.998766i	$0.515814\pi$
$542$		−	25.6662i		−	1.10246i
$543$	−20.9076	+	20.9076i	−0.897231	+	0.897231i
$544$		−	8.09027i		−	0.346867i
$545$	−6.35719	−	0.471000i	−0.272312	−	0.0201754i
$546$		−	4.64561i		−	0.198814i
$547$			24.7795i			1.05949i	0.848155	+	0.529747i	$0.177713\pi$
$547$			24.7795i			1.05949i	−0.848155	+	0.529747i	$0.822287\pi$
$548$	11.4519	−	11.4519i	0.489203	−	0.489203i
$549$	−2.82891	−	2.82891i	−0.120735	−	0.120735i
$550$	2.68680	−	18.0326i	0.114565	−	0.768913i
$551$	−8.39222			−0.357521
$552$	10.0446	−	10.0446i	0.427526	−	0.427526i
$553$			0.882399i			0.0375234i
$554$	−17.2625			−0.733415
$555$	−13.3019	−	20.9313i	−0.564634	−	0.888484i
$556$	−2.41427			−0.102388
$557$			28.3582i			1.20157i	0.799409	+	0.600787i	$0.205146\pi$
$557$			28.3582i			1.20157i	−0.799409	+	0.600787i	$0.794854\pi$
$558$	1.05154	−	1.05154i	0.0445153	−	0.0445153i
$559$	−33.9163			−1.43451
$560$	1.82861	+	0.135480i	0.0772728	+	0.00572509i
$561$	38.0344	+	38.0344i	1.60581	+	1.60581i
$562$	3.84098	−	3.84098i	0.162022	−	0.162022i
$563$		−	16.8486i		−	0.710085i	−0.934850	−	0.355043i	$-0.884466\pi$
$563$		−	16.8486i		−	0.710085i	0.934850	−	0.355043i	$-0.115534\pi$
$564$			10.6186i			0.447124i
$565$	17.3581	+	20.1360i	0.730261	+	0.847128i
$566$			20.5564i			0.864049i
$567$	5.72219	−	5.72219i	0.240309	−	0.240309i
$568$		−	0.00151598i		−	6.36090e-5i
$569$	−4.89447	−	4.89447i	−0.205187	−	0.205187i	0.597031	−	0.802218i	$-0.296347\pi$
$569$	−4.89447	−	4.89447i	−0.205187	−	0.205187i	−0.802218	+	0.597031i	$0.796347\pi$
$570$	−11.4914	−	13.3304i	−0.481320	−	0.558348i
$571$	−38.8520			−1.62590			−0.812952	−	0.582330i	$-0.802141\pi$
$571$	−38.8520			−1.62590			−0.812952	+	0.582330i	$0.802141\pi$
$572$	11.3293			0.473701
$573$	−0.713470			−0.0298056
$574$	−5.39894	+	5.39894i	−0.225347	+	0.225347i
$575$	38.5280	+	5.74055i	1.60673	+	0.239397i
$576$			0.324646i			0.0135269i
$577$	−18.6556			−0.776642			−0.388321	−	0.921524i	$-0.626945\pi$
$577$	−18.6556			−0.776642			−0.388321	+	0.921524i	$0.626945\pi$
$578$			48.4524i			2.01535i
$579$	−11.3302	−	11.3302i	−0.470867	−	0.470867i
$580$	−0.321204	+	4.33536i	−0.0133373	+	0.180016i
$581$	3.67597			0.152505
$582$	18.8504	+	18.8504i	0.781376	+	0.781376i
$583$	−1.62829	+	1.62829i	−0.0674368	+	0.0674368i
$584$	−9.32759	−	9.32759i	−0.385979	−	0.385979i
$585$	1.47267	+	1.70835i	0.0608876	+	0.0706317i
$586$	11.2671	−	11.2671i	0.465441	−	0.465441i
$587$			5.75904i			0.237701i	0.992912	+	0.118851i	$0.0379209\pi$
$587$			5.75904i			0.237701i	−0.992912	+	0.118851i	$0.962079\pi$
$588$	8.15820	+	8.15820i	0.336439	+	0.336439i
$589$		−	19.7733i		−	0.814746i
$590$	−1.44019	+	19.4386i	−0.0592919	+	0.800275i
$591$			21.6988i			0.892568i
$592$	3.63294	+	4.87870i	0.149313	+	0.200513i
$593$	−16.3572	−	16.3572i	−0.671709	−	0.671709i	0.286401	−	0.958110i	$-0.407541\pi$
$593$	−16.3572	−	16.3572i	−0.671709	−	0.671709i	−0.958110	+	0.286401i	$0.907541\pi$
$594$	12.5775	+	12.5775i	0.516062	+	0.516062i
$595$	−14.7939	−	1.09607i	−0.606492	−	0.0449346i
$596$			4.02923i			0.165044i
$597$	10.8332			0.443372
$598$			24.2059i			0.989852i
$599$			23.6157i			0.964910i	0.875921	+	0.482455i	$0.160255\pi$
$599$			23.6157i			0.964910i	−0.875921	+	0.482455i	$0.839745\pi$
$600$	−7.32620	+	5.42614i	−0.299091	+	0.221521i
$601$	30.4617			1.24256			0.621279	−	0.783589i	$-0.286613\pi$
$601$	30.4617			1.24256			0.621279	+	0.783589i	$0.286613\pi$
$602$	−6.32952	+	6.32952i	−0.257972	+	0.257972i
$603$	0.652617	−	0.652617i	0.0265766	−	0.0265766i
$604$		−	8.86568i		−	0.360739i
$605$	−3.35176	−	3.88816i	−0.136268	−	0.158076i
$606$	4.75588	−	4.75588i	0.193195	−	0.193195i
$607$			17.6781i			0.717530i	0.933428	+	0.358765i	$0.116802\pi$
$607$			17.6781i			0.717530i	−0.933428	+	0.358765i	$0.883198\pi$
$608$	3.05234	+	3.05234i	0.123789	+	0.123789i
$609$	2.05547	−	2.05547i	0.0832918	−	0.0832918i
$610$	−2.03599	+	27.4802i	−0.0824349	+	1.11264i
$611$	−12.7946	−	12.7946i	−0.517614	−	0.517614i
$612$		−	2.62647i		−	0.106169i
$613$	24.9613	−	24.9613i	1.00818	−	1.00818i	0.00821132	−	0.999966i	$-0.497386\pi$
$613$	24.9613	−	24.9613i	1.00818	−	1.00818i	0.999966	−	0.00821132i	$-0.00261377\pi$
$614$	9.43686	−	9.43686i	0.380841	−	0.380841i
$615$	2.80494	−	37.8589i	0.113106	−	1.52662i
$616$	2.11429	−	2.11429i	0.0851873	−	0.0851873i
$617$	6.37297	+	6.37297i	0.256566	+	0.256566i	0.823656	−	0.567090i	$-0.191931\pi$
$617$	6.37297	+	6.37297i	0.256566	+	0.256566i	−0.567090	+	0.823656i	$0.691931\pi$
$618$	−14.3814	−	14.3814i	−0.578506	−	0.578506i
$619$	2.43520			0.0978789			0.0489394	−	0.998802i	$-0.484416\pi$
$619$	2.43520			0.0978789			0.0489394	+	0.998802i	$0.484416\pi$
$620$	−10.2148	−	0.756805i	−0.410234	−	0.0303940i
$621$	−26.8729	+	26.8729i	−1.07837	+	1.07837i
$622$	6.70368	+	6.70368i	0.268793	+	0.268793i
$623$	6.72635			0.269485
$624$	−4.00594	−	4.00594i	−0.160366	−	0.160366i
$625$	−23.9141	−	7.28804i	−0.956564	−	0.291522i
$626$	23.2157			0.927885
$627$	−28.6997			−1.14616
$628$	−6.87897	+	6.87897i	−0.274501	+	0.274501i
$629$	−29.3915	−	39.4700i	−1.17191	−	1.57377i
$630$	0.593650	+	0.0439832i	0.0236516	+	0.00175233i
$631$	8.01035	−	8.01035i	0.318887	−	0.318887i	−0.529453	−	0.848340i	$-0.677603\pi$
$631$	8.01035	−	8.01035i	0.318887	−	0.318887i	0.848340	+	0.529453i	$0.177603\pi$
$632$	0.760897	+	0.760897i	0.0302669	+	0.0302669i
$633$	35.4433	−	35.4433i	1.40874	−	1.40874i
$634$	−15.3696	+	15.3696i	−0.610406	+	0.610406i
$635$	43.8414	+	3.24818i	1.73979	+	0.128900i
$636$	1.15150			0.0456598
$637$	−19.6600			−0.778957
$638$	5.01268	+	5.01268i	0.198454	+	0.198454i
$639$		0	0.000492156i		0	1.94694e-5i
$640$	1.69364	−	1.45999i	0.0669471	−	0.0577112i
$641$	20.0552			0.792134			0.396067	−	0.918222i	$-0.370375\pi$
$641$	20.0552			0.792134			0.396067	+	0.918222i	$0.370375\pi$
$642$	10.0131			0.395184
$643$	−2.02458			−0.0798417			−0.0399208	−	0.999203i	$-0.512711\pi$
$643$	−2.02458			−0.0798417			−0.0399208	+	0.999203i	$0.512711\pi$
$644$	4.51735	+	4.51735i	0.178009	+	0.178009i
$645$	3.28842	−	44.3844i	0.129481	−	1.74764i
$646$	−24.6943	−	24.6943i	−0.971583	−	0.971583i
$647$		−	37.8245i		−	1.48703i	−0.668717	−	0.743517i	$-0.733156\pi$
$647$		−	37.8245i		−	1.48703i	0.668717	−	0.743517i	$-0.266844\pi$
$648$		−	9.86854i		−	0.387673i
$649$	22.4755	+	22.4755i	0.882242	+	0.882242i
$650$	2.28942	−	15.3656i	0.0897983	−	0.602687i
$651$	4.84299	+	4.84299i	0.189812	+	0.189812i
$652$	10.6733			0.417997
$653$	24.2252			0.948006			0.474003	−	0.880523i	$-0.342808\pi$
$653$	24.2252			0.948006			0.474003	+	0.880523i	$0.342808\pi$
$654$	5.19806			0.203260
$655$	8.55422	+	0.633777i	0.334241	+	0.0247637i
$656$			9.31106i			0.363536i
$657$	−3.02816	−	3.02816i	−0.118140	−	0.118140i
$658$	−4.77550			−0.186169
$659$	−16.7841			−0.653814			−0.326907	−	0.945056i	$-0.606006\pi$
$659$	−16.7841			−0.653814			−0.326907	+	0.945056i	$0.606006\pi$
$660$	−1.09845	+	14.8260i	−0.0427572	+	0.577103i
$661$	2.96671	−	2.96671i	0.115392	−	0.115392i	−0.647053	−	0.762445i	$-0.723999\pi$
$661$	2.96671	−	2.96671i	0.115392	−	0.115392i	0.762445	+	0.647053i	$0.223999\pi$
$662$	5.72839	−	5.72839i	0.222640	−	0.222640i
$663$	32.4091	+	32.4091i	1.25866	+	1.25866i
$664$	3.16981	−	3.16981i	0.123012	−	0.123012i
$665$	5.99507	−	5.16800i	0.232479	−	0.200407i
$666$	1.17942	+	1.58385i	0.0457016	+	0.0613730i
$667$	−10.7100	+	10.7100i	−0.414692	+	0.414692i
$668$	0.864796			0.0334600
$669$	24.3077			0.939788
$670$	−6.33957	−	0.469695i	−0.244919	−	0.0181459i
$671$	31.7735	+	31.7735i	1.22660	+	1.22660i
$672$	−1.49519			−0.0576783
$673$	23.2071	+	23.2071i	0.894567	+	0.894567i	0.994949	−	0.100382i	$-0.0320066\pi$
$673$	23.2071	+	23.2071i	0.894567	+	0.894567i	−0.100382	+	0.994949i	$0.532007\pi$
$674$	5.31333	−	5.31333i	0.204662	−	0.204662i
$675$	19.6002	−	14.5168i	0.754411	−	0.558754i
$676$	−3.34633			−0.128705
$677$	−4.70869	−	4.70869i	−0.180970	−	0.180970i	0.610809	−	0.791778i	$-0.290844\pi$
$677$	−4.70869	−	4.70869i	−0.180970	−	0.180970i	−0.791778	+	0.610809i	$0.790844\pi$
$678$	−15.3288	−	15.3288i	−0.588701	−	0.588701i
$679$	−8.47761	+	8.47761i	−0.325341	+	0.325341i
$680$	−13.7020	+	11.8117i	−0.525448	+	0.452959i
$681$	−23.1544	+	23.1544i	−0.887277	+	0.887277i
$682$	−11.8106	+	11.8106i	−0.452252	+	0.452252i
$683$		−	46.0160i		−	1.76075i	−0.474277	−	0.880376i	$-0.657290\pi$
$683$		−	46.0160i		−	1.76075i	0.474277	−	0.880376i	$-0.342710\pi$
$684$	0.990930	+	0.990930i	0.0378892	+	0.0378892i
$685$	−36.1152	−	2.67576i	−1.37989	−	0.102235i
$686$	−7.72788	+	7.72788i	−0.295052	+	0.295052i
$687$	23.4233	+	23.4233i	0.893653	+	0.893653i
$688$			10.9160i			0.416167i
$689$	−1.38746	+	1.38746i	−0.0528581	+	0.0528581i
$690$	−31.6770	−	2.34693i	−1.20592	−	0.0893460i
$691$		−	37.9434i		−	1.44344i	−0.692187	−	0.721718i	$-0.743353\pi$
$691$		−	37.9434i		−	1.44344i	0.692187	−	0.721718i	$-0.256647\pi$
$692$	−2.14973	+	2.14973i	−0.0817206	+	0.0817206i
$693$	0.686397	−	0.686397i	0.0260741	−	0.0260741i
$694$	32.7620			1.24363
$695$	3.52481	+	4.08890i	0.133704	+	0.155101i
$696$		−	3.54488i		−	0.134368i
$697$		−	75.3290i		−	2.85329i
$698$	−14.0604			−0.532194
$699$		−	5.76801i		−	0.218166i
$700$	−2.44030	−	3.29481i	−0.0922345	−	0.124532i
$701$	11.9143	+	11.9143i	0.449995	+	0.449995i	0.895353	−	0.445358i	$-0.146923\pi$
$701$	11.9143	+	11.9143i	0.449995	+	0.449995i	−0.445358	+	0.895353i	$0.646923\pi$
$702$	10.7173	+	10.7173i	0.404498	+	0.404498i
$703$	25.9805	+	3.80249i	0.979871	+	0.143414i
$704$		−	3.64633i		−	0.137426i
$705$	17.9841	−	15.5031i	0.677322	−	0.583880i
$706$			6.79098i			0.255582i
$707$	2.13886	+	2.13886i	0.0804402	+	0.0804402i
$708$		−	15.8943i		−	0.597345i
$709$	13.4491	−	13.4491i	0.505093	−	0.505093i	−0.407923	−	0.913016i	$-0.633747\pi$
$709$	13.4491	−	13.4491i	0.505093	−	0.505093i	0.913016	+	0.407923i	$0.133747\pi$
$710$	−0.00256752	+	0.00221331i	−9.63574e−5	+	8.30642e-5i
$711$	0.247022	+	0.247022i	0.00926405	+	0.00926405i
$712$	5.80016	−	5.80016i	0.217370	−	0.217370i
$713$	−25.2343	−	25.2343i	−0.945032	−	0.945032i
$714$	12.0965			0.452700
$715$	−16.5407	−	19.1878i	−0.618586	−	0.717582i
$716$	−0.313292	−	0.313292i	−0.0117083	−	0.0117083i
$717$		−	11.6951i		−	0.436763i
$718$	4.91904			0.183577
$719$		−	15.0482i		−	0.561204i	−0.959824	−	0.280602i	$-0.909466\pi$
$719$		−	15.0482i		−	0.561204i	0.959824	−	0.280602i	$-0.0905342\pi$
$720$	0.549834	−	0.473980i	0.0204911	−	0.0176642i
$721$	6.46775	−	6.46775i	0.240872	−	0.240872i
$722$	−0.366413			−0.0136365
$723$	−7.61354			−0.283151
$724$	−16.2161			−0.602667
$725$	7.81150	−	5.78558i	0.290112	−	0.214871i
$726$	2.95992	+	2.95992i	0.109853	+	0.109853i
$727$			48.0498i			1.78207i	0.453938	+	0.891033i	$0.350019\pi$
$727$			48.0498i			1.78207i	−0.453938	+	0.891033i	$0.649981\pi$
$728$	1.80159	−	1.80159i	0.0667713	−	0.0667713i
$729$			23.4800i			0.869631i
$730$	−2.17940	+	29.4158i	−0.0806632	+	1.08873i
$731$		−	88.3130i		−	3.26637i
$732$		−	22.4697i		−	0.830502i
$733$	−17.9391	+	17.9391i	−0.662596	+	0.662596i	−0.955991	−	0.293395i	$-0.905215\pi$
$733$	−17.9391	+	17.9391i	−0.662596	+	0.662596i	0.293395	+	0.955991i	$0.405215\pi$
$734$	21.4924	+	21.4924i	0.793298	+	0.793298i
$735$	1.90617	−	25.7280i	0.0703102	−	0.948991i
$736$	7.79067			0.287168
$737$	−7.33001	+	7.33001i	−0.270004	+	0.270004i
$738$			3.02280i			0.111271i
$739$	−27.0049			−0.993391			−0.496696	−	0.867925i	$-0.665453\pi$
$739$	−27.0049			−0.993391			−0.496696	+	0.867925i	$0.665453\pi$
$740$	2.95871	−	13.2758i	0.108764	−	0.488027i
$741$	−24.4550			−0.898376
$742$			0.517862i			0.0190113i
$743$	−21.8683	+	21.8683i	−0.802270	+	0.802270i	−0.983450	−	0.181180i	$-0.942008\pi$
$743$	−21.8683	+	21.8683i	−0.802270	+	0.802270i	0.181180	+	0.983450i	$0.442008\pi$
$744$	8.35226			0.306209
$745$	6.82408	−	5.88265i	0.250015	−	0.215523i
$746$	−19.5734	−	19.5734i	−0.716632	−	0.716632i
$747$	1.02907	−	1.02907i	0.0376515	−	0.0376515i
$748$			29.4998i			1.07862i
$749$			4.50318i			0.164542i
$750$	19.8861	+	4.48584i	0.726139	+	0.163800i
$751$			17.0169i			0.620957i	0.950580	+	0.310479i	$0.100489\pi$
$751$			17.0169i			0.620957i	−0.950580	+	0.310479i	$0.899511\pi$
$752$	−4.11794	+	4.11794i	−0.150166	+	0.150166i
$753$		−	25.6085i		−	0.933227i
$754$	4.27130	+	4.27130i	0.155552	+	0.155552i
$755$	−15.0153	+	12.9438i	−0.546462	+	0.471074i
$756$	4.00017			0.145485
$757$	31.0722			1.12934			0.564669	−	0.825317i	$-0.309004\pi$
$757$	31.0722			1.12934			0.564669	+	0.825317i	$0.309004\pi$
$758$	1.90775			0.0692925
$759$	−36.6259	+	36.6259i	−1.32944	+	1.32944i
$760$	0.713182	−	9.62597i	0.0258698	−	0.349171i
$761$		−	14.8739i		−	0.539180i	−0.962975	−	0.269590i	$-0.913112\pi$
$761$		−	14.8739i		−	0.539180i	0.962975	−	0.269590i	$-0.0868882\pi$
$762$	−35.8476			−1.29862
$763$			2.33772i			0.0846312i
$764$	−0.276686	−	0.276686i	−0.0100102	−	0.0100102i
$765$	−4.44830	+	3.83463i	−0.160829	+	0.138641i
$766$	−12.0669			−0.435996
$767$	19.1514	+	19.1514i	0.691516	+	0.691516i
$768$	−1.28931	+	1.28931i	−0.0465240	+	0.0465240i
$769$	−21.6211	−	21.6211i	−0.779677	−	0.779677i	0.200099	−	0.979776i	$-0.435874\pi$
$769$	−21.6211	−	21.6211i	−0.779677	−	0.779677i	−0.979776	+	0.200099i	$0.935874\pi$
$770$	−6.66771	−	0.494007i	−0.240288	−	0.0178028i
$771$	19.4861	−	19.4861i	0.701773	−	0.701773i
$772$		−	8.78779i		−	0.316279i
$773$	8.11195	+	8.11195i	0.291766	+	0.291766i	0.837778	−	0.546011i	$-0.183854\pi$
$773$	8.11195	+	8.11195i	0.291766	+	0.291766i	−0.546011	+	0.837778i	$0.683854\pi$
$774$			3.54382i			0.127380i
$775$	13.6317	+	18.4051i	0.489665	+	0.661129i
$776$			14.6206i			0.524847i
$777$	−7.29460	+	5.43194i	−0.261692	+	0.194870i
$778$	16.8015	+	16.8015i	0.602361	+	0.602361i
$779$	28.4205	+	28.4205i	1.01827	+	1.01827i
$780$	−0.935990	+	12.6333i	−0.0335138	+	0.452343i
$781$			0.00552776i			0.000197799i
$782$	−63.0286			−2.25390
$783$			9.48381i			0.338924i
$784$			6.32757i			0.225985i
$785$	21.6937	+	1.60728i	0.774283	+	0.0573662i
$786$	−6.99450			−0.249486
$787$	−25.9363	+	25.9363i	−0.924530	+	0.924530i	−0.997345	−	0.0728158i	$-0.976801\pi$
$787$	−25.9363	+	25.9363i	−0.924530	+	0.924530i	0.0728158	+	0.997345i	$0.476801\pi$
$788$	−8.41487	+	8.41487i	−0.299767	+	0.299767i
$789$		−	25.1222i		−	0.894375i
$790$	0.177784	−	2.39959i	0.00632528	−	0.0853736i
$791$	6.89384	−	6.89384i	0.245117	−	0.245117i
$792$		−	1.18377i		−	0.0420633i
$793$	27.0742	+	27.0742i	0.961432	+	0.961432i
$794$	−6.99419	+	6.99419i	−0.248214	+	0.248214i
$795$	−1.68117	−	1.95022i	−0.0596251	−	0.0691673i
$796$	4.20114	+	4.20114i	0.148906	+	0.148906i
$797$		−	7.46766i		−	0.264518i	−0.991215	−	0.132259i	$-0.957777\pi$
$797$		−	7.46766i		−	0.264518i	0.991215	−	0.132259i	$-0.0422230\pi$
$798$	−4.56384	+	4.56384i	−0.161558	+	0.161558i
$799$	33.3152	−	33.3152i	1.17861	−	1.17861i
$800$	−4.94541	−	0.736849i	−0.174847	−	0.0260516i
$801$	1.88300	−	1.88300i	0.0665325	−	0.0665325i
$802$	0.759591	+	0.759591i	0.0268221	+	0.0268221i
$803$	34.0115	+	34.0115i	1.20024	+	1.20024i
$804$	5.18365			0.182813
$805$	1.05548	−	14.2461i	0.0372009	−	0.502108i
$806$	−10.0638	+	10.0638i	−0.354483	+	0.354483i
$807$	8.29566	+	8.29566i	0.292021	+	0.292021i
$808$	3.68870			0.129768
$809$	−13.5592	−	13.5592i	−0.476716	−	0.476716i	0.427364	−	0.904080i	$-0.359442\pi$
$809$	−13.5592	−	13.5592i	−0.476716	−	0.476716i	−0.904080	+	0.427364i	$0.859442\pi$
$810$	−16.7138	+	14.4080i	−0.587262	+	0.506245i
$811$	−19.5616			−0.686901			−0.343450	−	0.939171i	$-0.611596\pi$
$811$	−19.5616			−0.686901			−0.343450	+	0.939171i	$0.611596\pi$
$812$	1.59424			0.0559468
$813$	33.0918	−	33.0918i	1.16058	−	1.16058i
$814$	−13.2469	−	17.7894i	−0.464304	−	0.623517i
$815$	−15.5829	−	18.0767i	−0.545844	−	0.633199i
$816$	10.4309	−	10.4309i	0.365153	−	0.365153i
$817$	33.3192	+	33.3192i	1.16569	+	1.16569i
$818$	22.0320	−	22.0320i	0.770331	−	0.770331i
$819$	0.584878	−	0.584878i	0.0204373	−	0.0204373i
$820$	15.7696	−	13.5941i	0.550699	−	0.474726i
$821$	−3.12570			−0.109088			−0.0545438	−	0.998511i	$-0.517370\pi$
$821$	−3.12570			−0.109088			−0.0545438	+	0.998511i	$0.517370\pi$
$822$	29.5302			1.02999
$823$	−19.9647	−	19.9647i	−0.695926	−	0.695926i	0.267603	−	0.963529i	$-0.413768\pi$
$823$	−19.9647	−	19.9647i	−0.695926	−	0.695926i	−0.963529	+	0.267603i	$0.913768\pi$
$824$		−	11.1543i		−	0.388580i
$825$	26.7137	−	19.7855i	0.930053	−	0.688843i
$826$	7.14814			0.248716
$827$	18.4817			0.642673			0.321336	−	0.946965i	$-0.395868\pi$
$827$	18.4817			0.642673			0.321336	+	0.946965i	$0.395868\pi$
$828$	2.52921			0.0878961
$829$	21.6955	+	21.6955i	0.753515	+	0.753515i	0.975134	−	0.221618i	$-0.0711338\pi$
$829$	21.6955	+	21.6955i	0.753515	+	0.753515i	−0.221618	+	0.975134i	$0.571134\pi$
$830$	−9.99642	−	0.740629i	−0.346981	−	0.0257076i
$831$	−22.2568	−	22.2568i	−0.772079	−	0.772079i
$832$		−	3.10704i		−	0.107717i
$833$		−	51.1917i		−	1.77369i
$834$	−3.11274	−	3.11274i	−0.107785	−	0.107785i
$835$	−1.26260	−	1.46466i	−0.0436939	−	0.0506865i
$836$	−11.1299	−	11.1299i	−0.384934	−	0.384934i
$837$	−22.3453			−0.772365
$838$	13.7527			0.475079
$839$	−35.7782			−1.23520			−0.617600	−	0.786492i	$-0.711895\pi$
$839$	−35.7782			−1.23520			−0.617600	+	0.786492i	$0.711895\pi$
$840$	2.18297	+	2.53232i	0.0753195	+	0.0873733i
$841$		−	25.2203i		−	0.869665i
$842$	4.62725	+	4.62725i	0.159466	+	0.159466i
$843$	9.90444			0.341127
$844$	27.4901			0.946248
$845$	4.88561	+	5.66748i	0.168070	+	0.194967i
$846$	−1.33687	+	1.33687i	−0.0459626	+	0.0459626i
$847$	−1.33117	+	1.33117i	−0.0457394	+	0.0457394i
$848$	0.446555	+	0.446555i	0.0153348	+	0.0153348i
$849$	−26.5036	+	26.5036i	−0.909600	+	0.909600i
$850$	40.0097	+	5.96131i	1.37232	+	0.204471i
$851$	38.0084	−	28.3030i	1.30291	−	0.970216i
$852$	0.00195457	−	0.00195457i	6.69623e−5	−	6.69623e-5i
$853$	37.5829			1.28681			0.643407	−	0.765524i	$-0.277520\pi$
$853$	37.5829			1.28681			0.643407	+	0.765524i	$0.277520\pi$
$854$	10.1053			0.345795
$855$	0.231532	−	3.12503i	0.00791822	−	0.106874i
$856$	3.88311	+	3.88311i	0.132722	+	0.132722i
$857$	−24.8711			−0.849581			−0.424791	−	0.905292i	$-0.639652\pi$
$857$	−24.8711			−0.849581			−0.424791	+	0.905292i	$0.639652\pi$
$858$	14.6070	+	14.6070i	0.498674	+	0.498674i
$859$	15.0119	−	15.0119i	0.512199	−	0.512199i	−0.403000	−	0.915200i	$-0.632033\pi$
$859$	15.0119	−	15.0119i	0.512199	−	0.512199i	0.915200	+	0.403000i	$0.132033\pi$
$860$	18.4877	−	15.9372i	0.630426	−	0.543454i
$861$	−13.9218			−0.474454
$862$	2.01292	+	2.01292i	0.0685605	+	0.0685605i
$863$	28.2484	+	28.2484i	0.961586	+	0.961586i	0.999289	−	0.0377026i	$-0.0120039\pi$
$863$	28.2484	+	28.2484i	0.961586	+	0.961586i	−0.0377026	+	0.999289i	$0.512004\pi$
$864$	3.44936	−	3.44936i	0.117350	−	0.117350i
$865$	6.77948	+	0.502287i	0.230509	+	0.0170783i
$866$	23.2986	−	23.2986i	0.791720	−	0.791720i
$867$	−62.4702	+	62.4702i	−2.12160	+	2.12160i
$868$			3.75626i			0.127496i
$869$	−2.77448	−	2.77448i	−0.0941179	−	0.0941179i
$870$	−6.00376	+	5.17549i	−0.203546	+	0.175466i
$871$	−6.24589	+	6.24589i	−0.211634	+	0.211634i
$872$	2.01583	+	2.01583i	0.0682646	+	0.0682646i
$873$			4.74650i			0.160645i
$874$	23.7798	−	23.7798i	0.804363	−	0.804363i
$875$	−2.01741	+	8.94338i	−0.0682010	+	0.302341i
$876$		−	24.0523i		−	0.812653i
$877$	20.7098	−	20.7098i	0.699322	−	0.699322i	−0.264943	−	0.964264i	$-0.585353\pi$
$877$	20.7098	−	20.7098i	0.699322	−	0.699322i	0.964264	+	0.264943i	$0.0853530\pi$
$878$	−6.59762	+	6.59762i	−0.222659	+	0.222659i
$879$	29.0537			0.979955
$880$	−6.17558	+	5.32361i	−0.208179	+	0.179459i
$881$		−	2.51776i		−	0.0848254i	−0.999100	−	0.0424127i	$-0.986496\pi$
$881$		−	2.51776i		−	0.0848254i	0.999100	−	0.0424127i	$-0.0135044\pi$
$882$			2.05422i			0.0691691i
$883$	8.49437			0.285858			0.142929	−	0.989733i	$-0.454348\pi$
$883$	8.49437			0.285858			0.142929	+	0.989733i	$0.454348\pi$
$884$			25.1367i			0.845440i
$885$	−26.9193	+	23.2056i	−0.904881	+	0.780046i
$886$	28.2758	+	28.2758i	0.949945	+	0.949945i
$887$	−13.0043	−	13.0043i	−0.436643	−	0.436643i	0.454238	−	0.890881i	$-0.349912\pi$
$887$	−13.0043	−	13.0043i	−0.436643	−	0.436643i	−0.890881	+	0.454238i	$0.849912\pi$
$888$	−1.60617	+	10.9742i	−0.0538996	+	0.368269i
$889$		−	16.1217i		−	0.540706i
$890$	−18.2916	−	1.35521i	−0.613136	−	0.0454268i
$891$			35.9840i			1.20551i
$892$	9.42660	+	9.42660i	0.315626	+	0.315626i
$893$			25.1387i			0.841235i
$894$	−5.19493	+	5.19493i	−0.173745	+	0.173745i
$895$	−0.0732008	+	0.988007i	−0.00244683	+	0.0330254i
$896$	−0.579841	−	0.579841i	−0.0193711	−	0.0193711i
$897$	−31.2089	+	31.2089i	−1.04204	+	1.04204i
$898$	−11.7576	−	11.7576i	−0.392357	−	0.392357i
$899$	−8.90554			−0.297016
$900$	−1.60551	−	0.239215i	−0.0535169	−	0.00797383i
$901$	−3.61275	−	3.61275i	−0.120358	−	0.120358i
$902$		−	33.9512i		−	1.13045i
$903$	−16.3214			−0.543144
$904$		−	11.8892i		−	0.395428i
$905$	23.6754	+	27.4643i	0.786996	+	0.912944i
$906$	11.4306	−	11.4306i	0.379757	−	0.379757i
$907$	39.4216			1.30897			0.654487	−	0.756074i	$-0.272885\pi$
$907$	39.4216			1.30897			0.654487	+	0.756074i	$0.272885\pi$
$908$	−17.9587			−0.595981
$909$	1.19752			0.0397193
$910$	−5.68155	−	0.420942i	−0.188342	−	0.0139541i
$911$	−10.3558	−	10.3558i	−0.343105	−	0.343105i	0.514429	−	0.857533i	$-0.328004\pi$
$911$	−10.3558	−	10.3558i	−0.343105	−	0.343105i	−0.857533	+	0.514429i	$0.828004\pi$
$912$			7.87084i			0.260629i
$913$	−11.5582	+	11.5582i	−0.382520	+	0.382520i
$914$			31.9954i			1.05831i
$915$	−38.0556	+	32.8055i	−1.25808	+	1.08452i
$916$			18.1673i			0.600264i
$917$		−	3.14564i		−	0.103878i
$918$	−27.9063	+	27.9063i	−0.921044	+	0.921044i
$919$	−21.8092	−	21.8092i	−0.719419	−	0.719419i	0.249068	−	0.968486i	$-0.419876\pi$
$919$	−21.8092	−	21.8092i	−0.719419	−	0.719419i	−0.968486	+	0.249068i	$0.919876\pi$
$920$	−11.3743	−	13.1946i	−0.375000	−	0.435013i
$921$	24.3341			0.801836
$922$	17.2203	−	17.2203i	0.567122	−	0.567122i
$923$			0.00471020i			0.000155038i
$924$	5.45197			0.179357
$925$	−26.8041	+	14.3715i	−0.881313	+	0.472532i
$926$	13.3316			0.438102
$927$		−	3.62121i		−	0.118936i
$928$	1.37472	−	1.37472i	0.0451274	−	0.0451274i
$929$	16.6531			0.546370			0.273185	−	0.961962i	$-0.411923\pi$
$929$	16.6531			0.546370			0.273185	+	0.961962i	$0.411923\pi$
$930$	−12.1942	−	14.1457i	−0.399865	−	0.463857i
$931$	19.3139	+	19.3139i	0.632988	+	0.632988i
$932$	2.23686	−	2.23686i	0.0732706	−	0.0732706i
$933$			17.2862i			0.565926i
$934$			32.1997i			1.05361i
$935$	49.9621	−	43.0695i	1.63394	−	1.40852i
$936$		−	1.00869i		−	0.0329699i
$937$	17.3416	−	17.3416i	0.566526	−	0.566526i	−0.364627	−	0.931154i	$-0.618804\pi$
$937$	17.3416	−	17.3416i	0.566526	−	0.566526i	0.931154	+	0.364627i	$0.118804\pi$
$938$			2.33124i			0.0761178i
$939$	29.9322	+	29.9322i	0.976802	+	0.976802i
$940$	12.9865	+	0.962160i	0.423572	+	0.0313822i
$941$	−13.4862			−0.439637			−0.219818	−	0.975541i	$-0.570547\pi$
$941$	−13.4862			−0.439637			−0.219818	+	0.975541i	$0.570547\pi$
$942$	−17.7383			−0.577944
$943$	72.5394			2.36221
$944$	6.16388	−	6.16388i	0.200617	−	0.200617i
$945$	−5.84021	−	6.77485i	−0.189982	−	0.220386i
$946$		−	39.8032i		−	1.29411i
$947$	−22.9700			−0.746424			−0.373212	−	0.927746i	$-0.621744\pi$
$947$	−22.9700			−0.746424			−0.373212	+	0.927746i	$0.621744\pi$
$948$			1.96207i			0.0637249i
$949$	28.9812	+	28.9812i	0.940769	+	0.940769i
$950$	−17.3442	+	12.8460i	−0.562720	+	0.416778i
$951$	−39.6325			−1.28517
$952$	4.69107	+	4.69107i	0.152038	+	0.152038i
$953$	−24.2716	+	24.2716i	−0.786234	+	0.786234i	−0.980875	−	0.194641i	$-0.937646\pi$
$953$	−24.2716	+	24.2716i	−0.786234	+	0.786234i	0.194641	+	0.980875i	$0.437646\pi$
$954$	0.144972	+	0.144972i	0.00469365	+	0.00469365i
$955$	−0.0646480	+	0.872568i	−0.00209196	+	0.0282356i
$956$	4.53542	−	4.53542i	0.146686	−	0.146686i
$957$			12.9258i			0.417832i
$958$	−10.6512	−	10.6512i	−0.344124	−	0.344124i
$959$			13.2806i			0.428854i
$960$	4.06602	+	0.301249i	0.131230	+	0.00972276i
$961$			10.0172i			0.323136i
$962$	−11.2877	−	15.1583i	−0.363929	−	0.488723i
$963$	1.26064	+	1.26064i	0.0406234	+	0.0406234i
$964$	−2.95256	−	2.95256i	−0.0950957	−	0.0950957i
$965$	−14.8834	+	12.8301i	−0.479113	+	0.413016i
$966$			11.6485i			0.374786i
$967$	−20.1548			−0.648135			−0.324068	−	0.946034i	$-0.605051\pi$
$967$	−20.1548			−0.648135			−0.324068	+	0.946034i	$0.605051\pi$
$968$			2.29574i			0.0737879i
$969$		−	63.6772i		−	2.04561i
$970$	24.7620	−	21.3459i	0.795060	−	0.685375i
$971$	35.4771			1.13852			0.569258	−	0.822159i	$-0.307231\pi$
$971$	35.4771			1.13852			0.569258	+	0.822159i	$0.307231\pi$
$972$	2.37553	−	2.37553i	0.0761952	−	0.0761952i
$973$	1.39989	−	1.39989i	0.0448785	−	0.0448785i
$974$			17.1695i			0.550145i
$975$	22.7628	−	16.8592i	0.728992	−	0.539927i
$976$	8.71382	−	8.71382i	0.278923	−	0.278923i
$977$		−	2.60048i		−	0.0831967i	−0.999134	−	0.0415983i	$-0.986755\pi$
$977$		−	2.60048i		−	0.0831967i	0.999134	−	0.0415983i	$-0.0132450\pi$
$978$	13.7612	+	13.7612i	0.440033	+	0.440033i
$979$	−21.1493	+	21.1493i	−0.675935	+	0.675935i
$980$	10.7166	−	9.23820i	0.342330	−	0.295103i
$981$	0.654431	+	0.654431i	0.0208944	+	0.0208944i
$982$		−	9.04897i		−	0.288764i
$983$	−35.9359	+	35.9359i	−1.14618	+	1.14618i	−0.158880	+	0.987298i	$0.550788\pi$
$983$	−35.9359	+	35.9359i	−1.14618	+	1.14618i	−0.987298	+	0.158880i	$0.949212\pi$
$984$	−12.0049	+	12.0049i	−0.382701	+	0.382701i
$985$	26.5374	+	1.96614i	0.845552	+	0.0626465i
$986$	−11.1218	+	11.1218i	−0.354192	+	0.354192i
$987$	−6.15711	−	6.15711i	−0.195983	−	0.195983i
$988$	−9.48374	−	9.48374i	−0.301718	−	0.301718i
$989$	85.0426			2.70420
$990$	−2.00488	+	1.72829i	−0.0637192	+	0.0549286i
$991$	−24.9318	+	24.9318i	−0.791984	+	0.791984i	−0.981816	−	0.189833i	$-0.939205\pi$
$991$	−24.9318	+	24.9318i	−0.791984	+	0.791984i	0.189833	+	0.981816i	$0.439205\pi$
$992$	3.23904	+	3.23904i	0.102840	+	0.102840i
$993$	14.7713			0.468755
$994$	0.000879026	0	0.000879026i	2.78810e−5	0	2.78810e-5i
$995$	0.981600	−	13.2489i	0.0311188	−	0.420017i
$996$	8.17374			0.258995
$997$	23.9821			0.759520			0.379760	−	0.925085i	$-0.376007\pi$
$997$	23.9821			0.759520			0.379760	+	0.925085i	$0.376007\pi$
$998$	−8.81194	+	8.81194i	−0.278937	+	0.278937i
$999$	4.29708	−	29.3598i	0.135954	−	0.928902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.e.43.4	✓	20
5.2	odd	4		370.2.h.e.117.7	yes	20
37.31	odd	4		370.2.h.e.253.7	yes	20
185.142	even	4	inner	370.2.g.e.327.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.4	✓	20	1.1	even	1	trivial
370.2.g.e.327.4	yes	20	185.142	even	4	inner
370.2.h.e.117.7	yes	20	5.2	odd	4
370.2.h.e.253.7	yes	20	37.31	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.28931 + 1.28931i) q^{3} -1.00000 q^{4} +(1.45999 + 1.69364i) q^{5} +(-1.28931 - 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000i q^{8} -0.324646i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.28931 + 1.28931i) q^{3} -1.00000 q^{4} +(1.45999 + 1.69364i) q^{5} +(-1.28931 - 1.28931i) q^{6} +(0.579841 - 0.579841i) q^{7} -1.00000i q^{8} -0.324646i q^{9} +(-1.69364 + 1.45999i) q^{10} +3.64633i q^{11} +(1.28931 - 1.28931i) q^{12} +3.10704i q^{13} +(0.579841 + 0.579841i) q^{14} +(-4.06602 - 0.301249i) q^{15} +1.00000 q^{16} -8.09027 q^{17} +0.324646 q^{18} +(3.05234 - 3.05234i) q^{19} +(-1.45999 - 1.69364i) q^{20} +1.49519i q^{21} -3.64633 q^{22} -7.79067i q^{23} +(1.28931 + 1.28931i) q^{24} +(-0.736849 + 4.94541i) q^{25} -3.10704 q^{26} +(-3.44936 - 3.44936i) q^{27} +(-0.579841 + 0.579841i) q^{28} +(-1.37472 - 1.37472i) q^{29} +(0.301249 - 4.06602i) q^{30} +(3.23904 - 3.23904i) q^{31} +1.00000i q^{32} +(-4.70126 - 4.70126i) q^{33} -8.09027i q^{34} +(1.82861 + 0.135480i) q^{35} +0.324646i q^{36} +(3.63294 + 4.87870i) q^{37} +(3.05234 + 3.05234i) q^{38} +(-4.00594 - 4.00594i) q^{39} +(1.69364 - 1.45999i) q^{40} +9.31106i q^{41} -1.49519 q^{42} +10.9160i q^{43} -3.64633i q^{44} +(0.549834 - 0.473980i) q^{45} +7.79067 q^{46} +(-4.11794 + 4.11794i) q^{47} +(-1.28931 + 1.28931i) q^{48} +6.32757i q^{49} +(-4.94541 - 0.736849i) q^{50} +(10.4309 - 10.4309i) q^{51} -3.10704i q^{52} +(0.446555 + 0.446555i) q^{53} +(3.44936 - 3.44936i) q^{54} +(-6.17558 + 5.32361i) q^{55} +(-0.579841 - 0.579841i) q^{56} +7.87084i q^{57} +(1.37472 - 1.37472i) q^{58} +(6.16388 - 6.16388i) q^{59} +(4.06602 + 0.301249i) q^{60} +(8.71382 - 8.71382i) q^{61} +(3.23904 + 3.23904i) q^{62} +(-0.188243 - 0.188243i) q^{63} -1.00000 q^{64} +(-5.26221 + 4.53625i) q^{65} +(4.70126 - 4.70126i) q^{66} +(2.01024 + 2.01024i) q^{67} +8.09027 q^{68} +(10.0446 + 10.0446i) q^{69} +(-0.135480 + 1.82861i) q^{70} +0.00151598 q^{71} -0.324646 q^{72} +(9.32759 - 9.32759i) q^{73} +(-4.87870 + 3.63294i) q^{74} +(-5.42614 - 7.32620i) q^{75} +(-3.05234 + 3.05234i) q^{76} +(2.11429 + 2.11429i) q^{77} +(4.00594 - 4.00594i) q^{78} +(-0.760897 + 0.760897i) q^{79} +(1.45999 + 1.69364i) q^{80} +9.86854 q^{81} -9.31106 q^{82} +(3.16981 + 3.16981i) q^{83} -1.49519i q^{84} +(-11.8117 - 13.7020i) q^{85} -10.9160 q^{86} +3.54488 q^{87} +3.64633 q^{88} +(5.80016 + 5.80016i) q^{89} +(0.473980 + 0.549834i) q^{90} +(1.80159 + 1.80159i) q^{91} +7.79067i q^{92} +8.35226i q^{93} +(-4.11794 - 4.11794i) q^{94} +(9.62597 + 0.713182i) q^{95} +(-1.28931 - 1.28931i) q^{96} -14.6206 q^{97} -6.32757 q^{98} +1.18377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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