LMFDB - Embedded newform 370.2.h.e.253.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.7
Root			$1.28931 + 1.28931i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.28931	−	1.28931i	0.744384	−	0.744384i	−0.229034	−	0.973418i	$-0.573557\pi$
$3$	1.28931	−	1.28931i	0.744384	−	0.744384i	0.973418	+	0.229034i	$0.0735568\pi$
$4$	1.00000			0.500000
$5$	1.69364	−	1.45999i	0.757420	−	0.652928i
$5$	1.69364	−	1.45999i	0.757420	−	0.652928i
$6$	−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	$0.200472\pi$
$8$	−1.00000			−0.353553
$9$		−	0.324646i		−	0.108215i
$10$	−1.69364	+	1.45999i	−0.535577	+	0.461690i
$11$		−	3.64633i		−	1.09941i	−0.835359	−	0.549705i	$-0.814740\pi$
$11$		−	3.64633i		−	1.09941i	0.835359	−	0.549705i	$-0.185260\pi$
$12$	1.28931	−	1.28931i	0.372192	−	0.372192i
$13$	3.10704			0.861737			0.430868	−	0.902415i	$-0.358207\pi$
$13$	3.10704			0.861737			0.430868	+	0.902415i	$0.358207\pi$
$14$	−0.579841	+	0.579841i	−0.154969	+	0.154969i
$15$	0.301249	−	4.06602i	0.0777820	−	1.04984i
$16$	1.00000			0.250000
$17$			8.09027i			1.96218i	0.193558	+	0.981089i	$0.437997\pi$
$17$			8.09027i			1.96218i	−0.193558	+	0.981089i	$0.562003\pi$
$18$			0.324646i			0.0765198i
$19$	−3.05234	−	3.05234i	−0.700255	−	0.700255i	0.264210	−	0.964465i	$-0.414889\pi$
$19$	−3.05234	−	3.05234i	−0.700255	−	0.700255i	−0.964465	+	0.264210i	$0.914889\pi$
$20$	1.69364	−	1.45999i	0.378710	−	0.326464i
$21$		−	1.49519i		−	0.326278i
$22$			3.64633i			0.777401i
$23$	−7.79067			−1.62447			−0.812233	−	0.583333i	$-0.801748\pi$
$23$	−7.79067			−1.62447			−0.812233	+	0.583333i	$0.801748\pi$
$24$	−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	$-0.692225\pi$
$29$	1.37472	−	1.37472i	0.255279	−	0.255279i	0.823131	+	0.567852i	$0.192225\pi$
$30$	−0.301249	+	4.06602i	−0.0550002	+	0.742349i
$31$	3.23904	+	3.23904i	0.581749	+	0.581749i	0.935384	−	0.353635i	$-0.115054\pi$
$31$	3.23904	+	3.23904i	0.581749	+	0.581749i	−0.353635	+	0.935384i	$0.615054\pi$
$32$	−1.00000			−0.176777
$33$	−4.70126	−	4.70126i	−0.818384	−	0.818384i
$34$		−	8.09027i		−	1.38747i
$35$	0.135480	−	1.82861i	0.0229004	−	0.309091i
$36$		−	0.324646i		−	0.0541076i
$37$	−4.87870	−	3.63294i	−0.802054	−	0.597252i
$37$	−4.87870	−	3.63294i	−0.802054	−	0.597252i
$38$	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	$-0.740881\pi$
$41$		−	9.31106i		−	1.45414i	0.686562	−	0.727072i	$-0.259119\pi$
$42$			1.49519i			0.230713i
$43$	10.9160			1.66467			0.832334	−	0.554275i	$-0.187004\pi$
$43$	10.9160			1.66467			0.832334	+	0.554275i	$0.187004\pi$
$44$		−	3.64633i		−	0.549705i
$45$	−0.473980	−	0.549834i	−0.0706568	−	0.0819644i
$46$	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
$50$	−0.736849	+	4.94541i	−0.104206	+	0.699386i
$51$	10.4309	+	10.4309i	1.46061	+	1.46061i
$52$	3.10704			0.430868
$53$	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
$55$	−5.32361	−	6.17558i	−0.717836	−	0.832715i
$56$	−0.579841	+	0.579841i	−0.0774846	+	0.0774846i
$57$	−7.87084			−1.04252
$58$	−1.37472	+	1.37472i	−0.180509	+	0.180509i
$59$	−6.16388	−	6.16388i	−0.802468	−	0.802468i	0.181012	−	0.983481i	$-0.442063\pi$
$59$	−6.16388	−	6.16388i	−0.802468	−	0.802468i	−0.983481	+	0.181012i	$0.942063\pi$
$60$	0.301249	−	4.06602i	0.0388910	−	0.524920i
$61$	8.71382	+	8.71382i	1.11569	+	1.11569i	0.992366	+	0.123324i	$0.0393555\pi$
$61$	8.71382	+	8.71382i	1.11569	+	1.11569i	0.123324	+	0.992366i	$0.460644\pi$
$62$	−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	0.573568	−	0.819158i	$-0.305559\pi$
$67$	−2.01024	−	2.01024i	−0.245590	−	0.245590i	−0.819158	+	0.573568i	$0.805559\pi$
$68$			8.09027i			0.981089i
$69$	−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	$0.499971\pi$
$72$			0.324646i			0.0382599i
$73$	−9.32759	+	9.32759i	−1.09171	+	1.09171i	−0.0963663	+	0.995346i	$0.530722\pi$
$73$	−9.32759	+	9.32759i	−1.09171	+	1.09171i	−0.995346	+	0.0963663i	$0.969278\pi$
$74$	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	$-0.230720\pi$
$79$	0.760897	+	0.760897i	0.0856076	+	0.0856076i	−0.663006	+	0.748614i	$0.730720\pi$
$80$	1.69364	−	1.45999i	0.189355	−	0.163232i
$81$	9.86854			1.09650
$82$			9.31106i			1.02823i
$83$	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
$87$		−	3.54488i		−	0.380051i
$88$			3.64633i			0.388700i
$89$	−5.80016	+	5.80016i	−0.614816	+	0.614816i	−0.944197	−	0.329381i	$-0.893160\pi$
$89$	−5.80016	+	5.80016i	−0.614816	+	0.614816i	0.329381	+	0.944197i	$0.393160\pi$
$90$	0.473980	+	0.549834i	0.0499619	+	0.0579576i
$91$	1.80159	−	1.80159i	0.188858	−	0.188858i
$92$	−7.79067			−0.812233
$93$	8.35226			0.866089
$94$	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
$97$			14.6206i			1.48449i	0.670127	+	0.742246i	$0.266240\pi$
$97$			14.6206i			1.48449i	−0.670127	+	0.742246i	$0.733760\pi$
$98$		−	6.32757i		−	0.639181i
$99$	−1.18377			−0.118973
$100$	0.736849	−	4.94541i	0.0736849	−	0.494541i
$101$		−	3.68870i		−	0.367039i	−0.983016	−	0.183520i	$-0.941251\pi$
$101$		−	3.68870i		−	0.367039i	0.983016	−	0.183520i	$-0.0587491\pi$
$102$	−10.4309	−	10.4309i	−1.03281	−	1.03281i
$103$			11.1543i			1.09907i	0.835471	+	0.549535i	$0.185195\pi$
$103$			11.1543i			1.09907i	−0.835471	+	0.549535i	$0.814805\pi$
$104$	−3.10704			−0.304670
$105$	−2.18297	−	2.53232i	−0.213036	−	0.247129i
$106$	−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	$-0.206405\pi$
$109$	2.01583	+	2.01583i	0.193081	+	0.193081i	−0.603945	+	0.797026i	$0.706405\pi$
$110$	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
$113$			11.8892i			1.11844i	0.829019	+	0.559220i	$0.188899\pi$
$113$			11.8892i			1.11844i	−0.829019	+	0.559220i	$0.811101\pi$
$114$	7.87084			0.737171
$115$	−13.1946	+	11.3743i	−1.23040	+	1.06066i
$116$	1.37472	−	1.37472i	0.127639	−	0.127639i
$117$		−	1.00869i		−	0.0932531i
$118$	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
$125$	−5.97229	−	9.45154i	−0.534178	−	0.845372i
$126$	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	$-0.0873593\pi$
$128$	−1.00000			−0.0883883
$129$	14.0741	−	14.0741i	1.23915	−	1.23915i
$130$	−5.26221	+	4.53625i	−0.461526	+	0.397855i
$131$	2.71250	+	2.71250i	0.236992	+	0.236992i	0.815603	−	0.578611i	$-0.196405\pi$
$131$	2.71250	+	2.71250i	0.236992	+	0.236992i	−0.578611	+	0.815603i	$0.696405\pi$
$132$	−4.70126	−	4.70126i	−0.409192	−	0.409192i
$133$	−3.53975			−0.306935
$134$	2.01024	+	2.01024i	0.173658	+	0.173658i
$135$	10.8780	+	0.805947i	0.936232	+	0.0693648i
$136$		−	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	$-0.532648\pi$
$139$	−2.41427			−0.204775			−0.102388	+	0.994745i	$0.532648\pi$
$140$	0.135480	−	1.82861i	0.0114502	−	0.154546i
$141$			10.6186i			0.894248i
$142$	−0.00151598			−0.000127218
$143$		−	11.3293i		−	0.947403i
$144$		−	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
$148$	−4.87870	−	3.63294i	−0.401027	−	0.298626i
$149$		−	4.02923i		−	0.330088i	−0.986286	−	0.165044i	$-0.947223\pi$
$149$		−	4.02923i		−	0.330088i	0.986286	−	0.165044i	$-0.0527765\pi$
$150$	5.42614	+	7.32620i	0.443043	+	0.598181i
$151$		−	8.86568i		−	0.721479i	−0.932667	−	0.360739i	$-0.882524\pi$
$151$		−	8.86568i		−	0.721479i	0.932667	−	0.360739i	$-0.117476\pi$
$152$	3.05234	+	3.05234i	0.247578	+	0.247578i
$153$	2.62647			0.212338
$154$	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
$162$	−9.86854			−0.775346
$163$		−	10.6733i		−	0.835995i	−0.908448	−	0.417997i	$-0.862732\pi$
$163$		−	10.6733i		−	0.835995i	0.908448	−	0.417997i	$-0.137268\pi$
$164$		−	9.31106i		−	0.727072i
$165$	−14.8260	−	1.09845i	−1.15421	−	0.0855144i
$166$	−3.16981	−	3.16981i	−0.246025	−	0.246025i
$167$			0.864796i			0.0669199i	0.999440	+	0.0334600i	$0.0106526\pi$
$167$			0.864796i			0.0669199i	−0.999440	+	0.0334600i	$0.989347\pi$
$168$			1.49519i			0.115357i
$169$	−3.34633			−0.257410
$170$	−11.8117	−	13.7020i	−0.905918	−	1.05090i
$171$	−0.990930	+	0.990930i	−0.0757783	+	0.0757783i
$172$	10.9160			0.832334
$173$	−2.14973	+	2.14973i	−0.163441	+	0.163441i	−0.784089	−	0.620648i	$-0.786870\pi$
$173$	−2.14973	+	2.14973i	−0.163441	+	0.163441i	0.620648	+	0.784089i	$0.286870\pi$
$174$			3.54488i			0.268737i
$175$	−2.44030	−	3.29481i	−0.184469	−	0.249064i
$176$		−	3.64633i		−	0.274853i
$177$	−15.8943			−1.19469
$178$	5.80016	−	5.80016i	0.434741	−	0.434741i
$179$	−0.313292	+	0.313292i	−0.0234165	+	0.0234165i	−0.718718	−	0.695302i	$-0.755271\pi$
$179$	−0.313292	+	0.313292i	−0.0234165	+	0.0234165i	0.695302	+	0.718718i	$0.255271\pi$
$180$	−0.473980	−	0.549834i	−0.0353284	−	0.0409822i
$181$	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
$183$	22.4697			1.66100
$184$	7.79067			0.574336
$185$	−13.5668	+	0.969960i	−0.997454	+	0.0713129i
$186$	−8.35226			−0.612418
$187$	29.4998			2.15724
$188$	−4.11794	+	4.11794i	−0.300332	+	0.300332i
$189$	4.00017			0.290969
$190$	9.62597	+	0.713182i	0.698341	+	0.0517397i
$191$	0.276686	−	0.276686i	0.0200203	−	0.0200203i	−0.697026	−	0.717046i	$-0.745494\pi$
$191$	0.276686	−	0.276686i	0.0200203	−	0.0200203i	0.717046	+	0.697026i	$0.245494\pi$
$192$	1.28931	−	1.28931i	0.0930480	−	0.0930480i
$193$	8.78779			0.632559			0.316279	−	0.948666i	$-0.397566\pi$
$193$	8.78779			0.632559			0.316279	+	0.948666i	$0.397566\pi$
$194$		−	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	$0.110649\pi$
$198$	1.18377			0.0841266
$199$	4.20114	−	4.20114i	0.297811	−	0.297811i	−0.542345	−	0.840156i	$-0.682463\pi$
$199$	4.20114	−	4.20114i	0.297811	−	0.297811i	0.840156	+	0.542345i	$0.182463\pi$
$200$	−0.736849	+	4.94541i	−0.0521031	+	0.349693i
$201$	−5.18365			−0.365627
$202$			3.68870i			0.259536i
$203$		−	1.59424i		−	0.111894i
$204$	10.4309	+	10.4309i	0.730307	+	0.730307i
$205$	−13.5941	−	15.7696i	−0.949451	−	1.10140i
$206$		−	11.1543i		−	0.777160i
$207$			2.52921i			0.175792i
$208$	3.10704			0.215434
$209$	−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
$217$	3.75626			0.254992
$218$	−2.01583	−	2.01583i	−0.136529	−	0.136529i
$219$			24.0523i			1.62531i
$220$	−5.32361	−	6.17558i	−0.358918	−	0.416358i
$221$			25.1367i			1.69088i
$222$	10.9742	−	1.60617i	0.736537	−	0.107799i
$223$	−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
$227$		−	17.9587i		−	1.19196i	−0.802999	−	0.595981i	$-0.796763\pi$
$227$		−	17.9587i		−	1.19196i	0.802999	−	0.595981i	$-0.203237\pi$
$228$	−7.87084			−0.521259
$229$		−	18.1673i		−	1.20053i	−0.799802	−	0.600264i	$-0.795062\pi$
$229$		−	18.1673i		−	1.20053i	0.799802	−	0.600264i	$-0.204938\pi$
$230$	13.1946	−	11.3743i	0.870027	−	0.750000i
$231$	−5.45197			−0.358713
$232$	−1.37472	+	1.37472i	−0.0902547	+	0.0902547i
$233$	2.23686	−	2.23686i	0.146541	−	0.146541i	−0.630030	−	0.776571i	$-0.716957\pi$
$233$	2.23686	−	2.23686i	0.146541	−	0.146541i	0.776571	+	0.630030i	$0.216957\pi$
$234$			1.00869i			0.0659399i
$235$	−0.962160	+	12.9865i	−0.0627644	+	0.847144i
$236$	−6.16388	−	6.16388i	−0.401234	−	0.401234i
$237$	1.96207			0.127450
$238$	−4.69107	−	4.69107i	−0.304077	−	0.304077i
$239$	4.53542	+	4.53542i	0.293372	+	0.293372i	0.838411	−	0.545039i	$-0.183485\pi$
$239$	4.53542	+	4.53542i	0.293372	+	0.293372i	−0.545039	+	0.838411i	$0.683485\pi$
$240$	0.301249	−	4.06602i	0.0194455	−	0.262460i
$241$	2.95256	−	2.95256i	0.190191	−	0.190191i	−0.605587	−	0.795779i	$-0.707062\pi$
$241$	2.95256	−	2.95256i	0.190191	−	0.190191i	0.795779	+	0.605587i	$0.207062\pi$
$242$	2.29574			0.147576
$243$	2.37553	−	2.37553i	0.152390	−	0.152390i
$244$	8.71382	+	8.71382i	0.557845	+	0.557845i
$245$	9.23820	+	10.7166i	0.590207	+	0.684661i
$246$	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	0.320428	−	0.947273i	$-0.396173\pi$
$251$	−9.93109	−	9.93109i	−0.626845	−	0.626845i	−0.947273	+	0.320428i	$0.896173\pi$
$252$	−0.188243	−	0.188243i	−0.0118582	−	0.0118582i
$253$			28.4074i			1.78596i
$254$	−13.9019	+	13.9019i	−0.872280	+	0.872280i
$255$	32.8951	+	2.43718i	2.05997	+	0.152622i
$256$	1.00000			0.0625000
$257$			15.1135i			0.942757i	0.881931	+	0.471378i	$0.156243\pi$
$257$			15.1135i			0.942757i	−0.881931	+	0.471378i	$0.843757\pi$
$258$	−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	−0.339763	−	0.940511i	$-0.610347\pi$
$263$	9.74250	−	9.74250i	0.600749	−	0.600749i	0.940511	+	0.339763i	$0.110347\pi$
$264$	4.70126	+	4.70126i	0.289342	+	0.289342i
$265$	1.40827	+	0.104338i	0.0865094	+	0.00640942i
$266$	3.53975			0.217036
$267$			14.9564i			0.915319i
$268$	−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	$0.784555\pi$
$272$			8.09027i			0.490544i
$273$		−	4.64561i		−	0.281165i
$274$	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
$277$	−17.2625			−1.03720			−0.518602	−	0.855016i	$-0.673548\pi$
$277$	−17.2625			−1.03720			−0.518602	+	0.855016i	$0.673548\pi$
$278$	2.41427			0.144798
$279$	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	−0.812331	−	0.583197i	$-0.801802\pi$
$281$	−3.84098	+	3.84098i	−0.229134	+	0.229134i	0.583197	+	0.812331i	$0.301802\pi$
$282$		−	10.6186i		−	0.632329i
$283$			20.5564i			1.22195i	0.791650	+	0.610975i	$0.209222\pi$
$283$			20.5564i			1.22195i	−0.791650	+	0.610975i	$0.790778\pi$
$284$	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
$288$			0.324646i			0.0191299i
$289$	−48.4524			−2.85014
$290$	−0.321204	+	4.33536i	−0.0188618	+	0.254581i
$291$	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
$298$			4.02923i			0.233407i
$299$	−24.2059			−1.39986
$300$	−5.42614	−	7.32620i	−0.313278	−	0.422978i
$301$	6.32952	−	6.32952i	0.364828	−	0.364828i
$302$			8.86568i			0.510163i
$303$	−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	0.923115	−	0.384525i	$-0.125635\pi$
$307$	9.43686	+	9.43686i	0.538590	+	0.538590i	−0.384525	+	0.923115i	$0.625635\pi$
$308$	−2.11429	−	2.11429i	−0.120473	−	0.120473i
$309$	14.3814	+	14.3814i	0.818131	+	0.818131i
$310$	−10.2148	−	0.756805i	−0.580159	−	0.0429836i
$311$	6.70368	+	6.70368i	0.380131	+	0.380131i	0.871149	−	0.491019i	$-0.163375\pi$
$311$	6.70368	+	6.70368i	0.380131	+	0.380131i	−0.491019	+	0.871149i	$0.663375\pi$
$312$	−4.00594	+	4.00594i	−0.226791	+	0.226791i
$313$	−23.2157			−1.31223			−0.656114	−	0.754662i	$-0.727801\pi$
$313$	−23.2157			−1.31223			−0.656114	+	0.754662i	$0.727801\pi$
$314$	−6.87897	+	6.87897i	−0.388203	+	0.388203i
$315$	−0.593650	−	0.0439832i	−0.0334484	−	0.00247817i
$316$	0.760897	+	0.760897i	0.0428038	+	0.0428038i
$317$	−15.3696	−	15.3696i	−0.863245	−	0.863245i	0.128469	−	0.991714i	$-0.458994\pi$
$317$	−15.3696	−	15.3696i	−0.863245	−	0.863245i	−0.991714	+	0.128469i	$0.958994\pi$
$318$	−1.15150			−0.0645727
$319$	−5.01268	−	5.01268i	−0.280656	−	0.280656i
$320$	1.69364	−	1.45999i	0.0946775	−	0.0816160i
$321$			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
$325$	2.28942	−	15.3656i	0.126994	−	0.852328i
$326$			10.6733i			0.591137i
$327$	5.19806			0.287454
$328$			9.31106i			0.514117i
$329$			4.77550i			0.263282i
$330$	14.8260	+	1.09845i	0.816147	+	0.0604678i
$331$	−5.72839	+	5.72839i	−0.314861	+	0.314861i	−0.846789	−	0.531929i	$-0.821467\pi$
$331$	−5.72839	+	5.72839i	−0.314861	+	0.314861i	0.531929	+	0.846789i	$0.321467\pi$
$332$	3.16981	+	3.16981i	0.173966	+	0.173966i
$333$	−1.17942	+	1.58385i	−0.0646318	+	0.0867945i
$334$		−	0.864796i		−	0.0473195i
$335$	−6.33957	−	0.469695i	−0.346368	−	0.0256622i
$336$		−	1.49519i		−	0.0815694i
$337$	5.31333	+	5.31333i	0.289436	+	0.289436i	0.836857	−	0.547421i	$-0.184391\pi$
$337$	5.31333	+	5.31333i	0.289436	+	0.289436i	−0.547421	+	0.836857i	$0.684391\pi$
$338$	3.34633			0.182016
$339$	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
$347$	32.7620			1.75876			0.879379	−	0.476123i	$-0.157958\pi$
$347$	32.7620			1.75876			0.879379	+	0.476123i	$0.157958\pi$
$348$		−	3.54488i		−	0.190026i
$349$			14.0604i			0.752637i	0.926490	+	0.376318i	$0.122810\pi$
$349$			14.0604i			0.752637i	−0.926490	+	0.376318i	$0.877190\pi$
$350$	2.44030	+	3.29481i	0.130439	+	0.176115i
$351$	10.7173	+	10.7173i	0.572047	+	0.572047i
$352$			3.64633i			0.194350i
$353$			6.79098i			0.361447i	0.983534	+	0.180724i	$0.0578440\pi$
$353$			6.79098i			0.361447i	−0.983534	+	0.180724i	$0.942156\pi$
$354$	15.8943			0.844773
$355$	0.00256752	−	0.00221331i	0.000136270	−	0.000117471i
$356$	−5.80016	+	5.80016i	−0.307408	+	0.307408i
$357$	12.0965			0.640215
$358$	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
$362$	−16.2161			−0.852300
$363$	−2.95992	+	2.95992i	−0.155356	+	0.155356i
$364$	1.80159	−	1.80159i	0.0944289	−	0.0944289i
$365$	−2.17940	+	29.4158i	−0.114075	+	1.53969i
$366$	−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	$-0.0416378\pi$
$368$	−7.79067			−0.406117
$369$	−3.02280			−0.157361
$370$	13.5668	−	0.969960i	0.705306	−	0.0504258i
$371$	0.517862			0.0268860
$372$	8.35226			0.433045
$373$	19.5734	−	19.5734i	1.01347	−	1.01347i	0.0135632	−	0.999908i	$-0.495683\pi$
$373$	19.5734	−	19.5734i	1.01347	−	1.01347i	0.999908	−	0.0135632i	$-0.00431743\pi$
$374$	−29.4998			−1.52540
$375$	−19.8861	−	4.48584i	−1.02692	−	0.231648i
$376$	4.11794	−	4.11794i	0.212367	−	0.212367i
$377$	4.27130	−	4.27130i	0.219983	−	0.219983i
$378$	−4.00017			−0.205746
$379$		−	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
$383$	12.0669			0.616591			0.308295	−	0.951291i	$-0.400241\pi$
$383$	12.0669			0.616591			0.308295	+	0.951291i	$0.400241\pi$
$384$	−1.28931	+	1.28931i	−0.0657949	+	0.0657949i
$385$	−6.66771	−	0.494007i	−0.339818	−	0.0251769i
$386$	−8.78779			−0.447287
$387$		−	3.54382i		−	0.180142i
$388$			14.6206i			0.742246i
$389$	−16.8015	−	16.8015i	−0.851868	−	0.851868i	0.138495	−	0.990363i	$-0.455773\pi$
$389$	−16.8015	−	16.8015i	−0.851868	−	0.851868i	−0.990363	+	0.138495i	$0.955773\pi$
$390$	−0.935990	+	12.6333i	−0.0473957	+	0.639710i
$391$		−	63.0286i		−	3.18749i
$392$		−	6.32757i		−	0.319590i
$393$	6.99450			0.352826
$394$	−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	0.509464	−	0.860492i	$-0.329844\pi$
$397$	−6.99419	−	6.99419i	−0.351028	−	0.351028i	−0.860492	+	0.509464i	$0.829844\pi$
$398$	−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	0.725818	−	0.687886i	$-0.241461\pi$
$401$	0.759591	+	0.759591i	0.0379322	+	0.0379322i	−0.687886	+	0.725818i	$0.741461\pi$
$402$	5.18365			0.258537
$403$	10.0638	+	10.0638i	0.501315	+	0.501315i
$404$		−	3.68870i		−	0.183520i
$405$	16.7138	−	14.4080i	0.830515	−	0.715939i
$406$			1.59424i			0.0791207i
$407$	−13.2469	+	17.7894i	−0.656625	+	0.881786i
$408$	−10.4309	−	10.4309i	−0.516405	−	0.516405i
$409$	22.0320	−	22.0320i	1.08941	−	1.08941i	0.0938237	−	0.995589i	$-0.470091\pi$
$409$	22.0320	−	22.0320i	1.08941	−	1.08941i	0.995589	−	0.0938237i	$-0.0299090\pi$
$410$	13.5941	+	15.7696i	0.671363	+	0.778805i
$411$			29.5302i			1.45662i
$412$			11.1543i			0.549535i
$413$	−7.14814			−0.351737
$414$		−	2.52921i		−	0.124304i
$415$	9.99642	+	0.740629i	0.490705	+	0.0363560i
$416$	−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	$-0.109051\pi$
$420$	−2.18297	−	2.53232i	−0.106518	−	0.123565i
$421$	4.62725	+	4.62725i	0.225519	+	0.225519i	0.810818	−	0.585299i	$-0.199023\pi$
$421$	4.62725	+	4.62725i	0.225519	+	0.225519i	−0.585299	+	0.810818i	$0.699023\pi$
$422$	27.4901			1.33820
$423$	1.33687	+	1.33687i	0.0650010	+	0.0650010i
$424$	−0.446555	−	0.446555i	−0.0216866	−	0.0216866i
$425$	40.0097	+	5.96131i	1.94075	+	0.289166i
$426$	−0.00195457	+	0.00195457i	−9.46990e−5	+	9.46990e-5i
$427$	10.1053			0.489028
$428$	−3.88311	+	3.88311i	−0.187697	+	0.187697i
$429$	−14.6070	−	14.6070i	−0.705231	−	0.705231i
$430$	−18.4877	+	15.9372i	−0.891557	+	0.768560i
$431$	2.01292	+	2.01292i	0.0969591	+	0.0969591i	0.753922	−	0.656963i	$-0.228159\pi$
$431$	2.01292	+	2.01292i	0.0969591	+	0.0969591i	−0.656963	+	0.753922i	$0.728159\pi$
$432$	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
$438$		−	24.0523i		−	1.14927i
$439$	−6.59762	+	6.59762i	−0.314887	+	0.314887i	−0.846800	−	0.531912i	$-0.821474\pi$
$439$	−6.59762	+	6.59762i	−0.314887	+	0.314887i	0.531912	+	0.846800i	$0.321474\pi$
$440$	5.32361	+	6.17558i	0.253793	+	0.294409i
$441$	2.05422			0.0978199
$442$		−	25.1367i		−	1.19563i
$443$	−28.2758	+	28.2758i	−1.34343	+	1.34343i	−0.450801	+	0.892625i	$0.648862\pi$
$443$	−28.2758	+	28.2758i	−1.34343	+	1.34343i	−0.892625	+	0.450801i	$0.851138\pi$
$444$	−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	$-0.121660\pi$
$449$	11.7576	+	11.7576i	0.554876	+	0.554876i	−0.372968	+	0.927844i	$0.621660\pi$
$450$	1.60551	+	0.239215i	0.0756843	+	0.0112767i
$451$	−33.9512			−1.59870
$452$			11.8892i			0.559220i
$453$	−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
$457$		−	31.9954i		−	1.49668i	−0.663314	−	0.748341i	$-0.730851\pi$
$457$		−	31.9954i		−	1.49668i	0.663314	−	0.748341i	$-0.269149\pi$
$458$			18.1673i			0.848901i
$459$	−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	−0.983413	−	0.181382i	$-0.941943\pi$
$461$	−17.2203	+	17.2203i	−0.802031	+	0.802031i	0.181382	+	0.983413i	$0.441943\pi$
$462$	5.45197			0.253648
$463$	−13.3316			−0.619570			−0.309785	−	0.950807i	$-0.600257\pi$
$463$	−13.3316			−0.619570			−0.309785	+	0.950807i	$0.600257\pi$
$464$	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
$467$		−	32.1997i		−	1.49003i	−0.667050	−	0.745013i	$-0.732443\pi$
$467$		−	32.1997i		−	1.49003i	0.667050	−	0.745013i	$-0.267557\pi$
$468$		−	1.00869i		−	0.0466265i
$469$	−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
$473$		−	39.8032i		−	1.83015i
$474$	−1.96207			−0.0901207
$475$	−17.3442	+	12.8460i	−0.795806	+	0.589413i
$476$	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	$-0.138176\pi$
$479$	10.6512	+	10.6512i	0.486664	+	0.486664i	−0.420588	+	0.907252i	$0.638176\pi$
$480$	−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
$483$			11.6485i			0.530027i
$484$	−2.29574			−0.104352
$485$	21.3459	+	24.7620i	0.969267	+	1.12438i
$486$	−2.37553	+	2.37553i	−0.107756	+	0.107756i
$487$		−	17.1695i		−	0.778022i	−0.921233	−	0.389011i	$-0.872817\pi$
$487$		−	17.1695i		−	0.778022i	0.921233	−	0.389011i	$-0.127183\pi$
$488$	−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
$495$	−2.00488	+	1.72829i	−0.0901125	+	0.0776808i
$496$	3.23904	+	3.23904i	0.145437	+	0.145437i
$497$	0.000879026	0	0.000879026i	3.94297e−5	0	3.94297e-5i
$498$	−8.17374			−0.366274
$499$	−8.81194	+	8.81194i	−0.394477	+	0.394477i	−0.876280	−	0.481803i	$-0.839982\pi$
$499$	−8.81194	+	8.81194i	−0.394477	+	0.394477i	0.481803	+	0.876280i	$0.339982\pi$
$500$	−5.97229	−	9.45154i	−0.267089	−	0.422686i
$501$	1.11499	+	1.11499i	0.0498141	+	0.0498141i
$502$	9.93109	+	9.93109i	0.443246	+	0.443246i
$503$	13.2027			0.588678			0.294339	−	0.955701i	$-0.404900\pi$
$503$	13.2027			0.588678			0.294339	+	0.955701i	$0.404900\pi$
$504$	0.188243	+	0.188243i	0.00838501	+	0.00838501i
$505$	−5.38547	−	6.24734i	−0.239650	−	0.278003i
$506$		−	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	$-0.311334\pi$
$509$	25.2057			1.11722			0.558612	+	0.829429i	$0.311334\pi$
$510$	−32.8951	−	2.43718i	−1.45662	−	0.107920i
$511$			10.8170i			0.478518i
$512$	−1.00000			−0.0441942
$513$		−	21.0573i		−	0.929701i
$514$		−	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
$518$	4.93540	−	0.722344i	0.216849	−	0.0317380i
$519$			5.54335i			0.243326i
$520$	−5.26221	+	4.53625i	−0.230763	+	0.198928i
$521$			8.65279i			0.379086i	0.981872	+	0.189543i	$0.0607006\pi$
$521$			8.65279i			0.379086i	−0.981872	+	0.189543i	$0.939299\pi$
$522$	0.446297	+	0.446297i	0.0195339	+	0.0195339i
$523$	−28.4569			−1.24433			−0.622167	−	0.782884i	$-0.713748\pi$
$523$	−28.4569			−1.24433			−0.622167	+	0.782884i	$0.713748\pi$
$524$	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
$532$	−3.53975			−0.153468
$533$		−	28.9298i		−	1.25309i
$534$		−	14.9564i		−	0.647228i
$535$	−0.907292	+	12.2459i	−0.0392256	+	0.529437i
$536$	2.01024	+	2.01024i	0.0868292	+	0.0868292i
$537$			0.807861i			0.0348618i
$538$			6.43418i			0.277397i
$539$	23.0724			0.993799
$540$	10.8780	+	0.805947i	0.468116	+	0.0346824i
$541$	22.0757	−	22.0757i	0.949106	−	0.949106i	−0.0496598	−	0.998766i	$-0.515814\pi$
$541$	22.0757	−	22.0757i	0.949106	−	0.949106i	0.998766	+	0.0496598i	$0.0158137\pi$
$542$	25.6662			1.10246
$543$	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
$547$	−24.7795			−1.05949			−0.529747	−	0.848155i	$-0.677713\pi$
$547$	−24.7795			−1.05949			−0.529747	+	0.848155i	$0.677713\pi$
$548$	−11.4519	+	11.4519i	−0.489203	+	0.489203i
$549$	2.82891	−	2.82891i	0.120735	−	0.120735i
$550$	18.0326	+	2.68680i	0.768913	+	0.114565i
$551$	−8.39222			−0.357521
$552$	10.0446	−	10.0446i	0.427526	−	0.427526i
$553$	0.882399			0.0375234
$554$	17.2625			0.733415
$555$	−16.2413	+	18.7425i	−0.689405	+	0.795573i
$556$	−2.41427			−0.102388
$557$	−28.3582			−1.20157			−0.600787	−	0.799409i	$-0.705146\pi$
$557$	−28.3582			−1.20157			−0.600787	+	0.799409i	$0.705146\pi$
$558$	−1.05154	+	1.05154i	−0.0445153	+	0.0445153i
$559$	33.9163			1.43451
$560$	0.135480	−	1.82861i	0.00572509	−	0.0772728i
$561$	38.0344	−	38.0344i	1.60581	−	1.60581i
$562$	3.84098	−	3.84098i	0.162022	−	0.162022i
$563$	−16.8486			−0.710085			−0.355043	−	0.934850i	$-0.615534\pi$
$563$	−16.8486			−0.710085			−0.355043	+	0.934850i	$0.615534\pi$
$564$			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
$568$	−0.00151598			−6.36090e−5
$569$	4.89447	−	4.89447i	0.205187	−	0.205187i	−0.597031	−	0.802218i	$-0.703653\pi$
$569$	4.89447	−	4.89447i	0.205187	−	0.205187i	0.802218	+	0.597031i	$0.203653\pi$
$570$	13.3304	−	11.4914i	0.558348	−	0.481320i
$571$	−38.8520			−1.62590			−0.812952	−	0.582330i	$-0.802141\pi$
$571$	−38.8520			−1.62590			−0.812952	+	0.582330i	$0.802141\pi$
$572$		−	11.3293i		−	0.473701i
$573$		−	0.713470i		−	0.0298056i
$574$	5.39894	+	5.39894i	0.225347	+	0.225347i
$575$	−5.74055	+	38.5280i	−0.239397	+	1.60673i
$576$		−	0.324646i		−	0.0135269i
$577$			18.6556i			0.776642i	0.921524	+	0.388321i	$0.126945\pi$
$577$			18.6556i			0.776642i	−0.921524	+	0.388321i	$0.873055\pi$
$578$	48.4524			2.01535
$579$	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
$587$	−5.75904			−0.237701			−0.118851	−	0.992912i	$-0.537921\pi$
$587$	−5.75904			−0.237701			−0.118851	+	0.992912i	$0.537921\pi$
$588$	8.15820	+	8.15820i	0.336439	+	0.336439i
$589$		−	19.7733i		−	0.814746i
$590$	19.4386	+	1.44019i	0.800275	+	0.0592919i
$591$		−	21.6988i		−	0.892568i
$592$	−4.87870	−	3.63294i	−0.200513	−	0.149313i
$593$	−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
$597$		−	10.8332i		−	0.443372i
$598$	24.2059			0.989852
$599$			23.6157i			0.964910i	0.875921	+	0.482455i	$0.160255\pi$
$599$			23.6157i			0.964910i	−0.875921	+	0.482455i	$0.839745\pi$
$600$	5.42614	+	7.32620i	0.221521	+	0.299091i
$601$	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
$605$	−3.88816	+	3.35176i	−0.158076	+	0.136268i
$606$	4.75588	+	4.75588i	0.193195	+	0.193195i
$607$	−17.6781			−0.717530			−0.358765	−	0.933428i	$-0.616802\pi$
$607$	−17.6781			−0.717530			−0.358765	+	0.933428i	$0.616802\pi$
$608$	3.05234	+	3.05234i	0.123789	+	0.123789i
$609$	−2.05547	−	2.05547i	−0.0832918	−	0.0832918i
$610$	−27.4802	−	2.03599i	−1.11264	−	0.0824349i
$611$	−12.7946	+	12.7946i	−0.517614	+	0.517614i
$612$	2.62647			0.106169
$613$	−24.9613	+	24.9613i	−1.00818	+	1.00818i	−0.00821132	+	0.999966i	$0.502614\pi$
$613$	−24.9613	+	24.9613i	−1.00818	+	1.00818i	−0.999966	+	0.00821132i	$0.997386\pi$
$614$	−9.43686	−	9.43686i	−0.380841	−	0.380841i
$615$	−37.8589	−	2.80494i	−1.52662	−	0.113106i
$616$	2.11429	+	2.11429i	0.0851873	+	0.0851873i
$617$	−6.37297	−	6.37297i	−0.256566	−	0.256566i	0.567090	−	0.823656i	$-0.308069\pi$
$617$	−6.37297	−	6.37297i	−0.256566	−	0.256566i	−0.823656	+	0.567090i	$0.808069\pi$
$618$	−14.3814	−	14.3814i	−0.578506	−	0.578506i
$619$	−2.43520			−0.0978789			−0.0489394	−	0.998802i	$-0.515584\pi$
$619$	−2.43520			−0.0978789			−0.0489394	+	0.998802i	$0.515584\pi$
$620$	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
$623$			6.72635i			0.269485i
$624$	4.00594	−	4.00594i	0.160366	−	0.160366i
$625$	−23.9141	−	7.28804i	−0.956564	−	0.291522i
$626$	23.2157			0.927885
$627$			28.6997i			1.14616i
$628$	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	0.848340	−	0.529453i	$-0.177603\pi$
$631$	8.01035	+	8.01035i	0.318887	+	0.318887i	−0.529453	+	0.848340i	$0.677603\pi$
$632$	−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
$635$	3.24818	−	43.8414i	0.128900	−	1.73979i
$636$	1.15150			0.0456598
$637$			19.6600i			0.778957i
$638$	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	$0.370375\pi$
$642$		−	10.0131i		−	0.395184i
$643$		−	2.02458i		−	0.0798417i	−0.999203	−	0.0399208i	$-0.987289\pi$
$643$		−	2.02458i		−	0.0798417i	0.999203	−	0.0399208i	$-0.0127106\pi$
$644$	−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
$647$	37.8245			1.48703			0.743517	−	0.668717i	$-0.233156\pi$
$647$	37.8245			1.48703			0.743517	+	0.668717i	$0.233156\pi$
$648$	−9.86854			−0.387673
$649$	−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
$652$		−	10.6733i		−	0.417997i
$653$			24.2252i			0.948006i	0.880523	+	0.474003i	$0.157192\pi$
$653$			24.2252i			0.948006i	−0.880523	+	0.474003i	$0.842808\pi$
$654$	−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
$658$		−	4.77550i		−	0.186169i
$659$	16.7841			0.653814			0.326907	−	0.945056i	$-0.393994\pi$
$659$	16.7841			0.653814			0.326907	+	0.945056i	$0.393994\pi$
$660$	−14.8260	−	1.09845i	−0.577103	−	0.0427572i
$661$	2.96671	+	2.96671i	0.115392	+	0.115392i	0.762445	−	0.647053i	$-0.223999\pi$
$661$	2.96671	+	2.96671i	0.115392	+	0.115392i	−0.647053	+	0.762445i	$0.723999\pi$
$662$	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
$668$			0.864796i			0.0334600i
$669$	−24.3077			−0.939788
$670$	6.33957	+	0.469695i	0.244919	+	0.0181459i
$671$	31.7735	−	31.7735i	1.22660	−	1.22660i
$672$			1.49519i			0.0576783i
$673$	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	0.791778	−	0.610809i	$-0.209156\pi$
$677$	4.70869	+	4.70869i	0.180970	+	0.180970i	−0.610809	+	0.791778i	$0.709156\pi$
$678$	−15.3288	−	15.3288i	−0.588701	−	0.588701i
$679$	8.47761	+	8.47761i	0.325341	+	0.325341i
$680$	−11.8117	−	13.7020i	−0.452959	−	0.525448i
$681$	−23.1544	−	23.1544i	−0.887277	−	0.887277i
$682$	−11.8106	+	11.8106i	−0.452252	+	0.452252i
$683$	−46.0160			−1.76075			−0.880376	−	0.474277i	$-0.842710\pi$
$683$	−46.0160			−1.76075			−0.880376	+	0.474277i	$0.842710\pi$
$684$	−0.990930	+	0.990930i	−0.0378892	+	0.0378892i
$685$	−2.67576	+	36.1152i	−0.102235	+	1.37989i
$686$	−7.72788	−	7.72788i	−0.295052	−	0.295052i
$687$	−23.4233	−	23.4233i	−0.893653	−	0.893653i
$688$	10.9160			0.416167
$689$	1.38746	+	1.38746i	0.0528581	+	0.0528581i
$690$	2.34693	−	31.6770i	0.0893460	−	1.20592i
$691$			37.9434i			1.44344i	0.692187	+	0.721718i	$0.256647\pi$
$691$			37.9434i			1.44344i	−0.692187	+	0.721718i	$0.743353\pi$
$692$	−2.14973	+	2.14973i	−0.0817206	+	0.0817206i
$693$	−0.686397	+	0.686397i	−0.0260741	+	0.0260741i
$694$	−32.7620			−1.24363
$695$	−4.08890	+	3.52481i	−0.155101	+	0.133704i
$696$			3.54488i			0.134368i
$697$	75.3290			2.85329
$698$		−	14.0604i		−	0.532194i
$699$		−	5.76801i		−	0.218166i
$700$	−2.44030	−	3.29481i	−0.0922345	−	0.124532i
$701$	11.9143	−	11.9143i	0.449995	−	0.449995i	−0.445358	−	0.895353i	$-0.646923\pi$
$701$	11.9143	−	11.9143i	0.449995	−	0.449995i	0.895353	+	0.445358i	$0.146923\pi$
$702$	−10.7173	−	10.7173i	−0.404498	−	0.404498i
$703$	3.80249	+	25.9805i	0.143414	+	0.979871i
$704$		−	3.64633i		−	0.137426i
$705$	15.5031	+	17.9841i	0.583880	+	0.677322i
$706$		−	6.79098i		−	0.255582i
$707$	−2.13886	−	2.13886i	−0.0804402	−	0.0804402i
$708$	−15.8943			−0.597345
$709$	−13.4491	−	13.4491i	−0.505093	−	0.505093i	0.407923	−	0.913016i	$-0.366253\pi$
$709$	−13.4491	−	13.4491i	−0.505093	−	0.505093i	−0.913016	+	0.407923i	$0.866253\pi$
$710$	−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
$717$	11.6951			0.436763
$718$			4.91904i			0.183577i
$719$		−	15.0482i		−	0.561204i	−0.959824	−	0.280602i	$-0.909466\pi$
$719$		−	15.0482i		−	0.561204i	0.959824	−	0.280602i	$-0.0905342\pi$
$720$	−0.473980	−	0.549834i	−0.0176642	−	0.0204911i
$721$	6.46775	+	6.46775i	0.240872	+	0.240872i
$722$			0.366413i			0.0136365i
$723$		−	7.61354i		−	0.283151i
$724$	16.2161			0.602667
$725$	−5.78558	−	7.81150i	−0.214871	−	0.290112i
$726$	2.95992	−	2.95992i	0.109853	−	0.109853i
$727$	−48.0498			−1.78207			−0.891033	−	0.453938i	$-0.850019\pi$
$727$	−48.0498			−1.78207			−0.891033	+	0.453938i	$0.850019\pi$
$728$	−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
$732$	22.4697			0.830502
$733$	17.9391	−	17.9391i	0.662596	−	0.662596i	−0.293395	−	0.955991i	$-0.594785\pi$
$733$	17.9391	−	17.9391i	0.662596	−	0.662596i	0.955991	+	0.293395i	$0.0947851\pi$
$734$	−21.4924	+	21.4924i	−0.793298	+	0.793298i
$735$	25.7280	+	1.90617i	0.948991	+	0.0703102i
$736$	7.79067			0.287168
$737$	−7.33001	+	7.33001i	−0.270004	+	0.270004i
$738$	3.02280			0.111271
$739$	27.0049			0.993391			0.496696	−	0.867925i	$-0.334547\pi$
$739$	27.0049			0.993391			0.496696	+	0.867925i	$0.334547\pi$
$740$	−13.5668	+	0.969960i	−0.498727	+	0.0356564i
$741$	−24.4550			−0.898376
$742$	−0.517862			−0.0190113
$743$	21.8683	−	21.8683i	0.802270	−	0.802270i	−0.181180	−	0.983450i	$-0.557992\pi$
$743$	21.8683	−	21.8683i	0.802270	−	0.802270i	0.983450	+	0.181180i	$0.0579917\pi$
$744$	−8.35226			−0.306209
$745$	−5.88265	−	6.82408i	−0.215523	−	0.250015i
$746$	−19.5734	+	19.5734i	−0.716632	+	0.716632i
$747$	1.02907	−	1.02907i	0.0376515	−	0.0376515i
$748$	29.4998			1.07862
$749$			4.50318i			0.164542i
$750$	19.8861	+	4.48584i	0.726139	+	0.163800i
$751$		−	17.0169i		−	0.620957i	−0.950580	−	0.310479i	$-0.899511\pi$
$751$		−	17.0169i		−	0.620957i	0.950580	−	0.310479i	$-0.100489\pi$
$752$	−4.11794	+	4.11794i	−0.150166	+	0.150166i
$753$	−25.6085			−0.933227
$754$	−4.27130	+	4.27130i	−0.155552	+	0.155552i
$755$	−12.9438	−	15.0153i	−0.471074	−	0.546462i
$756$	4.00017			0.145485
$757$		−	31.0722i		−	1.12934i	−0.825317	−	0.564669i	$-0.809004\pi$
$757$		−	31.0722i		−	1.12934i	0.825317	−	0.564669i	$-0.190996\pi$
$758$			1.90775i			0.0692925i
$759$	36.6259	+	36.6259i	1.32944	+	1.32944i
$760$	9.62597	+	0.713182i	0.349171	+	0.0258698i
$761$			14.8739i			0.539180i	0.962975	+	0.269590i	$0.0868882\pi$
$761$			14.8739i			0.539180i	−0.962975	+	0.269590i	$0.913112\pi$
$762$			35.8476i			1.29862i
$763$	2.33772			0.0846312
$764$	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	$-0.564126\pi$
$769$	21.6211	−	21.6211i	0.779677	−	0.779677i	0.979776	+	0.200099i	$0.0641264\pi$
$770$	6.66771	+	0.494007i	0.240288	+	0.0178028i
$771$	19.4861	+	19.4861i	0.701773	+	0.701773i
$772$	8.78779			0.316279
$773$	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
$775$	18.4051	−	13.6317i	0.661129	−	0.489665i
$776$		−	14.6206i		−	0.524847i
$777$	−5.43194	+	7.29460i	−0.194870	+	0.261692i
$778$	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
$782$			63.0286i			2.25390i
$783$	9.48381			0.338924
$784$			6.32757i			0.225985i
$785$	1.60728	−	21.6937i	0.0573662	−	0.774283i
$786$	−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
$790$	−2.39959	−	0.177784i	−0.0853736	−	0.00632528i
$791$	6.89384	+	6.89384i	0.245117	+	0.245117i
$792$	1.18377			0.0420633
$793$	27.0742	+	27.0742i	0.961432	+	0.961432i
$794$	6.99419	+	6.99419i	0.248214	+	0.248214i
$795$	1.95022	−	1.68117i	0.0691673	−	0.0596251i
$796$	4.20114	−	4.20114i	0.148906	−	0.148906i
$797$	7.46766			0.264518			0.132259	−	0.991215i	$-0.457777\pi$
$797$	7.46766			0.264518			0.132259	+	0.991215i	$0.457777\pi$
$798$	4.56384	−	4.56384i	0.161558	−	0.161558i
$799$	−33.3152	−	33.3152i	−1.17861	−	1.17861i
$800$	−0.736849	+	4.94541i	−0.0260516	+	0.174847i
$801$	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
$808$			3.68870i			0.129768i
$809$	13.5592	−	13.5592i	0.476716	−	0.476716i	−0.427364	−	0.904080i	$-0.640558\pi$
$809$	13.5592	−	13.5592i	0.476716	−	0.476716i	0.904080	+	0.427364i	$0.140558\pi$
$810$	−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	$0.611596\pi$
$812$		−	1.59424i		−	0.0559468i
$813$	−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
$820$	−13.5941	−	15.7696i	−0.474726	−	0.550699i
$821$	−3.12570			−0.109088			−0.0545438	−	0.998511i	$-0.517370\pi$
$821$	−3.12570			−0.109088			−0.0545438	+	0.998511i	$0.517370\pi$
$822$		−	29.5302i		−	1.02999i
$823$	−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
$827$		−	18.4817i		−	0.642673i	−0.946965	−	0.321336i	$-0.895868\pi$
$827$		−	18.4817i		−	0.642673i	0.946965	−	0.321336i	$-0.104132\pi$
$828$			2.52921i			0.0878961i
$829$	−21.6955	+	21.6955i	−0.753515	+	0.753515i	−0.975134	−	0.221618i	$-0.928866\pi$
$829$	−21.6955	+	21.6955i	−0.753515	+	0.753515i	0.221618	+	0.975134i	$0.428866\pi$
$830$	−9.99642	−	0.740629i	−0.346981	−	0.0257076i
$831$	−22.2568	+	22.2568i	−0.772079	+	0.772079i
$832$	3.10704			0.107717
$833$	−51.1917			−1.77369
$834$	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
$837$			22.3453i			0.772365i
$838$			13.7527i			0.475079i
$839$	35.7782			1.23520			0.617600	−	0.786492i	$-0.288105\pi$
$839$	35.7782			1.23520			0.617600	+	0.786492i	$0.288105\pi$
$840$	2.18297	+	2.53232i	0.0753195	+	0.0873733i
$841$			25.2203i			0.869665i
$842$	−4.62725	−	4.62725i	−0.159466	−	0.159466i
$843$			9.90444i			0.341127i
$844$	−27.4901			−0.946248
$845$	−5.66748	+	4.88561i	−0.194967	+	0.168070i
$846$	−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
$853$			37.5829i			1.28681i	0.765524	+	0.643407i	$0.222480\pi$
$853$			37.5829i			1.28681i	−0.765524	+	0.643407i	$0.777520\pi$
$854$	−10.1053			−0.345795
$855$	−0.231532	+	3.12503i	−0.00791822	+	0.106874i
$856$	3.88311	−	3.88311i	0.132722	−	0.132722i
$857$			24.8711i			0.849581i	0.905292	+	0.424791i	$0.139652\pi$
$857$			24.8711i			0.849581i	−0.905292	+	0.424791i	$0.860348\pi$
$858$	14.6070	+	14.6070i	0.498674	+	0.498674i
$859$	−15.0119	−	15.0119i	−0.512199	−	0.512199i	0.403000	−	0.915200i	$-0.367967\pi$
$859$	−15.0119	−	15.0119i	−0.512199	−	0.512199i	−0.915200	+	0.403000i	$0.867967\pi$
$860$	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
$865$	−0.502287	+	6.77948i	−0.0170783	+	0.230509i
$866$	23.2986	+	23.2986i	0.791720	+	0.791720i
$867$	−62.4702	+	62.4702i	−2.12160	+	2.12160i
$868$	3.75626			0.127496
$869$	2.77448	−	2.77448i	0.0941179	−	0.0941179i
$870$	5.17549	+	6.00376i	0.175466	+	0.203546i
$871$	−6.24589	−	6.24589i	−0.211634	−	0.211634i
$872$	−2.01583	−	2.01583i	−0.0682646	−	0.0682646i
$873$	4.74650			0.160645
$874$	−23.7798	−	23.7798i	−0.804363	−	0.804363i
$875$	−8.94338	−	2.01741i	−0.302341	−	0.0682010i
$876$			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
$880$	−5.32361	−	6.17558i	−0.179459	−	0.208179i
$881$			2.51776i			0.0848254i	0.999100	+	0.0424127i	$0.0135044\pi$
$881$			2.51776i			0.0848254i	−0.999100	+	0.0424127i	$0.986496\pi$
$882$	−2.05422			−0.0691691
$883$			8.49437i			0.285858i	0.989733	+	0.142929i	$0.0456521\pi$
$883$			8.49437i			0.285858i	−0.989733	+	0.142929i	$0.954348\pi$
$884$			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	0.890881	−	0.454238i	$-0.150088\pi$
$887$	13.0043	+	13.0043i	0.436643	+	0.436643i	−0.454238	+	0.890881i	$0.650088\pi$
$888$	10.9742	−	1.60617i	0.368269	−	0.0538996i
$889$		−	16.1217i		−	0.540706i
$890$	1.35521	−	18.2916i	0.0454268	−	0.613136i
$891$		−	35.9840i		−	1.20551i
$892$	−9.42660	−	9.42660i	−0.315626	−	0.315626i
$893$	25.1387			0.841235
$894$	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
$902$	33.9512			1.13045
$903$		−	16.3214i		−	0.543144i
$904$		−	11.8892i		−	0.395428i
$905$	27.4643	−	23.6754i	0.912944	−	0.786996i
$906$	11.4306	+	11.4306i	0.379757	+	0.379757i
$907$		−	39.4216i		−	1.30897i	−0.756074	−	0.654487i	$-0.772885\pi$
$907$		−	39.4216i		−	1.30897i	0.756074	−	0.654487i	$-0.227115\pi$
$908$		−	17.9587i		−	0.595981i
$909$	−1.19752			−0.0397193
$910$	−0.420942	+	5.68155i	−0.0139541	+	0.188342i
$911$	−10.3558	+	10.3558i	−0.343105	+	0.343105i	−0.857533	−	0.514429i	$-0.828004\pi$
$911$	−10.3558	+	10.3558i	−0.343105	+	0.343105i	0.514429	+	0.857533i	$0.328004\pi$
$912$	−7.87084			−0.260629
$913$	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
$917$	3.14564			0.103878
$918$	27.9063	−	27.9063i	0.921044	−	0.921044i
$919$	21.8092	−	21.8092i	0.719419	−	0.719419i	−0.249068	−	0.968486i	$-0.580124\pi$
$919$	21.8092	−	21.8092i	0.719419	−	0.719419i	0.968486	+	0.249068i	$0.0801241\pi$
$920$	13.1946	−	11.3743i	0.435013	−	0.375000i
$921$	24.3341			0.801836
$922$	17.2203	−	17.2203i	0.567122	−	0.567122i
$923$	0.00471020			0.000155038
$924$	−5.45197			−0.179357
$925$	−21.5612	+	21.4502i	−0.708929	+	0.705280i
$926$	13.3316			0.438102
$927$	3.62121			0.118936
$928$	−1.37472	+	1.37472i	−0.0451274	+	0.0451274i
$929$	−16.6531			−0.546370			−0.273185	−	0.961962i	$-0.588077\pi$
$929$	−16.6531			−0.546370			−0.273185	+	0.961962i	$0.588077\pi$
$930$	−14.1457	+	12.1942i	−0.463857	+	0.399865i
$931$	19.3139	−	19.3139i	0.632988	−	0.632988i
$932$	2.23686	−	2.23686i	0.0732706	−	0.0732706i
$933$	17.2862			0.565926
$934$			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	$0.118804\pi$
$938$	2.33124			0.0761178
$939$	−29.9322	+	29.9322i	−0.976802	+	0.976802i
$940$	−0.962160	+	12.9865i	−0.0313822	+	0.423572i
$941$	−13.4862			−0.439637			−0.219818	−	0.975541i	$-0.570547\pi$
$941$	−13.4862			−0.439637			−0.219818	+	0.975541i	$0.570547\pi$
$942$			17.7383i			0.577944i
$943$			72.5394i			2.36221i
$944$	−6.16388	−	6.16388i	−0.200617	−	0.200617i
$945$	6.77485	−	5.84021i	0.220386	−	0.189982i
$946$			39.8032i			1.29411i
$947$			22.9700i			0.746424i	0.927746	+	0.373212i	$0.121744\pi$
$947$			22.9700i			0.746424i	−0.927746	+	0.373212i	$0.878256\pi$
$948$	1.96207			0.0637249
$949$	−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	−0.194641	−	0.980875i	$-0.562354\pi$
$953$	24.2716	−	24.2716i	0.786234	−	0.786234i	0.980875	+	0.194641i	$0.0623541\pi$
$954$	−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
$957$	−12.9258			−0.417832
$958$	−10.6512	−	10.6512i	−0.344124	−	0.344124i
$959$			13.2806i			0.428854i
$960$	0.301249	−	4.06602i	0.00972276	−	0.131230i
$961$		−	10.0172i		−	0.323136i
$962$	15.1583	+	11.2877i	0.488723	+	0.363929i
$963$	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
$967$			20.1548i			0.648135i	0.946034	+	0.324068i	$0.105051\pi$
$967$			20.1548i			0.648135i	−0.946034	+	0.324068i	$0.894949\pi$
$968$	2.29574			0.0737879
$969$		−	63.6772i		−	2.04561i
$970$	−21.3459	−	24.7620i	−0.685375	−	0.795060i
$971$	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
$975$	−16.8592	−	22.7628i	−0.539927	−	0.728992i
$976$	8.71382	+	8.71382i	0.278923	+	0.278923i
$977$	2.60048			0.0831967			0.0415983	−	0.999134i	$-0.486755\pi$
$977$	2.60048			0.0831967			0.0415983	+	0.999134i	$0.486755\pi$
$978$	13.7612	+	13.7612i	0.440033	+	0.440033i
$979$	21.1493	+	21.1493i	0.675935	+	0.675935i
$980$	9.23820	+	10.7166i	0.295103	+	0.342330i
$981$	0.654431	−	0.654431i	0.0208944	−	0.0208944i
$982$	9.04897			0.288764
$983$	35.9359	−	35.9359i	1.14618	−	1.14618i	0.158880	−	0.987298i	$-0.449212\pi$
$983$	35.9359	−	35.9359i	1.14618	−	1.14618i	0.987298	−	0.158880i	$-0.0507881\pi$
$984$	12.0049	+	12.0049i	0.382701	+	0.382701i
$985$	1.96614	−	26.5374i	0.0626465	−	0.845552i
$986$	−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	0.189833	−	0.981816i	$-0.439205\pi$
$991$	−24.9318	−	24.9318i	−0.791984	−	0.791984i	−0.981816	+	0.189833i	$0.939205\pi$
$992$	−3.23904	−	3.23904i	−0.102840	−	0.102840i
$993$			14.7713i			0.468755i
$994$	−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
$997$		−	23.9821i		−	0.759520i	−0.925085	−	0.379760i	$-0.876007\pi$
$997$		−	23.9821i		−	0.759520i	0.925085	−	0.379760i	$-0.123993\pi$
$998$	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.h.e.253.7	yes	20
5.2	odd	4		370.2.g.e.327.4	yes	20
37.6	odd	4		370.2.g.e.43.4	✓	20
185.117	even	4	inner	370.2.h.e.117.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.4	✓	20	37.6	odd	4
370.2.g.e.327.4	yes	20	5.2	odd	4
370.2.h.e.117.7	yes	20	185.117	even	4	inner
370.2.h.e.253.7	yes	20	1.1	even	1	trivial

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.h (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

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Database

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