LMFDB - Embedded newform 370.2.m.c.159.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.8
Root			$2.90925i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.c.249.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(2.51948 + 1.45462i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.19673 - 1.88887i) q^{5} -2.90925i q^{6} +(-0.191824 - 0.110750i) q^{7} +1.00000 q^{8} +(2.73187 + 4.73173i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(2.51948 + 1.45462i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.19673 - 1.88887i) q^{5} -2.90925i q^{6} +(-0.191824 - 0.110750i) q^{7} +1.00000 q^{8} +(2.73187 + 4.73173i) q^{9} +(-1.03745 + 1.98083i) q^{10} +6.08400 q^{11} +(-2.51948 + 1.45462i) q^{12} +(0.0723701 - 0.125349i) q^{13} +0.221499i q^{14} +(-0.267544 - 6.49978i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.31013 - 2.26922i) q^{17} +(2.73187 - 4.73173i) q^{18} +(3.28333 + 1.89563i) q^{19} +(2.23418 - 0.0919631i) q^{20} +(-0.322198 - 0.558064i) q^{21} +(-3.04200 - 5.26890i) q^{22} -0.277470 q^{23} +(2.51948 + 1.45462i) q^{24} +(-2.13567 + 4.52094i) q^{25} -0.144740 q^{26} +7.16761i q^{27} +(0.191824 - 0.110750i) q^{28} -1.60727i q^{29} +(-5.49520 + 3.48159i) q^{30} +0.776351i q^{31} +(-0.500000 + 0.866025i) q^{32} +(15.3285 + 8.84994i) q^{33} +(-1.31013 + 2.26922i) q^{34} +(0.0203698 + 0.494868i) q^{35} -5.46373 q^{36} +(-5.49268 + 2.61351i) q^{37} -3.79127i q^{38} +(0.364671 - 0.210543i) q^{39} +(-1.19673 - 1.88887i) q^{40} +(-5.07928 + 8.79757i) q^{41} +(-0.322198 + 0.558064i) q^{42} -6.51449 q^{43} +(-3.04200 + 5.26890i) q^{44} +(5.66833 - 10.8228i) q^{45} +(0.138735 + 0.240296i) q^{46} -7.42616i q^{47} -2.90925i q^{48} +(-3.47547 - 6.01969i) q^{49} +(4.98309 - 0.410924i) q^{50} -7.62301i q^{51} +(0.0723701 + 0.125349i) q^{52} +(3.13449 - 1.80970i) q^{53} +(6.20734 - 3.58381i) q^{54} +(-7.28091 - 11.4919i) q^{55} +(-0.191824 - 0.110750i) q^{56} +(5.51487 + 9.55204i) q^{57} +(-1.39194 + 0.803636i) q^{58} +(11.3301 - 6.54142i) q^{59} +(5.76274 + 3.01819i) q^{60} +(-8.82479 - 5.09500i) q^{61} +(0.672340 - 0.388176i) q^{62} -1.21021i q^{63} +1.00000 q^{64} +(-0.323375 + 0.0133108i) q^{65} -17.6999i q^{66} +(-12.9680 - 7.48709i) q^{67} +2.62027 q^{68} +(-0.699081 - 0.403615i) q^{69} +(0.418383 - 0.265075i) q^{70} +(-6.50051 + 11.2592i) q^{71} +(2.73187 + 4.73173i) q^{72} +5.99590i q^{73} +(5.00970 + 3.45005i) q^{74} +(-11.9571 + 8.28384i) q^{75} +(-3.28333 + 1.89563i) q^{76} +(-1.16706 - 0.673800i) q^{77} +(-0.364671 - 0.210543i) q^{78} +(5.73029 + 3.30838i) q^{79} +(-1.03745 + 1.98083i) q^{80} +(-2.23059 + 3.86349i) q^{81} +10.1586 q^{82} +(-3.52033 + 2.03246i) q^{83} +0.644396 q^{84} +(-2.71838 + 5.19032i) q^{85} +(3.25725 + 5.64172i) q^{86} +(2.33798 - 4.04950i) q^{87} +6.08400 q^{88} +(-10.8608 + 6.27049i) q^{89} +(-12.2069 + 0.502462i) q^{90} +(-0.0277646 + 0.0160299i) q^{91} +(0.138735 - 0.240296i) q^{92} +(-1.12930 + 1.95600i) q^{93} +(-6.43124 + 3.71308i) q^{94} +(-0.348657 - 8.47036i) q^{95} +(-2.51948 + 1.45462i) q^{96} -5.20777 q^{97} +(-3.47547 + 6.01969i) q^{98} +(16.6207 + 28.7879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	2.51948	+	1.45462i	1.45462	+	0.839828i	0.998739	−	0.0502101i	$-0.0159891\pi$
$3$	2.51948	+	1.45462i	1.45462	+	0.839828i	0.455886	+	0.890038i	$0.349322\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.19673	−	1.88887i	−0.535194	−	0.844729i
$5$	−1.19673	−	1.88887i	−0.535194	−	0.844729i
$6$		−	2.90925i		−	1.18770i
$7$	−0.191824	−	0.110750i	−0.0725026	−	0.0418594i	0.463310	−	0.886196i	$-0.346661\pi$
$7$	−0.191824	−	0.110750i	−0.0725026	−	0.0418594i	−0.535813	+	0.844337i	$0.679995\pi$
$8$	1.00000			0.353553
$9$	2.73187	+	4.73173i	0.910622	+	1.57724i
$10$	−1.03745	+	1.98083i	−0.328069	+	0.626395i
$11$	6.08400			1.83439			0.917197	−	0.398433i	$-0.130446\pi$
$11$	6.08400			1.83439			0.917197	+	0.398433i	$0.130446\pi$
$12$	−2.51948	+	1.45462i	−0.727312	+	0.419914i
$13$	0.0723701	−	0.125349i	0.0200719	−	0.0347655i	−0.855815	−	0.517282i	$-0.826944\pi$
$13$	0.0723701	−	0.125349i	0.0200719	−	0.0347655i	0.875887	+	0.482517i	$0.160277\pi$
$14$			0.221499i			0.0591981i
$15$	−0.267544	−	6.49978i	−0.0690795	−	1.67823i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.31013	−	2.26922i	−0.317754	−	0.550366i	0.662265	−	0.749270i	$-0.269595\pi$
$17$	−1.31013	−	2.26922i	−0.317754	−	0.550366i	−0.980019	+	0.198904i	$0.936262\pi$
$18$	2.73187	−	4.73173i	0.643907	−	1.11528i
$19$	3.28333	+	1.89563i	0.753249	+	0.434888i	0.826866	−	0.562398i	$-0.190121\pi$
$19$	3.28333	+	1.89563i	0.753249	+	0.434888i	−0.0736180	+	0.997287i	$0.523455\pi$
$20$	2.23418	−	0.0919631i	0.499577	−	0.0205636i
$21$	−0.322198	−	0.558064i	−0.0703094	−	0.121779i
$22$	−3.04200	−	5.26890i	−0.648557	−	1.12333i
$23$	−0.277470			−0.0578565			−0.0289282	−	0.999581i	$-0.509209\pi$
$23$	−0.277470			−0.0578565			−0.0289282	+	0.999581i	$0.509209\pi$
$24$	2.51948	+	1.45462i	0.514288	+	0.296924i
$25$	−2.13567	+	4.52094i	−0.427134	+	0.904188i
$26$	−0.144740			−0.0283859
$27$			7.16761i			1.37941i
$28$	0.191824	−	0.110750i	0.0362513	−	0.0209297i
$29$		−	1.60727i		−	0.298463i	−0.988802	−	0.149231i	$-0.952320\pi$
$29$		−	1.60727i		−	0.298463i	0.988802	−	0.149231i	$-0.0476800\pi$
$30$	−5.49520	+	3.48159i	−1.00328	+	0.635648i
$31$			0.776351i			0.139437i	0.997567	+	0.0697184i	$0.0222101\pi$
$31$			0.776351i			0.139437i	−0.997567	+	0.0697184i	$0.977790\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	15.3285	+	8.84994i	2.66836	+	1.54058i
$34$	−1.31013	+	2.26922i	−0.224686	+	0.389168i
$35$	0.0203698	+	0.494868i	0.00344312	+	0.0836480i
$36$	−5.46373			−0.910622
$37$	−5.49268	+	2.61351i	−0.902992	+	0.429658i
$37$	−5.49268	+	2.61351i	−0.902992	+	0.429658i
$38$		−	3.79127i		−	0.615025i
$39$	0.364671	−	0.210543i	0.0583940	−	0.0337138i
$40$	−1.19673	−	1.88887i	−0.189220	−	0.298657i
$41$	−5.07928	+	8.79757i	−0.793250	+	1.37395i	0.130694	+	0.991423i	$0.458279\pi$
$41$	−5.07928	+	8.79757i	−0.793250	+	1.37395i	−0.923944	+	0.382527i	$0.875054\pi$
$42$	−0.322198	+	0.558064i	−0.0497163	+	0.0861111i
$43$	−6.51449			−0.993451			−0.496726	−	0.867908i	$-0.665464\pi$
$43$	−6.51449			−0.993451			−0.496726	+	0.867908i	$0.665464\pi$
$44$	−3.04200	+	5.26890i	−0.458599	+	0.794316i
$45$	5.66833	−	10.8228i	0.844984	−	1.61336i
$46$	0.138735	+	0.240296i	0.0204553	+	0.0354297i
$47$		−	7.42616i		−	1.08322i	−0.840631	−	0.541608i	$-0.817816\pi$
$47$		−	7.42616i		−	1.08322i	0.840631	−	0.541608i	$-0.182184\pi$
$48$		−	2.90925i		−	0.419914i
$49$	−3.47547	−	6.01969i	−0.496496	−	0.859956i
$50$	4.98309	−	0.410924i	0.704715	−	0.0581134i
$51$		−	7.62301i		−	1.06743i
$52$	0.0723701	+	0.125349i	0.0100359	+	0.0173827i
$53$	3.13449	−	1.80970i	0.430556	−	0.248582i	−0.269028	−	0.963132i	$-0.586702\pi$
$53$	3.13449	−	1.80970i	0.430556	−	0.248582i	0.699583	+	0.714551i	$0.253369\pi$
$54$	6.20734	−	3.58381i	0.844711	−	0.487694i
$55$	−7.28091	−	11.4919i	−0.981757	−	1.54957i
$56$	−0.191824	−	0.110750i	−0.0256335	−	0.0147995i
$57$	5.51487	+	9.55204i	0.730463	+	1.26520i
$58$	−1.39194	+	0.803636i	−0.182770	+	0.105523i
$59$	11.3301	−	6.54142i	1.47505	−	0.851620i	0.475445	−	0.879746i	$-0.342287\pi$
$59$	11.3301	−	6.54142i	1.47505	−	0.851620i	0.999604	+	0.0281258i	$0.00895390\pi$
$60$	5.76274	+	3.01819i	0.743967	+	0.389646i
$61$	−8.82479	−	5.09500i	−1.12990	−	0.652347i	−0.185989	−	0.982552i	$-0.559549\pi$
$61$	−8.82479	−	5.09500i	−1.12990	−	0.652347i	−0.943909	+	0.330205i	$0.892882\pi$
$62$	0.672340	−	0.388176i	0.0853873	−	0.0492984i
$63$		−	1.21021i		−	0.152472i
$64$	1.00000			0.125000
$65$	−0.323375	+	0.0133108i	−0.0401097	+	0.00165100i
$66$		−	17.6999i		−	2.17870i
$67$	−12.9680	−	7.48709i	−1.58429	−	0.914693i	−0.994222	−	0.107343i	$-0.965766\pi$
$67$	−12.9680	−	7.48709i	−1.58429	−	0.914693i	−0.590073	−	0.807350i	$-0.700901\pi$
$68$	2.62027			0.317754
$69$	−0.699081	−	0.403615i	−0.0841594	−	0.0485895i
$70$	0.418383	−	0.265075i	0.0500064	−	0.0316825i
$71$	−6.50051	+	11.2592i	−0.771468	+	1.33622i	0.165290	+	0.986245i	$0.447144\pi$
$71$	−6.50051	+	11.2592i	−0.771468	+	1.33622i	−0.936758	+	0.349977i	$0.886189\pi$
$72$	2.73187	+	4.73173i	0.321954	+	0.557640i
$73$			5.99590i			0.701767i	0.936419	+	0.350884i	$0.114119\pi$
$73$			5.99590i			0.701767i	−0.936419	+	0.350884i	$0.885881\pi$
$74$	5.00970	+	3.45005i	0.582366	+	0.401060i
$75$	−11.9571	+	8.28384i	−1.38068	+	0.956535i
$76$	−3.28333	+	1.89563i	−0.376624	+	0.217444i
$77$	−1.16706	−	0.673800i	−0.132998	−	0.0767867i
$78$	−0.364671	−	0.210543i	−0.0412908	−	0.0238393i
$79$	5.73029	+	3.30838i	0.644707	+	0.372222i	0.786426	−	0.617685i	$-0.211929\pi$
$79$	5.73029	+	3.30838i	0.644707	+	0.372222i	−0.141718	+	0.989907i	$0.545263\pi$
$80$	−1.03745	+	1.98083i	−0.115990	+	0.221464i
$81$	−2.23059	+	3.86349i	−0.247843	+	0.429277i
$82$	10.1586			1.12183
$83$	−3.52033	+	2.03246i	−0.386406	+	0.223092i	−0.680602	−	0.732654i	$-0.738282\pi$
$83$	−3.52033	+	2.03246i	−0.386406	+	0.223092i	0.294196	+	0.955745i	$0.404948\pi$
$84$	0.644396			0.0703094
$85$	−2.71838	+	5.19032i	−0.294850	+	0.562969i
$86$	3.25725	+	5.64172i	0.351238	+	0.608362i
$87$	2.33798	−	4.04950i	0.250658	−	0.434152i
$88$	6.08400			0.648557
$89$	−10.8608	+	6.27049i	−1.15124	+	0.664671i	−0.949190	−	0.314704i	$-0.898095\pi$
$89$	−10.8608	+	6.27049i	−1.15124	+	0.664671i	−0.202053	+	0.979375i	$0.564761\pi$
$90$	−12.2069	+	0.502462i	−1.28672	+	0.0529641i
$91$	−0.0277646	+	0.0160299i	−0.00291052	+	0.00168039i
$92$	0.138735	−	0.240296i	0.0144641	−	0.0250526i
$93$	−1.12930	+	1.95600i	−0.117103	+	0.202828i
$94$	−6.43124	+	3.71308i	−0.663332	+	0.382975i
$95$	−0.348657	−	8.47036i	−0.0357714	−	0.869041i
$96$	−2.51948	+	1.45462i	−0.257144	+	0.148462i
$97$	−5.20777			−0.528769			−0.264385	−	0.964417i	$-0.585169\pi$
$97$	−5.20777			−0.528769			−0.264385	+	0.964417i	$0.585169\pi$
$98$	−3.47547	+	6.01969i	−0.351075	+	0.608080i
$99$	16.6207	+	28.7879i	1.67044	+	2.89329i
$100$	−2.84741	−	4.11002i	−0.284741	−	0.411002i
$101$	8.65668			0.861372			0.430686	−	0.902502i	$-0.358272\pi$
$101$	8.65668			0.861372			0.430686	+	0.902502i	$0.358272\pi$
$102$	−6.60172	+	3.81150i	−0.653668	+	0.377395i
$103$	−11.1036			−1.09407			−0.547035	−	0.837109i	$-0.684244\pi$
$103$	−11.1036			−1.09407			−0.547035	+	0.837109i	$0.684244\pi$
$104$	0.0723701	−	0.125349i	0.00709647	−	0.0122914i
$105$	−0.668526	+	1.27644i	−0.0652415	+	0.124568i
$106$	−3.13449	−	1.80970i	−0.304449	−	0.175774i
$107$	15.5556	+	8.98104i	1.50382	+	0.868230i	0.999990	+	0.00442608i	$0.00140887\pi$
$107$	15.5556	+	8.98104i	1.50382	+	0.868230i	0.503828	+	0.863804i	$0.331924\pi$
$108$	−6.20734	−	3.58381i	−0.597301	−	0.344852i
$109$	5.62967	−	3.25029i	0.539224	−	0.311321i	−0.205540	−	0.978649i	$-0.565895\pi$
$109$	5.62967	−	3.25029i	0.539224	−	0.311321i	0.744764	+	0.667327i	$0.232562\pi$
$110$	−6.31182	+	12.0514i	−0.601808	+	1.14906i
$111$	−17.6404	−	1.40511i	−1.67435	−	0.133367i
$112$			0.221499i			0.0209297i
$113$	−4.08400	−	7.07369i	−0.384190	−	0.665437i	0.607466	−	0.794346i	$-0.292186\pi$
$113$	−4.08400	−	7.07369i	−0.384190	−	0.665437i	−0.991657	+	0.128908i	$0.958853\pi$
$114$	5.51487	−	9.55204i	0.516515	−	0.894630i
$115$	0.332057	+	0.524105i	0.0309644	+	0.0488730i
$116$	1.39194	+	0.803636i	0.129238	+	0.0746157i
$117$	0.790822			0.0731115
$118$	−11.3301	−	6.54142i	−1.04302	−	0.602186i
$119$			0.580387i			0.0532040i
$120$	−0.267544	−	6.49978i	−0.0244233	−	0.593346i
$121$	26.0150			2.36500
$122$			10.1900i			0.922558i
$123$	−25.5943	+	14.7769i	−2.30776	+	1.33239i
$124$	−0.672340	−	0.388176i	−0.0603779	−	0.0348592i
$125$	11.0953	−	1.37634i	0.992394	−	0.123103i
$126$	−1.04807	+	0.605106i	−0.0933699	+	0.0539071i
$127$	−8.48756	+	4.90030i	−0.753150	+	0.434831i	−0.826831	−	0.562451i	$-0.809859\pi$
$127$	−8.48756	+	4.90030i	−0.753150	+	0.434831i	0.0736812	+	0.997282i	$0.476525\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−16.4132	−	9.47614i	−1.44510	−	0.834328i
$130$	0.173215	+	0.273396i	0.0151920	+	0.0239784i
$131$	1.84401	−	1.06464i	0.161112	−	0.0930179i	−0.417276	−	0.908780i	$-0.637015\pi$
$131$	1.84401	−	1.06464i	0.161112	−	0.0930179i	0.578388	+	0.815762i	$0.303682\pi$
$132$	−15.3285	+	8.84994i	−1.33418	+	0.770288i
$133$	−0.419881	−	0.727256i	−0.0364083	−	0.0630611i
$134$			14.9742i			1.29357i
$135$	13.5387	−	8.57770i	1.16523	−	0.738251i
$136$	−1.31013	−	2.26922i	−0.112343	−	0.194584i
$137$		−	11.3683i		−	0.971259i	−0.874165	−	0.485630i	$-0.838590\pi$
$137$		−	11.3683i		−	0.971259i	0.874165	−	0.485630i	$-0.161410\pi$
$138$			0.807229i			0.0687159i
$139$	−3.73056	−	6.46151i	−0.316422	−	0.548058i	0.663317	−	0.748339i	$-0.269148\pi$
$139$	−3.73056	−	6.46151i	−0.316422	−	0.548058i	−0.979739	+	0.200280i	$0.935815\pi$
$140$	−0.438753	−	0.229793i	−0.0370814	−	0.0194211i
$141$	10.8023	−	18.7101i	0.909716	−	1.57567i
$142$	13.0010			1.09102
$143$	0.440300	−	0.762621i	0.0368197	−	0.0637736i
$144$	2.73187	−	4.73173i	0.227656	−	0.394311i
$145$	−3.03593	+	1.92347i	−0.252120	+	0.159736i
$146$	5.19260	−	2.99795i	0.429743	−	0.248112i
$147$		−	20.2220i		−	1.66788i
$148$	0.482980	−	6.06356i	0.0397007	−	0.498421i
$149$	−10.5731			−0.866181			−0.433091	−	0.901350i	$-0.642577\pi$
$149$	−10.5731			−0.866181			−0.433091	+	0.901350i	$0.642577\pi$
$150$	13.1525	+	6.21320i	1.07390	+	0.507306i
$151$	−7.03678	+	12.1881i	−0.572645	+	0.991851i	0.423648	+	0.905827i	$0.360749\pi$
$151$	−7.03678	+	12.1881i	−0.572645	+	0.991851i	−0.996293	+	0.0860237i	$0.972584\pi$
$152$	3.28333	+	1.89563i	0.266314	+	0.153756i
$153$	7.15822	−	12.3984i	0.578708	−	1.00235i
$154$			1.34760i			0.108593i
$155$	1.46643	−	0.929083i	0.117786	−	0.0746258i
$156$			0.421085i			0.0337138i
$157$	13.2368	−	7.64224i	1.05641	−	0.609917i	0.131971	−	0.991254i	$-0.457869\pi$
$157$	13.2368	−	7.64224i	1.05641	−	0.609917i	0.924436	+	0.381336i	$0.124536\pi$
$158$		−	6.61676i		−	0.526401i
$159$	10.5297			0.835063
$160$	2.23418	−	0.0919631i	0.176627	−	0.00727032i
$161$	0.0532253	+	0.0307297i	0.00419475	+	0.00242184i
$162$	4.46118			0.350503
$163$	8.94061	+	15.4856i	0.700283	+	1.21293i	0.968367	+	0.249530i	$0.0802761\pi$
$163$	8.94061	+	15.4856i	0.700283	+	1.21293i	−0.268084	+	0.963395i	$0.586391\pi$
$164$	−5.07928	−	8.79757i	−0.396625	−	0.686975i
$165$	−1.62774	−	39.5446i	−0.126719	−	3.07855i
$166$	3.52033	+	2.03246i	0.273230	+	0.157750i
$167$	−3.85790	+	6.68208i	−0.298533	+	0.517075i	−0.975801	−	0.218662i	$-0.929831\pi$
$167$	−3.85790	+	6.68208i	−0.298533	+	0.517075i	0.677267	+	0.735737i	$0.263164\pi$
$168$	−0.322198	−	0.558064i	−0.0248581	−	0.0430555i
$169$	6.48953	+	11.2402i	0.499194	+	0.864630i
$170$	5.85414	−	0.240968i	0.448992	−	0.0184814i
$171$			20.7145i			1.58408i
$172$	3.25725	−	5.64172i	0.248363	−	0.430177i
$173$	−8.22699	+	4.74986i	−0.625487	+	0.361125i	−0.779002	−	0.627021i	$-0.784274\pi$
$173$	−8.22699	+	4.74986i	−0.625487	+	0.361125i	0.153515	+	0.988146i	$0.450941\pi$
$174$	−4.67596			−0.354483
$175$	0.910365	−	0.630700i	0.0688171	−	0.0476764i
$176$	−3.04200	−	5.26890i	−0.229299	−	0.397158i
$177$	38.0612			2.86086
$178$	10.8608	+	6.27049i	0.814052	+	0.469993i
$179$			10.8474i			0.810776i	0.914145	+	0.405388i	$0.132864\pi$
$179$			10.8474i			0.810776i	−0.914145	+	0.405388i	$0.867136\pi$
$180$	6.53862	+	10.3203i	0.487360	+	0.769229i
$181$	−8.45183	+	14.6390i	−0.628220	+	1.08811i	0.359689	+	0.933072i	$0.382883\pi$
$181$	−8.45183	+	14.6390i	−0.628220	+	1.08811i	−0.987909	+	0.155036i	$0.950451\pi$
$182$	0.0277646	+	0.0160299i	0.00205805	+	0.00118822i
$183$	−14.8226	−	25.6735i	−1.09572	−	1.89784i
$184$	−0.277470			−0.0204553
$185$	11.5098	+	7.24731i	0.846220	+	0.532833i
$186$	2.25860			0.165609
$187$	−7.97085	−	13.8059i	−0.582886	−	1.00959i
$188$	6.43124	+	3.71308i	0.469047	+	0.270804i
$189$	0.793810	−	1.37492i	0.0577412	−	0.100011i
$190$	−7.16122	+	4.53713i	−0.519529	+	0.329158i
$191$		−	20.7156i		−	1.49893i	−0.662044	−	0.749465i	$-0.730311\pi$
$191$		−	20.7156i		−	1.49893i	0.662044	−	0.749465i	$-0.269689\pi$
$192$	2.51948	+	1.45462i	0.181828	+	0.104979i
$193$	14.7238			1.05984			0.529922	−	0.848047i	$-0.322221\pi$
$193$	14.7238			1.05984			0.529922	+	0.848047i	$0.322221\pi$
$194$	2.60389	+	4.51006i	0.186948	+	0.323804i
$195$	−0.834101	−	0.436853i	−0.0597312	−	0.0312837i
$196$	6.95094			0.496496
$197$	18.3664	−	10.6038i	1.30855	−	0.755491i	0.326695	−	0.945130i	$-0.394065\pi$
$197$	18.3664	−	10.6038i	1.30855	−	0.755491i	0.981854	+	0.189639i	$0.0607317\pi$
$198$	16.6207	−	28.7879i	1.18118	−	2.04586i
$199$		−	14.0640i		−	0.996972i	−0.866898	−	0.498486i	$-0.833890\pi$
$199$		−	14.0640i		−	0.996972i	0.866898	−	0.498486i	$-0.166110\pi$
$200$	−2.13567	+	4.52094i	−0.151015	+	0.319679i
$201$	−21.7818	−	37.7272i	−1.53637	−	2.66107i
$202$	−4.32834	−	7.49690i	−0.304541	−	0.527480i
$203$	−0.178005	+	0.308313i	−0.0124935	+	0.0216393i
$204$	6.60172	+	3.81150i	0.462213	+	0.266859i
$205$	22.6960	−	0.934213i	1.58516	−	0.0652483i
$206$	5.55180	+	9.61601i	0.386812	+	0.669979i
$207$	−0.758011	−	1.31291i	−0.0526854	−	0.0912538i
$208$	−0.144740			−0.0100359
$209$	19.9758	+	11.5330i	1.38176	+	0.797757i
$210$	1.43969	−	0.0592607i	0.0993484	−	0.00408938i
$211$	−4.44627			−0.306094			−0.153047	−	0.988219i	$-0.548909\pi$
$211$	−4.44627			−0.306094			−0.153047	+	0.988219i	$0.548909\pi$
$212$			3.61940i			0.248582i
$213$	−32.7558	+	18.9116i	−2.24439	+	1.29580i
$214$		−	17.9621i		−	1.22786i
$215$	7.79609	+	12.3050i	0.531689	+	0.839197i
$216$			7.16761i			0.487694i
$217$	0.0859806	−	0.148923i	0.00583674	−	0.0101095i
$218$	−5.62967	−	3.25029i	−0.381289	−	0.220137i
$219$	−8.72179	+	15.1066i	−0.589364	+	1.02081i
$220$	13.5927	−	0.559504i	0.916421	−	0.0377217i
$221$	−0.379258			−0.0255116
$222$	7.60334	+	15.9796i	0.510303	+	1.07248i
$223$			10.8958i			0.729635i	0.931079	+	0.364818i	$0.118869\pi$
$223$			10.8958i			0.729635i	−0.931079	+	0.364818i	$0.881131\pi$
$224$	0.191824	−	0.110750i	0.0128168	−	0.00739977i
$225$	−27.2262	+	2.24518i	−1.81508	+	0.149678i
$226$	−4.08400	+	7.07369i	−0.271664	+	0.470535i
$227$	−1.84751	+	3.19999i	−0.122624	+	0.212391i	−0.920802	−	0.390031i	$-0.872464\pi$
$227$	−1.84751	+	3.19999i	−0.122624	+	0.212391i	0.798178	+	0.602422i	$0.205798\pi$
$228$	−11.0297			−0.730463
$229$	10.3979	−	18.0097i	0.687113	−	1.19011i	−0.285655	−	0.958333i	$-0.592211\pi$
$229$	10.3979	−	18.0097i	0.687113	−	1.19011i	0.972768	−	0.231782i	$-0.0744556\pi$
$230$	0.287860	−	0.549622i	0.0189809	−	0.0362410i
$231$	−1.96025	−	3.39526i	−0.128975	−	0.223392i
$232$		−	1.60727i		−	0.105523i
$233$		−	9.94711i		−	0.651657i	−0.945429	−	0.325828i	$-0.894357\pi$
$233$		−	9.94711i		−	0.651657i	0.945429	−	0.325828i	$-0.105643\pi$
$234$	−0.395411	−	0.684872i	−0.0258488	−	0.0447715i
$235$	−14.0271	+	8.88711i	−0.915025	+	0.579731i
$236$			13.0828i			0.851620i
$237$	9.62491	+	16.6708i	0.625205	+	1.08289i
$238$	0.502630	−	0.290193i	0.0325806	−	0.0188104i
$239$	−10.2828	+	5.93680i	−0.665142	+	0.384020i	−0.794233	−	0.607613i	$-0.792127\pi$
$239$	−10.2828	+	5.93680i	−0.665142	+	0.384020i	0.129091	+	0.991633i	$0.458794\pi$
$240$	−5.49520	+	3.48159i	−0.354714	+	0.224736i
$241$	7.68274	+	4.43563i	0.494889	+	0.285724i	0.726600	−	0.687060i	$-0.241099\pi$
$241$	7.68274	+	4.43563i	0.494889	+	0.285724i	−0.231712	+	0.972785i	$0.574433\pi$
$242$	−13.0075	−	22.5297i	−0.836155	−	1.44826i
$243$	7.38214	−	4.26208i	0.473564	−	0.273413i
$244$	8.82479	−	5.09500i	0.564949	−	0.326174i
$245$	−7.21122	+	13.7687i	−0.460708	+	0.879647i
$246$	25.5943	+	14.7769i	1.63183	+	0.942140i
$247$	0.475230	−	0.274374i	0.0302382	−	0.0174580i
$248$			0.776351i			0.0492984i
$249$	−11.8259			−0.749434
$250$	−6.73959	−	8.92064i	−0.426249	−	0.564191i
$251$		−	7.69687i		−	0.485822i	−0.970049	−	0.242911i	$-0.921898\pi$
$251$		−	7.69687i		−	0.485822i	0.970049	−	0.242911i	$-0.0781023\pi$
$252$	1.04807	+	0.605106i	0.0660225	+	0.0381181i
$253$	−1.68813			−0.106132
$254$	8.48756	+	4.90030i	0.532557	+	0.307472i
$255$	−14.3989	+	9.12269i	−0.901693	+	0.571285i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.0691	−	19.1723i	−0.690472	−	1.19593i	−0.971683	−	0.236287i	$-0.924070\pi$
$257$	−11.0691	−	19.1723i	−0.690472	−	1.19593i	0.281212	−	0.959646i	$-0.409264\pi$
$258$			18.9523i			1.17992i
$259$	1.34307	+	0.106980i	0.0834545	+	0.00664739i
$260$	0.150160	−	0.286706i	0.00931253	−	0.0177808i
$261$	7.60518	−	4.39085i	0.470749	−	0.271787i
$262$	−1.84401	−	1.06464i	−0.113923	−	0.0657736i
$263$	24.9793	+	14.4218i	1.54029	+	0.889287i	0.998820	+	0.0485661i	$0.0154652\pi$
$263$	24.9793	+	14.4218i	1.54029	+	0.889287i	0.541469	+	0.840720i	$0.317868\pi$
$264$	15.3285	+	8.84994i	0.943406	+	0.544676i
$265$	−7.16944	−	3.75493i	−0.440415	−	0.230664i
$266$	−0.419881	+	0.727256i	−0.0257446	+	0.0445909i
$267$	−36.4848			−2.23284
$268$	12.9680	−	7.48709i	0.792147	−	0.457347i
$269$	9.51308			0.580023			0.290011	−	0.957023i	$-0.406341\pi$
$269$	9.51308			0.580023			0.290011	+	0.957023i	$0.406341\pi$
$270$	−14.1979	−	7.43601i	−0.864054	−	0.452541i
$271$	−5.71516	−	9.89894i	−0.347171	−	0.601318i	0.638575	−	0.769560i	$-0.279524\pi$
$271$	−5.71516	−	9.89894i	−0.347171	−	0.601318i	−0.985746	+	0.168242i	$0.946191\pi$
$272$	−1.31013	+	2.26922i	−0.0794385	+	0.137592i
$273$	−0.0932700			−0.00564496
$274$	−9.84523	+	5.68415i	−0.594772	+	0.343392i
$275$	−12.9934	+	27.5054i	−0.783533	+	1.65864i
$276$	0.699081	−	0.403615i	0.0420797	−	0.0242947i
$277$	−15.7756	+	27.3242i	−0.947867	+	1.64175i	−0.197960	+	0.980210i	$0.563432\pi$
$277$	−15.7756	+	27.3242i	−0.947867	+	1.64175i	−0.749907	+	0.661544i	$0.769902\pi$
$278$	−3.73056	+	6.46151i	−0.223744	+	0.387536i
$279$	−3.67349	+	2.12089i	−0.219926	+	0.126974i
$280$	0.0203698	+	0.494868i	0.00121733	+	0.0295740i
$281$	12.3570	−	7.13433i	0.737158	−	0.425598i	−0.0838770	−	0.996476i	$-0.526730\pi$
$281$	12.3570	−	7.13433i	0.737158	−	0.425598i	0.821035	+	0.570878i	$0.193397\pi$
$282$	−21.6045			−1.28653
$283$	−2.27949	+	3.94820i	−0.135502	+	0.234696i	−0.925789	−	0.378041i	$-0.876598\pi$
$283$	−2.27949	+	3.94820i	−0.135502	+	0.234696i	0.790287	+	0.612737i	$0.209931\pi$
$284$	−6.50051	−	11.2592i	−0.385734	−	0.668111i
$285$	11.4428	−	21.8481i	0.677811	−	1.29417i
$286$	−0.880599			−0.0520709
$287$	1.94865	−	1.12506i	0.115025	−	0.0664100i
$288$	−5.46373			−0.321954
$289$	5.06710	−	8.77648i	0.298065	−	0.516263i
$290$	3.18374	+	1.66746i	0.186956	+	0.0979165i
$291$	−13.1209	−	7.57535i	−0.769161	−	0.444075i
$292$	−5.19260	−	2.99795i	−0.303874	−	0.175442i
$293$	5.06215	+	2.92263i	0.295734	+	0.170742i	0.640525	−	0.767938i	$-0.278717\pi$
$293$	5.06215	+	2.92263i	0.295734	+	0.170742i	−0.344791	+	0.938679i	$0.612050\pi$
$294$	−17.5128	+	10.1110i	−1.02137	+	0.589686i
$295$	−25.9149	−	13.5727i	−1.50883	−	0.790235i
$296$	−5.49268	+	2.61351i	−0.319256	+	0.151907i
$297$			43.6078i			2.53038i
$298$	5.28654	+	9.15656i	0.306241	+	0.530425i
$299$	−0.0200805	+	0.0347805i	−0.00116129	+	0.00201141i
$300$	−1.19548	−	14.4970i	−0.0690210	−	0.836987i
$301$	1.24964	+	0.721477i	0.0720278	+	0.0415853i
$302$	14.0736			0.809843
$303$	21.8104	+	12.5922i	1.25297	+	0.723404i
$304$		−	3.79127i		−	0.217444i
$305$	0.937103	+	22.7662i	0.0536584	+	1.30359i
$306$	−14.3164			−0.818416
$307$		−	33.1089i		−	1.88962i	−0.327614	−	0.944812i	$-0.606244\pi$
$307$		−	33.1089i		−	1.88962i	0.327614	−	0.944812i	$-0.393756\pi$
$308$	1.16706	−	0.673800i	0.0664992	−	0.0383933i
$309$	−27.9754	−	16.1516i	−1.59146	−	0.918831i
$310$	−1.53782	−	0.805422i	−0.0873425	−	0.0457449i
$311$	21.7793	−	12.5743i	1.23499	−	0.713022i	0.266924	−	0.963718i	$-0.413993\pi$
$311$	21.7793	−	12.5743i	1.23499	−	0.713022i	0.968066	+	0.250696i	$0.0806594\pi$
$312$	0.364671	−	0.210543i	0.0206454	−	0.0119196i
$313$	5.97122	+	10.3425i	0.337513	+	0.584590i	0.983964	−	0.178365i	$-0.0570809\pi$
$313$	5.97122	+	10.3425i	0.337513	+	0.584590i	−0.646451	+	0.762955i	$0.723748\pi$
$314$	−13.2368	−	7.64224i	−0.746993	−	0.431277i
$315$	−2.28594	+	1.44830i	−0.128798	+	0.0816023i
$316$	−5.73029	+	3.30838i	−0.322354	+	0.186111i
$317$	0.692689	−	0.399924i	0.0389053	−	0.0224620i	−0.480421	−	0.877038i	$-0.659516\pi$
$317$	0.692689	−	0.399924i	0.0389053	−	0.0224620i	0.519327	+	0.854576i	$0.326183\pi$
$318$	−5.26487	−	9.11902i	−0.295239	−	0.511369i
$319$		−	9.77864i		−	0.547499i
$320$	−1.19673	−	1.88887i	−0.0668993	−	0.105591i
$321$	26.1281	+	45.2552i	1.45833	+	2.52590i
$322$		−	0.0614593i		−	0.00342500i
$323$		−	9.93413i		−	0.552750i
$324$	−2.23059	−	3.86349i	−0.123922	−	0.214639i
$325$	0.412135	+	0.594885i	0.0228611	+	0.0329983i
$326$	8.94061	−	15.4856i	0.495175	−	0.857668i
$327$	18.9118			1.04583
$328$	−5.07928	+	8.79757i	−0.280456	+	0.485765i
$329$	−0.822444	+	1.42451i	−0.0453428	+	0.0785360i
$330$	−33.4328	+	21.1820i	−1.84041	+	1.16603i
$331$	−8.83765	+	5.10242i	−0.485761	+	0.280454i	−0.722814	−	0.691042i	$-0.757152\pi$
$331$	−8.83765	+	5.10242i	−0.485761	+	0.280454i	0.237053	+	0.971497i	$0.423818\pi$
$332$		−	4.06492i		−	0.223092i
$333$	−27.3717	−	18.8502i	−1.49996	−	1.03298i
$334$	7.71580			0.422190
$335$	1.37707	+	33.4549i	0.0752375	+	1.82784i
$336$	−0.322198	+	0.558064i	−0.0175774	+	0.0304449i
$337$	16.4969	+	9.52449i	0.898644	+	0.518832i	0.876760	−	0.480928i	$-0.159700\pi$
$337$	16.4969	+	9.52449i	0.898644	+	0.518832i	0.0218837	+	0.999761i	$0.493034\pi$
$338$	6.48953	−	11.2402i	0.352984	−	0.611386i
$339$		−	23.7627i		−	1.29062i
$340$	−3.13575	−	4.94935i	−0.170060	−	0.268416i
$341$			4.72332i			0.255782i
$342$	17.9393	−	10.3572i	0.970044	−	0.560055i
$343$			3.09012i			0.166851i
$344$	−6.51449			−0.351238
$345$	0.0742353	+	1.80349i	0.00399669	+	0.0970967i
$346$	8.22699	+	4.74986i	0.442286	+	0.255354i
$347$	−13.8443			−0.743199			−0.371600	−	0.928393i	$-0.621191\pi$
$347$	−13.8443			−0.743199			−0.371600	+	0.928393i	$0.621191\pi$
$348$	2.33798	+	4.04950i	0.125329	+	0.217076i
$349$	−4.07759	−	7.06260i	−0.218268	−	0.378052i	0.736010	−	0.676970i	$-0.236708\pi$
$349$	−4.07759	−	7.06260i	−0.218268	−	0.378052i	−0.954279	+	0.298918i	$0.903374\pi$
$350$	−1.00138	−	0.473050i	−0.0535263	−	0.0252856i
$351$	0.898451	+	0.518721i	0.0479558	+	0.0276873i
$352$	−3.04200	+	5.26890i	−0.162139	+	0.280833i
$353$	9.11593	+	15.7892i	0.485192	+	0.840377i	0.999855	−	0.0170155i	$-0.00541646\pi$
$353$	9.11593	+	15.7892i	0.485192	+	0.840377i	−0.514663	+	0.857392i	$0.672083\pi$
$354$	−19.0306	−	32.9620i	−1.01147	−	1.75191i
$355$	29.0465	−	1.19561i	1.54163	−	0.0634566i
$356$		−	12.5410i		−	0.664671i
$357$	−0.844245	+	1.46228i	−0.0446822	+	0.0773918i
$358$	9.39416	−	5.42372i	0.496497	−	0.286653i
$359$	10.2372			0.540301			0.270150	−	0.962818i	$-0.412927\pi$
$359$	10.2372			0.540301			0.270150	+	0.962818i	$0.412927\pi$
$360$	5.66833	−	10.8228i	0.298747	−	0.570409i
$361$	−2.31314	−	4.00648i	−0.121744	−	0.210868i
$362$	16.9037			0.888437
$363$	65.5445	+	37.8421i	3.44019	+	1.98620i
$364$		−	0.0320598i		−	0.00168039i
$365$	11.3255	−	7.17548i	0.592803	−	0.375582i
$366$	−14.8226	+	25.6735i	−0.774790	+	1.34198i
$367$	13.0111	+	7.51197i	0.679175	+	0.392122i	0.799544	−	0.600607i	$-0.205075\pi$
$367$	13.0111	+	7.51197i	0.679175	+	0.392122i	−0.120369	+	0.992729i	$0.538408\pi$
$368$	0.138735	+	0.240296i	0.00723206	+	0.0125263i
$369$	−55.5037			−2.88940
$370$	0.521439	−	13.5915i	0.0271083	−	0.706587i
$371$	−0.801694			−0.0416219
$372$	−1.12930	−	1.95600i	−0.0585515	−	0.101414i
$373$	7.24996	+	4.18576i	0.375389	+	0.216731i	0.675810	−	0.737076i	$-0.263794\pi$
$373$	7.24996	+	4.18576i	0.375389	+	0.216731i	−0.300421	+	0.953807i	$0.597127\pi$
$374$	−7.97085	+	13.8059i	−0.412163	+	0.713887i
$375$	29.9565	+	12.6718i	1.54695	+	0.654371i
$376$		−	7.42616i		−	0.382975i
$377$	−0.201469	−	0.116318i	−0.0103762	−	0.00599070i
$378$	−1.58762			−0.0816584
$379$	−7.69375	−	13.3260i	−0.395201	−	0.684509i	0.597926	−	0.801552i	$-0.295992\pi$
$379$	−7.69375	−	13.3260i	−0.395201	−	0.684509i	−0.993127	+	0.117043i	$0.962658\pi$
$380$	7.50987	+	3.93323i	0.385248	+	0.201771i
$381$	−28.5124			−1.46073
$382$	−17.9402	+	10.3578i	−0.917903	+	0.529952i
$383$	14.0817	−	24.3903i	0.719543	−	1.24629i	−0.241637	−	0.970367i	$-0.577684\pi$
$383$	14.0817	−	24.3903i	0.719543	−	1.24629i	0.961181	−	0.275919i	$-0.0889822\pi$
$384$		−	2.90925i		−	0.148462i
$385$	0.123930	+	3.01078i	0.00631604	+	0.153443i
$386$	−7.36191	−	12.7512i	−0.374711	−	0.649019i
$387$	−17.7967	−	30.8248i	−0.904659	−	1.56691i
$388$	2.60389	−	4.51006i	0.132192	−	0.228964i
$389$	−15.2311	−	8.79367i	−0.772246	−	0.445857i	0.0614289	−	0.998111i	$-0.480434\pi$
$389$	−15.2311	−	8.79367i	−0.772246	−	0.445857i	−0.833675	+	0.552255i	$0.813768\pi$
$390$	0.0387243	+	0.940779i	0.00196088	+	0.0476382i
$391$	0.363522	+	0.629639i	0.0183841	+	0.0318422i
$392$	−3.47547	−	6.01969i	−0.175538	−	0.304040i
$393$	6.19460			0.312476
$394$	−18.3664	−	10.6038i	−0.925284	−	0.534213i
$395$	−0.608498	−	14.7830i	−0.0306169	−	0.743814i
$396$	−33.2413			−1.67044
$397$			8.29560i			0.416344i	0.978092	+	0.208172i	$0.0667514\pi$
$397$			8.29560i			0.416344i	−0.978092	+	0.208172i	$0.933249\pi$
$398$	−12.1798	+	7.03201i	−0.610518	+	0.352483i
$399$		−	2.44308i		−	0.122307i
$400$	4.98309	−	0.410924i	0.249154	−	0.0205462i
$401$		−	12.0757i		−	0.603034i	−0.953461	−	0.301517i	$-0.902507\pi$
$401$		−	12.0757i		−	0.603034i	0.953461	−	0.301517i	$-0.0974930\pi$
$402$	−21.7818	+	37.7272i	−1.08638	+	1.88166i
$403$	0.0973146	+	0.0561846i	0.00484759	+	0.00279876i
$404$	−4.32834	+	7.49690i	−0.215343	+	0.372985i
$405$	9.96706	−	0.410264i	0.495267	−	0.0203862i
$406$	0.356009			0.0176685
$407$	−33.4175	+	15.9006i	−1.65644	+	0.788162i
$408$		−	7.62301i		−	0.377395i
$409$	−8.90476	+	5.14117i	−0.440312	+	0.254214i	−0.703730	−	0.710467i	$-0.748484\pi$
$409$	−8.90476	+	5.14117i	−0.440312	+	0.254214i	0.263418	+	0.964682i	$0.415150\pi$
$410$	−12.1571	−	19.1882i	−0.600394	−	0.947638i
$411$	16.5366	−	28.6422i	0.815691	−	1.41282i
$412$	5.55180	−	9.61601i	0.273518	−	0.473747i
$413$	−2.89784			−0.142593
$414$	−0.758011	+	1.31291i	−0.0372542	+	0.0645261i
$415$	8.05194	+	4.21714i	0.395254	+	0.207011i
$416$	0.0723701	+	0.125349i	0.00354824	+	0.00614572i
$417$		−	21.7062i		−	1.06296i
$418$		−	23.0661i		−	1.12820i
$419$	−1.28468	−	2.22513i	−0.0627606	−	0.108704i	0.832938	−	0.553367i	$-0.186657\pi$
$419$	−1.28468	−	2.22513i	−0.0627606	−	0.108704i	−0.895698	+	0.444662i	$0.853324\pi$
$420$	−0.771169	−	1.21718i	−0.0376292	−	0.0593924i
$421$			36.5506i			1.78137i	0.454624	+	0.890683i	$0.349774\pi$
$421$			36.5506i			1.78137i	−0.454624	+	0.890683i	$0.650226\pi$
$422$	2.22314	+	3.85059i	0.108221	+	0.187444i
$423$	35.1386	−	20.2873i	1.70850	−	0.986401i
$424$	3.13449	−	1.80970i	0.152224	−	0.0878868i
$425$	13.0570	−	1.07673i	0.633358	−	0.0522291i
$426$	32.7558	+	18.9116i	1.58703	+	0.916270i
$427$	1.12854	+	1.95468i	0.0546137	+	0.0945938i
$428$	−15.5556	+	8.98104i	−0.751909	+	0.434115i
$429$	2.21866	−	1.28094i	0.107118	−	0.0618444i
$430$	6.75843	−	12.9041i	0.325921	−	0.622293i
$431$	−12.9598	−	7.48236i	−0.624253	−	0.360413i	0.154270	−	0.988029i	$-0.450697\pi$
$431$	−12.9598	−	7.48236i	−0.624253	−	0.360413i	−0.778523	+	0.627616i	$0.784031\pi$
$432$	6.20734	−	3.58381i	0.298651	−	0.172426i
$433$		−	26.7819i		−	1.28706i	−0.765422	−	0.643528i	$-0.777470\pi$
$433$		−	26.7819i		−	1.28706i	0.765422	−	0.643528i	$-0.222530\pi$
$434$	−0.171961			−0.00825440
$435$	−10.4469	+	0.430016i	−0.500891	+	0.0206177i
$436$			6.50058i			0.311321i
$437$	−0.911026	−	0.525981i	−0.0435803	−	0.0251611i
$438$	17.4436			0.833486
$439$	27.5675	+	15.9161i	1.31572	+	0.759634i	0.983038	−	0.183404i	$-0.0587116\pi$
$439$	27.5675	+	15.9161i	1.31572	+	0.759634i	0.332687	+	0.943037i	$0.392045\pi$
$440$	−7.28091	−	11.4919i	−0.347104	−	0.547855i
$441$	18.9890	−	32.8900i	0.904240	−	1.56619i
$442$	0.189629	+	0.328447i	0.00901973	+	0.0156226i
$443$		−	4.63532i		−	0.220231i	−0.993919	−	0.110115i	$-0.964878\pi$
$443$		−	4.63532i		−	0.220231i	0.993919	−	0.110115i	$-0.0351220\pi$
$444$	10.0371	−	14.5745i	0.476338	−	0.691674i
$445$	24.8416	+	13.0106i	1.17761	+	0.616761i
$446$	9.43602	−	5.44789i	0.446808	−	0.257965i
$447$	−26.6387	−	15.3799i	−1.25997	−	0.727443i
$448$	−0.191824	−	0.110750i	−0.00906283	−	0.00523243i
$449$	−2.66572	−	1.53905i	−0.125803	−	0.0726324i	0.435778	−	0.900054i	$-0.356473\pi$
$449$	−2.66572	−	1.53905i	−0.125803	−	0.0726324i	−0.561581	+	0.827422i	$0.689807\pi$
$450$	15.5575	+	22.4560i	0.733388	+	1.05859i
$451$	−30.9023	+	53.5244i	−1.45513	+	2.52037i
$452$	8.16800			0.384190
$453$	−35.4581	+	20.4718i	−1.66597	+	0.961847i
$454$	3.69503			0.173416
$455$	0.0635052	+	0.0332603i	0.00297717	+	0.00155927i
$456$	5.51487	+	9.55204i	0.258258	+	0.447315i
$457$	−5.97845	+	10.3550i	−0.279660	+	0.484386i	−0.971300	−	0.237857i	$-0.923555\pi$
$457$	−5.97845	+	10.3550i	−0.279660	+	0.484386i	0.691640	+	0.722242i	$0.256889\pi$
$458$	−20.7958			−0.971725
$459$	16.2649	−	9.39053i	0.759179	−	0.438312i
$460$	−0.619917	+	0.0255170i	−0.0289038	+	0.00118974i
$461$	−20.8728	+	12.0509i	−0.972142	+	0.561266i	−0.899888	−	0.436120i	$-0.856352\pi$
$461$	−20.8728	+	12.0509i	−0.972142	+	0.561266i	−0.0722531	+	0.997386i	$0.523019\pi$
$462$	−1.96025	+	3.39526i	−0.0911992	+	0.157962i
$463$	−14.0877	+	24.4006i	−0.654712	+	1.13399i	0.327254	+	0.944936i	$0.393877\pi$
$463$	−14.0877	+	24.4006i	−0.654712	+	1.13399i	−0.981966	+	0.189057i	$0.939457\pi$
$464$	−1.39194	+	0.803636i	−0.0646191	+	0.0373079i
$465$	5.04611	−	0.207708i	0.234008	−	0.00963222i
$466$	−8.61445	+	4.97356i	−0.399057	+	0.230396i
$467$	−9.72748			−0.450134			−0.225067	−	0.974343i	$-0.572260\pi$
$467$	−9.72748			−0.450134			−0.225067	+	0.974343i	$0.572260\pi$
$468$	−0.395411	+	0.684872i	−0.0182779	+	0.0316582i
$469$	1.65838	+	2.87240i	0.0765770	+	0.132635i
$470$	14.7100	+	7.70424i	0.678521	+	0.355370i
$471$	44.4664			2.04890
$472$	11.3301	−	6.54142i	0.521509	−	0.301093i
$473$	−39.6342			−1.82238
$474$	9.62491	−	16.6708i	0.442087	−	0.765717i
$475$	−15.5822	+	10.7953i	−0.714959	+	0.495323i
$476$	−0.502630	−	0.290193i	−0.0230380	−	0.0133010i
$477$	17.1260	+	9.88772i	0.784147	+	0.452728i
$478$	10.2828	+	5.93680i	0.470326	+	0.271543i
$479$	12.3632	−	7.13788i	0.564888	−	0.326138i	−0.190217	−	0.981742i	$-0.560919\pi$
$479$	12.3632	−	7.13788i	0.564888	−	0.326138i	0.755105	+	0.655604i	$0.227586\pi$
$480$	5.76274	+	3.01819i	0.263032	+	0.137761i
$481$	−0.0699066	+	0.877641i	−0.00318747	+	0.0400170i
$482$		−	8.87126i		−	0.404075i
$483$	0.0894003	+	0.154846i	0.00406785	+	0.00704573i
$484$	−13.0075	+	22.5297i	−0.591251	+	1.02408i
$485$	6.23230	+	9.83681i	0.282994	+	0.446667i
$486$	−7.38214	−	4.26208i	−0.334861	−	0.193332i
$487$	8.42422			0.381738			0.190869	−	0.981616i	$-0.438869\pi$
$487$	8.42422			0.381738			0.190869	+	0.981616i	$0.438869\pi$
$488$	−8.82479	−	5.09500i	−0.399479	−	0.230640i
$489$			52.0209i			2.35247i
$490$	15.5296	−	0.639230i	0.701557	−	0.0288775i
$491$	−16.2253			−0.732237			−0.366119	−	0.930568i	$-0.619314\pi$
$491$	−16.2253			−0.732237			−0.366119	+	0.930568i	$0.619314\pi$
$492$		−	29.5538i		−	1.33239i
$493$	−3.64725	+	2.10574i	−0.164264	+	0.0948378i
$494$	−0.475230	−	0.274374i	−0.0213816	−	0.0123447i
$495$	34.4861	−	65.8456i	1.55003	−	2.95954i
$496$	0.672340	−	0.388176i	0.0301890	−	0.0174296i
$497$	2.49390	−	1.43986i	0.111867	−	0.0645864i
$498$	5.91294	+	10.2415i	0.264965	+	0.458933i
$499$	18.3628	+	10.6018i	0.822033	+	0.474601i	0.851117	−	0.524976i	$-0.175926\pi$
$499$	18.3628	+	10.6018i	0.822033	+	0.474601i	−0.0290841	+	0.999577i	$0.509259\pi$
$500$	−4.35571	+	10.2970i	−0.194793	+	0.460495i
$501$	−19.4398	+	11.2236i	−0.868507	+	0.501433i
$502$	−6.66569	+	3.84844i	−0.297504	+	0.171764i
$503$	−21.0542	−	36.4669i	−0.938760	−	1.62598i	−0.767788	−	0.640704i	$-0.778642\pi$
$503$	−21.0542	−	36.4669i	−0.938760	−	1.62598i	−0.170972	−	0.985276i	$-0.554691\pi$
$504$		−	1.21021i		−	0.0539071i
$505$	−10.3597	−	16.3514i	−0.461001	−	0.727626i
$506$	0.844063	+	1.46196i	0.0375232	+	0.0649921i
$507$			37.7593i			1.67695i
$508$		−	9.80060i		−	0.434831i
$509$	1.65619	+	2.86861i	0.0734095	+	0.127149i	0.900393	−	0.435076i	$-0.143279\pi$
$509$	1.65619	+	2.86861i	0.0734095	+	0.127149i	−0.826984	+	0.562225i	$0.809945\pi$
$510$	15.0999	+	7.90846i	0.668636	+	0.350192i
$511$	0.664044	−	1.15016i	0.0293756	−	0.0508800i
$512$	1.00000			0.0441942
$513$	−13.5872	+	23.5337i	−0.599888	+	1.03904i
$514$	−11.0691	+	19.1723i	−0.488237	+	0.845652i
$515$	13.2880	+	20.9733i	0.585540	+	0.924194i
$516$	16.4132	−	9.47614i	0.722549	−	0.417164i
$517$		−	45.1807i		−	1.98705i
$518$	−0.578889	−	1.21663i	−0.0254349	−	0.0534554i
$519$	−27.6370			−1.21313
$520$	−0.323375	+	0.0133108i	−0.0141809	+	0.000583716i
$521$	2.68321	−	4.64745i	0.117554	−	0.203609i	−0.801244	−	0.598338i	$-0.795828\pi$
$521$	2.68321	−	4.64745i	0.117554	−	0.203609i	0.918798	+	0.394729i	$0.129161\pi$
$522$	−7.60518	−	4.39085i	−0.332870	−	0.192182i
$523$	−17.5017	+	30.3138i	−0.765294	+	1.32553i	0.174796	+	0.984605i	$0.444073\pi$
$523$	−17.5017	+	30.3138i	−0.765294	+	1.32553i	−0.940091	+	0.340924i	$0.889260\pi$
$524$			2.12928i			0.0930179i
$525$	3.21108	−	0.264798i	0.140143	−	0.0115567i
$526$		−	28.8436i		−	1.25764i
$527$	1.76171	−	1.01712i	0.0767413	−	0.0443066i
$528$		−	17.6999i		−	0.770288i
$529$	−22.9230			−0.996653
$530$	0.332851	+	8.08638i	0.0144581	+	0.351250i
$531$	61.9045	+	35.7406i	2.68642	+	1.55101i
$532$	0.839763			0.0364083
$533$	0.735176	+	1.27336i	0.0318440	+	0.0551554i
$534$	18.2424	+	31.5968i	0.789427	+	1.36733i
$535$	−1.65185	−	40.1305i	−0.0714157	−	1.73499i
$536$	−12.9680	−	7.48709i	−0.560133	−	0.323393i
$537$	−15.7790	+	27.3300i	−0.680912	+	1.17937i
$538$	−4.75654	−	8.23857i	−0.205069	−	0.355190i
$539$	−21.1448	−	36.6238i	−0.910769	−	1.57750i
$540$	0.659156	+	16.0137i	0.0283656	+	0.689120i
$541$			30.8147i			1.32483i	0.749138	+	0.662414i	$0.230468\pi$
$541$			30.8147i			1.32483i	−0.749138	+	0.662414i	$0.769532\pi$
$542$	−5.71516	+	9.89894i	−0.245487	+	0.425196i
$543$	−42.5885	+	24.5885i	−1.82765	+	1.05519i
$544$	2.62027			0.112343
$545$	−12.8766	−	6.74400i	−0.551572	−	0.288881i
$546$	0.0466350	+	0.0807742i	0.00199579	+	0.00345682i
$547$	1.96309			0.0839356			0.0419678	−	0.999119i	$-0.486637\pi$
$547$	1.96309			0.0839356			0.0419678	+	0.999119i	$0.486637\pi$
$548$	9.84523	+	5.68415i	0.420568	+	0.242815i
$549$		−	55.6754i		−	2.37617i
$550$	30.3171	−	2.50006i	1.29273	−	0.106603i
$551$	3.04680	−	5.27721i	0.129798	−	0.224817i
$552$	−0.699081	−	0.403615i	−0.0297549	−	0.0171790i
$553$	−0.732804	−	1.26925i	−0.0311620	−	0.0539741i
$554$	31.5513			1.34049
$555$	18.4567	+	35.0020i	0.783445	+	1.48575i
$556$	7.46111			0.316422
$557$	11.0114	+	19.0723i	0.466567	+	0.808118i	0.999271	−	0.0381841i	$-0.0121573\pi$
$557$	11.0114	+	19.0723i	0.466567	+	0.808118i	−0.532704	+	0.846302i	$0.678824\pi$
$558$	3.67349	+	2.12089i	0.155511	+	0.0897843i
$559$	−0.471455	+	0.816583i	−0.0199404	+	0.0345378i
$560$	0.418383	−	0.265075i	0.0176799	−	0.0112015i
$561$		−	46.3784i		−	1.95810i
$562$	−12.3570	−	7.13433i	−0.521250	−	0.300944i
$563$	−15.7065			−0.661950			−0.330975	−	0.943639i	$-0.607378\pi$
$563$	−15.7065			−0.661950			−0.330975	+	0.943639i	$0.607378\pi$
$564$	10.8023	+	18.7101i	0.454858	+	0.787837i
$565$	−8.47385	+	16.1795i	−0.356498	+	0.680675i
$566$	4.55899			0.191629
$567$	0.855761	−	0.494074i	0.0359386	−	0.0207491i
$568$	−6.50051	+	11.2592i	−0.272755	+	0.472426i
$569$		−	4.82994i		−	0.202482i	−0.994862	−	0.101241i	$-0.967719\pi$
$569$		−	4.82994i		−	0.202482i	0.994862	−	0.101241i	$-0.0322813\pi$
$570$	−24.6424	+	1.01433i	−1.03216	+	0.0424856i
$571$	−0.111370	−	0.192898i	−0.00466068	−	0.00807253i	0.863686	−	0.504031i	$-0.168150\pi$
$571$	−0.111370	−	0.192898i	−0.00466068	−	0.00807253i	−0.868346	+	0.495958i	$0.834817\pi$
$572$	0.440300	+	0.762621i	0.0184099	+	0.0318868i
$573$	30.1334	−	52.1927i	1.25884	−	2.18038i
$574$	−1.94865	−	1.12506i	−0.0813353	−	0.0469589i
$575$	0.592585	−	1.25442i	0.0247125	−	0.0523131i
$576$	2.73187	+	4.73173i	0.113828	+	0.197155i
$577$	18.5090	+	32.0586i	0.770541	+	1.33462i	0.937267	+	0.348614i	$0.113347\pi$
$577$	18.5090	+	32.0586i	0.770541	+	1.33462i	−0.166725	+	0.986003i	$0.553319\pi$
$578$	−10.1342			−0.421527
$579$	37.0964	+	21.4176i	1.54167	+	0.890086i
$580$	−0.147810	−	3.59093i	−0.00613747	−	0.149105i
$581$	0.900377			0.0373539
$582$			15.1507i			0.628017i
$583$	19.0703	−	11.0102i	0.789809	−	0.455997i
$584$			5.99590i			0.248112i
$585$	−0.946400	−	1.49376i	−0.0391288	−	0.0617594i
$586$		−	5.84526i		−	0.241466i
$587$	4.12294	−	7.14114i	0.170172	−	0.294746i	−0.768308	−	0.640080i	$-0.778901\pi$
$587$	4.12294	−	7.14114i	0.170172	−	0.294746i	0.938480	+	0.345334i	$0.112234\pi$
$588$	17.5128	+	10.1110i	0.722215	+	0.416971i
$589$	−1.47168	+	2.54902i	−0.0606394	+	0.105031i
$590$	1.20314	+	29.2294i	0.0495324	+	1.20335i
$591$	61.6983			2.53793
$592$	5.00970	+	3.45005i	0.205898	+	0.141796i
$593$		−	17.9870i		−	0.738639i	−0.929302	−	0.369320i	$-0.879591\pi$
$593$		−	17.9870i		−	0.738639i	0.929302	−	0.369320i	$-0.120409\pi$
$594$	37.7654	−	21.8039i	1.54953	−	0.894624i
$595$	1.09628	−	0.694567i	0.0449429	−	0.0284745i
$596$	5.28654	−	9.15656i	0.216545	−	0.375067i
$597$	20.4579	−	35.4341i	0.837285	−	1.45022i
$598$	0.0401610			0.00164231
$599$	12.8394	−	22.2385i	0.524604	−	0.908640i	−0.474986	−	0.879993i	$-0.657547\pi$
$599$	12.8394	−	22.2385i	0.524604	−	0.908640i	0.999590	−	0.0286469i	$-0.00911982\pi$
$600$	−11.9571	+	8.28384i	−0.488145	+	0.338186i
$601$	12.2173	+	21.1611i	0.498356	+	0.863178i	0.999998	−	0.00189748i	$-0.000603988\pi$
$601$	12.2173	+	21.1611i	0.498356	+	0.863178i	−0.501642	+	0.865075i	$0.667271\pi$
$602$		−	1.44295i		−	0.0588105i
$603$		−	81.8149i		−	3.33176i
$604$	−7.03678	−	12.1881i	−0.286323	−	0.495925i
$605$	−31.1330	−	49.1391i	−1.26574	−	1.99779i
$606$		−	25.1844i		−	1.02305i
$607$	−8.34623	−	14.4561i	−0.338763	−	0.586755i	0.645437	−	0.763813i	$-0.276675\pi$
$607$	−8.34623	−	14.4561i	−0.338763	−	0.586755i	−0.984200	+	0.177059i	$0.943342\pi$
$608$	−3.28333	+	1.89563i	−0.133157	+	0.0768781i
$609$	−0.896960	+	0.517860i	−0.0363467	+	0.0209848i
$610$	19.2476	−	12.1947i	0.779312	−	0.493748i
$611$	−0.930859	−	0.537432i	−0.0376585	−	0.0217422i
$612$	7.15822	+	12.3984i	0.289354	+	0.501176i
$613$	28.6684	−	16.5517i	1.15791	−	0.668517i	0.207105	−	0.978319i	$-0.433596\pi$
$613$	28.6684	−	16.5517i	1.15791	−	0.668517i	0.950801	+	0.309801i	$0.100263\pi$
$614$	−28.6731	+	16.5544i	−1.15715	+	0.668083i
$615$	58.5412	+	30.6604i	2.36061	+	1.23635i
$616$	−1.16706	−	0.673800i	−0.0470220	−	0.0271482i
$617$	−4.91286	+	2.83644i	−0.197784	+	0.114191i	−0.595622	−	0.803265i	$-0.703094\pi$
$617$	−4.91286	+	2.83644i	−0.197784	+	0.114191i	0.397837	+	0.917456i	$0.369761\pi$
$618$			32.3032i			1.29942i
$619$	−34.6316			−1.39196			−0.695980	−	0.718061i	$-0.745030\pi$
$619$	−34.6316			−1.39196			−0.695980	+	0.718061i	$0.745030\pi$
$620$	0.0713957	+	1.73451i	0.00286732	+	0.0696594i
$621$		−	1.98880i		−	0.0798077i
$622$	−21.7793	−	12.5743i	−0.873270	−	0.504183i
$623$	2.77782			0.111291
$624$	−0.364671	−	0.210543i	−0.0145985	−	0.00842845i
$625$	−15.8778	−	19.3105i	−0.635112	−	0.772420i
$626$	5.97122	−	10.3425i	0.238658	−	0.413368i
$627$	33.5525	+	58.1146i	1.33996	+	2.32087i
$628$			15.2845i			0.609917i
$629$	13.1268	+	9.04005i	0.523398	+	0.360451i
$630$	2.39723	+	1.25553i	0.0955079	+	0.0500215i
$631$	−10.4928	+	6.05801i	−0.417711	+	0.241165i	−0.694097	−	0.719881i	$-0.744196\pi$
$631$	−10.4928	+	6.05801i	−0.417711	+	0.241165i	0.276387	+	0.961047i	$0.410863\pi$
$632$	5.73029	+	3.30838i	0.227939	+	0.131600i
$633$	−11.2023	−	6.46766i	−0.445252	−	0.257066i
$634$	−0.692689	−	0.399924i	−0.0275102	−	0.0158830i
$635$	19.4134	+	10.1676i	0.770396	+	0.403488i
$636$	−5.26487	+	9.11902i	−0.208766	+	0.361593i
$637$	−1.00608			−0.0398623
$638$	−8.46855	+	4.88932i	−0.335273	+	0.193570i
$639$	−71.0341			−2.81006
$640$	−1.03745	+	1.98083i	−0.0410086	+	0.0782994i
$641$	−0.0554737	−	0.0960833i	−0.00219108	−	0.00379506i	0.864928	−	0.501896i	$-0.167364\pi$
$641$	−0.0554737	−	0.0960833i	−0.00219108	−	0.00379506i	−0.867119	+	0.498101i	$0.834031\pi$
$642$	26.1281	−	45.2552i	1.03119	−	1.78608i
$643$	13.5510			0.534401			0.267200	−	0.963641i	$-0.413901\pi$
$643$	13.5510			0.534401			0.267200	+	0.963641i	$0.413901\pi$
$644$	−0.0532253	+	0.0307297i	−0.00209737	+	0.00121092i
$645$	1.74291	+	42.3428i	0.0686271	+	1.66724i
$646$	−8.60321	+	4.96707i	−0.338489	+	0.195427i
$647$	11.6638	−	20.2022i	0.458549	−	0.794231i	−0.540335	−	0.841450i	$-0.681703\pi$
$647$	11.6638	−	20.2022i	0.458549	−	0.794231i	0.998885	+	0.0472191i	$0.0150359\pi$
$648$	−2.23059	+	3.86349i	−0.0876258	+	0.151772i
$649$	68.9321	−	39.7980i	2.70582	−	1.56221i
$650$	0.309118	−	0.654362i	0.0121246	−	0.0256662i
$651$	0.433253	−	0.250139i	0.0169805	−	0.00980372i
$652$	−17.8812			−0.700283
$653$	−6.35214	+	11.0022i	−0.248578	+	0.430551i	−0.963132	−	0.269031i	$-0.913297\pi$
$653$	−6.35214	+	11.0022i	−0.248578	+	0.430551i	0.714553	+	0.699581i	$0.246630\pi$
$654$	−9.45590	−	16.3781i	−0.369755	−	0.640435i
$655$	−4.21775	−	2.20901i	−0.164801	−	0.0863131i
$656$	10.1586			0.396625
$657$	−28.3710	+	16.3800i	−1.10686	+	0.639045i
$658$	1.64489			0.0641244
$659$	−4.80410	+	8.32095i	−0.187141	+	0.324138i	−0.944296	−	0.329097i	$-0.893256\pi$
$659$	−4.80410	+	8.32095i	−0.187141	+	0.324138i	0.757155	+	0.653236i	$0.226589\pi$
$660$	35.0605	+	18.3627i	1.36473	+	0.714765i
$661$	7.07993	+	4.08760i	0.275377	+	0.158989i	0.631329	−	0.775515i	$-0.282510\pi$
$661$	7.07993	+	4.08760i	0.275377	+	0.158989i	−0.355951	+	0.934504i	$0.615843\pi$
$662$	8.83765	+	5.10242i	0.343485	+	0.198311i
$663$	−0.955534	−	0.551678i	−0.0371099	−	0.0214254i
$664$	−3.52033	+	2.03246i	−0.136615	+	0.0788748i
$665$	−0.871208	+	1.66343i	−0.0337840	+	0.0645051i
$666$	−2.63887	+	33.1297i	−0.102254	+	1.28375i
$667$			0.445970i			0.0172680i
$668$	−3.85790	−	6.68208i	−0.149267	−	0.258537i
$669$	−15.8493	+	27.4517i	−0.612768	+	1.06135i
$670$	28.2843	−	17.9200i	1.09272	−	0.692312i
$671$	−53.6900	−	30.9979i	−2.07268	−	1.19666i
$672$	0.644396			0.0248581
$673$	−24.0589	−	13.8904i	−0.927401	−	0.535435i	−0.0414126	−	0.999142i	$-0.513186\pi$
$673$	−24.0589	−	13.8904i	−0.927401	−	0.535435i	−0.885989	+	0.463707i	$0.846519\pi$
$674$		−	19.0490i		−	0.733739i
$675$	−32.4044	−	15.3077i	−1.24724	−	0.589193i
$676$	−12.9791			−0.499194
$677$			25.9326i			0.996672i	0.866984	+	0.498336i	$0.166055\pi$
$677$			25.9326i			0.996672i	−0.866984	+	0.498336i	$0.833945\pi$
$678$	−20.5791	+	11.8814i	−0.790337	+	0.456301i
$679$	0.998975	+	0.576759i	0.0383371	+	0.0221340i
$680$	−2.71838	+	5.19032i	−0.104245	+	0.199039i
$681$	−9.30956	+	5.37488i	−0.356743	+	0.205966i
$682$	4.09052	−	2.36166i	0.156634	−	0.0904326i
$683$	−11.0153	−	19.0791i	−0.421490	−	0.730041i	0.574596	−	0.818437i	$-0.305159\pi$
$683$	−11.0153	−	19.0791i	−0.421490	−	0.730041i	−0.996085	+	0.0883959i	$0.971826\pi$
$684$	−17.9393	−	10.3572i	−0.685925	−	0.396019i
$685$	−21.4733	+	13.6048i	−0.820451	+	0.519812i
$686$	2.67612	−	1.54506i	0.102175	−	0.0589907i
$687$	52.3947	−	30.2501i	1.99898	−	1.15411i
$688$	3.25725	+	5.64172i	0.124181	+	0.215088i
$689$		−	0.523873i		−	0.0199580i
$690$	1.52475	−	0.966036i	0.0580463	−	0.0367763i
$691$	1.38776	+	2.40367i	0.0527929	+	0.0914401i	0.891214	−	0.453583i	$-0.149854\pi$
$691$	1.38776	+	2.40367i	0.0527929	+	0.0914401i	−0.838421	+	0.545023i	$0.816521\pi$
$692$		−	9.49971i		−	0.361125i
$693$		−	7.36293i		−	0.279695i
$694$	6.92213	+	11.9895i	0.262761	+	0.455115i
$695$	−7.74050	+	14.7792i	−0.293614	+	0.560608i
$696$	2.33798	−	4.04950i	0.0886208	−	0.153496i
$697$	26.6181			1.00823
$698$	−4.07759	+	7.06260i	−0.154339	+	0.267323i
$699$	14.4693	−	25.0616i	0.547280	−	0.947916i
$700$	0.0910192	+	1.10375i	0.00344020	+	0.0417178i
$701$	2.68900	−	1.55249i	0.101562	−	0.0586369i	−0.448359	−	0.893854i	$-0.647991\pi$
$701$	2.68900	−	1.55249i	0.101562	−	0.0586369i	0.549921	+	0.835217i	$0.314658\pi$
$702$		−	1.03744i		−	0.0391557i
$703$	−22.9886	−	1.83111i	−0.867030	−	0.0690615i
$704$	6.08400			0.229299
$705$	−48.2684	+	1.98682i	−1.81789	+	0.0748280i
$706$	9.11593	−	15.7892i	0.343082	−	0.594236i
$707$	−1.66056	−	0.958724i	−0.0624517	−	0.0360565i
$708$	−19.0306	+	32.9620i	−0.715214	+	1.23879i
$709$			23.0858i			0.867006i	0.901152	+	0.433503i	$0.142723\pi$
$709$			23.0858i			0.867006i	−0.901152	+	0.433503i	$0.857277\pi$
$710$	−15.5587	−	24.5572i	−0.583908	−	0.921617i
$711$			36.1522i			1.35581i
$712$	−10.8608	+	6.27049i	−0.407026	+	0.234997i
$713$		−	0.215414i		−	0.00806732i
$714$	1.68849			0.0631902
$715$	−1.96741	+	0.0809827i	−0.0735771	+	0.00302858i
$716$	−9.39416	−	5.42372i	−0.351076	−	0.202694i
$717$	−34.5433			−1.29004
$718$	−5.11862	−	8.86571i	−0.191025	−	0.330865i
$719$	−6.87917	−	11.9151i	−0.256550	−	0.444357i	0.708766	−	0.705444i	$-0.249252\pi$
$719$	−6.87917	−	11.9151i	−0.256550	−	0.444357i	−0.965315	+	0.261087i	$0.915919\pi$
$720$	−12.2069	+	0.502462i	−0.454926	+	0.0187257i
$721$	2.12994	+	1.22972i	0.0793230	+	0.0457972i
$722$	−2.31314	+	4.00648i	−0.0860863	+	0.149106i
$723$	12.9044	+	22.3510i	0.479918	+	0.831243i
$724$	−8.45183	−	14.6390i	−0.314110	−	0.544054i
$725$	7.26638	+	3.43261i	0.269867	+	0.127484i
$726$		−	75.6843i		−	2.80891i
$727$	24.4548	−	42.3570i	0.906980	−	1.57094i	0.0887430	−	0.996055i	$-0.471715\pi$
$727$	24.4548	−	42.3570i	0.906980	−	1.57094i	0.818237	−	0.574881i	$-0.194952\pi$
$728$	−0.0277646	+	0.0160299i	−0.00102903	+	0.000594108i
$729$	38.1824			1.41416
$730$	−11.8769	−	6.22042i	−0.439584	−	0.230228i
$731$	8.53486	+	14.7828i	0.315673	+	0.546762i
$732$	29.6452			1.09572
$733$	−30.1463	−	17.4049i	−1.11348	−	0.642866i	−0.173749	−	0.984790i	$-0.555588\pi$
$733$	−30.1463	−	17.4049i	−1.11348	−	0.642866i	−0.939728	+	0.341924i	$0.888922\pi$
$734$		−	15.0239i		−	0.554544i
$735$	−38.1968	+	24.2003i	−1.40891	+	0.892641i
$736$	0.138735	−	0.240296i	0.00511384	−	0.00885743i
$737$	−78.8974	−	45.5514i	−2.90622	−	1.67791i
$738$	27.7518	+	48.0676i	1.02156	+	1.76939i
$739$	24.3924			0.897288			0.448644	−	0.893711i	$-0.351907\pi$
$739$	24.3924			0.897288			0.448644	+	0.893711i	$0.351907\pi$
$740$	−12.0313	+	6.34416i	−0.442279	+	0.233216i
$741$	1.59645			0.0586470
$742$	0.400847	+	0.694288i	0.0147156	+	0.0254881i
$743$	−9.95998	−	5.75040i	−0.365396	−	0.210962i	0.306049	−	0.952016i	$-0.400993\pi$
$743$	−9.95998	−	5.75040i	−0.365396	−	0.210962i	−0.671445	+	0.741054i	$0.734326\pi$
$744$	−1.12930	+	1.95600i	−0.0414021	+	0.0717106i
$745$	12.6531	+	19.9712i	0.463575	+	0.731688i
$746$		−	8.37153i		−	0.306503i
$747$	−19.2341	−	11.1048i	−0.703740	−	0.406304i
$748$	15.9417			0.582886
$749$	−1.98929	−	3.44556i	−0.0726872	−	0.125898i
$750$	−4.00410	−	32.2790i	−0.146209	−	1.17866i
$751$	−14.1263			−0.515477			−0.257738	−	0.966215i	$-0.582977\pi$
$751$	−14.1263			−0.515477			−0.257738	+	0.966215i	$0.582977\pi$
$752$	−6.43124	+	3.71308i	−0.234523	+	0.135402i
$753$	11.1961	−	19.3921i	0.408007	−	0.706689i
$754$			0.232637i			0.00847214i
$755$	31.4428	−	1.29425i	1.14432	−	0.0471025i
$756$	0.793810	+	1.37492i	0.0288706	+	0.0500053i
$757$	9.97530	+	17.2777i	0.362558	+	0.627970i	0.988381	−	0.151996i	$-0.0485700\pi$
$757$	9.97530	+	17.2777i	0.362558	+	0.627970i	−0.625823	+	0.779965i	$0.715237\pi$
$758$	−7.69375	+	13.3260i	−0.279449	+	0.484021i
$759$	−4.25321	−	2.45559i	−0.154382	−	0.0891323i
$760$	−0.348657	−	8.47036i	−0.0126471	−	0.307252i
$761$	10.8594	+	18.8091i	0.393654	+	0.681829i	0.992928	−	0.118715i	$-0.0378775\pi$
$761$	10.8594	+	18.8091i	0.393654	+	0.681829i	−0.599274	+	0.800544i	$0.704544\pi$
$762$	14.2562	+	24.6924i	0.516447	+	0.894513i
$763$	−1.43987			−0.0521269
$764$	17.9402	+	10.3578i	0.649055	+	0.374732i
$765$	−31.9854	+	1.31658i	−1.15644	+	0.0476012i
$766$	−28.1635			−1.01759
$767$		−	1.89361i		−	0.0683744i
$768$	−2.51948	+	1.45462i	−0.0909140	+	0.0524893i
$769$			0.619597i			0.0223432i	0.999938	+	0.0111716i	$0.00355611\pi$
$769$			0.619597i			0.0223432i	−0.999938	+	0.0111716i	$0.996444\pi$
$770$	2.54544	−	1.61271i	0.0917315	−	0.0581182i
$771$		−	64.4056i		−	2.31951i
$772$	−7.36191	+	12.7512i	−0.264961	+	0.458926i
$773$	42.5741	+	24.5802i	1.53128	+	0.884087i	0.999303	+	0.0373311i	$0.0118856\pi$
$773$	42.5741	+	24.5802i	1.53128	+	0.884087i	0.531981	+	0.846756i	$0.321448\pi$
$774$	−17.7967	+	30.8248i	−0.639690	+	1.10798i
$775$	−3.50984	−	1.65803i	−0.126077	−	0.0595583i
$776$	−5.20777			−0.186948
$777$	3.22824	+	2.22320i	0.115812	+	0.0797569i
$778$			17.5873i			0.630537i
$779$	−33.3539	+	19.2569i	−1.19503	+	0.689950i
$780$	0.795376	−	0.503926i	0.0284790	−	0.0180434i
$781$	−39.5491	+	68.5010i	−1.41518	+	2.45116i
$782$	0.363522	−	0.629639i	0.0129995	−	0.0225159i
$783$	11.5203			0.411702
$784$	−3.47547	+	6.01969i	−0.124124	+	0.214989i
$785$	−30.2760	−	15.8568i	−1.08060	−	0.565954i
$786$	−3.09730	−	5.36468i	−0.110477	−	0.191352i
$787$		−	17.0706i		−	0.608501i	−0.952592	−	0.304250i	$-0.901594\pi$
$787$		−	17.0706i		−	0.608501i	0.952592	−	0.304250i	$-0.0984060\pi$
$788$			21.2076i			0.755491i
$789$	41.9566	+	72.6710i	1.49370	+	2.58716i
$790$	−12.4982	+	7.91848i	−0.444667	+	0.281727i
$791$			1.80920i			0.0643279i
$792$	16.6207	+	28.7879i	0.590590	+	1.02293i
$793$	−1.27730	+	0.737451i	−0.0453583	+	0.0261876i
$794$	7.18420	−	4.14780i	0.254958	−	0.147200i
$795$	−12.6013	−	19.8893i	−0.446921	−	0.705402i
$796$	12.1798	+	7.03201i	0.431701	+	0.249243i
$797$	3.34890	+	5.80047i	0.118624	+	0.205463i	0.919223	−	0.393738i	$-0.128818\pi$
$797$	3.34890	+	5.80047i	0.118624	+	0.205463i	−0.800599	+	0.599201i	$0.795485\pi$
$798$	−2.11577	+	1.22154i	−0.0748974	+	0.0432420i
$799$	−16.8516	+	9.72926i	−0.596166	+	0.344196i
$800$	−2.84741	−	4.11002i	−0.100671	−	0.145311i
$801$	−59.3405	−	34.2603i	−2.09670	−	1.21053i
$802$	−10.4579	+	6.03787i	−0.369281	+	0.213205i
$803$			36.4791i			1.28732i
$804$	43.5636			1.53637
$805$	−0.00565199	−	0.137311i	−0.000199207	−	0.00483958i
$806$		−	0.112369i		−	0.00395804i
$807$	23.9681	+	13.8380i	0.843716	+	0.487120i
$808$	8.65668			0.304541
$809$	−15.2207	−	8.78766i	−0.535130	−	0.308958i	0.207973	−	0.978135i	$-0.433313\pi$
$809$	−15.2207	−	8.78766i	−0.535130	−	0.308958i	−0.743103	+	0.669177i	$0.766647\pi$
$810$	−5.33883	−	8.42659i	−0.187587	−	0.296080i
$811$	23.3915	−	40.5153i	0.821386	−	1.42268i	−0.0832636	−	0.996528i	$-0.526534\pi$
$811$	23.3915	−	40.5153i	0.821386	−	1.42268i	0.904650	−	0.426155i	$-0.140132\pi$
$812$	−0.178005	−	0.308313i	−0.00624674	−	0.0108197i
$813$		−	33.2536i		−	1.16626i
$814$	30.4790	+	20.9901i	1.06829	+	0.735703i
$815$	18.5508	−	35.4197i	0.649806	−	1.24070i
$816$	−6.60172	+	3.81150i	−0.231106	+	0.133429i
$817$	−21.3893	−	12.3491i	−0.748316	−	0.432040i
$818$	8.90476	+	5.14117i	0.311348	+	0.179757i
$819$	−0.151699	−	0.0875832i	−0.00530077	−	0.00306040i
$820$	−10.5390	+	20.1224i	−0.368036	+	0.702706i
$821$	−24.8327	+	43.0115i	−0.866667	+	1.50111i	−0.00128385	+	0.999999i	$0.500409\pi$
$821$	−24.8327	+	43.0115i	−0.866667	+	1.50111i	−0.865383	+	0.501111i	$0.832925\pi$
$822$	−33.0732			−1.15356
$823$	24.3430	−	14.0545i	0.848545	−	0.489907i	−0.0116149	−	0.999933i	$-0.503697\pi$
$823$	24.3430	−	14.0545i	0.848545	−	0.489907i	0.860160	+	0.510025i	$0.170364\pi$
$824$	−11.1036			−0.386812
$825$	−72.7468	+	50.3988i	−2.53272	+	1.75466i
$826$	1.44892	+	2.50960i	0.0504143	+	0.0873202i
$827$	−28.2038	+	48.8503i	−0.980741	+	1.69869i	−0.321223	+	0.947004i	$0.604094\pi$
$827$	−28.2038	+	48.8503i	−0.980741	+	1.69869i	−0.659518	+	0.751689i	$0.729240\pi$
$828$	1.51602			0.0526854
$829$	−10.8431	+	6.26029i	−0.376598	+	0.217429i	−0.676337	−	0.736592i	$-0.736434\pi$
$829$	−10.8431	+	6.26029i	−0.376598	+	0.217429i	0.299739	+	0.954021i	$0.403100\pi$
$830$	−0.373823	−	9.08175i	−0.0129756	−	0.315232i
$831$	−79.4930	+	45.8953i	−2.75758	+	1.59209i
$832$	0.0723701	−	0.125349i	0.00250898	−	0.00434568i
$833$	−9.10666	+	15.7732i	−0.315527	+	0.546509i
$834$	−18.7982	+	10.8531i	−0.650927	+	0.375813i
$835$	17.2385	−	0.709569i	0.596561	−	0.0245556i
$836$	−19.9758	+	11.5330i	−0.690878	+	0.398878i
$837$	−5.56459			−0.192340
$838$	−1.28468	+	2.22513i	−0.0443784	+	0.0768657i
$839$	6.73506	+	11.6655i	0.232520	+	0.402737i	0.958549	−	0.284927i	$-0.0919695\pi$
$839$	6.73506	+	11.6655i	0.232520	+	0.402737i	−0.726029	+	0.687664i	$0.758636\pi$
$840$	−0.668526	+	1.27644i	−0.0230663	+	0.0440415i
$841$	26.4167			0.910920
$842$	31.6537	−	18.2753i	1.09086	−	0.629808i
$843$	41.5111			1.42972
$844$	2.22314	−	3.85059i	0.0765235	−	0.132543i
$845$	13.4651	−	25.7094i	0.463212	−	0.884429i
$846$	−35.1386	−	20.2873i	−1.20809	−	0.697491i
$847$	−4.99031	−	2.88116i	−0.171469	−	0.0989977i
$848$	−3.13449	−	1.80970i	−0.107639	−	0.0621454i
$849$	−11.4863	+	6.63162i	−0.394209	+	0.227596i
$850$	−7.46098	−	10.7693i	−0.255910	−	0.369385i
$851$	1.52405	−	0.725169i	0.0522439	−	0.0248585i
$852$		−	37.8232i		−	1.29580i
$853$	15.6089	+	27.0354i	0.534439	+	0.925675i	0.999190	+	0.0402339i	$0.0128103\pi$
$853$	15.6089	+	27.0354i	0.534439	+	0.925675i	−0.464752	+	0.885441i	$0.653856\pi$
$854$	1.12854	−	1.95468i	0.0386177	−	0.0668879i
$855$	39.1270	−	24.7896i	1.33811	−	0.847788i
$856$	15.5556	+	8.98104i	0.531680	+	0.306966i
$857$	22.0143			0.751994			0.375997	−	0.926621i	$-0.377300\pi$
$857$	22.0143			0.751994			0.375997	+	0.926621i	$0.377300\pi$
$858$	−2.21866	−	1.28094i	−0.0757437	−	0.0437306i
$859$		−	32.2800i		−	1.10138i	−0.834710	−	0.550690i	$-0.814365\pi$
$859$		−	32.2800i		−	1.10138i	0.834710	−	0.550690i	$-0.185635\pi$
$860$	−14.5545	+	0.599093i	−0.496305	+	0.0204289i
$861$	6.54614			0.223092
$862$			14.9647i			0.509700i
$863$	2.05241	−	1.18496i	0.0698649	−	0.0403365i	−0.464661	−	0.885489i	$-0.653824\pi$
$863$	2.05241	−	1.18496i	0.0698649	−	0.0403365i	0.534526	+	0.845152i	$0.320490\pi$
$864$	−6.20734	−	3.58381i	−0.211178	−	0.121924i
$865$	18.8174	+	9.85543i	0.639809	+	0.335095i
$866$	−23.1938	+	13.3910i	−0.788158	+	0.455043i
$867$	25.5330	−	14.7415i	0.867145	−	0.500646i
$868$	0.0859806	+	0.148923i	0.00291837	+	0.00505477i
$869$	34.8631	+	20.1282i	1.18265	+	0.682802i
$870$	5.59586	+	8.83228i	0.189717	+	0.299442i
$871$	−1.87699	+	1.08368i	−0.0635995	+	0.0367192i
$872$	5.62967	−	3.25029i	0.190645	−	0.110069i
$873$	−14.2269	−	24.6418i	−0.481509	−	0.833998i
$874$			1.05196i			0.0355832i
$875$	−2.28077	−	0.964786i	−0.0771042	−	0.0326157i
$876$	−8.72179	−	15.1066i	−0.294682	−	0.510404i
$877$			10.1611i			0.343117i	0.985174	+	0.171558i	$0.0548802\pi$
$877$			10.1611i			0.343117i	−0.985174	+	0.171558i	$0.945120\pi$
$878$		−	31.8322i		−	1.07428i
$879$	8.50266	+	14.7270i	0.286788	+	0.496731i
$880$	−6.31182	+	12.0514i	−0.212771	+	0.406253i
$881$	14.8099	−	25.6516i	0.498959	−	0.864223i	−0.501040	−	0.865424i	$-0.667049\pi$
$881$	14.8099	−	25.6516i	0.498959	−	0.864223i	0.999999	+	0.00120108i	$0.000382314\pi$
$882$	−37.9781			−1.27879
$883$	7.92250	−	13.7222i	0.266613	−	0.461788i	−0.701372	−	0.712796i	$-0.747429\pi$
$883$	7.92250	−	13.7222i	0.266613	−	0.461788i	0.967985	+	0.251008i	$0.0807620\pi$
$884$	0.189629	−	0.328447i	0.00637791	−	0.0110469i
$885$	−45.5490	−	71.8928i	−1.53111	−	2.41665i
$886$	−4.01430	+	2.31766i	−0.134863	+	0.0778633i
$887$			40.5502i			1.36154i	0.732496	+	0.680771i	$0.238355\pi$
$887$			40.5502i			1.36154i	−0.732496	+	0.680771i	$0.761645\pi$
$888$	−17.6404	−	1.40511i	−0.591973	−	0.0471524i
$889$	2.17082			0.0728071
$890$	−1.15331	−	28.0188i	−0.0386590	−	0.939191i
$891$	−13.5709	+	23.5055i	−0.454642	+	0.787464i
$892$	−9.43602	−	5.44789i	−0.315941	−	0.182409i
$893$	14.0773	−	24.3826i	0.471078	−	0.815931i
$894$			30.7598i			1.02876i
$895$	20.4894	−	12.9815i	0.684886	−	0.433923i
$896$			0.221499i			0.00739977i
$897$	−0.101185	+	0.0584192i	−0.00337847	+	0.00195056i
$898$			3.07810i			0.102718i
$899$	1.24781			0.0416167
$900$	11.6687	−	24.7012i	0.388958	−	0.823374i
$901$	−8.21321	−	4.74190i	−0.273622	−	0.157976i
$902$	61.8047			2.05787
$903$	2.09896	+	3.63550i	0.0698489	+	0.120982i
$904$	−4.08400	−	7.07369i	−0.135832	−	0.235268i
$905$	37.7658	−	1.55451i	1.25538	−	0.0516738i
$906$	35.4581	+	20.4718i	1.17802	+	0.680129i
$907$	−10.4477	+	18.0960i	−0.346911	+	0.600868i	−0.985699	−	0.168515i	$-0.946103\pi$
$907$	−10.4477	+	18.0960i	−0.346911	+	0.600868i	0.638788	+	0.769383i	$0.279436\pi$
$908$	−1.84751	−	3.19999i	−0.0613119	−	0.106195i
$909$	23.6489	+	40.9611i	0.784384	+	1.35859i
$910$	−0.00294832	−	0.0716273i	−9.77359e−5	−	0.00237442i
$911$		−	58.1026i		−	1.92503i	−0.271236	−	0.962513i	$-0.587432\pi$
$911$		−	58.1026i		−	1.92503i	0.271236	−	0.962513i	$-0.412568\pi$
$912$	5.51487	−	9.55204i	0.182616	−	0.316300i
$913$	−21.4177	+	12.3655i	−0.708821	+	0.409238i
$914$	11.9569			0.395499
$915$	−30.7553	+	58.7223i	−1.01674	+	1.94130i
$916$	10.3979	+	18.0097i	0.343557	+	0.595057i
$917$	−0.471633			−0.0155747
$918$	−16.2649	−	9.39053i	−0.536821	−	0.309934i
$919$			19.8144i			0.653616i	0.945091	+	0.326808i	$0.105973\pi$
$919$			19.8144i			0.653616i	−0.945091	+	0.326808i	$0.894027\pi$
$920$	0.332057	+	0.524105i	0.0109476	+	0.0172792i
$921$	48.1610	−	83.4173i	1.58696	−	2.74869i
$922$	20.8728	+	12.0509i	0.687408	+	0.396875i
$923$	0.940884	+	1.62966i	0.0309696	+	0.0536409i
$924$	3.92051			0.128975
$925$	−0.0849288	−	30.4137i	−0.00279244	−	0.999996i
$926$	28.1754			0.925902
$927$	−30.3336	−	52.5393i	−0.996285	−	1.72562i
$928$	1.39194	+	0.803636i	0.0456926	+	0.0263806i
$929$	27.0154	−	46.7921i	0.886347	−	1.53520i	0.0421844	−	0.999110i	$-0.486568\pi$
$929$	27.0154	−	46.7921i	0.886347	−	1.53520i	0.844162	−	0.536088i	$-0.180098\pi$
$930$	−2.70293	−	4.26620i	−0.0886327	−	0.139894i
$931$		−	26.3529i		−	0.863680i
$932$	8.61445	+	4.97356i	0.282176	+	0.162914i
$933$	73.1634			2.39526
$934$	4.86374	+	8.42425i	0.159147	+	0.275650i
$935$	−16.5386	+	31.5779i	−0.540872	+	1.03271i
$936$	0.790822			0.0258488
$937$	12.6396	−	7.29747i	0.412917	−	0.238398i	−0.279125	−	0.960255i	$-0.590044\pi$
$937$	12.6396	−	7.29747i	0.412917	−	0.238398i	0.692042	+	0.721857i	$0.256711\pi$
$938$	1.65838	−	2.87240i	0.0541481	−	0.0937873i
$939$			34.7435i			1.13381i
$940$	−0.682933	−	16.5913i	−0.0222748	−	0.541150i
$941$	−18.8735	−	32.6899i	−0.615260	−	1.06566i	−0.990339	−	0.138668i	$-0.955718\pi$
$941$	−18.8735	−	32.6899i	−0.615260	−	1.06566i	0.375079	−	0.926993i	$-0.377615\pi$
$942$	−22.2332	−	38.5090i	−0.724397	−	1.25469i
$943$	1.40935	−	2.44106i	0.0458947	−	0.0794919i
$944$	−11.3301	−	6.54142i	−0.368762	−	0.212905i
$945$	−3.54702	+	0.146003i	−0.115385	+	0.00474946i
$946$	19.8171	+	34.3242i	0.644309	+	1.11598i
$947$	3.85463	+	6.67642i	0.125259	+	0.216955i	0.921834	−	0.387585i	$-0.126691\pi$
$947$	3.85463	+	6.67642i	0.125259	+	0.216955i	−0.796575	+	0.604539i	$0.793357\pi$
$948$	−19.2498			−0.625205
$949$	0.751579	+	0.433924i	0.0243973	+	0.0140858i
$950$	17.1401	+	8.09691i	0.556098	+	0.262698i
$951$	2.32696			0.0754568
$952$			0.580387i			0.0188104i
$953$	35.7363	−	20.6324i	1.15761	−	0.668348i	0.206882	−	0.978366i	$-0.433668\pi$
$953$	35.7363	−	20.6324i	1.15761	−	0.668348i	0.950731	+	0.310018i	$0.100335\pi$
$954$		−	19.7754i		−	0.640254i
$955$	−39.1291	+	24.7910i	−1.26619	+	0.802218i
$956$		−	11.8736i		−	0.384020i
$957$	14.2243	−	24.6371i	0.459805	−	0.796405i
$958$	−12.3632	−	7.13788i	−0.399436	−	0.230615i
$959$	−1.25903	+	2.18071i	−0.0406563	+	0.0704188i
$960$	−0.267544	−	6.49978i	−0.00863494	−	0.209779i
$961$	30.3973			0.980557
$962$	0.795012	−	0.378279i	0.0256322	−	0.0121962i
$963$			98.1400i			3.16252i
$964$	−7.68274	+	4.43563i	−0.247444	+	0.142862i
$965$	−17.6204	−	27.8114i	−0.567222	−	0.895281i
$966$	0.0894003	−	0.154846i	0.00287641	−	0.00498208i
$967$	−20.2368	+	35.0512i	−0.650773	+	1.12717i	0.332163	+	0.943222i	$0.392222\pi$
$967$	−20.2368	+	35.0512i	−0.650773	+	1.12717i	−0.982936	+	0.183950i	$0.941112\pi$
$968$	26.0150			0.836155
$969$	14.4504	−	25.0289i	0.464215	−	0.804044i
$970$	5.40278	−	10.3157i	0.173473	−	0.331218i
$971$	−10.5662	−	18.3012i	−0.339086	−	0.587314i	0.645175	−	0.764035i	$-0.276784\pi$
$971$	−10.5662	−	18.3012i	−0.339086	−	0.587314i	−0.984261	+	0.176721i	$0.943451\pi$
$972$			8.52416i			0.273413i
$973$			1.65263i			0.0529809i
$974$	−4.21211	−	7.29559i	−0.134965	−	0.233766i
$975$	0.173034	+	2.09830i	0.00554152	+	0.0671995i
$976$			10.1900i			0.326174i
$977$	5.43288	+	9.41002i	0.173813	+	0.301053i	0.939750	−	0.341863i	$-0.111058\pi$
$977$	5.43288	+	9.41002i	0.173813	+	0.301053i	−0.765937	+	0.642916i	$0.777724\pi$
$978$	45.0515	−	26.0105i	1.44059	−	0.831723i
$979$	−66.0771	+	38.1497i	−2.11183	+	1.21927i
$980$	−8.31840	−	13.1294i	−0.265722	−	0.419404i
$981$	30.7590	+	17.7587i	0.982059	+	0.566992i
$982$	8.11265	+	14.0515i	0.258885	+	0.448402i
$983$	−9.33874	+	5.39172i	−0.297860	+	0.171969i	−0.641481	−	0.767139i	$-0.721680\pi$
$983$	−9.33874	+	5.39172i	−0.297860	+	0.171969i	0.343621	+	0.939108i	$0.388346\pi$
$984$	−25.5943	+	14.7769i	−0.815917	+	0.471070i
$985$	−42.0088	−	22.0018i	−1.33851	−	0.701035i
$986$	3.64725	+	2.10574i	0.116152	+	0.0670604i
$987$	−4.14427	+	2.39269i	−0.131914	+	0.0761603i
$988$			0.548749i			0.0174580i
$989$	1.80758			0.0574776
$990$	−74.2670	+	3.05698i	−2.36036	+	0.0971571i
$991$			5.98300i			0.190056i	0.995475	+	0.0950282i	$0.0302941\pi$
$991$			5.98300i			0.190056i	−0.995475	+	0.0950282i	$0.969706\pi$
$992$	−0.672340	−	0.388176i	−0.0213468	−	0.0123246i
$993$	−29.6884			−0.942134
$994$	−2.49390	−	1.43986i	−0.0791019	−	0.0456695i
$995$	−26.5651	+	16.8308i	−0.842171	+	0.533573i
$996$	5.91294	−	10.2415i	0.187359	−	0.324515i
$997$	11.8896	+	20.5935i	0.376549	+	0.652202i	0.990558	−	0.137097i	$-0.0437773\pi$
$997$	11.8896	+	20.5935i	0.376549	+	0.652202i	−0.614009	+	0.789299i	$0.710444\pi$
$998$		−	21.2036i		−	0.671187i
$999$	−18.7326	−	39.3694i	−0.592673	−	1.24559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.159.8	✓	16
5.4	even	2		370.2.m.d.159.1	yes	16
37.27	even	6		370.2.m.d.249.1	yes	16
185.64	even	6	inner	370.2.m.c.249.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.8	✓	16	1.1	even	1	trivial
370.2.m.c.249.8	yes	16	185.64	even	6	inner
370.2.m.d.159.1	yes	16	5.4	even	2
370.2.m.d.249.1	yes	16	37.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.51948 + 1.45462i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.19673 - 1.88887i) q^{5} -2.90925i q^{6} +(-0.191824 - 0.110750i) q^{7} +1.00000 q^{8} +(2.73187 + 4.73173i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.51948 + 1.45462i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.19673 - 1.88887i) q^{5} -2.90925i q^{6} +(-0.191824 - 0.110750i) q^{7} +1.00000 q^{8} +(2.73187 + 4.73173i) q^{9} +(-1.03745 + 1.98083i) q^{10} +6.08400 q^{11} +(-2.51948 + 1.45462i) q^{12} +(0.0723701 - 0.125349i) q^{13} +0.221499i q^{14} +(-0.267544 - 6.49978i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.31013 - 2.26922i) q^{17} +(2.73187 - 4.73173i) q^{18} +(3.28333 + 1.89563i) q^{19} +(2.23418 - 0.0919631i) q^{20} +(-0.322198 - 0.558064i) q^{21} +(-3.04200 - 5.26890i) q^{22} -0.277470 q^{23} +(2.51948 + 1.45462i) q^{24} +(-2.13567 + 4.52094i) q^{25} -0.144740 q^{26} +7.16761i q^{27} +(0.191824 - 0.110750i) q^{28} -1.60727i q^{29} +(-5.49520 + 3.48159i) q^{30} +0.776351i q^{31} +(-0.500000 + 0.866025i) q^{32} +(15.3285 + 8.84994i) q^{33} +(-1.31013 + 2.26922i) q^{34} +(0.0203698 + 0.494868i) q^{35} -5.46373 q^{36} +(-5.49268 + 2.61351i) q^{37} -3.79127i q^{38} +(0.364671 - 0.210543i) q^{39} +(-1.19673 - 1.88887i) q^{40} +(-5.07928 + 8.79757i) q^{41} +(-0.322198 + 0.558064i) q^{42} -6.51449 q^{43} +(-3.04200 + 5.26890i) q^{44} +(5.66833 - 10.8228i) q^{45} +(0.138735 + 0.240296i) q^{46} -7.42616i q^{47} -2.90925i q^{48} +(-3.47547 - 6.01969i) q^{49} +(4.98309 - 0.410924i) q^{50} -7.62301i q^{51} +(0.0723701 + 0.125349i) q^{52} +(3.13449 - 1.80970i) q^{53} +(6.20734 - 3.58381i) q^{54} +(-7.28091 - 11.4919i) q^{55} +(-0.191824 - 0.110750i) q^{56} +(5.51487 + 9.55204i) q^{57} +(-1.39194 + 0.803636i) q^{58} +(11.3301 - 6.54142i) q^{59} +(5.76274 + 3.01819i) q^{60} +(-8.82479 - 5.09500i) q^{61} +(0.672340 - 0.388176i) q^{62} -1.21021i q^{63} +1.00000 q^{64} +(-0.323375 + 0.0133108i) q^{65} -17.6999i q^{66} +(-12.9680 - 7.48709i) q^{67} +2.62027 q^{68} +(-0.699081 - 0.403615i) q^{69} +(0.418383 - 0.265075i) q^{70} +(-6.50051 + 11.2592i) q^{71} +(2.73187 + 4.73173i) q^{72} +5.99590i q^{73} +(5.00970 + 3.45005i) q^{74} +(-11.9571 + 8.28384i) q^{75} +(-3.28333 + 1.89563i) q^{76} +(-1.16706 - 0.673800i) q^{77} +(-0.364671 - 0.210543i) q^{78} +(5.73029 + 3.30838i) q^{79} +(-1.03745 + 1.98083i) q^{80} +(-2.23059 + 3.86349i) q^{81} +10.1586 q^{82} +(-3.52033 + 2.03246i) q^{83} +0.644396 q^{84} +(-2.71838 + 5.19032i) q^{85} +(3.25725 + 5.64172i) q^{86} +(2.33798 - 4.04950i) q^{87} +6.08400 q^{88} +(-10.8608 + 6.27049i) q^{89} +(-12.2069 + 0.502462i) q^{90} +(-0.0277646 + 0.0160299i) q^{91} +(0.138735 - 0.240296i) q^{92} +(-1.12930 + 1.95600i) q^{93} +(-6.43124 + 3.71308i) q^{94} +(-0.348657 - 8.47036i) q^{95} +(-2.51948 + 1.45462i) q^{96} -5.20777 q^{97} +(-3.47547 + 6.01969i) q^{98} +(16.6207 + 28.7879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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