LMFDB - Embedded newform 775.2.ck.b.524.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(49,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 26]))

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

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

chi := DirichletCharacter("775.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			524.1
Character	$\chi$	$=$	775.524
Dual form			775.2.ck.b.599.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48042 - 2.03762i) q^{2} +(-1.93191 - 0.203052i) q^{3} +(-1.34222 + 4.13093i) q^{4} +(2.44628 + 4.23709i) q^{6} +(-0.173622 - 0.816826i) q^{7} +(5.61358 - 1.82396i) q^{8} +(0.756592 + 0.160819i) q^{9} +O(q^{10})$	\(q+(-1.48042 - 2.03762i) q^{2} +(-1.93191 - 0.203052i) q^{3} +(-1.34222 + 4.13093i) q^{4} +(2.44628 + 4.23709i) q^{6} +(-0.173622 - 0.816826i) q^{7} +(5.61358 - 1.82396i) q^{8} +(0.756592 + 0.160819i) q^{9} +(-3.03538 - 3.37113i) q^{11} +(3.43184 - 7.70804i) q^{12} +(-2.56093 - 5.75194i) q^{13} +(-1.40735 + 1.56302i) q^{14} +(-4.99902 - 3.63200i) q^{16} +(-0.961611 - 0.865839i) q^{17} +(-0.792384 - 1.77972i) q^{18} +(-0.526383 - 0.234361i) q^{19} +(0.169563 + 1.61329i) q^{21} +(-2.37545 + 11.1756i) q^{22} +(-2.24594 + 0.729749i) q^{23} +(-11.2153 + 2.38388i) q^{24} +(-7.92902 + 13.7335i) q^{26} +(4.11341 + 1.33653i) q^{27} +(3.60729 + 0.379142i) q^{28} +(0.640127 - 0.465079i) q^{29} +(4.56993 + 3.18053i) q^{31} +3.75801i q^{32} +(5.17955 + 7.12905i) q^{33} +(-0.340664 + 3.24120i) q^{34} +(-1.67985 + 2.90958i) q^{36} +(-9.77616 + 5.64427i) q^{37} +(0.301728 + 1.41952i) q^{38} +(3.77954 + 11.6322i) q^{39} +(-1.17622 - 11.1910i) q^{41} +(3.03624 - 2.73384i) q^{42} +(-4.54466 + 10.2075i) q^{43} +(18.0001 - 8.01414i) q^{44} +(4.81187 + 3.49603i) q^{46} +(4.89623 - 6.73909i) q^{47} +(8.92015 + 8.03174i) q^{48} +(5.75776 - 2.56352i) q^{49} +(1.68193 + 1.86798i) q^{51} +(27.1982 - 2.85865i) q^{52} +(-1.10989 + 5.22161i) q^{53} +(-3.36622 - 10.3602i) q^{54} +(-2.46450 - 4.26864i) q^{56} +(0.969336 + 0.559646i) q^{57} +(-1.89531 - 0.615823i) q^{58} +(-0.557834 + 5.30744i) q^{59} -4.18717 q^{61} +(-0.284685 - 14.0203i) q^{62} -0.645926i q^{63} +(-2.34063 + 1.70057i) q^{64} +(6.85838 - 21.1079i) q^{66} +(6.10094 + 3.52238i) q^{67} +(4.86742 - 2.81020i) q^{68} +(4.48712 - 0.953766i) q^{69} +(2.94921 + 0.626874i) q^{71} +(4.54052 - 0.477228i) q^{72} +(-7.69391 + 6.92763i) q^{73} +(25.9736 + 11.5642i) q^{74} +(1.67465 - 1.85989i) q^{76} +(-2.22662 + 3.06468i) q^{77} +(18.1067 - 24.9218i) q^{78} +(-0.856267 + 0.950981i) q^{79} +(-9.79521 - 4.36111i) q^{81} +(-21.0616 + 18.9640i) q^{82} +(13.0446 - 1.37104i) q^{83} +(-6.89197 - 1.46493i) q^{84} +(27.5269 - 5.85103i) q^{86} +(-1.33110 + 0.768511i) q^{87} +(-23.1882 - 13.3877i) q^{88} +(-1.14268 + 3.51681i) q^{89} +(-4.25370 + 3.09050i) q^{91} -10.2573i q^{92} +(-8.18286 - 7.07242i) q^{93} -20.9802 q^{94} +(0.763071 - 7.26013i) q^{96} +(5.15563 + 1.67517i) q^{97} +(-13.7473 - 7.93704i) q^{98} +(-1.75440 - 3.03871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) $ 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9	$ 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9} + 32 q^{11} + 20 q^{14} - 32 q^{16} + 18 q^{19} - 48 q^{21} - 220 q^{24} - 8 q^{26} + 44 q^{29} - 12 q^{31} + 32 q^{34} - 2 q^{36} + 110 q^{39} - 48 q^{41} + 104 q^{44} - 100 q^{46} - 186 q^{49} - 84 q^{51} - 204 q^{54} + 10 q^{56} - 62 q^{59} + 136 q^{61} + 46 q^{64} + 96 q^{69} - 60 q^{71} - 100 q^{74} + 28 q^{76} - 98 q^{79} + 50 q^{81} + 36 q^{84} + 326 q^{86} - 8 q^{89} - 74 q^{91} + 188 q^{94} + 44 q^{96} - 34 q^{99}+O(q^{100}) $ 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9 + 32 * q^11 + 20 * q^14 - 32 * q^16 + 18 * q^19 - 48 * q^21 - 220 * q^24 - 8 * q^26 + 44 * q^29 - 12 * q^31 + 32 * q^34 - 2 * q^36 + 110 * q^39 - 48 * q^41 + 104 * q^44 - 100 * q^46 - 186 * q^49 - 84 * q^51 - 204 * q^54 + 10 * q^56 - 62 * q^59 + 136 * q^61 + 46 * q^64 + 96 * q^69 - 60 * q^71 - 100 * q^74 + 28 * q^76 - 98 * q^79 + 50 * q^81 + 36 * q^84 + 326 * q^86 - 8 * q^89 - 74 * q^91 + 188 * q^94 + 44 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{8}{15}\right)$	$-1$

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 $

$2$	−1.48042	−	2.03762i	−1.04681	−	1.44081i	−0.891540	−	0.452942i	$-0.850375\pi$
$2$	−1.48042	−	2.03762i	−1.04681	−	1.44081i	−0.155272	−	0.987872i	$-0.549625\pi$
$3$	−1.93191	−	0.203052i	−1.11539	−	0.117232i	−0.471147	−	0.882055i	$-0.656160\pi$
$3$	−1.93191	−	0.203052i	−1.11539	−	0.117232i	−0.644240	+	0.764823i	$0.722826\pi$
$4$	−1.34222	+	4.13093i	−0.671111	+	2.06547i
$5$		0			0
$5$		0			0
$6$	2.44628	+	4.23709i	0.998692	+	1.72978i
$7$	−0.173622	−	0.816826i	−0.0656229	−	0.308731i	0.933079	−	0.359672i	$-0.117111\pi$
$7$	−0.173622	−	0.816826i	−0.0656229	−	0.308731i	−0.998702	+	0.0509406i	$0.983778\pi$
$8$	5.61358	−	1.82396i	1.98470	−	0.644868i
$9$	0.756592	+	0.160819i	0.252197	+	0.0536062i
$10$		0			0
$11$	−3.03538	−	3.37113i	−0.915201	−	1.01643i	−0.999800	−	0.0200184i	$-0.993628\pi$
$11$	−3.03538	−	3.37113i	−0.915201	−	1.01643i	0.0845988	−	0.996415i	$-0.473039\pi$
$12$	3.43184	−	7.70804i	0.990687	−	2.22512i
$13$	−2.56093	−	5.75194i	−0.710274	−	1.59530i	−0.800467	−	0.599377i	$-0.795415\pi$
$13$	−2.56093	−	5.75194i	−0.710274	−	1.59530i	0.0901931	−	0.995924i	$-0.471252\pi$
$14$	−1.40735	+	1.56302i	−0.376129	+	0.417734i
$15$		0			0
$16$	−4.99902	−	3.63200i	−1.24975	−	0.907999i
$17$	−0.961611	−	0.865839i	−0.233225	−	0.209997i	0.544229	−	0.838937i	$-0.316822\pi$
$17$	−0.961611	−	0.865839i	−0.233225	−	0.209997i	−0.777454	+	0.628940i	$0.783489\pi$
$18$	−0.792384	−	1.77972i	−0.186767	−	0.419485i
$19$	−0.526383	−	0.234361i	−0.120761	−	0.0537661i	0.345467	−	0.938431i	$-0.387721\pi$
$19$	−0.526383	−	0.234361i	−0.120761	−	0.0537661i	−0.466228	+	0.884665i	$0.654387\pi$
$20$		0			0
$21$	0.169563	+	1.61329i	0.0370017	+	0.352048i
$22$	−2.37545	+	11.1756i	−0.506448	+	2.38265i
$23$	−2.24594	+	0.729749i	−0.468310	+	0.152163i	−0.533660	−	0.845699i	$-0.679184\pi$
$23$	−2.24594	+	0.729749i	−0.468310	+	0.152163i	0.0653498	+	0.997862i	$0.479184\pi$
$24$	−11.2153	+	2.38388i	−2.28931	+	0.486608i
$25$		0			0
$26$	−7.92902	+	13.7335i	−1.55501	+	2.69335i
$27$	4.11341	+	1.33653i	0.791626	+	0.257215i
$28$	3.60729	+	0.379142i	0.681714	+	0.0716511i
$29$	0.640127	−	0.465079i	0.118869	−	0.0863630i	−0.526763	−	0.850012i	$-0.676594\pi$
$29$	0.640127	−	0.465079i	0.118869	−	0.0863630i	0.645631	+	0.763649i	$0.276594\pi$
$30$		0			0
$31$	4.56993	+	3.18053i	0.820783	+	0.571240i
$31$	4.56993	+	3.18053i	0.820783	+	0.571240i
$32$			3.75801i			0.664329i
$33$	5.17955	+	7.12905i	0.901645	+	1.24101i
$34$	−0.340664	+	3.24120i	−0.0584233	+	0.555861i
$35$		0			0
$36$	−1.67985	+	2.90958i	−0.279974	+	0.484930i
$37$	−9.77616	+	5.64427i	−1.60719	+	0.927912i	−0.617196	+	0.786810i	$0.711731\pi$
$37$	−9.77616	+	5.64427i	−1.60719	+	0.927912i	−0.989995	+	0.141102i	$0.954935\pi$
$38$	0.301728	+	1.41952i	0.0489468	+	0.230276i
$39$	3.77954	+	11.6322i	0.605210	+	1.86265i
$40$		0			0
$41$	−1.17622	−	11.1910i	−0.183695	−	1.74774i	−0.566639	−	0.823966i	$-0.691757\pi$
$41$	−1.17622	−	11.1910i	−0.183695	−	1.74774i	0.382944	−	0.923771i	$-0.374910\pi$
$42$	3.03624	−	2.73384i	0.468502	−	0.421841i
$43$	−4.54466	+	10.2075i	−0.693054	+	1.55663i	0.131797	+	0.991277i	$0.457925\pi$
$43$	−4.54466	+	10.2075i	−0.693054	+	1.55663i	−0.824852	+	0.565349i	$0.808741\pi$
$44$	18.0001	−	8.01414i	2.71361	−	1.20818i
$45$		0			0
$46$	4.81187	+	3.49603i	0.709471	+	0.515461i
$47$	4.89623	−	6.73909i	0.714189	−	0.982997i	−0.285508	−	0.958376i	$-0.592162\pi$
$47$	4.89623	−	6.73909i	0.714189	−	0.982997i	0.999697	−	0.0246207i	$-0.00783781\pi$
$48$	8.92015	+	8.03174i	1.28751	+	1.15928i
$49$	5.75776	−	2.56352i	0.822537	−	0.366217i
$50$		0			0
$51$	1.68193	+	1.86798i	0.235518	+	0.261569i
$52$	27.1982	−	2.85865i	3.77171	−	0.396423i
$53$	−1.10989	+	5.22161i	−0.152455	+	0.717244i	0.833807	+	0.552056i	$0.186156\pi$
$53$	−1.10989	+	5.22161i	−0.152455	+	0.717244i	−0.986262	+	0.165188i	$0.947177\pi$
$54$	−3.36622	−	10.3602i	−0.458085	−	1.40984i
$55$		0			0
$56$	−2.46450	−	4.26864i	−0.329333	−	0.570421i
$57$	0.969336	+	0.559646i	0.128392	+	0.0741270i
$58$	−1.89531	−	0.615823i	−0.248866	−	0.0808615i
$59$	−0.557834	+	5.30744i	−0.0726238	+	0.690969i	0.896273	+	0.443503i	$0.146265\pi$
$59$	−0.557834	+	5.30744i	−0.0726238	+	0.690969i	−0.968897	+	0.247466i	$0.920402\pi$
$60$		0			0
$61$	−4.18717			−0.536112			−0.268056	−	0.963403i	$-0.586381\pi$
$61$	−4.18717			−0.536112			−0.268056	+	0.963403i	$0.586381\pi$
$62$	−0.284685	−	14.0203i	−0.0361551	−	1.78058i
$63$		−	0.645926i		−	0.0813790i
$64$	−2.34063	+	1.70057i	−0.292579	+	0.212571i
$65$		0			0
$66$	6.85838	−	21.1079i	0.844208	−	2.59820i
$67$	6.10094	+	3.52238i	0.745348	+	0.430327i	0.824011	−	0.566574i	$-0.191732\pi$
$67$	6.10094	+	3.52238i	0.745348	+	0.430327i	−0.0786623	+	0.996901i	$0.525065\pi$
$68$	4.86742	−	2.81020i	0.590261	−	0.340787i
$69$	4.48712	−	0.953766i	0.540185	−	0.114820i
$70$		0			0
$71$	2.94921	+	0.626874i	0.350007	+	0.0743962i	0.379560	−	0.925167i	$-0.376075\pi$
$71$	2.94921	+	0.626874i	0.350007	+	0.0743962i	−0.0295537	+	0.999563i	$0.509409\pi$
$72$	4.54052	−	0.477228i	0.535105	−	0.0562418i
$73$	−7.69391	+	6.92763i	−0.900504	+	0.810818i	−0.982586	−	0.185808i	$-0.940510\pi$
$73$	−7.69391	+	6.92763i	−0.900504	+	0.810818i	0.0820820	+	0.996626i	$0.473843\pi$
$74$	25.9736	+	11.5642i	3.01938	+	1.34431i
$75$		0			0
$76$	1.67465	−	1.85989i	0.192096	−	0.213344i
$77$	−2.22662	+	3.06468i	−0.253747	+	0.349252i
$78$	18.1067	−	24.9218i	2.05018	−	2.82183i
$79$	−0.856267	+	0.950981i	−0.0963375	+	0.106994i	−0.789386	−	0.613898i	$-0.789601\pi$
$79$	−0.856267	+	0.950981i	−0.0963375	+	0.106994i	0.693048	+	0.720891i	$0.256267\pi$
$80$		0			0
$81$	−9.79521	−	4.36111i	−1.08836	−	0.484568i
$82$	−21.0616	+	18.9640i	−2.32587	+	2.09422i
$83$	13.0446	−	1.37104i	1.43183	−	0.150492i	0.643361	−	0.765563i	$-0.277539\pi$
$83$	13.0446	−	1.37104i	1.43183	−	0.150492i	0.788472	+	0.615071i	$0.210873\pi$
$84$	−6.89197	−	1.46493i	−0.751976	−	0.159837i
$85$		0			0
$86$	27.5269	−	5.85103i	2.96831	−	0.630933i
$87$	−1.33110	+	0.768511i	−0.142709	+	0.0823930i
$88$	−23.1882	−	13.3877i	−2.47187	−	1.42713i
$89$	−1.14268	+	3.51681i	−0.121124	+	0.372782i	−0.993175	−	0.116634i	$-0.962790\pi$
$89$	−1.14268	+	3.51681i	−0.121124	+	0.372782i	0.872051	+	0.489415i	$0.162790\pi$
$90$		0			0
$91$	−4.25370	+	3.09050i	−0.445909	+	0.323972i
$92$		−	10.2573i		−	1.06940i
$93$	−8.18286	−	7.07242i	−0.848523	−	0.733376i
$94$	−20.9802			−2.16394
$95$		0			0
$96$	0.763071	−	7.26013i	0.0778806	−	0.740984i
$97$	5.15563	+	1.67517i	0.523475	+	0.170087i	0.558822	−	0.829288i	$-0.311254\pi$
$97$	5.15563	+	1.67517i	0.523475	+	0.170087i	−0.0353469	+	0.999375i	$0.511254\pi$
$98$	−13.7473	−	7.93704i	−1.38869	−	0.801762i
$99$	−1.75440	−	3.03871i	−0.176324	−	0.305402i
$100$		0			0
$101$	0.705882	+	2.17248i	0.0702379	+	0.216170i	0.980014	−	0.198930i	$-0.0637466\pi$
$101$	0.705882	+	2.17248i	0.0702379	+	0.216170i	−0.909776	+	0.415100i	$0.863747\pi$
$102$	1.31626	−	6.19252i	0.130329	−	0.613151i
$103$	−6.51522	+	0.684777i	−0.641963	+	0.0674731i	−0.419916	−	0.907563i	$-0.637941\pi$
$103$	−6.51522	+	0.684777i	−0.641963	+	0.0674731i	−0.222047	+	0.975036i	$0.571274\pi$
$104$	−24.8673	−	27.6179i	−2.43844	−	2.70816i
$105$		0			0
$106$	12.2828	−	5.46863i	1.19301	−	0.531161i
$107$	3.44460	+	3.10153i	0.333002	+	0.299836i	0.818621	−	0.574334i	$-0.194739\pi$
$107$	3.44460	+	3.10153i	0.333002	+	0.299836i	−0.485619	+	0.874171i	$0.661406\pi$
$108$	−11.0422	+	15.1983i	−1.06254	+	1.46246i
$109$	−0.480316	−	0.348970i	−0.0460059	−	0.0334252i	0.564545	−	0.825403i	$-0.309052\pi$
$109$	−0.480316	−	0.348970i	−0.0460059	−	0.0334252i	−0.610551	+	0.791977i	$0.709052\pi$
$110$		0			0
$111$	20.0327	−	8.91914i	1.90142	−	0.846567i
$112$	−2.09877	+	4.71392i	−0.198315	+	0.445424i
$113$	7.17577	−	6.46109i	0.675039	−	0.607808i	−0.258616	−	0.965980i	$-0.583267\pi$
$113$	7.17577	−	6.46109i	0.675039	−	0.607808i	0.933656	+	0.358172i	$0.116600\pi$
$114$	−0.294675	−	2.80365i	−0.0275988	−	0.262585i
$115$		0			0
$116$	1.06202	+	3.26856i	0.0986060	+	0.303478i
$117$	−1.01256	−	4.76372i	−0.0936112	−	0.440406i
$118$	11.6404	−	6.72056i	1.07158	−	0.618678i
$119$	−0.540283	+	0.935798i	−0.0495277	+	0.0857844i
$120$		0			0
$121$	−1.00118	+	9.52556i	−0.0910160	+	0.865960i
$122$	6.19876	+	8.53186i	0.561209	+	0.772438i
$123$			21.8588i			1.97094i
$124$	−19.2724	+	14.6091i	−1.73071	+	1.31193i
$125$		0			0
$126$	−1.31615	+	0.956239i	−0.117252	+	0.0851886i
$127$	12.2066	+	1.28296i	1.08316	+	0.113845i	0.629250	−	0.777203i	$-0.283362\pi$
$127$	12.2066	+	1.28296i	1.08316	+	0.113845i	0.453910	+	0.891048i	$0.350029\pi$
$128$	14.0784	+	4.57435i	1.24437	+	0.404319i
$129$	10.8525	−	18.7971i	0.955510	−	1.65499i
$130$		0			0
$131$	−16.2500	+	3.45404i	−1.41977	+	0.301781i	−0.852919	−	0.522042i	$-0.825170\pi$
$131$	−16.2500	+	3.45404i	−1.41977	+	0.301781i	−0.566847	+	0.823823i	$0.691837\pi$
$132$	−36.4017	+	11.8276i	−3.16836	+	1.02946i
$133$	−0.100041	+	0.470654i	−0.00867461	+	0.0408108i
$134$	−1.85467	−	17.6460i	−0.160219	−	1.52438i
$135$		0			0
$136$	−6.97734	−	3.10651i	−0.598302	−	0.266381i
$137$	−1.19162	−	2.67643i	−0.101807	−	0.228663i	0.855459	−	0.517870i	$-0.173275\pi$
$137$	−1.19162	−	2.67643i	−0.101807	−	0.228663i	−0.957266	+	0.289207i	$0.906608\pi$
$138$	−8.58621	−	7.73106i	−0.730907	−	0.658111i
$139$	17.3423	+	12.6000i	1.47096	+	1.06871i	0.980335	+	0.197342i	$0.0632311\pi$
$139$	17.3423	+	12.6000i	1.47096	+	1.06871i	0.490624	+	0.871371i	$0.336769\pi$
$140$		0			0
$141$	−10.8275	+	12.0251i	−0.911836	+	1.01270i
$142$	−3.08873	−	6.93739i	−0.259200	−	0.582173i
$143$	−11.6171	+	26.0925i	−0.971474	+	2.18197i
$144$	−3.19812	−	3.55188i	−0.266510	−	0.295990i
$145$		0			0
$146$	25.5060	+	5.42148i	2.11090	+	0.448685i
$147$	−11.6440	+	3.78336i	−0.960379	+	0.312046i
$148$	−10.1943	−	47.9605i	−0.837968	−	3.94233i
$149$	−3.94968	−	6.84105i	−0.323571	−	0.560441i	0.657651	−	0.753322i	$-0.271550\pi$
$149$	−3.94968	−	6.84105i	−0.323571	−	0.560441i	−0.981222	+	0.192882i	$0.938217\pi$
$150$		0			0
$151$	−0.686047	+	2.11144i	−0.0558297	+	0.171826i	−0.975083	−	0.221840i	$-0.928794\pi$
$151$	−0.686047	+	2.11144i	−0.0558297	+	0.171826i	0.919253	+	0.393667i	$0.128794\pi$
$152$	−3.38236	−	0.355500i	−0.274346	−	0.0288349i
$153$	−0.588305	−	0.809732i	−0.0475616	−	0.0654629i
$154$	9.54097			0.768833
$155$		0			0
$156$	−53.1249			−4.25339
$157$	3.07376	+	4.23067i	0.245313	+	0.337644i	0.913863	−	0.406023i	$-0.133085\pi$
$157$	3.07376	+	4.23067i	0.245313	+	0.337644i	−0.668550	+	0.743667i	$0.733085\pi$
$158$	3.20537	+	0.336898i	0.255005	+	0.0268021i
$159$	3.20446	−	9.86231i	0.254130	−	0.782132i
$160$		0			0
$161$	0.986021	+	1.70784i	0.0777094	+	0.134597i
$162$	5.61471	+	26.4151i	0.441134	+	2.07537i
$163$	−12.6282	+	4.10314i	−0.989113	+	0.321382i	−0.758507	−	0.651665i	$-0.774071\pi$
$163$	−12.6282	+	4.10314i	−0.989113	+	0.321382i	−0.230606	+	0.973047i	$0.574071\pi$
$164$	47.8079	+	10.1619i	3.73317	+	0.793510i
$165$		0			0
$166$	−22.1051	−	24.5502i	−1.71569	−	1.90547i
$167$	2.58388	−	5.80350i	0.199947	−	0.449088i	−0.785546	−	0.618803i	$-0.787618\pi$
$167$	2.58388	−	5.80350i	0.199947	−	0.449088i	0.985493	+	0.169715i	$0.0542847\pi$
$168$	3.89443	+	8.74704i	0.300462	+	0.674849i
$169$	−17.8278	+	19.7997i	−1.37137	+	1.52306i
$170$		0			0
$171$	−0.360568	−	0.261968i	−0.0275733	−	0.0200332i
$172$	−36.0665	−	32.4744i	−2.75004	−	2.47615i
$173$	1.02551	+	2.30333i	0.0779679	+	0.175119i	0.948324	−	0.317305i	$-0.102778\pi$
$173$	1.02551	+	2.30333i	0.0779679	+	0.175119i	−0.870356	+	0.492423i	$0.836111\pi$
$174$	3.53651	+	1.57456i	0.268102	+	0.119367i
$175$		0			0
$176$	2.92997	+	27.8768i	0.220855	+	2.10129i
$177$	2.15537	−	10.1402i	0.162007	−	0.762184i
$178$	8.85757	−	2.87800i	0.663903	−	0.215715i
$179$	−11.6906	+	2.48491i	−0.873795	+	0.185731i	−0.622917	−	0.782288i	$-0.714053\pi$
$179$	−11.6906	+	2.48491i	−0.873795	+	0.185731i	−0.250878	+	0.968019i	$0.580719\pi$
$180$		0			0
$181$	−7.04742	+	12.2065i	−0.523830	+	0.907301i	0.475785	+	0.879562i	$0.342164\pi$
$181$	−7.04742	+	12.2065i	−0.523830	+	0.907301i	−0.999615	+	0.0277391i	$0.991169\pi$
$182$	12.5945	+	4.09220i	0.933567	+	0.303334i
$183$	8.08923	+	0.850212i	0.597973	+	0.0628495i
$184$	−11.2767	+	8.19301i	−0.831330	+	0.603997i
$185$		0			0
$186$	−2.29685	+	27.1437i	−0.168413	+	1.99027i
$187$			5.86986i			0.429247i
$188$	21.2669	+	29.2714i	1.55105	+	2.13483i
$189$	0.377533	−	3.59199i	0.0274615	−	0.261279i
$190$		0			0
$191$	−0.140704	+	0.243707i	−0.0101810	+	0.0176340i	−0.871071	−	0.491157i	$-0.836574\pi$
$191$	−0.140704	+	0.243707i	−0.0101810	+	0.0176340i	0.860890	+	0.508791i	$0.169907\pi$
$192$	4.86719	−	2.81007i	0.351259	−	0.202800i
$193$	−5.02930	−	23.6610i	−0.362017	−	1.70316i	−0.662243	−	0.749289i	$-0.730395\pi$
$193$	−5.02930	−	23.6610i	−0.362017	−	1.70316i	0.300226	−	0.953868i	$-0.402938\pi$
$194$	−4.21913	−	12.9851i	−0.302916	−	0.932279i
$195$		0			0
$196$	2.86154	+	27.2257i	0.204396	+	1.94469i
$197$	−9.46805	+	8.52507i	−0.674571	+	0.607386i	−0.933529	−	0.358502i	$-0.883287\pi$
$197$	−9.46805	+	8.52507i	−0.674571	+	0.607386i	0.258958	+	0.965889i	$0.416621\pi$
$198$	−3.59449	+	8.07337i	−0.255450	+	0.573749i
$199$	−9.87056	+	4.39466i	−0.699705	+	0.311529i	−0.725582	−	0.688136i	$-0.758429\pi$
$199$	−9.87056	+	4.39466i	−0.699705	+	0.311529i	0.0258761	+	0.999665i	$0.491762\pi$
$200$		0			0
$201$	−11.0712	−	8.04371i	−0.780904	−	0.567360i
$202$	3.38169	−	4.65449i	0.237935	−	0.327489i
$203$	−0.491029	−	0.442124i	−0.0344635	−	0.0310310i
$204$	−9.97401	+	4.44072i	−0.698320	+	0.310912i
$205$		0			0
$206$	11.0405	+	12.2618i	0.769231	+	0.854318i
$207$	−1.81661	+	0.190934i	−0.126263	+	0.0132708i
$208$	−8.08891	+	38.0553i	−0.560865	+	2.63866i
$209$	0.807711	+	2.48588i	0.0558705	+	0.171952i
$210$		0			0
$211$	2.19907	+	3.80891i	0.151391	+	0.262216i	0.931739	−	0.363129i	$-0.118292\pi$
$211$	2.19907	+	3.80891i	0.151391	+	0.262216i	−0.780348	+	0.625345i	$0.784958\pi$
$212$	−20.0804	−	11.5934i	−1.37913	−	0.796241i
$213$	−5.57031	−	1.80990i	−0.381671	−	0.124013i
$214$	1.22030	−	11.6103i	0.0834177	−	0.793667i
$215$		0			0
$216$	25.5287			1.73701
$217$	1.80450	−	4.28505i	0.122498	−	0.290888i
$218$			1.49532i			0.101276i
$219$	16.2706	−	11.8213i	1.09946	−	0.798808i
$220$		0			0
$221$	−2.51763	+	7.74848i	−0.169354	+	0.521219i
$222$	−47.8305	−	27.6150i	−3.21018	−	1.85340i
$223$	15.2399	−	8.79878i	1.02054	−	0.589210i	0.106281	−	0.994336i	$-0.466106\pi$
$223$	15.2399	−	8.79878i	1.02054	−	0.589210i	0.914261	+	0.405126i	$0.132772\pi$
$224$	3.06964	−	0.652473i	0.205099	−	0.0435952i
$225$		0			0
$226$	−23.7884	−	5.05637i	−1.58238	−	0.336345i
$227$	−22.2197	+	2.33539i	−1.47477	+	0.155005i	−0.807527	−	0.589831i	$-0.799194\pi$
$227$	−22.2197	+	2.33539i	−1.47477	+	0.155005i	−0.667248	+	0.744836i	$0.732528\pi$
$228$	−3.61292	+	3.25309i	−0.239272	+	0.215441i
$229$	−0.133599	−	0.0594822i	−0.00882849	−	0.00393070i	0.402318	−	0.915500i	$-0.368205\pi$
$229$	−0.133599	−	0.0594822i	−0.00882849	−	0.00393070i	−0.411146	+	0.911569i	$0.634871\pi$
$230$		0			0
$231$	4.92391	−	5.46855i	0.323969	−	0.359804i
$232$	2.74512	−	3.77833i	0.180226	−	0.248059i
$233$	5.10755	−	7.02994i	0.334607	−	0.460547i	−0.608250	−	0.793746i	$-0.708128\pi$
$233$	5.10755	−	7.02994i	0.334607	−	0.460547i	0.942856	+	0.333199i	$0.108128\pi$
$234$	−8.20763	+	9.11550i	−0.536549	+	0.595899i
$235$		0			0
$236$	−21.1759	−	9.42813i	−1.37844	−	0.613719i
$237$	1.84733	−	1.66334i	0.119997	−	0.108046i
$238$	2.70664	−	0.284480i	0.175446	−	0.0184401i
$239$	−10.2336	−	2.17521i	−0.661954	−	0.140703i	−0.135329	−	0.990801i	$-0.543209\pi$
$239$	−10.2336	−	2.17521i	−0.661954	−	0.140703i	−0.526624	+	0.850098i	$0.676543\pi$
$240$		0			0
$241$	−5.32178	+	1.13118i	−0.342806	+	0.0728657i	−0.376098	−	0.926580i	$-0.622734\pi$
$241$	−5.32178	+	1.13118i	−0.342806	+	0.0728657i	0.0332916	+	0.999446i	$0.489401\pi$
$242$	20.8916	−	12.0618i	1.34296	−	0.775360i
$243$	6.80098	+	3.92655i	0.436283	+	0.251888i
$244$	5.62011	−	17.2969i	0.359791	−	1.10732i
$245$		0			0
$246$	44.5398	−	32.3601i	2.83976	−	2.06320i
$247$			3.62790i			0.230838i
$248$	31.4548	+	9.51879i	1.99738	+	0.604444i
$249$	−25.4794			−1.61469
$250$		0			0
$251$	1.20823	−	11.4955i	0.0762626	−	0.725590i	−0.887857	−	0.460120i	$-0.847806\pi$
$251$	1.20823	−	11.4955i	0.0762626	−	0.725590i	0.964119	−	0.265470i	$-0.0855270\pi$
$252$	2.66828	+	0.866976i	0.168086	+	0.0546143i
$253$	9.27734	+	5.35627i	0.583261	+	0.336746i
$254$	−15.4566	−	26.7717i	−0.969836	−	1.67981i
$255$		0			0
$256$	−9.73302	−	29.9552i	−0.608314	−	1.87220i
$257$	−3.94450	+	18.5574i	−0.246051	+	1.15758i	0.665501	+	0.746397i	$0.268218\pi$
$257$	−3.94450	+	18.5574i	−0.246051	+	1.15758i	−0.911552	+	0.411184i	$0.865115\pi$
$258$	−54.3675	+	5.71426i	−3.38477	+	0.355754i
$259$	6.30774	+	7.00546i	0.391944	+	0.435298i
$260$		0			0
$261$	0.559108	−	0.248931i	0.0346079	−	0.0154084i
$262$	31.0947	+	27.9978i	1.92104	+	1.72971i
$263$	3.06516	−	4.21884i	0.189006	−	0.260145i	−0.703989	−	0.710211i	$-0.748600\pi$
$263$	3.06516	−	4.21884i	0.189006	−	0.260145i	0.892995	+	0.450066i	$0.148600\pi$
$264$	42.0790	+	30.5722i	2.58978	+	1.88159i
$265$		0			0
$266$	1.10711	−	0.492919i	0.0678815	−	0.0302228i
$267$	2.92165	−	6.56213i	0.178802	−	0.401596i
$268$	−22.7395	+	20.4748i	−1.38904	+	1.25069i
$269$	0.120184	+	1.14347i	0.00732773	+	0.0697187i	0.997575	−	0.0696049i	$-0.0221738\pi$
$269$	0.120184	+	1.14347i	0.00732773	+	0.0697187i	−0.990247	+	0.139324i	$0.955507\pi$
$270$		0			0
$271$	3.88599	+	11.9599i	0.236057	+	0.726509i	0.996979	+	0.0776663i	$0.0247469\pi$
$271$	3.88599	+	11.9599i	0.236057	+	0.726509i	−0.760922	+	0.648843i	$0.775253\pi$
$272$	1.66239	+	7.82091i	0.100797	+	0.474212i
$273$	8.84529	−	5.10683i	0.535341	−	0.309079i
$274$	−3.68944	+	6.39030i	−0.222887	+	0.386052i
$275$		0			0
$276$	−2.08276	+	19.8161i	−0.125367	+	1.19279i
$277$	−12.8237	−	17.6504i	−0.770503	−	1.06051i	−0.996267	−	0.0863249i	$-0.972488\pi$
$277$	−12.8237	−	17.6504i	−0.770503	−	1.06051i	0.225764	−	0.974182i	$-0.427512\pi$
$278$		−	53.9902i		−	3.23812i
$279$	2.94608	+	3.14129i	0.176377	+	0.188064i
$280$		0			0
$281$	25.1753	−	18.2909i	1.50183	−	1.09114i	0.532185	−	0.846628i	$-0.321371\pi$
$281$	25.1753	−	18.2909i	1.50183	−	1.09114i	0.969645	−	0.244515i	$-0.0786289\pi$
$282$	40.5317	+	4.26005i	2.41363	+	0.253683i
$283$	17.2425	+	5.60243i	1.02496	+	0.333030i	0.772796	−	0.634654i	$-0.218858\pi$
$283$	17.2425	+	5.60243i	1.02496	+	0.333030i	0.252165	+	0.967684i	$0.418858\pi$
$284$	−6.54806	+	11.3416i	−0.388556	+	0.672999i
$285$		0			0
$286$	70.3648	−	14.9565i	4.16076	−	0.884397i
$287$	−8.93687	+	2.90377i	−0.527527	+	0.171404i
$288$	−0.604359	+	2.84328i	−0.0356122	+	0.167542i
$289$	−1.60196	−	15.2417i	−0.0942332	−	0.896569i
$290$		0			0
$291$	−9.62005	−	4.28312i	−0.563937	−	0.251081i
$292$	−18.2906	−	41.0814i	−1.07038	−	2.40411i
$293$	−8.69944	−	7.83301i	−0.508226	−	0.457609i	0.374683	−	0.927153i	$-0.377752\pi$
$293$	−8.69944	−	7.83301i	−0.508226	−	0.457609i	−0.882909	+	0.469544i	$0.844418\pi$
$294$	24.9470	+	18.1250i	1.45494	+	1.05707i
$295$		0			0
$296$	−44.5843	+	49.5159i	−2.59141	+	2.87805i
$297$	−7.98014	−	17.9237i	−0.463055	−	1.04004i
$298$	−8.09227	+	18.1755i	−0.468773	+	1.05288i
$299$	9.94915	+	11.0497i	0.575374	+	0.639018i
$300$		0			0
$301$	9.12679	+	1.93996i	0.526059	+	0.111817i
$302$	5.31794	−	1.72790i	0.306013	−	0.0994296i
$303$	−0.922572	−	4.34036i	−0.0530004	−	0.249347i
$304$	1.78020	+	3.08339i	0.102101	+	0.176845i
$305$		0			0
$306$	−0.778988	+	2.39748i	−0.0445318	+	0.137055i
$307$	−11.6792	−	1.22753i	−0.666568	−	0.0700591i	−0.234800	−	0.972044i	$-0.575443\pi$
$307$	−11.6792	−	1.22753i	−0.666568	−	0.0700591i	−0.431768	+	0.901985i	$0.642110\pi$
$308$	−9.67136	−	13.3115i	−0.551077	−	0.758492i
$309$	12.7258			0.723947
$310$		0			0
$311$	−0.833220			−0.0472476			−0.0236238	−	0.999721i	$-0.507520\pi$
$311$	−0.833220			−0.0472476			−0.0236238	+	0.999721i	$0.507520\pi$
$312$	42.4335	+	58.4047i	2.40232	+	3.30651i
$313$	−10.5377	−	1.10756i	−0.595627	−	0.0626029i	−0.198082	−	0.980186i	$-0.563471\pi$
$313$	−10.5377	−	1.10756i	−0.595627	−	0.0626029i	−0.397545	+	0.917583i	$0.630138\pi$
$314$	4.07004	−	12.5263i	0.229686	−	0.706900i
$315$		0			0
$316$	−2.77914	−	4.81361i	−0.156339	−	0.270787i
$317$	6.46741	+	30.4268i	0.363246	+	1.70894i	0.657707	+	0.753274i	$0.271526\pi$
$317$	6.46741	+	30.4268i	0.363246	+	1.70894i	−0.294461	+	0.955663i	$0.595140\pi$
$318$	−24.8396	+	8.07086i	−1.39293	+	0.452591i
$319$	−3.51087	−	0.746258i	−0.196571	−	0.0417824i
$320$		0			0
$321$	−6.02488	−	6.69130i	−0.336276	−	0.373472i
$322$	2.02020	−	4.53745i	0.112581	−	0.252862i
$323$	0.303257	+	0.681127i	0.0168737	+	0.0378989i
$324$	31.1628	−	34.6098i	1.73127	−	1.92277i
$325$		0			0
$326$	27.0555	+	19.6570i	1.49847	+	1.08870i
$327$	0.857067	+	0.771706i	0.0473959	+	0.0426755i
$328$	−27.0147	−	60.6761i	−1.49164	−	3.35028i
$329$	−6.35476	−	2.82932i	−0.350349	−	0.155986i
$330$		0			0
$331$	0.934022	+	8.88662i	0.0513385	+	0.488453i	0.989737	+	0.142899i	$0.0456424\pi$
$331$	0.934022	+	8.88662i	0.0513385	+	0.488453i	−0.938399	+	0.345554i	$0.887691\pi$
$332$	−11.8451	+	55.7267i	−0.650083	+	3.05840i
$333$	−8.30427	+	2.69822i	−0.455071	+	0.147862i
$334$	−15.6505	+	3.32662i	−0.856359	+	0.182025i
$335$		0			0
$336$	5.01180	−	8.68070i	0.273416	−	0.473571i
$337$	−22.1613	−	7.20064i	−1.20720	−	0.392244i	−0.364796	−	0.931087i	$-0.618861\pi$
$337$	−22.1613	−	7.20064i	−1.20720	−	0.392244i	−0.842406	+	0.538843i	$0.818861\pi$
$338$	66.7368	+	7.01432i	3.63000	+	0.381529i
$339$	−15.1749	+	11.0252i	−0.824185	+	0.598805i
$340$		0			0
$341$	−3.14947	−	25.0599i	−0.170554	−	1.35707i
$342$			1.12252i			0.0606990i
$343$	−6.52953	−	8.98713i	−0.352562	−	0.485260i
$344$	−6.89377	+	65.5898i	−0.371687	+	3.53637i
$345$		0			0
$346$	3.17512	−	5.49947i	0.170696	−	0.295654i
$347$	16.6841	−	9.63256i	0.895648	−	0.517103i	0.0198624	−	0.999803i	$-0.493677\pi$
$347$	16.6841	−	9.63256i	0.895648	−	0.517103i	0.875786	+	0.482700i	$0.160344\pi$
$348$	−1.38804	−	6.53020i	−0.0744065	−	0.350055i
$349$	−10.0809	−	31.0259i	−0.539619	−	1.66078i	−0.733451	−	0.679743i	$-0.762092\pi$
$349$	−10.0809	−	31.0259i	−0.539619	−	1.66078i	0.193832	−	0.981035i	$-0.437908\pi$
$350$		0			0
$351$	−2.84652	−	27.0828i	−0.151936	−	1.44557i
$352$	12.6687	−	11.4070i	0.675247	−	0.607995i
$353$	5.17536	−	11.6241i	0.275457	−	0.618686i	−0.721848	−	0.692051i	$-0.756707\pi$
$353$	5.17536	−	11.6241i	0.275457	−	0.618686i	0.997305	+	0.0733652i	$0.0233739\pi$
$354$	−23.8527	+	10.6199i	−1.26776	+	0.564442i
$355$		0			0
$356$	−12.9940	−	9.44069i	−0.688680	−	0.500355i
$357$	1.23379	−	1.69817i	0.0652992	−	0.0898766i
$358$	22.3702	+	20.1422i	1.18230	+	1.06455i
$359$	5.85762	−	2.60798i	0.309153	−	0.137644i	−0.246295	−	0.969195i	$-0.579213\pi$
$359$	5.85762	−	2.60798i	0.309153	−	0.137644i	0.555449	+	0.831551i	$0.312547\pi$
$360$		0			0
$361$	−12.4913	−	13.8730i	−0.657438	−	0.730159i
$362$	35.3053	−	3.71073i	1.85560	−	0.195032i
$363$	3.86836	−	18.1992i	0.203036	−	0.955210i
$364$	−7.05722	−	21.7199i	−0.369899	−	1.13843i
$365$		0			0
$366$	−10.2430	−	17.7414i	−0.535411	−	0.927359i
$367$	18.9610	+	10.9471i	0.989754	+	0.571435i	0.905201	−	0.424984i	$-0.139720\pi$
$367$	18.9610	+	10.9471i	0.989754	+	0.571435i	0.0845536	+	0.996419i	$0.473054\pi$
$368$	13.8779	+	4.50921i	0.723436	+	0.235059i
$369$	0.909800	−	8.65617i	0.0473623	−	0.450622i
$370$		0			0
$371$	4.45785			0.231440
$372$	40.1989	−	24.3101i	2.08422	−	1.26042i
$373$			4.62775i			0.239616i	0.992797	+	0.119808i	$0.0382279\pi$
$373$			4.62775i			0.239616i	−0.992797	+	0.119808i	$0.961772\pi$
$374$	11.9605	−	8.68984i	0.618465	−	0.449341i
$375$		0			0
$376$	15.1936	−	46.7610i	0.783548	−	2.41151i
$377$	−4.31443	−	2.49093i	−0.222204	−	0.128290i
$378$	−7.87801	+	4.54837i	−0.405201	+	0.233943i
$379$	−14.1342	+	3.00432i	−0.726025	+	0.154321i	−0.556076	−	0.831131i	$-0.687694\pi$
$379$	−14.1342	+	3.00432i	−0.726025	+	0.154321i	−0.169949	+	0.985453i	$0.554360\pi$
$380$		0			0
$381$	−23.3215	−	4.95714i	−1.19480	−	0.253962i
$382$	0.704882	−	0.0740861i	0.0360649	−	0.00379057i
$383$	−15.1615	+	13.6515i	−0.774718	+	0.697560i	−0.958401	−	0.285426i	$-0.907865\pi$
$383$	−15.1615	+	13.6515i	−0.774718	+	0.697560i	0.183682	+	0.982986i	$0.441198\pi$
$384$	−26.2693	−	11.6959i	−1.34055	−	0.596852i
$385$		0			0
$386$	−40.7666	+	45.2759i	−2.07497	+	2.30449i
$387$	−5.08001	+	6.99203i	−0.258231	+	0.355425i
$388$	−13.8400	+	19.0491i	−0.702619	+	0.967072i
$389$	−4.17983	+	4.64217i	−0.211926	+	0.235367i	−0.839730	−	0.543004i	$-0.817287\pi$
$389$	−4.17983	+	4.64217i	−0.211926	+	0.235367i	0.627805	+	0.778371i	$0.283954\pi$
$390$		0			0
$391$	2.79156	+	1.24288i	0.141175	+	0.0628553i
$392$	27.6459	−	24.8925i	1.39633	−	1.25726i
$393$	32.0948	−	3.37330i	1.61897	−	0.170160i
$394$	31.3875	+	6.67162i	1.58128	+	0.336111i
$395$		0			0
$396$	14.9075	−	3.16869i	0.749131	−	0.159233i
$397$	27.3586	−	15.7955i	1.37309	−	0.792753i	0.381773	−	0.924256i	$-0.375314\pi$
$397$	27.3586	−	15.7955i	1.37309	−	0.792753i	0.991316	+	0.131503i	$0.0419804\pi$
$398$	23.5672	+	13.6065i	1.18132	+	0.682033i
$399$	0.288836	−	0.888946i	0.0144599	−	0.0445030i
$400$		0			0
$401$	−1.67599	+	1.21768i	−0.0836950	+	0.0608080i	−0.628846	−	0.777530i	$-0.716472\pi$
$401$	−1.67599	+	1.21768i	−0.0836950	+	0.0608080i	0.545151	+	0.838338i	$0.316472\pi$
$402$			34.4670i			1.71906i
$403$	6.59097	−	34.4311i	0.328320	−	1.71513i
$404$	−9.92182			−0.493629
$405$		0			0
$406$	−0.173954	+	1.65506i	−0.00863317	+	0.0821391i
$407$	48.7019	+	15.8242i	2.41406	+	0.784377i
$408$	12.8488	+	7.41825i	0.636110	+	0.367258i
$409$	11.9560	+	20.7083i	0.591184	+	1.02396i	0.994073	+	0.108712i	$0.0346725\pi$
$409$	11.9560	+	20.7083i	0.591184	+	1.02396i	−0.402890	+	0.915249i	$0.631994\pi$
$410$		0			0
$411$	1.75865	+	5.41258i	0.0867479	+	0.266983i
$412$	5.91609	−	27.8330i	0.291465	−	1.37124i
$413$	4.43211	−	0.465833i	0.218090	−	0.0229221i
$414$	3.07840	+	3.41891i	0.151295	+	0.168030i
$415$		0			0
$416$	21.6159	−	9.62401i	1.05981	−	0.471856i
$417$	−30.9454	−	27.8633i	−1.51540	−	1.36447i
$418$	3.86952	−	5.32594i	0.189265	−	0.260500i
$419$	−24.7274	−	17.9655i	−1.20801	−	0.877673i	−0.212965	−	0.977060i	$-0.568312\pi$
$419$	−24.7274	−	17.9655i	−1.20801	−	0.877673i	−0.995049	+	0.0993864i	$0.968312\pi$
$420$		0			0
$421$	20.5099	−	9.13160i	0.999592	−	0.445047i	0.159329	−	0.987226i	$-0.449067\pi$
$421$	20.5099	−	9.13160i	0.999592	−	0.445047i	0.840263	+	0.542178i	$0.182400\pi$
$422$	4.50555	−	10.1196i	0.219327	−	0.492616i
$423$	4.78822	−	4.31134i	0.232811	−	0.209624i
$424$	3.29358	+	31.3364i	0.159951	+	1.52183i
$425$		0			0
$426$	4.55848	+	14.0296i	0.220859	+	0.679735i
$427$	0.726984	+	3.42019i	0.0351812	+	0.165515i
$428$	−17.4356	+	10.0665i	−0.842783	+	0.486581i
$429$	27.7414	−	48.0495i	1.33937	−	2.31985i
$430$		0			0
$431$	1.72251	−	16.3886i	0.0829704	−	0.789411i	−0.871357	−	0.490649i	$-0.836760\pi$
$431$	1.72251	−	16.3886i	0.0829704	−	0.789411i	0.954328	−	0.298762i	$-0.0965736\pi$
$432$	−15.7087	−	21.6212i	−0.755787	−	1.04025i
$433$			30.3372i			1.45791i	0.684560	+	0.728957i	$0.259994\pi$
$433$			30.3372i			1.45791i	−0.684560	+	0.728957i	$0.740006\pi$
$434$	−11.4027	+	2.66676i	−0.547347	+	0.128009i
$435$		0			0
$436$	2.08626	−	1.51576i	0.0999138	−	0.0725916i
$437$	1.35325	+	0.142232i	0.0647346	+	0.00680388i
$438$	−48.1745	−	15.6528i	−2.30187	−	0.747921i
$439$	−8.25197	+	14.2928i	−0.393845	+	0.682160i	−0.992953	−	0.118508i	$-0.962189\pi$
$439$	−8.25197	+	14.2928i	−0.393845	+	0.682160i	0.599108	+	0.800668i	$0.295522\pi$
$440$		0			0
$441$	4.76854	−	1.01358i	0.227073	−	0.0482659i
$442$	19.5156	−	6.34100i	0.928262	−	0.301611i
$443$	−5.24879	+	24.6936i	−0.249377	+	1.17323i	0.658035	+	0.752987i	$0.271388\pi$
$443$	−5.24879	+	24.6936i	−0.249377	+	1.17323i	−0.907413	+	0.420241i	$0.861946\pi$
$444$	9.95602	+	94.7252i	0.472492	+	4.49546i
$445$		0			0
$446$	−40.4900	−	18.0273i	−1.91726	−	0.853618i
$447$	6.24133	+	14.0183i	0.295205	+	0.663041i
$448$	1.79546	+	1.61664i	0.0848273	+	0.0763788i
$449$	2.11185	+	1.53435i	0.0996644	+	0.0724104i	0.636501	−	0.771276i	$-0.280381\pi$
$449$	2.11185	+	1.53435i	0.0996644	+	0.0724104i	−0.536837	+	0.843686i	$0.680381\pi$
$450$		0			0
$451$	−34.1560	+	37.9340i	−1.60834	+	1.78624i
$452$	17.0589	+	38.3148i	0.802381	+	1.80218i
$453$	1.75411	−	3.93980i	0.0824153	−	0.185108i
$454$	37.6531	+	41.8180i	1.76715	+	1.96261i
$455$		0			0
$456$	6.46222	+	1.37359i	0.302621	+	0.0643241i
$457$	−8.90392	+	2.89306i	−0.416508	+	0.135332i	−0.509771	−	0.860310i	$-0.670270\pi$
$457$	−8.90392	+	2.89306i	−0.416508	+	0.135332i	0.0932637	+	0.995641i	$0.470270\pi$
$458$	0.0765805	+	0.360283i	0.00357837	+	0.0168349i
$459$	−2.79828	−	4.84677i	−0.130613	−	0.226228i
$460$		0			0
$461$	−5.44913	+	16.7707i	−0.253791	+	0.781089i	0.740274	+	0.672305i	$0.234696\pi$
$461$	−5.44913	+	16.7707i	−0.253791	+	0.781089i	−0.994065	+	0.108784i	$0.965304\pi$
$462$	−18.4323	−	1.93731i	−0.857546	−	0.0901318i
$463$	−3.41667	−	4.70265i	−0.158786	−	0.218551i	0.722210	−	0.691674i	$-0.243126\pi$
$463$	−3.41667	−	4.70265i	−0.158786	−	0.218551i	−0.880996	+	0.473123i	$0.843126\pi$
$464$	−4.88917			−0.226974
$465$		0			0
$466$	−21.8856			−1.01383
$467$	4.75472	+	6.54431i	0.220022	+	0.302834i	0.904732	−	0.425981i	$-0.140071\pi$
$467$	4.75472	+	6.54431i	0.220022	+	0.302834i	−0.684710	+	0.728816i	$0.740071\pi$
$468$	21.0377	+	2.21115i	0.972467	+	0.102210i
$469$	1.81792	−	5.59497i	0.0839436	−	0.258352i
$470$		0			0
$471$	−5.07918	−	8.79739i	−0.234036	−	0.405362i
$472$	6.54912	+	30.8112i	0.301448	+	1.41820i
$473$	48.2055	−	15.6629i	2.21649	−	0.720181i
$474$	−6.12406	−	1.30171i	−0.281287	−	0.0597895i
$475$		0			0
$476$	−3.14054	−	3.48792i	−0.143946	−	0.159869i
$477$	−1.67947	+	3.77214i	−0.0768975	+	0.172715i
$478$	10.7177	+	24.0723i	0.490215	+	1.10104i
$479$	−6.09262	+	6.76654i	−0.278379	+	0.309171i	−0.866078	−	0.499908i	$-0.833367\pi$
$479$	−6.09262	+	6.76654i	−0.278379	+	0.309171i	0.587700	+	0.809079i	$0.300034\pi$
$480$		0			0
$481$	57.5015	+	41.7773i	2.62184	+	1.90488i
$482$	10.1834	+	9.16915i	0.463840	+	0.417643i
$483$	−1.55812	−	3.49960i	−0.0708970	−	0.159237i
$484$	−38.0056	−	16.9212i	−1.72753	−	0.769145i
$485$		0			0
$486$	−2.06748	−	19.6707i	−0.0937826	−	0.892282i
$487$	−8.55495	+	40.2479i	−0.387662	+	1.82381i	0.160013	+	0.987115i	$0.448846\pi$
$487$	−8.55495	+	40.2479i	−0.387662	+	1.82381i	−0.547675	+	0.836691i	$0.684487\pi$
$488$	−23.5050	+	7.63725i	−1.06402	+	0.345722i
$489$	25.2296	−	5.36271i	1.14092	−	0.242510i
$490$		0			0
$491$	−9.46138	+	16.3876i	−0.426986	+	0.739562i	−0.996604	−	0.0823481i	$-0.973758\pi$
$491$	−9.46138	+	16.3876i	−0.426986	+	0.739562i	0.569617	+	0.821910i	$0.307091\pi$
$492$	−90.2971	−	29.3393i	−4.07091	−	1.32272i
$493$	−1.01824	−	0.107021i	−0.0458591	−	0.00481998i
$494$	7.39228	−	5.37081i	0.332595	−	0.241644i
$495$		0			0
$496$	−11.2935	−	32.4975i	−0.507091	−	1.45918i
$497$		−	2.51783i		−	0.112940i
$498$	37.7201	+	51.9172i	1.69028	+	2.32647i
$499$	0.831837	−	7.91440i	0.0372382	−	0.354297i	−0.959998	−	0.280006i	$-0.909664\pi$
$499$	0.831837	−	7.91440i	0.0372382	−	0.354297i	0.997237	−	0.0742919i	$-0.0236696\pi$
$500$		0			0
$501$	−6.17023	+	10.6872i	−0.275666	+	0.477467i
$502$	−25.2121	+	14.5562i	−1.12527	+	0.649676i
$503$	1.56422	+	7.35909i	0.0697452	+	0.328125i	0.999163	−	0.0409035i	$-0.0130236\pi$
$503$	1.56422	+	7.35909i	0.0697452	+	0.328125i	−0.929418	+	0.369029i	$0.879690\pi$
$504$	−1.17815	−	3.62596i	−0.0524788	−	0.161513i
$505$		0			0
$506$	−2.82028	−	26.8332i	−0.125377	−	1.19288i
$507$	38.4619	−	34.6313i	1.70816	−	1.53803i
$508$	−21.6838	+	48.7026i	−0.962062	+	2.16083i
$509$	−12.2699	+	5.46290i	−0.543852	+	0.242139i	−0.660226	−	0.751067i	$-0.729540\pi$
$509$	−12.2699	+	5.46290i	−0.543852	+	0.242139i	0.116374	+	0.993205i	$0.462873\pi$
$510$		0			0
$511$	6.99450	+	5.08180i	0.309418	+	0.224806i
$512$	−29.2264	+	40.2267i	−1.29164	+	1.77779i
$513$	−1.85200	−	1.66755i	−0.0817677	−	0.0736240i
$514$	43.6525	−	19.4353i	1.92543	−	0.857255i
$515$		0			0
$516$	63.0831	+	70.0608i	2.77708	+	3.08426i
$517$	−37.5803	+	3.94984i	−1.65278	+	0.173714i
$518$	4.93636	−	23.2238i	0.216891	−	1.02039i
$519$	−1.51349	−	4.65804i	−0.0664349	−	0.204465i
$520$		0			0
$521$	9.74556	+	16.8798i	0.426961	+	0.739518i	0.996601	−	0.0823761i	$-0.0262509\pi$
$521$	9.74556	+	16.8798i	0.426961	+	0.739518i	−0.569640	+	0.821894i	$0.692918\pi$
$522$	−1.33494	−	0.770727i	−0.0584287	−	0.0337338i
$523$	−5.95438	−	1.93469i	−0.260367	−	0.0845983i	0.175925	−	0.984404i	$-0.443708\pi$
$523$	−5.95438	−	1.93469i	−0.260367	−	0.0845983i	−0.436292	+	0.899805i	$0.643708\pi$
$524$	7.54266	−	71.7636i	0.329503	−	3.13501i
$525$		0			0
$526$	−13.1341			−0.572674
$527$	−1.64067	−	7.01525i	−0.0714685	−	0.305589i
$528$		−	54.4503i		−	2.36965i
$529$	−14.0957	+	10.2411i	−0.612856	+	0.445266i
$530$		0			0
$531$	−1.27559	+	3.92585i	−0.0553558	+	0.170368i
$532$	−1.80996	−	1.04498i	−0.0784718	−	0.0453057i
$533$	−61.3576	+	35.4248i	−2.65769	+	1.53442i
$534$	−17.6964	+	3.76148i	−0.765797	+	0.162775i
$535$		0			0
$536$	40.6728	+	8.64527i	1.75680	+	0.373419i
$537$	23.0897	−	2.42682i	0.996394	−	0.104725i
$538$	2.15204	−	1.93770i	0.0927809	−	0.0835403i
$539$	−26.1189	−	11.6289i	−1.12502	−	0.500892i
$540$		0			0
$541$	24.4535	−	27.1584i	1.05134	−	1.16763i	0.0658608	−	0.997829i	$-0.479021\pi$
$541$	24.4535	−	27.1584i	1.05134	−	1.16763i	0.985478	−	0.169802i	$-0.0543127\pi$
$542$	18.6167	−	25.6237i	0.799657	−	1.10063i
$543$	16.0935	−	22.1508i	0.690638	−	0.950582i
$544$	3.25383	−	3.61375i	0.139507	−	0.154938i
$545$		0			0
$546$	−23.5005	−	10.4631i	−1.00573	−	0.447779i
$547$	8.45322	−	7.61131i	0.361433	−	0.325436i	−0.468328	−	0.883555i	$-0.655143\pi$
$547$	8.45322	−	7.61131i	0.361433	−	0.325436i	0.829761	+	0.558119i	$0.188477\pi$
$548$	12.6556	−	1.33015i	0.540619	−	0.0568214i
$549$	−3.16798	−	0.673375i	−0.135206	−	0.0287390i
$550$		0			0
$551$	−0.445948	+	0.0947892i	−0.0189980	+	0.00403815i
$552$	23.4492	−	13.5384i	0.998062	−	0.576232i
$553$	0.925453	+	0.534310i	0.0393542	+	0.0227212i
$554$	−16.9802	+	52.2597i	−0.721420	+	2.22030i
$555$		0			0
$556$	−75.3268	+	54.7281i	−3.19457	+	2.32099i
$557$		−	17.9263i		−	0.759560i	−0.925077	−	0.379780i	$-0.876000\pi$
$557$		−	17.9263i		−	0.759560i	0.925077	−	0.379780i	$-0.124000\pi$
$558$	2.03933	−	10.6534i	0.0863317	−	0.450995i
$559$	70.3514			2.97555
$560$		0			0
$561$	1.19188	−	11.3400i	0.0503214	−	0.478776i
$562$	−74.5397	−	24.2194i	−3.14427	−	1.02163i
$563$	−28.7466	−	16.5969i	−1.21152	−	0.699474i	−0.248433	−	0.968649i	$-0.579916\pi$
$563$	−28.7466	−	16.5969i	−1.21152	−	0.699474i	−0.963091	+	0.269175i	$0.913249\pi$
$564$	−35.1421	−	60.8678i	−1.47975	−	2.56300i
$565$		0			0
$566$	−14.1105	−	43.4276i	−0.593108	−	1.82540i
$567$	−1.86161	+	8.75817i	−0.0781801	+	0.367808i
$568$	17.6990	−	1.86024i	0.742634	−	0.0780540i
$569$	−18.2648	−	20.2851i	−0.765699	−	0.850395i	0.226635	−	0.973980i	$-0.427228\pi$
$569$	−18.2648	−	20.2851i	−0.765699	−	0.850395i	−0.992334	+	0.123585i	$0.960561\pi$
$570$		0			0
$571$	27.0994	−	12.0654i	1.13408	−	0.504923i	0.248137	−	0.968725i	$-0.420182\pi$
$571$	27.0994	−	12.0654i	1.13408	−	0.504923i	0.885939	+	0.463802i	$0.153515\pi$
$572$	−92.1937	−	83.0116i	−3.85481	−	3.47089i
$573$	0.321312	−	0.442248i	0.0134230	−	0.0184752i
$574$	19.1471	+	13.9111i	0.799182	+	0.580640i
$575$		0			0
$576$	−2.04439	+	0.910221i	−0.0851829	+	0.0379259i
$577$	−0.821336	+	1.84475i	−0.0341926	+	0.0767979i	−0.929834	−	0.367978i	$-0.880050\pi$
$577$	−0.821336	+	1.84475i	−0.0341926	+	0.0767979i	0.895642	+	0.444776i	$0.146717\pi$
$578$	−28.6851	+	25.8282i	−1.19314	+	1.07431i
$579$	4.91174	+	46.7321i	0.204125	+	1.94212i
$580$		0			0
$581$	−3.38474	−	10.4171i	−0.140422	−	0.432176i
$582$	5.51431	+	25.9428i	0.228576	+	1.07536i
$583$	20.9717	−	12.1080i	0.868558	−	0.501462i
$584$	−30.5547	+	52.9222i	−1.26436	+	2.18994i
$585$		0			0
$586$	−3.08189	+	29.3222i	−0.127312	+	1.21129i
$587$	2.00517	+	2.75988i	0.0827623	+	0.113913i	0.848391	−	0.529371i	$-0.177572\pi$
$587$	2.00517	+	2.75988i	0.0827623	+	0.113913i	−0.765628	+	0.643283i	$0.777572\pi$
$588$		−	53.1786i		−	2.19305i
$589$	−1.66014	−	2.74519i	−0.0684049	−	0.113114i
$590$		0			0
$591$	20.0224	−	14.5471i	0.823612	−	0.598389i
$592$	69.3711	+	7.29120i	2.85114	+	0.299667i
$593$	−13.8014	−	4.48436i	−0.566757	−	0.184151i	0.0116020	−	0.999933i	$-0.496307\pi$
$593$	−13.8014	−	4.48436i	−0.566757	−	0.184151i	−0.578359	+	0.815782i	$0.696307\pi$
$594$	−24.7077	+	42.7950i	−1.01377	+	1.75590i
$595$		0			0
$596$	33.5613	−	7.13367i	1.37472	−	0.292206i
$597$	19.9613	−	6.48584i	0.816964	−	0.265448i
$598$	7.78609	−	36.6307i	0.318397	−	1.49794i
$599$	0.0589838	+	0.561194i	0.00241001	+	0.0229298i	0.995661	−	0.0930566i	$-0.0296638\pi$
$599$	0.0589838	+	0.561194i	0.00241001	+	0.0229298i	−0.993251	+	0.115986i	$0.962997\pi$
$600$		0			0
$601$	−19.9005	−	8.86028i	−0.811759	−	0.361419i	−0.0414913	−	0.999139i	$-0.513211\pi$
$601$	−19.9005	−	8.86028i	−0.811759	−	0.361419i	−0.770268	+	0.637720i	$0.779878\pi$
$602$	−9.55855	−	21.4689i	−0.389577	−	0.875005i
$603$	4.04946	+	3.64615i	0.164907	+	0.148483i
$604$	−7.80137	−	5.66803i	−0.317433	−	0.230629i
$605$		0			0
$606$	−7.47821	+	8.30539i	−0.303781	+	0.337384i
$607$	4.24026	+	9.52379i	0.172107	+	0.386559i	0.978919	−	0.204250i	$-0.0654755\pi$
$607$	4.24026	+	9.52379i	0.172107	+	0.386559i	−0.806812	+	0.590809i	$0.798809\pi$
$608$	0.880731	−	1.97815i	0.0357184	−	0.0802248i
$609$	0.858848	+	0.953847i	0.0348023	+	0.0386518i
$610$		0			0
$611$	−51.3017	−	10.9045i	−2.07545	−	0.441150i
$612$	4.13458	−	1.34341i	0.167131	−	0.0543040i
$613$	3.44801	+	16.2216i	0.139264	+	0.655184i	0.991291	+	0.131687i	$0.0420395\pi$
$613$	3.44801	+	16.2216i	0.139264	+	0.655184i	−0.852028	+	0.523497i	$0.824627\pi$
$614$	14.7888	+	25.6150i	0.596829	+	1.03374i
$615$		0			0
$616$	−6.90945	+	21.2651i	−0.278390	+	0.856795i
$617$	15.3315	+	1.61141i	0.617224	+	0.0648729i	0.407980	−	0.912991i	$-0.366233\pi$
$617$	15.3315	+	1.61141i	0.617224	+	0.0648729i	0.209244	+	0.977864i	$0.432900\pi$
$618$	−18.8395	−	25.9304i	−0.757837	−	1.04307i
$619$	−40.5205			−1.62866			−0.814328	−	0.580406i	$-0.802894\pi$
$619$	−40.5205			−1.62866			−0.814328	+	0.580406i	$0.802894\pi$
$620$		0			0
$621$	−10.2138			−0.409865
$622$	1.23351	+	1.69779i	0.0494594	+	0.0680750i
$623$	3.07102	+	0.322777i	0.123038	+	0.0129318i
$624$	23.3542	−	71.8769i	0.934917	−	2.87738i
$625$		0			0
$626$	13.3434	+	23.1115i	0.533310	+	0.923721i
$627$	−1.05566	−	4.96649i	−0.0421590	−	0.198343i
$628$	−21.6023	+	7.01901i	−0.862025	+	0.280089i
$629$	14.2879	+	3.03698i	0.569695	+	0.121093i
$630$		0			0
$631$	−5.30926	−	5.89653i	−0.211358	−	0.234737i	0.628139	−	0.778101i	$-0.283817\pi$
$631$	−5.30926	−	5.89653i	−0.211358	−	0.234737i	−0.839497	+	0.543364i	$0.817150\pi$
$632$	−3.07217	+	6.90021i	−0.122204	+	0.274475i
$633$	−3.47500	−	7.80498i	−0.138119	−	0.310220i
$634$	52.4237	−	58.2224i	2.08201	−	2.31231i
$635$		0			0
$636$	36.4394	+	26.4748i	1.44492	+	1.04979i
$637$	−29.4904	−	26.5533i	−1.16845	−	1.05208i
$638$	3.67696	+	8.25858i	0.145572	+	0.326960i
$639$	2.13053	+	0.948575i	0.0842827	+	0.0375251i
$640$		0			0
$641$	3.39369	+	32.2888i	0.134043	+	1.27533i	0.830210	+	0.557450i	$0.188220\pi$
$641$	3.39369	+	32.2888i	0.134043	+	1.27533i	−0.696168	+	0.717879i	$0.745113\pi$
$642$	−4.71500	+	22.1823i	−0.186086	+	0.875466i
$643$	33.9837	−	11.0420i	1.34019	−	0.435453i	0.450806	−	0.892622i	$-0.351137\pi$
$643$	33.9837	−	11.0420i	1.34019	−	0.435453i	0.889380	+	0.457169i	$0.151137\pi$
$644$	−8.37843	+	1.78089i	−0.330156	+	0.0701769i
$645$		0			0
$646$	0.938929	−	1.62627i	0.0369417	−	0.0639849i
$647$	4.46933	+	1.45217i	0.175708	+	0.0570909i	0.395550	−	0.918445i	$-0.370554\pi$
$647$	4.46933	+	1.45217i	0.175708	+	0.0570909i	−0.219842	+	0.975536i	$0.570554\pi$
$648$	−62.9407	−	6.61533i	−2.47254	−	0.259875i
$649$	19.5853	−	14.2295i	0.768790	−	0.558558i
$650$		0			0
$651$	−4.35622	+	7.91190i	−0.170734	+	0.310092i
$652$		−	57.6734i		−	2.25866i
$653$	−25.9985	−	35.7838i	−1.01740	−	1.40033i	−0.914011	−	0.405689i	$-0.867032\pi$
$653$	−25.9985	−	35.7838i	−1.01740	−	1.40033i	−0.103388	−	0.994641i	$-0.532968\pi$
$654$	0.303627	−	2.88882i	0.0118728	−	0.112962i
$655$		0			0
$656$	−34.7657	+	60.2159i	−1.35737	+	2.35104i
$657$	−6.93524	+	4.00407i	−0.270570	+	0.156213i
$658$	3.64261	+	17.1371i	0.142004	+	0.668075i
$659$	4.42186	+	13.6091i	0.172251	+	0.530135i	0.999497	−	0.0317052i	$-0.0100938\pi$
$659$	4.42186	+	13.6091i	0.172251	+	0.530135i	−0.827246	+	0.561840i	$0.810094\pi$
$660$		0			0
$661$	2.03732	+	19.3838i	0.0792424	+	0.753941i	0.959929	+	0.280242i	$0.0904148\pi$
$661$	2.03732	+	19.3838i	0.0792424	+	0.753941i	−0.880687	+	0.473699i	$0.842919\pi$
$662$	16.7248	−	15.0591i	0.650028	−	0.585288i
$663$	6.43718	−	14.4581i	0.249999	−	0.561507i
$664$	70.7263	−	31.4894i	2.74471	−	1.22202i
$665$		0			0
$666$	17.7917	+	12.9264i	0.689415	+	0.500889i
$667$	−1.09829	+	1.51167i	−0.0425260	+	0.0585321i
$668$	20.5057	+	18.4634i	0.793390	+	0.714371i
$669$	−31.2288	+	13.9039i	−1.20737	+	0.537557i
$670$		0			0
$671$	12.7096	+	14.1155i	0.490650	+	0.544923i
$672$	−6.06275	+	0.637221i	−0.233876	+	0.0245813i
$673$	−2.17735	+	10.2436i	−0.0839307	+	0.394863i	−0.999981	−	0.00620110i	$-0.998026\pi$
$673$	−2.17735	+	10.2436i	−0.0839307	+	0.394863i	0.916050	+	0.401064i	$0.131359\pi$
$674$	18.1358	+	55.8162i	0.698564	+	2.14996i
$675$		0			0
$676$	−57.8626	−	100.221i	−2.22548	−	3.85465i
$677$	−24.4920	−	14.1405i	−0.941304	−	0.543462i	−0.0509354	−	0.998702i	$-0.516220\pi$
$677$	−24.4920	−	14.1405i	−0.941304	−	0.543462i	−0.890369	+	0.455240i	$0.849554\pi$
$678$	44.9302	+	14.5987i	1.72553	+	0.560660i
$679$	0.473190	−	4.50210i	0.0181594	−	0.172775i
$680$		0			0
$681$	43.4006			1.66312
$682$	−46.4000	+	43.5165i	−1.77675	+	1.66633i
$683$			2.92111i			0.111773i	0.998437	+	0.0558866i	$0.0177985\pi$
$683$			2.92111i			0.111773i	−0.998437	+	0.0558866i	$0.982201\pi$
$684$	1.56613	−	1.13786i	0.0598826	−	0.0435072i
$685$		0			0
$686$	−8.64592	+	26.6094i	−0.330103	+	1.01595i
$687$	0.246023	+	0.142042i	0.00938638	+	0.00541923i
$688$	59.7924	−	34.5211i	2.27956	−	1.31611i
$689$	32.8768	−	6.98817i	1.25250	−	0.266228i
$690$		0			0
$691$	22.1035	+	4.69823i	0.840855	+	0.178729i	0.608154	−	0.793819i	$-0.291910\pi$
$691$	22.1035	+	4.69823i	0.840855	+	0.178729i	0.232701	+	0.972548i	$0.425244\pi$
$692$	−10.8913	+	1.14473i	−0.414027	+	0.0435160i
$693$	−2.17750	+	1.96063i	−0.0827164	+	0.0744782i
$694$	−44.3268	−	19.7356i	−1.68262	−	0.749152i
$695$		0			0
$696$	−6.07050	+	6.74198i	−0.230102	+	0.255554i
$697$	−8.55852	+	11.7798i	−0.324177	+	0.446191i
$698$	−48.2949	+	66.4723i	−1.82799	+	2.51601i
$699$	−11.2948	+	12.5441i	−0.427207	+	0.474461i
$700$		0			0
$701$	−25.8525	−	11.5103i	−0.976436	−	0.434737i	−0.144437	−	0.989514i	$-0.546137\pi$
$701$	−25.8525	−	11.5103i	−0.976436	−	0.434737i	−0.831999	+	0.554777i	$0.812804\pi$
$702$	−50.9704	+	45.8940i	−1.92376	+	1.73216i
$703$	6.46880	−	0.679898i	0.243975	−	0.0256428i
$704$	12.8375	+	2.72871i	0.483833	+	0.102842i
$705$		0			0
$706$	−31.3471	+	6.66303i	−1.17976	+	0.250766i
$707$	1.65198	−	0.953773i	0.0621292	−	0.0358703i
$708$	38.9955	+	22.5141i	1.46554	+	0.846131i
$709$	4.96572	−	15.2829i	0.186492	−	0.573962i	−0.813479	−	0.581594i	$-0.802429\pi$
$709$	4.96572	−	15.2829i	0.186492	−	0.573962i	0.999971	+	0.00763191i	$0.00242934\pi$
$710$		0			0
$711$	−0.800780	+	0.581801i	−0.0300316	+	0.0218192i
$712$			21.8261i			0.817969i
$713$	−12.5847	−	3.80837i	−0.471303	−	0.142625i
$714$	−5.28675			−0.197851
$715$		0			0
$716$	5.42636	−	51.6283i	0.202792	−	1.92944i
$717$	19.3286	+	6.28024i	0.721840	+	0.234540i
$718$	−13.9858	−	8.07470i	−0.521945	−	0.301345i
$719$	14.2609	+	24.7007i	0.531843	+	0.921179i	0.999309	+	0.0371679i	$0.0118336\pi$
$719$	14.2609	+	24.7007i	0.531843	+	0.921179i	−0.467466	+	0.884011i	$0.654833\pi$
$720$		0			0
$721$	1.69053	+	5.20291i	0.0629585	+	0.193766i
$722$	−9.77556	+	45.9904i	−0.363809	+	1.71159i
$723$	10.5109	−	1.10474i	0.390904	−	0.0410857i
$724$	−40.9650	−	45.4962i	−1.52245	−	1.69085i
$725$		0			0
$726$	−42.8098	+	19.0602i	−1.58882	+	0.707389i
$727$	−4.08346	−	3.67677i	−0.151447	−	0.136364i	0.589924	−	0.807459i	$-0.299158\pi$
$727$	−4.08346	−	3.67677i	−0.151447	−	0.136364i	−0.741371	+	0.671095i	$0.765824\pi$
$728$	−18.2416	+	25.1074i	−0.676077	+	0.930540i
$729$	13.6817	+	9.94036i	0.506731	+	0.368162i
$730$		0			0
$731$	13.2082	−	5.88068i	0.488524	−	0.217505i
$732$	−14.3697	+	32.2749i	−0.531119	+	1.19291i
$733$	−30.5031	+	27.4651i	−1.12666	+	1.01445i	−0.126911	+	0.991914i	$0.540506\pi$
$733$	−30.5031	+	27.4651i	−1.12666	+	1.01445i	−0.999746	+	0.0225327i	$0.992827\pi$
$734$	−5.76407	−	54.8415i	−0.212756	−	2.02424i
$735$		0			0
$736$	−2.74241	−	8.44026i	−0.101086	−	0.311112i
$737$	−6.64426	−	31.2588i	−0.244745	−	1.15143i
$738$	−18.9848	+	10.9609i	−0.698842	+	0.403476i
$739$	−6.42893	+	11.1352i	−0.236492	+	0.409616i	−0.959705	−	0.281009i	$-0.909331\pi$
$739$	−6.42893	+	11.1352i	−0.236492	+	0.409616i	0.723213	+	0.690625i	$0.242664\pi$
$740$		0			0
$741$	0.736652	−	7.00878i	0.0270616	−	0.257474i
$742$	−6.59948	−	9.08340i	−0.242274	−	0.333462i
$743$			5.08104i			0.186405i	0.995647	+	0.0932026i	$0.0297104\pi$
$743$			5.08104i			0.186405i	−0.995647	+	0.0932026i	$0.970290\pi$
$744$	−58.8350	−	24.7764i	−2.15700	−	0.908346i
$745$		0			0
$746$	9.42959	−	6.85100i	0.345242	−	0.250833i
$747$	10.0899	+	1.06050i	0.369172	+	0.0388015i
$748$	−24.2480	−	7.87865i	−0.886595	−	0.288072i
$749$	1.93536	−	3.35213i	0.0707164	−	0.122484i
$750$		0			0
$751$	6.81891	−	1.44940i	0.248825	−	0.0528895i	−0.0818103	−	0.996648i	$-0.526070\pi$
$751$	6.81891	−	1.44940i	0.248825	−	0.0528895i	0.330636	+	0.943758i	$0.392737\pi$
$752$	−48.9527	+	15.9057i	−1.78512	+	0.580021i
$753$	−4.66836	+	21.9629i	−0.170125	+	0.800373i
$754$	1.31157	+	12.4788i	0.0477646	+	0.454450i
$755$		0			0
$756$	14.3315	+	6.38081i	0.521233	+	0.232068i
$757$	5.96076	+	13.3881i	0.216648	+	0.486598i	0.988875	−	0.148748i	$-0.0475242\pi$
$757$	5.96076	+	13.3881i	0.216648	+	0.486598i	−0.772228	+	0.635346i	$0.780858\pi$
$758$	27.0461	+	24.3525i	0.982360	+	0.884521i
$759$	−16.8354	−	12.2316i	−0.611085	−	0.443979i
$760$		0			0
$761$	21.0905	−	23.4234i	0.764530	−	0.849097i	−0.227672	−	0.973738i	$-0.573111\pi$
$761$	21.0905	−	23.4234i	0.764530	−	0.849097i	0.992202	+	0.124641i	$0.0397779\pi$
$762$	24.4248	+	54.8589i	0.884816	+	1.98733i
$763$	−0.201654	+	0.452923i	−0.00730038	+	0.0163969i
$764$	−0.817880	−	0.908348i	−0.0295899	−	0.0328629i
$765$		0			0
$766$	50.2619	+	10.6835i	1.81604	+	0.386011i
$767$	31.9566	−	10.3833i	1.15389	−	0.374921i
$768$	12.7209	+	59.8469i	0.459024	+	2.15954i
$769$	21.8896	+	37.9139i	0.789358	+	1.36721i	0.926361	+	0.376638i	$0.122920\pi$
$769$	21.8896	+	37.9139i	0.789358	+	1.36721i	−0.137002	+	0.990571i	$0.543747\pi$
$770$		0			0
$771$	11.3885	−	35.0503i	0.410148	−	1.26231i
$772$	104.492	+	10.9826i	3.76077	+	0.395273i
$773$	−14.2806	−	19.6555i	−0.513637	−	0.706960i	0.470891	−	0.882192i	$-0.343933\pi$
$773$	−14.2806	−	19.6555i	−0.513637	−	0.706960i	−0.984527	+	0.175231i	$0.943933\pi$
$774$	21.7676			0.782421
$775$		0			0
$776$	31.9970			1.14862
$777$	−10.7635	−	14.8147i	−0.386138	−	0.531474i
$778$	15.6469	+	1.64455i	0.560967	+	0.0589600i
$779$	−2.00359	+	6.16640i	−0.0717859	+	0.220934i
$780$		0			0
$781$	−6.83869	−	11.8450i	−0.244708	−	0.423846i
$782$	−1.60015	−	7.52812i	−0.0572213	−	0.269205i
$783$	3.25469	−	1.05751i	0.116313	−	0.0377925i
$784$	−38.0938	−	8.09709i	−1.36049	−	0.289182i
$785$		0			0
$786$	−54.3871	−	60.4030i	−1.93992	−	2.15450i
$787$	5.90552	−	13.2640i	0.210509	−	0.472811i	−0.777173	−	0.629287i	$-0.783347\pi$
$787$	5.90552	−	13.2640i	0.210509	−	0.472811i	0.987682	+	0.156476i	$0.0500135\pi$
$788$	−22.5083	−	50.5544i	−0.801824	−	1.80093i
$789$	−6.77825	+	7.52801i	−0.241312	+	0.268004i
$790$		0			0
$791$	−6.52346	−	4.73957i	−0.231947	−	0.168520i
$792$	−15.3910	−	13.8581i	−0.546895	−	0.492426i
$793$	10.7230	+	24.0844i	0.380787	+	0.855261i
$794$	−72.6873	−	32.3625i	−2.57957	−	1.14850i
$795$		0			0
$796$	−4.90555	−	46.6732i	−0.173873	−	1.65429i
$797$	4.54149	−	21.3661i	0.160868	−	0.756824i	−0.821551	−	0.570135i	$-0.806891\pi$
$797$	4.54149	−	21.3661i	0.160868	−	0.756824i	0.982419	−	0.186689i	$-0.0597758\pi$
$798$	−2.23893	+	0.727472i	−0.0792572	+	0.0257522i
$799$	−10.5432	+	2.24103i	−0.372993	+	0.0792821i
$800$		0			0
$801$	−1.43011	+	2.47703i	−0.0505306	+	0.0875215i
$802$	4.96233	+	1.61236i	0.175226	+	0.0569344i
$803$	46.7078	+	4.90919i	1.64828	+	0.173242i
$804$	48.0881	−	34.9380i	1.69594	−	1.23217i
$805$		0			0
$806$	−79.9147	+	37.5424i	−2.81488	+	1.32238i
$807$		−	2.23349i		−	0.0786224i
$808$	7.92505	+	10.9079i	0.278802	+	0.383739i
$809$	2.04937	−	19.4984i	0.0720520	−	0.685529i	−0.897562	−	0.440888i	$-0.854663\pi$
$809$	2.04937	−	19.4984i	0.0720520	−	0.685529i	0.969614	−	0.244640i	$-0.0786699\pi$
$810$		0			0
$811$	−0.447413	+	0.774942i	−0.0157108	+	0.0272119i	−0.873774	−	0.486332i	$-0.838334\pi$
$811$	−0.447413	+	0.774942i	−0.0157108	+	0.0272119i	0.858063	+	0.513544i	$0.171668\pi$
$812$	2.48546	−	1.43498i	0.0872224	−	0.0503579i
$813$	−5.07891	−	23.8944i	−0.178125	−	0.838013i
$814$	−39.8554	−	122.662i	−1.39693	−	4.29931i
$815$		0			0
$816$	−1.62353	−	15.4468i	−0.0568348	−	0.540747i
$817$	4.78447	−	4.30795i	0.167387	−	0.150716i
$818$	24.4959	−	55.0186i	0.856477	−	1.92368i
$819$	−3.71533	+	1.65417i	−0.129824	+	0.0578014i
$820$		0			0
$821$	30.2838	+	22.0025i	1.05691	+	0.767892i	0.973515	−	0.228624i	$-0.0734228\pi$
$821$	30.2838	+	22.0025i	1.05691	+	0.767892i	0.0833978	+	0.996516i	$0.473423\pi$
$822$	8.42522	−	11.5963i	0.293863	−	0.404468i
$823$	−22.6647	−	20.4074i	−0.790041	−	0.711356i	0.171750	−	0.985141i	$-0.445058\pi$
$823$	−22.6647	−	20.4074i	−0.790041	−	0.711356i	−0.961791	+	0.273784i	$0.911725\pi$
$824$	−35.3247	+	15.7276i	−1.23059	+	0.547896i
$825$		0			0
$826$	−7.51055	−	8.34131i	−0.261325	−	0.290231i
$827$	−26.3577	+	2.77030i	−0.916546	+	0.0963329i	−0.551043	−	0.834477i	$-0.685770\pi$
$827$	−26.3577	+	2.77030i	−0.916546	+	0.0963329i	−0.365504	+	0.930810i	$0.619103\pi$
$828$	1.64956	−	7.76059i	0.0573263	−	0.269699i
$829$	11.3256	+	34.8565i	0.393354	+	1.21062i	0.930236	+	0.366961i	$0.119602\pi$
$829$	11.3256	+	34.8565i	0.393354	+	1.21062i	−0.536883	+	0.843657i	$0.680398\pi$
$830$		0			0
$831$	21.1903	+	36.7027i	0.735084	+	1.27320i
$832$	15.7758	+	9.10815i	0.546927	+	0.315768i
$833$	−7.75632	−	2.52018i	−0.268740	−	0.0873191i
$834$	−10.9628	+	104.304i	−0.379611	+	3.61176i
$835$		0			0
$836$	−11.3531			−0.392656
$837$	14.5471	+	19.1907i	0.502822	+	0.663326i
$838$			76.9815i			2.65928i
$839$	1.83042	−	1.32988i	0.0631933	−	0.0459126i	−0.555740	−	0.831356i	$-0.687565\pi$
$839$	1.83042	−	1.32988i	0.0631933	−	0.0459126i	0.618933	+	0.785443i	$0.287565\pi$
$840$		0			0
$841$	−8.76803	+	26.9852i	−0.302346	+	0.930525i
$842$	−48.9699	−	28.2728i	−1.68762	−	0.974345i
$843$	−52.3503	+	30.2244i	−1.80304	+	1.04098i
$844$	−18.6860	+	3.97183i	−0.643198	+	0.136716i
$845$		0			0
$846$	−15.8734	−	3.37400i	−0.545739	−	0.116001i
$847$	7.95455	−	0.836057i	0.273322	−	0.0287273i
$848$	24.5132	−	22.0718i	0.841788	−	0.757949i
$849$	−32.1733	−	14.3245i	−1.10419	−	0.491615i
$850$		0			0
$851$	17.8377	−	19.8108i	0.611469	−	0.679106i
$852$	14.9532	−	20.5813i	0.512287	−	0.705103i
$853$	−3.88984	+	5.35391i	−0.133186	+	0.183314i	−0.870401	−	0.492344i	$-0.836140\pi$
$853$	−3.88984	+	5.35391i	−0.133186	+	0.183314i	0.737215	+	0.675658i	$0.236140\pi$
$854$	5.89281	−	6.54462i	0.201648	−	0.223952i
$855$		0			0
$856$	24.9936	+	11.1279i	0.854265	+	0.380343i
$857$	−27.9942	+	25.2061i	−0.956263	+	0.861023i	−0.990377	−	0.138395i	$-0.955806\pi$
$857$	−27.9942	+	25.2061i	−0.956263	+	0.861023i	0.0341142	+	0.999418i	$0.489139\pi$
$858$	−138.975	+	14.6069i	−4.74454	+	0.498671i
$859$	16.0689	+	3.41555i	0.548264	+	0.116537i	0.473712	−	0.880680i	$-0.342914\pi$
$859$	16.0689	+	3.41555i	0.548264	+	0.116537i	0.0745524	+	0.997217i	$0.476247\pi$
$860$		0			0
$861$	17.8548	−	3.79516i	0.608491	−	0.129339i
$862$	−35.9437	+	20.7521i	−1.22425	+	0.706820i
$863$	−22.2659	−	12.8552i	−0.757941	−	0.437598i	0.0706147	−	0.997504i	$-0.477504\pi$
$863$	−22.2659	−	12.8552i	−0.757941	−	0.437598i	−0.828556	+	0.559906i	$0.810837\pi$
$864$	−5.02269	+	15.4582i	−0.170875	+	0.525900i
$865$		0			0
$866$	61.8156	−	44.9117i	2.10058	−	1.52616i
$867$			29.7708i			1.01107i
$868$	15.2792	+	13.2058i	0.518610	+	0.448233i
$869$	5.80497			0.196920
$870$		0			0
$871$	4.63644	−	44.1128i	0.157100	−	1.49471i
$872$	−3.33280	−	1.08289i	−0.112863	−	0.0366714i
$873$	3.63131	+	2.09654i	0.122901	+	0.0709571i
$874$	−1.71355	−	2.96796i	−0.0579618	−	0.100393i
$875$		0			0
$876$	26.9942	+	83.0795i	0.912048	+	2.80699i
$877$	3.63980	−	17.1239i	0.122907	−	0.578234i	−0.872989	−	0.487739i	$-0.837822\pi$
$877$	3.63980	−	17.1239i	0.122907	−	0.578234i	0.995897	−	0.0904951i	$-0.0288449\pi$
$878$	41.3397	−	4.34498i	1.39515	−	0.146636i
$879$	15.2160	+	16.8991i	0.513223	+	0.569992i
$880$		0			0
$881$	−8.66292	+	3.85698i	−0.291861	+	0.129945i	−0.547444	−	0.836842i	$-0.684399\pi$
$881$	−8.66292	+	3.85698i	−0.291861	+	0.129945i	0.255583	+	0.966787i	$0.417733\pi$
$882$	−9.12471	−	8.21593i	−0.307245	−	0.276645i
$883$	13.0142	−	17.9126i	0.437964	−	0.602806i	−0.531794	−	0.846874i	$-0.678482\pi$
$883$	13.0142	−	17.9126i	0.437964	−	0.602806i	0.969758	+	0.244068i	$0.0784819\pi$
$884$	−28.6292	−	20.8004i	−0.962905	−	0.699592i
$885$		0			0
$886$	58.0865	−	25.8618i	1.95145	−	0.868843i
$887$	−13.0095	+	29.2198i	−0.436816	+	0.981104i	0.552257	+	0.833674i	$0.313767\pi$
$887$	−13.0095	+	29.2198i	−0.436816	+	0.981104i	−0.989072	+	0.147430i	$0.952900\pi$
$888$	96.1871	−	86.6072i	3.22783	−	2.90635i
$889$	−1.07137	−	10.1934i	−0.0359326	−	0.341876i
$890$		0			0
$891$	15.0303	+	46.2585i	0.503534	+	1.54972i
$892$	15.8918	+	74.7651i	0.532097	+	2.50332i
$893$	−4.15667	+	2.39986i	−0.139098	+	0.0803081i
$894$	19.3241	−	33.4703i	0.646294	−	1.11941i
$895$		0			0
$896$	1.29213	−	12.2938i	0.0431671	−	0.410707i
$897$	−16.9772	−	23.3671i	−0.566852	−	0.780205i
$898$		−	6.57462i		−	0.219398i
$899$	4.40453	−	0.0894351i	0.146899	−	0.00298283i
$900$		0			0
$901$	5.58836	−	4.06018i	0.186175	−	0.135264i
$902$	127.860	+	13.4386i	4.25728	+	0.447458i
$903$	−17.2382	−	5.60103i	−0.573651	−	0.186391i
$904$	28.4970	−	49.3582i	0.947795	−	1.64163i
$905$		0			0
$906$	−10.6246	+	2.25833i	−0.352979	+	0.0750280i
$907$	−31.8148	+	10.3373i	−1.05639	+	0.343243i	−0.785174	−	0.619275i	$-0.787427\pi$
$907$	−31.8148	+	10.3373i	−1.05639	+	0.343243i	−0.271219	+	0.962518i	$0.587427\pi$
$908$	20.1765	−	94.9228i	0.669579	−	3.15012i
$909$	0.184689	+	1.75720i	0.00612576	+	0.0582827i
$910$		0			0
$911$	−40.9176	−	18.2177i	−1.35566	−	0.603579i	−0.405144	−	0.914253i	$-0.632779\pi$
$911$	−40.9176	−	18.2177i	−1.35566	−	0.603579i	−0.950517	+	0.310673i	$0.899445\pi$
$912$	−2.81309	−	6.31830i	−0.0931507	−	0.209220i
$913$	−44.2173	−	39.8134i	−1.46338	−	1.31763i
$914$	19.0765	+	13.8599i	0.630993	+	0.458443i
$915$		0			0
$916$	0.425037	−	0.472051i	0.0140436	−	0.0155970i
$917$	5.64270	+	12.6737i	0.186338	+	0.418523i
$918$	−5.73324	+	12.8771i	−0.189225	+	0.425007i
$919$	19.0879	+	21.1993i	0.629652	+	0.699300i	0.970577	−	0.240791i	$-0.0774068\pi$
$919$	19.0879	+	21.1993i	0.629652	+	0.699300i	−0.340925	+	0.940091i	$0.610740\pi$
$920$		0			0
$921$	22.3139	+	4.74297i	0.735268	+	0.156286i
$922$	42.2393	−	13.7244i	1.39108	−	0.451988i
$923$	−3.94697	−	18.5690i	−0.129916	−	0.611208i
$924$	15.9813	+	27.6803i	0.525745	+	0.910616i
$925$		0			0
$926$	−4.52410	+	13.9237i	−0.148671	+	0.457563i
$927$	−5.03949	−	0.529671i	−0.165518	−	0.0173967i
$928$	1.74777	+	2.40560i	0.0573735	+	0.0789678i
$929$	47.0642			1.54413			0.772064	−	0.635545i	$-0.219225\pi$
$929$	47.0642			1.54413			0.772064	+	0.635545i	$0.219225\pi$
$930$		0			0
$931$	−3.63157			−0.119020
$932$	22.1847	+	30.5347i	0.726685	+	1.00020i
$933$	1.60970	+	0.169187i	0.0526994	+	0.00553893i
$934$	6.29584	−	19.3766i	0.206006	−	0.634022i
$935$		0			0
$936$	−14.3729	−	24.8946i	−0.469794	−	0.813707i
$937$	−6.40434	−	30.1300i	−0.209221	−	0.984306i	−0.949926	−	0.312476i	$-0.898842\pi$
$937$	−6.40434	−	30.1300i	−0.209221	−	0.984306i	0.740705	−	0.671830i	$-0.234492\pi$
$938$	−14.0917	+	4.57867i	−0.460110	+	0.149499i
$939$	20.1330	+	4.27940i	0.657015	+	0.139653i
$940$		0			0
$941$	1.90260	+	2.11305i	0.0620230	+	0.0688835i	0.773358	−	0.633970i	$-0.218576\pi$
$941$	1.90260	+	2.11305i	0.0620230	+	0.0688835i	−0.711335	+	0.702853i	$0.751909\pi$
$942$	−10.4064	+	23.3732i	−0.339060	+	0.761541i
$943$	10.8083	+	24.2759i	0.351967	+	0.790531i
$944$	22.0652	−	24.5059i	0.718161	−	0.797599i
$945$		0			0
$946$	−103.279	−	75.0367i	−3.35790	−	2.43965i
$947$	−7.74812	−	6.97644i	−0.251780	−	0.226704i	0.533570	−	0.845756i	$-0.320850\pi$
$947$	−7.74812	−	6.97644i	−0.251780	−	0.226704i	−0.785350	+	0.619052i	$0.787517\pi$
$948$	4.39162	+	9.86375i	0.142633	+	0.320360i
$949$	59.5509	+	26.5138i	1.93310	+	0.860673i
$950$		0			0
$951$	−6.31623	−	60.0949i	−0.204818	−	1.94871i
$952$	−1.32606	+	6.23863i	−0.0429779	+	0.202195i
$953$	45.0649	−	14.6425i	1.45979	−	0.474316i	0.531788	−	0.846878i	$-0.321521\pi$
$953$	45.0649	−	14.6425i	1.45979	−	0.474316i	0.928007	+	0.372562i	$0.121521\pi$
$954$	10.1725	−	2.16223i	0.329347	−	0.0700048i
$955$		0			0
$956$	22.7213	−	39.3545i	0.734861	−	1.27282i
$957$	6.63114	+	2.15459i	0.214354	+	0.0696479i
$958$	22.8072	+	2.39714i	0.736868	+	0.0774480i
$959$	−1.97929	+	1.43804i	−0.0639145	+	0.0464366i
$960$		0			0
$961$	10.7684	+	29.0696i	0.347369	+	0.937728i
$962$		−	179.014i		−	5.77164i
$963$	2.10737	+	2.90055i	0.0679092	+	0.0934690i
$964$	2.47018	−	23.5022i	0.0795593	−	0.756956i
$965$		0			0
$966$	−4.82418	+	8.35572i	−0.155215	+	0.268841i
$967$	19.6633	−	11.3526i	0.632329	−	0.365075i	−0.149325	−	0.988788i	$-0.547710\pi$
$967$	19.6633	−	11.3526i	0.632329	−	0.365075i	0.781653	+	0.623713i	$0.214377\pi$
$968$	11.7541	+	55.2986i	0.377790	+	1.77736i
$969$	−0.447561	−	1.37745i	−0.0143777	−	0.0442501i
$970$		0			0
$971$	5.75452	+	54.7506i	0.184671	+	1.75703i	0.558475	+	0.829522i	$0.311387\pi$
$971$	5.75452	+	54.7506i	0.184671	+	1.75703i	−0.373803	+	0.927508i	$0.621947\pi$
$972$	−25.3487	+	22.8241i	−0.813060	+	0.732083i
$973$	7.28096	−	16.3533i	0.233417	−	0.524263i
$974$	94.6747	−	42.1519i	3.03357	−	1.35063i
$975$		0			0
$976$	20.9317	+	15.2078i	0.670008	+	0.486790i
$977$	−8.04457	+	11.0724i	−0.257369	+	0.354238i	−0.918075	−	0.396407i	$-0.870257\pi$
$977$	−8.04457	+	11.0724i	−0.257369	+	0.354238i	0.660706	+	0.750645i	$0.270257\pi$
$978$	−48.2774	−	43.4692i	−1.54374	−	1.38999i
$979$	15.3241	−	6.82273i	0.489761	−	0.218055i
$980$		0			0
$981$	−0.307282	−	0.341272i	−0.00981077	−	0.0108960i
$982$	47.3985	−	4.98178i	1.51255	−	0.158975i
$983$	8.57156	−	40.3260i	0.273390	−	1.28620i	−0.600322	−	0.799758i	$-0.704961\pi$
$983$	8.57156	−	40.3260i	0.273390	−	1.28620i	0.873713	−	0.486443i	$-0.161706\pi$
$984$	39.8696	+	122.706i	1.27100	+	3.91172i
$985$		0			0
$986$	1.28935	+	2.23321i	0.0410611	+	0.0711200i
$987$	11.7023	+	6.75633i	0.372488	+	0.215056i
$988$	−14.9866	−	4.86945i	−0.476788	−	0.154918i
$989$	2.75812	−	26.2418i	0.0877032	−	0.834441i
$990$		0			0
$991$	−34.9979			−1.11174			−0.555872	−	0.831268i	$-0.687616\pi$
$991$	−34.9979			−1.11174			−0.555872	+	0.831268i	$0.687616\pi$
$992$	−11.9525	+	17.1738i	−0.379492	+	0.545270i
$993$		−	17.3578i		−	0.550833i
$994$	−5.13038	+	3.72744i	−0.162726	+	0.118227i
$995$		0			0
$996$	34.1990	−	105.254i	1.08364	−	3.33509i
$997$	−1.78793	−	1.03226i	−0.0566242	−	0.0326920i	0.471421	−	0.881908i	$-0.343741\pi$
$997$	−1.78793	−	1.03226i	−0.0566242	−	0.0326920i	−0.528045	+	0.849216i	$0.677075\pi$
$998$	−17.3580	+	10.0216i	−0.549458	+	0.317230i
$999$	−47.7571	+	10.1511i	−1.51097	+	0.321166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.b.524.1		80
5.2	odd	4		155.2.q.b.121.5	yes	40
5.3	odd	4		775.2.bl.b.276.1		40
5.4	even	2	inner	775.2.ck.b.524.10		80
31.10	even	15	inner	775.2.ck.b.599.10		80
155.17	even	60		4805.2.a.z.1.2		20
155.72	odd	60		155.2.q.b.41.5	✓	40
155.103	odd	60		775.2.bl.b.351.1		40
155.107	odd	60		4805.2.a.ba.1.2		20
155.134	even	30	inner	775.2.ck.b.599.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.b.41.5	✓	40	155.72	odd	60
155.2.q.b.121.5	yes	40	5.2	odd	4
775.2.bl.b.276.1		40	5.3	odd	4
775.2.bl.b.351.1		40	155.103	odd	60
775.2.ck.b.524.1		80	1.1	even	1	trivial
775.2.ck.b.524.10		80	5.4	even	2	inner
775.2.ck.b.599.1		80	155.134	even	30	inner
775.2.ck.b.599.10		80	31.10	even	15	inner
4805.2.a.z.1.2		20	155.17	even	60
4805.2.a.ba.1.2		20	155.107	odd	60

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.48042 - 2.03762i) q^{2} +(-1.93191 - 0.203052i) q^{3} +(-1.34222 + 4.13093i) q^{4} +(2.44628 + 4.23709i) q^{6} +(-0.173622 - 0.816826i) q^{7} +(5.61358 - 1.82396i) q^{8} +(0.756592 + 0.160819i) q^{9} +O(q^{10})\)	\(q+(-1.48042 - 2.03762i) q^{2} +(-1.93191 - 0.203052i) q^{3} +(-1.34222 + 4.13093i) q^{4} +(2.44628 + 4.23709i) q^{6} +(-0.173622 - 0.816826i) q^{7} +(5.61358 - 1.82396i) q^{8} +(0.756592 + 0.160819i) q^{9} +(-3.03538 - 3.37113i) q^{11} +(3.43184 - 7.70804i) q^{12} +(-2.56093 - 5.75194i) q^{13} +(-1.40735 + 1.56302i) q^{14} +(-4.99902 - 3.63200i) q^{16} +(-0.961611 - 0.865839i) q^{17} +(-0.792384 - 1.77972i) q^{18} +(-0.526383 - 0.234361i) q^{19} +(0.169563 + 1.61329i) q^{21} +(-2.37545 + 11.1756i) q^{22} +(-2.24594 + 0.729749i) q^{23} +(-11.2153 + 2.38388i) q^{24} +(-7.92902 + 13.7335i) q^{26} +(4.11341 + 1.33653i) q^{27} +(3.60729 + 0.379142i) q^{28} +(0.640127 - 0.465079i) q^{29} +(4.56993 + 3.18053i) q^{31} +3.75801i q^{32} +(5.17955 + 7.12905i) q^{33} +(-0.340664 + 3.24120i) q^{34} +(-1.67985 + 2.90958i) q^{36} +(-9.77616 + 5.64427i) q^{37} +(0.301728 + 1.41952i) q^{38} +(3.77954 + 11.6322i) q^{39} +(-1.17622 - 11.1910i) q^{41} +(3.03624 - 2.73384i) q^{42} +(-4.54466 + 10.2075i) q^{43} +(18.0001 - 8.01414i) q^{44} +(4.81187 + 3.49603i) q^{46} +(4.89623 - 6.73909i) q^{47} +(8.92015 + 8.03174i) q^{48} +(5.75776 - 2.56352i) q^{49} +(1.68193 + 1.86798i) q^{51} +(27.1982 - 2.85865i) q^{52} +(-1.10989 + 5.22161i) q^{53} +(-3.36622 - 10.3602i) q^{54} +(-2.46450 - 4.26864i) q^{56} +(0.969336 + 0.559646i) q^{57} +(-1.89531 - 0.615823i) q^{58} +(-0.557834 + 5.30744i) q^{59} -4.18717 q^{61} +(-0.284685 - 14.0203i) q^{62} -0.645926i q^{63} +(-2.34063 + 1.70057i) q^{64} +(6.85838 - 21.1079i) q^{66} +(6.10094 + 3.52238i) q^{67} +(4.86742 - 2.81020i) q^{68} +(4.48712 - 0.953766i) q^{69} +(2.94921 + 0.626874i) q^{71} +(4.54052 - 0.477228i) q^{72} +(-7.69391 + 6.92763i) q^{73} +(25.9736 + 11.5642i) q^{74} +(1.67465 - 1.85989i) q^{76} +(-2.22662 + 3.06468i) q^{77} +(18.1067 - 24.9218i) q^{78} +(-0.856267 + 0.950981i) q^{79} +(-9.79521 - 4.36111i) q^{81} +(-21.0616 + 18.9640i) q^{82} +(13.0446 - 1.37104i) q^{83} +(-6.89197 - 1.46493i) q^{84} +(27.5269 - 5.85103i) q^{86} +(-1.33110 + 0.768511i) q^{87} +(-23.1882 - 13.3877i) q^{88} +(-1.14268 + 3.51681i) q^{89} +(-4.25370 + 3.09050i) q^{91} -10.2573i q^{92} +(-8.18286 - 7.07242i) q^{93} -20.9802 q^{94} +(0.763071 - 7.26013i) q^{96} +(5.15563 + 1.67517i) q^{97} +(-13.7473 - 7.93704i) q^{98} +(-1.75440 - 3.03871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) \) 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9	\( 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9} + 32 q^{11} + 20 q^{14} - 32 q^{16} + 18 q^{19} - 48 q^{21} - 220 q^{24} - 8 q^{26} + 44 q^{29} - 12 q^{31} + 32 q^{34} - 2 q^{36} + 110 q^{39} - 48 q^{41} + 104 q^{44} - 100 q^{46} - 186 q^{49} - 84 q^{51} - 204 q^{54} + 10 q^{56} - 62 q^{59} + 136 q^{61} + 46 q^{64} + 96 q^{69} - 60 q^{71} - 100 q^{74} + 28 q^{76} - 98 q^{79} + 50 q^{81} + 36 q^{84} + 326 q^{86} - 8 q^{89} - 74 q^{91} + 188 q^{94} + 44 q^{96} - 34 q^{99}+O(q^{100}) \) 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9 + 32 * q^11 + 20 * q^14 - 32 * q^16 + 18 * q^19 - 48 * q^21 - 220 * q^24 - 8 * q^26 + 44 * q^29 - 12 * q^31 + 32 * q^34 - 2 * q^36 + 110 * q^39 - 48 * q^41 + 104 * q^44 - 100 * q^46 - 186 * q^49 - 84 * q^51 - 204 * q^54 + 10 * q^56 - 62 * q^59 + 136 * q^61 + 46 * q^64 + 96 * q^69 - 60 * q^71 - 100 * q^74 + 28 * q^76 - 98 * q^79 + 50 * q^81 + 36 * q^84 + 326 * q^86 - 8 * q^89 - 74 * q^91 + 188 * q^94 + 44 * q^96 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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