LMFDB - Embedded newform 627.2.l.a.197.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(197,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("627.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.l (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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$76$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			197.15
Character	$\chi$	$=$	627.197
Dual form			627.2.l.a.296.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.873606 - 1.51313i) q^{2} +(-0.568916 + 1.63595i) q^{3} +(-0.526375 + 0.911708i) q^{4} +(3.14552 - 1.81607i) q^{5} +(2.97241 - 0.568333i) q^{6} +1.70419i q^{7} -1.65505 q^{8} +(-2.35267 - 1.86144i) q^{9} +(-5.49590 - 3.17306i) q^{10} +(0.771949 - 3.22554i) q^{11} +(-1.19205 - 1.37981i) q^{12} +(-5.39290 - 3.11359i) q^{13} +(2.57866 - 1.48879i) q^{14} +(1.18146 + 6.17911i) q^{15} +(2.49861 + 4.32772i) q^{16} +(0.177104 + 0.306754i) q^{17} +(-0.761289 + 5.18606i) q^{18} +(3.56291 - 2.51111i) q^{19} +3.82373i q^{20} +(-2.78797 - 0.969541i) q^{21} +(-5.55504 + 1.64979i) q^{22} +(-2.33830 - 1.35002i) q^{23} +(0.941582 - 2.70757i) q^{24} +(4.09621 - 7.09485i) q^{25} +10.8802i q^{26} +(4.38369 - 2.78985i) q^{27} +(-1.55372 - 0.897043i) q^{28} +(2.63722 - 4.56781i) q^{29} +(8.31767 - 7.18581i) q^{30} +5.28855 q^{31} +(2.71055 - 4.69481i) q^{32} +(4.83765 + 3.09793i) q^{33} +(0.309439 - 0.535964i) q^{34} +(3.09493 + 5.36057i) q^{35} +(2.93547 - 1.16513i) q^{36} -9.00338 q^{37} +(-6.91221 - 3.19743i) q^{38} +(8.16179 - 7.05115i) q^{39} +(-5.20599 + 3.00568i) q^{40} +(1.00090 + 1.73360i) q^{41} +(0.968548 + 5.06556i) q^{42} +(5.97582 - 3.45014i) q^{43} +(2.53441 + 2.40163i) q^{44} +(-10.7809 - 1.58258i) q^{45} +4.71754i q^{46} +(-4.99634 - 2.88464i) q^{47} +(-8.50143 + 1.62549i) q^{48} +4.09573 q^{49} -14.3139 q^{50} +(-0.602592 + 0.115217i) q^{51} +(5.67738 - 3.27783i) q^{52} +(-4.94884 - 2.85721i) q^{53} +(-8.05102 - 4.19586i) q^{54} +(-3.42962 - 11.5479i) q^{55} -2.82052i q^{56} +(2.08105 + 7.25736i) q^{57} -9.21558 q^{58} +(-3.56425 + 2.05782i) q^{59} +(-6.25544 - 2.17538i) q^{60} +(-7.30518 - 4.21765i) q^{61} +(-4.62011 - 8.00227i) q^{62} +(3.17224 - 4.00940i) q^{63} +0.522614 q^{64} -22.6180 q^{65} +(0.461373 - 10.0264i) q^{66} +(-1.49556 + 2.59038i) q^{67} -0.372893 q^{68} +(3.53886 - 3.05730i) q^{69} +(5.40750 - 9.36606i) q^{70} +(-3.24639 + 1.87430i) q^{71} +(3.89378 + 3.08076i) q^{72} +(9.93554 - 5.73629i) q^{73} +(7.86541 + 13.6233i) q^{74} +(9.27642 + 10.7376i) q^{75} +(0.413970 + 4.57012i) q^{76} +(5.49693 + 1.31555i) q^{77} +(-17.7995 - 6.18992i) q^{78} +(6.78568 - 3.91771i) q^{79} +(15.7189 + 9.07529i) q^{80} +(2.07011 + 8.75869i) q^{81} +(1.74878 - 3.02897i) q^{82} -2.90096 q^{83} +(2.35146 - 2.03148i) q^{84} +(1.11417 + 0.643268i) q^{85} +(-10.4410 - 6.02813i) q^{86} +(5.97235 + 6.91307i) q^{87} +(-1.27761 + 5.33842i) q^{88} +(10.1340 + 5.85087i) q^{89} +(7.02358 + 17.6954i) q^{90} +(5.30616 - 9.19053i) q^{91} +(2.46165 - 1.42123i) q^{92} +(-3.00874 + 8.65181i) q^{93} +10.0801i q^{94} +(6.64688 - 14.3692i) q^{95} +(6.13841 + 7.10528i) q^{96} +(-3.05823 - 5.29701i) q^{97} +(-3.57806 - 6.19738i) q^{98} +(-7.82027 + 6.15169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 76 q^{4} - 8 q^{9} - 14 q^{15} - 76 q^{16} + 4 q^{22} + 60 q^{25} + 12 q^{27} - 16 q^{31} + 16 q^{33} - 16 q^{34} - 10 q^{36} - 16 q^{37} + 50 q^{42} - 108 q^{45} + 54 q^{48} - 80 q^{49} + 32 q^{55}+ \cdots + 60 q^{99}+O(q^{100}) $ 152 * q - 76 * q^4 - 8 * q^9 - 14 * q^15 - 76 * q^16 + 4 * q^22 + 60 * q^25 + 12 * q^27 - 16 * q^31 + 16 * q^33 - 16 * q^34 - 10 * q^36 - 16 * q^37 + 50 * q^42 - 108 * q^45 + 54 * q^48 - 80 * q^49 + 32 * q^55 - 40 * q^58 + 2 * q^60 + 152 * q^64 - 10 * q^66 - 16 * q^67 - 32 * q^69 - 4 * q^70 - 20 * q^75 - 58 * q^78 + 16 * q^81 - 40 * q^82 - 120 * q^88 - 16 * q^91 - 12 * q^93 + 4 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.873606	−	1.51313i	−0.617733	−	1.06994i	−0.989898	−	0.141778i	$-0.954718\pi$
$2$	−0.873606	−	1.51313i	−0.617733	−	1.06994i	0.372166	−	0.928166i	$-0.378615\pi$
$3$	−0.568916	+	1.63595i	−0.328464	+	0.944517i
$3$	−0.568916	+	1.63595i	−0.328464	+	0.944517i
$4$	−0.526375	+	0.911708i	−0.263187	+	0.455854i
$5$	3.14552	−	1.81607i	1.40672	−	0.812171i	0.411651	−	0.911342i	$-0.364952\pi$
$5$	3.14552	−	1.81607i	1.40672	−	0.812171i	0.995070	+	0.0991710i	$0.0316191\pi$
$6$	2.97241	−	0.568333i	1.21348	−	0.232021i
$7$			1.70419i			0.644124i	0.946719	+	0.322062i	$0.104376\pi$
$7$			1.70419i			0.644124i	−0.946719	+	0.322062i	$0.895624\pi$
$8$	−1.65505			−0.585147
$9$	−2.35267	−	1.86144i	−0.784223	−	0.620479i
$10$	−5.49590	−	3.17306i	−1.73796	−	1.00341i
$11$	0.771949	−	3.22554i	0.232751	−	0.972536i
$11$	0.771949	−	3.22554i	0.232751	−	0.972536i
$12$	−1.19205	−	1.37981i	−0.344114	−	0.398316i
$13$	−5.39290	−	3.11359i	−1.49572	−	0.863555i	−0.495734	−	0.868475i	$-0.665101\pi$
$13$	−5.39290	−	3.11359i	−1.49572	−	0.863555i	−0.999988	+	0.00491948i	$0.998434\pi$
$14$	2.57866	−	1.48879i	0.689177	−	0.397896i
$15$	1.18146	+	6.17911i	0.305052	+	1.59544i
$16$	2.49861	+	4.32772i	0.624652	+	1.08193i
$17$	0.177104	+	0.306754i	0.0429541	+	0.0743988i	0.886703	−	0.462339i	$-0.152990\pi$
$17$	0.177104	+	0.306754i	0.0429541	+	0.0743988i	−0.843749	+	0.536738i	$0.819656\pi$
$18$	−0.761289	+	5.18606i	−0.179438	+	1.22237i
$19$	3.56291	−	2.51111i	0.817388	−	0.576088i
$19$	3.56291	−	2.51111i	0.817388	−	0.576088i
$20$			3.82373i			0.855013i
$21$	−2.78797	−	0.969541i	−0.608385	−	0.211571i
$22$	−5.55504	+	1.64979i	−1.18434	+	0.351737i
$23$	−2.33830	−	1.35002i	−0.487570	−	0.281499i	0.235996	−	0.971754i	$-0.424165\pi$
$23$	−2.33830	−	1.35002i	−0.487570	−	0.281499i	−0.723566	+	0.690256i	$0.757498\pi$
$24$	0.941582	−	2.70757i	0.192200	−	0.552681i
$25$	4.09621	−	7.09485i	0.819243	−	1.41897i
$26$			10.8802i			2.13379i
$27$	4.38369	−	2.78985i	0.843641	−	0.536907i
$28$	−1.55372	−	0.897043i	−0.293626	−	0.169525i
$29$	2.63722	−	4.56781i	0.489720	−	0.848220i	−0.510210	−	0.860050i	$-0.670432\pi$
$29$	2.63722	−	4.56781i	0.489720	−	0.848220i	0.999930	+	0.0118296i	$0.00376555\pi$
$30$	8.31767	−	7.18581i	1.51859	−	1.31194i
$31$	5.28855			0.949852			0.474926	−	0.880026i	$-0.342475\pi$
$31$	5.28855			0.949852			0.474926	+	0.880026i	$0.342475\pi$
$32$	2.71055	−	4.69481i	0.479163	−	0.829934i
$33$	4.83765	+	3.09793i	0.842126	+	0.539280i
$34$	0.309439	−	0.535964i	0.0530684	−	0.0919171i
$35$	3.09493	+	5.36057i	0.523138	+	0.906102i
$36$	2.93547	−	1.16513i	0.489246	−	0.194189i
$37$	−9.00338			−1.48015			−0.740073	−	0.672526i	$-0.765209\pi$
$37$	−9.00338			−1.48015			−0.740073	+	0.672526i	$0.765209\pi$
$38$	−6.91221	−	3.19743i	−1.12131	−	0.518692i
$39$	8.16179	−	7.05115i	1.30693	−	1.12909i
$40$	−5.20599	+	3.00568i	−0.823139	+	0.475240i
$41$	1.00090	+	1.73360i	0.156314	+	0.270743i	0.933537	−	0.358482i	$-0.116706\pi$
$41$	1.00090	+	1.73360i	0.156314	+	0.270743i	−0.777223	+	0.629225i	$0.783372\pi$
$42$	0.968548	+	5.06556i	0.149450	+	0.781633i
$43$	5.97582	−	3.45014i	0.911304	−	0.526141i	0.0304532	−	0.999536i	$-0.490305\pi$
$43$	5.97582	−	3.45014i	0.911304	−	0.526141i	0.880850	+	0.473395i	$0.156972\pi$
$44$	2.53441	+	2.40163i	0.382077	+	0.362060i
$45$	−10.7809	−	1.58258i	−1.60712	−	0.235917i
$46$			4.71754i			0.695563i
$47$	−4.99634	−	2.88464i	−0.728791	−	0.420767i	0.0891889	−	0.996015i	$-0.471573\pi$
$47$	−4.99634	−	2.88464i	−0.728791	−	0.420767i	−0.817980	+	0.575247i	$0.804906\pi$
$48$	−8.50143	+	1.62549i	−1.22708	+	0.234620i
$49$	4.09573			0.585105
$50$	−14.3139			−2.02429
$51$	−0.602592	+	0.115217i	−0.0843797	+	0.0161336i
$52$	5.67738	−	3.27783i	0.787310	−	0.454554i
$53$	−4.94884	−	2.85721i	−0.679775	−	0.392468i	0.119995	−	0.992774i	$-0.461712\pi$
$53$	−4.94884	−	2.85721i	−0.679775	−	0.392468i	−0.799770	+	0.600306i	$0.795045\pi$
$54$	−8.05102	−	4.19586i	−1.09561	−	0.570984i
$55$	−3.42962	−	11.5479i	−0.462449	−	1.55712i
$56$		−	2.82052i		−	0.376907i
$57$	2.08105	+	7.25736i	0.275642	+	0.961260i
$58$	−9.21558			−1.21007
$59$	−3.56425	+	2.05782i	−0.464026	+	0.267906i	−0.713736	−	0.700415i	$-0.752998\pi$
$59$	−3.56425	+	2.05782i	−0.464026	+	0.267906i	0.249709	+	0.968321i	$0.419665\pi$
$60$	−6.25544	−	2.17538i	−0.807574	−	0.280841i
$61$	−7.30518	−	4.21765i	−0.935333	−	0.540015i	−0.0468385	−	0.998902i	$-0.514915\pi$
$61$	−7.30518	−	4.21765i	−0.935333	−	0.540015i	−0.888494	+	0.458888i	$0.848248\pi$
$62$	−4.62011	−	8.00227i	−0.586755	−	1.01629i
$63$	3.17224	−	4.00940i	0.399665	−	0.505137i
$64$	0.522614			0.0653268
$65$	−22.6180			−2.80542
$66$	0.461373	−	10.0264i	0.0567910	−	1.23416i
$67$	−1.49556	+	2.59038i	−0.182711	+	0.316465i	−0.942803	−	0.333351i	$-0.891821\pi$
$67$	−1.49556	+	2.59038i	−0.182711	+	0.316465i	0.760092	+	0.649816i	$0.225154\pi$
$68$	−0.372893			−0.0452200
$69$	3.53886	−	3.05730i	0.426029	−	0.368056i
$70$	5.40750	−	9.36606i	0.646319	−	1.11946i
$71$	−3.24639	+	1.87430i	−0.385275	+	0.222439i	−0.680111	−	0.733109i	$-0.738068\pi$
$71$	−3.24639	+	1.87430i	−0.385275	+	0.222439i	0.294836	+	0.955548i	$0.404735\pi$
$72$	3.89378	+	3.08076i	0.458886	+	0.363072i
$73$	9.93554	−	5.73629i	1.16287	−	0.671382i	0.210878	−	0.977512i	$-0.432368\pi$
$73$	9.93554	−	5.73629i	1.16287	−	0.671382i	0.951990	+	0.306131i	$0.0990344\pi$
$74$	7.86541	+	13.6233i	0.914335	+	1.58367i
$75$	9.27642	+	10.7376i	1.07115	+	1.23987i
$76$	0.413970	+	4.57012i	0.0474856	+	0.524229i
$77$	5.49693	+	1.31555i	0.626434	+	0.149921i
$78$	−17.7995	−	6.18992i	−2.01540	−	0.700871i
$79$	6.78568	−	3.91771i	0.763449	−	0.440777i	−0.0670839	−	0.997747i	$-0.521370\pi$
$79$	6.78568	−	3.91771i	0.763449	−	0.440777i	0.830533	+	0.556970i	$0.188036\pi$
$80$	15.7189	+	9.07529i	1.75742	+	1.01465i
$81$	2.07011	+	8.75869i	0.230012	+	0.973188i
$82$	1.74878	−	3.02897i	0.193120	−	0.334494i
$83$	−2.90096			−0.318422			−0.159211	−	0.987245i	$-0.550895\pi$
$83$	−2.90096			−0.318422			−0.159211	+	0.987245i	$0.550895\pi$
$84$	2.35146	−	2.03148i	0.256565	−	0.221652i
$85$	1.11417	+	0.643268i	0.120849	+	0.0697722i
$86$	−10.4410	−	6.02813i	−1.12588	−	0.650030i
$87$	5.97235	+	6.91307i	0.640303	+	0.741159i
$88$	−1.27761	+	5.33842i	−0.136194	+	0.569077i
$89$	10.1340	+	5.85087i	1.07420	+	0.620191i	0.929327	−	0.369259i	$-0.120388\pi$
$89$	10.1340	+	5.85087i	1.07420	+	0.620191i	0.144876	+	0.989450i	$0.453722\pi$
$90$	7.02358	+	17.6954i	0.740351	+	1.86526i
$91$	5.30616	−	9.19053i	0.556236	−	0.963429i
$92$	2.46165	−	1.42123i	0.256644	−	0.148174i
$93$	−3.00874	+	8.65181i	−0.311992	+	0.897151i
$94$			10.0801i			1.03969i
$95$	6.64688	−	14.3692i	0.681955	−	1.47425i
$96$	6.13841	+	7.10528i	0.626499	+	0.725180i
$97$	−3.05823	−	5.29701i	−0.310516	−	0.537830i	0.667958	−	0.744199i	$-0.267169\pi$
$97$	−3.05823	−	5.29701i	−0.310516	−	0.537830i	−0.978474	+	0.206369i	$0.933835\pi$
$98$	−3.57806	−	6.19738i	−0.361438	−	0.626030i
$99$	−7.82027	+	6.15169i	−0.785967	+	0.618268i
$100$	4.31229	+	7.46910i	0.431229	+	0.746910i
$101$	−4.31493	+	7.47367i	−0.429351	+	0.743658i	−0.996816	−	0.0797398i	$-0.974591\pi$
$101$	−4.31493	+	7.47367i	−0.429351	+	0.743658i	0.567465	+	0.823398i	$0.307924\pi$
$102$	0.700766	+	0.811145i	0.0693862	+	0.0803154i
$103$	9.53114			0.939131			0.469566	−	0.882898i	$-0.344411\pi$
$103$	9.53114			0.939131			0.469566	+	0.882898i	$0.344411\pi$
$104$	8.92550	+	5.15314i	0.875217	+	0.505307i
$105$	−10.5304	+	2.01344i	−1.02766	+	0.196491i
$106$			9.98431i			0.969762i
$107$	−2.15811			−0.208633			−0.104316	−	0.994544i	$-0.533265\pi$
$107$	−2.15811			−0.208633			−0.104316	+	0.994544i	$0.533265\pi$
$108$	0.236066	+	5.46515i	0.0227154	+	0.525885i
$109$	−9.95573	+	5.74794i	−0.953586	+	0.550553i	−0.894193	−	0.447682i	$-0.852250\pi$
$109$	−9.95573	+	5.74794i	−0.953586	+	0.550553i	−0.0593927	+	0.998235i	$0.518916\pi$
$110$	−14.4774	+	15.2778i	−1.38036	+	1.45668i
$111$	5.12216	−	14.7291i	0.486174	−	1.39802i
$112$	−7.37526	+	4.25811i	−0.696896	+	0.402353i
$113$		−	2.78933i		−	0.262398i	−0.991356	−	0.131199i	$-0.958117\pi$
$113$		−	2.78933i		−	0.262398i	0.991356	−	0.131199i	$-0.0418827\pi$
$114$	9.16330	−	9.48897i	0.858222	−	0.888724i
$115$	−9.80691			−0.914499
$116$	2.77634	+	4.80876i	0.257777	+	0.446482i
$117$	6.89196	+	17.3638i	0.637162	+	1.60528i
$118$	6.22751	+	3.59545i	0.573289	+	0.330988i
$119$	−0.522767	+	0.301820i	−0.0479220	+	0.0276678i
$120$	−1.95537	−	10.2267i	−0.178500	−	0.933567i
$121$	−9.80819	−	4.97990i	−0.891654	−	0.452718i
$122$			14.7383i			1.33434i
$123$	−3.40551	+	0.651142i	−0.307065	+	0.0587115i
$124$	−2.78376	+	4.82162i	−0.249989	+	0.432994i
$125$		−	11.5953i		−	1.03712i
$126$	−8.83803	−	1.29738i	−0.787354	−	0.115580i
$127$	8.86864	+	5.12031i	0.786965	+	0.454354i	0.838893	−	0.544296i	$-0.183203\pi$
$127$	8.86864	+	5.12031i	0.786965	+	0.454354i	−0.0519281	+	0.998651i	$0.516537\pi$
$128$	−5.87766	−	10.1804i	−0.519517	−	0.899830i
$129$	2.24452	+	11.7390i	0.197619	+	1.03356i
$130$	19.7592	+	34.2240i	1.73300	+	3.00164i
$131$	0.0180427	+	0.0312509i	0.00157640	+	0.00273041i	0.866813	−	0.498634i	$-0.166165\pi$
$131$	0.0180427	+	0.0312509i	0.00157640	+	0.00273041i	−0.865236	+	0.501365i	$0.832832\pi$
$132$	−5.37082	+	2.77985i	−0.467470	+	0.241955i
$133$	4.27941	+	6.07188i	0.371072	+	0.526499i
$134$	5.22611			0.451467
$135$	8.72244	−	16.7366i	0.750708	−	1.44046i
$136$	−0.293116	−	0.507692i	−0.0251345	−	0.0435342i
$137$	18.9824	+	10.9595i	1.62178	+	0.936334i	0.986444	+	0.164096i	$0.0524707\pi$
$137$	18.9824	+	10.9595i	1.62178	+	0.936334i	0.635333	+	0.772238i	$0.280863\pi$
$138$	−7.71766	−	2.68388i	−0.656971	−	0.228467i
$139$	12.4076	+	7.16352i	1.05240	+	0.607602i	0.923320	−	0.384033i	$-0.125465\pi$
$139$	12.4076	+	7.16352i	1.05240	+	0.607602i	0.129078	+	0.991634i	$0.458798\pi$
$140$	−6.51637			−0.550734
$141$	7.56162	−	6.53265i	0.636803	−	0.550148i
$142$	5.67212	+	3.27480i	0.475994	+	0.274815i
$143$	−14.2061	+	14.9915i	−1.18797	+	1.25365i
$144$	2.17737	−	14.8327i	0.181447	−	1.23606i
$145$		−	19.1575i		−	1.59095i
$146$	−17.3595	−	10.0225i	−1.43668	−	0.829469i
$147$	−2.33013	+	6.70042i	−0.192186	+	0.552641i
$148$	4.73915	−	8.20845i	0.389556	−	0.674731i
$149$	8.83043	+	15.2948i	0.723417	+	1.25300i	0.959622	+	0.281292i	$0.0907630\pi$
$149$	8.83043	+	15.2948i	0.723417	+	1.25300i	−0.236205	+	0.971703i	$0.575904\pi$
$150$	8.14341	−	23.4168i	0.664906	−	1.91198i
$151$			4.10478i			0.334043i	0.985953	+	0.167021i	$0.0534149\pi$
$151$			4.10478i			0.334043i	−0.985953	+	0.167021i	$0.946585\pi$
$152$	−5.89678	+	4.15600i	−0.478292	+	0.337096i
$153$	0.154335	−	1.05136i	0.0124772	−	0.0849974i
$154$	−2.81156	−	9.46684i	−0.226562	−	0.762860i
$155$	16.6353	−	9.60438i	1.33618	−	0.771442i
$156$	2.13243	+	11.1527i	0.170731	+	0.892932i
$157$	−6.31614	−	10.9399i	−0.504083	−	0.873098i	−0.999989	−	0.00472125i	$-0.998497\pi$
$157$	−6.31614	−	10.9399i	−0.504083	−	0.873098i	0.495906	−	0.868376i	$-0.334836\pi$
$158$	−11.8560	−	6.84508i	−0.943215	−	0.544565i
$159$	7.48973	−	6.47054i	0.593974	−	0.513147i
$160$		−	19.6902i		−	1.55665i
$161$	2.30069	−	3.98491i	0.181320	−	0.314055i
$162$	11.4446	−	10.7840i	0.899171	−	0.847270i
$163$	−6.52105			−0.510768			−0.255384	−	0.966840i	$-0.582202\pi$
$163$	−6.52105			−0.510768			−0.255384	+	0.966840i	$0.582202\pi$
$164$	−2.10739			−0.164559
$165$	20.8430	+	0.959110i	1.62262	+	0.0746666i
$166$	2.53430	+	4.38953i	0.196699	+	0.340693i
$167$	9.77888	−	16.9375i	0.756712	−	1.31066i	−0.187806	−	0.982206i	$-0.560138\pi$
$167$	9.77888	−	16.9375i	0.756712	−	1.31066i	0.944519	−	0.328458i	$-0.106529\pi$
$168$	4.61422	+	1.60464i	0.355995	+	0.123800i
$169$	12.8889	+	22.3243i	0.991455	+	1.71725i
$170$		−	2.24785i		−	0.172402i
$171$	−13.0566	−	0.724326i	−0.998465	−	0.0553906i
$172$			7.26427i			0.553895i
$173$	3.56190	+	6.16940i	0.270806	+	0.469051i	0.969069	−	0.246792i	$-0.0793763\pi$
$173$	3.56190	+	6.16940i	0.270806	+	0.469051i	−0.698262	+	0.715842i	$0.746043\pi$
$174$	5.24289	−	15.0762i	0.397462	−	1.14293i
$175$	12.0910	+	6.98073i	0.913992	+	0.527693i
$176$	15.8880	−	4.71858i	1.19760	−	0.355676i
$177$	−1.33874	−	7.00167i	−0.100626	−	0.526278i
$178$		−	20.4454i		−	1.53245i
$179$			0.897550i			0.0670860i	0.999437	+	0.0335430i	$0.0106791\pi$
$179$			0.897550i			0.0670860i	−0.999437	+	0.0335430i	$0.989321\pi$
$180$	7.11764	−	8.99598i	0.530517	−	0.670521i
$181$	−8.62795	+	14.9440i	−0.641310	+	1.11078i	0.343830	+	0.939032i	$0.388276\pi$
$181$	−8.62795	+	14.9440i	−0.641310	+	1.11078i	−0.985141	+	0.171750i	$0.945058\pi$
$182$	−18.5420			−1.37442
$183$	11.0559	−	9.55143i	0.817276	−	0.706062i
$184$	3.87000	+	2.23435i	0.285300	+	0.164718i
$185$	−28.3203	+	16.3508i	−2.08215	+	1.20213i
$186$	15.7198	−	3.00566i	1.15263	−	0.220386i
$187$	1.12616	−	0.334459i	0.0823531	−	0.0244581i
$188$	5.25989	−	3.03680i	0.383617	−	0.221481i
$189$	4.75444	+	7.47064i	0.345835	+	0.543409i
$190$	−27.5493	+	2.49547i	−1.99864	+	0.181040i
$191$			8.70784i			0.630077i	0.949079	+	0.315038i	$0.102017\pi$
$191$			8.70784i			0.630077i	−0.949079	+	0.315038i	$0.897983\pi$
$192$	−0.297324	+	0.854972i	−0.0214575	+	0.0617023i
$193$	−19.3643	+	11.1800i	−1.39387	+	0.804751i	−0.993741	−	0.111708i	$-0.964368\pi$
$193$	−19.3643	+	11.1800i	−1.39387	+	0.804751i	−0.400129	+	0.916459i	$0.631035\pi$
$194$	−5.34338	+	9.25500i	−0.383632	+	0.664470i
$195$	12.8677	−	37.0019i	0.921478	−	2.64976i
$196$	−2.15589	+	3.73411i	−0.153992	+	0.266722i
$197$	−11.9769			−0.853320			−0.426660	−	0.904412i	$-0.640310\pi$
$197$	−11.9769			−0.853320			−0.426660	+	0.904412i	$0.640310\pi$
$198$	16.1401	+	6.45894i	1.14703	+	0.459017i
$199$	11.7476	−	20.3474i	0.832763	−	1.44239i	−0.0630757	−	0.998009i	$-0.520091\pi$
$199$	11.7476	−	20.3474i	0.832763	−	1.44239i	0.895839	−	0.444379i	$-0.146576\pi$
$200$	−6.77942	+	11.7423i	−0.479378	+	0.830306i
$201$	−3.38689	−	3.92036i	−0.238893	−	0.276521i
$202$	15.0782			1.06090
$203$	7.78441	+	4.49433i	0.546359	+	0.315440i
$204$	0.212145	−	0.610035i	0.0148531	−	0.0427110i
$205$	6.29668	+	3.63539i	0.439779	+	0.253907i
$206$	−8.32646	−	14.4219i	−0.580132	−	1.00482i
$207$	2.98828	+	7.52875i	0.207700	+	0.523284i
$208$		−	31.1186i		−	2.15769i
$209$	−5.34929	−	13.4308i	−0.370018	−	0.929025i
$210$	12.2460	+	14.1749i	0.845054	+	0.978161i
$211$	−1.84396	+	1.06461i	−0.126944	+	0.0732910i	−0.562127	−	0.827051i	$-0.690017\pi$
$211$	−1.84396	+	1.06461i	−0.126944	+	0.0732910i	0.435183	+	0.900342i	$0.356684\pi$
$212$	5.20989	−	3.00793i	0.357817	−	0.206586i
$213$	−1.21934	−	6.37725i	−0.0835481	−	0.436962i
$214$	1.88534	+	3.26550i	0.128879	+	0.223225i
$215$	12.5314	−	21.7050i	0.854633	−	1.48027i
$216$	−7.25521	+	4.61733i	−0.493655	+	0.314170i
$217$			9.01270i			0.611822i
$218$	17.3948	+	10.0429i	1.17812	+	0.680189i
$219$	3.73180	+	19.5175i	0.252172	+	1.31887i
$220$	12.3336	+	2.95173i	0.831531	+	0.199005i
$221$		−	2.20572i		−	0.148373i
$222$	−26.7618	+	5.11692i	−1.79613	+	0.343425i
$223$	6.45941	+	11.1880i	0.432554	+	0.749206i	0.997092	−	0.0762009i	$-0.0242790\pi$
$223$	6.45941	+	11.1880i	0.432554	+	0.749206i	−0.564538	+	0.825407i	$0.690946\pi$
$224$	8.00086	+	4.61930i	0.534580	+	0.308640i
$225$	−22.8436	+	9.06700i	−1.52291	+	0.604466i
$226$	−4.22062	+	2.43678i	−0.280751	+	0.162092i
$227$	28.7695			1.90950			0.954750	−	0.297408i	$-0.0961223\pi$
$227$	28.7695			1.90950			0.954750	+	0.297408i	$0.0961223\pi$
$228$	−7.71201	−	1.92278i	−0.510740	−	0.127339i
$229$	−1.54986			−0.102418			−0.0512089	−	0.998688i	$-0.516307\pi$
$229$	−1.54986			−0.102418			−0.0512089	+	0.998688i	$0.516307\pi$
$230$	8.56738	+	14.8391i	0.564916	+	0.978464i
$231$	−5.27946	+	8.24427i	−0.347363	+	0.542433i
$232$	−4.36473	+	7.55993i	−0.286559	+	0.496334i
$233$	−5.39617	−	9.34645i	−0.353515	−	0.612306i	0.633348	−	0.773867i	$-0.281680\pi$
$233$	−5.39617	−	9.34645i	−0.353515	−	0.612306i	−0.986863	+	0.161561i	$0.948347\pi$
$234$	20.2528	−	25.5975i	1.32397	−	1.67336i
$235$	−20.9548			−1.36694
$236$		−	4.33275i		−	0.282038i
$237$	2.54871	+	13.3299i	0.165556	+	0.865869i
$238$	0.913385	+	0.527343i	0.0592060	+	0.0341826i
$239$	10.2871			0.665418			0.332709	−	0.943029i	$-0.392037\pi$
$239$	10.2871			0.665418			0.332709	+	0.943029i	$0.392037\pi$
$240$	−23.7894	+	20.5522i	−1.53560	+	1.32664i
$241$	0.437927	+	0.252837i	0.0282093	+	0.0162867i	0.514038	−	0.857767i	$-0.328149\pi$
$241$	0.437927	+	0.252837i	0.0282093	+	0.0162867i	−0.485829	+	0.874054i	$0.661482\pi$
$242$	1.03326	+	19.1915i	0.0664203	+	1.23368i
$243$	−15.5065	−	1.59636i	−0.994743	−	0.102407i
$244$	7.69053	−	4.44013i	0.492336	−	0.284250i
$245$	12.8832	−	7.43813i	0.823079	−	0.475205i
$246$	3.96034	+	4.58414i	0.252502	+	0.292274i
$247$	−27.0330	+	2.44870i	−1.72007	+	0.155807i
$248$	−8.75280			−0.555803
$249$	1.65040	−	4.74583i	0.104590	−	0.300755i
$250$	−17.5452	+	10.1298i	−1.10966	+	0.640662i
$251$	−15.5501	−	8.97786i	−0.981514	−	0.566677i	−0.0787871	−	0.996891i	$-0.525105\pi$
$251$	−15.5501	−	8.97786i	−0.981514	−	0.566677i	−0.902727	+	0.430214i	$0.858438\pi$
$252$	1.98561	+	5.00261i	0.125082	+	0.315135i
$253$	−6.15959	+	6.50014i	−0.387250	+	0.408660i
$254$		−	17.8925i		−	1.12268i
$255$	−1.68622	+	1.45677i	−0.105595	+	0.0912262i
$256$	−9.74691	+	16.8821i	−0.609182	+	1.05513i
$257$	16.5970	+	9.58225i	1.03529	+	0.597725i	0.918495	−	0.395432i	$-0.129405\pi$
$257$	16.5970	+	9.58225i	1.03529	+	0.597725i	0.116794	+	0.993156i	$0.462738\pi$
$258$	15.8018	−	13.6515i	0.983776	−	0.849905i
$259$		−	15.3435i		−	0.953397i
$260$	11.9055	−	20.6210i	0.738351	−	1.27886i
$261$	−14.7072	+	5.83751i	−0.910353	+	0.361333i
$262$	0.0315245	−	0.0546020i	0.00194759	−	0.00337332i
$263$	14.1774	+	24.5560i	0.874217	+	1.51419i	0.857595	+	0.514326i	$0.171958\pi$
$263$	14.1774	+	24.5560i	0.874217	+	1.51419i	0.0166216	+	0.999862i	$0.494709\pi$
$264$	−8.00653	−	5.12722i	−0.492768	−	0.315558i
$265$	−20.7556			−1.27501
$266$	5.44903	−	11.7797i	0.334101	−	0.722262i
$267$	−15.3371	+	13.2501i	−0.938618	+	0.810892i
$268$	−1.57445	−	2.72702i	−0.0961747	−	0.166579i
$269$	−12.4224	+	7.17205i	−0.757404	+	0.437288i	−0.828363	−	0.560192i	$-0.810728\pi$
$269$	−12.4224	+	7.17205i	−0.757404	+	0.437288i	0.0709586	+	0.997479i	$0.477394\pi$
$270$	−32.9447	+	1.42304i	−2.00495	+	0.0866032i
$271$	−8.69831	+	5.02197i	−0.528385	+	0.305063i	−0.740358	−	0.672212i	$-0.765344\pi$
$271$	−8.69831	+	5.02197i	−0.528385	+	0.305063i	0.211974	+	0.977275i	$0.432011\pi$
$272$	−0.885029	+	1.53292i	−0.0536628	+	0.0929467i
$273$	12.0165	+	13.9092i	0.727272	+	0.841826i
$274$		−	38.2972i		−	2.31362i
$275$	−19.7226	−	18.6894i	−1.18932	−	1.12701i
$276$	0.924597	+	4.83570i	0.0556542	+	0.291075i
$277$			31.4966i			1.89245i	0.323513	+	0.946224i	$0.395136\pi$
$277$			31.4966i			1.89245i	−0.323513	+	0.946224i	$0.604864\pi$
$278$		−	25.0324i		−	1.50134i
$279$	−12.4422	−	9.84430i	−0.744896	−	0.589363i
$280$	−5.12225	−	8.87200i	−0.306113	−	0.530203i
$281$	7.51730	−	13.0203i	0.448444	−	0.776728i	−0.549841	−	0.835270i	$-0.685312\pi$
$281$	7.51730	−	13.0203i	0.448444	−	0.776728i	0.998285	+	0.0585413i	$0.0186449\pi$
$282$	−16.4906	−	5.73475i	−0.982002	−	0.341500i
$283$	−27.5872	+	15.9275i	−1.63989	+	0.946790i	−0.659018	+	0.752127i	$0.729028\pi$
$283$	−27.5872	+	15.9275i	−1.63989	+	0.946790i	−0.980870	+	0.194663i	$0.937639\pi$
$284$		−	3.94634i		−	0.234172i
$285$	19.7259	+	19.0489i	1.16846	+	1.12836i
$286$	35.0945	+	8.39897i	2.07518	+	0.496641i
$287$	−2.95439	+	1.70572i	−0.174392	+	0.100685i
$288$	−15.1161	+	5.99983i	−0.890727	+	0.353543i
$289$	8.43727	−	14.6138i	0.496310	−	0.859634i
$290$	−28.9878	+	16.7361i	−1.70222	+	0.982779i
$291$	10.4055	−	1.98956i	0.609983	−	0.116630i
$292$			12.0778i			0.706797i
$293$	4.06111			0.237253			0.118626	−	0.992939i	$-0.462151\pi$
$293$	4.06111			0.237253			0.118626	+	0.992939i	$0.462151\pi$
$294$	12.1742	−	2.32774i	0.710015	−	0.135757i
$295$	−7.47430	+	12.9459i	−0.435170	+	0.753737i
$296$	14.9010			0.866104
$297$	−5.61479	−	16.2934i	−0.325803	−	0.945438i
$298$	15.4286	−	26.7232i	0.893757	−	1.54803i
$299$	8.40682	+	14.5610i	0.486179	+	0.842087i
$300$	−14.6724	+	2.80540i	−0.847112	+	0.161970i
$301$	5.87970	+	10.1839i	0.338900	+	0.586992i
$302$	6.21107	−	3.58596i	0.357407	−	0.206349i
$303$	−9.77173	−	11.3109i	−0.561371	−	0.649794i
$304$	19.7697	+	9.14500i	1.13387	+	0.524502i
$305$	−30.6382			−1.75434
$306$	−1.72567	+	0.684945i	−0.0986500	+	0.0391557i
$307$	16.6169	−	9.59375i	0.948374	−	0.547544i	0.0557986	−	0.998442i	$-0.482230\pi$
$307$	16.6169	−	9.59375i	0.948374	−	0.547544i	0.892575	+	0.450898i	$0.148896\pi$
$308$	−4.09284	+	4.31913i	−0.233211	+	0.246105i
$309$	−5.42242	+	15.5925i	−0.308471	+	0.887025i
$310$	−29.0653	−	16.7809i	−1.65080	−	0.953090i
$311$			14.4857i			0.821408i	0.911769	+	0.410704i	$0.134717\pi$
$311$			14.4857i			0.821408i	−0.911769	+	0.410704i	$0.865283\pi$
$312$	−13.5081	+	11.6700i	−0.764748	+	0.660682i
$313$	7.77063	−	13.4591i	0.439222	−	0.760755i	−0.558408	−	0.829567i	$-0.688588\pi$
$313$	7.77063	−	13.4591i	0.439222	−	0.760755i	0.997630	+	0.0688120i	$0.0219209\pi$
$314$	−11.0356	+	19.1143i	−0.622777	+	1.07868i
$315$	2.69702	−	18.3727i	0.151960	−	1.03518i
$316$			8.24875i			0.464028i
$317$	−0.423867	−	0.244720i	−0.0238067	−	0.0137448i	0.488049	−	0.872816i	$-0.337709\pi$
$317$	−0.423867	−	0.244720i	−0.0238067	−	0.0137448i	−0.511856	+	0.859071i	$0.671042\pi$
$318$	−16.3338	−	5.68023i	−0.915957	−	0.318532i
$319$	−12.6978	−	12.0326i	−0.710942	−	0.673695i
$320$	1.64390	−	0.949104i	0.0918966	−	0.0530565i
$321$	1.22778	−	3.53056i	0.0685282	−	0.197057i
$322$	−8.03959			−0.448029
$323$	1.40130	+	0.648209i	0.0779704	+	0.0360673i
$324$	−9.07502	−	2.72302i	−0.504168	−	0.151279i
$325$	−44.1809	+	25.5079i	−2.45072	+	1.41492i
$326$	5.69683	+	9.86719i	0.315518	+	0.546493i
$327$	−3.73938	−	19.5572i	−0.206788	−	1.08151i
$328$	−1.65653	−	2.86919i	−0.0914665	−	0.158425i
$329$	4.91597	−	8.51471i	0.271026	−	0.469431i
$330$	−16.7573	−	32.3760i	−0.922459	−	1.78224i
$331$	6.80848			0.374228			0.187114	−	0.982338i	$-0.440087\pi$
$331$	6.80848			0.374228			0.187114	+	0.982338i	$0.440087\pi$
$332$	1.52699	−	2.64483i	0.0838046	−	0.145154i
$333$	21.1820	+	16.7592i	1.16077	+	0.918399i
$334$	−34.1715			−1.86978
$335$			10.8641i			0.593571i
$336$	−2.77015	−	14.4881i	−0.151124	−	0.790388i
$337$	27.0052	−	15.5915i	1.47107	−	0.849322i	0.471597	−	0.881814i	$-0.343678\pi$
$337$	27.0052	−	15.5915i	1.47107	−	0.849322i	0.999472	+	0.0324924i	$0.0103445\pi$
$338$	22.5197	−	39.0052i	1.22491	−	2.12160i
$339$	4.56321	+	1.58689i	0.247839	+	0.0861883i
$340$	−1.17295	+	0.677200i	−0.0636119	+	0.0367263i
$341$	4.08249	−	17.0584i	0.221079	−	0.923766i
$342$	10.3103	+	20.3891i	0.557519	+	1.10252i
$343$			18.9092i			1.02100i
$344$	−9.89026	+	5.71014i	−0.533247	+	0.307870i
$345$	5.57931	−	16.0436i	0.300380	−	0.863760i
$346$	6.22340	−	10.7792i	0.334572	−	0.579496i
$347$	11.6281	+	20.1404i	0.624228	+	1.08120i	0.988690	+	0.149977i	$0.0479199\pi$
$347$	11.6281	+	20.1404i	0.624228	+	1.08120i	−0.364461	+	0.931219i	$0.618747\pi$
$348$	−9.44639	+	1.80617i	−0.506380	+	0.0968211i
$349$		−	30.6015i		−	1.63806i	−0.573752	−	0.819029i	$-0.694512\pi$
$349$		−	30.6015i		−	1.63806i	0.573752	−	0.819029i	$-0.305488\pi$
$350$		−	24.3936i		−	1.30389i
$351$	−32.3273	+	1.39637i	−1.72550	+	0.0745325i
$352$	−13.0509	−	12.3671i	−0.695615	−	0.659171i
$353$			23.2012i			1.23488i	0.786619	+	0.617439i	$0.211830\pi$
$353$			23.2012i			1.23488i	−0.786619	+	0.617439i	$0.788170\pi$
$354$	−9.42491	+	8.14239i	−0.500928	+	0.432763i
$355$	−6.80772	+	11.7913i	−0.361316	+	0.625818i
$356$	−10.6686	+	6.15951i	−0.565433	+	0.326453i
$357$	−0.196352	−	1.02693i	−0.0103920	−	0.0543510i
$358$	1.35811	−	0.784105i	0.0717783	−	0.0414412i
$359$	−9.59917	−	16.6262i	−0.506625	−	0.877500i	−0.999971	−	0.00766656i	$-0.997560\pi$
$359$	−9.59917	−	16.6262i	−0.506625	−	0.877500i	0.493346	−	0.869833i	$-0.335774\pi$
$360$	17.8429	+	2.61925i	0.940401	+	0.138046i
$361$	6.38868	−	17.8937i	0.336246	−	0.941774i
$362$	30.1497			1.58463
$363$	13.7269	−	13.2126i	0.720476	−	0.693480i
$364$	5.58606	+	9.67533i	0.292789	+	0.507125i
$365$	20.8350	−	36.0873i	1.09055	−	1.88889i
$366$	−24.1111	−	8.38483i	−1.26031	−	0.438282i
$367$	0.0655163	−	0.113478i	0.00341992	−	0.00592348i	−0.864310	−	0.502959i	$-0.832245\pi$
$367$	0.0655163	−	0.113478i	0.00341992	−	0.00592348i	0.867730	+	0.497035i	$0.165578\pi$
$368$		−	13.4927i		−	0.703355i
$369$	0.872214	−	5.94170i	0.0454056	−	0.309312i
$370$	49.4816	+	28.5682i	2.57243	+	1.48519i
$371$	4.86924	−	8.43376i	0.252798	−	0.437859i
$372$	−6.30420	−	7.29719i	−0.326858	−	0.378342i
$373$			2.77235i			0.143547i	0.997421	+	0.0717735i	$0.0228659\pi$
$373$			2.77235i			0.143547i	−0.997421	+	0.0717735i	$0.977134\pi$
$374$	−1.48990	−	1.41184i	−0.0770410	−	0.0730047i
$375$	18.9694	+	6.59677i	0.979575	+	0.340656i
$376$	8.26917	+	4.77421i	0.426450	+	0.246211i
$377$	−28.4446	+	16.4225i	−1.46497	+	0.845801i
$378$	7.15055	−	13.7205i	0.367785	−	0.705705i
$379$	11.8167			0.606982			0.303491	−	0.952834i	$-0.401848\pi$
$379$	11.8167			0.606982			0.303491	+	0.952834i	$0.401848\pi$
$380$	9.60181	+	13.6236i	0.492562	+	0.698877i
$381$	−13.4221	+	11.5956i	−0.687635	+	0.594062i
$382$	13.1761	−	7.60722i	0.674147	−	0.389219i
$383$	10.5162	−	6.07151i	0.537351	−	0.310240i	−0.206654	−	0.978414i	$-0.566257\pi$
$383$	10.5162	−	6.07151i	0.537351	−	0.310240i	0.744005	+	0.668174i	$0.232924\pi$
$384$	19.9986	−	3.82377i	1.02055	−	0.195131i
$385$	19.6799	−	5.84472i	1.00298	−	0.297875i
$386$	33.8335	+	19.5338i	1.72208	+	0.994242i
$387$	−20.4813	−	3.00657i	−1.04113	−	0.152832i
$388$	6.43910			0.326896
$389$	5.81921	+	3.35972i	0.295046	+	0.170345i	0.640215	−	0.768196i	$-0.278845\pi$
$389$	5.81921	+	3.35972i	0.295046	+	0.170345i	−0.345169	+	0.938540i	$0.612179\pi$
$390$	−67.2301	+	12.8545i	−3.40433	+	0.650915i
$391$		−	0.956378i		−	0.0483661i
$392$	−6.77863			−0.342373
$393$	−0.0613898	+	0.0117379i	−0.00309670	+	0.000592097i
$394$	10.4631	+	18.1226i	0.527124	+	0.913005i
$395$	14.2297	−	24.6465i	0.715973	−	1.24010i
$396$	−1.49215	−	10.3679i	−0.0749834	−	0.521007i
$397$	−19.7742	−	34.2499i	−0.992437	−	1.71895i	−0.602525	−	0.798100i	$-0.705839\pi$
$397$	−19.7742	−	34.2499i	−0.992437	−	1.71895i	−0.389912	−	0.920852i	$-0.627495\pi$
$398$	−41.0510			−2.05770
$399$	−12.3679	+	3.54651i	−0.619170	+	0.177548i
$400$	40.9393			2.04697
$401$	12.0332	−	6.94738i	0.600910	−	0.346935i	−0.168490	−	0.985703i	$-0.553889\pi$
$401$	12.0332	−	6.94738i	0.600910	−	0.346935i	0.769399	+	0.638768i	$0.220556\pi$
$402$	−2.97322	+	8.54966i	−0.148291	+	0.426418i
$403$	−28.5206	−	16.4664i	−1.42071	−	0.820250i
$404$	−4.54254	−	7.86791i	−0.226000	−	0.391443i
$405$	22.4180	+	23.7912i	1.11396	+	1.18219i
$406$		−	15.7051i		−	0.779431i
$407$	−6.95015	+	29.0407i	−0.344506	+	1.43950i
$408$	0.997318	−	0.190690i	0.0493746	−	0.00944054i
$409$	8.95670	+	5.17115i	0.442880	+	0.255697i	0.704819	−	0.709388i	$-0.251028\pi$
$409$	8.95670	+	5.17115i	0.442880	+	0.255697i	−0.261938	+	0.965085i	$0.584362\pi$
$410$		−	12.7036i		−	0.627386i
$411$	−28.7286	+	24.8193i	−1.41708	+	1.22424i
$412$	−5.01696	+	8.68962i	−0.247168	+	0.428107i
$413$	−3.50692	−	6.07417i	−0.172564	−	0.298890i
$414$	8.78140	−	11.0988i	0.431582	−	0.545477i
$415$	−9.12504	+	5.26834i	−0.447930	+	0.258613i
$416$	−29.2355	+	16.8791i	−1.43339	+	0.827567i
$417$	−18.7780	+	16.2228i	−0.919564	+	0.794432i
$418$	−15.6493	+	19.8274i	−0.765433	+	0.969788i
$419$		−	6.77170i		−	0.330819i	−0.986225	−	0.165410i	$-0.947105\pi$
$419$		−	6.77170i		−	0.330819i	0.986225	−	0.165410i	$-0.0528946\pi$
$420$	3.70727	−	10.6605i	0.180896	−	0.520177i
$421$	4.84221	+	8.38695i	0.235995	+	0.408755i	0.959561	−	0.281500i	$-0.0908319\pi$
$421$	4.84221	+	8.38695i	0.235995	+	0.408755i	−0.723567	+	0.690255i	$0.757499\pi$
$422$	3.22180	+	1.86010i	0.156835	+	0.0905485i
$423$	6.38516	+	16.0870i	0.310457	+	0.782175i
$424$	8.19056	+	4.72882i	0.397769	+	0.229652i
$425$	2.90183			0.140759
$426$	−8.58438	+	7.41623i	−0.415914	+	0.359317i
$427$	7.18768	−	12.4494i	0.347836	−	0.602470i
$428$	1.13598	−	1.96757i	0.0549095	−	0.0951060i
$429$	−16.4433	−	31.7693i	−0.793888	−	1.53384i
$430$	−43.7900			−2.11174
$431$	−6.45736	+	11.1845i	−0.311040	+	0.538738i	−0.978588	−	0.205830i	$-0.934011\pi$
$431$	−6.45736	+	11.1845i	−0.311040	+	0.538738i	0.667548	+	0.744567i	$0.267344\pi$
$432$	23.0268	+	12.0006i	1.10788	+	0.577380i
$433$	2.59746	−	4.49893i	0.124826	−	0.216205i	−0.796839	−	0.604192i	$-0.793496\pi$
$433$	2.59746	−	4.49893i	0.124826	−	0.216205i	0.921665	+	0.387987i	$0.126829\pi$
$434$	13.6374	−	7.87355i	0.654616	−	0.377943i
$435$	31.3408	+	10.8990i	1.50267	+	0.522568i
$436$		−	12.1023i		−	0.579595i
$437$	−11.7212	+	1.06173i	−0.560701	+	0.0507894i
$438$	26.2724	−	22.6973i	1.25535	−	1.08452i
$439$	−14.4785	+	8.35919i	−0.691023	+	0.398962i	−0.803995	−	0.594636i	$-0.797296\pi$
$439$	−14.4785	+	8.35919i	−0.691023	+	0.398962i	0.112972	+	0.993598i	$0.463963\pi$
$440$	5.67617	+	19.1123i	0.270601	+	0.911145i
$441$	−9.63591	−	7.62395i	−0.458853	−	0.363045i
$442$	−3.33755	+	1.92693i	−0.158751	+	0.0916549i
$443$	32.6466	+	18.8485i	1.55109	+	0.895520i	0.998054	+	0.0623594i	$0.0198625\pi$
$443$	32.6466	+	18.8485i	1.55109	+	0.895520i	0.553032	+	0.833160i	$0.313471\pi$
$444$	10.7324	+	12.4229i	0.509339	+	0.589567i
$445$	42.5024			2.01480
$446$	11.2860	−	19.5479i	0.534406	−	0.925618i
$447$	−30.0452	+	5.74472i	−1.42109	+	0.271716i
$448$			0.890635i			0.0420785i
$449$		−	29.6615i		−	1.39981i	−0.714235	−	0.699906i	$-0.753225\pi$
$449$		−	29.6615i		−	1.39981i	0.714235	−	0.699906i	$-0.246775\pi$
$450$	33.6759	+	26.6444i	1.58750	+	1.25603i
$451$	6.36444	−	1.89018i	0.299690	−	0.0890049i
$452$	2.54306	+	1.46823i	0.119615	+	0.0690599i
$453$	−6.71523	−	2.33528i	−0.315509	−	0.109721i
$454$	−25.1332	−	43.5320i	−1.17956	−	2.04306i
$455$		−	38.5454i		−	1.80704i
$456$	−3.44424	−	12.0113i	−0.161291	−	0.562479i
$457$		−	8.24748i		−	0.385801i	−0.981218	−	0.192900i	$-0.938211\pi$
$457$		−	8.24748i		−	0.385801i	0.981218	−	0.192900i	$-0.0617894\pi$
$458$	1.35397	+	2.34514i	0.0632668	+	0.109581i
$459$	1.63217	+	0.850619i	0.0761831	+	0.0397035i
$460$	5.16211	−	8.94104i	0.240685	−	0.416878i
$461$	−6.88191	−	11.9198i	−0.320523	−	0.555161i	0.660073	−	0.751201i	$-0.270525\pi$
$461$	−6.88191	−	11.9198i	−0.320523	−	0.555161i	−0.980596	+	0.196040i	$0.937192\pi$
$462$	17.0868	+	0.786267i	0.794951	+	0.0365805i
$463$	−6.32105			−0.293764			−0.146882	−	0.989154i	$-0.546924\pi$
$463$	−6.32105			−0.293764			−0.146882	+	0.989154i	$0.546924\pi$
$464$	26.3576			1.22362
$465$	6.24822	+	32.6786i	0.289754	+	1.51543i
$466$	−9.42826	+	16.3302i	−0.436756	+	0.756483i
$467$			7.84566i			0.363054i	0.983386	+	0.181527i	$0.0581040\pi$
$467$			7.84566i			0.363054i	−0.983386	+	0.181527i	$0.941896\pi$
$468$	−19.4585	−	2.85641i	−0.899468	−	0.132038i
$469$	−4.41450	−	2.54871i	−0.203843	−	0.117689i
$470$	18.3062	+	31.7073i	0.844404	+	1.46255i
$471$	21.4905	−	4.10903i	0.990228	−	0.189334i
$472$	5.89901	−	3.40579i	0.271524	−	0.156764i
$473$	−6.51553	−	21.9386i	−0.299584	−	1.00874i
$474$	17.9433	−	15.5016i	0.824163	−	0.712012i
$475$	−3.22149	−	35.5644i	−0.147812	−	1.63180i
$476$		−	0.635482i		−	0.0291272i
$477$	6.32446	+	15.9340i	0.289577	+	0.729569i
$478$	−8.98689	−	15.5657i	−0.411051	−	0.711961i
$479$	−17.4479	+	30.2207i	−0.797217	+	1.38082i	0.124205	+	0.992257i	$0.460362\pi$
$479$	−17.4479	+	30.2207i	−0.797217	+	1.38082i	−0.921422	+	0.388563i	$0.872971\pi$
$480$	32.2122	+	11.2021i	1.47028	+	0.511302i
$481$	48.5543	+	28.0329i	2.21389	+	1.27819i
$482$		−	0.883520i		−	0.0402433i
$483$	5.21022	+	6.03090i	0.237073	+	0.274415i
$484$	9.70300	−	6.32091i	0.441046	−	0.287314i
$485$	−19.2395	−	11.1079i	−0.873620	−	0.504384i
$486$	11.1311	+	24.8579i	0.504916	+	1.12758i
$487$	36.8707			1.67077			0.835385	−	0.549665i	$-0.185245\pi$
$487$	36.8707			1.67077			0.835385	+	0.549665i	$0.185245\pi$
$488$	12.0904	+	6.98041i	0.547307	+	0.315988i
$489$	3.70993	−	10.6681i	0.167769	−	0.482429i
$490$	−22.5097	−	12.9960i	−1.01689	−	0.587099i
$491$	−14.8940	−	25.7972i	−0.672157	−	1.16421i	−0.977291	−	0.211900i	$-0.932035\pi$
$491$	−14.8940	−	25.7972i	−0.672157	−	1.16421i	0.305135	−	0.952309i	$-0.401299\pi$
$492$	1.19893	−	3.44758i	0.0540517	−	0.155429i
$493$	1.86826			0.0841421
$494$	27.3214	+	38.7652i	1.22925	+	1.74413i
$495$	−13.4270	+	33.5524i	−0.603497	+	1.50807i
$496$	13.2140	+	22.8874i	0.593327	+	1.02767i
$497$	−3.19417	−	5.53246i	−0.143278	−	0.248165i
$498$	−8.62285	+	1.64871i	−0.386399	+	0.0738805i
$499$	5.73063	+	9.92573i	0.256538	+	0.444337i	0.965312	−	0.261099i	$-0.0840848\pi$
$499$	5.73063	+	9.92573i	0.256538	+	0.444337i	−0.708774	+	0.705436i	$0.750751\pi$
$500$	10.5716	+	6.10349i	0.472774	+	0.272956i
$501$	22.1456	+	25.6338i	0.989391	+	1.14523i
$502$			31.3724i			1.40022i
$503$	6.82612	−	11.8232i	0.304362	−	0.527170i	−0.672757	−	0.739863i	$-0.734890\pi$
$503$	6.82612	−	11.8232i	0.304362	−	0.527170i	0.977119	+	0.212693i	$0.0682235\pi$
$504$	−5.25021	+	6.63574i	−0.233863	+	0.295579i
$505$			31.3448i			1.39483i
$506$	15.2166	+	3.64170i	0.676461	+	0.161893i
$507$	−43.8541	+	8.38501i	−1.94763	+	0.372391i
$508$	−9.33646	+	5.39041i	−0.414239	+	0.239161i
$509$	−25.5400	−	14.7455i	−1.13204	−	0.653585i	−0.187595	−	0.982247i	$-0.560069\pi$
$509$	−25.5400	−	14.7455i	−1.13204	−	0.653585i	−0.944448	+	0.328662i	$0.893402\pi$
$510$	3.67737	+	1.27884i	0.162837	+	0.0566279i
$511$	9.77573	+	16.9321i	0.432453	+	0.749030i
$512$	10.5492			0.466213
$513$	8.61308	−	20.9479i	0.380277	−	0.924873i
$514$		−	33.4845i		−	1.47694i
$515$	29.9804	−	17.3092i	1.32110	−	0.762735i
$516$	−11.8840	−	4.13276i	−0.523163	−	0.181935i
$517$	−13.1614	+	13.8891i	−0.578839	+	0.610841i
$518$	−23.2167	+	13.4042i	−1.02008	+	0.588945i
$519$	−12.1193	+	2.31723i	−0.531976	+	0.101715i
$520$	37.4338			1.64158
$521$		−	38.2989i		−	1.67790i	−0.544206	−	0.838952i	$-0.683169\pi$
$521$		−	38.2989i		−	1.67790i	0.544206	−	0.838952i	$-0.316831\pi$
$522$	21.6812	+	17.1542i	0.948961	+	0.750820i
$523$	−4.78340	−	2.76169i	−0.209163	−	0.120760i	0.391759	−	0.920068i	$-0.371867\pi$
$523$	−4.78340	−	2.76169i	−0.209163	−	0.120760i	−0.600922	+	0.799307i	$0.705200\pi$
$524$	−0.0379890			−0.00165956
$525$	−18.2989	+	15.8088i	−0.798628	+	0.689952i
$526$	24.7709	−	42.9045i	1.08006	−	1.87073i
$527$	0.936626	+	1.62228i	0.0408001	+	0.0706678i
$528$	−1.31958	+	28.6765i	−0.0574272	+	1.24798i
$529$	−7.85490	−	13.6051i	−0.341517	−	0.591525i
$530$	18.1322	+	31.4059i	0.787612	+	1.36418i
$531$	12.2160	+	1.79325i	0.530130	+	0.0778206i
$532$	−7.78836	+	0.705484i	−0.337668	+	0.0305866i
$533$		−	12.4655i		−	0.539942i
$534$	33.4477	+	11.6317i	1.44742	+	0.503354i
$535$	−6.78839	+	3.91928i	−0.293488	+	0.169445i
$536$	2.47522	−	4.28720i	0.106913	−	0.185179i
$537$	−1.46835	−	0.510630i	−0.0633638	−	0.0220353i
$538$	21.7045	+	12.5311i	0.935747	+	0.540254i
$539$	3.16170	−	13.2109i	0.136184	−	0.569036i
$540$	10.6676	+	16.7621i	0.459062	+	0.721324i
$541$	−18.0931	−	10.4461i	−0.777885	−	0.449112i	0.0577953	−	0.998328i	$-0.481593\pi$
$541$	−18.0931	−	10.4461i	−0.777885	−	0.449112i	−0.835680	+	0.549216i	$0.814926\pi$
$542$	15.1978	+	8.77445i	0.652801	+	0.376895i
$543$	−19.5391	−	22.6168i	−0.838505	−	0.970580i
$544$	1.92020			0.0823281
$545$	−20.8773	+	36.1606i	−0.894286	+	1.54895i
$546$	10.5488	−	30.3337i	0.451448	−	1.29816i
$547$	−20.0363	−	11.5680i	−0.856691	−	0.494611i	0.00621154	−	0.999981i	$-0.498023\pi$
$547$	−20.0363	−	11.5680i	−0.856691	−	0.494611i	−0.862903	+	0.505370i	$0.831356\pi$
$548$	−19.9837	+	11.5376i	−0.853663	+	0.492863i
$549$	9.33579	+	23.5209i	0.398442	+	1.00385i
$550$	−11.0496	+	46.1700i	−0.471157	+	1.96870i
$551$	−2.07406	−	22.8970i	−0.0883578	−	0.975447i
$552$	−5.85698	+	5.05997i	−0.249290	+	0.215367i
$553$	6.67653	+	11.5641i	0.283915	+	0.491755i
$554$	47.6585	−	27.5156i	2.02481	−	1.16903i
$555$	−10.6371	−	55.6329i	−0.451522	−	2.36148i
$556$	−13.0621	+	7.54140i	−0.553956	+	0.319826i
$557$	15.2516	−	26.4166i	0.646232	−	1.11931i	−0.337783	−	0.941224i	$-0.609677\pi$
$557$	15.2516	−	26.4166i	0.646232	−	1.11931i	0.984015	−	0.178083i	$-0.0569896\pi$
$558$	−4.02612	+	27.4267i	−0.170439	+	1.16107i
$559$	−42.9693			−1.81741
$560$	−15.4660	+	26.7879i	−0.653559	+	1.13200i
$561$	−0.0935332	+	2.03262i	−0.00394897	+	0.0858175i
$562$	−26.2686			−1.10807
$563$	−34.0359			−1.43444			−0.717222	−	0.696845i	$-0.754587\pi$
$563$	−34.0359			−1.43444			−0.717222	+	0.696845i	$0.754587\pi$
$564$	1.97562	+	10.3326i	0.0831886	+	0.435081i
$565$	−5.06562	−	8.77391i	−0.213112	−	0.369121i
$566$	48.2007	+	27.8287i	2.02603	+	1.16973i
$567$	−14.9265	+	3.52786i	−0.626853	+	0.148156i
$568$	5.37292	−	3.10206i	0.225443	−	0.130159i
$569$	−17.8409			−0.747929			−0.373964	−	0.927443i	$-0.622002\pi$
$569$	−17.8409			−0.747929			−0.373964	+	0.927443i	$0.622002\pi$
$570$	11.5908	−	46.4890i	0.485484	−	1.94721i
$571$		−	41.0108i		−	1.71625i	−0.513441	−	0.858125i	$-0.671630\pi$
$571$		−	41.0108i		−	1.71625i	0.513441	−	0.858125i	$-0.328370\pi$
$572$	−6.19014	−	20.8429i	−0.258823	−	0.871486i
$573$	−14.2456	−	4.95403i	−0.595118	−	0.206957i
$574$	5.16195	+	2.98025i	0.215455	+	0.124393i
$575$	−19.1564	+	11.0599i	−0.798876	+	0.461231i
$576$	−1.22954	−	0.972814i	−0.0512308	−	0.0405339i
$577$	−34.6605			−1.44294			−0.721468	−	0.692448i	$-0.756532\pi$
$577$	−34.6605			−1.44294			−0.721468	+	0.692448i	$0.756532\pi$
$578$	−29.4834			−1.22635
$579$	−7.27323	−	38.0394i	−0.302265	−	1.58086i
$580$	17.4661	+	10.0840i	0.725239	+	0.418717i
$581$		−	4.94379i		−	0.205103i
$582$	−12.1008	−	14.0068i	−0.501594	−	0.580601i
$583$	−13.0363	+	13.7570i	−0.539908	+	0.569758i
$584$	−16.4438	+	9.49383i	−0.680449	+	0.392857i
$585$	53.2127	+	42.1020i	2.20007	+	1.74070i
$586$	−3.54781	−	6.14499i	−0.146559	−	0.253847i
$587$	−4.97862	+	2.87441i	−0.205489	+	0.118639i	−0.599213	−	0.800589i	$-0.704520\pi$
$587$	−4.97862	+	2.87441i	−0.205489	+	0.118639i	0.393724	+	0.919229i	$0.371187\pi$
$588$	−4.88231	−	5.65133i	−0.201343	−	0.233057i
$589$	18.8426	−	13.2801i	0.776398	−	0.547198i
$590$	26.1184			1.07528
$591$	6.81386	−	19.5937i	0.280285	−	0.805975i
$592$	−22.4959	−	38.9641i	−0.924577	−	1.60141i
$593$	9.39335	−	16.2698i	0.385739	−	0.668119i	−0.606133	−	0.795363i	$-0.707280\pi$
$593$	9.39335	−	16.2698i	0.385739	−	0.668119i	0.991871	+	0.127245i	$0.0406133\pi$
$594$	−19.7489	+	22.7299i	−0.810307	+	0.932619i
$595$	−1.09625	+	1.89876i	−0.0449419	+	0.0778417i
$596$	−18.5925			−0.761577
$597$	26.6039	+	30.7944i	1.08883	+	1.26033i
$598$	14.6885	−	25.4412i	0.600657	−	1.04037i
$599$	16.0533	+	9.26841i	0.655922	+	0.378697i	0.790721	−	0.612176i	$-0.209706\pi$
$599$	16.0533	+	9.26841i	0.655922	+	0.378697i	−0.134799	+	0.990873i	$0.543039\pi$
$600$	−15.3529	−	17.7712i	−0.626780	−	0.725506i
$601$			42.2013i			1.72143i	0.509089	+	0.860714i	$0.329982\pi$
$601$			42.2013i			1.72143i	−0.509089	+	0.860714i	$0.670018\pi$
$602$	10.2731	−	17.7935i	0.418699	−	0.725209i
$603$	8.34038	−	3.31042i	0.339646	−	0.134811i
$604$	−3.74237	−	2.16066i	−0.152275	−	0.0879158i
$605$	−39.8957	+	2.14796i	−1.62199	+	0.0873268i
$606$	−8.57822	+	24.6672i	−0.348466	+	1.00203i
$607$		−	5.60937i		−	0.227677i	−0.993499	−	0.113839i	$-0.963685\pi$
$607$		−	5.60937i		−	0.227677i	0.993499	−	0.113839i	$-0.0363147\pi$
$608$	−2.13173	−	23.5337i	−0.0864530	−	0.954418i
$609$	−11.7812	+	10.1780i	−0.477398	+	0.412434i
$610$	26.7657	+	46.3595i	1.08371	+	1.87704i
$611$	17.9632	+	31.1131i	0.726712	+	1.25870i
$612$	0.877295	+	0.694117i	0.0354625	+	0.0280580i
$613$	15.3065	−	8.83723i	0.618225	−	0.356932i	−0.157953	−	0.987447i	$-0.550489\pi$
$613$	15.3065	−	8.83723i	0.618225	−	0.356932i	0.776178	+	0.630514i	$0.217156\pi$
$614$	−29.0332	−	16.7623i	−1.17168	−	0.676472i
$615$	−9.52960	+	8.23283i	−0.384271	+	0.331980i
$616$	−9.09768	−	2.17729i	−0.366556	−	0.0877257i
$617$	−11.0755	−	6.39445i	−0.445883	−	0.257431i	0.260207	−	0.965553i	$-0.416209\pi$
$617$	−11.0755	−	6.39445i	−0.445883	−	0.257431i	−0.706090	+	0.708122i	$0.749543\pi$
$618$	28.3305	−	5.41686i	1.13962	−	0.217898i
$619$	24.8020			0.996878			0.498439	−	0.866925i	$-0.333907\pi$
$619$	24.8020			0.996878			0.498439	+	0.866925i	$0.333907\pi$
$620$			20.2220i			0.812136i
$621$	−14.0167	+	0.605449i	−0.562473	+	0.0242958i
$622$	21.9187	−	12.6548i	0.878861	−	0.507411i
$623$	−9.97100	+	17.2703i	−0.399480	+	0.691919i
$624$	50.9085	+	17.7039i	2.03797	+	0.708722i
$625$	−0.576856	−	0.999144i	−0.0230742	−	0.0399658i
$626$	−27.1539			−1.08529
$627$	25.0153	−	1.11020i	0.999017	−	0.0443373i
$628$	13.2986			0.530674
$629$	−1.59454	−	2.76182i	−0.0635784	−	0.110121i
$630$	−30.1564	+	11.9695i	−1.20146	+	0.476877i
$631$	16.3795	−	28.3701i	0.652057	−	1.12940i	−0.330565	−	0.943783i	$-0.607239\pi$
$631$	16.3795	−	28.3701i	0.652057	−	1.12940i	0.982623	−	0.185613i	$-0.0594272\pi$
$632$	−11.2306	+	6.48400i	−0.446730	+	0.257920i
$633$	−0.692594	−	3.62231i	−0.0275282	−	0.143974i
$634$			0.855154i			0.0339625i
$635$	37.1954			1.47605
$636$	1.95684	+	10.2344i	0.0775937	+	0.405820i
$637$	−22.0879	−	12.7524i	−0.875154	−	0.505270i
$638$	−7.11396	+	29.7252i	−0.281644	+	1.17683i
$639$	11.1266	+	1.63333i	0.440160	+	0.0646135i
$640$	−36.9767	−	21.3485i	−1.46163	−	0.843873i
$641$	−20.8814	+	12.0559i	−0.824767	+	0.476179i	−0.852057	−	0.523448i	$-0.824645\pi$
$641$	−20.8814	+	12.0559i	−0.824767	+	0.476179i	0.0272907	+	0.999628i	$0.491312\pi$
$642$	−6.41480	+	1.22653i	−0.253172	+	0.0484071i
$643$	1.70104	+	2.94628i	0.0670824	+	0.116190i	0.897616	−	0.440779i	$-0.145298\pi$
$643$	1.70104	+	2.94628i	0.0670824	+	0.116190i	−0.830533	+	0.556969i	$0.811964\pi$
$644$	2.42205	+	4.19512i	0.0954422	+	0.165311i
$645$	28.3790	+	32.8490i	1.11742	+	1.29343i
$646$	−0.243360	−	2.68663i	−0.00957486	−	0.105704i
$647$			22.8749i			0.899305i	0.893203	+	0.449653i	$0.148452\pi$
$647$			22.8749i			0.899305i	−0.893203	+	0.449653i	$0.851548\pi$
$648$	−3.42613	−	14.4960i	−0.134591	−	0.569458i
$649$	3.88617	+	13.0852i	0.152545	+	0.513638i
$650$	77.1935	+	44.5677i	3.02778	+	1.74809i
$651$	−14.7443	−	5.12747i	−0.577876	−	0.200961i
$652$	3.43252	−	5.94529i	0.134428	−	0.232836i
$653$			42.1264i			1.64853i	0.566201	+	0.824267i	$0.308413\pi$
$653$			42.1264i			1.64853i	−0.566201	+	0.824267i	$0.691587\pi$
$654$	−26.3258	+	22.7434i	−1.02942	+	0.889339i
$655$	0.113508	+	0.0655337i	0.00443511	+	0.00256061i
$656$	−5.00169	+	8.66319i	−0.195283	+	0.338241i
$657$	−34.0528	−	4.99879i	−1.32853	−	0.195021i
$658$	−17.1785			−0.669687
$659$	−8.78735	+	15.2201i	−0.342306	+	0.592892i	−0.984861	−	0.173348i	$-0.944541\pi$
$659$	−8.78735	+	15.2201i	−0.342306	+	0.592892i	0.642554	+	0.766240i	$0.277875\pi$
$660$	−11.8457	+	18.4979i	−0.461092	+	0.720029i
$661$	5.26979	−	9.12755i	0.204971	−	0.355020i	−0.745152	−	0.666894i	$-0.767623\pi$
$661$	5.26979	−	9.12755i	0.204971	−	0.355020i	0.950124	+	0.311874i	$0.100957\pi$
$662$	−5.94793	−	10.3021i	−0.231173	−	0.400403i
$663$	3.60846	+	1.25487i	0.140141	+	0.0487352i
$664$	4.80122			0.186324
$665$	24.4879	+	11.3275i	0.949601	+	0.439263i
$666$	6.85417	−	46.6920i	0.265594	−	1.80928i
$667$	−12.3333	+	7.12061i	−0.477546	+	0.275711i
$668$	10.2947	+	17.8310i	0.398314	+	0.689901i
$669$	−21.9779	+	4.20223i	−0.849716	+	0.162468i
$670$	16.4388	−	9.49097i	0.635088	−	0.366668i
$671$	−19.2434	+	20.3073i	−0.742884	+	0.783956i
$672$	−12.1088	+	10.4610i	−0.467106	+	0.403543i
$673$		−	24.5417i		−	0.946015i	−0.881058	−	0.473007i	$-0.843168\pi$
$673$		−	24.5417i		−	0.946015i	0.881058	−	0.473007i	$-0.156832\pi$
$674$	−47.1839	−	27.2416i	−1.81745	−	1.04931i
$675$	−1.83705	−	42.5294i	−0.0707080	−	1.63696i
$676$	−27.1376			−1.04375
$677$	27.2728			1.04818			0.524089	−	0.851664i	$-0.324406\pi$
$677$	27.2728			1.04818			0.524089	+	0.851664i	$0.324406\pi$
$678$	−1.58527	−	8.29105i	−0.0608819	−	0.318416i
$679$	9.02712	−	5.21181i	0.346429	−	0.200011i
$680$	−1.84401	−	1.06464i	−0.0707145	−	0.0408270i
$681$	−16.3674	+	47.0655i	−0.627202	+	1.80356i
$682$	−29.3781	+	8.72500i	−1.12495	+	0.334098i
$683$		−	18.5618i		−	0.710247i	−0.934819	−	0.355124i	$-0.884439\pi$
$683$		−	18.5618i		−	0.710247i	0.934819	−	0.355124i	$-0.115561\pi$
$684$	7.53305	−	11.5226i	0.288033	−	0.440576i
$685$	79.6129			3.04185
$686$	28.6122	−	16.5192i	1.09242	−	0.630707i
$687$	0.881741	−	2.53550i	0.0336405	−	0.0967353i
$688$	29.8625	+	17.2411i	1.13850	+	0.657311i
$689$	17.7924	+	30.8173i	0.677836	+	1.17405i
$690$	−29.1502	+	5.57359i	−1.10973	+	0.212183i
$691$	−2.35530			−0.0895999			−0.0447999	−	0.998996i	$-0.514265\pi$
$691$	−2.35530			−0.0895999			−0.0447999	+	0.998996i	$0.514265\pi$
$692$	−7.49959			−0.285092
$693$	−10.4837	−	13.3272i	−0.398241	−	0.506260i
$694$	20.3167	−	35.1896i	0.771213	−	1.33578i
$695$	52.0378			1.97391
$696$	−9.88452	−	11.4414i	−0.374672	−	0.433687i
$697$	−0.354526	+	0.614057i	−0.0134286	+	0.0232591i
$698$	−46.3040	+	26.7336i	−1.75263	+	1.01188i
$699$	18.3603	−	3.51053i	0.694450	−	0.132781i
$700$	−12.7288	+	7.34896i	−0.481102	+	0.277765i
$701$	−8.94421	−	15.4918i	−0.337818	−	0.585118i	0.646204	−	0.763165i	$-0.276356\pi$
$701$	−8.94421	−	15.4918i	−0.337818	−	0.585118i	−0.984022	+	0.178047i	$0.943022\pi$
$702$	30.3542	+	47.6955i	1.14564	+	1.80015i
$703$	−32.0782	+	22.6085i	−1.20985	+	0.852694i
$704$	0.403432	−	1.68571i	0.0152049	−	0.0635327i
$705$	11.9215	−	34.2810i	0.448990	−	1.29110i
$706$	35.1065	−	20.2687i	1.32125	−	0.762824i
$707$	−12.7366	−	7.35346i	−0.479008	−	0.276555i
$708$	7.08816	+	2.46497i	0.266389	+	0.0926392i
$709$	7.48710	−	12.9680i	0.281184	−	0.487025i	−0.690493	−	0.723339i	$-0.742606\pi$
$709$	7.48710	−	12.9680i	0.281184	−	0.487025i	0.971677	+	0.236315i	$0.0759396\pi$
$710$	23.7891			0.892788
$711$	−23.2570	−	3.41403i	−0.872207	−	0.128036i
$712$	−16.7723	−	9.68347i	−0.628567	−	0.362903i
$713$	−12.3662	−	7.13965i	−0.463119	−	0.267382i
$714$	−1.38235	+	1.19424i	−0.0517330	+	0.0446933i
$715$	−17.4599	+	72.9552i	−0.652965	+	2.72837i
$716$	−0.818303	−	0.472448i	−0.0305814	−	0.0176562i
$717$	−5.85250	+	16.8292i	−0.218566	+	0.628499i
$718$	−16.7718	+	29.0496i	−0.625917	+	1.08412i
$719$	−4.45558	+	2.57243i	−0.166165	+	0.0959355i	−0.580776	−	0.814063i	$-0.697251\pi$
$719$	−4.45558	+	2.57243i	−0.166165	+	0.0959355i	0.414611	+	0.909999i	$0.363918\pi$
$720$	−20.0882	−	50.6108i	−0.748644	−	1.88615i
$721$			16.2429i			0.604917i
$722$	−32.6567	+	5.96516i	−1.21536	+	0.222000i
$723$	−0.662773	+	0.572584i	−0.0246488	+	0.0212946i
$724$	−9.08307	−	15.7323i	−0.337570	−	0.584688i
$725$	−21.6053	−	37.4214i	−0.802399	−	1.38980i
$726$	−31.9842	−	9.22801i	−1.18705	−	0.342484i
$727$	8.84051	+	15.3122i	0.327877	+	0.567899i	0.982090	−	0.188411i	$-0.0603337\pi$
$727$	8.84051	+	15.3122i	0.327877	+	0.567899i	−0.654214	+	0.756310i	$0.727000\pi$
$728$	−8.78194	+	15.2108i	−0.325480	+	0.563748i
$729$	11.4335	−	24.4597i	0.423462	−	0.905914i
$730$	−72.8063			−2.69468
$731$	2.11669	+	1.22207i	0.0782885	+	0.0451999i
$732$	2.88857	+	15.1074i	0.106765	+	0.558385i
$733$			37.4213i			1.38219i	0.722766	+	0.691093i	$0.242870\pi$
$733$			37.4213i			1.38219i	−0.722766	+	0.691093i	$0.757130\pi$
$734$	−0.228942			−0.00845039
$735$	4.83895	+	25.3080i	0.178487	+	0.933500i
$736$	−12.6762	+	7.31860i	−0.467250	+	0.269767i
$737$	7.20088	+	6.82361i	0.265248	+	0.251351i
$738$	−9.75253	+	3.87093i	−0.358996	+	0.142491i
$739$	12.9424	−	7.47230i	0.476094	−	0.274873i	−0.242693	−	0.970103i	$-0.578031\pi$
$739$	12.9424	−	7.47230i	0.476094	−	0.274873i	0.718787	+	0.695230i	$0.244697\pi$
$740$		−	34.4265i		−	1.26554i
$741$	11.3735	−	45.6177i	0.417818	−	1.67581i
$742$	−17.0152			−0.624647
$743$	4.96427	+	8.59837i	0.182121	+	0.315444i	0.942603	−	0.333916i	$-0.108370\pi$
$743$	4.96427	+	8.59837i	0.182121	+	0.315444i	−0.760481	+	0.649360i	$0.775037\pi$
$744$	4.97961	−	14.3192i	0.182561	−	0.524966i
$745$	55.5527	+	32.0733i	2.03529	+	1.17508i
$746$	4.19493	−	2.42194i	0.153587	−	0.0886737i
$747$	6.82500	+	5.39995i	0.249714	+	0.197574i
$748$	−0.287855	+	1.20278i	−0.0105250	+	0.0439781i
$749$		−	3.67783i		−	0.134385i
$750$	−6.59001	−	34.4661i	−0.240633	−	1.25853i
$751$	−17.0437	+	29.5205i	−0.621932	+	1.07722i	0.367193	+	0.930145i	$0.380319\pi$
$751$	−17.0437	+	29.5205i	−0.621932	+	1.07722i	−0.989126	+	0.147074i	$0.953015\pi$
$752$		−	28.8303i		−	1.05133i
$753$	23.5340	−	20.3316i	0.857628	−	0.740923i
$754$	49.6987	+	28.6936i	1.80992	+	1.04496i
$755$	7.45457	+	12.9117i	0.271300	+	0.469905i
$756$	−9.31366	+	0.402301i	−0.338735	+	0.0146315i
$757$	2.29611	+	3.97699i	0.0834537	+	0.144546i	0.904731	−	0.425983i	$-0.140072\pi$
$757$	2.29611	+	3.97699i	0.0834537	+	0.144546i	−0.821278	+	0.570529i	$0.806738\pi$
$758$	−10.3231	−	17.8802i	−0.374953	−	0.649437i
$759$	−7.12962	−	13.7748i	−0.258789	−	0.499994i
$760$	−11.0009	+	23.7818i	−0.399044	+	0.862655i
$761$	−35.6275			−1.29150			−0.645749	−	0.763550i	$-0.723455\pi$
$761$	−35.6275			−1.29150			−0.645749	+	0.763550i	$0.723455\pi$
$762$	29.2713	+	10.1794i	1.06039	+	0.368759i
$763$	−9.79559	−	16.9665i	−0.354624	−	0.614227i
$764$	−7.93901	−	4.58359i	−0.287223	−	0.165828i
$765$	−1.42388	−	3.58736i	−0.0514804	−	0.129701i
$766$	−18.3740	−	10.6082i	−0.663879	−	0.383291i
$767$	25.6289			0.925406
$768$	−22.0732	−	25.5500i	−0.796498	−	0.921956i
$769$	−3.72361	−	2.14983i	−0.134277	−	0.0775248i	0.431357	−	0.902181i	$-0.358035\pi$
$769$	−3.72361	−	2.14983i	−0.134277	−	0.0775248i	−0.565634	+	0.824657i	$0.691368\pi$
$770$	−26.0363	−	24.6722i	−0.938282	−	0.889124i
$771$	−25.1184	+	21.7003i	−0.904616	+	0.781517i
$772$		−	23.5394i		−	0.847202i
$773$	−8.58569	−	4.95695i	−0.308806	−	0.178289i	0.337586	−	0.941295i	$-0.390390\pi$
$773$	−8.58569	−	4.95695i	−0.308806	−	0.178289i	−0.646392	+	0.763006i	$0.723723\pi$
$774$	13.3433	+	33.6175i	0.479615	+	1.20836i
$775$	21.6630	−	37.5215i	0.778159	−	1.34781i
$776$	5.06151	+	8.76680i	0.181698	+	0.314710i
$777$	25.1012	+	8.72915i	0.900499	+	0.313156i
$778$		−	11.7403i		−	0.420910i
$779$	7.91937	+	3.66331i	0.283741	+	0.131252i
$780$	26.9617	+	31.2085i	0.965384	+	1.11744i
$781$	3.53959	+	11.9182i	0.126656	+	0.426467i
$782$	−1.44712	+	0.835497i	−0.0517490	+	0.0298773i
$783$	−1.18273	−	27.3813i	−0.0422672	−	0.978528i
$784$	10.2336	+	17.7252i	0.365487	+	0.633042i
$785$	−39.7352	−	22.9411i	−1.41821	−	0.818803i
$786$	0.0713914	+	0.0826364i	0.00254645	+	0.00294754i
$787$			17.3576i			0.618732i	0.950943	+	0.309366i	$0.100117\pi$
$787$			17.3576i			0.618732i	−0.950943	+	0.309366i	$0.899883\pi$
$788$	6.30435	−	10.9195i	0.224583	−	0.388990i
$789$	−48.2382	+	9.22325i	−1.71732	+	0.328356i
$790$	−49.7245			−1.76912
$791$	4.75355			0.169017
$792$	12.9429	−	10.1813i	0.459907	−	0.361778i
$793$	26.2641	+	45.4907i	0.932665	+	1.61542i
$794$	−34.5497	+	59.8418i	−1.22612	+	2.12371i
$795$	11.8082	−	33.9551i	0.418793	−	1.20426i
$796$	12.3673	+	21.4207i	0.438346	+	0.759237i
$797$			23.0045i			0.814863i	0.913236	+	0.407431i	$0.133575\pi$
$797$			23.0045i			0.814863i	−0.913236	+	0.407431i	$0.866425\pi$
$798$	16.1710	+	15.6160i	0.572448	+	0.552801i
$799$		−	2.04353i		−	0.0722948i
$800$	−22.2060	−	38.4619i	−0.785101	−	1.35983i
$801$	−12.9509	−	32.6290i	−0.457599	−	1.15289i
$802$	−21.0246	−	12.1385i	−0.742403	−	0.428627i
$803$	−10.8329	−	36.4756i	−0.382284	−	1.28720i
$804$	5.35700	−	1.02427i	0.188927	−	0.0361233i
$805$		−	16.7129i		−	0.589051i
$806$			57.5406i			2.02678i
$807$	−4.66585	−	24.4027i	−0.164246	−	0.859014i
$808$	7.14140	−	12.3693i	0.251234	−	0.435150i
$809$	10.7210			0.376930			0.188465	−	0.982080i	$-0.439649\pi$
$809$	10.7210			0.376930			0.188465	+	0.982080i	$0.439649\pi$
$810$	16.4147	−	54.7054i	0.576755	−	1.92215i
$811$	4.65556	+	2.68789i	0.163479	+	0.0943846i	0.579507	−	0.814967i	$-0.303245\pi$
$811$	4.65556	+	2.68789i	0.163479	+	0.0943846i	−0.416028	+	0.909352i	$0.636578\pi$
$812$	−8.19504	+	4.73141i	−0.287590	+	0.166040i
$813$	−3.26709	−	17.0871i	−0.114582	−	0.599270i
$814$	50.0141	−	14.8537i	1.75299	−	0.520621i
$815$	−20.5121	+	11.8427i	−0.718508	+	0.414831i
$816$	−2.00427	−	2.31996i	−0.0701634	−	0.0812150i
$817$	12.6276	−	27.2985i	0.441785	−	0.955052i
$818$		−	18.0702i		−	0.631810i
$819$	−29.5912	+	11.7452i	−1.03400	+	0.410411i
$820$	−6.62883	+	3.82716i	−0.231489	+	0.133650i
$821$	−27.4408	+	47.5289i	−0.957691	+	1.65877i	−0.229603	+	0.973284i	$0.573743\pi$
$821$	−27.4408	+	47.5289i	−0.957691	+	1.65877i	−0.728087	+	0.685485i	$0.759590\pi$
$822$	62.6523	+	21.7879i	2.18525	+	0.759939i
$823$	−1.13133	+	1.95952i	−0.0394357	+	0.0683047i	−0.885070	−	0.465459i	$-0.845889\pi$
$823$	−1.13133	+	1.95952i	−0.0394357	+	0.0683047i	0.845634	+	0.533763i	$0.179223\pi$
$824$	−15.7745			−0.549530
$825$	41.7954	−	21.6326i	1.45513	−	0.753150i
$826$	−6.12734	+	10.6129i	−0.213197	+	0.369269i
$827$	13.1262	−	22.7353i	0.456444	−	0.790584i	−0.542326	−	0.840168i	$-0.682456\pi$
$827$	13.1262	−	22.7353i	0.456444	−	0.790584i	0.998770	+	0.0495839i	$0.0157895\pi$
$828$	−8.43698	−	1.23851i	−0.293205	−	0.0430412i
$829$	−26.8473			−0.932446			−0.466223	−	0.884667i	$-0.654386\pi$
$829$	−26.8473			−0.932446			−0.466223	+	0.884667i	$0.654386\pi$
$830$	15.9434	+	9.20491i	0.553403	+	0.319507i
$831$	−51.5269	−	17.9189i	−1.78745	−	0.621600i
$832$	−2.81841	−	1.62721i	−0.0977107	−	0.0564133i
$833$	0.725373	+	1.25638i	0.0251327	+	0.0435311i
$834$	40.9517	+	14.2413i	1.41804	+	0.493136i
$835$		−	71.0365i		−	2.45832i
$836$	15.0607	+	2.19262i	0.520884	+	0.0758334i
$837$	23.1834	−	14.7543i	0.801334	−	0.509982i
$838$	−10.2465	+	5.91580i	−0.353958	+	0.204358i
$839$	26.5383	−	15.3219i	0.916205	−	0.528971i	0.0337827	−	0.999429i	$-0.489245\pi$
$839$	26.5383	−	15.3219i	0.916205	−	0.528971i	0.882422	+	0.470458i	$0.155911\pi$
$840$	17.4283	−	3.33233i	0.601333	−	0.114976i
$841$	0.590093	+	1.02207i	0.0203480	+	0.0352438i
$842$	8.46036	−	14.6538i	0.291563	−	0.505002i
$843$	17.0239	+	19.7054i	0.586335	+	0.678690i
$844$		−	2.24154i		−	0.0771571i
$845$	81.0848	+	46.8143i	2.78940	+	1.61046i
$846$	18.7635	−	23.7152i	0.645104	−	0.815347i
$847$	8.48670	−	16.7150i	0.291606	−	0.574335i
$848$		−	28.5562i		−	0.980625i
$849$	−10.3618	−	54.1927i	−0.355615	−	1.85989i
$850$	−2.53506	−	4.39085i	−0.0869517	−	0.150605i
$851$	21.0526	+	12.1547i	0.721674	+	0.416659i
$852$	6.45602	+	2.24514i	0.221180	+	0.0769171i
$853$	30.6277	−	17.6829i	1.04867	−	0.605452i	0.126396	−	0.991980i	$-0.459659\pi$
$853$	30.6277	−	17.6829i	1.04867	−	0.605452i	0.922278	+	0.386528i	$0.126326\pi$
$854$	−25.1168			−0.859479
$855$	−42.3853	+	21.4333i	−1.44955	+	0.733005i
$856$	3.57178			0.122081
$857$	−7.27617	−	12.6027i	−0.248549	−	0.430500i	0.714574	−	0.699560i	$-0.246620\pi$
$857$	−7.27617	−	12.6027i	−0.248549	−	0.430500i	−0.963124	+	0.269060i	$0.913287\pi$
$858$	−33.7061	+	52.6346i	−1.15071	+	1.79692i
$859$	0.506499	−	0.877283i	0.0172815	−	0.0299325i	−0.857255	−	0.514892i	$-0.827832\pi$
$859$	0.506499	−	0.877283i	0.0172815	−	0.0299325i	0.874537	+	0.484959i	$0.161166\pi$
$860$	13.1924	+	22.8499i	0.449858	+	0.779176i
$861$	−1.10967	−	5.80365i	−0.0378175	−	0.197788i
$862$	22.5648			0.768559
$863$			19.2866i			0.656522i	0.944587	+	0.328261i	$0.106463\pi$
$863$			19.2866i			0.656522i	−0.944587	+	0.328261i	$0.893537\pi$
$864$	−1.21561	−	28.1426i	−0.0413560	−	0.957432i
$865$	22.4081	+	12.9373i	0.761898	+	0.439882i
$866$	−9.07662			−0.308436
$867$	19.1073	+	22.1170i	0.648919	+	0.751131i
$868$	−8.21695	−	4.74406i	−0.278902	−	0.161024i
$869$	−7.39854	−	24.9117i	−0.250978	−	0.845073i
$870$	−10.8879	−	56.9441i	−0.369133	−	1.93059i
$871$	16.1308	−	9.31311i	0.546570	−	0.315563i
$872$	16.4772	−	9.51311i	0.557988	−	0.322155i
$873$	−2.66504	+	18.1548i	−0.0901980	+	0.614448i
$874$	11.8463	+	16.8082i	0.400705	+	0.568545i
$875$	19.7607			0.668032
$876$	−19.7586	−	6.87123i	−0.667582	−	0.232157i
$877$	26.0817	−	15.0583i	0.880718	−	0.508483i	0.00982272	−	0.999952i	$-0.496873\pi$
$877$	26.0817	−	15.0583i	0.880718	−	0.508483i	0.870895	+	0.491469i	$0.163540\pi$
$878$	25.2971	+	14.6053i	0.853735	+	0.492904i
$879$	−2.31043	+	6.64378i	−0.0779289	+	0.224089i
$880$	41.4069	−	43.6961i	1.39582	−	1.47300i
$881$			32.2795i			1.08752i	0.839239	+	0.543762i	$0.183001\pi$
$881$			32.2795i			1.08752i	−0.839239	+	0.543762i	$0.816999\pi$
$882$	−3.11804	+	21.2407i	−0.104990	+	0.715212i
$883$	−20.8517	+	36.1161i	−0.701714	+	1.21540i	0.266150	+	0.963932i	$0.414248\pi$
$883$	−20.8517	+	36.1161i	−0.701714	+	1.21540i	−0.967864	+	0.251473i	$0.919085\pi$
$884$	2.01098	+	1.16104i	0.0676365	+	0.0390499i
$885$	−16.9265	−	19.5927i	−0.568980	−	0.658601i
$886$		−	65.8647i		−	2.21277i
$887$	5.38330	−	9.32415i	0.180754	−	0.313074i	−0.761384	−	0.648301i	$-0.775480\pi$
$887$	5.38330	−	9.32415i	0.180754	−	0.313074i	0.942137	+	0.335227i	$0.108813\pi$
$888$	−8.47742	+	24.3773i	−0.284484	+	0.818049i
$889$	−8.72599	+	15.1139i	−0.292660	+	0.506903i
$890$	−37.1303	−	64.3116i	−1.24461	−	2.15573i
$891$	29.8495	+	0.0840462i	0.999996	+	0.00281565i
$892$	−13.6003			−0.455372
$893$	−25.0451	+	2.26864i	−0.838104	+	0.0759170i
$894$	34.9402	+	40.4437i	1.16858	+	1.35264i
$895$	1.63001	+	2.82326i	0.0544853	+	0.0943713i
$896$	17.3494	−	10.0167i	0.579602	−	0.334633i
$897$	−28.6039	+	5.46914i	−0.955057	+	0.182609i
$898$	−44.8817	+	25.9124i	−1.49772	+	0.864709i
$899$	13.9471	−	24.1571i	0.465162	−	0.805684i
$900$	3.75787	−	25.5994i	0.125262	−	0.853313i
$901$		−	2.02410i		−	0.0674326i
$902$	−8.42010	−	7.97896i	−0.280359	−	0.265670i
$903$	−20.0055	+	3.82509i	−0.665740	+	0.127291i
$904$			4.61647i			0.153542i
$905$			62.6758i			2.08341i
$906$	2.33288	+	12.2011i	0.0775049	+	0.405355i
$907$	20.9937	+	36.3621i	0.697084	+	1.20739i	0.969473	+	0.245198i	$0.0788529\pi$
$907$	20.9937	+	36.3621i	0.697084	+	1.20739i	−0.272389	+	0.962187i	$0.587814\pi$
$908$	−15.1436	+	26.2294i	−0.502557	+	0.870454i
$909$	24.0634	−	9.55112i	0.798131	−	0.316791i
$910$	−58.3242	+	33.6735i	−1.93343	+	1.11626i
$911$		−	55.6095i		−	1.84243i	−0.389058	−	0.921213i	$-0.627200\pi$
$911$		−	55.6095i		−	1.84243i	0.389058	−	0.921213i	$-0.372800\pi$
$912$	−26.2081	+	27.1395i	−0.867835	+	0.898679i
$913$	−2.23939	+	9.35715i	−0.0741131	+	0.309677i
$914$	−12.4795	+	7.20505i	−0.412785	+	0.238322i
$915$	17.4305	−	50.1225i	0.576236	−	1.65700i
$916$	0.815809	−	1.41302i	0.0269551	−	0.0466876i
$917$	−0.0532575	+	0.0307482i	−0.00175872	+	0.00101540i
$918$	−0.138775	−	3.21279i	−0.00458027	−	0.106038i
$919$			5.06389i			0.167042i	0.996506	+	0.0835211i	$0.0266166\pi$
$919$			5.06389i			0.167042i	−0.996506	+	0.0835211i	$0.973383\pi$
$920$	16.2309			0.535117
$921$	6.24130	+	32.6424i	0.205658	+	1.07560i
$922$	−12.0242	+	20.8265i	−0.395995	+	0.685883i
$923$	23.3432			0.768352
$924$	−4.73740	−	9.15291i	−0.155849	−	0.301109i
$925$	−36.8798	+	63.8776i	−1.21260	+	2.10028i
$926$	5.52211	+	9.56458i	0.181468	+	0.314312i
$927$	−22.4236	−	17.7416i	−0.736489	−	0.582711i
$928$	−14.2967	−	24.7626i	−0.469311	−	0.812871i
$929$	0.00513951	−	0.00296729i	0.000168622	−	9.73538e-5i	−0.499916	−	0.866074i	$-0.666636\pi$
$929$	0.00513951	−	0.00296729i	0.000168622	−	9.73538e-5i	0.500084	+	0.865977i	$0.333302\pi$
$930$	43.9884	−	38.0026i	1.44244	−	1.24615i
$931$	14.5927	−	10.2848i	0.478258	−	0.337072i
$932$	11.3616			0.372163
$933$	−23.6979	−	8.24114i	−0.775834	−	0.269803i
$934$	11.8715	−	6.85402i	0.388448	−	0.224270i
$935$	2.93497	−	3.09724i	0.0959837	−	0.101290i
$936$	−11.4065	−	28.7379i	−0.372834	−	0.939327i
$937$	−19.8827	−	11.4793i	−0.649541	−	0.375013i	0.138739	−	0.990329i	$-0.455695\pi$
$937$	−19.8827	−	11.4793i	−0.649541	−	0.375013i	−0.788280	+	0.615316i	$0.789028\pi$
$938$			8.90629i			0.290801i
$939$	17.5976	+	20.3695i	0.574277	+	0.664733i
$940$	11.0301	−	19.1047i	0.359762	−	0.623125i
$941$	21.4985	−	37.2365i	0.700832	−	1.21388i	−0.267343	−	0.963602i	$-0.586146\pi$
$941$	21.4985	−	37.2365i	0.700832	−	1.21388i	0.968175	−	0.250275i	$-0.0805211\pi$
$942$	−24.9917	−	28.9282i	−0.814273	−	0.942531i
$943$		−	5.40492i		−	0.176008i
$944$	−17.8114	−	10.2834i	−0.579710	−	0.334696i
$945$	28.5224	+	14.8647i	0.927834	+	0.483549i
$946$	−27.5039	+	29.0245i	−0.894228	+	0.943668i
$947$	26.5443	−	15.3254i	0.862574	−	0.498007i	−0.00229951	−	0.999997i	$-0.500732\pi$
$947$	26.5443	−	15.3254i	0.862574	−	0.498007i	0.864873	+	0.501990i	$0.167399\pi$
$948$	−13.4945	−	4.69284i	−0.438282	−	0.152416i
$949$	−71.4419			−2.31910
$950$	−50.9992	+	35.9438i	−1.65463	+	1.16617i
$951$	0.641494	−	0.554200i	0.0208019	−	0.0179712i
$952$	0.865204	−	0.499526i	0.0280414	−	0.0161897i
$953$	−26.8930	−	46.5801i	−0.871151	−	1.50888i	−0.860807	−	0.508932i	$-0.830041\pi$
$953$	−26.8930	−	46.5801i	−0.871151	−	1.50888i	−0.0103443	−	0.999946i	$-0.503293\pi$
$954$	18.5852	−	23.4898i	0.601717	−	0.760510i
$955$	15.8140	+	27.3907i	0.511730	+	0.886342i
$956$	−5.41488	+	9.37885i	−0.175130	+	0.303334i
$957$	26.9087	−	13.9275i	0.869835	−	0.450212i
$958$	60.9705			1.96987
$959$	−18.6771	+	32.3497i	−0.603115	+	1.04463i
$960$	0.617449	+	3.22929i	0.0199281	+	0.104225i
$961$	−3.03122			−0.0977812
$962$		−	97.9587i		−	3.15831i
$963$	5.07732	+	4.01719i	0.163614	+	0.129452i
$964$	−0.461027	+	0.266174i	−0.0148487	+	0.00857290i
$965$	−40.6072	+	70.3337i	−1.30719	+	2.26412i
$966$	4.57385	−	13.1524i	0.147161	−	0.423171i
$967$	7.21321	−	4.16455i	0.231961	−	0.133923i	−0.379515	−	0.925185i	$-0.623909\pi$
$967$	7.21321	−	4.16455i	0.231961	−	0.133923i	0.611476	+	0.791263i	$0.290576\pi$
$968$	16.2330	+	8.24197i	0.521749	+	0.264907i
$969$	−1.85766	+	1.92368i	−0.0596766	+	0.0617975i
$970$			38.8158i			1.24630i
$971$	−34.1584	+	19.7213i	−1.09619	+	0.632888i	−0.935219	−	0.354070i	$-0.884797\pi$
$971$	−34.1584	+	19.7213i	−1.09619	+	0.632888i	−0.160976	+	0.986958i	$0.551464\pi$
$972$	9.61765	−	13.2971i	0.308486	−	0.426505i
$973$	−12.2080	+	21.1449i	−0.391371	+	0.677874i
$974$	−32.2105	−	55.7902i	−1.03209	−	1.78763i
$975$	−16.5944	−	86.7897i	−0.531446	−	2.77949i
$976$		−	42.1530i		−	1.34929i
$977$		−	51.3981i		−	1.64437i	−0.569219	−	0.822186i	$-0.692754\pi$
$977$		−	51.3981i		−	1.64437i	0.569219	−	0.822186i	$-0.307246\pi$
$978$	−19.3833	+	3.70613i	−0.619808	+	0.118509i
$979$	26.6951	−	28.1711i	0.853181	−	0.900351i
$980$			15.6610i			0.500272i
$981$	34.1220	+	5.00895i	1.08943	+	0.159923i
$982$	−26.0230	+	45.0731i	−0.830426	+	1.43834i
$983$	23.3759	−	13.4961i	0.745576	−	0.430459i	−0.0785171	−	0.996913i	$-0.525019\pi$
$983$	23.3759	−	13.4961i	0.745576	−	0.430459i	0.824093	+	0.566454i	$0.191685\pi$
$984$	5.63628	−	1.07767i	0.179678	−	0.0343549i
$985$	−37.6737	+	21.7509i	−1.20038	+	0.693042i
$986$	−1.63212	−	2.82692i	−0.0519773	−	0.0900273i
$987$	11.1329	+	12.8864i	0.354363	+	0.410180i
$988$	11.9970	−	25.9351i	0.381675	−	0.825107i
$989$	−18.6310			−0.592432
$990$	62.4991	−	8.99488i	1.98635	−	0.285876i
$991$	24.5610	+	42.5409i	0.780206	+	1.35136i	0.931822	+	0.362916i	$0.118219\pi$
$991$	24.5610	+	42.5409i	0.780206	+	1.35136i	−0.151616	+	0.988439i	$0.548448\pi$
$992$	14.3349	−	24.8288i	0.455133	−	0.788314i
$993$	−3.87345	+	11.1383i	−0.122920	+	0.353464i
$994$	−5.58089	+	9.66638i	−0.177015	+	0.306599i
$995$		−	85.3376i		−	2.70538i
$996$	3.45808	+	4.00277i	0.109573	+	0.126833i
$997$	21.7860	+	12.5782i	0.689970	+	0.398355i	0.803601	−	0.595168i	$-0.202915\pi$
$997$	21.7860	+	12.5782i	0.689970	+	0.398355i	−0.113631	+	0.993523i	$0.536248\pi$
$998$	10.0126	−	17.3424i	0.316944	−	0.548963i
$999$	−39.4680	+	25.1181i	−1.24871	+	0.794701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.l.a.197.15	✓	152
3.2	odd	2	inner	627.2.l.a.197.62	yes	152
11.10	odd	2	inner	627.2.l.a.197.61	yes	152
19.11	even	3	inner	627.2.l.a.296.16	yes	152
33.32	even	2	inner	627.2.l.a.197.16	yes	152
57.11	odd	6	inner	627.2.l.a.296.61	yes	152
209.87	odd	6	inner	627.2.l.a.296.62	yes	152
627.296	even	6	inner	627.2.l.a.296.15	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.l.a.197.15	✓	152	1.1	even	1	trivial
627.2.l.a.197.16	yes	152	33.32	even	2	inner
627.2.l.a.197.61	yes	152	11.10	odd	2	inner
627.2.l.a.197.62	yes	152	3.2	odd	2	inner
627.2.l.a.296.15	yes	152	627.296	even	6	inner
627.2.l.a.296.16	yes	152	19.11	even	3	inner
627.2.l.a.296.61	yes	152	57.11	odd	6	inner
627.2.l.a.296.62	yes	152	209.87	odd	6	inner

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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.873606 - 1.51313i) q^{2} +(-0.568916 + 1.63595i) q^{3} +(-0.526375 + 0.911708i) q^{4} +(3.14552 - 1.81607i) q^{5} +(2.97241 - 0.568333i) q^{6} +1.70419i q^{7} -1.65505 q^{8} +(-2.35267 - 1.86144i) q^{9} +(-5.49590 - 3.17306i) q^{10} +(0.771949 - 3.22554i) q^{11} +(-1.19205 - 1.37981i) q^{12} +(-5.39290 - 3.11359i) q^{13} +(2.57866 - 1.48879i) q^{14} +(1.18146 + 6.17911i) q^{15} +(2.49861 + 4.32772i) q^{16} +(0.177104 + 0.306754i) q^{17} +(-0.761289 + 5.18606i) q^{18} +(3.56291 - 2.51111i) q^{19} +3.82373i q^{20} +(-2.78797 - 0.969541i) q^{21} +(-5.55504 + 1.64979i) q^{22} +(-2.33830 - 1.35002i) q^{23} +(0.941582 - 2.70757i) q^{24} +(4.09621 - 7.09485i) q^{25} +10.8802i q^{26} +(4.38369 - 2.78985i) q^{27} +(-1.55372 - 0.897043i) q^{28} +(2.63722 - 4.56781i) q^{29} +(8.31767 - 7.18581i) q^{30} +5.28855 q^{31} +(2.71055 - 4.69481i) q^{32} +(4.83765 + 3.09793i) q^{33} +(0.309439 - 0.535964i) q^{34} +(3.09493 + 5.36057i) q^{35} +(2.93547 - 1.16513i) q^{36} -9.00338 q^{37} +(-6.91221 - 3.19743i) q^{38} +(8.16179 - 7.05115i) q^{39} +(-5.20599 + 3.00568i) q^{40} +(1.00090 + 1.73360i) q^{41} +(0.968548 + 5.06556i) q^{42} +(5.97582 - 3.45014i) q^{43} +(2.53441 + 2.40163i) q^{44} +(-10.7809 - 1.58258i) q^{45} +4.71754i q^{46} +(-4.99634 - 2.88464i) q^{47} +(-8.50143 + 1.62549i) q^{48} +4.09573 q^{49} -14.3139 q^{50} +(-0.602592 + 0.115217i) q^{51} +(5.67738 - 3.27783i) q^{52} +(-4.94884 - 2.85721i) q^{53} +(-8.05102 - 4.19586i) q^{54} +(-3.42962 - 11.5479i) q^{55} -2.82052i q^{56} +(2.08105 + 7.25736i) q^{57} -9.21558 q^{58} +(-3.56425 + 2.05782i) q^{59} +(-6.25544 - 2.17538i) q^{60} +(-7.30518 - 4.21765i) q^{61} +(-4.62011 - 8.00227i) q^{62} +(3.17224 - 4.00940i) q^{63} +0.522614 q^{64} -22.6180 q^{65} +(0.461373 - 10.0264i) q^{66} +(-1.49556 + 2.59038i) q^{67} -0.372893 q^{68} +(3.53886 - 3.05730i) q^{69} +(5.40750 - 9.36606i) q^{70} +(-3.24639 + 1.87430i) q^{71} +(3.89378 + 3.08076i) q^{72} +(9.93554 - 5.73629i) q^{73} +(7.86541 + 13.6233i) q^{74} +(9.27642 + 10.7376i) q^{75} +(0.413970 + 4.57012i) q^{76} +(5.49693 + 1.31555i) q^{77} +(-17.7995 - 6.18992i) q^{78} +(6.78568 - 3.91771i) q^{79} +(15.7189 + 9.07529i) q^{80} +(2.07011 + 8.75869i) q^{81} +(1.74878 - 3.02897i) q^{82} -2.90096 q^{83} +(2.35146 - 2.03148i) q^{84} +(1.11417 + 0.643268i) q^{85} +(-10.4410 - 6.02813i) q^{86} +(5.97235 + 6.91307i) q^{87} +(-1.27761 + 5.33842i) q^{88} +(10.1340 + 5.85087i) q^{89} +(7.02358 + 17.6954i) q^{90} +(5.30616 - 9.19053i) q^{91} +(2.46165 - 1.42123i) q^{92} +(-3.00874 + 8.65181i) q^{93} +10.0801i q^{94} +(6.64688 - 14.3692i) q^{95} +(6.13841 + 7.10528i) q^{96} +(-3.05823 - 5.29701i) q^{97} +(-3.57806 - 6.19738i) q^{98} +(-7.82027 + 6.15169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 76 q^{4} - 8 q^{9} - 14 q^{15} - 76 q^{16} + 4 q^{22} + 60 q^{25} + 12 q^{27} - 16 q^{31} + 16 q^{33} - 16 q^{34} - 10 q^{36} - 16 q^{37} + 50 q^{42} - 108 q^{45} + 54 q^{48} - 80 q^{49} + 32 q^{55}+ \cdots + 60 q^{99}+O(q^{100}) \) 152 * q - 76 * q^4 - 8 * q^9 - 14 * q^15 - 76 * q^16 + 4 * q^22 + 60 * q^25 + 12 * q^27 - 16 * q^31 + 16 * q^33 - 16 * q^34 - 10 * q^36 - 16 * q^37 + 50 * q^42 - 108 * q^45 + 54 * q^48 - 80 * q^49 + 32 * q^55 - 40 * q^58 + 2 * q^60 + 152 * q^64 - 10 * q^66 - 16 * q^67 - 32 * q^69 - 4 * q^70 - 20 * q^75 - 58 * q^78 + 16 * q^81 - 40 * q^82 - 120 * q^88 - 16 * q^91 - 12 * q^93 + 4 * q^97 + 60 * q^99

Introduction

L-functions

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