LMFDB - Embedded newform 429.2.bb.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45613 - 2.00419i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.27843 + 3.93462i) q^{4} +(-2.20631 + 3.03673i) q^{5} +(1.45613 - 2.00419i) q^{6} +(-2.63274 - 0.855429i) q^{7} +(5.03515 - 1.63602i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.45613 - 2.00419i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.27843 + 3.93462i) q^{4} +(-2.20631 + 3.03673i) q^{5} +(1.45613 - 2.00419i) q^{6} +(-2.63274 - 0.855429i) q^{7} +(5.03515 - 1.63602i) q^{8} +(-0.809017 + 0.587785i) q^{9} +9.29887 q^{10} +(0.894146 - 3.19382i) q^{11} -4.13710 q^{12} +(3.56452 + 0.542421i) q^{13} +(2.11917 + 6.52213i) q^{14} +(-3.56989 - 1.15993i) q^{15} +(-3.91677 - 2.84570i) q^{16} +(-6.24007 - 4.53368i) q^{17} +(2.35607 + 0.765533i) q^{18} +(4.67948 - 1.52046i) q^{19} +(-9.12774 - 12.5633i) q^{20} -2.76822i q^{21} +(-7.70303 + 2.85858i) q^{22} -1.13110 q^{23} +(3.11189 + 4.28316i) q^{24} +(-2.80882 - 8.64467i) q^{25} +(-4.10329 - 7.93381i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(6.73156 - 9.26520i) q^{28} +(1.45298 - 4.47181i) q^{29} +(2.87351 + 8.84375i) q^{30} +(-2.05085 - 2.82276i) q^{31} +1.40512i q^{32} +(3.31381 - 0.136562i) q^{33} +19.1079i q^{34} +(8.40635 - 6.10757i) q^{35} +(-1.27843 - 3.93462i) q^{36} +(1.99803 + 0.649200i) q^{37} +(-9.86122 - 7.16460i) q^{38} +(0.585624 + 3.55767i) q^{39} +(-6.14097 + 18.9000i) q^{40} +(-5.53373 + 1.79802i) q^{41} +(-5.54805 + 4.03090i) q^{42} -1.07260 q^{43} +(11.4234 + 7.60121i) q^{44} -3.75360i q^{45} +(1.64703 + 2.26694i) q^{46} +(5.15657 - 1.67547i) q^{47} +(1.49607 - 4.60444i) q^{48} +(0.536434 + 0.389742i) q^{49} +(-13.2356 + 18.2172i) q^{50} +(2.38350 - 7.33564i) q^{51} +(-6.69122 + 13.3316i) q^{52} +(-2.80279 + 2.03635i) q^{53} +2.47732i q^{54} +(7.72601 + 9.76185i) q^{55} -14.6557 q^{56} +(2.89208 + 3.98061i) q^{57} +(-11.0781 + 3.59949i) q^{58} +(1.99145 + 0.647063i) q^{59} +(9.12774 - 12.5633i) q^{60} +(5.61374 + 4.07862i) q^{61} +(-2.67104 + 8.22060i) q^{62} +(2.63274 - 0.855429i) q^{63} +(-5.01741 + 3.64536i) q^{64} +(-9.51162 + 9.62772i) q^{65} +(-5.09904 - 6.44266i) q^{66} -6.16455i q^{67} +(25.8158 - 18.7563i) q^{68} +(-0.349529 - 1.07574i) q^{69} +(-24.4815 - 7.95452i) q^{70} +(5.33655 - 7.34513i) q^{71} +(-3.11189 + 4.28316i) q^{72} +(-15.3178 - 4.97707i) q^{73} +(-1.60827 - 4.94976i) q^{74} +(7.35359 - 5.34270i) q^{75} +20.3558i q^{76} +(-5.08614 + 7.64362i) q^{77} +(6.27752 - 6.35414i) q^{78} +(7.23952 - 5.25982i) q^{79} +(17.2832 - 5.61566i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6614 + 8.47251i) q^{82} +(-7.72682 + 10.6351i) q^{83} +(10.8919 + 3.53899i) q^{84} +(27.5351 - 8.94670i) q^{85} +(1.56184 + 2.14969i) q^{86} +4.70194 q^{87} +(-0.722998 - 17.5442i) q^{88} +2.28824i q^{89} +(-7.52294 + 5.46574i) q^{90} +(-8.92044 - 4.47724i) q^{91} +(1.44603 - 4.45044i) q^{92} +(2.05085 - 2.82276i) q^{93} +(-10.8666 - 7.89505i) q^{94} +(-5.70719 + 17.5649i) q^{95} +(-1.33634 + 0.434205i) q^{96} +(-4.37703 - 6.02447i) q^{97} -1.64263i q^{98} +(1.15390 + 3.10942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.45613	−	2.00419i	−1.02964	−	1.41718i	−0.905218	−	0.424948i	$-0.860292\pi$
$2$	−1.45613	−	2.00419i	−1.02964	−	1.41718i	−0.124422	−	0.992229i	$-0.539708\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−1.27843	+	3.93462i	−0.639217	+	1.96731i
$5$	−2.20631	+	3.03673i	−0.986693	+	1.35807i	−0.0535486	+	0.998565i	$0.517053\pi$
$5$	−2.20631	+	3.03673i	−0.986693	+	1.35807i	−0.933145	+	0.359501i	$0.882947\pi$
$6$	1.45613	−	2.00419i	0.594463	−	0.818208i
$7$	−2.63274	−	0.855429i	−0.995082	−	0.323322i	−0.234183	−	0.972193i	$-0.575242\pi$
$7$	−2.63274	−	0.855429i	−0.995082	−	0.323322i	−0.760898	+	0.648871i	$0.775242\pi$
$8$	5.03515	−	1.63602i	1.78019	−	0.578420i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	9.29887			2.94056
$11$	0.894146	−	3.19382i	0.269595	−	0.962974i
$11$	0.894146	−	3.19382i	0.269595	−	0.962974i
$12$	−4.13710			−1.19428
$13$	3.56452	+	0.542421i	0.988619	+	0.150440i
$13$	3.56452	+	0.542421i	0.988619	+	0.150440i
$14$	2.11917	+	6.52213i	0.566371	+	1.74311i
$15$	−3.56989	−	1.15993i	−0.921741	−	0.299492i
$16$	−3.91677	−	2.84570i	−0.979192	−	0.711425i
$17$	−6.24007	−	4.53368i	−1.51344	−	1.09958i	−0.964622	−	0.263636i	$-0.915078\pi$
$17$	−6.24007	−	4.53368i	−1.51344	−	1.09958i	−0.548817	−	0.835942i	$-0.684922\pi$
$18$	2.35607	+	0.765533i	0.555331	+	0.180438i
$19$	4.67948	−	1.52046i	1.07355	−	0.348817i	0.281679	−	0.959509i	$-0.409109\pi$
$19$	4.67948	−	1.52046i	1.07355	−	0.348817i	0.791868	+	0.610692i	$0.209109\pi$
$20$	−9.12774	−	12.5633i	−2.04102	−	2.80923i
$21$		−	2.76822i		−	0.604076i
$22$	−7.70303	+	2.85858i	−1.64229	+	0.609452i
$23$	−1.13110			−0.235850			−0.117925	−	0.993022i	$-0.537624\pi$
$23$	−1.13110			−0.235850			−0.117925	+	0.993022i	$0.537624\pi$
$24$	3.11189	+	4.28316i	0.635213	+	0.874296i
$25$	−2.80882	−	8.64467i	−0.561765	−	1.72893i
$26$	−4.10329	−	7.93381i	−0.804721	−	1.55595i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	6.73156	−	9.26520i	1.27215	−	1.75096i
$29$	1.45298	−	4.47181i	0.269811	−	0.830394i	−0.720734	−	0.693211i	$-0.756195\pi$
$29$	1.45298	−	4.47181i	0.269811	−	0.830394i	0.990546	−	0.137183i	$-0.0438048\pi$
$30$	2.87351	+	8.84375i	0.524628	+	1.61464i
$31$	−2.05085	−	2.82276i	−0.368344	−	0.506982i	0.584106	−	0.811678i	$-0.301445\pi$
$31$	−2.05085	−	2.82276i	−0.368344	−	0.506982i	−0.952450	+	0.304695i	$0.901445\pi$
$32$			1.40512i			0.248392i
$33$	3.31381	−	0.136562i	0.576861	−	0.0237724i
$34$			19.1079i			3.27698i
$35$	8.40635	−	6.10757i	1.42093	−	1.03237i
$36$	−1.27843	−	3.93462i	−0.213072	−	0.655769i
$37$	1.99803	+	0.649200i	0.328474	+	0.106728i	0.468612	−	0.883404i	$-0.344754\pi$
$37$	1.99803	+	0.649200i	0.328474	+	0.106728i	−0.140137	+	0.990132i	$0.544754\pi$
$38$	−9.86122	−	7.16460i	−1.59970	−	1.16225i
$39$	0.585624	+	3.55767i	0.0937748	+	0.569684i
$40$	−6.14097	+	18.9000i	−0.970973	+	2.98835i
$41$	−5.53373	+	1.79802i	−0.864224	+	0.280803i	−0.707392	−	0.706822i	$-0.750128\pi$
$41$	−5.53373	+	1.79802i	−0.864224	+	0.280803i	−0.156832	+	0.987625i	$0.550128\pi$
$42$	−5.54805	+	4.03090i	−0.856083	+	0.621981i
$43$	−1.07260			−0.163569			−0.0817847	−	0.996650i	$-0.526062\pi$
$43$	−1.07260			−0.163569			−0.0817847	+	0.996650i	$0.526062\pi$
$44$	11.4234	+	7.60121i	1.72214	+	1.14593i
$45$		−	3.75360i		−	0.559554i
$46$	1.64703	+	2.26694i	0.242841	+	0.334242i
$47$	5.15657	−	1.67547i	0.752163	−	0.244393i	0.0922513	−	0.995736i	$-0.470594\pi$
$47$	5.15657	−	1.67547i	0.752163	−	0.244393i	0.659912	+	0.751343i	$0.270594\pi$
$48$	1.49607	−	4.60444i	0.215939	−	0.664593i
$49$	0.536434	+	0.389742i	0.0766334	+	0.0556774i
$50$	−13.2356	+	18.2172i	−1.87179	+	2.57630i
$51$	2.38350	−	7.33564i	0.333756	−	1.02720i
$52$	−6.69122	+	13.3316i	−0.927905	+	1.84875i
$53$	−2.80279	+	2.03635i	−0.384993	+	0.279714i	−0.763401	−	0.645925i	$-0.776472\pi$
$53$	−2.80279	+	2.03635i	−0.384993	+	0.279714i	0.378408	+	0.925639i	$0.376472\pi$
$54$			2.47732i			0.337120i
$55$	7.72601	+	9.76185i	1.04177	+	1.31629i
$56$	−14.6557			−1.95845
$57$	2.89208	+	3.98061i	0.383065	+	0.527244i
$58$	−11.0781	+	3.59949i	−1.45462	+	0.472636i
$59$	1.99145	+	0.647063i	0.259265	+	0.0842404i	0.435766	−	0.900060i	$-0.356478\pi$
$59$	1.99145	+	0.647063i	0.259265	+	0.0842404i	−0.176500	+	0.984301i	$0.556478\pi$
$60$	9.12774	−	12.5633i	1.17839	−	1.62191i
$61$	5.61374	+	4.07862i	0.718766	+	0.522214i	0.885990	−	0.463705i	$-0.153480\pi$
$61$	5.61374	+	4.07862i	0.718766	+	0.522214i	−0.167224	+	0.985919i	$0.553480\pi$
$62$	−2.67104	+	8.22060i	−0.339222	+	1.04402i
$63$	2.63274	−	0.855429i	0.331694	−	0.107774i
$64$	−5.01741	+	3.64536i	−0.627177	+	0.455671i
$65$	−9.51162	+	9.62772i	−1.17977	+	1.19417i
$66$	−5.09904	−	6.44266i	−0.627648	−	0.793037i
$67$		−	6.16455i		−	0.753120i	−0.926392	−	0.376560i	$-0.877107\pi$
$67$		−	6.16455i		−	0.753120i	0.926392	−	0.376560i	$-0.122893\pi$
$68$	25.8158	−	18.7563i	3.13063	−	2.27453i
$69$	−0.349529	−	1.07574i	−0.0420783	−	0.129504i
$70$	−24.4815	−	7.95452i	−2.92610	−	0.950746i
$71$	5.33655	−	7.34513i	0.633332	−	0.871707i	−0.364906	−	0.931044i	$-0.618899\pi$
$71$	5.33655	−	7.34513i	0.633332	−	0.871707i	0.998238	+	0.0593375i	$0.0188988\pi$
$72$	−3.11189	+	4.28316i	−0.366740	+	0.504775i
$73$	−15.3178	−	4.97707i	−1.79282	−	0.582521i	−0.793167	−	0.609004i	$-0.791569\pi$
$73$	−15.3178	−	4.97707i	−1.79282	−	0.582521i	−0.999649	+	0.0264824i	$0.991569\pi$
$74$	−1.60827	−	4.94976i	−0.186958	−	0.575397i
$75$	7.35359	−	5.34270i	0.849120	−	0.616922i
$76$			20.3558i			2.33497i
$77$	−5.08614	+	7.64362i	−0.579619	+	0.871071i
$78$	6.27752	−	6.35414i	0.710789	−	0.719465i
$79$	7.23952	−	5.25982i	0.814510	−	0.591776i	−0.100625	−	0.994924i	$-0.532084\pi$
$79$	7.23952	−	5.25982i	0.814510	−	0.591776i	0.915135	+	0.403148i	$0.132084\pi$
$80$	17.2832	−	5.61566i	1.93232	−	0.627850i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	11.6614	+	8.47251i	1.28779	+	0.935632i
$83$	−7.72682	+	10.6351i	−0.848129	+	1.16735i	0.136143	+	0.990689i	$0.456529\pi$
$83$	−7.72682	+	10.6351i	−0.848129	+	1.16735i	−0.984272	+	0.176660i	$0.943471\pi$
$84$	10.8919	+	3.53899i	1.18840	+	0.386136i
$85$	27.5351	−	8.94670i	2.98660	−	0.970406i
$86$	1.56184	+	2.14969i	0.168418	+	0.231807i
$87$	4.70194			0.504101
$88$	−0.722998	−	17.5442i	−0.0770718	−	1.87022i
$89$			2.28824i			0.242553i	0.992619	+	0.121276i	$0.0386988\pi$
$89$			2.28824i			0.242553i	−0.992619	+	0.121276i	$0.961301\pi$
$90$	−7.52294	+	5.46574i	−0.792988	+	0.576139i
$91$	−8.92044	−	4.47724i	−0.935116	−	0.469342i
$92$	1.44603	−	4.45044i	0.150760	−	0.463990i
$93$	2.05085	−	2.82276i	0.212664	−	0.292706i
$94$	−10.8666	−	7.89505i	−1.12080	−	0.814312i
$95$	−5.70719	+	17.5649i	−0.585545	+	1.80212i
$96$	−1.33634	+	0.434205i	−0.136390	+	0.0443158i
$97$	−4.37703	−	6.02447i	−0.444420	−	0.611692i	0.526767	−	0.850010i	$-0.323404\pi$
$97$	−4.37703	−	6.02447i	−0.444420	−	0.611692i	−0.971187	+	0.238318i	$0.923404\pi$
$98$		−	1.64263i		−	0.165931i
$99$	1.15390	+	3.10942i	0.115972	+	0.312509i
$100$	37.6043			3.76043
$101$	10.0475	−	7.29994i	0.999764	−	0.726371i	0.0377266	−	0.999288i	$-0.487988\pi$
$101$	10.0475	−	7.29994i	0.999764	−	0.726371i	0.962038	+	0.272917i	$0.0879884\pi$
$102$	−18.1727	+	5.90467i	−1.79937	+	0.584650i
$103$	−3.16062	+	9.72738i	−0.311425	+	0.958468i	0.665776	+	0.746152i	$0.268101\pi$
$103$	−3.16062	+	9.72738i	−0.311425	+	0.958468i	−0.977201	+	0.212316i	$0.931899\pi$
$104$	18.8353	−	3.10045i	1.84695	−	0.304024i
$105$	8.40635	+	6.10757i	0.820376	+	0.596038i
$106$	8.16245	+	2.65214i	0.792808	+	0.257599i
$107$	−1.26247	−	3.88549i	−0.122048	−	0.375625i	0.871304	−	0.490744i	$-0.163275\pi$
$107$	−1.26247	−	3.88549i	−0.122048	−	0.375625i	−0.993352	+	0.115119i	$0.963275\pi$
$108$	3.34698	−	2.43173i	0.322064	−	0.233993i
$109$		−	20.3375i		−	1.94798i	−0.226593	−	0.973990i	$-0.572759\pi$
$109$		−	20.3375i		−	1.94798i	0.226593	−	0.973990i	$-0.427241\pi$
$110$	8.31454	−	29.6989i	0.792760	−	2.83168i
$111$			2.10085i			0.199404i
$112$	7.87753	+	10.8425i	0.744357	+	1.02452i
$113$	−1.88553	−	5.80307i	−0.177376	−	0.545907i	0.822358	−	0.568970i	$-0.192658\pi$
$113$	−1.88553	−	5.80307i	−0.177376	−	0.545907i	−0.999734	+	0.0230632i	$0.992658\pi$
$114$	3.76665	−	11.5926i	0.352779	−	1.08574i
$115$	2.49556	−	3.43484i	0.232712	−	0.320301i
$116$	15.7373	+	11.4338i	1.46117	+	1.06160i
$117$	−3.20258	+	1.65634i	−0.296079	+	0.153129i
$118$	−1.60298	−	4.93346i	−0.147566	−	0.454162i
$119$	12.5502	+	17.2739i	1.15048	+	1.58350i
$120$	−19.8726			−1.81411
$121$	−9.40101	−	5.71149i	−0.854637	−	0.519226i
$122$		−	17.1900i		−	1.55631i
$123$	−3.42003	−	4.70727i	−0.308374	−	0.424441i
$124$	13.7283	−	4.46061i	1.23284	−	0.400575i
$125$	14.5992	+	4.74357i	1.30579	+	0.424278i
$126$	−5.54805	−	4.03090i	−0.494260	−	0.359101i
$127$	−17.3704	−	12.6203i	−1.54137	−	1.11987i	−0.949467	−	0.313868i	$-0.898375\pi$
$127$	−17.3704	−	12.6203i	−1.54137	−	1.11987i	−0.591908	−	0.806006i	$-0.701625\pi$
$128$	17.2847	+	5.61614i	1.52777	+	0.496401i
$129$	−0.331451	−	1.02010i	−0.0291826	−	0.0898148i
$130$	33.1460	+	5.04390i	2.90709	+	0.442379i
$131$	−0.816806			−0.0713647			−0.0356823	−	0.999363i	$-0.511360\pi$
$131$	−0.816806			−0.0713647			−0.0356823	+	0.999363i	$0.511360\pi$
$132$	−3.69917	+	13.2132i	−0.321971	+	1.15006i
$133$	−13.6205			−1.18105
$134$	−12.3549	+	8.97639i	−1.06730	+	0.775442i
$135$	3.56989	−	1.15993i	0.307247	−	0.0998307i
$136$	−38.8369	−	12.6189i	−3.33024	−	1.08206i
$137$	−3.36800	+	4.63566i	−0.287748	+	0.396051i	−0.928281	−	0.371879i	$-0.878713\pi$
$137$	−3.36800	+	4.63566i	−0.287748	+	0.396051i	0.640533	+	0.767931i	$0.278713\pi$
$138$	−1.64703	+	2.26694i	−0.140204	+	0.192975i
$139$	−3.05155	+	9.39169i	−0.258829	+	0.796593i	0.734222	+	0.678909i	$0.237547\pi$
$139$	−3.05155	+	9.39169i	−0.258829	+	0.796593i	−0.993051	+	0.117684i	$0.962453\pi$
$140$	13.2840	+	40.8839i	1.12270	+	3.45532i
$141$	3.18694	+	4.38644i	0.268388	+	0.369405i
$142$	−22.4918			−1.88747
$143$	4.91959	−	10.8994i	0.411397	−	0.911456i
$144$	4.84139			0.403449
$145$	10.3739	+	14.2785i	0.861510	+	1.18577i
$146$	12.3298	+	37.9471i	1.02042	+	3.14053i
$147$	−0.204899	+	0.630616i	−0.0168998	+	0.0520123i
$148$	−5.10870	+	7.03152i	−0.419933	+	0.577988i
$149$	−7.88068	+	10.8468i	−0.645611	+	0.888607i	−0.998899	−	0.0469074i	$-0.985063\pi$
$149$	−7.88068	+	10.8468i	−0.645611	+	0.888607i	0.353288	+	0.935514i	$0.385063\pi$
$150$	−21.4156	−	6.95834i	−1.74858	−	0.568146i
$151$	−21.1728	+	6.87947i	−1.72302	+	0.559843i	−0.992412	−	0.122955i	$-0.960763\pi$
$151$	−21.1728	+	6.87947i	−1.72302	+	0.559843i	−0.730607	+	0.682798i	$0.760763\pi$
$152$	21.0744	−	15.3115i	1.70936	−	1.24192i
$153$	7.71315			0.623571
$154$	22.7254	−	0.936513i	1.83126	−	0.0754664i
$155$	13.0968			1.05196
$156$	−14.7468	−	2.24405i	−1.18069	−	0.179668i
$157$	0.811299	+	2.49692i	0.0647487	+	0.199276i	0.978197	−	0.207678i	$-0.0665908\pi$
$157$	0.811299	+	2.49692i	0.0647487	+	0.199276i	−0.913448	+	0.406954i	$0.866591\pi$
$158$	−21.0834	−	6.85041i	−1.67730	−	0.544989i
$159$	−2.80279	−	2.03635i	−0.222276	−	0.161493i
$160$	−4.26696	−	3.10013i	−0.337333	−	0.245086i
$161$	2.97789	+	0.967574i	0.234690	+	0.0762555i
$162$	−2.35607	+	0.765533i	−0.185110	+	0.0601460i
$163$	−1.26066	−	1.73515i	−0.0987423	−	0.135907i	0.756787	−	0.653662i	$-0.226768\pi$
$163$	−1.26066	−	1.73515i	−0.0987423	−	0.135907i	−0.855529	+	0.517755i	$0.826768\pi$
$164$		−	24.0718i		−	1.87969i
$165$	−6.89660	+	10.3644i	−0.536900	+	0.806871i
$166$	32.5660			2.52761
$167$	1.86447	+	2.56623i	0.144277	+	0.198581i	0.875040	−	0.484051i	$-0.160835\pi$
$167$	1.86447	+	2.56623i	0.144277	+	0.198581i	−0.730762	+	0.682632i	$0.760835\pi$
$168$	−4.52887	−	13.9384i	−0.349410	−	1.07537i
$169$	12.4116	+	3.86693i	0.954735	+	0.297456i
$170$	−58.0256	−	42.1581i	−4.45036	−	3.23338i
$171$	−2.89208	+	3.98061i	−0.221163	+	0.304405i
$172$	1.37124	−	4.22025i	0.104556	−	0.321791i
$173$	−4.99164	−	15.3627i	−0.379507	−	1.16800i	−0.940387	−	0.340106i	$-0.889537\pi$
$173$	−4.99164	−	15.3627i	−0.379507	−	1.16800i	0.560880	−	0.827897i	$-0.310463\pi$
$174$	−6.84664	−	9.42359i	−0.519042	−	0.714400i
$175$			25.1619i			1.90206i
$176$	−12.5908	+	9.96499i	−0.949069	+	0.751140i
$177$			2.09394i			0.157390i
$178$	4.58607	−	3.33198i	0.343741	−	0.249742i
$179$	−0.747643	−	2.30101i	−0.0558815	−	0.171985i	0.919220	−	0.393744i	$-0.128820\pi$
$179$	−0.747643	−	2.30101i	−0.0558815	−	0.171985i	−0.975102	+	0.221758i	$0.928820\pi$
$180$	14.7690	+	4.79873i	1.10082	+	0.357677i
$181$	8.58681	+	6.23868i	0.638253	+	0.463718i	0.859249	−	0.511557i	$-0.170931\pi$
$181$	8.58681	+	6.23868i	0.638253	+	0.463718i	−0.220997	+	0.975275i	$0.570931\pi$
$182$	4.01607	+	24.3977i	0.297691	+	1.80848i
$183$	−2.14426	+	6.59935i	−0.158508	+	0.487838i
$184$	−5.69525	+	1.85050i	−0.419860	+	0.136421i
$185$	−6.37972	+	4.63514i	−0.469047	+	0.340782i
$186$	−8.64366			−0.633784
$187$	−20.0593	+	15.8759i	−1.46688	+	1.16096i
$188$			22.4311i			1.63596i
$189$	1.62712	+	2.23954i	0.118356	+	0.162903i
$190$	43.5139	−	14.1385i	3.15683	−	1.02572i
$191$	−1.88874	+	5.81294i	−0.136664	+	0.420609i	−0.995845	−	0.0910626i	$-0.970974\pi$
$191$	−1.88874	+	5.81294i	−0.136664	+	0.420609i	0.859181	+	0.511672i	$0.170974\pi$
$192$	−5.01741	−	3.64536i	−0.362101	−	0.263082i
$193$	7.99099	−	10.9987i	0.575204	−	0.791701i	−0.417955	−	0.908468i	$-0.637253\pi$
$193$	7.99099	−	10.9987i	0.575204	−	0.791701i	0.993159	+	0.116767i	$0.0372531\pi$
$194$	−5.70066	+	17.5448i	−0.409284	+	1.25965i
$195$	−12.0958	−	6.07096i	−0.866196	−	0.434751i
$196$	−2.21928	+	1.61240i	−0.158520	+	0.115172i
$197$		−	5.51297i		−	0.392783i	−0.980526	−	0.196392i	$-0.937078\pi$
$197$		−	5.51297i		−	0.392783i	0.980526	−	0.196392i	$-0.0629224\pi$
$198$	4.55165	−	6.84037i	0.323471	−	0.486124i
$199$	−12.5315			−0.888336			−0.444168	−	0.895943i	$-0.646501\pi$
$199$	−12.5315			−0.888336			−0.444168	+	0.895943i	$0.646501\pi$
$200$	−28.2857	−	38.9319i	−2.00010	−	2.75290i
$201$	5.86284	−	1.90495i	0.413533	−	0.134365i
$202$	−29.2610	−	9.50746i	−2.05879	−	0.668943i
$203$	−7.65063	+	10.5302i	−0.536969	+	0.739074i
$204$	25.8158	+	18.7563i	1.80747	+	1.31320i
$205$	6.74905	−	20.7714i	0.471374	−	1.45074i
$206$	24.0978	−	7.82985i	1.67897	−	0.545532i
$207$	0.915078	−	0.664843i	0.0636023	−	0.0462098i
$208$	−12.4178	−	12.2681i	−0.861021	−	0.850638i
$209$	−0.671927	−	16.3049i	−0.0464782	−	1.12784i
$210$		−	25.7414i		−	1.77632i
$211$	4.90669	−	3.56492i	0.337791	−	0.245419i	−0.405938	−	0.913900i	$-0.633055\pi$
$211$	4.90669	−	3.56492i	0.337791	−	0.245419i	0.743729	+	0.668481i	$0.233055\pi$
$212$	−4.42906	−	13.6312i	−0.304189	−	0.936197i
$213$	8.63472	+	2.80559i	0.591641	+	0.192236i
$214$	−5.94894	+	8.18802i	−0.406661	+	0.559721i
$215$	2.36648	−	3.25719i	0.161393	−	0.222138i
$216$	−5.03515	−	1.63602i	−0.342599	−	0.111317i
$217$	2.98469	+	9.18594i	0.202614	+	0.623582i
$218$	−40.7602	+	29.6141i	−2.76063	+	2.00572i
$219$		−	16.1061i		−	1.08835i
$220$	−48.2863	+	17.9190i	−3.25546	+	1.20810i
$221$	−19.7837	−	19.5451i	−1.33079	−	1.31475i
$222$	4.21051	−	3.05912i	0.282591	−	0.205314i
$223$	12.0264	−	3.90762i	0.805348	−	0.261673i	0.122722	−	0.992441i	$-0.460838\pi$
$223$	12.0264	−	3.90762i	0.805348	−	0.261673i	0.682626	+	0.730768i	$0.260838\pi$
$224$	1.20198	−	3.69930i	0.0803104	−	0.247170i
$225$	7.35359	+	5.34270i	0.490240	+	0.356180i
$226$	−8.88489	+	12.2290i	−0.591014	+	0.813461i
$227$	9.28295	+	3.01621i	0.616131	+	0.200193i	0.600422	−	0.799684i	$-0.294999\pi$
$227$	9.28295	+	3.01621i	0.616131	+	0.200193i	0.0157092	+	0.999877i	$0.494999\pi$
$228$	−19.3595	+	6.29028i	−1.28211	+	0.416584i
$229$	−8.42025	−	11.5895i	−0.556426	−	0.765855i	0.434441	−	0.900701i	$-0.356946\pi$
$229$	−8.42025	−	11.5895i	−0.556426	−	0.765855i	−0.990867	+	0.134846i	$0.956946\pi$
$230$	−10.5179			−0.693532
$231$	−8.84122	−	2.47520i	−0.581710	−	0.162856i
$232$		−	24.8933i		−	1.63433i
$233$	−18.4681	+	13.4178i	−1.20988	+	0.879032i	−0.995220	−	0.0976559i	$-0.968866\pi$
$233$	−18.4681	+	13.4178i	−1.20988	+	0.879032i	−0.214664	+	0.976688i	$0.568866\pi$
$234$	7.98300	+	4.00674i	0.521865	+	0.261928i
$235$	−6.28905	+	19.3557i	−0.410253	+	1.26263i
$236$	−5.09188	+	7.00838i	−0.331453	+	0.456206i
$237$	7.23952	+	5.25982i	0.470258	+	0.341662i
$238$	16.3455	−	50.3062i	1.05952	−	3.26086i
$239$	16.1804	−	5.25732i	1.04662	−	0.340068i	0.265279	−	0.964172i	$-0.414536\pi$
$239$	16.1804	−	5.25732i	1.04662	−	0.340068i	0.781341	+	0.624104i	$0.214536\pi$
$240$	10.6816	+	14.7020i	0.689496	+	0.949010i
$241$		−	3.33664i		−	0.214932i	−0.994209	−	0.107466i	$-0.965726\pi$
$241$		−	3.33664i		−	0.214932i	0.994209	−	0.107466i	$-0.0342736\pi$
$242$	2.24218	+	27.1581i	0.144133	+	1.74579i
$243$	1.00000			0.0641500
$244$	−23.2246	+	16.8737i	−1.48680	+	1.08022i
$245$	−2.36708	+	0.769111i	−0.151227	+	0.0491367i
$246$	−4.45426	+	13.7088i	−0.283993	+	0.874042i
$247$	17.5048	−	2.88144i	1.11381	−	0.183342i
$248$	−14.9444	−	10.8578i	−0.948973	−	0.689469i
$249$	−12.5023	−	4.06223i	−0.792299	−	0.257433i
$250$	−11.7513	−	36.1669i	−0.743219	−	2.28739i
$251$	−13.3288	+	9.68397i	−0.841309	+	0.611247i	−0.922736	−	0.385433i	$-0.874052\pi$
$251$	−13.3288	+	9.68397i	−0.841309	+	0.611247i	0.0814271	+	0.996679i	$0.474052\pi$
$252$			11.4524i			0.721435i
$253$	−1.01137	+	3.61253i	−0.0635841	+	0.227118i
$254$			53.1905i			3.33747i
$255$	17.0176	+	23.4228i	1.06569	+	1.46679i
$256$	−10.0800	−	31.0230i	−0.630000	−	1.93894i
$257$	4.44121	−	13.6686i	0.277035	−	0.852626i	−0.711639	−	0.702546i	$-0.752047\pi$
$257$	4.44121	−	13.6686i	0.277035	−	0.852626i	0.988674	−	0.150080i	$-0.0479533\pi$
$258$	−1.56184	+	2.14969i	−0.0972359	+	0.133834i
$259$	−4.70495	−	3.41834i	−0.292351	−	0.212406i
$260$	−25.7214	−	49.7330i	−1.59517	−	3.08431i
$261$	1.45298	+	4.47181i	0.0899371	+	0.276798i
$262$	1.18938	+	1.63704i	0.0734799	+	0.101136i
$263$	22.9122			1.41283			0.706415	−	0.707798i	$-0.250311\pi$
$263$	22.9122			1.41283			0.706415	+	0.707798i	$0.250311\pi$
$264$	16.4621	−	6.10907i	1.01317	−	0.375988i
$265$		−	13.0041i		−	0.798837i
$266$	19.8332	+	27.2981i	1.21605	+	1.67375i
$267$	−2.17625	+	0.707105i	−0.133184	+	0.0432741i
$268$	24.2551	+	7.88097i	1.48162	+	0.481407i
$269$	21.8151	+	15.8496i	1.33009	+	0.966366i	0.999747	+	0.0225053i	$0.00716426\pi$
$269$	21.8151	+	15.8496i	1.33009	+	0.966366i	0.330343	+	0.943861i	$0.392836\pi$
$270$	−7.52294	−	5.46574i	−0.457832	−	0.332634i
$271$	6.68550	+	2.17225i	0.406115	+	0.131955i	0.504949	−	0.863149i	$-0.331511\pi$
$271$	6.68550	+	2.17225i	0.406115	+	0.131955i	−0.0988341	+	0.995104i	$0.531511\pi$
$272$	11.5394	+	35.5147i	0.699681	+	2.15340i
$273$	1.50154	−	9.86738i	0.0908775	−	0.597201i
$274$	14.1950			0.857552
$275$	−30.1210	+	1.24129i	−1.81637	+	0.0748525i
$276$	4.67947			0.281671
$277$	−12.6384	+	9.18230i	−0.759365	+	0.551711i	−0.898716	−	0.438532i	$-0.855499\pi$
$277$	−12.6384	+	9.18230i	−0.759365	+	0.551711i	0.139350	+	0.990243i	$0.455499\pi$
$278$	23.2662	−	7.55965i	1.39541	−	0.453397i
$279$	3.31835	+	1.07820i	0.198664	+	0.0645500i
$280$	32.3351	−	44.5055i	1.93239	−	2.65971i
$281$	1.15765	−	1.59337i	0.0690596	−	0.0950523i	−0.773090	−	0.634296i	$-0.781290\pi$
$281$	1.15765	−	1.59337i	0.0690596	−	0.0950523i	0.842150	+	0.539244i	$0.181290\pi$
$282$	4.15067	−	12.7745i	0.247169	−	0.760708i
$283$	2.47243	+	7.60935i	0.146971	+	0.452329i	0.997259	−	0.0739878i	$-0.0235726\pi$
$283$	2.47243	+	7.60935i	0.146971	+	0.452329i	−0.850289	+	0.526317i	$0.823573\pi$
$284$	22.0778	+	30.3875i	1.31008	+	1.80317i
$285$	−18.4689			−1.09400
$286$	−29.0081	+	6.01119i	−1.71529	+	0.355449i
$287$	16.1069			0.950763
$288$	−0.825906	−	1.13676i	−0.0486670	−	0.0669844i
$289$	13.1310	+	40.4130i	0.772410	+	2.37723i
$290$	13.5111	−	41.5828i	0.793397	−	2.44182i
$291$	4.37703	−	6.02447i	0.256586	−	0.353161i
$292$	39.1657	−	53.9069i	2.29200	−	3.15466i
$293$	−8.18482	−	2.65941i	−0.478162	−	0.155364i	0.0600125	−	0.998198i	$-0.480886\pi$
$293$	−8.18482	−	2.65941i	−0.478162	−	0.155364i	−0.538175	+	0.842833i	$0.680886\pi$
$294$	1.56223	−	0.507601i	0.0911114	−	0.0296039i
$295$	−6.35872	+	4.61988i	−0.370219	+	0.268980i
$296$	11.1225			0.646482
$297$	−2.60066	+	2.05829i	−0.150906	+	0.119434i
$298$	33.2144			1.92406
$299$	−4.03182	−	0.613531i	−0.233166	−	0.0354814i
$300$	11.6204	+	35.7639i	0.670903	+	2.06483i
$301$	2.82387	+	0.917530i	0.162765	+	0.0528855i
$302$	44.6182	+	32.4170i	2.56749	+	1.86539i
$303$	10.0475	+	7.29994i	0.577214	+	0.419371i
$304$	−22.6552	−	7.36112i	−1.29937	−	0.422189i
$305$	−24.7713	+	8.04869i	−1.41840	+	0.460867i
$306$	−11.2314	−	15.4586i	−0.642054	−	0.883711i
$307$			4.15328i			0.237040i	0.992952	+	0.118520i	$0.0378150\pi$
$307$			4.15328i			0.237040i	−0.992952	+	0.118520i	$0.962185\pi$
$308$	−23.5724	−	29.7839i	−1.34316	−	1.69709i
$309$	−10.2280			−0.581849
$310$	−19.0706	−	26.2484i	−1.08314	−	1.49081i
$311$	−0.658406	−	2.02637i	−0.0373348	−	0.114905i	0.930652	−	0.365905i	$-0.119240\pi$
$311$	−0.658406	−	2.02637i	−0.0373348	−	0.114905i	−0.967987	+	0.251000i	$0.919240\pi$
$312$	8.76913	+	16.9553i	0.496454	+	0.959907i
$313$	−3.95852	−	2.87603i	−0.223749	−	0.162563i	0.470264	−	0.882526i	$-0.344159\pi$
$313$	−3.95852	−	2.87603i	−0.223749	−	0.162563i	−0.694012	+	0.719963i	$0.744159\pi$
$314$	3.82295	−	5.26184i	0.215742	−	0.296943i
$315$	−3.21094	+	9.88226i	−0.180916	+	0.556802i
$316$	11.4401	+	35.2091i	0.643557	+	1.98067i
$317$	−10.7977	−	14.8618i	−0.606460	−	0.834721i	0.389820	−	0.920891i	$-0.372537\pi$
$317$	−10.7977	−	14.8618i	−0.606460	−	0.834721i	−0.996280	+	0.0861700i	$0.972537\pi$
$318$			8.58251i			0.481283i
$319$	−12.9830	−	8.63901i	−0.726908	−	0.483692i
$320$		−	23.2793i		−	1.30135i
$321$	3.30520	−	2.40137i	0.184478	−	0.134031i
$322$	−2.39699	−	7.37717i	−0.133579	−	0.411114i
$323$	−36.0936	−	11.7275i	−2.00830	−	0.652536i
$324$	3.34698	+	2.43173i	0.185944	+	0.135096i
$325$	−5.32305	−	32.3376i	−0.295270	−	1.79377i
$326$	−1.64188	+	5.05320i	−0.0909355	+	0.279871i
$327$	19.3421	−	6.28463i	1.06962	−	0.347541i
$328$	−24.9216	+	18.1066i	−1.37606	+	0.999769i
$329$	−15.0091			−0.827481
$330$	30.8147	−	1.26987i	1.69629	−	0.0699043i
$331$			19.7679i			1.08654i	0.839557	+	0.543272i	$0.182815\pi$
$331$			19.7679i			1.08654i	−0.839557	+	0.543272i	$0.817185\pi$
$332$	−31.9666	−	43.9983i	−1.75440	−	2.41472i
$333$	−1.99803	+	0.649200i	−0.109491	+	0.0355759i
$334$	2.42830	−	7.47353i	0.132870	−	0.408933i
$335$	18.7201	+	13.6009i	1.02279	+	0.743098i
$336$	−7.87753	+	10.8425i	−0.429755	+	0.591506i
$337$	6.05790	−	18.6443i	0.329995	−	1.01562i	−0.639141	−	0.769090i	$-0.720710\pi$
$337$	6.05790	−	18.6443i	0.329995	−	1.01562i	0.969135	−	0.246529i	$-0.0792902\pi$
$338$	−10.3228	−	30.5059i	−0.561485	−	1.65930i
$339$	4.93639	−	3.58650i	0.268108	−	0.194792i
$340$			119.778i			6.49586i
$341$	−10.8491	+	4.02610i	−0.587514	+	0.218026i
$342$	12.1891			0.659113
$343$	10.3110	+	14.1918i	0.556739	+	0.766286i
$344$	−5.40069	+	1.75479i	−0.291186	+	0.0946119i
$345$	4.03790	+	1.31199i	0.217393	+	0.0706353i
$346$	−23.5213	+	32.3743i	−1.26451	+	1.74045i
$347$	11.2032	+	8.13957i	0.601417	+	0.436955i	0.846381	−	0.532577i	$-0.178776\pi$
$347$	11.2032	+	8.13957i	0.601417	+	0.436955i	−0.244965	+	0.969532i	$0.578776\pi$
$348$	−6.01112	+	18.5003i	−0.322230	+	0.991721i
$349$	4.93654	−	1.60398i	0.264247	−	0.0858590i	−0.173897	−	0.984764i	$-0.555636\pi$
$349$	4.93654	−	1.60398i	0.264247	−	0.0858590i	0.438144	+	0.898905i	$0.355636\pi$
$350$	50.4293	−	36.6390i	2.69556	−	1.95844i
$351$	−2.56493	−	2.53400i	−0.136906	−	0.135255i
$352$	4.48769	+	1.25638i	0.239195	+	0.0669652i
$353$		−	15.1520i		−	0.806458i	−0.915099	−	0.403229i	$-0.867888\pi$
$353$		−	15.1520i		−	0.806458i	0.915099	−	0.403229i	$-0.132112\pi$
$354$	4.19665	−	3.04905i	0.223050	−	0.162055i
$355$	10.5311	+	32.4113i	0.558932	+	1.72021i
$356$	−9.00334	−	2.92536i	−0.477176	−	0.155044i
$357$	−12.5502	+	17.2739i	−0.664229	+	0.914233i
$358$	−3.52300	+	4.84899i	−0.186196	+	0.256277i
$359$	28.5781	+	9.28560i	1.50830	+	0.490075i	0.942425	−	0.334419i	$-0.108540\pi$
$359$	28.5781	+	9.28560i	1.50830	+	0.490075i	0.565871	+	0.824494i	$0.308540\pi$
$360$	−6.14097	−	18.9000i	−0.323658	−	0.996116i
$361$	4.21445	−	3.06198i	0.221813	−	0.161157i
$362$		−	26.2940i		−	1.38198i
$363$	2.52688	−	10.7058i	0.132627	−	0.561911i
$364$	29.0204	−	29.3746i	1.52108	−	1.53965i
$365$	48.9099	−	35.5351i	2.56006	−	1.85999i
$366$	16.3487	−	5.31200i	0.854559	−	0.277663i
$367$	1.33258	−	4.10126i	0.0695602	−	0.214084i	−0.910233	−	0.414096i	$-0.864098\pi$
$367$	1.33258	−	4.10126i	0.0695602	−	0.214084i	0.979794	+	0.200011i	$0.0640979\pi$
$368$	4.43025	+	3.21877i	0.230943	+	0.167790i
$369$	3.42003	−	4.70727i	0.178040	−	0.245051i
$370$	18.5794	+	6.03682i	0.965898	+	0.313839i
$371$	9.12096	−	2.96358i	0.473537	−	0.153861i
$372$	8.48458	+	11.6780i	0.439905	+	0.605477i
$373$	−14.5751			−0.754670			−0.377335	−	0.926077i	$-0.623159\pi$
$373$	−14.5751			−0.754670			−0.377335	+	0.926077i	$0.623159\pi$
$374$	61.0273	+	17.0853i	3.15565	+	0.883458i
$375$			15.3505i			0.792698i
$376$	23.2230	−	16.8725i	1.19764	−	0.870133i
$377$	7.60477	−	15.1517i	0.391666	−	0.780353i
$378$	2.11917	−	6.52213i	0.108998	−	0.335462i
$379$	−1.25989	+	1.73409i	−0.0647163	+	0.0890743i	−0.840148	−	0.542357i	$-0.817532\pi$
$379$	−1.25989	+	1.73409i	−0.0647163	+	0.0890743i	0.775432	+	0.631431i	$0.217532\pi$
$380$	−61.8150	−	44.9112i	−3.17104	−	2.30390i
$381$	6.63490	−	20.4201i	0.339916	−	1.04616i
$382$	14.4005	−	4.67900i	0.736793	−	0.239399i
$383$	2.76174	+	3.80121i	0.141118	+	0.194233i	0.873726	−	0.486418i	$-0.161697\pi$
$383$	2.76174	+	3.80121i	0.141118	+	0.194233i	−0.732608	+	0.680651i	$0.761697\pi$
$384$			18.1742i			0.927449i
$385$	−11.9900	−	32.3094i	−0.611067	−	1.64664i
$386$	−33.6793			−1.71423
$387$	0.867749	−	0.630456i	0.0441102	−	0.0320479i
$388$	29.2997	−	9.52006i	1.48747	−	0.483308i
$389$	1.39695	−	4.29937i	0.0708282	−	0.217987i	−0.909376	−	0.415974i	$-0.863441\pi$
$389$	1.39695	−	4.29937i	0.0708282	−	0.217987i	0.980205	+	0.197988i	$0.0634406\pi$
$390$	5.44564	+	33.0823i	0.275751	+	1.67519i
$391$	7.05814	+	5.12804i	0.356945	+	0.259336i
$392$	3.33865	+	1.08479i	0.168627	+	0.0547903i
$393$	−0.252407	−	0.776829i	−0.0127322	−	0.0391858i
$394$	−11.0491	+	8.02761i	−0.556643	+	0.404425i
$395$			33.5893i			1.69006i
$396$	−13.7096	+	0.564972i	−0.688932	+	0.0283909i
$397$			12.5301i			0.628867i	0.949280	+	0.314433i	$0.101814\pi$
$397$			12.5301i			0.628867i	−0.949280	+	0.314433i	$0.898186\pi$
$398$	18.2475	+	25.1156i	0.914666	+	1.25893i
$399$	−4.20896	−	12.9539i	−0.210712	−	0.648504i
$400$	−13.5986	+	41.8522i	−0.679931	+	2.09261i
$401$	12.0708	−	16.6140i	0.602785	−	0.829663i	−0.393174	−	0.919464i	$-0.628623\pi$
$401$	12.0708	−	16.6140i	0.602785	−	0.829663i	0.995960	+	0.0898010i	$0.0286231\pi$
$402$	−12.3549	−	8.97639i	−0.616209	−	0.447702i
$403$	−5.77918	−	11.1742i	−0.287881	−	0.556626i
$404$	15.8774	+	48.8656i	0.789929	+	2.43115i
$405$	2.20631	+	3.03673i	0.109633	+	0.150896i
$406$	32.2448			1.60028
$407$	3.85996	−	5.80088i	0.191331	−	0.287539i
$408$		−	40.8355i		−	2.02166i
$409$	−4.79355	−	6.59776i	−0.237026	−	0.326238i	0.673889	−	0.738833i	$-0.264623\pi$
$409$	−4.79355	−	6.59776i	−0.237026	−	0.326238i	−0.910915	+	0.412595i	$0.864623\pi$
$410$	−51.4574	+	16.7195i	−2.54130	+	0.825719i
$411$	−5.44955	−	1.77066i	−0.268806	−	0.0873405i
$412$	−34.2329	−	24.8716i	−1.68653	−	1.22534i
$413$	−4.68946	−	3.40709i	−0.230753	−	0.167652i
$414$	−2.66495	−	0.865893i	−0.130975	−	0.0425563i
$415$	−15.2480	−	46.9285i	−0.748495	−	2.30363i
$416$	−0.762164	+	5.00856i	−0.0373682	+	0.245565i
$417$	−9.87501			−0.483581
$418$	−31.6998	+	25.0888i	−1.55049	+	1.22713i
$419$	−39.0388			−1.90717			−0.953585	−	0.301125i	$-0.902638\pi$
$419$	−39.0388			−1.90717			−0.953585	+	0.301125i	$0.902638\pi$
$420$	−34.7779	+	25.2676i	−1.69699	+	1.23293i
$421$	−28.9676	+	9.41215i	−1.41180	+	0.458720i	−0.912986	−	0.407991i	$-0.866229\pi$
$421$	−28.9676	+	9.41215i	−1.41180	+	0.458720i	−0.498810	+	0.866711i	$0.666229\pi$
$422$	−14.2896	−	4.64296i	−0.695605	−	0.226016i
$423$	−3.18694	+	4.38644i	−0.154954	+	0.213276i
$424$	−10.7810	+	14.8387i	−0.523570	+	0.720632i
$425$	−21.6649	+	66.6776i	−1.05090	+	3.23434i
$426$	−6.95034	−	21.3909i	−0.336745	−	1.03639i
$427$	−11.2905	−	15.5401i	−0.546387	−	0.752038i
$428$	16.9019			0.816984
$429$	11.8862	+	1.31070i	0.573872	+	0.0632813i
$430$	−9.97393			−0.480986
$431$	−2.95368	−	4.06539i	−0.142274	−	0.195823i	0.731933	−	0.681376i	$-0.238618\pi$
$431$	−2.95368	−	4.06539i	−0.142274	−	0.195823i	−0.874207	+	0.485553i	$0.838618\pi$
$432$	1.49607	+	4.60444i	0.0719798	+	0.221531i
$433$	11.3980	−	35.0794i	0.547752	−	1.68581i	−0.166604	−	0.986024i	$-0.553280\pi$
$433$	11.3980	−	35.0794i	0.547752	−	1.68581i	0.714356	−	0.699783i	$-0.246720\pi$
$434$	14.0643	−	19.3578i	0.675107	−	0.929205i
$435$	−10.3739	+	14.2785i	−0.497393	+	0.684602i
$436$	80.0202	+	26.0001i	3.83227	+	1.24518i
$437$	−5.29296	+	1.71979i	−0.253196	+	0.0822685i
$438$	−32.2798	+	23.4526i	−1.54239	+	1.12061i
$439$	12.6191			0.602279			0.301139	−	0.953580i	$-0.402633\pi$
$439$	12.6191			0.602279			0.301139	+	0.953580i	$0.402633\pi$
$440$	54.8722	+	36.5125i	2.61593	+	1.74066i
$441$	−0.663069			−0.0315747
$442$	−10.3645	+	68.1105i	−0.492990	+	3.23969i
$443$	−7.89680	−	24.3039i	−0.375188	−	1.15471i	−0.943351	−	0.331795i	$-0.892346\pi$
$443$	−7.89680	−	24.3039i	−0.375188	−	1.15471i	0.568163	−	0.822916i	$-0.307654\pi$
$444$	−8.26605	−	2.68580i	−0.392289	−	0.127463i
$445$	−6.94876	−	5.04857i	−0.329403	−	0.239325i
$446$	−25.3436	−	18.4132i	−1.20006	−	0.871892i
$447$	−12.7512	−	4.14312i	−0.603112	−	0.195963i
$448$	16.3279	−	5.30525i	0.771420	−	0.250650i
$449$	−1.57866	−	2.17284i	−0.0745016	−	0.102543i	0.770140	−	0.637875i	$-0.220186\pi$
$449$	−1.57866	−	2.17284i	−0.0745016	−	0.102543i	−0.844641	+	0.535332i	$0.820186\pi$
$450$		−	22.5177i		−	1.06149i
$451$	0.794589	+	19.2815i	0.0374157	+	0.907928i
$452$	25.2434			1.18735
$453$	−13.0855	−	18.0107i	−0.614811	−	0.846215i
$454$	−7.47211	−	22.9968i	−0.350684	−	1.07929i
$455$	33.2774	−	17.2108i	1.56007	−	0.806853i
$456$	21.0744	+	15.3115i	0.986900	+	0.717025i
$457$	1.18746	−	1.63440i	0.0555470	−	0.0764539i	−0.780340	−	0.625356i	$-0.784954\pi$
$457$	1.18746	−	1.63440i	0.0555470	−	0.0764539i	0.835887	+	0.548902i	$0.184954\pi$
$458$	−10.9666	+	33.7516i	−0.512434	+	1.57711i
$459$	2.38350	+	7.33564i	0.111252	+	0.342399i
$460$	10.3244	+	14.2103i	0.481376	+	0.662558i
$461$		−	18.9148i		−	0.880949i	−0.897765	−	0.440475i	$-0.854810\pi$
$461$		−	18.9148i		−	0.880949i	0.897765	−	0.440475i	$-0.145190\pi$
$462$	7.91320	+	21.3237i	0.368155	+	0.992069i
$463$		−	12.4805i		−	0.580020i	−0.957024	−	0.290010i	$-0.906341\pi$
$463$		−	12.4805i		−	0.580020i	0.957024	−	0.290010i	$-0.0936587\pi$
$464$	−18.4164	+	13.3803i	−0.854960	+	0.621165i
$465$	4.04713	+	12.4558i	0.187681	+	0.577623i
$466$	53.7839	+	17.4754i	2.49149	+	0.809534i
$467$	15.1232	+	10.9877i	0.699820	+	0.508449i	0.879874	−	0.475208i	$-0.157627\pi$
$467$	15.1232	+	10.9877i	0.699820	+	0.508449i	−0.180053	+	0.983657i	$0.557627\pi$
$468$	−2.42278	−	14.7185i	−0.111993	−	0.680361i
$469$	−5.27333	+	16.2297i	−0.243500	+	0.749416i
$470$	47.9503	−	15.5800i	2.21178	−	0.718651i
$471$	−2.12401	+	1.54318i	−0.0978691	+	0.0711061i
$472$	11.0859			0.510269
$473$	−0.959058	+	3.42568i	−0.0440975	+	0.157513i
$474$		−	22.1684i		−	1.01823i
$475$	−26.2877	−	36.1819i	−1.20616	−	1.66014i
$476$	−84.0109	+	27.2968i	−3.85063	+	1.25115i
$477$	1.07057	−	3.29488i	0.0490180	−	0.150862i
$478$	−34.0974	−	24.7732i	−1.55958	−	1.13310i
$479$	−25.3152	+	34.8434i	−1.15668	+	1.59203i	−0.433893	+	0.900965i	$0.642860\pi$
$479$	−25.3152	+	34.8434i	−1.15668	+	1.59203i	−0.722788	+	0.691070i	$0.757140\pi$
$480$	1.62983	−	5.01611i	0.0743913	−	0.228953i
$481$	6.76987	+	3.39786i	0.308680	+	0.154929i
$482$	−6.68726	+	4.85858i	−0.304596	+	0.221302i
$483$			3.13114i			0.142472i
$484$	34.4911	−	29.6876i	1.56778	−	1.34944i
$485$	27.9518			1.26923
$486$	−1.45613	−	2.00419i	−0.0660514	−	0.0909120i
$487$	−24.8464	+	8.07310i	−1.12590	+	0.365827i	−0.812016	−	0.583635i	$-0.801630\pi$
$487$	−24.8464	+	8.07310i	−1.12590	+	0.365827i	−0.313883	+	0.949462i	$0.601630\pi$
$488$	34.9387	+	11.3523i	1.58160	+	0.513894i
$489$	1.26066	−	1.73515i	0.0570089	−	0.0784660i
$490$	4.98823	+	3.62416i	0.225345	+	0.163723i
$491$	5.70072	−	17.5450i	0.257270	−	0.791795i	−0.736104	−	0.676868i	$-0.763337\pi$
$491$	5.70072	−	17.5450i	0.257270	−	0.791795i	0.993374	−	0.114927i	$-0.0366633\pi$
$492$	22.8936	−	7.43858i	1.03212	−	0.335357i
$493$	−29.3404	+	21.3171i	−1.32143	+	0.960073i
$494$	−31.2643	−	30.8873i	−1.40665	−	1.38968i
$495$	−11.9883	−	3.35627i	−0.538836	−	0.150853i
$496$			16.8922i			0.758482i
$497$	−20.3330	+	14.7728i	−0.912059	+	0.662650i
$498$	10.0634	+	30.9721i	0.450953	+	1.38789i
$499$	−15.7609	−	5.12104i	−0.705557	−	0.229249i	−0.0658069	−	0.997832i	$-0.520962\pi$
$499$	−15.7609	−	5.12104i	−0.705557	−	0.229249i	−0.639750	+	0.768583i	$0.720962\pi$
$500$	−37.3283	+	51.3779i	−1.66937	+	2.29769i
$501$	−1.86447	+	2.56623i	−0.0832986	+	0.114651i
$502$	38.8171	+	12.6124i	1.73249	+	0.562920i
$503$	2.60838	+	8.02776i	0.116302	+	0.357940i	0.992216	−	0.124526i	$-0.0397411\pi$
$503$	2.60838	+	8.02776i	0.116302	+	0.357940i	−0.875915	+	0.482466i	$0.839741\pi$
$504$	11.8567	−	8.61442i	0.528141	−	0.383717i
$505$			46.6175i			2.07445i
$506$	8.71288	−	3.23334i	0.387335	−	0.143739i
$507$	0.157710	+	12.9990i	0.00700413	+	0.577308i
$508$	71.8631	−	52.2116i	3.18841	−	2.31651i
$509$	18.1790	−	5.90673i	0.805772	−	0.261811i	0.122966	−	0.992411i	$-0.460759\pi$
$509$	18.1790	−	5.90673i	0.805772	−	0.261811i	0.682806	+	0.730600i	$0.260759\pi$
$510$	22.1638	−	68.2132i	0.981430	−	3.02053i
$511$	36.0703	+	26.2066i	1.59566	+	1.15931i
$512$	−26.1333	+	35.9694i	−1.15494	+	1.58964i
$513$	−4.67948	−	1.52046i	−0.206604	−	0.0671298i
$514$	−33.8615	+	11.0023i	−1.49357	+	0.485290i
$515$	−22.5661	−	31.0596i	−0.994382	−	1.36865i
$516$	4.43744			0.195347
$517$	−0.740432	−	17.9673i	−0.0325642	−	0.790200i
$518$			14.4072i			0.633015i
$519$	13.0683	−	9.49466i	0.573634	−	0.416769i
$520$	−32.1413	+	64.0383i	−1.40949	+	2.80826i
$521$	−0.0929794	+	0.286161i	−0.00407350	+	0.0125369i	−0.953073	−	0.302742i	$-0.902098\pi$
$521$	−0.0929794	+	0.286161i	−0.00407350	+	0.0125369i	0.948999	+	0.315279i	$0.102098\pi$
$522$	6.84664	−	9.42359i	0.299669	−	0.412459i
$523$	14.9246	+	10.8434i	0.652607	+	0.474147i	0.864158	−	0.503220i	$-0.167851\pi$
$523$	14.9246	+	10.8434i	0.652607	+	0.474147i	−0.211551	+	0.977367i	$0.567851\pi$
$524$	1.04423	−	3.21382i	0.0456175	−	0.140396i
$525$	−23.9304	+	7.77545i	−1.04441	+	0.339349i
$526$	−33.3632	−	45.9205i	−1.45471	−	2.00223i
$527$			26.9121i			1.17231i
$528$	−13.3680	−	8.89523i	−0.581770	−	0.387115i
$529$	−21.7206			−0.944375
$530$	−26.0628	+	18.9357i	−1.13209	+	0.822515i
$531$	−1.99145	+	0.647063i	−0.0864217	+	0.0280801i
$532$	17.4129	−	53.5914i	0.754945	−	2.32348i
$533$	−20.7004	+	3.40746i	−0.896632	+	0.147593i
$534$	4.58607	+	3.33198i	0.198459	+	0.144189i
$535$	14.5846	+	4.73882i	0.630547	+	0.204877i
$536$	−10.0853	−	31.0395i	−0.435620	−	1.34070i
$537$	1.95735	−	1.42210i	0.0844661	−	0.0613682i
$538$		−	66.8007i		−	2.87998i
$539$	1.72442	−	1.36479i	0.0742759	−	0.0587856i
$540$			15.5290i			0.668263i
$541$	−7.45539	−	10.2615i	−0.320532	−	0.441175i	0.618097	−	0.786102i	$-0.287904\pi$
$541$	−7.45539	−	10.2615i	−0.320532	−	0.441175i	−0.938630	+	0.344927i	$0.887904\pi$
$542$	−5.38135	−	16.5621i	−0.231149	−	0.711403i
$543$	−3.27987	+	10.0944i	−0.140753	+	0.433192i
$544$	6.37034	−	8.76802i	0.273126	−	0.375926i
$545$	61.7595	+	44.8709i	2.64549	+	1.92206i
$546$	−21.9626	+	11.3588i	−0.939911	+	0.486113i
$547$	−8.88761	−	27.3532i	−0.380007	−	1.16954i	−0.940038	−	0.341069i	$-0.889211\pi$
$547$	−8.88761	−	27.3532i	−0.380007	−	1.16954i	0.560032	−	0.828471i	$-0.310789\pi$
$548$	−13.9338	−	19.1782i	−0.595221	−	0.819252i
$549$	−6.93896			−0.296148
$550$	46.3479	+	58.5608i	1.97628	+	2.49704i
$551$		−	23.1349i		−	0.985582i
$552$	−3.51986	−	4.84467i	−0.149815	−	0.206203i
$553$	−23.5592	+	7.65484i	−1.00184	+	0.325517i
$554$	36.8062	+	11.9591i	1.56374	+	0.508092i
$555$	−6.37972	−	4.63514i	−0.270804	−	0.196751i
$556$	−33.0515	−	24.0133i	−1.40170	−	1.01839i
$557$	−36.4334	−	11.8379i	−1.54373	−	0.501590i	−0.591330	−	0.806429i	$-0.701397\pi$
$557$	−36.4334	−	11.8379i	−1.54373	−	0.501590i	−0.952404	+	0.304840i	$0.901397\pi$
$558$	−2.67104	−	8.22060i	−0.113074	−	0.348006i
$559$	−3.82329	−	0.581798i	−0.161708	−	0.0246075i
$560$	−50.3060			−2.12582
$561$	−21.2976	−	14.1716i	−0.899183	−	0.598325i
$562$	−4.87910			−0.205812
$563$	−22.2107	+	16.1370i	−0.936069	+	0.680094i	−0.947471	−	0.319841i	$-0.896371\pi$
$563$	−22.2107	+	16.1370i	−0.936069	+	0.680094i	0.0114019	+	0.999935i	$0.496371\pi$
$564$	−21.3332	+	6.93159i	−0.898291	+	0.291873i
$565$	21.7824	+	7.07754i	0.916394	+	0.297754i
$566$	11.6504	−	16.0354i	0.489704	−	0.674019i
$567$	−1.62712	+	2.23954i	−0.0683327	+	0.0940519i
$568$	14.8536	−	45.7146i	0.623242	−	1.91814i
$569$	−1.22002	−	3.75482i	−0.0511457	−	0.157410i	0.922221	−	0.386662i	$-0.126372\pi$
$569$	−1.22002	−	3.75482i	−0.0511457	−	0.157410i	−0.973367	+	0.229252i	$0.926372\pi$
$570$	26.8931	+	37.0151i	1.12643	+	1.55039i
$571$	31.9034			1.33512			0.667558	−	0.744558i	$-0.267340\pi$
$571$	31.9034			1.33512			0.667558	+	0.744558i	$0.267340\pi$
$572$	36.5957	+	33.2909i	1.53014	+	1.39196i
$573$	−6.11208			−0.255336
$574$	−23.4538	−	32.2814i	−0.978943	−	1.34740i
$575$	3.17706	+	9.77797i	0.132492	+	0.407770i
$576$	1.91648	−	5.89832i	0.0798534	−	0.245763i
$577$	−13.8463	+	19.0579i	−0.576431	+	0.793389i	−0.993298	−	0.115578i	$-0.963128\pi$
$577$	−13.8463	+	19.0579i	−0.576431	+	0.793389i	0.416867	+	0.908967i	$0.363128\pi$
$578$	61.8749	−	85.1636i	2.57366	−	3.54234i
$579$	12.9297	+	4.20111i	0.537340	+	0.174592i
$580$	−69.4429	+	22.5634i	−2.88346	+	0.936892i
$581$	29.4402	−	21.3896i	1.22139	−	0.887389i
$582$	−18.4477			−0.764683
$583$	3.99762	+	10.7724i	0.165565	+	0.446147i
$584$	−85.2702			−3.52851
$585$	2.03603	−	13.3798i	0.0841796	−	0.553186i
$586$	6.58820	+	20.2764i	0.272156	+	0.837610i
$587$	22.4044	+	7.27963i	0.924728	+	0.300462i	0.732405	−	0.680869i	$-0.238398\pi$
$587$	22.4044	+	7.27963i	0.924728	+	0.300462i	0.192323	+	0.981332i	$0.438398\pi$
$588$	−2.21928	−	1.61240i	−0.0915216	−	0.0664943i
$589$	−13.8888	−	10.0908i	−0.572278	−	0.415785i
$590$	18.5183	+	6.01695i	0.762385	+	0.247714i
$591$	5.24315	−	1.70360i	0.215674	−	0.0700769i
$592$	−5.97840	−	8.22856i	−0.245711	−	0.338192i
$593$			13.2532i			0.544244i	0.962263	+	0.272122i	$0.0877255\pi$
$593$			13.2532i			0.544244i	−0.962263	+	0.272122i	$0.912275\pi$
$594$	7.91211	+	2.21508i	0.324638	+	0.0908859i
$595$	−80.1460			−3.28566
$596$	−32.6032	−	44.8744i	−1.33548	−	1.83813i
$597$	−3.87245	−	11.9182i	−0.158489	−	0.487779i
$598$	4.64122	+	8.97392i	0.189794	+	0.366971i
$599$	−12.4803	−	9.06745i	−0.509930	−	0.370486i	0.302867	−	0.953033i	$-0.402056\pi$
$599$	−12.4803	−	9.06745i	−0.509930	−	0.370486i	−0.812797	+	0.582547i	$0.802056\pi$
$600$	28.2857	−	38.9319i	1.15476	−	1.58939i
$601$	13.3211	−	40.9981i	0.543379	−	1.67235i	−0.181434	−	0.983403i	$-0.558074\pi$
$601$	13.3211	−	40.9981i	0.543379	−	1.67235i	0.724813	−	0.688945i	$-0.241926\pi$
$602$	−2.27301	−	6.99561i	−0.0926411	−	0.285120i
$603$	3.62343	+	4.98723i	0.147558	+	0.203096i
$604$		−	92.1018i		−	3.74757i
$605$	38.0858	−	15.9470i	1.54841	−	0.648337i
$606$		−	30.7668i		−	1.24982i
$607$	15.0807	−	10.9568i	0.612107	−	0.444722i	−0.238048	−	0.971253i	$-0.576508\pi$
$607$	15.0807	−	10.9568i	0.612107	−	0.444722i	0.850156	+	0.526531i	$0.176508\pi$
$608$	2.13642	+	6.57522i	0.0866432	+	0.266660i
$609$	−12.3790	−	4.02217i	−0.501621	−	0.162987i
$610$	52.2014	+	37.9265i	2.11357	+	1.53560i
$611$	19.2895	−	3.17522i	0.780369	−	0.128455i
$612$	−9.86076	+	30.3483i	−0.398597	+	1.22676i
$613$	20.4684	−	6.65058i	0.826710	−	0.268614i	0.135051	−	0.990839i	$-0.456880\pi$
$613$	20.4684	−	6.65058i	0.826710	−	0.268614i	0.691659	+	0.722224i	$0.256880\pi$
$614$	8.32397	−	6.04772i	0.335928	−	0.244066i
$615$	21.8404			0.880689
$616$	−13.1044	+	46.8078i	−0.527990	+	1.88594i
$617$			38.5461i			1.55181i	0.630851	+	0.775904i	$0.282706\pi$
$617$			38.5461i			1.55181i	−0.630851	+	0.775904i	$0.717294\pi$
$618$	14.8933	+	20.4988i	0.599095	+	0.824584i
$619$	22.4287	−	7.28752i	0.901485	−	0.292910i	0.178635	−	0.983915i	$-0.442832\pi$
$619$	22.4287	−	7.28752i	0.901485	−	0.292910i	0.722850	+	0.691005i	$0.242832\pi$
$620$	−16.7434	+	51.5308i	−0.672429	+	2.06953i
$621$	0.915078	+	0.664843i	0.0367208	+	0.0266792i
$622$	−3.10250	+	4.27022i	−0.124399	+	0.171220i
$623$	1.95743	−	6.02434i	0.0784226	−	0.241360i
$624$	7.83032	−	15.6011i	0.313463	−	0.624543i
$625$	−9.84741	+	7.15456i	−0.393896	+	0.286182i
$626$			12.1215i			0.484473i
$627$	15.2993	−	5.67755i	0.610995	−	0.226739i
$628$	−10.8616			−0.433426
$629$	−9.52459	−	13.1095i	−0.379770	−	0.522709i
$630$	24.4815	−	7.95452i	0.975366	−	0.316915i
$631$	−0.350782	−	0.113976i	−0.0139644	−	0.00453732i	0.302026	−	0.953300i	$-0.402337\pi$
$631$	−0.350782	−	0.113976i	−0.0139644	−	0.00453732i	−0.315991	+	0.948762i	$0.602337\pi$
$632$	27.8469	−	38.3280i	1.10769	−	1.52461i
$633$	4.90669	+	3.56492i	0.195023	+	0.141693i
$634$	−14.0630	+	43.2814i	−0.558512	+	1.71892i
$635$	76.6491	−	24.9048i	3.04173	−	0.988317i
$636$	11.5954	−	8.42456i	0.459788	−	0.334056i
$637$	1.70072	+	1.68021i	0.0673851	+	0.0665725i
$638$	1.59070	+	38.5999i	0.0629766	+	1.52819i
$639$			9.07908i			0.359163i
$640$	−55.1902	+	40.0980i	−2.18158	+	1.58501i
$641$	9.93324	+	30.5714i	0.392339	+	1.20750i	0.931014	+	0.364982i	$0.118925\pi$
$641$	9.93324	+	30.5714i	0.392339	+	1.20750i	−0.538675	+	0.842514i	$0.681075\pi$
$642$	−9.62559	−	3.12754i	−0.379892	−	0.123434i
$643$	−2.19190	+	3.01689i	−0.0864400	+	0.118974i	−0.850047	−	0.526707i	$-0.823427\pi$
$643$	−2.19190	+	3.01689i	−0.0864400	+	0.118974i	0.763607	+	0.645681i	$0.223427\pi$
$644$	−7.61406	+	10.4799i	−0.300036	+	0.412964i
$645$	3.82905	+	1.24413i	0.150769	+	0.0489877i
$646$	29.0528	+	89.4152i	1.14307	+	3.51799i
$647$	28.7939	−	20.9200i	1.13201	−	0.822450i	0.146020	−	0.989282i	$-0.453354\pi$
$647$	28.7939	−	20.9200i	1.13201	−	0.822450i	0.985985	+	0.166832i	$0.0533536\pi$
$648$		−	5.29427i		−	0.207979i
$649$	3.84725	−	5.78178i	0.151018	−	0.226955i
$650$	−57.0597	+	57.7562i	−2.23807	+	2.26539i
$651$	−7.81403	+	5.67722i	−0.306256	+	0.222508i
$652$	8.43880	−	2.74193i	0.330489	−	0.107382i
$653$	−2.48440	+	7.64620i	−0.0972221	+	0.299219i	−0.987826	−	0.155560i	$-0.950282\pi$
$653$	−2.48440	+	7.64620i	−0.0972221	+	0.299219i	0.890604	+	0.454779i	$0.150282\pi$
$654$	−40.7602	−	29.6141i	−1.59385	−	1.15800i
$655$	1.80213	−	2.48042i	0.0704150	−	0.0969180i
$656$	26.7910	+	8.70491i	1.04601	+	0.339870i
$657$	15.3178	−	4.97707i	0.597606	−	0.194174i
$658$	21.8553	+	30.0812i	0.852007	+	1.17269i
$659$	2.01044			0.0783155			0.0391577	−	0.999233i	$-0.487533\pi$
$659$	2.01044			0.0783155			0.0391577	+	0.999233i	$0.487533\pi$
$660$	−31.9633	−	40.3857i	−1.24417	−	1.57201i
$661$			2.40278i			0.0934573i	0.998908	+	0.0467287i	$0.0148796\pi$
$661$			2.40278i			0.0934573i	−0.998908	+	0.0467287i	$0.985120\pi$
$662$	39.6187	−	28.7847i	1.53982	−	1.11875i
$663$	12.4750	−	24.8552i	0.484489	−	0.965295i
$664$	−21.5066	+	66.1904i	−0.834616	+	2.56868i
$665$	30.0511	−	41.3618i	1.16533	−	1.60394i
$666$	4.21051	+	3.05912i	0.163154	+	0.118538i
$667$	−1.64346	+	5.05806i	−0.0636351	+	0.195849i
$668$	−12.4807	+	4.05524i	−0.482894	+	0.156902i
$669$	7.43273	+	10.2303i	0.287366	+	0.395525i
$670$		−	57.3233i		−	2.21459i
$671$	18.0459	−	14.2824i	0.696654	−	0.551366i
$672$	3.88968			0.150048
$673$	4.03665	−	2.93280i	0.155602	−	0.113051i	−0.507260	−	0.861793i	$-0.669342\pi$
$673$	4.03665	−	2.93280i	0.155602	−	0.113051i	0.662862	+	0.748742i	$0.269342\pi$
$674$	−46.1878	+	15.0073i	−1.77909	+	0.578061i
$675$	−2.80882	+	8.64467i	−0.108112	+	0.332733i
$676$	−31.0823	+	43.8911i	−1.19547	+	1.68812i
$677$	−7.77581	−	5.64946i	−0.298849	−	0.217126i	0.428248	−	0.903661i	$-0.359131\pi$
$677$	−7.77581	−	5.64946i	−0.298849	−	0.217126i	−0.727097	+	0.686535i	$0.759131\pi$
$678$	−14.3761	−	4.67106i	−0.552109	−	0.179391i
$679$	6.37008	+	19.6051i	0.244461	+	0.752374i
$680$	124.006	−	90.0960i	4.75543	−	3.45502i
$681$			9.76067i			0.374030i
$682$	23.8669	+	15.8812i	0.913909	+	0.608124i
$683$		−	14.0127i		−	0.536181i	−0.963394	−	0.268091i	$-0.913607\pi$
$683$		−	14.0127i		−	0.536181i	0.963394	−	0.268091i	$-0.0863926\pi$
$684$	−11.9648	−	16.4682i	−0.457486	−	0.629676i
$685$	−6.64637	−	20.4554i	−0.253945	−	0.781562i
$686$	13.4290	−	41.3303i	0.512722	−	1.57800i
$687$	8.42025	−	11.5895i	0.321253	−	0.442166i
$688$	4.20111	+	3.05229i	0.160166	+	0.116367i
$689$	−11.0951	+	5.73830i	−0.422691	+	0.218612i
$690$	−3.25022	−	10.0032i	−0.123734	−	0.380813i
$691$	−12.1699	−	16.7504i	−0.462964	−	0.637215i	0.512156	−	0.858892i	$-0.328847\pi$
$691$	−12.1699	−	16.7504i	−0.462964	−	0.637215i	−0.975120	+	0.221677i	$0.928847\pi$
$692$	66.8277			2.54041
$693$	−0.378035	−	9.17338i	−0.0143604	−	0.348468i
$694$		−	34.3055i		−	1.30222i
$695$	−21.7874	−	29.9877i	−0.826442	−	1.13750i
$696$	23.6750	−	7.69247i	0.897398	−	0.291582i
$697$	42.6825	+	13.8684i	1.61672	+	0.525303i
$698$	−10.4029	−	7.55817i	−0.393756	−	0.286081i
$699$	−18.4681	−	13.4178i	−0.698527	−	0.507509i
$700$	−99.0024	−	32.1678i	−3.74194	−	1.21583i
$701$	11.2290	+	34.5594i	0.424115	+	1.30529i	0.903839	+	0.427872i	$0.140737\pi$
$701$	11.2290	+	34.5594i	0.424115	+	1.30529i	−0.479725	+	0.877419i	$0.659263\pi$
$702$	−1.34375	+	8.83044i	−0.0507165	+	0.333283i
$703$	10.3368			0.389861
$704$	7.15635	+	19.2842i	0.269715	+	0.726801i
$705$	−20.3518			−0.766493
$706$	−30.3674	+	22.0632i	−1.14289	+	0.830361i
$707$	−32.6970	+	10.6239i	−1.22970	+	0.399553i
$708$	−8.23884	−	2.67696i	−0.309635	−	0.100606i
$709$	−13.3129	+	18.3236i	−0.499976	+	0.688158i	−0.982189	−	0.187896i	$-0.939833\pi$
$709$	−13.3129	+	18.3236i	−0.499976	+	0.688158i	0.482213	+	0.876054i	$0.339833\pi$
$710$	49.6239	−	68.3014i	1.86235	−	2.56331i
$711$	−2.76525	+	8.51057i	−0.103705	+	0.319171i
$712$	3.74361	+	11.5216i	0.140298	+	0.431791i
$713$	2.31972	+	3.19282i	0.0868741	+	0.119572i
$714$	52.8950			1.97955
$715$	22.2445	+	38.9870i	0.831896	+	1.45803i
$716$	10.0094			0.374069
$717$	10.0000	+	13.7638i	0.373457	+	0.514020i
$718$	−23.0034	−	70.7971i	−0.858478	−	2.64212i
$719$	−9.38811	+	28.8936i	−0.350118	+	1.07755i	0.608669	+	0.793424i	$0.291704\pi$
$719$	−9.38811	+	28.8936i	−0.350118	+	1.07755i	−0.958787	+	0.284127i	$0.908296\pi$
$720$	−10.6816	+	14.7020i	−0.398081	+	0.547911i
$721$	16.6422	−	22.9060i	0.619787	−	0.853063i
$722$	−12.2736	−	3.98793i	−0.456775	−	0.148415i
$723$	3.17333	−	1.03108i	0.118017	−	0.0383462i
$724$	−35.5245	+	25.8101i	−1.32026	+	0.959223i
$725$	−42.7385			−1.58727
$726$	−25.1360	+	10.5247i	−0.932885	+	0.390610i
$727$	39.0889			1.44973			0.724864	−	0.688892i	$-0.241903\pi$
$727$	39.0889			1.44973			0.724864	+	0.688892i	$0.241903\pi$
$728$	−52.2406	−	7.94957i	−1.93617	−	0.294631i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−142.438	−	46.2811i	−5.27188	−	1.71294i
$731$	6.69308	+	4.86281i	0.247553	+	0.179857i
$732$	−23.2246	−	16.8737i	−0.858406	−	0.623668i
$733$	37.4395	+	12.1648i	1.38286	+	0.449318i	0.903608	−	0.428360i	$-0.140908\pi$
$733$	37.4395	+	12.1648i	1.38286	+	0.449318i	0.479251	+	0.877678i	$0.340908\pi$
$734$	−10.1601	+	3.30123i	−0.375017	+	0.121850i
$735$	−1.46294	−	2.01356i	−0.0539612	−	0.0742713i
$736$		−	1.58932i		−	0.0585833i
$737$	−19.6885	−	5.51201i	−0.725235	−	0.203037i
$738$	−14.4143			−0.530598
$739$	8.13445	+	11.1961i	0.299231	+	0.411855i	0.931985	−	0.362497i	$-0.118076\pi$
$739$	8.13445	+	11.1961i	0.299231	+	0.411855i	−0.632754	+	0.774353i	$0.718076\pi$
$740$	−10.0814	−	31.0275i	−0.370601	−	1.14059i
$741$	8.14970	+	15.7577i	0.299387	+	0.578872i
$742$	−19.2209	−	13.9648i	−0.705621	−	0.512664i
$743$	−4.50309	+	6.19797i	−0.165202	+	0.227381i	−0.883590	−	0.468262i	$-0.844880\pi$
$743$	−4.50309	+	6.19797i	−0.165202	+	0.227381i	0.718388	+	0.695643i	$0.244880\pi$
$744$	5.70827	−	17.5682i	0.209275	−	0.644083i
$745$	−15.5516	−	47.8630i	−0.569768	−	1.75356i
$746$	21.2232	+	29.2113i	0.777038	+	1.06950i
$747$		−	13.1457i		−	0.480974i
$748$	−36.8211	−	99.2219i	−1.34631	−	3.62791i
$749$			11.3094i			0.413238i
$750$	30.7654	−	22.3524i	1.12339	−	0.816193i
$751$	5.46646	+	16.8240i	0.199474	+	0.613917i	0.999895	+	0.0144795i	$0.00460912\pi$
$751$	5.46646	+	16.8240i	0.199474	+	0.613917i	−0.800421	+	0.599438i	$0.795391\pi$
$752$	−24.9650	−	8.11161i	−0.910379	−	0.295800i
$753$	−13.3288	−	9.68397i	−0.485730	−	0.352903i
$754$	−41.4405	+	6.82146i	−1.50917	+	0.248423i
$755$	25.8228	−	79.4744i	0.939788	−	2.89237i
$756$	−10.8919	+	3.53899i	−0.396135	+	0.128712i
$757$	−39.3439	+	28.5850i	−1.42998	+	1.03894i	−0.439957	+	0.898019i	$0.645006\pi$
$757$	−39.3439	+	28.5850i	−1.42998	+	1.03894i	−0.990021	+	0.140921i	$0.954994\pi$
$758$	5.31002			0.192869
$759$	−3.74825	+	0.154465i	−0.136053	+	0.00560674i
$760$			97.7791i			3.54682i
$761$	14.4902	+	19.9441i	0.525270	+	0.722972i	0.986400	−	0.164360i	$-0.0525559\pi$
$761$	14.4902	+	19.9441i	0.525270	+	0.722972i	−0.461130	+	0.887332i	$0.652556\pi$
$762$	−50.5872	+	16.4368i	−1.83258	+	0.595441i
$763$	−17.3973	+	53.5433i	−0.629824	+	1.93840i
$764$	−20.4570	−	14.8629i	−0.740110	−	0.537721i
$765$	−17.0176	+	23.4228i	−0.615274	+	0.846852i
$766$	3.59690	−	11.0701i	0.129961	−	0.399980i
$767$	6.74759	+	3.38667i	0.243641	+	0.122286i
$768$	26.3898	−	19.1733i	0.952259	−	0.691857i
$769$		−	11.4079i		−	0.411380i	−0.978617	−	0.205690i	$-0.934056\pi$
$769$		−	11.4079i		−	0.411380i	0.978617	−	0.205690i	$-0.0659439\pi$
$770$	−47.2953	+	71.0770i	−1.70441	+	2.56144i
$771$	14.3721			0.517597
$772$	33.0595	+	45.5025i	1.18984	+	1.63767i
$773$	22.9767	−	7.46560i	0.826416	−	0.268519i	0.134881	−	0.990862i	$-0.456935\pi$
$773$	22.9767	−	7.46560i	0.826416	−	0.268519i	0.691535	+	0.722343i	$0.256935\pi$
$774$	−2.52711	−	0.821108i	−0.0908351	−	0.0295141i
$775$	−18.6413	+	25.6576i	−0.669616	+	0.921647i
$776$	−31.8952	−	23.1732i	−1.14497	−	0.831870i
$777$	1.79713	−	5.53100i	0.0644717	−	0.198423i
$778$	−10.6509	+	3.46069i	−0.381854	+	0.124072i
$779$	−23.1612	+	16.8276i	−0.829836	+	0.602911i
$780$	39.3505	−	39.8308i	1.40898	−	1.42617i
$781$	−18.6874	−	23.6116i	−0.668688	−	0.844890i
$782$		−	21.6129i		−	0.772877i
$783$	−3.80395	+	2.76373i	−0.135942	+	0.0987677i
$784$	−0.991998	−	3.05306i	−0.0354285	−	0.109038i
$785$	−9.37246	−	3.04530i	−0.334517	−	0.108691i
$786$	−1.18938	+	1.63704i	−0.0424236	+	0.0583911i
$787$	0.509828	−	0.701718i	0.0181734	−	0.0250135i	−0.799834	−	0.600222i	$-0.795079\pi$
$787$	0.509828	−	0.701718i	0.0181734	−	0.0250135i	0.818007	+	0.575208i	$0.195079\pi$
$788$	21.6914	+	7.04797i	0.772725	+	0.251074i
$789$	7.08027	+	21.7908i	0.252064	+	0.775775i
$790$	67.3194	−	48.9104i	2.39512	−	1.74015i
$791$			16.8909i			0.600572i
$792$	10.8972	+	13.7686i	0.387213	+	0.489246i
$793$	17.7979	+	17.5833i	0.632023	+	0.624402i
$794$	25.1127	−	18.2454i	0.891216	−	0.647506i
$795$	12.3677	−	4.01850i	0.438636	−	0.142521i
$796$	16.0207	−	49.3067i	0.567840	−	1.74763i
$797$	35.4224	+	25.7359i	1.25473	+	0.911611i	0.998486	−	0.0550022i	$-0.0175166\pi$
$797$	35.4224	+	25.7359i	1.25473	+	0.911611i	0.256239	+	0.966613i	$0.417517\pi$
$798$	−19.8332	+	27.2981i	−0.702088	+	0.966342i
$799$	−39.7734	−	12.9232i	−1.40708	−	0.457189i
$800$	12.1468	−	3.94672i	0.429453	−	0.139538i
$801$	−1.34499	−	1.85122i	−0.0475230	−	0.0654098i
$802$	−50.8742			−1.79643
$803$	−29.5922	+	44.4722i	−1.04429	+	1.56939i
$804$			25.5034i			0.899434i
$805$	−9.50841	+	6.90826i	−0.335127	+	0.243484i
$806$	−13.9800	+	27.8537i	−0.492424	+	0.981103i
$807$	−8.33262	+	25.6452i	−0.293322	+	0.902753i
$808$	38.6479	−	53.1942i	1.35963	−	1.87137i
$809$	−18.8544	−	13.6985i	−0.662885	−	0.481614i	0.204751	−	0.978814i	$-0.434361\pi$
$809$	−18.8544	−	13.6985i	−0.662885	−	0.481614i	−0.867636	+	0.497200i	$0.834361\pi$
$810$	2.87351	−	8.84375i	0.100965	−	0.310738i
$811$	12.7636	−	4.14714i	0.448190	−	0.145626i	−0.0762212	−	0.997091i	$-0.524286\pi$
$811$	12.7636	−	4.14714i	0.448190	−	0.145626i	0.524411	+	0.851465i	$0.324286\pi$
$812$	−31.6514	−	43.5644i	−1.11075	−	1.52881i
$813$			7.02955i			0.246537i
$814$	−17.2467	+	0.710736i	−0.604496	+	0.0249113i
$815$	8.05057			0.281999
$816$	−30.2106	+	21.9493i	−1.05758	+	0.768379i
$817$	−5.01920	+	1.63084i	−0.175599	+	0.0570557i
$818$	−6.24313	+	19.2144i	−0.218286	+	0.671815i
$819$	9.84844	−	1.62114i	0.344132	−	0.0566471i
$820$	73.0994	+	53.1098i	2.55274	+	1.85468i
$821$	−7.74204	−	2.51554i	−0.270199	−	0.0877930i	0.170784	−	0.985309i	$-0.445370\pi$
$821$	−7.74204	−	2.51554i	−0.270199	−	0.0877930i	−0.440983	+	0.897516i	$0.645370\pi$
$822$	4.38650	+	13.5003i	0.152997	+	0.470875i
$823$	16.3157	−	11.8540i	0.568729	−	0.413206i	−0.265914	−	0.963997i	$-0.585674\pi$
$823$	16.3157	−	11.8540i	0.568729	−	0.413206i	0.834643	+	0.550791i	$0.185674\pi$
$824$			54.1497i			1.88639i
$825$	−10.4884	−	28.2632i	−0.365161	−	0.983999i
$826$			14.3597i			0.499640i
$827$	20.2338	+	27.8494i	0.703598	+	0.968419i	0.999911	+	0.0133283i	$0.00424265\pi$
$827$	20.2338	+	27.8494i	0.703598	+	0.968419i	−0.296314	+	0.955091i	$0.595757\pi$
$828$	1.44603	+	4.45044i	0.0502532	+	0.154663i
$829$	13.0634	−	40.2051i	0.453711	−	1.39638i	−0.418930	−	0.908018i	$-0.637595\pi$
$829$	13.0634	−	40.2051i	0.453711	−	1.39638i	0.872642	−	0.488361i	$-0.162405\pi$
$830$	−71.8507	+	98.8940i	−2.49397	+	3.43266i
$831$	−12.6384	−	9.18230i	−0.438420	−	0.318531i
$832$	−19.8620	+	10.2724i	−0.688590	+	0.356132i
$833$	−1.58042	−	4.86404i	−0.0547583	−	0.168529i
$834$	14.3793	+	19.7914i	0.497914	+	0.685320i
$835$	−11.9066			−0.412043
$836$	65.0127	+	18.2010i	2.24851	+	0.629496i
$837$			3.48912i			0.120602i
$838$	56.8456	+	78.2412i	1.96370	+	2.70280i
$839$	22.0309	−	7.15828i	0.760592	−	0.247131i	0.0970593	−	0.995279i	$-0.469056\pi$
$839$	22.0309	−	7.15828i	0.760592	−	0.247131i	0.663533	+	0.748147i	$0.269056\pi$
$840$	52.3194	+	16.9996i	1.80519	+	0.586542i
$841$	5.57556	+	4.05088i	0.192261	+	0.139686i
$842$	61.0444	+	44.3514i	2.10373	+	1.52845i
$843$	1.87312	+	0.608612i	0.0645135	+	0.0209617i
$844$	7.75371	+	23.8635i	0.266894	+	0.821414i
$845$	−39.1266	+	29.1589i	−1.34600	+	1.00310i
$846$	13.4319			0.461797
$847$	19.8646	+	23.0787i	0.682556	+	0.792995i
$848$	16.7727			0.575977
$849$	−6.47290	+	4.70284i	−0.222149	+	0.161401i
$850$	165.182	−	53.6708i	5.66568	−	1.84089i
$851$	−2.25997	−	0.734309i	−0.0774708	−	0.0251718i
$852$	−22.0778	+	30.3875i	−0.756374	+	1.04106i
$853$	−23.1305	+	31.8364i	−0.791973	+	1.09006i	0.201887	+	0.979409i	$0.435293\pi$
$853$	−23.1305	+	31.8364i	−0.791973	+	1.09006i	−0.993860	+	0.110648i	$0.964707\pi$
$854$	−14.7048	+	45.2568i	−0.503189	+	1.54866i
$855$	−5.70719	−	17.5649i	−0.195182	−	0.600708i
$856$	−12.7135	−	17.4986i	−0.434538	−	0.598090i
$857$	−37.9122			−1.29505			−0.647527	−	0.762042i	$-0.724197\pi$
$857$	−37.9122			−1.29505			−0.647527	+	0.762042i	$0.724197\pi$
$858$	−14.6810	−	25.7308i	−0.501200	−	0.878435i
$859$	8.15109			0.278112			0.139056	−	0.990285i	$-0.455593\pi$
$859$	8.15109			0.278112			0.139056	+	0.990285i	$0.455593\pi$
$860$	9.79038	+	13.4753i	0.333849	+	0.459504i
$861$	4.97732	+	15.3186i	0.169627	+	0.522057i
$862$	−3.84688	+	11.8395i	−0.131025	+	0.403254i
$863$	−10.8076	+	14.8754i	−0.367895	+	0.506364i	−0.952327	−	0.305078i	$-0.901317\pi$
$863$	−10.8076	+	14.8754i	−0.367895	+	0.506364i	0.584432	+	0.811443i	$0.301317\pi$
$864$	0.825906	−	1.13676i	0.0280979	−	0.0386735i
$865$	57.6654	+	18.7366i	1.96068	+	0.637064i
$866$	−86.9027	+	28.2364i	−2.95307	+	0.959512i
$867$	−34.3773	+	24.9766i	−1.16752	+	0.848250i
$868$	−39.9589			−1.35629
$869$	−10.3257	−	27.8248i	−0.350277	−	0.943892i
$870$	43.7227			1.48234
$871$	3.34378	−	21.9736i	0.113300	−	0.744549i
$872$	−33.2726	−	102.402i	−1.12675	−	3.46778i
$873$	7.08219	+	2.30114i	0.239696	+	0.0778819i
$874$	11.1540	+	8.10387i	0.377290	+	0.274117i
$875$	−34.3781	−	24.9772i	−1.16219	−	0.844382i
$876$	63.3714	+	20.5906i	2.14112	+	0.695692i
$877$	33.0089	−	10.7252i	1.11463	−	0.362165i	0.306914	−	0.951737i	$-0.400703\pi$
$877$	33.0089	−	10.7252i	1.11463	−	0.362165i	0.807716	+	0.589572i	$0.200703\pi$
$878$	−18.3751	−	25.2912i	−0.620130	−	0.853536i
$879$		−	8.60603i		−	0.290274i
$880$	−2.48170	−	60.2208i	−0.0836581	−	2.03004i
$881$	11.5200			0.388120			0.194060	−	0.980990i	$-0.437834\pi$
$881$	11.5200			0.388120			0.194060	+	0.980990i	$0.437834\pi$
$882$	0.965514	+	1.32892i	0.0325106	+	0.0447469i
$883$	14.1917	+	43.6775i	0.477588	+	1.46986i	0.842436	+	0.538797i	$0.181121\pi$
$883$	14.1917	+	43.6775i	0.477588	+	1.46986i	−0.364848	+	0.931067i	$0.618879\pi$
$884$	102.195	−	52.8540i	3.43718	−	1.77767i
$885$	−6.35872	−	4.61988i	−0.213746	−	0.155296i
$886$	−37.2108	+	51.2163i	−1.25012	+	1.72065i
$887$	16.1328	−	49.6516i	0.541686	−	1.66714i	−0.187055	−	0.982349i	$-0.559894\pi$
$887$	16.1328	−	49.6516i	0.541686	−	1.66714i	0.728741	−	0.684789i	$-0.240106\pi$
$888$	3.43704	+	10.5781i	0.115339	+	0.354978i
$889$	34.9359	+	48.0852i	1.17171	+	1.61273i
$890$			21.2780i			0.713241i
$891$	−2.76120	−	1.83733i	−0.0925037	−	0.0615528i
$892$			52.3149i			1.75163i
$893$	21.5826	−	15.6807i	0.722234	−	0.524734i
$894$	10.2638	+	31.5888i	0.343274	+	1.05649i
$895$	8.63708	+	2.80636i	0.288706	+	0.0938061i
$896$	−40.7019	−	29.5717i	−1.35975	−	0.987920i
$897$	−0.662398	−	4.02408i	−0.0221168	−	0.134360i
$898$	−2.05605	+	6.32787i	−0.0686113	+	0.211164i
$899$	−15.6027	+	5.06962i	−0.520378	+	0.169081i
$900$	−30.4225	+	22.1033i	−1.01408	+	0.736776i
$901$	26.7217			0.890230
$902$	37.4867	−	29.6688i	1.24817	−	0.987863i
$903$			2.96919i			0.0988084i
$904$	−18.9879	−	26.1346i	−0.631528	−	0.869223i
$905$	−37.8904	+	12.3113i	−1.25952	+	0.409243i
$906$	−17.0426	+	52.4518i	−0.566203	+	1.74259i
$907$	16.2055	+	11.7740i	0.538094	+	0.390948i	0.823377	−	0.567495i	$-0.192088\pi$
$907$	16.2055	+	11.7740i	0.538094	+	0.390948i	−0.285283	+	0.958443i	$0.592088\pi$
$908$	−23.7353	+	32.6688i	−0.787683	+	1.08415i
$909$	−3.83781	+	11.8116i	−0.127292	+	0.391764i
$910$	−82.9500	−	41.6333i	−2.74976	−	1.38013i
$911$	−33.3169	+	24.2062i	−1.10384	+	0.801986i	−0.981682	−	0.190525i	$-0.938981\pi$
$911$	−33.3169	+	24.2062i	−1.10384	+	0.801986i	−0.122157	+	0.992511i	$0.538981\pi$
$912$		−	23.8211i		−	0.788795i
$913$	27.0576	+	34.1874i	0.895475	+	1.13144i
$914$	−5.00474			−0.165542
$915$	−15.3095	−	21.0718i	−0.506117	−	0.696611i
$916$	56.3649	−	18.3141i	1.86235	−	0.605114i
$917$	2.15044	+	0.698719i	0.0710137	+	0.0230737i
$918$	11.2314	−	15.4586i	0.370690	−	0.510211i
$919$	−40.6518	−	29.5353i	−1.34098	−	0.974278i	−0.999407	−	0.0344224i	$-0.989041\pi$
$919$	−40.6518	−	29.5353i	−1.34098	−	0.974278i	−0.341572	−	0.939856i	$-0.610959\pi$
$920$	6.94604	−	21.3777i	0.229004	−	0.704803i
$921$	−3.95000	+	1.28343i	−0.130157	+	0.0422906i
$922$	−37.9089	+	27.5424i	−1.24846	+	0.907060i
$923$	23.0064	−	23.2872i	0.757264	−	0.766507i
$924$	21.0419	−	31.6224i	0.692226	−	1.04030i
$925$		−	19.0958i		−	0.627866i
$926$	−25.0134	+	18.1733i	−0.821991	+	0.597212i
$927$	−3.16062	−	9.72738i	−0.103808	−	0.319489i
$928$	6.28341	+	2.04160i	0.206263	+	0.0670189i
$929$	−1.22972	+	1.69256i	−0.0403458	+	0.0555313i	−0.828713	−	0.559673i	$-0.810927\pi$
$929$	−1.22972	+	1.69256i	−0.0403458	+	0.0555313i	0.788367	+	0.615205i	$0.210927\pi$
$930$	19.0706	−	26.2484i	0.625350	−	0.860720i
$931$	3.10282	+	1.00817i	0.101691	+	0.0330413i
$932$	−29.1838	−	89.8186i	−0.955948	−	2.94211i
$933$	1.72373	−	1.25236i	0.0564324	−	0.0410005i
$934$		−	46.3094i		−	1.51529i
$935$	−3.95377	−	95.9419i	−0.129302	−	3.13764i
$936$	−13.4157	+	13.5794i	−0.438505	+	0.443857i
$937$	−37.0016	+	26.8832i	−1.20879	+	0.878236i	−0.995120	−	0.0986699i	$-0.968541\pi$
$937$	−37.0016	+	26.8832i	−1.20879	+	0.878236i	−0.213668	+	0.976906i	$0.568541\pi$
$938$	40.2060	−	13.0637i	1.31277	−	0.426546i
$939$	1.51202	−	4.65351i	0.0493429	−	0.151862i
$940$	−68.1172	−	49.4900i	−2.22174	−	1.61419i
$941$	3.90271	−	5.37162i	0.127225	−	0.175110i	−0.740653	−	0.671888i	$-0.765484\pi$
$941$	3.90271	−	5.37162i	0.127225	−	0.175110i	0.867878	+	0.496778i	$0.165484\pi$
$942$	6.18567	+	2.00984i	0.201540	+	0.0654843i
$943$	6.25920	−	2.03374i	0.203828	−	0.0662276i
$944$	−5.95872	−	8.20147i	−0.193940	−	0.266935i
$945$	−10.3908			−0.338013
$946$	8.26224	−	3.06611i	0.268629	−	0.0996877i
$947$		−	14.4104i		−	0.468276i	−0.972203	−	0.234138i	$-0.924773\pi$
$947$		−	14.4104i		−	0.468276i	0.972203	−	0.234138i	$-0.0752267\pi$
$948$	−29.9506	+	21.7604i	−0.972751	+	0.706745i
$949$	−51.9010	−	26.0495i	−1.68478	−	0.845604i
$950$	−34.2371	+	105.371i	−1.11080	+	3.41869i
$951$	10.7977	−	14.8618i	0.350140	−	0.481926i
$952$	91.4528	+	66.4444i	2.96400	+	2.15347i
$953$	11.4381	−	35.2030i	0.370518	−	1.14034i	−0.575935	−	0.817495i	$-0.695362\pi$
$953$	11.4381	−	35.2030i	0.370518	−	1.14034i	0.946453	−	0.322842i	$-0.104638\pi$
$954$	−8.16245	+	2.65214i	−0.264269	+	0.0858663i
$955$	−13.4852	−	18.5607i	−0.436370	−	0.600611i
$956$			70.3847i			2.27640i
$957$	4.20422	−	15.0172i	0.135903	−	0.485436i
$958$	106.695			3.44716
$959$	12.8326	−	9.32339i	0.414385	−	0.301068i
$960$	22.1400	−	7.19371i	0.714564	−	0.232176i
$961$	5.81757	−	17.9046i	0.187663	−	0.577569i
$962$	−3.04787	−	18.5158i	−0.0982672	−	0.596975i
$963$	3.30520	+	2.40137i	0.106508	+	0.0773829i
$964$	13.1284	+	4.26567i	0.422837	+	0.137388i
$965$	15.7693	+	48.5330i	0.507632	+	1.56233i
$966$	6.27540	−	4.55934i	0.201908	−	0.146694i
$967$			28.0563i			0.902230i	0.892466	+	0.451115i	$0.148974\pi$
$967$			28.0563i			0.902230i	−0.892466	+	0.451115i	$0.851026\pi$
$968$	−56.6796	−	13.3780i	−1.82175	−	0.429984i
$969$		−	37.9510i		−	1.21916i
$970$	−40.7015	−	56.0207i	−1.30685	−	1.79872i
$971$	−1.54487	−	4.75461i	−0.0495771	−	0.152583i	0.923203	−	0.384312i	$-0.125561\pi$
$971$	−1.54487	−	4.75461i	−0.0495771	−	0.152583i	−0.972780	+	0.231730i	$0.925561\pi$
$972$	−1.27843	+	3.93462i	−0.0410058	+	0.126203i
$973$	16.0678	−	22.1155i	0.515111	−	0.708990i
$974$	52.3597	+	38.0415i	1.67771	+	1.21893i
$975$	29.1100	−	15.0554i	0.932266	−	0.482159i
$976$	−10.3812	−	31.9500i	−0.332294	−	1.02269i
$977$	−9.08318	−	12.5019i	−0.290597	−	0.399972i	0.638611	−	0.769530i	$-0.279509\pi$
$977$	−9.08318	−	12.5019i	−0.290597	−	0.399972i	−0.929208	+	0.369557i	$0.879509\pi$
$978$	−5.31325			−0.169899
$979$	7.30823	+	2.04602i	0.233572	+	0.0653911i
$980$		−	10.2968i		−	0.328920i
$981$	11.9541	+	16.4534i	0.381664	+	0.525316i
$982$	−43.4645	+	14.1225i	−1.38701	+	0.450666i
$983$	−41.3610	−	13.4390i	−1.31921	−	0.428637i	−0.436987	−	0.899468i	$-0.643954\pi$
$983$	−41.3610	−	13.4390i	−1.31921	−	0.428637i	−0.882224	+	0.470830i	$0.843954\pi$
$984$	−24.9216	−	18.1066i	−0.794471	−	0.577217i
$985$	16.7414	+	12.1633i	0.533426	+	0.387556i
$986$	85.4470	+	27.7634i	2.72119	+	0.884167i
$987$	−4.63808	−	14.2745i	−0.147632	−	0.454364i
$988$	−11.0414	+	72.5585i	−0.351273	+	2.30839i
$989$	1.21321			0.0385779
$990$	10.7300	+	28.9141i	0.341021	+	0.918951i
$991$	10.3292			0.328117			0.164059	−	0.986451i	$-0.447541\pi$
$991$	10.3292			0.328117			0.164059	+	0.986451i	$0.447541\pi$
$992$	3.96630	−	2.88169i	0.125930	−	0.0914936i
$993$	−18.8004	+	6.10862i	−0.596613	+	0.193851i
$994$	59.2149	+	19.2401i	1.87818	+	0.610259i
$995$	27.6485	−	38.0548i	0.876515	−	1.20642i
$996$	31.9666	−	43.9983i	1.01290	−	1.39414i
$997$	5.00544	−	15.4052i	0.158524	−	0.487886i	−0.839977	−	0.542622i	$-0.817432\pi$
$997$	5.00544	−	15.4052i	0.158524	−	0.487886i	0.998501	+	0.0547358i	$0.0174317\pi$
$998$	12.6864	+	39.0449i	0.401582	+	1.23594i
$999$	−1.23485	−	1.69963i	−0.0390690	−	0.0537738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.1	✓	56
11.4	even	5	inner	429.2.bb.a.103.14	yes	56
13.12	even	2	inner	429.2.bb.a.25.14	yes	56
143.103	even	10	inner	429.2.bb.a.103.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.1	✓	56	1.1	even	1	trivial
429.2.bb.a.25.14	yes	56	13.12	even	2	inner
429.2.bb.a.103.1	yes	56	143.103	even	10	inner
429.2.bb.a.103.14	yes	56	11.4	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45613 - 2.00419i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.27843 + 3.93462i) q^{4} +(-2.20631 + 3.03673i) q^{5} +(1.45613 - 2.00419i) q^{6} +(-2.63274 - 0.855429i) q^{7} +(5.03515 - 1.63602i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.45613 - 2.00419i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.27843 + 3.93462i) q^{4} +(-2.20631 + 3.03673i) q^{5} +(1.45613 - 2.00419i) q^{6} +(-2.63274 - 0.855429i) q^{7} +(5.03515 - 1.63602i) q^{8} +(-0.809017 + 0.587785i) q^{9} +9.29887 q^{10} +(0.894146 - 3.19382i) q^{11} -4.13710 q^{12} +(3.56452 + 0.542421i) q^{13} +(2.11917 + 6.52213i) q^{14} +(-3.56989 - 1.15993i) q^{15} +(-3.91677 - 2.84570i) q^{16} +(-6.24007 - 4.53368i) q^{17} +(2.35607 + 0.765533i) q^{18} +(4.67948 - 1.52046i) q^{19} +(-9.12774 - 12.5633i) q^{20} -2.76822i q^{21} +(-7.70303 + 2.85858i) q^{22} -1.13110 q^{23} +(3.11189 + 4.28316i) q^{24} +(-2.80882 - 8.64467i) q^{25} +(-4.10329 - 7.93381i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(6.73156 - 9.26520i) q^{28} +(1.45298 - 4.47181i) q^{29} +(2.87351 + 8.84375i) q^{30} +(-2.05085 - 2.82276i) q^{31} +1.40512i q^{32} +(3.31381 - 0.136562i) q^{33} +19.1079i q^{34} +(8.40635 - 6.10757i) q^{35} +(-1.27843 - 3.93462i) q^{36} +(1.99803 + 0.649200i) q^{37} +(-9.86122 - 7.16460i) q^{38} +(0.585624 + 3.55767i) q^{39} +(-6.14097 + 18.9000i) q^{40} +(-5.53373 + 1.79802i) q^{41} +(-5.54805 + 4.03090i) q^{42} -1.07260 q^{43} +(11.4234 + 7.60121i) q^{44} -3.75360i q^{45} +(1.64703 + 2.26694i) q^{46} +(5.15657 - 1.67547i) q^{47} +(1.49607 - 4.60444i) q^{48} +(0.536434 + 0.389742i) q^{49} +(-13.2356 + 18.2172i) q^{50} +(2.38350 - 7.33564i) q^{51} +(-6.69122 + 13.3316i) q^{52} +(-2.80279 + 2.03635i) q^{53} +2.47732i q^{54} +(7.72601 + 9.76185i) q^{55} -14.6557 q^{56} +(2.89208 + 3.98061i) q^{57} +(-11.0781 + 3.59949i) q^{58} +(1.99145 + 0.647063i) q^{59} +(9.12774 - 12.5633i) q^{60} +(5.61374 + 4.07862i) q^{61} +(-2.67104 + 8.22060i) q^{62} +(2.63274 - 0.855429i) q^{63} +(-5.01741 + 3.64536i) q^{64} +(-9.51162 + 9.62772i) q^{65} +(-5.09904 - 6.44266i) q^{66} -6.16455i q^{67} +(25.8158 - 18.7563i) q^{68} +(-0.349529 - 1.07574i) q^{69} +(-24.4815 - 7.95452i) q^{70} +(5.33655 - 7.34513i) q^{71} +(-3.11189 + 4.28316i) q^{72} +(-15.3178 - 4.97707i) q^{73} +(-1.60827 - 4.94976i) q^{74} +(7.35359 - 5.34270i) q^{75} +20.3558i q^{76} +(-5.08614 + 7.64362i) q^{77} +(6.27752 - 6.35414i) q^{78} +(7.23952 - 5.25982i) q^{79} +(17.2832 - 5.61566i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6614 + 8.47251i) q^{82} +(-7.72682 + 10.6351i) q^{83} +(10.8919 + 3.53899i) q^{84} +(27.5351 - 8.94670i) q^{85} +(1.56184 + 2.14969i) q^{86} +4.70194 q^{87} +(-0.722998 - 17.5442i) q^{88} +2.28824i q^{89} +(-7.52294 + 5.46574i) q^{90} +(-8.92044 - 4.47724i) q^{91} +(1.44603 - 4.45044i) q^{92} +(2.05085 - 2.82276i) q^{93} +(-10.8666 - 7.89505i) q^{94} +(-5.70719 + 17.5649i) q^{95} +(-1.33634 + 0.434205i) q^{96} +(-4.37703 - 6.02447i) q^{97} -1.64263i q^{98} +(1.15390 + 3.10942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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