LMFDB - Embedded newform 429.2.n.a.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 9x^10 - 15x^9 + 29x^8 - 26x^7 + 43x^6 + 24x^5 + 16x^4 - 17x^3 + 14x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.2
Root			$0.275227 + 0.199964i$ of defining polynomial
Character	$\chi$	$=$	429.157
Dual form			429.2.n.a.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.275227 - 0.199964i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.582270 + 1.79204i) q^{4} +(3.18709 + 2.31555i) q^{5} +(0.275227 + 0.199964i) q^{6} +(-0.203890 + 0.627508i) q^{7} +(0.408342 + 1.25675i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.275227 - 0.199964i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.582270 + 1.79204i) q^{4} +(3.18709 + 2.31555i) q^{5} +(0.275227 + 0.199964i) q^{6} +(-0.203890 + 0.627508i) q^{7} +(0.408342 + 1.25675i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.34020 q^{10} +(-0.0920501 - 3.31535i) q^{11} -1.88426 q^{12} +(-0.809017 + 0.587785i) q^{13} +(0.0693631 + 0.213478i) q^{14} +(-1.21736 + 3.74665i) q^{15} +(-2.68511 - 1.95085i) q^{16} +(-0.812211 - 0.590106i) q^{17} +(-0.105127 + 0.323548i) q^{18} +(-1.57486 - 4.84691i) q^{19} +(-6.00532 + 4.36312i) q^{20} -0.659801 q^{21} +(-0.688284 - 0.894065i) q^{22} +3.10400 q^{23} +(-1.06905 + 0.776713i) q^{24} +(3.25065 + 10.0045i) q^{25} +(-0.105127 + 0.323548i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.00580 - 0.730758i) q^{28} +(-0.247787 + 0.762610i) q^{29} +(0.414144 + 1.27460i) q^{30} +(4.03228 - 2.92962i) q^{31} -3.77196 q^{32} +(3.12464 - 1.11204i) q^{33} -0.341542 q^{34} +(-2.10284 + 1.52781i) q^{35} +(-0.582270 - 1.79204i) q^{36} +(0.206975 - 0.637002i) q^{37} +(-1.40265 - 1.01908i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-1.60865 + 4.95090i) q^{40} +(-0.545701 - 1.67949i) q^{41} +(-0.181595 + 0.131936i) q^{42} +11.9438 q^{43} +(5.99484 + 1.76547i) q^{44} -3.93946 q^{45} +(0.854303 - 0.620687i) q^{46} +(1.78728 + 5.50070i) q^{47} +(1.02562 - 3.15654i) q^{48} +(5.31092 + 3.85861i) q^{49} +(2.89520 + 2.10348i) q^{50} +(0.310237 - 0.954811i) q^{51} +(-0.582270 - 1.79204i) q^{52} +(-9.61976 + 6.98917i) q^{53} -0.340199 q^{54} +(7.38350 - 10.7794i) q^{55} -0.871876 q^{56} +(4.12303 - 2.99555i) q^{57} +(0.0842969 + 0.259439i) q^{58} +(-0.106583 + 0.328029i) q^{59} +(-6.00532 - 4.36312i) q^{60} +(-3.47620 - 2.52561i) q^{61} +(0.523972 - 1.61262i) q^{62} +(-0.203890 - 0.627508i) q^{63} +(4.33208 - 3.14744i) q^{64} -3.93946 q^{65} +(0.637615 - 0.930879i) q^{66} -2.12212 q^{67} +(1.53042 - 1.11192i) q^{68} +(0.959188 + 2.95208i) q^{69} +(-0.273253 + 0.840986i) q^{70} +(-7.84151 - 5.69719i) q^{71} +(-1.06905 - 0.776713i) q^{72} +(3.20186 - 9.85431i) q^{73} +(-0.0704125 - 0.216708i) q^{74} +(-8.51031 + 6.18310i) q^{75} +9.60285 q^{76} +(2.09918 + 0.618203i) q^{77} -0.340199 q^{78} +(5.15995 - 3.74892i) q^{79} +(-4.04039 - 12.4351i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.486030 - 0.353121i) q^{82} +(6.22609 + 4.52352i) q^{83} +(0.384182 - 1.18239i) q^{84} +(-1.22216 - 3.76144i) q^{85} +(3.28726 - 2.38834i) q^{86} -0.801856 q^{87} +(4.12897 - 1.46948i) q^{88} -4.75754 q^{89} +(-1.08424 + 0.787749i) q^{90} +(-0.203890 - 0.627508i) q^{91} +(-1.80736 + 5.56249i) q^{92} +(4.03228 + 2.92962i) q^{93} +(1.59185 + 1.15655i) q^{94} +(6.20408 - 19.0942i) q^{95} +(-1.16560 - 3.58735i) q^{96} +(7.33533 - 5.32943i) q^{97} +2.23329 q^{98} +(2.02318 + 2.62807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

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 $

$2$	0.275227	−	0.199964i	0.194615	−	0.141396i	−0.486211	−	0.873842i	$-0.661621\pi$
$2$	0.275227	−	0.199964i	0.194615	−	0.141396i	0.680825	+	0.732446i	$0.261621\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.582270	+	1.79204i	−0.291135	+	0.896021i
$5$	3.18709	+	2.31555i	1.42531	+	1.03555i	0.990866	+	0.134848i	$0.0430546\pi$
$5$	3.18709	+	2.31555i	1.42531	+	1.03555i	0.434443	+	0.900700i	$0.356945\pi$
$6$	0.275227	+	0.199964i	0.112361	+	0.0816349i
$7$	−0.203890	+	0.627508i	−0.0770631	+	0.237176i	−0.982166	−	0.188017i	$-0.939794\pi$
$7$	−0.203890	+	0.627508i	−0.0770631	+	0.237176i	0.905103	+	0.425193i	$0.139794\pi$
$8$	0.408342	+	1.25675i	0.144371	+	0.444327i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.34020			0.423808
$11$	−0.0920501	−	3.31535i	−0.0277541	−	0.999615i
$11$	−0.0920501	−	3.31535i	−0.0277541	−	0.999615i
$12$	−1.88426			−0.543940
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	0.0693631	+	0.213478i	0.0185381	+	0.0570543i
$15$	−1.21736	+	3.74665i	−0.314321	+	0.967380i
$16$	−2.68511	−	1.95085i	−0.671278	−	0.487712i
$17$	−0.812211	−	0.590106i	−0.196990	−	0.143122i	0.484918	−	0.874560i	$-0.338850\pi$
$17$	−0.812211	−	0.590106i	−0.196990	−	0.143122i	−0.681908	+	0.731438i	$0.738850\pi$
$18$	−0.105127	+	0.323548i	−0.0247787	+	0.0762611i
$19$	−1.57486	−	4.84691i	−0.361297	−	1.11196i	−0.952268	−	0.305264i	$-0.901255\pi$
$19$	−1.57486	−	4.84691i	−0.361297	−	1.11196i	0.590971	−	0.806693i	$-0.298745\pi$
$20$	−6.00532	+	4.36312i	−1.34283	+	0.975623i
$21$	−0.659801			−0.143980
$22$	−0.688284	−	0.894065i	−0.146743	−	0.190615i
$23$	3.10400			0.647228			0.323614	−	0.946189i	$-0.395102\pi$
$23$	3.10400			0.647228			0.323614	+	0.946189i	$0.395102\pi$
$24$	−1.06905	+	0.776713i	−0.218220	+	0.158546i
$25$	3.25065	+	10.0045i	0.650130	+	2.00089i
$26$	−0.105127	+	0.323548i	−0.0206171	+	0.0634531i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.00580	−	0.730758i	−0.190079	−	0.138100i
$29$	−0.247787	+	0.762610i	−0.0460129	+	0.141613i	−0.971424	−	0.237353i	$-0.923720\pi$
$29$	−0.247787	+	0.762610i	−0.0460129	+	0.141613i	0.925411	+	0.378966i	$0.123720\pi$
$30$	0.414144	+	1.27460i	0.0756120	+	0.232710i
$31$	4.03228	−	2.92962i	0.724218	−	0.526176i	−0.163511	−	0.986542i	$-0.552282\pi$
$31$	4.03228	−	2.92962i	0.724218	−	0.526176i	0.887729	+	0.460366i	$0.152282\pi$
$32$	−3.77196			−0.666795
$33$	3.12464	−	1.11204i	0.543930	−	0.193582i
$34$	−0.341542			−0.0585740
$35$	−2.10284	+	1.52781i	−0.355445	+	0.258246i
$36$	−0.582270	−	1.79204i	−0.0970450	−	0.298674i
$37$	0.206975	−	0.637002i	0.0340264	−	0.104723i	−0.932601	−	0.360910i	$-0.882466\pi$
$37$	0.206975	−	0.637002i	0.0340264	−	0.104723i	0.966627	+	0.256187i	$0.0824663\pi$
$38$	−1.40265	−	1.01908i	−0.227540	−	0.165317i
$39$	−0.809017	−	0.587785i	−0.129546	−	0.0941210i
$40$	−1.60865	+	4.95090i	−0.254349	+	0.782806i
$41$	−0.545701	−	1.67949i	−0.0852241	−	0.262293i	0.899359	−	0.437211i	$-0.144034\pi$
$41$	−0.545701	−	1.67949i	−0.0852241	−	0.262293i	−0.984583	+	0.174918i	$0.944034\pi$
$42$	−0.181595	+	0.131936i	−0.0280207	+	0.0203582i
$43$	11.9438			1.82142			0.910709	−	0.413049i	$-0.135536\pi$
$43$	11.9438			1.82142			0.910709	+	0.413049i	$0.135536\pi$
$44$	5.99484	+	1.76547i	0.903756	+	0.266154i
$45$	−3.93946			−0.587260
$46$	0.854303	−	0.620687i	0.125960	−	0.0915153i
$47$	1.78728	+	5.50070i	0.260702	+	0.802359i	0.992652	+	0.121001i	$0.0386104\pi$
$47$	1.78728	+	5.50070i	0.260702	+	0.802359i	−0.731950	+	0.681358i	$0.761390\pi$
$48$	1.02562	−	3.15654i	0.148036	−	0.455607i
$49$	5.31092	+	3.85861i	0.758703	+	0.551230i
$50$	2.89520	+	2.10348i	0.409443	+	0.297478i
$51$	0.310237	−	0.954811i	0.0434419	−	0.133700i
$52$	−0.582270	−	1.79204i	−0.0807463	−	0.248512i
$53$	−9.61976	+	6.98917i	−1.32138	+	0.960036i	−0.321462	+	0.946922i	$0.604174\pi$
$53$	−9.61976	+	6.98917i	−1.32138	+	0.960036i	−0.999914	+	0.0131136i	$0.995826\pi$
$54$	−0.340199			−0.0462952
$55$	7.38350	−	10.7794i	0.995590	−	1.45350i
$56$	−0.871876			−0.116509
$57$	4.12303	−	2.99555i	0.546108	−	0.396771i
$58$	0.0842969	+	0.259439i	0.0110687	+	0.0340660i
$59$	−0.106583	+	0.328029i	−0.0138759	+	0.0427057i	−0.957755	−	0.287586i	$-0.907147\pi$
$59$	−0.106583	+	0.328029i	−0.0138759	+	0.0427057i	0.943879	+	0.330292i	$0.107147\pi$
$60$	−6.00532	−	4.36312i	−0.775283	−	0.563276i
$61$	−3.47620	−	2.52561i	−0.445082	−	0.323371i	0.342569	−	0.939493i	$-0.388703\pi$
$61$	−3.47620	−	2.52561i	−0.445082	−	0.323371i	−0.787651	+	0.616122i	$0.788703\pi$
$62$	0.523972	−	1.61262i	0.0665445	−	0.204803i
$63$	−0.203890	−	0.627508i	−0.0256877	−	0.0790586i
$64$	4.33208	−	3.14744i	0.541510	−	0.393430i
$65$	−3.93946			−0.488629
$66$	0.637615	−	0.930879i	0.0784850	−	0.114583i
$67$	−2.12212			−0.259259			−0.129629	−	0.991563i	$-0.541379\pi$
$67$	−2.12212			−0.259259			−0.129629	+	0.991563i	$0.541379\pi$
$68$	1.53042	−	1.11192i	0.185591	−	0.134840i
$69$	0.959188	+	2.95208i	0.115473	+	0.355388i
$70$	−0.273253	+	0.840986i	−0.0326600	+	0.100517i
$71$	−7.84151	−	5.69719i	−0.930616	−	0.676132i	0.0155275	−	0.999879i	$-0.495057\pi$
$71$	−7.84151	−	5.69719i	−0.930616	−	0.676132i	−0.946144	+	0.323747i	$0.895057\pi$
$72$	−1.06905	−	0.776713i	−0.125989	−	0.0915365i
$73$	3.20186	−	9.85431i	0.374749	−	1.15336i	−0.568898	−	0.822408i	$-0.692630\pi$
$73$	3.20186	−	9.85431i	0.374749	−	1.15336i	0.943648	−	0.330952i	$-0.107370\pi$
$74$	−0.0704125	−	0.216708i	−0.00818529	−	0.0251917i
$75$	−8.51031	+	6.18310i	−0.982686	+	0.713963i
$76$	9.60285			1.10152
$77$	2.09918	+	0.618203i	0.239223	+	0.0704508i
$78$	−0.340199			−0.0385199
$79$	5.15995	−	3.74892i	0.580540	−	0.421787i	−0.258379	−	0.966044i	$-0.583188\pi$
$79$	5.15995	−	3.74892i	0.580540	−	0.421787i	0.838919	+	0.544257i	$0.183188\pi$
$80$	−4.04039	−	12.4351i	−0.451730	−	1.39028i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.486030	−	0.353121i	−0.0536730	−	0.0389957i
$83$	6.22609	+	4.52352i	0.683403	+	0.496521i	0.874485	−	0.485053i	$-0.161200\pi$
$83$	6.22609	+	4.52352i	0.683403	+	0.496521i	−0.191082	+	0.981574i	$0.561200\pi$
$84$	0.384182	−	1.18239i	0.0419177	−	0.129009i
$85$	−1.22216	−	3.76144i	−0.132562	−	0.407985i
$86$	3.28726	−	2.38834i	0.354475	−	0.257541i
$87$	−0.801856			−0.0859680
$88$	4.12897	−	1.46948i	0.440149	−	0.156647i
$89$	−4.75754			−0.504299			−0.252149	−	0.967688i	$-0.581137\pi$
$89$	−4.75754			−0.504299			−0.252149	+	0.967688i	$0.581137\pi$
$90$	−1.08424	+	0.787749i	−0.114289	+	0.0830361i
$91$	−0.203890	−	0.627508i	−0.0213735	−	0.0657807i
$92$	−1.80736	+	5.56249i	−0.188431	+	0.579930i
$93$	4.03228	+	2.92962i	0.418128	+	0.303788i
$94$	1.59185	+	1.15655i	0.164187	+	0.119289i
$95$	6.20408	−	19.0942i	0.636525	−	1.95902i
$96$	−1.16560	−	3.58735i	−0.118964	−	0.366132i
$97$	7.33533	−	5.32943i	0.744790	−	0.541122i	−0.149418	−	0.988774i	$-0.547740\pi$
$97$	7.33533	−	5.32943i	0.744790	−	0.541122i	0.894208	+	0.447653i	$0.147740\pi$
$98$	2.23329			0.225596
$99$	2.02318	+	2.62807i	0.203337	+	0.264131i
$100$	−19.8212			−1.98212
$101$	−15.2148	+	11.0542i	−1.51393	+	1.09994i	−0.549539	+	0.835468i	$0.685197\pi$
$101$	−15.2148	+	11.0542i	−1.51393	+	1.09994i	−0.964394	+	0.264469i	$0.914803\pi$
$102$	−0.105542	−	0.324826i	−0.0104502	−	0.0321625i
$103$	−5.91976	+	18.2192i	−0.583292	+	1.79519i	0.0227335	+	0.999742i	$0.492763\pi$
$103$	−5.91976	+	18.2192i	−0.583292	+	1.79519i	−0.606025	+	0.795446i	$0.707237\pi$
$104$	−1.06905	−	0.776713i	−0.104829	−	0.0761630i
$105$	−2.10284	−	1.52781i	−0.205217	−	0.149099i
$106$	−1.25003	+	3.84721i	−0.121414	+	0.373674i
$107$	−6.13770	−	18.8899i	−0.593354	−	1.82616i	−0.562755	−	0.826624i	$-0.690259\pi$
$107$	−6.13770	−	18.8899i	−0.593354	−	1.82616i	−0.0305990	−	0.999532i	$-0.509741\pi$
$108$	1.52440	−	1.10754i	0.146686	−	0.106573i
$109$	−2.61734			−0.250696			−0.125348	−	0.992113i	$-0.540005\pi$
$109$	−2.61734			−0.250696			−0.125348	+	0.992113i	$0.540005\pi$
$110$	−0.123365	−	4.44322i	−0.0117624	−	0.423645i
$111$	0.669784			0.0635731
$112$	1.77164	−	1.28717i	0.167404	−	0.121626i
$113$	−2.94569	−	9.06589i	−0.277107	−	0.852847i	−0.988654	−	0.150209i	$-0.952005\pi$
$113$	−2.94569	−	9.06589i	−0.277107	−	0.852847i	0.711547	−	0.702638i	$-0.247995\pi$
$114$	0.535764	−	1.64891i	0.0501789	−	0.154435i
$115$	9.89271	+	7.18747i	0.922500	+	0.670235i
$116$	−1.22235	−	0.888090i	−0.113492	−	0.0824571i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	0.0362594	+	0.111595i	0.00333795	+	0.0102732i
$119$	0.535898	−	0.389352i	0.0491257	−	0.0356919i
$120$	−5.20569			−0.475212
$121$	−10.9831	+	0.610356i	−0.998459	+	0.0554869i
$122$	−1.46177			−0.132343
$123$	1.42866	−	1.03798i	0.128818	−	0.0935919i
$124$	2.90213	+	8.93184i	0.260619	+	0.802103i
$125$	−6.71899	+	20.6789i	−0.600965	+	1.84958i
$126$	−0.181595	−	0.131936i	−0.0161778	−	0.0117538i
$127$	−6.13021	−	4.45386i	−0.543968	−	0.395216i	0.281589	−	0.959535i	$-0.409139\pi$
$127$	−6.13021	−	4.45386i	−0.543968	−	0.395216i	−0.825557	+	0.564319i	$0.809139\pi$
$128$	2.89413	−	8.90721i	0.255807	−	0.787294i
$129$	3.69085	+	11.3593i	0.324961	+	1.00013i
$130$	−1.08424	+	0.787749i	−0.0950945	+	0.0690902i
$131$	19.9723			1.74499			0.872496	−	0.488622i	$-0.162500\pi$
$131$	19.9723			1.74499			0.872496	+	0.488622i	$0.162500\pi$
$132$	0.173447	+	6.24699i	0.0150966	+	0.543731i
$133$	3.36257			0.291572
$134$	−0.584065	+	0.424348i	−0.0504555	+	0.0366581i
$135$	−1.21736	−	3.74665i	−0.104774	−	0.322460i
$136$	0.409954	−	1.26171i	0.0351533	−	0.108191i
$137$	9.58097	+	6.96098i	0.818557	+	0.594717i	0.916299	−	0.400495i	$-0.131162\pi$
$137$	9.58097	+	6.96098i	0.818557	+	0.594717i	−0.0977417	+	0.995212i	$0.531162\pi$
$138$	0.854303	+	0.620687i	0.0727231	+	0.0528364i
$139$	0.728026	−	2.24063i	0.0617503	−	0.190048i	−0.915422	−	0.402495i	$-0.868143\pi$
$139$	0.728026	−	2.24063i	0.0617503	−	0.190048i	0.977173	+	0.212447i	$0.0681432\pi$
$140$	−1.51347	−	4.65798i	−0.127912	−	0.393671i
$141$	−4.67917	+	3.39962i	−0.394057	+	0.286299i
$142$	−3.29743			−0.276714
$143$	2.02318	+	2.62807i	0.169187	+	0.219770i
$144$	3.31898			0.276582
$145$	−2.55558	+	1.85674i	−0.212230	+	0.154194i
$146$	−1.08927	−	3.35243i	−0.0901485	−	0.277449i
$147$	−2.02859	+	6.24337i	−0.167315	+	0.514944i
$148$	1.02102	+	0.741815i	0.0839273	+	0.0609768i
$149$	13.1351	+	9.54324i	1.07607	+	0.781813i	0.976994	−	0.213267i	$-0.0684103\pi$
$149$	13.1351	+	9.54324i	1.07607	+	0.781813i	0.0990791	+	0.995080i	$0.468410\pi$
$150$	−1.10587	+	3.40351i	−0.0902937	+	0.277895i
$151$	−2.52549	−	7.77264i	−0.205521	−	0.632529i	−0.999692	−	0.0248338i	$-0.992094\pi$
$151$	−2.52549	−	7.77264i	−0.205521	−	0.632529i	0.794171	−	0.607695i	$-0.207906\pi$
$152$	5.44826	−	3.95839i	0.441912	−	0.321068i
$153$	1.00395			0.0811644
$154$	0.701367	−	0.249613i	0.0565178	−	0.0201144i
$155$	19.6349			1.57711
$156$	1.52440	−	1.10754i	0.122050	−	0.0886744i
$157$	−7.61129	−	23.4251i	−0.607447	−	1.86953i	−0.479003	−	0.877813i	$-0.659002\pi$
$157$	−7.61129	−	23.4251i	−0.607447	−	1.86953i	−0.128444	−	0.991717i	$-0.540998\pi$
$158$	0.670507	−	2.06361i	0.0533426	−	0.164172i
$159$	−9.61976	−	6.98917i	−0.762897	−	0.554277i
$160$	−12.0216	−	8.73418i	−0.950388	−	0.690497i
$161$	−0.632873	+	1.94778i	−0.0498774	+	0.153507i
$162$	−0.105127	−	0.323548i	−0.00825958	−	0.0254204i
$163$	17.5727	−	12.7673i	1.37640	−	1.00001i	0.379196	−	0.925317i	$-0.376201\pi$
$163$	17.5727	−	12.7673i	1.37640	−	1.00001i	0.997206	−	0.0746980i	$-0.0237993\pi$
$164$	3.32747			0.259832
$165$	12.5335	+	3.69109i	0.975731	+	0.287351i
$166$	2.61813			0.203206
$167$	−13.5302	+	9.83028i	−1.04700	+	0.760690i	−0.971640	−	0.236466i	$-0.924011\pi$
$167$	−13.5302	+	9.83028i	−1.04700	+	0.760690i	−0.0753602	+	0.997156i	$0.524011\pi$
$168$	−0.269425	−	0.829203i	−0.0207866	−	0.0639744i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−1.08852	−	0.790859i	−0.0834860	−	0.0606561i
$171$	4.12303	+	2.99555i	0.315296	+	0.229076i
$172$	−6.95454	+	21.4039i	−0.530278	+	1.63203i
$173$	−2.95988	−	9.10959i	−0.225036	−	0.692589i	−0.998288	−	0.0584904i	$-0.981371\pi$
$173$	−2.95988	−	9.10959i	−0.225036	−	0.692589i	0.773252	−	0.634099i	$-0.218629\pi$
$174$	−0.220692	+	0.160342i	−0.0167306	+	0.0121555i
$175$	−6.94066			−0.524664
$176$	−6.22058	+	9.08166i	−0.468894	+	0.684556i
$177$	−0.344910			−0.0259250
$178$	−1.30940	+	0.951337i	−0.0981439	+	0.0713057i
$179$	−0.259669	−	0.799178i	−0.0194086	−	0.0597334i	0.940883	−	0.338731i	$-0.109998\pi$
$179$	−0.259669	−	0.799178i	−0.0194086	−	0.0597334i	−0.960292	+	0.278998i	$0.909998\pi$
$180$	2.29383	−	7.05967i	0.170972	−	0.526197i
$181$	2.63862	+	1.91707i	0.196127	+	0.142495i	0.681515	−	0.731804i	$-0.261321\pi$
$181$	2.63862	+	1.91707i	0.196127	+	0.142495i	−0.485387	+	0.874299i	$0.661321\pi$
$182$	−0.181595	−	0.131936i	−0.0134607	−	0.00977978i
$183$	1.32779	−	4.08652i	0.0981530	−	0.302084i
$184$	1.26749	+	3.90094i	0.0934408	+	0.287581i
$185$	2.13466	−	1.55092i	0.156943	−	0.114026i
$186$	1.69561			0.124328
$187$	−1.88164	+	2.74708i	−0.137599	+	0.200886i
$188$	−10.8982			−0.794830
$189$	0.533790	−	0.387821i	0.0388275	−	0.0282099i
$190$	−2.11062	−	6.49582i	−0.153120	−	0.471256i
$191$	1.18850	−	3.65781i	0.0859965	−	0.264670i	−0.898806	−	0.438346i	$-0.855565\pi$
$191$	1.18850	−	3.65781i	0.0859965	−	0.264670i	0.984803	+	0.173676i	$0.0555645\pi$
$192$	4.33208	+	3.14744i	0.312641	+	0.227147i
$193$	17.0295	+	12.3727i	1.22581	+	0.890603i	0.996569	−	0.0827667i	$-0.0263756\pi$
$193$	17.0295	+	12.3727i	1.22581	+	0.890603i	0.229241	+	0.973370i	$0.426376\pi$
$194$	0.953185	−	2.93360i	0.0684347	−	0.210620i
$195$	−1.21736	−	3.74665i	−0.0871769	−	0.268303i
$196$	−10.0072	+	7.27065i	−0.714799	+	0.519332i
$197$	−10.2644			−0.731305			−0.365653	−	0.930751i	$-0.619154\pi$
$197$	−10.2644			−0.731305			−0.365653	+	0.930751i	$0.619154\pi$
$198$	1.08235	+	0.318751i	0.0769194	+	0.0226526i
$199$	−9.31129			−0.660060			−0.330030	−	0.943970i	$-0.607059\pi$
$199$	−9.31129			−0.660060			−0.330030	+	0.943970i	$0.607059\pi$
$200$	−11.2457	+	8.17049i	−0.795192	+	0.577741i
$201$	−0.655772	−	2.01826i	−0.0462546	−	0.142357i
$202$	−1.97708	+	6.08484i	−0.139107	+	0.428128i
$203$	−0.428023	−	0.310977i	−0.0300413	−	0.0218263i
$204$	1.53042	+	1.11192i	0.107151	+	0.0778496i
$205$	2.14976	−	6.61629i	0.150146	−	0.462102i
$206$	2.01390	+	6.19814i	0.140315	+	0.431845i
$207$	−2.51119	+	1.82448i	−0.174539	+	0.126810i
$208$	3.31898			0.230130
$209$	−15.9242	+	5.66735i	−1.10150	+	0.392019i
$210$	−0.884265			−0.0610201
$211$	−10.1240	+	7.35554i	−0.696967	+	0.506376i	−0.878943	−	0.476927i	$-0.841751\pi$
$211$	−10.1240	+	7.35554i	−0.696967	+	0.506376i	0.181976	+	0.983303i	$0.441751\pi$
$212$	−6.92359	−	21.3086i	−0.475514	−	1.46348i
$213$	2.99519	−	9.21825i	0.205227	−	0.631624i
$214$	−5.46656	−	3.97169i	−0.373686	−	0.271499i
$215$	38.0660	+	27.6566i	2.59608	+	1.88616i
$216$	0.408342	−	1.25675i	0.0277842	−	0.0855108i
$217$	1.01622	+	3.12761i	0.0689856	+	0.212316i
$218$	−0.720363	+	0.523374i	−0.0487891	+	0.0354474i
$219$	10.3614			0.700161
$220$	15.0180	+	19.5081i	1.01252	+	1.31523i
$221$	1.00395			0.0675328
$222$	0.184342	−	0.133933i	0.0123723	−	0.00898897i
$223$	−1.55273	−	4.77881i	−0.103978	−	0.320013i	0.885511	−	0.464619i	$-0.153809\pi$
$223$	−1.55273	−	4.77881i	−0.103978	−	0.320013i	−0.989489	+	0.144606i	$0.953809\pi$
$224$	0.769064	−	2.36694i	0.0513852	−	0.158148i
$225$	−8.51031	−	6.18310i	−0.567354	−	0.412207i
$226$	−2.62358	−	1.90614i	−0.174518	−	0.126795i
$227$	−1.40258	+	4.31670i	−0.0930925	+	0.286509i	−0.986752	−	0.162237i	$-0.948129\pi$
$227$	−1.40258	+	4.31670i	−0.0930925	+	0.286509i	0.893659	+	0.448746i	$0.148129\pi$
$228$	2.96744	+	9.13286i	0.196524	+	0.604838i
$229$	2.54757	−	1.85092i	0.168348	−	0.122312i	−0.500421	−	0.865782i	$-0.666821\pi$
$229$	2.54757	−	1.85092i	0.168348	−	0.122312i	0.668769	+	0.743470i	$0.266821\pi$
$230$	4.15997			0.274300
$231$	0.0607347	+	2.18747i	0.00399605	+	0.143925i
$232$	−1.05959			−0.0695655
$233$	1.46099	−	1.06147i	0.0957130	−	0.0695395i	−0.538899	−	0.842370i	$-0.681160\pi$
$233$	1.46099	−	1.06147i	0.0957130	−	0.0695395i	0.634612	+	0.772831i	$0.281160\pi$
$234$	−0.105127	−	0.323548i	−0.00687238	−	0.0211510i
$235$	−7.04093	+	21.6698i	−0.459300	+	1.41358i
$236$	−0.525781	−	0.382002i	−0.0342254	−	0.0248662i
$237$	5.15995	+	3.74892i	0.335175	+	0.243519i
$238$	0.0696369	−	0.214320i	0.00451389	−	0.0138923i
$239$	4.35768	+	13.4116i	0.281875	+	0.867522i	0.987318	+	0.158756i	$0.0507482\pi$
$239$	4.35768	+	13.4116i	0.281875	+	0.867522i	−0.705443	+	0.708767i	$0.749252\pi$
$240$	10.5779	−	7.68529i	0.682800	−	0.496083i
$241$	−8.19384			−0.527811			−0.263906	−	0.964548i	$-0.585011\pi$
$241$	−8.19384			−0.527811			−0.263906	+	0.964548i	$0.585011\pi$
$242$	−2.90078	+	2.36420i	−0.186469	+	0.151977i
$243$	1.00000			0.0641500
$244$	6.55008	−	4.75891i	0.419326	−	0.304658i
$245$	7.99155	+	24.5955i	0.510561	+	1.57135i
$246$	0.185647	−	0.571362i	0.0118364	−	0.0364287i
$247$	4.12303	+	2.99555i	0.262342	+	0.190602i
$248$	5.32834	+	3.87127i	0.338350	+	0.245826i
$249$	−2.37816	+	7.31921i	−0.150710	+	0.463836i
$250$	2.28579	+	7.03495i	0.144566	+	0.444929i
$251$	−3.99311	+	2.90116i	−0.252043	+	0.183120i	−0.706632	−	0.707582i	$-0.749786\pi$
$251$	−3.99311	+	2.90116i	−0.252043	+	0.183120i	0.454589	+	0.890701i	$0.349786\pi$
$252$	1.24324			0.0783168
$253$	−0.285723	−	10.2908i	−0.0179633	−	0.646979i
$254$	−2.57781			−0.161746
$255$	3.19967	−	2.32470i	0.200371	−	0.145578i
$256$	2.32484	+	7.15511i	0.145302	+	0.447195i
$257$	−3.08169	+	9.48446i	−0.192230	+	0.591624i	0.807767	+	0.589501i	$0.200676\pi$
$257$	−3.08169	+	9.48446i	−0.192230	+	0.591624i	−0.999998	+	0.00212277i	$0.999324\pi$
$258$	3.28726	+	2.38834i	0.204656	+	0.148691i
$259$	0.357524	+	0.259757i	0.0222155	+	0.0161405i
$260$	2.29383	−	7.05967i	0.142257	−	0.437822i
$261$	−0.247787	−	0.762610i	−0.0153376	−	0.0472044i
$262$	5.49692	−	3.99375i	0.339601	−	0.246735i
$263$	−20.3964			−1.25769			−0.628847	−	0.777529i	$-0.716473\pi$
$263$	−20.3964			−1.25769			−0.628847	+	0.777529i	$0.716473\pi$
$264$	2.67348	+	3.47279i	0.164541	+	0.213735i
$265$	−46.8428			−2.87753
$266$	0.925469	−	0.672393i	0.0567442	−	0.0412270i
$267$	−1.47016	−	4.52469i	−0.0899725	−	0.276907i
$268$	1.23565	−	3.80293i	0.0754792	−	0.232301i
$269$	11.7201	+	8.51518i	0.714590	+	0.519180i	0.884651	−	0.466254i	$-0.154397\pi$
$269$	11.7201	+	8.51518i	0.714590	+	0.519180i	−0.170061	+	0.985433i	$0.554397\pi$
$270$	−1.08424	−	0.787749i	−0.0659850	−	0.0479409i
$271$	−6.73152	+	20.7175i	−0.408911	+	1.25850i	0.508675	+	0.860959i	$0.330136\pi$
$271$	−6.73152	+	20.7175i	−0.408911	+	1.25850i	−0.917585	+	0.397539i	$0.869864\pi$
$272$	1.02967	+	3.16900i	0.0624330	+	0.192149i
$273$	0.533790	−	0.387821i	0.0323065	−	0.0234720i
$274$	4.02888			0.243394
$275$	32.8691	−	11.6979i	1.98208	−	0.705412i
$276$	−5.84875			−0.352053
$277$	−10.5400	+	7.65777i	−0.633288	+	0.460111i	−0.857538	−	0.514421i	$-0.828007\pi$
$277$	−10.5400	+	7.65777i	−0.633288	+	0.460111i	0.224250	+	0.974532i	$0.428007\pi$
$278$	−0.247674	−	0.762261i	−0.0148545	−	0.0457174i
$279$	−1.54019	+	4.74023i	−0.0922089	+	0.283790i
$280$	−2.77875	−	2.01888i	−0.166062	−	0.120651i
$281$	−24.2018	−	17.5836i	−1.44376	−	1.04895i	−0.987240	−	0.159239i	$-0.949096\pi$
$281$	−24.2018	−	17.5836i	−1.44376	−	1.04895i	−0.456519	−	0.889714i	$-0.650904\pi$
$282$	−0.608032	+	1.87133i	−0.0362078	+	0.111436i
$283$	−5.92466	−	18.2342i	−0.352184	−	1.08391i	−0.957624	−	0.288021i	$-0.907003\pi$
$283$	−5.92466	−	18.2342i	−0.352184	−	1.08391i	0.605440	−	0.795891i	$-0.292997\pi$
$284$	14.7755	−	10.7350i	0.876764	−	0.637006i
$285$	20.0768			1.18925
$286$	1.08235	+	0.318751i	0.0640008	+	0.0188481i
$287$	1.16516			0.0687772
$288$	3.05158	−	2.21710i	0.179816	−	0.130644i
$289$	−4.94183	−	15.2094i	−0.290696	−	0.894669i
$290$	−0.332084	+	1.02205i	−0.0195006	+	0.0600168i
$291$	7.33533	+	5.32943i	0.430005	+	0.312417i
$292$	15.7950	+	11.4757i	0.924332	+	0.671566i
$293$	−3.67687	+	11.3162i	−0.214805	+	0.661101i	0.784362	+	0.620303i	$0.212990\pi$
$293$	−3.67687	+	11.3162i	−0.214805	+	0.661101i	−0.999167	+	0.0407987i	$0.987010\pi$
$294$	0.690125	+	2.12399i	0.0402489	+	0.123873i
$295$	−1.09926	+	0.798657i	−0.0640013	+	0.0464996i
$296$	0.885068			0.0514435
$297$	−1.87424	+	2.73628i	−0.108755	+	0.158775i
$298$	5.52345			0.319965
$299$	−2.51119	+	1.82448i	−0.145226	+	0.105513i
$300$	−6.12508	−	18.8511i	−0.353632	−	1.08837i
$301$	−2.43523	+	7.49485i	−0.140364	+	0.431996i
$302$	−2.24933	−	1.63423i	−0.129434	−	0.0940396i
$303$	−15.2148	−	11.0542i	−0.874070	−	0.635049i
$304$	−5.22692	+	16.0868i	−0.299784	+	0.922641i
$305$	−5.23077	−	16.0987i	−0.299513	−	0.921806i
$306$	0.276313	−	0.200753i	0.0157958	−	0.0114763i
$307$	24.3043			1.38712			0.693560	−	0.720398i	$-0.256041\pi$
$307$	24.3043			1.38712			0.693560	+	0.720398i	$0.256041\pi$
$308$	−2.33013	+	3.40185i	−0.132772	+	0.193838i
$309$	−19.1568			−1.08979
$310$	5.40405	−	3.92628i	0.306930	−	0.222997i
$311$	−4.53712	−	13.9638i	−0.257276	−	0.791815i	−0.993373	−	0.114938i	$-0.963333\pi$
$311$	−4.53712	−	13.9638i	−0.257276	−	0.791815i	0.736096	−	0.676877i	$-0.236667\pi$
$312$	0.408342	−	1.25675i	0.0231178	−	0.0711493i
$313$	−5.90356	−	4.28919i	−0.333689	−	0.242439i	0.408305	−	0.912845i	$-0.366120\pi$
$313$	−5.90356	−	4.28919i	−0.333689	−	0.242439i	−0.741994	+	0.670406i	$0.766120\pi$
$314$	−6.77901	−	4.92524i	−0.382562	−	0.277947i
$315$	0.803215	−	2.47204i	0.0452560	−	0.139284i
$316$	3.71375	+	11.4297i	0.208914	+	0.642973i
$317$	4.48152	−	3.25601i	0.251707	−	0.182876i	−0.454776	−	0.890606i	$-0.650281\pi$
$317$	4.48152	−	3.25601i	0.251707	−	0.182876i	0.706483	+	0.707730i	$0.250281\pi$
$318$	−4.04520			−0.226843
$319$	2.55113	+	0.751302i	0.142836	+	0.0420648i
$320$	21.0948			1.17924
$321$	16.0687	−	11.6746i	0.896868	−	0.651613i
$322$	0.215303	+	0.662634i	0.0119984	+	0.0369271i
$323$	−1.58107	+	4.86604i	−0.0879732	+	0.270754i
$324$	1.52440	+	1.10754i	0.0846890	+	0.0615302i
$325$	−8.51031	−	6.18310i	−0.472067	−	0.342977i
$326$	2.28348	−	7.02782i	0.126470	−	0.389235i
$327$	−0.808804	−	2.48924i	−0.0447270	−	0.137655i
$328$	1.88787	−	1.37162i	0.104240	−	0.0757348i
$329$	−3.81614			−0.210391
$330$	4.18764	−	1.49036i	0.230522	−	0.0820416i
$331$	−26.0563			−1.43218			−0.716091	−	0.698007i	$-0.754071\pi$
$331$	−26.0563			−1.43218			−0.716091	+	0.698007i	$0.754071\pi$
$332$	−11.7316	+	8.52351i	−0.643856	+	0.467789i
$333$	0.206975	+	0.637002i	0.0113421	+	0.0349075i
$334$	−1.75818	+	5.41111i	−0.0962031	+	0.296083i
$335$	−6.76339	−	4.91389i	−0.369524	−	0.268475i
$336$	1.77164	+	1.28717i	0.0966509	+	0.0702210i
$337$	−4.31503	+	13.2803i	−0.235055	+	0.723424i	0.762059	+	0.647507i	$0.224188\pi$
$337$	−4.31503	+	13.2803i	−0.235055	+	0.723424i	−0.997114	+	0.0759172i	$0.975812\pi$
$338$	−0.105127	−	0.323548i	−0.00571817	−	0.0175987i
$339$	7.71191	−	5.60303i	0.418853	−	0.304315i
$340$	7.45228			0.404157
$341$	−10.0839	−	13.0987i	−0.546073	−	0.709336i
$342$	1.73377			0.0937515
$343$	−7.24069	+	5.26067i	−0.390960	+	0.284049i
$344$	4.87717	+	15.0104i	0.262959	+	0.809306i
$345$	−3.77868	+	11.6296i	−0.203437	+	0.626115i
$346$	−2.63623	−	1.91533i	−0.141724	−	0.102969i
$347$	−20.2001	−	14.6763i	−1.08440	−	0.787863i	−0.105955	−	0.994371i	$-0.533790\pi$
$347$	−20.2001	−	14.6763i	−1.08440	−	0.787863i	−0.978445	+	0.206508i	$0.933790\pi$
$348$	0.466896	−	1.43696i	0.0250283	−	0.0770291i
$349$	−9.31548	−	28.6701i	−0.498646	−	1.53468i	−0.811196	−	0.584774i	$-0.801183\pi$
$349$	−9.31548	−	28.6701i	−0.498646	−	1.53468i	0.312550	−	0.949901i	$-0.398817\pi$
$350$	−1.91025	+	1.38788i	−0.102107	+	0.0741854i
$351$	1.00000			0.0533761
$352$	0.347209	+	12.5054i	0.0185063	+	0.666538i
$353$	26.6798			1.42002			0.710011	−	0.704191i	$-0.248690\pi$
$353$	26.6798			1.42002			0.710011	+	0.704191i	$0.248690\pi$
$354$	−0.0949284	+	0.0689695i	−0.00504539	+	0.00366569i
$355$	−11.7994	−	36.3149i	−0.626248	−	1.92739i
$356$	2.77017	−	8.52572i	0.146819	−	0.451862i
$357$	0.535898	+	0.389352i	0.0283627	+	0.0206067i
$358$	−0.231275	−	0.168031i	−0.0122232	−	0.00888071i
$359$	4.51067	−	13.8824i	0.238064	−	0.732686i	−0.758636	−	0.651515i	$-0.774134\pi$
$359$	4.51067	−	13.8824i	0.238064	−	0.732686i	0.996700	−	0.0811716i	$-0.0258662\pi$
$360$	−1.60865	−	4.95090i	−0.0847831	−	0.260935i
$361$	−5.64102	+	4.09844i	−0.296896	+	0.215707i
$362$	1.10957			0.0583175
$363$	−3.97443	−	10.2569i	−0.208604	−	0.538347i
$364$	1.24324			0.0651635
$365$	33.0228	−	23.9925i	1.72849	−	1.25582i
$366$	−0.451713	−	1.39023i	−0.0236114	−	0.0726684i
$367$	6.78242	−	20.8741i	0.354039	−	1.08962i	−0.602525	−	0.798100i	$-0.705839\pi$
$367$	6.78242	−	20.8741i	0.354039	−	1.08962i	0.956564	−	0.291521i	$-0.0941614\pi$
$368$	−8.33458	−	6.05543i	−0.434470	−	0.315661i
$369$	1.42866	+	1.03798i	0.0743732	+	0.0540353i
$370$	0.277387	−	0.853710i	0.0144207	−	0.0443823i
$371$	−2.42439	−	7.46150i	−0.125868	−	0.387382i
$372$	−7.59788	+	5.52018i	−0.393932	+	0.286208i
$373$	8.28362			0.428909			0.214455	−	0.976734i	$-0.431203\pi$
$373$	8.28362			0.428909			0.214455	+	0.976734i	$0.431203\pi$
$374$	0.0314390	+	1.13233i	0.00162567	+	0.0585514i
$375$	−21.7431			−1.12281
$376$	−6.18316	+	4.49233i	−0.318872	+	0.231674i
$377$	−0.247787	−	0.762610i	−0.0127617	−	0.0392764i
$378$	0.0693631	−	0.213478i	0.00356765	−	0.0109801i
$379$	−15.9486	−	11.5873i	−0.819222	−	0.595200i	0.0972673	−	0.995258i	$-0.468990\pi$
$379$	−15.9486	−	11.5873i	−0.819222	−	0.595200i	−0.916490	+	0.400058i	$0.868990\pi$
$380$	30.6051	+	22.2359i	1.57001	+	1.14068i
$381$	2.34153	−	7.20649i	0.119960	−	0.369200i
$382$	−0.404325	−	1.24438i	−0.0206871	−	0.0636682i
$383$	7.88111	−	5.72596i	0.402706	−	0.292583i	−0.367936	−	0.929851i	$-0.619936\pi$
$383$	7.88111	−	5.72596i	0.402706	−	0.292583i	0.770642	+	0.637268i	$0.219936\pi$
$384$	9.36560			0.477936
$385$	5.25877	+	6.83102i	0.268012	+	0.348141i
$386$	7.16106			0.364488
$387$	−9.66277	+	7.02041i	−0.491186	+	0.356868i
$388$	5.27942	+	16.2484i	0.268022	+	0.824887i
$389$	−5.07773	+	15.6276i	−0.257451	+	0.792353i	0.735886	+	0.677106i	$0.236766\pi$
$389$	−5.07773	+	15.6276i	−0.257451	+	0.792353i	−0.993337	+	0.115247i	$0.963234\pi$
$390$	−1.08424	−	0.787749i	−0.0549028	−	0.0398892i
$391$	−2.52110	−	1.83169i	−0.127497	−	0.0926323i
$392$	−2.68063	+	8.25012i	−0.135392	+	0.416694i
$393$	6.17179	+	18.9948i	0.311326	+	0.958162i
$394$	−2.82503	+	2.05250i	−0.142323	+	0.103404i
$395$	25.1260			1.26423
$396$	−5.88764	+	2.09538i	−0.295865	+	0.105297i
$397$	18.1880			0.912832			0.456416	−	0.889767i	$-0.349133\pi$
$397$	18.1880			0.912832			0.456416	+	0.889767i	$0.349133\pi$
$398$	−2.56272	+	1.86192i	−0.128457	+	0.0933298i
$399$	1.03909	+	3.19799i	0.0520196	+	0.160100i
$400$	10.7888	−	33.2047i	0.539442	−	1.66023i
$401$	−0.433267	−	0.314787i	−0.0216363	−	0.0157197i	0.576915	−	0.816805i	$-0.304257\pi$
$401$	−0.433267	−	0.314787i	−0.0216363	−	0.0157197i	−0.598551	+	0.801085i	$0.704257\pi$
$402$	−0.584065	−	0.424348i	−0.0291305	−	0.0211646i
$403$	−1.54019	+	4.74023i	−0.0767225	+	0.236128i
$404$	−10.9505	−	33.7022i	−0.544808	−	1.67675i
$405$	3.18709	−	2.31555i	0.158368	−	0.115061i
$406$	−0.179987			−0.00893263
$407$	−2.13094	−	0.627557i	−0.105627	−	0.0311068i
$408$	1.32664			0.0656784
$409$	−14.8912	+	10.8191i	−0.736325	+	0.534971i	−0.891558	−	0.452907i	$-0.850387\pi$
$409$	−14.8912	+	10.8191i	−0.736325	+	0.534971i	0.155233	+	0.987878i	$0.450387\pi$
$410$	−0.731348	−	2.25086i	−0.0361187	−	0.111162i
$411$	−3.65960	+	11.2631i	−0.180515	+	0.555568i
$412$	−29.2026	−	21.2169i	−1.43871	−	1.04528i
$413$	−0.184110	−	0.133763i	−0.00905944	−	0.00658207i
$414$	−0.326315	+	1.00429i	−0.0160375	+	0.0493583i
$415$	9.36864	+	28.8337i	0.459889	+	1.41539i
$416$	3.05158	−	2.21710i	0.149616	−	0.108702i
$417$	2.35594			0.115371
$418$	−3.24950	+	4.74407i	−0.158938	+	0.232040i
$419$	−29.9674			−1.46400			−0.732001	−	0.681304i	$-0.761413\pi$
$419$	−29.9674			−1.46400			−0.732001	+	0.681304i	$0.761413\pi$
$420$	3.96231	−	2.87879i	0.193341	−	0.140471i
$421$	10.3326	+	31.8004i	0.503579	+	1.54986i	0.803146	+	0.595782i	$0.203158\pi$
$421$	10.3326	+	31.8004i	0.503579	+	1.54986i	−0.299567	+	0.954075i	$0.596842\pi$
$422$	−1.31556	+	4.04888i	−0.0640405	+	0.197096i
$423$	−4.67917	−	3.39962i	−0.227509	−	0.165295i
$424$	−12.7118	−	9.23564i	−0.617338	−	0.448523i
$425$	3.26348	−	10.0440i	0.158302	−	0.487204i
$426$	−1.01896	−	3.13604i	−0.0493688	−	0.151942i
$427$	2.29360	−	1.66640i	0.110995	−	0.0806426i
$428$	37.4253			1.80902
$429$	−1.87424	+	2.73628i	−0.0904893	+	0.132109i
$430$	16.0071			0.771932
$431$	−20.7326	+	15.0631i	−0.998652	+	0.725563i	−0.961799	−	0.273757i	$-0.911733\pi$
$431$	−20.7326	+	15.0631i	−0.998652	+	0.725563i	−0.0368535	+	0.999321i	$0.511733\pi$
$432$	1.02562	+	3.15654i	0.0493453	+	0.151869i
$433$	−2.13509	+	6.57112i	−0.102606	+	0.315788i	−0.989161	−	0.146835i	$-0.953091\pi$
$433$	−2.13509	+	6.57112i	−0.102606	+	0.315788i	0.886555	+	0.462623i	$0.153091\pi$
$434$	0.905100	+	0.657593i	0.0434462	+	0.0315655i
$435$	−2.55558	−	1.85674i	−0.122531	−	0.0890239i
$436$	1.52400	−	4.69039i	0.0729864	−	0.224629i
$437$	−4.88835	−	15.0448i	−0.233841	−	0.719690i
$438$	2.85174	−	2.07191i	0.136262	−	0.0989998i
$439$	26.9412			1.28583			0.642916	−	0.765936i	$-0.277724\pi$
$439$	26.9412			1.28583			0.642916	+	0.765936i	$0.277724\pi$
$440$	16.5620	+	4.87749i	0.789564	+	0.232525i
$441$	−6.56466			−0.312603
$442$	0.276313	−	0.200753i	0.0131429	−	0.00954886i
$443$	3.95952	+	12.1862i	0.188123	+	0.578982i	0.999988	−	0.00486252i	$-0.00154779\pi$
$443$	3.95952	+	12.1862i	0.188123	+	0.578982i	−0.811866	+	0.583844i	$0.801548\pi$
$444$	−0.389995	+	1.20028i	−0.0185083	+	0.0569628i
$445$	−15.1627	−	11.0164i	−0.718781	−	0.522225i
$446$	−1.38294	−	1.00477i	−0.0654842	−	0.0475770i
$447$	−5.01718	+	15.4413i	−0.237304	+	0.730348i
$448$	1.09178	+	3.36015i	0.0515817	+	0.158752i
$449$	−15.5283	+	11.2819i	−0.732824	+	0.532428i	−0.890456	−	0.455070i	$-0.849614\pi$
$449$	−15.5283	+	11.2819i	−0.732824	+	0.532428i	0.157631	+	0.987498i	$0.449614\pi$
$450$	−3.57866			−0.168700
$451$	−5.51787	+	1.96378i	−0.259827	+	0.0924710i
$452$	17.9616			0.844845
$453$	6.61181	−	4.80376i	0.310650	−	0.225700i
$454$	0.477156	+	1.46854i	0.0223940	+	0.0689218i
$455$	0.803215	−	2.47204i	0.0376553	−	0.115891i
$456$	5.44826	+	3.95839i	0.255138	+	0.185369i
$457$	1.34891	+	0.980037i	0.0630991	+	0.0458442i	0.618888	−	0.785479i	$-0.287584\pi$
$457$	1.34891	+	0.980037i	0.0630991	+	0.0458442i	−0.555789	+	0.831324i	$0.687584\pi$
$458$	0.331043	−	1.01885i	0.0154686	−	0.0476075i
$459$	0.310237	+	0.954811i	0.0144806	+	0.0445668i
$460$	−18.6405	+	13.5431i	−0.869117	+	0.631450i
$461$	−18.7395			−0.872787			−0.436394	−	0.899756i	$-0.643745\pi$
$461$	−18.7395			−0.872787			−0.436394	+	0.899756i	$0.643745\pi$
$462$	0.454131	+	0.589905i	0.0211281	+	0.0274449i
$463$	11.4490			0.532080			0.266040	−	0.963962i	$-0.414285\pi$
$463$	11.4490			0.532080			0.266040	+	0.963962i	$0.414285\pi$
$464$	2.15307	−	1.56430i	0.0999539	−	0.0726208i
$465$	6.06752	+	18.6739i	0.281375	+	0.865982i
$466$	0.189848	−	0.584293i	0.00879455	−	0.0270668i
$467$	−11.1486	−	8.09994i	−0.515896	−	0.374820i	0.299160	−	0.954203i	$-0.403294\pi$
$467$	−11.1486	−	8.09994i	−0.515896	−	0.374820i	−0.815056	+	0.579383i	$0.803294\pi$
$468$	1.52440	+	1.10754i	0.0704655	+	0.0511962i
$469$	0.432679	−	1.33165i	0.0199793	−	0.0614899i
$470$	2.39532	+	7.37203i	0.110488	+	0.340046i
$471$	19.9266	−	14.4775i	0.918170	−	0.667090i
$472$	−0.455772			−0.0209786
$473$	−1.09943	−	39.5980i	−0.0505519	−	1.82072i
$474$	2.16981			0.0996625
$475$	43.3714	−	31.5112i	1.99002	−	1.44583i
$476$	0.385699	+	1.18706i	0.0176785	+	0.0544088i
$477$	3.67442	−	11.3087i	0.168240	−	0.517790i
$478$	3.88118	+	2.81984i	0.177521	+	0.128977i
$479$	−12.3069	−	8.94147i	−0.562315	−	0.408546i	0.269990	−	0.962863i	$-0.412980\pi$
$479$	−12.3069	−	8.94147i	−0.562315	−	0.408546i	−0.832306	+	0.554317i	$0.812980\pi$
$480$	4.59183	−	14.1322i	0.209587	−	0.645044i
$481$	0.206975	+	0.637002i	0.00943723	+	0.0290448i
$482$	−2.25516	+	1.63847i	−0.102720	+	0.0746303i
$483$	−2.04802			−0.0931881
$484$	5.30132	−	20.0375i	0.240969	−	0.910795i
$485$	35.7189			1.62191
$486$	0.275227	−	0.199964i	0.0124845	−	0.00907055i
$487$	−6.43804	−	19.8143i	−0.291736	−	0.897870i	−0.984298	−	0.176512i	$-0.943518\pi$
$487$	−6.43804	−	19.8143i	−0.291736	−	0.897870i	0.692563	−	0.721358i	$-0.256482\pi$
$488$	1.75457	−	5.40002i	0.0794257	−	0.244447i
$489$	17.5727	+	12.7673i	0.794666	+	0.577359i
$490$	7.11769	+	5.17131i	0.321545	+	0.233616i
$491$	9.26355	−	28.5103i	0.418058	−	1.28665i	−0.491429	−	0.870918i	$-0.663525\pi$
$491$	9.26355	−	28.5103i	0.418058	−	1.28665i	0.909487	−	0.415732i	$-0.136475\pi$
$492$	1.02824	+	3.16461i	0.0463568	+	0.142672i
$493$	0.651276	−	0.473180i	0.0293320	−	0.0213109i
$494$	1.73377			0.0780060
$495$	0.362627	+	13.0607i	0.0162989	+	0.587033i
$496$	−16.5424			−0.742774
$497$	5.17384	−	3.75901i	0.232078	−	0.168615i
$498$	0.809046	+	2.48999i	0.0362542	+	0.111579i
$499$	7.49341	−	23.0624i	0.335451	−	1.03241i	−0.631048	−	0.775744i	$-0.717375\pi$
$499$	7.49341	−	23.0624i	0.335451	−	1.03241i	0.966499	−	0.256669i	$-0.0826251\pi$
$500$	−33.1453	−	24.0814i	−1.48230	−	1.07695i
$501$	−13.5302	−	9.83028i	−0.604486	−	0.439185i
$502$	−0.518882	+	1.59696i	−0.0231588	+	0.0712756i
$503$	−9.17099	−	28.2254i	−0.408914	−	1.25851i	−0.917582	−	0.397546i	$-0.869862\pi$
$503$	−9.17099	−	28.2254i	−0.408914	−	1.25851i	0.508668	−	0.860963i	$-0.330138\pi$
$504$	0.705363	−	0.512476i	0.0314193	−	0.0228275i
$505$	−74.0877			−3.29686
$506$	−2.13643	−	2.77518i	−0.0949760	−	0.123372i
$507$	1.00000			0.0444116
$508$	11.5509	−	8.39224i	0.512490	−	0.372346i
$509$	9.22302	+	28.3855i	0.408803	+	1.25817i	0.917678	+	0.397326i	$0.130062\pi$
$509$	9.22302	+	28.3855i	0.408803	+	1.25817i	−0.508875	+	0.860841i	$0.669938\pi$
$510$	0.415779	−	1.27964i	0.0184110	−	0.0566633i
$511$	5.53083	+	4.01839i	0.244670	+	0.177763i
$512$	17.2245	+	12.5143i	0.761222	+	0.553060i
$513$	−1.57486	+	4.84691i	−0.0695316	+	0.213996i
$514$	1.04839	+	3.22660i	0.0462423	+	0.142319i
$515$	−61.0543	+	44.3585i	−2.69037	+	1.95467i
$516$	−22.5053			−0.990743
$517$	18.0722	−	6.43181i	0.794814	−	0.282871i
$518$	0.150342			0.00660565
$519$	7.74908	−	5.63003i	0.340147	−	0.247131i
$520$	−1.60865	−	4.95090i	−0.0705438	−	0.217111i
$521$	−6.36929	+	19.6027i	−0.279044	+	0.858808i	0.709077	+	0.705131i	$0.249112\pi$
$521$	−6.36929	+	19.6027i	−0.279044	+	0.858808i	−0.988121	+	0.153678i	$0.950888\pi$
$522$	−0.220692	−	0.160342i	−0.00965943	−	0.00701799i
$523$	30.1568	+	21.9102i	1.31867	+	0.958067i	0.999948	+	0.0102173i	$0.00325232\pi$
$523$	30.1568	+	21.9102i	1.31867	+	0.958067i	0.318718	+	0.947850i	$0.396748\pi$
$524$	−11.6293	+	35.7913i	−0.508028	+	1.56355i
$525$	−2.14478	−	6.60096i	−0.0936059	−	0.288089i
$526$	−5.61362	+	4.07853i	−0.244766	+	0.177833i
$527$	−5.00385			−0.217971
$528$	−10.5594	−	3.10973i	−0.459540	−	0.135334i
$529$	−13.3652			−0.581096
$530$	−12.8924	+	9.36688i	−0.560010	+	0.406871i
$531$	−0.106583	−	0.328029i	−0.00462531	−	0.0142352i
$532$	−1.95792	+	6.02587i	−0.0848867	+	0.261255i
$533$	1.42866	+	1.03798i	0.0618823	+	0.0449601i
$534$	−1.30940	−	0.951337i	−0.0566634	−	0.0411684i
$535$	24.1792	−	74.4159i	1.04536	−	3.21728i
$536$	−0.866552	−	2.66697i	−0.0374293	−	0.115196i
$537$	0.679822	−	0.493919i	0.0293365	−	0.0213142i
$538$	4.92843			0.212479
$539$	12.3038	−	17.9627i	0.529961	−	0.773710i
$540$	7.42298			0.319434
$541$	11.0229	−	8.00863i	0.473913	−	0.344318i	−0.325051	−	0.945696i	$-0.605382\pi$
$541$	11.0229	−	8.00863i	0.473913	−	0.344318i	0.798964	+	0.601378i	$0.205382\pi$
$542$	2.29006	+	7.04807i	0.0983663	+	0.302740i
$543$	−1.00787	+	3.10189i	−0.0432516	+	0.133115i
$544$	3.06363	+	2.22585i	0.131352	+	0.0954327i
$545$	−8.34171	−	6.06060i	−0.357319	−	0.259608i
$546$	0.0693631	−	0.213478i	0.00296847	−	0.00913600i
$547$	5.04386	+	15.5234i	0.215660	+	0.663732i	0.999106	+	0.0422730i	$0.0134599\pi$
$547$	5.04386	+	15.5234i	0.215660	+	0.663732i	−0.783446	+	0.621459i	$0.786540\pi$
$548$	−18.0531	+	13.1163i	−0.771189	+	0.560302i
$549$	4.29682			0.183384
$550$	6.70728	−	9.79221i	0.285999	−	0.417541i
$551$	4.08653			0.174092
$552$	−3.31834	+	2.41091i	−0.141238	+	0.102615i
$553$	1.30042	+	4.00228i	0.0552994	+	0.170194i
$554$	−1.36962	+	4.21524i	−0.0581894	+	0.179089i
$555$	2.13466	+	1.55092i	0.0906113	+	0.0658329i
$556$	3.59140	+	2.60931i	0.152309	+	0.110659i
$557$	−5.34308	+	16.4443i	−0.226394	+	0.696768i	0.771753	+	0.635922i	$0.219380\pi$
$557$	−5.34308	+	16.4443i	−0.226394	+	0.696768i	−0.998147	+	0.0608464i	$0.980620\pi$
$558$	0.523972	+	1.61262i	0.0221815	+	0.0682677i
$559$	−9.66277	+	7.02041i	−0.408691	+	0.296932i
$560$	8.62689			0.364553
$561$	−3.19409	−	0.940653i	−0.134854	−	0.0397144i
$562$	−10.1771			−0.429294
$563$	0.465126	−	0.337934i	0.0196027	−	0.0142422i	−0.577941	−	0.816079i	$-0.696144\pi$
$563$	0.465126	−	0.337934i	0.0196027	−	0.0142422i	0.597543	+	0.801837i	$0.296144\pi$
$564$	−3.36772	−	10.3648i	−0.141806	−	0.436435i
$565$	11.6044	−	35.7147i	0.488201	−	1.50253i
$566$	−5.27681	−	3.83383i	−0.221801	−	0.161148i
$567$	0.533790	+	0.387821i	0.0224171	+	0.0162870i
$568$	3.95791	−	12.1812i	0.166070	−	0.511112i
$569$	11.8375	+	36.4320i	0.496253	+	1.52731i	0.814995	+	0.579468i	$0.196740\pi$
$569$	11.8375	+	36.4320i	0.496253	+	1.52731i	−0.318742	+	0.947841i	$0.603260\pi$
$570$	5.52567	−	4.01464i	0.231445	−	0.168155i
$571$	−20.0309			−0.838267			−0.419133	−	0.907925i	$-0.637666\pi$
$571$	−20.0309			−0.838267			−0.419133	+	0.907925i	$0.637666\pi$
$572$	−5.88764	+	2.09538i	−0.246175	+	0.0876124i
$573$	3.84605			0.160671
$574$	0.320683	−	0.232990i	0.0133850	−	0.00972480i
$575$	10.0900	+	31.0538i	0.420782	+	1.29503i
$576$	−1.65471	+	5.09267i	−0.0689462	+	0.212195i
$577$	23.0579	+	16.7525i	0.959911	+	0.697416i	0.953130	−	0.302561i	$-0.0978415\pi$
$577$	23.0579	+	16.7525i	0.959911	+	0.697416i	0.00678098	+	0.999977i	$0.497842\pi$
$578$	−4.40145	−	3.19784i	−0.183076	−	0.133013i
$579$	−6.50469	+	20.0194i	−0.270326	+	0.831977i
$580$	−1.83932	−	5.66084i	−0.0763735	−	0.235054i
$581$	−4.10798	+	2.98462i	−0.170428	+	0.123823i
$582$	3.08457			0.127860
$583$	24.0570	+	31.2495i	0.996340	+	1.29422i
$584$	13.6918			0.566572
$585$	3.18709	−	2.31555i	0.131770	−	0.0957364i
$586$	1.25087	+	3.84977i	0.0516728	+	0.159033i
$587$	−5.76814	+	17.7525i	−0.238076	+	0.732724i	0.758622	+	0.651531i	$0.225873\pi$
$587$	−5.76814	+	17.7525i	−0.238076	+	0.732724i	−0.996698	+	0.0811929i	$0.974127\pi$
$588$	−10.0072	−	7.27065i	−0.412689	−	0.299836i
$589$	−20.5499	−	14.9303i	−0.846742	−	0.615194i
$590$	−0.142842	+	0.439624i	−0.00588073	+	0.0180990i
$591$	−3.17186	−	9.76199i	−0.130473	−	0.401554i
$592$	−1.79845	+	1.30665i	−0.0739157	+	0.0537029i
$593$	29.4986			1.21136			0.605681	−	0.795708i	$-0.292901\pi$
$593$	29.4986			1.21136			0.605681	+	0.795708i	$0.292901\pi$
$594$	0.0313153	+	1.12788i	0.00128488	+	0.0462774i
$595$	2.60952			0.106980
$596$	−24.7501	+	17.9820i	−1.01380	+	0.736571i
$597$	−2.87735	−	8.85557i	−0.117762	−	0.362434i
$598$	−0.326315	+	1.00429i	−0.0133440	+	0.0410686i
$599$	9.53109	+	6.92474i	0.389430	+	0.282937i	0.765222	−	0.643767i	$-0.222629\pi$
$599$	9.53109	+	6.92474i	0.389430	+	0.282937i	−0.375792	+	0.926704i	$0.622629\pi$
$600$	−11.2457	−	8.17049i	−0.459104	−	0.333559i
$601$	−14.4309	+	44.4138i	−0.588650	+	1.81168i	−0.00455763	+	0.999990i	$0.501451\pi$
$601$	−14.4309	+	44.4138i	−0.588650	+	1.81168i	−0.584092	+	0.811687i	$0.698549\pi$
$602$	0.828461	+	2.54974i	0.0337656	+	0.103920i
$603$	1.71683	−	1.24735i	0.0699149	−	0.0507961i
$604$	15.3994			0.626594
$605$	−36.4173	−	23.4866i	−1.48057	−	0.954866i
$606$	−6.39798			−0.259900
$607$	3.41290	−	2.47962i	0.138525	−	0.100645i	−0.516364	−	0.856369i	$-0.672715\pi$
$607$	3.41290	−	2.47962i	0.138525	−	0.100645i	0.654890	+	0.755724i	$0.272715\pi$
$608$	5.94029	+	18.2823i	0.240911	+	0.741447i
$609$	0.163490	−	0.503171i	0.00662496	−	0.0203895i
$610$	−4.65880	−	3.38481i	−0.188629	−	0.137047i
$611$	−4.67917	−	3.39962i	−0.189299	−	0.137534i
$612$	−0.584568	+	1.79912i	−0.0236298	+	0.0727250i
$613$	9.91019	+	30.5004i	0.400269	+	1.23190i	0.924782	+	0.380498i	$0.124247\pi$
$613$	9.91019	+	30.5004i	0.400269	+	1.23190i	−0.524513	+	0.851402i	$0.675753\pi$
$614$	6.68920	−	4.85999i	0.269954	−	0.196133i
$615$	6.95678			0.280525
$616$	0.0802562	+	2.89057i	0.00323362	+	0.116464i
$617$	−15.7235			−0.633006			−0.316503	−	0.948591i	$-0.602509\pi$
$617$	−15.7235			−0.633006			−0.316503	+	0.948591i	$0.602509\pi$
$618$	−5.27245	+	3.83066i	−0.212089	+	0.154092i
$619$	−11.4230	−	35.1565i	−0.459131	−	1.41306i	−0.866216	−	0.499670i	$-0.833455\pi$
$619$	−11.4230	−	35.1565i	−0.459131	−	1.41306i	0.407085	−	0.913390i	$-0.366545\pi$
$620$	−11.4328	+	35.1866i	−0.459153	+	1.41313i
$621$	−2.51119	−	1.82448i	−0.100770	−	0.0732140i
$622$	−4.04099	−	2.93595i	−0.162029	−	0.117721i
$623$	0.970015	−	2.98540i	0.0388628	−	0.119607i
$624$	1.02562	+	3.15654i	0.0410577	+	0.126363i
$625$	−26.7457	+	19.4319i	−1.06983	+	0.777275i
$626$	−2.48250			−0.0992207
$627$	−10.3108	−	13.3935i	−0.411775	−	0.534886i
$628$	46.4107			1.85199
$629$	−0.544006	+	0.395243i	−0.0216909	+	0.0157594i
$630$	−0.273253	−	0.840986i	−0.0108867	−	0.0335057i
$631$	−9.64700	+	29.6904i	−0.384041	+	1.18196i	0.553133	+	0.833093i	$0.313432\pi$
$631$	−9.64700	+	29.6904i	−0.384041	+	1.18196i	−0.937174	+	0.348863i	$0.886568\pi$
$632$	6.81847	+	4.95391i	0.271224	+	0.197056i
$633$	−10.1240	−	7.35554i	−0.402394	−	0.292356i
$634$	0.582348	−	1.79228i	0.0231280	−	0.0711807i
$635$	−9.22436	−	28.3897i	−0.366057	−	1.12661i
$636$	18.1262	−	13.1694i	0.718750	−	0.522202i
$637$	−6.56466			−0.260101
$638$	0.852371	−	0.303355i	0.0337457	−	0.0120099i
$639$	9.69264			0.383435
$640$	29.8490	−	21.6866i	1.17988	−	0.857236i
$641$	11.2858	+	34.7342i	0.445763	+	1.37192i	0.881645	+	0.471914i	$0.156437\pi$
$641$	11.2858	+	34.7342i	0.445763	+	1.37192i	−0.435882	+	0.900004i	$0.643563\pi$
$642$	2.08804	−	6.42632i	0.0824083	−	0.253627i
$643$	29.4235	+	21.3774i	1.16035	+	0.843043i	0.989822	−	0.142310i	$-0.0454529\pi$
$643$	29.4235	+	21.3774i	1.16035	+	0.843043i	0.170527	+	0.985353i	$0.445453\pi$
$644$	−3.12201	−	2.26827i	−0.123024	−	0.0893824i
$645$	−14.5399	+	44.7493i	−0.572509	+	1.76200i
$646$	0.537879	+	1.65542i	0.0211626	+	0.0651317i
$647$	6.77898	−	4.92521i	0.266509	−	0.193630i	−0.446503	−	0.894782i	$-0.647331\pi$
$647$	6.77898	−	4.92521i	0.266509	−	0.193630i	0.713012	+	0.701152i	$0.247331\pi$
$648$	1.32142			0.0519104
$649$	1.09734	+	0.323165i	0.0430744	+	0.0126853i
$650$	−3.57866			−0.140367
$651$	−2.66050	+	1.93297i	−0.104273	+	0.0757590i
$652$	12.6475	+	38.9251i	0.495315	+	1.52442i
$653$	0.126996	−	0.390853i	0.00496973	−	0.0152952i	−0.948541	−	0.316655i	$-0.897440\pi$
$653$	0.126996	−	0.390853i	0.00496973	−	0.0152952i	0.953511	+	0.301359i	$0.0974404\pi$
$654$	−0.720363	−	0.523374i	−0.0281684	−	0.0204656i
$655$	63.6536	+	46.2470i	2.48715	+	1.80702i
$656$	−1.81117	+	5.57421i	−0.0707144	+	0.217636i
$657$	3.20186	+	9.85431i	0.124916	+	0.384453i
$658$	−1.05030	+	0.763090i	−0.0409451	+	0.0297484i
$659$	−47.2816			−1.84183			−0.920915	−	0.389764i	$-0.872557\pi$
$659$	−47.2816			−1.84183			−0.920915	+	0.389764i	$0.872557\pi$
$660$	−13.9125	+	20.3113i	−0.541542	+	0.790618i
$661$	17.5534			0.682749			0.341375	−	0.939927i	$-0.389108\pi$
$661$	17.5534			0.682749			0.341375	+	0.939927i	$0.389108\pi$
$662$	−7.17138	+	5.21032i	−0.278724	+	0.202505i
$663$	0.310237	+	0.954811i	0.0120486	+	0.0370818i
$664$	−3.14255	+	9.67177i	−0.121955	+	0.375338i
$665$	10.7168	+	7.78622i	0.415580	+	0.301936i
$666$	0.184342	+	0.133933i	0.00714312	+	0.00518978i
$667$	−0.769130	+	2.36714i	−0.0297808	+	0.0916560i
$668$	−9.73804	−	29.9706i	−0.376776	−	1.15960i
$669$	4.06510	−	2.95346i	0.157166	−	0.114188i
$670$	−2.84407			−0.109876
$671$	−8.05328	+	11.7573i	−0.310893	+	0.453885i
$672$	2.48874			0.0960053
$673$	2.76098	−	2.00597i	0.106428	−	0.0773246i	−0.533298	−	0.845927i	$-0.679048\pi$
$673$	2.76098	−	2.00597i	0.106428	−	0.0773246i	0.639726	+	0.768603i	$0.279048\pi$
$674$	1.46797	+	4.51795i	0.0565441	+	0.174025i
$675$	3.25065	−	10.0045i	0.125118	−	0.385072i
$676$	1.52440	+	1.10754i	0.0586309	+	0.0425978i
$677$	−27.7761	−	20.1805i	−1.06752	−	0.775601i	−0.0920579	−	0.995754i	$-0.529344\pi$
$677$	−27.7761	−	20.1805i	−1.06752	−	0.775601i	−0.975465	+	0.220153i	$0.929344\pi$
$678$	1.00212	−	3.08421i	0.0384862	−	0.118448i
$679$	1.84866	+	5.68960i	0.0709451	+	0.218347i
$680$	4.22812	−	3.07191i	0.162141	−	0.117802i
$681$	−4.53884			−0.173929
$682$	−5.39463	−	1.58871i	−0.206571	−	0.0608348i
$683$	2.04683			0.0783199			0.0391599	−	0.999233i	$-0.487532\pi$
$683$	2.04683			0.0783199			0.0391599	+	0.999233i	$0.487532\pi$
$684$	−7.76887	+	5.64442i	−0.297050	+	0.215820i
$685$	14.4168	+	44.3705i	0.550839	+	1.69531i
$686$	−0.940887	+	2.89575i	−0.0359232	+	0.110560i
$687$	2.54757	+	1.85092i	0.0971960	+	0.0706170i
$688$	−32.0706	−	23.3006i	−1.22268	−	0.888328i
$689$	3.67442	−	11.3087i	0.139984	−	0.430828i
$690$	1.28550	+	3.95637i	0.0489382	+	0.150616i
$691$	33.7843	−	24.5457i	1.28521	−	0.933763i	0.285517	−	0.958374i	$-0.407835\pi$
$691$	33.7843	−	24.5457i	1.28521	−	0.933763i	0.999697	+	0.0246107i	$0.00783461\pi$
$692$	18.0482			0.686090
$693$	−2.06164	+	0.733727i	−0.0783152	+	0.0278720i
$694$	−8.49434			−0.322441
$695$	7.50859	−	5.45531i	0.284817	−	0.206932i
$696$	−0.327431	−	1.00773i	−0.0124113	−	0.0381979i
$697$	−0.547855	+	1.68612i	−0.0207515	+	0.0638665i
$698$	−8.29686	−	6.02802i	−0.314041	−	0.228164i
$699$	1.46099	+	1.06147i	0.0552599	+	0.0401487i
$700$	4.04134	−	12.4380i	0.152748	−	0.470110i
$701$	12.7891	+	39.3607i	0.483036	+	1.48663i	0.834805	+	0.550546i	$0.185580\pi$
$701$	12.7891	+	39.3607i	0.483036	+	1.48663i	−0.351768	+	0.936087i	$0.614420\pi$
$702$	0.275227	−	0.199964i	0.0103878	−	0.00754715i
$703$	−3.41345			−0.128741
$704$	−10.8336	−	14.0726i	−0.408308	−	0.530382i
$705$	−22.7849			−0.858130
$706$	7.34299	−	5.33500i	0.276357	−	0.200785i
$707$	−3.83447	−	11.8013i	−0.144210	−	0.443833i
$708$	0.200831	−	0.618093i	0.00754768	−	0.0232294i
$709$	−21.1535	−	15.3689i	−0.794437	−	0.577192i	0.114840	−	0.993384i	$-0.463365\pi$
$709$	−21.1535	−	15.3689i	−0.794437	−	0.577192i	−0.909277	+	0.416192i	$0.863365\pi$
$710$	−10.5092	−	7.63537i	−0.394403	−	0.286550i
$711$	−1.97093	+	6.06588i	−0.0739155	+	0.227488i
$712$	−1.94271	−	5.97903i	−0.0728060	−	0.224074i
$713$	12.5162	−	9.09353i	0.468734	−	0.340556i
$714$	0.225350			0.00843350
$715$	0.362627	+	13.0607i	0.0135615	+	0.488441i
$716$	1.58336			0.0591729
$717$	−11.4086	+	8.28881i	−0.426061	+	0.309551i
$718$	−1.53453	−	4.72279i	−0.0572680	−	0.176253i
$719$	−4.91562	+	15.1287i	−0.183322	+	0.564206i	−0.999915	−	0.0130068i	$-0.995860\pi$
$719$	−4.91562	+	15.1287i	−0.183322	+	0.564206i	0.816594	+	0.577213i	$0.195860\pi$
$720$	10.5779	+	7.68529i	0.394215	+	0.286414i
$721$	−10.2257	−	7.42940i	−0.380825	−	0.276685i
$722$	−0.733019	+	2.25600i	−0.0272801	+	0.0839596i
$723$	−2.53203	−	7.79280i	−0.0941674	−	0.289817i
$724$	−4.97187	+	3.61227i	−0.184778	+	0.134249i
$725$	−8.43498			−0.313267
$726$	−3.14488	−	2.02823i	−0.116717	−	0.0752746i
$727$	−14.9983			−0.556256			−0.278128	−	0.960544i	$-0.589714\pi$
$727$	−14.9983			−0.556256			−0.278128	+	0.960544i	$0.589714\pi$
$728$	0.705363	−	0.512476i	0.0261425	−	0.0189936i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	4.29113	−	13.2067i	0.158822	−	0.488803i
$731$	−9.70091	−	7.04813i	−0.358801	−	0.260684i
$732$	6.55008	+	4.75891i	0.242098	+	0.175894i
$733$	3.00726	−	9.25541i	0.111076	−	0.341856i	−0.880033	−	0.474913i	$-0.842479\pi$
$733$	3.00726	−	9.25541i	0.111076	−	0.341856i	0.991108	+	0.133057i	$0.0424794\pi$
$734$	−2.30737	−	7.10136i	−0.0851666	−	0.262116i
$735$	−20.9222	+	15.2008i	−0.771725	+	0.560691i
$736$	−11.7081			−0.431568
$737$	0.195342	+	7.03557i	0.00719550	+	0.259159i
$738$	0.600766			0.0221145
$739$	4.76042	−	3.45865i	0.175115	−	0.127228i	−0.496775	−	0.867879i	$-0.665483\pi$
$739$	4.76042	−	3.45865i	0.175115	−	0.127228i	0.671890	+	0.740651i	$0.265483\pi$
$740$	1.53637	+	4.72846i	0.0564780	+	0.173821i
$741$	−1.57486	+	4.84691i	−0.0578538	+	0.178056i
$742$	−2.15929	−	1.56881i	−0.0792699	−	0.0575930i
$743$	−15.4545	−	11.2284i	−0.566971	−	0.411929i	0.267033	−	0.963688i	$-0.413957\pi$
$743$	−15.4545	−	11.2284i	−0.566971	−	0.411929i	−0.834004	+	0.551759i	$0.813957\pi$
$744$	−2.03525	+	6.26384i	−0.0746157	+	0.229644i
$745$	19.7650	+	60.8303i	0.724132	+	2.22865i
$746$	2.27987	−	1.65642i	0.0834721	−	0.0606460i
$747$	−7.69588			−0.281577
$748$	−3.82726	−	4.97152i	−0.139939	−	0.181777i
$749$	13.1050			0.478846
$750$	−5.98429	+	4.34784i	−0.218515	+	0.158761i
$751$	−9.54262	−	29.3692i	−0.348215	−	1.07170i	−0.959840	−	0.280548i	$-0.909484\pi$
$751$	−9.54262	−	29.3692i	−0.348215	−	1.07170i	0.611625	−	0.791148i	$-0.290516\pi$
$752$	5.93197	−	18.2567i	0.216317	−	0.665754i
$753$	−3.99311	−	2.90116i	−0.145517	−	0.105724i
$754$	−0.220692	−	0.160342i	−0.00803713	−	0.00583932i
$755$	9.94904	−	30.6200i	0.362083	−	1.11438i
$756$	0.384182	+	1.18239i	0.0139726	+	0.0430032i
$757$	2.86630	−	2.08249i	0.104178	−	0.0756895i	−0.534477	−	0.845183i	$-0.679491\pi$
$757$	2.86630	−	2.08249i	0.104178	−	0.0756895i	0.638654	+	0.769494i	$0.279491\pi$
$758$	−6.70651			−0.243591
$759$	9.69886	−	3.45178i	0.352046	−	0.125292i
$760$	26.5300			0.962342
$761$	36.8615	−	26.7814i	1.33623	−	0.970826i	0.336653	−	0.941629i	$-0.390705\pi$
$761$	36.8615	−	26.7814i	1.33623	−	0.970826i	0.999574	−	0.0291972i	$-0.00929509\pi$
$762$	−0.796586	−	2.45164i	−0.0288573	−	0.0888136i
$763$	0.533650	−	1.64240i	0.0193194	−	0.0594590i
$764$	5.86293	+	4.25967i	0.212113	+	0.154109i
$765$	3.19967	+	2.32470i	0.115684	+	0.0840496i
$766$	1.02411	−	3.15188i	0.0370025	−	0.113882i
$767$	−0.106583	−	0.328029i	−0.00384849	−	0.0118444i
$768$	−6.08650	+	4.42210i	−0.219628	+	0.159569i
$769$	27.0550			0.975629			0.487815	−	0.872947i	$-0.337794\pi$
$769$	27.0550			0.975629			0.487815	+	0.872947i	$0.337794\pi$
$770$	2.81331	+	0.828515i	0.101385	+	0.0298576i
$771$	−9.97255			−0.359152
$772$	−32.0881	+	23.3134i	−1.15488	+	0.839066i
$773$	8.51708	+	26.2129i	0.306338	+	0.942811i	0.979175	+	0.203020i	$0.0650757\pi$
$773$	8.51708	+	26.2129i	0.306338	+	0.942811i	−0.672837	+	0.739791i	$0.734924\pi$
$774$	−1.25562	+	3.86441i	−0.0451324	+	0.138903i
$775$	42.4168	+	30.8176i	1.52366	+	1.10700i
$776$	9.69307	+	7.04243i	0.347961	+	0.252809i
$777$	−0.136562	+	0.420295i	−0.00489914	+	0.0150780i
$778$	1.72744	+	5.31651i	0.0619316	+	0.190606i
$779$	−7.28095	+	5.28992i	−0.260867	+	0.189531i
$780$	7.42298			0.265785
$781$	−18.1664	+	26.5218i	−0.650043	+	0.949023i
$782$	−1.06014			−0.0379107
$783$	0.648715	−	0.471319i	0.0231832	−	0.0168436i
$784$	−6.73286	−	20.7216i	−0.240459	−	0.740058i
$785$	29.9843	−	92.2823i	1.07019	−	3.29370i
$786$	5.49692	+	3.99375i	0.196069	+	0.142452i
$787$	28.6431	+	20.8105i	1.02102	+	0.741813i	0.966491	−	0.256700i	$-0.0826351\pi$
$787$	28.6431	+	20.8105i	1.02102	+	0.741813i	0.0545264	+	0.998512i	$0.482635\pi$
$788$	5.97663	−	18.3942i	0.212908	−	0.655265i
$789$	−6.30282	−	19.3981i	−0.224386	−	0.690590i
$790$	6.91536	−	5.02430i	0.246037	−	0.178757i
$791$	6.28952			0.223629
$792$	−2.47667	+	3.61578i	−0.0880045	+	0.128481i
$793$	4.29682			0.152584
$794$	5.00583	−	3.63695i	0.177650	−	0.129071i
$795$	−14.4752	−	44.5502i	−0.513384	−	1.58003i
$796$	5.42169	−	16.6862i	0.192167	−	0.591428i
$797$	25.9464	+	18.8512i	0.919070	+	0.667743i	0.943292	−	0.331963i	$-0.107711\pi$
$797$	25.9464	+	18.8512i	0.919070	+	0.667743i	−0.0242225	+	0.999707i	$0.507711\pi$
$798$	0.925469	+	0.672393i	0.0327613	+	0.0238024i
$799$	1.79434	−	5.52241i	0.0634792	−	0.195369i
$800$	−12.2613	−	37.7364i	−0.433503	−	1.33418i
$801$	3.84893	−	2.79641i	0.135995	−	0.0988064i
$802$	−0.182193			−0.00643345
$803$	−32.9652	−	9.70818i	−1.16332	−	0.342594i
$804$	3.99864			0.141021
$805$	−6.52722	+	4.74230i	−0.230054	+	0.167144i
$806$	0.523972	+	1.61262i	0.0184561	+	0.0568021i
$807$	−4.47670	+	13.7779i	−0.157587	+	0.485003i
$808$	−20.1052	−	14.6073i	−0.707300	−	0.513883i
$809$	−2.90853	−	2.11317i	−0.102259	−	0.0742952i	0.535481	−	0.844547i	$-0.320130\pi$
$809$	−2.90853	−	2.11317i	−0.102259	−	0.0742952i	−0.637740	+	0.770252i	$0.720130\pi$
$810$	0.414144	−	1.27460i	0.0145515	−	0.0447851i
$811$	2.38932	+	7.35357i	0.0839004	+	0.258219i	0.984202	−	0.177047i	$-0.0566544\pi$
$811$	2.38932	+	7.35357i	0.0839004	+	0.258219i	−0.900302	+	0.435266i	$0.856654\pi$
$812$	0.806508	−	0.585962i	0.0283029	−	0.0205633i
$813$	−21.7837			−0.763986
$814$	−0.711979	+	0.253390i	−0.0249549	+	0.00888131i
$815$	85.5693			2.99736
$816$	−2.69571	+	1.95855i	−0.0943689	+	0.0685630i
$817$	−18.8098	−	57.8907i	−0.658072	−	2.02534i
$818$	−1.93503	+	5.95542i	−0.0676569	+	0.208226i
$819$	0.533790	+	0.387821i	0.0186521	+	0.0135516i
$820$	10.6049	+	7.70494i	0.370340	+	0.269068i
$821$	−7.94062	+	24.4387i	−0.277130	+	0.852918i	0.711518	+	0.702668i	$0.248008\pi$
$821$	−7.94062	+	24.4387i	−0.277130	+	0.852918i	−0.988648	+	0.150250i	$0.951992\pi$
$822$	1.24499	+	3.83169i	0.0434241	+	0.133646i
$823$	−11.5438	+	8.38708i	−0.402392	+	0.292355i	−0.770515	−	0.637422i	$-0.780001\pi$
$823$	−11.5438	+	8.38708i	−0.402392	+	0.292355i	0.368122	+	0.929777i	$0.380001\pi$
$824$	−25.3142			−0.881861
$825$	21.2825	+	27.6455i	0.740962	+	0.962492i
$826$	−0.0774197			−0.00269378
$827$	−3.82042	+	2.77570i	−0.132849	+	0.0965205i	−0.652225	−	0.758025i	$-0.726164\pi$
$827$	−3.82042	+	2.77570i	−0.132849	+	0.0965205i	0.519376	+	0.854546i	$0.326164\pi$
$828$	−1.80736	−	5.56249i	−0.0628102	−	0.193310i
$829$	13.8510	−	42.6289i	0.481064	−	1.48056i	−0.356536	−	0.934281i	$-0.616042\pi$
$829$	13.8510	−	42.6289i	0.481064	−	1.48056i	0.837601	−	0.546283i	$-0.183958\pi$
$830$	8.34420	+	6.06242i	0.289632	+	0.210430i
$831$	−10.5400	−	7.65777i	−0.365629	−	0.265645i
$832$	−1.65471	+	5.09267i	−0.0573667	+	0.176557i
$833$	−2.03660	−	6.26801i	−0.0705640	−	0.217174i
$834$	0.648418	−	0.471103i	0.0224529	−	0.0163130i
$835$	−65.8845			−2.28003
$836$	−0.883943	−	31.8368i	−0.0305718	−	1.10110i
$837$	−4.98417			−0.172278
$838$	−8.24782	+	5.99239i	−0.284916	+	0.207004i
$839$	1.59373	+	4.90500i	0.0550217	+	0.169339i	0.974791	−	0.223120i	$-0.0716243\pi$
$839$	1.59373	+	4.90500i	0.0550217	+	0.169339i	−0.919769	+	0.392460i	$0.871624\pi$
$840$	1.06139	−	3.26661i	0.0366213	−	0.112709i
$841$	22.9413	+	16.6678i	0.791080	+	0.574753i
$842$	9.20274	+	6.68618i	0.317147	+	0.230421i
$843$	9.24427	−	28.4509i	0.318390	−	0.979902i
$844$	−7.28652	−	22.4256i	−0.250812	−	0.771921i
$845$	3.18709	−	2.31555i	0.109639	−	0.0796575i
$846$	−1.96763			−0.0676486
$847$	1.85633	−	7.01640i	0.0637842	−	0.241086i
$848$	39.4650			1.35523
$849$	15.5110	−	11.2694i	0.532335	−	0.386764i
$850$	−1.11023	−	3.41695i	−0.0380807	−	0.117200i
$851$	0.642448	−	1.97725i	0.0220229	−	0.0677794i
$852$	14.7755	+	10.7350i	0.506200	+	0.367776i
$853$	15.3270	+	11.1357i	0.524788	+	0.381281i	0.818405	−	0.574643i	$-0.194859\pi$
$853$	15.3270	+	11.1357i	0.524788	+	0.381281i	−0.293617	+	0.955923i	$0.594859\pi$
$854$	0.298040	−	0.917274i	0.0101987	−	0.0313885i
$855$	6.20408	+	19.0942i	0.212175	+	0.653007i
$856$	21.2336	−	15.4271i	0.725748	−	0.527287i
$857$	−34.9448			−1.19369			−0.596846	−	0.802356i	$-0.703580\pi$
$857$	−34.9448			−1.19369			−0.596846	+	0.802356i	$0.703580\pi$
$858$	0.0313153	+	1.12788i	0.00106909	+	0.0385051i
$859$	−43.3058			−1.47757			−0.738787	−	0.673938i	$-0.764601\pi$
$859$	−43.3058			−1.47757			−0.738787	+	0.673938i	$0.764601\pi$
$860$	−71.7265	+	52.1124i	−2.44585	+	1.77702i
$861$	0.360054	+	1.10813i	0.0122706	+	0.0377650i
$862$	−2.69408	+	8.29153i	−0.0917608	+	0.282411i
$863$	23.6969	+	17.2168i	0.806653	+	0.586068i	0.912858	−	0.408276i	$-0.133870\pi$
$863$	23.6969	+	17.2168i	0.806653	+	0.586068i	−0.106205	+	0.994344i	$0.533870\pi$
$864$	3.05158	+	2.21710i	0.103817	+	0.0754274i
$865$	11.6603	−	35.8868i	0.396463	−	1.22019i
$866$	0.726354	+	2.23549i	0.0246825	+	0.0759650i
$867$	12.9379	−	9.39991i	0.439393	−	0.319238i
$868$	−6.19652			−0.210324
$869$	−12.9040	−	16.7619i	−0.437737	−	0.568610i
$870$	−1.07465			−0.0364339
$871$	1.71683	−	1.24735i	0.0581727	−	0.0422649i
$872$	−1.06877	−	3.28934i	−0.0361932	−	0.111391i
$873$	−2.80185	+	8.62320i	−0.0948282	+	0.291851i
$874$	−4.35382	−	3.16323i	−0.147270	−	0.106998i
$875$	−11.6063	−	8.43244i	−0.392363	−	0.285069i
$876$	−6.03315	+	18.5681i	−0.203841	+	0.627359i
$877$	−3.16523	−	9.74156i	−0.106882	−	0.328949i	0.883286	−	0.468835i	$-0.155326\pi$
$877$	−3.16523	−	9.74156i	−0.106882	−	0.328949i	−0.990168	+	0.139886i	$0.955326\pi$
$878$	7.41493	−	5.38726i	0.250242	−	0.181811i
$879$	−11.8986			−0.401330
$880$	−40.8546	+	14.5400i	−1.37721	+	0.490142i
$881$	−40.9069			−1.37819			−0.689094	−	0.724672i	$-0.741991\pi$
$881$	−40.9069			−1.37819			−0.689094	+	0.724672i	$0.741991\pi$
$882$	−1.80677	+	1.31270i	−0.0608371	+	0.0442008i
$883$	−9.59469	−	29.5294i	−0.322887	−	0.993744i	−0.972385	−	0.233381i	$-0.925021\pi$
$883$	−9.59469	−	29.5294i	−0.322887	−	0.993744i	0.649498	−	0.760363i	$-0.274979\pi$
$884$	−0.584568	+	1.79912i	−0.0196612	+	0.0605108i
$885$	−1.09926	−	0.798657i	−0.0369511	−	0.0268466i
$886$	3.52656	+	2.56219i	0.118477	+	0.0860786i
$887$	1.62682	−	5.00683i	0.0546232	−	0.168113i	−0.920023	−	0.391864i	$-0.871830\pi$
$887$	1.62682	−	5.00683i	0.0546232	−	0.168113i	0.974646	+	0.223751i	$0.0718303\pi$
$888$	0.273501	+	0.841749i	0.00917809	+	0.0282473i
$889$	4.04472	−	2.93866i	0.135655	−	0.0985595i
$890$	−6.37606			−0.213726
$891$	−3.18153	−	0.936954i	−0.106585	−	0.0313891i
$892$	9.46793			0.317010
$893$	23.8467	−	17.3256i	0.797998	−	0.579779i
$894$	1.70684	+	5.25311i	0.0570852	+	0.175690i
$895$	1.02295	−	3.14833i	0.0341936	−	0.105237i
$896$	4.99927	+	3.63218i	0.167014	+	0.121343i
$897$	−2.51119	−	1.82448i	−0.0838461	−	0.0609177i
$898$	−2.01781	+	6.21019i	−0.0673353	+	0.207237i
$899$	1.23501	+	3.80098i	0.0411900	+	0.126770i
$900$	16.0357	−	11.6506i	0.534522	−	0.388353i
$901$	11.9376			0.397700
$902$	−1.12598	+	1.64386i	−0.0374910	+	0.0547346i
$903$	−7.88056			−0.262248
$904$	10.1907	−	7.40397i	0.338937	−	0.246252i
$905$	3.97044	+	12.2198i	0.131982	+	0.406199i
$906$	0.859167	−	2.64425i	0.0285439	−	0.0878492i
$907$	18.1418	+	13.1808i	0.602387	+	0.437660i	0.846725	−	0.532030i	$-0.178571\pi$
$907$	18.1418	+	13.1808i	0.602387	+	0.437660i	−0.244338	+	0.969690i	$0.578571\pi$
$908$	−6.91902	−	5.02696i	−0.229616	−	0.166826i
$909$	5.81155	−	17.8861i	0.192757	−	0.593245i
$910$	−0.273253	−	0.840986i	−0.00905824	−	0.0278784i
$911$	−20.5237	+	14.9114i	−0.679982	+	0.494036i	−0.873352	−	0.487090i	$-0.838058\pi$
$911$	−20.5237	+	14.9114i	−0.679982	+	0.494036i	0.193370	+	0.981126i	$0.438058\pi$
$912$	−16.9147			−0.560100
$913$	14.4239	−	21.0581i	0.477363	−	0.696920i
$914$	0.567227			0.0187622
$915$	13.6943	−	9.94952i	0.452721	−	0.328921i
$916$	1.83355	+	5.64310i	0.0605823	+	0.186453i
$917$	−4.07216	+	12.5328i	−0.134474	+	0.413870i
$918$	0.276313	+	0.200753i	0.00911970	+	0.00662585i
$919$	23.1138	+	16.7932i	0.762455	+	0.553956i	0.899662	−	0.436586i	$-0.143813\pi$
$919$	23.1138	+	16.7932i	0.762455	+	0.553956i	−0.137207	+	0.990542i	$0.543813\pi$
$920$	−4.99323	+	15.3676i	−0.164622	+	0.506654i
$921$	7.51045	+	23.1148i	0.247478	+	0.761658i
$922$	−5.15762	+	3.74723i	−0.169857	+	0.123409i
$923$	9.69264			0.319037
$924$	−3.95540	−	1.16486i	−0.130123	−	0.0383210i
$925$	7.04567			0.231660
$926$	3.15107	−	2.28939i	0.103551	−	0.0752340i
$927$	−5.91976	−	18.2192i	−0.194431	−	0.598396i
$928$	0.934643	−	2.87653i	0.0306811	−	0.0944269i
$929$	41.7745	+	30.3510i	1.37058	+	0.995783i	0.997692	+	0.0679061i	$0.0216318\pi$
$929$	41.7745	+	30.3510i	1.37058	+	0.995783i	0.372886	+	0.927877i	$0.378368\pi$
$930$	5.40405	+	3.92628i	0.177206	+	0.128748i
$931$	10.3384	−	31.8183i	0.338827	−	1.04280i
$932$	1.05151	+	3.23623i	0.0344435	+	0.106006i
$933$	11.8783	−	8.63011i	0.388879	−	0.282537i
$934$	−4.68809			−0.153399
$935$	−12.3580	+	4.39814i	−0.404149	+	0.143835i
$936$	1.32142			0.0431921
$937$	0.162230	−	0.117867i	0.00529983	−	0.00385055i	−0.585132	−	0.810938i	$-0.698957\pi$
$937$	0.162230	−	0.117867i	0.00529983	−	0.00385055i	0.590432	+	0.807087i	$0.298957\pi$
$938$	−0.147197	−	0.453026i	−0.00480615	−	0.0147918i
$939$	2.25496	−	6.94005i	0.0735878	−	0.226480i
$940$	−34.7334	−	25.2353i	−1.13288	−	0.823084i
$941$	0.626931	+	0.455492i	0.0204374	+	0.0148486i	0.597957	−	0.801528i	$-0.295979\pi$
$941$	0.626931	+	0.455492i	0.0204374	+	0.0148486i	−0.577520	+	0.816377i	$0.695979\pi$
$942$	2.58935	−	7.96921i	0.0843657	−	0.259651i
$943$	−1.69385	−	5.21314i	−0.0551594	−	0.169763i
$944$	0.926122	−	0.672867i	0.0301427	−	0.0219000i
$945$	2.59926			0.0845539
$946$	−8.22076	−	10.6786i	−0.267280	−	0.347190i
$947$	−4.68762			−0.152327			−0.0761637	−	0.997095i	$-0.524267\pi$
$947$	−4.68762			−0.152327			−0.0761637	+	0.997095i	$0.524267\pi$
$948$	−9.72271	+	7.06396i	−0.315779	+	0.229427i
$949$	3.20186	+	9.85431i	0.103937	+	0.319884i
$950$	5.63587	−	17.3454i	0.182852	−	0.562760i
$951$	4.48152	+	3.25601i	0.145323	+	0.105583i
$952$	0.708147	+	0.514499i	0.0229512	+	0.0166750i
$953$	−4.15847	+	12.7984i	−0.134706	+	0.414582i	−0.995544	−	0.0942965i	$-0.969940\pi$
$953$	−4.15847	+	12.7984i	−0.134706	+	0.414582i	0.860838	+	0.508879i	$0.169940\pi$
$954$	−1.25003	−	3.84721i	−0.0404714	−	0.124558i
$955$	12.2577	−	8.90574i	0.396650	−	0.288183i
$956$	−26.5715			−0.859382
$957$	0.0738109	+	2.65843i	0.00238597	+	0.0859348i
$958$	−5.17515			−0.167202
$959$	−6.32153	+	4.59286i	−0.204133	+	0.148311i
$960$	6.51865	+	20.0623i	0.210389	+	0.647510i
$961$	−1.90294	+	5.85666i	−0.0613853	+	0.188924i
$962$	0.184342	+	0.133933i	0.00594344	+	0.00431816i
$963$	16.0687	+	11.6746i	0.517807	+	0.376209i
$964$	4.77102	−	14.6837i	0.153664	−	0.472930i
$965$	25.6249	+	78.8654i	0.824896	+	2.53877i
$966$	−0.563670	+	0.409530i	−0.0181358	+	0.0131764i
$967$	−21.8025			−0.701120			−0.350560	−	0.936540i	$-0.614009\pi$
$967$	−21.8025			−0.701120			−0.350560	+	0.936540i	$0.614009\pi$
$968$	−5.25191	−	13.5537i	−0.168803	−	0.435632i
$969$	−5.11646			−0.164364
$970$	9.83080	−	7.14250i	0.315648	−	0.229332i
$971$	−8.74469	−	26.9134i	−0.280630	−	0.863692i	−0.987674	−	0.156522i	$-0.949972\pi$
$971$	−8.74469	−	26.9134i	−0.280630	−	0.863692i	0.707044	−	0.707170i	$-0.250028\pi$
$972$	−0.582270	+	1.79204i	−0.0186763	+	0.0574798i
$973$	1.25758	+	0.913684i	0.0403161	+	0.0292914i
$974$	−5.73406	−	4.16604i	−0.183731	−	0.133488i
$975$	3.25065	−	10.0045i	0.104104	−	0.320399i
$976$	4.40691	+	13.5631i	0.141062	+	0.434144i
$977$	38.5788	−	28.0292i	1.23425	−	0.896732i	0.237045	−	0.971499i	$-0.423821\pi$
$977$	38.5788	−	28.0292i	1.23425	−	0.896732i	0.997201	+	0.0747664i	$0.0238211\pi$
$978$	7.38949			0.236290
$979$	0.437932	+	15.7729i	0.0139964	+	0.504104i
$980$	−48.7294			−1.55660
$981$	2.11748	−	1.53844i	0.0676058	−	0.0491185i
$982$	−3.15145	−	9.69916i	−0.100567	−	0.309513i
$983$	7.01481	−	21.5894i	0.223738	−	0.688594i	−0.774680	−	0.632354i	$-0.782089\pi$
$983$	7.01481	−	21.5894i	0.223738	−	0.688594i	0.998417	−	0.0562399i	$-0.0179112\pi$
$984$	1.88787	+	1.37162i	0.0601830	+	0.0437255i
$985$	−32.7134	−	23.7677i	−1.04234	−	0.757301i
$986$	0.0846297	−	0.260463i	0.00269516	−	0.00829484i
$987$	−1.17925	−	3.62937i	−0.0375360	−	0.115524i
$988$	−7.76887	+	5.64442i	−0.247161	+	0.179573i
$989$	37.0736			1.17887
$990$	2.71147	+	3.52213i	0.0861761	+	0.111941i
$991$	−5.00165			−0.158883			−0.0794413	−	0.996840i	$-0.525314\pi$
$991$	−5.00165			−0.158883			−0.0794413	+	0.996840i	$0.525314\pi$
$992$	−15.2096	+	11.0504i	−0.482905	+	0.350851i
$993$	−8.05183	−	24.7810i	−0.255517	−	0.786401i
$994$	0.672311	−	2.06916i	0.0213244	−	0.0656298i
$995$	−29.6759	−	21.5608i	−0.940789	−	0.683524i
$996$	−11.7316	−	8.52351i	−0.371730	−	0.270078i
$997$	12.6302	−	38.8719i	0.400004	−	1.23108i	−0.524992	−	0.851107i	$-0.675932\pi$
$997$	12.6302	−	38.8719i	0.400004	−	1.23108i	0.924996	−	0.379978i	$-0.124068\pi$
$998$	−2.54925	−	7.84579i	−0.0806951	−	0.248354i
$999$	−0.541867	+	0.393689i	−0.0171439	+	0.0124558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.a.157.2	✓	12
11.2	odd	10		4719.2.a.bh.1.4		6
11.4	even	5	inner	429.2.n.a.235.2	yes	12
11.9	even	5		4719.2.a.bg.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.a.157.2	✓	12	1.1	even	1	trivial
429.2.n.a.235.2	yes	12	11.4	even	5	inner
4719.2.a.bg.1.3		6	11.9	even	5
4719.2.a.bh.1.4		6	11.2	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.275227 - 0.199964i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.582270 + 1.79204i) q^{4} +(3.18709 + 2.31555i) q^{5} +(0.275227 + 0.199964i) q^{6} +(-0.203890 + 0.627508i) q^{7} +(0.408342 + 1.25675i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.275227 - 0.199964i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.582270 + 1.79204i) q^{4} +(3.18709 + 2.31555i) q^{5} +(0.275227 + 0.199964i) q^{6} +(-0.203890 + 0.627508i) q^{7} +(0.408342 + 1.25675i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.34020 q^{10} +(-0.0920501 - 3.31535i) q^{11} -1.88426 q^{12} +(-0.809017 + 0.587785i) q^{13} +(0.0693631 + 0.213478i) q^{14} +(-1.21736 + 3.74665i) q^{15} +(-2.68511 - 1.95085i) q^{16} +(-0.812211 - 0.590106i) q^{17} +(-0.105127 + 0.323548i) q^{18} +(-1.57486 - 4.84691i) q^{19} +(-6.00532 + 4.36312i) q^{20} -0.659801 q^{21} +(-0.688284 - 0.894065i) q^{22} +3.10400 q^{23} +(-1.06905 + 0.776713i) q^{24} +(3.25065 + 10.0045i) q^{25} +(-0.105127 + 0.323548i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.00580 - 0.730758i) q^{28} +(-0.247787 + 0.762610i) q^{29} +(0.414144 + 1.27460i) q^{30} +(4.03228 - 2.92962i) q^{31} -3.77196 q^{32} +(3.12464 - 1.11204i) q^{33} -0.341542 q^{34} +(-2.10284 + 1.52781i) q^{35} +(-0.582270 - 1.79204i) q^{36} +(0.206975 - 0.637002i) q^{37} +(-1.40265 - 1.01908i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-1.60865 + 4.95090i) q^{40} +(-0.545701 - 1.67949i) q^{41} +(-0.181595 + 0.131936i) q^{42} +11.9438 q^{43} +(5.99484 + 1.76547i) q^{44} -3.93946 q^{45} +(0.854303 - 0.620687i) q^{46} +(1.78728 + 5.50070i) q^{47} +(1.02562 - 3.15654i) q^{48} +(5.31092 + 3.85861i) q^{49} +(2.89520 + 2.10348i) q^{50} +(0.310237 - 0.954811i) q^{51} +(-0.582270 - 1.79204i) q^{52} +(-9.61976 + 6.98917i) q^{53} -0.340199 q^{54} +(7.38350 - 10.7794i) q^{55} -0.871876 q^{56} +(4.12303 - 2.99555i) q^{57} +(0.0842969 + 0.259439i) q^{58} +(-0.106583 + 0.328029i) q^{59} +(-6.00532 - 4.36312i) q^{60} +(-3.47620 - 2.52561i) q^{61} +(0.523972 - 1.61262i) q^{62} +(-0.203890 - 0.627508i) q^{63} +(4.33208 - 3.14744i) q^{64} -3.93946 q^{65} +(0.637615 - 0.930879i) q^{66} -2.12212 q^{67} +(1.53042 - 1.11192i) q^{68} +(0.959188 + 2.95208i) q^{69} +(-0.273253 + 0.840986i) q^{70} +(-7.84151 - 5.69719i) q^{71} +(-1.06905 - 0.776713i) q^{72} +(3.20186 - 9.85431i) q^{73} +(-0.0704125 - 0.216708i) q^{74} +(-8.51031 + 6.18310i) q^{75} +9.60285 q^{76} +(2.09918 + 0.618203i) q^{77} -0.340199 q^{78} +(5.15995 - 3.74892i) q^{79} +(-4.04039 - 12.4351i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.486030 - 0.353121i) q^{82} +(6.22609 + 4.52352i) q^{83} +(0.384182 - 1.18239i) q^{84} +(-1.22216 - 3.76144i) q^{85} +(3.28726 - 2.38834i) q^{86} -0.801856 q^{87} +(4.12897 - 1.46948i) q^{88} -4.75754 q^{89} +(-1.08424 + 0.787749i) q^{90} +(-0.203890 - 0.627508i) q^{91} +(-1.80736 + 5.56249i) q^{92} +(4.03228 + 2.92962i) q^{93} +(1.59185 + 1.15655i) q^{94} +(6.20408 - 19.0942i) q^{95} +(-1.16560 - 3.58735i) q^{96} +(7.33533 - 5.32943i) q^{97} +2.23329 q^{98} +(2.02318 + 2.62807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

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