LMFDB - Embedded newform 429.2.i.e.133.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 6x^{7} + 46x^{6} - 31x^{5} + 111x^{4} - 36x^{3} + 145x^{2} - 72x + 81 $ x^10 - 2x^9 + 10x^8 - 6x^7 + 46x^6 - 31x^5 + 111x^4 - 36x^3 + 145x^2 - 72*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.4
Root			$0.779885 + 1.35080i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.e.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.779885 + 1.35080i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.216440 + 0.374886i) q^{4} +1.18322 q^{5} +(-0.779885 + 1.35080i) q^{6} +(-1.45667 + 2.52303i) q^{7} +2.44434 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.779885 + 1.35080i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.216440 + 0.374886i) q^{4} +1.18322 q^{5} +(-0.779885 + 1.35080i) q^{6} +(-1.45667 + 2.52303i) q^{7} +2.44434 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.922773 + 1.59829i) q^{10} +(0.500000 + 0.866025i) q^{11} -0.432881 q^{12} +(0.0453878 - 3.60527i) q^{13} -4.54414 q^{14} +(0.591609 + 1.02470i) q^{15} +(2.33919 + 4.05159i) q^{16} +(0.0735520 - 0.127396i) q^{17} -1.55977 q^{18} +(-1.11702 + 1.93473i) q^{19} +(-0.256096 + 0.443571i) q^{20} -2.91334 q^{21} +(-0.779885 + 1.35080i) q^{22} +(1.04171 + 1.80430i) q^{23} +(1.22217 + 2.11686i) q^{24} -3.60000 q^{25} +(4.90539 - 2.75038i) q^{26} -1.00000 q^{27} +(-0.630564 - 1.09217i) q^{28} +(-2.93861 - 5.08983i) q^{29} +(-0.922773 + 1.59829i) q^{30} +6.91010 q^{31} +(-1.20425 + 2.08582i) q^{32} +(-0.500000 + 0.866025i) q^{33} +0.229448 q^{34} +(-1.72356 + 2.98529i) q^{35} +(-0.216440 - 0.374886i) q^{36} +(2.57561 + 4.46109i) q^{37} -3.48457 q^{38} +(3.14495 - 1.76333i) q^{39} +2.89219 q^{40} +(-4.93494 - 8.54756i) q^{41} +(-2.27207 - 3.93534i) q^{42} +(5.24679 - 9.08771i) q^{43} -0.432881 q^{44} +(-0.591609 + 1.02470i) q^{45} +(-1.62483 + 2.81429i) q^{46} -11.0402 q^{47} +(-2.33919 + 4.05159i) q^{48} +(-0.743771 - 1.28825i) q^{49} +(-2.80758 - 4.86288i) q^{50} +0.147104 q^{51} +(1.34174 + 0.797340i) q^{52} -5.94502 q^{53} +(-0.779885 - 1.35080i) q^{54} +(0.591609 + 1.02470i) q^{55} +(-3.56060 + 6.16714i) q^{56} -2.23403 q^{57} +(4.58356 - 7.93896i) q^{58} +(5.32541 - 9.22387i) q^{59} -0.512192 q^{60} +(2.30229 - 3.98768i) q^{61} +(5.38908 + 9.33417i) q^{62} +(-1.45667 - 2.52303i) q^{63} +5.60005 q^{64} +(0.0537036 - 4.26581i) q^{65} -1.55977 q^{66} +(7.06633 + 12.2393i) q^{67} +(0.0318392 + 0.0551471i) q^{68} +(-1.04171 + 1.80430i) q^{69} -5.37670 q^{70} +(6.84208 - 11.8508i) q^{71} +(-1.22217 + 2.11686i) q^{72} -3.10942 q^{73} +(-4.01736 + 6.95827i) q^{74} +(-1.80000 - 3.11769i) q^{75} +(-0.483534 - 0.837506i) q^{76} -2.91334 q^{77} +(4.83460 + 2.87300i) q^{78} -12.2513 q^{79} +(2.76777 + 4.79391i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.69736 - 13.3322i) q^{82} +6.52042 q^{83} +(0.630564 - 1.09217i) q^{84} +(0.0870280 - 0.150737i) q^{85} +16.3676 q^{86} +(2.93861 - 5.08983i) q^{87} +(1.22217 + 2.11686i) q^{88} +(1.92712 + 3.33787i) q^{89} -1.84555 q^{90} +(9.03006 + 5.36619i) q^{91} -0.901874 q^{92} +(3.45505 + 5.98432i) q^{93} +(-8.61010 - 14.9131i) q^{94} +(-1.32167 + 2.28920i) q^{95} -2.40850 q^{96} +(5.82173 - 10.0835i) q^{97} +(1.16011 - 2.00937i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.779885	+	1.35080i	0.551462	+	0.955160i	0.998169	+	0.0604798i	$0.0192631\pi$
$2$	0.779885	+	1.35080i	0.551462	+	0.955160i	−0.446708	+	0.894680i	$0.647404\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.216440	+	0.374886i	−0.108220	+	0.187443i
$5$	1.18322			0.529151			0.264575	−	0.964365i	$-0.414768\pi$
$5$	1.18322			0.529151			0.264575	+	0.964365i	$0.414768\pi$
$6$	−0.779885	+	1.35080i	−0.318387	+	0.551462i
$7$	−1.45667	+	2.52303i	−0.550569	+	0.953614i	0.447664	+	0.894202i	$0.352256\pi$
$7$	−1.45667	+	2.52303i	−0.550569	+	0.953614i	−0.998234	+	0.0594122i	$0.981077\pi$
$8$	2.44434			0.864206
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.922773	+	1.59829i	0.291806	+	0.505424i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−0.432881			−0.124962
$13$	0.0453878	−	3.60527i	0.0125883	−	0.999921i
$13$	0.0453878	−	3.60527i	0.0125883	−	0.999921i
$14$	−4.54414			−1.21447
$15$	0.591609	+	1.02470i	0.152753	+	0.264575i
$16$	2.33919	+	4.05159i	0.584797	+	1.01290i
$17$	0.0735520	−	0.127396i	0.0178390	−	0.0308980i	−0.856968	−	0.515369i	$-0.827655\pi$
$17$	0.0735520	−	0.127396i	0.0178390	−	0.0308980i	0.874807	+	0.484471i	$0.160988\pi$
$18$	−1.55977			−0.367641
$19$	−1.11702	+	1.93473i	−0.256261	+	0.443857i	−0.965237	−	0.261375i	$-0.915824\pi$
$19$	−1.11702	+	1.93473i	−0.256261	+	0.443857i	0.708976	+	0.705232i	$0.249157\pi$
$20$	−0.256096	+	0.443571i	−0.0572648	+	0.0991855i
$21$	−2.91334			−0.635743
$22$	−0.779885	+	1.35080i	−0.166272	+	0.287992i
$23$	1.04171	+	1.80430i	0.217212	+	0.376222i	0.953955	−	0.299951i	$-0.0969703\pi$
$23$	1.04171	+	1.80430i	0.217212	+	0.376222i	−0.736742	+	0.676173i	$0.763637\pi$
$24$	1.22217	+	2.11686i	0.249475	+	0.432103i
$25$	−3.60000			−0.719999
$26$	4.90539	−	2.75038i	0.962026	−	0.539394i
$27$	−1.00000			−0.192450
$28$	−0.630564	−	1.09217i	−0.119165	−	0.206400i
$29$	−2.93861	−	5.08983i	−0.545687	−	0.945157i	−0.998563	−	0.0535839i	$-0.982936\pi$
$29$	−2.93861	−	5.08983i	−0.545687	−	0.945157i	0.452877	−	0.891573i	$-0.350398\pi$
$30$	−0.922773	+	1.59829i	−0.168475	+	0.291806i
$31$	6.91010			1.24109			0.620546	−	0.784170i	$-0.286911\pi$
$31$	6.91010			1.24109			0.620546	+	0.784170i	$0.286911\pi$
$32$	−1.20425	+	2.08582i	−0.212883	+	0.368724i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	0.229448			0.0393500
$35$	−1.72356	+	2.98529i	−0.291334	+	0.504606i
$36$	−0.216440	−	0.374886i	−0.0360734	−	0.0624809i
$37$	2.57561	+	4.46109i	0.423428	+	0.733398i	0.996272	−	0.0862660i	$-0.0274935\pi$
$37$	2.57561	+	4.46109i	0.423428	+	0.733398i	−0.572845	+	0.819664i	$0.694160\pi$
$38$	−3.48457			−0.565272
$39$	3.14495	−	1.76333i	0.503594	−	0.282358i
$40$	2.89219			0.457296
$41$	−4.93494	−	8.54756i	−0.770708	−	1.33491i	−0.937176	−	0.348858i	$-0.886569\pi$
$41$	−4.93494	−	8.54756i	−0.770708	−	1.33491i	0.166468	−	0.986047i	$-0.446764\pi$
$42$	−2.27207	−	3.93534i	−0.350588	−	0.607236i
$43$	5.24679	−	9.08771i	0.800129	−	1.38586i	−0.119402	−	0.992846i	$-0.538098\pi$
$43$	5.24679	−	9.08771i	0.800129	−	1.38586i	0.919531	−	0.393018i	$-0.128569\pi$
$44$	−0.432881			−0.0652592
$45$	−0.591609	+	1.02470i	−0.0881918	+	0.152753i
$46$	−1.62483	+	2.81429i	−0.239568	+	0.414945i
$47$	−11.0402			−1.61038			−0.805191	−	0.593015i	$-0.797937\pi$
$47$	−11.0402			−1.61038			−0.805191	+	0.593015i	$0.797937\pi$
$48$	−2.33919	+	4.05159i	−0.337633	+	0.584797i
$49$	−0.743771	−	1.28825i	−0.106253	−	0.184036i
$50$	−2.80758	−	4.86288i	−0.397052	−	0.687714i
$51$	0.147104			0.0205987
$52$	1.34174	+	0.797340i	0.186066	+	0.110571i
$53$	−5.94502			−0.816611			−0.408306	−	0.912845i	$-0.633880\pi$
$53$	−5.94502			−0.816611			−0.408306	+	0.912845i	$0.633880\pi$
$54$	−0.779885	−	1.35080i	−0.106129	−	0.183821i
$55$	0.591609	+	1.02470i	0.0797725	+	0.138170i
$56$	−3.56060	+	6.16714i	−0.475806	+	0.824119i
$57$	−2.23403			−0.295905
$58$	4.58356	−	7.93896i	0.601851	−	1.04244i
$59$	5.32541	−	9.22387i	0.693309	−	1.20085i	−0.277439	−	0.960743i	$-0.589486\pi$
$59$	5.32541	−	9.22387i	0.693309	−	1.20085i	0.970748	−	0.240103i	$-0.0771811\pi$
$60$	−0.512192			−0.0661237
$61$	2.30229	−	3.98768i	0.294778	−	0.510570i	−0.680155	−	0.733068i	$-0.738088\pi$
$61$	2.30229	−	3.98768i	0.294778	−	0.510570i	0.974933	+	0.222498i	$0.0714210\pi$
$62$	5.38908	+	9.33417i	0.684414	+	1.18544i
$63$	−1.45667	−	2.52303i	−0.183523	−	0.317871i
$64$	5.60005			0.700006
$65$	0.0537036	−	4.26581i	0.00666111	−	0.529109i
$66$	−1.55977			−0.191994
$67$	7.06633	+	12.2393i	0.863290	+	1.49526i	0.868735	+	0.495277i	$0.164934\pi$
$67$	7.06633	+	12.2393i	0.863290	+	1.49526i	−0.00544478	+	0.999985i	$0.501733\pi$
$68$	0.0318392	+	0.0551471i	0.00386107	+	0.00668757i
$69$	−1.04171	+	1.80430i	−0.125407	+	0.217212i
$70$	−5.37670			−0.642639
$71$	6.84208	−	11.8508i	0.812005	−	1.40643i	−0.0994532	−	0.995042i	$-0.531709\pi$
$71$	6.84208	−	11.8508i	0.812005	−	1.40643i	0.911458	−	0.411392i	$-0.134957\pi$
$72$	−1.22217	+	2.11686i	−0.144034	+	0.249475i
$73$	−3.10942			−0.363930			−0.181965	−	0.983305i	$-0.558246\pi$
$73$	−3.10942			−0.363930			−0.181965	+	0.983305i	$0.558246\pi$
$74$	−4.01736	+	6.95827i	−0.467008	+	0.808882i
$75$	−1.80000	−	3.11769i	−0.207846	−	0.360000i
$76$	−0.483534	−	0.837506i	−0.0554652	−	0.0960685i
$77$	−2.91334			−0.332006
$78$	4.83460	+	2.87300i	0.547410	+	0.325303i
$79$	−12.2513			−1.37838			−0.689188	−	0.724582i	$-0.742033\pi$
$79$	−12.2513			−1.37838			−0.689188	+	0.724582i	$0.742033\pi$
$80$	2.76777	+	4.79391i	0.309446	+	0.535976i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.69736	−	13.3322i	0.850032	−	1.47230i
$83$	6.52042			0.715709			0.357855	−	0.933777i	$-0.383508\pi$
$83$	6.52042			0.715709			0.357855	+	0.933777i	$0.383508\pi$
$84$	0.630564	−	1.09217i	0.0688002	−	0.119165i
$85$	0.0870280	−	0.150737i	0.00943951	−	0.0163497i
$86$	16.3676			1.76496
$87$	2.93861	−	5.08983i	0.315052	−	0.545687i
$88$	1.22217	+	2.11686i	0.130284	+	0.225659i
$89$	1.92712	+	3.33787i	0.204274	+	0.353814i	0.949901	−	0.312550i	$-0.101183\pi$
$89$	1.92712	+	3.33787i	0.204274	+	0.353814i	−0.745627	+	0.666364i	$0.767850\pi$
$90$	−1.84555			−0.194538
$91$	9.03006	+	5.36619i	0.946608	+	0.562530i
$92$	−0.901874			−0.0940269
$93$	3.45505	+	5.98432i	0.358272	+	0.620546i
$94$	−8.61010	−	14.9131i	−0.888064	−	1.53817i
$95$	−1.32167	+	2.28920i	−0.135601	+	0.234867i
$96$	−2.40850			−0.245816
$97$	5.82173	−	10.0835i	0.591107	−	1.02383i	−0.402977	−	0.915210i	$-0.632024\pi$
$97$	5.82173	−	10.0835i	0.591107	−	1.02383i	0.994084	−	0.108617i	$-0.0346423\pi$
$98$	1.16011	−	2.00937i	0.117189	−	0.202977i
$99$	−1.00000			−0.100504
$100$	0.779184	−	1.34959i	0.0779184	−	0.134959i
$101$	1.86928	+	3.23768i	0.186000	+	0.322161i	0.943913	−	0.330194i	$-0.107114\pi$
$101$	1.86928	+	3.23768i	0.186000	+	0.322161i	−0.757913	+	0.652356i	$0.773781\pi$
$102$	0.114724	+	0.198708i	0.0113594	+	0.0196750i
$103$	7.53705			0.742648			0.371324	−	0.928503i	$-0.378904\pi$
$103$	7.53705			0.742648			0.371324	+	0.928503i	$0.378904\pi$
$104$	0.110943	−	8.81251i	0.0108789	−	0.864138i
$105$	−3.44711			−0.336404
$106$	−4.63643	−	8.03053i	−0.450330	−	0.779994i
$107$	−3.54552	−	6.14102i	−0.342758	−	0.593675i	0.642185	−	0.766549i	$-0.278028\pi$
$107$	−3.54552	−	6.14102i	−0.342758	−	0.593675i	−0.984944	+	0.172874i	$0.944695\pi$
$108$	0.216440	−	0.374886i	0.0208270	−	0.0360734i
$109$	5.90734			0.565820			0.282910	−	0.959146i	$-0.408700\pi$
$109$	5.90734			0.565820			0.282910	+	0.959146i	$0.408700\pi$
$110$	−0.922773	+	1.59829i	−0.0879830	+	0.152391i
$111$	−2.57561	+	4.46109i	−0.244466	+	0.423428i
$112$	−13.6297			−1.28788
$113$	−7.45698	+	12.9159i	−0.701493	+	1.21502i	0.266449	+	0.963849i	$0.414150\pi$
$113$	−7.45698	+	12.9159i	−0.701493	+	1.21502i	−0.967942	+	0.251173i	$0.919184\pi$
$114$	−1.74229	−	3.01773i	−0.163180	−	0.282636i
$115$	1.23257	+	2.13488i	0.114938	+	0.199078i
$116$	2.54414			0.236217
$117$	3.09956	+	1.84194i	0.286554	+	0.170287i
$118$	16.6128			1.52933
$119$	0.214282	+	0.371147i	0.0196432	+	0.0340230i
$120$	1.44610	+	2.50471i	0.132010	+	0.228648i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	7.18208			0.650235
$123$	4.93494	−	8.54756i	0.444968	−	0.770708i
$124$	−1.49562	+	2.59050i	−0.134311	+	0.232634i
$125$	−10.1757			−0.910139
$126$	2.27207	−	3.93534i	0.202412	−	0.350588i
$127$	1.68851	+	2.92459i	0.149831	+	0.259515i	0.931165	−	0.364598i	$-0.118794\pi$
$127$	1.68851	+	2.92459i	0.149831	+	0.259515i	−0.781334	+	0.624113i	$0.785460\pi$
$128$	6.77589	+	11.7362i	0.598910	+	1.03734i
$129$	10.4936			0.923909
$130$	5.80414	−	3.25430i	0.509057	−	0.285421i
$131$	−1.07103			−0.0935762			−0.0467881	−	0.998905i	$-0.514899\pi$
$131$	−1.07103			−0.0935762			−0.0467881	+	0.998905i	$0.514899\pi$
$132$	−0.216440	−	0.374886i	−0.0188387	−	0.0326296i
$133$	−3.25424	−	5.63652i	−0.282179	−	0.488748i
$134$	−11.0219	+	19.0904i	−0.952143	+	1.64916i
$135$	−1.18322			−0.101835
$136$	0.179786	−	0.311399i	0.0154166	−	0.0267023i
$137$	−3.10758	+	5.38249i	−0.265499	+	0.459857i	−0.967694	−	0.252127i	$-0.918870\pi$
$137$	−3.10758	+	5.38249i	−0.265499	+	0.459857i	0.702196	+	0.711984i	$0.252203\pi$
$138$	−3.24966			−0.276630
$139$	−11.4782	+	19.8809i	−0.973572	+	1.68628i	−0.289002	+	0.957329i	$0.593323\pi$
$139$	−11.4782	+	19.8809i	−0.973572	+	1.68628i	−0.684570	+	0.728947i	$0.740010\pi$
$140$	−0.746094	−	1.29227i	−0.0630565	−	0.109217i
$141$	−5.52011	−	9.56112i	−0.464877	−	0.805191i
$142$	21.3441			1.79116
$143$	3.14495	−	1.76333i	0.262994	−	0.147457i
$144$	−4.67838			−0.389865
$145$	−3.47702	−	6.02237i	−0.288751	−	0.500131i
$146$	−2.42499	−	4.20021i	−0.200694	−	0.347611i
$147$	0.743771	−	1.28825i	0.0613452	−	0.106253i
$148$	−2.22986			−0.183294
$149$	0.850361	−	1.47287i	0.0696643	−	0.120662i	−0.829089	−	0.559116i	$-0.811141\pi$
$149$	0.850361	−	1.47287i	0.0696643	−	0.120662i	0.898754	+	0.438454i	$0.144474\pi$
$150$	2.80758	−	4.86288i	0.229238	−	0.397052i
$151$	−18.0544			−1.46925			−0.734625	−	0.678474i	$-0.762642\pi$
$151$	−18.0544			−1.46925			−0.734625	+	0.678474i	$0.762642\pi$
$152$	−2.73037	+	4.72914i	−0.221462	+	0.383584i
$153$	0.0735520	+	0.127396i	0.00594632	+	0.0102993i
$154$	−2.27207	−	3.93534i	−0.183088	−	0.317119i
$155$	8.17615			0.656724
$156$	−0.0196475	+	1.56065i	−0.00157306	+	0.124952i
$157$	0.871222			0.0695311			0.0347655	−	0.999395i	$-0.488932\pi$
$157$	0.871222			0.0695311			0.0347655	+	0.999395i	$0.488932\pi$
$158$	−9.55458	−	16.5490i	−0.760122	−	1.31657i
$159$	−2.97251	−	5.14854i	−0.235735	−	0.408306i
$160$	−1.42489	+	2.46798i	−0.112647	+	0.195111i
$161$	−6.06972			−0.478361
$162$	0.779885	−	1.35080i	0.0612735	−	0.106129i
$163$	−1.63369	+	2.82963i	−0.127960	+	0.221634i	−0.922886	−	0.385073i	$-0.874176\pi$
$163$	−1.63369	+	2.82963i	−0.127960	+	0.221634i	0.794926	+	0.606707i	$0.207510\pi$
$164$	4.27248			0.333624
$165$	−0.591609	+	1.02470i	−0.0460567	+	0.0797725i
$166$	5.08518	+	8.80778i	0.394686	+	0.683617i
$167$	−3.09505	−	5.36078i	−0.239502	−	0.414830i	0.721069	−	0.692863i	$-0.243651\pi$
$167$	−3.09505	−	5.36078i	−0.239502	−	0.414830i	−0.960572	+	0.278033i	$0.910318\pi$
$168$	−7.12120			−0.549413
$169$	−12.9959	−	0.327270i	−0.999683	−	0.0251746i
$170$	0.271487			0.0208221
$171$	−1.11702	−	1.93473i	−0.0854203	−	0.147952i
$172$	2.27124	+	3.93389i	0.173180	+	0.299957i
$173$	2.91771	−	5.05363i	0.221830	−	0.384220i	−0.733534	−	0.679653i	$-0.762130\pi$
$173$	2.91771	−	5.05363i	0.221830	−	0.384220i	0.955364	+	0.295433i	$0.0954638\pi$
$174$	9.16712			0.694957
$175$	5.24401	−	9.08288i	0.396410	−	0.686601i
$176$	−2.33919	+	4.05159i	−0.176323	+	0.305400i
$177$	10.6508			0.800564
$178$	−3.00586	+	5.20631i	−0.225299	+	0.390229i
$179$	−8.28183	−	14.3446i	−0.619013	−	1.07216i	−0.989666	−	0.143391i	$-0.954199\pi$
$179$	−8.28183	−	14.3446i	−0.619013	−	1.07216i	0.370653	−	0.928771i	$-0.379134\pi$
$180$	−0.256096	−	0.443571i	−0.0190883	−	0.0330618i
$181$	−11.0302			−0.819870			−0.409935	−	0.912115i	$-0.634449\pi$
$181$	−11.0302			−0.819870			−0.409935	+	0.912115i	$0.634449\pi$
$182$	−0.206248	+	16.3828i	−0.0152881	+	1.21438i
$183$	4.60458			0.340380
$184$	2.54631	+	4.41033i	0.187716	+	0.325134i
$185$	3.04751	+	5.27843i	0.224057	+	0.388078i
$186$	−5.38908	+	9.33417i	−0.395147	+	0.684414i
$187$	0.147104			0.0107573
$188$	2.38955	−	4.13882i	0.174276	−	0.301855i
$189$	1.45667	−	2.52303i	0.105957	−	0.183523i
$190$	−4.12301			−0.299114
$191$	−9.91310	+	17.1700i	−0.717287	+	1.24238i	0.244784	+	0.969578i	$0.421283\pi$
$191$	−9.91310	+	17.1700i	−0.717287	+	1.24238i	−0.962071	+	0.272800i	$0.912050\pi$
$192$	2.80003	+	4.84979i	0.202074	+	0.350003i
$193$	1.35964	+	2.35496i	0.0978687	+	0.169514i	0.910802	−	0.412843i	$-0.135464\pi$
$193$	1.35964	+	2.35496i	0.0978687	+	0.169514i	−0.812934	+	0.582356i	$0.802131\pi$
$194$	18.1611			1.30389
$195$	3.72115	−	2.08640i	0.266477	−	0.149410i
$196$	0.643928			0.0459949
$197$	−2.02576	−	3.50872i	−0.144330	−	0.249986i	0.784793	−	0.619758i	$-0.212769\pi$
$197$	−2.02576	−	3.50872i	−0.144330	−	0.249986i	−0.929123	+	0.369772i	$0.879436\pi$
$198$	−0.779885	−	1.35080i	−0.0554240	−	0.0959972i
$199$	5.05274	−	8.75160i	0.358179	−	0.620384i	−0.629478	−	0.777019i	$-0.716731\pi$
$199$	5.05274	−	8.75160i	0.358179	−	0.620384i	0.987657	+	0.156634i	$0.0500644\pi$
$200$	−8.79963			−0.622228
$201$	−7.06633	+	12.2393i	−0.498421	+	0.863290i
$202$	−2.91564	+	5.05004i	−0.205144	+	0.355319i
$203$	17.1223			1.20175
$204$	−0.0318392	+	0.0551471i	−0.00222919	+	0.00386107i
$205$	−5.83910	−	10.1136i	−0.407821	−	0.706366i
$206$	5.87803	+	10.1810i	0.409542	+	0.709347i
$207$	−2.08343			−0.144808
$208$	14.7132	−	8.24950i	1.02018	−	0.572000i
$209$	−2.23403			−0.154531
$210$	−2.68835	−	4.65636i	−0.185514	−	0.321319i
$211$	1.64620	+	2.85130i	0.113329	+	0.196291i	0.917110	−	0.398633i	$-0.130515\pi$
$211$	1.64620	+	2.85130i	0.113329	+	0.196291i	−0.803782	+	0.594924i	$0.797182\pi$
$212$	1.28674	−	2.22870i	0.0883738	−	0.153068i
$213$	13.6842			0.937623
$214$	5.53019	−	9.57858i	0.378036	−	0.654778i
$215$	6.20810	−	10.7527i	0.423389	−	0.733331i
$216$	−2.44434			−0.166317
$217$	−10.0657	+	17.4344i	−0.683307	+	1.18352i
$218$	4.60704	+	7.97963i	0.312028	+	0.540449i
$219$	−1.55471	−	2.69284i	−0.105058	−	0.181965i
$220$	−0.512192			−0.0345320
$221$	−0.455957	−	0.270957i	−0.0306710	−	0.0182265i
$222$	−8.03471			−0.539255
$223$	8.70034	+	15.0694i	0.582618	+	1.00912i	0.995168	+	0.0981887i	$0.0313049\pi$
$223$	8.70034	+	15.0694i	0.582618	+	1.00912i	−0.412550	+	0.910935i	$0.635362\pi$
$224$	−3.50838	−	6.07670i	−0.234414	−	0.406017i
$225$	1.80000	−	3.11769i	0.120000	−	0.207846i
$226$	−23.2623			−1.54739
$227$	−3.21741	+	5.57271i	−0.213547	+	0.369874i	−0.952822	−	0.303530i	$-0.901835\pi$
$227$	−3.21741	+	5.57271i	−0.213547	+	0.369874i	0.739275	+	0.673403i	$0.235168\pi$
$228$	0.483534	−	0.837506i	0.0320228	−	0.0554652i
$229$	−15.5366			−1.02669			−0.513343	−	0.858183i	$-0.671593\pi$
$229$	−15.5366			−1.02669			−0.513343	+	0.858183i	$0.671593\pi$
$230$	−1.92253	+	3.32992i	−0.126768	+	0.219568i
$231$	−1.45667	−	2.52303i	−0.0958418	−	0.166003i
$232$	−7.18298	−	12.4413i	−0.471586	−	0.816811i
$233$	−14.4570			−0.947110			−0.473555	−	0.880764i	$-0.657029\pi$
$233$	−14.4570			−0.947110			−0.473555	+	0.880764i	$0.657029\pi$
$234$	−0.0707945	+	5.62338i	−0.00462798	+	0.367612i
$235$	−13.0630			−0.852135
$236$	2.30526	+	3.99284i	0.150060	+	0.259911i
$237$	−6.12564	−	10.6099i	−0.397903	−	0.689188i
$238$	−0.334230	+	0.578904i	−0.0216649	+	0.0375248i
$239$	−2.21188			−0.143075			−0.0715374	−	0.997438i	$-0.522791\pi$
$239$	−2.21188			−0.143075			−0.0715374	+	0.997438i	$0.522791\pi$
$240$	−2.76777	+	4.79391i	−0.178659	+	0.309446i
$241$	−7.62746	+	13.2111i	−0.491328	+	0.851005i	−0.999950	−	0.00998485i	$-0.996822\pi$
$241$	−7.62746	+	13.2111i	−0.491328	+	0.851005i	0.508622	+	0.860990i	$0.330155\pi$
$242$	−1.55977			−0.100266
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.996616	+	1.72619i	0.0638018	+	0.110508i
$245$	−0.880043	−	1.52428i	−0.0562239	−	0.0973826i
$246$	15.3947			0.981532
$247$	6.92451	+	4.11495i	0.440596	+	0.261828i
$248$	16.8907			1.07256
$249$	3.26021	+	5.64685i	0.206607	+	0.357855i
$250$	−7.93585	−	13.7453i	−0.501907	−	0.869328i
$251$	−6.92877	+	12.0010i	−0.437340	+	0.757495i	−0.997483	−	0.0709004i	$-0.977413\pi$
$251$	−6.92877	+	12.0010i	−0.437340	+	0.757495i	0.560143	+	0.828396i	$0.310746\pi$
$252$	1.26113			0.0794436
$253$	−1.04171	+	1.80430i	−0.0654919	+	0.113435i
$254$	−2.63369	+	4.56168i	−0.165252	+	0.286225i
$255$	0.174056			0.0108998
$256$	−4.96878	+	8.60617i	−0.310549	+	0.537886i
$257$	10.1770	+	17.6271i	0.634826	+	1.09955i	0.986552	+	0.163448i	$0.0522616\pi$
$257$	10.1770	+	17.6271i	0.634826	+	1.09955i	−0.351726	+	0.936103i	$0.614405\pi$
$258$	8.18379	+	14.1747i	0.509500	+	0.882481i
$259$	−15.0072			−0.932505
$260$	1.58757	+	0.943426i	0.0984568	+	0.0585088i
$261$	5.87723			0.363791
$262$	−0.835279	−	1.44675i	−0.0516037	−	0.0893802i
$263$	−1.86999	−	3.23891i	−0.115308	−	0.199720i	0.802595	−	0.596525i	$-0.203452\pi$
$263$	−1.86999	−	3.23891i	−0.115308	−	0.199720i	−0.917903	+	0.396805i	$0.870119\pi$
$264$	−1.22217	+	2.11686i	−0.0752195	+	0.130284i
$265$	−7.03425			−0.432110
$266$	5.07587	−	8.79167i	0.311222	−	0.539052i
$267$	−1.92712	+	3.33787i	−0.117938	+	0.204274i
$268$	−6.11776			−0.373702
$269$	5.22290	−	9.04634i	0.318446	−	0.551565i	−0.661718	−	0.749753i	$-0.730172\pi$
$269$	5.22290	−	9.04634i	0.318446	−	0.551565i	0.980164	+	0.198188i	$0.0635057\pi$
$270$	−0.922773	−	1.59829i	−0.0561582	−	0.0972688i
$271$	4.00808	+	6.94220i	0.243474	+	0.421709i	0.961701	−	0.274099i	$-0.0883797\pi$
$271$	4.00808	+	6.94220i	0.243474	+	0.421709i	−0.718228	+	0.695808i	$0.755046\pi$
$272$	0.688207			0.0417287
$273$	−0.132230	+	10.5034i	−0.00800292	+	0.635692i
$274$	−9.69422			−0.585649
$275$	−1.80000	−	3.11769i	−0.108544	−	0.188004i
$276$	−0.450937	−	0.781046i	−0.0271432	−	0.0470135i
$277$	−11.0438	+	19.1284i	−0.663558	+	1.14932i	0.316116	+	0.948720i	$0.397621\pi$
$277$	−11.0438	+	19.1284i	−0.663558	+	1.14932i	−0.979674	+	0.200595i	$0.935712\pi$
$278$	−35.8068			−2.14755
$279$	−3.45505	+	5.98432i	−0.206849	+	0.358272i
$280$	−4.21297	+	7.29707i	−0.251773	+	0.436083i
$281$	−6.48212			−0.386691			−0.193346	−	0.981131i	$-0.561934\pi$
$281$	−6.48212			−0.386691			−0.193346	+	0.981131i	$0.561934\pi$
$282$	8.61010	−	14.9131i	0.512724	−	0.888064i
$283$	6.94493	+	12.0290i	0.412833	+	0.715049i	0.995198	−	0.0978790i	$-0.0312058\pi$
$283$	6.94493	+	12.0290i	0.412833	+	0.715049i	−0.582365	+	0.812928i	$0.697872\pi$
$284$	2.96180	+	5.12999i	0.175751	+	0.304409i
$285$	−2.64334			−0.156578
$286$	4.83460	+	2.87300i	0.285876	+	0.169884i
$287$	28.7543			1.69731
$288$	−1.20425	−	2.08582i	−0.0709610	−	0.122908i
$289$	8.48918	+	14.7037i	0.499364	+	0.864923i
$290$	5.42335	−	9.39351i	0.318470	−	0.551606i
$291$	11.6435			0.682552
$292$	0.673004	−	1.16568i	0.0393846	−	0.0682161i
$293$	14.1927	−	24.5825i	0.829147	−	1.43613i	−0.0695604	−	0.997578i	$-0.522160\pi$
$293$	14.1927	−	24.5825i	0.829147	−	1.43613i	0.898708	−	0.438548i	$-0.144507\pi$
$294$	2.32022			0.135318
$295$	6.30111	−	10.9138i	0.366865	−	0.635429i
$296$	6.29568	+	10.9044i	0.365929	+	0.633807i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	2.65273			0.153669
$299$	6.55226	−	3.67376i	0.378927	−	0.212459i
$300$	1.55837			0.0899725
$301$	15.2857	+	26.4756i	0.881052	+	1.52603i
$302$	−14.0804	−	24.3879i	−0.810235	−	1.40337i
$303$	−1.86928	+	3.23768i	−0.107387	+	0.186000i
$304$	−10.4516			−0.599442
$305$	2.72411	−	4.71829i	0.155982	−	0.270169i
$306$	−0.114724	+	0.198708i	−0.00655834	+	0.0113594i
$307$	19.5549			1.11606			0.558029	−	0.829822i	$-0.311558\pi$
$307$	19.5549			1.11606			0.558029	+	0.829822i	$0.311558\pi$
$308$	0.630564	−	1.09217i	0.0359297	−	0.0622321i
$309$	3.76853	+	6.52728i	0.214384	+	0.371324i
$310$	6.37646	+	11.0443i	0.362158	+	0.627277i
$311$	−16.9041			−0.958544			−0.479272	−	0.877667i	$-0.659099\pi$
$311$	−16.9041			−0.958544			−0.479272	+	0.877667i	$0.659099\pi$
$312$	7.68733	−	4.31018i	0.435209	−	0.244016i
$313$	−5.29817			−0.299470			−0.149735	−	0.988726i	$-0.547842\pi$
$313$	−5.29817			−0.299470			−0.149735	+	0.988726i	$0.547842\pi$
$314$	0.679453	+	1.17685i	0.0383437	+	0.0664133i
$315$	−1.72356	−	2.98529i	−0.0971114	−	0.168202i
$316$	2.65167	−	4.59283i	0.149168	−	0.258367i
$317$	21.7382			1.22094			0.610470	−	0.792040i	$-0.290981\pi$
$317$	21.7382			1.22094			0.610470	+	0.792040i	$0.290981\pi$
$318$	4.63643	−	8.03053i	0.259998	−	0.450330i
$319$	2.93861	−	5.08983i	0.164531	−	0.284976i
$320$	6.62608			0.370409
$321$	3.54552	−	6.14102i	0.197892	−	0.342758i
$322$	−4.73369	−	8.19898i	−0.263798	−	0.456911i
$323$	0.164317	+	0.284606i	0.00914286	+	0.0158359i
$324$	0.432881			0.0240489
$325$	−0.163396	+	12.9789i	−0.00906357	+	0.719942i
$326$	−5.09635			−0.282261
$327$	2.95367	+	5.11590i	0.163338	+	0.282910i
$328$	−12.0627	−	20.8932i	−0.666051	−	1.15363i
$329$	16.0820	−	27.8548i	0.886627	−	1.53568i
$330$	−1.84555			−0.101594
$331$	4.19047	−	7.25810i	0.230329	−	0.398941i	−0.727576	−	0.686027i	$-0.759353\pi$
$331$	4.19047	−	7.25810i	0.230329	−	0.398941i	0.957905	+	0.287086i	$0.0926865\pi$
$332$	−1.41128	+	2.44441i	−0.0774541	+	0.134155i
$333$	−5.15122			−0.282285
$334$	4.82756	−	8.36159i	0.264153	−	0.457526i
$335$	8.36101	+	14.4817i	0.456811	+	0.791219i
$336$	−6.81485	−	11.8037i	−0.371780	−	0.643942i
$337$	−9.85686			−0.536937			−0.268469	−	0.963288i	$-0.586518\pi$
$337$	−9.85686			−0.536937			−0.268469	+	0.963288i	$0.586518\pi$
$338$	−9.69321	−	17.8101i	−0.527241	−	0.968740i
$339$	−14.9140			−0.810015
$340$	0.0376727	+	0.0652511i	0.00204309	+	0.00353874i
$341$	3.45505	+	5.98432i	0.187102	+	0.324069i
$342$	1.74229	−	3.01773i	0.0942121	−	0.163180i
$343$	−16.0597			−0.867140
$344$	12.8250	−	22.2135i	0.691476	−	1.19767i
$345$	−1.23257	+	2.13488i	−0.0663595	+	0.114938i
$346$	9.10192			0.489322
$347$	−13.8576	+	24.0021i	−0.743915	+	1.28850i	0.206785	+	0.978386i	$0.433700\pi$
$347$	−13.8576	+	24.0021i	−0.743915	+	1.28850i	−0.950700	+	0.310112i	$0.899633\pi$
$348$	1.27207	+	2.20329i	0.0681900	+	0.118109i
$349$	−14.6495	−	25.3738i	−0.784172	−	1.35823i	−0.929492	−	0.368842i	$-0.879754\pi$
$349$	−14.6495	−	25.3738i	−0.784172	−	1.35823i	0.145320	−	0.989385i	$-0.453579\pi$
$350$	16.3589			0.874419
$351$	−0.0453878	+	3.60527i	−0.00242262	+	0.192435i
$352$	−2.40850			−0.128373
$353$	−3.72960	−	6.45985i	−0.198506	−	0.343823i	0.749538	−	0.661961i	$-0.230276\pi$
$353$	−3.72960	−	6.45985i	−0.198506	−	0.343823i	−0.948044	+	0.318138i	$0.896942\pi$
$354$	8.30640	+	14.3871i	0.441480	+	0.764666i
$355$	8.09566	−	14.0221i	0.429673	−	0.744216i
$356$	−1.66843			−0.0884264
$357$	−0.214282	+	0.371147i	−0.0113410	+	0.0196432i
$358$	12.9177	−	22.3742i	0.682724	−	1.18251i
$359$	32.8828			1.73549			0.867744	−	0.497011i	$-0.165569\pi$
$359$	32.8828			1.73549			0.867744	+	0.497011i	$0.165569\pi$
$360$	−1.44610	+	2.50471i	−0.0762159	+	0.132010i
$361$	7.00455	+	12.1322i	0.368661	+	0.638539i
$362$	−8.60231	−	14.8996i	−0.452127	−	0.783107i
$363$	−1.00000			−0.0524864
$364$	−3.96618	+	2.22378i	−0.207884	+	0.116558i
$365$	−3.67912			−0.192574
$366$	3.59104	+	6.21987i	0.187707	+	0.325118i
$367$	12.7559	+	22.0938i	0.665852	+	1.15329i	0.979054	+	0.203602i	$0.0652650\pi$
$367$	12.7559	+	22.0938i	0.665852	+	1.15329i	−0.313202	+	0.949687i	$0.601402\pi$
$368$	−4.87352	+	8.44119i	−0.254050	+	0.440027i
$369$	9.86988			0.513805
$370$	−4.75341	+	8.23314i	−0.247118	+	0.428021i
$371$	8.65993	−	14.9994i	0.449601	−	0.778732i
$372$	−2.99125			−0.155089
$373$	−11.1008	+	19.2271i	−0.574777	+	0.995543i	0.421289	+	0.906927i	$0.361578\pi$
$373$	−11.1008	+	19.2271i	−0.574777	+	0.995543i	−0.996066	+	0.0886168i	$0.971755\pi$
$374$	0.114724	+	0.198708i	0.00593224	+	0.0102749i
$375$	−5.08783	−	8.81238i	−0.262735	−	0.455070i
$376$	−26.9861			−1.39170
$377$	−18.4836	+	10.3635i	−0.951951	+	0.533746i
$378$	4.54414			0.233725
$379$	17.3367	+	30.0280i	0.890526	+	1.54244i	0.839246	+	0.543751i	$0.182997\pi$
$379$	17.3367	+	30.0280i	0.890526	+	1.54244i	0.0512792	+	0.998684i	$0.483670\pi$
$380$	−0.572126	−	0.990951i	−0.0293494	−	0.0508347i
$381$	−1.68851	+	2.92459i	−0.0865050	+	0.149831i
$382$	−30.9243			−1.58223
$383$	14.7587	−	25.5627i	0.754132	−	1.30619i	−0.191673	−	0.981459i	$-0.561391\pi$
$383$	14.7587	−	25.5627i	0.754132	−	1.30619i	0.945805	−	0.324736i	$-0.105275\pi$
$384$	−6.77589	+	11.7362i	−0.345781	+	0.598910i
$385$	−3.44711			−0.175681
$386$	−2.12072	+	3.67319i	−0.107942	+	0.186960i
$387$	5.24679	+	9.08771i	0.266710	+	0.461954i
$388$	2.52011	+	4.36497i	0.127939	+	0.221598i
$389$	11.6528			0.590819			0.295409	−	0.955371i	$-0.404544\pi$
$389$	11.6528			0.590819			0.295409	+	0.955371i	$0.404544\pi$
$390$	5.72038	+	3.39938i	0.289663	+	0.172135i
$391$	0.306480			0.0154994
$392$	−1.81803	−	3.14893i	−0.0918246	−	0.159045i
$393$	−0.535514	−	0.927538i	−0.0270131	−	0.0467881i
$394$	3.15972	−	5.47280i	0.159184	−	0.275716i
$395$	−14.4959			−0.729369
$396$	0.216440	−	0.374886i	0.0108765	−	0.0188387i
$397$	12.5319	−	21.7058i	0.628956	−	1.08938i	−0.358806	−	0.933412i	$-0.616816\pi$
$397$	12.5319	−	21.7058i	0.628956	−	1.08938i	0.987762	−	0.155971i	$-0.0498508\pi$
$398$	15.7622			0.790088
$399$	3.25424	−	5.63652i	0.162916	−	0.282179i
$400$	−8.42107	−	14.5857i	−0.421053	−	0.729286i
$401$	−2.70849	−	4.69124i	−0.135256	−	0.234270i	0.790439	−	0.612540i	$-0.209852\pi$
$401$	−2.70849	−	4.69124i	−0.135256	−	0.234270i	−0.925695	+	0.378271i	$0.876519\pi$
$402$	−22.0437			−1.09944
$403$	0.313634	−	24.9128i	0.0156232	−	1.24099i
$404$	−1.61835			−0.0805158
$405$	−0.591609	−	1.02470i	−0.0293973	−	0.0509176i
$406$	13.3535	+	23.1289i	0.662721	+	1.14787i
$407$	−2.57561	+	4.46109i	−0.127668	+	0.221128i
$408$	0.359573			0.0178015
$409$	13.2014	−	22.8656i	0.652769	−	1.13063i	−0.329679	−	0.944093i	$-0.606941\pi$
$409$	13.2014	−	22.8656i	0.652769	−	1.13063i	0.982448	−	0.186536i	$-0.0597261\pi$
$410$	9.10765	−	15.7749i	0.449795	−	0.779068i
$411$	−6.21516			−0.306571
$412$	−1.63132	+	2.82553i	−0.0803694	+	0.139204i
$413$	15.5147	+	26.8723i	0.763429	+	1.32230i
$414$	−1.62483	−	2.81429i	−0.0798561	−	0.138315i
$415$	7.71507			0.378718
$416$	7.46528	+	4.43631i	0.366015	+	0.217508i
$417$	−22.9565			−1.12418
$418$	−1.74229	−	3.01773i	−0.0852180	−	0.147602i
$419$	−17.9722	−	31.1288i	−0.878002	−	1.52074i	−0.853530	−	0.521043i	$-0.825543\pi$
$419$	−17.9722	−	31.1288i	−0.878002	−	1.52074i	−0.0244714	−	0.999701i	$-0.507790\pi$
$420$	0.746094	−	1.29227i	0.0364057	−	0.0630565i
$421$	6.37033			0.310471			0.155235	−	0.987878i	$-0.450386\pi$
$421$	6.37033			0.310471			0.155235	+	0.987878i	$0.450386\pi$
$422$	−2.56769	+	4.44736i	−0.124993	+	0.216494i
$423$	5.52011	−	9.56112i	0.268397	−	0.464877i
$424$	−14.5317			−0.705721
$425$	−0.264787	+	0.458624i	−0.0128441	+	0.0222465i
$426$	10.6721	+	18.4846i	0.517063	+	0.895580i
$427$	6.70735	+	11.6175i	0.324591	+	0.562209i
$428$	3.06957			0.148373
$429$	3.09956	+	1.84194i	0.149648	+	0.0889297i
$430$	19.3664			0.933931
$431$	−14.6847	−	25.4346i	−0.707337	−	1.22514i	−0.965842	−	0.259133i	$-0.916563\pi$
$431$	−14.6847	−	25.4346i	−0.707337	−	1.22514i	0.258505	−	0.966010i	$-0.416770\pi$
$432$	−2.33919	−	4.05159i	−0.112544	−	0.194932i
$433$	5.66363	−	9.80969i	0.272177	−	0.471424i	−0.697242	−	0.716835i	$-0.745590\pi$
$433$	5.66363	−	9.80969i	0.272177	−	0.471424i	0.969419	+	0.245412i	$0.0789232\pi$
$434$	−31.4005			−1.50727
$435$	3.47702	−	6.02237i	0.166710	−	0.288751i
$436$	−1.27859	+	2.21457i	−0.0612331	+	0.106059i
$437$	−4.65444			−0.222652
$438$	2.42499	−	4.20021i	0.115870	−	0.200694i
$439$	−6.22344	−	10.7793i	−0.297029	−	0.514469i	0.678426	−	0.734669i	$-0.262662\pi$
$439$	−6.22344	−	10.7793i	−0.297029	−	0.514469i	−0.975455	+	0.220200i	$0.929329\pi$
$440$	1.44610	+	2.50471i	0.0689399	+	0.119407i
$441$	1.48754			0.0708354
$442$	0.0104141	−	0.827222i	0.000495350	−	0.0393469i
$443$	−3.78245			−0.179710			−0.0898549	−	0.995955i	$-0.528640\pi$
$443$	−3.78245			−0.179710			−0.0898549	+	0.995955i	$0.528640\pi$
$444$	−1.11493	−	1.93112i	−0.0529123	−	0.0916468i
$445$	2.28020	+	3.94943i	0.108092	+	0.187221i
$446$	−13.5705	+	23.5048i	−0.642583	+	1.11299i
$447$	1.70072			0.0804414
$448$	−8.15742	+	14.1291i	−0.385402	+	0.667536i
$449$	−3.44013	+	5.95848i	−0.162350	+	0.281198i	−0.935711	−	0.352768i	$-0.885241\pi$
$449$	−3.44013	+	5.95848i	−0.162350	+	0.281198i	0.773361	+	0.633966i	$0.218574\pi$
$450$	5.61517			0.264701
$451$	4.93494	−	8.54756i	0.232377	−	0.402489i
$452$	−3.22798	−	5.59103i	−0.151831	−	0.262980i
$453$	−9.02722	−	15.6356i	−0.424136	−	0.734625i
$454$	−10.0368			−0.471051
$455$	10.6845	+	6.34937i	0.500898	+	0.297663i
$456$	−5.46074			−0.255723
$457$	1.44220	+	2.49797i	0.0674634	+	0.116850i	0.897784	−	0.440436i	$-0.145176\pi$
$457$	1.44220	+	2.49797i	0.0674634	+	0.116850i	−0.830321	+	0.557286i	$0.811843\pi$
$458$	−12.1167	−	20.9868i	−0.566178	−	0.980650i
$459$	−0.0735520	+	0.127396i	−0.00343311	+	0.00594632i
$460$	−1.06711			−0.0497544
$461$	−16.4644	+	28.5172i	−0.766824	+	1.32818i	0.172453	+	0.985018i	$0.444831\pi$
$461$	−16.4644	+	28.5172i	−0.766824	+	1.32818i	−0.939277	+	0.343160i	$0.888503\pi$
$462$	2.27207	−	3.93534i	0.105706	−	0.183088i
$463$	32.0246			1.48831			0.744155	−	0.668007i	$-0.232852\pi$
$463$	32.0246			1.48831			0.744155	+	0.668007i	$0.232852\pi$
$464$	13.7479	−	23.8121i	0.638232	−	1.10545i
$465$	4.08808	+	7.08076i	0.189580	+	0.328362i
$466$	−11.2748	−	19.5285i	−0.522295	−	0.904641i
$467$	14.3058			0.661993			0.330996	−	0.943632i	$-0.392615\pi$
$467$	14.3058			0.661993			0.330996	+	0.943632i	$0.392615\pi$
$468$	−1.36139	+	0.763309i	−0.0629301	+	0.0352840i
$469$	−41.1733			−1.90120
$470$	−10.1876	−	17.6455i	−0.469920	−	0.813925i
$471$	0.435611	+	0.754500i	0.0200719	+	0.0347655i
$472$	13.0171	−	22.5463i	0.599162	−	1.03778i
$473$	10.4936			0.482496
$474$	9.55458	−	16.5490i	0.438856	−	0.760122i
$475$	4.02125	−	6.96501i	0.184508	−	0.319577i
$476$	−0.185517			−0.00850315
$477$	2.97251	−	5.14854i	0.136102	−	0.235735i
$478$	−1.72501	−	2.98781i	−0.0789003	−	0.136659i
$479$	13.8811	+	24.0428i	0.634245	+	1.09855i	0.986674	+	0.162707i	$0.0520225\pi$
$479$	13.8811	+	24.0428i	0.634245	+	1.09855i	−0.352429	+	0.935839i	$0.614644\pi$
$480$	−2.84978			−0.130074
$481$	16.2003	−	9.08328i	0.738670	−	0.414162i
$482$	−23.7942			−1.08379
$483$	−3.03486	−	5.25654i	−0.138091	−	0.239181i
$484$	−0.216440	−	0.374886i	−0.00983819	−	0.0170403i
$485$	6.88837	−	11.9310i	0.312785	−	0.541759i
$486$	1.55977			0.0707526
$487$	2.52008	−	4.36491i	0.114196	−	0.197793i	−0.803262	−	0.595626i	$-0.796904\pi$
$487$	2.52008	−	4.36491i	0.114196	−	0.197793i	0.917458	+	0.397833i	$0.130238\pi$
$488$	5.62759	−	9.74727i	0.254749	−	0.441238i
$489$	−3.26738			−0.147756
$490$	1.37266	−	2.37752i	0.0620107	−	0.107406i
$491$	3.31222	+	5.73694i	0.149478	+	0.258904i	0.931035	−	0.364930i	$-0.118907\pi$
$491$	3.31222	+	5.73694i	0.149478	+	0.258904i	−0.781556	+	0.623835i	$0.785574\pi$
$492$	2.13624	+	3.70007i	0.0963091	+	0.166812i
$493$	−0.864563			−0.0389380
$494$	−0.158157	+	12.5628i	−0.00711582	+	0.565228i
$495$	−1.18322			−0.0531817
$496$	16.1640	+	27.9969i	0.725786	+	1.25710i
$497$	19.9333	+	34.5255i	0.894130	+	1.54868i
$498$	−5.08518	+	8.80778i	−0.227872	+	0.394686i
$499$	−26.3525			−1.17970			−0.589851	−	0.807512i	$-0.700813\pi$
$499$	−26.3525			−1.17970			−0.589851	+	0.807512i	$0.700813\pi$
$500$	2.20242	−	3.81471i	0.0984954	−	0.170599i
$501$	3.09505	−	5.36078i	0.138277	−	0.239502i
$502$	−21.6146			−0.964705
$503$	14.1357	−	24.4837i	0.630279	−	1.09168i	−0.357215	−	0.934022i	$-0.616274\pi$
$503$	14.1357	−	24.4837i	0.630279	−	1.09168i	0.987494	−	0.157654i	$-0.0503930\pi$
$504$	−3.56060	−	6.16714i	−0.158602	−	0.274706i
$505$	2.21176	+	3.83088i	0.0984220	+	0.170472i
$506$	−3.24966			−0.144465
$507$	−6.21452	−	11.4184i	−0.275996	−	0.507109i
$508$	−1.46185			−0.0648589
$509$	−13.1660	−	22.8041i	−0.583572	−	1.01078i	−0.995052	−	0.0993571i	$-0.968321\pi$
$509$	−13.1660	−	22.8041i	−0.583572	−	1.01078i	0.411480	−	0.911419i	$-0.365012\pi$
$510$	0.135744	+	0.235115i	0.00601083	+	0.0104111i
$511$	4.52940	−	7.84515i	0.200369	−	0.347049i
$512$	11.6033			0.512797
$513$	1.11702	−	1.93473i	0.0493174	−	0.0854203i
$514$	−15.8738	+	27.4943i	−0.700165	+	1.21272i
$515$	8.91797			0.392973
$516$	−2.27124	+	3.93389i	−0.0999856	+	0.173180i
$517$	−5.52011	−	9.56112i	−0.242774	−	0.420497i
$518$	−11.7039	−	20.2718i	−0.514241	−	0.890691i
$519$	5.83543			0.256147
$520$	0.131270	−	10.4271i	0.00575658	−	0.457259i
$521$	−6.62006			−0.290030			−0.145015	−	0.989429i	$-0.546323\pi$
$521$	−6.62006			−0.290030			−0.145015	+	0.989429i	$0.546323\pi$
$522$	4.58356	+	7.93896i	0.200617	+	0.347479i
$523$	18.2249	+	31.5665i	0.796920	+	1.38031i	0.921613	+	0.388111i	$0.126872\pi$
$523$	18.2249	+	31.5665i	0.796920	+	1.38031i	−0.124692	+	0.992195i	$0.539794\pi$
$524$	0.231814	−	0.401513i	0.0101268	−	0.0175402i
$525$	10.4880			0.457734
$526$	2.91675	−	5.05196i	0.127176	−	0.220276i
$527$	0.508252	−	0.880318i	0.0221398	−	0.0383472i
$528$	−4.67838			−0.203600
$529$	9.32967	−	16.1595i	0.405638	−	0.702585i
$530$	−5.48590	−	9.50186i	−0.238292	−	0.412734i
$531$	5.32541	+	9.22387i	0.231103	+	0.400282i
$532$	2.81740			0.122150
$533$	−31.0402	+	17.4038i	−1.34450	+	0.753843i
$534$	−6.01173			−0.260153
$535$	−4.19512	−	7.26616i	−0.181371	−	0.314144i
$536$	17.2726	+	29.9170i	0.746061	+	1.29222i
$537$	8.28183	−	14.3446i	0.357387	−	0.619013i
$538$	16.2931			0.702443
$539$	0.743771	−	1.28825i	0.0320365	−	0.0554889i
$540$	0.256096	−	0.443571i	0.0110206	−	0.0190883i
$541$	−30.3876			−1.30646			−0.653232	−	0.757158i	$-0.726587\pi$
$541$	−30.3876			−1.30646			−0.653232	+	0.757158i	$0.726587\pi$
$542$	−6.25168	+	10.8282i	−0.268533	+	0.465112i
$543$	−5.51511	−	9.55246i	−0.236676	−	0.409935i
$544$	0.177150	+	0.306832i	0.00759523	+	0.0131553i
$545$	6.98966			0.299404
$546$	−14.2911	+	8.01279i	−0.611601	+	0.342916i
$547$	15.4262			0.659575			0.329788	−	0.944055i	$-0.393023\pi$
$547$	15.4262			0.659575			0.329788	+	0.944055i	$0.393023\pi$
$548$	−1.34521	−	2.32997i	−0.0574646	−	0.0995316i
$549$	2.30229	+	3.98768i	0.0982593	+	0.170190i
$550$	2.80758	−	4.86288i	0.119716	−	0.207354i
$551$	13.1299			0.559353
$552$	−2.54631	+	4.41033i	−0.108378	+	0.187716i
$553$	17.8461	−	30.9103i	0.758892	−	1.31444i
$554$	−34.4516			−1.46371
$555$	−3.04751	+	5.27843i	−0.129359	+	0.224057i
$556$	−4.96871	−	8.60605i	−0.210720	−	0.364978i
$557$	9.13975	+	15.8305i	0.387264	+	0.670761i	0.992080	−	0.125604i	$-0.0400869\pi$
$557$	9.13975	+	15.8305i	0.387264	+	0.670761i	−0.604817	+	0.796365i	$0.706754\pi$
$558$	−10.7782			−0.456276
$559$	−32.5255	−	19.3286i	−1.37568	−	0.817511i
$560$	−16.1269			−0.681485
$561$	0.0735520	+	0.127396i	0.00310537	+	0.00537865i
$562$	−5.05531	−	8.75605i	−0.213245	−	0.369352i
$563$	−0.432620	+	0.749319i	−0.0182327	+	0.0315800i	−0.874998	−	0.484127i	$-0.839137\pi$
$563$	−0.432620	+	0.749319i	−0.0182327	+	0.0315800i	0.856765	+	0.515707i	$0.172471\pi$
$564$	4.77910			0.201236
$565$	−8.82322	+	15.2823i	−0.371196	+	0.642930i
$566$	−10.8325	+	18.7624i	−0.455324	+	0.788644i
$567$	2.91334			0.122349
$568$	16.7244	−	28.9675i	0.701740	−	1.21545i
$569$	1.65714	+	2.87025i	0.0694708	+	0.120327i	0.898668	−	0.438629i	$-0.144536\pi$
$569$	1.65714	+	2.87025i	0.0694708	+	0.120327i	−0.829198	+	0.558955i	$0.811202\pi$
$570$	−2.06150	−	3.57063i	−0.0863469	−	0.149557i
$571$	1.97305			0.0825695			0.0412847	−	0.999147i	$-0.486855\pi$
$571$	1.97305			0.0825695			0.0412847	+	0.999147i	$0.486855\pi$
$572$	−0.0196475	+	1.56065i	−0.000821503	+	0.0652540i
$573$	−19.8262			−0.828252
$574$	22.4250	+	38.8413i	0.936003	+	1.62120i
$575$	−3.75016	−	6.49547i	−0.156393	−	0.270880i
$576$	−2.80003	+	4.84979i	−0.116668	+	0.202074i
$577$	−8.41078			−0.350145			−0.175073	−	0.984556i	$-0.556016\pi$
$577$	−8.41078			−0.350145			−0.175073	+	0.984556i	$0.556016\pi$
$578$	−13.2412	+	22.9344i	−0.550760	+	0.953944i
$579$	−1.35964	+	2.35496i	−0.0565045	+	0.0978687i
$580$	3.01027			0.124995
$581$	−9.49810	+	16.4512i	−0.394047	+	0.682510i
$582$	9.08056	+	15.7280i	0.376401	+	0.651946i
$583$	−2.97251	−	5.14854i	−0.123109	−	0.213231i
$584$	−7.60050			−0.314511
$585$	3.66745	+	2.17941i	0.151630	+	0.0901077i
$586$	44.2747			1.82897
$587$	13.3102	+	23.0540i	0.549372	+	0.951541i	0.998318	+	0.0579816i	$0.0184665\pi$
$587$	13.3102	+	23.0540i	0.549372	+	0.951541i	−0.448945	+	0.893559i	$0.648200\pi$
$588$	0.321964	+	0.557658i	0.0132776	+	0.0229974i
$589$	−7.71869	+	13.3692i	−0.318043	+	0.550867i
$590$	19.6566			0.809248
$591$	2.02576	−	3.50872i	0.0833287	−	0.144330i
$592$	−12.0497	+	20.8706i	−0.495238	+	0.857778i
$593$	10.9886			0.451249			0.225624	−	0.974214i	$-0.427558\pi$
$593$	10.9886			0.451249			0.225624	+	0.974214i	$0.427558\pi$
$594$	0.779885	−	1.35080i	0.0319991	−	0.0554240i
$595$	0.253542	+	0.439148i	0.0103942	+	0.0180033i
$596$	0.368105	+	0.637576i	0.0150782	+	0.0261161i
$597$	10.1055			0.413590
$598$	10.0725	+	5.98568i	0.411896	+	0.244773i
$599$	−11.3528			−0.463862			−0.231931	−	0.972732i	$-0.574504\pi$
$599$	−11.3528			−0.463862			−0.231931	+	0.972732i	$0.574504\pi$
$600$	−4.39982	−	7.62071i	−0.179622	−	0.311114i
$601$	−0.436471	−	0.755990i	−0.0178040	−	0.0308375i	0.856986	−	0.515339i	$-0.172334\pi$
$601$	−0.436471	−	0.755990i	−0.0178040	−	0.0308375i	−0.874790	+	0.484502i	$0.839001\pi$
$602$	−23.8422	+	41.2958i	−0.971734	+	1.68309i
$603$	−14.1327			−0.575527
$604$	3.90771	−	6.76835i	0.159002	−	0.275400i
$605$	−0.591609	+	1.02470i	−0.0240523	+	0.0416598i
$606$	−5.83128			−0.236880
$607$	10.1906	−	17.6507i	0.413624	−	0.716418i	−0.581659	−	0.813433i	$-0.697596\pi$
$607$	10.1906	−	17.6507i	0.413624	−	0.716418i	0.995283	+	0.0970148i	$0.0309294\pi$
$608$	−2.69033	−	4.65978i	−0.109107	−	0.188979i
$609$	8.56117	+	14.8284i	0.346916	+	0.600877i
$610$	8.49796			0.344072
$611$	−0.501091	+	39.8030i	−0.0202720	+	1.61026i
$612$	−0.0636784			−0.00257405
$613$	0.500673	+	0.867192i	0.0202220	+	0.0350255i	0.875959	−	0.482385i	$-0.160229\pi$
$613$	0.500673	+	0.867192i	0.0202220	+	0.0350255i	−0.855737	+	0.517411i	$0.826896\pi$
$614$	15.2506	+	26.4148i	0.615463	+	1.06601i
$615$	5.83910	−	10.1136i	0.235455	−	0.407821i
$616$	−7.12120			−0.286922
$617$	−15.7239	+	27.2345i	−0.633019	+	1.09642i	0.353912	+	0.935279i	$0.384851\pi$
$617$	−15.7239	+	27.2345i	−0.633019	+	1.09642i	−0.986931	+	0.161143i	$0.948482\pi$
$618$	−5.87803	+	10.1810i	−0.236449	+	0.409542i
$619$	48.0210			1.93013			0.965064	−	0.262014i	$-0.0843867\pi$
$619$	48.0210			1.93013			0.965064	+	0.262014i	$0.0843867\pi$
$620$	−1.76965	+	3.06512i	−0.0710708	+	0.123098i
$621$	−1.04171	−	1.80430i	−0.0418025	−	0.0724040i
$622$	−13.1832	−	22.8341i	−0.528600	−	0.915562i
$623$	−11.2287			−0.449869
$624$	14.5009	+	8.61729i	0.580500	+	0.344968i
$625$	5.95996			0.238399
$626$	−4.13196	−	7.15677i	−0.165147	−	0.286042i
$627$	−1.11702	−	1.93473i	−0.0446093	−	0.0772656i
$628$	−0.188568	+	0.326609i	−0.00752466	+	0.0130331i
$629$	0.757765			0.0302140
$630$	2.68835	−	4.65636i	0.107106	−	0.185514i
$631$	10.1548	−	17.5887i	0.404257	−	0.700194i	−0.589978	−	0.807420i	$-0.700863\pi$
$631$	10.1548	−	17.5887i	0.404257	−	0.700194i	0.994235	+	0.107226i	$0.0341968\pi$
$632$	−29.9463			−1.19120
$633$	−1.64620	+	2.85130i	−0.0654304	+	0.113329i
$634$	16.9533	+	29.3640i	0.673301	+	1.16619i
$635$	1.99787	+	3.46042i	0.0792832	+	0.137323i
$636$	2.57348			0.102045
$637$	−4.67824	+	2.62302i	−0.185359	+	0.103928i
$638$	9.16712			0.362930
$639$	6.84208	+	11.8508i	0.270668	+	0.468811i
$640$	8.01735	+	13.8865i	0.316914	+	0.548911i
$641$	−22.0302	+	38.1574i	−0.870140	+	1.50713i	−0.00828942	+	0.999966i	$0.502639\pi$
$641$	−22.0302	+	38.1574i	−0.870140	+	1.50713i	−0.861851	+	0.507162i	$0.830695\pi$
$642$	11.0604			0.436519
$643$	−5.65674	+	9.79777i	−0.223080	+	0.386386i	−0.955742	−	0.294207i	$-0.904945\pi$
$643$	−5.65674	+	9.79777i	−0.223080	+	0.386386i	0.732662	+	0.680593i	$0.238278\pi$
$644$	1.31373	−	2.27545i	0.0517683	−	0.0896654i
$645$	12.4162			0.488887
$646$	−0.256297	+	0.443920i	−0.0100839	+	0.0174658i
$647$	10.8448	+	18.7837i	0.426353	+	0.738464i	0.996546	−	0.0830464i	$-0.0264650\pi$
$647$	10.8448	+	18.7837i	0.426353	+	0.738464i	−0.570193	+	0.821511i	$0.693132\pi$
$648$	−1.22217	−	2.11686i	−0.0480115	−	0.0831583i
$649$	10.6508			0.418081
$650$	−17.6594	+	9.90137i	−0.692658	+	0.388364i
$651$	−20.1315			−0.789015
$652$	−0.707192	−	1.22489i	−0.0276958	−	0.0479705i
$653$	−13.4935	−	23.3714i	−0.528041	−	0.914594i	−0.999466	−	0.0326875i	$-0.989593\pi$
$653$	−13.4935	−	23.3714i	−0.528041	−	0.914594i	0.471425	−	0.881906i	$-0.343740\pi$
$654$	−4.60704	+	7.97963i	−0.180150	+	0.312028i
$655$	−1.26726			−0.0495159
$656$	23.0875	−	39.9887i	0.901415	−	1.56130i
$657$	1.55471	−	2.69284i	0.0606550	−	0.105058i
$658$	50.1683			1.95576
$659$	−5.60060	+	9.70052i	−0.218168	+	0.377878i	−0.954248	−	0.299016i	$-0.903341\pi$
$659$	−5.60060	+	9.70052i	−0.218168	+	0.377878i	0.736080	+	0.676895i	$0.236675\pi$
$660$	−0.256096	−	0.443571i	−0.00996852	−	0.0172660i
$661$	−7.21844	−	12.5027i	−0.280765	−	0.486299i	0.690809	−	0.723038i	$-0.257255\pi$
$661$	−7.21844	−	12.5027i	−0.280765	−	0.486299i	−0.971573	+	0.236739i	$0.923921\pi$
$662$	13.0723			0.508070
$663$	0.00667672	−	0.530349i	0.000259302	−	0.0205970i
$664$	15.9382			0.618520
$665$	−3.85048	−	6.66922i	−0.149315	−	0.258621i
$666$	−4.01736	−	6.95827i	−0.155669	−	0.269627i
$667$	6.12238	−	10.6043i	0.237060	−	0.410599i
$668$	2.67957			0.103676
$669$	−8.70034	+	15.0694i	−0.336375	+	0.582618i
$670$	−13.0412	+	22.5881i	−0.503827	+	0.872654i
$671$	4.60458			0.177758
$672$	3.50838	−	6.07670i	0.135339	−	0.234414i
$673$	−20.5071	−	35.5193i	−0.790490	−	1.36917i	−0.925664	−	0.378347i	$-0.876493\pi$
$673$	−20.5071	−	35.5193i	−0.790490	−	1.36917i	0.135174	−	0.990822i	$-0.456841\pi$
$674$	−7.68722	−	13.3146i	−0.296100	−	0.512861i
$675$	3.60000			0.138564
$676$	2.93552	−	4.80113i	0.112905	−	0.184659i
$677$	22.8840			0.879505			0.439752	−	0.898119i	$-0.355066\pi$
$677$	22.8840			0.879505			0.439752	+	0.898119i	$0.355066\pi$
$678$	−11.6312	−	20.1458i	−0.446692	−	0.773693i
$679$	16.9607	+	29.3767i	0.650891	+	1.12738i
$680$	0.212726	−	0.368453i	0.00815768	−	0.0141295i
$681$	−6.43481			−0.246583
$682$	−5.38908	+	9.33417i	−0.206359	+	0.357424i
$683$	−12.6120	+	21.8446i	−0.482584	+	0.835860i	−0.999800	−	0.0199950i	$-0.993635\pi$
$683$	−12.6120	+	21.8446i	−0.482584	+	0.835860i	0.517216	+	0.855855i	$0.326968\pi$
$684$	0.967068			0.0369768
$685$	−3.67694	+	6.36865i	−0.140489	+	0.243334i
$686$	−12.5247	−	21.6934i	−0.478194	−	0.828257i
$687$	−7.76829	−	13.4551i	−0.296379	−	0.513343i
$688$	49.0929			1.87165
$689$	−0.269831	+	21.4334i	−0.0102797	+	0.816546i
$690$	−3.84506			−0.146379
$691$	17.7920	+	30.8166i	0.676839	+	1.17232i	0.975928	+	0.218095i	$0.0699842\pi$
$691$	17.7920	+	30.8166i	0.676839	+	1.17232i	−0.299088	+	0.954225i	$0.596683\pi$
$692$	1.26302	+	2.18762i	0.0480129	+	0.0831608i
$693$	1.45667	−	2.52303i	0.0553343	−	0.0958418i
$694$	−43.2293			−1.64096
$695$	−13.5813	+	23.5234i	−0.515166	+	0.892294i
$696$	7.18298	−	12.4413i	0.272270	−	0.471586i
$697$	−1.45190			−0.0549945
$698$	22.8499	−	39.5772i	0.864882	−	1.49802i
$699$	−7.22850	−	12.5201i	−0.273407	−	0.473555i
$700$	2.27003	+	3.93180i	0.0857990	+	0.148608i
$701$	−20.6495			−0.779919			−0.389960	−	0.920832i	$-0.627511\pi$
$701$	−20.6495			−0.779919			−0.389960	+	0.920832i	$0.627511\pi$
$702$	−4.90539	+	2.75038i	−0.185142	+	0.103806i
$703$	−11.5080			−0.434032
$704$	2.80003	+	4.84979i	0.105530	+	0.182783i
$705$	−6.53149	−	11.3129i	−0.245990	−	0.426068i
$706$	5.81731	−	10.0759i	0.218937	−	0.379211i
$707$	−10.8917			−0.409623
$708$	−2.30526	+	3.99284i	−0.0866371	+	0.150060i
$709$	−17.6013	+	30.4864i	−0.661031	+	1.14494i	0.319314	+	0.947649i	$0.396548\pi$
$709$	−17.6013	+	30.4864i	−0.661031	+	1.14494i	−0.980345	+	0.197291i	$0.936786\pi$
$710$	25.2547			0.947793
$711$	6.12564	−	10.6099i	0.229729	−	0.397903i
$712$	4.71055	+	8.15891i	0.176535	+	0.305768i
$713$	7.19834	+	12.4679i	0.269580	+	0.466926i
$714$	−0.668460			−0.0250165
$715$	3.72115	−	2.08640i	0.139163	−	0.0780268i
$716$	7.17009			0.267959
$717$	−1.10594	−	1.91555i	−0.0413022	−	0.0715374i
$718$	25.6448	+	44.4181i	0.957055	+	1.65767i
$719$	7.91297	−	13.7057i	0.295104	−	0.511135i	−0.679905	−	0.733300i	$-0.737979\pi$
$719$	7.91297	−	13.7057i	0.295104	−	0.511135i	0.975009	+	0.222165i	$0.0713123\pi$
$720$	−5.53553			−0.206297
$721$	−10.9790	+	19.0162i	−0.408879	+	0.708199i
$722$	−10.9255	+	18.9235i	−0.406605	+	0.704260i
$723$	−15.2549			−0.567337
$724$	2.38739	−	4.13507i	0.0887265	−	0.153679i
$725$	10.5790	+	18.3234i	0.392894	+	0.680513i
$726$	−0.779885	−	1.35080i	−0.0289442	−	0.0501329i
$727$	11.7907			0.437294			0.218647	−	0.975804i	$-0.429836\pi$
$727$	11.7907			0.437294			0.218647	+	0.975804i	$0.429836\pi$
$728$	22.0726	+	13.1168i	0.818064	+	0.486142i
$729$	1.00000			0.0370370
$730$	−2.86929	−	4.96976i	−0.106197	−	0.183939i
$731$	−0.771824	−	1.33684i	−0.0285469	−	0.0494448i
$732$	−0.996616	+	1.72619i	−0.0368360	+	0.0638018i
$733$	6.75455			0.249485			0.124742	−	0.992189i	$-0.460190\pi$
$733$	6.75455			0.249485			0.124742	+	0.992189i	$0.460190\pi$
$734$	−19.8962	+	34.4613i	−0.734383	+	1.27199i
$735$	0.880043	−	1.52428i	0.0324609	−	0.0562239i
$736$	−5.01792			−0.184963
$737$	−7.06633	+	12.2393i	−0.260292	+	0.450839i
$738$	7.69736	+	13.3322i	0.283344	+	0.490766i
$739$	20.1809	+	34.9543i	0.742366	+	1.28582i	0.951415	+	0.307911i	$0.0996298\pi$
$739$	20.1809	+	34.9543i	0.742366	+	1.28582i	−0.209049	+	0.977905i	$0.567037\pi$
$740$	−2.63841			−0.0969899
$741$	−0.101398	+	8.05427i	−0.00372494	+	0.295881i
$742$	27.0150			0.991751
$743$	2.24872	+	3.89490i	0.0824975	+	0.142890i	0.904322	−	0.426851i	$-0.140377\pi$
$743$	2.24872	+	3.89490i	0.0824975	+	0.142890i	−0.821825	+	0.569741i	$0.807044\pi$
$744$	8.44534	+	14.6278i	0.309621	+	0.536279i
$745$	1.00616	−	1.74272i	0.0368629	−	0.0638484i
$746$	−34.6294			−1.26787
$747$	−3.26021	+	5.64685i	−0.119285	+	0.206607i
$748$	−0.0318392	+	0.0551471i	−0.00116416	+	0.00201638i
$749$	20.6586			0.754849
$750$	7.93585	−	13.7453i	0.289776	−	0.501907i
$751$	−10.4369	−	18.0773i	−0.380848	−	0.659648i	0.610336	−	0.792143i	$-0.291035\pi$
$751$	−10.4369	−	18.0773i	−0.380848	−	0.659648i	−0.991184	+	0.132495i	$0.957701\pi$
$752$	−25.8252	−	44.7305i	−0.941747	−	1.63115i
$753$	−13.8575			−0.504997
$754$	−28.4140	−	16.8853i	−1.03478	−	0.614925i
$755$	−21.3623			−0.777455
$756$	0.630564	+	1.09217i	0.0229334	+	0.0397218i
$757$	−17.1078	−	29.6316i	−0.621795	−	1.07698i	−0.989151	−	0.146900i	$-0.953070\pi$
$757$	−17.1078	−	29.6316i	−0.621795	−	1.07698i	0.367357	−	0.930080i	$-0.380263\pi$
$758$	−27.0412	+	46.8368i	−0.982182	+	1.70119i
$759$	−2.08343			−0.0756236
$760$	−3.23062	+	5.59560i	−0.117187	+	0.202974i
$761$	25.2785	−	43.7836i	0.916344	−	1.58715i	0.111423	−	0.993773i	$-0.464459\pi$
$761$	25.2785	−	43.7836i	0.916344	−	1.58715i	0.804921	−	0.593382i	$-0.202208\pi$
$762$	−5.26737			−0.190817
$763$	−8.60503	+	14.9044i	−0.311523	+	0.539574i
$764$	−4.29119	−	7.43256i	−0.155250	−	0.268901i
$765$	0.0870280	+	0.150737i	0.00314650	+	0.00544990i
$766$	46.0402			1.66350
$767$	−33.0128	−	19.6182i	−1.19202	−	0.708370i
$768$	−9.93755			−0.358591
$769$	−12.1452	−	21.0361i	−0.437966	−	0.758580i	0.559566	−	0.828786i	$-0.310968\pi$
$769$	−12.1452	−	21.0361i	−0.437966	−	0.758580i	−0.997533	+	0.0702059i	$0.977634\pi$
$770$	−2.68835	−	4.65636i	−0.0968814	−	0.167804i
$771$	−10.1770	+	17.6271i	−0.366517	+	0.634826i
$772$	−1.17712			−0.0423654
$773$	9.78072	−	16.9407i	0.351788	−	0.609315i	−0.634775	−	0.772697i	$-0.718907\pi$
$773$	9.78072	−	16.9407i	0.351788	−	0.609315i	0.986563	+	0.163382i	$0.0522404\pi$
$774$	−8.18379	+	14.1747i	−0.294160	+	0.509500i
$775$	−24.8764			−0.893585
$776$	14.2303	−	24.6476i	0.510839	−	0.884798i
$777$	−7.50362	−	12.9967i	−0.269191	−	0.466252i
$778$	9.08782	+	15.7406i	0.325814	+	0.564326i
$779$	22.0496			0.790009
$780$	−0.0232472	+	1.84659i	−0.000832385	+	0.0661184i
$781$	13.6842			0.489658
$782$	0.239019	+	0.413993i	0.00854731	+	0.0148044i
$783$	2.93861	+	5.08983i	0.105017	+	0.181896i
$784$	3.47964	−	6.02692i	0.124273	−	0.215247i
$785$	1.03084			0.0367924
$786$	0.835279	−	1.44675i	0.0297934	−	0.0516037i
$787$	15.7307	−	27.2463i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$787$	15.7307	−	27.2463i	0.560737	−	0.971226i	0.997432	−	0.0716159i	$-0.0228156\pi$
$788$	1.75383			0.0624774
$789$	1.86999	−	3.23891i	0.0665733	−	0.115308i
$790$	−11.3051	−	19.5811i	−0.402219	−	0.696664i
$791$	−21.7247	−	37.6283i	−0.772441	−	1.33791i
$792$	−2.44434			−0.0868560
$793$	−14.2722	−	8.48136i	−0.506819	−	0.301182i
$794$	39.0936			1.38738
$795$	−3.51712	−	6.09184i	−0.124740	−	0.216055i
$796$	2.18723	+	3.78840i	0.0775244	+	0.134276i
$797$	19.2206	−	33.2910i	0.680827	−	1.17923i	−0.293901	−	0.955836i	$-0.594954\pi$
$797$	19.2206	−	33.2910i	0.680827	−	1.17923i	0.974729	−	0.223392i	$-0.0717129\pi$
$798$	10.1517			0.359368
$799$	−0.812031	+	1.40648i	−0.0287276	+	0.0497576i
$800$	4.33529	−	7.50894i	0.153276	−	0.265481i
$801$	−3.85424			−0.136183
$802$	4.22462	−	7.31726i	0.149177	−	0.258381i
$803$	−1.55471	−	2.69284i	−0.0548645	−	0.0950282i
$804$	−3.05888	−	5.29813i	−0.107878	−	0.186851i
$805$	−7.18180			−0.253125
$806$	33.8967	−	19.0054i	1.19396	−	0.669437i
$807$	10.4458			0.367710
$808$	4.56916	+	7.91401i	0.160742	+	0.278414i
$809$	−13.8245	−	23.9447i	−0.486043	−	0.841851i	0.513828	−	0.857893i	$-0.328227\pi$
$809$	−13.8245	−	23.9447i	−0.486043	−	0.841851i	−0.999871	+	0.0160417i	$0.994894\pi$
$810$	0.922773	−	1.59829i	0.0324229	−	0.0561582i
$811$	−13.5052			−0.474233			−0.237116	−	0.971481i	$-0.576202\pi$
$811$	−13.5052			−0.474233			−0.237116	+	0.971481i	$0.576202\pi$
$812$	−3.70597	+	6.41892i	−0.130054	+	0.225260i
$813$	−4.00808	+	6.94220i	−0.140570	+	0.243474i
$814$	−8.03471			−0.281617
$815$	−1.93301	+	3.34807i	−0.0677103	+	0.117278i
$816$	0.344104	+	0.596005i	0.0120460	+	0.0208644i
$817$	11.7215	+	20.3022i	0.410083	+	0.710285i
$818$	41.1824			1.43991
$819$	−9.16229	+	5.13717i	−0.320156	+	0.179507i
$820$	5.05527			0.176538
$821$	6.64101	+	11.5026i	0.231773	+	0.401442i	0.958330	−	0.285664i	$-0.0922141\pi$
$821$	6.64101	+	11.5026i	0.231773	+	0.401442i	−0.726557	+	0.687106i	$0.758881\pi$
$822$	−4.84711	−	8.39544i	−0.169062	−	0.292825i
$823$	0.981280	−	1.69963i	0.0342053	−	0.0592453i	−0.848416	−	0.529330i	$-0.822443\pi$
$823$	0.981280	−	1.69963i	0.0342053	−	0.0592453i	0.882621	+	0.470085i	$0.155777\pi$
$824$	18.4232			0.641801
$825$	1.80000	−	3.11769i	0.0626679	−	0.108544i
$826$	−24.1994	+	41.9145i	−0.842004	+	1.45839i
$827$	−47.2714			−1.64379			−0.821893	−	0.569642i	$-0.807082\pi$
$827$	−47.2714			−1.64379			−0.821893	+	0.569642i	$0.807082\pi$
$828$	0.450937	−	0.781046i	0.0156712	−	0.0271432i
$829$	−9.01826	−	15.6201i	−0.313217	−	0.542508i	0.665840	−	0.746095i	$-0.268073\pi$
$829$	−9.01826	−	15.6201i	−0.313217	−	0.542508i	−0.979057	+	0.203587i	$0.934740\pi$
$830$	6.01687	+	10.4215i	0.208849	+	0.361736i
$831$	−22.0876			−0.766210
$832$	0.254174	−	20.1897i	0.00881189	−	0.699951i
$833$	−0.218823			−0.00758178
$834$	−17.9034	−	31.0096i	−0.619944	−	1.07378i
$835$	−3.66212	−	6.34297i	−0.126733	−	0.219508i
$836$	0.483534	−	0.837506i	0.0167234	−	0.0289657i
$837$	−6.91010			−0.238848
$838$	28.0326	−	48.5538i	0.968369	−	1.67726i
$839$	23.0528	−	39.9286i	0.795871	−	1.37849i	−0.126414	−	0.991978i	$-0.540347\pi$
$839$	23.0528	−	39.9286i	0.795871	−	1.37849i	0.922285	−	0.386511i	$-0.126320\pi$
$840$	−8.42593			−0.290722
$841$	−2.77089	+	4.79932i	−0.0955479	+	0.165494i
$842$	4.96812	+	8.60504i	0.171213	+	0.296549i
$843$	−3.24106	−	5.61368i	−0.111628	−	0.193346i
$844$	−1.42521			−0.0490579
$845$	−15.3769	−	0.387231i	−0.528983	−	0.0133212i
$846$	17.2202			0.592043
$847$	−1.45667	−	2.52303i	−0.0500518	−	0.0866922i
$848$	−13.9065	−	24.0868i	−0.477552	−	0.827144i
$849$	−6.94493	+	12.0290i	−0.238350	+	0.412833i
$850$	−0.826013			−0.0283320
$851$	−5.36609	+	9.29434i	−0.183947	+	0.318606i
$852$	−2.96180	+	5.12999i	−0.101470	+	0.175751i
$853$	−43.0488			−1.47396			−0.736981	−	0.675913i	$-0.763749\pi$
$853$	−43.0488			−1.47396			−0.736981	+	0.675913i	$0.763749\pi$
$854$	−10.4619	+	18.1206i	−0.357999	+	0.620073i
$855$	−1.32167	−	2.28920i	−0.0452002	−	0.0782891i
$856$	−8.66648	−	15.0108i	−0.296214	−	0.513058i
$857$	8.75471			0.299055			0.149528	−	0.988758i	$-0.452225\pi$
$857$	8.75471			0.299055			0.149528	+	0.988758i	$0.452225\pi$
$858$	−0.0707945	+	5.62338i	−0.00241688	+	0.191979i
$859$	−44.3901			−1.51457			−0.757286	−	0.653083i	$-0.773475\pi$
$859$	−44.3901			−1.51457			−0.757286	+	0.653083i	$0.773475\pi$
$860$	2.68736	+	4.65465i	0.0916384	+	0.158722i
$861$	14.3771	+	24.9019i	0.489972	+	0.848656i
$862$	22.9047	−	39.6722i	0.780138	−	1.35124i
$863$	12.3187			0.419333			0.209666	−	0.977773i	$-0.432762\pi$
$863$	12.3187			0.419333			0.209666	+	0.977773i	$0.432762\pi$
$864$	1.20425	−	2.08582i	0.0409694	−	0.0709610i
$865$	3.45229	−	5.97954i	0.117381	−	0.203310i
$866$	17.6679			0.600380
$867$	−8.48918	+	14.7037i	−0.288308	+	0.499364i
$868$	−4.35726	−	7.54700i	−0.147895	−	0.256162i
$869$	−6.12564	−	10.6099i	−0.207798	−	0.359917i
$870$	10.8467			0.367737
$871$	44.4465	−	24.9205i	1.50601	−	0.844399i
$872$	14.4396			0.488985
$873$	5.82173	+	10.0835i	0.197036	+	0.341276i
$874$	−3.62992	−	6.28721i	−0.122784	−	0.212668i
$875$	14.8226	−	25.6735i	0.501095	−	0.867921i
$876$	1.34601			0.0454774
$877$	27.8606	−	48.2560i	0.940785	−	1.62949i	0.176808	−	0.984245i	$-0.443423\pi$
$877$	27.8606	−	48.2560i	0.940785	−	1.62949i	0.763978	−	0.645243i	$-0.223244\pi$
$878$	9.70714	−	16.8133i	0.327600	−	0.567420i
$879$	28.3854			0.957417
$880$	−2.76777	+	4.79391i	−0.0933014	+	0.161603i
$881$	−10.6355	−	18.4212i	−0.358319	−	0.620626i	0.629361	−	0.777113i	$-0.283317\pi$
$881$	−10.6355	−	18.4212i	−0.358319	−	0.620626i	−0.987680	+	0.156487i	$0.949983\pi$
$882$	1.16011	+	2.00937i	0.0390630	+	0.0676591i
$883$	−50.3917			−1.69581			−0.847907	−	0.530145i	$-0.822138\pi$
$883$	−50.3917			−1.69581			−0.847907	+	0.530145i	$0.822138\pi$
$884$	0.200265	−	0.112286i	0.00673565	−	0.00377658i
$885$	12.6022			0.423619
$886$	−2.94988	−	5.10934i	−0.0991030	−	0.171652i
$887$	11.7201	+	20.2998i	0.393522	+	0.681600i	0.992911	−	0.118857i	$-0.0379232\pi$
$887$	11.7201	+	20.2998i	0.393522	+	0.681600i	−0.599389	+	0.800458i	$0.704590\pi$
$888$	−6.29568	+	10.9044i	−0.211269	+	0.365929i
$889$	−9.83840			−0.329969
$890$	−3.55659	+	6.16020i	−0.119217	+	0.206490i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−7.53242			−0.252204
$893$	12.3321	−	21.3598i	0.412678	−	0.714779i
$894$	1.32637	+	2.29733i	0.0443603	+	0.0768344i
$895$	−9.79920	−	16.9727i	−0.327551	−	0.567335i
$896$	−39.4809			−1.31897
$897$	6.45770	+	3.83754i	0.215616	+	0.128132i
$898$	−10.7316			−0.358119
$899$	−20.3061	−	35.1712i	−0.677247	−	1.17303i
$900$	0.779184	+	1.34959i	0.0259728	+	0.0449862i
$901$	−0.437268	+	0.757370i	−0.0145675	+	0.0252317i
$902$	15.3947			0.512588
$903$	−15.2857	+	26.4756i	−0.508676	+	0.881052i
$904$	−18.2274	+	31.5708i	−0.606235	+	1.05003i
$905$	−13.0512			−0.433835
$906$	14.0804	−	24.3879i	0.467789	−	0.810235i
$907$	8.08381	+	14.0016i	0.268419	+	0.464915i	0.968454	−	0.249194i	$-0.0801656\pi$
$907$	8.08381	+	14.0016i	0.268419	+	0.464915i	−0.700035	+	0.714108i	$0.746832\pi$
$908$	−1.39275	−	2.41232i	−0.0462201	−	0.0800556i
$909$	−3.73855			−0.124000
$910$	−0.244036	+	19.3844i	−0.00808973	+	0.642588i
$911$	−46.6321			−1.54499			−0.772496	−	0.635020i	$-0.780992\pi$
$911$	−46.6321			−1.54499			−0.772496	+	0.635020i	$0.780992\pi$
$912$	−5.22582	−	9.05138i	−0.173044	−	0.299721i
$913$	3.26021	+	5.64685i	0.107897	+	0.186883i
$914$	−2.24950	+	3.89626i	−0.0744070	+	0.128877i
$915$	5.44822			0.180113
$916$	3.36274	−	5.82444i	0.111108	−	0.192445i
$917$	1.56013	−	2.70223i	0.0515202	−	0.0892356i
$918$	−0.229448			−0.00757292
$919$	12.2482	−	21.2145i	0.404032	−	0.699803i	−0.590177	−	0.807274i	$-0.700942\pi$
$919$	12.2482	−	21.2145i	0.404032	−	0.699803i	0.994208	+	0.107471i	$0.0342752\pi$
$920$	3.01283	+	5.21838i	0.0993301	+	0.172045i
$921$	9.77746	+	16.9350i	0.322178	+	0.558029i
$922$	−51.3614			−1.69150
$923$	−42.4148	−	25.2054i	−1.39610	−	0.829646i
$924$	1.26113			0.0414881
$925$	−9.27219	−	16.0599i	−0.304868	−	0.528046i
$926$	24.9755	+	43.2588i	0.820746	+	1.42157i
$927$	−3.76853	+	6.52728i	−0.123775	+	0.214384i
$928$	14.1553			0.464670
$929$	−11.3790	+	19.7090i	−0.373333	+	0.646632i	−0.990076	−	0.140532i	$-0.955119\pi$
$929$	−11.3790	+	19.7090i	−0.373333	+	0.646632i	0.616743	+	0.787165i	$0.288452\pi$
$930$	−6.37646	+	11.0443i	−0.209092	+	0.362158i
$931$	3.32322			0.108914
$932$	3.12908	−	5.41972i	0.102496	−	0.177529i
$933$	−8.45205	−	14.6394i	−0.276708	−	0.479272i
$934$	11.1569	+	19.3243i	0.365064	+	0.632309i
$935$	0.174056			0.00569224
$936$	7.57639	+	4.50234i	0.247642	+	0.147163i
$937$	26.5835			0.868446			0.434223	−	0.900805i	$-0.357023\pi$
$937$	26.5835			0.868446			0.434223	+	0.900805i	$0.357023\pi$
$938$	−32.1104	−	55.6168i	−1.04844	−	1.81595i
$939$	−2.64909	−	4.58835i	−0.0864497	−	0.149735i
$940$	2.82736	−	4.89713i	0.0922182	−	0.159727i
$941$	−9.01994			−0.294042			−0.147021	−	0.989133i	$-0.546968\pi$
$941$	−9.01994			−0.294042			−0.147021	+	0.989133i	$0.546968\pi$
$942$	−0.679453	+	1.17685i	−0.0221378	+	0.0383437i
$943$	10.2816	−	17.8082i	0.334814	−	0.579915i
$944$	49.8285			1.62178
$945$	1.72356	−	2.98529i	0.0560673	−	0.0971114i
$946$	8.18379	+	14.1747i	0.266078	+	0.460861i
$947$	8.74502	+	15.1468i	0.284175	+	0.492205i	0.972409	−	0.233283i	$-0.0749470\pi$
$947$	8.74502	+	15.1468i	0.284175	+	0.492205i	−0.688234	+	0.725489i	$0.741614\pi$
$948$	5.30334			0.172244
$949$	−0.141130	+	11.2103i	−0.00458126	+	0.363901i
$950$	12.5445			0.406996
$951$	10.8691	+	18.8258i	0.352455	+	0.610470i
$952$	0.523779	+	0.907211i	0.0169758	+	0.0294029i
$953$	−4.22537	+	7.31855i	−0.136873	+	0.237071i	−0.926311	−	0.376759i	$-0.877039\pi$
$953$	−4.22537	+	7.31855i	−0.136873	+	0.237071i	0.789438	+	0.613830i	$0.210372\pi$
$954$	9.27286			0.300220
$955$	−11.7294	+	20.3158i	−0.379553	+	0.657405i
$956$	0.478741	−	0.829203i	0.0154836	−	0.0268184i
$957$	5.87723			0.189984
$958$	−21.6514	+	37.5013i	−0.699524	+	1.21161i
$959$	−9.05344	−	15.6810i	−0.292351	−	0.506366i
$960$	3.31304	+	5.73835i	0.106928	+	0.185204i
$961$	16.7495			0.540307
$962$	24.9041	+	14.7995i	0.802939	+	0.477154i
$963$	7.09104			0.228506
$964$	−3.30178	−	5.71885i	−0.106343	−	0.184192i
$965$	1.60874	+	2.78643i	0.0517873	+	0.0896982i
$966$	4.73369	−	8.19898i	0.152304	−	0.263798i
$967$	−31.9335			−1.02691			−0.513456	−	0.858116i	$-0.671635\pi$
$967$	−31.9335			−1.02691			−0.513456	+	0.858116i	$0.671635\pi$
$968$	−1.22217	+	2.11686i	−0.0392821	+	0.0680386i
$969$	−0.164317	+	0.284606i	−0.00527863	+	0.00914286i
$970$	21.4885			0.689955
$971$	3.40850	−	5.90370i	0.109384	−	0.189459i	−0.806137	−	0.591729i	$-0.798446\pi$
$971$	3.40850	−	5.90370i	0.109384	−	0.189459i	0.915521	+	0.402270i	$0.131779\pi$
$972$	0.216440	+	0.374886i	0.00694233	+	0.0120245i
$973$	−33.4400	−	57.9198i	−1.07204	−	1.85682i
$974$	7.86149			0.251899
$975$	−11.3218	+	6.34797i	−0.362588	+	0.203298i
$976$	21.5420			0.689541
$977$	−1.84312	−	3.19238i	−0.0589667	−	0.102133i	0.835035	−	0.550197i	$-0.185447\pi$
$977$	−1.84312	−	3.19238i	−0.0589667	−	0.102133i	−0.894002	+	0.448063i	$0.852114\pi$
$978$	−2.54818	−	4.41357i	−0.0814817	−	0.141130i
$979$	−1.92712	+	3.33787i	−0.0615911	+	0.106679i
$980$	0.761907			0.0243382
$981$	−2.95367	+	5.11590i	−0.0943034	+	0.163338i
$982$	−5.16630	+	8.94830i	−0.164863	+	0.285552i
$983$	−48.4143			−1.54418			−0.772089	−	0.635515i	$-0.780788\pi$
$983$	−48.4143			−1.54418			−0.772089	+	0.635515i	$0.780788\pi$
$984$	12.0627	−	20.8932i	0.384545	−	0.666051i
$985$	−2.39692	−	4.15158i	−0.0763721	−	0.132280i
$986$	−0.674259	−	1.16785i	−0.0214728	−	0.0371920i
$987$	32.1639			1.02379
$988$	−3.04138	+	1.70526i	−0.0967591	+	0.0542514i
$989$	21.8626			0.695191
$990$	−0.922773	−	1.59829i	−0.0293277	−	0.0507970i
$991$	−10.5072	−	18.1991i	−0.333773	−	0.578112i	0.649475	−	0.760383i	$-0.274989\pi$
$991$	−10.5072	−	18.1991i	−0.333773	−	0.578112i	−0.983248	+	0.182271i	$0.941655\pi$
$992$	−8.32148	+	14.4132i	−0.264207	+	0.457620i
$993$	8.38093			0.265961
$994$	−31.0913	+	53.8518i	−0.986157	+	1.70807i
$995$	5.97849	−	10.3550i	0.189531	−	0.328277i
$996$	−2.82256			−0.0894363
$997$	9.35351	−	16.2008i	0.296229	−	0.513083i	−0.679041	−	0.734100i	$-0.737604\pi$
$997$	9.35351	−	16.2008i	0.296229	−	0.513083i	0.975270	+	0.221017i	$0.0709376\pi$
$998$	−20.5519	−	35.5970i	−0.650560	−	1.12680i
$999$	−2.57561	−	4.46109i	−0.0814887	−	0.141143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.e.133.4	yes	10
13.3	even	3		5577.2.a.o.1.2		5
13.9	even	3	inner	429.2.i.e.100.4	✓	10
13.10	even	6		5577.2.a.u.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.e.100.4	✓	10	13.9	even	3	inner
429.2.i.e.133.4	yes	10	1.1	even	1	trivial
5577.2.a.o.1.2		5	13.3	even	3
5577.2.a.u.1.4		5	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.779885 + 1.35080i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.216440 + 0.374886i) q^{4} +1.18322 q^{5} +(-0.779885 + 1.35080i) q^{6} +(-1.45667 + 2.52303i) q^{7} +2.44434 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.779885 + 1.35080i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.216440 + 0.374886i) q^{4} +1.18322 q^{5} +(-0.779885 + 1.35080i) q^{6} +(-1.45667 + 2.52303i) q^{7} +2.44434 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.922773 + 1.59829i) q^{10} +(0.500000 + 0.866025i) q^{11} -0.432881 q^{12} +(0.0453878 - 3.60527i) q^{13} -4.54414 q^{14} +(0.591609 + 1.02470i) q^{15} +(2.33919 + 4.05159i) q^{16} +(0.0735520 - 0.127396i) q^{17} -1.55977 q^{18} +(-1.11702 + 1.93473i) q^{19} +(-0.256096 + 0.443571i) q^{20} -2.91334 q^{21} +(-0.779885 + 1.35080i) q^{22} +(1.04171 + 1.80430i) q^{23} +(1.22217 + 2.11686i) q^{24} -3.60000 q^{25} +(4.90539 - 2.75038i) q^{26} -1.00000 q^{27} +(-0.630564 - 1.09217i) q^{28} +(-2.93861 - 5.08983i) q^{29} +(-0.922773 + 1.59829i) q^{30} +6.91010 q^{31} +(-1.20425 + 2.08582i) q^{32} +(-0.500000 + 0.866025i) q^{33} +0.229448 q^{34} +(-1.72356 + 2.98529i) q^{35} +(-0.216440 - 0.374886i) q^{36} +(2.57561 + 4.46109i) q^{37} -3.48457 q^{38} +(3.14495 - 1.76333i) q^{39} +2.89219 q^{40} +(-4.93494 - 8.54756i) q^{41} +(-2.27207 - 3.93534i) q^{42} +(5.24679 - 9.08771i) q^{43} -0.432881 q^{44} +(-0.591609 + 1.02470i) q^{45} +(-1.62483 + 2.81429i) q^{46} -11.0402 q^{47} +(-2.33919 + 4.05159i) q^{48} +(-0.743771 - 1.28825i) q^{49} +(-2.80758 - 4.86288i) q^{50} +0.147104 q^{51} +(1.34174 + 0.797340i) q^{52} -5.94502 q^{53} +(-0.779885 - 1.35080i) q^{54} +(0.591609 + 1.02470i) q^{55} +(-3.56060 + 6.16714i) q^{56} -2.23403 q^{57} +(4.58356 - 7.93896i) q^{58} +(5.32541 - 9.22387i) q^{59} -0.512192 q^{60} +(2.30229 - 3.98768i) q^{61} +(5.38908 + 9.33417i) q^{62} +(-1.45667 - 2.52303i) q^{63} +5.60005 q^{64} +(0.0537036 - 4.26581i) q^{65} -1.55977 q^{66} +(7.06633 + 12.2393i) q^{67} +(0.0318392 + 0.0551471i) q^{68} +(-1.04171 + 1.80430i) q^{69} -5.37670 q^{70} +(6.84208 - 11.8508i) q^{71} +(-1.22217 + 2.11686i) q^{72} -3.10942 q^{73} +(-4.01736 + 6.95827i) q^{74} +(-1.80000 - 3.11769i) q^{75} +(-0.483534 - 0.837506i) q^{76} -2.91334 q^{77} +(4.83460 + 2.87300i) q^{78} -12.2513 q^{79} +(2.76777 + 4.79391i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.69736 - 13.3322i) q^{82} +6.52042 q^{83} +(0.630564 - 1.09217i) q^{84} +(0.0870280 - 0.150737i) q^{85} +16.3676 q^{86} +(2.93861 - 5.08983i) q^{87} +(1.22217 + 2.11686i) q^{88} +(1.92712 + 3.33787i) q^{89} -1.84555 q^{90} +(9.03006 + 5.36619i) q^{91} -0.901874 q^{92} +(3.45505 + 5.98432i) q^{93} +(-8.61010 - 14.9131i) q^{94} +(-1.32167 + 2.28920i) q^{95} -2.40850 q^{96} +(5.82173 - 10.0835i) q^{97} +(1.16011 - 2.00937i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Introduction

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