LMFDB - Embedded newform 429.2.n.d.157.5

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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	429.157
Dual form			429.2.n.d.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167740 - 0.121870i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.604750 + 1.86123i) q^{4} +(0.762452 + 0.553954i) q^{5} +(0.167740 + 0.121870i) q^{6} +(0.163043 - 0.501795i) q^{7} +(0.253530 + 0.780285i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.167740 - 0.121870i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.604750 + 1.86123i) q^{4} +(0.762452 + 0.553954i) q^{5} +(0.167740 + 0.121870i) q^{6} +(0.163043 - 0.501795i) q^{7} +(0.253530 + 0.780285i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.195404 q^{10} +(0.840162 + 3.20845i) q^{11} -1.95701 q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.0338051 - 0.104041i) q^{14} +(-0.291231 + 0.896316i) q^{15} +(-3.02889 - 2.20062i) q^{16} +(-2.85444 - 2.07387i) q^{17} +(-0.0640711 + 0.197191i) q^{18} +(2.13338 + 6.56587i) q^{19} +(-1.49213 + 1.08409i) q^{20} +0.527618 q^{21} +(0.531944 + 0.435795i) q^{22} -0.338811 q^{23} +(-0.663750 + 0.482243i) q^{24} +(-1.27062 - 3.91056i) q^{25} +(0.0640711 - 0.197191i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.835354 + 0.606920i) q^{28} +(-3.12617 + 9.62136i) q^{29} +(0.0603833 + 0.185841i) q^{30} +(0.714328 - 0.518990i) q^{31} -2.41714 q^{32} +(-2.79179 + 1.79051i) q^{33} -0.731548 q^{34} +(0.402283 - 0.292276i) q^{35} +(-0.604750 - 1.86123i) q^{36} +(2.40458 - 7.40053i) q^{37} +(1.15804 + 0.841365i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-0.238937 + 0.735374i) q^{40} +(-0.0218930 - 0.0673798i) q^{41} +(0.0885028 - 0.0643011i) q^{42} +5.35730 q^{43} +(-6.47974 - 0.376575i) q^{44} -0.942442 q^{45} +(-0.0568323 + 0.0412911i) q^{46} +(0.210799 + 0.648774i) q^{47} +(1.15693 - 3.56067i) q^{48} +(5.43790 + 3.95087i) q^{49} +(-0.689715 - 0.501107i) q^{50} +(1.09030 - 3.35559i) q^{51} +(0.604750 + 1.86123i) q^{52} +(3.88510 - 2.82269i) q^{53} -0.207338 q^{54} +(-1.13675 + 2.91170i) q^{55} +0.432879 q^{56} +(-5.58526 + 4.05793i) q^{57} +(0.648175 + 1.99488i) q^{58} +(3.14757 - 9.68724i) q^{59} +(-1.49213 - 1.08409i) q^{60} +(8.83599 + 6.41972i) q^{61} +(0.0565721 - 0.174111i) q^{62} +(0.163043 + 0.501795i) q^{63} +(5.65233 - 4.10666i) q^{64} +0.942442 q^{65} +(-0.250086 + 0.640577i) q^{66} +11.4772 q^{67} +(5.58617 - 4.05859i) q^{68} +(-0.104698 - 0.322229i) q^{69} +(0.0318593 - 0.0980529i) q^{70} +(-2.23972 - 1.62725i) q^{71} +(-0.663750 - 0.482243i) q^{72} +(0.319512 - 0.983356i) q^{73} +(-0.498562 - 1.53441i) q^{74} +(3.32652 - 2.41686i) q^{75} -13.5107 q^{76} +(1.74696 + 0.101526i) q^{77} +0.207338 q^{78} +(9.74462 - 7.07988i) q^{79} +(-1.09034 - 3.35573i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0118839 - 0.00863419i) q^{82} +(-10.0084 - 7.27154i) q^{83} +(-0.319077 + 0.982017i) q^{84} +(-1.02754 - 3.16245i) q^{85} +(0.898635 - 0.652897i) q^{86} -10.1165 q^{87} +(-2.29050 + 1.46900i) q^{88} -12.8752 q^{89} +(-0.158086 + 0.114856i) q^{90} +(-0.163043 - 0.501795i) q^{91} +(0.204896 - 0.630605i) q^{92} +(0.714328 + 0.518990i) q^{93} +(0.114426 + 0.0831353i) q^{94} +(-2.01059 + 6.18795i) q^{95} +(-0.746937 - 2.29883i) q^{96} +(-3.71413 + 2.69847i) q^{97} +1.39365 q^{98} +(-2.56558 - 2.10185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

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 $

$2$	0.167740	−	0.121870i	0.118610	−	0.0861754i	−0.526899	−	0.849928i	$-0.676645\pi$
$2$	0.167740	−	0.121870i	0.118610	−	0.0861754i	0.645509	+	0.763753i	$0.276645\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.604750	+	1.86123i	−0.302375	+	0.930614i
$5$	0.762452	+	0.553954i	0.340979	+	0.247736i	0.745075	−	0.666981i	$-0.232414\pi$
$5$	0.762452	+	0.553954i	0.340979	+	0.247736i	−0.404096	+	0.914717i	$0.632414\pi$
$6$	0.167740	+	0.121870i	0.0684797	+	0.0497534i
$7$	0.163043	−	0.501795i	0.0616244	−	0.189661i	−0.915505	−	0.402307i	$-0.868208\pi$
$7$	0.163043	−	0.501795i	0.0616244	−	0.189661i	0.977129	+	0.212647i	$0.0682084\pi$
$8$	0.253530	+	0.780285i	0.0896364	+	0.275872i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.195404			0.0617923
$11$	0.840162	+	3.20845i	0.253318	+	0.967383i
$11$	0.840162	+	3.20845i	0.253318	+	0.967383i
$12$	−1.95701			−0.564940
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−0.0338051	−	0.104041i	−0.00903478	−	0.0278062i
$15$	−0.291231	+	0.896316i	−0.0751954	+	0.231428i
$16$	−3.02889	−	2.20062i	−0.757222	−	0.550154i
$17$	−2.85444	−	2.07387i	−0.692303	−	0.502988i	0.185113	−	0.982717i	$-0.440735\pi$
$17$	−2.85444	−	2.07387i	−0.692303	−	0.502988i	−0.877416	+	0.479730i	$0.840735\pi$
$18$	−0.0640711	+	0.197191i	−0.0151017	+	0.0464783i
$19$	2.13338	+	6.56587i	0.489431	+	1.50631i	0.825459	+	0.564461i	$0.190916\pi$
$19$	2.13338	+	6.56587i	0.489431	+	1.50631i	−0.336029	+	0.941852i	$0.609084\pi$
$20$	−1.49213	+	1.08409i	−0.333650	+	0.242411i
$21$	0.527618			0.115136
$22$	0.531944	+	0.435795i	0.113411	+	0.0929118i
$23$	−0.338811			−0.0706470			−0.0353235	−	0.999376i	$-0.511246\pi$
$23$	−0.338811			−0.0706470			−0.0353235	+	0.999376i	$0.511246\pi$
$24$	−0.663750	+	0.482243i	−0.135487	+	0.0984374i
$25$	−1.27062	−	3.91056i	−0.254123	−	0.782111i
$26$	0.0640711	−	0.197191i	0.0125654	−	0.0386723i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.835354	+	0.606920i	0.157867	+	0.114697i
$29$	−3.12617	+	9.62136i	−0.580515	+	1.78664i	0.0360642	+	0.999349i	$0.488518\pi$
$29$	−3.12617	+	9.62136i	−0.580515	+	1.78664i	−0.616579	+	0.787293i	$0.711482\pi$
$30$	0.0603833	+	0.185841i	0.0110244	+	0.0339297i
$31$	0.714328	−	0.518990i	0.128297	−	0.0932133i	−0.521786	−	0.853076i	$-0.674734\pi$
$31$	0.714328	−	0.518990i	0.128297	−	0.0932133i	0.650083	+	0.759863i	$0.274734\pi$
$32$	−2.41714			−0.427294
$33$	−2.79179	+	1.79051i	−0.485988	+	0.311687i
$34$	−0.731548			−0.125459
$35$	0.402283	−	0.292276i	0.0679983	−	0.0494036i
$36$	−0.604750	−	1.86123i	−0.100792	−	0.310205i
$37$	2.40458	−	7.40053i	0.395310	−	1.21664i	−0.533409	−	0.845857i	$-0.679089\pi$
$37$	2.40458	−	7.40053i	0.395310	−	1.21664i	0.928720	−	0.370783i	$-0.120911\pi$
$38$	1.15804	+	0.841365i	0.187859	+	0.136487i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	−0.238937	+	0.735374i	−0.0377793	+	0.116273i
$41$	−0.0218930	−	0.0673798i	−0.00341911	−	0.0105230i	0.949332	−	0.314274i	$-0.101761\pi$
$41$	−0.0218930	−	0.0673798i	−0.00341911	−	0.0105230i	−0.952752	+	0.303751i	$0.901761\pi$
$42$	0.0885028	−	0.0643011i	0.0136563	−	0.00992187i
$43$	5.35730			0.816981			0.408490	−	0.912763i	$-0.366055\pi$
$43$	5.35730			0.816981			0.408490	+	0.912763i	$0.366055\pi$
$44$	−6.47974	−	0.376575i	−0.976857	−	0.0567707i
$45$	−0.942442			−0.140491
$46$	−0.0568323	+	0.0412911i	−0.00837947	+	0.00608804i
$47$	0.210799	+	0.648774i	0.0307483	+	0.0946334i	0.965253	−	0.261318i	$-0.0841570\pi$
$47$	0.210799	+	0.648774i	0.0307483	+	0.0946334i	−0.934505	+	0.355951i	$0.884157\pi$
$48$	1.15693	−	3.56067i	0.166989	−	0.513939i
$49$	5.43790	+	3.95087i	0.776843	+	0.564410i
$50$	−0.689715	−	0.501107i	−0.0975404	−	0.0708673i
$51$	1.09030	−	3.35559i	0.152672	−	0.469877i
$52$	0.604750	+	1.86123i	0.0838637	+	0.258106i
$53$	3.88510	−	2.82269i	0.533660	−	0.387727i	−0.288065	−	0.957611i	$-0.593012\pi$
$53$	3.88510	−	2.82269i	0.533660	−	0.387727i	0.821725	+	0.569884i	$0.193012\pi$
$54$	−0.207338			−0.0282152
$55$	−1.13675	+	2.91170i	−0.153279	+	0.392613i
$56$	0.432879			0.0578459
$57$	−5.58526	+	4.05793i	−0.739786	+	0.537486i
$58$	0.648175	+	1.99488i	0.0851096	+	0.261940i
$59$	3.14757	−	9.68724i	0.409779	−	1.26117i	−0.507059	−	0.861911i	$-0.669267\pi$
$59$	3.14757	−	9.68724i	0.409779	−	1.26117i	0.916838	−	0.399259i	$-0.130733\pi$
$60$	−1.49213	−	1.08409i	−0.192633	−	0.139956i
$61$	8.83599	+	6.41972i	1.13133	+	0.821961i	0.985888	−	0.167406i	$-0.0535389\pi$
$61$	8.83599	+	6.41972i	1.13133	+	0.821961i	0.145444	+	0.989366i	$0.453539\pi$
$62$	0.0565721	−	0.174111i	0.00718466	−	0.0221121i
$63$	0.163043	+	0.501795i	0.0205415	+	0.0632202i
$64$	5.65233	−	4.10666i	0.706541	−	0.513332i
$65$	0.942442			0.116896
$66$	−0.250086	+	0.640577i	−0.0307834	+	0.0788495i
$67$	11.4772			1.40217			0.701083	−	0.713080i	$-0.252700\pi$
$67$	11.4772			1.40217			0.701083	+	0.713080i	$0.252700\pi$
$68$	5.58617	−	4.05859i	0.677422	−	0.492176i
$69$	−0.104698	−	0.322229i	−0.0126042	−	0.0387918i
$70$	0.0318593	−	0.0980529i	0.00380792	−	0.0117196i
$71$	−2.23972	−	1.62725i	−0.265806	−	0.193119i	0.446897	−	0.894586i	$-0.352529\pi$
$71$	−2.23972	−	1.62725i	−0.265806	−	0.193119i	−0.712703	+	0.701466i	$0.752529\pi$
$72$	−0.663750	−	0.482243i	−0.0782237	−	0.0568329i
$73$	0.319512	−	0.983356i	0.0373960	−	0.115093i	−0.930616	−	0.365997i	$-0.880728\pi$
$73$	0.319512	−	0.983356i	0.0373960	−	0.115093i	0.968012	+	0.250904i	$0.0807279\pi$
$74$	−0.498562	−	1.53441i	−0.0579566	−	0.178372i
$75$	3.32652	−	2.41686i	0.384113	−	0.279075i
$76$	−13.5107			−1.54979
$77$	1.74696	+	0.101526i	0.199085	+	0.0115700i
$78$	0.207338			0.0234765
$79$	9.74462	−	7.07988i	1.09635	−	0.796548i	0.115894	−	0.993262i	$-0.463027\pi$
$79$	9.74462	−	7.07988i	1.09635	−	0.796548i	0.980461	+	0.196713i	$0.0630268\pi$
$80$	−1.09034	−	3.35573i	−0.121904	−	0.375182i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.0118839	−	0.00863419i	−0.00131236	−	0.000953487i
$83$	−10.0084	−	7.27154i	−1.09857	−	0.798155i	−0.117741	−	0.993044i	$-0.537565\pi$
$83$	−10.0084	−	7.27154i	−1.09857	−	0.798155i	−0.980825	+	0.194889i	$0.937565\pi$
$84$	−0.319077	+	0.982017i	−0.0348141	+	0.107147i
$85$	−1.02754	−	3.16245i	−0.111453	−	0.343016i
$86$	0.898635	−	0.652897i	0.0969023	−	0.0704037i
$87$	−10.1165			−1.08460
$88$	−2.29050	+	1.46900i	−0.244168	+	0.156596i
$89$	−12.8752			−1.36477			−0.682384	−	0.730994i	$-0.739057\pi$
$89$	−12.8752			−1.36477			−0.682384	+	0.730994i	$0.739057\pi$
$90$	−0.158086	+	0.114856i	−0.0166637	+	0.0121069i
$91$	−0.163043	−	0.501795i	−0.0170915	−	0.0526024i
$92$	0.204896	−	0.630605i	0.0213619	−	0.0657451i
$93$	0.714328	+	0.518990i	0.0740724	+	0.0538167i
$94$	0.114426	+	0.0831353i	0.0118021	+	0.00857476i
$95$	−2.01059	+	6.18795i	−0.206282	+	0.634870i
$96$	−0.746937	−	2.29883i	−0.0762339	−	0.234624i
$97$	−3.71413	+	2.69847i	−0.377113	+	0.273989i	−0.760154	−	0.649743i	$-0.774877\pi$
$97$	−3.71413	+	2.69847i	−0.377113	+	0.273989i	0.383041	+	0.923731i	$0.374877\pi$
$98$	1.39365			0.140780
$99$	−2.56558	−	2.10185i	−0.257851	−	0.211244i
$100$	8.04684			0.804684
$101$	7.01749	−	5.09851i	0.698267	−	0.507321i	−0.181100	−	0.983465i	$-0.557966\pi$
$101$	7.01749	−	5.09851i	0.698267	−	0.507321i	0.879367	+	0.476144i	$0.157966\pi$
$102$	−0.226061	−	0.695743i	−0.0223833	−	0.0688889i
$103$	4.59979	−	14.1567i	0.453231	−	1.39490i	−0.419969	−	0.907538i	$-0.637959\pi$
$103$	4.59979	−	14.1567i	0.453231	−	1.39490i	0.873200	−	0.487362i	$-0.162041\pi$
$104$	0.663750	+	0.482243i	0.0650861	+	0.0472878i
$105$	0.402283	+	0.292276i	0.0392588	+	0.0285232i
$106$	0.307686	−	0.946959i	0.0298851	−	0.0919768i
$107$	4.13248	+	12.7185i	0.399502	+	1.22954i	0.925400	+	0.378992i	$0.123729\pi$
$107$	4.13248	+	12.7185i	0.399502	+	1.22954i	−0.525898	+	0.850548i	$0.676271\pi$
$108$	1.58325	−	1.15030i	0.152349	−	0.110688i
$109$	0.774287			0.0741632			0.0370816	−	0.999312i	$-0.488194\pi$
$109$	0.774287			0.0741632			0.0370816	+	0.999312i	$0.488194\pi$
$110$	0.164171	+	0.626945i	0.0156531	+	0.0597768i
$111$	7.78138			0.738576
$112$	−1.59810	+	1.16108i	−0.151006	+	0.109712i
$113$	3.97991	+	12.2489i	0.374398	+	1.15228i	0.943884	+	0.330278i	$0.107142\pi$
$113$	3.97991	+	12.2489i	0.374398	+	1.15228i	−0.569486	+	0.822001i	$0.692858\pi$
$114$	−0.442332	+	1.36136i	−0.0414281	+	0.127503i
$115$	−0.258327	−	0.187686i	−0.0240891	−	0.0175018i
$116$	−16.0170	−	11.6370i	−1.48714	−	1.08047i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	−0.652613	−	2.00854i	−0.0600779	−	0.184901i
$119$	−1.50605	+	1.09421i	−0.138060	+	0.100306i
$120$	−0.773218			−0.0705848
$121$	−9.58826	+	5.39123i	−0.871660	+	0.490112i
$122$	2.26453			0.205021
$123$	0.0573167	−	0.0416430i	0.00516807	−	0.00375482i
$124$	0.533969	+	1.64339i	0.0479518	+	0.147580i
$125$	2.65364	−	8.16705i	0.237348	−	0.730483i
$126$	0.0885028	+	0.0643011i	0.00788446	+	0.00572839i
$127$	−11.4142	−	8.29288i	−1.01284	−	0.735874i	−0.0480403	−	0.998845i	$-0.515298\pi$
$127$	−11.4142	−	8.29288i	−1.01284	−	0.735874i	−0.964804	+	0.262971i	$0.915298\pi$
$128$	1.94152	−	5.97537i	0.171607	−	0.528153i
$129$	1.65550	+	5.09509i	0.145758	+	0.448598i
$130$	0.158086	−	0.114856i	0.0138650	−	0.0100735i
$131$	6.40993			0.560038			0.280019	−	0.959994i	$-0.409659\pi$
$131$	6.40993			0.560038			0.280019	+	0.959994i	$0.409659\pi$
$132$	−1.64421	−	6.27896i	−0.143110	−	0.546514i
$133$	3.64255			0.315849
$134$	1.92519	−	1.39873i	0.166311	−	0.120832i
$135$	−0.291231	−	0.896316i	−0.0250651	−	0.0771426i
$136$	0.894525	−	2.75306i	0.0767049	−	0.236073i
$137$	−16.7628	−	12.1789i	−1.43214	−	1.04051i	−0.989613	−	0.143759i	$-0.954081\pi$
$137$	−16.7628	−	12.1789i	−1.43214	−	1.04051i	−0.442530	−	0.896754i	$-0.645919\pi$
$138$	−0.0568323	−	0.0412911i	−0.00483789	−	0.00351493i
$139$	1.67284	−	5.14846i	0.141888	−	0.436687i	−0.854710	−	0.519106i	$-0.826265\pi$
$139$	1.67284	−	5.14846i	0.141888	−	0.436687i	0.996598	+	0.0824198i	$0.0262648\pi$
$140$	0.300711	+	0.925495i	0.0254148	+	0.0782186i
$141$	−0.551880	+	0.400964i	−0.0464767	+	0.0337673i
$142$	−0.574006			−0.0481695
$143$	2.56558	+	2.10185i	0.214545	+	0.175766i
$144$	3.74391			0.311993
$145$	−7.71334	+	5.60407i	−0.640558	+	0.465393i
$146$	−0.0662470	−	0.203887i	−0.00548264	−	0.0168738i
$147$	−2.07709	+	6.39264i	−0.171316	+	0.527256i
$148$	12.3199	+	8.95094i	1.01269	+	0.735762i
$149$	16.5863	+	12.0506i	1.35880	+	0.987226i	0.998520	+	0.0543816i	$0.0173187\pi$
$149$	16.5863	+	12.0506i	1.35880	+	0.987226i	0.360280	+	0.932844i	$0.382681\pi$
$150$	0.263448	−	0.810809i	0.0215104	−	0.0662023i
$151$	1.13501	+	3.49319i	0.0923656	+	0.284272i	0.986558	−	0.163410i	$-0.0522495\pi$
$151$	1.13501	+	3.49319i	0.0923656	+	0.284272i	−0.894193	+	0.447683i	$0.852249\pi$
$152$	−4.58237	+	3.32929i	−0.371680	+	0.270041i
$153$	3.52828			0.285244
$154$	0.305409	−	0.195873i	0.0246106	−	0.0157839i
$155$	0.832137			0.0668389
$156$	−1.58325	+	1.15030i	−0.126762	+	0.0920979i
$157$	−0.859302	−	2.64466i	−0.0685798	−	0.211067i	0.910893	−	0.412642i	$-0.135394\pi$
$157$	−0.859302	−	2.64466i	−0.0685798	−	0.211067i	−0.979473	+	0.201575i	$0.935394\pi$
$158$	0.771737	−	2.37516i	0.0613961	−	0.188958i
$159$	3.88510	+	2.82269i	0.308109	+	0.223854i
$160$	−1.84295	−	1.33898i	−0.145698	−	0.105856i
$161$	−0.0552408	+	0.170014i	−0.00435358	+	0.0133990i
$162$	−0.0640711	−	0.197191i	−0.00503390	−	0.0154928i
$163$	0.499565	−	0.362955i	0.0391290	−	0.0284289i	−0.568049	−	0.822995i	$-0.692302\pi$
$163$	0.499565	−	0.362955i	0.0391290	−	0.0284289i	0.607178	+	0.794566i	$0.292302\pi$
$164$	0.138649			0.0108267
$165$	−3.12046	−	0.181348i	−0.242928	−	0.0141179i
$166$	−2.56500			−0.199083
$167$	9.80970	−	7.12716i	0.759097	−	0.551516i	−0.139536	−	0.990217i	$-0.544561\pi$
$167$	9.80970	−	7.12716i	0.759097	−	0.551516i	0.898633	+	0.438701i	$0.144561\pi$
$168$	0.133767	+	0.411693i	0.0103203	+	0.0317628i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−0.557770	−	0.405244i	−0.0427790	−	0.0310808i
$171$	−5.58526	−	4.05793i	−0.427116	−	0.310318i
$172$	−3.23982	+	9.97116i	−0.247034	+	0.760293i
$173$	5.71720	+	17.5957i	0.434671	+	1.33778i	0.893424	+	0.449215i	$0.148296\pi$
$173$	5.71720	+	17.5957i	0.434671	+	1.33778i	−0.458753	+	0.888564i	$0.651704\pi$
$174$	−1.69694	+	1.23290i	−0.128645	+	0.0934661i
$175$	−2.16946			−0.163996
$176$	4.51580	−	11.5669i	0.340392	−	0.871888i
$177$	10.1858			0.765609
$178$	−2.15969	+	1.56911i	−0.161876	+	0.117610i
$179$	4.33249	+	13.3340i	0.323826	+	0.996632i	0.971968	+	0.235113i	$0.0755461\pi$
$179$	4.33249	+	13.3340i	0.323826	+	0.996632i	−0.648142	+	0.761519i	$0.724454\pi$
$180$	0.569942	−	1.75410i	0.0424809	−	0.130743i
$181$	−19.7922	−	14.3799i	−1.47114	−	1.06885i	−0.980280	−	0.197613i	$-0.936681\pi$
$181$	−19.7922	−	14.3799i	−1.47114	−	1.06885i	−0.490864	−	0.871236i	$-0.663319\pi$
$182$	−0.0885028	−	0.0643011i	−0.00656026	−	0.00476631i
$183$	−3.37505	+	10.3873i	−0.249491	+	0.767853i
$184$	−0.0858988	−	0.264369i	−0.00633255	−	0.0194896i
$185$	5.93293	−	4.31052i	0.436197	−	0.316916i
$186$	0.183071			0.0134234
$187$	4.25571	−	10.9007i	0.311209	−	0.797138i
$188$	−1.33500			−0.0973647
$189$	−0.426852	+	0.310126i	−0.0310489	+	0.0225584i
$190$	0.416872	+	1.28300i	0.0302431	+	0.0930786i
$191$	−1.27394	+	3.92078i	−0.0921790	+	0.283698i	−0.986508	−	0.163712i	$-0.947653\pi$
$191$	−1.27394	+	3.92078i	−0.0921790	+	0.283698i	0.894329	+	0.447409i	$0.147653\pi$
$192$	5.65233	+	4.10666i	0.407922	+	0.296372i
$193$	−4.71481	−	3.42551i	−0.339380	−	0.246574i	0.405020	−	0.914308i	$-0.367264\pi$
$193$	−4.71481	−	3.42551i	−0.339380	−	0.246574i	−0.744400	+	0.667734i	$0.767264\pi$
$194$	−0.294145	+	0.905286i	−0.0211184	+	0.0649957i
$195$	0.291231	+	0.896316i	0.0208555	+	0.0641865i
$196$	−10.6420	+	7.73189i	−0.760146	+	0.552278i
$197$	−20.0109			−1.42572			−0.712860	−	0.701306i	$-0.752601\pi$
$197$	−20.0109			−1.42572			−0.712860	+	0.701306i	$0.752601\pi$
$198$	−0.686505	−	0.0398967i	−0.0487878	−	0.00283534i
$199$	21.7784			1.54383			0.771915	−	0.635726i	$-0.219299\pi$
$199$	21.7784			1.54383			0.771915	+	0.635726i	$0.219299\pi$
$200$	2.72921	−	1.98289i	0.192984	−	0.140211i
$201$	3.54666	+	10.9155i	0.250162	+	0.769919i
$202$	0.555759	−	1.71045i	0.0391031	−	0.120347i
$203$	4.31825	+	3.13739i	0.303082	+	0.220202i
$204$	5.58617	+	4.05859i	0.391110	+	0.284158i
$205$	0.0206329	−	0.0635015i	0.00144106	−	0.00443514i
$206$	−0.953713	−	2.93523i	−0.0664483	−	0.204507i
$207$	0.274104	−	0.199148i	0.0190516	−	0.0138418i
$208$	−3.74391			−0.259594
$209$	−19.2739	+	12.3612i	−1.33320	+	0.855044i
$210$	0.103099			0.00711450
$211$	−0.255831	+	0.185872i	−0.0176121	+	0.0127959i	−0.596556	−	0.802571i	$-0.703465\pi$
$211$	−0.255831	+	0.185872i	−0.0176121	+	0.0127959i	0.578944	+	0.815367i	$0.303465\pi$
$212$	2.90416	+	8.93809i	0.199459	+	0.613870i
$213$	0.855498	−	2.63295i	0.0586177	−	0.180407i
$214$	2.24319	+	1.62977i	0.153341	+	0.111409i
$215$	4.08468	+	2.96770i	0.278573	+	0.202395i
$216$	0.253530	−	0.780285i	0.0172505	−	0.0530917i
$217$	−0.143960	−	0.443064i	−0.00977265	−	0.0300771i
$218$	0.129879	−	0.0943627i	0.00879652	−	0.00639105i
$219$	1.03396			0.0698686
$220$	−4.73188	−	3.87659i	−0.319023	−	0.261360i
$221$	−3.52828			−0.237338
$222$	1.30525	−	0.948320i	0.0876027	−	0.0636471i
$223$	6.49818	+	19.9993i	0.435150	+	1.33926i	0.892932	+	0.450191i	$0.148644\pi$
$223$	6.49818	+	19.9993i	0.435150	+	1.33926i	−0.457782	+	0.889065i	$0.651356\pi$
$224$	−0.394097	+	1.21291i	−0.0263317	+	0.0810407i
$225$	3.32652	+	2.41686i	0.221768	+	0.161124i
$226$	2.16037	+	1.56960i	0.143706	+	0.104408i
$227$	−2.38985	+	7.35521i	−0.158620	+	0.488182i	−0.998510	−	0.0545750i	$-0.982620\pi$
$227$	−2.38985	+	7.35521i	−0.158620	+	0.488182i	0.839890	+	0.542757i	$0.182620\pi$
$228$	−4.17505	−	12.8495i	−0.276499	−	0.850977i
$229$	−15.8766	+	11.5350i	−1.04915	+	0.762254i	−0.972051	−	0.234769i	$-0.924567\pi$
$229$	−15.8766	+	11.5350i	−1.04915	+	0.762254i	−0.0771015	+	0.997023i	$0.524567\pi$
$230$	−0.0662052			−0.00436544
$231$	0.443284	+	1.69283i	0.0291660	+	0.111380i
$232$	−8.29998			−0.544921
$233$	7.95550	−	5.78001i	0.521182	−	0.378661i	−0.295867	−	0.955229i	$-0.595609\pi$
$233$	7.95550	−	5.78001i	0.521182	−	0.378661i	0.817049	+	0.576568i	$0.195609\pi$
$234$	0.0640711	+	0.197191i	0.00418846	+	0.0128908i
$235$	−0.198666	+	0.611432i	−0.0129596	+	0.0398854i
$236$	16.1267	+	11.7167i	1.04976	+	0.762692i
$237$	9.74462	+	7.07988i	0.632981	+	0.459887i
$238$	−0.119274	+	0.367087i	−0.00773137	+	0.0237947i
$239$	−0.348901	−	1.07381i	−0.0225685	−	0.0694588i	0.939138	−	0.343540i	$-0.111626\pi$
$239$	−0.348901	−	1.07381i	−0.0225685	−	0.0694588i	−0.961706	+	0.274082i	$0.911626\pi$
$240$	2.85455	−	2.07395i	0.184261	−	0.133873i
$241$	−25.7065			−1.65590			−0.827951	−	0.560800i	$-0.810494\pi$
$241$	−25.7065			−1.65590			−0.827951	+	0.560800i	$0.810494\pi$
$242$	−0.951306	+	2.07285i	−0.0611523	+	0.133248i
$243$	1.00000			0.0641500
$244$	−17.2921	+	12.5635i	−1.10701	+	0.804293i
$245$	1.95754	+	6.02469i	0.125063	+	0.384904i
$246$	0.00453926	−	0.0139704i	0.000289413	−	0.000890721i
$247$	5.58526	+	4.05793i	0.355382	+	0.258200i
$248$	0.586064	+	0.425800i	0.0372151	+	0.0270383i
$249$	3.82287	−	11.7656i	0.242265	−	0.745615i
$250$	−0.550201	−	1.69334i	−0.0347978	−	0.107096i
$251$	−9.08084	+	6.59761i	−0.573177	+	0.416438i	−0.836258	−	0.548336i	$-0.815261\pi$
$251$	−9.08084	+	6.59761i	−0.573177	+	0.416438i	0.263081	+	0.964774i	$0.415261\pi$
$252$	−1.03255			−0.0650448
$253$	−0.284656	−	1.08706i	−0.0178962	−	0.0683427i
$254$	−2.92527			−0.183548
$255$	2.69014	−	1.95450i	0.168463	−	0.122396i
$256$	3.91544	+	12.0505i	0.244715	+	0.753156i
$257$	6.51602	−	20.0542i	0.406458	−	1.25095i	−0.513214	−	0.858261i	$-0.671545\pi$
$257$	6.51602	−	20.0542i	0.406458	−	1.25095i	0.919672	−	0.392688i	$-0.128455\pi$
$258$	0.898635	+	0.652897i	0.0559466	+	0.0406476i
$259$	−3.32150	−	2.41321i	−0.206388	−	0.149949i
$260$	−0.569942	+	1.75410i	−0.0353463	+	0.108785i
$261$	−3.12617	−	9.62136i	−0.193505	−	0.595547i
$262$	1.07520	−	0.781181i	0.0664263	−	0.0482615i
$263$	0.650490			0.0401109			0.0200555	−	0.999799i	$-0.493616\pi$
$263$	0.650490			0.0401109			0.0200555	+	0.999799i	$0.493616\pi$
$264$	−2.10491	−	1.72445i	−0.129548	−	0.106132i
$265$	4.52585			0.278020
$266$	0.611002	−	0.443919i	0.0374630	−	0.0272184i
$267$	−3.97866	−	12.2450i	−0.243490	−	0.749385i
$268$	−6.94084	+	21.3617i	−0.423980	+	1.30487i
$269$	−0.907149	−	0.659082i	−0.0553099	−	0.0401850i	0.559787	−	0.828637i	$-0.310883\pi$
$269$	−0.907149	−	0.659082i	−0.0553099	−	0.0401850i	−0.615097	+	0.788452i	$0.710883\pi$
$270$	−0.158086	−	0.114856i	−0.00962078	−	0.00698991i
$271$	1.83804	−	5.65691i	0.111653	−	0.343633i	−0.879581	−	0.475749i	$-0.842177\pi$
$271$	1.83804	−	5.65691i	0.111653	−	0.343633i	0.991234	+	0.132116i	$0.0421771\pi$
$272$	4.08198	+	12.5630i	0.247507	+	0.761747i
$273$	0.426852	−	0.310126i	0.0258343	−	0.0187697i
$274$	−4.29605			−0.259534
$275$	11.4793	−	7.36221i	0.692227	−	0.443958i
$276$	0.663057			0.0399114
$277$	−6.61545	+	4.80640i	−0.397484	+	0.288789i	−0.768515	−	0.639831i	$-0.779004\pi$
$277$	−6.61545	+	4.80640i	−0.397484	+	0.288789i	0.371032	+	0.928620i	$0.379004\pi$
$278$	−0.346843	−	1.06747i	−0.0208023	−	0.0640228i
$279$	−0.272849	+	0.839743i	−0.0163350	+	0.0502741i
$280$	0.330049	+	0.239795i	0.0197242	+	0.0143305i
$281$	−8.93811	−	6.49392i	−0.533203	−	0.387395i	0.288352	−	0.957525i	$-0.406893\pi$
$281$	−8.93811	−	6.49392i	−0.533203	−	0.387395i	−0.821555	+	0.570130i	$0.806893\pi$
$282$	−0.0437068	+	0.134516i	−0.00260270	+	0.00801030i
$283$	2.03622	+	6.26683i	0.121040	+	0.372524i	0.993159	−	0.116771i	$-0.0372542\pi$
$283$	2.03622	+	6.26683i	0.121040	+	0.372524i	−0.872118	+	0.489295i	$0.837254\pi$
$284$	4.38316	−	3.18455i	0.260093	−	0.188968i
$285$	−6.50640			−0.385406
$286$	0.686505	+	0.0398967i	0.0405939	+	0.00235914i
$287$	−0.0373803			−0.00220649
$288$	1.95551	−	1.42076i	0.115229	−	0.0837190i
$289$	−1.40641	−	4.32849i	−0.0827301	−	0.254617i
$290$	−0.610868	+	1.88006i	−0.0358714	+	0.110401i
$291$	−3.71413	−	2.69847i	−0.217726	−	0.158187i
$292$	1.63702	+	1.18937i	0.0957996	+	0.0696025i
$293$	−2.24869	+	6.92076i	−0.131370	+	0.404315i	−0.995008	−	0.0997976i	$-0.968180\pi$
$293$	−2.24869	+	6.92076i	−0.131370	+	0.404315i	0.863638	+	0.504113i	$0.168180\pi$
$294$	0.430662	+	1.32544i	0.0251167	+	0.0773012i
$295$	7.76615	−	5.64244i	0.452163	−	0.328516i
$296$	6.38416			0.371072
$297$	1.20617	−	3.08952i	0.0699892	−	0.179272i
$298$	4.25080			0.246242
$299$	−0.274104	+	0.199148i	−0.0158518	+	0.0115170i
$300$	2.48661	+	7.65300i	0.143565	+	0.441846i
$301$	0.873470	−	2.68826i	0.0503460	−	0.154949i
$302$	0.616104	+	0.447626i	0.0354528	+	0.0257580i
$303$	7.01749	+	5.09851i	0.403145	+	0.292902i
$304$	7.98719	−	24.5820i	0.458097	−	1.40988i
$305$	3.18079	+	9.78945i	0.182131	+	0.560543i
$306$	0.591835	−	0.429993i	0.0338329	−	0.0245811i
$307$	−11.8523			−0.676446			−0.338223	−	0.941066i	$-0.609826\pi$
$307$	−11.8523			−0.676446			−0.338223	+	0.941066i	$0.609826\pi$
$308$	−1.24544	+	3.19010i	−0.0709654	+	0.181773i
$309$	14.8852			0.846791
$310$	0.139583	−	0.101413i	0.00792778	−	0.00575987i
$311$	−8.21412	−	25.2805i	−0.465780	−	1.43352i	−0.857999	−	0.513652i	$-0.828292\pi$
$311$	−8.21412	−	25.2805i	−0.465780	−	1.43352i	0.392219	−	0.919872i	$-0.371708\pi$
$312$	−0.253530	+	0.780285i	−0.0143533	+	0.0441749i
$313$	9.96279	+	7.23839i	0.563130	+	0.409138i	0.832603	−	0.553870i	$-0.186850\pi$
$313$	9.96279	+	7.23839i	0.563130	+	0.409138i	−0.269473	+	0.963008i	$0.586850\pi$
$314$	−0.466446	−	0.338893i	−0.0263231	−	0.0191248i
$315$	−0.153659	+	0.472912i	−0.00865768	+	0.0266456i
$316$	7.28421	+	22.4185i	0.409769	+	1.26114i
$317$	−15.3712	+	11.1678i	−0.863331	+	0.627246i	−0.928789	−	0.370609i	$-0.879149\pi$
$317$	−15.3712	+	11.1678i	−0.863331	+	0.627246i	0.0654585	+	0.997855i	$0.479149\pi$
$318$	0.995691			0.0558356
$319$	−33.4961	−	1.94665i	−1.87542	−	0.108992i
$320$	6.58452			0.368086
$321$	−10.8190	+	7.86044i	−0.603856	+	0.438727i
$322$	0.0114535	+	0.0352504i	0.000638281	+	0.00196443i
$323$	7.52716	−	23.1662i	0.418822	−	1.28900i
$324$	1.58325	+	1.15030i	0.0879586	+	0.0639057i
$325$	−3.32652	−	2.41686i	−0.184522	−	0.134063i
$326$	0.0395637	−	0.121764i	0.00219123	−	0.00674391i
$327$	0.239268	+	0.736390i	0.0132315	+	0.0407225i
$328$	0.0470249	−	0.0341656i	0.00259652	−	0.00188648i
$329$	0.359921			0.0198431
$330$	−0.545528	+	0.349873i	−0.0300303	+	0.0192599i
$331$	4.05070			0.222647			0.111323	−	0.993784i	$-0.464491\pi$
$331$	4.05070			0.222647			0.111323	+	0.993784i	$0.464491\pi$
$332$	19.5866	−	14.2305i	1.07495	−	0.780999i
$333$	2.40458	+	7.40053i	0.131770	+	0.405547i
$334$	0.776891	−	2.39102i	0.0425096	−	0.130831i
$335$	8.75083	+	6.35785i	0.478109	+	0.347366i
$336$	−1.59810	−	1.16108i	−0.0871833	−	0.0633424i
$337$	4.18555	−	12.8818i	0.228001	−	0.701716i	−0.769972	−	0.638078i	$-0.779730\pi$
$337$	4.18555	−	12.8818i	0.228001	−	0.701716i	0.997973	−	0.0636380i	$-0.0202703\pi$
$338$	−0.0640711	−	0.197191i	−0.00348501	−	0.0107258i
$339$	−10.4195	+	7.57023i	−0.565911	+	0.411159i
$340$	6.50745			0.352916
$341$	2.26530	+	1.85585i	0.122673	+	0.100500i
$342$	−1.43142			−0.0774021
$343$	5.85710	−	4.25543i	0.316254	−	0.229772i
$344$	1.35824	+	4.18022i	0.0732312	+	0.225382i
$345$	0.0986722	−	0.303682i	0.00531233	−	0.0163497i
$346$	3.10341	+	2.25476i	0.166840	+	0.121216i
$347$	−24.0021	−	17.4386i	−1.28850	−	0.936151i	−0.288727	−	0.957411i	$-0.593232\pi$
$347$	−24.0021	−	17.4386i	−1.28850	−	0.936151i	−0.999774	+	0.0212604i	$0.993232\pi$
$348$	6.11795	−	18.8291i	0.327956	−	1.00935i
$349$	−6.90707	−	21.2578i	−0.369727	−	1.13790i	−0.946968	−	0.321329i	$-0.895871\pi$
$349$	−6.90707	−	21.2578i	−0.369727	−	1.13790i	0.577241	−	0.816574i	$-0.304129\pi$
$350$	−0.363906	+	0.264393i	−0.0194516	+	0.0141324i
$351$	−1.00000			−0.0533761
$352$	−2.03079	−	7.75526i	−0.108241	−	0.413357i
$353$	−1.62522			−0.0865020			−0.0432510	−	0.999064i	$-0.513772\pi$
$353$	−1.62522			−0.0865020			−0.0432510	+	0.999064i	$0.513772\pi$
$354$	1.70856	−	1.24134i	0.0908091	−	0.0659767i
$355$	−0.806257	−	2.48140i	−0.0427917	−	0.131699i
$356$	7.78627	−	23.9637i	0.412672	−	1.27007i
$357$	−1.50605	−	1.09421i	−0.0797088	−	0.0579118i
$358$	2.35176	+	1.70865i	0.124294	+	0.0903051i
$359$	2.00472	−	6.16988i	0.105805	−	0.325634i	−0.884114	−	0.467272i	$-0.845237\pi$
$359$	2.00472	−	6.16988i	0.105805	−	0.325634i	0.989919	+	0.141638i	$0.0452369\pi$
$360$	−0.238937	−	0.735374i	−0.0125931	−	0.0387576i
$361$	−23.1880	+	16.8471i	−1.22042	+	0.886687i
$362$	−5.07244			−0.266601
$363$	−8.09030	−	7.45299i	−0.424630	−	0.391181i
$364$	1.03255			0.0541205
$365$	0.788346	−	0.572767i	0.0412639	−	0.0299800i
$366$	0.699777	+	2.15369i	0.0365779	+	0.112575i
$367$	0.214010	−	0.658656i	0.0111712	−	0.0343816i	−0.945316	−	0.326157i	$-0.894246\pi$
$367$	0.214010	−	0.658656i	0.0111712	−	0.0343816i	0.956487	+	0.291776i	$0.0942461\pi$
$368$	1.02622	+	0.745594i	0.0534955	+	0.0388668i
$369$	0.0573167	+	0.0416430i	0.00298379	+	0.00216785i
$370$	0.469865	−	1.44610i	0.0244271	−	0.0751790i
$371$	−0.782973	−	2.40974i	−0.0406499	−	0.125108i
$372$	−1.39795	+	1.01567i	−0.0724802	+	0.0526600i
$373$	6.50359			0.336743			0.168371	−	0.985724i	$-0.446149\pi$
$373$	6.50359			0.336743			0.168371	+	0.985724i	$0.446149\pi$
$374$	−0.614618	−	2.34713i	−0.0317812	−	0.121367i
$375$	8.58735			0.443449
$376$	−0.452785	+	0.328967i	−0.0233506	+	0.0169652i
$377$	3.12617	+	9.62136i	0.161006	+	0.495525i
$378$	−0.0338051	+	0.104041i	−0.00173874	+	0.00535131i
$379$	−26.6599	−	19.3696i	−1.36943	−	0.994948i	−0.997781	−	0.0665742i	$-0.978793\pi$
$379$	−26.6599	−	19.3696i	−1.36943	−	0.994948i	−0.371647	−	0.928374i	$-0.621207\pi$
$380$	−10.3013	−	7.48432i	−0.528445	−	0.383938i
$381$	4.35983	−	13.4182i	0.223361	−	0.687433i
$382$	0.264137	+	0.812929i	0.0135144	+	0.0415931i
$383$	29.5464	−	21.4667i	1.50975	−	1.09690i	0.543465	−	0.839432i	$-0.317112\pi$
$383$	29.5464	−	21.4667i	1.50975	−	1.09690i	0.966287	−	0.257467i	$-0.0828878\pi$
$384$	6.28288			0.320622
$385$	1.27573	+	1.04515i	0.0650175	+	0.0532655i
$386$	−1.20833			−0.0615026
$387$	−4.33415	+	3.14894i	−0.220317	+	0.160070i
$388$	−2.77636	−	8.54475i	−0.140948	−	0.433794i
$389$	−5.28650	+	16.2702i	−0.268036	+	0.824931i	0.722942	+	0.690909i	$0.242789\pi$
$389$	−5.28650	+	16.2702i	−0.268036	+	0.824931i	−0.990978	+	0.134022i	$0.957211\pi$
$390$	0.158086	+	0.114856i	0.00800497	+	0.00581595i
$391$	0.967116	+	0.702651i	0.0489091	+	0.0355346i
$392$	−1.70413	+	5.24478i	−0.0860717	+	0.264901i
$393$	1.98078	+	6.09620i	0.0999169	+	0.307513i
$394$	−3.35664	+	2.43874i	−0.169105	+	0.122862i
$395$	11.3517			0.571167
$396$	5.46356	−	3.50404i	0.274554	−	0.176085i
$397$	11.2995			0.567108			0.283554	−	0.958956i	$-0.408486\pi$
$397$	11.2995			0.567108			0.283554	+	0.958956i	$0.408486\pi$
$398$	3.65312	−	2.65414i	0.183114	−	0.133040i
$399$	1.12561	+	3.46427i	0.0563510	+	0.173430i
$400$	−4.75708	+	14.6408i	−0.237854	+	0.732039i
$401$	15.2574	+	11.0852i	0.761919	+	0.553567i	0.899498	−	0.436924i	$-0.143932\pi$
$401$	15.2574	+	11.0852i	0.761919	+	0.553567i	−0.137579	+	0.990491i	$0.543932\pi$
$402$	1.92519	+	1.39873i	0.0960199	+	0.0697625i
$403$	0.272849	−	0.839743i	0.0135916	−	0.0418306i
$404$	5.24566	+	16.1445i	0.260981	+	0.803218i
$405$	0.762452	−	0.553954i	0.0378865	−	0.0275262i
$406$	1.10670			0.0549246
$407$	25.7644	+	1.49732i	1.27710	+	0.0742193i
$408$	2.89474			0.143311
$409$	−2.30814	+	1.67696i	−0.114130	+	0.0829206i	−0.643386	−	0.765542i	$-0.722471\pi$
$409$	−2.30814	+	1.67696i	−0.114130	+	0.0829206i	0.529256	+	0.848462i	$0.322471\pi$
$410$	−0.00427799	−	0.0131663i	−0.000211275	−	0.000650238i
$411$	6.40282	−	19.7059i	0.315828	−	0.972018i
$412$	23.5671	+	17.1225i	1.16107	+	0.843565i
$413$	−4.34781	−	3.15887i	−0.213942	−	0.155438i
$414$	0.0217080	−	0.0668104i	0.00106689	−	0.00328355i
$415$	−3.60284	−	11.0884i	−0.176856	−	0.544308i
$416$	−1.95551	+	1.42076i	−0.0958765	+	0.0696584i
$417$	5.41341			0.265096
$418$	−1.72653	+	4.42239i	−0.0844475	+	0.216306i
$419$	17.6109			0.860349			0.430175	−	0.902746i	$-0.358452\pi$
$419$	17.6109			0.860349			0.430175	+	0.902746i	$0.358452\pi$
$420$	−0.787273	+	0.571987i	−0.0384150	+	0.0279101i
$421$	−1.98884	−	6.12101i	−0.0969300	−	0.298320i	0.890822	−	0.454353i	$-0.150129\pi$
$421$	−1.98884	−	6.12101i	−0.0969300	−	0.298320i	−0.987752	+	0.156033i	$0.950129\pi$
$422$	−0.0202608	+	0.0623564i	−0.000986282	+	0.00303546i
$423$	−0.551880	−	0.400964i	−0.0268333	−	0.0194956i
$424$	3.18750	+	2.31585i	0.154798	+	0.112468i
$425$	−4.48309	+	13.7975i	−0.217462	+	0.669279i
$426$	−0.177378	−	0.545912i	−0.00859397	−	0.0264495i
$427$	4.66203	−	3.38716i	0.225611	−	0.163916i
$428$	−26.1711			−1.26503
$429$	−1.20617	+	3.08952i	−0.0582346	+	0.149164i
$430$	1.04684			0.0504831
$431$	−19.7612	+	14.3573i	−0.951863	+	0.691569i	−0.951247	−	0.308431i	$-0.900196\pi$
$431$	−19.7612	+	14.3573i	−0.951863	+	0.691569i	−0.000616153		1.00000i	$0.500196\pi$
$432$	1.15693	+	3.56067i	0.0556629	+	0.171313i
$433$	4.79538	−	14.7587i	0.230451	−	0.709257i	−0.767241	−	0.641359i	$-0.778371\pi$
$433$	4.79538	−	14.7587i	0.230451	−	0.709257i	0.997692	−	0.0678975i	$-0.0216291\pi$
$434$	−0.0781443	−	0.0567751i	−0.00375105	−	0.00272529i
$435$	−7.71334	−	5.60407i	−0.369826	−	0.268695i
$436$	−0.468250	+	1.44112i	−0.0224251	+	0.0690173i
$437$	−0.722813	−	2.22459i	−0.0345768	−	0.106417i
$438$	0.173437	−	0.126009i	0.00828714	−	0.00602096i
$439$	−10.4724			−0.499822			−0.249911	−	0.968269i	$-0.580401\pi$
$439$	−10.4724			−0.499822			−0.249911	+	0.968269i	$0.580401\pi$
$440$	−2.56015	−	0.148785i	−0.122051	−	0.00709305i
$441$	−6.72162			−0.320077
$442$	−0.591835	+	0.429993i	−0.0281507	+	0.0204527i
$443$	−11.8375	−	36.4322i	−0.562418	−	1.73095i	−0.675500	−	0.737360i	$-0.736072\pi$
$443$	−11.8375	−	36.4322i	−0.562418	−	1.73095i	0.113081	−	0.993586i	$-0.463928\pi$
$444$	−4.70579	+	14.4829i	−0.223327	+	0.687329i
$445$	−9.81672	−	7.13226i	−0.465357	−	0.338102i
$446$	3.52734	+	2.56276i	0.167024	+	0.121350i
$447$	−6.33539	+	19.4983i	−0.299654	+	0.922239i
$448$	−1.13913	−	3.50587i	−0.0538186	−	0.165637i
$449$	18.1476	−	13.1850i	0.856438	−	0.622238i	−0.0704759	−	0.997513i	$-0.522452\pi$
$449$	18.1476	−	13.1850i	0.856438	−	0.622238i	0.926913	+	0.375275i	$0.122452\pi$
$450$	0.852535			0.0401889
$451$	0.197791	−	0.126852i	0.00931360	−	0.00597325i
$452$	−25.2048			−1.18554
$453$	−2.97149	+	2.15891i	−0.139613	+	0.101435i
$454$	0.495508	+	1.52502i	0.0232553	+	0.0715726i
$455$	0.153659	−	0.472912i	0.00720362	−	0.0221705i
$456$	−4.58237	−	3.32929i	−0.214589	−	0.155908i
$457$	−26.1719	−	19.0150i	−1.22427	−	0.889484i	−0.227822	−	0.973703i	$-0.573160\pi$
$457$	−26.1719	−	19.0150i	−1.22427	−	0.889484i	−0.996447	+	0.0842192i	$0.973160\pi$
$458$	−1.25736	+	3.86977i	−0.0587527	+	0.180822i
$459$	1.09030	+	3.35559i	0.0508908	+	0.156626i
$460$	0.505549	−	0.367303i	0.0235714	−	0.0171256i
$461$	−12.0012			−0.558953			−0.279476	−	0.960153i	$-0.590161\pi$
$461$	−12.0012			−0.558953			−0.279476	+	0.960153i	$0.590161\pi$
$462$	0.280663	+	0.229933i	0.0130576	+	0.0106975i
$463$	−5.62191			−0.261272			−0.130636	−	0.991430i	$-0.541702\pi$
$463$	−5.62191			−0.261272			−0.130636	+	0.991430i	$0.541702\pi$
$464$	30.6418	−	22.2625i	1.42251	−	1.03351i
$465$	0.257144	+	0.791409i	0.0119248	+	0.0367007i
$466$	0.630046	−	1.93908i	0.0291863	−	0.0898262i
$467$	−12.4293	−	9.03044i	−0.575161	−	0.417879i	0.261815	−	0.965118i	$-0.415679\pi$
$467$	−12.4293	−	9.03044i	−0.575161	−	0.417879i	−0.836976	+	0.547239i	$0.815679\pi$
$468$	−1.58325	−	1.15030i	−0.0731860	−	0.0531727i
$469$	1.87128	−	5.75921i	0.0864077	−	0.265935i
$470$	0.0411912	+	0.126773i	0.00190001	+	0.00584762i
$471$	2.24968	−	1.63449i	0.103660	−	0.0753133i
$472$	8.35681			0.384653
$473$	4.50100	+	17.1886i	0.206956	+	0.790333i
$474$	2.49739			0.114709
$475$	22.9655	−	16.6854i	1.05373	−	0.765579i
$476$	−1.12579	−	3.46483i	−0.0516006	−	0.158810i
$477$	−1.48398	+	4.56721i	−0.0679467	+	0.209118i
$478$	−0.189390	−	0.137600i	−0.00866250	−	0.00629368i
$479$	−3.32788	−	2.41785i	−0.152055	−	0.110474i	0.509157	−	0.860674i	$-0.329957\pi$
$479$	−3.32788	−	2.41785i	−0.152055	−	0.110474i	−0.661212	+	0.750200i	$0.729957\pi$
$480$	0.703945	−	2.16652i	0.0321305	−	0.0988876i
$481$	−2.40458	−	7.40053i	−0.109639	−	0.337435i
$482$	−4.31202	+	3.13287i	−0.196407	+	0.142698i
$483$	−0.178763			−0.00813399
$484$	−4.23581	−	21.1063i	−0.192537	−	0.959376i
$485$	−4.32668			−0.196464
$486$	0.167740	−	0.121870i	0.00760885	−	0.00552816i
$487$	12.5572	+	38.6472i	0.569023	+	1.75127i	0.655685	+	0.755035i	$0.272380\pi$
$487$	12.5572	+	38.6472i	0.569023	+	1.75127i	−0.0866619	+	0.996238i	$0.527620\pi$
$488$	−2.76902	+	8.52218i	−0.125348	+	0.385781i
$489$	0.499565	+	0.362955i	0.0225911	+	0.0164134i
$490$	1.06259	+	0.772017i	0.0480030	+	0.0348762i
$491$	0.454521	−	1.39887i	0.0205123	−	0.0631302i	−0.940276	−	0.340412i	$-0.889434\pi$
$491$	0.454521	−	1.39887i	0.0205123	−	0.0631302i	0.960789	+	0.277282i	$0.0894335\pi$
$492$	0.0428449	+	0.131863i	0.00193160	+	0.00594484i
$493$	28.8769	−	20.9803i	1.30055	−	0.944906i
$494$	1.43142			0.0644024
$495$	−0.791804	−	3.02378i	−0.0355889	−	0.135909i
$496$	−3.30572			−0.148431
$497$	−1.18172	+	0.858568i	−0.0530073	+	0.0385120i
$498$	−0.792629	−	2.43946i	−0.0355185	−	0.109315i
$499$	10.3322	−	31.7994i	0.462534	−	1.42353i	−0.399523	−	0.916723i	$-0.630824\pi$
$499$	10.3322	−	31.7994i	0.462534	−	1.42353i	0.862057	−	0.506811i	$-0.169176\pi$
$500$	13.5960	+	9.87804i	0.608030	+	0.441760i
$501$	9.80970	+	7.12716i	0.438265	+	0.318418i
$502$	−0.719168	+	2.21337i	−0.0320980	+	0.0987876i
$503$	5.88072	+	18.0990i	0.262208	+	0.806994i	0.992323	+	0.123670i	$0.0394665\pi$
$503$	5.88072	+	18.0990i	0.262208	+	0.806994i	−0.730115	+	0.683324i	$0.760534\pi$
$504$	−0.350207	+	0.254440i	−0.0155994	+	0.0113337i
$505$	8.17484			0.363776
$506$	−0.180229	−	0.147652i	−0.00801214	−	0.00656394i
$507$	1.00000			0.0444116
$508$	22.3377	−	16.2293i	0.991073	−	0.720057i
$509$	−9.34297	−	28.7547i	−0.414120	−	1.27453i	−0.913036	−	0.407880i	$-0.866268\pi$
$509$	−9.34297	−	28.7547i	−0.414120	−	1.27453i	0.498916	−	0.866651i	$-0.333732\pi$
$510$	0.213049	−	0.655698i	0.00943398	−	0.0290348i
$511$	−0.441348	−	0.320658i	−0.0195241	−	0.0141851i
$512$	12.2913	+	8.93014i	0.543203	+	0.394660i
$513$	2.13338	−	6.56587i	0.0941910	−	0.289890i
$514$	−1.35102	−	4.15801i	−0.0595910	−	0.183402i
$515$	11.3493	−	8.24573i	0.500109	−	0.363350i
$516$	−10.4843			−0.461545
$517$	−1.90445	+	1.22141i	−0.0837577	+	0.0537177i
$518$	−0.851248			−0.0374017
$519$	−14.9678	+	10.8748i	−0.657015	+	0.477349i
$520$	0.238937	+	0.735374i	0.0104781	+	0.0322483i
$521$	−7.43374	+	22.8787i	−0.325678	+	1.00233i	0.645456	+	0.763798i	$0.276668\pi$
$521$	−7.43374	+	22.8787i	−0.325678	+	1.00233i	−0.971134	+	0.238536i	$0.923332\pi$
$522$	−1.69694	−	1.23290i	−0.0742733	−	0.0539627i
$523$	33.7788	+	24.5418i	1.47705	+	1.07314i	0.978494	+	0.206276i	$0.0661344\pi$
$523$	33.7788	+	24.5418i	1.47705	+	1.07314i	0.498551	+	0.866860i	$0.333866\pi$
$524$	−3.87640	+	11.9303i	−0.169341	+	0.521179i
$525$	−0.670400	−	2.06328i	−0.0292587	−	0.0900489i
$526$	0.109113	−	0.0792755i	0.00475757	−	0.00345658i
$527$	−3.11532			−0.135706
$528$	12.3962	+	0.720416i	0.539477	+	0.0313521i
$529$	−22.8852			−0.995009
$530$	0.759167	−	0.551567i	0.0329761	−	0.0239585i
$531$	3.14757	+	9.68724i	0.136593	+	0.420390i
$532$	−2.20283	+	6.77961i	−0.0955048	+	0.293934i
$533$	−0.0573167	−	0.0416430i	−0.00248266	−	0.00180376i
$534$	−2.15969	−	1.56911i	−0.0934589	−	0.0679019i
$535$	−3.89462	+	11.9864i	−0.168379	+	0.518218i
$536$	2.90982	+	8.95551i	0.125685	+	0.386819i
$537$	−11.3426	+	8.24089i	−0.489470	+	0.355620i
$538$	−0.232488			−0.0100233
$539$	−8.10743	+	20.7666i	−0.349212	+	0.894480i
$540$	1.84437			0.0793690
$541$	−14.1733	+	10.2975i	−0.609360	+	0.442726i	−0.849189	−	0.528089i	$-0.822909\pi$
$541$	−14.1733	+	10.2975i	−0.609360	+	0.442726i	0.239829	+	0.970815i	$0.422909\pi$
$542$	−0.381097	−	1.17290i	−0.0163695	−	0.0503802i
$543$	7.55996	−	23.2672i	0.324429	−	0.998489i
$544$	6.89957	+	5.01283i	0.295817	+	0.214923i
$545$	0.590356	+	0.428919i	0.0252881	+	0.0183729i
$546$	0.0338051	−	0.104041i	0.00144672	−	0.00445256i
$547$	−2.56635	−	7.89842i	−0.109729	−	0.337712i	0.881082	−	0.472964i	$-0.156816\pi$
$547$	−2.56635	−	7.89842i	−0.109729	−	0.337712i	−0.990811	+	0.135251i	$0.956816\pi$
$548$	32.8050	−	23.8342i	1.40136	−	1.01815i
$549$	−10.9219			−0.466134
$550$	1.02830	−	2.63392i	0.0438470	−	0.112311i
$551$	−69.8419			−2.97536
$552$	0.224886	−	0.163389i	0.00957179	−	0.00695431i
$553$	−1.96385	−	6.04412i	−0.0835115	−	0.257022i
$554$	−0.523919	+	1.61246i	−0.0222592	+	0.0685067i
$555$	5.93293	+	4.31052i	0.251839	+	0.182972i
$556$	8.57081	+	6.22706i	0.363483	+	0.264086i
$557$	−0.857123	+	2.63795i	−0.0363175	+	0.111774i	−0.967572	−	0.252596i	$-0.918716\pi$
$557$	−0.857123	+	2.63795i	−0.0363175	+	0.111774i	0.931254	+	0.364370i	$0.118716\pi$
$558$	0.0565721	+	0.174111i	0.00239489	+	0.00737071i
$559$	4.33415	−	3.14894i	0.183315	−	0.133186i
$560$	−1.86166			−0.0786694
$561$	11.6823	+	0.678923i	0.493226	+	0.0286642i
$562$	−2.29070			−0.0966273
$563$	2.40671	−	1.74858i	0.101431	−	0.0736938i	−0.535914	−	0.844273i	$-0.680033\pi$
$563$	2.40671	−	1.74858i	0.101431	−	0.0736938i	0.637345	+	0.770579i	$0.280033\pi$
$564$	−0.412537	−	1.26966i	−0.0173709	−	0.0534622i
$565$	−3.75083	+	11.5439i	−0.157799	+	0.485654i
$566$	1.10530	+	0.803045i	0.0464591	+	0.0337545i
$567$	−0.426852	−	0.310126i	−0.0179261	−	0.0130241i
$568$	0.701885	−	2.16018i	0.0294504	−	0.0906391i
$569$	0.149422	+	0.459873i	0.00626409	+	0.0192789i	0.954140	−	0.299362i	$-0.0967737\pi$
$569$	0.149422	+	0.459873i	0.00626409	+	0.0192789i	−0.947876	+	0.318641i	$0.896774\pi$
$570$	−1.09138	+	0.792938i	−0.0457131	+	0.0332125i
$571$	20.5258			0.858979			0.429489	−	0.903072i	$-0.358694\pi$
$571$	20.5258			0.858979			0.429489	+	0.903072i	$0.358694\pi$
$572$	−5.46356	+	3.50404i	−0.228443	+	0.146511i
$573$	−4.12255			−0.172222
$574$	−0.00627018	+	0.00455556i	−0.000261712	+	0.000190145i
$575$	0.430499	+	1.32494i	0.0179531	+	0.0552538i
$576$	−2.15900	+	6.64471i	−0.0899582	+	0.276863i
$577$	10.1834	+	7.39868i	0.423941	+	0.308011i	0.779222	−	0.626748i	$-0.215615\pi$
$577$	10.1834	+	7.39868i	0.423941	+	0.308011i	−0.355280	+	0.934760i	$0.615615\pi$
$578$	−0.763427	−	0.554662i	−0.0317544	−	0.0230709i
$579$	1.80090	−	5.54260i	0.0748428	−	0.230342i
$580$	−5.76581	−	17.7453i	−0.239412	−	0.736835i
$581$	−5.28062	+	3.83660i	−0.219077	+	0.159169i
$582$	−0.951874			−0.0394564
$583$	12.3206	+	10.0936i	0.510266	+	0.418035i
$584$	0.848304			0.0351031
$585$	−0.762452	+	0.553954i	−0.0315235	+	0.0229032i
$586$	0.466240	+	1.43494i	0.0192602	+	0.0592768i
$587$	2.39113	−	7.35916i	0.0986927	−	0.303745i	−0.889506	−	0.456924i	$-0.848951\pi$
$587$	2.39113	−	7.35916i	0.0986927	−	0.303745i	0.988198	+	0.153179i	$0.0489511\pi$
$588$	−10.6420	−	7.73189i	−0.438870	−	0.318858i
$589$	4.93155	+	3.58298i	0.203201	+	0.147634i
$590$	0.615050	−	1.89293i	0.0253212	−	0.0779307i
$591$	−6.18372	−	19.0315i	−0.254364	−	0.782853i
$592$	−23.5689	+	17.1238i	−0.968677	+	0.703785i
$593$	27.4083			1.12552			0.562762	−	0.826619i	$-0.309739\pi$
$593$	27.4083			1.12552			0.562762	+	0.826619i	$0.309739\pi$
$594$	−0.174198	−	0.665234i	−0.00714742	−	0.0272949i
$595$	−1.75444			−0.0719248
$596$	−32.4595	+	23.5832i	−1.32959	+	0.966006i
$597$	6.72990	+	20.7125i	0.275436	+	0.847706i
$598$	−0.0217080	+	0.0668104i	−0.000887707	+	0.00273208i
$599$	−8.14899	−	5.92059i	−0.332959	−	0.241909i	0.408726	−	0.912657i	$-0.365973\pi$
$599$	−8.14899	−	5.92059i	−0.332959	−	0.241909i	−0.741685	+	0.670748i	$0.765973\pi$
$600$	2.72921	+	1.98289i	0.111420	+	0.0809510i
$601$	−6.27513	+	19.3129i	−0.255968	+	0.787788i	0.737670	+	0.675162i	$0.235926\pi$
$601$	−6.27513	+	19.3129i	−0.255968	+	0.787788i	−0.993637	+	0.112626i	$0.964074\pi$
$602$	−0.181104	−	0.557380i	−0.00738124	−	0.0227171i
$603$	−9.28527	+	6.74614i	−0.378125	+	0.274724i
$604$	−7.18802			−0.292477
$605$	−10.2971	−	1.20090i	−0.418636	−	0.0488235i
$606$	1.79847			0.0730580
$607$	1.74297	−	1.26634i	0.0707450	−	0.0513992i	−0.551851	−	0.833943i	$-0.686078\pi$
$607$	1.74297	−	1.26634i	0.0707450	−	0.0513992i	0.622596	+	0.782544i	$0.286078\pi$
$608$	−5.15667	−	15.8706i	−0.209131	−	0.643638i
$609$	−1.64942	+	5.07640i	−0.0668380	+	0.205706i
$610$	1.72659	+	1.25444i	0.0699076	+	0.0507909i
$611$	0.551880	+	0.400964i	0.0223267	+	0.0162213i
$612$	−2.13373	+	6.56693i	−0.0862507	+	0.265452i
$613$	11.9621	+	36.8157i	0.483147	+	1.48697i	0.834647	+	0.550785i	$0.185671\pi$
$613$	11.9621	+	36.8157i	0.483147	+	1.48697i	−0.351501	+	0.936188i	$0.614329\pi$
$614$	−1.98811	+	1.44444i	−0.0802334	+	0.0582930i
$615$	0.0667695			0.00269241
$616$	0.363688	+	1.38887i	0.0146534	+	0.0559591i
$617$	−18.5980			−0.748729			−0.374364	−	0.927282i	$-0.622139\pi$
$617$	−18.5980			−0.748729			−0.374364	+	0.927282i	$0.622139\pi$
$618$	2.49685	−	1.81407i	0.100438	−	0.0729726i
$619$	−0.244394	−	0.752167i	−0.00982301	−	0.0302321i	0.946025	−	0.324094i	$-0.105059\pi$
$619$	−0.244394	−	0.752167i	−0.00982301	−	0.0302321i	−0.955848	+	0.293862i	$0.905059\pi$
$620$	−0.503235	+	1.54880i	−0.0202104	+	0.0622012i
$621$	0.274104	+	0.199148i	0.0109994	+	0.00799154i
$622$	−4.45878	−	3.23949i	−0.178781	−	0.129892i
$623$	−2.09921	+	6.46071i	−0.0841031	+	0.258843i
$624$	−1.15693	−	3.56067i	−0.0463144	−	0.142541i
$625$	−10.0852	+	7.32729i	−0.403406	+	0.293092i
$626$	2.55331			0.102051
$627$	−17.7122	−	14.5107i	−0.707356	−	0.579501i
$628$	5.44198			0.217159
$629$	−22.2115	+	16.1376i	−0.885629	+	0.643447i
$630$	0.0318593	+	0.0980529i	0.00126931	+	0.00390652i
$631$	−13.8914	+	42.7533i	−0.553007	+	1.70198i	0.148142	+	0.988966i	$0.452671\pi$
$631$	−13.8914	+	42.7533i	−0.553007	+	1.70198i	−0.701149	+	0.713015i	$0.747329\pi$
$632$	7.99488	+	5.80862i	0.318019	+	0.231054i
$633$	−0.255831	−	0.185872i	−0.0101684	−	0.00738774i
$634$	−1.21734	+	3.74658i	−0.0483467	+	0.148796i
$635$	−4.10888	−	12.6458i	−0.163056	−	0.501835i
$636$	−7.60319	+	5.52404i	−0.301486	+	0.219042i
$637$	6.72162			0.266320
$638$	−5.85589	+	3.75566i	−0.231837	+	0.148688i
$639$	2.76845			0.109518
$640$	4.79039	−	3.48042i	0.189357	−	0.137576i
$641$	−11.5217	−	35.4603i	−0.455082	−	1.40060i	−0.871039	−	0.491213i	$-0.836554\pi$
$641$	−11.5217	−	35.4603i	−0.455082	−	1.40060i	0.415958	−	0.909384i	$-0.363446\pi$
$642$	−0.856821	+	2.63702i	−0.0338160	+	0.104075i
$643$	6.31172	+	4.58573i	0.248910	+	0.180844i	0.705244	−	0.708965i	$-0.250838\pi$
$643$	6.31172	+	4.58573i	0.248910	+	0.180844i	−0.456334	+	0.889809i	$0.650838\pi$
$644$	−0.283027	−	0.205631i	−0.0111528	−	0.00810301i
$645$	−1.56021	+	4.80183i	−0.0614332	+	0.189072i
$646$	−1.56067	−	4.80325i	−0.0614037	−	0.188981i
$647$	3.68715	−	2.67887i	0.144957	−	0.105317i	−0.512943	−	0.858423i	$-0.671445\pi$
$647$	3.68715	−	2.67887i	0.144957	−	0.105317i	0.657900	+	0.753105i	$0.271445\pi$
$648$	0.820440			0.0322299
$649$	33.7254	+	1.95998i	1.32384	+	0.0769359i
$650$	−0.852535			−0.0334392
$651$	0.376892	−	0.273828i	0.0147716	−	0.0107322i
$652$	0.373431	+	1.14930i	0.0146247	+	0.0450101i
$653$	−2.16562	+	6.66509i	−0.0847472	+	0.260825i	−0.984446	−	0.175685i	$-0.943786\pi$
$653$	−2.16562	+	6.66509i	−0.0847472	+	0.260825i	0.899699	+	0.436511i	$0.143786\pi$
$654$	0.129879	+	0.0943627i	0.00507867	+	0.00368987i
$655$	4.88726	+	3.55080i	0.190961	+	0.138741i
$656$	−0.0819655	+	0.252264i	−0.00320022	+	0.00984926i
$657$	0.319512	+	0.983356i	0.0124653	+	0.0383644i
$658$	0.0603732	−	0.0438637i	0.00235359	−	0.00170999i
$659$	0.866629			0.0337591			0.0168795	−	0.999858i	$-0.494627\pi$
$659$	0.866629			0.0337591			0.0168795	+	0.999858i	$0.494627\pi$
$660$	2.22463	−	5.69822i	0.0865935	−	0.221803i
$661$	40.6341			1.58048			0.790241	−	0.612796i	$-0.209955\pi$
$661$	40.6341			1.58048			0.790241	+	0.612796i	$0.209955\pi$
$662$	0.679466	−	0.493661i	0.0264082	−	0.0191867i
$663$	−1.09030	−	3.35559i	−0.0423437	−	0.130320i
$664$	3.13644	−	9.65297i	0.121718	−	0.374608i
$665$	2.77727	+	2.01780i	0.107698	+	0.0782471i
$666$	1.30525	+	0.948320i	0.0505774	+	0.0367467i
$667$	1.05918	−	3.25983i	0.0410117	−	0.126221i
$668$	7.33286	+	22.5682i	0.283717	+	0.873191i
$669$	−17.0125	+	12.3603i	−0.657740	+	0.477876i
$670$	2.24270			0.0866431
$671$	−13.1737	+	33.7434i	−0.508564	+	1.30265i
$672$	−1.27533			−0.0491967
$673$	−37.0448	+	26.9146i	−1.42797	+	1.03748i	−0.437583	+	0.899178i	$0.644165\pi$
$673$	−37.0448	+	26.9146i	−1.42797	+	1.03748i	−0.990390	+	0.138305i	$0.955835\pi$
$674$	−0.867825	−	2.67089i	−0.0334274	−	0.102879i
$675$	−1.27062	+	3.91056i	−0.0489061	+	0.150517i
$676$	1.58325	+	1.15030i	0.0608944	+	0.0442424i
$677$	34.8327	+	25.3075i	1.33873	+	0.972645i	0.999490	+	0.0319455i	$0.0101703\pi$
$677$	34.8327	+	25.3075i	1.33873	+	0.972645i	0.339241	+	0.940699i	$0.389830\pi$
$678$	−0.825188	+	2.53967i	−0.0316911	+	0.0975353i
$679$	0.748517	+	2.30370i	0.0287254	+	0.0884078i
$680$	2.20710	−	1.60355i	0.0846385	−	0.0614935i
$681$	−7.73372			−0.296357
$682$	0.606156	+	0.0352272i	0.0232109	+	0.00134892i
$683$	−34.3677			−1.31504			−0.657522	−	0.753436i	$-0.728395\pi$
$683$	−34.3677			−1.31504			−0.657522	+	0.753436i	$0.728395\pi$
$684$	10.9304	−	7.94141i	0.417935	−	0.303647i
$685$	−6.03429	−	18.5716i	−0.230558	−	0.709586i
$686$	0.463860	−	1.42761i	0.0177103	−	0.0545066i
$687$	−15.8766	−	11.5350i	−0.605729	−	0.440088i
$688$	−16.2267	−	11.7894i	−0.618636	−	0.449465i
$689$	1.48398	−	4.56721i	0.0565350	−	0.173997i
$690$	−0.0204585	−	0.0629649i	−0.000778844	−	0.00239703i
$691$	7.58417	−	5.51022i	0.288515	−	0.209619i	−0.434108	−	0.900861i	$-0.642936\pi$
$691$	7.58417	−	5.51022i	0.288515	−	0.209619i	0.722623	+	0.691242i	$0.242936\pi$
$692$	−36.2072			−1.37639
$693$	−1.47300	+	0.944703i	−0.0559546	+	0.0358863i
$694$	−6.15137			−0.233503
$695$	4.12746	−	2.99878i	0.156564	−	0.113750i
$696$	−2.56484	−	7.89375i	−0.0972199	−	0.299212i
$697$	−0.0772447	+	0.237735i	−0.00292585	+	0.00900484i
$698$	−3.74929	−	2.72402i	−0.141913	−	0.103106i
$699$	7.95550	+	5.78001i	0.300905	+	0.218620i
$700$	1.31198	−	4.03786i	0.0495882	−	0.152617i
$701$	8.40420	+	25.8655i	0.317422	+	0.976925i	0.974746	+	0.223317i	$0.0716884\pi$
$701$	8.40420	+	25.8655i	0.317422	+	0.976925i	−0.657324	+	0.753608i	$0.728312\pi$
$702$	−0.167740	+	0.121870i	−0.00633095	+	0.00459970i
$703$	53.7208			2.02612
$704$	17.9249	+	14.6849i	0.675568	+	0.553459i
$705$	−0.642898			−0.0242129
$706$	−0.272616	+	0.198067i	−0.0102600	+	0.00745434i
$707$	−1.41425	−	4.35262i	−0.0531884	−	0.163697i
$708$	−6.15984	+	18.9580i	−0.231501	+	0.712486i
$709$	−3.23196	−	2.34816i	−0.121379	−	0.0881869i	0.525440	−	0.850831i	$-0.323901\pi$
$709$	−3.23196	−	2.34816i	−0.121379	−	0.0881869i	−0.646818	+	0.762644i	$0.723901\pi$
$710$	−0.437652	−	0.317973i	−0.0164248	−	0.0119333i
$711$	−3.72211	+	11.4555i	−0.139590	+	0.429614i
$712$	−3.26425	−	10.0463i	−0.122333	−	0.376502i
$713$	−0.242022	+	0.175840i	−0.00906381	+	0.00658524i
$714$	−0.385978			−0.0144449
$715$	0.791804	+	3.02378i	0.0296118	+	0.113083i
$716$	−27.4377			−1.02540
$717$	0.913435	−	0.663649i	0.0341128	−	0.0247844i
$718$	−0.415655	−	1.27925i	−0.0155121	−	0.0477413i
$719$	0.500790	−	1.54127i	0.0186763	−	0.0574798i	−0.941284	−	0.337616i	$-0.890380\pi$
$719$	0.500790	−	1.54127i	0.0186763	−	0.0574798i	0.959960	+	0.280136i	$0.0903795\pi$
$720$	2.85455	+	2.07395i	0.106383	+	0.0772917i
$721$	−6.35379	−	4.61630i	−0.236627	−	0.171920i
$722$	−1.83640	+	5.65186i	−0.0683438	+	0.210340i
$723$	−7.94375	−	24.4484i	−0.295431	−	0.909244i
$724$	38.7336	−	28.1416i	1.43952	−	1.04587i
$725$	41.5970			1.54488
$726$	−2.26537	−	0.264199i	−0.0840757	−	0.00980536i
$727$	40.0709			1.48615			0.743074	−	0.669210i	$-0.233367\pi$
$727$	40.0709			1.48615			0.743074	+	0.669210i	$0.233367\pi$
$728$	0.350207	−	0.254440i	0.0129795	−	0.00943017i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.0624340	−	0.192152i	0.00231079	−	0.00711187i
$731$	−15.2921	−	11.1103i	−0.565598	−	0.410931i
$732$	−17.2921	−	12.5635i	−0.639135	−	0.464359i
$733$	−6.86238	+	21.1202i	−0.253468	+	0.780093i	0.740660	+	0.671880i	$0.234513\pi$
$733$	−6.86238	+	21.1202i	−0.253468	+	0.780093i	−0.994128	+	0.108213i	$0.965487\pi$
$734$	−0.0443726	−	0.136565i	−0.00163782	−	0.00504070i
$735$	−5.12491	+	3.72347i	−0.189035	+	0.137342i
$736$	0.818954			0.0301870
$737$	9.64272	+	36.8240i	0.355194	+	1.35643i
$738$	0.0146894			0.000540723
$739$	−25.4295	+	18.4756i	−0.935440	+	0.679637i	−0.947319	−	0.320292i	$-0.896219\pi$
$739$	−25.4295	+	18.4756i	−0.935440	+	0.679637i	0.0118784	+	0.999929i	$0.496219\pi$
$740$	4.43493	+	13.6493i	0.163031	+	0.501759i
$741$	−2.13338	+	6.56587i	−0.0783717	+	0.241203i
$742$	−0.425013	−	0.308790i	−0.0156027	−	0.0113360i
$743$	−9.80734	−	7.12545i	−0.359797	−	0.261407i	0.393171	−	0.919465i	$-0.371378\pi$
$743$	−9.80734	−	7.12545i	−0.359797	−	0.261407i	−0.752967	+	0.658058i	$0.771378\pi$
$744$	−0.223856	+	0.688959i	−0.00820697	+	0.0252585i
$745$	5.97074	+	18.3760i	0.218751	+	0.673246i
$746$	1.09091	−	0.792595i	0.0399412	−	0.0290190i
$747$	12.3711			0.452634
$748$	17.7150	+	14.5130i	0.647726	+	0.530650i
$749$	7.05582			0.257814
$750$	1.44044	−	1.04654i	0.0525976	−	0.0382144i
$751$	11.4856	+	35.3490i	0.419115	+	1.28990i	0.908518	+	0.417846i	$0.137215\pi$
$751$	11.4856	+	35.3490i	0.419115	+	1.28990i	−0.489403	+	0.872058i	$0.662785\pi$
$752$	0.789215	−	2.42895i	0.0287797	−	0.0885748i
$753$	−9.08084	−	6.59761i	−0.330924	−	0.240430i
$754$	1.69694	+	1.23290i	0.0617991	+	0.0448997i
$755$	−1.06968	+	3.29213i	−0.0389296	+	0.119813i
$756$	−0.319077	−	0.982017i	−0.0116047	−	0.0357156i
$757$	−1.21517	+	0.882871i	−0.0441660	+	0.0320885i	−0.609649	−	0.792671i	$-0.708690\pi$
$757$	−1.21517	+	0.882871i	−0.0441660	+	0.0320885i	0.565483	+	0.824760i	$0.308690\pi$
$758$	−6.83252			−0.248168
$759$	0.945890	−	0.606644i	0.0343336	−	0.0220198i
$760$	−5.33811			−0.193634
$761$	34.9984	−	25.4278i	1.26869	−	0.921758i	0.269541	−	0.962989i	$-0.413128\pi$
$761$	34.9984	−	25.4278i	1.26869	−	0.921758i	0.999150	+	0.0412312i	$0.0131280\pi$
$762$	−0.903959	−	2.78210i	−0.0327470	−	0.100785i
$763$	0.126242	−	0.388533i	0.00457027	−	0.0140658i
$764$	−6.52705	−	4.74218i	−0.236141	−	0.171566i
$765$	2.69014	+	1.95450i	0.0972623	+	0.0706652i
$766$	2.33997	−	7.20167i	0.0845464	−	0.260207i
$767$	−3.14757	−	9.68724i	−0.113652	−	0.349786i
$768$	−10.2508	+	7.44761i	−0.369892	+	0.268743i
$769$	−1.90908			−0.0688432			−0.0344216	−	0.999407i	$-0.510959\pi$
$769$	−1.90908			−0.0688432			−0.0344216	+	0.999407i	$0.510959\pi$
$770$	0.341364	+	0.0198386i	0.0123019	+	0.000714935i
$771$	21.0863			0.759403
$772$	9.22694	−	6.70377i	0.332085	−	0.241274i
$773$	−10.1888	−	31.3580i	−0.366467	−	1.12787i	−0.949057	−	0.315103i	$-0.897961\pi$
$773$	−10.1888	−	31.3580i	−0.366467	−	1.12787i	0.582590	−	0.812766i	$-0.302039\pi$
$774$	−0.343248	+	1.05641i	−0.0123378	+	0.0379718i
$775$	−2.93718	−	2.13398i	−0.105506	−	0.0766550i
$776$	−3.04722	−	2.21394i	−0.109389	−	0.0794757i
$777$	1.26870	−	3.90465i	0.0455143	−	0.140079i
$778$	1.09610	+	3.37343i	0.0392969	+	0.120943i
$779$	0.395701	−	0.287493i	0.0141774	−	0.0103005i
$780$	−1.84437			−0.0660390
$781$	3.33923	−	8.55318i	0.119487	−	0.306057i
$782$	0.247857			0.00886334
$783$	8.18442	−	5.94633i	0.292487	−	0.212504i
$784$	−7.77646	−	23.9335i	−0.277731	−	0.854767i
$785$	0.809843	−	2.49244i	0.0289045	−	0.0889590i
$786$	1.07520	+	0.781181i	0.0383512	+	0.0278638i
$787$	−7.84726	−	5.70137i	−0.279724	−	0.203232i	0.439073	−	0.898452i	$-0.355307\pi$
$787$	−7.84726	−	5.70137i	−0.279724	−	0.203232i	−0.718797	+	0.695220i	$0.755307\pi$
$788$	12.1016	−	37.2449i	0.431102	−	1.32680i
$789$	0.201012	+	0.618652i	0.00715623	+	0.0220246i
$790$	1.90414	−	1.38344i	0.0677463	−	0.0492206i
$791$	6.79532			0.241614
$792$	0.989593	−	2.53477i	0.0351636	−	0.0900691i
$793$	10.9219			0.387847
$794$	1.89539	−	1.37708i	0.0672648	−	0.0488708i
$795$	1.39856	+	4.30433i	0.0496019	+	0.152659i
$796$	−13.1705	+	40.5346i	−0.466815	+	1.43671i
$797$	−35.5820	−	25.8518i	−1.26038	−	0.915718i	−0.261601	−	0.965176i	$-0.584251\pi$
$797$	−35.5820	−	25.8518i	−1.26038	−	0.915718i	−0.998776	+	0.0494582i	$0.984251\pi$
$798$	0.611002	+	0.443919i	0.0216292	+	0.0157146i
$799$	0.743760	−	2.28906i	0.0263123	−	0.0809810i
$800$	3.07126	+	9.45235i	0.108585	+	0.334191i
$801$	10.4163	−	7.56785i	0.368040	−	0.267397i
$802$	3.91024			0.138075
$803$	3.42349	+	0.198958i	0.120812	+	0.00702109i
$804$	−22.4610			−0.792140
$805$	−0.136298	+	0.0990264i	−0.00480388	+	0.00349022i
$806$	−0.0565721	−	0.174111i	−0.00199267	−	0.00613280i
$807$	0.346500	−	1.06642i	0.0121974	−	0.0375397i
$808$	5.75744	+	4.18302i	0.202546	+	0.147158i
$809$	−1.62708	−	1.18214i	−0.0572051	−	0.0415619i	0.558815	−	0.829292i	$-0.311256\pi$
$809$	−1.62708	−	1.18214i	−0.0572051	−	0.0415619i	−0.616020	+	0.787730i	$0.711256\pi$
$810$	0.0603833	−	0.185841i	0.00212165	−	0.00652978i
$811$	−14.7482	−	45.3903i	−0.517880	−	1.59387i	−0.777980	−	0.628289i	$-0.783756\pi$
$811$	−14.7482	−	45.3903i	−0.517880	−	1.59387i	0.260100	−	0.965582i	$-0.416244\pi$
$812$	−8.45086	+	6.13991i	−0.296567	+	0.215468i
$813$	5.94803			0.208606
$814$	4.50421	−	2.88876i	0.157873	−	0.101251i
$815$	0.581955			0.0203850
$816$	−10.6868	+	7.76439i	−0.374112	+	0.271808i
$817$	11.4292	+	35.1753i	0.399855	+	1.23063i
$818$	−0.182796	+	0.562589i	−0.00639132	+	0.0196705i
$819$	0.426852	+	0.310126i	0.0149154	+	0.0108367i
$820$	0.105713	+	0.0768051i	0.00369166	+	0.00268215i
$821$	−0.193309	+	0.594945i	−0.00674655	+	0.0207637i	−0.954373	−	0.298617i	$-0.903475\pi$
$821$	−0.193309	+	0.594945i	−0.00674655	+	0.0207637i	0.947627	+	0.319380i	$0.103475\pi$
$822$	−1.32755	−	4.08578i	−0.0463037	−	0.142508i
$823$	14.5304	−	10.5570i	0.506500	−	0.367993i	−0.304995	−	0.952354i	$-0.598655\pi$
$823$	14.5304	−	10.5570i	0.506500	−	0.367993i	0.811494	+	0.584361i	$0.198655\pi$
$824$	12.2124			0.425441
$825$	10.5492	+	8.64241i	0.367275	+	0.300890i
$826$	−1.11428			−0.0387706
$827$	21.2843	−	15.4640i	0.740128	−	0.537734i	−0.152623	−	0.988284i	$-0.548772\pi$
$827$	21.2843	−	15.4640i	0.740128	−	0.537734i	0.892751	+	0.450550i	$0.148772\pi$
$828$	0.204896	+	0.630605i	0.00712063	+	0.0219150i
$829$	10.5479	−	32.4631i	0.366344	−	1.12749i	−0.582791	−	0.812622i	$-0.698039\pi$
$829$	10.5479	−	32.4631i	0.366344	−	1.12749i	0.949135	−	0.314869i	$-0.101961\pi$
$830$	−1.95569	−	1.42089i	−0.0678830	−	0.0493199i
$831$	−6.61545	−	4.80640i	−0.229487	−	0.166732i
$832$	2.15900	−	6.64471i	0.0748497	−	0.230364i
$833$	−7.32857	−	22.5550i	−0.253920	−	0.781485i
$834$	0.908047	−	0.659735i	0.0314431	−	0.0228448i
$835$	11.4275			0.395466
$836$	−11.3512	−	43.3485i	−0.392589	−	1.49924i
$837$	−0.882958			−0.0305195
$838$	2.95406	−	2.14625i	0.102046	−	0.0741410i
$839$	7.28810	+	22.4305i	0.251613	+	0.774386i	0.994478	+	0.104945i	$0.0334665\pi$
$839$	7.28810	+	22.4305i	0.251613	+	0.774386i	−0.742865	+	0.669441i	$0.766534\pi$
$840$	−0.126068	+	0.387996i	−0.00434975	+	0.0133871i
$841$	−59.3362	−	43.1103i	−2.04608	−	1.48656i
$842$	−1.07958	−	0.784360i	−0.0372047	−	0.0270308i
$843$	3.41405	−	10.5074i	0.117586	−	0.361893i
$844$	−0.191236	−	0.588565i	−0.00658263	−	0.0202592i
$845$	0.762452	−	0.553954i	0.0262291	−	0.0190566i
$846$	−0.141438			−0.00486275
$847$	1.14199	+	5.69034i	0.0392393	+	0.195522i
$848$	−17.9792			−0.617409
$849$	−5.33088	+	3.87311i	−0.182955	+	0.132925i
$850$	0.929517	+	2.86076i	0.0318822	+	0.0981232i
$851$	−0.814698	+	2.50738i	−0.0279275	+	0.0859520i
$852$	4.38316	+	3.18455i	0.150165	+	0.109101i
$853$	16.6584	+	12.1030i	0.570373	+	0.414400i	0.835241	−	0.549885i	$-0.185328\pi$
$853$	16.6584	+	12.1030i	0.570373	+	0.414400i	−0.264868	+	0.964285i	$0.585328\pi$
$854$	0.369215	−	1.13633i	0.0126343	−	0.0388843i
$855$	−2.01059	−	6.18795i	−0.0687606	−	0.211623i
$856$	−8.87632	+	6.44902i	−0.303386	+	0.220423i
$857$	14.6799			0.501457			0.250729	−	0.968057i	$-0.419330\pi$
$857$	14.6799			0.501457			0.250729	+	0.968057i	$0.419330\pi$
$858$	0.174198	+	0.665234i	0.00594701	+	0.0227107i
$859$	10.7418			0.366505			0.183253	−	0.983066i	$-0.441337\pi$
$859$	10.7418			0.366505			0.183253	+	0.983066i	$0.441337\pi$
$860$	−7.99377	+	5.80781i	−0.272585	+	0.198045i
$861$	−0.0115512	−	0.0355508i	−0.000393662	−	0.00121157i
$862$	−1.56501	+	4.81661i	−0.0533045	+	0.164054i
$863$	27.7749	+	20.1797i	0.945469	+	0.686924i	0.949731	−	0.313067i	$-0.101357\pi$
$863$	27.7749	+	20.1797i	0.945469	+	0.686924i	−0.00426159	+	0.999991i	$0.501357\pi$
$864$	1.95551	+	1.42076i	0.0665276	+	0.0483352i
$865$	−5.38813	+	16.5830i	−0.183202	+	0.563838i
$866$	−0.994267	−	3.06004i	−0.0337866	−	0.103984i
$867$	3.68203	−	2.67515i	0.125048	−	0.0908530i
$868$	0.911702			0.0309452
$869$	30.9025	+	25.3168i	1.04829	+	0.858815i
$870$	−1.97681			−0.0670201
$871$	9.28527	−	6.74614i	0.314619	−	0.228584i
$872$	0.196305	+	0.604164i	0.00664772	+	0.0204596i
$873$	1.41867	−	4.36622i	0.0480148	−	0.147774i
$874$	−0.392357	−	0.285064i	−0.0132717	−	0.00964243i
$875$	−3.66553	−	2.66316i	−0.123917	−	0.0900313i
$876$	−0.625288	+	1.92444i	−0.0211265	+	0.0650207i
$877$	−13.9346	−	42.8863i	−0.470538	−	1.44817i	−0.851881	−	0.523735i	$-0.824538\pi$
$877$	−13.9346	−	42.8863i	−0.470538	−	1.44817i	0.381343	−	0.924434i	$-0.375462\pi$
$878$	−1.75665	+	1.27628i	−0.0592841	+	0.0430724i
$879$	−7.27692			−0.245444
$880$	9.85061	−	6.31766i	0.332064	−	0.212968i
$881$	38.7731			1.30630			0.653149	−	0.757229i	$-0.273447\pi$
$881$	38.7731			1.30630			0.653149	+	0.757229i	$0.273447\pi$
$882$	−1.12749	+	0.819167i	−0.0379644	+	0.0275828i
$883$	2.30941	+	7.10764i	0.0777179	+	0.239191i	0.982366	−	0.186968i	$-0.0598662\pi$
$883$	2.30941	+	7.10764i	0.0777179	+	0.239191i	−0.904648	+	0.426160i	$0.859866\pi$
$884$	2.13373	−	6.56693i	0.0717650	−	0.220870i
$885$	7.76615	+	5.64244i	0.261056	+	0.189669i
$886$	−6.42564	−	4.66850i	−0.215874	−	0.156841i
$887$	8.84968	−	27.2365i	0.297143	−	0.914512i	−0.685350	−	0.728214i	$-0.740351\pi$
$887$	8.84968	−	27.2365i	0.297143	−	0.914512i	0.982493	−	0.186298i	$-0.0596491\pi$
$888$	1.97281	+	6.07169i	0.0662033	+	0.203753i
$889$	−6.02232	+	4.37547i	−0.201982	+	0.146749i
$890$	−2.51587			−0.0843322
$891$	3.31104	+	0.192423i	0.110924	+	0.00644642i
$892$	−41.1531			−1.37791
$893$	−3.81005	+	2.76816i	−0.127498	+	0.0926330i
$894$	1.31357	+	4.04275i	0.0439323	+	0.135210i
$895$	−4.08312	+	12.5666i	−0.136484	+	0.420054i
$896$	−2.68186	−	1.94848i	−0.0895946	−	0.0650943i
$897$	−0.274104	−	0.199148i	−0.00915207	−	0.00664937i
$898$	1.43722	−	4.42331i	0.0479607	−	0.147608i
$899$	2.76028	+	8.49526i	0.0920604	+	0.283333i
$900$	−6.51003	+	4.72982i	−0.217001	+	0.157661i
$901$	−16.9437			−0.564476
$902$	0.0177179	−	0.0453831i	0.000589942	−	0.00151109i
$903$	2.82661			0.0940636
$904$	−8.54860	+	6.21092i	−0.284322	+	0.206572i
$905$	−7.12482	−	21.9279i	−0.236837	−	0.728910i
$906$	−0.235331	+	0.724273i	−0.00781834	+	0.0240624i
$907$	11.8286	+	8.59395i	0.392761	+	0.285358i	0.766586	−	0.642142i	$-0.221954\pi$
$907$	11.8286	+	8.59395i	0.392761	+	0.285358i	−0.373825	+	0.927499i	$0.621954\pi$
$908$	−12.2445	−	8.89612i	−0.406346	−	0.295228i
$909$	−2.68044	+	8.24956i	−0.0889047	+	0.273621i
$910$	−0.0318593	−	0.0980529i	−0.00105613	−	0.00325042i
$911$	9.43623	−	6.85583i	0.312636	−	0.227144i	−0.420391	−	0.907343i	$-0.638107\pi$
$911$	9.43623	−	6.85583i	0.312636	−	0.227144i	0.733027	+	0.680200i	$0.238107\pi$
$912$	25.8471			0.855882
$913$	14.9217	−	38.2207i	0.493835	−	1.26492i
$914$	−6.70745			−0.221863
$915$	−8.32741	+	6.05022i	−0.275296	+	0.200014i
$916$	−11.8679	−	36.5257i	−0.392127	−	1.20684i
$917$	1.04509	−	3.21647i	0.0345120	−	0.106217i
$918$	0.591835	+	0.429993i	0.0195335	+	0.0141919i
$919$	−6.25518	−	4.54466i	−0.206339	−	0.149914i	0.479817	−	0.877369i	$-0.340703\pi$
$919$	−6.25518	−	4.54466i	−0.206339	−	0.149914i	−0.686156	+	0.727455i	$0.740703\pi$
$920$	0.0809547	−	0.249153i	0.00266900	−	0.00821433i
$921$	−3.66256	−	11.2722i	−0.120685	−	0.371431i
$922$	−2.01309	+	1.46259i	−0.0662976	+	0.0481680i
$923$	−2.76845			−0.0911246
$924$	−3.41883	−	0.198687i	−0.112471	−	0.00653634i
$925$	−31.9955			−1.05201
$926$	−0.943021	+	0.685145i	−0.0309896	+	0.0225153i
$927$	4.59979	+	14.1567i	0.151077	+	0.464967i
$928$	7.55638	−	23.2562i	0.248050	−	0.763421i
$929$	−41.5363	−	30.1779i	−1.36276	−	0.990104i	−0.998264	−	0.0588993i	$-0.981241\pi$
$929$	−41.5363	−	30.1779i	−1.36276	−	0.990104i	−0.364497	−	0.931205i	$-0.618759\pi$
$930$	0.139583	+	0.101413i	0.00457710	+	0.00332546i
$931$	−14.3398	+	44.1333i	−0.469967	+	1.44641i
$932$	5.94683	+	18.3025i	0.194795	+	0.599517i
$933$	21.5048	−	15.6242i	0.704037	−	0.511513i
$934$	−3.18545			−0.104231
$935$	9.28326	−	5.95379i	0.303595	−	0.194710i
$936$	−0.820440			−0.0268169
$937$	12.2603	−	8.90760i	0.400525	−	0.290999i	−0.369230	−	0.929338i	$-0.620378\pi$
$937$	12.2603	−	8.90760i	0.400525	−	0.290999i	0.769755	+	0.638340i	$0.220378\pi$
$938$	−0.387988	−	1.19410i	−0.0126683	−	0.0389889i
$939$	−3.80545	+	11.7120i	−0.124186	+	0.382205i
$940$	−1.01787	−	0.739527i	−0.0331993	−	0.0241207i
$941$	22.4319	+	16.2977i	0.731257	+	0.531290i	0.889961	−	0.456037i	$-0.150731\pi$
$941$	22.4319	+	16.2977i	0.731257	+	0.531290i	−0.158704	+	0.987326i	$0.550731\pi$
$942$	0.178166	−	0.548340i	0.00580498	−	0.0178659i
$943$	0.00741760	+	0.0228290i	0.000241550	+	0.000743415i
$944$	−30.8515	+	22.4150i	−1.00413	+	0.729545i
$945$	−0.497249			−0.0161755
$946$	2.84978	+	2.33468i	0.0926544	+	0.0759071i
$947$	−17.8975			−0.581591			−0.290795	−	0.956785i	$-0.593920\pi$
$947$	−17.8975			−0.581591			−0.290795	+	0.956785i	$0.593920\pi$
$948$	−19.0703	+	13.8554i	−0.619375	+	0.450002i
$949$	−0.319512	−	0.983356i	−0.0103718	−	0.0319211i
$950$	1.81878	−	5.59763i	0.0590090	−	0.181611i
$951$	−15.3712	−	11.1678i	−0.498444	−	0.362141i
$952$	−1.23563	−	0.897735i	−0.0400469	−	0.0290958i
$953$	−13.7957	+	42.4589i	−0.446888	+	1.37538i	0.433512	+	0.901148i	$0.357274\pi$
$953$	−13.7957	+	42.4589i	−0.446888	+	1.37538i	−0.880400	+	0.474231i	$0.842726\pi$
$954$	0.307686	+	0.946959i	0.00996169	+	0.0306589i
$955$	−3.14325	+	2.28370i	−0.101713	+	0.0738989i
$956$	2.20960			0.0714635
$957$	−8.49949	−	32.4582i	−0.274750	−	1.04923i
$958$	−0.852885			−0.0275555
$959$	−8.84436	+	6.42580i	−0.285599	+	0.207500i
$960$	2.03473	+	6.26225i	0.0656706	+	0.202113i
$961$	−9.33861	+	28.7413i	−0.301246	+	0.927139i
$962$	−1.30525	−	0.948320i	−0.0420830	−	0.0305751i
$963$	−10.8190	−	7.86044i	−0.348636	−	0.253299i
$964$	15.5460	−	47.8457i	0.500703	−	1.54101i
$965$	−1.69724	−	5.22358i	−0.0546362	−	0.168153i
$966$	−0.0299857	+	0.0217859i	−0.000964776	+	0.000700951i
$967$	57.1296			1.83717			0.918583	−	0.395229i	$-0.129335\pi$
$967$	57.1296			1.83717			0.918583	+	0.395229i	$0.129335\pi$
$968$	−6.63761	−	6.11474i	−0.213341	−	0.196535i
$969$	24.3584			0.782505
$970$	−0.725758	+	0.527294i	−0.0233027	+	0.0169304i
$971$	−9.35289	−	28.7852i	−0.300149	−	0.923762i	−0.981443	−	0.191753i	$-0.938583\pi$
$971$	−9.35289	−	28.7852i	−0.300149	−	0.923762i	0.681295	−	0.732009i	$-0.261417\pi$
$972$	−0.604750	+	1.86123i	−0.0193974	+	0.0596989i
$973$	−2.31072	−	1.67884i	−0.0740784	−	0.0538211i
$974$	6.81631	+	4.95234i	0.218409	+	0.158683i
$975$	1.27062	−	3.91056i	0.0406923	−	0.125238i
$976$	−12.6359	−	38.8892i	−0.404465	−	1.24481i
$977$	27.0956	−	19.6861i	0.866865	−	0.629815i	−0.0628785	−	0.998021i	$-0.520028\pi$
$977$	27.0956	−	19.6861i	0.866865	−	0.629815i	0.929744	+	0.368207i	$0.120028\pi$
$978$	0.128031			0.00409397
$979$	−10.8172	−	41.3094i	−0.345721	−	1.32025i
$980$	−12.3972			−0.396012
$981$	−0.626411	+	0.455114i	−0.0199998	+	0.0145307i
$982$	−0.0942397	−	0.290040i	−0.00300731	−	0.00925555i
$983$	−4.31257	+	13.2727i	−0.137550	+	0.423334i	−0.995978	−	0.0895996i	$-0.971441\pi$
$983$	−4.31257	+	13.2727i	−0.137550	+	0.423334i	0.858428	+	0.512934i	$0.171441\pi$
$984$	0.0470249	+	0.0341656i	0.00149910	+	0.00108916i
$985$	−15.2574	−	11.0851i	−0.486140	−	0.353202i
$986$	2.28694	−	7.03849i	0.0728311	−	0.224151i
$987$	0.111222	+	0.342305i	0.00354022	+	0.0108957i
$988$	−10.9304	+	7.94141i	−0.347743	+	0.252650i
$989$	−1.81511			−0.0577173
$990$	−0.501326	−	0.410712i	−0.0159332	−	0.0130533i
$991$	27.5990			0.876710			0.438355	−	0.898802i	$-0.355561\pi$
$991$	27.5990			0.876710			0.438355	+	0.898802i	$0.355561\pi$
$992$	−1.72663	+	1.25447i	−0.0548205	+	0.0398295i
$993$	1.25174	+	3.85245i	0.0397227	+	0.122254i
$994$	−0.0935876	+	0.288033i	−0.00296842	+	0.00913585i
$995$	16.6050	+	12.0642i	0.526413	+	0.382462i
$996$	19.5866	+	14.2305i	0.620624	+	0.450910i
$997$	16.3964	−	50.4630i	0.519280	−	1.59818i	−0.256078	−	0.966656i	$-0.582430\pi$
$997$	16.3964	−	50.4630i	0.519280	−	1.59818i	0.775358	−	0.631522i	$-0.217570\pi$
$998$	−2.14227	−	6.59323i	−0.0678124	−	0.208705i
$999$	−6.29527	+	4.57378i	−0.199173	+	0.144708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.157.5	✓	36
11.2	odd	10		4719.2.a.br.1.10		18
11.4	even	5	inner	429.2.n.d.235.5	yes	36
11.9	even	5		4719.2.a.bq.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.5	✓	36	1.1	even	1	trivial
429.2.n.d.235.5	yes	36	11.4	even	5	inner
4719.2.a.bq.1.9		18	11.9	even	5
4719.2.a.br.1.10		18	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)

\(f(q)\)	\(=\)	\(q+(0.167740 - 0.121870i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.604750 + 1.86123i) q^{4} +(0.762452 + 0.553954i) q^{5} +(0.167740 + 0.121870i) q^{6} +(0.163043 - 0.501795i) q^{7} +(0.253530 + 0.780285i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.167740 - 0.121870i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.604750 + 1.86123i) q^{4} +(0.762452 + 0.553954i) q^{5} +(0.167740 + 0.121870i) q^{6} +(0.163043 - 0.501795i) q^{7} +(0.253530 + 0.780285i) q^{8} +(-0.809017 + 0.587785i) q^{9} +0.195404 q^{10} +(0.840162 + 3.20845i) q^{11} -1.95701 q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.0338051 - 0.104041i) q^{14} +(-0.291231 + 0.896316i) q^{15} +(-3.02889 - 2.20062i) q^{16} +(-2.85444 - 2.07387i) q^{17} +(-0.0640711 + 0.197191i) q^{18} +(2.13338 + 6.56587i) q^{19} +(-1.49213 + 1.08409i) q^{20} +0.527618 q^{21} +(0.531944 + 0.435795i) q^{22} -0.338811 q^{23} +(-0.663750 + 0.482243i) q^{24} +(-1.27062 - 3.91056i) q^{25} +(0.0640711 - 0.197191i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.835354 + 0.606920i) q^{28} +(-3.12617 + 9.62136i) q^{29} +(0.0603833 + 0.185841i) q^{30} +(0.714328 - 0.518990i) q^{31} -2.41714 q^{32} +(-2.79179 + 1.79051i) q^{33} -0.731548 q^{34} +(0.402283 - 0.292276i) q^{35} +(-0.604750 - 1.86123i) q^{36} +(2.40458 - 7.40053i) q^{37} +(1.15804 + 0.841365i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-0.238937 + 0.735374i) q^{40} +(-0.0218930 - 0.0673798i) q^{41} +(0.0885028 - 0.0643011i) q^{42} +5.35730 q^{43} +(-6.47974 - 0.376575i) q^{44} -0.942442 q^{45} +(-0.0568323 + 0.0412911i) q^{46} +(0.210799 + 0.648774i) q^{47} +(1.15693 - 3.56067i) q^{48} +(5.43790 + 3.95087i) q^{49} +(-0.689715 - 0.501107i) q^{50} +(1.09030 - 3.35559i) q^{51} +(0.604750 + 1.86123i) q^{52} +(3.88510 - 2.82269i) q^{53} -0.207338 q^{54} +(-1.13675 + 2.91170i) q^{55} +0.432879 q^{56} +(-5.58526 + 4.05793i) q^{57} +(0.648175 + 1.99488i) q^{58} +(3.14757 - 9.68724i) q^{59} +(-1.49213 - 1.08409i) q^{60} +(8.83599 + 6.41972i) q^{61} +(0.0565721 - 0.174111i) q^{62} +(0.163043 + 0.501795i) q^{63} +(5.65233 - 4.10666i) q^{64} +0.942442 q^{65} +(-0.250086 + 0.640577i) q^{66} +11.4772 q^{67} +(5.58617 - 4.05859i) q^{68} +(-0.104698 - 0.322229i) q^{69} +(0.0318593 - 0.0980529i) q^{70} +(-2.23972 - 1.62725i) q^{71} +(-0.663750 - 0.482243i) q^{72} +(0.319512 - 0.983356i) q^{73} +(-0.498562 - 1.53441i) q^{74} +(3.32652 - 2.41686i) q^{75} -13.5107 q^{76} +(1.74696 + 0.101526i) q^{77} +0.207338 q^{78} +(9.74462 - 7.07988i) q^{79} +(-1.09034 - 3.35573i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-0.0118839 - 0.00863419i) q^{82} +(-10.0084 - 7.27154i) q^{83} +(-0.319077 + 0.982017i) q^{84} +(-1.02754 - 3.16245i) q^{85} +(0.898635 - 0.652897i) q^{86} -10.1165 q^{87} +(-2.29050 + 1.46900i) q^{88} -12.8752 q^{89} +(-0.158086 + 0.114856i) q^{90} +(-0.163043 - 0.501795i) q^{91} +(0.204896 - 0.630605i) q^{92} +(0.714328 + 0.518990i) q^{93} +(0.114426 + 0.0831353i) q^{94} +(-2.01059 + 6.18795i) q^{95} +(-0.746937 - 2.29883i) q^{96} +(-3.71413 + 2.69847i) q^{97} +1.39365 q^{98} +(-2.56558 - 2.10185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

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