LMFDB - Embedded newform 429.2.i.f.133.3

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} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 $ x^10 - x^9 + 7x^8 + 4x^7 + 32x^6 + 3x^5 + 30x^4 - 7x^3 + 26x^2 - 5x + 1
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			133.3
Root			$0.100998 + 0.174933i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.f.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.399002 + 0.691092i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.681594 - 1.18056i) q^{4} +1.11866 q^{5} +(0.399002 - 0.691092i) q^{6} +(-0.394706 + 0.683651i) q^{7} +2.68384 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.399002 + 0.691092i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.681594 - 1.18056i) q^{4} +1.11866 q^{5} +(0.399002 - 0.691092i) q^{6} +(-0.394706 + 0.683651i) q^{7} +2.68384 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.446346 + 0.773094i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.36319 q^{12} +(2.79509 + 2.27761i) q^{13} -0.629954 q^{14} +(-0.559328 - 0.968784i) q^{15} +(-0.292331 - 0.506332i) q^{16} +(3.74431 - 6.48534i) q^{17} -0.798005 q^{18} +(0.206292 - 0.357308i) q^{19} +(0.762469 - 1.32064i) q^{20} +0.789412 q^{21} +(0.399002 - 0.691092i) q^{22} +(-1.39557 - 2.41720i) q^{23} +(-1.34192 - 2.32427i) q^{24} -3.74861 q^{25} +(-0.458791 + 2.84043i) q^{26} +1.00000 q^{27} +(0.538059 + 0.931945i) q^{28} +(-0.370913 - 0.642441i) q^{29} +(0.446346 - 0.773094i) q^{30} +2.32468 q^{31} +(2.91712 - 5.05260i) q^{32} +(-0.500000 + 0.866025i) q^{33} +5.97596 q^{34} +(-0.441540 + 0.764770i) q^{35} +(0.681594 + 1.18056i) q^{36} +(2.71398 + 4.70075i) q^{37} +0.329243 q^{38} +(0.574923 - 3.55942i) q^{39} +3.00229 q^{40} +(2.19838 + 3.80771i) q^{41} +(0.314977 + 0.545556i) q^{42} +(-2.10352 + 3.64341i) q^{43} -1.36319 q^{44} +(-0.559328 + 0.968784i) q^{45} +(1.11367 - 1.92894i) q^{46} -8.63637 q^{47} +(-0.292331 + 0.506332i) q^{48} +(3.18841 + 5.52250i) q^{49} +(-1.49570 - 2.59063i) q^{50} -7.48863 q^{51} +(4.59396 - 1.74735i) q^{52} -0.894984 q^{53} +(0.399002 + 0.691092i) q^{54} +(-0.559328 - 0.968784i) q^{55} +(-1.05933 + 1.83481i) q^{56} -0.412583 q^{57} +(0.295991 - 0.512671i) q^{58} +(-3.47187 + 6.01346i) q^{59} -1.52494 q^{60} +(-1.94721 + 3.37267i) q^{61} +(0.927552 + 1.60657i) q^{62} +(-0.394706 - 0.683651i) q^{63} +3.48643 q^{64} +(3.12674 + 2.54786i) q^{65} -0.798005 q^{66} +(5.30978 + 9.19680i) q^{67} +(-5.10421 - 8.84074i) q^{68} +(-1.39557 + 2.41720i) q^{69} -0.704702 q^{70} +(1.31044 - 2.26975i) q^{71} +(-1.34192 + 2.32427i) q^{72} -4.87688 q^{73} +(-2.16577 + 3.75122i) q^{74} +(1.87430 + 3.24639i) q^{75} +(-0.281215 - 0.487078i) q^{76} +0.789412 q^{77} +(2.68928 - 1.02289i) q^{78} -10.2541 q^{79} +(-0.327017 - 0.566411i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.75432 + 3.03857i) q^{82} -8.52577 q^{83} +(0.538059 - 0.931945i) q^{84} +(4.18860 - 7.25486i) q^{85} -3.35724 q^{86} +(-0.370913 + 0.642441i) q^{87} +(-1.34192 - 2.32427i) q^{88} +(5.28512 + 9.15409i) q^{89} -0.892692 q^{90} +(-2.66033 + 1.01188i) q^{91} -3.80486 q^{92} +(-1.16234 - 2.01323i) q^{93} +(-3.44593 - 5.96853i) q^{94} +(0.230769 - 0.399704i) q^{95} -5.83424 q^{96} +(1.74041 - 3.01448i) q^{97} +(-2.54437 + 4.40698i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * 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 $

$2$	0.399002	+	0.691092i	0.282137	+	0.488676i	0.971911	−	0.235349i	$-0.0756233\pi$
$2$	0.399002	+	0.691092i	0.282137	+	0.488676i	−0.689774	+	0.724025i	$0.742290\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.681594	−	1.18056i	0.340797	−	0.590278i
$5$	1.11866			0.500278			0.250139	−	0.968210i	$-0.419524\pi$
$5$	1.11866			0.500278			0.250139	+	0.968210i	$0.419524\pi$
$6$	0.399002	−	0.691092i	0.162892	−	0.282137i
$7$	−0.394706	+	0.683651i	−0.149185	+	0.258396i	−0.930926	−	0.365207i	$-0.880998\pi$
$7$	−0.394706	+	0.683651i	−0.149185	+	0.258396i	0.781742	+	0.623603i	$0.214332\pi$
$8$	2.68384			0.948881
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.446346	+	0.773094i	0.141147	+	0.244474i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.36319			−0.393519
$13$	2.79509	+	2.27761i	0.775217	+	0.631695i
$13$	2.79509	+	2.27761i	0.775217	+	0.631695i
$14$	−0.629954			−0.168362
$15$	−0.559328	−	0.968784i	−0.144418	−	0.250139i
$16$	−0.292331	−	0.506332i	−0.0730827	−	0.126583i
$17$	3.74431	−	6.48534i	0.908129	−	1.57293i	0.0914690	−	0.995808i	$-0.470844\pi$
$17$	3.74431	−	6.48534i	0.908129	−	1.57293i	0.816660	−	0.577118i	$-0.195823\pi$
$18$	−0.798005			−0.188091
$19$	0.206292	−	0.357308i	0.0473266	−	0.0819720i	−0.841392	−	0.540426i	$-0.818263\pi$
$19$	0.206292	−	0.357308i	0.0473266	−	0.0819720i	0.888718	+	0.458454i	$0.151597\pi$
$20$	0.762469	−	1.32064i	0.170493	−	0.295303i
$21$	0.789412			0.172264
$22$	0.399002	−	0.691092i	0.0850676	−	0.147341i
$23$	−1.39557	−	2.41720i	−0.290997	−	0.504022i	0.683049	−	0.730373i	$-0.260654\pi$
$23$	−1.39557	−	2.41720i	−0.290997	−	0.504022i	−0.974046	+	0.226351i	$0.927320\pi$
$24$	−1.34192	−	2.32427i	−0.273918	−	0.474440i
$25$	−3.74861			−0.749722
$26$	−0.458791	+	2.84043i	−0.0899763	+	0.557055i
$27$	1.00000			0.192450
$28$	0.538059	+	0.931945i	0.101684	+	0.176121i
$29$	−0.370913	−	0.642441i	−0.0688769	−	0.119298i	0.829530	−	0.558462i	$-0.188608\pi$
$29$	−0.370913	−	0.642441i	−0.0688769	−	0.119298i	−0.898407	+	0.439163i	$0.855275\pi$
$30$	0.446346	−	0.773094i	0.0814913	−	0.141147i
$31$	2.32468			0.417525			0.208762	−	0.977966i	$-0.433056\pi$
$31$	2.32468			0.417525			0.208762	+	0.977966i	$0.433056\pi$
$32$	2.91712	−	5.05260i	0.515679	−	0.893182i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	5.97596			1.02487
$35$	−0.441540	+	0.764770i	−0.0746339	+	0.129270i
$36$	0.681594	+	1.18056i	0.113599	+	0.196759i
$37$	2.71398	+	4.70075i	0.446175	+	0.772799i	0.998133	−	0.0610735i	$-0.0194524\pi$
$37$	2.71398	+	4.70075i	0.446175	+	0.772799i	−0.551958	+	0.833872i	$0.686119\pi$
$38$	0.329243			0.0534103
$39$	0.574923	−	3.55942i	0.0920613	−	0.569963i
$40$	3.00229			0.474704
$41$	2.19838	+	3.80771i	0.343330	+	0.594665i	0.985049	−	0.172275i	$-0.0551118\pi$
$41$	2.19838	+	3.80771i	0.343330	+	0.594665i	−0.641719	+	0.766940i	$0.721778\pi$
$42$	0.314977	+	0.545556i	0.0486020	+	0.0841812i
$43$	−2.10352	+	3.64341i	−0.320784	+	0.555614i	−0.980650	−	0.195769i	$-0.937280\pi$
$43$	−2.10352	+	3.64341i	−0.320784	+	0.555614i	0.659866	+	0.751383i	$0.270613\pi$
$44$	−1.36319			−0.205508
$45$	−0.559328	+	0.968784i	−0.0833797	+	0.144418i
$46$	1.11367	−	1.92894i	0.164202	−	0.284407i
$47$	−8.63637			−1.25974			−0.629872	−	0.776699i	$-0.716893\pi$
$47$	−8.63637			−1.25974			−0.629872	+	0.776699i	$0.716893\pi$
$48$	−0.292331	+	0.506332i	−0.0421943	+	0.0730827i
$49$	3.18841	+	5.52250i	0.455488	+	0.788928i
$50$	−1.49570	−	2.59063i	−0.211524	−	0.366371i
$51$	−7.48863			−1.04862
$52$	4.59396	−	1.74735i	0.637067	−	0.242314i
$53$	−0.894984			−0.122936			−0.0614678	−	0.998109i	$-0.519578\pi$
$53$	−0.894984			−0.122936			−0.0614678	+	0.998109i	$0.519578\pi$
$54$	0.399002	+	0.691092i	0.0542973	+	0.0940457i
$55$	−0.559328	−	0.968784i	−0.0754197	−	0.130631i
$56$	−1.05933	+	1.83481i	−0.141559	+	0.245187i
$57$	−0.412583			−0.0546480
$58$	0.295991	−	0.512671i	0.0388655	−	0.0673170i
$59$	−3.47187	+	6.01346i	−0.452000	+	0.782886i	−0.998510	−	0.0545660i	$-0.982622\pi$
$59$	−3.47187	+	6.01346i	−0.452000	+	0.782886i	0.546511	+	0.837452i	$0.315956\pi$
$60$	−1.52494			−0.196869
$61$	−1.94721	+	3.37267i	−0.249315	+	0.431827i	−0.963336	−	0.268298i	$-0.913539\pi$
$61$	−1.94721	+	3.37267i	−0.249315	+	0.431827i	0.714021	+	0.700124i	$0.246872\pi$
$62$	0.927552	+	1.60657i	0.117799	+	0.204034i
$63$	−0.394706	−	0.683651i	−0.0497283	−	0.0861319i
$64$	3.48643			0.435804
$65$	3.12674	+	2.54786i	0.387824	+	0.316023i
$66$	−0.798005			−0.0982276
$67$	5.30978	+	9.19680i	0.648692	+	1.12357i	0.983435	+	0.181259i	$0.0580172\pi$
$67$	5.30978	+	9.19680i	0.648692	+	1.12357i	−0.334743	+	0.942309i	$0.608650\pi$
$68$	−5.10421	−	8.84074i	−0.618976	−	1.07210i
$69$	−1.39557	+	2.41720i	−0.168007	+	0.290997i
$70$	−0.704702			−0.0842280
$71$	1.31044	−	2.26975i	0.155521	−	0.269370i	−0.777728	−	0.628601i	$-0.783628\pi$
$71$	1.31044	−	2.26975i	0.155521	−	0.269370i	0.933248	+	0.359232i	$0.116961\pi$
$72$	−1.34192	+	2.32427i	−0.158147	+	0.273918i
$73$	−4.87688			−0.570795			−0.285398	−	0.958409i	$-0.592126\pi$
$73$	−4.87688			−0.570795			−0.285398	+	0.958409i	$0.592126\pi$
$74$	−2.16577	+	3.75122i	−0.251765	+	0.436070i
$75$	1.87430	+	3.24639i	0.216426	+	0.374861i
$76$	−0.281215	−	0.487078i	−0.0322575	−	0.0558717i
$77$	0.789412			0.0899619
$78$	2.68928	−	1.02289i	0.304501	−	0.115820i
$79$	−10.2541			−1.15367			−0.576837	−	0.816860i	$-0.695713\pi$
$79$	−10.2541			−1.15367			−0.576837	+	0.816860i	$0.695713\pi$
$80$	−0.327017	−	0.566411i	−0.0365616	−	0.0633266i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.75432	+	3.03857i	−0.193732	+	0.335554i
$83$	−8.52577			−0.935825			−0.467912	−	0.883775i	$-0.654994\pi$
$83$	−8.52577			−0.935825			−0.467912	+	0.883775i	$0.654994\pi$
$84$	0.538059	−	0.931945i	0.0587070	−	0.101684i
$85$	4.18860	−	7.25486i	0.454317	−	0.786900i
$86$	−3.35724			−0.362020
$87$	−0.370913	+	0.642441i	−0.0397661	+	0.0688769i
$88$	−1.34192	−	2.32427i	−0.143049	−	0.247768i
$89$	5.28512	+	9.15409i	0.560221	+	0.970332i	0.997477	+	0.0709942i	$0.0226172\pi$
$89$	5.28512	+	9.15409i	0.560221	+	0.970332i	−0.437256	+	0.899337i	$0.644049\pi$
$90$	−0.892692			−0.0940980
$91$	−2.66033	+	1.01188i	−0.278878	+	0.106074i
$92$	−3.80486			−0.396684
$93$	−1.16234	−	2.01323i	−0.120529	−	0.208762i
$94$	−3.44593	−	5.96853i	−0.355421	−	0.615607i
$95$	0.230769	−	0.399704i	0.0236764	−	0.0410088i
$96$	−5.83424			−0.595455
$97$	1.74041	−	3.01448i	0.176712	−	0.306074i	−0.764040	−	0.645168i	$-0.776787\pi$
$97$	1.74041	−	3.01448i	0.176712	−	0.306074i	0.940752	+	0.339094i	$0.110121\pi$
$98$	−2.54437	+	4.40698i	−0.257020	+	0.445172i
$99$	1.00000			0.100504
$100$	−2.55503	+	4.42544i	−0.255503	+	0.442544i
$101$	−4.48551	−	7.76914i	−0.446325	−	0.773058i	0.551818	−	0.833964i	$-0.313934\pi$
$101$	−4.48551	−	7.76914i	−0.446325	−	0.773058i	−0.998143	+	0.0609063i	$0.980601\pi$
$102$	−2.98798	−	5.17533i	−0.295854	−	0.512434i
$103$	−8.05171			−0.793359			−0.396679	−	0.917957i	$-0.629837\pi$
$103$	−8.05171			−0.793359			−0.396679	+	0.917957i	$0.629837\pi$
$104$	7.50156	+	6.11273i	0.735589	+	0.599403i
$105$	0.883080			0.0861798
$106$	−0.357101	−	0.618517i	−0.0346847	−	0.0600756i
$107$	−3.30569	−	5.72563i	−0.319573	−	0.553517i	0.660826	−	0.750539i	$-0.270206\pi$
$107$	−3.30569	−	5.72563i	−0.319573	−	0.553517i	−0.980399	+	0.197022i	$0.936873\pi$
$108$	0.681594	−	1.18056i	0.0655865	−	0.113599i
$109$	10.0166			0.959412			0.479706	−	0.877429i	$-0.340743\pi$
$109$	10.0166			0.959412			0.479706	+	0.877429i	$0.340743\pi$
$110$	0.446346	−	0.773094i	0.0425574	−	0.0737116i
$111$	2.71398	−	4.70075i	0.257600	−	0.446175i
$112$	0.461539			0.0436113
$113$	−2.98459	+	5.16946i	−0.280766	+	0.486302i	−0.971574	−	0.236737i	$-0.923922\pi$
$113$	−2.98459	+	5.16946i	−0.280766	+	0.486302i	0.690807	+	0.723039i	$0.257255\pi$
$114$	−0.164622	−	0.285133i	−0.0154182	−	0.0267052i
$115$	−1.56117	−	2.70402i	−0.145580	−	0.252151i
$116$	−1.01125			−0.0938922
$117$	−3.37001	+	1.28181i	−0.311557	+	0.118504i
$118$	−5.54114			−0.510104
$119$	2.95581	+	5.11961i	0.270958	+	0.469314i
$120$	−1.50115	−	2.60006i	−0.137035	−	0.237352i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.10777			−0.281364
$123$	2.19838	−	3.80771i	0.198222	−	0.343330i
$124$	1.58449	−	2.74441i	0.142291	−	0.246456i
$125$	−9.78668			−0.875347
$126$	0.314977	−	0.545556i	0.0280604	−	0.0486020i
$127$	4.09006	+	7.08419i	0.362934	+	0.628620i	0.988442	−	0.151598i	$-0.0484418\pi$
$127$	4.09006	+	7.08419i	0.362934	+	0.628620i	−0.625508	+	0.780217i	$0.715108\pi$
$128$	−4.44315	−	7.69576i	−0.392723	−	0.680216i
$129$	4.20704			0.370409
$130$	−0.513229	+	3.17747i	−0.0450132	+	0.278682i
$131$	8.48279			0.741145			0.370572	−	0.928804i	$-0.379162\pi$
$131$	8.48279			0.741145			0.370572	+	0.928804i	$0.379162\pi$
$132$	0.681594	+	1.18056i	0.0593252	+	0.102754i
$133$	0.162849	+	0.282063i	0.0141208	+	0.0244580i
$134$	−4.23723	+	7.33909i	−0.366041	+	0.634001i
$135$	1.11866			0.0962785
$136$	10.0491	−	17.4056i	0.861706	−	1.49252i
$137$	−2.35012	+	4.07052i	−0.200784	+	0.347768i	−0.948781	−	0.315934i	$-0.897682\pi$
$137$	−2.35012	+	4.07052i	−0.200784	+	0.347768i	0.747997	+	0.663702i	$0.231016\pi$
$138$	−2.22735			−0.189604
$139$	−7.05745	+	12.2239i	−0.598605	+	1.03681i	0.394422	+	0.918929i	$0.370945\pi$
$139$	−7.05745	+	12.2239i	−0.598605	+	1.03681i	−0.993027	+	0.117885i	$0.962388\pi$
$140$	0.601902	+	1.04253i	0.0508700	+	0.0881095i
$141$	4.31819	+	7.47932i	0.363657	+	0.629872i
$142$	2.09147			0.175513
$143$	0.574923	−	3.55942i	0.0480775	−	0.297654i
$144$	0.584661			0.0487218
$145$	−0.414924	−	0.718670i	−0.0344576	−	0.0596823i
$146$	−1.94589	−	3.37037i	−0.161043	−	0.278934i
$147$	3.18841	−	5.52250i	0.262976	−	0.455488i
$148$	7.39933			0.608221
$149$	11.7705	−	20.3872i	0.964280	−	1.67018i	0.252742	−	0.967534i	$-0.418668\pi$
$149$	11.7705	−	20.3872i	0.964280	−	1.67018i	0.711538	−	0.702648i	$-0.247999\pi$
$150$	−1.49570	+	2.59063i	−0.122124	+	0.211524i
$151$	14.3170			1.16510			0.582551	−	0.812794i	$-0.302055\pi$
$151$	14.3170			1.16510			0.582551	+	0.812794i	$0.302055\pi$
$152$	0.553654	−	0.958957i	0.0449073	−	0.0777817i
$153$	3.74431	+	6.48534i	0.302710	+	0.524309i
$154$	0.314977	+	0.545556i	0.0253816	+	0.0439622i
$155$	2.60051			0.208878
$156$	−3.81023	−	3.10481i	−0.305063	−	0.248584i
$157$	−21.7452			−1.73546			−0.867729	−	0.497038i	$-0.834421\pi$
$157$	−21.7452			−1.73546			−0.867729	+	0.497038i	$0.834421\pi$
$158$	−4.09140	−	7.08651i	−0.325494	−	0.563772i
$159$	0.447492	+	0.775079i	0.0354884	+	0.0614678i
$160$	3.26325	−	5.65212i	0.257983	−	0.446839i
$161$	2.20337			0.173650
$162$	0.399002	−	0.691092i	0.0313486	−	0.0542973i
$163$	0.634009	−	1.09814i	0.0496594	−	0.0860127i	−0.840127	−	0.542389i	$-0.817520\pi$
$163$	0.634009	−	1.09814i	0.0496594	−	0.0860127i	0.889787	+	0.456377i	$0.150853\pi$
$164$	5.99363			0.468024
$165$	−0.559328	+	0.968784i	−0.0435436	+	0.0754197i
$166$	−3.40180	−	5.89209i	−0.264031	−	0.457315i
$167$	−9.25169	−	16.0244i	−0.715917	−	1.24000i	−0.962605	−	0.270910i	$-0.912676\pi$
$167$	−9.25169	−	16.0244i	−0.715917	−	1.24000i	0.246688	−	0.969095i	$-0.420658\pi$
$168$	2.11866			0.163458
$169$	2.62501	+	12.7322i	0.201924	+	0.979401i
$170$	6.68504			0.512719
$171$	0.206292	+	0.357308i	0.0157755	+	0.0273240i
$172$	2.86750	+	4.96665i	0.218645	+	0.378704i
$173$	−5.38923	+	9.33441i	−0.409735	+	0.709682i	−0.994860	−	0.101261i	$-0.967712\pi$
$173$	−5.38923	+	9.33441i	−0.409735	+	0.709682i	0.585125	+	0.810943i	$0.301046\pi$
$174$	−0.591981			−0.0448780
$175$	1.47960	−	2.56274i	0.111847	−	0.193725i
$176$	−0.292331	+	0.506332i	−0.0220353	+	0.0381662i
$177$	6.94375			0.521924
$178$	−4.21755	+	7.30500i	−0.316118	+	0.547533i
$179$	6.07695	+	10.5256i	0.454212	+	0.786719i	0.998643	−	0.0520872i	$-0.0165874\pi$
$179$	6.07695	+	10.5256i	0.454212	+	0.786719i	−0.544430	+	0.838806i	$0.683254\pi$
$180$	0.762469	+	1.32064i	0.0568311	+	0.0984344i
$181$	18.8225			1.39906			0.699532	−	0.714601i	$-0.253392\pi$
$181$	18.8225			1.39906			0.699532	+	0.714601i	$0.253392\pi$
$182$	−1.76078	−	1.43479i	−0.130517	−	0.106354i
$183$	3.89443			0.287884
$184$	−3.74550	−	6.48739i	−0.276122	−	0.478257i
$185$	3.03601	+	5.25852i	0.223212	+	0.386614i
$186$	0.927552	−	1.60657i	0.0680114	−	0.117799i
$187$	−7.48863			−0.547623
$188$	−5.88650	+	10.1957i	−0.429317	+	0.743599i
$189$	−0.394706	+	0.683651i	−0.0287106	+	0.0497283i
$190$	0.368310			0.0267200
$191$	−2.33606	+	4.04618i	−0.169032	+	0.292771i	−0.938080	−	0.346420i	$-0.887397\pi$
$191$	−2.33606	+	4.04618i	−0.169032	+	0.292771i	0.769048	+	0.639191i	$0.220731\pi$
$192$	−1.74321	−	3.01934i	−0.125806	−	0.217902i
$193$	6.88940	+	11.9328i	0.495910	+	0.858941i	0.999989	−	0.00471629i	$-0.00150125\pi$
$193$	6.88940	+	11.9328i	0.495910	+	0.858941i	−0.504079	+	0.863658i	$0.668168\pi$
$194$	2.77771			0.199428
$195$	0.643141	−	3.98176i	0.0460563	−	0.285140i
$196$	8.69282			0.620916
$197$	11.2917	+	19.5578i	0.804501	+	1.39344i	0.916627	+	0.399743i	$0.130901\pi$
$197$	11.2917	+	19.5578i	0.804501	+	1.39344i	−0.112126	+	0.993694i	$0.535766\pi$
$198$	0.399002	+	0.691092i	0.0283559	+	0.0491138i
$199$	−12.8815	+	22.3113i	−0.913142	+	1.58161i	−0.103544	+	0.994625i	$0.533018\pi$
$199$	−12.8815	+	22.3113i	−0.913142	+	1.58161i	−0.809599	+	0.586984i	$0.800315\pi$
$200$	−10.0607			−0.711397
$201$	5.30978	−	9.19680i	0.374523	−	0.648692i
$202$	3.57946	−	6.19981i	0.251850	−	0.436217i
$203$	0.585607			0.0411016
$204$	−5.10421	+	8.84074i	−0.357366	+	0.618976i
$205$	2.45923	+	4.25952i	0.171760	+	0.297498i
$206$	−3.21265	−	5.56447i	−0.223836	−	0.387695i
$207$	2.79115			0.193998
$208$	0.336135	−	2.08105i	0.0233068	−	0.144295i
$209$	−0.412583			−0.0285390
$210$	0.352351	+	0.610290i	0.0243145	+	0.0421140i
$211$	−11.6299	−	20.1436i	−0.800637	−	1.38674i	−0.919198	−	0.393796i	$-0.871161\pi$
$211$	−11.6299	−	20.1436i	−0.800637	−	1.38674i	0.118561	−	0.992947i	$-0.462172\pi$
$212$	−0.610016	+	1.05658i	−0.0418961	+	0.0725662i
$213$	−2.62088			−0.179580
$214$	2.63796	−	4.56908i	0.180327	−	0.312336i
$215$	−2.35312	+	4.07572i	−0.160481	+	0.277962i
$216$	2.68384			0.182612
$217$	−0.917565	+	1.58927i	−0.0622884	+	0.107887i
$218$	3.99663	+	6.92236i	0.270686	+	0.468842i
$219$	2.43844	+	4.22350i	0.164774	+	0.285398i
$220$	−1.52494			−0.102811
$221$	25.2367	−	9.59901i	1.69761	−	0.645699i
$222$	4.33154			0.290714
$223$	−14.5471	−	25.1963i	−0.974146	−	1.68727i	−0.682726	−	0.730675i	$-0.739206\pi$
$223$	−14.5471	−	25.1963i	−0.974146	−	1.68727i	−0.291420	−	0.956595i	$-0.594128\pi$
$224$	2.30281	+	3.98858i	0.153863	+	0.266499i
$225$	1.87430	−	3.24639i	0.124954	−	0.216426i
$226$	−4.76343			−0.316859
$227$	5.60444	−	9.70717i	0.371980	−	0.644288i	−0.617890	−	0.786264i	$-0.712012\pi$
$227$	5.60444	−	9.70717i	0.371980	−	0.644288i	0.989870	+	0.141977i	$0.0453458\pi$
$228$	−0.281215	+	0.487078i	−0.0186239	+	0.0322575i
$229$	−13.0914			−0.865105			−0.432553	−	0.901609i	$-0.642387\pi$
$229$	−13.0914			−0.865105			−0.432553	+	0.901609i	$0.642387\pi$
$230$	1.24582	−	2.15782i	0.0821468	−	0.142282i
$231$	−0.394706	−	0.683651i	−0.0259697	−	0.0449809i
$232$	−0.995472	−	1.72421i	−0.0653560	−	0.113200i
$233$	2.44561			0.160217			0.0801085	−	0.996786i	$-0.474473\pi$
$233$	2.44561			0.160217			0.0801085	+	0.996786i	$0.474473\pi$
$234$	−2.23049	−	1.81754i	−0.145812	−	0.118816i
$235$	−9.66112			−0.630222
$236$	4.73282	+	8.19749i	0.308080	+	0.533611i
$237$	5.12704	+	8.88029i	0.333037	+	0.576837i
$238$	−2.35875	+	4.08547i	−0.152895	+	0.264822i
$239$	4.97047			0.321513			0.160757	−	0.986994i	$-0.448607\pi$
$239$	4.97047			0.321513			0.160757	+	0.986994i	$0.448607\pi$
$240$	−0.327017	+	0.566411i	−0.0211089	+	0.0365616i
$241$	9.71664	−	16.8297i	0.625904	−	1.08410i	−0.362461	−	0.931999i	$-0.618064\pi$
$241$	9.71664	−	16.8297i	0.625904	−	1.08410i	0.988365	−	0.152099i	$-0.0486031\pi$
$242$	−0.798005			−0.0512977
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	2.65442	+	4.59759i	0.169932	+	0.294331i
$245$	3.56674	+	6.17777i	0.227870	+	0.394683i
$246$	3.50864			0.223703
$247$	1.39041	−	0.528854i	0.0884697	−	0.0336502i
$248$	6.23907			0.396181
$249$	4.26288	+	7.38353i	0.270149	+	0.467912i
$250$	−3.90491	−	6.76350i	−0.246968	−	0.427761i
$251$	14.5731	−	25.2413i	0.919844	−	1.59322i	0.120193	−	0.992751i	$-0.461649\pi$
$251$	14.5731	−	25.2413i	0.919844	−	1.59322i	0.799651	−	0.600466i	$-0.205018\pi$
$252$	−1.07612			−0.0677890
$253$	−1.39557	+	2.41720i	−0.0877390	+	0.151968i
$254$	−3.26388	+	5.65321i	−0.204794	+	0.354714i
$255$	−8.37719			−0.524600
$256$	7.03208	−	12.1799i	0.439505	−	0.761245i
$257$	9.06680	+	15.7042i	0.565572	+	0.979599i	0.996996	+	0.0774498i	$0.0246778\pi$
$257$	9.06680	+	15.7042i	0.565572	+	0.979599i	−0.431425	+	0.902149i	$0.641989\pi$
$258$	1.67862	+	2.90745i	0.104506	+	0.181010i
$259$	−4.28490			−0.266250
$260$	5.13906	−	1.95468i	0.318711	−	0.121224i
$261$	0.741827			0.0459179
$262$	3.38465	+	5.86239i	0.209105	+	0.362180i
$263$	−2.99188	−	5.18209i	−0.184487	−	0.319541i	0.758916	−	0.651188i	$-0.225729\pi$
$263$	−2.99188	−	5.18209i	−0.184487	−	0.319541i	−0.943404	+	0.331647i	$0.892396\pi$
$264$	−1.34192	+	2.32427i	−0.0825895	+	0.143049i
$265$	−1.00118			−0.0615019
$266$	−0.129954	+	0.225088i	−0.00796801	+	0.0138010i
$267$	5.28512	−	9.15409i	0.323444	−	0.560221i
$268$	14.4765			0.884290
$269$	5.27952	−	9.14440i	0.321898	−	0.557544i	−0.658982	−	0.752159i	$-0.729012\pi$
$269$	5.27952	−	9.14440i	0.321898	−	0.557544i	0.980880	+	0.194615i	$0.0623458\pi$
$270$	0.446346	+	0.773094i	0.0271638	+	0.0470490i
$271$	2.58979	+	4.48565i	0.157318	+	0.272484i	0.933901	−	0.357532i	$-0.116382\pi$
$271$	2.58979	+	4.48565i	0.157318	+	0.272484i	−0.776582	+	0.630016i	$0.783048\pi$
$272$	−4.37831			−0.265474
$273$	2.20647	+	1.79797i	0.133542	+	0.108818i
$274$	−3.75081			−0.226595
$275$	1.87430	+	3.24639i	0.113025	+	0.195765i
$276$	1.90243	+	3.29511i	0.114513	+	0.198342i
$277$	14.3988	−	24.9394i	0.865137	−	1.49846i	−0.00177310	−	0.999998i	$-0.500564\pi$
$277$	14.3988	−	24.9394i	0.865137	−	1.49846i	0.866911	−	0.498464i	$-0.166102\pi$
$278$	−11.2638			−0.675555
$279$	−1.16234	+	2.01323i	−0.0695874	+	0.120529i
$280$	−1.18502	+	2.05252i	−0.0708187	+	0.122662i
$281$	−8.66501			−0.516911			−0.258455	−	0.966023i	$-0.583214\pi$
$281$	−8.66501			−0.516911			−0.258455	+	0.966023i	$0.583214\pi$
$282$	−3.44593	+	5.96853i	−0.205202	+	0.355421i
$283$	4.29859	+	7.44538i	0.255525	+	0.442582i	0.965038	−	0.262110i	$-0.0844184\pi$
$283$	4.29859	+	7.44538i	0.255525	+	0.442582i	−0.709513	+	0.704692i	$0.751085\pi$
$284$	−1.78638	−	3.09410i	−0.106002	−	0.183601i
$285$	−0.461539			−0.0273392
$286$	2.68928	−	1.02289i	0.159021	−	0.0604848i
$287$	−3.47086			−0.204879
$288$	2.91712	+	5.05260i	0.171893	+	0.297727i
$289$	−19.5398	−	33.8439i	−1.14940	−	1.99082i
$290$	0.331112	−	0.573502i	0.0194435	−	0.0336772i
$291$	−3.48082			−0.204050
$292$	−3.32405	+	5.75743i	−0.194525	+	0.336928i
$293$	10.9311	−	18.9332i	0.638600	−	1.10609i	−0.347140	−	0.937813i	$-0.612847\pi$
$293$	10.9311	−	18.9332i	0.638600	−	1.10609i	0.985740	−	0.168274i	$-0.0538195\pi$
$294$	5.08874			0.296781
$295$	−3.88383	+	6.72699i	−0.226125	+	0.391661i
$296$	7.28389	+	12.6161i	0.423367	+	0.733294i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	18.7859			1.08824
$299$	1.60469	−	9.93486i	0.0928019	−	0.574548i
$300$	5.11006			0.295030
$301$	−1.66055	−	2.87615i	−0.0957122	−	0.165778i
$302$	5.71252	+	9.89438i	0.328719	+	0.569358i
$303$	−4.48551	+	7.76914i	−0.257686	+	0.446325i
$304$	−0.241222			−0.0138350
$305$	−2.17826	+	3.77286i	−0.124727	+	0.216033i
$306$	−2.98798	+	5.17533i	−0.170811	+	0.295854i
$307$	−31.0201			−1.77041			−0.885204	−	0.465202i	$-0.845982\pi$
$307$	−31.0201			−1.77041			−0.885204	+	0.465202i	$0.845982\pi$
$308$	0.538059	−	0.931945i	0.0306587	−	0.0531025i
$309$	4.02586	+	6.97299i	0.229023	+	0.396679i
$310$	1.03761	+	1.79720i	0.0589324	+	0.102074i
$311$	14.9824			0.849572			0.424786	−	0.905294i	$-0.360349\pi$
$311$	14.9824			0.849572			0.424786	+	0.905294i	$0.360349\pi$
$312$	1.54300	−	9.55291i	0.0873552	−	0.540827i
$313$	−25.7272			−1.45419			−0.727094	−	0.686538i	$-0.759130\pi$
$313$	−25.7272			−1.45419			−0.727094	+	0.686538i	$0.759130\pi$
$314$	−8.67639	−	15.0280i	−0.489637	−	0.848077i
$315$	−0.441540	−	0.764770i	−0.0248780	−	0.0430899i
$316$	−6.98912	+	12.1055i	−0.393169	+	0.680988i
$317$	−19.7902			−1.11153			−0.555763	−	0.831341i	$-0.687574\pi$
$317$	−19.7902			−1.11153			−0.555763	+	0.831341i	$0.687574\pi$
$318$	−0.357101	+	0.618517i	−0.0200252	+	0.0346847i
$319$	−0.370913	+	0.642441i	−0.0207672	+	0.0359698i
$320$	3.90011			0.218023
$321$	−3.30569	+	5.72563i	−0.184506	+	0.319573i
$322$	0.879148	+	1.52273i	0.0489930	+	0.0848584i
$323$	−1.54484	−	2.67574i	−0.0859573	−	0.148882i
$324$	−1.36319			−0.0757327
$325$	−10.4777	−	8.53786i	−0.581197	−	0.473595i
$326$	1.01188			0.0560431
$327$	−5.00828	−	8.67459i	−0.276958	−	0.479706i
$328$	5.90011	+	10.2193i	0.325779	+	0.564266i
$329$	3.40883	−	5.90426i	0.187935	−	0.325513i
$330$	−0.892692			−0.0491411
$331$	10.5599	−	18.2904i	0.580427	−	1.00533i	−0.415002	−	0.909821i	$-0.636219\pi$
$331$	10.5599	−	18.2904i	0.580427	−	1.00533i	0.995429	−	0.0955081i	$-0.0304476\pi$
$332$	−5.81112	+	10.0651i	−0.318926	+	0.552397i
$333$	−5.42796			−0.297450
$334$	7.38289	−	12.7875i	0.403974	−	0.699703i
$335$	5.93981	+	10.2881i	0.324527	+	0.562096i
$336$	−0.230769	−	0.399704i	−0.0125895	−	0.0218057i
$337$	26.7711			1.45832			0.729158	−	0.684346i	$-0.239912\pi$
$337$	26.7711			1.45832			0.729158	+	0.684346i	$0.239912\pi$
$338$	−7.75175	+	6.89431i	−0.421640	+	0.375001i
$339$	5.96918			0.324201
$340$	−5.70985	−	9.88975i	−0.309660	−	0.536347i
$341$	−1.16234	−	2.01323i	−0.0629442	−	0.109023i
$342$	−0.164622	+	0.285133i	−0.00890172	+	0.0154182i
$343$	−10.5598			−0.570177
$344$	−5.64551	+	9.77832i	−0.304386	+	0.527212i
$345$	−1.56117	+	2.70402i	−0.0840504	+	0.145580i
$346$	−8.60125			−0.462406
$347$	4.86438	−	8.42536i	0.261134	−	0.452297i	−0.705410	−	0.708800i	$-0.749237\pi$
$347$	4.86438	−	8.42536i	0.261134	−	0.452297i	0.966543	+	0.256503i	$0.0825703\pi$
$348$	0.505625	+	0.875768i	0.0271043	+	0.0469461i
$349$	−5.04144	−	8.73204i	−0.269862	−	0.467415i	0.698964	−	0.715157i	$-0.253645\pi$
$349$	−5.04144	−	8.73204i	−0.269862	−	0.467415i	−0.968826	+	0.247742i	$0.920312\pi$
$350$	2.36145			0.126225
$351$	2.79509	+	2.27761i	0.149191	+	0.121570i
$352$	−5.83424			−0.310966
$353$	−1.75124	−	3.03323i	−0.0932089	−	0.161443i	0.815651	−	0.578545i	$-0.196379\pi$
$353$	−1.75124	−	3.03323i	−0.0932089	−	0.161443i	−0.908860	+	0.417102i	$0.863046\pi$
$354$	2.77057	+	4.79877i	0.147254	+	0.255052i
$355$	1.46593	−	2.53907i	0.0778035	−	0.134760i
$356$	14.4092			0.763687
$357$	2.95581	−	5.11961i	0.156438	−	0.270958i
$358$	−4.84943	+	8.39946i	−0.256300	+	0.443925i
$359$	−1.76139			−0.0929628			−0.0464814	−	0.998919i	$-0.514801\pi$
$359$	−1.76139			−0.0929628			−0.0464814	+	0.998919i	$0.514801\pi$
$360$	−1.50115	+	2.60006i	−0.0791173	+	0.137035i
$361$	9.41489	+	16.3071i	0.495520	+	0.858266i
$362$	7.51022	+	13.0081i	0.394728	+	0.683689i
$363$	1.00000			0.0524864
$364$	−0.618685	+	3.83035i	−0.0324279	+	0.200765i
$365$	−5.45555			−0.285556
$366$	1.55389	+	2.69141i	0.0812229	+	0.140682i
$367$	−4.56617	−	7.90883i	−0.238352	−	0.412838i	0.721890	−	0.692008i	$-0.243274\pi$
$367$	−4.56617	−	7.90883i	−0.238352	−	0.412838i	−0.960242	+	0.279171i	$0.909941\pi$
$368$	−0.815938	+	1.41325i	−0.0425337	+	0.0736706i
$369$	−4.39677			−0.228887
$370$	−2.42275	+	4.19632i	−0.125953	+	0.218156i
$371$	0.353256	−	0.611857i	0.0183401	−	0.0317660i
$372$	−3.16898			−0.164304
$373$	−4.27623	+	7.40665i	−0.221415	+	0.383502i	−0.955238	−	0.295839i	$-0.904401\pi$
$373$	−4.27623	+	7.40665i	−0.221415	+	0.383502i	0.733823	+	0.679341i	$0.237734\pi$
$374$	−2.98798	−	5.17533i	−0.154505	−	0.267610i
$375$	4.89334	+	8.47551i	0.252691	+	0.437674i
$376$	−23.1786			−1.19535
$377$	0.426493	−	2.64047i	0.0219655	−	0.135991i
$378$	−0.629954			−0.0324014
$379$	−3.03518	−	5.25709i	−0.155907	−	0.270039i	0.777482	−	0.628905i	$-0.216497\pi$
$379$	−3.03518	−	5.25709i	−0.155907	−	0.270039i	−0.933389	+	0.358867i	$0.883163\pi$
$380$	−0.314582	−	0.544872i	−0.0161377	−	0.0279514i
$381$	4.09006	−	7.08419i	0.209540	−	0.362934i
$382$	−3.72838			−0.190760
$383$	−0.744236	+	1.28905i	−0.0380287	+	0.0658676i	−0.884413	−	0.466705i	$-0.845441\pi$
$383$	−0.744236	+	1.28905i	−0.0380287	+	0.0658676i	0.846385	+	0.532572i	$0.178774\pi$
$384$	−4.44315	+	7.69576i	−0.226739	+	0.392723i
$385$	0.883080			0.0450059
$386$	−5.49777	+	9.52242i	−0.279829	+	0.484679i
$387$	−2.10352	−	3.64341i	−0.106928	−	0.185205i
$388$	−2.37251	−	4.10931i	−0.120446	−	0.208619i
$389$	2.83887			0.143936			0.0719682	−	0.997407i	$-0.477072\pi$
$389$	2.83887			0.143936			0.0719682	+	0.997407i	$0.477072\pi$
$390$	3.00838	−	1.14426i	0.152335	−	0.0579420i
$391$	−20.9019			−1.05705
$392$	8.55719	+	14.8215i	0.432204	+	0.748598i
$393$	−4.24140	−	7.34631i	−0.213950	−	0.370572i
$394$	−9.01084	+	15.6072i	−0.453960	+	0.786281i
$395$	−11.4708			−0.577157
$396$	0.681594	−	1.18056i	0.0342514	−	0.0593252i
$397$	8.20396	−	14.2097i	0.411745	−	0.713163i	−0.583336	−	0.812231i	$-0.698253\pi$
$397$	8.20396	−	14.2097i	0.411745	−	0.713163i	0.995081	+	0.0990682i	$0.0315862\pi$
$398$	−20.5589			−1.03053
$399$	0.162849	−	0.282063i	0.00815266	−	0.0141208i
$400$	1.09583	+	1.89804i	0.0547917	+	0.0949020i
$401$	3.78266	+	6.55176i	0.188897	+	0.327179i	0.944883	−	0.327409i	$-0.106175\pi$
$401$	3.78266	+	6.55176i	0.188897	+	0.327179i	−0.755986	+	0.654588i	$0.772842\pi$
$402$	8.47445			0.422667
$403$	6.49768	+	5.29471i	0.323672	+	0.263748i
$404$	−12.2292			−0.608426
$405$	−0.559328	−	0.968784i	−0.0277932	−	0.0481393i
$406$	0.233659	+	0.404708i	0.0115963	+	0.0200853i
$407$	2.71398	−	4.70075i	0.134527	−	0.233008i
$408$	−20.0983			−0.995013
$409$	−12.5085	+	21.6653i	−0.618503	+	1.07128i	0.371256	+	0.928531i	$0.378927\pi$
$409$	−12.5085	+	21.6653i	−0.618503	+	1.07128i	−0.989759	+	0.142748i	$0.954406\pi$
$410$	−1.96248	+	3.39912i	−0.0969200	+	0.167870i
$411$	4.70023			0.231845
$412$	−5.48800	+	9.50550i	−0.270374	+	0.468302i
$413$	−2.74074	−	4.74710i	−0.134863	−	0.233590i
$414$	1.11367	+	1.92894i	0.0547341	+	0.0948022i
$415$	−9.53740			−0.468172
$416$	19.6614	−	7.47840i	0.963982	−	0.366659i
$417$	14.1149			0.691210
$418$	−0.164622	−	0.285133i	−0.00805191	−	0.0139463i
$419$	7.70086	+	13.3383i	0.376212	+	0.651618i	0.990508	−	0.137458i	$-0.0438932\pi$
$419$	7.70086	+	13.3383i	0.376212	+	0.651618i	−0.614296	+	0.789076i	$0.710560\pi$
$420$	0.601902	−	1.04253i	0.0293698	−	0.0508700i
$421$	3.88693			0.189437			0.0947187	−	0.995504i	$-0.469805\pi$
$421$	3.88693			0.189437			0.0947187	+	0.995504i	$0.469805\pi$
$422$	9.28073	−	16.0747i	0.451779	−	0.782504i
$423$	4.31819	−	7.47932i	0.209957	−	0.363657i
$424$	−2.40199			−0.116651
$425$	−14.0360	+	24.3110i	−0.680845	+	1.17926i
$426$	−1.04574	−	1.81127i	−0.0506661	−	0.0877563i
$427$	−1.53715	−	2.66243i	−0.0743881	−	0.128844i
$428$	−9.01257			−0.435639
$429$	−3.37001	+	1.28181i	−0.162706	+	0.0618865i
$430$	−3.75559			−0.181111
$431$	11.4709	+	19.8682i	0.552534	+	0.957017i	0.998091	+	0.0617633i	$0.0196724\pi$
$431$	11.4709	+	19.8682i	0.552534	+	0.957017i	−0.445557	+	0.895254i	$0.646994\pi$
$432$	−0.292331	−	0.506332i	−0.0140648	−	0.0243609i
$433$	−8.87577	+	15.3733i	−0.426542	+	0.738793i	−0.996563	−	0.0828374i	$-0.973602\pi$
$433$	−8.87577	+	15.3733i	−0.426542	+	0.738793i	0.570021	+	0.821630i	$0.306935\pi$
$434$	−1.46444			−0.0702954
$435$	−0.414924	+	0.718670i	−0.0198941	+	0.0344576i
$436$	6.82723	−	11.8251i	0.326965	−	0.566320i
$437$	−1.15158			−0.0550876
$438$	−1.94589	+	3.37037i	−0.0929780	+	0.161043i
$439$	0.513035	+	0.888602i	0.0244858	+	0.0424107i	0.878009	−	0.478645i	$-0.158872\pi$
$439$	0.513035	+	0.888602i	0.0244858	+	0.0424107i	−0.853523	+	0.521055i	$0.825538\pi$
$440$	−1.50115	−	2.60006i	−0.0715643	−	0.123953i
$441$	−6.37683			−0.303659
$442$	16.7033	+	13.6109i	0.794496	+	0.647404i
$443$	−21.6894			−1.03049			−0.515247	−	0.857042i	$-0.672300\pi$
$443$	−21.6894			−1.03049			−0.515247	+	0.857042i	$0.672300\pi$
$444$	−3.69967	−	6.40801i	−0.175578	−	0.304111i
$445$	5.91222	+	10.2403i	0.280266	+	0.485435i
$446$	11.6087	−	20.1068i	0.549686	−	0.952083i
$447$	−23.5411			−1.11345
$448$	−1.37611	+	2.38350i	−0.0650153	+	0.112610i
$449$	13.4835	−	23.3540i	0.636324	−	1.10214i	−0.349909	−	0.936784i	$-0.613788\pi$
$449$	13.4835	−	23.3540i	0.636324	−	1.10214i	0.986233	−	0.165361i	$-0.0528790\pi$
$450$	2.99141			0.141016
$451$	2.19838	−	3.80771i	0.103518	−	0.179298i
$452$	4.06856	+	7.04695i	0.191369	+	0.331460i
$453$	−7.15851	−	12.3989i	−0.336336	−	0.582551i
$454$	8.94473			0.419797
$455$	−2.97599	+	1.13194i	−0.139516	+	0.0530663i
$456$	−1.10731			−0.0518544
$457$	−8.53189	−	14.7777i	−0.399105	−	0.691270i	0.594511	−	0.804088i	$-0.297346\pi$
$457$	−8.53189	−	14.7777i	−0.399105	−	0.691270i	−0.993616	+	0.112817i	$0.964013\pi$
$458$	−5.22351	−	9.04738i	−0.244078	−	0.422756i
$459$	3.74431	−	6.48534i	0.174770	−	0.302710i
$460$	−4.25633			−0.198452
$461$	−10.7323	+	18.5890i	−0.499855	+	0.865774i	−1.00000		0.000167448i	$-0.999947\pi$
$461$	−10.7323	+	18.5890i	−0.499855	+	0.865774i	0.500145	+	0.865942i	$0.333280\pi$
$462$	0.314977	−	0.545556i	0.0146541	−	0.0253816i
$463$	13.5790			0.631070			0.315535	−	0.948914i	$-0.397816\pi$
$463$	13.5790			0.631070			0.315535	+	0.948914i	$0.397816\pi$
$464$	−0.216859	+	0.375610i	−0.0100674	+	0.0174373i
$465$	−1.30026	−	2.25211i	−0.0602980	−	0.104439i
$466$	0.975803	+	1.69014i	0.0452032	+	0.0782942i
$467$	−17.8761			−0.827205			−0.413603	−	0.910457i	$-0.635730\pi$
$467$	−17.8761			−0.827205			−0.413603	+	0.910457i	$0.635730\pi$
$468$	−0.783728	+	4.85216i	−0.0362279	+	0.224291i
$469$	−8.38320			−0.387100
$470$	−3.85481	−	6.67673i	−0.177809	−	0.307974i
$471$	10.8726	+	18.8319i	0.500984	+	0.867729i
$472$	−9.31795	+	16.1392i	−0.428894	+	0.742866i
$473$	4.20704			0.193440
$474$	−4.09140	+	7.08651i	−0.187924	+	0.325494i
$475$	−0.773307	+	1.33941i	−0.0354818	+	0.0614562i
$476$	8.05864			0.369367
$477$	0.447492	−	0.775079i	0.0204893	−	0.0354884i
$478$	1.98323	+	3.43505i	0.0907108	+	0.157116i
$479$	−3.25226	−	5.63308i	−0.148600	−	0.257382i	0.782110	−	0.623140i	$-0.214143\pi$
$479$	−3.25226	−	5.63308i	−0.148600	−	0.257382i	−0.930710	+	0.365758i	$0.880810\pi$
$480$	−6.52651			−0.297893
$481$	−3.12066	+	19.3204i	−0.142290	+	0.880934i
$482$	15.5078			0.706363
$483$	−1.10168	−	1.90817i	−0.0501283	−	0.0868248i
$484$	0.681594	+	1.18056i	0.0309816	+	0.0536616i
$485$	1.94692	−	3.37217i	0.0884052	−	0.153122i
$486$	−0.798005			−0.0361982
$487$	−10.2045	+	17.6748i	−0.462412	+	0.800921i	−0.999081	−	0.0428722i	$-0.986349\pi$
$487$	−10.2045	+	17.6748i	−0.462412	+	0.800921i	0.536669	+	0.843793i	$0.319683\pi$
$488$	−5.22601	+	9.05172i	−0.236570	+	0.409752i
$489$	−1.26802			−0.0573418
$490$	−2.84627	+	4.92989i	−0.128581	+	0.222710i
$491$	−20.8084	−	36.0412i	−0.939070	−	1.62652i	−0.767210	−	0.641396i	$-0.778356\pi$
$491$	−20.8084	−	36.0412i	−0.939070	−	1.62652i	−0.171860	−	0.985121i	$-0.554978\pi$
$492$	−2.99681	−	5.19063i	−0.135107	−	0.234012i
$493$	−5.55527			−0.250197
$494$	0.920264	+	0.749887i	0.0414046	+	0.0337390i
$495$	1.11866			0.0502798
$496$	−0.679575	−	1.17706i	−0.0305138	−	0.0528515i
$497$	1.03448	+	1.79177i	0.0464026	+	0.0803717i
$498$	−3.40180	+	5.89209i	−0.152438	+	0.264031i
$499$	9.77223			0.437465			0.218732	−	0.975785i	$-0.429808\pi$
$499$	9.77223			0.437465			0.218732	+	0.975785i	$0.429808\pi$
$500$	−6.67055	+	11.5537i	−0.298316	+	0.516698i
$501$	−9.25169	+	16.0244i	−0.413335	+	0.715917i
$502$	23.2587			1.03809
$503$	−3.18229	+	5.51188i	−0.141891	+	0.245763i	−0.928209	−	0.372060i	$-0.878652\pi$
$503$	−3.18229	+	5.51188i	−0.141891	+	0.245763i	0.786318	+	0.617822i	$0.211985\pi$
$504$	−1.05933	−	1.83481i	−0.0471862	−	0.0817289i
$505$	−5.01774	−	8.69099i	−0.223287	−	0.386744i
$506$	−2.22735			−0.0990177
$507$	9.71392	−	8.63943i	0.431410	−	0.383691i
$508$	11.1510			0.494747
$509$	14.7574	+	25.5606i	0.654112	+	1.13296i	0.982116	+	0.188279i	$0.0602910\pi$
$509$	14.7574	+	25.5606i	0.654112	+	1.13296i	−0.328003	+	0.944677i	$0.606376\pi$
$510$	−3.34252	−	5.78941i	−0.148009	−	0.256360i
$511$	1.92493	−	3.33408i	0.0851540	−	0.147491i
$512$	−6.54933			−0.289442
$513$	0.206292	−	0.357308i	0.00910800	−	0.0157755i
$514$	−7.23535	+	12.5320i	−0.319138	+	0.552763i
$515$	−9.00709			−0.396900
$516$	2.86750	−	4.96665i	0.126235	−	0.218645i
$517$	4.31819	+	7.47932i	0.189914	+	0.328940i
$518$	−1.70968	−	2.96126i	−0.0751192	−	0.130110i
$519$	10.7785			0.473122
$520$	8.39166	+	6.83804i	0.367999	+	0.299868i
$521$	−36.7600			−1.61048			−0.805242	−	0.592946i	$-0.797965\pi$
$521$	−36.7600			−1.61048			−0.805242	+	0.592946i	$0.797965\pi$
$522$	0.295991	+	0.512671i	0.0129552	+	0.0224390i
$523$	11.2928	+	19.5597i	0.493799	+	0.855285i	0.999974	−	0.00714550i	$-0.00227450\pi$
$523$	11.2928	+	19.5597i	0.493799	+	0.855285i	−0.506175	+	0.862431i	$0.668941\pi$
$524$	5.78182	−	10.0144i	0.252580	−	0.437482i
$525$	−2.95920			−0.129150
$526$	2.38753	−	4.13533i	0.104101	−	0.180309i
$527$	8.70433	−	15.0763i	0.379166	−	0.656736i
$528$	0.584661			0.0254441
$529$	7.60475	−	13.1718i	0.330641	−	0.572687i
$530$	−0.399473	−	0.691907i	−0.0173520	−	0.0300545i
$531$	−3.47187	−	6.01346i	−0.150667	−	0.260962i
$532$	0.443988			0.0192493
$533$	−2.52780	+	15.6499i	−0.109491	+	0.677874i
$534$	8.43509			0.365022
$535$	−3.69793	−	6.40500i	−0.159875	−	0.276912i
$536$	14.2506	+	24.6827i	0.615532	+	1.06613i
$537$	6.07695	−	10.5256i	0.262240	−	0.454212i
$538$	8.42616			0.363278
$539$	3.18841	−	5.52250i	0.137335	−	0.237871i
$540$	0.762469	−	1.32064i	0.0328115	−	0.0568311i
$541$	11.4157			0.490800			0.245400	−	0.969422i	$-0.421081\pi$
$541$	11.4157			0.490800			0.245400	+	0.969422i	$0.421081\pi$
$542$	−2.06666	+	3.57957i	−0.0887708	+	0.153755i
$543$	−9.41125	−	16.3008i	−0.403875	−	0.699532i
$544$	−21.8452	−	37.8371i	−0.936607	−	1.62225i
$545$	11.2051			0.479973
$546$	−0.362175	+	2.24227i	−0.0154997	+	0.0959604i
$547$	33.0422			1.41278			0.706390	−	0.707822i	$-0.250322\pi$
$547$	33.0422			1.41278			0.706390	+	0.707822i	$0.250322\pi$
$548$	3.20365	+	5.54889i	0.136853	+	0.237037i
$549$	−1.94721	−	3.37267i	−0.0831051	−	0.143942i
$550$	−1.49570	+	2.59063i	−0.0637770	+	0.110465i
$551$	−0.306065			−0.0130388
$552$	−3.74550	+	6.48739i	−0.159419	+	0.276122i
$553$	4.04734	−	7.01021i	0.172111	−	0.298104i
$554$	22.9805			0.976350
$555$	3.03601	−	5.25852i	0.128871	−	0.223212i
$556$	9.62064	+	16.6634i	0.408006	+	0.706687i
$557$	−5.84184	−	10.1184i	−0.247527	−	0.428729i	0.715312	−	0.698805i	$-0.246284\pi$
$557$	−5.84184	−	10.1184i	−0.247527	−	0.428729i	−0.962839	+	0.270076i	$0.912951\pi$
$558$	−1.85510			−0.0785328
$559$	−14.1778	+	5.39264i	−0.599656	+	0.228084i
$560$	0.516303			0.0218178
$561$	3.74431	+	6.48534i	0.158085	+	0.273811i
$562$	−3.45736	−	5.98832i	−0.145840	−	0.252602i
$563$	13.5051	−	23.3916i	0.569173	−	0.985837i	−0.427475	−	0.904027i	$-0.640597\pi$
$563$	13.5051	−	23.3916i	0.569173	−	0.985837i	0.996648	−	0.0818097i	$-0.0260700\pi$
$564$	11.7730			0.495733
$565$	−3.33873	+	5.78284i	−0.140461	+	0.243286i
$566$	−3.43030	+	5.94145i	−0.144186	+	0.249738i
$567$	0.789412			0.0331522
$568$	3.51701	−	6.09164i	0.147570	−	0.255600i
$569$	10.7461	+	18.6128i	0.450500	+	0.780288i	0.998417	−	0.0562441i	$-0.0179125\pi$
$569$	10.7461	+	18.6128i	0.450500	+	0.780288i	−0.547917	+	0.836532i	$0.684579\pi$
$570$	−0.184155	−	0.318966i	−0.00771340	−	0.0133600i
$571$	29.3958			1.23018			0.615089	−	0.788458i	$-0.289120\pi$
$571$	29.3958			1.23018			0.615089	+	0.788458i	$0.289120\pi$
$572$	−3.81023	−	3.10481i	−0.159314	−	0.129819i
$573$	4.67213			0.195181
$574$	−1.38488	−	2.39869i	−0.0578039	−	0.100119i
$575$	5.23146	+	9.06116i	0.218167	+	0.377876i
$576$	−1.74321	+	3.01934i	−0.0726339	+	0.125806i
$577$	43.7240			1.82026			0.910128	−	0.414328i	$-0.135983\pi$
$577$	43.7240			1.82026			0.910128	+	0.414328i	$0.135983\pi$
$578$	15.5928	−	27.0076i	0.648576	−	1.12337i
$579$	6.88940	−	11.9328i	0.286314	−	0.495910i
$580$	−1.13124			−0.0469722
$581$	3.36517	−	5.82865i	0.139611	−	0.241813i
$582$	−1.38886	−	2.40557i	−0.0575700	−	0.0997141i
$583$	0.447492	+	0.775079i	0.0185332	+	0.0321005i
$584$	−13.0888			−0.541617
$585$	−3.76988	+	1.43391i	−0.155865	+	0.0592847i
$586$	17.4461			0.720691
$587$	15.7280	+	27.2416i	0.649162	+	1.12438i	0.983323	+	0.181866i	$0.0582136\pi$
$587$	15.7280	+	27.2416i	0.649162	+	1.12438i	−0.334161	+	0.942516i	$0.608453\pi$
$588$	−4.34641	−	7.52820i	−0.179243	−	0.310458i
$589$	0.479562	−	0.830626i	0.0197600	−	0.0342253i
$590$	−6.19863			−0.255194
$591$	11.2917	−	19.5578i	0.464479	−	0.804501i
$592$	1.58676	−	2.74835i	0.0652154	−	0.112956i
$593$	−30.2101			−1.24058			−0.620290	−	0.784373i	$-0.712985\pi$
$593$	−30.2101			−1.24058			−0.620290	+	0.784373i	$0.712985\pi$
$594$	0.399002	−	0.691092i	0.0163713	−	0.0283559i
$595$	3.30653	+	5.72708i	0.135554	+	0.234787i
$596$	−16.0455	−	27.7916i	−0.657248	−	1.13839i
$597$	25.7629			1.05441
$598$	7.50618	−	2.85504i	0.306951	−	0.116751i
$599$	−32.7313			−1.33736			−0.668682	−	0.743548i	$-0.733141\pi$
$599$	−32.7313			−1.33736			−0.668682	+	0.743548i	$0.733141\pi$
$600$	5.03033	+	8.71279i	0.205363	+	0.355698i
$601$	2.14656	+	3.71795i	0.0875601	+	0.151658i	0.906479	−	0.422250i	$-0.138760\pi$
$601$	2.14656	+	3.71795i	0.0875601	+	0.151658i	−0.818919	+	0.573909i	$0.805426\pi$
$602$	1.32512	−	2.29518i	0.0540080	−	0.0935445i
$603$	−10.6196			−0.432462
$604$	9.75840	−	16.9020i	0.397064	−	0.687734i
$605$	−0.559328	+	0.968784i	−0.0227399	+	0.0393867i
$606$	−7.15892			−0.290811
$607$	17.0645	−	29.5566i	0.692628	−	1.19967i	−0.278346	−	0.960481i	$-0.589786\pi$
$607$	17.0645	−	29.5566i	0.692628	−	1.19967i	0.970974	−	0.239186i	$-0.0768806\pi$
$608$	−1.20356	−	2.08462i	−0.0488106	−	0.0845425i
$609$	−0.292804	−	0.507151i	−0.0118650	−	0.0205508i
$610$	−3.47652			−0.140760
$611$	−24.1394	−	19.6703i	−0.976576	−	0.795774i
$612$	10.2084			0.412651
$613$	−17.7127	−	30.6792i	−0.715408	−	1.23912i	−0.962802	−	0.270208i	$-0.912908\pi$
$613$	−17.7127	−	30.6792i	−0.715408	−	1.23912i	0.247394	−	0.968915i	$-0.420426\pi$
$614$	−12.3771	−	21.4377i	−0.499498	−	0.865156i
$615$	2.45923	−	4.25952i	0.0991659	−	0.171760i
$616$	2.11866			0.0853631
$617$	12.8829	−	22.3139i	0.518646	−	0.898322i	−0.481119	−	0.876655i	$-0.659769\pi$
$617$	12.8829	−	22.3139i	0.518646	−	0.898322i	0.999765	−	0.0216665i	$-0.00689721\pi$
$618$	−3.21265	+	5.56447i	−0.129232	+	0.223836i
$619$	32.7419			1.31601			0.658004	−	0.753014i	$-0.271401\pi$
$619$	32.7419			1.31601			0.658004	+	0.753014i	$0.271401\pi$
$620$	1.77250	−	3.07005i	0.0711852	−	0.123296i
$621$	−1.39557	−	2.41720i	−0.0560024	−	0.0969991i
$622$	5.97800	+	10.3542i	0.239696	+	0.415165i
$623$	−8.34427			−0.334306
$624$	−1.97031	+	0.749426i	−0.0788757	+	0.0300010i
$625$	7.79513			0.311805
$626$	−10.2652	−	17.7799i	−0.410281	−	0.710627i
$627$	0.206292	+	0.357308i	0.00823850	+	0.0142695i
$628$	−14.8214	+	25.6715i	−0.591439	+	1.02440i
$629$	40.6480			1.62074
$630$	0.352351	−	0.610290i	0.0140380	−	0.0243145i
$631$	−2.09784	+	3.63356i	−0.0835136	+	0.144650i	−0.904757	−	0.425928i	$-0.859948\pi$
$631$	−2.09784	+	3.63356i	−0.0835136	+	0.144650i	0.821243	+	0.570578i	$0.193281\pi$
$632$	−27.5203			−1.09470
$633$	−11.6299	+	20.1436i	−0.462248	+	0.800637i
$634$	−7.89632	−	13.6768i	−0.313603	−	0.543176i
$635$	4.57536	+	7.92476i	0.181568	+	0.314485i
$636$	1.22003			0.0483774
$637$	−3.66618	+	22.6978i	−0.145260	+	0.899320i
$638$	−0.591981			−0.0234368
$639$	1.31044	+	2.26975i	0.0518402	+	0.0897898i
$640$	−4.97035	−	8.60890i	−0.196470	−	0.340297i
$641$	−14.4845	+	25.0880i	−0.572105	+	0.990915i	0.424245	+	0.905548i	$0.360540\pi$
$641$	−14.4845	+	25.0880i	−0.572105	+	0.990915i	−0.996350	+	0.0853673i	$0.972794\pi$
$642$	−5.27591			−0.208224
$643$	0.961673	−	1.66567i	0.0379247	−	0.0656875i	−0.846440	−	0.532484i	$-0.821259\pi$
$643$	0.961673	−	1.66567i	0.0379247	−	0.0656875i	0.884365	+	0.466797i	$0.154592\pi$
$644$	1.50180	−	2.60120i	0.0591793	−	0.102502i
$645$	4.70623			0.185308
$646$	1.23279	−	2.13526i	0.0485035	−	0.0840105i
$647$	−24.0727	−	41.6951i	−0.946394	−	1.63920i	−0.752936	−	0.658094i	$-0.771363\pi$
$647$	−24.0727	−	41.6951i	−0.946394	−	1.63920i	−0.193458	−	0.981108i	$-0.561970\pi$
$648$	−1.34192	−	2.32427i	−0.0527156	−	0.0913061i
$649$	6.94375			0.272566
$650$	1.71983	−	10.6477i	0.0674572	−	0.417636i
$651$	1.83513			0.0719244
$652$	−0.864274	−	1.49697i	−0.0338476	−	0.0586258i
$653$	12.8381	+	22.2363i	0.502394	+	0.870172i	0.999996	+	0.00276656i	$0.000880625\pi$
$653$	12.8381	+	22.2363i	0.502394	+	0.870172i	−0.497602	+	0.867405i	$0.665786\pi$
$654$	3.99663	−	6.92236i	0.156281	−	0.270686i
$655$	9.48932			0.370778
$656$	1.28531	−	2.22622i	0.0501829	−	0.0869194i
$657$	2.43844	−	4.22350i	0.0951326	−	0.164774i
$658$	5.44052			0.212094
$659$	9.91074	−	17.1659i	0.386068	−	0.668689i	−0.605849	−	0.795580i	$-0.707166\pi$
$659$	9.91074	−	17.1659i	0.386068	−	0.668689i	0.991917	+	0.126891i	$0.0404998\pi$
$660$	0.762469	+	1.32064i	0.0296791	+	0.0514057i
$661$	−9.45771	−	16.3812i	−0.367862	−	0.637156i	0.621369	−	0.783518i	$-0.286577\pi$
$661$	−9.45771	−	16.3812i	−0.367862	−	0.637156i	−0.989231	+	0.146362i	$0.953244\pi$
$662$	16.8538			0.655040
$663$	−20.9314	−	17.0562i	−0.812907	−	0.662406i
$664$	−22.8818			−0.887986
$665$	0.182172	+	0.315531i	0.00706433	+	0.0122358i
$666$	−2.16577	−	3.75122i	−0.0839218	−	0.145357i
$667$	−1.03527	+	1.79315i	−0.0400860	+	0.0694309i
$668$	−25.2236			−0.975930
$669$	−14.5471	+	25.1963i	−0.562423	+	0.974146i
$670$	−4.74000	+	8.20991i	−0.183122	+	0.317177i
$671$	3.89443			0.150343
$672$	2.30281	−	3.98858i	0.0888328	−	0.153863i
$673$	11.0526	+	19.1436i	0.426046	+	0.737933i	0.996517	−	0.0833845i	$-0.0265730\pi$
$673$	11.0526	+	19.1436i	0.426046	+	0.737933i	−0.570472	+	0.821317i	$0.693240\pi$
$674$	10.6817	+	18.5013i	0.411445	+	0.712644i
$675$	−3.74861			−0.144284
$676$	16.8203	+	5.57924i	0.646934	+	0.214586i
$677$	−11.5681			−0.444600			−0.222300	−	0.974978i	$-0.571356\pi$
$677$	−11.5681			−0.444600			−0.222300	+	0.974978i	$0.571356\pi$
$678$	2.38171	+	4.12525i	0.0914692	+	0.158429i
$679$	1.37390	+	2.37967i	0.0527255	+	0.0913233i
$680$	11.2415	−	19.4709i	0.431093	−	0.746675i
$681$	−11.2089			−0.429525
$682$	0.927552	−	1.60657i	0.0355178	−	0.0615186i
$683$	5.71888	−	9.90538i	0.218827	−	0.379019i	−0.735623	−	0.677391i	$-0.763110\pi$
$683$	5.71888	−	9.90538i	0.218827	−	0.379019i	0.954450	+	0.298372i	$0.0964437\pi$
$684$	0.562429			0.0215050
$685$	−2.62897	+	4.55351i	−0.100448	+	0.173981i
$686$	−4.21340	−	7.29782i	−0.160868	−	0.278632i
$687$	6.54571	+	11.3375i	0.249734	+	0.432553i
$688$	2.45970			0.0937750
$689$	−2.50156	−	2.03842i	−0.0953018	−	0.0776577i
$690$	−2.49164			−0.0948549
$691$	14.6136	+	25.3115i	0.555928	+	0.962896i	0.997831	+	0.0658329i	$0.0209704\pi$
$691$	14.6136	+	25.3115i	0.555928	+	0.962896i	−0.441902	+	0.897063i	$0.645696\pi$
$692$	7.34653	+	12.7246i	0.279273	+	0.483716i
$693$	−0.394706	+	0.683651i	−0.0149936	+	0.0259697i
$694$	7.76360			0.294702
$695$	−7.89486	+	13.6743i	−0.299469	+	0.518696i
$696$	−0.995472	+	1.72421i	−0.0377333	+	0.0653560i
$697$	32.9258			1.24715
$698$	4.02309	−	6.96820i	0.152276	−	0.263750i
$699$	−1.22280	−	2.11796i	−0.0462507	−	0.0801085i
$700$	−2.01697	−	3.49350i	−0.0762344	−	0.132042i
$701$	17.7950			0.672107			0.336054	−	0.941843i	$-0.390908\pi$
$701$	17.7950			0.672107			0.336054	+	0.941843i	$0.390908\pi$
$702$	−0.458791	+	2.84043i	−0.0173160	+	0.107205i
$703$	2.23949			0.0844638
$704$	−1.74321	−	3.01934i	−0.0656999	−	0.113795i
$705$	4.83056	+	8.36678i	0.181930	+	0.315111i
$706$	1.39749	−	2.42053i	0.0525954	−	0.0910979i
$707$	7.08184			0.266340
$708$	4.73282	−	8.19749i	0.177870	−	0.308080i
$709$	6.10585	−	10.5757i	0.229310	−	0.397177i	−0.728294	−	0.685265i	$-0.759686\pi$
$709$	6.10585	−	10.5757i	0.229310	−	0.397177i	0.957604	+	0.288088i	$0.0930196\pi$
$710$	2.33964			0.0878051
$711$	5.12704	−	8.88029i	0.192279	−	0.333037i
$712$	14.1844	+	24.5681i	0.531583	+	0.920729i
$713$	−3.24426	−	5.61922i	−0.121499	−	0.210442i
$714$	4.71749			0.176548
$715$	0.643141	−	3.98176i	0.0240521	−	0.148910i
$716$	16.5681			0.619177
$717$	−2.48524	−	4.30455i	−0.0928128	−	0.160757i
$718$	−0.702800	−	1.21728i	−0.0262283	−	0.0454287i
$719$	−10.0757	+	17.4517i	−0.375761	+	0.650838i	−0.990441	−	0.137939i	$-0.955952\pi$
$719$	−10.0757	+	17.4517i	−0.375761	+	0.650838i	0.614679	+	0.788777i	$0.289285\pi$
$720$	0.654035			0.0243744
$721$	3.17806	−	5.50456i	0.118357	−	0.205000i
$722$	−7.51312	+	13.0131i	−0.279609	+	0.484298i
$723$	−19.4333			−0.722732
$724$	12.8293	−	22.2210i	0.476797	−	0.825837i
$725$	1.39041	+	2.40826i	0.0516385	+	0.0894405i
$726$	0.399002	+	0.691092i	0.0148084	+	0.0256488i
$727$	4.73751			0.175705			0.0878523	−	0.996134i	$-0.472000\pi$
$727$	4.73751			0.175705			0.0878523	+	0.996134i	$0.472000\pi$
$728$	−7.13989	+	2.71572i	−0.264622	+	0.100651i
$729$	1.00000			0.0370370
$730$	−2.17678	−	3.77028i	−0.0805661	−	0.139545i
$731$	15.7525	+	27.2841i	0.582627	+	1.00914i
$732$	2.65442	−	4.59759i	0.0981102	−	0.169932i
$733$	7.54526			0.278691			0.139345	−	0.990244i	$-0.455500\pi$
$733$	7.54526			0.278691			0.139345	+	0.990244i	$0.455500\pi$
$734$	3.64382	−	6.31128i	0.134496	−	0.232954i
$735$	3.56674	−	6.17777i	0.131561	−	0.227870i
$736$	−16.2842			−0.600245
$737$	5.30978	−	9.19680i	0.195588	−	0.338769i
$738$	−1.75432	−	3.03857i	−0.0645774	−	0.111851i
$739$	13.4165	+	23.2381i	0.493535	+	0.854827i	0.999972	−	0.00744958i	$-0.00237130\pi$
$739$	13.4165	+	23.2381i	0.493535	+	0.854827i	−0.506438	+	0.862277i	$0.669038\pi$
$740$	8.27730			0.304280
$741$	−1.15321	−	0.939703i	−0.0423641	−	0.0345209i
$742$	0.563799			0.0206977
$743$	0.776831	+	1.34551i	0.0284992	+	0.0493620i	0.879923	−	0.475116i	$-0.157594\pi$
$743$	0.776831	+	1.34551i	0.0284992	+	0.0493620i	−0.851424	+	0.524478i	$0.824261\pi$
$744$	−3.11953	−	5.40319i	−0.114368	−	0.198091i
$745$	13.1672	−	22.8062i	0.482408	−	0.835555i
$746$	−6.82491			−0.249878
$747$	4.26288	−	7.38353i	0.155971	−	0.270149i
$748$	−5.10421	+	8.84074i	−0.186628	+	0.323250i
$749$	5.21911			0.190702
$750$	−3.90491	+	6.76350i	−0.142587	+	0.246968i
$751$	−2.44586	−	4.23635i	−0.0892505	−	0.154586i	0.817944	−	0.575298i	$-0.195114\pi$
$751$	−2.44586	−	4.23635i	−0.0892505	−	0.154586i	−0.907195	+	0.420711i	$0.861781\pi$
$752$	2.52468	+	4.37287i	0.0920655	+	0.159462i
$753$	−29.1461			−1.06214
$754$	1.99498	−	0.758808i	0.0726530	−	0.0276342i
$755$	16.0158			0.582875
$756$	0.538059	+	0.931945i	0.0195690	+	0.0338945i
$757$	−20.3876	−	35.3124i	−0.741000	−	1.28345i	−0.952040	−	0.305973i	$-0.901018\pi$
$757$	−20.3876	−	35.3124i	−0.741000	−	1.28345i	0.211040	−	0.977477i	$-0.432315\pi$
$758$	2.42209	−	4.19518i	0.0879743	−	0.152376i
$759$	2.79115			0.101312
$760$	0.619348	−	1.07274i	0.0224661	−	0.0389125i
$761$	−6.75585	+	11.7015i	−0.244899	+	0.424178i	−0.962103	−	0.272685i	$-0.912088\pi$
$761$	−6.75585	+	11.7015i	−0.244899	+	0.424178i	0.717204	+	0.696863i	$0.245422\pi$
$762$	6.52777			0.236476
$763$	−3.95359	+	6.84783i	−0.143130	+	0.247908i
$764$	3.18450	+	5.51571i	0.115211	+	0.199551i
$765$	4.18860	+	7.25486i	0.151439	+	0.262300i
$766$	−1.18781			−0.0429172
$767$	−23.4005	+	8.90058i	−0.844943	+	0.321381i
$768$	−14.0642			−0.507497
$769$	4.78602	+	8.28964i	0.172588	+	0.298932i	0.939324	−	0.343031i	$-0.111454\pi$
$769$	4.78602	+	8.28964i	0.172588	+	0.298932i	−0.766736	+	0.641963i	$0.778120\pi$
$770$	0.352351	+	0.610290i	0.0126978	+	0.0219933i
$771$	9.06680	−	15.7042i	0.326533	−	0.565572i
$772$	18.7831			0.676019
$773$	−15.8161	+	27.3942i	−0.568864	+	0.985302i	0.427814	+	0.903867i	$0.359284\pi$
$773$	−15.8161	+	27.3942i	−0.568864	+	0.985302i	−0.996679	+	0.0814352i	$0.974050\pi$
$774$	1.67862	−	2.90745i	0.0603367	−	0.104506i
$775$	−8.71431			−0.313027
$776$	4.67099	−	8.09039i	0.167679	−	0.290428i
$777$	2.14245	+	3.71083i	0.0768599	+	0.133125i
$778$	1.13272	+	1.96192i	0.0406098	+	0.0703382i
$779$	1.81403			0.0649945
$780$	−4.26233	−	3.47321i	−0.152616	−	0.124361i
$781$	−2.62088			−0.0937824
$782$	−8.33989	−	14.4451i	−0.298234	−	0.516556i
$783$	−0.370913	−	0.642441i	−0.0132554	−	0.0229590i
$784$	1.86414	−	3.22879i	0.0665765	−	0.115314i
$785$	−24.3254			−0.868211
$786$	3.38465	−	5.86239i	0.120727	−	0.209105i
$787$	−3.47440	+	6.01783i	−0.123849	+	0.214513i	−0.921282	−	0.388894i	$-0.872857\pi$
$787$	−3.47440	+	6.01783i	−0.123849	+	0.214513i	0.797433	+	0.603407i	$0.206190\pi$
$788$	30.7855			1.09669
$789$	−2.99188	+	5.18209i	−0.106514	+	0.184487i
$790$	−4.57686	−	7.92736i	−0.162838	−	0.282043i
$791$	−2.35607	−	4.08083i	−0.0837722	−	0.145098i
$792$	2.68384			0.0953661
$793$	−13.1243	+	4.99192i	−0.466056	+	0.177268i
$794$	13.0936			0.464674
$795$	0.500590	+	0.867047i	0.0177541	+	0.0307510i
$796$	17.5599	+	30.4146i	0.622393	+	1.07802i
$797$	−8.65577	+	14.9922i	−0.306603	+	0.531052i	−0.977617	−	0.210393i	$-0.932526\pi$
$797$	−8.65577	+	14.9922i	−0.306603	+	0.531052i	0.671014	+	0.741445i	$0.265859\pi$
$798$	0.259909			0.00920067
$799$	−32.3373	+	56.0098i	−1.14401	+	1.98149i
$800$	−10.9351	+	18.9402i	−0.386616	+	0.669638i
$801$	−10.5702			−0.373481
$802$	−3.01858	+	5.22833i	−0.106590	+	0.184619i
$803$	2.43844	+	4.22350i	0.0860506	+	0.149044i
$804$	−7.23823	−	12.5370i	−0.255273	−	0.442145i
$805$	2.46481			0.0868730
$806$	−1.06654	+	6.60309i	−0.0375673	+	0.232584i
$807$	−10.5590			−0.371696
$808$	−12.0384	−	20.8511i	−0.423509	−	0.733540i
$809$	10.9594	+	18.9822i	0.385312	+	0.667380i	0.991812	−	0.127703i	$-0.0407605\pi$
$809$	10.9594	+	18.9822i	0.385312	+	0.667380i	−0.606500	+	0.795083i	$0.707427\pi$
$810$	0.446346	−	0.773094i	0.0156830	−	0.0271638i
$811$	35.3904			1.24272			0.621362	−	0.783524i	$-0.286580\pi$
$811$	35.3904			1.24272			0.621362	+	0.783524i	$0.286580\pi$
$812$	0.399147	−	0.691342i	0.0140073	−	0.0242613i
$813$	2.58979	−	4.48565i	0.0908278	−	0.157318i
$814$	4.33154			0.151820
$815$	0.709238	−	1.22844i	0.0248435	−	0.0430302i
$816$	2.18916	+	3.79173i	0.0766358	+	0.132737i
$817$	0.867878	+	1.50321i	0.0303632	+	0.0525906i
$818$	−19.9636			−0.698011
$819$	0.453851	−	2.80985i	0.0158588	−	0.0981840i
$820$	6.70480			0.234142
$821$	9.22252	+	15.9739i	0.321868	+	0.557492i	0.980874	−	0.194646i	$-0.0623559\pi$
$821$	9.22252	+	15.9739i	0.321868	+	0.557492i	−0.659005	+	0.752138i	$0.729023\pi$
$822$	1.87540	+	3.24830i	0.0654122	+	0.113297i
$823$	−27.5860	+	47.7803i	−0.961586	+	1.66552i	−0.243067	+	0.970010i	$0.578153\pi$
$823$	−27.5860	+	47.7803i	−0.961586	+	1.66552i	−0.718520	+	0.695507i	$0.755180\pi$
$824$	−21.6095			−0.752803
$825$	1.87430	−	3.24639i	0.0652549	−	0.113025i
$826$	2.18712	−	3.78821i	0.0760997	−	0.131809i
$827$	32.8428			1.14206			0.571028	−	0.820930i	$-0.306545\pi$
$827$	32.8428			1.14206			0.571028	+	0.820930i	$0.306545\pi$
$828$	1.90243	−	3.29511i	0.0661140	−	0.114513i
$829$	−18.2748	−	31.6528i	−0.634709	−	1.09935i	−0.986577	−	0.163298i	$-0.947787\pi$
$829$	−18.2748	−	31.6528i	−0.634709	−	1.09935i	0.351868	−	0.936050i	$-0.385547\pi$
$830$	−3.80544	−	6.59122i	−0.132089	−	0.228785i
$831$	−28.7975			−0.998975
$832$	9.74487	+	7.94072i	0.337842	+	0.275295i
$833$	47.7537			1.65457
$834$	5.63188	+	9.75470i	0.195016	+	0.337778i
$835$	−10.3494	−	17.9258i	−0.358157	−	0.620347i
$836$	−0.281215	+	0.487078i	−0.00972601	+	0.0168459i
$837$	2.32468			0.0803527
$838$	−6.14532	+	10.6440i	−0.212287	+	0.367691i
$839$	−9.21621	+	15.9629i	−0.318179	+	0.551102i	−0.980108	−	0.198464i	$-0.936405\pi$
$839$	−9.21621	+	15.9629i	−0.318179	+	0.551102i	0.661929	+	0.749566i	$0.269738\pi$
$840$	2.37005			0.0817743
$841$	14.2248	−	24.6382i	0.490512	−	0.849592i
$842$	1.55089	+	2.68623i	0.0534473	+	0.0925735i
$843$	4.33250	+	7.50411i	0.149219	+	0.258455i
$844$	−31.7075			−1.09142
$845$	2.93648	+	14.2430i	0.101018	+	0.489973i
$846$	6.89186			0.236947
$847$	−0.394706	−	0.683651i	−0.0135623	−	0.0234905i
$848$	0.261631	+	0.453159i	0.00898446	+	0.0155615i
$849$	4.29859	−	7.44538i	0.147527	−	0.255525i
$850$	−22.4015			−0.768366
$851$	7.57512	−	13.1205i	0.259672	−	0.449765i
$852$	−1.78638	+	3.09410i	−0.0612003	+	0.106002i
$853$	21.3401			0.730673			0.365336	−	0.930876i	$-0.380954\pi$
$853$	21.3401			0.730673			0.365336	+	0.930876i	$0.380954\pi$
$854$	1.22666	−	2.12463i	0.0419753	−	0.0727034i
$855$	0.230769	+	0.399704i	0.00789215	+	0.0136696i
$856$	−8.87195	−	15.3667i	−0.303237	−	0.525222i
$857$	−37.9175			−1.29524			−0.647619	−	0.761964i	$-0.724235\pi$
$857$	−37.9175			−1.29524			−0.647619	+	0.761964i	$0.724235\pi$
$858$	−2.23049	−	1.81754i	−0.0761477	−	0.0620498i
$859$	−24.0448			−0.820397			−0.410198	−	0.911996i	$-0.634541\pi$
$859$	−24.0448			−0.820397			−0.410198	+	0.911996i	$0.634541\pi$
$860$	3.20774	+	5.55597i	0.109383	+	0.189457i
$861$	1.73543	+	3.00585i	0.0591433	+	0.102439i
$862$	−9.15383	+	15.8549i	−0.311781	+	0.540020i
$863$	−27.4294			−0.933707			−0.466853	−	0.884335i	$-0.654612\pi$
$863$	−27.4294			−0.933707			−0.466853	+	0.884335i	$0.654612\pi$
$864$	2.91712	−	5.05260i	0.0992425	−	0.171893i
$865$	−6.02869	+	10.4420i	−0.204982	+	0.355038i
$866$	−14.1658			−0.481374
$867$	−19.5398	+	33.8439i	−0.663605	+	1.14940i
$868$	1.25081	+	2.16647i	0.0424554	+	0.0735349i
$869$	5.12704	+	8.88029i	0.173923	+	0.301243i
$870$	−0.662223			−0.0224515
$871$	−6.10542	+	37.7994i	−0.206874	+	1.28079i
$872$	26.8828			0.910367
$873$	1.74041	+	3.01448i	0.0589040	+	0.102025i
$874$	−0.459484	−	0.795849i	−0.0155423	−	0.0269200i
$875$	3.86286	−	6.69067i	0.130589	−	0.226186i
$876$	6.64810			0.224619
$877$	12.4663	−	21.5923i	0.420957	−	0.729119i	−0.575076	−	0.818100i	$-0.695028\pi$
$877$	12.4663	−	21.5923i	0.420957	−	0.729119i	0.996033	+	0.0889809i	$0.0283610\pi$
$878$	−0.409404	+	0.709108i	−0.0138167	+	0.0239312i
$879$	−21.8621			−0.737392
$880$	−0.327017	+	0.566411i	−0.0110238	+	0.0190937i
$881$	−28.0005	−	48.4983i	−0.943362	−	1.63395i	−0.758999	−	0.651092i	$-0.774311\pi$
$881$	−28.0005	−	48.4983i	−0.943362	−	1.63395i	−0.184363	−	0.982858i	$-0.559022\pi$
$882$	−2.54437	−	4.40698i	−0.0856734	−	0.148391i
$883$	−2.70589			−0.0910605			−0.0455303	−	0.998963i	$-0.514498\pi$
$883$	−2.70589			−0.0910605			−0.0455303	+	0.998963i	$0.514498\pi$
$884$	5.86905	−	36.3360i	0.197398	−	1.22211i
$885$	7.76766			0.261107
$886$	−8.65411	−	14.9894i	−0.290741	−	0.503577i
$887$	−20.2181	−	35.0187i	−0.678856	−	1.17581i	−0.975326	−	0.220771i	$-0.929143\pi$
$887$	−20.2181	−	35.0187i	−0.678856	−	1.17581i	0.296469	−	0.955042i	$-0.404191\pi$
$888$	7.28389	−	12.6161i	0.244431	−	0.423367i
$889$	−6.45748			−0.216577
$890$	−4.71798	+	8.17178i	−0.158147	+	0.273919i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−39.6609			−1.32794
$893$	−1.78161	+	3.08584i	−0.0596194	+	0.103264i
$894$	−9.39294	−	16.2690i	−0.314147	−	0.544118i
$895$	6.79801	+	11.7745i	0.227232	+	0.393578i
$896$	7.01495			0.234353
$897$	−9.40619	+	3.57773i	−0.314064	+	0.119457i
$898$	21.5197			0.718122
$899$	−0.862255	−	1.49347i	−0.0287578	−	0.0498100i
$900$	−2.55503	−	4.42544i	−0.0851677	−	0.147515i
$901$	−3.35110	+	5.80428i	−0.111641	+	0.193369i
$902$	3.50864			0.116825
$903$	−1.66055	+	2.87615i	−0.0552595	+	0.0957122i
$904$	−8.01016	+	13.8740i	−0.266414	+	0.461442i
$905$	21.0559			0.699921
$906$	5.71252	−	9.89438i	0.189786	−	0.328719i
$907$	−1.21275	−	2.10055i	−0.0402688	−	0.0697476i	0.845189	−	0.534468i	$-0.179488\pi$
$907$	−1.21275	−	2.10055i	−0.0402688	−	0.0697476i	−0.885457	+	0.464721i	$0.846155\pi$
$908$	−7.63991	−	13.2327i	−0.253539	−	0.439143i
$909$	8.97103			0.297550
$910$	−1.96970	−	1.60503i	−0.0652950	−	0.0532064i
$911$	−16.0657			−0.532279			−0.266140	−	0.963934i	$-0.585748\pi$
$911$	−16.0657			−0.532279			−0.266140	+	0.963934i	$0.585748\pi$
$912$	0.120611	+	0.208904i	0.00399382	+	0.00691750i
$913$	4.26288	+	7.38353i	0.141081	+	0.244359i
$914$	6.80849	−	11.7927i	0.225205	−	0.390066i
$915$	4.35652			0.144022
$916$	−8.92304	+	15.4552i	−0.294825	+	0.510653i
$917$	−3.34821	+	5.79927i	−0.110568	+	0.191509i
$918$	5.97596			0.197236
$919$	−2.29016	+	3.96668i	−0.0755455	+	0.130849i	−0.901323	−	0.433147i	$-0.857403\pi$
$919$	−2.29016	+	3.96668i	−0.0755455	+	0.130849i	0.825778	+	0.563996i	$0.190736\pi$
$920$	−4.18992	−	7.25716i	−0.138138	−	0.239261i
$921$	15.5100	+	26.8642i	0.511073	+	0.885204i
$922$	−17.1289			−0.564111
$923$	8.83239	−	3.35947i	0.290722	−	0.110578i
$924$	−1.07612			−0.0354017
$925$	−10.1737	−	17.6213i	−0.334508	−	0.579384i
$926$	5.41805	+	9.38434i	0.178048	+	0.308389i
$927$	4.02586	−	6.97299i	0.132226	−	0.229023i
$928$	−4.32800			−0.142073
$929$	16.5511	−	28.6673i	0.543024	−	0.940545i	−0.455705	−	0.890131i	$-0.650613\pi$
$929$	16.5511	−	28.6673i	0.543024	−	0.940545i	0.998728	−	0.0504139i	$-0.0160540\pi$
$930$	1.03761	−	1.79720i	0.0340246	−	0.0589324i
$931$	2.63097			0.0862267
$932$	1.66691	−	2.88718i	0.0546015	−	0.0945726i
$933$	−7.49118	−	12.9751i	−0.245250	−	0.424786i
$934$	−7.13259	−	12.3540i	−0.233385	−	0.404235i
$935$	−8.37719			−0.273964
$936$	−9.04456	+	3.44018i	−0.295631	+	0.112446i
$937$	2.34244			0.0765242			0.0382621	−	0.999268i	$-0.487818\pi$
$937$	2.34244			0.0765242			0.0382621	+	0.999268i	$0.487818\pi$
$938$	−3.34492	−	5.79357i	−0.109215	−	0.189167i
$939$	12.8636	+	22.2804i	0.419788	+	0.727094i
$940$	−6.58497	+	11.4055i	−0.214778	+	0.372006i
$941$	4.60126			0.149997			0.0749984	−	0.997184i	$-0.476105\pi$
$941$	4.60126			0.149997			0.0749984	+	0.997184i	$0.476105\pi$
$942$	−8.67639	+	15.0280i	−0.282692	+	0.489637i
$943$	6.13602	−	10.6279i	0.199816	−	0.346092i
$944$	4.05974			0.132133
$945$	−0.441540	+	0.764770i	−0.0143633	+	0.0248780i
$946$	1.67862	+	2.90745i	0.0545766	+	0.0945295i
$947$	13.1784	+	22.8257i	0.428241	+	0.741736i	0.996717	−	0.0809643i	$-0.0258000\pi$
$947$	13.1784	+	22.8257i	0.428241	+	0.741736i	−0.568476	+	0.822700i	$0.692467\pi$
$948$	13.9782			0.453992
$949$	−13.6313	−	11.1076i	−0.442490	−	0.360568i
$950$	−1.23421			−0.0400429
$951$	9.89508	+	17.1388i	0.320870	+	0.555763i
$952$	7.93291	+	13.7402i	0.257107	+	0.445323i
$953$	−18.9540	+	32.8292i	−0.613979	+	1.06344i	0.376584	+	0.926383i	$0.377099\pi$
$953$	−18.9540	+	32.8292i	−0.613979	+	1.06344i	−0.990563	+	0.137060i	$0.956235\pi$
$954$	0.714201			0.0231231
$955$	−2.61325	+	4.52628i	−0.0845628	+	0.146467i
$956$	3.38785	−	5.86792i	0.109571	−	0.189782i
$957$	0.741827			0.0239799
$958$	2.59532	−	4.49523i	0.0838510	−	0.145234i
$959$	−1.85521	−	3.21332i	−0.0599079	−	0.103764i
$960$	−1.95006	−	3.37760i	−0.0629378	−	0.109011i
$961$	−25.5959			−0.825673
$962$	−14.5973	+	5.55221i	−0.470636	+	0.179011i
$963$	6.61138			0.213049
$964$	−13.2456	−	22.9421i	−0.426613	−	0.738915i
$965$	7.70687	+	13.3487i	0.248093	+	0.429709i
$966$	0.879148	−	1.52273i	0.0282861	−	0.0489930i
$967$	34.5168			1.10999			0.554993	−	0.831855i	$-0.312721\pi$
$967$	34.5168			1.10999			0.554993	+	0.831855i	$0.312721\pi$
$968$	−1.34192	+	2.32427i	−0.0431309	+	0.0747050i
$969$	−1.54484	+	2.67574i	−0.0496275	+	0.0859573i
$970$	3.10730			0.0997695
$971$	−10.6558	+	18.4563i	−0.341960	+	0.592292i	−0.984797	−	0.173711i	$-0.944424\pi$
$971$	−10.6558	+	18.4563i	−0.341960	+	0.592292i	0.642836	+	0.766003i	$0.277757\pi$
$972$	0.681594	+	1.18056i	0.0218622	+	0.0378664i
$973$	−5.57124	−	9.64967i	−0.178606	−	0.309354i
$974$	−16.2865			−0.521854
$975$	−2.15516	+	13.3429i	−0.0690204	+	0.427314i
$976$	2.27692			0.0728825
$977$	−27.6669	−	47.9204i	−0.885142	−	1.53311i	−0.845551	−	0.533894i	$-0.820728\pi$
$977$	−27.6669	−	47.9204i	−0.885142	−	1.53311i	−0.0395903	−	0.999216i	$-0.512605\pi$
$978$	−0.505942	−	0.876318i	−0.0161782	−	0.0280215i
$979$	5.28512	−	9.15409i	0.168913	−	0.292566i
$980$	9.72427			0.310630
$981$	−5.00828	+	8.67459i	−0.159902	+	0.276958i
$982$	16.6052	−	28.7611i	0.529893	−	0.917802i
$983$	7.06432			0.225317			0.112658	−	0.993634i	$-0.464063\pi$
$983$	7.06432			0.225317			0.112658	+	0.993634i	$0.464063\pi$
$984$	5.90011	−	10.2193i	0.188089	−	0.325779i
$985$	12.6315	+	21.8785i	0.402474	+	0.697106i
$986$	−2.21656	−	3.83920i	−0.0705898	−	0.122265i
$987$	−6.81766			−0.217008
$988$	0.323353	−	2.00192i	0.0102872	−	0.0636896i
$989$	11.7425			0.373389
$990$	0.446346	+	0.773094i	0.0141858	+	0.0245705i
$991$	22.3086	+	38.6396i	0.708655	+	1.22743i	0.965356	+	0.260935i	$0.0840310\pi$
$991$	22.3086	+	38.6396i	0.708655	+	1.22743i	−0.256701	+	0.966491i	$0.582636\pi$
$992$	6.78137	−	11.7457i	0.215309	−	0.372926i
$993$	−21.1199			−0.670219
$994$	−0.825517	+	1.42984i	−0.0261838	+	0.0453517i
$995$	−14.4099	+	24.9587i	−0.456825	+	0.791244i
$996$	11.6222			0.368264
$997$	−8.83622	+	15.3048i	−0.279846	+	0.484707i	−0.971346	−	0.237669i	$-0.923617\pi$
$997$	−8.83622	+	15.3048i	−0.279846	+	0.484707i	0.691500	+	0.722376i	$0.256950\pi$
$998$	3.89914	+	6.75351i	0.123425	+	0.213779i
$999$	2.71398	+	4.70075i	0.0858665	+	0.148725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.f.133.3	yes	10
13.3	even	3		5577.2.a.n.1.3		5
13.9	even	3	inner	429.2.i.f.100.3	✓	10
13.10	even	6		5577.2.a.w.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.f.100.3	✓	10	13.9	even	3	inner
429.2.i.f.133.3	yes	10	1.1	even	1	trivial
5577.2.a.n.1.3		5	13.3	even	3
5577.2.a.w.1.3		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)

\(f(q)\)	\(=\)	\(q+(0.399002 + 0.691092i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.681594 - 1.18056i) q^{4} +1.11866 q^{5} +(0.399002 - 0.691092i) q^{6} +(-0.394706 + 0.683651i) q^{7} +2.68384 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.399002 + 0.691092i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.681594 - 1.18056i) q^{4} +1.11866 q^{5} +(0.399002 - 0.691092i) q^{6} +(-0.394706 + 0.683651i) q^{7} +2.68384 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.446346 + 0.773094i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.36319 q^{12} +(2.79509 + 2.27761i) q^{13} -0.629954 q^{14} +(-0.559328 - 0.968784i) q^{15} +(-0.292331 - 0.506332i) q^{16} +(3.74431 - 6.48534i) q^{17} -0.798005 q^{18} +(0.206292 - 0.357308i) q^{19} +(0.762469 - 1.32064i) q^{20} +0.789412 q^{21} +(0.399002 - 0.691092i) q^{22} +(-1.39557 - 2.41720i) q^{23} +(-1.34192 - 2.32427i) q^{24} -3.74861 q^{25} +(-0.458791 + 2.84043i) q^{26} +1.00000 q^{27} +(0.538059 + 0.931945i) q^{28} +(-0.370913 - 0.642441i) q^{29} +(0.446346 - 0.773094i) q^{30} +2.32468 q^{31} +(2.91712 - 5.05260i) q^{32} +(-0.500000 + 0.866025i) q^{33} +5.97596 q^{34} +(-0.441540 + 0.764770i) q^{35} +(0.681594 + 1.18056i) q^{36} +(2.71398 + 4.70075i) q^{37} +0.329243 q^{38} +(0.574923 - 3.55942i) q^{39} +3.00229 q^{40} +(2.19838 + 3.80771i) q^{41} +(0.314977 + 0.545556i) q^{42} +(-2.10352 + 3.64341i) q^{43} -1.36319 q^{44} +(-0.559328 + 0.968784i) q^{45} +(1.11367 - 1.92894i) q^{46} -8.63637 q^{47} +(-0.292331 + 0.506332i) q^{48} +(3.18841 + 5.52250i) q^{49} +(-1.49570 - 2.59063i) q^{50} -7.48863 q^{51} +(4.59396 - 1.74735i) q^{52} -0.894984 q^{53} +(0.399002 + 0.691092i) q^{54} +(-0.559328 - 0.968784i) q^{55} +(-1.05933 + 1.83481i) q^{56} -0.412583 q^{57} +(0.295991 - 0.512671i) q^{58} +(-3.47187 + 6.01346i) q^{59} -1.52494 q^{60} +(-1.94721 + 3.37267i) q^{61} +(0.927552 + 1.60657i) q^{62} +(-0.394706 - 0.683651i) q^{63} +3.48643 q^{64} +(3.12674 + 2.54786i) q^{65} -0.798005 q^{66} +(5.30978 + 9.19680i) q^{67} +(-5.10421 - 8.84074i) q^{68} +(-1.39557 + 2.41720i) q^{69} -0.704702 q^{70} +(1.31044 - 2.26975i) q^{71} +(-1.34192 + 2.32427i) q^{72} -4.87688 q^{73} +(-2.16577 + 3.75122i) q^{74} +(1.87430 + 3.24639i) q^{75} +(-0.281215 - 0.487078i) q^{76} +0.789412 q^{77} +(2.68928 - 1.02289i) q^{78} -10.2541 q^{79} +(-0.327017 - 0.566411i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.75432 + 3.03857i) q^{82} -8.52577 q^{83} +(0.538059 - 0.931945i) q^{84} +(4.18860 - 7.25486i) q^{85} -3.35724 q^{86} +(-0.370913 + 0.642441i) q^{87} +(-1.34192 - 2.32427i) q^{88} +(5.28512 + 9.15409i) q^{89} -0.892692 q^{90} +(-2.66033 + 1.01188i) q^{91} -3.80486 q^{92} +(-1.16234 - 2.01323i) q^{93} +(-3.44593 - 5.96853i) q^{94} +(0.230769 - 0.399704i) q^{95} -5.83424 q^{96} +(1.74041 - 3.01448i) q^{97} +(-2.54437 + 4.40698i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 4 q^{2} - 5 q^{3} - 6 q^{4} - 8 q^{5} + 4 q^{6} + 3 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} - 5 q^{11} + 12 q^{12} + 5 q^{13} + 14 q^{14} + 4 q^{15} - 12 q^{16} - 9 q^{17} - 8 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} + 4 q^{22} + 9 q^{23} + 9 q^{24} + 2 q^{25} - 12 q^{26} + 10 q^{27} - q^{28} - 8 q^{29} + 5 q^{30} - 12 q^{31} + 27 q^{32} - 5 q^{33} - 14 q^{34} + 2 q^{35} - 6 q^{36} + 17 q^{37} - 2 q^{38} + 2 q^{39} + 46 q^{40} + 6 q^{41} - 7 q^{42} - 13 q^{43} + 12 q^{44} + 4 q^{45} - 6 q^{46} - 32 q^{47} - 12 q^{48} + 18 q^{49} - 8 q^{50} + 18 q^{51} + 7 q^{52} - 26 q^{53} + 4 q^{54} + 4 q^{55} - q^{56} - 18 q^{57} + 11 q^{58} + 8 q^{59} - 12 q^{60} - 4 q^{61} + 22 q^{62} + 3 q^{63} + 22 q^{64} + 26 q^{65} - 8 q^{66} + 5 q^{67} - 34 q^{68} + 9 q^{69} + 8 q^{70} + 19 q^{71} + 9 q^{72} - 4 q^{73} - 27 q^{74} - q^{75} - 6 q^{76} - 6 q^{77} - 3 q^{78} - 16 q^{79} + 32 q^{80} - 5 q^{81} - 16 q^{82} - 20 q^{83} - q^{84} + 21 q^{85} + 8 q^{86} - 8 q^{87} + 9 q^{88} + 32 q^{89} - 10 q^{90} - 17 q^{91} - 84 q^{92} + 6 q^{93} - 66 q^{94} - 11 q^{95} - 54 q^{96} - 5 q^{97} - 18 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 5 * q^3 - 6 * q^4 - 8 * q^5 + 4 * q^6 + 3 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 - 5 * q^11 + 12 * q^12 + 5 * q^13 + 14 * q^14 + 4 * q^15 - 12 * q^16 - 9 * q^17 - 8 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 + 4 * q^22 + 9 * q^23 + 9 * q^24 + 2 * q^25 - 12 * q^26 + 10 * q^27 - q^28 - 8 * q^29 + 5 * q^30 - 12 * q^31 + 27 * q^32 - 5 * q^33 - 14 * q^34 + 2 * q^35 - 6 * q^36 + 17 * q^37 - 2 * q^38 + 2 * q^39 + 46 * q^40 + 6 * q^41 - 7 * q^42 - 13 * q^43 + 12 * q^44 + 4 * q^45 - 6 * q^46 - 32 * q^47 - 12 * q^48 + 18 * q^49 - 8 * q^50 + 18 * q^51 + 7 * q^52 - 26 * q^53 + 4 * q^54 + 4 * q^55 - q^56 - 18 * q^57 + 11 * q^58 + 8 * q^59 - 12 * q^60 - 4 * q^61 + 22 * q^62 + 3 * q^63 + 22 * q^64 + 26 * q^65 - 8 * q^66 + 5 * q^67 - 34 * q^68 + 9 * q^69 + 8 * q^70 + 19 * q^71 + 9 * q^72 - 4 * q^73 - 27 * q^74 - q^75 - 6 * q^76 - 6 * q^77 - 3 * q^78 - 16 * q^79 + 32 * q^80 - 5 * q^81 - 16 * q^82 - 20 * q^83 - q^84 + 21 * q^85 + 8 * q^86 - 8 * q^87 + 9 * q^88 + 32 * q^89 - 10 * q^90 - 17 * q^91 - 84 * q^92 + 6 * q^93 - 66 * q^94 - 11 * q^95 - 54 * q^96 - 5 * q^97 - 18 * q^98 + 10 * q^99

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