LMFDB - Embedded newform 665.2.i.h.596.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(106,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, 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("665.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.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:	$5.31005173442$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 20 x^{18} - 43 x^{17} + 207 x^{16} - 401 x^{15} + 1351 x^{14} - 2135 x^{13} + \cdots + 1024 $ x^20 - 3x^19 + 20x^18 - 43x^17 + 207x^16 - 401x^15 + 1351x^14 - 2135x^13 + 5714x^12 - 7983x^11 + 16723x^10 - 18718x^9 + 30867x^8 - 28726x^7 + 37857x^6 - 24848x^5 + 21360x^4 - 7488x^3 + 5888x^2 - 1536*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			596.5
Root			$0.302407 + 0.523784i$ of defining polynomial
Character	$\chi$	$=$	665.596
Dual form			665.2.i.h.106.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.302407 + 0.523784i) q^{2} +(0.354617 + 0.614215i) q^{3} +(0.817100 - 1.41526i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.214477 + 0.371485i) q^{6} -1.00000 q^{7} +2.19801 q^{8} +(1.24849 - 2.16245i) q^{9} +O(q^{10})$	\(q+(0.302407 + 0.523784i) q^{2} +(0.354617 + 0.614215i) q^{3} +(0.817100 - 1.41526i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.214477 + 0.371485i) q^{6} -1.00000 q^{7} +2.19801 q^{8} +(1.24849 - 2.16245i) q^{9} +(-0.302407 + 0.523784i) q^{10} -0.340028 q^{11} +1.15903 q^{12} +(3.17154 - 5.49327i) q^{13} +(-0.302407 - 0.523784i) q^{14} +(-0.354617 + 0.614215i) q^{15} +(-0.969507 - 1.67924i) q^{16} +(2.54874 + 4.41454i) q^{17} +1.51021 q^{18} +(-4.22294 + 1.08018i) q^{19} +1.63420 q^{20} +(-0.354617 - 0.614215i) q^{21} +(-0.102827 - 0.178101i) q^{22} +(2.28550 - 3.95860i) q^{23} +(0.779453 + 1.35005i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.83638 q^{26} +3.89865 q^{27} +(-0.817100 + 1.41526i) q^{28} +(-4.46480 + 7.73326i) q^{29} -0.428954 q^{30} +6.98333 q^{31} +(2.78438 - 4.82269i) q^{32} +(-0.120580 - 0.208850i) q^{33} +(-1.54151 + 2.66997i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-2.04029 - 3.53388i) q^{36} -5.09691 q^{37} +(-1.84283 - 1.88525i) q^{38} +4.49873 q^{39} +(1.09901 + 1.90354i) q^{40} +(5.15105 + 8.92188i) q^{41} +(0.214477 - 0.371485i) q^{42} +(-1.54282 - 2.67224i) q^{43} +(-0.277837 + 0.481228i) q^{44} +2.49699 q^{45} +2.76460 q^{46} +(3.43135 - 5.94328i) q^{47} +(0.687607 - 1.19097i) q^{48} +1.00000 q^{49} -0.604813 q^{50} +(-1.80765 + 3.13094i) q^{51} +(-5.18294 - 8.97711i) q^{52} +(-3.62686 + 6.28190i) q^{53} +(1.17898 + 2.04205i) q^{54} +(-0.170014 - 0.294473i) q^{55} -2.19801 q^{56} +(-2.16099 - 2.21074i) q^{57} -5.40074 q^{58} +(-6.28915 - 10.8931i) q^{59} +(0.579515 + 1.00375i) q^{60} +(-4.62027 + 8.00254i) q^{61} +(2.11180 + 3.65775i) q^{62} +(-1.24849 + 2.16245i) q^{63} -0.509963 q^{64} +6.34309 q^{65} +(0.0729282 - 0.126315i) q^{66} +(1.37608 - 2.38344i) q^{67} +8.33030 q^{68} +3.24191 q^{69} +(0.302407 - 0.523784i) q^{70} +(1.65141 + 2.86033i) q^{71} +(2.74421 - 4.75310i) q^{72} +(4.01184 + 6.94871i) q^{73} +(-1.54134 - 2.66968i) q^{74} -0.709234 q^{75} +(-1.92183 + 6.85917i) q^{76} +0.340028 q^{77} +(1.36045 + 2.35636i) q^{78} +(-1.89495 - 3.28215i) q^{79} +(0.969507 - 1.67924i) q^{80} +(-2.36295 - 4.09276i) q^{81} +(-3.11542 + 5.39607i) q^{82} +2.93027 q^{83} -1.15903 q^{84} +(-2.54874 + 4.41454i) q^{85} +(0.933117 - 1.61621i) q^{86} -6.33317 q^{87} -0.747386 q^{88} +(-8.59029 + 14.8788i) q^{89} +(0.755106 + 1.30788i) q^{90} +(-3.17154 + 5.49327i) q^{91} +(-3.73497 - 6.46915i) q^{92} +(2.47641 + 4.28926i) q^{93} +4.15066 q^{94} +(-3.04693 - 3.11708i) q^{95} +3.94956 q^{96} +(1.81490 + 3.14350i) q^{97} +(0.302407 + 0.523784i) q^{98} +(-0.424523 + 0.735295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/665\mathbb{Z}\right)^\times$.

$n$	$211$	$267$	$381$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.302407	+	0.523784i	0.213834	+	0.370371i	0.952911	−	0.303250i	$-0.0980716\pi$
$2$	0.302407	+	0.523784i	0.213834	+	0.370371i	−0.739077	+	0.673621i	$0.764738\pi$
$3$	0.354617	+	0.614215i	0.204738	+	0.354617i	0.950049	−	0.312100i	$-0.101032\pi$
$3$	0.354617	+	0.614215i	0.204738	+	0.354617i	−0.745311	+	0.666717i	$0.767699\pi$
$4$	0.817100	−	1.41526i	0.408550	−	0.707630i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.214477	+	0.371485i	−0.0875599	+	0.151658i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.19801			0.777115
$9$	1.24849	−	2.16245i	0.416165	−	0.720818i
$10$	−0.302407	+	0.523784i	−0.0956294	+	0.165635i
$11$	−0.340028			−0.102522			−0.0512611	−	0.998685i	$-0.516324\pi$
$11$	−0.340028			−0.102522			−0.0512611	+	0.998685i	$0.516324\pi$
$12$	1.15903			0.334583
$13$	3.17154	−	5.49327i	0.879628	−	1.52356i	0.0278777	−	0.999611i	$-0.491125\pi$
$13$	3.17154	−	5.49327i	0.879628	−	1.52356i	0.851750	−	0.523949i	$-0.175542\pi$
$14$	−0.302407	−	0.523784i	−0.0808216	−	0.139987i
$15$	−0.354617	+	0.614215i	−0.0915617	+	0.158590i
$16$	−0.969507	−	1.67924i	−0.242377	−	0.419809i
$17$	2.54874	+	4.41454i	0.618160	+	1.07068i	0.989821	+	0.142316i	$0.0454548\pi$
$17$	2.54874	+	4.41454i	0.618160	+	1.07068i	−0.371662	+	0.928368i	$0.621212\pi$
$18$	1.51021			0.355960
$19$	−4.22294	+	1.08018i	−0.968808	+	0.247811i
$19$	−4.22294	+	1.08018i	−0.968808	+	0.247811i
$20$	1.63420			0.365418
$21$	−0.354617	−	0.614215i	−0.0773838	−	0.134033i
$22$	−0.102827	−	0.178101i	−0.0219227	−	0.0379713i
$23$	2.28550	−	3.95860i	0.476560	−	0.825426i	−0.523079	−	0.852284i	$-0.675217\pi$
$23$	2.28550	−	3.95860i	0.476560	−	0.825426i	0.999639	+	0.0268580i	$0.00855021\pi$
$24$	0.779453	+	1.35005i	0.159105	+	0.275578i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.83638			0.752377
$27$	3.89865			0.750295
$28$	−0.817100	+	1.41526i	−0.154417	+	0.267459i
$29$	−4.46480	+	7.73326i	−0.829092	+	1.43603i	0.0696594	+	0.997571i	$0.477809\pi$
$29$	−4.46480	+	7.73326i	−0.829092	+	1.43603i	−0.898751	+	0.438459i	$0.855525\pi$
$30$	−0.428954			−0.0783159
$31$	6.98333			1.25424			0.627121	−	0.778922i	$-0.284233\pi$
$31$	6.98333			1.25424			0.627121	+	0.778922i	$0.284233\pi$
$32$	2.78438	−	4.82269i	0.492214	−	0.852540i
$33$	−0.120580	−	0.208850i	−0.0209902	−	0.0363561i
$34$	−1.54151	+	2.66997i	−0.264367	+	0.457897i
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−2.04029	−	3.53388i	−0.340048	−	0.588981i
$37$	−5.09691			−0.837927			−0.418964	−	0.908003i	$-0.637607\pi$
$37$	−5.09691			−0.837927			−0.418964	+	0.908003i	$0.637607\pi$
$38$	−1.84283	−	1.88525i	−0.298946	−	0.305828i
$39$	4.49873			0.720373
$40$	1.09901	+	1.90354i	0.173768	+	0.300975i
$41$	5.15105	+	8.92188i	0.804459	+	1.39336i	0.916656	+	0.399677i	$0.130878\pi$
$41$	5.15105	+	8.92188i	0.804459	+	1.39336i	−0.112197	+	0.993686i	$0.535789\pi$
$42$	0.214477	−	0.371485i	0.0330945	−	0.0573214i
$43$	−1.54282	−	2.67224i	−0.235278	−	0.407513i	0.724076	−	0.689720i	$-0.242267\pi$
$43$	−1.54282	−	2.67224i	−0.235278	−	0.407513i	−0.959353	+	0.282208i	$0.908933\pi$
$44$	−0.277837	+	0.481228i	−0.0418855	+	0.0725478i
$45$	2.49699			0.372229
$46$	2.76460			0.407618
$47$	3.43135	−	5.94328i	0.500514	−	0.866917i	−0.499485	−	0.866322i	$-0.666478\pi$
$47$	3.43135	−	5.94328i	0.500514	−	0.866917i	1.00000		0.000594186i	$-0.000189135\pi$
$48$	0.687607	−	1.19097i	0.0992476	−	0.171902i
$49$	1.00000			0.142857
$50$	−0.604813			−0.0855335
$51$	−1.80765	+	3.13094i	−0.253122	+	0.438420i
$52$	−5.18294	−	8.97711i	−0.718744	−	1.24490i
$53$	−3.62686	+	6.28190i	−0.498187	+	0.862886i	−0.999998	−	0.00209198i	$-0.999334\pi$
$53$	−3.62686	+	6.28190i	−0.498187	+	0.862886i	0.501811	+	0.864978i	$0.332667\pi$
$54$	1.17898	+	2.04205i	0.160439	+	0.277888i
$55$	−0.170014	−	0.294473i	−0.0229247	−	0.0397067i
$56$	−2.19801			−0.293722
$57$	−2.16099	−	2.21074i	−0.286230	−	0.292820i
$58$	−5.40074			−0.709152
$59$	−6.28915	−	10.8931i	−0.818778	−	1.41816i	−0.906583	−	0.422027i	$-0.861319\pi$
$59$	−6.28915	−	10.8931i	−0.818778	−	1.41816i	0.0878058	−	0.996138i	$-0.472015\pi$
$60$	0.579515	+	1.00375i	0.0748151	+	0.129584i
$61$	−4.62027	+	8.00254i	−0.591565	+	1.02462i	0.402457	+	0.915439i	$0.368156\pi$
$61$	−4.62027	+	8.00254i	−0.591565	+	1.02462i	−0.994022	+	0.109182i	$0.965177\pi$
$62$	2.11180	+	3.65775i	0.268199	+	0.464535i
$63$	−1.24849	+	2.16245i	−0.157295	+	0.272444i
$64$	−0.509963			−0.0637454
$65$	6.34309			0.786763
$66$	0.0729282	−	0.126315i	0.00897684	−	0.0155483i
$67$	1.37608	−	2.38344i	0.168115	−	0.291184i	−0.769642	−	0.638476i	$-0.779565\pi$
$67$	1.37608	−	2.38344i	0.168115	−	0.291184i	0.937757	+	0.347292i	$0.112899\pi$
$68$	8.33030			1.01020
$69$	3.24191			0.390280
$70$	0.302407	−	0.523784i	0.0361445	−	0.0626041i
$71$	1.65141	+	2.86033i	0.195987	+	0.339459i	0.947224	−	0.320574i	$-0.103876\pi$
$71$	1.65141	+	2.86033i	0.195987	+	0.339459i	−0.751237	+	0.660033i	$0.770542\pi$
$72$	2.74421	−	4.75310i	0.323408	−	0.560159i
$73$	4.01184	+	6.94871i	0.469550	+	0.813284i	0.999394	−	0.0348107i	$-0.0110828\pi$
$73$	4.01184	+	6.94871i	0.469550	+	0.813284i	−0.529844	+	0.848095i	$0.677749\pi$
$74$	−1.54134	−	2.66968i	−0.179177	−	0.310344i
$75$	−0.709234			−0.0818953
$76$	−1.92183	+	6.85917i	−0.220449	+	0.786801i
$77$	0.340028			0.0387498
$78$	1.36045	+	2.35636i	0.154040	+	0.266805i
$79$	−1.89495	−	3.28215i	−0.213198	−	0.369270i	0.739515	−	0.673140i	$-0.235055\pi$
$79$	−1.89495	−	3.28215i	−0.213198	−	0.369270i	−0.952714	+	0.303869i	$0.901721\pi$
$80$	0.969507	−	1.67924i	0.108394	−	0.187744i
$81$	−2.36295	−	4.09276i	−0.262550	−	0.454751i
$82$	−3.11542	+	5.39607i	−0.344041	+	0.595896i
$83$	2.93027			0.321639			0.160820	−	0.986984i	$-0.448586\pi$
$83$	2.93027			0.321639			0.160820	+	0.986984i	$0.448586\pi$
$84$	−1.15903			−0.126461
$85$	−2.54874	+	4.41454i	−0.276449	+	0.478824i
$86$	0.933117	−	1.61621i	0.100621	−	0.174280i
$87$	−6.33317			−0.678987
$88$	−0.747386			−0.0796716
$89$	−8.59029	+	14.8788i	−0.910569	+	1.57715i	−0.0973075	+	0.995254i	$0.531023\pi$
$89$	−8.59029	+	14.8788i	−0.910569	+	1.57715i	−0.813262	+	0.581898i	$0.802310\pi$
$90$	0.755106	+	1.30788i	0.0795951	+	0.137863i
$91$	−3.17154	+	5.49327i	−0.332468	+	0.575851i
$92$	−3.73497	−	6.46915i	−0.389397	−	0.674456i
$93$	2.47641	+	4.28926i	0.256791	+	0.444776i
$94$	4.15066			0.428108
$95$	−3.04693	−	3.11708i	−0.312609	−	0.319806i
$96$	3.94956			0.403100
$97$	1.81490	+	3.14350i	0.184275	+	0.319175i	0.943332	−	0.331850i	$-0.107673\pi$
$97$	1.81490	+	3.14350i	0.184275	+	0.319175i	−0.759057	+	0.651025i	$0.774339\pi$
$98$	0.302407	+	0.523784i	0.0305477	+	0.0529101i
$99$	−0.424523	+	0.735295i	−0.0426661	+	0.0738999i
$100$	0.817100	+	1.41526i	0.0817100	+	0.141526i
$101$	−1.16576	+	2.01915i	−0.115997	+	0.200913i	−0.918178	−	0.396168i	$-0.870340\pi$
$101$	−1.16576	+	2.01915i	−0.115997	+	0.200913i	0.802181	+	0.597081i	$0.203673\pi$
$102$	−2.18658			−0.216504
$103$	−2.33442			−0.230017			−0.115009	−	0.993364i	$-0.536690\pi$
$103$	−2.33442			−0.230017			−0.115009	+	0.993364i	$0.536690\pi$
$104$	6.97109	−	12.0743i	0.683572	−	1.18398i
$105$	0.354617	−	0.614215i	0.0346071	−	0.0599412i
$106$	−4.38714			−0.426117
$107$	−2.77391			−0.268164			−0.134082	−	0.990970i	$-0.542809\pi$
$107$	−2.77391			−0.268164			−0.134082	+	0.990970i	$0.542809\pi$
$108$	3.18559	−	5.51760i	0.306533	−	0.530931i
$109$	−2.38388	−	4.12900i	−0.228334	−	0.395487i	0.728980	−	0.684535i	$-0.239995\pi$
$109$	−2.38388	−	4.12900i	−0.228334	−	0.395487i	−0.957315	+	0.289048i	$0.906661\pi$
$110$	0.102827	−	0.178101i	0.00980414	−	0.0169813i
$111$	−1.80745	−	3.13060i	−0.171556	−	0.297143i
$112$	0.969507	+	1.67924i	0.0916098	+	0.158673i
$113$	−1.49863			−0.140979			−0.0704895	−	0.997513i	$-0.522456\pi$
$113$	−1.49863			−0.140979			−0.0704895	+	0.997513i	$0.522456\pi$
$114$	0.504451	−	1.80043i	0.0472462	−	0.168626i
$115$	4.57100			0.426248
$116$	7.29638	+	12.6377i	0.677451	+	1.17338i
$117$	−7.91930	−	13.7166i	−0.732140	−	1.26810i
$118$	3.80376	−	6.58831i	0.350165	−	0.606503i
$119$	−2.54874	−	4.41454i	−0.233642	−	0.404680i
$120$	−0.779453	+	1.35005i	−0.0711540	+	0.123242i
$121$	−10.8844			−0.989489
$122$	−5.58880			−0.505986
$123$	−3.65330	+	6.32770i	−0.329407	+	0.570549i
$124$	5.70608	−	9.88322i	0.512421	−	0.887539i
$125$	−1.00000			−0.0894427
$126$	−1.51021			−0.134540
$127$	−2.30494	+	3.99228i	−0.204531	+	0.354258i	−0.949983	−	0.312301i	$-0.898900\pi$
$127$	−2.30494	+	3.99228i	−0.204531	+	0.354258i	0.745452	+	0.666559i	$0.232234\pi$
$128$	−5.72298	−	9.91250i	−0.505845	−	0.876149i
$129$	1.09422	−	1.89524i	0.0963406	−	0.166867i
$130$	1.91819	+	3.32240i	0.168237	+	0.291394i
$131$	−5.53149	−	9.58082i	−0.483288	−	0.837080i	0.516528	−	0.856271i	$-0.327224\pi$
$131$	−5.53149	−	9.58082i	−0.483288	−	0.837080i	−0.999816	+	0.0191906i	$0.993891\pi$
$132$	−0.394103			−0.0343022
$133$	4.22294	−	1.08018i	0.366175	−	0.0936637i
$134$	1.66454			0.143795
$135$	1.94932	+	3.37633i	0.167771	+	0.290588i
$136$	5.60216	+	9.70322i	0.480381	+	0.832044i
$137$	−2.57319	+	4.45689i	−0.219842	+	0.380778i	−0.954760	−	0.297379i	$-0.903888\pi$
$137$	−2.57319	+	4.45689i	−0.219842	+	0.380778i	0.734917	+	0.678157i	$0.237221\pi$
$138$	0.980375	+	1.69806i	0.0834551	+	0.144548i
$139$	−7.49336	+	12.9789i	−0.635578	+	1.10085i	0.350814	+	0.936445i	$0.385905\pi$
$139$	−7.49336	+	12.9789i	−0.635578	+	1.10085i	−0.986392	+	0.164409i	$0.947428\pi$
$140$	−1.63420			−0.138115
$141$	4.86727			0.409898
$142$	−0.998798	+	1.72997i	−0.0838172	+	0.145176i
$143$	−1.07841	+	1.86787i	−0.0901814	+	0.156199i
$144$	−4.84169			−0.403474
$145$	−8.92959			−0.741562
$146$	−2.42641	+	4.20267i	−0.200811	+	0.347815i
$147$	0.354617	+	0.614215i	0.0292483	+	0.0506596i
$148$	−4.16469	+	7.21345i	−0.342335	+	0.592942i
$149$	−3.08865	−	5.34970i	−0.253032	−	0.438265i	0.711327	−	0.702861i	$-0.248095\pi$
$149$	−3.08865	−	5.34970i	−0.253032	−	0.438265i	−0.964359	+	0.264596i	$0.914761\pi$
$150$	−0.214477	−	0.371485i	−0.0175120	−	0.0303316i
$151$	0.451833			0.0367696			0.0183848	−	0.999831i	$-0.494148\pi$
$151$	0.451833			0.0367696			0.0183848	+	0.999831i	$0.494148\pi$
$152$	−9.28207	+	2.37426i	−0.752876	+	0.192578i
$153$	12.7283			1.02902
$154$	0.102827	+	0.178101i	0.00828601	+	0.0143518i
$155$	3.49166	+	6.04774i	0.280457	+	0.485766i
$156$	3.67591	−	6.36687i	0.294309	−	0.509758i
$157$	−9.82667	−	17.0203i	−0.784254	−	1.35837i	−0.929444	−	0.368963i	$-0.879713\pi$
$157$	−9.82667	−	17.0203i	−0.784254	−	1.35837i	0.145190	−	0.989404i	$-0.453621\pi$
$158$	1.14609	−	1.98509i	0.0911780	−	0.157925i
$159$	−5.14458			−0.407992
$160$	5.56877			0.440250
$161$	−2.28550	+	3.95860i	−0.180123	+	0.311982i
$162$	1.42915	−	2.47535i	0.112284	−	0.194482i
$163$	−24.8892			−1.94947			−0.974735	−	0.223364i	$-0.928296\pi$
$163$	−24.8892			−1.94947			−0.974735	+	0.223364i	$0.928296\pi$
$164$	16.8357			1.31465
$165$	0.120580	−	0.208850i	0.00938711	−	0.0162590i
$166$	0.886133	+	1.53483i	0.0687773	+	0.119126i
$167$	6.21897	−	10.7716i	0.481238	−	0.833529i	−0.518530	−	0.855059i	$-0.673521\pi$
$167$	6.21897	−	10.7716i	0.481238	−	0.833529i	0.999768	+	0.0215304i	$0.00685385\pi$
$168$	−0.779453	−	1.35005i	−0.0601361	−	0.104159i
$169$	−13.6174	−	23.5860i	−1.04749	−	1.81431i
$170$	−3.08302			−0.236457
$171$	−2.93647	+	10.4805i	−0.224557	+	0.801465i
$172$	−5.04255			−0.384491
$173$	−1.52284	−	2.63763i	−0.115779	−	0.200536i	0.802312	−	0.596905i	$-0.203603\pi$
$173$	−1.52284	−	2.63763i	−0.115779	−	0.200536i	−0.918091	+	0.396370i	$0.870270\pi$
$174$	−1.91519	−	3.31721i	−0.145190	−	0.251477i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	0.329660	+	0.570987i	0.0248490	+	0.0430398i
$177$	4.46048	−	7.72577i	0.335270	−	0.580705i
$178$	−10.3910			−0.778842
$179$	5.99193			0.447858			0.223929	−	0.974605i	$-0.428112\pi$
$179$	5.99193			0.447858			0.223929	+	0.974605i	$0.428112\pi$
$180$	2.04029	−	3.53388i	0.152074	−	0.263400i
$181$	4.48959	−	7.77619i	0.333708	−	0.578000i	−0.649528	−	0.760338i	$-0.725033\pi$
$181$	4.48959	−	7.77619i	0.333708	−	0.578000i	0.983236	+	0.182338i	$0.0583666\pi$
$182$	−3.83638			−0.284372
$183$	−6.55371			−0.484464
$184$	5.02356	−	8.70106i	0.370342	−	0.641451i
$185$	−2.54846	−	4.41406i	−0.187366	−	0.324528i
$186$	−1.49776	+	2.59420i	−0.109821	+	0.190216i
$187$	−0.866642	−	1.50107i	−0.0633751	−	0.109769i
$188$	−5.60752	−	9.71251i	−0.408971	−	0.708358i
$189$	−3.89865			−0.283585
$190$	0.711263	−	2.53856i	0.0516004	−	0.184167i
$191$	−2.09231			−0.151394			−0.0756970	−	0.997131i	$-0.524118\pi$
$191$	−2.09231			−0.151394			−0.0756970	+	0.997131i	$0.524118\pi$
$192$	−0.180842	−	0.313227i	−0.0130511	−	0.0226052i
$193$	8.96066	+	15.5203i	0.645002	+	1.11718i	0.984301	+	0.176498i	$0.0564769\pi$
$193$	8.96066	+	15.5203i	0.645002	+	1.11718i	−0.339299	+	0.940679i	$0.610190\pi$
$194$	−1.09768	+	1.90123i	−0.0788087	+	0.136501i
$195$	2.24937	+	3.89602i	0.161080	+	0.278999i
$196$	0.817100	−	1.41526i	0.0583643	−	0.101090i
$197$	−1.65811			−0.118135			−0.0590677	−	0.998254i	$-0.518813\pi$
$197$	−1.65811			−0.118135			−0.0590677	+	0.998254i	$0.518813\pi$
$198$	−0.513514			−0.0364939
$199$	−2.02600	+	3.50914i	−0.143619	+	0.248756i	−0.928857	−	0.370438i	$-0.879207\pi$
$199$	−2.02600	+	3.50914i	−0.143619	+	0.248756i	0.785238	+	0.619195i	$0.212541\pi$
$200$	−1.09901	+	1.90354i	−0.0777115	+	0.134600i
$201$	1.95193			0.137678
$202$	−1.41013			−0.0992164
$203$	4.46480	−	7.73326i	0.313367	−	0.542768i
$204$	2.95406	+	5.11659i	0.206826	+	0.358233i
$205$	−5.15105	+	8.92188i	−0.359765	+	0.623131i
$206$	−0.705945	−	1.22273i	−0.0491855	−	0.0851918i
$207$	−5.70687	−	9.88458i	−0.396655	−	0.687026i
$208$	−12.2993			−0.852805
$209$	1.43592	−	0.367292i	0.0993245	−	0.0254061i
$210$	0.428954			0.0296006
$211$	10.5608	+	18.2918i	0.727035	+	1.25926i	0.958131	+	0.286330i	$0.0924354\pi$
$211$	10.5608	+	18.2918i	0.727035	+	1.25926i	−0.231096	+	0.972931i	$0.574231\pi$
$212$	5.92701	+	10.2659i	0.407069	+	0.705064i
$213$	−1.17124	+	2.02865i	−0.0802520	+	0.139001i
$214$	−0.838849	−	1.45293i	−0.0573425	−	0.0993202i
$215$	1.54282	−	2.67224i	0.105219	−	0.182245i
$216$	8.56928			0.583066
$217$	−6.98333			−0.474059
$218$	1.44180	−	2.49728i	0.0976513	−	0.169137i
$219$	−2.84533	+	4.92826i	−0.192270	+	0.333021i
$220$	−0.555674			−0.0374635
$221$	32.3337			2.17500
$222$	1.09317	−	1.89343i	0.0733688	−	0.127079i
$223$	0.274427	+	0.475322i	0.0183770	+	0.0318299i	0.875068	−	0.484001i	$-0.160817\pi$
$223$	0.274427	+	0.475322i	0.0183770	+	0.0318299i	−0.856691	+	0.515831i	$0.827483\pi$
$224$	−2.78438	+	4.82269i	−0.186039	+	0.322230i
$225$	1.24849	+	2.16245i	0.0832329	+	0.144164i
$226$	−0.453195	−	0.784956i	−0.0301461	−	0.0522145i
$227$	24.6610			1.63681			0.818406	−	0.574641i	$-0.194858\pi$
$227$	24.6610			1.63681			0.818406	+	0.574641i	$0.194858\pi$
$228$	−4.89451	+	1.25196i	−0.324147	+	0.0829134i
$229$	10.3427			0.683463			0.341731	−	0.939798i	$-0.388987\pi$
$229$	10.3427			0.683463			0.341731	+	0.939798i	$0.388987\pi$
$230$	1.38230	+	2.39422i	0.0911463	+	0.157870i
$231$	0.120580	+	0.208850i	0.00793356	+	0.0137413i
$232$	−9.81368	+	16.9978i	−0.644300	+	1.11596i
$233$	0.643808	+	1.11511i	0.0421773	+	0.0730531i	0.886343	−	0.463028i	$-0.153237\pi$
$233$	0.643808	+	1.11511i	0.0421773	+	0.0730531i	−0.844166	+	0.536082i	$0.819904\pi$
$234$	4.78970	−	8.29600i	0.313112	−	0.542327i
$235$	6.86271			0.447674
$236$	−20.5555			−1.33805
$237$	1.34396	−	2.32781i	0.0872997	−	0.151207i
$238$	1.54151	−	2.66997i	0.0999213	−	0.173069i
$239$	−24.0906			−1.55829			−0.779147	−	0.626841i	$-0.784347\pi$
$239$	−24.0906			−1.55829			−0.779147	+	0.626841i	$0.784347\pi$
$240$	1.37521			0.0887697
$241$	−6.05265	+	10.4835i	−0.389886	+	0.675302i	−0.992434	−	0.122781i	$-0.960819\pi$
$241$	−6.05265	+	10.4835i	−0.389886	+	0.675302i	0.602548	+	0.798082i	$0.294152\pi$
$242$	−3.29151	−	5.70106i	−0.211586	−	0.366478i
$243$	7.52386	−	13.0317i	0.482656	−	0.835985i
$244$	7.55045	+	13.0778i	0.483368	+	0.837218i
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	−4.41913			−0.281753
$247$	−7.45949	+	26.6236i	−0.474636	+	1.69402i
$248$	15.3494			0.974690
$249$	1.03912	+	1.79982i	0.0658518	+	0.114059i
$250$	−0.302407	−	0.523784i	−0.0191259	−	0.0331270i
$251$	−1.82370	+	3.15874i	−0.115111	+	0.199378i	−0.917824	−	0.396987i	$-0.870056\pi$
$251$	−1.82370	+	3.15874i	−0.115111	+	0.199378i	0.802713	+	0.596365i	$0.203389\pi$
$252$	2.04029	+	3.53388i	0.128526	+	0.222614i
$253$	−0.777134	+	1.34604i	−0.0488580	+	0.0846246i
$254$	−2.78812			−0.174942
$255$	−3.61530			−0.226399
$256$	2.95137	−	5.11193i	0.184461	−	0.319496i
$257$	2.93771	−	5.08827i	0.183249	−	0.317397i	−0.759736	−	0.650232i	$-0.774672\pi$
$257$	2.93771	−	5.08827i	0.183249	−	0.317397i	0.942985	+	0.332835i	$0.108005\pi$
$258$	1.32360			0.0824035
$259$	5.09691			0.316707
$260$	5.18294	−	8.97711i	0.321432	−	0.556737i
$261$	11.1485	+	19.3098i	0.690077	+	1.19525i
$262$	3.34552	−	5.79461i	0.206687	−	0.357992i
$263$	11.7659	+	20.3791i	0.725514	+	1.25663i	0.958762	+	0.284210i	$0.0917314\pi$
$263$	11.7659	+	20.3791i	0.725514	+	1.25663i	−0.233248	+	0.972417i	$0.574935\pi$
$264$	−0.265036	−	0.459055i	−0.0163118	−	0.0282529i
$265$	−7.25372			−0.445592
$266$	1.84283	+	1.88525i	0.112991	+	0.115592i
$267$	−12.1851			−0.745713
$268$	−2.24879	−	3.89502i	−0.137367	−	0.237926i
$269$	13.0527	+	22.6080i	0.795839	+	1.37843i	0.922305	+	0.386463i	$0.126303\pi$
$269$	13.0527	+	22.6080i	0.795839	+	1.37843i	−0.126466	+	0.991971i	$0.540364\pi$
$270$	−1.17898	+	2.04205i	−0.0717503	+	0.124275i
$271$	4.91212	+	8.50804i	0.298390	+	0.516826i	0.975768	−	0.218809i	$-0.0702171\pi$
$271$	4.91212	+	8.50804i	0.298390	+	0.516826i	−0.677378	+	0.735635i	$0.736884\pi$
$272$	4.94204	−	8.55986i	0.299655	−	0.519018i
$273$	−4.49873			−0.272276
$274$	−3.11260			−0.188039
$275$	0.170014	−	0.294473i	0.0102522	−	0.0177574i
$276$	2.64897	−	4.58814i	0.159449	−	0.276174i
$277$	16.9041			1.01567			0.507836	−	0.861454i	$-0.330446\pi$
$277$	16.9041			1.01567			0.507836	+	0.861454i	$0.330446\pi$
$278$	−9.06416			−0.543632
$279$	8.71864	−	15.1011i	0.521971	−	0.904081i
$280$	−1.09901	−	1.90354i	−0.0656782	−	0.113758i
$281$	4.50692	−	7.80621i	0.268860	−	0.465680i	−0.699707	−	0.714429i	$-0.746686\pi$
$281$	4.50692	−	7.80621i	0.268860	−	0.465680i	0.968568	+	0.248750i	$0.0800197\pi$
$282$	1.47189	+	2.54939i	0.0876500	+	0.151814i
$283$	−1.04105	−	1.80315i	−0.0618838	−	0.107186i	0.833424	−	0.552635i	$-0.186377\pi$
$283$	−1.04105	−	1.80315i	−0.0618838	−	0.107186i	−0.895307	+	0.445449i	$0.853044\pi$
$284$	5.39749			0.320282
$285$	0.834061	−	2.97684i	0.0494055	−	0.176333i
$286$	−1.30448			−0.0771354
$287$	−5.15105	−	8.92188i	−0.304057	−	0.526642i
$288$	−6.95257	−	12.0422i	−0.409684	−	0.709594i
$289$	−4.49212	+	7.78058i	−0.264242	+	0.457681i
$290$	−2.70037	−	4.67718i	−0.158571	−	0.274653i
$291$	−1.28719	+	2.22948i	−0.0754565	+	0.130694i
$292$	13.1123			0.767339
$293$	19.5343			1.14121			0.570604	−	0.821226i	$-0.306709\pi$
$293$	19.5343			1.14121			0.570604	+	0.821226i	$0.306709\pi$
$294$	−0.214477	+	0.371485i	−0.0125086	+	0.0216655i
$295$	6.28915	−	10.8931i	0.366168	−	0.634222i
$296$	−11.2031			−0.651166
$297$	−1.32565			−0.0769220
$298$	1.86806	−	3.23557i	0.108214	−	0.187432i
$299$	−14.4971	−	25.1098i	−0.838391	−	1.45213i
$300$	−0.579515	+	1.00375i	−0.0334583	+	0.0579515i
$301$	1.54282	+	2.67224i	0.0889266	+	0.154025i
$302$	0.136637	+	0.236663i	0.00786259	+	0.0136184i
$303$	−1.65359			−0.0949962
$304$	5.90805	+	6.04406i	0.338850	+	0.346651i
$305$	−9.24054			−0.529112
$306$	3.84913	+	6.66689i	0.220040	+	0.381121i
$307$	2.56580	+	4.44410i	0.146438	+	0.253638i	0.929909	−	0.367791i	$-0.119886\pi$
$307$	2.56580	+	4.44410i	0.146438	+	0.253638i	−0.783470	+	0.621429i	$0.786552\pi$
$308$	0.277837	−	0.481228i	0.0158312	−	0.0274205i
$309$	−0.827825	−	1.43384i	−0.0470933	−	0.0815681i
$310$	−2.11180	+	3.65775i	−0.119942	+	0.207746i
$311$	8.74396			0.495825			0.247912	−	0.968782i	$-0.420256\pi$
$311$	8.74396			0.495825			0.247912	+	0.968782i	$0.420256\pi$
$312$	9.88827			0.559813
$313$	−15.7118	+	27.2136i	−0.888082	+	1.53820i	−0.0459427	+	0.998944i	$0.514629\pi$
$313$	−15.7118	+	27.2136i	−0.888082	+	1.53820i	−0.842140	+	0.539260i	$0.818704\pi$
$314$	5.94330	−	10.2941i	0.335400	−	0.580930i
$315$	−2.49699			−0.140689
$316$	−6.19345			−0.348409
$317$	0.265488	−	0.459838i	0.0149113	−	0.0258271i	−0.858473	−	0.512858i	$-0.828587\pi$
$317$	0.265488	−	0.459838i	0.0149113	−	0.0258271i	0.873385	+	0.487031i	$0.161920\pi$
$318$	−1.55576	−	2.69465i	−0.0872424	−	0.151108i
$319$	1.51816	−	2.62952i	0.0850004	−	0.147225i
$320$	−0.254982	−	0.441641i	−0.0142539	−	0.0246885i
$321$	−0.983676	−	1.70378i	−0.0549034	−	0.0950955i
$322$	−2.76460			−0.154065
$323$	−15.5317	−	15.8892i	−0.864205	−	0.884101i
$324$	−7.72308			−0.429060
$325$	3.17154	+	5.49327i	0.175926	+	0.304712i
$326$	−7.52665	−	13.0365i	−0.416863	−	0.722027i
$327$	1.69073	−	2.92843i	0.0934976	−	0.161943i
$328$	11.3221	+	19.6104i	0.625157	+	1.08280i
$329$	−3.43135	+	5.94328i	−0.189177	+	0.327664i
$330$	0.145856			0.00802913
$331$	−8.06440			−0.443259			−0.221630	−	0.975131i	$-0.571138\pi$
$331$	−8.06440			−0.443259			−0.221630	+	0.975131i	$0.571138\pi$
$332$	2.39433	−	4.14709i	0.131406	−	0.227601i
$333$	−6.36346	+	11.0218i	−0.348716	+	0.603993i
$334$	7.52263			0.411620
$335$	2.75216			0.150367
$336$	−0.687607	+	1.19097i	−0.0375120	+	0.0649728i
$337$	−12.7830	−	22.1408i	−0.696335	−	1.20609i	−0.969729	−	0.244185i	$-0.921479\pi$
$337$	−12.7830	−	22.1408i	−0.696335	−	1.20609i	0.273394	−	0.961902i	$-0.411854\pi$
$338$	8.23596	−	14.2651i	0.447977	−	0.775920i
$339$	−0.531438	−	0.920478i	−0.0288638	−	0.0499935i
$340$	4.16515	+	7.21425i	0.225887	+	0.391248i
$341$	−2.37453			−0.128588
$342$	−6.37753	+	1.63130i	−0.344857	+	0.0882108i
$343$	−1.00000			−0.0539949
$344$	−3.39114	−	5.87362i	−0.182838	−	0.316684i
$345$	1.62095	+	2.80758i	0.0872693	+	0.151155i
$346$	0.921033	−	1.59528i	0.0495151	−	0.0857626i
$347$	−11.7205	−	20.3005i	−0.629190	−	1.08979i	−0.987715	−	0.156268i	$-0.950054\pi$
$347$	−11.7205	−	20.3005i	−0.629190	−	1.08979i	0.358525	−	0.933520i	$-0.383280\pi$
$348$	−5.17484	+	8.96308i	−0.277400	+	0.480471i
$349$	4.63994			0.248370			0.124185	−	0.992259i	$-0.460368\pi$
$349$	4.63994			0.248370			0.124185	+	0.992259i	$0.460368\pi$
$350$	0.604813			0.0323286
$351$	12.3647	−	21.4163i	0.659981	−	1.14312i
$352$	−0.946768	+	1.63985i	−0.0504629	+	0.0874043i
$353$	12.7297			0.677535			0.338768	−	0.940870i	$-0.389990\pi$
$353$	12.7297			0.677535			0.338768	+	0.940870i	$0.389990\pi$
$354$	5.39551			0.286768
$355$	−1.65141	+	2.86033i	−0.0876480	+	0.151811i
$356$	14.0383	+	24.3150i	0.744027	+	1.28869i
$357$	1.80765	−	3.13094i	0.0956710	−	0.165707i
$358$	1.81200	+	3.13847i	0.0957671	+	0.165874i
$359$	−3.16968	−	5.49005i	−0.167289	−	0.289754i	0.770177	−	0.637831i	$-0.220168\pi$
$359$	−3.16968	−	5.49005i	−0.167289	−	0.289754i	−0.937466	+	0.348077i	$0.886835\pi$
$360$	5.48841			0.289265
$361$	16.6664	−	9.12309i	0.877180	−	0.480163i
$362$	5.43072			0.285432
$363$	−3.85979	−	6.68534i	−0.202586	−	0.350890i
$364$	5.18294	+	8.97711i	0.271660	+	0.470529i
$365$	−4.01184	+	6.94871i	−0.209989	+	0.363712i
$366$	−1.98188	−	3.43272i	−0.103595	−	0.179431i
$367$	−11.6253	+	20.1356i	−0.606837	+	1.05107i	0.384921	+	0.922949i	$0.374229\pi$
$367$	−11.6253	+	20.1356i	−0.606837	+	1.05107i	−0.991758	+	0.128123i	$0.959105\pi$
$368$	−8.86324			−0.462028
$369$	25.7242			1.33915
$370$	1.54134	−	2.66968i	0.0801305	−	0.138790i
$371$	3.62686	−	6.28190i	0.188297	−	0.326140i
$372$	8.09389			0.419649
$373$	11.0296			0.571091			0.285545	−	0.958365i	$-0.407825\pi$
$373$	11.0296			0.571091			0.285545	+	0.958365i	$0.407825\pi$
$374$	0.524157	−	0.907866i	0.0271035	−	0.0469446i
$375$	−0.354617	−	0.614215i	−0.0183123	−	0.0317179i
$376$	7.54216	−	13.0634i	0.388957	−	0.673694i
$377$	28.3206	+	49.0527i	1.45858	+	2.52634i
$378$	−1.17898	−	2.04205i	−0.0606401	−	0.105032i
$379$	27.6497			1.42027			0.710135	−	0.704065i	$-0.248634\pi$
$379$	27.6497			1.42027			0.710135	+	0.704065i	$0.248634\pi$
$380$	−6.90113	+	1.76524i	−0.354020	+	0.0905547i
$381$	−3.26949			−0.167501
$382$	−0.632727	−	1.09592i	−0.0323731	−	0.0560719i
$383$	8.21387	+	14.2268i	0.419709	+	0.726958i	0.995910	−	0.0903505i	$-0.0287987\pi$
$383$	8.21387	+	14.2268i	0.419709	+	0.726958i	−0.576201	+	0.817308i	$0.695465\pi$
$384$	4.05893	−	7.03028i	0.207132	−	0.358762i
$385$	0.170014	+	0.294473i	0.00866471	+	0.0150077i
$386$	−5.41953	+	9.38689i	−0.275847	+	0.477780i
$387$	−7.70480			−0.391657
$388$	5.93183			0.301143
$389$	−8.14129	+	14.1011i	−0.412780	+	0.714956i	−0.995193	−	0.0979375i	$-0.968775\pi$
$389$	−8.14129	+	14.1011i	−0.412780	+	0.714956i	0.582413	+	0.812893i	$0.302109\pi$
$390$	−1.36045	+	2.35636i	−0.0688889	+	0.119319i
$391$	23.3006			1.17836
$392$	2.19801			0.111016
$393$	3.92312	−	6.79504i	0.197895	−	0.342764i
$394$	−0.501423	−	0.868490i	−0.0252613	−	0.0437539i
$395$	1.89495	−	3.28215i	0.0953452	−	0.165143i
$396$	0.693755	+	1.20162i	0.0348625	+	0.0603837i
$397$	−18.2601	−	31.6275i	−0.916450	−	1.58734i	−0.804764	−	0.593595i	$-0.797708\pi$
$397$	−18.2601	−	31.6275i	−0.916450	−	1.58734i	−0.111686	−	0.993743i	$-0.535625\pi$
$398$	−2.45071			−0.122843
$399$	2.16099	+	2.21074i	0.108185	+	0.110675i
$400$	1.93901			0.0969507
$401$	−0.760627	−	1.31744i	−0.0379839	−	0.0657900i	0.846408	−	0.532534i	$-0.178760\pi$
$401$	−0.760627	−	1.31744i	−0.0379839	−	0.0657900i	−0.884392	+	0.466744i	$0.845427\pi$
$402$	0.590276	+	1.02239i	0.0294403	+	0.0509921i
$403$	22.1479	−	38.3613i	1.10327	−	1.91091i
$404$	1.90508	+	3.29970i	0.0947813	+	0.164166i
$405$	2.36295	−	4.09276i	0.117416	−	0.203371i
$406$	5.40074			0.268034
$407$	1.73309			0.0859062
$408$	−3.97324	+	6.88185i	−0.196705	+	0.340702i
$409$	−3.34756	+	5.79815i	−0.165526	+	0.286700i	−0.936842	−	0.349753i	$-0.886266\pi$
$409$	−3.34756	+	5.79815i	−0.165526	+	0.286700i	0.771316	+	0.636453i	$0.219599\pi$
$410$	−6.23085			−0.307720
$411$	−3.64999			−0.180040
$412$	−1.90746	+	3.30381i	−0.0939737	+	0.162767i
$413$	6.28915	+	10.8931i	0.309469	+	0.536016i
$414$	3.45159	−	5.97833i	0.169636	−	0.293819i
$415$	1.46514	+	2.53769i	0.0719207	+	0.124570i
$416$	−17.6616	−	30.5908i	−0.865930	−	1.49984i
$417$	−10.6291			−0.520509
$418$	0.626613	+	0.641038i	0.0306486	+	0.0313542i
$419$	−6.48768			−0.316944			−0.158472	−	0.987363i	$-0.550657\pi$
$419$	−6.48768			−0.316944			−0.158472	+	0.987363i	$0.550657\pi$
$420$	−0.579515	−	1.00375i	−0.0282774	−	0.0489780i
$421$	17.8737	+	30.9582i	0.871111	+	1.50881i	0.860849	+	0.508861i	$0.169933\pi$
$421$	17.8737	+	30.9582i	0.871111	+	1.50881i	0.0102619	+	0.999947i	$0.496733\pi$
$422$	−6.38731	+	11.0631i	−0.310929	+	0.538545i
$423$	−8.56805	−	14.8403i	−0.416593	−	0.721560i
$424$	−7.97188	+	13.8077i	−0.387149	+	0.670561i
$425$	−5.09747			−0.247264
$426$	−1.41676			−0.0686423
$427$	4.62027	−	8.00254i	0.223591	−	0.387270i
$428$	−2.26656	+	3.92580i	−0.109558	+	0.189761i
$429$	−1.52969			−0.0738543
$430$	1.86623			0.0899978
$431$	16.2790	−	28.1960i	0.784132	−	1.35816i	−0.145385	−	0.989375i	$-0.546442\pi$
$431$	16.2790	−	28.1960i	0.784132	−	1.35816i	0.929516	−	0.368781i	$-0.120225\pi$
$432$	−3.77977	−	6.54675i	−0.181854	−	0.314981i
$433$	17.5581	−	30.4115i	0.843787	−	1.46148i	−0.0428831	−	0.999080i	$-0.513654\pi$
$433$	17.5581	−	30.4115i	0.843787	−	1.46148i	0.886670	−	0.462402i	$-0.153012\pi$
$434$	−2.11180	−	3.65775i	−0.101370	−	0.175578i
$435$	−3.16659	−	5.48469i	−0.151826	−	0.262971i
$436$	−7.79148			−0.373144
$437$	−5.37551	+	19.1857i	−0.257146	+	0.917776i
$438$	−3.44179			−0.164455
$439$	9.80258	+	16.9786i	0.467852	+	0.810343i	0.999325	−	0.0367321i	$-0.0116948\pi$
$439$	9.80258	+	16.9786i	0.467852	+	0.810343i	−0.531474	+	0.847075i	$0.678362\pi$
$440$	−0.373693	−	0.647255i	−0.0178151	−	0.0308567i
$441$	1.24849	−	2.16245i	0.0594521	−	0.102974i
$442$	9.77793	+	16.9359i	0.465089	+	0.805557i
$443$	3.28259	−	5.68561i	0.155961	−	0.270132i	−0.777448	−	0.628947i	$-0.783486\pi$
$443$	3.28259	−	5.68561i	0.155961	−	0.270132i	0.933408	+	0.358816i	$0.116819\pi$
$444$	−5.90748			−0.280357
$445$	−17.1806			−0.814438
$446$	−0.165977	+	0.287481i	−0.00785925	+	0.0136126i
$447$	2.19058	−	3.79419i	0.103611	−	0.179459i
$448$	0.509963			0.0240935
$449$	−22.0291			−1.03962			−0.519809	−	0.854283i	$-0.673997\pi$
$449$	−22.0291			−1.03962			−0.519809	+	0.854283i	$0.673997\pi$
$450$	−0.755106	+	1.30788i	−0.0355960	+	0.0616541i
$451$	−1.75150	−	3.03369i	−0.0824749	−	0.142851i
$452$	−1.22453	+	2.12095i	−0.0575970	+	0.0997609i
$453$	0.160228	+	0.277522i	0.00752815	+	0.0130391i
$454$	7.45767	+	12.9171i	0.350006	+	0.606227i
$455$	−6.34309			−0.297368
$456$	−4.74988	−	4.85923i	−0.222434	−	0.227554i
$457$	41.1881			1.92670			0.963349	−	0.268252i	$-0.0864460\pi$
$457$	41.1881			1.92670			0.963349	+	0.268252i	$0.0864460\pi$
$458$	3.12769	+	5.41732i	0.146147	+	0.253135i
$459$	9.93663	+	17.2108i	0.463802	+	0.803329i
$460$	3.73497	−	6.46915i	0.174144	−	0.301626i
$461$	−18.8229	−	32.6022i	−0.876668	−	1.51843i	−0.854975	−	0.518670i	$-0.826427\pi$
$461$	−18.8229	−	32.6022i	−0.876668	−	1.51843i	−0.0216937	−	0.999765i	$-0.506906\pi$
$462$	−0.0729282	+	0.126315i	−0.00339293	+	0.00587672i
$463$	5.84422			0.271604			0.135802	−	0.990736i	$-0.456639\pi$
$463$	5.84422			0.271604			0.135802	+	0.990736i	$0.456639\pi$
$464$	17.3146			0.803811
$465$	−2.47641	+	4.28926i	−0.114841	+	0.198910i
$466$	−0.389384	+	0.674432i	−0.0180378	+	0.0312425i
$467$	10.4493			0.483536			0.241768	−	0.970334i	$-0.422273\pi$
$467$	10.4493			0.483536			0.241768	+	0.970334i	$0.422273\pi$
$468$	−25.8835			−1.19646
$469$	−1.37608	+	2.38344i	−0.0635415	+	0.110057i
$470$	2.07533	+	3.59458i	0.0957278	+	0.165805i
$471$	6.96941	−	12.0714i	0.321133	−	0.556219i
$472$	−13.8236	−	23.9432i	−0.636284	−	1.10208i
$473$	0.524601	+	0.908636i	0.0241212	+	0.0417791i
$474$	1.62569			0.0746705
$475$	1.17600	−	4.19726i	0.0539587	−	0.192584i
$476$	−8.33030			−0.381819
$477$	9.05622	+	15.6858i	0.414656	+	0.718205i
$478$	−7.28517	−	12.6183i	−0.333216	−	0.577147i
$479$	−14.7362	+	25.5239i	−0.673315	+	1.16622i	0.303643	+	0.952786i	$0.401797\pi$
$479$	−14.7362	+	25.5239i	−0.673315	+	1.16622i	−0.976958	+	0.213430i	$0.931536\pi$
$480$	1.97478	+	3.42042i	0.0901359	+	0.156120i
$481$	−16.1651	+	27.9987i	−0.737064	+	1.27663i
$482$	−7.32145			−0.333483
$483$	−3.24191			−0.147512
$484$	−8.89363	+	15.4042i	−0.404256	+	0.700192i
$485$	−1.81490	+	3.14350i	−0.0824105	+	0.142739i
$486$	9.10106			0.412833
$487$	29.5669			1.33981			0.669903	−	0.742449i	$-0.266336\pi$
$487$	29.5669			1.33981			0.669903	+	0.742449i	$0.266336\pi$
$488$	−10.1554	+	17.5897i	−0.459714	+	0.796248i
$489$	−8.82612	−	15.2873i	−0.399131	−	0.691315i
$490$	−0.302407	+	0.523784i	−0.0136613	+	0.0236621i
$491$	5.61178	+	9.71988i	0.253256	+	0.438652i	0.964420	−	0.264374i	$-0.0851652\pi$
$491$	5.61178	+	9.71988i	0.253256	+	0.438652i	−0.711164	+	0.703026i	$0.751832\pi$
$492$	5.97022	+	10.3407i	0.269158	+	0.466196i
$493$	−45.5184			−2.05004
$494$	−16.2008	+	4.14399i	−0.728909	+	0.186447i
$495$	−0.849046			−0.0381618
$496$	−6.77038	−	11.7266i	−0.303999	−	0.526542i
$497$	−1.65141	−	2.86033i	−0.0740761	−	0.128304i
$498$	−0.628476	+	1.08855i	−0.0281627	+	0.0487792i
$499$	−21.1802	−	36.6853i	−0.948158	−	1.64226i	−0.749302	−	0.662229i	$-0.769611\pi$
$499$	−21.1802	−	36.6853i	−0.948158	−	1.64226i	−0.198856	−	0.980029i	$-0.563723\pi$
$500$	−0.817100	+	1.41526i	−0.0365418	+	0.0632923i
$501$	8.82141			0.394111
$502$	−2.20600			−0.0984584
$503$	−9.89887	+	17.1453i	−0.441369	+	0.764473i	−0.997791	−	0.0664265i	$-0.978840\pi$
$503$	−9.89887	+	17.1453i	−0.441369	+	0.764473i	0.556423	+	0.830899i	$0.312174\pi$
$504$	−2.74421	+	4.75310i	−0.122237	+	0.211720i
$505$	−2.33151			−0.103751
$506$	−0.940042			−0.0417900
$507$	9.65790	−	16.7280i	0.428922	−	0.742915i
$508$	3.76674	+	6.52419i	0.167122	+	0.289464i
$509$	5.93011	−	10.2712i	0.262847	−	0.455265i	−0.704150	−	0.710051i	$-0.748672\pi$
$509$	5.93011	−	10.2712i	0.262847	−	0.455265i	0.966997	+	0.254786i	$0.0820051\pi$
$510$	−1.09329	−	1.89364i	−0.0484117	−	0.0838516i
$511$	−4.01184	−	6.94871i	−0.177473	−	0.307393i
$512$	−19.3219			−0.853914
$513$	−16.4638	+	4.21125i	−0.726893	+	0.185931i
$514$	3.55353			0.156740
$515$	−1.16721	−	2.02167i	−0.0514335	−	0.0890854i
$516$	−1.78817	−	3.09721i	−0.0787200	−	0.136347i
$517$	−1.16676	+	2.02088i	−0.0513139	+	0.0888783i
$518$	1.54134	+	2.66968i	0.0677226	+	0.117299i
$519$	1.08005	−	1.87070i	0.0474089	−	0.0821146i
$520$	13.9422			0.611405
$521$	2.06682			0.0905488			0.0452744	−	0.998975i	$-0.485584\pi$
$521$	2.06682			0.0905488			0.0452744	+	0.998975i	$0.485584\pi$
$522$	−6.74279	+	11.6788i	−0.295124	+	0.511169i
$523$	−8.16171	+	14.1365i	−0.356887	+	0.618146i	−0.987439	−	0.158001i	$-0.949495\pi$
$523$	−8.16171	+	14.1365i	−0.356887	+	0.618146i	0.630552	+	0.776147i	$0.282828\pi$
$524$	−18.0791			−0.789790
$525$	0.709234			0.0309535
$526$	−7.11615	+	12.3255i	−0.310279	+	0.537419i
$527$	17.7987	+	30.8282i	0.775322	+	1.34290i
$528$	−0.233806	+	0.404963i	−0.0101751	+	0.0176238i
$529$	1.05297	+	1.82380i	0.0457814	+	0.0792956i
$530$	−2.19357	−	3.79938i	−0.0952827	−	0.165034i
$531$	−31.4079			−1.36298
$532$	1.92183	−	6.85917i	0.0833217	−	0.297383i
$533$	65.3471			2.83050
$534$	−3.68484	−	6.38233i	−0.159459	−	0.276191i
$535$	−1.38696	−	2.40228i	−0.0599633	−	0.103860i
$536$	3.02464	−	5.23884i	0.130645	−	0.226283i
$537$	2.12484	+	3.68033i	0.0916936	+	0.158818i
$538$	−7.89446	+	13.6736i	−0.340355	+	0.589511i
$539$	−0.340028			−0.0146460
$540$	6.37118			0.274172
$541$	−5.73419	+	9.93190i	−0.246532	+	0.427006i	−0.962561	−	0.271064i	$-0.912624\pi$
$541$	−5.73419	+	9.93190i	−0.246532	+	0.427006i	0.716029	+	0.698070i	$0.245958\pi$
$542$	−2.97091	+	5.14577i	−0.127612	+	0.221030i
$543$	6.36833			0.273291
$544$	28.3866			1.21707
$545$	2.38388	−	4.12900i	0.102114	−	0.176867i
$546$	−1.36045	−	2.35636i	−0.0582217	−	0.100843i
$547$	3.33887	−	5.78310i	0.142760	−	0.247268i	−0.785775	−	0.618512i	$-0.787736\pi$
$547$	3.33887	−	5.78310i	0.142760	−	0.247268i	0.928535	+	0.371245i	$0.121069\pi$
$548$	4.20511	+	7.28346i	0.179633	+	0.311134i
$549$	11.5368	+	19.9823i	0.492377	+	0.852822i
$550$	0.205653			0.00876909
$551$	10.5012	−	37.4799i	0.447368	−	1.59670i
$552$	7.12576			0.303292
$553$	1.89495	+	3.28215i	0.0805814	+	0.139571i
$554$	5.11193	+	8.85411i	0.217185	+	0.376175i
$555$	1.80745	−	3.13060i	0.0767221	−	0.132886i
$556$	12.2457	+	21.2101i	0.519331	+	0.899508i
$557$	22.1410	−	38.3494i	0.938145	−	1.62491i	0.169216	−	0.985579i	$-0.445876\pi$
$557$	22.1410	−	38.3494i	0.938145	−	1.62491i	0.768928	−	0.639335i	$-0.220790\pi$
$558$	10.5463			0.446460
$559$	−19.5725			−0.827827
$560$	−0.969507	+	1.67924i	−0.0409692	+	0.0709607i
$561$	0.614652	−	1.06461i	0.0259506	−	0.0449478i
$562$	5.45169			0.229966
$563$	18.1283			0.764018			0.382009	−	0.924159i	$-0.375232\pi$
$563$	18.1283			0.764018			0.382009	+	0.924159i	$0.375232\pi$
$564$	3.97704	−	6.88844i	0.167464	−	0.290056i
$565$	−0.749313	−	1.29785i	−0.0315239	−	0.0546009i
$566$	0.629639	−	1.09057i	0.0264657	−	0.0458399i
$567$	2.36295	+	4.09276i	0.0992347	+	0.171880i
$568$	3.62983	+	6.28705i	0.152304	+	0.263799i
$569$	−46.2871			−1.94045			−0.970227	−	0.242196i	$-0.922132\pi$
$569$	−46.2871			−1.94045			−0.970227	+	0.242196i	$0.922132\pi$
$570$	1.81145	−	0.463349i	0.0758731	−	0.0194075i
$571$	−37.6756			−1.57667			−0.788337	−	0.615244i	$-0.789058\pi$
$571$	−37.6756			−1.57667			−0.788337	+	0.615244i	$0.789058\pi$
$572$	1.76234	+	3.05247i	0.0736873	+	0.127630i
$573$	−0.741967	−	1.28512i	−0.0309961	−	0.0536868i
$574$	3.11542	−	5.39607i	0.130035	−	0.225228i
$575$	2.28550	+	3.95860i	0.0953120	+	0.165085i
$576$	−0.636686	+	1.10277i	−0.0265286	+	0.0459489i
$577$	−30.4662			−1.26832			−0.634161	−	0.773201i	$-0.718654\pi$
$577$	−30.4662			−1.26832			−0.634161	+	0.773201i	$0.718654\pi$
$578$	−5.43379			−0.226016
$579$	−6.35520	+	11.0075i	−0.264113	+	0.457457i
$580$	−7.29638	+	12.6377i	−0.302965	+	0.524752i
$581$	−2.93027			−0.121568
$582$	−1.55702			−0.0645406
$583$	1.23323	−	2.13602i	0.0510753	−	0.0884650i
$584$	8.81807	+	15.2733i	0.364894	+	0.632016i
$585$	7.91930	−	13.7166i	0.327423	−	0.567113i
$586$	5.90731	+	10.2318i	0.244029	+	0.422670i
$587$	11.2989	+	19.5702i	0.466354	+	0.807749i	0.999261	−	0.0384247i	$-0.0122340\pi$
$587$	11.2989	+	19.5702i	0.466354	+	0.807749i	−0.532907	+	0.846174i	$0.678901\pi$
$588$	1.15903			0.0477976
$589$	−29.4902	+	7.54327i	−1.21512	+	0.310815i
$590$	7.60752			0.313197
$591$	−0.587993	−	1.01843i	−0.0241868	−	0.0418928i
$592$	4.94149	+	8.55892i	0.203094	+	0.351769i
$593$	14.0541	−	24.3423i	0.577131	−	0.999620i	−0.418676	−	0.908136i	$-0.637506\pi$
$593$	14.0541	−	24.3423i	0.577131	−	0.999620i	0.995807	−	0.0914842i	$-0.0291611\pi$
$594$	−0.400885	−	0.694354i	−0.0164485	−	0.0284897i
$595$	2.54874	−	4.41454i	0.104488	−	0.180979i
$596$	−10.0950			−0.413506
$597$	−2.87382			−0.117618
$598$	8.76806	−	15.1867i	0.358552	−	0.621031i
$599$	−8.64053	+	14.9658i	−0.353042	+	0.611488i	−0.986781	−	0.162060i	$-0.948186\pi$
$599$	−8.64053	+	14.9658i	−0.353042	+	0.611488i	0.633738	+	0.773547i	$0.281520\pi$
$600$	−1.55891			−0.0636420
$601$	−21.8909			−0.892950			−0.446475	−	0.894796i	$-0.647321\pi$
$601$	−21.8909			−0.892950			−0.446475	+	0.894796i	$0.647321\pi$
$602$	−0.933117	+	1.61621i	−0.0380310	+	0.0658717i
$603$	−3.43606	−	5.95143i	−0.139927	−	0.242361i
$604$	0.369193	−	0.639460i	0.0150222	−	0.0260193i
$605$	−5.44219	−	9.42615i	−0.221257	−	0.383228i
$606$	−0.500056	−	0.866123i	−0.0203134	−	0.0351838i
$607$	−31.0668			−1.26096			−0.630482	−	0.776204i	$-0.717143\pi$
$607$	−31.0668			−1.26096			−0.630482	+	0.776204i	$0.717143\pi$
$608$	−6.54889	+	23.3736i	−0.265593	+	0.947924i
$609$	6.33317			0.256633
$610$	−2.79440	−	4.84005i	−0.113142	−	0.195968i
$611$	−21.7654	−	37.6987i	−0.880533	−	1.52513i
$612$	10.4003	−	18.0139i	0.420408	−	0.728168i
$613$	−15.9442	−	27.6162i	−0.643980	−	1.11541i	−0.984536	−	0.175182i	$-0.943949\pi$
$613$	−15.9442	−	27.6162i	−0.643980	−	1.11541i	0.340556	−	0.940224i	$-0.389385\pi$
$614$	−1.55183	+	2.68785i	−0.0626268	+	0.108473i
$615$	−7.30660			−0.294630
$616$	0.747386			0.0301130
$617$	8.85317	−	15.3341i	0.356415	−	0.617329i	−0.630944	−	0.775828i	$-0.717332\pi$
$617$	8.85317	−	15.3341i	0.356415	−	0.617329i	0.987359	+	0.158499i	$0.0506655\pi$
$618$	0.500680	−	0.867203i	0.0201403	−	0.0348840i
$619$	−25.3388			−1.01845			−0.509226	−	0.860633i	$-0.670068\pi$
$619$	−25.3388			−1.01845			−0.509226	+	0.860633i	$0.670068\pi$
$620$	11.4122			0.458323
$621$	8.91037	−	15.4332i	0.357561	−	0.619313i
$622$	2.64423	+	4.57994i	0.106024	+	0.183639i
$623$	8.59029	−	14.8788i	0.344163	−	0.596108i
$624$	−4.36155	−	7.55443i	−0.174602	−	0.302419i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−19.0054			−0.759608
$627$	0.734797	+	0.751713i	0.0293450	+	0.0300205i
$628$	−32.1175			−1.28163
$629$	−12.9907	−	22.5005i	−0.517973	−	0.897155i
$630$	−0.755106	−	1.30788i	−0.0300841	−	0.0521072i
$631$	19.2624	−	33.3634i	0.766824	−	1.32818i	−0.172453	−	0.985018i	$-0.555169\pi$
$631$	19.2624	−	33.3634i	0.766824	−	1.32818i	0.939277	−	0.343160i	$-0.111497\pi$
$632$	−4.16512	−	7.21420i	−0.165680	−	0.286965i
$633$	−7.49007	+	12.9732i	−0.297704	+	0.515638i
$634$	0.321141			0.0127541
$635$	−4.60989			−0.182938
$636$	−4.20364	+	7.28092i	−0.166685	+	0.288707i
$637$	3.17154	−	5.49327i	0.125661	−	0.217651i
$638$	1.83640			0.0727038
$639$	8.24712			0.326251
$640$	5.72298	−	9.91250i	0.226221	−	0.391826i
$641$	5.29324	+	9.16816i	0.209070	+	0.362121i	0.951422	−	0.307890i	$-0.0996229\pi$
$641$	5.29324	+	9.16816i	0.209070	+	0.362121i	−0.742352	+	0.670011i	$0.766290\pi$
$642$	0.594940	−	1.03047i	0.0234804	−	0.0406693i
$643$	−16.3808	−	28.3723i	−0.645994	−	1.11890i	−0.984071	−	0.177776i	$-0.943110\pi$
$643$	−16.3808	−	28.3723i	−0.645994	−	1.11890i	0.338077	−	0.941119i	$-0.390224\pi$
$644$	3.73497	+	6.46915i	0.147178	+	0.254920i
$645$	2.18844			0.0861697
$646$	3.62564	−	12.9402i	0.142649	−	0.509127i
$647$	−8.21699			−0.323043			−0.161522	−	0.986869i	$-0.551640\pi$
$647$	−8.21699			−0.323043			−0.161522	+	0.986869i	$0.551640\pi$
$648$	−5.19380	−	8.99593i	−0.204032	−	0.353394i
$649$	2.13849	+	3.70397i	0.0839430	+	0.145393i
$650$	−1.91819	+	3.32240i	−0.0752377	+	0.130315i
$651$	−2.47641	−	4.28926i	−0.0970580	−	0.168109i
$652$	−20.3370	+	35.2246i	−0.796456	+	1.37950i
$653$	−20.4633			−0.800790			−0.400395	−	0.916343i	$-0.631127\pi$
$653$	−20.4633			−0.800790			−0.400395	+	0.916343i	$0.631127\pi$
$654$	2.04515			0.0799718
$655$	5.53149	−	9.58082i	0.216133	−	0.374354i
$656$	9.98796	−	17.2996i	0.389964	−	0.675438i
$657$	20.0350			0.781640
$658$	−4.15066			−0.161809
$659$	15.3092	−	26.5164i	0.596363	−	1.03293i	−0.396989	−	0.917823i	$-0.629945\pi$
$659$	15.3092	−	26.5164i	0.596363	−	1.03293i	0.993353	−	0.115109i	$-0.0367216\pi$
$660$	−0.197051	−	0.341303i	−0.00767022	−	0.0132852i
$661$	−6.27446	+	10.8677i	−0.244048	+	0.422704i	−0.961864	−	0.273529i	$-0.911809\pi$
$661$	−6.27446	+	10.8677i	−0.244048	+	0.422704i	0.717815	+	0.696234i	$0.245142\pi$
$662$	−2.43873	−	4.22400i	−0.0947838	−	0.164170i
$663$	11.4661	+	19.8598i	0.445306	+	0.771292i
$664$	6.44077			0.249951
$665$	3.04693	+	3.11708i	0.118155	+	0.120875i
$666$	−7.69742			−0.298269
$667$	20.4086	+	35.3487i	0.790224	+	1.36871i
$668$	−10.1630	−	17.6029i	−0.393220	−	0.681077i
$669$	−0.194633	+	0.337114i	−0.00752495	+	0.0130336i
$670$	0.832272	+	1.44154i	0.0321535	+	0.0556915i
$671$	1.57102	−	2.72109i	0.0606486	−	0.105046i
$672$	−3.94956			−0.152358
$673$	−20.1514			−0.776779			−0.388390	−	0.921495i	$-0.626969\pi$
$673$	−20.1514			−0.776779			−0.388390	+	0.921495i	$0.626969\pi$
$674$	7.73133	−	13.3911i	0.297800	−	0.515805i
$675$	−1.94932	+	3.37633i	−0.0750295	+	0.129955i
$676$	−44.5070			−1.71181
$677$	34.7489			1.33551			0.667755	−	0.744381i	$-0.267255\pi$
$677$	34.7489			1.33551			0.667755	+	0.744381i	$0.267255\pi$
$678$	0.321421	−	0.556718i	0.0123441	−	0.0213806i
$679$	−1.81490	−	3.14350i	−0.0696496	−	0.120637i
$680$	−5.60216	+	9.70322i	−0.214833	+	0.372102i
$681$	8.74523	+	15.1472i	0.335118	+	0.580441i
$682$	−0.718072	−	1.24374i	−0.0274964	−	0.0476252i
$683$	−5.41800			−0.207314			−0.103657	−	0.994613i	$-0.533054\pi$
$683$	−5.41800			−0.207314			−0.103657	+	0.994613i	$0.533054\pi$
$684$	12.4333	+	12.7195i	0.475397	+	0.486342i
$685$	−5.14638			−0.196633
$686$	−0.302407	−	0.523784i	−0.0115459	−	0.0199982i
$687$	3.66769	+	6.35262i	0.139931	+	0.242367i
$688$	−2.99155	+	5.18151i	−0.114052	+	0.197543i
$689$	23.0055	+	39.8466i	0.876439	+	1.51804i
$690$	−0.980375	+	1.69806i	−0.0373222	+	0.0646440i
$691$	−33.9677			−1.29219			−0.646095	−	0.763257i	$-0.723599\pi$
$691$	−33.9677			−1.29219			−0.646095	+	0.763257i	$0.723599\pi$
$692$	−4.97725			−0.189207
$693$	0.424523	−	0.735295i	0.0161263	−	0.0279315i
$694$	7.08872	−	12.2780i	0.269084	−	0.466067i
$695$	−14.9867			−0.568479
$696$	−13.9204			−0.527651
$697$	−26.2573	+	45.4790i	−0.994567	+	1.72264i
$698$	1.40315	+	2.43033i	0.0531100	+	0.0919892i
$699$	−0.456610	+	0.790872i	−0.0172706	+	0.0299135i
$700$	−0.817100	−	1.41526i	−0.0308835	−	0.0534918i
$701$	3.68735	+	6.38668i	0.139269	+	0.241221i	0.927220	−	0.374517i	$-0.122191\pi$
$701$	3.68735	+	6.38668i	0.139269	+	0.241221i	−0.787951	+	0.615738i	$0.788858\pi$
$702$	14.9567			0.564505
$703$	21.5239	−	5.50560i	0.811791	−	0.207648i
$704$	0.173402			0.00653533
$705$	2.43363	+	4.21518i	0.0916559	+	0.158753i
$706$	3.84956	+	6.66763i	0.144880	+	0.250939i
$707$	1.16576	−	2.01915i	0.0438428	−	0.0759380i
$708$	−7.28932	−	12.6255i	−0.273949	−	0.474494i
$709$	23.1576	−	40.1102i	0.869703	−	1.50637i	0.00740328	−	0.999973i	$-0.497643\pi$
$709$	23.1576	−	40.1102i	0.869703	−	1.50637i	0.862300	−	0.506398i	$-0.169023\pi$
$710$	−1.99760			−0.0749684
$711$	−9.46332			−0.354902
$712$	−18.8816	+	32.7039i	−0.707617	+	1.22563i
$713$	15.9604	−	27.6442i	0.597722	−	1.03528i
$714$	2.18658			0.0818308
$715$	−2.15683			−0.0806607
$716$	4.89601	−	8.48013i	0.182972	−	0.316917i
$717$	−8.54295	−	14.7968i	−0.319042	−	0.552597i
$718$	1.91707	−	3.32046i	0.0715443	−	0.123918i
$719$	16.3198	+	28.2668i	0.608627	+	1.05417i	0.991467	+	0.130359i	$0.0416129\pi$
$719$	16.3198	+	28.2668i	0.608627	+	1.05417i	−0.382839	+	0.923815i	$0.625054\pi$
$720$	−2.42085	−	4.19303i	−0.0902196	−	0.156265i
$721$	2.33442			0.0869384
$722$	9.81856	+	5.97071i	0.365409	+	0.222207i
$723$	−8.58549			−0.319298
$724$	−7.33689	−	12.7079i	−0.272673	−	0.472284i
$725$	−4.46480	−	7.73326i	−0.165818	−	0.287206i
$726$	2.33445	−	4.04339i	0.0866396	−	0.150064i
$727$	10.5055	+	18.1960i	0.389626	+	0.674852i	0.992399	−	0.123060i	$-0.0392709\pi$
$727$	10.5055	+	18.1960i	0.389626	+	0.674852i	−0.602773	+	0.797913i	$0.705938\pi$
$728$	−6.97109	+	12.0743i	−0.258366	+	0.447503i
$729$	−3.50537			−0.129829
$730$	−4.85282			−0.179611
$731$	7.86448	−	13.6217i	0.290878	−	0.503816i
$732$	−5.35504	+	9.27519i	−0.197928	+	0.342821i
$733$	14.7475			0.544712			0.272356	−	0.962197i	$-0.412197\pi$
$733$	14.7475			0.544712			0.272356	+	0.962197i	$0.412197\pi$
$734$	−14.0623			−0.519049
$735$	−0.354617	+	0.614215i	−0.0130802	+	0.0226556i
$736$	−12.7274	−	22.0445i	−0.469139	−	0.812573i
$737$	−0.467906	+	0.810437i	−0.0172355	+	0.0298528i
$738$	7.77917	+	13.4739i	0.286355	+	0.495982i
$739$	−15.3699	−	26.6215i	−0.565392	−	0.979287i	−0.997013	−	0.0772323i	$-0.975392\pi$
$739$	−15.3699	−	26.6215i	−0.565392	−	0.979287i	0.431621	−	0.902055i	$-0.357942\pi$
$740$	−8.32938			−0.306194
$741$	−18.9979	+	4.85945i	−0.697904	+	0.178516i
$742$	4.38714			0.161057
$743$	2.11168	+	3.65753i	0.0774700	+	0.134182i	0.902158	−	0.431406i	$-0.141982\pi$
$743$	2.11168	+	3.65753i	0.0774700	+	0.134182i	−0.824688	+	0.565588i	$0.808649\pi$
$744$	5.44317	+	9.42785i	0.199556	+	0.345642i
$745$	3.08865	−	5.34970i	0.113159	−	0.195998i
$746$	3.33542	+	5.77712i	0.122118	+	0.211515i
$747$	3.65842	−	6.33658i	0.133855	−	0.231843i
$748$	−2.83253			−0.103568
$749$	2.77391			0.101356
$750$	0.214477	−	0.371485i	0.00783159	−	0.0135647i
$751$	22.0548	−	38.2001i	0.804791	−	1.39394i	−0.111640	−	0.993749i	$-0.535610\pi$
$751$	22.0548	−	38.2001i	0.804791	−	1.39394i	0.916432	−	0.400191i	$-0.131056\pi$
$752$	−13.3069			−0.485252
$753$	−2.58686			−0.0942704
$754$	−17.1287	+	29.6677i	−0.623789	+	1.08043i
$755$	0.225916	+	0.391299i	0.00822194	+	0.0142408i
$756$	−3.18559	+	5.51760i	−0.115859	+	0.200673i
$757$	17.4971	+	30.3058i	0.635942	+	1.10148i	0.986315	+	0.164873i	$0.0527216\pi$
$757$	17.4971	+	30.3058i	0.635942	+	1.10148i	−0.350373	+	0.936610i	$0.613945\pi$
$758$	8.36146	+	14.4825i	0.303702	+	0.526027i
$759$	−1.10234			−0.0400124
$760$	−6.69720	−	6.85138i	−0.242933	−	0.248526i
$761$	−15.8276			−0.573749			−0.286874	−	0.957968i	$-0.592616\pi$
$761$	−15.8276			−0.573749			−0.286874	+	0.957968i	$0.592616\pi$
$762$	−0.988715	−	1.71251i	−0.0358174	−	0.0620375i
$763$	2.38388	+	4.12900i	0.0863023	+	0.149480i
$764$	−1.70962	+	2.96115i	−0.0618520	+	0.107131i
$765$	6.36416	+	11.0231i	0.230097	+	0.398539i
$766$	−4.96786	+	8.60458i	−0.179496	+	0.310896i
$767$	−79.7852			−2.88088
$768$	4.18643			0.151065
$769$	16.3912	−	28.3903i	0.591080	−	1.02378i	−0.403007	−	0.915197i	$-0.632035\pi$
$769$	16.3912	−	28.3903i	0.591080	−	1.02378i	0.994087	−	0.108584i	$-0.0346317\pi$
$770$	−0.102827	+	0.178101i	−0.00370562	+	0.00641832i
$771$	4.16705			0.150073
$772$	29.2870			1.05406
$773$	−19.3120	+	33.4493i	−0.694604	+	1.20309i	0.275710	+	0.961241i	$0.411087\pi$
$773$	−19.3120	+	33.4493i	−0.694604	+	1.20309i	−0.970314	+	0.241848i	$0.922246\pi$
$774$	−2.32998	−	4.03565i	−0.0837495	−	0.145058i
$775$	−3.49166	+	6.04774i	−0.125424	+	0.217241i
$776$	3.98918	+	6.90946i	0.143203	+	0.248035i
$777$	1.80745	+	3.13060i	0.0648420	+	0.112310i
$778$	−9.84792			−0.353065
$779$	−31.3898	−	32.1125i	−1.12466	−	1.15055i
$780$	7.35183			0.263238
$781$	−0.561527	−	0.972594i	−0.0200930	−	0.0348021i
$782$	7.04625	+	12.2045i	0.251973	+	0.436430i
$783$	−17.4067	+	30.1493i	−0.622064	+	1.07745i
$784$	−0.969507	−	1.67924i	−0.0346253	−	0.0599727i
$785$	9.82667	−	17.0203i	0.350729	−	0.607480i
$786$	4.74551			0.169267
$787$	−48.1787			−1.71738			−0.858692	−	0.512491i	$-0.828723\pi$
$787$	−48.1787			−1.71738			−0.858692	+	0.512491i	$0.828723\pi$
$788$	−1.35484	+	2.34665i	−0.0482642	+	0.0835961i
$789$	−8.34475	+	14.4535i	−0.297081	+	0.514559i
$790$	2.29218			0.0815521
$791$	1.49863			0.0532850
$792$	−0.933107	+	1.61619i	−0.0331565	+	0.0574287i
$793$	29.3068	+	50.7608i	1.04071	+	1.80257i
$794$	11.0440	−	19.1287i	0.391936	−	0.678853i
$795$	−2.57229	−	4.45534i	−0.0912297	−	0.158015i
$796$	3.31089	+	5.73464i	0.117352	+	0.203259i
$797$	5.88269			0.208376			0.104188	−	0.994558i	$-0.466776\pi$
$797$	5.88269			0.208376			0.104188	+	0.994558i	$0.466776\pi$
$798$	−0.504451	+	1.80043i	−0.0178574	+	0.0637346i
$799$	34.9825			1.23759
$800$	2.78438	+	4.82269i	0.0984428	+	0.170508i
$801$	21.4499	+	37.1522i	0.757893	+	1.31271i
$802$	0.460037	−	0.796808i	0.0162445	−	0.0281363i
$803$	−1.36414	−	2.36275i	−0.0481393	−	0.0833798i
$804$	1.59492	−	2.76248i	0.0562485	−	0.0974253i
$805$	−4.57100			−0.161107
$806$	26.7907			0.943662
$807$	−9.25744	+	16.0344i	−0.325877	+	0.564436i
$808$	−2.56235	+	4.43812i	−0.0901431	+	0.156132i
$809$	16.5249			0.580985			0.290492	−	0.956877i	$-0.406181\pi$
$809$	16.5249			0.580985			0.290492	+	0.956877i	$0.406181\pi$
$810$	2.85829			0.100430
$811$	8.62462	−	14.9383i	0.302851	−	0.524554i	−0.673929	−	0.738796i	$-0.735395\pi$
$811$	8.62462	−	14.9383i	0.302851	−	0.524554i	0.976781	+	0.214242i	$0.0687281\pi$
$812$	−7.29638	−	12.6377i	−0.256053	−	0.443496i
$813$	−3.48384	+	6.03419i	−0.122184	+	0.211628i
$814$	0.524099	+	0.907766i	0.0183697	+	0.0318172i
$815$	−12.4446	−	21.5547i	−0.435915	−	0.755027i
$816$	7.01012			0.245403
$817$	9.40173	+	9.61818i	0.328925	+	0.336497i
$818$	−4.04930			−0.141581
$819$	7.91930	+	13.7166i	0.276723	+	0.479298i
$820$	8.41785	+	14.5801i	0.293964	+	0.509161i
$821$	−7.16224	+	12.4054i	−0.249964	+	0.432950i	−0.963516	−	0.267653i	$-0.913752\pi$
$821$	−7.16224	+	12.4054i	−0.249964	+	0.432950i	0.713552	+	0.700603i	$0.247085\pi$
$822$	−1.10378	−	1.91180i	−0.0384987	−	0.0666818i
$823$	−1.72986	+	2.99621i	−0.0602992	+	0.104441i	−0.894599	−	0.446870i	$-0.852539\pi$
$823$	−1.72986	+	2.99621i	−0.0602992	+	0.104441i	0.834300	+	0.551311i	$0.185872\pi$
$824$	−5.13109			−0.178750
$825$	0.241159			0.00839609
$826$	−3.80376	+	6.58831i	−0.132350	+	0.229237i
$827$	9.54635	−	16.5348i	0.331959	−	0.574970i	−0.650937	−	0.759132i	$-0.725624\pi$
$827$	9.54635	−	16.5348i	0.331959	−	0.574970i	0.982896	+	0.184162i	$0.0589570\pi$
$828$	−18.6523			−0.648213
$829$	42.3771			1.47182			0.735909	−	0.677080i	$-0.236755\pi$
$829$	42.3771			1.47182			0.735909	+	0.677080i	$0.236755\pi$
$830$	−0.886133	+	1.53483i	−0.0307581	+	0.0532747i
$831$	5.99450	+	10.3828i	0.207947	+	0.360174i
$832$	−1.61737	+	2.80137i	−0.0560722	+	0.0971200i
$833$	2.54874	+	4.41454i	0.0883085	+	0.152955i
$834$	−3.21431	−	5.56734i	−0.111302	−	0.192781i
$835$	12.4379			0.430433
$836$	0.653475	−	2.33231i	0.0226009	−	0.0806646i
$837$	27.2255			0.941052
$838$	−1.96192	−	3.39814i	−0.0677733	−	0.117387i
$839$	−12.7255	−	22.0412i	−0.439332	−	0.760945i	0.558306	−	0.829635i	$-0.311451\pi$
$839$	−12.7255	−	22.0412i	−0.439332	−	0.760945i	−0.997638	+	0.0686898i	$0.978118\pi$
$840$	0.779453	−	1.35005i	0.0268937	−	0.0465812i
$841$	−25.3688	−	43.9401i	−0.874787	−	1.51518i
$842$	−10.8103	+	18.7239i	−0.372546	+	0.645268i
$843$	6.39292			0.220184
$844$	34.5169			1.18812
$845$	13.6174	−	23.5860i	0.468452	−	0.811382i
$846$	5.18207	−	8.97561i	0.178163	−	0.308588i
$847$	10.8844			0.373992
$848$	14.0651			0.482996
$849$	0.738345	−	1.27885i	0.0253399	−	0.0438901i
$850$	−1.54151	−	2.66997i	−0.0528734	−	0.0915793i
$851$	−11.6490	+	20.1767i	−0.399323	+	0.691647i
$852$	1.91404	+	3.31521i	0.0655739	+	0.113577i
$853$	4.94533	+	8.56557i	0.169325	+	0.293280i	0.938183	−	0.346140i	$-0.112508\pi$
$853$	4.94533	+	8.56557i	0.169325	+	0.293280i	−0.768858	+	0.639420i	$0.779175\pi$
$854$	5.58880			0.191245
$855$	−10.5446	+	2.69720i	−0.360618	+	0.0922424i
$856$	−6.09709			−0.208394
$857$	3.54060	+	6.13250i	0.120945	+	0.209482i	0.920140	−	0.391588i	$-0.128074\pi$
$857$	3.54060	+	6.13250i	0.120945	+	0.209482i	−0.799196	+	0.601071i	$0.794741\pi$
$858$	−0.462590	−	0.801229i	−0.0157926	−	0.0273535i
$859$	−19.2087	+	33.2704i	−0.655392	+	1.13517i	0.326403	+	0.945231i	$0.394163\pi$
$859$	−19.2087	+	33.2704i	−0.655392	+	1.13517i	−0.981795	+	0.189942i	$0.939170\pi$
$860$	−2.52128	−	4.36698i	−0.0859748	−	0.148913i
$861$	3.65330	−	6.32770i	0.124504	−	0.215647i
$862$	19.6915			0.670695
$863$	31.5146			1.07277			0.536385	−	0.843974i	$-0.319790\pi$
$863$	31.5146			1.07277			0.536385	+	0.843974i	$0.319790\pi$
$864$	10.8553	−	18.8020i	0.369306	−	0.639657i
$865$	1.52284	−	2.63763i	0.0517781	−	0.0896823i
$866$	21.2387			0.721721
$867$	−6.37193			−0.216402
$868$	−5.70608	+	9.88322i	−0.193677	+	0.335458i
$869$	0.644335	+	1.11602i	0.0218576	+	0.0378584i
$870$	1.91519	−	3.31721i	0.0649311	−	0.112464i
$871$	−8.72860	−	15.1184i	−0.295757	−	0.512267i
$872$	−5.23980	−	9.07561i	−0.177442	−	0.307339i
$873$	9.06358			0.306756
$874$	−11.6747	+	2.98628i	−0.394904	+	0.101012i
$875$	1.00000			0.0338062
$876$	4.64984	+	8.05376i	0.157104	+	0.272111i
$877$	0.556083	+	0.963165i	0.0187776	+	0.0325238i	0.875262	−	0.483650i	$-0.160689\pi$
$877$	0.556083	+	0.963165i	0.0187776	+	0.0325238i	−0.856484	+	0.516174i	$0.827356\pi$
$878$	−5.92873	+	10.2689i	−0.200085	+	0.346557i
$879$	6.92720	+	11.9983i	0.233649	+	0.404691i
$880$	−0.329660	+	0.570987i	−0.0111128	+	0.0192480i
$881$	−24.1428			−0.813391			−0.406696	−	0.913564i	$-0.633319\pi$
$881$	−24.1428			−0.813391			−0.406696	+	0.913564i	$0.633319\pi$
$882$	1.51021			0.0508515
$883$	12.4661	−	21.5919i	0.419518	−	0.726626i	−0.576373	−	0.817186i	$-0.695533\pi$
$883$	12.4661	−	21.5919i	0.419518	−	0.726626i	0.995891	+	0.0905607i	$0.0288659\pi$
$884$	26.4199	−	45.7606i	0.888597	−	1.53910i
$885$	8.92096			0.299875
$886$	3.97071			0.133399
$887$	7.21480	−	12.4964i	0.242249	−	0.419588i	−0.719105	−	0.694901i	$-0.755448\pi$
$887$	7.21480	−	12.4964i	0.242249	−	0.419588i	0.961355	+	0.275313i	$0.0887815\pi$
$888$	−3.97280	−	6.88110i	−0.133319	−	0.230914i
$889$	2.30494	−	3.99228i	0.0773054	−	0.133897i
$890$	−5.19552	−	8.99891i	−0.174154	−	0.301644i
$891$	0.803470	+	1.39165i	0.0269173	+	0.0466221i
$892$	0.896939			0.0300317
$893$	−8.07057	+	28.8046i	−0.270071	+	0.963909i
$894$	2.64978			0.0886219
$895$	2.99596	+	5.18916i	0.100144	+	0.173455i
$896$	5.72298	+	9.91250i	0.191191	+	0.331153i
$897$	10.2819	−	17.8087i	0.343301	−	0.594615i
$898$	−6.66174	−	11.5385i	−0.222305	−	0.385044i
$899$	−31.1791	+	54.0038i	−1.03988	+	1.80113i
$900$	4.08058			0.136019
$901$	−36.9756			−1.23184
$902$	1.05933	−	1.83481i	0.0352719	−	0.0610926i
$903$	−1.09422	+	1.89524i	−0.0364133	+	0.0630697i
$904$	−3.29400			−0.109557
$905$	8.97917			0.298478
$906$	−0.0969077	+	0.167849i	−0.00321954	+	0.00557641i
$907$	−21.6884	−	37.5653i	−0.720150	−	1.24734i	−0.960939	−	0.276759i	$-0.910740\pi$
$907$	−21.6884	−	37.5653i	−0.720150	−	1.24734i	0.240789	−	0.970577i	$-0.422594\pi$
$908$	20.1506	−	34.9018i	0.668720	−	1.15826i
$909$	2.91088	+	5.04179i	0.0965478	+	0.167226i
$910$	−1.91819	−	3.32240i	−0.0635874	−	0.110137i
$911$	−8.72436			−0.289051			−0.144525	−	0.989501i	$-0.546166\pi$
$911$	−8.72436			−0.289051			−0.144525	+	0.989501i	$0.546166\pi$
$912$	−1.61726	+	5.77214i	−0.0535527	+	0.191135i
$913$	−0.996374			−0.0329752
$914$	12.4556	+	21.5736i	0.411993	+	0.713593i
$915$	−3.27685	−	5.67568i	−0.108329	−	0.187632i
$916$	8.45100	−	14.6376i	0.279229	−	0.483639i
$917$	5.53149	+	9.58082i	0.182666	+	0.316386i
$918$	−6.00981	+	10.4093i	−0.198353	+	0.343558i
$919$	15.8401			0.522515			0.261258	−	0.965269i	$-0.415863\pi$
$919$	15.8401			0.522515			0.261258	+	0.965269i	$0.415863\pi$
$920$	10.0471			0.331244
$921$	−1.81975	+	3.15191i	−0.0599629	+	0.103859i
$922$	11.3843	−	19.7182i	0.374923	−	0.649385i
$923$	20.9501			0.689582
$924$	0.394103			0.0129650
$925$	2.54846	−	4.41406i	0.0837927	−	0.145133i
$926$	1.76733	+	3.06111i	0.0580781	+	0.100594i
$927$	−2.91451	+	5.04808i	−0.0957251	+	0.165801i
$928$	24.8634	+	43.0647i	0.816182	+	1.41367i
$929$	−4.56608	−	7.90868i	−0.149808	−	0.259475i	0.781348	−	0.624095i	$-0.214532\pi$
$929$	−4.56608	−	7.90868i	−0.149808	−	0.259475i	−0.931156	+	0.364620i	$0.881199\pi$
$930$	−2.99553			−0.0982272
$931$	−4.22294	+	1.08018i	−0.138401	+	0.0354016i
$932$	2.10422			0.0689261
$933$	3.10076	+	5.37067i	0.101514	+	0.175828i
$934$	3.15994	+	5.47317i	0.103396	+	0.179088i
$935$	0.866642	−	1.50107i	0.0283422	−	0.0490902i
$936$	−17.4067	−	30.1493i	−0.568957	−	0.985462i
$937$	−11.8760	+	20.5698i	−0.387972	+	0.671986i	−0.992177	−	0.124842i	$-0.960157\pi$
$937$	−11.8760	+	20.5698i	−0.387972	+	0.671986i	0.604205	+	0.796829i	$0.293491\pi$
$938$	−1.66454			−0.0543493
$939$	−22.2867			−0.727297
$940$	5.60752	−	9.71251i	0.182897	−	0.316787i
$941$	9.11205	−	15.7825i	0.297044	−	0.514496i	−0.678414	−	0.734680i	$-0.737332\pi$
$941$	9.11205	−	15.7825i	0.297044	−	0.514496i	0.975458	+	0.220184i	$0.0706657\pi$
$942$	8.43038			0.274677
$943$	47.0909			1.53349
$944$	−12.1948	+	21.1219i	−0.396905	+	0.687460i
$945$	−1.94932	−	3.37633i	−0.0634115	−	0.109832i
$946$	−0.317286	+	0.549555i	−0.0103159	+	0.0178676i
$947$	16.1301	+	27.9382i	0.524159	+	0.907870i	0.999604	+	0.0281246i	$0.00895351\pi$
$947$	16.1301	+	27.9382i	0.524159	+	0.907870i	−0.475446	+	0.879745i	$0.657713\pi$
$948$	−2.19630	−	3.80411i	−0.0713326	−	0.123552i
$949$	50.8948			1.65212
$950$	2.55409	−	0.653309i	0.0828656	−	0.0211961i
$951$	0.376586			0.0122116
$952$	−5.60216	−	9.70322i	−0.181567	−	0.314483i
$953$	−7.37274	−	12.7700i	−0.238827	−	0.413660i	0.721551	−	0.692361i	$-0.243429\pi$
$953$	−7.37274	−	12.7700i	−0.238827	−	0.413660i	−0.960378	+	0.278701i	$0.910096\pi$
$954$	−5.47732	+	9.48700i	−0.177335	+	0.307153i
$955$	−1.04615	−	1.81199i	−0.0338527	−	0.0586346i
$956$	−19.6845	+	34.0945i	−0.636641	+	1.10269i
$957$	2.15346			0.0696113
$958$	−17.8253			−0.575910
$959$	2.57319	−	4.45689i	0.0830926	−	0.143921i
$960$	0.180842	−	0.313227i	0.00583664	−	0.0101094i
$961$	17.7668			0.573124
$962$	−19.5537			−0.630437
$963$	−3.46321	+	5.99846i	−0.111600	+	0.193298i
$964$	9.89125	+	17.1321i	0.318576	+	0.551789i
$965$	−8.96066	+	15.5203i	−0.288454	+	0.499617i
$966$	−0.980375	−	1.69806i	−0.0315430	−	0.0546342i
$967$	17.5915	+	30.4693i	0.565703	+	0.979826i	0.996984	+	0.0776086i	$0.0247284\pi$
$967$	17.5915	+	30.4693i	0.565703	+	0.979826i	−0.431281	+	0.902218i	$0.641938\pi$
$968$	−23.9240			−0.768947
$969$	4.25161	−	15.1744i	0.136581	−	0.487471i
$970$	−2.19536			−0.0704886
$971$	6.80414	+	11.7851i	0.218355	+	0.378202i	0.954305	−	0.298834i	$-0.0965975\pi$
$971$	6.80414	+	11.7851i	0.218355	+	0.378202i	−0.735950	+	0.677036i	$0.763264\pi$
$972$	−12.2955	−	21.2964i	−0.394378	−	0.683083i
$973$	7.49336	−	12.9789i	0.240226	−	0.416084i
$974$	8.94123	+	15.4867i	0.286496	+	0.496225i
$975$	−2.24937	+	3.89602i	−0.0720373	+	0.124772i
$976$	17.9175			0.573527
$977$	26.8804			0.859980			0.429990	−	0.902834i	$-0.358517\pi$
$977$	26.8804			0.859980			0.429990	+	0.902834i	$0.358517\pi$
$978$	5.33815	−	9.24596i	0.170695	−	0.295653i
$979$	2.92094	−	5.05922i	0.0933536	−	0.161693i
$980$	1.63420			0.0522026
$981$	−11.9050			−0.380099
$982$	−3.39408	+	5.87872i	−0.108309	+	0.187597i
$983$	26.6814	+	46.2135i	0.851003	+	1.47398i	0.880304	+	0.474411i	$0.157339\pi$
$983$	26.6814	+	46.2135i	0.851003	+	1.47398i	−0.0293003	+	0.999571i	$0.509328\pi$
$984$	−8.03000	+	13.9084i	−0.255987	+	0.443382i
$985$	−0.829054	−	1.43596i	−0.0264159	−	0.0457536i
$986$	−13.7651	−	23.8418i	−0.438369	−	0.759277i
$987$	−4.86727			−0.154927
$988$	31.5841	+	32.3113i	1.00483	+	1.02796i
$989$	−14.1045			−0.448495
$990$	−0.256757	−	0.444716i	−0.00816027	−	0.0141340i
$991$	−25.8407	−	44.7573i	−0.820856	−	1.42176i	−0.905046	−	0.425314i	$-0.860164\pi$
$991$	−25.8407	−	44.7573i	−0.820856	−	1.42176i	0.0841903	−	0.996450i	$-0.473170\pi$
$992$	19.4443	−	33.6784i	0.617356	−	1.06929i
$993$	−2.85977	−	4.95327i	−0.0907521	−	0.157187i
$994$	0.998798	−	1.72997i	0.0316799	−	0.0548713i
$995$	−4.05200			−0.128457
$996$	3.39627			0.107615
$997$	26.4864	−	45.8758i	0.838833	−	1.45290i	−0.0520384	−	0.998645i	$-0.516572\pi$
$997$	26.4864	−	45.8758i	0.838833	−	1.45290i	0.890871	−	0.454256i	$-0.150095\pi$
$998$	12.8101	−	22.1877i	0.405496	−	0.702340i
$999$	−19.8711			−0.628693

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.i.h.596.5	yes	20
19.11	even	3	inner	665.2.i.h.106.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.i.h.106.5	✓	20	19.11	even	3	inner
665.2.i.h.596.5	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.302407 + 0.523784i) q^{2} +(0.354617 + 0.614215i) q^{3} +(0.817100 - 1.41526i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.214477 + 0.371485i) q^{6} -1.00000 q^{7} +2.19801 q^{8} +(1.24849 - 2.16245i) q^{9} +O(q^{10})\)	\(q+(0.302407 + 0.523784i) q^{2} +(0.354617 + 0.614215i) q^{3} +(0.817100 - 1.41526i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.214477 + 0.371485i) q^{6} -1.00000 q^{7} +2.19801 q^{8} +(1.24849 - 2.16245i) q^{9} +(-0.302407 + 0.523784i) q^{10} -0.340028 q^{11} +1.15903 q^{12} +(3.17154 - 5.49327i) q^{13} +(-0.302407 - 0.523784i) q^{14} +(-0.354617 + 0.614215i) q^{15} +(-0.969507 - 1.67924i) q^{16} +(2.54874 + 4.41454i) q^{17} +1.51021 q^{18} +(-4.22294 + 1.08018i) q^{19} +1.63420 q^{20} +(-0.354617 - 0.614215i) q^{21} +(-0.102827 - 0.178101i) q^{22} +(2.28550 - 3.95860i) q^{23} +(0.779453 + 1.35005i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.83638 q^{26} +3.89865 q^{27} +(-0.817100 + 1.41526i) q^{28} +(-4.46480 + 7.73326i) q^{29} -0.428954 q^{30} +6.98333 q^{31} +(2.78438 - 4.82269i) q^{32} +(-0.120580 - 0.208850i) q^{33} +(-1.54151 + 2.66997i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-2.04029 - 3.53388i) q^{36} -5.09691 q^{37} +(-1.84283 - 1.88525i) q^{38} +4.49873 q^{39} +(1.09901 + 1.90354i) q^{40} +(5.15105 + 8.92188i) q^{41} +(0.214477 - 0.371485i) q^{42} +(-1.54282 - 2.67224i) q^{43} +(-0.277837 + 0.481228i) q^{44} +2.49699 q^{45} +2.76460 q^{46} +(3.43135 - 5.94328i) q^{47} +(0.687607 - 1.19097i) q^{48} +1.00000 q^{49} -0.604813 q^{50} +(-1.80765 + 3.13094i) q^{51} +(-5.18294 - 8.97711i) q^{52} +(-3.62686 + 6.28190i) q^{53} +(1.17898 + 2.04205i) q^{54} +(-0.170014 - 0.294473i) q^{55} -2.19801 q^{56} +(-2.16099 - 2.21074i) q^{57} -5.40074 q^{58} +(-6.28915 - 10.8931i) q^{59} +(0.579515 + 1.00375i) q^{60} +(-4.62027 + 8.00254i) q^{61} +(2.11180 + 3.65775i) q^{62} +(-1.24849 + 2.16245i) q^{63} -0.509963 q^{64} +6.34309 q^{65} +(0.0729282 - 0.126315i) q^{66} +(1.37608 - 2.38344i) q^{67} +8.33030 q^{68} +3.24191 q^{69} +(0.302407 - 0.523784i) q^{70} +(1.65141 + 2.86033i) q^{71} +(2.74421 - 4.75310i) q^{72} +(4.01184 + 6.94871i) q^{73} +(-1.54134 - 2.66968i) q^{74} -0.709234 q^{75} +(-1.92183 + 6.85917i) q^{76} +0.340028 q^{77} +(1.36045 + 2.35636i) q^{78} +(-1.89495 - 3.28215i) q^{79} +(0.969507 - 1.67924i) q^{80} +(-2.36295 - 4.09276i) q^{81} +(-3.11542 + 5.39607i) q^{82} +2.93027 q^{83} -1.15903 q^{84} +(-2.54874 + 4.41454i) q^{85} +(0.933117 - 1.61621i) q^{86} -6.33317 q^{87} -0.747386 q^{88} +(-8.59029 + 14.8788i) q^{89} +(0.755106 + 1.30788i) q^{90} +(-3.17154 + 5.49327i) q^{91} +(-3.73497 - 6.46915i) q^{92} +(2.47641 + 4.28926i) q^{93} +4.15066 q^{94} +(-3.04693 - 3.11708i) q^{95} +3.94956 q^{96} +(1.81490 + 3.14350i) q^{97} +(0.302407 + 0.523784i) q^{98} +(-0.424523 + 0.735295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

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