LMFDB - Embedded newform 304.2.k.b.229.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	304.229
Dual form			304.2.k.b.77.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.738388 + 1.20614i) q^{2} +(-0.325366 + 0.325366i) q^{3} +(-0.909565 - 1.78121i) q^{4} +(-0.432056 - 0.432056i) q^{5} +(-0.152192 - 0.632685i) q^{6} +0.877228i q^{7} +(2.82000 + 0.218155i) q^{8} +2.78827i q^{9} +O(q^{10})$	\(q+(-0.738388 + 1.20614i) q^{2} +(-0.325366 + 0.325366i) q^{3} +(-0.909565 - 1.78121i) q^{4} +(-0.432056 - 0.432056i) q^{5} +(-0.152192 - 0.632685i) q^{6} +0.877228i q^{7} +(2.82000 + 0.218155i) q^{8} +2.78827i q^{9} +(0.840146 - 0.202096i) q^{10} +(-0.148426 - 0.148426i) q^{11} +(0.875485 + 0.283602i) q^{12} +(-4.57140 + 4.57140i) q^{13} +(-1.05806 - 0.647735i) q^{14} +0.281153 q^{15} +(-2.34538 + 3.24024i) q^{16} -4.80073 q^{17} +(-3.36306 - 2.05883i) q^{18} +(0.707107 - 0.707107i) q^{19} +(-0.376597 + 1.16256i) q^{20} +(-0.285420 - 0.285420i) q^{21} +(0.288619 - 0.0694269i) q^{22} +5.90304i q^{23} +(-0.988513 + 0.846553i) q^{24} -4.62666i q^{25} +(-2.13830 - 8.88923i) q^{26} +(-1.88331 - 1.88331i) q^{27} +(1.56252 - 0.797896i) q^{28} +(-4.03905 + 4.03905i) q^{29} +(-0.207600 + 0.339110i) q^{30} +9.44915 q^{31} +(-2.17640 - 5.22143i) q^{32} +0.0965854 q^{33} +(3.54480 - 5.79037i) q^{34} +(0.379011 - 0.379011i) q^{35} +(4.96649 - 2.53612i) q^{36} +(-2.05541 - 2.05541i) q^{37} +(0.330753 + 1.37499i) q^{38} -2.97476i q^{39} +(-1.12414 - 1.31265i) q^{40} +11.4085i q^{41} +(0.555009 - 0.133507i) q^{42} +(-3.98068 - 3.98068i) q^{43} +(-0.129374 + 0.399380i) q^{44} +(1.20469 - 1.20469i) q^{45} +(-7.11992 - 4.35874i) q^{46} -6.46743 q^{47} +(-0.291158 - 1.81737i) q^{48} +6.23047 q^{49} +(5.58041 + 3.41627i) q^{50} +(1.56199 - 1.56199i) q^{51} +(12.3006 + 3.98461i) q^{52} +(1.81402 + 1.81402i) q^{53} +(3.66215 - 0.880927i) q^{54} +0.128256i q^{55} +(-0.191372 + 2.47378i) q^{56} +0.460137i q^{57} +(-1.88929 - 7.85406i) q^{58} +(3.14983 + 3.14983i) q^{59} +(-0.255727 - 0.500790i) q^{60} +(-4.49166 + 4.49166i) q^{61} +(-6.97714 + 11.3970i) q^{62} -2.44595 q^{63} +(7.90482 + 1.23039i) q^{64} +3.95020 q^{65} +(-0.0713176 + 0.116496i) q^{66} +(10.7741 - 10.7741i) q^{67} +(4.36658 + 8.55108i) q^{68} +(-1.92065 - 1.92065i) q^{69} +(0.177285 + 0.737000i) q^{70} +2.42744i q^{71} +(-0.608276 + 7.86294i) q^{72} +3.14290i q^{73} +(3.99681 - 0.961430i) q^{74} +(1.50536 + 1.50536i) q^{75} +(-1.90266 - 0.616342i) q^{76} +(0.130203 - 0.130203i) q^{77} +(3.58798 + 2.19652i) q^{78} +15.3181 q^{79} +(2.41330 - 0.386630i) q^{80} -7.13929 q^{81} +(-13.7602 - 8.42388i) q^{82} +(4.96065 - 4.96065i) q^{83} +(-0.248784 + 0.768000i) q^{84} +(2.07418 + 2.07418i) q^{85} +(7.74055 - 1.86198i) q^{86} -2.62834i q^{87} +(-0.386181 - 0.450941i) q^{88} -6.03742i q^{89} +(0.563500 + 2.34256i) q^{90} +(-4.01016 - 4.01016i) q^{91} +(10.5145 - 5.36920i) q^{92} +(-3.07443 + 3.07443i) q^{93} +(4.77547 - 7.80065i) q^{94} -0.611019 q^{95} +(2.40700 + 0.990750i) q^{96} +6.45317 q^{97} +(-4.60051 + 7.51484i) q^{98} +(0.413852 - 0.413852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.738388	+	1.20614i	−0.522119	+	0.852872i
$2$	−0.738388	+	1.20614i	−0.522119	+	0.852872i
$3$	−0.325366	+	0.325366i	−0.187850	+	0.187850i	−0.794766	−	0.606916i	$-0.792406\pi$
$3$	−0.325366	+	0.325366i	−0.187850	+	0.187850i	0.606916	+	0.794766i	$0.292406\pi$
$4$	−0.909565	−	1.78121i	−0.454783	−	0.890603i
$5$	−0.432056	−	0.432056i	−0.193221	−	0.193221i	0.603865	−	0.797086i	$-0.293626\pi$
$5$	−0.432056	−	0.432056i	−0.193221	−	0.193221i	−0.797086	+	0.603865i	$0.793626\pi$
$6$	−0.152192	−	0.632685i	−0.0621320	−	0.258292i
$7$			0.877228i			0.331561i	0.986163	+	0.165781i	$0.0530143\pi$
$7$			0.877228i			0.331561i	−0.986163	+	0.165781i	$0.946986\pi$
$8$	2.82000	+	0.218155i	0.997021	+	0.0771294i
$9$			2.78827i			0.929425i
$10$	0.840146	−	0.202096i	0.265678	−	0.0639085i
$11$	−0.148426	−	0.148426i	−0.0447521	−	0.0447521i	0.684377	−	0.729129i	$-0.260074\pi$
$11$	−0.148426	−	0.148426i	−0.0447521	−	0.0447521i	−0.729129	+	0.684377i	$0.760074\pi$
$12$	0.875485	+	0.283602i	0.252731	+	0.0818689i
$13$	−4.57140	+	4.57140i	−1.26788	+	1.26788i	−0.320695	+	0.947183i	$0.603916\pi$
$13$	−4.57140	+	4.57140i	−1.26788	+	1.26788i	−0.947183	+	0.320695i	$0.896084\pi$
$14$	−1.05806	−	0.647735i	−0.282779	−	0.173114i
$15$	0.281153			0.0725933
$16$	−2.34538	+	3.24024i	−0.586346	+	0.810061i
$17$	−4.80073			−1.16435			−0.582174	−	0.813064i	$-0.697798\pi$
$17$	−4.80073			−1.16435			−0.582174	+	0.813064i	$0.697798\pi$
$18$	−3.36306	−	2.05883i	−0.792681	−	0.485271i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$19$	0.707107	−	0.707107i	0.162221	−	0.162221i
$20$	−0.376597	+	1.16256i	−0.0842096	+	0.259957i
$21$	−0.285420	−	0.285420i	−0.0622838	−	0.0622838i
$22$	0.288619	−	0.0694269i	0.0615337	−	0.0148019i
$23$			5.90304i			1.23087i	0.788188	+	0.615435i	$0.211019\pi$
$23$			5.90304i			1.23087i	−0.788188	+	0.615435i	$0.788981\pi$
$24$	−0.988513	+	0.846553i	−0.201779	+	0.172802i
$25$		−	4.62666i		−	0.925331i
$26$	−2.13830	−	8.88923i	−0.419354	−	1.74332i
$27$	−1.88331	−	1.88331i	−0.362443	−	0.362443i
$28$	1.56252	−	0.797896i	0.295289	−	0.150788i
$29$	−4.03905	+	4.03905i	−0.750032	+	0.750032i	−0.974485	−	0.224453i	$-0.927941\pi$
$29$	−4.03905	+	4.03905i	−0.750032	+	0.750032i	0.224453	+	0.974485i	$0.427941\pi$
$30$	−0.207600	+	0.339110i	−0.0379024	+	0.0619128i
$31$	9.44915			1.69712			0.848559	−	0.529101i	$-0.177471\pi$
$31$	9.44915			1.69712			0.848559	+	0.529101i	$0.177471\pi$
$32$	−2.17640	−	5.22143i	−0.384736	−	0.923027i
$33$	0.0965854			0.0168134
$34$	3.54480	−	5.79037i	0.607929	−	0.993040i
$35$	0.379011	−	0.379011i	0.0640646	−	0.0640646i
$36$	4.96649	−	2.53612i	0.827748	−	0.422686i
$37$	−2.05541	−	2.05541i	−0.337908	−	0.337908i	0.517672	−	0.855579i	$-0.326799\pi$
$37$	−2.05541	−	2.05541i	−0.337908	−	0.337908i	−0.855579	+	0.517672i	$0.826799\pi$
$38$	0.330753	+	1.37499i	0.0536552	+	0.223053i
$39$		−	2.97476i		−	0.476342i
$40$	−1.12414	−	1.31265i	−0.177743	−	0.207549i
$41$			11.4085i			1.78170i	0.454295	+	0.890851i	$0.349891\pi$
$41$			11.4085i			1.78170i	−0.454295	+	0.890851i	$0.650109\pi$
$42$	0.555009	−	0.133507i	0.0856397	−	0.0206006i
$43$	−3.98068	−	3.98068i	−0.607047	−	0.607047i	0.335126	−	0.942173i	$-0.391221\pi$
$43$	−3.98068	−	3.98068i	−0.607047	−	0.607047i	−0.942173	+	0.335126i	$0.891221\pi$
$44$	−0.129374	+	0.399380i	−0.0195038	+	0.0602087i
$45$	1.20469	−	1.20469i	0.179585	−	0.179585i
$46$	−7.11992	−	4.35874i	−1.04977	−	0.642661i
$47$	−6.46743			−0.943372			−0.471686	−	0.881767i	$-0.656354\pi$
$47$	−6.46743			−0.943372			−0.471686	+	0.881767i	$0.656354\pi$
$48$	−0.291158	−	1.81737i	−0.0420250	−	0.262315i
$49$	6.23047			0.890067
$50$	5.58041	+	3.41627i	0.789189	+	0.483133i
$51$	1.56199	−	1.56199i	0.218723	−	0.218723i
$52$	12.3006	+	3.98461i	1.70578	+	0.552566i
$53$	1.81402	+	1.81402i	0.249175	+	0.249175i	0.820632	−	0.571457i	$-0.193622\pi$
$53$	1.81402	+	1.81402i	0.249175	+	0.249175i	−0.571457	+	0.820632i	$0.693622\pi$
$54$	3.66215	−	0.880927i	0.498356	−	0.119879i
$55$			0.128256i			0.0172941i
$56$	−0.191372	+	2.47378i	−0.0255731	+	0.330573i
$57$			0.460137i			0.0609467i
$58$	−1.88929	−	7.85406i	−0.248075	−	1.03129i
$59$	3.14983	+	3.14983i	0.410073	+	0.410073i	0.881764	−	0.471691i	$-0.156356\pi$
$59$	3.14983	+	3.14983i	0.410073	+	0.410073i	−0.471691	+	0.881764i	$0.656356\pi$
$60$	−0.255727	−	0.500790i	−0.0330142	−	0.0646517i
$61$	−4.49166	+	4.49166i	−0.575098	+	0.575098i	−0.933549	−	0.358451i	$-0.883305\pi$
$61$	−4.49166	+	4.49166i	−0.575098	+	0.575098i	0.358451	+	0.933549i	$0.383305\pi$
$62$	−6.97714	+	11.3970i	−0.886098	+	1.44742i
$63$	−2.44595			−0.308161
$64$	7.90482	+	1.23039i	0.988102	+	0.153799i
$65$	3.95020			0.489962
$66$	−0.0713176	+	0.116496i	−0.00877858	+	0.0143397i
$67$	10.7741	−	10.7741i	1.31626	−	1.31626i	0.399549	−	0.916712i	$-0.369167\pi$
$67$	10.7741	−	10.7741i	1.31626	−	1.31626i	0.916712	−	0.399549i	$-0.130833\pi$
$68$	4.36658	+	8.55108i	0.529525	+	1.03697i
$69$	−1.92065	−	1.92065i	−0.231219	−	0.231219i
$70$	0.177285	+	0.737000i	0.0211896	+	0.0880883i
$71$			2.42744i			0.288085i	0.989572	+	0.144042i	$0.0460101\pi$
$71$			2.42744i			0.288085i	−0.989572	+	0.144042i	$0.953990\pi$
$72$	−0.608276	+	7.86294i	−0.0716860	+	0.926656i
$73$			3.14290i			0.367849i	0.982940	+	0.183925i	$0.0588802\pi$
$73$			3.14290i			0.367849i	−0.982940	+	0.183925i	$0.941120\pi$
$74$	3.99681	−	0.961430i	0.464620	−	0.111764i
$75$	1.50536	+	1.50536i	0.173824	+	0.173824i
$76$	−1.90266	−	0.616342i	−0.218250	−	0.0706993i
$77$	0.130203	−	0.130203i	0.0148380	−	0.0148380i
$78$	3.58798	+	2.19652i	0.406259	+	0.248707i
$79$	15.3181			1.72342			0.861711	−	0.507399i	$-0.169393\pi$
$79$	15.3181			1.72342			0.861711	+	0.507399i	$0.169393\pi$
$80$	2.41330	−	0.386630i	0.269815	−	0.0432265i
$81$	−7.13929			−0.793255
$82$	−13.7602	−	8.42388i	−1.51956	−	0.930262i
$83$	4.96065	−	4.96065i	0.544502	−	0.544502i	−0.380344	−	0.924845i	$-0.624194\pi$
$83$	4.96065	−	4.96065i	0.544502	−	0.544502i	0.924845	+	0.380344i	$0.124194\pi$
$84$	−0.248784	+	0.768000i	−0.0271445	+	0.0837957i
$85$	2.07418	+	2.07418i	0.224977	+	0.224977i
$86$	7.74055	−	1.86198i	0.834685	−	0.200783i
$87$		−	2.62834i		−	0.281787i
$88$	−0.386181	−	0.450941i	−0.0411670	−	0.0480704i
$89$		−	6.03742i		−	0.639965i	−0.947423	−	0.319983i	$-0.896323\pi$
$89$		−	6.03742i		−	0.639965i	0.947423	−	0.319983i	$-0.103677\pi$
$90$	0.563500	+	2.34256i	0.0593981	+	0.246927i
$91$	−4.01016	−	4.01016i	−0.420379	−	0.420379i
$92$	10.5145	−	5.36920i	1.09622	−	0.559778i
$93$	−3.07443	+	3.07443i	−0.318804	+	0.318804i
$94$	4.77547	−	7.80065i	0.492553	−	0.804576i
$95$	−0.611019			−0.0626892
$96$	2.40700	+	0.990750i	0.245663	+	0.101118i
$97$	6.45317			0.655220			0.327610	−	0.944813i	$-0.393757\pi$
$97$	6.45317			0.655220			0.327610	+	0.944813i	$0.393757\pi$
$98$	−4.60051	+	7.51484i	−0.464721	+	0.759114i
$99$	0.413852	−	0.413852i	0.0415937	−	0.0415937i
$100$	−8.24102	+	4.20824i	−0.824102	+	0.420824i
$101$	−3.94735	−	3.94735i	−0.392776	−	0.392776i	0.482900	−	0.875676i	$-0.339584\pi$
$101$	−3.94735	−	3.94735i	−0.392776	−	0.392776i	−0.875676	+	0.482900i	$0.839584\pi$
$102$	0.730631	+	3.03735i	0.0723433	+	0.300742i
$103$			18.4066i			1.81366i	0.421501	+	0.906828i	$0.361503\pi$
$103$			18.4066i			1.81366i	−0.421501	+	0.906828i	$0.638497\pi$
$104$	−13.8886	+	11.8941i	−1.36189	+	1.16631i
$105$			0.246635i			0.0240691i
$106$	−3.52742	+	0.848517i	−0.342613	+	0.0824153i
$107$	−7.72317	−	7.72317i	−0.746627	−	0.746627i	0.227217	−	0.973844i	$-0.427037\pi$
$107$	−7.72317	−	7.72317i	−0.746627	−	0.746627i	−0.973844	+	0.227217i	$0.927037\pi$
$108$	−1.64157	+	5.06755i	−0.157960	+	0.487625i
$109$	6.06425	−	6.06425i	0.580849	−	0.580849i	−0.354287	−	0.935137i	$-0.615276\pi$
$109$	6.06425	−	6.06425i	0.580849	−	0.580849i	0.935137	+	0.354287i	$0.115276\pi$
$110$	−0.154696	−	0.0947030i	−0.0147496	−	0.00902958i
$111$	1.33752			0.126952
$112$	−2.84243	−	2.05744i	−0.268585	−	0.194409i
$113$	16.0659			1.51136			0.755679	−	0.654943i	$-0.227307\pi$
$113$	16.0659			1.51136			0.755679	+	0.654943i	$0.227307\pi$
$114$	−0.554991	−	0.339760i	−0.0519797	−	0.0318214i
$115$	2.55044	−	2.55044i	0.237830	−	0.237830i
$116$	10.8681	+	3.52060i	1.00908	+	0.326879i
$117$	−12.7463	−	12.7463i	−1.17840	−	1.17840i
$118$	−6.12495	+	1.47335i	−0.563847	+	0.135633i
$119$		−	4.21133i		−	0.386052i
$120$	0.792850	+	0.0613348i	0.0723770	+	0.00559908i
$121$		−	10.9559i		−	0.995995i
$122$	−2.10100	−	8.73417i	−0.190215	−	0.790754i
$123$	−3.71193	−	3.71193i	−0.334693	−	0.334693i
$124$	−8.59462	−	16.8309i	−0.771819	−	1.51146i
$125$	−4.15925	+	4.15925i	−0.372015	+	0.372015i
$126$	1.80606	−	2.95017i	0.160897	−	0.262822i
$127$	−10.5074			−0.932377			−0.466188	−	0.884686i	$-0.654373\pi$
$127$	−10.5074			−0.932377			−0.466188	+	0.884686i	$0.654373\pi$
$128$	−7.32086	+	8.62584i	−0.647078	+	0.762423i
$129$	2.59035			0.228068
$130$	−2.91678	+	4.76450i	−0.255818	+	0.417875i
$131$	5.64719	−	5.64719i	0.493397	−	0.493397i	−0.415978	−	0.909375i	$-0.636561\pi$
$131$	5.64719	−	5.64719i	0.493397	−	0.493397i	0.909375	+	0.415978i	$0.136561\pi$
$132$	−0.0878507	−	0.172038i	−0.00764642	−	0.0149740i
$133$	0.620294	+	0.620294i	0.0537863	+	0.0537863i
$134$	5.03962	+	20.9505i	0.435357	+	1.80985i
$135$			1.62739i			0.140063i
$136$	−13.5381	−	1.04730i	−1.16088	−	0.0898054i
$137$			11.9904i			1.02441i	0.858864	+	0.512204i	$0.171171\pi$
$137$			11.9904i			1.02441i	−0.858864	+	0.512204i	$0.828829\pi$
$138$	3.73476	−	0.898394i	0.317924	−	0.0764764i
$139$	−0.167866	−	0.167866i	−0.0142382	−	0.0142382i	0.699952	−	0.714190i	$-0.253205\pi$
$139$	−0.167866	−	0.167866i	−0.0142382	−	0.0142382i	−0.714190	+	0.699952i	$0.753205\pi$
$140$	−1.01983	−	0.330361i	−0.0861916	−	0.0279206i
$141$	2.10428	−	2.10428i	0.177213	−	0.177213i
$142$	−2.92785	−	1.79240i	−0.245699	−	0.150415i
$143$	1.35703			0.113480
$144$	−9.03469	−	6.53957i	−0.752891	−	0.544964i
$145$	3.49019			0.289844
$146$	−3.79079	−	2.32068i	−0.313728	−	0.192061i
$147$	−2.02718	+	2.02718i	−0.167199	+	0.167199i
$148$	−1.79158	+	5.53064i	−0.147267	+	0.454616i
$149$	−3.98948	−	3.98948i	−0.326831	−	0.326831i	0.524549	−	0.851380i	$-0.324234\pi$
$149$	−3.98948	−	3.98948i	−0.326831	−	0.326831i	−0.851380	+	0.524549i	$0.824234\pi$
$150$	−2.92721	+	0.704139i	−0.239006	+	0.0574927i
$151$		−	5.04645i		−	0.410674i	−0.978691	−	0.205337i	$-0.934171\pi$
$151$		−	5.04645i		−	0.410674i	0.978691	−	0.205337i	$-0.0658291\pi$
$152$	2.14830	−	1.83978i	0.174250	−	0.149226i
$153$		−	13.3857i		−	1.08217i
$154$	0.0609033	+	0.253184i	0.00490772	+	0.0204022i
$155$	−4.08256	−	4.08256i	−0.327919	−	0.327919i
$156$	−5.29865	+	2.70573i	−0.424231	+	0.216632i
$157$	−7.87764	+	7.87764i	−0.628704	+	0.628704i	−0.947742	−	0.319038i	$-0.896640\pi$
$157$	−7.87764	+	7.87764i	−0.628704	+	0.628704i	0.319038	+	0.947742i	$0.396640\pi$
$158$	−11.3107	+	18.4758i	−0.899832	+	1.46986i
$159$	−1.18044			−0.0936150
$160$	−1.31562	+	3.19627i	−0.104009	+	0.252687i
$161$	−5.17831			−0.408108
$162$	5.27157	−	8.61101i	0.414174	−	0.676545i
$163$	−12.4666	+	12.4666i	−0.976459	+	0.976459i	−0.999729	−	0.0232699i	$-0.992592\pi$
$163$	−12.4666	+	12.4666i	−0.976459	+	0.976459i	0.0232699	+	0.999729i	$0.492592\pi$
$164$	20.3208	−	10.3767i	1.58679	−	0.810287i
$165$	−0.0417303	−	0.0417303i	−0.00324870	−	0.00324870i
$166$	2.32037	+	9.64614i	0.180096	+	0.748685i
$167$		−	8.36505i		−	0.647307i	−0.946176	−	0.323654i	$-0.895089\pi$
$167$		−	8.36505i		−	0.647307i	0.946176	−	0.323654i	$-0.104911\pi$
$168$	−0.742620	−	0.867151i	−0.0572944	−	0.0669022i
$169$		−	28.7953i		−	2.21503i
$170$	−4.03331	+	0.970210i	−0.309341	+	0.0744117i
$171$	1.97161	+	1.97161i	0.150773	+	0.150773i
$172$	−3.46972	+	10.7111i	−0.264563	+	0.816712i
$173$	−12.6708	+	12.6708i	−0.963343	+	0.963343i	−0.999351	−	0.0360084i	$-0.988536\pi$
$173$	−12.6708	+	12.6708i	−0.963343	+	0.963343i	0.0360084	+	0.999351i	$0.488536\pi$
$174$	3.17015	+	1.94073i	0.240329	+	0.147127i
$175$	4.05863			0.306804
$176$	0.829051	−	0.132820i	0.0624921	−	0.0100117i
$177$	−2.04970			−0.154065
$178$	7.28200	+	4.45796i	0.545809	+	0.334138i
$179$	−6.16078	+	6.16078i	−0.460478	+	0.460478i	−0.898812	−	0.438334i	$-0.855569\pi$
$179$	−6.16078	+	6.16078i	−0.460478	+	0.460478i	0.438334	+	0.898812i	$0.355569\pi$
$180$	−3.24154	−	1.05006i	−0.241610	−	0.0782665i
$181$	7.94569	+	7.94569i	0.590599	+	0.590599i	0.937793	−	0.347195i	$-0.112866\pi$
$181$	7.94569	+	7.94569i	0.590599	+	0.590599i	−0.347195	+	0.937793i	$0.612866\pi$
$182$	7.79788	−	1.87577i	0.578017	−	0.139042i
$183$		−	2.92286i		−	0.216064i
$184$	−1.28778	+	16.6466i	−0.0949362	+	1.22720i
$185$			1.77610i			0.130582i
$186$	−1.43808	−	5.97833i	−0.105445	−	0.438353i
$187$	0.712552	+	0.712552i	0.0521069	+	0.0521069i
$188$	5.88255	+	11.5198i	0.429029	+	0.840169i
$189$	1.65209	−	1.65209i	0.120172	−	0.120172i
$190$	0.451169	−	0.736977i	0.0327313	−	0.0534659i
$191$	−5.33845			−0.386276			−0.193138	−	0.981172i	$-0.561867\pi$
$191$	−5.33845			−0.386276			−0.193138	+	0.981172i	$0.561867\pi$
$192$	−2.97229	+	2.17163i	−0.214506	+	0.156724i
$193$	−0.104888			−0.00754999			−0.00377499	−	0.999993i	$-0.501202\pi$
$193$	−0.104888			−0.00754999			−0.00377499	+	0.999993i	$0.501202\pi$
$194$	−4.76495	+	7.78345i	−0.342103	+	0.558819i
$195$	−1.28526	+	1.28526i	−0.0920394	+	0.0920394i
$196$	−5.66702	−	11.0977i	−0.404787	−	0.792696i
$197$	10.3045	+	10.3045i	0.734162	+	0.734162i	0.971441	−	0.237279i	$-0.0762557\pi$
$197$	10.3045	+	10.3045i	0.734162	+	0.734162i	−0.237279	+	0.971441i	$0.576256\pi$
$198$	0.193581	+	0.804748i	0.0137572	+	0.0571909i
$199$			10.1833i			0.721872i	0.932591	+	0.360936i	$0.117543\pi$
$199$			10.1833i			0.721872i	−0.932591	+	0.360936i	$0.882457\pi$
$200$	1.00933	−	13.0472i	0.0713702	−	0.922575i
$201$			7.01103i			0.494520i
$202$	7.67575	−	1.84639i	0.540064	−	0.129912i
$203$	−3.54317	−	3.54317i	−0.248682	−	0.248682i
$204$	−4.20297	−	1.36150i	−0.294267	−	0.0953238i
$205$	4.92909	−	4.92909i	0.344263	−	0.344263i
$206$	−22.2010	−	13.5912i	−1.54682	−	0.946945i
$207$	−16.4593			−1.14400
$208$	−4.09077	−	25.5341i	−0.283644	−	1.77047i
$209$	−0.209906			−0.0145195
$210$	−0.297477	−	0.182112i	−0.0205279	−	0.0125669i
$211$	5.44187	−	5.44187i	0.374634	−	0.374634i	−0.494528	−	0.869162i	$-0.664659\pi$
$211$	5.44187	−	5.44187i	0.374634	−	0.374634i	0.869162	+	0.494528i	$0.164659\pi$
$212$	1.58117	−	4.88111i	0.108595	−	0.335236i
$213$	−0.789808	−	0.789808i	−0.0541168	−	0.0541168i
$214$	15.0180	−	3.61256i	1.02661	−	0.246949i
$215$			3.43975i			0.234589i
$216$	−4.90008	−	5.72178i	−0.333408	−	0.389318i
$217$			8.28906i			0.562698i
$218$	2.83658	+	11.7921i	0.192118	+	0.798663i
$219$	−1.02259	−	1.02259i	−0.0691005	−	0.0691005i
$220$	0.228451	−	0.116658i	0.0154022	−	0.00786505i
$221$	21.9460	−	21.9460i	1.47625	−	1.47625i
$222$	−0.987611	+	1.61324i	−0.0662841	+	0.108274i
$223$	16.7858			1.12406			0.562030	−	0.827117i	$-0.310021\pi$
$223$	16.7858			1.12406			0.562030	+	0.827117i	$0.310021\pi$
$224$	4.58038	−	1.90920i	0.306040	−	0.127564i
$225$	12.9004			0.860026
$226$	−11.8629	+	19.3778i	−0.789109	+	1.28899i
$227$	−7.45061	+	7.45061i	−0.494514	+	0.494514i	−0.909725	−	0.415211i	$-0.863708\pi$
$227$	−7.45061	+	7.45061i	−0.494514	+	0.494514i	0.415211	+	0.909725i	$0.363708\pi$
$228$	0.819599	−	0.418525i	0.0542792	−	0.0277175i
$229$	−4.41201	−	4.41201i	−0.291554	−	0.291554i	0.546140	−	0.837694i	$-0.316097\pi$
$229$	−4.41201	−	4.41201i	−0.291554	−	0.291554i	−0.837694	+	0.546140i	$0.816097\pi$
$230$	1.19298	+	4.95942i	0.0786630	+	0.327014i
$231$			0.0847274i			0.00557466i
$232$	−12.2713	+	10.5090i	−0.805648	+	0.689949i
$233$			5.29823i			0.347099i	0.984825	+	0.173549i	$0.0555236\pi$
$233$			5.29823i			0.347099i	−0.984825	+	0.173549i	$0.944476\pi$
$234$	24.7856	−	5.96215i	1.62029	−	0.389758i
$235$	2.79429	+	2.79429i	0.182279	+	0.182279i
$236$	2.74552	−	8.47548i	0.178718	−	0.551706i
$237$	−4.98399	+	4.98399i	−0.323745	+	0.323745i
$238$	5.07947	+	3.10960i	0.329253	+	0.201565i
$239$	3.04336			0.196859			0.0984293	−	0.995144i	$-0.468618\pi$
$239$	3.04336			0.196859			0.0984293	+	0.995144i	$0.468618\pi$
$240$	−0.659410	+	0.911003i	−0.0425647	+	0.0588050i
$241$	−3.80993			−0.245419			−0.122710	−	0.992443i	$-0.539158\pi$
$241$	−3.80993			−0.245419			−0.122710	+	0.992443i	$0.539158\pi$
$242$	13.2144	+	8.08974i	0.849456	+	0.520028i
$243$	7.97281	−	7.97281i	0.511456	−	0.511456i
$244$	12.0860	+	3.91511i	0.773728	+	0.250639i
$245$	−2.69191	−	2.69191i	−0.171980	−	0.171980i
$246$	7.21796	−	1.73627i	0.460200	−	0.110701i
$247$			6.46493i			0.411354i
$248$	26.6466	+	2.06138i	1.69206	+	0.130898i
$249$			3.22805i			0.204570i
$250$	−1.94551	−	8.08780i	−0.123045	−	0.511517i
$251$	12.5083	+	12.5083i	0.789518	+	0.789518i	0.981415	−	0.191897i	$-0.0614639\pi$
$251$	12.5083	+	12.5083i	0.789518	+	0.789518i	−0.191897	+	0.981415i	$0.561464\pi$
$252$	2.22475	+	4.35674i	0.140146	+	0.274449i
$253$	0.876163	−	0.876163i	0.0550839	−	0.0550839i
$254$	7.75851	−	12.6734i	0.486812	−	0.795198i
$255$	−1.34974			−0.0845238
$256$	−4.99836	−	15.1992i	−0.312398	−	0.949951i
$257$	19.6430			1.22530			0.612648	−	0.790356i	$-0.290104\pi$
$257$	19.6430			1.22530			0.612648	+	0.790356i	$0.290104\pi$
$258$	−1.91269	+	3.12434i	−0.119079	+	0.194513i
$259$	1.80307	−	1.80307i	0.112037	−	0.112037i
$260$	−3.59296	−	7.03611i	−0.222826	−	0.436361i
$261$	−11.2620	−	11.2620i	−0.697099	−	0.697099i
$262$	2.64150	+	10.9811i	0.163193	+	0.678417i
$263$			17.6575i			1.08881i	0.838823	+	0.544405i	$0.183244\pi$
$263$			17.6575i			1.08881i	−0.838823	+	0.544405i	$0.816756\pi$
$264$	0.272371	+	0.0210706i	0.0167633	+	0.00129680i
$265$		−	1.56751i		−	0.0962917i
$266$	−1.20618	+	0.290146i	−0.0739557	+	0.0177900i
$267$	1.96437	+	1.96437i	0.120218	+	0.120218i
$268$	−28.9905	−	9.39110i	−1.77088	−	0.573653i
$269$	−2.00039	+	2.00039i	−0.121966	+	0.121966i	−0.765455	−	0.643489i	$-0.777486\pi$
$269$	−2.00039	+	2.00039i	−0.121966	+	0.121966i	0.643489	+	0.765455i	$0.277486\pi$
$270$	−1.96286	−	1.20164i	−0.119456	−	0.0731297i
$271$	−23.0434			−1.39979			−0.699894	−	0.714247i	$-0.746770\pi$
$271$	−23.0434			−1.39979			−0.699894	+	0.714247i	$0.746770\pi$
$272$	11.2595	−	15.5555i	0.682710	−	0.943193i
$273$	2.60954			0.157936
$274$	−14.4621	−	8.85356i	−0.873689	−	0.534863i
$275$	−0.686715	+	0.686715i	−0.0414105	+	0.0414105i
$276$	−1.67411	+	5.16803i	−0.100770	+	0.311079i
$277$	−7.65088	−	7.65088i	−0.459697	−	0.459697i	0.438859	−	0.898556i	$-0.355383\pi$
$277$	−7.65088	−	7.65088i	−0.459697	−	0.459697i	−0.898556	+	0.438859i	$0.855383\pi$
$278$	0.326420	−	0.0785200i	0.0195774	−	0.00470932i
$279$			26.3468i			1.57734i
$280$	1.15150	−	0.986129i	0.0688150	−	0.0589325i
$281$			3.92451i			0.234117i	0.993125	+	0.117058i	$0.0373465\pi$
$281$			3.92451i			0.234117i	−0.993125	+	0.117058i	$0.962654\pi$
$282$	0.984289	+	4.09184i	0.0586136	+	0.243666i
$283$	12.3057	+	12.3057i	0.731500	+	0.731500i	0.970917	−	0.239417i	$-0.0769563\pi$
$283$	12.3057	+	12.3057i	0.731500	+	0.731500i	−0.239417	+	0.970917i	$0.576956\pi$
$284$	4.32378	−	2.20792i	0.256569	−	0.131016i
$285$	0.198805	−	0.198805i	0.0117762	−	0.0117762i
$286$	−1.00201	+	1.63677i	−0.0592502	+	0.0967842i
$287$	−10.0078			−0.590743
$288$	14.5588	−	6.06839i	0.857884	−	0.357583i
$289$	6.04700			0.355706
$290$	−2.57711	+	4.20967i	−0.151333	+	0.247200i
$291$	−2.09964	+	2.09964i	−0.123083	+	0.123083i
$292$	5.59816	−	2.85868i	0.327607	−	0.167291i
$293$	16.4010	+	16.4010i	0.958155	+	0.958155i	0.999159	−	0.0410037i	$-0.0130555\pi$
$293$	16.4010	+	16.4010i	0.958155	+	0.958155i	−0.0410037	+	0.999159i	$0.513056\pi$
$294$	−0.948226	−	3.94192i	−0.0553017	−	0.229898i
$295$		−	2.72181i		−	0.158470i
$296$	−5.34787	−	6.24466i	−0.310838	−	0.362964i
$297$			0.559063i			0.0324401i
$298$	7.75768	−	1.86610i	0.449390	−	0.108100i
$299$	−26.9851	−	26.9851i	−1.56059	−	1.56059i
$300$	1.31213	−	4.05057i	0.0757558	−	0.233860i
$301$	3.49196	−	3.49196i	0.201273	−	0.201273i
$302$	6.08674	+	3.72624i	0.350253	+	0.214421i
$303$	2.56867			0.147566
$304$	0.632763	+	3.94963i	0.0362914	+	0.226527i
$305$	3.88129			0.222242
$306$	16.1451	+	9.88388i	0.922956	+	0.565024i
$307$	−11.5944	+	11.5944i	−0.661726	+	0.661726i	−0.955787	−	0.294061i	$-0.904993\pi$
$307$	−11.5944	+	11.5944i	−0.661726	+	0.661726i	0.294061	+	0.955787i	$0.404993\pi$
$308$	−0.350347	−	0.113490i	−0.0199629	−	0.00646671i
$309$	−5.98888	−	5.98888i	−0.340696	−	0.340696i
$310$	7.93867	−	1.90964i	0.450886	−	0.108460i
$311$		−	16.6570i		−	0.944535i	−0.881455	−	0.472267i	$-0.843436\pi$
$311$		−	16.6570i		−	0.944535i	0.881455	−	0.472267i	$-0.156564\pi$
$312$	0.648957	−	8.38881i	0.0367400	−	0.474923i
$313$			4.42443i			0.250084i	0.992151	+	0.125042i	$0.0399065\pi$
$313$			4.42443i			0.250084i	−0.992151	+	0.125042i	$0.960094\pi$
$314$	−3.68481	−	15.3183i	−0.207946	−	0.864463i
$315$	1.05679	+	1.05679i	0.0595432	+	0.0595432i
$316$	−13.9328	−	27.2847i	−0.783782	−	1.53488i
$317$	8.13182	−	8.13182i	0.456729	−	0.456729i	−0.440851	−	0.897580i	$-0.645323\pi$
$317$	8.13182	−	8.13182i	0.456729	−	0.456729i	0.897580	+	0.440851i	$0.145323\pi$
$318$	0.871624	−	1.42378i	0.0488782	−	0.0798417i
$319$	1.19900			0.0671310
$320$	−2.88372	−	3.94692i	−0.161205	−	0.220640i
$321$	5.02572			0.280508
$322$	3.82361	−	6.24579i	0.213081	−	0.348064i
$323$	−3.39463	+	3.39463i	−0.188882	+	0.188882i
$324$	6.49365	+	12.7165i	0.360758	+	0.706475i
$325$	21.1503	+	21.1503i	1.17321	+	1.17321i
$326$	−5.83132	−	24.2417i	−0.322967	−	1.34262i
$327$			3.94620i			0.218225i
$328$	−2.48881	+	32.1719i	−0.137422	+	1.77640i
$329$		−	5.67341i		−	0.312785i
$330$	0.0811459	−	0.0195196i	0.00446693	−	0.00107452i
$331$	23.5352	+	23.5352i	1.29361	+	1.29361i	0.932537	+	0.361075i	$0.117590\pi$
$331$	23.5352	+	23.5352i	1.29361	+	1.29361i	0.361075	+	0.932537i	$0.382410\pi$
$332$	−13.3480	−	4.32390i	−0.732564	−	0.237305i
$333$	5.73105	−	5.73105i	0.314060	−	0.314060i
$334$	10.0895	+	6.17666i	0.552070	+	0.337972i
$335$	−9.30999			−0.508659
$336$	1.59425	−	0.255412i	0.0869735	−	0.0139338i
$337$	−8.45484			−0.460565			−0.230282	−	0.973124i	$-0.573965\pi$
$337$	−8.45484			−0.460565			−0.230282	+	0.973124i	$0.573965\pi$
$338$	34.7313	+	21.2621i	1.88913	+	1.15651i
$339$	−5.22731	+	5.22731i	−0.283909	+	0.283909i
$340$	1.80794	−	5.58115i	0.0980493	−	0.302680i
$341$	−1.40250	−	1.40250i	−0.0759495	−	0.0759495i
$342$	−3.83385	+	0.922230i	−0.207311	+	0.0498685i
$343$			11.6061i			0.626673i
$344$	−10.3571	−	12.0939i	−0.558418	−	0.652060i
$345$			1.65965i			0.0893528i
$346$	−5.92683	−	24.6388i	−0.318629	−	1.32459i
$347$	−10.8869	−	10.8869i	−0.584440	−	0.584440i	0.351680	−	0.936120i	$-0.385611\pi$
$347$	−10.8869	−	10.8869i	−0.584440	−	0.584440i	−0.936120	+	0.351680i	$0.885611\pi$
$348$	−4.68161	+	2.39065i	−0.250961	+	0.128152i
$349$	−7.49760	+	7.49760i	−0.401337	+	0.401337i	−0.878704	−	0.477367i	$-0.841591\pi$
$349$	−7.49760	+	7.49760i	−0.401337	+	0.401337i	0.477367	+	0.878704i	$0.341591\pi$
$350$	−2.99685	+	4.89529i	−0.160188	+	0.261664i
$351$	17.2187			0.919066
$352$	−0.451961	+	1.09803i	−0.0240896	+	0.0585251i
$353$	−6.11644			−0.325545			−0.162773	−	0.986664i	$-0.552044\pi$
$353$	−6.11644			−0.325545			−0.162773	+	0.986664i	$0.552044\pi$
$354$	1.51347	−	2.47223i	0.0804402	−	0.131398i
$355$	1.04879	−	1.04879i	0.0556640	−	0.0556640i
$356$	−10.7539	+	5.49143i	−0.569955	+	0.291045i
$357$	1.37023	+	1.37023i	0.0725200	+	0.0725200i
$358$	−2.88174	−	11.9798i	−0.152304	−	0.633153i
$359$		−	9.48528i		−	0.500614i	−0.968167	−	0.250307i	$-0.919468\pi$
$359$		−	9.48528i		−	0.500614i	0.968167	−	0.250307i	$-0.0805315\pi$
$360$	3.66004	−	3.13442i	0.192901	−	0.165198i
$361$		−	1.00000i		−	0.0526316i
$362$	−15.4507	+	3.71664i	−0.812068	+	0.195342i
$363$	3.56469	+	3.56469i	0.187098	+	0.187098i
$364$	−3.49541	+	10.7904i	−0.183209	+	0.565571i
$365$	1.35791	−	1.35791i	0.0710762	−	0.0710762i
$366$	3.52539	+	2.15821i	0.184275	+	0.112811i
$367$	16.9825			0.886479			0.443240	−	0.896403i	$-0.353829\pi$
$367$	16.9825			0.886479			0.443240	+	0.896403i	$0.353829\pi$
$368$	−19.1273	−	13.8449i	−0.997079	−	0.721715i
$369$	−31.8099			−1.65596
$370$	−2.14224	−	1.31146i	−0.111370	−	0.0681793i
$371$	−1.59131	+	1.59131i	−0.0826166	+	0.0826166i
$372$	8.27259	+	2.67980i	0.428914	+	0.138941i
$373$	−16.2127	−	16.2127i	−0.839464	−	0.839464i	0.149325	−	0.988788i	$-0.452290\pi$
$373$	−16.2127	−	16.2127i	−0.839464	−	0.839464i	−0.988788	+	0.149325i	$0.952290\pi$
$374$	−1.38558	+	0.333300i	−0.0716466	+	0.0172345i
$375$		−	2.70656i		−	0.139766i
$376$	−18.2382	−	1.41090i	−0.940561	−	0.0727617i
$377$		−	36.9282i		−	1.90190i
$378$	0.772774	+	3.21254i	0.0397472	+	0.165235i
$379$	5.87391	+	5.87391i	0.301723	+	0.301723i	0.841688	−	0.539965i	$-0.181563\pi$
$379$	5.87391	+	5.87391i	0.301723	+	0.301723i	−0.539965	+	0.841688i	$0.681563\pi$
$380$	0.555762	+	1.08835i	0.0285100	+	0.0558312i
$381$	3.41874	−	3.41874i	0.175147	−	0.175147i
$382$	3.94185	−	6.43893i	0.201682	−	0.329444i
$383$	−17.7096			−0.904920			−0.452460	−	0.891785i	$-0.649454\pi$
$383$	−17.7096			−0.904920			−0.452460	+	0.891785i	$0.649454\pi$
$384$	−0.424596	−	5.18851i	−0.0216676	−	0.264775i
$385$	−0.112510			−0.00573405
$386$	0.0774479	−	0.126510i	0.00394199	−	0.00643917i
$387$	11.0992	−	11.0992i	0.564205	−	0.564205i
$388$	−5.86958	−	11.4944i	−0.297983	−	0.583541i
$389$	16.2003	+	16.2003i	0.821390	+	0.821390i	0.986307	−	0.164917i	$-0.0527357\pi$
$389$	16.2003	+	16.2003i	0.821390	+	0.821390i	−0.164917	+	0.986307i	$0.552736\pi$
$390$	−0.601187	−	2.49923i	−0.0304423	−	0.126553i
$391$		−	28.3389i		−	1.43316i
$392$	17.5699	+	1.35921i	0.887416	+	0.0686504i
$393$			3.67481i			0.185370i
$394$	−20.0373	+	4.81996i	−1.00947	+	0.242826i
$395$	−6.61828	−	6.61828i	−0.333002	−	0.333002i
$396$	−1.11358	−	0.360730i	−0.0559595	−	0.0181273i
$397$	16.1866	−	16.1866i	0.812383	−	0.812383i	−0.172608	−	0.984991i	$-0.555219\pi$
$397$	16.1866	−	16.1866i	0.812383	−	0.812383i	0.984991	+	0.172608i	$0.0552193\pi$
$398$	−12.2825	−	7.51920i	−0.615665	−	0.376904i
$399$	−0.403645			−0.0202075
$400$	14.9915	+	10.8513i	0.749575	+	0.542564i
$401$	−20.6502			−1.03122			−0.515610	−	0.856823i	$-0.672435\pi$
$401$	−20.6502			−1.03122			−0.515610	+	0.856823i	$0.672435\pi$
$402$	−8.45631	−	5.17686i	−0.421762	−	0.258198i
$403$	−43.1958	+	43.1958i	−2.15174	+	2.15174i
$404$	−3.44067	+	10.6214i	−0.171180	+	0.528435i
$405$	3.08457	+	3.08457i	0.153274	+	0.153274i
$406$	6.88980	−	1.65733i	0.341935	−	0.0822521i
$407$			0.610152i			0.0302441i
$408$	4.74558	−	4.06407i	0.234941	−	0.201201i
$409$			21.9832i			1.08700i	0.839409	+	0.543500i	$0.182901\pi$
$409$			21.9832i			1.08700i	−0.839409	+	0.543500i	$0.817099\pi$
$410$	2.30561	+	9.58478i	0.113866	+	0.473358i
$411$	−3.90126	−	3.90126i	−0.192435	−	0.192435i
$412$	32.7859	−	16.7420i	1.61525	−	0.824819i
$413$	−2.76312	+	2.76312i	−0.135964	+	0.135964i
$414$	12.1534	−	19.8523i	0.597305	−	0.975686i
$415$	−4.28655			−0.210419
$416$	33.8184	+	13.9200i	1.65808	+	0.682486i
$417$	0.109236			0.00534929
$418$	0.154992	−	0.253176i	0.00758090	−	0.0123833i
$419$	−21.7865	+	21.7865i	−1.06434	+	1.06434i	−0.0665555	+	0.997783i	$0.521201\pi$
$419$	−21.7865	+	21.7865i	−1.06434	+	1.06434i	−0.997783	+	0.0665555i	$0.978799\pi$
$420$	0.439307	−	0.224330i	0.0214360	−	0.0109462i
$421$	24.5524	+	24.5524i	1.19661	+	1.19661i	0.975175	+	0.221435i	$0.0710740\pi$
$421$	24.5524	+	24.5524i	1.19661	+	1.19661i	0.221435	+	0.975175i	$0.428926\pi$
$422$	2.54546	+	10.5819i	0.123911	+	0.515118i
$423$		−	18.0330i		−	0.876793i
$424$	4.71980	+	5.51127i	0.229214	+	0.267651i
$425$			22.2113i			1.07741i
$426$	1.53581	−	0.369437i	0.0744101	−	0.0178993i
$427$	−3.94021	−	3.94021i	−0.190680	−	0.190680i
$428$	−6.73183	+	20.7813i	−0.325395	+	1.00450i
$429$	−0.441530	+	0.441530i	−0.0213173	+	0.0213173i
$430$	−4.14883	−	2.53987i	−0.200074	−	0.122483i
$431$	−7.65152			−0.368561			−0.184280	−	0.982874i	$-0.558995\pi$
$431$	−7.65152			−0.368561			−0.184280	+	0.982874i	$0.558995\pi$
$432$	10.5195	−	1.68530i	0.506118	−	0.0810840i
$433$	−29.2772			−1.40697			−0.703485	−	0.710710i	$-0.748374\pi$
$433$	−29.2772			−1.40697			−0.703485	+	0.710710i	$0.748374\pi$
$434$	−9.99780	−	6.12055i	−0.479910	−	0.293796i
$435$	−1.13559	+	1.13559i	−0.0544473	+	0.0544473i
$436$	−16.3175	−	5.28584i	−0.781466	−	0.253146i
$437$	4.17408	+	4.17408i	0.199673	+	0.199673i
$438$	1.98847	−	0.478324i	0.0950127	−	0.0228552i
$439$		−	6.28684i		−	0.300055i	−0.988682	−	0.150027i	$-0.952064\pi$
$439$		−	6.28684i		−	0.300055i	0.988682	−	0.150027i	$-0.0479362\pi$
$440$	−0.0279798	+	0.361683i	−0.00133388	+	0.0172426i
$441$			17.3723i			0.827250i
$442$	10.2654	+	42.6748i	0.488274	+	2.02983i
$443$	0.532494	+	0.532494i	0.0252996	+	0.0252996i	0.719643	−	0.694344i	$-0.244305\pi$
$443$	0.532494	+	0.532494i	0.0252996	+	0.0252996i	−0.694344	+	0.719643i	$0.744305\pi$
$444$	−1.21656	−	2.38240i	−0.0577356	−	0.113064i
$445$	−2.60850	+	2.60850i	−0.123655	+	0.123655i
$446$	−12.3944	+	20.2461i	−0.586893	+	0.958679i
$447$	2.59608			0.122791
$448$	−1.07934	+	6.93433i	−0.0509939	+	0.327616i
$449$	−17.7086			−0.835718			−0.417859	−	0.908512i	$-0.637219\pi$
$449$	−17.7086			−0.835718			−0.417859	+	0.908512i	$0.637219\pi$
$450$	−9.52549	+	15.5597i	−0.449036	+	0.733492i
$451$	1.69331	−	1.69331i	0.0797348	−	0.0797348i
$452$	−14.6130	−	28.6167i	−0.687339	−	1.34602i
$453$	1.64194	+	1.64194i	0.0771452	+	0.0771452i
$454$	−3.48506	−	14.4879i	−0.163562	−	0.679953i
$455$			3.46522i			0.162452i
$456$	−0.100381	+	1.29759i	−0.00470078	+	0.0607651i
$457$		−	7.11641i		−	0.332891i	−0.986051	−	0.166446i	$-0.946771\pi$
$457$		−	7.11641i		−	0.332891i	0.986051	−	0.166446i	$-0.0532290\pi$
$458$	8.57929	−	2.06374i	0.400884	−	0.0964322i
$459$	9.04125	+	9.04125i	0.422009	+	0.422009i
$460$	−6.86265	−	2.22307i	−0.319973	−	0.103651i
$461$	10.7807	−	10.7807i	0.502109	−	0.502109i	−0.409984	−	0.912093i	$-0.634466\pi$
$461$	10.7807	−	10.7807i	0.502109	−	0.502109i	0.912093	+	0.409984i	$0.134466\pi$
$462$	−0.102193	−	0.0625618i	−0.00475447	−	0.00291064i
$463$	16.2805			0.756617			0.378309	−	0.925680i	$-0.376506\pi$
$463$	16.2805			0.756617			0.378309	+	0.925680i	$0.376506\pi$
$464$	−3.61439	−	22.5606i	−0.167794	−	1.04735i
$465$	2.65665			0.123199
$466$	−6.39043	−	3.91216i	−0.296031	−	0.181227i
$467$	12.2276	−	12.2276i	0.565827	−	0.565827i	−0.365130	−	0.930957i	$-0.618975\pi$
$467$	12.2276	−	12.2276i	0.565827	−	0.565827i	0.930957	+	0.365130i	$0.118975\pi$
$468$	−11.1102	+	34.2974i	−0.513569	+	1.58540i
$469$	9.45131	+	9.45131i	0.436421	+	0.436421i
$470$	−5.43359	+	1.30704i	−0.250633	+	0.0602894i
$471$		−	5.12623i		−	0.236204i
$472$	8.19538	+	9.56968i	0.377223	+	0.440480i
$473$			1.18167i			0.0543332i
$474$	−2.33129	−	9.69154i	−0.107080	−	0.445147i
$475$	−3.27154	−	3.27154i	−0.150109	−	0.150109i
$476$	−7.50125	+	3.83048i	−0.343819	+	0.175570i
$477$	−5.05798	+	5.05798i	−0.231589	+	0.231589i
$478$	−2.24718	+	3.67073i	−0.102784	+	0.167895i
$479$	5.29784			0.242064			0.121032	−	0.992649i	$-0.461380\pi$
$479$	5.29784			0.242064			0.121032	+	0.992649i	$0.461380\pi$
$480$	−0.611899	−	1.46802i	−0.0279293	−	0.0670055i
$481$	18.7922			0.856851
$482$	2.81321	−	4.59532i	0.128138	−	0.209311i
$483$	1.68485	−	1.68485i	0.0766632	−	0.0766632i
$484$	−19.5148	+	9.96514i	−0.887035	+	0.452961i
$485$	−2.78813	−	2.78813i	−0.126602	−	0.126602i
$486$	3.72932	+	15.5034i	0.169166	+	0.703248i
$487$		−	8.14586i		−	0.369124i	−0.982821	−	0.184562i	$-0.940913\pi$
$487$		−	8.14586i		−	0.369124i	0.982821	−	0.184562i	$-0.0590867\pi$
$488$	−13.6464	+	11.6866i	−0.617741	+	0.529027i
$489$		−	8.11242i		−	0.366856i
$490$	5.23451	−	1.25916i	0.236471	−	0.0568828i
$491$	29.4320	+	29.4320i	1.32825	+	1.32825i	0.906898	+	0.421351i	$0.138444\pi$
$491$	29.4320	+	29.4320i	1.32825	+	1.32825i	0.421351	+	0.906898i	$0.361556\pi$
$492$	−3.23546	+	9.98794i	−0.145866	+	0.450291i
$493$	19.3904	−	19.3904i	0.873299	−	0.873299i
$494$	−7.79764	−	4.77363i	−0.350832	−	0.214776i
$495$	−0.357614			−0.0160735
$496$	−22.1619	+	30.6176i	−0.995097	+	1.37477i
$497$	−2.12942			−0.0955176
$498$	−3.89349	−	2.38356i	−0.174472	−	0.106810i
$499$	20.3065	−	20.3065i	0.909042	−	0.909042i	−0.0871531	−	0.996195i	$-0.527777\pi$
$499$	20.3065	−	20.3065i	0.909042	−	0.909042i	0.996195	+	0.0871531i	$0.0277769\pi$
$500$	11.1916	+	3.62537i	0.500503	+	0.162131i
$501$	2.72170	+	2.72170i	0.121597	+	0.121597i
$502$	−24.3228	+	5.85083i	−1.08558	+	0.261135i
$503$		−	28.2743i		−	1.26069i	−0.776316	−	0.630343i	$-0.782914\pi$
$503$		−	28.2743i		−	1.26069i	0.776316	−	0.630343i	$-0.217086\pi$
$504$	−6.89759	−	0.533596i	−0.307243	−	0.0237683i
$505$			3.41095i			0.151785i
$506$	0.409830	+	1.70373i	0.0182192	+	0.0757399i
$507$	9.36903	+	9.36903i	0.416093	+	0.416093i
$508$	9.55712	+	18.7157i	0.424029	+	0.830377i
$509$	−20.2643	+	20.2643i	−0.898198	+	0.898198i	−0.995277	−	0.0970786i	$-0.969050\pi$
$509$	−20.2643	+	20.2643i	−0.898198	+	0.898198i	0.0970786	+	0.995277i	$0.469050\pi$
$510$	0.996630	−	1.62798i	0.0441315	−	0.0720880i
$511$	−2.75704			−0.121964
$512$	22.0232	+	5.19419i	0.973296	+	0.229553i
$513$	−2.66340			−0.117592
$514$	−14.5042	+	23.6923i	−0.639751	+	1.04502i
$515$	7.95267	−	7.95267i	0.350437	−	0.350437i
$516$	−2.35610	−	4.61395i	−0.103721	−	0.203118i
$517$	0.959933	+	0.959933i	0.0422178	+	0.0422178i
$518$	0.843393	+	3.50612i	0.0370566	+	0.154050i
$519$		−	8.24530i		−	0.361928i
$520$	11.1396	+	0.861755i	0.488502	+	0.0377904i
$521$		−	6.85416i		−	0.300286i	−0.988664	−	0.150143i	$-0.952027\pi$
$521$		−	6.85416i		−	0.300286i	0.988664	−	0.150143i	$-0.0479734\pi$
$522$	21.8993	−	5.26785i	0.958505	−	0.230567i
$523$	5.65969	+	5.65969i	0.247481	+	0.247481i	0.819936	−	0.572455i	$-0.194009\pi$
$523$	5.65969	+	5.65969i	0.247481	+	0.247481i	−0.572455	+	0.819936i	$0.694009\pi$
$524$	−15.1953	−	4.92232i	−0.663809	−	0.215032i
$525$	−1.32054	+	1.32054i	−0.0576332	+	0.0576332i
$526$	−21.2975	−	13.0381i	−0.928616	−	0.568489i
$527$	−45.3628			−1.97603
$528$	−0.226530	+	0.312960i	−0.00985844	+	0.0136198i
$529$	−11.8459			−0.515039
$530$	1.89065	+	1.15743i	0.0821245	+	0.0502757i
$531$	−8.78260	+	8.78260i	−0.381132	+	0.381132i
$532$	0.540673	−	1.66907i	0.0234411	−	0.0723633i
$533$	−52.1526	−	52.1526i	−2.25898	−	2.25898i
$534$	−3.81978	+	0.918845i	−0.165298	+	0.0397623i
$535$			6.67368i			0.288528i
$536$	32.7333	−	28.0324i	1.41386	−	1.21082i
$537$		−	4.00901i		−	0.173002i
$538$	−0.935692	−	3.88982i	−0.0403405	−	0.167702i
$539$	−0.924762	−	0.924762i	−0.0398323	−	0.0398323i
$540$	2.89871	−	1.48022i	0.124741	−	0.0636983i
$541$	−3.19539	+	3.19539i	−0.137381	+	0.137381i	−0.772453	−	0.635072i	$-0.780970\pi$
$541$	−3.19539	+	3.19539i	−0.137381	+	0.137381i	0.635072	+	0.772453i	$0.280970\pi$
$542$	17.0150	−	27.7937i	0.730857	−	1.19384i
$543$	−5.17052			−0.221888
$544$	10.4483	+	25.0667i	0.447967	+	1.07472i
$545$	−5.24018			−0.224465
$546$	−1.92685	+	3.14748i	−0.0824617	+	0.134700i
$547$	15.4558	−	15.4558i	0.660841	−	0.660841i	−0.294738	−	0.955578i	$-0.595232\pi$
$547$	15.4558	−	15.4558i	0.660841	−	0.660841i	0.955578	+	0.294738i	$0.0952322\pi$
$548$	21.3573	−	10.9060i	0.912340	−	0.465883i
$549$	−12.5240	−	12.5240i	−0.534510	−	0.534510i
$550$	−0.321215	−	1.33534i	−0.0136966	−	0.0569391i
$551$			5.71208i			0.243343i
$552$	−4.99723	−	5.83523i	−0.212696	−	0.248364i
$553$			13.4375i			0.571420i
$554$	14.8774	−	3.57874i	0.632079	−	0.152046i
$555$	−0.577884	−	0.577884i	−0.0245298	−	0.0245298i
$556$	−0.146318	+	0.451688i	−0.00620528	+	0.0191558i
$557$	11.8584	−	11.8584i	0.502457	−	0.502457i	−0.409744	−	0.912201i	$-0.634382\pi$
$557$	11.8584	−	11.8584i	0.502457	−	0.502457i	0.912201	+	0.409744i	$0.134382\pi$
$558$	−31.7780	−	19.4542i	−1.34527	−	0.823561i
$559$	36.3945			1.53932
$560$	0.339163	+	2.11702i	0.0143322	+	0.0894603i
$561$	−0.463680			−0.0195766
$562$	−4.73353	−	2.89782i	−0.199672	−	0.122237i
$563$	14.8608	−	14.8608i	0.626307	−	0.626307i	−0.320830	−	0.947137i	$-0.603962\pi$
$563$	14.8608	−	14.8608i	0.626307	−	0.626307i	0.947137	+	0.320830i	$0.103962\pi$
$564$	−5.66214	−	1.83418i	−0.238419	−	0.0772328i
$565$	−6.94138	−	6.94138i	−0.292026	−	0.292026i
$566$	−23.9289	+	5.75607i	−1.00581	+	0.241946i
$567$		−	6.26279i		−	0.263012i
$568$	−0.529559	+	6.84540i	−0.0222198	+	0.287226i
$569$			1.80315i			0.0755920i	0.999285	+	0.0377960i	$0.0120337\pi$
$569$			1.80315i			0.0755920i	−0.999285	+	0.0377960i	$0.987966\pi$
$570$	0.0929920	+	0.386582i	0.00389501	+	0.0161922i
$571$	−11.3994	−	11.3994i	−0.477052	−	0.477052i	0.427136	−	0.904188i	$-0.359523\pi$
$571$	−11.3994	−	11.3994i	−0.477052	−	0.477052i	−0.904188	+	0.427136i	$0.859523\pi$
$572$	−1.23430	−	2.41714i	−0.0516088	−	0.101066i
$573$	1.73695	−	1.73695i	0.0725621	−	0.0725621i
$574$	7.38966	−	12.0709i	0.308439	−	0.503829i
$575$	27.3113			1.13896
$576$	−3.43068	+	22.0408i	−0.142945	+	0.918366i
$577$	−37.7912			−1.57327			−0.786634	−	0.617419i	$-0.788178\pi$
$577$	−37.7912			−1.57327			−0.786634	+	0.617419i	$0.788178\pi$
$578$	−4.46503	+	7.29355i	−0.185721	+	0.303372i
$579$	0.0341269	−	0.0341269i	0.00141827	−	0.00141827i
$580$	−3.17455	−	6.21674i	−0.131816	−	0.258136i
$581$	4.35162	+	4.35162i	0.180536	+	0.180536i
$582$	−0.982119	−	4.08282i	−0.0407101	−	0.169238i
$583$		−	0.538494i		−	0.0223022i
$584$	−0.685640	+	8.86299i	−0.0283720	+	0.366753i
$585$			11.0142i			0.455382i
$586$	−31.8922	+	7.67164i	−1.31746	+	0.316913i
$587$	−22.8736	−	22.8736i	−0.944095	−	0.944095i	0.0544226	−	0.998518i	$-0.482668\pi$
$587$	−22.8736	−	22.8736i	−0.944095	−	0.944095i	−0.998518	+	0.0544226i	$0.982668\pi$
$588$	5.45469	+	1.76697i	0.224947	+	0.0728688i
$589$	6.68156	−	6.68156i	0.275309	−	0.275309i
$590$	3.28289	+	2.00975i	0.135154	+	0.0827401i
$591$	−6.70544			−0.275825
$592$	11.4808	−	1.83931i	0.471856	−	0.0755951i
$593$	22.5456			0.925836			0.462918	−	0.886401i	$-0.346802\pi$
$593$	22.5456			0.925836			0.462918	+	0.886401i	$0.346802\pi$
$594$	−0.674310	−	0.412806i	−0.0276673	−	0.0169376i
$595$	−1.81953	+	1.81953i	−0.0745935	+	0.0745935i
$596$	−3.47739	+	10.7348i	−0.142440	+	0.439714i
$597$	−3.31329	−	3.31329i	−0.135604	−	0.135604i
$598$	52.4735	−	12.6224i	2.14580	−	0.516170i
$599$		−	42.7512i		−	1.74677i	−0.487034	−	0.873383i	$-0.661921\pi$
$599$		−	42.7512i		−	1.74677i	0.487034	−	0.873383i	$-0.338079\pi$
$600$	3.91671	+	4.57351i	0.159899	+	0.186713i
$601$		−	39.1369i		−	1.59643i	−0.602375	−	0.798213i	$-0.705779\pi$
$601$		−	39.1369i		−	1.59643i	0.602375	−	0.798213i	$-0.294221\pi$
$602$	1.63338	+	6.79023i	0.0665717	+	0.276749i
$603$	30.0410	+	30.0410i	1.22337	+	1.22337i
$604$	−8.98876	+	4.59007i	−0.365747	+	0.186767i
$605$	−4.73358	+	4.73358i	−0.192447	+	0.192447i
$606$	−1.89668	+	3.09818i	−0.0770472	+	0.125855i
$607$	27.9592			1.13483			0.567414	−	0.823432i	$-0.307944\pi$
$607$	27.9592			1.13483			0.567414	+	0.823432i	$0.307944\pi$
$608$	−5.23105	−	2.15316i	−0.212147	−	0.0873222i
$609$	2.30565			0.0934297
$610$	−2.86590	+	4.68139i	−0.116037	+	0.189544i
$611$	29.5652	−	29.5652i	1.19608	−	1.19608i
$612$	−23.8428	+	12.1752i	−0.963786	+	0.492154i
$613$	−0.729775	−	0.729775i	−0.0294753	−	0.0294753i	0.692216	−	0.721691i	$-0.256635\pi$
$613$	−0.729775	−	0.729775i	−0.0294753	−	0.0294753i	−0.721691	+	0.692216i	$0.756635\pi$
$614$	−5.42333	−	22.5456i	−0.218868	−	0.909867i
$615$			3.20752i			0.129340i
$616$	0.395578	−	0.338769i	0.0159383	−	0.0136494i
$617$			42.4958i			1.71082i	0.517954	+	0.855408i	$0.326694\pi$
$617$			42.4958i			1.71082i	−0.517954	+	0.855408i	$0.673306\pi$
$618$	11.6456	−	2.80133i	0.468454	−	0.112686i
$619$	−2.71819	−	2.71819i	−0.109253	−	0.109253i	0.650367	−	0.759620i	$-0.274615\pi$
$619$	−2.71819	−	2.71819i	−0.109253	−	0.109253i	−0.759620	+	0.650367i	$0.774615\pi$
$620$	−3.55852	+	10.9852i	−0.142914	+	0.441177i
$621$	11.1172	−	11.1172i	0.446120	−	0.446120i
$622$	20.0908	+	12.2994i	0.805567	+	0.493160i
$623$	5.29620			0.212188
$624$	9.63893	+	6.97694i	0.385866	+	0.279301i
$625$	−19.5392			−0.781569
$626$	−5.33650	−	3.26695i	−0.213289	−	0.130574i
$627$	0.0682962	−	0.0682962i	0.00272749	−	0.00272749i
$628$	21.1969	+	6.86647i	0.845849	+	0.274002i
$629$	9.86748	+	9.86748i	0.393442	+	0.393442i
$630$	−2.05496	+	0.494318i	−0.0818715	+	0.0196941i
$631$		−	28.4054i		−	1.13080i	−0.824816	−	0.565401i	$-0.808721\pi$
$631$		−	28.4054i		−	1.13080i	0.824816	−	0.565401i	$-0.191279\pi$
$632$	43.1971	+	3.34172i	1.71829	+	0.132927i
$633$			3.54120i			0.140750i
$634$	3.80370	+	15.8126i	0.151064	+	0.627998i
$635$	4.53976	+	4.53976i	0.180155	+	0.180155i
$636$	1.07369	+	2.10261i	0.0425745	+	0.0833738i
$637$	−28.4820	+	28.4820i	−1.12850	+	1.12850i
$638$	−0.885326	+	1.44616i	−0.0350504	+	0.0572542i
$639$	−6.76838			−0.267753
$640$	6.88986	−	0.563823i	0.272346	−	0.0222871i
$641$	1.32506			0.0523368			0.0261684	−	0.999658i	$-0.491669\pi$
$641$	1.32506			0.0523368			0.0261684	+	0.999658i	$0.491669\pi$
$642$	−3.71093	+	6.06174i	−0.146459	+	0.239238i
$643$	7.25465	−	7.25465i	0.286096	−	0.286096i	−0.549439	−	0.835534i	$-0.685158\pi$
$643$	7.25465	−	7.25465i	0.286096	−	0.286096i	0.835534	+	0.549439i	$0.185158\pi$
$644$	4.71001	+	9.22364i	0.185601	+	0.363462i
$645$	−1.11918	−	1.11918i	−0.0440676	−	0.0440676i
$646$	−1.58786	−	6.60096i	−0.0624733	−	0.259711i
$647$		−	50.3850i		−	1.98084i	−0.138094	−	0.990419i	$-0.544098\pi$
$647$		−	50.3850i		−	1.98084i	0.138094	−	0.990419i	$-0.455902\pi$
$648$	−20.1328	−	1.55747i	−0.790892	−	0.0611833i
$649$		−	0.935033i		−	0.0367032i
$650$	−41.1274	+	9.89316i	−1.61315	+	0.388041i
$651$	−2.69698	−	2.69698i	−0.105703	−	0.105703i
$652$	33.5448	+	10.8664i	1.31371	+	0.425560i
$653$	22.6802	−	22.6802i	0.887544	−	0.887544i	−0.106742	−	0.994287i	$-0.534042\pi$
$653$	22.6802	−	22.6802i	0.887544	−	0.887544i	0.994287	+	0.106742i	$0.0340420\pi$
$654$	−4.75968	−	2.91383i	−0.186118	−	0.113940i
$655$	−4.87980			−0.190670
$656$	−36.9662	−	26.7572i	−1.44329	−	1.04469i
$657$	−8.76328			−0.341888
$658$	6.84295	+	4.18918i	0.266766	+	0.163311i
$659$	22.0987	−	22.0987i	0.860844	−	0.860844i	−0.130592	−	0.991436i	$-0.541688\pi$
$659$	22.0987	−	22.0987i	0.860844	−	0.860844i	0.991436	+	0.130592i	$0.0416879\pi$
$660$	−0.0363738	+	0.112287i	−0.00141585	+	0.00437075i
$661$	26.2953	+	26.2953i	1.02277	+	1.02277i	0.999735	+	0.0230347i	$0.00733281\pi$
$661$	26.2953	+	26.2953i	1.02277	+	1.02277i	0.0230347	+	0.999735i	$0.492667\pi$
$662$	−45.7649	+	11.0087i	−1.77871	+	0.427866i
$663$			14.2810i			0.554628i
$664$	15.0712	−	12.9068i	0.584877	−	0.500883i
$665$		−	0.536003i		−	0.0207853i
$666$	2.68073	+	11.1442i	0.103876	+	0.431829i
$667$	−23.8427	−	23.8427i	−0.923192	−	0.923192i
$668$	−14.8999	+	7.60856i	−0.576493	+	0.294384i
$669$	−5.46153	+	5.46153i	−0.211155	+	0.211155i
$670$	6.87439	−	11.2292i	0.265581	−	0.433821i
$671$	1.33335			0.0514736
$672$	−0.869113	+	2.11149i	−0.0335268	+	0.0814524i
$673$	28.8587			1.11242			0.556211	−	0.831041i	$-0.312254\pi$
$673$	28.8587			1.11242			0.556211	+	0.831041i	$0.312254\pi$
$674$	6.24296	−	10.1978i	0.240470	−	0.392803i
$675$	−8.71342	+	8.71342i	−0.335380	+	0.335380i
$676$	−51.2904	+	26.1912i	−1.97271	+	1.00736i
$677$	26.5863	+	26.5863i	1.02180	+	1.02180i	0.999757	+	0.0220382i	$0.00701553\pi$
$677$	26.5863	+	26.5863i	1.02180	+	1.02180i	0.0220382	+	0.999757i	$0.492984\pi$
$678$	−2.44510	−	10.1647i	−0.0939036	−	0.390372i
$679$			5.66090i			0.217246i
$680$	5.39670	+	6.30169i	0.206954	+	0.241659i
$681$		−	4.84835i		−	0.185789i
$682$	2.72720	−	0.656025i	0.104430	−	0.0251205i
$683$	30.9645	+	30.9645i	1.18482	+	1.18482i	0.978480	+	0.206344i	$0.0661565\pi$
$683$	30.9645	+	30.9645i	1.18482	+	1.18482i	0.206344	+	0.978480i	$0.433843\pi$
$684$	1.71853	−	5.30514i	0.0657097	−	0.202847i
$685$	5.18051	−	5.18051i	0.197937	−	0.197937i
$686$	−13.9987	−	8.56984i	−0.534472	−	0.327198i
$687$	2.87103			0.109537
$688$	22.2346	−	3.56215i	0.847685	−	0.135806i
$689$	−16.5852			−0.631846
$690$	−2.00178	−	1.22547i	−0.0762065	−	0.0466528i
$691$	−20.6100	+	20.6100i	−0.784043	+	0.784043i	−0.980510	−	0.196467i	$-0.937053\pi$
$691$	−20.6100	+	20.6100i	−0.784043	+	0.784043i	0.196467	+	0.980510i	$0.437053\pi$
$692$	34.0942	+	11.0444i	1.29607	+	0.419844i
$693$	0.363042	+	0.363042i	0.0137908	+	0.0137908i
$694$	21.1700	−	5.09241i	0.803601	−	0.193305i
$695$			0.145055i			0.00550224i
$696$	0.573385	−	7.41192i	0.0217341	−	0.280948i
$697$		−	54.7689i		−	2.07452i
$698$	−3.50704	−	14.5793i	−0.132743	−	0.551835i
$699$	−1.72387	−	1.72387i	−0.0652026	−	0.0652026i
$700$	−3.69159	−	7.22926i	−0.139529	−	0.273240i
$701$	20.6437	−	20.6437i	0.779701	−	0.779701i	−0.200079	−	0.979780i	$-0.564120\pi$
$701$	20.6437	−	20.6437i	0.779701	−	0.779701i	0.979780	+	0.200079i	$0.0641198\pi$
$702$	−12.7141	+	20.7682i	−0.479862	+	0.783846i
$703$	−2.90679			−0.109632
$704$	−0.990656	−	1.35590i	−0.0373368	−	0.0511024i
$705$	−1.81833			−0.0684824
$706$	4.51631	−	7.37730i	0.169973	−	0.277648i
$707$	3.46273	−	3.46273i	0.130229	−	0.130229i
$708$	1.86433	+	3.65093i	0.0700659	+	0.137210i
$709$	−3.18323	−	3.18323i	−0.119549	−	0.119549i	0.644801	−	0.764350i	$-0.276940\pi$
$709$	−3.18323	−	3.18323i	−0.119549	−	0.119549i	−0.764350	+	0.644801i	$0.776940\pi$
$710$	0.490578	+	2.03941i	0.0184110	+	0.0765376i
$711$			42.7111i			1.60179i
$712$	1.31709	−	17.0255i	0.0493601	−	0.638059i
$713$			55.7787i			2.08893i
$714$	−2.66445	+	0.640930i	−0.0997144	+	0.0239862i
$715$	−0.586311	−	0.586311i	−0.0219268	−	0.0219268i
$716$	16.5772	+	5.36998i	0.619520	+	0.200685i
$717$	−0.990206	+	0.990206i	−0.0369799	+	0.0369799i
$718$	11.4406	+	7.00382i	0.426960	+	0.261380i
$719$	−21.1221			−0.787722			−0.393861	−	0.919170i	$-0.628861\pi$
$719$	−21.1221			−0.787722			−0.393861	+	0.919170i	$0.628861\pi$
$720$	1.07803	+	6.72895i	0.0401758	+	0.250773i
$721$	−16.1468			−0.601338
$722$	1.20614	+	0.738388i	0.0448880	+	0.0274800i
$723$	1.23962	−	1.23962i	0.0461020	−	0.0461020i
$724$	6.92578	−	21.3800i	0.257395	−	0.794582i
$725$	18.6873	+	18.6873i	0.694028	+	0.694028i
$726$	−6.93166	+	1.66740i	−0.257258	+	0.0618831i
$727$		−	21.8358i		−	0.809844i	−0.914351	−	0.404922i	$-0.867299\pi$
$727$		−	21.8358i		−	0.809844i	0.914351	−	0.404922i	$-0.132701\pi$
$728$	−10.4338	−	12.1835i	−0.386703	−	0.451550i
$729$		−	16.2297i		−	0.601101i
$730$	0.635169	+	2.64050i	0.0235087	+	0.0977292i
$731$	19.1101	+	19.1101i	0.706814	+	0.706814i
$732$	−5.20622	+	2.65854i	−0.192427	+	0.0982623i
$733$	−16.3781	+	16.3781i	−0.604938	+	0.604938i	−0.941619	−	0.336681i	$-0.890696\pi$
$733$	−16.3781	+	16.3781i	−0.604938	+	0.604938i	0.336681	+	0.941619i	$0.390696\pi$
$734$	−12.5397	+	20.4833i	−0.462848	+	0.756054i
$735$	1.75171			0.0646129
$736$	30.8223	−	12.8474i	1.13612	−	0.473560i
$737$	−3.19830			−0.117811
$738$	23.4881	−	38.3673i	0.864608	−	1.41232i
$739$	−25.3921	+	25.3921i	−0.934063	+	0.934063i	−0.997957	−	0.0638939i	$-0.979648\pi$
$739$	−25.3921	+	25.3921i	−0.934063	+	0.934063i	0.0638939	+	0.997957i	$0.479648\pi$
$740$	3.16361	−	1.61548i	0.116296	−	0.0593863i
$741$	−2.10347	−	2.10347i	−0.0772729	−	0.0772729i
$742$	−0.744343	−	3.09435i	−0.0273257	−	0.113597i
$743$		−	2.56210i		−	0.0939944i	−0.998895	−	0.0469972i	$-0.985035\pi$
$743$		−	2.56210i		−	0.0939944i	0.998895	−	0.0469972i	$-0.0149652\pi$
$744$	−9.34061	+	7.99920i	−0.342443	+	0.293265i
$745$			3.44736i			0.126301i
$746$	31.5262	−	7.58359i	1.15426	−	0.277655i
$747$	13.8316	+	13.8316i	0.506073	+	0.506073i
$748$	0.621089	−	1.91731i	0.0227092	−	0.0701039i
$749$	6.77499	−	6.77499i	0.247553	−	0.247553i
$750$	3.26450	+	1.99849i	0.119203	+	0.0729746i
$751$	48.2987			1.76245			0.881223	−	0.472701i	$-0.156721\pi$
$751$	48.2987			1.76245			0.881223	+	0.472701i	$0.156721\pi$
$752$	15.1686	−	20.9560i	0.553142	−	0.764188i
$753$	−8.13957			−0.296622
$754$	44.5407	+	27.2673i	1.62208	+	0.993018i
$755$	−2.18035	+	2.18035i	−0.0793509	+	0.0793509i
$756$	−4.44540	−	1.44003i	−0.161678	−	0.0523733i
$757$	17.6938	+	17.6938i	0.643091	+	0.643091i	0.951314	−	0.308223i	$-0.0997344\pi$
$757$	17.6938	+	17.6938i	0.643091	+	0.643091i	−0.308223	+	0.951314i	$0.599734\pi$
$758$	−11.4220	+	2.74755i	−0.414866	+	0.0997956i
$759$			0.570148i			0.0206950i
$760$	−1.72307	−	0.133297i	−0.0625025	−	0.00483518i
$761$			21.6720i			0.785608i	0.919622	+	0.392804i	$0.128495\pi$
$761$			21.6720i			0.785608i	−0.919622	+	0.392804i	$0.871505\pi$
$762$	1.59913	+	6.64784i	0.0579304	+	0.240826i
$763$	5.31973	+	5.31973i	0.192587	+	0.192587i
$764$	4.85566	+	9.50887i	0.175672	+	0.344019i
$765$	−5.78339	+	5.78339i	−0.209099	+	0.209099i
$766$	13.0766	−	21.3604i	0.472477	−	0.771782i
$767$	−28.7983			−1.03985
$768$	6.57161	+	3.31901i	0.237133	+	0.119765i
$769$	−15.8063			−0.569991			−0.284995	−	0.958529i	$-0.591992\pi$
$769$	−15.8063			−0.569991			−0.284995	+	0.958529i	$0.591992\pi$
$770$	0.0830762	−	0.135703i	0.00299386	−	0.00489041i
$771$	−6.39116	+	6.39116i	−0.230172	+	0.230172i
$772$	0.0954023	+	0.186827i	0.00343360	+	0.00672404i
$773$	11.1253	+	11.1253i	0.400150	+	0.400150i	0.878286	−	0.478136i	$-0.158687\pi$
$773$	11.1253	+	11.1253i	0.400150	+	0.400150i	−0.478136	+	0.878286i	$0.658687\pi$
$774$	5.19172	+	21.5828i	0.186612	+	0.775777i
$775$		−	43.7180i		−	1.57040i
$776$	18.1980	+	1.40779i	0.653268	+	0.0505367i
$777$			1.17331i			0.0420924i
$778$	−31.5021	+	7.57780i	−1.12940	+	0.271677i
$779$	8.06700	+	8.06700i	0.289030	+	0.289030i
$780$	3.45834	+	1.12028i	0.123828	+	0.0401126i
$781$	0.360295	−	0.360295i	0.0128924	−	0.0128924i
$782$	34.1808	+	20.9251i	1.22230	+	0.748281i
$783$	15.2135			0.543688
$784$	−14.6128	+	20.1882i	−0.521887	+	0.721009i
$785$	6.80716			0.242958
$786$	−4.43235	−	2.71344i	−0.158097	−	0.0967851i
$787$	−29.9966	+	29.9966i	−1.06926	+	1.06926i	−0.0718466	+	0.997416i	$0.522889\pi$
$787$	−29.9966	+	29.9966i	−1.06926	+	1.06926i	−0.997416	+	0.0718466i	$0.977111\pi$
$788$	8.98177	−	27.7269i	0.319962	−	0.987731i
$789$	−5.74516	−	5.74516i	−0.204533	−	0.204533i
$790$	12.8695	−	3.09573i	0.457875	−	0.110141i
$791$			14.0935i			0.501107i
$792$	1.25735	−	1.07678i	0.0446778	−	0.0382617i
$793$		−	41.0663i		−	1.45831i
$794$	7.57137	+	31.4754i	0.268698	+	1.11702i
$795$	0.510016	+	0.510016i	0.0180884	+	0.0180884i
$796$	18.1385	−	9.26234i	0.642901	−	0.328295i
$797$	−24.2464	+	24.2464i	−0.858851	+	0.858851i	−0.991203	−	0.132352i	$-0.957747\pi$
$797$	−24.2464	+	24.2464i	−0.858851	+	0.858851i	0.132352	+	0.991203i	$0.457747\pi$
$798$	0.298047	−	0.486854i	0.0105507	−	0.0172344i
$799$	31.0484			1.09841
$800$	−24.1577	+	10.0694i	−0.854105	+	0.356008i
$801$	16.8340			0.594800
$802$	15.2478	−	24.9071i	0.538420	−	0.879499i
$803$	0.466488	−	0.466488i	0.0164620	−	0.0164620i
$804$	12.4881	−	6.37699i	0.440420	−	0.224899i
$805$	2.23732	+	2.23732i	0.0788552	+	0.0788552i
$806$	−20.2051	−	83.9957i	−0.711693	−	2.95862i
$807$		−	1.30172i		−	0.0458226i
$808$	−10.2704	−	11.9927i	−0.361312	−	0.421901i
$809$		−	2.98508i		−	0.104950i	−0.998622	−	0.0524750i	$-0.983289\pi$
$809$		−	2.98508i		−	0.104950i	0.998622	−	0.0524750i	$-0.0167110\pi$
$810$	−5.99805	+	1.44282i	−0.210750	+	0.0506957i
$811$	−18.6270	−	18.6270i	−0.654081	−	0.654081i	0.299892	−	0.953973i	$-0.403049\pi$
$811$	−18.6270	−	18.6270i	−0.654081	−	0.654081i	−0.953973	+	0.299892i	$0.903049\pi$
$812$	−3.08837	+	9.53385i	−0.108380	+	0.334572i
$813$	7.49755	−	7.49755i	0.262951	−	0.262951i
$814$	−0.735931	−	0.450529i	−0.0257944	−	0.0157910i
$815$	10.7725			0.377345
$816$	1.39777	+	8.72472i	0.0489317	+	0.305426i
$817$	−5.62953			−0.196952
$818$	−26.5149	−	16.2322i	−0.927072	−	0.567544i
$819$	11.1814	−	11.1814i	0.390710	−	0.390710i
$820$	−13.2631	−	4.29639i	−0.463166	−	0.150037i
$821$	−29.9374	−	29.9374i	−1.04482	−	1.04482i	−0.998947	−	0.0458735i	$-0.985393\pi$
$821$	−29.9374	−	29.9374i	−1.04482	−	1.04482i	−0.0458735	−	0.998947i	$-0.514607\pi$
$822$	7.58613	−	1.82484i	0.264597	−	0.0636485i
$823$			9.14454i			0.318759i	0.987217	+	0.159379i	$0.0509493\pi$
$823$			9.14454i			0.318759i	−0.987217	+	0.159379i	$0.949051\pi$
$824$	−4.01549	+	51.9066i	−0.139886	+	1.80825i
$825$		−	0.446867i		−	0.0155579i
$826$	−1.29246	−	5.37298i	−0.0449706	−	0.186950i
$827$	−40.0271	−	40.0271i	−1.39188	−	1.39188i	−0.821115	−	0.570763i	$-0.806647\pi$
$827$	−40.0271	−	40.0271i	−1.39188	−	1.39188i	−0.570763	−	0.821115i	$-0.693353\pi$
$828$	14.9708	+	29.3174i	0.520271	+	1.01885i
$829$	−37.8937	+	37.8937i	−1.31610	+	1.31610i	−0.399268	+	0.916834i	$0.630736\pi$
$829$	−37.8937	+	37.8937i	−1.31610	+	1.31610i	−0.916834	+	0.399268i	$0.869264\pi$
$830$	3.16514	−	5.17020i	0.109864	−	0.179460i
$831$	4.97867			0.172708
$832$	−41.7607	+	30.5114i	−1.44779	+	1.05779i
$833$	−29.9108			−1.03635
$834$	−0.0806583	+	0.131754i	−0.00279297	+	0.00456226i
$835$	−3.61417	+	3.61417i	−0.125073	+	0.125073i
$836$	0.190923	+	0.373885i	0.00660321	+	0.0129311i
$837$	−17.7957	−	17.7957i	−0.615108	−	0.615108i
$838$	−10.1907	−	42.3645i	−0.352033	−	1.46346i
$839$		−	14.4505i		−	0.498887i	−0.968389	−	0.249444i	$-0.919752\pi$
$839$		−	14.4505i		−	0.498887i	0.968389	−	0.249444i	$-0.0802477\pi$
$840$	−0.0538046	+	0.695511i	−0.00185644	+	0.0239974i
$841$		−	3.62782i		−	0.125097i
$842$	−47.7429	+	11.4845i	−1.64533	+	0.395782i
$843$	−1.27690	−	1.27690i	−0.0439789	−	0.0439789i
$844$	−14.6428	−	4.74335i	−0.504027	−	0.163273i
$845$	−12.4412	+	12.4412i	−0.427990	+	0.427990i
$846$	21.7503	+	13.3153i	0.747792	+	0.457791i
$847$	9.61086			0.330233
$848$	−10.1324	+	1.62330i	−0.347949	+	0.0557442i
$849$	−8.00773			−0.274825
$850$	−26.7900	−	16.4006i	−0.918891	−	0.562535i
$851$	12.1332	−	12.1332i	0.415920	−	0.415920i
$852$	−0.688428	+	2.12519i	−0.0235852	+	0.0728079i
$853$	−9.65508	−	9.65508i	−0.330584	−	0.330584i	0.522224	−	0.852808i	$-0.325102\pi$
$853$	−9.65508	−	9.65508i	−0.330584	−	0.330584i	−0.852808	+	0.522224i	$0.825102\pi$
$854$	7.66186	−	1.84305i	0.262183	−	0.0630680i
$855$		−	1.70369i		−	0.0582649i
$856$	−20.0945	−	23.4642i	−0.686816	−	0.801990i
$857$			25.3214i			0.864963i	0.901643	+	0.432482i	$0.142362\pi$
$857$			25.3214i			0.864963i	−0.901643	+	0.432482i	$0.857638\pi$
$858$	−0.206528	−	0.858570i	−0.00705075	−	0.0293111i
$859$	16.6946	+	16.6946i	0.569614	+	0.569614i	0.932020	−	0.362407i	$-0.118045\pi$
$859$	16.6946	+	16.6946i	0.569614	+	0.569614i	−0.362407	+	0.932020i	$0.618045\pi$
$860$	6.12689	−	3.12867i	0.208925	−	0.106687i
$861$	3.25621	−	3.25621i	0.110971	−	0.110971i
$862$	5.64979	−	9.22883i	0.192433	−	0.314335i
$863$	−25.5746			−0.870570			−0.435285	−	0.900293i	$-0.643352\pi$
$863$	−25.5746			−0.870570			−0.435285	+	0.900293i	$0.643352\pi$
$864$	−5.73473	+	13.9324i	−0.195099	+	0.473989i
$865$	10.9490			0.372277
$866$	21.6179	−	35.3125i	0.734607	−	1.19997i
$867$	−1.96749	+	1.96749i	−0.0668194	+	0.0668194i
$868$	14.7645	−	7.53944i	0.501140	−	0.255905i
$869$	−2.27360	−	2.27360i	−0.0771267	−	0.0771267i
$870$	−0.531178	−	2.20819i	−0.0180086	−	0.0748646i
$871$			98.5050i			3.33771i
$872$	18.4241	−	15.7782i	0.623920	−	0.534319i
$873$			17.9932i			0.608978i
$874$	−8.11663	+	1.95245i	−0.274549	+	0.0660425i
$875$	−3.64861	−	3.64861i	−0.123346	−	0.123346i
$876$	−0.891334	+	2.75157i	−0.0301154	+	0.0929668i
$877$	−5.75569	+	5.75569i	−0.194356	+	0.194356i	−0.797575	−	0.603220i	$-0.793884\pi$
$877$	−5.75569	+	5.75569i	−0.194356	+	0.194356i	0.603220	+	0.797575i	$0.293884\pi$
$878$	7.58284	+	4.64213i	0.255908	+	0.156664i
$879$	−10.6726			−0.359979
$880$	−0.415582	−	0.300810i	−0.0140093	−	0.0101403i
$881$	19.3698			0.652586			0.326293	−	0.945269i	$-0.394200\pi$
$881$	19.3698			0.652586			0.326293	+	0.945269i	$0.394200\pi$
$882$	−20.9534	−	12.8275i	−0.705539	−	0.431924i
$883$	29.7245	−	29.7245i	1.00031	−	1.00031i	0.000309805	−	1.00000i	$-0.499901\pi$
$883$	29.7245	−	29.7245i	1.00031	−	1.00031i	1.00000		0.000309805i	$-9.86140e-5\pi$
$884$	−59.0517	−	19.1290i	−1.98613	−	0.643379i
$885$	0.885583	+	0.885583i	0.0297686	+	0.0297686i
$886$	−1.03545	+	0.249077i	−0.0347867	+	0.00836791i
$887$			47.1761i			1.58402i	0.610510	+	0.792008i	$0.290964\pi$
$887$			47.1761i			1.58402i	−0.610510	+	0.792008i	$0.709036\pi$
$888$	3.77182	+	0.291787i	0.126574	+	0.00979173i
$889$		−	9.21734i		−	0.309140i
$890$	−1.22014	−	5.07232i	−0.0408992	−	0.170024i
$891$	1.05965	+	1.05965i	0.0354998	+	0.0354998i
$892$	−15.2678	−	29.8989i	−0.511203	−	1.00109i
$893$	−4.57316	+	4.57316i	−0.153035	+	0.153035i
$894$	−1.91692	+	3.13125i	−0.0641113	+	0.104725i
$895$	5.32360			0.177948
$896$	−7.56683	−	6.42206i	−0.252790	−	0.214546i
$897$	17.5601			0.586315
$898$	13.0758	−	21.3591i	0.436345	−	0.712761i
$899$	−38.1656	+	38.1656i	−1.27289	+	1.27289i
$900$	−11.7337	−	22.9782i	−0.391125	−	0.765941i
$901$	−8.70861	−	8.70861i	−0.290126	−	0.290126i
$902$	0.792055	+	3.29270i	0.0263725	+	0.109635i
$903$			2.27233i			0.0756184i
$904$	45.3060	+	3.50486i	1.50686	+	0.116570i
$905$		−	6.86596i		−	0.228232i
$906$	−3.19281	+	0.768027i	−0.106074	+	0.0255160i
$907$	−7.60558	−	7.60558i	−0.252539	−	0.252539i	0.569472	−	0.822011i	$-0.307148\pi$
$907$	−7.60558	−	7.60558i	−0.252539	−	0.252539i	−0.822011	+	0.569472i	$0.807148\pi$
$908$	20.0479	+	6.49425i	0.665312	+	0.215519i
$909$	11.0063	−	11.0063i	0.365056	−	0.365056i
$910$	−4.17956	−	2.55868i	−0.138551	−	0.0848194i
$911$	−17.6243			−0.583920			−0.291960	−	0.956430i	$-0.594307\pi$
$911$	−17.6243			−0.583920			−0.291960	+	0.956430i	$0.594307\pi$
$912$	−1.49096	−	1.07920i	−0.0493705	−	0.0357358i
$913$	−1.47258			−0.0487351
$914$	8.58341	+	5.25467i	0.283914	+	0.173809i
$915$	−1.26284	+	1.26284i	−0.0417482	+	0.0417482i
$916$	−3.84568	+	11.8717i	−0.127065	+	0.392252i
$917$	4.95387	+	4.95387i	0.163591	+	0.163591i
$918$	−17.5810	+	4.22909i	−0.580260	+	0.139581i
$919$			38.9615i			1.28522i	0.766193	+	0.642610i	$0.222149\pi$
$919$			38.9615i			1.28522i	−0.766193	+	0.642610i	$0.777851\pi$
$920$	7.74864	−	6.63586i	0.255465	−	0.218778i
$921$		−	7.54483i		−	0.248611i
$922$	5.04275	+	20.9635i	0.166074	+	0.690396i
$923$	−11.0968	−	11.0968i	−0.365256	−	0.365256i
$924$	0.150917	−	0.0770651i	0.00496480	−	0.00253526i
$925$	−9.50968	+	9.50968i	−0.312676	+	0.312676i
$926$	−12.0213	+	19.6366i	−0.395045	+	0.645298i
$927$	−51.3226			−1.68566
$928$	29.8802	+	12.2990i	0.980864	+	0.403735i
$929$	−2.38543			−0.0782634			−0.0391317	−	0.999234i	$-0.512459\pi$
$929$	−2.38543			−0.0782634			−0.0391317	+	0.999234i	$0.512459\pi$
$930$	−1.96164	+	3.20430i	−0.0643247	+	0.105073i
$931$	4.40561	−	4.40561i	0.144388	−	0.144388i
$932$	9.43724	−	4.81909i	0.309127	−	0.157855i
$933$	5.41964	+	5.41964i	0.177431	+	0.177431i
$934$	5.71954	+	23.7770i	0.187149	+	0.778008i
$935$		−	0.615724i		−	0.0201363i
$936$	−33.1639	−	38.7253i	−1.08400	−	1.26578i
$937$			10.7674i			0.351757i	0.984412	+	0.175878i	$0.0562766\pi$
$937$			10.7674i			0.351757i	−0.984412	+	0.175878i	$0.943723\pi$
$938$	−18.3784	+	4.42090i	−0.600075	+	0.144347i
$939$	−1.43956	−	1.43956i	−0.0469783	−	0.0469783i
$940$	2.43561	−	7.51879i	0.0794410	−	0.245236i
$941$	−22.5540	+	22.5540i	−0.735240	+	0.735240i	−0.971653	−	0.236413i	$-0.924028\pi$
$941$	−22.5540	+	22.5540i	−0.735240	+	0.735240i	0.236413	+	0.971653i	$0.424028\pi$
$942$	6.18297	+	3.78515i	0.201452	+	0.123327i
$943$	−67.3446			−2.19304
$944$	−17.5938	+	2.81866i	−0.572629	+	0.0917397i
$945$	−1.42759			−0.0464395
$946$	−1.42526	−	0.872531i	−0.0463393	−	0.0283684i
$947$	0.681177	−	0.681177i	0.0221353	−	0.0221353i	−0.695953	−	0.718088i	$-0.745018\pi$
$947$	0.681177	−	0.681177i	0.0221353	−	0.0221353i	0.718088	+	0.695953i	$0.245018\pi$
$948$	13.4108	+	4.34425i	0.435562	+	0.141095i
$949$	−14.3675	−	14.3675i	−0.466388	−	0.466388i
$950$	6.36161	−	1.53028i	0.206398	−	0.0496488i
$951$			5.29164i			0.171593i
$952$	0.918723	−	11.8760i	0.0297760	−	0.384902i
$953$			20.0787i			0.650412i	0.945643	+	0.325206i	$0.105434\pi$
$953$			20.0787i			0.650412i	−0.945643	+	0.325206i	$0.894566\pi$
$954$	−2.36590	−	9.83541i	−0.0765988	−	0.318433i
$955$	2.30651	+	2.30651i	0.0746368	+	0.0746368i
$956$	−2.76813	−	5.42085i	−0.0895278	−	0.175323i
$957$	−0.390113	+	0.390113i	−0.0126106	+	0.0126106i
$958$	−3.91186	+	6.38995i	−0.126386	+	0.206450i
$959$	−10.5183			−0.339654
$960$	2.22246	+	0.345928i	0.0717296	+	0.0111648i
$961$	58.2864			1.88021
$962$	−13.8759	+	22.6661i	−0.447379	+	0.730785i
$963$	21.5343	−	21.5343i	0.693934	−	0.693934i
$964$	3.46538	+	6.78627i	0.111612	+	0.218571i
$965$	0.0453174	+	0.0453174i	0.00145882	+	0.00145882i
$966$	0.788096	+	3.27624i	0.0253566	+	0.105411i
$967$		−	34.2552i		−	1.10157i	−0.834646	−	0.550787i	$-0.814328\pi$
$967$		−	34.2552i		−	1.10157i	0.834646	−	0.550787i	$-0.185672\pi$
$968$	2.39009	−	30.8958i	0.0768205	−	0.993028i
$969$		−	2.20899i		−	0.0709631i
$970$	5.42161	−	1.30416i	0.174077	−	0.0418741i
$971$	−19.8808	−	19.8808i	−0.638004	−	0.638004i	0.312059	−	0.950063i	$-0.398981\pi$
$971$	−19.8808	−	19.8808i	−0.638004	−	0.638004i	−0.950063	+	0.312059i	$0.898981\pi$
$972$	−21.4530	−	6.94942i	−0.688105	−	0.222903i
$973$	0.147256	−	0.147256i	0.00472083	−	0.00472083i
$974$	9.82508	+	6.01481i	0.314816	+	0.192727i
$975$	−13.7632			−0.440774
$976$	−4.01941	−	25.0887i	−0.128658	−	0.803070i
$977$	24.4843			0.783323			0.391662	−	0.920109i	$-0.371900\pi$
$977$	24.4843			0.783323			0.391662	+	0.920109i	$0.371900\pi$
$978$	9.78474	+	5.99011i	0.312881	+	0.191543i
$979$	−0.896109	+	0.896109i	−0.0286398	+	0.0286398i
$980$	−2.34638	+	7.24331i	−0.0749522	+	0.231379i
$981$	16.9088	+	16.9088i	0.539856	+	0.539856i
$982$	−57.2315	+	13.7670i	−1.82633	+	0.439322i
$983$		−	10.8056i		−	0.344644i	−0.985041	−	0.172322i	$-0.944873\pi$
$983$		−	10.8056i		−	0.344644i	0.985041	−	0.172322i	$-0.0551270\pi$
$984$	−9.65786	−	11.2774i	−0.307881	−	0.359511i
$985$		−	8.90420i		−	0.283711i
$986$	9.06995	+	37.7052i	0.288846	+	1.20078i
$987$	1.84594	+	1.84594i	0.0587568	+	0.0587568i
$988$	11.5154	−	5.88028i	0.366353	−	0.187077i
$989$	23.4981	−	23.4981i	0.747196	−	0.747196i
$990$	0.264058	−	0.431334i	0.00839231	−	0.0137087i
$991$	−1.18500			−0.0376426			−0.0188213	−	0.999823i	$-0.505991\pi$
$991$	−1.18500			−0.0376426			−0.0188213	+	0.999823i	$0.505991\pi$
$992$	−20.5651	−	49.3380i	−0.652942	−	1.56648i
$993$	−15.3151			−0.486010
$994$	1.57234	−	2.56839i	0.0498716	−	0.0814644i
$995$	4.39974	−	4.39974i	0.139481	−	0.139481i
$996$	5.74982	−	2.93612i	0.182190	−	0.0930346i
$997$	25.9355	+	25.9355i	0.821386	+	0.821386i	0.986307	−	0.164921i	$-0.0527369\pi$
$997$	25.9355	+	25.9355i	0.821386	+	0.821386i	−0.164921	+	0.986307i	$0.552737\pi$
$998$	9.49845	+	39.4866i	0.300668	+	1.24993i
$999$			7.74195i			0.244944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.229.11	yes	68
4.3	odd	2		1216.2.k.b.305.22		68
16.3	odd	4		1216.2.k.b.913.22		68
16.13	even	4	inner	304.2.k.b.77.11	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.11	✓	68	16.13	even	4	inner
304.2.k.b.229.11	yes	68	1.1	even	1	trivial
1216.2.k.b.305.22		68	4.3	odd	2
1216.2.k.b.913.22		68	16.3	odd	4

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.738388 + 1.20614i) q^{2} +(-0.325366 + 0.325366i) q^{3} +(-0.909565 - 1.78121i) q^{4} +(-0.432056 - 0.432056i) q^{5} +(-0.152192 - 0.632685i) q^{6} +0.877228i q^{7} +(2.82000 + 0.218155i) q^{8} +2.78827i q^{9} +O(q^{10})\)	\(q+(-0.738388 + 1.20614i) q^{2} +(-0.325366 + 0.325366i) q^{3} +(-0.909565 - 1.78121i) q^{4} +(-0.432056 - 0.432056i) q^{5} +(-0.152192 - 0.632685i) q^{6} +0.877228i q^{7} +(2.82000 + 0.218155i) q^{8} +2.78827i q^{9} +(0.840146 - 0.202096i) q^{10} +(-0.148426 - 0.148426i) q^{11} +(0.875485 + 0.283602i) q^{12} +(-4.57140 + 4.57140i) q^{13} +(-1.05806 - 0.647735i) q^{14} +0.281153 q^{15} +(-2.34538 + 3.24024i) q^{16} -4.80073 q^{17} +(-3.36306 - 2.05883i) q^{18} +(0.707107 - 0.707107i) q^{19} +(-0.376597 + 1.16256i) q^{20} +(-0.285420 - 0.285420i) q^{21} +(0.288619 - 0.0694269i) q^{22} +5.90304i q^{23} +(-0.988513 + 0.846553i) q^{24} -4.62666i q^{25} +(-2.13830 - 8.88923i) q^{26} +(-1.88331 - 1.88331i) q^{27} +(1.56252 - 0.797896i) q^{28} +(-4.03905 + 4.03905i) q^{29} +(-0.207600 + 0.339110i) q^{30} +9.44915 q^{31} +(-2.17640 - 5.22143i) q^{32} +0.0965854 q^{33} +(3.54480 - 5.79037i) q^{34} +(0.379011 - 0.379011i) q^{35} +(4.96649 - 2.53612i) q^{36} +(-2.05541 - 2.05541i) q^{37} +(0.330753 + 1.37499i) q^{38} -2.97476i q^{39} +(-1.12414 - 1.31265i) q^{40} +11.4085i q^{41} +(0.555009 - 0.133507i) q^{42} +(-3.98068 - 3.98068i) q^{43} +(-0.129374 + 0.399380i) q^{44} +(1.20469 - 1.20469i) q^{45} +(-7.11992 - 4.35874i) q^{46} -6.46743 q^{47} +(-0.291158 - 1.81737i) q^{48} +6.23047 q^{49} +(5.58041 + 3.41627i) q^{50} +(1.56199 - 1.56199i) q^{51} +(12.3006 + 3.98461i) q^{52} +(1.81402 + 1.81402i) q^{53} +(3.66215 - 0.880927i) q^{54} +0.128256i q^{55} +(-0.191372 + 2.47378i) q^{56} +0.460137i q^{57} +(-1.88929 - 7.85406i) q^{58} +(3.14983 + 3.14983i) q^{59} +(-0.255727 - 0.500790i) q^{60} +(-4.49166 + 4.49166i) q^{61} +(-6.97714 + 11.3970i) q^{62} -2.44595 q^{63} +(7.90482 + 1.23039i) q^{64} +3.95020 q^{65} +(-0.0713176 + 0.116496i) q^{66} +(10.7741 - 10.7741i) q^{67} +(4.36658 + 8.55108i) q^{68} +(-1.92065 - 1.92065i) q^{69} +(0.177285 + 0.737000i) q^{70} +2.42744i q^{71} +(-0.608276 + 7.86294i) q^{72} +3.14290i q^{73} +(3.99681 - 0.961430i) q^{74} +(1.50536 + 1.50536i) q^{75} +(-1.90266 - 0.616342i) q^{76} +(0.130203 - 0.130203i) q^{77} +(3.58798 + 2.19652i) q^{78} +15.3181 q^{79} +(2.41330 - 0.386630i) q^{80} -7.13929 q^{81} +(-13.7602 - 8.42388i) q^{82} +(4.96065 - 4.96065i) q^{83} +(-0.248784 + 0.768000i) q^{84} +(2.07418 + 2.07418i) q^{85} +(7.74055 - 1.86198i) q^{86} -2.62834i q^{87} +(-0.386181 - 0.450941i) q^{88} -6.03742i q^{89} +(0.563500 + 2.34256i) q^{90} +(-4.01016 - 4.01016i) q^{91} +(10.5145 - 5.36920i) q^{92} +(-3.07443 + 3.07443i) q^{93} +(4.77547 - 7.80065i) q^{94} -0.611019 q^{95} +(2.40700 + 0.990750i) q^{96} +6.45317 q^{97} +(-4.60051 + 7.51484i) q^{98} +(0.413852 - 0.413852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more