LMFDB - Embedded newform 570.2.k.a.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.4
Character	$\chi$	$=$	570.77
Dual form			570.2.k.a.533.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +(-2.23388 - 0.0989549i) q^{10} +0.944248i q^{11} +(1.55987 + 0.752859i) q^{12} +(-4.86057 + 4.86057i) q^{13} -0.433689 q^{14} +(-3.70964 + 1.11292i) q^{15} -1.00000 q^{16} +(2.18295 - 2.18295i) q^{17} +(2.98055 + 0.341054i) q^{18} +1.00000i q^{19} +(1.64956 - 1.50962i) q^{20} +(-0.709233 + 0.247482i) q^{21} +(-0.667684 - 0.667684i) q^{22} +(5.00219 + 5.00219i) q^{23} +(-1.63535 + 0.570645i) q^{24} +(-0.442106 + 4.98042i) q^{25} -6.87388i q^{26} +(5.06886 - 1.14309i) q^{27} +(0.306664 - 0.306664i) q^{28} -1.77850 q^{29} +(1.83615 - 3.41007i) q^{30} -10.9563 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.47291 - 0.710886i) q^{33} +3.08715i q^{34} +(-0.0429156 + 0.968808i) q^{35} +(-2.34873 + 1.86641i) q^{36} +(-3.09818 - 3.09818i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-3.92254 - 11.2412i) q^{39} +(-0.0989549 + 2.23388i) q^{40} -6.08532i q^{41} +(0.326507 - 0.676500i) q^{42} +(-3.19643 + 3.19643i) q^{43} +0.944248 q^{44} +(1.05681 - 6.62444i) q^{45} -7.07416 q^{46} +(-4.22008 + 4.22008i) q^{47} +(0.752859 - 1.55987i) q^{48} -6.81191i q^{49} +(-3.20907 - 3.83430i) q^{50} +(1.76167 + 5.04857i) q^{51} +(4.86057 + 4.86057i) q^{52} +(-5.08232 - 5.08232i) q^{53} +(-2.77594 + 4.39251i) q^{54} +(-1.55759 + 1.42545i) q^{55} +0.433689i q^{56} +(-1.55987 - 0.752859i) q^{57} +(1.25759 - 1.25759i) q^{58} +7.52893 q^{59} +(1.11292 + 3.70964i) q^{60} +4.53489 q^{61} +(7.74725 - 7.74725i) q^{62} +(0.147911 - 1.29263i) q^{63} +1.00000i q^{64} +(-15.3554 - 0.680204i) q^{65} +(1.54417 - 0.538830i) q^{66} +(7.65067 + 7.65067i) q^{67} +(-2.18295 - 2.18295i) q^{68} +(-11.5687 + 4.03683i) q^{69} +(-0.654705 - 0.715397i) q^{70} +12.9834i q^{71} +(0.341054 - 2.98055i) q^{72} +(2.53764 - 2.53764i) q^{73} +4.38149 q^{74} +(-7.43597 - 4.43918i) q^{75} +1.00000 q^{76} +(-0.289567 + 0.289567i) q^{77} +(10.7224 + 5.17507i) q^{78} -9.50297i q^{79} +(-1.50962 - 1.64956i) q^{80} +(-2.03306 + 8.76736i) q^{81} +(4.30297 + 4.30297i) q^{82} +(7.84806 + 7.84806i) q^{83} +(0.247482 + 0.709233i) q^{84} +(6.89632 + 0.305489i) q^{85} -4.52043i q^{86} +(1.33896 - 2.77424i) q^{87} +(-0.667684 + 0.667684i) q^{88} -8.88554 q^{89} +(3.93690 + 5.43146i) q^{90} -2.98113 q^{91} +(5.00219 - 5.00219i) q^{92} +(8.24852 - 17.0904i) q^{93} -5.96810i q^{94} +(-1.64956 + 1.50962i) q^{95} +(0.570645 + 1.63535i) q^{96} +(-0.722973 - 0.722973i) q^{97} +(4.81675 + 4.81675i) q^{98} +(2.21778 - 1.76235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.752859	+	1.55987i	−0.434663	+	0.900593i
$3$	−0.752859	+	1.55987i	−0.434663	+	0.900593i
$4$		−	1.00000i		−	0.500000i
$5$	1.50962	+	1.64956i	0.675122	+	0.737706i
$5$	1.50962	+	1.64956i	0.675122	+	0.737706i
$6$	−0.570645	−	1.63535i	−0.232965	−	0.667628i
$7$	0.306664	+	0.306664i	0.115908	+	0.115908i	0.762682	−	0.646774i	$-0.223882\pi$
$7$	0.306664	+	0.306664i	0.115908	+	0.115908i	−0.646774	+	0.762682i	$0.723882\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.86641	−	2.34873i	−0.622135	−	0.782910i
$10$	−2.23388	−	0.0989549i	−0.706414	−	0.0312923i
$11$			0.944248i			0.284701i	0.989816	+	0.142351i	$0.0454661\pi$
$11$			0.944248i			0.284701i	−0.989816	+	0.142351i	$0.954534\pi$
$12$	1.55987	+	0.752859i	0.450296	+	0.217332i
$13$	−4.86057	+	4.86057i	−1.34808	+	1.34808i	−0.460332	+	0.887747i	$0.652270\pi$
$13$	−4.86057	+	4.86057i	−1.34808	+	1.34808i	−0.887747	+	0.460332i	$0.847730\pi$
$14$	−0.433689			−0.115908
$15$	−3.70964	+	1.11292i	−0.957824	+	0.287356i
$16$	−1.00000			−0.250000
$17$	2.18295	−	2.18295i	0.529443	−	0.529443i	−0.390964	−	0.920406i	$-0.627858\pi$
$17$	2.18295	−	2.18295i	0.529443	−	0.529443i	0.920406	+	0.390964i	$0.127858\pi$
$18$	2.98055	+	0.341054i	0.702523	+	0.0803872i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.64956	−	1.50962i	0.368853	−	0.337561i
$21$	−0.709233	+	0.247482i	−0.154767	+	0.0540051i
$22$	−0.667684	−	0.667684i	−0.142351	−	0.142351i
$23$	5.00219	+	5.00219i	1.04303	+	1.04303i	0.999032	+	0.0439961i	$0.0140089\pi$
$23$	5.00219	+	5.00219i	1.04303	+	1.04303i	0.0439961	+	0.999032i	$0.485991\pi$
$24$	−1.63535	+	0.570645i	−0.333814	+	0.116482i
$25$	−0.442106	+	4.98042i	−0.0884212	+	0.996083i
$26$		−	6.87388i		−	1.34808i
$27$	5.06886	−	1.14309i	0.975502	−	0.219988i
$28$	0.306664	−	0.306664i	0.0579541	−	0.0579541i
$29$	−1.77850			−0.330260			−0.165130	−	0.986272i	$-0.552804\pi$
$29$	−1.77850			−0.330260			−0.165130	+	0.986272i	$0.552804\pi$
$30$	1.83615	−	3.41007i	0.335234	−	0.622590i
$31$	−10.9563			−1.96780			−0.983901	−	0.178714i	$-0.942806\pi$
$31$	−10.9563			−1.96780			−0.983901	+	0.178714i	$0.942806\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.47291	−	0.710886i	−0.256400	−	0.123749i
$34$			3.08715i			0.529443i
$35$	−0.0429156	+	0.968808i	−0.00725407	+	0.163758i
$36$	−2.34873	+	1.86641i	−0.391455	+	0.311068i
$37$	−3.09818	−	3.09818i	−0.509338	−	0.509338i	0.404985	−	0.914323i	$-0.367277\pi$
$37$	−3.09818	−	3.09818i	−0.509338	−	0.509338i	−0.914323	+	0.404985i	$0.867277\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$	−3.92254	−	11.2412i	−0.628110	−	1.80003i
$40$	−0.0989549	+	2.23388i	−0.0156461	+	0.353207i
$41$		−	6.08532i		−	0.950368i	−0.879886	−	0.475184i	$-0.842382\pi$
$41$		−	6.08532i		−	0.950368i	0.879886	−	0.475184i	$-0.157618\pi$
$42$	0.326507	−	0.676500i	0.0503811	−	0.104386i
$43$	−3.19643	+	3.19643i	−0.487451	+	0.487451i	−0.907501	−	0.420050i	$-0.862013\pi$
$43$	−3.19643	+	3.19643i	−0.487451	+	0.487451i	0.420050	+	0.907501i	$0.362013\pi$
$44$	0.944248			0.142351
$45$	1.05681	−	6.62444i	0.157540	−	0.987513i
$46$	−7.07416			−1.04303
$47$	−4.22008	+	4.22008i	−0.615562	+	0.615562i	−0.944390	−	0.328828i	$-0.893346\pi$
$47$	−4.22008	+	4.22008i	−0.615562	+	0.615562i	0.328828	+	0.944390i	$0.393346\pi$
$48$	0.752859	−	1.55987i	0.108666	−	0.225148i
$49$		−	6.81191i		−	0.973131i
$50$	−3.20907	−	3.83430i	−0.453831	−	0.542252i
$51$	1.76167	+	5.04857i	0.246683	+	0.706942i
$52$	4.86057	+	4.86057i	0.674040	+	0.674040i
$53$	−5.08232	−	5.08232i	−0.698110	−	0.698110i	0.265893	−	0.964003i	$-0.414333\pi$
$53$	−5.08232	−	5.08232i	−0.698110	−	0.698110i	−0.964003	+	0.265893i	$0.914333\pi$
$54$	−2.77594	+	4.39251i	−0.377757	+	0.597745i
$55$	−1.55759	+	1.42545i	−0.210026	+	0.192208i
$56$			0.433689i			0.0579541i
$57$	−1.55987	−	0.752859i	−0.206610	−	0.0997186i
$58$	1.25759	−	1.25759i	0.165130	−	0.165130i
$59$	7.52893			0.980183			0.490092	−	0.871671i	$-0.336963\pi$
$59$	7.52893			0.980183			0.490092	+	0.871671i	$0.336963\pi$
$60$	1.11292	+	3.70964i	0.143678	+	0.478912i
$61$	4.53489			0.580633			0.290316	−	0.956931i	$-0.406239\pi$
$61$	4.53489			0.580633			0.290316	+	0.956931i	$0.406239\pi$
$62$	7.74725	−	7.74725i	0.983901	−	0.983901i
$63$	0.147911	−	1.29263i	0.0186351	−	0.162856i
$64$			1.00000i			0.125000i
$65$	−15.3554	−	0.680204i	−1.90460	−	0.0843689i
$66$	1.54417	−	0.538830i	0.190075	−	0.0663254i
$67$	7.65067	+	7.65067i	0.934678	+	0.934678i	0.997994	−	0.0633153i	$-0.0201674\pi$
$67$	7.65067	+	7.65067i	0.934678	+	0.934678i	−0.0633153	+	0.997994i	$0.520167\pi$
$68$	−2.18295	−	2.18295i	−0.264721	−	0.264721i
$69$	−11.5687	+	4.03683i	−1.39271	+	0.485977i
$70$	−0.654705	−	0.715397i	−0.0782522	−	0.0855062i
$71$			12.9834i			1.54085i	0.637531	+	0.770425i	$0.279956\pi$
$71$			12.9834i			1.54085i	−0.637531	+	0.770425i	$0.720044\pi$
$72$	0.341054	−	2.98055i	0.0401936	−	0.351261i
$73$	2.53764	−	2.53764i	0.297009	−	0.297009i	−0.542832	−	0.839841i	$-0.682648\pi$
$73$	2.53764	−	2.53764i	0.297009	−	0.297009i	0.839841	+	0.542832i	$0.182648\pi$
$74$	4.38149			0.509338
$75$	−7.43597	−	4.43918i	−0.858632	−	0.512593i
$76$	1.00000			0.114708
$77$	−0.289567	+	0.289567i	−0.0329992	+	0.0329992i
$78$	10.7224	+	5.17507i	1.21407	+	0.585961i
$79$		−	9.50297i		−	1.06917i	−0.845115	−	0.534584i	$-0.820468\pi$
$79$		−	9.50297i		−	1.06917i	0.845115	−	0.534584i	$-0.179532\pi$
$80$	−1.50962	−	1.64956i	−0.168780	−	0.184427i
$81$	−2.03306	+	8.76736i	−0.225895	+	0.974152i
$82$	4.30297	+	4.30297i	0.475184	+	0.475184i
$83$	7.84806	+	7.84806i	0.861436	+	0.861436i	0.991505	−	0.130069i	$-0.0415197\pi$
$83$	7.84806	+	7.84806i	0.861436	+	0.861436i	−0.130069	+	0.991505i	$0.541520\pi$
$84$	0.247482	+	0.709233i	0.0270025	+	0.0773836i
$85$	6.89632	+	0.305489i	0.748011	+	0.0331349i
$86$		−	4.52043i		−	0.487451i
$87$	1.33896	−	2.77424i	0.143552	−	0.297430i
$88$	−0.667684	+	0.667684i	−0.0711753	+	0.0711753i
$89$	−8.88554			−0.941866			−0.470933	−	0.882169i	$-0.656083\pi$
$89$	−8.88554			−0.941866			−0.470933	+	0.882169i	$0.656083\pi$
$90$	3.93690	+	5.43146i	0.414986	+	0.572526i
$91$	−2.98113			−0.312507
$92$	5.00219	−	5.00219i	0.521514	−	0.521514i
$93$	8.24852	−	17.0904i	0.855332	−	1.77219i
$94$		−	5.96810i		−	0.615562i
$95$	−1.64956	+	1.50962i	−0.169241	+	0.154884i
$96$	0.570645	+	1.63535i	0.0582412	+	0.166907i
$97$	−0.722973	−	0.722973i	−0.0734067	−	0.0734067i	0.669450	−	0.742857i	$-0.266530\pi$
$97$	−0.722973	−	0.722973i	−0.0734067	−	0.0734067i	−0.742857	+	0.669450i	$0.766530\pi$
$98$	4.81675	+	4.81675i	0.486565	+	0.486565i
$99$	2.21778	−	1.76235i	0.222895	−	0.177123i
$100$	4.98042	+	0.442106i	0.498042	+	0.0442106i
$101$		−	1.65814i		−	0.164991i	−0.996591	−	0.0824956i	$-0.973711\pi$
$101$		−	1.65814i		−	0.164991i	0.996591	−	0.0824956i	$-0.0262890\pi$
$102$	−4.81557	−	2.32419i	−0.476812	−	0.230129i
$103$	−1.69267	+	1.69267i	−0.166784	+	0.166784i	−0.785564	−	0.618780i	$-0.787627\pi$
$103$	−1.69267	+	1.69267i	−0.166784	+	0.166784i	0.618780	+	0.785564i	$0.287627\pi$
$104$	−6.87388			−0.674040
$105$	−1.47891	−	0.796319i	−0.144327	−	0.0777128i
$106$	7.18748			0.698110
$107$	7.42775	−	7.42775i	0.718067	−	0.718067i	−0.250142	−	0.968209i	$-0.580477\pi$
$107$	7.42775	−	7.42775i	0.718067	−	0.718067i	0.968209	+	0.250142i	$0.0804773\pi$
$108$	−1.14309	−	5.06886i	−0.109994	−	0.487751i
$109$			7.49186i			0.717590i	0.933416	+	0.358795i	$0.116812\pi$
$109$			7.49186i			0.717590i	−0.933416	+	0.358795i	$0.883188\pi$
$110$	0.0934379	−	2.10933i	0.00890895	−	0.201117i
$111$	7.16526	−	2.50027i	0.680097	−	0.237315i
$112$	−0.306664	−	0.306664i	−0.0289771	−	0.0289771i
$113$	11.8230	+	11.8230i	1.11222	+	1.11222i	0.992850	+	0.119367i	$0.0380865\pi$
$113$	11.8230	+	11.8230i	1.11222	+	1.11222i	0.119367	+	0.992850i	$0.461913\pi$
$114$	1.63535	−	0.570645i	0.153164	−	0.0534458i
$115$	−0.700022	+	15.8028i	−0.0652774	+	1.47362i
$116$			1.77850i			0.165130i
$117$	20.4880	+	2.34436i	1.89411	+	0.216737i
$118$	−5.32376	+	5.32376i	−0.490092	+	0.490092i
$119$	1.33886			0.122734
$120$	−3.41007	−	1.83615i	−0.311295	−	0.167617i
$121$	10.1084			0.918945
$122$	−3.20665	+	3.20665i	−0.290316	+	0.290316i
$123$	9.49233	+	4.58139i	0.855895	+	0.413090i
$124$			10.9563i			0.983901i
$125$	−8.88291	+	6.78925i	−0.794512	+	0.607249i
$126$	0.809440	+	1.01862i	0.0721106	+	0.0907457i
$127$	1.42736	+	1.42736i	0.126658	+	0.126658i	0.767594	−	0.640936i	$-0.221454\pi$
$127$	1.42736	+	1.42736i	0.126658	+	0.126658i	−0.640936	+	0.767594i	$0.721454\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−2.57956	−	7.39249i	−0.227118	−	0.650872i
$130$	11.3389	−	10.3769i	0.994486	−	0.910117i
$131$			18.5477i			1.62052i	0.586073	+	0.810258i	$0.300673\pi$
$131$			18.5477i			1.62052i	−0.586073	+	0.810258i	$0.699327\pi$
$132$	−0.710886	+	1.47291i	−0.0618746	+	0.128200i
$133$	−0.306664	+	0.306664i	−0.0265912	+	0.0265912i
$134$	−10.8197			−0.934678
$135$	9.53765	+	6.63576i	0.820870	+	0.571115i
$136$	3.08715			0.264721
$137$	2.22249	−	2.22249i	0.189880	−	0.189880i	−0.605764	−	0.795644i	$-0.707132\pi$
$137$	2.22249	−	2.22249i	0.189880	−	0.189880i	0.795644	+	0.605764i	$0.207132\pi$
$138$	5.32585	−	11.0348i	0.453366	−	0.939343i
$139$			18.9629i			1.60841i	0.594350	+	0.804206i	$0.297409\pi$
$139$			18.9629i			1.60841i	−0.594350	+	0.804206i	$0.702591\pi$
$140$	0.968808	+	0.0429156i	0.0818792	+	0.00362703i
$141$	−3.40566	−	9.75992i	−0.286809	−	0.821933i
$142$	−9.18067	−	9.18067i	−0.770425	−	0.770425i
$143$	−4.58958	−	4.58958i	−0.383800	−	0.383800i
$144$	1.86641	+	2.34873i	0.155534	+	0.195727i
$145$	−2.68486	−	2.93375i	−0.222966	−	0.243635i
$146$			3.58877i			0.297009i
$147$	10.6257	+	5.12841i	0.876395	+	0.422984i
$148$	−3.09818	+	3.09818i	−0.254669	+	0.254669i
$149$	12.9585			1.06160			0.530799	−	0.847498i	$-0.321892\pi$
$149$	12.9585			1.06160			0.530799	+	0.847498i	$0.321892\pi$
$150$	8.39700	−	2.11905i	0.685612	−	0.173020i
$151$	4.35166			0.354133			0.177067	−	0.984199i	$-0.443339\pi$
$151$	4.35166			0.354133			0.177067	+	0.984199i	$0.443339\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	−9.20142	−	1.05289i	−0.743891	−	0.0851208i
$154$		−	0.409510i		−	0.0329992i
$155$	−16.5398	−	18.0730i	−1.32851	−	1.45166i
$156$	−11.2412	+	3.92254i	−0.900016	+	0.314055i
$157$	−5.26086	−	5.26086i	−0.419863	−	0.419863i	0.465294	−	0.885156i	$-0.345949\pi$
$157$	−5.26086	−	5.26086i	−0.419863	−	0.419863i	−0.885156	+	0.465294i	$0.845949\pi$
$158$	6.71962	+	6.71962i	0.534584	+	0.534584i
$159$	11.7540	−	4.10150i	0.932156	−	0.325270i
$160$	2.23388	+	0.0989549i	0.176604	+	0.00782307i
$161$			3.06798i			0.241791i
$162$	−4.76187	−	7.63705i	−0.374128	−	0.600023i
$163$	−2.53089	+	2.53089i	−0.198234	+	0.198234i	−0.799243	−	0.601008i	$-0.794766\pi$
$163$	−2.53089	+	2.53089i	−0.198234	+	0.198234i	0.601008	+	0.799243i	$0.294766\pi$
$164$	−6.08532			−0.475184
$165$	−1.05088	−	3.50281i	−0.0818106	−	0.272694i
$166$	−11.0988			−0.861436
$167$	−3.33084	+	3.33084i	−0.257749	+	0.257749i	−0.824138	−	0.566389i	$-0.808340\pi$
$167$	−3.33084	+	3.33084i	−0.257749	+	0.257749i	0.566389	+	0.824138i	$0.308340\pi$
$168$	−0.676500	−	0.326507i	−0.0521931	−	0.0251905i
$169$		−	34.2502i		−	2.63463i
$170$	−5.09245	+	4.66042i	−0.390573	+	0.357438i
$171$	2.34873	−	1.86641i	0.179612	−	0.142728i
$172$	3.19643	+	3.19643i	0.243725	+	0.243725i
$173$	9.61343	+	9.61343i	0.730896	+	0.730896i	0.970797	−	0.239902i	$-0.0771152\pi$
$173$	9.61343	+	9.61343i	0.730896	+	0.730896i	−0.239902	+	0.970797i	$0.577115\pi$
$174$	1.01489	+	2.90847i	0.0769389	+	0.220491i
$175$	−1.66289	+	1.39174i	−0.125703	+	0.105206i
$176$		−	0.944248i		−	0.0711753i
$177$	−5.66823	+	11.7442i	−0.426050	+	0.882746i
$178$	6.28303	−	6.28303i	0.470933	−	0.470933i
$179$	22.6680			1.69429			0.847143	−	0.531365i	$-0.178321\pi$
$179$	22.6680			1.69429			0.847143	+	0.531365i	$0.178321\pi$
$180$	−6.62444	−	1.05681i	−0.493756	−	0.0787702i
$181$	3.95190			0.293743			0.146871	−	0.989156i	$-0.453080\pi$
$181$	3.95190			0.293743			0.146871	+	0.989156i	$0.453080\pi$
$182$	2.10797	−	2.10797i	0.156253	−	0.156253i
$183$	−3.41413	+	7.07384i	−0.252380	+	0.522914i
$184$			7.07416i			0.521514i
$185$	0.433570	−	9.78771i	0.0318767	−	0.719607i
$186$	6.25213	+	17.9173i	0.458429	+	1.31376i
$187$	2.06124	+	2.06124i	0.150733	+	0.150733i
$188$	4.22008	+	4.22008i	0.307781	+	0.307781i
$189$	1.90498	+	1.20389i	0.138567	+	0.0875703i
$190$	0.0989549	−	2.23388i	0.00717894	−	0.162062i
$191$			3.21978i			0.232975i	0.993192	+	0.116487i	$0.0371635\pi$
$191$			3.21978i			0.232975i	−0.993192	+	0.116487i	$0.962837\pi$
$192$	−1.55987	−	0.752859i	−0.112574	−	0.0543329i
$193$	−8.96414	+	8.96414i	−0.645253	+	0.645253i	−0.951842	−	0.306589i	$-0.900812\pi$
$193$	−8.96414	+	8.96414i	−0.645253	+	0.645253i	0.306589	+	0.951842i	$0.400812\pi$
$194$	1.02244			0.0734067
$195$	12.6215	−	23.4404i	0.903844	−	1.67860i
$196$	−6.81191			−0.486565
$197$	6.36112	−	6.36112i	0.453211	−	0.453211i	−0.443208	−	0.896419i	$-0.646160\pi$
$197$	6.36112	−	6.36112i	0.453211	−	0.453211i	0.896419	+	0.443208i	$0.146160\pi$
$198$	−0.322039	+	2.81438i	−0.0228863	+	0.200009i
$199$		−	21.5251i		−	1.52588i	−0.646472	−	0.762938i	$-0.723756\pi$
$199$		−	21.5251i		−	1.52588i	0.646472	−	0.762938i	$-0.276244\pi$
$200$	−3.83430	+	3.20907i	−0.271126	+	0.226915i
$201$	−17.6940	+	6.17419i	−1.24804	+	0.435494i
$202$	1.17248	+	1.17248i	0.0824956	+	0.0824956i
$203$	−0.545404	−	0.545404i	−0.0382798	−	0.0382798i
$204$	5.04857	−	1.76167i	0.353471	−	0.123341i
$205$	10.0381	−	9.18652i	0.701092	−	0.641614i
$206$		−	2.39380i		−	0.166784i
$207$	2.41267	−	21.0849i	0.167692	−	1.46550i
$208$	4.86057	−	4.86057i	0.337020	−	0.337020i
$209$	−0.944248			−0.0653150
$210$	1.60883	−	0.482663i	0.111020	−	0.0333069i
$211$	−1.03406			−0.0711877			−0.0355938	−	0.999366i	$-0.511332\pi$
$211$	−1.03406			−0.0711877			−0.0355938	+	0.999366i	$0.511332\pi$
$212$	−5.08232	+	5.08232i	−0.349055	+	0.349055i
$213$	−20.2525	−	9.77470i	−1.38768	−	0.669751i
$214$			10.5044i			0.718067i
$215$	−10.0981	−	0.447319i	−0.688684	−	0.0305069i
$216$	4.39251	+	2.77594i	0.298873	+	0.188879i
$217$	−3.35989	−	3.35989i	−0.228085	−	0.228085i
$218$	−5.29755	−	5.29755i	−0.358795	−	0.358795i
$219$	2.04791	+	5.86889i	0.138385	+	0.396583i
$220$	1.42545	+	1.55759i	0.0961040	+	0.105013i
$221$			21.2207i			1.42746i
$222$	−3.29864	+	6.83457i	−0.221391	+	0.458706i
$223$	−4.32004	+	4.32004i	−0.289291	+	0.289291i	−0.836800	−	0.547509i	$-0.815576\pi$
$223$	−4.32004	+	4.32004i	−0.289291	+	0.289291i	0.547509	+	0.836800i	$0.315576\pi$
$224$	0.433689			0.0289771
$225$	12.5228	−	8.25709i	0.834853	−	0.550473i
$226$	−16.7203			−1.11222
$227$	−8.83516	+	8.83516i	−0.586410	+	0.586410i	−0.936657	−	0.350247i	$-0.886098\pi$
$227$	−8.83516	+	8.83516i	−0.586410	+	0.586410i	0.350247	+	0.936657i	$0.386098\pi$
$228$	−0.752859	+	1.55987i	−0.0498593	+	0.103305i
$229$			21.6673i			1.43182i	0.698194	+	0.715908i	$0.253987\pi$
$229$			21.6673i			1.43182i	−0.698194	+	0.715908i	$0.746013\pi$
$230$	−10.6793	−	11.6693i	−0.704171	−	0.769448i
$231$	−0.233685	−	0.669691i	−0.0153753	−	0.0440624i
$232$	−1.25759	−	1.25759i	−0.0825649	−	0.0825649i
$233$	−10.5947	−	10.5947i	−0.694079	−	0.694079i	0.269048	−	0.963127i	$-0.413291\pi$
$233$	−10.5947	−	10.5947i	−0.694079	−	0.694079i	−0.963127	+	0.269048i	$0.913291\pi$
$234$	−16.1449	+	12.8295i	−1.05542	+	0.838688i
$235$	−13.3320	−	0.590572i	−0.869683	−	0.0385247i
$236$		−	7.52893i		−	0.490092i
$237$	14.8234	+	7.15440i	0.962885	+	0.464728i
$238$	−0.946720	+	0.946720i	−0.0613668	+	0.0613668i
$239$	11.6073			0.750812			0.375406	−	0.926860i	$-0.377503\pi$
$239$	11.6073			0.750812			0.375406	+	0.926860i	$0.377503\pi$
$240$	3.70964	−	1.11292i	0.239456	−	0.0718390i
$241$	20.6897			1.33274			0.666369	−	0.745622i	$-0.267848\pi$
$241$	20.6897			1.33274			0.666369	+	0.745622i	$0.267848\pi$
$242$	−7.14772	+	7.14772i	−0.459473	+	0.459473i
$243$	−12.1454	−	9.77190i	−0.779126	−	0.626868i
$244$		−	4.53489i		−	0.290316i
$245$	11.2367	−	10.2834i	0.717885	−	0.656982i
$246$	−9.95162	+	3.47256i	−0.634492	+	0.221402i
$247$	−4.86057	−	4.86057i	−0.309271	−	0.309271i
$248$	−7.74725	−	7.74725i	−0.491951	−	0.491951i
$249$	−18.1505	+	6.33349i	−1.15024	+	0.401369i
$250$	1.48045	−	11.0819i	0.0936317	−	0.700880i
$251$		−	15.5598i		−	0.982128i	−0.871123	−	0.491064i	$-0.836608\pi$
$251$		−	15.5598i		−	0.982128i	0.871123	−	0.491064i	$-0.163392\pi$
$252$	−1.29263	−	0.147911i	−0.0814282	−	0.00931754i
$253$	−4.72330	+	4.72330i	−0.296951	+	0.296951i
$254$	−2.01860			−0.126658
$255$	−5.66848	+	10.5274i	−0.354974	+	0.659251i
$256$	1.00000			0.0625000
$257$	−2.98574	+	2.98574i	−0.186245	+	0.186245i	−0.794071	−	0.607825i	$-0.792042\pi$
$257$	−2.98574	+	2.98574i	−0.186245	+	0.186245i	0.607825	+	0.794071i	$0.292042\pi$
$258$	7.05130	+	3.40325i	0.438995	+	0.211877i
$259$		−	1.90020i		−	0.118073i
$260$	−0.680204	+	15.3554i	−0.0421845	+	0.952302i
$261$	3.31941	+	4.17722i	0.205466	+	0.258564i
$262$	−13.1152	−	13.1152i	−0.810258	−	0.810258i
$263$	8.55701	+	8.55701i	0.527648	+	0.527648i	0.919870	−	0.392222i	$-0.128294\pi$
$263$	8.55701	+	8.55701i	0.527648	+	0.527648i	−0.392222	+	0.919870i	$0.628294\pi$
$264$	−0.538830	−	1.54417i	−0.0331627	−	0.0950373i
$265$	0.711236	−	16.0560i	0.0436909	−	0.986309i
$266$		−	0.433689i		−	0.0265912i
$267$	6.68956	−	13.8603i	0.409395	−	0.848237i
$268$	7.65067	−	7.65067i	0.467339	−	0.467339i
$269$	11.0350			0.672814			0.336407	−	0.941717i	$-0.390788\pi$
$269$	11.0350			0.672814			0.336407	+	0.941717i	$0.390788\pi$
$270$	−11.4363	+	2.05194i	−0.695993	+	0.124877i
$271$	−12.1851			−0.740190			−0.370095	−	0.928994i	$-0.620675\pi$
$271$	−12.1851			−0.740190			−0.370095	+	0.928994i	$0.620675\pi$
$272$	−2.18295	+	2.18295i	−0.132361	+	0.132361i
$273$	2.24437	−	4.65018i	0.135835	−	0.281442i
$274$			3.14308i			0.189880i
$275$	−4.70275	−	0.417458i	−0.283586	−	0.0251736i
$276$	4.03683	+	11.5687i	0.242989	+	0.696355i
$277$	4.80867	+	4.80867i	0.288925	+	0.288925i	0.836655	−	0.547730i	$-0.184508\pi$
$277$	4.80867	+	4.80867i	0.288925	+	0.288925i	−0.547730	+	0.836655i	$0.684508\pi$
$278$	−13.4088	−	13.4088i	−0.804206	−	0.804206i
$279$	20.4488	+	25.7333i	1.22424	+	1.54061i
$280$	−0.715397	+	0.654705i	−0.0427531	+	0.0391261i
$281$		−	32.0631i		−	1.91273i	−0.292180	−	0.956363i	$-0.594381\pi$
$281$		−	32.0631i		−	1.91273i	0.292180	−	0.956363i	$-0.405619\pi$
$282$	9.30947	+	4.49314i	0.554371	+	0.267562i
$283$	8.65468	−	8.65468i	0.514467	−	0.514467i	−0.401425	−	0.915892i	$-0.631485\pi$
$283$	8.65468	−	8.65468i	0.514467	−	0.514467i	0.915892	+	0.401425i	$0.131485\pi$
$284$	12.9834			0.770425
$285$	−1.11292	−	3.70964i	−0.0659240	−	0.219740i
$286$	6.49065			0.383800
$287$	1.86615	−	1.86615i	0.110155	−	0.110155i
$288$	−2.98055	−	0.341054i	−0.175631	−	0.0200968i
$289$			7.46948i			0.439381i
$290$	3.97296	+	0.175992i	0.233300	+	0.0103346i
$291$	1.67204	−	0.583449i	0.0980168	−	0.0342024i
$292$	−2.53764	−	2.53764i	−0.148504	−	0.148504i
$293$	−7.19596	−	7.19596i	−0.420392	−	0.420392i	0.464947	−	0.885339i	$-0.346074\pi$
$293$	−7.19596	−	7.19596i	−0.420392	−	0.420392i	−0.885339	+	0.464947i	$0.846074\pi$
$294$	−11.1399	+	3.88718i	−0.649689	+	0.226705i
$295$	11.3658	+	12.4194i	0.661743	+	0.723087i
$296$		−	4.38149i		−	0.254669i
$297$	1.07936	+	4.78626i	0.0626310	+	0.277727i
$298$	−9.16302	+	9.16302i	−0.530799	+	0.530799i
$299$	−48.6269			−2.81217
$300$	−4.43918	+	7.43597i	−0.256296	+	0.429316i
$301$	−1.96046			−0.112999
$302$	−3.07709	+	3.07709i	−0.177067	+	0.177067i
$303$	2.58649	+	1.24835i	0.148590	+	0.0717156i
$304$		−	1.00000i		−	0.0573539i
$305$	6.84595	+	7.48057i	0.391998	+	0.428336i
$306$	7.25089	−	5.76188i	0.414506	−	0.329385i
$307$	−1.61182	−	1.61182i	−0.0919916	−	0.0919916i	0.659613	−	0.751605i	$-0.270720\pi$
$307$	−1.61182	−	1.61182i	−0.0919916	−	0.0919916i	−0.751605	+	0.659613i	$0.770720\pi$
$308$	0.289567	+	0.289567i	0.0164996	+	0.0164996i
$309$	−1.36601	−	3.91469i	−0.0777094	−	0.222699i
$310$	24.4749	+	1.08418i	1.39008	+	0.0615770i
$311$		−	24.1698i		−	1.37055i	−0.728286	−	0.685273i	$-0.759683\pi$
$311$		−	24.1698i		−	1.37055i	0.728286	−	0.685273i	$-0.240317\pi$
$312$	5.17507	−	10.7224i	0.292980	−	0.607035i
$313$	−20.5330	+	20.5330i	−1.16059	+	1.16059i	−0.176245	+	0.984346i	$0.556395\pi$
$313$	−20.5330	+	20.5330i	−1.16059	+	1.16059i	−0.984346	+	0.176245i	$0.943605\pi$
$314$	7.43999			0.419863
$315$	2.35557	−	1.70739i	0.132721	−	0.0962006i
$316$	−9.50297			−0.534584
$317$	−18.3162	+	18.3162i	−1.02874	+	1.02874i	−0.0291663	+	0.999575i	$0.509285\pi$
$317$	−18.3162	+	18.3162i	−1.02874	+	1.02874i	−0.999575	+	0.0291663i	$0.990715\pi$
$318$	−5.41116	+	11.2116i	−0.303443	+	0.628713i
$319$		−	1.67935i		−	0.0940254i
$320$	−1.64956	+	1.50962i	−0.0922133	+	0.0843902i
$321$	5.99429	+	17.1784i	0.334569	+	0.958804i
$322$	−2.16939	−	2.16939i	−0.120896	−	0.120896i
$323$	2.18295	+	2.18295i	0.121462	+	0.121462i
$324$	8.76736	+	2.03306i	0.487076	+	0.112948i
$325$	−22.0588	−	26.3565i	−1.22360	−	1.46200i
$326$		−	3.57921i		−	0.198234i
$327$	−11.6864	−	5.64032i	−0.646257	−	0.311910i
$328$	4.30297	−	4.30297i	0.237592	−	0.237592i
$329$	−2.58830			−0.142697
$330$	3.21995	+	1.73378i	0.177252	+	0.0954416i
$331$	16.5637			0.910424			0.455212	−	0.890383i	$-0.349563\pi$
$331$	16.5637			0.910424			0.455212	+	0.890383i	$0.349563\pi$
$332$	7.84806	−	7.84806i	0.430718	−	0.430718i
$333$	−1.49432	+	13.0593i	−0.0818885	+	0.715643i
$334$		−	4.71053i		−	0.257749i
$335$	−1.07066	+	24.1698i	−0.0584964	+	1.32054i
$336$	0.709233	−	0.247482i	0.0386918	−	0.0135013i
$337$	25.3948	+	25.3948i	1.38334	+	1.38334i	0.838608	+	0.544735i	$0.183370\pi$
$337$	25.3948	+	25.3948i	1.38334	+	1.38334i	0.544735	+	0.838608i	$0.316630\pi$
$338$	24.2186	+	24.2186i	1.31732	+	1.31732i
$339$	−27.3435	+	9.54135i	−1.48510	+	0.518215i
$340$	0.305489	−	6.89632i	0.0165675	−	0.374006i
$341$		−	10.3454i		−	0.560236i
$342$	−0.341054	+	2.98055i	−0.0184421	+	0.161170i
$343$	4.23562	−	4.23562i	0.228702	−	0.228702i
$344$	−4.52043			−0.243725
$345$	−24.1233	−	12.9892i	−1.29876	−	0.699317i
$346$	−13.5954			−0.730896
$347$	5.68399	−	5.68399i	0.305133	−	0.305133i	−0.537885	−	0.843018i	$-0.680777\pi$
$347$	5.68399	−	5.68399i	0.305133	−	0.305133i	0.843018	+	0.537885i	$0.180777\pi$
$348$	−2.77424	−	1.33896i	−0.148715	−	0.0717759i
$349$		−	18.1493i		−	0.971512i	−0.874094	−	0.485756i	$-0.838544\pi$
$349$		−	18.1493i		−	0.971512i	0.874094	−	0.485756i	$-0.161456\pi$
$350$	0.191737	−	2.15995i	0.0102487	−	0.115454i
$351$	−19.0815	+	30.1936i	−1.01849	+	1.61162i
$352$	0.667684	+	0.667684i	0.0355877	+	0.0355877i
$353$	−8.86486	−	8.86486i	−0.471829	−	0.471829i	0.430677	−	0.902506i	$-0.358275\pi$
$353$	−8.86486	−	8.86486i	−0.471829	−	0.471829i	−0.902506	+	0.430677i	$0.858275\pi$
$354$	−4.29635	−	12.3124i	−0.228348	−	0.654398i
$355$	−21.4170	+	19.6000i	−1.13669	+	1.04026i
$356$			8.88554i			0.470933i
$357$	−1.00798	+	2.08846i	−0.0533478	+	0.110533i
$358$	−16.0287	+	16.0287i	−0.847143	+	0.847143i
$359$	−10.7838			−0.569150			−0.284575	−	0.958654i	$-0.591852\pi$
$359$	−10.7838			−0.569150			−0.284575	+	0.958654i	$0.591852\pi$
$360$	5.43146	−	3.93690i	0.286263	−	0.207493i
$361$	−1.00000			−0.0526316
$362$	−2.79442	+	2.79442i	−0.146871	+	0.146871i
$363$	−7.61020	+	15.7678i	−0.399432	+	0.827596i
$364$			2.98113i			0.156253i
$365$	8.01687	+	0.355126i	0.419622	+	0.0185882i
$366$	−2.58781	−	7.41612i	−0.135267	−	0.387647i
$367$	−9.27545	−	9.27545i	−0.484175	−	0.484175i	0.422287	−	0.906462i	$-0.361227\pi$
$367$	−9.27545	−	9.27545i	−0.484175	−	0.484175i	−0.906462	+	0.422287i	$0.861227\pi$
$368$	−5.00219	−	5.00219i	−0.260757	−	0.260757i
$369$	−14.2928	+	11.3577i	−0.744052	+	0.591257i
$370$	6.61438	+	7.22754i	0.343865	+	0.375742i
$371$		−	3.11713i		−	0.161833i
$372$	−17.0904	−	8.24852i	−0.886094	−	0.427666i
$373$	−4.66943	+	4.66943i	−0.241774	+	0.241774i	−0.817584	−	0.575810i	$-0.804687\pi$
$373$	−4.66943	+	4.66943i	−0.241774	+	0.241774i	0.575810	+	0.817584i	$0.304687\pi$
$374$	−2.91504			−0.150733
$375$	−3.90277	−	18.9676i	−0.201538	−	0.979481i
$376$	−5.96810			−0.307781
$377$	8.64454	−	8.64454i	0.445216	−	0.445216i
$378$	−2.19831	+	0.495747i	−0.113069	+	0.0254985i
$379$		−	21.6246i		−	1.11078i	−0.831590	−	0.555390i	$-0.812569\pi$
$379$		−	21.6246i		−	1.11078i	0.831590	−	0.555390i	$-0.187431\pi$
$380$	1.50962	+	1.64956i	0.0774418	+	0.0846207i
$381$	−3.30111	+	1.15190i	−0.169121	+	0.0590138i
$382$	−2.27673	−	2.27673i	−0.116487	−	0.116487i
$383$	19.8243	+	19.8243i	1.01297	+	1.01297i	0.999915	+	0.0130600i	$0.00415723\pi$
$383$	19.8243	+	19.8243i	1.01297	+	1.01297i	0.0130600	+	0.999915i	$0.495843\pi$
$384$	1.63535	−	0.570645i	0.0834535	−	0.0291206i
$385$	−0.914795	−	0.0405230i	−0.0466222	−	0.00206524i
$386$		−	12.6772i		−	0.645253i
$387$	13.4734	+	1.54171i	0.684891	+	0.0783696i
$388$	−0.722973	+	0.722973i	−0.0367034	+	0.0367034i
$389$	18.0320			0.914258			0.457129	−	0.889400i	$-0.348878\pi$
$389$	18.0320			0.914258			0.457129	+	0.889400i	$0.348878\pi$
$390$	7.65011	+	25.4996i	0.387378	+	1.29122i
$391$	21.8390			1.10445
$392$	4.81675	−	4.81675i	0.243283	−	0.243283i
$393$	−28.9320	−	13.9638i	−1.45943	−	0.704379i
$394$			8.99598i			0.453211i
$395$	15.6757	−	14.3459i	0.788732	−	0.721819i
$396$	−1.76235	−	2.21778i	−0.0885614	−	0.111448i
$397$	−15.1322	−	15.1322i	−0.759462	−	0.759462i	0.216763	−	0.976224i	$-0.430450\pi$
$397$	−15.1322	−	15.1322i	−0.759462	−	0.759462i	−0.976224	+	0.216763i	$0.930450\pi$
$398$	15.2206	+	15.2206i	0.762938	+	0.762938i
$399$	−0.247482	−	0.709233i	−0.0123896	−	0.0355060i
$400$	0.442106	−	4.98042i	0.0221053	−	0.249021i
$401$		−	10.1310i		−	0.505916i	−0.967477	−	0.252958i	$-0.918597\pi$
$401$		−	10.1310i		−	0.505916i	0.967477	−	0.252958i	$-0.0814034\pi$
$402$	8.14570	−	16.8773i	0.406270	−	0.841765i
$403$	53.2536	−	53.2536i	2.65275	−	2.65275i
$404$	−1.65814			−0.0824956
$405$	−17.5314	+	9.88172i	−0.871145	+	0.491027i
$406$	0.771317			0.0382798
$407$	2.92545	−	2.92545i	0.145009	−	0.145009i
$408$	−2.32419	+	4.81557i	−0.115065	+	0.238406i
$409$		−	8.93136i		−	0.441627i	−0.975316	−	0.220814i	$-0.929129\pi$
$409$		−	8.93136i		−	0.441627i	0.975316	−	0.220814i	$-0.0708713\pi$
$410$	−0.602172	+	13.5939i	−0.0297392	+	0.671353i
$411$	1.79358	+	5.14003i	0.0884709	+	0.253539i
$412$	1.69267	+	1.69267i	0.0833918	+	0.0833918i
$413$	2.30886	+	2.30886i	0.113611	+	0.113611i
$414$	13.2033	+	16.6153i	0.648904	+	0.816597i
$415$	−1.09828	+	24.7934i	−0.0539126	+	1.21706i
$416$			6.87388i			0.337020i
$417$	−29.5797	−	14.2764i	−1.44853	−	0.699118i
$418$	0.667684	−	0.667684i	0.0326575	−	0.0326575i
$419$	20.6060			1.00667			0.503333	−	0.864092i	$-0.332107\pi$
$419$	20.6060			1.00667			0.503333	+	0.864092i	$0.332107\pi$
$420$	−0.796319	+	1.47891i	−0.0388564	+	0.0721633i
$421$	15.1039			0.736120			0.368060	−	0.929802i	$-0.380022\pi$
$421$	15.1039			0.736120			0.368060	+	0.929802i	$0.380022\pi$
$422$	0.731191	−	0.731191i	0.0355938	−	0.0355938i
$423$	17.7882	+	2.03544i	0.864892	+	0.0989666i
$424$		−	7.18748i		−	0.349055i
$425$	9.90689	+	11.8371i	0.480555	+	0.574183i
$426$	21.2324	−	7.40893i	1.02871	−	0.358964i
$427$	1.39069	+	1.39069i	0.0673001	+	0.0673001i
$428$	−7.42775	−	7.42775i	−0.359034	−	0.359034i
$429$	10.6145	−	3.70385i	0.512471	−	0.178824i
$430$	7.45673	−	6.82413i	0.359596	−	0.329089i
$431$		−	7.39471i		−	0.356191i	−0.984013	−	0.178095i	$-0.943006\pi$
$431$		−	7.39471i		−	0.356191i	0.984013	−	0.178095i	$-0.0569936\pi$
$432$	−5.06886	+	1.14309i	−0.243876	+	0.0549971i
$433$	−6.52218	+	6.52218i	−0.313436	+	0.313436i	−0.846239	−	0.532803i	$-0.821139\pi$
$433$	−6.52218	+	6.52218i	−0.313436	+	0.313436i	0.532803	+	0.846239i	$0.321139\pi$
$434$	4.75161			0.228085
$435$	6.59760	−	1.97934i	0.316331	−	0.0949021i
$436$	7.49186			0.358795
$437$	−5.00219	+	5.00219i	−0.239287	+	0.239287i
$438$	−5.59802	−	2.70184i	−0.267484	−	0.129099i
$439$			32.0835i			1.53126i	0.643279	+	0.765632i	$0.277574\pi$
$439$			32.0835i			1.53126i	−0.643279	+	0.765632i	$0.722426\pi$
$440$	−2.10933	−	0.0934379i	−0.100559	−	0.00445448i
$441$	−15.9993	+	12.7138i	−0.761873	+	0.605419i
$442$	−15.0053	−	15.0053i	−0.713730	−	0.713730i
$443$	5.56755	+	5.56755i	0.264522	+	0.264522i	0.826888	−	0.562366i	$-0.190109\pi$
$443$	5.56755	+	5.56755i	0.264522	+	0.264522i	−0.562366	+	0.826888i	$0.690109\pi$
$444$	−2.50027	−	7.16526i	−0.118658	−	0.340048i
$445$	−13.4138	−	14.6572i	−0.635874	−	0.694820i
$446$		−	6.10946i		−	0.289291i
$447$	−9.75590	+	20.2136i	−0.461438	+	0.956068i
$448$	−0.306664	+	0.306664i	−0.0144885	+	0.0144885i
$449$	22.1426			1.04497			0.522487	−	0.852647i	$-0.325004\pi$
$449$	22.1426			1.04497			0.522487	+	0.852647i	$0.325004\pi$
$450$	−3.01631	+	14.6936i	−0.142190	+	0.692663i
$451$	5.74605			0.270571
$452$	11.8230	−	11.8230i	0.556109	−	0.556109i
$453$	−3.27619	+	6.78804i	−0.153929	+	0.318930i
$454$		−	12.4948i		−	0.586410i
$455$	−4.50036	−	4.91755i	−0.210980	−	0.230538i
$456$	−0.570645	−	1.63535i	−0.0267229	−	0.0765822i
$457$	1.27154	+	1.27154i	0.0594803	+	0.0594803i	0.736221	−	0.676741i	$-0.236608\pi$
$457$	1.27154	+	1.27154i	0.0594803	+	0.0594803i	−0.676741	+	0.736221i	$0.736608\pi$
$458$	−15.3211	−	15.3211i	−0.715908	−	0.715908i
$459$	8.56974	−	13.5604i	0.400001	−	0.632944i
$460$	15.8028	+	0.700022i	0.736809	+	0.0326387i
$461$		−	31.2805i		−	1.45688i	−0.685111	−	0.728439i	$-0.740246\pi$
$461$		−	31.2805i		−	1.45688i	0.685111	−	0.728439i	$-0.259754\pi$
$462$	0.638783	+	0.308303i	0.0297189	+	0.0143436i
$463$	12.3092	−	12.3092i	0.572056	−	0.572056i	−0.360647	−	0.932702i	$-0.617444\pi$
$463$	12.3092	−	12.3092i	0.572056	−	0.572056i	0.932702	+	0.360647i	$0.117444\pi$
$464$	1.77850			0.0825649
$465$	40.6437	−	12.1935i	1.88481	−	0.565460i
$466$	14.9831			0.694079
$467$	−3.08706	+	3.08706i	−0.142852	+	0.142852i	−0.774916	−	0.632064i	$-0.782208\pi$
$467$	−3.08706	+	3.08706i	−0.142852	+	0.142852i	0.632064	+	0.774916i	$0.282208\pi$
$468$	2.34436	−	20.4880i	0.108368	−	0.947056i
$469$			4.69238i			0.216674i
$470$	9.84474	−	9.00955i	0.454104	−	0.415579i
$471$	12.1670	−	4.24559i	0.560624	−	0.195626i
$472$	5.32376	+	5.32376i	0.245046	+	0.245046i
$473$	−3.01822	−	3.01822i	−0.138778	−	0.138778i
$474$	−15.5407	+	5.42282i	−0.713807	+	0.249078i
$475$	−4.98042	−	0.442106i	−0.228517	−	0.0202852i
$476$		−	1.33886i		−	0.0613668i
$477$	−2.45132	+	21.4227i	−0.112238	+	0.980876i
$478$	−8.20758	+	8.20758i	−0.375406	+	0.375406i
$479$	−3.14915			−0.143888			−0.0719441	−	0.997409i	$-0.522920\pi$
$479$	−3.14915			−0.143888			−0.0719441	+	0.997409i	$0.522920\pi$
$480$	−1.83615	+	3.41007i	−0.0838085	+	0.155647i
$481$	30.1178			1.37326
$482$	−14.6298	+	14.6298i	−0.666369	+	0.666369i
$483$	−4.78567	−	2.30976i	−0.217755	−	0.105098i
$484$		−	10.1084i		−	0.459473i
$485$	0.101175	−	2.28400i	0.00459413	−	0.103711i
$486$	15.4978	−	1.67829i	0.702997	−	0.0761289i
$487$	−14.2900	−	14.2900i	−0.647541	−	0.647541i	0.304857	−	0.952398i	$-0.401391\pi$
$487$	−14.2900	−	14.2900i	−0.647541	−	0.647541i	−0.952398	+	0.304857i	$0.901391\pi$
$488$	3.20665	+	3.20665i	0.145158	+	0.145158i
$489$	−2.04246	−	5.85326i	−0.0923632	−	0.264694i
$490$	−0.674072	+	15.2170i	−0.0304515	+	0.687433i
$491$			3.56231i			0.160765i	0.996764	+	0.0803823i	$0.0256141\pi$
$491$			3.56231i			0.160765i	−0.996764	+	0.0803823i	$0.974386\pi$
$492$	4.58139	−	9.49233i	0.206545	−	0.427947i
$493$	−3.88238	+	3.88238i	−0.174854	+	0.174854i
$494$	6.87388			0.309271
$495$	6.25511	+	0.997893i	0.281146	+	0.0448520i
$496$	10.9563			0.491951
$497$	−3.98156	+	3.98156i	−0.178597	+	0.178597i
$498$	8.35586	−	17.3128i	0.374435	−	0.775804i
$499$		−	22.7927i		−	1.02034i	−0.860074	−	0.510170i	$-0.829583\pi$
$499$		−	22.7927i		−	1.02034i	0.860074	−	0.510170i	$-0.170417\pi$
$500$	6.78925	+	8.88291i	0.303624	+	0.397256i
$501$	−2.68804	−	7.70335i	−0.120093	−	0.344160i
$502$	11.0025	+	11.0025i	0.491064	+	0.491064i
$503$	2.87058	+	2.87058i	0.127993	+	0.127993i	0.768201	−	0.640208i	$-0.221152\pi$
$503$	2.87058	+	2.87058i	0.127993	+	0.127993i	−0.640208	+	0.768201i	$0.721152\pi$
$504$	1.01862	−	0.809440i	0.0453728	−	0.0360553i
$505$	2.73521	−	2.50316i	0.121715	−	0.111389i
$506$		−	6.67976i		−	0.296951i
$507$	53.4260	+	25.7856i	2.37273	+	1.14518i
$508$	1.42736	−	1.42736i	0.0633291	−	0.0633291i
$509$	−12.2215			−0.541709			−0.270854	−	0.962620i	$-0.587306\pi$
$509$	−12.2215			−0.541709			−0.270854	+	0.962620i	$0.587306\pi$
$510$	−3.43577	−	11.4522i	−0.152138	−	0.507113i
$511$	1.55641			0.0688515
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.14309	+	5.06886i	0.0504688	+	0.223796i
$514$		−	4.22247i		−	0.186245i
$515$	−5.34745	−	0.236878i	−0.235637	−	0.0104381i
$516$	−7.39249	+	2.57956i	−0.325436	+	0.113559i
$517$	−3.98480	−	3.98480i	−0.175251	−	0.175251i
$518$	1.34365	+	1.34365i	0.0590365	+	0.0590365i
$519$	−22.2333	+	7.75817i	−0.975933	+	0.340546i
$520$	−10.3769	−	11.3389i	−0.455059	−	0.497243i
$521$			41.4157i			1.81446i	0.420639	+	0.907228i	$0.361806\pi$
$521$			41.4157i			1.81446i	−0.420639	+	0.907228i	$0.638194\pi$
$522$	−5.30092	−	0.606566i	−0.232015	−	0.0265487i
$523$	−0.411090	+	0.411090i	−0.0179757	+	0.0179757i	−0.716038	−	0.698062i	$-0.754046\pi$
$523$	−0.411090	+	0.411090i	−0.0179757	+	0.0179757i	0.698062	+	0.716038i	$0.254046\pi$
$524$	18.5477			0.810258
$525$	−0.919009	−	3.64169i	−0.0401088	−	0.158936i
$526$	−12.1014			−0.527648
$527$	−23.9169	+	23.9169i	−1.04184	+	1.04184i
$528$	1.47291	+	0.710886i	0.0641000	+	0.0309373i
$529$			27.0437i			1.17581i
$530$	10.8504	+	11.8562i	0.471309	+	0.515000i
$531$	−14.0520	−	17.6834i	−0.609807	−	0.767395i
$532$	0.306664	+	0.306664i	0.0132956	+	0.0132956i
$533$	29.5781	+	29.5781i	1.28117	+	1.28117i
$534$	5.07049	+	14.5310i	0.219421	+	0.628816i
$535$	23.4656	+	1.03946i	1.01451	+	0.0449399i
$536$			10.8197i			0.467339i
$537$	−17.0658	+	35.3592i	−0.736444	+	1.52586i
$538$	−7.80290	+	7.80290i	−0.336407	+	0.336407i
$539$	6.43213			0.277052
$540$	6.63576	−	9.53765i	0.285558	−	0.410435i
$541$	−0.975280			−0.0419306			−0.0209653	−	0.999780i	$-0.506674\pi$
$541$	−0.975280			−0.0419306			−0.0209653	+	0.999780i	$0.506674\pi$
$542$	8.61614	−	8.61614i	0.370095	−	0.370095i
$543$	−2.97523	+	6.16447i	−0.127679	+	0.264543i
$544$		−	3.08715i		−	0.132361i
$545$	−12.3583	+	11.3099i	−0.529371	+	0.484461i
$546$	1.70116	+	4.87518i	0.0728031	+	0.208638i
$547$	−8.86543	−	8.86543i	−0.379058	−	0.379058i	0.491704	−	0.870762i	$-0.336374\pi$
$547$	−8.86543	−	8.86543i	−0.379058	−	0.379058i	−0.870762	+	0.491704i	$0.836374\pi$
$548$	−2.22249	−	2.22249i	−0.0949402	−	0.0949402i
$549$	−8.46394	−	10.6512i	−0.361232	−	0.454583i
$550$	3.62053	−	3.03016i	0.154380	−	0.129206i
$551$		−	1.77850i		−	0.0757668i
$552$	−11.0348	−	5.32585i	−0.469672	−	0.226683i
$553$	2.91422	−	2.91422i	0.123925	−	0.123925i
$554$	−6.80049			−0.288925
$555$	14.9412	+	8.04508i	0.634217	+	0.341495i
$556$	18.9629			0.804206
$557$	−18.8971	+	18.8971i	−0.800694	+	0.800694i	−0.983204	−	0.182510i	$-0.941578\pi$
$557$	−18.8971	+	18.8971i	−0.800694	+	0.800694i	0.182510	+	0.983204i	$0.441578\pi$
$558$	−32.6557	−	3.73668i	−1.38243	−	0.158186i
$559$		−	31.0729i		−	1.31424i
$560$	0.0429156	−	0.968808i	0.00181352	−	0.0409396i
$561$	−4.76710	+	1.66345i	−0.201267	+	0.0702310i
$562$	22.6721	+	22.6721i	0.956363	+	0.956363i
$563$	−1.06006	−	1.06006i	−0.0446761	−	0.0446761i	0.684416	−	0.729092i	$-0.260057\pi$
$563$	−1.06006	−	1.06006i	−0.0446761	−	0.0446761i	−0.729092	+	0.684416i	$0.760057\pi$
$564$	−9.75992	+	3.40566i	−0.410967	+	0.143404i
$565$	−1.65455	+	37.3511i	−0.0696076	+	1.57137i
$566$			12.2396i			0.514467i
$567$	−3.31210	+	2.06517i	−0.139095	+	0.0867291i
$568$	−9.18067	+	9.18067i	−0.385212	+	0.385212i
$569$	−5.21442			−0.218600			−0.109300	−	0.994009i	$-0.534861\pi$
$569$	−5.21442			−0.218600			−0.109300	+	0.994009i	$0.534861\pi$
$570$	3.41007	+	1.83615i	0.142832	+	0.0769080i
$571$	27.0533			1.13215			0.566073	−	0.824355i	$-0.308462\pi$
$571$	27.0533			1.13215			0.566073	+	0.824355i	$0.308462\pi$
$572$	−4.58958	+	4.58958i	−0.191900	+	0.191900i
$573$	−5.02244	−	2.42404i	−0.209816	−	0.101266i
$574$			2.63914i			0.110155i
$575$	−27.1245	+	22.7015i	−1.13117	+	0.946717i
$576$	2.34873	−	1.86641i	0.0978637	−	0.0777669i
$577$	−31.9330	−	31.9330i	−1.32939	−	1.32939i	−0.905903	−	0.423484i	$-0.860807\pi$
$577$	−31.9330	−	31.9330i	−1.32939	−	1.32939i	−0.423484	−	0.905903i	$-0.639193\pi$
$578$	−5.28172	−	5.28172i	−0.219691	−	0.219691i
$579$	−7.23419	−	20.7317i	−0.300642	−	0.861578i
$580$	−2.93375	+	2.68486i	−0.121817	+	0.111483i
$581$			4.81344i			0.199695i
$582$	−0.769752	+	1.59487i	−0.0319072	+	0.0661096i
$583$	4.79897	−	4.79897i	0.198753	−	0.198753i
$584$	3.58877			0.148504
$585$	27.0618	+	37.3352i	1.11887	+	1.54362i
$586$	10.1766			0.420392
$587$	4.54157	−	4.54157i	0.187450	−	0.187450i	−0.607142	−	0.794593i	$-0.707684\pi$
$587$	4.54157	−	4.54157i	0.187450	−	0.187450i	0.794593	+	0.607142i	$0.207684\pi$
$588$	5.12841	−	10.6257i	0.211492	−	0.438197i
$589$		−	10.9563i		−	0.451445i
$590$	−16.8187	−	0.745024i	−0.692415	−	0.0306722i
$591$	5.13351	+	14.7116i	0.211164	+	0.605153i
$592$	3.09818	+	3.09818i	0.127334	+	0.127334i
$593$	6.70785	+	6.70785i	0.275458	+	0.275458i	0.831293	−	0.555835i	$-0.187601\pi$
$593$	6.70785	+	6.70785i	0.275458	+	0.275458i	−0.555835	+	0.831293i	$0.687601\pi$
$594$	−4.14762	−	2.62117i	−0.170179	−	0.107548i
$595$	2.02117	+	2.20854i	0.0828601	+	0.0905413i
$596$		−	12.9585i		−	0.530799i
$597$	33.5765	+	16.2054i	1.37419	+	0.663243i
$598$	34.3844	−	34.3844i	1.40608	−	1.40608i
$599$	−25.3428			−1.03548			−0.517740	−	0.855538i	$-0.673226\pi$
$599$	−25.3428			−1.03548			−0.517740	+	0.855538i	$0.673226\pi$
$600$	−2.11905	−	8.39700i	−0.0865099	−	0.342806i
$601$	10.1452			0.413833			0.206916	−	0.978359i	$-0.433657\pi$
$601$	10.1452			0.413833			0.206916	+	0.978359i	$0.433657\pi$
$602$	1.38626	−	1.38626i	0.0564996	−	0.0564996i
$603$	3.69010	−	32.2486i	0.150272	−	1.31327i
$604$		−	4.35166i		−	0.177067i
$605$	15.2598	+	16.6744i	0.620400	+	0.677912i
$606$	−2.71164	+	0.946209i	−0.110153	+	0.0384371i
$607$	16.7036	+	16.7036i	0.677979	+	0.677979i	0.959543	−	0.281564i	$-0.0908530\pi$
$607$	16.7036	+	16.7036i	0.677979	+	0.677979i	−0.281564	+	0.959543i	$0.590853\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$	1.26137	−	0.440148i	0.0511134	−	0.0178357i
$610$	−10.1304	−	0.448749i	−0.410167	−	0.0181693i
$611$		−	41.0240i		−	1.65965i
$612$	−1.05289	+	9.20142i	−0.0425604	+	0.371945i
$613$	22.7706	−	22.7706i	0.919695	−	0.919695i	−0.0773118	−	0.997007i	$-0.524634\pi$
$613$	22.7706	−	22.7706i	0.919695	−	0.919695i	0.997007	+	0.0773118i	$0.0246337\pi$
$614$	2.27946			0.0919916
$615$	6.77251	+	22.5743i	0.273094	+	0.910285i
$616$	−0.409510			−0.0164996
$617$	−6.58274	+	6.58274i	−0.265011	+	0.265011i	−0.827086	−	0.562075i	$-0.810003\pi$
$617$	−6.58274	+	6.58274i	−0.265011	+	0.265011i	0.562075	+	0.827086i	$0.310003\pi$
$618$	3.73402	+	1.80219i	0.150204	+	0.0724948i
$619$			27.5771i			1.10842i	0.832378	+	0.554209i	$0.186979\pi$
$619$			27.5771i			1.10842i	−0.832378	+	0.554209i	$0.813021\pi$
$620$	−18.0730	+	16.5398i	−0.725830	+	0.664253i
$621$	31.0733	+	19.6374i	1.24693	+	0.788022i
$622$	17.0907	+	17.0907i	0.685273	+	0.685273i
$623$	−2.72488	−	2.72488i	−0.109170	−	0.109170i
$624$	3.92254	+	11.2412i	0.157027	+	0.450008i
$625$	−24.6091	−	4.40374i	−0.984363	−	0.176150i
$626$		−	29.0380i		−	1.16059i
$627$	0.710886	−	1.47291i	0.0283900	−	0.0588222i
$628$	−5.26086	+	5.26086i	−0.209931	+	0.209931i
$629$	−13.5263			−0.539330
$630$	−0.458328	+	2.87294i	−0.0182602	+	0.114461i
$631$	−30.6726			−1.22106			−0.610529	−	0.791994i	$-0.709043\pi$
$631$	−30.6726			−1.22106			−0.610529	+	0.791994i	$0.709043\pi$
$632$	6.71962	−	6.71962i	0.267292	−	0.267292i
$633$	0.778502	−	1.61300i	0.0309427	−	0.0641111i
$634$		−	25.9030i		−	1.02874i
$635$	−0.199750	+	4.50930i	−0.00792684	+	0.178946i
$636$	−4.10150	−	11.7540i	−0.162635	−	0.466078i
$637$	33.1098	+	33.1098i	1.31186	+	1.31186i
$638$	1.18748	+	1.18748i	0.0470127	+	0.0470127i
$639$	30.4946	−	24.2324i	1.20635	−	0.958617i
$640$	0.0989549	−	2.23388i	0.00391153	−	0.0883018i
$641$		−	49.7149i		−	1.96362i	−0.189862	−	0.981811i	$-0.560804\pi$
$641$		−	49.7149i		−	1.96362i	0.189862	−	0.981811i	$-0.439196\pi$
$642$	−16.3856	−	7.90835i	−0.646686	−	0.312118i
$643$	−2.40899	+	2.40899i	−0.0950012	+	0.0950012i	−0.753010	−	0.658009i	$-0.771399\pi$
$643$	−2.40899	+	2.40899i	−0.0950012	+	0.0950012i	0.658009	+	0.753010i	$0.271399\pi$
$644$	3.06798			0.120896
$645$	8.30021	−	15.4150i	0.326820	−	0.606964i
$646$	−3.08715			−0.121462
$647$	−5.87644	+	5.87644i	−0.231027	+	0.231027i	−0.813121	−	0.582094i	$-0.802233\pi$
$647$	−5.87644	+	5.87644i	−0.231027	+	0.231027i	0.582094	+	0.813121i	$0.302233\pi$
$648$	−7.63705	+	4.76187i	−0.300012	+	0.187064i
$649$			7.10918i			0.279060i
$650$	34.2348	+	3.03898i	1.34280	+	0.119199i
$651$	7.77054	−	2.71148i	0.304551	−	0.106271i
$652$	2.53089	+	2.53089i	0.0991172	+	0.0991172i
$653$	−6.59638	−	6.59638i	−0.258136	−	0.258136i	0.566159	−	0.824296i	$-0.308429\pi$
$653$	−6.59638	−	6.59638i	−0.258136	−	0.258136i	−0.824296	+	0.566159i	$0.808429\pi$
$654$	12.2518	−	4.27519i	0.479084	−	0.167173i
$655$	−30.5955	+	27.9999i	−1.19547	+	1.09405i
$656$			6.08532i			0.237592i
$657$	−10.6965	−	1.22396i	−0.417311	−	0.0477514i
$658$	1.83020	−	1.83020i	0.0713487	−	0.0713487i
$659$	26.7046			1.04026			0.520132	−	0.854086i	$-0.325883\pi$
$659$	26.7046			1.04026			0.520132	+	0.854086i	$0.325883\pi$
$660$	−3.50281	+	1.05088i	−0.136347	+	0.0409053i
$661$	−20.8028			−0.809135			−0.404568	−	0.914508i	$-0.632578\pi$
$661$	−20.8028			−0.809135			−0.404568	+	0.914508i	$0.632578\pi$
$662$	−11.7123	+	11.7123i	−0.455212	+	0.455212i
$663$	−33.1016	−	15.9762i	−1.28556	−	0.620465i
$664$			11.0988i			0.430718i
$665$	−0.968808	−	0.0429156i	−0.0375688	−	0.00166420i
$666$	−8.17764	−	10.2909i	−0.316877	−	0.398766i
$667$	−8.89640	−	8.89640i	−0.344470	−	0.344470i
$668$	3.33084	+	3.33084i	0.128874	+	0.128874i
$669$	−3.48633	−	9.99110i	−0.134789	−	0.386278i
$670$	−16.3336	−	17.8477i	−0.631022	−	0.689518i
$671$			4.28205i			0.165307i
$672$	−0.326507	+	0.676500i	−0.0125953	+	0.0260965i
$673$	29.5002	−	29.5002i	1.13715	−	1.13715i	0.148188	−	0.988959i	$-0.452656\pi$
$673$	29.5002	−	29.5002i	1.13715	−	1.13715i	0.988959	−	0.148188i	$-0.0473442\pi$
$674$	−35.9137			−1.38334
$675$	3.45211	+	25.7504i	0.132872	+	0.991133i
$676$	−34.2502			−1.31732
$677$	35.0885	−	35.0885i	1.34856	−	1.34856i	0.461331	−	0.887228i	$-0.347372\pi$
$677$	35.0885	−	35.0885i	1.34856	−	1.34856i	0.887228	−	0.461331i	$-0.152628\pi$
$678$	12.5880	−	26.0815i	0.483440	−	1.00165i
$679$		−	0.443420i		−	0.0170169i
$680$	4.66042	+	5.09245i	0.178719	+	0.195287i
$681$	−7.13009	−	20.4333i	−0.273226	−	0.783008i
$682$	7.31532	+	7.31532i	0.280118	+	0.280118i
$683$	−16.7946	−	16.7946i	−0.642629	−	0.642629i	0.308572	−	0.951201i	$-0.400149\pi$
$683$	−16.7946	−	16.7946i	−0.642629	−	0.642629i	−0.951201	+	0.308572i	$0.900149\pi$
$684$	−1.86641	−	2.34873i	−0.0713638	−	0.0898059i
$685$	7.02125	+	0.311023i	0.268268	+	0.0118836i
$686$			5.99007i			0.228702i
$687$	−33.7983	−	16.3124i	−1.28948	−	0.622358i
$688$	3.19643	−	3.19643i	0.121863	−	0.121863i
$689$	49.4059			1.88221
$690$	26.2426	−	7.87301i	0.999037	−	0.299720i
$691$	−30.1709			−1.14776			−0.573878	−	0.818941i	$-0.694562\pi$
$691$	−30.1709			−1.14776			−0.573878	+	0.818941i	$0.694562\pi$
$692$	9.61343	−	9.61343i	0.365448	−	0.365448i
$693$	1.22056	+	0.139665i	0.0463654	+	0.00530543i
$694$			8.03838i			0.305133i
$695$	−31.2805	+	28.6267i	−1.18654	+	1.08587i
$696$	2.90847	−	1.01489i	0.110245	−	0.0384694i
$697$	−13.2839	−	13.2839i	−0.503165	−	0.503165i
$698$	12.8335	+	12.8335i	0.485756	+	0.485756i
$699$	24.5026	−	8.55003i	0.926774	−	0.323392i
$700$	1.39174	+	1.66289i	0.0526028	+	0.0628515i
$701$		−	39.5966i		−	1.49554i	−0.663957	−	0.747771i	$-0.731124\pi$
$701$		−	39.5966i		−	1.49554i	0.663957	−	0.747771i	$-0.268876\pi$
$702$	−7.85749	−	34.8427i	−0.296562	−	1.31505i
$703$	3.09818	−	3.09818i	0.116850	−	0.116850i
$704$	−0.944248			−0.0355877
$705$	10.9583	−	20.3516i	0.412715	−	0.766485i
$706$	12.5368			0.471829
$707$	0.508493	−	0.508493i	0.0191238	−	0.0191238i
$708$	11.7442	+	5.66823i	0.441373	+	0.213025i
$709$			39.9962i			1.50209i	0.660252	+	0.751044i	$0.270449\pi$
$709$			39.9962i			1.50209i	−0.660252	+	0.751044i	$0.729551\pi$
$710$	1.28477	−	29.0034i	0.0482167	−	1.08848i
$711$	−22.3199	+	17.7364i	−0.837062	+	0.665167i
$712$	−6.28303	−	6.28303i	−0.235466	−	0.235466i
$713$	−54.8052	−	54.8052i	−2.05247	−	2.05247i
$714$	−0.764016	−	2.18951i	−0.0285926	−	0.0819404i
$715$	0.642281	−	14.4993i	0.0240199	−	0.542243i
$716$		−	22.6680i		−	0.847143i
$717$	−8.73865	+	18.1059i	−0.326351	+	0.676176i
$718$	7.62533	−	7.62533i	0.284575	−	0.284575i
$719$	−34.6703			−1.29298			−0.646491	−	0.762921i	$-0.723764\pi$
$719$	−34.6703			−1.29298			−0.646491	+	0.762921i	$0.723764\pi$
$720$	−1.05681	+	6.62444i	−0.0393851	+	0.246878i
$721$	−1.03816			−0.0386632
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	−15.5764	+	32.2732i	−0.579293	+	1.20025i
$724$		−	3.95190i		−	0.146871i
$725$	0.786287	−	8.85768i	0.0292020	−	0.328966i
$726$	−5.76830	−	16.5308i	−0.214082	−	0.613514i
$727$	2.33610	+	2.33610i	0.0866412	+	0.0866412i	0.749099	−	0.662458i	$-0.230487\pi$
$727$	2.33610	+	2.33610i	0.0866412	+	0.0866412i	−0.662458	+	0.749099i	$0.730487\pi$
$728$	−2.10797	−	2.10797i	−0.0781267	−	0.0781267i
$729$	24.3867	−	11.5884i	0.903210	−	0.429198i
$730$	−5.91990	+	5.41767i	−0.219105	+	0.200517i
$731$			13.9553i			0.516155i
$732$	7.07384	+	3.41413i	0.261457	+	0.126190i
$733$	−25.5392	+	25.5392i	−0.943311	+	0.943311i	−0.998477	−	0.0551665i	$-0.982431\pi$
$733$	−25.5392	+	25.5392i	−0.943311	+	0.943311i	0.0551665	+	0.998477i	$0.482431\pi$
$734$	13.1175			0.484175
$735$	7.58115	+	25.2697i	0.279635	+	0.932088i
$736$	7.07416			0.260757
$737$	−7.22413	+	7.22413i	−0.266104	+	0.266104i
$738$	2.07542	−	18.1376i	0.0763974	−	0.667655i
$739$			6.43422i			0.236686i	0.992973	+	0.118343i	$0.0377583\pi$
$739$			6.43422i			0.236686i	−0.992973	+	0.118343i	$0.962242\pi$
$740$	−9.78771	−	0.433570i	−0.359803	−	0.0159383i
$741$	11.2412	−	3.92254i	0.412955	−	0.144098i
$742$	2.20414	+	2.20414i	0.0809167	+	0.0809167i
$743$	−2.23501	−	2.23501i	−0.0819944	−	0.0819944i	0.664920	−	0.746915i	$-0.268466\pi$
$743$	−2.23501	−	2.23501i	−0.0819944	−	0.0819944i	−0.746915	+	0.664920i	$0.768466\pi$
$744$	17.9173	−	6.25213i	0.656880	−	0.229214i
$745$	19.5623	+	21.3758i	0.716708	+	0.783148i
$746$		−	6.60357i		−	0.241774i
$747$	3.78530	−	33.0806i	0.138497	−	1.21036i
$748$	2.06124	−	2.06124i	0.0753665	−	0.0753665i
$749$	4.55565			0.166460
$750$	16.1718	+	10.6524i	0.590510	+	0.388971i
$751$	−33.0311			−1.20532			−0.602660	−	0.797998i	$-0.705893\pi$
$751$	−33.0311			−1.20532			−0.602660	+	0.797998i	$0.705893\pi$
$752$	4.22008	−	4.22008i	0.153891	−	0.153891i
$753$	24.2714	+	11.7144i	0.884498	+	0.426895i
$754$			12.2252i			0.445216i
$755$	6.56935	+	7.17833i	0.239083	+	0.261246i
$756$	1.20389	−	1.90498i	0.0437852	−	0.0692836i
$757$	−22.2750	−	22.2750i	−0.809598	−	0.809598i	0.174975	−	0.984573i	$-0.444016\pi$
$757$	−22.2750	−	22.2750i	−0.809598	−	0.809598i	−0.984573	+	0.174975i	$0.944016\pi$
$758$	15.2909	+	15.2909i	0.555390	+	0.555390i
$759$	−3.81177	−	10.9237i	−0.138358	−	0.396506i
$760$	−2.23388	−	0.0989549i	−0.0810312	−	0.00358947i
$761$		−	19.7060i		−	0.714342i	−0.934039	−	0.357171i	$-0.883741\pi$
$761$		−	19.7060i		−	0.714342i	0.934039	−	0.357171i	$-0.116259\pi$
$762$	1.51972	−	3.14876i	0.0550537	−	0.114067i
$763$	−2.29749	+	2.29749i	−0.0831746	+	0.0831746i
$764$	3.21978			0.116487
$765$	−12.1538	−	16.7678i	−0.439423	−	0.606240i
$766$	−28.0358			−1.01297
$767$	−36.5949	+	36.5949i	−1.32136	+	1.32136i
$768$	−0.752859	+	1.55987i	−0.0271665	+	0.0562871i
$769$		−	1.48367i		−	0.0535024i	−0.999642	−	0.0267512i	$-0.991484\pi$
$769$		−	1.48367i		−	0.0535024i	0.999642	−	0.0267512i	$-0.00851619\pi$
$770$	0.675512	−	0.618203i	0.0243437	−	0.0222785i
$771$	−2.40953	−	6.90521i	−0.0867771	−	0.248685i
$772$	8.96414	+	8.96414i	0.322627	+	0.322627i
$773$	9.99213	+	9.99213i	0.359392	+	0.359392i	0.863589	−	0.504197i	$-0.168211\pi$
$773$	9.99213	+	9.99213i	0.359392	+	0.359392i	−0.504197	+	0.863589i	$0.668211\pi$
$774$	−10.6173	+	8.43697i	−0.381630	+	0.303260i
$775$	4.84383	−	54.5667i	0.173995	−	1.96009i
$776$		−	1.02244i		−	0.0367034i
$777$	2.96408	+	1.43059i	0.106336	+	0.0513220i
$778$	−12.7505	+	12.7505i	−0.457129	+	0.457129i
$779$	6.08532			0.218029
$780$	−23.4404	−	12.6215i	−0.839300	−	0.451922i
$781$	−12.2596			−0.438682
$782$	−15.4425	+	15.4425i	−0.552223	+	0.552223i
$783$	−9.01498	+	2.03299i	−0.322169	+	0.0726533i
$784$			6.81191i			0.243283i
$785$	0.736223	−	16.6200i	0.0262769	−	0.593194i
$786$	30.3319	−	10.5841i	1.08190	−	0.377523i
$787$	1.19902	+	1.19902i	0.0427405	+	0.0427405i	0.728154	−	0.685414i	$-0.240379\pi$
$787$	1.19902	+	1.19902i	0.0427405	+	0.0427405i	−0.685414	+	0.728154i	$0.740379\pi$
$788$	−6.36112	−	6.36112i	−0.226605	−	0.226605i
$789$	−19.7901	+	6.90563i	−0.704546	+	0.245847i
$790$	−0.940365	+	21.2285i	−0.0334567	+	0.755275i
$791$			7.25141i			0.257830i
$792$	2.81438	+	0.322039i	0.100005	+	0.0114432i
$793$	−22.0421	+	22.0421i	−0.782739	+	0.782739i
$794$	21.4001			0.759462
$795$	24.5098	+	13.1973i	0.869272	+	0.468060i
$796$	−21.5251			−0.762938
$797$	−18.6007	+	18.6007i	−0.658871	+	0.658871i	−0.955113	−	0.296242i	$-0.904266\pi$
$797$	−18.6007	+	18.6007i	−0.658871	+	0.658871i	0.296242	+	0.955113i	$0.404266\pi$
$798$	0.676500	+	0.326507i	0.0239478	+	0.0115582i
$799$			18.4244i			0.651810i
$800$	3.20907	+	3.83430i	0.113458	+	0.135563i
$801$	16.5840	+	20.8697i	0.585968	+	0.737396i
$802$	7.16366	+	7.16366i	0.252958	+	0.252958i
$803$	2.39616	+	2.39616i	0.0845588	+	0.0845588i
$804$	6.17419	+	17.6940i	0.217747	+	0.624018i
$805$	−5.06083	+	4.63149i	−0.178371	+	0.163238i
$806$			75.3120i			2.65275i
$807$	−8.30778	+	17.2131i	−0.292448	+	0.605931i
$808$	1.17248	−	1.17248i	0.0412478	−	0.0412478i
$809$	29.5206			1.03789			0.518945	−	0.854808i	$-0.326325\pi$
$809$	29.5206			1.03789			0.518945	+	0.854808i	$0.326325\pi$
$810$	5.40917	−	19.3840i	0.190059	−	0.681086i
$811$	−19.0909			−0.670373			−0.335186	−	0.942152i	$-0.608799\pi$
$811$	−19.0909			−0.670373			−0.335186	+	0.942152i	$0.608799\pi$
$812$	−0.545404	+	0.545404i	−0.0191399	+	0.0191399i
$813$	9.17363	−	19.0071i	0.321733	−	0.666610i
$814$			4.13721i			0.145009i
$815$	−7.99553	−	0.354181i	−0.280071	−	0.0124064i
$816$	−1.76167	−	5.04857i	−0.0616707	−	0.176735i
$817$	−3.19643	−	3.19643i	−0.111829	−	0.111829i
$818$	6.31543	+	6.31543i	0.220814	+	0.220814i
$819$	5.56399	+	7.00186i	0.194422	+	0.244665i
$820$	−9.18652	−	10.0381i	−0.320807	−	0.350546i
$821$			36.9019i			1.28789i	0.765074	+	0.643943i	$0.222703\pi$
$821$			36.9019i			1.28789i	−0.765074	+	0.643943i	$0.777297\pi$
$822$	−4.90280	−	2.36630i	−0.171005	−	0.0825341i
$823$	−1.58603	+	1.58603i	−0.0552855	+	0.0552855i	−0.734209	−	0.678924i	$-0.762447\pi$
$823$	−1.58603	+	1.58603i	−0.0552855	+	0.0552855i	0.678924	+	0.734209i	$0.262447\pi$
$824$	−2.39380			−0.0833918
$825$	4.19169	−	7.02140i	0.145936	−	0.244454i
$826$	−3.26521			−0.113611
$827$	14.6947	−	14.6947i	0.510984	−	0.510984i	−0.403844	−	0.914828i	$-0.632326\pi$
$827$	14.6947	−	14.6947i	0.510984	−	0.510984i	0.914828	+	0.403844i	$0.132326\pi$
$828$	−21.0849	−	2.41267i	−0.732751	−	0.0838461i
$829$			7.51933i			0.261157i	0.991438	+	0.130579i	$0.0416835\pi$
$829$			7.51933i			0.261157i	−0.991438	+	0.130579i	$0.958316\pi$
$830$	−16.7550	−	18.3082i	−0.581575	−	0.635487i
$831$	−11.1212	+	3.88066i	−0.385789	+	0.134619i
$832$	−4.86057	−	4.86057i	−0.168510	−	0.168510i
$833$	−14.8701	−	14.8701i	−0.515217	−	0.515217i
$834$	31.0110	−	10.8211i	1.07382	−	0.374703i
$835$	−10.5227	−	0.466130i	−0.364154	−	0.0161311i
$836$			0.944248i			0.0326575i
$837$	−55.5357	+	12.5240i	−1.91960	+	0.432894i
$838$	−14.5706	+	14.5706i	−0.503333	+	0.503333i
$839$	−5.59026			−0.192997			−0.0964985	−	0.995333i	$-0.530764\pi$
$839$	−5.59026			−0.192997			−0.0964985	+	0.995333i	$0.530764\pi$
$840$	−0.482663	−	1.60883i	−0.0166535	−	0.0555098i
$841$	−25.8369			−0.890929
$842$	−10.6801	+	10.6801i	−0.368060	+	0.368060i
$843$	50.0144	+	24.1390i	1.72259	+	0.831392i
$844$			1.03406i			0.0355938i
$845$	56.4979	−	51.7048i	1.94359	−	1.77870i
$846$	−14.0174	+	11.1389i	−0.481930	+	0.382963i
$847$	3.09989	+	3.09989i	0.106513	+	0.106513i
$848$	5.08232	+	5.08232i	0.174527	+	0.174527i
$849$	6.98445	+	20.0160i	0.239706	+	0.686946i
$850$	−15.3753	−	1.36485i	−0.527369	−	0.0468140i
$851$		−	30.9954i		−	1.06251i
$852$	−9.77470	+	20.2525i	−0.334876	+	0.693839i
$853$	12.5659	−	12.5659i	0.430247	−	0.430247i	−0.458465	−	0.888712i	$-0.651601\pi$
$853$	12.5659	−	12.5659i	0.430247	−	0.430247i	0.888712	+	0.458465i	$0.151601\pi$
$854$	−1.96673			−0.0673001
$855$	6.62444	+	1.05681i	0.226551	+	0.0361422i
$856$	10.5044			0.359034
$857$	20.9298	−	20.9298i	0.714948	−	0.714948i	−0.252618	−	0.967566i	$-0.581292\pi$
$857$	20.9298	−	20.9298i	0.714948	−	0.714948i	0.967566	+	0.252618i	$0.0812916\pi$
$858$	−4.88654	+	10.1246i	−0.166824	+	0.345648i
$859$			32.5560i			1.11080i	0.831585	+	0.555398i	$0.187434\pi$
$859$			32.5560i			1.11080i	−0.831585	+	0.555398i	$0.812566\pi$
$860$	−0.447319	+	10.0981i	−0.0152535	+	0.344342i
$861$	1.50601	+	4.31591i	0.0513247	+	0.147086i
$862$	5.22885	+	5.22885i	0.178095	+	0.178095i
$863$	−29.9371	−	29.9371i	−1.01907	−	1.01907i	−0.999815	−	0.0192563i	$-0.993870\pi$
$863$	−29.9371	−	29.9371i	−1.01907	−	1.01907i	−0.0192563	−	0.999815i	$-0.506130\pi$
$864$	2.77594	−	4.39251i	0.0944393	−	0.149436i
$865$	−1.34534	+	30.3706i	−0.0457428	+	1.03263i
$866$		−	9.22376i		−	0.313436i
$867$	−11.6514	−	5.62347i	−0.395704	−	0.190983i
$868$	−3.35989	+	3.35989i	−0.114042	+	0.114042i
$869$	8.97316			0.304394
$870$	−3.26560	+	6.06481i	−0.110714	+	0.205616i
$871$	−74.3732			−2.52004
$872$	−5.29755	+	5.29755i	−0.179398	+	0.179398i
$873$	−0.348706	+	3.04743i	−0.0118019	+	0.103140i
$874$		−	7.07416i		−	0.239287i
$875$	−4.80609	−	0.642054i	−0.162476	−	0.0217054i
$876$	5.86889	−	2.04791i	0.198291	−	0.0691926i
$877$	−1.12380	−	1.12380i	−0.0379481	−	0.0379481i	0.687878	−	0.725826i	$-0.258542\pi$
$877$	−1.12380	−	1.12380i	−0.0379481	−	0.0379481i	−0.725826	+	0.687878i	$0.758542\pi$
$878$	−22.6865	−	22.6865i	−0.765632	−	0.765632i
$879$	16.6423	−	5.80723i	0.561331	−	0.195873i
$880$	1.55759	−	1.42545i	0.0525065	−	0.0480520i
$881$			52.9484i			1.78388i	0.452158	+	0.891938i	$0.350654\pi$
$881$			52.9484i			1.78388i	−0.452158	+	0.891938i	$0.649346\pi$
$882$	2.32323	−	20.3033i	0.0782272	−	0.683646i
$883$	−15.4219	+	15.4219i	−0.518989	+	0.518989i	−0.917266	−	0.398276i	$-0.869609\pi$
$883$	−15.4219	+	15.4219i	−0.518989	+	0.518989i	0.398276	+	0.917266i	$0.369609\pi$
$884$	21.2207			0.713730
$885$	−27.9296	+	8.37913i	−0.938843	+	0.281661i
$886$	−7.87370			−0.264522
$887$	−14.7809	+	14.7809i	−0.496293	+	0.496293i	−0.910282	−	0.413989i	$-0.864135\pi$
$887$	−14.7809	+	14.7809i	−0.496293	+	0.496293i	0.413989	+	0.910282i	$0.364135\pi$
$888$	6.83457	+	3.29864i	0.229353	+	0.110695i
$889$			0.875444i			0.0293614i
$890$	19.8492	+	0.879268i	0.665347	+	0.0294731i
$891$	−8.27856	−	1.91971i	−0.277342	−	0.0643127i
$892$	4.32004	+	4.32004i	0.144646	+	0.144646i
$893$	−4.22008	−	4.22008i	−0.141220	−	0.141220i
$894$	−7.39468	−	21.1916i	−0.247315	−	0.708753i
$895$	34.2200	+	37.3923i	1.14385	+	1.24989i
$896$		−	0.433689i		−	0.0144885i
$897$	36.6092	−	75.8518i	1.22235	−	2.53262i
$898$	−15.6572	+	15.6572i	−0.522487	+	0.522487i
$899$	19.4857			0.649886
$900$	−8.25709	−	12.5228i	−0.275236	−	0.417427i
$901$	−22.1889			−0.739218
$902$	−4.06307	+	4.06307i	−0.135286	+	0.135286i
$903$	1.47595	−	3.05807i	0.0491166	−	0.101766i
$904$			16.7203i			0.556109i
$905$	5.96587	+	6.51891i	0.198312	+	0.216696i
$906$	−2.48325	−	7.11648i	−0.0825006	−	0.236429i
$907$	−22.2347	−	22.2347i	−0.738290	−	0.738290i	0.233957	−	0.972247i	$-0.424833\pi$
$907$	−22.2347	−	22.2347i	−0.738290	−	0.738290i	−0.972247	+	0.233957i	$0.924833\pi$
$908$	8.83516	+	8.83516i	0.293205	+	0.293205i
$909$	−3.89452	+	3.09476i	−0.129173	+	0.102647i
$910$	6.65947	+	0.294997i	0.220759	+	0.00977906i
$911$		−	10.9407i		−	0.362480i	−0.983439	−	0.181240i	$-0.941989\pi$
$911$		−	10.9407i		−	0.362480i	0.983439	−	0.181240i	$-0.0580111\pi$
$912$	1.55987	+	0.752859i	0.0516525	+	0.0249297i
$913$	−7.41051	+	7.41051i	−0.245252	+	0.245252i
$914$	−1.79823			−0.0594803
$915$	−16.8228	+	5.04699i	−0.556144	+	0.166848i
$916$	21.6673			0.715908
$917$	−5.68791	+	5.68791i	−0.187831	+	0.187831i
$918$	3.52891	+	15.6484i	0.116471	+	0.516473i
$919$			20.3908i			0.672632i	0.941749	+	0.336316i	$0.109181\pi$
$919$			20.3908i			0.672632i	−0.941749	+	0.336316i	$0.890819\pi$
$920$	−11.6693	+	10.6793i	−0.384724	+	0.352085i
$921$	3.72772	−	1.30076i	0.122832	−	0.0428616i
$922$	22.1186	+	22.1186i	0.728439	+	0.728439i
$923$	−63.1069	−	63.1069i	−2.07719	−	2.07719i
$924$	−0.669691	+	0.233685i	−0.0220312	+	0.00768766i
$925$	16.8000	−	14.0605i	0.552379	−	0.462307i
$926$			17.4078i			0.572056i
$927$	7.13483	+	0.816414i	0.234339	+	0.0268145i
$928$	−1.25759	+	1.25759i	−0.0412825	+	0.0412825i
$929$	−7.33339			−0.240601			−0.120300	−	0.992738i	$-0.538386\pi$
$929$	−7.33339			−0.240601			−0.120300	+	0.992738i	$0.538386\pi$
$930$	−20.1174	+	37.3616i	−0.659674	+	1.22513i
$931$	6.81191			0.223251
$932$	−10.5947	+	10.5947i	−0.347040	+	0.347040i
$933$	37.7019	+	18.1965i	1.23430	+	0.595726i
$934$		−	4.36576i		−	0.142852i
$935$	−0.288457	+	6.51184i	−0.00943356	+	0.212960i
$936$	12.8295	+	16.1449i	0.419344	+	0.527712i
$937$	16.6534	+	16.6534i	0.544044	+	0.544044i	0.924712	−	0.380668i	$-0.124306\pi$
$937$	16.6534	+	16.6534i	0.544044	+	0.544044i	−0.380668	+	0.924712i	$0.624306\pi$
$938$	−3.31801	−	3.31801i	−0.108337	−	0.108337i
$939$	−16.5704	−	47.4872i	−0.540754	−	1.54969i
$940$	−0.590572	+	13.3320i	−0.0192623	+	0.434842i
$941$			41.0823i			1.33924i	0.742702	+	0.669622i	$0.233544\pi$
$941$			41.0823i			1.33924i	−0.742702	+	0.669622i	$0.766456\pi$
$942$	−5.60126	+	11.6054i	−0.182499	+	0.378125i
$943$	30.4399	−	30.4399i	0.991260	−	0.991260i
$944$	−7.52893			−0.245046
$945$	0.889905	+	4.95981i	0.0289486	+	0.161343i
$946$	4.26841			0.138778
$947$	−43.3537	+	43.3537i	−1.40880	+	1.40880i	−0.642619	+	0.766186i	$0.722152\pi$
$947$	−43.3537	+	43.3537i	−1.40880	+	1.40880i	−0.766186	+	0.642619i	$0.777848\pi$
$948$	7.15440	−	14.8234i	0.232364	−	0.481443i
$949$			24.6688i			0.800782i
$950$	3.83430	−	3.20907i	0.124401	−	0.104116i
$951$	−14.7814	−	42.3605i	−0.479321	−	1.37363i
$952$	0.946720	+	0.946720i	0.0306834	+	0.0306834i
$953$	33.0634	+	33.0634i	1.07103	+	1.07103i	0.997277	+	0.0737523i	$0.0234974\pi$
$953$	33.0634	+	33.0634i	1.07103	+	1.07103i	0.0737523	+	0.997277i	$0.476503\pi$
$954$	−13.4148	−	16.8814i	−0.434319	−	0.546557i
$955$	−5.31122	+	4.86063i	−0.171867	+	0.157286i
$956$		−	11.6073i		−	0.375406i
$957$	2.61957	+	1.26431i	0.0846786	+	0.0408694i
$958$	2.22678	−	2.22678i	0.0719441	−	0.0719441i
$959$	1.36312			0.0440174
$960$	−1.11292	−	3.70964i	−0.0359195	−	0.119728i
$961$	89.0396			2.87225
$962$	−21.2965	+	21.2965i	−0.686628	+	0.686628i
$963$	−31.3090	−	3.58257i	−1.00892	−	0.115447i
$964$		−	20.6897i		−	0.666369i
$965$	−28.3193	−	1.25447i	−0.911632	−	0.0403829i
$966$	5.01722	−	1.75073i	0.161427	−	0.0563288i
$967$	−8.96271	−	8.96271i	−0.288221	−	0.288221i	0.548155	−	0.836377i	$-0.315330\pi$
$967$	−8.96271	−	8.96271i	−0.288221	−	0.288221i	−0.836377	+	0.548155i	$0.815330\pi$
$968$	7.14772	+	7.14772i	0.229736	+	0.229736i
$969$	−5.04857	+	1.76167i	−0.162184	+	0.0565929i
$970$	1.54349	+	1.68657i	0.0495585	+	0.0541526i
$971$		−	56.8504i		−	1.82442i	−0.409726	−	0.912209i	$-0.634376\pi$
$971$		−	56.8504i		−	1.82442i	0.409726	−	0.912209i	$-0.365624\pi$
$972$	−9.77190	+	12.1454i	−0.313434	+	0.389563i
$973$	−5.81525	+	5.81525i	−0.186428	+	0.186428i
$974$	20.2091			0.647541
$975$	57.7200	−	14.5661i	1.84852	−	0.466489i
$976$	−4.53489			−0.145158
$977$	20.1899	−	20.1899i	0.645933	−	0.645933i	−0.306074	−	0.952008i	$-0.599016\pi$
$977$	20.1899	−	20.1899i	0.645933	−	0.645933i	0.952008	+	0.306074i	$0.0990156\pi$
$978$	5.58312	+	2.69464i	0.178528	+	0.0861652i
$979$		−	8.39015i		−	0.268150i
$980$	−10.2834	−	11.2367i	−0.328491	−	0.358942i
$981$	17.5964	−	13.9829i	0.561808	−	0.446438i
$982$	−2.51893	−	2.51893i	−0.0803823	−	0.0803823i
$983$	12.2333	+	12.2333i	0.390180	+	0.390180i	0.874752	−	0.484571i	$-0.161024\pi$
$983$	12.2333	+	12.2333i	0.390180	+	0.390180i	−0.484571	+	0.874752i	$0.661024\pi$
$984$	3.47256	+	9.95162i	0.110701	+	0.317246i
$985$	20.0959	+	0.890196i	0.640309	+	0.0283640i
$986$		−	5.49051i		−	0.174854i
$987$	1.94862	−	4.03741i	0.0620254	−	0.128512i
$988$	−4.86057	+	4.86057i	−0.154635	+	0.154635i
$989$	−31.9783			−1.01685
$990$	−5.12865	+	3.71741i	−0.162999	+	0.118147i
$991$	25.1249			0.798118			0.399059	−	0.916925i	$-0.369337\pi$
$991$	25.1249			0.798118			0.399059	+	0.916925i	$0.369337\pi$
$992$	−7.74725	+	7.74725i	−0.245975	+	0.245975i
$993$	−12.4701	+	25.8373i	−0.395728	+	0.819921i
$994$		−	5.63077i		−	0.178597i
$995$	35.5070	−	32.4947i	1.12565	−	1.03015i
$996$	6.33349	+	18.1505i	0.200684	+	0.575119i
$997$	−28.2711	−	28.2711i	−0.895354	−	0.895354i	0.0996671	−	0.995021i	$-0.468222\pi$
$997$	−28.2711	−	28.2711i	−0.895354	−	0.895354i	−0.995021	+	0.0996671i	$0.968222\pi$
$998$	16.1168	+	16.1168i	0.510170	+	0.510170i
$999$	−19.2458	−	12.1627i	−0.608909	−	0.384812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.77.4	✓	36
3.2	odd	2	inner	570.2.k.a.77.10	yes	36
5.3	odd	4	inner	570.2.k.a.533.10	yes	36
15.8	even	4	inner	570.2.k.a.533.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.4	✓	36	1.1	even	1	trivial
570.2.k.a.77.10	yes	36	3.2	odd	2	inner
570.2.k.a.533.4	yes	36	15.8	even	4	inner
570.2.k.a.533.10	yes	36	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +(-2.23388 - 0.0989549i) q^{10} +0.944248i q^{11} +(1.55987 + 0.752859i) q^{12} +(-4.86057 + 4.86057i) q^{13} -0.433689 q^{14} +(-3.70964 + 1.11292i) q^{15} -1.00000 q^{16} +(2.18295 - 2.18295i) q^{17} +(2.98055 + 0.341054i) q^{18} +1.00000i q^{19} +(1.64956 - 1.50962i) q^{20} +(-0.709233 + 0.247482i) q^{21} +(-0.667684 - 0.667684i) q^{22} +(5.00219 + 5.00219i) q^{23} +(-1.63535 + 0.570645i) q^{24} +(-0.442106 + 4.98042i) q^{25} -6.87388i q^{26} +(5.06886 - 1.14309i) q^{27} +(0.306664 - 0.306664i) q^{28} -1.77850 q^{29} +(1.83615 - 3.41007i) q^{30} -10.9563 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.47291 - 0.710886i) q^{33} +3.08715i q^{34} +(-0.0429156 + 0.968808i) q^{35} +(-2.34873 + 1.86641i) q^{36} +(-3.09818 - 3.09818i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-3.92254 - 11.2412i) q^{39} +(-0.0989549 + 2.23388i) q^{40} -6.08532i q^{41} +(0.326507 - 0.676500i) q^{42} +(-3.19643 + 3.19643i) q^{43} +0.944248 q^{44} +(1.05681 - 6.62444i) q^{45} -7.07416 q^{46} +(-4.22008 + 4.22008i) q^{47} +(0.752859 - 1.55987i) q^{48} -6.81191i q^{49} +(-3.20907 - 3.83430i) q^{50} +(1.76167 + 5.04857i) q^{51} +(4.86057 + 4.86057i) q^{52} +(-5.08232 - 5.08232i) q^{53} +(-2.77594 + 4.39251i) q^{54} +(-1.55759 + 1.42545i) q^{55} +0.433689i q^{56} +(-1.55987 - 0.752859i) q^{57} +(1.25759 - 1.25759i) q^{58} +7.52893 q^{59} +(1.11292 + 3.70964i) q^{60} +4.53489 q^{61} +(7.74725 - 7.74725i) q^{62} +(0.147911 - 1.29263i) q^{63} +1.00000i q^{64} +(-15.3554 - 0.680204i) q^{65} +(1.54417 - 0.538830i) q^{66} +(7.65067 + 7.65067i) q^{67} +(-2.18295 - 2.18295i) q^{68} +(-11.5687 + 4.03683i) q^{69} +(-0.654705 - 0.715397i) q^{70} +12.9834i q^{71} +(0.341054 - 2.98055i) q^{72} +(2.53764 - 2.53764i) q^{73} +4.38149 q^{74} +(-7.43597 - 4.43918i) q^{75} +1.00000 q^{76} +(-0.289567 + 0.289567i) q^{77} +(10.7224 + 5.17507i) q^{78} -9.50297i q^{79} +(-1.50962 - 1.64956i) q^{80} +(-2.03306 + 8.76736i) q^{81} +(4.30297 + 4.30297i) q^{82} +(7.84806 + 7.84806i) q^{83} +(0.247482 + 0.709233i) q^{84} +(6.89632 + 0.305489i) q^{85} -4.52043i q^{86} +(1.33896 - 2.77424i) q^{87} +(-0.667684 + 0.667684i) q^{88} -8.88554 q^{89} +(3.93690 + 5.43146i) q^{90} -2.98113 q^{91} +(5.00219 - 5.00219i) q^{92} +(8.24852 - 17.0904i) q^{93} -5.96810i q^{94} +(-1.64956 + 1.50962i) q^{95} +(0.570645 + 1.63535i) q^{96} +(-0.722973 - 0.722973i) q^{97} +(4.81675 + 4.81675i) q^{98} +(2.21778 - 1.76235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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