LMFDB - Embedded newform 366.2.o.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,2,Mod(29,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 7]))

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

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

chi := DirichletCharacter("366.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	366.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.92252471398$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	366.101
Dual form			366.2.o.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.49583 - 0.873213i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.97711 - 3.42446i) q^{5} +(1.67086 + 0.456310i) q^{6} +(1.24820 + 4.65833i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47500 + 2.61235i) q^{9} +(-1.02343 + 3.81948i) q^{10} +(-0.138932 + 0.138932i) q^{11} +(-1.73203 - 0.00831075i) q^{12} +(2.68018 - 4.64222i) q^{13} +(-2.41133 - 4.17654i) q^{14} +(-5.94770 + 3.39596i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.70446 + 0.992608i) q^{17} +(-2.10087 - 2.14158i) q^{18} +(-1.71846 + 0.992153i) q^{19} -3.95422i q^{20} +(2.20063 - 8.05799i) q^{21} +(0.0982399 - 0.170156i) q^{22} +(0.658382 + 0.658382i) q^{23} +(1.67516 - 0.440255i) q^{24} +(-5.31794 - 9.21093i) q^{25} +(-1.38737 + 5.17772i) q^{26} +(0.0747944 - 5.19561i) q^{27} +(3.41013 + 3.41013i) q^{28} +(0.815390 + 0.218483i) q^{29} +(4.86609 - 4.81962i) q^{30} +(2.60251 - 9.71268i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.329136 - 0.0865012i) q^{33} -3.83514 q^{34} +(18.4201 + 4.93564i) q^{35} +(2.58356 + 1.52486i) q^{36} +(3.63140 + 3.63140i) q^{37} +(1.40312 - 1.40312i) q^{38} +(-8.06274 + 4.60358i) q^{39} +(1.02343 + 3.81948i) q^{40} -3.85786 q^{41} +(-0.0400799 + 8.35299i) q^{42} +(4.11970 - 1.10387i) q^{43} +(-0.0508527 + 0.189785i) q^{44} +(11.8621 + 0.113838i) q^{45} +(-0.806350 - 0.465546i) q^{46} +(5.38640 - 3.10984i) q^{47} +(-1.50414 + 0.858818i) q^{48} +(-14.0799 + 8.12901i) q^{49} +(7.52070 + 7.52070i) q^{50} +(-4.67448 - 4.71955i) q^{51} -5.36037i q^{52} +(-0.492458 - 0.492458i) q^{53} +(1.27248 + 5.03794i) q^{54} +(0.201083 + 0.750451i) q^{55} +(-4.17654 - 2.41133i) q^{56} +(3.43688 + 0.0164911i) q^{57} -0.844154 q^{58} +(-0.527818 - 1.96984i) q^{59} +(-3.45288 + 5.91483i) q^{60} +(-3.63436 - 6.91313i) q^{61} +10.0553i q^{62} +(-10.3281 + 10.1318i) q^{63} -1.00000i q^{64} +(-10.5980 - 18.3564i) q^{65} +(-0.295533 + 0.168740i) q^{66} +(-7.60992 + 2.03907i) q^{67} +(3.70446 - 0.992608i) q^{68} +(-0.409918 - 1.55973i) q^{69} -19.0699 q^{70} +(-13.1618 - 3.52668i) q^{71} +(-2.89019 - 0.804229i) q^{72} +(4.81771 + 8.34453i) q^{73} +(-4.44753 - 2.56778i) q^{74} +(-0.0883920 + 18.4217i) q^{75} +(-0.992153 + 1.71846i) q^{76} +(-0.820606 - 0.473777i) q^{77} +(6.59651 - 6.53351i) q^{78} +(2.50818 + 9.36065i) q^{79} +(-1.97711 - 3.42446i) q^{80} +(-4.64876 + 7.70643i) q^{81} +(3.72641 - 0.998487i) q^{82} +(8.96193 + 5.17418i) q^{83} +(-2.12320 - 8.07874i) q^{84} +(10.7233 - 10.7233i) q^{85} +(-3.69363 + 2.13252i) q^{86} +(-1.02890 - 1.03882i) q^{87} -0.196480i q^{88} +(-1.89629 + 1.89629i) q^{89} +(-11.4874 + 2.96018i) q^{90} +(24.9704 + 6.69079i) q^{91} +(0.899366 + 0.240984i) q^{92} +(-12.3741 + 12.2560i) q^{93} +(-4.39798 + 4.39798i) q^{94} +7.84639i q^{95} +(1.23061 - 1.21885i) q^{96} +(-7.87693 + 4.54774i) q^{97} +(11.4962 - 11.4962i) q^{98} +(-0.567864 - 0.158015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{6} + 16 q^{7} + 16 q^{10} - 16 q^{15} + 40 q^{16} - 8 q^{18} + 4 q^{21} - 4 q^{24} - 32 q^{25} - 8 q^{28} + 12 q^{30} + 44 q^{33} + 12 q^{36} - 36 q^{39} - 16 q^{40} - 24 q^{43} + 60 q^{45}+ \cdots + 52 q^{99}+O(q^{100}) $ 80 * q - 8 * q^6 + 16 * q^7 + 16 * q^10 - 16 * q^15 + 40 * q^16 - 8 * q^18 + 4 * q^21 - 4 * q^24 - 32 * q^25 - 8 * q^28 + 12 * q^30 + 44 * q^33 + 12 * q^36 - 36 * q^39 - 16 * q^40 - 24 * q^43 + 60 * q^45 + 48 * q^46 - 144 * q^49 - 32 * q^51 - 4 * q^54 + 32 * q^55 + 56 * q^57 - 48 * q^58 - 48 * q^61 - 8 * q^63 - 48 * q^66 - 64 * q^67 - 32 * q^69 - 96 * q^70 - 8 * q^72 + 32 * q^73 + 8 * q^76 + 32 * q^78 + 16 * q^79 + 40 * q^81 + 64 * q^82 + 32 * q^84 - 80 * q^85 - 8 * q^87 - 56 * q^90 + 96 * q^91 - 100 * q^93 - 48 * q^94 - 4 * q^96 - 144 * q^97 + 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/366\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.49583	−	0.873213i	−0.863616	−	0.504150i
$3$	−1.49583	−	0.873213i	−0.863616	−	0.504150i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.97711	−	3.42446i	0.884191	−	1.53146i	0.0375527	−	0.999295i	$-0.488044\pi$
$5$	1.97711	−	3.42446i	0.884191	−	1.53146i	0.846638	−	0.532169i	$-0.178623\pi$
$6$	1.67086	+	0.456310i	0.682127	+	0.186288i
$7$	1.24820	+	4.65833i	0.471773	+	1.76068i	0.633394	+	0.773830i	$0.281661\pi$
$7$	1.24820	+	4.65833i	0.471773	+	1.76068i	−0.161620	+	0.986853i	$0.551672\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.47500	+	2.61235i	0.491666	+	0.870784i
$10$	−1.02343	+	3.81948i	−0.323636	+	1.20783i
$11$	−0.138932	+	0.138932i	−0.0418896	+	0.0418896i	−0.727741	−	0.685852i	$-0.759430\pi$
$11$	−0.138932	+	0.138932i	−0.0418896	+	0.0418896i	0.685852	+	0.727741i	$0.259430\pi$
$12$	−1.73203	−	0.00831075i	−0.499994	−	0.00239911i
$13$	2.68018	−	4.64222i	0.743350	−	1.28752i	−0.207612	−	0.978211i	$-0.566569\pi$
$13$	2.68018	−	4.64222i	0.743350	−	1.28752i	0.950962	−	0.309308i	$-0.100097\pi$
$14$	−2.41133	−	4.17654i	−0.644455	−	1.11623i
$15$	−5.94770	+	3.39596i	−1.53569	+	0.876832i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.70446	+	0.992608i	0.898464	+	0.240743i	0.678356	−	0.734733i	$-0.262693\pi$
$17$	3.70446	+	0.992608i	0.898464	+	0.240743i	0.220107	+	0.975476i	$0.429359\pi$
$18$	−2.10087	−	2.14158i	−0.495179	−	0.504775i
$19$	−1.71846	+	0.992153i	−0.394242	+	0.227615i	−0.683996	−	0.729485i	$-0.739760\pi$
$19$	−1.71846	+	0.992153i	−0.394242	+	0.227615i	0.289755	+	0.957101i	$0.406426\pi$
$20$		−	3.95422i		−	0.884191i
$21$	2.20063	−	8.05799i	0.480216	−	1.75840i
$22$	0.0982399	−	0.170156i	0.0209448	−	0.0362775i
$23$	0.658382	+	0.658382i	0.137282	+	0.137282i	0.772408	−	0.635126i	$-0.219052\pi$
$23$	0.658382	+	0.658382i	0.137282	+	0.137282i	−0.635126	+	0.772408i	$0.719052\pi$
$24$	1.67516	−	0.440255i	0.341941	−	0.0898667i
$25$	−5.31794	−	9.21093i	−1.06359	−	1.84219i
$26$	−1.38737	+	5.17772i	−0.272085	+	1.01543i
$27$	0.0747944	−	5.19561i	0.0143942	−	0.999896i
$28$	3.41013	+	3.41013i	0.644455	+	0.644455i
$29$	0.815390	+	0.218483i	0.151414	+	0.0405713i	0.333730	−	0.942669i	$-0.391693\pi$
$29$	0.815390	+	0.218483i	0.151414	+	0.0405713i	−0.182316	+	0.983240i	$0.558359\pi$
$30$	4.86609	−	4.81962i	0.888423	−	0.879938i
$31$	2.60251	−	9.71268i	0.467424	−	1.74445i	−0.181302	−	0.983427i	$-0.558031\pi$
$31$	2.60251	−	9.71268i	0.467424	−	1.74445i	0.648726	−	0.761022i	$-0.275302\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.329136	−	0.0865012i	0.0572952	−	0.0150579i
$34$	−3.83514			−0.657721
$35$	18.4201	+	4.93564i	3.11356	+	0.834276i
$36$	2.58356	+	1.52486i	0.430594	+	0.254144i
$37$	3.63140	+	3.63140i	0.596998	+	0.596998i	0.939512	−	0.342515i	$-0.111279\pi$
$37$	3.63140	+	3.63140i	0.596998	+	0.596998i	−0.342515	+	0.939512i	$0.611279\pi$
$38$	1.40312	−	1.40312i	0.227615	−	0.227615i
$39$	−8.06274	+	4.60358i	−1.29107	+	0.737163i
$40$	1.02343	+	3.81948i	0.161818	+	0.603914i
$41$	−3.85786			−0.602496			−0.301248	−	0.953546i	$-0.597403\pi$
$41$	−3.85786			−0.602496			−0.301248	+	0.953546i	$0.597403\pi$
$42$	−0.0400799	+	8.35299i	−0.00618446	+	1.28889i
$43$	4.11970	−	1.10387i	0.628249	−	0.168339i	0.0693740	−	0.997591i	$-0.477900\pi$
$43$	4.11970	−	1.10387i	0.628249	−	0.168339i	0.558875	+	0.829252i	$0.311233\pi$
$44$	−0.0508527	+	0.189785i	−0.00766633	+	0.0286111i
$45$	11.8621	+	0.113838i	1.76830	+	0.0169699i
$46$	−0.806350	−	0.465546i	−0.118890	−	0.0686410i
$47$	5.38640	−	3.10984i	0.785687	−	0.453617i	−0.0527547	−	0.998608i	$-0.516800\pi$
$47$	5.38640	−	3.10984i	0.785687	−	0.453617i	0.838442	+	0.544991i	$0.183467\pi$
$48$	−1.50414	+	0.858818i	−0.217104	+	0.123960i
$49$	−14.0799	+	8.12901i	−2.01141	+	1.16129i
$50$	7.52070	+	7.52070i	1.06359	+	1.06359i
$51$	−4.67448	−	4.71955i	−0.654558	−	0.660870i
$52$		−	5.36037i		−	0.743350i
$53$	−0.492458	−	0.492458i	−0.0676444	−	0.0676444i	0.672475	−	0.740120i	$-0.265231\pi$
$53$	−0.492458	−	0.492458i	−0.0676444	−	0.0676444i	−0.740120	+	0.672475i	$0.765231\pi$
$54$	1.27248	+	5.03794i	0.173162	+	0.685576i
$55$	0.201083	+	0.750451i	0.0271140	+	0.101191i
$56$	−4.17654	−	2.41133i	−0.558114	−	0.322227i
$57$	3.43688	+	0.0164911i	0.455226	+	0.00218429i
$58$	−0.844154			−0.110843
$59$	−0.527818	−	1.96984i	−0.0687161	−	0.256452i	0.923019	−	0.384754i	$-0.125714\pi$
$59$	−0.527818	−	1.96984i	−0.0687161	−	0.256452i	−0.991735	+	0.128302i	$0.959047\pi$
$60$	−3.45288	+	5.91483i	−0.445764	+	0.763602i
$61$	−3.63436	−	6.91313i	−0.465333	−	0.885136i
$61$	−3.63436	−	6.91313i	−0.465333	−	0.885136i
$62$			10.0553i			1.27703i
$63$	−10.3281	+	10.1318i	−1.30122	+	1.27648i
$64$		−	1.00000i		−	0.125000i
$65$	−10.5980	−	18.3564i	−1.31453	−	2.27683i
$66$	−0.295533	+	0.168740i	−0.0363776	+	0.0207705i
$67$	−7.60992	+	2.03907i	−0.929700	+	0.249112i	−0.691727	−	0.722159i	$-0.743150\pi$
$67$	−7.60992	+	2.03907i	−0.929700	+	0.249112i	−0.237973	+	0.971272i	$0.576483\pi$
$68$	3.70446	−	0.992608i	0.449232	−	0.120371i
$69$	−0.409918	−	1.55973i	−0.0493483	−	0.187770i
$70$	−19.0699			−2.27928
$71$	−13.1618	−	3.52668i	−1.56201	−	0.418541i	−0.628714	−	0.777637i	$-0.716418\pi$
$71$	−13.1618	−	3.52668i	−1.56201	−	0.418541i	−0.933301	+	0.359096i	$0.883085\pi$
$72$	−2.89019	−	0.804229i	−0.340613	−	0.0947793i
$73$	4.81771	+	8.34453i	0.563871	+	0.976653i	0.997154	+	0.0753950i	$0.0240218\pi$
$73$	4.81771	+	8.34453i	0.563871	+	0.976653i	−0.433283	+	0.901258i	$0.642645\pi$
$74$	−4.44753	−	2.56778i	−0.517015	−	0.298499i
$75$	−0.0883920	+	18.4217i	−0.0102066	+	2.12715i
$76$	−0.992153	+	1.71846i	−0.113808	+	0.197121i
$77$	−0.820606	−	0.473777i	−0.0935167	−	0.0539919i
$78$	6.59651	−	6.53351i	0.746908	−	0.739774i
$79$	2.50818	+	9.36065i	0.282192	+	1.05316i	0.950867	+	0.309600i	$0.100195\pi$
$79$	2.50818	+	9.36065i	0.282192	+	1.05316i	−0.668675	+	0.743555i	$0.733138\pi$
$80$	−1.97711	−	3.42446i	−0.221048	−	0.382866i
$81$	−4.64876	+	7.70643i	−0.516528	+	0.856270i
$82$	3.72641	−	0.998487i	0.411513	−	0.110264i
$83$	8.96193	+	5.17418i	0.983700	+	0.567940i	0.903385	−	0.428830i	$-0.141074\pi$
$83$	8.96193	+	5.17418i	0.983700	+	0.567940i	0.0803149	+	0.996770i	$0.474407\pi$
$84$	−2.12320	−	8.07874i	−0.231660	−	0.881463i
$85$	10.7233	−	10.7233i	1.16310	−	1.16310i
$86$	−3.69363	+	2.13252i	−0.398294	+	0.229955i
$87$	−1.02890	−	1.03882i	−0.110310	−	0.111373i
$88$		−	0.196480i		−	0.0209448i
$89$	−1.89629	+	1.89629i	−0.201006	+	0.201006i	−0.800431	−	0.599425i	$-0.795396\pi$
$89$	−1.89629	+	1.89629i	−0.201006	+	0.201006i	0.599425	+	0.800431i	$0.295396\pi$
$90$	−11.4874	+	2.96018i	−1.21088	+	0.312031i
$91$	24.9704	+	6.69079i	2.61761	+	0.701385i
$92$	0.899366	+	0.240984i	0.0937654	+	0.0251244i
$93$	−12.3741	+	12.2560i	−1.28314	+	1.27088i
$94$	−4.39798	+	4.39798i	−0.453617	+	0.453617i
$95$			7.84639i			0.805022i
$96$	1.23061	−	1.21885i	0.125598	−	0.124399i
$97$	−7.87693	+	4.54774i	−0.799781	+	0.461754i	−0.843394	−	0.537295i	$-0.819446\pi$
$97$	−7.87693	+	4.54774i	−0.799781	+	0.461754i	0.0436139	+	0.999048i	$0.486113\pi$
$98$	11.4962	−	11.4962i	1.16129	−	1.16129i
$99$	−0.567864	−	0.158015i	−0.0570725	−	0.0158811i
$100$	−9.21093	−	5.31794i	−0.921093	−	0.531794i
$101$	14.6789	−	3.93321i	1.46061	−	0.391369i	0.560910	−	0.827877i	$-0.310452\pi$
$101$	14.6789	−	3.93321i	1.46061	−	0.391369i	0.899700	+	0.436508i	$0.143785\pi$
$102$	5.73671	+	3.34889i	0.568019	+	0.331590i
$103$	−3.55587	−	6.15895i	−0.350371	−	0.606860i	0.635944	−	0.771735i	$-0.280611\pi$
$103$	−3.55587	−	6.15895i	−0.350371	−	0.606860i	−0.986314	+	0.164876i	$0.947278\pi$
$104$	1.38737	+	5.17772i	0.136042	+	0.507717i
$105$	−23.2434	−	23.4675i	−2.26832	−	2.29019i
$106$	0.603136	+	0.348221i	0.0585817	+	0.0338222i
$107$	−5.03053	+	8.71314i	−0.486320	+	0.842331i	−0.999876	−	0.0157248i	$-0.994994\pi$
$107$	−5.03053	+	8.71314i	−0.486320	+	0.842331i	0.513556	+	0.858056i	$0.328328\pi$
$108$	−2.53303	−	4.53693i	−0.243741	−	0.436566i
$109$	0.0969251	+	0.0559597i	0.00928374	+	0.00535997i	0.504635	−	0.863333i	$-0.331627\pi$
$109$	0.0969251	+	0.0559597i	0.00928374	+	0.00535997i	−0.495351	+	0.868693i	$0.664961\pi$
$110$	−0.388462	−	0.672836i	−0.0370384	−	0.0641524i
$111$	−2.26096	−	8.60292i	−0.214601	−	0.816553i
$112$	4.65833	+	1.24820i	0.440171	+	0.117943i
$113$	10.4712			0.985045			0.492522	−	0.870300i	$-0.336075\pi$
$113$	10.4712			0.985045			0.492522	+	0.870300i	$0.336075\pi$
$114$	−3.32404	+	0.873601i	−0.311325	+	0.0818202i
$115$	3.55629	−	0.952906i	0.331626	−	0.0888589i
$116$	0.815390	−	0.218483i	0.0757071	−	0.0202857i
$117$	16.0804	+	0.154319i	1.48663	+	0.0142668i
$118$	1.01967	+	1.76611i	0.0938679	+	0.162584i
$119$			18.4956i			1.69549i
$120$	1.80435	−	6.60696i	0.164714	−	0.603130i
$121$			10.9614i			0.996491i
$122$	5.29978	+	5.73693i	0.479819	+	0.519397i
$123$	5.77069	+	3.36873i	0.520326	+	0.303748i
$124$	−2.60251	−	9.71268i	−0.233712	−	0.872225i
$125$	−22.2855			−1.99327
$126$	7.35389	−	12.4596i	0.655137	−	1.10999i
$127$	4.46109	+	2.57561i	0.395858	+	0.228548i	0.684695	−	0.728830i	$-0.259935\pi$
$127$	4.46109	+	2.57561i	0.395858	+	0.228548i	−0.288838	+	0.957378i	$0.593269\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−7.12628	−	1.94618i	−0.627434	−	0.171351i
$130$	14.9879	+	14.9879i	1.31453	+	1.31453i
$131$			8.90487i			0.778022i	0.921233	+	0.389011i	$0.127183\pi$
$131$			8.90487i			0.778022i	−0.921233	+	0.389011i	$0.872817\pi$
$132$	0.241789	−	0.239480i	0.0210451	−	0.0208441i
$133$	−6.76675	−	6.76675i	−0.586751	−	0.586751i
$134$	6.82287	−	3.93919i	0.589406	−	0.340294i
$135$	−17.6443	−	10.5284i	−1.51858	−	0.906143i
$136$	−3.32133	+	1.91757i	−0.284802	+	0.164430i
$137$	9.89586	+	5.71338i	0.845460	+	0.488127i	0.859116	−	0.511780i	$-0.171014\pi$
$137$	9.89586	+	5.71338i	0.845460	+	0.488127i	−0.0136564	+	0.999907i	$0.504347\pi$
$138$	0.799639	+	1.40049i	0.0680698	+	0.119218i
$139$	1.90004	−	7.09103i	0.161159	−	0.601453i	−0.837340	−	0.546682i	$-0.815891\pi$
$139$	1.90004	−	7.09103i	0.161159	−	0.601453i	0.998499	−	0.0547708i	$-0.0174428\pi$
$140$	18.4201	−	4.93564i	1.55678	−	0.417138i
$141$	−10.7727	−	0.0516902i	−0.907223	−	0.00435310i
$142$	13.6261			1.14347
$143$	0.272589	+	1.01732i	0.0227951	+	0.0850723i
$144$	2.99986	+	0.0287889i	0.249988	+	0.00239908i
$145$	2.36030	−	2.36030i	0.196013	−	0.196013i
$146$	−6.81328	−	6.81328i	−0.563871	−	0.563871i
$147$	28.1594	+	0.135116i	2.32255	+	0.0111442i
$148$	4.96058	+	1.32918i	0.407757	+	0.109258i
$149$	−11.4579			−0.938671			−0.469335	−	0.883020i	$-0.655506\pi$
$149$	−11.4579			−0.938671			−0.469335	+	0.883020i	$0.655506\pi$
$150$	−4.68250	−	17.8168i	−0.382324	−	1.45474i
$151$	−1.68275	+	6.28010i	−0.136940	+	0.511067i	0.863042	+	0.505132i	$0.168556\pi$
$151$	−1.68275	+	6.28010i	−0.136940	+	0.511067i	−0.999982	+	0.00593561i	$0.998111\pi$
$152$	0.513576	−	1.91669i	0.0416565	−	0.155464i
$153$	2.87104	+	11.1414i	0.232110	+	0.900733i
$154$	0.915267	+	0.245245i	0.0737543	+	0.0197624i
$155$	−28.1152	−	28.1152i	−2.25827	−	2.25827i
$156$	−4.68074	+	8.01819i	−0.374759	+	0.641969i
$157$	−1.95018	+	7.27818i	−0.155642	+	0.580862i	0.843408	+	0.537274i	$0.180546\pi$
$157$	−1.95018	+	7.27818i	−0.155642	+	0.580862i	−0.999050	+	0.0435885i	$0.986121\pi$
$158$	−4.84543	−	8.39253i	−0.385482	−	0.667674i
$159$	0.306612	+	1.16665i	0.0243159	+	0.0925216i
$160$	2.79606	+	2.79606i	0.221048	+	0.221048i
$161$	−2.24517	+	3.88875i	−0.176944	+	0.306476i
$162$	2.49578	−	8.64703i	0.196087	−	0.679375i
$163$			0.322970i			0.0252970i	0.999920	+	0.0126485i	$0.00402625\pi$
$163$			0.322970i			0.0252970i	−0.999920	+	0.0126485i	$0.995974\pi$
$164$	−3.34100	+	1.92893i	−0.260889	+	0.150624i
$165$	0.354519	−	1.29813i	0.0275992	−	0.101060i
$166$	−9.99574	−	2.67835i	−0.775820	−	0.207880i
$167$	7.99365	−	13.8454i	0.618567	−	1.07139i	−0.371180	−	0.928561i	$-0.621047\pi$
$167$	7.99365	−	13.8454i	0.618567	−	1.07139i	0.989747	−	0.142829i	$-0.0456199\pi$
$168$	4.14178	+	7.25394i	0.319546	+	0.559654i
$169$	−7.86678	−	13.6257i	−0.605137	−	1.04813i
$170$	−7.58250	+	13.1333i	−0.581551	+	1.00728i
$171$	−5.12658	−	3.02579i	−0.392039	−	0.231388i
$172$	3.01583	−	3.01583i	0.229955	−	0.229955i
$173$	−3.59448	+	13.4148i	−0.273284	+	1.01991i	0.683699	+	0.729764i	$0.260370\pi$
$173$	−3.59448	+	13.4148i	−0.273284	+	1.01991i	−0.956983	+	0.290144i	$0.906297\pi$
$174$	1.26271	+	0.737126i	0.0957257	+	0.0558814i
$175$	36.2697	−	36.2697i	2.74173	−	2.74173i
$176$	0.0508527	+	0.189785i	0.00383317	+	0.0143056i
$177$	−0.930568	+	3.40745i	−0.0699458	+	0.256119i
$178$	1.34088	−	2.32247i	0.100503	−	0.174076i
$179$	−4.73171	+	2.73185i	−0.353664	+	0.204188i	−0.666298	−	0.745686i	$-0.732122\pi$
$179$	−4.73171	+	2.73185i	−0.353664	+	0.204188i	0.312634	+	0.949874i	$0.398789\pi$
$180$	10.3298	−	5.83247i	0.769939	−	0.434727i
$181$	−2.04026	+	0.546686i	−0.151651	+	0.0406349i	−0.333846	−	0.942628i	$-0.608347\pi$
$181$	−2.04026	+	0.546686i	−0.151651	+	0.0406349i	0.182195	+	0.983262i	$0.441680\pi$
$182$	−25.8512			−1.91622
$183$	−0.600255	+	13.5144i	−0.0443721	+	0.999015i
$184$	−0.931092			−0.0686410
$185$	19.6152	−	5.25588i	1.44214	−	0.386420i
$186$	8.78042	−	15.0410i	0.643812	−	1.10286i
$187$	−0.652574	+	0.376764i	−0.0477209	+	0.0275517i
$188$	3.10984	−	5.38640i	0.226808	−	0.392844i
$189$	24.2962	−	6.13672i	1.76729	−	0.446381i
$190$	−2.03079	−	7.57903i	−0.147329	−	0.549840i
$191$	−6.23151	+	6.23151i	−0.450896	+	0.450896i	−0.895652	−	0.444756i	$-0.853290\pi$
$191$	−6.23151	+	6.23151i	−0.450896	+	0.450896i	0.444756	+	0.895652i	$0.353290\pi$
$192$	−0.873213	+	1.49583i	−0.0630187	+	0.107952i
$193$	−1.99642	+	7.45072i	−0.143705	+	0.536315i	0.856104	+	0.516803i	$0.172878\pi$
$193$	−1.99642	+	7.45072i	−0.143705	+	0.536315i	−0.999810	+	0.0195121i	$0.993789\pi$
$194$	6.43148	−	6.43148i	0.461754	−	0.461754i
$195$	−0.176155	+	36.7123i	−0.0126147	+	2.62902i
$196$	−8.12901	+	14.0799i	−0.580643	+	1.00570i
$197$	−7.60238	−	13.1677i	−0.541647	−	0.938161i	−0.998810	−	0.0487774i	$-0.984468\pi$
$197$	−7.60238	−	13.1677i	−0.541647	−	0.938161i	0.457162	−	0.889383i	$-0.348866\pi$
$198$	0.589412	+	0.00565644i	0.0418877	+	0.000401986i
$199$	−5.68947	+	9.85446i	−0.403316	+	0.698564i	−0.994124	−	0.108248i	$-0.965476\pi$
$199$	−5.68947	+	9.85446i	−0.403316	+	0.698564i	0.590808	+	0.806812i	$0.298809\pi$
$200$	10.2735	+	2.75277i	0.726443	+	0.194650i
$201$	13.1637	+	3.59498i	0.928494	+	0.253570i
$202$	−13.1608	+	7.59838i	−0.925990	+	0.534620i
$203$			4.07107i			0.285733i
$204$	−6.40799	−	1.75001i	−0.448649	−	0.122525i
$205$	−7.62741	+	13.2111i	−0.532722	+	0.922701i
$206$	5.02876	+	5.02876i	0.350371	+	0.350371i
$207$	−0.748812	+	2.69104i	−0.0520460	+	0.187040i
$208$	−2.68018	−	4.64222i	−0.185837	−	0.321880i
$209$	0.100907	−	0.376591i	0.00697990	−	0.0260494i
$210$	28.5252	+	16.6520i	1.96843	+	1.14910i
$211$	−6.37518	−	6.37518i	−0.438885	−	0.438885i	0.452751	−	0.891637i	$-0.350442\pi$
$211$	−6.37518	−	6.37518i	−0.438885	−	0.438885i	−0.891637	+	0.452751i	$0.850442\pi$
$212$	−0.672711	−	0.180252i	−0.0462020	−	0.0123798i
$213$	16.6082	+	16.7683i	1.13797	+	1.14895i
$214$	2.60400	−	9.71825i	0.178005	−	0.664326i
$215$	4.36495	−	16.2902i	0.297687	−	1.11098i
$216$	3.62097	+	3.72674i	0.246376	+	0.253573i
$217$	48.4933			3.29194
$218$	−0.108106	−	0.0289669i	−0.00732186	−	0.00196189i
$219$	0.0800776	−	16.6889i	0.00541114	−	1.12773i
$220$	0.549369	+	0.549369i	0.0370384	+	0.0370384i
$221$	14.5365	−	14.5365i	0.977834	−	0.977834i
$222$	4.41052	+	7.72460i	0.296015	+	0.518441i
$223$	−0.642741	−	2.39874i	−0.0430411	−	0.160632i	0.941060	−	0.338239i	$-0.109831\pi$
$223$	−0.642741	−	2.39874i	−0.0430411	−	0.160632i	−0.984102	+	0.177607i	$0.943164\pi$
$224$	−4.82266			−0.322227
$225$	16.2182	−	27.4784i	1.08122	−	1.83190i
$226$	−10.1144	+	2.71014i	−0.672798	+	0.180276i
$227$	−5.25923	+	19.6277i	−0.349068	+	1.30274i	0.538720	+	0.842485i	$0.318908\pi$
$227$	−5.25923	+	19.6277i	−0.349068	+	1.30274i	−0.887788	+	0.460253i	$0.847759\pi$
$228$	2.98467	−	1.70416i	0.197665	−	0.112861i
$229$	3.39286	+	1.95887i	0.224207	+	0.129446i	0.607897	−	0.794016i	$-0.292014\pi$
$229$	3.39286	+	1.95887i	0.224207	+	0.129446i	−0.383690	+	0.923462i	$0.625347\pi$
$230$	−3.18849	+	1.84087i	−0.210243	+	0.121384i
$231$	0.813777	+	1.42525i	0.0535426	+	0.0937747i
$232$	−0.731059	+	0.422077i	−0.0479964	+	0.0277107i
$233$	−5.61705	−	5.61705i	−0.367985	−	0.367985i	0.498757	−	0.866742i	$-0.333790\pi$
$233$	−5.61705	−	5.61705i	−0.367985	−	0.367985i	−0.866742	+	0.498757i	$0.833790\pi$
$234$	−15.5724	+	4.01284i	−1.01800	+	0.262328i
$235$		−	24.5940i		−	1.60434i
$236$	−1.44203	−	1.44203i	−0.0938679	−	0.0938679i
$237$	4.42204	−	16.1921i	0.287242	−	1.05179i
$238$	−4.78700	−	17.8653i	−0.310295	−	1.15804i
$239$	−10.4350	−	6.02462i	−0.674981	−	0.389701i	0.122980	−	0.992409i	$-0.460755\pi$
$239$	−10.4350	−	6.02462i	−0.674981	−	0.389701i	−0.797961	+	0.602709i	$0.794088\pi$
$240$	−0.0328625	+	6.84883i	−0.00212127	+	0.442090i
$241$	−25.2368			−1.62564			−0.812821	−	0.582513i	$-0.802070\pi$
$241$	−25.2368			−1.62564			−0.812821	+	0.582513i	$0.802070\pi$
$242$	−2.83702	−	10.5879i	−0.182370	−	0.680616i
$243$	13.6831	−	7.46814i	0.877771	−	0.479081i
$244$	−6.60402	−	4.16977i	−0.422779	−	0.266942i
$245$			64.2878i			4.10720i
$246$	−6.44595	−	1.76038i	−0.410979	−	0.112238i
$247$			10.6366i			0.676791i
$248$	5.02765	+	8.70815i	0.319256	+	0.552968i
$249$	−8.88735	−	15.5653i	−0.563213	−	0.986414i
$250$	21.5261	−	5.76791i	1.36143	−	0.364794i
$251$	−20.8599	+	5.58939i	−1.31666	+	0.352799i	−0.847727	−	0.530432i	$-0.822030\pi$
$251$	−20.8599	+	5.58939i	−1.31666	+	0.352799i	−0.468937	+	0.883231i	$0.655363\pi$
$252$	−3.87852	+	13.9384i	−0.244324	+	0.878037i
$253$	−0.182941			−0.0115014
$254$	−4.97570	−	1.33323i	−0.312203	−	0.0836545i
$255$	−25.4039	+	6.67647i	−1.59085	+	0.418097i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.75900	−	2.17026i	−0.234480	−	0.135377i	0.378157	−	0.925741i	$-0.376558\pi$
$257$	−3.75900	−	2.17026i	−0.234480	−	0.135377i	−0.612637	+	0.790364i	$0.709891\pi$
$258$	7.38717	+	0.0354456i	0.459905	+	0.00220675i
$259$	−12.3835	+	21.4489i	−0.769476	+	1.33277i
$260$	−18.3564	−	10.5980i	−1.13841	−	0.657263i
$261$	0.631945	+	2.45235i	0.0391164	+	0.151797i
$262$	−2.30475	−	8.60145i	−0.142388	−	0.531399i
$263$	−8.27735	−	14.3368i	−0.510403	−	0.884045i	−0.999927	−	0.0120549i	$-0.996163\pi$
$263$	−8.27735	−	14.3368i	−0.510403	−	0.884045i	0.489524	−	0.871990i	$-0.337171\pi$
$264$	−0.171569	+	0.293900i	−0.0105593	+	0.0180883i
$265$	−2.66005	+	0.712757i	−0.163405	+	0.0437843i
$266$	8.28754	+	4.78481i	0.508142	+	0.293376i
$267$	4.49238	−	1.18066i	0.274929	−	0.0722550i
$268$	−5.57085	+	5.57085i	−0.340294	+	0.340294i
$269$	8.78886	−	5.07425i	0.535866	−	0.309382i	−0.207536	−	0.978227i	$-0.566544\pi$
$269$	8.78886	−	5.07425i	0.535866	−	0.309382i	0.743402	+	0.668845i	$0.233211\pi$
$270$	19.7680	+	5.60301i	1.20304	+	0.340988i
$271$			3.03921i			0.184619i	0.995730	+	0.0923093i	$0.0294249\pi$
$271$			3.03921i			0.184619i	−0.995730	+	0.0923093i	$0.970575\pi$
$272$	2.71185	−	2.71185i	0.164430	−	0.164430i
$273$	−31.5089	−	31.8127i	−1.90700	−	1.92539i
$274$	−11.0374	−	2.95746i	−0.666793	−	0.178667i
$275$	2.01853	+	0.540863i	0.121722	+	0.0326153i
$276$	−1.13487	−	1.14581i	−0.0683109	−	0.0689696i
$277$	−0.442446	+	0.442446i	−0.0265840	+	0.0265840i	−0.720274	−	0.693690i	$-0.755984\pi$
$277$	−0.442446	+	0.442446i	−0.0265840	+	0.0265840i	0.693690	+	0.720274i	$0.255984\pi$
$278$			7.34117i			0.440294i
$279$	29.2116	−	7.52754i	1.74885	−	0.450662i
$280$	−16.5150	+	9.53493i	−0.986959	+	0.569821i
$281$	18.7798	−	18.7798i	1.12031	−	1.12031i	0.128614	−	0.991695i	$-0.458947\pi$
$281$	18.7798	−	18.7798i	1.12031	−	1.12031i	0.991695	−	0.128614i	$-0.0410527\pi$
$282$	10.4190	−	2.73825i	0.620442	−	0.163060i
$283$	−14.6438	−	8.45461i	−0.870484	−	0.502574i	−0.00297519	−	0.999996i	$-0.500947\pi$
$283$	−14.6438	−	8.45461i	−0.870484	−	0.502574i	−0.867509	+	0.497421i	$0.834280\pi$
$284$	−13.1618	+	3.52668i	−0.781007	+	0.209270i
$285$	6.85156	−	11.7368i	0.405852	−	0.695230i
$286$	−0.526602	−	0.912102i	−0.0311386	−	0.0539337i
$287$	−4.81536	−	17.9712i	−0.284242	−	1.06080i
$288$	−2.90510	+	0.748613i	−0.171184	+	0.0441125i
$289$	−1.98466	−	1.14585i	−0.116745	−	0.0674028i
$290$	−1.66899	+	2.89077i	−0.0980063	+	0.169752i
$291$	15.7537	+	0.0755903i	0.923496	+	0.00443118i
$292$	8.34453	+	4.81771i	0.488326	+	0.281935i
$293$	−13.8747	−	24.0316i	−0.810567	−	1.40394i	−0.912468	−	0.409148i	$-0.865826\pi$
$293$	−13.8747	−	24.0316i	−0.810567	−	1.40394i	0.101901	−	0.994795i	$-0.467507\pi$
$294$	−27.2348	+	7.15767i	−1.58837	+	0.417444i
$295$	−7.78920	−	2.08711i	−0.453505	−	0.121516i
$296$	−5.13557			−0.298499
$297$	0.711447	+	0.732229i	0.0412823	+	0.0424883i
$298$	11.0675	−	2.96553i	0.641124	−	0.171789i
$299$	4.82094	−	1.29177i	0.278802	−	0.0747047i
$300$	9.13428	+	15.9978i	0.527368	+	0.923634i
$301$	10.2844	+	17.8131i	0.592782	+	1.02673i
$302$		−	6.50164i		−	0.374127i
$303$	−25.3917	−	6.93444i	−1.45872	−	0.398373i
$304$			1.98431i			0.113808i
$305$	−30.8593	−	1.22231i	−1.76700	−	0.0699893i
$306$	−5.65683	−	10.0187i	−0.323379	−	0.572733i
$307$	0.328052	+	1.22431i	0.0187229	+	0.0698750i	0.974655	−	0.223712i	$-0.0718176\pi$
$307$	0.328052	+	1.22431i	0.0187229	+	0.0698750i	−0.955932	+	0.293587i	$0.905151\pi$
$308$	−0.947554			−0.0539919
$309$	−0.0591039	+	12.3178i	−0.00336230	+	0.700733i
$310$	34.4340	+	19.8805i	1.95572	+	1.12913i
$311$	1.78665	+	6.66789i	0.101312	+	0.378101i	0.997901	−	0.0647629i	$-0.0206291\pi$
$311$	1.78665	+	6.66789i	0.101312	+	0.378101i	−0.896589	+	0.442864i	$0.853962\pi$
$312$	2.44599	−	8.95644i	0.138477	−	0.507059i
$313$	18.4606	+	18.4606i	1.04345	+	1.04345i	0.999012	+	0.0444420i	$0.0141510\pi$
$313$	18.4606	+	18.4606i	1.04345	+	1.04345i	0.0444420	+	0.999012i	$0.485849\pi$
$314$		−	7.53493i		−	0.425221i
$315$	14.2759	+	55.3997i	0.804358	+	3.12142i
$316$	6.85247	+	6.85247i	0.385482	+	0.385482i
$317$	5.75499	−	3.32264i	0.323232	−	0.186618i	−0.329600	−	0.944121i	$-0.606914\pi$
$317$	5.75499	−	3.32264i	0.323232	−	0.186618i	0.652832	+	0.757502i	$0.273581\pi$
$318$	−0.598116	−	1.04754i	−0.0335407	−	0.0587433i
$319$	−0.143638	+	0.0829296i	−0.00804220	+	0.00464317i
$320$	−3.42446	−	1.97711i	−0.191433	−	0.110524i
$321$	15.1332	−	8.64063i	0.844655	−	0.482273i
$322$	1.16219	−	4.33733i	0.0647660	−	0.241710i
$323$	−7.35078	+	1.96964i	−0.409009	+	0.109594i
$324$	−0.172726	+	8.99834i	−0.00959587	+	0.499908i
$325$	−57.0122			−3.16247
$326$	−0.0835909	−	0.311965i	−0.00462967	−	0.0172782i
$327$	−0.0961185	−	0.168342i	−0.00531536	−	0.00930935i
$328$	2.72792	−	2.72792i	0.150624	−	0.150624i
$329$	21.2099	+	21.2099i	1.16934	+	1.16934i
$330$	−0.00645682	+	1.34566i	−0.000355436	+	0.0740760i
$331$	4.23408	+	1.13452i	0.232726	+	0.0623588i	0.373297	−	0.927712i	$-0.378227\pi$
$331$	4.23408	+	1.13452i	0.232726	+	0.0623588i	−0.140571	+	0.990071i	$0.544894\pi$
$332$	10.3484			0.567940
$333$	−4.13018	+	14.8428i	−0.226332	+	0.813380i
$334$	−4.13782	+	15.4425i	−0.226411	+	0.844979i
$335$	−8.06294	+	30.0913i	−0.440526	+	1.64406i
$336$	−5.87811	−	5.93480i	−0.320677	−	0.323770i
$337$	15.1164	+	4.05043i	0.823444	+	0.220641i	0.645852	−	0.763463i	$-0.276503\pi$
$337$	15.1164	+	4.05043i	0.823444	+	0.220641i	0.177592	+	0.984104i	$0.443169\pi$
$338$	11.1253	+	11.1253i	0.605137	+	0.605137i
$339$	−15.6631	−	9.14356i	−0.850701	−	0.496610i
$340$	3.92499	−	14.6483i	0.212862	−	0.794414i
$341$	0.987832	+	1.71098i	0.0534941	+	0.0926545i
$342$	5.73503	+	1.59584i	0.310115	+	0.0862930i
$343$	−31.5711	−	31.5711i	−1.70468	−	1.70468i
$344$	−2.13252	+	3.69363i	−0.114978	+	0.199147i
$345$	−6.15169	−	1.68002i	−0.331196	−	0.0904491i
$346$		−	13.8880i		−	0.746624i
$347$	−11.7304	+	6.77254i	−0.629720	+	0.363569i	−0.780644	−	0.624976i	$-0.785109\pi$
$347$	−11.7304	+	6.77254i	−0.629720	+	0.363569i	0.150924	+	0.988545i	$0.451775\pi$
$348$	−1.41047	−	0.385196i	−0.0756089	−	0.0206487i
$349$	4.35282	+	1.16633i	0.233001	+	0.0624324i	0.373430	−	0.927658i	$-0.378182\pi$
$349$	4.35282	+	1.16633i	0.233001	+	0.0624324i	−0.140429	+	0.990091i	$0.544848\pi$
$350$	−25.6466	+	44.4212i	−1.37087	+	2.37441i
$351$	−23.9187	−	14.2724i	−1.27669	−	0.761805i
$352$	−0.0982399	−	0.170156i	−0.00523620	−	0.00906937i
$353$	−5.59115	+	9.68415i	−0.297587	+	0.515435i	−0.975583	−	0.219630i	$-0.929515\pi$
$353$	−5.59115	+	9.68415i	−0.297587	+	0.515435i	0.677997	+	0.735065i	$0.262848\pi$
$354$	0.0169484	−	3.53219i	0.000900796	−	0.187734i
$355$	−38.0993	+	38.0993i	−2.02210	+	2.02210i
$356$	−0.694090	+	2.59038i	−0.0367867	+	0.137290i
$357$	16.1506	−	27.6662i	0.854779	−	1.46425i
$358$	3.86342	−	3.86342i	0.204188	−	0.204188i
$359$	7.80558	+	29.1308i	0.411963	+	1.53747i	0.790842	+	0.612020i	$0.209643\pi$
$359$	7.80558	+	29.1308i	0.411963	+	1.53747i	−0.378879	+	0.925446i	$0.623690\pi$
$360$	−8.46828	+	8.30729i	−0.446318	+	0.437833i
$361$	−7.53127	+	13.0445i	−0.396382	+	0.686554i
$362$	1.82925	−	1.05612i	0.0961431	−	0.0555083i
$363$	9.57163	−	16.3964i	0.502380	−	0.860585i
$364$	24.9704	−	6.69079i	1.30880	−	0.350693i
$365$	38.1006			1.99428
$366$	−2.91799	−	13.2093i	−0.152526	−	0.690461i
$367$	1.36248			0.0711211			0.0355605	−	0.999368i	$-0.488678\pi$
$367$	1.36248			0.0711211			0.0355605	+	0.999368i	$0.488678\pi$
$368$	0.899366	−	0.240984i	0.0468827	−	0.0125622i
$369$	−5.69034	−	10.0781i	−0.296227	−	0.524644i
$370$	−17.5865	+	10.1536i	−0.914280	+	0.527860i
$371$	1.67935	−	2.90872i	0.0871874	−	0.151013i
$372$	−4.58834	+	16.8010i	−0.237894	+	0.871093i
$373$	3.50470	+	13.0797i	0.181467	+	0.677242i	0.995359	+	0.0962273i	$0.0306776\pi$
$373$	3.50470	+	13.0797i	0.181467	+	0.677242i	−0.813893	+	0.581015i	$0.802656\pi$
$374$	0.532824	−	0.532824i	0.0275517	−	0.0275517i
$375$	33.3352	+	19.4600i	1.72142	+	1.00491i
$376$	−1.60977	+	6.00775i	−0.0830177	+	0.309826i
$377$	3.19964	−	3.19964i	0.164790	−	0.164790i
$378$	−21.8801	+	12.2159i	−1.12539	+	0.628321i
$379$	19.2372	−	33.3197i	0.988147	−	1.71152i	0.361127	−	0.932517i	$-0.382392\pi$
$379$	19.2372	−	33.3197i	0.988147	−	1.71152i	0.627020	−	0.779003i	$-0.284274\pi$
$380$	3.92319	+	6.79517i	0.201256	+	0.348585i
$381$	−4.42396	−	7.74815i	−0.226646	−	0.396950i
$382$	4.40634	−	7.63201i	0.225448	−	0.390487i
$383$	2.02348	+	0.542190i	0.103395	+	0.0277046i	0.310146	−	0.950689i	$-0.399622\pi$
$383$	2.02348	+	0.542190i	0.103395	+	0.0277046i	−0.206751	+	0.978394i	$0.566289\pi$
$384$	0.456310	−	1.67086i	0.0232860	−	0.0852658i
$385$	−3.24486	+	1.87342i	−0.165373	+	0.0954783i
$386$		−	7.71356i		−	0.392610i
$387$	8.96026	+	9.13390i	0.455476	+	0.464302i
$388$	−4.54774	+	7.87693i	−0.230877	+	0.399890i
$389$	7.14278	+	7.14278i	0.362153	+	0.362153i	0.864605	−	0.502452i	$-0.167569\pi$
$389$	7.14278	+	7.14278i	0.362153	+	0.362153i	−0.502452	+	0.864605i	$0.667569\pi$
$390$	−9.33168	−	35.5069i	−0.472528	−	1.79796i
$391$	1.78544	+	3.09246i	0.0902933	+	0.156393i
$392$	4.20788	−	15.7040i	0.212530	−	0.793174i
$393$	7.77585	−	13.3202i	0.392240	−	0.671913i
$394$	10.7514	+	10.7514i	0.541647	+	0.541647i
$395$	37.0141	+	9.91790i	1.86238	+	0.499024i
$396$	−0.570792	+	0.147087i	−0.0286834	+	0.00739142i
$397$	−8.14528	+	30.3986i	−0.408800	+	1.52566i	0.388138	+	0.921601i	$0.373118\pi$
$397$	−8.14528	+	30.3986i	−0.408800	+	1.52566i	−0.796938	+	0.604061i	$0.793548\pi$
$398$	2.94509	−	10.9912i	0.147624	−	0.550940i
$399$	4.21308	+	16.0307i	0.210918	+	0.802538i
$400$	−10.6359			−0.531794
$401$	−2.20313	−	0.590327i	−0.110019	−	0.0294795i	0.203389	−	0.979098i	$-0.434804\pi$
$401$	−2.20313	−	0.590327i	−0.110019	−	0.0294795i	−0.313409	+	0.949618i	$0.601471\pi$
$402$	−13.6456	−	0.0654751i	−0.680580	−	0.00326560i
$403$	−38.1132	−	38.1132i	−1.89855	−	1.89855i
$404$	10.7457	−	10.7457i	0.534620	−	0.534620i
$405$	17.1992	+	31.1559i	0.854637	+	1.54815i
$406$	−1.05367	−	3.93235i	−0.0522927	−	0.195159i
$407$	−1.00904			−0.0500160
$408$	6.64258	+	0.0318729i	0.328857	+	0.00157794i
$409$	4.07360	−	1.09152i	0.201427	−	0.0539721i	−0.156695	−	0.987647i	$-0.550084\pi$
$409$	4.07360	−	1.09152i	0.201427	−	0.0539721i	0.358122	+	0.933675i	$0.383417\pi$
$410$	3.94824	−	14.7350i	0.194990	−	0.727711i
$411$	−9.81350	−	17.1874i	−0.484064	−	0.847792i
$412$	−6.15895	−	3.55587i	−0.303430	−	0.175185i
$413$	8.51736	−	4.91750i	0.419112	−	0.241974i
$414$	0.0268052	−	2.79315i	0.00131740	−	0.137276i
$415$	35.4375	−	20.4598i	1.73956	−	1.00433i
$416$	3.79035	+	3.79035i	0.185837	+	0.185837i
$417$	−9.03410	+	8.94782i	−0.442402	+	0.438177i
$418$			0.389876i			0.0190695i
$419$	−14.6265	−	14.6265i	−0.714552	−	0.714552i	0.252932	−	0.967484i	$-0.418605\pi$
$419$	−14.6265	−	14.6265i	−0.714552	−	0.714552i	−0.967484	+	0.252932i	$0.918605\pi$
$420$	−31.8631	−	8.70177i	−1.55476	−	0.424603i
$421$	−2.64311	−	9.86420i	−0.128817	−	0.480752i	0.871130	−	0.491053i	$-0.163388\pi$
$421$	−2.64311	−	9.86420i	−0.128817	−	0.480752i	−0.999947	+	0.0103008i	$0.996721\pi$
$422$	7.80797	+	4.50793i	0.380086	+	0.219443i
$423$	16.0689	+	9.48416i	0.781298	+	0.461136i
$424$	0.696441			0.0338222
$425$	−10.5572	−	39.4002i	−0.512102	−	1.91119i
$426$	−20.3822	−	11.8985i	−0.987523	−	0.576482i
$427$	27.6672	−	25.5590i	1.33891	−	1.23689i
$428$			10.0611i			0.486320i
$429$	0.480588	−	1.75976i	0.0232030	−	0.0849620i
$430$			16.8649i			0.813297i
$431$	16.5013	+	28.5810i	0.794838	+	1.37670i	0.922942	+	0.384939i	$0.125778\pi$
$431$	16.5013	+	28.5810i	0.794838	+	1.37670i	−0.128104	+	0.991761i	$0.540889\pi$
$432$	−4.46214	−	2.66258i	−0.214685	−	0.128103i
$433$	−32.5939	+	8.73352i	−1.56636	+	0.419706i	−0.934671	−	0.355513i	$-0.884306\pi$
$433$	−32.5939	+	8.73352i	−1.56636	+	0.419706i	−0.631693	+	0.775219i	$0.717640\pi$
$434$	−46.8409	+	12.5510i	−2.24844	+	0.602467i
$435$	−5.59165	+	1.46956i	−0.268099	+	0.0704600i
$436$	0.111919			0.00535997
$437$	−1.78462	−	0.478187i	−0.0853698	−	0.0228748i
$438$	4.24205	+	16.1409i	0.202693	+	0.771243i
$439$	5.30512	+	9.18874i	0.253200	+	0.438555i	0.964405	−	0.264430i	$-0.0851837\pi$
$439$	5.30512	+	9.18874i	0.253200	+	0.438555i	−0.711205	+	0.702984i	$0.751850\pi$
$440$	−0.672836	−	0.388462i	−0.0320762	−	0.0185192i
$441$	−42.0036	−	24.7912i	−2.00017	−	1.18054i
$442$	−10.2789	+	17.8036i	−0.488917	+	0.846829i
$443$	−11.5175	−	6.64965i	−0.547215	−	0.315935i	0.200783	−	0.979636i	$-0.435651\pi$
$443$	−11.5175	−	6.64965i	−0.547215	−	0.315935i	−0.747998	+	0.663701i	$0.768985\pi$
$444$	−6.25951	−	6.31987i	−0.297063	−	0.299928i
$445$	2.74458	+	10.2429i	0.130106	+	0.485561i
$446$	1.24168	+	2.15065i	0.0587953	+	0.101836i
$447$	17.1391	+	10.0052i	0.810652	+	0.473231i
$448$	4.65833	−	1.24820i	0.220085	−	0.0589717i
$449$	−27.0556	−	15.6205i	−1.27683	−	0.737179i	−0.300567	−	0.953761i	$-0.597176\pi$
$449$	−27.0556	−	15.6205i	−1.27683	−	0.737179i	−0.976264	+	0.216582i	$0.930509\pi$
$450$	−8.55368	+	30.7397i	−0.403224	+	1.44908i
$451$	0.535981	−	0.535981i	0.0252383	−	0.0252383i
$452$	9.06830	−	5.23558i	0.426537	−	0.246261i
$453$	8.00096	−	7.92455i	0.375918	−	0.372328i
$454$		−	20.3201i		−	0.953670i
$455$	72.2815	−	72.2815i	3.38861	−	3.38861i
$456$	−2.44190	+	2.41858i	−0.114353	+	0.113260i
$457$	−6.73588	−	1.80487i	−0.315091	−	0.0844285i	0.0978075	−	0.995205i	$-0.468817\pi$
$457$	−6.73588	−	1.80487i	−0.315091	−	0.0844285i	−0.412899	+	0.910777i	$0.635484\pi$
$458$	−3.78425	−	1.01399i	−0.176826	−	0.0473804i
$459$	5.43428	−	19.1727i	0.253650	−	0.894906i
$460$	2.60339	−	2.60339i	0.121384	−	0.121384i
$461$			1.31636i			0.0613089i	0.999530	+	0.0306545i	$0.00975915\pi$
$461$			1.31636i			0.0613089i	−0.999530	+	0.0306545i	$0.990241\pi$
$462$	−1.15493	−	1.16607i	−0.0537322	−	0.0542504i
$463$	5.03584	−	2.90744i	0.234035	−	0.135120i	−0.378397	−	0.925643i	$-0.623525\pi$
$463$	5.03584	−	2.90744i	0.234035	−	0.135120i	0.612432	+	0.790523i	$0.290191\pi$
$464$	0.596907	−	0.596907i	0.0277107	−	0.0277107i
$465$	17.5049	+	66.6061i	0.811772	+	3.08878i
$466$	6.87946	+	3.97186i	0.318685	+	0.183993i
$467$	−1.22193	+	0.327414i	−0.0565440	+	0.0151509i	−0.286980	−	0.957937i	$-0.592651\pi$
$467$	−1.22193	+	0.327414i	−0.0565440	+	0.0151509i	0.230436	+	0.973087i	$0.425985\pi$
$468$	14.0032	−	7.90654i	0.647297	−	0.365480i
$469$	−18.9973	−	32.9044i	−0.877215	−	1.51938i
$470$	6.36540	+	23.7560i	0.293614	+	1.09578i
$471$	9.27254	−	9.18398i	0.427256	−	0.423175i
$472$	1.76611	+	1.01967i	0.0812920	+	0.0469340i
$473$	−0.418996	+	0.725723i	−0.0192655	+	0.0333688i
$474$	−0.0805383	+	16.7849i	−0.00369925	+	0.770955i
$475$	18.2773	+	10.5524i	0.838620	+	0.484178i
$476$	9.24778	+	16.0176i	0.423871	+	0.734167i
$477$	0.560099	−	2.01285i	0.0256451	−	0.0921621i
$478$	11.6387	+	3.11857i	0.532341	+	0.142640i
$479$	33.0397			1.50962			0.754811	−	0.655942i	$-0.227728\pi$
$479$	33.0397			1.50962			0.754811	+	0.655942i	$0.227728\pi$
$480$	−1.74087	−	6.62397i	−0.0794593	−	0.302342i
$481$	26.5905	−	7.12491i	1.21242	−	0.324868i
$482$	24.3768	−	6.53175i	1.11033	−	0.297513i
$483$	6.75409	−	3.85638i	0.307322	−	0.175472i
$484$	5.48070	+	9.49285i	0.249123	+	0.431493i
$485$			35.9656i			1.63311i
$486$	−11.2840	+	10.7551i	−0.511851	+	0.487862i
$487$			39.2696i			1.77948i	0.456471	+	0.889738i	$0.349113\pi$
$487$			39.2696i			1.77948i	−0.456471	+	0.889738i	$0.650887\pi$
$488$	7.45821	+	2.31844i	0.337617	+	0.104951i
$489$	0.282022	−	0.483108i	0.0127535	−	0.0218469i
$490$	−16.6389	−	62.0972i	−0.751669	−	2.80527i
$491$	−13.8005			−0.622808			−0.311404	−	0.950278i	$-0.600799\pi$
$491$	−13.8005			−0.622808			−0.311404	+	0.950278i	$0.600799\pi$
$492$	6.68193	+	0.0320617i	0.301245	+	0.00144545i
$493$	2.80371	+	1.61873i	0.126273	+	0.0729037i
$494$	−2.75296	−	10.2742i	−0.123861	−	0.462257i
$495$	−1.66385	+	1.63221i	−0.0747843	+	0.0733626i
$496$	−7.11018	−	7.11018i	−0.319256	−	0.319256i
$497$		−	65.7138i		−	2.94767i
$498$	12.6131	+	12.7348i	0.565208	+	0.570658i
$499$	−0.427990	−	0.427990i	−0.0191595	−	0.0191595i	0.697462	−	0.716622i	$-0.254313\pi$
$499$	−0.427990	−	0.427990i	−0.0191595	−	0.0191595i	−0.716622	+	0.697462i	$0.754313\pi$
$500$	−19.2998	+	11.1427i	−0.863113	+	0.498319i
$501$	−24.0471	+	13.7302i	−1.07435	+	0.613419i
$502$	18.7025	−	10.7979i	0.834732	−	0.481933i
$503$	−21.0914	−	12.1771i	−0.940421	−	0.542952i	−0.0503286	−	0.998733i	$-0.516027\pi$
$503$	−21.0914	−	12.1771i	−0.940421	−	0.542952i	−0.890092	+	0.455781i	$0.849360\pi$
$504$	0.138839	−	14.4673i	0.00618439	−	0.644425i
$505$	15.5528	−	58.0438i	0.692090	−	2.58292i
$506$	0.176707	−	0.0473486i	0.00785560	−	0.00210490i
$507$	−0.130758	+	27.2510i	−0.00580715	+	1.21026i
$508$	5.15122			0.228548
$509$	5.29411	+	19.7579i	0.234657	+	0.875753i	0.978303	+	0.207179i	$0.0664283\pi$
$509$	5.29411	+	19.7579i	0.234657	+	0.875753i	−0.743646	+	0.668574i	$0.766905\pi$
$510$	22.8103	−	13.0240i	1.01005	−	0.576711i
$511$	−32.8581	+	32.8581i	−1.45356	+	1.45356i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.02631	+	9.00266i	0.221917	+	0.397477i
$514$	4.19262	+	1.12341i	0.184929	+	0.0495515i
$515$	−28.1214			−1.23918
$516$	−7.14463	+	1.87770i	−0.314525	+	0.0826612i
$517$	−0.316288	+	1.18040i	−0.0139103	+	0.0519140i
$518$	6.41019	−	23.9232i	0.281648	−	1.05112i
$519$	17.0907	−	16.9275i	0.750198	−	0.743033i
$520$	20.4739	+	5.48595i	0.897838	+	0.240575i
$521$	−19.1368	−	19.1368i	−0.838400	−	0.838400i	0.150248	−	0.988648i	$-0.451993\pi$
$521$	−19.1368	−	19.1368i	−0.838400	−	0.838400i	−0.988648	+	0.150248i	$0.951993\pi$
$522$	−1.24513	−	2.20523i	−0.0544977	−	0.0965202i
$523$	7.54304	−	28.1510i	0.329834	−	1.23096i	−0.579528	−	0.814952i	$-0.696763\pi$
$523$	7.54304	−	28.1510i	0.329834	−	1.23096i	0.909362	−	0.416005i	$-0.136570\pi$
$524$	4.45244	+	7.71185i	0.194506	+	0.336894i
$525$	−85.9244	+	22.5821i	−3.75005	+	0.985562i
$526$	11.7059	+	11.7059i	0.510403	+	0.510403i
$527$	19.2818	−	33.3970i	0.839927	−	1.45480i
$528$	0.0896557	−	0.328291i	0.00390176	−	0.0142870i
$529$		−	22.1331i		−	0.962307i
$530$	2.38493	−	1.37694i	0.103595	−	0.0598105i
$531$	4.36739	−	4.28437i	0.189529	−	0.185926i
$532$	−9.24355	−	2.47680i	−0.400759	−	0.107383i
$533$	−10.3398	+	17.9090i	−0.447865	+	0.775725i
$534$	−4.03373	+	2.30314i	−0.174557	+	0.0996667i
$535$	19.8918	+	34.4537i	0.860000	+	1.48956i
$536$	3.93919	−	6.82287i	0.170147	−	0.294703i
$537$	9.46330	+	0.0454074i	0.408372	+	0.00195948i
$538$	−7.17607	+	7.17607i	−0.309382	+	0.309382i
$539$	0.826764	−	3.08552i	0.0356112	−	0.132903i
$540$	−20.5446	−	0.295754i	−0.884099	−	0.0127272i
$541$	3.73419	−	3.73419i	0.160546	−	0.160546i	−0.622263	−	0.782808i	$-0.713786\pi$
$541$	3.73419	−	3.73419i	0.160546	−	0.160546i	0.782808	+	0.622263i	$0.213786\pi$
$542$	−0.786604	−	2.93565i	−0.0337876	−	0.126097i
$543$	3.52925	+	0.963834i	0.151455	+	0.0413621i
$544$	−1.91757	+	3.32133i	−0.0822152	+	0.142401i
$545$	0.383263	−	0.221277i	0.0164172	−	0.00947847i
$546$	38.6690	+	22.5736i	1.65488	+	0.966062i
$547$	36.6700	−	9.82569i	1.56789	−	0.420116i	0.632742	−	0.774362i	$-0.281929\pi$
$547$	36.6700	−	9.82569i	1.56789	−	0.420116i	0.935152	+	0.354246i	$0.115263\pi$
$548$	11.4268			0.488127
$549$	12.6988	−	19.6911i	0.541974	−	0.840396i
$550$	−2.08973			−0.0891065
$551$	−1.61798	+	0.433537i	−0.0689284	+	0.0184693i
$552$	1.39275	+	0.813042i	0.0592795	+	0.0346054i
$553$	−40.4743	+	23.3678i	−1.72114	+	0.993702i
$554$	0.312856	−	0.541883i	0.0132920	−	0.0230224i
$555$	−33.9305	−	9.26637i	−1.44027	−	0.393336i
$556$	−1.90004	−	7.09103i	−0.0805794	−	0.300727i
$557$	−26.4833	+	26.4833i	−1.12213	+	1.12213i	−0.130714	+	0.991420i	$0.541727\pi$
$557$	−26.4833	+	26.4833i	−1.12213	+	1.12213i	−0.991420	+	0.130714i	$0.958273\pi$
$558$	−26.2680	+	14.8316i	−1.11201	+	0.627870i
$559$	5.91716	−	22.0831i	0.250269	−	0.934017i
$560$	13.4844	−	13.4844i	0.569821	−	0.569821i
$561$	1.30513	+	0.00626238i	0.0551028	+	0.000264398i
$562$	−13.2793	+	23.0005i	−0.560154	+	0.970216i
$563$	−12.5981	−	21.8205i	−0.530946	−	0.919626i	−0.999348	−	0.0361100i	$-0.988503\pi$
$563$	−12.5981	−	21.8205i	−0.530946	−	0.919626i	0.468402	−	0.883516i	$-0.344830\pi$
$564$	−9.35526	+	5.34157i	−0.393927	+	0.224921i
$565$	20.7027	−	35.8581i	0.870967	−	1.50856i
$566$	16.3331	+	4.37643i	0.686529	+	0.183955i
$567$	−41.7016	−	12.0363i	−1.75130	−	0.505477i
$568$	11.8005	−	6.81303i	0.495139	−	0.285868i
$569$			20.7618i			0.870381i	0.900338	+	0.435190i	$0.143319\pi$
$569$			20.7618i			0.870381i	−0.900338	+	0.435190i	$0.856681\pi$
$570$	−3.58039	+	13.1102i	−0.149966	+	0.549127i
$571$	−11.2233	+	19.4393i	−0.469681	+	0.813511i	−0.999399	−	0.0346628i	$-0.988964\pi$
$571$	−11.2233	+	19.4393i	−0.469681	+	0.813511i	0.529718	+	0.848174i	$0.322298\pi$
$572$	0.744728	+	0.744728i	0.0311386	+	0.0311386i
$573$	14.7627	−	3.87983i	0.616720	−	0.162082i
$574$	9.30256	+	16.1125i	0.388281	+	0.672523i
$575$	2.56308	−	9.56554i	0.106888	−	0.398911i
$576$	2.61235	−	1.47500i	0.108848	−	0.0614583i
$577$	10.6584	+	10.6584i	0.443714	+	0.443714i	0.893258	−	0.449544i	$-0.148414\pi$
$577$	10.6584	+	10.6584i	0.443714	+	0.443714i	−0.449544	+	0.893258i	$0.648414\pi$
$578$	2.21361	+	0.593134i	0.0920739	+	0.0246711i
$579$	9.49236	−	9.40170i	0.394489	−	0.390721i
$580$	0.863931	−	3.22423i	0.0358728	−	0.133879i
$581$	−12.9168	+	48.2060i	−0.535878	+	1.99992i
$582$	−15.2364	+	4.00433i	−0.631571	+	0.165985i
$583$	0.136837			0.00566719
$584$	−9.30711	−	2.49383i	−0.385131	−	0.103196i
$585$	32.3211	−	54.7614i	1.33631	−	2.26411i
$586$	19.6217	+	19.6217i	0.810567	+	0.810567i
$587$	−14.7998	+	14.7998i	−0.610855	+	0.610855i	−0.943169	−	0.332314i	$-0.892171\pi$
$587$	−14.7998	+	14.7998i	−0.610855	+	0.610855i	0.332314	+	0.943169i	$0.392171\pi$
$588$	24.4543	−	13.9627i	1.00848	−	0.575811i
$589$	5.16417	+	19.2729i	0.212786	+	0.794127i
$590$	8.06398			0.331989
$591$	−0.126363	+	26.3351i	−0.00519788	+	1.08328i
$592$	4.96058	−	1.32918i	0.203879	−	0.0546291i
$593$	−3.29900	+	12.3120i	−0.135474	+	0.505595i	0.864522	+	0.502595i	$0.167621\pi$
$593$	−3.29900	+	12.3120i	−0.135474	+	0.505595i	−0.999996	+	0.00299961i	$0.999045\pi$
$594$	−0.876720	−	0.523143i	−0.0359722	−	0.0214648i
$595$	63.3373	+	36.5678i	2.59657	+	1.49913i
$596$	−9.92287	+	5.72897i	−0.406456	+	0.234668i
$597$	17.1155	−	9.77244i	0.700491	−	0.399960i
$598$	−4.32233	+	2.49550i	−0.176753	+	0.102049i
$599$	7.35235	+	7.35235i	0.300409	+	0.300409i	0.841174	−	0.540765i	$-0.181865\pi$
$599$	7.35235	+	7.35235i	0.300409	+	0.300409i	−0.540765	+	0.841174i	$0.681865\pi$
$600$	−12.9636	−	13.0886i	−0.529236	−	0.534339i
$601$		−	10.8870i		−	0.444090i	−0.975036	−	0.222045i	$-0.928727\pi$
$601$		−	10.8870i		−	0.444090i	0.975036	−	0.222045i	$-0.0712732\pi$
$602$	−14.5443	−	14.5443i	−0.592782	−	0.592782i
$603$	−16.5514	−	16.8722i	−0.674025	−	0.687087i
$604$	1.68275	+	6.28010i	0.0684700	+	0.255534i
$605$	37.5368	+	21.6719i	1.52609	+	0.881088i
$606$	26.3213	+	0.126296i	1.06923	+	0.00513044i
$607$	−44.0702			−1.78876			−0.894378	−	0.447313i	$-0.852381\pi$
$607$	−44.0702			−1.78876			−0.894378	+	0.447313i	$0.852381\pi$
$608$	−0.513576	−	1.91669i	−0.0208283	−	0.0777321i
$609$	3.55491	−	6.08961i	0.144052	−	0.246764i
$610$	30.1241	−	6.80630i	1.21969	−	0.275579i
$611$		−	33.3398i		−	1.34878i
$612$	8.05712	+	8.21326i	0.325690	+	0.332001i
$613$		−	14.9809i		−	0.605071i	−0.953138	−	0.302535i	$-0.902167\pi$
$613$		−	14.9809i		−	0.605071i	0.953138	−	0.302535i	$-0.0978331\pi$
$614$	−0.633749	−	1.09768i	−0.0255760	−	0.0442990i
$615$	22.9454	−	13.1011i	0.925247	−	0.528288i
$616$	0.915267	−	0.245245i	0.0368772	−	0.00988121i
$617$	46.7691	−	12.5318i	1.88285	−	0.504509i	0.883506	−	0.468419i	$-0.155176\pi$
$617$	46.7691	−	12.5318i	1.88285	−	0.504509i	0.999349	−	0.0360903i	$-0.0114904\pi$
$618$	−3.13098	−	11.9133i	−0.125947	−	0.479225i
$619$	−24.5923			−0.988447			−0.494223	−	0.869335i	$-0.664548\pi$
$619$	−24.5923			−0.988447			−0.494223	+	0.869335i	$0.664548\pi$
$620$	−38.4061	−	10.2909i	−1.54243	−	0.413292i
$621$	3.46994	−	3.37145i	0.139244	−	0.135292i
$622$	−3.45155	−	5.97826i	−0.138395	−	0.239707i
$623$	−11.2005	−	6.46660i	−0.448737	−	0.259079i
$624$	−0.0445487	+	9.28433i	−0.00178337	+	0.371670i
$625$	−17.4712	+	30.2610i	−0.698848	+	1.21044i
$626$	−22.6095	−	13.0536i	−0.903658	−	0.521727i
$627$	−0.479784	+	0.475202i	−0.0191607	+	0.0189777i
$628$	1.95018	+	7.27818i	0.0778208	+	0.290431i
$629$	9.84781	+	17.0569i	0.392658	+	0.680104i
$630$	−28.1280	−	49.8171i	−1.12065	−	1.98476i
$631$	−6.58195	+	1.76363i	−0.262023	+	0.0702089i	−0.387439	−	0.921895i	$-0.626640\pi$
$631$	−6.58195	+	1.76363i	−0.262023	+	0.0702089i	0.125416	+	0.992104i	$0.459974\pi$
$632$	−8.39253	−	4.84543i	−0.333837	−	0.192741i
$633$	3.96928	+	15.1030i	0.157765	+	0.600292i
$634$	−4.69893	+	4.69893i	−0.186618	+	0.186618i
$635$	17.6401	−	10.1845i	0.700027	−	0.404161i
$636$	0.848860	+	0.857046i	0.0336595	+	0.0339841i
$637$			87.1490i			3.45297i
$638$	0.117280	−	0.117280i	0.00464317	−	0.00464317i
$639$	−10.2007	−	39.5850i	−0.403532	−	1.56596i
$640$	3.81948	+	1.02343i	0.150978	+	0.0404545i
$641$	11.7788	+	3.15612i	0.465235	+	0.124659i	0.483819	−	0.875168i	$-0.339249\pi$
$641$	11.7788	+	3.15612i	0.465235	+	0.124659i	−0.0185844	+	0.999827i	$0.505916\pi$
$642$	−12.3812	+	12.2630i	−0.488648	+	0.483981i
$643$	−3.47780	+	3.47780i	−0.137151	+	0.137151i	−0.772349	−	0.635198i	$-0.780918\pi$
$643$	−3.47780	+	3.47780i	−0.137151	+	0.137151i	0.635198	+	0.772349i	$0.280918\pi$
$644$			4.49034i			0.176944i
$645$	−20.7540	+	20.5558i	−0.817190	+	0.809385i
$646$	6.59053	−	3.80505i	0.259301	−	0.149708i
$647$	−12.5731	+	12.5731i	−0.494301	+	0.494301i	−0.909658	−	0.415357i	$-0.863657\pi$
$647$	−12.5731	+	12.5731i	−0.494301	+	0.494301i	0.415357	+	0.909658i	$0.363657\pi$
$648$	−2.16210	−	8.73644i	−0.0849354	−	0.343200i
$649$	0.347006	+	0.200344i	0.0136212	+	0.00786418i
$650$	55.0696	−	14.7558i	2.16001	−	0.578772i
$651$	−72.5376	−	42.3450i	−2.84297	−	1.65963i
$652$	0.161485	+	0.279700i	0.00632425	+	0.0109539i
$653$	12.5754	+	46.9319i	0.492112	+	1.83659i	0.545638	+	0.838021i	$0.316287\pi$
$653$	12.5754	+	46.9319i	0.492112	+	1.83659i	−0.0535257	+	0.998566i	$0.517046\pi$
$654$	0.136414	+	0.137729i	0.00533419	+	0.00538563i
$655$	30.4943	+	17.6059i	1.19151	+	0.687920i
$656$	−1.92893	+	3.34100i	−0.0753120	+	0.130444i
$657$	−14.6927	+	24.8937i	−0.573217	+	0.971197i
$658$	−25.9768	−	14.9977i	−1.01268	−	0.584671i
$659$	13.2109	+	22.8819i	0.514623	+	0.891352i	0.999856	+	0.0169678i	$0.00540126\pi$
$659$	13.2109	+	22.8819i	0.514623	+	0.891352i	−0.485234	+	0.874385i	$0.661265\pi$
$660$	−0.342045	−	1.30148i	−0.0133141	−	0.0506599i
$661$	26.5744	+	7.12058i	1.03362	+	0.276959i	0.735469	−	0.677559i	$-0.236962\pi$
$661$	26.5744	+	7.12058i	1.03362	+	0.276959i	0.298155	+	0.954517i	$0.403629\pi$
$662$	−4.38344			−0.170367
$663$	−34.4376	+	9.05066i	−1.33745	+	0.351499i
$664$	−9.99574	+	2.67835i	−0.387910	+	0.103940i
$665$	−36.5510	+	9.79382i	−1.41739	+	0.379788i
$666$	0.147848	−	15.4060i	0.00572898	−	0.596970i
$667$	0.392993	+	0.680684i	0.0152167	+	0.0263562i
$668$		−	15.9873i		−	0.618567i
$669$	−1.13318	+	4.14936i	−0.0438114	+	0.160423i
$670$		−	31.1528i		−	1.20354i
$671$	1.46539	+	0.455527i	0.0565706	+	0.0175854i
$672$	7.21386	+	4.21120i	0.278281	+	0.162451i
$673$	6.23750	+	23.2787i	0.240438	+	0.897327i	0.975622	+	0.219459i	$0.0704292\pi$
$673$	6.23750	+	23.2787i	0.240438	+	0.897327i	−0.735184	+	0.677868i	$0.762904\pi$
$674$	−15.6497			−0.602803
$675$	−48.2542	+	26.9410i	−1.85731	+	1.03696i
$676$	−13.6257	−	7.86678i	−0.524064	−	0.302568i
$677$	−10.4633	−	39.0497i	−0.402139	−	1.50080i	−0.809273	−	0.587433i	$-0.800139\pi$
$677$	−10.4633	−	39.0497i	−0.402139	−	1.50080i	0.407134	−	0.913368i	$-0.366528\pi$
$678$	17.4959	+	4.77810i	0.671925	+	0.183502i
$679$	−31.0168	−	31.0168i	−1.19032	−	1.19032i
$680$			15.1650i			0.581551i
$681$	25.0061	−	24.7673i	0.958235	−	0.949083i
$682$	−1.39701	−	1.39701i	−0.0534941	−	0.0534941i
$683$	18.9100	−	10.9177i	0.723569	−	0.417753i	−0.0924956	−	0.995713i	$-0.529484\pi$
$683$	18.9100	−	10.9177i	0.723569	−	0.417753i	0.816065	+	0.577960i	$0.196151\pi$
$684$	−5.95264	−	0.0571261i	−0.227605	−	0.00218427i
$685$	39.1304	−	22.5920i	1.49510	−	0.863194i
$686$	38.6665	+	22.3241i	1.47629	+	0.852338i
$687$	−3.36463	−	5.89282i	−0.128368	−	0.224825i
$688$	1.10387	−	4.11970i	0.0420847	−	0.157062i
$689$	−3.60598	+	0.966219i	−0.137377	+	0.0368100i
$690$	6.37690	+	0.0305981i	0.242764	+	0.00116485i
$691$	22.4726			0.854900			0.427450	−	0.904039i	$-0.359412\pi$
$691$	22.4726			0.854900			0.427450	+	0.904039i	$0.359412\pi$
$692$	3.59448	+	13.4148i	0.136642	+	0.509954i
$693$	0.0272791	−	2.84253i	0.00103625	−	0.107979i
$694$	9.57782	−	9.57782i	0.363569	−	0.363569i
$695$	−20.5263	−	20.5263i	−0.778608	−	0.778608i
$696$	1.46210	+	0.00701555i	0.0554208	+	0.000265924i
$697$	−14.2913	−	3.82934i	−0.541321	−	0.145047i
$698$	−4.50637			−0.170568
$699$	3.49726	+	13.3070i	0.132279	+	0.503318i
$700$	13.2756	−	49.5454i	0.501772	−	1.87264i
$701$	10.3933	−	38.7882i	0.392548	−	1.46501i	−0.433369	−	0.901217i	$-0.642675\pi$
$701$	10.3933	−	38.7882i	0.392548	−	1.46501i	0.825917	−	0.563792i	$-0.190658\pi$
$702$	26.7977	+	7.59548i	1.01141	+	0.286673i
$703$	−9.84330	−	2.63751i	−0.371247	−	0.0994754i
$704$	0.138932	+	0.138932i	0.00523620	+	0.00523620i
$705$	−21.4758	+	36.7884i	−0.808825	+	1.38553i
$706$	2.89419	−	10.8013i	0.108924	−	0.406511i
$707$	36.6444	+	63.4699i	1.37815	+	2.38703i
$708$	0.897827	+	3.41622i	0.0337424	+	0.128389i
$709$	−28.2432	−	28.2432i	−1.06070	−	1.06070i	−0.998035	−	0.0626615i	$-0.980041\pi$
$709$	−28.2432	−	28.2432i	−1.06070	−	1.06070i	−0.0626615	−	0.998035i	$-0.519959\pi$
$710$	26.9402	−	46.6619i	1.01105	−	1.75119i
$711$	−20.7537	+	20.3592i	−0.778326	+	0.763530i
$712$		−	2.68176i		−	0.100503i
$713$	8.10810	−	4.68121i	0.303651	−	0.175313i
$714$	−8.43971	+	30.9035i	−0.315848	+	1.15654i
$715$	4.02270	+	1.07788i	0.150440	+	0.0403104i
$716$	−2.73185	+	4.73171i	−0.102094	+	0.176832i
$717$	10.3481	+	18.1237i	0.386457	+	0.676843i
$718$	−15.0792	−	26.1180i	−0.562752	−	0.974715i
$719$	7.25574	−	12.5673i	0.270593	−	0.468681i	−0.698421	−	0.715688i	$-0.746113\pi$
$719$	7.25574	−	12.5673i	0.270593	−	0.468681i	0.969014	+	0.247006i	$0.0794468\pi$
$720$	6.02965	−	10.2160i	0.224712	−	0.380727i
$721$	24.2520	−	24.2520i	0.903192	−	0.903192i
$722$	3.89847	−	14.5493i	0.145086	−	0.541468i
$723$	37.7498	+	22.0371i	1.40393	+	0.819567i
$724$	−1.49357	+	1.49357i	−0.0555083	+	0.0555083i
$725$	−2.32376	−	8.67239i	−0.0863022	−	0.322084i
$726$	−5.00180	+	18.3150i	−0.185634	+	0.679733i
$727$	−14.5496	+	25.2006i	−0.539613	+	0.934637i	0.459312	+	0.888275i	$0.348096\pi$
$727$	−14.5496	+	25.2006i	−0.539613	+	0.934637i	−0.998925	+	0.0463621i	$0.985237\pi$
$728$	−22.3878	+	12.9256i	−0.829748	+	0.479055i
$729$	−26.9888	−	0.777206i	−0.999586	−	0.0287854i
$730$	−36.8024	+	9.86117i	−1.36212	+	0.364978i
$731$	16.3570			0.604985
$732$	6.23738	+	12.0040i	0.230540	+	0.443679i
$733$	−5.60747			−0.207116			−0.103558	−	0.994623i	$-0.533023\pi$
$733$	−5.60747			−0.207116			−0.103558	+	0.994623i	$0.533023\pi$
$734$	−1.31606	+	0.352637i	−0.0485766	+	0.0130161i
$735$	56.1369	−	96.1634i	2.07064	−	3.54704i
$736$	−0.806350	+	0.465546i	−0.0297224	+	0.0171603i
$737$	0.773970	−	1.34056i	0.0285096	−	0.0493800i
$738$	8.10484	+	8.26191i	0.298343	+	0.304125i
$739$	−7.58271	−	28.2991i	−0.278934	−	1.04100i	−0.953159	−	0.302471i	$-0.902189\pi$
$739$	−7.58271	−	28.2991i	−0.278934	−	1.04100i	0.674224	−	0.738527i	$-0.264478\pi$
$740$	14.3593	−	14.3593i	0.527860	−	0.527860i
$741$	9.28803	−	15.9105i	0.341204	−	0.584488i
$742$	−0.869295	+	3.24425i	−0.0319128	+	0.119100i
$743$	−9.88451	+	9.88451i	−0.362627	+	0.362627i	−0.864779	−	0.502152i	$-0.832542\pi$
$743$	−9.88451	+	9.88451i	−0.362627	+	0.362627i	0.502152	+	0.864779i	$0.332542\pi$
$744$	0.0835671	−	17.4161i	0.00306372	−	0.638505i
$745$	−22.6536	+	39.2372i	−0.829964	+	1.43754i
$746$	−6.77056	−	11.7270i	−0.247888	−	0.429354i
$747$	−0.297918	+	31.0436i	−0.0109003	+	1.13583i
$748$	−0.376764	+	0.652574i	−0.0137758	+	0.0238605i
$749$	−46.8678	−	12.5582i	−1.71251	−	0.458866i
$750$	−37.2360	−	10.1691i	−1.35967	−	0.371323i
$751$	34.9510	−	20.1790i	1.27538	−	0.736342i	0.299386	−	0.954132i	$-0.403218\pi$
$751$	34.9510	−	20.1790i	1.27538	−	0.736342i	0.975996	+	0.217791i	$0.0698850\pi$
$752$		−	6.21968i		−	0.226808i
$753$	36.0835	+	9.85436i	1.31496	+	0.359113i
$754$	−2.26249	+	3.91875i	−0.0823950	+	0.142712i
$755$	18.1789	+	18.1789i	0.661600	+	0.661600i
$756$	17.9728	−	17.4627i	0.653664	−	0.635111i
$757$	24.1627	+	41.8510i	0.878209	+	1.52110i	0.853305	+	0.521412i	$0.174595\pi$
$757$	24.1627	+	41.8510i	0.878209	+	1.52110i	0.0249036	+	0.999690i	$0.492072\pi$
$758$	−9.95789	+	37.1633i	−0.361687	+	1.34983i
$759$	0.273648	+	0.159746i	0.00993279	+	0.00579842i
$760$	−5.54823	−	5.54823i	−0.201256	−	0.201256i
$761$	41.7423	+	11.1848i	1.51316	+	0.405449i	0.917483	−	0.397776i	$-0.130218\pi$
$761$	41.7423	+	11.1848i	1.51316	+	0.405449i	0.595675	+	0.803225i	$0.296884\pi$
$762$	6.27859	+	6.33913i	0.227449	+	0.229642i
$763$	−0.139697	+	0.521358i	−0.00505738	+	0.0188744i
$764$	−2.28089	+	8.51240i	−0.0825197	+	0.307968i
$765$	43.8298	+	12.1961i	1.58467	+	0.440952i
$766$	−2.09486			−0.0756904
$767$	−10.5591	−	2.82930i	−0.381267	−	0.102160i
$768$	−0.00831075	+	1.73203i	−0.000299888	+	0.0624993i
$769$	−17.5183	−	17.5183i	−0.631726	−	0.631726i	0.316775	−	0.948501i	$-0.397400\pi$
$769$	−17.5183	−	17.5183i	−0.631726	−	0.631726i	−0.948501	+	0.316775i	$0.897400\pi$
$770$	2.64942	−	2.64942i	0.0954783	−	0.0954783i
$771$	3.72772	+	6.52874i	0.134250	+	0.235127i
$772$	1.99642	+	7.45072i	0.0718526	+	0.268157i
$773$	0.123332			0.00443594			0.00221797	−	0.999998i	$-0.499294\pi$
$773$	0.123332			0.00443594			0.00221797	+	0.999998i	$0.499294\pi$
$774$	−11.0190	−	6.50359i	−0.396069	−	0.233767i
$775$	−103.303	+	27.6799i	−3.71075	+	0.994292i
$776$	2.35409	−	8.78557i	0.0845068	−	0.315384i
$777$	37.2531	−	21.2704i	1.33645	−	0.763072i
$778$	−8.74808	−	5.05071i	−0.313634	−	0.181077i
$779$	6.62957	−	3.82759i	0.237529	−	0.137137i
$780$	18.2036	+	31.8818i	0.651793	+	1.14155i
$781$	2.31856	−	1.33862i	0.0829647	−	0.0478997i
$782$	−2.52499	−	2.52499i	−0.0902933	−	0.0902933i
$783$	1.19614	−	4.22011i	0.0427466	−	0.150815i
$784$			16.2580i			0.580643i
$785$	21.0681	+	21.0681i	0.751952	+	0.751952i
$786$	−4.06338	+	14.8788i	−0.144936	+	0.530710i
$787$	−14.2982	−	53.3617i	−0.509677	−	1.90214i	−0.423598	−	0.905850i	$-0.639233\pi$
$787$	−14.2982	−	53.3617i	−0.509677	−	1.90214i	−0.0860786	−	0.996288i	$-0.527434\pi$
$788$	−13.1677	−	7.60238i	−0.469080	−	0.270824i
$789$	−0.137582	+	28.6733i	−0.00489805	+	1.02080i
$790$	−38.3198			−1.36336
$791$	13.0701	+	48.7781i	0.464718	+	1.73435i
$792$	0.513274	−	0.289807i	0.0182384	−	0.0102979i
$793$	−41.8330	−	1.65697i	−1.48553	−	0.0588408i
$794$		−	31.4710i		−	1.11686i
$795$	4.60136	+	1.25662i	0.163193	+	0.0445679i
$796$			11.3789i			0.403316i
$797$	−2.77647	−	4.80900i	−0.0983478	−	0.170343i	0.812653	−	0.582748i	$-0.198022\pi$
$797$	−2.77647	−	4.80900i	−0.0983478	−	0.170343i	−0.911001	+	0.412404i	$0.864689\pi$
$798$	−8.21857	−	14.3940i	−0.290934	−	0.509543i
$799$	23.0406	−	6.17370i	0.815117	−	0.218410i
$800$	10.2735	−	2.75277i	0.363222	−	0.0973250i
$801$	−7.75079	−	2.15675i	−0.273861	−	0.0762049i
$802$	2.28085			0.0805395
$803$	−1.82866	−	0.489988i	−0.0645320	−	0.0172913i
$804$	13.1976	−	3.46849i	0.465442	−	0.122324i
$805$	8.87790	+	15.3770i	0.312905	+	0.541967i
$806$	46.6789	+	26.9501i	1.64419	+	0.949276i
$807$	−17.5775	−	0.0843416i	−0.618758	−	0.00296896i
$808$	−7.59838	+	13.1608i	−0.267310	+	0.462995i
$809$	2.91683	+	1.68403i	0.102550	+	0.0592074i	0.550398	−	0.834902i	$-0.314476\pi$
$809$	2.91683	+	1.68403i	0.102550	+	0.0592074i	−0.447848	+	0.894110i	$0.647809\pi$
$810$	−24.6769	−	25.6428i	−0.867059	−	0.900997i
$811$	0.980277	+	3.65844i	0.0344222	+	0.128465i	0.980999	−	0.194013i	$-0.0621506\pi$
$811$	0.980277	+	3.65844i	0.0344222	+	0.128465i	−0.946577	+	0.322479i	$0.895484\pi$
$812$	2.03553	+	3.52565i	0.0714332	+	0.123726i
$813$	2.65387	−	4.54613i	0.0930754	−	0.159440i
$814$	0.974653	−	0.261158i	0.0341616	−	0.00915357i
$815$	1.10600	+	0.638548i	0.0387414	+	0.0223674i
$816$	−6.42449	+	1.68844i	−0.224902	+	0.0591072i
$817$	−5.98433	+	5.98433i	−0.209365	+	0.209365i
$818$	−3.65229	+	2.10865i	−0.127699	+	0.0737273i
$819$	19.3526	+	75.1003i	0.676233	+	2.62422i
$820$			15.2548i			0.532722i
$821$	−10.1166	+	10.1166i	−0.353071	+	0.353071i	−0.861251	−	0.508180i	$-0.830318\pi$
$821$	−10.1166	+	10.1166i	−0.353071	+	0.353071i	0.508180	+	0.861251i	$0.330318\pi$
$822$	13.9275	+	14.0618i	0.485779	+	0.490463i
$823$	29.3478	+	7.86373i	1.02300	+	0.274112i	0.731052	−	0.682322i	$-0.239030\pi$
$823$	29.3478	+	7.86373i	1.02300	+	0.274112i	0.291949	+	0.956434i	$0.405696\pi$
$824$	6.86942	+	1.84066i	0.239308	+	0.0641223i
$825$	−2.54708	−	2.57164i	−0.0886779	−	0.0895331i
$826$	−6.95440	+	6.95440i	−0.241974	+	0.241974i
$827$		−	28.4760i		−	0.990209i	−0.868833	−	0.495104i	$-0.835130\pi$
$827$		−	28.4760i		−	0.990209i	0.868833	−	0.495104i	$-0.164870\pi$
$828$	0.697028	+	2.70491i	0.0242234	+	0.0940022i
$829$	8.22754	−	4.75017i	0.285754	−	0.164980i	−0.350271	−	0.936648i	$-0.613911\pi$
$829$	8.22754	−	4.75017i	0.285754	−	0.164980i	0.636026	+	0.771668i	$0.280577\pi$
$830$	−28.9346	+	28.9346i	−1.00433	+	1.00433i
$831$	1.04817	−	0.275473i	0.0363607	−	0.00955606i
$832$	−4.64222	−	2.68018i	−0.160940	−	0.0929187i
$833$	−60.2272	+	16.1378i	−2.08675	+	0.559143i
$834$	6.41041	−	10.9811i	0.221974	−	0.380245i
$835$	−31.6087	−	54.7478i	−1.09386	−	1.89463i
$836$	−0.100907	−	0.376591i	−0.00348995	−	0.0130247i
$837$	−50.2687	−	14.2481i	−1.73754	−	0.492485i
$838$	17.9138	+	10.3425i	0.618820	+	0.357276i
$839$	13.8906	−	24.0592i	0.479555	−	0.830614i	−0.520170	−	0.854063i	$-0.674131\pi$
$839$	13.8906	−	24.0592i	0.479555	−	0.830614i	0.999725	+	0.0234487i	$0.00746464\pi$
$840$	33.0296	+	0.158485i	1.13963	+	0.00546824i
$841$	−24.4976	−	14.1437i	−0.844745	−	0.487714i
$842$	5.10609	+	8.84400i	0.175967	+	0.304784i
$843$	−44.4901	+	11.6926i	−1.53232	+	0.402714i
$844$	−8.70865	−	2.33348i	−0.299764	−	0.0803216i
$845$	−62.2140			−2.14023
$846$	−17.9761	−	5.00205i	−0.618030	−	0.171974i
$847$	−51.0618	+	13.6820i	−1.75450	+	0.470118i
$848$	−0.672711	+	0.180252i	−0.0231010	+	0.00618989i
$849$	14.5219	+	25.4338i	0.498392	+	0.872886i
$850$	20.3950	+	35.3252i	0.699544	+	1.21165i
$851$			4.78169i			0.163914i
$852$	22.7673	+	6.21771i	0.779994	+	0.213015i
$853$		−	9.75471i		−	0.333995i	−0.985957	−	0.166997i	$-0.946593\pi$
$853$		−	9.75471i		−	0.333995i	0.985957	−	0.166997i	$-0.0534072\pi$
$854$	−20.1094	+	31.8489i	−0.688128	+	1.08985i
$855$	−20.4975	+	11.5734i	−0.701000	+	0.395802i
$856$	−2.60400	−	9.71825i	−0.0890027	−	0.332163i
$857$	−35.5782			−1.21533			−0.607664	−	0.794194i	$-0.707893\pi$
$857$	−35.5782			−1.21533			−0.607664	+	0.794194i	$0.707893\pi$
$858$	−0.00875291	+	1.82418i	−0.000298820	+	0.0622765i
$859$	−39.1654	−	22.6121i	−1.33631	−	0.771516i	−0.350048	−	0.936732i	$-0.613835\pi$
$859$	−39.1654	−	22.6121i	−1.33631	−	0.771516i	−0.986257	+	0.165216i	$0.947168\pi$
$860$	−4.36495	−	16.2902i	−0.148844	−	0.555492i
$861$	−8.48971	+	31.0866i	−0.289328	+	1.05943i
$862$	−23.3363	−	23.3363i	−0.794838	−	0.794838i
$863$		−	22.6530i		−	0.771118i	−0.922683	−	0.385559i	$-0.874009\pi$
$863$		−	22.6530i		−	0.771118i	0.922683	−	0.385559i	$-0.125991\pi$
$864$	4.99922	+	1.41697i	0.170077	+	0.0482063i
$865$	38.8317	+	38.8317i	1.32032	+	1.32032i
$866$	29.2229	−	16.8719i	0.993035	−	0.573329i
$867$	1.96815	+	3.44702i	0.0668418	+	0.117067i
$868$	41.9964	−	24.2466i	1.42545	−	0.822985i
$869$	−1.64896	−	0.952029i	−0.0559372	−	0.0322954i
$870$	5.02077	−	2.86671i	0.170220	−	0.0971906i
$871$	−10.9302	+	40.7920i	−0.370355	+	1.38218i
$872$	−0.108106	+	0.0289669i	−0.00366093	+	0.000980943i
$873$	−23.4988	−	13.8694i	−0.795313	−	0.469407i
$874$	1.84757			0.0624951
$875$	−27.8166	−	103.813i	−0.940374	−	3.50952i
$876$	−8.27508	−	14.4930i	−0.279589	−	0.489674i
$877$	−16.1591	+	16.1591i	−0.545653	+	0.545653i	−0.925181	−	0.379527i	$-0.876087\pi$
$877$	−16.1591	+	16.1591i	−0.545653	+	0.545653i	0.379527	+	0.925181i	$0.376087\pi$
$878$	−7.50257	−	7.50257i	−0.253200	−	0.253200i
$879$	−0.230618	+	48.0627i	−0.00777854	+	1.62111i
$880$	0.750451	+	0.201083i	0.0252977	+	0.00677850i
$881$	41.0080			1.38159			0.690797	−	0.723049i	$-0.257260\pi$
$881$	41.0080			1.38159			0.690797	+	0.723049i	$0.257260\pi$
$882$	46.9888	+	13.0752i	1.58220	+	0.440264i
$883$	−0.251650	+	0.939172i	−0.00846871	+	0.0316057i	−0.970031	−	0.242982i	$-0.921875\pi$
$883$	−0.251650	+	0.939172i	−0.00846871	+	0.0316057i	0.961562	+	0.274587i	$0.0885412\pi$
$884$	5.32074	−	19.8573i	0.178956	−	0.667873i
$885$	9.82881	+	9.92359i	0.330392	+	0.333578i
$886$	12.8461	+	3.44211i	0.431575	+	0.115640i
$887$	19.0084	+	19.0084i	0.638241	+	0.638241i	0.950121	−	0.311880i	$-0.100959\pi$
$887$	19.0084	+	19.0084i	0.638241	+	0.638241i	−0.311880	+	0.950121i	$0.600959\pi$
$888$	7.68192	+	4.48444i	0.257788	+	0.150488i
$889$	−6.42973	+	23.9961i	−0.215646	+	0.804803i
$890$	−5.30213	−	9.18356i	−0.177728	−	0.307834i
$891$	−0.424809	−	1.71653i	−0.0142316	−	0.0575060i
$892$	−1.75600	−	1.75600i	−0.0587953	−	0.0587953i
$893$	−6.17087	+	10.6883i	−0.206500	+	0.357669i
$894$	−19.1446	−	5.22837i	−0.640293	−	0.174863i
$895$			21.6047i			0.722165i
$896$	−4.17654	+	2.41133i	−0.139529	+	0.0805568i
$897$	−8.33927	−	2.27744i	−0.278440	−	0.0760416i
$898$	30.1766	+	8.08579i	1.00701	+	0.269826i
$899$	4.24412	−	7.35102i	0.141549	−	0.245170i
$900$	0.306195	−	31.9061i	0.0102065	−	1.06354i
$901$	−1.33548	−	2.31311i	−0.0444911	−	0.0770609i
$902$	−0.378996	+	0.656440i	−0.0126192	+	0.0218570i
$903$	0.170942	−	35.6258i	0.00568859	−	1.18555i
$904$	−7.40423	+	7.40423i	−0.246261	+	0.246261i
$905$	−2.16172	+	8.06764i	−0.0718580	+	0.268178i
$906$	−5.67731	+	9.72533i	−0.188616	+	0.323102i
$907$	24.0254	−	24.0254i	0.797750	−	0.797750i	−0.184990	−	0.982740i	$-0.559225\pi$
$907$	24.0254	−	24.0254i	0.797750	−	0.797750i	0.982740	+	0.184990i	$0.0592253\pi$
$908$	5.25923	+	19.6277i	0.174534	+	0.651369i
$909$	31.9264	+	32.5451i	1.05893	+	1.07945i
$910$	−51.1107	+	88.5264i	−1.69430	+	2.93462i
$911$	−3.31329	+	1.91293i	−0.109774	+	0.0633782i	−0.553882	−	0.832595i	$-0.686854\pi$
$911$	−3.31329	+	1.91293i	−0.109774	+	0.0633782i	0.444108	+	0.895973i	$0.353521\pi$
$912$	1.73272	−	2.96818i	0.0573761	−	0.0982862i
$913$	−1.96396	+	0.526242i	−0.0649976	+	0.0174161i
$914$	6.97350			0.230663
$915$	45.0928	+	28.7751i	1.49072	+	0.951274i
$916$	3.91774			0.129446
$917$	−41.4818	+	11.1150i	−1.36985	+	0.367050i
$918$	−0.286847	+	19.9259i	−0.00946737	+	0.657653i
$919$	25.4229	−	14.6779i	0.838625	−	0.484181i	−0.0181713	−	0.999835i	$-0.505784\pi$
$919$	25.4229	−	14.6779i	0.838625	−	0.484181i	0.856797	+	0.515654i	$0.172451\pi$
$920$	−1.84087	+	3.18849i	−0.0606918	+	0.105121i
$921$	0.578372	−	2.11781i	0.0190580	−	0.0697843i
$922$	−0.340699	−	1.27150i	−0.0112203	−	0.0418748i
$923$	−51.6476	+	51.6476i	−1.70000	+	1.70000i
$924$	1.41738	+	0.827417i	0.0466283	+	0.0272200i
$925$	14.1370	−	52.7601i	0.464822	−	1.73474i
$926$	−4.11175	+	4.11175i	−0.135120	+	0.135120i
$927$	10.8444	−	18.3736i	0.356178	−	0.603469i
$928$	−0.422077	+	0.731059i	−0.0138554	+	0.0239982i
$929$	−16.7271	−	28.9722i	−0.548798	−	0.950547i	−0.998357	−	0.0572961i	$-0.981752\pi$
$929$	−16.7271	−	28.9722i	−0.548798	−	0.950547i	0.449559	−	0.893251i	$-0.351581\pi$
$930$	−34.1474	−	59.8059i	−1.11974	−	1.96111i
$931$	16.1304	−	27.9387i	0.528654	−	0.915655i
$932$	−7.67304	−	2.05598i	−0.251339	−	0.0673460i
$933$	3.14996	−	11.5341i	0.103125	−	0.377611i
$934$	1.09555	−	0.632516i	0.0358475	−	0.0206965i
$935$			2.97962i			0.0974438i
$936$	−11.4797	+	11.2614i	−0.375224	+	0.368091i
$937$	18.4707	−	31.9921i	0.603411	−	1.04514i	−0.388890	−	0.921284i	$-0.627141\pi$
$937$	18.4707	−	31.9921i	0.603411	−	1.04514i	0.992301	−	0.123854i	$-0.0395253\pi$
$938$	26.8663	+	26.8663i	0.877215	+	0.877215i
$939$	−11.4938	−	43.7339i	−0.375087	−	1.42720i
$940$	−12.2970	−	21.2990i	−0.401084	−	0.694698i
$941$	−3.79895	+	14.1779i	−0.123842	+	0.462186i	−0.999796	−	0.0202099i	$-0.993567\pi$
$941$	−3.79895	+	14.1779i	−0.123842	+	0.462186i	0.875953	+	0.482396i	$0.160233\pi$
$942$	−6.57959	+	11.2709i	−0.214375	+	0.367227i
$943$	−2.53994	−	2.53994i	−0.0827119	−	0.0827119i
$944$	−1.96984	−	0.527818i	−0.0641130	−	0.0171790i
$945$	27.0214	−	95.3344i	0.879006	−	3.10123i
$946$	0.216888	−	0.809438i	0.00705165	−	0.0263171i
$947$	−2.76283	+	10.3110i	−0.0897800	+	0.335063i	−0.996176	−	0.0873648i	$-0.972155\pi$
$947$	−2.76283	+	10.3110i	−0.0897800	+	0.335063i	0.906396	+	0.422428i	$0.138822\pi$
$948$	−4.26645	−	16.2338i	−0.138568	−	0.527249i
$949$	51.6495			1.67661
$950$	−20.3857	−	5.46233i	−0.661399	−	0.177221i
$951$	−11.5098	−	0.0552273i	−0.373232	−	0.00179087i
$952$	−13.0783	−	13.0783i	−0.423871	−	0.423871i
$953$	−25.5495	+	25.5495i	−0.827628	+	0.827628i	−0.987188	−	0.159560i	$-0.948992\pi$
$953$	−25.5495	+	25.5495i	−0.827628	+	0.827628i	0.159560	+	0.987188i	$0.448992\pi$
$954$	−0.0200498	+	2.08923i	−0.000649136	+	0.0676412i
$955$	9.01914	+	33.6599i	0.291853	+	1.08921i
$956$	−12.0492			−0.389701
$957$	0.287273	+	0.00137841i	0.00928623	+	4.45578e-5i
$958$	−31.9139	+	8.55130i	−1.03109	+	0.276280i
$959$	−14.2628	+	53.2296i	−0.460570	+	1.71887i
$960$	3.39596	+	5.94770i	0.109604	+	0.191961i
$961$	−60.7164	−	35.0546i	−1.95859	−	1.13079i
$962$	−23.8404	+	13.7643i	−0.768646	+	0.443778i
$963$	−30.1818	−	0.289647i	−0.972595	−	0.00933376i
$964$	−21.8557	+	12.6184i	−0.703924	+	0.406411i
$965$	21.5675	+	21.5675i	0.694284	+	0.694284i
$966$	−5.52584	+	5.47307i	−0.177791	+	0.176093i
$967$			7.48330i			0.240647i	0.992735	+	0.120323i	$0.0383931\pi$
$967$			7.48330i			0.240647i	−0.992735	+	0.120323i	$0.961607\pi$
$968$	−7.75088	−	7.75088i	−0.249123	−	0.249123i
$969$	12.7154	+	3.47256i	0.408478	+	0.111555i
$970$	−9.30858	−	34.7401i	−0.298880	−	1.11544i
$971$	49.7228	+	28.7075i	1.59568	+	0.921266i	0.992306	+	0.123807i	$0.0395104\pi$
$971$	49.7228	+	28.7075i	1.59568	+	0.921266i	0.603373	+	0.797459i	$0.293823\pi$
$972$	8.11584	−	13.3091i	0.260316	−	0.426891i
$973$	35.4040			1.13500
$974$	−10.1637	−	37.9315i	−0.325667	−	1.21540i
$975$	85.2804	+	49.7838i	2.73116	+	1.59436i
$976$	−7.80413	−	0.309115i	−0.249804	−	0.00989454i
$977$		−	56.9187i		−	1.82099i	−0.413520	−	0.910495i	$-0.635701\pi$
$977$		−	56.9187i		−	1.82099i	0.413520	−	0.910495i	$-0.364299\pi$
$978$	−0.147375	+	0.539639i	−0.00471252	+	0.0172557i
$979$		−	0.526911i		−	0.0168401i
$980$	32.1439	+	55.6749i	1.02680	+	1.77847i
$981$	−0.00322204	+	0.335743i	−0.000102872	+	0.0107194i
$982$	13.3303	−	3.57183i	0.425386	−	0.113982i
$983$	−41.0296	+	10.9939i	−1.30864	+	0.350650i	−0.844712	−	0.535222i	$-0.820228\pi$
$983$	−41.0296	+	10.9939i	−1.30864	+	0.350650i	−0.463931	+	0.885871i	$0.653561\pi$
$984$	−6.46255	+	1.69844i	−0.206018	+	0.0541443i
$985$	−60.1230			−1.91568
$986$	−3.12714	−	0.837914i	−0.0995883	−	0.0266846i
$987$	−13.2056	−	50.2472i	−0.420339	−	1.59939i
$988$	5.31831	+	9.21158i	0.169198	+	0.293059i
$989$	3.43911	+	1.98557i	0.109357	+	0.0631374i
$990$	1.18470	−	2.00723i	0.0376523	−	0.0637940i
$991$	5.92533	−	10.2630i	0.188224	−	0.326014i	−0.756434	−	0.654070i	$-0.773060\pi$
$991$	5.92533	−	10.2630i	0.188224	−	0.326014i	0.944658	+	0.328056i	$0.106393\pi$
$992$	8.70815	+	5.02765i	0.276484	+	0.159628i
$993$	−5.34278	−	5.39430i	−0.169548	−	0.171183i
$994$	17.0080	+	63.4747i	0.539461	+	2.01329i
$995$	22.4974	+	38.9667i	0.713217	+	1.23533i
$996$	−15.4793	−	9.03631i	−0.490482	−	0.286326i
$997$	39.6058	−	10.6123i	1.25433	−	0.336096i	0.430321	−	0.902676i	$-0.358400\pi$
$997$	39.6058	−	10.6123i	1.25433	−	0.336096i	0.824007	+	0.566580i	$0.191734\pi$
$998$	0.524179	+	0.302635i	0.0165926	+	0.00957974i
$999$	19.1389	−	18.5957i	0.605529	−	0.588343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.2.o.a.101.2	yes	80
3.2	odd	2	inner	366.2.o.a.101.19	yes	80
61.29	odd	12	inner	366.2.o.a.29.19	yes	80
183.29	even	12	inner	366.2.o.a.29.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.2.o.a.29.2	✓	80	183.29	even	12	inner
366.2.o.a.29.19	yes	80	61.29	odd	12	inner
366.2.o.a.101.2	yes	80	1.1	even	1	trivial
366.2.o.a.101.19	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	366.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.49583 - 0.873213i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.97711 - 3.42446i) q^{5} +(1.67086 + 0.456310i) q^{6} +(1.24820 + 4.65833i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47500 + 2.61235i) q^{9} +(-1.02343 + 3.81948i) q^{10} +(-0.138932 + 0.138932i) q^{11} +(-1.73203 - 0.00831075i) q^{12} +(2.68018 - 4.64222i) q^{13} +(-2.41133 - 4.17654i) q^{14} +(-5.94770 + 3.39596i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.70446 + 0.992608i) q^{17} +(-2.10087 - 2.14158i) q^{18} +(-1.71846 + 0.992153i) q^{19} -3.95422i q^{20} +(2.20063 - 8.05799i) q^{21} +(0.0982399 - 0.170156i) q^{22} +(0.658382 + 0.658382i) q^{23} +(1.67516 - 0.440255i) q^{24} +(-5.31794 - 9.21093i) q^{25} +(-1.38737 + 5.17772i) q^{26} +(0.0747944 - 5.19561i) q^{27} +(3.41013 + 3.41013i) q^{28} +(0.815390 + 0.218483i) q^{29} +(4.86609 - 4.81962i) q^{30} +(2.60251 - 9.71268i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.329136 - 0.0865012i) q^{33} -3.83514 q^{34} +(18.4201 + 4.93564i) q^{35} +(2.58356 + 1.52486i) q^{36} +(3.63140 + 3.63140i) q^{37} +(1.40312 - 1.40312i) q^{38} +(-8.06274 + 4.60358i) q^{39} +(1.02343 + 3.81948i) q^{40} -3.85786 q^{41} +(-0.0400799 + 8.35299i) q^{42} +(4.11970 - 1.10387i) q^{43} +(-0.0508527 + 0.189785i) q^{44} +(11.8621 + 0.113838i) q^{45} +(-0.806350 - 0.465546i) q^{46} +(5.38640 - 3.10984i) q^{47} +(-1.50414 + 0.858818i) q^{48} +(-14.0799 + 8.12901i) q^{49} +(7.52070 + 7.52070i) q^{50} +(-4.67448 - 4.71955i) q^{51} -5.36037i q^{52} +(-0.492458 - 0.492458i) q^{53} +(1.27248 + 5.03794i) q^{54} +(0.201083 + 0.750451i) q^{55} +(-4.17654 - 2.41133i) q^{56} +(3.43688 + 0.0164911i) q^{57} -0.844154 q^{58} +(-0.527818 - 1.96984i) q^{59} +(-3.45288 + 5.91483i) q^{60} +(-3.63436 - 6.91313i) q^{61} +10.0553i q^{62} +(-10.3281 + 10.1318i) q^{63} -1.00000i q^{64} +(-10.5980 - 18.3564i) q^{65} +(-0.295533 + 0.168740i) q^{66} +(-7.60992 + 2.03907i) q^{67} +(3.70446 - 0.992608i) q^{68} +(-0.409918 - 1.55973i) q^{69} -19.0699 q^{70} +(-13.1618 - 3.52668i) q^{71} +(-2.89019 - 0.804229i) q^{72} +(4.81771 + 8.34453i) q^{73} +(-4.44753 - 2.56778i) q^{74} +(-0.0883920 + 18.4217i) q^{75} +(-0.992153 + 1.71846i) q^{76} +(-0.820606 - 0.473777i) q^{77} +(6.59651 - 6.53351i) q^{78} +(2.50818 + 9.36065i) q^{79} +(-1.97711 - 3.42446i) q^{80} +(-4.64876 + 7.70643i) q^{81} +(3.72641 - 0.998487i) q^{82} +(8.96193 + 5.17418i) q^{83} +(-2.12320 - 8.07874i) q^{84} +(10.7233 - 10.7233i) q^{85} +(-3.69363 + 2.13252i) q^{86} +(-1.02890 - 1.03882i) q^{87} -0.196480i q^{88} +(-1.89629 + 1.89629i) q^{89} +(-11.4874 + 2.96018i) q^{90} +(24.9704 + 6.69079i) q^{91} +(0.899366 + 0.240984i) q^{92} +(-12.3741 + 12.2560i) q^{93} +(-4.39798 + 4.39798i) q^{94} +7.84639i q^{95} +(1.23061 - 1.21885i) q^{96} +(-7.87693 + 4.54774i) q^{97} +(11.4962 - 11.4962i) q^{98} +(-0.567864 - 0.158015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{6} + 16 q^{7} + 16 q^{10} - 16 q^{15} + 40 q^{16} - 8 q^{18} + 4 q^{21} - 4 q^{24} - 32 q^{25} - 8 q^{28} + 12 q^{30} + 44 q^{33} + 12 q^{36} - 36 q^{39} - 16 q^{40} - 24 q^{43} + 60 q^{45}+ \cdots + 52 q^{99}+O(q^{100}) \) 80 * q - 8 * q^6 + 16 * q^7 + 16 * q^10 - 16 * q^15 + 40 * q^16 - 8 * q^18 + 4 * q^21 - 4 * q^24 - 32 * q^25 - 8 * q^28 + 12 * q^30 + 44 * q^33 + 12 * q^36 - 36 * q^39 - 16 * q^40 - 24 * q^43 + 60 * q^45 + 48 * q^46 - 144 * q^49 - 32 * q^51 - 4 * q^54 + 32 * q^55 + 56 * q^57 - 48 * q^58 - 48 * q^61 - 8 * q^63 - 48 * q^66 - 64 * q^67 - 32 * q^69 - 96 * q^70 - 8 * q^72 + 32 * q^73 + 8 * q^76 + 32 * q^78 + 16 * q^79 + 40 * q^81 + 64 * q^82 + 32 * q^84 - 80 * q^85 - 8 * q^87 - 56 * q^90 + 96 * q^91 - 100 * q^93 - 48 * q^94 - 4 * q^96 - 144 * q^97 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more