LMFDB - Embedded newform 495.2.u.b.34.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(34,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("495.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			34.11
Character	$\chi$	$=$	495.34
Dual form			495.2.u.b.364.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20576 - 0.696146i) q^{2} +(-1.69928 - 0.335329i) q^{3} +(-0.0307612 - 0.0532800i) q^{4} +(-1.62199 + 1.53920i) q^{5} +(1.81549 + 1.58727i) q^{6} +(0.764219 + 0.441222i) q^{7} +2.87024i q^{8} +(2.77511 + 1.13964i) q^{9} +O(q^{10})$	\(q+(-1.20576 - 0.696146i) q^{2} +(-1.69928 - 0.335329i) q^{3} +(-0.0307612 - 0.0532800i) q^{4} +(-1.62199 + 1.53920i) q^{5} +(1.81549 + 1.58727i) q^{6} +(0.764219 + 0.441222i) q^{7} +2.87024i q^{8} +(2.77511 + 1.13964i) q^{9} +(3.02724 - 0.726768i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.0344056 + 0.100853i) q^{12} +(3.73070 - 2.15392i) q^{13} +(-0.614310 - 1.06402i) q^{14} +(3.27236 - 2.07164i) q^{15} +(1.93659 - 3.35426i) q^{16} -2.04321i q^{17} +(-2.55276 - 3.30601i) q^{18} -5.96276 q^{19} +(0.131903 + 0.0390719i) q^{20} +(-1.15067 - 1.00602i) q^{21} +(-1.20576 + 0.696146i) q^{22} +(-2.07499 + 1.19800i) q^{23} +(0.962476 - 4.87735i) q^{24} +(0.261708 - 4.99315i) q^{25} -5.99778 q^{26} +(-4.33353 - 2.86714i) q^{27} -0.0542900i q^{28} +(-3.41677 + 5.91802i) q^{29} +(-5.38784 + 0.219859i) q^{30} +(2.56034 + 4.43465i) q^{31} +(0.301289 - 0.173949i) q^{32} +(-1.14004 + 1.30396i) q^{33} +(-1.42237 + 2.46362i) q^{34} +(-1.91869 + 0.460630i) q^{35} +(-0.0246458 - 0.182914i) q^{36} -9.09483i q^{37} +(7.18966 + 4.15095i) q^{38} +(-7.06178 + 2.40910i) q^{39} +(-4.41788 - 4.65551i) q^{40} +(-2.64290 - 4.57763i) q^{41} +(0.687089 + 2.01406i) q^{42} +(-1.70538 - 0.984603i) q^{43} -0.0615224 q^{44} +(-6.25533 + 2.42297i) q^{45} +3.33593 q^{46} +(4.06750 + 2.34837i) q^{47} +(-4.41558 + 5.05044i) q^{48} +(-3.11065 - 5.38780i) q^{49} +(-3.79152 + 5.83835i) q^{50} +(-0.685148 + 3.47199i) q^{51} +(-0.229522 - 0.132514i) q^{52} -11.5804i q^{53} +(3.22926 + 6.47386i) q^{54} +(0.521994 + 2.17429i) q^{55} +(-1.26641 + 2.19349i) q^{56} +(10.1324 + 1.99949i) q^{57} +(8.23962 - 4.75715i) q^{58} +(-3.33721 - 5.78021i) q^{59} +(-0.211038 - 0.110625i) q^{60} +(4.98490 - 8.63409i) q^{61} -7.12950i q^{62} +(1.61796 + 2.09537i) q^{63} -8.23072 q^{64} +(-2.73584 + 9.23595i) q^{65} +(2.28236 - 0.778621i) q^{66} +(-0.516070 + 0.297953i) q^{67} +(-0.108862 + 0.0628516i) q^{68} +(3.92772 - 1.33993i) q^{69} +(2.63414 + 0.780276i) q^{70} +2.23907 q^{71} +(-3.27103 + 7.96523i) q^{72} -1.97352i q^{73} +(-6.33133 + 10.9662i) q^{74} +(-2.11906 + 8.39700i) q^{75} +(0.183422 + 0.317696i) q^{76} +(0.764219 - 0.441222i) q^{77} +(10.1919 + 2.01123i) q^{78} +(7.89895 - 13.6814i) q^{79} +(2.02177 + 8.42138i) q^{80} +(6.40245 + 6.32523i) q^{81} +7.35937i q^{82} +(-6.81352 - 3.93379i) q^{83} +(-0.0182050 + 0.0922540i) q^{84} +(3.14491 + 3.31407i) q^{85} +(1.37086 + 2.37439i) q^{86} +(7.79054 - 8.91064i) q^{87} +(2.48570 + 1.43512i) q^{88} -14.6980 q^{89} +(9.22918 + 1.43310i) q^{90} +3.80143 q^{91} +(0.127659 + 0.0737037i) q^{92} +(-2.86368 - 8.39427i) q^{93} +(-3.26962 - 5.66315i) q^{94} +(9.67154 - 9.17790i) q^{95} +(-0.570305 + 0.194557i) q^{96} +(13.6309 + 7.86980i) q^{97} +8.66186i q^{98} +(2.37451 - 1.83350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9	$ 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9} + 34 q^{11} - 10 q^{14} - 28 q^{15} - 52 q^{16} - 40 q^{19} + q^{20} - 14 q^{21} + 20 q^{24} + 2 q^{25} - 24 q^{26} - 6 q^{29} + 22 q^{30} - 36 q^{31} + 34 q^{34} - 16 q^{36} - 12 q^{39} + 15 q^{40} + 6 q^{41} + 80 q^{44} + 50 q^{45} + 84 q^{46} + 60 q^{49} - 19 q^{50} + 48 q^{51} - 50 q^{54} - 4 q^{55} + 30 q^{56} - 103 q^{60} - 62 q^{61} - 164 q^{64} - 17 q^{65} + 2 q^{66} - 20 q^{69} + 28 q^{70} - 60 q^{71} + 14 q^{74} + 11 q^{75} - 86 q^{76} + 32 q^{79} + 50 q^{80} - 112 q^{81} - 36 q^{84} + q^{85} + 14 q^{86} + 20 q^{89} + 101 q^{90} + 104 q^{91} + 38 q^{94} + 6 q^{95} + 40 q^{96} + 4 q^{99}+O(q^{100}) $ 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9 + 34 * q^11 - 10 * q^14 - 28 * q^15 - 52 * q^16 - 40 * q^19 + q^20 - 14 * q^21 + 20 * q^24 + 2 * q^25 - 24 * q^26 - 6 * q^29 + 22 * q^30 - 36 * q^31 + 34 * q^34 - 16 * q^36 - 12 * q^39 + 15 * q^40 + 6 * q^41 + 80 * q^44 + 50 * q^45 + 84 * q^46 + 60 * q^49 - 19 * q^50 + 48 * q^51 - 50 * q^54 - 4 * q^55 + 30 * q^56 - 103 * q^60 - 62 * q^61 - 164 * q^64 - 17 * q^65 + 2 * q^66 - 20 * q^69 + 28 * q^70 - 60 * q^71 + 14 * q^74 + 11 * q^75 - 86 * q^76 + 32 * q^79 + 50 * q^80 - 112 * q^81 - 36 * q^84 + q^85 + 14 * q^86 + 20 * q^89 + 101 * q^90 + 104 * q^91 + 38 * q^94 + 6 * q^95 + 40 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.20576	−	0.696146i	−0.852601	−	0.492250i	0.00892635	−	0.999960i	$-0.497159\pi$
$2$	−1.20576	−	0.696146i	−0.852601	−	0.492250i	−0.861528	+	0.507711i	$0.830492\pi$
$3$	−1.69928	−	0.335329i	−0.981080	−	0.193603i
$3$	−1.69928	−	0.335329i	−0.981080	−	0.193603i
$4$	−0.0307612	−	0.0532800i	−0.0153806	−	0.0266400i
$5$	−1.62199	+	1.53920i	−0.725376	+	0.688353i
$5$	−1.62199	+	1.53920i	−0.725376	+	0.688353i
$6$	1.81549	+	1.58727i	0.741169	+	0.648002i
$7$	0.764219	+	0.441222i	0.288847	+	0.166766i	0.637422	−	0.770515i	$-0.280001\pi$
$7$	0.764219	+	0.441222i	0.288847	+	0.166766i	−0.348574	+	0.937281i	$0.613334\pi$
$8$			2.87024i			1.01478i
$9$	2.77511	+	1.13964i	0.925036	+	0.379879i
$10$	3.02724	−	0.726768i	0.957298	−	0.229824i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.0344056	+	0.100853i	0.00993203	+	0.0291137i
$13$	3.73070	−	2.15392i	1.03471	−	0.597390i	0.116380	−	0.993205i	$-0.462871\pi$
$13$	3.73070	−	2.15392i	1.03471	−	0.597390i	0.918330	+	0.395815i	$0.129538\pi$
$14$	−0.614310	−	1.06402i	−0.164181	−	0.284370i
$15$	3.27236	−	2.07164i	0.844919	−	0.534894i
$16$	1.93659	−	3.35426i	0.484146	−	0.838566i
$17$		−	2.04321i		−	0.495551i	−0.968817	−	0.247776i	$-0.920300\pi$
$17$		−	2.04321i		−	0.495551i	0.968817	−	0.247776i	$-0.0796996\pi$
$18$	−2.55276	−	3.30601i	−0.601692	−	0.779234i
$19$	−5.96276			−1.36795			−0.683975	−	0.729505i	$-0.739750\pi$
$19$	−5.96276			−1.36795			−0.683975	+	0.729505i	$0.739750\pi$
$20$	0.131903	+	0.0390719i	0.0294944	+	0.00873673i
$21$	−1.15067	−	1.00602i	−0.251096	−	0.219533i
$22$	−1.20576	+	0.696146i	−0.257069	+	0.148419i
$23$	−2.07499	+	1.19800i	−0.432666	+	0.249800i	−0.700482	−	0.713670i	$-0.747032\pi$
$23$	−2.07499	+	1.19800i	−0.432666	+	0.249800i	0.267816	+	0.963470i	$0.413698\pi$
$24$	0.962476	−	4.87735i	0.196465	−	0.995584i
$25$	0.261708	−	4.99315i	0.0523416	−	0.998629i
$26$	−5.99778			−1.17626
$27$	−4.33353	−	2.86714i	−0.833989	−	0.551781i
$28$		−	0.0542900i		−	0.0102599i
$29$	−3.41677	+	5.91802i	−0.634479	+	1.09895i	0.352147	+	0.935945i	$0.385452\pi$
$29$	−3.41677	+	5.91802i	−0.634479	+	1.09895i	−0.986625	+	0.163004i	$0.947881\pi$
$30$	−5.38784	+	0.219859i	−0.983681	+	0.0401405i
$31$	2.56034	+	4.43465i	0.459851	+	0.796486i	0.998953	−	0.0457549i	$-0.0145693\pi$
$31$	2.56034	+	4.43465i	0.459851	+	0.796486i	−0.539101	+	0.842241i	$0.681236\pi$
$32$	0.301289	−	0.173949i	0.0532608	−	0.0307502i
$33$	−1.14004	+	1.30396i	−0.198456	+	0.226989i
$34$	−1.42237	+	2.46362i	−0.243935	+	0.422508i
$35$	−1.91869	+	0.460630i	−0.324317	+	0.0778607i
$36$	−0.0246458	−	0.182914i	−0.00410764	−	0.0304857i
$37$		−	9.09483i		−	1.49518i	−0.664160	−	0.747590i	$-0.731211\pi$
$37$		−	9.09483i		−	1.49518i	0.664160	−	0.747590i	$-0.268789\pi$
$38$	7.18966	+	4.15095i	1.16632	+	0.673373i
$39$	−7.06178	+	2.40910i	−1.13079	+	0.385765i
$40$	−4.41788	−	4.65551i	−0.698529	−	0.736100i
$41$	−2.64290	−	4.57763i	−0.412751	−	0.714906i	0.582439	−	0.812875i	$-0.302099\pi$
$41$	−2.64290	−	4.57763i	−0.412751	−	0.714906i	−0.995189	+	0.0979692i	$0.968765\pi$
$42$	0.687089	+	2.01406i	0.106020	+	0.310776i
$43$	−1.70538	−	0.984603i	−0.260068	−	0.150151i	0.364297	−	0.931283i	$-0.381309\pi$
$43$	−1.70538	−	0.984603i	−0.260068	−	0.150151i	−0.624366	+	0.781132i	$0.714643\pi$
$44$	−0.0615224			−0.00927485
$45$	−6.25533	+	2.42297i	−0.932490	+	0.361196i
$46$	3.33593			0.491856
$47$	4.06750	+	2.34837i	0.593306	+	0.342546i	0.766404	−	0.642359i	$-0.222044\pi$
$47$	4.06750	+	2.34837i	0.593306	+	0.342546i	−0.173097	+	0.984905i	$0.555378\pi$
$48$	−4.41558	+	5.05044i	−0.637335	+	0.728968i
$49$	−3.11065	−	5.38780i	−0.444378	−	0.769685i
$50$	−3.79152	+	5.83835i	−0.536201	+	0.825668i
$51$	−0.685148	+	3.47199i	−0.0959399	+	0.486175i
$52$	−0.229522	−	0.132514i	−0.0318289	−	0.0183764i
$53$		−	11.5804i		−	1.59069i	−0.606160	−	0.795343i	$-0.707291\pi$
$53$		−	11.5804i		−	1.59069i	0.606160	−	0.795343i	$-0.292709\pi$
$54$	3.22926	+	6.47386i	0.439446	+	0.880980i
$55$	0.521994	+	2.17429i	0.0703856	+	0.293181i
$56$	−1.26641	+	2.19349i	−0.169232	+	0.293118i
$57$	10.1324	+	1.99949i	1.34207	+	0.264839i
$58$	8.23962	−	4.75715i	1.08191	−	0.624644i
$59$	−3.33721	−	5.78021i	−0.434467	−	0.752519i	0.562785	−	0.826603i	$-0.309730\pi$
$59$	−3.33721	−	5.78021i	−0.434467	−	0.752519i	−0.997252	+	0.0740843i	$0.976397\pi$
$60$	−0.211038	−	0.110625i	−0.0272449	−	0.0142816i
$61$	4.98490	−	8.63409i	0.638251	−	1.10548i	−0.347566	−	0.937656i	$-0.612992\pi$
$61$	4.98490	−	8.63409i	0.638251	−	1.10548i	0.985816	−	0.167827i	$-0.0536750\pi$
$62$		−	7.12950i		−	0.905447i
$63$	1.61796	+	2.09537i	0.203843	+	0.263992i
$64$	−8.23072			−1.02884
$65$	−2.73584	+	9.23595i	−0.339339	+	1.14558i
$66$	2.28236	−	0.778621i	0.280940	−	0.0958416i
$67$	−0.516070	+	0.297953i	−0.0630480	+	0.0364008i	−0.531193	−	0.847251i	$-0.678256\pi$
$67$	−0.516070	+	0.297953i	−0.0630480	+	0.0364008i	0.468145	+	0.883652i	$0.344923\pi$
$68$	−0.108862	+	0.0628516i	−0.0132015	+	0.00762187i
$69$	3.92772	−	1.33993i	0.472842	−	0.161308i
$70$	2.63414	+	0.780276i	0.314840	+	0.0932608i
$71$	2.23907			0.265728			0.132864	−	0.991134i	$-0.457583\pi$
$71$	2.23907			0.265728			0.132864	+	0.991134i	$0.457583\pi$
$72$	−3.27103	+	7.96523i	−0.385495	+	0.938712i
$73$		−	1.97352i		−	0.230983i	−0.993308	−	0.115491i	$-0.963156\pi$
$73$		−	1.97352i		−	0.230983i	0.993308	−	0.115491i	$-0.0368443\pi$
$74$	−6.33133	+	10.9662i	−0.736002	+	1.27479i
$75$	−2.11906	+	8.39700i	−0.244688	+	0.969602i
$76$	0.183422	+	0.317696i	0.0210399	+	0.0364422i
$77$	0.764219	−	0.441222i	0.0870908	−	0.0502819i
$78$	10.1919	+	2.01123i	1.15401	+	0.227727i
$79$	7.89895	−	13.6814i	0.888702	−	1.53928i	0.0472903	−	0.998881i	$-0.484941\pi$
$79$	7.89895	−	13.6814i	0.888702	−	1.53928i	0.841411	−	0.540395i	$-0.181725\pi$
$80$	2.02177	+	8.42138i	0.226041	+	0.941539i
$81$	6.40245	+	6.32523i	0.711384	+	0.702804i
$82$			7.35937i			0.812706i
$83$	−6.81352	−	3.93379i	−0.747881	−	0.431789i	0.0770466	−	0.997027i	$-0.475451\pi$
$83$	−6.81352	−	3.93379i	−0.747881	−	0.431789i	−0.824928	+	0.565238i	$0.808784\pi$
$84$	−0.0182050	+	0.0922540i	−0.00198633	+	0.0100657i
$85$	3.14491	+	3.31407i	0.341114	+	0.359461i
$86$	1.37086	+	2.37439i	0.147823	+	0.256037i
$87$	7.79054	−	8.91064i	0.835234	−	0.955321i
$88$	2.48570	+	1.43512i	0.264977	+	0.152984i
$89$	−14.6980			−1.55799			−0.778994	−	0.627031i	$-0.784270\pi$
$89$	−14.6980			−1.55799			−0.778994	+	0.627031i	$0.784270\pi$
$90$	9.22918	+	1.43310i	0.972841	+	0.151062i
$91$	3.80143			0.398498
$92$	0.127659	+	0.0737037i	0.0133093	+	0.00768415i
$93$	−2.86368	−	8.39427i	−0.296949	−	0.870445i
$94$	−3.26962	−	5.66315i	−0.337236	−	0.584110i
$95$	9.67154	−	9.17790i	0.992279	−	0.941633i
$96$	−0.570305	+	0.194557i	−0.0582065	+	0.0198569i
$97$	13.6309	+	7.86980i	1.38401	+	0.799057i	0.992631	−	0.121174i	$-0.0386659\pi$
$97$	13.6309	+	7.86980i	1.38401	+	0.799057i	0.391376	+	0.920231i	$0.371999\pi$
$98$			8.66186i			0.874980i
$99$	2.37451	−	1.83350i	0.238647	−	0.184273i
$100$	−0.274085	+	0.139651i	−0.0274085	+	0.0139651i
$101$	7.57795	−	13.1254i	0.754035	−	1.30603i	−0.191818	−	0.981430i	$-0.561438\pi$
$101$	7.57795	−	13.1254i	0.754035	−	1.30603i	0.945853	−	0.324596i	$-0.105228\pi$
$102$	3.24313	−	3.70942i	0.321118	−	0.367287i
$103$	−15.2670	+	8.81438i	−1.50430	+	0.868507i	−0.504311	+	0.863522i	$0.668253\pi$
$103$	−15.2670	+	8.81438i	−1.50430	+	0.868507i	−0.999988	+	0.00498465i	$0.998413\pi$
$104$	6.18227	+	10.7080i	0.606222	+	1.05001i
$105$	3.41485	−	0.139348i	0.333255	−	0.0135990i
$106$	−8.06163	+	13.9631i	−0.783014	+	1.35622i
$107$		−	11.1265i		−	1.07564i	−0.843061	−	0.537819i	$-0.819249\pi$
$107$		−	11.1265i		−	1.07564i	0.843061	−	0.537819i	$-0.180751\pi$
$108$	−0.0194564	+	0.319087i	−0.00187219	+	0.0307042i
$109$	−2.14160			−0.205128			−0.102564	−	0.994726i	$-0.532705\pi$
$109$	−2.14160			−0.205128			−0.102564	+	0.994726i	$0.532705\pi$
$110$	0.884222	−	2.98505i	0.0843073	−	0.284614i
$111$	−3.04976	+	15.4547i	−0.289471	+	1.46689i
$112$	2.95995	−	1.70893i	0.279689	−	0.161478i
$113$	2.36167	−	1.36351i	0.222168	−	0.128268i	−0.384786	−	0.923006i	$-0.625725\pi$
$113$	2.36167	−	1.36351i	0.222168	−	0.128268i	0.606953	+	0.794737i	$0.292391\pi$
$114$	−10.8253	−	9.46454i	−1.01388	−	0.886435i
$115$	1.52166	−	5.13698i	0.141895	−	0.479026i
$116$	0.420416			0.0390346
$117$	12.8078	−	1.72572i	1.18408	−	0.159543i
$118$			9.29273i			0.855465i
$119$	0.901509	−	1.56146i	0.0826412	−	0.143139i
$120$	5.94610	+	9.39246i	0.542802	+	0.857410i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−12.0212	+	6.94043i	−1.08835	+	0.628357i
$123$	2.95601	+	8.66492i	0.266534	+	0.781289i
$124$	0.157519	−	0.272830i	0.0141456	−	0.0245009i
$125$	7.26098	+	8.50166i	0.649442	+	0.760411i
$126$	−0.492184	−	3.65285i	−0.0438472	−	0.325422i
$127$			14.4141i			1.27905i	0.768771	+	0.639524i	$0.220868\pi$
$127$			14.4141i			1.27905i	−0.768771	+	0.639524i	$0.779132\pi$
$128$	9.32169	+	5.38188i	0.823929	+	0.475696i
$129$	2.56776	+	2.24498i	0.226078	+	0.197660i
$130$	9.72834	−	9.23179i	0.853231	−	0.809682i
$131$	−3.21425	−	5.56725i	−0.280831	−	0.486413i	0.690759	−	0.723085i	$-0.257277\pi$
$131$	−3.21425	−	5.56725i	−0.280831	−	0.486413i	−0.971590	+	0.236672i	$0.923943\pi$
$132$	0.104544	+	0.0206303i	0.00909937	+	0.00179563i
$133$	−4.55685	−	2.63090i	−0.395129	−	0.228128i
$134$	0.829676			0.0716731
$135$	11.4421	−	2.01972i	0.984776	−	0.173829i
$136$	5.86451			0.502877
$137$	4.64758	+	2.68328i	0.397069	+	0.229248i	0.685219	−	0.728337i	$-0.259707\pi$
$137$	4.64758	+	2.68328i	0.397069	+	0.229248i	−0.288149	+	0.957585i	$0.593040\pi$
$138$	−5.66868	−	1.11863i	−0.482550	−	0.0952245i
$139$	7.21353	+	12.4942i	0.611844	+	1.05974i	0.990929	+	0.134383i	$0.0429052\pi$
$139$	7.21353	+	12.4942i	0.611844	+	1.05974i	−0.379086	+	0.925362i	$0.623761\pi$
$140$	0.0835634	+	0.0880579i	0.00706240	+	0.00744225i
$141$	−6.12435	−	5.35450i	−0.515763	−	0.450930i
$142$	−2.69978	−	1.55872i	−0.226560	−	0.130805i
$143$		−	4.30784i		−	0.360240i
$144$	9.19688	−	7.10144i	0.766407	−	0.591787i
$145$	−3.56707	−	14.8581i	−0.296229	−	1.23390i
$146$	−1.37386	+	2.37959i	−0.113701	+	0.196936i
$147$	3.47917	+	10.1985i	0.286957	+	0.841156i
$148$	−0.484572	+	0.279768i	−0.0398316	+	0.0229968i
$149$	−0.160627	−	0.278215i	−0.0131591	−	0.0227922i	0.859371	−	0.511353i	$-0.170855\pi$
$149$	−0.160627	−	0.278215i	−0.0131591	−	0.0227922i	−0.872530	+	0.488561i	$0.837522\pi$
$150$	8.40062	−	8.64959i	0.685908	−	0.706236i
$151$	3.12415	−	5.41118i	0.254239	−	0.440356i	−0.710449	−	0.703748i	$-0.751508\pi$
$151$	3.12415	−	5.41118i	0.254239	−	0.440356i	0.964689	+	0.263393i	$0.0848416\pi$
$152$		−	17.1146i		−	1.38817i
$153$	2.32852	−	5.67013i	0.188250	−	0.458403i
$154$	−1.22862			−0.0990050
$155$	−10.9787	−	3.25207i	−0.881829	−	0.261212i
$156$	0.345586	+	0.302144i	0.0276690	+	0.0241909i
$157$	−17.8188	+	10.2877i	−1.42209	+	0.821046i	−0.996478	−	0.0838575i	$-0.973276\pi$
$157$	−17.8188	+	10.2877i	−1.42209	+	0.821046i	−0.425616	+	0.904904i	$0.639943\pi$
$158$	−19.0485	+	10.9977i	−1.51542	+	0.874926i
$159$	−3.88324	+	19.6783i	−0.307961	+	1.56059i
$160$	−0.220945	+	0.745889i	−0.0174672	+	0.0589677i
$161$	−2.11433			−0.166633
$162$	−3.31654	−	12.0838i	−0.260572	−	0.949390i
$163$		−	3.92898i		−	0.307741i	−0.988091	−	0.153871i	$-0.950826\pi$
$163$		−	3.92898i		−	0.307741i	0.988091	−	0.153871i	$-0.0491739\pi$
$164$	−0.162597	+	0.281627i	−0.0126967	+	0.0219914i
$165$	−0.157911	−	3.86976i	−0.0122934	−	0.301261i
$166$	5.47698	+	9.48641i	0.425096	+	0.736289i
$167$	1.97228	−	1.13870i	0.152620	−	0.0881150i	−0.421745	−	0.906714i	$-0.638582\pi$
$167$	1.97228	−	1.13870i	0.152620	−	0.0881150i	0.574365	+	0.818599i	$0.305249\pi$
$168$	2.88753	−	3.30269i	0.222778	−	0.254808i
$169$	2.77875	−	4.81294i	0.213750	−	0.370226i
$170$	−1.48494	−	6.18529i	−0.113890	−	0.474390i
$171$	−16.5473	−	6.79538i	−1.26540	−	0.519656i
$172$			0.121150i			0.00923762i
$173$	10.1988	+	5.88825i	0.775397	+	0.447676i	0.834796	−	0.550559i	$-0.185585\pi$
$173$	10.1988	+	5.88825i	0.775397	+	0.447676i	−0.0593996	+	0.998234i	$0.518919\pi$
$174$	−15.5966	+	5.32074i	−1.18238	+	0.403364i
$175$	2.40309	−	3.70038i	0.181656	−	0.279723i
$176$	−1.93659	−	3.35426i	−0.145976	−	0.252837i
$177$	3.73257	+	10.9413i	0.280557	+	0.822395i
$178$	17.7223	+	10.2320i	1.32834	+	0.766919i
$179$	−8.85749			−0.662040			−0.331020	−	0.943624i	$-0.607393\pi$
$179$	−8.85749			−0.662040			−0.331020	+	0.943624i	$0.607393\pi$
$180$	0.321517	+	0.258750i	0.0239645	+	0.0192861i
$181$	5.76906			0.428811			0.214406	−	0.976745i	$-0.431219\pi$
$181$	5.76906			0.428811			0.214406	+	0.976745i	$0.431219\pi$
$182$	−4.58361	−	2.64635i	−0.339760	−	0.196160i
$183$	−11.3660	+	13.0002i	−0.840199	+	0.961000i
$184$	−3.43855	−	5.95574i	−0.253493	−	0.439063i
$185$	13.9988	+	14.7517i	1.02921	+	1.08457i
$186$	−2.39073	+	12.1150i	−0.175297	+	0.888316i
$187$	−1.76947	−	1.02160i	−0.129397	−	0.0747071i
$188$		−	0.288955i		−	0.0210742i
$189$	−2.04672	−	4.10317i	−0.148877	−	0.298462i
$190$	−18.0507	+	4.33354i	−1.30954	+	0.314388i
$191$	1.98696	−	3.44151i	0.143771	−	0.249019i	−0.785143	−	0.619315i	$-0.787410\pi$
$191$	1.98696	−	3.44151i	0.143771	−	0.249019i	0.928914	+	0.370296i	$0.120744\pi$
$192$	13.9863	+	2.76000i	1.00937	+	0.199186i
$193$	11.8218	−	6.82530i	0.850950	−	0.491296i	−0.0100214	−	0.999950i	$-0.503190\pi$
$193$	11.8218	−	6.82530i	0.850950	−	0.491296i	0.860971	+	0.508654i	$0.169857\pi$
$194$	−10.9571	−	18.9782i	−0.786671	−	1.36255i
$195$	7.74604	−	14.7771i	0.554706	−	1.05821i
$196$	−0.191374	+	0.331470i	−0.0136696	+	0.0236764i
$197$		−	19.1331i		−	1.36318i	−0.731737	−	0.681588i	$-0.761290\pi$
$197$		−	19.1331i		−	1.36318i	0.731737	−	0.681588i	$-0.238710\pi$
$198$	−4.13947	+	0.557751i	−0.294179	+	0.0396377i
$199$	−17.9435			−1.27198			−0.635991	−	0.771697i	$-0.719408\pi$
$199$	−17.9435			−1.27198			−0.635991	+	0.771697i	$0.719408\pi$
$200$	14.3315	+	0.751165i	1.01339	+	0.0531154i
$201$	0.976861	−	0.333253i	0.0689025	−	0.0235058i
$202$	−18.2744	+	10.5507i	−1.28578	+	0.742346i
$203$	−5.22232	+	3.01511i	−0.366535	+	0.211619i
$204$	0.206063	−	0.0702978i	0.0144273	−	0.00492183i
$205$	11.3327	+	3.35692i	0.791507	+	0.234457i
$206$	24.5444			1.71009
$207$	−7.12362	+	0.959835i	−0.495126	+	0.0667131i
$208$		−	16.6850i		−	1.15690i
$209$	−2.98138	+	5.16390i	−0.206226	+	0.357195i
$210$	−4.21449	−	2.20921i	−0.290828	−	0.152450i
$211$	2.73134	+	4.73083i	0.188034	+	0.325684i	0.944595	−	0.328240i	$-0.106455\pi$
$211$	2.73134	+	4.73083i	0.188034	+	0.325684i	−0.756561	+	0.653923i	$0.773122\pi$
$212$	−0.617001	+	0.356226i	−0.0423758	+	0.0244657i
$213$	−3.80480	−	0.750825i	−0.260701	−	0.0514456i
$214$	−7.74566	+	13.4159i	−0.529482	+	0.917090i
$215$	4.28162	−	1.02791i	0.292004	−	0.0701031i
$216$	8.22938	−	12.4383i	0.559938	−	0.846318i
$217$			4.51872i			0.306751i
$218$	2.58225	+	1.49087i	0.174892	+	0.100974i
$219$	−0.661779	+	3.35356i	−0.0447189	+	0.226613i
$220$	0.0997887	−	0.0946955i	0.00672776	−	0.00638437i
$221$	−4.40091	−	7.62260i	−0.296037	−	0.512752i
$222$	14.4360	−	16.5115i	0.968880	−	1.10818i
$223$	−20.0827	−	11.5948i	−1.34484	−	0.776443i	−0.357326	−	0.933980i	$-0.616311\pi$
$223$	−20.0827	−	11.5948i	−1.34484	−	0.776443i	−0.987513	+	0.157537i	$0.949645\pi$
$224$	0.307001			0.0205124
$225$	6.41664	−	13.5583i	0.427776	−	0.903885i
$226$	−3.79682			−0.252560
$227$	−12.6466	−	7.30149i	−0.839381	−	0.484617i	0.0176726	−	0.999844i	$-0.494374\pi$
$227$	−12.6466	−	7.30149i	−0.839381	−	0.484617i	−0.857054	+	0.515227i	$0.827708\pi$
$228$	−0.205152	−	0.601361i	−0.0135865	−	0.0398261i
$229$	3.81070	+	6.60033i	0.251818	+	0.436162i	0.964027	−	0.265806i	$-0.0856381\pi$
$229$	3.81070	+	6.60033i	0.251818	+	0.436162i	−0.712208	+	0.701968i	$0.752305\pi$
$230$	−5.41084	+	5.13467i	−0.356781	+	0.338570i
$231$	−1.44658	+	0.493495i	−0.0951777	+	0.0324696i
$232$	−16.9862	−	9.80696i	−1.11520	−	0.643859i
$233$		−	19.6294i		−	1.28597i	−0.765880	−	0.642983i	$-0.777697\pi$
$233$		−	19.6294i		−	1.28597i	0.765880	−	0.642983i	$-0.222303\pi$
$234$	−16.6445	−	6.83529i	−1.08808	−	0.446837i
$235$	−10.2121	+	2.45167i	−0.666162	+	0.159929i
$236$	−0.205313	+	0.355612i	−0.0133647	+	0.0231484i
$237$	−18.0103	+	20.5998i	−1.16990	+	1.33810i
$238$	−2.17401	+	1.25516i	−0.140920	+	0.0813602i
$239$	6.25928	+	10.8414i	0.404879	+	0.701271i	0.994307	−	0.106550i	$-0.0339803\pi$
$239$	6.25928	+	10.8414i	0.404879	+	0.701271i	−0.589428	+	0.807821i	$0.700647\pi$
$240$	−0.611617	−	14.9882i	−0.0394797	−	0.967487i
$241$	−0.00696979	+	0.0120720i	−0.000448964	+	0.000777628i	−0.866250	−	0.499611i	$-0.833476\pi$
$241$	−0.00696979	+	0.0120720i	−0.000448964	+	0.000777628i	0.865801	+	0.500389i	$0.166810\pi$
$242$			1.39229i			0.0894999i
$243$	−8.75853	−	12.8953i	−0.561860	−	0.827233i
$244$	−0.613365			−0.0392667
$245$	13.3384	+	3.95104i	0.852156	+	0.252423i
$246$	2.46781	−	12.5056i	0.157342	−	0.797330i
$247$	−22.2453	+	12.8433i	−1.41543	+	0.817201i
$248$	−12.7285	+	7.34881i	−0.808261	+	0.466650i
$249$	10.2590	+	8.96939i	0.650136	+	0.568412i
$250$	−2.83660	−	15.3057i	−0.179403	−	0.968015i
$251$	1.84666			0.116560			0.0582799	−	0.998300i	$-0.481438\pi$
$251$	1.84666			0.116560			0.0582799	+	0.998300i	$0.481438\pi$
$252$	0.0618710	−	0.150661i	0.00389750	−	0.00949074i
$253$			2.39600i			0.150635i
$254$	10.0343	−	17.3800i	0.629611	−	1.09052i
$255$	−4.23279	−	6.68611i	−0.265067	−	0.418701i
$256$	0.737563	+	1.27750i	0.0460977	+	0.0798435i
$257$	−3.29799	+	1.90410i	−0.205723	+	0.118774i	−0.599322	−	0.800508i	$-0.704563\pi$
$257$	−3.29799	+	1.90410i	−0.205723	+	0.118774i	0.393599	+	0.919282i	$0.371230\pi$
$258$	−1.53326	−	4.49445i	−0.0954569	−	0.279812i
$259$	4.01284	−	6.95044i	0.249346	−	0.431879i
$260$	0.576248	−	0.138343i	0.0357374	−	0.00857969i
$261$	−16.2263	+	12.5293i	−1.00438	+	0.775543i
$262$			8.95036i			0.552955i
$263$	8.35948	+	4.82635i	0.515468	+	0.297605i	0.735078	−	0.677982i	$-0.237145\pi$
$263$	8.35948	+	4.82635i	0.515468	+	0.297605i	−0.219611	+	0.975588i	$0.570479\pi$
$264$	−3.74267	−	3.27220i	−0.230345	−	0.201390i
$265$	17.8245	+	18.7832i	1.09495	+	1.15385i
$266$	3.66298	+	6.34447i	0.224592	+	0.389004i
$267$	24.9761	+	4.92868i	1.52851	+	0.301631i
$268$	0.0317499	+	0.0183308i	0.00193943	+	0.00111973i
$269$	−5.80782			−0.354109			−0.177055	−	0.984201i	$-0.556657\pi$
$269$	−5.80782			−0.354109			−0.177055	+	0.984201i	$0.556657\pi$
$270$	−15.2024	−	5.53005i	−0.925189	−	0.336548i
$271$	18.8578			1.14553			0.572764	−	0.819720i	$-0.305871\pi$
$271$	18.8578			1.14553			0.572764	+	0.819720i	$0.305871\pi$
$272$	−6.85346	−	3.95685i	−0.415552	−	0.239919i
$273$	−6.45969	−	1.27473i	−0.390958	−	0.0771502i
$274$	−3.73591	−	6.47078i	−0.225694	−	0.390914i
$275$	−4.19334	−	2.72322i	−0.252868	−	0.164216i
$276$	−0.192213	−	0.168051i	−0.0115698	−	0.0101155i
$277$	−9.79637	−	5.65594i	−0.588607	−	0.339832i	0.175940	−	0.984401i	$-0.443704\pi$
$277$	−9.79637	−	5.65594i	−0.588607	−	0.339832i	−0.764546	+	0.644569i	$0.777037\pi$
$278$		−	20.0867i		−	1.20472i
$279$	2.05134	+	15.2245i	0.122811	+	0.911466i
$280$	−1.32212	−	5.50709i	−0.0790117	−	0.329112i
$281$	6.78559	−	11.7530i	0.404794	−	0.701124i	−0.589503	−	0.807766i	$-0.700676\pi$
$281$	6.78559	−	11.7530i	0.404794	−	0.701124i	0.994298	+	0.106642i	$0.0340098\pi$
$282$	3.65698	+	10.7197i	0.217770	+	0.638348i
$283$	−5.53656	+	3.19653i	−0.329114	+	0.190014i	−0.655448	−	0.755241i	$-0.727520\pi$
$283$	−5.53656	+	3.19653i	−0.329114	+	0.190014i	0.326334	+	0.945255i	$0.394187\pi$
$284$	−0.0688763	−	0.119297i	−0.00408706	−	0.00707899i
$285$	−19.5123	+	12.3527i	−1.15581	+	0.731709i
$286$	−2.99889	+	5.19423i	−0.177328	+	0.307141i
$287$		−	4.66441i		−	0.275332i
$288$	1.03435	−	0.139368i	0.0609496	−	0.00821233i
$289$	12.8253			0.754429
$290$	−6.04237	+	20.3985i	−0.354820	+	1.19784i
$291$	−20.5237	−	17.9438i	−1.20312	−	1.05189i
$292$	−0.105149	+	0.0607078i	−0.00615338	+	0.00355265i
$293$	−5.37870	+	3.10539i	−0.314227	+	0.181419i	−0.648816	−	0.760945i	$-0.724736\pi$
$293$	−5.37870	+	3.10539i	−0.314227	+	0.181419i	0.334590	+	0.942364i	$0.391402\pi$
$294$	2.90458	−	14.7189i	0.169398	−	0.858425i
$295$	14.3098	+	4.23881i	0.833151	+	0.246793i
$296$	26.1044			1.51728
$297$	−4.64978	+	2.31938i	−0.269808	+	0.134584i
$298$			0.447280i			0.0259102i
$299$	−5.16079	+	8.93875i	−0.298456	+	0.516941i
$300$	0.512577	−	0.145398i	0.0295936	−	0.00839456i
$301$	−0.868857	−	1.50490i	−0.0500801	−	0.0867413i
$302$	−7.53394	+	4.34972i	−0.433530	+	0.250298i
$303$	−17.2784	+	19.7626i	−0.992618	+	1.13533i
$304$	−11.5474	+	20.0007i	−0.662288	+	1.14712i
$305$	5.20417	+	21.6772i	0.297990	+	1.24123i
$306$	−6.75487	+	5.21583i	−0.386150	+	0.298169i
$307$			5.96779i			0.340600i	0.985392	+	0.170300i	$0.0544736\pi$
$307$			5.96779i			0.340600i	−0.985392	+	0.170300i	$0.945526\pi$
$308$	−0.0470166	−	0.0271450i	−0.00267902	−	0.00154673i
$309$	28.8986	−	9.85865i	1.64398	−	0.560839i
$310$	10.9737	+	11.5640i	0.623267	+	0.656790i
$311$	−10.6137	−	18.3834i	−0.601846	−	1.04243i	−0.992541	−	0.121908i	$-0.961099\pi$
$311$	−10.6137	−	18.3834i	−0.601846	−	1.04243i	0.390695	−	0.920520i	$-0.372235\pi$
$312$	−6.91471	−	20.2690i	−0.391468	−	1.14751i
$313$	−11.2337	−	6.48580i	−0.634969	−	0.366599i	0.147705	−	0.989031i	$-0.452811\pi$
$313$	−11.2337	−	6.48580i	−0.634969	−	0.366599i	−0.782674	+	0.622432i	$0.786145\pi$
$314$	28.6469			1.61664
$315$	−5.84951	−	0.908308i	−0.329583	−	0.0511773i
$316$	−0.971925			−0.0546751
$317$	−2.23781	−	1.29200i	−0.125688	−	0.0725661i	0.435838	−	0.900025i	$-0.356452\pi$
$317$	−2.23781	−	1.29200i	−0.125688	−	0.0725661i	−0.561526	+	0.827459i	$0.689785\pi$
$318$	18.3812	−	21.0240i	1.03077	−	1.17897i
$319$	3.41677	+	5.91802i	0.191303	+	0.331346i
$320$	13.3501	−	12.6687i	0.746296	−	0.708204i
$321$	−3.73104	+	18.9070i	−0.208246	+	1.05529i
$322$	2.54938	+	1.47188i	0.142071	+	0.0820249i
$323$			12.1832i			0.677890i
$324$	0.140061	−	0.535694i	0.00778117	−	0.0297608i
$325$	−9.77849	−	19.1916i	−0.542413	−	1.06456i
$326$	−2.73514	+	4.73741i	−0.151486	+	0.262381i
$327$	3.63918	+	0.718141i	0.201247	+	0.0397133i
$328$	13.1389	−	7.58575i	0.725474	−	0.418853i
$329$	2.07231	+	3.58934i	0.114250	+	0.197887i
$330$	−2.50352	+	4.77594i	−0.137814	+	0.262907i
$331$	−14.6716	+	25.4119i	−0.806422	+	1.39676i	0.108905	+	0.994052i	$0.465266\pi$
$331$	−14.6716	+	25.4119i	−0.806422	+	1.39676i	−0.915327	+	0.402711i	$0.868068\pi$
$332$			0.484032i			0.0265647i
$333$	10.3648	−	25.2391i	0.567988	−	1.38310i
$334$	−3.17080			−0.173498
$335$	0.378451	−	1.27761i	0.0206770	−	0.0698036i
$336$	−5.60284	+	1.91139i	−0.305660	+	0.104275i
$337$	16.1320	−	9.31379i	0.878764	−	0.507355i	0.00851343	−	0.999964i	$-0.497290\pi$
$337$	16.1320	−	9.31379i	0.878764	−	0.507355i	0.870251	+	0.492609i	$0.163957\pi$
$338$	−6.70102	+	3.86884i	−0.364487	+	0.210437i
$339$	−4.47037	+	1.52505i	−0.242797	+	0.0828294i
$340$	0.0798320	−	0.269506i	0.00432950	−	0.0146160i
$341$	5.12069			0.277301
$342$	15.2215	+	19.7129i	0.823085	+	1.06595i
$343$		−	11.6670i		−	0.629961i
$344$	2.82605	−	4.89486i	0.152370	−	0.263913i
$345$	−4.30831	+	8.21891i	−0.231951	+	0.442491i
$346$	−8.19817	−	14.1996i	−0.440736	−	0.763378i
$347$	−8.74919	+	5.05135i	−0.469681	+	0.271171i	−0.716106	−	0.697991i	$-0.754077\pi$
$347$	−8.74919	+	5.05135i	−0.469681	+	0.271171i	0.246425	+	0.969162i	$0.420744\pi$
$348$	−0.714405	−	0.140978i	−0.0382961	−	0.00755721i
$349$	1.18227	−	2.04775i	0.0632855	−	0.109614i	−0.832647	−	0.553805i	$-0.813175\pi$
$349$	1.18227	−	2.04775i	0.0632855	−	0.109614i	0.895932	+	0.444191i	$0.146509\pi$
$350$	−5.47356	+	2.78888i	−0.292574	+	0.149072i
$351$	−22.3427	−	1.36235i	−1.19257	−	0.0727168i
$352$		−	0.347898i		−	0.0185430i
$353$	20.9626	+	12.1028i	1.11573	+	0.644166i	0.940307	−	0.340327i	$-0.110538\pi$
$353$	20.9626	+	12.1028i	1.11573	+	0.644166i	0.175422	+	0.984493i	$0.443871\pi$
$354$	3.11613	−	15.7910i	0.165620	−	0.839280i
$355$	−3.63174	+	3.44638i	−0.192753	+	0.182915i
$356$	0.452129	+	0.783111i	0.0239628	+	0.0415048i
$357$	−2.05552	+	2.35105i	−0.108790	+	0.124431i
$358$	10.6800	+	6.16611i	0.564456	+	0.325889i
$359$	24.2457			1.27964			0.639819	−	0.768525i	$-0.279009\pi$
$359$	24.2457			1.27964			0.639819	+	0.768525i	$0.279009\pi$
$360$	−6.95452	−	17.9543i	−0.366535	−	0.946276i
$361$	16.5545			0.871290
$362$	−6.95611	−	4.01611i	−0.365605	−	0.211082i
$363$	0.559236	+	1.63928i	0.0293523	+	0.0860401i
$364$	−0.116936	−	0.202540i	−0.00612914	−	0.0106160i
$365$	3.03765	+	3.20103i	0.158998	+	0.167549i
$366$	22.7547	−	7.76269i	1.18941	−	0.405762i
$367$	−20.5304	−	11.8532i	−1.07168	−	0.618734i	−0.143039	−	0.989717i	$-0.545687\pi$
$367$	−20.5304	−	11.8532i	−1.07168	−	0.618734i	−0.928639	+	0.370983i	$0.879021\pi$
$368$			9.28011i			0.483759i
$369$	−2.11748	−	15.7154i	−0.110232	−	0.818109i
$370$	−6.60983	−	27.5323i	−0.343629	−	1.43133i
$371$	5.10951	−	8.84993i	0.265273	−	0.459466i
$372$	−0.359156	+	0.410794i	−0.0186214	+	0.0212987i
$373$	17.8563	−	10.3094i	0.924566	−	0.533798i	0.0394770	−	0.999220i	$-0.487431\pi$
$373$	17.8563	−	10.3094i	0.924566	−	0.533798i	0.885089	+	0.465422i	$0.154097\pi$
$374$	1.42237	+	2.46362i	0.0735491	+	0.127391i
$375$	−9.48758	−	16.8815i	−0.489937	−	0.871758i
$376$	−6.74040	+	11.6747i	−0.347610	+	0.602078i
$377$			29.4378i			1.51613i
$378$	−0.388549	+	6.37226i	−0.0199848	+	0.327754i
$379$	3.70151			0.190134			0.0950668	−	0.995471i	$-0.469694\pi$
$379$	3.70151			0.190134			0.0950668	+	0.995471i	$0.469694\pi$
$380$	−0.786506	−	0.232976i	−0.0403469	−	0.0119514i
$381$	4.83348	−	24.4937i	0.247627	−	1.25485i
$382$	−4.79159	+	2.76643i	−0.245159	+	0.141543i
$383$	16.0597	−	9.27205i	0.820611	−	0.473780i	−0.0300162	−	0.999549i	$-0.509556\pi$
$383$	16.0597	−	9.27205i	0.820611	−	0.473780i	0.850627	+	0.525770i	$0.176223\pi$
$384$	−14.0355	−	12.2712i	−0.716245	−	0.626210i
$385$	−0.560426	+	1.89195i	−0.0285619	+	0.0964225i
$386$	−19.0056			−0.967361
$387$	−3.61053	−	4.67590i	−0.183534	−	0.237689i
$388$		−	0.968338i		−	0.0491599i
$389$	14.4886	−	25.0950i	0.734602	−	1.27237i	−0.220296	−	0.975433i	$-0.570702\pi$
$389$	14.4886	−	25.0950i	0.734602	−	1.27237i	0.954898	−	0.296935i	$-0.0959643\pi$
$390$	−19.6269	+	12.4252i	−0.993845	+	0.629175i
$391$	2.44776	+	4.23965i	0.123789	+	0.214408i
$392$	15.4643	−	8.92831i	0.781064	−	0.450948i
$393$	3.59505	+	10.5381i	0.181346	+	0.531579i
$394$	−13.3194	+	23.0699i	−0.671022	+	1.16224i
$395$	8.24641	+	34.3492i	0.414922	+	1.72829i
$396$	−0.170731	−	0.0701132i	−0.00857957	−	0.00352332i
$397$			22.4973i			1.12911i	0.825396	+	0.564554i	$0.190952\pi$
$397$			22.4973i			1.12911i	−0.825396	+	0.564554i	$0.809048\pi$
$398$	21.6356	+	12.4913i	1.08449	+	0.626132i
$399$	6.86115	+	5.99868i	0.343487	+	0.300310i
$400$	−16.2415	−	10.5475i	−0.812076	−	0.527374i
$401$	8.72676	+	15.1152i	0.435794	+	0.754817i	0.997360	−	0.0726151i	$-0.0231345\pi$
$401$	8.72676	+	15.1152i	0.435794	+	0.754817i	−0.561567	+	0.827432i	$0.689801\pi$
$402$	−1.40985	−	0.278215i	−0.0703171	−	0.0138761i
$403$	19.1038	+	11.0296i	0.951626	+	0.549421i
$404$	−0.932428			−0.0463900
$405$	−20.1205	−	0.404796i	−0.999798	−	0.0201145i
$406$	8.39583			0.416678
$407$	−7.87635	−	4.54741i	−0.390416	−	0.225407i
$408$	−9.96544	−	1.96654i	−0.493363	−	0.0973583i
$409$	−0.279054	−	0.483337i	−0.0137984	−	0.0238995i	0.859044	−	0.511902i	$-0.171059\pi$
$409$	−0.279054	−	0.483337i	−0.0137984	−	0.0238995i	−0.872842	+	0.488003i	$0.837726\pi$
$410$	−11.3276	−	11.9368i	−0.559428	−	0.589518i
$411$	−6.99775	−	6.11811i	−0.345174	−	0.301784i
$412$	0.939260	+	0.542282i	0.0462740	+	0.0267163i
$413$		−	5.88979i		−	0.289818i
$414$	9.25756	+	3.80175i	0.454984	+	0.186846i
$415$	17.1064	−	4.10683i	0.839719	−	0.201596i
$416$	0.749346	−	1.29790i	0.0367397	−	0.0636350i
$417$	−8.06814	−	23.6501i	−0.395098	−	1.15815i
$418$	7.18966	−	4.15095i	0.351658	−	0.203030i
$419$	−12.5513	−	21.7395i	−0.613173	−	1.06205i	−0.990702	−	0.136049i	$-0.956560\pi$
$419$	−12.5513	−	21.7395i	−0.613173	−	1.06205i	0.377529	−	0.925998i	$-0.376774\pi$
$420$	−0.112469	−	0.177656i	−0.00548794	−	0.00866875i
$421$	−11.0673	+	19.1692i	−0.539389	+	0.934249i	0.459548	+	0.888153i	$0.348011\pi$
$421$	−11.0673	+	19.1692i	−0.539389	+	0.934249i	−0.998937	+	0.0460961i	$0.985322\pi$
$422$		−	7.60566i		−	0.370238i
$423$	8.61147	+	11.1525i	0.418704	+	0.542252i
$424$	33.2384			1.61420
$425$	−10.2020	−	0.534724i	−0.494872	−	0.0259379i
$426$	4.06499	+	3.55401i	0.196950	+	0.172192i
$427$	7.61910	−	4.39889i	0.368714	−	0.212877i
$428$	−0.592818	+	0.342264i	−0.0286550	+	0.0165439i
$429$	−1.44455	+	7.32023i	−0.0697433	+	0.353424i
$430$	−5.87819	−	1.74122i	−0.283471	−	0.0839689i
$431$	−26.9147			−1.29644			−0.648218	−	0.761455i	$-0.724485\pi$
$431$	−26.9147			−1.29644			−0.648218	+	0.761455i	$0.724485\pi$
$432$	−18.0094	+	8.98336i	−0.866478	+	0.432212i
$433$			13.4179i			0.644823i	0.946600	+	0.322411i	$0.104493\pi$
$433$			13.4179i			0.644823i	−0.946600	+	0.322411i	$0.895507\pi$
$434$	3.14569	−	5.44849i	0.150998	−	0.261536i
$435$	1.07909	+	26.4442i	0.0517386	+	1.26790i
$436$	0.0658781	+	0.114104i	0.00315499	+	0.00546460i
$437$	12.3727	−	7.14338i	0.591866	−	0.341714i
$438$	3.13252	−	3.58290i	0.149677	−	0.171197i
$439$	19.1877	−	33.2341i	0.915780	−	1.58618i	0.110026	−	0.993929i	$-0.464907\pi$
$439$	19.1877	−	33.2341i	0.915780	−	1.58618i	0.805755	−	0.592249i	$-0.201760\pi$
$440$	−6.24073	+	1.49825i	−0.297515	+	0.0714262i
$441$	−2.49225	−	18.4967i	−0.118678	−	0.880797i
$442$			12.2547i			0.582897i
$443$	21.0700	+	12.1648i	1.00107	+	0.577966i	0.908564	−	0.417747i	$-0.137180\pi$
$443$	21.0700	+	12.1648i	1.00107	+	0.577966i	0.0925027	+	0.995712i	$0.470513\pi$
$444$	0.917238	−	0.312913i	0.0435302	−	0.0148502i
$445$	23.8401	−	22.6233i	1.13013	−	1.07245i
$446$	16.1433	+	27.9610i	0.764407	+	1.32399i
$447$	0.179657	+	0.526628i	0.00849750	+	0.0249086i
$448$	−6.29007	−	3.63157i	−0.297178	−	0.171576i
$449$	3.16563			0.149395			0.0746977	−	0.997206i	$-0.476201\pi$
$449$	3.16563			0.149395			0.0746977	+	0.997206i	$0.476201\pi$
$450$	−17.1755	+	11.8811i	−0.809660	+	0.560081i
$451$	−5.28579			−0.248898
$452$	−0.145296	−	0.0838866i	−0.00683414	−	0.00394569i
$453$	−7.12333	+	8.14749i	−0.334683	+	0.382803i
$454$	10.1658	+	17.6077i	0.477105	+	0.826370i
$455$	−6.16588	+	5.85117i	−0.289061	+	0.274307i
$456$	−5.73902	+	29.0824i	−0.268754	+	1.36191i
$457$	31.2209	+	18.0254i	1.46045	+	0.843192i	0.999032	−	0.0439902i	$-0.0140070\pi$
$457$	31.2209	+	18.0254i	1.46045	+	0.843192i	0.461419	+	0.887182i	$0.347340\pi$
$458$		−	10.6112i		−	0.495830i
$459$	−5.85817	+	8.85432i	−0.273436	+	0.413284i
$460$	−0.320506	+	0.0769458i	−0.0149437	+	0.00358761i
$461$	−17.8472	+	30.9123i	−0.831228	+	1.43973i	0.0658373	+	0.997830i	$0.479028\pi$
$461$	−17.8472	+	30.9123i	−0.831228	+	1.43973i	−0.897065	+	0.441898i	$0.854305\pi$
$462$	2.08777	+	0.411992i	0.0971318	+	0.0191676i
$463$	−14.2147	+	8.20685i	−0.660612	+	0.381405i	−0.792510	−	0.609859i	$-0.791226\pi$
$463$	−14.2147	+	8.20685i	−0.660612	+	0.381405i	0.131898	+	0.991263i	$0.457893\pi$
$464$	13.2337	+	22.9215i	0.614361	+	1.06410i
$465$	17.5653	+	9.20764i	0.814573	+	0.426994i
$466$	−13.6649	+	23.6684i	−0.633016	+	1.09642i
$467$			21.2464i			0.983166i	0.870831	+	0.491583i	$0.163582\pi$
$467$			21.2464i			0.983166i	−0.870831	+	0.491583i	$0.836418\pi$
$468$	−0.485929	−	0.629313i	−0.0224621	−	0.0290900i
$469$	−0.525854			−0.0242817
$470$	14.0200	+	4.15297i	0.646696	+	0.191562i
$471$	33.7289	−	11.5065i	1.55414	−	0.530191i
$472$	16.5906	−	9.57859i	0.763644	−	0.440890i
$473$	−1.70538	+	0.984603i	−0.0784136	+	0.0452721i
$474$	36.0566	−	12.3006i	1.65613	−	0.564984i
$475$	−1.56050	+	29.7729i	−0.0716007	+	1.36608i
$476$	−0.110926			−0.00508428
$477$	13.1974	−	32.1368i	0.604268	−	1.47144i
$478$		−	17.4295i		−	0.797206i
$479$	−9.07984	+	15.7267i	−0.414868	+	0.718573i	−0.995415	−	0.0956541i	$-0.969506\pi$
$479$	−9.07984	+	15.7267i	−0.414868	+	0.718573i	0.580546	+	0.814227i	$0.302839\pi$
$480$	0.625565	−	1.19338i	0.0285530	−	0.0544703i
$481$	−19.5895	−	33.9301i	−0.893206	−	1.54708i
$482$	0.0168078	−	0.00970398i	0.000765574	−	0.000442004i
$483$	3.59284	+	0.708998i	0.163480	+	0.0322605i
$484$	−0.0307612	+	0.0532800i	−0.00139824	+	0.00242182i
$485$	−34.2224	+	8.21597i	−1.55396	+	0.373068i
$486$	1.58369	+	21.6458i	0.0718375	+	0.981875i
$487$			2.26938i			0.102835i	0.998677	+	0.0514177i	$0.0163740\pi$
$487$			2.26938i			0.102835i	−0.998677	+	0.0514177i	$0.983626\pi$
$488$	24.7819	+	14.3079i	1.12183	+	0.647686i
$489$	−1.31750	+	6.67644i	−0.0595795	+	0.301919i
$490$	−13.3324	−	14.0495i	−0.602295	−	0.634690i
$491$	−14.8209	−	25.6705i	−0.668858	−	1.15850i	−0.978224	−	0.207552i	$-0.933450\pi$
$491$	−14.8209	−	25.6705i	−0.668858	−	1.15850i	0.309366	−	0.950943i	$-0.399883\pi$
$492$	0.370736	−	0.424039i	0.0167141	−	0.0191172i
$493$	12.0918	+	6.98118i	0.544586	+	0.314417i
$494$	35.7633			1.60907
$495$	−1.02931	+	6.62876i	−0.0462640	+	0.297941i
$496$	19.8333			0.890541
$497$	1.71114	+	0.987925i	0.0767549	+	0.0443145i
$498$	−6.12586	−	17.9567i	−0.274506	−	0.804658i
$499$	6.59250	+	11.4186i	0.295121	+	0.511165i	0.975013	−	0.222148i	$-0.0713067\pi$
$499$	6.59250	+	11.4186i	0.295121	+	0.511165i	−0.679892	+	0.733312i	$0.737973\pi$
$500$	0.229612	−	0.648386i	0.0102685	−	0.0289967i
$501$	−3.73329	+	1.27360i	−0.166791	+	0.0569003i
$502$	−2.22662	−	1.28554i	−0.0993791	−	0.0573765i
$503$			36.6771i			1.63535i	0.575679	+	0.817676i	$0.304738\pi$
$503$			36.6771i			1.63535i	−0.575679	+	0.817676i	$0.695262\pi$
$504$	−6.01422	+	4.64393i	−0.267895	+	0.206857i
$505$	7.91129	+	32.9533i	0.352048	+	1.46640i
$506$	1.66796	−	2.88900i	0.0741500	−	0.128432i
$507$	−6.33580	+	7.24674i	−0.281383	+	0.321839i
$508$	0.767984	−	0.443396i	0.0340738	−	0.0196725i
$509$	11.0457	+	19.1318i	0.489594	+	0.848001i	0.999928	−	0.0119750i	$-0.00381184\pi$
$509$	11.0457	+	19.1318i	0.489594	+	0.848001i	−0.510335	+	0.859976i	$0.670479\pi$
$510$	0.449217	+	11.0085i	0.0198917	+	0.487464i
$511$	0.870759	−	1.50820i	0.0385201	−	0.0667188i
$512$		−	23.5813i		−	1.04216i
$513$	25.8398	+	17.0961i	1.14086	+	0.754810i
$514$	5.30212			0.233867
$515$	11.1957	−	37.7958i	0.493343	−	1.66548i
$516$	0.0406253	−	0.205868i	0.00178843	−	0.00906285i
$517$	4.06750	−	2.34837i	0.178889	−	0.103281i
$518$	−9.67704	+	5.58704i	−0.425185	+	0.245481i
$519$	−15.3560	−	13.4257i	−0.674055	−	0.589324i
$520$	−26.5094	−	7.85252i	−1.16251	−	0.344356i
$521$	−35.9213			−1.57374			−0.786870	−	0.617119i	$-0.788300\pi$
$521$	−35.9213			−1.57374			−0.786870	+	0.617119i	$0.788300\pi$
$522$	28.2873	−	3.81142i	1.23810	−	0.166821i
$523$			4.17379i			0.182507i	0.995828	+	0.0912537i	$0.0290874\pi$
$523$			4.17379i			0.182507i	−0.995828	+	0.0912537i	$0.970913\pi$
$524$	−0.197748	+	0.342510i	−0.00863868	+	0.0149626i
$525$	−5.32437	+	5.48216i	−0.232374	+	0.239261i
$526$	−6.71969	−	11.6388i	−0.292992	−	0.507478i
$527$	9.06091	−	5.23132i	0.394700	−	0.227880i
$528$	2.16602	+	6.34923i	0.0942638	+	0.276315i
$529$	−8.62960	+	14.9469i	−0.375200	+	0.649865i
$530$	−8.41623	−	35.0566i	−0.365578	−	1.52276i
$531$	−2.67376	−	19.8439i	−0.116031	−	0.861152i
$532$			0.323718i			0.0140350i
$533$	−19.7197	−	11.3852i	−0.854155	−	0.493147i
$534$	−26.6841	−	23.3298i	−1.15473	−	1.00958i
$535$	17.1259	+	18.0470i	0.740418	+	0.780242i
$536$	−0.855198	−	1.48125i	−0.0369389	−	0.0639801i
$537$	15.0514	+	2.97018i	0.649514	+	0.128173i
$538$	7.00284	+	4.04309i	0.301914	+	0.174310i
$539$	−6.22129			−0.267970
$540$	−0.459582	−	0.547504i	−0.0197773	−	0.0235608i
$541$	−17.4012			−0.748137			−0.374068	−	0.927401i	$-0.622038\pi$
$541$	−17.4012			−0.748137			−0.374068	+	0.927401i	$0.622038\pi$
$542$	−22.7379	−	13.1278i	−0.976678	−	0.563886i
$543$	−9.80326	−	1.93454i	−0.420698	−	0.0830189i
$544$	−0.355415	−	0.615596i	−0.0152383	−	0.0263935i
$545$	3.47365	−	3.29636i	0.148795	−	0.141200i
$546$	6.90144	+	6.03391i	0.295354	+	0.258227i
$547$	8.69703	+	5.02123i	0.371858	+	0.214692i	0.674270	−	0.738485i	$-0.264458\pi$
$547$	8.69703	+	5.02123i	0.371858	+	0.214692i	−0.302412	+	0.953177i	$0.597792\pi$
$548$		−	0.330163i		−	0.0141039i
$549$	23.6734	−	18.2796i	1.01035	−	0.780153i
$550$	3.16040	+	6.20272i	0.134760	+	0.264485i
$551$	20.3734	−	35.2878i	0.867936	−	1.50331i
$552$	3.84592	+	11.2735i	0.163693	+	0.479832i
$553$	12.0731	−	6.97038i	0.513398	−	0.296411i
$554$	7.87472	+	13.6394i	0.334565	+	0.579483i
$555$	−18.8412	−	29.7615i	−0.799764	−	1.26331i
$556$	0.443794	−	0.768673i	0.0188210	−	0.0325990i
$557$		−	16.3788i		−	0.693991i	−0.937867	−	0.346996i	$-0.887202\pi$
$557$		−	16.3788i		−	0.693991i	0.937867	−	0.346996i	$-0.112798\pi$
$558$	8.12504	−	19.7851i	0.343960	−	0.837571i
$559$	−8.48303			−0.358794
$560$	−2.17062	+	7.32783i	−0.0917256	+	0.309657i
$561$	2.66425	+	2.32935i	0.112485	+	0.0983452i
$562$	−16.3636	+	9.44752i	−0.690256	+	0.398520i
$563$	−27.6982	+	15.9916i	−1.16734	+	0.673964i	−0.953052	−	0.302806i	$-0.902077\pi$
$563$	−27.6982	+	15.9916i	−1.16734	+	0.673964i	−0.214288	+	0.976770i	$0.568743\pi$
$564$	−0.0968952	+	0.491016i	−0.00408002	+	0.0206755i
$565$	−1.73189	+	5.84670i	−0.0728611	+	0.245972i
$566$	8.90102			0.374138
$567$	2.10204	+	7.65876i	0.0882775	+	0.321638i
$568$			6.42666i			0.269657i
$569$	−19.0749	+	33.0388i	−0.799663	+	1.38506i	0.120173	+	0.992753i	$0.461655\pi$
$569$	−19.0749	+	33.0388i	−0.799663	+	1.38506i	−0.919836	+	0.392304i	$0.871678\pi$
$570$	32.1264	−	1.31096i	1.34563	−	0.0549103i
$571$	−16.7618	−	29.0323i	−0.701459	−	1.21496i	−0.967954	−	0.251126i	$-0.919199\pi$
$571$	−16.7618	−	29.0323i	−0.701459	−	1.21496i	0.266495	−	0.963836i	$-0.414134\pi$
$572$	−0.229522	+	0.132514i	−0.00959678	+	0.00554070i
$573$	−4.53044	+	5.18181i	−0.189262	+	0.216473i
$574$	−3.24711	+	5.62416i	−0.135532	+	0.234748i
$575$	5.43874	+	10.6743i	0.226811	+	0.445148i
$576$	−22.8411	−	9.38003i	−0.951714	−	0.390835i
$577$			1.92436i			0.0801123i	0.999197	+	0.0400561i	$0.0127537\pi$
$577$			1.92436i			0.0801123i	−0.999197	+	0.0400561i	$0.987246\pi$
$578$	−15.4642	−	8.92828i	−0.643227	−	0.371367i
$579$	−22.3772	+	7.63392i	−0.929966	+	0.317255i
$580$	−0.681911	+	0.647106i	−0.0283148	+	0.0268696i
$581$	−3.47135	−	6.01255i	−0.144016	−	0.249443i
$582$	12.2552	+	35.9235i	0.507993	+	1.48908i
$583$	−10.0289	−	5.79018i	−0.415354	−	0.239805i
$584$	5.66447			0.234398
$585$	−18.1179	+	22.5129i	−0.749082	+	0.930793i
$586$	8.64723			0.357214
$587$	−15.9625	−	9.21595i	−0.658843	−	0.380383i	0.132993	−	0.991117i	$-0.457541\pi$
$587$	−15.9625	−	9.21595i	−0.658843	−	0.380383i	−0.791836	+	0.610734i	$0.790875\pi$
$588$	0.436351	−	0.499087i	0.0179948	−	0.0205820i
$589$	−15.2667	−	26.4427i	−0.629054	−	1.08955i
$590$	−14.3034	−	15.0727i	−0.588862	−	0.620534i
$591$	−6.41588	+	32.5125i	−0.263914	+	1.33738i
$592$	−30.5065	−	17.6129i	−1.25381	−	0.723886i
$593$		−	25.6627i		−	1.05384i	−0.849914	−	0.526921i	$-0.823346\pi$
$593$		−	25.6627i		−	1.05384i	0.849914	−	0.526921i	$-0.176654\pi$
$594$	7.22115	+	0.440310i	0.296287	+	0.0180661i
$595$	0.941164	+	3.92028i	0.0385839	+	0.160716i
$596$	−0.00988217	+	0.0171164i	−0.000404790	+	0.000701116i
$597$	30.4910	+	6.01698i	1.24792	+	0.246259i
$598$	12.4454	−	7.18533i	0.508928	−	0.293830i
$599$	2.26827	+	3.92876i	0.0926790	+	0.160525i	0.908638	−	0.417586i	$-0.137124\pi$
$599$	2.26827	+	3.92876i	0.0926790	+	0.160525i	−0.815959	+	0.578110i	$0.803790\pi$
$600$	−24.1014	−	6.08222i	−0.983936	−	0.248306i
$601$	−13.5452	+	23.4610i	−0.552520	+	0.956992i	0.445572	+	0.895246i	$0.353000\pi$
$601$	−13.5452	+	23.4610i	−0.552520	+	0.956992i	−0.998092	+	0.0617461i	$0.980333\pi$
$602$			2.41941i			0.0986076i
$603$	−1.77171	+	0.238720i	−0.0721496	+	0.00972142i
$604$	−0.384410			−0.0156414
$605$	2.14398	+	0.635084i	0.0871654	+	0.0258198i
$606$	34.5913	−	11.8007i	1.40517	−	0.479371i
$607$	−13.8908	+	8.01985i	−0.563810	+	0.325516i	−0.754673	−	0.656101i	$-0.772205\pi$
$607$	−13.8908	+	8.01985i	−0.563810	+	0.325516i	0.190863	+	0.981617i	$0.438871\pi$
$608$	−1.79651	+	1.03722i	−0.0728582	+	0.0420647i
$609$	9.88524	−	3.37232i	0.400570	−	0.136653i
$610$	8.81551	−	29.7604i	0.356930	−	1.20496i
$611$	20.2328			0.818533
$612$	−0.373732	+	0.0503566i	−0.0151072	+	0.00203554i
$613$		−	28.9382i		−	1.16880i	−0.811464	−	0.584402i	$-0.801329\pi$
$613$		−	28.9382i		−	1.16880i	0.811464	−	0.584402i	$-0.198671\pi$
$614$	4.15445	−	7.19572i	0.167660	−	0.290396i
$615$	−18.1317	−	9.50452i	−0.731140	−	0.383259i
$616$	1.26641	+	2.19349i	0.0510252	+	0.0883783i
$617$	21.0481	−	12.1521i	0.847364	−	0.489226i	−0.0123964	−	0.999923i	$-0.503946\pi$
$617$	21.0481	−	12.1521i	0.847364	−	0.489226i	0.859761	+	0.510697i	$0.170613\pi$
$618$	−41.7078	−	8.23046i	−1.67773	−	0.331078i
$619$	4.13107	−	7.15522i	0.166042	−	0.287593i	−0.770983	−	0.636856i	$-0.780235\pi$
$619$	4.13107	−	7.15522i	0.166042	−	0.287593i	0.937025	+	0.349263i	$0.113568\pi$
$620$	0.164447	+	0.684981i	0.00660436	+	0.0275095i
$621$	12.4269	+	0.757730i	0.498674	+	0.0304067i
$622$			29.5547i			1.18503i
$623$	−11.2325	−	6.48510i	−0.450021	−	0.259820i
$624$	−5.59497	+	28.3525i	−0.223978	+	1.13501i
$625$	−24.8630	−	2.61349i	−0.994521	−	0.104540i
$626$	9.03013	+	15.6407i	0.360917	+	0.625126i
$627$	6.79781	−	7.77517i	0.271478	−	0.310510i
$628$	1.09625	+	0.632923i	0.0437453	+	0.0252564i
$629$	−18.5826			−0.740939
$630$	6.42079	+	5.16732i	0.255811	+	0.205871i
$631$	27.6887			1.10227			0.551135	−	0.834416i	$-0.314195\pi$
$631$	27.6887			1.10227			0.551135	+	0.834416i	$0.314195\pi$
$632$	39.2689	+	22.6719i	1.56203	+	0.901840i
$633$	−3.05494	−	8.95490i	−0.121423	−	0.355925i
$634$	1.79884	+	3.11569i	0.0714413	+	0.123740i
$635$	−22.1863	−	23.3796i	−0.880436	−	0.927791i
$636$	1.16791	−	0.398429i	0.0463107	−	0.0157987i
$637$	−23.2098	−	13.4002i	−0.919605	−	0.530934i
$638$		−	9.51429i		−	0.376674i
$639$	6.21365	+	2.55172i	0.245808	+	0.100945i
$640$	−23.4035	+	5.61862i	−0.925105	+	0.222095i
$641$	−23.4985	+	40.7005i	−0.928133	+	1.60757i	−0.141690	+	0.989911i	$0.545254\pi$
$641$	−23.4985	+	40.7005i	−0.928133	+	1.60757i	−0.786443	+	0.617662i	$0.788080\pi$
$642$	17.6608	−	20.2000i	0.697015	−	0.797230i
$643$	−8.50977	+	4.91312i	−0.335593	+	0.193755i	−0.658321	−	0.752737i	$-0.728733\pi$
$643$	−8.50977	+	4.91312i	−0.335593	+	0.193755i	0.322729	+	0.946492i	$0.395400\pi$
$644$	0.0650394	+	0.112652i	0.00256291	+	0.00443909i
$645$	−7.62036	+	0.310960i	−0.300052	+	0.0122440i
$646$	8.48127	−	14.6900i	0.333691	−	0.577970i
$647$		−	9.76321i		−	0.383831i	−0.981411	−	0.191916i	$-0.938530\pi$
$647$		−	9.76321i		−	0.383831i	0.981411	−	0.191916i	$-0.0614700\pi$
$648$	−18.1550	+	18.3766i	−0.713194	+	0.721901i
$649$	−6.67441			−0.261994
$650$	−1.56966	+	29.9478i	−0.0615673	+	1.17465i
$651$	1.51526	−	7.67857i	0.0593877	−	0.300947i
$652$	−0.209336	+	0.120860i	−0.00819822	+	0.00473325i
$653$	4.83231	−	2.78994i	0.189103	−	0.109179i	−0.402460	−	0.915438i	$-0.631845\pi$
$653$	4.83231	−	2.78994i	0.189103	−	0.109179i	0.591563	+	0.806259i	$0.298511\pi$
$654$	−3.88804	−	3.39930i	−0.152035	−	0.132923i
$655$	13.7826	+	4.08264i	0.538531	+	0.159522i
$656$	−20.4728			−0.799327
$657$	2.24910	−	5.47673i	0.0877456	−	0.213667i
$658$		−	5.77052i		−	0.224958i
$659$	18.5007	−	32.0441i	0.720684	−	1.24826i	−0.240042	−	0.970762i	$-0.577161\pi$
$659$	18.5007	−	32.0441i	0.720684	−	1.24826i	0.960726	−	0.277499i	$-0.0895054\pi$
$660$	−0.201323	+	0.127452i	−0.00783650	+	0.00496106i
$661$	−22.7622	−	39.4253i	−0.885348	−	1.53347i	−0.845314	−	0.534269i	$-0.820587\pi$
$661$	−22.7622	−	39.4253i	−0.885348	−	1.53347i	−0.0400336	−	0.999198i	$-0.512746\pi$
$662$	35.3808	−	20.4271i	1.37511	−	0.793922i
$663$	4.92230	+	14.4287i	0.191166	+	0.560364i
$664$	11.2909	−	19.5565i	0.438173	−	0.758938i
$665$	11.4407	−	2.74663i	0.443650	−	0.106510i
$666$	−30.0676	+	23.2169i	−1.16510	+	0.899638i
$667$		−	16.3732i		−	0.633971i
$668$	−0.121339	−	0.0700553i	−0.00469476	−	0.00271052i
$669$	30.2381	+	26.4371i	1.16907	+	1.02212i
$670$	−1.34573	+	1.27704i	−0.0519900	+	0.0493364i
$671$	−4.98490	−	8.63409i	−0.192440	−	0.333315i
$672$	−0.521680	−	0.102946i	−0.0201243	−	0.00397124i
$673$	−16.7969	−	9.69770i	−0.647473	−	0.373819i	0.140014	−	0.990149i	$-0.455285\pi$
$673$	−16.7969	−	9.69770i	−0.647473	−	0.373819i	−0.787487	+	0.616331i	$0.788618\pi$
$674$	−25.9350			−0.998981
$675$	−15.4502	+	20.8876i	−0.594677	+	0.803965i
$676$	−0.341911			−0.0131504
$677$	−39.5670	−	22.8440i	−1.52068	−	0.877968i	−0.999702	−	0.0244006i	$-0.992232\pi$
$677$	−39.5670	−	22.8440i	−1.52068	−	0.877968i	−0.520983	−	0.853567i	$-0.674434\pi$
$678$	6.45186	+	1.27318i	0.247782	+	0.0488963i
$679$	6.94465	+	12.0285i	0.266511	+	0.461611i
$680$	−9.51217	+	9.02666i	−0.364775	+	0.346157i
$681$	19.0416	+	16.6480i	0.729677	+	0.637954i
$682$	−6.17432	−	3.56475i	−0.236427	−	0.136501i
$683$		−	37.9861i		−	1.45350i	−0.686903	−	0.726749i	$-0.741030\pi$
$683$		−	37.9861i		−	1.45350i	0.686903	−	0.726749i	$-0.258970\pi$
$684$	0.146957	+	1.09067i	0.00561905	+	0.0417030i
$685$	−11.6684	+	2.80131i	−0.445828	+	0.107033i
$686$	−8.12197	+	14.0677i	−0.310098	+	0.537106i
$687$	−4.26217	−	12.4937i	−0.162612	−	0.476663i
$688$	−6.60524	+	3.81354i	−0.251822	+	0.145390i
$689$	−24.9432	−	43.2029i	−0.950260	−	1.64590i
$690$	10.9163	−	6.91083i	0.415578	−	0.263091i
$691$	16.0557	−	27.8093i	0.610787	−	1.05791i	−0.380321	−	0.924855i	$-0.624187\pi$
$691$	16.0557	−	27.8093i	0.610787	−	1.05791i	0.991108	−	0.133060i	$-0.0424802\pi$
$692$		−	0.724519i		−	0.0275421i
$693$	2.62362	−	0.353506i	0.0996632	−	0.0134286i
$694$	14.0659			0.533934
$695$	−30.9314	−	9.16239i	−1.17329	−	0.347549i
$696$	25.5757	+	22.3607i	0.969444	+	0.847582i
$697$	−9.35306	+	5.39999i	−0.354272	+	0.204539i
$698$	−2.85107	+	1.64607i	−0.107915	+	0.0623045i
$699$	−6.58232	+	33.3559i	−0.248966	+	1.26164i
$700$	−0.271078	−	0.0142081i	−0.0102458	−	0.000537017i
$701$	19.3534			0.730970			0.365485	−	0.930817i	$-0.380903\pi$
$701$	19.3534			0.730970			0.365485	+	0.930817i	$0.380903\pi$
$702$	25.9916	+	17.1965i	0.980988	+	0.649038i
$703$			54.2303i			2.04533i
$704$	−4.11536	+	7.12801i	−0.155103	+	0.268647i
$705$	18.1753	−	0.741670i	0.684521	−	0.0279329i
$706$	−16.8506	−	29.1861i	−0.634181	−	1.09843i
$707$	11.5824	−	6.68712i	0.435602	−	0.251495i
$708$	0.468131	−	0.535438i	0.0175935	−	0.0201230i
$709$	20.0935	−	34.8030i	0.754628	−	1.30705i	−0.190930	−	0.981604i	$-0.561150\pi$
$709$	20.0935	−	34.8030i	0.754628	−	1.30705i	0.945559	−	0.325451i	$-0.105516\pi$
$710$	6.77819	−	1.62728i	0.254381	−	0.0610707i
$711$	37.5123	−	28.9654i	1.40682	−	1.08629i
$712$		−	42.1869i		−	1.58102i
$713$	−10.6254	−	6.13458i	−0.397924	−	0.229742i
$714$	4.11514	−	1.40387i	0.154005	−	0.0525384i
$715$	6.63064	+	6.98728i	0.247972	+	0.261309i
$716$	0.272467	+	0.471927i	0.0101826	+	0.0176367i
$717$	−7.00083	−	20.5215i	−0.261451	−	0.766388i
$718$	−29.2345	−	16.8785i	−1.09102	−	0.629901i
$719$	−21.9739			−0.819487			−0.409743	−	0.912201i	$-0.634382\pi$
$719$	−21.9739			−0.819487			−0.409743	+	0.912201i	$0.634382\pi$
$720$	−3.98669	+	25.6743i	−0.148575	+	0.956826i
$721$	−15.5564			−0.579350
$722$	−19.9608	−	11.5244i	−0.742863	−	0.428892i
$723$	0.0158917	−	0.0181766i	0.000591020	−	0.000675995i
$724$	−0.177463	−	0.307375i	−0.00659537	−	0.0114235i
$725$	28.6554	+	18.6092i	1.06423	+	0.691130i
$726$	0.466877	−	2.36590i	0.0173274	−	0.0878066i
$727$	42.0721	+	24.2904i	1.56037	+	0.900879i	0.997219	+	0.0745242i	$0.0237438\pi$
$727$	42.0721	+	24.2904i	1.56037	+	0.900879i	0.563149	+	0.826355i	$0.309590\pi$
$728$			10.9110i			0.404389i
$729$	10.5590	+	24.8497i	0.391075	+	0.920359i
$730$	−1.43429	−	5.97432i	−0.0530854	−	0.221119i
$731$	−2.01175	+	3.48446i	−0.0744073	+	0.128877i
$732$	1.04228	+	0.205679i	0.0385238	+	0.00760213i
$733$	−37.1153	+	21.4286i	−1.37089	+	0.791482i	−0.991040	−	0.133568i	$-0.957357\pi$
$733$	−37.1153	+	21.4286i	−1.37089	+	0.791482i	−0.379847	+	0.925049i	$0.624023\pi$
$734$	16.5032	+	28.5843i	0.609143	+	1.05507i
$735$	−21.3407	−	11.1867i	−0.787164	−	0.412627i
$736$	−0.416782	+	0.721887i	−0.0153628	+	0.0266091i
$737$			0.595907i			0.0219505i
$738$	−8.38701	+	20.4230i	−0.308730	+	0.751782i
$739$	49.8356			1.83323			0.916615	−	0.399770i	$-0.130910\pi$
$739$	49.8356			1.83323			0.916615	+	0.399770i	$0.130910\pi$
$740$	0.355352	−	1.19964i	0.0130630	−	0.0440995i
$741$	42.1077	−	14.3649i	1.54687	−	0.527708i
$742$	−12.3217	+	7.11393i	−0.452343	+	0.261161i
$743$	27.6053	−	15.9379i	1.01274	−	0.584705i	0.100747	−	0.994912i	$-0.467877\pi$
$743$	27.6053	−	15.9379i	1.01274	−	0.584705i	0.911993	+	0.410207i	$0.134543\pi$
$744$	24.0936	−	8.21944i	0.883313	−	0.301339i
$745$	0.688765	+	0.204024i	0.0252344	+	0.00747484i
$746$	−28.7073			−1.05105
$747$	−14.4252	−	18.6816i	−0.527789	−	0.683525i
$748$			0.125703i			0.00459616i
$749$	4.90925	−	8.50306i	0.179380	−	0.310695i
$750$	−0.312254	+	26.9598i	−0.0114019	+	0.984433i
$751$	6.26461	+	10.8506i	0.228599	+	0.395945i	0.957393	−	0.288788i	$-0.0932523\pi$
$751$	6.26461	+	10.8506i	0.228599	+	0.395945i	−0.728794	+	0.684733i	$0.759919\pi$
$752$	15.7541	−	9.09565i	0.574494	−	0.331684i
$753$	−3.13798	−	0.619238i	−0.114355	−	0.0225663i
$754$	20.4930	−	35.4950i	0.746312	−	1.29265i
$755$	3.26157	+	13.5856i	0.118701	+	0.494430i
$756$	−0.155657	+	0.235268i	−0.00566119	+	0.00855660i
$757$			27.4041i			0.996019i	0.867172	+	0.498010i	$0.165936\pi$
$757$			27.4041i			0.996019i	−0.867172	+	0.498010i	$0.834064\pi$
$758$	−4.46313	−	2.57679i	−0.162108	−	0.0935932i
$759$	0.803448	−	4.07147i	0.0291633	−	0.147785i
$760$	26.3428	+	27.7597i	0.955553	+	1.00695i
$761$	16.0240	+	27.7545i	0.580871	+	1.00610i	0.995376	+	0.0960512i	$0.0306213\pi$
$761$	16.0240	+	27.7545i	0.580871	+	1.00610i	−0.414505	+	0.910047i	$0.636045\pi$
$762$	−22.8792	+	26.1687i	−0.828825	+	0.947991i
$763$	−1.63665	−	0.944920i	−0.0592507	−	0.0342084i
$764$	−0.244485			−0.00884515
$765$	4.95064	+	12.7810i	0.178991	+	0.462097i
$766$	−25.8188			−0.932872
$767$	−24.9002	−	14.3762i	−0.899095	−	0.519093i
$768$	−0.824944	−	2.41815i	−0.0297676	−	0.0872575i
$769$	1.89786	+	3.28719i	0.0684385	+	0.118539i	0.898214	−	0.439558i	$-0.144865\pi$
$769$	1.89786	+	3.28719i	0.0684385	+	0.118539i	−0.829776	+	0.558097i	$0.811532\pi$
$770$	1.99281	−	1.89109i	0.0718159	−	0.0681503i
$771$	6.24272	−	2.12968i	0.224826	−	0.0766986i
$772$	−0.727304	−	0.419909i	−0.0261762	−	0.0151129i
$773$			25.8442i			0.929552i	0.885428	+	0.464776i	$0.153865\pi$
$773$			25.8442i			0.929552i	−0.885428	+	0.464776i	$0.846135\pi$
$774$	1.09833	+	8.15147i	0.0394786	+	0.292999i
$775$	22.8129	−	11.6236i	0.819464	−	0.417532i
$776$	−22.5882	+	39.1239i	−0.810870	+	1.40447i
$777$	−9.14962	+	10.4651i	−0.328241	+	0.375434i
$778$	−34.9396	+	20.1724i	−1.25264	+	0.723215i
$779$	15.7590	+	27.2953i	0.564623	+	0.977956i
$780$	−1.02560	+	0.0418510i	−0.0367223	+	0.00149851i
$781$	1.11953	−	1.93909i	0.0400600	−	0.0693860i
$782$		−	6.81600i		−	0.243740i
$783$	31.7745	−	15.8496i	1.13553	−	0.566418i
$784$	−24.0961			−0.860576
$785$	13.0671	−	44.1133i	0.466384	−	1.57447i
$786$	3.00132	−	15.2092i	0.107053	−	0.542493i
$787$	23.8927	−	13.7944i	0.851682	−	0.491719i	−0.00953602	−	0.999955i	$-0.503035\pi$
$787$	23.8927	−	13.7944i	0.851682	−	0.491719i	0.861218	+	0.508236i	$0.169702\pi$
$788$	−1.01941	+	0.588556i	−0.0363150	+	0.0209664i
$789$	−12.5867	−	11.0045i	−0.448098	−	0.391771i
$790$	13.9689	−	47.1576i	0.496990	−	1.67779i
$791$	2.40645			0.0855634
$792$	5.26258	+	6.81541i	0.186997	+	0.242175i
$793$		−	42.9483i		−	1.52514i
$794$	15.6614	−	27.1264i	0.555803	−	0.962679i
$795$	−23.9903	−	37.8951i	−0.850849	−	1.34400i
$796$	0.551964	+	0.956029i	0.0195638	+	0.0338855i
$797$	−33.5574	+	19.3744i	−1.18866	+	0.686275i	−0.958003	−	0.286760i	$-0.907422\pi$
$797$	−33.5574	+	19.3744i	−1.18866	+	0.686275i	−0.230660	+	0.973034i	$0.574089\pi$
$798$	−4.09695	−	12.0093i	−0.145030	−	0.425126i
$799$	4.79822	−	8.31076i	0.169749	−	0.294014i
$800$	−0.789704	−	1.54990i	−0.0279203	−	0.0547974i
$801$	−40.7886	−	16.7504i	−1.44120	−	0.591847i
$802$		−	24.3004i		−	0.858077i
$803$	−1.70912	−	0.986759i	−0.0603134	−	0.0348220i
$804$	−0.0478051	−	0.0417958i	−0.00168596	−	0.00147403i
$805$	3.42943	−	3.25439i	0.120871	−	0.114702i
$806$	−15.3564	−	26.5980i	−0.540905	−	0.936875i
$807$	9.86912	+	1.94753i	0.347410	+	0.0685564i
$808$	37.6731	+	21.7506i	1.32533	+	0.765182i
$809$	42.8694			1.50721			0.753603	−	0.657329i	$-0.228314\pi$
$809$	42.8694			1.50721			0.753603	+	0.657329i	$0.228314\pi$
$810$	23.9788	+	14.4949i	0.842528	+	0.509300i
$811$	−9.49238			−0.333322			−0.166661	−	0.986014i	$-0.553299\pi$
$811$	−9.49238			−0.333322			−0.166661	+	0.986014i	$0.553299\pi$
$812$	0.321290	+	0.185497i	0.0112751	+	0.00650966i
$813$	−32.0446	−	6.32356i	−1.12385	−	0.221777i
$814$	6.33133	+	10.9662i	0.221913	+	0.384365i
$815$	6.04750	+	6.37277i	0.211835	+	0.223228i
$816$	10.3191	+	9.02197i	0.361241	+	0.315832i
$817$	10.1688	+	5.87095i	0.355761	+	0.205399i
$818$			0.777051i			0.0271689i
$819$	10.5494	+	4.33225i	0.368625	+	0.151381i
$820$	−0.169749	−	0.707066i	−0.00592791	−	0.0246918i
$821$	−20.6924	+	35.8402i	−0.722168	+	1.25083i	0.237960	+	0.971275i	$0.423521\pi$
$821$	−20.6924	+	35.8402i	−0.722168	+	1.25083i	−0.960129	+	0.279558i	$0.909812\pi$
$822$	4.17851	+	12.2484i	0.145742	+	0.427213i
$823$	15.1515	−	8.74774i	0.528149	−	0.304927i	−0.212113	−	0.977245i	$-0.568035\pi$
$823$	15.1515	−	8.74774i	0.528149	−	0.304927i	0.740262	+	0.672318i	$0.234701\pi$
$824$	−25.2994	−	43.8199i	−0.881347	−	1.52654i
$825$	6.21248	+	6.03366i	0.216291	+	0.210065i
$826$	−4.10016	+	7.10168i	−0.142663	+	0.247099i
$827$			31.4699i			1.09431i	0.837030	+	0.547157i	$0.184290\pi$
$827$			31.4699i			1.09431i	−0.837030	+	0.547157i	$0.815710\pi$
$828$	0.270271	+	0.350020i	0.00939257	+	0.0121640i
$829$	−21.4640			−0.745474			−0.372737	−	0.927937i	$-0.621581\pi$
$829$	−21.4640			−0.745474			−0.372737	+	0.927937i	$0.621581\pi$
$830$	−23.4851	−	6.95669i	−0.815181	−	0.241470i
$831$	14.7502	+	12.8960i	0.511678	+	0.447358i
$832$	−30.7063	+	17.7283i	−1.06455	+	0.614619i
$833$	−11.0084	+	6.35570i	−0.381418	+	0.220212i
$834$	−6.73566	+	34.1329i	−0.233237	+	1.18193i
$835$	−1.44633	+	4.88269i	−0.0500525	+	0.168973i
$836$	0.366843			0.0126875
$837$	1.61941	−	26.5586i	0.0559750	−	0.917998i
$838$			34.9503i			1.20734i
$839$	2.87916	−	4.98685i	0.0993996	−	0.172165i	−0.812037	−	0.583606i	$-0.801641\pi$
$839$	2.87916	−	4.98685i	0.0993996	−	0.172165i	0.911436	+	0.411441i	$0.134974\pi$
$840$	0.399962	+	9.80144i	0.0138000	+	0.338182i
$841$	−8.84867	−	15.3263i	−0.305126	−	0.528494i
$842$	26.6891	−	15.4090i	0.919767	−	0.531028i
$843$	−15.4717	+	17.6962i	−0.532875	+	0.609490i
$844$	0.168039	−	0.291052i	0.00578414	−	0.0100184i
$845$	2.90098	+	12.0836i	0.0997968	+	0.415689i
$846$	−2.61962	−	19.4420i	−0.0900643	−	0.668431i
$847$		−	0.882444i		−	0.0303211i
$848$	−38.8436	−	22.4264i	−1.33389	−	0.770124i
$849$	10.4801	−	3.57524i	0.359675	−	0.122702i
$850$	11.9290	+	7.74686i	0.409160	+	0.265715i
$851$	10.8956	+	18.8717i	0.373496	+	0.646914i
$852$	0.0770363	+	0.225816i	0.00263922	+	0.00773632i
$853$	−2.65784	−	1.53451i	−0.0910028	−	0.0525405i	0.453808	−	0.891099i	$-0.350065\pi$
$853$	−2.65784	−	1.53451i	−0.0910028	−	0.0525405i	−0.544811	+	0.838559i	$0.683399\pi$
$854$	−12.2491			−0.419155
$855$	37.2991	−	14.4476i	1.27560	−	0.494098i
$856$	31.9357			1.09154
$857$	−7.57503	−	4.37344i	−0.258758	−	0.149394i	0.365010	−	0.931004i	$-0.381066\pi$
$857$	−7.57503	−	4.37344i	−0.258758	−	0.149394i	−0.623768	+	0.781610i	$0.714399\pi$
$858$	6.83773	−	7.82083i	0.233436	−	0.266999i
$859$	14.6151	+	25.3141i	0.498661	+	0.863707i	0.999999	−	0.00154519i	$-0.000491850\pi$
$859$	14.6151	+	25.3141i	0.498661	+	0.863707i	−0.501338	+	0.865252i	$0.667159\pi$
$860$	−0.186475	−	0.196505i	−0.00635874	−	0.00670075i
$861$	−1.56411	+	7.92615i	−0.0533049	+	0.270122i
$862$	32.4527	+	18.7366i	1.10534	+	0.638170i
$863$		−	20.5969i		−	0.701125i	−0.936539	−	0.350563i	$-0.885990\pi$
$863$		−	20.5969i		−	0.701125i	0.936539	−	0.350563i	$-0.114010\pi$
$864$	−1.80438	−	0.110022i	−0.0613863	−	0.00374303i
$865$	−25.6055	+	6.14726i	−0.870613	+	0.209013i
$866$	9.34081	−	16.1788i	0.317414	−	0.549777i
$867$	−21.7938	−	4.30070i	−0.740155	−	0.146059i
$868$	0.240757	−	0.139001i	0.00817183	−	0.00471801i
$869$	−7.89895	−	13.6814i	−0.267954	−	0.464109i
$870$	17.1079	−	32.6366i	0.580012	−	1.10648i
$871$	−1.28354	+	2.22315i	−0.0434910	+	0.0753286i
$872$		−	6.14691i		−	0.208160i
$873$	28.8585	+	37.3738i	0.976712	+	1.26491i
$874$	−19.8913			−0.672835
$875$	1.79786	+	9.70083i	0.0607787	+	0.327948i
$876$	0.199035	−	0.0679000i	0.00672476	−	0.00229413i
$877$	11.7224	−	6.76793i	0.395837	−	0.228537i	−0.288849	−	0.957375i	$-0.593273\pi$
$877$	11.7224	−	6.76793i	0.395837	−	0.228537i	0.684686	+	0.728838i	$0.259939\pi$
$878$	−46.2716	+	26.7149i	−1.56159	+	0.901585i
$879$	10.1812	−	3.47330i	0.343405	−	0.117151i
$880$	8.30402	+	2.45979i	0.279928	+	0.0829194i
$881$	−9.36084			−0.315375			−0.157687	−	0.987489i	$-0.550404\pi$
$881$	−9.36084			−0.315375			−0.157687	+	0.987489i	$0.550404\pi$
$882$	−9.87138	+	24.0376i	−0.332387	+	0.809388i
$883$			15.0653i			0.506987i	0.967337	+	0.253494i	$0.0815797\pi$
$883$			15.0653i			0.506987i	−0.967337	+	0.253494i	$0.918420\pi$
$884$	−0.270755	+	0.468961i	−0.00910646	+	0.0157729i
$885$	−22.8950	−	12.0014i	−0.769608	−	0.403424i
$886$	−16.9369	−	29.3356i	−0.569007	−	0.985549i
$887$	25.1643	−	14.5286i	0.844935	−	0.487823i	−0.0140038	−	0.999902i	$-0.504458\pi$
$887$	25.1643	−	14.5286i	0.844935	−	0.487823i	0.858939	+	0.512079i	$0.171124\pi$
$888$	−44.3586	−	8.75356i	−1.48858	−	0.293750i
$889$	−6.35983	+	11.0155i	−0.213302	+	0.369450i
$890$	−44.4945	+	10.6821i	−1.49146	+	0.358063i
$891$	8.67904	−	2.38207i	0.290759	−	0.0798023i
$892$			1.42668i			0.0477686i
$893$	−24.2535	−	14.0028i	−0.811614	−	0.468586i
$894$	0.149986	−	0.760055i	0.00501629	−	0.0254200i
$895$	14.3668	−	13.6335i	0.480228	−	0.455717i
$896$	4.74921	+	8.22587i	0.158660	+	0.274807i
$897$	11.7671	−	13.4589i	0.392890	−	0.449379i
$898$	−3.81700	−	2.20374i	−0.127375	−	0.0735399i
$899$	−34.9925			−1.16706
$900$	−0.919768	+	0.0751901i	−0.0306589	+	0.00250634i
$901$	−23.6611			−0.788266
$902$	6.37340	+	3.67968i	0.212211	+	0.122520i
$903$	0.971793	+	2.84861i	0.0323392	+	0.0947957i
$904$	3.91361	+	6.77857i	0.130165	+	0.225452i
$905$	−9.35737	+	8.87976i	−0.311049	+	0.295173i
$906$	14.2609	−	4.86505i	0.473786	−	0.161630i
$907$	−19.2356	−	11.1057i	−0.638706	−	0.368757i	0.145410	−	0.989372i	$-0.453550\pi$
$907$	−19.2356	−	11.1057i	−0.638706	−	0.368757i	−0.784116	+	0.620614i	$0.786883\pi$
$908$			0.898410i			0.0298148i
$909$	35.9878	−	27.7883i	1.19364	−	0.921679i
$910$	11.5078	−	2.76275i	0.381481	−	0.0915844i
$911$	−5.94219	+	10.2922i	−0.196874	+	0.340995i	−0.947513	−	0.319717i	$-0.896412\pi$
$911$	−5.94219	+	10.2922i	−0.196874	+	0.340995i	0.750640	+	0.660712i	$0.229745\pi$
$912$	26.3291	−	30.1146i	0.871843	−	0.997193i
$913$	−6.81352	+	3.93379i	−0.225495	+	0.130189i
$914$	−25.0966	−	43.4686i	−0.830122	−	1.43781i
$915$	−1.57434	−	38.5807i	−0.0520462	−	1.27544i
$916$	0.234444	−	0.406068i	0.00774624	−	0.0134169i
$917$		−	5.67279i		−	0.187332i
$918$	13.2274	−	6.59805i	0.436571	−	0.217768i
$919$	−21.6546			−0.714321			−0.357160	−	0.934043i	$-0.616255\pi$
$919$	−21.6546			−0.714321			−0.357160	+	0.934043i	$0.616255\pi$
$920$	14.7444	+	4.36753i	0.486108	+	0.143993i
$921$	2.00117	−	10.1409i	0.0659409	−	0.334155i
$922$	43.0389	−	24.8485i	1.41741	−	0.818343i
$923$	8.35328	−	4.82277i	0.274952	−	0.158743i
$924$	0.0707918	+	0.0618930i	0.00232888	+	0.00203613i
$925$	−45.4118	−	2.38019i	−1.49313	−	0.0782601i
$926$	22.8527			0.750985
$927$	−52.4127	+	7.06207i	−1.72146	+	0.231949i
$928$			2.37738i			0.0780413i
$929$	−3.71538	+	6.43523i	−0.121898	+	0.211133i	−0.920516	−	0.390705i	$-0.872231\pi$
$929$	−3.71538	+	6.43523i	−0.121898	+	0.211133i	0.798618	+	0.601838i	$0.205565\pi$
$930$	−14.7697	−	23.3303i	−0.484318	−	0.765029i
$931$	18.5480	+	32.1261i	0.607887	+	1.05289i
$932$	−1.04585	+	0.603824i	−0.0342581	+	0.0197789i
$933$	11.8711	+	34.7977i	0.388643	+	1.13923i
$934$	14.7906	−	25.6181i	0.483963	−	0.838249i
$935$	4.44252	−	1.06654i	0.145286	−	0.0348797i
$936$	4.95323	+	36.7614i	0.161901	+	1.20159i
$937$		−	36.0122i		−	1.17647i	−0.808691	−	0.588233i	$-0.799824\pi$
$937$		−	36.0122i		−	1.17647i	0.808691	−	0.588233i	$-0.200176\pi$
$938$	0.634054	+	0.366071i	0.0207026	+	0.0119527i
$939$	16.9144	+	14.7882i	0.551980	+	0.482595i
$940$	0.444761	+	0.468683i	0.0145065	+	0.0152867i
$941$	10.8456	+	18.7851i	0.353555	+	0.612375i	0.986870	−	0.161519i	$-0.0516393\pi$
$941$	10.8456	+	18.7851i	0.353555	+	0.612375i	−0.633314	+	0.773895i	$0.718306\pi$
$942$	−48.6791	−	9.60615i	−1.58605	−	0.312985i
$943$	10.9680	+	6.33237i	0.357167	+	0.206210i
$944$	−25.8511			−0.841383
$945$	9.63538	+	3.50498i	0.313439	+	0.114017i
$946$	2.74171			0.0891407
$947$	29.5791	+	17.0775i	0.961190	+	0.554944i	0.896539	−	0.442964i	$-0.146073\pi$
$947$	29.5791	+	17.0775i	0.961190	+	0.554944i	0.0646512	+	0.997908i	$0.479407\pi$
$948$	1.65157	+	0.325915i	0.0536406	+	0.0105852i
$949$	−4.25080	−	7.36261i	−0.137987	−	0.239000i
$950$	22.6079	−	34.8127i	0.733497	−	1.12947i
$951$	3.36943	+	2.94588i	0.109261	+	0.0955267i
$952$	4.48176	+	2.58755i	0.145255	+	0.0838629i
$953$			37.2181i			1.20561i	0.797888	+	0.602806i	$0.205951\pi$
$953$			37.2181i			1.20561i	−0.797888	+	0.602806i	$0.794049\pi$
$954$	−38.2848	+	29.5619i	−1.23952	+	0.957102i
$955$	2.07436	+	8.64044i	0.0671247	+	0.279598i
$956$	0.385086	−	0.666988i	0.0124546	−	0.0215719i
$957$	−3.82157	−	11.2021i	−0.123534	−	0.362113i
$958$	21.8962	−	12.6418i	0.707435	−	0.408438i
$959$	2.36784	+	4.10122i	0.0764616	+	0.132435i
$960$	−26.9338	+	17.0511i	−0.869286	+	0.550320i
$961$	2.38927	−	4.13834i	0.0770733	−	0.133495i
$962$			54.5487i			1.75872i
$963$	12.6802	−	30.8772i	0.408612	−	0.995003i
$964$	0.000857596	0		2.76213e−5	0
$965$	−8.66928	+	29.2667i	−0.279074	+	0.942128i
$966$	−3.83854	−	3.35603i	−0.123503	−	0.107978i
$967$	1.98147	−	1.14400i	0.0637197	−	0.0367886i	−0.467802	−	0.883833i	$-0.654954\pi$
$967$	1.98147	−	1.14400i	0.0637197	−	0.0367886i	0.531521	+	0.847045i	$0.321621\pi$
$968$	2.48570	−	1.43512i	0.0798935	−	0.0461265i
$969$	4.08537	−	20.7026i	0.131241	−	0.665064i
$970$	46.9835	+	13.9173i	1.50855	+	0.446858i
$971$	−25.1219			−0.806200			−0.403100	−	0.915156i	$-0.632067\pi$
$971$	−25.1219			−0.806200			−0.403100	+	0.915156i	$0.632067\pi$
$972$	−0.417637	+	0.863328i	−0.0133957	+	0.0276913i
$973$			12.7311i			0.408139i
$974$	1.57982	−	2.73633i	0.0506207	−	0.0876776i
$975$	10.1809	+	35.8910i	0.326049	+	1.14943i
$976$	−19.3074	−	33.4413i	−0.618013	−	1.07043i
$977$	−36.0189	+	20.7955i	−1.15235	+	0.665307i	−0.949458	−	0.313895i	$-0.898366\pi$
$977$	−36.0189	+	20.7955i	−1.15235	+	0.665307i	−0.202888	+	0.979202i	$0.565033\pi$
$978$	6.23637	−	7.13301i	0.199417	−	0.228088i
$979$	−7.34902	+	12.7289i	−0.234876	+	0.406817i
$980$	−0.199792	−	0.832206i	−0.00638214	−	0.0265838i
$981$	−5.94317	−	2.44065i	−0.189751	−	0.0779238i
$982$			41.2700i			1.31698i
$983$	9.90116	+	5.71644i	0.315798	+	0.182326i	0.649518	−	0.760346i	$-0.274971\pi$
$983$	9.90116	+	5.71644i	0.315798	+	0.182326i	−0.333720	+	0.942672i	$0.608304\pi$
$984$	−24.8704	+	8.48445i	−0.792840	+	0.270475i
$985$	29.4497	+	31.0337i	0.938345	+	0.988815i
$986$	−9.71985	−	16.8353i	−0.309543	−	0.536144i
$987$	−2.31782	−	6.79421i	−0.0737770	−	0.216262i
$988$	1.36858	+	0.790151i	0.0435404	+	0.0251381i
$989$	4.71821			0.150030
$990$	5.85569	−	7.27615i	0.186106	−	0.231251i
$991$	−48.6261			−1.54466			−0.772330	−	0.635221i	$-0.780909\pi$
$991$	−48.6261			−1.54466			−0.772330	+	0.635221i	$0.780909\pi$
$992$	1.54281	+	0.890740i	0.0489842	+	0.0282810i
$993$	33.4524	−	38.2621i	1.06158	−	1.21421i
$994$	−1.37548	−	2.38240i	−0.0436276	−	0.0755652i
$995$	29.1042	−	27.6187i	0.922665	−	0.875571i
$996$	0.162310	−	0.822507i	0.00514300	−	0.0260621i
$997$	33.2689	+	19.2078i	1.05364	+	0.608317i	0.923665	−	0.383201i	$-0.125178\pi$
$997$	33.2689	+	19.2078i	1.05364	+	0.608317i	0.129971	+	0.991518i	$0.458512\pi$
$998$		−	18.3574i		−	0.581093i
$999$	−26.0761	+	39.4127i	−0.825013	+	1.24696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.u.b.34.11	✓	68
5.4	even	2	inner	495.2.u.b.34.24	yes	68
9.4	even	3	inner	495.2.u.b.364.24	yes	68
45.4	even	6	inner	495.2.u.b.364.11	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.u.b.34.11	✓	68	1.1	even	1	trivial
495.2.u.b.34.24	yes	68	5.4	even	2	inner
495.2.u.b.364.11	yes	68	45.4	even	6	inner
495.2.u.b.364.24	yes	68	9.4	even	3	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20576 - 0.696146i) q^{2} +(-1.69928 - 0.335329i) q^{3} +(-0.0307612 - 0.0532800i) q^{4} +(-1.62199 + 1.53920i) q^{5} +(1.81549 + 1.58727i) q^{6} +(0.764219 + 0.441222i) q^{7} +2.87024i q^{8} +(2.77511 + 1.13964i) q^{9} +O(q^{10})\)	\(q+(-1.20576 - 0.696146i) q^{2} +(-1.69928 - 0.335329i) q^{3} +(-0.0307612 - 0.0532800i) q^{4} +(-1.62199 + 1.53920i) q^{5} +(1.81549 + 1.58727i) q^{6} +(0.764219 + 0.441222i) q^{7} +2.87024i q^{8} +(2.77511 + 1.13964i) q^{9} +(3.02724 - 0.726768i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.0344056 + 0.100853i) q^{12} +(3.73070 - 2.15392i) q^{13} +(-0.614310 - 1.06402i) q^{14} +(3.27236 - 2.07164i) q^{15} +(1.93659 - 3.35426i) q^{16} -2.04321i q^{17} +(-2.55276 - 3.30601i) q^{18} -5.96276 q^{19} +(0.131903 + 0.0390719i) q^{20} +(-1.15067 - 1.00602i) q^{21} +(-1.20576 + 0.696146i) q^{22} +(-2.07499 + 1.19800i) q^{23} +(0.962476 - 4.87735i) q^{24} +(0.261708 - 4.99315i) q^{25} -5.99778 q^{26} +(-4.33353 - 2.86714i) q^{27} -0.0542900i q^{28} +(-3.41677 + 5.91802i) q^{29} +(-5.38784 + 0.219859i) q^{30} +(2.56034 + 4.43465i) q^{31} +(0.301289 - 0.173949i) q^{32} +(-1.14004 + 1.30396i) q^{33} +(-1.42237 + 2.46362i) q^{34} +(-1.91869 + 0.460630i) q^{35} +(-0.0246458 - 0.182914i) q^{36} -9.09483i q^{37} +(7.18966 + 4.15095i) q^{38} +(-7.06178 + 2.40910i) q^{39} +(-4.41788 - 4.65551i) q^{40} +(-2.64290 - 4.57763i) q^{41} +(0.687089 + 2.01406i) q^{42} +(-1.70538 - 0.984603i) q^{43} -0.0615224 q^{44} +(-6.25533 + 2.42297i) q^{45} +3.33593 q^{46} +(4.06750 + 2.34837i) q^{47} +(-4.41558 + 5.05044i) q^{48} +(-3.11065 - 5.38780i) q^{49} +(-3.79152 + 5.83835i) q^{50} +(-0.685148 + 3.47199i) q^{51} +(-0.229522 - 0.132514i) q^{52} -11.5804i q^{53} +(3.22926 + 6.47386i) q^{54} +(0.521994 + 2.17429i) q^{55} +(-1.26641 + 2.19349i) q^{56} +(10.1324 + 1.99949i) q^{57} +(8.23962 - 4.75715i) q^{58} +(-3.33721 - 5.78021i) q^{59} +(-0.211038 - 0.110625i) q^{60} +(4.98490 - 8.63409i) q^{61} -7.12950i q^{62} +(1.61796 + 2.09537i) q^{63} -8.23072 q^{64} +(-2.73584 + 9.23595i) q^{65} +(2.28236 - 0.778621i) q^{66} +(-0.516070 + 0.297953i) q^{67} +(-0.108862 + 0.0628516i) q^{68} +(3.92772 - 1.33993i) q^{69} +(2.63414 + 0.780276i) q^{70} +2.23907 q^{71} +(-3.27103 + 7.96523i) q^{72} -1.97352i q^{73} +(-6.33133 + 10.9662i) q^{74} +(-2.11906 + 8.39700i) q^{75} +(0.183422 + 0.317696i) q^{76} +(0.764219 - 0.441222i) q^{77} +(10.1919 + 2.01123i) q^{78} +(7.89895 - 13.6814i) q^{79} +(2.02177 + 8.42138i) q^{80} +(6.40245 + 6.32523i) q^{81} +7.35937i q^{82} +(-6.81352 - 3.93379i) q^{83} +(-0.0182050 + 0.0922540i) q^{84} +(3.14491 + 3.31407i) q^{85} +(1.37086 + 2.37439i) q^{86} +(7.79054 - 8.91064i) q^{87} +(2.48570 + 1.43512i) q^{88} -14.6980 q^{89} +(9.22918 + 1.43310i) q^{90} +3.80143 q^{91} +(0.127659 + 0.0737037i) q^{92} +(-2.86368 - 8.39427i) q^{93} +(-3.26962 - 5.66315i) q^{94} +(9.67154 - 9.17790i) q^{95} +(-0.570305 + 0.194557i) q^{96} +(13.6309 + 7.86980i) q^{97} +8.66186i q^{98} +(2.37451 - 1.83350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9	\( 68 q + 40 q^{4} - 2 q^{5} + 4 q^{6} - 4 q^{9} + 34 q^{11} - 10 q^{14} - 28 q^{15} - 52 q^{16} - 40 q^{19} + q^{20} - 14 q^{21} + 20 q^{24} + 2 q^{25} - 24 q^{26} - 6 q^{29} + 22 q^{30} - 36 q^{31} + 34 q^{34} - 16 q^{36} - 12 q^{39} + 15 q^{40} + 6 q^{41} + 80 q^{44} + 50 q^{45} + 84 q^{46} + 60 q^{49} - 19 q^{50} + 48 q^{51} - 50 q^{54} - 4 q^{55} + 30 q^{56} - 103 q^{60} - 62 q^{61} - 164 q^{64} - 17 q^{65} + 2 q^{66} - 20 q^{69} + 28 q^{70} - 60 q^{71} + 14 q^{74} + 11 q^{75} - 86 q^{76} + 32 q^{79} + 50 q^{80} - 112 q^{81} - 36 q^{84} + q^{85} + 14 q^{86} + 20 q^{89} + 101 q^{90} + 104 q^{91} + 38 q^{94} + 6 q^{95} + 40 q^{96} + 4 q^{99}+O(q^{100}) \) 68 * q + 40 * q^4 - 2 * q^5 + 4 * q^6 - 4 * q^9 + 34 * q^11 - 10 * q^14 - 28 * q^15 - 52 * q^16 - 40 * q^19 + q^20 - 14 * q^21 + 20 * q^24 + 2 * q^25 - 24 * q^26 - 6 * q^29 + 22 * q^30 - 36 * q^31 + 34 * q^34 - 16 * q^36 - 12 * q^39 + 15 * q^40 + 6 * q^41 + 80 * q^44 + 50 * q^45 + 84 * q^46 + 60 * q^49 - 19 * q^50 + 48 * q^51 - 50 * q^54 - 4 * q^55 + 30 * q^56 - 103 * q^60 - 62 * q^61 - 164 * q^64 - 17 * q^65 + 2 * q^66 - 20 * q^69 + 28 * q^70 - 60 * q^71 + 14 * q^74 + 11 * q^75 - 86 * q^76 + 32 * q^79 + 50 * q^80 - 112 * q^81 - 36 * q^84 + q^85 + 14 * q^86 + 20 * q^89 + 101 * q^90 + 104 * q^91 + 38 * q^94 + 6 * q^95 + 40 * q^96 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more