LMFDB - Embedded newform 360.2.bm.b.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21368 + 0.725941i) q^{2} +(-0.452164 + 1.67199i) q^{3} +(0.946019 - 1.76211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.664985 - 2.35750i) q^{6} +(-0.550736 - 0.317967i) q^{7} +(0.131031 + 2.82539i) q^{8} +(-2.59109 - 1.51203i) q^{9} +O(q^{10})$	\(q+(-1.21368 + 0.725941i) q^{2} +(-0.452164 + 1.67199i) q^{3} +(0.946019 - 1.76211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.664985 - 2.35750i) q^{6} +(-0.550736 - 0.317967i) q^{7} +(0.131031 + 2.82539i) q^{8} +(-2.59109 - 1.51203i) q^{9} +(-1.23552 - 0.688104i) q^{10} +(4.49782 + 2.59682i) q^{11} +(2.51848 + 2.37850i) q^{12} +(-5.73863 + 3.31320i) q^{13} +(0.899240 - 0.0138923i) q^{14} +(-1.67407 + 0.444409i) q^{15} +(-2.21010 - 3.33399i) q^{16} +4.95756i q^{17} +(4.24239 - 0.0458709i) q^{18} -0.264402 q^{19} +(1.99905 - 0.0617811i) q^{20} +(0.780661 - 0.777050i) q^{21} +(-7.34404 + 0.113458i) q^{22} +(-3.14782 - 5.45218i) q^{23} +(-4.78327 - 1.05846i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.55965 - 8.18706i) q^{26} +(3.69969 - 3.64860i) q^{27} +(-1.08130 + 0.669656i) q^{28} +(-1.68113 + 2.91181i) q^{29} +(1.70916 - 1.75464i) q^{30} +(-1.81704 + 1.04907i) q^{31} +(5.10262 + 2.44198i) q^{32} +(-6.37561 + 6.34612i) q^{33} +(-3.59889 - 6.01687i) q^{34} -0.635935i q^{35} +(-5.11559 + 3.13540i) q^{36} -2.07249i q^{37} +(0.320898 - 0.191940i) q^{38} +(-2.94483 - 11.0930i) q^{39} +(-2.38134 + 1.52617i) q^{40} +(-9.24285 + 5.33636i) q^{41} +(-0.383377 + 1.50980i) q^{42} +(2.19807 - 3.80716i) q^{43} +(8.83092 - 5.46904i) q^{44} +(0.0139069 - 2.99997i) q^{45} +(7.77839 + 4.33205i) q^{46} +(-3.26632 + 5.65743i) q^{47} +(6.57372 - 2.18775i) q^{48} +(-3.29779 - 5.71195i) q^{49} +(-0.0218455 - 1.41404i) q^{50} +(-8.28898 - 2.24163i) q^{51} +(0.409386 + 13.2465i) q^{52} +3.24812 q^{53} +(-1.84156 + 7.11398i) q^{54} +5.19364i q^{55} +(0.826218 - 1.59771i) q^{56} +(0.119553 - 0.442077i) q^{57} +(-0.0734505 - 4.75440i) q^{58} +(-0.776635 + 0.448390i) q^{59} +(-0.800600 + 3.37032i) q^{60} +(6.09659 + 3.51987i) q^{61} +(1.44374 - 2.59230i) q^{62} +(0.946233 + 1.65661i) q^{63} +(-7.96566 + 0.740430i) q^{64} +(-5.73863 - 3.31320i) q^{65} +(3.13101 - 12.3305i) q^{66} +(5.19945 + 9.00572i) q^{67} +(8.73578 + 4.68994i) q^{68} +(10.5393 - 2.79783i) q^{69} +(0.461651 + 0.771819i) q^{70} +16.0496 q^{71} +(3.93255 - 7.51898i) q^{72} +8.48226 q^{73} +(1.50451 + 2.51533i) q^{74} +(-1.22190 - 1.22758i) q^{75} +(-0.250129 + 0.465906i) q^{76} +(-1.65141 - 2.86032i) q^{77} +(11.6270 + 11.3256i) q^{78} +(-2.27891 - 1.31573i) q^{79} +(1.78227 - 3.58099i) q^{80} +(4.42754 + 7.83561i) q^{81} +(7.34394 - 13.1864i) q^{82} +(9.82573 + 5.67289i) q^{83} +(-0.630732 - 2.11072i) q^{84} +(-4.29337 + 2.47878i) q^{85} +(0.0960358 + 6.21633i) q^{86} +(-4.10836 - 4.12745i) q^{87} +(-6.74767 + 13.0484i) q^{88} +9.84392i q^{89} +(2.16092 + 3.65108i) q^{90} +4.21396 q^{91} +(-12.5853 + 0.388951i) q^{92} +(-0.932431 - 3.51242i) q^{93} +(-0.142709 - 9.23743i) q^{94} +(-0.132201 - 0.228979i) q^{95} +(-6.39019 + 7.42735i) q^{96} +(2.80646 - 4.86094i) q^{97} +(8.14899 + 4.53845i) q^{98} +(-7.72782 - 13.5294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.21368	+	0.725941i	−0.858199	+	0.513318i
$2$	−1.21368	+	0.725941i	−0.858199	+	0.513318i
$3$	−0.452164	+	1.67199i	−0.261057	+	0.965323i
$3$	−0.452164	+	1.67199i	−0.261057	+	0.965323i
$4$	0.946019	−	1.76211i	0.473009	−	0.881057i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.664985	−	2.35750i	−0.271479	−	0.962444i
$7$	−0.550736	−	0.317967i	−0.208159	−	0.120180i	0.392297	−	0.919839i	$-0.371681\pi$
$7$	−0.550736	−	0.317967i	−0.208159	−	0.120180i	−0.600455	+	0.799658i	$0.705014\pi$
$8$	0.131031	+	2.82539i	0.0463266	+	0.998926i
$9$	−2.59109	−	1.51203i	−0.863698	−	0.504009i
$10$	−1.23552	−	0.688104i	−0.390706	−	0.217597i
$11$	4.49782	+	2.59682i	1.35614	+	0.782971i	0.989102	−	0.147233i	$-0.0470369\pi$
$11$	4.49782	+	2.59682i	1.35614	+	0.782971i	0.367043	+	0.930204i	$0.380370\pi$
$12$	2.51848	+	2.37850i	0.727023	+	0.686613i
$13$	−5.73863	+	3.31320i	−1.59161	+	0.918916i	−0.598579	+	0.801064i	$0.704268\pi$
$13$	−5.73863	+	3.31320i	−1.59161	+	0.918916i	−0.993031	+	0.117853i	$0.962399\pi$
$14$	0.899240	−	0.0138923i	0.240332	−	0.00371288i
$15$	−1.67407	+	0.444409i	−0.432242	+	0.114746i
$16$	−2.21010	−	3.33399i	−0.552524	−	0.833497i
$17$			4.95756i			1.20238i	0.799105	+	0.601192i	$0.205307\pi$
$17$			4.95756i			1.20238i	−0.799105	+	0.601192i	$0.794693\pi$
$18$	4.24239	−	0.0458709i	0.999942	−	0.0108119i
$19$	−0.264402			−0.0606579			−0.0303290	−	0.999540i	$-0.509655\pi$
$19$	−0.264402			−0.0606579			−0.0303290	+	0.999540i	$0.509655\pi$
$20$	1.99905	−	0.0617811i	0.447000	−	0.0138147i
$21$	0.780661	−	0.777050i	0.170354	−	0.169566i
$22$	−7.34404	+	0.113458i	−1.56575	+	0.0241893i
$23$	−3.14782	−	5.45218i	−0.656365	−	1.13686i	−0.981550	−	0.191207i	$-0.938760\pi$
$23$	−3.14782	−	5.45218i	−0.656365	−	1.13686i	0.325184	−	0.945651i	$-0.394574\pi$
$24$	−4.78327	−	1.05846i	−0.976381	−	0.216057i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.55965	−	8.18706i	0.894221	−	1.60561i
$27$	3.69969	−	3.64860i	0.712006	−	0.702173i
$28$	−1.08130	+	0.669656i	−0.204347	+	0.126553i
$29$	−1.68113	+	2.91181i	−0.312179	+	0.540709i	−0.978834	−	0.204657i	$-0.934392\pi$
$29$	−1.68113	+	2.91181i	−0.312179	+	0.540709i	0.666655	+	0.745366i	$0.267725\pi$
$30$	1.70916	−	1.75464i	0.312049	−	0.320352i
$31$	−1.81704	+	1.04907i	−0.326350	+	0.188418i	−0.654220	−	0.756305i	$-0.727003\pi$
$31$	−1.81704	+	1.04907i	−0.326350	+	0.188418i	0.327869	+	0.944723i	$0.393669\pi$
$32$	5.10262	+	2.44198i	0.902024	+	0.431685i
$33$	−6.37561	+	6.34612i	−1.10985	+	1.10472i
$34$	−3.59889	−	6.01687i	−0.617205	−	1.03188i
$35$		−	0.635935i		−	0.107493i
$36$	−5.11559	+	3.13540i	−0.852598	+	0.522567i
$37$		−	2.07249i		−	0.340715i	−0.985382	−	0.170358i	$-0.945508\pi$
$37$		−	2.07249i		−	0.340715i	0.985382	−	0.170358i	$-0.0544923\pi$
$38$	0.320898	−	0.191940i	0.0520565	−	0.0311368i
$39$	−2.94483	−	11.0930i	−0.471550	−	1.77631i
$40$	−2.38134	+	1.52617i	−0.376524	+	0.241309i
$41$	−9.24285	+	5.33636i	−1.44349	+	0.833400i	−0.998081	−	0.0619273i	$-0.980275\pi$
$41$	−9.24285	+	5.33636i	−1.44349	+	0.833400i	−0.445410	+	0.895327i	$0.646942\pi$
$42$	−0.383377	+	1.50980i	−0.0591563	+	0.232967i
$43$	2.19807	−	3.80716i	0.335202	−	0.580587i	−0.648322	−	0.761366i	$-0.724529\pi$
$43$	2.19807	−	3.80716i	0.335202	−	0.580587i	0.983524	+	0.180780i	$0.0578622\pi$
$44$	8.83092	−	5.46904i	1.33131	−	0.824489i
$45$	0.0139069	−	2.99997i	0.00207312	−	0.447209i
$46$	7.77839	+	4.33205i	1.14686	+	0.638726i
$47$	−3.26632	+	5.65743i	−0.476441	+	0.825220i	−0.999636	−	0.0269930i	$-0.991407\pi$
$47$	−3.26632	+	5.65743i	−0.476441	+	0.825220i	0.523194	+	0.852213i	$0.324740\pi$
$48$	6.57372	−	2.18775i	0.948834	−	0.315774i
$49$	−3.29779	−	5.71195i	−0.471113	−	0.815992i
$50$	−0.0218455	−	1.41404i	−0.00308942	−	0.199976i
$51$	−8.28898	−	2.24163i	−1.16069	−	0.313891i
$52$	0.409386	+	13.2465i	0.0567717	+	1.83696i
$53$	3.24812			0.446163			0.223082	−	0.974800i	$-0.428388\pi$
$53$	3.24812			0.446163			0.223082	+	0.974800i	$0.428388\pi$
$54$	−1.84156	+	7.11398i	−0.250605	+	0.968089i
$55$			5.19364i			0.700310i
$56$	0.826218	−	1.59771i	0.110408	−	0.213503i
$57$	0.119553	−	0.442077i	0.0158352	−	0.0585545i
$58$	−0.0734505	−	4.75440i	−0.00964452	−	0.624283i
$59$	−0.776635	+	0.448390i	−0.101109	+	0.0583754i	−0.549702	−	0.835361i	$-0.685259\pi$
$59$	−0.776635	+	0.448390i	−0.101109	+	0.0583754i	0.448593	+	0.893736i	$0.351925\pi$
$60$	−0.800600	+	3.37032i	−0.103357	+	0.435106i
$61$	6.09659	+	3.51987i	0.780588	+	0.450673i	0.836639	−	0.547755i	$-0.184517\pi$
$61$	6.09659	+	3.51987i	0.780588	+	0.450673i	−0.0560504	+	0.998428i	$0.517851\pi$
$62$	1.44374	−	2.59230i	0.183355	−	0.329222i
$63$	0.946233	+	1.65661i	0.119214	+	0.208713i
$64$	−7.96566	+	0.740430i	−0.995708	+	0.0925538i
$65$	−5.73863	−	3.31320i	−0.711790	−	0.410952i
$66$	3.13101	−	12.3305i	0.385401	−	1.51777i
$67$	5.19945	+	9.00572i	0.635214	+	1.10022i	0.986470	+	0.163944i	$0.0524216\pi$
$67$	5.19945	+	9.00572i	0.635214	+	1.10022i	−0.351255	+	0.936280i	$0.614245\pi$
$68$	8.73578	+	4.68994i	1.05937	+	0.568739i
$69$	10.5393	−	2.79783i	1.26878	−	0.336820i
$70$	0.461651	+	0.771819i	0.0551779	+	0.0922500i
$71$	16.0496			1.90474			0.952368	−	0.304950i	$-0.0986397\pi$
$71$	16.0496			1.90474			0.952368	+	0.304950i	$0.0986397\pi$
$72$	3.93255	−	7.51898i	0.463456	−	0.886120i
$73$	8.48226			0.992774			0.496387	−	0.868101i	$-0.334660\pi$
$73$	8.48226			0.992774			0.496387	+	0.868101i	$0.334660\pi$
$74$	1.50451	+	2.51533i	0.174895	+	0.292401i
$75$	−1.22190	−	1.22758i	−0.141093	−	0.141749i
$76$	−0.250129	+	0.465906i	−0.0286918	+	0.0534431i
$77$	−1.65141	−	2.86032i	−0.188195	−	0.325964i
$78$	11.6270	+	11.3256i	1.31649	+	1.28237i
$79$	−2.27891	−	1.31573i	−0.256398	−	0.148031i	0.366292	−	0.930500i	$-0.380627\pi$
$79$	−2.27891	−	1.31573i	−0.256398	−	0.148031i	−0.622690	+	0.782468i	$0.713960\pi$
$80$	1.78227	−	3.58099i	0.199264	−	0.400367i
$81$	4.42754	+	7.83561i	0.491949	+	0.870624i
$82$	7.34394	−	13.1864i	0.811002	−	1.45619i
$83$	9.82573	+	5.67289i	1.07851	+	0.622680i	0.930495	−	0.366304i	$-0.119377\pi$
$83$	9.82573	+	5.67289i	1.07851	+	0.622680i	0.148019	+	0.988985i	$0.452710\pi$
$84$	−0.630732	−	2.11072i	−0.0688185	−	0.230298i
$85$	−4.29337	+	2.47878i	−0.465681	+	0.268861i
$86$	0.0960358	+	6.21633i	0.0103558	+	0.670324i
$87$	−4.10836	−	4.12745i	−0.440463	−	0.442509i
$88$	−6.74767	+	13.0484i	−0.719304	+	1.39096i
$89$			9.84392i			1.04345i	0.853113	+	0.521727i	$0.174712\pi$
$89$			9.84392i			1.04345i	−0.853113	+	0.521727i	$0.825288\pi$
$90$	2.16092	+	3.65108i	0.227781	+	0.384858i
$91$	4.21396			0.441743
$92$	−12.5853	+	0.388951i	−1.31210	+	0.0405510i
$93$	−0.932431	−	3.51242i	−0.0966886	−	0.364221i
$94$	−0.142709	−	9.23743i	−0.0147193	−	0.952769i
$95$	−0.132201	−	0.228979i	−0.0135635	−	0.0234927i
$96$	−6.39019	+	7.42735i	−0.652196	+	0.758051i
$97$	2.80646	−	4.86094i	0.284953	−	0.493553i	−0.687645	−	0.726047i	$-0.741355\pi$
$97$	2.80646	−	4.86094i	0.284953	−	0.493553i	0.972598	+	0.232494i	$0.0746886\pi$
$98$	8.14899	+	4.53845i	0.823172	+	0.458452i
$99$	−7.72782	−	13.5294i	−0.776676	−	1.35976i
$100$	1.05303	+	1.70033i	0.105303	+	0.170033i
$101$	−3.90875	+	6.77015i	−0.388935	+	0.673655i	−0.992307	−	0.123805i	$-0.960490\pi$
$101$	−3.90875	+	6.77015i	−0.388935	+	0.673655i	0.603372	+	0.797460i	$0.293824\pi$
$102$	11.6874	−	3.29670i	1.15723	−	0.326422i
$103$	1.88935	−	1.09082i	0.186163	−	0.107482i	−0.404022	−	0.914749i	$-0.632388\pi$
$103$	1.88935	−	1.09082i	0.186163	−	0.107482i	0.590185	+	0.807268i	$0.299055\pi$
$104$	−10.1130	−	15.7797i	−0.991664	−	1.54733i
$105$	1.06328	+	0.287547i	0.103765	+	0.0280617i
$106$	−3.94216	+	2.35794i	−0.382897	+	0.229024i
$107$		−	0.309074i		−	0.0298793i	−0.999888	−	0.0149397i	$-0.995244\pi$
$107$		−	0.309074i		−	0.0298793i	0.999888	−	0.0149397i	$-0.00475562\pi$
$108$	−2.92927	−	9.97093i	−0.281869	−	0.959453i
$109$			2.65467i			0.254272i	0.991885	+	0.127136i	$0.0405784\pi$
$109$			2.65467i			0.254272i	−0.991885	+	0.127136i	$0.959422\pi$
$110$	−3.77028	−	6.30339i	−0.359482	−	0.601005i
$111$	3.46518	+	0.937106i	0.328901	+	0.0889462i
$112$	0.157080	+	2.53888i	0.0148427	+	0.239902i
$113$	3.68245	−	2.12606i	0.346416	−	0.200003i	−0.316690	−	0.948529i	$-0.602571\pi$
$113$	3.68245	−	2.12606i	0.346416	−	0.200003i	0.663105	+	0.748526i	$0.269238\pi$
$114$	0.175823	+	0.623326i	0.0164673	+	0.0583799i
$115$	3.14782	−	5.45218i	0.293535	−	0.508418i
$116$	3.54056	+	5.71698i	0.328733	+	0.530808i
$117$	19.8790	+	0.0921527i	1.83781	+	0.00851952i
$118$	0.617078	−	1.10799i	0.0568066	−	0.101999i
$119$	1.57634	−	2.73030i	0.144503	−	0.250286i
$120$	−1.47498	−	4.67166i	−0.134647	−	0.426462i
$121$	7.98694	+	13.8338i	0.726086	+	1.25762i
$122$	−9.95450	+	0.153787i	−0.901238	+	0.0139232i
$123$	−4.74305	−	17.8669i	−0.427666	−	1.61100i
$124$	0.129625	+	4.19427i	0.0116407	+	0.376657i
$125$	−1.00000			−0.0894427
$126$	−2.35102	−	1.32368i	−0.209446	−	0.117923i
$127$			0.222417i			0.0197364i	0.999951	+	0.00986818i	$0.00314119\pi$
$127$			0.222417i			0.0197364i	−0.999951	+	0.00986818i	$0.996859\pi$
$128$	9.13022	−	6.68124i	0.807005	−	0.590544i
$129$	5.37164	+	5.39660i	0.472947	+	0.475144i
$130$	9.37003	−	0.144757i	0.821806	−	0.0126960i
$131$	7.92211	−	4.57383i	0.692158	−	0.399618i	−0.112262	−	0.993679i	$-0.535810\pi$
$131$	7.92211	−	4.57383i	0.692158	−	0.399618i	0.804420	+	0.594061i	$0.202476\pi$
$132$	5.15115	+	17.2381i	0.448350	+	1.50038i
$133$	0.145615	+	0.0840711i	0.0126265	+	0.00728989i
$134$	−12.8481	−	7.15553i	−1.10990	−	0.618143i
$135$	5.00963	+	1.37973i	0.431160	+	0.118748i
$136$	−14.0070	+	0.649596i	−1.20109	+	0.0557024i
$137$	−15.9278	−	9.19594i	−1.36081	−	0.785662i	−0.371075	−	0.928603i	$-0.621011\pi$
$137$	−15.9278	−	9.19594i	−1.36081	−	0.785662i	−0.989731	+	0.142941i	$0.954344\pi$
$138$	−10.7602	+	11.0466i	−0.915973	+	0.940348i
$139$	−5.04647	−	8.74074i	−0.428036	−	0.741380i	0.568663	−	0.822571i	$-0.307461\pi$
$139$	−5.04647	−	8.74074i	−0.428036	−	0.741380i	−0.996699	+	0.0811909i	$0.974128\pi$
$140$	−1.12059	−	0.601606i	−0.0947071	−	0.0508450i
$141$	−7.98224	−	8.01933i	−0.672226	−	0.675349i
$142$	−19.4790	+	11.6511i	−1.63464	+	0.977736i
$143$	−34.4151			−2.87794
$144$	0.685490	+	11.9804i	0.0571242	+	0.998367i
$145$	−3.36227			−0.279221
$146$	−10.2947	+	6.15762i	−0.851997	+	0.509608i
$147$	11.0415	−	2.93114i	0.910684	−	0.241756i
$148$	−3.65197	−	1.96062i	−0.300190	−	0.161162i
$149$	7.27801	+	12.6059i	0.596237	+	1.03271i	0.993371	+	0.114953i	$0.0366717\pi$
$149$	7.27801	+	12.6059i	0.596237	+	1.03271i	−0.397133	+	0.917761i	$0.629995\pi$
$150$	2.37415	+	0.602855i	0.193848	+	0.0492229i
$151$	18.8772	+	10.8988i	1.53621	+	0.886929i	0.999056	+	0.0434423i	$0.0138325\pi$
$151$	18.8772	+	10.8988i	1.53621	+	0.886929i	0.537150	+	0.843487i	$0.319501\pi$
$152$	−0.0346449	−	0.747038i	−0.00281008	−	0.0605928i
$153$	7.49596	−	12.8455i	0.606013	−	1.03850i
$154$	4.08070	+	2.27268i	0.328832	+	0.183138i
$155$	−1.81704	−	1.04907i	−0.145948	−	0.0842633i
$156$	−22.3331	−	5.30509i	−1.78808	−	0.424748i
$157$	12.8763	−	7.43414i	1.02764	−	0.593309i	0.111334	−	0.993783i	$-0.464488\pi$
$157$	12.8763	−	7.43414i	1.02764	−	0.593309i	0.916308	+	0.400474i	$0.131154\pi$
$158$	3.72100	−	0.0574857i	0.296027	−	0.00457331i
$159$	−1.46868	+	5.43082i	−0.116474	+	0.430692i
$160$	0.436494	+	5.63999i	0.0345079	+	0.445880i
$161$			4.00361i			0.315529i
$162$	−11.0618	−	6.29576i	−0.869097	−	0.494642i
$163$	−6.49946			−0.509077			−0.254538	−	0.967063i	$-0.581924\pi$
$163$	−6.49946			−0.509077			−0.254538	+	0.967063i	$0.581924\pi$
$164$	0.659373	+	21.3353i	0.0514884	+	1.66600i
$165$	−8.68371	−	2.34838i	−0.676026	−	0.182821i
$166$	−16.0434	+	0.247854i	−1.24521	+	0.0192372i
$167$	−6.96462	−	12.0631i	−0.538938	−	0.933469i	−0.998962	−	0.0455619i	$-0.985492\pi$
$167$	−6.96462	−	12.0631i	−0.538938	−	0.933469i	0.460023	−	0.887907i	$-0.347841\pi$
$168$	2.29776	+	2.10385i	0.177276	+	0.162316i
$169$	15.4546	−	26.7681i	1.18881	−	2.05909i
$170$	3.41131	−	6.12517i	0.261636	−	0.469779i
$171$	0.685090	+	0.399783i	0.0523901	+	0.0305721i
$172$	−4.62924	−	7.47489i	−0.352976	−	0.569955i
$173$	−9.36448	+	16.2198i	−0.711968	+	1.23317i	0.252149	+	0.967689i	$0.418863\pi$
$173$	−9.36448	+	16.2198i	−0.711968	+	1.23317i	−0.964117	+	0.265477i	$0.914471\pi$
$174$	7.98251	+	2.02696i	0.605153	+	0.153663i
$175$	0.550736	−	0.317967i	0.0416317	−	0.0240361i
$176$	−1.28286	−	20.7349i	−0.0966994	−	1.56295i
$177$	−0.398537	−	1.50127i	−0.0299559	−	0.112842i
$178$	−7.14610	−	11.9473i	−0.535623	−	0.895490i
$179$			10.8924i			0.814140i	0.913397	+	0.407070i	$0.133449\pi$
$179$			10.8924i			0.814140i	−0.913397	+	0.407070i	$0.866551\pi$
$180$	−5.27313	−	2.86253i	−0.393036	−	0.213360i
$181$			0.681477i			0.0506538i	0.999679	+	0.0253269i	$0.00806267\pi$
$181$			0.681477i			0.0506538i	−0.999679	+	0.0253269i	$0.991937\pi$
$182$	−5.11438	+	3.05909i	−0.379103	+	0.226755i
$183$	−8.64184	+	8.60187i	−0.638823	+	0.635869i
$184$	14.9921	−	9.60822i	1.10523	−	0.708327i
$185$	1.79483	−	1.03625i	0.131959	−	0.0761863i
$186$	3.68148	+	3.58606i	0.269939	+	0.262942i
$187$	−12.8739	+	22.2982i	−0.941431	+	1.63061i
$188$	6.87904	+	11.1077i	0.501705	+	0.810109i
$189$	−3.19769	+	0.833031i	−0.232598	+	0.0605941i
$190$	0.326674	+	0.181936i	0.0236994	+	0.0131990i
$191$	6.73163	−	11.6595i	0.487083	−	0.843653i	−0.512806	−	0.858504i	$-0.671394\pi$
$191$	6.73163	−	11.6595i	0.487083	−	0.843653i	0.999890	+	0.0148511i	$0.00472744\pi$
$192$	2.36380	−	13.6533i	0.170592	−	0.985342i
$193$	−5.74299	−	9.94714i	−0.413389	−	0.716011i	0.581869	−	0.813283i	$-0.302322\pi$
$193$	−5.74299	−	9.94714i	−0.413389	−	0.716011i	−0.995258	+	0.0972717i	$0.968988\pi$
$194$	0.122617	+	7.93693i	0.00880341	+	0.569838i
$195$	8.13444	−	8.09682i	0.582519	−	0.579825i
$196$	−13.1849	+	0.407483i	−0.941777	+	0.0291059i
$197$	8.23340			0.586606			0.293303	−	0.956020i	$-0.405246\pi$
$197$	8.23340			0.586606			0.293303	+	0.956020i	$0.405246\pi$
$198$	19.2007	+	10.8104i	1.36453	+	0.768262i
$199$		−	0.174548i		−	0.0123734i	−0.999981	−	0.00618669i	$-0.998031\pi$
$199$		−	0.174548i		−	0.0123734i	0.999981	−	0.00618669i	$-0.00196930\pi$
$200$	−2.51238	−	1.29922i	−0.177652	−	0.0918686i
$201$	−17.4085	+	4.62137i	−1.22790	+	0.325966i
$202$	−0.170777	−	11.0543i	−0.0120159	−	0.777777i
$203$	1.85172	−	1.06909i	0.129965	−	0.0750355i
$204$	−11.7915	+	12.4855i	−0.825573	+	0.874160i
$205$	−9.24285	−	5.33636i	−0.645549	−	0.372708i
$206$	−1.50119	+	2.69546i	−0.104593	+	0.187801i
$207$	−0.0875528	+	18.8867i	−0.00608534	+	1.31272i
$208$	23.7291	+	11.8100i	1.64532	+	0.818878i
$209$	−1.18923	−	0.686604i	−0.0822609	−	0.0474934i
$210$	−1.49921	+	0.422887i	−0.103456	+	0.0291820i
$211$	3.50564	+	6.07195i	0.241338	+	0.418010i	0.961096	−	0.276215i	$-0.0890803\pi$
$211$	3.50564	+	6.07195i	0.241338	+	0.418010i	−0.719757	+	0.694226i	$0.755747\pi$
$212$	3.07278	−	5.72356i	0.211040	−	0.393096i
$213$	−7.25706	+	26.8348i	−0.497245	+	1.83869i
$214$	0.224370	+	0.375116i	0.0153376	+	0.0256424i
$215$	4.39613			0.299814
$216$	10.7935	+	9.97500i	0.734404	+	0.678713i
$217$	1.33428			0.0905768
$218$	−1.92714	−	3.22191i	−0.130522	−	0.218216i
$219$	−3.83538	+	14.1822i	−0.259171	+	0.958347i
$220$	9.15179	+	4.91328i	0.617013	+	0.331253i
$221$	−16.4254	−	28.4496i	−1.10489	−	1.91373i
$222$	−4.88589	+	1.37817i	−0.327920	+	0.0924970i
$223$	18.9074	+	10.9162i	1.26613	+	0.731003i	0.974254	−	0.225452i	$-0.0723860\pi$
$223$	18.9074	+	10.9162i	1.26613	+	0.731003i	0.291880	+	0.956455i	$0.405719\pi$
$224$	−2.03373	−	2.96735i	−0.135884	−	0.198265i
$225$	2.60500	−	1.48794i	0.173667	−	0.0991960i
$226$	−2.92590	+	5.25359i	−0.194628	+	0.349464i
$227$	2.68573	+	1.55060i	0.178258	+	0.102917i	0.586474	−	0.809968i	$-0.300516\pi$
$227$	2.68573	+	1.55060i	0.178258	+	0.102917i	−0.408216	+	0.912885i	$0.633849\pi$
$228$	−0.665891	−	0.628879i	−0.0440997	−	0.0416485i
$229$	−17.4319	+	10.0643i	−1.15193	+	0.665070i	−0.949358	−	0.314197i	$-0.898265\pi$
$229$	−17.4319	+	10.0643i	−1.15193	+	0.665070i	−0.202577	+	0.979266i	$0.564931\pi$
$230$	0.137531	+	8.90231i	0.00906856	+	0.587001i
$231$	5.52913	−	1.46780i	0.363790	−	0.0965741i
$232$	−8.44728	−	4.36832i	−0.554591	−	0.286794i
$233$		−	10.2128i		−	0.669064i	−0.942384	−	0.334532i	$-0.891422\pi$
$233$		−	10.2128i		−	0.669064i	0.942384	−	0.334532i	$-0.108578\pi$
$234$	−24.1935	+	14.3191i	−1.58158	+	0.936071i
$235$	−6.53263			−0.426142
$236$	0.0554041	+	1.79270i	0.00360650	+	0.116695i
$237$	3.23033	−	3.21539i	0.209833	−	0.208862i
$238$	0.0688720	+	4.45803i	0.00446431	+	0.288971i
$239$	1.53438	+	2.65763i	0.0992511	+	0.171908i	0.911375	−	0.411577i	$-0.135022\pi$
$239$	1.53438	+	2.65763i	0.0992511	+	0.171908i	−0.812124	+	0.583485i	$0.801689\pi$
$240$	5.18150	+	4.59913i	0.334465	+	0.296873i
$241$	13.6118	−	23.5763i	0.876813	−	1.51869i	0.0219950	−	0.999758i	$-0.492998\pi$
$241$	13.6118	−	23.5763i	0.876813	−	1.51869i	0.854818	−	0.518927i	$-0.173668\pi$
$242$	−19.7361	−	10.9917i	−1.26868	−	0.706572i
$243$	−15.1030	+	3.85982i	−0.968860	+	0.247608i
$244$	11.9699	−	7.41303i	0.766294	−	0.474571i
$245$	3.29779	−	5.71195i	0.210688	−	0.364923i
$246$	18.7268	+	18.2414i	1.19398	+	1.16303i
$247$	1.51730	−	0.876016i	0.0965437	−	0.0557396i
$248$	−3.20212	−	4.99639i	−0.203335	−	0.317271i
$249$	−13.9278	+	13.8634i	−0.882641	+	0.878559i
$250$	1.21368	−	0.725941i	0.0767596	−	0.0459126i
$251$		−	17.8638i		−	1.12755i	−0.825927	−	0.563777i	$-0.809348\pi$
$251$		−	17.8638i		−	1.12755i	0.825927	−	0.563777i	$-0.190652\pi$
$252$	3.81429	−	0.100186i	0.240278	−	0.00631110i
$253$		−	32.6973i		−	2.05566i
$254$	−0.161462	−	0.269943i	−0.0101310	−	0.0169377i
$255$	−2.20318	−	8.29928i	−0.137969	−	0.519721i
$256$	−6.23094	+	14.7369i	−0.389434	+	0.921054i
$257$	−3.52545	+	2.03542i	−0.219912	+	0.126966i	−0.605909	−	0.795534i	$-0.707191\pi$
$257$	−3.52545	+	2.03542i	−0.219912	+	0.126966i	0.385998	+	0.922500i	$0.373857\pi$
$258$	−10.4371	−	2.65023i	−0.649783	−	0.164996i
$259$	−0.658984	+	1.14139i	−0.0409473	+	0.0709228i
$260$	−11.2671	+	6.97778i	−0.698755	+	0.432743i
$261$	8.75871	−	5.00285i	0.542151	−	0.309669i
$262$	−6.29454	+	11.3021i	−0.388878	+	0.698248i
$263$	8.86011	−	15.3462i	0.546338	−	0.946285i	−0.452184	−	0.891925i	$-0.649355\pi$
$263$	8.86011	−	15.3462i	0.546338	−	0.946285i	0.998521	−	0.0543598i	$-0.0173118\pi$
$264$	−18.7657	−	17.1820i	−1.15495	−	1.05748i
$265$	1.62406	+	2.81295i	0.0997652	+	0.172798i
$266$	−0.237761	+	0.00367316i	−0.0145780	+	0.000225216i
$267$	−16.4589	−	4.45107i	−1.00727	−	0.272401i
$268$	20.7879	−	0.642456i	1.26982	−	0.0392443i
$269$	8.37523			0.510647			0.255323	−	0.966856i	$-0.417818\pi$
$269$	8.37523			0.510647			0.255323	+	0.966856i	$0.417818\pi$
$270$	−7.08166	+	1.96215i	−0.430976	+	0.119412i
$271$		−	14.4241i		−	0.876200i	−0.898926	−	0.438100i	$-0.855652\pi$
$271$		−	14.4241i		−	0.876200i	0.898926	−	0.438100i	$-0.144348\pi$
$272$	16.5284	−	10.9567i	1.00218	−	0.664346i
$273$	−1.90540	+	7.04569i	−0.115320	+	0.426425i
$274$	26.0069	−	0.401780i	1.57114	−	0.0242724i
$275$	−4.49782	+	2.59682i	−0.271229	+	0.156594i
$276$	5.04028	−	21.2183i	0.303389	−	1.27719i
$277$	8.28685	+	4.78441i	0.497908	+	0.287468i	0.727849	−	0.685737i	$-0.240520\pi$
$277$	8.28685	+	4.78441i	0.497908	+	0.287468i	−0.229941	+	0.973205i	$0.573853\pi$
$278$	12.4700	+	6.94499i	0.747903	+	0.416533i
$279$	6.29435	+	0.0291786i	0.376833	+	0.00174688i
$280$	1.79676	−	0.0833275i	0.107377	−	0.00497977i
$281$	7.39997	+	4.27238i	0.441445	+	0.254869i	0.704210	−	0.709991i	$-0.251301\pi$
$281$	7.39997	+	4.27238i	0.441445	+	0.254869i	−0.262765	+	0.964860i	$0.584634\pi$
$282$	15.5094	+	3.93823i	0.923572	+	0.234518i
$283$	9.57105	+	16.5776i	0.568940	+	0.985433i	0.996671	+	0.0815271i	$0.0259797\pi$
$283$	9.57105	+	16.5776i	0.568940	+	0.985433i	−0.427731	+	0.903906i	$0.640687\pi$
$284$	15.1832	−	28.2812i	0.900958	−	1.67818i
$285$	0.442626	−	0.117502i	0.0262189	−	0.00696024i
$286$	41.7688	−	24.9834i	2.46984	−	1.47730i
$287$	6.78715			0.400633
$288$	−9.52903	−	14.0427i	−0.561504	−	0.827474i
$289$	−7.57736			−0.445727
$290$	4.08070	−	2.44081i	0.239627	−	0.143329i
$291$	6.85845	+	6.89032i	0.402049	+	0.403918i
$292$	8.02438	−	14.9467i	0.469591	−	0.874690i
$293$	−6.93773	−	12.0165i	−0.405306	−	0.702011i	0.589051	−	0.808096i	$-0.299502\pi$
$293$	−6.93773	−	12.0165i	−0.405306	−	0.702011i	−0.994357	+	0.106085i	$0.966168\pi$
$294$	−11.2729	+	11.5729i	−0.657450	+	0.674945i
$295$	−0.776635	−	0.448390i	−0.0452174	−	0.0261063i
$296$	5.85560	−	0.271562i	0.340350	−	0.0157842i
$297$	26.1153	−	6.80331i	1.51536	−	0.394768i
$298$	−17.9843	−	10.0160i	−1.04180	−	0.580214i
$299$	36.1283	+	20.8587i	2.08936	+	1.20629i
$300$	−3.31908	+	0.991819i	−0.191627	+	0.0572627i
$301$	−2.42111	+	1.39783i	−0.139550	+	0.0805694i
$302$	−30.8227	+	0.476179i	−1.77365	+	0.0274010i
$303$	−9.55222	−	9.59661i	−0.548761	−	0.551311i
$304$	0.584353	+	0.881512i	0.0335150	+	0.0505582i
$305$			7.03974i			0.403094i
$306$	0.227408	+	21.0319i	0.0130000	+	1.20231i
$307$	−12.9457			−0.738852			−0.369426	−	0.929260i	$-0.620446\pi$
$307$	−12.9457			−0.738852			−0.369426	+	0.929260i	$0.620446\pi$
$308$	−6.60248	+	0.204052i	−0.376211	+	0.0116269i
$309$	0.969538	+	3.65221i	0.0551551	+	0.207767i
$310$	2.96686	−	0.0458349i	0.168506	−	0.00260325i
$311$	4.31699	+	7.47725i	0.244794	+	0.423996i	0.962074	−	0.272790i	$-0.0879463\pi$
$311$	4.31699	+	7.47725i	0.244794	+	0.423996i	−0.717280	+	0.696785i	$0.754613\pi$
$312$	30.9563	−	9.77383i	1.75256	−	0.553334i
$313$	−1.63851	+	2.83799i	−0.0926143	+	0.160413i	−0.908610	−	0.417645i	$-0.862856\pi$
$313$	−1.63851	+	2.83799i	−0.0926143	+	0.160413i	0.815996	+	0.578057i	$0.196189\pi$
$314$	−10.2309	+	18.3701i	−0.577364	+	1.03668i
$315$	−0.961551	+	1.64777i	−0.0541773	+	0.0928412i
$316$	−4.47436	+	2.77100i	−0.251703	+	0.155881i
$317$	−10.8462	+	18.7861i	−0.609181	+	1.05513i	0.382195	+	0.924082i	$0.375168\pi$
$317$	−10.8462	+	18.7861i	−0.609181	+	1.05513i	−0.991376	+	0.131051i	$0.958165\pi$
$318$	−2.15995	−	7.65743i	−0.121124	−	0.429408i
$319$	−15.1229	+	8.73120i	−0.846719	+	0.488853i
$320$	−4.62406	−	6.52825i	−0.258493	−	0.364940i
$321$	0.516769	+	0.139752i	0.0288432	+	0.00780021i
$322$	−2.90639	−	4.85909i	−0.161967	−	0.270786i
$323$		−	1.31079i		−	0.0729341i
$324$	17.9958	−	0.389205i	0.999766	−	0.0216225i
$325$		−	6.62640i		−	0.367567i
$326$	7.88824	−	4.71822i	0.436889	−	0.261318i
$327$	−4.43859	−	1.20035i	−0.245454	−	0.0663795i
$328$	−16.2884	−	25.4154i	−0.899377	−	1.40333i
$329$	3.59775	−	2.07716i	0.198351	−	0.114518i
$330$	12.2440	−	3.45369i	0.674010	−	0.190119i
$331$	−3.95718	+	6.85404i	−0.217506	+	0.376732i	−0.954045	−	0.299663i	$-0.903126\pi$
$331$	−3.95718	+	6.85404i	−0.217506	+	0.376732i	0.736539	+	0.676396i	$0.236459\pi$
$332$	19.2916	−	11.9474i	1.05876	−	0.655699i
$333$	−3.13366	+	5.37002i	−0.171724	+	0.294275i
$334$	17.2099	+	9.58476i	0.941683	+	0.524455i
$335$	−5.19945	+	9.00572i	−0.284077	+	0.492035i
$336$	−4.31601	−	0.885357i	−0.235458	−	0.0483002i
$337$	8.26957	+	14.3233i	0.450472	+	0.780241i	0.998415	−	0.0562748i	$-0.0179223\pi$
$337$	8.26957	+	14.3233i	0.450472	+	0.780241i	−0.547943	+	0.836516i	$0.684589\pi$
$338$	0.675228	+	43.7070i	0.0367275	+	2.37735i
$339$	1.88968	+	7.11834i	0.102633	+	0.386615i
$340$	0.306283	+	9.91038i	0.0166105	+	0.537466i
$341$	−10.8970			−0.590104
$342$	−1.12170	+	0.0121283i	−0.0606544	+	0.000655826i
$343$			8.64591i			0.466835i
$344$	11.0447	+	5.71153i	0.595492	+	0.307945i
$345$	7.69265	+	7.72840i	0.414159	+	0.416083i
$346$	−0.409144	−	26.4836i	−0.0219957	−	1.42377i
$347$	−9.05298	+	5.22674i	−0.485989	+	0.280586i	−0.722909	−	0.690943i	$-0.757195\pi$
$347$	−9.05298	+	5.22674i	−0.485989	+	0.280586i	0.236920	+	0.971529i	$0.423862\pi$
$348$	−11.1596	+	3.33476i	−0.598219	+	0.178762i
$349$	4.32681	+	2.49809i	0.231609	+	0.133720i	0.611314	−	0.791388i	$-0.290641\pi$
$349$	4.32681	+	2.49809i	0.231609	+	0.133720i	−0.379705	+	0.925108i	$0.623975\pi$
$350$	−0.437589	+	0.785711i	−0.0233901	+	0.0419980i
$351$	−9.14265	+	33.1958i	−0.487998	+	1.77186i
$352$	16.6093	+	24.2342i	0.885279	+	1.29169i
$353$	−19.1212	−	11.0397i	−1.01772	−	0.587581i	−0.104278	−	0.994548i	$-0.533253\pi$
$353$	−19.1212	−	11.0397i	−1.01772	−	0.587581i	−0.913443	+	0.406967i	$0.866586\pi$
$354$	1.57353	+	1.53274i	0.0836321	+	0.0814643i
$355$	8.02480	+	13.8994i	0.425912	+	0.737701i
$356$	17.3461	+	9.31253i	0.919342	+	0.493563i
$357$	3.85227	+	3.87017i	0.203884	+	0.204831i
$358$	−7.90727	−	13.2199i	−0.417912	−	0.698693i
$359$	13.7313			0.724710			0.362355	−	0.932040i	$-0.381973\pi$
$359$	13.7313			0.724710			0.362355	+	0.932040i	$0.381973\pi$
$360$	8.47790	−	0.353798i	0.446825	−	0.0186468i
$361$	−18.9301			−0.996321
$362$	−0.494713	−	0.827093i	−0.0260015	−	0.0434710i
$363$	−26.7414	+	7.09893i	−1.40356	+	0.372597i
$364$	3.98648	−	7.42548i	0.208949	−	0.389201i
$365$	4.24113	+	7.34585i	0.221991	+	0.384500i
$366$	4.24394	−	16.7134i	0.221834	−	0.873621i
$367$	−11.6292	−	6.71410i	−0.607037	−	0.350473i	0.164768	−	0.986332i	$-0.447312\pi$
$367$	−11.6292	−	6.71410i	−0.607037	−	0.350473i	−0.771805	+	0.635859i	$0.780646\pi$
$368$	−11.2205	+	22.5446i	−0.584910	+	1.17522i
$369$	32.0178	+	0.148425i	1.66678	+	0.00772667i
$370$	−1.42609	+	2.56061i	−0.0741388	+	0.133120i
$371$	−1.78885	−	1.03280i	−0.0928727	−	0.0536201i
$372$	−7.07139	−	1.67977i	−0.366635	−	0.0870920i
$373$	22.7101	−	13.1117i	1.17589	−	0.678898i	0.220827	−	0.975313i	$-0.429124\pi$
$373$	22.7101	−	13.1117i	1.17589	−	0.678898i	0.955059	+	0.296415i	$0.0957911\pi$
$374$	−0.562473	−	36.4085i	−0.0290848	−	1.88264i
$375$	0.452164	−	1.67199i	0.0233497	−	0.0863411i
$376$	−16.4124	−	8.48732i	−0.846406	−	0.437700i
$377$		−	22.2797i		−	1.14746i
$378$	3.27623	−	3.33236i	0.168511	−	0.171398i
$379$	−16.1844			−0.831335			−0.415667	−	0.909517i	$-0.636452\pi$
$379$	−16.1844			−0.831335			−0.415667	+	0.909517i	$0.636452\pi$
$380$	−0.528551	+	0.0163350i	−0.0271141	+	0.000837970i
$381$	−0.371880	−	0.100569i	−0.0190520	−	0.00515232i
$382$	0.294112	+	19.0376i	0.0150481	+	0.974051i
$383$	9.27409	+	16.0632i	0.473884	+	0.820791i	0.999553	−	0.0298979i	$-0.00951823\pi$
$383$	9.27409	+	16.0632i	0.473884	+	0.820791i	−0.525669	+	0.850689i	$0.676185\pi$
$384$	7.04261	+	18.2867i	0.359391	+	0.933187i
$385$	1.65141	−	2.86032i	0.0841635	−	0.145776i
$386$	14.1912	+	7.90354i	0.722311	+	0.402280i
$387$	−11.4519	+	6.54118i	−0.582134	+	0.332507i
$388$	−5.91056	−	9.54385i	−0.300063	−	0.484515i
$389$	7.85367	−	13.6030i	0.398197	−	0.689697i	−0.595307	−	0.803499i	$-0.702969\pi$
$389$	7.85367	−	13.6030i	0.398197	−	0.689697i	0.993504	+	0.113801i	$0.0363027\pi$
$390$	−3.99476	+	15.7320i	−0.202283	+	0.796623i
$391$	27.0295	−	15.6055i	1.36694	−	0.789203i
$392$	15.7064	−	10.0660i	0.793291	−	0.508410i
$393$	4.06530	+	15.3138i	0.205067	+	0.772479i
$394$	−9.99268	+	5.97697i	−0.503424	+	0.301115i
$395$		−	2.63146i		−	0.132403i
$396$	−31.1511	+	0.818210i	−1.56540	+	0.0411166i
$397$			17.5080i			0.878701i	0.898316	+	0.439350i	$0.144791\pi$
$397$			17.5080i			0.878701i	−0.898316	+	0.439350i	$0.855209\pi$
$398$	0.126712	+	0.211845i	0.00635148	+	0.0106188i
$399$	−0.206408	+	0.205453i	−0.0103333	+	0.0102855i
$400$	3.99237	−	0.247007i	0.199618	−	0.0123503i
$401$	12.7667	−	7.37088i	0.637540	−	0.368084i	−0.146126	−	0.989266i	$-0.546681\pi$
$401$	12.7667	−	7.37088i	0.637540	−	0.368084i	0.783666	+	0.621182i	$0.213347\pi$
$402$	17.7734	−	18.2464i	0.886457	−	0.910046i
$403$	6.95155	−	12.0404i	0.346282	−	0.599777i
$404$	8.23203	+	13.2924i	0.409559	+	0.661319i
$405$	−4.57207	+	7.75217i	−0.227188	+	0.385209i
$406$	−1.47129	+	2.64177i	−0.0730190	+	0.131109i
$407$	5.38188	−	9.32170i	0.266770	−	0.462059i
$408$	5.24736	−	23.7133i	0.259783	−	1.17398i
$409$	0.548950	+	0.950809i	0.0271438	+	0.0470145i	0.879278	−	0.476309i	$-0.158025\pi$
$409$	0.548950	+	0.950809i	0.0271438	+	0.0470145i	−0.852134	+	0.523323i	$0.824692\pi$
$410$	15.0917	−	0.233151i	0.745326	−	0.0115145i
$411$	22.5775	−	22.4731i	1.11367	−	1.10852i
$412$	−0.134784	−	4.36119i	−0.00664033	−	0.214860i
$413$	0.570294			0.0280623
$414$	−13.6044	−	22.9859i	−0.668618	−	1.12970i
$415$			11.3458i			0.556942i
$416$	−37.3728	+	2.89238i	−1.83235	+	0.141811i
$417$	16.8963	−	4.48539i	0.827413	−	0.219650i
$418$	1.94178	−	0.0299984i	0.0949754	−	0.00146727i
$419$	−29.5085	+	17.0367i	−1.44158	+	0.832298i	−0.997955	−	0.0639134i	$-0.979642\pi$
$419$	−29.5085	+	17.0367i	−1.44158	+	0.832298i	−0.443627	+	0.896211i	$0.646309\pi$
$420$	1.51257	−	1.60159i	0.0738058	−	0.0781496i
$421$	−34.1945	−	19.7422i	−1.66654	−	0.962177i	−0.969483	−	0.245160i	$-0.921159\pi$
$421$	−34.1945	−	19.7422i	−1.66654	−	0.962177i	−0.697056	−	0.717016i	$-0.745507\pi$
$422$	−8.66260	−	4.82449i	−0.421689	−	0.234853i
$423$	17.0175	−	9.72017i	0.827420	−	0.472611i
$424$	0.425606	+	9.17720i	0.0206692	+	0.445684i
$425$	−4.29337	−	2.47878i	−0.208259	−	0.120238i
$426$	−10.6727	−	37.8369i	−0.517096	−	1.83320i
$427$	−2.23841	−	3.87703i	−0.108324	−	0.187623i
$428$	−0.544624	−	0.292390i	−0.0263254	−	0.0141332i
$429$	15.5613	−	57.5417i	0.751306	−	2.77814i
$430$	−5.33548	+	3.19133i	−0.257300	+	0.153900i
$431$	0.916514			0.0441469			0.0220735	−	0.999756i	$-0.492973\pi$
$431$	0.916514			0.0441469			0.0220735	+	0.999756i	$0.492973\pi$
$432$	−20.3411	−	4.27098i	−0.978660	−	0.205488i
$433$	−8.33823			−0.400710			−0.200355	−	0.979723i	$-0.564209\pi$
$433$	−8.33823			−0.400710			−0.200355	+	0.979723i	$0.564209\pi$
$434$	−1.61938	+	0.968608i	−0.0777328	+	0.0464947i
$435$	1.52030	−	5.62167i	0.0728927	−	0.269539i
$436$	4.67784	+	2.51137i	0.224028	+	0.120273i
$437$	0.832288	+	1.44157i	0.0398138	+	0.0689594i
$438$	−5.64057	−	19.9969i	−0.269517	−	0.955489i
$439$	−19.9492	−	11.5177i	−0.952125	−	0.549710i	−0.0583848	−	0.998294i	$-0.518595\pi$
$439$	−19.9492	−	11.5177i	−0.952125	−	0.549710i	−0.893740	+	0.448584i	$0.851928\pi$
$440$	−14.6741	+	0.680530i	−0.699558	+	0.0324430i
$441$	−0.0917242	+	19.7865i	−0.00436782	+	0.942217i
$442$	40.5878	+	22.6047i	1.93057	+	1.07520i
$443$	−11.9699	−	6.91085i	−0.568709	−	0.328344i	0.187925	−	0.982183i	$-0.439824\pi$
$443$	−11.9699	−	6.91085i	−0.568709	−	0.328344i	−0.756633	+	0.653839i	$0.773157\pi$
$444$	4.92942	−	5.21953i	0.233940	−	0.247708i
$445$	−8.52508	+	4.92196i	−0.404128	+	0.233323i
$446$	−30.8720	+	0.476940i	−1.46183	+	0.0225838i
$447$	−24.3677	+	6.46882i	−1.15255	+	0.305965i
$448$	4.62241	+	2.12504i	0.218388	+	0.100399i
$449$			11.8035i			0.557040i	0.960430	+	0.278520i	$0.0898439\pi$
$449$			11.8035i			0.557040i	−0.960430	+	0.278520i	$0.910156\pi$
$450$	−2.08147	+	3.69696i	−0.0981215	+	0.174276i
$451$	−55.4303			−2.61011
$452$	−0.262701	−	8.50019i	−0.0123564	−	0.399815i
$453$	−26.7582	+	26.6345i	−1.25721	+	1.25140i
$454$	−4.38525	+	0.0677476i	−0.205810	+	0.00317955i
$455$	2.10698	+	3.64940i	0.0987767	+	0.171086i
$456$	1.26470	+	0.279858i	0.0592252	+	0.0131056i
$457$	−9.61902	+	16.6606i	−0.449959	+	0.779352i	−0.998383	−	0.0568489i	$-0.981895\pi$
$457$	−9.61902	+	16.6606i	−0.449959	+	0.779352i	0.548424	+	0.836200i	$0.315228\pi$
$458$	13.8506	−	24.8694i	0.647196	−	1.16207i
$459$	18.0881	+	18.3414i	0.844281	+	0.856105i
$460$	−6.62947	−	10.7047i	−0.309101	−	0.499108i
$461$	−12.7289	+	22.0471i	−0.592843	+	1.02683i	0.401004	+	0.916076i	$0.368661\pi$
$461$	−12.7289	+	22.0471i	−0.592843	+	1.02683i	−0.993847	+	0.110758i	$0.964672\pi$
$462$	−5.64504	+	5.79526i	−0.262631	+	0.269620i
$463$	−9.81774	+	5.66827i	−0.456269	+	0.263427i	−0.710474	−	0.703723i	$-0.751519\pi$
$463$	−9.81774	+	5.66827i	−0.456269	+	0.263427i	0.254205	+	0.967150i	$0.418186\pi$
$464$	13.4234	−	0.830502i	0.623166	−	0.0385551i
$465$	2.57563	−	2.56372i	0.119442	−	0.118890i
$466$	7.41391	+	12.3951i	0.343443	+	0.574190i
$467$		−	16.8107i		−	0.777906i	−0.921258	−	0.388953i	$-0.872837\pi$
$467$		−	16.8107i		−	0.777906i	0.921258	−	0.388953i	$-0.127163\pi$
$468$	18.9683	−	34.9419i	0.876809	−	1.61519i
$469$		−	6.61303i		−	0.305361i
$470$	7.92850	−	4.74231i	0.365714	−	0.218746i
$471$	6.60760	+	24.8905i	0.304462	+	1.14689i
$472$	−1.36864	−	2.13554i	−0.0629968	−	0.0982963i
$473$	19.7730	−	11.4160i	0.909164	−	0.524906i
$474$	−1.58639	+	6.24747i	−0.0728653	+	0.286956i
$475$	0.132201	−	0.228979i	0.00606579	−	0.0105063i
$476$	−3.31986	−	5.36061i	−0.152165	−	0.245703i
$477$	−8.41618	−	4.91125i	−0.385351	−	0.224870i
$478$	−3.79153	−	2.11163i	−0.173421	−	0.0965838i
$479$	−5.25587	+	9.10343i	−0.240147	+	0.415947i	−0.960756	−	0.277395i	$-0.910529\pi$
$479$	−5.25587	+	9.10343i	−0.240147	+	0.415947i	0.720609	+	0.693342i	$0.243862\pi$
$480$	−9.62737	−	1.82039i	−0.439427	−	0.0830890i
$481$	6.86658	+	11.8933i	0.313089	+	0.542286i
$482$	0.594714	+	38.4954i	0.0270885	+	1.75342i
$483$	−6.69400	−	1.81029i	−0.304587	−	0.0823711i
$484$	31.9325	−	0.986884i	1.45148	−	0.0448584i
$485$	5.61293			0.254870
$486$	15.5282	−	15.6485i	0.704373	−	0.709830i
$487$		−	34.8994i		−	1.58144i	−0.612177	−	0.790721i	$-0.709706\pi$
$487$		−	34.8994i		−	1.58144i	0.612177	−	0.790721i	$-0.290294\pi$
$488$	−9.14616	+	17.6865i	−0.414027	+	0.800628i
$489$	2.93882	−	10.8670i	0.132898	−	0.491424i
$490$	0.144084	+	9.32646i	0.00650906	+	0.421326i
$491$	−5.76638	+	3.32922i	−0.260233	+	0.150246i	−0.624441	−	0.781072i	$-0.714673\pi$
$491$	−5.76638	+	3.32922i	−0.260233	+	0.150246i	0.364208	+	0.931318i	$0.381340\pi$
$492$	−35.9705	−	8.54458i	−1.62167	−	0.385219i
$493$	−14.4355	−	8.33431i	−0.650140	−	0.375359i
$494$	−1.20558	+	2.16467i	−0.0542416	+	0.0973932i
$495$	7.85293	−	13.4572i	0.352963	−	0.604857i
$496$	7.51342	+	3.73945i	0.337363	+	0.167906i
$497$	−8.83909	−	5.10325i	−0.396487	−	0.228912i
$498$	6.83986	−	26.9365i	0.306501	−	1.20705i
$499$	−1.72229	−	2.98309i	−0.0771003	−	0.133542i	0.824897	−	0.565282i	$-0.191233\pi$
$499$	−1.72229	−	2.98309i	−0.0771003	−	0.133542i	−0.901998	+	0.431741i	$0.857899\pi$
$500$	−0.946019	+	1.76211i	−0.0423072	+	0.0788042i
$501$	23.3185	−	6.19028i	1.04179	−	0.276561i
$502$	12.9681	+	21.6809i	0.578794	+	0.967665i
$503$	−26.1689			−1.16681			−0.583407	−	0.812180i	$-0.698281\pi$
$503$	−26.1689			−1.16681			−0.583407	+	0.812180i	$0.698281\pi$
$504$	−4.55659	+	2.89055i	−0.202967	+	0.128755i
$505$	−7.81750			−0.347874
$506$	23.7363	+	39.6839i	1.05521	+	1.76416i
$507$	37.7680	+	37.9435i	1.67734	+	1.68513i
$508$	0.391925	+	0.210411i	0.0173889	+	0.00933548i
$509$	15.3256	+	26.5448i	0.679297	+	1.17658i	0.975193	+	0.221357i	$0.0710485\pi$
$509$	15.3256	+	26.5448i	0.679297	+	1.17658i	−0.295896	+	0.955220i	$0.595618\pi$
$510$	8.69874	+	8.47326i	0.385187	+	0.375202i
$511$	−4.67148	−	2.69708i	−0.206654	−	0.119312i
$512$	−3.13576	−	22.4091i	−0.138582	−	0.990351i
$513$	−0.978206	+	0.964695i	−0.0431888	+	0.0425923i
$514$	2.80116	−	5.02961i	0.123554	−	0.221847i
$515$	1.88935	+	1.09082i	0.0832548	+	0.0480672i
$516$	14.5911	−	4.36017i	0.642338	−	0.191946i
$517$	−29.3826	+	16.9641i	−1.29225	+	0.746079i
$518$	−0.0287917	−	1.86367i	−0.00126504	−	0.0818848i
$519$	−22.8850	−	22.9913i	−1.00454	−	1.00921i
$520$	8.60914	−	16.6480i	0.377536	−	0.730063i
$521$			30.1254i			1.31982i	0.751346	+	0.659909i	$0.229405\pi$
$521$			30.1254i			1.31982i	−0.751346	+	0.659909i	$0.770595\pi$
$522$	−6.99846	+	12.4302i	−0.306314	+	0.544053i
$523$	6.25220			0.273389			0.136695	−	0.990613i	$-0.456352\pi$
$523$	6.25220			0.273389			0.136695	+	0.990613i	$0.456352\pi$
$524$	−0.565153	−	18.2866i	−0.0246888	−	0.798854i
$525$	0.282615	+	1.06460i	0.0123343	+	0.0464628i
$526$	0.387107	+	25.0572i	0.0168787	+	1.09254i
$527$	−5.20082	−	9.00808i	−0.226551	−	0.392398i
$528$	35.2486	+	7.23065i	1.53400	+	0.314674i
$529$	−8.31751	+	14.4063i	−0.361631	+	0.626363i
$530$	−4.01312	−	2.23504i	−0.174319	−	0.0970840i
$531$	2.69031	+	0.0124714i	0.116750	+	0.000541214i
$532$	0.285898	−	0.177058i	0.0123952	−	0.00767645i
$533$	35.3609	−	61.2468i	1.53165	−	2.65289i
$534$	23.2070	−	6.54605i	1.00427	−	0.283275i
$535$	0.267666	−	0.154537i	0.0115722	−	0.00668122i
$536$	−24.7634	+	15.8705i	−1.06962	+	0.685502i
$537$	−18.2120	−	4.92518i	−0.785908	−	0.212537i
$538$	−10.1648	+	6.07992i	−0.438236	+	0.262124i
$539$		−	34.2551i		−	1.47547i
$540$	7.17044	−	7.52228i	0.308567	−	0.323708i
$541$			17.1597i			0.737754i	0.929478	+	0.368877i	$0.120258\pi$
$541$			17.1597i			0.737754i	−0.929478	+	0.368877i	$0.879742\pi$
$542$	10.4710	+	17.5061i	0.449769	+	0.751953i
$543$	−1.13942	−	0.308140i	−0.0488973	−	0.0132235i
$544$	−12.1063	+	25.2965i	−0.519051	+	1.08458i
$545$	−2.29902	+	1.32734i	−0.0984790	+	0.0568569i
$546$	−2.80222	−	9.93440i	−0.119924	−	0.425153i
$547$	−3.70465	+	6.41665i	−0.158400	+	0.274356i	−0.934292	−	0.356509i	$-0.883967\pi$
$547$	−3.70465	+	6.41665i	−0.158400	+	0.274356i	0.775892	+	0.630866i	$0.217300\pi$
$548$	−31.2723	+	19.3671i	−1.33589	+	0.827323i
$549$	−10.4747	−	18.3385i	−0.447050	−	0.782669i
$550$	3.57376	−	6.41685i	0.152386	−	0.273616i
$551$	0.444495	−	0.769887i	0.0189361	−	0.0327983i
$552$	9.28596	+	29.4111i	0.395237	+	1.25182i
$553$	0.836719	+	1.44924i	0.0355809	+	0.0616279i
$554$	−13.5307	+	0.209036i	−0.574866	+	0.00888109i
$555$	0.921033	+	3.46949i	0.0390957	+	0.147272i
$556$	−20.1762	+	0.623553i	−0.855663	+	0.0264445i
$557$	29.5488			1.25202			0.626011	−	0.779814i	$-0.284687\pi$
$557$	29.5488			1.25202			0.626011	+	0.779814i	$0.284687\pi$
$558$	−7.66048	+	4.53391i	−0.324294	+	0.191936i
$559$			29.1305i			1.23209i
$560$	−2.12020	+	1.40548i	−0.0895947	+	0.0593923i
$561$	−31.4613	−	31.6074i	−1.32830	−	1.33447i
$562$	−12.0827	+	0.186665i	−0.509676	+	0.00787397i
$563$	26.7132	−	15.4229i	1.12583	−	0.649997i	0.182945	−	0.983123i	$-0.441437\pi$
$563$	26.7132	−	15.4229i	1.12583	−	0.649997i	0.942882	+	0.333126i	$0.108104\pi$
$564$	−21.6823	+	6.47919i	−0.912991	+	0.272823i
$565$	3.68245	+	2.12606i	0.154922	+	0.0894441i
$566$	−23.6505	−	13.1718i	−0.994104	−	0.553650i
$567$	0.0530627	−	5.72317i	0.00222843	−	0.240350i
$568$	2.10300	+	45.3464i	0.0882400	+	1.90269i
$569$	−10.9256	−	6.30788i	−0.458024	−	0.264440i	0.253189	−	0.967417i	$-0.418520\pi$
$569$	−10.9256	−	6.30788i	−0.458024	−	0.264440i	−0.711213	+	0.702977i	$0.751854\pi$
$570$	−0.451905	+	0.463931i	−0.0189282	+	0.0194319i
$571$	7.60971	+	13.1804i	0.318456	+	0.551583i	0.980166	−	0.198177i	$-0.0635022\pi$
$571$	7.60971	+	13.1804i	0.318456	+	0.551583i	−0.661710	+	0.749760i	$0.730169\pi$
$572$	−32.5574	+	60.6434i	−1.36129	+	2.53563i
$573$	16.4508	+	16.5272i	0.687241	+	0.690435i
$574$	−8.23741	+	4.92708i	−0.343823	+	0.205652i
$575$	6.29563			0.262546
$576$	21.7593	+	10.1258i	0.906639	+	0.421907i
$577$	29.9725			1.24777			0.623887	−	0.781515i	$-0.285553\pi$
$577$	29.9725			1.24777			0.623887	+	0.781515i	$0.285553\pi$
$578$	9.19646	−	5.50072i	0.382522	−	0.228800i
$579$	19.2283	−	5.10447i	0.799100	−	0.212134i
$580$	−3.18077	+	5.92470i	−0.132074	+	0.246010i
$581$	−3.60759	−	6.24852i	−0.149668	−	0.259232i
$582$	−13.3259	−	3.38378i	−0.552376	−	0.140262i
$583$	14.6095	+	8.43478i	0.605062	+	0.349333i
$584$	1.11144	+	23.9657i	0.0459918	+	0.991708i
$585$	9.85969	+	17.2618i	0.407648	+	0.713687i
$586$	17.1434	+	9.54775i	0.708188	+	0.394414i
$587$	−11.6112	−	6.70371i	−0.479244	−	0.276692i	0.240857	−	0.970561i	$-0.422571\pi$
$587$	−11.6112	−	6.70371i	−0.479244	−	0.276692i	−0.720102	+	0.693869i	$0.755905\pi$
$588$	5.28043	−	22.2292i	0.217761	−	0.916718i
$589$	0.480429	−	0.277376i	0.0197957	−	0.0114291i
$590$	1.26809	−	0.0195906i	0.0522063	−	0.000806534i
$591$	−3.72285	+	13.7662i	−0.153138	+	0.566264i
$592$	−6.90966	+	4.58041i	−0.283985	+	0.188254i
$593$		−	15.9732i		−	0.655941i	−0.944688	−	0.327970i	$-0.893635\pi$
$593$		−	15.9732i		−	0.655941i	0.944688	−	0.327970i	$-0.106365\pi$
$594$	−26.7567	+	27.2152i	−1.09784	+	1.11665i
$595$	3.15268			0.129247
$596$	29.0981	−	0.899287i	1.19191	−	0.0368362i
$597$	0.291842	+	0.0789244i	0.0119443	+	0.00323016i
$598$	−58.9903	+	0.911339i	−2.41229	+	0.0372674i
$599$	21.4901	+	37.2220i	0.878062	+	1.52085i	0.853465	+	0.521150i	$0.174497\pi$
$599$	21.4901	+	37.2220i	0.878062	+	1.52085i	0.0245970	+	0.999697i	$0.492170\pi$
$600$	3.30829	−	3.61320i	0.135060	−	0.147508i
$601$	−2.92749	+	5.07055i	−0.119415	+	0.206832i	−0.919536	−	0.393006i	$-0.871435\pi$
$601$	−2.92749	+	5.07055i	−0.119415	+	0.206832i	0.800121	+	0.599838i	$0.204768\pi$
$602$	1.92370	−	3.45409i	0.0784041	−	0.140778i
$603$	0.144617	−	31.1964i	0.00588925	−	1.27042i
$604$	37.0631	−	22.9534i	1.50808	−	0.933960i
$605$	−7.98694	+	13.8338i	−0.324715	+	0.562424i
$606$	18.5599	+	4.71282i	0.753943	+	0.191445i
$607$	−32.0275	+	18.4911i	−1.29996	+	0.750531i	−0.980396	−	0.197035i	$-0.936869\pi$
$607$	−32.0275	+	18.4911i	−1.29996	+	0.750531i	−0.319561	+	0.947566i	$0.603535\pi$
$608$	−1.34914	−	0.645664i	−0.0547149	−	0.0261851i
$609$	0.950227	+	3.57946i	0.0385051	+	0.145047i
$610$	−5.11043	−	8.54396i	−0.206915	−	0.345935i
$611$		−	43.2878i		−	1.75124i
$612$	−15.5439	−	25.3608i	−0.628326	−	1.02515i
$613$			7.76568i			0.313653i	0.987626	+	0.156826i	$0.0501263\pi$
$613$			7.76568i			0.313653i	−0.987626	+	0.156826i	$0.949874\pi$
$614$	15.7119	−	9.39784i	0.634082	−	0.379266i
$615$	13.1016	−	13.0410i	0.528308	−	0.525865i
$616$	7.86514	−	5.04066i	0.316896	−	0.203094i
$617$	41.1771	−	23.7736i	1.65773	−	0.957090i	0.683970	−	0.729510i	$-0.260252\pi$
$617$	41.1771	−	23.7736i	1.65773	−	0.957090i	0.973759	−	0.227580i	$-0.0730813\pi$
$618$	−3.82799	−	3.72877i	−0.153984	−	0.149993i
$619$	6.69864	−	11.6024i	0.269241	−	0.466339i	−0.699425	−	0.714706i	$-0.746561\pi$
$619$	6.69864	−	11.6024i	0.269241	−	0.466339i	0.968666	+	0.248367i	$0.0798939\pi$
$620$	−3.56754	+	2.20940i	−0.143276	+	0.0887315i
$621$	−31.5388	−	8.68628i	−1.26561	−	0.348568i
$622$	−10.6675	−	5.94107i	−0.427727	−	0.238215i
$623$	3.13004	−	5.42140i	0.125403	−	0.217204i
$624$	−30.4757	+	34.3347i	−1.22000	+	1.37449i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.0715885	−	4.63387i	−0.00286125	−	0.185207i
$627$	1.68572	−	1.67793i	0.0673213	−	0.0670099i
$628$	−0.918579	−	29.7224i	−0.0366553	−	1.18605i
$629$	10.2745			0.409671
$630$	−0.0291709	−	2.69788i	−0.00116220	−	0.107486i
$631$		−	38.0305i		−	1.51397i	−0.653433	−	0.756985i	$-0.726672\pi$
$631$		−	38.0305i		−	1.51397i	0.653433	−	0.756985i	$-0.273328\pi$
$632$	3.41884	−	6.61122i	0.135994	−	0.262980i
$633$	−11.7374	+	3.11588i	−0.466518	+	0.123845i
$634$	−0.473880	−	30.6739i	−0.0188202	−	1.21822i
$635$	−0.192619	+	0.111209i	−0.00764386	+	0.00441318i
$636$	8.18033	+	7.72565i	0.324371	+	0.306342i
$637$	37.8496	+	21.8525i	1.49966	+	0.865828i
$638$	12.0159	−	21.5752i	0.475716	−	0.854169i
$639$	−41.5860	−	24.2674i	−1.64512	−	0.960005i
$640$	10.3512	+	4.56638i	0.409169	+	0.180502i
$641$	−21.9853	−	12.6932i	−0.868367	−	0.501352i	−0.00156193	−	0.999999i	$-0.500497\pi$
$641$	−21.9853	−	12.6932i	−0.868367	−	0.501352i	−0.866805	+	0.498647i	$0.833831\pi$
$642$	−0.728641	+	0.205530i	−0.0287572	+	0.00811161i
$643$	6.81817	+	11.8094i	0.268882	+	0.465718i	0.968573	−	0.248728i	$-0.0800124\pi$
$643$	6.81817	+	11.8094i	0.268882	+	0.465718i	−0.699691	+	0.714445i	$0.746679\pi$
$644$	7.05483	+	3.78749i	0.277999	+	0.149248i
$645$	−1.98777	+	7.35028i	−0.0782685	+	0.289417i
$646$	0.951554	+	1.59087i	0.0374384	+	0.0625919i
$647$	5.92873			0.233082			0.116541	−	0.993186i	$-0.462819\pi$
$647$	5.92873			0.233082			0.116541	+	0.993186i	$0.462819\pi$
$648$	−21.5585	+	13.5363i	−0.846899	+	0.531754i
$649$	−4.65755			−0.182825
$650$	4.81038	+	8.04230i	0.188679	+	0.315445i
$651$	−0.603313	+	2.23090i	−0.0236457	+	0.0874359i
$652$	−6.14861	+	11.4528i	−0.240798	+	0.448526i
$653$	22.0758	+	38.2364i	0.863892	+	1.49630i	0.868144	+	0.496313i	$0.165313\pi$
$653$	22.0758	+	38.2364i	0.863892	+	1.49630i	−0.00425191	+	0.999991i	$0.501353\pi$
$654$	6.25839	−	1.76532i	0.244722	−	0.0690294i
$655$	7.92211	+	4.57383i	0.309542	+	0.178714i
$656$	38.2190	+	19.0217i	1.49220	+	0.742671i
$657$	−21.9783	−	12.8254i	−0.857457	−	0.500367i
$658$	−2.85861	+	5.13276i	−0.111440	+	0.200096i
$659$	−15.7714	−	9.10561i	−0.614366	−	0.354704i	0.160306	−	0.987067i	$-0.448752\pi$
$659$	−15.7714	−	9.10561i	−0.614366	−	0.354704i	−0.774672	+	0.632363i	$0.782085\pi$
$660$	−12.3531	+	13.0801i	−0.480842	+	0.509141i
$661$	−2.33282	+	1.34685i	−0.0907361	+	0.0523865i	−0.544681	−	0.838643i	$-0.683349\pi$
$661$	−2.33282	+	1.34685i	−0.0907361	+	0.0523865i	0.453945	+	0.891030i	$0.350016\pi$
$662$	−0.172894	−	11.1913i	−0.00671970	−	0.434961i
$663$	54.9944	−	14.5992i	2.13580	−	0.566984i
$664$	−14.7406	+	28.5048i	−0.572048	+	1.10620i
$665$			0.168142i			0.00652028i
$666$	−0.0950670	−	8.79232i	−0.00368377	−	0.340695i
$667$	21.1676			0.819613
$668$	−27.8452	+	0.860564i	−1.07736	+	0.0332962i
$669$	−26.8010	+	26.6771i	−1.03619	+	1.03140i
$670$	−0.227170	−	14.7045i	−0.00877633	−	0.568085i
$671$	18.2809	+	31.6635i	0.705727	+	1.22236i
$672$	5.88096	−	2.05864i	0.226863	−	0.0794136i
$673$	−20.0619	+	34.7483i	−0.773330	+	1.33945i	0.162398	+	0.986725i	$0.448077\pi$
$673$	−20.0619	+	34.7483i	−0.773330	+	1.33945i	−0.935728	+	0.352722i	$0.885256\pi$
$674$	−20.4345	−	11.3806i	−0.787106	−	0.438366i
$675$	1.30993	+	5.02833i	0.0504193	+	0.193540i
$676$	−32.5482	−	52.5559i	−1.25185	−	2.02138i
$677$	−2.92803	+	5.07150i	−0.112533	+	0.194914i	−0.916791	−	0.399367i	$-0.869230\pi$
$677$	−2.92803	+	5.07150i	−0.112533	+	0.194914i	0.804258	+	0.594281i	$0.202563\pi$
$678$	−7.46096	−	7.26756i	−0.286536	−	0.279109i
$679$	−3.09124	+	1.78473i	−0.118631	+	0.0684916i
$680$	−7.56608	−	11.8056i	−0.290146	−	0.452726i
$681$	−3.80698	+	3.78938i	−0.145884	+	0.145209i
$682$	13.2254	−	7.91056i	0.506427	−	0.302911i
$683$			19.7354i			0.755156i	0.925978	+	0.377578i	$0.123243\pi$
$683$			19.7354i			0.755156i	−0.925978	+	0.377578i	$0.876757\pi$
$684$	1.35257	−	0.829005i	0.0517168	−	0.0316978i
$685$		−	18.3919i		−	0.702717i
$686$	−6.27642	−	10.4933i	−0.239635	−	0.400637i
$687$	−8.94535	−	33.6967i	−0.341286	−	1.28561i
$688$	−17.5510	+	1.08587i	−0.669124	+	0.0413985i
$689$	−18.6398	+	10.7617i	−0.710118	+	0.409987i
$690$	−14.9468	−	3.79536i	−0.569013	−	0.144487i
$691$	24.2787	−	42.0520i	0.923606	−	1.59973i	0.129817	−	0.991538i	$-0.458561\pi$
$691$	24.2787	−	42.0520i	0.923606	−	1.59973i	0.793788	−	0.608194i	$-0.208106\pi$
$692$	19.7221	+	31.8455i	0.749722	+	1.21058i
$693$	−0.0459319	+	9.90834i	−0.00174481	+	0.376387i
$694$	7.19308	−	12.9155i	0.273045	−	0.490266i
$695$	5.04647	−	8.74074i	0.191423	−	0.331555i
$696$	11.1233	−	12.1486i	0.421629	−	0.460490i
$697$	−26.4553	−	45.8219i	−1.00207	−	1.73563i
$698$	−7.06481	+	0.109144i	−0.267407	+	0.00413116i
$699$	17.0757	+	4.61787i	0.645863	+	0.174664i
$700$	−0.0392888	−	1.27126i	−0.00148498	−	0.0480492i
$701$	−43.2675			−1.63419			−0.817096	−	0.576502i	$-0.804417\pi$
$701$	−43.2675			−1.63419			−0.817096	+	0.576502i	$0.804417\pi$
$702$	−13.0020	−	46.9259i	−0.490728	−	1.77111i
$703$			0.547970i			0.0206671i
$704$	−37.7509	−	17.3551i	−1.42279	−	0.654093i
$705$	2.95382	−	10.9225i	0.111247	−	0.411365i
$706$	31.2211	−	0.482334i	1.17502	−	0.0181529i
$707$	4.30537	−	2.48571i	0.161920	−	0.0934847i
$708$	−3.02243	−	0.717962i	−0.113590	−	0.0269827i
$709$	−10.9589	−	6.32714i	−0.411571	−	0.237621i	0.279894	−	0.960031i	$-0.409701\pi$
$709$	−10.9589	−	6.32714i	−0.411571	−	0.237621i	−0.691464	+	0.722410i	$0.743034\pi$
$710$	−19.8296	−	11.0438i	−0.744192	−	0.414466i
$711$	3.91546	+	6.85496i	0.146841	+	0.257081i
$712$	−27.8129	+	1.28986i	−1.04233	+	0.0483397i
$713$	11.4394	+	6.60456i	0.428410	+	0.247343i
$714$	−7.48492	−	1.90061i	−0.280116	−	0.0711286i
$715$	−17.2076	−	29.8044i	−0.643526	−	1.11462i
$716$	19.1937	+	10.3045i	0.717304	+	0.385096i
$717$	−5.13733	+	1.36379i	−0.191857	+	0.0509316i
$718$	−16.6653	+	9.96812i	−0.621945	+	0.372007i
$719$	8.61000			0.321099			0.160549	−	0.987028i	$-0.448673\pi$
$719$	8.61000			0.321099			0.160549	+	0.987028i	$0.448673\pi$
$720$	−10.0326	+	6.58385i	−0.373893	+	0.245366i
$721$	−1.38738			−0.0516687
$722$	22.9750	−	13.7421i	0.855041	−	0.511429i
$723$	33.2646	+	33.4192i	1.23712	+	1.24287i
$724$	1.20084	+	0.644690i	0.0446289	+	0.0239597i
$725$	−1.68113	−	2.91181i	−0.0624357	−	0.108142i
$726$	27.3019	−	28.0285i	1.01327	−	1.04023i
$727$	0.778073	+	0.449221i	0.0288571	+	0.0166607i	0.514359	−	0.857575i	$-0.328030\pi$
$727$	0.778073	+	0.449221i	0.0288571	+	0.0166607i	−0.485502	+	0.874236i	$0.661363\pi$
$728$	0.552161	+	11.9061i	0.0204645	+	0.441269i
$729$	0.375476	−	26.9974i	0.0139065	−	0.999903i
$730$	−10.4800	−	5.83667i	−0.387883	−	0.216025i
$731$	18.8742	+	10.8970i	0.698088	+	0.403041i
$732$	6.98214	+	23.3654i	0.258067	+	0.863612i
$733$	37.9597	−	21.9160i	1.40207	−	0.809488i	0.407469	−	0.913219i	$-0.366412\pi$
$733$	37.9597	−	21.9160i	1.40207	−	0.809488i	0.994605	+	0.103732i	$0.0330783\pi$
$734$	18.9881	−	0.293346i	0.700862	−	0.0108276i
$735$	8.05917	+	8.09661i	0.297267	+	0.298648i
$736$	−2.74800	−	35.5073i	−0.101293	−	1.30882i
$737$			54.0082i			1.98942i
$738$	−38.9670	+	23.0629i	−1.43440	+	0.848958i
$739$	46.6601			1.71642			0.858210	−	0.513299i	$-0.171577\pi$
$739$	46.6601			1.71642			0.858210	+	0.513299i	$0.171577\pi$
$740$	−0.128041	−	4.14300i	−0.00470687	−	0.152300i
$741$	0.778618	+	2.93302i	0.0286033	+	0.107747i
$742$	2.92084	−	0.0451239i	0.107227	−	0.00165655i
$743$	−16.3801	−	28.3712i	−0.600928	−	1.04084i	−0.992681	−	0.120767i	$-0.961465\pi$
$743$	−16.3801	−	28.3712i	−0.600928	−	1.04084i	0.391753	−	0.920070i	$-0.371869\pi$
$744$	9.80179	−	3.09472i	0.359351	−	0.113458i
$745$	−7.27801	+	12.6059i	−0.266646	+	0.461844i
$746$	−18.0444	+	32.3996i	−0.660653	+	1.18623i
$747$	−16.8818	−	29.5558i	−0.617674	−	1.08139i
$748$	27.1131	+	43.7798i	0.991352	+	1.60075i
$749$	−0.0982755	+	0.170218i	−0.00359091	+	0.00621963i
$750$	0.664985	+	2.35750i	0.0242818	+	0.0860836i
$751$	−22.4669	+	12.9713i	−0.819829	+	0.473328i	−0.850357	−	0.526205i	$-0.823614\pi$
$751$	−22.4669	+	12.9713i	−0.819829	+	0.473328i	0.0305285	+	0.999534i	$0.490281\pi$
$752$	26.0807	−	1.61360i	0.951064	−	0.0588420i
$753$	29.8681	+	8.07738i	1.08845	+	0.294356i
$754$	16.1738	+	27.0404i	0.589014	+	0.984752i
$755$			21.7975i			0.793293i
$756$	−1.55718	+	6.42276i	−0.0566340	+	0.233593i
$757$		−	2.42716i		−	0.0882167i	−0.999027	−	0.0441084i	$-0.985955\pi$
$757$		−	2.42716i		−	0.0882167i	0.999027	−	0.0441084i	$-0.0140447\pi$
$758$	19.6426	−	11.7489i	0.713450	−	0.426739i
$759$	54.6694	+	14.7845i	1.98438	+	0.536644i
$760$	0.629632	−	0.403522i	0.0228391	−	0.0146373i
$761$	1.32882	−	0.767194i	0.0481696	−	0.0278108i	−0.475722	−	0.879596i	$-0.657813\pi$
$761$	1.32882	−	0.767194i	0.0481696	−	0.0278108i	0.523891	+	0.851785i	$0.324480\pi$
$762$	0.524349	−	0.147904i	0.0189952	−	0.00535801i
$763$	0.844100	−	1.46202i	0.0305585	−	0.0529288i
$764$	−14.1772	−	22.8920i	−0.512912	−	0.828204i
$765$	14.8725	+	0.0689443i	0.537717	+	0.00249269i
$766$	−22.9167	−	12.7631i	−0.828014	−	0.461149i
$767$	2.97121	−	5.14629i	0.107284	−	0.185822i
$768$	−21.8225	−	17.0816i	−0.787451	−	0.616378i
$769$	−13.3873	−	23.1875i	−0.482758	−	0.836161i	0.517046	−	0.855958i	$-0.327032\pi$
$769$	−13.3873	−	23.1875i	−0.482758	−	0.836161i	−0.999804	+	0.0197963i	$0.993698\pi$
$770$	0.0721517	+	4.67033i	0.00260017	+	0.168307i
$771$	−1.80912	−	6.81486i	−0.0651538	−	0.245431i
$772$	−22.9610	+	0.709616i	−0.826384	+	0.0255396i
$773$	20.2189			0.727223			0.363612	−	0.931551i	$-0.381543\pi$
$773$	20.2189			0.727223			0.363612	+	0.931551i	$0.381543\pi$
$774$	9.15042	−	16.2523i	0.328905	−	0.584177i
$775$		−	2.09814i		−	0.0753674i
$776$	14.1018	+	7.29242i	0.506224	+	0.261783i
$777$	−1.61043	−	1.61791i	−0.0577739	−	0.0580423i
$778$	0.343135	+	22.2109i	0.0123020	+	0.796299i
$779$	2.44383	−	1.41094i	0.0875591	−	0.0505523i
$780$	−6.57219	−	21.9936i	−0.235322	−	0.787496i
$781$	72.1882	+	41.6779i	2.58310	+	1.49135i
$782$	−21.4764	+	38.5618i	−0.767994	+	1.37897i
$783$	4.40434	+	16.9066i	0.157398	+	0.604192i
$784$	−11.7551	+	23.6188i	−0.419825	+	0.843527i
$785$	12.8763	+	7.43414i	0.459575	+	0.265336i
$786$	−16.0509	−	15.6348i	−0.572516	−	0.557676i
$787$	−12.2401	−	21.2005i	−0.436313	−	0.755716i	0.561089	−	0.827756i	$-0.310383\pi$
$787$	−12.2401	−	21.2005i	−0.436313	−	0.755716i	−0.997402	+	0.0720395i	$0.977049\pi$
$788$	7.78895	−	14.5082i	0.277470	−	0.516833i
$789$	21.6524	+	21.7530i	0.770845	+	0.774427i
$790$	1.91029	+	3.19374i	0.0679649	+	0.113628i
$791$	−2.70407			−0.0961458
$792$	37.2134	−	23.6069i	1.32232	−	0.838835i
$793$	−46.6481			−1.65652
$794$	−12.7098	−	21.2490i	−0.451053	−	0.754100i
$795$	−5.43757	+	1.44349i	−0.192851	+	0.0511954i
$796$	−0.307574	−	0.165126i	−0.0109017	−	0.00585272i
$797$	−24.9028	−	43.1330i	−0.882103	−	1.52785i	−0.848998	−	0.528396i	$-0.822794\pi$
$797$	−24.9028	−	43.1330i	−0.882103	−	1.52785i	−0.0331053	−	0.999452i	$-0.510540\pi$
$798$	0.101365	−	0.399194i	0.00358830	−	0.0141313i
$799$	−28.0470	−	16.1929i	−0.992232	−	0.572865i
$800$	−4.66613	+	3.19801i	−0.164972	+	0.113067i
$801$	14.8843	−	25.5065i	0.525910	−	0.901229i
$802$	−10.1439	+	18.2138i	−0.358192	+	0.643150i
$803$	38.1517	+	22.0269i	1.34634	+	0.777312i
$804$	−8.32536	+	35.0476i	−0.293613	+	1.23603i
$805$	−3.46723	+	2.00181i	−0.122204	+	0.0705544i
$806$	0.303721	+	19.6596i	0.0106981	+	0.692480i
$807$	−3.78698	+	14.0033i	−0.133308	+	0.492939i
$808$	−19.6405	−	10.1566i	−0.690950	−	0.357309i
$809$		−	12.3412i		−	0.433893i	−0.976183	−	0.216947i	$-0.930390\pi$
$809$		−	12.3412i		−	0.433893i	0.976183	−	0.216947i	$-0.0696097\pi$
$810$	−0.0786126	−	12.7277i	−0.00276217	−	0.447205i
$811$	25.3981			0.891846			0.445923	−	0.895071i	$-0.352875\pi$
$811$	25.3981			0.891846			0.445923	+	0.895071i	$0.352875\pi$
$812$	−0.132099	−	4.27432i	−0.00463578	−	0.149999i
$813$	24.1169	+	6.52205i	0.845816	+	0.228738i
$814$	0.235140	+	15.2205i	0.00824166	+	0.533477i
$815$	−3.24973	−	5.62870i	−0.113833	−	0.197165i
$816$	10.8459	+	32.5896i	0.379682	+	1.14086i
$817$	−0.581172	+	1.00662i	−0.0203326	+	0.0352172i
$818$	−1.35648	−	0.755469i	−0.0474282	−	0.0264143i
$819$	−10.9188	−	6.37162i	−0.381533	−	0.222642i
$820$	−18.1472	+	11.2387i	−0.633727	+	0.392471i
$821$	−2.67347	+	4.63059i	−0.0933048	+	0.161609i	−0.908900	−	0.417014i	$-0.863076\pi$
$821$	−2.67347	+	4.63059i	−0.0933048	+	0.161609i	0.815595	+	0.578623i	$0.196410\pi$
$822$	−11.0876	+	43.6650i	−0.386726	+	1.52299i
$823$	30.0747	−	17.3637i	1.04834	−	0.605259i	0.126155	−	0.992010i	$-0.459736\pi$
$823$	30.0747	−	17.3637i	1.04834	−	0.605259i	0.922184	+	0.386751i	$0.126403\pi$
$824$	3.32955	+	5.19523i	0.115990	+	0.180984i
$825$	−2.30810	−	8.69450i	−0.0803577	−	0.302704i
$826$	−0.692152	+	0.414000i	−0.0240830	+	0.0144049i
$827$		−	4.45118i		−	0.154783i	−0.997001	−	0.0773914i	$-0.975341\pi$
$827$		−	4.45118i		−	0.154783i	0.997001	−	0.0773914i	$-0.0246591\pi$
$828$	33.1977	+	18.0215i	1.15370	+	0.626289i
$829$			14.8316i			0.515124i	0.966262	+	0.257562i	$0.0829192\pi$
$829$			14.8316i			0.515124i	−0.966262	+	0.257562i	$0.917081\pi$
$830$	−8.23636	−	13.7701i	−0.285888	−	0.477967i
$831$	−11.7465	+	11.6922i	−0.407482	+	0.405597i
$832$	43.2588	−	30.6409i	1.49973	−	1.06228i
$833$	28.3173	−	16.3490i	0.981136	−	0.566459i
$834$	−17.2504	+	17.7095i	−0.597334	+	0.613230i
$835$	6.96462	−	12.0631i	0.241021	−	0.417460i
$836$	−2.33491	+	1.44602i	−0.0807546	+	0.0500118i
$837$	−2.89487	+	10.5109i	−0.100061	+	0.363309i
$838$	23.4461	−	42.0985i	0.809930	−	1.45427i
$839$	25.7912	−	44.6717i	0.890413	−	1.54224i	0.0510312	−	0.998697i	$-0.483749\pi$
$839$	25.7912	−	44.6717i	0.890413	−	1.54224i	0.839381	−	0.543543i	$-0.182917\pi$
$840$	−0.673110	+	3.04185i	−0.0232245	+	0.104954i
$841$	8.84758	+	15.3245i	0.305089	+	0.528430i
$842$	55.8328	−	0.862558i	1.92412	−	0.0297257i
$843$	−10.4894	+	10.4409i	−0.361273	+	0.359602i
$844$	14.0159	−	0.433165i	0.482447	−	0.0149102i
$845$	30.9092			1.06331
$846$	−13.5975	+	24.1508i	−0.467491	+	0.830323i
$847$		−	10.1583i		−	0.349045i
$848$	−7.17866	−	10.8292i	−0.246516	−	0.371876i
$849$	−32.0452	+	8.50692i	−1.09979	+	0.291957i
$850$	7.01021	−	0.108300i	0.240448	−	0.00371467i
$851$	−11.2996	+	6.52382i	−0.387345	+	0.223634i
$852$	40.4206	+	38.1739i	1.38479	+	1.30782i
$853$	−22.5836	−	13.0386i	−0.773246	−	0.446434i	0.0607851	−	0.998151i	$-0.480640\pi$
$853$	−22.5836	−	13.0386i	−0.773246	−	0.446434i	−0.834031	+	0.551717i	$0.813973\pi$
$854$	5.53120	+	3.08051i	0.189274	+	0.105413i
$855$	−0.00367701	+	0.793197i	−0.000125751	+	0.0271268i
$856$	0.873255	−	0.0404984i	0.0298472	−	0.00138421i
$857$	6.55553	+	3.78484i	0.223933	+	0.129288i	0.607770	−	0.794113i	$-0.292064\pi$
$857$	6.55553	+	3.78484i	0.223933	+	0.129288i	−0.383837	+	0.923401i	$0.625398\pi$
$858$	22.8855	+	81.1336i	0.781299	+	2.76986i
$859$	−22.0843	−	38.2511i	−0.753506	−	1.30511i	−0.946114	−	0.323835i	$-0.895028\pi$
$859$	−22.0843	−	38.2511i	−0.753506	−	1.30511i	0.192607	−	0.981276i	$-0.438306\pi$
$860$	4.15882	−	7.74649i	0.141815	−	0.264153i
$861$	−3.06891	+	11.3480i	−0.104588	+	0.386740i
$862$	−1.11235	+	0.665335i	−0.0378868	+	0.0226614i
$863$	−54.8876			−1.86839			−0.934197	−	0.356757i	$-0.883882\pi$
$863$	−54.8876			−1.86839			−0.934197	+	0.356757i	$0.883882\pi$
$864$	27.7879	−	9.58283i	0.945365	−	0.326014i
$865$	−18.7290			−0.636804
$866$	10.1199	−	6.05306i	0.343888	−	0.205691i
$867$	3.42621	−	12.6693i	0.116360	−	0.430271i
$868$	1.26225	−	2.35115i	0.0428437	−	0.0798033i
$869$	−6.83343	−	11.8358i	−0.231808	−	0.401504i
$870$	2.23586	+	7.92654i	0.0758026	+	0.268735i
$871$	−59.6755	−	34.4537i	−2.02203	−	1.16742i
$872$	−7.50049	+	0.347846i	−0.253999	+	0.0117795i
$873$	−14.6217	+	8.35170i	−0.494869	+	0.282662i
$874$	−2.05662	−	1.14540i	−0.0695662	−	0.0387438i
$875$	0.550736	+	0.317967i	0.0186183	+	0.0107493i
$876$	21.3624	+	20.1750i	0.721769	+	0.681652i
$877$	19.7220	−	11.3865i	0.665965	−	0.384495i	−0.128581	−	0.991699i	$-0.541042\pi$
$877$	19.7220	−	11.3865i	0.665965	−	0.384495i	0.794546	+	0.607204i	$0.207709\pi$
$878$	32.5731	−	0.503220i	1.09929	−	0.0169829i
$879$	23.2284	−	6.16637i	0.783476	−	0.207987i
$880$	17.3155	−	11.4784i	0.583706	−	0.386938i
$881$		−	13.4097i		−	0.451783i	−0.974152	−	0.225891i	$-0.927471\pi$
$881$		−	13.4097i		−	0.451783i	0.974152	−	0.225891i	$-0.0725295\pi$
$882$	−14.2525	−	24.0810i	−0.479908	−	0.810851i
$883$	47.1600			1.58706			0.793530	−	0.608531i	$-0.208241\pi$
$883$	47.1600			1.58706			0.793530	+	0.608531i	$0.208241\pi$
$884$	−65.6701	+	2.02956i	−2.20873	+	0.0682614i
$885$	1.10087	−	1.09578i	0.0370053	−	0.0368342i
$886$	19.5445	−	0.301942i	0.656610	−	0.0101439i
$887$	15.0822	+	26.1232i	0.506411	+	0.877130i	0.999972	+	0.00741869i	$0.00236146\pi$
$887$	15.0822	+	26.1232i	0.506411	+	0.877130i	−0.493561	+	0.869711i	$0.664305\pi$
$888$	−2.19364	+	9.91328i	−0.0736139	+	0.332668i
$889$	0.0707215	−	0.122493i	0.00237192	−	0.00410829i
$890$	6.77363	−	12.1624i	0.227053	−	0.407684i
$891$	−0.433360	+	46.7407i	−0.0145181	+	1.56587i
$892$	37.1224	−	22.9901i	1.24295	−	0.769765i
$893$	0.863620	−	1.49583i	0.0288999	−	0.0500561i
$894$	24.8786	−	25.5406i	0.832064	−	0.854205i
$895$	−9.43313	+	5.44622i	−0.315315	+	0.182047i
$896$	−7.15276	+	0.776486i	−0.238957	+	0.0259406i
$897$	−51.2115	+	50.9746i	−1.70990	+	1.70199i
$898$	−8.56862	−	14.3256i	−0.285939	−	0.478051i
$899$		−	7.05450i		−	0.235281i
$900$	−0.157541	−	5.99793i	−0.00525136	−	0.199931i
$901$			16.1027i			0.536460i
$902$	67.2744	−	40.2391i	2.23999	−	1.33982i
$903$	−1.24241	−	4.68011i	−0.0413449	−	0.155744i
$904$	6.48947	+	10.1258i	0.215837	+	0.336778i
$905$	−0.590177	+	0.340739i	−0.0196181	+	0.0113265i
$906$	13.1408	−	51.7505i	0.436572	−	1.71930i
$907$	14.3915	−	24.9268i	0.477861	−	0.827679i	−0.521817	−	0.853057i	$-0.674746\pi$
$907$	14.3915	−	24.9268i	0.477861	−	0.827679i	0.999678	+	0.0253782i	$0.00807900\pi$
$908$	5.27309	−	3.26566i	0.174994	−	0.108375i
$909$	20.3646	−	11.6320i	0.675451	−	0.385808i
$910$	−5.20644	−	2.89964i	−0.172592	−	0.0961221i
$911$	0.279655	−	0.484376i	0.00926538	−	0.0160481i	−0.861356	−	0.508003i	$-0.830384\pi$
$911$	0.279655	−	0.484376i	0.00926538	−	0.0160481i	0.870621	+	0.491954i	$0.163717\pi$
$912$	−1.73810	+	0.578444i	−0.0575543	+	0.0191542i
$913$	29.4629	+	51.0313i	0.975080	+	1.68889i
$914$	−0.420265	−	27.2035i	−0.0139011	−	0.899810i
$915$	−11.7704	−	3.18312i	−0.389116	−	0.105231i
$916$	1.24357	+	40.2381i	0.0410887	+	1.32950i
$917$	−5.81732			−0.192105
$918$	−35.2679	−	9.12965i	−1.16402	−	0.301323i
$919$			16.4311i			0.542012i	0.962578	+	0.271006i	$0.0873562\pi$
$919$			16.4311i			0.542012i	−0.962578	+	0.271006i	$0.912644\pi$
$920$	15.8170	+	8.17941i	0.521471	+	0.269667i
$921$	5.85360	−	21.6451i	0.192883	−	0.713231i
$922$	−0.556138	−	35.9984i	−0.0183154	−	1.18554i
$923$	−92.1027	+	53.1755i	−3.03160	+	1.75029i
$924$	2.64423	−	11.1315i	0.0869889	−	0.366201i
$925$	1.79483	+	1.03625i	0.0590136	+	0.0340715i
$926$	7.80072	−	14.0065i	0.256348	−	0.460284i
$927$	−6.54484	−	0.0303398i	−0.214961	−	0.000996490i
$928$	−15.6888	+	10.7526i	−0.515009	+	0.352970i
$929$	34.3337	+	19.8226i	1.12645	+	0.650357i	0.943040	−	0.332679i	$-0.107953\pi$
$929$	34.3337	+	19.8226i	1.12645	+	0.650357i	0.183411	+	0.983036i	$0.441286\pi$
$930$	−1.26487	+	4.98129i	−0.0414768	+	0.163343i
$931$	0.871942	+	1.51025i	0.0285768	+	0.0494964i
$932$	−17.9962	−	9.66152i	−0.589484	−	0.316474i
$933$	−14.4539	+	3.83702i	−0.473198	+	0.125618i
$934$	12.2036	+	20.4027i	0.399313	+	0.667598i
$935$	−25.7478			−0.842042
$936$	2.34441	+	56.1780i	0.0766293	+	1.83623i
$937$	32.2140			1.05239			0.526193	−	0.850365i	$-0.323619\pi$
$937$	32.2140			1.05239			0.526193	+	0.850365i	$0.323619\pi$
$938$	4.80067	+	8.02607i	0.156747	+	0.262061i
$939$	−4.00421	−	4.02282i	−0.130673	−	0.131280i
$940$	−6.17999	+	11.5112i	−0.201569	+	0.375455i
$941$	−9.46132	−	16.3875i	−0.308430	−	0.534217i	0.669589	−	0.742732i	$-0.266470\pi$
$941$	−9.46132	−	16.3875i	−0.308430	−	0.534217i	−0.978019	+	0.208515i	$0.933137\pi$
$942$	−26.0885	−	25.4123i	−0.850010	−	0.827977i
$943$	58.1896	+	33.5958i	1.89491	+	1.09403i
$944$	3.21137	+	1.59830i	0.104521	+	0.0520204i
$945$	−2.32027	−	2.35276i	−0.0754784	−	0.0765354i
$946$	−15.7107	+	28.2093i	−0.510800	+	0.917164i
$947$	−26.3475	−	15.2117i	−0.856179	−	0.494315i	0.00655204	−	0.999979i	$-0.497914\pi$
$947$	−26.3475	−	15.2117i	−0.856179	−	0.494315i	−0.862731	+	0.505664i	$0.831248\pi$
$948$	−2.60993	−	8.73403i	−0.0847667	−	0.283668i
$949$	−48.6766	+	28.1034i	−1.58011	+	0.912276i
$950$	0.00577600	+	0.373876i	0.000187398	+	0.0121301i
$951$	−26.5059	−	26.6291i	−0.859513	−	0.863507i
$952$	7.92072	+	4.09602i	0.256712	+	0.132753i
$953$			23.2450i			0.752979i	0.926421	+	0.376489i	$0.122869\pi$
$953$			23.2450i			0.752979i	−0.926421	+	0.376489i	$0.877131\pi$
$954$	13.7798	−	0.148994i	0.446137	−	0.00482386i
$955$	13.4633			0.435661
$956$	6.13461	−	0.189592i	0.198407	−	0.00613184i
$957$	−7.76044	−	29.2332i	−0.250860	−	0.944976i
$958$	−0.229635	−	14.8641i	−0.00741915	−	0.480236i
$959$	5.84801	+	10.1291i	0.188842	+	0.327084i
$960$	13.0060	−	4.77954i	0.419767	−	0.154259i
$961$	−13.2989	+	23.0344i	−0.428997	+	0.743045i
$962$	−16.9676	−	9.44983i	−0.547058	−	0.304675i
$963$	−0.467329	+	0.800840i	−0.0150595	+	0.0258067i
$964$	−28.6672	−	46.2892i	−0.923308	−	1.49088i
$965$	5.74299	−	9.94714i	0.184873	−	0.320210i
$966$	9.43851	−	2.66234i	0.303679	−	0.0856594i
$967$	42.1905	−	24.3587i	1.35675	−	0.783322i	0.367569	−	0.929996i	$-0.380190\pi$
$967$	42.1905	−	24.3587i	1.35675	−	0.783322i	0.989185	+	0.146674i	$0.0468567\pi$
$968$	−38.0393	+	24.3789i	−1.22263	+	0.783567i
$969$	2.19162	+	0.592691i	0.0704050	+	0.0190400i
$970$	−6.81227	+	4.07465i	−0.218729	+	0.130829i
$971$		−	0.0189290i		−	0.000607459i	−1.00000		0.000303730i	$-0.999903\pi$
$971$		−	0.0189290i		−	0.000607459i	1.00000		0.000303730i	$-9.66802e-5\pi$
$972$	−7.48631	+	30.2648i	−0.240123	+	0.970742i
$973$			6.41845i			0.205766i
$974$	25.3349	+	42.3565i	0.811782	+	1.35719i
$975$	11.0793	+	2.99622i	0.354821	+	0.0959559i
$976$	−1.73886	−	28.1052i	−0.0556596	−	0.899626i
$977$	−5.29534	+	3.05727i	−0.169413	+	0.0978106i	−0.582309	−	0.812968i	$-0.697851\pi$
$977$	−5.29534	+	3.05727i	−0.169413	+	0.0978106i	0.412896	+	0.910778i	$0.364517\pi$
$978$	4.32204	+	15.3225i	0.138204	+	0.489958i
$979$	−25.5629	+	44.2762i	−0.816993	+	1.41507i
$980$	−6.94533	−	11.2147i	−0.221860	−	0.358240i
$981$	4.01394	−	6.87851i	0.128155	−	0.219614i
$982$	4.58170	−	8.22666i	0.146208	−	0.262523i
$983$	−22.1595	+	38.3814i	−0.706779	+	1.22418i	0.259266	+	0.965806i	$0.416519\pi$
$983$	−22.1595	+	38.3814i	−0.706779	+	1.22418i	−0.966046	+	0.258372i	$0.916814\pi$
$984$	49.8593	−	15.7421i	1.58946	−	0.501840i
$985$	4.11670	+	7.13034i	0.131169	+	0.227191i
$986$	23.5702	−	0.364135i	0.750628	−	0.0115964i
$987$	1.84622	+	6.95462i	0.0587658	+	0.221368i
$988$	−0.108242	−	3.50239i	−0.00344365	−	0.111426i
$989$	−27.6764			−0.880059
$990$	0.238237	+	22.0335i	0.00757166	+	0.700269i
$991$		−	9.14014i		−	0.290346i	−0.989406	−	0.145173i	$-0.953626\pi$
$991$		−	9.14014i		−	0.290346i	0.989406	−	0.145173i	$-0.0463739\pi$
$992$	−11.8335	+	0.915824i	−0.375713	+	0.0290774i
$993$	−9.67059	−	9.71552i	−0.306887	−	0.308313i
$994$	14.4324	−	0.222966i	0.457769	−	0.00707206i
$995$	0.151163	−	0.0872740i	0.00479219	−	0.00276677i
$996$	11.2530	+	37.6575i	0.356563	+	1.19322i
$997$	−39.4045	−	22.7502i	−1.24795	−	0.720506i	−0.277253	−	0.960797i	$-0.589424\pi$
$997$	−39.4045	−	22.7502i	−1.24795	−	0.720506i	−0.970701	+	0.240291i	$0.922757\pi$
$998$	4.25585	+	2.37023i	0.134717	+	0.0750282i
$999$	−7.56168	−	7.66758i	−0.239241	−	0.242592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.4	yes	48
3.2	odd	2		1080.2.bm.a.251.21		48
4.3	odd	2		1440.2.cc.b.911.14		48
8.3	odd	2		360.2.bm.a.11.12	✓	48
8.5	even	2		1440.2.cc.a.911.14		48
9.4	even	3		1080.2.bm.b.611.13		48
9.5	odd	6		360.2.bm.a.131.12	yes	48
12.11	even	2		4320.2.cc.a.1871.13		48
24.5	odd	2		4320.2.cc.b.1871.12		48
24.11	even	2		1080.2.bm.b.251.13		48
36.23	even	6		1440.2.cc.a.1391.14		48
36.31	odd	6		4320.2.cc.b.3311.12		48
72.5	odd	6		1440.2.cc.b.1391.14		48
72.13	even	6		4320.2.cc.a.3311.13		48
72.59	even	6	inner	360.2.bm.b.131.4	yes	48
72.67	odd	6		1080.2.bm.a.611.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.12	✓	48	8.3	odd	2
360.2.bm.a.131.12	yes	48	9.5	odd	6
360.2.bm.b.11.4	yes	48	1.1	even	1	trivial
360.2.bm.b.131.4	yes	48	72.59	even	6	inner
1080.2.bm.a.251.21		48	3.2	odd	2
1080.2.bm.a.611.21		48	72.67	odd	6
1080.2.bm.b.251.13		48	24.11	even	2
1080.2.bm.b.611.13		48	9.4	even	3
1440.2.cc.a.911.14		48	8.5	even	2
1440.2.cc.a.1391.14		48	36.23	even	6
1440.2.cc.b.911.14		48	4.3	odd	2
1440.2.cc.b.1391.14		48	72.5	odd	6
4320.2.cc.a.1871.13		48	12.11	even	2
4320.2.cc.a.3311.13		48	72.13	even	6
4320.2.cc.b.1871.12		48	24.5	odd	2
4320.2.cc.b.3311.12		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21368 + 0.725941i) q^{2} +(-0.452164 + 1.67199i) q^{3} +(0.946019 - 1.76211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.664985 - 2.35750i) q^{6} +(-0.550736 - 0.317967i) q^{7} +(0.131031 + 2.82539i) q^{8} +(-2.59109 - 1.51203i) q^{9} +O(q^{10})\)	\(q+(-1.21368 + 0.725941i) q^{2} +(-0.452164 + 1.67199i) q^{3} +(0.946019 - 1.76211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.664985 - 2.35750i) q^{6} +(-0.550736 - 0.317967i) q^{7} +(0.131031 + 2.82539i) q^{8} +(-2.59109 - 1.51203i) q^{9} +(-1.23552 - 0.688104i) q^{10} +(4.49782 + 2.59682i) q^{11} +(2.51848 + 2.37850i) q^{12} +(-5.73863 + 3.31320i) q^{13} +(0.899240 - 0.0138923i) q^{14} +(-1.67407 + 0.444409i) q^{15} +(-2.21010 - 3.33399i) q^{16} +4.95756i q^{17} +(4.24239 - 0.0458709i) q^{18} -0.264402 q^{19} +(1.99905 - 0.0617811i) q^{20} +(0.780661 - 0.777050i) q^{21} +(-7.34404 + 0.113458i) q^{22} +(-3.14782 - 5.45218i) q^{23} +(-4.78327 - 1.05846i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(4.55965 - 8.18706i) q^{26} +(3.69969 - 3.64860i) q^{27} +(-1.08130 + 0.669656i) q^{28} +(-1.68113 + 2.91181i) q^{29} +(1.70916 - 1.75464i) q^{30} +(-1.81704 + 1.04907i) q^{31} +(5.10262 + 2.44198i) q^{32} +(-6.37561 + 6.34612i) q^{33} +(-3.59889 - 6.01687i) q^{34} -0.635935i q^{35} +(-5.11559 + 3.13540i) q^{36} -2.07249i q^{37} +(0.320898 - 0.191940i) q^{38} +(-2.94483 - 11.0930i) q^{39} +(-2.38134 + 1.52617i) q^{40} +(-9.24285 + 5.33636i) q^{41} +(-0.383377 + 1.50980i) q^{42} +(2.19807 - 3.80716i) q^{43} +(8.83092 - 5.46904i) q^{44} +(0.0139069 - 2.99997i) q^{45} +(7.77839 + 4.33205i) q^{46} +(-3.26632 + 5.65743i) q^{47} +(6.57372 - 2.18775i) q^{48} +(-3.29779 - 5.71195i) q^{49} +(-0.0218455 - 1.41404i) q^{50} +(-8.28898 - 2.24163i) q^{51} +(0.409386 + 13.2465i) q^{52} +3.24812 q^{53} +(-1.84156 + 7.11398i) q^{54} +5.19364i q^{55} +(0.826218 - 1.59771i) q^{56} +(0.119553 - 0.442077i) q^{57} +(-0.0734505 - 4.75440i) q^{58} +(-0.776635 + 0.448390i) q^{59} +(-0.800600 + 3.37032i) q^{60} +(6.09659 + 3.51987i) q^{61} +(1.44374 - 2.59230i) q^{62} +(0.946233 + 1.65661i) q^{63} +(-7.96566 + 0.740430i) q^{64} +(-5.73863 - 3.31320i) q^{65} +(3.13101 - 12.3305i) q^{66} +(5.19945 + 9.00572i) q^{67} +(8.73578 + 4.68994i) q^{68} +(10.5393 - 2.79783i) q^{69} +(0.461651 + 0.771819i) q^{70} +16.0496 q^{71} +(3.93255 - 7.51898i) q^{72} +8.48226 q^{73} +(1.50451 + 2.51533i) q^{74} +(-1.22190 - 1.22758i) q^{75} +(-0.250129 + 0.465906i) q^{76} +(-1.65141 - 2.86032i) q^{77} +(11.6270 + 11.3256i) q^{78} +(-2.27891 - 1.31573i) q^{79} +(1.78227 - 3.58099i) q^{80} +(4.42754 + 7.83561i) q^{81} +(7.34394 - 13.1864i) q^{82} +(9.82573 + 5.67289i) q^{83} +(-0.630732 - 2.11072i) q^{84} +(-4.29337 + 2.47878i) q^{85} +(0.0960358 + 6.21633i) q^{86} +(-4.10836 - 4.12745i) q^{87} +(-6.74767 + 13.0484i) q^{88} +9.84392i q^{89} +(2.16092 + 3.65108i) q^{90} +4.21396 q^{91} +(-12.5853 + 0.388951i) q^{92} +(-0.932431 - 3.51242i) q^{93} +(-0.142709 - 9.23743i) q^{94} +(-0.132201 - 0.228979i) q^{95} +(-6.39019 + 7.42735i) q^{96} +(2.80646 - 4.86094i) q^{97} +(8.14899 + 4.53845i) q^{98} +(-7.72782 - 13.5294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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