LMFDB - Embedded newform 312.2.ba.a.179.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,2,Mod(179,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("312.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	312.ba (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:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.10
Character	$\chi$	$=$	312.179
Dual form			312.2.ba.a.251.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16902 + 0.795859i) q^{2} +(1.00378 - 1.41153i) q^{3} +(0.733216 - 1.86075i) q^{4} -0.119305i q^{5} +(-0.0500653 + 2.44898i) q^{6} +(0.682422 - 1.18199i) q^{7} +(0.623752 + 2.75879i) q^{8} +(-0.984833 - 2.83374i) q^{9} +O(q^{10})$	\(q+(-1.16902 + 0.795859i) q^{2} +(1.00378 - 1.41153i) q^{3} +(0.733216 - 1.86075i) q^{4} -0.119305i q^{5} +(-0.0500653 + 2.44898i) q^{6} +(0.682422 - 1.18199i) q^{7} +(0.623752 + 2.75879i) q^{8} +(-0.984833 - 2.83374i) q^{9} +(0.0949496 + 0.139469i) q^{10} +(1.19826 + 2.07544i) q^{11} +(-1.89051 - 2.90275i) q^{12} +(1.75966 - 3.14700i) q^{13} +(0.142932 + 1.92488i) q^{14} +(-0.168402 - 0.119756i) q^{15} +(-2.92479 - 2.72866i) q^{16} +(1.73687 + 1.00278i) q^{17} +(3.40655 + 2.52892i) q^{18} +(-5.15721 - 2.97752i) q^{19} +(-0.221996 - 0.0874760i) q^{20} +(-0.983408 - 2.14972i) q^{21} +(-3.05255 - 1.47259i) q^{22} +(-2.69692 - 4.67120i) q^{23} +(4.52023 + 1.88879i) q^{24} +4.98577 q^{25} +(0.447488 + 5.07935i) q^{26} +(-4.98847 - 1.45435i) q^{27} +(-1.69903 - 2.13647i) q^{28} +(-2.87305 - 4.97627i) q^{29} +(0.292174 + 0.00597301i) q^{30} +5.63702 q^{31} +(5.59077 + 0.862142i) q^{32} +(4.13234 + 0.391921i) q^{33} +(-2.82851 + 0.210031i) q^{34} +(-0.141017 - 0.0814160i) q^{35} +(-5.99499 - 0.245218i) q^{36} +(4.57129 + 7.91771i) q^{37} +(8.39857 - 0.623637i) q^{38} +(-2.67576 - 5.64272i) q^{39} +(0.329136 - 0.0744165i) q^{40} +(2.46267 + 4.26547i) q^{41} +(2.86050 + 1.73041i) q^{42} +(-0.354899 + 0.614703i) q^{43} +(4.74046 - 0.707911i) q^{44} +(-0.338078 + 0.117495i) q^{45} +(6.87037 + 3.31436i) q^{46} +3.88604i q^{47} +(-6.78745 + 1.38944i) q^{48} +(2.56860 + 4.44895i) q^{49} +(-5.82846 + 3.96797i) q^{50} +(3.15890 - 1.44507i) q^{51} +(-4.56557 - 5.58172i) q^{52} -4.82108 q^{53} +(6.98908 - 2.26996i) q^{54} +(0.247610 - 0.142957i) q^{55} +(3.68652 + 1.14539i) q^{56} +(-9.37958 + 4.29077i) q^{57} +(7.31907 + 3.53082i) q^{58} +(4.24834 - 7.35834i) q^{59} +(-0.346311 + 0.225547i) q^{60} +(-1.33324 - 0.769745i) q^{61} +(-6.58979 + 4.48628i) q^{62} +(-4.02153 - 0.769747i) q^{63} +(-7.22187 + 3.44161i) q^{64} +(-0.375451 - 0.209936i) q^{65} +(-5.14270 + 2.83060i) q^{66} +(-4.07532 + 2.35289i) q^{67} +(3.13943 - 2.49663i) q^{68} +(-9.30067 - 0.882098i) q^{69} +(0.229647 - 0.0170525i) q^{70} +(2.07930 + 1.20048i) q^{71} +(7.20342 - 4.48450i) q^{72} +9.66594i q^{73} +(-11.6453 - 5.61786i) q^{74} +(5.00464 - 7.03756i) q^{75} +(-9.32177 + 7.41312i) q^{76} +3.27087 q^{77} +(7.61883 + 4.46693i) q^{78} +4.53066i q^{79} +(-0.325542 + 0.348941i) q^{80} +(-7.06021 + 5.58153i) q^{81} +(-6.27363 - 3.02648i) q^{82} -13.8145 q^{83} +(-4.72115 + 0.253669i) q^{84} +(0.119636 - 0.207216i) q^{85} +(-0.0743332 - 1.00105i) q^{86} +(-9.90808 - 0.939707i) q^{87} +(-4.97830 + 4.60030i) q^{88} +(4.65921 + 8.06999i) q^{89} +(0.301711 - 0.406417i) q^{90} +(-2.51889 - 4.22748i) q^{91} +(-10.6694 + 1.59330i) q^{92} +(5.65836 - 7.95682i) q^{93} +(-3.09274 - 4.54285i) q^{94} +(-0.355231 + 0.615279i) q^{95} +(6.82887 - 7.02613i) q^{96} +(-3.05451 - 1.76352i) q^{97} +(-6.54348 - 3.15666i) q^{98} +(4.70119 - 5.43951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9}+O(q^{10}) $ 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9	$ 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + 6 q^{10} + 8 q^{12} - 6 q^{16} - 12 q^{19} + 8 q^{22} - 36 q^{24} - 88 q^{25} + 16 q^{27} + 12 q^{28} + 14 q^{30} - 6 q^{33} + 22 q^{36} + 4 q^{40} + 26 q^{42} - 20 q^{43} - 36 q^{46} + 14 q^{48} - 24 q^{49} - 20 q^{51} - 16 q^{52} - 36 q^{54} - 66 q^{58} + 28 q^{64} + 32 q^{66} - 12 q^{67} - 66 q^{72} + 2 q^{75} - 60 q^{76} - 14 q^{78} - 2 q^{81} + 50 q^{82} - 90 q^{84} + 24 q^{88} + 8 q^{90} + 44 q^{91} + 72 q^{94} + 12 q^{97}+O(q^{100}) $ 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9 + 6 * q^10 + 8 * q^12 - 6 * q^16 - 12 * q^19 + 8 * q^22 - 36 * q^24 - 88 * q^25 + 16 * q^27 + 12 * q^28 + 14 * q^30 - 6 * q^33 + 22 * q^36 + 4 * q^40 + 26 * q^42 - 20 * q^43 - 36 * q^46 + 14 * q^48 - 24 * q^49 - 20 * q^51 - 16 * q^52 - 36 * q^54 - 66 * q^58 + 28 * q^64 + 32 * q^66 - 12 * q^67 - 66 * q^72 + 2 * q^75 - 60 * q^76 - 14 * q^78 - 2 * q^81 + 50 * q^82 - 90 * q^84 + 24 * q^88 + 8 * q^90 + 44 * q^91 + 72 * q^94 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−1.16902	+	0.795859i	−0.826622	+	0.562758i
$2$	−1.16902	+	0.795859i	−0.826622	+	0.562758i
$3$	1.00378	−	1.41153i	0.579535	−	0.814947i
$3$	1.00378	−	1.41153i	0.579535	−	0.814947i
$4$	0.733216	−	1.86075i	0.366608	−	0.930376i
$5$		−	0.119305i		−	0.0533546i	−0.999644	−	0.0266773i	$-0.991507\pi$
$5$		−	0.119305i		−	0.0533546i	0.999644	−	0.0266773i	$-0.00849266\pi$
$6$	−0.0500653	+	2.44898i	−0.0204391	+	0.999791i
$7$	0.682422	−	1.18199i	0.257931	−	0.446750i	−0.707756	−	0.706457i	$-0.750293\pi$
$7$	0.682422	−	1.18199i	0.257931	−	0.446750i	0.965688	+	0.259707i	$0.0836259\pi$
$8$	0.623752	+	2.75879i	0.220530	+	0.975380i
$9$	−0.984833	−	2.83374i	−0.328278	−	0.944581i
$10$	0.0949496	+	0.139469i	0.0300257	+	0.0441041i
$11$	1.19826	+	2.07544i	0.361288	+	0.625769i	0.988173	−	0.153343i	$-0.0490038\pi$
$11$	1.19826	+	2.07544i	0.361288	+	0.625769i	−0.626885	+	0.779112i	$0.715670\pi$
$12$	−1.89051	−	2.90275i	−0.545745	−	0.837952i
$13$	1.75966	−	3.14700i	0.488042	−	0.872820i
$13$	1.75966	−	3.14700i	0.488042	−	0.872820i
$14$	0.142932	+	1.92488i	0.0382003	+	0.514446i
$15$	−0.168402	−	0.119756i	−0.0434812	−	0.0309209i
$16$	−2.92479	−	2.72866i	−0.731197	−	0.682166i
$17$	1.73687	+	1.00278i	0.421253	+	0.243210i	0.695613	−	0.718417i	$-0.255133\pi$
$17$	1.73687	+	1.00278i	0.421253	+	0.243210i	−0.274360	+	0.961627i	$0.588466\pi$
$18$	3.40655	+	2.52892i	0.802932	+	0.596071i
$19$	−5.15721	−	2.97752i	−1.18315	−	0.683089i	−0.226405	−	0.974033i	$-0.572697\pi$
$19$	−5.15721	−	2.97752i	−1.18315	−	0.683089i	−0.956740	+	0.290944i	$0.906031\pi$
$20$	−0.221996	−	0.0874760i	−0.0496398	−	0.0195602i
$21$	−0.983408	−	2.14972i	−0.214597	−	0.469108i
$22$	−3.05255	−	1.47259i	−0.650805	−	0.313957i
$23$	−2.69692	−	4.67120i	−0.562346	−	0.974013i	−0.997291	−	0.0735555i	$-0.976565\pi$
$23$	−2.69692	−	4.67120i	−0.562346	−	0.974013i	0.434945	−	0.900457i	$-0.356768\pi$
$24$	4.52023	+	1.88879i	0.922688	+	0.385547i
$25$	4.98577			0.997153
$26$	0.447488	+	5.07935i	0.0877596	+	0.996142i
$27$	−4.98847	−	1.45435i	−0.960032	−	0.279889i
$28$	−1.69903	−	2.13647i	−0.321086	−	0.403755i
$29$	−2.87305	−	4.97627i	−0.533512	−	0.924070i	−0.999234	−	0.0391390i	$-0.987538\pi$
$29$	−2.87305	−	4.97627i	−0.533512	−	0.924070i	0.465722	−	0.884931i	$-0.345795\pi$
$30$	0.292174	+	0.00597301i	0.0533435	+	0.00109052i
$31$	5.63702			1.01244			0.506220	−	0.862405i	$-0.331043\pi$
$31$	5.63702			1.01244			0.506220	+	0.862405i	$0.331043\pi$
$32$	5.59077	+	0.862142i	0.988318	+	0.152407i
$33$	4.13234	+	0.391921i	0.719348	+	0.0682248i
$34$	−2.82851	+	0.210031i	−0.485085	+	0.0360201i
$35$	−0.141017	−	0.0814160i	−0.0238362	−	0.0137618i
$36$	−5.99499	−	0.245218i	−0.999164	−	0.0408696i
$37$	4.57129	+	7.91771i	0.751516	+	1.30166i	0.947088	+	0.320974i	$0.104010\pi$
$37$	4.57129	+	7.91771i	0.751516	+	1.30166i	−0.195572	+	0.980689i	$0.562656\pi$
$38$	8.39857	−	0.623637i	1.36243	−	0.101167i
$39$	−2.67576	−	5.64272i	−0.428464	−	0.903559i
$40$	0.329136	−	0.0744165i	0.0520410	−	0.0117663i
$41$	2.46267	+	4.26547i	0.384605	+	0.666155i	0.991714	−	0.128463i	$-0.0410044\pi$
$41$	2.46267	+	4.26547i	0.384605	+	0.666155i	−0.607109	+	0.794618i	$0.707671\pi$
$42$	2.86050	+	1.73041i	0.441385	+	0.267008i
$43$	−0.354899	+	0.614703i	−0.0541216	+	0.0937414i	−0.891817	−	0.452396i	$-0.850569\pi$
$43$	−0.354899	+	0.614703i	−0.0541216	+	0.0937414i	0.837695	+	0.546138i	$0.183903\pi$
$44$	4.74046	−	0.707911i	0.714651	−	0.106722i
$45$	−0.338078	+	0.117495i	−0.0503978	+	0.0175151i
$46$	6.87037	+	3.31436i	1.01298	+	0.488676i
$47$			3.88604i			0.566837i	0.958996	+	0.283418i	$0.0914685\pi$
$47$			3.88604i			0.566837i	−0.958996	+	0.283418i	$0.908532\pi$
$48$	−6.78745	+	1.38944i	−0.979684	+	0.200548i
$49$	2.56860	+	4.44895i	0.366943	+	0.635564i
$50$	−5.82846	+	3.96797i	−0.824269	+	0.561156i
$51$	3.15890	−	1.44507i	0.442334	−	0.202350i
$52$	−4.56557	−	5.58172i	−0.633130	−	0.774045i
$53$	−4.82108			−0.662226			−0.331113	−	0.943591i	$-0.607424\pi$
$53$	−4.82108			−0.662226			−0.331113	+	0.943591i	$0.607424\pi$
$54$	6.98908	−	2.26996i	0.951094	−	0.308903i
$55$	0.247610	−	0.142957i	0.0333877	−	0.0192764i
$56$	3.68652	+	1.14539i	0.492633	+	0.153059i
$57$	−9.37958	+	4.29077i	−1.24236	+	0.568327i
$58$	7.31907	+	3.53082i	0.961041	+	0.463619i
$59$	4.24834	−	7.35834i	0.553087	−	0.957975i	−0.444963	−	0.895549i	$-0.646783\pi$
$59$	4.24834	−	7.35834i	0.553087	−	0.957975i	0.998050	−	0.0624257i	$-0.0198836\pi$
$60$	−0.346311	+	0.225547i	−0.0447086	+	0.0291180i
$61$	−1.33324	−	0.769745i	−0.170704	−	0.0985558i	0.412214	−	0.911087i	$-0.364756\pi$
$61$	−1.33324	−	0.769745i	−0.170704	−	0.0985558i	−0.582918	+	0.812531i	$0.698089\pi$
$62$	−6.58979	+	4.48628i	−0.836904	+	0.569758i
$63$	−4.02153	−	0.769747i	−0.506665	−	0.0969790i
$64$	−7.22187	+	3.44161i	−0.902733	+	0.430201i
$65$	−0.375451	−	0.209936i	−0.0465690	−	0.0260393i
$66$	−5.14270	+	2.83060i	−0.633023	+	0.348422i
$67$	−4.07532	+	2.35289i	−0.497880	+	0.287451i	−0.727838	−	0.685750i	$-0.759475\pi$
$67$	−4.07532	+	2.35289i	−0.497880	+	0.287451i	0.229958	+	0.973201i	$0.426141\pi$
$68$	3.13943	−	2.49663i	0.380712	−	0.302760i
$69$	−9.30067	−	0.882098i	−1.11967	−	0.106192i
$70$	0.229647	−	0.0170525i	0.0274481	−	0.00203816i
$71$	2.07930	+	1.20048i	0.246768	+	0.142471i	0.618283	−	0.785955i	$-0.287828\pi$
$71$	2.07930	+	1.20048i	0.246768	+	0.142471i	−0.371516	+	0.928427i	$0.621162\pi$
$72$	7.20342	−	4.48450i	0.848931	−	0.528504i
$73$			9.66594i			1.13131i	0.824641	+	0.565656i	$0.191377\pi$
$73$			9.66594i			1.13131i	−0.824641	+	0.565656i	$0.808623\pi$
$74$	−11.6453	−	5.61786i	−1.35374	−	0.653062i
$75$	5.00464	−	7.03756i	0.577886	−	0.812627i
$76$	−9.32177	+	7.41312i	−1.06928	+	0.850344i
$77$	3.27087			0.372750
$78$	7.61883	+	4.46693i	0.862663	+	0.505780i
$79$			4.53066i			0.509739i	0.966975	+	0.254870i	$0.0820325\pi$
$79$			4.53066i			0.509739i	−0.966975	+	0.254870i	$0.917967\pi$
$80$	−0.325542	+	0.348941i	−0.0363967	+	0.0390127i
$81$	−7.06021	+	5.58153i	−0.784468	+	0.620170i
$82$	−6.27363	−	3.02648i	−0.692807	−	0.334219i
$83$	−13.8145			−1.51634			−0.758169	−	0.652058i	$-0.773906\pi$
$83$	−13.8145			−1.51634			−0.758169	+	0.652058i	$0.773906\pi$
$84$	−4.72115	+	0.253669i	−0.515119	+	0.0276775i
$85$	0.119636	−	0.207216i	0.0129764	−	0.0224758i
$86$	−0.0743332	−	1.00105i	−0.00801555	−	0.107946i
$87$	−9.90808	−	0.939707i	−1.06226	−	0.100747i
$88$	−4.97830	+	4.60030i	−0.530688	+	0.490394i
$89$	4.65921	+	8.06999i	0.493876	+	0.855418i	0.999975	−	0.00705746i	$-0.00224648\pi$
$89$	4.65921	+	8.06999i	0.493876	+	0.855418i	−0.506099	+	0.862475i	$0.668913\pi$
$90$	0.301711	−	0.406417i	0.0318031	−	0.0428401i
$91$	−2.51889	−	4.22748i	−0.264051	−	0.443160i
$92$	−10.6694	+	1.59330i	−1.11236	+	0.166113i
$93$	5.65836	−	7.95682i	0.586744	−	0.825084i
$94$	−3.09274	−	4.54285i	−0.318992	−	0.468560i
$95$	−0.355231	+	0.615279i	−0.0364460	+	0.0631263i
$96$	6.82887	−	7.02613i	0.696969	−	0.717102i
$97$	−3.05451	−	1.76352i	−0.310138	−	0.179058i	0.336850	−	0.941558i	$-0.390638\pi$
$97$	−3.05451	−	1.76352i	−0.310138	−	0.179058i	−0.646988	+	0.762500i	$0.723972\pi$
$98$	−6.54348	−	3.15666i	−0.660992	−	0.318871i
$99$	4.70119	−	5.43951i	0.472487	−	0.546692i
$100$	3.65564	−	9.27727i	0.365564	−	0.927727i
$101$	8.02999	+	13.9084i	0.799014	+	1.38393i	0.920259	+	0.391311i	$0.127978\pi$
$101$	8.02999	+	13.9084i	0.799014	+	1.38393i	−0.121245	+	0.992623i	$0.538689\pi$
$102$	−2.54275	+	4.20335i	−0.251770	+	0.416194i
$103$			12.4174i			1.22352i	0.791044	+	0.611759i	$0.209538\pi$
$103$			12.4174i			1.22352i	−0.791044	+	0.611759i	$0.790462\pi$
$104$	9.77950	+	2.89159i	0.958959	+	0.283544i
$105$	−0.256471	+	0.117325i	−0.0250291	+	0.0114498i
$106$	5.63593	−	3.83690i	0.547410	−	0.372672i
$107$	−12.7438	+	7.35762i	−1.23199	+	0.711288i	−0.967444	−	0.253086i	$-0.918555\pi$
$107$	−12.7438	+	7.35762i	−1.23199	+	0.711288i	−0.264543	+	0.964374i	$0.585221\pi$
$108$	−6.36381	+	8.21596i	−0.612358	+	0.790581i
$109$	8.22718			0.788021			0.394010	−	0.919106i	$-0.371087\pi$
$109$	8.22718			0.788021			0.394010	+	0.919106i	$0.371087\pi$
$110$	−0.175687	+	0.364182i	−0.0167511	+	0.0347234i
$111$	15.7647	+	1.49516i	1.49632	+	0.141914i
$112$	−5.22119	+	1.59497i	−0.493356	+	0.150710i
$113$	9.32277	+	5.38251i	0.877013	+	0.506344i	0.869672	−	0.493629i	$-0.164330\pi$
$113$	9.32277	+	5.38251i	0.877013	+	0.506344i	0.00734049	+	0.999973i	$0.497663\pi$
$114$	7.55007	−	12.4808i	0.707129	−	1.16894i
$115$	−0.557295	+	0.321755i	−0.0519681	+	0.0300038i
$116$	−11.3662	+	1.69735i	−1.05532	+	0.157595i
$117$	−10.6508	−	1.88716i	−0.984663	−	0.174468i
$118$	0.889810	+	11.9831i	0.0819137	+	1.10314i
$119$	2.37056	−	1.36864i	0.217308	−	0.125463i
$120$	0.225341	−	0.539284i	0.0205707	−	0.0492297i
$121$	2.62836	−	4.55246i	0.238942	−	0.413860i
$122$	2.17119	−	0.161222i	0.196570	−	0.0145964i
$123$	8.49284	+	0.805482i	0.765773	+	0.0726279i
$124$	4.13315	−	10.4891i	0.371168	−	0.941949i
$125$		−	1.19135i		−	0.106557i
$126$	5.31385	−	2.30072i	0.473396	−	0.204964i
$127$	11.1556	−	6.44067i	0.989896	−	0.571517i	0.0846527	−	0.996411i	$-0.473022\pi$
$127$	11.1556	−	6.44067i	0.989896	−	0.571517i	0.905243	+	0.424894i	$0.139689\pi$
$128$	5.70347	−	9.77090i	0.504121	−	0.863633i
$129$	0.511430	+	1.11798i	0.0450289	+	0.0984327i
$130$	0.605989	−	0.0533873i	0.0531487	−	0.00468238i
$131$		−	6.86179i		−	0.599517i	−0.954015	−	0.299759i	$-0.903094\pi$
$131$		−	6.86179i		−	0.599517i	0.954015	−	0.299759i	$-0.0969061\pi$
$132$	3.75916	−	7.40189i	0.327193	−	0.644252i
$133$	−7.03879	+	4.06385i	−0.610340	+	0.352380i
$134$	2.89156	−	5.99396i	0.249793	−	0.517799i
$135$	−0.173510	+	0.595148i	−0.0149334	+	0.0512221i
$136$	−1.68309	+	5.41715i	−0.144324	+	0.464517i
$137$	8.09347	−	14.0183i	0.691472	−	1.19766i	−0.279884	−	0.960034i	$-0.590296\pi$
$137$	8.09347	−	14.0183i	0.691472	−	1.19766i	0.971356	−	0.237631i	$-0.0763708\pi$
$138$	11.5747	−	6.37083i	0.985303	−	0.542321i
$139$	3.81522	−	6.60816i	0.323603	−	0.560497i	−0.657626	−	0.753345i	$-0.728439\pi$
$139$	3.81522	−	6.60816i	0.323603	−	0.560497i	0.981229	+	0.192848i	$0.0617724\pi$
$140$	−0.254891	+	0.202701i	−0.0215422	+	0.0171314i
$141$	5.48526	+	3.90074i	0.461942	+	0.328502i
$142$	−3.38616	+	0.251440i	−0.284160	+	0.0211004i
$143$	8.63993	−	0.118836i	0.722508	−	0.00993760i
$144$	−4.85191	+	10.9754i	−0.404326	+	0.914615i
$145$	−0.593692	+	0.342768i	−0.0493034	+	0.0284653i
$146$	−7.69273	−	11.2997i	−0.636655	−	0.935168i
$147$	8.85814	+	0.840129i	0.730607	+	0.0692926i
$148$	18.0846	−	2.70065i	1.48655	−	0.221992i
$149$	9.16688	+	5.29250i	0.750980	+	0.433579i	0.826048	−	0.563600i	$-0.190584\pi$
$149$	9.16688	+	5.29250i	0.750980	+	0.433579i	−0.0750678	+	0.997178i	$0.523917\pi$
$150$	−0.249614	+	12.2100i	−0.0203809	+	0.996945i
$151$	−17.8395			−1.45176			−0.725879	−	0.687822i	$-0.758567\pi$
$151$	−17.8395			−1.45176			−0.725879	+	0.687822i	$0.758567\pi$
$152$	4.99753	−	16.0849i	0.405353	−	1.30466i
$153$	1.13110	−	5.90942i	0.0914442	−	0.477748i
$154$	−3.82371	+	2.60315i	−0.308123	+	0.209768i
$155$		−	0.672522i		−	0.0540183i
$156$	−12.4616	+	0.841589i	−0.997727	+	0.0673811i
$157$			19.0939i			1.52386i	0.647659	+	0.761931i	$0.275748\pi$
$157$			19.0939i			1.52386i	−0.647659	+	0.761931i	$0.724252\pi$
$158$	−3.60577	−	5.29643i	−0.286859	−	0.421361i
$159$	−4.83932	+	6.80509i	−0.383783	+	0.539679i
$160$	0.102857	−	0.667004i	0.00813160	−	0.0527313i
$161$	−7.36174			−0.580187
$162$	3.81142	−	12.1439i	0.299453	−	0.954111i
$163$	5.77541	+	3.33443i	0.452365	+	0.261173i	0.708829	−	0.705381i	$-0.249224\pi$
$163$	5.77541	+	3.33443i	0.452365	+	0.261173i	−0.256463	+	0.966554i	$0.582557\pi$
$164$	9.74266	−	1.45491i	0.760774	−	0.113609i
$165$	0.0467580	−	0.493007i	0.00364010	−	0.0383805i
$166$	16.1494	−	10.9944i	1.25344	−	0.853330i
$167$	−7.79054	+	4.49787i	−0.602850	+	0.348056i	−0.770162	−	0.637848i	$-0.779825\pi$
$167$	−7.79054	+	4.49787i	−0.602850	+	0.348056i	0.167312	+	0.985904i	$0.446491\pi$
$168$	5.31723	−	4.05391i	0.410233	−	0.312766i
$169$	−6.80718	−	11.0753i	−0.523630	−	0.851946i
$170$	0.0250577	+	0.337454i	0.00192184	+	0.0258815i
$171$	−3.35853	+	17.5466i	−0.256833	+	1.34182i
$172$	0.883592	+	1.11109i	0.0673733	+	0.0847197i
$173$	3.01904	−	5.22913i	0.229533	−	0.397563i	−0.728137	−	0.685432i	$-0.759613\pi$
$173$	3.01904	−	5.22913i	0.229533	−	0.397563i	0.957670	+	0.287869i	$0.0929467\pi$
$174$	12.3306	−	6.78690i	0.934782	−	0.514514i
$175$	3.40240	−	5.89312i	0.257197	−	0.445478i
$176$	2.15853	−	9.33987i	0.162706	−	0.704019i
$177$	−6.12210	−	13.3829i	−0.460165	−	1.00592i
$178$	−11.8693	−	5.72591i	−0.889641	−	0.429175i
$179$	5.41835	−	3.12828i	0.404986	−	0.233819i	−0.283647	−	0.958929i	$-0.591544\pi$
$179$	5.41835	−	3.12828i	0.404986	−	0.233819i	0.688633	+	0.725110i	$0.258211\pi$
$180$	−0.0292556	+	0.715229i	−0.00218058	+	0.0533100i
$181$		−	16.1268i		−	1.19869i	−0.800489	−	0.599347i	$-0.795427\pi$
$181$		−	16.1268i		−	1.19869i	0.800489	−	0.599347i	$-0.204573\pi$
$182$	6.30911	+	2.93733i	0.467662	+	0.217729i
$183$	−2.42480	+	1.10925i	−0.179247	+	0.0819979i
$184$	11.2047	−	10.3539i	0.826019	−	0.763300i
$185$	0.944619	−	0.545376i	0.0694497	−	0.0400968i
$186$	−0.282219	+	13.8049i	−0.0206933	+	1.01223i
$187$			4.80636i			0.351476i
$188$	7.23095	+	2.84930i	0.527371	+	0.207807i
$189$	−5.12327	+	4.90384i	−0.372663	+	0.356702i
$190$	−0.0744028	−	1.00199i	−0.00539774	−	0.0726918i
$191$	1.29050	−	2.23522i	0.0933776	−	0.161735i	−0.815553	−	0.578683i	$-0.803567\pi$
$191$	1.29050	−	2.23522i	0.0933776	−	0.161735i	0.908930	+	0.416948i	$0.136900\pi$
$192$	−2.39127	+	13.6485i	−0.172575	+	0.984996i
$193$	−6.29813	+	3.63622i	−0.453349	+	0.261741i	−0.709244	−	0.704964i	$-0.750963\pi$
$193$	−6.29813	+	3.63622i	−0.453349	+	0.261741i	0.255895	+	0.966705i	$0.417630\pi$
$194$	4.97429	−	0.369367i	0.357134	−	0.0265190i
$195$	−0.673202	+	0.319230i	−0.0482090	+	0.0228605i
$196$	10.1617	−	1.51749i	0.725837	−	0.108392i
$197$	−22.9762	+	13.2653i	−1.63699	+	0.945114i	−0.655123	+	0.755522i	$0.727383\pi$
$197$	−22.9762	+	13.2653i	−1.63699	+	0.945114i	−0.981863	+	0.189592i	$0.939284\pi$
$198$	−1.16669	+	10.1004i	−0.0829133	+	0.717803i
$199$	20.0773	+	11.5916i	1.42324	+	0.821708i	0.996574	−	0.0827016i	$-0.0263548\pi$
$199$	20.0773	+	11.5916i	1.42324	+	0.821708i	0.426665	+	0.904410i	$0.359688\pi$
$200$	3.10988	+	13.7547i	0.219902	+	0.972604i
$201$	−0.769574	+	8.11423i	−0.0542816	+	0.572334i
$202$	−20.4563	−	9.86840i	−1.43930	−	0.694338i
$203$	−7.84253			−0.550438
$204$	−0.372752	−	6.93747i	−0.0260979	−	0.485720i
$205$	0.508890	−	0.293808i	0.0355424	−	0.0205204i
$206$	−9.88247	−	14.5161i	−0.688544	−	1.01139i
$207$	−10.5810	+	12.2427i	−0.735428	+	0.850928i
$208$	−13.7337	+	4.40278i	−0.952263	+	0.305278i
$209$		−	14.2713i		−	0.987168i
$210$	0.206446	−	0.341271i	0.0142461	−	0.0235499i
$211$	0.328697	+	0.569319i	0.0226284	+	0.0391936i	0.877118	−	0.480275i	$-0.159463\pi$
$211$	0.328697	+	0.569319i	0.0226284	+	0.0391936i	−0.854489	+	0.519469i	$0.826130\pi$
$212$	−3.53489	+	8.97082i	−0.242777	+	0.616119i
$213$	3.78169	−	1.72997i	0.259117	−	0.118535i
$214$	9.04210	−	18.7435i	0.618105	−	1.28128i
$215$	0.0733369	+	0.0423411i	0.00500153	+	0.00288764i
$216$	0.900673	−	14.6693i	0.0612830	−	0.998120i
$217$	3.84683	−	6.66290i	0.261140	−	0.452307i
$218$	−9.61774	+	6.54768i	−0.651395	+	0.443465i
$219$	13.6438	+	9.70252i	0.921960	+	0.655635i
$220$	−0.0844570	−	0.565558i	−0.00569409	−	0.0381299i
$221$	6.21205	−	3.70137i	0.417868	−	0.248981i
$222$	−19.6192	+	10.7986i	−1.31675	+	0.724754i
$223$	−5.70473	−	9.88088i	−0.382017	−	0.661673i	0.609333	−	0.792914i	$-0.291437\pi$
$223$	−5.70473	−	9.88088i	−0.382017	−	0.661673i	−0.991350	+	0.131241i	$0.958104\pi$
$224$	4.83431	−	6.01989i	0.323006	−	0.402220i
$225$	−4.91015	−	14.1284i	−0.327343	−	0.941892i
$226$	−15.1822	+	1.12736i	−1.00991	+	0.0749908i
$227$	−8.68945	+	15.0506i	−0.576739	+	0.998941i	0.419111	+	0.907935i	$0.362342\pi$
$227$	−8.68945	+	15.0506i	−0.576739	+	0.998941i	−0.995850	+	0.0910063i	$0.970992\pi$
$228$	1.10680	+	20.5991i	0.0732995	+	1.36421i
$229$	5.42276			0.358346			0.179173	−	0.983818i	$-0.442658\pi$
$229$	5.42276			0.358346			0.179173	+	0.983818i	$0.442658\pi$
$230$	0.395418	−	0.819666i	0.0260731	−	0.0540472i
$231$	3.28324	−	4.61692i	0.216022	−	0.303771i
$232$	11.9364	−	11.0301i	0.783665	−	0.724162i
$233$		−	10.1875i		−	0.667404i	−0.942679	−	0.333702i	$-0.891702\pi$
$233$		−	10.1875i		−	0.667404i	0.942679	−	0.333702i	$-0.108298\pi$
$234$	13.9529	−	6.27037i	0.912127	−	0.409907i
$235$	0.463622			0.0302433
$236$	−10.5771	−	13.3004i	−0.688510	−	0.865780i
$237$	6.39516	+	4.54781i	0.415410	+	0.295412i
$238$	−1.68198	+	3.48660i	−0.109027	+	0.226002i
$239$			18.3272i			1.18549i	0.805391	+	0.592744i	$0.201955\pi$
$239$			18.3272i			1.18549i	−0.805391	+	0.592744i	$0.798045\pi$
$240$	0.165766	+	0.809773i	0.0107001	+	0.0522707i
$241$	−3.43169	−	1.98129i	−0.221055	−	0.127626i	0.385384	−	0.922756i	$-0.374069\pi$
$241$	−3.43169	−	1.98129i	−0.221055	−	0.127626i	−0.606439	+	0.795130i	$0.707402\pi$
$242$	0.550507	+	7.41372i	0.0353880	+	0.476572i
$243$	0.791560	+	15.5683i	0.0507786	+	0.998710i
$244$	−2.40986	+	1.91643i	−0.154275	+	0.122687i
$245$	0.530780	−	0.306446i	0.0339103	−	0.0195781i
$246$	−10.5693	+	5.81748i	−0.673877	+	0.370909i
$247$	−18.4452	+	10.9903i	−1.17364	+	0.699297i
$248$	3.51611	+	15.5514i	0.223273	+	0.987513i
$249$	−13.8668	+	19.4996i	−0.878771	+	1.23573i
$250$	0.948145	+	1.39271i	0.0599659	+	0.0880826i
$251$	−16.1695	−	9.33547i	−1.02061	−	0.589250i	−0.106330	−	0.994331i	$-0.533910\pi$
$251$	−16.1695	−	9.33547i	−1.02061	−	0.589250i	−0.914281	+	0.405081i	$0.867243\pi$
$252$	−4.38095	+	6.91867i	−0.275974	+	0.435835i
$253$	6.46320	−	11.1946i	0.406338	−	0.703798i
$254$	−7.91521	+	16.4075i	−0.496644	+	1.02950i
$255$	−0.172403	−	0.376871i	−0.0107963	−	0.0236006i
$256$	1.10878	+	15.9615i	0.0692991	+	0.997596i
$257$	19.2368	−	11.1064i	1.19996	−	0.692795i	0.239411	−	0.970918i	$-0.423046\pi$
$257$	19.2368	−	11.1064i	1.19996	−	0.692795i	0.960545	+	0.278123i	$0.0897123\pi$
$258$	−1.48763	−	0.899915i	−0.0926156	−	0.0560263i
$259$	12.4782			0.775357
$260$	−0.665924	+	0.544693i	−0.0412989	+	0.0337804i
$261$	−11.2720	+	13.0423i	−0.697719	+	0.807297i
$262$	5.46102	+	8.02157i	0.337383	+	0.495574i
$263$	−14.1937	−	24.5842i	−0.875221	−	1.51593i	−0.856527	−	0.516103i	$-0.827382\pi$
$263$	−14.1937	−	24.5842i	−0.875221	−	1.51593i	−0.0186946	−	0.999825i	$-0.505951\pi$
$264$	1.49633	+	11.6447i	0.0920925	+	0.716683i
$265$			0.575176i			0.0353328i
$266$	4.99423	−	10.3526i	0.306216	−	0.634759i
$267$	16.0679	+	1.52392i	0.983339	+	0.0932623i
$268$	1.39005	+	9.30833i	0.0849108	+	0.568597i
$269$	13.5230	−	23.4225i	0.824511	−	1.42809i	−0.0777817	−	0.996970i	$-0.524784\pi$
$269$	13.5230	−	23.4225i	0.824511	−	1.42809i	0.902293	−	0.431124i	$-0.141883\pi$
$270$	−0.270817	−	0.833829i	−0.0164814	−	0.0507452i
$271$	−11.1921	−	19.3853i	−0.679871	−	1.17757i	−0.975019	−	0.222120i	$-0.928702\pi$
$271$	−11.1921	−	19.3853i	−0.679871	−	1.17757i	0.295148	−	0.955452i	$-0.404631\pi$
$272$	−2.34372	−	7.67226i	−0.142109	−	0.465199i
$273$	−8.49563	−	0.687998i	−0.514179	−	0.0416395i
$274$	1.69517	+	22.8289i	0.102409	+	1.37915i
$275$	5.97423	+	10.3477i	0.360259	+	0.623988i
$276$	−8.46076	+	16.6595i	−0.509278	+	1.00278i
$277$	−28.0636	−	16.2025i	−1.68618	−	0.973516i	−0.957398	−	0.288770i	$-0.906754\pi$
$277$	−28.0636	−	16.2025i	−1.68618	−	0.973516i	−0.728781	−	0.684746i	$-0.759913\pi$
$278$	0.799094	+	10.7615i	0.0479265	+	0.645429i
$279$	−5.55152	−	15.9739i	−0.332361	−	0.956331i
$280$	0.136650	−	0.439819i	0.00816642	−	0.0262842i
$281$	1.92218			0.114667			0.0573337	−	0.998355i	$-0.481740\pi$
$281$	1.92218			0.114667			0.0573337	+	0.998355i	$0.481740\pi$
$282$	−9.51682	−	0.194555i	−0.566718	−	0.0115856i
$283$	13.6728	+	23.6820i	0.812764	+	1.40775i	0.910922	+	0.412578i	$0.135372\pi$
$283$	13.6728	+	23.6820i	0.812764	+	1.40775i	−0.0981576	+	0.995171i	$0.531295\pi$
$284$	3.75838	−	2.98885i	0.223019	−	0.177355i
$285$	0.511908	+	1.11903i	0.0303228	+	0.0662854i
$286$	−10.0057	+	7.01509i	−0.591648	+	0.414811i
$287$	6.72233			0.396806
$288$	−3.06288	−	16.6919i	−0.180482	−	0.983578i
$289$	−6.48886	−	11.2390i	−0.381697	−	0.661119i
$290$	0.421242	−	0.873198i	0.0247362	−	0.0512759i
$291$	−5.55533	+	2.54133i	−0.325659	+	0.148976i
$292$	17.9859	+	7.08722i	1.05255	+	0.414748i
$293$	−15.1710	−	8.75898i	−0.886299	−	0.511705i	−0.0135687	−	0.999908i	$-0.504319\pi$
$293$	−15.1710	−	8.75898i	−0.886299	−	0.511705i	−0.872730	+	0.488203i	$0.837653\pi$
$294$	−11.0240	+	6.06771i	−0.642931	+	0.353876i
$295$	−0.877884	−	0.506846i	−0.0511124	−	0.0295097i
$296$	−18.9920	+	17.5499i	−1.10389	+	1.02007i
$297$	−2.95906	−	12.0960i	−0.171702	−	0.701879i
$298$	−14.9284	+	1.10851i	−0.864776	+	0.0642141i
$299$	−19.4459	+	0.267465i	−1.12459	+	0.0154679i
$300$	−9.42567	−	14.4724i	−0.544191	−	0.835566i
$301$	0.484382	+	0.838974i	0.0279193	+	0.0483576i
$302$	20.8547	−	14.1977i	1.20006	−	0.816988i
$303$	27.6924	+	2.62642i	1.59089	+	0.150884i
$304$	6.95911	+	22.7809i	0.399132	+	1.30657i
$305$	−0.0918341	+	0.159061i	−0.00525841	+	0.00910783i
$306$	3.38078	+	7.80842i	0.193266	+	0.446378i
$307$			16.7637i			0.956757i	0.878154	+	0.478379i	$0.158775\pi$
$307$			16.7637i			0.956757i	−0.878154	+	0.478379i	$0.841225\pi$
$308$	2.39825	−	6.08627i	0.136653	−	0.346797i
$309$	17.5275	+	12.4644i	0.997103	+	0.709072i
$310$	0.535233	+	0.786192i	0.0303992	+	0.0446527i
$311$	17.4325			0.988505			0.494253	−	0.869318i	$-0.335442\pi$
$311$	17.4325			0.988505			0.494253	+	0.869318i	$0.335442\pi$
$312$	13.8981	−	10.9015i	0.786824	−	0.617177i
$313$	−5.60731			−0.316944			−0.158472	−	0.987364i	$-0.550657\pi$
$313$	−5.60731			−0.316944			−0.158472	+	0.987364i	$0.550657\pi$
$314$	−15.1961	−	22.3212i	−0.857564	−	1.25966i
$315$	−0.0918343	+	0.479786i	−0.00517428	+	0.0270329i
$316$	8.43043	+	3.32195i	0.474249	+	0.186874i
$317$		−	16.3453i		−	0.918046i	−0.888425	−	0.459023i	$-0.848200\pi$
$317$		−	16.3453i		−	0.918046i	0.888425	−	0.459023i	$-0.151800\pi$
$318$	0.241368	−	11.8067i	0.0135353	−	0.662087i
$319$	6.88531	−	11.9257i	0.385503	−	0.667711i
$320$	0.410599	+	0.861601i	0.0229532	+	0.0481650i
$321$	−2.40650	+	25.3737i	−0.134318	+	1.41622i
$322$	8.60603	−	5.85891i	0.479595	−	0.326504i
$323$	−5.97160	−	10.3431i	−0.332269	−	0.575506i
$324$	5.20917	+	17.2298i	0.289399	+	0.957209i
$325$	8.77326	−	15.6902i	0.486653	−	0.870335i
$326$	−9.40531	+	0.698393i	−0.520912	+	0.0386804i
$327$	8.25832	−	11.6129i	0.456686	−	0.642195i
$328$	−10.2315	+	9.45460i	−0.564938	+	0.522043i
$329$	4.59325	+	2.65192i	0.253234	+	0.146205i
$330$	0.337703	+	0.613548i	0.0185899	+	0.0337747i
$331$	−5.22085	−	3.01426i	−0.286964	−	0.165679i	0.349608	−	0.936896i	$-0.386315\pi$
$331$	−5.22085	−	3.01426i	−0.286964	−	0.165679i	−0.636572	+	0.771217i	$0.719648\pi$
$332$	−10.1290	+	25.7053i	−0.555901	+	1.41076i
$333$	17.9348	−	20.7515i	0.982821	−	1.13717i
$334$	5.52763	−	11.4583i	0.302458	−	0.626969i
$335$	0.280710	+	0.486204i	0.0153368	+	0.0265642i
$336$	−2.98960	+	8.97087i	−0.163096	+	0.489401i
$337$	−7.45794			−0.406260			−0.203130	−	0.979152i	$-0.565111\pi$
$337$	−7.45794			−0.406260			−0.203130	+	0.979152i	$0.565111\pi$
$338$	16.7721	+	7.52969i	0.912283	+	0.409561i
$339$	16.9556	−	7.75650i	0.920903	−	0.421275i
$340$	−0.297859	−	0.374548i	−0.0161537	−	0.0203127i
$341$	6.75460	+	11.6993i	0.365782	+	0.633553i
$342$	−10.0384	−	23.1852i	−0.542815	−	1.25371i
$343$	16.5654			0.894447
$344$	−1.91721	−	0.595670i	−0.103369	−	0.0321164i
$345$	−0.105238	+	1.10961i	−0.00566584	+	0.0597395i
$346$	0.632334	+	8.51569i	0.0339945	+	0.457806i
$347$	18.5065	+	10.6847i	0.993480	+	0.573586i	0.906313	−	0.422608i	$-0.138885\pi$
$347$	18.5065	+	10.6847i	0.993480	+	0.573586i	0.0871670	+	0.996194i	$0.472219\pi$
$348$	−9.01332	+	17.7475i	−0.483165	+	0.951364i
$349$	11.5682	+	20.0367i	0.619233	+	1.07254i	0.989626	+	0.143667i	$0.0458895\pi$
$349$	11.5682	+	20.0367i	0.619233	+	1.07254i	−0.370394	+	0.928875i	$0.620777\pi$
$350$	0.712628	+	9.59701i	0.0380915	+	0.512982i
$351$	−13.3549	+	13.1396i	−0.712829	+	0.701337i
$352$	4.90985	+	12.6364i	0.261696	+	0.673521i
$353$	10.6121	+	18.3808i	0.564827	+	0.978309i	0.997066	+	0.0765500i	$0.0243905\pi$
$353$	10.6121	+	18.3808i	0.564827	+	0.978309i	−0.432239	+	0.901759i	$0.642276\pi$
$354$	17.8077	+	10.7725i	0.946470	+	0.572552i
$355$	0.143223	−	0.248070i	0.00760150	−	0.0131662i
$356$	18.4325	−	2.75259i	0.976918	−	0.145887i
$357$	0.447650	−	4.71993i	0.0236921	−	0.249805i
$358$	−3.84448	+	7.96927i	−0.203187	+	0.421189i
$359$		−	20.0575i		−	1.05859i	−0.848437	−	0.529297i	$-0.822456\pi$
$359$		−	20.0575i		−	1.05859i	0.848437	−	0.529297i	$-0.177544\pi$
$360$	−0.535021	−	0.859400i	−0.0281981	−	0.0452944i
$361$	8.23122	+	14.2569i	0.433222	+	0.750363i
$362$	12.8346	+	18.8525i	0.674574	+	0.990867i
$363$	−3.78762	−	8.27970i	−0.198798	−	0.434571i
$364$	−9.71317	+	1.58736i	−0.509109	+	0.0832005i
$365$	1.15319			0.0603607
$366$	1.95184	−	3.22653i	0.102024	−	0.168654i
$367$	−7.37242	+	4.25647i	−0.384837	+	0.222186i	−0.679921	−	0.733286i	$-0.737986\pi$
$367$	−7.37242	+	4.25647i	−0.384837	+	0.222186i	0.295084	+	0.955471i	$0.404653\pi$
$368$	−4.85822	+	21.0213i	−0.253252	+	1.09581i
$369$	9.66194	−	11.1794i	0.502981	−	0.581974i
$370$	−0.670236	+	1.38934i	−0.0348439	+	0.0722283i
$371$	−3.29001	+	5.69846i	−0.170809	+	0.295849i
$372$	−10.6569	−	16.3629i	−0.552533	−	0.848375i
$373$	−3.48849	−	2.01408i	−0.180627	−	0.104285i	0.406960	−	0.913446i	$-0.366589\pi$
$373$	−3.48849	−	2.01408i	−0.180627	−	0.104285i	−0.587587	+	0.809161i	$0.699922\pi$
$374$	−3.82519	−	5.61873i	−0.197796	−	0.290538i
$375$	−1.68162	−	1.19586i	−0.0868386	−	0.0617537i
$376$	−10.7208	+	2.42392i	−0.552881	+	0.125004i
$377$	−20.7159	+	0.284933i	−1.06692	+	0.0146748i
$378$	2.08643	−	9.81009i	0.107315	−	0.504577i
$379$	20.0015	−	11.5479i	1.02741	−	0.593175i	0.111167	−	0.993802i	$-0.464541\pi$
$379$	20.0015	−	11.5479i	1.02741	−	0.593175i	0.916241	+	0.400627i	$0.131208\pi$
$380$	0.884419	+	1.11213i	0.0453698	+	0.0570510i
$381$	2.10659	−	22.2114i	0.107924	−	1.13793i
$382$	0.270295	+	3.64008i	0.0138295	+	0.186242i
$383$	−23.6645	−	13.6627i	−1.20920	−	0.698131i	−0.246614	−	0.969114i	$-0.579318\pi$
$383$	−23.6645	−	13.6627i	−1.20920	−	0.698131i	−0.962584	+	0.270983i	$0.912651\pi$
$384$	−8.06685	−	17.8585i	−0.411660	−	0.911338i
$385$		−	0.390229i		−	0.0198879i
$386$	4.46871	−	9.26324i	0.227451	−	0.471487i
$387$	2.09143	+	0.400313i	0.106313	+	0.0203491i
$388$	−5.52109	+	4.39064i	−0.280291	+	0.222901i
$389$	−26.8012			−1.35888			−0.679438	−	0.733733i	$-0.737776\pi$
$389$	−26.8012			−1.35888			−0.679438	+	0.733733i	$0.737776\pi$
$390$	0.532925	−	0.908961i	0.0269857	−	0.0460270i
$391$		−	10.8177i		−	0.547074i
$392$	−10.6716	+	9.86128i	−0.538995	+	0.498070i
$393$	−9.68562	−	6.88776i	−0.488575	−	0.347441i
$394$	16.3023	−	33.7932i	0.821298	−	1.70248i
$395$	0.540528			0.0271969
$396$	−6.67460	−	12.7361i	−0.335411	−	0.640012i
$397$	−4.82003	+	8.34853i	−0.241910	+	0.419001i	−0.961258	−	0.275649i	$-0.911107\pi$
$397$	−4.82003	+	8.34853i	−0.241910	+	0.419001i	0.719348	+	0.694650i	$0.244441\pi$
$398$	−32.6960	+	2.42785i	−1.63890	+	0.121697i
$399$	−1.32919	+	14.0147i	−0.0665426	+	0.701612i
$400$	−14.5823	−	13.6045i	−0.729116	−	0.680224i
$401$	4.18561	+	7.24969i	0.209019	+	0.362032i	0.951406	−	0.307940i	$-0.0996395\pi$
$401$	4.18561	+	7.24969i	0.209019	+	0.362032i	−0.742387	+	0.669972i	$0.766306\pi$
$402$	−5.55814	−	10.0982i	−0.277215	−	0.503651i
$403$	9.91925	−	17.7397i	0.494113	−	0.883677i
$404$	31.7677	−	4.74399i	1.58050	−	0.236022i
$405$	0.665901	+	0.842315i	0.0330889	+	0.0418550i
$406$	9.16808	−	6.24155i	0.455004	−	0.309763i
$407$	−10.9552	+	18.9749i	−0.543027	+	0.940551i
$408$	5.95701	+	7.81338i	0.294916	+	0.386820i
$409$	−30.6518	−	17.6968i	−1.51563	−	0.875051i	−0.999832	−	0.0183420i	$-0.994161\pi$
$409$	−30.6518	−	17.6968i	−1.51563	−	0.875051i	−0.515800	−	0.856709i	$-0.672505\pi$
$410$	−0.361073	+	0.748473i	−0.0178321	+	0.0369644i
$411$	−11.6631	−	25.4955i	−0.575301	−	1.25760i
$412$	23.1056	+	9.10460i	1.13833	+	0.448552i
$413$	−5.79832	−	10.0430i	−0.285317	−	0.494183i
$414$	2.62588	−	22.7330i	0.129055	−	1.11726i
$415$			1.64813i			0.0809036i
$416$	12.5510	−	16.0771i	0.615364	−	0.788243i
$417$	−5.49795	−	12.0185i	−0.269236	−	0.588547i
$418$	11.3580	+	16.6835i	0.555536	+	0.816015i
$419$	14.0614	−	8.11836i	0.686945	−	0.396608i	−0.115522	−	0.993305i	$-0.536854\pi$
$419$	14.0614	−	8.11836i	0.686945	−	0.396608i	0.802466	+	0.596697i	$0.203521\pi$
$420$	0.0302638	+	0.563254i	0.00147672	+	0.0274840i
$421$	−28.0298			−1.36609			−0.683045	−	0.730376i	$-0.739345\pi$
$421$	−28.0298			−1.36609			−0.683045	+	0.730376i	$0.739345\pi$
$422$	−0.837351	−	0.403949i	−0.0407616	−	0.0196640i
$423$	11.0120	−	3.82710i	0.535423	−	0.186080i
$424$	−3.00716	−	13.3003i	−0.146040	−	0.645922i
$425$	8.65963	+	4.99964i	0.420054	+	0.242518i
$426$	−3.04406	+	5.03206i	−0.147485	+	0.243804i
$427$	−1.81966	+	1.05058i	−0.0880596	+	0.0508412i
$428$	4.34677	+	29.1077i	0.210109	+	1.40697i
$429$	8.50489	−	12.3148i	0.410620	−	0.594565i
$430$	−0.119430	+	0.00886829i	−0.00575942	+	0.000427667i
$431$	−0.314807	+	0.181754i	−0.0151637	+	0.00875478i	−0.507563	−	0.861615i	$-0.669453\pi$
$431$	−0.314807	+	0.181754i	−0.0151637	+	0.00875478i	0.492399	+	0.870370i	$0.336120\pi$
$432$	10.6218	+	17.8655i	0.511042	+	0.859556i
$433$	−10.5568	+	18.2848i	−0.507325	+	0.878713i	0.492639	+	0.870234i	$0.336032\pi$
$433$	−10.5568	+	18.2848i	−0.507325	+	0.878713i	−0.999964	+	0.00847907i	$0.997301\pi$
$434$	0.805713	+	10.8506i	0.0386755	+	0.520845i
$435$	−0.112111	+	1.18208i	−0.00537533	+	0.0566763i
$436$	6.03230	−	15.3087i	0.288895	−	0.733155i
$437$			32.1205i			1.53653i
$438$	−23.6717	−	0.483928i	−1.13108	−	0.0231230i
$439$	−18.7505	+	10.8256i	−0.894912	+	0.516678i	−0.875546	−	0.483135i	$-0.839498\pi$
$439$	−18.7505	+	10.8256i	−0.894912	+	0.516678i	−0.0193663	+	0.999812i	$0.506165\pi$
$440$	0.548837	+	0.593933i	0.0261648	+	0.0283147i
$441$	10.0775	−	11.6602i	0.479883	−	0.555249i
$442$	−4.31625	+	9.27089i	−0.205303	+	0.440971i
$443$			7.23483i			0.343737i	0.985120	+	0.171868i	$0.0549804\pi$
$443$			7.23483i			0.343737i	−0.985120	+	0.171868i	$0.945020\pi$
$444$	14.3410	−	28.2379i	0.680595	−	1.34011i
$445$	0.962787	−	0.555865i	0.0456405	−	0.0263505i
$446$	14.5327	+	7.01079i	0.688145	+	0.331970i
$447$	16.6721	−	7.62679i	0.788563	−	0.360735i
$448$	−0.860418	+	10.8848i	−0.0406509	+	0.514258i
$449$	−5.12694	+	8.88012i	−0.241955	+	0.419079i	−0.961271	−	0.275604i	$-0.911122\pi$
$449$	−5.12694	+	8.88012i	−0.241955	+	0.419079i	0.719316	+	0.694683i	$0.244455\pi$
$450$	16.9843	+	12.6086i	0.800646	+	0.594374i
$451$	−5.90183	+	10.2223i	−0.277906	+	0.481348i
$452$	16.8511	−	13.4008i	0.792609	−	0.630322i
$453$	−17.9070	+	25.1810i	−0.841346	+	1.18311i
$454$	−1.81999	−	24.5100i	−0.0854166	−	1.15031i
$455$	−0.504358	+	0.300514i	−0.0236446	+	0.0140883i
$456$	−17.6879	−	23.1999i	−0.828311	−	1.08644i
$457$	10.7284	−	6.19403i	0.501852	−	0.289745i	−0.227626	−	0.973749i	$-0.573096\pi$
$457$	10.7284	−	6.19403i	0.501852	−	0.289745i	0.729478	+	0.684004i	$0.239763\pi$
$458$	−6.33931	+	4.31575i	−0.296217	+	0.201662i
$459$	−7.20593	−	7.52837i	−0.336344	−	0.351394i
$460$	0.190088	+	1.27290i	0.00886288	+	0.0593494i
$461$	19.6931	+	11.3698i	0.917197	+	0.529544i	0.882740	−	0.469862i	$-0.155696\pi$
$461$	19.6931	+	11.3698i	0.917197	+	0.529544i	0.0344572	+	0.999406i	$0.489030\pi$
$462$	−0.163757	+	8.01028i	−0.00761865	+	0.372672i
$463$	−19.1612			−0.890494			−0.445247	−	0.895408i	$-0.646884\pi$
$463$	−19.1612			−0.890494			−0.445247	+	0.895408i	$0.646884\pi$
$464$	−5.17550	+	22.3941i	−0.240267	+	1.03962i
$465$	−0.949285	−	0.675068i	−0.0440220	−	0.0313055i
$466$	8.10780	+	11.9094i	0.375587	+	0.551691i
$467$		−	5.62089i		−	0.260104i	−0.991507	−	0.130052i	$-0.958486\pi$
$467$		−	5.62089i		−	0.260104i	0.991507	−	0.130052i	$-0.0415144\pi$
$468$	−11.3208	+	18.4347i	−0.523306	+	0.852145i
$469$			6.42265i			0.296570i
$470$	−0.541983	+	0.368978i	−0.0249998	+	0.0170197i
$471$	26.9516	+	19.1662i	1.24187	+	0.883131i
$472$	22.9501	+	7.13051i	1.05636	+	0.328208i
$473$	−1.70104			−0.0782139
$474$	−11.0955	−	0.226829i	−0.509633	−	0.0104186i
$475$	−25.7127	−	14.8452i	−1.17978	−	0.681145i
$476$	−0.808571	−	5.41452i	−0.0370608	−	0.248174i
$477$	4.74795	+	13.6617i	0.217394	+	0.625526i
$478$	−14.5859	−	21.4248i	−0.667142	−	0.979950i
$479$	8.90456	−	5.14105i	0.406860	−	0.234901i	−0.282580	−	0.959244i	$-0.591190\pi$
$479$	8.90456	−	5.14105i	0.406860	−	0.234901i	0.689440	+	0.724343i	$0.257857\pi$
$480$	−0.838250	−	0.814715i	−0.0382607	−	0.0371865i
$481$	32.9609	−	0.453355i	1.50289	−	0.0206712i
$482$	5.58854	−	0.414978i	0.254551	−	0.0189017i
$483$	−7.38961	+	10.3913i	−0.336239	+	0.472822i
$484$	−6.54383	−	8.22866i	−0.297447	−	0.374030i
$485$	−0.210396	+	0.364417i	−0.00955359	+	0.0165473i
$486$	−13.3156	−	17.5697i	−0.604006	−	0.796980i
$487$	−7.21480	+	12.4964i	−0.326934	+	0.566266i	−0.981902	−	0.189390i	$-0.939349\pi$
$487$	−7.21480	+	12.4964i	−0.326934	+	0.566266i	0.654968	+	0.755657i	$0.272682\pi$
$488$	1.29196	−	4.15826i	0.0584841	−	0.188235i
$489$	10.5039	−	4.80511i	0.475004	−	0.217295i
$490$	−0.376604	+	0.780667i	−0.0170132	+	0.0352669i
$491$	33.1043	−	19.1128i	1.49397	−	0.862547i	0.493999	−	0.869463i	$-0.335535\pi$
$491$	33.1043	−	19.1128i	1.49397	−	0.862547i	0.999976	+	0.00691567i	$0.00220135\pi$
$492$	7.72588	−	15.2125i	0.348310	−	0.685831i
$493$		−	11.5242i		−	0.519023i
$494$	12.8161	−	27.5277i	0.576621	−	1.23853i
$495$	−0.648959	−	0.560873i	−0.0291685	−	0.0252094i
$496$	−16.4871	−	15.3815i	−0.740293	−	0.690652i
$497$	2.83792	−	1.63847i	0.127298	−	0.0734956i
$498$	0.691626	−	33.8314i	0.0309925	−	1.51602i
$499$		−	27.9280i		−	1.25023i	−0.780534	−	0.625114i	$-0.785053\pi$
$499$		−	27.9280i		−	1.25023i	0.780534	−	0.625114i	$-0.214947\pi$
$500$	−2.21680	−	0.873515i	−0.0991383	−	0.0390648i
$501$	−1.47115	+	15.5115i	−0.0657260	+	0.693002i
$502$	26.3322	−	1.95530i	1.17526	−	0.0872695i
$503$	−8.63677	+	14.9593i	−0.385094	+	0.667003i	−0.991782	−	0.127937i	$-0.959164\pi$
$503$	−8.63677	+	14.9593i	−0.385094	+	0.667003i	0.606688	+	0.794940i	$0.292498\pi$
$504$	−0.384863	−	11.5747i	−0.0171432	−	0.515577i
$505$	1.65933	−	0.958015i	0.0738392	−	0.0426311i
$506$	1.35371	+	18.2305i	0.0601797	+	0.810445i
$507$	−22.4661	−	1.50867i	−0.997753	−	0.0670025i
$508$	−3.80504	−	25.4801i	−0.168821	−	1.13050i
$509$	−9.35481	+	5.40100i	−0.414645	+	0.239395i	−0.692783	−	0.721146i	$-0.743616\pi$
$509$	−9.35481	+	5.40100i	−0.414645	+	0.239395i	0.278139	+	0.960541i	$0.410282\pi$
$510$	0.501479	+	0.303361i	0.0222059	+	0.0134331i
$511$	11.4250	+	6.59625i	0.505414	+	0.291801i
$512$	−13.9993	−	17.7769i	−0.618689	−	0.785636i
$513$	21.3963	+	22.3537i	0.944668	+	0.986938i
$514$	−13.6491	+	28.2933i	−0.602035	+	1.24796i
$515$	1.48145			0.0652803
$516$	2.45527	−	0.131922i	0.108087	−	0.00580756i
$517$	−8.06524	+	4.65647i	−0.354709	+	0.204791i
$518$	−14.5873	+	9.93089i	−0.640927	+	0.436338i
$519$	−4.35061	−	9.51039i	−0.190970	−	0.417460i
$520$	0.344980	−	1.16674i	0.0151284	−	0.0511649i
$521$			3.13114i			0.137178i	0.997645	+	0.0685890i	$0.0218497\pi$
$521$			3.13114i			0.137178i	−0.997645	+	0.0685890i	$0.978150\pi$
$522$	2.79737	−	24.2176i	0.122438	−	1.05998i
$523$	−3.12985	−	5.42105i	−0.136859	−	0.237046i	0.789447	−	0.613818i	$-0.210367\pi$
$523$	−3.12985	−	5.42105i	−0.136859	−	0.237046i	−0.926306	+	0.376772i	$0.877034\pi$
$524$	−12.7681	−	5.03117i	−0.557776	−	0.219788i
$525$	−4.90304	−	10.7180i	−0.213986	−	0.467772i
$526$	36.1583	+	17.4433i	1.57658	+	0.760562i
$527$	9.79077	+	5.65270i	0.426493	+	0.246236i
$528$	−11.0168	−	12.4221i	−0.479445	−	0.540600i
$529$	−3.04674	+	5.27712i	−0.132467	+	0.229440i
$530$	−0.457759	−	0.672392i	−0.0198838	−	0.0292069i
$531$	−25.0356	−	4.79198i	−1.08645	−	0.207954i
$532$	2.40086	+	16.0771i	0.104090	+	0.697031i
$533$	17.7569	−	0.244234i	0.769137	−	0.0105790i
$534$	−19.9965	+	11.0063i	−0.865333	+	0.476289i
$535$	0.877798	+	1.52039i	0.0379505	+	0.0657322i
$536$	−9.03312	−	9.77535i	−0.390171	−	0.422231i
$537$	1.02319	−	10.7883i	0.0441538	−	0.465549i
$538$	2.83237	+	38.1438i	0.122112	+	1.64449i
$539$	−6.15569	+	10.6620i	−0.265144	+	0.459243i
$540$	0.980201	+	0.759231i	0.0421811	+	0.0326721i
$541$	13.2584			0.570024			0.285012	−	0.958524i	$-0.408002\pi$
$541$	13.2584			0.570024			0.285012	+	0.958524i	$0.408002\pi$
$542$	28.5117	+	13.7544i	1.22468	+	0.590804i
$543$	−22.7634	−	16.1878i	−0.976872	−	0.694686i
$544$	8.84590	+	7.10375i	0.379265	+	0.304571i
$545$		−	0.981540i		−	0.0420445i
$546$	10.4791	−	5.95705i	0.448465	−	0.254938i
$547$	7.11989			0.304424			0.152212	−	0.988348i	$-0.451360\pi$
$547$	7.11989			0.304424			0.152212	+	0.988348i	$0.451360\pi$
$548$	−20.1503	−	25.3384i	−0.860779	−	1.08240i
$549$	−0.868245	+	4.53613i	−0.0370558	+	0.193597i
$550$	−15.2193	−	7.34198i	−0.648952	−	0.313063i
$551$			34.2182i			1.45775i
$552$	−3.36778	−	26.2088i	−0.143342	−	1.11552i
$553$	5.35519	+	3.09182i	0.227726	+	0.131478i
$554$	45.7019	−	3.39360i	1.94169	−	0.144180i
$555$	0.178380	−	1.88080i	0.00757179	−	0.0798354i
$556$	−9.49876	−	11.9444i	−0.402837	−	0.506555i
$557$	29.3568	−	16.9492i	1.24389	−	0.718160i	0.274006	−	0.961728i	$-0.411651\pi$
$557$	29.3568	−	16.9492i	1.24389	−	0.718160i	0.969884	+	0.243568i	$0.0783180\pi$
$558$	19.2028	+	14.2556i	0.812919	+	0.603486i
$559$	1.30997	+	2.19854i	0.0554057	+	0.0929882i
$560$	0.190287	+	0.622912i	0.00804110	+	0.0263228i
$561$	6.78432	+	4.82455i	0.286434	+	0.203693i
$562$	−2.24706	+	1.52978i	−0.0947866	+	0.0645299i
$563$	1.07613	+	0.621306i	0.0453536	+	0.0261849i	0.522505	−	0.852636i	$-0.324997\pi$
$563$	1.07613	+	0.621306i	0.0453536	+	0.0261849i	−0.477152	+	0.878821i	$0.658331\pi$
$564$	11.2802	−	7.34661i	0.474982	−	0.309348i
$565$	0.642157	−	1.11225i	0.0270158	−	0.0467927i
$566$	−34.8313	−	16.8031i	−1.46407	−	0.706287i
$567$	1.77926	+	12.1540i	0.0747220	+	0.510422i
$568$	−2.01492	+	6.48516i	−0.0845441	+	0.272111i
$569$	10.6528	−	6.15040i	0.446589	−	0.257838i	−0.259800	−	0.965663i	$-0.583656\pi$
$569$	10.6528	−	6.15040i	0.446589	−	0.257838i	0.706389	+	0.707824i	$0.250323\pi$
$570$	−1.48902	−	0.900758i	−0.0623682	−	0.0377286i
$571$	−24.0389			−1.00599			−0.502997	−	0.864288i	$-0.667769\pi$
$571$	−24.0389			−1.00599			−0.502997	+	0.864288i	$0.667769\pi$
$572$	6.11381	−	16.1639i	0.255631	−	0.675847i
$573$	−1.85969	−	4.06526i	−0.0776897	−	0.169829i
$574$	−7.85853	+	5.35003i	−0.328009	+	0.223306i
$575$	−13.4462	−	23.2895i	−0.560746	−	0.971240i
$576$	16.8650	+	17.0755i	0.702707	+	0.711480i
$577$		−	34.5344i		−	1.43769i	−0.695172	−	0.718843i	$-0.744672\pi$
$577$		−	34.5344i		−	1.43769i	0.695172	−	0.718843i	$-0.255328\pi$
$578$	16.5303	+	7.97443i	0.687569	+	0.331693i
$579$	−1.18932	+	12.5400i	−0.0494266	+	0.521144i
$580$	0.202502	+	1.35604i	0.00840843	+	0.0563063i
$581$	−9.42731	+	16.3286i	−0.391111	+	0.677424i
$582$	4.47175	−	7.39213i	0.185360	−	0.306414i
$583$	−5.77689	−	10.0059i	−0.239254	−	0.414400i
$584$	−26.6663	+	6.02915i	−1.10346	+	0.249488i
$585$	−0.225147	+	1.27068i	−0.00930869	+	0.0525363i
$586$	24.7061	−	1.83456i	1.02060	−	0.0757848i
$587$	18.7413	+	32.4609i	0.773538	+	1.33981i	0.935613	+	0.353028i	$0.114848\pi$
$587$	18.7413	+	32.4609i	0.773538	+	1.33981i	−0.162075	+	0.986778i	$0.551819\pi$
$588$	8.05820	−	15.8668i	0.332315	−	0.654336i
$589$	−29.0713	−	16.7843i	−1.19786	−	0.691586i
$590$	1.42964	−	0.106158i	0.0588574	−	0.00437047i
$591$	−4.33877	+	45.7471i	−0.178473	+	1.88178i
$592$	8.23470	−	35.6311i	0.338444	−	1.46443i
$593$	−27.1783			−1.11608			−0.558040	−	0.829814i	$-0.688446\pi$
$593$	−27.1783			−1.11608			−0.558040	+	0.829814i	$0.688446\pi$
$594$	13.0859	+	11.7854i	0.536920	+	0.483562i
$595$	−0.163285	−	0.282818i	−0.00669403	−	0.0115944i
$596$	16.5693	−	13.1767i	0.678706	−	0.539740i
$597$	36.5152	−	16.7042i	1.49447	−	0.683656i
$598$	22.5198	−	15.7889i	0.920903	−	0.645656i
$599$	44.3738			1.81306			0.906532	−	0.422138i	$-0.138720\pi$
$599$	44.3738			1.81306			0.906532	+	0.422138i	$0.138720\pi$
$600$	22.5368	+	9.41706i	0.920061	+	0.384450i
$601$	21.2244	+	36.7618i	0.865762	+	1.49954i	0.866288	+	0.499545i	$0.166499\pi$
$601$	21.2244	+	36.7618i	0.865762	+	1.49954i	−0.000525868		1.00000i	$0.500167\pi$
$602$	−1.23396	−	0.595277i	−0.0502923	−	0.0242617i
$603$	10.6810	+	9.23122i	0.434964	+	0.375924i
$604$	−13.0802	+	33.1949i	−0.532226	+	1.35068i
$605$	−0.543129	−	0.313576i	−0.0220813	−	0.0127487i
$606$	−34.4633	+	18.9690i	−1.39998	+	0.770561i
$607$	−4.12102	−	2.37927i	−0.167267	−	0.0965716i	0.414030	−	0.910263i	$-0.364121\pi$
$607$	−4.12102	−	2.37927i	−0.167267	−	0.0965716i	−0.581296	+	0.813692i	$0.697454\pi$
$608$	−26.2657	−	21.0929i	−1.06522	−	0.855429i
$609$	−7.87221	+	11.0700i	−0.318998	+	0.448578i
$610$	−0.0192345	−	0.259033i	−0.000778784	−	0.0104879i
$611$	12.2293	+	6.83811i	0.494746	+	0.276640i
$612$	−10.1666	−	6.43758i	−0.410961	−	0.260224i
$613$	6.23475	+	10.7989i	0.251819	+	0.436163i	0.964027	−	0.265805i	$-0.0856379\pi$
$613$	6.23475	+	10.7989i	0.251819	+	0.436163i	−0.712208	+	0.701969i	$0.752305\pi$
$614$	−13.3416	−	19.5971i	−0.538422	−	0.790876i
$615$	0.0960976	−	1.01323i	0.00387503	−	0.0408575i
$616$	2.04021	+	9.02364i	0.0822024	+	0.363573i
$617$	−23.1708	+	40.1330i	−0.932822	+	1.61570i	−0.154350	+	0.988016i	$0.549328\pi$
$617$	−23.1708	+	40.1330i	−0.932822	+	1.61570i	−0.778472	+	0.627679i	$0.784005\pi$
$618$	−30.4098	−	0.621678i	−1.22326	−	0.0250076i
$619$			18.2414i			0.733182i	0.930382	+	0.366591i	$0.119475\pi$
$619$			18.2414i			0.733182i	−0.930382	+	0.366591i	$0.880525\pi$
$620$	−1.25140	−	0.493104i	−0.0502573	−	0.0198035i
$621$	6.65996	+	27.2244i	0.267255	+	1.09248i
$622$	−20.3789	+	13.8738i	−0.817120	+	0.556289i
$623$	12.7182			0.509544
$624$	−7.57106	+	23.8050i	−0.303085	+	0.952964i
$625$	24.7867			0.991468
$626$	6.55505	−	4.46263i	0.261993	−	0.178362i
$627$	−20.1444	−	14.3253i	−0.804490	−	0.572099i
$628$	35.5290	+	14.0000i	1.41776	+	0.558660i
$629$			18.3360i			0.731106i
$630$	−0.274486	−	0.633967i	−0.0109358	−	0.0252578i
$631$	16.2255	−	28.1034i	0.645928	−	1.11878i	−0.338158	−	0.941089i	$-0.609804\pi$
$631$	16.2255	−	28.1034i	0.645928	−	1.11878i	0.984086	−	0.177691i	$-0.0568627\pi$
$632$	−12.4991	+	2.82601i	−0.497189	+	0.112413i
$633$	1.13355	+	0.107509i	0.0450547	+	0.00427310i
$634$	13.0086	+	19.1080i	0.516637	+	0.758877i
$635$	−0.768401	−	1.33091i	−0.0304930	−	0.0528155i
$636$	9.11431	+	13.9944i	0.361406	+	0.554913i
$637$	18.5207	−	0.254740i	0.733817	−	0.0100932i
$638$	1.44212	+	19.4211i	0.0570940	+	0.768889i
$639$	1.35410	−	7.07448i	0.0535675	−	0.279862i
$640$	−1.16571	−	0.680450i	−0.0460788	−	0.0268972i
$641$	−40.3967	−	23.3230i	−1.59557	−	0.921204i	−0.992326	−	0.123649i	$-0.960540\pi$
$641$	−40.3967	−	23.3230i	−1.59557	−	0.921204i	−0.603246	−	0.797555i	$-0.706126\pi$
$642$	−17.3806	−	31.5776i	−0.685959	−	1.24627i
$643$	−35.6303	−	20.5712i	−1.40512	−	0.811247i	−0.410209	−	0.911992i	$-0.634544\pi$
$643$	−35.6303	−	20.5712i	−1.40512	−	0.811247i	−0.994912	+	0.100744i	$0.967878\pi$
$644$	−5.39775	+	13.6984i	−0.212701	+	0.539792i
$645$	0.133380	−	0.0610159i	0.00525184	−	0.00240250i
$646$	15.2126	+	7.33876i	0.598531	+	0.288740i
$647$	6.02259	+	10.4314i	0.236772	+	0.410102i	0.959786	−	0.280732i	$-0.0905771\pi$
$647$	6.02259	+	10.4314i	0.236772	+	0.410102i	−0.723014	+	0.690833i	$0.757244\pi$
$648$	−19.8021	−	15.9962i	−0.777900	−	0.628389i
$649$	20.3624			0.799295
$650$	2.23107	+	25.3244i	0.0875098	+	0.993306i
$651$	−5.54349	−	12.1180i	−0.217267	−	0.474943i
$652$	10.4392	−	8.30174i	0.408830	−	0.325121i
$653$	−8.64101	−	14.9667i	−0.338149	−	0.585691i	0.645936	−	0.763392i	$-0.276467\pi$
$653$	−8.64101	−	14.9667i	−0.338149	−	0.585691i	−0.984085	+	0.177701i	$0.943134\pi$
$654$	−0.411896	+	20.1482i	−0.0161064	+	0.787856i
$655$	−0.818642			−0.0319870
$656$	4.43625	−	19.1954i	0.173206	−	0.749455i
$657$	27.3908	−	9.51933i	1.06862	−	0.371384i
$658$	−7.48016	+	0.555441i	−0.291607	+	0.0216533i
$659$	−6.33974	−	3.66025i	−0.246961	−	0.142583i	0.371411	−	0.928469i	$-0.378874\pi$
$659$	−6.33974	−	3.66025i	−0.246961	−	0.142583i	−0.618372	+	0.785886i	$0.712207\pi$
$660$	−0.883079	−	0.448485i	−0.0343738	−	0.0174573i
$661$	−5.16276	−	8.94217i	−0.200808	−	0.347810i	0.747981	−	0.663720i	$-0.231023\pi$
$661$	−5.16276	−	8.94217i	−0.200808	−	0.347810i	−0.948789	+	0.315910i	$0.897690\pi$
$662$	8.50220	−	0.631333i	0.330447	−	0.0245374i
$663$	1.01098	−	12.4839i	0.0392631	−	0.484834i
$664$	−8.61682	−	38.1113i	−0.334397	−	1.47901i
$665$	0.484835	+	0.839759i	0.0188011	+	0.0325645i
$666$	−4.45088	+	38.5325i	−0.172468	+	1.49310i
$667$	−15.4968	+	26.8412i	−0.600037	+	1.03930i
$668$	2.65727	+	17.7942i	0.102813	+	0.688477i
$669$	−19.6735	−	1.86588i	−0.760621	−	0.0721392i
$670$	−0.715106	−	0.344977i	−0.0276270	−	0.0133276i
$671$		−	3.68941i		−	0.142428i
$672$	−3.64464	−	12.8664i	−0.140595	−	0.496334i
$673$	8.50404	+	14.7294i	0.327807	+	0.567778i	0.982076	−	0.188483i	$-0.0603572\pi$
$673$	8.50404	+	14.7294i	0.327807	+	0.567778i	−0.654270	+	0.756261i	$0.727024\pi$
$674$	8.71849	−	5.93547i	0.335824	−	0.228626i
$675$	−24.8714	−	7.25104i	−0.957299	−	0.279093i
$676$	−25.5995	+	4.54589i	−0.984597	+	0.174842i
$677$	−4.84344			−0.186149			−0.0930743	−	0.995659i	$-0.529669\pi$
$677$	−4.84344			−0.186149			−0.0930743	+	0.995659i	$0.529669\pi$
$678$	−13.6484	+	22.5618i	−0.524163	+	0.866480i
$679$	−4.16892	+	2.40693i	−0.159989	+	0.0923695i
$680$	0.646290	+	0.200800i	0.0247841	+	0.00770034i
$681$	12.5220	+	27.3729i	0.479844	+	1.04893i
$682$	−17.2073	−	8.30102i	−0.658900	−	0.317862i
$683$	16.2078	−	28.0726i	0.620172	−	1.07417i	−0.369281	−	0.929318i	$-0.620396\pi$
$683$	16.2078	−	28.0726i	0.620172	−	1.07417i	0.989453	−	0.144852i	$-0.0462707\pi$
$684$	30.1873	+	19.1148i	1.15424	+	0.730873i
$685$	−1.67245	−	0.965588i	−0.0639009	−	0.0368932i
$686$	−19.3653	+	13.1837i	−0.739369	+	0.503357i
$687$	5.44328	−	7.65438i	0.207674	−	0.292033i
$688$	2.71532	−	0.829477i	0.103521	−	0.0316235i
$689$	−8.48346	+	15.1719i	−0.323194	+	0.578004i
$690$	−0.760069	−	1.38091i	−0.0289353	−	0.0525705i
$691$	−17.1436	+	9.89786i	−0.652173	+	0.376532i	−0.789288	−	0.614023i	$-0.789550\pi$
$691$	−17.1436	+	9.89786i	−0.652173	+	0.376532i	0.137115	+	0.990555i	$0.456217\pi$
$692$	−7.51650	−	9.45176i	−0.285735	−	0.359302i
$693$	−3.22125	−	9.26880i	−0.122365	−	0.352092i
$694$	−30.1380	+	2.23790i	−1.14402	+	0.0849496i
$695$	−0.788384	−	0.455173i	−0.0299051	−	0.0172657i
$696$	−3.58773	−	27.9205i	−0.135993	−	1.05832i
$697$			9.87810i			0.374160i
$698$	−29.4699	−	14.2167i	−1.11545	−	0.538109i
$699$	−14.3799	−	10.2260i	−0.543899	−	0.386784i
$700$	−8.47094	−	10.6519i	−0.320172	−	0.402606i
$701$	8.73947			0.330085			0.165043	−	0.986286i	$-0.447224\pi$
$701$	8.73947			0.330085			0.165043	+	0.986286i	$0.447224\pi$
$702$	5.15486	−	25.9890i	0.194558	−	0.980891i
$703$		−	54.4444i		−	2.05341i
$704$	−15.7965	−	10.8646i	−0.595353	−	0.409476i
$705$	0.465376	−	0.654416i	0.0175271	−	0.0246467i
$706$	−27.0343	−	13.0417i	−1.01745	−	0.490831i
$707$	21.9194			0.824363
$708$	−29.3910	+	1.57919i	−1.10458	+	0.0593495i
$709$	−24.3967	+	42.2563i	−0.916237	+	1.58697i	−0.111156	+	0.993803i	$0.535455\pi$
$709$	−24.3967	+	42.2563i	−0.916237	+	1.58697i	−0.805081	+	0.593165i	$0.797878\pi$
$710$	0.0299979	+	0.403984i	0.00112580	+	0.0151613i
$711$	12.8387	−	4.46194i	0.481490	−	0.167336i
$712$	−19.3572	+	17.8875i	−0.725443	+	0.670362i
$713$	−15.2026	−	26.3317i	−0.569342	−	0.986129i
$714$	3.23309	+	5.87396i	0.120995	+	0.219827i
$715$	−0.0141777	−	1.03078i	−0.000530217	−	0.0385491i
$716$	−1.84814	−	12.3759i	−0.0690682	−	0.462509i
$717$	25.8694	+	18.3965i	0.966109	+	0.687032i
$718$	15.9629	+	23.4476i	0.595731	+	0.875056i
$719$	−25.8702	+	44.8086i	−0.964797	+	1.67108i	−0.254638	+	0.967036i	$0.581956\pi$
$719$	−25.8702	+	44.8086i	−0.964797	+	1.67108i	−0.710159	+	0.704041i	$0.751377\pi$
$720$	1.30941	+	0.578855i	0.0487989	+	0.0215726i
$721$	14.6772	+	8.47387i	0.546607	+	0.315584i
$722$	−20.9689	−	10.1157i	−0.780383	−	0.376467i
$723$	−6.24133	+	2.85515i	−0.232117	+	0.106184i
$724$	−30.0079	−	11.8244i	−1.11524	−	0.439451i
$725$	−14.3244	−	24.8105i	−0.531993	−	0.921440i
$726$	11.0173	+	6.66472i	0.408890	+	0.247351i
$727$			40.2916i			1.49433i	0.664638	+	0.747166i	$0.268586\pi$
$727$			40.2916i			1.49433i	−0.664638	+	0.747166i	$0.731414\pi$
$728$	10.0916	−	9.58598i	0.374019	−	0.355280i
$729$	22.7697	+	14.5100i	0.843324	+	0.537406i
$730$	−1.34810	+	0.917777i	−0.0498955	+	0.0339685i
$731$	−1.23283	+	0.711773i	−0.0455977	+	0.0263259i
$732$	0.286128	+	5.32527i	0.0105756	+	0.196828i
$733$	−17.5209			−0.647149			−0.323575	−	0.946203i	$-0.604885\pi$
$733$	−17.5209			−0.647149			−0.323575	+	0.946203i	$0.604885\pi$
$734$	5.23096	−	10.8433i	0.193078	−	0.400234i
$735$	0.100231	−	1.05682i	0.00369708	−	0.0389813i
$736$	−11.0506	−	28.4407i	−0.407331	−	1.04834i
$737$	−9.76656	−	5.63873i	−0.359756	−	0.207705i
$738$	−2.39780	+	20.7584i	−0.0882644	+	0.764129i
$739$	−6.26640	+	3.61791i	−0.230513	+	0.133087i	−0.610809	−	0.791778i	$-0.709156\pi$
$739$	−6.26640	+	3.61791i	−0.230513	+	0.133087i	0.380296	+	0.924865i	$0.375822\pi$
$740$	−0.322199	−	2.15758i	−0.0118443	−	0.0793141i
$741$	−3.00185	+	37.0678i	−0.110276	+	1.36172i
$742$	−0.689088	−	9.28000i	−0.0252972	−	0.340679i
$743$	−8.54135	+	4.93135i	−0.313352	+	0.180914i	−0.648425	−	0.761278i	$-0.724572\pi$
$743$	−8.54135	+	4.93135i	−0.313352	+	0.180914i	0.335074	+	0.942192i	$0.391239\pi$
$744$	25.4806	+	10.6471i	0.934165	+	0.390343i
$745$	0.631419	−	1.09365i	0.0231334	−	0.0400683i
$746$	5.68104	−	0.421847i	0.207998	−	0.0154449i
$747$	13.6050	+	39.1467i	0.497779	+	1.43230i
$748$	8.94344	+	3.52410i	0.327005	+	0.128854i
$749$			20.0840i			0.733853i
$750$	2.91758	+	0.0596451i	0.106535	+	0.00217793i
$751$	−32.8744	+	18.9801i	−1.19961	+	0.692593i	−0.960467	−	0.278393i	$-0.910198\pi$
$751$	−32.8744	+	18.9801i	−1.19961	+	0.692593i	−0.239138	+	0.970986i	$0.576865\pi$
$752$	10.6037	−	11.3658i	0.386677	−	0.414469i
$753$	−29.4080	+	13.4529i	−1.07169	+	0.490253i
$754$	23.9905	−	16.8200i	0.873684	−	0.612550i
$755$			2.12833i			0.0774580i
$756$	5.36837	+	13.1287i	0.195246	+	0.477486i
$757$	40.3934	−	23.3212i	1.46812	−	0.847622i	0.468762	−	0.883325i	$-0.344700\pi$
$757$	40.3934	−	23.3212i	1.46812	−	0.847622i	0.999362	+	0.0357030i	$0.0113670\pi$
$758$	−14.1917	+	29.4181i	−0.515465	+	1.06851i
$759$	−9.31384	−	20.3600i	−0.338071	−	0.739020i
$760$	−1.91900	−	0.596228i	−0.0696095	−	0.0216275i
$761$	−8.95153	+	15.5045i	−0.324493	+	0.562038i	−0.981410	−	0.191925i	$-0.938527\pi$
$761$	−8.95153	+	15.5045i	−0.324493	+	0.562038i	0.656917	+	0.753963i	$0.271860\pi$
$762$	15.2145	+	27.6422i	0.551165	+	1.00137i
$763$	5.61441	−	9.72444i	0.203255	−	0.352048i
$764$	−3.21297	−	4.04021i	−0.116241	−	0.146170i
$765$	−0.705020	−	0.134946i	−0.0254901	−	0.00487897i
$766$	38.5378	−	2.86164i	1.39243	−	0.103395i
$767$	−15.6810	−	26.3177i	−0.566210	−	0.950278i
$768$	23.6432	+	14.4569i	0.853149	+	0.521667i
$769$	−17.2413	+	9.95426i	−0.621736	+	0.358960i	−0.777545	−	0.628828i	$-0.783535\pi$
$769$	−17.2413	+	9.95426i	−0.621736	+	0.358960i	0.155808	+	0.987787i	$0.450202\pi$
$770$	0.310567	+	0.456186i	0.0111921	+	0.0164398i
$771$	3.63263	−	38.3017i	0.130826	−	1.37940i
$772$	2.14822	+	14.3854i	0.0773163	+	0.517741i
$773$	−7.33492	−	4.23482i	−0.263819	−	0.152316i	0.362257	−	0.932078i	$-0.382006\pi$
$773$	−7.33492	−	4.23482i	−0.263819	−	0.152316i	−0.626075	+	0.779763i	$0.715340\pi$
$774$	−2.76351	+	1.19651i	−0.0993325	+	0.0430076i
$775$	28.1049			1.00956
$776$	2.95993	−	9.52675i	0.106255	−	0.341990i
$777$	12.5254	−	17.6133i	0.449347	−	0.631875i
$778$	31.3312	−	21.3300i	1.12328	−	0.764718i
$779$		−	29.3306i		−	1.05088i
$780$	0.100405	+	1.48673i	0.00359509	+	0.0532333i
$781$			5.75395i			0.205893i
$782$	8.60936	+	12.6461i	0.307870	+	0.452223i
$783$	7.09491	+	29.0024i	0.253551	+	1.03646i
$784$	4.62707	−	20.0211i	0.165252	−	0.715039i
$785$	2.27799			0.0813050
$786$	16.8044	+	0.343537i	0.599392	+	0.0122536i
$787$	26.7905	+	15.4675i	0.954977	+	0.551356i	0.894623	−	0.446821i	$-0.147444\pi$
$787$	26.7905	+	15.4675i	0.954977	+	0.551356i	0.0603535	+	0.998177i	$0.480777\pi$
$788$	7.83693	+	52.4793i	0.279179	+	1.86950i
$789$	−48.9488	−	4.64243i	−1.74262	−	0.165275i
$790$	−0.631888	+	0.430184i	−0.0224816	+	0.0153053i
$791$	12.7241	−	7.34628i	0.452418	−	0.261204i
$792$	17.9389	+	9.57669i	0.637430	+	0.340293i
$793$	−4.76843	+	2.84121i	−0.169332	+	0.100894i
$794$	−1.00955	−	13.5957i	−0.0358276	−	0.482492i
$795$	0.811878	+	0.577353i	0.0287944	+	0.0204766i
$796$	36.2901	−	28.8596i	1.28627	−	1.02290i
$797$	9.36951	−	16.2285i	0.331885	−	0.574842i	−0.650997	−	0.759081i	$-0.725649\pi$
$797$	9.36951	−	16.2285i	0.331885	−	0.574842i	0.982881	+	0.184239i	$0.0589821\pi$
$798$	−9.59987	−	17.4413i	−0.339832	−	0.617415i
$799$	−3.89685	+	6.74954i	−0.137861	+	0.238781i
$800$	27.8743	+	4.29844i	0.985504	+	0.151973i
$801$	18.2798	−	21.1506i	0.645883	−	0.747320i
$802$	−10.6628	−	5.14388i	−0.376516	−	0.181637i
$803$	−20.0611	+	11.5823i	−0.707940	+	0.408730i
$804$	14.5343	+	7.38147i	0.512585	+	0.260324i
$805$			0.878289i			0.0309556i
$806$	2.52250	+	28.6324i	0.0888512	+	1.00853i
$807$	−19.4874	−	42.5992i	−0.685988	−	1.49956i
$808$	−33.3615	+	30.8284i	−1.17365	+	1.08454i
$809$	1.04048	−	0.600720i	0.0365812	−	0.0211202i	−0.481598	−	0.876392i	$-0.659943\pi$
$809$	1.04048	−	0.600720i	0.0365812	−	0.0211202i	0.518179	+	0.855272i	$0.326610\pi$
$810$	−1.44882	−	0.454719i	−0.0509062	−	0.0159772i
$811$		−	25.5475i		−	0.897094i	−0.893759	−	0.448547i	$-0.851942\pi$
$811$		−	25.5475i		−	0.897094i	0.893759	−	0.448547i	$-0.148058\pi$
$812$	−5.75027	+	14.5930i	−0.201795	+	0.512114i
$813$	−38.5973	−	3.66067i	−1.35367	−	0.128385i
$814$	−2.29455	−	30.9008i	−0.0804238	−	1.08307i
$815$	0.397813	−	0.689033i	0.0139348	−	0.0241358i
$816$	−13.1822	−	4.39306i	−0.461470	−	0.153788i
$817$	3.66058	−	2.11344i	0.128067	−	0.0739398i
$818$	49.9167	−	3.70657i	1.74530	−	0.129597i
$819$	−9.49892	+	11.3012i	−0.331919	+	0.394897i
$820$	−0.173577	−	1.16234i	−0.00606158	−	0.0405908i
$821$	−9.56060	+	5.51981i	−0.333667	+	0.192643i	−0.657468	−	0.753482i	$-0.728373\pi$
$821$	−9.56060	+	5.51981i	−0.333667	+	0.192643i	0.323801	+	0.946125i	$0.395039\pi$
$822$	33.9253	+	20.5226i	1.18328	+	0.715807i
$823$	39.7370	+	22.9422i	1.38514	+	0.799713i	0.992763	−	0.120090i	$-0.0383182\pi$
$823$	39.7370	+	22.9422i	1.38514	+	0.799713i	0.392381	+	0.919803i	$0.371652\pi$
$824$	−34.2569	+	7.74535i	−1.19340	+	0.269822i
$825$	20.6029	+	1.95403i	0.717300	+	0.0680305i
$826$	14.7712	+	7.12581i	0.513954	+	0.247939i
$827$	24.3898			0.848117			0.424058	−	0.905635i	$-0.360605\pi$
$827$	24.3898			0.848117			0.424058	+	0.905635i	$0.360605\pi$
$828$	15.0225	+	28.6651i	0.522069	+	0.996182i
$829$	40.6462	−	23.4671i	1.41170	−	0.815047i	0.416154	−	0.909294i	$-0.363378\pi$
$829$	40.6462	−	23.4671i	1.41170	−	0.815047i	0.995549	+	0.0942474i	$0.0300445\pi$
$830$	−1.31168	−	1.92670i	−0.0455291	−	0.0668767i
$831$	−51.0402	+	23.3488i	−1.77057	+	0.809960i
$832$	−1.87732	+	28.7833i	−0.0650842	+	0.997880i
$833$			10.3030i			0.356977i
$834$	15.9922	+	9.67424i	0.553766	+	0.334991i
$835$	0.536617	+	0.929447i	0.0185704	+	0.0321648i
$836$	−26.5554	−	10.4640i	−0.918437	−	0.361903i
$837$	−28.1201	−	8.19819i	−0.971974	−	0.283371i
$838$	−9.97700	+	20.6814i	−0.344650	+	0.714428i
$839$	−4.79758	−	2.76988i	−0.165631	−	0.0956270i	0.414893	−	0.909870i	$-0.363819\pi$
$839$	−4.79758	−	2.76988i	−0.165631	−	0.0956270i	−0.580524	+	0.814243i	$0.697152\pi$
$840$	−0.483650	−	0.634370i	−0.0166875	−	0.0218878i
$841$	−2.00885	+	3.47943i	−0.0692706	+	0.119980i
$842$	32.7674	−	22.3078i	1.12924	−	0.768778i
$843$	1.92945	−	2.71321i	0.0664538	−	0.0934479i
$844$	1.30037	−	0.194189i	0.0447605	−	0.00668425i
$845$	−1.32133	+	0.812128i	−0.0454552	+	0.0279380i
$846$	−9.82746	+	13.2380i	−0.337875	+	0.455131i
$847$	−3.58730	−	6.21339i	−0.123261	−	0.213495i
$848$	14.1006	+	13.1551i	0.484218	+	0.451748i
$849$	47.1524	+	4.47205i	1.61827	+	0.153481i
$850$	−14.1023	+	1.04717i	−0.483704	+	0.0359176i
$851$	24.6568	−	42.7068i	0.845224	−	1.46397i
$852$	−0.446242	−	8.30522i	−0.0152880	−	0.284532i
$853$	6.05163			0.207204			0.103602	−	0.994619i	$-0.466963\pi$
$853$	6.05163			0.207204			0.103602	+	0.994619i	$0.466963\pi$
$854$	1.29111	−	2.67635i	0.0441807	−	0.0915827i
$855$	2.09339	+	0.400688i	0.0715923	+	0.0137032i
$856$	−28.2471	−	30.5681i	−0.965466	−	1.04480i
$857$		−	21.9501i		−	0.749801i	−0.927065	−	0.374901i	$-0.877677\pi$
$857$		−	21.9501i		−	0.749801i	0.927065	−	0.374901i	$-0.122323\pi$
$858$	−0.141533	+	21.1650i	−0.00483185	+	0.722560i
$859$	−2.37658			−0.0810878			−0.0405439	−	0.999178i	$-0.512909\pi$
$859$	−2.37658			−0.0810878			−0.0405439	+	0.999178i	$0.512909\pi$
$860$	0.132558	−	0.105417i	0.00452019	−	0.00359467i
$861$	6.74777	−	9.48876i	0.229963	−	0.323376i
$862$	0.223365	−	0.463016i	0.00760785	−	0.0157704i
$863$		−	41.6036i		−	1.41620i	−0.706111	−	0.708101i	$-0.749552\pi$
$863$		−	41.6036i		−	1.41620i	0.706111	−	0.708101i	$-0.250448\pi$
$864$	−26.6356	−	12.4317i	−0.906160	−	0.422935i
$865$	−0.623859	−	0.360185i	−0.0212118	−	0.0122467i
$866$	−2.21110	−	29.7770i	−0.0751362	−	1.01186i
$867$	−22.3776	−	2.12235i	−0.759984	−	0.0720788i
$868$	−9.57744	−	12.0433i	−0.325080	−	0.408777i
$869$	−9.40312	+	5.42889i	−0.318979	+	0.184163i
$870$	−0.809708	−	1.47110i	−0.0274517	−	0.0498749i
$871$	0.233346	+	16.9653i	0.00790664	+	0.574848i
$872$	5.13172	+	22.6971i	0.173782	+	0.768620i
$873$	−1.98919	+	10.3925i	−0.0673238	+	0.351732i
$874$	−25.5634	−	37.5495i	−0.864695	−	1.27013i
$875$	−1.40816	−	0.813001i	−0.0476045	−	0.0274845i
$876$	28.0578	−	18.2736i	0.947985	−	0.617408i
$877$	4.32509	−	7.49127i	0.146048	−	0.252962i	−0.783716	−	0.621120i	$-0.786678\pi$
$877$	4.32509	−	7.49127i	0.146048	−	0.252962i	0.929763	+	0.368158i	$0.120011\pi$
$878$	13.3040	−	27.5781i	0.448990	−	0.930716i
$879$	−27.5920	+	12.6222i	−0.930654	+	0.425736i
$880$	−1.11429	−	0.257523i	−0.0375627	−	0.00868109i
$881$	−34.3798	+	19.8492i	−1.15829	+	0.668736i	−0.950893	−	0.309521i	$-0.899831\pi$
$881$	−34.3798	+	19.8492i	−1.15829	+	0.668736i	−0.207393	+	0.978258i	$0.566498\pi$
$882$	−2.50094	+	21.6513i	−0.0842111	+	0.729039i
$883$	35.2624			1.18668			0.593338	−	0.804954i	$-0.297810\pi$
$883$	35.2624			1.18668			0.593338	+	0.804954i	$0.297810\pi$
$884$	−2.33255	−	14.2730i	−0.0784520	−	0.480053i
$885$	−1.59664	+	0.730394i	−0.0536703	+	0.0245519i
$886$	−5.75790	−	8.45766i	−0.193441	−	0.284141i
$887$	−1.26936	−	2.19859i	−0.0426209	−	0.0738216i	0.843928	−	0.536456i	$-0.180237\pi$
$887$	−1.26936	−	2.19859i	−0.0426209	−	0.0738216i	−0.886549	+	0.462635i	$0.846904\pi$
$888$	5.70841	+	44.4241i	0.191562	+	1.49077i
$889$		−	17.5810i		−	0.589648i
$890$	−0.683127	+	1.41606i	−0.0228985	+	0.0474665i
$891$	−20.0441	−	7.96495i	−0.671502	−	0.266836i
$892$	−22.5687	+	3.37026i	−0.755655	+	0.112845i
$893$	11.5707	−	20.0411i	0.387200	−	0.670650i
$894$	−13.4202	+	22.1845i	−0.448837	+	0.741961i
$895$	−0.373218	−	0.646433i	−0.0124753	−	0.0216079i
$896$	−7.65692	−	13.4093i	−0.255800	−	0.447974i
$897$	−19.1420	+	27.7170i	−0.639132	+	0.925443i
$898$	−1.07383	−	14.4614i	−0.0358342	−	0.482582i
$899$	−16.1955	−	28.0513i	−0.540149	−	0.935565i
$900$	−29.8896	−	1.22260i	−0.996320	−	0.0407532i
$901$	−8.37358	−	4.83449i	−0.278964	−	0.161060i
$902$	−1.23613	−	16.6471i	−0.0411586	−	0.554286i
$903$	1.67045	+	0.158430i	0.0555891	+	0.00527221i
$904$	−9.03411	+	29.0769i	−0.300470	+	0.967085i
$905$	−1.92400			−0.0639559
$906$	0.893140	−	43.6886i	0.0296726	−	1.45146i
$907$	−6.91458	−	11.9764i	−0.229595	−	0.397670i	0.728093	−	0.685478i	$-0.240407\pi$
$907$	−6.91458	−	11.9764i	−0.229595	−	0.397670i	−0.957688	+	0.287808i	$0.907073\pi$
$908$	21.6341	+	27.2042i	0.717953	+	0.902803i
$909$	31.5045	−	36.4523i	1.04494	−	1.20905i
$910$	0.350437	−	0.752705i	0.0116169	−	0.0249519i
$911$	5.21479			0.172774			0.0863868	−	0.996262i	$-0.472468\pi$
$911$	5.21479			0.172774			0.0863868	+	0.996262i	$0.472468\pi$
$912$	39.1414	+	13.0441i	1.29610	+	0.431934i
$913$	−16.5533	−	28.6712i	−0.547834	−	0.948877i
$914$	−7.61211	+	15.7792i	−0.251786	+	0.521930i
$915$	0.132338	+	0.289290i	0.00437496	+	0.00956363i
$916$	3.97605	−	10.0904i	0.131372	−	0.333396i
$917$	−8.11056	−	4.68263i	−0.267834	−	0.154634i
$918$	14.4154	+	3.06590i	0.475779	+	0.101190i
$919$	39.9492	+	23.0647i	1.31780	+	0.760834i	0.983375	−	0.181586i	$-0.0581232\pi$
$919$	39.9492	+	23.0647i	1.31780	+	0.760834i	0.334429	+	0.942421i	$0.391457\pi$
$920$	−1.23527	−	1.33677i	−0.0407256	−	0.0440719i
$921$	23.6625	+	16.8272i	0.779706	+	0.554475i
$922$	−32.0703	+	2.38139i	−1.05618	+	0.0784269i
$923$	7.43679	−	4.43111i	0.244785	−	0.145852i
$924$	−6.18362	−	9.49450i	−0.203426	−	0.312346i
$925$	22.7914	+	39.4758i	0.749376	+	1.29796i
$926$	22.3998	−	15.2496i	0.736102	−	0.501132i
$927$	35.1876	−	12.2290i	1.15571	−	0.401654i
$928$	−11.7723	−	30.2982i	−0.386445	−	0.994586i
$929$	24.7925	−	42.9419i	0.813416	−	1.40888i	−0.0970441	−	0.995280i	$-0.530939\pi$
$929$	24.7925	−	42.9419i	0.813416	−	1.40888i	0.910460	−	0.413597i	$-0.135728\pi$
$930$	1.64699	+	0.0336700i	0.0540070	+	0.00110408i
$931$		−	30.5922i		−	1.00262i
$932$	−18.9564	−	7.46962i	−0.620936	−	0.244676i
$933$	17.4985	−	24.6065i	0.572874	−	0.805579i
$934$	4.47344	+	6.57093i	0.146375	+	0.215008i
$935$	0.573421			0.0187529
$936$	−1.43714	−	30.5603i	−0.0469744	−	0.998896i
$937$	−52.4495			−1.71345			−0.856725	−	0.515773i	$-0.827505\pi$
$937$	−52.4495			−1.71345			−0.856725	+	0.515773i	$0.827505\pi$
$938$	−5.11152	−	7.50820i	−0.166897	−	0.245152i
$939$	−5.62853	+	7.91488i	−0.183680	+	0.258292i
$940$	0.339935	−	0.862685i	0.0110875	−	0.0281377i
$941$		−	32.7557i		−	1.06781i	−0.845546	−	0.533903i	$-0.820725\pi$
$941$		−	32.7557i		−	1.06781i	0.845546	−	0.533903i	$-0.179275\pi$
$942$	−46.7606	−	0.955943i	−1.52354	−	0.0311463i
$943$	13.2833	−	23.0073i	0.432562	−	0.749220i
$944$	−32.5040	+	9.92931i	−1.05791	+	0.323171i
$945$	0.585051	+	0.611229i	0.0190317	+	0.0198833i
$946$	1.98855	−	1.35379i	0.0646534	−	0.0440155i
$947$	18.8648	+	32.6748i	0.613023	+	1.06179i	0.990728	+	0.135861i	$0.0433800\pi$
$947$	18.8648	+	32.6748i	0.613023	+	1.06179i	−0.377705	+	0.925926i	$0.623287\pi$
$948$	13.1514	−	8.56528i	0.427137	−	0.278187i
$949$	30.4187	+	17.0088i	0.987432	+	0.552128i
$950$	41.8733	−	3.10931i	1.35855	−	0.100879i
$951$	−23.0719	−	16.4072i	−0.748159	−	0.532040i
$952$	5.25443	+	5.68618i	0.170297	+	0.184290i
$953$	21.8338	+	12.6058i	0.707267	+	0.408341i	0.810048	−	0.586363i	$-0.199441\pi$
$953$	21.8338	+	12.6058i	0.707267	+	0.408341i	−0.102781	+	0.994704i	$0.532774\pi$
$954$	−16.4232	−	12.1921i	−0.531722	−	0.394734i
$955$	−0.266672	−	0.153963i	−0.00862930	−	0.00498213i
$956$	34.1023	+	13.4378i	1.10295	+	0.434609i
$957$	−9.92211	−	21.6896i	−0.320736	−	0.701127i
$958$	−6.31806	+	13.0968i	−0.204127	+	0.423137i
$959$	−11.0463	−	19.1328i	−0.356704	−	0.617830i
$960$	1.62833	+	0.285289i	0.0525541	+	0.00920768i
$961$	0.776019			0.0250329
$962$	−38.1712	+	26.7622i	−1.23069	+	0.862850i
$963$	33.4001	+	28.8666i	1.07630	+	0.930212i
$964$	−6.20285	+	4.93281i	−0.199780	+	0.158875i
$965$	0.433818	+	0.751395i	0.0139651	+	0.0241883i
$966$	0.368568	−	18.0288i	0.0118585	−	0.580066i
$967$	6.99039			0.224796			0.112398	−	0.993663i	$-0.464147\pi$
$967$	6.99039			0.224796			0.112398	+	0.993663i	$0.464147\pi$
$968$	14.1987	+	4.41150i	0.456364	+	0.141791i
$969$	−20.5938	−	1.95317i	−0.661569	−	0.0627449i
$970$	−0.0440672	−	0.593456i	−0.00141491	−	0.0190547i
$971$	10.4697	+	6.04466i	0.335987	+	0.193982i	0.658496	−	0.752584i	$-0.271193\pi$
$971$	10.4697	+	6.04466i	0.335987	+	0.193982i	−0.322509	+	0.946566i	$0.604526\pi$
$972$	29.5492	+	9.94206i	0.947791	+	0.318892i
$973$	−5.20718	−	9.01911i	−0.166935	−	0.289139i
$974$	−1.51113	−	20.3505i	−0.0484198	−	0.652073i
$975$	−13.3407	−	28.1333i	−0.427245	−	0.900986i
$976$	1.79906	+	5.88930i	0.0575866	+	0.188512i
$977$	−4.02911	−	6.97862i	−0.128903	−	0.223266i	0.794349	−	0.607462i	$-0.207812\pi$
$977$	−4.02911	−	6.97862i	−0.128903	−	0.223266i	−0.923252	+	0.384196i	$0.874479\pi$
$978$	−8.45511	+	13.9769i	−0.270364	+	0.446932i
$979$	−11.1659	+	19.3398i	−0.356863	+	0.618104i
$980$	−0.181043	−	1.21234i	−0.00578322	−	0.0387268i
$981$	−8.10239	−	23.3137i	−0.258690	−	0.744350i
$982$	−23.4885	+	48.6895i	−0.749548	+	1.55375i
$983$		−	28.8328i		−	0.919623i	−0.888017	−	0.459811i	$-0.847917\pi$
$983$		−	28.8328i		−	0.919623i	0.888017	−	0.459811i	$-0.152083\pi$
$984$	3.07527	+	23.9324i	0.0980360	+	0.762937i
$985$	1.58261	+	2.74116i	0.0504262	+	0.0873407i
$986$	9.17162	+	13.4720i	0.292084	+	0.429036i
$987$	8.35390	−	3.82156i	0.265907	−	0.121642i
$988$	6.92593	+	42.3802i	0.220343	+	1.34829i
$989$	3.82854			0.121740
$990$	1.20502	+	0.139192i	0.0382981	+	0.00442381i
$991$	21.4026	−	12.3568i	0.679875	−	0.392526i	−0.119933	−	0.992782i	$-0.538268\pi$
$991$	21.4026	−	12.3568i	0.679875	−	0.392526i	0.799808	+	0.600256i	$0.204935\pi$
$992$	31.5153	+	4.85991i	1.00061	+	0.154302i
$993$	−9.49532	+	4.34372i	−0.301325	+	0.137844i
$994$	−2.01359	+	4.17399i	−0.0638672	+	0.132391i
$995$	1.38293	−	2.39531i	0.0438419	−	0.0759364i
$996$	26.1165	+	40.1000i	0.827533	+	1.27062i
$997$	3.27051	+	1.88823i	0.103578	+	0.0598008i	0.550894	−	0.834575i	$-0.314287\pi$
$997$	3.27051	+	1.88823i	0.103578	+	0.0598008i	−0.447316	+	0.894376i	$0.647620\pi$
$998$	22.2267	+	32.6484i	0.703575	+	1.03347i
$999$	−11.2887	−	46.1455i	−0.357157	−	1.45998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.ba.a.179.10	yes	104
3.2	odd	2	inner	312.2.ba.a.179.43	yes	104
8.3	odd	2	inner	312.2.ba.a.179.45	yes	104
13.4	even	6	inner	312.2.ba.a.251.8	yes	104
24.11	even	2	inner	312.2.ba.a.179.8	✓	104
39.17	odd	6	inner	312.2.ba.a.251.45	yes	104
104.43	odd	6	inner	312.2.ba.a.251.43	yes	104
312.251	even	6	inner	312.2.ba.a.251.10	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.ba.a.179.8	✓	104	24.11	even	2	inner
312.2.ba.a.179.10	yes	104	1.1	even	1	trivial
312.2.ba.a.179.43	yes	104	3.2	odd	2	inner
312.2.ba.a.179.45	yes	104	8.3	odd	2	inner
312.2.ba.a.251.8	yes	104	13.4	even	6	inner
312.2.ba.a.251.10	yes	104	312.251	even	6	inner
312.2.ba.a.251.43	yes	104	104.43	odd	6	inner
312.2.ba.a.251.45	yes	104	39.17	odd	6	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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	312.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16902 + 0.795859i) q^{2} +(1.00378 - 1.41153i) q^{3} +(0.733216 - 1.86075i) q^{4} -0.119305i q^{5} +(-0.0500653 + 2.44898i) q^{6} +(0.682422 - 1.18199i) q^{7} +(0.623752 + 2.75879i) q^{8} +(-0.984833 - 2.83374i) q^{9} +O(q^{10})\)	\(q+(-1.16902 + 0.795859i) q^{2} +(1.00378 - 1.41153i) q^{3} +(0.733216 - 1.86075i) q^{4} -0.119305i q^{5} +(-0.0500653 + 2.44898i) q^{6} +(0.682422 - 1.18199i) q^{7} +(0.623752 + 2.75879i) q^{8} +(-0.984833 - 2.83374i) q^{9} +(0.0949496 + 0.139469i) q^{10} +(1.19826 + 2.07544i) q^{11} +(-1.89051 - 2.90275i) q^{12} +(1.75966 - 3.14700i) q^{13} +(0.142932 + 1.92488i) q^{14} +(-0.168402 - 0.119756i) q^{15} +(-2.92479 - 2.72866i) q^{16} +(1.73687 + 1.00278i) q^{17} +(3.40655 + 2.52892i) q^{18} +(-5.15721 - 2.97752i) q^{19} +(-0.221996 - 0.0874760i) q^{20} +(-0.983408 - 2.14972i) q^{21} +(-3.05255 - 1.47259i) q^{22} +(-2.69692 - 4.67120i) q^{23} +(4.52023 + 1.88879i) q^{24} +4.98577 q^{25} +(0.447488 + 5.07935i) q^{26} +(-4.98847 - 1.45435i) q^{27} +(-1.69903 - 2.13647i) q^{28} +(-2.87305 - 4.97627i) q^{29} +(0.292174 + 0.00597301i) q^{30} +5.63702 q^{31} +(5.59077 + 0.862142i) q^{32} +(4.13234 + 0.391921i) q^{33} +(-2.82851 + 0.210031i) q^{34} +(-0.141017 - 0.0814160i) q^{35} +(-5.99499 - 0.245218i) q^{36} +(4.57129 + 7.91771i) q^{37} +(8.39857 - 0.623637i) q^{38} +(-2.67576 - 5.64272i) q^{39} +(0.329136 - 0.0744165i) q^{40} +(2.46267 + 4.26547i) q^{41} +(2.86050 + 1.73041i) q^{42} +(-0.354899 + 0.614703i) q^{43} +(4.74046 - 0.707911i) q^{44} +(-0.338078 + 0.117495i) q^{45} +(6.87037 + 3.31436i) q^{46} +3.88604i q^{47} +(-6.78745 + 1.38944i) q^{48} +(2.56860 + 4.44895i) q^{49} +(-5.82846 + 3.96797i) q^{50} +(3.15890 - 1.44507i) q^{51} +(-4.56557 - 5.58172i) q^{52} -4.82108 q^{53} +(6.98908 - 2.26996i) q^{54} +(0.247610 - 0.142957i) q^{55} +(3.68652 + 1.14539i) q^{56} +(-9.37958 + 4.29077i) q^{57} +(7.31907 + 3.53082i) q^{58} +(4.24834 - 7.35834i) q^{59} +(-0.346311 + 0.225547i) q^{60} +(-1.33324 - 0.769745i) q^{61} +(-6.58979 + 4.48628i) q^{62} +(-4.02153 - 0.769747i) q^{63} +(-7.22187 + 3.44161i) q^{64} +(-0.375451 - 0.209936i) q^{65} +(-5.14270 + 2.83060i) q^{66} +(-4.07532 + 2.35289i) q^{67} +(3.13943 - 2.49663i) q^{68} +(-9.30067 - 0.882098i) q^{69} +(0.229647 - 0.0170525i) q^{70} +(2.07930 + 1.20048i) q^{71} +(7.20342 - 4.48450i) q^{72} +9.66594i q^{73} +(-11.6453 - 5.61786i) q^{74} +(5.00464 - 7.03756i) q^{75} +(-9.32177 + 7.41312i) q^{76} +3.27087 q^{77} +(7.61883 + 4.46693i) q^{78} +4.53066i q^{79} +(-0.325542 + 0.348941i) q^{80} +(-7.06021 + 5.58153i) q^{81} +(-6.27363 - 3.02648i) q^{82} -13.8145 q^{83} +(-4.72115 + 0.253669i) q^{84} +(0.119636 - 0.207216i) q^{85} +(-0.0743332 - 1.00105i) q^{86} +(-9.90808 - 0.939707i) q^{87} +(-4.97830 + 4.60030i) q^{88} +(4.65921 + 8.06999i) q^{89} +(0.301711 - 0.406417i) q^{90} +(-2.51889 - 4.22748i) q^{91} +(-10.6694 + 1.59330i) q^{92} +(5.65836 - 7.95682i) q^{93} +(-3.09274 - 4.54285i) q^{94} +(-0.355231 + 0.615279i) q^{95} +(6.82887 - 7.02613i) q^{96} +(-3.05451 - 1.76352i) q^{97} +(-6.54348 - 3.15666i) q^{98} +(4.70119 - 5.43951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9}+O(q^{10}) \) 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9	\( 104 q - 2 q^{3} - 2 q^{4} - 12 q^{6} - 2 q^{9} + 6 q^{10} + 8 q^{12} - 6 q^{16} - 12 q^{19} + 8 q^{22} - 36 q^{24} - 88 q^{25} + 16 q^{27} + 12 q^{28} + 14 q^{30} - 6 q^{33} + 22 q^{36} + 4 q^{40} + 26 q^{42} - 20 q^{43} - 36 q^{46} + 14 q^{48} - 24 q^{49} - 20 q^{51} - 16 q^{52} - 36 q^{54} - 66 q^{58} + 28 q^{64} + 32 q^{66} - 12 q^{67} - 66 q^{72} + 2 q^{75} - 60 q^{76} - 14 q^{78} - 2 q^{81} + 50 q^{82} - 90 q^{84} + 24 q^{88} + 8 q^{90} + 44 q^{91} + 72 q^{94} + 12 q^{97}+O(q^{100}) \) 104 * q - 2 * q^3 - 2 * q^4 - 12 * q^6 - 2 * q^9 + 6 * q^10 + 8 * q^12 - 6 * q^16 - 12 * q^19 + 8 * q^22 - 36 * q^24 - 88 * q^25 + 16 * q^27 + 12 * q^28 + 14 * q^30 - 6 * q^33 + 22 * q^36 + 4 * q^40 + 26 * q^42 - 20 * q^43 - 36 * q^46 + 14 * q^48 - 24 * q^49 - 20 * q^51 - 16 * q^52 - 36 * q^54 - 66 * q^58 + 28 * q^64 + 32 * q^66 - 12 * q^67 - 66 * q^72 + 2 * q^75 - 60 * q^76 - 14 * q^78 - 2 * q^81 + 50 * q^82 - 90 * q^84 + 24 * q^88 + 8 * q^90 + 44 * q^91 + 72 * q^94 + 12 * q^97

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