LMFDB - Embedded newform 234.2.y.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.46728 - 0.920381i) q^{3} -1.00000i q^{4} +(-3.62177 - 0.970449i) q^{5} +(-0.386713 + 1.68833i) q^{6} +(-3.13748 - 0.840685i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.30580 - 2.70091i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46728 - 0.920381i) q^{3} -1.00000i q^{4} +(-3.62177 - 0.970449i) q^{5} +(-0.386713 + 1.68833i) q^{6} +(-3.13748 - 0.840685i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.30580 - 2.70091i) q^{9} +(3.24719 - 1.87476i) q^{10} +(-1.54706 - 1.54706i) q^{11} +(-0.920381 - 1.46728i) q^{12} +(0.305736 - 3.59257i) q^{13} +(2.81299 - 1.62408i) q^{14} +(-6.20731 + 1.90949i) q^{15} -1.00000 q^{16} +(-3.50770 + 6.07551i) q^{17} +(0.986492 + 2.83317i) q^{18} +(4.70354 - 1.26031i) q^{19} +(-0.970449 + 3.62177i) q^{20} +(-5.37730 + 1.65416i) q^{21} +2.18787 q^{22} +(0.415879 - 0.720323i) q^{23} +(1.68833 + 0.386713i) q^{24} +(7.84529 + 4.52948i) q^{25} +(2.32414 + 2.75652i) q^{26} +(-0.569900 - 5.16481i) q^{27} +(-0.840685 + 3.13748i) q^{28} -9.26729i q^{29} +(3.03902 - 5.73945i) q^{30} +(-0.141470 + 0.527973i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.69385 - 0.846078i) q^{33} +(-1.81572 - 6.77635i) q^{34} +(10.5474 + 6.08953i) q^{35} +(-2.70091 - 1.30580i) q^{36} +(1.90093 + 0.509353i) q^{37} +(-2.43473 + 4.21708i) q^{38} +(-2.85793 - 5.55268i) q^{39} +(-1.87476 - 3.24719i) q^{40} +(0.455940 + 1.70159i) q^{41} +(2.63266 - 4.97199i) q^{42} +(0.0503260 - 0.0290558i) q^{43} +(-1.54706 + 1.54706i) q^{44} +(-7.35038 + 8.51484i) q^{45} +(0.215275 + 0.803416i) q^{46} +(5.83570 - 1.56367i) q^{47} +(-1.46728 + 0.920381i) q^{48} +(3.07486 + 1.77527i) q^{49} +(-8.75029 + 2.34463i) q^{50} +(0.445026 + 12.1429i) q^{51} +(-3.59257 - 0.305736i) q^{52} -1.62324i q^{53} +(4.05505 + 3.24909i) q^{54} +(4.10174 + 7.10443i) q^{55} +(-1.62408 - 2.81299i) q^{56} +(5.74143 - 6.17827i) q^{57} +(6.55297 + 6.55297i) q^{58} +(2.06291 + 2.06291i) q^{59} +(1.90949 + 6.20731i) q^{60} +(-1.78999 - 3.10035i) q^{61} +(-0.273299 - 0.473367i) q^{62} +(-6.36752 + 7.37628i) q^{63} +1.00000i q^{64} +(-4.59371 + 12.7147i) q^{65} +(3.21021 - 2.01368i) q^{66} +(-12.5547 + 3.36401i) q^{67} +(6.07551 + 3.50770i) q^{68} +(-0.0527631 - 1.43968i) q^{69} +(-11.7641 + 3.15217i) q^{70} +(-2.31786 - 8.65035i) q^{71} +(2.83317 - 0.986492i) q^{72} +(3.38343 - 3.38343i) q^{73} +(-1.70433 + 0.983995i) q^{74} +(15.6801 - 0.574661i) q^{75} +(-1.26031 - 4.70354i) q^{76} +(3.55328 + 6.15446i) q^{77} +(5.94720 + 1.90547i) q^{78} +(-5.86001 + 10.1498i) q^{79} +(3.62177 + 0.970449i) q^{80} +(-5.58979 - 7.05367i) q^{81} +(-1.52561 - 0.880809i) q^{82} +(3.75798 + 14.0250i) q^{83} +(1.65416 + 5.37730i) q^{84} +(18.6000 - 18.6000i) q^{85} +(-0.0150404 + 0.0561314i) q^{86} +(-8.52944 - 13.5977i) q^{87} -2.18787i q^{88} +(3.50606 - 13.0848i) q^{89} +(-0.823397 - 11.2184i) q^{90} +(-3.97946 + 11.0146i) q^{91} +(-0.720323 - 0.415879i) q^{92} +(0.278361 + 0.904888i) q^{93} +(-3.02078 + 5.23214i) q^{94} -18.2582 q^{95} +(0.386713 - 1.68833i) q^{96} +(2.55453 - 9.53363i) q^{97} +(-3.42956 + 0.918947i) q^{98} +(-6.19861 + 2.15832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.46728	−	0.920381i	0.847132	−	0.531382i
$3$	1.46728	−	0.920381i	0.847132	−	0.531382i
$4$		−	1.00000i		−	0.500000i
$5$	−3.62177	−	0.970449i	−1.61970	−	0.433998i	−0.668789	−	0.743452i	$-0.733187\pi$
$5$	−3.62177	−	0.970449i	−1.61970	−	0.433998i	−0.950914	+	0.309454i	$0.899854\pi$
$6$	−0.386713	+	1.68833i	−0.157875	+	0.689257i
$7$	−3.13748	−	0.840685i	−1.18586	−	0.317749i	−0.388609	−	0.921403i	$-0.627044\pi$
$7$	−3.13748	−	0.840685i	−1.18586	−	0.317749i	−0.797247	+	0.603653i	$0.793711\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.30580	−	2.70091i	0.435266	−	0.900302i
$10$	3.24719	−	1.87476i	1.02685	−	0.592852i
$11$	−1.54706	−	1.54706i	−0.466456	−	0.466456i	0.434308	−	0.900764i	$-0.356993\pi$
$11$	−1.54706	−	1.54706i	−0.466456	−	0.466456i	−0.900764	+	0.434308i	$0.856993\pi$
$12$	−0.920381	−	1.46728i	−0.265691	−	0.423566i
$13$	0.305736	−	3.59257i	0.0847958	−	0.996398i
$13$	0.305736	−	3.59257i	0.0847958	−	0.996398i
$14$	2.81299	−	1.62408i	0.751803	−	0.434054i
$15$	−6.20731	+	1.90949i	−1.60272	+	0.493028i
$16$	−1.00000			−0.250000
$17$	−3.50770	+	6.07551i	−0.850742	+	1.47353i	0.0297983	+	0.999556i	$0.490513\pi$
$17$	−3.50770	+	6.07551i	−0.850742	+	1.47353i	−0.880540	+	0.473972i	$0.842820\pi$
$18$	0.986492	+	2.83317i	0.232518	+	0.667784i
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.324853	−	0.945765i	$-0.394685\pi$
$19$	4.70354	−	1.26031i	1.07907	−	0.289135i	0.754213	+	0.656630i	$0.228019\pi$
$20$	−0.970449	+	3.62177i	−0.216999	+	0.809852i
$21$	−5.37730	+	1.65416i	−1.17342	+	0.360968i
$22$	2.18787			0.466456
$23$	0.415879	−	0.720323i	0.0867167	−	0.150198i	−0.819405	−	0.573215i	$-0.805696\pi$
$23$	0.415879	−	0.720323i	0.0867167	−	0.150198i	0.906121	+	0.423018i	$0.139029\pi$
$24$	1.68833	+	0.386713i	0.344629	+	0.0789374i
$25$	7.84529	+	4.52948i	1.56906	+	0.905896i
$26$	2.32414	+	2.75652i	0.455801	+	0.540597i
$27$	−0.569900	−	5.16481i	−0.109677	−	0.993967i
$28$	−0.840685	+	3.13748i	−0.158875	+	0.592928i
$29$		−	9.26729i		−	1.72089i	−0.509541	−	0.860447i	$-0.670185\pi$
$29$		−	9.26729i		−	1.72089i	0.509541	−	0.860447i	$-0.329815\pi$
$30$	3.03902	−	5.73945i	0.554847	−	1.04787i
$31$	−0.141470	+	0.527973i	−0.0254087	+	0.0948267i	−0.977466	−	0.211094i	$-0.932297\pi$
$31$	−0.141470	+	0.527973i	−0.0254087	+	0.0948267i	0.952057	+	0.305920i	$0.0989641\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.69385	−	0.846078i	−0.643016	−	0.147283i
$34$	−1.81572	−	6.77635i	−0.311393	−	1.16213i
$35$	10.5474	+	6.08953i	1.78283	+	1.02932i
$36$	−2.70091	−	1.30580i	−0.450151	−	0.217633i
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	0.411666	−	0.911335i	$-0.364947\pi$
$37$	1.90093	+	0.509353i	0.312511	+	0.0837372i	−0.0991544	+	0.995072i	$0.531614\pi$
$38$	−2.43473	+	4.21708i	−0.394966	+	0.684100i
$39$	−2.85793	−	5.55268i	−0.457635	−	0.889140i
$40$	−1.87476	−	3.24719i	−0.296426	−	0.513425i
$41$	0.455940	+	1.70159i	0.0712059	+	0.265744i	0.992346	−	0.123487i	$-0.0394076\pi$
$41$	0.455940	+	1.70159i	0.0712059	+	0.265744i	−0.921140	+	0.389231i	$0.872741\pi$
$42$	2.63266	−	4.97199i	0.406228	−	0.767195i
$43$	0.0503260	−	0.0290558i	0.00767465	−	0.00443096i	−0.496158	−	0.868232i	$-0.665256\pi$
$43$	0.0503260	−	0.0290558i	0.00767465	−	0.00443096i	0.503832	+	0.863801i	$0.331923\pi$
$44$	−1.54706	+	1.54706i	−0.233228	+	0.233228i
$45$	−7.35038	+	8.51484i	−1.09573	+	1.26932i
$46$	0.215275	+	0.803416i	0.0317405	+	0.118457i
$47$	5.83570	−	1.56367i	0.851224	−	0.228085i	0.193272	−	0.981145i	$-0.438090\pi$
$47$	5.83570	−	1.56367i	0.851224	−	0.228085i	0.657951	+	0.753060i	$0.271423\pi$
$48$	−1.46728	+	0.920381i	−0.211783	+	0.132846i
$49$	3.07486	+	1.77527i	0.439265	+	0.253610i
$50$	−8.75029	+	2.34463i	−1.23748	+	0.331581i
$51$	0.445026	+	12.1429i	0.0623161	+	1.70034i
$52$	−3.59257	−	0.305736i	−0.498199	−	0.0423979i
$53$		−	1.62324i		−	0.222969i	−0.993766	−	0.111484i	$-0.964440\pi$
$53$		−	1.62324i		−	0.222969i	0.993766	−	0.111484i	$-0.0355605\pi$
$54$	4.05505	+	3.24909i	0.551822	+	0.442145i
$55$	4.10174	+	7.10443i	0.553079	+	0.957961i
$56$	−1.62408	−	2.81299i	−0.217027	−	0.375901i
$57$	5.74143	−	6.17827i	0.760470	−	0.818332i
$58$	6.55297	+	6.55297i	0.860447	+	0.860447i
$59$	2.06291	+	2.06291i	0.268568	+	0.268568i	0.828523	−	0.559955i	$-0.189182\pi$
$59$	2.06291	+	2.06291i	0.268568	+	0.268568i	−0.559955	+	0.828523i	$0.689182\pi$
$60$	1.90949	+	6.20731i	0.246514	+	0.801361i
$61$	−1.78999	−	3.10035i	−0.229185	−	0.396959i	0.728382	−	0.685171i	$-0.240273\pi$
$61$	−1.78999	−	3.10035i	−0.229185	−	0.396959i	−0.957567	+	0.288212i	$0.906939\pi$
$62$	−0.273299	−	0.473367i	−0.0347090	−	0.0601177i
$63$	−6.36752	+	7.37628i	−0.802233	+	0.929324i
$64$			1.00000i			0.125000i
$65$	−4.59371	+	12.7147i	−0.569779	+	1.57707i
$66$	3.21021	−	2.01368i	0.395150	−	0.247866i
$67$	−12.5547	+	3.36401i	−1.53380	+	0.410979i	−0.924255	−	0.381775i	$-0.875313\pi$
$67$	−12.5547	+	3.36401i	−1.53380	+	0.410979i	−0.609541	+	0.792755i	$0.708646\pi$
$68$	6.07551	+	3.50770i	0.736764	+	0.425371i
$69$	−0.0527631	−	1.43968i	−0.00635193	−	0.173317i
$70$	−11.7641	+	3.15217i	−1.40608	+	0.376757i
$71$	−2.31786	−	8.65035i	−0.275079	−	1.02661i	−0.955789	−	0.294055i	$-0.904995\pi$
$71$	−2.31786	−	8.65035i	−0.275079	−	1.02661i	0.680710	−	0.732553i	$-0.261671\pi$
$72$	2.83317	−	0.986492i	0.333892	−	0.116259i
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	−0.480819	−	0.876820i	$-0.659661\pi$
$73$	3.38343	−	3.38343i	0.396001	−	0.396001i	0.876820	+	0.480819i	$0.159661\pi$
$74$	−1.70433	+	0.983995i	−0.198124	+	0.114387i
$75$	15.6801	−	0.574661i	1.81058	−	0.0663562i
$76$	−1.26031	−	4.70354i	−0.144567	−	0.539533i
$77$	3.55328	+	6.15446i	0.404934	+	0.701366i
$78$	5.94720	+	1.90547i	0.673388	+	0.215752i
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	0.321494	+	0.946911i	$0.395815\pi$
$79$	−5.86001	+	10.1498i	−0.659302	+	1.14194i	−0.980797	+	0.195033i	$0.937518\pi$
$80$	3.62177	+	0.970449i	0.404926	+	0.108500i
$81$	−5.58979	−	7.05367i	−0.621088	−	0.783741i
$82$	−1.52561	−	0.880809i	−0.168475	−	0.0972691i
$83$	3.75798	+	14.0250i	0.412492	+	1.53944i	0.789807	+	0.613356i	$0.210181\pi$
$83$	3.75798	+	14.0250i	0.412492	+	1.53944i	−0.377315	+	0.926085i	$0.623152\pi$
$84$	1.65416	+	5.37730i	0.180484	+	0.586712i
$85$	18.6000	−	18.6000i	2.01746	−	2.01746i
$86$	−0.0150404	+	0.0561314i	−0.00162184	+	0.00605280i
$87$	−8.52944	−	13.5977i	−0.914452	−	1.45782i
$88$		−	2.18787i		−	0.233228i
$89$	3.50606	−	13.0848i	0.371642	−	1.38699i	−0.486548	−	0.873654i	$-0.661744\pi$
$89$	3.50606	−	13.0848i	0.371642	−	1.38699i	0.858190	−	0.513332i	$-0.171589\pi$
$90$	−0.823397	−	11.2184i	−0.0867936	−	1.18252i
$91$	−3.97946	+	11.0146i	−0.417160	+	1.15464i
$92$	−0.720323	−	0.415879i	−0.0750989	−	0.0433583i
$93$	0.278361	+	0.904888i	0.0288647	+	0.0938325i
$94$	−3.02078	+	5.23214i	−0.311570	+	0.539654i
$95$	−18.2582			−1.87325
$96$	0.386713	−	1.68833i	0.0394687	−	0.172314i
$97$	2.55453	−	9.53363i	0.259373	−	0.967993i	−0.706232	−	0.707980i	$-0.749607\pi$
$97$	2.55453	−	9.53363i	0.259373	−	0.967993i	0.965605	−	0.260013i	$-0.0837268\pi$
$98$	−3.42956	+	0.918947i	−0.346438	+	0.0928277i
$99$	−6.19861	+	2.15832i	−0.622983	+	0.216919i
$100$	4.52948	−	7.84529i	0.452948	−	0.784529i
$101$	4.39893			0.437710			0.218855	−	0.975757i	$-0.429768\pi$
$101$	4.39893			0.437710			0.218855	+	0.975757i	$0.429768\pi$
$102$	−8.90099	−	8.27162i	−0.881329	−	0.819013i
$103$	−8.09876	+	4.67582i	−0.797994	+	0.460722i	−0.842769	−	0.538275i	$-0.819076\pi$
$103$	−8.09876	+	4.67582i	−0.797994	+	0.460722i	0.0447750	+	0.998997i	$0.485743\pi$
$104$	2.75652	−	2.32414i	0.270299	−	0.227901i
$105$	21.0806	−	0.772587i	2.05726	−	0.0753968i
$106$	1.14780	+	1.14780i	0.111484	+	0.111484i
$107$	4.41803	−	2.55075i	0.427107	−	0.246590i	−0.271007	−	0.962577i	$-0.587357\pi$
$107$	4.41803	−	2.55075i	0.427107	−	0.246590i	0.698113	+	0.715987i	$0.254023\pi$
$108$	−5.16481	+	0.569900i	−0.496984	+	0.0548386i
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	0.661516	−	0.749931i	$-0.269913\pi$
$109$	−0.923072	−	0.923072i	−0.0884142	−	0.0884142i	−0.749931	+	0.661516i	$0.769913\pi$
$110$	−7.92396	−	2.12322i	−0.755520	−	0.202441i
$111$	3.25799	−	1.00222i	0.309235	−	0.0951266i
$112$	3.13748	+	0.840685i	0.296464	+	0.0794373i
$113$		−	11.5693i		−	1.08835i	−0.838971	−	0.544176i	$-0.816842\pi$
$113$		−	11.5693i		−	1.08835i	0.838971	−	0.544176i	$-0.183158\pi$
$114$	0.308898	+	8.42850i	0.0289309	+	0.789401i
$115$	−2.20525	+	2.20525i	−0.205641	+	0.205641i
$116$	−9.26729			−0.860447
$117$	−9.30395	−	5.51692i	−0.860151	−	0.510040i
$118$	−2.91739			−0.268568
$119$	16.1129	−	16.1129i	1.47707	−	1.47707i
$120$	−5.73945	−	3.03902i	−0.523937	−	0.277423i
$121$		−	6.21322i		−	0.564838i
$122$	3.45799	+	0.926566i	0.313072	+	0.0838874i
$123$	2.23510	+	2.07707i	0.201533	+	0.187283i
$124$	0.527973	+	0.141470i	0.0474133	+	0.0127044i
$125$	−10.7616	−	10.7616i	−0.962547	−	0.962547i
$126$	−0.713296	−	9.71834i	−0.0635455	−	0.865778i
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	−0.367678	−	0.929953i	$-0.619847\pi$
$127$	2.86070	−	1.65163i	0.253846	−	0.146558i	0.621524	+	0.783395i	$0.286514\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.0470998	−	0.0889519i	0.00414691	−	0.00783178i
$130$	−5.74243	−	12.2389i	−0.503645	−	1.07342i
$131$	9.54763	−	5.51233i	0.834181	−	0.481614i	−0.0211014	−	0.999777i	$-0.506717\pi$
$131$	9.54763	−	5.51233i	0.834181	−	0.481614i	0.855282	+	0.518163i	$0.173384\pi$
$132$	−0.846078	+	3.69385i	−0.0736416	+	0.321508i
$133$	−15.8168			−1.37149
$134$	6.49877	−	11.2562i	0.561408	−	0.972388i
$135$	−2.94814	+	19.2588i	−0.253735	+	1.65753i
$136$	−6.77635	+	1.81572i	−0.581067	+	0.155697i
$137$	2.94490	−	10.9905i	0.251600	−	0.938984i	−0.718350	−	0.695682i	$-0.755102\pi$
$137$	2.94490	−	10.9905i	0.251600	−	0.938984i	0.969950	−	0.243303i	$-0.0782309\pi$
$138$	1.05532	+	0.980698i	0.0898345	+	0.0834825i
$139$	3.67668			0.311852			0.155926	−	0.987769i	$-0.450164\pi$
$139$	3.67668			0.311852			0.155926	+	0.987769i	$0.450164\pi$
$140$	6.08953	−	10.5474i	0.514659	−	0.891416i
$141$	7.12340	−	7.66540i	0.599899	−	0.645543i
$142$	7.75569	+	4.47775i	0.650843	+	0.375765i
$143$	−6.03090	+	5.08492i	−0.504329	+	0.425222i
$144$	−1.30580	+	2.70091i	−0.108816	+	0.225076i
$145$	−8.99344	+	33.5640i	−0.746864	+	2.78734i
$146$			4.78490i			0.396001i
$147$	6.14559	−	0.225231i	0.506879	−	0.0185767i
$148$	0.509353	−	1.90093i	0.0418686	−	0.156256i
$149$	6.41670	−	6.41670i	0.525676	−	0.525676i	−0.393604	−	0.919280i	$-0.628772\pi$
$149$	6.41670	−	6.41670i	0.525676	−	0.525676i	0.919280	+	0.393604i	$0.128772\pi$
$150$	−10.6811	+	11.4938i	−0.872110	+	0.938467i
$151$	4.88320	+	18.2244i	0.397389	+	1.48308i	0.817672	+	0.575684i	$0.195264\pi$
$151$	4.88320	+	18.2244i	0.397389	+	1.48308i	−0.420283	+	0.907393i	$0.638069\pi$
$152$	4.21708	+	2.43473i	0.342050	+	0.197483i
$153$	11.8290	+	17.4073i	0.956322	+	1.40730i
$154$	−6.86441	−	1.83931i	−0.553150	−	0.148216i
$155$	1.02474	−	1.77490i	0.0823092	−	0.142564i
$156$	−5.55268	+	2.85793i	−0.444570	+	0.228818i
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.851407	+	0.524506i	$0.175750\pi$
$157$	11.0256	+	19.0969i	0.879939	+	1.52410i	0.0285320	+	0.999593i	$0.490917\pi$
$158$	−3.03336	−	11.3207i	−0.241321	−	0.900623i
$159$	−1.49400	−	2.38174i	−0.118482	−	0.188884i
$160$	−3.24719	+	1.87476i	−0.256713	+	0.148213i
$161$	−1.91038	+	1.91038i	−0.150559	+	0.150559i
$162$	8.94028	+	1.03512i	0.702414	+	0.0813266i
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	0.871158	−	0.491003i	$-0.163370\pi$
$163$	−1.64426	−	6.13647i	−0.128789	−	0.480646i	−0.999946	+	0.0103577i	$0.996703\pi$
$164$	1.70159	−	0.455940i	0.132872	−	0.0356030i
$165$	12.5572	+	6.64899i	0.977574	+	0.517623i
$166$	−12.5744	−	7.25986i	−0.975967	−	0.563475i
$167$	−8.50863	+	2.27988i	−0.658417	+	0.176422i	−0.572532	−	0.819883i	$-0.694039\pi$
$167$	−8.50863	+	2.27988i	−0.658417	+	0.176422i	−0.0858858	+	0.996305i	$0.527372\pi$
$168$	−4.97199	−	2.63266i	−0.383598	−	0.203114i
$169$	−12.8131	−	2.19675i	−0.985619	−	0.168981i
$170$			26.3044i			2.01746i
$171$	2.73789	−	14.3495i	0.209372	−	1.09734i
$172$	−0.0290558	−	0.0503260i	−0.00221548	−	0.00383732i
$173$	−0.0252410	−	0.0437187i	−0.00191904	−	0.00332387i	0.865064	−	0.501661i	$-0.167278\pi$
$173$	−0.0252410	−	0.0437187i	−0.00191904	−	0.00332387i	−0.866983	+	0.498337i	$0.833944\pi$
$174$	15.6462	+	3.58378i	1.18614	+	0.271686i
$175$	−20.8066	−	20.8066i	−1.57283	−	1.57283i
$176$	1.54706	+	1.54706i	0.116614	+	0.116614i
$177$	4.92552	+	1.12819i	0.370224	+	0.0848002i
$178$	6.77319	+	11.7315i	0.507672	+	0.879314i
$179$	−3.55609	−	6.15933i	−0.265795	−	0.460370i	0.701977	−	0.712200i	$-0.252301\pi$
$179$	−3.55609	−	6.15933i	−0.265795	−	0.460370i	−0.967772	+	0.251830i	$0.918968\pi$
$180$	8.51484	+	7.35038i	0.634659	+	0.547865i
$181$		−	20.6330i		−	1.53364i	−0.641863	−	0.766820i	$-0.721838\pi$
$181$		−	20.6330i		−	1.53364i	0.641863	−	0.766820i	$-0.278162\pi$
$182$	−4.97458	−	10.6024i	−0.368741	−	0.785901i
$183$	−5.47991	−	2.90160i	−0.405087	−	0.214492i
$184$	0.803416	−	0.215275i	0.0592286	−	0.0158703i
$185$	−6.39043	−	3.68952i	−0.469834	−	0.271259i
$186$	−0.836683	−	0.443021i	−0.0613486	−	0.0324839i
$187$	14.8258	−	3.97256i	1.08417	−	0.290502i
$188$	−1.56367	−	5.83570i	−0.114042	−	0.425612i
$189$	−2.55393	+	16.6836i	−0.185771	+	1.21355i
$190$	12.9105	−	12.9105i	0.936625	−	0.936625i
$191$	−19.4788	+	11.2461i	−1.40944	+	0.813738i	−0.995334	−	0.0964927i	$-0.969238\pi$
$191$	−19.4788	+	11.2461i	−1.40944	+	0.813738i	−0.414102	+	0.910231i	$0.635904\pi$
$192$	0.920381	+	1.46728i	0.0664228	+	0.105892i
$193$	1.74990	+	6.53071i	0.125961	+	0.470091i	0.999872	−	0.0159939i	$-0.00509122\pi$
$193$	1.74990	+	6.53071i	0.125961	+	0.470091i	−0.873912	+	0.486085i	$0.838425\pi$
$194$	4.93497	+	8.54762i	0.354310	+	0.613683i
$195$	4.96217	+	22.8840i	0.355348	+	1.63876i
$196$	1.77527	−	3.07486i	0.126805	−	0.219633i
$197$	−5.95380	−	1.59532i	−0.424191	−	0.113662i	0.0404072	−	0.999183i	$-0.487134\pi$
$197$	−5.95380	−	1.59532i	−0.424191	−	0.113662i	−0.464598	+	0.885522i	$0.653801\pi$
$198$	2.85692	−	5.90924i	0.203032	−	0.419951i
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	0.612310	−	0.790618i	$-0.290241\pi$
$199$	3.29772	+	1.90394i	0.233769	+	0.134967i	−0.378541	+	0.925585i	$0.623574\pi$
$200$	2.34463	+	8.75029i	0.165791	+	0.618739i
$201$	−15.3250	+	16.4910i	−1.08094	+	1.16319i
$202$	−3.11051	+	3.11051i	−0.218855	+	0.218855i
$203$	−7.79088	+	29.0760i	−0.546813	+	2.04073i
$204$	12.1429	−	0.445026i	0.850171	−	0.0311581i
$205$		−	6.60524i		−	0.461330i
$206$	2.42038	−	9.03299i	0.168636	−	0.629358i
$207$	−1.40247	−	2.06384i	−0.0974785	−	0.143447i
$208$	−0.305736	+	3.59257i	−0.0211989	+	0.249100i
$209$	−9.22643	−	5.32688i	−0.638205	−	0.368468i
$210$	−14.3599	+	15.4525i	−0.990930	+	1.06633i
$211$	9.59387	−	16.6171i	0.660469	−	1.14397i	−0.320024	−	0.947410i	$-0.603691\pi$
$211$	9.59387	−	16.6171i	0.660469	−	1.14397i	0.980493	−	0.196556i	$-0.0629758\pi$
$212$	−1.62324			−0.111484
$213$	−11.3626	−	10.5591i	−0.778549	−	0.723501i
$214$	−1.32036	+	4.92767i	−0.0902582	+	0.336848i
$215$	−0.210466	+	0.0563943i	−0.0143537	+	0.00384606i
$216$	3.24909	−	4.05505i	0.221072	−	0.275911i
$217$	0.887718	−	1.53757i	0.0602622	−	0.104377i
$218$	1.30542			0.0884142
$219$	1.85038	−	8.07848i	0.125037	−	0.545893i
$220$	7.10443	−	4.10174i	0.478980	−	0.276539i
$221$	20.7542	+	14.4591i	1.39608	+	0.972627i
$222$	−1.59507	+	3.01243i	−0.107054	+	0.202181i
$223$	0.198374	+	0.198374i	0.0132841	+	0.0132841i	0.713718	−	0.700434i	$-0.247010\pi$
$223$	0.198374	+	0.198374i	0.0132841	+	0.0132841i	−0.700434	+	0.713718i	$0.747010\pi$
$224$	−2.81299	+	1.62408i	−0.187951	+	0.108513i
$225$	22.4781	−	15.2748i	1.49854	−	1.01832i
$226$	8.18076	+	8.18076i	0.544176	+	0.544176i
$227$	12.3064	+	3.29749i	0.816804	+	0.218862i	0.642949	−	0.765909i	$-0.277711\pi$
$227$	12.3064	+	3.29749i	0.816804	+	0.218862i	0.173856	+	0.984771i	$0.444377\pi$
$228$	−6.17827	−	5.74143i	−0.409166	−	0.380235i
$229$	4.16011	+	1.11470i	0.274908	+	0.0736613i	0.393639	−	0.919265i	$-0.371216\pi$
$229$	4.16011	+	1.11470i	0.274908	+	0.0736613i	−0.118731	+	0.992926i	$0.537883\pi$
$230$		−	3.11870i		−	0.205641i
$231$	10.8781	+	5.75992i	0.715725	+	0.378975i
$232$	6.55297	−	6.55297i	0.430223	−	0.430223i
$233$	−21.0744			−1.38063			−0.690313	−	0.723511i	$-0.742527\pi$
$233$	−21.0744			−1.38063			−0.690313	+	0.723511i	$0.742527\pi$
$234$	10.4799	−	2.67784i	0.685095	−	0.175056i
$235$	−22.6530			−1.47772
$236$	2.06291	−	2.06291i	0.134284	−	0.134284i
$237$	0.743467	+	20.2860i	0.0482933	+	1.31772i
$238$			22.7871i			1.47707i
$239$	12.5730	+	3.36892i	0.813278	+	0.217917i	0.641406	−	0.767202i	$-0.278352\pi$
$239$	12.5730	+	3.36892i	0.813278	+	0.217917i	0.171873	+	0.985119i	$0.445018\pi$
$240$	6.20731	−	1.90949i	0.400680	−	0.123257i
$241$	−1.20385	−	0.322572i	−0.0775471	−	0.0207787i	0.219837	−	0.975537i	$-0.429447\pi$
$241$	−1.20385	−	0.322572i	−0.0775471	−	0.0207787i	−0.297384	+	0.954758i	$0.596114\pi$
$242$	4.39341	+	4.39341i	0.282419	+	0.282419i
$243$	−14.6938	−	5.20494i	−0.942610	−	0.333897i
$244$	−3.10035	+	1.78999i	−0.198480	+	0.114592i
$245$	−9.41360	−	9.41360i	−0.601413	−	0.601413i
$246$	−3.04917	+	0.111749i	−0.194408	+	0.00712488i
$247$	−3.08971	−	17.2831i	−0.196593	−	1.09970i
$248$	−0.473367	+	0.273299i	−0.0300588	+	0.0173545i
$249$	18.4223	+	17.1197i	1.16747	+	1.08492i
$250$	15.2192			0.962547
$251$	5.64794	−	9.78252i	0.356495	−	0.617467i	−0.630878	−	0.775882i	$-0.717305\pi$
$251$	5.64794	−	9.78252i	0.356495	−	0.617467i	0.987373	+	0.158415i	$0.0506384\pi$
$252$	7.37628	+	6.36752i	0.464662	+	0.401116i
$253$	−1.75777	+	0.470993i	−0.110510	+	0.0296111i
$254$	−0.854944	+	3.19070i	−0.0536440	+	0.200202i
$255$	10.1723	−	44.4105i	0.637012	−	2.78109i
$256$	1.00000			0.0625000
$257$	−0.813117	+	1.40836i	−0.0507209	+	0.0878511i	−0.890271	−	0.455431i	$-0.849485\pi$
$257$	−0.813117	+	1.40836i	−0.0507209	+	0.0878511i	0.839550	+	0.543282i	$0.182819\pi$
$258$	0.0295939	+	0.0962031i	0.00184244	+	0.00598934i
$259$	−5.53593	−	3.19617i	−0.343986	−	0.198601i
$260$	12.7147	+	4.59371i	0.788534	+	0.284890i
$261$	−25.0301	−	12.1012i	−1.54932	−	0.749046i
$262$	−2.85339	+	10.6490i	−0.176283	+	0.657897i
$263$			11.3766i			0.701511i	0.936467	+	0.350755i	$0.114075\pi$
$263$			11.3766i			0.701511i	−0.936467	+	0.350755i	$0.885925\pi$
$264$	−2.01368	−	3.21021i	−0.123933	−	0.197575i
$265$	−1.57527	+	5.87898i	−0.0967680	+	0.361143i
$266$	11.1842	−	11.1842i	0.685745	−	0.685745i
$267$	−6.89865	−	22.4259i	−0.422190	−	1.37244i
$268$	3.36401	+	12.5547i	0.205490	+	0.766898i
$269$	10.3721	+	5.98835i	0.632400	+	0.365116i	0.781681	−	0.623678i	$-0.214363\pi$
$269$	10.3721	+	5.98835i	0.632400	+	0.365116i	−0.149281	+	0.988795i	$0.547696\pi$
$270$	−11.5334	−	15.7027i	−0.701898	−	0.955633i
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.898502	−	0.438970i	$-0.144657\pi$
$271$	23.9876	+	6.42745i	1.45714	+	0.390440i	0.558640	+	0.829410i	$0.311323\pi$
$272$	3.50770	−	6.07551i	0.212685	−	0.368382i
$273$	4.29865	+	19.8240i	0.260166	+	1.19981i
$274$	5.68912	+	9.85384i	0.343692	+	0.595292i
$275$	−5.12975	−	19.1445i	−0.309336	−	1.15446i
$276$	−1.43968	+	0.0527631i	−0.0866585	+	0.00317596i
$277$	−13.5548	+	7.82589i	−0.814432	+	0.470212i	−0.848493	−	0.529207i	$-0.822489\pi$
$277$	−13.5548	+	7.82589i	−0.814432	+	0.470212i	0.0340608	+	0.999420i	$0.489156\pi$
$278$	−2.59981	+	2.59981i	−0.155926	+	0.155926i
$279$	1.24127	+	1.07152i	0.0743131	+	0.0641503i
$280$	3.15217	+	11.7641i	0.188378	+	0.703038i
$281$	4.25406	−	1.13987i	0.253776	−	0.0679991i	−0.129688	−	0.991555i	$-0.541398\pi$
$281$	4.25406	−	1.13987i	0.253776	−	0.0679991i	0.383464	+	0.923556i	$0.374731\pi$
$282$	0.383250	+	10.4573i	0.0228222	+	0.622721i
$283$	15.8083	+	9.12694i	0.939707	+	0.542540i	0.889868	−	0.456217i	$-0.150796\pi$
$283$	15.8083	+	9.12694i	0.939707	+	0.542540i	0.0498385	+	0.998757i	$0.484129\pi$
$284$	−8.65035	+	2.31786i	−0.513304	+	0.137539i
$285$	−26.7898	+	16.8045i	−1.58689	+	0.995412i
$286$	0.668910	−	7.86007i	0.0395535	−	0.464776i
$287$		−	5.72202i		−	0.337760i
$288$	−0.986492	−	2.83317i	−0.0581296	−	0.166946i
$289$	−16.1079	−	27.8997i	−0.947523	−	1.64116i
$290$	−17.3740	−	30.0926i	−1.02024	−	1.76710i
$291$	−5.02638	−	16.3396i	−0.294651	−	0.957844i
$292$	−3.38343	−	3.38343i	−0.198000	−	0.198000i
$293$	7.90296	+	7.90296i	0.461696	+	0.461696i	0.899211	−	0.437515i	$-0.144141\pi$
$293$	7.90296	+	7.90296i	0.461696	+	0.461696i	−0.437515	+	0.899211i	$0.644141\pi$
$294$	−4.18632	+	4.50485i	−0.244151	+	0.262728i
$295$	−5.46942	−	9.47332i	−0.318442	−	0.551558i
$296$	0.983995	+	1.70433i	0.0571936	+	0.0990622i
$297$	−7.10859	+	8.87193i	−0.412482	+	0.514801i
$298$			9.07458i			0.525676i
$299$	−2.46066	−	1.71430i	−0.142304	−	0.0991405i
$300$	−0.574661	−	15.6801i	−0.0331781	−	0.905289i
$301$	−0.182324	+	0.0488535i	−0.0105090	+	0.00281587i
$302$	−16.3395	−	9.43362i	−0.940234	−	0.542844i
$303$	6.45444	−	4.04869i	0.370798	−	0.232591i
$304$	−4.70354	+	1.26031i	−0.269767	+	0.0722837i
$305$	3.47419	+	12.9658i	0.198931	+	0.742422i
$306$	−20.6732	−	3.94445i	−1.18181	−	0.225489i
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	−0.990723	−	0.135900i	$-0.956608\pi$
$307$	−14.9777	+	14.9777i	−0.854823	+	0.854823i	0.135900	+	0.990723i	$0.456608\pi$
$308$	6.15446	−	3.55328i	0.350683	−	0.202467i
$309$	−7.57957	+	14.3147i	−0.431187	+	0.814333i
$310$	0.530445	+	1.97965i	0.0301273	+	0.112436i
$311$	6.94304	+	12.0257i	0.393704	+	0.681915i	0.992935	−	0.118661i	$-0.0378603\pi$
$311$	6.94304	+	12.0257i	0.393704	+	0.681915i	−0.599231	+	0.800576i	$0.704527\pi$
$312$	1.90547	−	5.94720i	0.107876	−	0.336694i
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	−0.698267	−	0.715838i	$-0.746045\pi$
$313$	4.79094	−	8.29816i	0.270800	−	0.469040i	0.969067	+	0.246798i	$0.0793784\pi$
$314$	−21.2998	−	5.70727i	−1.20202	−	0.322080i
$315$	30.2200	−	20.5358i	1.70270	−	1.15706i
$316$	10.1498	+	5.86001i	0.570972	+	0.329651i
$317$	4.16793	+	15.5549i	0.234095	+	0.873653i	0.978555	+	0.205986i	$0.0660402\pi$
$317$	4.16793	+	15.5549i	0.234095	+	0.873653i	−0.744460	+	0.667667i	$0.767293\pi$
$318$	2.74056	+	0.627727i	0.153683	+	0.0352012i
$319$	−14.3370	+	14.3370i	−0.802721	+	0.802721i
$320$	0.970449	−	3.62177i	0.0542498	−	0.202463i
$321$	4.13480	−	7.80892i	0.230782	−	0.435851i
$322$		−	2.70168i		−	0.150559i
$323$	−8.84157	+	32.9972i	−0.491958	+	1.83601i
$324$	−7.05367	+	5.58979i	−0.391870	+	0.310544i
$325$	18.6710	−	26.7999i	1.03568	−	1.48659i
$326$	5.50181	+	3.17647i	0.304717	+	0.175928i
$327$	−2.20398	−	0.504823i	−0.121880	−	0.0279168i
$328$	−0.880809	+	1.52561i	−0.0486345	+	0.0842375i
$329$	−19.6239			−1.08190
$330$	−13.5808	+	4.17772i	−0.747599	+	0.229976i
$331$	1.91411	−	7.14356i	0.105209	−	0.392646i	−0.893160	−	0.449740i	$-0.851517\pi$
$331$	1.91411	−	7.14356i	0.105209	−	0.392646i	0.998369	+	0.0570939i	$0.0181834\pi$
$332$	14.0250	−	3.75798i	0.769721	−	0.206246i
$333$	3.85795	−	4.46913i	0.211414	−	0.244907i
$334$	4.40439	−	7.62863i	0.240998	−	0.417420i
$335$	48.7346			2.66266
$336$	5.37730	−	1.65416i	0.293356	−	0.0902419i
$337$	−16.2869	+	9.40326i	−0.887205	+	0.512228i	−0.873027	−	0.487671i	$-0.837846\pi$
$337$	−16.2869	+	9.40326i	−0.887205	+	0.512228i	−0.0141778	+	0.999899i	$0.504513\pi$
$338$	10.6135	−	7.50686i	0.577300	−	0.408319i
$339$	−10.6482	−	16.9754i	−0.578331	−	0.921979i
$340$	−18.6000	−	18.6000i	−1.00873	−	1.00873i
$341$	1.03567	−	0.597942i	0.0560845	−	0.0323804i
$342$	8.21067	+	12.0826i	0.443982	+	0.653354i
$343$	7.92271	+	7.92271i	0.427786	+	0.427786i
$344$	0.0561314	+	0.0150404i	0.00302640	+	0.000810922i
$345$	−1.20604	+	5.26539i	−0.0649310	+	0.283479i
$346$	0.0487619	+	0.0130657i	0.00262145	+	0.000702417i
$347$			24.7596i			1.32916i	0.747215	+	0.664582i	$0.231390\pi$
$347$			24.7596i			1.32916i	−0.747215	+	0.664582i	$0.768610\pi$
$348$	−13.5977	+	8.52944i	−0.728912	+	0.457226i
$349$	2.41492	−	2.41492i	0.129267	−	0.129267i	−0.639513	−	0.768780i	$-0.720864\pi$
$349$	2.41492	−	2.41492i	0.129267	−	0.129267i	0.768780	+	0.639513i	$0.220864\pi$
$350$	29.4250			1.57283
$351$	−18.7291	+	0.468337i	−0.999688	+	0.0249980i
$352$	−2.18787			−0.116614
$353$	3.14228	−	3.14228i	0.167247	−	0.167247i	−0.618521	−	0.785768i	$-0.712268\pi$
$353$	3.14228	−	3.14228i	0.167247	−	0.167247i	0.785768	+	0.618521i	$0.212268\pi$
$354$	−4.28062	+	2.68511i	−0.227512	+	0.142712i
$355$			33.5789i			1.78218i
$356$	−13.0848	−	3.50606i	−0.693493	−	0.185821i
$357$	8.81207	−	38.4721i	0.466384	−	2.03616i
$358$	6.86984	+	1.84077i	0.363082	+	0.0972876i
$359$	−1.76025	−	1.76025i	−0.0929022	−	0.0929022i	0.659128	−	0.752031i	$-0.270925\pi$
$359$	−1.76025	−	1.76025i	−0.0929022	−	0.0929022i	−0.752031	+	0.659128i	$0.770925\pi$
$360$	−11.2184	+	0.823397i	−0.591262	+	0.0433968i
$361$	4.08043	−	2.35584i	0.214759	−	0.123991i
$362$	14.5897	+	14.5897i	0.766820	+	0.766820i
$363$	−5.71853	−	9.11650i	−0.300145	−	0.478492i
$364$	11.0146	+	3.97946i	0.577321	+	0.208580i
$365$	−15.5375	+	8.97055i	−0.813268	+	0.469540i
$366$	5.92662	−	1.82314i	0.309790	−	0.0952972i
$367$	8.15098			0.425478			0.212739	−	0.977109i	$-0.431762\pi$
$367$	8.15098			0.425478			0.212739	+	0.977109i	$0.431762\pi$
$368$	−0.415879	+	0.720323i	−0.0216792	+	0.0375494i
$369$	5.19121	+	0.990482i	0.270243	+	0.0515624i
$370$	7.12760	−	1.90984i	0.370546	−	0.0992876i
$371$	−1.36463	+	5.09287i	−0.0708481	+	0.264409i
$372$	0.904888	−	0.278361i	0.0469162	−	0.0144323i
$373$	23.6763			1.22591			0.612956	−	0.790117i	$-0.289980\pi$
$373$	23.6763			1.22591			0.612956	+	0.790117i	$0.289980\pi$
$374$	−7.67439	+	13.2924i	−0.396833	+	0.687336i
$375$	−25.6950	−	5.88546i	−1.32688	−	0.303924i
$376$	5.23214	+	3.02078i	0.269827	+	0.155785i
$377$	−33.2934	−	2.83334i	−1.71470	−	0.145925i
$378$	−9.99118	−	13.6030i	−0.513891	−	0.699662i
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	−0.849057	−	0.528302i	$-0.822829\pi$
$379$	2.92796	−	10.9273i	0.150399	−	0.561297i	0.999456	−	0.0329946i	$-0.0105044\pi$
$380$			18.2582i			0.936625i
$381$	2.67731	−	5.05633i	0.137163	−	0.259043i
$382$	5.82140	−	21.7258i	0.297849	−	1.11159i
$383$	−21.2432	+	21.2432i	−1.08548	+	1.08548i	−0.0894896	+	0.995988i	$0.528524\pi$
$383$	−21.2432	+	21.2432i	−1.08548	+	1.08548i	−0.995988	+	0.0894896i	$0.971476\pi$
$384$	−1.68833	−	0.386713i	−0.0861572	−	0.0197344i
$385$	−6.89655	−	25.7383i	−0.351481	−	1.31174i
$386$	−5.85528	−	3.38055i	−0.298026	−	0.172065i
$387$	−0.0127613	−	0.173867i	−0.000648693	−	0.00883815i
$388$	−9.53363	−	2.55453i	−0.483997	−	0.129687i
$389$	4.55590	−	7.89104i	0.230993	−	0.400092i	−0.727108	−	0.686524i	$-0.759136\pi$
$389$	4.55590	−	7.89104i	0.230993	−	0.400092i	0.958101	+	0.286432i	$0.0924692\pi$
$390$	−19.6902	−	12.6726i	−0.997052	−	0.641704i
$391$	2.91755	+	5.05335i	0.147547	+	0.255559i
$392$	0.918947	+	3.42956i	0.0464138	+	0.173219i
$393$	8.93557	−	16.8756i	0.450740	−	0.851260i
$394$	5.33803	−	3.08191i	0.268926	−	0.155265i
$395$	31.0735	−	31.0735i	1.56348	−	1.56348i
$396$	2.15832	+	6.19861i	0.108460	+	0.311492i
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	−0.999927	−	0.0121147i	$-0.996144\pi$
$397$	−2.78992	−	10.4121i	−0.140022	−	0.522570i	0.859904	−	0.510455i	$-0.170523\pi$
$398$	−3.67812	+	0.985551i	−0.184368	+	0.0494012i
$399$	−23.2076	+	14.5575i	−1.16183	+	0.728785i
$400$	−7.84529	−	4.52948i	−0.392265	−	0.226474i
$401$	11.4714	−	3.07374i	0.572852	−	0.153495i	0.0392478	−	0.999230i	$-0.487504\pi$
$401$	11.4714	−	3.07374i	0.572852	−	0.153495i	0.533604	+	0.845734i	$0.320837\pi$
$402$	−0.824507	−	22.4973i	−0.0411227	−	1.12206i
$403$	1.85352	+	0.669660i	0.0923306	+	0.0333581i
$404$		−	4.39893i		−	0.218855i
$405$	13.3997	+	30.9713i	0.665836	+	1.53898i
$406$	−15.0508	−	26.0688i	−0.746960	−	1.29377i
$407$	−2.15286	−	3.72885i	−0.106713	−	0.184832i
$408$	−8.27162	+	8.90099i	−0.409506	+	0.440664i
$409$	−15.1835	−	15.1835i	−0.750777	−	0.750777i	0.223847	−	0.974624i	$-0.428138\pi$
$409$	−15.1835	−	15.1835i	−0.750777	−	0.750777i	−0.974624	+	0.223847i	$0.928138\pi$
$410$	4.67061	+	4.67061i	0.230665	+	0.230665i
$411$	−5.79449	−	18.8366i	−0.285821	−	0.929140i
$412$	4.67582	+	8.09876i	0.230361	+	0.398997i
$413$	−4.73808	−	8.20659i	−0.233146	−	0.403820i
$414$	2.45106	+	0.467661i	0.120463	+	0.0229843i
$415$		−	54.4421i		−	2.67246i
$416$	−2.32414	−	2.75652i	−0.113950	−	0.135149i
$417$	5.39470	−	3.38395i	0.264180	−	0.165713i
$418$	10.2907	−	2.75740i	0.503337	−	0.134869i
$419$	−9.35158	−	5.39914i	−0.456855	−	0.263765i	0.253866	−	0.967239i	$-0.418298\pi$
$419$	−9.35158	−	5.39914i	−0.456855	−	0.263765i	−0.710721	+	0.703474i	$0.751631\pi$
$420$	−0.772587	−	21.0806i	−0.0376984	−	1.02863i
$421$	6.34283	−	1.69956i	0.309131	−	0.0828313i	−0.100919	−	0.994895i	$-0.532178\pi$
$421$	6.34283	−	1.69956i	0.309131	−	0.0828313i	0.410049	+	0.912063i	$0.365512\pi$
$422$	4.96615	+	18.5339i	0.241748	+	0.902217i
$423$	3.39691	−	17.8035i	0.165163	−	0.865636i
$424$	1.14780	−	1.14780i	0.0557422	−	0.0557422i
$425$	−55.0378	+	31.7761i	−2.66973	+	1.54137i
$426$	15.5010	−	0.568098i	0.751025	−	0.0275244i
$427$	3.00963	+	11.2321i	0.145646	+	0.543560i
$428$	−2.55075	−	4.41803i	−0.123295	−	0.213553i
$429$	−4.16893	+	13.0117i	−0.201278	+	0.628211i
$430$	0.108945	−	0.188699i	0.00525381	−	0.00909987i
$431$	5.36331	+	1.43709i	0.258341	+	0.0692224i	0.385665	−	0.922639i	$-0.373972\pi$
$431$	5.36331	+	1.43709i	0.258341	+	0.0692224i	−0.127324	+	0.991861i	$0.540639\pi$
$432$	0.569900	+	5.16481i	0.0274193	+	0.248492i
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.999997	−	0.00257012i	$-0.000818096\pi$
$433$	31.1666	+	17.9940i	1.49777	+	0.864737i	0.497773	+	0.867308i	$0.334151\pi$
$434$	0.459516	+	1.71494i	0.0220575	+	0.0823197i
$435$	17.6958	+	57.5250i	0.848448	+	2.75811i
$436$	−0.923072	+	0.923072i	−0.0442071	+	0.0442071i
$437$	1.04827	−	3.91220i	0.0501456	−	0.187146i
$438$	4.40393	+	7.02076i	0.210428	+	0.335465i
$439$		−	20.3140i		−	0.969533i	−0.874644	−	0.484767i	$-0.838905\pi$
$439$		−	20.3140i		−	0.969533i	0.874644	−	0.484767i	$-0.161095\pi$
$440$	−2.12322	+	7.92396i	−0.101220	+	0.377760i
$441$	8.80997	−	5.98676i	0.419523	−	0.285084i
$442$	−24.8996	+	4.45131i	−1.18435	+	0.211727i
$443$	−16.2468	−	9.38011i	−0.771910	−	0.445662i	0.0616456	−	0.998098i	$-0.480365\pi$
$443$	−16.2468	−	9.38011i	−0.771910	−	0.445662i	−0.833556	+	0.552436i	$0.813698\pi$
$444$	−1.00222	−	3.25799i	−0.0475633	−	0.154617i
$445$	−25.3963	+	43.9876i	−1.20390	+	2.08521i
$446$	−0.280543			−0.0132841
$447$	3.50926	−	15.3209i	0.165982	−	0.724652i
$448$	0.840685	−	3.13748i	0.0397187	−	0.148232i
$449$	15.3460	−	4.11194i	0.724221	−	0.194055i	0.122167	−	0.992510i	$-0.461016\pi$
$449$	15.3460	−	4.11194i	0.724221	−	0.194055i	0.602054	+	0.798455i	$0.294349\pi$
$450$	−5.09346	+	26.6953i	−0.240108	+	1.25843i
$451$	1.92710	−	3.33783i	0.0907435	−	0.157172i
$452$	−11.5693			−0.544176
$453$	23.9384	+	22.2458i	1.12472	+	1.04520i
$454$	−11.0336	+	6.37026i	−0.517833	+	0.298971i
$455$	25.1018	−	36.0304i	1.17679	−	1.68913i
$456$	8.42850	−	0.308898i	0.394701	−	0.0144655i
$457$	−0.620379	−	0.620379i	−0.0290201	−	0.0290201i	0.692448	−	0.721468i	$-0.256532\pi$
$457$	−0.620379	−	0.620379i	−0.0290201	−	0.0290201i	−0.721468	+	0.692448i	$0.756532\pi$
$458$	−3.72985	+	2.15343i	−0.174285	+	0.100623i
$459$	33.3779	+	14.6541i	1.55795	+	0.683997i
$460$	2.20525	+	2.20525i	0.102820	+	0.102820i
$461$	22.4997	+	6.02877i	1.04792	+	0.280788i	0.741390	−	0.671074i	$-0.234167\pi$
$461$	22.4997	+	6.02877i	1.04792	+	0.280788i	0.306525	+	0.951863i	$0.400834\pi$
$462$	−11.7648	+	3.61909i	−0.547350	+	0.168375i
$463$	−17.4167	−	4.66680i	−0.809424	−	0.216885i	−0.169707	−	0.985495i	$-0.554282\pi$
$463$	−17.4167	−	4.66680i	−0.809424	−	0.216885i	−0.639718	+	0.768610i	$0.720949\pi$
$464$			9.26729i			0.430223i
$465$	−0.130010	−	3.54743i	−0.00602908	−	0.164508i
$466$	14.9018	−	14.9018i	0.690313	−	0.690313i
$467$	24.8989			1.15218			0.576091	−	0.817386i	$-0.304577\pi$
$467$	24.8989			1.15218			0.576091	+	0.817386i	$0.304577\pi$
$468$	−5.51692	+	9.30395i	−0.255020	+	0.430075i
$469$	42.2181			1.94945
$470$	16.0181	−	16.0181i	0.738859	−	0.738859i
$471$	33.7540	+	17.8727i	1.55530	+	0.823529i
$472$			2.91739i			0.134284i
$473$	−0.122808	−	0.0329064i	−0.00564673	−	0.00151304i
$474$	−14.8701	−	13.8187i	−0.683006	−	0.634713i
$475$	42.6092	+	11.4171i	1.95504	+	0.523852i
$476$	−16.1129	−	16.1129i	−0.738535	−	0.738535i
$477$	−4.38421	−	2.11962i	−0.200739	−	0.0970506i
$478$	−11.2726	+	6.50825i	−0.515598	+	0.297681i
$479$	−5.37507	−	5.37507i	−0.245593	−	0.245593i	0.573566	−	0.819159i	$-0.305560\pi$
$479$	−5.37507	−	5.37507i	−0.245593	−	0.245593i	−0.819159	+	0.573566i	$0.805560\pi$
$480$	−3.03902	+	5.73945i	−0.138712	+	0.261969i
$481$	2.41107	−	6.67350i	0.109935	−	0.304285i
$482$	1.07935	−	0.623161i	0.0491629	−	0.0283842i
$483$	−1.04477	+	4.56132i	−0.0475389	+	0.207547i
$484$	−6.21322			−0.282419
$485$	−18.5038	+	32.0495i	−0.840215	+	1.45529i
$486$	14.0706	−	6.70966i	0.638253	−	0.304356i
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.896660	−	0.442720i	$-0.854014\pi$
$487$	−32.0391	+	8.58485i	−1.45183	+	0.389017i	−0.555171	+	0.831736i	$0.687347\pi$
$488$	0.926566	−	3.45799i	0.0419437	−	0.156536i
$489$	−8.06048	−	7.49055i	−0.364508	−	0.338734i
$490$	13.3128			0.601413
$491$	−12.9239	+	22.3849i	−0.583248	+	1.01022i	0.411843	+	0.911255i	$0.364885\pi$
$491$	−12.9239	+	22.3849i	−0.583248	+	1.01022i	−0.995091	+	0.0989607i	$0.968448\pi$
$492$	2.07707	−	2.23510i	0.0936414	−	0.100766i
$493$	56.3035	+	32.5069i	2.53578	+	1.46404i
$494$	14.4057	+	10.0362i	0.648145	+	0.451552i
$495$	24.5444	−	1.80149i	1.10319	−	0.0809708i
$496$	0.141470	−	0.527973i	0.00635218	−	0.0237067i
$497$			29.0889i			1.30482i
$498$	−25.1320	+	0.921068i	−1.12619	+	0.0412741i
$499$	−4.22357	+	15.7626i	−0.189073	+	0.705629i	0.804649	+	0.593751i	$0.202353\pi$
$499$	−4.22357	+	15.7626i	−0.189073	+	0.705629i	−0.993722	+	0.111879i	$0.964313\pi$
$500$	−10.7616	+	10.7616i	−0.481273	+	0.481273i
$501$	−10.3861	+	11.1764i	−0.464019	+	0.499325i
$502$	2.92359	+	10.9110i	0.130486	+	0.486981i
$503$	−6.80210	−	3.92720i	−0.303291	−	0.175105i	0.340630	−	0.940198i	$-0.389360\pi$
$503$	−6.80210	−	3.92720i	−0.303291	−	0.175105i	−0.643920	+	0.765093i	$0.722693\pi$
$504$	−9.71834	+	0.713296i	−0.432889	+	0.0317727i
$505$	−15.9319	−	4.26894i	−0.708960	−	0.189965i
$506$	0.909889	−	1.57597i	0.0404495	−	0.0700606i
$507$	−20.8221	+	8.56965i	−0.924743	+	0.380592i
$508$	−1.65163	−	2.86070i	−0.0732790	−	0.126923i
$509$	−6.70498	−	25.0233i	−0.297193	−	1.10914i	−0.939460	−	0.342659i	$-0.888672\pi$
$509$	−6.70498	−	25.0233i	−0.297193	−	1.10914i	0.642267	−	0.766481i	$-0.277994\pi$
$510$	24.2101	+	38.5958i	1.07204	+	1.70905i
$511$	−13.4599	+	7.77105i	−0.595429	+	0.343771i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−9.18980	−	23.5746i	−0.405740	−	1.04084i
$514$	−0.420900	−	1.57082i	−0.0185651	−	0.0692860i
$515$	33.8695	−	9.07529i	1.49247	−	0.399905i
$516$	−0.0889519	−	0.0470998i	−0.00391589	−	0.00207345i
$517$	−11.4473	−	6.60908i	−0.503450	−	0.290667i
$518$	6.17453	−	1.65446i	0.271293	−	0.0726928i
$519$	−0.0772734	−	0.0409160i	−0.00339193	−	0.00179602i
$520$	−12.2389	+	5.74243i	−0.536712	+	0.251822i
$521$			44.6910i			1.95795i	0.203981	+	0.978975i	$0.434612\pi$
$521$			44.6910i			1.95795i	−0.203981	+	0.978975i	$0.565388\pi$
$522$	26.2558	−	9.14211i	1.14918	−	0.400139i
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	0.913429	−	0.406998i	$-0.133424\pi$
$523$	2.38397	+	4.12916i	0.104244	+	0.180556i	−0.809185	+	0.587554i	$0.800091\pi$
$524$	−5.51233	−	9.54763i	−0.240807	−	0.417090i
$525$	−49.6790	−	11.3790i	−2.16817	−	0.496621i
$526$	−8.04447	−	8.04447i	−0.350755	−	0.350755i
$527$	−2.71147	−	2.71147i	−0.118113	−	0.118113i
$528$	3.69385	+	0.846078i	0.160754	+	0.0368208i
$529$	11.1541	+	19.3195i	0.484960	+	0.839976i
$530$	−3.04319	−	5.27095i	−0.132188	−	0.228956i
$531$	8.26546	−	2.87798i	0.358690	−	0.124894i
$532$			15.8168i			0.685745i
$533$	6.25248	−	1.11776i	0.270825	−	0.0484155i
$534$	20.7356	+	10.9794i	0.897317	+	0.475127i
$535$	−18.4764	+	4.95074i	−0.798806	+	0.214039i
$536$	−11.2562	−	6.49877i	−0.486194	−	0.280704i
$537$	−10.8867	−	5.76448i	−0.469796	−	0.248756i
$538$	−11.5686	+	3.09980i	−0.498758	+	0.133642i
$539$	−2.01054	−	7.50343i	−0.0866000	−	0.323196i
$540$	19.2588	+	2.94814i	0.828766	+	0.126868i
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.437565	+	0.899187i	$0.644159\pi$
$541$	−31.0921	+	31.0921i	−1.33675	+	1.33675i	−0.899187	+	0.437565i	$0.855841\pi$
$542$	−21.5067	+	12.4169i	−0.923791	+	0.533351i
$543$	−18.9902	−	30.2743i	−0.814949	−	1.29920i
$544$	1.81572	+	6.77635i	0.0778483	+	0.290534i
$545$	2.44736	+	4.23894i	0.104833	+	0.181576i
$546$	−17.0573	−	10.9781i	−0.729986	−	0.469820i
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	−0.671751	−	0.740777i	$-0.734458\pi$
$547$	7.14869	−	12.3819i	0.305656	−	0.529412i	0.977407	+	0.211365i	$0.0677910\pi$
$548$	−10.9905	−	2.94490i	−0.469492	−	0.125800i
$549$	−10.7111	+	0.786163i	−0.457139	+	0.0335526i
$550$	17.1645	+	9.90992i	0.731896	+	0.422561i
$551$	−11.6797	−	43.5891i	−0.497570	−	1.85696i
$552$	0.980698	−	1.05532i	0.0417413	−	0.0449172i
$553$	26.9185	−	26.9185i	1.14469	−	1.14469i
$554$	4.05098	−	15.1185i	0.172110	−	0.642322i
$555$	−12.7723	+	0.468094i	−0.542154	+	0.0198695i
$556$		−	3.67668i		−	0.155926i
$557$	11.2642	−	42.0386i	0.477280	−	1.78123i	−0.135277	−	0.990808i	$-0.543193\pi$
$557$	11.2642	−	42.0386i	0.477280	−	1.78123i	0.612557	−	0.790426i	$-0.290141\pi$
$558$	−1.63539	+	0.120033i	−0.0692317	+	0.00508140i
$559$	−0.0889982	−	0.189683i	−0.00376422	−	0.00802273i
$560$	−10.5474	−	6.08953i	−0.445708	−	0.257330i
$561$	18.0973	−	19.4742i	0.764067	−	0.822202i
$562$	−2.20206	+	3.81409i	−0.0928885	+	0.160888i
$563$	7.46962			0.314807			0.157403	−	0.987534i	$-0.449688\pi$
$563$	7.46962			0.314807			0.157403	+	0.987534i	$0.449688\pi$
$564$	−7.66540	−	7.12340i	−0.322772	−	0.299949i
$565$	−11.2275	+	41.9015i	−0.472343	+	1.76281i
$566$	−17.6319	+	4.72445i	−0.741124	+	0.198583i
$567$	11.6079	+	26.8300i	0.487488	+	1.12675i
$568$	4.47775	−	7.75569i	0.187882	−	0.325422i
$569$	−41.3056			−1.73162			−0.865810	−	0.500373i	$-0.833196\pi$
$569$	−41.3056			−1.73162			−0.865810	+	0.500373i	$0.833196\pi$
$570$	7.06068	−	30.8258i	0.295739	−	1.29115i
$571$	38.0908	−	21.9917i	1.59405	−	0.920326i	0.601449	−	0.798911i	$-0.294590\pi$
$571$	38.0908	−	21.9917i	1.59405	−	0.920326i	0.992602	−	0.121415i	$-0.0387432\pi$
$572$	5.08492	+	6.03090i	0.212611	+	0.252165i
$573$	−18.2301	+	34.4290i	−0.761572	+	1.43829i
$574$	4.04608	+	4.04608i	0.168880	+	0.168880i
$575$	6.52538	−	3.76743i	0.272127	−	0.157113i
$576$	2.70091	+	1.30580i	0.112538	+	0.0544082i
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.984952	−	0.172831i	$-0.944709\pi$
$577$	−27.8109	−	27.8109i	−1.15778	−	1.15778i	−0.172831	−	0.984952i	$-0.555291\pi$
$578$	31.1180	+	8.33806i	1.29434	+	0.346817i
$579$	8.57833	+	7.97178i	0.356503	+	0.331296i
$580$	33.5640	+	8.99344i	1.39367	+	0.373432i
$581$		−	47.1624i		−	1.95663i
$582$	15.1080	+	7.99966i	0.626248	+	0.331597i
$583$	−2.51124	+	2.51124i	−0.104005	+	0.104005i
$584$	4.78490			0.198000
$585$	28.3429	+	29.0100i	1.17183	+	1.19942i
$586$	−11.1765			−0.461696
$587$	7.42299	−	7.42299i	0.306380	−	0.306380i	−0.537124	−	0.843503i	$-0.680489\pi$
$587$	7.42299	−	7.42299i	0.306380	−	0.306380i	0.843503	+	0.537124i	$0.180489\pi$
$588$	−0.225231	−	6.14559i	−0.00928836	−	0.253440i
$589$			2.66164i			0.109671i
$590$	10.5661	+	2.83118i	0.435000	+	0.116558i
$591$	−10.2042	+	3.13900i	−0.419743	+	0.129121i
$592$	−1.90093	−	0.509353i	−0.0781279	−	0.0209343i
$593$	24.8672	+	24.8672i	1.02117	+	1.02117i	0.999771	+	0.0214039i	$0.00681360\pi$
$593$	24.8672	+	24.8672i	1.02117	+	1.02117i	0.0214039	+	0.999771i	$0.493186\pi$
$594$	−1.24687	−	11.2999i	−0.0511596	−	0.463642i
$595$	−73.9940	+	42.7205i	−3.03346	+	1.75137i
$596$	−6.41670	−	6.41670i	−0.262838	−	0.262838i
$597$	6.59101	−	0.241555i	0.269752	−	0.00988619i
$598$	2.95214	−	0.527755i	0.120722	−	0.0215815i
$599$	5.46701	−	3.15638i	0.223376	−	0.128966i	−0.384137	−	0.923276i	$-0.625501\pi$
$599$	5.46701	−	3.15638i	0.223376	−	0.128966i	0.607512	+	0.794310i	$0.292167\pi$
$600$	11.4938	+	10.6811i	0.469233	+	0.436055i
$601$	33.7487			1.37664			0.688318	−	0.725409i	$-0.258349\pi$
$601$	33.7487			1.37664			0.688318	+	0.725409i	$0.258349\pi$
$602$	0.0943777	−	0.163467i	0.00384655	−	0.00666242i
$603$	−7.30795	+	38.3017i	−0.297603	+	1.55976i
$604$	18.2244	−	4.88320i	0.741539	−	0.198695i
$605$	−6.02961	+	22.5028i	−0.245139	+	0.914870i
$606$	−1.70112	+	7.42683i	−0.0691033	+	0.301695i
$607$	25.8145			1.04778			0.523888	−	0.851787i	$-0.324481\pi$
$607$	25.8145			1.04778			0.523888	+	0.851787i	$0.324481\pi$
$608$	2.43473	−	4.21708i	0.0987414	−	0.171025i
$609$	15.3296	+	49.8330i	0.621187	+	2.01934i
$610$	−11.6249	−	6.71161i	−0.470677	−	0.271745i
$611$	−3.83341	−	21.4432i	−0.155083	−	0.867499i
$612$	17.4073	−	11.8290i	0.703650	−	0.478161i
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	−0.818715	−	0.574200i	$-0.805313\pi$
$613$	4.39253	−	16.3932i	0.177413	−	0.662113i	0.996128	−	0.0879138i	$-0.0280200\pi$
$614$		−	21.1817i		−	0.854823i
$615$	−6.07934	−	9.69171i	−0.245143	−	0.390807i
$616$	−1.83931	+	6.86441i	−0.0741080	+	0.276575i
$617$	32.7229	−	32.7229i	1.31737	−	1.31737i	0.401528	−	0.915847i	$-0.368479\pi$
$617$	32.7229	−	32.7229i	1.31737	−	1.31737i	0.915847	−	0.401528i	$-0.131521\pi$
$618$	−4.76243	−	15.4816i	−0.191573	−	0.622760i
$619$	−8.87599	−	33.1257i	−0.356756	−	1.33143i	−0.878260	−	0.478183i	$-0.841295\pi$
$619$	−8.87599	−	33.1257i	−0.356756	−	1.33143i	0.521504	−	0.853249i	$-0.325371\pi$
$620$	−1.77490	−	1.02474i	−0.0712819	−	0.0411546i
$621$	−3.95734	−	1.73742i	−0.158802	−	0.0697203i
$622$	−13.4129	−	3.59398i	−0.537809	−	0.144106i
$623$	−22.0004	+	38.1058i	−0.881428	+	1.52668i
$624$	2.85793	+	5.55268i	0.114409	+	0.222285i
$625$	5.88500	+	10.1931i	0.235400	+	0.407725i
$626$	2.47997	+	9.25539i	0.0991197	+	0.369920i
$627$	−18.4405	+	0.675828i	−0.736442	+	0.0269900i
$628$	19.0969	−	11.0256i	0.762049	−	0.439969i
$629$	−9.76248	+	9.76248i	−0.389256	+	0.389256i
$630$	−6.84776	+	35.8898i	−0.272821	+	1.42988i
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	0.898097	−	0.439798i	$-0.144950\pi$
$631$	−2.50134	−	9.33512i	−0.0995767	−	0.371625i	−0.997674	+	0.0681724i	$0.978283\pi$
$632$	−11.3207	+	3.03336i	−0.450312	+	0.120661i
$633$	−1.21719	−	33.2118i	−0.0483788	−	1.32005i
$634$	−13.9462	−	8.05183i	−0.553874	−	0.319779i
$635$	−11.9636	+	3.20564i	−0.474761	+	0.127212i
$636$	−2.38174	+	1.49400i	−0.0944420	+	0.0592408i
$637$	7.31786	−	10.5039i	0.289944	−	0.416178i
$638$		−	20.2756i		−	0.802721i
$639$	−26.3904	−	5.03529i	−1.04399	−	0.199193i
$640$	1.87476	+	3.24719i	0.0741066	+	0.128356i
$641$	−11.1614	−	19.3321i	−0.440848	−	0.763570i	0.556905	−	0.830576i	$-0.311989\pi$
$641$	−11.1614	−	19.3321i	−0.440848	−	0.763570i	−0.997753	+	0.0670058i	$0.978655\pi$
$642$	2.59799	+	8.44548i	0.102535	+	0.333317i
$643$	−26.4365	−	26.4365i	−1.04255	−	1.04255i	−0.999053	−	0.0434999i	$-0.986149\pi$
$643$	−26.4365	−	26.4365i	−1.04255	−	1.04255i	−0.0434999	−	0.999053i	$-0.513851\pi$
$644$	1.91038	+	1.91038i	0.0752794	+	0.0752794i
$645$	−0.256908	+	0.276455i	−0.0101157	+	0.0108854i
$646$	−17.0806	−	29.5845i	−0.672027	−	1.16399i
$647$	−1.97324	−	3.41775i	−0.0775760	−	0.134366i	0.824628	−	0.565676i	$-0.191385\pi$
$647$	−1.97324	−	3.41775i	−0.0775760	−	0.134366i	−0.902204	+	0.431310i	$0.858051\pi$
$648$	1.03512	−	8.94028i	0.0406633	−	0.351207i
$649$		−	6.38288i		−	0.250550i
$650$	5.74797	+	32.1528i	0.225454	+	1.26114i
$651$	−0.112626	−	3.07308i	−0.00441416	−	0.120444i
$652$	−6.13647	+	1.64426i	−0.240323	+	0.0643943i
$653$	12.8636	+	7.42680i	0.503391	+	0.290633i	0.730113	−	0.683326i	$-0.239467\pi$
$653$	12.8636	+	7.42680i	0.503391	+	0.290633i	−0.226722	+	0.973960i	$0.572801\pi$
$654$	1.91541	−	1.20148i	0.0748985	−	0.0469818i
$655$	−39.9287	+	10.6989i	−1.56014	+	0.418039i
$656$	−0.455940	−	1.70159i	−0.0178015	−	0.0664360i
$657$	−4.72026	−	13.5564i	−0.184155	−	0.528886i
$658$	13.8762	−	13.8762i	0.540951	−	0.540951i
$659$	34.6644	−	20.0135i	1.35033	−	0.779615i	0.362037	−	0.932164i	$-0.382081\pi$
$659$	34.6644	−	20.0135i	1.35033	−	0.779615i	0.988296	+	0.152548i	$0.0487479\pi$
$660$	6.64899	−	12.5572i	0.258811	−	0.488787i
$661$	1.32797	+	4.95604i	0.0516519	+	0.192768i	0.986931	−	0.161144i	$-0.0515182\pi$
$661$	1.32797	+	4.95604i	0.0516519	+	0.192768i	−0.935279	+	0.353911i	$0.884852\pi$
$662$	3.69778	+	6.40474i	0.143718	+	0.248927i
$663$	43.7601	+	2.11372i	1.69950	+	0.0820902i
$664$	−7.25986	+	12.5744i	−0.281737	+	0.487983i
$665$	57.2847	+	15.3494i	2.22141	+	0.595224i
$666$	0.432171	+	5.88813i	0.0167463	+	0.228161i
$667$	−6.67544	−	3.85407i	−0.258474	−	0.149230i
$668$	2.27988	+	8.50863i	0.0882112	+	0.329209i
$669$	0.473648	+	0.108489i	0.0183123	+	0.00419445i
$670$	−34.4606	+	34.4606i	−1.33133	+	1.33133i
$671$	−2.02721	+	7.56564i	−0.0782595	+	0.292068i
$672$	−2.63266	+	4.97199i	−0.101557	+	0.191799i
$673$		−	40.5684i		−	1.56380i	−0.623405	−	0.781899i	$-0.714251\pi$
$673$		−	40.5684i		−	1.56380i	0.623405	−	0.781899i	$-0.285749\pi$
$674$	4.86748	−	18.1657i	0.187489	−	0.699717i
$675$	18.9229	−	43.1008i	0.728341	−	1.65895i
$676$	−2.19675	+	12.8131i	−0.0844904	+	0.492810i
$677$	−11.0747	−	6.39397i	−0.425635	−	0.245740i	0.271851	−	0.962339i	$-0.412364\pi$
$677$	−11.0747	−	6.39397i	−0.425635	−	0.245740i	−0.697485	+	0.716599i	$0.745698\pi$
$678$	19.5329	+	4.47402i	0.750155	+	0.171824i
$679$	−16.0296	+	27.7640i	−0.615158	+	1.06549i
$680$	26.3044			1.00873
$681$	21.0918	−	6.48825i	0.808241	−	0.248630i
$682$	−0.309518	+	1.15514i	−0.0118520	+	0.0442324i
$683$	−31.3371	+	8.39675i	−1.19908	+	0.321293i	−0.802469	−	0.596693i	$-0.796481\pi$
$683$	−31.3371	+	8.39675i	−1.19908	+	0.321293i	−0.396612	+	0.917986i	$0.629814\pi$
$684$	−14.3495	−	2.73789i	−0.548668	−	0.104686i
$685$	−21.3315	+	36.9473i	−0.815035	+	1.41168i
$686$	−11.2044			−0.427786
$687$	7.12998	−	2.19332i	0.272026	−	0.0836803i
$688$	−0.0503260	+	0.0290558i	−0.00191866	+	0.00110774i
$689$	−5.83158	−	0.496281i	−0.222166	−	0.0189068i
$690$	−2.87039	−	4.57599i	−0.109274	−	0.174205i
$691$	−6.81892	−	6.81892i	−0.259404	−	0.259404i	0.565408	−	0.824812i	$-0.308719\pi$
$691$	−6.81892	−	6.81892i	−0.259404	−	0.259404i	−0.824812	+	0.565408i	$0.808719\pi$
$692$	−0.0437187	+	0.0252410i	−0.00166194	+	0.000959519i
$693$	21.2625	−	1.56060i	0.807694	−	0.0592823i
$694$	−17.5077	−	17.5077i	−0.664582	−	0.664582i
$695$	−13.3161	−	3.56803i	−0.505108	−	0.135343i
$696$	3.58378	−	15.6462i	0.135843	−	0.593069i
$697$	−11.9373	−	3.19860i	−0.452159	−	0.121156i
$698$			3.41521i			0.129267i
$699$	−30.9219	+	19.3964i	−1.16957	+	0.733641i
$700$	−20.8066	+	20.8066i	−0.786415	+	0.786415i
$701$	−45.7174			−1.72672			−0.863360	−	0.504588i	$-0.831645\pi$
$701$	−45.7174			−1.72672			−0.863360	+	0.504588i	$0.831645\pi$
$702$	12.9123	−	13.5747i	0.487345	−	0.512343i
$703$	9.58306			0.361432
$704$	1.54706	−	1.54706i	0.0583070	−	0.0583070i
$705$	−33.2382	+	20.8494i	−1.25182	+	0.785233i
$706$			4.44385i			0.167247i
$707$	−13.8016	−	3.69811i	−0.519061	−	0.139082i
$708$	1.12819	−	4.92552i	0.0424001	−	0.185112i
$709$	−15.4828	−	4.14860i	−0.581468	−	0.155804i	−0.0439170	−	0.999035i	$-0.513984\pi$
$709$	−15.4828	−	4.14860i	−0.581468	−	0.155804i	−0.537551	+	0.843231i	$0.680650\pi$
$710$	−23.7439	−	23.7439i	−0.891092	−	0.891092i
$711$	19.7618	+	29.0809i	0.741124	+	1.09062i
$712$	11.7315	−	6.77319i	0.439657	−	0.253836i
$713$	0.321476	+	0.321476i	0.0120394	+	0.0120394i
$714$	20.9728	+	33.4350i	0.784889	+	1.25127i
$715$	26.7772	−	12.5637i	1.00141	−	0.469856i
$716$	−6.15933	+	3.55609i	−0.230185	+	0.132897i
$717$	21.5487	−	6.62880i	0.804752	−	0.247557i
$718$	2.48936			0.0929022
$719$	−10.0799	+	17.4589i	−0.375917	+	0.651107i	−0.990464	−	0.137773i	$-0.956006\pi$
$719$	−10.0799	+	17.4589i	−0.375917	+	0.651107i	0.614547	+	0.788880i	$0.289339\pi$
$720$	7.35038	−	8.51484i	0.273933	−	0.317329i
$721$	29.3406	−	7.86179i	1.09270	−	0.292788i
$722$	−1.21947	+	4.55112i	−0.0453840	+	0.169375i
$723$	−2.06327	+	0.634703i	−0.0767340	+	0.0236049i
$724$	−20.6330			−0.766820
$725$	41.9760	−	72.7046i	1.55895	−	2.70018i
$726$	10.4900	+	2.40273i	0.389319	+	0.0891737i
$727$	−19.8457	−	11.4579i	−0.736036	−	0.424950i	0.0845905	−	0.996416i	$-0.473042\pi$
$727$	−19.8457	−	11.4579i	−0.736036	−	0.424950i	−0.820626	+	0.571465i	$0.806375\pi$
$728$	−10.6024	+	4.97458i	−0.392950	+	0.184370i
$729$	−26.3504	+	5.88684i	−0.975942	+	0.218031i
$730$	4.64350	−	17.3298i	0.171864	−	0.641404i
$731$			0.407675i			0.0150784i
$732$	−2.90160	+	5.47991i	−0.107246	+	0.202543i
$733$	7.04796	−	26.3034i	0.260322	−	0.971536i	−0.704729	−	0.709476i	$-0.748931\pi$
$733$	7.04796	−	26.3034i	0.260322	−	0.971536i	0.965052	−	0.262060i	$-0.0844018\pi$
$734$	−5.76362	+	5.76362i	−0.212739	+	0.212739i
$735$	−22.4765	−	5.14825i	−0.829056	−	0.189896i
$736$	−0.215275	−	0.803416i	−0.00793513	−	0.0296143i
$737$	24.6271	+	14.2185i	0.907152	+	0.523744i
$738$	−4.37111	+	2.97036i	−0.160903	+	0.109341i
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.660513	−	0.750815i	$-0.270339\pi$
$739$	23.3006	+	6.24337i	0.857126	+	0.229666i	0.196613	+	0.980481i	$0.437006\pi$
$740$	−3.68952	+	6.39043i	−0.135629	+	0.234917i
$741$	−20.4405	−	22.5154i	−0.750900	−	0.827123i
$742$	−2.63627	−	4.56615i	−0.0967804	−	0.167628i
$743$	−11.8113	−	44.0805i	−0.433316	−	1.61716i	−0.745064	−	0.666993i	$-0.767581\pi$
$743$	−11.8113	−	44.0805i	−0.433316	−	1.61716i	0.311747	−	0.950165i	$-0.399086\pi$
$744$	−0.443021	+	0.836683i	−0.0162419	+	0.0306743i
$745$	−29.4669	+	17.0127i	−1.07958	+	0.623297i
$746$	−16.7417	+	16.7417i	−0.612956	+	0.612956i
$747$	42.7873	+	8.16381i	1.56551	+	0.298698i
$748$	−3.97256	−	14.8258i	−0.145251	−	0.542084i
$749$	−16.0058	+	4.28875i	−0.584841	+	0.156708i
$750$	22.3308	−	14.0075i	0.815404	−	0.511480i
$751$	27.0510	+	15.6179i	0.987104	+	0.569905i	0.904407	−	0.426670i	$-0.140313\pi$
$751$	27.0510	+	15.6179i	0.987104	+	0.569905i	0.0826964	+	0.996575i	$0.473647\pi$
$752$	−5.83570	+	1.56367i	−0.212806	+	0.0570212i
$753$	−0.716562	−	19.5519i	−0.0261130	−	0.712512i
$754$	25.5454	−	21.5385i	0.930310	−	0.784385i
$755$		−	70.7433i		−	2.57461i
$756$	16.6836	+	2.55393i	0.606776	+	0.0928854i
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	0.994826	−	0.101598i	$-0.0323956\pi$
$757$	11.2648	+	19.5112i	0.409426	+	0.709147i	−0.585399	+	0.810745i	$0.699062\pi$
$758$	5.65638	+	9.79713i	0.205449	+	0.355848i
$759$	−2.14564	+	2.30890i	−0.0778818	+	0.0838076i
$760$	−12.9105	−	12.9105i	−0.468313	−	0.468313i
$761$	23.2943	+	23.2943i	0.844417	+	0.844417i	0.989430	−	0.145013i	$-0.0463223\pi$
$761$	23.2943	+	23.2943i	0.844417	+	0.844417i	−0.145013	+	0.989430i	$0.546322\pi$
$762$	1.68222	+	5.46851i	0.0609403	+	0.198103i
$763$	2.12011	+	3.67213i	0.0767530	+	0.132940i
$764$	11.2461	+	19.4788i	0.406869	+	0.704718i
$765$	−25.9491	−	74.5248i	−0.938191	−	2.69445i
$766$		−	30.0424i		−	1.08548i
$767$	8.04183	−	6.78043i	0.290374	−	0.244827i
$768$	1.46728	−	0.920381i	0.0529458	−	0.0332114i
$769$	−50.4684	+	13.5230i	−1.81994	+

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46728 - 0.920381i) q^{3} -1.00000i q^{4} +(-3.62177 - 0.970449i) q^{5} +(-0.386713 + 1.68833i) q^{6} +(-3.13748 - 0.840685i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.30580 - 2.70091i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.46728 - 0.920381i) q^{3} -1.00000i q^{4} +(-3.62177 - 0.970449i) q^{5} +(-0.386713 + 1.68833i) q^{6} +(-3.13748 - 0.840685i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.30580 - 2.70091i) q^{9} +(3.24719 - 1.87476i) q^{10} +(-1.54706 - 1.54706i) q^{11} +(-0.920381 - 1.46728i) q^{12} +(0.305736 - 3.59257i) q^{13} +(2.81299 - 1.62408i) q^{14} +(-6.20731 + 1.90949i) q^{15} -1.00000 q^{16} +(-3.50770 + 6.07551i) q^{17} +(0.986492 + 2.83317i) q^{18} +(4.70354 - 1.26031i) q^{19} +(-0.970449 + 3.62177i) q^{20} +(-5.37730 + 1.65416i) q^{21} +2.18787 q^{22} +(0.415879 - 0.720323i) q^{23} +(1.68833 + 0.386713i) q^{24} +(7.84529 + 4.52948i) q^{25} +(2.32414 + 2.75652i) q^{26} +(-0.569900 - 5.16481i) q^{27} +(-0.840685 + 3.13748i) q^{28} -9.26729i q^{29} +(3.03902 - 5.73945i) q^{30} +(-0.141470 + 0.527973i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.69385 - 0.846078i) q^{33} +(-1.81572 - 6.77635i) q^{34} +(10.5474 + 6.08953i) q^{35} +(-2.70091 - 1.30580i) q^{36} +(1.90093 + 0.509353i) q^{37} +(-2.43473 + 4.21708i) q^{38} +(-2.85793 - 5.55268i) q^{39} +(-1.87476 - 3.24719i) q^{40} +(0.455940 + 1.70159i) q^{41} +(2.63266 - 4.97199i) q^{42} +(0.0503260 - 0.0290558i) q^{43} +(-1.54706 + 1.54706i) q^{44} +(-7.35038 + 8.51484i) q^{45} +(0.215275 + 0.803416i) q^{46} +(5.83570 - 1.56367i) q^{47} +(-1.46728 + 0.920381i) q^{48} +(3.07486 + 1.77527i) q^{49} +(-8.75029 + 2.34463i) q^{50} +(0.445026 + 12.1429i) q^{51} +(-3.59257 - 0.305736i) q^{52} -1.62324i q^{53} +(4.05505 + 3.24909i) q^{54} +(4.10174 + 7.10443i) q^{55} +(-1.62408 - 2.81299i) q^{56} +(5.74143 - 6.17827i) q^{57} +(6.55297 + 6.55297i) q^{58} +(2.06291 + 2.06291i) q^{59} +(1.90949 + 6.20731i) q^{60} +(-1.78999 - 3.10035i) q^{61} +(-0.273299 - 0.473367i) q^{62} +(-6.36752 + 7.37628i) q^{63} +1.00000i q^{64} +(-4.59371 + 12.7147i) q^{65} +(3.21021 - 2.01368i) q^{66} +(-12.5547 + 3.36401i) q^{67} +(6.07551 + 3.50770i) q^{68} +(-0.0527631 - 1.43968i) q^{69} +(-11.7641 + 3.15217i) q^{70} +(-2.31786 - 8.65035i) q^{71} +(2.83317 - 0.986492i) q^{72} +(3.38343 - 3.38343i) q^{73} +(-1.70433 + 0.983995i) q^{74} +(15.6801 - 0.574661i) q^{75} +(-1.26031 - 4.70354i) q^{76} +(3.55328 + 6.15446i) q^{77} +(5.94720 + 1.90547i) q^{78} +(-5.86001 + 10.1498i) q^{79} +(3.62177 + 0.970449i) q^{80} +(-5.58979 - 7.05367i) q^{81} +(-1.52561 - 0.880809i) q^{82} +(3.75798 + 14.0250i) q^{83} +(1.65416 + 5.37730i) q^{84} +(18.6000 - 18.6000i) q^{85} +(-0.0150404 + 0.0561314i) q^{86} +(-8.52944 - 13.5977i) q^{87} -2.18787i q^{88} +(3.50606 - 13.0848i) q^{89} +(-0.823397 - 11.2184i) q^{90} +(-3.97946 + 11.0146i) q^{91} +(-0.720323 - 0.415879i) q^{92} +(0.278361 + 0.904888i) q^{93} +(-3.02078 + 5.23214i) q^{94} -18.2582 q^{95} +(0.386713 - 1.68833i) q^{96} +(2.55453 - 9.53363i) q^{97} +(-3.42956 + 0.918947i) q^{98} +(-6.19861 + 2.15832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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