LMFDB - Embedded newform 234.2.y.a.11.14

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			11.14
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.72982 + 0.0878497i) q^{3} -1.00000i q^{4} +(-2.64098 - 0.707650i) q^{5} +(1.28529 - 1.16105i) q^{6} +(3.36644 + 0.902034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98456 + 0.303929i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.72982 + 0.0878497i) q^{3} -1.00000i q^{4} +(-2.64098 - 0.707650i) q^{5} +(1.28529 - 1.16105i) q^{6} +(3.36644 + 0.902034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98456 + 0.303929i) q^{9} +(-2.36784 + 1.36707i) q^{10} +(-1.29045 - 1.29045i) q^{11} +(0.0878497 - 1.72982i) q^{12} +(2.77764 - 2.29885i) q^{13} +(3.01826 - 1.74260i) q^{14} +(-4.50627 - 1.45612i) q^{15} -1.00000 q^{16} +(-0.419403 + 0.726428i) q^{17} +(2.32532 - 1.89550i) q^{18} +(-6.94825 + 1.86178i) q^{19} +(-0.707650 + 2.64098i) q^{20} +(5.74409 + 1.85610i) q^{21} -1.82497 q^{22} +(-3.18965 + 5.52464i) q^{23} +(-1.16105 - 1.28529i) q^{24} +(2.14391 + 1.23778i) q^{25} +(0.338562 - 3.58962i) q^{26} +(5.13606 + 0.787935i) q^{27} +(0.902034 - 3.36644i) q^{28} +6.05100i q^{29} +(-4.21604 + 2.15678i) q^{30} +(-1.99320 + 7.43873i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.11888 - 2.34561i) q^{33} +(0.217099 + 0.810225i) q^{34} +(-8.25239 - 4.76452i) q^{35} +(0.303929 - 2.98456i) q^{36} +(-4.09570 - 1.09744i) q^{37} +(-3.59668 + 6.22963i) q^{38} +(5.00678 - 3.73258i) q^{39} +(1.36707 + 2.36784i) q^{40} +(-1.07586 - 4.01515i) q^{41} +(5.37415 - 2.74923i) q^{42} +(7.47357 - 4.31487i) q^{43} +(-1.29045 + 1.29045i) q^{44} +(-7.66712 - 2.91470i) q^{45} +(1.65109 + 6.16194i) q^{46} +(7.46630 - 2.00059i) q^{47} +(-1.72982 - 0.0878497i) q^{48} +(4.45706 + 2.57328i) q^{49} +(2.39122 - 0.640725i) q^{50} +(-0.789309 + 1.21975i) q^{51} +(-2.29885 - 2.77764i) q^{52} -3.92979i q^{53} +(4.18890 - 3.07459i) q^{54} +(2.49486 + 4.32123i) q^{55} +(-1.74260 - 3.01826i) q^{56} +(-12.1828 + 2.61014i) q^{57} +(4.27871 + 4.27871i) q^{58} +(-5.26591 - 5.26591i) q^{59} +(-1.45612 + 4.50627i) q^{60} +(0.247438 + 0.428575i) q^{61} +(3.85057 + 6.66938i) q^{62} +(9.77320 + 3.71534i) q^{63} +1.00000i q^{64} +(-8.96250 + 4.10562i) q^{65} +(-3.15687 - 0.160323i) q^{66} +(5.34607 - 1.43247i) q^{67} +(0.726428 + 0.419403i) q^{68} +(-6.00287 + 9.27644i) q^{69} +(-9.20434 + 2.46630i) q^{70} +(1.48865 + 5.55573i) q^{71} +(-1.89550 - 2.32532i) q^{72} +(-9.66963 + 9.66963i) q^{73} +(-3.67210 + 2.12009i) q^{74} +(3.59984 + 2.32949i) q^{75} +(1.86178 + 6.94825i) q^{76} +(-3.18018 - 5.50823i) q^{77} +(0.900999 - 6.17966i) q^{78} +(-0.892374 + 1.54564i) q^{79} +(2.64098 + 0.707650i) q^{80} +(8.81525 + 1.81419i) q^{81} +(-3.59989 - 2.07840i) q^{82} +(-4.07375 - 15.2034i) q^{83} +(1.85610 - 5.74409i) q^{84} +(1.62169 - 1.62169i) q^{85} +(2.23354 - 8.33569i) q^{86} +(-0.531579 + 10.4672i) q^{87} +1.82497i q^{88} +(0.385644 - 1.43924i) q^{89} +(-7.48247 + 3.36047i) q^{90} +(11.4244 - 5.23339i) q^{91} +(5.52464 + 3.18965i) q^{92} +(-4.10137 + 12.6926i) q^{93} +(3.86484 - 6.69410i) q^{94} +19.6677 q^{95} +(-1.28529 + 1.16105i) q^{96} +(4.50154 - 16.8000i) q^{97} +(4.97120 - 1.33203i) q^{98} +(-3.45922 - 4.24362i) 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
$3$	1.72982	+	0.0878497i	0.998713	+	0.0507201i
$3$	1.72982	+	0.0878497i	0.998713	+	0.0507201i
$4$		−	1.00000i		−	0.500000i
$5$	−2.64098	−	0.707650i	−1.18108	−	0.316471i	−0.385728	−	0.922613i	$-0.626050\pi$
$5$	−2.64098	−	0.707650i	−1.18108	−	0.316471i	−0.795356	+	0.606142i	$0.792716\pi$
$6$	1.28529	−	1.16105i	0.524716	−	0.473996i
$7$	3.36644	+	0.902034i	1.27239	+	0.340937i	0.830947	−	0.556351i	$-0.187799\pi$
$7$	3.36644	+	0.902034i	1.27239	+	0.340937i	0.441446	+	0.897288i	$0.354466\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.98456	+	0.303929i	0.994855	+	0.101310i
$10$	−2.36784	+	1.36707i	−0.748777	+	0.432307i
$11$	−1.29045	−	1.29045i	−0.389084	−	0.389084i	0.485277	−	0.874361i	$-0.338719\pi$
$11$	−1.29045	−	1.29045i	−0.389084	−	0.389084i	−0.874361	+	0.485277i	$0.838719\pi$
$12$	0.0878497	−	1.72982i	0.0253600	−	0.499356i
$13$	2.77764	−	2.29885i	0.770380	−	0.637585i
$13$	2.77764	−	2.29885i	0.770380	−	0.637585i
$14$	3.01826	−	1.74260i	0.806665	−	0.465728i
$15$	−4.50627	−	1.45612i	−1.16351	−	0.375968i
$16$	−1.00000			−0.250000
$17$	−0.419403	+	0.726428i	−0.101720	+	0.176185i	−0.912393	−	0.409314i	$-0.865768\pi$
$17$	−0.419403	+	0.726428i	−0.101720	+	0.176185i	0.810673	+	0.585499i	$0.199101\pi$
$18$	2.32532	−	1.89550i	0.548082	−	0.446773i
$19$	−6.94825	+	1.86178i	−1.59404	+	0.427121i	−0.943235	−	0.332126i	$-0.892234\pi$
$19$	−6.94825	+	1.86178i	−1.59404	+	0.427121i	−0.650802	+	0.759247i	$0.725567\pi$
$20$	−0.707650	+	2.64098i	−0.158235	+	0.590542i
$21$	5.74409	+	1.85610i	1.25346	+	0.405034i
$22$	−1.82497			−0.389084
$23$	−3.18965	+	5.52464i	−0.665089	+	1.15197i	0.314172	+	0.949366i	$0.398273\pi$
$23$	−3.18965	+	5.52464i	−0.665089	+	1.15197i	−0.979261	+	0.202602i	$0.935060\pi$
$24$	−1.16105	−	1.28529i	−0.236998	−	0.262358i
$25$	2.14391	+	1.23778i	0.428781	+	0.247557i
$26$	0.338562	−	3.58962i	0.0663975	−	0.703983i
$27$	5.13606	+	0.787935i	0.988436	+	0.151638i
$28$	0.902034	−	3.36644i	0.170468	−	0.636197i
$29$			6.05100i			1.12364i	0.827258	+	0.561822i	$0.189899\pi$
$29$			6.05100i			1.12364i	−0.827258	+	0.561822i	$0.810101\pi$
$30$	−4.21604	+	2.15678i	−0.769740	+	0.393772i
$31$	−1.99320	+	7.43873i	−0.357990	+	1.33604i	0.518691	+	0.854962i	$0.326420\pi$
$31$	−1.99320	+	7.43873i	−0.357990	+	1.33604i	−0.876680	+	0.481074i	$0.840247\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.11888	−	2.34561i	−0.368849	−	0.408318i
$34$	0.217099	+	0.810225i	0.0372322	+	0.138952i
$35$	−8.25239	−	4.76452i	−1.39491	−	0.805350i
$36$	0.303929	−	2.98456i	0.0506548	−	0.497427i
$37$	−4.09570	−	1.09744i	−0.673328	−	0.180418i	−0.0940746	−	0.995565i	$-0.529989\pi$
$37$	−4.09570	−	1.09744i	−0.673328	−	0.180418i	−0.579254	+	0.815147i	$0.696656\pi$
$38$	−3.59668	+	6.22963i	−0.583458	+	1.01058i
$39$	5.00678	−	3.73258i	0.801727	−	0.597691i
$40$	1.36707	+	2.36784i	0.216153	+	0.374389i
$41$	−1.07586	−	4.01515i	−0.168021	−	0.627062i	−0.997636	−	0.0687257i	$-0.978107\pi$
$41$	−1.07586	−	4.01515i	−0.168021	−	0.627062i	0.829615	−	0.558336i	$-0.188560\pi$
$42$	5.37415	−	2.74923i	0.829249	−	0.424215i
$43$	7.47357	−	4.31487i	1.13971	−	0.658011i	0.193351	−	0.981130i	$-0.438065\pi$
$43$	7.47357	−	4.31487i	1.13971	−	0.658011i	0.946359	+	0.323118i	$0.104731\pi$
$44$	−1.29045	+	1.29045i	−0.194542	+	0.194542i
$45$	−7.66712	−	2.91470i	−1.14295	−	0.434497i
$46$	1.65109	+	6.16194i	0.243439	+	0.908528i
$47$	7.46630	−	2.00059i	1.08907	−	0.291816i	0.330765	−	0.943713i	$-0.392693\pi$
$47$	7.46630	−	2.00059i	1.08907	−	0.291816i	0.758307	+	0.651897i	$0.226027\pi$
$48$	−1.72982	−	0.0878497i	−0.249678	−	0.0126800i
$49$	4.45706	+	2.57328i	0.636722	+	0.367612i
$50$	2.39122	−	0.640725i	0.338169	−	0.0906121i
$51$	−0.789309	+	1.21975i	−0.110525	+	0.170799i
$52$	−2.29885	−	2.77764i	−0.318792	−	0.385190i
$53$		−	3.92979i		−	0.539798i	−0.962889	−	0.269899i	$-0.913010\pi$
$53$		−	3.92979i		−	0.539798i	0.962889	−	0.269899i	$-0.0869903\pi$
$54$	4.18890	−	3.07459i	0.570037	−	0.418399i
$55$	2.49486	+	4.32123i	0.336408	+	0.582675i
$56$	−1.74260	−	3.01826i	−0.232864	−	0.403333i
$57$	−12.1828	+	2.61014i	−1.61365	+	0.345722i
$58$	4.27871	+	4.27871i	0.561822	+	0.561822i
$59$	−5.26591	−	5.26591i	−0.685564	−	0.685564i	0.275685	−	0.961248i	$-0.411095\pi$
$59$	−5.26591	−	5.26591i	−0.685564	−	0.685564i	−0.961248	+	0.275685i	$0.911095\pi$
$60$	−1.45612	+	4.50627i	−0.187984	+	0.581756i
$61$	0.247438	+	0.428575i	0.0316812	+	0.0548734i	0.881431	−	0.472312i	$-0.156581\pi$
$61$	0.247438	+	0.428575i	0.0316812	+	0.0548734i	−0.849750	+	0.527186i	$0.823247\pi$
$62$	3.85057	+	6.66938i	0.489023	+	0.847013i
$63$	9.77320	+	3.71534i	1.23131	+	0.468088i
$64$			1.00000i			0.125000i
$65$	−8.96250	+	4.10562i	−1.11166	+	0.509239i
$66$	−3.15687	−	0.160323i	−0.388583	−	0.0197344i
$67$	5.34607	−	1.43247i	0.653126	−	0.175005i	0.0829842	−	0.996551i	$-0.473555\pi$
$67$	5.34607	−	1.43247i	0.653126	−	0.175005i	0.570142	+	0.821546i	$0.306888\pi$
$68$	0.726428	+	0.419403i	0.0880923	+	0.0508601i
$69$	−6.00287	+	9.27644i	−0.722661	+	1.11675i
$70$	−9.20434	+	2.46630i	−1.10013	+	0.294779i
$71$	1.48865	+	5.55573i	0.176671	+	0.659344i	0.996261	+	0.0863938i	$0.0275343\pi$
$71$	1.48865	+	5.55573i	0.176671	+	0.659344i	−0.819591	+	0.572950i	$0.805799\pi$
$72$	−1.89550	−	2.32532i	−0.223386	−	0.274041i
$73$	−9.66963	+	9.66963i	−1.13174	+	1.13174i	−0.141858	+	0.989887i	$0.545307\pi$
$73$	−9.66963	+	9.66963i	−1.13174	+	1.13174i	−0.989887	+	0.141858i	$0.954693\pi$
$74$	−3.67210	+	2.12009i	−0.426873	+	0.246455i
$75$	3.59984	+	2.32949i	0.415673	+	0.268986i
$76$	1.86178	+	6.94825i	0.213560	+	0.797018i
$77$	−3.18018	−	5.50823i	−0.362415	−	0.627721i
$78$	0.900999	−	6.17966i	0.102018	−	0.699709i
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	−0.911849	−	0.410525i	$-0.865346\pi$
$79$	−0.892374	+	1.54564i	−0.100400	+	0.173898i	0.811450	+	0.584422i	$0.198679\pi$
$80$	2.64098	+	0.707650i	0.295271	+	0.0791177i
$81$	8.81525	+	1.81419i	0.979473	+	0.201577i
$82$	−3.59989	−	2.07840i	−0.397541	−	0.229520i
$83$	−4.07375	−	15.2034i	−0.447152	−	1.66879i	−0.710191	−	0.704009i	$-0.751391\pi$
$83$	−4.07375	−	15.2034i	−0.447152	−	1.66879i	0.263039	−	0.964785i	$-0.415275\pi$
$84$	1.85610	−	5.74409i	0.202517	−	0.626732i
$85$	1.62169	−	1.62169i	0.175897	−	0.175897i
$86$	2.23354	−	8.33569i	0.240849	−	0.898860i
$87$	−0.531579	+	10.4672i	−0.0569912	+	1.12220i
$88$			1.82497i			0.194542i
$89$	0.385644	−	1.43924i	0.0408782	−	0.152559i	−0.942470	−	0.334290i	$-0.891503\pi$
$89$	0.385644	−	1.43924i	0.0408782	−	0.152559i	0.983348	+	0.181731i	$0.0581700\pi$
$90$	−7.48247	+	3.36047i	−0.788722	+	0.354224i
$91$	11.4244	−	5.23339i	1.19760	−	0.548608i
$92$	5.52464	+	3.18965i	0.575984	+	0.332544i
$93$	−4.10137	+	12.6926i	−0.425293	+	1.31616i
$94$	3.86484	−	6.69410i	0.398628	−	0.690444i
$95$	19.6677			2.01786
$96$	−1.28529	+	1.16105i	−0.131179	+	0.118499i
$97$	4.50154	−	16.8000i	0.457062	−	1.70578i	−0.224892	−	0.974384i	$-0.572203\pi$
$97$	4.50154	−	16.8000i	0.457062	−	1.70578i	0.681954	−	0.731395i	$-0.261130\pi$
$98$	4.97120	−	1.33203i	0.502167	−	0.134555i
$99$	−3.45922	−	4.24362i	−0.347664	−	0.426500i
$100$	1.23778	−	2.14391i	0.123778	−	0.214391i
$101$	0.0847306			0.00843101			0.00421550	−	0.999991i	$-0.498658\pi$
$101$	0.0847306			0.00843101			0.00421550	+	0.999991i	$0.498658\pi$
$102$	0.304365	+	1.42062i	0.0301366	+	0.140662i
$103$	−7.73765	+	4.46733i	−0.762413	+	0.440179i	−0.830161	−	0.557523i	$-0.811752\pi$
$103$	−7.73765	+	4.46733i	−0.762413	+	0.440179i	0.0677484	+	0.997702i	$0.478418\pi$
$104$	−3.58962	−	0.338562i	−0.351991	−	0.0331988i
$105$	−13.8566	−	8.96673i	−1.35226	−	0.875064i
$106$	−2.77878	−	2.77878i	−0.269899	−	0.269899i
$107$	12.3692	−	7.14138i	1.19578	−	0.690384i	0.236168	−	0.971712i	$-0.424108\pi$
$107$	12.3692	−	7.14138i	1.19578	−	0.690384i	0.959611	+	0.281329i	$0.0907751\pi$
$108$	0.787935	−	5.13606i	0.0758191	−	0.494218i
$109$	−9.68492	−	9.68492i	−0.927647	−	0.927647i	0.0699067	−	0.997554i	$-0.477730\pi$
$109$	−9.68492	−	9.68492i	−0.927647	−	0.927647i	−0.997554	+	0.0699067i	$0.977730\pi$
$110$	4.81971	+	1.29144i	0.459541	+	0.123134i
$111$	−6.98841	−	2.25818i	−0.663311	−	0.214337i
$112$	−3.36644	−	0.902034i	−0.318098	−	0.0852342i
$113$			7.95653i			0.748487i	0.927330	+	0.374244i	$0.122098\pi$
$113$			7.95653i			0.748487i	−0.927330	+	0.374244i	$0.877902\pi$
$114$	−6.76888	+	10.4602i	−0.633964	+	0.979685i
$115$	12.3333	−	12.3333i	1.15009	−	1.15009i
$116$	6.05100			0.561822
$117$	8.98875	−	6.01685i	0.831010	−	0.556258i
$118$	−7.44713			−0.685564
$119$	−2.06716	+	2.06716i	−0.189496	+	0.189496i
$120$	2.15678	+	4.21604i	0.196886	+	0.384870i
$121$		−	7.66950i		−	0.697227i
$122$	0.478014	+	0.128083i	0.0432773	+	0.0115961i
$123$	−1.50831	−	7.04001i	−0.136000	−	0.634777i
$124$	7.43873	+	1.99320i	0.668018	+	0.178995i
$125$	4.88057	+	4.88057i	0.436531	+	0.436531i
$126$	9.53783	−	4.28355i	0.849698	−	0.381609i
$127$	10.0640	−	5.81045i	0.893035	−	0.515594i	0.0181011	−	0.999836i	$-0.494238\pi$
$127$	10.0640	−	5.81045i	0.893035	−	0.515594i	0.874934	+	0.484242i	$0.160905\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	13.3070	−	6.80740i	1.17162	−	0.599358i
$130$	−3.43433	+	9.24055i	−0.301211	+	0.810450i
$131$	−4.16625	+	2.40538i	−0.364007	+	0.210159i	−0.670837	−	0.741605i	$-0.734065\pi$
$131$	−4.16625	+	2.40538i	−0.364007	+	0.210159i	0.306830	+	0.951764i	$0.400732\pi$
$132$	−2.34561	+	2.11888i	−0.204159	+	0.184425i
$133$	−25.0702			−2.17386
$134$	2.76733	−	4.79315i	0.239061	−	0.414065i
$135$	−13.0067	−	5.71546i	−1.11944	−	0.491909i
$136$	0.810225	−	0.217099i	0.0694762	−	0.0186161i
$137$	2.00715	−	7.49077i	0.171482	−	0.639980i	−0.825642	−	0.564194i	$-0.809187\pi$
$137$	2.00715	−	7.49077i	0.171482	−	0.639980i	0.997124	−	0.0757856i	$-0.0241465\pi$
$138$	2.31476	+	10.8041i	0.197045	+	0.919706i
$139$	−4.82707			−0.409427			−0.204713	−	0.978822i	$-0.565626\pi$
$139$	−4.82707			−0.409427			−0.204713	+	0.978822i	$0.565626\pi$
$140$	−4.76452	+	8.25239i	−0.402675	+	0.697454i
$141$	13.0911	−	2.80475i	1.10247	−	0.236203i
$142$	4.98113	+	2.87586i	0.418007	+	0.241336i
$143$	−6.55094	−	0.617865i	−0.547817	−	0.0516685i
$144$	−2.98456	−	0.303929i	−0.248714	−	0.0253274i
$145$	4.28199	−	15.9806i	0.355600	−	1.32712i
$146$			13.6749i			1.13174i
$147$	7.48385	+	4.84287i	0.617257	+	0.399433i
$148$	−1.09744	+	4.09570i	−0.0902089	+	0.336664i
$149$	−9.23003	+	9.23003i	−0.756153	+	0.756153i	−0.975620	−	0.219467i	$-0.929568\pi$
$149$	−9.23003	+	9.23003i	−0.756153	+	0.756153i	0.219467	+	0.975620i	$0.429568\pi$
$150$	4.19267	−	0.898272i	0.342330	−	0.0733436i
$151$	2.95315	+	11.0213i	0.240324	+	0.896900i	0.975676	+	0.219216i	$0.0703498\pi$
$151$	2.95315	+	11.0213i	0.240324	+	0.896900i	−0.735353	+	0.677685i	$0.762984\pi$
$152$	6.22963	+	3.59668i	0.505289	+	0.291729i
$153$	−1.47252	+	2.04060i	−0.119046	+	0.164973i
$154$	−6.14363	−	1.64618i	−0.495068	−	0.132653i
$155$	10.5280	−	18.2351i	0.845632	−	1.46468i
$156$	−3.73258	−	5.00678i	−0.298845	−	0.400863i
$157$	2.16879	+	3.75646i	0.173089	+	0.299798i	0.939498	−	0.342554i	$-0.111292\pi$
$157$	2.16879	+	3.75646i	0.173089	+	0.299798i	−0.766409	+	0.642352i	$0.777959\pi$
$158$	0.461927	+	1.72393i	0.0367489	+	0.137149i
$159$	0.345231	−	6.79783i	0.0273786	−	0.539103i
$160$	2.36784	−	1.36707i	0.187194	−	0.108077i
$161$	−15.7212	+	15.7212i	−1.23900	+	1.23900i
$162$	7.51615	−	4.95050i	0.590525	−	0.388948i
$163$	4.75149	+	17.7328i	0.372166	+	1.38894i	0.857442	+	0.514580i	$0.172052\pi$
$163$	4.75149	+	17.7328i	0.372166	+	1.38894i	−0.485277	+	0.874361i	$0.661281\pi$
$164$	−4.01515	+	1.07586i	−0.313531	+	0.0840103i
$165$	3.93605	+	7.69413i	0.306421	+	0.598988i
$166$	−13.6310	−	7.86988i	−1.05797	−	0.610821i
$167$	2.35159	−	0.630107i	0.181972	−	0.0487591i	−0.166682	−	0.986011i	$-0.553305\pi$
$167$	2.35159	−	0.630107i	0.181972	−	0.0487591i	0.348654	+	0.937251i	$0.386639\pi$
$168$	−2.74923	−	5.37415i	−0.212107	−	0.414624i
$169$	2.43062	−	12.7708i	0.186971	−	0.982365i
$170$		−	2.29342i		−	0.175897i
$171$	−21.3033	+	3.44482i	−1.62911	+	0.263432i
$172$	−4.31487	−	7.47357i	−0.329006	−	0.569855i
$173$	5.08757	+	8.81194i	0.386801	+	0.669959i	0.992017	−	0.126102i	$-0.0402467\pi$
$173$	5.08757	+	8.81194i	0.386801	+	0.669959i	−0.605216	+	0.796061i	$0.706913\pi$
$174$	7.02551	+	7.77728i	0.532603	+	0.589594i
$175$	6.10080	+	6.10080i	0.461177	+	0.461177i
$176$	1.29045	+	1.29045i	0.0972710	+	0.0972710i
$177$	−8.64648	−	9.57170i	−0.649909	−	0.719453i
$178$	−0.745007	−	1.29039i	−0.0558406	−	0.0967188i
$179$	6.54598	+	11.3380i	0.489270	+	0.847440i	0.999924	−	0.0123463i	$-0.00393003\pi$
$179$	6.54598	+	11.3380i	0.489270	+	0.847440i	−0.510654	+	0.859786i	$0.670597\pi$
$180$	−2.91470	+	7.66712i	−0.217249	+	0.571473i
$181$		−	10.0606i		−	0.747798i	−0.927469	−	0.373899i	$-0.878021\pi$
$181$		−	10.0606i		−	0.747798i	0.927469	−	0.373899i	$-0.121979\pi$
$182$	4.37771	−	11.7788i	0.324497	−	0.873105i
$183$	0.390373	+	0.763096i	0.0288572	+	0.0564097i
$184$	6.16194	−	1.65109i	0.454264	−	0.121720i
$185$	10.0401	+	5.79664i	0.738160	+	0.426177i
$186$	6.07490	+	11.8751i	0.445433	+	0.870726i
$187$	1.47863	−	0.396198i	0.108128	−	0.0289729i
$188$	−2.00059	−	7.46630i	−0.145908	−	0.544536i
$189$	16.5795	+	7.28544i	1.20598	+	0.529938i
$190$	13.9072	−	13.9072i	1.00893	−	1.00893i
$191$	16.1899	−	9.34724i	1.17146	−	0.676343i	0.217437	−	0.976074i	$-0.430230\pi$
$191$	16.1899	−	9.34724i	1.17146	−	0.676343i	0.954024	+	0.299732i	$0.0968972\pi$
$192$	−0.0878497	+	1.72982i	−0.00634001	+	0.124839i
$193$	−1.33858	−	4.99566i	−0.0963533	−	0.359595i	0.900868	−	0.434093i	$-0.142931\pi$
$193$	−1.33858	−	4.99566i	−0.0963533	−	0.359595i	−0.997221	+	0.0744981i	$0.976265\pi$
$194$	−8.69631	−	15.0624i	−0.624358	−	1.08142i
$195$	−15.8642	+	6.31463i	−1.13606	+	0.452200i
$196$	2.57328	−	4.45706i	0.183806	−	0.318361i
$197$	8.85907	+	2.37378i	0.631183	+	0.169125i	0.560206	−	0.828353i	$-0.310722\pi$
$197$	8.85907	+	2.37378i	0.631183	+	0.169125i	0.0709764	+	0.997478i	$0.477388\pi$
$198$	−5.44673	−	0.554660i	−0.387082	−	0.0394179i
$199$	−11.5728	−	6.68158i	−0.820376	−	0.473644i	0.0301700	−	0.999545i	$-0.490395\pi$
$199$	−11.5728	−	6.68158i	−0.820376	−	0.473644i	−0.850546	+	0.525900i	$0.823728\pi$
$200$	−0.640725	−	2.39122i	−0.0453061	−	0.169085i
$201$	9.37359	−	2.00827i	0.661162	−	0.141653i
$202$	0.0599135	−	0.0599135i	0.00421550	−	0.00421550i
$203$	−5.45821	+	20.3703i	−0.383091	+	1.42972i
$204$	1.21975	+	0.789309i	0.0853993	+	0.0552627i
$205$			11.3653i			0.793786i
$206$	−2.31246	+	8.63023i	−0.161117	+	0.601296i
$207$	−11.1988	+	15.5192i	−0.778372	+	1.07866i
$208$	−2.77764	+	2.29885i	−0.192595	+	0.159396i
$209$	11.3689	+	6.56381i	0.786401	+	0.454029i
$210$	−16.1385	+	3.45765i	−1.11366	+	0.238601i
$211$	5.98953	−	10.3742i	0.412336	−	0.714187i	−0.582809	−	0.812609i	$-0.698046\pi$
$211$	5.98953	−	10.3742i	0.412336	−	0.714187i	0.995145	+	0.0984226i	$0.0313797\pi$
$212$	−3.92979			−0.269899
$213$	2.08703	+	9.74119i	0.143001	+	0.667456i
$214$	3.69665	−	13.7961i	0.252698	−	0.943081i
$215$	−22.7910	+	6.10683i	−1.55433	+	0.416483i
$216$	−3.07459	−	4.18890i	−0.209199	−	0.285019i
$217$	−13.4200	+	23.2441i	−0.911007	+	1.57791i
$218$	−13.6965			−0.927647
$219$	−17.5762	+	15.8773i	−1.18769	+	1.07289i
$220$	4.32123	−	2.49486i	0.291337	−	0.168204i
$221$	0.504992	+	2.98190i	0.0339694	+	0.200584i
$222$	−6.53833	+	3.34478i	−0.438824	+	0.224487i
$223$	−1.24226	−	1.24226i	−0.0831878	−	0.0831878i	0.664288	−	0.747476i	$-0.268735\pi$
$223$	−1.24226	−	1.24226i	−0.0831878	−	0.0831878i	−0.747476	+	0.664288i	$0.768735\pi$
$224$	−3.01826	+	1.74260i	−0.201666	+	0.116432i
$225$	6.02243	+	4.34584i	0.401495	+	0.289723i
$226$	5.62611	+	5.62611i	0.374244	+	0.374244i
$227$	10.4293	+	2.79453i	0.692218	+	0.185479i	0.587742	−	0.809048i	$-0.300017\pi$
$227$	10.4293	+	2.79453i	0.692218	+	0.185479i	0.104476	+	0.994527i	$0.466684\pi$
$228$	2.61014	+	12.1828i	0.172861	+	0.806824i
$229$	2.29318	+	0.614457i	0.151538	+	0.0406044i	0.333790	−	0.942647i	$-0.391672\pi$
$229$	2.29318	+	0.614457i	0.151538	+	0.0406044i	−0.182253	+	0.983252i	$0.558339\pi$
$230$		−	17.4420i		−	1.15009i
$231$	−5.01725	−	9.80764i	−0.330111	−	0.645295i
$232$	4.27871	−	4.27871i	0.280911	−	0.280911i
$233$	−14.8461			−0.972602			−0.486301	−	0.873791i	$-0.661654\pi$
$233$	−14.8461			−0.972602			−0.486301	+	0.873791i	$0.661654\pi$
$234$	2.10145	−	10.6106i	0.137376	−	0.693634i
$235$	−21.1341			−1.37864
$236$	−5.26591	+	5.26591i	−0.342782	+	0.342782i
$237$	−1.67943	+	2.59528i	−0.109091	+	0.168582i
$238$			2.92340i			0.189496i
$239$	28.5302	+	7.64464i	1.84546	+	0.494491i	0.999264	−	0.0383723i	$-0.0122173\pi$
$239$	28.5302	+	7.64464i	1.84546	+	0.494491i	0.846201	+	0.532863i	$0.178884\pi$
$240$	4.50627	+	1.45612i	0.290878	+	0.0939920i
$241$	−19.8922	−	5.33009i	−1.28137	−	0.343341i	−0.446992	−	0.894538i	$-0.647505\pi$
$241$	−19.8922	−	5.33009i	−1.28137	−	0.343341i	−0.834376	+	0.551196i	$0.814171\pi$
$242$	−5.42315	−	5.42315i	−0.348614	−	0.348614i
$243$	15.0894	+	3.91264i	0.967988	+	0.250996i
$244$	0.428575	−	0.247438i	0.0274367	−	0.0158406i
$245$	−9.95003	−	9.95003i	−0.635684	−	0.635684i
$246$	−6.04458	−	3.91150i	−0.385388	−	0.249388i
$247$	−15.0198	+	21.1443i	−0.955688	+	1.34538i
$248$	6.66938	−	3.85057i	0.423506	−	0.244511i
$249$	−5.71124	−	26.6571i	−0.361935	−	1.68933i
$250$	6.90217			0.436531
$251$	10.3116	−	17.8602i	0.650861	−	1.12732i	−0.332053	−	0.943261i	$-0.607741\pi$
$251$	10.3116	−	17.8602i	0.650861	−	1.12732i	0.982914	−	0.184064i	$-0.0589253\pi$
$252$	3.71534	−	9.77320i	0.234044	−	0.615653i
$253$	11.2453	−	3.01318i	0.706988	−	0.189437i
$254$	3.00771	−	11.2249i	0.188721	−	0.704315i
$255$	2.94771	−	2.66278i	0.184593	−	0.166749i
$256$	1.00000			0.0625000
$257$	−4.26967	+	7.39529i	−0.266335	+	0.461305i	−0.967912	−	0.251288i	$-0.919146\pi$
$257$	−4.26967	+	7.39529i	−0.266335	+	0.461305i	0.701578	+	0.712593i	$0.252479\pi$
$258$	4.59591	−	14.2230i	0.286129	−	0.885487i
$259$	−12.7980	−	7.38891i	−0.795227	−	0.459125i
$260$	4.10562	+	8.96250i	0.254620	+	0.555830i
$261$	−1.83907	+	18.0596i	−0.113836	+	1.11786i
$262$	−1.24512	+	4.64685i	−0.0769237	+	0.287083i
$263$		−	2.64515i		−	0.163107i	−0.996669	−	0.0815535i	$-0.974012\pi$
$263$		−	2.64515i		−	0.163107i	0.996669	−	0.0815535i	$-0.0259881\pi$
$264$	−0.160323	+	3.15687i	−0.00986718	+	0.194292i
$265$	−2.78091	+	10.3785i	−0.170830	+	0.637547i
$266$	−17.7273	+	17.7273i	−1.08693	+	1.08693i
$267$	0.793533	−	2.45576i	0.0485634	−	0.150290i
$268$	−1.43247	−	5.34607i	−0.0875023	−	0.326563i
$269$	−14.9308	−	8.62028i	−0.910345	−	0.525588i	−0.0298029	−	0.999556i	$-0.509488\pi$
$269$	−14.9308	−	8.62028i	−0.910345	−	0.525588i	−0.880542	+	0.473968i	$0.842821\pi$
$270$	−13.2386	+	5.15568i	−0.805673	+	0.313764i
$271$	14.5522	+	3.89924i	0.883981	+	0.236862i	0.672124	−	0.740439i	$-0.265382\pi$
$271$	14.5522	+	3.89924i	0.883981	+	0.236862i	0.211857	+	0.977301i	$0.432049\pi$
$272$	0.419403	−	0.726428i	0.0254301	−	0.0440461i
$273$	20.2219	−	8.04920i	1.22389	−	0.487160i
$274$	−3.87751	−	6.71604i	−0.234249	−	0.405731i
$275$	−1.16930	−	4.36389i	−0.0705115	−	0.263153i
$276$	9.27644	+	6.00287i	0.558376	+	0.361330i
$277$	−11.8455	+	6.83901i	−0.711728	+	0.410916i	−0.811700	−	0.584074i	$-0.801458\pi$
$277$	−11.8455	+	6.83901i	−0.711728	+	0.410916i	0.0999726	+	0.994990i	$0.468124\pi$
$278$	−3.41325	+	3.41325i	−0.204713	+	0.204713i
$279$	−8.20968	+	21.5956i	−0.491501	+	1.29289i
$280$	2.46630	+	9.20434i	0.147389	+	0.550065i
$281$	−12.8651	+	3.44720i	−0.767468	+	0.205643i	−0.621253	−	0.783610i	$-0.713376\pi$
$281$	−12.8651	+	3.44720i	−0.767468	+	0.205643i	−0.146216	+	0.989253i	$0.546709\pi$
$282$	7.27356	−	11.2401i	0.433134	−	0.669337i
$283$	−2.19846	−	1.26928i	−0.130685	−	0.0754510i	0.433232	−	0.901282i	$-0.357373\pi$
$283$	−2.19846	−	1.26928i	−0.130685	−	0.0754510i	−0.563917	+	0.825831i	$0.690706\pi$
$284$	5.55573	−	1.48865i	0.329672	−	0.0883353i
$285$	34.0216	+	1.72780i	2.01527	+	0.102346i
$286$	−5.06911	+	4.19532i	−0.299743	+	0.248074i
$287$		−	14.4872i		−	0.855154i
$288$	−2.32532	+	1.89550i	−0.137021	+	0.111693i
$289$	8.14820	+	14.1131i	0.479306	+	0.830182i
$290$	−8.27217	−	14.3278i	−0.485759	−	0.841359i
$291$	9.26273	−	28.6655i	0.542991	−	1.68040i
$292$	9.66963	+	9.66963i	0.565872	+	0.565872i
$293$	−9.85394	−	9.85394i	−0.575674	−	0.575674i	0.358035	−	0.933708i	$-0.383447\pi$
$293$	−9.85394	−	9.85394i	−0.575674	−	0.575674i	−0.933708	+	0.358035i	$0.883447\pi$
$294$	8.71631	−	1.86745i	0.508345	−	0.108912i
$295$	10.1808	+	17.6336i	0.592748	+	1.02667i
$296$	2.12009	+	3.67210i	0.123228	+	0.213436i
$297$	−5.61103	−	7.64460i	−0.325585	−	0.443585i
$298$			13.0532i			0.756153i
$299$	3.84057	+	22.6780i	0.222106	+	1.31150i
$300$	2.32949	−	3.59984i	0.134493	−	0.207837i
$301$	29.0515	−	7.78432i	1.67450	−	0.448681i
$302$	9.88142	+	5.70504i	0.568612	+	0.328288i
$303$	0.146569	+	0.00744355i	0.00842015	+	0.000427621i
$304$	6.94825	−	1.86178i	0.398509	−	0.106780i
$305$	−0.350199	−	1.30696i	−0.0200523	−	0.0748363i
$306$	0.401696	+	2.48415i	0.0229634	+	0.142009i
$307$	−6.54395	+	6.54395i	−0.373483	+	0.373483i	−0.868744	−	0.495261i	$-0.835072\pi$
$307$	−6.54395	+	6.54395i	−0.373483	+	0.373483i	0.495261	+	0.868744i	$0.335072\pi$
$308$	−5.50823	+	3.18018i	−0.313861	+	0.181208i
$309$	−13.7772	+	7.04794i	−0.783758	+	0.400943i
$310$	−5.44971	−	20.3386i	−0.309523	−	1.15515i
$311$	−8.02003	−	13.8911i	−0.454774	−	0.787692i	0.543901	−	0.839149i	$-0.316947\pi$
$311$	−8.02003	−	13.8911i	−0.454774	−	0.787692i	−0.998675	+	0.0514573i	$0.983613\pi$
$312$	−6.17966	−	0.900999i	−0.349854	−	0.0510091i
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	0.473670	+	0.880702i	$0.342929\pi$
$313$	−9.30369	+	16.1145i	−0.525875	+	0.910843i	−0.999546	+	0.0301408i	$0.990404\pi$
$314$	4.18979	+	1.12265i	0.236444	+	0.0633549i
$315$	−23.1817	−	16.7281i	−1.30614	−	0.942524i
$316$	1.54564	+	0.892374i	0.0869489	+	0.0501999i
$317$	1.93565	+	7.22395i	0.108717	+	0.405737i	0.998740	−	0.0501776i	$-0.0159787\pi$
$317$	1.93565	+	7.22395i	0.108717	+	0.405737i	−0.890023	+	0.455915i	$0.849312\pi$
$318$	−4.56268	−	5.05091i	−0.255862	−	0.283241i
$319$	7.80849	−	7.80849i	0.437192	−	0.437192i
$320$	0.707650	−	2.64098i	0.0395588	−	0.147636i
$321$	22.0239	−	11.2667i	1.22926	−	0.628845i
$322$			22.2331i			1.23900i
$323$	1.56167	−	5.82823i	0.0868937	−	0.324292i
$324$	1.81419	−	8.81525i	0.100788	−	0.489736i
$325$	8.80049	−	1.49038i	0.488163	−	0.0826715i
$326$	15.8988	+	9.17918i	0.880553	+	0.508388i
$327$	−15.9024	−	17.6040i	−0.879403	−	0.973503i
$328$	−2.07840	+	3.59989i	−0.114760	+	0.198771i
$329$	26.9394			1.48522
$330$	8.22378	+	2.65737i	0.452704	+	0.146283i
$331$	−2.94858	+	11.0042i	−0.162069	+	0.604848i	0.836327	+	0.548230i	$0.184698\pi$
$331$	−2.94858	+	11.0042i	−0.162069	+	0.604848i	−0.998396	+	0.0566177i	$0.981968\pi$
$332$	−15.2034	+	4.07375i	−0.834397	+	0.223576i
$333$	−11.8903	−	4.52017i	−0.651586	−	0.247704i
$334$	1.21727	−	2.10838i	0.0666062	−	0.115365i
$335$	−15.1326			−0.826781
$336$	−5.74409	−	1.85610i	−0.313366	−	0.101258i
$337$	−14.3804	+	8.30252i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$337$	−14.3804	+	8.30252i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$338$	−7.31158	−	10.7490i	−0.397697	−	0.584668i
$339$	−0.698979	+	13.7634i	−0.0379633	+	0.747524i
$340$	−1.62169	−	1.62169i	−0.0879487	−	0.0879487i
$341$	12.1714	−	7.02716i	0.659118	−	0.380542i
$342$	−12.6279	+	17.4996i	−0.682837	+	0.946270i
$343$	−4.56761	−	4.56761i	−0.246628	−	0.246628i
$344$	−8.33569	−	2.23354i	−0.449430	−	0.120424i
$345$	22.4180	−	20.2510i	1.20694	−	1.09028i
$346$	9.82844	+	2.63352i	0.528380	+	0.141579i
$347$			14.0776i			0.755726i	0.925862	+	0.377863i	$0.123341\pi$
$347$			14.0776i			0.755726i	−0.925862	+	0.377863i	$0.876659\pi$
$348$	10.4672	+	0.531579i	0.561098	+	0.0284956i
$349$	−1.81786	+	1.81786i	−0.0973080	+	0.0973080i	−0.754085	−	0.656777i	$-0.771919\pi$
$349$	−1.81786	+	1.81786i	−0.0973080	+	0.0973080i	0.656777	+	0.754085i	$0.271919\pi$
$350$	8.62784			0.461177
$351$	16.0775	−	9.61841i	0.858154	−	0.513393i
$352$	1.82497			0.0972710
$353$	4.48187	−	4.48187i	0.238546	−	0.238546i	−0.577702	−	0.816248i	$-0.696050\pi$
$353$	4.48187	−	4.48187i	0.238546	−	0.238546i	0.816248	+	0.577702i	$0.196050\pi$
$354$	−12.8822	−	0.654228i	−0.684681	−	0.0347718i
$355$		−	15.7260i		−	0.834651i
$356$	−1.43924	−	0.385644i	−0.0762797	−	0.0204391i
$357$	−3.75741	+	3.39421i	−0.198863	+	0.179641i
$358$	12.6459	+	3.38845i	0.668355	+	0.179085i
$359$	−15.0107	−	15.0107i	−0.792236	−	0.792236i	0.189622	−	0.981857i	$-0.439274\pi$
$359$	−15.0107	−	15.0107i	−0.792236	−	0.792236i	−0.981857	+	0.189622i	$0.939274\pi$
$360$	3.36047	+	7.48247i	0.177112	+	0.394361i
$361$	28.3574	−	16.3722i	1.49250	−	0.861693i
$362$	−7.11392	−	7.11392i	−0.373899	−	0.373899i
$363$	0.673763	−	13.2669i	0.0353634	−	0.696330i
$364$	−5.23339	−	11.4244i	−0.274304	−	0.598801i
$365$	32.3801	−	18.6946i	1.69485	−	0.978522i
$366$	0.815626	+	0.263555i	0.0426335	+	0.0137762i
$367$	16.7751			0.875655			0.437828	−	0.899059i	$-0.355748\pi$
$367$	16.7751			0.875655			0.437828	+	0.899059i	$0.355748\pi$
$368$	3.18965	−	5.52464i	0.166272	−	0.287992i
$369$	−1.99065	−	12.3105i	−0.103629	−	0.640857i
$370$	11.1982	−	3.00056i	0.582169	−	0.155992i
$371$	3.54480	−	13.2294i	0.184037	−	0.686835i
$372$	12.6926	+	4.10137i	0.658079	+	0.212646i
$373$	−10.9205			−0.565440			−0.282720	−	0.959202i	$-0.591237\pi$
$373$	−10.9205			−0.565440			−0.282720	+	0.959202i	$0.591237\pi$
$374$	0.765397	−	1.32571i	0.0395777	−	0.0685506i
$375$	8.01376	+	8.87127i	0.413829	+	0.458110i
$376$	−6.69410	−	3.86484i	−0.345222	−	0.199314i
$377$	13.9103	+	16.8075i	0.716418	+	0.865632i
$378$	16.8751	−	6.57189i	0.867959	−	0.338021i
$379$	1.57730	−	5.88656i	0.0810203	−	0.302372i	−0.913511	−	0.406815i	$-0.866639\pi$
$379$	1.57730	−	5.88656i	0.0810203	−	0.302372i	0.994531	+	0.104443i	$0.0333060\pi$
$380$		−	19.6677i		−	1.00893i
$381$	17.9194	−	9.16692i	0.918037	−	0.469636i
$382$	4.83849	−	18.0575i	0.247559	−	0.923901i
$383$	−22.6794	+	22.6794i	−1.15886	+	1.15886i	−0.174143	+	0.984720i	$0.555715\pi$
$383$	−22.6794	+	22.6794i	−1.15886	+	1.15886i	−0.984720	+	0.174143i	$0.944285\pi$
$384$	1.16105	+	1.28529i	0.0592496	+	0.0655896i
$385$	4.50091	+	16.7976i	0.229387	+	0.856086i
$386$	−4.47898	−	2.58594i	−0.227974	−	0.131621i
$387$	23.6168	−	10.6066i	1.20051	−	0.539162i
$388$	−16.8000	−	4.50154i	−0.852889	−	0.228531i
$389$	−16.7063	+	28.9362i	−0.847043	+	1.46712i	0.0367925	+	0.999323i	$0.488286\pi$
$389$	−16.7063	+	28.9362i	−0.847043	+	1.46712i	−0.883835	+	0.467798i	$0.845047\pi$
$390$	−6.75256	+	15.6828i	−0.341929	+	0.794129i
$391$	−2.67550	−	4.63411i	−0.135306	−	0.234357i
$392$	−1.33203	−	4.97120i	−0.0672776	−	0.251083i
$393$	−7.41818	+	3.79488i	−0.374198	+	0.191426i
$394$	7.94283	−	4.58579i	0.400154	−	0.231029i
$395$	3.45052	−	3.45052i	0.173614	−	0.173614i
$396$	−4.24362	+	3.45922i	−0.213250	+	0.173832i
$397$	−5.37105	−	20.0450i	−0.269565	−	1.00603i	−0.959397	−	0.282061i	$-0.908982\pi$
$397$	−5.37105	−	20.0450i	−0.269565	−	1.00603i	0.689832	−	0.723970i	$-0.257685\pi$
$398$	−12.9078	+	3.45864i	−0.647010	+	0.173366i
$399$	−43.3670	−	2.20241i	−2.17107	−	0.110258i
$400$	−2.14391	−	1.23778i	−0.107195	−	0.0618892i
$401$	19.5869	−	5.24830i	0.978125	−	0.262088i	0.265870	−	0.964009i	$-0.414341\pi$
$401$	19.5869	−	5.24830i	0.978125	−	0.262088i	0.712255	+	0.701921i	$0.247674\pi$
$402$	5.20806	−	8.04819i	0.259754	−	0.401407i
$403$	11.5641	+	25.2442i	0.576048	+	1.25750i
$404$		−	0.0847306i		−	0.00421550i
$405$	−21.9971	−	11.0294i	−1.09305	−	0.548053i
$406$	10.5445	+	18.2635i	0.523313	+	0.906404i
$407$	3.86909	+	6.70146i	0.191784	+	0.332179i
$408$	1.42062	−	0.304365i	0.0703310	−	0.0150683i
$409$	3.94732	+	3.94732i	0.195183	+	0.195183i	0.797931	−	0.602749i	$-0.205928\pi$
$409$	3.94732	+	3.94732i	0.195183	+	0.195183i	−0.602749	+	0.797931i	$0.705928\pi$
$410$	8.03647	+	8.03647i	0.396893	+	0.396893i
$411$	4.13007	−	12.7814i	0.203721	−	0.630459i
$412$	4.46733	+	7.73765i	0.220090	+	0.381207i
$413$	−12.9773	−	22.4774i	−0.638573	−	1.10604i
$414$	3.05498	+	18.8925i	0.150144	+	0.928517i
$415$			43.0348i			2.11250i
$416$	−0.338562	+	3.58962i	−0.0165994	+	0.175996i
$417$	−8.34997	−	0.424057i	−0.408900	−	0.0207661i
$418$	12.6803	−	3.39768i	0.620215	−	0.166186i
$419$	−27.1430	−	15.6710i	−1.32602	−	0.765578i	−0.341339	−	0.939940i	$-0.610880\pi$
$419$	−27.1430	−	15.6710i	−1.32602	−	0.765578i	−0.984682	+	0.174362i	$0.944214\pi$
$420$	−8.96673	+	13.8566i	−0.437532	+	0.676132i
$421$	26.5626	−	7.11743i	1.29458	−	0.346882i	0.455183	−	0.890398i	$-0.349574\pi$
$421$	26.5626	−	7.11743i	1.29458	−	0.346882i	0.839399	+	0.543516i	$0.182907\pi$
$422$	−3.10041	−	11.5709i	−0.150925	−	0.563261i
$423$	22.8917	−	3.70167i	1.11303	−	0.179981i
$424$	−2.77878	+	2.77878i	−0.134949	+	0.134949i
$425$	−1.79832	+	1.03826i	−0.0872314	+	0.0503631i
$426$	8.36382	+	5.41231i	0.405228	+	0.262227i
$427$	0.446395	+	1.66597i	0.0216026	+	0.0806219i
$428$	−7.14138	−	12.3692i	−0.345192	−	0.597890i
$429$	−11.2777	−	1.64429i	−0.544491	−	0.0793873i
$430$	−11.7975	+	20.4339i	−0.568926	+	0.985408i
$431$	26.7454	+	7.16641i	1.28828	+	0.345194i	0.837007	−	0.547192i	$-0.184303\pi$
$431$	26.7454	+	7.16641i	1.28828	+	0.345194i	0.451274	+	0.892386i	$0.350970\pi$
$432$	−5.13606	−	0.787935i	−0.247109	−	0.0379096i
$433$	−27.2596	−	15.7383i	−1.31001	−	0.756336i	−0.327914	−	0.944708i	$-0.606346\pi$
$433$	−27.2596	−	15.7383i	−1.31001	−	0.756336i	−0.982098	+	0.188372i	$0.939679\pi$
$434$	6.94669	+	25.9254i	0.333452	+	1.24446i
$435$	8.81097	−	27.2674i	0.422454	−	1.30737i
$436$	−9.68492	+	9.68492i	−0.463823	+	0.463823i
$437$	11.8768	−	44.3250i	0.568147	−	2.12035i
$438$	−1.20134	+	23.6552i	−0.0574021	+	1.13029i
$439$		−	26.2573i		−	1.25319i	−0.779344	−	0.626596i	$-0.784448\pi$
$439$		−	26.2573i		−	1.25319i	0.779344	−	0.626596i	$-0.215552\pi$
$440$	1.29144	−	4.81971i	0.0615669	−	0.229771i
$441$	12.5203	+	9.03475i	0.596204	+	0.430226i
$442$	2.46561	+	1.75144i	0.117277	+	0.0833075i
$443$	−23.2806	−	13.4410i	−1.10609	−	0.638604i	−0.168279	−	0.985739i	$-0.553821\pi$
$443$	−23.2806	−	13.4410i	−1.10609	−	0.638604i	−0.937815	+	0.347136i	$0.887154\pi$
$444$	−2.25818	+	6.98841i	−0.107168	+	0.331655i
$445$	−2.03696	+	3.52812i	−0.0965612	+	0.167249i
$446$	−1.75682			−0.0831878
$447$	−16.7772	+	15.1554i	−0.793532	+	0.716828i
$448$	−0.902034	+	3.36644i	−0.0426171	+	0.159049i
$449$	−1.60200	+	0.429254i	−0.0756029	+	0.0202577i	−0.296422	−	0.955057i	$-0.595794\pi$
$449$	−1.60200	+	0.429254i	−0.0756029	+	0.0202577i	0.220819	+	0.975315i	$0.429127\pi$
$450$	7.33148	−	1.18552i	0.345609	−	0.0558862i
$451$	−3.79300	+	6.56968i	−0.178606	+	0.309354i
$452$	7.95653			0.374244
$453$	4.14020	+	19.3243i	0.194524	+	0.907935i
$454$	9.35067	−	5.39861i	0.438849	−	0.253369i
$455$	−33.8751	+	5.73682i	−1.58809	+	0.268946i
$456$	10.4602	+	6.76888i	0.489843	+	0.316982i
$457$	25.6564	+	25.6564i	1.20015	+	1.20015i	0.974119	+	0.226036i	$0.0725767\pi$
$457$	25.6564	+	25.6564i	1.20015	+	1.20015i	0.226036	+	0.974119i	$0.427423\pi$
$458$	2.05601	−	1.18704i	0.0960711	−	0.0554667i
$459$	−2.72646	+	3.40052i	−0.127260	+	0.158723i
$460$	−12.3333	−	12.3333i	−0.575045	−	0.575045i
$461$	−21.4084	−	5.73636i	−0.997087	−	0.267169i	−0.276863	−	0.960910i	$-0.589295\pi$
$461$	−21.4084	−	5.73636i	−0.997087	−	0.267169i	−0.720225	+	0.693741i	$0.755961\pi$
$462$	−10.4828	−	3.38732i	−0.487703	−	0.157592i
$463$	−28.8741	−	7.73679i	−1.34189	−	0.359559i	−0.484756	−	0.874649i	$-0.661092\pi$
$463$	−28.8741	−	7.73679i	−1.34189	−	0.359559i	−0.857136	+	0.515090i	$0.827758\pi$
$464$		−	6.05100i		−	0.280911i
$465$	19.8136	−	30.6186i	0.918832	−	1.41990i
$466$	−10.4978	+	10.4978i	−0.486301	+	0.486301i
$467$	−36.5666			−1.69210			−0.846051	−	0.533102i	$-0.821026\pi$
$467$	−36.5666			−1.69210			−0.846051	+	0.533102i	$0.821026\pi$
$468$	−6.01685	−	8.98875i	−0.278129	−	0.415505i
$469$	19.2893			0.890699
$470$	−14.9441	+	14.9441i	−0.689318	+	0.689318i
$471$	3.42162	+	6.68854i	0.157660	+	0.308192i
$472$			7.44713i			0.342782i
$473$	−15.2123	−	4.07614i	−0.699465	−	0.187421i
$474$	0.647604	+	3.02268i	0.0297454	+	0.138836i
$475$	−17.2009	−	4.60896i	−0.789230	−	0.211474i
$476$	2.06716	+	2.06716i	0.0947480	+	0.0947480i
$477$	1.19438	−	11.7287i	0.0546867	−	0.537021i
$478$	25.5795	−	14.7683i	1.16998	−	0.675487i
$479$	24.0481	+	24.0481i	1.09879	+	1.09879i	0.994553	+	0.104234i	$0.0332390\pi$
$479$	24.0481	+	24.0481i	1.09879	+	1.09879i	0.104234	+	0.994553i	$0.466761\pi$
$480$	4.21604	−	2.15678i	0.192435	−	0.0984431i
$481$	−13.8992	+	6.36708i	−0.633750	+	0.290314i
$482$	−17.8348	+	10.2969i	−0.812355	+	0.469013i
$483$	−28.5759	+	25.8137i	−1.30025	+	1.17457i
$484$	−7.66950			−0.348614
$485$	−23.7770	+	41.1830i	−1.07966	+	1.87002i
$486$	13.4365	−	7.90319i	0.609492	−	0.358496i
$487$	12.0435	−	3.22705i	0.545744	−	0.146232i	0.0245951	−	0.999697i	$-0.492170\pi$
$487$	12.0435	−	3.22705i	0.545744	−	0.146232i	0.521149	+	0.853466i	$0.325504\pi$
$488$	0.128083	−	0.478014i	0.00579806	−	0.0216387i
$489$	6.66141	+	31.0920i	0.301239	+	1.40603i
$490$	−14.0715			−0.635684
$491$	−2.76676	+	4.79216i	−0.124862	+	0.216267i	−0.921679	−	0.387953i	$-0.873182\pi$
$491$	−2.76676	+	4.79216i	−0.124862	+	0.216267i	0.796817	+	0.604221i	$0.206515\pi$
$492$	−7.04001	+	1.50831i	−0.317388	+	0.0679999i
$493$	−4.39562	−	2.53781i	−0.197969	−	0.114297i
$494$	4.33066	+	25.5719i	0.194846	+	1.15053i
$495$	6.13274	+	13.6553i	0.275646	+	0.613758i
$496$	1.99320	−	7.43873i	0.0894974	−	0.334009i
$497$			20.0458i			0.899178i
$498$	−22.8879	−	14.8110i	−1.02563	−	0.663695i
$499$	−0.641188	+	2.39294i	−0.0287035	+	0.107123i	−0.978791	−	0.204859i	$-0.934326\pi$
$499$	−0.641188	+	2.39294i	−0.0287035	+	0.107123i	0.950088	+	0.311982i	$0.100993\pi$
$500$	4.88057	−	4.88057i	0.218266	−	0.218266i
$501$	4.12319	−	0.883386i	0.184210	−	0.0394668i
$502$	−5.33767	−	19.9204i	−0.238232	−	0.889093i
$503$	32.0788	+	18.5207i	1.43032	+	0.825798i	0.997145	−	0.0755096i	$-0.0240583\pi$
$503$	32.0788	+	18.5207i	1.43032	+	0.825798i	0.433179	+	0.901308i	$0.357392\pi$
$504$	−4.28355	−	9.53783i	−0.190805	−	0.424849i
$505$	−0.223772	−	0.0599596i	−0.00995773	−	0.00266817i
$506$	5.82101	−	10.0823i	0.258776	−	0.448212i
$507$	5.32645	−	21.8776i	0.236556	−	0.971618i
$508$	−5.81045	−	10.0640i	−0.257797	−	0.446518i
$509$	8.65075	+	32.2850i	0.383438	+	1.43101i	0.840615	+	0.541634i	$0.182194\pi$
$509$	8.65075	+	32.2850i	0.383438	+	1.43101i	−0.457177	+	0.889376i	$0.651139\pi$
$510$	0.201476	−	3.96721i	0.00892153	−	0.175671i
$511$	−41.2745	+	23.8299i	−1.82588	+	1.05417i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−37.1536	+	4.08744i	−1.64037	+	0.180465i
$514$	2.21014	+	8.24837i	0.0974853	+	0.363820i
$515$	23.5963	−	6.32261i	1.03978	−	0.278608i
$516$	−6.80740	−	13.3070i	−0.299679	−	0.585808i
$517$	−12.2165	−	7.05321i	−0.537282	−	0.310200i
$518$	−14.2743	+	3.82478i	−0.627176	+	0.168051i
$519$	8.02647	+	15.6900i	0.352323	+	0.688715i
$520$	9.24055	+	3.43433i	0.405225	+	0.150605i
$521$			6.65944i			0.291755i	0.989303	+	0.145878i	$0.0466006\pi$
$521$			6.65944i			0.291755i	−0.989303	+	0.145878i	$0.953399\pi$
$522$	11.4697	+	14.0705i	0.502013	+	0.615849i
$523$	0.581243	+	1.00674i	0.0254160	+	0.0440218i	0.878454	−	0.477828i	$-0.158576\pi$
$523$	0.581243	+	1.00674i	0.0254160	+	0.0440218i	−0.853038	+	0.521849i	$0.825242\pi$
$524$	2.40538	+	4.16625i	0.105080	+	0.182003i
$525$	10.0173	+	11.0893i	0.437193	+	0.483975i
$526$	−1.87040	−	1.87040i	−0.0815535	−	0.0815535i
$527$	−4.56774	−	4.56774i	−0.198974	−	0.198974i
$528$	2.11888	+	2.34561i	0.0922123	+	0.102079i
$529$	−8.84778	−	15.3248i	−0.384686	−	0.666296i
$530$	5.37231	+	9.30512i	0.233358	+	0.404189i
$531$	−14.1160	−	17.3169i	−0.612582	−	0.751490i
$532$			25.0702i			1.08693i
$533$	−12.2186	−	8.67944i	−0.529245	−	0.375948i
$534$	−1.17537	−	2.29759i	−0.0508632	−	0.0994266i
$535$	−37.7206	+	10.1072i	−1.63080	+	0.436972i
$536$	−4.79315	−	2.76733i	−0.207033	−	0.119530i
$537$	10.3273	+	20.1877i	0.445658	+	0.871165i
$538$	−16.6531	+	4.46219i	−0.717967	+	0.192379i
$539$	−2.43091	−	9.07227i	−0.104707	−	0.390770i
$540$	−5.71546	+	13.0067i	−0.245954	+	0.559719i
$541$	15.5641	−	15.5641i	0.669152	−	0.669152i	−0.288368	−	0.957520i	$-0.593113\pi$
$541$	15.5641	−	15.5641i	0.669152	−	0.669152i	0.957520	+	0.288368i	$0.0931126\pi$
$542$	13.0471	−	7.53275i	0.560421	−	0.323559i
$543$	0.883820	−	17.4030i	0.0379284	−	0.746836i
$544$	−0.217099	−	0.810225i	−0.00930805	−	0.0347381i
$545$	18.7242	+	32.4313i	0.802056	+	1.38920i
$546$	8.60742	−	19.9907i	0.368364	−	0.855523i
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	−0.940935	−	0.338588i	$-0.890051\pi$
$547$	−4.14533	+	7.17992i	−0.177241	+	0.306991i	0.763693	+	0.645579i	$0.223384\pi$
$548$	−7.49077	−	2.00715i	−0.319990	−	0.0857411i
$549$	0.608239	+	1.35431i	0.0259590	+	0.0578007i
$550$	−3.91256	−	2.25892i	−0.166832	−	0.0963205i
$551$	−11.2656	−	42.0439i	−0.479932	−	1.79113i
$552$	10.8041	−	2.31476i	0.459853	−	0.0985227i
$553$	−4.39834	+	4.39834i	−0.187036	+	0.187036i
$554$	−3.54013	+	13.2120i	−0.150406	+	0.561322i
$555$	16.8583	+	10.9092i	0.715595	+	0.463068i
$556$			4.82707i			0.204713i
$557$	5.76476	−	21.5144i	0.244261	−	0.911594i	−0.729493	−	0.683989i	$-0.760244\pi$
$557$	5.76476	−	21.5144i	0.244261	−	0.911594i	0.973754	−	0.227605i	$-0.0730895\pi$
$558$	9.46526	+	21.0755i	0.400696	+	0.892197i
$559$	10.8397	−	29.1658i	0.458471	−	1.23358i
$560$	8.25239	+	4.76452i	0.348727	+	0.201338i
$561$	2.59258	−	0.555455i	0.109459	−	0.0234513i
$562$	−6.65947	+	11.5345i	−0.280913	+	0.486555i
$563$	28.1745			1.18741			0.593707	−	0.804682i	$-0.297664\pi$
$563$	28.1745			1.18741			0.593707	+	0.804682i	$0.297664\pi$
$564$	−2.80475	−	13.0911i	−0.118101	−	0.551236i
$565$	5.63043	−	21.0131i	0.236874	−	0.884026i
$566$	−2.45206	+	0.657028i	−0.103068	+	0.0276170i
$567$	28.0395	+	14.0590i	1.17755	+	0.590423i
$568$	2.87586	−	4.98113i	0.120668	−	0.209004i
$569$	29.1878			1.22362			0.611808	−	0.791007i	$-0.290443\pi$
$569$	29.1878			1.22362			0.611808	+	0.791007i	$0.290443\pi$
$570$	25.2787	−	22.8352i	1.05881	−	0.956460i
$571$	36.5099	−	21.0790i	1.52789	−	0.882129i	0.528443	−	0.848969i	$-0.322776\pi$
$571$	36.5099	−	21.0790i	1.52789	−	0.882129i	0.999450	−	0.0331604i	$-0.0105572\pi$
$572$	−0.617865	+	6.55094i	−0.0258342	+	0.273908i
$573$	28.8268	−	14.7468i	1.20426	−	0.616056i
$574$	−10.2440	−	10.2440i	−0.427577	−	0.427577i
$575$	−13.6766	+	7.89621i	−0.570355	+	0.329295i
$576$	−0.303929	+	2.98456i	−0.0126637	+	0.124357i
$577$	13.8702	+	13.8702i	0.577425	+	0.577425i	0.934193	−	0.356768i	$-0.116121\pi$
$577$	13.8702	+	13.8702i	0.577425	+	0.577425i	−0.356768	+	0.934193i	$0.616121\pi$
$578$	15.7411	+	4.21782i	0.654744	+	0.175438i
$579$	−1.87664	−	8.75919i	−0.0779905	−	0.364019i
$580$	−15.9806	−	4.28199i	−0.663559	−	0.177800i
$581$		−	54.8561i		−	2.27581i
$582$	−13.7198	−	26.8193i	−0.568705	−	1.11170i
$583$	−5.07118	+	5.07118i	−0.210027	+	0.210027i
$584$	13.6749			0.565872
$585$	−27.9970	+	9.52952i	−1.15753	+	0.393997i
$586$	−13.9356			−0.575674
$587$	−5.61049	+	5.61049i	−0.231570	+	0.231570i	−0.813348	−	0.581778i	$-0.802357\pi$
$587$	−5.61049	+	5.61049i	−0.231570	+	0.231570i	0.581778	+	0.813348i	$0.302357\pi$
$588$	4.84287	−	7.48385i	0.199717	−	0.308629i
$589$		−	55.3970i		−	2.28259i
$590$	19.6678	+	5.26996i	0.809708	+	0.216961i
$591$	15.1161	+	4.88448i	0.621792	+	0.200921i
$592$	4.09570	+	1.09744i	0.168332	+	0.0451044i
$593$	23.8412	+	23.8412i	0.979040	+	0.979040i	0.999785	−	0.0207452i	$-0.00660388\pi$
$593$	23.8412	+	23.8412i	0.979040	+	0.979040i	−0.0207452	+	0.999785i	$0.506604\pi$
$594$	−9.37315	−	1.43796i	−0.384585	−	0.0590000i
$595$	6.92215	−	3.99651i	0.283781	−	0.163841i
$596$	9.23003	+	9.23003i	0.378077	+	0.378077i
$597$	−19.4320	−	12.5746i	−0.795297	−	0.514644i
$598$	18.7515	+	13.3201i	0.766805	+	0.544699i
$599$	5.64668	−	3.26011i	0.230717	−	0.133205i	−0.380186	−	0.924910i	$-0.624140\pi$
$599$	5.64668	−	3.26011i	0.230717	−	0.133205i	0.610903	+	0.791706i	$0.290807\pi$
$600$	−0.898272	−	4.19267i	−0.0366718	−	0.171165i
$601$	−27.5743			−1.12478			−0.562390	−	0.826872i	$-0.690118\pi$
$601$	−27.5743			−1.12478			−0.562390	+	0.826872i	$0.690118\pi$
$602$	15.0381	−	26.0468i	0.612909	−	1.06159i
$603$	16.3911	−	2.65049i	0.667495	−	0.107936i
$604$	11.0213	−	2.95315i	0.448450	−	0.120162i
$605$	−5.42732	+	20.2550i	−0.220652	+	0.823484i
$606$	0.108903	−	0.0983764i	0.00442389	−	0.00399627i
$607$	5.91621			0.240132			0.120066	−	0.992766i	$-0.461689\pi$
$607$	5.91621			0.240132			0.120066	+	0.992766i	$0.461689\pi$
$608$	3.59668	−	6.22963i	0.145865	−	0.252645i
$609$	−11.2313	+	34.7575i	−0.455114	+	1.40845i
$610$	−1.17179	−	0.676532i	−0.0474443	−	0.0273920i
$611$	16.1397	−	22.7208i	0.652942	−	0.919185i
$612$	2.04060	+	1.47252i	0.0824864	+	0.0595230i
$613$	4.10104	−	15.3053i	0.165639	−	0.618175i	−0.832318	−	0.554298i	$-0.812987\pi$
$613$	4.10104	−	15.3053i	0.165639	−	0.618175i	0.997958	−	0.0638768i	$-0.0203465\pi$
$614$			9.25454i			0.373483i
$615$	−0.998438	+	19.6599i	−0.0402609	+	0.792765i
$616$	−1.64618	+	6.14363i	−0.0663266	+	0.247534i
$617$	−18.4697	+	18.4697i	−0.743561	+	0.743561i	−0.973261	−	0.229700i	$-0.926225\pi$
$617$	−18.4697	+	18.4697i	−0.743561	+	0.743561i	0.229700	+	0.973261i	$0.426225\pi$
$618$	−4.75831	+	14.7256i	−0.191407	+	0.592351i
$619$	−3.16658	−	11.8178i	−0.127276	−	0.474999i	0.872635	−	0.488373i	$-0.162409\pi$
$619$	−3.16658	−	11.8178i	−0.127276	−	0.474999i	−0.999911	+	0.0133740i	$0.995743\pi$
$620$	−18.2351	−	10.5280i	−0.732339	−	0.422816i
$621$	−20.7353	+	25.8617i	−0.832080	+	1.03779i
$622$	−15.4935	−	4.15147i	−0.621233	−	0.166459i
$623$	2.59649	−	4.49726i	0.104026	−	0.180179i
$624$	−5.00678	+	3.73258i	−0.200432	+	0.149423i
$625$	−15.6247	−	27.0628i	−0.624988	−	1.08251i
$626$	4.81594	+	17.9733i	0.192484	+	0.718359i
$627$	19.0895	+	12.3530i	0.762360	+	0.493330i
$628$	3.75646	−	2.16879i	0.149899	−	0.0865443i
$629$	2.51496	−	2.51496i	0.100278	−	0.100278i
$630$	−28.2205	+	4.56336i	−1.12433	+	0.181808i
$631$	2.72399	+	10.1661i	0.108440	+	0.404704i	0.998713	−	0.0507238i	$-0.0161528\pi$
$631$	2.72399	+	10.1661i	0.108440	+	0.404704i	−0.890272	+	0.455428i	$0.849486\pi$
$632$	1.72393	−	0.461927i	0.0685744	−	0.0183745i
$633$	11.2722	−	17.4193i	0.448029	−	0.692354i
$634$	6.47682	+	3.73939i	0.257227	+	0.148510i
$635$	−30.6906	+	8.22353i	−1.21792	+	0.326341i
$636$	−6.79783	−	0.345231i	−0.269552	−	0.0136893i
$637$	18.2957	−	3.09842i	0.724902	−	0.122764i
$638$		−	11.0429i		−	0.437192i
$639$	2.75444	+	17.0339i	0.108964	+	0.673850i
$640$	−1.36707	−	2.36784i	−0.0540384	−	0.0935972i
$641$	2.46006	+	4.26095i	0.0971666	+	0.168297i	0.910511	−	0.413485i	$-0.135689\pi$
$641$	2.46006	+	4.26095i	0.0971666	+	0.168297i	−0.813344	+	0.581783i	$0.802355\pi$
$642$	7.60653	−	23.5400i	0.300206	−	0.929051i
$643$	23.8644	+	23.8644i	0.941119	+	0.941119i	0.998360	−	0.0572415i	$-0.0182305\pi$
$643$	23.8644	+	23.8644i	0.941119	+	0.941119i	−0.0572415	+	0.998360i	$0.518230\pi$
$644$	15.7212	+	15.7212i	0.619501	+	0.619501i
$645$	−39.9609	+	8.56155i	−1.57346	+	0.337111i
$646$	−3.01692	−	5.22545i	−0.118699	−	0.205593i
$647$	−2.54755	−	4.41248i	−0.100154	−	0.173473i	0.811594	−	0.584222i	$-0.198600\pi$
$647$	−2.54755	−	4.41248i	−0.100154	−	0.173473i	−0.911748	+	0.410750i	$0.865267\pi$
$648$	−4.95050	−	7.51615i	−0.194474	−	0.295262i
$649$			13.5908i			0.533484i
$650$	5.16902	−	7.27674i	0.202746	−	0.285417i
$651$	−25.2562	+	39.0292i	−0.989867	+	1.52967i
$652$	17.7328	−	4.75149i	0.694470	−	0.186083i
$653$	−34.2634	−	19.7820i	−1.34083	−	0.774129i	−0.353901	−	0.935283i	$-0.615145\pi$
$653$	−34.2634	−	19.7820i	−1.34083	−	0.774129i	−0.986929	+	0.161154i	$0.948478\pi$
$654$	−23.6926	−	1.20324i	−0.926453	−	0.0470503i
$655$	12.7052	−	3.40434i	0.496432	−	0.133019i
$656$	1.07586	+	4.01515i	0.0420052	+	0.156765i
$657$	−31.7985	+	25.9208i	−1.24058	+	1.01127i
$658$	19.0491	−	19.0491i	0.742609	−	0.742609i
$659$	13.1719	−	7.60483i	0.513106	−	0.296242i	−0.221003	−	0.975273i	$-0.570933\pi$
$659$	13.1719	−	7.60483i	0.513106	−	0.296242i	0.734110	+	0.679031i	$0.237600\pi$
$660$	7.69413	−	3.93605i	0.299494	−	0.153211i
$661$	3.06267	+	11.4300i	0.119124	+	0.444577i	0.999562	−	0.0295837i	$-0.00941817\pi$
$661$	3.06267	+	11.4300i	0.119124	+	0.444577i	−0.880438	+	0.474161i	$0.842752\pi$
$662$	5.69622	+	9.86614i	0.221390	+	0.383458i
$663$	0.611586	+	5.20252i	0.0237520	+	0.202049i
$664$	−7.86988	+	13.6310i	−0.305411	+	0.528987i
$665$	66.2101	+	17.7409i	2.56752	+	0.687964i
$666$	−11.6040	+	5.21148i	−0.449645	+	0.201941i
$667$	−33.4296	−	19.3006i	−1.29440	−	0.747323i
$668$	−0.630107	−	2.35159i	−0.0243796	−	0.0909858i
$669$	−2.03975	−	2.25802i	−0.0788615	−	0.0873000i
$670$	−10.7003	+	10.7003i	−0.413390	+	0.413390i
$671$	0.233748	−	0.872359i	0.00902373	−	0.0336770i
$672$	−5.37415	+	2.74923i	−0.207312	+	0.106054i
$673$		−	19.5423i		−	0.753299i	−0.926356	−	0.376650i	$-0.877076\pi$
$673$		−	19.5423i		−	0.753299i	0.926356	−	0.376650i	$-0.122924\pi$
$674$	−4.29770	+	16.0392i	−0.165541	+	0.617808i
$675$	10.0359	+	8.04660i	0.386284	+	0.309714i
$676$	−12.7708	−	2.43062i	−0.491183	−	0.0934854i
$677$	−7.33732	−	4.23620i	−0.281996	−	0.162811i	0.352331	−	0.935876i	$-0.385389\pi$
$677$	−7.33732	−	4.23620i	−0.281996	−	0.162811i	−0.634327	+	0.773065i	$0.718723\pi$
$678$	9.23792	+	10.2264i	0.354780	+	0.392743i
$679$	30.3083	−	52.4955i	1.16313	−	2.01459i
$680$	−2.29342			−0.0879487
$681$	17.7954	+	5.75024i	0.681919	+	0.220350i
$682$	3.63753	−	13.5754i	0.139288	−	0.519830i
$683$	13.4051	−	3.59188i	0.512930	−	0.137439i	0.00693584	−	0.999976i	$-0.497792\pi$
$683$	13.4051	−	3.59188i	0.512930	−	0.137439i	0.505995	+	0.862537i	$0.331126\pi$
$684$	3.44482	+	21.3033i	0.131716	+	0.814554i
$685$	−10.6017	+	18.3627i	−0.405070	+	0.701601i
$686$	−6.45958			−0.246628
$687$	3.91282	+	1.26436i	0.149283	+	0.0482382i
$688$	−7.47357	+	4.31487i	−0.284927	+	0.164503i
$689$	−9.03398	−	10.9156i	−0.344167	−	0.415850i
$690$	1.53227	−	30.1715i	0.0583326	−	1.14861i
$691$	3.25059	+	3.25059i	0.123658	+	0.123658i	0.766228	−	0.642569i	$-0.222132\pi$
$691$	3.25059	+	3.25059i	0.123658	+	0.123658i	−0.642569	+	0.766228i	$0.722132\pi$
$692$	8.81194	−	5.08757i	0.334980	−	0.193401i
$693$	−7.81734	−	17.4062i	−0.296956	−	0.661208i
$694$	9.95438	+	9.95438i	0.377863	+	0.377863i
$695$	12.7482	+	3.41587i	0.483567	+	0.129571i
$696$	7.77728	−	7.02551i	0.294797	−	0.266301i
$697$	3.36794	+	0.902436i	0.127570	+	0.0341822i
$698$			2.57085i			0.0973080i
$699$	−25.6812	−	1.30423i	−0.971351	−	0.0493304i
$700$	6.10080	−	6.10080i	0.230589	−	0.230589i
$701$	−3.27106			−0.123546			−0.0617731	−	0.998090i	$-0.519676\pi$
$701$	−3.27106			−0.123546			−0.0617731	+	0.998090i	$0.519676\pi$
$702$	4.56727	−	18.1698i	0.172380	−	0.685773i
$703$	30.5011			1.15037
$704$	1.29045	−	1.29045i	0.0486355	−	0.0486355i
$705$	−36.5582	−	1.85662i	−1.37686	−	0.0699245i
$706$		−	6.33832i		−	0.238546i
$707$	0.285240	+	0.0764298i	0.0107276	+	0.00287444i
$708$	−9.57170	+	8.64648i	−0.359727	+	0.324955i
$709$	17.9894	+	4.82025i	0.675606	+	0.181028i	0.580279	−	0.814418i	$-0.302944\pi$
$709$	17.9894	+	4.82025i	0.675606	+	0.181028i	0.0953275	+	0.995446i	$0.469610\pi$
$710$	−11.1200	−	11.1200i	−0.417326	−	0.417326i
$711$	−3.13311	+	4.34184i	−0.117501	+	0.162832i
$712$	−1.29039	+	0.745007i	−0.0483594	+	0.0279203i
$713$	−34.7387	−	34.7387i	−1.30097	−	1.30097i
$714$	−0.256820	+	5.05696i	−0.00961125	+	0.189252i
$715$	16.8637	+	6.26754i	0.630666	+	0.234393i
$716$	11.3380	−	6.54598i	0.423720	−	0.244635i
$717$	48.6806	+	15.7302i	1.81801	+	0.587456i
$718$	−21.2284			−0.792236
$719$	−6.22658	+	10.7848i	−0.232212	+	0.402204i	−0.958459	−	0.285231i	$-0.907930\pi$
$719$	−6.22658	+	10.7848i	−0.232212	+	0.402204i	0.726247	+	0.687434i	$0.241263\pi$
$720$	7.66712	+	2.91470i	0.285737	+	0.108624i
$721$	−30.0780	+	8.05937i	−1.12016	+	0.300147i
$722$	8.47486	−	31.6286i	0.315402	−	1.17709i
$723$	−33.9417	−	10.9676i	−1.26230	−	0.407891i
$724$	−10.0606			−0.373899
$725$	−7.48984	+	12.9728i	−0.278166	+	0.481797i
$726$	−8.90467	−	9.85751i	−0.330483	−	0.365847i
$727$	0.202128	+	0.116699i	0.00749650	+	0.00432811i	0.503744	−	0.863853i	$-0.331956\pi$
$727$	0.202128	+	0.116699i	0.00749650	+	0.00432811i	−0.496247	+	0.868181i	$0.665289\pi$
$728$	−11.7788	−	4.37771i	−0.436553	−	0.162249i
$729$	25.7583	+	8.09377i	0.954012	+	0.299769i
$730$	9.67706	−	36.1153i	0.358164	−	1.33669i
$731$			7.23868i			0.267732i
$732$	0.763096	−	0.390373i	0.0282048	−	0.0144286i
$733$	−7.31715	+	27.3080i	−0.270265	+	1.00864i	0.688684	+	0.725062i	$0.258189\pi$
$733$	−7.31715	+	27.3080i	−0.270265	+	1.00864i	−0.958948	+	0.283580i	$0.908478\pi$
$734$	11.8618	−	11.8618i	0.437828	−	0.437828i
$735$	−16.3377	−	18.0859i	−0.602624	−	0.667108i
$736$	−1.65109	−	6.16194i	−0.0608599	−	0.227132i
$737$	−8.74734	−	5.05028i	−0.322213	−	0.186030i
$738$	−10.1124	−	7.29722i	−0.372243	−	0.268614i
$739$	34.3558	+	9.20561i	1.26380	+	0.338634i	0.827652	−	0.561242i	$-0.189676\pi$
$739$	34.3558	+	9.20561i	1.26380	+	0.338634i	0.436146	+	0.899876i	$0.356343\pi$
$740$	5.79664	−	10.0401i	0.213089	−	0.369080i
$741$	−27.8391	+	35.2564i	−1.02270	+	1.29518i
$742$	−6.84803	−	11.8611i	−0.251399	−	0.435436i
$743$	6.78006	+	25.3035i	0.248736	+	0.928297i	0.971469	+	0.237168i	$0.0762193\pi$
$743$	6.78006	+	25.3035i	0.248736	+	0.928297i	−0.722732	+	0.691128i	$0.757114\pi$
$744$	11.8751	−	6.07490i	0.435363	−	0.222716i
$745$	30.9080	−	17.8447i	1.13238	−	0.653781i
$746$	−7.72193	+	7.72193i	−0.282720	+	0.282720i
$747$	−7.53761	−	46.6138i	−0.275787	−	1.70551i
$748$	−0.396198	−	1.47863i	−0.0144865	−	0.0540642i
$749$	48.0820	−	12.8835i	1.75688	−	0.470754i
$750$	11.9395	+	0.606353i	0.435970	+	0.0221409i
$751$	25.3210	+	14.6191i	0.923975	+	0.533457i	0.884901	−	0.465779i	$-0.154226\pi$
$751$	25.3210	+	14.6191i	0.923975	+	0.533457i	0.0390742	+	0.999236i	$0.487559\pi$
$752$	−7.46630	+	2.00059i	−0.272268	+	0.0729540i
$753$	19.4062	−	29.9891i	0.707201	−	1.09286i
$754$	21.7208	+	2.04864i	0.791025	+	0.0746071i
$755$		−	31.1969i		−	1.13537i
$756$	7.28544	−	16.5795i	0.264969	−	0.602990i
$757$	0.560080	+	0.970087i	0.0203565	+	0.0352584i	0.876024	−	0.482267i	$-0.160187\pi$
$757$	0.560080	+	0.970087i	0.0203565	+	0.0352584i	−0.855668	+	0.517526i	$0.826853\pi$
$758$	−3.04711	−	5.27774i	−0.110676	−	0.191696i
$759$	19.7171	−	4.22436i	0.715686	−	0.153335i
$760$	−13.9072	−	13.9072i	−0.504466	−	0.504466i
$761$	−8.74376	−	8.74376i	−0.316961	−	0.316961i	0.530638	−	0.847599i	$-0.321952\pi$
$761$	−8.74376	−	8.74376i	−0.316961	−	0.316961i	−0.847599	+	0.530638i	$0.821952\pi$
$762$	6.18891	−	19.1529i	0.224201	−	0.693836i
$763$	−23.8675	−	41.3398i	−0.864063	−	1.49660i
$764$	−9.34724	−	16.1899i	−0.338171	−	0.585730i
$765$	5.33293	−	4.34717i	0.192812	−	0.157172i
$766$			32.0735i			1.15886i
$767$	−26.7324	−	2.52132i	−0.965250	−	0.0910395i
$768$	1.72982	+	0.0878497i	0.0624196	+	0.00317000i
$769$	−21.2688	+	5.69895i	−0.766971	+	0.205509i	−0.621033	−	0.783785i	$-0.713287\pi$

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.72982 + 0.0878497i) q^{3} -1.00000i q^{4} +(-2.64098 - 0.707650i) q^{5} +(1.28529 - 1.16105i) q^{6} +(3.36644 + 0.902034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98456 + 0.303929i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.72982 + 0.0878497i) q^{3} -1.00000i q^{4} +(-2.64098 - 0.707650i) q^{5} +(1.28529 - 1.16105i) q^{6} +(3.36644 + 0.902034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98456 + 0.303929i) q^{9} +(-2.36784 + 1.36707i) q^{10} +(-1.29045 - 1.29045i) q^{11} +(0.0878497 - 1.72982i) q^{12} +(2.77764 - 2.29885i) q^{13} +(3.01826 - 1.74260i) q^{14} +(-4.50627 - 1.45612i) q^{15} -1.00000 q^{16} +(-0.419403 + 0.726428i) q^{17} +(2.32532 - 1.89550i) q^{18} +(-6.94825 + 1.86178i) q^{19} +(-0.707650 + 2.64098i) q^{20} +(5.74409 + 1.85610i) q^{21} -1.82497 q^{22} +(-3.18965 + 5.52464i) q^{23} +(-1.16105 - 1.28529i) q^{24} +(2.14391 + 1.23778i) q^{25} +(0.338562 - 3.58962i) q^{26} +(5.13606 + 0.787935i) q^{27} +(0.902034 - 3.36644i) q^{28} +6.05100i q^{29} +(-4.21604 + 2.15678i) q^{30} +(-1.99320 + 7.43873i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.11888 - 2.34561i) q^{33} +(0.217099 + 0.810225i) q^{34} +(-8.25239 - 4.76452i) q^{35} +(0.303929 - 2.98456i) q^{36} +(-4.09570 - 1.09744i) q^{37} +(-3.59668 + 6.22963i) q^{38} +(5.00678 - 3.73258i) q^{39} +(1.36707 + 2.36784i) q^{40} +(-1.07586 - 4.01515i) q^{41} +(5.37415 - 2.74923i) q^{42} +(7.47357 - 4.31487i) q^{43} +(-1.29045 + 1.29045i) q^{44} +(-7.66712 - 2.91470i) q^{45} +(1.65109 + 6.16194i) q^{46} +(7.46630 - 2.00059i) q^{47} +(-1.72982 - 0.0878497i) q^{48} +(4.45706 + 2.57328i) q^{49} +(2.39122 - 0.640725i) q^{50} +(-0.789309 + 1.21975i) q^{51} +(-2.29885 - 2.77764i) q^{52} -3.92979i q^{53} +(4.18890 - 3.07459i) q^{54} +(2.49486 + 4.32123i) q^{55} +(-1.74260 - 3.01826i) q^{56} +(-12.1828 + 2.61014i) q^{57} +(4.27871 + 4.27871i) q^{58} +(-5.26591 - 5.26591i) q^{59} +(-1.45612 + 4.50627i) q^{60} +(0.247438 + 0.428575i) q^{61} +(3.85057 + 6.66938i) q^{62} +(9.77320 + 3.71534i) q^{63} +1.00000i q^{64} +(-8.96250 + 4.10562i) q^{65} +(-3.15687 - 0.160323i) q^{66} +(5.34607 - 1.43247i) q^{67} +(0.726428 + 0.419403i) q^{68} +(-6.00287 + 9.27644i) q^{69} +(-9.20434 + 2.46630i) q^{70} +(1.48865 + 5.55573i) q^{71} +(-1.89550 - 2.32532i) q^{72} +(-9.66963 + 9.66963i) q^{73} +(-3.67210 + 2.12009i) q^{74} +(3.59984 + 2.32949i) q^{75} +(1.86178 + 6.94825i) q^{76} +(-3.18018 - 5.50823i) q^{77} +(0.900999 - 6.17966i) q^{78} +(-0.892374 + 1.54564i) q^{79} +(2.64098 + 0.707650i) q^{80} +(8.81525 + 1.81419i) q^{81} +(-3.59989 - 2.07840i) q^{82} +(-4.07375 - 15.2034i) q^{83} +(1.85610 - 5.74409i) q^{84} +(1.62169 - 1.62169i) q^{85} +(2.23354 - 8.33569i) q^{86} +(-0.531579 + 10.4672i) q^{87} +1.82497i q^{88} +(0.385644 - 1.43924i) q^{89} +(-7.48247 + 3.36047i) q^{90} +(11.4244 - 5.23339i) q^{91} +(5.52464 + 3.18965i) q^{92} +(-4.10137 + 12.6926i) q^{93} +(3.86484 - 6.69410i) q^{94} +19.6677 q^{95} +(-1.28529 + 1.16105i) q^{96} +(4.50154 - 16.8000i) q^{97} +(4.97120 - 1.33203i) q^{98} +(-3.45922 - 4.24362i) 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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