LMFDB - Embedded newform 756.2.bp.a.193.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.7
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985812 + 1.42414i) q^{3} +(-1.13435 + 0.412871i) q^{5} +(-2.60567 - 0.458792i) q^{7} +(-1.05635 - 2.80787i) q^{9} +O(q^{10})$	\(q+(-0.985812 + 1.42414i) q^{3} +(-1.13435 + 0.412871i) q^{5} +(-2.60567 - 0.458792i) q^{7} +(-1.05635 - 2.80787i) q^{9} +(1.14789 + 0.417800i) q^{11} +(-1.33860 + 0.487212i) q^{13} +(0.530273 - 2.02249i) q^{15} +(1.27085 + 2.20117i) q^{17} +(3.29707 - 5.71070i) q^{19} +(3.22208 - 3.25855i) q^{21} +(1.48918 - 8.44558i) q^{23} +(-2.71393 + 2.27725i) q^{25} +(5.04016 + 1.26364i) q^{27} +(-3.96187 - 1.44200i) q^{29} +(6.69268 - 2.43594i) q^{31} +(-1.72661 + 1.22289i) q^{33} +(3.14517 - 0.555372i) q^{35} -11.3959 q^{37} +(0.625754 - 2.38666i) q^{39} +(10.2365 - 3.72579i) q^{41} +(0.269511 + 1.52847i) q^{43} +(2.35756 + 2.74898i) q^{45} +(10.4781 + 3.81373i) q^{47} +(6.57902 + 2.39092i) q^{49} +(-4.38759 - 0.360077i) q^{51} +(6.20454 - 10.7466i) q^{53} -1.47462 q^{55} +(4.88254 + 10.3252i) q^{57} +(-4.50330 - 3.77872i) q^{59} +(-6.26425 - 2.28000i) q^{61} +(1.46427 + 7.80102i) q^{63} +(1.31730 - 1.10534i) q^{65} +(0.341369 - 1.93600i) q^{67} +(10.5596 + 10.4466i) q^{69} +(0.665025 - 1.15186i) q^{71} -11.3954 q^{73} +(-0.567708 - 6.10996i) q^{75} +(-2.79935 - 1.61529i) q^{77} +(-2.89374 - 16.4112i) q^{79} +(-6.76825 + 5.93218i) q^{81} +(-9.56572 - 3.48164i) q^{83} +(-2.35039 - 1.97221i) q^{85} +(5.95928 - 4.22072i) q^{87} +(2.06682 - 3.57984i) q^{89} +(3.71149 - 0.655372i) q^{91} +(-3.12861 + 11.9327i) q^{93} +(-1.38226 + 7.83921i) q^{95} +(1.44888 + 8.21701i) q^{97} +(-0.0394521 - 3.66448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.985812	+	1.42414i	−0.569159	+	0.822228i
$3$	−0.985812	+	1.42414i	−0.569159	+	0.822228i
$4$		0			0
$5$	−1.13435	+	0.412871i	−0.507298	+	0.184642i	−0.582974	−	0.812491i	$-0.698111\pi$
$5$	−1.13435	+	0.412871i	−0.507298	+	0.184642i	0.0756754	+	0.997133i	$0.475889\pi$
$6$		0			0
$7$	−2.60567	−	0.458792i	−0.984850	−	0.173407i
$7$	−2.60567	−	0.458792i	−0.984850	−	0.173407i
$8$		0			0
$9$	−1.05635	−	2.80787i	−0.352117	−	0.935956i
$10$		0			0
$11$	1.14789	+	0.417800i	0.346103	+	0.125971i	0.509222	−	0.860635i	$-0.329933\pi$
$11$	1.14789	+	0.417800i	0.346103	+	0.125971i	−0.163119	+	0.986606i	$0.552155\pi$
$12$		0			0
$13$	−1.33860	+	0.487212i	−0.371262	+	0.135128i	−0.520911	−	0.853611i	$-0.674408\pi$
$13$	−1.33860	+	0.487212i	−0.371262	+	0.135128i	0.149649	+	0.988739i	$0.452186\pi$
$14$		0			0
$15$	0.530273	−	2.02249i	0.136916	−	0.522205i
$16$		0			0
$17$	1.27085	+	2.20117i	0.308225	+	0.533862i	0.977974	−	0.208726i	$-0.0669316\pi$
$17$	1.27085	+	2.20117i	0.308225	+	0.533862i	−0.669749	+	0.742588i	$0.733598\pi$
$18$		0			0
$19$	3.29707	−	5.71070i	0.756400	−	1.31012i	−0.188275	−	0.982116i	$-0.560290\pi$
$19$	3.29707	−	5.71070i	0.756400	−	1.31012i	0.944675	−	0.328007i	$-0.106377\pi$
$20$		0			0
$21$	3.22208	−	3.25855i	0.703116	−	0.711075i
$22$		0			0
$23$	1.48918	−	8.44558i	0.310516	−	1.76103i	−0.285812	−	0.958286i	$-0.592263\pi$
$23$	1.48918	−	8.44558i	0.310516	−	1.76103i	0.596329	−	0.802740i	$-0.296626\pi$
$24$		0			0
$25$	−2.71393	+	2.27725i	−0.542785	+	0.455451i
$26$		0			0
$27$	5.04016	+	1.26364i	0.969979	+	0.243188i
$28$		0			0
$29$	−3.96187	−	1.44200i	−0.735701	−	0.267773i	−0.0531252	−	0.998588i	$-0.516918\pi$
$29$	−3.96187	−	1.44200i	−0.735701	−	0.267773i	−0.682576	+	0.730814i	$0.739140\pi$
$30$		0			0
$31$	6.69268	−	2.43594i	1.20204	−	0.437507i	0.338105	−	0.941108i	$-0.390214\pi$
$31$	6.69268	−	2.43594i	1.20204	−	0.437507i	0.863936	+	0.503601i	$0.167992\pi$
$32$		0			0
$33$	−1.72661	+	1.22289i	−0.300565	+	0.212878i
$34$		0			0
$35$	3.14517	−	0.555372i	0.531631	−	0.0938751i
$36$		0			0
$37$	−11.3959			−1.87347			−0.936736	−	0.350035i	$-0.886170\pi$
$37$	−11.3959			−1.87347			−0.936736	+	0.350035i	$0.886170\pi$
$38$		0			0
$39$	0.625754	−	2.38666i	0.100201	−	0.382172i
$40$		0			0
$41$	10.2365	−	3.72579i	1.59867	−	0.581870i	0.619519	−	0.784982i	$-0.287328\pi$
$41$	10.2365	−	3.72579i	1.59867	−	0.581870i	0.979156	+	0.203112i	$0.0651055\pi$
$42$		0			0
$43$	0.269511	+	1.52847i	0.0411000	+	0.233090i	0.998437	−	0.0558830i	$-0.0177974\pi$
$43$	0.269511	+	1.52847i	0.0411000	+	0.233090i	−0.957337	+	0.288973i	$0.906686\pi$
$44$		0			0
$45$	2.35756	+	2.74898i	0.351445	+	0.409794i
$46$		0			0
$47$	10.4781	+	3.81373i	1.52839	+	0.556290i	0.963228	−	0.268687i	$-0.0865897\pi$
$47$	10.4781	+	3.81373i	1.52839	+	0.556290i	0.565166	+	0.824977i	$0.308812\pi$
$48$		0			0
$49$	6.57902	+	2.39092i	0.939860	+	0.341560i
$50$		0			0
$51$	−4.38759	−	0.360077i	−0.614385	−	0.0504208i
$52$		0			0
$53$	6.20454	−	10.7466i	0.852260	−	1.47616i	−0.0269043	−	0.999638i	$-0.508565\pi$
$53$	6.20454	−	10.7466i	0.852260	−	1.47616i	0.879164	−	0.476519i	$-0.158102\pi$
$54$		0			0
$55$	−1.47462			−0.198837
$56$		0			0
$57$	4.88254	+	10.3252i	0.646708	+	1.36760i
$58$		0			0
$59$	−4.50330	−	3.77872i	−0.586280	−	0.491947i	0.300723	−	0.953712i	$-0.402772\pi$
$59$	−4.50330	−	3.77872i	−0.586280	−	0.491947i	−0.887003	+	0.461764i	$0.847217\pi$
$60$		0			0
$61$	−6.26425	−	2.28000i	−0.802055	−	0.291924i	−0.0917174	−	0.995785i	$-0.529236\pi$
$61$	−6.26425	−	2.28000i	−0.802055	−	0.291924i	−0.710338	+	0.703861i	$0.751458\pi$
$62$		0			0
$63$	1.46427	+	7.80102i	0.184481	+	0.982836i
$64$		0			0
$65$	1.31730	−	1.10534i	0.163390	−	0.137101i
$66$		0			0
$67$	0.341369	−	1.93600i	0.0417048	−	0.236520i	−0.956829	−	0.290652i	$-0.906128\pi$
$67$	0.341369	−	1.93600i	0.0417048	−	0.236520i	0.998534	+	0.0541317i	$0.0172391\pi$
$68$		0			0
$69$	10.5596	+	10.4466i	1.27123	+	1.25762i
$70$		0			0
$71$	0.665025	−	1.15186i	0.0789240	−	0.136700i	−0.823862	−	0.566791i	$-0.808185\pi$
$71$	0.665025	−	1.15186i	0.0789240	−	0.136700i	0.902786	+	0.430090i	$0.141518\pi$
$72$		0			0
$73$	−11.3954			−1.33373			−0.666867	−	0.745177i	$-0.732365\pi$
$73$	−11.3954			−1.33373			−0.666867	+	0.745177i	$0.732365\pi$
$74$		0			0
$75$	−0.567708	−	6.10996i	−0.0655533	−	0.705517i
$76$		0			0
$77$	−2.79935	−	1.61529i	−0.319016	−	0.184080i
$78$		0			0
$79$	−2.89374	−	16.4112i	−0.325571	−	1.84640i	−0.505633	−	0.862749i	$-0.668741\pi$
$79$	−2.89374	−	16.4112i	−0.325571	−	1.84640i	0.180062	−	0.983655i	$-0.442370\pi$
$80$		0			0
$81$	−6.76825	+	5.93218i	−0.752028	+	0.659131i
$82$		0			0
$83$	−9.56572	−	3.48164i	−1.04997	−	0.382159i	−0.241321	−	0.970445i	$-0.577581\pi$
$83$	−9.56572	−	3.48164i	−1.04997	−	0.382159i	−0.808653	+	0.588286i	$0.799803\pi$
$84$		0			0
$85$	−2.35039	−	1.97221i	−0.254935	−	0.213916i
$86$		0			0
$87$	5.95928	−	4.22072i	0.638902	−	0.452508i
$88$		0			0
$89$	2.06682	−	3.57984i	0.219082	−	0.379462i	−0.735445	−	0.677584i	$-0.763027\pi$
$89$	2.06682	−	3.57984i	0.219082	−	0.379462i	0.954528	+	0.298122i	$0.0963603\pi$
$90$		0			0
$91$	3.71149	−	0.655372i	0.389070	−	0.0687017i
$92$		0			0
$93$	−3.12861	+	11.9327i	−0.324422	+	1.23736i
$94$		0			0
$95$	−1.38226	+	7.83921i	−0.141817	+	0.804286i
$96$		0			0
$97$	1.44888	+	8.21701i	0.147111	+	0.834311i	0.965648	+	0.259855i	$0.0836749\pi$
$97$	1.44888	+	8.21701i	0.147111	+	0.834311i	−0.818536	+	0.574455i	$0.805214\pi$
$98$		0			0
$99$	−0.0394521	−	3.66448i	−0.00396509	−	0.368294i
$100$		0			0
$101$	1.40097	+	7.94531i	0.139402	+	0.790588i	0.971693	+	0.236249i	$0.0759180\pi$
$101$	1.40097	+	7.94531i	0.139402	+	0.790588i	−0.832291	+	0.554340i	$0.812971\pi$
$102$		0			0
$103$	−11.2700	+	4.10194i	−1.11046	+	0.404176i	−0.831164	−	0.556028i	$-0.812325\pi$
$103$	−11.2700	+	4.10194i	−1.11046	+	0.404176i	−0.279301	+	0.960204i	$0.590103\pi$
$104$		0			0
$105$	−2.30962	+	5.02666i	−0.225396	+	0.490552i
$106$		0			0
$107$	1.40726	+	2.43744i	0.136045	+	0.235636i	0.925996	−	0.377533i	$-0.123228\pi$
$107$	1.40726	+	2.43744i	0.136045	+	0.235636i	−0.789951	+	0.613170i	$0.789894\pi$
$108$		0			0
$109$	−0.123885	+	0.214575i	−0.0118660	+	0.0205526i	−0.871897	−	0.489689i	$-0.837110\pi$
$109$	−0.123885	+	0.214575i	−0.0118660	+	0.0205526i	0.860031	+	0.510241i	$0.170444\pi$
$110$		0			0
$111$	11.2342	−	16.2293i	1.06630	−	1.54042i
$112$		0			0
$113$	2.76266	−	15.6678i	0.259889	−	1.47390i	−0.523315	−	0.852139i	$-0.675305\pi$
$113$	2.76266	−	15.6678i	0.259889	−	1.47390i	0.783204	−	0.621765i	$-0.213584\pi$
$114$		0			0
$115$	1.79767	+	10.1951i	0.167634	+	0.950700i
$116$		0			0
$117$	2.78206	+	3.24396i	0.257202	+	0.299904i
$118$		0			0
$119$	−2.30152	−	6.31857i	−0.210980	−	0.579222i
$120$		0			0
$121$	−7.28338	−	6.11148i	−0.662126	−	0.555589i
$122$		0			0
$123$	−4.78523	+	18.2511i	−0.431470	+	1.64565i
$124$		0			0
$125$	5.15622	−	8.93084i	0.461187	−	0.798799i
$126$		0			0
$127$	−3.23555	−	5.60414i	−0.287109	−	0.497287i	0.686010	−	0.727593i	$-0.259361\pi$
$127$	−3.23555	−	5.60414i	−0.287109	−	0.497287i	−0.973118	+	0.230305i	$0.926027\pi$
$128$		0			0
$129$	−2.44245	−	1.12296i	−0.215045	−	0.0988715i
$130$		0			0
$131$	−0.614181	+	3.48320i	−0.0536613	+	0.304328i	−0.999812	−	0.0193987i	$-0.993825\pi$
$131$	−0.614181	+	3.48320i	−0.0536613	+	0.304328i	0.946151	+	0.323727i	$0.104936\pi$
$132$		0			0
$133$	−11.2111	+	13.3675i	−0.972126	+	1.15911i
$134$		0			0
$135$	−6.23904	+	0.647521i	−0.536971	+	0.0557297i
$136$		0			0
$137$	−3.89825	+	3.27102i	−0.333050	+	0.279462i	−0.793941	−	0.607994i	$-0.791974\pi$
$137$	−3.89825	+	3.27102i	−0.333050	+	0.279462i	0.460891	+	0.887457i	$0.347530\pi$
$138$		0			0
$139$	9.60142	+	8.05655i	0.814382	+	0.683348i	0.951649	−	0.307186i	$-0.0993875\pi$
$139$	9.60142	+	8.05655i	0.814382	+	0.683348i	−0.137267	+	0.990534i	$0.543832\pi$
$140$		0			0
$141$	−15.7608	+	11.1627i	−1.32730	+	0.940070i
$142$		0			0
$143$	−1.74013			−0.145517
$144$		0			0
$145$	5.08953			0.422662
$146$		0			0
$147$	−9.89068	+	7.01245i	−0.815770	+	0.578377i
$148$		0			0
$149$	−4.74511	−	3.98162i	−0.388734	−	0.326187i	0.427386	−	0.904069i	$-0.359435\pi$
$149$	−4.74511	−	3.98162i	−0.388734	−	0.326187i	−0.816120	+	0.577883i	$0.803879\pi$
$150$		0			0
$151$	−2.91826	−	1.06216i	−0.237485	−	0.0864374i	0.220536	−	0.975379i	$-0.429219\pi$
$151$	−2.91826	−	1.06216i	−0.237485	−	0.0864374i	−0.458021	+	0.888941i	$0.651442\pi$
$152$		0			0
$153$	4.83814	−	5.89357i	0.391140	−	0.476467i
$154$		0			0
$155$	−6.58614	+	5.52643i	−0.529011	+	0.443893i
$156$		0			0
$157$	−1.95803	−	1.64298i	−0.156268	−	0.131124i	0.561301	−	0.827612i	$-0.310301\pi$
$157$	−1.95803	−	1.64298i	−0.156268	−	0.131124i	−0.717569	+	0.696487i	$0.754745\pi$
$158$		0			0
$159$	9.18813	+	19.4303i	0.728666	+	1.54092i
$160$		0			0
$161$	−7.75509	+	21.3232i	−0.611187	+	1.68050i
$162$		0			0
$163$	−1.93202	−	3.34636i	−0.151328	−	0.262108i	0.780388	−	0.625296i	$-0.215022\pi$
$163$	−1.93202	−	3.34636i	−0.151328	−	0.262108i	−0.931716	+	0.363188i	$0.881688\pi$
$164$		0			0
$165$	1.45369	−	2.10006i	0.113170	−	0.163489i
$166$		0			0
$167$	2.37370	−	13.4619i	0.183683	−	1.04172i	−0.743954	−	0.668231i	$-0.767052\pi$
$167$	2.37370	−	13.4619i	0.183683	−	1.04172i	0.927636	−	0.373485i	$-0.121837\pi$
$168$		0			0
$169$	−8.40409	+	7.05187i	−0.646469	+	0.542451i
$170$		0			0
$171$	−19.5177	−	3.22525i	−1.49256	−	0.246641i
$172$		0			0
$173$	−12.4270	+	10.4275i	−0.944806	+	0.792786i	−0.978415	−	0.206649i	$-0.933744\pi$
$173$	−12.4270	+	10.4275i	−0.944806	+	0.792786i	0.0336095	+	0.999435i	$0.489300\pi$
$174$		0			0
$175$	8.11638	−	4.68864i	0.613541	−	0.354428i
$176$		0			0
$177$	9.82083	−	2.68823i	0.738179	−	0.202059i
$178$		0			0
$179$	9.50031	+	16.4550i	0.710087	+	1.22991i	0.964824	+	0.262896i	$0.0846777\pi$
$179$	9.50031	+	16.4550i	0.710087	+	1.22991i	−0.254737	+	0.967010i	$0.581989\pi$
$180$		0			0
$181$	−1.42054	−	2.46045i	−0.105588	−	0.182884i	0.808390	−	0.588647i	$-0.200339\pi$
$181$	−1.42054	−	2.46045i	−0.105588	−	0.182884i	−0.913978	+	0.405763i	$0.867006\pi$
$182$		0			0
$183$	9.42242	−	6.67352i	0.696525	−	0.493321i
$184$		0			0
$185$	12.9270	−	4.70503i	0.950410	−	0.345921i
$186$		0			0
$187$	0.539149	+	3.05767i	0.0394265	+	0.223599i
$188$		0			0
$189$	−12.5532	−	5.60501i	−0.913114	−	0.407705i
$190$		0			0
$191$	−3.31726	−	18.8131i	−0.240029	−	1.36127i	−0.831760	−	0.555135i	$-0.812667\pi$
$191$	−3.31726	−	18.8131i	−0.240029	−	1.36127i	0.591732	−	0.806135i	$-0.298445\pi$
$192$		0			0
$193$	4.88027	−	1.77627i	0.351290	−	0.127859i	−0.160348	−	0.987061i	$-0.551261\pi$
$193$	4.88027	−	1.77627i	0.351290	−	0.127859i	0.511637	+	0.859202i	$0.329039\pi$
$194$		0			0
$195$	0.275556	+	2.96567i	0.0197330	+	0.212376i
$196$		0			0
$197$	12.8017	+	22.1732i	0.912085	+	1.57978i	0.811114	+	0.584888i	$0.198862\pi$
$197$	12.8017	+	22.1732i	0.912085	+	1.57978i	0.100971	+	0.994889i	$0.467805\pi$
$198$		0			0
$199$	−6.17903	−	10.7024i	−0.438020	−	0.758673i	0.559517	−	0.828819i	$-0.310987\pi$
$199$	−6.17903	−	10.7024i	−0.438020	−	0.758673i	−0.997537	+	0.0701463i	$0.977653\pi$
$200$		0			0
$201$	2.42061	+	2.39469i	0.170737	+	0.168908i
$202$		0			0
$203$	9.66175	+	5.57506i	0.678122	+	0.391293i
$204$		0			0
$205$	−10.0736	+	8.45272i	−0.703568	+	0.590363i
$206$		0			0
$207$	−25.2872	+	4.74006i	−1.75758	+	0.329457i
$208$		0			0
$209$	6.17062	−	5.17776i	0.426831	−	0.358153i
$210$		0			0
$211$	1.34718	−	7.64025i	0.0927439	−	0.525977i	−0.902672	−	0.430330i	$-0.858397\pi$
$211$	1.34718	−	7.64025i	0.0927439	−	0.525977i	0.995415	−	0.0956464i	$-0.0304918\pi$
$212$		0			0
$213$	0.984817	+	2.08260i	0.0674785	+	0.142698i
$214$		0			0
$215$	−0.936782	−	1.62255i	−0.0638880	−	0.110657i
$216$		0			0
$217$	−18.5565	+	3.27669i	−1.25970	+	0.222436i
$218$		0			0
$219$	11.2338	−	16.2287i	0.759107	−	1.09663i
$220$		0			0
$221$	−2.77360	−	2.32732i	−0.186572	−	0.156553i
$222$		0			0
$223$	−5.87637	+	4.93086i	−0.393511	+	0.330195i	−0.817979	−	0.575248i	$-0.804905\pi$
$223$	−5.87637	+	4.93086i	−0.393511	+	0.330195i	0.424468	+	0.905443i	$0.360461\pi$
$224$		0			0
$225$	9.26109	+	5.21477i	0.617406	+	0.347651i
$226$		0			0
$227$	−0.558974	−	0.203450i	−0.0371004	−	0.0135035i	0.323403	−	0.946261i	$-0.395173\pi$
$227$	−0.558974	−	0.203450i	−0.0371004	−	0.0135035i	−0.360504	+	0.932758i	$0.617395\pi$
$228$		0			0
$229$	4.09079	+	3.43258i	0.270327	+	0.226831i	0.767866	−	0.640610i	$-0.221319\pi$
$229$	4.09079	+	3.43258i	0.270327	+	0.226831i	−0.497539	+	0.867441i	$0.665763\pi$
$230$		0			0
$231$	5.06004	−	2.39429i	0.332926	−	0.157533i
$232$		0			0
$233$	−3.16281			−0.207203			−0.103601	−	0.994619i	$-0.533037\pi$
$233$	−3.16281			−0.207203			−0.103601	+	0.994619i	$0.533037\pi$
$234$		0			0
$235$	−13.4605			−0.878066
$236$		0			0
$237$	26.2245	+	12.0573i	1.70347	+	0.783204i
$238$		0			0
$239$	1.27452	+	1.06945i	0.0824421	+	0.0691772i	0.683077	−	0.730346i	$-0.260641\pi$
$239$	1.27452	+	1.06945i	0.0824421	+	0.0691772i	−0.600635	+	0.799523i	$0.705086\pi$
$240$		0			0
$241$	8.07839	−	6.77858i	0.520375	−	0.436646i	−0.344388	−	0.938828i	$-0.611913\pi$
$241$	8.07839	−	6.77858i	0.520375	−	0.436646i	0.864762	+	0.502181i	$0.167469\pi$
$242$		0			0
$243$	−1.77604	−	15.4870i	−0.113933	−	0.993488i
$244$		0			0
$245$	−8.45008	+	0.00413620i	−0.539856	+	0.000264252i
$246$		0			0
$247$	−1.63115	+	9.25074i	−0.103788	+	0.588610i
$248$		0			0
$249$	14.3883	−	10.1907i	0.911824	−	0.645808i
$250$		0			0
$251$	1.73221	+	3.00028i	0.109336	+	0.189376i	0.915502	−	0.402314i	$-0.131794\pi$
$251$	1.73221	+	3.00028i	0.109336	+	0.189376i	−0.806165	+	0.591690i	$0.798461\pi$
$252$		0			0
$253$	5.23799	−	9.07246i	0.329310	−	0.570381i
$254$		0			0
$255$	5.12574	−	1.40305i	0.320986	−	0.0878626i
$256$		0			0
$257$	12.9905	+	10.9004i	0.810327	+	0.679945i	0.950686	−	0.310155i	$-0.100381\pi$
$257$	12.9905	+	10.9004i	0.810327	+	0.679945i	−0.140359	+	0.990101i	$0.544826\pi$
$258$		0			0
$259$	29.6939	+	5.22835i	1.84509	+	0.324874i
$260$		0			0
$261$	0.136166	+	12.6477i	0.00842847	+	0.782872i
$262$		0			0
$263$	0.139148	+	0.789148i	0.00858024	+	0.0486610i	0.988797	−	0.149265i	$-0.0476906\pi$
$263$	0.139148	+	0.789148i	0.00858024	+	0.0486610i	−0.980217	+	0.197926i	$0.936580\pi$
$264$		0			0
$265$	−2.60119	+	14.7521i	−0.159790	+	0.906215i
$266$		0			0
$267$	3.06069	+	6.47249i	0.187311	+	0.396110i
$268$		0			0
$269$	12.1374	−	21.0225i	0.740029	−	1.28177i	−0.212453	−	0.977171i	$-0.568145\pi$
$269$	12.1374	−	21.0225i	0.740029	−	1.28177i	0.952482	−	0.304596i	$-0.0985214\pi$
$270$		0			0
$271$	10.7864	+	18.6826i	0.655227	+	1.13489i	0.981837	+	0.189727i	$0.0607603\pi$
$271$	10.7864	+	18.6826i	0.655227	+	1.13489i	−0.326610	+	0.945159i	$0.605906\pi$
$272$		0			0
$273$	−2.72549	+	5.93176i	−0.164954	+	0.359006i
$274$		0			0
$275$	−4.06674	+	1.48017i	−0.245234	+	0.0892577i
$276$		0			0
$277$	4.56603	+	25.8952i	0.274346	+	1.55589i	0.741031	+	0.671471i	$0.234337\pi$
$277$	4.56603	+	25.8952i	0.274346	+	1.55589i	−0.466685	+	0.884424i	$0.654552\pi$
$278$		0			0
$279$	−13.9096	−	16.2190i	−0.832746	−	0.971004i
$280$		0			0
$281$	−1.74183	−	9.87843i	−0.103909	−	0.589298i	−0.991650	−	0.128955i	$-0.958838\pi$
$281$	−1.74183	−	9.87843i	−0.103909	−	0.589298i	0.887741	−	0.460343i	$-0.152273\pi$
$282$		0			0
$283$	3.13848	−	17.7992i	0.186563	−	1.05805i	−0.737367	−	0.675493i	$-0.763931\pi$
$283$	3.13848	−	17.7992i	0.186563	−	1.05805i	0.923930	−	0.382561i	$-0.124958\pi$
$284$		0			0
$285$	−9.80148	−	9.69653i	−0.580590	−	0.574373i
$286$		0			0
$287$	−28.3823	+	5.01173i	−1.67536	+	0.295833i
$288$		0			0
$289$	5.26990	−	9.12774i	0.309994	−	0.536926i
$290$		0			0
$291$	−13.1305	−	6.03702i	−0.769723	−	0.353896i
$292$		0			0
$293$	−10.0250	−	8.41200i	−0.585668	−	0.491434i	0.301135	−	0.953582i	$-0.402635\pi$
$293$	−10.0250	−	8.41200i	−0.585668	−	0.491434i	−0.886803	+	0.462147i	$0.847079\pi$
$294$		0			0
$295$	6.66846	+	2.42712i	0.388253	+	0.141312i
$296$		0			0
$297$	5.25762	+	3.55630i	0.305078	+	0.206358i
$298$		0			0
$299$	2.12136	+	12.0308i	0.122682	+	0.695762i
$300$		0			0
$301$	−0.00100500	−	4.10634i	−5.79272e−5	−	0.236686i
$302$		0			0
$303$	−12.6963	−	5.83740i	−0.729386	−	0.335350i
$304$		0			0
$305$	8.04722			0.460783
$306$		0			0
$307$	−3.12591	+	5.41424i	−0.178405	+	0.309007i	−0.941334	−	0.337475i	$-0.890427\pi$
$307$	−3.12591	+	5.41424i	−0.178405	+	0.309007i	0.762929	+	0.646482i	$0.223760\pi$
$308$		0			0
$309$	5.26835	−	20.0938i	0.299706	−	1.14309i
$310$		0			0
$311$	0.200272	−	1.13580i	0.0113564	−	0.0644051i	−0.978603	−	0.205758i	$-0.934034\pi$
$311$	0.200272	−	1.13580i	0.0113564	−	0.0644051i	0.989959	+	0.141353i	$0.0451452\pi$
$312$		0			0
$313$	18.2712	−	15.3314i	1.03275	−	0.866580i	0.0415747	−	0.999135i	$-0.486763\pi$
$313$	18.2712	−	15.3314i	1.03275	−	0.866580i	0.991176	+	0.132555i	$0.0423181\pi$
$314$		0			0
$315$	−4.88181	−	8.24456i	−0.275059	−	0.464528i
$316$		0			0
$317$	−9.14060	−	3.32691i	−0.513387	−	0.186858i	0.0723184	−	0.997382i	$-0.476960\pi$
$317$	−9.14060	−	3.32691i	−0.513387	−	0.186858i	−0.585705	+	0.810524i	$0.699182\pi$
$318$		0			0
$319$	−3.94534	−	3.31054i	−0.220897	−	0.185354i
$320$		0			0
$321$	−4.85855	−	0.398727i	−0.271178	−	0.0222548i
$322$		0			0
$323$	16.7603			0.932567
$324$		0			0
$325$	2.52337	−	4.37060i	0.139971	−	0.242437i
$326$		0			0
$327$	−0.183458	−	0.387960i	−0.0101452	−	0.0214542i
$328$		0			0
$329$	−25.5529	−	14.7446i	−1.40877	−	0.812897i
$330$		0			0
$331$	−12.4858	−	4.54447i	−0.686284	−	0.249787i	−0.0247405	−	0.999694i	$-0.507876\pi$
$331$	−12.4858	−	4.54447i	−0.686284	−	0.249787i	−0.661543	+	0.749907i	$0.730098\pi$
$332$		0			0
$333$	12.0380	+	31.9982i	0.659681	+	1.75349i
$334$		0			0
$335$	0.412085	+	2.33705i	0.0225146	+	0.127687i
$336$		0			0
$337$	22.9087	−	8.33807i	1.24791	−	0.454203i	0.368218	−	0.929740i	$-0.379968\pi$
$337$	22.9087	−	8.33807i	1.24791	−	0.454203i	0.879696	+	0.475536i	$0.157746\pi$
$338$		0			0
$339$	19.5897	+	19.3799i	1.06397	+	1.05257i
$340$		0			0
$341$	8.70023			0.471144
$342$		0			0
$343$	−16.0458	−	9.24835i	−0.866392	−	0.499364i
$344$		0			0
$345$	−16.2914	−	7.49033i	−0.877102	−	0.403266i
$346$		0			0
$347$	24.9994	−	9.09905i	1.34204	−	0.488463i	0.431586	−	0.902072i	$-0.357954\pi$
$347$	24.9994	−	9.09905i	1.34204	−	0.488463i	0.910455	+	0.413609i	$0.135732\pi$
$348$		0			0
$349$	−25.2893	−	9.20456i	−1.35371	−	0.492709i	−0.439603	−	0.898192i	$-0.644881\pi$
$349$	−25.2893	−	9.20456i	−1.35371	−	0.492709i	−0.914102	+	0.405483i	$0.867103\pi$
$350$		0			0
$351$	−7.36244	+	0.764113i	−0.392978	+	0.0407853i
$352$		0			0
$353$	−7.09806	+	5.95598i	−0.377792	+	0.317005i	−0.811835	−	0.583887i	$-0.801531\pi$
$353$	−7.09806	+	5.95598i	−0.377792	+	0.317005i	0.434043	+	0.900892i	$0.357087\pi$
$354$		0			0
$355$	−0.278805	+	1.58118i	−0.0147975	+	0.0839205i
$356$		0			0
$357$	11.2674	+	2.95123i	0.596334	+	0.156196i
$358$		0			0
$359$	13.6173	−	23.5859i	0.718695	−	1.24482i	−0.242822	−	0.970071i	$-0.578073\pi$
$359$	13.6173	−	23.5859i	0.718695	−	1.24482i	0.961517	−	0.274745i	$-0.0885936\pi$
$360$		0			0
$361$	−12.2414	−	21.2027i	−0.644282	−	1.11593i
$362$		0			0
$363$	15.8837	−	4.34778i	0.833676	−	0.228199i
$364$		0			0
$365$	12.9264	−	4.70484i	0.676601	−	0.246263i
$366$		0			0
$367$	−11.6601	−	4.24392i	−0.608650	−	0.221531i	0.0192622	−	0.999814i	$-0.493868\pi$
$367$	−11.6601	−	4.24392i	−0.608650	−	0.221531i	−0.627913	+	0.778284i	$0.716090\pi$
$368$		0			0
$369$	−21.2748	−	24.8070i	−1.10752	−	1.29140i
$370$		0			0
$371$	−21.0974	+	25.1554i	−1.09532	+	1.30601i
$372$		0			0
$373$	0.988924	−	0.359939i	0.0512046	−	0.0186369i	−0.316291	−	0.948662i	$-0.602438\pi$
$373$	0.988924	−	0.359939i	0.0512046	−	0.0186369i	0.367495	+	0.930025i	$0.380215\pi$
$374$		0			0
$375$	7.63570	+	16.1473i	0.394306	+	0.833844i
$376$		0			0
$377$	6.00594			0.309322
$378$		0			0
$379$	1.75486			0.0901411			0.0450705	−	0.998984i	$-0.485649\pi$
$379$	1.75486			0.0901411			0.0450705	+	0.998984i	$0.485649\pi$
$380$		0			0
$381$	11.1707	+	0.916750i	0.572294	+	0.0469665i
$382$		0			0
$383$	−17.7207	+	6.44982i	−0.905487	+	0.329570i	−0.752449	−	0.658650i	$-0.771128\pi$
$383$	−17.7207	+	6.44982i	−0.905487	+	0.329570i	−0.153038	+	0.988220i	$0.548906\pi$
$384$		0			0
$385$	3.84236	+	0.676542i	0.195825	+	0.0344798i
$386$		0			0
$387$	4.00705	−	2.37135i	0.203690	−	0.120543i
$388$		0			0
$389$	18.2331	+	6.63632i	0.924457	+	0.336475i	0.760010	−	0.649911i	$-0.225194\pi$
$389$	18.2331	+	6.63632i	0.924457	+	0.336475i	0.164447	+	0.986386i	$0.447416\pi$
$390$		0			0
$391$	20.4827	−	7.45509i	1.03585	−	0.377020i
$392$		0			0
$393$	−4.35509	−	4.30846i	−0.219685	−	0.217333i
$394$		0			0
$395$	10.0582	+	17.4214i	0.506084	+	0.876564i
$396$		0			0
$397$	8.30655	−	14.3874i	0.416894	−	0.722082i	−0.578731	−	0.815518i	$-0.696452\pi$
$397$	8.30655	−	14.3874i	0.416894	−	0.722082i	0.995625	+	0.0934368i	$0.0297853\pi$
$398$		0			0
$399$	−7.98517	−	29.1440i	−0.399759	−	1.45903i
$400$		0			0
$401$	−1.06786	+	6.05616i	−0.0533266	+	0.302430i	−0.999792	−	0.0203738i	$-0.993514\pi$
$401$	−1.06786	+	6.05616i	−0.0533266	+	0.302430i	0.946466	+	0.322804i	$0.104625\pi$
$402$		0			0
$403$	−7.77204	+	6.52151i	−0.387153	+	0.324860i
$404$		0			0
$405$	5.22836	−	9.52361i	0.259800	−	0.473232i
$406$		0			0
$407$	−13.0813	−	4.76120i	−0.648415	−	0.236004i
$408$		0			0
$409$	14.3913	−	5.23801i	0.711605	−	0.259003i	0.0392475	−	0.999230i	$-0.487504\pi$
$409$	14.3913	−	5.23801i	0.711605	−	0.259003i	0.672358	+	0.740226i	$0.265282\pi$
$410$		0			0
$411$	−0.815450	−	8.77627i	−0.0402232	−	0.432902i
$412$		0			0
$413$	10.0005	+	11.9122i	0.492091	+	0.586159i
$414$		0			0
$415$	12.2884			0.603212
$416$		0			0
$417$	−20.9388	+	5.73153i	−1.02538	+	0.280674i
$418$		0			0
$419$	−21.9431	+	7.98663i	−1.07199	+	0.390172i	−0.816920	−	0.576750i	$-0.804320\pi$
$419$	−21.9431	+	7.98663i	−1.07199	+	0.390172i	−0.255069	+	0.966923i	$0.582098\pi$
$420$		0			0
$421$	1.90088	+	10.7804i	0.0926431	+	0.525405i	0.995444	+	0.0953466i	$0.0303959\pi$
$421$	1.90088	+	10.7804i	0.0926431	+	0.525405i	−0.902801	+	0.430058i	$0.858493\pi$
$422$		0			0
$423$	−0.360124	−	33.4499i	−0.0175099	−	1.62639i
$424$		0			0
$425$	−8.46160	−	3.07977i	−0.410448	−	0.149391i
$426$		0			0
$427$	15.2765	+	8.81492i	0.739283	+	0.426584i
$428$		0			0
$429$	1.71545	−	2.47820i	0.0828225	−	0.119648i
$430$		0			0
$431$	−2.23273	+	3.86721i	−0.107547	+	0.186277i	−0.914776	−	0.403962i	$-0.867633\pi$
$431$	−2.23273	+	3.86721i	−0.107547	+	0.186277i	0.807229	+	0.590238i	$0.200966\pi$
$432$		0			0
$433$	19.1320			0.919423			0.459712	−	0.888068i	$-0.347953\pi$
$433$	19.1320			0.919423			0.459712	+	0.888068i	$0.347953\pi$
$434$		0			0
$435$	−5.01732	+	7.24820i	−0.240562	+	0.347524i
$436$		0			0
$437$	−43.3202	−	36.3500i	−2.07229	−	1.73886i
$438$		0			0
$439$	29.8527	+	10.8655i	1.42479	+	0.518582i	0.935434	−	0.353501i	$-0.115009\pi$
$439$	29.8527	+	10.8655i	1.42479	+	0.518582i	0.489358	+	0.872083i	$0.337231\pi$
$440$		0			0
$441$	−0.236353	−	20.9987i	−0.0112549	−	0.999937i
$442$		0			0
$443$	2.78858	−	2.33989i	0.132489	−	0.111172i	−0.574135	−	0.818761i	$-0.694662\pi$
$443$	2.78858	−	2.33989i	0.132489	−	0.111172i	0.706624	+	0.707589i	$0.250217\pi$
$444$		0			0
$445$	−0.866494	+	4.91413i	−0.0410757	+	0.232952i
$446$		0			0
$447$	10.3482	−	2.83257i	0.489451	−	0.133976i
$448$		0			0
$449$	−6.66096	+	11.5371i	−0.314350	+	0.544470i	−0.979299	−	0.202418i	$-0.935120\pi$
$449$	−6.66096	+	11.5371i	−0.314350	+	0.544470i	0.664949	+	0.746889i	$0.268453\pi$
$450$		0			0
$451$	13.3071			0.626605
$452$		0			0
$453$	4.38952	−	3.10892i	0.206238	−	0.146070i
$454$		0			0
$455$	−3.93956	+	2.27579i	−0.184689	+	0.106691i
$456$		0			0
$457$	2.56706	+	14.5585i	0.120082	+	0.681020i	0.984108	+	0.177572i	$0.0568243\pi$
$457$	2.56706	+	14.5585i	0.120082	+	0.681020i	−0.864026	+	0.503448i	$0.832065\pi$
$458$		0			0
$459$	3.62378	+	12.7001i	0.169143	+	0.592792i
$460$		0			0
$461$	−12.7289	−	4.63295i	−0.592846	−	0.215778i	0.0281350	−	0.999604i	$-0.491043\pi$
$461$	−12.7289	−	4.63295i	−0.592846	−	0.215778i	−0.620981	+	0.783826i	$0.713265\pi$
$462$		0			0
$463$	21.8512	+	18.3354i	1.01551	+	0.852117i	0.989057	−	0.147533i	$-0.0471333\pi$
$463$	21.8512	+	18.3354i	1.01551	+	0.852117i	0.0264563	+	0.999650i	$0.491578\pi$
$464$		0			0
$465$	−1.37771	−	14.8276i	−0.0638898	−	0.687614i
$466$		0			0
$467$	−19.9458	+	34.5471i	−0.922980	+	1.59865i	−0.128202	+	0.991748i	$0.540921\pi$
$467$	−19.9458	+	34.5471i	−0.922980	+	1.59865i	−0.794778	+	0.606900i	$0.792413\pi$
$468$		0			0
$469$	−1.77772	+	4.88795i	−0.0820873	+	0.225705i
$470$		0			0
$471$	4.27009	−	1.16884i	0.196755	−	0.0538572i
$472$		0			0
$473$	−0.329225	+	1.86713i	−0.0151378	+	0.0858506i
$474$		0			0
$475$	4.05670	+	23.0067i	0.186134	+	1.05562i
$476$		0			0
$477$	−36.7292	−	6.06939i	−1.68171	−	0.277898i
$478$		0			0
$479$	−1.21097	−	6.86775i	−0.0553306	−	0.313795i	0.944564	−	0.328328i	$-0.106485\pi$
$479$	−1.21097	−	6.86775i	−0.0553306	−	0.313795i	−0.999894	+	0.0145325i	$0.995374\pi$
$480$		0			0
$481$	15.2546	−	5.55222i	0.695550	−	0.253159i
$482$		0			0
$483$	−22.7221	−	32.0650i	−1.03389	−	1.45901i
$484$		0			0
$485$	−5.03611	−	8.72279i	−0.228678	−	0.396082i
$486$		0			0
$487$	20.1799	−	34.9526i	0.914438	−	1.58385i	0.106715	−	0.994290i	$-0.465967\pi$
$487$	20.1799	−	34.9526i	0.914438	−	1.58385i	0.807722	−	0.589563i	$-0.200700\pi$
$488$		0			0
$489$	6.67031	+	0.547413i	0.301642	+	0.0247549i
$490$		0			0
$491$	−3.51327	+	19.9247i	−0.158551	+	0.899190i	0.796915	+	0.604091i	$0.206464\pi$
$491$	−3.51327	+	19.9247i	−0.158551	+	0.899190i	−0.955467	+	0.295099i	$0.904647\pi$
$492$		0			0
$493$	−1.86083	−	10.5533i	−0.0838078	−	0.475297i
$494$		0			0
$495$	1.55771	+	4.14053i	0.0700139	+	0.186103i
$496$		0			0
$497$	−2.26130	+	2.69625i	−0.101433	+	0.120943i
$498$		0			0
$499$	−7.27898	−	6.10779i	−0.325852	−	0.273422i	0.465155	−	0.885229i	$-0.345998\pi$
$499$	−7.27898	−	6.10779i	−0.325852	−	0.273422i	−0.791007	+	0.611807i	$0.790443\pi$
$500$		0			0
$501$	16.8317	+	16.6514i	0.751983	+	0.743931i
$502$		0			0
$503$	−7.67986	+	13.3019i	−0.342428	+	0.593103i	−0.984883	−	0.173220i	$-0.944583\pi$
$503$	−7.67986	+	13.3019i	−0.342428	+	0.593103i	0.642455	+	0.766324i	$0.277916\pi$
$504$		0			0
$505$	−4.86959	−	8.43438i	−0.216694	−	0.375325i
$506$		0			0
$507$	−1.75800	−	18.9204i	−0.0780754	−	0.840285i
$508$		0			0
$509$	5.84800	−	33.1656i	0.259208	−	1.47004i	−0.525828	−	0.850591i	$-0.676245\pi$
$509$	5.84800	−	33.1656i	0.259208	−	1.47004i	0.785036	−	0.619450i	$-0.212644\pi$
$510$		0			0
$511$	29.6927	+	5.22813i	1.31353	+	0.231279i
$512$		0			0
$513$	23.8340	−	24.6165i	1.05230	−	1.08685i
$514$		0			0
$515$	11.0906	−	9.30610i	0.488709	−	0.410076i
$516$		0			0
$517$	10.4344	+	8.75552i	0.458906	+	0.385068i
$518$		0			0
$519$	−2.59952	−	27.9773i	−0.114106	−	1.22807i
$520$		0			0
$521$	36.3385			1.59202			0.796010	−	0.605284i	$-0.206940\pi$
$521$	36.3385			1.59202			0.796010	+	0.605284i	$0.206940\pi$
$522$		0			0
$523$	16.7090			0.730634			0.365317	−	0.930883i	$-0.380961\pi$
$523$	16.7090			0.730634			0.365317	+	0.930883i	$0.380961\pi$
$524$		0			0
$525$	−1.32394	+	16.1810i	−0.0577815	+	0.706196i
$526$		0			0
$527$	13.8673	+	11.6360i	0.604068	+	0.506873i
$528$		0			0
$529$	−47.4973	−	17.2876i	−2.06510	−	0.751635i
$530$		0			0
$531$	−5.85308	+	16.6363i	−0.254002	+	0.721955i
$532$		0			0
$533$	−11.8874	+	9.97471i	−0.514900	+	0.432053i
$534$		0			0
$535$	−2.60268	−	2.18391i	−0.112524	−	0.0944185i
$536$		0			0
$537$	−32.7998	−	2.69178i	−1.41542	−	0.116159i
$538$		0			0
$539$	6.55310	+	5.49324i	0.282262	+	0.236610i
$540$		0			0
$541$	7.18915	+	12.4520i	0.309086	+	0.535352i	0.978163	−	0.207841i	$-0.0666437\pi$
$541$	7.18915	+	12.4520i	0.309086	+	0.535352i	−0.669077	+	0.743193i	$0.733310\pi$
$542$		0			0
$543$	4.90442	+	0.402492i	0.210469	+	0.0172726i
$544$		0			0
$545$	0.0519375	−	0.294552i	0.00222476	−	0.0126172i
$546$		0			0
$547$	5.21279	−	4.37405i	0.222883	−	0.187021i	−0.524508	−	0.851405i	$-0.675751\pi$
$547$	5.21279	−	4.37405i	0.222883	−	0.187021i	0.747391	+	0.664385i	$0.231306\pi$
$548$		0			0
$549$	0.215297	+	19.9977i	0.00918864	+	0.853480i
$550$		0			0
$551$	−21.2974	+	17.8707i	−0.907301	+	0.761316i
$552$		0			0
$553$	0.0107907	+	44.0898i	0.000458866	+	1.87489i
$554$		0			0
$555$	−6.04294	+	23.0481i	−0.256508	+	0.978337i
$556$		0			0
$557$	−16.3290	−	28.2826i	−0.691881	−	1.19837i	−0.971221	−	0.238180i	$-0.923449\pi$
$557$	−16.3290	−	28.2826i	−0.691881	−	1.19837i	0.279340	−	0.960192i	$-0.409884\pi$
$558$		0			0
$559$	−1.10546	−	1.91471i	−0.0467559	−	0.0809837i
$560$		0			0
$561$	−4.88605	−	2.24646i	−0.206289	−	0.0948457i
$562$		0			0
$563$	16.5062	−	6.00776i	0.695652	−	0.253197i	0.0300988	−	0.999547i	$-0.490418\pi$
$563$	16.5062	−	6.00776i	0.695652	−	0.253197i	0.665553	+	0.746350i	$0.268196\pi$
$564$		0			0
$565$	3.33495	+	18.9135i	0.140303	+	0.795695i
$566$		0			0
$567$	20.3575	−	12.3521i	0.854933	−	0.518739i
$568$		0			0
$569$	7.47536	+	42.3949i	0.313384	+	1.77729i	0.581144	+	0.813801i	$0.302605\pi$
$569$	7.47536	+	42.3949i	0.313384	+	1.77729i	−0.267760	+	0.963486i	$0.586283\pi$
$570$		0			0
$571$	6.75203	−	2.45754i	0.282564	−	0.102845i	−0.196850	−	0.980434i	$-0.563071\pi$
$571$	6.75203	−	2.45754i	0.282564	−	0.102845i	0.479414	+	0.877589i	$0.340849\pi$
$572$		0			0
$573$	30.0627	+	13.8220i	1.25589	+	0.577421i
$574$		0			0
$575$	15.1912	+	26.3119i	0.633517	+	1.09728i
$576$		0			0
$577$	0.184049	+	0.318783i	0.00766207	+	0.0132711i	0.869831	−	0.493350i	$-0.164228\pi$
$577$	0.184049	+	0.318783i	0.00766207	+	0.0132711i	−0.862169	+	0.506621i	$0.830894\pi$
$578$		0			0
$579$	−2.28137	+	8.70126i	−0.0948104	+	0.361612i
$580$		0			0
$581$	23.3277	+	13.4607i	0.967798	+	0.558442i
$582$		0			0
$583$	11.6121	−	9.74369i	0.480923	−	0.403543i
$584$		0			0
$585$	−4.49518	−	2.53116i	−0.185853	−	0.104651i
$586$		0			0
$587$	−4.89969	+	4.11133i	−0.202232	+	0.169693i	−0.738279	−	0.674495i	$-0.764361\pi$
$587$	−4.89969	+	4.11133i	−0.202232	+	0.169693i	0.536047	+	0.844188i	$0.319917\pi$
$588$		0			0
$589$	8.15536	−	46.2513i	0.336036	−	1.90575i
$590$		0			0
$591$	−44.1979	−	3.62719i	−1.81806	−	0.149203i
$592$		0			0
$593$	−12.8441	−	22.2467i	−0.527444	−	0.913561i	−0.999488	−	0.0319856i	$-0.989817\pi$
$593$	−12.8441	−	22.2467i	−0.527444	−	0.913561i	0.472044	−	0.881575i	$-0.343516\pi$
$594$		0			0
$595$	5.21950	+	6.21726i	0.213978	+	0.254883i
$596$		0			0
$597$	21.3331	+	1.75074i	0.873104	+	0.0716532i
$598$		0			0
$599$	2.81900	+	2.36542i	0.115181	+	0.0966486i	0.698559	−	0.715552i	$-0.253825\pi$
$599$	2.81900	+	2.36542i	0.115181	+	0.0966486i	−0.583378	+	0.812201i	$0.698269\pi$
$600$		0			0
$601$	−20.8118	+	17.4631i	−0.848930	+	0.712336i	−0.959554	−	0.281526i	$-0.909159\pi$
$601$	−20.8118	+	17.4631i	−0.848930	+	0.712336i	0.110624	+	0.993862i	$0.464715\pi$
$602$		0			0
$603$	−5.79663	+	1.08657i	−0.236057	+	0.0442487i
$604$		0			0
$605$	10.7852	+	3.92549i	0.438480	+	0.159594i
$606$		0			0
$607$	2.72351	+	2.28530i	0.110544	+	0.0927574i	0.696384	−	0.717669i	$-0.254791\pi$
$607$	2.72351	+	2.28530i	0.110544	+	0.0927574i	−0.585840	+	0.810427i	$0.699235\pi$
$608$		0			0
$609$	−17.4643	+	8.26372i	−0.707690	+	0.334863i
$610$		0			0
$611$	−15.8842			−0.642605
$612$		0			0
$613$	−26.5797			−1.07355			−0.536773	−	0.843727i	$-0.680357\pi$
$613$	−26.5797			−1.07355			−0.536773	+	0.843727i	$0.680357\pi$
$614$		0			0
$615$	−2.10722	−	22.6789i	−0.0849713	−	0.914503i
$616$		0			0
$617$	16.6754	+	13.9923i	0.671326	+	0.563309i	0.913458	−	0.406934i	$-0.133402\pi$
$617$	16.6754	+	13.9923i	0.671326	+	0.563309i	−0.242132	+	0.970243i	$0.577847\pi$
$618$		0			0
$619$	6.52677	−	5.47661i	0.262333	−	0.220123i	−0.502128	−	0.864793i	$-0.667450\pi$
$619$	6.52677	−	5.47661i	0.262333	−	0.220123i	0.764461	+	0.644670i	$0.223005\pi$
$620$		0			0
$621$	18.1779	−	40.6853i	0.729454	−	1.63265i
$622$		0			0
$623$	−7.02785	+	8.37963i	−0.281565	+	0.335723i
$624$		0			0
$625$	0.914289	−	5.18519i	0.0365716	−	0.207408i
$626$		0			0
$627$	1.29079	+	13.8921i	0.0515492	+	0.554798i
$628$		0			0
$629$	−14.4824	−	25.0843i	−0.577452	−	1.00018i
$630$		0			0
$631$	8.98748	−	15.5668i	0.357786	−	0.619703i	−0.629805	−	0.776754i	$-0.716865\pi$
$631$	8.98748	−	15.5668i	0.357786	−	0.619703i	0.987591	+	0.157050i	$0.0501984\pi$
$632$		0			0
$633$	9.55272	+	9.45043i	0.379687	+	0.375621i
$634$		0			0
$635$	5.98405	+	5.02121i	0.237470	+	0.199261i
$636$		0			0
$637$	−9.97159	+	0.00488096i	−0.395089	+	0.000193391i
$638$		0			0
$639$	−3.93676	−	0.650539i	−0.155736	−	0.0257349i
$640$		0			0
$641$	3.45979	+	19.6214i	0.136653	+	0.775000i	0.973694	+	0.227859i	$0.0731725\pi$
$641$	3.45979	+	19.6214i	0.136653	+	0.775000i	−0.837041	+	0.547140i	$0.815716\pi$
$642$		0			0
$643$	−3.93605	+	22.3225i	−0.155223	+	0.880312i	0.803359	+	0.595495i	$0.203044\pi$
$643$	−3.93605	+	22.3225i	−0.155223	+	0.880312i	−0.958582	+	0.284817i	$0.908067\pi$
$644$		0			0
$645$	3.23424	+	0.265424i	0.127348	+	0.0104511i
$646$		0			0
$647$	−8.75034	+	15.1560i	−0.344011	+	0.595845i	−0.985174	−	0.171560i	$-0.945119\pi$
$647$	−8.75034	+	15.1560i	−0.344011	+	0.595845i	0.641162	+	0.767405i	$0.278453\pi$
$648$		0			0
$649$	−3.59057	−	6.21905i	−0.140942	−	0.244119i
$650$		0			0
$651$	13.6267	−	29.6573i	0.534074	−	1.16236i
$652$		0			0
$653$	−36.9659	+	13.4545i	−1.44659	+	0.526515i	−0.941636	−	0.336633i	$-0.890712\pi$
$653$	−36.9659	+	13.4545i	−1.44659	+	0.526515i	−0.504951	+	0.863148i	$0.668490\pi$
$654$		0			0
$655$	−0.741411	−	4.20475i	−0.0289693	−	0.164293i
$656$		0			0
$657$	12.0376	+	31.9969i	0.469630	+	1.24832i
$658$		0			0
$659$	1.59405	+	9.04031i	0.0620954	+	0.352161i	0.999986	+	0.00523031i	$0.00166487\pi$
$659$	1.59405	+	9.04031i	0.0620954	+	0.352161i	−0.937891	+	0.346930i	$0.887224\pi$
$660$		0			0
$661$	−1.76873	+	10.0310i	−0.0687958	+	0.390160i	0.930895	+	0.365287i	$0.119029\pi$
$661$	−1.76873	+	10.0310i	−0.0687958	+	0.390160i	−0.999691	+	0.0248730i	$0.992082\pi$
$662$		0			0
$663$	6.04868	−	1.65569i	0.234911	−	0.0643015i
$664$		0			0
$665$	7.19829	−	19.7922i	0.279138	−	0.767509i
$666$		0			0
$667$	−18.0785	+	31.3129i	−0.700003	+	1.21244i
$668$		0			0
$669$	−1.22924	−	13.2297i	−0.0475251	−	0.511488i
$670$		0			0
$671$	−6.23812	−	5.23440i	−0.240820	−	0.202072i
$672$		0			0
$673$	−33.3067	−	12.1226i	−1.28388	−	0.467294i	−0.392166	−	0.919895i	$-0.628274\pi$
$673$	−33.3067	−	12.1226i	−1.28388	−	0.467294i	−0.891713	+	0.452601i	$0.850496\pi$
$674$		0			0
$675$	−16.5563	+	8.04830i	−0.637251	+	0.309779i
$676$		0			0
$677$	7.65883	+	43.4354i	0.294353	+	1.66936i	0.669821	+	0.742522i	$0.266371\pi$
$677$	7.65883	+	43.4354i	0.294353	+	1.66936i	−0.375469	+	0.926835i	$0.622518\pi$
$678$		0			0
$679$	−0.00540284	−	22.0755i	−0.000207342	−	0.847181i
$680$		0			0
$681$	0.840785	−	0.595494i	0.0322189	−	0.0228194i
$682$		0			0
$683$	−28.9739			−1.10865			−0.554327	−	0.832299i	$-0.687024\pi$
$683$	−28.9739			−1.10865			−0.554327	+	0.832299i	$0.687024\pi$
$684$		0			0
$685$	3.07149	−	5.31997i	0.117356	−	0.203266i
$686$		0			0
$687$	−8.92122	+	2.44198i	−0.340366	+	0.0931673i
$688$		0			0
$689$	−3.06956	+	17.4084i	−0.116941	+	0.663206i
$690$		0			0
$691$	17.4008	−	14.6010i	0.661956	−	0.555447i	−0.248717	−	0.968576i	$-0.580009\pi$
$691$	17.4008	−	14.6010i	0.661956	−	0.555447i	0.910672	+	0.413130i	$0.135564\pi$
$692$		0			0
$693$	−1.57844	+	9.56652i	−0.0599598	+	0.363402i
$694$		0			0
$695$	−14.2177	−	5.17483i	−0.539309	−	0.196292i
$696$		0			0
$697$	21.2101	+	17.7974i	0.803390	+	0.674124i
$698$		0			0
$699$	3.11794	−	4.50429i	0.117931	−	0.170368i
$700$		0			0
$701$	−7.95748			−0.300550			−0.150275	−	0.988644i	$-0.548016\pi$
$701$	−7.95748			−0.300550			−0.150275	+	0.988644i	$0.548016\pi$
$702$		0			0
$703$	−37.5731	+	65.0785i	−1.41710	+	2.45448i
$704$		0			0
$705$	13.2695	−	19.1696i	0.499759	−	0.721970i
$706$		0			0
$707$	−0.00522419	−	21.3456i	−0.000196476	−	0.802784i
$708$		0			0
$709$	−4.98107	−	1.81296i	−0.187068	−	0.0680872i	0.246788	−	0.969070i	$-0.420625\pi$
$709$	−4.98107	−	1.81296i	−0.187068	−	0.0680872i	−0.433856	+	0.900982i	$0.642847\pi$
$710$		0			0
$711$	−43.0237	+	25.4612i	−1.61351	+	0.954869i
$712$		0			0
$713$	−10.6063	−	60.1512i	−0.397208	−	2.25268i
$714$		0			0
$715$	1.97393	−	0.718451i	0.0738207	−	0.0268685i
$716$		0			0
$717$	−2.77949	+	0.760822i	−0.103802	+	0.0284134i
$718$		0			0
$719$	23.3953			0.872498			0.436249	−	0.899826i	$-0.356307\pi$
$719$	23.3953			0.872498			0.436249	+	0.899826i	$0.356307\pi$
$720$		0			0
$721$	31.2478	−	5.51771i	1.16373	−	0.205490i
$722$		0			0
$723$	1.68987	+	18.1872i	0.0628468	+	0.676388i
$724$		0			0
$725$	14.0360	−	5.10870i	0.521285	−	0.189732i
$726$		0			0
$727$	3.94940	+	1.43746i	0.146475	+	0.0533126i	0.414217	−	0.910178i	$-0.364055\pi$
$727$	3.94940	+	1.43746i	0.146475	+	0.0533126i	−0.267742	+	0.963491i	$0.586278\pi$
$728$		0			0
$729$	23.8064	+	12.7379i	0.881719	+	0.471774i
$730$		0			0
$731$	−3.02192	+	2.53569i	−0.111770	+	0.0937859i
$732$		0			0
$733$	−4.23541	+	24.0202i	−0.156438	+	0.887207i	0.801020	+	0.598637i	$0.204291\pi$
$733$	−4.23541	+	24.0202i	−0.156438	+	0.887207i	−0.957459	+	0.288570i	$0.906820\pi$
$734$		0			0
$735$	8.32430	−	12.0382i	0.307046	−	0.444035i
$736$		0			0
$737$	1.20071	−	2.07970i	0.0442289	−	0.0766067i
$738$		0			0
$739$	−11.7296	−	20.3162i	−0.431480	−	0.747345i	0.565521	−	0.824734i	$-0.308675\pi$
$739$	−11.7296	−	20.3162i	−0.431480	−	0.747345i	−0.997001	+	0.0773887i	$0.975342\pi$
$740$		0			0
$741$	−11.5663	−	11.4425i	−0.424900	−	0.420350i
$742$		0			0
$743$	17.2444	−	6.27646i	0.632636	−	0.230261i	−0.00574196	−	0.999984i	$-0.501828\pi$
$743$	17.2444	−	6.27646i	0.632636	−	0.230261i	0.638378	+	0.769723i	$0.279606\pi$
$744$		0			0
$745$	7.02652	+	2.55745i	0.257432	+	0.0936975i
$746$		0			0
$747$	0.328765	+	30.5371i	0.0120289	+	1.11729i
$748$		0			0
$749$	−2.54857	−	6.99681i	−0.0931227	−	0.255658i
$750$		0			0
$751$	−30.7714	+	11.1999i	−1.12287	+	0.408690i	−0.835697	−	0.549190i	$-0.814936\pi$
$751$	−30.7714	+	11.1999i	−1.12287	+	0.408690i	−0.287169	+	0.957880i	$0.592714\pi$
$752$		0			0
$753$	−5.98045	−	0.490798i	−0.217940	−	0.0178857i
$754$		0			0
$755$	3.74888			0.136436
$756$		0			0
$757$	−40.9371			−1.48789			−0.743943	−	0.668243i	$-0.767047\pi$
$757$	−40.9371			−1.48789			−0.743943	+	0.668243i	$0.767047\pi$
$758$		0			0
$759$	7.75678	+	16.4034i	0.281553	+	0.595405i
$760$		0			0
$761$	−45.1309	+	16.4263i	−1.63599	+	0.595452i	−0.986332	−	0.164772i	$-0.947311\pi$
$761$	−45.1309	+	16.4263i	−1.63599	+	0.595452i	−0.649660	+	0.760224i	$0.725089\pi$
$762$		0			0
$763$	0.421248	−	0.502274i	0.0152502	−	0.0181835i
$764$		0			0
$765$	−3.05487	+	8.68292i	−0.110449	+	0.313932i
$766$		0			0
$767$	7.86918	+	2.86415i	0.284140	+	0.103418i
$768$		0			0
$769$	−28.9757	+	10.5463i	−1.04489	+	0.380309i	−0.806732	−	0.590917i	$-0.798766\pi$
$769$	−28.9757	+	10.5463i	−1.04489	+	0.380309i	−0.238158	+	0.971226i	$0.576544\pi$
$770$		0			0
$771$	−28.3299	+	7.75464i	−1.02027	+	0.279277i
$772$		0			0
$773$	1.06406	+	1.84301i	0.0382717	+	0.0662886i	0.884527	−	0.466489i	$-0.154481\pi$
$773$	1.06406	+	1.84301i	0.0382717	+	0.0662886i	−0.846255	+	0.532778i	$0.821148\pi$
$774$		0			0
$775$	−12.6162	+	21.8519i	−0.453187	+	0.784943i
$776$		0			0
$777$	−36.7185	+	37.1341i	−1.31727	+	1.33218i
$778$		0			0
$779$	12.4737	−	70.7418i	0.446916	−	2.53459i
$780$		0			0
$781$	1.24462	−	1.04436i	0.0445362	−	0.0373703i
$782$		0			0
$783$	−18.1463	−	12.2743i	−0.648496	−	0.438648i
$784$		0			0
$785$	2.89944	+	1.05531i	0.103486	+	0.0376656i
$786$		0			0
$787$	−35.3716	+	12.8742i	−1.26086	+	0.458916i	−0.884058	−	0.467376i	$-0.845199\pi$
$787$	−35.3716	+	12.8742i	−1.26086	+	0.458916i	−0.376804	+	0.926293i	$0.622977\pi$
$788$		0			0
$789$	−1.26103	−	0.579786i	−0.0448939	−	0.0206409i
$790$		0			0
$791$	−14.3868	+	39.5577i	−0.511537	+	1.40651i
$792$		0			0
$793$	9.49620			0.337220
$794$		0			0
$795$	−18.4448	−	18.2473i	−0.654169	−	0.647164i
$796$		0			0
$797$	−6.16107	+	2.24245i	−0.218236	+	0.0794315i	−0.448825	−	0.893620i	$-0.648157\pi$
$797$	−6.16107	+	2.24245i	−0.218236	+	0.0794315i	0.230588	+	0.973051i	$0.425935\pi$
$798$		0			0
$799$	4.92143	+	27.9108i	0.174108	+	0.987414i
$800$		0			0
$801$	−12.2350	−	2.02180i	−0.432302	−	0.0714367i
$802$		0			0
$803$	−13.0808	−	4.76101i	−0.461610	−	0.168012i
$804$		0			0
$805$	−0.00670348	−	27.3899i	−0.000236267	−	0.965366i
$806$		0			0
$807$	17.9739	+	38.0096i	0.632711	+	1.33800i
$808$		0			0
$809$	3.29662	−	5.70991i	0.115903	−	0.200750i	−0.802237	−	0.597005i	$-0.796357\pi$
$809$	3.29662	−	5.70991i	0.115903	−	0.200750i	0.918140	+	0.396255i	$0.129690\pi$
$810$		0			0
$811$	−3.35495			−0.117808			−0.0589041	−	0.998264i	$-0.518761\pi$
$811$	−3.35495			−0.117808			−0.0589041	+	0.998264i	$0.518761\pi$
$812$		0			0
$813$	−37.2400	−	3.05618i	−1.30606	−	0.107185i
$814$		0			0
$815$	3.57322	+	2.99828i	0.125164	+	0.105025i
$816$		0			0
$817$	9.61724	+	3.50039i	0.336465	+	0.122463i
$818$		0			0
$819$	−5.76083	−	9.72907i	−0.201300	−	0.339961i
$820$		0			0
$821$	30.5363	−	25.6230i	1.06572	−	0.894248i	0.0710651	−	0.997472i	$-0.477360\pi$
$821$	30.5363	−	25.6230i	1.06572	−	0.894248i	0.994658	+	0.103224i	$0.0329157\pi$
$822$		0			0
$823$	9.36796	−	53.1283i	0.326546	−	1.85194i	−0.172031	−	0.985092i	$-0.555033\pi$
$823$	9.36796	−	53.1283i	0.326546	−	1.85194i	0.498577	−	0.866845i	$-0.333856\pi$
$824$		0			0
$825$	1.90107	−	7.25077i	0.0661867	−	0.252440i
$826$		0			0
$827$	−7.30251	+	12.6483i	−0.253933	+	0.439825i	−0.964605	−	0.263698i	$-0.915058\pi$
$827$	−7.30251	+	12.6483i	−0.253933	+	0.439825i	0.710672	+	0.703523i	$0.248391\pi$
$828$		0			0
$829$	−21.0842			−0.732286			−0.366143	−	0.930559i	$-0.619322\pi$
$829$	−21.0842			−0.732286			−0.366143	+	0.930559i	$0.619322\pi$
$830$		0			0
$831$	−41.3797	−	19.0252i	−1.43545	−	0.659976i
$832$		0			0
$833$	3.09810	+	17.5200i	0.107343	+	0.607033i
$834$		0			0
$835$	2.86542	+	16.2506i	0.0991621	+	0.562376i
$836$		0			0
$837$	36.8103	−	3.82037i	1.27235	−	0.132051i
$838$		0			0
$839$	−2.21902	−	0.807659i	−0.0766092	−	0.0278835i	0.303431	−	0.952853i	$-0.401868\pi$
$839$	−2.21902	−	0.807659i	−0.0766092	−	0.0278835i	−0.380040	+	0.924970i	$0.624090\pi$
$840$		0			0
$841$	−8.59823	−	7.21477i	−0.296491	−	0.248785i
$842$		0			0
$843$	15.7854	+	7.25766i	0.543678	+	0.249967i
$844$		0			0
$845$	6.62170	−	11.4691i	0.227793	−	0.394550i
$846$		0			0
$847$	16.1742	+	19.2661i	0.555751	+	0.661990i
$848$		0			0
$849$	22.2546	+	22.0163i	0.763777	+	0.755598i
$850$		0			0
$851$	−16.9706	+	96.2450i	−0.581744	+	3.29923i
$852$		0			0
$853$	0.460804	+	2.61335i	0.0157776	+	0.0894793i	0.991680	−	0.128729i	$-0.0410898\pi$
$853$	0.460804	+	2.61335i	0.0157776	+	0.0894793i	−0.975902	+	0.218209i	$0.929979\pi$
$854$		0			0
$855$	23.4716	−	4.39973i	0.802713	−	0.150468i
$856$		0			0
$857$	2.90845	+	16.4947i	0.0993509	+	0.563447i	0.993327	+	0.115332i	$0.0367933\pi$
$857$	2.90845	+	16.4947i	0.0993509	+	0.563447i	−0.893976	+	0.448115i	$0.852096\pi$
$858$		0			0
$859$	−11.4126	+	4.15386i	−0.389394	+	0.141728i	−0.529295	−	0.848438i	$-0.677544\pi$
$859$	−11.4126	+	4.15386i	−0.389394	+	0.141728i	0.139901	+	0.990165i	$0.455321\pi$
$860$		0			0
$861$	20.8422	−	45.3610i	0.710301	−	1.54590i
$862$		0			0
$863$	20.6817	+	35.8218i	0.704015	+	1.21939i	0.967046	+	0.254602i	$0.0819445\pi$
$863$	20.6817	+	35.8218i	0.704015	+	1.21939i	−0.263031	+	0.964787i	$0.584722\pi$
$864$		0			0
$865$	9.79139	−	16.9592i	0.332917	−	0.576629i
$866$		0			0
$867$	7.80405	+	16.5033i	0.265039	+	0.560482i
$868$		0			0
$869$	3.53488	−	20.0473i	0.119913	−	0.680059i
$870$		0			0
$871$	0.486284	+	2.75786i	0.0164771	+	0.0934464i
$872$		0			0
$873$	21.5418	−	12.7483i	0.729078	−	0.431465i
$874$		0			0
$875$	−17.5328	+	20.9052i	−0.592717	+	0.706724i
$876$		0			0
$877$	13.4411	+	11.2784i	0.453874	+	0.380845i	0.840871	−	0.541235i	$-0.182043\pi$
$877$	13.4411	+	11.2784i	0.453874	+	0.380845i	−0.386997	+	0.922081i	$0.626488\pi$
$878$		0			0
$879$	21.8627	−	5.98440i	0.737409	−	0.201849i
$880$		0			0
$881$	−4.99602	+	8.65336i	−0.168320	+	0.291539i	−0.937829	−	0.347097i	$-0.887168\pi$
$881$	−4.99602	+	8.65336i	−0.168320	+	0.291539i	0.769509	+	0.638636i	$0.220501\pi$
$882$		0			0
$883$	17.9754	+	31.1343i	0.604920	+	1.04775i	0.992064	+	0.125733i	$0.0401284\pi$
$883$	17.9754	+	31.1343i	0.604920	+	1.04775i	−0.387144	+	0.922019i	$0.626538\pi$
$884$		0			0
$885$	−10.0304	+	7.10414i	−0.337168	+	0.238803i
$886$		0			0
$887$	−2.64854	+	15.0206i	−0.0889293	+	0.504343i	0.907510	+	0.420030i	$0.137981\pi$
$887$	−2.64854	+	15.0206i	−0.0889293	+	0.504343i	−0.996439	+	0.0843126i	$0.973131\pi$
$888$		0			0
$889$	5.85964	+	16.0870i	0.196526	+	0.539540i
$890$		0			0
$891$	−10.2477	+	3.98175i	−0.343311	+	0.133394i
$892$		0			0
$893$	56.3262	−	47.2633i	1.88489	−	1.58161i
$894$		0			0
$895$	−17.5705	−	14.7434i	−0.587318	−	0.492818i
$896$		0			0
$897$	−19.2249	−	8.83904i	−0.641900	−	0.295127i
$898$		0			0
$899$	−30.0282			−1.00150
$900$		0			0
$901$	31.5401			1.05075
$902$		0			0
$903$	5.84900	+	4.04665i	0.194642	+	0.134664i
$904$		0			0
$905$	2.62725	+	2.20452i	0.0873327	+	0.0732809i
$906$		0			0
$907$	−8.89566	−	3.23776i	−0.295376	−	0.107508i	0.190082	−	0.981768i	$-0.439125\pi$
$907$	−8.89566	−	3.23776i	−0.295376	−	0.107508i	−0.485457	+	0.874260i	$0.661347\pi$
$908$		0			0
$909$	20.8295	−	12.3268i	0.690870	−	0.408853i
$910$		0			0
$911$	26.0760	−	21.8804i	0.863937	−	0.724930i	−0.0988751	−	0.995100i	$-0.531524\pi$
$911$	26.0760	−	21.8804i	0.863937	−	0.724930i	0.962813	+	0.270170i	$0.0870800\pi$
$912$		0			0
$913$	−9.52581	−	7.99310i	−0.315258	−	0.264533i
$914$		0			0
$915$	−7.93305	+	11.4604i	−0.262258	+	0.378868i
$916$		0			0
$917$	3.19842	−	8.79427i	0.105621	−	0.290412i
$918$		0			0
$919$	−13.0898	−	22.6722i	−0.431793	−	0.747888i	0.565234	−	0.824930i	$-0.308786\pi$
$919$	−13.0898	−	22.6722i	−0.431793	−	0.747888i	−0.997028	+	0.0770422i	$0.975452\pi$
$920$		0			0
$921$	−4.62907	−	9.78916i	−0.152533	−	0.322564i
$922$		0			0
$923$	−0.329007	+	1.86589i	−0.0108294	+	0.0614166i
$924$		0			0
$925$	30.9276	−	25.9513i	1.01689	−	0.853275i
$926$		0			0
$927$	23.4227	+	27.3115i	0.769304	+	0.897029i
$928$		0			0
$929$	9.44173	−	7.92256i	0.309773	−	0.259931i	−0.474625	−	0.880188i	$-0.657416\pi$
$929$	9.44173	−	7.92256i	0.309773	−	0.259931i	0.784398	+	0.620257i	$0.212972\pi$
$930$		0			0
$931$	35.3453	−	29.6877i	1.15840	−	0.972976i
$932$		0			0
$933$	1.42010	+	1.40490i	0.0464921	+	0.0459943i
$934$		0			0
$935$	−1.87401	−	3.24588i	−0.0612866	−	0.106152i
$936$		0			0
$937$	16.7156	+	28.9523i	0.546075	+	0.945830i	0.998538	+	0.0540471i	$0.0172121\pi$
$937$	16.7156	+	28.9523i	0.546075	+	0.945830i	−0.452463	+	0.891783i	$0.649455\pi$
$938$		0			0
$939$	3.82204	+	41.1346i	0.124727	+	1.34238i
$940$		0			0
$941$	40.0557	−	14.5791i	1.30578	−	0.475264i	0.406904	−	0.913471i	$-0.366608\pi$
$941$	40.0557	−	14.5791i	1.30578	−	0.475264i	0.898874	+	0.438206i	$0.144386\pi$
$942$		0			0
$943$	−16.2224	−	92.0017i	−0.528273	−	2.99599i
$944$		0			0
$945$	16.5540	+	1.17520i	0.538500	+	0.0382293i
$946$		0			0
$947$	−6.48918	−	36.8020i	−0.210870	−	1.19590i	−0.887931	−	0.459977i	$-0.847858\pi$
$947$	−6.48918	−	36.8020i	−0.210870	−	1.19590i	0.677061	−	0.735927i	$-0.263253\pi$
$948$		0			0
$949$	15.2540	−	5.55199i	0.495165	−	0.180225i
$950$		0			0
$951$	13.7489	−	9.73779i	0.445838	−	0.315769i
$952$		0			0
$953$	−17.9054	−	31.0130i	−0.580012	−	1.00461i	−0.995477	−	0.0950012i	$-0.969715\pi$
$953$	−17.9054	−	31.0130i	−0.580012	−	1.00461i	0.415465	−	0.909609i	$-0.363619\pi$
$954$		0			0
$955$	11.5303	+	19.9711i	0.373113	+	0.646251i
$956$		0			0
$957$	8.60404	−	2.35516i	0.278129	−	0.0761314i
$958$		0			0
$959$	11.6583	−	6.73472i	0.376465	−	0.217475i
$960$		0			0
$961$	15.1108	−	12.6795i	0.487445	−	0.409015i
$962$		0			0
$963$	5.35746	−	6.52619i	0.172642	−	0.210303i
$964$		0			0
$965$	−4.80258	+	4.02984i	−0.154601	+	0.129725i
$966$		0			0
$967$	−0.0727281	+	0.412461i	−0.00233878	+	0.0132639i	−0.985955	−	0.167012i	$-0.946588\pi$
$967$	−0.0727281	+	0.412461i	−0.00233878	+	0.0132639i	0.983616	+	0.180276i	$0.0576991\pi$
$968$		0			0
$969$	−16.5225	+	23.8690i	−0.530778	+	0.766782i
$970$		0			0
$971$	−12.1008	−	20.9592i	−0.388334	−	0.672614i	0.603892	−	0.797066i	$-0.293616\pi$
$971$	−12.1008	−	20.9592i	−0.388334	−	0.672614i	−0.992226	+	0.124453i	$0.960283\pi$
$972$		0			0
$973$	−21.3218	−	25.3978i	−0.683547	−	0.814215i
$974$		0			0
$975$	3.73678	+	7.90222i	0.119673	+	0.253074i
$976$		0			0
$977$	14.9794	+	12.5692i	0.479232	+	0.402124i	0.850149	−	0.526543i	$-0.176512\pi$
$977$	14.9794	+	12.5692i	0.479232	+	0.402124i	−0.370916	+	0.928666i	$0.620956\pi$
$978$		0			0
$979$	3.86815	−	3.24576i	0.123626	−	0.103735i
$980$		0			0
$981$	0.733364	+	0.121186i	0.0234145	+	0.00386918i
$982$		0			0
$983$	−2.83304	−	1.03114i	−0.0903601	−	0.0328884i	0.296445	−	0.955050i	$-0.404199\pi$
$983$	−2.83304	−	1.03114i	−0.0903601	−	0.0328884i	−0.386805	+	0.922162i	$0.626421\pi$
$984$		0			0
$985$	−23.6764	−	19.8668i	−0.754392	−	0.633010i
$986$		0			0
$987$	46.1887	−	21.8554i	1.47020	−	0.695666i
$988$		0			0
$989$	13.3102			0.423240
$990$		0			0
$991$	17.5183			0.556489			0.278244	−	0.960510i	$-0.410248\pi$
$991$	17.5183			0.556489			0.278244	+	0.960510i	$0.410248\pi$
$992$		0			0
$993$	18.7807	−	13.3016i	0.595986	−	0.422113i
$994$		0			0
$995$	11.4279	+	9.58916i	0.362289	+	0.303997i
$996$		0			0
$997$	13.6549	−	11.4578i	0.432454	−	0.362872i	−0.400423	−	0.916330i	$-0.631137\pi$
$997$	13.6549	−	11.4578i	0.432454	−	0.362872i	0.832877	+	0.553459i	$0.186692\pi$
$998$		0			0
$999$	−57.4371	−	14.4003i	−1.81723	−	0.455606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.7	✓	144
7.2	even	3		756.2.bq.a.625.9	yes	144
27.7	even	9		756.2.bq.a.277.9	yes	144
189.142	even	9	inner	756.2.bp.a.709.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.7	✓	144	1.1	even	1	trivial
756.2.bp.a.709.7	yes	144	189.142	even	9	inner
756.2.bq.a.277.9	yes	144	27.7	even	9
756.2.bq.a.625.9	yes	144	7.2	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.985812 + 1.42414i) q^{3} +(-1.13435 + 0.412871i) q^{5} +(-2.60567 - 0.458792i) q^{7} +(-1.05635 - 2.80787i) q^{9} +O(q^{10})\)	\(q+(-0.985812 + 1.42414i) q^{3} +(-1.13435 + 0.412871i) q^{5} +(-2.60567 - 0.458792i) q^{7} +(-1.05635 - 2.80787i) q^{9} +(1.14789 + 0.417800i) q^{11} +(-1.33860 + 0.487212i) q^{13} +(0.530273 - 2.02249i) q^{15} +(1.27085 + 2.20117i) q^{17} +(3.29707 - 5.71070i) q^{19} +(3.22208 - 3.25855i) q^{21} +(1.48918 - 8.44558i) q^{23} +(-2.71393 + 2.27725i) q^{25} +(5.04016 + 1.26364i) q^{27} +(-3.96187 - 1.44200i) q^{29} +(6.69268 - 2.43594i) q^{31} +(-1.72661 + 1.22289i) q^{33} +(3.14517 - 0.555372i) q^{35} -11.3959 q^{37} +(0.625754 - 2.38666i) q^{39} +(10.2365 - 3.72579i) q^{41} +(0.269511 + 1.52847i) q^{43} +(2.35756 + 2.74898i) q^{45} +(10.4781 + 3.81373i) q^{47} +(6.57902 + 2.39092i) q^{49} +(-4.38759 - 0.360077i) q^{51} +(6.20454 - 10.7466i) q^{53} -1.47462 q^{55} +(4.88254 + 10.3252i) q^{57} +(-4.50330 - 3.77872i) q^{59} +(-6.26425 - 2.28000i) q^{61} +(1.46427 + 7.80102i) q^{63} +(1.31730 - 1.10534i) q^{65} +(0.341369 - 1.93600i) q^{67} +(10.5596 + 10.4466i) q^{69} +(0.665025 - 1.15186i) q^{71} -11.3954 q^{73} +(-0.567708 - 6.10996i) q^{75} +(-2.79935 - 1.61529i) q^{77} +(-2.89374 - 16.4112i) q^{79} +(-6.76825 + 5.93218i) q^{81} +(-9.56572 - 3.48164i) q^{83} +(-2.35039 - 1.97221i) q^{85} +(5.95928 - 4.22072i) q^{87} +(2.06682 - 3.57984i) q^{89} +(3.71149 - 0.655372i) q^{91} +(-3.12861 + 11.9327i) q^{93} +(-1.38226 + 7.83921i) q^{95} +(1.44888 + 8.21701i) q^{97} +(-0.0394521 - 3.66448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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