LMFDB - Embedded newform 672.2.bi.c.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26610 + 1.18195i) q^{3} +(-1.54900 + 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(0.206000 - 2.99292i) q^{9} +O(q^{10})$	\(q+(-1.26610 + 1.18195i) q^{3} +(-1.54900 + 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(0.206000 - 2.99292i) q^{9} +(0.501346 - 0.868358i) q^{11} -2.47302 q^{13} +(0.904151 - 2.96313i) q^{15} +(3.32963 - 5.76708i) q^{17} +(1.85941 + 3.22059i) q^{19} +(3.06518 - 3.40656i) q^{21} +(6.85244 - 3.95626i) q^{23} +(-0.900394 + 1.55953i) q^{25} +(3.27666 + 4.03281i) q^{27} -0.748403 q^{29} +(-2.87254 - 1.65846i) q^{31} +(0.391600 + 1.69199i) q^{33} +(3.87702 - 2.71353i) q^{35} +(3.22429 - 1.86155i) q^{37} +(3.13108 - 2.92298i) q^{39} -2.01044 q^{41} -9.19651i q^{43} +(2.35752 + 4.82027i) q^{45} +(1.19840 + 2.07569i) q^{47} +(6.89415 - 1.21270i) q^{49} +(2.60076 + 11.2371i) q^{51} +(6.33884 - 10.9792i) q^{53} +1.79345i q^{55} +(-6.16075 - 1.87985i) q^{57} +(-7.34922 - 4.24308i) q^{59} +(2.02442 + 3.50640i) q^{61} +(0.145558 + 7.93592i) q^{63} +(3.83071 - 2.21166i) q^{65} +(-6.89843 - 3.98281i) q^{67} +(-3.99976 + 13.1082i) q^{69} -5.46843i q^{71} +(-5.68546 - 3.28250i) q^{73} +(-0.703295 - 3.03873i) q^{75} +(-1.12165 + 2.40409i) q^{77} +(-2.53988 - 4.39920i) q^{79} +(-8.91513 - 1.23308i) q^{81} -5.65457i q^{83} +11.9110i q^{85} +(0.947550 - 0.884573i) q^{87} +(7.39495 + 12.8084i) q^{89} +(6.51821 - 0.568916i) q^{91} +(5.59713 - 1.29542i) q^{93} +(-5.76045 - 3.32580i) q^{95} -1.75577i q^{97} +(-2.49565 - 1.67937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.26610	+	1.18195i	−0.730981	+	0.682398i
$3$	−1.26610	+	1.18195i	−0.730981	+	0.682398i
$4$		0			0
$5$	−1.54900	+	0.894317i	−0.692735	+	0.399951i	−0.804636	−	0.593769i	$-0.797639\pi$
$5$	−1.54900	+	0.894317i	−0.692735	+	0.399951i	0.111901	+	0.993719i	$0.464306\pi$
$6$		0			0
$7$	−2.63573	+	0.230049i	−0.996213	+	0.0869505i
$7$	−2.63573	+	0.230049i	−0.996213	+	0.0869505i
$8$		0			0
$9$	0.206000	−	2.99292i	0.0686667	−	0.997640i
$10$		0			0
$11$	0.501346	−	0.868358i	0.151162	−	0.261820i	−0.780493	−	0.625164i	$-0.785032\pi$
$11$	0.501346	−	0.868358i	0.151162	−	0.261820i	0.931655	+	0.363345i	$0.118365\pi$
$12$		0			0
$13$	−2.47302			−0.685891			−0.342946	−	0.939355i	$-0.611425\pi$
$13$	−2.47302			−0.685891			−0.342946	+	0.939355i	$0.611425\pi$
$14$		0			0
$15$	0.904151	−	2.96313i	0.233451	−	0.765077i
$16$		0			0
$17$	3.32963	−	5.76708i	0.807553	−	1.39872i	−0.107001	−	0.994259i	$-0.534125\pi$
$17$	3.32963	−	5.76708i	0.807553	−	1.39872i	0.914554	−	0.404464i	$-0.132542\pi$
$18$		0			0
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	0.996566	−	0.0827988i	$-0.0263859\pi$
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	−0.569989	+	0.821652i	$0.693053\pi$
$20$		0			0
$21$	3.06518	−	3.40656i	0.668878	−	0.743372i
$22$		0			0
$23$	6.85244	−	3.95626i	1.42883	−	0.824936i	0.431803	−	0.901968i	$-0.357877\pi$
$23$	6.85244	−	3.95626i	1.42883	−	0.824936i	0.997029	+	0.0770314i	$0.0245442\pi$
$24$		0			0
$25$	−0.900394	+	1.55953i	−0.180079	+	0.311906i
$26$		0			0
$27$	3.27666	+	4.03281i	0.630593	+	0.776114i
$28$		0			0
$29$	−0.748403			−0.138975			−0.0694875	−	0.997583i	$-0.522136\pi$
$29$	−0.748403			−0.138975			−0.0694875	+	0.997583i	$0.522136\pi$
$30$		0			0
$31$	−2.87254	−	1.65846i	−0.515924	−	0.297869i	0.219341	−	0.975648i	$-0.429609\pi$
$31$	−2.87254	−	1.65846i	−0.515924	−	0.297869i	−0.735265	+	0.677779i	$0.762942\pi$
$32$		0			0
$33$	0.391600	+	1.69199i	0.0681688	+	0.294538i
$34$		0			0
$35$	3.87702	−	2.71353i	0.655335	−	0.458670i
$36$		0			0
$37$	3.22429	−	1.86155i	0.530071	−	0.306036i	−0.210975	−	0.977492i	$-0.567664\pi$
$37$	3.22429	−	1.86155i	0.530071	−	0.306036i	0.741045	+	0.671455i	$0.234330\pi$
$38$		0			0
$39$	3.13108	−	2.92298i	0.501374	−	0.468051i
$40$		0			0
$41$	−2.01044			−0.313978			−0.156989	−	0.987600i	$-0.550179\pi$
$41$	−2.01044			−0.313978			−0.156989	+	0.987600i	$0.550179\pi$
$42$		0			0
$43$		−	9.19651i		−	1.40245i	−0.712938	−	0.701227i	$-0.752636\pi$
$43$		−	9.19651i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$44$		0			0
$45$	2.35752	+	4.82027i	0.351439	+	0.718563i
$46$		0			0
$47$	1.19840	+	2.07569i	0.174805	+	0.302771i	0.940094	−	0.340916i	$-0.110737\pi$
$47$	1.19840	+	2.07569i	0.174805	+	0.302771i	−0.765289	+	0.643687i	$0.777404\pi$
$48$		0			0
$49$	6.89415	−	1.21270i	0.984879	−	0.173242i
$50$		0			0
$51$	2.60076	+	11.2371i	0.364179	+	1.57351i
$52$		0			0
$53$	6.33884	−	10.9792i	0.870707	−	1.50811i	0.00943963	−	0.999955i	$-0.496995\pi$
$53$	6.33884	−	10.9792i	0.870707	−	1.50811i	0.861267	−	0.508153i	$-0.169671\pi$
$54$		0			0
$55$			1.79345i			0.241829i
$56$		0			0
$57$	−6.16075	−	1.87985i	−0.816012	−	0.248993i
$58$		0			0
$59$	−7.34922	−	4.24308i	−0.956787	−	0.552401i	−0.0616046	−	0.998101i	$-0.519622\pi$
$59$	−7.34922	−	4.24308i	−0.956787	−	0.552401i	−0.895183	+	0.445699i	$0.852955\pi$
$60$		0			0
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	0.966028	−	0.258438i	$-0.0832077\pi$
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	−0.706828	+	0.707386i	$0.749874\pi$
$62$		0			0
$63$	0.145558	+	7.93592i	0.0183386	+	0.999832i
$64$		0			0
$65$	3.83071	−	2.21166i	0.475141	−	0.274323i
$66$		0			0
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	0.0154303	−	0.999881i	$-0.495088\pi$
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	−0.858207	+	0.513303i	$0.828422\pi$
$68$		0			0
$69$	−3.99976	+	13.1082i	−0.481514	+	1.57804i
$70$		0			0
$71$		−	5.46843i		−	0.648984i	−0.945889	−	0.324492i	$-0.894807\pi$
$71$		−	5.46843i		−	0.648984i	0.945889	−	0.324492i	$-0.105193\pi$
$72$		0			0
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	0.128911	−	0.991656i	$-0.458852\pi$
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	−0.794344	+	0.607468i	$0.792185\pi$
$74$		0			0
$75$	−0.703295	−	3.03873i	−0.0812095	−	0.350883i
$76$		0			0
$77$	−1.12165	+	2.40409i	−0.127824	+	0.273972i
$78$		0			0
$79$	−2.53988	−	4.39920i	−0.285759	−	0.494949i	0.687034	−	0.726625i	$-0.258912\pi$
$79$	−2.53988	−	4.39920i	−0.285759	−	0.494949i	−0.972793	+	0.231676i	$0.925579\pi$
$80$		0			0
$81$	−8.91513	−	1.23308i	−0.990570	−	0.137009i
$82$		0			0
$83$		−	5.65457i		−	0.620669i	−0.950627	−	0.310335i	$-0.899559\pi$
$83$		−	5.65457i		−	0.620669i	0.950627	−	0.310335i	$-0.100441\pi$
$84$		0			0
$85$			11.9110i			1.29193i
$86$		0			0
$87$	0.947550	−	0.884573i	0.101588	−	0.0948362i
$88$		0			0
$89$	7.39495	+	12.8084i	0.783863	+	1.35769i	0.929676	+	0.368379i	$0.120087\pi$
$89$	7.39495	+	12.8084i	0.783863	+	1.35769i	−0.145812	+	0.989312i	$0.546580\pi$
$90$		0			0
$91$	6.51821	−	0.568916i	0.683294	−	0.0596386i
$92$		0			0
$93$	5.59713	−	1.29542i	0.580396	−	0.134329i
$94$		0			0
$95$	−5.76045	−	3.32580i	−0.591010	−	0.341220i
$96$		0			0
$97$		−	1.75577i		−	0.178271i	−0.996019	−	0.0891356i	$-0.971590\pi$
$97$		−	1.75577i		−	0.178271i	0.996019	−	0.0891356i	$-0.0284105\pi$
$98$		0			0
$99$	−2.49565	−	1.67937i	−0.250822	−	0.168783i
$100$		0			0
$101$	−12.6803	−	7.32100i	−1.26174	−	0.728467i	−0.288330	−	0.957531i	$-0.593100\pi$
$101$	−12.6803	−	7.32100i	−1.26174	−	0.728467i	−0.973411	+	0.229064i	$0.926433\pi$
$102$		0			0
$103$	8.54056	−	4.93089i	0.841526	−	0.485855i	−0.0162566	−	0.999868i	$-0.505175\pi$
$103$	8.54056	−	4.93089i	0.841526	−	0.485855i	0.857783	+	0.514013i	$0.171842\pi$
$104$		0			0
$105$	−1.70143	+	8.01802i	−0.166043	+	0.782478i
$106$		0			0
$107$	−3.48110	−	6.02945i	−0.336531	−	0.582889i	0.647247	−	0.762281i	$-0.275920\pi$
$107$	−3.48110	−	6.02945i	−0.336531	−	0.582889i	−0.983778	+	0.179392i	$0.942587\pi$
$108$		0			0
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	0.382508	−	0.923952i	$-0.375061\pi$
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	−0.608912	+	0.793238i	$0.708394\pi$
$110$		0			0
$111$	−1.88202	+	6.16785i	−0.178633	+	0.585426i
$112$		0			0
$113$		−	0.531154i		−	0.0499667i	−0.999688	−	0.0249834i	$-0.992047\pi$
$113$		−	0.531154i		−	0.0499667i	0.999688	−	0.0249834i	$-0.00795328\pi$
$114$		0			0
$115$	−7.07629	+	12.2565i	−0.659868	+	1.14292i
$116$		0			0
$117$	−0.509442	+	7.40154i	−0.0470979	+	0.684272i
$118$		0			0
$119$	−7.44929	+	15.9665i	−0.682875	+	1.46364i
$120$		0			0
$121$	4.99730	+	8.65558i	0.454300	+	0.786871i
$122$		0			0
$123$	2.54541	−	2.37623i	0.229512	−	0.214258i
$124$		0			0
$125$		−	12.1641i		−	1.08799i
$126$		0			0
$127$	4.52393			0.401434			0.200717	−	0.979649i	$-0.435673\pi$
$127$	4.52393			0.401434			0.200717	+	0.979649i	$0.435673\pi$
$128$		0			0
$129$	10.8698	+	11.6437i	0.957031	+	1.02517i
$130$		0			0
$131$	−13.3927	+	7.73228i	−1.17013	+	0.675573i	−0.953710	−	0.300729i	$-0.902770\pi$
$131$	−13.3927	+	7.73228i	−1.17013	+	0.675573i	−0.216416	+	0.976301i	$0.569437\pi$
$132$		0			0
$133$	−5.64179	−	8.06085i	−0.489205	−	0.698964i
$134$		0			0
$135$	−8.68216	−	3.31646i	−0.747241	−	0.285435i
$136$		0			0
$137$	−9.71195	−	5.60719i	−0.829748	−	0.479055i	0.0240187	−	0.999712i	$-0.492354\pi$
$137$	−9.71195	−	5.60719i	−0.829748	−	0.479055i	−0.853766	+	0.520657i	$0.825687\pi$
$138$		0			0
$139$	17.9824			1.52525			0.762625	−	0.646840i	$-0.223910\pi$
$139$	17.9824			1.52525			0.762625	+	0.646840i	$0.223910\pi$
$140$		0			0
$141$	−3.97066	−	1.21158i	−0.334390	−	0.102033i
$142$		0			0
$143$	−1.23984	+	2.14746i	−0.103680	+	0.179580i
$144$		0			0
$145$	1.15928	−	0.669310i	0.0962728	−	0.0555831i
$146$		0			0
$147$	−7.29532	+	9.68392i	−0.601708	+	0.798716i
$148$		0			0
$149$	0.462495	+	0.801066i	0.0378891	+	0.0656258i	0.884348	−	0.466828i	$-0.154603\pi$
$149$	0.462495	+	0.801066i	0.0378891	+	0.0656258i	−0.846459	+	0.532454i	$0.821270\pi$
$150$		0			0
$151$	−9.56720	+	16.5709i	−0.778568	+	1.34852i	0.154200	+	0.988040i	$0.450720\pi$
$151$	−9.56720	+	16.5709i	−0.778568	+	1.34852i	−0.932767	+	0.360479i	$0.882613\pi$
$152$		0			0
$153$	−16.5745	−	11.1533i	−1.33997	−	0.901693i
$154$		0			0
$155$	5.93277			0.476531
$156$		0			0
$157$	5.46873	−	9.47212i	0.436452	−	0.755957i	−0.560961	−	0.827842i	$-0.689568\pi$
$157$	5.46873	−	9.47212i	0.436452	−	0.755957i	0.997413	+	0.0718851i	$0.0229015\pi$
$158$		0			0
$159$	4.95125	+	21.3929i	0.392659	+	1.69657i
$160$		0			0
$161$	−17.1510	+	12.0040i	−1.35169	+	0.946050i
$162$		0			0
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	−0.815316	−	0.579017i	$-0.803437\pi$
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	0.0937855	+	0.995592i	$0.470103\pi$
$164$		0			0
$165$	−2.11976	−	2.27068i	−0.165023	−	0.176772i
$166$		0			0
$167$	−7.93040			−0.613673			−0.306836	−	0.951762i	$-0.599270\pi$
$167$	−7.93040			−0.613673			−0.306836	+	0.951762i	$0.599270\pi$
$168$		0			0
$169$	−6.88419			−0.529553
$170$		0			0
$171$	10.0220	−	4.90161i	0.766401	−	0.374836i
$172$		0			0
$173$	−3.69882	+	2.13552i	−0.281216	+	0.162360i	−0.633974	−	0.773354i	$-0.718577\pi$
$173$	−3.69882	+	2.13552i	−0.281216	+	0.162360i	0.352758	+	0.935715i	$0.385244\pi$
$174$		0			0
$175$	2.01443	−	4.31763i	0.152276	−	0.326382i
$176$		0			0
$177$	14.3199	−	3.31425i	1.07635	−	0.249115i
$178$		0			0
$179$	3.77825	−	6.54412i	0.282399	−	0.489130i	−0.689576	−	0.724214i	$-0.742203\pi$
$179$	3.77825	−	6.54412i	0.282399	−	0.489130i	0.971975	+	0.235083i	$0.0755363\pi$
$180$		0			0
$181$	−5.00239			−0.371824			−0.185912	−	0.982566i	$-0.559524\pi$
$181$	−5.00239			−0.371824			−0.185912	+	0.982566i	$0.559524\pi$
$182$		0			0
$183$	−6.70749	−	2.04668i	−0.495832	−	0.151295i
$184$		0			0
$185$	−3.32963	+	5.76708i	−0.244799	+	0.424004i
$186$		0			0
$187$	−3.33859	−	5.78261i	−0.244142	−	0.422867i
$188$		0			0
$189$	−9.56413	−	9.87560i	−0.695688	−	0.718344i
$190$		0			0
$191$	10.4891	−	6.05587i	0.758963	−	0.438188i	−0.0699601	−	0.997550i	$-0.522287\pi$
$191$	10.4891	−	6.05587i	0.758963	−	0.438188i	0.828923	+	0.559362i	$0.188954\pi$
$192$		0			0
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	−0.843915	−	0.536476i	$-0.819755\pi$
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	0.886560	+	0.462614i	$0.153088\pi$
$194$		0			0
$195$	−2.23598	+	7.32787i	−0.160122	+	0.524760i
$196$		0			0
$197$	19.5111			1.39011			0.695054	−	0.718957i	$-0.255380\pi$
$197$	19.5111			1.39011			0.695054	+	0.718957i	$0.255380\pi$
$198$		0			0
$199$	12.7632	+	7.36884i	0.904760	+	0.522363i	0.878741	−	0.477298i	$-0.158384\pi$
$199$	12.7632	+	7.36884i	0.904760	+	0.522363i	0.0260186	+	0.999661i	$0.491717\pi$
$200$		0			0
$201$	13.4415	−	3.11096i	0.948093	−	0.219430i
$202$		0			0
$203$	1.97259	−	0.172170i	0.138449	−	0.0120839i
$204$		0			0
$205$	3.11418	−	1.79797i	0.217503	−	0.125576i
$206$		0			0
$207$	−10.4292	−	21.3238i	−0.724876	−	1.48211i
$208$		0			0
$209$	3.72883			0.257929
$210$		0			0
$211$			14.9240i			1.02741i	0.857967	+	0.513704i	$0.171727\pi$
$211$			14.9240i			1.02741i	−0.857967	+	0.513704i	$0.828273\pi$
$212$		0			0
$213$	6.46340	+	6.92356i	0.442865	+	0.474395i
$214$		0			0
$215$	8.22459	+	14.2454i	0.560913	+	0.971529i
$216$		0			0
$217$	7.95278	+	3.71044i	0.539870	+	0.251881i
$218$		0			0
$219$	11.0781	−	2.56395i	0.748587	−	0.173256i
$220$		0			0
$221$	−8.23422	+	14.2621i	−0.553894	+	0.959372i
$222$		0			0
$223$			7.62187i			0.510398i	0.966889	+	0.255199i	$0.0821410\pi$
$223$			7.62187i			0.510398i	−0.966889	+	0.255199i	$0.917859\pi$
$224$		0			0
$225$	4.48206	+	3.01607i	0.298804	+	0.201071i
$226$		0			0
$227$	13.6531	+	7.88264i	0.906190	+	0.523189i	0.879203	−	0.476446i	$-0.158075\pi$
$227$	13.6531	+	7.88264i	0.906190	+	0.523189i	0.0269870	+	0.999636i	$0.491409\pi$
$228$		0			0
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	−0.995125	−	0.0986198i	$-0.968557\pi$
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	0.412155	−	0.911114i	$-0.364776\pi$
$230$		0			0
$231$	−1.42139	−	4.36954i	−0.0935208	−	0.287495i
$232$		0			0
$233$	15.7079	−	9.06896i	1.02906	−	0.594127i	0.112344	−	0.993669i	$-0.464164\pi$
$233$	15.7079	−	9.06896i	1.02906	−	0.594127i	0.916715	+	0.399542i	$0.130831\pi$
$234$		0			0
$235$	−3.71266	−	2.14350i	−0.242187	−	0.139827i
$236$		0			0
$237$	8.41536	+	2.56781i	0.546637	+	0.166797i
$238$		0			0
$239$			5.41040i			0.349970i	0.984571	+	0.174985i	$0.0559877\pi$
$239$			5.41040i			0.349970i	−0.984571	+	0.174985i	$0.944012\pi$
$240$		0			0
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.238117	−	0.971236i	$-0.576530\pi$
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.960174	+	0.279403i	$0.909863\pi$
$242$		0			0
$243$	12.7449	−	8.97601i	0.817583	−	0.575811i
$244$		0			0
$245$	−9.59453	+	8.04403i	−0.612972	+	0.513914i
$246$		0			0
$247$	−4.59834	−	7.96457i	−0.292586	−	0.506773i
$248$		0			0
$249$	6.68340	+	7.15923i	0.423543	+	0.453698i
$250$		0			0
$251$		−	19.8553i		−	1.25325i	−0.779319	−	0.626627i	$-0.784435\pi$
$251$		−	19.8553i		−	1.25325i	0.779319	−	0.626627i	$-0.215565\pi$
$252$		0			0
$253$		−	7.93382i		−	0.498795i
$254$		0			0
$255$	−14.0781	−	15.0804i	−0.881607	−	0.944373i
$256$		0			0
$257$	4.36616	+	7.56240i	0.272353	+	0.471730i	0.969464	−	0.245234i	$-0.0788647\pi$
$257$	4.36616	+	7.56240i	0.272353	+	0.471730i	−0.697111	+	0.716964i	$0.745531\pi$
$258$		0			0
$259$	−8.07012	+	5.64828i	−0.501453	+	0.350967i
$260$		0			0
$261$	−0.154171	+	2.23991i	−0.00954295	+	0.138647i
$262$		0			0
$263$	−17.1429	−	9.89747i	−1.05708	−	0.610304i	−0.132455	−	0.991189i	$-0.542286\pi$
$263$	−17.1429	−	9.89747i	−1.05708	−	0.610304i	−0.924623	+	0.380885i	$0.875619\pi$
$264$		0			0
$265$			22.6757i			1.39296i
$266$		0			0
$267$	−24.5016	−	7.47627i	−1.49947	−	0.457540i
$268$		0			0
$269$	0.805574	+	0.465098i	0.0491167	+	0.0283575i	0.524357	−	0.851498i	$-0.324306\pi$
$269$	0.805574	+	0.465098i	0.0491167	+	0.0283575i	−0.475241	+	0.879856i	$0.657639\pi$
$270$		0			0
$271$	7.45646	−	4.30499i	0.452948	−	0.261509i	−0.256127	−	0.966643i	$-0.582446\pi$
$271$	7.45646	−	4.30499i	0.452948	−	0.261509i	0.709074	+	0.705134i	$0.249113\pi$
$272$		0			0
$273$	−7.58025	+	8.42448i	−0.458777	+	0.509873i
$274$		0			0
$275$	0.902819	+	1.56373i	0.0544420	+	0.0942964i
$276$		0			0
$277$	25.5583	+	14.7561i	1.53565	+	0.886607i	0.999086	+	0.0427456i	$0.0136105\pi$
$277$	25.5583	+	14.7561i	1.53565	+	0.886607i	0.536562	+	0.843861i	$0.319723\pi$
$278$		0			0
$279$	−5.55539	+	8.25565i	−0.332593	+	0.494253i
$280$		0			0
$281$		−	21.3260i		−	1.27220i	−0.771605	−	0.636102i	$-0.780546\pi$
$281$		−	21.3260i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$282$		0			0
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	−0.369860	−	0.929088i	$-0.620594\pi$
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	0.989543	−	0.144236i	$-0.0460724\pi$
$284$		0			0
$285$	11.2242	−	2.59777i	0.664865	−	0.153879i
$286$		0			0
$287$	5.29898	−	0.462500i	0.312789	−	0.0273005i
$288$		0			0
$289$	−13.6728	−	23.6820i	−0.804284	−	1.39306i
$290$		0			0
$291$	2.07523	+	2.22297i	0.121652	+	0.130313i
$292$		0			0
$293$		−	13.1058i		−	0.765652i	−0.923821	−	0.382826i	$-0.874951\pi$
$293$		−	13.1058i		−	0.765652i	0.923821	−	0.382826i	$-0.125049\pi$
$294$		0			0
$295$	15.1786			0.883733
$296$		0			0
$297$	5.14466	−	0.823477i	0.298523	−	0.0477830i
$298$		0			0
$299$	−16.9462	+	9.78389i	−0.980023	+	0.565817i
$300$		0			0
$301$	2.11565	+	24.2395i	0.121944	+	1.39714i
$302$		0			0
$303$	24.7076	−	5.71841i	1.41941	−	0.328514i
$304$		0			0
$305$	−6.27166	−	3.62094i	−0.359114	−	0.207335i
$306$		0			0
$307$	−18.6425			−1.06398			−0.531992	−	0.846750i	$-0.678556\pi$
$307$	−18.6425			−1.06398			−0.531992	+	0.846750i	$0.678556\pi$
$308$		0			0
$309$	−4.98511	+	16.3375i	−0.283593	+	0.929406i
$310$		0			0
$311$	9.92896	−	17.1975i	0.563020	−	0.975179i	−0.434211	−	0.900811i	$-0.642973\pi$
$311$	9.92896	−	17.1975i	0.563020	−	0.975179i	0.997231	−	0.0743677i	$-0.0236939\pi$
$312$		0			0
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	−0.432671	−	0.901552i	$-0.642429\pi$
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	0.564431	+	0.825480i	$0.309096\pi$
$314$		0			0
$315$	−7.32270	−	12.1626i	−0.412587	−	0.685284i
$316$		0			0
$317$	5.35288	+	9.27147i	0.300648	+	0.520737i	0.976283	−	0.216499i	$-0.0694638\pi$
$317$	5.35288	+	9.27147i	0.300648	+	0.520737i	−0.675635	+	0.737236i	$0.736130\pi$
$318$		0			0
$319$	−0.375209	+	0.649881i	−0.0210077	+	0.0363864i
$320$		0			0
$321$	11.5339	+	3.51938i	0.643760	+	0.196433i
$322$		0			0
$323$	24.7645			1.37794
$324$		0			0
$325$	2.22669	−	3.85674i	0.123514	−	0.213933i
$326$		0			0
$327$	4.60572	−	1.06596i	0.254697	−	0.0589479i
$328$		0			0
$329$	−3.63618	−	5.19528i	−0.200469	−	0.286425i
$330$		0			0
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.117465	−	0.993077i	$-0.462523\pi$
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.918762	+	0.394811i	$0.129190\pi$
$332$		0			0
$333$	−4.90725	−	10.0335i	−0.268916	−	0.549834i
$334$		0			0
$335$	14.2476			0.778428
$336$		0			0
$337$	−11.3104			−0.616116			−0.308058	−	0.951368i	$-0.599679\pi$
$337$	−11.3104			−0.616116			−0.308058	+	0.951368i	$0.599679\pi$
$338$		0			0
$339$	0.627796	+	0.672492i	0.0340972	+	0.0365247i
$340$		0			0
$341$	−2.88028	+	1.66293i	−0.155976	+	0.0900527i
$342$		0			0
$343$	−17.8922	+	4.78234i	−0.966086	+	0.258222i
$344$		0			0
$345$	−5.52727	−	23.8817i	−0.297578	−	1.28575i
$346$		0			0
$347$	−9.94032	+	17.2171i	−0.533624	+	0.924265i	0.465604	+	0.884993i	$0.345837\pi$
$347$	−9.94032	+	17.2171i	−0.533624	+	0.924265i	−0.999229	+	0.0392715i	$0.987496\pi$
$348$		0			0
$349$	−9.45348			−0.506033			−0.253017	−	0.967462i	$-0.581423\pi$
$349$	−9.45348			−0.506033			−0.253017	+	0.967462i	$0.581423\pi$
$350$		0			0
$351$	−8.10323	−	9.97319i	−0.432518	−	0.532330i
$352$		0			0
$353$	8.48135	−	14.6901i	0.451417	−	0.781877i	−0.547057	−	0.837095i	$-0.684252\pi$
$353$	8.48135	−	14.6901i	0.451417	−	0.781877i	0.998474	+	0.0552182i	$0.0175854\pi$
$354$		0			0
$355$	4.89051	+	8.47062i	0.259561	+	0.449574i
$356$		0			0
$357$	−9.44000	−	29.0197i	−0.499618	−	1.53589i
$358$		0			0
$359$	18.2162	−	10.5171i	0.961413	−	0.555072i	0.0648056	−	0.997898i	$-0.479357\pi$
$359$	18.2162	−	10.5171i	0.961413	−	0.555072i	0.896608	+	0.442826i	$0.146024\pi$
$360$		0			0
$361$	2.58521	−	4.47771i	0.136064	−	0.235669i
$362$		0			0
$363$	−16.5575	−	5.05225i	−0.869044	−	0.265174i
$364$		0			0
$365$	11.7424			0.614625
$366$		0			0
$367$	−1.24875	−	0.720966i	−0.0651842	−	0.0376341i	0.467054	−	0.884229i	$-0.345315\pi$
$367$	−1.24875	−	0.720966i	−0.0651842	−	0.0376341i	−0.532238	+	0.846595i	$0.678649\pi$
$368$		0			0
$369$	−0.414151	+	6.01708i	−0.0215598	+	0.313237i
$370$		0			0
$371$	−14.1817	+	30.3964i	−0.736278	+	1.57810i
$372$		0			0
$373$	−18.8362	+	10.8751i	−0.975302	+	0.563091i	−0.900848	−	0.434134i	$-0.857055\pi$
$373$	−18.8362	+	10.8751i	−0.975302	+	0.563091i	−0.0744535	+	0.997224i	$0.523721\pi$
$374$		0			0
$375$	14.3774	+	15.4010i	0.742443	+	0.795302i
$376$		0			0
$377$	1.85081			0.0953217
$378$		0			0
$379$		−	1.82298i		−	0.0936402i	−0.998903	−	0.0468201i	$-0.985091\pi$
$379$		−	1.82298i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149087\pi$
$380$		0			0
$381$	−5.72774	+	5.34705i	−0.293441	+	0.273938i
$382$		0			0
$383$	−4.81069	−	8.33236i	−0.245815	−	0.425763i	0.716546	−	0.697540i	$-0.245722\pi$
$383$	−4.81069	−	8.33236i	−0.245815	−	0.425763i	−0.962360	+	0.271777i	$0.912389\pi$
$384$		0			0
$385$	−0.412582	−	4.72705i	−0.0210271	−	0.240913i
$386$		0			0
$387$	−27.5244	−	1.89448i	−1.39914	−	0.0963019i
$388$		0			0
$389$	−14.0629	+	24.3576i	−0.713017	+	1.23498i	0.250703	+	0.968064i	$0.419338\pi$
$389$	−14.0629	+	24.3576i	−0.713017	+	1.23498i	−0.963719	+	0.266917i	$0.913995\pi$
$390$		0			0
$391$		−	52.6914i		−	2.66472i
$392$		0			0
$393$	7.81730	−	25.6193i	0.394331	−	1.29232i
$394$		0			0
$395$	7.86857	+	4.54292i	0.395911	+	0.228579i
$396$		0			0
$397$	9.42646	+	16.3271i	0.473101	+	0.819434i	0.999526	−	0.0307871i	$-0.00980139\pi$
$397$	9.42646	+	16.3271i	0.473101	+	0.819434i	−0.526425	+	0.850221i	$0.676468\pi$
$398$		0			0
$399$	16.6706	+	3.53751i	0.834571	+	0.177097i
$400$		0			0
$401$	5.22718	−	3.01791i	0.261033	−	0.150707i	−0.363773	−	0.931488i	$-0.618512\pi$
$401$	5.22718	−	3.01791i	0.261033	−	0.150707i	0.624806	+	0.780780i	$0.285178\pi$
$402$		0			0
$403$	7.10385	+	4.10141i	0.353868	+	0.204306i
$404$		0			0
$405$	14.9123	−	6.06290i	0.740999	−	0.301268i
$406$		0			0
$407$		−	3.73312i		−	0.185044i
$408$		0			0
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.941556	−	0.336856i	$-0.109364\pi$
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.179052	+	0.983840i	$0.442697\pi$
$410$		0			0
$411$	18.9237	−	4.37976i	0.933436	−	0.216038i
$412$		0			0
$413$	20.3467	+	9.49292i	1.00120	+	0.467116i
$414$		0			0
$415$	5.05698	+	8.75894i	0.248237	+	0.429959i
$416$		0			0
$417$	−22.7675	+	21.2543i	−1.11493	+	1.04083i
$418$		0			0
$419$			2.51866i			0.123045i	0.998106	+	0.0615223i	$0.0195955\pi$
$419$			2.51866i			0.123045i	−0.998106	+	0.0615223i	$0.980404\pi$
$420$		0			0
$421$		−	33.4873i		−	1.63207i	−0.578003	−	0.816034i	$-0.696168\pi$
$421$		−	33.4873i		−	1.63207i	0.578003	−	0.816034i	$-0.303832\pi$
$422$		0			0
$423$	6.45926	−	3.15913i	0.314060	−	0.153602i
$424$		0			0
$425$	5.99595	+	10.3853i	0.290846	+	0.503761i
$426$		0			0
$427$	−6.14247	−	8.77620i	−0.297255	−	0.424710i
$428$		0			0
$429$	−0.968433	−	4.18432i	−0.0467564	−	0.202021i
$430$		0			0
$431$	−12.0003	−	6.92836i	−0.578033	−	0.333727i	0.182319	−	0.983240i	$-0.441640\pi$
$431$	−12.0003	−	6.92836i	−0.578033	−	0.333727i	−0.760351	+	0.649512i	$0.774973\pi$
$432$		0			0
$433$		−	9.79368i		−	0.470654i	−0.971916	−	0.235327i	$-0.924384\pi$
$433$		−	9.79368i		−	0.470654i	0.971916	−	0.235327i	$-0.0756161\pi$
$434$		0			0
$435$	−0.676669	+	2.21762i	−0.0324438	+	0.106327i
$436$		0			0
$437$	25.4829	+	14.7126i	1.21901	+	0.703798i
$438$		0			0
$439$	−6.99463	+	4.03835i	−0.333835	+	0.192740i	−0.657543	−	0.753417i	$-0.728404\pi$
$439$	−6.99463	+	4.03835i	−0.333835	+	0.192740i	0.323707	+	0.946157i	$0.395071\pi$
$440$		0			0
$441$	−2.20931	−	20.8835i	−0.105205	−	0.994451i
$442$		0			0
$443$	8.84884	+	15.3266i	0.420421	+	0.728191i	0.995981	−	0.0895692i	$-0.0285490\pi$
$443$	8.84884	+	15.3266i	0.420421	+	0.728191i	−0.575559	+	0.817760i	$0.695216\pi$
$444$		0			0
$445$	−22.9096	−	13.2269i	−1.08602	−	0.627014i
$446$		0			0
$447$	−1.53238	−	0.467581i	−0.0724791	−	0.0221158i
$448$		0			0
$449$			19.4650i			0.918609i	0.888279	+	0.459305i	$0.151901\pi$
$449$			19.4650i			0.918609i	−0.888279	+	0.459305i	$0.848099\pi$
$450$		0			0
$451$	−1.00793	+	1.74578i	−0.0474614	+	0.0822056i
$452$		0			0
$453$	−7.47291	−	32.2882i	−0.351108	−	1.51703i
$454$		0			0
$455$	−9.58793	+	6.71059i	−0.449489	+	0.314597i
$456$		0			0
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	0.988424	−	0.151715i	$-0.0484797\pi$
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	−0.625601	+	0.780143i	$0.715146\pi$
$458$		0			0
$459$	34.1676	−	5.46902i	1.59481	−	0.255272i
$460$		0			0
$461$			0.857290i			0.0399280i	0.999801	+	0.0199640i	$0.00635516\pi$
$461$			0.857290i			0.0399280i	−0.999801	+	0.0199640i	$0.993645\pi$
$462$		0			0
$463$	−37.5731			−1.74617			−0.873086	−	0.487566i	$-0.837885\pi$
$463$	−37.5731			−1.74617			−0.873086	+	0.487566i	$0.837885\pi$
$464$		0			0
$465$	−7.51146	+	7.01222i	−0.348335	+	0.325184i
$466$		0			0
$467$	8.69155	−	5.01807i	0.402197	−	0.232208i	−0.285235	−	0.958458i	$-0.592072\pi$
$467$	8.69155	−	5.01807i	0.402197	−	0.232208i	0.687431	+	0.726249i	$0.258738\pi$
$468$		0			0
$469$	19.0986	+	8.91063i	0.881893	+	0.411455i
$470$		0			0
$471$	4.27161	+	18.4564i	0.196825	+	0.850424i
$472$		0			0
$473$	−7.98586	−	4.61064i	−0.367190	−	0.211997i
$474$		0			0
$475$	−6.69680			−0.307270
$476$		0			0
$477$	−31.5540	−	21.2333i	−1.44476	−	0.972208i
$478$		0			0
$479$	−11.0594	+	19.1555i	−0.505318	+	0.875237i	0.494663	+	0.869085i	$0.335292\pi$
$479$	−11.0594	+	19.1555i	−0.505318	+	0.875237i	−0.999981	+	0.00615194i	$0.998042\pi$
$480$		0			0
$481$	−7.97373	+	4.60364i	−0.363571	+	0.209908i
$482$		0			0
$483$	7.52675	−	35.4699i	0.342479	−	1.61394i
$484$		0			0
$485$	1.57021	+	2.71969i	0.0712997	+	0.123495i
$486$		0			0
$487$	−11.2659	+	19.5131i	−0.510506	+	0.884223i	0.489419	+	0.872049i	$0.337209\pi$
$487$	−11.2659	+	19.5131i	−0.510506	+	0.884223i	−0.999926	+	0.0121746i	$0.996125\pi$
$488$		0			0
$489$	5.37696	−	17.6217i	0.243155	−	0.796879i
$490$		0			0
$491$	25.1085			1.13313			0.566565	−	0.824017i	$-0.308272\pi$
$491$	25.1085			1.13313			0.566565	+	0.824017i	$0.308272\pi$
$492$		0			0
$493$	−2.49190	+	4.31610i	−0.112230	+	0.194387i
$494$		0			0
$495$	5.36765	+	0.369451i	0.241258	+	0.0166056i
$496$		0			0
$497$	1.25801	+	14.4133i	0.0564295	+	0.646526i
$498$		0			0
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	−0.279813	−	0.960054i	$-0.590273\pi$
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	0.691525	+	0.722353i	$0.256939\pi$
$500$		0			0
$501$	10.0407	−	9.37332i	0.448583	−	0.418769i
$502$		0			0
$503$	−13.3046			−0.593223			−0.296612	−	0.954998i	$-0.595857\pi$
$503$	−13.3046			−0.593223			−0.296612	+	0.954998i	$0.595857\pi$
$504$		0			0
$505$	26.1892			1.16540
$506$		0			0
$507$	8.71605	−	8.13675i	0.387093	−	0.361366i
$508$		0			0
$509$	−20.2595	+	11.6968i	−0.897985	+	0.518452i	−0.876546	−	0.481318i	$-0.840158\pi$
$509$	−20.2595	+	11.6968i	−0.897985	+	0.518452i	−0.0214392	+	0.999770i	$0.506825\pi$
$510$		0			0
$511$	15.7405	+	7.34385i	0.696318	+	0.324873i
$512$		0			0
$513$	−6.89536	+	18.0514i	−0.304438	+	0.796988i
$514$		0			0
$515$	−8.81956	+	15.2759i	−0.388636	+	0.673138i
$516$		0			0
$517$	2.40326			0.105695
$518$		0			0
$519$	2.15900	−	7.07558i	0.0947695	−	0.310584i
$520$		0			0
$521$	−0.735700	+	1.27427i	−0.0322316	+	0.0558267i	−0.881691	−	0.471827i	$-0.843595\pi$
$521$	−0.735700	+	1.27427i	−0.0322316	+	0.0558267i	0.849460	+	0.527654i	$0.176928\pi$
$522$		0			0
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	0.958372	−	0.285523i	$-0.0921674\pi$
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	−0.726456	+	0.687213i	$0.758834\pi$
$524$		0			0
$525$	2.55275	+	7.84749i	0.111411	+	0.342492i
$526$		0			0
$527$	−19.1290	+	11.0441i	−0.833272	+	0.481090i
$528$		0			0
$529$	19.8039	−	34.3014i	0.861040	−	1.49137i
$530$		0			0
$531$	−14.2131	+	21.1216i	−0.616797	+	0.916597i
$532$		0			0
$533$	4.97185			0.215355
$534$		0			0
$535$	10.7845	+	6.22642i	0.466254	+	0.269192i
$536$		0			0
$537$	2.95118	+	12.7512i	0.127353	+	0.550254i
$538$		0			0
$539$	2.40331	−	6.59457i	0.103518	−	0.284048i
$540$		0			0
$541$	14.0009	−	8.08343i	0.601946	−	0.347534i	−0.167861	−	0.985811i	$-0.553686\pi$
$541$	14.0009	−	8.08343i	0.601946	−	0.347534i	0.769807	+	0.638277i	$0.220353\pi$
$542$		0			0
$543$	6.33350	−	5.91256i	0.271797	−	0.253732i
$544$		0			0
$545$	4.88190			0.209118
$546$		0			0
$547$			12.4170i			0.530914i	0.964123	+	0.265457i	$0.0855228\pi$
$547$			12.4170i			0.530914i	−0.964123	+	0.265457i	$0.914477\pi$
$548$		0			0
$549$	10.9114	−	5.33660i	0.465687	−	0.227761i
$550$		0			0
$551$	−1.39159	−	2.41030i	−0.0592836	−	0.102682i
$552$		0			0
$553$	7.70648	+	11.0108i	0.327713	+	0.468228i
$554$		0			0
$555$	−2.60076	−	11.2371i	−0.110396	−	0.476989i
$556$		0			0
$557$	10.7167	−	18.5619i	0.454081	−	0.786492i	−0.544554	−	0.838726i	$-0.683301\pi$
$557$	10.7167	−	18.5619i	0.454081	−	0.786492i	0.998635	+	0.0522341i	$0.0166342\pi$
$558$		0			0
$559$			22.7431i			0.961931i
$560$		0			0
$561$	11.0617	+	3.37530i	0.467026	+	0.142505i
$562$		0			0
$563$	−17.9430	−	10.3594i	−0.756205	−	0.436595i	0.0717262	−	0.997424i	$-0.477149\pi$
$563$	−17.9430	−	10.3594i	−0.756205	−	0.436595i	−0.827932	+	0.560829i	$0.810483\pi$
$564$		0			0
$565$	0.475020	+	0.822758i	0.0199842	+	0.0346137i
$566$		0			0
$567$	23.7815	+	1.19916i	0.998731	+	0.0503598i
$568$		0			0
$569$	−23.8691	+	13.7808i	−1.00064	+	0.577722i	−0.908439	−	0.418018i	$-0.862725\pi$
$569$	−23.8691	+	13.7808i	−1.00064	+	0.577722i	−0.0922056	+	0.995740i	$0.529392\pi$
$570$		0			0
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	0.492870	−	0.870103i	$-0.335948\pi$
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	−0.507096	+	0.861889i	$0.669281\pi$
$572$		0			0
$573$	−6.12246	+	20.0649i	−0.255770	+	0.838222i
$574$		0			0
$575$			14.2488i			0.594214i
$576$		0			0
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	0.209493	−	0.977810i	$-0.432819\pi$
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	−0.742062	+	0.670331i	$0.766152\pi$
$578$		0			0
$579$	0.462751	+	1.99941i	0.0192313	+	0.0830926i
$580$		0			0
$581$	1.30083	+	14.9039i	0.0539675	+	0.618319i
$582$		0			0
$583$	−6.35591	−	11.0088i	−0.263235	−	0.455936i
$584$		0			0
$585$	−5.83019	−	11.9206i	−0.241049	−	0.492856i
$586$		0			0
$587$			3.51421i			0.145047i	0.997367	+	0.0725236i	$0.0231052\pi$
$587$			3.51421i			0.145047i	−0.997367	+	0.0725236i	$0.976895\pi$
$588$		0			0
$589$		−	12.3350i		−	0.508256i
$590$		0			0
$591$	−24.7029	+	23.0611i	−1.01614	+	0.948607i
$592$		0			0
$593$	−17.8824	−	30.9732i	−0.734342	−	1.27192i	−0.955012	−	0.296568i	$-0.904158\pi$
$593$	−17.8824	−	30.9732i	−0.734342	−	1.27192i	0.220670	−	0.975349i	$-0.429176\pi$
$594$		0			0
$595$	−2.74011	−	31.3941i	−0.112334	−	1.28703i
$596$		0			0
$597$	−24.8690	+	5.75578i	−1.01782	+	0.235568i
$598$		0			0
$599$	35.4819	+	20.4855i	1.44975	+	0.837014i	0.998466	−	0.0553669i	$-0.0176328\pi$
$599$	35.4819	+	20.4855i	1.44975	+	0.837014i	0.451284	+	0.892380i	$0.350966\pi$
$600$		0			0
$601$			36.1540i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$601$			36.1540i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$602$		0			0
$603$	−13.3413	+	19.8260i	−0.543300	+	0.807376i
$604$		0			0
$605$	−15.4817	−	8.93835i	−0.629419	−	0.363395i
$606$		0			0
$607$	−9.04038	+	5.21946i	−0.366938	+	0.211851i	−0.672120	−	0.740443i	$-0.734616\pi$
$607$	−9.04038	+	5.21946i	−0.366938	+	0.211851i	0.305182	+	0.952294i	$0.401283\pi$
$608$		0			0
$609$	−2.29399	+	2.54948i	−0.0929573	+	0.103310i
$610$		0			0
$611$	−2.96367	−	5.13323i	−0.119897	−	0.207668i
$612$		0			0
$613$	5.37925	+	3.10571i	0.217266	+	0.125439i	0.604684	−	0.796466i	$-0.293300\pi$
$613$	5.37925	+	3.10571i	0.217266	+	0.125439i	−0.387418	+	0.921904i	$0.626633\pi$
$614$		0			0
$615$	−1.81774	+	5.95720i	−0.0732984	+	0.240217i
$616$		0			0
$617$			22.4963i			0.905669i	0.891595	+	0.452834i	$0.149587\pi$
$617$			22.4963i			0.905669i	−0.891595	+	0.452834i	$0.850413\pi$
$618$		0			0
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	0.427407	+	0.904059i	$0.359427\pi$
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	−0.996642	+	0.0818842i	$0.973906\pi$
$620$		0			0
$621$	38.4079	+	14.6712i	1.54126	+	0.588737i
$622$		0			0
$623$	−22.4377	−	32.0584i	−0.898947	−	1.28439i
$624$		0			0
$625$	6.37661	+	11.0446i	0.255064	+	0.441785i
$626$		0			0
$627$	−4.72106	+	4.40728i	−0.188541	+	0.176010i
$628$		0			0
$629$		−	24.7930i		−	0.988563i
$630$		0			0
$631$	−8.51542			−0.338993			−0.169497	−	0.985531i	$-0.554214\pi$
$631$	−8.51542			−0.338993			−0.169497	+	0.985531i	$0.554214\pi$
$632$		0			0
$633$	−17.6393	−	18.8952i	−0.701101	−	0.751016i
$634$		0			0
$635$	−7.00758	+	4.04583i	−0.278087	+	0.160554i
$636$		0			0
$637$	−17.0494	+	2.99902i	−0.675520	+	0.118825i
$638$		0			0
$639$	−16.3666	−	1.12650i	−0.647452	−	0.0445636i
$640$		0			0
$641$	−0.0793494	−	0.0458124i	−0.00313411	−	0.00180948i	0.498432	−	0.866929i	$-0.333909\pi$
$641$	−0.0793494	−	0.0458124i	−0.00313411	−	0.00180948i	−0.501566	+	0.865119i	$0.667243\pi$
$642$		0			0
$643$	5.89351			0.232417			0.116209	−	0.993225i	$-0.462926\pi$
$643$	5.89351			0.232417			0.116209	+	0.993225i	$0.462926\pi$
$644$		0			0
$645$	−27.2505	−	8.31503i	−1.07299	−	0.327404i
$646$		0			0
$647$	−4.05903	+	7.03045i	−0.159577	+	0.276396i	−0.934716	−	0.355395i	$-0.884346\pi$
$647$	−4.05903	+	7.03045i	−0.159577	+	0.276396i	0.775139	+	0.631791i	$0.217680\pi$
$648$		0			0
$649$	−7.36901	+	4.25450i	−0.289259	+	0.167004i
$650$		0			0
$651$	−14.4545	+	4.70200i	−0.566518	+	0.184286i
$652$		0			0
$653$	−16.7312	−	28.9792i	−0.654741	−	1.13404i	−0.981959	−	0.189095i	$-0.939444\pi$
$653$	−16.7312	−	28.9792i	−0.654741	−	1.13404i	0.327218	−	0.944949i	$-0.393889\pi$
$654$		0			0
$655$	13.8302	−	23.9547i	0.540392	−	0.935986i
$656$		0			0
$657$	−10.9955	+	16.3399i	−0.428974	+	0.637481i
$658$		0			0
$659$	−15.5448			−0.605540			−0.302770	−	0.953064i	$-0.597911\pi$
$659$	−15.5448			−0.605540			−0.302770	+	0.953064i	$0.597911\pi$
$660$		0			0
$661$	−15.4190	+	26.7065i	−0.599731	+	1.03876i	0.393130	+	0.919483i	$0.371392\pi$
$661$	−15.4190	+	26.7065i	−0.599731	+	1.03876i	−0.992861	+	0.119281i	$0.961941\pi$
$662$		0			0
$663$	−6.43172	−	27.7896i	−0.249787	−	1.07926i
$664$		0			0
$665$	15.9481	+	7.44072i	0.618441	+	0.288539i
$666$		0			0
$667$	−5.12838	+	2.96087i	−0.198572	+	0.114646i
$668$		0			0
$669$	−9.00865	−	9.65002i	−0.348294	−	0.373091i
$670$		0			0
$671$	4.05974			0.156725
$672$		0			0
$673$	3.84855			0.148351			0.0741753	−	0.997245i	$-0.476368\pi$
$673$	3.84855			0.148351			0.0741753	+	0.997245i	$0.476368\pi$
$674$		0			0
$675$	−9.23956	+	1.47893i	−0.355631	+	0.0569239i
$676$		0			0
$677$	−32.5497	+	18.7926i	−1.25099	+	0.722257i	−0.971305	−	0.237836i	$-0.923562\pi$
$677$	−32.5497	+	18.7926i	−1.25099	+	0.722257i	−0.279680	+	0.960093i	$0.590228\pi$
$678$		0			0
$679$	0.403913	+	4.62773i	0.0155008	+	0.177596i
$680$		0			0
$681$	−26.6031	+	6.15711i	−1.01943	+	0.235941i
$682$		0			0
$683$	1.02051	−	1.76757i	0.0390487	−	0.0676343i	−0.845841	−	0.533436i	$-0.820901\pi$
$683$	1.02051	−	1.76757i	0.0390487	−	0.0676343i	0.884889	+	0.465802i	$0.154234\pi$
$684$		0			0
$685$	20.0584			0.766394
$686$		0			0
$687$	29.2296	+	8.91894i	1.11518	+	0.340279i
$688$		0			0
$689$	−15.6761	+	27.1517i	−0.597210	+	1.03440i
$690$		0			0
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	0.551786	−	0.833986i	$-0.313947\pi$
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	−0.998146	+	0.0608673i	$0.980613\pi$
$692$		0			0
$693$	6.96419	+	3.85225i	0.264548	+	0.146335i
$694$		0			0
$695$	−27.8548	+	16.0820i	−1.05659	+	0.610025i
$696$		0			0
$697$	−6.69401	+	11.5944i	−0.253554	+	0.439168i
$698$		0			0
$699$	−9.16868	+	30.0481i	−0.346791	+	1.13652i
$700$		0			0
$701$	15.4603			0.583926			0.291963	−	0.956430i	$-0.405692\pi$
$701$	15.4603			0.583926			0.291963	+	0.956430i	$0.405692\pi$
$702$		0			0
$703$	11.9906	+	6.92275i	0.452232	+	0.261096i
$704$		0			0
$705$	7.23409	−	1.67428i	0.272452	−	0.0630572i
$706$		0			0
$707$	35.1062	+	16.3791i	1.32030	+	0.615999i
$708$		0			0
$709$	−41.7153	+	24.0843i	−1.56665	+	0.904505i	−0.570093	+	0.821580i	$0.693093\pi$
$709$	−41.7153	+	24.0843i	−1.56665	+	0.904505i	−0.996556	+	0.0829254i	$0.973574\pi$
$710$		0			0
$711$	−13.6897	+	6.69542i	−0.513403	+	0.251098i
$712$		0			0
$713$	−26.2452			−0.982891
$714$		0			0
$715$		−	4.43523i		−	0.165868i
$716$		0			0
$717$	−6.39481	−	6.85009i	−0.238819	−	0.255821i
$718$		0			0
$719$	6.49021	+	11.2414i	0.242044	+	0.419232i	0.961296	−	0.275517i	$-0.0888489\pi$
$719$	6.49021	+	11.2414i	0.242044	+	0.419232i	−0.719252	+	0.694749i	$0.755516\pi$
$720$		0			0
$721$	−21.3763	+	14.9613i	−0.796094	+	0.557186i
$722$		0			0
$723$	36.2468	−	8.38909i	1.34803	−	0.311994i
$724$		0			0
$725$	0.673858	−	1.16716i	0.0250264	−	0.0433471i
$726$		0			0
$727$		−	12.0095i		−	0.445406i	−0.974886	−	0.222703i	$-0.928512\pi$
$727$		−	12.0095i		−	0.445406i	0.974886	−	0.222703i	$-0.0714880\pi$
$728$		0			0
$729$	−5.52704	+	26.4282i	−0.204705	+	0.978824i
$730$		0			0
$731$	−53.0370	−	30.6209i	−1.96164	−	1.13256i
$732$		0			0
$733$	4.29808	+	7.44449i	0.158753	+	0.274968i	0.934419	−	0.356175i	$-0.115919\pi$
$733$	4.29808	+	7.44449i	0.158753	+	0.274968i	−0.775666	+	0.631143i	$0.782586\pi$
$734$		0			0
$735$	2.63998	−	21.5247i	0.0973770	−	0.793952i
$736$		0			0
$737$	−6.91700	+	3.99353i	−0.254791	+	0.147104i
$738$		0			0
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	0.540875	−	0.841103i	$-0.318093\pi$
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	−0.457979	+	0.888963i	$0.651426\pi$
$740$		0			0
$741$	15.2356	+	4.64891i	0.559695	+	0.170782i
$742$		0			0
$743$			13.4061i			0.491823i	0.969292	+	0.245911i	$0.0790872\pi$
$743$			13.4061i			0.491823i	−0.969292	+	0.245911i	$0.920913\pi$
$744$		0			0
$745$	−1.43281	−	0.827235i	−0.0524942	−	0.0303075i
$746$		0			0
$747$	−16.9237	−	1.16484i	−0.619204	−	0.0426193i
$748$		0			0
$749$	10.5623	+	15.0912i	0.385939	+	0.551420i
$750$		0			0
$751$	7.86182	+	13.6171i	0.286882	+	0.496894i	0.973064	−	0.230536i	$-0.0740480\pi$
$751$	7.86182	+	13.6171i	0.286882	+	0.496894i	−0.686182	+	0.727430i	$0.740715\pi$
$752$		0			0
$753$	23.4679	+	25.1387i	0.855218	+	0.916105i
$754$		0			0
$755$		−	34.2244i		−	1.24555i
$756$		0			0
$757$			48.7626i			1.77231i	0.463391	+	0.886154i	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$		0			0
$759$	9.37736	+	10.0450i	0.340377	+	0.364610i
$760$		0			0
$761$	−21.7170	−	37.6149i	−0.787240	−	1.36354i	−0.927652	−	0.373447i	$-0.878176\pi$
$761$	−21.7170	−	37.6149i	−0.787240	−	1.36354i	0.140411	−	0.990093i	$-0.455158\pi$
$762$		0			0
$763$	6.54411	+	3.05321i	0.236913	+	0.110534i
$764$		0			0
$765$	35.6486	+	2.45366i	1.28888	+	0.0887123i
$766$		0			0
$767$	18.1747	+	10.4932i	0.656252	+	0.378887i
$768$		0			0
$769$		−	23.9226i		−	0.862670i	−0.902192	−	0.431335i	$-0.858043\pi$
$769$		−	23.9226i		−	0.862670i	0.902192	−	0.431335i	$-0.141957\pi$
$770$		0			0
$771$	−14.4663	−	4.41417i	−0.520993	−	0.158972i
$772$		0			0
$773$	−14.3402	−	8.27930i	−0.515780	−	0.297786i	0.219427	−	0.975629i	$-0.429581\pi$
$773$	−14.3402	−	8.27930i	−0.515780	−	0.297786i	−0.735206	+	0.677843i	$0.762915\pi$
$774$		0			0
$775$	5.17284	−	2.98654i	0.185814	−	0.107280i
$776$		0			0
$777$	3.54158	−	16.6897i	0.127053	−	0.598741i
$778$		0			0
$779$	−3.73823	−	6.47480i	−0.133936	−	0.231984i
$780$		0			0
$781$	−4.74856	−	2.74158i	−0.169917	−	0.0981014i
$782$		0			0
$783$	−2.45226	−	3.01816i	−0.0876366	−	0.107860i
$784$		0			0
$785$			19.5631i			0.698237i
$786$		0			0
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	−0.743658	−	0.668561i	$-0.766911\pi$
$787$	5.81161	−	10.0660i	0.207162	−	0.358814i	0.950819	+	0.309746i	$0.100244\pi$
$788$		0			0
$789$	33.4029	−	7.73088i	1.18917	−	0.275227i
$790$		0			0
$791$	0.122192	+	1.39998i	0.00434463	+	0.0497775i
$792$		0			0
$793$	−5.00642	−	8.67137i	−0.177783	−	0.307930i
$794$		0			0
$795$	−26.8015	−	28.7097i	−0.950552	−	1.01823i
$796$		0			0
$797$		−	2.35681i		−	0.0834824i	−0.999128	−	0.0417412i	$-0.986709\pi$
$797$		−	2.35681i		−	0.0834824i	0.999128	−	0.0417412i	$-0.0132905\pi$
$798$		0			0
$799$	15.9609			0.564657
$800$		0			0
$801$	39.8580	−	19.4940i	1.40831	−	0.688785i
$802$		0			0
$803$	−5.70077	+	3.29134i	−0.201176	+	0.116149i
$804$		0			0
$805$	15.8316	−	33.9327i	0.557991	−	1.19597i
$806$		0			0
$807$	−1.56966	+	0.363287i	−0.0552545	+	0.0127883i
$808$		0			0
$809$	39.6070	+	22.8671i	1.39251	+	0.803964i	0.993592	−	0.113024i	$-0.0360538\pi$
$809$	39.6070	+	22.8671i	1.39251	+	0.803964i	0.398914	+	0.916988i	$0.369387\pi$
$810$		0			0
$811$	−0.844573			−0.0296570			−0.0148285	−	0.999890i	$-0.504720\pi$
$811$	−0.844573			−0.0296570			−0.0148285	+	0.999890i	$0.504720\pi$
$812$		0			0
$813$	−4.35233	+	14.2637i	−0.152643	+	0.500249i
$814$		0			0
$815$	9.51282	−	16.4767i	0.333219	−	0.577153i
$816$		0			0
$817$	29.6182	−	17.1000i	1.03621	−	0.598255i
$818$		0			0
$819$	−0.359968	−	19.6257i	−0.0125783	−	0.685776i
$820$		0			0
$821$	18.4890	+	32.0239i	0.645272	+	1.11764i	0.984239	+	0.176845i	$0.0565892\pi$
$821$	18.4890	+	32.0239i	0.645272	+	1.11764i	−0.338967	+	0.940798i	$0.610078\pi$
$822$		0			0
$823$	3.62518	−	6.27899i	0.126366	−	0.218872i	−0.795900	−	0.605428i	$-0.793002\pi$
$823$	3.62518	−	6.27899i	0.126366	−	0.218872i	0.922266	+	0.386556i	$0.126335\pi$
$824$		0			0
$825$	−2.99130	−	0.912746i	−0.104144	−	0.0317777i
$826$		0			0
$827$	43.4014			1.50921			0.754607	−	0.656176i	$-0.227827\pi$
$827$	43.4014			1.50921			0.754607	+	0.656176i	$0.227827\pi$
$828$		0			0
$829$	12.7789	−	22.1338i	0.443830	−	0.768737i	−0.554139	−	0.832424i	$-0.686953\pi$
$829$	12.7789	−	22.1338i	0.443830	−	0.768737i	0.997970	+	0.0636869i	$0.0202859\pi$
$830$		0			0
$831$	−49.8001	+	11.5259i	−1.72755	+	0.399830i
$832$		0			0
$833$	15.9612	−	43.7970i	0.553024	−	1.51748i
$834$		0			0
$835$	12.2842	−	7.09229i	0.425113	−	0.245439i
$836$		0			0
$837$	−2.72408	−	17.0186i	−0.0941579	−	0.588250i
$838$		0			0
$839$	19.2288			0.663854			0.331927	−	0.943305i	$-0.392301\pi$
$839$	19.2288			0.663854			0.331927	+	0.943305i	$0.392301\pi$
$840$		0			0
$841$	−28.4399			−0.980686
$842$		0			0
$843$	25.2062	+	27.0008i	0.868149	+	0.929956i
$844$		0			0
$845$	10.6636	−	6.15665i	0.366840	−	0.211795i
$846$		0			0
$847$	−15.1628	−	21.6642i	−0.520999	−	0.744389i
$848$		0			0
$849$	8.14269	+	35.1822i	0.279457	+	1.20745i
$850$		0			0
$851$	14.7295	−	25.5123i	0.504921	−	0.874549i
$852$		0			0
$853$	43.5472			1.49103			0.745514	−	0.666489i	$-0.232204\pi$
$853$	43.5472			1.49103			0.745514	+	0.666489i	$0.232204\pi$
$854$		0			0
$855$	−11.1405	+	16.5555i	−0.380997	+	0.566185i
$856$		0			0
$857$	4.41603	−	7.64878i	0.150849	−	0.261277i	−0.780691	−	0.624917i	$-0.785133\pi$
$857$	4.41603	−	7.64878i	0.150849	−	0.261277i	0.931540	+	0.363640i	$0.118466\pi$
$858$		0			0
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	0.911892	−	0.410429i	$-0.134621\pi$
$859$	2.94564	+	5.10200i	0.100504	+	0.174078i	−0.811388	+	0.584507i	$0.801288\pi$
$860$		0			0
$861$	−6.16237	+	6.84868i	−0.210013	+	0.233403i
$862$		0			0
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	−0.547037	−	0.837109i	$-0.684244\pi$
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	0.451439	+	0.892302i	$0.350911\pi$
$864$		0			0
$865$	3.81966	−	6.61584i	0.129872	−	0.224945i
$866$		0			0
$867$	45.3020	+	13.8232i	1.53854	+	0.469460i
$868$		0			0
$869$	−5.09344			−0.172783
$870$		0			0
$871$	17.0599	+	9.84955i	0.578053	+	0.333739i
$872$		0			0
$873$	−5.25487	−	0.361689i	−0.177850	−	0.0122413i
$874$		0			0
$875$	2.79835	+	32.0614i	0.0946015	+	1.08387i
$876$		0			0
$877$	39.1526	−	22.6048i	1.32209	−	0.763309i	0.338028	−	0.941136i	$-0.390240\pi$
$877$	39.1526	−	22.6048i	1.32209	−	0.763309i	0.984062	+	0.177828i	$0.0569070\pi$
$878$		0			0
$879$	15.4904	+	16.5933i	0.522479	+	0.559677i
$880$		0			0
$881$	28.1014			0.946759			0.473380	−	0.880859i	$-0.343034\pi$
$881$	28.1014			0.946759			0.473380	+	0.880859i	$0.343034\pi$
$882$		0			0
$883$		−	5.45102i		−	0.183442i	−0.995785	−	0.0917208i	$-0.970763\pi$
$883$		−	5.45102i		−	0.183442i	0.995785	−	0.0917208i	$-0.0292367\pi$
$884$		0			0
$885$	−19.2176	+	17.9403i	−0.645992	+	0.603058i
$886$		0			0
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	−0.879290	−	0.476287i	$-0.841982\pi$
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	0.0271684	−	0.999631i	$-0.491351\pi$
$888$		0			0
$889$	−11.9239	+	1.04073i	−0.399914	+	0.0349049i
$890$		0			0
$891$	−5.54033	+	7.12332i	−0.185608	+	0.238640i
$892$		0			0
$893$	−4.45664	+	7.71912i	−0.149136	+	0.258311i
$894$		0			0
$895$			13.5158i			0.451783i
$896$		0			0
$897$	9.89147	−	32.4168i	0.330266	−	1.08237i
$898$		0			0
$899$	2.14982	+	1.24120i	0.0717005	+	0.0413963i
$900$		0			0
$901$	−42.2119	−	73.1132i	−1.40628	−	2.43575i
$902$		0			0
$903$	−31.3285	−	28.1890i	−1.04255	−	0.938070i
$904$		0			0
$905$	7.74871	−	4.47372i	0.257576	−	0.148711i
$906$		0			0
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	0.349167	−	0.937060i	$-0.386464\pi$
$907$	−8.66652	−	5.00362i	−0.287767	−	0.166142i	−0.636934	+	0.770918i	$0.719798\pi$
$908$		0			0
$909$	−24.5233	+	36.4431i	−0.813387	+	1.20874i
$910$		0			0
$911$		−	14.5940i		−	0.483521i	−0.970336	−	0.241761i	$-0.922275\pi$
$911$		−	14.5940i		−	0.483521i	0.970336	−	0.241761i	$-0.0777249\pi$
$912$		0			0
$913$	−4.91019	−	2.83490i	−0.162503	−	0.0938214i
$914$		0			0
$915$	12.2203	−	2.82831i	0.403990	−	0.0935010i
$916$		0			0
$917$	33.5208	−	23.4612i	1.10695	−	0.774757i
$918$		0			0
$919$	1.14316	+	1.98001i	0.0377093	+	0.0653145i	0.884264	−	0.466987i	$-0.154661\pi$
$919$	1.14316	+	1.98001i	0.0377093	+	0.0653145i	−0.846555	+	0.532302i	$0.821327\pi$
$920$		0			0
$921$	23.6032	−	22.0344i	0.777751	−	0.726060i
$922$		0			0
$923$			13.5235i			0.445132i
$924$		0			0
$925$			6.70450i			0.220443i
$926$		0			0
$927$	−12.9984	−	26.5770i	−0.426924	−	0.872902i
$928$		0			0
$929$	−9.71753	−	16.8313i	−0.318822	−	0.552216i	0.661421	−	0.750015i	$-0.269954\pi$
$929$	−9.71753	−	16.8313i	−0.318822	−	0.552216i	−0.980242	+	0.197799i	$0.936621\pi$
$930$		0			0
$931$	16.7246	+	19.9483i	0.548128	+	0.653780i
$932$		0			0
$933$	7.75548	+	33.5092i	0.253903	+	1.09704i
$934$		0			0
$935$	10.3430	+	5.97152i	0.338252	+	0.195290i
$936$		0			0
$937$		−	21.6552i		−	0.707445i	−0.935350	−	0.353723i	$-0.884916\pi$
$937$		−	21.6552i		−	0.707445i	0.935350	−	0.353723i	$-0.115084\pi$
$938$		0			0
$939$	−1.36065	+	4.45918i	−0.0444030	+	0.145520i
$940$		0			0
$941$	−5.82024	−	3.36032i	−0.189735	−	0.109543i	0.402124	−	0.915585i	$-0.368272\pi$
$941$	−5.82024	−	3.36032i	−0.189735	−	0.109543i	−0.591858	+	0.806042i	$0.701605\pi$
$942$		0			0
$943$	−13.7764	+	7.95381i	−0.448622	+	0.259012i
$944$		0			0
$945$	23.6468	+	6.74396i	0.769230	+	0.219381i
$946$		0			0
$947$	−10.5673	−	18.3031i	−0.343392	−	0.594772i	0.641668	−	0.766982i	$-0.278243\pi$
$947$	−10.5673	−	18.3031i	−0.343392	−	0.594772i	−0.985060	+	0.172210i	$0.944909\pi$
$948$		0			0
$949$	14.0602	+	8.11768i	0.456414	+	0.263511i
$950$		0			0
$951$	−17.7357	−	5.41174i	−0.575118	−	0.175488i
$952$		0			0
$953$		−	2.18327i		−	0.0707230i	−0.999375	−	0.0353615i	$-0.988742\pi$
$953$		−	2.18327i		−	0.0707230i	0.999375	−	0.0353615i	$-0.0112583\pi$
$954$		0			0
$955$	−10.8317	+	18.7611i	−0.350507	+	0.607096i
$956$		0			0
$957$	−0.293075	−	1.26629i	−0.00947376	−	0.0409333i
$958$		0			0
$959$	26.8880	+	12.5448i	0.868259	+	0.405094i
$960$		0			0
$961$	−9.99900	−	17.3188i	−0.322548	−	0.558670i
$962$		0			0
$963$	−18.7628	+	9.17660i	−0.604622	+	0.295712i
$964$		0			0
$965$			2.11931i			0.0682229i
$966$		0			0
$967$	25.1413			0.808490			0.404245	−	0.914651i	$-0.367534\pi$
$967$	25.1413			0.808490			0.404245	+	0.914651i	$0.367534\pi$
$968$		0			0
$969$	−31.3543	+	29.2704i	−1.00724	+	0.940300i
$970$		0			0
$971$	30.0100	−	17.3263i	0.963065	−	0.556026i	0.0659503	−	0.997823i	$-0.478992\pi$
$971$	30.0100	−	17.3263i	0.963065	−	0.556026i	0.897115	+	0.441797i	$0.145659\pi$
$972$		0			0
$973$	−47.3969	+	4.13685i	−1.51947	+	0.132621i
$974$		0			0
$975$	1.73926	+	7.51483i	0.0557009	+	0.240667i
$976$		0			0
$977$	−3.22538	−	1.86218i	−0.103189	−	0.0595763i	0.447517	−	0.894275i	$-0.352308\pi$
$977$	−3.22538	−	1.86218i	−0.103189	−	0.0595763i	−0.550706	+	0.834699i	$0.685642\pi$
$978$		0			0
$979$	14.8297			0.473960
$980$		0			0
$981$	−4.57137	+	6.79333i	−0.145953	+	0.216894i
$982$		0			0
$983$	27.3018	−	47.2881i	0.870792	−	1.50826i	0.00961355	−	0.999954i	$-0.496940\pi$
$983$	27.3018	−	47.2881i	0.870792	−	1.50826i	0.861179	−	0.508302i	$-0.169727\pi$
$984$		0			0
$985$	−30.2227	+	17.4491i	−0.962977	+	0.555975i
$986$		0			0
$987$	10.7443	+	2.27995i	0.341995	+	0.0725717i
$988$		0			0
$989$	−36.3837	−	63.0185i	−1.15694	−	2.00387i
$990$		0			0
$991$	25.1790	−	43.6114i	0.799839	−	1.38536i	−0.119882	−	0.992788i	$-0.538252\pi$
$991$	25.1790	−	43.6114i	0.799839	−	1.38536i	0.919721	−	0.392573i	$-0.128415\pi$
$992$		0			0
$993$	−11.0042	+	36.0635i	−0.349207	+	1.14444i
$994$		0			0
$995$	−26.3603			−0.835679
$996$		0			0
$997$	12.7609	−	22.1025i	0.404141	−	0.699993i	−0.590080	−	0.807345i	$-0.700904\pi$
$997$	12.7609	−	22.1025i	0.404141	−	0.699993i	0.994221	+	0.107352i	$0.0342372\pi$
$998$		0			0
$999$	18.0722	+	6.90330i	0.571778	+	0.218411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.5		48
3.2	odd	2	inner	672.2.bi.c.17.11		48
4.3	odd	2		168.2.ba.c.101.18	yes	48
7.5	odd	6	inner	672.2.bi.c.593.14		48
8.3	odd	2		168.2.ba.c.101.10	yes	48
8.5	even	2	inner	672.2.bi.c.17.20		48
12.11	even	2		168.2.ba.c.101.7	yes	48
21.5	even	6	inner	672.2.bi.c.593.20		48
24.5	odd	2	inner	672.2.bi.c.17.14		48
24.11	even	2		168.2.ba.c.101.15	yes	48
28.19	even	6		168.2.ba.c.5.15	yes	48
56.5	odd	6	inner	672.2.bi.c.593.11		48
56.19	even	6		168.2.ba.c.5.7	✓	48
84.47	odd	6		168.2.ba.c.5.10	yes	48
168.5	even	6	inner	672.2.bi.c.593.5		48
168.131	odd	6		168.2.ba.c.5.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	56.19	even	6
168.2.ba.c.5.10	yes	48	84.47	odd	6
168.2.ba.c.5.15	yes	48	28.19	even	6
168.2.ba.c.5.18	yes	48	168.131	odd	6
168.2.ba.c.101.7	yes	48	12.11	even	2
168.2.ba.c.101.10	yes	48	8.3	odd	2
168.2.ba.c.101.15	yes	48	24.11	even	2
168.2.ba.c.101.18	yes	48	4.3	odd	2
672.2.bi.c.17.5		48	1.1	even	1	trivial
672.2.bi.c.17.11		48	3.2	odd	2	inner
672.2.bi.c.17.14		48	24.5	odd	2	inner
672.2.bi.c.17.20		48	8.5	even	2	inner
672.2.bi.c.593.5		48	168.5	even	6	inner
672.2.bi.c.593.11		48	56.5	odd	6	inner
672.2.bi.c.593.14		48	7.5	odd	6	inner
672.2.bi.c.593.20		48	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26610 + 1.18195i) q^{3} +(-1.54900 + 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(0.206000 - 2.99292i) q^{9} +O(q^{10})\)	\(q+(-1.26610 + 1.18195i) q^{3} +(-1.54900 + 0.894317i) q^{5} +(-2.63573 + 0.230049i) q^{7} +(0.206000 - 2.99292i) q^{9} +(0.501346 - 0.868358i) q^{11} -2.47302 q^{13} +(0.904151 - 2.96313i) q^{15} +(3.32963 - 5.76708i) q^{17} +(1.85941 + 3.22059i) q^{19} +(3.06518 - 3.40656i) q^{21} +(6.85244 - 3.95626i) q^{23} +(-0.900394 + 1.55953i) q^{25} +(3.27666 + 4.03281i) q^{27} -0.748403 q^{29} +(-2.87254 - 1.65846i) q^{31} +(0.391600 + 1.69199i) q^{33} +(3.87702 - 2.71353i) q^{35} +(3.22429 - 1.86155i) q^{37} +(3.13108 - 2.92298i) q^{39} -2.01044 q^{41} -9.19651i q^{43} +(2.35752 + 4.82027i) q^{45} +(1.19840 + 2.07569i) q^{47} +(6.89415 - 1.21270i) q^{49} +(2.60076 + 11.2371i) q^{51} +(6.33884 - 10.9792i) q^{53} +1.79345i q^{55} +(-6.16075 - 1.87985i) q^{57} +(-7.34922 - 4.24308i) q^{59} +(2.02442 + 3.50640i) q^{61} +(0.145558 + 7.93592i) q^{63} +(3.83071 - 2.21166i) q^{65} +(-6.89843 - 3.98281i) q^{67} +(-3.99976 + 13.1082i) q^{69} -5.46843i q^{71} +(-5.68546 - 3.28250i) q^{73} +(-0.703295 - 3.03873i) q^{75} +(-1.12165 + 2.40409i) q^{77} +(-2.53988 - 4.39920i) q^{79} +(-8.91513 - 1.23308i) q^{81} -5.65457i q^{83} +11.9110i q^{85} +(0.947550 - 0.884573i) q^{87} +(7.39495 + 12.8084i) q^{89} +(6.51821 - 0.568916i) q^{91} +(5.59713 - 1.29542i) q^{93} +(-5.76045 - 3.32580i) q^{95} -1.75577i q^{97} +(-2.49565 - 1.67937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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