LMFDB - Embedded newform 680.2.bo.a.121.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(121,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			121.5
Character	$\chi$	$=$	680.121
Dual form			680.2.bo.a.281.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0428807 + 0.0177618i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.01246 + 2.44430i) q^{7} +(-2.11980 + 2.11980i) q^{9} +(-2.19039 - 0.907288i) q^{11} -4.92162i q^{13} +(0.0328194 + 0.0328194i) q^{15} +(-2.99715 - 2.83145i) q^{17} +(-3.28719 - 3.28719i) q^{19} -0.122796i q^{21} +(2.35333 + 0.974780i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(0.106532 - 0.257192i) q^{27} +(-2.20034 - 5.31209i) q^{29} +(-1.46319 + 0.606071i) q^{31} +0.110040 q^{33} +2.64569 q^{35} +(-10.2267 + 4.23603i) q^{37} +(0.0874165 + 0.211042i) q^{39} +(1.27713 - 3.08326i) q^{41} +(-6.83895 + 6.83895i) q^{43} +(2.76965 + 1.14723i) q^{45} +10.8173i q^{47} +(0.000225088 + 0.000225088i) q^{49} +(0.178811 + 0.0681797i) q^{51} +(-4.84149 - 4.84149i) q^{53} +2.37086i q^{55} +(0.199343 + 0.0825705i) q^{57} +(8.18933 - 8.18933i) q^{59} +(0.722571 - 1.74444i) q^{61} +(-3.03521 - 7.32763i) q^{63} +(-4.54698 + 1.88342i) q^{65} +12.0951 q^{67} -0.118226 q^{69} +(-8.91550 + 3.69292i) q^{71} +(-1.64242 - 3.96516i) q^{73} +(0.0177618 - 0.0428807i) q^{75} +(4.43537 - 4.43537i) q^{77} +(-2.83076 - 1.17254i) q^{79} -8.98062i q^{81} +(1.35431 + 1.35431i) q^{83} +(-1.46896 + 3.85255i) q^{85} +(0.188704 + 0.188704i) q^{87} -13.6178i q^{89} +(12.0299 + 4.98295i) q^{91} +(0.0519775 - 0.0519775i) q^{93} +(-1.77901 + 4.29492i) q^{95} +(5.71594 + 13.7995i) q^{97} +(6.56644 - 2.71991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0428807	+	0.0177618i	−0.0247572	+	0.0102548i	−0.395028	−	0.918669i	$-0.629265\pi$
$3$	−0.0428807	+	0.0177618i	−0.0247572	+	0.0102548i	0.370271	+	0.928924i	$0.379265\pi$
$4$		0			0
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$		0			0
$7$	−1.01246	+	2.44430i	−0.382675	+	0.923859i	0.608772	+	0.793345i	$0.291662\pi$
$7$	−1.01246	+	2.44430i	−0.382675	+	0.923859i	−0.991447	+	0.130513i	$0.958338\pi$
$8$		0			0
$9$	−2.11980	+	2.11980i	−0.706599	+	0.706599i
$10$		0			0
$11$	−2.19039	−	0.907288i	−0.660426	−	0.273558i	0.0271916	−	0.999630i	$-0.491344\pi$
$11$	−2.19039	−	0.907288i	−0.660426	−	0.273558i	−0.687618	+	0.726073i	$0.741344\pi$
$12$		0			0
$13$		−	4.92162i		−	1.36501i	−0.730880	−	0.682505i	$-0.760890\pi$
$13$		−	4.92162i		−	1.36501i	0.730880	−	0.682505i	$-0.239110\pi$
$14$		0			0
$15$	0.0328194	+	0.0328194i	0.00847394	+	0.00847394i
$16$		0			0
$17$	−2.99715	−	2.83145i	−0.726916	−	0.686727i
$17$	−2.99715	−	2.83145i	−0.726916	−	0.686727i
$18$		0			0
$19$	−3.28719	−	3.28719i	−0.754132	−	0.754132i	0.221115	−	0.975248i	$-0.429030\pi$
$19$	−3.28719	−	3.28719i	−0.754132	−	0.754132i	−0.975248	+	0.221115i	$0.929030\pi$
$20$		0			0
$21$		−	0.122796i		−	0.0267963i
$22$		0			0
$23$	2.35333	+	0.974780i	0.490702	+	0.203256i	0.614293	−	0.789078i	$-0.289441\pi$
$23$	2.35333	+	0.974780i	0.490702	+	0.203256i	−0.123591	+	0.992333i	$0.539441\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	0.106532	−	0.257192i	0.0205021	−	0.0494965i
$28$		0			0
$29$	−2.20034	−	5.31209i	−0.408593	−	0.986431i	−0.985508	−	0.169627i	$-0.945744\pi$
$29$	−2.20034	−	5.31209i	−0.408593	−	0.986431i	0.576915	−	0.816804i	$-0.304256\pi$
$30$		0			0
$31$	−1.46319	+	0.606071i	−0.262796	+	0.108854i	−0.510191	−	0.860061i	$-0.670425\pi$
$31$	−1.46319	+	0.606071i	−0.262796	+	0.108854i	0.247395	+	0.968915i	$0.420425\pi$
$32$		0			0
$33$	0.110040			0.0191555
$34$		0			0
$35$	2.64569			0.447203
$36$		0			0
$37$	−10.2267	+	4.23603i	−1.68126	+	0.696399i	−0.999385	−	0.0350720i	$-0.988834\pi$
$37$	−10.2267	+	4.23603i	−1.68126	+	0.696399i	−0.681872	+	0.731471i	$0.738834\pi$
$38$		0			0
$39$	0.0874165	+	0.211042i	0.0139978	+	0.0337938i
$40$		0			0
$41$	1.27713	−	3.08326i	0.199454	−	0.481524i	−0.792230	−	0.610223i	$-0.791080\pi$
$41$	1.27713	−	3.08326i	0.199454	−	0.481524i	0.991684	+	0.128698i	$0.0410799\pi$
$42$		0			0
$43$	−6.83895	+	6.83895i	−1.04293	+	1.04293i	−0.0438932	+	0.999036i	$0.513976\pi$
$43$	−6.83895	+	6.83895i	−1.04293	+	1.04293i	−0.999036	+	0.0438932i	$0.986024\pi$
$44$		0			0
$45$	2.76965	+	1.14723i	0.412875	+	0.171018i
$46$		0			0
$47$			10.8173i			1.57787i	0.614479	+	0.788933i	$0.289366\pi$
$47$			10.8173i			1.57787i	−0.614479	+	0.788933i	$0.710634\pi$
$48$		0			0
$49$	0.000225088	0	0.000225088i	3.21554e−5	0	3.21554e-5i
$50$		0			0
$51$	0.178811	+	0.0681797i	0.0250386	+	0.00954707i
$52$		0			0
$53$	−4.84149	−	4.84149i	−0.665029	−	0.665029i	0.291532	−	0.956561i	$-0.405835\pi$
$53$	−4.84149	−	4.84149i	−0.665029	−	0.665029i	−0.956561	+	0.291532i	$0.905835\pi$
$54$		0			0
$55$			2.37086i			0.319686i
$56$		0			0
$57$	0.199343	+	0.0825705i	0.0264036	+	0.0109367i
$58$		0			0
$59$	8.18933	−	8.18933i	1.06616	−	1.06616i	0.0685094	−	0.997650i	$-0.478176\pi$
$59$	8.18933	−	8.18933i	1.06616	−	1.06616i	0.997650	−	0.0685094i	$-0.0218243\pi$
$60$		0			0
$61$	0.722571	−	1.74444i	0.0925158	−	0.223353i	−0.870847	−	0.491554i	$-0.836429\pi$
$61$	0.722571	−	1.74444i	0.0925158	−	0.223353i	0.963363	+	0.268201i	$0.0864291\pi$
$62$		0			0
$63$	−3.03521	−	7.32763i	−0.382400	−	0.923195i
$64$		0			0
$65$	−4.54698	+	1.88342i	−0.563984	+	0.233610i
$66$		0			0
$67$	12.0951			1.47766			0.738828	−	0.673894i	$-0.235379\pi$
$67$	12.0951			1.47766			0.738828	+	0.673894i	$0.235379\pi$
$68$		0			0
$69$	−0.118226			−0.0142327
$70$		0			0
$71$	−8.91550	+	3.69292i	−1.05808	+	0.438269i	−0.842768	−	0.538277i	$-0.819075\pi$
$71$	−8.91550	+	3.69292i	−1.05808	+	0.438269i	−0.215307	+	0.976546i	$0.569075\pi$
$72$		0			0
$73$	−1.64242	−	3.96516i	−0.192231	−	0.464087i	0.798149	−	0.602460i	$-0.205813\pi$
$73$	−1.64242	−	3.96516i	−0.192231	−	0.464087i	−0.990380	+	0.138373i	$0.955813\pi$
$74$		0			0
$75$	0.0177618	−	0.0428807i	0.00205095	−	0.00495143i
$76$		0			0
$77$	4.43537	−	4.43537i	0.505457	−	0.505457i
$78$		0			0
$79$	−2.83076	−	1.17254i	−0.318486	−	0.131921i	0.217713	−	0.976013i	$-0.430140\pi$
$79$	−2.83076	−	1.17254i	−0.318486	−	0.131921i	−0.536199	+	0.844092i	$0.680140\pi$
$80$		0			0
$81$		−	8.98062i		−	0.997846i
$82$		0			0
$83$	1.35431	+	1.35431i	0.148655	+	0.148655i	0.777517	−	0.628862i	$-0.216479\pi$
$83$	1.35431	+	1.35431i	0.148655	+	0.148655i	−0.628862	+	0.777517i	$0.716479\pi$
$84$		0			0
$85$	−1.46896	+	3.85255i	−0.159331	+	0.417868i
$86$		0			0
$87$	0.188704	+	0.188704i	0.0202312	+	0.0202312i
$88$		0			0
$89$		−	13.6178i		−	1.44349i	−0.692161	−	0.721743i	$-0.743341\pi$
$89$		−	13.6178i		−	1.44349i	0.692161	−	0.721743i	$-0.256659\pi$
$90$		0			0
$91$	12.0299	+	4.98295i	1.26108	+	0.522355i
$92$		0			0
$93$	0.0519775	−	0.0519775i	0.00538981	−	0.00538981i
$94$		0			0
$95$	−1.77901	+	4.29492i	−0.182523	+	0.440649i
$96$		0			0
$97$	5.71594	+	13.7995i	0.580366	+	1.40113i	0.892482	+	0.451084i	$0.148962\pi$
$97$	5.71594	+	13.7995i	0.580366	+	1.40113i	−0.312116	+	0.950044i	$0.601038\pi$
$98$		0			0
$99$	6.56644	−	2.71991i	0.659952	−	0.273361i
$100$		0			0
$101$	−4.24135			−0.422030			−0.211015	−	0.977483i	$-0.567677\pi$
$101$	−4.24135			−0.422030			−0.211015	+	0.977483i	$0.567677\pi$
$102$		0			0
$103$	−0.0507186			−0.00499745			−0.00249873	−	0.999997i	$-0.500795\pi$
$103$	−0.0507186			−0.00499745			−0.00249873	+	0.999997i	$0.500795\pi$
$104$		0			0
$105$	−0.113449	+	0.0469921i	−0.0110715	+	0.00458596i
$106$		0			0
$107$	1.75802	+	4.24424i	0.169954	+	0.410306i	0.985791	−	0.167976i	$-0.0537231\pi$
$107$	1.75802	+	4.24424i	0.169954	+	0.410306i	−0.815837	+	0.578283i	$0.803723\pi$
$108$		0			0
$109$	−1.71511	+	4.14064i	−0.164278	+	0.396602i	−0.984486	−	0.175463i	$-0.943858\pi$
$109$	−1.71511	+	4.14064i	−0.164278	+	0.396602i	0.820208	+	0.572065i	$0.193858\pi$
$110$		0			0
$111$	0.363288	−	0.363288i	0.0344817	−	0.0344817i
$112$		0			0
$113$	10.7624	+	4.45795i	1.01245	+	0.419369i	0.826347	−	0.563162i	$-0.190415\pi$
$113$	10.7624	+	4.45795i	1.01245	+	0.419369i	0.186100	+	0.982531i	$0.440415\pi$
$114$		0			0
$115$		−	2.54722i		−	0.237530i
$116$		0			0
$117$	10.4328	+	10.4328i	0.964515	+	0.964515i
$118$		0			0
$119$	9.95541	−	4.45920i	0.912611	−	0.408774i
$120$		0			0
$121$	−3.80355	−	3.80355i	−0.345778	−	0.345778i
$122$		0			0
$123$			0.154896i			0.0139665i
$124$		0			0
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$		0			0
$127$	−13.3521	+	13.3521i	−1.18481	+	1.18481i	−0.206328	+	0.978483i	$0.566151\pi$
$127$	−13.3521	+	13.3521i	−1.18481	+	1.18481i	−0.978483	+	0.206328i	$0.933849\pi$
$128$		0			0
$129$	0.171787	−	0.414730i	0.0151250	−	0.0365150i
$130$		0			0
$131$	5.09577	+	12.3023i	0.445220	+	1.07486i	0.974092	+	0.226154i	$0.0726151\pi$
$131$	5.09577	+	12.3023i	0.445220	+	1.07486i	−0.528872	+	0.848702i	$0.677385\pi$
$132$		0			0
$133$	11.3630	−	4.70672i	0.985299	−	0.408124i
$134$		0			0
$135$	−0.278382			−0.0239593
$136$		0			0
$137$	6.00853			0.513344			0.256672	−	0.966499i	$-0.417374\pi$
$137$	6.00853			0.513344			0.256672	+	0.966499i	$0.417374\pi$
$138$		0			0
$139$	−11.4042	+	4.72378i	−0.967293	+	0.400666i	−0.809704	−	0.586839i	$-0.800372\pi$
$139$	−11.4042	+	4.72378i	−0.967293	+	0.400666i	−0.157589	+	0.987505i	$0.550372\pi$
$140$		0			0
$141$	−0.192134	−	0.463853i	−0.0161806	−	0.0390635i
$142$		0			0
$143$	−4.46532	+	10.7802i	−0.373409	+	0.901489i
$144$		0			0
$145$	−4.06570	+	4.06570i	−0.337638	+	0.337638i
$146$		0			0
$147$	−1.36499e−5	0	5.65396e-6i	−1.12582e−6	0	4.66331e-7i
$148$		0			0
$149$		−	1.01511i		−	0.0831610i	−0.999135	−	0.0415805i	$-0.986761\pi$
$149$		−	1.01511i		−	0.0831610i	0.999135	−	0.0415805i	$-0.0132393\pi$
$150$		0			0
$151$	−7.54390	−	7.54390i	−0.613914	−	0.613914i	0.330050	−	0.943964i	$-0.392934\pi$
$151$	−7.54390	−	7.54390i	−0.613914	−	0.613914i	−0.943964	+	0.330050i	$0.892934\pi$
$152$		0			0
$153$	12.3554	−	0.351257i	0.998878	−	0.0283975i
$154$		0			0
$155$	1.11987	+	1.11987i	0.0899504	+	0.0899504i
$156$		0			0
$157$		−	6.83156i		−	0.545218i	−0.962125	−	0.272609i	$-0.912113\pi$
$157$		−	6.83156i		−	0.545218i	0.962125	−	0.272609i	$-0.0878865\pi$
$158$		0			0
$159$	0.293599	+	0.121613i	0.0232840	+	0.00964453i
$160$		0			0
$161$	−4.76531	+	4.76531i	−0.375559	+	0.375559i
$162$		0			0
$163$	3.61062	−	8.71680i	0.282805	−	0.682753i	−0.717093	−	0.696977i	$-0.754528\pi$
$163$	3.61062	−	8.71680i	0.282805	−	0.682753i	0.999899	+	0.0142245i	$0.00452795\pi$
$164$		0			0
$165$	−0.0421106	−	0.101664i	−0.00327830	−	0.00791453i
$166$		0			0
$167$	8.20249	−	3.39758i	0.634728	−	0.262913i	−0.0420324	−	0.999116i	$-0.513383\pi$
$167$	8.20249	−	3.39758i	0.634728	−	0.262913i	0.676760	+	0.736203i	$0.263383\pi$
$168$		0			0
$169$	−11.2223			−0.863255
$170$		0			0
$171$	13.9363			1.06574
$172$		0			0
$173$	11.9048	−	4.93112i	0.905103	−	0.374906i	0.118923	−	0.992903i	$-0.462056\pi$
$173$	11.9048	−	4.93112i	0.905103	−	0.374906i	0.786180	+	0.617998i	$0.212056\pi$
$174$		0			0
$175$	−1.01246	−	2.44430i	−0.0765349	−	0.184772i
$176$		0			0
$177$	−0.205707	+	0.496621i	−0.0154619	+	0.0373283i
$178$		0			0
$179$	17.5607	−	17.5607i	1.31255	−	1.31255i	0.393017	−	0.919531i	$-0.371431\pi$
$179$	17.5607	−	17.5607i	1.31255	−	1.31255i	0.919531	−	0.393017i	$-0.128569\pi$
$180$		0			0
$181$	20.5508	+	8.51240i	1.52753	+	0.632722i	0.979082	−	0.203466i	$-0.0652205\pi$
$181$	20.5508	+	8.51240i	1.52753	+	0.632722i	0.548444	+	0.836188i	$0.315221\pi$
$182$		0			0
$183$			0.0876369i			0.00647831i
$184$		0			0
$185$	7.82717	+	7.82717i	0.575465	+	0.575465i
$186$		0			0
$187$	3.99598	+	8.92124i	0.292215	+	0.652386i
$188$		0			0
$189$	0.520794	+	0.520794i	0.0378822	+	0.0378822i
$190$		0			0
$191$		−	10.7977i		−	0.781293i	−0.920541	−	0.390647i	$-0.872251\pi$
$191$		−	10.7977i		−	0.781293i	0.920541	−	0.390647i	$-0.127749\pi$
$192$		0			0
$193$	−19.0863	−	7.90581i	−1.37386	−	0.569073i	−0.431030	−	0.902338i	$-0.641850\pi$
$193$	−19.0863	−	7.90581i	−1.37386	−	0.569073i	−0.942833	+	0.333265i	$0.891850\pi$
$194$		0			0
$195$	0.161525	−	0.161525i	0.0115670	−	0.0115670i
$196$		0			0
$197$	−6.61641	+	15.9734i	−0.471400	+	1.13806i	0.492145	+	0.870513i	$0.336213\pi$
$197$	−6.61641	+	15.9734i	−0.471400	+	1.13806i	−0.963545	+	0.267547i	$0.913787\pi$
$198$		0			0
$199$	−3.59789	−	8.68607i	−0.255048	−	0.615739i	0.743550	−	0.668680i	$-0.233141\pi$
$199$	−3.59789	−	8.68607i	−0.255048	−	0.615739i	−0.998598	+	0.0529409i	$0.983141\pi$
$200$		0			0
$201$	−0.518648	+	0.214831i	−0.0365826	+	0.0151530i
$202$		0			0
$203$	15.2121			1.06768
$204$		0			0
$205$	−3.33730			−0.233087
$206$		0			0
$207$	−7.05491	+	2.92224i	−0.490350	+	0.203110i
$208$		0			0
$209$	4.21778	+	10.1826i	0.291750	+	0.704347i
$210$		0			0
$211$	−3.07946	+	7.43448i	−0.211999	+	0.511811i	−0.993730	−	0.111805i	$-0.964337\pi$
$211$	−3.07946	+	7.43448i	−0.211999	+	0.511811i	0.781731	+	0.623615i	$0.214337\pi$
$212$		0			0
$213$	0.316710	−	0.316710i	0.0217006	−	0.0217006i
$214$		0			0
$215$	8.93551	+	3.70121i	0.609397	+	0.252420i
$216$		0			0
$217$		−	4.19009i		−	0.284442i
$218$		0			0
$219$	0.140856	+	0.140856i	0.00951820	+	0.00951820i
$220$		0			0
$221$	−13.9353	+	14.7508i	−0.937390	+	0.992248i
$222$		0			0
$223$	−9.98887	−	9.98887i	−0.668904	−	0.668904i	0.288558	−	0.957462i	$-0.406824\pi$
$223$	−9.98887	−	9.98887i	−0.668904	−	0.668904i	−0.957462	+	0.288558i	$0.906824\pi$
$224$		0			0
$225$		−	2.99785i		−	0.199856i
$226$		0			0
$227$	−17.9596	−	7.43910i	−1.19202	−	0.493750i	−0.303607	−	0.952797i	$-0.598191\pi$
$227$	−17.9596	−	7.43910i	−1.19202	−	0.493750i	−0.888412	+	0.459047i	$0.848191\pi$
$228$		0			0
$229$	2.78527	−	2.78527i	0.184056	−	0.184056i	−0.609065	−	0.793121i	$-0.708455\pi$
$229$	2.78527	−	2.78527i	0.184056	−	0.184056i	0.793121	+	0.609065i	$0.208455\pi$
$230$		0			0
$231$	−0.111412	+	0.268971i	−0.00733034	+	0.0176970i
$232$		0			0
$233$	−2.56233	−	6.18602i	−0.167864	−	0.405260i	0.817453	−	0.575996i	$-0.195385\pi$
$233$	−2.56233	−	6.18602i	−0.167864	−	0.405260i	−0.985317	+	0.170736i	$0.945385\pi$
$234$		0			0
$235$	9.99389	−	4.13960i	0.651929	−	0.270038i
$236$		0			0
$237$	0.142211			0.00923762
$238$		0			0
$239$	15.9469			1.03152			0.515758	−	0.856734i	$-0.327510\pi$
$239$	15.9469			1.03152			0.515758	+	0.856734i	$0.327510\pi$
$240$		0			0
$241$	0.919910	−	0.381039i	0.0592566	−	0.0245449i	−0.352858	−	0.935677i	$-0.614790\pi$
$241$	0.919910	−	0.381039i	0.0592566	−	0.0245449i	0.412115	+	0.911132i	$0.364790\pi$
$242$		0			0
$243$	0.479108	+	1.15667i	0.0307348	+	0.0742004i
$244$		0			0
$245$	0.000121817	0	0.000294091i	7.78258e−6	0	1.87888e-5i
$246$		0			0
$247$	−16.1783	+	16.1783i	−1.02940	+	1.02940i
$248$		0			0
$249$	−0.0821285	−	0.0340187i	−0.00520468	−	0.00215585i
$250$		0			0
$251$		−	26.0343i		−	1.64327i	−0.570016	−	0.821634i	$-0.693063\pi$
$251$		−	26.0343i		−	1.64327i	0.570016	−	0.821634i	$-0.306937\pi$
$252$		0			0
$253$	−4.27029	−	4.27029i	−0.268471	−	0.268471i
$254$		0			0
$255$	−0.00543829	−	0.191291i	−0.000340559	−	0.0119791i
$256$		0			0
$257$	11.1355	+	11.1355i	0.694611	+	0.694611i	0.963243	−	0.268632i	$-0.0865714\pi$
$257$	11.1355	+	11.1355i	0.694611	+	0.694611i	−0.268632	+	0.963243i	$0.586571\pi$
$258$		0			0
$259$		−	29.2859i		−	1.81974i
$260$		0			0
$261$	15.9248	+	6.59628i	0.985722	+	0.408300i
$262$		0			0
$263$	−10.3325	+	10.3325i	−0.637131	+	0.637131i	−0.949847	−	0.312716i	$-0.898761\pi$
$263$	−10.3325	+	10.3325i	−0.637131	+	0.637131i	0.312716	+	0.949847i	$0.398761\pi$
$264$		0			0
$265$	−2.62019	+	6.32571i	−0.160957	+	0.388585i
$266$		0			0
$267$	0.241876	+	0.583941i	0.0148026	+	0.0357366i
$268$		0			0
$269$	−25.9188	+	10.7359i	−1.58030	+	0.654580i	−0.988461	−	0.151478i	$-0.951597\pi$
$269$	−25.9188	+	10.7359i	−1.58030	+	0.654580i	−0.591836	+	0.806058i	$0.701597\pi$
$270$		0			0
$271$	−25.3199			−1.53807			−0.769036	−	0.639206i	$-0.779263\pi$
$271$	−25.3199			−1.53807			−0.769036	+	0.639206i	$0.779263\pi$
$272$		0			0
$273$	−0.604356			−0.0365773
$274$		0			0
$275$	2.19039	−	0.907288i	0.132085	−	0.0547115i
$276$		0			0
$277$	8.70896	+	21.0253i	0.523271	+	1.26329i	0.935861	+	0.352371i	$0.114624\pi$
$277$	8.70896	+	21.0253i	0.523271	+	1.26329i	−0.412590	+	0.910917i	$0.635376\pi$
$278$		0			0
$279$	1.81691	−	4.38641i	0.108775	−	0.262607i
$280$		0			0
$281$	21.2873	−	21.2873i	1.26989	−	1.26989i	0.323752	−	0.946142i	$-0.395056\pi$
$281$	21.2873	−	21.2873i	1.26989	−	1.26989i	0.946142	−	0.323752i	$-0.104944\pi$
$282$		0			0
$283$	−18.1016	−	7.49794i	−1.07603	−	0.445706i	−0.226915	−	0.973915i	$-0.572864\pi$
$283$	−18.1016	−	7.49794i	−1.07603	−	0.445706i	−0.849115	+	0.528208i	$0.822864\pi$
$284$		0			0
$285$		−	0.215767i		−	0.0127809i
$286$		0			0
$287$	6.24337	+	6.24337i	0.368534	+	0.368534i
$288$		0			0
$289$	0.965817	+	16.9725i	0.0568128	+	0.998385i
$290$		0			0
$291$	−0.490207	−	0.490207i	−0.0287364	−	0.0287364i
$292$		0			0
$293$		−	10.2106i		−	0.596508i	−0.954487	−	0.298254i	$-0.903596\pi$
$293$		−	10.2106i		−	0.596508i	0.954487	−	0.298254i	$-0.0964042\pi$
$294$		0			0
$295$	−10.6999	−	4.43203i	−0.622971	−	0.258043i
$296$		0			0
$297$	−0.466694	+	0.466694i	−0.0270803	+	0.0270803i
$298$		0			0
$299$	4.79749	−	11.5822i	0.277446	−	0.669814i
$300$		0			0
$301$	−9.79226	−	23.6406i	−0.564417	−	1.36262i
$302$		0			0
$303$	0.181872	−	0.0753339i	0.0104483	−	0.00432782i
$304$		0			0
$305$	−1.88817			−0.108116
$306$		0			0
$307$	−17.4086			−0.993563			−0.496782	−	0.867876i	$-0.665485\pi$
$307$	−17.4086			−0.993563			−0.496782	+	0.867876i	$0.665485\pi$
$308$		0			0
$309$	0.00217485		0.000900852i	0.000123723		5.12477e-5i
$310$		0			0
$311$	4.06555	+	9.81512i	0.230536	+	0.556564i	0.996241	−	0.0866287i	$-0.0276094\pi$
$311$	4.06555	+	9.81512i	0.230536	+	0.556564i	−0.765704	+	0.643193i	$0.777609\pi$
$312$		0			0
$313$	−8.87602	+	21.4286i	−0.501702	+	1.21122i	0.446854	+	0.894607i	$0.352544\pi$
$313$	−8.87602	+	21.4286i	−0.501702	+	1.21122i	−0.948556	+	0.316610i	$0.897456\pi$
$314$		0			0
$315$	−5.60833	+	5.60833i	−0.315994	+	0.315994i
$316$		0			0
$317$	−4.91368	−	2.03531i	−0.275980	−	0.114315i	0.240401	−	0.970674i	$-0.422721\pi$
$317$	−4.91368	−	2.03531i	−0.275980	−	0.114315i	−0.516381	+	0.856359i	$0.672721\pi$
$318$		0			0
$319$			13.6319i			0.763239i
$320$		0			0
$321$	−0.150770	−	0.150770i	−0.00841518	−	0.00841518i
$322$		0			0
$323$	0.544697	+	19.1597i	0.0303078	+	1.06607i
$324$		0			0
$325$	3.48011	+	3.48011i	0.193042	+	0.193042i
$326$		0			0
$327$		−	0.208017i		−	0.0115034i
$328$		0			0
$329$	−26.4407	−	10.9521i	−1.45773	−	0.603810i
$330$		0			0
$331$	−21.1906	+	21.1906i	−1.16474	+	1.16474i	−0.181314	+	0.983425i	$0.558035\pi$
$331$	−21.1906	+	21.1906i	−1.16474	+	1.16474i	−0.983425	+	0.181314i	$0.941965\pi$
$332$		0			0
$333$	12.6990	−	30.6580i	0.695899	−	1.68005i
$334$		0			0
$335$	−4.62861	−	11.1745i	−0.252888	−	0.610526i
$336$		0			0
$337$	10.3439	−	4.28458i	0.563467	−	0.233396i	−0.0827226	−	0.996573i	$-0.526362\pi$
$337$	10.3439	−	4.28458i	0.563467	−	0.233396i	0.646190	+	0.763177i	$0.276362\pi$
$338$		0			0
$339$	−0.540682			−0.0293658
$340$		0			0
$341$	3.75482			0.203335
$342$		0			0
$343$	−17.1109	+	7.08756i	−0.923901	+	0.382692i
$344$		0			0
$345$	0.0452431	+	0.109227i	0.00243581	+	0.00588056i
$346$		0			0
$347$	5.96576	−	14.4026i	0.320259	−	0.773173i	−0.678980	−	0.734157i	$-0.737578\pi$
$347$	5.96576	−	14.4026i	0.320259	−	0.773173i	0.999239	−	0.0390162i	$-0.0124224\pi$
$348$		0			0
$349$	−5.71106	+	5.71106i	−0.305706	+	0.305706i	−0.843241	−	0.537535i	$-0.819355\pi$
$349$	−5.71106	+	5.71106i	−0.305706	+	0.305706i	0.537535	+	0.843241i	$0.319355\pi$
$350$		0			0
$351$	−1.26580	−	0.524311i	−0.0675633	−	0.0279856i
$352$		0			0
$353$			1.06908i			0.0569015i	0.999595	+	0.0284507i	$0.00905738\pi$
$353$			1.06908i			0.0569015i	−0.999595	+	0.0284507i	$0.990943\pi$
$354$		0			0
$355$	6.82363	+	6.82363i	0.362161	+	0.362161i
$356$		0			0
$357$	−0.347691	+	0.368039i	−0.0184018	+	0.0194787i
$358$		0			0
$359$	−18.8161	−	18.8161i	−0.993077	−	0.993077i	0.00689921	−	0.999976i	$-0.497804\pi$
$359$	−18.8161	−	18.8161i	−0.993077	−	0.993077i	−0.999976	+	0.00689921i	$0.997804\pi$
$360$		0			0
$361$			2.61118i			0.137431i
$362$		0			0
$363$	0.230657	+	0.0955411i	0.0121063	+	0.00501461i
$364$		0			0
$365$	−3.03480	+	3.03480i	−0.158849	+	0.158849i
$366$		0			0
$367$	11.7048	−	28.2578i	0.610984	−	1.47505i	−0.250936	−	0.968004i	$-0.580738\pi$
$367$	11.7048	−	28.2578i	0.610984	−	1.47505i	0.861921	−	0.507043i	$-0.169262\pi$
$368$		0			0
$369$	3.82863	+	9.24314i	0.199311	+	0.481178i
$370$		0			0
$371$	16.7359	−	6.93222i	0.868883	−	0.359903i
$372$		0			0
$373$	3.74661			0.193992			0.0969959	−	0.995285i	$-0.469077\pi$
$373$	3.74661			0.193992			0.0969959	+	0.995285i	$0.469077\pi$
$374$		0			0
$375$	−0.0464137			−0.00239679
$376$		0			0
$377$	−26.1441	+	10.8292i	−1.34649	+	0.557734i
$378$		0			0
$379$	−5.34437	−	12.9024i	−0.274522	−	0.662754i	0.725144	−	0.688597i	$-0.241773\pi$
$379$	−5.34437	−	12.9024i	−0.274522	−	0.662754i	−0.999666	+	0.0258428i	$0.991773\pi$
$380$		0			0
$381$	0.335391	−	0.809706i	0.0171826	−	0.0414825i
$382$		0			0
$383$	−3.62564	+	3.62564i	−0.185261	+	0.185261i	−0.793644	−	0.608383i	$-0.791819\pi$
$383$	−3.62564	+	3.62564i	−0.185261	+	0.185261i	0.608383	+	0.793644i	$0.291819\pi$
$384$		0			0
$385$	−5.79509	−	2.40040i	−0.295345	−	0.122336i
$386$		0			0
$387$		−	28.9944i		−	1.47387i
$388$		0			0
$389$	−8.65691	−	8.65691i	−0.438923	−	0.438923i	0.452727	−	0.891649i	$-0.350451\pi$
$389$	−8.65691	−	8.65691i	−0.438923	−	0.438923i	−0.891649	+	0.452727i	$0.850451\pi$
$390$		0			0
$391$	−4.29323	−	9.58488i	−0.217118	−	0.484728i
$392$		0			0
$393$	−0.437020	−	0.437020i	−0.0220447	−	0.0220447i
$394$		0			0
$395$			3.06400i			0.154166i
$396$		0			0
$397$	−19.0772	−	7.90203i	−0.957457	−	0.396592i	−0.151428	−	0.988468i	$-0.548387\pi$
$397$	−19.0772	−	7.90203i	−0.957457	−	0.396592i	−0.806029	+	0.591877i	$0.798387\pi$
$398$		0			0
$399$	−0.403654	+	0.403654i	−0.0202080	+	0.0202080i
$400$		0			0
$401$	0.172151	−	0.415610i	0.00859683	−	0.0207546i	−0.919523	−	0.393037i	$-0.871425\pi$
$401$	0.172151	−	0.415610i	0.00859683	−	0.0207546i	0.928120	+	0.372282i	$0.121425\pi$
$402$		0			0
$403$	2.98285	+	7.20124i	0.148586	+	0.358719i
$404$		0			0
$405$	−8.29701	+	3.43673i	−0.412282	+	0.170773i
$406$		0			0
$407$	26.2437			1.30085
$408$		0			0
$409$	30.4454			1.50543			0.752714	−	0.658347i	$-0.228744\pi$
$409$	30.4454			1.50543			0.752714	+	0.658347i	$0.228744\pi$
$410$		0			0
$411$	−0.257650	+	0.106722i	−0.0127089	+	0.00526421i
$412$		0			0
$413$	11.7258	+	28.3086i	0.576988	+	1.39297i
$414$		0			0
$415$	0.732946	−	1.76949i	0.0359789	−	0.0868608i
$416$		0			0
$417$	0.405118	−	0.405118i	0.0198387	−	0.0198387i
$418$		0			0
$419$	8.22105	+	3.40527i	0.401625	+	0.166358i	0.574347	−	0.818612i	$-0.305256\pi$
$419$	8.22105	+	3.40527i	0.401625	+	0.166358i	−0.172722	+	0.984971i	$0.555256\pi$
$420$		0			0
$421$			4.18156i			0.203797i	0.994795	+	0.101898i	$0.0324916\pi$
$421$			4.18156i			0.203797i	−0.994795	+	0.101898i	$0.967508\pi$
$422$		0			0
$423$	−22.9305	−	22.9305i	−1.11492	−	1.11492i
$424$		0			0
$425$	4.12144	−	0.117170i	0.199919	−	0.00568357i
$426$		0			0
$427$	3.53236	+	3.53236i	0.170943	+	0.170943i
$428$		0			0
$429$		−	0.541576i		−	0.0261475i
$430$		0			0
$431$	−25.3483	−	10.4996i	−1.22098	−	0.505748i	−0.323262	−	0.946310i	$-0.604779\pi$
$431$	−25.3483	−	10.4996i	−1.22098	−	0.505748i	−0.897723	+	0.440561i	$0.854779\pi$
$432$		0			0
$433$	12.1973	−	12.1973i	0.586165	−	0.586165i	−0.350426	−	0.936591i	$-0.613963\pi$
$433$	12.1973	−	12.1973i	0.586165	−	0.586165i	0.936591	+	0.350426i	$0.113963\pi$
$434$		0			0
$435$	0.102126	−	0.246554i	0.00489656	−	0.0118214i
$436$		0			0
$437$	−4.53154	−	10.9401i	−0.216773	−	0.523336i
$438$		0			0
$439$	2.65428	−	1.09944i	0.126682	−	0.0524733i	−0.318442	−	0.947942i	$-0.603160\pi$
$439$	2.65428	−	1.09944i	0.126682	−	0.0524733i	0.445124	+	0.895469i	$0.353160\pi$
$440$		0			0
$441$	−0.000954281	0		−4.54419e−5	0
$442$		0			0
$443$	17.6741			0.839724			0.419862	−	0.907588i	$-0.362078\pi$
$443$	17.6741			0.839724			0.419862	+	0.907588i	$0.362078\pi$
$444$		0			0
$445$	−12.5812	+	5.21132i	−0.596407	+	0.247040i
$446$		0			0
$447$	0.0180301	+	0.0435285i	0.000852795	+	0.00205883i
$448$		0			0
$449$	−11.5287	+	27.8327i	−0.544072	+	1.31351i	0.377755	+	0.925906i	$0.376696\pi$
$449$	−11.5287	+	27.8327i	−0.544072	+	1.31351i	−0.921827	+	0.387601i	$0.873304\pi$
$450$		0			0
$451$	−5.59481	+	5.59481i	−0.263449	+	0.263449i
$452$		0			0
$453$	0.457480	+	0.189495i	0.0214943	+	0.00890323i
$454$		0			0
$455$		−	13.0211i		−	0.610438i
$456$		0			0
$457$	−18.4395	−	18.4395i	−0.862563	−	0.862563i	0.129072	−	0.991635i	$-0.458800\pi$
$457$	−18.4395	−	18.4395i	−0.862563	−	0.862563i	−0.991635	+	0.129072i	$0.958800\pi$
$458$		0			0
$459$	−1.04752	+	0.469201i	−0.0488939	+	0.0219004i
$460$		0			0
$461$	−22.1455	−	22.1455i	−1.03142	−	1.03142i	−0.999490	−	0.0319303i	$-0.989835\pi$
$461$	−22.1455	−	22.1455i	−1.03142	−	1.03142i	−0.0319303	−	0.999490i	$-0.510165\pi$
$462$		0			0
$463$			19.7237i			0.916639i	0.888787	+	0.458320i	$0.151549\pi$
$463$			19.7237i			0.916639i	−0.888787	+	0.458320i	$0.848451\pi$
$464$		0			0
$465$	−0.0679119	−	0.0281300i	−0.00314934	−	0.00130450i
$466$		0			0
$467$	−12.4081	+	12.4081i	−0.574180	+	0.574180i	−0.933294	−	0.359114i	$-0.883079\pi$
$467$	−12.4081	+	12.4081i	−0.574180	+	0.574180i	0.359114	+	0.933294i	$0.383079\pi$
$468$		0			0
$469$	−12.2459	+	29.5642i	−0.565462	+	1.36515i
$470$		0			0
$471$	0.121340	+	0.292942i	0.00559107	+	0.0134980i
$472$		0			0
$473$	21.1848	−	8.77504i	0.974079	−	0.403477i
$474$		0			0
$475$	4.64878			0.213301
$476$		0			0
$477$	20.5259			0.939818
$478$		0			0
$479$	−23.2625	+	9.63566i	−1.06289	+	0.440264i	−0.844477	−	0.535592i	$-0.820089\pi$
$479$	−23.2625	+	9.63566i	−1.06289	+	0.440264i	−0.218415	+	0.975856i	$0.570089\pi$
$480$		0			0
$481$	20.8481	+	50.3318i	0.950593	+	2.29493i
$482$		0			0
$483$	0.119699	−	0.288980i	0.00544651	−	0.0131490i
$484$		0			0
$485$	10.5617	−	10.5617i	0.479581	−	0.479581i
$486$		0			0
$487$	11.2288	+	4.65110i	0.508823	+	0.210762i	0.622300	−	0.782779i	$-0.286199\pi$
$487$	11.2288	+	4.65110i	0.508823	+	0.210762i	−0.113476	+	0.993541i	$0.536199\pi$
$488$		0			0
$489$			0.437913i			0.0198031i
$490$		0			0
$491$	−0.708515	−	0.708515i	−0.0319748	−	0.0319748i	0.690939	−	0.722913i	$-0.257197\pi$
$491$	−0.708515	−	0.708515i	−0.0319748	−	0.0319748i	−0.722913	+	0.690939i	$0.757197\pi$
$492$		0			0
$493$	−8.44616	+	22.1513i	−0.380396	+	0.997644i
$494$		0			0
$495$	−5.02574	−	5.02574i	−0.225890	−	0.225890i
$496$		0			0
$497$		−	25.5311i		−	1.14523i
$498$		0			0
$499$	36.2598	+	15.0193i	1.62321	+	0.672357i	0.994447	−	0.105239i	$-0.0335607\pi$
$499$	36.2598	+	15.0193i	1.62321	+	0.672357i	0.628765	+	0.777595i	$0.283561\pi$
$500$		0			0
$501$	−0.291381	+	0.291381i	−0.0130180	+	0.0130180i
$502$		0			0
$503$	−6.90768	+	16.6766i	−0.307998	+	0.743573i	0.691772	+	0.722116i	$0.256831\pi$
$503$	−6.90768	+	16.6766i	−0.307998	+	0.743573i	−0.999770	+	0.0214570i	$0.993169\pi$
$504$		0			0
$505$	1.62310	+	3.91850i	0.0722268	+	0.174371i
$506$		0			0
$507$	0.481220	−	0.199328i	0.0213717	−	0.00885246i
$508$		0			0
$509$	13.1870			0.584504			0.292252	−	0.956341i	$-0.405595\pi$
$509$	13.1870			0.584504			0.292252	+	0.956341i	$0.405595\pi$
$510$		0			0
$511$	11.3549			0.502313
$512$		0			0
$513$	−1.19563	+	0.495245i	−0.0527883	+	0.0218656i
$514$		0			0
$515$	0.0194092	+	0.0468579i	0.000855271	+	0.00206481i
$516$		0			0
$517$	9.81441	−	23.6941i	0.431637	−	1.04206i
$518$		0			0
$519$	−0.422899	+	0.422899i	−0.0185632	+	0.0185632i
$520$		0			0
$521$	−7.97279	−	3.30244i	−0.349294	−	0.144682i	0.201137	−	0.979563i	$-0.435537\pi$
$521$	−7.97279	−	3.30244i	−0.349294	−	0.144682i	−0.550431	+	0.834881i	$0.685537\pi$
$522$		0			0
$523$		−	43.5509i		−	1.90435i	−0.305559	−	0.952173i	$-0.598843\pi$
$523$		−	43.5509i		−	1.90435i	0.305559	−	0.952173i	$-0.401157\pi$
$524$		0			0
$525$	0.0868301	+	0.0868301i	0.00378958	+	0.00378958i
$526$		0			0
$527$	6.10145	+	2.32645i	0.265783	+	0.101342i
$528$		0			0
$529$	−11.6755	−	11.6755i	−0.507631	−	0.507631i
$530$		0			0
$531$			34.7194i			1.50670i
$532$		0			0
$533$	−15.1746	−	6.28553i	−0.657286	−	0.272257i
$534$		0			0
$535$	3.24840	−	3.24840i	0.140441	−	0.140441i
$536$		0			0
$537$	−0.441106	+	1.06492i	−0.0190351	+	0.0459548i
$538$		0			0
$539$	−0.000288810	0	0.000697248i	−1.24399e−5	0	3.00326e-5i
$540$		0			0
$541$	−0.702711	+	0.291073i	−0.0302119	+	0.0125142i	−0.397738	−	0.917499i	$-0.630205\pi$
$541$	−0.702711	+	0.291073i	−0.0302119	+	0.0125142i	0.367526	+	0.930013i	$0.380205\pi$
$542$		0			0
$543$	−1.03243			−0.0443056
$544$		0			0
$545$	4.48180			0.191979
$546$		0			0
$547$	−17.2898	+	7.16168i	−0.739260	+	0.306212i	−0.720351	−	0.693610i	$-0.756019\pi$
$547$	−17.2898	+	7.16168i	−0.739260	+	0.306212i	−0.0189090	+	0.999821i	$0.506019\pi$
$548$		0			0
$549$	2.16616	+	5.22957i	0.0924493	+	0.223192i
$550$		0			0
$551$	−10.2289	+	24.6948i	−0.435766	+	1.05203i
$552$		0			0
$553$	5.73208	−	5.73208i	0.243753	−	0.243753i
$554$		0			0
$555$	−0.474658	−	0.196610i	−0.0201481	−	0.00834563i
$556$		0			0
$557$		−	18.2983i		−	0.775324i	−0.921802	−	0.387662i	$-0.873283\pi$
$557$		−	18.2983i		−	0.775324i	0.921802	−	0.387662i	$-0.126717\pi$
$558$		0			0
$559$	33.6587	+	33.6587i	1.42361	+	1.42361i
$560$		0			0
$561$	−0.329807	−	0.311573i	−0.0139245	−	0.0131546i
$562$		0			0
$563$	−7.87431	−	7.87431i	−0.331863	−	0.331863i	0.521431	−	0.853293i	$-0.325398\pi$
$563$	−7.87431	−	7.87431i	−0.331863	−	0.331863i	−0.853293	+	0.521431i	$0.825398\pi$
$564$		0			0
$565$		−	11.6492i		−	0.490085i
$566$		0			0
$567$	21.9513	+	9.09253i	0.921869	+	0.381851i
$568$		0			0
$569$	24.8909	−	24.8909i	1.04348	−	1.04348i	0.0444710	−	0.999011i	$-0.485840\pi$
$569$	24.8909	−	24.8909i	1.04348	−	1.04348i	0.999011	−	0.0444710i	$-0.0141602\pi$
$570$		0			0
$571$	1.32607	−	3.20142i	0.0554944	−	0.133975i	−0.893701	−	0.448664i	$-0.851900\pi$
$571$	1.32607	−	3.20142i	0.0554944	−	0.133975i	0.949195	+	0.314689i	$0.101900\pi$
$572$		0			0
$573$	0.191786	+	0.463012i	0.00801197	+	0.0193426i
$574$		0			0
$575$	−2.35333	+	0.974780i	−0.0981405	+	0.0406511i
$576$		0			0
$577$	7.17791			0.298820			0.149410	−	0.988775i	$-0.452263\pi$
$577$	7.17791			0.298820			0.149410	+	0.988775i	$0.452263\pi$
$578$		0			0
$579$	0.958855			0.0398486
$580$		0			0
$581$	−4.68152	+	1.93915i	−0.194222	+	0.0804495i
$582$		0			0
$583$	6.21211	+	14.9973i	0.257279	+	0.621127i
$584$		0			0
$585$	5.64621	−	13.6311i	0.233442	−	0.563579i
$586$		0			0
$587$	4.59581	−	4.59581i	0.189689	−	0.189689i	−0.605872	−	0.795562i	$-0.707176\pi$
$587$	4.59581	−	4.59581i	0.189689	−	0.189689i	0.795562	+	0.605872i	$0.207176\pi$
$588$		0			0
$589$	6.80203	+	2.81749i	0.280273	+	0.116093i
$590$		0			0
$591$		−	0.802471i		−	0.0330092i
$592$		0			0
$593$	12.4388	+	12.4388i	0.510800	+	0.510800i	0.914772	−	0.403971i	$-0.132370\pi$
$593$	12.4388	+	12.4388i	0.510800	+	0.510800i	−0.403971	+	0.914772i	$0.632370\pi$
$594$		0			0
$595$	−7.92953	−	7.49113i	−0.325079	−	0.307107i
$596$		0			0
$597$	0.308560	+	0.308560i	0.0126285	+	0.0126285i
$598$		0			0
$599$			19.3164i			0.789248i	0.918843	+	0.394624i	$0.129125\pi$
$599$			19.3164i			0.789248i	−0.918843	+	0.394624i	$0.870875\pi$
$600$		0			0
$601$	−14.2096	−	5.88583i	−0.579623	−	0.240088i	0.0735559	−	0.997291i	$-0.476565\pi$
$601$	−14.2096	−	5.88583i	−0.579623	−	0.240088i	−0.653179	+	0.757203i	$0.726565\pi$
$602$		0			0
$603$	−25.6392	+	25.6392i	−1.04411	+	1.04411i
$604$		0			0
$605$	−2.05847	+	4.96958i	−0.0836886	+	0.202042i
$606$		0			0
$607$	6.77408	+	16.3541i	0.274952	+	0.663792i	0.999681	−	0.0252414i	$-0.00803545\pi$
$607$	6.77408	+	16.3541i	0.274952	+	0.663792i	−0.724730	+	0.689033i	$0.758035\pi$
$608$		0			0
$609$	−0.652305	+	0.270194i	−0.0264327	+	0.0109488i
$610$		0			0
$611$	53.2386			2.15380
$612$		0			0
$613$	0.172428			0.00696430			0.00348215	−	0.999994i	$-0.498892\pi$
$613$	0.172428			0.00696430			0.00348215	+	0.999994i	$0.498892\pi$
$614$		0			0
$615$	0.143105	−	0.0592762i	0.00577057	−	0.00239025i
$616$		0			0
$617$	−7.57029	−	18.2763i	−0.304768	−	0.735776i	−0.999858	−	0.0168527i	$-0.994635\pi$
$617$	−7.57029	−	18.2763i	−0.304768	−	0.735776i	0.695090	−	0.718923i	$-0.255365\pi$
$618$		0			0
$619$	−1.06571	+	2.57284i	−0.0428344	+	0.103411i	−0.943849	−	0.330378i	$-0.892824\pi$
$619$	−1.06571	+	2.57284i	−0.0428344	+	0.103411i	0.901014	+	0.433789i	$0.142824\pi$
$620$		0			0
$621$	0.501410	−	0.501410i	0.0201209	−	0.0201209i
$622$		0			0
$623$	33.2860	+	13.7875i	1.33358	+	0.552386i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−0.361723	−	0.361723i	−0.0144458	−	0.0144458i
$628$		0			0
$629$	42.6450	+	16.2603i	1.70037	+	0.648340i
$630$		0			0
$631$	−20.1667	−	20.1667i	−0.802823	−	0.802823i	0.180712	−	0.983536i	$-0.442160\pi$
$631$	−20.1667	−	20.1667i	−0.802823	−	0.802823i	−0.983536	+	0.180712i	$0.942160\pi$
$632$		0			0
$633$		−	0.373492i		−	0.0148450i
$634$		0			0
$635$	17.4454	+	7.22613i	0.692300	+	0.286760i
$636$		0			0
$637$	0.00110780	−	0.00110780i	4.38925e−5	−	4.38925e-5i
$638$		0			0
$639$	11.0708	−	26.7273i	0.437954	−	1.05732i
$640$		0			0
$641$	−10.3402	−	24.9635i	−0.408414	−	0.985998i	−0.985555	−	0.169354i	$-0.945832\pi$
$641$	−10.3402	−	24.9635i	−0.408414	−	0.985998i	0.577142	−	0.816644i	$-0.304168\pi$
$642$		0			0
$643$	−7.97587	+	3.30371i	−0.314537	+	0.130286i	−0.534367	−	0.845253i	$-0.679450\pi$
$643$	−7.97587	+	3.30371i	−0.314537	+	0.130286i	0.219829	+	0.975538i	$0.429450\pi$
$644$		0			0
$645$	−0.448901			−0.0176754
$646$		0			0
$647$	3.64937			0.143471			0.0717357	−	0.997424i	$-0.477146\pi$
$647$	3.64937			0.143471			0.0717357	+	0.997424i	$0.477146\pi$
$648$		0			0
$649$	−25.3679	+	10.5077i	−0.995776	+	0.412464i
$650$		0			0
$651$	0.0744233	+	0.179674i	0.00291688	+	0.00704197i
$652$		0			0
$653$	2.49072	−	6.01313i	0.0974694	−	0.235312i	−0.867622	−	0.497224i	$-0.834353\pi$
$653$	2.49072	−	6.01313i	0.0974694	−	0.235312i	0.965092	+	0.261912i	$0.0843529\pi$
$654$		0			0
$655$	9.41576	−	9.41576i	0.367904	−	0.367904i
$656$		0			0
$657$	11.8869	+	4.92374i	0.463754	+	0.192093i
$658$		0			0
$659$			16.5602i			0.645092i	0.946554	+	0.322546i	$0.104539\pi$
$659$			16.5602i			0.645092i	−0.946554	+	0.322546i	$0.895461\pi$
$660$		0			0
$661$	19.0713	+	19.0713i	0.741788	+	0.741788i	0.972922	−	0.231134i	$-0.0742436\pi$
$661$	19.0713	+	19.0713i	0.741788	+	0.741788i	−0.231134	+	0.972922i	$0.574244\pi$
$662$		0			0
$663$	0.335554	−	0.880040i	0.0130318	−	0.0341779i
$664$		0			0
$665$	−8.69688	−	8.69688i	−0.337251	−	0.337251i
$666$		0			0
$667$		−	14.6459i		−	0.567093i
$668$		0			0
$669$	0.605749	+	0.250909i	0.0234196	+	0.00970072i
$670$		0			0
$671$	−3.16542	+	3.16542i	−0.122200	+	0.122200i
$672$		0			0
$673$	11.0722	−	26.7307i	0.426802	−	1.03039i	−0.553493	−	0.832854i	$-0.686705\pi$
$673$	11.0722	−	26.7307i	0.426802	−	1.03039i	0.980295	−	0.197538i	$-0.0632946\pi$
$674$		0			0
$675$	0.106532	+	0.257192i	0.00410043	+	0.00989931i
$676$		0			0
$677$	9.18323	−	3.80382i	0.352940	−	0.146193i	−0.199167	−	0.979965i	$-0.563824\pi$
$677$	9.18323	−	3.80382i	0.352940	−	0.146193i	0.552108	+	0.833773i	$0.313824\pi$
$678$		0			0
$679$	−39.5173			−1.51654
$680$		0			0
$681$	0.902250			0.0345743
$682$		0			0
$683$	17.2893	−	7.16147i	0.661557	−	0.274026i	−0.0265366	−	0.999648i	$-0.508448\pi$
$683$	17.2893	−	7.16147i	0.661557	−	0.274026i	0.688094	+	0.725622i	$0.258448\pi$
$684$		0			0
$685$	−2.29937	−	5.55116i	−0.0878543	−	0.212099i
$686$		0			0
$687$	−0.0699629	+	0.168905i	−0.00266925	+	0.00644414i
$688$		0			0
$689$	−23.8279	+	23.8279i	−0.907772	+	0.907772i
$690$		0			0
$691$	15.9249	+	6.59633i	0.605813	+	0.250936i	0.664437	−	0.747344i	$-0.268671\pi$
$691$	15.9249	+	6.59633i	0.605813	+	0.250936i	−0.0586240	+	0.998280i	$0.518671\pi$
$692$		0			0
$693$			18.8042i			0.714311i
$694$		0			0
$695$	8.72841	+	8.72841i	0.331087	+	0.331087i
$696$		0			0
$697$	−12.5578	+	5.62487i	−0.475662	+	0.213057i
$698$		0			0
$699$	0.219749	+	0.219749i	0.00831167	+	0.00831167i
$700$		0			0
$701$		−	31.3063i		−	1.18242i	−0.806517	−	0.591211i	$-0.798650\pi$
$701$		−	31.3063i		−	1.18242i	0.806517	−	0.591211i	$-0.201350\pi$
$702$		0			0
$703$	47.5416	+	19.6924i	1.79307	+	0.742713i
$704$		0			0
$705$	−0.355018	+	0.355018i	−0.0133707	+	0.0133707i
$706$		0			0
$707$	4.29421	−	10.3671i	0.161500	−	0.389896i
$708$		0			0
$709$	−4.69124	−	11.3257i	−0.176183	−	0.425344i	0.810977	−	0.585078i	$-0.198936\pi$
$709$	−4.69124	−	11.3257i	−0.176183	−	0.425344i	−0.987160	+	0.159734i	$0.948936\pi$
$710$		0			0
$711$	8.48619	−	3.51510i	0.318257	−	0.131826i
$712$		0			0
$713$	−4.03414			−0.151080
$714$		0			0
$715$	11.6685			0.436375
$716$		0			0
$717$	−0.683812	+	0.283244i	−0.0255374	+	0.0105779i
$718$		0			0
$719$	12.2748	+	29.6340i	0.457773	+	1.10516i	0.969297	+	0.245893i	$0.0790813\pi$
$719$	12.2748	+	29.6340i	0.457773	+	1.10516i	−0.511524	+	0.859269i	$0.670919\pi$
$720$		0			0
$721$	0.0513507	−	0.123972i	0.00191240	−	0.00461694i
$722$		0			0
$723$	−0.0326784	+	0.0326784i	−0.00121532	+	0.00121532i
$724$		0			0
$725$	5.31209	+	2.20034i	0.197286	+	0.0817186i
$726$		0			0
$727$			4.75521i			0.176361i	0.996105	+	0.0881805i	$0.0281052\pi$
$727$			4.75521i			0.176361i	−0.996105	+	0.0881805i	$0.971895\pi$
$728$		0			0
$729$	19.0097	+	19.0097i	0.704062	+	0.704062i
$730$		0			0
$731$	39.8615	−	1.13324i	1.47433	−	0.0419142i
$732$		0			0
$733$	8.87653	+	8.87653i	0.327862	+	0.327862i	0.851773	−	0.523911i	$-0.175528\pi$
$733$	8.87653	+	8.87653i	0.327862	+	0.327862i	−0.523911	+	0.851773i	$0.675528\pi$
$734$		0			0
$735$		0	1.47745e-5i		0	5.44966e-7i
$736$		0			0
$737$	−26.4930	−	10.9738i	−0.975883	−	0.404224i
$738$		0			0
$739$	−23.6516	+	23.6516i	−0.870038	+	0.870038i	−0.992476	−	0.122438i	$-0.960929\pi$
$739$	−23.6516	+	23.6516i	−0.870038	+	0.870038i	0.122438	+	0.992476i	$0.460929\pi$
$740$		0			0
$741$	0.406381	−	0.981089i	0.0149288	−	0.0360412i
$742$		0			0
$743$	9.97338	+	24.0779i	0.365888	+	0.883331i	0.994415	+	0.105543i	$0.0336582\pi$
$743$	9.97338	+	24.0779i	0.365888	+	0.883331i	−0.628527	+	0.777788i	$0.716342\pi$
$744$		0			0
$745$	−0.937838	+	0.388465i	−0.0343597	+	0.0142323i
$746$		0			0
$747$	−5.74172			−0.210078
$748$		0			0
$749$	−12.1541			−0.444102
$750$		0			0
$751$	19.0426	−	7.88770i	0.694874	−	0.287826i	−0.00715519	−	0.999974i	$-0.502278\pi$
$751$	19.0426	−	7.88770i	0.694874	−	0.287826i	0.702029	+	0.712148i	$0.252278\pi$
$752$		0			0
$753$	0.462414	+	1.11637i	0.0168513	+	0.0406826i
$754$		0			0
$755$	−4.08273	+	9.85658i	−0.148586	+	0.358718i
$756$		0			0
$757$	8.03416	−	8.03416i	0.292006	−	0.292006i	−0.545866	−	0.837872i	$-0.683799\pi$
$757$	8.03416	−	8.03416i	0.292006	−	0.292006i	0.837872	+	0.545866i	$0.183799\pi$
$758$		0			0
$759$	0.258961	+	0.107265i	0.00939967	+	0.00389347i
$760$		0			0
$761$		−	7.45322i		−	0.270179i	−0.990833	−	0.135090i	$-0.956868\pi$
$761$		−	7.45322i		−	0.270179i	0.990833	−	0.135090i	$-0.0431322\pi$
$762$		0			0
$763$	−8.38449	−	8.38449i	−0.303539	−	0.303539i
$764$		0			0
$765$	−5.05274	−	11.2805i	−0.182682	−	0.407848i
$766$		0			0
$767$	−40.3047	−	40.3047i	−1.45532	−	1.45532i
$768$		0			0
$769$		−	15.1949i		−	0.547943i	−0.961738	−	0.273972i	$-0.911663\pi$
$769$		−	15.1949i		−	0.547943i	0.961738	−	0.273972i	$-0.0883374\pi$
$770$		0			0
$771$	−0.675282	−	0.279711i	−0.0243197	−	0.0100735i
$772$		0			0
$773$	−27.9242	+	27.9242i	−1.00436	+	1.00436i	−0.00437428	+	0.999990i	$0.501392\pi$
$773$	−27.9242	+	27.9242i	−1.00436	+	1.00436i	−0.999990	+	0.00437428i	$0.998608\pi$
$774$		0			0
$775$	0.606071	−	1.46319i	0.0217707	−	0.0525592i
$776$		0			0
$777$	0.520169	+	1.25580i	0.0186610	+	0.0450515i
$778$		0			0
$779$	−14.3334	+	5.93709i	−0.513548	+	0.212718i
$780$		0			0
$781$	22.8789			0.818673
$782$		0			0
$783$	−1.60063			−0.0572019
$784$		0			0
$785$	−6.31154	+	2.61432i	−0.225268	+	0.0933093i
$786$		0			0
$787$	−16.2435	−	39.2153i	−0.579019	−	1.39788i	−0.893694	−	0.448676i	$-0.851896\pi$
$787$	−16.2435	−	39.2153i	−0.579019	−	1.39788i	0.314675	−	0.949199i	$-0.398104\pi$
$788$		0			0
$789$	0.259542	−	0.626589i	0.00923993	−	0.0223072i
$790$		0			0
$791$	−21.7931	+	21.7931i	−0.774875	+	0.774875i
$792$		0			0
$793$	−8.58547	−	3.55622i	−0.304879	−	0.126285i
$794$		0			0
$795$		−	0.317790i		−	0.0112708i
$796$		0			0
$797$	7.46528	+	7.46528i	0.264434	+	0.264434i	0.826852	−	0.562419i	$-0.190129\pi$
$797$	7.46528	+	7.46528i	0.264434	+	0.264434i	−0.562419	+	0.826852i	$0.690129\pi$
$798$		0			0
$799$	30.6286	−	32.4211i	1.08356	−	1.14698i
$800$		0			0
$801$	28.8670	+	28.8670i	1.01997	+	1.01997i
$802$		0			0
$803$			10.1754i			0.359082i
$804$		0			0
$805$	6.22617	+	2.57897i	0.219444	+	0.0908966i
$806$		0			0
$807$	0.920726	−	0.920726i	0.0324111	−	0.0324111i
$808$		0			0
$809$	−16.9009	+	40.8024i	−0.594204	+	1.43453i	0.285205	+	0.958467i	$0.407938\pi$
$809$	−16.9009	+	40.8024i	−0.594204	+	1.43453i	−0.879408	+	0.476068i	$0.842062\pi$
$810$		0			0
$811$	16.3850	+	39.5568i	0.575354	+	1.38903i	0.896942	+	0.442147i	$0.145783\pi$
$811$	16.3850	+	39.5568i	0.575354	+	1.38903i	−0.321589	+	0.946879i	$0.604217\pi$
$812$		0			0
$813$	1.08573	−	0.449725i	0.0380783	−	0.0157725i
$814$		0			0
$815$	−9.43500			−0.330494
$816$		0			0
$817$	44.9618			1.57301
$818$		0			0
$819$	−36.0638	+	14.9381i	−1.26017	+	0.521980i
$820$		0			0
$821$	−7.02173	−	16.9519i	−0.245060	−	0.591627i	0.752712	−	0.658350i	$-0.228745\pi$
$821$	−7.02173	−	16.9519i	−0.245060	−	0.591627i	−0.997772	+	0.0667234i	$0.978745\pi$
$822$		0			0
$823$	−12.3818	+	29.8924i	−0.431604	+	1.04198i	0.547167	+	0.837024i	$0.315706\pi$
$823$	−12.3818	+	29.8924i	−0.431604	+	1.04198i	−0.978770	+	0.204960i	$0.934294\pi$
$824$		0			0
$825$	−0.0778102	+	0.0778102i	−0.00270900	+	0.00270900i
$826$		0			0
$827$	−10.1388	−	4.19965i	−0.352562	−	0.146036i	0.199372	−	0.979924i	$-0.436110\pi$
$827$	−10.1388	−	4.19965i	−0.352562	−	0.146036i	−0.551934	+	0.833888i	$0.686110\pi$
$828$		0			0
$829$		−	23.0619i		−	0.800973i	−0.916303	−	0.400487i	$-0.868841\pi$
$829$		−	23.0619i		−	0.800973i	0.916303	−	0.400487i	$-0.131159\pi$
$830$		0			0
$831$	−0.746892	−	0.746892i	−0.0259094	−	0.0259094i
$832$		0			0
$833$	−3.72978e−5	−	0.00131195i	−1.29229e−6	−	4.54562e-5i
$834$		0			0
$835$	−6.27792	−	6.27792i	−0.217256	−	0.217256i
$836$		0			0
$837$			0.440885i			0.0152392i
$838$		0			0
$839$	41.4693	+	17.1771i	1.43168	+	0.593021i	0.957765	−	0.287551i	$-0.0928411\pi$
$839$	41.4693	+	17.1771i	1.43168	+	0.593021i	0.473913	+	0.880572i	$0.342841\pi$
$840$		0			0
$841$	−2.87073	+	2.87073i	−0.0989905	+	0.0989905i
$842$		0			0
$843$	−0.534714	+	1.29091i	−0.0184165	+	0.0444614i
$844$		0			0
$845$	4.29459	+	10.3681i	0.147739	+	0.356672i
$846$		0			0
$847$	13.1480	−	5.44607i	0.451770	−	0.187129i
$848$		0			0
$849$	0.909386			0.0312101
$850$		0			0
$851$	−28.1959			−0.966544
$852$		0			0
$853$	−36.5727	+	15.1489i	−1.25222	+	0.518688i	−0.907514	−	0.420021i	$-0.862023\pi$
$853$	−36.5727	+	15.1489i	−1.25222	+	0.518688i	−0.344710	+	0.938709i	$0.612023\pi$
$854$		0			0
$855$	−5.33320	−	12.8755i	−0.182392	−	0.440333i
$856$		0			0
$857$	2.86679	−	6.92105i	0.0979278	−	0.236419i	−0.867322	−	0.497747i	$-0.834161\pi$
$857$	2.86679	−	6.92105i	0.0979278	−	0.236419i	0.965250	+	0.261329i	$0.0841607\pi$
$858$		0			0
$859$	−31.9984	+	31.9984i	−1.09177	+	1.09177i	−0.0964306	+	0.995340i	$0.530743\pi$
$859$	−31.9984	+	31.9984i	−1.09177	+	1.09177i	−0.995340	+	0.0964306i	$0.969257\pi$
$860$		0			0
$861$	−0.378613	−	0.156827i	−0.0129031	−	0.00534464i
$862$		0			0
$863$		−	22.3654i		−	0.761328i	−0.924713	−	0.380664i	$-0.875696\pi$
$863$		−	22.3654i		−	0.761328i	0.924713	−	0.380664i	$-0.124304\pi$
$864$		0			0
$865$	−9.11152	−	9.11152i	−0.309801	−	0.309801i
$866$		0			0
$867$	−0.342877	−	0.710639i	−0.0116447	−	0.0241346i
$868$		0			0
$869$	5.13663	+	5.13663i	0.174248	+	0.174248i
$870$		0			0
$871$		−	59.5277i		−	2.01702i
$872$		0			0
$873$	−41.3688	−	17.1355i	−1.40012	−	0.579949i
$874$		0			0
$875$	−1.87079	+	1.87079i	−0.0632441	+	0.0632441i
$876$		0			0
$877$	17.4383	−	42.0999i	0.588851	−	1.42161i	−0.295751	−	0.955265i	$-0.595570\pi$
$877$	17.4383	−	42.0999i	0.588851	−	1.42161i	0.884602	−	0.466347i	$-0.154430\pi$
$878$		0			0
$879$	0.181358	+	0.437836i	0.00611704	+	0.0147678i
$880$		0			0
$881$	9.15563	−	3.79239i	0.308461	−	0.127769i	−0.223083	−	0.974799i	$-0.571612\pi$
$881$	9.15563	−	3.79239i	0.308461	−	0.127769i	0.531544	+	0.847031i	$0.321612\pi$
$882$		0			0
$883$	−14.6843			−0.494167			−0.247083	−	0.968994i	$-0.579472\pi$
$883$	−14.6843			−0.494167			−0.247083	+	0.968994i	$0.579472\pi$
$884$		0			0
$885$	0.537538			0.0180692
$886$		0			0
$887$	14.7394	−	6.10526i	0.494901	−	0.204995i	−0.121251	−	0.992622i	$-0.538691\pi$
$887$	14.7394	−	6.10526i	0.494901	−	0.204995i	0.616152	+	0.787627i	$0.288691\pi$
$888$		0			0
$889$	−19.1181	−	46.1552i	−0.641200	−	1.54799i
$890$		0			0
$891$	−8.14800	+	19.6710i	−0.272968	+	0.659004i
$892$		0			0
$893$	35.5585	−	35.5585i	1.18992	−	1.18992i
$894$		0			0
$895$	−22.9442	−	9.50378i	−0.766939	−	0.317676i
$896$		0			0
$897$			0.581863i			0.0194278i
$898$		0			0
$899$	6.43901	+	6.43901i	0.214753	+	0.214753i
$900$		0			0
$901$	0.802250	+	28.2191i	0.0267268	+	0.940114i
$902$		0			0
$903$	0.839797	+	0.839797i	0.0279467	+	0.0279467i
$904$		0			0
$905$		−	22.2440i		−	0.739415i
$906$		0			0
$907$	−31.0500	−	12.8613i	−1.03100	−	0.427054i	−0.197926	−	0.980217i	$-0.563421\pi$
$907$	−31.0500	−	12.8613i	−1.03100	−	0.427054i	−0.833073	+	0.553163i	$0.813421\pi$
$908$		0			0
$909$	8.99081	−	8.99081i	0.298206	−	0.298206i
$910$		0			0
$911$	6.27104	−	15.1396i	0.207769	−	0.501598i	−0.785302	−	0.619112i	$-0.787493\pi$
$911$	6.27104	−	15.1396i	0.207769	−	0.501598i	0.993071	+	0.117514i	$0.0374926\pi$
$912$		0			0
$913$	−1.73771	−	4.19521i	−0.0575098	−	0.138841i
$914$		0			0
$915$	0.0809660	−	0.0335372i	0.00267665	−	0.00110871i
$916$		0			0
$917$	−35.2297			−1.16339
$918$		0			0
$919$	45.4361			1.49880			0.749399	−	0.662118i	$-0.230342\pi$
$919$	45.4361			1.49880			0.749399	+	0.662118i	$0.230342\pi$
$920$		0			0
$921$	0.746494	−	0.309208i	0.0245978	−	0.0101887i
$922$		0			0
$923$	18.1751	+	43.8787i	0.598242	+	1.44428i
$924$		0			0
$925$	4.23603	−	10.2267i	0.139280	−	0.336251i
$926$		0			0
$927$	0.107513	−	0.107513i	0.00353120	−	0.00353120i
$928$		0			0
$929$	−2.79655	−	1.15837i	−0.0917520	−	0.0380049i	0.336335	−	0.941742i	$-0.390812\pi$
$929$	−2.79655	−	1.15837i	−0.0917520	−	0.0380049i	−0.428087	+	0.903737i	$0.640812\pi$
$930$		0			0
$931$		−	0.00147981i		−	4.84988e-5i
$932$		0			0
$933$	−0.348667	−	0.348667i	−0.0114149	−	0.0114149i
$934$		0			0
$935$	6.71296	−	7.10581i	0.219537	−	0.232385i
$936$		0			0
$937$	−11.0166	−	11.0166i	−0.359898	−	0.359898i	0.503877	−	0.863775i	$-0.331906\pi$
$937$	−11.0166	−	11.0166i	−0.359898	−	0.359898i	−0.863775	+	0.503877i	$0.831906\pi$
$938$		0			0
$939$		−	1.07653i		−	0.0351311i
$940$		0			0
$941$	−40.9831	−	16.9757i	−1.33601	−	0.553393i	−0.403646	−	0.914915i	$-0.632257\pi$
$941$	−40.9831	−	16.9757i	−1.33601	−	0.553393i	−0.932364	+	0.361522i	$0.882257\pi$
$942$		0			0
$943$	6.01100	−	6.01100i	0.195745	−	0.195745i
$944$		0			0
$945$	0.281851	−	0.680450i	0.00916863	−	0.0221350i
$946$		0			0
$947$	−16.7470	−	40.4307i	−0.544203	−	1.31382i	−0.921733	−	0.387825i	$-0.873227\pi$
$947$	−16.7470	−	40.4307i	−0.544203	−	1.31382i	0.377530	−	0.925997i	$-0.376773\pi$
$948$		0			0
$949$	−19.5150	+	8.08338i	−0.633484	+	0.262398i
$950$		0			0
$951$	0.246853			0.00800474
$952$		0			0
$953$	−14.4469			−0.467980			−0.233990	−	0.972239i	$-0.575178\pi$
$953$	−14.4469			−0.467980			−0.233990	+	0.972239i	$0.575178\pi$
$954$		0			0
$955$	−9.97576	+	4.13210i	−0.322808	+	0.133712i
$956$		0			0
$957$	−0.242126	−	0.584544i	−0.00782682	−	0.0188956i
$958$		0			0
$959$	−6.08341	+	14.6867i	−0.196444	+	0.474257i
$960$		0			0
$961$	−20.1467	+	20.1467i	−0.649894	+	0.649894i
$962$		0			0
$963$	−12.7236	−	5.27028i	−0.410012	−	0.169832i
$964$		0			0
$965$			20.6589i			0.665033i
$966$		0			0
$967$	22.8881	+	22.8881i	0.736030	+	0.736030i	0.971807	−	0.235777i	$-0.0757635\pi$
$967$	22.8881	+	22.8881i	0.736030	+	0.736030i	−0.235777	+	0.971807i	$0.575763\pi$
$968$		0			0
$969$	−0.363667	−	0.811905i	−0.0116827	−	0.0260821i
$970$		0			0
$971$	3.78792	+	3.78792i	0.121560	+	0.121560i	0.765270	−	0.643710i	$-0.222606\pi$
$971$	3.78792	+	3.78792i	0.121560	+	0.121560i	−0.643710	+	0.765270i	$0.722606\pi$
$972$		0			0
$973$		−	32.6580i		−	1.04697i
$974$		0			0
$975$	−0.211042	−	0.0874165i	−0.00675876	−	0.00279957i
$976$		0			0
$977$	0.777635	−	0.777635i	0.0248788	−	0.0248788i	−0.694558	−	0.719437i	$-0.744400\pi$
$977$	0.777635	−	0.777635i	0.0248788	−	0.0248788i	0.719437	+	0.694558i	$0.244400\pi$
$978$		0			0
$979$	−12.3553	+	29.8283i	−0.394877	+	0.953317i
$980$		0			0
$981$	−5.14164	−	12.4130i	−0.164160	−	0.396317i
$982$		0			0
$983$	18.1518	−	7.51873i	0.578953	−	0.239810i	−0.0739370	−	0.997263i	$-0.523556\pi$
$983$	18.1518	−	7.51873i	0.578953	−	0.239810i	0.652890	+	0.757453i	$0.273556\pi$
$984$		0			0
$985$	17.2895			0.550890
$986$		0			0
$987$	1.32833			0.0422811
$988$		0			0
$989$	−22.7607	+	9.42780i	−0.723749	+	0.299787i
$990$		0			0
$991$	−11.6083	−	28.0248i	−0.368748	−	0.890237i	−0.993956	−	0.109779i	$-0.964986\pi$
$991$	−11.6083	−	28.0248i	−0.368748	−	0.890237i	0.625208	−	0.780458i	$-0.285014\pi$
$992$		0			0
$993$	0.532284	−	1.28505i	0.0168915	−	0.0407798i
$994$		0			0
$995$	−6.64803	+	6.64803i	−0.210757	+	0.210757i
$996$		0			0
$997$	20.2309	+	8.37993i	0.640720	+	0.265395i	0.679300	−	0.733861i	$-0.262283\pi$
$997$	20.2309	+	8.37993i	0.640720	+	0.265395i	−0.0385800	+	0.999256i	$0.512283\pi$
$998$		0			0
$999$			3.08149i			0.0974941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bo.a.121.5	✓	32
17.9	even	8	inner	680.2.bo.a.281.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bo.a.121.5	✓	32	1.1	even	1	trivial
680.2.bo.a.281.5	yes	32	17.9	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0428807 + 0.0177618i) q^{3} +(-0.382683 - 0.923880i) q^{5} +(-1.01246 + 2.44430i) q^{7} +(-2.11980 + 2.11980i) q^{9} +(-2.19039 - 0.907288i) q^{11} -4.92162i q^{13} +(0.0328194 + 0.0328194i) q^{15} +(-2.99715 - 2.83145i) q^{17} +(-3.28719 - 3.28719i) q^{19} -0.122796i q^{21} +(2.35333 + 0.974780i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(0.106532 - 0.257192i) q^{27} +(-2.20034 - 5.31209i) q^{29} +(-1.46319 + 0.606071i) q^{31} +0.110040 q^{33} +2.64569 q^{35} +(-10.2267 + 4.23603i) q^{37} +(0.0874165 + 0.211042i) q^{39} +(1.27713 - 3.08326i) q^{41} +(-6.83895 + 6.83895i) q^{43} +(2.76965 + 1.14723i) q^{45} +10.8173i q^{47} +(0.000225088 + 0.000225088i) q^{49} +(0.178811 + 0.0681797i) q^{51} +(-4.84149 - 4.84149i) q^{53} +2.37086i q^{55} +(0.199343 + 0.0825705i) q^{57} +(8.18933 - 8.18933i) q^{59} +(0.722571 - 1.74444i) q^{61} +(-3.03521 - 7.32763i) q^{63} +(-4.54698 + 1.88342i) q^{65} +12.0951 q^{67} -0.118226 q^{69} +(-8.91550 + 3.69292i) q^{71} +(-1.64242 - 3.96516i) q^{73} +(0.0177618 - 0.0428807i) q^{75} +(4.43537 - 4.43537i) q^{77} +(-2.83076 - 1.17254i) q^{79} -8.98062i q^{81} +(1.35431 + 1.35431i) q^{83} +(-1.46896 + 3.85255i) q^{85} +(0.188704 + 0.188704i) q^{87} -13.6178i q^{89} +(12.0299 + 4.98295i) q^{91} +(0.0519775 - 0.0519775i) q^{93} +(-1.77901 + 4.29492i) q^{95} +(5.71594 + 13.7995i) q^{97} +(6.56644 - 2.71991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^11 - 8 * q^17 + 8 * q^19 + 8 * q^23 - 24 * q^27 - 32 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^35 + 16 * q^37 - 24 * q^39 - 16 * q^41 - 8 * q^49 + 16 * q^51 + 16 * q^53 + 48 * q^57 + 24 * q^59 - 24 * q^61 - 48 * q^63 - 16 * q^67 - 80 * q^69 - 64 * q^71 + 16 * q^73 - 8 * q^79 - 56 * q^83 + 16 * q^85 + 96 * q^87 - 48 * q^91 + 32 * q^93 + 24 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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