LMFDB - Embedded newform 680.2.bo.a.121.6

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			121.6
Character	$\chi$	$=$	680.121
Dual form			680.2.bo.a.281.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.46749 - 0.607854i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-1.67090 + 4.03391i) q^{7} +(-0.337282 + 0.337282i) q^{9} +(3.64531 + 1.50994i) q^{11} +1.55040i q^{13} +(1.12317 + 1.12317i) q^{15} +(-4.11036 + 0.323974i) q^{17} +(-3.33014 - 3.33014i) q^{19} +6.93538i q^{21} +(-1.81673 - 0.752515i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-2.11350 + 5.10244i) q^{27} +(3.94646 + 9.52759i) q^{29} +(5.18852 - 2.14916i) q^{31} +6.26727 q^{33} -4.36627 q^{35} +(2.96423 - 1.22783i) q^{37} +(0.942417 + 2.27520i) q^{39} +(1.52629 - 3.68478i) q^{41} +(4.89107 - 4.89107i) q^{43} +(-0.440680 - 0.182536i) q^{45} -8.02179i q^{47} +(-8.53078 - 8.53078i) q^{49} +(-5.83498 + 2.97393i) q^{51} +(8.66749 + 8.66749i) q^{53} +3.94565i q^{55} +(-6.91118 - 2.86270i) q^{57} +(6.65674 - 6.65674i) q^{59} +(2.87731 - 6.94644i) q^{61} +(-0.797001 - 1.92413i) q^{63} +(-1.43238 + 0.593312i) q^{65} +6.67116 q^{67} -3.12345 q^{69} +(7.26969 - 3.01120i) q^{71} +(2.19937 + 5.30975i) q^{73} +(-0.607854 + 1.46749i) q^{75} +(-12.1819 + 12.1819i) q^{77} +(5.87417 + 2.43316i) q^{79} +7.34151i q^{81} +(-11.3675 - 11.3675i) q^{83} +(-1.87228 - 3.67350i) q^{85} +(11.5828 + 11.5828i) q^{87} +1.49862i q^{89} +(-6.25418 - 2.59056i) q^{91} +(6.30773 - 6.30773i) q^{93} +(1.80226 - 4.35103i) q^{95} +(4.07938 + 9.84849i) q^{97} +(-1.73877 + 0.720223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.46749	−	0.607854i	0.847255	−	0.350945i	0.0835452	−	0.996504i	$-0.473376\pi$
$3$	1.46749	−	0.607854i	0.847255	−	0.350945i	0.763710	+	0.645559i	$0.223376\pi$
$4$		0			0
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$		0			0
$7$	−1.67090	+	4.03391i	−0.631541	+	1.52467i	0.206144	+	0.978522i	$0.433908\pi$
$7$	−1.67090	+	4.03391i	−0.631541	+	1.52467i	−0.837685	+	0.546153i	$0.816092\pi$
$8$		0			0
$9$	−0.337282	+	0.337282i	−0.112427	+	0.112427i
$10$		0			0
$11$	3.64531	+	1.50994i	1.09910	+	0.455263i	0.857171	−	0.515031i	$-0.172220\pi$
$11$	3.64531	+	1.50994i	1.09910	+	0.455263i	0.241930	+	0.970294i	$0.422220\pi$
$12$		0			0
$13$			1.55040i			0.430004i	0.976614	+	0.215002i	$0.0689757\pi$
$13$			1.55040i			0.430004i	−0.976614	+	0.215002i	$0.931024\pi$
$14$		0			0
$15$	1.12317	+	1.12317i	0.290001	+	0.290001i
$16$		0			0
$17$	−4.11036	+	0.323974i	−0.996908	+	0.0785754i
$17$	−4.11036	+	0.323974i	−0.996908	+	0.0785754i
$18$		0			0
$19$	−3.33014	−	3.33014i	−0.763986	−	0.763986i	0.213054	−	0.977040i	$-0.431659\pi$
$19$	−3.33014	−	3.33014i	−0.763986	−	0.763986i	−0.977040	+	0.213054i	$0.931659\pi$
$20$		0			0
$21$			6.93538i			1.51342i
$22$		0			0
$23$	−1.81673	−	0.752515i	−0.378815	−	0.156910i	0.185148	−	0.982711i	$-0.440724\pi$
$23$	−1.81673	−	0.752515i	−0.378815	−	0.156910i	−0.563962	+	0.825801i	$0.690724\pi$
$24$		0			0
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$		0			0
$27$	−2.11350	+	5.10244i	−0.406744	+	0.981966i
$28$		0			0
$29$	3.94646	+	9.52759i	0.732838	+	1.76923i	0.632898	+	0.774235i	$0.281865\pi$
$29$	3.94646	+	9.52759i	0.732838	+	1.76923i	0.0999406	+	0.994993i	$0.468135\pi$
$30$		0			0
$31$	5.18852	−	2.14916i	0.931886	−	0.386000i	0.135493	−	0.990778i	$-0.456738\pi$
$31$	5.18852	−	2.14916i	0.931886	−	0.386000i	0.796394	+	0.604778i	$0.206738\pi$
$32$		0			0
$33$	6.26727			1.09099
$34$		0			0
$35$	−4.36627			−0.738035
$36$		0			0
$37$	2.96423	−	1.22783i	0.487317	−	0.201853i	−0.125476	−	0.992097i	$-0.540046\pi$
$37$	2.96423	−	1.22783i	0.487317	−	0.201853i	0.612793	+	0.790243i	$0.290046\pi$
$38$		0			0
$39$	0.942417	+	2.27520i	0.150907	+	0.364323i
$40$		0			0
$41$	1.52629	−	3.68478i	0.238366	−	0.575466i	−0.758748	−	0.651384i	$-0.774189\pi$
$41$	1.52629	−	3.68478i	0.238366	−	0.575466i	0.997114	+	0.0759180i	$0.0241887\pi$
$42$		0			0
$43$	4.89107	−	4.89107i	0.745881	−	0.745881i	−0.227822	−	0.973703i	$-0.573160\pi$
$43$	4.89107	−	4.89107i	0.745881	−	0.745881i	0.973703	+	0.227822i	$0.0731603\pi$
$44$		0			0
$45$	−0.440680	−	0.182536i	−0.0656928	−	0.0272108i
$46$		0			0
$47$		−	8.02179i		−	1.17010i	−0.810998	−	0.585049i	$-0.801075\pi$
$47$		−	8.02179i		−	1.17010i	0.810998	−	0.585049i	$-0.198925\pi$
$48$		0			0
$49$	−8.53078	−	8.53078i	−1.21868	−	1.21868i
$50$		0			0
$51$	−5.83498	+	2.97393i	−0.817060	+	0.416433i
$52$		0			0
$53$	8.66749	+	8.66749i	1.19057	+	1.19057i	0.976907	+	0.213663i	$0.0685396\pi$
$53$	8.66749	+	8.66749i	1.19057	+	1.19057i	0.213663	+	0.976907i	$0.431460\pi$
$54$		0			0
$55$			3.94565i			0.532031i
$56$		0			0
$57$	−6.91118	−	2.86270i	−0.915408	−	0.379174i
$58$		0			0
$59$	6.65674	−	6.65674i	0.866634	−	0.866634i	−0.125465	−	0.992098i	$-0.540042\pi$
$59$	6.65674	−	6.65674i	0.866634	−	0.866634i	0.992098	+	0.125465i	$0.0400421\pi$
$60$		0			0
$61$	2.87731	−	6.94644i	0.368402	−	0.889401i	−0.625611	−	0.780135i	$-0.715150\pi$
$61$	2.87731	−	6.94644i	0.368402	−	0.889401i	0.994013	−	0.109265i	$-0.0348499\pi$
$62$		0			0
$63$	−0.797001	−	1.92413i	−0.100413	−	0.242418i
$64$		0			0
$65$	−1.43238	+	0.593312i	−0.177665	+	0.0735914i
$66$		0			0
$67$	6.67116			0.815012			0.407506	−	0.913203i	$-0.366399\pi$
$67$	6.67116			0.815012			0.407506	+	0.913203i	$0.366399\pi$
$68$		0			0
$69$	−3.12345			−0.376020
$70$		0			0
$71$	7.26969	−	3.01120i	0.862753	−	0.357364i	0.0929695	−	0.995669i	$-0.470364\pi$
$71$	7.26969	−	3.01120i	0.862753	−	0.357364i	0.769784	+	0.638305i	$0.220364\pi$
$72$		0			0
$73$	2.19937	+	5.30975i	0.257417	+	0.621459i	0.998766	−	0.0496600i	$-0.0158138\pi$
$73$	2.19937	+	5.30975i	0.257417	+	0.621459i	−0.741349	+	0.671119i	$0.765814\pi$
$74$		0			0
$75$	−0.607854	+	1.46749i	−0.0701889	+	0.169451i
$76$		0			0
$77$	−12.1819	+	12.1819i	−1.38825	+	1.38825i
$78$		0			0
$79$	5.87417	+	2.43316i	0.660896	+	0.273752i	0.687816	−	0.725886i	$-0.258570\pi$
$79$	5.87417	+	2.43316i	0.660896	+	0.273752i	−0.0269195	+	0.999638i	$0.508570\pi$
$80$		0			0
$81$			7.34151i			0.815724i
$82$		0			0
$83$	−11.3675	−	11.3675i	−1.24774	−	1.24774i	−0.956714	−	0.291031i	$-0.906002\pi$
$83$	−11.3675	−	11.3675i	−1.24774	−	1.24774i	−0.291031	−	0.956714i	$-0.593998\pi$
$84$		0			0
$85$	−1.87228	−	3.67350i	−0.203077	−	0.398447i
$86$		0			0
$87$	11.5828	+	11.5828i	1.24180	+	1.24180i
$88$		0			0
$89$			1.49862i			0.158854i	0.996841	+	0.0794269i	$0.0253090\pi$
$89$			1.49862i			0.158854i	−0.996841	+	0.0794269i	$0.974691\pi$
$90$		0			0
$91$	−6.25418	−	2.59056i	−0.655616	−	0.271565i
$92$		0			0
$93$	6.30773	−	6.30773i	0.654081	−	0.654081i
$94$		0			0
$95$	1.80226	−	4.35103i	0.184908	−	0.446407i
$96$		0			0
$97$	4.07938	+	9.84849i	0.414198	+	0.999963i	0.983998	+	0.178179i	$0.0570208\pi$
$97$	4.07938	+	9.84849i	0.414198	+	0.999963i	−0.569800	+	0.821784i	$0.692979\pi$
$98$		0			0
$99$	−1.73877	+	0.720223i	−0.174753	+	0.0723851i
$100$		0			0
$101$	−19.0954			−1.90007			−0.950033	−	0.312149i	$-0.898951\pi$
$101$	−19.0954			−1.90007			−0.950033	+	0.312149i	$0.898951\pi$
$102$		0			0
$103$	0.668860			0.0659047			0.0329524	−	0.999457i	$-0.489509\pi$
$103$	0.668860			0.0659047			0.0329524	+	0.999457i	$0.489509\pi$
$104$		0			0
$105$	−6.40746	+	2.65406i	−0.625304	+	0.259009i
$106$		0			0
$107$	−0.323027	−	0.779856i	−0.0312282	−	0.0753915i	0.907496	−	0.420061i	$-0.137991\pi$
$107$	−0.323027	−	0.779856i	−0.0312282	−	0.0753915i	−0.938724	+	0.344669i	$0.887991\pi$
$108$		0			0
$109$	−5.35444	+	12.9268i	−0.512863	+	1.23816i	0.429348	+	0.903139i	$0.358743\pi$
$109$	−5.35444	+	12.9268i	−0.512863	+	1.23816i	−0.942211	+	0.335021i	$0.891257\pi$
$110$		0			0
$111$	3.60364	−	3.60364i	0.342043	−	0.342043i
$112$		0			0
$113$	−10.7873	−	4.46823i	−1.01478	−	0.420336i	−0.187584	−	0.982249i	$-0.560066\pi$
$113$	−10.7873	−	4.46823i	−1.01478	−	0.420336i	−0.827196	+	0.561913i	$0.810066\pi$
$114$		0			0
$115$		−	1.96642i		−	0.183369i
$116$		0			0
$117$	−0.522922	−	0.522922i	−0.0483442	−	0.0483442i
$118$		0			0
$119$	5.56111	−	17.1221i	0.509786	−	1.56958i
$120$		0			0
$121$	3.23018	+	3.23018i	0.293653	+	0.293653i
$122$		0			0
$123$		−	6.33513i		−	0.571220i
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$		0			0
$127$	−10.2856	+	10.2856i	−0.912696	+	0.912696i	−0.996484	−	0.0837878i	$-0.973298\pi$
$127$	−10.2856	+	10.2856i	−0.912696	+	0.912696i	0.0837878	+	0.996484i	$0.473298\pi$
$128$		0			0
$129$	4.20454	−	10.1506i	0.370189	−	0.893715i
$130$		0			0
$131$	−3.07012	−	7.41192i	−0.268238	−	0.647583i	0.731163	−	0.682203i	$-0.238978\pi$
$131$	−3.07012	−	7.41192i	−0.268238	−	0.647583i	−0.999401	+	0.0346201i	$0.988978\pi$
$132$		0			0
$133$	18.9978	−	7.86915i	1.64732	−	0.682342i
$134$		0			0
$135$	−5.52285			−0.475331
$136$		0			0
$137$	−5.62626			−0.480684			−0.240342	−	0.970688i	$-0.577260\pi$
$137$	−5.62626			−0.480684			−0.240342	+	0.970688i	$0.577260\pi$
$138$		0			0
$139$	19.4834	−	8.07027i	1.65256	−	0.684511i	0.655084	−	0.755556i	$-0.272633\pi$
$139$	19.4834	−	8.07027i	1.65256	−	0.684511i	0.997473	+	0.0710448i	$0.0226333\pi$
$140$		0			0
$141$	−4.87608	−	11.7719i	−0.410640	−	0.991372i
$142$		0			0
$143$	−2.34100	+	5.65168i	−0.195765	+	0.472618i
$144$		0			0
$145$	−7.29210	+	7.29210i	−0.605576	+	0.605576i
$146$		0			0
$147$	−17.7043	−	7.33336i	−1.46023	−	0.604845i
$148$		0			0
$149$		−	10.5546i		−	0.864663i	−0.901715	−	0.432331i	$-0.857691\pi$
$149$		−	10.5546i		−	0.864663i	0.901715	−	0.432331i	$-0.142309\pi$
$150$		0			0
$151$	−7.44464	−	7.44464i	−0.605836	−	0.605836i	0.336019	−	0.941855i	$-0.390919\pi$
$151$	−7.44464	−	7.44464i	−0.605836	−	0.605836i	−0.941855	+	0.336019i	$0.890919\pi$
$152$		0			0
$153$	1.27708	−	1.49562i	0.103246	−	0.120914i
$154$		0			0
$155$	3.97112	+	3.97112i	0.318968	+	0.318968i
$156$		0			0
$157$		−	1.49458i		−	0.119280i	−0.998220	−	0.0596402i	$-0.981005\pi$
$157$		−	1.49458i		−	0.119280i	0.998220	−	0.0596402i	$-0.0189953\pi$
$158$		0			0
$159$	17.9880	+	7.45088i	1.42654	+	0.590893i
$160$		0			0
$161$	6.07115	−	6.07115i	0.478474	−	0.478474i
$162$		0			0
$163$	−5.69807	+	13.7563i	−0.446307	+	1.07748i	0.527388	+	0.849625i	$0.323171\pi$
$163$	−5.69807	+	13.7563i	−0.446307	+	1.07748i	−0.973695	+	0.227856i	$0.926829\pi$
$164$		0			0
$165$	2.39838	+	5.79020i	0.186714	+	0.450766i
$166$		0			0
$167$	−7.28069	+	3.01576i	−0.563397	+	0.233367i	−0.646159	−	0.763203i	$-0.723626\pi$
$167$	−7.28069	+	3.01576i	−0.563397	+	0.233367i	0.0827624	+	0.996569i	$0.473626\pi$
$168$		0			0
$169$	10.5963			0.815097
$170$		0			0
$171$	2.24639			0.171786
$172$		0			0
$173$	10.5199	−	4.35749i	0.799814	−	0.331294i	0.0549319	−	0.998490i	$-0.482506\pi$
$173$	10.5199	−	4.35749i	0.799814	−	0.331294i	0.744882	+	0.667196i	$0.232506\pi$
$174$		0			0
$175$	−1.67090	−	4.03391i	−0.126308	−	0.304935i
$176$		0			0
$177$	5.72237	−	13.8150i	0.430119	−	1.03840i
$178$		0			0
$179$	4.97401	−	4.97401i	0.371775	−	0.371775i	−0.496348	−	0.868123i	$-0.665326\pi$
$179$	4.97401	−	4.97401i	0.371775	−	0.371775i	0.868123	+	0.496348i	$0.165326\pi$
$180$		0			0
$181$	1.68857	+	0.699427i	0.125510	+	0.0519880i	0.444555	−	0.895752i	$-0.353362\pi$
$181$	1.68857	+	0.699427i	0.125510	+	0.0519880i	−0.319044	+	0.947740i	$0.603362\pi$
$182$		0			0
$183$		−	11.9428i		−	0.882838i
$184$		0			0
$185$	2.26873	+	2.26873i	0.166800	+	0.166800i
$186$		0			0
$187$	−15.4727	−	5.02539i	−1.13148	−	0.367493i
$188$		0			0
$189$	−17.0514	−	17.0514i	−1.24030	−	1.24030i
$190$		0			0
$191$			3.68371i			0.266544i	0.991080	+	0.133272i	$0.0425484\pi$
$191$			3.68371i			0.266544i	−0.991080	+	0.133272i	$0.957452\pi$
$192$		0			0
$193$	2.89719	+	1.20006i	0.208544	+	0.0863819i	0.484511	−	0.874785i	$-0.338998\pi$
$193$	2.89719	+	1.20006i	0.208544	+	0.0863819i	−0.275966	+	0.961167i	$0.588998\pi$
$194$		0			0
$195$	−1.74136	+	1.74136i	−0.124701	+	0.124701i
$196$		0			0
$197$	−5.80103	+	14.0049i	−0.413307	+	0.997810i	0.570937	+	0.820994i	$0.306580\pi$
$197$	−5.80103	+	14.0049i	−0.413307	+	0.997810i	−0.984244	+	0.176817i	$0.943420\pi$
$198$		0			0
$199$	−2.00499	−	4.84047i	−0.142130	−	0.343132i	0.836745	−	0.547593i	$-0.184456\pi$
$199$	−2.00499	−	4.84047i	−0.142130	−	0.343132i	−0.978875	+	0.204461i	$0.934456\pi$
$200$		0			0
$201$	9.78985	−	4.05509i	0.690523	−	0.286024i
$202$		0			0
$203$	−45.0276			−3.16032
$204$		0			0
$205$	3.98838			0.278560
$206$		0			0
$207$	0.866561	−	0.358941i	0.0602302	−	0.0249481i
$208$		0			0
$209$	−7.11108	−	17.1677i	−0.491884	−	1.18751i
$210$		0			0
$211$	−5.23435	+	12.6368i	−0.360347	+	0.869955i	0.634902	+	0.772593i	$0.281041\pi$
$211$	−5.23435	+	12.6368i	−0.360347	+	0.869955i	−0.995249	+	0.0973624i	$0.968959\pi$
$212$		0			0
$213$	8.83781	−	8.83781i	0.605557	−	0.605557i
$214$		0			0
$215$	6.39049	+	2.64703i	0.435828	+	0.180526i
$216$		0			0
$217$			24.5211i			1.66460i
$218$		0			0
$219$	6.45511	+	6.45511i	0.436196	+	0.436196i
$220$		0			0
$221$	−0.502290	−	6.37270i	−0.0337877	−	0.428674i
$222$		0			0
$223$	14.0307	+	14.0307i	0.939565	+	0.939565i	0.998275	−	0.0587100i	$-0.0186987\pi$
$223$	14.0307	+	14.0307i	0.939565	+	0.939565i	−0.0587100	+	0.998275i	$0.518699\pi$
$224$		0			0
$225$		−	0.476989i		−	0.0317993i
$226$		0			0
$227$	−20.2103	−	8.37137i	−1.34140	−	0.555627i	−0.407516	−	0.913198i	$-0.633605\pi$
$227$	−20.2103	−	8.37137i	−1.34140	−	0.555627i	−0.933886	+	0.357571i	$0.883605\pi$
$228$		0			0
$229$	16.3720	−	16.3720i	1.08189	−	1.08189i	0.0855592	−	0.996333i	$-0.472732\pi$
$229$	16.3720	−	16.3720i	1.08189	−	1.08189i	0.996333	−	0.0855592i	$-0.0272677\pi$
$230$		0			0
$231$	−10.4720	+	25.2816i	−0.689006	+	1.66341i
$232$		0			0
$233$	−1.92852	−	4.65586i	−0.126342	−	0.305015i	0.848034	−	0.529941i	$-0.177786\pi$
$233$	−1.92852	−	4.65586i	−0.126342	−	0.305015i	−0.974376	+	0.224926i	$0.927786\pi$
$234$		0			0
$235$	7.41117	−	3.06981i	0.483451	−	0.200252i
$236$		0			0
$237$	10.0993			0.656019
$238$		0			0
$239$	18.0660			1.16859			0.584297	−	0.811540i	$-0.301370\pi$
$239$	18.0660			1.16859			0.584297	+	0.811540i	$0.301370\pi$
$240$		0			0
$241$	15.5932	−	6.45890i	1.00444	−	0.416054i	0.181019	−	0.983480i	$-0.442061\pi$
$241$	15.5932	−	6.45890i	1.00444	−	0.416054i	0.823425	+	0.567425i	$0.192061\pi$
$242$		0			0
$243$	−1.87794	−	4.53374i	−0.120470	−	0.290839i
$244$		0			0
$245$	4.61682	−	11.1460i	0.294958	−	0.712092i
$246$		0			0
$247$	5.16305	−	5.16305i	0.328517	−	0.328517i
$248$		0			0
$249$	−23.5915	−	9.77190i	−1.49505	−	0.619269i
$250$		0			0
$251$			8.94113i			0.564359i	0.959362	+	0.282179i	$0.0910574\pi$
$251$			8.94113i			0.564359i	−0.959362	+	0.282179i	$0.908943\pi$
$252$		0			0
$253$	−5.48629	−	5.48629i	−0.344920	−	0.344920i
$254$		0			0
$255$	−4.98050	−	4.25274i	−0.311891	−	0.266317i
$256$		0			0
$257$	0.221345	+	0.221345i	0.0138071	+	0.0138071i	0.713977	−	0.700170i	$-0.246892\pi$
$257$	0.221345	+	0.221345i	0.0138071	+	0.0138071i	−0.700170	+	0.713977i	$0.746892\pi$
$258$		0			0
$259$			14.0090i			0.870478i
$260$		0			0
$261$	−4.54456	−	1.88242i	−0.281301	−	0.116519i
$262$		0			0
$263$	5.55489	−	5.55489i	0.342529	−	0.342529i	−0.514788	−	0.857317i	$-0.672129\pi$
$263$	5.55489	−	5.55489i	0.342529	−	0.342529i	0.857317	+	0.514788i	$0.172129\pi$
$264$		0			0
$265$	−4.69081	+	11.3246i	−0.288154	+	0.695666i
$266$		0			0
$267$	0.910944	+	2.19921i	0.0557489	+	0.134590i
$268$		0			0
$269$	−5.94376	+	2.46198i	−0.362397	+	0.150110i	−0.556450	−	0.830881i	$-0.687837\pi$
$269$	−5.94376	+	2.46198i	−0.362397	+	0.150110i	0.194052	+	0.980991i	$0.437837\pi$
$270$		0			0
$271$	21.9350			1.33246			0.666229	−	0.745747i	$-0.267907\pi$
$271$	21.9350			1.33246			0.666229	+	0.745747i	$0.267907\pi$
$272$		0			0
$273$	−10.7526			−0.650778
$274$		0			0
$275$	−3.64531	+	1.50994i	−0.219820	+	0.0910525i
$276$		0			0
$277$	−10.4006	−	25.1093i	−0.624912	−	1.50867i	−0.845870	−	0.533389i	$-0.820918\pi$
$277$	−10.4006	−	25.1093i	−0.624912	−	1.50867i	0.220958	−	0.975283i	$-0.429082\pi$
$278$		0			0
$279$	−1.02512	+	2.47487i	−0.0613726	+	0.148167i
$280$		0			0
$281$	−2.96185	+	2.96185i	−0.176689	+	0.176689i	−0.789911	−	0.613222i	$-0.789873\pi$
$281$	−2.96185	+	2.96185i	−0.176689	+	0.176689i	0.613222	+	0.789911i	$0.289873\pi$
$282$		0			0
$283$	6.23839	+	2.58402i	0.370834	+	0.153604i	0.560314	−	0.828280i	$-0.310680\pi$
$283$	6.23839	+	2.58402i	0.370834	+	0.153604i	−0.189481	+	0.981884i	$0.560680\pi$
$284$		0			0
$285$		−	7.48060i		−	0.443113i
$286$		0			0
$287$	12.3138	+	12.3138i	0.726861	+	0.726861i
$288$		0			0
$289$	16.7901	−	2.66330i	0.987652	−	0.156665i
$290$		0			0
$291$	11.9729	+	11.9729i	0.701863	+	0.701863i
$292$		0			0
$293$			17.6481i			1.03101i	0.856885	+	0.515507i	$0.172396\pi$
$293$			17.6481i			1.03101i	−0.856885	+	0.515507i	$0.827604\pi$
$294$		0			0
$295$	8.69745	+	3.60260i	0.506385	+	0.209752i
$296$		0			0
$297$	−15.4087	+	15.4087i	−0.894105	+	0.894105i
$298$		0			0
$299$	1.16670	−	2.81666i	0.0674719	−	0.162892i
$300$		0			0
$301$	11.5576	+	27.9026i	0.666172	+	1.60828i
$302$		0			0
$303$	−28.0223	+	11.6072i	−1.60984	+	0.666818i
$304$		0			0
$305$	7.51878			0.430524
$306$		0			0
$307$	−15.2841			−0.872311			−0.436155	−	0.899871i	$-0.643660\pi$
$307$	−15.2841			−0.872311			−0.436155	+	0.899871i	$0.643660\pi$
$308$		0			0
$309$	0.981545	−	0.406569i	0.0558381	−	0.0231289i
$310$		0			0
$311$	−11.7364	−	28.3343i	−0.665513	−	1.60669i	−0.789035	−	0.614348i	$-0.789419\pi$
$311$	−11.7364	−	28.3343i	−0.665513	−	1.60669i	0.123523	−	0.992342i	$-0.460581\pi$
$312$		0			0
$313$	4.68300	−	11.3058i	0.264699	−	0.639039i	−0.734519	−	0.678588i	$-0.762592\pi$
$313$	4.68300	−	11.3058i	0.264699	−	0.639039i	0.999218	+	0.0395489i	$0.0125921\pi$
$314$		0			0
$315$	1.47267	−	1.47267i	0.0829753	−	0.0829753i
$316$		0			0
$317$	13.8509	+	5.73724i	0.777945	+	0.322236i	0.736086	−	0.676888i	$-0.236672\pi$
$317$	13.8509	+	5.73724i	0.777945	+	0.322236i	0.0418594	+	0.999124i	$0.486672\pi$
$318$		0			0
$319$			40.6899i			2.27820i
$320$		0			0
$321$	−0.948077	−	0.948077i	−0.0529165	−	0.0529165i
$322$		0			0
$323$	14.7669	+	12.6092i	0.821654	+	0.701593i
$324$		0			0
$325$	−1.09630	−	1.09630i	−0.0608117	−	0.0608117i
$326$		0			0
$327$			22.2246i			1.22902i
$328$		0			0
$329$	32.3592	+	13.4036i	1.78402	+	0.738965i
$330$		0			0
$331$	7.81279	−	7.81279i	0.429430	−	0.429430i	−0.459004	−	0.888434i	$-0.651794\pi$
$331$	7.81279	−	7.81279i	0.429430	−	0.429430i	0.888434	+	0.459004i	$0.151794\pi$
$332$		0			0
$333$	−0.585659	+	1.41391i	−0.0320939	+	0.0774816i
$334$		0			0
$335$	2.55294	+	6.16335i	0.139482	+	0.336740i
$336$		0			0
$337$	1.38300	−	0.572856i	0.0753367	−	0.0312055i	−0.344697	−	0.938714i	$-0.612018\pi$
$337$	1.38300	−	0.572856i	0.0753367	−	0.0312055i	0.420034	+	0.907509i	$0.362018\pi$
$338$		0			0
$339$	−18.5462			−1.00729
$340$		0			0
$341$	22.1588			1.19997
$342$		0			0
$343$	20.4291	−	8.46201i	1.10307	−	0.456905i
$344$		0			0
$345$	−1.19529	−	2.88569i	−0.0643524	−	0.155361i
$346$		0			0
$347$	5.42311	−	13.0925i	0.291128	−	0.702845i	−0.708869	−	0.705340i	$-0.750794\pi$
$347$	5.42311	−	13.0925i	0.291128	−	0.702845i	0.999997	+	0.00249540i	$0.000794312\pi$
$348$		0			0
$349$	−21.1619	+	21.1619i	−1.13277	+	1.13277i	−0.143055	+	0.989715i	$0.545693\pi$
$349$	−21.1619	+	21.1619i	−1.13277	+	1.13277i	−0.989715	+	0.143055i	$0.954307\pi$
$350$		0			0
$351$	−7.91083	−	3.27677i	−0.422249	−	0.174901i
$352$		0			0
$353$			30.3154i			1.61353i	0.590875	+	0.806763i	$0.298783\pi$
$353$			30.3154i			1.61353i	−0.590875	+	0.806763i	$0.701217\pi$
$354$		0			0
$355$	5.56398	+	5.56398i	0.295305	+	0.295305i
$356$		0			0
$357$	−2.24689	−	28.5069i	−0.118918	−	1.50875i
$358$		0			0
$359$	16.4428	+	16.4428i	0.867819	+	0.867819i	0.992231	−	0.124412i	$-0.0397044\pi$
$359$	16.4428	+	16.4428i	0.867819	+	0.867819i	−0.124412	+	0.992231i	$0.539704\pi$
$360$		0			0
$361$			3.17963i			0.167349i
$362$		0			0
$363$	6.70373	+	2.77678i	0.351854	+	0.145743i
$364$		0			0
$365$	−4.06391	+	4.06391i	−0.212715	+	0.212715i
$366$		0			0
$367$	−7.79215	+	18.8119i	−0.406747	+	0.981974i	0.579241	+	0.815157i	$0.303349\pi$
$367$	−7.79215	+	18.8119i	−0.406747	+	0.981974i	−0.985988	+	0.166818i	$0.946651\pi$
$368$		0			0
$369$	0.728022	+	1.75760i	0.0378993	+	0.0914970i
$370$		0			0
$371$	−49.4464	+	20.4814i	−2.56713	+	1.06334i
$372$		0			0
$373$	−7.82030			−0.404920			−0.202460	−	0.979291i	$-0.564894\pi$
$373$	−7.82030			−0.404920			−0.202460	+	0.979291i	$0.564894\pi$
$374$		0			0
$375$	−1.58840			−0.0820246
$376$		0			0
$377$	−14.7716	+	6.11859i	−0.760775	+	0.315123i
$378$		0			0
$379$	−6.30403	−	15.2193i	−0.323816	−	0.781762i	−0.999026	−	0.0441356i	$-0.985947\pi$
$379$	−6.30403	−	15.2193i	−0.323816	−	0.781762i	0.675209	−	0.737626i	$-0.264053\pi$
$380$		0			0
$381$	−8.84183	+	21.3461i	−0.452981	+	1.09359i
$382$		0			0
$383$	−19.4193	+	19.4193i	−0.992281	+	0.992281i	−0.999970	−	0.00768945i	$-0.997552\pi$
$383$	−19.4193	+	19.4193i	−0.992281	+	0.992281i	0.00768945	+	0.999970i	$0.497552\pi$
$384$		0			0
$385$	−15.9164	−	6.59279i	−0.811175	−	0.336000i
$386$		0			0
$387$			3.29934i			0.167715i
$388$		0			0
$389$	−2.10200	−	2.10200i	−0.106575	−	0.106575i	0.651808	−	0.758384i	$-0.274011\pi$
$389$	−2.10200	−	2.10200i	−0.106575	−	0.106575i	−0.758384	+	0.651808i	$0.774011\pi$
$390$		0			0
$391$	7.71121	+	2.50453i	0.389973	+	0.126660i
$392$		0			0
$393$	−9.01073	−	9.01073i	−0.454531	−	0.454531i
$394$		0			0
$395$			6.35816i			0.319914i
$396$		0			0
$397$	6.74218	+	2.79270i	0.338380	+	0.140162i	0.545402	−	0.838175i	$-0.316377\pi$
$397$	6.74218	+	2.79270i	0.338380	+	0.140162i	−0.207022	+	0.978336i	$0.566377\pi$
$398$		0			0
$399$	23.0958	−	23.0958i	1.15624	−	1.15624i
$400$		0			0
$401$	7.94504	−	19.1810i	0.396756	−	0.957855i	−0.591674	−	0.806178i	$-0.701533\pi$
$401$	7.94504	−	19.1810i	0.396756	−	0.957855i	0.988430	−	0.151677i	$-0.0484674\pi$
$402$		0			0
$403$	3.33205	+	8.04429i	0.165981	+	0.400715i
$404$		0			0
$405$	−6.78267	+	2.80948i	−0.337034	+	0.139604i
$406$		0			0
$407$	12.6595			0.627507
$408$		0			0
$409$	−1.91681			−0.0947799			−0.0473900	−	0.998876i	$-0.515090\pi$
$409$	−1.91681			−0.0947799			−0.0473900	+	0.998876i	$0.515090\pi$
$410$		0			0
$411$	−8.25647	+	3.41994i	−0.407262	+	0.168693i
$412$		0			0
$413$	15.7299	+	37.9754i	0.774020	+	1.86865i
$414$		0			0
$415$	6.15204	−	14.8523i	0.301992	−	0.729073i
$416$		0			0
$417$	23.6861	−	23.6861i	1.15991	−	1.15991i
$418$		0			0
$419$	−2.78902	−	1.15525i	−0.136252	−	0.0564376i	0.313515	−	0.949583i	$-0.398493\pi$
$419$	−2.78902	−	1.15525i	−0.136252	−	0.0564376i	−0.449768	+	0.893146i	$0.648493\pi$
$420$		0			0
$421$		−	10.6132i		−	0.517258i	−0.965977	−	0.258629i	$-0.916729\pi$
$421$		−	10.6132i		−	0.517258i	0.965977	−	0.258629i	$-0.0832707\pi$
$422$		0			0
$423$	2.70561	+	2.70561i	0.131551	+	0.131551i
$424$		0			0
$425$	2.67738	−	3.13555i	0.129872	−	0.152096i
$426$		0			0
$427$	23.2136	+	23.2136i	1.12339	+	1.12339i
$428$		0			0
$429$			9.71677i			0.469130i
$430$		0			0
$431$	−11.3842	−	4.71551i	−0.548360	−	0.227138i	0.0912632	−	0.995827i	$-0.470910\pi$
$431$	−11.3842	−	4.71551i	−0.548360	−	0.227138i	−0.639623	+	0.768689i	$0.720910\pi$
$432$		0			0
$433$	23.9426	−	23.9426i	1.15061	−	1.15061i	0.164174	−	0.986431i	$-0.447504\pi$
$433$	23.9426	−	23.9426i	1.15061	−	1.15061i	0.986431	−	0.164174i	$-0.0524960\pi$
$434$		0			0
$435$	−6.26855	+	15.1336i	−0.300554	+	0.725601i
$436$		0			0
$437$	3.54399	+	8.55594i	0.169532	+	0.409286i
$438$		0			0
$439$	8.35988	−	3.46278i	0.398995	−	0.165269i	−0.174157	−	0.984718i	$-0.555720\pi$
$439$	8.35988	−	3.46278i	0.398995	−	0.165269i	0.573153	+	0.819449i	$0.305720\pi$
$440$		0			0
$441$	5.75456			0.274027
$442$		0			0
$443$	−25.6397			−1.21818			−0.609090	−	0.793101i	$-0.708465\pi$
$443$	−25.6397			−1.21818			−0.609090	+	0.793101i	$0.708465\pi$
$444$		0			0
$445$	−1.38455	+	0.573498i	−0.0656339	+	0.0271864i
$446$		0			0
$447$	−6.41563	−	15.4887i	−0.303449	−	0.732590i
$448$		0			0
$449$	4.93839	−	11.9223i	0.233057	−	0.562649i	−0.763477	−	0.645835i	$-0.776509\pi$
$449$	4.93839	−	11.9223i	0.233057	−	0.562649i	0.996534	+	0.0831857i	$0.0265095\pi$
$450$		0			0
$451$	11.1276	−	11.1276i	0.523976	−	0.523976i
$452$		0			0
$453$	−15.4502	−	6.39967i	−0.725913	−	0.300683i
$454$		0			0
$455$		−	6.76947i		−	0.317358i
$456$		0			0
$457$	28.1021	+	28.1021i	1.31456	+	1.31456i	0.918016	+	0.396544i	$0.129791\pi$
$457$	28.1021	+	28.1021i	1.31456	+	1.31456i	0.396544	+	0.918016i	$0.370209\pi$
$458$		0			0
$459$	7.03419	−	21.6576i	0.328328	−	1.01089i
$460$		0			0
$461$	−4.54917	−	4.54917i	−0.211876	−	0.211876i	0.593188	−	0.805064i	$-0.297869\pi$
$461$	−4.54917	−	4.54917i	−0.211876	−	0.211876i	−0.805064	+	0.593188i	$0.797869\pi$
$462$		0			0
$463$		−	20.2801i		−	0.942498i	−0.882000	−	0.471249i	$-0.843803\pi$
$463$		−	20.2801i		−	0.942498i	0.882000	−	0.471249i	$-0.156197\pi$
$464$		0			0
$465$	8.24144	+	3.41372i	0.382188	+	0.158307i
$466$		0			0
$467$	23.6662	−	23.6662i	1.09514	−	1.09514i	0.100173	−	0.994970i	$-0.468061\pi$
$467$	23.6662	−	23.6662i	1.09514	−	1.09514i	0.994970	−	0.100173i	$-0.0319395\pi$
$468$		0			0
$469$	−11.1468	+	26.9108i	−0.514713	+	1.24263i
$470$		0			0
$471$	−0.908486	−	2.19328i	−0.0418608	−	0.101061i
$472$		0			0
$473$	25.2146	−	10.4442i	1.15937	−	0.480227i
$474$		0			0
$475$	4.70953			0.216088
$476$		0			0
$477$	−5.84678			−0.267706
$478$		0			0
$479$	−36.5438	+	15.1369i	−1.66973	+	0.691624i	−0.998756	−	0.0498594i	$-0.984123\pi$
$479$	−36.5438	+	15.1369i	−1.66973	+	0.691624i	−0.670971	+	0.741483i	$0.734123\pi$
$480$		0			0
$481$	1.90362	+	4.59575i	0.0867977	+	0.209548i
$482$		0			0
$483$	5.21898	−	12.5997i	0.237472	−	0.573307i
$484$		0			0
$485$	−7.53771	+	7.53771i	−0.342270	+	0.342270i
$486$		0			0
$487$	25.1478	+	10.4165i	1.13955	+	0.472019i	0.871018	−	0.491251i	$-0.163460\pi$
$487$	25.1478	+	10.4165i	1.13955	+	0.472019i	0.268536	+	0.963270i	$0.413460\pi$
$488$		0			0
$489$			23.6509i			1.06953i
$490$		0			0
$491$	−12.9721	−	12.9721i	−0.585420	−	0.585420i	0.350967	−	0.936388i	$-0.385853\pi$
$491$	−12.9721	−	12.9721i	−0.585420	−	0.585420i	−0.936388	+	0.350967i	$0.885853\pi$
$492$		0			0
$493$	−19.3080	−	37.8832i	−0.869590	−	1.70618i
$494$		0			0
$495$	−1.33080	−	1.33080i	−0.0598149	−	0.0598149i
$496$		0			0
$497$			34.3567i			1.54111i
$498$		0			0
$499$	4.31220	+	1.78617i	0.193041	+	0.0799601i	0.477110	−	0.878844i	$-0.341684\pi$
$499$	4.31220	+	1.78617i	0.193041	+	0.0799601i	−0.284069	+	0.958804i	$0.591684\pi$
$500$		0			0
$501$	−8.85119	+	8.85119i	−0.395442	+	0.395442i
$502$		0			0
$503$	6.59330	−	15.9176i	0.293981	−	0.709732i	−0.706018	−	0.708194i	$-0.749510\pi$
$503$	6.59330	−	15.9176i	0.293981	−	0.709732i	0.999999	−	0.00153827i	$-0.000489647\pi$
$504$		0			0
$505$	−7.30750	−	17.6419i	−0.325180	−	0.785053i
$506$		0			0
$507$	15.5499	−	6.44098i	0.690595	−	0.286054i
$508$		0			0
$509$	−30.5288			−1.35317			−0.676583	−	0.736367i	$-0.736540\pi$
$509$	−30.5288			−1.35317			−0.676583	+	0.736367i	$0.736540\pi$
$510$		0			0
$511$	−25.0940			−1.11009
$512$		0			0
$513$	24.0301	−	9.95359i	1.06095	−	0.439462i
$514$		0			0
$515$	0.255962	+	0.617946i	0.0112790	+	0.0272300i
$516$		0			0
$517$	12.1124	−	29.2419i	0.532702	−	1.28606i
$518$		0			0
$519$	12.7891	−	12.7891i	0.561381	−	0.561381i
$520$		0			0
$521$	−6.55302	−	2.71435i	−0.287093	−	0.118918i	0.234490	−	0.972119i	$-0.424658\pi$
$521$	−6.55302	−	2.71435i	−0.287093	−	0.118918i	−0.521583	+	0.853201i	$0.674658\pi$
$522$		0			0
$523$		−	24.7012i		−	1.08011i	−0.841631	−	0.540053i	$-0.818404\pi$
$523$		−	24.7012i		−	1.08011i	0.841631	−	0.540053i	$-0.181596\pi$
$524$		0			0
$525$	−4.90406	−	4.90406i	−0.214031	−	0.214031i
$526$		0			0
$527$	−20.6304	+	10.5148i	−0.898675	+	0.458030i
$528$		0			0
$529$	−13.5292	−	13.5292i	−0.588227	−	0.588227i
$530$		0			0
$531$			4.49040i			0.194867i
$532$		0			0
$533$	5.71288	+	2.36635i	0.247452	+	0.102498i
$534$		0			0
$535$	0.596876	−	0.596876i	0.0258052	−	0.0258052i
$536$		0			0
$537$	4.27584	−	10.3228i	0.184516	−	0.445461i
$538$		0			0
$539$	−18.2164	−	43.9782i	−0.784635	−	1.89428i
$540$		0			0
$541$	−31.3452	+	12.9836i	−1.34764	+	0.558209i	−0.935633	−	0.352974i	$-0.885170\pi$
$541$	−31.3452	+	12.9836i	−1.34764	+	0.558209i	−0.412002	+	0.911183i	$0.635170\pi$
$542$		0			0
$543$	2.90310			0.124584
$544$		0			0
$545$	−13.9918			−0.599344
$546$		0			0
$547$	10.0303	−	4.15469i	0.428865	−	0.177642i	−0.157800	−	0.987471i	$-0.550440\pi$
$547$	10.0303	−	4.15469i	0.428865	−	0.177642i	0.586666	+	0.809829i	$0.300440\pi$
$548$		0			0
$549$	1.37245	+	3.31338i	0.0585746	+	0.141411i
$550$		0			0
$551$	18.5859	−	44.8704i	0.791787	−	1.91154i
$552$		0			0
$553$	−19.6303	+	19.6303i	−0.834766	+	0.834766i
$554$		0			0
$555$	4.70838	+	1.95028i	0.199860	+	0.0827846i
$556$		0			0
$557$		−	39.0477i		−	1.65451i	−0.561829	−	0.827253i	$-0.689902\pi$
$557$		−	39.0477i		−	1.65451i	0.561829	−	0.827253i	$-0.310098\pi$
$558$		0			0
$559$	7.58312	+	7.58312i	0.320732	+	0.320732i
$560$		0			0
$561$	−25.7607	+	2.03043i	−1.08762	+	0.0857250i
$562$		0			0
$563$	19.7750	+	19.7750i	0.833419	+	0.833419i	0.987983	−	0.154564i	$-0.0493973\pi$
$563$	19.7750	+	19.7750i	0.833419	+	0.833419i	−0.154564	+	0.987983i	$0.549397\pi$
$564$		0			0
$565$		−	11.6760i		−	0.491215i
$566$		0			0
$567$	−29.6150	−	12.2669i	−1.24371	−	0.515163i
$568$		0			0
$569$	−25.4541	+	25.4541i	−1.06709	+	1.06709i	−0.0695089	+	0.997581i	$0.522143\pi$
$569$	−25.4541	+	25.4541i	−1.06709	+	1.06709i	−0.997581	+	0.0695089i	$0.977857\pi$
$570$		0			0
$571$	5.03077	−	12.1453i	0.210531	−	0.508267i	−0.782974	−	0.622054i	$-0.786298\pi$
$571$	5.03077	−	12.1453i	0.210531	−	0.508267i	0.993505	+	0.113788i	$0.0362983\pi$
$572$		0			0
$573$	2.23916	+	5.40581i	0.0935422	+	0.225831i
$574$		0			0
$575$	1.81673	−	0.752515i	0.0757629	−	0.0313820i
$576$		0			0
$577$	−3.15568			−0.131373			−0.0656864	−	0.997840i	$-0.520924\pi$
$577$	−3.15568			−0.131373			−0.0656864	+	0.997840i	$0.520924\pi$
$578$		0			0
$579$	4.98106			0.207006
$580$		0			0
$581$	64.8494	−	26.8615i	2.69041	−	1.11440i
$582$		0			0
$583$	18.5083	+	44.6830i	0.766535	+	1.85058i
$584$		0			0
$585$	0.283004	−	0.683231i	0.0117008	−	0.0282481i
$586$		0			0
$587$	−11.6311	+	11.6311i	−0.480067	+	0.480067i	−0.905153	−	0.425086i	$-0.860244\pi$
$587$	−11.6311	+	11.6311i	−0.480067	+	0.480067i	0.425086	+	0.905153i	$0.360244\pi$
$588$		0			0
$589$	−24.4355	−	10.1215i	−1.00685	−	0.417049i
$590$		0			0
$591$			24.0783i			0.990448i
$592$		0			0
$593$	−2.18100	−	2.18100i	−0.0895631	−	0.0895631i	0.660906	−	0.750469i	$-0.270172\pi$
$593$	−2.18100	−	2.18100i	−0.0895631	−	0.0895631i	−0.750469	+	0.660906i	$0.770172\pi$
$594$		0			0
$595$	17.9469	−	1.41456i	0.735753	−	0.0579913i
$596$		0			0
$597$	−5.88460	−	5.88460i	−0.240841	−	0.240841i
$598$		0			0
$599$			10.5002i			0.429028i	0.976721	+	0.214514i	$0.0688167\pi$
$599$			10.5002i			0.429028i	−0.976721	+	0.214514i	$0.931183\pi$
$600$		0			0
$601$	31.3363	+	12.9799i	1.27823	+	0.529461i	0.915457	−	0.402415i	$-0.131829\pi$
$601$	31.3363	+	12.9799i	1.27823	+	0.529461i	0.362776	+	0.931876i	$0.381829\pi$
$602$		0			0
$603$	−2.25006	+	2.25006i	−0.0916296	+	0.0916296i
$604$		0			0
$605$	−1.74816	+	4.22043i	−0.0710728	+	0.171585i
$606$		0			0
$607$	−0.558189	−	1.34759i	−0.0226562	−	0.0546969i	0.912147	−	0.409864i	$-0.134424\pi$
$607$	−0.558189	−	1.34759i	−0.0226562	−	0.0546969i	−0.934803	+	0.355167i	$0.884424\pi$
$608$		0			0
$609$	−66.0775	+	27.3702i	−2.67759	+	1.10910i
$610$		0			0
$611$	12.4370			0.503147
$612$		0			0
$613$	−25.4615			−1.02838			−0.514190	−	0.857676i	$-0.671907\pi$
$613$	−25.4615			−1.02838			−0.514190	+	0.857676i	$0.671907\pi$
$614$		0			0
$615$	5.85290	−	2.42435i	0.236012	−	0.0977593i
$616$		0			0
$617$	−16.2086	−	39.1309i	−0.652532	−	1.57535i	−0.809092	−	0.587682i	$-0.800040\pi$
$617$	−16.2086	−	39.1309i	−0.652532	−	1.57535i	0.156560	−	0.987668i	$-0.449960\pi$
$618$		0			0
$619$	−15.3557	+	37.0720i	−0.617198	+	1.49005i	0.237745	+	0.971328i	$0.423592\pi$
$619$	−15.3557	+	37.0720i	−0.617198	+	1.49005i	−0.854944	+	0.518721i	$0.826408\pi$
$620$		0			0
$621$	7.67933	−	7.67933i	0.308161	−	0.308161i
$622$		0			0
$623$	−6.04531	−	2.50405i	−0.242200	−	0.100323i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$		0			0
$627$	−20.8709	−	20.8709i	−0.833502	−	0.833502i
$628$		0			0
$629$	−11.7863	+	6.00714i	−0.469950	+	0.239520i
$630$		0			0
$631$	−16.8532	−	16.8532i	−0.670915	−	0.670915i	0.287012	−	0.957927i	$-0.407338\pi$
$631$	−16.8532	−	16.8532i	−0.670915	−	0.670915i	−0.957927	+	0.287012i	$0.907338\pi$
$632$		0			0
$633$			21.7261i			0.863536i
$634$		0			0
$635$	−13.4387	−	5.56650i	−0.533300	−	0.220900i
$636$		0			0
$637$	13.2261	−	13.2261i	0.524038	−	0.524038i
$638$		0			0
$639$	−1.43631	+	3.46756i	−0.0568196	+	0.137175i
$640$		0			0
$641$	−7.01505	−	16.9358i	−0.277078	−	0.668925i	0.722674	−	0.691189i	$-0.242913\pi$
$641$	−7.01505	−	16.9358i	−0.277078	−	0.668925i	−0.999752	+	0.0222638i	$0.992913\pi$
$642$		0			0
$643$	−15.2451	+	6.31474i	−0.601209	+	0.249029i	−0.662465	−	0.749093i	$-0.730490\pi$
$643$	−15.2451	+	6.31474i	−0.601209	+	0.249029i	0.0612555	+	0.998122i	$0.480490\pi$
$644$		0			0
$645$	10.9870			0.432612
$646$		0			0
$647$	5.26603			0.207029			0.103515	−	0.994628i	$-0.466991\pi$
$647$	5.26603			0.207029			0.103515	+	0.994628i	$0.466991\pi$
$648$		0			0
$649$	34.3171	−	14.2146i	1.34706	−	0.557972i
$650$		0			0
$651$	14.9052	+	35.9844i	0.584182	+	1.41034i
$652$		0			0
$653$	−8.31888	+	20.0836i	−0.325543	+	0.785931i	0.673369	+	0.739306i	$0.264846\pi$
$653$	−8.31888	+	20.0836i	−0.325543	+	0.785931i	−0.998912	+	0.0466244i	$0.985154\pi$
$654$		0			0
$655$	5.67284	−	5.67284i	0.221656	−	0.221656i
$656$		0			0
$657$	−2.53269	−	1.04908i	−0.0988098	−	0.0409284i
$658$		0			0
$659$			32.8555i			1.27987i	0.768430	+	0.639934i	$0.221038\pi$
$659$			32.8555i			1.27987i	−0.768430	+	0.639934i	$0.778962\pi$
$660$		0			0
$661$	25.9634	+	25.9634i	1.00986	+	1.00986i	0.999951	+	0.00991014i	$0.00315455\pi$
$661$	25.9634	+	25.9634i	1.00986	+	1.00986i	0.00991014	+	0.999951i	$0.496845\pi$
$662$		0			0
$663$	−4.61078	−	9.04655i	−0.179068	−	0.351339i
$664$		0			0
$665$	14.5403	+	14.5403i	0.563848	+	0.563848i
$666$		0			0
$667$		−	20.2788i		−	0.785200i
$668$		0			0
$669$	29.1185	+	12.0613i	1.12579	+	0.466316i
$670$		0			0
$671$	20.9774	−	20.9774i	0.809822	−	0.809822i
$672$		0			0
$673$	9.27659	−	22.3957i	0.357586	−	0.863290i	−0.638052	−	0.769993i	$-0.720260\pi$
$673$	9.27659	−	22.3957i	0.357586	−	0.863290i	0.995638	−	0.0932966i	$-0.0297405\pi$
$674$		0			0
$675$	−2.11350	−	5.10244i	−0.0813487	−	0.196393i
$676$		0			0
$677$	16.7557	−	6.94043i	0.643973	−	0.266742i	−0.0367037	−	0.999326i	$-0.511686\pi$
$677$	16.7557	−	6.94043i	0.643973	−	0.266742i	0.680677	+	0.732584i	$0.261686\pi$
$678$		0			0
$679$	−46.5442			−1.78620
$680$		0			0
$681$	−34.7469			−1.33150
$682$		0			0
$683$	28.4240	−	11.7736i	1.08761	−	0.450505i	0.234440	−	0.972131i	$-0.424674\pi$
$683$	28.4240	−	11.7736i	1.08761	−	0.450505i	0.853174	+	0.521626i	$0.174674\pi$
$684$		0			0
$685$	−2.15308	−	5.19799i	−0.0822648	−	0.198605i
$686$		0			0
$687$	14.0739	−	33.9775i	0.536955	−	1.29632i
$688$		0			0
$689$	−13.4381	+	13.4381i	−0.511950	+	0.511950i
$690$		0			0
$691$	−9.30901	−	3.85592i	−0.354131	−	0.146686i	0.198524	−	0.980096i	$-0.436385\pi$
$691$	−9.30901	−	3.85592i	−0.354131	−	0.146686i	−0.552655	+	0.833410i	$0.686385\pi$
$692$		0			0
$693$		−	8.21747i		−	0.312156i
$694$		0			0
$695$	14.9119	+	14.9119i	0.565641	+	0.565641i
$696$		0			0
$697$	−5.07981	+	15.6402i	−0.192411	+	0.592416i
$698$		0			0
$699$	−5.66016	−	5.66016i	−0.214087	−	0.214087i
$700$		0			0
$701$			32.0760i			1.21150i	0.795657	+	0.605748i	$0.207126\pi$
$701$			32.0760i			1.21150i	−0.795657	+	0.605748i	$0.792874\pi$
$702$		0			0
$703$	−13.9601	−	5.78248i	−0.526516	−	0.218090i
$704$		0			0
$705$	9.00981	−	9.00981i	0.339329	−	0.339329i
$706$		0			0
$707$	31.9066	−	77.0293i	1.19997	−	2.89698i
$708$		0			0
$709$	3.29129	+	7.94589i	0.123607	+	0.298414i	0.973555	−	0.228453i	$-0.0733667\pi$
$709$	3.29129	+	7.94589i	0.123607	+	0.298414i	−0.849948	+	0.526867i	$0.823367\pi$
$710$		0			0
$711$	−2.80192	+	1.16059i	−0.105080	+	0.0435256i
$712$		0			0
$713$	−11.0434			−0.413580
$714$		0			0
$715$	−6.11734			−0.228775
$716$		0			0
$717$	26.5117	−	10.9815i	0.990098	−	0.410112i
$718$		0			0
$719$	−8.47004	−	20.4485i	−0.315879	−	0.762600i	−0.999464	−	0.0327288i	$-0.989580\pi$
$719$	−8.47004	−	20.4485i	−0.315879	−	0.762600i	0.683585	−	0.729871i	$-0.260420\pi$
$720$		0			0
$721$	−1.11760	+	2.69812i	−0.0416215	+	0.100483i
$722$		0			0
$723$	18.9567	−	18.9567i	0.705008	−	0.705008i
$724$		0			0
$725$	−9.52759	−	3.94646i	−0.353846	−	0.146568i
$726$		0			0
$727$			19.9059i			0.738270i	0.929376	+	0.369135i	$0.120346\pi$
$727$			19.9059i			0.738270i	−0.929376	+	0.369135i	$0.879654\pi$
$728$		0			0
$729$	−21.0854	−	21.0854i	−0.780941	−	0.780941i
$730$		0			0
$731$	−18.5195	+	21.6886i	−0.684967	+	0.802183i
$732$		0			0
$733$	−4.88790	−	4.88790i	−0.180539	−	0.180539i	0.611052	−	0.791591i	$-0.290747\pi$
$733$	−4.88790	−	4.88790i	−0.180539	−	0.180539i	−0.791591	+	0.611052i	$0.790747\pi$
$734$		0			0
$735$		−	19.1630i		−	0.706837i
$736$		0			0
$737$	24.3184	+	10.0730i	0.895780	+	0.371044i
$738$		0			0
$739$	5.23246	−	5.23246i	0.192479	−	0.192479i	−0.604287	−	0.796766i	$-0.706542\pi$
$739$	5.23246	−	5.23246i	0.192479	−	0.192479i	0.796766	+	0.604287i	$0.206542\pi$
$740$		0			0
$741$	4.43834	−	10.7151i	0.163046	−	0.393629i
$742$		0			0
$743$	4.94938	+	11.9488i	0.181575	+	0.438361i	0.988291	−	0.152578i	$-0.0487575\pi$
$743$	4.94938	+	11.9488i	0.181575	+	0.438361i	−0.806716	+	0.590939i	$0.798758\pi$
$744$		0			0
$745$	9.75114	−	4.03905i	0.357254	−	0.147979i
$746$		0			0
$747$	7.66811			0.280561
$748$		0			0
$749$	3.68562			0.134669
$750$		0			0
$751$	12.7137	−	5.26620i	0.463931	−	0.192166i	−0.138460	−	0.990368i	$-0.544215\pi$
$751$	12.7137	−	5.26620i	0.463931	−	0.192166i	0.602390	+	0.798202i	$0.294215\pi$
$752$		0			0
$753$	5.43490	+	13.1210i	0.198059	+	0.478156i
$754$		0			0
$755$	4.02901	−	9.72689i	0.146631	−	0.353998i
$756$		0			0
$757$	3.61651	−	3.61651i	0.131444	−	0.131444i	−0.638324	−	0.769768i	$-0.720372\pi$
$757$	3.61651	−	3.61651i	0.131444	−	0.131444i	0.769768	+	0.638324i	$0.220372\pi$
$758$		0			0
$759$	−11.3859	−	4.71621i	−0.413283	−	0.171188i
$760$		0			0
$761$			10.0575i			0.364585i	0.983244	+	0.182292i	$0.0583518\pi$
$761$			10.0575i			0.364585i	−0.983244	+	0.182292i	$0.941648\pi$
$762$		0			0
$763$	−43.1987	−	43.1987i	−1.56390	−	1.56390i
$764$		0			0
$765$	1.87049	+	0.607518i	0.0676278	+	0.0219649i
$766$		0			0
$767$	10.3206	+	10.3206i	0.372656	+	0.372656i
$768$		0			0
$769$		−	19.4115i		−	0.699997i	−0.936750	−	0.349998i	$-0.886182\pi$
$769$		−	19.4115i		−	0.699997i	0.936750	−	0.349998i	$-0.113818\pi$
$770$		0			0
$771$	0.459366	+	0.190276i	0.0165437	+	0.00685262i
$772$		0			0
$773$	−15.6614	+	15.6614i	−0.563302	+	0.563302i	−0.930244	−	0.366942i	$-0.880405\pi$
$773$	−15.6614	+	15.6614i	−0.563302	+	0.563302i	0.366942	+	0.930244i	$0.380405\pi$
$774$		0			0
$775$	−2.14916	+	5.18852i	−0.0772000	+	0.186377i
$776$		0			0
$777$	8.51544	+	20.5581i	0.305490	+	0.737517i
$778$		0			0
$779$	−17.3536	+	7.18808i	−0.621756	+	0.257540i
$780$		0			0
$781$	31.0470			1.11095
$782$		0			0
$783$	−56.9548			−2.03540
$784$		0			0
$785$	1.38081	−	0.571951i	0.0492833	−	0.0204138i
$786$		0			0
$787$	−4.04832	−	9.77350i	−0.144307	−	0.348388i	0.835156	−	0.550014i	$-0.185377\pi$
$787$	−4.04832	−	9.77350i	−0.144307	−	0.348388i	−0.979463	+	0.201626i	$0.935377\pi$
$788$		0			0
$789$	4.77518	−	11.5283i	0.170001	−	0.410419i
$790$		0			0
$791$	36.0489	−	36.0489i	1.28175	−	1.28175i
$792$		0			0
$793$	10.7698	+	4.46098i	0.382446	+	0.158414i
$794$		0			0
$795$			19.4701i			0.690533i
$796$		0			0
$797$	−25.0674	−	25.0674i	−0.887934	−	0.887934i	0.106391	−	0.994324i	$-0.466071\pi$
$797$	−25.0674	−	25.0674i	−0.887934	−	0.887934i	−0.994324	+	0.106391i	$0.966071\pi$
$798$		0			0
$799$	2.59886	+	32.9724i	0.0919409	+	1.16648i
$800$		0			0
$801$	−0.505459	−	0.505459i	−0.0178595	−	0.0178595i
$802$		0			0
$803$			22.6766i			0.800239i
$804$		0			0
$805$	7.93234	+	3.28568i	0.279578	+	0.115805i
$806$		0			0
$807$	−7.22587	+	7.22587i	−0.254363	+	0.254363i
$808$		0			0
$809$	−10.0126	+	24.1724i	−0.352023	+	0.849858i	0.644348	+	0.764733i	$0.277129\pi$
$809$	−10.0126	+	24.1724i	−0.352023	+	0.849858i	−0.996370	+	0.0851252i	$0.972871\pi$
$810$		0			0
$811$	14.8001	+	35.7307i	0.519703	+	1.25467i	0.938086	+	0.346403i	$0.112597\pi$
$811$	14.8001	+	35.7307i	0.519703	+	1.25467i	−0.418383	+	0.908271i	$0.637403\pi$
$812$		0			0
$813$	32.1894	−	13.3333i	1.12893	−	0.467619i
$814$		0			0
$815$	−14.8898			−0.521566
$816$		0			0
$817$	−32.5759			−1.13969
$818$		0			0
$819$	2.98317	−	1.23567i	0.104241	−	0.0431778i
$820$		0			0
$821$	−18.9919	−	45.8505i	−0.662822	−	1.60019i	−0.793361	−	0.608751i	$-0.791671\pi$
$821$	−18.9919	−	45.8505i	−0.662822	−	1.60019i	0.130539	−	0.991443i	$-0.458329\pi$
$822$		0			0
$823$	6.69230	−	16.1566i	0.233279	−	0.563185i	−0.763280	−	0.646067i	$-0.776413\pi$
$823$	6.69230	−	16.1566i	0.233279	−	0.563185i	0.996559	+	0.0828822i	$0.0264125\pi$
$824$		0			0
$825$	−4.43163	+	4.43163i	−0.154289	+	0.154289i
$826$		0			0
$827$	−5.53017	−	2.29067i	−0.192303	−	0.0796544i	0.284454	−	0.958690i	$-0.408188\pi$
$827$	−5.53017	−	2.29067i	−0.192303	−	0.0796544i	−0.476757	+	0.879035i	$0.658188\pi$
$828$		0			0
$829$			17.0473i			0.592076i	0.955176	+	0.296038i	$0.0956655\pi$
$829$			17.0473i			0.592076i	−0.955176	+	0.296038i	$0.904334\pi$
$830$		0			0
$831$	−30.5256	−	30.5256i	−1.05892	−	1.05892i
$832$		0			0
$833$	37.8283	+	32.3008i	1.31067	+	1.11916i
$834$		0			0
$835$	−5.57240	−	5.57240i	−0.192841	−	0.192841i
$836$		0			0
$837$			31.0164i			1.07208i
$838$		0			0
$839$	−43.1837	−	17.8873i	−1.49087	−	0.617537i	−0.519361	−	0.854555i	$-0.673830\pi$
$839$	−43.1837	−	17.8873i	−1.49087	−	0.617537i	−0.971505	+	0.237017i	$0.923830\pi$
$840$		0			0
$841$	−54.6943	+	54.6943i	−1.88601	+	1.88601i
$842$		0			0
$843$	−2.54611	+	6.14686i	−0.0876928	+	0.211709i
$844$		0			0
$845$	4.05501	+	9.78967i	0.139497	+	0.336775i
$846$		0			0
$847$	−18.4276	+	7.63294i	−0.633178	+	0.262271i
$848$		0			0
$849$	10.7255			0.368097
$850$		0			0
$851$	−6.30917			−0.216276
$852$		0			0
$853$	−51.7113	+	21.4195i	−1.77056	+	0.733390i	−0.775820	+	0.630954i	$0.782664\pi$
$853$	−51.7113	+	21.4195i	−1.77056	+	0.733390i	−0.994740	+	0.102436i	$0.967336\pi$
$854$		0			0
$855$	0.859657	+	2.07540i	0.0293996	+	0.0709770i
$856$		0			0
$857$	0.986747	−	2.38222i	0.0337066	−	0.0813750i	−0.906130	−	0.423000i	$-0.860977\pi$
$857$	0.986747	−	2.38222i	0.0337066	−	0.0813750i	0.939836	+	0.341625i	$0.110977\pi$
$858$		0			0
$859$	24.7536	−	24.7536i	0.844581	−	0.844581i	−0.144870	−	0.989451i	$-0.546276\pi$
$859$	24.7536	−	24.7536i	0.844581	−	0.844581i	0.989451	+	0.144870i	$0.0462764\pi$
$860$		0			0
$861$	25.5554	+	10.5854i	0.870924	+	0.360749i
$862$		0			0
$863$		−	21.9363i		−	0.746720i	−0.927687	−	0.373360i	$-0.878206\pi$
$863$		−	21.9363i		−	0.746720i	0.927687	−	0.373360i	$-0.121794\pi$
$864$		0			0
$865$	8.05159	+	8.05159i	0.273762	+	0.273762i
$866$		0			0
$867$	23.0204	−	14.1143i	0.781813	−	0.479346i
$868$		0			0
$869$	17.7392	+	17.7392i	0.601762	+	0.601762i
$870$		0			0
$871$			10.3430i			0.350458i
$872$		0			0
$873$	−4.69762	−	1.94582i	−0.158990	−	0.0658560i
$874$		0			0
$875$	3.08742	−	3.08742i	0.104374	−	0.104374i
$876$		0			0
$877$	−5.09326	+	12.2962i	−0.171987	+	0.415214i	−0.986245	−	0.165290i	$-0.947144\pi$
$877$	−5.09326	+	12.2962i	−0.171987	+	0.415214i	0.814258	+	0.580503i	$0.197144\pi$
$878$		0			0
$879$	10.7275	+	25.8984i	0.361829	+	0.873532i
$880$		0			0
$881$	36.5719	−	15.1486i	1.23214	−	0.510369i	0.330890	−	0.943670i	$-0.392651\pi$
$881$	36.5719	−	15.1486i	1.23214	−	0.510369i	0.901249	+	0.433301i	$0.142651\pi$
$882$		0			0
$883$	48.3602			1.62745			0.813725	−	0.581250i	$-0.197436\pi$
$883$	48.3602			1.62745			0.813725	+	0.581250i	$0.197436\pi$
$884$		0			0
$885$	14.9533			0.502649
$886$		0			0
$887$	33.1140	−	13.7163i	1.11186	−	0.460547i	0.250282	−	0.968173i	$-0.419477\pi$
$887$	33.1140	−	13.7163i	1.11186	−	0.460547i	0.861578	+	0.507626i	$0.169477\pi$
$888$		0			0
$889$	−24.3049	−	58.6772i	−0.815160	−	1.96797i
$890$		0			0
$891$	−11.0852	+	26.7621i	−0.371369	+	0.896563i
$892$		0			0
$893$	−26.7137	+	26.7137i	−0.893939	+	0.893939i
$894$		0			0
$895$	6.49886	+	2.69192i	0.217233	+	0.0899809i
$896$		0			0
$897$		−	4.84260i		−	0.161690i
$898$		0			0
$899$	40.9526	+	40.9526i	1.36584	+	1.36584i
$900$		0			0
$901$	−38.4345	−	32.8184i	−1.28044	−	1.09334i
$902$		0			0
$903$	33.9214	+	33.9214i	1.12883	+	1.12883i
$904$		0			0
$905$			1.82769i			0.0607545i
$906$		0			0
$907$	1.65667	+	0.686216i	0.0550089	+	0.0227854i	0.410018	−	0.912077i	$-0.365522\pi$
$907$	1.65667	+	0.686216i	0.0550089	+	0.0227854i	−0.355009	+	0.934863i	$0.615522\pi$
$908$		0			0
$909$	6.44055	−	6.44055i	0.213620	−	0.213620i
$910$		0			0
$911$	5.79680	−	13.9947i	0.192057	−	0.463666i	−0.798291	−	0.602272i	$-0.794262\pi$
$911$	5.79680	−	13.9947i	0.192057	−	0.463666i	0.990348	+	0.138606i	$0.0442623\pi$
$912$		0			0
$913$	−24.2738	−	58.6022i	−0.803346	−	1.93945i
$914$		0			0
$915$	11.0337	−	4.57032i	0.364764	−	0.151090i
$916$		0			0
$917$	35.0289			1.15676
$918$		0			0
$919$	−32.8285			−1.08291			−0.541457	−	0.840729i	$-0.682127\pi$
$919$	−32.8285			−1.08291			−0.541457	+	0.840729i	$0.682127\pi$
$920$		0			0
$921$	−22.4293	+	9.29051i	−0.739070	+	0.306133i
$922$		0			0
$923$	4.66857	+	11.2709i	0.153668	+	0.370987i
$924$		0			0
$925$	−1.22783	+	2.96423i	−0.0403707	+	0.0974634i
$926$		0			0
$927$	−0.225595	+	0.225595i	−0.00740950	+	0.00740950i
$928$		0			0
$929$	32.9725	+	13.6577i	1.08179	+	0.448093i	0.851138	−	0.524942i	$-0.175913\pi$
$929$	32.9725	+	13.6577i	1.08179	+	0.448093i	0.230655	+	0.973036i	$0.425913\pi$
$930$		0			0
$931$			56.8173i			1.86211i
$932$		0			0
$933$	−34.4462	−	34.4462i	−1.12772	−	1.12772i
$934$		0			0
$935$	−1.27829	−	16.2180i	−0.0418046	−	0.530387i
$936$		0			0
$937$	−16.6155	−	16.6155i	−0.542804	−	0.542804i	0.381546	−	0.924350i	$-0.375392\pi$
$937$	−16.6155	−	16.6155i	−0.542804	−	0.542804i	−0.924350	+	0.381546i	$0.875392\pi$
$938$		0			0
$939$		−	19.4377i		−	0.634324i
$940$		0			0
$941$	−13.4597	−	5.57517i	−0.438772	−	0.181745i	0.152351	−	0.988326i	$-0.451315\pi$
$941$	−13.4597	−	5.57517i	−0.438772	−	0.181745i	−0.591124	+	0.806581i	$0.701315\pi$
$942$		0			0
$943$	−5.54570	+	5.54570i	−0.180593	+	0.180593i
$944$		0			0
$945$	9.22812	−	22.2787i	0.300191	−	0.724725i
$946$		0			0
$947$	−10.3654	−	25.0243i	−0.336830	−	0.813180i	−0.998016	−	0.0629578i	$-0.979947\pi$
$947$	−10.3654	−	25.0243i	−0.336830	−	0.813180i	0.661186	−	0.750222i	$-0.270053\pi$
$948$		0			0
$949$	−8.23224	+	3.40991i	−0.267230	+	0.110690i
$950$		0			0
$951$	23.8135			0.772205
$952$		0			0
$953$	−30.3486			−0.983089			−0.491544	−	0.870853i	$-0.663567\pi$
$953$	−30.3486			−0.983089			−0.491544	+	0.870853i	$0.663567\pi$
$954$		0			0
$955$	−3.40330	+	1.40969i	−0.110128	+	0.0456167i
$956$		0			0
$957$	24.7335	+	59.7119i	0.799520	+	1.93021i
$958$		0			0
$959$	9.40092	−	22.6958i	0.303572	−	0.732886i
$960$		0			0
$961$	0.381591	−	0.381591i	0.0123094	−	0.0123094i
$962$		0			0
$963$	0.371983	+	0.154080i	0.0119870	+	0.00496517i
$964$		0			0
$965$			3.13590i			0.100948i
$966$		0			0
$967$	12.6496	+	12.6496i	0.406784	+	0.406784i	0.880616	−	0.473831i	$-0.157129\pi$
$967$	12.6496	+	12.6496i	0.406784	+	0.406784i	−0.473831	+	0.880616i	$0.657129\pi$
$968$		0			0
$969$	29.3349	+	9.52769i	0.942371	+	0.306073i
$970$		0			0
$971$	14.6184	+	14.6184i	0.469128	+	0.469128i	0.901632	−	0.432504i	$-0.142370\pi$
$971$	14.6184	+	14.6184i	0.469128	+	0.469128i	−0.432504	+	0.901632i	$0.642370\pi$
$972$		0			0
$973$			92.0787i			2.95191i
$974$		0			0
$975$	−2.27520	−	0.942417i	−0.0728646	−	0.0301815i
$976$		0			0
$977$	−39.6482	+	39.6482i	−1.26846	+	1.26846i	−0.321572	+	0.946885i	$0.604211\pi$
$977$	−39.6482	+	39.6482i	−1.26846	+	1.26846i	−0.946885	+	0.321572i	$0.895789\pi$
$978$		0			0
$979$	−2.26282	+	5.46294i	−0.0723202	+	0.174596i
$980$		0			0
$981$	−2.55401	−	6.16593i	−0.0815433	−	0.196863i
$982$		0			0
$983$	−0.614437	+	0.254508i	−0.0195975	+	0.00811754i	−0.392461	−	0.919769i	$-0.628376\pi$
$983$	−0.614437	+	0.254508i	−0.0195975	+	0.00811754i	0.372863	+	0.927886i	$0.378376\pi$
$984$		0			0
$985$	−15.1588			−0.483001
$986$		0			0
$987$	55.6342			1.77086
$988$		0			0
$989$	−12.5664	+	5.20516i	−0.399587	+	0.165514i
$990$		0			0
$991$	−2.74076	−	6.61678i	−0.0870631	−	0.210189i	0.874351	−	0.485294i	$-0.161287\pi$
$991$	−2.74076	−	6.61678i	−0.0870631	−	0.210189i	−0.961414	+	0.275105i	$0.911287\pi$
$992$		0			0
$993$	6.71615	−	16.2142i	0.213131	−	0.514543i
$994$		0			0
$995$	3.70474	−	3.70474i	0.117448	−	0.117448i
$996$		0			0
$997$	−11.1118	−	4.60266i	−0.351914	−	0.145768i	0.199722	−	0.979853i	$-0.435996\pi$
$997$	−11.1118	−	4.60266i	−0.351914	−	0.145768i	−0.551636	+	0.834085i	$0.685996\pi$
$998$		0			0
$999$			17.7198i			0.560631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bo.a.121.6	✓	32
17.9	even	8	inner	680.2.bo.a.281.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bo.a.121.6	✓	32	1.1	even	1	trivial
680.2.bo.a.281.6	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)

\(f(q)\)	\(=\)	\(q+(1.46749 - 0.607854i) q^{3} +(0.382683 + 0.923880i) q^{5} +(-1.67090 + 4.03391i) q^{7} +(-0.337282 + 0.337282i) q^{9} +(3.64531 + 1.50994i) q^{11} +1.55040i q^{13} +(1.12317 + 1.12317i) q^{15} +(-4.11036 + 0.323974i) q^{17} +(-3.33014 - 3.33014i) q^{19} +6.93538i q^{21} +(-1.81673 - 0.752515i) q^{23} +(-0.707107 + 0.707107i) q^{25} +(-2.11350 + 5.10244i) q^{27} +(3.94646 + 9.52759i) q^{29} +(5.18852 - 2.14916i) q^{31} +6.26727 q^{33} -4.36627 q^{35} +(2.96423 - 1.22783i) q^{37} +(0.942417 + 2.27520i) q^{39} +(1.52629 - 3.68478i) q^{41} +(4.89107 - 4.89107i) q^{43} +(-0.440680 - 0.182536i) q^{45} -8.02179i q^{47} +(-8.53078 - 8.53078i) q^{49} +(-5.83498 + 2.97393i) q^{51} +(8.66749 + 8.66749i) q^{53} +3.94565i q^{55} +(-6.91118 - 2.86270i) q^{57} +(6.65674 - 6.65674i) q^{59} +(2.87731 - 6.94644i) q^{61} +(-0.797001 - 1.92413i) q^{63} +(-1.43238 + 0.593312i) q^{65} +6.67116 q^{67} -3.12345 q^{69} +(7.26969 - 3.01120i) q^{71} +(2.19937 + 5.30975i) q^{73} +(-0.607854 + 1.46749i) q^{75} +(-12.1819 + 12.1819i) q^{77} +(5.87417 + 2.43316i) q^{79} +7.34151i q^{81} +(-11.3675 - 11.3675i) q^{83} +(-1.87228 - 3.67350i) q^{85} +(11.5828 + 11.5828i) q^{87} +1.49862i q^{89} +(-6.25418 - 2.59056i) q^{91} +(6.30773 - 6.30773i) q^{93} +(1.80226 - 4.35103i) q^{95} +(4.07938 + 9.84849i) q^{97} +(-1.73877 + 0.720223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 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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