LMFDB - Embedded newform 680.2.bo.a.161.1

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			161.1
Character	$\chi$	$=$	680.161
Dual form			680.2.bo.a.321.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.805905 + 1.94563i) q^{3} +(0.923880 + 0.382683i) q^{5} +(4.50228 - 1.86491i) q^{7} +(-1.01466 - 1.01466i) q^{9} +(0.738530 + 1.78297i) q^{11} -4.49602i q^{13} +(-1.48912 + 1.48912i) q^{15} +(2.20201 - 3.48585i) q^{17} +(5.38608 - 5.38608i) q^{19} +10.2627i q^{21} +(1.69771 + 4.09864i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-3.04502 + 1.26129i) q^{27} +(-8.52562 - 3.53143i) q^{29} +(1.27746 - 3.08407i) q^{31} -4.06418 q^{33} +4.87323 q^{35} +(-3.96828 + 9.58028i) q^{37} +(8.74757 + 3.62336i) q^{39} +(-1.90308 + 0.788283i) q^{41} +(5.75531 + 5.75531i) q^{43} +(-0.549128 - 1.32571i) q^{45} +6.13313i q^{47} +(11.8429 - 11.8429i) q^{49} +(5.00755 + 7.09355i) q^{51} +(-4.96199 + 4.96199i) q^{53} +1.92987i q^{55} +(6.13863 + 14.8200i) q^{57} +(5.21179 + 5.21179i) q^{59} +(-6.49304 + 2.68951i) q^{61} +(-6.46051 - 2.67603i) q^{63} +(1.72055 - 4.15378i) q^{65} -5.65422 q^{67} -9.34261 q^{69} +(-1.11027 + 2.68043i) q^{71} +(-5.42509 - 2.24715i) q^{73} +(-1.94563 + 0.805905i) q^{75} +(6.65014 + 6.65014i) q^{77} +(-3.64109 - 8.79037i) q^{79} -11.2458i q^{81} +(0.0745559 - 0.0745559i) q^{83} +(3.36837 - 2.37783i) q^{85} +(13.7417 - 13.7417i) q^{87} -10.3056i q^{89} +(-8.38465 - 20.2423i) q^{91} +(4.97093 + 4.97093i) q^{93} +(7.03725 - 2.91493i) q^{95} +(8.24633 + 3.41574i) q^{97} +(1.05975 - 2.55846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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
$3$	−0.805905	+	1.94563i	−0.465289	+	1.12331i	0.500907	+	0.865501i	$0.333000\pi$
$3$	−0.805905	+	1.94563i	−0.465289	+	1.12331i	−0.966197	+	0.257807i	$0.917000\pi$
$4$		0			0
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$6$		0			0
$7$	4.50228	−	1.86491i	1.70170	−	0.704868i	0.701730	−	0.712443i	$-0.252411\pi$
$7$	4.50228	−	1.86491i	1.70170	−	0.704868i	0.999971	+	0.00757473i	$0.00241114\pi$
$8$		0			0
$9$	−1.01466	−	1.01466i	−0.338219	−	0.338219i
$10$		0			0
$11$	0.738530	+	1.78297i	0.222675	+	0.537586i	0.995252	−	0.0973364i	$-0.0310323\pi$
$11$	0.738530	+	1.78297i	0.222675	+	0.537586i	−0.772576	+	0.634922i	$0.781032\pi$
$12$		0			0
$13$		−	4.49602i		−	1.24697i	−0.781835	−	0.623485i	$-0.785716\pi$
$13$		−	4.49602i		−	1.24697i	0.781835	−	0.623485i	$-0.214284\pi$
$14$		0			0
$15$	−1.48912	+	1.48912i	−0.384488	+	0.384488i
$16$		0			0
$17$	2.20201	−	3.48585i	0.534066	−	0.845443i
$17$	2.20201	−	3.48585i	0.534066	−	0.845443i
$18$		0			0
$19$	5.38608	−	5.38608i	1.23565	−	1.23565i	0.273891	−	0.961761i	$-0.411689\pi$
$19$	5.38608	−	5.38608i	1.23565	−	1.23565i	0.961761	−	0.273891i	$-0.0883107\pi$
$20$		0			0
$21$			10.2627i			2.23950i
$22$		0			0
$23$	1.69771	+	4.09864i	0.353997	+	0.854625i	0.996119	+	0.0880219i	$0.0280546\pi$
$23$	1.69771	+	4.09864i	0.353997	+	0.854625i	−0.642121	+	0.766603i	$0.721945\pi$
$24$		0			0
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$		0			0
$27$	−3.04502	+	1.26129i	−0.586014	+	0.242735i
$28$		0			0
$29$	−8.52562	−	3.53143i	−1.58317	−	0.655769i	−0.594256	−	0.804276i	$-0.702553\pi$
$29$	−8.52562	−	3.53143i	−1.58317	−	0.655769i	−0.988911	+	0.148507i	$0.952553\pi$
$30$		0			0
$31$	1.27746	−	3.08407i	0.229439	−	0.553915i	−0.766670	−	0.642041i	$-0.778088\pi$
$31$	1.27746	−	3.08407i	0.229439	−	0.553915i	0.996109	+	0.0881263i	$0.0280879\pi$
$32$		0			0
$33$	−4.06418			−0.707482
$34$		0			0
$35$	4.87323			0.823727
$36$		0			0
$37$	−3.96828	+	9.58028i	−0.652382	+	1.57499i	0.156930	+	0.987610i	$0.449840\pi$
$37$	−3.96828	+	9.58028i	−0.652382	+	1.57499i	−0.809312	+	0.587379i	$0.800160\pi$
$38$		0			0
$39$	8.74757	+	3.62336i	1.40073	+	0.580202i
$40$		0			0
$41$	−1.90308	+	0.788283i	−0.297212	+	0.123109i	−0.526306	−	0.850295i	$-0.676423\pi$
$41$	−1.90308	+	0.788283i	−0.297212	+	0.123109i	0.229095	+	0.973404i	$0.426423\pi$
$42$		0			0
$43$	5.75531	+	5.75531i	0.877676	+	0.877676i	0.993294	−	0.115617i	$-0.0368846\pi$
$43$	5.75531	+	5.75531i	0.877676	+	0.877676i	−0.115617	+	0.993294i	$0.536885\pi$
$44$		0			0
$45$	−0.549128	−	1.32571i	−0.0818592	−	0.197626i
$46$		0			0
$47$			6.13313i			0.894608i	0.894382	+	0.447304i	$0.147616\pi$
$47$			6.13313i			0.894608i	−0.894382	+	0.447304i	$0.852384\pi$
$48$		0			0
$49$	11.8429	−	11.8429i	1.69184	−	1.69184i
$50$		0			0
$51$	5.00755	+	7.09355i	0.701198	+	0.993295i
$52$		0			0
$53$	−4.96199	+	4.96199i	−0.681581	+	0.681581i	−0.960356	−	0.278775i	$-0.910072\pi$
$53$	−4.96199	+	4.96199i	−0.681581	+	0.681581i	0.278775	+	0.960356i	$0.410072\pi$
$54$		0			0
$55$			1.92987i			0.260224i
$56$		0			0
$57$	6.13863	+	14.8200i	0.813081	+	1.96295i
$58$		0			0
$59$	5.21179	+	5.21179i	0.678518	+	0.678518i	0.959665	−	0.281147i	$-0.0907148\pi$
$59$	5.21179	+	5.21179i	0.678518	+	0.678518i	−0.281147	+	0.959665i	$0.590715\pi$
$60$		0			0
$61$	−6.49304	+	2.68951i	−0.831349	+	0.344356i	−0.757437	−	0.652909i	$-0.773548\pi$
$61$	−6.49304	+	2.68951i	−0.831349	+	0.344356i	−0.0739123	+	0.997265i	$0.523548\pi$
$62$		0			0
$63$	−6.46051	−	2.67603i	−0.813947	−	0.337148i
$64$		0			0
$65$	1.72055	−	4.15378i	0.213408	−	0.515213i
$66$		0			0
$67$	−5.65422			−0.690773			−0.345387	−	0.938460i	$-0.612252\pi$
$67$	−5.65422			−0.690773			−0.345387	+	0.938460i	$0.612252\pi$
$68$		0			0
$69$	−9.34261			−1.12472
$70$		0			0
$71$	−1.11027	+	2.68043i	−0.131765	+	0.318109i	−0.975968	−	0.217915i	$-0.930074\pi$
$71$	−1.11027	+	2.68043i	−0.131765	+	0.318109i	0.844203	+	0.536024i	$0.180074\pi$
$72$		0			0
$73$	−5.42509	−	2.24715i	−0.634959	−	0.263009i	0.0418995	−	0.999122i	$-0.486659\pi$
$73$	−5.42509	−	2.24715i	−0.634959	−	0.263009i	−0.676858	+	0.736113i	$0.736659\pi$
$74$		0			0
$75$	−1.94563	+	0.805905i	−0.224661	+	0.0930578i
$76$		0			0
$77$	6.65014	+	6.65014i	0.757854	+	0.757854i
$78$		0			0
$79$	−3.64109	−	8.79037i	−0.409655	−	0.988994i	−0.985229	−	0.171244i	$-0.945221\pi$
$79$	−3.64109	−	8.79037i	−0.409655	−	0.988994i	0.575574	−	0.817750i	$-0.304779\pi$
$80$		0			0
$81$		−	11.2458i		−	1.24953i
$82$		0			0
$83$	0.0745559	−	0.0745559i	0.00818357	−	0.00818357i	−0.703003	−	0.711187i	$-0.748158\pi$
$83$	0.0745559	−	0.0745559i	0.00818357	−	0.00818357i	0.711187	+	0.703003i	$0.248158\pi$
$84$		0			0
$85$	3.36837	−	2.37783i	0.365351	−	0.257912i
$86$		0			0
$87$	13.7417	−	13.7417i	1.47326	−	1.47326i
$88$		0			0
$89$		−	10.3056i		−	1.09240i	−0.837656	−	0.546198i	$-0.816074\pi$
$89$		−	10.3056i		−	1.09240i	0.837656	−	0.546198i	$-0.183926\pi$
$90$		0			0
$91$	−8.38465	−	20.2423i	−0.878950	−	2.12197i
$92$		0			0
$93$	4.97093	+	4.97093i	0.515461	+	0.515461i
$94$		0			0
$95$	7.03725	−	2.91493i	0.722007	−	0.299065i
$96$		0			0
$97$	8.24633	+	3.41574i	0.837288	+	0.346816i	0.759784	−	0.650176i	$-0.225305\pi$
$97$	8.24633	+	3.41574i	0.837288	+	0.346816i	0.0775046	+	0.996992i	$0.475305\pi$
$98$		0			0
$99$	1.05975	−	2.55846i	0.106509	−	0.257135i
$100$		0			0
$101$	3.69319			0.367486			0.183743	−	0.982974i	$-0.441179\pi$
$101$	3.69319			0.367486			0.183743	+	0.982974i	$0.441179\pi$
$102$		0			0
$103$	−15.2035			−1.49804			−0.749022	−	0.662545i	$-0.769477\pi$
$103$	−15.2035			−1.49804			−0.749022	+	0.662545i	$0.769477\pi$
$104$		0			0
$105$	−3.92736	+	9.48149i	−0.383271	+	0.925298i
$106$		0			0
$107$	−13.2473	−	5.48720i	−1.28066	−	0.530468i	−0.364474	−	0.931214i	$-0.618751\pi$
$107$	−13.2473	−	5.48720i	−1.28066	−	0.530468i	−0.916189	+	0.400746i	$0.868751\pi$
$108$		0			0
$109$	−11.2681	+	4.66739i	−1.07929	+	0.447055i	−0.850259	−	0.526365i	$-0.823555\pi$
$109$	−11.2681	+	4.66739i	−1.07929	+	0.447055i	−0.229028	+	0.973420i	$0.573555\pi$
$110$		0			0
$111$	−15.4416	−	15.4416i	−1.46565	−	1.46565i
$112$		0			0
$113$	3.21308	+	7.75706i	0.302261	+	0.729723i	0.999912	+	0.0132846i	$0.00422874\pi$
$113$	3.21308	+	7.75706i	0.302261	+	0.729723i	−0.697651	+	0.716438i	$0.745771\pi$
$114$		0			0
$115$			4.43633i			0.413690i
$116$		0			0
$117$	−4.56191	+	4.56191i	−0.421749	+	0.421749i
$118$		0			0
$119$	3.41328	−	19.8008i	0.312895	−	1.81514i
$120$		0			0
$121$	5.14462	−	5.14462i	0.467693	−	0.467693i
$122$		0			0
$123$		−	4.33797i		−	0.391141i
$124$		0			0
$125$	0.382683	+	0.923880i	0.0342282	+	0.0826343i
$126$		0			0
$127$	7.22978	+	7.22978i	0.641539	+	0.641539i	0.950934	−	0.309395i	$-0.100126\pi$
$127$	7.22978	+	7.22978i	0.641539	+	0.641539i	−0.309395	+	0.950934i	$0.600126\pi$
$128$		0			0
$129$	−15.8359	+	6.55945i	−1.39427	+	0.577527i
$130$		0			0
$131$	4.82026	+	1.99662i	0.421148	+	0.174445i	0.583185	−	0.812339i	$-0.301806\pi$
$131$	4.82026	+	1.99662i	0.421148	+	0.174445i	−0.162037	+	0.986785i	$0.551806\pi$
$132$		0			0
$133$	14.2051	−	34.2942i	1.23174	−	2.97368i
$134$		0			0
$135$	−3.29590			−0.283666
$136$		0			0
$137$	−11.9884			−1.02423			−0.512117	−	0.858915i	$-0.671139\pi$
$137$	−11.9884			−1.02423			−0.512117	+	0.858915i	$0.671139\pi$
$138$		0			0
$139$	−6.23967	+	15.0639i	−0.529242	+	1.27770i	0.402779	+	0.915297i	$0.368044\pi$
$139$	−6.23967	+	15.0639i	−0.529242	+	1.27770i	−0.932021	+	0.362405i	$0.881956\pi$
$140$		0			0
$141$	−11.9328	−	4.94271i	−1.00492	−	0.416252i
$142$		0			0
$143$	8.01626	−	3.32044i	0.670353	−	0.277669i
$144$		0			0
$145$	−6.52522	−	6.52522i	−0.541890	−	0.541890i
$146$		0			0
$147$	13.4976	+	32.5861i	1.11326	+	2.68766i
$148$		0			0
$149$		−	6.90596i		−	0.565759i	−0.959156	−	0.282879i	$-0.908710\pi$
$149$		−	6.90596i		−	0.565759i	0.959156	−	0.282879i	$-0.0912896\pi$
$150$		0			0
$151$	8.59590	−	8.59590i	0.699525	−	0.699525i	−0.264783	−	0.964308i	$-0.585300\pi$
$151$	8.59590	−	8.59590i	0.699525	−	0.699525i	0.964308	+	0.264783i	$0.0853004\pi$
$152$		0			0
$153$	−5.77123	+	1.30266i	−0.466576	+	0.105314i
$154$		0			0
$155$	2.36044	−	2.36044i	0.189595	−	0.189595i
$156$		0			0
$157$		−	7.37348i		−	0.588467i	−0.955733	−	0.294234i	$-0.904936\pi$
$157$		−	7.37348i		−	0.588467i	0.955733	−	0.294234i	$-0.0950644\pi$
$158$		0			0
$159$	−5.65528	−	13.6531i	−0.448493	−	1.08276i
$160$		0			0
$161$	15.2871	+	15.2871i	1.20480	+	1.20480i
$162$		0			0
$163$	−0.296443	+	0.122791i	−0.0232192	+	0.00961771i	−0.394263	−	0.918998i	$-0.629000\pi$
$163$	−0.296443	+	0.122791i	−0.0232192	+	0.00961771i	0.371044	+	0.928615i	$0.379000\pi$
$164$		0			0
$165$	−3.75481	−	1.55529i	−0.292311	−	0.121079i
$166$		0			0
$167$	−6.02818	+	14.5533i	−0.466474	+	1.12617i	0.499217	+	0.866477i	$0.333621\pi$
$167$	−6.02818	+	14.5533i	−0.466474	+	1.12617i	−0.965692	+	0.259692i	$0.916379\pi$
$168$		0			0
$169$	−7.21417			−0.554936
$170$		0			0
$171$	−10.9300			−0.835842
$172$		0			0
$173$	6.99455	−	16.8863i	0.531786	−	1.28384i	−0.398554	−	0.917145i	$-0.630488\pi$
$173$	6.99455	−	16.8863i	0.531786	−	1.28384i	0.930339	−	0.366700i	$-0.119512\pi$
$174$		0			0
$175$	4.50228	+	1.86491i	0.340340	+	0.140974i
$176$		0			0
$177$	−14.3404	+	5.93999i	−1.07789	+	0.446477i
$178$		0			0
$179$	−2.53267	−	2.53267i	−0.189301	−	0.189301i	0.606093	−	0.795394i	$-0.292736\pi$
$179$	−2.53267	−	2.53267i	−0.189301	−	0.189301i	−0.795394	+	0.606093i	$0.792736\pi$
$180$		0			0
$181$	5.54803	+	13.3941i	0.412382	+	0.995578i	0.984496	+	0.175404i	$0.0561233\pi$
$181$	5.54803	+	13.3941i	0.412382	+	0.995578i	−0.572114	+	0.820174i	$0.693877\pi$
$182$		0			0
$183$		−	14.8005i		−	1.09409i
$184$		0			0
$185$	−7.33243	+	7.33243i	−0.539091	+	0.539091i
$186$		0			0
$187$	7.84142	+	1.35171i	0.573421	+	0.0988467i
$188$		0			0
$189$	−11.3573	+	11.3573i	−0.826125	+	0.826125i
$190$		0			0
$191$			12.6684i			0.916651i	0.888785	+	0.458325i	$0.151551\pi$
$191$			12.6684i			0.916651i	−0.888785	+	0.458325i	$0.848449\pi$
$192$		0			0
$193$	1.18935	+	2.87136i	0.0856116	+	0.206685i	0.960887	−	0.276939i	$-0.0893201\pi$
$193$	1.18935	+	2.87136i	0.0856116	+	0.206685i	−0.875276	+	0.483624i	$0.839320\pi$
$194$		0			0
$195$	6.69510	+	6.69510i	0.479446	+	0.479446i
$196$		0			0
$197$	17.7596	−	7.35626i	1.26532	−	0.524112i	0.353781	−	0.935328i	$-0.384896\pi$
$197$	17.7596	−	7.35626i	1.26532	−	0.524112i	0.911538	+	0.411216i	$0.134896\pi$
$198$		0			0
$199$	−8.53405	−	3.53492i	−0.604963	−	0.250584i	0.0591104	−	0.998251i	$-0.481174\pi$
$199$	−8.53405	−	3.53492i	−0.604963	−	0.250584i	−0.664073	+	0.747668i	$0.731174\pi$
$200$		0			0
$201$	4.55676	−	11.0010i	0.321409	−	0.775951i
$202$		0			0
$203$	−44.9705			−3.15631
$204$		0			0
$205$	−2.05988			−0.143868
$206$		0			0
$207$	2.43612	−	5.88130i	0.169322	−	0.408779i
$208$		0			0
$209$	13.5810	+	5.62543i	0.939417	+	0.389119i
$210$		0			0
$211$	18.3924	−	7.61840i	1.26619	−	0.524472i	0.354385	−	0.935100i	$-0.384690\pi$
$211$	18.3924	−	7.61840i	1.26619	−	0.524472i	0.911803	+	0.410627i	$0.134690\pi$
$212$		0			0
$213$	−4.32035	−	4.32035i	−0.296025	−	0.296025i
$214$		0			0
$215$	3.11475	+	7.51967i	0.212424	+	0.512838i
$216$		0			0
$217$		−	16.2677i		−	1.10432i
$218$		0			0
$219$	8.74421	−	8.74421i	0.590879	−	0.590879i
$220$		0			0
$221$	−15.6724	−	9.90027i	−1.05424	−	0.665964i
$222$		0			0
$223$	−4.85127	+	4.85127i	−0.324865	+	0.324865i	−0.850630	−	0.525765i	$-0.823779\pi$
$223$	−4.85127	+	4.85127i	−0.324865	+	0.324865i	0.525765	+	0.850630i	$0.323779\pi$
$224$		0			0
$225$		−	1.43494i		−	0.0956628i
$226$		0			0
$227$	4.79974	+	11.5876i	0.318570	+	0.769096i	0.999330	+	0.0365898i	$0.0116495\pi$
$227$	4.79974	+	11.5876i	0.318570	+	0.769096i	−0.680760	+	0.732506i	$0.738351\pi$
$228$		0			0
$229$	−12.2712	−	12.2712i	−0.810906	−	0.810906i	0.173864	−	0.984770i	$-0.444375\pi$
$229$	−12.2712	−	12.2712i	−0.810906	−	0.810906i	−0.984770	+	0.173864i	$0.944375\pi$
$230$		0			0
$231$	−18.2981	+	7.57930i	−1.20392	+	0.498682i
$232$		0			0
$233$	5.25730	+	2.17765i	0.344417	+	0.142662i	0.548185	−	0.836357i	$-0.315319\pi$
$233$	5.25730	+	2.17765i	0.344417	+	0.142662i	−0.203768	+	0.979019i	$0.565319\pi$
$234$		0			0
$235$	−2.34705	+	5.66627i	−0.153104	+	0.369627i
$236$		0			0
$237$	20.0371			1.30155
$238$		0			0
$239$	−11.8013			−0.763364			−0.381682	−	0.924294i	$-0.624655\pi$
$239$	−11.8013			−0.763364			−0.381682	+	0.924294i	$0.624655\pi$
$240$		0			0
$241$	−5.89823	+	14.2396i	−0.379938	+	0.917252i	0.612038	+	0.790828i	$0.290350\pi$
$241$	−5.89823	+	14.2396i	−0.379938	+	0.917252i	−0.991976	+	0.126424i	$0.959650\pi$
$242$		0			0
$243$	12.7450	+	5.27915i	0.817592	+	0.338658i
$244$		0			0
$245$	15.4735	−	6.40933i	0.988565	−	0.409477i
$246$		0			0
$247$	−24.2159	−	24.2159i	−1.54082	−	1.54082i
$248$		0			0
$249$	0.0849729	+	0.205143i	0.00538494	+	0.0130004i
$250$		0			0
$251$		−	4.28826i		−	0.270673i	−0.990800	−	0.135336i	$-0.956788\pi$
$251$		−	4.28826i		−	0.270673i	0.990800	−	0.135336i	$-0.0432115\pi$
$252$		0			0
$253$	−6.05393	+	6.05393i	−0.380608	+	0.380608i
$254$		0			0
$255$	1.91179	+	8.46989i	0.119721	+	0.530405i
$256$		0			0
$257$	2.91648	−	2.91648i	0.181925	−	0.181925i	−0.610269	−	0.792194i	$-0.708939\pi$
$257$	2.91648	−	2.91648i	0.181925	−	0.181925i	0.792194	+	0.610269i	$0.208939\pi$
$258$		0			0
$259$			50.5336i			3.14000i
$260$		0			0
$261$	5.06739	+	12.2338i	0.313663	+	0.757251i
$262$		0			0
$263$	−5.09744	−	5.09744i	−0.314322	−	0.314322i	0.532260	−	0.846581i	$-0.321343\pi$
$263$	−5.09744	−	5.09744i	−0.314322	−	0.314322i	−0.846581	+	0.532260i	$0.821343\pi$
$264$		0			0
$265$	−6.48315	+	2.68541i	−0.398257	+	0.164963i
$266$		0			0
$267$	20.0509	+	8.30537i	1.22710	+	0.508280i
$268$		0			0
$269$	0.588473	−	1.42070i	0.0358799	−	0.0866216i	−0.904924	−	0.425574i	$-0.860072\pi$
$269$	0.588473	−	1.42070i	0.0358799	−	0.0866216i	0.940804	+	0.338952i	$0.110072\pi$
$270$		0			0
$271$	−2.06053			−0.125168			−0.0625841	−	0.998040i	$-0.519934\pi$
$271$	−2.06053			−0.125168			−0.0625841	+	0.998040i	$0.519934\pi$
$272$		0			0
$273$	46.1412			2.79259
$274$		0			0
$275$	−0.738530	+	1.78297i	−0.0445350	+	0.107517i
$276$		0			0
$277$	−16.3007	−	6.75199i	−0.979417	−	0.405688i	−0.165207	−	0.986259i	$-0.552829\pi$
$277$	−16.3007	−	6.75199i	−0.979417	−	0.405688i	−0.814209	+	0.580571i	$0.802829\pi$
$278$		0			0
$279$	−4.42545	+	1.83308i	−0.264945	+	0.109744i
$280$		0			0
$281$	5.90111	+	5.90111i	0.352031	+	0.352031i	0.860865	−	0.508834i	$-0.169923\pi$
$281$	5.90111	+	5.90111i	0.352031	+	0.352031i	−0.508834	+	0.860865i	$0.669923\pi$
$282$		0			0
$283$	3.05540	+	7.37638i	0.181625	+	0.438481i	0.988302	−	0.152512i	$-0.0487363\pi$
$283$	3.05540	+	7.37638i	0.181625	+	0.438481i	−0.806677	+	0.590993i	$0.798736\pi$
$284$		0			0
$285$			16.0410i			0.950188i
$286$		0			0
$287$	−7.09814	+	7.09814i	−0.418990	+	0.418990i
$288$		0			0
$289$	−7.30231	−	15.3517i	−0.429548	−	0.903044i
$290$		0			0
$291$	−13.2915	+	13.2915i	−0.779163	+	0.779163i
$292$		0			0
$293$			24.9469i			1.45741i	0.684826	+	0.728706i	$0.259878\pi$
$293$			24.9469i			1.45741i	−0.684826	+	0.728706i	$0.740122\pi$
$294$		0			0
$295$	2.82060	+	6.80954i	0.164222	+	0.396467i
$296$		0			0
$297$	−4.49768	−	4.49768i	−0.260982	−	0.260982i
$298$		0			0
$299$	18.4275	−	7.63294i	1.06569	−	0.441424i
$300$		0			0
$301$	36.6451	+	15.1789i	2.11219	+	0.874898i
$302$		0			0
$303$	−2.97636	+	7.18556i	−0.170987	+	0.412800i
$304$		0			0
$305$	−7.02802			−0.402423
$306$		0			0
$307$	15.5974			0.890188			0.445094	−	0.895484i	$-0.353170\pi$
$307$	15.5974			0.890188			0.445094	+	0.895484i	$0.353170\pi$
$308$		0			0
$309$	12.2526	−	29.5803i	0.697024	−	1.68277i
$310$		0			0
$311$	13.9339	+	5.77163i	0.790121	+	0.327279i	0.740992	−	0.671514i	$-0.234355\pi$
$311$	13.9339	+	5.77163i	0.790121	+	0.327279i	0.0491289	+	0.998792i	$0.484355\pi$
$312$		0			0
$313$	11.6841	−	4.83973i	0.660426	−	0.273558i	−0.0271916	−	0.999630i	$-0.508656\pi$
$313$	11.6841	−	4.83973i	0.660426	−	0.273558i	0.687618	+	0.726073i	$0.258656\pi$
$314$		0			0
$315$	−4.94466	−	4.94466i	−0.278600	−	0.278600i
$316$		0			0
$317$	5.47967	+	13.2291i	0.307769	+	0.743020i	0.999777	+	0.0211298i	$0.00672631\pi$
$317$	5.47967	+	13.2291i	0.307769	+	0.743020i	−0.692008	+	0.721890i	$0.743274\pi$
$318$		0			0
$319$		−	17.8090i		−	0.997111i
$320$		0			0
$321$	21.3521	−	21.3521i	1.19176	−	1.19176i
$322$		0			0
$323$	−6.91488	−	30.6353i	−0.384754	−	1.70459i
$324$		0			0
$325$	3.17916	−	3.17916i	0.176348	−	0.176348i
$326$		0			0
$327$		−	25.6849i		−	1.42038i
$328$		0			0
$329$	11.4377	+	27.6130i	0.630581	+	1.52236i
$330$		0			0
$331$	−17.7379	−	17.7379i	−0.974963	−	0.974963i	0.0247316	−	0.999694i	$-0.492127\pi$
$331$	−17.7379	−	17.7379i	−0.974963	−	0.974963i	−0.999694	+	0.0247316i	$0.992127\pi$
$332$		0			0
$333$	13.7471	−	5.69425i	0.753339	−	0.312043i
$334$		0			0
$335$	−5.22382	−	2.16378i	−0.285408	−	0.118220i
$336$		0			0
$337$	0.938317	−	2.26530i	0.0511134	−	0.123399i	−0.896260	−	0.443528i	$-0.853727\pi$
$337$	0.938317	−	2.26530i	0.0511134	−	0.123399i	0.947374	+	0.320130i	$0.103727\pi$
$338$		0			0
$339$	−17.6818			−0.960342
$340$		0			0
$341$	6.44224			0.348867
$342$		0			0
$343$	18.1798	−	43.8900i	0.981618	−	2.36984i
$344$		0			0
$345$	−8.63144	−	3.57526i	−0.464701	−	0.192486i
$346$		0			0
$347$	−24.2176	+	10.0313i	−1.30007	+	0.538506i	−0.921971	−	0.387259i	$-0.873422\pi$
$347$	−24.2176	+	10.0313i	−1.30007	+	0.538506i	−0.378098	+	0.925766i	$0.623422\pi$
$348$		0			0
$349$	−4.96740	−	4.96740i	−0.265899	−	0.265899i	0.561546	−	0.827445i	$-0.310207\pi$
$349$	−4.96740	−	4.96740i	−0.265899	−	0.265899i	−0.827445	+	0.561546i	$0.810207\pi$
$350$		0			0
$351$	5.67077	+	13.6905i	0.302683	+	0.730742i
$352$		0			0
$353$		−	2.92576i		−	0.155723i	−0.996964	−	0.0778613i	$-0.975191\pi$
$353$		−	2.92576i		−	0.155723i	0.996964	−	0.0778613i	$-0.0248091\pi$
$354$		0			0
$355$	−2.05152	+	2.05152i	−0.108883	+	0.108883i
$356$		0			0
$357$	35.7742	+	22.5985i	1.89337	+	1.19604i
$358$		0			0
$359$	−3.23173	+	3.23173i	−0.170564	+	0.170564i	−0.787227	−	0.616663i	$-0.788484\pi$
$359$	−3.23173	+	3.23173i	−0.170564	+	0.170564i	0.616663	+	0.787227i	$0.288484\pi$
$360$		0			0
$361$		−	39.0197i		−	2.05367i
$362$		0			0
$363$	5.86343	+	14.1556i	0.307750	+	0.742975i
$364$		0			0
$365$	−4.15218	−	4.15218i	−0.217335	−	0.217335i
$366$		0			0
$367$	12.5626	−	5.20360i	0.655763	−	0.271626i	−0.0298914	−	0.999553i	$-0.509516\pi$
$367$	12.5626	−	5.20360i	0.655763	−	0.271626i	0.685654	+	0.727927i	$0.259516\pi$
$368$		0			0
$369$	2.73081	+	1.13114i	0.142160	+	0.0588848i
$370$		0			0
$371$	−13.0866	+	31.5939i	−0.679423	+	1.64027i
$372$		0			0
$373$	−8.36556			−0.433152			−0.216576	−	0.976266i	$-0.569489\pi$
$373$	−8.36556			−0.433152			−0.216576	+	0.976266i	$0.569489\pi$
$374$		0			0
$375$	−2.10593			−0.108750
$376$		0			0
$377$	−15.8773	+	38.3313i	−0.817725	+	1.97416i
$378$		0			0
$379$	5.15268	+	2.13431i	0.264675	+	0.109632i	0.511075	−	0.859536i	$-0.329247\pi$
$379$	5.15268	+	2.13431i	0.264675	+	0.109632i	−0.246399	+	0.969168i	$0.579247\pi$
$380$		0			0
$381$	−19.8930	+	8.23993i	−1.01915	+	0.422144i
$382$		0			0
$383$	−5.21690	−	5.21690i	−0.266571	−	0.266571i	0.561146	−	0.827717i	$-0.310361\pi$
$383$	−5.21690	−	5.21690i	−0.266571	−	0.266571i	−0.827717	+	0.561146i	$0.810361\pi$
$384$		0			0
$385$	3.59903	+	8.68882i	0.183423	+	0.442823i
$386$		0			0
$387$		−	11.6793i		−	0.593694i
$388$		0			0
$389$	−6.65024	+	6.65024i	−0.337181	+	0.337181i	−0.855305	−	0.518125i	$-0.826630\pi$
$389$	−6.65024	+	6.65024i	−0.337181	+	0.337181i	0.518125	+	0.855305i	$0.326630\pi$
$390$		0			0
$391$	18.0256	+	3.10727i	0.911595	+	0.157141i
$392$		0			0
$393$	−7.76934	+	7.76934i	−0.391912	+	0.391912i
$394$		0			0
$395$		−	9.51463i		−	0.478733i
$396$		0			0
$397$	−1.18424	−	2.85900i	−0.0594351	−	0.143489i	0.891372	−	0.453272i	$-0.149743\pi$
$397$	−1.18424	−	2.85900i	−0.0594351	−	0.143489i	−0.950807	+	0.309783i	$0.899743\pi$
$398$		0			0
$399$	55.2757	+	55.2757i	2.76724	+	2.76724i
$400$		0			0
$401$	−15.7055	+	6.50542i	−0.784294	+	0.324865i	−0.738647	−	0.674092i	$-0.764535\pi$
$401$	−15.7055	+	6.50542i	−0.784294	+	0.324865i	−0.0456472	+	0.998958i	$0.514535\pi$
$402$		0			0
$403$	−13.8660	−	5.74349i	−0.690715	−	0.286104i
$404$		0			0
$405$	4.30357	−	10.3897i	0.213846	−	0.516270i
$406$		0			0
$407$	−20.0120			−0.991960
$408$		0			0
$409$	−15.2403			−0.753582			−0.376791	−	0.926298i	$-0.622973\pi$
$409$	−15.2403			−0.753582			−0.376791	+	0.926298i	$0.622973\pi$
$410$		0			0
$411$	9.66147	−	23.3249i	0.476565	−	1.15053i
$412$		0			0
$413$	33.1845	+	13.7455i	1.63290	+	0.676370i
$414$		0			0
$415$	0.0974120	−	0.0403494i	0.00478177	−	0.00198067i
$416$		0			0
$417$	−24.2801	−	24.2801i	−1.18900	−	1.18900i
$418$		0			0
$419$	−2.51035	−	6.06051i	−0.122638	−	0.296075i	0.850623	−	0.525776i	$-0.176225\pi$
$419$	−2.51035	−	6.06051i	−0.122638	−	0.296075i	−0.973261	+	0.229701i	$0.926225\pi$
$420$		0			0
$421$		−	26.3710i		−	1.28524i	−0.766184	−	0.642622i	$-0.777847\pi$
$421$		−	26.3710i		−	1.28524i	0.766184	−	0.642622i	$-0.222153\pi$
$422$		0			0
$423$	6.22302	−	6.22302i	0.302573	−	0.302573i
$424$		0			0
$425$	4.02192	−	0.907813i	0.195092	−	0.0440354i
$426$		0			0
$427$	−24.2178	+	24.2178i	−1.17198	+	1.17198i
$428$		0			0
$429$			18.2726i			0.882210i
$430$		0			0
$431$	−5.24667	−	12.6666i	−0.252723	−	0.610128i	0.745699	−	0.666283i	$-0.232116\pi$
$431$	−5.24667	−	12.6666i	−0.252723	−	0.610128i	−0.998422	+	0.0561551i	$0.982116\pi$
$432$		0			0
$433$	5.55460	+	5.55460i	0.266937	+	0.266937i	0.827865	−	0.560928i	$-0.189555\pi$
$433$	5.55460	+	5.55460i	0.266937	+	0.266937i	−0.560928	+	0.827865i	$0.689555\pi$
$434$		0			0
$435$	17.9543	−	7.43693i	0.860845	−	0.356574i
$436$		0			0
$437$	31.2196	+	12.9316i	1.49344	+	0.618601i
$438$		0			0
$439$	3.29798	−	7.96202i	0.157404	−	0.380006i	−0.825429	−	0.564506i	$-0.809067\pi$
$439$	3.29798	−	7.96202i	0.157404	−	0.380006i	0.982833	+	0.184500i	$0.0590666\pi$
$440$		0			0
$441$	−24.0330			−1.14443
$442$		0			0
$443$	25.8387			1.22763			0.613817	−	0.789448i	$-0.289633\pi$
$443$	25.8387			1.22763			0.613817	+	0.789448i	$0.289633\pi$
$444$		0			0
$445$	3.94380	−	9.52118i	0.186954	−	0.451347i
$446$		0			0
$447$	13.4364	+	5.56555i	0.635521	+	0.263241i
$448$		0			0
$449$	−11.1602	+	4.62270i	−0.526681	+	0.218159i	−0.630149	−	0.776474i	$-0.717006\pi$
$449$	−11.1602	+	4.62270i	−0.526681	+	0.218159i	0.103468	+	0.994633i	$0.467006\pi$
$450$		0			0
$451$	−2.81097	−	2.81097i	−0.132363	−	0.132363i
$452$		0			0
$453$	9.79693	+	23.6519i	0.460300	+	1.11126i
$454$		0			0
$455$		−	21.9101i		−	1.02716i
$456$		0			0
$457$	13.5484	−	13.5484i	0.633769	−	0.633769i	−0.315242	−	0.949011i	$-0.602086\pi$
$457$	13.5484	−	13.5484i	0.633769	−	0.633769i	0.949011	+	0.315242i	$0.102086\pi$
$458$		0			0
$459$	−2.30850	+	13.3918i	−0.107751	+	0.625078i
$460$		0			0
$461$	13.8643	−	13.8643i	0.645726	−	0.645726i	−0.306231	−	0.951957i	$-0.599068\pi$
$461$	13.8643	−	13.8643i	0.645726	−	0.645726i	0.951957	+	0.306231i	$0.0990681\pi$
$462$		0			0
$463$			17.7003i			0.822601i	0.911500	+	0.411300i	$0.134925\pi$
$463$			17.7003i			0.822601i	−0.911500	+	0.411300i	$0.865075\pi$
$464$		0			0
$465$	2.69025	+	6.49483i	0.124757	+	0.301190i
$466$		0			0
$467$	17.5299	+	17.5299i	0.811188	+	0.811188i	0.984812	−	0.173624i	$-0.0555478\pi$
$467$	17.5299	+	17.5299i	0.811188	+	0.811188i	−0.173624	+	0.984812i	$0.555548\pi$
$468$		0			0
$469$	−25.4569	+	10.5446i	−1.17549	+	0.486904i
$470$		0			0
$471$	14.3460	+	5.94232i	0.661030	+	0.273808i
$472$		0			0
$473$	−6.01107	+	14.5120i	−0.276389	+	0.667263i
$474$		0			0
$475$	7.61707			0.349495
$476$		0			0
$477$	10.0694			0.461047
$478$		0			0
$479$	6.17703	−	14.9127i	0.282236	−	0.681377i	−0.717652	−	0.696402i	$-0.754783\pi$
$479$	6.17703	−	14.9127i	0.282236	−	0.681377i	0.999887	+	0.0150254i	$0.00478293\pi$
$480$		0			0
$481$	43.0731	+	17.8415i	1.96396	+	0.813501i
$482$		0			0
$483$	−42.0630	+	17.4231i	−1.91393	+	0.792777i
$484$		0			0
$485$	6.31147	+	6.31147i	0.286589	+	0.286589i
$486$		0			0
$487$	−3.11081	−	7.51016i	−0.140964	−	0.340318i	0.837592	−	0.546296i	$-0.183962\pi$
$487$	−3.11081	−	7.51016i	−0.140964	−	0.340318i	−0.978557	+	0.205978i	$0.933962\pi$
$488$		0			0
$489$		−	0.675725i		−	0.0305573i
$490$		0			0
$491$	−0.950951	+	0.950951i	−0.0429158	+	0.0429158i	−0.728239	−	0.685323i	$-0.759661\pi$
$491$	−0.950951	+	0.950951i	−0.0429158	+	0.0429158i	0.685323	+	0.728239i	$0.259661\pi$
$492$		0			0
$493$	−31.0835	+	21.9428i	−1.39993	+	0.988254i
$494$		0			0
$495$	1.95816	−	1.95816i	0.0880127	−	0.0880127i
$496$		0			0
$497$			14.1386i			0.634203i
$498$		0			0
$499$	−9.95716	−	24.0387i	−0.445744	−	1.07612i	−0.973901	−	0.226974i	$-0.927117\pi$
$499$	−9.95716	−	24.0387i	−0.445744	−	1.07612i	0.528157	−	0.849147i	$-0.322883\pi$
$500$		0			0
$501$	−23.4572	−	23.4572i	−1.04799	−	1.04799i
$502$		0			0
$503$	−19.1675	+	7.93942i	−0.854635	+	0.354001i	−0.766607	−	0.642117i	$-0.778056\pi$
$503$	−19.1675	+	7.93942i	−0.854635	+	0.354001i	−0.0880277	+	0.996118i	$0.528056\pi$
$504$		0			0
$505$	3.41206	+	1.41332i	0.151835	+	0.0628920i
$506$		0			0
$507$	5.81393	−	14.0361i	0.258206	−	0.623364i
$508$		0			0
$509$	−2.60349			−0.115397			−0.0576987	−	0.998334i	$-0.518376\pi$
$509$	−2.60349			−0.115397			−0.0576987	+	0.998334i	$0.518376\pi$
$510$		0			0
$511$	−28.6160			−1.26590
$512$		0			0
$513$	−9.60732	+	23.1941i	−0.424173	+	1.02405i
$514$		0			0
$515$	−14.0462	−	5.81813i	−0.618949	−	0.256377i
$516$		0			0
$517$	−10.9352	+	4.52950i	−0.480928	+	0.199207i
$518$		0			0
$519$	27.2176	+	27.2176i	1.19472	+	1.19472i
$520$		0			0
$521$	9.96740	+	24.0634i	0.436680	+	1.05424i	0.977088	+	0.212835i	$0.0682697\pi$
$521$	9.96740	+	24.0634i	0.436680	+	1.05424i	−0.540409	+	0.841403i	$0.681730\pi$
$522$		0			0
$523$			44.9469i			1.96539i	0.185229	+	0.982695i	$0.440697\pi$
$523$			44.9469i			1.96539i	−0.185229	+	0.982695i	$0.559303\pi$
$524$		0			0
$525$	−7.25681	+	7.25681i	−0.316713	+	0.316713i
$526$		0			0
$527$	−7.93761	−	11.2442i	−0.345768	−	0.489804i
$528$		0			0
$529$	2.34685	−	2.34685i	0.102037	−	0.102037i
$530$		0			0
$531$		−	10.5764i		−	0.458975i
$532$		0			0
$533$	3.54413	+	8.55629i	0.153513	+	0.370614i
$534$		0			0
$535$	−10.1390	−	10.1390i	−0.438349	−	0.438349i
$536$		0			0
$537$	6.96873	−	2.88654i	0.300723	−	0.124564i
$538$		0			0
$539$	29.8619	+	12.3692i	1.28624	+	0.532779i
$540$		0			0
$541$	4.44860	−	10.7399i	0.191260	−	0.461743i	−0.798938	−	0.601414i	$-0.794604\pi$
$541$	4.44860	−	10.7399i	0.191260	−	0.461743i	0.990198	+	0.139671i	$0.0446044\pi$
$542$		0			0
$543$	−30.5312			−1.31022
$544$		0			0
$545$	−12.1965			−0.522440
$546$		0			0
$547$	−12.4848	+	30.1411i	−0.533813	+	1.28874i	0.395167	+	0.918609i	$0.370687\pi$
$547$	−12.4848	+	30.1411i	−0.533813	+	1.28874i	−0.928980	+	0.370129i	$0.879313\pi$
$548$		0			0
$549$	9.31713	+	3.85928i	0.397646	+	0.164710i
$550$		0			0
$551$	−64.9402	+	26.8991i	−2.76655	+	1.14594i
$552$		0			0
$553$	−32.7864	−	32.7864i	−1.39422	−	1.39422i
$554$		0			0
$555$	−8.35693	−	20.1754i	−0.354732	−	0.856398i
$556$		0			0
$557$		−	34.7475i		−	1.47230i	−0.676818	−	0.736150i	$-0.736642\pi$
$557$		−	34.7475i		−	1.47230i	0.676818	−	0.736150i	$-0.263358\pi$
$558$		0			0
$559$	25.8760	−	25.8760i	1.09444	−	1.09444i
$560$		0			0
$561$	−8.94935	+	14.1671i	−0.377842	+	0.598136i
$562$		0			0
$563$	26.3555	−	26.3555i	1.11075	−	1.11075i	0.117703	−	0.993049i	$-0.462447\pi$
$563$	26.3555	−	26.3555i	1.11075	−	1.11075i	0.993049	−	0.117703i	$-0.0375529\pi$
$564$		0			0
$565$			8.39618i			0.353230i
$566$		0			0
$567$	−20.9723	−	50.6316i	−0.880753	−	2.12633i
$568$		0			0
$569$	−15.0353	−	15.0353i	−0.630311	−	0.630311i	0.317835	−	0.948146i	$-0.397044\pi$
$569$	−15.0353	−	15.0353i	−0.630311	−	0.630311i	−0.948146	+	0.317835i	$0.897044\pi$
$570$		0			0
$571$	27.1423	−	11.2427i	1.13587	−	0.470493i	0.266098	−	0.963946i	$-0.414265\pi$
$571$	27.1423	−	11.2427i	1.13587	−	0.470493i	0.869773	+	0.493453i	$0.164265\pi$
$572$		0			0
$573$	−24.6479	−	10.2095i	−1.02968	−	0.426508i
$574$		0			0
$575$	−1.69771	+	4.09864i	−0.0707995	+	0.170925i
$576$		0			0
$577$	−15.1029			−0.628740			−0.314370	−	0.949300i	$-0.601793\pi$
$577$	−15.1029			−0.628740			−0.314370	+	0.949300i	$0.601793\pi$
$578$		0			0
$579$	−6.54509			−0.272005
$580$		0			0
$581$	0.196632	−	0.474711i	0.00815766	−	0.0196943i
$582$		0			0
$583$	−12.5116	−	5.18249i	−0.518179	−	0.214637i
$584$		0			0
$585$	−5.96043	+	2.46889i	−0.246433	+	0.102076i
$586$		0			0
$587$	−25.2735	−	25.2735i	−1.04315	−	1.04315i	−0.999026	−	0.0441247i	$-0.985950\pi$
$587$	−25.2735	−	25.2735i	−1.04315	−	1.04315i	−0.0441247	−	0.999026i	$-0.514050\pi$
$588$		0			0
$589$	−9.73052	−	23.4915i	−0.400939	−	0.967952i
$590$		0			0
$591$			40.4820i			1.66521i
$592$		0			0
$593$	7.93268	−	7.93268i	0.325756	−	0.325756i	−0.525214	−	0.850970i	$-0.676015\pi$
$593$	7.93268	−	7.93268i	0.325756	−	0.325756i	0.850970	+	0.525214i	$0.176015\pi$
$594$		0			0
$595$	10.7309	−	16.9874i	0.439924	−	0.696414i
$596$		0			0
$597$	13.7553	−	13.7553i	0.562965	−	0.562965i
$598$		0			0
$599$			24.6116i			1.00560i	0.864402	+	0.502801i	$0.167697\pi$
$599$			24.6116i			1.00560i	−0.864402	+	0.502801i	$0.832303\pi$
$600$		0			0
$601$	−11.9527	−	28.8563i	−0.487559	−	1.17707i	−0.955945	−	0.293547i	$-0.905164\pi$
$601$	−11.9527	−	28.8563i	−0.487559	−	1.17707i	0.468386	−	0.883524i	$-0.344836\pi$
$602$		0			0
$603$	5.73709	+	5.73709i	0.233633	+	0.233633i
$604$		0			0
$605$	6.72177	−	2.78425i	0.273279	−	0.113196i
$606$		0			0
$607$	24.1345	+	9.99684i	0.979589	+	0.405759i	0.814273	−	0.580482i	$-0.197136\pi$
$607$	24.1345	+	9.99684i	0.979589	+	0.405759i	0.165316	+	0.986241i	$0.447136\pi$
$608$		0			0
$609$	36.2419	−	87.4957i	1.46860	−	3.54551i
$610$		0			0
$611$	27.5746			1.11555
$612$		0			0
$613$	30.7925			1.24370			0.621849	−	0.783137i	$-0.286382\pi$
$613$	30.7925			1.24370			0.621849	+	0.783137i	$0.286382\pi$
$614$		0			0
$615$	1.66007	−	4.00776i	0.0669404	−	0.161608i
$616$		0			0
$617$	−34.6954	−	14.3713i	−1.39679	−	0.578568i	−0.447871	−	0.894098i	$-0.647817\pi$
$617$	−34.6954	−	14.3713i	−1.39679	−	0.578568i	−0.948915	+	0.315531i	$0.897817\pi$
$618$		0			0
$619$	18.6108	−	7.70886i	0.748033	−	0.309845i	0.0240941	−	0.999710i	$-0.492330\pi$
$619$	18.6108	−	7.70886i	0.748033	−	0.309845i	0.723939	+	0.689864i	$0.242330\pi$
$620$		0			0
$621$	−10.3391	−	10.3391i	−0.414895	−	0.414895i
$622$		0			0
$623$	−19.2191	−	46.3989i	−0.769995	−	1.85893i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$		0			0
$627$	−21.8900	+	21.8900i	−0.874202	+	0.874202i
$628$		0			0
$629$	24.6572	+	34.9287i	0.983149	+	1.39270i
$630$		0			0
$631$	−3.50409	+	3.50409i	−0.139496	+	0.139496i	−0.773406	−	0.633911i	$-0.781449\pi$
$631$	−3.50409	+	3.50409i	−0.139496	+	0.139496i	0.633911	+	0.773406i	$0.281449\pi$
$632$		0			0
$633$			41.9245i			1.66635i
$634$		0			0
$635$	3.91273	+	9.44616i	0.155272	+	0.374859i
$636$		0			0
$637$	−53.2459	−	53.2459i	−2.10968	−	2.10968i
$638$		0			0
$639$	3.84626	−	1.59318i	0.152156	−	0.0630250i
$640$		0			0
$641$	3.73965	+	1.54901i	0.147707	+	0.0611823i	0.455312	−	0.890332i	$-0.349528\pi$
$641$	3.73965	+	1.54901i	0.147707	+	0.0611823i	−0.307605	+	0.951514i	$0.599528\pi$
$642$		0			0
$643$	−1.87783	+	4.53349i	−0.0740545	+	0.178783i	−0.956572	−	0.291496i	$-0.905847\pi$
$643$	−1.87783	+	4.53349i	−0.0740545	+	0.178783i	0.882517	+	0.470280i	$0.155847\pi$
$644$		0			0
$645$	−17.1407			−0.674913
$646$		0			0
$647$	−37.6354			−1.47960			−0.739800	−	0.672827i	$-0.765080\pi$
$647$	−37.6354			−1.47960			−0.739800	+	0.672827i	$0.765080\pi$
$648$		0			0
$649$	−5.44340	+	13.1415i	−0.213672	+	0.515851i
$650$		0			0
$651$	31.6508	+	13.1102i	1.24049	+	0.513829i
$652$		0			0
$653$	−38.9988	+	16.1538i	−1.52614	+	0.632149i	−0.978811	−	0.204767i	$-0.934356\pi$
$653$	−38.9988	+	16.1538i	−1.52614	+	0.632149i	−0.547331	+	0.836916i	$0.684356\pi$
$654$		0			0
$655$	3.68927	+	3.68927i	0.144152	+	0.144152i
$656$		0			0
$657$	3.22452	+	7.78469i	0.125801	+	0.303710i
$658$		0			0
$659$		−	16.4870i		−	0.642242i	−0.947038	−	0.321121i	$-0.895940\pi$
$659$		−	16.4870i		−	0.642242i	0.947038	−	0.321121i	$-0.104060\pi$
$660$		0			0
$661$	−14.3736	+	14.3736i	−0.559070	+	0.559070i	−0.929043	−	0.369973i	$-0.879367\pi$
$661$	−14.3736	+	14.3736i	−0.559070	+	0.559070i	0.369973	+	0.929043i	$0.379367\pi$
$662$		0			0
$663$	31.8927	−	22.5140i	1.23861	−	0.874373i
$664$		0			0
$665$	26.2476	−	26.2476i	1.01784	−	1.01784i
$666$		0			0
$667$		−	40.9387i		−	1.58515i
$668$		0			0
$669$	−5.52909	−	13.3484i	−0.213767	−	0.516079i
$670$		0			0
$671$	−9.59062	−	9.59062i	−0.370242	−	0.370242i
$672$		0			0
$673$	15.5797	−	6.45334i	0.600555	−	0.248758i	−0.0616291	−	0.998099i	$-0.519630\pi$
$673$	15.5797	−	6.45334i	0.600555	−	0.248758i	0.662184	+	0.749341i	$0.269630\pi$
$674$		0			0
$675$	−3.04502	−	1.26129i	−0.117203	−	0.0485470i
$676$		0			0
$677$	3.19803	−	7.72072i	0.122910	−	0.296731i	−0.850434	−	0.526082i	$-0.823660\pi$
$677$	3.19803	−	7.72072i	0.122910	−	0.296731i	0.973344	+	0.229351i	$0.0736603\pi$
$678$		0			0
$679$	43.4973			1.66927
$680$		0			0
$681$	−26.4133			−1.01216
$682$		0			0
$683$	18.1884	−	43.9107i	0.695961	−	1.68020i	−0.0364503	−	0.999335i	$-0.511605\pi$
$683$	18.1884	−	43.9107i	0.695961	−	1.68020i	0.732411	−	0.680863i	$-0.238395\pi$
$684$		0			0
$685$	−11.0758	−	4.58775i	−0.423185	−	0.175289i
$686$		0			0
$687$	33.7647	−	13.9858i	1.28820	−	0.533591i
$688$		0			0
$689$	22.3092	+	22.3092i	0.849912	+	0.849912i
$690$		0			0
$691$	−0.197091	−	0.475819i	−0.00749769	−	0.0181010i	0.920086	−	0.391716i	$-0.128118\pi$
$691$	−0.197091	−	0.475819i	−0.00749769	−	0.0181010i	−0.927584	+	0.373615i	$0.878118\pi$
$692$		0			0
$693$		−	13.4952i		−	0.512641i
$694$		0			0
$695$	−11.5294	+	11.5294i	−0.437335	+	0.437335i
$696$		0			0
$697$	−1.44277	+	8.36967i	−0.0546488	+	0.317024i
$698$		0			0
$699$	−8.47377	+	8.47377i	−0.320507	+	0.320507i
$700$		0			0
$701$			24.5219i			0.926179i	0.886312	+	0.463089i	$0.153259\pi$
$701$			24.5219i			0.926179i	−0.886312	+	0.463089i	$0.846741\pi$
$702$		0			0
$703$	30.2267	+	72.9737i	1.14002	+	2.75225i
$704$		0			0
$705$	−9.13294	−	9.13294i	−0.343967	−	0.343967i
$706$		0			0
$707$	16.6278	−	6.88744i	0.625351	−	0.259029i
$708$		0			0
$709$	8.89780	+	3.68559i	0.334164	+	0.138415i	0.543455	−	0.839438i	$-0.317116\pi$
$709$	8.89780	+	3.68559i	0.334164	+	0.138415i	−0.209291	+	0.977853i	$0.567116\pi$
$710$		0			0
$711$	−5.22475	+	12.6137i	−0.195943	+	0.473049i
$712$		0			0
$713$	14.8092			0.554610
$714$		0			0
$715$	8.67674			0.324492
$716$		0			0
$717$	9.51074	−	22.9610i	0.355185	−	0.857493i
$718$		0			0
$719$	−44.4214	−	18.3999i	−1.65664	−	0.686202i	−0.658825	−	0.752296i	$-0.728946\pi$
$719$	−44.4214	−	18.3999i	−1.65664	−	0.686202i	−0.997813	+	0.0660937i	$0.978946\pi$
$720$		0			0
$721$	−68.4504	+	28.3531i	−2.54923	+	1.05592i
$722$		0			0
$723$	−22.9515	−	22.9515i	−0.853575	−	0.853575i
$724$		0			0
$725$	−3.53143	−	8.52562i	−0.131154	−	0.316633i
$726$		0			0
$727$			28.6934i			1.06418i	0.846688	+	0.532089i	$0.178593\pi$
$727$			28.6934i			1.06418i	−0.846688	+	0.532089i	$0.821407\pi$
$728$		0			0
$729$	3.31337	−	3.31337i	0.122717	−	0.122717i
$730$		0			0
$731$	32.7354	−	7.38891i	1.21076	−	0.273289i
$732$		0			0
$733$	−15.8642	+	15.8642i	−0.585959	+	0.585959i	−0.936534	−	0.350576i	$-0.885986\pi$
$733$	−15.8642	+	15.8642i	−0.585959	+	0.585959i	0.350576	+	0.936534i	$0.385986\pi$
$734$		0			0
$735$			35.2709i			1.30099i
$736$		0			0
$737$	−4.17581	−	10.0813i	−0.153818	−	0.371350i
$738$		0			0
$739$	4.86213	+	4.86213i	0.178856	+	0.178856i	0.790857	−	0.612001i	$-0.209635\pi$
$739$	4.86213	+	4.86213i	0.178856	+	0.178856i	−0.612001	+	0.790857i	$0.709635\pi$
$740$		0			0
$741$	66.6308	−	27.5994i	2.44774	−	1.01389i
$742$		0			0
$743$	34.0930	+	14.1218i	1.25075	+	0.518078i	0.907058	−	0.421005i	$-0.138323\pi$
$743$	34.0930	+	14.1218i	1.25075	+	0.518078i	0.343692	+	0.939083i	$0.388323\pi$
$744$		0			0
$745$	2.64280	−	6.38028i	0.0968246	−	0.233755i
$746$		0			0
$747$	−0.151297			−0.00553568
$748$		0			0
$749$	−69.8761			−2.55322
$750$		0			0
$751$	−1.62083	+	3.91302i	−0.0591448	+	0.142788i	−0.950689	−	0.310145i	$-0.899622\pi$
$751$	−1.62083	+	3.91302i	−0.0591448	+	0.142788i	0.891544	+	0.452933i	$0.149622\pi$
$752$		0			0
$753$	8.34335	+	3.45593i	0.304049	+	0.125941i
$754$		0			0
$755$	11.2311	−	4.65207i	0.408741	−	0.169306i
$756$		0			0
$757$	−11.3288	−	11.3288i	−0.411753	−	0.411753i	0.470596	−	0.882349i	$-0.344039\pi$
$757$	−11.3288	−	11.3288i	−0.411753	−	0.411753i	−0.882349	+	0.470596i	$0.844039\pi$
$758$		0			0
$759$	−6.89980	−	16.6576i	−0.250447	−	0.604632i
$760$		0			0
$761$			14.9621i			0.542377i	0.962526	+	0.271188i	$0.0874166\pi$
$761$			14.9621i			0.542377i	−0.962526	+	0.271188i	$0.912583\pi$
$762$		0			0
$763$	−42.0278	+	42.0278i	−1.52151	+	1.52151i
$764$		0			0
$765$	−5.83042	−	1.00505i	−0.210799	−	0.0363377i
$766$		0			0
$767$	23.4323	−	23.4323i	0.846092	−	0.846092i
$768$		0			0
$769$			48.3875i			1.74490i	0.488706	+	0.872449i	$0.337469\pi$
$769$			48.3875i			1.74490i	−0.488706	+	0.872449i	$0.662531\pi$
$770$		0			0
$771$	3.32397	+	8.02477i	0.119710	+	0.289005i
$772$		0			0
$773$	−29.8720	−	29.8720i	−1.07442	−	1.07442i	−0.996998	−	0.0774218i	$-0.975331\pi$
$773$	−29.8720	−	29.8720i	−1.07442	−	1.07442i	−0.0774218	−	0.996998i	$-0.524669\pi$
$774$		0			0
$775$	3.08407	−	1.27746i	0.110783	−	0.0458878i
$776$		0			0
$777$	−98.3194	−	40.7252i	−3.52719	−	1.46101i
$778$		0			0
$779$	−6.00440	+	14.4959i	−0.215130	+	0.519370i
$780$		0			0
$781$	−5.59910			−0.200352
$782$		0			0
$783$	30.4148			1.08694
$784$		0			0
$785$	2.82171	−	6.81220i	0.100711	−	0.243138i
$786$		0			0
$787$	−26.6747	−	11.0490i	−0.950850	−	0.393855i	−0.147300	−	0.989092i	$-0.547058\pi$
$787$	−26.6747	−	11.0490i	−0.950850	−	0.393855i	−0.803550	+	0.595237i	$0.797058\pi$
$788$		0			0
$789$	14.0258	−	5.80966i	0.499330	−	0.206829i
$790$		0			0
$791$	28.9324	+	28.9324i	1.02872	+	1.02872i
$792$		0			0
$793$	12.0921	+	29.1928i	0.429402	+	1.03667i
$794$		0			0
$795$		−	14.7780i		−	0.524120i
$796$		0			0
$797$	8.65980	−	8.65980i	0.306746	−	0.306746i	−0.536900	−	0.843646i	$-0.680405\pi$
$797$	8.65980	−	8.65980i	0.306746	−	0.306746i	0.843646	+	0.536900i	$0.180405\pi$
$798$		0			0
$799$	21.3792	+	13.5052i	0.756340	+	0.477780i
$800$		0			0
$801$	−10.4567	+	10.4567i	−0.369469	+	0.369469i
$802$		0			0
$803$		−	11.3324i		−	0.399910i
$804$		0			0
$805$	8.27334	+	19.9736i	0.291597	+	0.703977i
$806$		0			0
$807$	2.28990	+	2.28990i	0.0806082	+	0.0806082i
$808$		0			0
$809$	2.13669	−	0.885046i	0.0751220	−	0.0311166i	−0.344806	−	0.938674i	$-0.612055\pi$
$809$	2.13669	−	0.885046i	0.0751220	−	0.0311166i	0.419928	+	0.907557i	$0.362055\pi$
$810$		0			0
$811$	−14.9952	−	6.21123i	−0.526554	−	0.218106i	0.103539	−	0.994625i	$-0.466983\pi$
$811$	−14.9952	−	6.21123i	−0.526554	−	0.218106i	−0.630093	+	0.776520i	$0.716983\pi$
$812$		0			0
$813$	1.66059	−	4.00902i	0.0582394	−	0.140602i
$814$		0			0
$815$	−0.320868			−0.0112395
$816$		0			0
$817$	61.9971			2.16900
$818$		0			0
$819$	−12.0315	+	29.0465i	−0.420414	+	1.01497i
$820$		0			0
$821$	−38.8126	−	16.0767i	−1.35457	−	0.561081i	−0.417008	−	0.908903i	$-0.636921\pi$
$821$	−38.8126	−	16.0767i	−1.35457	−	0.561081i	−0.937561	+	0.347822i	$0.886921\pi$
$822$		0			0
$823$	16.4663	−	6.82056i	0.573979	−	0.237750i	−0.0767623	−	0.997049i	$-0.524458\pi$
$823$	16.4663	−	6.82056i	0.573979	−	0.237750i	0.650741	+	0.759300i	$0.274458\pi$
$824$		0			0
$825$	−2.87381	−	2.87381i	−0.100053	−	0.100053i
$826$		0			0
$827$	−10.8359	−	26.1602i	−0.376802	−	0.909681i	−0.992561	−	0.121746i	$-0.961151\pi$
$827$	−10.8359	−	26.1602i	−0.376802	−	0.909681i	0.615759	−	0.787934i	$-0.288849\pi$
$828$		0			0
$829$			27.0236i			0.938570i	0.883047	+	0.469285i	$0.155488\pi$
$829$			27.0236i			0.938570i	−0.883047	+	0.469285i	$0.844512\pi$
$830$		0			0
$831$	26.2737	−	26.2737i	0.911424	−	0.911424i
$832$		0			0
$833$	−15.2044	−	67.3608i	−0.526802	−	2.33391i
$834$		0			0
$835$	−11.1386	+	11.1386i	−0.385468	+	0.385468i
$836$		0			0
$837$			11.0023i			0.380295i
$838$		0			0
$839$	11.3532	+	27.4090i	0.391955	+	0.946262i	0.989514	+	0.144438i	$0.0461373\pi$
$839$	11.3532	+	27.4090i	0.391955	+	0.946262i	−0.597559	+	0.801825i	$0.703863\pi$
$840$		0			0
$841$	39.7091	+	39.7091i	1.36928	+	1.36928i
$842$		0			0
$843$	−16.2371	+	6.72562i	−0.559235	+	0.231643i
$844$		0			0
$845$	−6.66502	−	2.76074i	−0.229284	−	0.0949724i
$846$		0			0
$847$	13.5683	−	32.7568i	0.466212	−	1.12554i
$848$		0			0
$849$	−16.8140			−0.577056
$850$		0			0
$851$	−46.0031			−1.57697
$852$		0			0
$853$	6.79304	−	16.3999i	0.232589	−	0.561521i	−0.763891	−	0.645345i	$-0.776714\pi$
$853$	6.79304	−	16.3999i	0.232589	−	0.561521i	0.996481	+	0.0838246i	$0.0267136\pi$
$854$		0			0
$855$	−10.0980	−	4.18275i	−0.345346	−	0.143047i
$856$		0			0
$857$	0.300132	−	0.124319i	0.0102523	−	0.00424665i	−0.377551	−	0.925989i	$-0.623234\pi$
$857$	0.300132	−	0.124319i	0.0102523	−	0.00424665i	0.387804	+	0.921742i	$0.373234\pi$
$858$		0			0
$859$	−15.6278	−	15.6278i	−0.533213	−	0.533213i	0.388314	−	0.921527i	$-0.373058\pi$
$859$	−15.6278	−	15.6278i	−0.533213	−	0.533213i	−0.921527	+	0.388314i	$0.873058\pi$
$860$		0			0
$861$	−8.08990	−	19.5307i	−0.275703	−	0.665606i
$862$		0			0
$863$			16.3972i			0.558167i	0.960267	+	0.279084i	$0.0900307\pi$
$863$			16.3972i			0.558167i	−0.960267	+	0.279084i	$0.909969\pi$
$864$		0			0
$865$	12.9242	−	12.9242i	0.439438	−	0.439438i
$866$		0			0
$867$	35.7537	−	1.83552i	1.21426	−	0.0623377i
$868$		0			0
$869$	12.9839	−	12.9839i	0.440449	−	0.440449i
$870$		0			0
$871$			25.4215i			0.861374i
$872$		0			0
$873$	−4.90139	−	11.8330i	−0.165887	−	0.400487i
$874$		0			0
$875$	3.44590	+	3.44590i	0.116493	+	0.116493i
$876$		0			0
$877$	−48.8964	+	20.2535i	−1.65111	+	0.683913i	−0.997348	−	0.0727838i	$-0.976812\pi$
$877$	−48.8964	+	20.2535i	−1.65111	+	0.683913i	−0.653765	+	0.756697i	$0.726812\pi$
$878$		0			0
$879$	−48.5373	−	20.1048i	−1.63712	−	0.678118i
$880$		0			0
$881$	3.48852	−	8.42203i	0.117531	−	0.283746i	−0.854156	−	0.520017i	$-0.825926\pi$
$881$	3.48852	−	8.42203i	0.117531	−	0.283746i	0.971687	+	0.236272i	$0.0759255\pi$
$882$		0			0
$883$	53.7479			1.80876			0.904380	−	0.426728i	$-0.140334\pi$
$883$	53.7479			1.80876			0.904380	+	0.426728i	$0.140334\pi$
$884$		0			0
$885$	−15.5219			−0.521765
$886$		0			0
$887$	16.9141	−	40.8342i	0.567919	−	1.37108i	−0.335386	−	0.942081i	$-0.608867\pi$
$887$	16.9141	−	40.8342i	0.567919	−	1.37108i	0.903305	−	0.428998i	$-0.141133\pi$
$888$		0			0
$889$	46.0333	+	19.0676i	1.54391	+	0.639508i
$890$		0			0
$891$	20.0509	−	8.30534i	0.671729	−	0.278239i
$892$		0			0
$893$	33.0335	+	33.0335i	1.10542	+	1.10542i
$894$		0			0
$895$	−1.37067	−	3.30910i	−0.0458166	−	0.110611i
$896$		0			0
$897$			42.0045i			1.40249i
$898$		0			0
$899$	−21.7823	+	21.7823i	−0.726480	+	0.726480i
$900$		0			0
$901$	6.37041	+	28.2231i	0.212229	+	0.940247i
$902$		0			0
$903$	−59.0649	+	59.0649i	−1.96556	+	1.96556i
$904$		0			0
$905$			14.4977i			0.481920i
$906$		0			0
$907$	8.58242	+	20.7198i	0.284974	+	0.687989i	0.999938	−	0.0111729i	$-0.00355652\pi$
$907$	8.58242	+	20.7198i	0.284974	+	0.687989i	−0.714963	+	0.699162i	$0.753557\pi$
$908$		0			0
$909$	−3.74732	−	3.74732i	−0.124291	−	0.124291i
$910$		0			0
$911$	33.6148	−	13.9237i	1.11371	−	0.461312i	0.251494	−	0.967859i	$-0.419078\pi$
$911$	33.6148	−	13.9237i	1.11371	−	0.461312i	0.862213	+	0.506546i	$0.169078\pi$
$912$		0			0
$913$	0.187993	+	0.0778691i	0.00622165	+	0.00257709i
$914$		0			0
$915$	5.66391	−	13.6739i	0.187243	−	0.452045i
$916$		0			0
$917$	25.4257			0.839630
$918$		0			0
$919$	0.262467			0.00865797			0.00432899	−	0.999991i	$-0.498622\pi$
$919$	0.262467			0.00865797			0.00432899	+	0.999991i	$0.498622\pi$
$920$		0			0
$921$	−12.5700	+	30.3466i	−0.414195	+	0.999955i
$922$		0			0
$923$	12.0513	+	4.99180i	0.396673	+	0.164307i
$924$		0			0
$925$	−9.58028	+	3.96828i	−0.314998	+	0.130476i
$926$		0			0
$927$	15.4263	+	15.4263i	0.506667	+	0.506667i
$928$		0			0
$929$	15.1196	+	36.5020i	0.496059	+	1.19759i	0.951589	+	0.307372i	$0.0994496\pi$
$929$	15.1196	+	36.5020i	0.496059	+	1.19759i	−0.455531	+	0.890220i	$0.650550\pi$
$930$		0			0
$931$		−	127.574i		−	4.18106i
$932$		0			0
$933$	−22.4588	+	22.4588i	−0.735270	+	0.735270i
$934$		0			0
$935$	6.72725	+	4.24960i	0.220005	+	0.138977i
$936$		0			0
$937$	−19.5534	+	19.5534i	−0.638781	+	0.638781i	−0.950255	−	0.311474i	$-0.899177\pi$
$937$	−19.5534	+	19.5534i	−0.638781	+	0.638781i	0.311474	+	0.950255i	$0.399177\pi$
$938$		0			0
$939$			26.6333i			0.869145i
$940$		0			0
$941$	−7.62313	−	18.4039i	−0.248507	−	0.599949i	0.749571	−	0.661924i	$-0.230260\pi$
$941$	−7.62313	−	18.4039i	−0.248507	−	0.599949i	−0.998078	+	0.0619755i	$0.980260\pi$
$942$		0			0
$943$	−6.46177	−	6.46177i	−0.210424	−	0.210424i
$944$		0			0
$945$	−14.8391	+	6.14655i	−0.482715	+	0.199947i
$946$		0			0
$947$	13.5253	+	5.60234i	0.439512	+	0.182052i	0.591456	−	0.806337i	$-0.298553\pi$
$947$	13.5253	+	5.60234i	0.439512	+	0.182052i	−0.151944	+	0.988389i	$0.548553\pi$
$948$		0			0
$949$	−10.1032	+	24.3913i	−0.327964	+	0.791775i
$950$		0			0
$951$	−30.1549			−0.977841
$952$		0			0
$953$	22.9246			0.742601			0.371301	−	0.928513i	$-0.378912\pi$
$953$	22.9246			0.742601			0.371301	+	0.928513i	$0.378912\pi$
$954$		0			0
$955$	−4.84797	+	11.7040i	−0.156877	+	0.378734i
$956$		0			0
$957$	34.6496	+	14.3523i	1.12006	+	0.463945i
$958$		0			0
$959$	−53.9750	+	22.3572i	−1.74294	+	0.721950i
$960$		0			0
$961$	14.0408	+	14.0408i	0.452928	+	0.452928i
$962$		0			0
$963$	7.87382	+	19.0091i	0.253730	+	0.612559i
$964$		0			0
$965$			3.10793i			0.100048i
$966$		0			0
$967$	−8.92138	+	8.92138i	−0.286892	+	0.286892i	−0.835850	−	0.548958i	$-0.815025\pi$
$967$	−8.92138	+	8.92138i	−0.286892	+	0.286892i	0.548958	+	0.835850i	$0.315025\pi$
$968$		0			0
$969$	65.1775	+	11.2353i	2.09380	+	0.360931i
$970$		0			0
$971$	−4.29938	+	4.29938i	−0.137974	+	0.137974i	−0.772720	−	0.634747i	$-0.781104\pi$
$971$	−4.29938	+	4.29938i	−0.137974	+	0.137974i	0.634747	+	0.772720i	$0.281104\pi$
$972$		0			0
$973$			79.4582i			2.54731i
$974$		0			0
$975$	3.62336	+	8.74757i	0.116040	+	0.280146i
$976$		0			0
$977$	5.82173	+	5.82173i	0.186254	+	0.186254i	0.794074	−	0.607821i	$-0.207956\pi$
$977$	5.82173	+	5.82173i	0.186254	+	0.186254i	−0.607821	+	0.794074i	$0.707956\pi$
$978$		0			0
$979$	18.3747	−	7.61103i	0.587257	−	0.243250i
$980$		0			0
$981$	16.1690	+	6.69743i	0.516238	+	0.213833i
$982$		0			0
$983$	8.27003	−	19.9656i	0.263773	−	0.636804i	−0.735393	−	0.677641i	$-0.763002\pi$
$983$	8.27003	−	19.9656i	0.263773	−	0.636804i	0.999166	+	0.0408369i	$0.0130024\pi$
$984$		0			0
$985$	19.2228			0.612491
$986$		0			0
$987$	−62.9423			−2.00348
$988$		0			0
$989$	−13.8181	+	33.3598i	−0.439389	+	1.06078i
$990$		0			0
$991$	11.5935	+	4.80217i	0.368279	+	0.152546i	0.559145	−	0.829070i	$-0.311130\pi$
$991$	11.5935	+	4.80217i	0.368279	+	0.152546i	−0.190866	+	0.981616i	$0.561130\pi$
$992$		0			0
$993$	48.8063	−	20.2162i	1.54882	−	0.641543i
$994$		0			0
$995$	−6.53168	−	6.53168i	−0.207068	−	0.207068i
$996$		0			0
$997$	−5.95724	−	14.3821i	−0.188668	−	0.455484i	0.801036	−	0.598616i	$-0.204283\pi$
$997$	−5.95724	−	14.3821i	−0.188668	−	0.455484i	−0.989704	+	0.143132i	$0.954283\pi$
$998$		0			0
$999$		−	34.1773i		−	1.08132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.bo.a.161.1	✓	32
17.15	even	8	inner	680.2.bo.a.321.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.bo.a.161.1	✓	32	1.1	even	1	trivial
680.2.bo.a.321.1	yes	32	17.15	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)

\(f(q)\)	\(=\)	\(q+(-0.805905 + 1.94563i) q^{3} +(0.923880 + 0.382683i) q^{5} +(4.50228 - 1.86491i) q^{7} +(-1.01466 - 1.01466i) q^{9} +(0.738530 + 1.78297i) q^{11} -4.49602i q^{13} +(-1.48912 + 1.48912i) q^{15} +(2.20201 - 3.48585i) q^{17} +(5.38608 - 5.38608i) q^{19} +10.2627i q^{21} +(1.69771 + 4.09864i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-3.04502 + 1.26129i) q^{27} +(-8.52562 - 3.53143i) q^{29} +(1.27746 - 3.08407i) q^{31} -4.06418 q^{33} +4.87323 q^{35} +(-3.96828 + 9.58028i) q^{37} +(8.74757 + 3.62336i) q^{39} +(-1.90308 + 0.788283i) q^{41} +(5.75531 + 5.75531i) q^{43} +(-0.549128 - 1.32571i) q^{45} +6.13313i q^{47} +(11.8429 - 11.8429i) q^{49} +(5.00755 + 7.09355i) q^{51} +(-4.96199 + 4.96199i) q^{53} +1.92987i q^{55} +(6.13863 + 14.8200i) q^{57} +(5.21179 + 5.21179i) q^{59} +(-6.49304 + 2.68951i) q^{61} +(-6.46051 - 2.67603i) q^{63} +(1.72055 - 4.15378i) q^{65} -5.65422 q^{67} -9.34261 q^{69} +(-1.11027 + 2.68043i) q^{71} +(-5.42509 - 2.24715i) q^{73} +(-1.94563 + 0.805905i) q^{75} +(6.65014 + 6.65014i) q^{77} +(-3.64109 - 8.79037i) q^{79} -11.2458i q^{81} +(0.0745559 - 0.0745559i) q^{83} +(3.36837 - 2.37783i) q^{85} +(13.7417 - 13.7417i) q^{87} -10.3056i q^{89} +(-8.38465 - 20.2423i) q^{91} +(4.97093 + 4.97093i) q^{93} +(7.03725 - 2.91493i) q^{95} +(8.24633 + 3.41574i) q^{97} +(1.05975 - 2.55846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} + 8 q^{11} - 8 q^{17} + 8 q^{19} + 8 q^{23} - 24 q^{27} - 32 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{35} + 16 q^{37} - 24 q^{39} - 16 q^{41} - 8 q^{49} + 16 q^{51} + 16 q^{53} + 48 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 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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