LMFDB - Embedded newform 320.2.s.b.303.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,2,Mod(207,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("320.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			303.5
Root			$-1.37691 + 0.322680i$ of defining polynomial
Character	$\chi$	$=$	320.303
Dual form			320.2.s.b.207.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.614566 q^{3} +(0.832020 + 2.07551i) q^{5} +(-2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +O(q^{10})$	\(q-0.614566 q^{3} +(0.832020 + 2.07551i) q^{5} +(-2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +(-1.95928 - 1.95928i) q^{11} -2.05493i q^{13} +(-0.511331 - 1.27554i) q^{15} +(-4.06774 + 4.06774i) q^{17} +(0.683479 + 0.683479i) q^{19} +(1.74297 - 1.74297i) q^{21} +(4.95014 + 4.95014i) q^{23} +(-3.61549 + 3.45373i) q^{25} +3.45528 q^{27} +(0.835439 - 0.835439i) q^{29} +2.35978i q^{31} +(1.20411 + 1.20411i) q^{33} +(-8.24604 - 3.52666i) q^{35} +4.54384i q^{37} +1.26289i q^{39} -5.07255i q^{41} +0.849753i q^{43} +(-2.18181 - 5.44263i) q^{45} +(2.72646 + 2.72646i) q^{47} -9.08690i q^{49} +(2.49989 - 2.49989i) q^{51} +5.17605 q^{53} +(2.43634 - 5.69666i) q^{55} +(-0.420043 - 0.420043i) q^{57} +(4.16328 - 4.16328i) q^{59} +(5.55706 + 5.55706i) q^{61} +(7.43712 - 7.43712i) q^{63} +(4.26502 - 1.70974i) q^{65} -1.73609i q^{67} +(-3.04219 - 3.04219i) q^{69} -2.33526 q^{71} +(-4.39686 + 4.39686i) q^{73} +(2.22195 - 2.12255i) q^{75} +11.1134 q^{77} -14.0993 q^{79} +5.74343 q^{81} +2.75725 q^{83} +(-11.8271 - 5.05819i) q^{85} +(-0.513433 + 0.513433i) q^{87} +11.6448 q^{89} +(5.82797 + 5.82797i) q^{91} -1.45024i q^{93} +(-0.849899 + 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(5.13783 + 5.13783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} + 2 q^{19} - 16 q^{21} + 2 q^{23} - 6 q^{25} + 24 q^{27} + 14 q^{29} - 8 q^{33} - 2 q^{35} - 14 q^{45} - 38 q^{47} - 8 q^{51} + 12 q^{53} + 6 q^{55} - 24 q^{57} - 10 q^{59} + 14 q^{61} + 6 q^{63} - 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{75} - 44 q^{77} + 16 q^{79} + 2 q^{81} - 40 q^{83} + 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9 + 2 * q^11 + 20 * q^15 - 6 * q^17 + 2 * q^19 - 16 * q^21 + 2 * q^23 - 6 * q^25 + 24 * q^27 + 14 * q^29 - 8 * q^33 - 2 * q^35 - 14 * q^45 - 38 * q^47 - 8 * q^51 + 12 * q^53 + 6 * q^55 - 24 * q^57 - 10 * q^59 + 14 * q^61 + 6 * q^63 - 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^75 - 44 * q^77 + 16 * q^79 + 2 * q^81 - 40 * q^83 + 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.614566			−0.354820			−0.177410	−	0.984137i	$-0.556772\pi$
$3$	−0.614566			−0.354820			−0.177410	+	0.984137i	$0.556772\pi$
$4$		0			0
$5$	0.832020	+	2.07551i	0.372091	+	0.928196i
$5$	0.832020	+	2.07551i	0.372091	+	0.928196i
$6$		0			0
$7$	−2.83610	+	2.83610i	−1.07194	+	1.07194i	−0.0747413	+	0.997203i	$0.523813\pi$
$7$	−2.83610	+	2.83610i	−1.07194	+	1.07194i	−0.997203	+	0.0747413i	$0.976187\pi$
$8$		0			0
$9$	−2.62231			−0.874103
$10$		0			0
$11$	−1.95928	−	1.95928i	−0.590745	−	0.590745i	0.347088	−	0.937833i	$-0.387171\pi$
$11$	−1.95928	−	1.95928i	−0.590745	−	0.590745i	−0.937833	+	0.347088i	$0.887171\pi$
$12$		0			0
$13$		−	2.05493i		−	0.569934i	−0.958537	−	0.284967i	$-0.908017\pi$
$13$		−	2.05493i		−	0.569934i	0.958537	−	0.284967i	$-0.0919826\pi$
$14$		0			0
$15$	−0.511331	−	1.27554i	−0.132025	−	0.329343i
$16$		0			0
$17$	−4.06774	+	4.06774i	−0.986571	+	0.986571i	−0.999911	−	0.0133401i	$-0.995754\pi$
$17$	−4.06774	+	4.06774i	−0.986571	+	0.986571i	0.0133401	+	0.999911i	$0.495754\pi$
$18$		0			0
$19$	0.683479	+	0.683479i	0.156801	+	0.156801i	0.781147	−	0.624347i	$-0.214635\pi$
$19$	0.683479	+	0.683479i	0.156801	+	0.156801i	−0.624347	+	0.781147i	$0.714635\pi$
$20$		0			0
$21$	1.74297	−	1.74297i	0.380347	−	0.380347i
$22$		0			0
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.999465	+	0.0327113i	$0.0104142\pi$
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.0327113	+	0.999465i	$0.489586\pi$
$24$		0			0
$25$	−3.61549	+	3.45373i	−0.723097	+	0.690746i
$26$		0			0
$27$	3.45528			0.664969
$28$		0			0
$29$	0.835439	−	0.835439i	0.155137	−	0.155137i	−0.625271	−	0.780408i	$-0.715011\pi$
$29$	0.835439	−	0.835439i	0.155137	−	0.155137i	0.780408	+	0.625271i	$0.215011\pi$
$30$		0			0
$31$			2.35978i			0.423829i	0.977288	+	0.211915i	$0.0679698\pi$
$31$			2.35978i			0.423829i	−0.977288	+	0.211915i	$0.932030\pi$
$32$		0			0
$33$	1.20411	+	1.20411i	0.209608	+	0.209608i
$34$		0			0
$35$	−8.24604	−	3.52666i	−1.39384	−	0.596114i
$36$		0			0
$37$			4.54384i			0.747002i	0.927630	+	0.373501i	$0.121843\pi$
$37$			4.54384i			0.747002i	−0.927630	+	0.373501i	$0.878157\pi$
$38$		0			0
$39$			1.26289i			0.202224i
$40$		0			0
$41$		−	5.07255i		−	0.792199i	−0.918208	−	0.396100i	$-0.870364\pi$
$41$		−	5.07255i		−	0.792199i	0.918208	−	0.396100i	$-0.129636\pi$
$42$		0			0
$43$			0.849753i			0.129586i	0.997899	+	0.0647930i	$0.0206387\pi$
$43$			0.849753i			0.129586i	−0.997899	+	0.0647930i	$0.979361\pi$
$44$		0			0
$45$	−2.18181	−	5.44263i	−0.325245	−	0.811339i
$46$		0			0
$47$	2.72646	+	2.72646i	0.397696	+	0.397696i	0.877419	−	0.479724i	$-0.159263\pi$
$47$	2.72646	+	2.72646i	0.397696	+	0.397696i	−0.479724	+	0.877419i	$0.659263\pi$
$48$		0			0
$49$		−	9.08690i		−	1.29813i
$50$		0			0
$51$	2.49989	−	2.49989i	0.350055	−	0.350055i
$52$		0			0
$53$	5.17605			0.710985			0.355492	−	0.934679i	$-0.384313\pi$
$53$	5.17605			0.710985			0.355492	+	0.934679i	$0.384313\pi$
$54$		0			0
$55$	2.43634	−	5.69666i	0.328517	−	0.768138i
$56$		0			0
$57$	−0.420043	−	0.420043i	−0.0556360	−	0.0556360i
$58$		0			0
$59$	4.16328	−	4.16328i	0.542013	−	0.542013i	−0.382105	−	0.924119i	$-0.624801\pi$
$59$	4.16328	−	4.16328i	0.542013	−	0.542013i	0.924119	+	0.382105i	$0.124801\pi$
$60$		0			0
$61$	5.55706	+	5.55706i	0.711509	+	0.711509i	0.966851	−	0.255342i	$-0.0821880\pi$
$61$	5.55706	+	5.55706i	0.711509	+	0.711509i	−0.255342	+	0.966851i	$0.582188\pi$
$62$		0			0
$63$	7.43712	−	7.43712i	0.936990	−	0.936990i
$64$		0			0
$65$	4.26502	−	1.70974i	0.529011	−	0.212067i
$66$		0			0
$67$		−	1.73609i		−	0.212097i	−0.994361	−	0.106048i	$-0.966180\pi$
$67$		−	1.73609i		−	0.212097i	0.994361	−	0.106048i	$-0.0338198\pi$
$68$		0			0
$69$	−3.04219	−	3.04219i	−0.366237	−	0.366237i
$70$		0			0
$71$	−2.33526			−0.277144			−0.138572	−	0.990352i	$-0.544251\pi$
$71$	−2.33526			−0.277144			−0.138572	+	0.990352i	$0.544251\pi$
$72$		0			0
$73$	−4.39686	+	4.39686i	−0.514613	+	0.514613i	−0.915936	−	0.401323i	$-0.868550\pi$
$73$	−4.39686	+	4.39686i	−0.514613	+	0.514613i	0.401323	+	0.915936i	$0.368550\pi$
$74$		0			0
$75$	2.22195	−	2.12255i	0.256569	−	0.245091i
$76$		0			0
$77$	11.1134			1.26649
$78$		0			0
$79$	−14.0993			−1.58629			−0.793146	−	0.609032i	$-0.791558\pi$
$79$	−14.0993			−1.58629			−0.793146	+	0.609032i	$0.791558\pi$
$80$		0			0
$81$	5.74343			0.638159
$82$		0			0
$83$	2.75725			0.302648			0.151324	−	0.988484i	$-0.451646\pi$
$83$	2.75725			0.302648			0.151324	+	0.988484i	$0.451646\pi$
$84$		0			0
$85$	−11.8271	−	5.05819i	−1.28283	−	0.548638i
$86$		0			0
$87$	−0.513433	+	0.513433i	−0.0550458	+	0.0550458i
$88$		0			0
$89$	11.6448			1.23435			0.617173	−	0.786828i	$-0.288278\pi$
$89$	11.6448			1.23435			0.617173	+	0.786828i	$0.288278\pi$
$90$		0			0
$91$	5.82797	+	5.82797i	0.610937	+	0.610937i
$92$		0			0
$93$		−	1.45024i		−	0.150383i
$94$		0			0
$95$	−0.849899	+	1.98724i	−0.0871978	+	0.203886i
$96$		0			0
$97$	−3.52933	+	3.52933i	−0.358349	+	0.358349i	−0.863204	−	0.504855i	$-0.831546\pi$
$97$	−3.52933	+	3.52933i	−0.358349	+	0.358349i	0.504855	+	0.863204i	$0.331546\pi$
$98$		0			0
$99$	5.13783	+	5.13783i	0.516372	+	0.516372i
$100$		0			0
$101$	7.39467	−	7.39467i	0.735797	−	0.735797i	−0.235964	−	0.971762i	$-0.575825\pi$
$101$	7.39467	−	7.39467i	0.735797	−	0.735797i	0.971762	+	0.235964i	$0.0758249\pi$
$102$		0			0
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	0.499294	−	0.866433i	$-0.333593\pi$
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	−0.866433	+	0.499294i	$0.833593\pi$
$104$		0			0
$105$	5.06774	+	2.16737i	0.494560	+	0.211513i
$106$		0			0
$107$	−16.4605			−1.59130			−0.795649	−	0.605758i	$-0.792870\pi$
$107$	−16.4605			−1.59130			−0.795649	+	0.605758i	$0.792870\pi$
$108$		0			0
$109$	−12.8554	+	12.8554i	−1.23133	+	1.23133i	−0.267870	+	0.963455i	$0.586320\pi$
$109$	−12.8554	+	12.8554i	−1.23133	+	1.23133i	−0.963455	+	0.267870i	$0.913680\pi$
$110$		0			0
$111$		−	2.79249i		−	0.265051i
$112$		0			0
$113$	0.863630	+	0.863630i	0.0812435	+	0.0812435i	0.746561	−	0.665317i	$-0.231704\pi$
$113$	0.863630	+	0.863630i	0.0812435	+	0.0812435i	−0.665317	+	0.746561i	$0.731704\pi$
$114$		0			0
$115$	−6.15546	+	14.3927i	−0.573999	+	1.34213i
$116$		0			0
$117$			5.38865i			0.498181i
$118$		0			0
$119$		−	23.0730i		−	2.11510i
$120$		0			0
$121$		−	3.32246i		−	0.302042i
$122$		0			0
$123$			3.11742i			0.281088i
$124$		0			0
$125$	−10.1764	−	4.63041i	−0.910206	−	0.414156i
$126$		0			0
$127$	11.7944	+	11.7944i	1.04659	+	1.04659i	0.998860	+	0.0477265i	$0.0151976\pi$
$127$	11.7944	+	11.7944i	1.04659	+	1.04659i	0.0477265	+	0.998860i	$0.484802\pi$
$128$		0			0
$129$		−	0.522229i		−	0.0459797i
$130$		0			0
$131$	15.9756	−	15.9756i	1.39579	−	1.39579i	0.584132	−	0.811659i	$-0.301435\pi$
$131$	15.9756	−	15.9756i	1.39579	−	1.39579i	0.811659	−	0.584132i	$-0.198565\pi$
$132$		0			0
$133$	−3.87683			−0.336163
$134$		0			0
$135$	2.87486	+	7.17147i	0.247429	+	0.617222i
$136$		0			0
$137$	1.29423	+	1.29423i	0.110573	+	0.110573i	0.760229	−	0.649655i	$-0.225087\pi$
$137$	1.29423	+	1.29423i	0.110573	+	0.110573i	−0.649655	+	0.760229i	$0.725087\pi$
$138$		0			0
$139$	−8.61413	+	8.61413i	−0.730641	+	0.730641i	−0.970747	−	0.240106i	$-0.922818\pi$
$139$	−8.61413	+	8.61413i	−0.730641	+	0.730641i	0.240106	+	0.970747i	$0.422818\pi$
$140$		0			0
$141$	−1.67559	−	1.67559i	−0.141110	−	0.141110i
$142$		0			0
$143$	−4.02617	+	4.02617i	−0.336685	+	0.336685i
$144$		0			0
$145$	2.42906	+	1.03886i	0.201723	+	0.0862727i
$146$		0			0
$147$			5.58450i			0.460602i
$148$		0			0
$149$	0.0806133	+	0.0806133i	0.00660410	+	0.00660410i	0.710401	−	0.703797i	$-0.248514\pi$
$149$	0.0806133	+	0.0806133i	0.00660410	+	0.00660410i	−0.703797	+	0.710401i	$0.748514\pi$
$150$		0			0
$151$	3.25198			0.264643			0.132321	−	0.991207i	$-0.457757\pi$
$151$	3.25198			0.264643			0.132321	+	0.991207i	$0.457757\pi$
$152$		0			0
$153$	10.6669	−	10.6669i	0.862364	−	0.862364i
$154$		0			0
$155$	−4.89775	+	1.96338i	−0.393397	+	0.157703i
$156$		0			0
$157$	−9.06652			−0.723587			−0.361793	−	0.932258i	$-0.617835\pi$
$157$	−9.06652			−0.723587			−0.361793	+	0.932258i	$0.617835\pi$
$158$		0			0
$159$	−3.18102			−0.252271
$160$		0			0
$161$	−28.0782			−2.21287
$162$		0			0
$163$	−3.93313			−0.308067			−0.154033	−	0.988066i	$-0.549226\pi$
$163$	−3.93313			−0.308067			−0.154033	+	0.988066i	$0.549226\pi$
$164$		0			0
$165$	−1.49729	+	3.50097i	−0.116564	+	0.272550i
$166$		0			0
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	−0.947888	−	0.318603i	$-0.896786\pi$
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	0.318603	+	0.947888i	$0.396786\pi$
$168$		0			0
$169$	8.77728			0.675175
$170$		0			0
$171$	−1.79229	−	1.79229i	−0.137060	−	0.137060i
$172$		0			0
$173$			6.86735i			0.522115i	0.965323	+	0.261057i	$0.0840712\pi$
$173$			6.86735i			0.522115i	−0.965323	+	0.261057i	$0.915929\pi$
$174$		0			0
$175$	0.458751	−	20.0490i	0.0346784	−	1.51556i
$176$		0			0
$177$	−2.55861	+	2.55861i	−0.192317	+	0.192317i
$178$		0			0
$179$	15.7117	+	15.7117i	1.17435	+	1.17435i	0.981163	+	0.193183i	$0.0618811\pi$
$179$	15.7117	+	15.7117i	1.17435	+	1.17435i	0.193183	+	0.981163i	$0.438119\pi$
$180$		0			0
$181$	−13.9112	+	13.9112i	−1.03401	+	1.03401i	−0.0346142	+	0.999401i	$0.511020\pi$
$181$	−13.9112	+	13.9112i	−1.03401	+	1.03401i	−0.999401	+	0.0346142i	$0.988980\pi$
$182$		0			0
$183$	−3.41518	−	3.41518i	−0.252458	−	0.252458i
$184$		0			0
$185$	−9.43078	+	3.78056i	−0.693365	+	0.277953i
$186$		0			0
$187$	15.9397			1.16562
$188$		0			0
$189$	−9.79951	+	9.79951i	−0.712810	+	0.712810i
$190$		0			0
$191$			10.3393i			0.748123i	0.927404	+	0.374061i	$0.122035\pi$
$191$			10.3393i			0.748123i	−0.927404	+	0.374061i	$0.877965\pi$
$192$		0			0
$193$	13.2080	+	13.2080i	0.950734	+	0.950734i	0.998842	−	0.0481079i	$-0.0153191\pi$
$193$	13.2080	+	13.2080i	0.950734	+	0.950734i	−0.0481079	+	0.998842i	$0.515319\pi$
$194$		0			0
$195$	−2.62114	+	1.05075i	−0.187704	+	0.0752456i
$196$		0			0
$197$		−	15.2437i		−	1.08607i	−0.839709	−	0.543036i	$-0.817275\pi$
$197$		−	15.2437i		−	1.08607i	0.839709	−	0.543036i	$-0.182725\pi$
$198$		0			0
$199$			4.98761i			0.353562i	0.984250	+	0.176781i	$0.0565684\pi$
$199$			4.98761i			0.353562i	−0.984250	+	0.176781i	$0.943432\pi$
$200$		0			0
$201$			1.06694i			0.0752561i
$202$		0			0
$203$			4.73878i			0.332597i
$204$		0			0
$205$	10.5281	−	4.22046i	0.735316	−	0.294770i
$206$		0			0
$207$	−12.9808	−	12.9808i	−0.902228	−	0.902228i
$208$		0			0
$209$		−	2.67825i		−	0.185258i
$210$		0			0
$211$	−10.3803	+	10.3803i	−0.714608	+	0.714608i	−0.967496	−	0.252887i	$-0.918620\pi$
$211$	−10.3803	+	10.3803i	−0.714608	+	0.714608i	0.252887	+	0.967496i	$0.418620\pi$
$212$		0			0
$213$	1.43517			0.0983362
$214$		0			0
$215$	−1.76367	+	0.707011i	−0.120281	+	0.0482178i
$216$		0			0
$217$	−6.69257	−	6.69257i	−0.454321	−	0.454321i
$218$		0			0
$219$	2.70216	−	2.70216i	0.182595	−	0.182595i
$220$		0			0
$221$	8.35890	+	8.35890i	0.562280	+	0.562280i
$222$		0			0
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	−0.755499	−	0.655150i	$-0.772605\pi$
$223$	−1.49853	+	1.49853i	−0.100349	+	0.100349i	0.655150	+	0.755499i	$0.272605\pi$
$224$		0			0
$225$	9.48092	−	9.05675i	0.632061	−	0.603783i
$226$		0			0
$227$		−	15.6346i		−	1.03771i	−0.854864	−	0.518853i	$-0.826359\pi$
$227$		−	15.6346i		−	1.03771i	0.854864	−	0.518853i	$-0.173641\pi$
$228$		0			0
$229$	9.74097	+	9.74097i	0.643702	+	0.643702i	0.951463	−	0.307762i	$-0.0995800\pi$
$229$	9.74097	+	9.74097i	0.643702	+	0.643702i	−0.307762	+	0.951463i	$0.599580\pi$
$230$		0			0
$231$	−6.82992			−0.449376
$232$		0			0
$233$	−0.509123	+	0.509123i	−0.0333538	+	0.0333538i	−0.723587	−	0.690233i	$-0.757508\pi$
$233$	−0.509123	+	0.509123i	−0.0333538	+	0.0333538i	0.690233	+	0.723587i	$0.257508\pi$
$234$		0			0
$235$	−3.39033	+	7.92727i	−0.221161	+	0.517118i
$236$		0			0
$237$	8.66493			0.562848
$238$		0			0
$239$	8.19486			0.530081			0.265041	−	0.964237i	$-0.414615\pi$
$239$	8.19486			0.530081			0.265041	+	0.964237i	$0.414615\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$		0			0
$243$	−13.8956			−0.891400
$244$		0			0
$245$	18.8600	−	7.56048i	1.20492	−	0.483022i
$246$		0			0
$247$	1.40450	−	1.40450i	0.0893661	−	0.0893661i
$248$		0			0
$249$	−1.69451			−0.107385
$250$		0			0
$251$	−14.7484	−	14.7484i	−0.930911	−	0.930911i	0.0668521	−	0.997763i	$-0.478704\pi$
$251$	−14.7484	−	14.7484i	−0.930911	−	0.930911i	−0.997763	+	0.0668521i	$0.978704\pi$
$252$		0			0
$253$		−	19.3974i		−	1.21951i
$254$		0			0
$255$	7.26851	+	3.10859i	0.455172	+	0.194668i
$256$		0			0
$257$	3.61143	−	3.61143i	0.225275	−	0.225275i	−0.585440	−	0.810715i	$-0.699078\pi$
$257$	3.61143	−	3.61143i	0.225275	−	0.225275i	0.810715	+	0.585440i	$0.199078\pi$
$258$		0			0
$259$	−12.8868	−	12.8868i	−0.800745	−	0.800745i
$260$		0			0
$261$	−2.19078	+	2.19078i	−0.135606	+	0.135606i
$262$		0			0
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	0.884973	−	0.465642i	$-0.154177\pi$
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	−0.465642	+	0.884973i	$0.654177\pi$
$264$		0			0
$265$	4.30657	+	10.7429i	0.264551	+	0.659933i
$266$		0			0
$267$	−7.15650			−0.437970
$268$		0			0
$269$	1.20010	−	1.20010i	0.0731711	−	0.0731711i	−0.669574	−	0.742745i	$-0.733523\pi$
$269$	1.20010	−	1.20010i	0.0731711	−	0.0731711i	0.742745	+	0.669574i	$0.233523\pi$
$270$		0			0
$271$			2.79591i			0.169840i	0.996388	+	0.0849199i	$0.0270634\pi$
$271$			2.79591i			0.169840i	−0.996388	+	0.0849199i	$0.972937\pi$
$272$		0			0
$273$	−3.58167	−	3.58167i	−0.216773	−	0.216773i
$274$		0			0
$275$	13.8506	+	0.316922i	0.835220	+	0.0191111i
$276$		0			0
$277$		−	13.8115i		−	0.829852i	−0.909855	−	0.414926i	$-0.863807\pi$
$277$		−	13.8115i		−	0.829852i	0.909855	−	0.414926i	$-0.136193\pi$
$278$		0			0
$279$		−	6.18807i		−	0.370470i
$280$		0			0
$281$			7.21718i			0.430541i	0.976554	+	0.215270i	$0.0690633\pi$
$281$			7.21718i			0.430541i	−0.976554	+	0.215270i	$0.930937\pi$
$282$		0			0
$283$		−	25.2988i		−	1.50386i	−0.659243	−	0.751930i	$-0.729123\pi$
$283$		−	25.2988i		−	1.50386i	0.659243	−	0.751930i	$-0.270877\pi$
$284$		0			0
$285$	0.522319	−	1.22129i	0.0309395	−	0.0723428i
$286$		0			0
$287$	14.3862	+	14.3862i	0.849193	+	0.849193i
$288$		0			0
$289$		−	16.0930i		−	0.946644i
$290$		0			0
$291$	2.16901	−	2.16901i	0.127149	−	0.127149i
$292$		0			0
$293$	−14.1276			−0.825344			−0.412672	−	0.910880i	$-0.635404\pi$
$293$	−14.1276			−0.825344			−0.412672	+	0.910880i	$0.635404\pi$
$294$		0			0
$295$	12.1049	+	5.17700i	0.704773	+	0.301417i
$296$		0			0
$297$	−6.76985	−	6.76985i	−0.392827	−	0.392827i
$298$		0			0
$299$	10.1722	−	10.1722i	0.588272	−	0.588272i
$300$		0			0
$301$	−2.40998	−	2.40998i	−0.138909	−	0.138909i
$302$		0			0
$303$	−4.54451	+	4.54451i	−0.261076	+	0.261076i
$304$		0			0
$305$	−6.91016	+	16.1573i	−0.395674	+	0.925166i
$306$		0			0
$307$		−	22.6081i		−	1.29031i	−0.764051	−	0.645156i	$-0.776792\pi$
$307$		−	22.6081i		−	1.29031i	0.764051	−	0.645156i	$-0.223208\pi$
$308$		0			0
$309$	2.28990	+	2.28990i	0.130268	+	0.130268i
$310$		0			0
$311$	10.7903			0.611859			0.305929	−	0.952054i	$-0.401033\pi$
$311$	10.7903			0.611859			0.305929	+	0.952054i	$0.401033\pi$
$312$		0			0
$313$	−20.6842	+	20.6842i	−1.16914	+	1.16914i	−0.186727	+	0.982412i	$0.559788\pi$
$313$	−20.6842	+	20.6842i	−1.16914	+	1.16914i	−0.982412	+	0.186727i	$0.940212\pi$
$314$		0			0
$315$	21.6237	+	9.24799i	1.21836	+	0.521065i
$316$		0			0
$317$	23.8207			1.33791			0.668953	−	0.743305i	$-0.266743\pi$
$317$	23.8207			1.33791			0.668953	+	0.743305i	$0.266743\pi$
$318$		0			0
$319$	−3.27372			−0.183293
$320$		0			0
$321$	10.1161			0.564624
$322$		0			0
$323$	−5.56042			−0.309390
$324$		0			0
$325$	7.09716	+	7.42956i	0.393680	+	0.412118i
$326$		0			0
$327$	7.90050	−	7.90050i	0.436899	−	0.436899i
$328$		0			0
$329$	−15.4650			−0.852615
$330$		0			0
$331$	19.7688	+	19.7688i	1.08659	+	1.08659i	0.995877	+	0.0907155i	$0.0289154\pi$
$331$	19.7688	+	19.7688i	1.08659	+	1.08659i	0.0907155	+	0.995877i	$0.471085\pi$
$332$		0			0
$333$		−	11.9153i		−	0.652957i
$334$		0			0
$335$	3.60326	−	1.44446i	0.196867	−	0.0789191i
$336$		0			0
$337$	7.26955	−	7.26955i	0.395998	−	0.395998i	−0.480821	−	0.876819i	$-0.659661\pi$
$337$	7.26955	−	7.26955i	0.395998	−	0.395998i	0.876819	+	0.480821i	$0.159661\pi$
$338$		0			0
$339$	−0.530758	−	0.530758i	−0.0288268	−	0.0288268i
$340$		0			0
$341$	4.62347	−	4.62347i	0.250375	−	0.250375i
$342$		0			0
$343$	5.91866	+	5.91866i	0.319578	+	0.319578i
$344$		0			0
$345$	3.78293	−	8.84526i	0.203666	−	0.476213i
$346$		0			0
$347$	23.4667			1.25976			0.629880	−	0.776692i	$-0.283104\pi$
$347$	23.4667			1.25976			0.629880	+	0.776692i	$0.283104\pi$
$348$		0			0
$349$	23.2089	−	23.2089i	1.24234	−	1.24234i	0.283315	−	0.959027i	$-0.408566\pi$
$349$	23.2089	−	23.2089i	1.24234	−	1.24234i	0.959027	−	0.283315i	$-0.0914342\pi$
$350$		0			0
$351$		−	7.10035i		−	0.378988i
$352$		0			0
$353$	−13.3220	−	13.3220i	−0.709059	−	0.709059i	0.257278	−	0.966337i	$-0.417174\pi$
$353$	−13.3220	−	13.3220i	−0.709059	−	0.709059i	−0.966337	+	0.257278i	$0.917174\pi$
$354$		0			0
$355$	−1.94298	−	4.84685i	−0.103123	−	0.257244i
$356$		0			0
$357$			14.1799i			0.750479i
$358$		0			0
$359$			26.9902i			1.42449i	0.701932	+	0.712244i	$0.252321\pi$
$359$			26.9902i			1.42449i	−0.701932	+	0.712244i	$0.747679\pi$
$360$		0			0
$361$		−	18.0657i		−	0.950827i
$362$		0			0
$363$			2.04187i			0.107170i
$364$		0			0
$365$	−12.7840	−	5.46745i	−0.669145	−	0.286179i
$366$		0			0
$367$	−19.4758	−	19.4758i	−1.01663	−	1.01663i	−0.999859	−	0.0167684i	$-0.994662\pi$
$367$	−19.4758	−	19.4758i	−1.01663	−	1.01663i	−0.0167684	−	0.999859i	$-0.505338\pi$
$368$		0			0
$369$			13.3018i			0.692464i
$370$		0			0
$371$	−14.6798	+	14.6798i	−0.762136	+	0.762136i
$372$		0			0
$373$	4.87069			0.252195			0.126097	−	0.992018i	$-0.459755\pi$
$373$	4.87069			0.252195			0.126097	+	0.992018i	$0.459755\pi$
$374$		0			0
$375$	6.25408	+	2.84569i	0.322959	+	0.146951i
$376$		0			0
$377$	−1.71677	−	1.71677i	−0.0884180	−	0.0884180i
$378$		0			0
$379$	2.54450	−	2.54450i	0.130702	−	0.130702i	−0.638729	−	0.769432i	$-0.720540\pi$
$379$	2.54450	−	2.54450i	0.130702	−	0.130702i	0.769432	+	0.638729i	$0.220540\pi$
$380$		0			0
$381$	−7.24846	−	7.24846i	−0.371350	−	0.371350i
$382$		0			0
$383$	0.193238	−	0.193238i	0.00987399	−	0.00987399i	−0.702153	−	0.712027i	$-0.747778\pi$
$383$	0.193238	−	0.193238i	0.00987399	−	0.00987399i	0.712027	+	0.702153i	$0.247778\pi$
$384$		0			0
$385$	9.24658	+	23.0660i	0.471249	+	1.17555i
$386$		0			0
$387$		−	2.22831i		−	0.113272i
$388$		0			0
$389$	−2.01528	−	2.01528i	−0.102179	−	0.102179i	0.654169	−	0.756348i	$-0.273018\pi$
$389$	−2.01528	−	2.01528i	−0.102179	−	0.102179i	−0.756348	+	0.654169i	$0.773018\pi$
$390$		0			0
$391$	−40.2718			−2.03663
$392$		0			0
$393$	−9.81803	+	9.81803i	−0.495254	+	0.495254i
$394$		0			0
$395$	−11.7309	−	29.2632i	−0.590244	−	1.47239i
$396$		0			0
$397$	−21.5509			−1.08161			−0.540804	−	0.841149i	$-0.681880\pi$
$397$	−21.5509			−1.08161			−0.540804	+	0.841149i	$0.681880\pi$
$398$		0			0
$399$	2.38257			0.119277
$400$		0			0
$401$	−10.3965			−0.519176			−0.259588	−	0.965719i	$-0.583587\pi$
$401$	−10.3965			−0.519176			−0.259588	+	0.965719i	$0.583587\pi$
$402$		0			0
$403$	4.84917			0.241555
$404$		0			0
$405$	4.77865	+	11.9205i	0.237453	+	0.592337i
$406$		0			0
$407$	8.90264	−	8.90264i	0.441288	−	0.441288i
$408$		0			0
$409$	0.330732			0.0163536			0.00817682	−	0.999967i	$-0.497397\pi$
$409$	0.330732			0.0163536			0.00817682	+	0.999967i	$0.497397\pi$
$410$		0			0
$411$	−0.795389	−	0.795389i	−0.0392337	−	0.0392337i
$412$		0			0
$413$			23.6150i			1.16202i
$414$		0			0
$415$	2.29409	+	5.72270i	0.112612	+	0.280917i
$416$		0			0
$417$	5.29395	−	5.29395i	0.259246	−	0.259246i
$418$		0			0
$419$	−6.71354	−	6.71354i	−0.327978	−	0.327978i	0.523839	−	0.851817i	$-0.324499\pi$
$419$	−6.71354	−	6.71354i	−0.327978	−	0.327978i	−0.851817	+	0.523839i	$0.824499\pi$
$420$		0			0
$421$	2.99831	−	2.99831i	0.146129	−	0.146129i	−0.630258	−	0.776386i	$-0.717051\pi$
$421$	2.99831	−	2.99831i	0.146129	−	0.146129i	0.776386	+	0.630258i	$0.217051\pi$
$422$		0			0
$423$	−7.14963	−	7.14963i	−0.347627	−	0.347627i
$424$		0			0
$425$	0.657974	−	28.7557i	0.0319164	−	1.39486i
$426$		0			0
$427$	−31.5208			−1.52540
$428$		0			0
$429$	2.47435	−	2.47435i	0.119463	−	0.119463i
$430$		0			0
$431$			19.9548i			0.961191i	0.876942	+	0.480596i	$0.159580\pi$
$431$			19.9548i			0.961191i	−0.876942	+	0.480596i	$0.840420\pi$
$432$		0			0
$433$	−16.1910	−	16.1910i	−0.778092	−	0.778092i	0.201414	−	0.979506i	$-0.435446\pi$
$433$	−16.1910	−	16.1910i	−0.778092	−	0.778092i	−0.979506	+	0.201414i	$0.935446\pi$
$434$		0			0
$435$	−1.49282	−	0.638449i	−0.0715753	−	0.0306113i
$436$		0			0
$437$			6.76664i			0.323692i
$438$		0			0
$439$			29.3734i			1.40191i	0.713204	+	0.700957i	$0.247243\pi$
$439$			29.3734i			1.40191i	−0.713204	+	0.700957i	$0.752757\pi$
$440$		0			0
$441$			23.8287i			1.13470i
$442$		0			0
$443$			19.8713i			0.944115i	0.881568	+	0.472057i	$0.156489\pi$
$443$			19.8713i			0.944115i	−0.881568	+	0.472057i	$0.843511\pi$
$444$		0			0
$445$	9.68870	+	24.1689i	0.459288	+	1.14572i
$446$		0			0
$447$	−0.0495422	−	0.0495422i	−0.00234326	−	0.00234326i
$448$		0			0
$449$			16.7577i			0.790844i	0.918500	+	0.395422i	$0.129402\pi$
$449$			16.7577i			0.790844i	−0.918500	+	0.395422i	$0.870598\pi$
$450$		0			0
$451$	−9.93854	+	9.93854i	−0.467987	+	0.467987i
$452$		0			0
$453$	−1.99856			−0.0939005
$454$		0			0
$455$	−7.24703	+	16.9450i	−0.339746	+	0.794394i
$456$		0			0
$457$	5.00267	+	5.00267i	0.234015	+	0.234015i	0.814366	−	0.580351i	$-0.197085\pi$
$457$	5.00267	+	5.00267i	0.234015	+	0.234015i	−0.580351	+	0.814366i	$0.697085\pi$
$458$		0			0
$459$	−14.0552	+	14.0552i	−0.656039	+	0.656039i
$460$		0			0
$461$	2.71518	+	2.71518i	0.126459	+	0.126459i	0.767503	−	0.641045i	$-0.221499\pi$
$461$	2.71518	+	2.71518i	0.126459	+	0.126459i	−0.641045	+	0.767503i	$0.721499\pi$
$462$		0			0
$463$	9.18551	−	9.18551i	0.426887	−	0.426887i	−0.460680	−	0.887566i	$-0.652394\pi$
$463$	9.18551	−	9.18551i	0.426887	−	0.426887i	0.887566	+	0.460680i	$0.152394\pi$
$464$		0			0
$465$	3.00999	−	1.20663i	0.139585	−	0.0559561i
$466$		0			0
$467$		−	1.06405i		−	0.0492385i	−0.999697	−	0.0246193i	$-0.992163\pi$
$467$		−	1.06405i		−	0.0492385i	0.999697	−	0.0246193i	$-0.00783735\pi$
$468$		0			0
$469$	4.92371	+	4.92371i	0.227356	+	0.227356i
$470$		0			0
$471$	5.57197			0.256743
$472$		0			0
$473$	1.66490	−	1.66490i	0.0765523	−	0.0765523i
$474$		0			0
$475$	−4.83166	−	0.110556i	−0.221692	−	0.00507265i
$476$		0			0
$477$	−13.5732			−0.621474
$478$		0			0
$479$	15.8658			0.724926			0.362463	−	0.931998i	$-0.381936\pi$
$479$	15.8658			0.724926			0.362463	+	0.931998i	$0.381936\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$		0			0
$483$	17.2559			0.785170
$484$		0			0
$485$	−10.2616	−	4.38869i	−0.465957	−	0.199280i
$486$		0			0
$487$	13.7947	−	13.7947i	0.625099	−	0.625099i	−0.321732	−	0.946831i	$-0.604265\pi$
$487$	13.7947	−	13.7947i	0.625099	−	0.625099i	0.946831	+	0.321732i	$0.104265\pi$
$488$		0			0
$489$	2.41717			0.109308
$490$		0			0
$491$	−19.4471	−	19.4471i	−0.877637	−	0.877637i	0.115652	−	0.993290i	$-0.463104\pi$
$491$	−19.4471	−	19.4471i	−0.877637	−	0.877637i	−0.993290	+	0.115652i	$0.963104\pi$
$492$		0			0
$493$			6.79669i			0.306108i
$494$		0			0
$495$	−6.38885	+	14.9384i	−0.287157	+	0.671431i
$496$		0			0
$497$	6.62302	−	6.62302i	0.297083	−	0.297083i
$498$		0			0
$499$	23.0141	+	23.0141i	1.03025	+	1.03025i	0.999528	+	0.0307258i	$0.00978185\pi$
$499$	23.0141	+	23.0141i	1.03025	+	1.03025i	0.0307258	+	0.999528i	$0.490218\pi$
$500$		0			0
$501$	4.99775	−	4.99775i	0.223283	−	0.223283i
$502$		0			0
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	0.543579	−	0.839358i	$-0.317069\pi$
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	−0.839358	+	0.543579i	$0.817069\pi$
$504$		0			0
$505$	21.5002	+	9.19520i	0.956748	+	0.409181i
$506$		0			0
$507$	−5.39422			−0.239566
$508$		0			0
$509$	−8.04140	+	8.04140i	−0.356429	+	0.356429i	−0.862495	−	0.506066i	$-0.831099\pi$
$509$	−8.04140	+	8.04140i	−0.356429	+	0.356429i	0.506066	+	0.862495i	$0.331099\pi$
$510$		0			0
$511$		−	24.9398i		−	1.10327i
$512$		0			0
$513$	2.36161	+	2.36161i	0.104268	+	0.104268i
$514$		0			0
$515$	4.63331	−	10.8336i	0.204168	−	0.477386i
$516$		0			0
$517$		−	10.6838i		−	0.469873i
$518$		0			0
$519$		−	4.22044i		−	0.185257i
$520$		0			0
$521$			32.8549i			1.43940i	0.694285	+	0.719700i	$0.255721\pi$
$521$			32.8549i			1.43940i	−0.694285	+	0.719700i	$0.744279\pi$
$522$		0			0
$523$			2.46341i			0.107717i	0.998549	+	0.0538587i	$0.0171521\pi$
$523$			2.46341i			0.107717i	−0.998549	+	0.0538587i	$0.982848\pi$
$524$		0			0
$525$	−0.281933	+	12.3214i	−0.0123046	+	0.537751i
$526$		0			0
$527$	−9.59896	−	9.59896i	−0.418137	−	0.418137i
$528$		0			0
$529$			26.0078i			1.13078i
$530$		0			0
$531$	−10.9174	+	10.9174i	−0.473775	+	0.473775i
$532$		0			0
$533$	−10.4237			−0.451501
$534$		0			0
$535$	−13.6955	−	34.1640i	−0.592107	−	1.47704i
$536$		0			0
$537$	−9.65586	−	9.65586i	−0.416681	−	0.416681i
$538$		0			0
$539$	−17.8038	+	17.8038i	−0.766863	+	0.766863i
$540$		0			0
$541$	−18.0772	−	18.0772i	−0.777198	−	0.777198i	0.202156	−	0.979353i	$-0.435205\pi$
$541$	−18.0772	−	18.0772i	−0.777198	−	0.777198i	−0.979353	+	0.202156i	$0.935205\pi$
$542$		0			0
$543$	8.54938	−	8.54938i	0.366889	−	0.366889i
$544$		0			0
$545$	−37.3775	−	15.9856i	−1.60108	−	0.684747i
$546$		0			0
$547$			43.6742i			1.86738i	0.358089	+	0.933688i	$0.383428\pi$
$547$			43.6742i			1.86738i	−0.358089	+	0.933688i	$0.616572\pi$
$548$		0			0
$549$	−14.5723	−	14.5723i	−0.621932	−	0.621932i
$550$		0			0
$551$	1.14201			0.0486513
$552$		0			0
$553$	39.9869	−	39.9869i	1.70042	−	1.70042i
$554$		0			0
$555$	5.79584	−	2.32341i	0.246020	−	0.0986231i
$556$		0			0
$557$	−5.18948			−0.219885			−0.109943	−	0.993938i	$-0.535067\pi$
$557$	−5.18948			−0.219885			−0.109943	+	0.993938i	$0.535067\pi$
$558$		0			0
$559$	1.74618			0.0738555
$560$		0			0
$561$	−9.79597			−0.413586
$562$		0			0
$563$	−11.3756			−0.479423			−0.239711	−	0.970844i	$-0.577053\pi$
$563$	−11.3756			−0.479423			−0.239711	+	0.970844i	$0.577053\pi$
$564$		0			0
$565$	−1.07392	+	2.51103i	−0.0451800	+	0.105640i
$566$		0			0
$567$	−16.2889	+	16.2889i	−0.684071	+	0.684071i
$568$		0			0
$569$	7.51787			0.315165			0.157583	−	0.987506i	$-0.449630\pi$
$569$	7.51787			0.315165			0.157583	+	0.987506i	$0.449630\pi$
$570$		0			0
$571$	7.76889	+	7.76889i	0.325118	+	0.325118i	0.850726	−	0.525609i	$-0.176162\pi$
$571$	7.76889	+	7.76889i	0.325118	+	0.325118i	−0.525609	+	0.850726i	$0.676162\pi$
$572$		0			0
$573$		−	6.35416i		−	0.265449i
$574$		0			0
$575$	−34.9936	−	0.800708i	−1.45934	−	0.0333918i
$576$		0			0
$577$	−9.84819	+	9.84819i	−0.409986	+	0.409986i	−0.881733	−	0.471748i	$-0.843623\pi$
$577$	−9.84819	+	9.84819i	−0.409986	+	0.409986i	0.471748	+	0.881733i	$0.343623\pi$
$578$		0			0
$579$	−8.11720	−	8.11720i	−0.337339	−	0.337339i
$580$		0			0
$581$	−7.81984	+	7.81984i	−0.324421	+	0.324421i
$582$		0			0
$583$	−10.1413	−	10.1413i	−0.420010	−	0.420010i
$584$		0			0
$585$	−11.1842	+	4.48346i	−0.462410	+	0.185368i
$586$		0			0
$587$	33.0447			1.36390			0.681951	−	0.731398i	$-0.261132\pi$
$587$	33.0447			1.36390			0.681951	+	0.731398i	$0.261132\pi$
$588$		0			0
$589$	−1.61286	+	1.61286i	−0.0664567	+	0.0664567i
$590$		0			0
$591$			9.36829i			0.385360i
$592$		0			0
$593$	18.5424	+	18.5424i	0.761445	+	0.761445i	0.976584	−	0.215139i	$-0.0690203\pi$
$593$	18.5424	+	18.5424i	0.761445	+	0.761445i	−0.215139	+	0.976584i	$0.569020\pi$
$594$		0			0
$595$	47.8882	−	19.1972i	1.96323	−	0.787008i
$596$		0			0
$597$		−	3.06521i		−	0.125451i
$598$		0			0
$599$		−	28.3117i		−	1.15678i	−0.815759	−	0.578392i	$-0.803681\pi$
$599$		−	28.3117i		−	1.15678i	0.815759	−	0.578392i	$-0.196319\pi$
$600$		0			0
$601$		−	41.7630i		−	1.70355i	−0.523909	−	0.851774i	$-0.675527\pi$
$601$		−	41.7630i		−	1.70355i	0.523909	−	0.851774i	$-0.324473\pi$
$602$		0			0
$603$			4.55255i			0.185394i
$604$		0			0
$605$	6.89579	−	2.76435i	0.280354	−	0.112387i
$606$		0			0
$607$	4.01973	+	4.01973i	0.163156	+	0.163156i	0.783963	−	0.620807i	$-0.213195\pi$
$607$	4.01973	+	4.01973i	0.163156	+	0.163156i	−0.620807	+	0.783963i	$0.713195\pi$
$608$		0			0
$609$		−	2.91229i		−	0.118012i
$610$		0			0
$611$	5.60268	−	5.60268i	0.226660	−	0.226660i
$612$		0			0
$613$	21.5230			0.869305			0.434652	−	0.900598i	$-0.356871\pi$
$613$	21.5230			0.869305			0.434652	+	0.900598i	$0.356871\pi$
$614$		0			0
$615$	−6.47023	+	2.59375i	−0.260905	+	0.104590i
$616$		0			0
$617$	26.4655	+	26.4655i	1.06546	+	1.06546i	0.997702	+	0.0677580i	$0.0215846\pi$
$617$	26.4655	+	26.4655i	1.06546	+	1.06546i	0.0677580	+	0.997702i	$0.478415\pi$
$618$		0			0
$619$	21.7935	−	21.7935i	0.875955	−	0.875955i	−0.117158	−	0.993113i	$-0.537378\pi$
$619$	21.7935	−	21.7935i	0.875955	−	0.875955i	0.993113	+	0.117158i	$0.0373784\pi$
$620$		0			0
$621$	17.1041	+	17.1041i	0.686365	+	0.686365i
$622$		0			0
$623$	−33.0258	+	33.0258i	−1.32315	+	1.32315i
$624$		0			0
$625$	1.14348	−	24.9738i	0.0457391	−	0.998953i
$626$		0			0
$627$			1.64596i			0.0657334i
$628$		0			0
$629$	−18.4831	−	18.4831i	−0.736971	−	0.736971i
$630$		0			0
$631$	42.7412			1.70150			0.850751	−	0.525570i	$-0.176148\pi$
$631$	42.7412			1.70150			0.850751	+	0.525570i	$0.176148\pi$
$632$		0			0
$633$	6.37937	−	6.37937i	0.253557	−	0.253557i
$634$		0			0
$635$	−14.6663	+	34.2927i	−0.582013	+	1.36086i
$636$		0			0
$637$	−18.6729			−0.739848
$638$		0			0
$639$	6.12376			0.242252
$640$		0			0
$641$	45.4930			1.79687			0.898433	−	0.439110i	$-0.144706\pi$
$641$	45.4930			1.79687			0.898433	+	0.439110i	$0.144706\pi$
$642$		0			0
$643$	31.3531			1.23645			0.618224	−	0.786002i	$-0.287853\pi$
$643$	31.3531			1.23645			0.618224	+	0.786002i	$0.287853\pi$
$644$		0			0
$645$	1.08389	−	0.434505i	0.0426782	−	0.0171086i
$646$		0			0
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	−0.0536292	−	0.998561i	$-0.517079\pi$
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	0.998561	+	0.0536292i	$0.0170789\pi$
$648$		0			0
$649$	−16.3141			−0.640383
$650$		0			0
$651$	4.11303	+	4.11303i	0.161202	+	0.161202i
$652$		0			0
$653$			15.4153i			0.603248i	0.953427	+	0.301624i	$0.0975288\pi$
$653$			15.4153i			0.603248i	−0.953427	+	0.301624i	$0.902471\pi$
$654$		0			0
$655$	46.4494	+	19.8654i	1.81493	+	0.776207i
$656$		0			0
$657$	11.5299	−	11.5299i	0.449825	−	0.449825i
$658$		0			0
$659$	−30.4355	−	30.4355i	−1.18560	−	1.18560i	−0.978272	−	0.207327i	$-0.933524\pi$
$659$	−30.4355	−	30.4355i	−1.18560	−	1.18560i	−0.207327	−	0.978272i	$-0.566476\pi$
$660$		0			0
$661$	−11.2208	+	11.2208i	−0.436437	+	0.436437i	−0.890811	−	0.454374i	$-0.849863\pi$
$661$	−11.2208	+	11.2208i	−0.436437	+	0.436437i	0.454374	+	0.890811i	$0.349863\pi$
$662$		0			0
$663$	−5.13709	−	5.13709i	−0.199508	−	0.199508i
$664$		0			0
$665$	−3.22560	−	8.04639i	−0.125083	−	0.312026i
$666$		0			0
$667$	8.27109			0.320258
$668$		0			0
$669$	0.920946	−	0.920946i	0.0356058	−	0.0356058i
$670$		0			0
$671$		−	21.7757i		−	0.840640i
$672$		0			0
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.990291	−	0.139006i	$-0.955609\pi$
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.139006	−	0.990291i	$-0.544391\pi$
$674$		0			0
$675$	−12.4925	+	11.9336i	−0.480837	+	0.459325i
$676$		0			0
$677$		−	2.74511i		−	0.105503i	−0.998608	−	0.0527516i	$-0.983201\pi$
$677$		−	2.74511i		−	0.105503i	0.998608	−	0.0527516i	$-0.0167991\pi$
$678$		0			0
$679$		−	20.0191i		−	0.768261i
$680$		0			0
$681$			9.60850i			0.368199i
$682$		0			0
$683$			33.0796i			1.26576i	0.774251	+	0.632878i	$0.218127\pi$
$683$			33.0796i			1.26576i	−0.774251	+	0.632878i	$0.781873\pi$
$684$		0			0
$685$	−1.60936	+	3.76301i	−0.0614905	+	0.143777i
$686$		0			0
$687$	−5.98647	−	5.98647i	−0.228398	−	0.228398i
$688$		0			0
$689$		−	10.6364i		−	0.405214i
$690$		0			0
$691$	30.8216	−	30.8216i	1.17251	−	1.17251i	0.190899	−	0.981610i	$-0.438860\pi$
$691$	30.8216	−	30.8216i	1.17251	−	1.17251i	0.981610	−	0.190899i	$-0.0611404\pi$
$692$		0			0
$693$	−29.1428			−1.10704
$694$		0			0
$695$	−25.0458	−	10.7116i	−0.950043	−	0.406314i
$696$		0			0
$697$	20.6338	+	20.6338i	0.781561	+	0.781561i
$698$		0			0
$699$	0.312890	−	0.312890i	0.0118346	−	0.0118346i
$700$		0			0
$701$	−22.1242	−	22.1242i	−0.835619	−	0.835619i	0.152660	−	0.988279i	$-0.451216\pi$
$701$	−22.1242	−	22.1242i	−0.835619	−	0.835619i	−0.988279	+	0.152660i	$0.951216\pi$
$702$		0			0
$703$	−3.10562	+	3.10562i	−0.117131	+	0.117131i
$704$		0			0
$705$	2.08358	−	4.87183i	0.0784723	−	0.183484i
$706$		0			0
$707$			41.9440i			1.57747i
$708$		0			0
$709$	7.09244	+	7.09244i	0.266362	+	0.266362i	0.827632	−	0.561270i	$-0.189687\pi$
$709$	7.09244	+	7.09244i	0.266362	+	0.266362i	−0.561270	+	0.827632i	$0.689687\pi$
$710$		0			0
$711$	36.9726			1.38658
$712$		0			0
$713$	−11.6812	+	11.6812i	−0.437466	+	0.437466i
$714$		0			0
$715$	−11.7062	−	5.00651i	−0.437788	−	0.187233i
$716$		0			0
$717$	−5.03628			−0.188083
$718$		0			0
$719$	30.2949			1.12981			0.564905	−	0.825156i	$-0.308913\pi$
$719$	30.2949			1.12981			0.564905	+	0.825156i	$0.308913\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$		0			0
$723$	−3.48320			−0.129542
$724$		0			0
$725$	−0.135136	+	5.90590i	−0.00501883	+	0.219340i
$726$		0			0
$727$	−15.9503	+	15.9503i	−0.591566	+	0.591566i	−0.938054	−	0.346489i	$-0.887374\pi$
$727$	−15.9503	+	15.9503i	−0.591566	+	0.591566i	0.346489	+	0.938054i	$0.387374\pi$
$728$		0			0
$729$	−8.69055			−0.321872
$730$		0			0
$731$	−3.45657	−	3.45657i	−0.127846	−	0.127846i
$732$		0			0
$733$			35.8535i			1.32428i	0.749380	+	0.662140i	$0.230352\pi$
$733$			35.8535i			1.32428i	−0.749380	+	0.662140i	$0.769648\pi$
$734$		0			0
$735$	−11.5907	+	4.64642i	−0.427529	+	0.171386i
$736$		0			0
$737$	−3.40147	+	3.40147i	−0.125295	+	0.125295i
$738$		0			0
$739$	−21.4532	−	21.4532i	−0.789168	−	0.789168i	0.192190	−	0.981358i	$-0.438441\pi$
$739$	−21.4532	−	21.4532i	−0.789168	−	0.789168i	−0.981358	+	0.192190i	$0.938441\pi$
$740$		0			0
$741$	−0.863157	+	0.863157i	−0.0317089	+	0.0317089i
$742$		0			0
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	0.426449	−	0.904512i	$-0.359765\pi$
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	−0.904512	+	0.426449i	$0.859765\pi$
$744$		0			0
$745$	−0.100242	+	0.234385i	−0.00367258	+	0.00858722i
$746$		0			0
$747$	−7.23036			−0.264545
$748$		0			0
$749$	46.6836	−	46.6836i	1.70578	−	1.70578i
$750$		0			0
$751$		−	22.4879i		−	0.820595i	−0.911952	−	0.410297i	$-0.865425\pi$
$751$		−	22.4879i		−	0.820595i	0.911952	−	0.410297i	$-0.134575\pi$
$752$		0			0
$753$	9.06387	+	9.06387i	0.330306	+	0.330306i
$754$		0			0
$755$	2.70571	+	6.74952i	0.0984710	+	0.245640i
$756$		0			0
$757$		−	15.8781i		−	0.577100i	−0.957465	−	0.288550i	$-0.906827\pi$
$757$		−	15.8781i		−	0.577100i	0.957465	−	0.288550i	$-0.0931731\pi$
$758$		0			0
$759$			11.9210i			0.432705i
$760$		0			0
$761$		−	19.5227i		−	0.707696i	−0.935303	−	0.353848i	$-0.884873\pi$
$761$		−	19.5227i		−	0.707696i	0.935303	−	0.353848i	$-0.115127\pi$
$762$		0			0
$763$		−	72.9184i		−	2.63982i
$764$		0			0
$765$	31.0142	+	13.2641i	1.12132	+	0.479566i
$766$		0			0
$767$	−8.55524	−	8.55524i	−0.308912	−	0.308912i
$768$		0			0
$769$			8.03843i			0.289873i	0.989441	+	0.144937i	$0.0462978\pi$
$769$			8.03843i			0.289873i	−0.989441	+	0.144937i	$0.953702\pi$
$770$		0			0
$771$	−2.21946	+	2.21946i	−0.0799320	+	0.0799320i
$772$		0			0
$773$	40.5118			1.45711			0.728554	−	0.684988i	$-0.240193\pi$
$773$	40.5118			1.45711			0.728554	+	0.684988i	$0.240193\pi$
$774$		0			0
$775$	−8.15005	−	8.53175i	−0.292758	−	0.306470i
$776$		0			0
$777$	7.91977	+	7.91977i	0.284120	+	0.284120i
$778$		0			0
$779$	3.46698	−	3.46698i	0.124217	−	0.124217i
$780$		0			0
$781$	4.57542	+	4.57542i	0.163721	+	0.163721i
$782$		0			0
$783$	2.88668	−	2.88668i	0.103161	−	0.103161i
$784$		0			0
$785$	−7.54352	−	18.8176i	−0.269240	−	0.671631i
$786$		0			0
$787$			15.8333i			0.564396i	0.959356	+	0.282198i	$0.0910635\pi$
$787$			15.8333i			0.564396i	−0.959356	+	0.282198i	$0.908937\pi$
$788$		0			0
$789$	−4.17930	−	4.17930i	−0.148787	−	0.148787i
$790$		0			0
$791$	−4.89868			−0.174177
$792$		0			0
$793$	11.4194	−	11.4194i	0.405513	−	0.405513i
$794$		0			0
$795$	−2.64667	−	6.60224i	−0.0938678	−	0.234157i
$796$		0			0
$797$	−10.2670			−0.363674			−0.181837	−	0.983329i	$-0.558204\pi$
$797$	−10.2670			−0.363674			−0.181837	+	0.983329i	$0.558204\pi$
$798$		0			0
$799$	−22.1811			−0.784710
$800$		0			0
$801$	−30.5362			−1.07895
$802$		0			0
$803$	17.2293			0.608010
$804$		0			0
$805$	−23.3616	−	58.2766i	−0.823388	−	2.05398i
$806$		0			0
$807$	−0.737538	+	0.737538i	−0.0259626	+	0.0259626i
$808$		0			0
$809$	9.16442			0.322204			0.161102	−	0.986938i	$-0.448495\pi$
$809$	9.16442			0.322204			0.161102	+	0.986938i	$0.448495\pi$
$810$		0			0
$811$	22.1702	+	22.1702i	0.778502	+	0.778502i	0.979576	−	0.201074i	$-0.0644432\pi$
$811$	22.1702	+	22.1702i	0.778502	+	0.778502i	−0.201074	+	0.979576i	$0.564443\pi$
$812$		0			0
$813$		−	1.71827i		−	0.0602625i
$814$		0			0
$815$	−3.27245	−	8.16326i	−0.114629	−	0.285947i
$816$		0			0
$817$	−0.580788	+	0.580788i	−0.0203192	+	0.0203192i
$818$		0			0
$819$	−15.2827	−	15.2827i	−0.534022	−	0.534022i
$820$		0			0
$821$	13.3258	−	13.3258i	0.465074	−	0.465074i	−0.435240	−	0.900314i	$-0.643337\pi$
$821$	13.3258	−	13.3258i	0.465074	−	0.465074i	0.900314	+	0.435240i	$0.143337\pi$
$822$		0			0
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.970255	+	0.242084i	$0.0778308\pi$
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.242084	+	0.970255i	$0.422169\pi$
$824$		0			0
$825$	−8.51209	−	0.194769i	−0.296353	−	0.00678100i
$826$		0			0
$827$	−16.5717			−0.576253			−0.288127	−	0.957592i	$-0.593032\pi$
$827$	−16.5717			−0.576253			−0.288127	+	0.957592i	$0.593032\pi$
$828$		0			0
$829$	11.9869	−	11.9869i	0.416321	−	0.416321i	−0.467613	−	0.883933i	$-0.654886\pi$
$829$	11.9869	−	11.9869i	0.416321	−	0.416321i	0.883933	+	0.467613i	$0.154886\pi$
$830$		0			0
$831$			8.48807i			0.294448i
$832$		0			0
$833$	36.9631	+	36.9631i	1.28070	+	1.28070i
$834$		0			0
$835$	−23.6445	−	10.1123i	−0.818252	−	0.349949i
$836$		0			0
$837$			8.15370i			0.281833i
$838$		0			0
$839$			4.44215i			0.153360i	0.997056	+	0.0766800i	$0.0244320\pi$
$839$			4.44215i			0.153360i	−0.997056	+	0.0766800i	$0.975568\pi$
$840$		0			0
$841$			27.6041i			0.951865i
$842$		0			0
$843$		−	4.43543i		−	0.152764i
$844$		0			0
$845$	7.30287	+	18.2173i	0.251226	+	0.626695i
$846$		0			0
$847$	9.42281	+	9.42281i	0.323772	+	0.323772i
$848$		0			0
$849$			15.5478i			0.533599i
$850$		0			0
$851$	−22.4926	+	22.4926i	−0.771038	+	0.771038i
$852$		0			0
$853$	35.6748			1.22148			0.610742	−	0.791830i	$-0.290871\pi$
$853$	35.6748			1.22148			0.610742	+	0.791830i	$0.290871\pi$
$854$		0			0
$855$	2.22870	−	5.21114i	0.0762199	−	0.178217i
$856$		0			0
$857$	13.8568	+	13.8568i	0.473340	+	0.473340i	0.902994	−	0.429654i	$-0.141364\pi$
$857$	13.8568	+	13.8568i	0.473340	+	0.473340i	−0.429654	+	0.902994i	$0.641364\pi$
$858$		0			0
$859$	−19.4217	+	19.4217i	−0.662660	+	0.662660i	−0.956006	−	0.293346i	$-0.905231\pi$
$859$	−19.4217	+	19.4217i	−0.662660	+	0.662660i	0.293346	+	0.956006i	$0.405231\pi$
$860$		0			0
$861$	−8.84130	−	8.84130i	−0.301311	−	0.301311i
$862$		0			0
$863$	9.22041	−	9.22041i	0.313866	−	0.313866i	−0.532539	−	0.846405i	$-0.678762\pi$
$863$	9.22041	−	9.22041i	0.313866	−	0.313866i	0.846405	+	0.532539i	$0.178762\pi$
$864$		0			0
$865$	−14.2532	+	5.71377i	−0.484625	+	0.194274i
$866$		0			0
$867$			9.89018i			0.335888i
$868$		0			0
$869$	27.6244	+	27.6244i	0.937093	+	0.937093i
$870$		0			0
$871$	−3.56753			−0.120881
$872$		0			0
$873$	9.25500	−	9.25500i	0.313234	−	0.313234i
$874$		0			0
$875$	41.9936	−	15.7290i	1.41964	−	0.531738i
$876$		0			0
$877$	10.4267			0.352084			0.176042	−	0.984383i	$-0.443670\pi$
$877$	10.4267			0.352084			0.176042	+	0.984383i	$0.443670\pi$
$878$		0			0
$879$	8.68236			0.292849
$880$		0			0
$881$	−12.7405			−0.429239			−0.214619	−	0.976698i	$-0.568851\pi$
$881$	−12.7405			−0.429239			−0.214619	+	0.976698i	$0.568851\pi$
$882$		0			0
$883$	−27.9073			−0.939156			−0.469578	−	0.882891i	$-0.655594\pi$
$883$	−27.9073			−0.939156			−0.469578	+	0.882891i	$0.655594\pi$
$884$		0			0
$885$	−7.43924	−	3.18161i	−0.250067	−	0.106949i
$886$		0			0
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.606811	+	0.794846i	$0.707552\pi$
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.794846	+	0.606811i	$0.792448\pi$
$888$		0			0
$889$	−66.9004			−2.24377
$890$		0			0
$891$	−11.2530	−	11.2530i	−0.376989	−	0.376989i
$892$		0			0
$893$			3.72696i			0.124718i
$894$		0			0
$895$	−19.5373	+	45.6822i	−0.653061	+	1.52699i
$896$		0			0
$897$	−6.25148	+	6.25148i	−0.208731	+	0.208731i
$898$		0			0
$899$	1.97145	+	1.97145i	0.0657516	+	0.0657516i
$900$		0			0
$901$	−21.0548	+	21.0548i	−0.701437	+	0.701437i
$902$		0			0
$903$	1.48109	+	1.48109i	0.0492877	+	0.0492877i
$904$		0			0
$905$	−40.4474	−	17.2985i	−1.34452	−	0.575022i
$906$		0			0
$907$	−26.7614			−0.888597			−0.444298	−	0.895879i	$-0.646547\pi$
$907$	−26.7614			−0.888597			−0.444298	+	0.895879i	$0.646547\pi$
$908$		0			0
$909$	−19.3911	+	19.3911i	−0.643163	+	0.643163i
$910$		0			0
$911$		−	19.2403i		−	0.637459i	−0.947846	−	0.318729i	$-0.896744\pi$
$911$		−	19.2403i		−	0.637459i	0.947846	−	0.318729i	$-0.103256\pi$
$912$		0			0
$913$	−5.40222	−	5.40222i	−0.178787	−	0.178787i
$914$		0			0
$915$	4.24675	−	9.92975i	0.140393	−	0.328267i
$916$		0			0
$917$			90.6165i			2.99242i
$918$		0			0
$919$			42.6903i			1.40822i	0.710090	+	0.704111i	$0.248654\pi$
$919$			42.6903i			1.40822i	−0.710090	+	0.704111i	$0.751346\pi$
$920$		0			0
$921$			13.8942i			0.457828i
$922$		0			0
$923$			4.79878i			0.157954i
$924$		0			0
$925$	−15.6932	−	16.4282i	−0.515989	−	0.540155i
$926$		0			0
$927$	9.77085	+	9.77085i	0.320917	+	0.320917i
$928$		0			0
$929$		−	5.58037i		−	0.183086i	−0.995801	−	0.0915430i	$-0.970820\pi$
$929$		−	5.58037i		−	0.183086i	0.995801	−	0.0915430i	$-0.0291799\pi$
$930$		0			0
$931$	6.21070	−	6.21070i	0.203548	−	0.203548i
$932$		0			0
$933$	−6.63132			−0.217100
$934$		0			0
$935$	13.2621	+	33.0829i	0.433717	+	1.08193i
$936$		0			0
$937$	−41.0680	−	41.0680i	−1.34163	−	1.34163i	−0.894435	−	0.447197i	$-0.852422\pi$
$937$	−41.0680	−	41.0680i	−1.34163	−	1.34163i	−0.447197	−	0.894435i	$-0.647578\pi$
$938$		0			0
$939$	12.7118	−	12.7118i	0.414834	−	0.414834i
$940$		0			0
$941$	−31.5476	−	31.5476i	−1.02842	−	1.02842i	−0.999584	−	0.0288377i	$-0.990819\pi$
$941$	−31.5476	−	31.5476i	−1.02842	−	1.02842i	−0.0288377	−	0.999584i	$-0.509181\pi$
$942$		0			0
$943$	25.1098	−	25.1098i	0.817689	−	0.817689i
$944$		0			0
$945$	−28.4924	−	12.1856i	−0.926857	−	0.396398i
$946$		0			0
$947$		−	34.7892i		−	1.13050i	−0.824921	−	0.565248i	$-0.808780\pi$
$947$		−	34.7892i		−	1.13050i	0.824921	−	0.565248i	$-0.191220\pi$
$948$		0			0
$949$	9.03522	+	9.03522i	0.293296	+	0.293296i
$950$		0			0
$951$	−14.6394			−0.474715
$952$		0			0
$953$	−26.7047	+	26.7047i	−0.865050	+	0.865050i	−0.991919	−	0.126870i	$-0.959507\pi$
$953$	−26.7047	+	26.7047i	−0.865050	+	0.865050i	0.126870	+	0.991919i	$0.459507\pi$
$954$		0			0
$955$	−21.4592	+	8.60247i	−0.694405	+	0.278369i
$956$		0			0
$957$	2.01191			0.0650360
$958$		0			0
$959$	−7.34112			−0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$		0			0
$963$	43.1645			1.39096
$964$		0			0
$965$	−16.4241	+	38.4027i	−0.528709	+	1.23623i
$966$		0			0
$967$	12.8711	−	12.8711i	0.413906	−	0.413906i	−0.469191	−	0.883097i	$-0.655454\pi$
$967$	12.8711	−	12.8711i	0.413906	−	0.413906i	0.883097	+	0.469191i	$0.155454\pi$
$968$		0			0
$969$	3.41725			0.109778
$970$		0			0
$971$	23.9028	+	23.9028i	0.767078	+	0.767078i	0.977591	−	0.210513i	$-0.0675134\pi$
$971$	23.9028	+	23.9028i	0.767078	+	0.767078i	−0.210513	+	0.977591i	$0.567513\pi$
$972$		0			0
$973$		−	48.8610i		−	1.56641i
$974$		0			0
$975$	−4.36168	−	4.56595i	−0.139685	−	0.146228i
$976$		0			0
$977$	2.71449	−	2.71449i	0.0868441	−	0.0868441i	−0.662350	−	0.749194i	$-0.730441\pi$
$977$	2.71449	−	2.71449i	0.0868441	−	0.0868441i	0.749194	+	0.662350i	$0.230441\pi$
$978$		0			0
$979$	−22.8154	−	22.8154i	−0.729183	−	0.729183i
$980$		0			0
$981$	33.7109	−	33.7109i	1.07630	−	1.07630i
$982$		0			0
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	0.891572	−	0.452880i	$-0.149603\pi$
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	−0.452880	+	0.891572i	$0.649603\pi$
$984$		0			0
$985$	31.6386	−	12.6831i	1.00809	−	0.404117i
$986$		0			0
$987$	9.50428			0.302525
$988$		0			0
$989$	−4.20640	+	4.20640i	−0.133756	+	0.133756i
$990$		0			0
$991$		−	26.5971i		−	0.844883i	−0.906390	−	0.422442i	$-0.861173\pi$
$991$		−	26.5971i		−	0.844883i	0.906390	−	0.422442i	$-0.138827\pi$
$992$		0			0
$993$	−12.1492	−	12.1492i	−0.385545	−	0.385545i
$994$		0			0
$995$	−10.3518	+	4.14979i	−0.328175	+	0.131557i
$996$		0			0
$997$			25.4590i			0.806295i	0.915135	+	0.403148i	$0.132084\pi$
$997$			25.4590i			0.806295i	−0.915135	+	0.403148i	$0.867916\pi$
$998$		0			0
$999$			15.7002i			0.496733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.s.b.303.5		18
4.3	odd	2		80.2.s.b.3.3	yes	18
5.2	odd	4		320.2.j.b.47.5		18
5.3	odd	4		1600.2.j.d.1007.5		18
5.4	even	2		1600.2.s.d.943.5		18
8.3	odd	2		640.2.s.d.223.5		18
8.5	even	2		640.2.s.c.223.5		18
12.11	even	2		720.2.z.g.163.7		18
16.3	odd	4		640.2.j.c.543.5		18
16.5	even	4		80.2.j.b.43.7	✓	18
16.11	odd	4		320.2.j.b.143.5		18
16.13	even	4		640.2.j.d.543.5		18
20.3	even	4		400.2.j.d.307.3		18
20.7	even	4		80.2.j.b.67.7	yes	18
20.19	odd	2		400.2.s.d.243.7		18
40.27	even	4		640.2.j.d.607.5		18
40.37	odd	4		640.2.j.c.607.5		18
48.5	odd	4		720.2.bd.g.523.3		18
60.47	odd	4		720.2.bd.g.307.3		18
80.27	even	4	inner	320.2.s.b.207.5		18
80.37	odd	4		80.2.s.b.27.3	yes	18
80.43	even	4		1600.2.s.d.207.5		18
80.53	odd	4		400.2.s.d.107.7		18
80.59	odd	4		1600.2.j.d.143.5		18
80.67	even	4		640.2.s.c.287.5		18
80.69	even	4		400.2.j.d.43.3		18
80.77	odd	4		640.2.s.d.287.5		18
240.197	even	4		720.2.z.g.667.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	16.5	even	4
80.2.j.b.67.7	yes	18	20.7	even	4
80.2.s.b.3.3	yes	18	4.3	odd	2
80.2.s.b.27.3	yes	18	80.37	odd	4
320.2.j.b.47.5		18	5.2	odd	4
320.2.j.b.143.5		18	16.11	odd	4
320.2.s.b.207.5		18	80.27	even	4	inner
320.2.s.b.303.5		18	1.1	even	1	trivial
400.2.j.d.43.3		18	80.69	even	4
400.2.j.d.307.3		18	20.3	even	4
400.2.s.d.107.7		18	80.53	odd	4
400.2.s.d.243.7		18	20.19	odd	2
640.2.j.c.543.5		18	16.3	odd	4
640.2.j.c.607.5		18	40.37	odd	4
640.2.j.d.543.5		18	16.13	even	4
640.2.j.d.607.5		18	40.27	even	4
640.2.s.c.223.5		18	8.5	even	2
640.2.s.c.287.5		18	80.67	even	4
640.2.s.d.223.5		18	8.3	odd	2
640.2.s.d.287.5		18	80.77	odd	4
720.2.z.g.163.7		18	12.11	even	2
720.2.z.g.667.7		18	240.197	even	4
720.2.bd.g.307.3		18	60.47	odd	4
720.2.bd.g.523.3		18	48.5	odd	4
1600.2.j.d.143.5		18	80.59	odd	4
1600.2.j.d.1007.5		18	5.3	odd	4
1600.2.s.d.207.5		18	80.43	even	4
1600.2.s.d.943.5		18	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.614566 q^{3} +(0.832020 + 2.07551i) q^{5} +(-2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +O(q^{10})\)	\(q-0.614566 q^{3} +(0.832020 + 2.07551i) q^{5} +(-2.83610 + 2.83610i) q^{7} -2.62231 q^{9} +(-1.95928 - 1.95928i) q^{11} -2.05493i q^{13} +(-0.511331 - 1.27554i) q^{15} +(-4.06774 + 4.06774i) q^{17} +(0.683479 + 0.683479i) q^{19} +(1.74297 - 1.74297i) q^{21} +(4.95014 + 4.95014i) q^{23} +(-3.61549 + 3.45373i) q^{25} +3.45528 q^{27} +(0.835439 - 0.835439i) q^{29} +2.35978i q^{31} +(1.20411 + 1.20411i) q^{33} +(-8.24604 - 3.52666i) q^{35} +4.54384i q^{37} +1.26289i q^{39} -5.07255i q^{41} +0.849753i q^{43} +(-2.18181 - 5.44263i) q^{45} +(2.72646 + 2.72646i) q^{47} -9.08690i q^{49} +(2.49989 - 2.49989i) q^{51} +5.17605 q^{53} +(2.43634 - 5.69666i) q^{55} +(-0.420043 - 0.420043i) q^{57} +(4.16328 - 4.16328i) q^{59} +(5.55706 + 5.55706i) q^{61} +(7.43712 - 7.43712i) q^{63} +(4.26502 - 1.70974i) q^{65} -1.73609i q^{67} +(-3.04219 - 3.04219i) q^{69} -2.33526 q^{71} +(-4.39686 + 4.39686i) q^{73} +(2.22195 - 2.12255i) q^{75} +11.1134 q^{77} -14.0993 q^{79} +5.74343 q^{81} +2.75725 q^{83} +(-11.8271 - 5.05819i) q^{85} +(-0.513433 + 0.513433i) q^{87} +11.6448 q^{89} +(5.82797 + 5.82797i) q^{91} -1.45024i q^{93} +(-0.849899 + 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(5.13783 + 5.13783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{5} - 2 q^{7} + 10 q^{9} + 2 q^{11} + 20 q^{15} - 6 q^{17} + 2 q^{19} - 16 q^{21} + 2 q^{23} - 6 q^{25} + 24 q^{27} + 14 q^{29} - 8 q^{33} - 2 q^{35} - 14 q^{45} - 38 q^{47} - 8 q^{51} + 12 q^{53} + 6 q^{55} - 24 q^{57} - 10 q^{59} + 14 q^{61} + 6 q^{63} - 32 q^{69} - 24 q^{71} - 14 q^{73} - 16 q^{75} - 44 q^{77} + 16 q^{79} + 2 q^{81} - 40 q^{83} + 14 q^{85} - 24 q^{87} + 12 q^{89} - 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^5 - 2 * q^7 + 10 * q^9 + 2 * q^11 + 20 * q^15 - 6 * q^17 + 2 * q^19 - 16 * q^21 + 2 * q^23 - 6 * q^25 + 24 * q^27 + 14 * q^29 - 8 * q^33 - 2 * q^35 - 14 * q^45 - 38 * q^47 - 8 * q^51 + 12 * q^53 + 6 * q^55 - 24 * q^57 - 10 * q^59 + 14 * q^61 + 6 * q^63 - 32 * q^69 - 24 * q^71 - 14 * q^73 - 16 * q^75 - 44 * q^77 + 16 * q^79 + 2 * q^81 - 40 * q^83 + 14 * q^85 - 24 * q^87 + 12 * q^89 - 34 * q^95 + 18 * q^97 - 22 * q^99

Introduction

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