LMFDB - Embedded newform 640.2.s.c.223.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(223,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("640.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.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:	$5.11042572936$
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			223.6
Root			$-0.635486 - 1.26339i$ of defining polynomial
Character	$\chi$	$=$	640.223
Dual form			640.2.s.c.287.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.692712 q^{3} +(0.245325 + 2.22257i) q^{5} +(0.343872 - 0.343872i) q^{7} -2.52015 q^{9} +O(q^{10})$	\(q+0.692712 q^{3} +(0.245325 + 2.22257i) q^{5} +(0.343872 - 0.343872i) q^{7} -2.52015 q^{9} +(0.843672 + 0.843672i) q^{11} +3.68390i q^{13} +(0.169939 + 1.53960i) q^{15} +(0.412137 - 0.412137i) q^{17} +(5.37721 + 5.37721i) q^{19} +(0.238204 - 0.238204i) q^{21} +(3.08788 + 3.08788i) q^{23} +(-4.87963 + 1.09050i) q^{25} -3.82387 q^{27} +(-4.22969 + 4.22969i) q^{29} -8.75966i q^{31} +(0.584422 + 0.584422i) q^{33} +(0.848640 + 0.679919i) q^{35} -5.41752i q^{37} +2.55188i q^{39} +2.54777i q^{41} +4.30732i q^{43} +(-0.618255 - 5.60121i) q^{45} +(4.56972 + 4.56972i) q^{47} +6.76350i q^{49} +(0.285492 - 0.285492i) q^{51} -6.07536 q^{53} +(-1.66815 + 2.08209i) q^{55} +(3.72486 + 3.72486i) q^{57} +(7.33694 - 7.33694i) q^{59} +(4.81576 + 4.81576i) q^{61} +(-0.866609 + 0.866609i) q^{63} +(-8.18773 + 0.903753i) q^{65} -14.3626i q^{67} +(2.13901 + 2.13901i) q^{69} +2.97605 q^{71} +(6.87152 - 6.87152i) q^{73} +(-3.38018 + 0.755404i) q^{75} +0.580231 q^{77} +10.1654 q^{79} +4.91161 q^{81} -7.15276 q^{83} +(1.01711 + 0.814896i) q^{85} +(-2.92996 + 2.92996i) q^{87} -1.10953 q^{89} +(1.26679 + 1.26679i) q^{91} -6.06792i q^{93} +(-10.6321 + 13.2704i) q^{95} +(7.15920 - 7.15920i) q^{97} +(-2.12618 - 2.12618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$	0.692712			0.399937			0.199969	−	0.979802i	$-0.435916\pi$
$3$	0.692712			0.399937			0.199969	+	0.979802i	$0.435916\pi$
$4$		0			0
$5$	0.245325	+	2.22257i	0.109713	+	0.993963i
$5$	0.245325	+	2.22257i	0.109713	+	0.993963i
$6$		0			0
$7$	0.343872	−	0.343872i	0.129971	−	0.129971i	−0.639129	−	0.769100i	$-0.720705\pi$
$7$	0.343872	−	0.343872i	0.129971	−	0.129971i	0.769100	+	0.639129i	$0.220705\pi$
$8$		0			0
$9$	−2.52015			−0.840050
$10$		0			0
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	0.822762	−	0.568386i	$-0.192432\pi$
$11$	0.843672	+	0.843672i	0.254377	+	0.254377i	−0.568386	+	0.822762i	$0.692432\pi$
$12$		0			0
$13$			3.68390i			1.02173i	0.859661	+	0.510865i	$0.170675\pi$
$13$			3.68390i			1.02173i	−0.859661	+	0.510865i	$0.829325\pi$
$14$		0			0
$15$	0.169939	+	1.53960i	0.0438782	+	0.397523i
$16$		0			0
$17$	0.412137	−	0.412137i	0.0999579	−	0.0999579i	−0.655359	−	0.755317i	$-0.727483\pi$
$17$	0.412137	−	0.412137i	0.0999579	−	0.0999579i	0.755317	+	0.655359i	$0.227483\pi$
$18$		0			0
$19$	5.37721	+	5.37721i	1.23362	+	1.23362i	0.962565	+	0.271052i	$0.0873714\pi$
$19$	5.37721	+	5.37721i	1.23362	+	1.23362i	0.271052	+	0.962565i	$0.412629\pi$
$20$		0			0
$21$	0.238204	−	0.238204i	0.0519804	−	0.0519804i
$22$		0			0
$23$	3.08788	+	3.08788i	0.643868	+	0.643868i	0.951504	−	0.307636i	$-0.0995380\pi$
$23$	3.08788	+	3.08788i	0.643868	+	0.643868i	−0.307636	+	0.951504i	$0.599538\pi$
$24$		0			0
$25$	−4.87963	+	1.09050i	−0.975926	+	0.218101i
$26$		0			0
$27$	−3.82387			−0.735905
$28$		0			0
$29$	−4.22969	+	4.22969i	−0.785434	+	0.785434i	−0.980742	−	0.195308i	$-0.937429\pi$
$29$	−4.22969	+	4.22969i	−0.785434	+	0.785434i	0.195308	+	0.980742i	$0.437429\pi$
$30$		0			0
$31$		−	8.75966i		−	1.57328i	−0.617411	−	0.786641i	$-0.711818\pi$
$31$		−	8.75966i		−	1.57328i	0.617411	−	0.786641i	$-0.288182\pi$
$32$		0			0
$33$	0.584422	+	0.584422i	0.101735	+	0.101735i
$34$		0			0
$35$	0.848640	+	0.679919i	0.143446	+	0.114927i
$36$		0			0
$37$		−	5.41752i		−	0.890634i	−0.895373	−	0.445317i	$-0.853091\pi$
$37$		−	5.41752i		−	0.890634i	0.895373	−	0.445317i	$-0.146909\pi$
$38$		0			0
$39$			2.55188i			0.408628i
$40$		0			0
$41$			2.54777i			0.397895i	0.980010	+	0.198948i	$0.0637524\pi$
$41$			2.54777i			0.397895i	−0.980010	+	0.198948i	$0.936248\pi$
$42$		0			0
$43$			4.30732i			0.656861i	0.944528	+	0.328430i	$0.106520\pi$
$43$			4.30732i			0.656861i	−0.944528	+	0.328430i	$0.893480\pi$
$44$		0			0
$45$	−0.618255	−	5.60121i	−0.0921641	−	0.834979i
$46$		0			0
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	0.956919	−	0.290356i	$-0.0937738\pi$
$47$	4.56972	+	4.56972i	0.666562	+	0.666562i	−0.290356	+	0.956919i	$0.593774\pi$
$48$		0			0
$49$			6.76350i			0.966215i
$50$		0			0
$51$	0.285492	−	0.285492i	0.0399769	−	0.0399769i
$52$		0			0
$53$	−6.07536			−0.834515			−0.417257	−	0.908788i	$-0.637009\pi$
$53$	−6.07536			−0.834515			−0.417257	+	0.908788i	$0.637009\pi$
$54$		0			0
$55$	−1.66815	+	2.08209i	−0.224933	+	0.280749i
$56$		0			0
$57$	3.72486	+	3.72486i	0.493369	+	0.493369i
$58$		0			0
$59$	7.33694	−	7.33694i	0.955189	−	0.955189i	−0.0438495	−	0.999038i	$-0.513962\pi$
$59$	7.33694	−	7.33694i	0.955189	−	0.955189i	0.999038	+	0.0438495i	$0.0139622\pi$
$60$		0			0
$61$	4.81576	+	4.81576i	0.616595	+	0.616595i	0.944656	−	0.328062i	$-0.106395\pi$
$61$	4.81576	+	4.81576i	0.616595	+	0.616595i	−0.328062	+	0.944656i	$0.606395\pi$
$62$		0			0
$63$	−0.866609	+	0.866609i	−0.109183	+	0.109183i
$64$		0			0
$65$	−8.18773	+	0.903753i	−1.01556	+	0.112097i
$66$		0			0
$67$		−	14.3626i		−	1.75467i	−0.479880	−	0.877334i	$-0.659320\pi$
$67$		−	14.3626i		−	1.75467i	0.479880	−	0.877334i	$-0.340680\pi$
$68$		0			0
$69$	2.13901	+	2.13901i	0.257507	+	0.257507i
$70$		0			0
$71$	2.97605			0.353193			0.176596	−	0.984283i	$-0.443491\pi$
$71$	2.97605			0.353193			0.176596	+	0.984283i	$0.443491\pi$
$72$		0			0
$73$	6.87152	−	6.87152i	0.804250	−	0.804250i	−0.179507	−	0.983757i	$-0.557450\pi$
$73$	6.87152	−	6.87152i	0.804250	−	0.804250i	0.983757	+	0.179507i	$0.0574501\pi$
$74$		0			0
$75$	−3.38018	+	0.755404i	−0.390309	+	0.0872266i
$76$		0			0
$77$	0.580231			0.0661234
$78$		0			0
$79$	10.1654			1.14369			0.571847	−	0.820360i	$-0.306227\pi$
$79$	10.1654			1.14369			0.571847	+	0.820360i	$0.306227\pi$
$80$		0			0
$81$	4.91161			0.545734
$82$		0			0
$83$	−7.15276			−0.785118			−0.392559	−	0.919727i	$-0.628410\pi$
$83$	−7.15276			−0.785118			−0.392559	+	0.919727i	$0.628410\pi$
$84$		0			0
$85$	1.01711	+	0.814896i	0.110321	+	0.0883878i
$86$		0			0
$87$	−2.92996	+	2.92996i	−0.314124	+	0.314124i
$88$		0			0
$89$	−1.10953			−0.117610			−0.0588050	−	0.998269i	$-0.518729\pi$
$89$	−1.10953			−0.117610			−0.0588050	+	0.998269i	$0.518729\pi$
$90$		0			0
$91$	1.26679	+	1.26679i	0.132796	+	0.132796i
$92$		0			0
$93$		−	6.06792i		−	0.629214i
$94$		0			0
$95$	−10.6321	+	13.2704i	−1.09083	+	1.36151i
$96$		0			0
$97$	7.15920	−	7.15920i	0.726906	−	0.726906i	−0.243096	−	0.970002i	$-0.578163\pi$
$97$	7.15920	−	7.15920i	0.726906	−	0.726906i	0.970002	+	0.243096i	$0.0781630\pi$
$98$		0			0
$99$	−2.12618	−	2.12618i	−0.213689	−	0.213689i
$100$		0			0
$101$	−0.953394	+	0.953394i	−0.0948663	+	0.0948663i	−0.752947	−	0.658081i	$-0.771368\pi$
$101$	−0.953394	+	0.953394i	−0.0948663	+	0.0948663i	0.658081	+	0.752947i	$0.271368\pi$
$102$		0			0
$103$	−9.59425	−	9.59425i	−0.945350	−	0.945350i	0.0532322	−	0.998582i	$-0.483048\pi$
$103$	−9.59425	−	9.59425i	−0.945350	−	0.945350i	−0.998582	+	0.0532322i	$0.983048\pi$
$104$		0			0
$105$	0.587863	+	0.470988i	0.0573696	+	0.0459637i
$106$		0			0
$107$	−5.28201			−0.510631			−0.255316	−	0.966858i	$-0.582179\pi$
$107$	−5.28201			−0.510631			−0.255316	+	0.966858i	$0.582179\pi$
$108$		0			0
$109$	1.53980	−	1.53980i	0.147486	−	0.147486i	−0.629508	−	0.776994i	$-0.716744\pi$
$109$	1.53980	−	1.53980i	0.147486	−	0.147486i	0.776994	+	0.629508i	$0.216744\pi$
$110$		0			0
$111$		−	3.75278i		−	0.356198i
$112$		0			0
$113$	−2.99656	−	2.99656i	−0.281893	−	0.281893i	0.551971	−	0.833863i	$-0.313876\pi$
$113$	−2.99656	−	2.99656i	−0.281893	−	0.281893i	−0.833863	+	0.551971i	$0.813876\pi$
$114$		0			0
$115$	−6.10550	+	7.62056i	−0.569340	+	0.710621i
$116$		0			0
$117$		−	9.28399i		−	0.858305i
$118$		0			0
$119$		−	0.283445i		−	0.0259833i
$120$		0			0
$121$		−	9.57643i		−	0.870585i
$122$		0			0
$123$			1.76487i			0.159133i
$124$		0			0
$125$	−3.62081	−	10.5778i	−0.323855	−	0.946107i
$126$		0			0
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	0.0617330	−	0.998093i	$-0.480337\pi$
$127$	−10.5522	−	10.5522i	−0.936360	−	0.936360i	−0.998093	+	0.0617330i	$0.980337\pi$
$128$		0			0
$129$			2.98373i			0.262703i
$130$		0			0
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	−0.743285	−	0.668975i	$-0.766733\pi$
$131$	−0.850513	+	0.850513i	−0.0743096	+	0.0743096i	0.668975	+	0.743285i	$0.266733\pi$
$132$		0			0
$133$	3.69814			0.320670
$134$		0			0
$135$	−0.938091	−	8.49883i	−0.0807380	−	0.731463i
$136$		0			0
$137$	5.50145	+	5.50145i	0.470021	+	0.470021i	0.901921	−	0.431901i	$-0.142157\pi$
$137$	5.50145	+	5.50145i	0.470021	+	0.470021i	−0.431901	+	0.901921i	$0.642157\pi$
$138$		0			0
$139$	−3.03517	+	3.03517i	−0.257440	+	0.257440i	−0.824012	−	0.566572i	$-0.808269\pi$
$139$	−3.03517	+	3.03517i	−0.257440	+	0.257440i	0.566572	+	0.824012i	$0.308269\pi$
$140$		0			0
$141$	3.16550	+	3.16550i	0.266583	+	0.266583i
$142$		0			0
$143$	−3.10801	+	3.10801i	−0.259905	+	0.259905i
$144$		0			0
$145$	−10.4384	−	8.36313i	−0.866864	−	0.694520i
$146$		0			0
$147$			4.68516i			0.386425i
$148$		0			0
$149$	11.1571	+	11.1571i	0.914023	+	0.914023i	0.996586	−	0.0825625i	$-0.0263104\pi$
$149$	11.1571	+	11.1571i	0.914023	+	0.914023i	−0.0825625	+	0.996586i	$0.526310\pi$
$150$		0			0
$151$	−3.18265			−0.259000			−0.129500	−	0.991579i	$-0.541337\pi$
$151$	−3.18265			−0.259000			−0.129500	+	0.991579i	$0.541337\pi$
$152$		0			0
$153$	−1.03865	+	1.03865i	−0.0839696	+	0.0839696i
$154$		0			0
$155$	19.4690	−	2.14896i	1.56378	−	0.172609i
$156$		0			0
$157$	7.05454			0.563014			0.281507	−	0.959559i	$-0.409166\pi$
$157$	7.05454			0.563014			0.281507	+	0.959559i	$0.409166\pi$
$158$		0			0
$159$	−4.20847			−0.333754
$160$		0			0
$161$	2.12367			0.167369
$162$		0			0
$163$	−16.0208			−1.25484			−0.627422	−	0.778680i	$-0.715890\pi$
$163$	−16.0208			−1.25484			−0.627422	+	0.778680i	$0.715890\pi$
$164$		0			0
$165$	−1.15554	+	1.44229i	−0.0899591	+	0.112282i
$166$		0			0
$167$	16.6023	−	16.6023i	1.28473	−	1.28473i	0.346780	−	0.937946i	$-0.387275\pi$
$167$	16.6023	−	16.6023i	1.28473	−	1.28473i	0.937946	−	0.346780i	$-0.112725\pi$
$168$		0			0
$169$	−0.571141			−0.0439339
$170$		0			0
$171$	−13.5514	−	13.5514i	−1.03630	−	1.03630i
$172$		0			0
$173$		−	14.9958i		−	1.14011i	−0.821607	−	0.570054i	$-0.806922\pi$
$173$		−	14.9958i		−	1.14011i	0.821607	−	0.570054i	$-0.193078\pi$
$174$		0			0
$175$	−1.30298	+	2.05296i	−0.0984957	+	0.155189i
$176$		0			0
$177$	5.08239	−	5.08239i	0.382016	−	0.382016i
$178$		0			0
$179$	9.91310	+	9.91310i	0.740940	+	0.740940i	0.972759	−	0.231819i	$-0.0744678\pi$
$179$	9.91310	+	9.91310i	0.740940	+	0.740940i	−0.231819	+	0.972759i	$0.574468\pi$
$180$		0			0
$181$	−1.04015	+	1.04015i	−0.0773139	+	0.0773139i	−0.744706	−	0.667392i	$-0.767410\pi$
$181$	−1.04015	+	1.04015i	−0.0773139	+	0.0773139i	0.667392	+	0.744706i	$0.267410\pi$
$182$		0			0
$183$	3.33593	+	3.33593i	0.246599	+	0.246599i
$184$		0			0
$185$	12.0408	−	1.32905i	0.885258	−	0.0977138i
$186$		0			0
$187$	0.695417			0.0508539
$188$		0			0
$189$	−1.31492	+	1.31492i	−0.0956466	+	0.0956466i
$190$		0			0
$191$			3.08419i			0.223164i	0.993755	+	0.111582i	$0.0355918\pi$
$191$			3.08419i			0.223164i	−0.993755	+	0.111582i	$0.964408\pi$
$192$		0			0
$193$	−12.0915	−	12.0915i	−0.870368	−	0.870368i	0.122144	−	0.992512i	$-0.461023\pi$
$193$	−12.0915	−	12.0915i	−0.870368	−	0.870368i	−0.992512	+	0.122144i	$0.961023\pi$
$194$		0			0
$195$	−5.67174	+	0.626040i	−0.406162	+	0.0448317i
$196$		0			0
$197$			13.0186i			0.927540i	0.885956	+	0.463770i	$0.153504\pi$
$197$			13.0186i			0.927540i	−0.885956	+	0.463770i	$0.846496\pi$
$198$		0			0
$199$		−	10.6279i		−	0.753395i	−0.926336	−	0.376697i	$-0.877060\pi$
$199$		−	10.6279i		−	0.753395i	0.926336	−	0.376697i	$-0.122940\pi$
$200$		0			0
$201$		−	9.94913i		−	0.701758i
$202$		0			0
$203$			2.90894i			0.204168i
$204$		0			0
$205$	−5.66260	+	0.625032i	−0.395493	+	0.0436541i
$206$		0			0
$207$	−7.78192	−	7.78192i	−0.540881	−	0.540881i
$208$		0			0
$209$			9.07320i			0.627607i
$210$		0			0
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	−0.191225	−	0.981546i	$-0.561246\pi$
$211$	11.4801	−	11.4801i	0.790321	−	0.790321i	0.981546	+	0.191225i	$0.0612460\pi$
$212$		0			0
$213$	2.06155			0.141255
$214$		0			0
$215$	−9.57332	+	1.05669i	−0.652895	+	0.0720659i
$216$		0			0
$217$	−3.01220	−	3.01220i	−0.204482	−	0.204482i
$218$		0			0
$219$	4.75998	−	4.75998i	0.321650	−	0.321650i
$220$		0			0
$221$	1.51827	+	1.51827i	0.102130	+	0.102130i
$222$		0			0
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	−0.630388	−	0.776280i	$-0.717104\pi$
$223$	2.17863	−	2.17863i	0.145892	−	0.145892i	0.776280	+	0.630388i	$0.217104\pi$
$224$		0			0
$225$	12.2974	−	2.74823i	0.819827	−	0.183215i
$226$		0			0
$227$		−	9.32318i		−	0.618801i	−0.950932	−	0.309401i	$-0.899872\pi$
$227$		−	9.32318i		−	0.618801i	0.950932	−	0.309401i	$-0.100128\pi$
$228$		0			0
$229$	−2.72259	−	2.72259i	−0.179914	−	0.179914i	0.611404	−	0.791318i	$-0.290605\pi$
$229$	−2.72259	−	2.72259i	−0.179914	−	0.179914i	−0.791318	+	0.611404i	$0.790605\pi$
$230$		0			0
$231$	0.401933			0.0264452
$232$		0			0
$233$	−12.3897	+	12.3897i	−0.811679	+	0.811679i	−0.984886	−	0.173206i	$-0.944587\pi$
$233$	−12.3897	+	12.3897i	−0.811679	+	0.811679i	0.173206	+	0.984886i	$0.444587\pi$
$234$		0			0
$235$	−9.03546	+	11.2776i	−0.589408	+	0.735669i
$236$		0			0
$237$	7.04168			0.457406
$238$		0			0
$239$	25.2180			1.63122			0.815609	−	0.578604i	$-0.196402\pi$
$239$	25.2180			1.63122			0.815609	+	0.578604i	$0.196402\pi$
$240$		0			0
$241$	12.0218			0.774391			0.387195	−	0.921998i	$-0.373444\pi$
$241$	12.0218			0.774391			0.387195	+	0.921998i	$0.373444\pi$
$242$		0			0
$243$	14.8740			0.954164
$244$		0			0
$245$	−15.0324	+	1.65926i	−0.960382	+	0.106006i
$246$		0			0
$247$	−19.8091	+	19.8091i	−1.26042	+	1.26042i
$248$		0			0
$249$	−4.95480			−0.313998
$250$		0			0
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	0.902790	−	0.430081i	$-0.141515\pi$
$251$	7.48911	+	7.48911i	0.472709	+	0.472709i	−0.430081	+	0.902790i	$0.641515\pi$
$252$		0			0
$253$			5.21032i			0.327570i
$254$		0			0
$255$	0.704565	+	0.564488i	0.0441215	+	0.0353496i
$256$		0			0
$257$	−10.0809	+	10.0809i	−0.628832	+	0.628832i	−0.947774	−	0.318942i	$-0.896672\pi$
$257$	−10.0809	+	10.0809i	−0.628832	+	0.628832i	0.318942	+	0.947774i	$0.396672\pi$
$258$		0			0
$259$	−1.86293	−	1.86293i	−0.115757	−	0.115757i
$260$		0			0
$261$	10.6595	−	10.6595i	0.659804	−	0.659804i
$262$		0			0
$263$	3.83599	+	3.83599i	0.236537	+	0.236537i	0.815415	−	0.578877i	$-0.196509\pi$
$263$	3.83599	+	3.83599i	0.236537	+	0.236537i	−0.578877	+	0.815415i	$0.696509\pi$
$264$		0			0
$265$	−1.49044	−	13.5029i	−0.0915568	−	0.829477i
$266$		0			0
$267$	−0.768585			−0.0470367
$268$		0			0
$269$	−13.4250	+	13.4250i	−0.818539	+	0.818539i	−0.985896	−	0.167357i	$-0.946477\pi$
$269$	−13.4250	+	13.4250i	−0.818539	+	0.818539i	0.167357	+	0.985896i	$0.446477\pi$
$270$		0			0
$271$			12.3519i			0.750326i	0.926959	+	0.375163i	$0.122413\pi$
$271$			12.3519i			0.750326i	−0.926959	+	0.375163i	$0.877587\pi$
$272$		0			0
$273$	0.877522	+	0.877522i	0.0531100	+	0.0531100i
$274$		0			0
$275$	−5.03684	−	3.19678i	−0.303733	−	0.192773i
$276$		0			0
$277$		−	6.78804i		−	0.407854i	−0.978986	−	0.203927i	$-0.934630\pi$
$277$		−	6.78804i		−	0.407854i	0.978986	−	0.203927i	$-0.0653705\pi$
$278$		0			0
$279$			22.0757i			1.32164i
$280$		0			0
$281$			21.5509i			1.28562i	0.766026	+	0.642810i	$0.222232\pi$
$281$			21.5509i			1.28562i	−0.766026	+	0.642810i	$0.777768\pi$
$282$		0			0
$283$		−	9.86809i		−	0.586597i	−0.956021	−	0.293299i	$-0.905247\pi$
$283$		−	9.86809i		−	0.586597i	0.956021	−	0.293299i	$-0.0947530\pi$
$284$		0			0
$285$	−7.36495	+	9.19255i	−0.436262	+	0.544520i
$286$		0			0
$287$	0.876108	+	0.876108i	0.0517150	+	0.0517150i
$288$		0			0
$289$			16.6603i			0.980017i
$290$		0			0
$291$	4.95926	−	4.95926i	0.290717	−	0.290717i
$292$		0			0
$293$	−14.1972			−0.829410			−0.414705	−	0.909956i	$-0.636115\pi$
$293$	−14.1972			−0.829410			−0.414705	+	0.909956i	$0.636115\pi$
$294$		0			0
$295$	18.1068	+	14.5069i	1.05422	+	0.844626i
$296$		0			0
$297$	−3.22610	−	3.22610i	−0.187197	−	0.187197i
$298$		0			0
$299$	−11.3755	+	11.3755i	−0.657859	+	0.657859i
$300$		0			0
$301$	1.48117	+	1.48117i	0.0853731	+	0.0853731i
$302$		0			0
$303$	−0.660428	+	0.660428i	−0.0379406	+	0.0379406i
$304$		0			0
$305$	−9.52194	+	11.8848i	−0.545224	+	0.680521i
$306$		0			0
$307$			20.4161i			1.16521i	0.812756	+	0.582604i	$0.197966\pi$
$307$			20.4161i			1.16521i	−0.812756	+	0.582604i	$0.802034\pi$
$308$		0			0
$309$	−6.64605	−	6.64605i	−0.378081	−	0.378081i
$310$		0			0
$311$	6.81074			0.386202			0.193101	−	0.981179i	$-0.438146\pi$
$311$	6.81074			0.386202			0.193101	+	0.981179i	$0.438146\pi$
$312$		0			0
$313$	1.20933	−	1.20933i	0.0683555	−	0.0683555i	−0.672103	−	0.740458i	$-0.734609\pi$
$313$	1.20933	−	1.20933i	0.0683555	−	0.0683555i	0.740458	+	0.672103i	$0.234609\pi$
$314$		0			0
$315$	−2.13870	−	1.71350i	−0.120502	−	0.0965447i
$316$		0			0
$317$	3.44178			0.193310			0.0966548	−	0.995318i	$-0.469186\pi$
$317$	3.44178			0.193310			0.0966548	+	0.995318i	$0.469186\pi$
$318$		0			0
$319$	−7.13694			−0.399592
$320$		0			0
$321$	−3.65891			−0.204221
$322$		0			0
$323$	4.43229			0.246619
$324$		0			0
$325$	−4.01731	−	17.9761i	−0.222840	−	0.997134i
$326$		0			0
$327$	1.06664	−	1.06664i	0.0589852	−	0.0589852i
$328$		0			0
$329$	3.14280			0.173268
$330$		0			0
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	0.665128	−	0.746730i	$-0.268377\pi$
$331$	−1.48462	−	1.48462i	−0.0816019	−	0.0816019i	−0.746730	+	0.665128i	$0.768377\pi$
$332$		0			0
$333$			13.6530i			0.748177i
$334$		0			0
$335$	31.9218	−	3.52350i	1.74408	−	0.192509i
$336$		0			0
$337$	6.21211	−	6.21211i	0.338395	−	0.338395i	−0.517368	−	0.855763i	$-0.673088\pi$
$337$	6.21211	−	6.21211i	0.338395	−	0.338395i	0.855763	+	0.517368i	$0.173088\pi$
$338$		0			0
$339$	−2.07575	−	2.07575i	−0.112739	−	0.112739i
$340$		0			0
$341$	7.39028	−	7.39028i	0.400206	−	0.400206i
$342$		0			0
$343$	4.73288	+	4.73288i	0.255552	+	0.255552i
$344$		0			0
$345$	−4.22935	+	5.27886i	−0.227701	+	0.284204i
$346$		0			0
$347$	10.1502			0.544889			0.272445	−	0.962171i	$-0.412168\pi$
$347$	10.1502			0.544889			0.272445	+	0.962171i	$0.412168\pi$
$348$		0			0
$349$	−3.99595	+	3.99595i	−0.213898	+	0.213898i	−0.805921	−	0.592023i	$-0.798329\pi$
$349$	−3.99595	+	3.99595i	−0.213898	+	0.213898i	0.592023	+	0.805921i	$0.298329\pi$
$350$		0			0
$351$		−	14.0868i		−	0.751897i
$352$		0			0
$353$	22.6637	+	22.6637i	1.20627	+	1.20627i	0.972226	+	0.234043i	$0.0751957\pi$
$353$	22.6637	+	22.6637i	1.20627	+	1.20627i	0.234043	+	0.972226i	$0.424804\pi$
$354$		0			0
$355$	0.730100	+	6.61449i	0.0387497	+	0.351061i
$356$		0			0
$357$		−	0.196346i		−	0.0103917i
$358$		0			0
$359$			4.31874i			0.227934i	0.993485	+	0.113967i	$0.0363559\pi$
$359$			4.31874i			0.227934i	−0.993485	+	0.113967i	$0.963644\pi$
$360$		0			0
$361$			38.8288i			2.04362i
$362$		0			0
$363$		−	6.63371i		−	0.348180i
$364$		0			0
$365$	16.9582	+	13.5867i	0.887632	+	0.711159i
$366$		0			0
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	0.517801	−	0.855501i	$-0.326751\pi$
$367$	−6.46940	−	6.46940i	−0.337700	−	0.337700i	−0.855501	+	0.517801i	$0.826751\pi$
$368$		0			0
$369$		−	6.42077i		−	0.334252i
$370$		0			0
$371$	−2.08915	+	2.08915i	−0.108463	+	0.108463i
$372$		0			0
$373$	16.7831			0.868995			0.434497	−	0.900673i	$-0.356926\pi$
$373$	16.7831			0.868995			0.434497	+	0.900673i	$0.356926\pi$
$374$		0			0
$375$	−2.50818	−	7.32736i	−0.129522	−	0.378383i
$376$		0			0
$377$	−15.5818	−	15.5818i	−0.802502	−	0.802502i
$378$		0			0
$379$	7.31046	−	7.31046i	0.375513	−	0.375513i	−0.493967	−	0.869480i	$-0.664454\pi$
$379$	7.31046	−	7.31046i	0.375513	−	0.375513i	0.869480	+	0.493967i	$0.164454\pi$
$380$		0			0
$381$	−7.30966	−	7.30966i	−0.374485	−	0.374485i
$382$		0			0
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	−0.829736	−	0.558156i	$-0.811509\pi$
$383$	−5.31492	+	5.31492i	−0.271580	+	0.271580i	0.558156	+	0.829736i	$0.311509\pi$
$384$		0			0
$385$	0.142345	+	1.28960i	0.00725457	+	0.0657242i
$386$		0			0
$387$		−	10.8551i		−	0.551796i
$388$		0			0
$389$	−1.28845	−	1.28845i	−0.0653271	−	0.0653271i	0.673688	−	0.739016i	$-0.264709\pi$
$389$	−1.28845	−	1.28845i	−0.0653271	−	0.0653271i	−0.739016	+	0.673688i	$0.764709\pi$
$390$		0			0
$391$	2.54526			0.128719
$392$		0			0
$393$	−0.589160	+	0.589160i	−0.0297192	+	0.0297192i
$394$		0			0
$395$	2.49382	+	22.5933i	0.125478	+	1.13679i
$396$		0			0
$397$	−9.53832			−0.478715			−0.239357	−	0.970932i	$-0.576937\pi$
$397$	−9.53832			−0.478715			−0.239357	+	0.970932i	$0.576937\pi$
$398$		0			0
$399$	2.56175			0.128248
$400$		0			0
$401$	−24.6103			−1.22898			−0.614491	−	0.788924i	$-0.710638\pi$
$401$	−24.6103			−1.22898			−0.614491	+	0.788924i	$0.710638\pi$
$402$		0			0
$403$	32.2697			1.60747
$404$		0			0
$405$	1.20494	+	10.9164i	0.0598739	+	0.542440i
$406$		0			0
$407$	4.57061	−	4.57061i	0.226557	−	0.226557i
$408$		0			0
$409$	16.9457			0.837911			0.418955	−	0.908007i	$-0.362396\pi$
$409$	16.9457			0.837911			0.418955	+	0.908007i	$0.362396\pi$
$410$		0			0
$411$	3.81092	+	3.81092i	0.187979	+	0.187979i
$412$		0			0
$413$		−	5.04594i		−	0.248294i
$414$		0			0
$415$	−1.75475	−	15.8975i	−0.0861373	−	0.780378i
$416$		0			0
$417$	−2.10250	+	2.10250i	−0.102960	+	0.102960i
$418$		0			0
$419$	6.56956	+	6.56956i	0.320944	+	0.320944i	0.849129	−	0.528185i	$-0.177127\pi$
$419$	6.56956	+	6.56956i	0.320944	+	0.320944i	−0.528185	+	0.849129i	$0.677127\pi$
$420$		0			0
$421$	−13.8805	+	13.8805i	−0.676493	+	0.676493i	−0.959205	−	0.282712i	$-0.908766\pi$
$421$	−13.8805	+	13.8805i	−0.676493	+	0.676493i	0.282712	+	0.959205i	$0.408766\pi$
$422$		0			0
$423$	−11.5164	−	11.5164i	−0.559946	−	0.559946i
$424$		0			0
$425$	−1.56164	+	2.46051i	−0.0757507	+	0.119352i
$426$		0			0
$427$	3.31201			0.160279
$428$		0			0
$429$	−2.15295	+	2.15295i	−0.103946	+	0.103946i
$430$		0			0
$431$			12.3740i			0.596035i	0.954560	+	0.298017i	$0.0963254\pi$
$431$			12.3740i			0.596035i	−0.954560	+	0.298017i	$0.903675\pi$
$432$		0			0
$433$	−0.145326	−	0.145326i	−0.00698392	−	0.00698392i	0.703606	−	0.710590i	$-0.251572\pi$
$433$	−0.145326	−	0.145326i	−0.00698392	−	0.00698392i	−0.710590	+	0.703606i	$0.751572\pi$
$434$		0			0
$435$	−7.23082	−	5.79324i	−0.346691	−	0.277765i
$436$		0			0
$437$			33.2084i			1.58857i
$438$		0			0
$439$		−	3.65842i		−	0.174607i	−0.996182	−	0.0873035i	$-0.972175\pi$
$439$		−	3.65842i		−	0.174607i	0.996182	−	0.0873035i	$-0.0278250\pi$
$440$		0			0
$441$		−	17.0450i		−	0.811669i
$442$		0			0
$443$			3.94027i			0.187208i	0.995610	+	0.0936039i	$0.0298387\pi$
$443$			3.94027i			0.187208i	−0.995610	+	0.0936039i	$0.970161\pi$
$444$		0			0
$445$	−0.272195	−	2.46601i	−0.0129033	−	0.116900i
$446$		0			0
$447$	7.72864	+	7.72864i	0.365552	+	0.365552i
$448$		0			0
$449$		−	38.0014i		−	1.79340i	−0.442642	−	0.896698i	$-0.645959\pi$
$449$		−	38.0014i		−	1.79340i	0.442642	−	0.896698i	$-0.354041\pi$
$450$		0			0
$451$	−2.14949	+	2.14949i	−0.101215	+	0.101215i
$452$		0			0
$453$	−2.20466			−0.103584
$454$		0			0
$455$	−2.50476	+	3.12631i	−0.117425	+	0.146564i
$456$		0			0
$457$	−18.1142	−	18.1142i	−0.847348	−	0.847348i	0.142454	−	0.989801i	$-0.454501\pi$
$457$	−18.1142	−	18.1142i	−0.847348	−	0.847348i	−0.989801	+	0.142454i	$0.954501\pi$
$458$		0			0
$459$	−1.57596	+	1.57596i	−0.0735595	+	0.0735595i
$460$		0			0
$461$	−12.4144	−	12.4144i	−0.578197	−	0.578197i	0.356209	−	0.934406i	$-0.384069\pi$
$461$	−12.4144	−	12.4144i	−0.578197	−	0.578197i	−0.934406	+	0.356209i	$0.884069\pi$
$462$		0			0
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	−0.877557	−	0.479472i	$-0.840828\pi$
$463$	−8.56578	+	8.56578i	−0.398085	+	0.398085i	0.479472	+	0.877557i	$0.340828\pi$
$464$		0			0
$465$	13.4864	−	1.48861i	0.625416	−	0.0690327i
$466$		0			0
$467$			34.3465i			1.58937i	0.607023	+	0.794684i	$0.292364\pi$
$467$			34.3465i			1.58937i	−0.607023	+	0.794684i	$0.707636\pi$
$468$		0			0
$469$	−4.93889	−	4.93889i	−0.228057	−	0.228057i
$470$		0			0
$471$	4.88677			0.225170
$472$		0			0
$473$	−3.63397	+	3.63397i	−0.167090	+	0.167090i
$474$		0			0
$475$	−32.1027	−	20.3749i	−1.47297	−	0.934866i
$476$		0			0
$477$	15.3108			0.701034
$478$		0			0
$479$	−23.4504			−1.07148			−0.535738	−	0.844384i	$-0.679966\pi$
$479$	−23.4504			−1.07148			−0.535738	+	0.844384i	$0.679966\pi$
$480$		0			0
$481$	19.9576			0.909988
$482$		0			0
$483$	1.47109			0.0669370
$484$		0			0
$485$	17.6681	+	14.1555i	0.802269	+	0.642767i
$486$		0			0
$487$	5.31215	−	5.31215i	0.240716	−	0.240716i	−0.576430	−	0.817146i	$-0.695555\pi$
$487$	5.31215	−	5.31215i	0.240716	−	0.240716i	0.817146	+	0.576430i	$0.195555\pi$
$488$		0			0
$489$	−11.0978			−0.501859
$490$		0			0
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	0.618171	−	0.786044i	$-0.287874\pi$
$491$	−3.71980	−	3.71980i	−0.167872	−	0.167872i	−0.786044	+	0.618171i	$0.787874\pi$
$492$		0			0
$493$			3.48642i			0.157021i
$494$		0			0
$495$	4.20398	−	5.24719i	0.188955	−	0.235844i
$496$		0			0
$497$	1.02338	−	1.02338i	0.0459050	−	0.0459050i
$498$		0			0
$499$	−13.6065	−	13.6065i	−0.609111	−	0.609111i	0.333603	−	0.942714i	$-0.391736\pi$
$499$	−13.6065	−	13.6065i	−0.609111	−	0.609111i	−0.942714	+	0.333603i	$0.891736\pi$
$500$		0			0
$501$	11.5006	−	11.5006i	0.513810	−	0.513810i
$502$		0			0
$503$	9.31208	+	9.31208i	0.415205	+	0.415205i	0.883547	−	0.468342i	$-0.155148\pi$
$503$	9.31208	+	9.31208i	0.415205	+	0.415205i	−0.468342	+	0.883547i	$0.655148\pi$
$504$		0			0
$505$	−2.35288	−	1.88509i	−0.104702	−	0.0838856i
$506$		0			0
$507$	−0.395636			−0.0175708
$508$		0			0
$509$	7.94836	−	7.94836i	0.352305	−	0.352305i	−0.508662	−	0.860966i	$-0.669860\pi$
$509$	7.94836	−	7.94836i	0.352305	−	0.352305i	0.860966	+	0.508662i	$0.169860\pi$
$510$		0			0
$511$		−	4.72585i		−	0.209059i
$512$		0			0
$513$	−20.5618	−	20.5618i	−0.907824	−	0.907824i
$514$		0			0
$515$	18.9702	−	23.6776i	0.835926	−	1.04336i
$516$		0			0
$517$			7.71069i			0.339116i
$518$		0			0
$519$		−	10.3878i		−	0.455972i
$520$		0			0
$521$		−	29.3979i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$521$		−	29.3979i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$522$		0			0
$523$		−	19.5121i		−	0.853205i	−0.904439	−	0.426602i	$-0.859710\pi$
$523$		−	19.5121i		−	0.853205i	0.904439	−	0.426602i	$-0.140290\pi$
$524$		0			0
$525$	−0.902587	+	1.42211i	−0.0393921	+	0.0620660i
$526$		0			0
$527$	−3.61018	−	3.61018i	−0.157262	−	0.157262i
$528$		0			0
$529$		−	3.92999i		−	0.170869i
$530$		0			0
$531$	−18.4902	+	18.4902i	−0.802406	+	0.802406i
$532$		0			0
$533$	−9.38575			−0.406542
$534$		0			0
$535$	−1.29581	−	11.7396i	−0.0560227	−	0.507549i
$536$		0			0
$537$	6.86692	+	6.86692i	0.296329	+	0.296329i
$538$		0			0
$539$	−5.70618	+	5.70618i	−0.245783	+	0.245783i
$540$		0			0
$541$	−8.47183	−	8.47183i	−0.364232	−	0.364232i	0.501136	−	0.865369i	$-0.332916\pi$
$541$	−8.47183	−	8.47183i	−0.364232	−	0.364232i	−0.865369	+	0.501136i	$0.832916\pi$
$542$		0			0
$543$	−0.720526	+	0.720526i	−0.0309207	+	0.0309207i
$544$		0			0
$545$	3.80006	+	3.04456i	0.162777	+	0.130415i
$546$		0			0
$547$		−	9.97988i		−	0.426709i	−0.976975	−	0.213355i	$-0.931561\pi$
$547$		−	9.97988i		−	0.426709i	0.976975	−	0.213355i	$-0.0684389\pi$
$548$		0			0
$549$	−12.1364	−	12.1364i	−0.517971	−	0.517971i
$550$		0			0
$551$	−45.4879			−1.93785
$552$		0			0
$553$	3.49559	−	3.49559i	0.148648	−	0.148648i
$554$		0			0
$555$	8.34081	−	0.920650i	0.354048	−	0.0390794i
$556$		0			0
$557$	−13.4866			−0.571445			−0.285722	−	0.958312i	$-0.592234\pi$
$557$	−13.4866			−0.571445			−0.285722	+	0.958312i	$0.592234\pi$
$558$		0			0
$559$	−15.8678			−0.671135
$560$		0			0
$561$	0.481724			0.0203384
$562$		0			0
$563$	−20.3451			−0.857445			−0.428723	−	0.903436i	$-0.641036\pi$
$563$	−20.3451			−0.857445			−0.428723	+	0.903436i	$0.641036\pi$
$564$		0			0
$565$	5.92493	−	7.39519i	0.249264	−	0.311118i
$566$		0			0
$567$	1.68896	−	1.68896i	0.0709298	−	0.0709298i
$568$		0			0
$569$	17.1460			0.718797			0.359399	−	0.933184i	$-0.382982\pi$
$569$	17.1460			0.718797			0.359399	+	0.933184i	$0.382982\pi$
$570$		0			0
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	0.825571	−	0.564298i	$-0.190853\pi$
$571$	6.24329	+	6.24329i	0.261274	+	0.261274i	−0.564298	+	0.825571i	$0.690853\pi$
$572$		0			0
$573$			2.13645i			0.0892516i
$574$		0			0
$575$	−18.4351	−	11.7004i	−0.768795	−	0.487939i
$576$		0			0
$577$	−10.0373	+	10.0373i	−0.417859	+	0.417859i	−0.884465	−	0.466606i	$-0.845477\pi$
$577$	−10.0373	+	10.0373i	−0.417859	+	0.417859i	0.466606	+	0.884465i	$0.345477\pi$
$578$		0			0
$579$	−8.37596	−	8.37596i	−0.348093	−	0.348093i
$580$		0			0
$581$	−2.45963	+	2.45963i	−0.102043	+	0.102043i
$582$		0			0
$583$	−5.12561	−	5.12561i	−0.212281	−	0.212281i
$584$		0			0
$585$	20.6343	−	2.27759i	0.853124	−	0.0941669i
$586$		0			0
$587$	30.6857			1.26654			0.633268	−	0.773933i	$-0.281713\pi$
$587$	30.6857			1.26654			0.633268	+	0.773933i	$0.281713\pi$
$588$		0			0
$589$	47.1025	−	47.1025i	1.94083	−	1.94083i
$590$		0			0
$591$			9.01817i			0.370958i
$592$		0			0
$593$	−2.10671	−	2.10671i	−0.0865123	−	0.0865123i	0.662526	−	0.749039i	$-0.269484\pi$
$593$	−2.10671	−	2.10671i	−0.0865123	−	0.0865123i	−0.749039	+	0.662526i	$0.769484\pi$
$594$		0			0
$595$	0.629976	−	0.0695360i	0.0258265	−	0.00285070i
$596$		0			0
$597$		−	7.36210i		−	0.301311i
$598$		0			0
$599$		−	32.1322i		−	1.31289i	−0.754375	−	0.656444i	$-0.772060\pi$
$599$		−	32.1322i		−	1.31289i	0.754375	−	0.656444i	$-0.227940\pi$
$600$		0			0
$601$			14.9811i			0.611091i	0.952177	+	0.305546i	$0.0988388\pi$
$601$			14.9811i			0.611091i	−0.952177	+	0.305546i	$0.901161\pi$
$602$		0			0
$603$			36.1959i			1.47401i
$604$		0			0
$605$	21.2843	−	2.34934i	0.865330	−	0.0955141i
$606$		0			0
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.993213	+	0.116310i	$0.0371067\pi$
$607$	27.3357	+	27.3357i	1.10952	+	1.10952i	0.116310	+	0.993213i	$0.462893\pi$
$608$		0			0
$609$			2.01506i			0.0816544i
$610$		0			0
$611$	−16.8344	+	16.8344i	−0.681047	+	0.681047i
$612$		0			0
$613$	48.3829			1.95417			0.977083	−	0.212859i	$-0.0682775\pi$
$613$	48.3829			1.95417			0.977083	+	0.212859i	$0.0682775\pi$
$614$		0			0
$615$	−3.92255	+	0.432967i	−0.158173	+	0.0174589i
$616$		0			0
$617$	31.1565	+	31.1565i	1.25432	+	1.25432i	0.953766	+	0.300549i	$0.0971699\pi$
$617$	31.1565	+	31.1565i	1.25432	+	1.25432i	0.300549	+	0.953766i	$0.402830\pi$
$618$		0			0
$619$	−0.198272	+	0.198272i	−0.00796922	+	0.00796922i	−0.711080	−	0.703111i	$-0.751794\pi$
$619$	−0.198272	+	0.198272i	−0.00796922	+	0.00796922i	0.703111	+	0.711080i	$0.251794\pi$
$620$		0			0
$621$	−11.8077	−	11.8077i	−0.473825	−	0.473825i
$622$		0			0
$623$	−0.381537	+	0.381537i	−0.0152859	+	0.0152859i
$624$		0			0
$625$	22.6216	−	10.6425i	0.904864	−	0.425700i
$626$		0			0
$627$			6.28512i			0.251003i
$628$		0			0
$629$	−2.23276	−	2.23276i	−0.0890259	−	0.0890259i
$630$		0			0
$631$	32.3314			1.28709			0.643547	−	0.765407i	$-0.277462\pi$
$631$	32.3314			1.28709			0.643547	+	0.765407i	$0.277462\pi$
$632$		0			0
$633$	7.95239	−	7.95239i	0.316079	−	0.316079i
$634$		0			0
$635$	20.8644	−	26.0418i	0.827977	−	1.03344i
$636$		0			0
$637$	−24.9161			−0.987212
$638$		0			0
$639$	−7.50010			−0.296700
$640$		0			0
$641$	−46.5662			−1.83926			−0.919628	−	0.392790i	$-0.871510\pi$
$641$	−46.5662			−1.83926			−0.919628	+	0.392790i	$0.871510\pi$
$642$		0			0
$643$	−40.2247			−1.58631			−0.793154	−	0.609021i	$-0.791563\pi$
$643$	−40.2247			−1.58631			−0.793154	+	0.609021i	$0.791563\pi$
$644$		0			0
$645$	−6.63156	+	0.731984i	−0.261117	+	0.0288218i
$646$		0			0
$647$	10.7938	−	10.7938i	0.424349	−	0.424349i	−0.462349	−	0.886698i	$-0.652993\pi$
$647$	10.7938	−	10.7938i	0.424349	−	0.424349i	0.886698	+	0.462349i	$0.152993\pi$
$648$		0			0
$649$	12.3799			0.485956
$650$		0			0
$651$	−2.08659	−	2.08659i	−0.0817799	−	0.0817799i
$652$		0			0
$653$			3.92443i			0.153575i	0.997047	+	0.0767875i	$0.0244663\pi$
$653$			3.92443i			0.153575i	−0.997047	+	0.0767875i	$0.975534\pi$
$654$		0			0
$655$	−2.09898	−	1.68167i	−0.0820138	−	0.0657084i
$656$		0			0
$657$	−17.3173	+	17.3173i	−0.675610	+	0.675610i
$658$		0			0
$659$	−34.6142	−	34.6142i	−1.34838	−	1.34838i	−0.887425	−	0.460952i	$-0.847508\pi$
$659$	−34.6142	−	34.6142i	−1.34838	−	1.34838i	−0.460952	−	0.887425i	$-0.652492\pi$
$660$		0			0
$661$	−21.7641	+	21.7641i	−0.846525	+	0.846525i	−0.989698	−	0.143173i	$-0.954270\pi$
$661$	−21.7641	+	21.7641i	−0.846525	+	0.846525i	0.143173	+	0.989698i	$0.454270\pi$
$662$		0			0
$663$	1.05173	+	1.05173i	0.0408456	+	0.0408456i
$664$		0			0
$665$	0.907246	+	8.21938i	0.0351815	+	0.318734i
$666$		0			0
$667$	−26.1216			−1.01143
$668$		0			0
$669$	1.50917	−	1.50917i	0.0583477	−	0.0583477i
$670$		0			0
$671$			8.12584i			0.313695i
$672$		0			0
$673$	29.4450	+	29.4450i	1.13502	+	1.13502i	0.989330	+	0.145691i	$0.0465405\pi$
$673$	29.4450	+	29.4450i	1.13502	+	1.13502i	0.145691	+	0.989330i	$0.453459\pi$
$674$		0			0
$675$	18.6591	−	4.16995i	0.718189	−	0.160501i
$676$		0			0
$677$		−	34.7351i		−	1.33498i	−0.744619	−	0.667490i	$-0.767369\pi$
$677$		−	34.7351i		−	1.33498i	0.744619	−	0.667490i	$-0.232631\pi$
$678$		0			0
$679$		−	4.92370i		−	0.188954i
$680$		0			0
$681$		−	6.45828i		−	0.247482i
$682$		0			0
$683$		−	22.2693i		−	0.852110i	−0.904697	−	0.426055i	$-0.859903\pi$
$683$		−	22.2693i		−	0.852110i	0.904697	−	0.426055i	$-0.140097\pi$
$684$		0			0
$685$	−10.8777	+	13.5770i	−0.415616	+	0.518750i
$686$		0			0
$687$	−1.88597	−	1.88597i	−0.0719543	−	0.0719543i
$688$		0			0
$689$		−	22.3810i		−	0.852650i
$690$		0			0
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	−0.342205	−	0.939625i	$-0.611174\pi$
$691$	15.7043	−	15.7043i	0.597420	−	0.597420i	0.939625	+	0.342205i	$0.111174\pi$
$692$		0			0
$693$	−1.46227			−0.0555470
$694$		0			0
$695$	−7.49048	−	6.00128i	−0.284130	−	0.227641i
$696$		0			0
$697$	1.05003	+	1.05003i	0.0397728	+	0.0397728i
$698$		0			0
$699$	−8.58253	+	8.58253i	−0.324621	+	0.324621i
$700$		0			0
$701$	21.5588	+	21.5588i	0.814266	+	0.814266i	0.985270	−	0.171004i	$-0.0547011\pi$
$701$	21.5588	+	21.5588i	0.814266	+	0.814266i	−0.171004	+	0.985270i	$0.554701\pi$
$702$		0			0
$703$	29.1311	−	29.1311i	1.09870	−	1.09870i
$704$		0			0
$705$	−6.25897	+	7.81212i	−0.235726	+	0.294221i
$706$		0			0
$707$			0.655691i			0.0246598i
$708$		0			0
$709$	−2.96687	−	2.96687i	−0.111423	−	0.111423i	0.649197	−	0.760620i	$-0.275105\pi$
$709$	−2.96687	−	2.96687i	−0.111423	−	0.111423i	−0.760620	+	0.649197i	$0.775105\pi$
$710$		0			0
$711$	−25.6183			−0.960760
$712$		0			0
$713$	27.0488	−	27.0488i	1.01299	−	1.01299i
$714$		0			0
$715$	−7.67023	−	6.14529i	−0.286850	−	0.229821i
$716$		0			0
$717$	17.4688			0.652385
$718$		0			0
$719$	−25.8357			−0.963509			−0.481755	−	0.876306i	$-0.660000\pi$
$719$	−25.8357			−0.963509			−0.481755	+	0.876306i	$0.660000\pi$
$720$		0			0
$721$	−6.59839			−0.245737
$722$		0			0
$723$	8.32763			0.309708
$724$		0			0
$725$	16.0268	−	25.2518i	0.595222	−	0.937829i
$726$		0			0
$727$	−28.9620	+	28.9620i	−1.07414	+	1.07414i	−0.0771198	+	0.997022i	$0.524572\pi$
$727$	−28.9620	+	28.9620i	−1.07414	+	1.07414i	−0.997022	+	0.0771198i	$0.975428\pi$
$728$		0			0
$729$	−4.43146			−0.164128
$730$		0			0
$731$	1.77521	+	1.77521i	0.0656584	+	0.0656584i
$732$		0			0
$733$		−	21.1673i		−	0.781832i	−0.920426	−	0.390916i	$-0.872158\pi$
$733$		−	21.1673i		−	0.781832i	0.920426	−	0.390916i	$-0.127842\pi$
$734$		0			0
$735$	−10.4131	+	1.14939i	−0.384093	+	0.0423957i
$736$		0			0
$737$	12.1173	−	12.1173i	0.446347	−	0.446347i
$738$		0			0
$739$	−2.23302	−	2.23302i	−0.0821431	−	0.0821431i	0.664841	−	0.746985i	$-0.268499\pi$
$739$	−2.23302	−	2.23302i	−0.0821431	−	0.0821431i	−0.746985	+	0.664841i	$0.768499\pi$
$740$		0			0
$741$	−13.7220	+	13.7220i	−0.504091	+	0.504091i
$742$		0			0
$743$	18.4514	+	18.4514i	0.676915	+	0.676915i	0.959301	−	0.282386i	$-0.0911258\pi$
$743$	18.4514	+	18.4514i	0.676915	+	0.676915i	−0.282386	+	0.959301i	$0.591126\pi$
$744$		0			0
$745$	−22.0603	+	27.5345i	−0.808226	+	1.00879i
$746$		0			0
$747$	18.0260			0.659538
$748$		0			0
$749$	−1.81634	+	1.81634i	−0.0663675	+	0.0663675i
$750$		0			0
$751$			42.4243i			1.54808i	0.633134	+	0.774042i	$0.281768\pi$
$751$			42.4243i			1.54808i	−0.633134	+	0.774042i	$0.718232\pi$
$752$		0			0
$753$	5.18780	+	5.18780i	0.189054	+	0.189054i
$754$		0			0
$755$	−0.780782	−	7.07365i	−0.0284156	−	0.257437i
$756$		0			0
$757$		−	19.7595i		−	0.718170i	−0.933305	−	0.359085i	$-0.883089\pi$
$757$		−	19.7595i		−	0.718170i	0.933305	−	0.359085i	$-0.116911\pi$
$758$		0			0
$759$			3.60925i			0.131007i
$760$		0			0
$761$		−	48.0351i		−	1.74127i	−0.491928	−	0.870636i	$-0.663708\pi$
$761$		−	48.0351i		−	1.74127i	0.491928	−	0.870636i	$-0.336292\pi$
$762$		0			0
$763$		−	1.05899i		−	0.0383379i
$764$		0			0
$765$	−2.56327	−	2.05366i	−0.0926753	−	0.0742502i
$766$		0			0
$767$	27.0286	+	27.0286i	0.975946	+	0.975946i
$768$		0			0
$769$		−	24.0184i		−	0.866127i	−0.901363	−	0.433064i	$-0.857433\pi$
$769$		−	24.0184i		−	0.866127i	0.901363	−	0.433064i	$-0.142567\pi$
$770$		0			0
$771$	−6.98319	+	6.98319i	−0.251493	+	0.251493i
$772$		0			0
$773$	−22.4630			−0.807937			−0.403969	−	0.914773i	$-0.632370\pi$
$773$	−22.4630			−0.807937			−0.403969	+	0.914773i	$0.632370\pi$
$774$		0			0
$775$	9.55244	+	42.7439i	0.343134	+	1.53541i
$776$		0			0
$777$	−1.29048	−	1.29048i	−0.0462956	−	0.0462956i
$778$		0			0
$779$	−13.6999	+	13.6999i	−0.490850	+	0.490850i
$780$		0			0
$781$	2.51081	+	2.51081i	0.0898440	+	0.0898440i
$782$		0			0
$783$	16.1738	−	16.1738i	0.578005	−	0.578005i
$784$		0			0
$785$	1.73065	+	15.6792i	0.0617697	+	0.559615i
$786$		0			0
$787$		−	26.1054i		−	0.930556i	−0.885165	−	0.465278i	$-0.845954\pi$
$787$		−	26.1054i		−	0.930556i	0.885165	−	0.465278i	$-0.154046\pi$
$788$		0			0
$789$	2.65724	+	2.65724i	0.0946001	+	0.0946001i
$790$		0			0
$791$	−2.06087			−0.0732759
$792$		0			0
$793$	−17.7408	+	17.7408i	−0.629994	+	0.629994i
$794$		0			0
$795$	−1.03244	−	9.35363i	−0.0366170	−	0.331739i
$796$		0			0
$797$	−43.4888			−1.54045			−0.770227	−	0.637770i	$-0.779857\pi$
$797$	−43.4888			−1.54045			−0.770227	+	0.637770i	$0.779857\pi$
$798$		0			0
$799$	3.76670			0.133256
$800$		0			0
$801$	2.79618			0.0987983
$802$		0			0
$803$	11.5946			0.409165
$804$		0			0
$805$	0.520989	+	4.72001i	0.0183625	+	0.166358i
$806$		0			0
$807$	−9.29969	+	9.29969i	−0.327364	+	0.327364i
$808$		0			0
$809$	−36.6271			−1.28774			−0.643870	−	0.765135i	$-0.722672\pi$
$809$	−36.6271			−1.28774			−0.643870	+	0.765135i	$0.722672\pi$
$810$		0			0
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	0.955338	−	0.295516i	$-0.0954917\pi$
$811$	18.7904	+	18.7904i	0.659821	+	0.659821i	−0.295516	+	0.955338i	$0.595492\pi$
$812$		0			0
$813$			8.55633i			0.300084i
$814$		0			0
$815$	−3.93029	−	35.6073i	−0.137672	−	1.24727i
$816$		0			0
$817$	−23.1614	+	23.1614i	−0.810314	+	0.810314i
$818$		0			0
$819$	−3.19250	−	3.19250i	−0.111555	−	0.111555i
$820$		0			0
$821$	−3.91048	+	3.91048i	−0.136477	+	0.136477i	−0.772045	−	0.635568i	$-0.780766\pi$
$821$	−3.91048	+	3.91048i	−0.136477	+	0.136477i	0.635568	+	0.772045i	$0.280766\pi$
$822$		0			0
$823$	−35.4412	−	35.4412i	−1.23540	−	1.23540i	−0.961860	−	0.273542i	$-0.911805\pi$
$823$	−35.4412	−	35.4412i	−1.23540	−	1.23540i	−0.273542	−	0.961860i	$-0.588195\pi$
$824$		0			0
$825$	−3.48908	−	2.21445i	−0.121474	−	0.0770972i
$826$		0			0
$827$	−44.0700			−1.53246			−0.766232	−	0.642565i	$-0.777870\pi$
$827$	−44.0700			−1.53246			−0.766232	+	0.642565i	$0.777870\pi$
$828$		0			0
$829$	15.1609	−	15.1609i	0.526561	−	0.526561i	−0.392984	−	0.919545i	$-0.628557\pi$
$829$	15.1609	−	15.1609i	0.526561	−	0.526561i	0.919545	+	0.392984i	$0.128557\pi$
$830$		0			0
$831$		−	4.70216i		−	0.163116i
$832$		0			0
$833$	2.78749	+	2.78749i	0.0965808	+	0.0965808i
$834$		0			0
$835$	40.9728	+	32.8269i	1.41792	+	1.13602i
$836$		0			0
$837$			33.4958i			1.15779i
$838$		0			0
$839$			40.3143i			1.39180i	0.718137	+	0.695901i	$0.244995\pi$
$839$			40.3143i			1.39180i	−0.718137	+	0.695901i	$0.755005\pi$
$840$		0			0
$841$		−	6.78056i		−	0.233812i
$842$		0			0
$843$			14.9286i			0.514168i
$844$		0			0
$845$	−0.140115	−	1.26940i	−0.00482011	−	0.0436687i
$846$		0			0
$847$	−3.29307	−	3.29307i	−0.113151	−	0.113151i
$848$		0			0
$849$		−	6.83575i		−	0.234602i
$850$		0			0
$851$	16.7286	−	16.7286i	0.573450	−	0.573450i
$852$		0			0
$853$	−28.6203			−0.979941			−0.489971	−	0.871739i	$-0.662992\pi$
$853$	−28.6203			−0.979941			−0.489971	+	0.871739i	$0.662992\pi$
$854$		0			0
$855$	26.7944	−	33.4434i	0.916349	−	1.14374i
$856$		0			0
$857$	7.19794	+	7.19794i	0.245877	+	0.245877i	0.819276	−	0.573399i	$-0.194376\pi$
$857$	7.19794	+	7.19794i	0.245877	+	0.245877i	−0.573399	+	0.819276i	$0.694376\pi$
$858$		0			0
$859$	18.8135	−	18.8135i	0.641910	−	0.641910i	−0.309115	−	0.951025i	$-0.600033\pi$
$859$	18.8135	−	18.8135i	0.641910	−	0.641910i	0.951025	+	0.309115i	$0.100033\pi$
$860$		0			0
$861$	0.606890	+	0.606890i	0.0206828	+	0.0206828i
$862$		0			0
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	−0.299428	−	0.954119i	$-0.596796\pi$
$863$	19.2328	−	19.2328i	0.654691	−	0.654691i	0.954119	+	0.299428i	$0.0967958\pi$
$864$		0			0
$865$	33.3292	−	3.67883i	1.13323	−	0.125084i
$866$		0			0
$867$			11.5408i			0.391945i
$868$		0			0
$869$	8.57624	+	8.57624i	0.290929	+	0.290929i
$870$		0			0
$871$	52.9103			1.79280
$872$		0			0
$873$	−18.0423	+	18.0423i	−0.610638	+	0.610638i
$874$		0			0
$875$	−4.88250	−	2.39231i	−0.165059	−	0.0808749i
$876$		0			0
$877$	−35.4397			−1.19671			−0.598357	−	0.801229i	$-0.704180\pi$
$877$	−35.4397			−1.19671			−0.598357	+	0.801229i	$0.704180\pi$
$878$		0			0
$879$	−9.83458			−0.331712
$880$		0			0
$881$	30.2010			1.01750			0.508748	−	0.860915i	$-0.330108\pi$
$881$	30.2010			1.01750			0.508748	+	0.860915i	$0.330108\pi$
$882$		0			0
$883$	28.9931			0.975696			0.487848	−	0.872928i	$-0.337782\pi$
$883$	28.9931			0.975696			0.487848	+	0.872928i	$0.337782\pi$
$884$		0			0
$885$	12.5428	+	10.0491i	0.421622	+	0.337798i
$886$		0			0
$887$	−5.33418	+	5.33418i	−0.179104	+	0.179104i	−0.790965	−	0.611861i	$-0.790421\pi$
$887$	−5.33418	+	5.33418i	−0.179104	+	0.179104i	0.611861	+	0.790965i	$0.290421\pi$
$888$		0			0
$889$	−7.25724			−0.243400
$890$		0			0
$891$	4.14379	+	4.14379i	0.138822	+	0.138822i
$892$		0			0
$893$			49.1447i			1.64456i
$894$		0			0
$895$	−19.6006	+	24.4645i	−0.655176	+	0.817757i
$896$		0			0
$897$	−7.87991	+	7.87991i	−0.263103	+	0.263103i
$898$		0			0
$899$	37.0507	+	37.0507i	1.23571	+	1.23571i
$900$		0			0
$901$	−2.50388	+	2.50388i	−0.0834163	+	0.0834163i
$902$		0			0
$903$	1.02602	+	1.02602i	0.0341439	+	0.0341439i
$904$		0			0
$905$	−2.56699	−	2.05664i	−0.0853295	−	0.0683649i
$906$		0			0
$907$	26.2683			0.872226			0.436113	−	0.899892i	$-0.356355\pi$
$907$	26.2683			0.872226			0.436113	+	0.899892i	$0.356355\pi$
$908$		0			0
$909$	2.40270	−	2.40270i	0.0796924	−	0.0796924i
$910$		0			0
$911$		−	33.5196i		−	1.11055i	−0.831665	−	0.555277i	$-0.812612\pi$
$911$		−	33.5196i		−	1.11055i	0.831665	−	0.555277i	$-0.187388\pi$
$912$		0			0
$913$	−6.03459	−	6.03459i	−0.199716	−	0.199716i
$914$		0			0
$915$	−6.59596	+	8.23273i	−0.218056	+	0.272166i
$916$		0			0
$917$			0.584935i			0.0193163i
$918$		0			0
$919$		−	25.7545i		−	0.849564i	−0.905296	−	0.424782i	$-0.860351\pi$
$919$		−	25.7545i		−	0.849564i	0.905296	−	0.424782i	$-0.139649\pi$
$920$		0			0
$921$			14.1425i			0.466011i
$922$		0			0
$923$			10.9635i			0.360868i
$924$		0			0
$925$	5.90782	+	26.4355i	0.194248	+	0.869193i
$926$		0			0
$927$	24.1790	+	24.1790i	0.794141	+	0.794141i
$928$		0			0
$929$		−	9.06425i		−	0.297388i	−0.988883	−	0.148694i	$-0.952493\pi$
$929$		−	9.06425i		−	0.297388i	0.988883	−	0.148694i	$-0.0475070\pi$
$930$		0			0
$931$	−36.3688	+	36.3688i	−1.19194	+	1.19194i
$932$		0			0
$933$	4.71788			0.154456
$934$		0			0
$935$	0.170603	+	1.54561i	0.00557931	+	0.0505469i
$936$		0			0
$937$	3.38621	+	3.38621i	0.110623	+	0.110623i	0.760251	−	0.649629i	$-0.225076\pi$
$937$	3.38621	+	3.38621i	0.110623	+	0.110623i	−0.649629	+	0.760251i	$0.725076\pi$
$938$		0			0
$939$	0.837719	−	0.837719i	0.0273379	−	0.0273379i
$940$		0			0
$941$	16.9347	+	16.9347i	0.552054	+	0.552054i	0.927033	−	0.374979i	$-0.122350\pi$
$941$	16.9347	+	16.9347i	0.552054	+	0.552054i	−0.374979	+	0.927033i	$0.622350\pi$
$942$		0			0
$943$	−7.86722	+	7.86722i	−0.256192	+	0.256192i
$944$		0			0
$945$	−3.24509	−	2.59993i	−0.105563	−	0.0845756i
$946$		0			0
$947$			1.08633i			0.0353011i	0.999844	+	0.0176505i	$0.00561863\pi$
$947$			1.08633i			0.0353011i	−0.999844	+	0.0176505i	$0.994381\pi$
$948$		0			0
$949$	25.3140	+	25.3140i	0.821727	+	0.821727i
$950$		0			0
$951$	2.38416			0.0773117
$952$		0			0
$953$	−10.7914	+	10.7914i	−0.349567	+	0.349567i	−0.859948	−	0.510381i	$-0.829504\pi$
$953$	−10.7914	+	10.7914i	−0.349567	+	0.349567i	0.510381	+	0.859948i	$0.329504\pi$
$954$		0			0
$955$	−6.85482	+	0.756627i	−0.221817	+	0.0244839i
$956$		0			0
$957$	−4.94385			−0.159812
$958$		0			0
$959$	3.78359			0.122178
$960$		0			0
$961$	−45.7317			−1.47522
$962$		0			0
$963$	13.3115			0.428956
$964$		0			0
$965$	23.9079	−	29.8407i	0.769624	−	0.960605i
$966$		0			0
$967$	31.4724	−	31.4724i	1.01208	−	1.01208i	0.0121587	−	0.999926i	$-0.496130\pi$
$967$	31.4724	−	31.4724i	1.01208	−	1.01208i	0.999926	−	0.0121587i	$-0.00387033\pi$
$968$		0			0
$969$	3.07030			0.0986323
$970$		0			0
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	0.230909	−	0.972975i	$-0.425830\pi$
$971$	−23.1234	−	23.1234i	−0.742066	−	0.742066i	−0.972975	+	0.230909i	$0.925830\pi$
$972$		0			0
$973$			2.08742i			0.0669196i
$974$		0			0
$975$	−2.78284	−	12.4523i	−0.0891221	−	0.398791i
$976$		0			0
$977$	15.3820	−	15.3820i	0.492114	−	0.492114i	−0.416858	−	0.908972i	$-0.636869\pi$
$977$	15.3820	−	15.3820i	0.492114	−	0.492114i	0.908972	+	0.416858i	$0.136869\pi$
$978$		0			0
$979$	−0.936080	−	0.936080i	−0.0299173	−	0.0299173i
$980$		0			0
$981$	−3.88052	+	3.88052i	−0.123896	+	0.123896i
$982$		0			0
$983$	38.5198	+	38.5198i	1.22859	+	1.22859i	0.964497	+	0.264093i	$0.0850726\pi$
$983$	38.5198	+	38.5198i	1.22859	+	1.22859i	0.264093	+	0.964497i	$0.414927\pi$
$984$		0			0
$985$	−28.9348	+	3.19380i	−0.921941	+	0.101763i
$986$		0			0
$987$	2.17705			0.0692964
$988$		0			0
$989$	−13.3005	+	13.3005i	−0.422931	+	0.422931i
$990$		0			0
$991$		−	22.0556i		−	0.700619i	−0.936634	−	0.350310i	$-0.886076\pi$
$991$		−	22.0556i		−	0.700619i	0.936634	−	0.350310i	$-0.113924\pi$
$992$		0			0
$993$	−1.02841	−	1.02841i	−0.0326356	−	0.0326356i
$994$		0			0
$995$	23.6213	−	2.60730i	0.748847	−	0.0826569i
$996$		0			0
$997$			0.840040i			0.0266043i	0.999912	+	0.0133022i	$0.00423434\pi$
$997$			0.840040i			0.0266043i	−0.999912	+	0.0133022i	$0.995766\pi$
$998$		0			0
$999$			20.7159i			0.655422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.s.c.223.6		18
4.3	odd	2		640.2.s.d.223.4		18
5.2	odd	4		640.2.j.c.607.4		18
8.3	odd	2		80.2.s.b.3.7	yes	18
8.5	even	2		320.2.s.b.303.4		18
16.3	odd	4		320.2.j.b.143.4		18
16.5	even	4		640.2.j.d.543.4		18
16.11	odd	4		640.2.j.c.543.6		18
16.13	even	4		80.2.j.b.43.3	✓	18
20.7	even	4		640.2.j.d.607.6		18
24.11	even	2		720.2.z.g.163.3		18
40.3	even	4		400.2.j.d.307.7		18
40.13	odd	4		1600.2.j.d.1007.4		18
40.19	odd	2		400.2.s.d.243.3		18
40.27	even	4		80.2.j.b.67.3	yes	18
40.29	even	2		1600.2.s.d.943.6		18
40.37	odd	4		320.2.j.b.47.6		18
48.29	odd	4		720.2.bd.g.523.7		18
80.3	even	4		1600.2.s.d.207.6		18
80.13	odd	4		400.2.s.d.107.3		18
80.19	odd	4		1600.2.j.d.143.6		18
80.27	even	4	inner	640.2.s.c.287.6		18
80.29	even	4		400.2.j.d.43.7		18
80.37	odd	4		640.2.s.d.287.4		18
80.67	even	4		320.2.s.b.207.4		18
80.77	odd	4		80.2.s.b.27.7	yes	18
120.107	odd	4		720.2.bd.g.307.7		18
240.77	even	4		720.2.z.g.667.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.3	✓	18	16.13	even	4
80.2.j.b.67.3	yes	18	40.27	even	4
80.2.s.b.3.7	yes	18	8.3	odd	2
80.2.s.b.27.7	yes	18	80.77	odd	4
320.2.j.b.47.6		18	40.37	odd	4
320.2.j.b.143.4		18	16.3	odd	4
320.2.s.b.207.4		18	80.67	even	4
320.2.s.b.303.4		18	8.5	even	2
400.2.j.d.43.7		18	80.29	even	4
400.2.j.d.307.7		18	40.3	even	4
400.2.s.d.107.3		18	80.13	odd	4
400.2.s.d.243.3		18	40.19	odd	2
640.2.j.c.543.6		18	16.11	odd	4
640.2.j.c.607.4		18	5.2	odd	4
640.2.j.d.543.4		18	16.5	even	4
640.2.j.d.607.6		18	20.7	even	4
640.2.s.c.223.6		18	1.1	even	1	trivial
640.2.s.c.287.6		18	80.27	even	4	inner
640.2.s.d.223.4		18	4.3	odd	2
640.2.s.d.287.4		18	80.37	odd	4
720.2.z.g.163.3		18	24.11	even	2
720.2.z.g.667.3		18	240.77	even	4
720.2.bd.g.307.7		18	120.107	odd	4
720.2.bd.g.523.7		18	48.29	odd	4
1600.2.j.d.143.6		18	80.19	odd	4
1600.2.j.d.1007.4		18	40.13	odd	4
1600.2.s.d.207.6		18	80.3	even	4
1600.2.s.d.943.6		18	40.29	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.692712 q^{3} +(0.245325 + 2.22257i) q^{5} +(0.343872 - 0.343872i) q^{7} -2.52015 q^{9} +O(q^{10})\)	\(q+0.692712 q^{3} +(0.245325 + 2.22257i) q^{5} +(0.343872 - 0.343872i) q^{7} -2.52015 q^{9} +(0.843672 + 0.843672i) q^{11} +3.68390i q^{13} +(0.169939 + 1.53960i) q^{15} +(0.412137 - 0.412137i) q^{17} +(5.37721 + 5.37721i) q^{19} +(0.238204 - 0.238204i) q^{21} +(3.08788 + 3.08788i) q^{23} +(-4.87963 + 1.09050i) q^{25} -3.82387 q^{27} +(-4.22969 + 4.22969i) q^{29} -8.75966i q^{31} +(0.584422 + 0.584422i) q^{33} +(0.848640 + 0.679919i) q^{35} -5.41752i q^{37} +2.55188i q^{39} +2.54777i q^{41} +4.30732i q^{43} +(-0.618255 - 5.60121i) q^{45} +(4.56972 + 4.56972i) q^{47} +6.76350i q^{49} +(0.285492 - 0.285492i) q^{51} -6.07536 q^{53} +(-1.66815 + 2.08209i) q^{55} +(3.72486 + 3.72486i) q^{57} +(7.33694 - 7.33694i) q^{59} +(4.81576 + 4.81576i) q^{61} +(-0.866609 + 0.866609i) q^{63} +(-8.18773 + 0.903753i) q^{65} -14.3626i q^{67} +(2.13901 + 2.13901i) q^{69} +2.97605 q^{71} +(6.87152 - 6.87152i) q^{73} +(-3.38018 + 0.755404i) q^{75} +0.580231 q^{77} +10.1654 q^{79} +4.91161 q^{81} -7.15276 q^{83} +(1.01711 + 0.814896i) q^{85} +(-2.92996 + 2.92996i) q^{87} -1.10953 q^{89} +(1.26679 + 1.26679i) q^{91} -6.06792i q^{93} +(-10.6321 + 13.2704i) q^{95} +(7.15920 - 7.15920i) q^{97} +(-2.12618 - 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{5} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) 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

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