LMFDB - Embedded newform 1680.2.cz.d.433.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(97,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1680.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.5
Root			$1.40927 + 0.118126i$ of defining polynomial
Character	$\chi$	$=$	1680.433
Dual form			1680.2.cz.d.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-2.23450 + 0.0836010i) q^{5} +(0.0627175 - 2.64501i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23450 + 0.0836010i) q^{5} +(0.0627175 - 2.64501i) q^{7} -1.00000i q^{9} -3.98602 q^{11} +(-0.500437 + 0.500437i) q^{13} +(-1.52092 + 1.63915i) q^{15} +(1.67840 + 1.67840i) q^{17} -7.21850 q^{19} +(-1.82596 - 1.91465i) q^{21} +(5.16007 + 5.16007i) q^{23} +(4.98602 - 0.373614i) q^{25} +(-0.707107 - 0.707107i) q^{27} +3.65191i q^{29} +4.93821i q^{31} +(-2.81854 + 2.81854i) q^{33} +(0.0809828 + 5.91553i) q^{35} +(0.292275 - 0.292275i) q^{37} +0.707725i q^{39} +7.63184i q^{41} +(-3.65191 - 3.65191i) q^{43} +(0.0836010 + 2.23450i) q^{45} +(-0.305303 - 0.305303i) q^{47} +(-6.99213 - 0.331777i) q^{49} +2.37361 q^{51} +(5.39653 + 5.39653i) q^{53} +(8.90678 - 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +6.10959 q^{59} -7.11047i q^{61} +(-2.64501 - 0.0627175i) q^{63} +(1.07639 - 1.16007i) q^{65} +(-0.944185 + 0.944185i) q^{67} +7.29744 q^{69} -1.19297 q^{71} +(-1.38298 + 1.38298i) q^{73} +(3.26147 - 3.78983i) q^{75} +(-0.249993 + 10.5431i) q^{77} +8.64027i q^{79} -1.00000 q^{81} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(2.58229 + 2.58229i) q^{87} -7.82581 q^{89} +(1.29227 + 1.35505i) q^{91} +(3.49184 + 3.49184i) q^{93} +(16.1298 - 0.603474i) q^{95} +(-7.43671 - 7.43671i) q^{97} +3.98602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−2.23450	+	0.0836010i	−0.999301	+	0.0373875i
$5$	−2.23450	+	0.0836010i	−0.999301	+	0.0373875i
$6$		0			0
$7$	0.0627175	−	2.64501i	0.0237050	−	0.999719i
$7$	0.0627175	−	2.64501i	0.0237050	−	0.999719i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−3.98602			−1.20183			−0.600915	−	0.799313i	$-0.705197\pi$
$11$	−3.98602			−1.20183			−0.600915	+	0.799313i	$0.705197\pi$
$12$		0			0
$13$	−0.500437	+	0.500437i	−0.138796	+	0.138796i	−0.773091	−	0.634295i	$-0.781291\pi$
$13$	−0.500437	+	0.500437i	−0.138796	+	0.138796i	0.634295	+	0.773091i	$0.281291\pi$
$14$		0			0
$15$	−1.52092	+	1.63915i	−0.392699	+	0.423226i
$16$		0			0
$17$	1.67840	+	1.67840i	0.407071	+	0.407071i	0.880716	−	0.473645i	$-0.157062\pi$
$17$	1.67840	+	1.67840i	0.407071	+	0.407071i	−0.473645	+	0.880716i	$0.657062\pi$
$18$		0			0
$19$	−7.21850			−1.65604			−0.828019	−	0.560700i	$-0.810532\pi$
$19$	−7.21850			−1.65604			−0.828019	+	0.560700i	$0.810532\pi$
$20$		0			0
$21$	−1.82596	−	1.91465i	−0.398456	−	0.417811i
$22$		0			0
$23$	5.16007	+	5.16007i	1.07595	+	1.07595i	0.996868	+	0.0790800i	$0.0251983\pi$
$23$	5.16007	+	5.16007i	1.07595	+	1.07595i	0.0790800	+	0.996868i	$0.474802\pi$
$24$		0			0
$25$	4.98602	−	0.373614i	0.997204	−	0.0747227i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			3.65191i			0.678143i	0.940761	+	0.339071i	$0.110113\pi$
$29$			3.65191i			0.678143i	−0.940761	+	0.339071i	$0.889887\pi$
$30$		0			0
$31$			4.93821i			0.886929i	0.896292	+	0.443465i	$0.146251\pi$
$31$			4.93821i			0.886929i	−0.896292	+	0.443465i	$0.853749\pi$
$32$		0			0
$33$	−2.81854	+	2.81854i	−0.490645	+	0.490645i
$34$		0			0
$35$	0.0809828	+	5.91553i	0.0136886	+	0.999906i
$36$		0			0
$37$	0.292275	−	0.292275i	0.0480497	−	0.0480497i	−0.682674	−	0.730723i	$-0.739183\pi$
$37$	0.292275	−	0.292275i	0.0480497	−	0.0480497i	0.730723	+	0.682674i	$0.239183\pi$
$38$		0			0
$39$			0.707725i			0.113327i
$40$		0			0
$41$			7.63184i			1.19189i	0.803024	+	0.595947i	$0.203223\pi$
$41$			7.63184i			1.19189i	−0.803024	+	0.595947i	$0.796777\pi$
$42$		0			0
$43$	−3.65191	−	3.65191i	−0.556911	−	0.556911i	0.371516	−	0.928427i	$-0.378838\pi$
$43$	−3.65191	−	3.65191i	−0.556911	−	0.556911i	−0.928427	+	0.371516i	$0.878838\pi$
$44$		0			0
$45$	0.0836010	+	2.23450i	0.0124625	+	0.333100i
$46$		0			0
$47$	−0.305303	−	0.305303i	−0.0445331	−	0.0445331i	0.684490	−	0.729023i	$-0.260025\pi$
$47$	−0.305303	−	0.305303i	−0.0445331	−	0.0445331i	−0.729023	+	0.684490i	$0.760025\pi$
$48$		0			0
$49$	−6.99213	−	0.331777i	−0.998876	−	0.0473967i
$50$		0			0
$51$	2.37361			0.332372
$52$		0			0
$53$	5.39653	+	5.39653i	0.741270	+	0.741270i	0.972822	−	0.231553i	$-0.0743805\pi$
$53$	5.39653	+	5.39653i	0.741270	+	0.741270i	−0.231553	+	0.972822i	$0.574381\pi$
$54$		0			0
$55$	8.90678	−	0.333235i	1.20099	−	0.0449335i
$56$		0			0
$57$	−5.10425	+	5.10425i	−0.676075	+	0.676075i
$58$		0			0
$59$	6.10959			0.795401			0.397701	−	0.917515i	$-0.369808\pi$
$59$	6.10959			0.795401			0.397701	+	0.917515i	$0.369808\pi$
$60$		0			0
$61$		−	7.11047i		−	0.910402i	−0.890389	−	0.455201i	$-0.849567\pi$
$61$		−	7.11047i		−	0.910402i	0.890389	−	0.455201i	$-0.150433\pi$
$62$		0			0
$63$	−2.64501	−	0.0627175i	−0.333240	−	0.00790166i
$64$		0			0
$65$	1.07639	−	1.16007i	0.133510	−	0.143889i
$66$		0			0
$67$	−0.944185	+	0.944185i	−0.115351	+	0.115351i	−0.762426	−	0.647075i	$-0.775992\pi$
$67$	−0.944185	+	0.944185i	−0.115351	+	0.115351i	0.647075	+	0.762426i	$0.275992\pi$
$68$		0			0
$69$	7.29744			0.878508
$70$		0			0
$71$	−1.19297			−0.141579			−0.0707897	−	0.997491i	$-0.522552\pi$
$71$	−1.19297			−0.141579			−0.0707897	+	0.997491i	$0.522552\pi$
$72$		0			0
$73$	−1.38298	+	1.38298i	−0.161865	+	0.161865i	−0.783393	−	0.621527i	$-0.786513\pi$
$73$	−1.38298	+	1.38298i	−0.161865	+	0.161865i	0.621527	+	0.783393i	$0.286513\pi$
$74$		0			0
$75$	3.26147	−	3.78983i	0.376602	−	0.437612i
$76$		0			0
$77$	−0.249993	+	10.5431i	−0.0284894	+	1.20149i
$78$		0			0
$79$			8.64027i			0.972106i	0.873929	+	0.486053i	$0.161564\pi$
$79$			8.64027i			0.972106i	−0.873929	+	0.486053i	$0.838436\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−11.9895	+	11.9895i	−1.31602	+	1.31602i	−0.399122	+	0.916898i	$0.630685\pi$
$83$	−11.9895	+	11.9895i	−1.31602	+	1.31602i	−0.916898	+	0.399122i	$0.869315\pi$
$84$		0			0
$85$	−3.89070	−	3.61007i	−0.422006	−	0.391567i
$86$		0			0
$87$	2.58229	+	2.58229i	0.276851	+	0.276851i
$88$		0			0
$89$	−7.82581			−0.829534			−0.414767	−	0.909928i	$-0.636137\pi$
$89$	−7.82581			−0.829534			−0.414767	+	0.909928i	$0.636137\pi$
$90$		0			0
$91$	1.29227	+	1.35505i	0.135467	+	0.142048i
$92$		0			0
$93$	3.49184	+	3.49184i	0.362087	+	0.362087i
$94$		0			0
$95$	16.1298	−	0.603474i	1.65488	−	0.0619151i
$96$		0			0
$97$	−7.43671	−	7.43671i	−0.755083	−	0.755083i	0.220340	−	0.975423i	$-0.429283\pi$
$97$	−7.43671	−	7.43671i	−0.755083	−	0.755083i	−0.975423	+	0.220340i	$0.929283\pi$
$98$		0			0
$99$			3.98602i			0.400610i
$100$		0			0
$101$		−	6.31633i		−	0.628498i	−0.949341	−	0.314249i	$-0.898247\pi$
$101$		−	6.31633i		−	0.628498i	0.949341	−	0.314249i	$-0.101753\pi$
$102$		0			0
$103$	−12.5410	+	12.5410i	−1.23570	+	1.23570i	−0.273954	+	0.961743i	$0.588332\pi$
$103$	−12.5410	+	12.5410i	−1.23570	+	1.23570i	−0.961743	+	0.273954i	$0.911668\pi$
$104$		0			0
$105$	4.24017	+	4.12564i	0.413798	+	0.402622i
$106$		0			0
$107$	−7.48020	+	7.48020i	−0.723138	+	0.723138i	−0.969243	−	0.246105i	$-0.920849\pi$
$107$	−7.48020	+	7.48020i	−0.723138	+	0.723138i	0.246105	+	0.969243i	$0.420849\pi$
$108$		0			0
$109$		−	0.668223i		−	0.0640042i	−0.999488	−	0.0320021i	$-0.989812\pi$
$109$		−	0.668223i		−	0.0640042i	0.999488	−	0.0320021i	$-0.0101883\pi$
$110$		0			0
$111$		−	0.413339i		−	0.0392324i
$112$		0			0
$113$	−3.39653	−	3.39653i	−0.319518	−	0.319518i	0.529064	−	0.848582i	$-0.322543\pi$
$113$	−3.39653	−	3.39653i	−0.319518	−	0.319518i	−0.848582	+	0.529064i	$0.822543\pi$
$114$		0			0
$115$	−11.9616	−	11.0988i	−1.11542	−	1.03497i
$116$		0			0
$117$	0.500437	+	0.500437i	0.0462655	+	0.0462655i
$118$		0			0
$119$	4.54464	−	4.33411i	0.416607	−	0.397307i
$120$		0			0
$121$	4.88837			0.444397
$122$		0			0
$123$	5.39653	+	5.39653i	0.486588	+	0.486588i
$124$		0			0
$125$	−11.1101	+	1.25168i	−0.993713	+	0.111953i
$126$		0			0
$127$	5.88837	−	5.88837i	0.522508	−	0.522508i	−0.395820	−	0.918328i	$-0.629540\pi$
$127$	5.88837	−	5.88837i	0.522508	−	0.522508i	0.918328	+	0.395820i	$0.129540\pi$
$128$		0			0
$129$	−5.16458			−0.454716
$130$		0			0
$131$		−	18.8144i		−	1.64383i	−0.569613	−	0.821913i	$-0.692907\pi$
$131$		−	18.8144i		−	1.64383i	0.569613	−	0.821913i	$-0.307093\pi$
$132$		0			0
$133$	−0.452726	+	19.0930i	−0.0392564	+	1.65557i
$134$		0			0
$135$	1.63915	+	1.52092i	0.141075	+	0.130900i
$136$		0			0
$137$	−0.811977	+	0.811977i	−0.0693719	+	0.0693719i	−0.740941	−	0.671570i	$-0.765620\pi$
$137$	−0.811977	+	0.811977i	−0.0693719	+	0.0693719i	0.671570	+	0.740941i	$0.265620\pi$
$138$		0			0
$139$	−0.442439			−0.0375272			−0.0187636	−	0.999824i	$-0.505973\pi$
$139$	−0.442439			−0.0375272			−0.0187636	+	0.999824i	$0.505973\pi$
$140$		0			0
$141$	−0.431764			−0.0363611
$142$		0			0
$143$	1.99475	−	1.99475i	0.166810	−	0.166810i
$144$		0			0
$145$	−0.305303	−	8.16021i	−0.0253541	−	0.677669i
$146$		0			0
$147$	−5.17879	+	4.70958i	−0.427139	+	0.388440i
$148$		0			0
$149$			3.14114i			0.257332i	0.991688	+	0.128666i	$0.0410696\pi$
$149$			3.14114i			0.257332i	−0.991688	+	0.128666i	$0.958930\pi$
$150$		0			0
$151$	14.7239			1.19822			0.599109	−	0.800668i	$-0.295522\pi$
$151$	14.7239			1.19822			0.599109	+	0.800668i	$0.295522\pi$
$152$		0			0
$153$	1.67840	−	1.67840i	0.135690	−	0.135690i
$154$		0			0
$155$	−0.412839	−	11.0345i	−0.0331601	−	0.886309i
$156$		0			0
$157$	7.96508	+	7.96508i	0.635682	+	0.635682i	0.949487	−	0.313805i	$-0.101604\pi$
$157$	7.96508	+	7.96508i	0.635682	+	0.635682i	−0.313805	+	0.949487i	$0.601604\pi$
$158$		0			0
$159$	7.63184			0.605244
$160$		0			0
$161$	13.9720	−	13.3248i	1.10115	−	1.05014i
$162$		0			0
$163$	−10.4450	−	10.4450i	−0.818113	−	0.818113i	0.167722	−	0.985834i	$-0.446359\pi$
$163$	−10.4450	−	10.4450i	−0.818113	−	0.818113i	−0.985834	+	0.167722i	$0.946359\pi$
$164$		0			0
$165$	6.06241	−	6.53368i	0.471958	−	0.508646i
$166$		0			0
$167$	4.63621	+	4.63621i	0.358761	+	0.358761i	0.863356	−	0.504595i	$-0.168358\pi$
$167$	4.63621	+	4.63621i	0.358761	+	0.358761i	−0.504595	+	0.863356i	$0.668358\pi$
$168$		0			0
$169$			12.4991i			0.961471i
$170$		0			0
$171$			7.21850i			0.552013i
$172$		0			0
$173$	2.48531	−	2.48531i	0.188954	−	0.188954i	−0.606290	−	0.795244i	$-0.707343\pi$
$173$	2.48531	−	2.48531i	0.188954	−	0.188954i	0.795244	+	0.606290i	$0.207343\pi$
$174$		0			0
$175$	−0.675500	−	13.2115i	−0.0510630	−	0.998695i
$176$		0			0
$177$	4.32013	−	4.32013i	0.324721	−	0.324721i
$178$		0			0
$179$			22.1109i			1.65264i	0.563199	+	0.826321i	$0.309570\pi$
$179$			22.1109i			1.65264i	−0.563199	+	0.826321i	$0.690430\pi$
$180$		0			0
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		0			0
$183$	−5.02786	−	5.02786i	−0.371670	−	0.371670i
$184$		0			0
$185$	−0.628655	+	0.677524i	−0.0462196	+	0.0498125i
$186$		0			0
$187$	−6.69013	−	6.69013i	−0.489231	−	0.489231i
$188$		0			0
$189$	−1.91465	+	1.82596i	−0.139270	+	0.132819i
$190$		0			0
$191$	−15.2898			−1.10633			−0.553167	−	0.833070i	$-0.686581\pi$
$191$	−15.2898			−1.10633			−0.553167	+	0.833070i	$0.686581\pi$
$192$		0			0
$193$	−8.92787	−	8.92787i	−0.642642	−	0.642642i	0.308562	−	0.951204i	$-0.400152\pi$
$193$	−8.92787	−	8.92787i	−0.642642	−	0.642642i	−0.951204	+	0.308562i	$0.900152\pi$
$194$		0			0
$195$	−0.0591665	−	1.58142i	−0.00423700	−	0.113248i
$196$		0			0
$197$	−2.68715	+	2.68715i	−0.191451	+	0.191451i	−0.796323	−	0.604872i	$-0.793224\pi$
$197$	−2.68715	+	2.68715i	−0.191451	+	0.191451i	0.604872	+	0.796323i	$0.293224\pi$
$198$		0			0
$199$	0.616637			0.0437122			0.0218561	−	0.999761i	$-0.493042\pi$
$199$	0.616637			0.0437122			0.0218561	+	0.999761i	$0.493042\pi$
$200$		0			0
$201$			1.33528i			0.0941833i
$202$		0			0
$203$	9.65933	+	0.229039i	0.677952	+	0.0160754i
$204$		0			0
$205$	−0.638029	−	17.0534i	−0.0445619	−	1.19106i
$206$		0			0
$207$	5.16007	−	5.16007i	0.358649	−	0.358649i
$208$		0			0
$209$	28.7731			1.99028
$210$		0			0
$211$	−9.30849			−0.640823			−0.320411	−	0.947278i	$-0.603821\pi$
$211$	−9.30849			−0.640823			−0.320411	+	0.947278i	$0.603821\pi$
$212$		0			0
$213$	−0.843557	+	0.843557i	−0.0577996	+	0.0577996i
$214$		0			0
$215$	8.46551	+	7.85491i	0.577343	+	0.535700i
$216$		0			0
$217$	13.0616	+	0.309712i	0.886680	+	0.0210246i
$218$		0			0
$219$			1.95583i			0.132163i
$220$		0			0
$221$	−1.67987			−0.113000
$222$		0			0
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	−0.751020	−	0.660279i	$-0.770438\pi$
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	0.660279	+	0.751020i	$0.270438\pi$
$224$		0			0
$225$	−0.373614	−	4.98602i	−0.0249076	−	0.332401i
$226$		0			0
$227$	4.15437	+	4.15437i	0.275735	+	0.275735i	0.831404	−	0.555668i	$-0.187538\pi$
$227$	4.15437	+	4.15437i	0.275735	+	0.275735i	−0.555668	+	0.831404i	$0.687538\pi$
$228$		0			0
$229$	−12.9900			−0.858403			−0.429202	−	0.903209i	$-0.641205\pi$
$229$	−12.9900			−0.858403			−0.429202	+	0.903209i	$0.641205\pi$
$230$		0			0
$231$	7.27830	+	7.63184i	0.478877	+	0.502138i
$232$		0			0
$233$	−16.4639	−	16.4639i	−1.07859	−	1.07859i	−0.996637	−	0.0819485i	$-0.973886\pi$
$233$	−16.4639	−	16.4639i	−1.07859	−	1.07859i	−0.0819485	−	0.996637i	$-0.526114\pi$
$234$		0			0
$235$	0.707725	+	0.656678i	0.0461669	+	0.0428370i
$236$		0			0
$237$	6.10959	+	6.10959i	0.396861	+	0.396861i
$238$		0			0
$239$			5.48048i			0.354503i	0.984166	+	0.177251i	$0.0567205\pi$
$239$			5.48048i			0.354503i	−0.984166	+	0.177251i	$0.943279\pi$
$240$		0			0
$241$		−	14.6507i		−	0.943737i	−0.881669	−	0.471868i	$-0.843580\pi$
$241$		−	14.6507i		−	0.943737i	0.881669	−	0.471868i	$-0.156420\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	15.6517	+	0.156807i	0.999950	+	0.0100180i
$246$		0			0
$247$	3.61241	−	3.61241i	0.229852	−	0.229852i
$248$		0			0
$249$			16.9557i			1.07453i
$250$		0			0
$251$		−	21.1506i		−	1.33501i	−0.744604	−	0.667507i	$-0.767361\pi$
$251$		−	21.1506i		−	1.33501i	0.744604	−	0.667507i	$-0.232639\pi$
$252$		0			0
$253$	−20.5681	−	20.5681i	−1.29311	−	1.29311i
$254$		0			0
$255$	−5.30385	+	0.198436i	−0.332140	+	0.0124266i
$256$		0			0
$257$	9.39248	+	9.39248i	0.585887	+	0.585887i	0.936515	−	0.350628i	$-0.114032\pi$
$257$	9.39248	+	9.39248i	0.585887	+	0.585887i	−0.350628	+	0.936515i	$0.614032\pi$
$258$		0			0
$259$	−0.754738	−	0.791399i	−0.0468971	−	0.0491752i
$260$		0			0
$261$	3.65191			0.226048
$262$		0			0
$263$	−15.3779	−	15.3779i	−0.948241	−	0.948241i	0.0504843	−	0.998725i	$-0.483924\pi$
$263$	−15.3779	−	15.3779i	−0.948241	−	0.948241i	−0.998725	+	0.0504843i	$0.983924\pi$
$264$		0			0
$265$	−12.5097	−	11.6074i	−0.768466	−	0.713037i
$266$		0			0
$267$	−5.53368	+	5.53368i	−0.338656	+	0.338656i
$268$		0			0
$269$	22.9851			1.40143			0.700714	−	0.713442i	$-0.252865\pi$
$269$	22.9851			1.40143			0.700714	+	0.713442i	$0.252865\pi$
$270$		0			0
$271$		−	15.7596i		−	0.957330i	−0.877998	−	0.478665i	$-0.841121\pi$
$271$		−	15.7596i		−	0.957330i	0.877998	−	0.478665i	$-0.158879\pi$
$272$		0			0
$273$	1.87194	+	0.0443868i	0.113295	+	0.00268641i
$274$		0			0
$275$	−19.8744	+	1.48923i	−1.19847	+	0.0898041i
$276$		0			0
$277$	4.80771	−	4.80771i	0.288867	−	0.288867i	−0.547765	−	0.836632i	$-0.684521\pi$
$277$	4.80771	−	4.80771i	0.288867	−	0.288867i	0.836632	+	0.547765i	$0.184521\pi$
$278$		0			0
$279$	4.93821			0.295643
$280$		0			0
$281$	−9.65658			−0.576063			−0.288032	−	0.957621i	$-0.593001\pi$
$281$	−9.65658			−0.576063			−0.288032	+	0.957621i	$0.593001\pi$
$282$		0			0
$283$	14.9095	−	14.9095i	0.886278	−	0.886278i	−0.107885	−	0.994163i	$-0.534408\pi$
$283$	14.9095	−	14.9095i	0.886278	−	0.886278i	0.994163	+	0.107885i	$0.0344079\pi$
$284$		0			0
$285$	10.9788	−	11.8322i	0.650325	−	0.700879i
$286$		0			0
$287$	20.1863	+	0.478650i	1.19156	+	0.0282538i
$288$		0			0
$289$		−	11.3660i		−	0.668586i
$290$		0			0
$291$	−10.5171			−0.616523
$292$		0			0
$293$	−4.79236	+	4.79236i	−0.279973	+	0.279973i	−0.833098	−	0.553125i	$-0.813435\pi$
$293$	−4.79236	+	4.79236i	−0.279973	+	0.279973i	0.553125	+	0.833098i	$0.313435\pi$
$294$		0			0
$295$	−13.6519	+	0.510768i	−0.794845	+	0.0297381i
$296$		0			0
$297$	2.81854	+	2.81854i	0.163548	+	0.163548i
$298$		0			0
$299$	−5.16458			−0.298675
$300$		0			0
$301$	−9.88837	+	9.43029i	−0.569956	+	0.543553i
$302$		0			0
$303$	−4.46632	−	4.46632i	−0.256583	−	0.256583i
$304$		0			0
$305$	0.594442	+	15.8884i	0.0340377	+	0.909765i
$306$		0			0
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	0.929933	−	0.367728i	$-0.119864\pi$
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	−0.367728	+	0.929933i	$0.619864\pi$
$308$		0			0
$309$			17.7356i			1.00894i
$310$		0			0
$311$			27.3063i			1.54840i	0.632941	+	0.774200i	$0.281848\pi$
$311$			27.3063i			1.54840i	−0.632941	+	0.774200i	$0.718152\pi$
$312$		0			0
$313$	−18.5080	+	18.5080i	−1.04613	+	1.04613i	−0.0472492	+	0.998883i	$0.515045\pi$
$313$	−18.5080	+	18.5080i	−1.04613	+	1.04613i	−0.998883	+	0.0472492i	$0.984955\pi$
$314$		0			0
$315$	5.91553	−	0.0809828i	0.333302	−	0.00456286i
$316$		0			0
$317$	−21.8793	+	21.8793i	−1.22887	+	1.22887i	−0.264473	+	0.964393i	$0.585198\pi$
$317$	−21.8793	+	21.8793i	−1.22887	+	1.22887i	−0.964393	+	0.264473i	$0.914802\pi$
$318$		0			0
$319$		−	14.5566i		−	0.815013i
$320$		0			0
$321$			10.5786i			0.590440i
$322$		0			0
$323$	−12.1155	−	12.1155i	−0.674126	−	0.674126i
$324$		0			0
$325$	−2.30822	+	2.68216i	−0.128037	+	0.148780i
$326$		0			0
$327$	−0.472505	−	0.472505i	−0.0261296	−	0.0261296i
$328$		0			0
$329$	−0.826678	+	0.788382i	−0.0455762	+	0.0434649i
$330$		0			0
$331$	16.6913			0.917438			0.458719	−	0.888581i	$-0.348309\pi$
$331$	16.6913			0.917438			0.458719	+	0.888581i	$0.348309\pi$
$332$		0			0
$333$	−0.292275	−	0.292275i	−0.0160166	−	0.0160166i
$334$		0			0
$335$	2.03085	−	2.18872i	0.110957	−	0.119583i
$336$		0			0
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	−0.634525	−	0.772903i	$-0.718804\pi$
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	0.772903	+	0.634525i	$0.218804\pi$
$338$		0			0
$339$	−4.80341			−0.260886
$340$		0			0
$341$		−	19.6838i		−	1.06594i
$342$		0			0
$343$	−1.31608	+	18.4734i	−0.0710617	+	0.997472i
$344$		0			0
$345$	−16.3062	+	0.610073i	−0.877894	+	0.0328452i
$346$		0			0
$347$	−13.6980	+	13.6980i	−0.735348	+	0.735348i	−0.971674	−	0.236326i	$-0.924057\pi$
$347$	−13.6980	+	13.6980i	−0.735348	+	0.735348i	0.236326	+	0.971674i	$0.424057\pi$
$348$		0			0
$349$	−0.508601			−0.0272248			−0.0136124	−	0.999907i	$-0.504333\pi$
$349$	−0.508601			−0.0272248			−0.0136124	+	0.999907i	$0.504333\pi$
$350$		0			0
$351$	0.707725			0.0377756
$352$		0			0
$353$	−10.9217	+	10.9217i	−0.581305	+	0.581305i	−0.935262	−	0.353957i	$-0.884836\pi$
$353$	−10.9217	+	10.9217i	−0.581305	+	0.581305i	0.353957	+	0.935262i	$0.384836\pi$
$354$		0			0
$355$	2.66570	−	0.0997335i	0.141480	−	0.00529330i
$356$		0			0
$357$	0.148867	−	6.27823i	0.00787888	−	0.332279i
$358$		0			0
$359$		−	15.9860i		−	0.843710i	−0.906663	−	0.421855i	$-0.861379\pi$
$359$		−	15.9860i		−	0.843710i	0.906663	−	0.421855i	$-0.138621\pi$
$360$		0			0
$361$	33.1068			1.74246
$362$		0			0
$363$	3.45660	−	3.45660i	0.181424	−	0.181424i
$364$		0			0
$365$	2.97465	−	3.20589i	0.155701	−	0.167804i
$366$		0			0
$367$	0.410036	+	0.410036i	0.0214037	+	0.0214037i	0.717728	−	0.696324i	$-0.245182\pi$
$367$	0.410036	+	0.410036i	0.0214037	+	0.0214037i	−0.696324	+	0.717728i	$0.745182\pi$
$368$		0			0
$369$	7.63184			0.397298
$370$		0			0
$371$	14.6123	−	13.9354i	0.758633	−	0.723490i
$372$		0			0
$373$	−3.44496	−	3.44496i	−0.178373	−	0.178373i	0.612273	−	0.790646i	$-0.290255\pi$
$373$	−3.44496	−	3.44496i	−0.178373	−	0.178373i	−0.790646	+	0.612273i	$0.790255\pi$
$374$		0			0
$375$	−6.97092	+	8.74106i	−0.359977	+	0.451387i
$376$		0			0
$377$	−1.82755	−	1.82755i	−0.0941237	−	0.0941237i
$378$		0			0
$379$		−	12.9179i		−	0.663547i	−0.943359	−	0.331773i	$-0.892353\pi$
$379$		−	12.9179i		−	0.663547i	0.943359	−	0.331773i	$-0.107647\pi$
$380$		0			0
$381$		−	8.32741i		−	0.426626i
$382$		0			0
$383$	−10.0770	+	10.0770i	−0.514910	+	0.514910i	−0.916027	−	0.401117i	$-0.868622\pi$
$383$	−10.0770	+	10.0770i	−0.514910	+	0.514910i	0.401117	+	0.916027i	$0.368622\pi$
$384$		0			0
$385$	−0.322799	−	23.5794i	−0.0164514	−	1.20172i
$386$		0			0
$387$	−3.65191	+	3.65191i	−0.185637	+	0.185637i
$388$		0			0
$389$		−	24.3300i		−	1.23358i	−0.787127	−	0.616791i	$-0.788433\pi$
$389$		−	24.3300i		−	1.23358i	0.787127	−	0.616791i	$-0.211567\pi$
$390$		0			0
$391$			17.3213i			0.875976i
$392$		0			0
$393$	−13.3038	−	13.3038i	−0.671089	−	0.671089i
$394$		0			0
$395$	−0.722335	−	19.3067i	−0.0363446	−	0.971426i
$396$		0			0
$397$	−6.80633	−	6.80633i	−0.341600	−	0.341600i	0.515369	−	0.856969i	$-0.327655\pi$
$397$	−6.80633	−	6.80633i	−0.341600	−	0.341600i	−0.856969	+	0.515369i	$0.827655\pi$
$398$		0			0
$399$	13.1807	+	13.8209i	0.659858	+	0.691911i
$400$		0			0
$401$	−8.83090			−0.440994			−0.220497	−	0.975388i	$-0.570768\pi$
$401$	−8.83090			−0.440994			−0.220497	+	0.975388i	$0.570768\pi$
$402$		0			0
$403$	−2.47127	−	2.47127i	−0.123103	−	0.123103i
$404$		0			0
$405$	2.23450	−	0.0836010i	0.111033	−	0.00415417i
$406$		0			0
$407$	−1.16501	+	1.16501i	−0.0577476	+	0.0577476i
$408$		0			0
$409$	23.1985			1.14709			0.573546	−	0.819174i	$-0.305568\pi$
$409$	23.1985			1.14709			0.573546	+	0.819174i	$0.305568\pi$
$410$		0			0
$411$			1.14831i			0.0566419i
$412$		0			0
$413$	0.383178	−	16.1599i	0.0188550	−	0.795178i
$414$		0			0
$415$	25.7883	−	27.7930i	1.26590	−	1.36430i
$416$		0			0
$417$	−0.312852	+	0.312852i	−0.0153204	+	0.0153204i
$418$		0			0
$419$	13.0393			0.637009			0.318505	−	0.947921i	$-0.396819\pi$
$419$	13.0393			0.637009			0.318505	+	0.947921i	$0.396819\pi$
$420$		0			0
$421$	−31.3549			−1.52814			−0.764071	−	0.645132i	$-0.776802\pi$
$421$	−31.3549			−1.52814			−0.764071	+	0.645132i	$0.776802\pi$
$422$		0			0
$423$	−0.305303	+	0.305303i	−0.0148444	+	0.0148444i
$424$		0			0
$425$	8.99560	+	7.74146i	0.436351	+	0.375516i
$426$		0			0
$427$	−18.8072	−	0.445951i	−0.910146	−	0.0215811i
$428$		0			0
$429$		−	2.82101i		−	0.136200i
$430$		0			0
$431$	22.5558			1.08648			0.543238	−	0.839579i	$-0.317198\pi$
$431$	22.5558			1.08648			0.543238	+	0.839579i	$0.317198\pi$
$432$		0			0
$433$	19.9639	−	19.9639i	0.959405	−	0.959405i	−0.0398028	−	0.999208i	$-0.512673\pi$
$433$	19.9639	−	19.9639i	0.959405	−	0.959405i	0.999208	+	0.0398028i	$0.0126730\pi$
$434$		0			0
$435$	−5.98602	−	5.55426i	−0.287008	−	0.266306i
$436$		0			0
$437$	−37.2479	−	37.2479i	−1.78181	−	1.78181i
$438$		0			0
$439$	30.1943			1.44110			0.720548	−	0.693405i	$-0.243890\pi$
$439$	30.1943			1.44110			0.720548	+	0.693405i	$0.243890\pi$
$440$		0			0
$441$	−0.331777	+	6.99213i	−0.0157989	+	0.332959i
$442$		0			0
$443$	12.7423	+	12.7423i	0.605404	+	0.605404i	0.941742	−	0.336337i	$-0.109188\pi$
$443$	12.7423	+	12.7423i	0.605404	+	0.605404i	−0.336337	+	0.941742i	$0.609188\pi$
$444$		0			0
$445$	17.4868	−	0.654245i	0.828954	−	0.0310142i
$446$		0			0
$447$	2.22112	+	2.22112i	0.105056	+	0.105056i
$448$		0			0
$449$		−	30.4170i		−	1.43547i	−0.696318	−	0.717734i	$-0.745180\pi$
$449$		−	30.4170i		−	1.43547i	0.696318	−	0.717734i	$-0.254820\pi$
$450$		0			0
$451$		−	30.4207i		−	1.43245i
$452$		0			0
$453$	10.4114	−	10.4114i	0.489170	−	0.489170i
$454$		0			0
$455$	−3.00088	−	2.91982i	−0.140683	−	0.136883i
$456$		0			0
$457$	1.31546	−	1.31546i	0.0615348	−	0.0615348i	−0.675670	−	0.737204i	$-0.736145\pi$
$457$	1.31546	−	1.31546i	0.0615348	−	0.0615348i	0.737204	+	0.675670i	$0.236145\pi$
$458$		0			0
$459$		−	2.37361i		−	0.110791i
$460$		0			0
$461$		−	1.29957i		−	0.0605272i	−0.999542	−	0.0302636i	$-0.990365\pi$
$461$		−	1.29957i		−	0.0605272i	0.999542	−	0.0302636i	$-0.00963467\pi$
$462$		0			0
$463$	−16.5240	−	16.5240i	−0.767934	−	0.767934i	0.209809	−	0.977742i	$-0.432716\pi$
$463$	−16.5240	−	16.5240i	−0.767934	−	0.767934i	−0.977742	+	0.209809i	$0.932716\pi$
$464$		0			0
$465$	−8.09446	−	7.51062i	−0.375372	−	0.348297i
$466$		0			0
$467$	20.1009	+	20.1009i	0.930157	+	0.930157i	0.997715	−	0.0675588i	$-0.0215210\pi$
$467$	20.1009	+	20.1009i	0.930157	+	0.930157i	−0.0675588	+	0.997715i	$0.521521\pi$
$468$		0			0
$469$	2.43816	+	2.55659i	0.112584	+	0.118052i
$470$		0			0
$471$	11.2643			0.519032
$472$		0			0
$473$	14.5566	+	14.5566i	0.669313	+	0.669313i
$474$		0			0
$475$	−35.9916	+	2.69693i	−1.65141	+	0.123744i
$476$		0			0
$477$	5.39653	−	5.39653i	0.247090	−	0.247090i
$478$		0			0
$479$	−11.0836			−0.506425			−0.253212	−	0.967411i	$-0.581487\pi$
$479$	−11.0836			−0.506425			−0.253212	+	0.967411i	$0.581487\pi$
$480$		0			0
$481$			0.292530i			0.0133382i
$482$		0			0
$483$	0.457677	−	19.3018i	0.0208250	−	0.878261i
$484$		0			0
$485$	17.2391	+	15.9956i	0.782786	+	0.726325i
$486$		0			0
$487$	13.6519	−	13.6519i	0.618627	−	0.618627i	−0.326552	−	0.945179i	$-0.605887\pi$
$487$	13.6519	−	13.6519i	0.618627	−	0.618627i	0.945179	+	0.326552i	$0.105887\pi$
$488$		0			0
$489$	−14.7714			−0.667986
$490$		0			0
$491$	−32.1155			−1.44935			−0.724677	−	0.689089i	$-0.758011\pi$
$491$	−32.1155			−1.44935			−0.724677	+	0.689089i	$0.758011\pi$
$492$		0			0
$493$	−6.12936	+	6.12936i	−0.276052	+	0.276052i
$494$		0			0
$495$	−0.333235	−	8.90678i	−0.0149778	−	0.400330i
$496$		0			0
$497$	−0.0748201	+	3.15541i	−0.00335614	+	0.141540i
$498$		0			0
$499$			4.27431i			0.191344i	0.995413	+	0.0956722i	$0.0305000\pi$
$499$			4.27431i			0.191344i	−0.995413	+	0.0956722i	$0.969500\pi$
$500$		0			0
$501$	6.55659			0.292927
$502$		0			0
$503$	17.5637	−	17.5637i	0.783128	−	0.783128i	−0.197229	−	0.980357i	$-0.563194\pi$
$503$	17.5637	−	17.5637i	0.783128	−	0.783128i	0.980357	+	0.197229i	$0.0631943\pi$
$504$		0			0
$505$	0.528051	+	14.1139i	0.0234980	+	0.628059i
$506$		0			0
$507$	8.83822	+	8.83822i	0.392519	+	0.392519i
$508$		0			0
$509$	27.9162			1.23736			0.618682	−	0.785641i	$-0.287667\pi$
$509$	27.9162			1.23736			0.618682	+	0.785641i	$0.287667\pi$
$510$		0			0
$511$	3.57125	+	3.74473i	0.157983	+	0.165657i
$512$		0			0
$513$	5.10425	+	5.10425i	0.225358	+	0.225358i
$514$		0			0
$515$	26.9744	−	29.0713i	1.18863	−	1.28103i
$516$		0			0
$517$	1.21695	+	1.21695i	0.0535212	+	0.0535212i
$518$		0			0
$519$		−	3.51476i		−	0.154281i
$520$		0			0
$521$			28.8647i			1.26458i	0.774730	+	0.632292i	$0.217886\pi$
$521$			28.8647i			1.26458i	−0.774730	+	0.632292i	$0.782114\pi$
$522$		0			0
$523$	−3.54707	+	3.54707i	−0.155103	+	0.155103i	−0.780392	−	0.625290i	$-0.784981\pi$
$523$	−3.54707	+	3.54707i	−0.155103	+	0.155103i	0.625290	+	0.780392i	$0.284981\pi$
$524$		0			0
$525$	−9.81959	−	8.86429i	−0.428562	−	0.386869i
$526$		0			0
$527$	−8.28829	+	8.28829i	−0.361043	+	0.361043i
$528$		0			0
$529$			30.2526i			1.31533i
$530$		0			0
$531$		−	6.10959i		−	0.265134i
$532$		0			0
$533$	−3.81926	−	3.81926i	−0.165430	−	0.165430i
$534$		0			0
$535$	16.0892	−	17.3399i	0.695596	−	0.749669i
$536$		0			0
$537$	15.6347	+	15.6347i	0.674688	+	0.674688i
$538$		0			0
$539$	27.8708	+	1.32247i	1.20048	+	0.0569628i
$540$		0			0
$541$	−4.08698			−0.175713			−0.0878565	−	0.996133i	$-0.528002\pi$
$541$	−4.08698			−0.175713			−0.0878565	+	0.996133i	$0.528002\pi$
$542$		0			0
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$		0			0
$545$	0.0558641	+	1.49315i	0.00239296	+	0.0639594i
$546$		0			0
$547$	−28.2200	+	28.2200i	−1.20660	+	1.20660i	−0.234482	+	0.972121i	$0.575339\pi$
$547$	−28.2200	+	28.2200i	−1.20660	+	1.20660i	−0.972121	+	0.234482i	$0.924661\pi$
$548$		0			0
$549$	−7.11047			−0.303467
$550$		0			0
$551$		−	26.3613i		−	1.12303i
$552$		0			0
$553$	22.8536	+	0.541896i	0.971833	+	0.0230438i
$554$		0			0
$555$	0.0345555	+	0.923607i	0.00146680	+	0.0392050i
$556$		0			0
$557$	28.1616	−	28.1616i	1.19325	−	1.19325i	0.217096	−	0.976150i	$-0.430342\pi$
$557$	28.1616	−	28.1616i	1.19325	−	1.19325i	0.976150	−	0.217096i	$-0.0696584\pi$
$558$		0			0
$559$	3.65510			0.154594
$560$		0			0
$561$	−9.46128			−0.399455
$562$		0			0
$563$	−27.3645	+	27.3645i	−1.15328	+	1.15328i	−0.167386	+	0.985891i	$0.553533\pi$
$563$	−27.3645	+	27.3645i	−1.15328	+	1.15328i	−0.985891	+	0.167386i	$0.946467\pi$
$564$		0			0
$565$	7.87351	+	7.30560i	0.331241	+	0.307349i
$566$		0			0
$567$	−0.0627175	+	2.64501i	−0.00263389	+	0.111080i
$568$		0			0
$569$			17.7767i			0.745240i	0.927984	+	0.372620i	$0.121540\pi$
$569$			17.7767i			0.745240i	−0.927984	+	0.372620i	$0.878460\pi$
$570$		0			0
$571$	16.8866			0.706683			0.353342	−	0.935494i	$-0.385045\pi$
$571$	16.8866			0.706683			0.353342	+	0.935494i	$0.385045\pi$
$572$		0			0
$573$	−10.8116	+	10.8116i	−0.451659	+	0.451659i
$574$		0			0
$575$	27.6561	+	23.8003i	1.15334	+	0.992543i
$576$		0			0
$577$	−3.89677	−	3.89677i	−0.162225	−	0.162225i	0.621327	−	0.783552i	$-0.286594\pi$
$577$	−3.89677	−	3.89677i	−0.162225	−	0.162225i	−0.783552	+	0.621327i	$0.786594\pi$
$578$		0			0
$579$	−12.6259			−0.524715
$580$		0			0
$581$	30.9604	+	32.4643i	1.28445	+	1.34685i
$582$		0			0
$583$	−21.5107	−	21.5107i	−0.890881	−	0.890881i
$584$		0			0
$585$	−1.16007	−	1.07639i	−0.0479629	−	0.0445034i
$586$		0			0
$587$	−15.1058	−	15.1058i	−0.623484	−	0.623484i	0.322937	−	0.946420i	$-0.395330\pi$
$587$	−15.1058	−	15.1058i	−0.623484	−	0.623484i	−0.946420	+	0.322937i	$0.895330\pi$
$588$		0			0
$589$		−	35.6465i		−	1.46879i
$590$		0			0
$591$			3.80020i			0.156319i
$592$		0			0
$593$	3.43032	−	3.43032i	0.140866	−	0.140866i	−0.633157	−	0.774023i	$-0.718241\pi$
$593$	3.43032	−	3.43032i	0.140866	−	0.140866i	0.774023	+	0.633157i	$0.218241\pi$
$594$		0			0
$595$	−9.79269	+	10.0645i	−0.401461	+	0.412605i
$596$		0			0
$597$	0.436028	−	0.436028i	0.0178454	−	0.0178454i
$598$		0			0
$599$			10.1010i			0.412714i	0.978477	+	0.206357i	$0.0661608\pi$
$599$			10.1010i			0.412714i	−0.978477	+	0.206357i	$0.933839\pi$
$600$		0			0
$601$		−	38.4063i		−	1.56663i	−0.621628	−	0.783313i	$-0.713528\pi$
$601$		−	38.4063i		−	1.56663i	0.621628	−	0.783313i	$-0.286472\pi$
$602$		0			0
$603$	0.944185	+	0.944185i	0.0384502	+	0.0384502i
$604$		0			0
$605$	−10.9231	+	0.408673i	−0.444087	+	0.0166149i
$606$		0			0
$607$	10.2931	+	10.2931i	0.417783	+	0.417783i	0.884439	−	0.466656i	$-0.154541\pi$
$607$	10.2931	+	10.2931i	0.417783	+	0.417783i	−0.466656	+	0.884439i	$0.654541\pi$
$608$		0			0
$609$	6.99213	−	6.66822i	0.283336	−	0.270210i
$610$		0			0
$611$	0.305570			0.0123621
$612$		0			0
$613$	−14.4155	−	14.4155i	−0.582235	−	0.582235i	0.353282	−	0.935517i	$-0.385066\pi$
$613$	−14.4155	−	14.4155i	−0.582235	−	0.582235i	−0.935517	+	0.353282i	$0.885066\pi$
$614$		0			0
$615$	−12.5097	−	11.6074i	−0.504440	−	0.468056i
$616$		0			0
$617$	−25.4196	+	25.4196i	−1.02336	+	1.02336i	−0.0236346	+	0.999721i	$0.507524\pi$
$617$	−25.4196	+	25.4196i	−1.02336	+	1.02336i	−0.999721	+	0.0236346i	$0.992476\pi$
$618$		0			0
$619$	−11.1991			−0.450129			−0.225064	−	0.974344i	$-0.572259\pi$
$619$	−11.1991			−0.450129			−0.225064	+	0.974344i	$0.572259\pi$
$620$		0			0
$621$		−	7.29744i		−	0.292836i
$622$		0			0
$623$	−0.490815	+	20.6993i	−0.0196641	+	0.829301i
$624$		0			0
$625$	24.7208	−	3.72569i	0.988833	−	0.149028i
$626$		0			0
$627$	20.3457	−	20.3457i	0.812527	−	0.812527i
$628$		0			0
$629$	0.981107			0.0391193
$630$		0			0
$631$	−21.2015			−0.844020			−0.422010	−	0.906591i	$-0.638675\pi$
$631$	−21.2015			−0.844020			−0.422010	+	0.906591i	$0.638675\pi$
$632$		0			0
$633$	−6.58210	+	6.58210i	−0.261615	+	0.261615i
$634$		0			0
$635$	−12.6653	+	13.6499i	−0.502608	+	0.541678i
$636$		0			0
$637$	3.66516	−	3.33309i	0.145219	−	0.132062i
$638$		0			0
$639$			1.19297i			0.0471931i
$640$		0			0
$641$	−29.8969			−1.18086			−0.590428	−	0.807090i	$-0.701041\pi$
$641$	−29.8969			−1.18086			−0.590428	+	0.807090i	$0.701041\pi$
$642$		0			0
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	−0.448761	−	0.893652i	$-0.648134\pi$
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	0.893652	+	0.448761i	$0.148134\pi$
$644$		0			0
$645$	11.5403	−	0.431764i	0.454398	−	0.0170007i
$646$		0			0
$647$	−26.2395	−	26.2395i	−1.03158	−	1.03158i	−0.999485	−	0.0320982i	$-0.989781\pi$
$647$	−26.2395	−	26.2395i	−1.03158	−	1.03158i	−0.0320982	−	0.999485i	$-0.510219\pi$
$648$		0			0
$649$	−24.3530			−0.955937
$650$		0			0
$651$	9.45495	−	9.01695i	0.370569	−	0.353402i
$652$		0			0
$653$	−1.97641	−	1.97641i	−0.0773427	−	0.0773427i	0.667377	−	0.744720i	$-0.267417\pi$
$653$	−1.97641	−	1.97641i	−0.0773427	−	0.0773427i	−0.744720	+	0.667377i	$0.767417\pi$
$654$		0			0
$655$	1.57291	+	42.0410i	0.0614585	+	1.64268i
$656$		0			0
$657$	1.38298	+	1.38298i	0.0539552	+	0.0539552i
$658$		0			0
$659$		−	15.1044i		−	0.588385i	−0.955746	−	0.294193i	$-0.904949\pi$
$659$		−	15.1044i		−	0.588385i	0.955746	−	0.294193i	$-0.0950507\pi$
$660$		0			0
$661$		−	1.10054i		−	0.0428062i	−0.999771	−	0.0214031i	$-0.993187\pi$
$661$		−	1.10054i		−	0.0428062i	0.999771	−	0.0214031i	$-0.00681333\pi$
$662$		0			0
$663$	−1.18785	+	1.18785i	−0.0461321	+	0.0461321i
$664$		0			0
$665$	−0.584574	−	42.7012i	−0.0226688	−	1.65588i
$666$		0			0
$667$	−18.8441	+	18.8441i	−0.729646	+	0.729646i
$668$		0			0
$669$			1.91633i			0.0740894i
$670$		0			0
$671$			28.3425i			1.09415i
$672$		0			0
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	0.451411	−	0.892316i	$-0.350921\pi$
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	−0.892316	+	0.451411i	$0.850921\pi$
$674$		0			0
$675$	−3.78983	−	3.26147i	−0.145871	−	0.125534i
$676$		0			0
$677$	24.6007	+	24.6007i	0.945481	+	0.945481i	0.998589	−	0.0531077i	$-0.0169127\pi$
$677$	24.6007	+	24.6007i	0.945481	+	0.945481i	−0.0531077	+	0.998589i	$0.516913\pi$
$678$		0			0
$679$	−20.1366	+	19.2037i	−0.772770	+	0.736972i
$680$		0			0
$681$	5.87517			0.225137
$682$		0			0
$683$	13.8654	+	13.8654i	0.530543	+	0.530543i	0.920734	−	0.390191i	$-0.127591\pi$
$683$	13.8654	+	13.8654i	0.530543	+	0.530543i	−0.390191	+	0.920734i	$0.627591\pi$
$684$		0			0
$685$	1.74648	−	1.88225i	0.0667297	−	0.0719170i
$686$		0			0
$687$	−9.18531	+	9.18531i	−0.350442	+	0.350442i
$688$		0			0
$689$	−5.40125			−0.205771
$690$		0			0
$691$			12.4060i			0.471947i	0.971759	+	0.235974i	$0.0758279\pi$
$691$			12.4060i			0.471947i	−0.971759	+	0.235974i	$0.924172\pi$
$692$		0			0
$693$	10.5431	+	0.249993i	0.400498	+	0.00949646i
$694$		0			0
$695$	0.988633	−	0.0369884i	0.0375010	−	0.00140305i
$696$		0			0
$697$	−12.8093	+	12.8093i	−0.485186	+	0.485186i
$698$		0			0
$699$	−23.2835			−0.880661
$700$		0			0
$701$	1.45193			0.0548388			0.0274194	−	0.999624i	$-0.491271\pi$
$701$	1.45193			0.0548388			0.0274194	+	0.999624i	$0.491271\pi$
$702$		0			0
$703$	−2.10979	+	2.10979i	−0.0795720	+	0.0795720i
$704$		0			0
$705$	0.964779	−	0.0360959i	0.0363357	−	0.00135945i
$706$		0			0
$707$	−16.7067	−	0.396144i	−0.628322	−	0.0148985i
$708$		0			0
$709$			48.5284i			1.82252i	0.411827	+	0.911262i	$0.364891\pi$
$709$			48.5284i			1.82252i	−0.411827	+	0.911262i	$0.635109\pi$
$710$		0			0
$711$	8.64027			0.324035
$712$		0			0
$713$	−25.4815	+	25.4815i	−0.954290	+	0.954290i
$714$		0			0
$715$	−4.29052	+	4.62405i	−0.160457	+	0.172930i
$716$		0			0
$717$	3.87528	+	3.87528i	0.144725	+	0.144725i
$718$		0			0
$719$	43.5872			1.62553			0.812764	−	0.582593i	$-0.197962\pi$
$719$	43.5872			1.62553			0.812764	+	0.582593i	$0.197962\pi$
$720$		0			0
$721$	32.3844	+	33.9575i	1.20606	+	1.26464i
$722$		0			0
$723$	−10.3596	−	10.3596i	−0.385279	−	0.385279i
$724$		0			0
$725$	1.36440	+	18.2085i	0.0506727	+	0.676247i
$726$		0			0
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	0.873817	−	0.486254i	$-0.161637\pi$
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	−0.486254	+	0.873817i	$0.661637\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	12.2587i		−	0.453405i
$732$		0			0
$733$	−18.8687	+	18.8687i	−0.696933	+	0.696933i	−0.963748	−	0.266815i	$-0.914029\pi$
$733$	−18.8687	+	18.8687i	−0.696933	+	0.696933i	0.266815	+	0.963748i	$0.414029\pi$
$734$		0			0
$735$	11.1783	−	10.9565i	0.412318	−	0.404138i
$736$		0			0
$737$	3.76354	−	3.76354i	0.138632	−	0.138632i
$738$		0			0
$739$			20.9689i			0.771354i	0.922634	+	0.385677i	$0.126032\pi$
$739$			20.9689i			0.771354i	−0.922634	+	0.385677i	$0.873968\pi$
$740$		0			0
$741$		−	5.10872i		−	0.187673i
$742$		0			0
$743$	−9.18724	−	9.18724i	−0.337047	−	0.337047i	0.518208	−	0.855255i	$-0.326599\pi$
$743$	−9.18724	−	9.18724i	−0.337047	−	0.337047i	−0.855255	+	0.518208i	$0.826599\pi$
$744$		0			0
$745$	−0.262603	−	7.01890i	−0.00962102	−	0.257152i
$746$		0			0
$747$	11.9895	+	11.9895i	0.438673	+	0.438673i
$748$		0			0
$749$	19.3160	+	20.2543i	0.705793	+	0.740077i
$750$		0			0
$751$	−11.1969			−0.408579			−0.204290	−	0.978910i	$-0.565488\pi$
$751$	−11.1969			−0.408579			−0.204290	+	0.978910i	$0.565488\pi$
$752$		0			0
$753$	−14.9557	−	14.9557i	−0.545017	−	0.545017i
$754$		0			0
$755$	−32.9007	+	1.23094i	−1.19738	+	0.0447984i
$756$		0			0
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	−0.913414	−	0.407031i	$-0.866564\pi$
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	0.407031	+	0.913414i	$0.366564\pi$
$758$		0			0
$759$	−29.0877			−1.05582
$760$		0			0
$761$		−	8.78825i		−	0.318574i	−0.987232	−	0.159287i	$-0.949081\pi$
$761$		−	8.78825i		−	0.318574i	0.987232	−	0.159287i	$-0.0509195\pi$
$762$		0			0
$763$	−1.76746	−	0.0419093i	−0.0639862	−	0.00151722i
$764$		0			0
$765$	−3.61007	+	3.89070i	−0.130522	+	0.140669i
$766$		0			0
$767$	−3.05747	+	3.05747i	−0.110399	+	0.110399i
$768$		0			0
$769$	11.2183			0.404543			0.202271	−	0.979330i	$-0.435168\pi$
$769$	11.2183			0.404543			0.202271	+	0.979330i	$0.435168\pi$
$770$		0			0
$771$	13.2830			0.478374
$772$		0			0
$773$	−21.5065	+	21.5065i	−0.773535	+	0.773535i	−0.978723	−	0.205188i	$-0.934219\pi$
$773$	−21.5065	+	21.5065i	−0.773535	+	0.773535i	0.205188	+	0.978723i	$0.434219\pi$
$774$		0			0
$775$	1.84498	+	24.6220i	0.0662738	+	0.884450i
$776$		0			0
$777$	−1.09328	−	0.0259236i	−0.0392214	−	0.000930003i
$778$		0			0
$779$		−	55.0905i		−	1.97382i
$780$		0			0
$781$	4.75520			0.170155
$782$		0			0
$783$	2.58229	−	2.58229i	0.0922835	−	0.0922835i
$784$		0			0
$785$	−18.4639	−	17.1321i	−0.659004	−	0.611471i
$786$		0			0
$787$	37.4673	+	37.4673i	1.33557	+	1.33557i	0.900304	+	0.435262i	$0.143344\pi$
$787$	37.4673	+	37.4673i	1.33557	+	1.33557i	0.435262	+	0.900304i	$0.356656\pi$
$788$		0			0
$789$	−21.7476			−0.774235
$790$		0			0
$791$	−9.19686	+	8.77082i	−0.327003	+	0.311854i
$792$		0			0
$793$	3.55834	+	3.55834i	0.126360	+	0.126360i
$794$		0			0
$795$	−17.0534	+	0.638029i	−0.604821	+	0.0226286i
$796$		0			0
$797$	−6.96365	−	6.96365i	−0.246665	−	0.246665i	0.572935	−	0.819601i	$-0.305805\pi$
$797$	−6.96365	−	6.96365i	−0.246665	−	0.246665i	−0.819601	+	0.572935i	$0.805805\pi$
$798$		0			0
$799$		−	1.02484i		−	0.0362563i
$800$		0			0
$801$			7.82581i			0.276511i
$802$		0			0
$803$	5.51258	−	5.51258i	0.194535	−	0.194535i
$804$		0			0
$805$	−30.1066	+	30.9424i	−1.06112	+	1.09058i
$806$		0			0
$807$	16.2530	−	16.2530i	0.572131	−	0.572131i
$808$		0			0
$809$			42.2409i			1.48511i	0.669784	+	0.742556i	$0.266387\pi$
$809$			42.2409i			1.48511i	−0.669784	+	0.742556i	$0.733613\pi$
$810$		0			0
$811$			34.9480i			1.22719i	0.789620	+	0.613596i	$0.210277\pi$
$811$			34.9480i			1.22719i	−0.789620	+	0.613596i	$0.789723\pi$
$812$		0			0
$813$	−11.1438	−	11.1438i	−0.390828	−	0.390828i
$814$		0			0
$815$	24.2125	+	22.4661i	0.848128	+	0.786953i
$816$		0			0
$817$	26.3613	+	26.3613i	0.922266	+	0.922266i
$818$		0			0
$819$	1.35505	−	1.29227i	0.0473492	−	0.0451557i
$820$		0			0
$821$	−4.13417			−0.144284			−0.0721418	−	0.997394i	$-0.522983\pi$
$821$	−4.13417			−0.144284			−0.0721418	+	0.997394i	$0.522983\pi$
$822$		0			0
$823$	5.72102	+	5.72102i	0.199422	+	0.199422i	0.799752	−	0.600330i	$-0.204964\pi$
$823$	5.72102	+	5.72102i	0.199422	+	0.199422i	−0.600330	+	0.799752i	$0.704964\pi$
$824$		0			0
$825$	−13.0003	+	15.1064i	−0.452611	+	0.525936i
$826$		0			0
$827$	−17.0630	+	17.0630i	−0.593339	+	0.593339i	−0.938532	−	0.345193i	$-0.887813\pi$
$827$	−17.0630	+	17.0630i	−0.593339	+	0.593339i	0.345193	+	0.938532i	$0.387813\pi$
$828$		0			0
$829$	37.7146			1.30988			0.654940	−	0.755680i	$-0.272694\pi$
$829$	37.7146			1.30988			0.654940	+	0.755680i	$0.272694\pi$
$830$		0			0
$831$		−	6.79913i		−	0.235859i
$832$		0			0
$833$	−11.1787	−	12.2924i	−0.387320	−	0.425908i
$834$		0			0
$835$	−10.7472	−	9.97204i	−0.371923	−	0.345097i
$836$		0			0
$837$	3.49184	−	3.49184i	0.120696	−	0.120696i
$838$		0			0
$839$	22.3652			0.772133			0.386066	−	0.922471i	$-0.373834\pi$
$839$	22.3652			0.772133			0.386066	+	0.922471i	$0.373834\pi$
$840$		0			0
$841$	15.6636			0.540123
$842$		0			0
$843$	−6.82823	+	6.82823i	−0.235177	+	0.235177i
$844$		0			0
$845$	−1.04494	−	27.9294i	−0.0359470	−	0.960799i
$846$		0			0
$847$	0.306586	−	12.9298i	0.0105344	−	0.444272i
$848$		0			0
$849$		−	21.0852i		−	0.723643i
$850$		0			0
$851$	3.01631			0.103398
$852$		0			0
$853$	−24.1276	+	24.1276i	−0.826114	+	0.826114i	−0.986977	−	0.160863i	$-0.948572\pi$
$853$	−24.1276	+	24.1276i	−0.826114	+	0.826114i	0.160863	+	0.986977i	$0.448572\pi$
$854$		0			0
$855$	−0.603474	−	16.1298i	−0.0206384	−	0.551627i
$856$		0			0
$857$	1.53096	+	1.53096i	0.0522968	+	0.0522968i	0.732772	−	0.680475i	$-0.238226\pi$
$857$	1.53096	+	1.53096i	0.0522968	+	0.0522968i	−0.680475	+	0.732772i	$0.738226\pi$
$858$		0			0
$859$	−41.8095			−1.42652			−0.713261	−	0.700899i	$-0.752782\pi$
$859$	−41.8095			−1.42652			−0.713261	+	0.700899i	$0.752782\pi$
$860$		0			0
$861$	14.6123	−	13.9354i	0.497986	−	0.474917i
$862$		0			0
$863$	14.0647	+	14.0647i	0.478770	+	0.478770i	0.904738	−	0.425968i	$-0.140067\pi$
$863$	14.0647	+	14.0647i	0.478770	+	0.478770i	−0.425968	+	0.904738i	$0.640067\pi$
$864$		0			0
$865$	−5.34566	+	5.76121i	−0.181758	+	0.195887i
$866$		0			0
$867$	−8.03695	−	8.03695i	−0.272949	−	0.272949i
$868$		0			0
$869$		−	34.4403i		−	1.16831i
$870$		0			0
$871$		−	0.945011i		−	0.0320205i
$872$		0			0
$873$	−7.43671	+	7.43671i	−0.251694	+	0.251694i
$874$		0			0
$875$	2.61390	+	29.4647i	0.0883660	+	0.996088i
$876$		0			0
$877$	−39.3844	+	39.3844i	−1.32992	+	1.32992i	−0.424477	+	0.905438i	$0.639542\pi$
$877$	−39.3844	+	39.3844i	−1.32992	+	1.32992i	−0.905438	+	0.424477i	$0.860458\pi$
$878$		0			0
$879$			6.77742i			0.228597i
$880$		0			0
$881$		−	25.7205i		−	0.866546i	−0.901263	−	0.433273i	$-0.857359\pi$
$881$		−	25.7205i		−	0.866546i	0.901263	−	0.433273i	$-0.142641\pi$
$882$		0			0
$883$	25.0968	+	25.0968i	0.844574	+	0.844574i	0.989450	−	0.144876i	$-0.0462784\pi$
$883$	25.0968	+	25.0968i	0.844574	+	0.844574i	−0.144876	+	0.989450i	$0.546278\pi$
$884$		0			0
$885$	−9.29219	+	10.0145i	−0.312354	+	0.336635i
$886$		0			0
$887$	−37.8947	−	37.8947i	−1.27238	−	1.27238i	−0.944837	−	0.327541i	$-0.893780\pi$
$887$	−37.8947	−	37.8947i	−1.27238	−	1.27238i	−0.327541	−	0.944837i	$-0.606220\pi$
$888$		0			0
$889$	−15.2055	−	15.9441i	−0.509975	−	0.534748i
$890$		0			0
$891$	3.98602			0.133537
$892$		0			0
$893$	2.20383	+	2.20383i	0.0737484	+	0.0737484i
$894$		0			0
$895$	−1.84849	−	49.4068i	−0.0617882	−	1.65149i
$896$		0			0
$897$	−3.65191	+	3.65191i	−0.121934	+	0.121934i
$898$		0			0
$899$	−18.0339			−0.601464
$900$		0			0
$901$			18.1150i			0.603499i
$902$		0			0
$903$	−0.323910	+	13.6604i	−0.0107790	+	0.454588i
$904$		0			0
$905$	−0.709378	−	18.9604i	−0.0235805	−	0.630265i
$906$		0			0
$907$	30.5961	−	30.5961i	1.01593	−	1.01593i	0.0160555	−	0.999871i	$-0.494889\pi$
$907$	30.5961	−	30.5961i	1.01593	−	1.01593i	0.999871	−	0.0160555i	$-0.00511086\pi$
$908$		0			0
$909$	−6.31633			−0.209499
$910$		0			0
$911$	−20.7843			−0.688614			−0.344307	−	0.938857i	$-0.611886\pi$
$911$	−20.7843			−0.688614			−0.344307	+	0.938857i	$0.611886\pi$
$912$		0			0
$913$	47.7905	−	47.7905i	1.58163	−	1.58163i
$914$		0			0
$915$	11.6551	+	10.8144i	0.385306	+	0.357514i
$916$		0			0
$917$	−49.7643	−	1.17999i	−1.64336	−	0.0389669i
$918$		0			0
$919$			47.6045i			1.57033i	0.619288	+	0.785164i	$0.287421\pi$
$919$			47.6045i			1.57033i	−0.619288	+	0.785164i	$0.712579\pi$
$920$		0			0
$921$	13.9309			0.459038
$922$		0			0
$923$	0.597007	−	0.597007i	0.0196507	−	0.0196507i
$924$		0			0
$925$	1.34809	−	1.56649i	0.0443249	−	0.0515057i
$926$		0			0
$927$	12.5410	+	12.5410i	0.411899	+	0.411899i
$928$		0			0
$929$	−40.6532			−1.33379			−0.666895	−	0.745152i	$-0.732377\pi$
$929$	−40.6532			−1.33379			−0.666895	+	0.745152i	$0.732377\pi$
$930$		0			0
$931$	50.4727	+	2.39493i	1.65418	+	0.0784906i
$932$		0			0
$933$	19.3085	+	19.3085i	0.632132	+	0.632132i
$934$		0			0
$935$	15.5084	+	14.3898i	0.507180	+	0.470598i
$936$		0			0
$937$	8.25994	+	8.25994i	0.269841	+	0.269841i	0.829036	−	0.559195i	$-0.188890\pi$
$937$	8.25994	+	8.25994i	0.269841	+	0.269841i	−0.559195	+	0.829036i	$0.688890\pi$
$938$		0			0
$939$			26.1742i			0.854163i
$940$		0			0
$941$		−	28.7824i		−	0.938281i	−0.883124	−	0.469140i	$-0.844564\pi$
$941$		−	28.7824i		−	0.938281i	0.883124	−	0.469140i	$-0.155436\pi$
$942$		0			0
$943$	−39.3808	+	39.3808i	−1.28242	+	1.28242i
$944$		0			0
$945$	4.12564	−	4.24017i	0.134207	−	0.137933i
$946$		0			0
$947$	−4.26936	+	4.26936i	−0.138736	+	0.138736i	−0.773064	−	0.634328i	$-0.781277\pi$
$947$	−4.26936	+	4.26936i	−0.138736	+	0.138736i	0.634328	+	0.773064i	$0.281277\pi$
$948$		0			0
$949$		−	1.38419i		−	0.0449327i
$950$		0			0
$951$			30.9421i			1.00336i
$952$		0			0
$953$	31.8382	+	31.8382i	1.03134	+	1.03134i	0.999493	+	0.0318472i	$0.0101390\pi$
$953$	31.8382	+	31.8382i	1.03134	+	1.03134i	0.0318472	+	0.999493i	$0.489861\pi$
$954$		0			0
$955$	34.1652	−	1.27825i	1.10556	−	0.0413631i
$956$		0			0
$957$	−10.2931	−	10.2931i	−0.332728	−	0.332728i
$958$		0			0
$959$	2.09676	+	2.19861i	0.0677079	+	0.0709968i
$960$		0			0
$961$	6.61406			0.213357
$962$		0			0
$963$	7.48020	+	7.48020i	0.241046	+	0.241046i
$964$		0			0
$965$	20.6957	+	19.2030i	0.666220	+	0.618166i
$966$		0			0
$967$	17.5518	−	17.5518i	0.564429	−	0.564429i	−0.366134	−	0.930562i	$-0.619319\pi$
$967$	17.5518	−	17.5518i	0.564429	−	0.564429i	0.930562	+	0.366134i	$0.119319\pi$
$968$		0			0
$969$	−17.1339			−0.550421
$970$		0			0
$971$		−	0.0930634i		−	0.00298655i	−0.999999	−	0.00149327i	$-0.999525\pi$
$971$		−	0.0930634i		−	0.00298655i	0.999999	−	0.00149327i	$-0.000475324\pi$
$972$		0			0
$973$	−0.0277487	+	1.17026i	−0.000889582	+	0.0375167i
$974$		0			0
$975$	0.264416	+	3.52873i	0.00846808	+	0.113010i
$976$		0			0
$977$	5.19792	−	5.19792i	0.166296	−	0.166296i	−0.619053	−	0.785349i	$-0.712483\pi$
$977$	5.19792	−	5.19792i	0.166296	−	0.166296i	0.785349	+	0.619053i	$0.212483\pi$
$978$		0			0
$979$	31.1938			0.996959
$980$		0			0
$981$	−0.668223			−0.0213347
$982$		0			0
$983$	−30.3939	+	30.3939i	−0.969415	+	0.969415i	−0.999546	−	0.0301305i	$-0.990408\pi$
$983$	−30.3939	+	30.3939i	−0.969415	+	0.969415i	0.0301305	+	0.999546i	$0.490408\pi$
$984$		0			0
$985$	5.77980	−	6.22909i	0.184160	−	0.198475i
$986$		0			0
$987$	−0.0270792	+	1.14202i	−0.000861939	+	0.0363509i
$988$		0			0
$989$		−	37.6882i		−	1.19842i
$990$		0			0
$991$	−34.2648			−1.08846			−0.544228	−	0.838937i	$-0.683177\pi$
$991$	−34.2648			−1.08846			−0.544228	+	0.838937i	$0.683177\pi$
$992$		0			0
$993$	11.8025	−	11.8025i	0.374542	−	0.374542i
$994$		0			0
$995$	−1.37788	+	0.0515514i	−0.0436817	+	0.00163429i
$996$		0			0
$997$	21.1809	+	21.1809i	0.670805	+	0.670805i	0.957902	−	0.287097i	$-0.0926901\pi$
$997$	21.1809	+	21.1809i	0.670805	+	0.670805i	−0.287097	+	0.957902i	$0.592690\pi$
$998$		0			0
$999$	−0.413339			−0.0130775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.d.433.5		16
4.3	odd	2		105.2.m.a.13.3	✓	16
5.2	odd	4	inner	1680.2.cz.d.97.4		16
7.6	odd	2	inner	1680.2.cz.d.433.4		16
12.11	even	2		315.2.p.e.118.6		16
20.3	even	4		525.2.m.b.307.5		16
20.7	even	4		105.2.m.a.97.4	yes	16
20.19	odd	2		525.2.m.b.118.6		16
28.3	even	6		735.2.v.a.313.3		32
28.11	odd	6		735.2.v.a.313.4		32
28.19	even	6		735.2.v.a.178.6		32
28.23	odd	6		735.2.v.a.178.5		32
28.27	even	2		105.2.m.a.13.4	yes	16
35.27	even	4	inner	1680.2.cz.d.97.5		16
60.47	odd	4		315.2.p.e.307.5		16
84.83	odd	2		315.2.p.e.118.5		16
140.27	odd	4		105.2.m.a.97.3	yes	16
140.47	odd	12		735.2.v.a.472.4		32
140.67	even	12		735.2.v.a.607.6		32
140.83	odd	4		525.2.m.b.307.6		16
140.87	odd	12		735.2.v.a.607.5		32
140.107	even	12		735.2.v.a.472.3		32
140.139	even	2		525.2.m.b.118.5		16
420.167	even	4		315.2.p.e.307.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	4.3	odd	2
105.2.m.a.13.4	yes	16	28.27	even	2
105.2.m.a.97.3	yes	16	140.27	odd	4
105.2.m.a.97.4	yes	16	20.7	even	4
315.2.p.e.118.5		16	84.83	odd	2
315.2.p.e.118.6		16	12.11	even	2
315.2.p.e.307.5		16	60.47	odd	4
315.2.p.e.307.6		16	420.167	even	4
525.2.m.b.118.5		16	140.139	even	2
525.2.m.b.118.6		16	20.19	odd	2
525.2.m.b.307.5		16	20.3	even	4
525.2.m.b.307.6		16	140.83	odd	4
735.2.v.a.178.5		32	28.23	odd	6
735.2.v.a.178.6		32	28.19	even	6
735.2.v.a.313.3		32	28.3	even	6
735.2.v.a.313.4		32	28.11	odd	6
735.2.v.a.472.3		32	140.107	even	12
735.2.v.a.472.4		32	140.47	odd	12
735.2.v.a.607.5		32	140.87	odd	12
735.2.v.a.607.6		32	140.67	even	12
1680.2.cz.d.97.4		16	5.2	odd	4	inner
1680.2.cz.d.97.5		16	35.27	even	4	inner
1680.2.cz.d.433.4		16	7.6	odd	2	inner
1680.2.cz.d.433.5		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23450 + 0.0836010i) q^{5} +(0.0627175 - 2.64501i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-2.23450 + 0.0836010i) q^{5} +(0.0627175 - 2.64501i) q^{7} -1.00000i q^{9} -3.98602 q^{11} +(-0.500437 + 0.500437i) q^{13} +(-1.52092 + 1.63915i) q^{15} +(1.67840 + 1.67840i) q^{17} -7.21850 q^{19} +(-1.82596 - 1.91465i) q^{21} +(5.16007 + 5.16007i) q^{23} +(4.98602 - 0.373614i) q^{25} +(-0.707107 - 0.707107i) q^{27} +3.65191i q^{29} +4.93821i q^{31} +(-2.81854 + 2.81854i) q^{33} +(0.0809828 + 5.91553i) q^{35} +(0.292275 - 0.292275i) q^{37} +0.707725i q^{39} +7.63184i q^{41} +(-3.65191 - 3.65191i) q^{43} +(0.0836010 + 2.23450i) q^{45} +(-0.305303 - 0.305303i) q^{47} +(-6.99213 - 0.331777i) q^{49} +2.37361 q^{51} +(5.39653 + 5.39653i) q^{53} +(8.90678 - 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +6.10959 q^{59} -7.11047i q^{61} +(-2.64501 - 0.0627175i) q^{63} +(1.07639 - 1.16007i) q^{65} +(-0.944185 + 0.944185i) q^{67} +7.29744 q^{69} -1.19297 q^{71} +(-1.38298 + 1.38298i) q^{73} +(3.26147 - 3.78983i) q^{75} +(-0.249993 + 10.5431i) q^{77} +8.64027i q^{79} -1.00000 q^{81} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(2.58229 + 2.58229i) q^{87} -7.82581 q^{89} +(1.29227 + 1.35505i) q^{91} +(3.49184 + 3.49184i) q^{93} +(16.1298 - 0.603474i) q^{95} +(-7.43671 - 7.43671i) q^{97} +3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

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