LMFDB - Embedded newform 1680.2.cz.a.433.4

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.4
Root			$-1.69230i$ of defining polynomial
Character	$\chi$	$=$	1680.433
Dual form			1680.2.cz.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.19663 + 1.88893i) q^{5} +(-0.510472 - 2.59604i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(1.19663 + 1.88893i) q^{5} +(-0.510472 - 2.59604i) q^{7} -1.00000i q^{9} -4.79881 q^{11} +(0.585786 - 0.585786i) q^{13} +(2.18183 + 0.489528i) q^{15} +(-4.10651 - 4.10651i) q^{17} +2.36365 q^{19} +(-2.19663 - 1.47472i) q^{21} +(-2.97906 - 2.97906i) q^{23} +(-2.13613 + 4.52072i) q^{25} +(-0.707107 - 0.707107i) q^{27} -9.94900i q^{29} -3.02094i q^{31} +(-3.39327 + 3.39327i) q^{33} +(4.29289 - 4.07076i) q^{35} +(-6.10651 + 6.10651i) q^{37} -0.828427i q^{39} -10.9996i q^{41} +(5.74825 + 5.74825i) q^{43} +(1.88893 - 1.19663i) q^{45} +(-0.363651 - 0.363651i) q^{47} +(-6.47884 + 2.65041i) q^{49} -5.80748 q^{51} +(2.36365 + 2.36365i) q^{53} +(-5.74242 - 9.06462i) q^{55} +(1.67135 - 1.67135i) q^{57} +2.07912 q^{59} -5.55573i q^{61} +(-2.59604 + 0.510472i) q^{63} +(1.80748 + 0.405538i) q^{65} +(0.979056 - 0.979056i) q^{67} -4.21302 q^{69} -5.25132 q^{71} +(6.11519 - 6.11519i) q^{73} +(1.68616 + 4.70711i) q^{75} +(2.44966 + 12.4579i) q^{77} +5.10069i q^{79} -1.00000 q^{81} +(3.22170 - 3.22170i) q^{83} +(2.84293 - 12.6709i) q^{85} +(-7.03500 - 7.03500i) q^{87} +11.8989 q^{89} +(-1.81975 - 1.22170i) q^{91} +(-2.13613 - 2.13613i) q^{93} +(2.82843 + 4.46478i) q^{95} +(8.05595 + 8.05595i) q^{97} +4.79881i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 16 q^{23} - 4 q^{25} - 8 q^{33} + 40 q^{35} - 28 q^{37} - 4 q^{45} + 24 q^{47} - 4 q^{49} - 16 q^{51} - 8 q^{53} + 28 q^{55} - 4 q^{57} + 8 q^{59} + 4 q^{63} - 16 q^{65} + 8 q^{69} - 8 q^{71} + 28 q^{73} + 44 q^{77} - 8 q^{81} - 16 q^{83} + 28 q^{85} - 12 q^{87} + 64 q^{89} + 8 q^{91} - 4 q^{93} + 28 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 16 * q^23 - 4 * q^25 - 8 * q^33 + 40 * q^35 - 28 * q^37 - 4 * q^45 + 24 * q^47 - 4 * q^49 - 16 * q^51 - 8 * q^53 + 28 * q^55 - 4 * q^57 + 8 * q^59 + 4 * q^63 - 16 * q^65 + 8 * q^69 - 8 * q^71 + 28 * q^73 + 44 * q^77 - 8 * q^81 - 16 * q^83 + 28 * q^85 - 12 * q^87 + 64 * q^89 + 8 * q^91 - 4 * q^93 + 28 * q^97

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
$5$	1.19663	+	1.88893i	0.535151	+	0.844756i
$5$	1.19663	+	1.88893i	0.535151	+	0.844756i
$6$		0			0
$7$	−0.510472	−	2.59604i	−0.192940	−	0.981211i
$7$	−0.510472	−	2.59604i	−0.192940	−	0.981211i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−4.79881			−1.44690			−0.723448	−	0.690379i	$-0.757444\pi$
$11$	−4.79881			−1.44690			−0.723448	+	0.690379i	$0.757444\pi$
$12$		0			0
$13$	0.585786	−	0.585786i	0.162468	−	0.162468i	−0.621191	−	0.783659i	$-0.713351\pi$
$13$	0.585786	−	0.585786i	0.162468	−	0.162468i	0.783659	+	0.621191i	$0.213351\pi$
$14$		0			0
$15$	2.18183	+	0.489528i	0.563345	+	0.126396i
$16$		0			0
$17$	−4.10651	−	4.10651i	−0.995975	−	0.995975i	0.00401675	−	0.999992i	$-0.498721\pi$
$17$	−4.10651	−	4.10651i	−0.995975	−	0.995975i	−0.999992	+	0.00401675i	$0.998721\pi$
$18$		0			0
$19$	2.36365			0.542259			0.271129	−	0.962543i	$-0.412603\pi$
$19$	2.36365			0.542259			0.271129	+	0.962543i	$0.412603\pi$
$20$		0			0
$21$	−2.19663	−	1.47472i	−0.479345	−	0.321810i
$22$		0			0
$23$	−2.97906	−	2.97906i	−0.621176	−	0.621176i	0.324656	−	0.945832i	$-0.394751\pi$
$23$	−2.97906	−	2.97906i	−0.621176	−	0.621176i	−0.945832	+	0.324656i	$0.894751\pi$
$24$		0			0
$25$	−2.13613	+	4.52072i	−0.427226	+	0.904145i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	9.94900i		−	1.84748i	−0.383017	−	0.923741i	$-0.625115\pi$
$29$		−	9.94900i		−	1.84748i	0.383017	−	0.923741i	$-0.374885\pi$
$30$		0			0
$31$		−	3.02094i		−	0.542578i	−0.962498	−	0.271289i	$-0.912550\pi$
$31$		−	3.02094i		−	0.542578i	0.962498	−	0.271289i	$-0.0874498\pi$
$32$		0			0
$33$	−3.39327	+	3.39327i	−0.590692	+	0.590692i
$34$		0			0
$35$	4.29289	−	4.07076i	0.725631	−	0.688084i
$36$		0			0
$37$	−6.10651	+	6.10651i	−1.00390	+	1.00390i	−0.00391185	+	0.999992i	$0.501245\pi$
$37$	−6.10651	+	6.10651i	−1.00390	+	1.00390i	−0.999992	+	0.00391185i	$0.998755\pi$
$38$		0			0
$39$		−	0.828427i		−	0.132655i
$40$		0			0
$41$		−	10.9996i		−	1.71784i	−0.512107	−	0.858921i	$-0.671135\pi$
$41$		−	10.9996i		−	1.71784i	0.512107	−	0.858921i	$-0.328865\pi$
$42$		0			0
$43$	5.74825	+	5.74825i	0.876599	+	0.876599i	0.993181	−	0.116582i	$-0.0371937\pi$
$43$	5.74825	+	5.74825i	0.876599	+	0.876599i	−0.116582	+	0.993181i	$0.537194\pi$
$44$		0			0
$45$	1.88893	−	1.19663i	0.281585	−	0.178384i
$46$		0			0
$47$	−0.363651	−	0.363651i	−0.0530439	−	0.0530439i	0.680087	−	0.733131i	$-0.261942\pi$
$47$	−0.363651	−	0.363651i	−0.0530439	−	0.0530439i	−0.733131	+	0.680087i	$0.761942\pi$
$48$		0			0
$49$	−6.47884	+	2.65041i	−0.925548	+	0.378630i
$50$		0			0
$51$	−5.80748			−0.813210
$52$		0			0
$53$	2.36365	+	2.36365i	0.324672	+	0.324672i	0.850556	−	0.525884i	$-0.176265\pi$
$53$	2.36365	+	2.36365i	0.324672	+	0.324672i	−0.525884	+	0.850556i	$0.676265\pi$
$54$		0			0
$55$	−5.74242	−	9.06462i	−0.774308	−	1.22227i
$56$		0			0
$57$	1.67135	−	1.67135i	0.221376	−	0.221376i
$58$		0			0
$59$	2.07912			0.270679			0.135339	−	0.990799i	$-0.456788\pi$
$59$	2.07912			0.270679			0.135339	+	0.990799i	$0.456788\pi$
$60$		0			0
$61$		−	5.55573i		−	0.711338i	−0.934612	−	0.355669i	$-0.884253\pi$
$61$		−	5.55573i		−	0.711338i	0.934612	−	0.355669i	$-0.115747\pi$
$62$		0			0
$63$	−2.59604	+	0.510472i	−0.327070	+	0.0643134i
$64$		0			0
$65$	1.80748	+	0.405538i	0.224191	+	0.0503008i
$66$		0			0
$67$	0.979056	−	0.979056i	0.119611	−	0.119611i	−0.644768	−	0.764379i	$-0.723046\pi$
$67$	0.979056	−	0.979056i	0.119611	−	0.119611i	0.764379	+	0.644768i	$0.223046\pi$
$68$		0			0
$69$	−4.21302			−0.507188
$70$		0			0
$71$	−5.25132			−0.623217			−0.311608	−	0.950211i	$-0.600868\pi$
$71$	−5.25132			−0.623217			−0.311608	+	0.950211i	$0.600868\pi$
$72$		0			0
$73$	6.11519	−	6.11519i	0.715728	−	0.715728i	−0.251999	−	0.967727i	$-0.581088\pi$
$73$	6.11519	−	6.11519i	0.715728	−	0.715728i	0.967727	+	0.251999i	$0.0810880\pi$
$74$		0			0
$75$	1.68616	+	4.70711i	0.194701	+	0.543530i
$76$		0			0
$77$	2.44966	+	12.4579i	0.279164	+	1.41971i
$78$		0			0
$79$			5.10069i			0.573872i	0.957950	+	0.286936i	$0.0926367\pi$
$79$			5.10069i			0.573872i	−0.957950	+	0.286936i	$0.907363\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	3.22170	−	3.22170i	0.353627	−	0.353627i	−0.507830	−	0.861457i	$-0.669552\pi$
$83$	3.22170	−	3.22170i	0.353627	−	0.353627i	0.861457	+	0.507830i	$0.169552\pi$
$84$		0			0
$85$	2.84293	−	12.6709i	0.308359	−	1.37435i
$86$		0			0
$87$	−7.03500	−	7.03500i	−0.754232	−	0.754232i
$88$		0			0
$89$	11.8989			1.26128			0.630639	−	0.776076i	$-0.282793\pi$
$89$	11.8989			1.26128			0.630639	+	0.776076i	$0.282793\pi$
$90$		0			0
$91$	−1.81975	−	1.22170i	−0.190762	−	0.128069i
$92$		0			0
$93$	−2.13613	−	2.13613i	−0.221506	−	0.221506i
$94$		0			0
$95$	2.82843	+	4.46478i	0.290191	+	0.458076i
$96$		0			0
$97$	8.05595	+	8.05595i	0.817958	+	0.817958i	0.985812	−	0.167854i	$-0.0536838\pi$
$97$	8.05595	+	8.05595i	0.817958	+	0.817958i	−0.167854	+	0.985812i	$0.553684\pi$
$98$		0			0
$99$			4.79881i			0.482298i
$100$		0			0
$101$		−	4.89020i		−	0.486593i	−0.969952	−	0.243297i	$-0.921771\pi$
$101$		−	4.89020i		−	0.486593i	0.969952	−	0.243297i	$-0.0782288\pi$
$102$		0			0
$103$	−1.06462	+	1.06462i	−0.104900	+	0.104900i	−0.757609	−	0.652709i	$-0.773633\pi$
$103$	−1.06462	+	1.06462i	−0.104900	+	0.104900i	0.652709	+	0.757609i	$0.273633\pi$
$104$		0			0
$105$	0.157074	−	5.91399i	0.0153288	−	0.577147i
$106$		0			0
$107$	−2.15063	+	2.15063i	−0.207909	+	0.207909i	−0.803378	−	0.595469i	$-0.796966\pi$
$107$	−2.15063	+	2.15063i	−0.207909	+	0.207909i	0.595469	+	0.803378i	$0.296966\pi$
$108$		0			0
$109$			12.8984i			1.23545i	0.786396	+	0.617723i	$0.211945\pi$
$109$			12.8984i			1.23545i	−0.786396	+	0.617723i	$0.788055\pi$
$110$		0			0
$111$			8.63591i			0.819684i
$112$		0			0
$113$	−11.5853	−	11.5853i	−1.08986	−	1.08986i	−0.995542	−	0.0943155i	$-0.969934\pi$
$113$	−11.5853	−	11.5853i	−1.08986	−	1.08986i	−0.0943155	−	0.995542i	$-0.530066\pi$
$114$		0			0
$115$	2.06239	−	9.19208i	0.192319	−	0.857166i
$116$		0			0
$117$	−0.585786	−	0.585786i	−0.0541560	−	0.0541560i
$118$		0			0
$119$	−8.56440	+	12.7569i	−0.785098	+	1.16943i
$120$		0			0
$121$	12.0286			1.09351
$122$		0			0
$123$	−7.77786	−	7.77786i	−0.701306	−	0.701306i
$124$		0			0
$125$	−11.0955	+	1.37465i	−0.992413	+	0.122953i
$126$		0			0
$127$	−0.399714	+	0.399714i	−0.0354689	+	0.0354689i	−0.724619	−	0.689150i	$-0.757984\pi$
$127$	−0.399714	+	0.399714i	−0.0354689	+	0.0354689i	0.689150	+	0.724619i	$0.257984\pi$
$128$		0			0
$129$	8.12925			0.715740
$130$		0			0
$131$		−	22.2039i		−	1.93996i	−0.243176	−	0.969982i	$-0.578189\pi$
$131$		−	22.2039i		−	1.93996i	0.243176	−	0.969982i	$-0.421811\pi$
$132$		0			0
$133$	−1.20658	−	6.13613i	−0.104624	−	0.532070i
$134$		0			0
$135$	0.489528	−	2.18183i	0.0421319	−	0.187782i
$136$		0			0
$137$	−5.92849	+	5.92849i	−0.506505	+	0.506505i	−0.913452	−	0.406947i	$-0.866594\pi$
$137$	−5.92849	+	5.92849i	−0.506505	+	0.506505i	0.406947	+	0.913452i	$0.366594\pi$
$138$		0			0
$139$	8.46478			0.717973			0.358986	−	0.933343i	$-0.383122\pi$
$139$	8.46478			0.717973			0.358986	+	0.933343i	$0.383122\pi$
$140$		0			0
$141$	−0.514280			−0.0433102
$142$		0			0
$143$	−2.81108	+	2.81108i	−0.235074	+	0.235074i
$144$		0			0
$145$	18.7930	−	11.9053i	1.56067	−	0.988683i
$146$		0			0
$147$	−2.70711	+	6.45535i	−0.223278	+	0.532428i
$148$		0			0
$149$			4.43516i			0.363342i	0.983359	+	0.181671i	$0.0581506\pi$
$149$			4.43516i			0.363342i	−0.983359	+	0.181671i	$0.941849\pi$
$150$		0			0
$151$	−7.61497			−0.619697			−0.309849	−	0.950786i	$-0.600278\pi$
$151$	−7.61497			−0.619697			−0.309849	+	0.950786i	$0.600278\pi$
$152$		0			0
$153$	−4.10651	+	4.10651i	−0.331992	+	0.331992i
$154$		0			0
$155$	5.70636	−	3.61497i	0.458346	−	0.290361i
$156$		0			0
$157$	−6.30188	−	6.30188i	−0.502945	−	0.502945i	0.409407	−	0.912352i	$-0.365736\pi$
$157$	−6.30188	−	6.30188i	−0.502945	−	0.502945i	−0.912352	+	0.409407i	$0.865736\pi$
$158$		0			0
$159$	3.34271			0.265094
$160$		0			0
$161$	−6.21302	+	9.25447i	−0.489655	+	0.729354i
$162$		0			0
$163$	−10.8489	−	10.8489i	−0.849754	−	0.849754i	0.140348	−	0.990102i	$-0.455178\pi$
$163$	−10.8489	−	10.8489i	−0.849754	−	0.849754i	−0.990102	+	0.140348i	$0.955178\pi$
$164$		0			0
$165$	−10.4702	−	2.34915i	−0.815101	−	0.182881i
$166$		0			0
$167$	−5.63635	−	5.63635i	−0.436154	−	0.436154i	0.454562	−	0.890715i	$-0.349796\pi$
$167$	−5.63635	−	5.63635i	−0.436154	−	0.436154i	−0.890715	+	0.454562i	$0.849796\pi$
$168$		0			0
$169$			12.3137i			0.947208i
$170$		0			0
$171$		−	2.36365i		−	0.180753i
$172$		0			0
$173$	−12.6923	+	12.6923i	−0.964977	+	0.964977i	−0.999407	−	0.0344296i	$-0.989039\pi$
$173$	−12.6923	+	12.6923i	−0.964977	+	0.964977i	0.0344296	+	0.999407i	$0.489039\pi$
$174$		0			0
$175$	12.8264	+	3.23777i	0.969586	+	0.244753i
$176$		0			0
$177$	1.47016	−	1.47016i	0.110504	−	0.110504i
$178$		0			0
$179$		−	5.72836i		−	0.428158i	−0.976816	−	0.214079i	$-0.931325\pi$
$179$		−	5.72836i		−	0.428158i	0.976816	−	0.214079i	$-0.0686750\pi$
$180$		0			0
$181$		−	8.91220i		−	0.662439i	−0.943554	−	0.331219i	$-0.892540\pi$
$181$		−	8.91220i		−	0.662439i	0.943554	−	0.331219i	$-0.107460\pi$
$182$		0			0
$183$	−3.92849	−	3.92849i	−0.290403	−	0.290403i
$184$		0			0
$185$	−18.8420	−	4.22752i	−1.38530	−	0.310814i
$186$		0			0
$187$	19.7064	+	19.7064i	1.44107	+	1.44107i
$188$		0			0
$189$	−1.47472	+	2.19663i	−0.107270	+	0.159782i
$190$		0			0
$191$	7.67824			0.555578			0.277789	−	0.960642i	$-0.410398\pi$
$191$	7.67824			0.555578			0.277789	+	0.960642i	$0.410398\pi$
$192$		0			0
$193$	−4.59762	−	4.59762i	−0.330944	−	0.330944i	0.522001	−	0.852945i	$-0.325186\pi$
$193$	−4.59762	−	4.59762i	−0.330944	−	0.330944i	−0.852945	+	0.522001i	$0.825186\pi$
$194$		0			0
$195$	1.56484	−	0.991325i	0.112061	−	0.0709902i
$196$		0			0
$197$	−5.25132	+	5.25132i	−0.374141	+	0.374141i	−0.868983	−	0.494842i	$-0.835226\pi$
$197$	−5.25132	+	5.25132i	−0.374141	+	0.374141i	0.494842	+	0.868983i	$0.335226\pi$
$198$		0			0
$199$	−4.12163			−0.292175			−0.146087	−	0.989272i	$-0.546668\pi$
$199$	−4.12163			−0.292175			−0.146087	+	0.989272i	$0.546668\pi$
$200$		0			0
$201$		−	1.38459i		−	0.0976618i
$202$		0			0
$203$	−25.8280	+	5.07868i	−1.81277	+	0.356454i
$204$		0			0
$205$	20.7774	−	13.1625i	1.45116	−	0.919306i
$206$		0			0
$207$	−2.97906	+	2.97906i	−0.207059	+	0.207059i
$208$		0			0
$209$	−11.3427			−0.784591
$210$		0			0
$211$	27.6560			1.90392			0.951958	−	0.306229i	$-0.0990672\pi$
$211$	27.6560			1.90392			0.951958	+	0.306229i	$0.0990672\pi$
$212$		0			0
$213$	−3.71324	+	3.71324i	−0.254427	+	0.254427i
$214$		0			0
$215$	−3.97949	+	17.7366i	−0.271399	+	1.20963i
$216$		0			0
$217$	−7.84249	+	1.54211i	−0.532383	+	0.104685i
$218$		0			0
$219$		−	8.64818i		−	0.584390i
$220$		0			0
$221$	−4.81108			−0.323628
$222$		0			0
$223$	−15.3271	+	15.3271i	−1.02638	+	1.02638i	−0.0267394	+	0.999642i	$0.508512\pi$
$223$	−15.3271	+	15.3271i	−1.02638	+	1.02638i	−0.999642	+	0.0267394i	$0.991488\pi$
$224$		0			0
$225$	4.52072	+	2.13613i	0.301382	+	0.142409i
$226$		0			0
$227$	18.8984	+	18.8984i	1.25433	+	1.25433i	0.953758	+	0.300575i	$0.0971786\pi$
$227$	18.8984	+	18.8984i	1.25433	+	1.25433i	0.300575	+	0.953758i	$0.402821\pi$
$228$		0			0
$229$	−13.3137			−0.879795			−0.439897	−	0.898048i	$-0.644985\pi$
$229$	−13.3137			−0.879795			−0.439897	+	0.898048i	$0.644985\pi$
$230$		0			0
$231$	10.5412	+	7.07689i	0.693562	+	0.465625i
$232$		0			0
$233$	7.35498	+	7.35498i	0.481840	+	0.481840i	0.905719	−	0.423879i	$-0.139332\pi$
$233$	7.35498	+	7.35498i	0.481840	+	0.481840i	−0.423879	+	0.905719i	$0.639332\pi$
$234$		0			0
$235$	0.251755	−	1.12207i	0.0164227	−	0.0731957i
$236$		0			0
$237$	3.60673	+	3.60673i	0.234282	+	0.234282i
$238$		0			0
$239$		−	13.0491i		−	0.844074i	−0.906579	−	0.422037i	$-0.861315\pi$
$239$		−	13.0491i		−	0.844074i	0.906579	−	0.422037i	$-0.138685\pi$
$240$		0			0
$241$			24.4542i			1.57523i	0.616167	+	0.787616i	$0.288685\pi$
$241$			24.4542i			1.57523i	−0.616167	+	0.787616i	$0.711315\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−12.7592	−	9.06651i	−0.815158	−	0.579238i
$246$		0			0
$247$	1.38459	−	1.38459i	0.0880996	−	0.0880996i
$248$		0			0
$249$		−	4.55617i		−	0.288735i
$250$		0			0
$251$			4.32326i			0.272882i	0.990648	+	0.136441i	$0.0435664\pi$
$251$			4.32326i			0.272882i	−0.990648	+	0.136441i	$0.956434\pi$
$252$		0			0
$253$	14.2959	+	14.2959i	0.898777	+	0.898777i
$254$		0			0
$255$	−6.94944	−	10.9699i	−0.435191	−	0.686964i
$256$		0			0
$257$	5.06418	+	5.06418i	0.315895	+	0.315895i	0.847188	−	0.531293i	$-0.178294\pi$
$257$	5.06418	+	5.06418i	0.315895	+	0.315895i	−0.531293	+	0.847188i	$0.678294\pi$
$258$		0			0
$259$	18.9699	+	12.7355i	1.17873	+	0.791348i
$260$		0			0
$261$	−9.94900			−0.615828
$262$		0			0
$263$	4.17113	+	4.17113i	0.257203	+	0.257203i	0.823916	−	0.566712i	$-0.191785\pi$
$263$	4.17113	+	4.17113i	0.257203	+	0.257203i	−0.566712	+	0.823916i	$0.691785\pi$
$264$		0			0
$265$	−1.63635	+	7.29320i	−0.100520	+	0.448018i
$266$		0			0
$267$	8.41377	−	8.41377i	0.514915	−	0.514915i
$268$		0			0
$269$	24.7484			1.50894			0.754469	−	0.656336i	$-0.227894\pi$
$269$	24.7484			1.50894			0.754469	+	0.656336i	$0.227894\pi$
$270$		0			0
$271$		−	21.9960i		−	1.33616i	−0.744089	−	0.668080i	$-0.767116\pi$
$271$		−	21.9960i		−	1.33616i	0.744089	−	0.668080i	$-0.232884\pi$
$272$		0			0
$273$	−2.15063	+	0.422889i	−0.130162	+	0.0255944i
$274$		0			0
$275$	10.2509	−	21.6941i	0.618151	−	1.30820i
$276$		0			0
$277$	12.0646	−	12.0646i	0.724893	−	0.724893i	−0.244705	−	0.969598i	$-0.578691\pi$
$277$	12.0646	−	12.0646i	0.724893	−	0.724893i	0.969598	+	0.244705i	$0.0786910\pi$
$278$		0			0
$279$	−3.02094			−0.180859
$280$		0			0
$281$	14.3668			0.857052			0.428526	−	0.903530i	$-0.359033\pi$
$281$	14.3668			0.857052			0.428526	+	0.903530i	$0.359033\pi$
$282$		0			0
$283$	11.0833	−	11.0833i	0.658836	−	0.658836i	−0.296269	−	0.955105i	$-0.595742\pi$
$283$	11.0833	−	11.0833i	0.658836	−	0.658836i	0.955105	+	0.296269i	$0.0957424\pi$
$284$		0			0
$285$	5.15707	+	1.15707i	0.305479	+	0.0685391i
$286$		0			0
$287$	−28.5553	+	5.61497i	−1.68557	+	0.331441i
$288$		0			0
$289$			16.7269i			0.983933i
$290$		0			0
$291$	11.3928			0.667860
$292$		0			0
$293$	6.35827	−	6.35827i	0.371454	−	0.371454i	−0.496553	−	0.868007i	$-0.665401\pi$
$293$	6.35827	−	6.35827i	0.371454	−	0.371454i	0.868007	+	0.496553i	$0.165401\pi$
$294$		0			0
$295$	2.48795	+	3.92732i	0.144854	+	0.228658i
$296$		0			0
$297$	3.39327	+	3.39327i	0.196897	+	0.196897i
$298$		0			0
$299$	−3.49018			−0.201842
$300$		0			0
$301$	11.9884	−	17.8570i	0.690997	−	1.02926i
$302$		0			0
$303$	−3.45789	−	3.45789i	−0.198651	−	0.198651i
$304$		0			0
$305$	10.4944	−	6.64818i	0.600907	−	0.380674i
$306$		0			0
$307$	−16.8663	−	16.8663i	−0.962610	−	0.962610i	0.0367161	−	0.999326i	$-0.488310\pi$
$307$	−16.8663	−	16.8663i	−0.962610	−	0.962610i	−0.999326	+	0.0367161i	$0.988310\pi$
$308$		0			0
$309$			1.50560i			0.0856509i
$310$		0			0
$311$			0.0592379i			0.00335907i	0.999999	+	0.00167954i	$0.000534613\pi$
$311$			0.0592379i			0.00335907i	−0.999999	+	0.00167954i	$0.999465\pi$
$312$		0			0
$313$	−0.458332	+	0.458332i	−0.0259064	+	0.0259064i	−0.719941	−	0.694035i	$-0.755831\pi$
$313$	−0.458332	+	0.458332i	−0.0259064	+	0.0259064i	0.694035	+	0.719941i	$0.255831\pi$
$314$		0			0
$315$	−4.07076	−	4.29289i	−0.229361	−	0.241877i
$316$		0			0
$317$	13.1130	−	13.1130i	0.736497	−	0.736497i	−0.235401	−	0.971898i	$-0.575640\pi$
$317$	13.1130	−	13.1130i	0.736497	−	0.736497i	0.971898	+	0.235401i	$0.0756404\pi$
$318$		0			0
$319$			47.7433i			2.67311i
$320$		0			0
$321$			3.04145i			0.169757i
$322$		0			0
$323$	−9.70636	−	9.70636i	−0.540076	−	0.540076i
$324$		0			0
$325$	1.39686	+	3.89949i	0.0774840	+	0.216305i
$326$		0			0
$327$	9.12057	+	9.12057i	0.504369	+	0.504369i
$328$		0			0
$329$	−0.758418	+	1.12969i	−0.0418130	+	0.0622816i
$330$		0			0
$331$	25.1288			1.38120			0.690602	−	0.723235i	$-0.257346\pi$
$331$	25.1288			1.38120			0.690602	+	0.723235i	$0.257346\pi$
$332$		0			0
$333$	6.10651	+	6.10651i	0.334635	+	0.334635i
$334$		0			0
$335$	3.02094	+	0.677798i	0.165052	+	0.0370321i
$336$		0			0
$337$	16.5976	−	16.5976i	0.904130	−	0.904130i	−0.0916605	−	0.995790i	$-0.529217\pi$
$337$	16.5976	−	16.5976i	0.904130	−	0.904130i	0.995790	+	0.0916605i	$0.0292175\pi$
$338$		0			0
$339$	−16.3842			−0.889865
$340$		0			0
$341$			14.4969i			0.785053i
$342$		0			0
$343$	10.1878	+	15.4664i	0.550091	+	0.835105i
$344$		0			0
$345$	−5.04145	−	7.95811i	−0.271422	−	0.428450i
$346$		0			0
$347$	−14.4214	+	14.4214i	−0.774181	+	0.774181i	−0.978834	−	0.204654i	$-0.934393\pi$
$347$	−14.4214	+	14.4214i	−0.774181	+	0.774181i	0.204654	+	0.978834i	$0.434393\pi$
$348$		0			0
$349$	28.6672			1.53452			0.767260	−	0.641337i	$-0.221620\pi$
$349$	28.6672			1.53452			0.767260	+	0.641337i	$0.221620\pi$
$350$		0			0
$351$	−0.828427			−0.0442182
$352$		0			0
$353$	−5.06506	+	5.06506i	−0.269586	+	0.269586i	−0.828933	−	0.559347i	$-0.811052\pi$
$353$	−5.06506	+	5.06506i	−0.269586	+	0.269586i	0.559347	+	0.828933i	$0.311052\pi$
$354$		0			0
$355$	−6.28391	−	9.91938i	−0.333515	−	0.526466i
$356$		0			0
$357$	2.96456	+	15.0765i	0.156901	+	0.797931i
$358$		0			0
$359$			8.46478i			0.446754i	0.974732	+	0.223377i	$0.0717081\pi$
$359$			8.46478i			0.446754i	−0.974732	+	0.223377i	$0.928292\pi$
$360$		0			0
$361$	−13.4132			−0.705956
$362$		0			0
$363$	8.50548	−	8.50548i	0.446422	−	0.446422i
$364$		0			0
$365$	18.8688	+	4.23353i	0.987639	+	0.221593i
$366$		0			0
$367$	18.1685	+	18.1685i	0.948386	+	0.948386i	0.998732	−	0.0503457i	$-0.0160323\pi$
$367$	18.1685	+	18.1685i	0.948386	+	0.948386i	−0.0503457	+	0.998732i	$0.516032\pi$
$368$		0			0
$369$	−10.9996			−0.572614
$370$		0			0
$371$	4.92955	−	7.34271i	0.255930	−	0.381214i
$372$		0			0
$373$	−15.4492	−	15.4492i	−0.799930	−	0.799930i	0.183154	−	0.983084i	$-0.441369\pi$
$373$	−15.4492	−	15.4492i	−0.799930	−	0.799930i	−0.983084	+	0.183154i	$0.941369\pi$
$374$		0			0
$375$	−6.87368	+	8.81774i	−0.354956	+	0.455346i
$376$		0			0
$377$	−5.82799	−	5.82799i	−0.300157	−	0.300157i
$378$		0			0
$379$		−	32.3833i		−	1.66342i	−0.555212	−	0.831709i	$-0.687363\pi$
$379$		−	32.3833i		−	1.66342i	0.555212	−	0.831709i	$-0.312637\pi$
$380$		0			0
$381$			0.565281i			0.0289602i
$382$		0			0
$383$	−16.1916	+	16.1916i	−0.827354	+	0.827354i	−0.987150	−	0.159796i	$-0.948916\pi$
$383$	−16.1916	+	16.1916i	−0.827354	+	0.827354i	0.159796	+	0.987150i	$0.448916\pi$
$384$		0			0
$385$	−20.6008	+	19.5348i	−1.04991	+	0.995585i
$386$		0			0
$387$	5.74825	−	5.74825i	0.292200	−	0.292200i
$388$		0			0
$389$			12.0091i			0.608886i	0.952531	+	0.304443i	$0.0984704\pi$
$389$			12.0091i			0.608886i	−0.952531	+	0.304443i	$0.901530\pi$
$390$		0			0
$391$			24.4671i			1.23735i
$392$		0			0
$393$	−15.7005	−	15.7005i	−0.791987	−	0.791987i
$394$		0			0
$395$	−9.63485	+	6.10366i	−0.484782	+	0.307108i
$396$		0			0
$397$	2.62680	+	2.62680i	0.131835	+	0.131835i	0.769945	−	0.638110i	$-0.220284\pi$
$397$	2.62680	+	2.62680i	0.131835	+	0.131835i	−0.638110	+	0.769945i	$0.720284\pi$
$398$		0			0
$399$	−5.19208	−	3.48572i	−0.259929	−	0.174504i
$400$		0			0
$401$	19.7571			0.986623			0.493311	−	0.869853i	$-0.335786\pi$
$401$	19.7571			0.986623			0.493311	+	0.869853i	$0.335786\pi$
$402$		0			0
$403$	−1.76963	−	1.76963i	−0.0881514	−	0.0881514i
$404$		0			0
$405$	−1.19663	−	1.88893i	−0.0594613	−	0.0938618i
$406$		0			0
$407$	29.3040	−	29.3040i	1.45254	−	1.45254i
$408$		0			0
$409$	15.3846			0.760719			0.380360	−	0.924839i	$-0.375800\pi$
$409$	15.3846			0.760719			0.380360	+	0.924839i	$0.375800\pi$
$410$		0			0
$411$			8.38416i			0.413560i
$412$		0			0
$413$	−1.06133	−	5.39748i	−0.0522248	−	0.265593i
$414$		0			0
$415$	9.94076	+	2.23037i	0.487973	+	0.109485i
$416$		0			0
$417$	5.98550	−	5.98550i	0.293111	−	0.293111i
$418$		0			0
$419$	28.0782			1.37171			0.685856	−	0.727737i	$-0.259428\pi$
$419$	28.0782			1.37171			0.685856	+	0.727737i	$0.259428\pi$
$420$		0			0
$421$	11.4836			0.559677			0.279838	−	0.960047i	$-0.409719\pi$
$421$	11.4836			0.559677			0.279838	+	0.960047i	$0.409719\pi$
$422$		0			0
$423$	−0.363651	+	0.363651i	−0.0176813	+	0.0176813i
$424$		0			0
$425$	27.3364	−	9.79236i	1.32601	−	0.474999i
$426$		0			0
$427$	−14.4229	+	2.83604i	−0.697973	+	0.137246i
$428$		0			0
$429$			3.97546i			0.191937i
$430$		0			0
$431$	−11.3330			−0.545890			−0.272945	−	0.962030i	$-0.587998\pi$
$431$	−11.3330			−0.545890			−0.272945	+	0.962030i	$0.587998\pi$
$432$		0			0
$433$	−4.91337	+	4.91337i	−0.236122	+	0.236122i	−0.815242	−	0.579120i	$-0.803396\pi$
$433$	−4.91337	+	4.91337i	−0.236122	+	0.236122i	0.579120	+	0.815242i	$0.303396\pi$
$434$		0			0
$435$	4.87031	−	21.7070i	0.233514	−	1.04077i
$436$		0			0
$437$	−7.04145	−	7.04145i	−0.336838	−	0.336838i
$438$		0			0
$439$	−22.7723			−1.08686			−0.543432	−	0.839453i	$-0.682876\pi$
$439$	−22.7723			−1.08686			−0.543432	+	0.839453i	$0.682876\pi$
$440$		0			0
$441$	2.65041	+	6.47884i	0.126210	+	0.308516i
$442$		0			0
$443$	25.8189	+	25.8189i	1.22669	+	1.22669i	0.965208	+	0.261484i	$0.0842118\pi$
$443$	25.8189	+	25.8189i	1.22669	+	1.22669i	0.261484	+	0.965208i	$0.415788\pi$
$444$		0			0
$445$	14.2386	+	22.4762i	0.674975	+	1.06547i
$446$		0			0
$447$	3.13613	+	3.13613i	0.148334	+	0.148334i
$448$		0			0
$449$		−	9.55573i		−	0.450963i	−0.974247	−	0.225481i	$-0.927605\pi$
$449$		−	9.55573i		−	0.450963i	0.974247	−	0.225481i	$-0.0723955\pi$
$450$		0			0
$451$			52.7848i			2.48554i
$452$		0			0
$453$	−5.38459	+	5.38459i	−0.252990	+	0.252990i
$454$		0			0
$455$	0.130124	−	4.89931i	0.00610031	−	0.229683i
$456$		0			0
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	−0.979690	−	0.200516i	$-0.935738\pi$
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	0.200516	+	0.979690i	$0.435738\pi$
$458$		0			0
$459$			5.80748i			0.271070i
$460$		0			0
$461$			24.4762i			1.13997i	0.821656	+	0.569984i	$0.193051\pi$
$461$			24.4762i			1.13997i	−0.821656	+	0.569984i	$0.806949\pi$
$462$		0			0
$463$	−6.83022	−	6.83022i	−0.317427	−	0.317427i	0.530351	−	0.847778i	$-0.322060\pi$
$463$	−6.83022	−	6.83022i	−0.317427	−	0.317427i	−0.847778	+	0.530351i	$0.822060\pi$
$464$		0			0
$465$	1.47884	−	6.59117i	0.0685794	−	0.305658i
$466$		0			0
$467$	20.2503	+	20.2503i	0.937070	+	0.937070i	0.998134	−	0.0610637i	$-0.0194493\pi$
$467$	20.2503	+	20.2503i	0.937070	+	0.937070i	−0.0610637	+	0.998134i	$0.519449\pi$
$468$		0			0
$469$	−3.04145	−	2.04189i	−0.140441	−	0.0942856i
$470$		0			0
$471$	−8.91220			−0.410653
$472$		0			0
$473$	−27.5847	−	27.5847i	−1.26835	−	1.26835i
$474$		0			0
$475$	−5.04907	+	10.6854i	−0.231667	+	0.490280i
$476$		0			0
$477$	2.36365	−	2.36365i	0.108224	−	0.108224i
$478$		0			0
$479$	−6.82843			−0.311999			−0.155999	−	0.987757i	$-0.549860\pi$
$479$	−6.82843			−0.311999			−0.155999	+	0.987757i	$0.549860\pi$
$480$		0			0
$481$			7.15422i			0.326204i
$482$		0			0
$483$	2.15063	+	10.9372i	0.0978570	+	0.497658i
$484$		0			0
$485$	−5.57711	+	24.8572i	−0.253244	+	1.12871i
$486$		0			0
$487$	−0.327587	+	0.327587i	−0.0148444	+	0.0148444i	−0.714490	−	0.699646i	$-0.753341\pi$
$487$	−0.327587	+	0.327587i	−0.0148444	+	0.0148444i	0.699646	+	0.714490i	$0.253341\pi$
$488$		0			0
$489$	−15.3427			−0.693821
$490$		0			0
$491$	−3.38521			−0.152773			−0.0763863	−	0.997078i	$-0.524338\pi$
$491$	−3.38521			−0.152773			−0.0763863	+	0.997078i	$0.524338\pi$
$492$		0			0
$493$	−40.8557	+	40.8557i	−1.84005	+	1.84005i
$494$		0			0
$495$	−9.06462	+	5.74242i	−0.407425	+	0.258103i
$496$		0			0
$497$	2.68065	+	13.6326i	0.120244	+	0.611507i
$498$		0			0
$499$		−	4.17771i		−	0.187020i	−0.995618	−	0.0935101i	$-0.970191\pi$
$499$		−	4.17771i		−	0.187020i	0.995618	−	0.0935101i	$-0.0298087\pi$
$500$		0			0
$501$	−7.97100			−0.356118
$502$		0			0
$503$	−8.57667	+	8.57667i	−0.382415	+	0.382415i	−0.871972	−	0.489557i	$-0.837159\pi$
$503$	−8.57667	+	8.57667i	−0.382415	+	0.382415i	0.489557	+	0.871972i	$0.337159\pi$
$504$		0			0
$505$	9.23726	−	5.85178i	0.411052	−	0.260401i
$506$		0			0
$507$	8.70711	+	8.70711i	0.386696	+	0.386696i
$508$		0			0
$509$	−3.29829			−0.146194			−0.0730970	−	0.997325i	$-0.523288\pi$
$509$	−3.29829			−0.146194			−0.0730970	+	0.997325i	$0.523288\pi$
$510$		0			0
$511$	−18.9969	−	12.7536i	−0.840373	−	0.564187i
$512$		0			0
$513$	−1.67135	−	1.67135i	−0.0737921	−	0.0737921i
$514$		0			0
$515$	−3.28497	−	0.737036i	−0.144753	−	0.0324777i
$516$		0			0
$517$	1.74509	+	1.74509i	0.0767490	+	0.0767490i
$518$		0			0
$519$			17.9496i			0.787901i
$520$		0			0
$521$		−	15.6386i		−	0.685141i	−0.939492	−	0.342570i	$-0.888702\pi$
$521$		−	15.6386i		−	0.685141i	0.939492	−	0.342570i	$-0.111298\pi$
$522$		0			0
$523$	25.2794	−	25.2794i	1.10539	−	1.10539i	0.111644	−	0.993748i	$-0.464388\pi$
$523$	25.2794	−	25.2794i	1.10539	−	1.10539i	0.993748	−	0.111644i	$-0.0356118\pi$
$524$		0			0
$525$	11.3591	−	6.78019i	0.495752	−	0.295912i
$526$		0			0
$527$	−12.4055	+	12.4055i	−0.540394	+	0.540394i
$528$		0			0
$529$		−	5.25045i		−	0.228280i
$530$		0			0
$531$		−	2.07912i		−	0.0902262i
$532$		0			0
$533$	−6.44339	−	6.44339i	−0.279094	−	0.279094i
$534$		0			0
$535$	−6.63591	−	1.48887i	−0.286895	−	0.0643697i
$536$		0			0
$537$	−4.05056	−	4.05056i	−0.174795	−	0.174795i
$538$		0			0
$539$	31.0907	−	12.7188i	1.33917	−	0.547838i
$540$		0			0
$541$	−2.70276			−0.116201			−0.0581005	−	0.998311i	$-0.518504\pi$
$541$	−2.70276			−0.116201			−0.0581005	+	0.998311i	$0.518504\pi$
$542$		0			0
$543$	−6.30188	−	6.30188i	−0.270439	−	0.270439i
$544$		0			0
$545$	−24.3643	+	15.4347i	−1.04365	+	0.661151i
$546$		0			0
$547$	−1.65370	+	1.65370i	−0.0707071	+	0.0707071i	−0.741576	−	0.670869i	$-0.765921\pi$
$547$	−1.65370	+	1.65370i	−0.0707071	+	0.0707071i	0.670869	+	0.741576i	$0.265921\pi$
$548$		0			0
$549$	−5.55573			−0.237113
$550$		0			0
$551$		−	23.5160i		−	1.00181i
$552$		0			0
$553$	13.2416	−	2.60376i	0.563089	−	0.110723i
$554$		0			0
$555$	−16.3126	+	10.3340i	−0.692433	+	0.438655i
$556$		0			0
$557$	−27.6462	+	27.6462i	−1.17141	+	1.17141i	−0.189535	+	0.981874i	$0.560698\pi$
$557$	−27.6462	+	27.6462i	−1.17141	+	1.17141i	−0.981874	+	0.189535i	$0.939302\pi$
$558$		0			0
$559$	6.73449			0.284839
$560$		0			0
$561$	27.8690			1.17663
$562$		0			0
$563$	3.25447	−	3.25447i	0.137160	−	0.137160i	−0.635193	−	0.772353i	$-0.719080\pi$
$563$	3.25447	−	3.25447i	0.137160	−	0.137160i	0.772353	+	0.635193i	$0.219080\pi$
$564$		0			0
$565$	8.02051	−	35.7474i	0.337425	−	1.50390i
$566$		0			0
$567$	0.510472	+	2.59604i	0.0214378	+	0.109023i
$568$		0			0
$569$		−	24.2411i		−	1.01624i	−0.861286	−	0.508121i	$-0.830340\pi$
$569$		−	24.2411i		−	1.01624i	0.861286	−	0.508121i	$-0.169660\pi$
$570$		0			0
$571$	−17.3801			−0.727336			−0.363668	−	0.931529i	$-0.618476\pi$
$571$	−17.3801			−0.727336			−0.363668	+	0.931529i	$0.618476\pi$
$572$		0			0
$573$	5.42933	−	5.42933i	0.226814	−	0.226814i
$574$		0			0
$575$	19.8311	−	7.10384i	0.827016	−	0.296251i
$576$		0			0
$577$	22.7961	+	22.7961i	0.949016	+	0.949016i	0.998762	−	0.0497462i	$-0.0158413\pi$
$577$	22.7961	+	22.7961i	0.949016	+	0.949016i	−0.0497462	+	0.998762i	$0.515841\pi$
$578$		0			0
$579$	−6.50201			−0.270214
$580$		0			0
$581$	−10.0082	−	6.71907i	−0.415212	−	0.278754i
$582$		0			0
$583$	−11.3427	−	11.3427i	−0.469767	−	0.469767i
$584$		0			0
$585$	0.405538	−	1.80748i	0.0167669	−	0.0747302i
$586$		0			0
$587$	−0.690067	−	0.690067i	−0.0284821	−	0.0284821i	0.692722	−	0.721204i	$-0.256411\pi$
$587$	−0.690067	−	0.690067i	−0.0284821	−	0.0284821i	−0.721204	+	0.692722i	$0.756411\pi$
$588$		0			0
$589$		−	7.14046i		−	0.294217i
$590$		0			0
$591$			7.42648i			0.305485i
$592$		0			0
$593$	−16.0464	+	16.0464i	−0.658946	+	0.658946i	−0.955131	−	0.296184i	$-0.904286\pi$
$593$	−16.0464	+	16.0464i	−0.658946	+	0.658946i	0.296184	+	0.955131i	$0.404286\pi$
$594$		0			0
$595$	−34.3454	−	0.912202i	−1.40803	−	0.0373966i
$596$		0			0
$597$	−2.91443	+	2.91443i	−0.119280	+	0.119280i
$598$		0			0
$599$		−	0.262525i		−	0.0107265i	−0.999986	−	0.00536325i	$-0.998293\pi$
$599$		−	0.262525i		−	0.0107265i	0.999986	−	0.00536325i	$-0.00170718\pi$
$600$		0			0
$601$		−	6.35838i		−	0.259364i	−0.991556	−	0.129682i	$-0.958604\pi$
$601$		−	6.35838i		−	0.259364i	0.991556	−	0.129682i	$-0.0413956\pi$
$602$		0			0
$603$	−0.979056	−	0.979056i	−0.0398703	−	0.0398703i
$604$		0			0
$605$	14.3938	+	22.7211i	0.585191	+	0.923745i
$606$		0			0
$607$	−22.5571	−	22.5571i	−0.915564	−	0.915564i	0.0811391	−	0.996703i	$-0.474144\pi$
$607$	−22.5571	−	22.5571i	−0.915564	−	0.915564i	−0.996703	+	0.0811391i	$0.974144\pi$
$608$		0			0
$609$	−14.6720	+	21.8543i	−0.594538	+	0.885582i
$610$		0			0
$611$	−0.426043			−0.0172359
$612$		0			0
$613$	−4.17864	−	4.17864i	−0.168774	−	0.168774i	0.617667	−	0.786440i	$-0.288078\pi$
$613$	−4.17864	−	4.17864i	−0.168774	−	0.168774i	−0.786440	+	0.617667i	$0.788078\pi$
$614$		0			0
$615$	5.38459	−	23.9991i	0.217128	−	0.967738i
$616$		0			0
$617$	10.9152	−	10.9152i	0.439428	−	0.439428i	−0.452391	−	0.891819i	$-0.649429\pi$
$617$	10.9152	−	10.9152i	0.439428	−	0.439428i	0.891819	+	0.452391i	$0.149429\pi$
$618$		0			0
$619$	2.48720			0.0999688			0.0499844	−	0.998750i	$-0.484083\pi$
$619$	2.48720			0.0999688			0.0499844	+	0.998750i	$0.484083\pi$
$620$		0			0
$621$			4.21302i			0.169063i
$622$		0			0
$623$	−6.07404	−	30.8899i	−0.243351	−	1.23758i
$624$		0			0
$625$	−15.8739	−	19.3137i	−0.634956	−	0.772548i
$626$		0			0
$627$	−8.02051	+	8.02051i	−0.320308	+	0.320308i
$628$		0			0
$629$	50.1529			1.99973
$630$		0			0
$631$	34.6801			1.38059			0.690296	−	0.723527i	$-0.257480\pi$
$631$	34.6801			1.38059			0.690296	+	0.723527i	$0.257480\pi$
$632$		0			0
$633$	19.5557	−	19.5557i	0.777270	−	0.777270i
$634$		0			0
$635$	−1.23335	−	0.276721i	−0.0489438	−	0.0109813i
$636$		0			0
$637$	−2.24264	+	5.34779i	−0.0888567	+	0.211887i
$638$		0			0
$639$			5.25132i			0.207739i
$640$		0			0
$641$	−17.9572			−0.709268			−0.354634	−	0.935005i	$-0.615395\pi$
$641$	−17.9572			−0.709268			−0.354634	+	0.935005i	$0.615395\pi$
$642$		0			0
$643$	3.76560	−	3.76560i	0.148501	−	0.148501i	−0.628947	−	0.777448i	$-0.716514\pi$
$643$	3.76560	−	3.76560i	0.148501	−	0.148501i	0.777448	+	0.628947i	$0.216514\pi$
$644$		0			0
$645$	9.72774	+	15.3556i	0.383029	+	0.604626i
$646$		0			0
$647$	−24.7759	−	24.7759i	−0.974042	−	0.974042i	0.0256293	−	0.999672i	$-0.491841\pi$
$647$	−24.7759	−	24.7759i	−0.974042	−	0.974042i	−0.999672	+	0.0256293i	$0.991841\pi$
$648$		0			0
$649$	−9.97731			−0.391644
$650$		0			0
$651$	−4.45504	+	6.63591i	−0.174607	+	0.260082i
$652$		0			0
$653$	−15.9566	−	15.9566i	−0.624431	−	0.624431i	0.322231	−	0.946661i	$-0.395567\pi$
$653$	−15.9566	−	15.9566i	−0.624431	−	0.624431i	−0.946661	+	0.322231i	$0.895567\pi$
$654$		0			0
$655$	41.9417	−	26.5700i	1.63880	−	1.03817i
$656$		0			0
$657$	−6.11519	−	6.11519i	−0.238576	−	0.238576i
$658$		0			0
$659$			15.8705i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$659$			15.8705i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$660$		0			0
$661$		−	15.8409i		−	0.616139i	−0.951364	−	0.308069i	$-0.900317\pi$
$661$		−	15.8409i		−	0.616139i	0.951364	−	0.308069i	$-0.0996829\pi$
$662$		0			0
$663$	−3.40194	+	3.40194i	−0.132121	+	0.132121i
$664$		0			0
$665$	10.1469	−	9.62185i	0.393480	−	0.373119i
$666$		0			0
$667$	−29.6386	+	29.6386i	−1.14761	+	1.14761i
$668$		0			0
$669$			21.6759i			0.838037i
$670$		0			0
$671$			26.6609i			1.02923i
$672$		0			0
$673$	4.25535	+	4.25535i	0.164032	+	0.164032i	0.784350	−	0.620318i	$-0.212997\pi$
$673$	4.25535	+	4.25535i	0.164032	+	0.164032i	−0.620318	+	0.784350i	$0.712997\pi$
$674$		0			0
$675$	4.70711	−	1.68616i	0.181177	−	0.0649004i
$676$		0			0
$677$	−34.7614	−	34.7614i	−1.33599	−	1.33599i	−0.899906	−	0.436085i	$-0.856365\pi$
$677$	−34.7614	−	34.7614i	−1.33599	−	1.33599i	−0.436085	−	0.899906i	$-0.643635\pi$
$678$		0			0
$679$	16.8012	−	25.0259i	0.644772	−	0.960406i
$680$		0			0
$681$	26.7264			1.02416
$682$		0			0
$683$	−8.10025	−	8.10025i	−0.309947	−	0.309947i	0.534942	−	0.844889i	$-0.320334\pi$
$683$	−8.10025	−	8.10025i	−0.309947	−	0.309947i	−0.844889	+	0.534942i	$0.820334\pi$
$684$		0			0
$685$	−18.2928	−	4.10428i	−0.698931	−	0.156816i
$686$		0			0
$687$	−9.41421	+	9.41421i	−0.359175	+	0.359175i
$688$		0			0
$689$	2.76919			0.105498
$690$		0			0
$691$		−	39.2567i		−	1.49340i	−0.665163	−	0.746699i	$-0.731638\pi$
$691$		−	39.2567i		−	1.49340i	0.665163	−	0.746699i	$-0.268362\pi$
$692$		0			0
$693$	12.4579	−	2.44966i	0.473236	−	0.0930548i
$694$		0			0
$695$	10.1292	+	15.9894i	0.384224	+	0.606512i
$696$		0			0
$697$	−45.1698	+	45.1698i	−1.71093	+	1.71093i
$698$		0			0
$699$	10.4015			0.393421
$700$		0			0
$701$	27.9663			1.05627			0.528137	−	0.849159i	$-0.322891\pi$
$701$	27.9663			1.05627			0.528137	+	0.849159i	$0.322891\pi$
$702$		0			0
$703$	−14.4337	+	14.4337i	−0.544376	+	0.544376i
$704$		0			0
$705$	−0.615405	−	0.971440i	−0.0231775	−	0.0365865i
$706$		0			0
$707$	−12.6951	+	2.49631i	−0.477450	+	0.0938834i
$708$		0			0
$709$		−	23.3998i		−	0.878799i	−0.898292	−	0.439399i	$-0.855191\pi$
$709$		−	23.3998i		−	0.878799i	0.898292	−	0.439399i	$-0.144809\pi$
$710$		0			0
$711$	5.10069			0.191291
$712$		0			0
$713$	−8.99956	+	8.99956i	−0.337036	+	0.337036i
$714$		0			0
$715$	−8.67377	−	1.94610i	−0.324380	−	0.0727800i
$716$		0			0
$717$	−9.22708	−	9.22708i	−0.344592	−	0.344592i
$718$		0			0
$719$	50.8254			1.89547			0.947734	−	0.319060i	$-0.103367\pi$
$719$	50.8254			1.89547			0.947734	+	0.319060i	$0.103367\pi$
$720$		0			0
$721$	3.30726	+	2.22034i	0.123169	+	0.0826899i
$722$		0			0
$723$	17.2917	+	17.2917i	0.643085	+	0.643085i
$724$		0			0
$725$	44.9767	+	21.2524i	1.67039	+	0.789293i
$726$		0			0
$727$	5.10248	+	5.10248i	0.189240	+	0.189240i	0.795368	−	0.606127i	$-0.207278\pi$
$727$	5.10248	+	5.10248i	0.189240	+	0.189240i	−0.606127	+	0.795368i	$0.707278\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	47.2105i		−	1.74614i
$732$		0			0
$733$	−1.79925	+	1.79925i	−0.0664567	+	0.0664567i	−0.739554	−	0.673097i	$-0.764964\pi$
$733$	−1.79925	+	1.79925i	−0.0664567	+	0.0664567i	0.673097	+	0.739554i	$0.264964\pi$
$734$		0			0
$735$	−15.4331	+	2.61116i	−0.569260	+	0.0963140i
$736$		0			0
$737$	−4.69830	+	4.69830i	−0.173064	+	0.173064i
$738$		0			0
$739$			10.9122i			0.401412i	0.979652	+	0.200706i	$0.0643236\pi$
$739$			10.9122i			0.401412i	−0.979652	+	0.200706i	$0.935676\pi$
$740$		0			0
$741$		−	1.95811i		−	0.0719331i
$742$		0			0
$743$	12.3076	+	12.3076i	0.451521	+	0.451521i	0.895859	−	0.444338i	$-0.146561\pi$
$743$	12.3076	+	12.3076i	0.451521	+	0.451521i	−0.444338	+	0.895859i	$0.646561\pi$
$744$		0			0
$745$	−8.37771	+	5.30726i	−0.306936	+	0.194443i
$746$		0			0
$747$	−3.22170	−	3.22170i	−0.117876	−	0.117876i
$748$		0			0
$749$	6.68095	+	4.48528i	0.244117	+	0.163889i
$750$		0			0
$751$	12.4787			0.455354			0.227677	−	0.973737i	$-0.426887\pi$
$751$	12.4787			0.455354			0.227677	+	0.973737i	$0.426887\pi$
$752$		0			0
$753$	3.05701	+	3.05701i	0.111404	+	0.111404i
$754$		0			0
$755$	−9.11233	−	14.3842i	−0.331632	−	0.523493i
$756$		0			0
$757$	30.1930	−	30.1930i	1.09738	−	1.09738i	0.102667	−	0.994716i	$-0.467262\pi$
$757$	30.1930	−	30.1930i	1.09738	−	1.09738i	0.994716	−	0.102667i	$-0.0327377\pi$
$758$		0			0
$759$	20.2175			0.733848
$760$		0			0
$761$		−	33.4920i		−	1.21409i	−0.794669	−	0.607043i	$-0.792356\pi$
$761$		−	33.4920i		−	1.21409i	0.794669	−	0.607043i	$-0.207644\pi$
$762$		0			0
$763$	33.4848	−	6.58429i	1.21223	−	0.238367i
$764$		0			0
$765$	−12.6709	−	2.84293i	−0.458118	−	0.102786i
$766$		0			0
$767$	1.21792	−	1.21792i	0.0439766	−	0.0439766i
$768$		0			0
$769$	31.8992			1.15032			0.575158	−	0.818042i	$-0.304941\pi$
$769$	31.8992			1.15032			0.575158	+	0.818042i	$0.304941\pi$
$770$		0			0
$771$	7.16184			0.257927
$772$		0			0
$773$	11.0809	−	11.0809i	0.398553	−	0.398553i	−0.479170	−	0.877722i	$-0.659062\pi$
$773$	11.0809	−	11.0809i	0.398553	−	0.398553i	0.877722	+	0.479170i	$0.159062\pi$
$774$		0			0
$775$	13.6569	+	6.45313i	0.490569	+	0.231803i
$776$		0			0
$777$	22.4192	−	4.40839i	0.804283	−	0.158150i
$778$		0			0
$779$		−	25.9991i		−	0.931515i
$780$		0			0
$781$	25.2001			0.901729
$782$		0			0
$783$	−7.03500	+	7.03500i	−0.251411	+	0.251411i
$784$		0			0
$785$	4.36277	−	19.4449i	0.155714	−	0.694017i
$786$		0			0
$787$	27.9894	+	27.9894i	0.997714	+	0.997714i	0.999997	−	0.00228344i	$-0.000726843\pi$
$787$	27.9894	+	27.9894i	0.997714	+	0.997714i	−0.00228344	+	0.999997i	$0.500727\pi$
$788$		0			0
$789$	5.89887			0.210005
$790$		0			0
$791$	−24.1620	+	35.9900i	−0.859103	+	1.27966i
$792$		0			0
$793$	−3.25447	−	3.25447i	−0.115570	−	0.115570i
$794$		0			0
$795$	4.00000	+	6.31415i	0.141865	+	0.223940i
$796$		0			0
$797$	−6.43293	−	6.43293i	−0.227866	−	0.227866i	0.583935	−	0.811801i	$-0.301512\pi$
$797$	−6.43293	−	6.43293i	−0.227866	−	0.227866i	−0.811801	+	0.583935i	$0.801512\pi$
$798$		0			0
$799$			2.98667i			0.105661i
$800$		0			0
$801$		−	11.8989i		−	0.420426i
$802$		0			0
$803$	−29.3456	+	29.3456i	−1.03558	+	1.03558i
$804$		0			0
$805$	−24.9158	−	0.661754i	−0.878166	−	0.0233238i
$806$		0			0
$807$	17.4998	−	17.4998i	0.616021	−	0.616021i
$808$		0			0
$809$			36.3842i			1.27920i	0.768708	+	0.639599i	$0.220900\pi$
$809$			36.3842i			1.27920i	−0.768708	+	0.639599i	$0.779100\pi$
$810$		0			0
$811$		−	26.5629i		−	0.932750i	−0.884587	−	0.466375i	$-0.845560\pi$
$811$		−	26.5629i		−	0.932750i	0.884587	−	0.466375i	$-0.154440\pi$
$812$		0			0
$813$	−15.5535	−	15.5535i	−0.545485	−	0.545485i
$814$		0			0
$815$	7.51069	−	33.4751i	0.263088	−	1.17258i
$816$		0			0
$817$	13.5868	+	13.5868i	0.475344	+	0.475344i
$818$		0			0
$819$	−1.22170	+	1.81975i	−0.0426895	+	0.0635873i
$820$		0			0
$821$	−45.9655			−1.60421			−0.802103	−	0.597186i	$-0.796286\pi$
$821$	−45.9655			−1.60421			−0.802103	+	0.597186i	$0.796286\pi$
$822$		0			0
$823$	−36.5397	−	36.5397i	−1.27369	−	1.27369i	−0.944134	−	0.329561i	$-0.893099\pi$
$823$	−36.5397	−	36.5397i	−1.27369	−	1.27369i	−0.329561	−	0.944134i	$-0.606901\pi$
$824$		0			0
$825$	−8.09157	−	22.5885i	−0.281712	−	0.786431i
$826$		0			0
$827$	−15.7275	+	15.7275i	−0.546898	+	0.546898i	−0.925542	−	0.378644i	$-0.876390\pi$
$827$	−15.7275	+	15.7275i	−0.546898	+	0.546898i	0.378644	+	0.925542i	$0.376390\pi$
$828$		0			0
$829$	−29.2892			−1.01725			−0.508627	−	0.860987i	$-0.669847\pi$
$829$	−29.2892			−1.01725			−0.508627	+	0.860987i	$0.669847\pi$
$830$		0			0
$831$		−	17.0620i		−	0.591873i
$832$		0			0
$833$	37.4894	+	15.7215i	1.29893	+	0.544717i
$834$		0			0
$835$	3.90203	−	17.3913i	0.135035	−	0.601852i
$836$		0			0
$837$	−2.13613	+	2.13613i	−0.0738354	+	0.0738354i
$838$		0			0
$839$	−2.41886			−0.0835082			−0.0417541	−	0.999128i	$-0.513295\pi$
$839$	−2.41886			−0.0835082			−0.0417541	+	0.999128i	$0.513295\pi$
$840$		0			0
$841$	−69.9826			−2.41319
$842$		0			0
$843$	10.1589	−	10.1589i	0.349890	−	0.349890i
$844$		0			0
$845$	−23.2598	+	14.7350i	−0.800160	+	0.506900i
$846$		0			0
$847$	−6.14024	−	31.2266i	−0.210981	−	1.07296i
$848$		0			0
$849$		−	15.6742i		−	0.537937i
$850$		0			0
$851$	36.3833			1.24720
$852$		0			0
$853$	28.0222	−	28.0222i	0.959461	−	0.959461i	−0.0397491	−	0.999210i	$-0.512656\pi$
$853$	28.0222	−	28.0222i	0.959461	−	0.959461i	0.999210	+	0.0397491i	$0.0126559\pi$
$854$		0			0
$855$	4.46478	−	2.82843i	0.152692	−	0.0967302i
$856$		0			0
$857$	−19.1782	−	19.1782i	−0.655115	−	0.655115i	0.299105	−	0.954220i	$-0.403312\pi$
$857$	−19.1782	−	19.1782i	−0.655115	−	0.655115i	−0.954220	+	0.299105i	$0.903312\pi$
$858$		0			0
$859$	−45.5754			−1.55501			−0.777506	−	0.628876i	$-0.783515\pi$
$859$	−45.5754			−1.55501			−0.777506	+	0.628876i	$0.783515\pi$
$860$		0			0
$861$	−16.2213	+	24.1620i	−0.552819	+	0.823439i
$862$		0			0
$863$	−4.69515	−	4.69515i	−0.159825	−	0.159825i	0.622664	−	0.782489i	$-0.286050\pi$
$863$	−4.69515	−	4.69515i	−0.159825	−	0.159825i	−0.782489	+	0.622664i	$0.786050\pi$
$864$		0			0
$865$	−39.1629	−	8.78684i	−1.33158	−	0.298762i
$866$		0			0
$867$	11.8277	+	11.8277i	0.401689	+	0.401689i
$868$		0			0
$869$		−	24.4772i		−	0.830333i
$870$		0			0
$871$		−	1.14704i		−	0.0388658i
$872$		0			0
$873$	8.05595	−	8.05595i	0.272653	−	0.272653i
$874$		0			0
$875$	9.23260	+	28.1027i	0.312119	+	0.950043i
$876$		0			0
$877$	17.5321	−	17.5321i	0.592017	−	0.592017i	−0.346159	−	0.938176i	$-0.612514\pi$
$877$	17.5321	−	17.5321i	0.592017	−	0.592017i	0.938176	+	0.346159i	$0.112514\pi$
$878$		0			0
$879$		−	8.99195i		−	0.303291i
$880$		0			0
$881$			3.93358i			0.132526i	0.997802	+	0.0662628i	$0.0211076\pi$
$881$			3.93358i			0.132526i	−0.997802	+	0.0662628i	$0.978892\pi$
$882$		0			0
$883$	−34.7362	−	34.7362i	−1.16896	−	1.16896i	−0.982453	−	0.186512i	$-0.940282\pi$
$883$	−34.7362	−	34.7362i	−1.16896	−	1.16896i	−0.186512	−	0.982453i	$-0.559718\pi$
$884$		0			0
$885$	4.53628	+	1.01779i	0.152485	+	0.0342126i
$886$		0			0
$887$	−33.3213	−	33.3213i	−1.11882	−	1.11882i	−0.991915	−	0.126906i	$-0.959495\pi$
$887$	−33.3213	−	33.3213i	−1.11882	−	1.11882i	−0.126906	−	0.991915i	$-0.540505\pi$
$888$		0			0
$889$	1.24172	+	0.833631i	0.0416458	+	0.0279591i
$890$		0			0
$891$	4.79881			0.160766
$892$		0			0
$893$	−0.859544	−	0.859544i	−0.0287635	−	0.0287635i
$894$		0			0
$895$	10.8205	−	6.85476i	0.361689	−	0.229129i
$896$		0			0
$897$	−2.46793	+	2.46793i	−0.0824018	+	0.0824018i
$898$		0			0
$899$	−30.0554			−1.00240
$900$		0			0
$901$		−	19.4127i		−	0.646731i
$902$		0			0
$903$	−4.14975	−	21.1038i	−0.138095	−	0.702292i
$904$		0			0
$905$	16.8345	−	10.6647i	0.559599	−	0.354505i
$906$		0			0
$907$	0.932707	−	0.932707i	0.0309700	−	0.0309700i	−0.691452	−	0.722422i	$-0.743029\pi$
$907$	0.932707	−	0.932707i	0.0309700	−	0.0309700i	0.722422	+	0.691452i	$0.243029\pi$
$908$		0			0
$909$	−4.89020			−0.162198
$910$		0			0
$911$	−45.5690			−1.50977			−0.754885	−	0.655857i	$-0.772307\pi$
$911$	−45.5690			−1.50977			−0.754885	+	0.655857i	$0.772307\pi$
$912$		0			0
$913$	−15.4603	+	15.4603i	−0.511661	+	0.511661i
$914$		0			0
$915$	2.71969	−	12.1216i	0.0899100	−	0.400729i
$916$		0			0
$917$	−57.6422	+	11.3345i	−1.90351	+	0.374297i
$918$		0			0
$919$			20.8574i			0.688023i	0.938965	+	0.344011i	$0.111786\pi$
$919$			20.8574i			0.688023i	−0.938965	+	0.344011i	$0.888214\pi$
$920$		0			0
$921$	−23.8525			−0.785967
$922$		0			0
$923$	−3.07615	+	3.07615i	−0.101253	+	0.101253i
$924$		0			0
$925$	−14.5616	−	40.6502i	−0.478781	−	1.33657i
$926$		0			0
$927$	1.06462	+	1.06462i	0.0349668	+	0.0349668i
$928$		0			0
$929$	−9.10069			−0.298584			−0.149292	−	0.988793i	$-0.547699\pi$
$929$	−9.10069			−0.298584			−0.149292	+	0.988793i	$0.547699\pi$
$930$		0			0
$931$	−15.3137	+	6.26464i	−0.501887	+	0.205315i
$932$		0			0
$933$	0.0418875	+	0.0418875i	0.00137134	+	0.00137134i
$934$		0			0
$935$	−13.6427	+	60.8053i	−0.446163	+	1.98855i
$936$		0			0
$937$	−3.34154	−	3.34154i	−0.109163	−	0.109163i	0.650415	−	0.759579i	$-0.274595\pi$
$937$	−3.34154	−	3.34154i	−0.109163	−	0.109163i	−0.759579	+	0.650415i	$0.774595\pi$
$938$		0			0
$939$			0.648179i			0.0211525i
$940$		0			0
$941$		−	42.2862i		−	1.37849i	−0.724528	−	0.689245i	$-0.757942\pi$
$941$		−	42.2862i		−	1.37849i	0.724528	−	0.689245i	$-0.242058\pi$
$942$		0			0
$943$	−32.7683	+	32.7683i	−1.06708	+	1.06708i
$944$		0			0
$945$	−5.91399	−	0.157074i	−0.192382	−	0.00510960i
$946$		0			0
$947$	0.00253441	−	0.00253441i	8.23572e−5	−	8.23572e-5i	−0.707066	−	0.707148i	$-0.749981\pi$
$947$	0.00253441	−	0.00253441i	8.23572e−5	−	8.23572e-5i	0.707148	+	0.707066i	$0.249981\pi$
$948$		0			0
$949$		−	7.16439i		−	0.232566i
$950$		0			0
$951$		−	18.5445i		−	0.601347i
$952$		0			0
$953$	14.4673	+	14.4673i	0.468642	+	0.468642i	0.901474	−	0.432832i	$-0.142486\pi$
$953$	14.4673	+	14.4673i	0.468642	+	0.468642i	−0.432832	+	0.901474i	$0.642486\pi$
$954$		0			0
$955$	9.18805	+	14.5037i	0.297318	+	0.469328i
$956$		0			0
$957$	33.7596	+	33.7596i	1.09129	+	1.09129i
$958$		0			0
$959$	18.4169	+	12.3643i	0.594714	+	0.399263i
$960$		0			0
$961$	21.8739			0.705610
$962$		0			0
$963$	2.15063	+	2.15063i	0.0693031	+	0.0693031i
$964$		0			0
$965$	3.18292	−	14.1863i	0.102462	−	0.456672i
$966$		0			0
$967$	4.38595	−	4.38595i	0.141043	−	0.141043i	−0.633060	−	0.774103i	$-0.718201\pi$
$967$	4.38595	−	4.38595i	0.141043	−	0.141043i	0.774103	+	0.633060i	$0.218201\pi$
$968$		0			0
$969$	−13.7269			−0.440970
$970$		0			0
$971$			24.3630i			0.781847i	0.920423	+	0.390923i	$0.127844\pi$
$971$			24.3630i			0.781847i	−0.920423	+	0.390923i	$0.872156\pi$
$972$		0			0
$973$	−4.32103	−	21.9749i	−0.138526	−	0.704483i
$974$		0			0
$975$	3.74509	+	1.76963i	0.119939	+	0.0566734i
$976$		0			0
$977$	38.9763	−	38.9763i	1.24696	−	1.24696i	0.289905	−	0.957055i	$-0.406376\pi$
$977$	38.9763	−	38.9763i	1.24696	−	1.24696i	0.957055	−	0.289905i	$-0.0936239\pi$
$978$		0			0
$979$	−57.1004			−1.82494
$980$		0			0
$981$	12.8984			0.411815
$982$		0			0
$983$	14.5896	−	14.5896i	0.465335	−	0.465335i	−0.435065	−	0.900399i	$-0.643274\pi$
$983$	14.5896	−	14.5896i	0.465335	−	0.465335i	0.900399	+	0.435065i	$0.143274\pi$
$984$		0			0
$985$	−16.2033	−	3.63547i	−0.516280	−	0.115836i
$986$		0			0
$987$	0.262525	+	1.33509i	0.00835628	+	0.0424964i
$988$		0			0
$989$		−	34.2487i		−	1.08905i
$990$		0			0
$991$	−47.6560			−1.51384			−0.756921	−	0.653506i	$-0.773297\pi$
$991$	−47.6560			−1.51384			−0.756921	+	0.653506i	$0.773297\pi$
$992$		0			0
$993$	17.7688	−	17.7688i	0.563874	−	0.563874i
$994$		0			0
$995$	−4.93209	−	7.78548i	−0.156358	−	0.246816i
$996$		0			0
$997$	0.631258	+	0.631258i	0.0199921	+	0.0199921i	0.717032	−	0.697040i	$-0.245500\pi$
$997$	0.631258	+	0.631258i	0.0199921	+	0.0199921i	−0.697040	+	0.717032i	$0.745500\pi$
$998$		0			0
$999$	8.63591			0.273228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.a.433.4		8
4.3	odd	2		210.2.m.b.13.4	yes	8
5.2	odd	4		1680.2.cz.b.97.1		8
7.6	odd	2		1680.2.cz.b.433.1		8
12.11	even	2		630.2.p.c.433.1		8
20.3	even	4		1050.2.m.b.307.2		8
20.7	even	4		210.2.m.a.97.3	yes	8
20.19	odd	2		1050.2.m.a.643.2		8
28.27	even	2		210.2.m.a.13.3	✓	8
35.27	even	4	inner	1680.2.cz.a.97.4		8
60.47	odd	4		630.2.p.b.307.2		8
84.83	odd	2		630.2.p.b.433.2		8
140.27	odd	4		210.2.m.b.97.4	yes	8
140.83	odd	4		1050.2.m.a.307.2		8
140.139	even	2		1050.2.m.b.643.2		8
420.167	even	4		630.2.p.c.307.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.3	✓	8	28.27	even	2
210.2.m.a.97.3	yes	8	20.7	even	4
210.2.m.b.13.4	yes	8	4.3	odd	2
210.2.m.b.97.4	yes	8	140.27	odd	4
630.2.p.b.307.2		8	60.47	odd	4
630.2.p.b.433.2		8	84.83	odd	2
630.2.p.c.307.1		8	420.167	even	4
630.2.p.c.433.1		8	12.11	even	2
1050.2.m.a.307.2		8	140.83	odd	4
1050.2.m.a.643.2		8	20.19	odd	2
1050.2.m.b.307.2		8	20.3	even	4
1050.2.m.b.643.2		8	140.139	even	2
1680.2.cz.a.97.4		8	35.27	even	4	inner
1680.2.cz.a.433.4		8	1.1	even	1	trivial
1680.2.cz.b.97.1		8	5.2	odd	4
1680.2.cz.b.433.1		8	7.6	odd	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.19663 + 1.88893i) q^{5} +(-0.510472 - 2.59604i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.19663 + 1.88893i) q^{5} +(-0.510472 - 2.59604i) q^{7} -1.00000i q^{9} -4.79881 q^{11} +(0.585786 - 0.585786i) q^{13} +(2.18183 + 0.489528i) q^{15} +(-4.10651 - 4.10651i) q^{17} +2.36365 q^{19} +(-2.19663 - 1.47472i) q^{21} +(-2.97906 - 2.97906i) q^{23} +(-2.13613 + 4.52072i) q^{25} +(-0.707107 - 0.707107i) q^{27} -9.94900i q^{29} -3.02094i q^{31} +(-3.39327 + 3.39327i) q^{33} +(4.29289 - 4.07076i) q^{35} +(-6.10651 + 6.10651i) q^{37} -0.828427i q^{39} -10.9996i q^{41} +(5.74825 + 5.74825i) q^{43} +(1.88893 - 1.19663i) q^{45} +(-0.363651 - 0.363651i) q^{47} +(-6.47884 + 2.65041i) q^{49} -5.80748 q^{51} +(2.36365 + 2.36365i) q^{53} +(-5.74242 - 9.06462i) q^{55} +(1.67135 - 1.67135i) q^{57} +2.07912 q^{59} -5.55573i q^{61} +(-2.59604 + 0.510472i) q^{63} +(1.80748 + 0.405538i) q^{65} +(0.979056 - 0.979056i) q^{67} -4.21302 q^{69} -5.25132 q^{71} +(6.11519 - 6.11519i) q^{73} +(1.68616 + 4.70711i) q^{75} +(2.44966 + 12.4579i) q^{77} +5.10069i q^{79} -1.00000 q^{81} +(3.22170 - 3.22170i) q^{83} +(2.84293 - 12.6709i) q^{85} +(-7.03500 - 7.03500i) q^{87} +11.8989 q^{89} +(-1.81975 - 1.22170i) q^{91} +(-2.13613 - 2.13613i) q^{93} +(2.82843 + 4.46478i) q^{95} +(8.05595 + 8.05595i) q^{97} +4.79881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 12 q^{17} - 8 q^{19} - 8 q^{21} - 16 q^{23} - 4 q^{25} - 8 q^{33} + 40 q^{35} - 28 q^{37} - 4 q^{45} + 24 q^{47} - 4 q^{49} - 16 q^{51} - 8 q^{53} + 28 q^{55} - 4 q^{57} + 8 q^{59} + 4 q^{63} - 16 q^{65} + 8 q^{69} - 8 q^{71} + 28 q^{73} + 44 q^{77} - 8 q^{81} - 16 q^{83} + 28 q^{85} - 12 q^{87} + 64 q^{89} + 8 q^{91} - 4 q^{93} + 28 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 12 * q^17 - 8 * q^19 - 8 * q^21 - 16 * q^23 - 4 * q^25 - 8 * q^33 + 40 * q^35 - 28 * q^37 - 4 * q^45 + 24 * q^47 - 4 * q^49 - 16 * q^51 - 8 * q^53 + 28 * q^55 - 4 * q^57 + 8 * q^59 + 4 * q^63 - 16 * q^65 + 8 * q^69 - 8 * q^71 + 28 * q^73 + 44 * q^77 - 8 * q^81 - 16 * q^83 + 28 * q^85 - 12 * q^87 + 64 * q^89 + 8 * q^91 - 4 * q^93 + 28 * q^97

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