LMFDB - Embedded newform 1456.2.cc.c.225.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(225,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1456.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1456.cc (of order $6$, 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:	$11.6262185343$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.6
Root			$-1.08105 - 0.911778i$ of defining polynomial
Character	$\chi$	$=$	1456.225
Dual form			1456.2.cc.c.673.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33015 - 2.30388i) q^{3} +3.16209i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-2.03858 - 3.53092i) q^{9} +O(q^{10})$	\(q+(1.33015 - 2.30388i) q^{3} +3.16209i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-2.03858 - 3.53092i) q^{9} +(-5.14653 - 2.97135i) q^{11} +(-0.0766193 - 3.60474i) q^{13} +(7.28508 + 4.20604i) q^{15} +(-1.34982 - 2.33796i) q^{17} +(-1.69485 + 0.978524i) q^{19} +2.66029i q^{21} +(1.36471 - 2.36374i) q^{23} -4.99883 q^{25} -2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} -1.15155i q^{31} +(-13.6913 + 7.90465i) q^{33} +(-1.58105 - 2.73845i) q^{35} +(-5.63310 - 3.25227i) q^{37} +(-8.40680 - 4.61830i) q^{39} +(-3.23351 - 1.86687i) q^{41} +(-3.49562 - 6.05460i) q^{43} +(11.1651 - 6.44617i) q^{45} +0.456071i q^{47} +(0.500000 - 0.866025i) q^{49} -7.18184 q^{51} +0.399286 q^{53} +(9.39568 - 16.2738i) q^{55} +5.20632i q^{57} +(-4.16200 + 2.40293i) q^{59} +(0.578514 + 1.00201i) q^{61} +(3.53092 + 2.03858i) q^{63} +(11.3985 - 0.242277i) q^{65} +(5.43793 + 3.13959i) q^{67} +(-3.63052 - 6.28825i) q^{69} +(-3.90335 + 2.25360i) q^{71} -8.30575i q^{73} +(-6.64917 + 11.5167i) q^{75} +5.94270 q^{77} +7.91410 q^{79} +(2.30414 - 3.99089i) q^{81} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +(-7.97882 - 13.8197i) q^{87} +(3.08423 + 1.78068i) q^{89} +(1.86872 + 3.08348i) q^{91} +(-2.65303 - 1.53173i) q^{93} +(-3.09418 - 5.35928i) q^{95} +(-2.96831 + 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^9	$ 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

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
$3$	1.33015	−	2.30388i	0.767960	−	1.33015i	−0.170707	−	0.985322i	$-0.554605\pi$
$3$	1.33015	−	2.30388i	0.767960	−	1.33015i	0.938667	−	0.344824i	$-0.112061\pi$
$4$		0			0
$5$			3.16209i			1.41413i	0.707148	+	0.707065i	$0.249981\pi$
$5$			3.16209i			1.41413i	−0.707148	+	0.707065i	$0.750019\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		0			0
$9$	−2.03858	−	3.53092i	−0.679526	−	1.17697i
$10$		0			0
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.998001	−	0.0632025i	$-0.979869\pi$
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.553735	−	0.832693i	$-0.686798\pi$
$12$		0			0
$13$	−0.0766193	−	3.60474i	−0.0212504	−	0.999774i
$13$	−0.0766193	−	3.60474i	−0.0212504	−	0.999774i
$14$		0			0
$15$	7.28508	+	4.20604i	1.88100	+	1.08600i
$16$		0			0
$17$	−1.34982	−	2.33796i	−0.327380	−	0.567038i	0.654611	−	0.755966i	$-0.272832\pi$
$17$	−1.34982	−	2.33796i	−0.327380	−	0.567038i	−0.981991	+	0.188927i	$0.939499\pi$
$18$		0			0
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	−0.681651	−	0.731677i	$-0.738738\pi$
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	0.292825	+	0.956166i	$0.405405\pi$
$20$		0			0
$21$			2.66029i			0.580523i
$22$		0			0
$23$	1.36471	−	2.36374i	0.284561	−	0.492874i	−0.687941	−	0.725766i	$-0.741485\pi$
$23$	1.36471	−	2.36374i	0.284561	−	0.492874i	0.972503	+	0.232892i	$0.0748188\pi$
$24$		0			0
$25$	−4.99883			−0.999766
$26$		0			0
$27$	−2.86554			−0.551474
$28$		0			0
$29$	2.99923	−	5.19481i	0.556942	−	0.964652i	−0.440807	−	0.897602i	$-0.645308\pi$
$29$	2.99923	−	5.19481i	0.556942	−	0.964652i	0.997750	−	0.0670505i	$-0.0213589\pi$
$30$		0			0
$31$		−	1.15155i		−	0.206824i	−0.994639	−	0.103412i	$-0.967024\pi$
$31$		−	1.15155i		−	0.206824i	0.994639	−	0.103412i	$-0.0329760\pi$
$32$		0			0
$33$	−13.6913	+	7.90465i	−2.38334	+	1.37602i
$34$		0			0
$35$	−1.58105	−	2.73845i	−0.267246	−	0.462883i
$36$		0			0
$37$	−5.63310	−	3.25227i	−0.926075	−	0.534670i	−0.0405072	−	0.999179i	$-0.512897\pi$
$37$	−5.63310	−	3.25227i	−0.926075	−	0.534670i	−0.885568	+	0.464509i	$0.846231\pi$
$38$		0			0
$39$	−8.40680	−	4.61830i	−1.34617	−	0.739521i
$40$		0			0
$41$	−3.23351	−	1.86687i	−0.504990	−	0.291556i	0.225782	−	0.974178i	$-0.427506\pi$
$41$	−3.23351	−	1.86687i	−0.504990	−	0.291556i	−0.730772	+	0.682622i	$0.760840\pi$
$42$		0			0
$43$	−3.49562	−	6.05460i	−0.533078	−	0.923318i	−0.999254	−	0.0386258i	$-0.987702\pi$
$43$	−3.49562	−	6.05460i	−0.533078	−	0.923318i	0.466176	−	0.884692i	$-0.345631\pi$
$44$		0			0
$45$	11.1651	−	6.44617i	1.66439	−	0.960938i
$46$		0			0
$47$			0.456071i			0.0665248i	0.999447	+	0.0332624i	$0.0105897\pi$
$47$			0.456071i			0.0665248i	−0.999447	+	0.0332624i	$0.989410\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$		0			0
$51$	−7.18184			−1.00566
$52$		0			0
$53$	0.399286			0.0548462			0.0274231	−	0.999624i	$-0.491270\pi$
$53$	0.399286			0.0548462			0.0274231	+	0.999624i	$0.491270\pi$
$54$		0			0
$55$	9.39568	−	16.2738i	1.26691	−	2.19436i
$56$		0			0
$57$			5.20632i			0.689594i
$58$		0			0
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	−0.745827	−	0.666140i	$-0.767945\pi$
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	0.203981	+	0.978975i	$0.434612\pi$
$60$		0			0
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	0.900682	−	0.434479i	$-0.143067\pi$
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	−0.826611	+	0.562774i	$0.809734\pi$
$62$		0			0
$63$	3.53092	+	2.03858i	0.444854	+	0.256837i
$64$		0			0
$65$	11.3985	−	0.242277i	1.41381	−	0.0300508i
$66$		0			0
$67$	5.43793	+	3.13959i	0.664349	+	0.383562i	0.793932	−	0.608007i	$-0.208031\pi$
$67$	5.43793	+	3.13959i	0.664349	+	0.383562i	−0.129583	+	0.991569i	$0.541364\pi$
$68$		0			0
$69$	−3.63052	−	6.28825i	−0.437063	−	0.757016i
$70$		0			0
$71$	−3.90335	+	2.25360i	−0.463242	+	0.267453i	−0.713406	−	0.700751i	$-0.752849\pi$
$71$	−3.90335	+	2.25360i	−0.463242	+	0.267453i	0.250165	+	0.968203i	$0.419515\pi$
$72$		0			0
$73$		−	8.30575i		−	0.972115i	−0.873927	−	0.486057i	$-0.838435\pi$
$73$		−	8.30575i		−	0.972115i	0.873927	−	0.486057i	$-0.161565\pi$
$74$		0			0
$75$	−6.64917	+	11.5167i	−0.767780	+	1.32983i
$76$		0			0
$77$	5.94270			0.677233
$78$		0			0
$79$	7.91410			0.890405			0.445203	−	0.895430i	$-0.353132\pi$
$79$	7.91410			0.890405			0.445203	+	0.895430i	$0.353132\pi$
$80$		0			0
$81$	2.30414	−	3.99089i	0.256016	−	0.443432i
$82$		0			0
$83$			6.19795i			0.680313i	0.940369	+	0.340156i	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		0			0
$85$	7.39284	−	4.26826i	0.801866	−	0.462958i
$86$		0			0
$87$	−7.97882	−	13.8197i	−0.855419	−	1.48163i
$88$		0			0
$89$	3.08423	+	1.78068i	0.326928	+	0.188752i	0.654476	−	0.756083i	$-0.272889\pi$
$89$	3.08423	+	1.78068i	0.326928	+	0.188752i	−0.327549	+	0.944834i	$0.606222\pi$
$90$		0			0
$91$	1.86872	+	3.08348i	0.195895	+	0.323237i
$92$		0			0
$93$	−2.65303	−	1.53173i	−0.275106	−	0.158833i
$94$		0			0
$95$	−3.09418	−	5.35928i	−0.317457	−	0.549851i
$96$		0			0
$97$	−2.96831	+	1.71375i	−0.301386	+	0.174005i	−0.643065	−	0.765811i	$-0.722338\pi$
$97$	−2.96831	+	1.71375i	−0.301386	+	0.174005i	0.341679	+	0.939817i	$0.389004\pi$
$98$		0			0
$99$			24.2293i			2.43513i
$100$		0			0
$101$	−6.66474	+	11.5437i	−0.663167	+	1.14864i	0.316612	+	0.948555i	$0.397455\pi$
$101$	−6.66474	+	11.5437i	−0.663167	+	1.14864i	−0.979779	+	0.200084i	$0.935879\pi$
$102$		0			0
$103$	11.6450			1.14741			0.573706	−	0.819061i	$-0.305505\pi$
$103$	11.6450			1.14741			0.573706	+	0.819061i	$0.305505\pi$
$104$		0			0
$105$	−8.41209			−0.820936
$106$		0			0
$107$	1.96483	−	3.40318i	0.189947	−	0.328998i	−0.755285	−	0.655396i	$-0.772502\pi$
$107$	1.96483	−	3.40318i	0.189947	−	0.328998i	0.945232	+	0.326398i	$0.105835\pi$
$108$		0			0
$109$		−	11.2533i		−	1.07787i	−0.842346	−	0.538936i	$-0.818826\pi$
$109$		−	11.2533i		−	1.07787i	0.842346	−	0.538936i	$-0.181174\pi$
$110$		0			0
$111$	−14.9857	+	8.65199i	−1.42238	+	0.821210i
$112$		0			0
$113$	2.88709	+	5.00059i	0.271595	+	0.470416i	0.969270	−	0.245998i	$-0.0791157\pi$
$113$	2.88709	+	5.00059i	0.271595	+	0.470416i	−0.697676	+	0.716414i	$0.745782\pi$
$114$		0			0
$115$	7.47437	+	4.31533i	0.696989	+	0.402407i
$116$		0			0
$117$	−12.5718	+	7.61907i	−1.16227	+	0.704383i
$118$		0			0
$119$	2.33796	+	1.34982i	0.214320	+	0.123738i
$120$		0			0
$121$	12.1578	+	21.0580i	1.10526	+	1.91436i
$122$		0			0
$123$	−8.60209	+	4.96642i	−0.775625	+	0.447807i
$124$		0			0
$125$			0.00370455i			0.000331345i
$126$		0			0
$127$	−3.06558	+	5.30975i	−0.272027	+	0.471164i	−0.969381	−	0.245563i	$-0.921027\pi$
$127$	−3.06558	+	5.30975i	−0.272027	+	0.471164i	0.697354	+	0.716727i	$0.254361\pi$
$128$		0			0
$129$	−18.5988			−1.63753
$130$		0			0
$131$	−10.2217			−0.893073			−0.446537	−	0.894765i	$-0.647343\pi$
$131$	−10.2217			−0.893073			−0.446537	+	0.894765i	$0.647343\pi$
$132$		0			0
$133$	0.978524	−	1.69485i	0.0848488	−	0.146962i
$134$		0			0
$135$		−	9.06111i		−	0.779856i
$136$		0			0
$137$	−17.2751	+	9.97376i	−1.47591	+	0.852116i	−0.999631	−	0.0271788i	$-0.991348\pi$
$137$	−17.2751	+	9.97376i	−1.47591	+	0.852116i	−0.476278	+	0.879295i	$0.658014\pi$
$138$		0			0
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	−0.869921	−	0.493192i	$-0.835830\pi$
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	0.00784365	−	0.999969i	$-0.497503\pi$
$140$		0			0
$141$	1.05073	+	0.606641i	0.0884877	+	0.0510884i
$142$		0			0
$143$	−10.3166	+	18.7795i	−0.862718	+	1.57042i
$144$		0			0
$145$	16.4265	+	9.48383i	1.36414	+	0.787589i
$146$		0			0
$147$	−1.33015	−	2.30388i	−0.109709	−	0.190021i
$148$		0			0
$149$	−9.28046	+	5.35808i	−0.760285	+	0.438951i	−0.829398	−	0.558658i	$-0.811316\pi$
$149$	−9.28046	+	5.35808i	−0.760285	+	0.438951i	0.0691132	+	0.997609i	$0.477983\pi$
$150$		0			0
$151$		−	8.74416i		−	0.711590i	−0.934564	−	0.355795i	$-0.884210\pi$
$151$		−	8.74416i		−	0.711590i	0.934564	−	0.355795i	$-0.115790\pi$
$152$		0			0
$153$	−5.50343	+	9.53222i	−0.444926	+	0.770634i
$154$		0			0
$155$	3.64130			0.292476
$156$		0			0
$157$	6.50734			0.519342			0.259671	−	0.965697i	$-0.416386\pi$
$157$	6.50734			0.519342			0.259671	+	0.965697i	$0.416386\pi$
$158$		0			0
$159$	0.531109	−	0.919907i	0.0421197	−	0.0729534i
$160$		0			0
$161$			2.72941i			0.215108i
$162$		0			0
$163$	−2.26264	+	1.30634i	−0.177224	+	0.102320i	−0.585988	−	0.810320i	$-0.699293\pi$
$163$	−2.26264	+	1.30634i	−0.177224	+	0.102320i	0.408764	+	0.912640i	$0.365960\pi$
$164$		0			0
$165$	−24.9952	−	43.2930i	−1.94588	−	3.37036i
$166$		0			0
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	0.624534	−	0.780998i	$-0.285289\pi$
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	−0.364097	+	0.931361i	$0.618622\pi$
$168$		0			0
$169$	−12.9883	+	0.552385i	−0.999097	+	0.0424911i
$170$		0			0
$171$	6.91018	+	3.98959i	0.528434	+	0.305092i
$172$		0			0
$173$	6.98838	+	12.1042i	0.531317	+	0.920267i	0.999332	+	0.0365470i	$0.0116358\pi$
$173$	6.98838	+	12.1042i	0.531317	+	0.920267i	−0.468015	+	0.883720i	$0.655031\pi$
$174$		0			0
$175$	4.32911	−	2.49941i	0.327250	−	0.188938i
$176$		0			0
$177$			12.7850i			0.960979i
$178$		0			0
$179$	12.6422	−	21.8968i	0.944919	−	1.63665i	0.189005	−	0.981976i	$-0.439474\pi$
$179$	12.6422	−	21.8968i	0.944919	−	1.63665i	0.755914	−	0.654671i	$-0.227193\pi$
$180$		0			0
$181$	−0.864474			−0.0642559			−0.0321279	−	0.999484i	$-0.510228\pi$
$181$	−0.864474			−0.0642559			−0.0321279	+	0.999484i	$0.510228\pi$
$182$		0			0
$183$	3.07803			0.227535
$184$		0			0
$185$	10.2840	−	17.8124i	0.756093	−	1.30959i
$186$		0			0
$187$			16.0432i			1.17319i
$188$		0			0
$189$	2.48163	−	1.43277i	0.180512	−	0.104219i
$190$		0			0
$191$	7.33382	+	12.7026i	0.530657	+	0.919125i	0.999360	+	0.0357690i	$0.0113881\pi$
$191$	7.33382	+	12.7026i	0.530657	+	0.919125i	−0.468703	+	0.883356i	$0.655279\pi$
$192$		0			0
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.916503	−	0.400029i	$-0.131000\pi$
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.111816	+	0.993729i	$0.464333\pi$
$194$		0			0
$195$	14.6035	−	26.5831i	1.04578	−	1.90365i
$196$		0			0
$197$	9.53510	+	5.50509i	0.679348	+	0.392222i	0.799609	−	0.600521i	$-0.205040\pi$
$197$	9.53510	+	5.50509i	0.679348	+	0.392222i	−0.120262	+	0.992742i	$0.538373\pi$
$198$		0			0
$199$	10.6059	+	18.3699i	0.751829	+	1.30221i	0.946935	+	0.321425i	$0.104162\pi$
$199$	10.6059	+	18.3699i	0.751829	+	1.30221i	−0.195106	+	0.980782i	$0.562505\pi$
$200$		0			0
$201$	14.4665	−	8.35223i	1.02039	−	0.589121i
$202$		0			0
$203$			5.99845i			0.421009i
$204$		0			0
$205$	5.90322	−	10.2247i	0.412299	−	0.714122i
$206$		0			0
$207$	−11.1282			−0.773466
$208$		0			0
$209$	11.6301			0.804474
$210$		0			0
$211$	−8.96788	+	15.5328i	−0.617375	+	1.06932i	0.372588	+	0.927997i	$0.378470\pi$
$211$	−8.96788	+	15.5328i	−0.617375	+	1.06932i	−0.989963	+	0.141327i	$0.954863\pi$
$212$		0			0
$213$			11.9905i			0.821572i
$214$		0			0
$215$	19.1452	−	11.0535i	1.30569	−	0.753842i
$216$		0			0
$217$	0.575774	+	0.997270i	0.0390861	+	0.0676991i
$218$		0			0
$219$	−19.1355	−	11.0479i	−1.29305	−	0.746545i
$220$		0			0
$221$	−8.32431	+	5.04488i	−0.559953	+	0.339356i
$222$		0			0
$223$	13.8834	+	8.01558i	0.929700	+	0.536763i	0.886717	−	0.462313i	$-0.152980\pi$
$223$	13.8834	+	8.01558i	0.929700	+	0.536763i	0.0429835	+	0.999076i	$0.486314\pi$
$224$		0			0
$225$	10.1905	+	17.6505i	0.679366	+	1.17670i
$226$		0			0
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.0508902	−	0.998704i	$-0.483794\pi$
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.890348	+	0.455280i	$0.150461\pi$
$228$		0			0
$229$		−	27.0104i		−	1.78490i	−0.451148	−	0.892449i	$-0.648985\pi$
$229$		−	27.0104i		−	1.78490i	0.451148	−	0.892449i	$-0.351015\pi$
$230$		0			0
$231$	7.90465	−	13.6913i	0.520088	−	0.900819i
$232$		0			0
$233$	−11.5681			−0.757853			−0.378926	−	0.925427i	$-0.623707\pi$
$233$	−11.5681			−0.757853			−0.378926	+	0.925427i	$0.623707\pi$
$234$		0			0
$235$	−1.44214			−0.0940747
$236$		0			0
$237$	10.5269	−	18.2331i	0.683796	−	1.18437i
$238$		0			0
$239$		−	14.6731i		−	0.949122i	−0.880223	−	0.474561i	$-0.842607\pi$
$239$		−	14.6731i		−	0.949122i	0.880223	−	0.474561i	$-0.157393\pi$
$240$		0			0
$241$	12.4246	−	7.17334i	0.800338	−	0.462076i	−0.0432510	−	0.999064i	$-0.513772\pi$
$241$	12.4246	−	7.17334i	0.800338	−	0.462076i	0.843589	+	0.536989i	$0.180438\pi$
$242$		0			0
$243$	−10.4280	−	18.0618i	−0.668956	−	1.15867i
$244$		0			0
$245$	2.73845	+	1.58105i	0.174953	+	0.101009i
$246$		0			0
$247$	3.65718	+	6.03453i	0.232701	+	0.383968i
$248$		0			0
$249$	14.2793	+	8.24417i	0.904916	+	0.522453i
$250$		0			0
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	0.697469	−	0.716615i	$-0.254309\pi$
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	−0.969341	+	0.245719i	$0.920976\pi$
$252$		0			0
$253$	−14.0470	+	8.11004i	−0.883128	+	0.509874i
$254$		0			0
$255$		−	22.7096i		−	1.42213i
$256$		0			0
$257$	5.18197	−	8.97544i	0.323243	−	0.559873i	−0.657912	−	0.753094i	$-0.728560\pi$
$257$	5.18197	−	8.97544i	0.323243	−	0.559873i	0.981155	+	0.193222i	$0.0618936\pi$
$258$		0			0
$259$	6.50454			0.404172
$260$		0			0
$261$	−24.4566			−1.51383
$262$		0			0
$263$	−11.0413	+	19.1241i	−0.680835	+	1.17924i	0.293891	+	0.955839i	$0.405050\pi$
$263$	−11.0413	+	19.1241i	−0.680835	+	1.17924i	−0.974726	+	0.223403i	$0.928284\pi$
$264$		0			0
$265$			1.26258i			0.0775596i
$266$		0			0
$267$	8.20495	−	4.73713i	0.502135	−	0.289908i
$268$		0			0
$269$	−6.46995	−	11.2063i	−0.394480	−	0.683259i	0.598555	−	0.801082i	$-0.295742\pi$
$269$	−6.46995	−	11.2063i	−0.394480	−	0.683259i	−0.993035	+	0.117823i	$0.962409\pi$
$270$		0			0
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.886757	−	0.462235i	$-0.152952\pi$
$271$	15.3069	+	8.83745i	0.929829	+	0.536837i	0.0430712	+	0.999072i	$0.486286\pi$
$272$		0			0
$273$	9.58965	−	0.203830i	0.580392	−	0.0123363i
$274$		0			0
$275$	25.7266	+	14.8533i	1.55137	+	0.895685i
$276$		0			0
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	−0.998835	−	0.0482562i	$-0.984634\pi$
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	0.457626	−	0.889145i	$-0.348700\pi$
$278$		0			0
$279$	−4.06602	+	2.34752i	−0.243426	+	0.140542i
$280$		0			0
$281$		−	2.44178i		−	0.145665i	−0.997344	−	0.0728323i	$-0.976796\pi$
$281$		−	2.44178i		−	0.145665i	0.997344	−	0.0728323i	$-0.0232038\pi$
$282$		0			0
$283$	14.3620	−	24.8757i	0.853732	−	1.47871i	−0.0240853	−	0.999710i	$-0.507667\pi$
$283$	14.3620	−	24.8757i	0.853732	−	1.47871i	0.877817	−	0.478996i	$-0.158999\pi$
$284$		0			0
$285$	−16.4629			−0.975176
$286$		0			0
$287$	3.73374			0.220396
$288$		0			0
$289$	4.85596	−	8.41078i	0.285645	−	0.494752i
$290$		0			0
$291$			9.11818i			0.534517i
$292$		0			0
$293$	25.4013	−	14.6654i	1.48396	−	0.856763i	0.484124	−	0.874999i	$-0.339138\pi$
$293$	25.4013	−	14.6654i	1.48396	−	0.856763i	0.999834	+	0.0182359i	$0.00580499\pi$
$294$		0			0
$295$	−7.59829	−	13.1606i	−0.442390	−	0.766241i
$296$		0			0
$297$	14.7476	+	8.51453i	0.855742	+	0.494063i
$298$		0			0
$299$	−8.62523	−	4.73830i	−0.498810	−	0.274023i
$300$		0			0
$301$	6.05460	+	3.49562i	0.348981	+	0.201484i
$302$		0			0
$303$	17.7302	+	30.7096i	1.01857	+	1.76422i
$304$		0			0
$305$	−3.16846	+	1.82931i	−0.181426	+	0.104746i
$306$		0			0
$307$		−	7.06910i		−	0.403455i	−0.979442	−	0.201728i	$-0.935344\pi$
$307$		−	7.06910i		−	0.403455i	0.979442	−	0.201728i	$-0.0646555\pi$
$308$		0			0
$309$	15.4895	−	26.8286i	0.881166	−	1.52623i
$310$		0			0
$311$	−22.2686			−1.26274			−0.631368	−	0.775483i	$-0.717506\pi$
$311$	−22.2686			−1.26274			−0.631368	+	0.775483i	$0.717506\pi$
$312$		0			0
$313$	−28.0840			−1.58740			−0.793700	−	0.608309i	$-0.791848\pi$
$313$	−28.0840			−1.58740			−0.793700	+	0.608309i	$0.791848\pi$
$314$		0			0
$315$	−6.44617	+	11.1651i	−0.363200	+	0.629082i
$316$		0			0
$317$			19.5155i			1.09610i	0.836446	+	0.548049i	$0.184629\pi$
$317$			19.5155i			1.09610i	−0.836446	+	0.548049i	$0.815371\pi$
$318$		0			0
$319$	−30.8712	+	17.8235i	−1.72845	+	0.997924i
$320$		0			0
$321$	−5.22702	−	9.05346i	−0.291744	−	0.505315i
$322$		0			0
$323$	4.57550	+	2.64167i	0.254588	+	0.146986i
$324$		0			0
$325$	0.383007	+	18.0195i	0.0212454	+	0.999540i
$326$		0			0
$327$	−25.9263	−	14.9686i	−1.43373	−	0.827764i
$328$		0			0
$329$	−0.228035	−	0.394969i	−0.0125720	−	0.0217753i
$330$		0			0
$331$	−13.5367	+	7.81539i	−0.744042	+	0.429573i	−0.823537	−	0.567263i	$-0.808002\pi$
$331$	−13.5367	+	7.81539i	−0.744042	+	0.429573i	0.0794953	+	0.996835i	$0.474669\pi$
$332$		0			0
$333$			26.5200i			1.45329i
$334$		0			0
$335$	−9.92767	+	17.1952i	−0.542407	+	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$		0			0
$339$	15.3610			0.834295
$340$		0			0
$341$	−3.42165	+	5.92647i	−0.185293	+	0.320937i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$	19.8840	−	11.4800i	1.07052	−	0.618065i
$346$		0			0
$347$	−7.97952	−	13.8209i	−0.428363	−	0.741946i	0.568365	−	0.822777i	$-0.307576\pi$
$347$	−7.97952	−	13.8209i	−0.428363	−	0.741946i	−0.996728	+	0.0808303i	$0.974243\pi$
$348$		0			0
$349$	5.90375	+	3.40853i	0.316021	+	0.182455i	0.649617	−	0.760261i	$-0.274929\pi$
$349$	5.90375	+	3.40853i	0.316021	+	0.182455i	−0.333597	+	0.942716i	$0.608262\pi$
$350$		0			0
$351$	0.219556	+	10.3295i	0.0117190	+	0.551349i
$352$		0			0
$353$	12.1272	+	7.00163i	0.645465	+	0.372659i	0.786716	−	0.617314i	$-0.211779\pi$
$353$	12.1272	+	7.00163i	0.645465	+	0.372659i	−0.141252	+	0.989974i	$0.545113\pi$
$354$		0			0
$355$	−7.12608	−	12.3427i	−0.378213	−	0.655085i
$356$		0			0
$357$	6.21965	−	3.59092i	0.329179	−	0.190052i
$358$		0			0
$359$			5.41494i			0.285789i	0.989738	+	0.142895i	$0.0456410\pi$
$359$			5.41494i			0.285789i	−0.989738	+	0.142895i	$0.954359\pi$
$360$		0			0
$361$	−7.58498	+	13.1376i	−0.399210	+	0.691451i
$362$		0			0
$363$	64.6867			3.39517
$364$		0			0
$365$	26.2636			1.37470
$366$		0			0
$367$	15.0159	−	26.0083i	0.783822	−	1.35762i	−0.145878	−	0.989303i	$-0.546601\pi$
$367$	15.0159	−	26.0083i	0.783822	−	1.35762i	0.929700	−	0.368317i	$-0.120066\pi$
$368$		0			0
$369$			15.2230i			0.792480i
$370$		0			0
$371$	−0.345792	+	0.199643i	−0.0179526	+	0.0103649i
$372$		0			0
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	−0.997959	−	0.0638526i	$-0.979661\pi$
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	0.443682	−	0.896184i	$-0.353672\pi$
$374$		0			0
$375$	0.00853484	+	0.00492759i	0.000440737	+	0.000254460i
$376$		0			0
$377$	−18.9557	−	10.4134i	−0.976270	−	0.536317i
$378$		0			0
$379$	8.20693	+	4.73827i	0.421562	+	0.243389i	0.695745	−	0.718289i	$-0.255074\pi$
$379$	8.20693	+	4.73827i	0.421562	+	0.243389i	−0.274184	+	0.961677i	$0.588408\pi$
$380$		0			0
$381$	8.15535	+	14.1255i	0.417811	+	0.723670i
$382$		0			0
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	−0.375007	−	0.927022i	$-0.622360\pi$
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	0.615321	+	0.788277i	$0.289026\pi$
$384$		0			0
$385$			18.7914i			0.957696i
$386$		0			0
$387$	−14.2522	+	24.6855i	−0.724480	+	1.25484i
$388$		0			0
$389$	10.6422			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$389$	10.6422			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$390$		0			0
$391$	−7.36845			−0.372638
$392$		0			0
$393$	−13.5963	+	23.5495i	−0.685845	+	1.18792i
$394$		0			0
$395$			25.0251i			1.25915i
$396$		0			0
$397$	32.2035	−	18.5927i	1.61625	−	0.933140i	0.628367	−	0.777917i	$-0.283724\pi$
$397$	32.2035	−	18.5927i	1.61625	−	0.933140i	0.987879	−	0.155223i	$-0.0496097\pi$
$398$		0			0
$399$	−2.60316	−	4.50880i	−0.130321	−	0.225723i
$400$		0			0
$401$	−0.776487	−	0.448305i	−0.0387759	−	0.0223873i	0.480487	−	0.877002i	$-0.340460\pi$
$401$	−0.776487	−	0.448305i	−0.0387759	−	0.0223873i	−0.519263	+	0.854615i	$0.673793\pi$
$402$		0			0
$403$	−4.15103	+	0.0882308i	−0.206777	+	0.00439509i
$404$		0			0
$405$	12.6196	+	7.28590i	0.627071	+	0.362039i
$406$		0			0
$407$	19.3273	+	33.4758i	0.958016	+	1.65933i
$408$		0			0
$409$	21.2846	−	12.2886i	1.05245	−	0.607635i	0.129119	−	0.991629i	$-0.458785\pi$
$409$	21.2846	−	12.2886i	1.05245	−	0.607635i	0.923335	+	0.383995i	$0.125452\pi$
$410$		0			0
$411$			53.0662i			2.61756i
$412$		0			0
$413$	2.40293	−	4.16200i	0.118241	−	0.204799i
$414$		0			0
$415$	−19.5985			−0.962052
$416$		0			0
$417$	−54.0770			−2.64816
$418$		0			0
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	−0.944167	−	0.329468i	$-0.893131\pi$
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	0.757411	+	0.652938i	$0.226464\pi$
$420$		0			0
$421$		−	25.0780i		−	1.22223i	−0.791544	−	0.611113i	$-0.790722\pi$
$421$		−	25.0780i		−	1.22223i	0.791544	−	0.611113i	$-0.209278\pi$
$422$		0			0
$423$	1.61035	−	0.929736i	0.0782979	−	0.0452053i
$424$		0			0
$425$	6.74753	+	11.6871i	0.327303	+	0.566906i
$426$		0			0
$427$	−1.00201	−	0.578514i	−0.0484909	−	0.0279962i
$428$		0			0
$429$	29.5432	+	48.7478i	1.42636	+	2.35356i
$430$		0			0
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	0.329474	−	0.944165i	$-0.393129\pi$
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	−0.652934	+	0.757415i	$0.726462\pi$
$432$		0			0
$433$	17.9880	+	31.1561i	0.864448	+	1.49727i	0.867594	+	0.497273i	$0.165665\pi$
$433$	17.9880	+	31.1561i	0.864448	+	1.49727i	−0.00314644	+	0.999995i	$0.501002\pi$
$434$		0			0
$435$	43.6992	−	25.2298i	2.09522	−	1.20967i
$436$		0			0
$437$			5.34160i			0.255523i
$438$		0			0
$439$	14.1175	−	24.4523i	0.673792	−	1.16704i	−0.303028	−	0.952982i	$-0.597998\pi$
$439$	14.1175	−	24.4523i	0.673792	−	1.16704i	0.976820	−	0.214061i	$-0.0686691\pi$
$440$		0			0
$441$	−4.07715			−0.194150
$442$		0			0
$443$	−28.7918			−1.36794			−0.683970	−	0.729511i	$-0.739748\pi$
$443$	−28.7918			−1.36794			−0.683970	+	0.729511i	$0.739748\pi$
$444$		0			0
$445$	−5.63068	+	9.75262i	−0.266920	+	0.462319i
$446$		0			0
$447$			28.5081i			1.34839i
$448$		0			0
$449$	−25.2795	+	14.5951i	−1.19301	+	0.688785i	−0.958988	−	0.283446i	$-0.908522\pi$
$449$	−25.2795	+	14.5951i	−1.19301	+	0.688785i	−0.234023	+	0.972231i	$0.575189\pi$
$450$		0			0
$451$	11.0942	+	19.2158i	0.522408	+	0.904836i
$452$		0			0
$453$	−20.1455	−	11.6310i	−0.946518	−	0.546473i
$454$		0			0
$455$	−9.75026	+	5.90907i	−0.457099	+	0.277022i
$456$		0			0
$457$	−27.4399	−	15.8424i	−1.28358	−	0.741077i	−0.306081	−	0.952006i	$-0.599018\pi$
$457$	−27.4399	−	15.8424i	−1.28358	−	0.741077i	−0.977501	+	0.210929i	$0.932351\pi$
$458$		0			0
$459$	3.86797	+	6.69952i	0.180541	+	0.312707i
$460$		0			0
$461$	−19.1407	+	11.0509i	−0.891471	+	0.514691i	−0.874424	−	0.485163i	$-0.838760\pi$
$461$	−19.1407	+	11.0509i	−0.891471	+	0.514691i	−0.0170480	+	0.999855i	$0.505427\pi$
$462$		0			0
$463$		−	38.8811i		−	1.80696i	−0.428632	−	0.903479i	$-0.641004\pi$
$463$		−	38.8811i		−	1.80696i	0.428632	−	0.903479i	$-0.358996\pi$
$464$		0			0
$465$	4.84346	−	8.38913i	0.224610	−	0.389036i
$466$		0			0
$467$	13.2823			0.614632			0.307316	−	0.951607i	$-0.400569\pi$
$467$	13.2823			0.614632			0.307316	+	0.951607i	$0.400569\pi$
$468$		0			0
$469$	−6.27918			−0.289946
$470$		0			0
$471$	8.65571	−	14.9921i	0.398834	−	0.690801i
$472$		0			0
$473$			41.5469i			1.91033i
$474$		0			0
$475$	8.47228	−	4.89147i	0.388735	−	0.224436i
$476$		0			0
$477$	−0.813975	−	1.40985i	−0.0372694	−	0.0645524i
$478$		0			0
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	0.362947	−	0.931810i	$-0.381770\pi$
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	−0.625497	+	0.780226i	$0.715104\pi$
$480$		0			0
$481$	−11.2920	+	20.5550i	−0.514870	+	0.937228i
$482$		0			0
$483$	6.28825	+	3.63052i	0.286125	+	0.165194i
$484$		0			0
$485$	−5.41905	−	9.38607i	−0.246066	−	0.426200i
$486$		0			0
$487$	−28.9860	+	16.7351i	−1.31348	+	0.758338i	−0.982671	−	0.185359i	$-0.940655\pi$
$487$	−28.9860	+	16.7351i	−1.31348	+	0.758338i	−0.330809	+	0.943698i	$0.607322\pi$
$488$		0			0
$489$			6.95047i			0.314311i
$490$		0			0
$491$	18.6643	−	32.3276i	0.842310	−	1.45892i	−0.0456264	−	0.998959i	$-0.514528\pi$
$491$	18.6643	−	32.3276i	0.842310	−	1.45892i	0.887937	−	0.459966i	$-0.152138\pi$
$492$		0			0
$493$	−16.1937			−0.729327
$494$		0			0
$495$	−76.6152			−3.44360
$496$		0			0
$497$	2.25360	−	3.90335i	0.101088	−	0.175089i
$498$		0			0
$499$		−	34.1327i		−	1.52799i	−0.645223	−	0.763994i	$-0.723236\pi$
$499$		−	34.1327i		−	1.52799i	0.645223	−	0.763994i	$-0.276764\pi$
$500$		0			0
$501$	8.95342	−	5.16926i	0.400009	−	0.230946i
$502$		0			0
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	0.984674	−	0.174407i	$-0.0558008\pi$
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	−0.643378	+	0.765549i	$0.722467\pi$
$504$		0			0
$505$	−36.5022	−	21.0745i	−1.62433	−	0.937805i
$506$		0			0
$507$	−16.0037	+	30.6581i	−0.710747	+	1.36158i
$508$		0			0
$509$	−16.0189	−	9.24851i	−0.710025	−	0.409933i	0.101046	−	0.994882i	$-0.467781\pi$
$509$	−16.0189	−	9.24851i	−0.710025	−	0.409933i	−0.811070	+	0.584949i	$0.801115\pi$
$510$		0			0
$511$	4.15288	+	7.19299i	0.183712	+	0.318199i
$512$		0			0
$513$	4.85668	−	2.80400i	0.214427	−	0.123800i
$514$		0			0
$515$			36.8224i			1.62259i
$516$		0			0
$517$	1.35515	−	2.34718i	0.0595992	−	0.103229i
$518$		0			0
$519$	37.1823			1.63212
$520$		0			0
$521$	23.5865			1.03334			0.516671	−	0.856184i	$-0.327171\pi$
$521$	23.5865			1.03334			0.516671	+	0.856184i	$0.327171\pi$
$522$		0			0
$523$	6.15294	−	10.6572i	0.269049	−	0.466007i	−0.699567	−	0.714567i	$-0.746624\pi$
$523$	6.15294	−	10.6572i	0.269049	−	0.466007i	0.968617	+	0.248560i	$0.0799572\pi$
$524$		0			0
$525$		−	13.2983i		−	0.580387i
$526$		0			0
$527$	−2.69227	+	1.55438i	−0.117277	+	0.0677101i
$528$		0			0
$529$	7.77515	+	13.4670i	0.338050	+	0.585520i
$530$		0			0
$531$	16.9691	+	9.79712i	0.736397	+	0.425159i
$532$		0			0
$533$	−6.48183	+	11.7990i	−0.280759	+	0.511072i
$534$		0			0
$535$	10.7612	+	6.21297i	0.465246	+	0.268610i
$536$		0			0
$537$	−33.6318	−	58.2520i	−1.45132	−	2.51376i
$538$		0			0
$539$	−5.14653	+	2.97135i	−0.221677	+	0.127985i
$540$		0			0
$541$		−	19.4411i		−	0.835838i	−0.908484	−	0.417919i	$-0.862760\pi$
$541$		−	19.4411i		−	0.835838i	0.908484	−	0.417919i	$-0.137240\pi$
$542$		0			0
$543$	−1.14988	+	1.99165i	−0.0493460	+	0.0854697i
$544$		0			0
$545$	35.5841			1.52425
$546$		0			0
$547$	−40.2163			−1.71953			−0.859763	−	0.510693i	$-0.829389\pi$
$547$	−40.2163			−1.71953			−0.859763	+	0.510693i	$0.829389\pi$
$548$		0			0
$549$	2.35869	−	4.08537i	0.100666	−	0.174359i
$550$		0			0
$551$			11.7393i			0.500109i
$552$		0			0
$553$	−6.85381	+	3.95705i	−0.291454	+	0.168271i
$554$		0			0
$555$	−27.3584	−	47.3861i	−1.16130	−	2.01143i
$556$		0			0
$557$	6.89702	+	3.98199i	0.292236	+	0.168722i	0.638950	−	0.769248i	$-0.279369\pi$
$557$	6.89702	+	3.98199i	0.292236	+	0.168722i	−0.346714	+	0.937971i	$0.612703\pi$
$558$		0			0
$559$	−21.5574	+	13.0647i	−0.911781	+	0.552578i
$560$		0			0
$561$	36.9615	+	21.3397i	1.56052	+	0.900965i
$562$		0			0
$563$	0.711981	+	1.23319i	0.0300064	+	0.0519726i	0.880639	−	0.473789i	$-0.157114\pi$
$563$	0.711981	+	1.23319i	0.0300064	+	0.0519726i	−0.850632	+	0.525761i	$0.823781\pi$
$564$		0			0
$565$	−15.8123	+	9.12924i	−0.665229	+	0.384070i
$566$		0			0
$567$			4.60828i			0.193530i
$568$		0			0
$569$	−9.25946	+	16.0379i	−0.388177	+	0.672342i	−0.992204	−	0.124622i	$-0.960228\pi$
$569$	−9.25946	+	16.0379i	−0.388177	+	0.672342i	0.604028	+	0.796963i	$0.293562\pi$
$570$		0			0
$571$	4.35766			0.182362			0.0911812	−	0.995834i	$-0.470936\pi$
$571$	4.35766			0.182362			0.0911812	+	0.995834i	$0.470936\pi$
$572$		0			0
$573$	39.0202			1.63009
$574$		0			0
$575$	−6.82194	+	11.8159i	−0.284494	+	0.492759i
$576$		0			0
$577$		−	9.56416i		−	0.398161i	−0.979983	−	0.199081i	$-0.936204\pi$
$577$		−	9.56416i		−	0.398161i	0.979983	−	0.199081i	$-0.0637955\pi$
$578$		0			0
$579$	38.0046	−	21.9419i	1.57942	−	0.911876i
$580$		0			0
$581$	−3.09897	−	5.36758i	−0.128567	−	0.222685i
$582$		0			0
$583$	−2.05494	−	1.18642i	−0.0851068	−	0.0491364i
$584$		0			0
$585$	−24.0922	−	39.7533i	−0.996090	−	1.64360i
$586$		0			0
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	0.541595	−	0.840640i	$-0.317821\pi$
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	−0.457218	+	0.889355i	$0.651154\pi$
$588$		0			0
$589$	1.12682	+	1.95171i	0.0464297	+	0.0804186i
$590$		0			0
$591$	25.3661	−	14.6452i	1.04342	−	0.602421i
$592$		0			0
$593$		−	40.4292i		−	1.66023i	−0.557594	−	0.830114i	$-0.688275\pi$
$593$		−	40.4292i		−	1.66023i	0.557594	−	0.830114i	$-0.311725\pi$
$594$		0			0
$595$	−4.26826	+	7.39284i	−0.174982	+	0.303077i
$596$		0			0
$597$	56.4294			2.30950
$598$		0			0
$599$	38.5873			1.57663			0.788316	−	0.615270i	$-0.210953\pi$
$599$	38.5873			1.57663			0.788316	+	0.615270i	$0.210953\pi$
$600$		0			0
$601$	−4.08115	+	7.06877i	−0.166474	+	0.288341i	−0.937178	−	0.348852i	$-0.886571\pi$
$601$	−4.08115	+	7.06877i	−0.166474	+	0.288341i	0.770704	+	0.637193i	$0.219905\pi$
$602$		0			0
$603$		−	25.6012i		−	1.04256i
$604$		0			0
$605$	−66.5872	+	38.4442i	−2.70716	+	1.56298i
$606$		0			0
$607$	3.79263	+	6.56902i	0.153938	+	0.266628i	0.932672	−	0.360726i	$-0.117471\pi$
$607$	3.79263	+	6.56902i	0.153938	+	0.266628i	−0.778734	+	0.627354i	$0.784138\pi$
$608$		0			0
$609$	13.8197	+	7.97882i	0.560003	+	0.323318i
$610$		0			0
$611$	1.64402	−	0.0349438i	0.0665098	−	0.00141368i
$612$		0			0
$613$	−13.4908	−	7.78892i	−0.544889	−	0.314592i	0.202169	−	0.979351i	$-0.435201\pi$
$613$	−13.4908	−	7.78892i	−0.544889	−	0.314592i	−0.747058	+	0.664759i	$0.768534\pi$
$614$		0			0
$615$	−15.7043	−	27.2006i	−0.633258	−	1.09683i
$616$		0			0
$617$	20.6709	−	11.9343i	0.832177	−	0.480458i	−0.0224202	−	0.999749i	$-0.507137\pi$
$617$	20.6709	−	11.9343i	0.832177	−	0.480458i	0.854598	+	0.519291i	$0.173804\pi$
$618$		0			0
$619$		−	19.4963i		−	0.783622i	−0.920046	−	0.391811i	$-0.871849\pi$
$619$		−	19.4963i		−	0.783622i	0.920046	−	0.391811i	$-0.128151\pi$
$620$		0			0
$621$	−3.91063	+	6.77341i	−0.156928	+	0.271807i
$622$		0			0
$623$	−3.56136			−0.142683
$624$		0			0
$625$	−25.0059			−1.00023
$626$		0			0
$627$	15.4698	−	26.7945i	0.617804	−	1.07007i
$628$		0			0
$629$			17.5599i			0.700161i
$630$		0			0
$631$	22.2239	−	12.8309i	0.884718	−	0.510792i	0.0125066	−	0.999922i	$-0.496019\pi$
$631$	22.2239	−	12.8309i	0.884718	−	0.510792i	0.872211	+	0.489130i	$0.162686\pi$
$632$		0			0
$633$	23.8572	+	41.3219i	0.948238	+	1.64240i
$634$		0			0
$635$	−16.7899	−	9.69366i	−0.666287	−	0.384681i
$636$		0			0
$637$	−3.16010	−	1.73601i	−0.125208	−	0.0687834i
$638$		0			0
$639$	15.9145	+	9.18826i	0.629569	+	0.363482i
$640$		0			0
$641$	−0.553020	−	0.957859i	−0.0218430	−	0.0378332i	0.854897	−	0.518797i	$-0.173620\pi$
$641$	−0.553020	−	0.957859i	−0.0218430	−	0.0378332i	−0.876740	+	0.480964i	$0.840287\pi$
$642$		0			0
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	−0.700018	−	0.714125i	$-0.746825\pi$
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	0.268442	+	0.963296i	$0.413491\pi$
$644$		0			0
$645$		−	58.8110i		−	2.31568i
$646$		0			0
$647$	−12.8574	+	22.2697i	−0.505477	+	0.875512i	0.494503	+	0.869176i	$0.335350\pi$
$647$	−12.8574	+	22.2697i	−0.505477	+	0.875512i	−0.999980	+	0.00633579i	$0.997983\pi$
$648$		0			0
$649$	28.5598			1.12107
$650$		0			0
$651$	3.06345			0.120066
$652$		0			0
$653$	−12.6303	+	21.8764i	−0.494263	+	0.856089i	−0.999978	−	0.00661158i	$-0.997895\pi$
$653$	−12.6303	+	21.8764i	−0.494263	+	0.856089i	0.505715	+	0.862701i	$0.331229\pi$
$654$		0			0
$655$		−	32.3219i		−	1.26292i
$656$		0			0
$657$	−29.3269	+	16.9319i	−1.14415	+	0.660577i
$658$		0			0
$659$	11.4882	+	19.8982i	0.447517	+	0.775123i	0.998224	−	0.0595764i	$-0.0189750\pi$
$659$	11.4882	+	19.8982i	0.447517	+	0.775123i	−0.550707	+	0.834699i	$0.685642\pi$
$660$		0			0
$661$	26.3554	+	15.2163i	1.02511	+	0.591845i	0.915579	−	0.402138i	$-0.131733\pi$
$661$	26.3554	+	15.2163i	1.02511	+	0.591845i	0.109528	+	0.993984i	$0.465066\pi$
$662$		0			0
$663$	0.550267	+	25.8886i	0.0213706	+	1.00543i
$664$		0			0
$665$	5.35928	+	3.09418i	0.207824	+	0.119987i
$666$		0			0
$667$	−8.18613	−	14.1788i	−0.316968	−	0.549005i
$668$		0			0
$669$	36.9339	−	21.3238i	1.42795	−	0.824425i
$670$		0			0
$671$		−	6.87586i		−	0.265440i
$672$		0			0
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	−0.742468	−	0.669881i	$-0.766345\pi$
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	0.951368	+	0.308056i	$0.0996784\pi$
$674$		0			0
$675$	14.3244			0.551345
$676$		0			0
$677$	−18.1209			−0.696442			−0.348221	−	0.937412i	$-0.613214\pi$
$677$	−18.1209			−0.696442			−0.348221	+	0.937412i	$0.613214\pi$
$678$		0			0
$679$	1.71375	−	2.96831i	0.0657679	−	0.113913i
$680$		0			0
$681$		−	43.5624i		−	1.66931i
$682$		0			0
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.971855	−	0.235580i	$-0.924301\pi$
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.281909	+	0.959441i	$0.590968\pi$
$684$		0			0
$685$	−31.5380	−	54.6254i	−1.20500	−	2.08713i
$686$		0			0
$687$	−62.2288	−	35.9278i	−2.37418	−	1.37073i
$688$		0			0
$689$	−0.0305930	−	1.43932i	−0.00116550	−	0.0548338i
$690$		0			0
$691$	−26.0034	−	15.0131i	−0.989216	−	0.571124i	−0.0841761	−	0.996451i	$-0.526826\pi$
$691$	−26.0034	−	15.0131i	−0.989216	−	0.571124i	−0.905040	+	0.425327i	$0.860159\pi$
$692$		0			0
$693$	−12.1146	−	20.9832i	−0.460197	−	0.797085i
$694$		0			0
$695$	55.6658	−	32.1387i	2.11152	−	1.21909i
$696$		0			0
$697$			10.0798i			0.381798i
$698$		0			0
$699$	−15.3873	+	26.6516i	−0.582001	+	1.00805i
$700$		0			0
$701$	0.116177			0.00438796			0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177			0.00438796			0.00219398	+	0.999998i	$0.499302\pi$
$702$		0			0
$703$	12.7297			0.480110
$704$		0			0
$705$	−1.91825	+	3.32251i	−0.0722456	+	0.125133i
$706$		0			0
$707$		−	13.3295i		−	0.501307i
$708$		0			0
$709$	5.82829	−	3.36497i	0.218886	−	0.126374i	−0.386548	−	0.922269i	$-0.626333\pi$
$709$	5.82829	−	3.36497i	0.218886	−	0.126374i	0.605434	+	0.795895i	$0.292999\pi$
$710$		0			0
$711$	−16.1335	−	27.9440i	−0.605053	−	1.04798i
$712$		0			0
$713$	−2.72196	−	1.57153i	−0.101938	−	0.0588541i
$714$		0			0
$715$	−59.3826	−	32.6221i	−2.22078	−	1.22000i
$716$		0			0
$717$	−33.8050	−	19.5173i	−1.26247	−	0.728888i
$718$		0			0
$719$	−23.4039	−	40.5367i	−0.872818	−	1.51177i	−0.859069	−	0.511860i	$-0.828957\pi$
$719$	−23.4039	−	40.5367i	−0.872818	−	1.51177i	−0.0137492	−	0.999905i	$-0.504377\pi$
$720$		0			0
$721$	−10.0848	+	5.82248i	−0.375579	+	0.216840i
$722$		0			0
$723$		−	38.1664i		−	1.41942i
$724$		0			0
$725$	−14.9926	+	25.9680i	−0.556812	+	0.964426i
$726$		0			0
$727$	−13.3362			−0.494611			−0.247305	−	0.968938i	$-0.579545\pi$
$727$	−13.3362			−0.494611			−0.247305	+	0.968938i	$0.579545\pi$
$728$		0			0
$729$	−41.6582			−1.54290
$730$		0			0
$731$	−9.43694	+	16.3453i	−0.349038	+	0.604551i
$732$		0			0
$733$		−	29.4612i		−	1.08817i	−0.839029	−	0.544087i	$-0.816876\pi$
$733$		−	29.4612i		−	1.08817i	0.839029	−	0.544087i	$-0.183124\pi$
$734$		0			0
$735$	7.28508	−	4.20604i	0.268714	−	0.155142i
$736$		0			0
$737$	−18.6576	−	32.3160i	−0.687263	−	1.19037i
$738$		0			0
$739$	10.4184	+	6.01509i	0.383249	+	0.221269i	0.679231	−	0.733925i	$-0.262314\pi$
$739$	10.4184	+	6.01509i	0.383249	+	0.221269i	−0.295982	+	0.955193i	$0.595647\pi$
$740$		0			0
$741$	18.7674	−	0.398904i	0.689438	−	0.0146541i
$742$		0			0
$743$	18.9509	+	10.9413i	0.695242	+	0.401398i	0.805573	−	0.592497i	$-0.201858\pi$
$743$	18.9509	+	10.9413i	0.695242	+	0.401398i	−0.110331	+	0.993895i	$0.535191\pi$
$744$		0			0
$745$	−16.9427	−	29.3457i	−0.620734	−	1.07514i
$746$		0			0
$747$	21.8844	−	12.6350i	0.800710	−	0.462290i
$748$		0			0
$749$			3.92966i			0.143587i
$750$		0			0
$751$	−17.3746	+	30.0937i	−0.634008	+	1.09813i	0.352717	+	0.935730i	$0.385258\pi$
$751$	−17.3746	+	30.0937i	−0.634008	+	1.09813i	−0.986724	+	0.162403i	$0.948075\pi$
$752$		0			0
$753$	−22.9172			−0.835147
$754$		0			0
$755$	27.6498			1.00628
$756$		0			0
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	0.122481	+	0.992471i	$0.460915\pi$
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	−0.920745	+	0.390164i	$0.872418\pi$
$758$		0			0
$759$			43.1502i			1.56625i
$760$		0			0
$761$	0.122449	−	0.0706957i	0.00443876	−	0.00256272i	−0.497779	−	0.867304i	$-0.665851\pi$
$761$	0.122449	−	0.0706957i	0.00443876	−	0.00256272i	0.502218	+	0.864741i	$0.332518\pi$
$762$		0			0
$763$	5.62666	+	9.74566i	0.203699	+	0.352817i
$764$		0			0
$765$	−30.1418	−	17.4024i	−1.08978	−	0.629183i
$766$		0			0
$767$	8.98082	+	14.8188i	0.324279	+	0.535076i
$768$		0			0
$769$	11.8200	+	6.82429i	0.426241	+	0.246090i	0.697744	−	0.716347i	$-0.254187\pi$
$769$	11.8200	+	6.82429i	0.426241	+	0.246090i	−0.271503	+	0.962438i	$0.587521\pi$
$770$		0			0
$771$	−13.7856	−	23.8773i	−0.496475	−	0.859920i
$772$		0			0
$773$	15.2328	−	8.79469i	0.547887	−	0.316323i	−0.200382	−	0.979718i	$-0.564218\pi$
$773$	15.2328	−	8.79469i	0.547887	−	0.316323i	0.748269	+	0.663395i	$0.230885\pi$
$774$		0			0
$775$			5.75639i			0.206776i
$776$		0			0
$777$	8.65199	−	14.9857i	0.310388	−	0.537608i
$778$		0			0
$779$	7.30711			0.261804
$780$		0			0
$781$	26.7849			0.958439
$782$		0			0
$783$	−8.59441	+	14.8860i	−0.307139	+	0.531981i
$784$		0			0
$785$			20.5768i			0.734418i
$786$		0			0
$787$	−2.57075	+	1.48422i	−0.0916374	+	0.0529069i	−0.545118	−	0.838359i	$-0.683515\pi$
$787$	−2.57075	+	1.48422i	−0.0916374	+	0.0529069i	0.453481	+	0.891266i	$0.350182\pi$
$788$		0			0
$789$	29.3731	+	50.8756i	1.04571	+	1.81122i
$790$		0			0
$791$	−5.00059	−	2.88709i	−0.177800	−	0.102653i
$792$		0			0
$793$	3.56768	−	2.16216i	0.126692	−	0.0767807i
$794$		0			0
$795$	2.90883	+	1.67941i	0.103166	+	0.0595627i
$796$		0			0
$797$	4.72611	+	8.18586i	0.167407	+	0.289958i	0.937508	−	0.347965i	$-0.113127\pi$
$797$	4.72611	+	8.18586i	0.167407	+	0.289958i	−0.770100	+	0.637923i	$0.779794\pi$
$798$		0			0
$799$	1.06628	−	0.615614i	0.0377221	−	0.0217789i
$800$		0			0
$801$		−	14.5202i		−	0.513047i
$802$		0			0
$803$	−24.6793	+	42.7458i	−0.870913	+	1.50847i
$804$		0			0
$805$	−8.63066			−0.304191
$806$		0			0
$807$	−34.4239			−1.21178
$808$		0			0
$809$	0.581273	−	1.00679i	0.0204365	−	0.0353970i	−0.855626	−	0.517594i	$-0.826828\pi$
$809$	0.581273	−	1.00679i	0.0204365	−	0.0353970i	0.876063	+	0.482197i	$0.160161\pi$
$810$		0			0
$811$			19.5561i			0.686706i	0.939206	+	0.343353i	$0.111563\pi$
$811$			19.5561i			0.686706i	−0.939206	+	0.343353i	$0.888437\pi$
$812$		0			0
$813$	40.7209	−	23.5102i	1.42814	−	0.824538i
$814$		0			0
$815$	−4.13075	−	7.15467i	−0.144694	−	0.250617i
$816$		0			0
$817$	11.8491	+	6.84111i	0.414549	+	0.239340i
$818$		0			0
$819$	7.07800	−	12.8842i	0.247325	−	0.450211i
$820$		0			0
$821$	10.9283	+	6.30945i	0.381400	+	0.220201i	0.678427	−	0.734668i	$-0.262662\pi$
$821$	10.9283	+	6.30945i	0.381400	+	0.220201i	−0.297027	+	0.954869i	$0.595995\pi$
$822$		0			0
$823$	3.28404	+	5.68812i	0.114474	+	0.198275i	0.917570	−	0.397575i	$-0.130148\pi$
$823$	3.28404	+	5.68812i	0.114474	+	0.198275i	−0.803095	+	0.595851i	$0.796815\pi$
$824$		0			0
$825$	68.4403	−	39.5140i	2.38278	−	1.37570i
$826$		0			0
$827$		−	17.3050i		−	0.601754i	−0.953663	−	0.300877i	$-0.902721\pi$
$827$		−	17.3050i		−	0.601754i	0.953663	−	0.300877i	$-0.0972794\pi$
$828$		0			0
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	−0.896800	−	0.442437i	$-0.854114\pi$
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	0.831561	+	0.555433i	$0.187447\pi$
$830$		0			0
$831$	−47.9252			−1.66251
$832$		0			0
$833$	−2.69964			−0.0935371
$834$		0			0
$835$	−6.14432	+	10.6423i	−0.212633	+	0.368291i
$836$		0			0
$837$			3.29981i			0.114058i
$838$		0			0
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.392766	−	0.919638i	$-0.371518\pi$
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.992813	+	0.119674i	$0.0381849\pi$
$840$		0			0
$841$	−3.49071	−	6.04609i	−0.120369	−	0.208486i
$842$		0			0
$843$	−5.62558	−	3.24793i	−0.193755	−	0.111865i
$844$		0			0
$845$	−1.74669	−	41.0701i	−0.0600880	−	1.41285i
$846$		0			0
$847$	−21.0580	−	12.1578i	−0.723560	−	0.417748i
$848$		0			0
$849$	−38.2071	−	66.1766i	−1.31126	−	2.27118i
$850$		0			0
$851$	−15.3751	+	8.87679i	−0.527050	+	0.304293i
$852$		0			0
$853$			15.3103i			0.524215i	0.965039	+	0.262107i	$0.0844174\pi$
$853$			15.3103i			0.524215i	−0.965039	+	0.262107i	$0.915583\pi$
$854$		0			0
$855$	−12.6155	+	21.8506i	−0.431440	+	0.747275i
$856$		0			0
$857$	−2.59248			−0.0885574			−0.0442787	−	0.999019i	$-0.514099\pi$
$857$	−2.59248			−0.0885574			−0.0442787	+	0.999019i	$0.514099\pi$
$858$		0			0
$859$	13.7738			0.469955			0.234978	−	0.972001i	$-0.424498\pi$
$859$	13.7738			0.469955			0.234978	+	0.972001i	$0.424498\pi$
$860$		0			0
$861$	4.96642	−	8.60209i	0.169255	−	0.293159i
$862$		0			0
$863$			29.7592i			1.01302i	0.862235	+	0.506508i	$0.169064\pi$
$863$			29.7592i			1.01302i	−0.862235	+	0.506508i	$0.830936\pi$
$864$		0			0
$865$	−38.2747	+	22.0979i	−1.30138	+	0.751351i
$866$		0			0
$867$	−12.9183	−	22.3751i	−0.438728	−	0.759899i
$868$		0			0
$869$	−40.7301	−	23.5155i	−1.38167	−	0.797710i
$870$		0			0
$871$	10.9007	−	19.8429i	0.369358	−	0.672350i
$872$		0			0
$873$	12.1023	+	6.98724i	0.409599	+	0.236482i
$874$		0			0
$875$	−0.00185228	−	0.00320824i	−6.26183e−5	−	0.000108458i
$876$		0			0
$877$	−1.24995	+	0.721660i	−0.0422079	+	0.0243687i	−0.520955	−	0.853584i	$-0.674424\pi$
$877$	−1.24995	+	0.721660i	−0.0422079	+	0.0243687i	0.478748	+	0.877953i	$0.341091\pi$
$878$		0			0
$879$		−	78.0286i		−	2.63184i
$880$		0			0
$881$	−17.9402	+	31.0733i	−0.604420	+	1.04689i	0.387723	+	0.921776i	$0.373262\pi$
$881$	−17.9402	+	31.0733i	−0.604420	+	1.04689i	−0.992143	+	0.125110i	$0.960072\pi$
$882$		0			0
$883$	−10.5626			−0.355458			−0.177729	−	0.984079i	$-0.556875\pi$
$883$	−10.5626			−0.355458			−0.177729	+	0.984079i	$0.556875\pi$
$884$		0			0
$885$	−40.4273			−1.35895
$886$		0			0
$887$	6.11401	−	10.5898i	0.205288	−	0.355570i	−0.744936	−	0.667136i	$-0.767520\pi$
$887$	6.11401	−	10.5898i	0.205288	−	0.355570i	0.950225	+	0.311566i	$0.100853\pi$
$888$		0			0
$889$		−	6.13117i		−	0.205633i
$890$		0			0
$891$	−23.7166	+	13.6928i	−0.794537	+	0.458726i
$892$		0			0
$893$	−0.446276	−	0.772973i	−0.0149341	−	0.0258666i
$894$		0			0
$895$	69.2399	+	39.9757i	2.31443	+	1.33624i
$896$		0			0
$897$	−22.3893	+	13.5689i	−0.747557	+	0.453051i
$898$		0			0
$899$	−5.98208	−	3.45375i	−0.199513	−	0.115189i
$900$		0			0
$901$	−0.538965	−	0.933515i	−0.0179555	−	0.0310999i
$902$		0			0
$903$	16.1070	−	9.29938i	0.536008	−	0.309464i
$904$		0			0
$905$		−	2.73355i		−	0.0908662i
$906$		0			0
$907$	−2.26278	+	3.91924i	−0.0751343	+	0.130136i	−0.901145	−	0.433519i	$-0.857272\pi$
$907$	−2.26278	+	3.91924i	−0.0751343	+	0.130136i	0.826010	+	0.563655i	$0.190605\pi$
$908$		0			0
$909$	54.3464			1.80256
$910$		0			0
$911$	57.2723			1.89751			0.948757	−	0.316006i	$-0.102342\pi$
$911$	57.2723			1.89751			0.948757	+	0.316006i	$0.102342\pi$
$912$		0			0
$913$	18.4163	−	31.8979i	0.609489	−	1.05567i
$914$		0			0
$915$			9.73302i			0.321764i
$916$		0			0
$917$	8.85224	−	5.11084i	0.292327	−	0.168775i
$918$		0			0
$919$	−20.3775	−	35.2949i	−0.672193	−	1.16427i	−0.977281	−	0.211948i	$-0.932019\pi$
$919$	−20.3775	−	35.2949i	−0.672193	−	1.16427i	0.305088	−	0.952324i	$-0.401314\pi$
$920$		0			0
$921$	−16.2864	−	9.40294i	−0.536654	−	0.309837i
$922$		0			0
$923$	8.42270	+	13.8979i	0.277236	+	0.457454i
$924$		0			0
$925$	28.1589	+	16.2575i	0.925858	+	0.534545i
$926$		0			0
$927$	−23.7391	−	41.1174i	−0.779696	−	1.35047i
$928$		0			0
$929$	45.2751	−	26.1396i	1.48543	−	0.857611i	0.485564	−	0.874201i	$-0.338614\pi$
$929$	45.2751	−	26.1396i	1.48543	−	0.857611i	0.999862	+	0.0165897i	$0.00528089\pi$
$930$		0			0
$931$			1.95705i			0.0641397i
$932$		0			0
$933$	−29.6205	+	51.3042i	−0.969731	+	1.67962i
$934$		0			0
$935$	−50.7300			−1.65905
$936$		0			0
$937$	−6.38634			−0.208633			−0.104316	−	0.994544i	$-0.533265\pi$
$937$	−6.38634			−0.208633			−0.104316	+	0.994544i	$0.533265\pi$
$938$		0			0
$939$	−37.3558	+	64.7021i	−1.21906	+	2.11147i
$940$		0			0
$941$			25.3711i			0.827073i	0.910488	+	0.413536i	$0.135707\pi$
$941$			25.3711i			0.827073i	−0.910488	+	0.413536i	$0.864293\pi$
$942$		0			0
$943$	−8.82560	+	5.09546i	−0.287401	+	0.165931i
$944$		0			0
$945$	4.53056	+	7.84715i	0.147379	+	0.255268i
$946$		0			0
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	0.0656800	−	0.997841i	$-0.479078\pi$
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	−0.831315	+	0.555801i	$0.812412\pi$
$948$		0			0
$949$	−29.9401	+	0.636381i	−0.971895	+	0.0206578i
$950$		0			0
$951$	44.9613	+	25.9584i	1.45797	+	0.841760i
$952$		0			0
$953$	13.2939	+	23.0258i	0.430633	+	0.745878i	0.996928	−	0.0783248i	$-0.0249571\pi$
$953$	13.2939	+	23.0258i	0.430633	+	0.745878i	−0.566295	+	0.824203i	$0.691624\pi$
$954$		0			0
$955$	−40.1667	+	23.1902i	−1.29976	+	0.750418i
$956$		0			0
$957$			94.8314i			3.06546i
$958$		0			0
$959$	9.97376	−	17.2751i	0.322070	−	0.557841i
$960$		0			0
$961$	29.6739			0.957224
$962$		0			0
$963$	−16.0218			−0.516296
$964$		0			0
$965$	−26.0808	+	45.1732i	−0.839569	+	1.45418i
$966$		0			0
$967$			35.2467i			1.13346i	0.823904	+	0.566729i	$0.191791\pi$
$967$			35.2467i			1.13346i	−0.823904	+	0.566729i	$0.808209\pi$
$968$		0			0
$969$	12.1722	−	7.02760i	0.391026	−	0.225759i
$970$		0			0
$971$	18.4891	+	32.0241i	0.593344	+	1.02770i	0.993778	+	0.111377i	$0.0355261\pi$
$971$	18.4891	+	32.0241i	0.593344	+	1.02770i	−0.400434	+	0.916326i	$0.631141\pi$
$972$		0			0
$973$	17.6041	+	10.1637i	0.564362	+	0.325834i
$974$		0			0
$975$	42.0241	+	23.0861i	1.34585	+	0.739347i
$976$		0			0
$977$	−21.4363	−	12.3762i	−0.685807	−	0.395951i	0.116232	−	0.993222i	$-0.462918\pi$
$977$	−21.4363	−	12.3762i	−0.685807	−	0.395951i	−0.802039	+	0.597271i	$0.796252\pi$
$978$		0			0
$979$	−10.5820	−	18.3286i	−0.338204	−	0.585786i
$980$		0			0
$981$	−39.7346	+	22.9408i	−1.26863	+	0.732442i
$982$		0			0
$983$			4.55736i			0.145357i	0.997355	+	0.0726786i	$0.0231547\pi$
$983$			4.55736i			0.145357i	−0.997355	+	0.0726786i	$0.976845\pi$
$984$		0			0
$985$	−17.4076	+	30.1509i	−0.554652	+	0.960686i
$986$		0			0
$987$	−1.21328			−0.0386192
$988$		0			0
$989$	−19.0820			−0.606773
$990$		0			0
$991$	−13.5982	+	23.5527i	−0.431960	+	0.748176i	−0.997042	−	0.0768584i	$-0.975511\pi$
$991$	−13.5982	+	23.5527i	−0.431960	+	0.748176i	0.565082	+	0.825034i	$0.308844\pi$
$992$		0			0
$993$			41.5824i			1.31958i
$994$		0			0
$995$	−58.0873	+	33.5367i	−1.84149	+	1.06319i
$996$		0			0
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	0.999700	−	0.0244727i	$-0.00779070\pi$
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	−0.521044	+	0.853530i	$0.674457\pi$
$998$		0			0
$999$	16.1419	+	9.31952i	0.510707	+	0.294857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.2.cc.c.225.6		12
4.3	odd	2		91.2.q.a.43.4	yes	12
12.11	even	2		819.2.ct.a.316.3		12
13.10	even	6	inner	1456.2.cc.c.673.6		12
28.3	even	6		637.2.u.i.30.3		12
28.11	odd	6		637.2.u.h.30.3		12
28.19	even	6		637.2.k.g.459.3		12
28.23	odd	6		637.2.k.h.459.3		12
28.27	even	2		637.2.q.h.589.4		12
52.7	even	12		1183.2.a.m.1.5		6
52.19	even	12		1183.2.a.p.1.2		6
52.23	odd	6		91.2.q.a.36.4	✓	12
52.35	odd	6		1183.2.c.i.337.5		12
52.43	odd	6		1183.2.c.i.337.8		12
156.23	even	6		819.2.ct.a.127.3		12
364.23	odd	6		637.2.u.h.361.3		12
364.75	even	6		637.2.u.i.361.3		12
364.111	odd	12		8281.2.a.by.1.5		6
364.179	odd	6		637.2.k.h.569.4		12
364.279	odd	12		8281.2.a.ch.1.2		6
364.283	even	6		637.2.k.g.569.4		12
364.335	even	6		637.2.q.h.491.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	52.23	odd	6
91.2.q.a.43.4	yes	12	4.3	odd	2
637.2.k.g.459.3		12	28.19	even	6
637.2.k.g.569.4		12	364.283	even	6
637.2.k.h.459.3		12	28.23	odd	6
637.2.k.h.569.4		12	364.179	odd	6
637.2.q.h.491.4		12	364.335	even	6
637.2.q.h.589.4		12	28.27	even	2
637.2.u.h.30.3		12	28.11	odd	6
637.2.u.h.361.3		12	364.23	odd	6
637.2.u.i.30.3		12	28.3	even	6
637.2.u.i.361.3		12	364.75	even	6
819.2.ct.a.127.3		12	156.23	even	6
819.2.ct.a.316.3		12	12.11	even	2
1183.2.a.m.1.5		6	52.7	even	12
1183.2.a.p.1.2		6	52.19	even	12
1183.2.c.i.337.5		12	52.35	odd	6
1183.2.c.i.337.8		12	52.43	odd	6
1456.2.cc.c.225.6		12	1.1	even	1	trivial
1456.2.cc.c.673.6		12	13.10	even	6	inner
8281.2.a.by.1.5		6	364.111	odd	12
8281.2.a.ch.1.2		6	364.279	odd	12

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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.33015 - 2.30388i) q^{3} +3.16209i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-2.03858 - 3.53092i) q^{9} +O(q^{10})\)	\(q+(1.33015 - 2.30388i) q^{3} +3.16209i q^{5} +(-0.866025 + 0.500000i) q^{7} +(-2.03858 - 3.53092i) q^{9} +(-5.14653 - 2.97135i) q^{11} +(-0.0766193 - 3.60474i) q^{13} +(7.28508 + 4.20604i) q^{15} +(-1.34982 - 2.33796i) q^{17} +(-1.69485 + 0.978524i) q^{19} +2.66029i q^{21} +(1.36471 - 2.36374i) q^{23} -4.99883 q^{25} -2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} -1.15155i q^{31} +(-13.6913 + 7.90465i) q^{33} +(-1.58105 - 2.73845i) q^{35} +(-5.63310 - 3.25227i) q^{37} +(-8.40680 - 4.61830i) q^{39} +(-3.23351 - 1.86687i) q^{41} +(-3.49562 - 6.05460i) q^{43} +(11.1651 - 6.44617i) q^{45} +0.456071i q^{47} +(0.500000 - 0.866025i) q^{49} -7.18184 q^{51} +0.399286 q^{53} +(9.39568 - 16.2738i) q^{55} +5.20632i q^{57} +(-4.16200 + 2.40293i) q^{59} +(0.578514 + 1.00201i) q^{61} +(3.53092 + 2.03858i) q^{63} +(11.3985 - 0.242277i) q^{65} +(5.43793 + 3.13959i) q^{67} +(-3.63052 - 6.28825i) q^{69} +(-3.90335 + 2.25360i) q^{71} -8.30575i q^{73} +(-6.64917 + 11.5167i) q^{75} +5.94270 q^{77} +7.91410 q^{79} +(2.30414 - 3.99089i) q^{81} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +(-7.97882 - 13.8197i) q^{87} +(3.08423 + 1.78068i) q^{89} +(1.86872 + 3.08348i) q^{91} +(-2.65303 - 1.53173i) q^{93} +(-3.09418 - 5.35928i) q^{95} +(-2.96831 + 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^9	\( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q - 4 * q^9 - 6 * q^11 + 4 * q^13 - 6 * q^15 - 4 * q^17 + 12 * q^23 - 20 * q^25 - 12 * q^27 + 8 * q^29 - 30 * q^33 - 6 * q^35 - 42 * q^37 + 4 * q^39 + 30 * q^41 - 2 * q^43 + 6 * q^49 - 52 * q^51 - 44 * q^53 + 6 * q^55 - 18 * q^59 + 14 * q^61 - 12 * q^63 + 60 * q^65 + 24 * q^67 + 4 * q^69 + 24 * q^71 - 46 * q^75 + 8 * q^77 + 56 * q^79 + 2 * q^81 - 48 * q^85 + 2 * q^87 - 12 * q^89 - 14 * q^91 - 18 * q^93 + 22 * q^95 + 6 * q^97

Introduction

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