LMFDB - Embedded newform 644.2.y.a.261.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(9,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 22, 30]))

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

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

chi := DirichletCharacter("644.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			261.11
Character	$\chi$	$=$	644.261
Dual form			644.2.y.a.417.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557850 - 0.783391i) q^{3} +(-1.41067 + 0.271884i) q^{5} +(-2.57253 - 0.618153i) q^{7} +(0.678699 + 1.96097i) q^{9} +O(q^{10})$	\(q+(0.557850 - 0.783391i) q^{3} +(-1.41067 + 0.271884i) q^{5} +(-2.57253 - 0.618153i) q^{7} +(0.678699 + 1.96097i) q^{9} +(-0.981903 + 0.772177i) q^{11} +(-3.18951 + 2.04977i) q^{13} +(-0.573949 + 1.25677i) q^{15} +(-4.14845 - 3.95554i) q^{17} +(0.601062 - 0.573112i) q^{19} +(-1.91934 + 1.67046i) q^{21} +(0.125147 + 4.79420i) q^{23} +(-2.72578 + 1.09124i) q^{25} +(4.68310 + 1.37508i) q^{27} +(-6.30916 + 1.85254i) q^{29} +(-1.75433 + 0.167518i) q^{31} +(0.0571618 + 1.19997i) q^{33} +(3.79704 + 0.172579i) q^{35} +(2.48693 + 7.18551i) q^{37} +(-0.173494 + 3.64210i) q^{39} +(-0.661736 - 0.763684i) q^{41} +(-2.66495 - 5.83543i) q^{43} +(-1.49057 - 2.58175i) q^{45} +(-1.11018 + 1.92288i) q^{47} +(6.23577 + 3.18043i) q^{49} +(-5.41295 + 1.04326i) q^{51} +(0.297785 - 6.25128i) q^{53} +(1.17519 - 1.35625i) q^{55} +(-0.113668 - 0.790577i) q^{57} +(3.34078 + 1.72229i) q^{59} +(-1.20492 - 1.69207i) q^{61} +(-0.533791 - 5.46419i) q^{63} +(3.94203 - 3.75872i) q^{65} +(1.81537 - 0.726764i) q^{67} +(3.82555 + 2.57641i) q^{69} +(0.195716 - 1.36123i) q^{71} +(-1.64822 - 6.79404i) q^{73} +(-0.665712 + 2.74410i) q^{75} +(3.00329 - 1.37948i) q^{77} +(0.678857 + 14.2510i) q^{79} +(-1.20372 + 0.946616i) q^{81} +(1.84198 - 2.12576i) q^{83} +(6.92753 + 4.45205i) q^{85} +(-2.06831 + 5.97598i) q^{87} +(-10.5349 - 1.00596i) q^{89} +(9.47216 - 3.30149i) q^{91} +(-0.847420 + 1.46777i) q^{93} +(-0.692078 + 0.971888i) q^{95} +(-2.88852 - 3.33354i) q^{97} +(-2.18063 - 1.40141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.557850	−	0.783391i	0.322075	−	0.452291i	−0.621517	−	0.783400i	$-0.713483\pi$
$3$	0.557850	−	0.783391i	0.322075	−	0.452291i	0.943592	+	0.331109i	$0.107423\pi$
$4$		0			0
$5$	−1.41067	+	0.271884i	−0.630869	+	0.121590i	−0.494655	−	0.869089i	$-0.664706\pi$
$5$	−1.41067	+	0.271884i	−0.630869	+	0.121590i	−0.136214	+	0.990679i	$0.543493\pi$
$6$		0			0
$7$	−2.57253	−	0.618153i	−0.972323	−	0.233640i
$7$	−2.57253	−	0.618153i	−0.972323	−	0.233640i
$8$		0			0
$9$	0.678699	+	1.96097i	0.226233	+	0.653657i
$10$		0			0
$11$	−0.981903	+	0.772177i	−0.296055	+	0.232820i	−0.755126	−	0.655579i	$-0.772425\pi$
$11$	−0.981903	+	0.772177i	−0.296055	+	0.232820i	0.459072	+	0.888399i	$0.348182\pi$
$12$		0			0
$13$	−3.18951	+	2.04977i	−0.884610	+	0.568504i	−0.902189	−	0.431341i	$-0.858040\pi$
$13$	−3.18951	+	2.04977i	−0.884610	+	0.568504i	0.0175791	+	0.999845i	$0.494404\pi$
$14$		0			0
$15$	−0.573949	+	1.25677i	−0.148193	+	0.324498i
$16$		0			0
$17$	−4.14845	−	3.95554i	−1.00615	−	0.959360i	−0.00697299	−	0.999976i	$-0.502220\pi$
$17$	−4.14845	−	3.95554i	−1.00615	−	0.959360i	−0.999175	+	0.0406157i	$0.987068\pi$
$18$		0			0
$19$	0.601062	−	0.573112i	0.137893	−	0.131481i	−0.617994	−	0.786183i	$-0.712054\pi$
$19$	0.601062	−	0.573112i	0.137893	−	0.131481i	0.755887	+	0.654702i	$0.227206\pi$
$20$		0			0
$21$	−1.91934	+	1.67046i	−0.418834	+	0.364524i
$22$		0			0
$23$	0.125147	+	4.79420i	0.0260949	+	0.999659i
$23$	0.125147	+	4.79420i	0.0260949	+	0.999659i
$24$		0			0
$25$	−2.72578	+	1.09124i	−0.545156	+	0.218248i
$26$		0			0
$27$	4.68310	+	1.37508i	0.901263	+	0.264635i
$28$		0			0
$29$	−6.30916	+	1.85254i	−1.17158	+	0.344007i	−0.808923	−	0.587915i	$-0.799949\pi$
$29$	−6.30916	+	1.85254i	−1.17158	+	0.344007i	−0.362658	+	0.931922i	$0.618131\pi$
$30$		0			0
$31$	−1.75433	+	0.167518i	−0.315086	+	0.0300871i	−0.251401	−	0.967883i	$-0.580891\pi$
$31$	−1.75433	+	0.167518i	−0.315086	+	0.0300871i	−0.0636851	+	0.997970i	$0.520285\pi$
$32$		0			0
$33$	0.0571618	+	1.19997i	0.00995059	+	0.208889i
$34$		0			0
$35$	3.79704	+	0.172579i	0.641817	+	0.0291712i
$36$		0			0
$37$	2.48693	+	7.18551i	0.408849	+	1.18129i	0.942099	+	0.335334i	$0.108849\pi$
$37$	2.48693	+	7.18551i	0.408849	+	1.18129i	−0.533250	+	0.845957i	$0.679030\pi$
$38$		0			0
$39$	−0.173494	+	3.64210i	−0.0277813	+	0.583202i
$40$		0			0
$41$	−0.661736	−	0.763684i	−0.103346	−	0.119267i	0.701720	−	0.712453i	$-0.252416\pi$
$41$	−0.661736	−	0.763684i	−0.103346	−	0.119267i	−0.805066	+	0.593185i	$0.797870\pi$
$42$		0			0
$43$	−2.66495	−	5.83543i	−0.406401	−	0.889895i	−0.996581	−	0.0826228i	$-0.973670\pi$
$43$	−2.66495	−	5.83543i	−0.406401	−	0.889895i	0.590180	−	0.807272i	$-0.299057\pi$
$44$		0			0
$45$	−1.49057	−	2.58175i	−0.222202	−	0.384864i
$46$		0			0
$47$	−1.11018	+	1.92288i	−0.161936	+	0.280481i	−0.935563	−	0.353160i	$-0.885107\pi$
$47$	−1.11018	+	1.92288i	−0.161936	+	0.280481i	0.773627	+	0.633641i	$0.218440\pi$
$48$		0			0
$49$	6.23577	+	3.18043i	0.890825	+	0.454347i
$50$		0			0
$51$	−5.41295	+	1.04326i	−0.757965	+	0.146086i
$52$		0			0
$53$	0.297785	−	6.25128i	0.0409039	−	0.858679i	−0.881437	−	0.472302i	$-0.843423\pi$
$53$	0.297785	−	6.25128i	0.0409039	−	0.858679i	0.922341	−	0.386377i	$-0.126274\pi$
$54$		0			0
$55$	1.17519	−	1.35625i	0.158463	−	0.182876i
$56$		0			0
$57$	−0.113668	−	0.790577i	−0.0150557	−	0.104715i
$58$		0			0
$59$	3.34078	+	1.72229i	0.434932	+	0.224223i	0.661766	−	0.749710i	$-0.269807\pi$
$59$	3.34078	+	1.72229i	0.434932	+	0.224223i	−0.226834	+	0.973933i	$0.572837\pi$
$60$		0			0
$61$	−1.20492	−	1.69207i	−0.154274	−	0.216647i	0.730205	−	0.683229i	$-0.239425\pi$
$61$	−1.20492	−	1.69207i	−0.154274	−	0.216647i	−0.884478	+	0.466582i	$0.845485\pi$
$62$		0			0
$63$	−0.533791	−	5.46419i	−0.0672513	−	0.688423i
$64$		0			0
$65$	3.94203	−	3.75872i	0.488948	−	0.466211i
$66$		0			0
$67$	1.81537	−	0.726764i	0.221783	−	0.0887884i	−0.258110	−	0.966115i	$-0.583100\pi$
$67$	1.81537	−	0.726764i	0.221783	−	0.0887884i	0.479893	+	0.877327i	$0.340676\pi$
$68$		0			0
$69$	3.82555	+	2.57641i	0.460542	+	0.310163i
$70$		0			0
$71$	0.195716	−	1.36123i	0.0232272	−	0.161549i	−0.974907	−	0.222614i	$-0.928541\pi$
$71$	0.195716	−	1.36123i	0.0232272	−	0.161549i	0.998134	+	0.0610659i	$0.0194500\pi$
$72$		0			0
$73$	−1.64822	−	6.79404i	−0.192909	−	0.795182i	−0.983212	−	0.182466i	$-0.941592\pi$
$73$	−1.64822	−	6.79404i	−0.192909	−	0.795182i	0.790303	−	0.612716i	$-0.209923\pi$
$74$		0			0
$75$	−0.665712	+	2.74410i	−0.0768698	+	0.316862i
$76$		0			0
$77$	3.00329	−	1.37948i	0.342257	−	0.157206i
$78$		0			0
$79$	0.678857	+	14.2510i	0.0763774	+	1.60336i	0.634046	+	0.773295i	$0.281393\pi$
$79$	0.678857	+	14.2510i	0.0763774	+	1.60336i	−0.557669	+	0.830064i	$0.688304\pi$
$80$		0			0
$81$	−1.20372	+	0.946616i	−0.133747	+	0.105180i
$82$		0			0
$83$	1.84198	−	2.12576i	0.202184	−	0.233333i	−0.645598	−	0.763677i	$-0.723392\pi$
$83$	1.84198	−	2.12576i	0.202184	−	0.233333i	0.847782	+	0.530344i	$0.177937\pi$
$84$		0			0
$85$	6.92753	+	4.45205i	0.751396	+	0.482893i
$86$		0			0
$87$	−2.06831	+	5.97598i	−0.221746	+	0.640692i
$88$		0			0
$89$	−10.5349	−	1.00596i	−1.11670	−	0.106632i	−0.479653	−	0.877458i	$-0.659237\pi$
$89$	−10.5349	−	1.00596i	−1.11670	−	0.106632i	−0.637045	+	0.770826i	$0.719844\pi$
$90$		0			0
$91$	9.47216	−	3.30149i	0.992952	−	0.346090i
$92$		0			0
$93$	−0.847420	+	1.46777i	−0.0878734	+	0.152201i
$94$		0			0
$95$	−0.692078	+	0.971888i	−0.0710057	+	0.0997136i
$96$		0			0
$97$	−2.88852	−	3.33354i	−0.293285	−	0.338469i	0.589915	−	0.807465i	$-0.299161\pi$
$97$	−2.88852	−	3.33354i	−0.293285	−	0.338469i	−0.883200	+	0.468996i	$0.844616\pi$
$98$		0			0
$99$	−2.18063	−	1.40141i	−0.219162	−	0.140847i
$100$		0			0
$101$	−11.7412	−	2.26293i	−1.16829	−	0.225170i	−0.432026	−	0.901861i	$-0.642201\pi$
$101$	−11.7412	−	2.26293i	−1.16829	−	0.225170i	−0.736267	+	0.676691i	$0.763413\pi$
$102$		0			0
$103$	8.59801	+	3.44212i	0.847187	+	0.339162i	0.754313	−	0.656515i	$-0.227970\pi$
$103$	8.59801	+	3.44212i	0.847187	+	0.339162i	0.0928742	+	0.995678i	$0.470395\pi$
$104$		0			0
$105$	2.25338	−	2.87829i	0.219907	−	0.280893i
$106$		0			0
$107$	−9.65556	−	13.5593i	−0.933438	−	1.31083i	−0.950418	−	0.310974i	$-0.899345\pi$
$107$	−9.65556	−	13.5593i	−0.933438	−	1.31083i	0.0169805	−	0.999856i	$-0.494595\pi$
$108$		0			0
$109$	−1.50324	−	1.43334i	−0.143984	−	0.137289i	0.614664	−	0.788789i	$-0.289292\pi$
$109$	−1.50324	−	1.43334i	−0.143984	−	0.137289i	−0.758649	+	0.651500i	$0.774140\pi$
$110$		0			0
$111$	7.01641	+	2.06020i	0.665968	+	0.195546i
$112$		0			0
$113$	1.97403	−	13.7296i	0.185701	−	1.29158i	−0.657286	−	0.753642i	$-0.728295\pi$
$113$	1.97403	−	13.7296i	0.185701	−	1.29158i	0.842986	−	0.537935i	$-0.180795\pi$
$114$		0			0
$115$	−1.48000	−	6.72899i	−0.138011	−	0.627481i
$116$		0			0
$117$	−6.18426	−	4.86335i	−0.571735	−	0.449617i
$118$		0			0
$119$	8.22687	+	12.7401i	0.754156	+	1.16788i
$120$		0			0
$121$	−2.22547	+	9.17352i	−0.202316	+	0.833957i
$122$		0			0
$123$	−0.967413	+	0.0923768i	−0.0872287	+	0.00832933i
$124$		0			0
$125$	9.59132	−	6.16397i	0.857874	−	0.551322i
$126$		0			0
$127$	−0.501602	−	3.48872i	−0.0445100	−	0.309574i	−0.999899	−	0.0142230i	$-0.995473\pi$
$127$	−0.501602	−	3.48872i	−0.0445100	−	0.309574i	0.955389	−	0.295351i	$-0.0954366\pi$
$128$		0			0
$129$	−6.05807	−	1.16760i	−0.533383	−	0.102801i
$130$		0			0
$131$	8.66939	−	4.46938i	0.757448	−	0.390492i	−0.0358247	−	0.999358i	$-0.511406\pi$
$131$	8.66939	−	4.46938i	0.757448	−	0.390492i	0.793273	+	0.608867i	$0.208375\pi$
$132$		0			0
$133$	−1.90052	+	1.10280i	−0.164796	+	0.0956245i
$134$		0			0
$135$	−6.98016	−	0.666524i	−0.600756	−	0.0573653i
$136$		0			0
$137$	6.60511	+	11.4404i	0.564313	+	0.977418i	0.997113	+	0.0759285i	$0.0241921\pi$
$137$	6.60511	+	11.4404i	0.564313	+	0.977418i	−0.432801	+	0.901490i	$0.642475\pi$
$138$		0			0
$139$	11.7198			0.994058			0.497029	−	0.867734i	$-0.334424\pi$
$139$	11.7198			0.994058			0.497029	+	0.867734i	$0.334424\pi$
$140$		0			0
$141$	0.887057	+	1.94238i	0.0747037	+	0.163578i
$142$		0			0
$143$	1.54900	−	4.47554i	0.129534	−	0.374263i
$144$		0			0
$145$	8.39644	−	4.32866i	0.697286	−	0.359476i
$146$		0			0
$147$	5.97015	−	3.11085i	0.492410	−	0.256579i
$148$		0			0
$149$	−14.3521	−	5.74570i	−1.17577	−	0.470706i	−0.300235	−	0.953865i	$-0.597065\pi$
$149$	−14.3521	−	5.74570i	−1.17577	−	0.470706i	−0.875532	+	0.483159i	$0.839489\pi$
$150$		0			0
$151$	18.8580	+	9.72197i	1.53464	+	0.791163i	0.998593	−	0.0530238i	$-0.0168859\pi$
$151$	18.8580	+	9.72197i	1.53464	+	0.791163i	0.536049	+	0.844187i	$0.319916\pi$
$152$		0			0
$153$	4.94116	−	10.8196i	0.399469	−	0.874715i
$154$		0			0
$155$	2.42922	−	0.713285i	0.195120	−	0.0572924i
$156$		0			0
$157$	−5.58264	−	23.0119i	−0.445543	−	1.83655i	−0.540869	−	0.841107i	$-0.681904\pi$
$157$	−5.58264	−	23.0119i	−0.445543	−	1.83655i	0.0953260	−	0.995446i	$-0.469611\pi$
$158$		0			0
$159$	−4.73108	−	3.72056i	−0.375199	−	0.295060i
$160$		0			0
$161$	2.64160	−	12.4106i	0.208187	−	0.978089i
$162$		0			0
$163$	13.0879	+	10.2924i	1.02512	+	0.806164i	0.981224	−	0.192872i	$-0.0617801\pi$
$163$	13.0879	+	10.2924i	1.02512	+	0.806164i	0.0438974	+	0.999036i	$0.486023\pi$
$164$		0			0
$165$	−0.406889	−	1.67722i	−0.0316763	−	0.130571i
$166$		0			0
$167$	−7.20387	+	2.11525i	−0.557452	+	0.163683i	−0.548309	−	0.836276i	$-0.684728\pi$
$167$	−7.20387	+	2.11525i	−0.557452	+	0.163683i	−0.00914252	+	0.999958i	$0.502910\pi$
$168$		0			0
$169$	0.570990	−	1.25029i	0.0439223	−	0.0961765i
$170$		0			0
$171$	1.53180	+	0.789696i	0.117139	+	0.0603895i
$172$		0			0
$173$	−1.54004	−	0.616540i	−0.117087	−	0.0468746i	0.312379	−	0.949958i	$-0.398874\pi$
$173$	−1.54004	−	0.616540i	−0.117087	−	0.0468746i	−0.429466	+	0.903083i	$0.641298\pi$
$174$		0			0
$175$	7.68670	−	1.12229i	0.581060	−	0.0848371i
$176$		0			0
$177$	3.21288	−	1.65636i	0.241495	−	0.124499i
$178$		0			0
$179$	−1.81424	+	5.24190i	−0.135603	+	0.391798i	−0.992274	−	0.124064i	$-0.960407\pi$
$179$	−1.81424	+	5.24190i	−0.135603	+	0.391798i	0.856672	+	0.515862i	$0.172528\pi$
$180$		0			0
$181$	10.3058	+	22.5666i	0.766025	+	1.67736i	0.735213	+	0.677836i	$0.237082\pi$
$181$	10.3058	+	22.5666i	0.766025	+	1.67736i	0.0308126	+	0.999525i	$0.490191\pi$
$182$		0			0
$183$	−1.99771			−0.147675
$184$		0			0
$185$	−5.46185	−	9.46021i	−0.401563	−	0.695528i
$186$		0			0
$187$	7.12776	+	0.680618i	0.521233	+	0.0497717i
$188$		0			0
$189$	−11.1974	−	6.43231i	−0.814490	−	0.467882i
$190$		0			0
$191$	−7.67997	+	3.95930i	−0.555703	+	0.286485i	−0.713114	−	0.701048i	$-0.752716\pi$
$191$	−7.67997	+	3.95930i	−0.555703	+	0.286485i	0.157411	+	0.987533i	$0.449685\pi$
$192$		0			0
$193$	2.75002	+	0.530022i	0.197950	+	0.0381518i	0.287263	−	0.957852i	$-0.407255\pi$
$193$	2.75002	+	0.530022i	0.197950	+	0.0381518i	−0.0893122	+	0.996004i	$0.528467\pi$
$194$		0			0
$195$	−0.745483	−	5.18495i	−0.0533852	−	0.371302i
$196$		0			0
$197$	−14.7523	+	9.48073i	−1.05106	+	0.675474i	−0.947698	−	0.319170i	$-0.896596\pi$
$197$	−14.7523	+	9.48073i	−1.05106	+	0.675474i	−0.103361	+	0.994644i	$0.532960\pi$
$198$		0			0
$199$	16.2205	−	1.54887i	1.14984	−	0.109796i	0.497319	−	0.867568i	$-0.334318\pi$
$199$	16.2205	−	1.54887i	1.14984	−	0.109796i	0.652520	+	0.757771i	$0.273712\pi$
$200$		0			0
$201$	0.443364	−	1.82757i	0.0312725	−	0.128907i
$202$		0			0
$203$	17.3756	−	0.865674i	1.21953	−	0.0607584i
$204$		0			0
$205$	1.14112	+	0.897388i	0.0796994	+	0.0626763i
$206$		0			0
$207$	−9.31635	+	3.49923i	−0.647531	+	0.243213i
$208$		0			0
$209$	−0.147641	+	1.02687i	−0.0102125	+	0.0710298i
$210$		0			0
$211$	−1.07451	−	0.315505i	−0.0739725	−	0.0217203i	0.244537	−	0.969640i	$-0.421364\pi$
$211$	−1.07451	−	0.315505i	−0.0739725	−	0.0217203i	−0.318509	+	0.947920i	$0.603182\pi$
$212$		0			0
$213$	−0.957197	−	0.912686i	−0.0655861	−	0.0625362i
$214$		0			0
$215$	5.34591	+	7.50729i	0.364588	+	0.511993i
$216$		0			0
$217$	4.61660	+	0.653498i	0.313395	+	0.0443623i
$218$		0			0
$219$	−6.24185	−	2.49886i	−0.421785	−	0.168857i
$220$		0			0
$221$	21.3395	+	4.11285i	1.43545	+	0.276660i
$222$		0			0
$223$	−2.00765	−	1.29024i	−0.134442	−	0.0864007i	0.471691	−	0.881764i	$-0.343644\pi$
$223$	−2.00765	−	1.29024i	−0.134442	−	0.0864007i	−0.606133	+	0.795363i	$0.707280\pi$
$224$		0			0
$225$	−3.98987	−	4.60456i	−0.265992	−	0.306971i
$226$		0			0
$227$	−11.1804	+	15.7007i	−0.742072	+	1.04209i	0.255098	+	0.966915i	$0.417892\pi$
$227$	−11.1804	+	15.7007i	−0.742072	+	1.04209i	−0.997170	+	0.0751794i	$0.976047\pi$
$228$		0			0
$229$	−0.391240	+	0.677647i	−0.0258539	+	0.0447802i	−0.878663	−	0.477443i	$-0.841564\pi$
$229$	−0.391240	+	0.677647i	−0.0258539	+	0.0447802i	0.852809	+	0.522223i	$0.174897\pi$
$230$		0			0
$231$	0.594716	−	3.12230i	0.0391295	−	0.205432i
$232$		0			0
$233$	14.8262	+	1.41573i	0.971299	+	0.0927478i	0.568626	−	0.822596i	$-0.307475\pi$
$233$	14.8262	+	1.41573i	0.971299	+	0.0927478i	0.402673	+	0.915344i	$0.368081\pi$
$234$		0			0
$235$	1.04329	−	3.01438i	0.0680566	−	0.196637i
$236$		0			0
$237$	11.5428	+	7.41810i	0.749784	+	0.481857i
$238$		0			0
$239$	−11.8471	+	13.6723i	−0.766325	+	0.884386i	−0.996043	−	0.0888714i	$-0.971674\pi$
$239$	−11.8471	+	13.6723i	−0.766325	+	0.884386i	0.229719	+	0.973257i	$0.426219\pi$
$240$		0			0
$241$	−5.75460	+	4.52547i	−0.370686	+	0.291511i	−0.786073	−	0.618134i	$-0.787889\pi$
$241$	−5.75460	+	4.52547i	−0.370686	+	0.291511i	0.415386	+	0.909645i	$0.363646\pi$
$242$		0			0
$243$	0.766790	+	16.0969i	0.0491896	+	1.03262i
$244$		0			0
$245$	−9.66130	−	2.79111i	−0.617238	−	0.178318i
$246$		0			0
$247$	−0.742344	+	3.05998i	−0.0472342	+	0.194702i
$248$		0			0
$249$	−0.637753	−	2.62885i	−0.0404159	−	0.166597i
$250$		0			0
$251$	1.27682	−	8.88049i	0.0805923	−	0.560532i	−0.909018	−	0.416757i	$-0.863167\pi$
$251$	1.27682	−	8.88049i	0.0805923	−	0.560532i	0.989610	−	0.143775i	$-0.0459242\pi$
$252$		0			0
$253$	−3.82485	−	4.61080i	−0.240466	−	0.289879i
$254$		0			0
$255$	7.35222	−	2.94339i	0.460414	−	0.184322i
$256$		0			0
$257$	−15.9920	+	15.2484i	−0.997555	+	0.951167i	−0.998807	−	0.0488321i	$-0.984450\pi$
$257$	−15.9920	+	15.2484i	−0.997555	+	0.951167i	0.00125165	+	0.999999i	$0.499602\pi$
$258$		0			0
$259$	−1.95595	−	20.0222i	−0.121537	−	1.24412i
$260$		0			0
$261$	−7.91479	−	11.1148i	−0.489913	−	0.687987i
$262$		0			0
$263$	−14.9210	−	7.69231i	−0.920068	−	0.474328i	−0.0679566	−	0.997688i	$-0.521648\pi$
$263$	−14.9210	−	7.69231i	−0.920068	−	0.474328i	−0.852112	+	0.523360i	$0.824678\pi$
$264$		0			0
$265$	1.27954	+	8.89943i	0.0786018	+	0.546687i
$266$		0			0
$267$	−6.66497	+	7.69178i	−0.407889	+	0.470729i
$268$		0			0
$269$	1.01430	−	21.2927i	0.0618428	−	1.29824i	−0.728275	−	0.685285i	$-0.759678\pi$
$269$	1.01430	−	21.2927i	0.0618428	−	1.29824i	0.790118	−	0.612955i	$-0.210019\pi$
$270$		0			0
$271$	−21.7650	+	4.19485i	−1.32213	+	0.254819i	−0.801003	−	0.598661i	$-0.795700\pi$
$271$	−21.7650	+	4.19485i	−1.32213	+	0.254819i	−0.521125	+	0.853480i	$0.674488\pi$
$272$		0			0
$273$	2.69769	−	9.26214i	0.163272	−	0.560570i
$274$		0			0
$275$	1.83382	−	3.17628i	0.110584	−	0.191537i
$276$		0			0
$277$	2.02178	+	3.50183i	0.121477	+	0.210404i	0.920350	−	0.391095i	$-0.127904\pi$
$277$	2.02178	+	3.50183i	0.121477	+	0.210404i	−0.798873	+	0.601499i	$0.794570\pi$
$278$		0			0
$279$	−1.51916	−	3.32649i	−0.0909496	−	0.199152i
$280$		0			0
$281$	5.76192	+	6.64962i	0.343728	+	0.396683i	0.901122	−	0.433565i	$-0.142744\pi$
$281$	5.76192	+	6.64962i	0.343728	+	0.396683i	−0.557395	+	0.830248i	$0.688199\pi$
$282$		0			0
$283$	1.14277	−	23.9897i	0.0679305	−	1.42604i	−0.665563	−	0.746342i	$-0.731809\pi$
$283$	1.14277	−	23.9897i	0.0679305	−	1.42604i	0.733494	−	0.679696i	$-0.237888\pi$
$284$		0			0
$285$	0.375292	+	1.08434i	0.0222304	+	0.0642305i
$286$		0			0
$287$	1.23026	+	2.37365i	0.0726199	+	0.140112i
$288$		0			0
$289$	0.754458	+	15.8380i	0.0443799	+	0.931649i
$290$		0			0
$291$	−4.22283	+	0.403231i	−0.247547	+	0.0236378i
$292$		0			0
$293$	8.73029	−	2.56344i	0.510029	−	0.149758i	−0.0165851	−	0.999862i	$-0.505279\pi$
$293$	8.73029	−	2.56344i	0.510029	−	0.149758i	0.526614	+	0.850104i	$0.323461\pi$
$294$		0			0
$295$	−5.18098	−	1.52127i	−0.301649	−	0.0885720i
$296$		0			0
$297$	−5.66016	+	2.26599i	−0.328436	+	0.131486i
$298$		0			0
$299$	−10.2262	−	15.0346i	−0.591394	−	0.869473i
$300$		0			0
$301$	3.24847	+	16.6591i	0.187239	+	0.960217i
$302$		0			0
$303$	−8.32260	+	7.93558i	−0.478121	+	0.455887i
$304$		0			0
$305$	2.15978	+	2.05934i	0.123669	+	0.117918i
$306$		0			0
$307$	−9.64541	+	21.1205i	−0.550493	+	1.20541i	0.406059	+	0.913847i	$0.366903\pi$
$307$	−9.64541	+	21.1205i	−0.550493	+	1.20541i	−0.956551	+	0.291564i	$0.905824\pi$
$308$		0			0
$309$	7.49293	−	4.81541i	0.426258	−	0.273939i
$310$		0			0
$311$	−12.3631	+	9.72242i	−0.701045	+	0.551308i	−0.903818	−	0.427918i	$-0.859247\pi$
$311$	−12.3631	+	9.72242i	−0.701045	+	0.551308i	0.202772	+	0.979226i	$0.435005\pi$
$312$		0			0
$313$	7.85013	+	22.6815i	0.443716	+	1.28203i	0.916210	+	0.400699i	$0.131233\pi$
$313$	7.85013	+	22.6815i	0.443716	+	1.28203i	−0.472494	+	0.881334i	$0.656646\pi$
$314$		0			0
$315$	2.23862	+	7.56302i	0.126132	+	0.426128i
$316$		0			0
$317$	−27.0593	+	5.21526i	−1.51980	+	0.292918i	−0.879759	−	0.475420i	$-0.842296\pi$
$317$	−27.0593	+	5.21526i	−1.51980	+	0.292918i	−0.640044	+	0.768338i	$0.721084\pi$
$318$		0			0
$319$	4.76449	−	6.69079i	0.266760	−	0.374613i
$320$		0			0
$321$	−16.0086			−0.893514
$322$		0			0
$323$	−4.76045			−0.264878
$324$		0			0
$325$	6.45711	−	9.06774i	0.358176	−	0.502988i
$326$		0			0
$327$	−1.96145	+	0.378038i	−0.108468	+	0.0209056i
$328$		0			0
$329$	4.04459	−	4.26041i	0.222986	−	0.234884i
$330$		0			0
$331$	−0.759898	−	2.19558i	−0.0417677	−	0.120680i	0.922189	−	0.386741i	$-0.126399\pi$
$331$	−0.759898	−	2.19558i	−0.0417677	−	0.120680i	−0.963956	+	0.266061i	$0.914278\pi$
$332$		0			0
$333$	−12.4027	+	9.75360i	−0.679665	+	0.534494i
$334$		0			0
$335$	−2.36328	+	1.51879i	−0.129120	+	0.0829804i
$336$		0			0
$337$	−13.9654	+	30.5799i	−0.760743	+	1.66580i	−0.0147055	+	0.999892i	$0.504681\pi$
$337$	−13.9654	+	30.5799i	−0.760743	+	1.66580i	−0.746038	+	0.665904i	$0.768046\pi$
$338$		0			0
$339$	−9.65448	−	9.20552i	−0.524359	−	0.499975i
$340$		0			0
$341$	1.59323	−	1.51914i	0.0862780	−	0.0822659i
$342$		0			0
$343$	−14.0757	−	12.0364i	−0.760016	−	0.649904i
$344$		0			0
$345$	−6.09705	−	2.59435i	−0.328254	−	0.139675i
$346$		0			0
$347$	4.53854	−	1.81696i	0.243642	−	0.0975395i	−0.246628	−	0.969110i	$-0.579323\pi$
$347$	4.53854	−	1.81696i	0.243642	−	0.0975395i	0.490270	+	0.871571i	$0.336898\pi$
$348$		0			0
$349$	−16.3539	−	4.80194i	−0.875405	−	0.257042i	−0.186993	−	0.982361i	$-0.559874\pi$
$349$	−16.3539	−	4.80194i	−0.875405	−	0.257042i	−0.688413	+	0.725319i	$0.741692\pi$
$350$		0			0
$351$	−17.7554	+	5.21345i	−0.947712	+	0.278273i
$352$		0			0
$353$	16.2368	−	1.55042i	0.864195	−	0.0825206i	0.346463	−	0.938064i	$-0.387383\pi$
$353$	16.2368	−	1.55042i	0.864195	−	0.0825206i	0.517732	+	0.855543i	$0.326776\pi$
$354$		0			0
$355$	0.0940073	+	1.97346i	0.00498939	+	0.104740i
$356$		0			0
$357$	14.5699	+	0.662215i	0.771119	+	0.0350481i
$358$		0			0
$359$	10.5827	+	30.5767i	0.558534	+	1.61378i	0.771157	+	0.636645i	$0.219678\pi$
$359$	10.5827	+	30.5767i	0.558534	+	1.61378i	−0.212623	+	0.977134i	$0.568201\pi$
$360$		0			0
$361$	−0.871238	+	18.2895i	−0.0458546	+	0.962607i
$362$		0			0
$363$	5.94498	+	6.86087i	0.312030	+	0.360102i
$364$		0			0
$365$	4.17227	+	9.13599i	0.218386	+	0.478200i
$366$		0			0
$367$	0.945578	+	1.63779i	0.0493588	+	0.0854919i	0.889649	−	0.456645i	$-0.150949\pi$
$367$	0.945578	+	1.63779i	0.0493588	+	0.0854919i	−0.840290	+	0.542136i	$0.817616\pi$
$368$		0			0
$369$	1.04844	−	1.81596i	0.0545798	−	0.0945350i
$370$		0			0
$371$	−4.63030	+	15.8975i	−0.240393	+	0.825357i
$372$		0			0
$373$	−3.81977	+	0.736201i	−0.197780	+	0.0381190i	−0.287179	−	0.957877i	$-0.592718\pi$
$373$	−3.81977	+	0.736201i	−0.197780	+	0.0381190i	0.0893989	+	0.995996i	$0.471505\pi$
$374$		0			0
$375$	0.521724	−	10.9523i	0.0269417	−	0.565576i
$376$		0			0
$377$	16.3258	−	18.8410i	0.840822	−	0.970361i
$378$		0			0
$379$	1.69832	+	11.8121i	0.0872369	+	0.606746i	0.985803	+	0.167907i	$0.0537009\pi$
$379$	1.69832	+	11.8121i	0.0872369	+	0.606746i	−0.898566	+	0.438839i	$0.855390\pi$
$380$		0			0
$381$	−3.01285	−	1.55323i	−0.154353	−	0.0795746i
$382$		0			0
$383$	−9.35494	−	13.1372i	−0.478015	−	0.671278i	0.503206	−	0.864167i	$-0.332154\pi$
$383$	−9.35494	−	13.1372i	−0.478015	−	0.671278i	−0.981221	+	0.192889i	$0.938214\pi$
$384$		0			0
$385$	−3.86159	+	2.76253i	−0.196805	+	0.140792i
$386$		0			0
$387$	9.63442	−	9.18640i	0.489745	−	0.466971i
$388$		0			0
$389$	−8.64719	+	3.46181i	−0.438430	+	0.175521i	−0.580367	−	0.814355i	$-0.697091\pi$
$389$	−8.64719	+	3.46181i	−0.438430	+	0.175521i	0.141938	+	0.989876i	$0.454667\pi$
$390$		0			0
$391$	18.4445	−	20.3835i	0.932778	−	1.03084i
$392$		0			0
$393$	1.33495	−	9.28477i	0.0673392	−	0.468355i
$394$		0			0
$395$	−4.83224	−	19.9188i	−0.243137	−	1.00222i
$396$		0			0
$397$	−2.15383	+	8.87821i	−0.108098	+	0.445585i	−0.999978	−	0.00668748i	$-0.997871\pi$
$397$	−2.15383	+	8.87821i	−0.108098	+	0.445585i	0.891880	+	0.452272i	$0.149386\pi$
$398$		0			0
$399$	−0.196284	+	2.10404i	−0.00982649	+	0.105334i
$400$		0			0
$401$	0.495083	+	10.3931i	0.0247233	+	0.519005i	0.976931	+	0.213554i	$0.0685041\pi$
$401$	0.495083	+	10.3931i	0.0247233	+	0.519005i	−0.952208	+	0.305451i	$0.901193\pi$
$402$		0			0
$403$	5.25206	−	4.13027i	0.261624	−	0.205743i
$404$		0			0
$405$	1.44068	−	1.66263i	0.0715878	−	0.0826168i
$406$		0			0
$407$	−7.99041	−	5.13513i	−0.396070	−	0.254539i
$408$		0			0
$409$	−5.24116	+	15.1433i	−0.259159	+	0.748790i	0.738093	+	0.674699i	$0.235727\pi$
$409$	−5.24116	+	15.1433i	−0.259159	+	0.748790i	−0.997252	+	0.0740905i	$0.976395\pi$
$410$		0			0
$411$	12.6470	+	1.20764i	0.623829	+	0.0595684i
$412$		0			0
$413$	−7.52960	−	6.49575i	−0.370507	−	0.319635i
$414$		0			0
$415$	−2.02046	+	3.49955i	−0.0991807	+	0.171786i
$416$		0			0
$417$	6.53788	−	9.18116i	0.320161	−	0.449604i
$418$		0			0
$419$	−3.86968	−	4.46585i	−0.189046	−	0.218171i	0.653312	−	0.757089i	$-0.273379\pi$
$419$	−3.86968	−	4.46585i	−0.189046	−	0.218171i	−0.842359	+	0.538917i	$0.818833\pi$
$420$		0			0
$421$	11.2553	+	7.23335i	0.548550	+	0.352532i	0.785375	−	0.619021i	$-0.212470\pi$
$421$	11.2553	+	7.23335i	0.548550	+	0.352532i	−0.236824	+	0.971552i	$0.576107\pi$
$422$		0			0
$423$	−4.52419	−	0.871967i	−0.219974	−	0.0423965i
$424$		0			0
$425$	15.6242	+	6.25499i	0.757886	+	0.303412i
$426$		0			0
$427$	2.05372	+	5.09771i	0.0993865	+	0.246695i
$428$		0			0
$429$	−2.64199	−	3.71015i	−0.127556	−	0.179128i
$430$		0			0
$431$	−18.1965	−	17.3504i	−0.876497	−	0.835738i	0.110928	−	0.993828i	$-0.464618\pi$
$431$	−18.1965	−	17.3504i	−0.876497	−	0.835738i	−0.987425	+	0.158090i	$0.949466\pi$
$432$		0			0
$433$	−32.4013	−	9.51389i	−1.55711	−	0.457208i	−0.613893	−	0.789389i	$-0.710397\pi$
$433$	−32.4013	−	9.51389i	−1.55711	−	0.457208i	−0.943216	+	0.332181i	$0.892216\pi$
$434$		0			0
$435$	1.29292	−	8.99244i	0.0619907	−	0.431155i
$436$		0			0
$437$	2.82283	+	2.80989i	0.135034	+	0.134415i
$438$		0			0
$439$	31.0818	+	24.4430i	1.48346	+	1.16660i	0.946374	+	0.323072i	$0.104716\pi$
$439$	31.0818	+	24.4430i	1.48346	+	1.16660i	0.537081	+	0.843530i	$0.319527\pi$
$440$		0			0
$441$	−2.00451	+	14.3867i	−0.0954530	+	0.685083i
$442$		0			0
$443$	−2.25345	+	9.28886i	−0.107065	+	0.441327i	−0.999960	−	0.00893723i	$-0.997155\pi$
$443$	−2.25345	+	9.28886i	−0.107065	+	0.441327i	0.892895	+	0.450264i	$0.148670\pi$
$444$		0			0
$445$	15.1347	−	1.44519i	0.717456	−	0.0685087i
$446$		0			0
$447$	−12.5074	+	8.03804i	−0.591582	+	0.380186i
$448$		0			0
$449$	0.917558	+	6.38175i	0.0433022	+	0.301174i	0.999951	+	0.00992854i	$0.00316040\pi$
$449$	0.917558	+	6.38175i	0.0433022	+	0.301174i	−0.956648	+	0.291245i	$0.905931\pi$
$450$		0			0
$451$	1.23946	+	0.238886i	0.0583639	+	0.0112487i
$452$		0			0
$453$	18.1361	−	9.34979i	0.852106	−	0.439291i
$454$		0			0
$455$	−12.4644	+	7.23262i	−0.584341	+	0.339070i
$456$		0			0
$457$	2.40824	+	0.229959i	0.112653	+	0.0107571i	0.151230	−	0.988499i	$-0.451677\pi$
$457$	2.40824	+	0.229959i	0.112653	+	0.0107571i	−0.0385773	+	0.999256i	$0.512283\pi$
$458$		0			0
$459$	−13.9884	−	24.2287i	−0.652924	−	1.13090i
$460$		0			0
$461$	29.7041			1.38346			0.691730	−	0.722156i	$-0.256849\pi$
$461$	29.7041			1.38346			0.691730	+	0.722156i	$0.256849\pi$
$462$		0			0
$463$	−12.1461	−	26.5963i	−0.564478	−	1.23603i	−0.949686	−	0.313205i	$-0.898597\pi$
$463$	−12.1461	−	26.5963i	−0.564478	−	1.23603i	0.385208	−	0.922830i	$-0.374130\pi$
$464$		0			0
$465$	0.796363	−	2.30094i	0.0369304	−	0.106703i
$466$		0			0
$467$	28.4127	−	14.6478i	1.31478	−	0.677818i	0.348989	−	0.937127i	$-0.386525\pi$
$467$	28.4127	−	14.6478i	1.31478	−	0.677818i	0.965795	+	0.259308i	$0.0834946\pi$
$468$		0			0
$469$	−5.11934	+	0.747444i	−0.236389	+	0.0345138i
$470$		0			0
$471$	−21.1416	−	8.46383i	−0.974155	−	0.389993i
$472$		0			0
$473$	7.12271	+	3.67201i	0.327502	+	0.168839i
$474$		0			0
$475$	−1.01296	+	2.21808i	−0.0464779	+	0.101772i
$476$		0			0
$477$	12.4607	−	3.65879i	0.570536	−	0.167524i
$478$		0			0
$479$	6.67477	+	27.5138i	0.304978	+	1.25714i	0.893650	+	0.448765i	$0.148136\pi$
$479$	6.67477	+	27.5138i	0.304978	+	1.25714i	−0.588672	+	0.808372i	$0.700349\pi$
$480$		0			0
$481$	−22.6607	−	17.8206i	−1.03324	−	0.812549i
$482$		0			0
$483$	−8.24870	−	8.99264i	−0.375329	−	0.409179i
$484$		0			0
$485$	4.98108	+	3.91716i	0.226179	+	0.177869i
$486$		0			0
$487$	4.52802	+	18.6647i	0.205184	+	0.845781i	0.977567	+	0.210624i	$0.0675494\pi$
$487$	4.52802	+	18.6647i	0.205184	+	0.845781i	−0.772383	+	0.635157i	$0.780935\pi$
$488$		0			0
$489$	15.3641	−	4.51130i	0.694787	−	0.204008i
$490$		0			0
$491$	1.13504	−	2.48539i	0.0512235	−	0.112164i	−0.882290	−	0.470707i	$-0.843999\pi$
$491$	1.13504	−	2.48539i	0.0512235	−	0.112164i	0.933513	+	0.358543i	$0.116726\pi$
$492$		0			0
$493$	33.5010	+	17.2710i	1.50881	+	0.777846i
$494$		0			0
$495$	3.45717	+	1.38404i	0.155388	+	0.0622080i
$496$		0			0
$497$	−1.34493	+	3.38082i	−0.0603285	+	0.151651i
$498$		0			0
$499$	26.4409	−	13.6312i	1.18366	−	0.610217i	0.249950	−	0.968259i	$-0.419586\pi$
$499$	26.4409	−	13.6312i	1.18366	−	0.610217i	0.933706	+	0.358042i	$0.116556\pi$
$500$		0			0
$501$	−2.36161	+	6.82344i	−0.105509	+	0.304849i
$502$		0			0
$503$	−2.08860	−	4.57340i	−0.0931261	−	0.203918i	0.857337	−	0.514756i	$-0.172117\pi$
$503$	−2.08860	−	4.57340i	−0.0931261	−	0.203918i	−0.950463	+	0.310838i	$0.899390\pi$
$504$		0			0
$505$	17.1782			0.764419
$506$		0			0
$507$	−0.660942	−	1.14479i	−0.0293535	−	0.0508417i
$508$		0			0
$509$	−32.2236	−	3.07698i	−1.42829	−	0.136385i	−0.647921	−	0.761707i	$-0.724361\pi$
$509$	−32.2236	−	3.07698i	−1.42829	−	0.136385i	−0.780366	+	0.625322i	$0.784967\pi$
$510$		0			0
$511$	0.0403253	+	18.4967i	0.00178389	+	0.818245i
$512$		0			0
$513$	3.60291	−	1.85743i	0.159072	−	0.0820075i
$514$		0			0
$515$	−13.0648	−	2.51803i	−0.575703	−	0.110958i
$516$		0			0
$517$	−0.394720	−	2.74534i	−0.0173598	−	0.120740i
$518$		0			0
$519$	−1.34210	+	0.862518i	−0.0589118	+	0.0378603i
$520$		0			0
$521$	−25.6399	+	2.44831i	−1.12330	+	0.107262i	−0.640133	−	0.768264i	$-0.721121\pi$
$521$	−25.6399	+	2.44831i	−1.12330	+	0.107262i	−0.483170	+	0.875527i	$0.660515\pi$
$522$		0			0
$523$	10.1609	−	41.8836i	0.444303	−	1.83144i	−0.103230	−	0.994658i	$-0.532918\pi$
$523$	10.1609	−	41.8836i	0.444303	−	1.83144i	0.547533	−	0.836784i	$-0.315567\pi$
$524$		0			0
$525$	3.40883	−	6.64776i	0.148774	−	0.290132i
$526$		0			0
$527$	7.94037	+	6.24438i	0.345888	+	0.272009i
$528$		0			0
$529$	−22.9687	+	1.19996i	−0.998638	+	0.0521720i
$530$		0			0
$531$	−1.10998	+	7.72009i	−0.0481691	+	0.335023i
$532$		0			0
$533$	3.67599	+	1.07937i	0.159225	+	0.0467526i
$534$		0			0
$535$	17.3073	+	16.5025i	0.748261	+	0.713465i
$536$		0			0
$537$	3.09439	+	4.34546i	0.133533	+	0.187520i
$538$		0			0
$539$	−8.57878	+	1.69225i	−0.369514	+	0.0728904i
$540$		0			0
$541$	16.2141	+	6.49116i	0.697101	+	0.279077i	0.693024	−	0.720915i	$-0.256278\pi$
$541$	16.2141	+	6.49116i	0.697101	+	0.279077i	0.00407675	+	0.999992i	$0.498702\pi$
$542$		0			0
$543$	23.4276	+	4.51530i	1.00537	+	0.193770i
$544$		0			0
$545$	2.51027	+	1.61325i	0.107528	+	0.0691042i
$546$		0			0
$547$	−20.6685	−	23.8528i	−0.883722	−	1.01987i	−0.999646	−	0.0266119i	$-0.991528\pi$
$547$	−20.6685	−	23.8528i	−0.883722	−	1.01987i	0.115923	−	0.993258i	$-0.463017\pi$
$548$		0			0
$549$	2.50032	−	3.51121i	0.106711	−	0.149855i
$550$		0			0
$551$	−2.73049	+	4.72934i	−0.116323	+	0.201477i
$552$		0			0
$553$	7.06289	−	37.0806i	0.300345	−	1.57683i
$554$		0			0
$555$	−10.4579	−	0.998612i	−0.443915	−	0.0423887i
$556$		0			0
$557$	−8.06499	+	23.3023i	−0.341725	+	0.987349i	0.634937	+	0.772564i	$0.281026\pi$
$557$	−8.06499	+	23.3023i	−0.341725	+	0.987349i	−0.976661	+	0.214785i	$0.931095\pi$
$558$		0			0
$559$	20.4612	+	13.1496i	0.865415	+	0.556169i
$560$		0			0
$561$	4.50941	−	5.20414i	0.190388	−	0.219719i
$562$		0			0
$563$	11.0835	−	8.71619i	0.467115	−	0.367343i	−0.356684	−	0.934225i	$-0.616093\pi$
$563$	11.0835	−	8.71619i	0.467115	−	0.367343i	0.823799	+	0.566882i	$0.191850\pi$
$564$		0			0
$565$	0.948175	+	19.9046i	0.0398900	+	0.837395i
$566$		0			0
$567$	3.68175	−	1.69111i	0.154619	−	0.0710200i
$568$		0			0
$569$	7.15855	−	29.5079i	0.300102	−	1.23704i	−0.599517	−	0.800362i	$-0.704641\pi$
$569$	7.15855	−	29.5079i	0.300102	−	1.23704i	0.899619	−	0.436676i	$-0.143844\pi$
$570$		0			0
$571$	1.48787	+	6.13306i	0.0622652	+	0.256661i	0.994434	−	0.105364i	$-0.0336008\pi$
$571$	1.48787	+	6.13306i	0.0622652	+	0.256661i	−0.932169	+	0.362025i	$0.882086\pi$
$572$		0			0
$573$	−1.18259	+	8.22512i	−0.0494035	+	0.343609i
$574$		0			0
$575$	−5.57274	−	12.9314i	−0.232399	−	0.539276i
$576$		0			0
$577$	3.83136	−	1.53385i	0.159502	−	0.0638549i	−0.290538	−	0.956864i	$-0.593834\pi$
$577$	3.83136	−	1.53385i	0.159502	−	0.0638549i	0.450039	+	0.893009i	$0.351410\pi$
$578$		0			0
$579$	1.94931	−	1.85867i	0.0810107	−	0.0772435i
$580$		0			0
$581$	−6.05260	+	4.32995i	−0.251104	+	0.179637i
$582$		0			0
$583$	4.53470	+	6.36809i	0.187808	+	0.263739i
$584$		0			0
$585$	10.0462	+	5.17917i	0.415359	+	0.214132i
$586$		0			0
$587$	−0.774293	−	5.38532i	−0.0319585	−	0.222276i	0.967583	−	0.252553i	$-0.0812702\pi$
$587$	−0.774293	−	5.38532i	−0.0319585	−	0.222276i	−0.999542	+	0.0302769i	$0.990361\pi$
$588$		0			0
$589$	−0.958453	+	1.10611i	−0.0394924	+	0.0455766i
$590$		0			0
$591$	−0.802458	+	16.8457i	−0.0330087	+	0.692938i
$592$		0			0
$593$	−44.3077	+	8.53961i	−1.81950	+	0.350680i	−0.980968	−	0.194172i	$-0.937798\pi$
$593$	−44.3077	+	8.53961i	−1.81950	+	0.350680i	−0.838533	+	0.544851i	$0.816586\pi$
$594$		0			0
$595$	−15.0692	−	15.7353i	−0.617777	−	0.645084i
$596$		0			0
$597$	7.83523	−	13.5710i	0.320675	−	0.555425i
$598$		0			0
$599$	−3.15303	−	5.46121i	−0.128829	−	0.223139i	0.794394	−	0.607403i	$-0.207789\pi$
$599$	−3.15303	−	5.46121i	−0.128829	−	0.223139i	−0.923223	+	0.384264i	$0.874455\pi$
$600$		0			0
$601$	10.9481	+	23.9730i	0.446582	+	0.977878i	0.990343	+	0.138638i	$0.0442724\pi$
$601$	10.9481	+	23.9730i	0.446582	+	0.977878i	−0.543761	+	0.839240i	$0.683000\pi$
$602$		0			0
$603$	2.65725	+	3.06663i	0.108212	+	0.124883i
$604$		0			0
$605$	0.645268	−	13.5458i	0.0262339	−	0.550717i
$606$		0			0
$607$	−15.8183	−	45.7040i	−0.642045	−	1.85507i	−0.501875	−	0.864940i	$-0.667356\pi$
$607$	−15.8183	−	45.7040i	−0.642045	−	1.85507i	−0.140170	−	0.990127i	$-0.544765\pi$
$608$		0			0
$609$	9.01483	−	14.0948i	0.365299	−	0.571151i
$610$		0			0
$611$	−0.400553	−	8.40865i	−0.0162047	−	0.340178i
$612$		0			0
$613$	40.2284	−	3.84134i	1.62481	−	0.155150i	0.757470	−	0.652870i	$-0.226435\pi$
$613$	40.2284	−	3.84134i	1.62481	−	0.155150i	0.867338	+	0.497719i	$0.165829\pi$
$614$		0			0
$615$	1.33958	−	0.393337i	0.0540171	−	0.0158609i
$616$		0			0
$617$	26.1419	+	7.67596i	1.05243	+	0.309023i	0.761801	−	0.647812i	$-0.224316\pi$
$617$	26.1419	+	7.67596i	1.05243	+	0.309023i	0.290634	+	0.956834i	$0.406134\pi$
$618$		0			0
$619$	−19.9571	+	7.98960i	−0.802142	+	0.321129i	−0.736261	−	0.676698i	$-0.763410\pi$
$619$	−19.9571	+	7.98960i	−0.802142	+	0.321129i	−0.0658816	+	0.997827i	$0.520986\pi$
$620$		0			0
$621$	−6.00635	+	22.6238i	−0.241026	+	0.907862i
$622$		0			0
$623$	26.4795	+	9.10004i	1.06088	+	0.364586i
$624$		0			0
$625$	−1.22948	+	1.17231i	−0.0491793	+	0.0468924i
$626$		0			0
$627$	0.722076	+	0.688498i	0.0288370	+	0.0274960i
$628$		0			0
$629$	18.1057	−	39.6459i	0.721921	−	1.58079i
$630$		0			0
$631$	3.64657	−	2.34351i	0.145168	−	0.0932936i	−0.466041	−	0.884763i	$-0.654320\pi$
$631$	3.64657	−	2.34351i	0.145168	−	0.0932936i	0.611209	+	0.791470i	$0.290684\pi$
$632$		0			0
$633$	−0.846581	+	0.665759i	−0.0336486	+	0.0264615i
$634$		0			0
$635$	1.65612	+	4.78504i	0.0657211	+	0.189889i
$636$		0			0
$637$	−26.4082	+	2.63792i	−1.04633	+	0.104518i
$638$		0			0
$639$	2.80217	−	0.540074i	0.110852	−	0.0213650i
$640$		0			0
$641$	−3.22744	+	4.53231i	−0.127476	+	0.179015i	−0.873381	−	0.487037i	$-0.838078\pi$
$641$	−3.22744	+	4.53231i	−0.127476	+	0.179015i	0.745905	+	0.666052i	$0.232017\pi$
$642$		0			0
$643$	−24.2773			−0.957405			−0.478702	−	0.877977i	$-0.658893\pi$
$643$	−24.2773			−0.957405			−0.478702	+	0.877977i	$0.658893\pi$
$644$		0			0
$645$	8.86336			0.348995
$646$		0			0
$647$	17.4077	−	24.4457i	0.684368	−	0.961060i	−0.315559	−	0.948906i	$-0.602192\pi$
$647$	17.4077	−	24.4457i	0.684368	−	0.961060i	0.999926	−	0.0121537i	$-0.00386874\pi$
$648$		0			0
$649$	−4.61023	+	0.888550i	−0.180967	+	0.0348786i
$650$		0			0
$651$	3.08732	−	3.25205i	0.121002	−	0.127458i
$652$		0			0
$653$	−4.69869	−	13.5760i	−0.183874	−	0.531269i	0.814961	−	0.579515i	$-0.196758\pi$
$653$	−4.69869	−	13.5760i	−0.183874	−	0.531269i	−0.998835	+	0.0482459i	$0.984637\pi$
$654$		0			0
$655$	−11.0145	+	8.66187i	−0.430371	+	0.338447i
$656$		0			0
$657$	12.2043	−	7.84321i	0.476134	−	0.305993i
$658$		0			0
$659$	7.25486	−	15.8859i	0.282609	−	0.618828i	−0.714086	−	0.700058i	$-0.753158\pi$
$659$	7.25486	−	15.8859i	0.282609	−	0.618828i	0.996695	+	0.0812299i	$0.0258848\pi$
$660$		0			0
$661$	5.11714	+	4.87918i	0.199034	+	0.189778i	0.783041	−	0.621970i	$-0.213668\pi$
$661$	5.11714	+	4.87918i	0.199034	+	0.189778i	−0.584007	+	0.811748i	$0.698516\pi$
$662$		0			0
$663$	15.1262	−	14.4228i	0.587453	−	0.560135i
$664$		0			0
$665$	2.38116	−	2.07240i	0.0923376	−	0.0803641i
$666$		0			0
$667$	−9.67099	−	30.0155i	−0.374462	−	1.16221i
$668$		0			0
$669$	−2.13073	+	0.853015i	−0.0823787	+	0.0329795i
$670$		0			0
$671$	2.48968	+	0.731037i	0.0961132	+	0.0282214i
$672$		0			0
$673$	42.3660	−	12.4398i	1.63309	−	0.479518i	0.668595	−	0.743627i	$-0.266896\pi$
$673$	42.3660	−	12.4398i	1.63309	−	0.479518i	0.964493	+	0.264109i	$0.0850779\pi$
$674$		0			0
$675$	−14.2657	+	1.36221i	−0.549086	+	0.0524313i
$676$		0			0
$677$	−0.215973	−	4.53382i	−0.00830050	−	0.174249i	−0.999211	−	0.0397239i	$-0.987352\pi$
$677$	−0.215973	−	4.53382i	−0.00830050	−	0.174249i	0.990910	−	0.134525i	$-0.0429509\pi$
$678$		0			0
$679$	5.37017	+	10.3612i	0.206088	+	0.397625i
$680$		0			0
$681$	6.06281	+	17.5173i	0.232327	+	0.671266i
$682$		0			0
$683$	1.93219	−	40.5617i	0.0739333	−	1.55205i	−0.591937	−	0.805984i	$-0.701637\pi$
$683$	1.93219	−	40.5617i	0.0739333	−	1.55205i	0.665870	−	0.746068i	$-0.268060\pi$
$684$		0			0
$685$	−12.4281	−	14.3427i	−0.474852	−	0.548008i
$686$		0			0
$687$	0.312610	+	0.684520i	0.0119268	+	0.0261161i
$688$		0			0
$689$	11.8639	+	20.5489i	0.451979	+	0.782850i
$690$		0			0
$691$	11.8993	−	20.6101i	0.452669	−	0.784046i	−0.545882	−	0.837862i	$-0.683805\pi$
$691$	11.8993	−	20.6101i	0.452669	−	0.784046i	0.998551	+	0.0538161i	$0.0171385\pi$
$692$		0			0
$693$	4.74345	+	4.95312i	0.180189	+	0.188154i
$694$		0			0
$695$	−16.5327	+	3.18641i	−0.627120	+	0.120868i
$696$		0			0
$697$	−0.275604	+	5.78563i	−0.0104392	+	0.219147i
$698$		0			0
$699$	9.37989	−	10.8250i	0.354780	−	0.409438i
$700$		0			0
$701$	−4.06917	−	28.3017i	−0.153690	−	1.06894i	−0.909965	−	0.414686i	$-0.863892\pi$
$701$	−4.06917	−	28.3017i	−0.153690	−	1.06894i	0.756274	−	0.654255i	$-0.227018\pi$
$702$		0			0
$703$	5.61290	+	2.89365i	0.211695	+	0.109136i
$704$		0			0
$705$	−1.77944	−	2.49888i	−0.0670177	−	0.0941132i
$706$		0			0
$707$	28.8057	+	13.0793i	1.08335	+	0.491898i
$708$		0			0
$709$	28.4017	−	27.0810i	1.06665	−	1.01705i	0.0668342	−	0.997764i	$-0.478710\pi$
$709$	28.4017	−	27.0810i	1.06665	−	1.01705i	0.999814	−	0.0192830i	$-0.00613835\pi$
$710$		0			0
$711$	−27.4850	+	11.0033i	−1.03077	+	0.412657i
$712$		0			0
$713$	−1.02266	−	8.38963i	−0.0382990	−	0.314194i
$714$		0			0
$715$	−0.968294	+	6.73464i	−0.0362122	+	0.251861i
$716$		0			0
$717$	4.10183	+	16.9080i	0.153186	+	0.631440i
$718$		0			0
$719$	0.892234	−	3.67784i	0.0332747	−	0.137160i	−0.952751	−	0.303751i	$-0.901761\pi$
$719$	0.892234	−	3.67784i	0.0332747	−	0.137160i	0.986026	+	0.166591i	$0.0532760\pi$
$720$		0			0
$721$	−19.9908	−	14.1698i	−0.744498	−	0.527712i
$722$		0			0
$723$	0.335006	+	7.03264i	0.0124590	+	0.261547i
$724$		0			0
$725$	15.1758	−	11.9344i	0.563616	−	0.443233i
$726$		0			0
$727$	−22.5009	+	25.9675i	−0.834514	+	0.963080i	−0.999731	−	0.0231769i	$-0.992622\pi$
$727$	−22.5009	+	25.9675i	−0.834514	+	0.963080i	0.165218	+	0.986257i	$0.447167\pi$
$728$		0			0
$729$	9.17317	+	5.89524i	0.339747	+	0.218342i
$730$		0			0
$731$	−12.0269	+	34.7493i	−0.444830	+	1.28525i
$732$		0			0
$733$	−12.8996	−	1.23177i	−0.476459	−	0.0454963i	−0.145935	−	0.989294i	$-0.546619\pi$
$733$	−12.8996	−	1.23177i	−0.476459	−	0.0454963i	−0.330523	+	0.943798i	$0.607225\pi$
$734$		0			0
$735$	−7.57610	+	6.01155i	−0.279448	+	0.221740i
$736$		0			0
$737$	−1.22133	+	2.11540i	−0.0449881	+	0.0779217i
$738$		0			0
$739$	9.46502	−	13.2918i	0.348176	−	0.488945i	−0.602936	−	0.797789i	$-0.706003\pi$
$739$	9.46502	−	13.2918i	0.348176	−	0.488945i	0.951113	+	0.308844i	$0.0999421\pi$
$740$		0			0
$741$	1.98305	+	2.28856i	0.0728490	+	0.0840723i
$742$		0			0
$743$	9.52643	+	6.12226i	0.349491	+	0.224604i	0.703594	−	0.710602i	$-0.251577\pi$
$743$	9.52643	+	6.12226i	0.349491	+	0.224604i	−0.354103	+	0.935206i	$0.615214\pi$
$744$		0			0
$745$	21.8081	+	4.20317i	0.798988	+	0.153992i
$746$		0			0
$747$	5.41871	+	2.16933i	0.198260	+	0.0793715i
$748$		0			0
$749$	16.4574	+	40.8503i	0.601341	+	1.49264i
$750$		0			0
$751$	−13.6730	−	19.2010i	−0.498933	−	0.700654i	0.485928	−	0.873999i	$-0.338482\pi$
$751$	−13.6730	−	19.2010i	−0.498933	−	0.700654i	−0.984861	+	0.173345i	$0.944542\pi$
$752$		0			0
$753$	−6.24462	−	5.95424i	−0.227567	−	0.216984i
$754$		0			0
$755$	−29.2456	−	8.58728i	−1.06436	−	0.312523i
$756$		0			0
$757$	0.352611	−	2.45247i	0.0128159	−	0.0891364i	−0.982410	−	0.186739i	$-0.940208\pi$
$757$	0.352611	−	2.45247i	0.0128159	−	0.0891364i	0.995225	+	0.0976023i	$0.0311173\pi$
$758$		0			0
$759$	−5.74576	+	0.424218i	−0.208558	+	0.0153981i
$760$		0			0
$761$	14.4298	+	11.3477i	0.523080	+	0.411355i	0.844479	−	0.535589i	$-0.179910\pi$
$761$	14.4298	+	11.3477i	0.523080	+	0.411355i	−0.321399	+	0.946944i	$0.604153\pi$
$762$		0			0
$763$	2.98111	+	4.61653i	0.107923	+	0.167130i
$764$		0			0
$765$	−4.02864	+	16.6063i	−0.145656	+	0.600402i
$766$		0			0
$767$	−14.1857	+	1.35457i	−0.512217	+	0.0489108i
$768$		0			0
$769$	−23.2234	+	14.9248i	−0.837457	+	0.538201i	−0.887640	−	0.460539i	$-0.847656\pi$
$769$	−23.2234	+	14.9248i	−0.837457	+	0.538201i	0.0501822	+	0.998740i	$0.484020\pi$
$770$		0			0
$771$	3.02428	+	21.0343i	0.108917	+	0.757533i
$772$		0			0
$773$	8.36114	+	1.61148i	0.300729	+	0.0579608i	0.337384	−	0.941367i	$-0.390458\pi$
$773$	8.36114	+	1.61148i	0.300729	+	0.0579608i	−0.0366545	+	0.999328i	$0.511670\pi$
$774$		0			0
$775$	4.59911	−	2.37101i	0.165205	−	0.0851691i
$776$		0			0
$777$	−16.7764	−	9.63713i	−0.601849	−	0.345730i
$778$		0			0
$779$	−0.835421	−	0.0797730i	−0.0299321	−	0.00285816i
$780$		0			0
$781$	0.858938	+	1.48772i	0.0307352	+	0.0532350i
$782$		0			0
$783$	−32.0938			−1.14694
$784$		0			0
$785$	14.1318	+	30.9443i	0.504386	+	1.10445i
$786$		0			0
$787$	−15.5589	+	44.9543i	−0.554613	+	1.60245i	0.223758	+	0.974645i	$0.428168\pi$
$787$	−15.5589	+	44.9543i	−0.554613	+	1.60245i	−0.778371	+	0.627805i	$0.783954\pi$
$788$		0			0
$789$	−14.3498	+	7.39782i	−0.510866	+	0.263369i
$790$		0			0
$791$	−13.5652	+	34.0996i	−0.482325	+	1.21244i
$792$		0			0
$793$	7.31143	+	2.92706i	0.259637	+	0.103943i
$794$		0			0
$795$	7.68553	+	3.96217i	0.272578	+	0.140524i
$796$		0			0
$797$	−15.8840	+	34.7812i	−0.562641	+	1.23201i	0.387982	+	0.921667i	$0.373172\pi$
$797$	−15.8840	+	34.7812i	−0.562641	+	1.23201i	−0.950624	+	0.310346i	$0.899555\pi$
$798$		0			0
$799$	12.2116	−	3.58564i	0.432014	−	0.126851i
$800$		0			0
$801$	−5.17737	−	21.3414i	−0.182933	−	0.754062i
$802$		0			0
$803$	6.86458	+	5.39837i	0.242246	+	0.190504i
$804$		0			0
$805$	−0.352192	+	18.2254i	−0.0124131	+	0.642359i
$806$		0			0
$807$	−16.1147	−	12.6727i	−0.567264	−	0.446102i
$808$		0			0
$809$	−8.61482	−	35.5108i	−0.302881	−	1.24849i	−0.896245	−	0.443558i	$-0.853716\pi$
$809$	−8.61482	−	35.5108i	−0.302881	−	1.24849i	0.593364	−	0.804934i	$-0.297799\pi$
$810$		0			0
$811$	−40.4120	+	11.8660i	−1.41906	+	0.416673i	−0.899184	−	0.437570i	$-0.855839\pi$
$811$	−40.4120	+	11.8660i	−1.41906	+	0.416673i	−0.519874	+	0.854243i	$0.674021\pi$
$812$		0			0
$813$	−8.85539	+	19.3906i	−0.310572	+	0.680058i
$814$		0			0
$815$	−21.2610	−	10.9608i	−0.744739	−	0.383940i
$816$		0			0
$817$	−4.94615	−	1.98014i	−0.173044	−	0.0692764i
$818$		0			0
$819$	12.9029	+	16.3339i	0.450863	+	0.570753i
$820$		0			0
$821$	37.8938	−	19.5356i	1.32250	−	0.681797i	0.355049	−	0.934848i	$-0.384464\pi$
$821$	37.8938	−	19.5356i	1.32250	−	0.681797i	0.967453	+	0.253051i	$0.0814340\pi$
$822$		0			0
$823$	9.71109	−	28.0583i	0.338507	−	0.978052i	−0.639375	−	0.768895i	$-0.720807\pi$
$823$	9.71109	−	28.0583i	0.338507	−	0.978052i	0.977882	−	0.209157i	$-0.0670720\pi$
$824$		0			0
$825$	−1.46527	−	3.20849i	−0.0510141	−	0.111705i
$826$		0			0
$827$	39.2883			1.36619			0.683095	−	0.730330i	$-0.260634\pi$
$827$	39.2883			1.36619			0.683095	+	0.730330i	$0.260634\pi$
$828$		0			0
$829$	−12.9194	−	22.3771i	−0.448710	−	0.777189i	0.549592	−	0.835433i	$-0.314783\pi$
$829$	−12.9194	−	22.3771i	−0.448710	−	0.777189i	−0.998302	+	0.0582440i	$0.981450\pi$
$830$		0			0
$831$	3.87115	+	0.369650i	0.134289	+	0.0128230i
$832$		0			0
$833$	−13.2885	−	37.8597i	−0.460420	−	1.31176i
$834$		0			0
$835$	9.58715	−	4.94252i	0.331777	−	0.171043i
$836$		0			0
$837$	−8.44604	−	1.62784i	−0.291938	−	0.0562664i
$838$		0			0
$839$	−2.05954	−	14.3244i	−0.0711032	−	0.494534i	−0.993991	−	0.109464i	$-0.965087\pi$
$839$	−2.05954	−	14.3244i	−0.0711032	−	0.494534i	0.922888	−	0.385070i	$-0.125823\pi$
$840$		0			0
$841$	11.9772	−	7.69728i	0.413007	−	0.265424i
$842$		0			0
$843$	8.42354	−	0.804351i	0.290122	−	0.0277033i
$844$		0			0
$845$	−0.465542	+	1.91899i	−0.0160151	+	0.0660153i
$846$		0			0
$847$	11.3957	−	22.2234i	0.391562	−	0.763606i
$848$		0			0
$849$	−18.1558	−	14.2779i	−0.623106	−	0.490016i
$850$		0			0
$851$	−34.1376	+	12.8221i	−1.17022	+	0.439535i
$852$		0			0
$853$	−5.84009	+	40.6187i	−0.199961	+	1.39076i	0.604430	+	0.796659i	$0.293401\pi$
$853$	−5.84009	+	40.6187i	−0.199961	+	1.39076i	−0.804391	+	0.594101i	$0.797508\pi$
$854$		0			0
$855$	−2.37556	−	0.697527i	−0.0812424	−	0.0238549i
$856$		0			0
$857$	21.1993	+	20.2135i	0.724154	+	0.690480i	0.959587	−	0.281411i	$-0.0908024\pi$
$857$	21.1993	+	20.2135i	0.724154	+	0.690480i	−0.235433	+	0.971891i	$0.575651\pi$
$858$		0			0
$859$	−2.30022	−	3.23021i	−0.0784826	−	0.110213i	0.773469	−	0.633835i	$-0.218520\pi$
$859$	−2.30022	−	3.23021i	−0.0784826	−	0.110213i	−0.851951	+	0.523621i	$0.824581\pi$
$860$		0			0
$861$	2.54580	+	0.360367i	0.0867606	+	0.0122813i
$862$		0			0
$863$	40.7095	+	16.2976i	1.38577	+	0.554778i	0.940247	−	0.340494i	$-0.110594\pi$
$863$	40.7095	+	16.2976i	1.38577	+	0.554778i	0.445521	+	0.895271i	$0.353018\pi$
$864$		0			0
$865$	2.34011	+	0.451019i	0.0795662	+	0.0153351i
$866$		0			0
$867$	12.8282	+	8.24421i	0.435670	+	0.279988i
$868$		0			0
$869$	−11.6708	−	13.4689i	−0.395906	−	0.456900i
$870$		0			0
$871$	−4.30043	+	6.03911i	−0.145715	+	0.204627i
$872$		0			0
$873$	4.57653	−	7.92678i	0.154892	−	0.268281i
$874$		0			0
$875$	−28.4842	+	9.92806i	−0.962941	+	0.335630i
$876$		0			0
$877$	48.6313	+	4.64372i	1.64216	+	0.156807i	0.874826	−	0.484438i	$-0.160976\pi$
$877$	48.6313	+	4.64372i	1.64216	+	0.156807i	0.767336	+	0.641246i	$0.221582\pi$
$878$		0			0
$879$	2.86202	−	8.26925i	0.0965334	−	0.278915i
$880$		0			0
$881$	−16.4900	−	10.5975i	−0.555561	−	0.357037i	0.232537	−	0.972588i	$-0.425297\pi$
$881$	−16.4900	−	10.5975i	−0.555561	−	0.357037i	−0.788098	+	0.615550i	$0.788934\pi$
$882$		0			0
$883$	−6.12835	+	7.07249i	−0.206235	+	0.238008i	−0.849439	−	0.527687i	$-0.823059\pi$
$883$	−6.12835	+	7.07249i	−0.206235	+	0.238008i	0.643204	+	0.765695i	$0.277605\pi$
$884$		0			0
$885$	−4.08197	+	3.21009i	−0.137214	+	0.107906i
$886$		0			0
$887$	0.197785	+	4.15201i	0.00664096	+	0.139411i	0.999753	+	0.0222395i	$0.00707964\pi$
$887$	0.197785	+	4.15201i	0.00664096	+	0.139411i	−0.993112	+	0.117171i	$0.962617\pi$
$888$		0			0
$889$	−0.866177	+	9.28489i	−0.0290506	+	0.311405i
$890$		0			0
$891$	0.450981	−	1.85897i	0.0151084	−	0.0622778i
$892$		0			0
$893$	0.434741	+	1.79203i	0.0145481	+	0.0599679i
$894$		0			0
$895$	1.13410	−	7.88784i	0.0379088	−	0.263661i
$896$		0			0
$897$	−17.4826	−	0.375970i	−0.583729	−	0.0125533i
$898$		0			0
$899$	10.7580	−	4.30685i	0.358799	−	0.143641i
$900$		0			0
$901$	−25.9625	+	24.7552i	−0.864938	+	0.824716i
$902$		0			0
$903$	14.8628	+	6.74849i	0.494603	+	0.224576i
$904$		0			0
$905$	−20.6736	−	29.0319i	−0.687212	−	0.965054i
$906$		0			0
$907$	−6.71383	−	3.46122i	−0.222929	−	0.114928i	0.343145	−	0.939283i	$-0.388508\pi$
$907$	−6.71383	−	3.46122i	−0.222929	−	0.114928i	−0.566074	+	0.824355i	$0.691538\pi$
$908$		0			0
$909$	−3.53120	−	24.5600i	−0.117122	−	0.814605i
$910$		0			0
$911$	−0.657109	+	0.758344i	−0.0217710	+	0.0251251i	−0.766531	−	0.642208i	$-0.778019\pi$
$911$	−0.657109	+	0.758344i	−0.0217710	+	0.0251251i	0.744760	+	0.667333i	$0.232564\pi$
$912$		0			0
$913$	−0.167184	+	3.50963i	−0.00553299	+	0.116152i
$914$		0			0
$915$	2.81811	−	0.543145i	0.0931637	−	0.0179558i
$916$		0			0
$917$	−25.0650	+	6.13859i	−0.827719	+	0.202714i
$918$		0			0
$919$	−21.4085	+	37.0806i	−0.706200	+	1.22317i	0.260056	+	0.965593i	$0.416259\pi$
$919$	−21.4085	+	37.0806i	−0.706200	+	1.22317i	−0.966257	+	0.257581i	$0.917074\pi$
$920$		0			0
$921$	11.1649	+	19.3382i	0.367897	+	0.637216i
$922$		0			0
$923$	2.16598	+	4.74283i	0.0712940	+	0.156112i
$924$		0			0
$925$	−14.6199	−	16.8723i	−0.480701	−	0.554758i
$926$		0			0
$927$	−0.914448	+	19.1966i	−0.0300344	+	0.630500i
$928$		0			0
$929$	16.6315	+	48.0536i	0.545663	+	1.57659i	0.794002	+	0.607915i	$0.207994\pi$
$929$	16.6315	+	48.0536i	0.545663	+	1.57659i	−0.248339	+	0.968673i	$0.579885\pi$
$930$		0			0
$931$	5.57083	−	1.66216i	0.182576	−	0.0544751i
$932$		0			0
$933$	0.719720	+	15.1088i	0.0235626	+	0.494639i
$934$		0			0
$935$	−10.2399	+	0.977795i	−0.334882	+	0.0319773i
$936$		0			0
$937$	−16.0953	+	4.72602i	−0.525812	+	0.154392i	−0.533856	−	0.845575i	$-0.679258\pi$
$937$	−16.0953	+	4.72602i	−0.525812	+	0.154392i	0.00804417	+	0.999968i	$0.497439\pi$
$938$		0			0
$939$	22.1477	+	6.50314i	0.722762	+	0.212222i
$940$		0			0
$941$	−18.6800	+	7.47836i	−0.608952	+	0.243788i	−0.655581	−	0.755125i	$-0.727576\pi$
$941$	−18.6800	+	7.47836i	−0.608952	+	0.243788i	0.0466293	+	0.998912i	$0.485152\pi$
$942$		0			0
$943$	3.57844	−	3.26807i	0.116530	−	0.106423i
$944$		0			0
$945$	17.5446	+	6.02945i	0.570726	+	0.196138i
$946$		0			0
$947$	10.0461	−	9.57892i	0.326454	−	0.311273i	−0.509072	−	0.860724i	$-0.670011\pi$
$947$	10.0461	−	9.57892i	0.326454	−	0.311273i	0.835526	+	0.549451i	$0.185163\pi$
$948$		0			0
$949$	19.1832	+	18.2912i	0.622713	+	0.593756i
$950$		0			0
$951$	−11.0095	+	24.1074i	−0.357006	+	0.781735i
$952$		0			0
$953$	−11.8148	+	7.59291i	−0.382719	+	0.245958i	−0.717827	−	0.696221i	$-0.754863\pi$
$953$	−11.8148	+	7.59291i	−0.382719	+	0.245958i	0.335109	+	0.942180i	$0.391227\pi$
$954$		0			0
$955$	9.75740	−	7.67330i	0.315742	−	0.248302i
$956$		0			0
$957$	−2.58364	−	7.46492i	−0.0835171	−	0.241307i
$958$		0			0
$959$	−9.91991	−	33.5137i	−0.320331	−	1.08221i
$960$		0			0
$961$	−27.3902	+	5.27903i	−0.883554	+	0.170291i
$962$		0			0
$963$	20.0363	−	28.1370i	0.645659	−	0.906702i
$964$		0			0
$965$	−4.02346			−0.129520
$966$		0			0
$967$	−33.7236			−1.08448			−0.542239	−	0.840224i	$-0.682423\pi$
$967$	−33.7236			−1.08448			−0.542239	+	0.840224i	$0.682423\pi$
$968$		0			0
$969$	−2.65562	+	3.72929i	−0.0853107	+	0.119802i
$970$		0			0
$971$	10.9478	−	2.11002i	0.351332	−	0.0677136i	−0.0105324	−	0.999945i	$-0.503353\pi$
$971$	10.9478	−	2.11002i	0.351332	−	0.0677136i	0.361864	+	0.932231i	$0.382140\pi$
$972$		0			0
$973$	−30.1494	−	7.24460i	−0.966545	−	0.232251i
$974$		0			0
$975$	−3.50149	−	10.1169i	−0.112137	−	0.324000i
$976$		0			0
$977$	−23.6056	+	18.5636i	−0.755209	+	0.593903i	−0.919767	−	0.392465i	$-0.871623\pi$
$977$	−23.6056	+	18.5636i	−0.755209	+	0.593903i	0.164558	+	0.986367i	$0.447380\pi$
$978$		0			0
$979$	11.1210	−	7.14706i	0.355430	−	0.228421i
$980$		0			0
$981$	1.79049	−	3.92062i	0.0571658	−	0.125176i
$982$		0			0
$983$	−6.46796	−	6.16719i	−0.206296	−	0.196703i	0.579887	−	0.814697i	$-0.303097\pi$
$983$	−6.46796	−	6.16719i	−0.206296	−	0.196703i	−0.786182	+	0.617995i	$0.787945\pi$
$984$		0			0
$985$	18.2329	−	17.3851i	0.580949	−	0.553934i
$986$		0			0
$987$	−1.08129	−	5.54517i	−0.0344177	−	0.176505i
$988$		0			0
$989$	27.6427	−	13.5066i	0.878987	−	0.429485i
$990$		0			0
$991$	32.4001	−	12.9710i	1.02922	−	0.412039i	0.205275	−	0.978704i	$-0.434191\pi$
$991$	32.4001	−	12.9710i	1.02922	−	0.412039i	0.823948	+	0.566666i	$0.191767\pi$
$992$		0			0
$993$	−2.14391	−	0.629508i	−0.0680348	−	0.0199768i
$994$		0			0
$995$	−22.4606	+	6.59502i	−0.712048	+	0.209076i
$996$		0			0
$997$	2.09774	−	0.200310i	0.0664362	−	0.00634389i	−0.0617850	−	0.998089i	$-0.519679\pi$
$997$	2.09774	−	0.200310i	0.0664362	−	0.00634389i	0.128221	+	0.991746i	$0.459073\pi$
$998$		0			0
$999$	1.76587	+	37.0702i	0.0558698	+	1.17285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.y.a.261.11	yes	320
7.4	even	3	inner	644.2.y.a.445.6	yes	320
23.3	even	11	inner	644.2.y.a.233.6	✓	320
161.95	even	33	inner	644.2.y.a.417.11	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.y.a.233.6	✓	320	23.3	even	11	inner
644.2.y.a.261.11	yes	320	1.1	even	1	trivial
644.2.y.a.417.11	yes	320	161.95	even	33	inner
644.2.y.a.445.6	yes	320	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.557850 - 0.783391i) q^{3} +(-1.41067 + 0.271884i) q^{5} +(-2.57253 - 0.618153i) q^{7} +(0.678699 + 1.96097i) q^{9} +O(q^{10})\)	\(q+(0.557850 - 0.783391i) q^{3} +(-1.41067 + 0.271884i) q^{5} +(-2.57253 - 0.618153i) q^{7} +(0.678699 + 1.96097i) q^{9} +(-0.981903 + 0.772177i) q^{11} +(-3.18951 + 2.04977i) q^{13} +(-0.573949 + 1.25677i) q^{15} +(-4.14845 - 3.95554i) q^{17} +(0.601062 - 0.573112i) q^{19} +(-1.91934 + 1.67046i) q^{21} +(0.125147 + 4.79420i) q^{23} +(-2.72578 + 1.09124i) q^{25} +(4.68310 + 1.37508i) q^{27} +(-6.30916 + 1.85254i) q^{29} +(-1.75433 + 0.167518i) q^{31} +(0.0571618 + 1.19997i) q^{33} +(3.79704 + 0.172579i) q^{35} +(2.48693 + 7.18551i) q^{37} +(-0.173494 + 3.64210i) q^{39} +(-0.661736 - 0.763684i) q^{41} +(-2.66495 - 5.83543i) q^{43} +(-1.49057 - 2.58175i) q^{45} +(-1.11018 + 1.92288i) q^{47} +(6.23577 + 3.18043i) q^{49} +(-5.41295 + 1.04326i) q^{51} +(0.297785 - 6.25128i) q^{53} +(1.17519 - 1.35625i) q^{55} +(-0.113668 - 0.790577i) q^{57} +(3.34078 + 1.72229i) q^{59} +(-1.20492 - 1.69207i) q^{61} +(-0.533791 - 5.46419i) q^{63} +(3.94203 - 3.75872i) q^{65} +(1.81537 - 0.726764i) q^{67} +(3.82555 + 2.57641i) q^{69} +(0.195716 - 1.36123i) q^{71} +(-1.64822 - 6.79404i) q^{73} +(-0.665712 + 2.74410i) q^{75} +(3.00329 - 1.37948i) q^{77} +(0.678857 + 14.2510i) q^{79} +(-1.20372 + 0.946616i) q^{81} +(1.84198 - 2.12576i) q^{83} +(6.92753 + 4.45205i) q^{85} +(-2.06831 + 5.97598i) q^{87} +(-10.5349 - 1.00596i) q^{89} +(9.47216 - 3.30149i) q^{91} +(-0.847420 + 1.46777i) q^{93} +(-0.692078 + 0.971888i) q^{95} +(-2.88852 - 3.33354i) q^{97} +(-2.18063 - 1.40141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more