LMFDB - Embedded newform 780.2.r.a.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [780,2,Mod(73,780)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(780, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("780.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.r (of order $4$, degree $2$, 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:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	780.73
Dual form			780.2.r.a.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-0.705075 + 2.12200i) q^{5} +3.56717i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.705075 + 2.12200i) q^{5} +3.56717i q^{7} +1.00000i q^{9} +(2.90982 - 2.90982i) q^{11} +(-3.59366 - 0.292543i) q^{13} +(1.99904 - 1.00191i) q^{15} +(-2.74138 - 2.74138i) q^{17} +(-3.05307 + 3.05307i) q^{19} +(2.52237 - 2.52237i) q^{21} +(-3.58638 + 3.58638i) q^{23} +(-4.00574 - 2.99233i) q^{25} +(0.707107 - 0.707107i) q^{27} +4.28689i q^{29} +(-6.44632 - 6.44632i) q^{31} -4.11510 q^{33} +(-7.56951 - 2.51512i) q^{35} -10.5790i q^{37} +(2.33424 + 2.74796i) q^{39} +(5.79628 + 5.79628i) q^{41} +(-7.39231 + 7.39231i) q^{43} +(-2.12200 - 0.705075i) q^{45} +12.7460i q^{47} -5.72467 q^{49} +3.87689i q^{51} +(6.34720 + 6.34720i) q^{53} +(4.12298 + 8.22626i) q^{55} +4.31770 q^{57} +(-3.62177 - 3.62177i) q^{59} +0.559190 q^{61} -3.56717 q^{63} +(3.15458 - 7.41948i) q^{65} -9.61529 q^{67} +5.07190 q^{69} +(0.724767 + 0.724767i) q^{71} +3.21489 q^{73} +(0.716586 + 4.94838i) q^{75} +(10.3798 + 10.3798i) q^{77} +6.90252i q^{79} -1.00000 q^{81} -4.46117i q^{83} +(7.75007 - 3.88432i) q^{85} +(3.03129 - 3.03129i) q^{87} +(-6.82030 - 6.82030i) q^{89} +(1.04355 - 12.8192i) q^{91} +9.11647i q^{93} +(-4.32596 - 8.63125i) q^{95} -12.1805 q^{97} +(2.90982 + 2.90982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) $ 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−0.705075	+	2.12200i	−0.315319	+	0.948986i
$5$	−0.705075	+	2.12200i	−0.315319	+	0.948986i
$6$		0			0
$7$			3.56717i			1.34826i	0.738612	+	0.674131i	$0.235482\pi$
$7$			3.56717i			1.34826i	−0.738612	+	0.674131i	$0.764518\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	2.90982	−	2.90982i	0.877343	−	0.877343i	−0.115916	−	0.993259i	$-0.536980\pi$
$11$	2.90982	−	2.90982i	0.877343	−	0.877343i	0.993259	+	0.115916i	$0.0369804\pi$
$12$		0			0
$13$	−3.59366	−	0.292543i	−0.996703	−	0.0811369i
$13$	−3.59366	−	0.292543i	−0.996703	−	0.0811369i
$14$		0			0
$15$	1.99904	−	1.00191i	0.516150	−	0.258693i
$16$		0			0
$17$	−2.74138	−	2.74138i	−0.664881	−	0.664881i	0.291645	−	0.956527i	$-0.405797\pi$
$17$	−2.74138	−	2.74138i	−0.664881	−	0.664881i	−0.956527	+	0.291645i	$0.905797\pi$
$18$		0			0
$19$	−3.05307	+	3.05307i	−0.700423	+	0.700423i	−0.964501	−	0.264079i	$-0.914932\pi$
$19$	−3.05307	+	3.05307i	−0.700423	+	0.700423i	0.264079	+	0.964501i	$0.414932\pi$
$20$		0			0
$21$	2.52237	−	2.52237i	0.550426	−	0.550426i
$22$		0			0
$23$	−3.58638	+	3.58638i	−0.747811	+	0.747811i	−0.974068	−	0.226256i	$-0.927351\pi$
$23$	−3.58638	+	3.58638i	−0.747811	+	0.747811i	0.226256	+	0.974068i	$0.427351\pi$
$24$		0			0
$25$	−4.00574	−	2.99233i	−0.801148	−	0.598467i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			4.28689i			0.796055i	0.917373	+	0.398028i	$0.130305\pi$
$29$			4.28689i			0.796055i	−0.917373	+	0.398028i	$0.869695\pi$
$30$		0			0
$31$	−6.44632	−	6.44632i	−1.15779	−	1.15779i	−0.984949	−	0.172844i	$-0.944704\pi$
$31$	−6.44632	−	6.44632i	−1.15779	−	1.15779i	−0.172844	−	0.984949i	$-0.555296\pi$
$32$		0			0
$33$	−4.11510			−0.716347
$34$		0			0
$35$	−7.56951	−	2.51512i	−1.27948	−	0.425133i
$36$		0			0
$37$		−	10.5790i		−	1.73917i	−0.493781	−	0.869586i	$-0.664386\pi$
$37$		−	10.5790i		−	1.73917i	0.493781	−	0.869586i	$-0.335614\pi$
$38$		0			0
$39$	2.33424	+	2.74796i	0.373778	+	0.440026i
$40$		0			0
$41$	5.79628	+	5.79628i	0.905228	+	0.905228i	0.995882	−	0.0906548i	$-0.0288960\pi$
$41$	5.79628	+	5.79628i	0.905228	+	0.905228i	−0.0906548	+	0.995882i	$0.528896\pi$
$42$		0			0
$43$	−7.39231	+	7.39231i	−1.12732	+	1.12732i	−0.136705	+	0.990612i	$0.543651\pi$
$43$	−7.39231	+	7.39231i	−1.12732	+	1.12732i	−0.990612	+	0.136705i	$0.956349\pi$
$44$		0			0
$45$	−2.12200	−	0.705075i	−0.316329	−	0.105106i
$46$		0			0
$47$			12.7460i			1.85919i	0.368583	+	0.929595i	$0.379843\pi$
$47$			12.7460i			1.85919i	−0.368583	+	0.929595i	$0.620157\pi$
$48$		0			0
$49$	−5.72467			−0.817810
$50$		0			0
$51$			3.87689i			0.542873i
$52$		0			0
$53$	6.34720	+	6.34720i	0.871855	+	0.871855i	0.992674	−	0.120820i	$-0.0385523\pi$
$53$	6.34720	+	6.34720i	0.871855	+	0.871855i	−0.120820	+	0.992674i	$0.538552\pi$
$54$		0			0
$55$	4.12298	+	8.22626i	0.555943	+	1.10923i
$56$		0			0
$57$	4.31770			0.571893
$58$		0			0
$59$	−3.62177	−	3.62177i	−0.471514	−	0.471514i	0.430891	−	0.902404i	$-0.358200\pi$
$59$	−3.62177	−	3.62177i	−0.471514	−	0.471514i	−0.902404	+	0.430891i	$0.858200\pi$
$60$		0			0
$61$	0.559190			0.0715970			0.0357985	−	0.999359i	$-0.488603\pi$
$61$	0.559190			0.0715970			0.0357985	+	0.999359i	$0.488603\pi$
$62$		0			0
$63$	−3.56717			−0.449421
$64$		0			0
$65$	3.15458	−	7.41948i	0.391277	−	0.920273i
$66$		0			0
$67$	−9.61529			−1.17469			−0.587347	−	0.809335i	$-0.699828\pi$
$67$	−9.61529			−1.17469			−0.587347	+	0.809335i	$0.699828\pi$
$68$		0			0
$69$	5.07190			0.610585
$70$		0			0
$71$	0.724767	+	0.724767i	0.0860140	+	0.0860140i	0.748805	−	0.662791i	$-0.230628\pi$
$71$	0.724767	+	0.724767i	0.0860140	+	0.0860140i	−0.662791	+	0.748805i	$0.730628\pi$
$72$		0			0
$73$	3.21489			0.376275			0.188137	−	0.982143i	$-0.439755\pi$
$73$	3.21489			0.376275			0.188137	+	0.982143i	$0.439755\pi$
$74$		0			0
$75$	0.716586	+	4.94838i	0.0827442	+	0.571390i
$76$		0			0
$77$	10.3798	+	10.3798i	1.18289	+	1.18289i
$78$		0			0
$79$			6.90252i			0.776594i	0.921534	+	0.388297i	$0.126937\pi$
$79$			6.90252i			0.776594i	−0.921534	+	0.388297i	$0.873063\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$		−	4.46117i		−	0.489677i	−0.969564	−	0.244838i	$-0.921265\pi$
$83$		−	4.46117i		−	0.489677i	0.969564	−	0.244838i	$-0.0787349\pi$
$84$		0			0
$85$	7.75007	−	3.88432i	0.840613	−	0.421313i
$86$		0			0
$87$	3.03129	−	3.03129i	0.324988	−	0.324988i
$88$		0			0
$89$	−6.82030	−	6.82030i	−0.722951	−	0.722951i	0.246254	−	0.969205i	$-0.420800\pi$
$89$	−6.82030	−	6.82030i	−0.722951	−	0.722951i	−0.969205	+	0.246254i	$0.920800\pi$
$90$		0			0
$91$	1.04355	−	12.8192i	0.109394	−	1.34382i
$92$		0			0
$93$			9.11647i			0.945334i
$94$		0			0
$95$	−4.32596	−	8.63125i	−0.443834	−	0.885548i
$96$		0			0
$97$	−12.1805			−1.23674			−0.618369	−	0.785888i	$-0.712206\pi$
$97$	−12.1805			−1.23674			−0.618369	+	0.785888i	$0.712206\pi$
$98$		0			0
$99$	2.90982	+	2.90982i	0.292448	+	0.292448i
$100$		0			0
$101$		−	2.97899i		−	0.296421i	−0.988956	−	0.148210i	$-0.952649\pi$
$101$		−	2.97899i		−	0.296421i	0.988956	−	0.148210i	$-0.0473513\pi$
$102$		0			0
$103$	−6.27661	+	6.27661i	−0.618452	+	0.618452i	−0.945134	−	0.326682i	$-0.894069\pi$
$103$	−6.27661	+	6.27661i	−0.618452	+	0.618452i	0.326682	+	0.945134i	$0.394069\pi$
$104$		0			0
$105$	3.57400	+	7.13091i	0.348786	+	0.695906i
$106$		0			0
$107$	7.53335	−	7.53335i	0.728276	−	0.728276i	−0.242000	−	0.970276i	$-0.577803\pi$
$107$	7.53335	−	7.53335i	0.728276	−	0.728276i	0.970276	+	0.242000i	$0.0778035\pi$
$108$		0			0
$109$	10.1797	−	10.1797i	0.975034	−	0.975034i	−0.0246615	−	0.999696i	$-0.507851\pi$
$109$	10.1797	−	10.1797i	0.975034	−	0.975034i	0.999696	+	0.0246615i	$0.00785079\pi$
$110$		0			0
$111$	−7.48046	+	7.48046i	−0.710014	+	0.710014i
$112$		0			0
$113$	−5.00839	−	5.00839i	−0.471149	−	0.471149i	0.431137	−	0.902286i	$-0.358113\pi$
$113$	−5.00839	−	5.00839i	−0.471149	−	0.471149i	−0.902286	+	0.431137i	$0.858113\pi$
$114$		0			0
$115$	−5.08162	−	10.1389i	−0.473863	−	0.945461i
$116$		0			0
$117$	0.292543	−	3.59366i	0.0270456	−	0.332234i
$118$		0			0
$119$	9.77894	−	9.77894i	0.896434	−	0.896434i
$120$		0			0
$121$		−	5.93407i		−	0.539461i
$122$		0			0
$123$		−	8.19718i		−	0.739115i
$124$		0			0
$125$	9.17407	−	6.39035i	0.820553	−	0.571570i
$126$		0			0
$127$	12.9441	+	12.9441i	1.14860	+	1.14860i	0.986828	+	0.161774i	$0.0517216\pi$
$127$	12.9441	+	12.9441i	1.14860	+	1.14860i	0.161774	+	0.986828i	$0.448278\pi$
$128$		0			0
$129$	10.4543			0.920450
$130$		0			0
$131$	−5.60619			−0.489815			−0.244907	−	0.969546i	$-0.578758\pi$
$131$	−5.60619			−0.489815			−0.244907	+	0.969546i	$0.578758\pi$
$132$		0			0
$133$	−10.8908	−	10.8908i	−0.944353	−	0.944353i
$134$		0			0
$135$	1.00191	+	1.99904i	0.0862311	+	0.172050i
$136$		0			0
$137$			18.9286i			1.61718i	0.588371	+	0.808591i	$0.299769\pi$
$137$			18.9286i			1.61718i	−0.588371	+	0.808591i	$0.700231\pi$
$138$		0			0
$139$			7.66873i			0.650453i	0.945636	+	0.325227i	$0.105441\pi$
$139$			7.66873i			0.650453i	−0.945636	+	0.325227i	$0.894559\pi$
$140$		0			0
$141$	9.01276	−	9.01276i	0.759011	−	0.759011i
$142$		0			0
$143$	−11.3082	+	9.60566i	−0.945635	+	0.803265i
$144$		0			0
$145$	−9.09676	−	3.02258i	−0.755445	−	0.251011i
$146$		0			0
$147$	4.04795	+	4.04795i	0.333869	+	0.333869i
$148$		0			0
$149$	9.94182	−	9.94182i	0.814466	−	0.814466i	−0.170834	−	0.985300i	$-0.554646\pi$
$149$	9.94182	−	9.94182i	0.814466	−	0.814466i	0.985300	+	0.170834i	$0.0546462\pi$
$150$		0			0
$151$	1.86906	−	1.86906i	0.152102	−	0.152102i	−0.626954	−	0.779056i	$-0.715699\pi$
$151$	1.86906	−	1.86906i	0.152102	−	0.152102i	0.779056	+	0.626954i	$0.215699\pi$
$152$		0			0
$153$	2.74138	−	2.74138i	0.221627	−	0.221627i
$154$		0			0
$155$	18.2242	−	9.13393i	1.46380	−	0.733655i
$156$		0			0
$157$	−8.08132	+	8.08132i	−0.644960	+	0.644960i	−0.951771	−	0.306811i	$-0.900738\pi$
$157$	−8.08132	+	8.08132i	−0.644960	+	0.644960i	0.306811	+	0.951771i	$0.400738\pi$
$158$		0			0
$159$		−	8.97629i		−	0.711866i
$160$		0			0
$161$	−12.7932	−	12.7932i	−1.00825	−	1.00825i
$162$		0			0
$163$	9.86494			0.772682			0.386341	−	0.922356i	$-0.373739\pi$
$163$	9.86494			0.772682			0.386341	+	0.922356i	$0.373739\pi$
$164$		0			0
$165$	2.90146	−	8.73223i	0.225878	−	0.679804i
$166$		0			0
$167$			17.4695i			1.35183i	0.736979	+	0.675915i	$0.236251\pi$
$167$			17.4695i			1.35183i	−0.736979	+	0.675915i	$0.763749\pi$
$168$		0			0
$169$	12.8288	+	2.10260i	0.986834	+	0.161739i
$170$		0			0
$171$	−3.05307	−	3.05307i	−0.233474	−	0.233474i
$172$		0			0
$173$	11.8883	−	11.8883i	0.903852	−	0.903852i	−0.0919148	−	0.995767i	$-0.529299\pi$
$173$	11.8883	−	11.8883i	0.903852	−	0.903852i	0.995767	+	0.0919148i	$0.0292987\pi$
$174$		0			0
$175$	10.6741	−	14.2891i	0.806890	−	1.08016i
$176$		0			0
$177$			5.12195i			0.384989i
$178$		0			0
$179$	14.0398			1.04939			0.524693	−	0.851292i	$-0.324180\pi$
$179$	14.0398			1.04939			0.524693	+	0.851292i	$0.324180\pi$
$180$		0			0
$181$			16.0670i			1.19425i	0.802148	+	0.597126i	$0.203691\pi$
$181$			16.0670i			1.19425i	−0.802148	+	0.597126i	$0.796309\pi$
$182$		0			0
$183$	−0.395407	−	0.395407i	−0.0292294	−	0.0292294i
$184$		0			0
$185$	22.4485	+	7.45897i	1.65045	+	0.548394i
$186$		0			0
$187$	−15.9538			−1.16666
$188$		0			0
$189$	2.52237	+	2.52237i	0.183475	+	0.183475i
$190$		0			0
$191$	8.99994			0.651212			0.325606	−	0.945505i	$-0.394432\pi$
$191$	8.99994			0.651212			0.325606	+	0.945505i	$0.394432\pi$
$192$		0			0
$193$	−16.7246			−1.20386			−0.601930	−	0.798549i	$-0.705601\pi$
$193$	−16.7246			−1.20386			−0.601930	+	0.798549i	$0.705601\pi$
$194$		0			0
$195$	−7.47699	+	3.01574i	−0.535438	+	0.215962i
$196$		0			0
$197$	16.3197			1.16273			0.581366	−	0.813642i	$-0.302518\pi$
$197$	16.3197			1.16273			0.581366	+	0.813642i	$0.302518\pi$
$198$		0			0
$199$	−13.9059			−0.985764			−0.492882	−	0.870096i	$-0.664057\pi$
$199$	−13.9059			−0.985764			−0.492882	+	0.870096i	$0.664057\pi$
$200$		0			0
$201$	6.79904	+	6.79904i	0.479567	+	0.479567i
$202$		0			0
$203$	−15.2920			−1.07329
$204$		0			0
$205$	−16.3865	+	8.21288i	−1.14448	+	0.573613i
$206$		0			0
$207$	−3.58638	−	3.58638i	−0.249270	−	0.249270i
$208$		0			0
$209$			17.7678i			1.22902i
$210$		0			0
$211$	7.69845			0.529983			0.264992	−	0.964251i	$-0.414631\pi$
$211$	7.69845			0.529983			0.264992	+	0.964251i	$0.414631\pi$
$212$		0			0
$213$		−	1.02497i		−	0.0702301i
$214$		0			0
$215$	−10.4743	−	20.8986i	−0.714343	−	1.42527i
$216$		0			0
$217$	22.9951	−	22.9951i	1.56101	−	1.56101i
$218$		0			0
$219$	−2.27327	−	2.27327i	−0.153613	−	0.153613i
$220$		0			0
$221$	9.04961	+	10.6536i	0.608743	+	0.716636i
$222$		0			0
$223$		−	8.40252i		−	0.562674i	−0.959609	−	0.281337i	$-0.909222\pi$
$223$		−	8.40252i		−	0.562674i	0.959609	−	0.281337i	$-0.0907780\pi$
$224$		0			0
$225$	2.99233	−	4.00574i	0.199489	−	0.267049i
$226$		0			0
$227$	−0.552512			−0.0366715			−0.0183358	−	0.999832i	$-0.505837\pi$
$227$	−0.552512			−0.0366715			−0.0183358	+	0.999832i	$0.505837\pi$
$228$		0			0
$229$	18.5955	+	18.5955i	1.22883	+	1.22883i	0.964409	+	0.264416i	$0.0851793\pi$
$229$	18.5955	+	18.5955i	1.22883	+	1.22883i	0.264416	+	0.964409i	$0.414821\pi$
$230$		0			0
$231$		−	14.6793i		−	0.965824i
$232$		0			0
$233$	−2.40942	+	2.40942i	−0.157846	+	0.157846i	−0.781612	−	0.623765i	$-0.785602\pi$
$233$	−2.40942	+	2.40942i	−0.157846	+	0.157846i	0.623765	+	0.781612i	$0.285602\pi$
$234$		0			0
$235$	−27.0469	−	8.98686i	−1.76434	−	0.586238i
$236$		0			0
$237$	4.88082	−	4.88082i	0.317043	−	0.317043i
$238$		0			0
$239$	−20.7767	+	20.7767i	−1.34393	+	1.34393i	−0.451826	+	0.892106i	$0.649227\pi$
$239$	−20.7767	+	20.7767i	−1.34393	+	1.34393i	−0.892106	+	0.451826i	$0.850773\pi$
$240$		0			0
$241$	12.4441	−	12.4441i	0.801597	−	0.801597i	−0.181748	−	0.983345i	$-0.558176\pi$
$241$	12.4441	−	12.4441i	0.801597	−	0.801597i	0.983345	+	0.181748i	$0.0581755\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	4.03632	−	12.1477i	0.257871	−	0.776090i
$246$		0			0
$247$	11.8649	−	10.0786i	0.754943	−	0.641283i
$248$		0			0
$249$	−3.15452	+	3.15452i	−0.199910	+	0.199910i
$250$		0			0
$251$			25.7439i			1.62494i	0.583002	+	0.812471i	$0.301878\pi$
$251$			25.7439i			1.62494i	−0.583002	+	0.812471i	$0.698122\pi$
$252$		0			0
$253$			20.8714i			1.31217i
$254$		0			0
$255$	−8.22675	−	2.73350i	−0.515179	−	0.171178i
$256$		0			0
$257$	−5.00394	−	5.00394i	−0.312137	−	0.312137i	0.533600	−	0.845737i	$-0.320839\pi$
$257$	−5.00394	−	5.00394i	−0.312137	−	0.312137i	−0.845737	+	0.533600i	$0.820839\pi$
$258$		0			0
$259$	37.7369			2.34486
$260$		0			0
$261$	−4.28689			−0.265352
$262$		0			0
$263$	−1.27460	−	1.27460i	−0.0785953	−	0.0785953i	0.666716	−	0.745312i	$-0.267699\pi$
$263$	−1.27460	−	1.27460i	−0.0785953	−	0.0785953i	−0.745312	+	0.666716i	$0.767699\pi$
$264$		0			0
$265$	−17.9440	+	8.99348i	−1.10229	+	0.552465i
$266$		0			0
$267$			9.64537i			0.590287i
$268$		0			0
$269$			3.51908i			0.214562i	0.994229	+	0.107281i	$0.0342144\pi$
$269$			3.51908i			0.214562i	−0.994229	+	0.107281i	$0.965786\pi$
$270$		0			0
$271$	2.03265	−	2.03265i	0.123475	−	0.123475i	−0.642669	−	0.766144i	$-0.722173\pi$
$271$	2.03265	−	2.03265i	0.123475	−	0.123475i	0.766144	+	0.642669i	$0.222173\pi$
$272$		0			0
$273$	−9.80244	+	8.32664i	−0.593271	+	0.503951i
$274$		0			0
$275$	−20.3631	+	2.94883i	−1.22794	+	0.177821i
$276$		0			0
$277$	5.10792	+	5.10792i	0.306905	+	0.306905i	0.843708	−	0.536803i	$-0.180368\pi$
$277$	5.10792	+	5.10792i	0.306905	+	0.306905i	−0.536803	+	0.843708i	$0.680368\pi$
$278$		0			0
$279$	6.44632	−	6.44632i	0.385931	−	0.385931i
$280$		0			0
$281$	6.95567	−	6.95567i	0.414941	−	0.414941i	−0.468515	−	0.883456i	$-0.655211\pi$
$281$	6.95567	−	6.95567i	0.414941	−	0.414941i	0.883456	+	0.468515i	$0.155211\pi$
$282$		0			0
$283$	−0.558903	+	0.558903i	−0.0332233	+	0.0332233i	−0.723523	−	0.690300i	$-0.757479\pi$
$283$	−0.558903	+	0.558903i	−0.0332233	+	0.0332233i	0.690300	+	0.723523i	$0.257479\pi$
$284$		0			0
$285$	−3.04430	+	9.16213i	−0.180329	+	0.542718i
$286$		0			0
$287$	−20.6763	+	20.6763i	−1.22048	+	1.22048i
$288$		0			0
$289$		−	1.96971i		−	0.115865i
$290$		0			0
$291$	8.61288	+	8.61288i	0.504896	+	0.504896i
$292$		0			0
$293$	−1.35533			−0.0791794			−0.0395897	−	0.999216i	$-0.512605\pi$
$293$	−1.35533			−0.0791794			−0.0395897	+	0.999216i	$0.512605\pi$
$294$		0			0
$295$	10.2390	−	5.13176i	0.596137	−	0.298782i
$296$		0			0
$297$		−	4.11510i		−	0.238782i
$298$		0			0
$299$	13.9374	−	11.8391i	0.806021	−	0.684671i
$300$		0			0
$301$	−26.3696	−	26.3696i	−1.51992	−	1.51992i
$302$		0			0
$303$	−2.10646	+	2.10646i	−0.121013	+	0.121013i
$304$		0			0
$305$	−0.394271	+	1.18660i	−0.0225759	+	0.0679445i
$306$		0			0
$307$		−	8.52682i		−	0.486651i	−0.969945	−	0.243326i	$-0.921762\pi$
$307$		−	8.52682i		−	0.486651i	0.969945	−	0.243326i	$-0.0782383\pi$
$308$		0			0
$309$	8.87646			0.504964
$310$		0			0
$311$			12.5203i			0.709962i	0.934874	+	0.354981i	$0.115513\pi$
$311$			12.5203i			0.709962i	−0.934874	+	0.354981i	$0.884487\pi$
$312$		0			0
$313$	0.393638	+	0.393638i	0.0222497	+	0.0222497i	0.718144	−	0.695894i	$-0.244992\pi$
$313$	0.393638	+	0.393638i	0.0222497	+	0.0222497i	−0.695894	+	0.718144i	$0.744992\pi$
$314$		0			0
$315$	2.51512	−	7.56951i	0.141711	−	0.426494i
$316$		0			0
$317$	15.8511			0.890284			0.445142	−	0.895460i	$-0.353153\pi$
$317$	15.8511			0.890284			0.445142	+	0.895460i	$0.353153\pi$
$318$		0			0
$319$	12.4741	+	12.4741i	0.698413	+	0.698413i
$320$		0			0
$321$	−10.6538			−0.594635
$322$		0			0
$323$	16.7392			0.931396
$324$		0			0
$325$	13.5199	+	11.9253i	0.749949	+	0.661496i
$326$		0			0
$327$	−14.3962			−0.796112
$328$		0			0
$329$	−45.4669			−2.50667
$330$		0			0
$331$	7.12597	+	7.12597i	0.391679	+	0.391679i	0.875285	−	0.483607i	$-0.160673\pi$
$331$	7.12597	+	7.12597i	0.391679	+	0.391679i	−0.483607	+	0.875285i	$0.660673\pi$
$332$		0			0
$333$	10.5790			0.579724
$334$		0			0
$335$	6.77950	−	20.4036i	0.370404	−	1.11477i
$336$		0			0
$337$	−6.23426	−	6.23426i	−0.339602	−	0.339602i	0.516616	−	0.856217i	$-0.327192\pi$
$337$	−6.23426	−	6.23426i	−0.339602	−	0.339602i	−0.856217	+	0.516616i	$0.827192\pi$
$338$		0			0
$339$			7.08293i			0.384692i
$340$		0			0
$341$	−37.5152			−2.03156
$342$		0			0
$343$			4.54932i			0.245640i
$344$		0			0
$345$	−3.57607	+	10.7626i	−0.192529	+	0.579437i
$346$		0			0
$347$	11.1857	−	11.1857i	0.600479	−	0.600479i	−0.339960	−	0.940440i	$-0.610414\pi$
$347$	11.1857	−	11.1857i	0.600479	−	0.600479i	0.940440	+	0.339960i	$0.110414\pi$
$348$		0			0
$349$	−12.2610	−	12.2610i	−0.656315	−	0.656315i	0.298191	−	0.954506i	$-0.403617\pi$
$349$	−12.2610	−	12.2610i	−0.656315	−	0.656315i	−0.954506	+	0.298191i	$0.903617\pi$
$350$		0			0
$351$	−2.74796	+	2.33424i	−0.146675	+	0.124593i
$352$		0			0
$353$		−	6.49007i		−	0.345431i	−0.984972	−	0.172716i	$-0.944746\pi$
$353$		−	6.49007i		−	0.345431i	0.984972	−	0.172716i	$-0.0552542\pi$
$354$		0			0
$355$	−2.04897	+	1.02694i	−0.108748	+	0.0545042i
$356$		0			0
$357$	−13.8295			−0.731935
$358$		0			0
$359$	−9.00119	−	9.00119i	−0.475064	−	0.475064i	0.428485	−	0.903549i	$-0.359048\pi$
$359$	−9.00119	−	9.00119i	−0.475064	−	0.475064i	−0.903549	+	0.428485i	$0.859048\pi$
$360$		0			0
$361$			0.357508i			0.0188162i
$362$		0			0
$363$	−4.19602	+	4.19602i	−0.220234	+	0.220234i
$364$		0			0
$365$	−2.26674	+	6.82199i	−0.118647	+	0.357079i
$366$		0			0
$367$	3.31749	−	3.31749i	0.173171	−	0.173171i	−0.615200	−	0.788371i	$-0.710925\pi$
$367$	3.31749	−	3.31749i	0.173171	−	0.173171i	0.788371	+	0.615200i	$0.210925\pi$
$368$		0			0
$369$	−5.79628	+	5.79628i	−0.301743	+	0.301743i
$370$		0			0
$371$	−22.6415	+	22.6415i	−1.17549	+	1.17549i
$372$		0			0
$373$	−15.6723	−	15.6723i	−0.811482	−	0.811482i	0.173374	−	0.984856i	$-0.444533\pi$
$373$	−15.6723	−	15.6723i	−0.811482	−	0.811482i	−0.984856	+	0.173374i	$0.944533\pi$
$374$		0			0
$375$	−11.0057	−	1.96839i	−0.568332	−	0.101647i
$376$		0			0
$377$	1.25410	−	15.4056i	0.0645895	−	0.793431i
$378$		0			0
$379$	−10.7056	+	10.7056i	−0.549911	+	0.549911i	−0.926415	−	0.376504i	$-0.877126\pi$
$379$	−10.7056	+	10.7056i	−0.549911	+	0.549911i	0.376504	+	0.926415i	$0.377126\pi$
$380$		0			0
$381$		−	18.3057i		−	0.937830i
$382$		0			0
$383$			8.61332i			0.440120i	0.975486	+	0.220060i	$0.0706253\pi$
$383$			8.61332i			0.440120i	−0.975486	+	0.220060i	$0.929375\pi$
$384$		0			0
$385$	−29.3444	+	14.7074i	−1.49553	+	0.749557i
$386$		0			0
$387$	−7.39231	−	7.39231i	−0.375772	−	0.375772i
$388$		0			0
$389$	−4.91848			−0.249377			−0.124689	−	0.992196i	$-0.539793\pi$
$389$	−4.91848			−0.249377			−0.124689	+	0.992196i	$0.539793\pi$
$390$		0			0
$391$	19.6632			0.994412
$392$		0			0
$393$	3.96417	+	3.96417i	0.199966	+	0.199966i
$394$		0			0
$395$	−14.6471	−	4.86679i	−0.736977	−	0.244875i
$396$		0			0
$397$			30.0410i			1.50771i	0.657039	+	0.753857i	$0.271809\pi$
$397$			30.0410i			1.50771i	−0.657039	+	0.753857i	$0.728191\pi$
$398$		0			0
$399$			15.4019i			0.771061i
$400$		0			0
$401$	7.43646	−	7.43646i	0.371359	−	0.371359i	−0.496613	−	0.867972i	$-0.665423\pi$
$401$	7.43646	−	7.43646i	0.371359	−	0.371359i	0.867972	+	0.496613i	$0.165423\pi$
$402$		0			0
$403$	21.2801	+	25.0517i	1.06004	+	1.24792i
$404$		0			0
$405$	0.705075	−	2.12200i	0.0350355	−	0.105443i
$406$		0			0
$407$	−30.7829	−	30.7829i	−1.52585	−	1.52585i
$408$		0			0
$409$	−6.25648	+	6.25648i	−0.309363	+	0.309363i	−0.844662	−	0.535299i	$-0.820199\pi$
$409$	−6.25648	+	6.25648i	−0.309363	+	0.309363i	0.535299	+	0.844662i	$0.320199\pi$
$410$		0			0
$411$	13.3846	−	13.3846i	0.660212	−	0.660212i
$412$		0			0
$413$	12.9194	−	12.9194i	0.635724	−	0.635724i
$414$		0			0
$415$	9.46658	+	3.14546i	0.464696	+	0.154404i
$416$		0			0
$417$	5.42261	−	5.42261i	0.265546	−	0.265546i
$418$		0			0
$419$		−	12.3202i		−	0.601882i	−0.953643	−	0.300941i	$-0.902699\pi$
$419$		−	12.3202i		−	0.601882i	0.953643	−	0.300941i	$-0.0973007\pi$
$420$		0			0
$421$	−3.05534	−	3.05534i	−0.148908	−	0.148908i	0.628722	−	0.777630i	$-0.283578\pi$
$421$	−3.05534	−	3.05534i	−0.148908	−	0.148908i	−0.777630	+	0.628722i	$0.783578\pi$
$422$		0			0
$423$	−12.7460			−0.619730
$424$		0			0
$425$	2.77813	+	19.1843i	0.134759	+	0.930578i
$426$		0			0
$427$			1.99472i			0.0965315i
$428$		0			0
$429$	14.7883	+	1.20385i	0.713986	+	0.0581222i
$430$		0			0
$431$	19.5337	+	19.5337i	0.940907	+	0.940907i	0.998349	−	0.0574423i	$-0.0182945\pi$
$431$	19.5337	+	19.5337i	0.940907	+	0.940907i	−0.0574423	+	0.998349i	$0.518295\pi$
$432$		0			0
$433$	−5.34009	+	5.34009i	−0.256628	+	0.256628i	−0.823681	−	0.567053i	$-0.808083\pi$
$433$	−5.34009	+	5.34009i	−0.256628	+	0.256628i	0.567053	+	0.823681i	$0.308083\pi$
$434$		0			0
$435$	4.29510	+	8.56967i	0.205934	+	0.410884i
$436$		0			0
$437$		−	21.8989i		−	1.04757i
$438$		0			0
$439$	1.14079			0.0544471			0.0272236	−	0.999629i	$-0.491333\pi$
$439$	1.14079			0.0544471			0.0272236	+	0.999629i	$0.491333\pi$
$440$		0			0
$441$		−	5.72467i		−	0.272603i
$442$		0			0
$443$	−9.51142	−	9.51142i	−0.451901	−	0.451901i	0.444084	−	0.895985i	$-0.353529\pi$
$443$	−9.51142	−	9.51142i	−0.451901	−	0.451901i	−0.895985	+	0.444084i	$0.853529\pi$
$444$		0			0
$445$	19.2815	−	9.66384i	0.914030	−	0.458110i
$446$		0			0
$447$	−14.0599			−0.665008
$448$		0			0
$449$	7.19092	+	7.19092i	0.339360	+	0.339360i	0.856127	−	0.516766i	$-0.172864\pi$
$449$	7.19092	+	7.19092i	0.339360	+	0.339360i	−0.516766	+	0.856127i	$0.672864\pi$
$450$		0			0
$451$	33.7323			1.58839
$452$		0			0
$453$	−2.64324			−0.124190
$454$		0			0
$455$	26.4665	+	11.2529i	1.24077	+	0.527544i
$456$		0			0
$457$	−3.01755			−0.141155			−0.0705776	−	0.997506i	$-0.522484\pi$
$457$	−3.01755			−0.141155			−0.0705776	+	0.997506i	$0.522484\pi$
$458$		0			0
$459$	−3.87689			−0.180958
$460$		0			0
$461$	−14.7347	−	14.7347i	−0.686264	−	0.686264i	0.275140	−	0.961404i	$-0.411276\pi$
$461$	−14.7347	−	14.7347i	−0.686264	−	0.686264i	−0.961404	+	0.275140i	$0.911276\pi$
$462$		0			0
$463$	−18.7770			−0.872643			−0.436322	−	0.899791i	$-0.643719\pi$
$463$	−18.7770			−0.872643			−0.436322	+	0.899791i	$0.643719\pi$
$464$		0			0
$465$	−19.3451	−	6.42780i	−0.897109	−	0.298082i
$466$		0			0
$467$	28.0068	+	28.0068i	1.29600	+	1.29600i	0.931012	+	0.364989i	$0.118927\pi$
$467$	28.0068	+	28.0068i	1.29600	+	1.29600i	0.364989	+	0.931012i	$0.381073\pi$
$468$		0			0
$469$		−	34.2993i		−	1.58380i
$470$		0			0
$471$	11.4287			0.526607
$472$		0			0
$473$			43.0206i			1.97809i
$474$		0			0
$475$	21.3656	−	3.09400i	0.980322	−	0.141962i
$476$		0			0
$477$	−6.34720	+	6.34720i	−0.290618	+	0.290618i
$478$		0			0
$479$	−27.4587	−	27.4587i	−1.25462	−	1.25462i	−0.953627	−	0.300991i	$-0.902683\pi$
$479$	−27.4587	−	27.4587i	−1.25462	−	1.25462i	−0.300991	−	0.953627i	$-0.597317\pi$
$480$		0			0
$481$	−3.09481	+	38.0173i	−0.141111	+	1.73344i
$482$		0			0
$483$			18.0923i			0.823229i
$484$		0			0
$485$	8.58813	−	25.8469i	0.389967	−	1.17365i
$486$		0			0
$487$	−34.7589			−1.57508			−0.787538	−	0.616266i	$-0.788645\pi$
$487$	−34.7589			−1.57508			−0.787538	+	0.616266i	$0.788645\pi$
$488$		0			0
$489$	−6.97556	−	6.97556i	−0.315446	−	0.315446i
$490$		0			0
$491$			2.90611i			0.131151i	0.997848	+	0.0655754i	$0.0208883\pi$
$491$			2.90611i			0.131151i	−0.997848	+	0.0655754i	$0.979112\pi$
$492$		0			0
$493$	11.7520	−	11.7520i	0.529282	−	0.529282i
$494$		0			0
$495$	−8.22626	+	4.12298i	−0.369743	+	0.185314i
$496$		0			0
$497$	−2.58536	+	2.58536i	−0.115969	+	0.115969i
$498$		0			0
$499$	−14.8969	+	14.8969i	−0.666876	+	0.666876i	−0.956992	−	0.290116i	$-0.906306\pi$
$499$	−14.8969	+	14.8969i	−0.666876	+	0.666876i	0.290116	+	0.956992i	$0.406306\pi$
$500$		0			0
$501$	12.3528	−	12.3528i	0.551882	−	0.551882i
$502$		0			0
$503$	1.88427	+	1.88427i	0.0840156	+	0.0840156i	0.747866	−	0.663850i	$-0.231079\pi$
$503$	1.88427	+	1.88427i	0.0840156	+	0.0840156i	−0.663850	+	0.747866i	$0.731079\pi$
$504$		0			0
$505$	6.32141	+	2.10041i	0.281299	+	0.0934671i
$506$		0			0
$507$	−7.58459	−	10.5581i	−0.336844	−	0.468903i
$508$		0			0
$509$	−7.55425	+	7.55425i	−0.334836	+	0.334836i	−0.854420	−	0.519583i	$-0.826087\pi$
$509$	−7.55425	+	7.55425i	−0.334836	+	0.334836i	0.519583	+	0.854420i	$0.326087\pi$
$510$		0			0
$511$			11.4680i			0.507317i
$512$		0			0
$513$			4.31770i			0.190631i
$514$		0			0
$515$	−8.89346	−	17.7444i	−0.391893	−	0.781912i
$516$		0			0
$517$	37.0884	+	37.0884i	1.63115	+	1.63115i
$518$		0			0
$519$	−16.8126			−0.737992
$520$		0			0
$521$	−27.9787			−1.22577			−0.612884	−	0.790173i	$-0.709991\pi$
$521$	−27.9787			−1.22577			−0.612884	+	0.790173i	$0.709991\pi$
$522$		0			0
$523$	−2.40116	−	2.40116i	−0.104996	−	0.104996i	0.652657	−	0.757653i	$-0.273654\pi$
$523$	−2.40116	−	2.40116i	−0.104996	−	0.104996i	−0.757653	+	0.652657i	$0.773654\pi$
$524$		0			0
$525$	−17.6517	+	2.55618i	−0.770384	+	0.111561i
$526$		0			0
$527$			35.3436i			1.53959i
$528$		0			0
$529$		−	2.72420i		−	0.118443i
$530$		0			0
$531$	3.62177	−	3.62177i	0.157171	−	0.157171i
$532$		0			0
$533$	−19.1342	−	22.5256i	−0.828796	−	0.975690i
$534$		0			0
$535$	10.6742	+	21.2973i	0.461484	+	0.920763i
$536$		0			0
$537$	−9.92765	−	9.92765i	−0.428410	−	0.428410i
$538$		0			0
$539$	−16.6577	+	16.6577i	−0.717500	+	0.717500i
$540$		0			0
$541$	−24.5185	+	24.5185i	−1.05413	+	1.05413i	−0.0556864	+	0.998448i	$0.517735\pi$
$541$	−24.5185	+	24.5185i	−1.05413	+	1.05413i	−0.998448	+	0.0556864i	$0.982265\pi$
$542$		0			0
$543$	11.3611	−	11.3611i	0.487551	−	0.487551i
$544$		0			0
$545$	14.4238	+	28.7786i	0.617847	+	1.23274i
$546$		0			0
$547$	−3.59650	+	3.59650i	−0.153775	+	0.153775i	−0.779802	−	0.626027i	$-0.784680\pi$
$547$	−3.59650	+	3.59650i	−0.153775	+	0.153775i	0.626027	+	0.779802i	$0.284680\pi$
$548$		0			0
$549$			0.559190i			0.0238657i
$550$		0			0
$551$	−13.0882	−	13.0882i	−0.557575	−	0.557575i
$552$		0			0
$553$	−24.6224			−1.04705
$554$		0			0
$555$	−10.5992	−	21.1478i	−0.449912	−	0.897674i
$556$		0			0
$557$		−	12.7752i		−	0.541301i	−0.962678	−	0.270651i	$-0.912761\pi$
$557$		−	12.7752i		−	0.541301i	0.962678	−	0.270651i	$-0.0872388\pi$
$558$		0			0
$559$	28.7281	−	24.4029i	1.21507	−	1.03213i
$560$		0			0
$561$	11.2810	+	11.2810i	0.476286	+	0.476286i
$562$		0			0
$563$	2.14220	−	2.14220i	0.0902831	−	0.0902831i	−0.660523	−	0.750806i	$-0.729665\pi$
$563$	2.14220	−	2.14220i	0.0902831	−	0.0902831i	0.750806	+	0.660523i	$0.229665\pi$
$564$		0			0
$565$	14.1591	−	7.09649i	0.595677	−	0.298552i
$566$		0			0
$567$		−	3.56717i		−	0.149807i
$568$		0			0
$569$	−37.6615			−1.57885			−0.789426	−	0.613846i	$-0.789621\pi$
$569$	−37.6615			−1.57885			−0.789426	+	0.613846i	$0.789621\pi$
$570$		0			0
$571$			18.8599i			0.789264i	0.918839	+	0.394632i	$0.129128\pi$
$571$			18.8599i			0.789264i	−0.918839	+	0.394632i	$0.870872\pi$
$572$		0			0
$573$	−6.36392	−	6.36392i	−0.265856	−	0.265856i
$574$		0			0
$575$	25.0977	−	3.63446i	1.04665	−	0.151567i
$576$		0			0
$577$	8.24924			0.343420			0.171710	−	0.985147i	$-0.445071\pi$
$577$	8.24924			0.343420			0.171710	+	0.985147i	$0.445071\pi$
$578$		0			0
$579$	11.8261	+	11.8261i	0.491474	+	0.491474i
$580$		0			0
$581$	15.9137			0.660212
$582$		0			0
$583$	36.9384			1.52983
$584$		0			0
$585$	7.41948	+	3.15458i	0.306758	+	0.130426i
$586$		0			0
$587$	−33.1763			−1.36933			−0.684665	−	0.728858i	$-0.740052\pi$
$587$	−33.1763			−1.36933			−0.684665	+	0.728858i	$0.740052\pi$
$588$		0			0
$589$	39.3622			1.62189
$590$		0			0
$591$	−11.5398	−	11.5398i	−0.474683	−	0.474683i
$592$		0			0
$593$	26.7275			1.09757			0.548784	−	0.835964i	$-0.315091\pi$
$593$	26.7275			1.09757			0.548784	+	0.835964i	$0.315091\pi$
$594$		0			0
$595$	13.8560	+	27.6458i	0.568040	+	1.13337i
$596$		0			0
$597$	9.83297	+	9.83297i	0.402436	+	0.402436i
$598$		0			0
$599$		−	23.2813i		−	0.951249i	−0.879648	−	0.475624i	$-0.842222\pi$
$599$		−	23.2813i		−	0.951249i	0.879648	−	0.475624i	$-0.157778\pi$
$600$		0			0
$601$	−29.8301			−1.21680			−0.608398	−	0.793632i	$-0.708187\pi$
$601$	−29.8301			−1.21680			−0.608398	+	0.793632i	$0.708187\pi$
$602$		0			0
$603$		−	9.61529i		−	0.391565i
$604$		0			0
$605$	12.5921	+	4.18397i	0.511941	+	0.170102i
$606$		0			0
$607$	4.40523	−	4.40523i	0.178803	−	0.178803i	−0.612031	−	0.790834i	$-0.709647\pi$
$607$	4.40523	−	4.40523i	0.178803	−	0.178803i	0.790834	+	0.612031i	$0.209647\pi$
$608$		0			0
$609$	10.8131	+	10.8131i	0.438169	+	0.438169i
$610$		0			0
$611$	3.72875	−	45.8047i	0.150849	−	1.85306i
$612$		0			0
$613$		−	13.3001i		−	0.537187i	−0.963254	−	0.268593i	$-0.913441\pi$
$613$		−	13.3001i		−	0.537187i	0.963254	−	0.268593i	$-0.0865588\pi$
$614$		0			0
$615$	17.3944	+	5.77963i	0.701410	+	0.233057i
$616$		0			0
$617$	2.47243			0.0995363			0.0497681	−	0.998761i	$-0.484152\pi$
$617$	2.47243			0.0995363			0.0497681	+	0.998761i	$0.484152\pi$
$618$		0			0
$619$	11.1176	+	11.1176i	0.446853	+	0.446853i	0.894307	−	0.447454i	$-0.147669\pi$
$619$	11.1176	+	11.1176i	0.446853	+	0.446853i	−0.447454	+	0.894307i	$0.647669\pi$
$620$		0			0
$621$			5.07190i			0.203528i
$622$		0			0
$623$	24.3291	−	24.3291i	0.974727	−	0.974727i
$624$		0			0
$625$	7.09189	+	23.9730i	0.283675	+	0.958920i
$626$		0			0
$627$	12.5637	−	12.5637i	0.501746	−	0.501746i
$628$		0			0
$629$	−29.0009	+	29.0009i	−1.15634	+	1.15634i
$630$		0			0
$631$	21.1318	−	21.1318i	0.841243	−	0.841243i	−0.147778	−	0.989021i	$-0.547212\pi$
$631$	21.1318	−	21.1318i	0.841243	−	0.841243i	0.989021	+	0.147778i	$0.0472121\pi$
$632$		0			0
$633$	−5.44363	−	5.44363i	−0.216365	−	0.216365i
$634$		0			0
$635$	−36.5939	+	18.3408i	−1.45218	+	0.727831i
$636$		0			0
$637$	20.5725	+	1.67471i	0.815113	+	0.0663546i
$638$		0			0
$639$	−0.724767	+	0.724767i	−0.0286713	+	0.0286713i
$640$		0			0
$641$			21.2771i			0.840395i	0.907433	+	0.420198i	$0.138039\pi$
$641$			21.2771i			0.840395i	−0.907433	+	0.420198i	$0.861961\pi$
$642$		0			0
$643$		−	16.6976i		−	0.658488i	−0.944245	−	0.329244i	$-0.893206\pi$
$643$		−	16.6976i		−	0.658488i	0.944245	−	0.329244i	$-0.106794\pi$
$644$		0			0
$645$	−7.37107	+	22.1840i	−0.290236	+	0.873494i
$646$		0			0
$647$	10.4078	+	10.4078i	0.409171	+	0.409171i	0.881449	−	0.472279i	$-0.156568\pi$
$647$	10.4078	+	10.4078i	0.409171	+	0.409171i	−0.472279	+	0.881449i	$0.656568\pi$
$648$		0			0
$649$	−21.0774			−0.827358
$650$		0			0
$651$	−32.5200			−1.27456
$652$		0			0
$653$	−1.24912	−	1.24912i	−0.0488817	−	0.0488817i	0.682243	−	0.731125i	$-0.261004\pi$
$653$	−1.24912	−	1.24912i	−0.0488817	−	0.0488817i	−0.731125	+	0.682243i	$0.761004\pi$
$654$		0			0
$655$	3.95278	−	11.8963i	0.154448	−	0.464827i
$656$		0			0
$657$			3.21489i			0.125425i
$658$		0			0
$659$		−	34.8485i		−	1.35751i	−0.734367	−	0.678753i	$-0.762521\pi$
$659$		−	34.8485i		−	1.35751i	0.734367	−	0.678753i	$-0.237479\pi$
$660$		0			0
$661$	27.9461	−	27.9461i	1.08698	−	1.08698i	0.0911400	−	0.995838i	$-0.470949\pi$
$661$	27.9461	−	27.9461i	1.08698	−	1.08698i	0.995838	−	0.0911400i	$-0.0290511\pi$
$662$		0			0
$663$	1.13416	−	13.9322i	0.0440471	−	0.541084i
$664$		0			0
$665$	30.7891	−	15.4314i	1.19395	−	0.598405i
$666$		0			0
$667$	−15.3744	−	15.3744i	−0.595299	−	0.595299i
$668$		0			0
$669$	−5.94148	+	5.94148i	−0.229711	+	0.229711i
$670$		0			0
$671$	1.62714	−	1.62714i	0.0628151	−	0.0628151i
$672$		0			0
$673$	8.89048	−	8.89048i	0.342703	−	0.342703i	−0.514680	−	0.857382i	$-0.672089\pi$
$673$	8.89048	−	8.89048i	0.342703	−	0.342703i	0.857382	+	0.514680i	$0.172089\pi$
$674$		0			0
$675$	−4.94838	+	0.716586i	−0.190463	+	0.0275814i
$676$		0			0
$677$	4.54300	−	4.54300i	0.174602	−	0.174602i	−0.614396	−	0.788998i	$-0.710600\pi$
$677$	4.54300	−	4.54300i	0.174602	−	0.174602i	0.788998	+	0.614396i	$0.210600\pi$
$678$		0			0
$679$		−	43.4497i		−	1.66745i
$680$		0			0
$681$	0.390685	+	0.390685i	0.0149711	+	0.0149711i
$682$		0			0
$683$	18.6587			0.713954			0.356977	−	0.934113i	$-0.383807\pi$
$683$	18.6587			0.713954			0.356977	+	0.934113i	$0.383807\pi$
$684$		0			0
$685$	−40.1665	−	13.3461i	−1.53468	−	0.509928i
$686$		0			0
$687$		−	26.2980i		−	1.00333i
$688$		0			0
$689$	−20.9529	−	24.6665i	−0.798241	−	0.939720i
$690$		0			0
$691$	−19.1435	−	19.1435i	−0.728253	−	0.728253i	0.242018	−	0.970272i	$-0.422191\pi$
$691$	−19.1435	−	19.1435i	−0.728253	−	0.728253i	−0.970272	+	0.242018i	$0.922191\pi$
$692$		0			0
$693$	−10.3798	+	10.3798i	−0.394296	+	0.394296i
$694$		0			0
$695$	−16.2730	−	5.40703i	−0.617271	−	0.205100i
$696$		0			0
$697$		−	31.7796i		−	1.20374i
$698$		0			0
$699$	3.40743			0.128881
$700$		0			0
$701$			34.7674i			1.31314i	0.754263	+	0.656572i	$0.227994\pi$
$701$			34.7674i			1.31314i	−0.754263	+	0.656572i	$0.772006\pi$
$702$		0			0
$703$	32.2984	+	32.2984i	1.21816	+	1.21816i
$704$		0			0
$705$	12.7704	+	25.4797i	0.480960	+	0.959621i
$706$		0			0
$707$	10.6266			0.399653
$708$		0			0
$709$	−4.07550	−	4.07550i	−0.153059	−	0.153059i	0.626424	−	0.779483i	$-0.284518\pi$
$709$	−4.07550	−	4.07550i	−0.153059	−	0.153059i	−0.779483	+	0.626424i	$0.784518\pi$
$710$		0			0
$711$	−6.90252			−0.258865
$712$		0			0
$713$	46.2379			1.73162
$714$		0			0
$715$	−12.4101	−	30.7686i	−0.464111	−	1.15068i
$716$		0			0
$717$	29.3827			1.09732
$718$		0			0
$719$	21.5044			0.801980			0.400990	−	0.916082i	$-0.368666\pi$
$719$	21.5044			0.801980			0.400990	+	0.916082i	$0.368666\pi$
$720$		0			0
$721$	−22.3897	−	22.3897i	−0.833836	−	0.833836i
$722$		0			0
$723$	−17.5987			−0.654501
$724$		0			0
$725$	12.8278	−	17.1722i	0.476413	−	0.637758i
$726$		0			0
$727$	10.2775	+	10.2775i	0.381173	+	0.381173i	0.871525	−	0.490352i	$-0.163132\pi$
$727$	10.2775	+	10.2775i	0.381173	+	0.381173i	−0.490352	+	0.871525i	$0.663132\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	40.5302			1.49906
$732$		0			0
$733$		−	28.1259i		−	1.03885i	−0.854515	−	0.519427i	$-0.826145\pi$
$733$		−	28.1259i		−	1.03885i	0.854515	−	0.519427i	$-0.173855\pi$
$734$		0			0
$735$	−11.4438	+	5.73563i	−0.422113	+	0.211562i
$736$		0			0
$737$	−27.9787	+	27.9787i	−1.03061	+	1.03061i
$738$		0			0
$739$	−4.57708	−	4.57708i	−0.168371	−	0.168371i	0.617892	−	0.786263i	$-0.287987\pi$
$739$	−4.57708	−	4.57708i	−0.168371	−	0.168371i	−0.786263	+	0.617892i	$0.787987\pi$
$740$		0			0
$741$	−15.5163	−	1.26311i	−0.570007	−	0.0464016i
$742$		0			0
$743$			36.9937i			1.35717i	0.734524	+	0.678583i	$0.237406\pi$
$743$			36.9937i			1.35717i	−0.734524	+	0.678583i	$0.762594\pi$
$744$		0			0
$745$	14.0868	+	28.1062i	0.516100	+	1.02973i
$746$		0			0
$747$	4.46117			0.163226
$748$		0			0
$749$	26.8727	+	26.8727i	0.981907	+	0.981907i
$750$		0			0
$751$			41.0304i			1.49722i	0.663010	+	0.748610i	$0.269279\pi$
$751$			41.0304i			1.49722i	−0.663010	+	0.748610i	$0.730721\pi$
$752$		0			0
$753$	18.2037	−	18.2037i	0.663380	−	0.663380i
$754$		0			0
$755$	2.64831	+	5.28395i	0.0963817	+	0.192303i
$756$		0			0
$757$	−2.56168	+	2.56168i	−0.0931059	+	0.0931059i	−0.752126	−	0.659020i	$-0.770971\pi$
$757$	−2.56168	+	2.56168i	−0.0931059	+	0.0931059i	0.659020	+	0.752126i	$0.270971\pi$
$758$		0			0
$759$	14.7583	−	14.7583i	0.535693	−	0.535693i
$760$		0			0
$761$	−27.7277	+	27.7277i	−1.00513	+	1.00513i	−0.00514320	+	0.999987i	$0.501637\pi$
$761$	−27.7277	+	27.7277i	−1.00513	+	1.00513i	−0.999987	+	0.00514320i	$0.998363\pi$
$762$		0			0
$763$	36.3125	+	36.3125i	1.31460	+	1.31460i
$764$		0			0
$765$	3.88432	+	7.75007i	0.140438	+	0.280204i
$766$		0			0
$767$	11.9559	+	14.0749i	0.431702	+	0.508216i
$768$		0			0
$769$	12.0487	−	12.0487i	0.434486	−	0.434486i	−0.455665	−	0.890151i	$-0.650599\pi$
$769$	12.0487	−	12.0487i	0.434486	−	0.434486i	0.890151	+	0.455665i	$0.150599\pi$
$770$		0			0
$771$			7.07664i			0.254859i
$772$		0			0
$773$		−	20.4650i		−	0.736074i	−0.929811	−	0.368037i	$-0.880030\pi$
$773$		−	20.4650i		−	0.736074i	0.929811	−	0.368037i	$-0.119970\pi$
$774$		0			0
$775$	6.53274	+	45.1118i	0.234663	+	1.62046i
$776$		0			0
$777$	−26.6840	−	26.6840i	−0.957285	−	0.957285i
$778$		0			0
$779$	−35.3929			−1.26808
$780$		0			0
$781$	4.21788			0.150927
$782$		0			0
$783$	3.03129	+	3.03129i	0.108329	+	0.108329i
$784$		0			0
$785$	−11.4506	−	22.8465i	−0.408689	−	0.815426i
$786$		0			0
$787$		−	49.6055i		−	1.76825i	−0.467255	−	0.884123i	$-0.654757\pi$
$787$		−	49.6055i		−	1.76825i	0.467255	−	0.884123i	$-0.345243\pi$
$788$		0			0
$789$			1.80256i			0.0641728i
$790$		0			0
$791$	17.8657	−	17.8657i	0.635233	−	0.635233i
$792$		0			0
$793$	−2.00954	−	0.163587i	−0.0713609	−	0.00580916i
$794$		0			0
$795$	19.0477	+	6.32896i	0.675551	+	0.224465i
$796$		0			0
$797$	17.1618	+	17.1618i	0.607901	+	0.607901i	0.942397	−	0.334496i	$-0.108566\pi$
$797$	17.1618	+	17.1618i	0.607901	+	0.607901i	−0.334496	+	0.942397i	$0.608566\pi$
$798$		0			0
$799$	34.9415	−	34.9415i	1.23614	−	1.23614i
$800$		0			0
$801$	6.82030	−	6.82030i	0.240984	−	0.240984i
$802$		0			0
$803$	9.35475	−	9.35475i	0.330122	−	0.330122i
$804$		0			0
$805$	36.1673	−	18.1270i	1.27473	−	0.638891i
$806$		0			0
$807$	2.48836	−	2.48836i	0.0875945	−	0.0875945i
$808$		0			0
$809$		−	11.6016i		−	0.407892i	−0.978982	−	0.203946i	$-0.934623\pi$
$809$		−	11.6016i		−	0.407892i	0.978982	−	0.203946i	$-0.0653767\pi$
$810$		0			0
$811$	−6.50396	−	6.50396i	−0.228385	−	0.228385i	0.583633	−	0.812018i	$-0.301631\pi$
$811$	−6.50396	−	6.50396i	−0.228385	−	0.228385i	−0.812018	+	0.583633i	$0.801631\pi$
$812$		0			0
$813$	−2.87460			−0.100817
$814$		0			0
$815$	−6.95552	+	20.9334i	−0.243641	+	0.733264i
$816$		0			0
$817$		−	45.1385i		−	1.57920i
$818$		0			0
$819$	12.8192	+	1.04355i	0.447939	+	0.0364646i
$820$		0			0
$821$	−26.5832	−	26.5832i	−0.927760	−	0.927760i	0.0698013	−	0.997561i	$-0.477763\pi$
$821$	−26.5832	−	26.5832i	−0.927760	−	0.927760i	−0.997561	+	0.0698013i	$0.977763\pi$
$822$		0			0
$823$	29.9348	−	29.9348i	1.04346	−	1.04346i	0.0444506	−	0.999012i	$-0.485846\pi$
$823$	29.9348	−	29.9348i	1.04346	−	1.04346i	0.999012	−	0.0444506i	$-0.0141537\pi$
$824$		0			0
$825$	16.4840	+	12.3138i	0.573900	+	0.428710i
$826$		0			0
$827$		−	14.4083i		−	0.501024i	−0.968113	−	0.250512i	$-0.919401\pi$
$827$		−	14.4083i		−	0.501024i	0.968113	−	0.250512i	$-0.0805990\pi$
$828$		0			0
$829$	1.98514			0.0689468			0.0344734	−	0.999406i	$-0.489025\pi$
$829$	1.98514			0.0689468			0.0344734	+	0.999406i	$0.489025\pi$
$830$		0			0
$831$		−	7.22369i		−	0.250587i
$832$		0			0
$833$	15.6935	+	15.6935i	0.543747	+	0.543747i
$834$		0			0
$835$	−37.0702	−	12.3173i	−1.28287	−	0.426258i
$836$		0			0
$837$	−9.11647			−0.315111
$838$		0			0
$839$	−8.65703	−	8.65703i	−0.298874	−	0.298874i	0.541699	−	0.840573i	$-0.317781\pi$
$839$	−8.65703	−	8.65703i	−0.298874	−	0.298874i	−0.840573	+	0.541699i	$0.817781\pi$
$840$		0			0
$841$	10.6226			0.366296
$842$		0			0
$843$	−9.83681			−0.338798
$844$		0			0
$845$	−13.5070	+	25.7403i	−0.464655	+	0.885492i
$846$		0			0
$847$	21.1678			0.727335
$848$		0			0
$849$	0.790409			0.0271267
$850$		0			0
$851$	37.9402	+	37.9402i	1.30057	+	1.30057i
$852$		0			0
$853$	−54.7187			−1.87353			−0.936767	−	0.349954i	$-0.886197\pi$
$853$	−54.7187			−1.87353			−0.936767	+	0.349954i	$0.886197\pi$
$854$		0			0
$855$	8.63125	−	4.32596i	0.295183	−	0.147945i
$856$		0			0
$857$	37.1891	+	37.1891i	1.27036	+	1.27036i	0.945901	+	0.324455i	$0.105181\pi$
$857$	37.1891	+	37.1891i	1.27036	+	1.27036i	0.324455	+	0.945901i	$0.394819\pi$
$858$		0			0
$859$			42.8168i			1.46089i	0.682972	+	0.730445i	$0.260687\pi$
$859$			42.8168i			1.46089i	−0.682972	+	0.730445i	$0.739313\pi$
$860$		0			0
$861$	29.2407			0.996521
$862$		0			0
$863$		−	48.5169i		−	1.65154i	−0.564011	−	0.825768i	$-0.690742\pi$
$863$		−	48.5169i		−	1.65154i	0.564011	−	0.825768i	$-0.309258\pi$
$864$		0			0
$865$	16.8448	+	33.6091i	0.572741	+	1.14274i
$866$		0			0
$867$	−1.39280	+	1.39280i	−0.0473019	+	0.0473019i
$868$		0			0
$869$	20.0851	+	20.0851i	0.681339	+	0.681339i
$870$		0			0
$871$	34.5541	+	2.81289i	1.17082	+	0.0953111i
$872$		0			0
$873$		−	12.1805i		−	0.412246i
$874$		0			0
$875$	22.7954	+	32.7254i	0.770626	+	1.10632i
$876$		0			0
$877$	−13.5916			−0.458956			−0.229478	−	0.973314i	$-0.573702\pi$
$877$	−13.5916			−0.458956			−0.229478	+	0.973314i	$0.573702\pi$
$878$		0			0
$879$	0.958366	+	0.958366i	0.0323249	+	0.0323249i
$880$		0			0
$881$			30.4810i			1.02693i	0.858111	+	0.513465i	$0.171638\pi$
$881$			30.4810i			1.02693i	−0.858111	+	0.513465i	$0.828362\pi$
$882$		0			0
$883$	31.1770	−	31.1770i	1.04919	−	1.04919i	0.0504636	−	0.998726i	$-0.483930\pi$
$883$	31.1770	−	31.1770i	1.04919	−	1.04919i	0.998726	−	0.0504636i	$-0.0160699\pi$
$884$		0			0
$885$	−10.8688	−	3.61136i	−0.365349	−	0.121394i
$886$		0			0
$887$	−4.17680	+	4.17680i	−0.140243	+	0.140243i	−0.773743	−	0.633500i	$-0.781618\pi$
$887$	−4.17680	+	4.17680i	−0.140243	+	0.140243i	0.633500	+	0.773743i	$0.281618\pi$
$888$		0			0
$889$	−46.1737	+	46.1737i	−1.54862	+	1.54862i
$890$		0			0
$891$	−2.90982	+	2.90982i	−0.0974825	+	0.0974825i
$892$		0			0
$893$	−38.9143	−	38.9143i	−1.30222	−	1.30222i
$894$		0			0
$895$	−9.89912	+	29.7924i	−0.330891	+	0.995852i
$896$		0			0
$897$	−18.2267	−	1.48375i	−0.608572	−	0.0495410i
$898$		0			0
$899$	27.6347	−	27.6347i	0.921667	−	0.921667i
$900$		0			0
$901$		−	34.8001i		−	1.15936i
$902$		0			0
$903$			37.2922i			1.24101i
$904$		0			0
$905$	−34.0941	−	11.3284i	−1.13333	−	0.376570i
$906$		0			0
$907$	−8.18396	−	8.18396i	−0.271744	−	0.271744i	0.558058	−	0.829802i	$-0.311547\pi$
$907$	−8.18396	−	8.18396i	−0.271744	−	0.271744i	−0.829802	+	0.558058i	$0.811547\pi$
$908$		0			0
$909$	2.97899			0.0988069
$910$		0			0
$911$	22.3772			0.741391			0.370695	−	0.928755i	$-0.379119\pi$
$911$	22.3772			0.741391			0.370695	+	0.928755i	$0.379119\pi$
$912$		0			0
$913$	−12.9812	−	12.9812i	−0.429614	−	0.429614i
$914$		0			0
$915$	1.11784	−	0.560261i	0.0369548	−	0.0185217i
$916$		0			0
$917$		−	19.9982i		−	0.660398i
$918$		0			0
$919$			52.8543i			1.74350i	0.489949	+	0.871751i	$0.337015\pi$
$919$			52.8543i			1.74350i	−0.489949	+	0.871751i	$0.662985\pi$
$920$		0			0
$921$	−6.02937	+	6.02937i	−0.198674	+	0.198674i
$922$		0			0
$923$	−2.39254	−	2.81659i	−0.0787515	−	0.0927093i
$924$		0			0
$925$	−31.6558	+	42.3766i	−1.04084	+	1.39333i
$926$		0			0
$927$	−6.27661	−	6.27661i	−0.206151	−	0.206151i
$928$		0			0
$929$	−11.3787	+	11.3787i	−0.373324	+	0.373324i	−0.868686	−	0.495363i	$-0.835035\pi$
$929$	−11.3787	+	11.3787i	−0.373324	+	0.373324i	0.495363	+	0.868686i	$0.335035\pi$
$930$		0			0
$931$	17.4778	−	17.4778i	0.572813	−	0.572813i
$932$		0			0
$933$	8.85320	−	8.85320i	0.289841	−	0.289841i
$934$		0			0
$935$	11.2486	−	33.8539i	0.367870	−	1.10714i
$936$		0			0
$937$	2.51977	−	2.51977i	0.0823173	−	0.0823173i	−0.664749	−	0.747067i	$-0.731462\pi$
$937$	2.51977	−	2.51977i	0.0823173	−	0.0823173i	0.747067	+	0.664749i	$0.231462\pi$
$938$		0			0
$939$		−	0.556688i		−	0.0181668i
$940$		0			0
$941$	15.1005	+	15.1005i	0.492262	+	0.492262i	0.909018	−	0.416756i	$-0.136833\pi$
$941$	15.1005	+	15.1005i	0.492262	+	0.492262i	−0.416756	+	0.909018i	$0.636833\pi$
$942$		0			0
$943$	−41.5753			−1.35388
$944$		0			0
$945$	−7.13091	+	3.57400i	−0.231969	+	0.116262i
$946$		0			0
$947$		−	29.4849i		−	0.958131i	−0.877779	−	0.479066i	$-0.840976\pi$
$947$		−	29.4849i		−	0.958131i	0.877779	−	0.479066i	$-0.159024\pi$
$948$		0			0
$949$	−11.5532	−	0.940495i	−0.375034	−	0.0305298i
$950$		0			0
$951$	−11.2084	−	11.2084i	−0.363457	−	0.363457i
$952$		0			0
$953$	25.2218	−	25.2218i	0.817014	−	0.817014i	−0.168661	−	0.985674i	$-0.553944\pi$
$953$	25.2218	−	25.2218i	0.817014	−	0.817014i	0.985674	+	0.168661i	$0.0539442\pi$
$954$		0			0
$955$	−6.34563	+	19.0978i	−0.205340	+	0.617991i
$956$		0			0
$957$		−	17.6410i		−	0.570252i
$958$		0			0
$959$	−67.5215			−2.18038
$960$		0			0
$961$			52.1101i			1.68097i
$962$		0			0
$963$	7.53335	+	7.53335i	0.242759	+	0.242759i
$964$		0			0
$965$	11.7921	−	35.4895i	0.379600	−	1.14245i
$966$		0			0
$967$	−19.1628			−0.616235			−0.308117	−	0.951348i	$-0.599699\pi$
$967$	−19.1628			−0.616235			−0.308117	+	0.951348i	$0.599699\pi$
$968$		0			0
$969$	−11.8364	−	11.8364i	−0.380241	−	0.380241i
$970$		0			0
$971$	−17.1250			−0.549568			−0.274784	−	0.961506i	$-0.588606\pi$
$971$	−17.1250			−0.549568			−0.274784	+	0.961506i	$0.588606\pi$
$972$		0			0
$973$	−27.3556			−0.876981
$974$		0			0
$975$	−1.12755	−	17.9925i	−0.0361106	−	0.576220i
$976$		0			0
$977$	−50.4566			−1.61425			−0.807125	−	0.590381i	$-0.798978\pi$
$977$	−50.4566			−1.61425			−0.807125	+	0.590381i	$0.798978\pi$
$978$		0			0
$979$	−39.6917			−1.26855
$980$		0			0
$981$	10.1797	+	10.1797i	0.325011	+	0.325011i
$982$		0			0
$983$	13.7540			0.438685			0.219343	−	0.975648i	$-0.429609\pi$
$983$	13.7540			0.438685			0.219343	+	0.975648i	$0.429609\pi$
$984$		0			0
$985$	−11.5066	+	34.6304i	−0.366632	+	1.10342i
$986$		0			0
$987$	32.1500	+	32.1500i	1.02335	+	1.02335i
$988$		0			0
$989$		−	53.0232i		−	1.68604i
$990$		0			0
$991$	−49.7636			−1.58079			−0.790396	−	0.612596i	$-0.790125\pi$
$991$	−49.7636			−1.58079			−0.790396	+	0.612596i	$0.790125\pi$
$992$		0			0
$993$		−	10.0776i		−	0.319804i
$994$		0			0
$995$	9.80471	−	29.5083i	0.310830	−	0.935476i
$996$		0			0
$997$	13.7400	−	13.7400i	0.435151	−	0.435151i	−0.455225	−	0.890376i	$-0.650441\pi$
$997$	13.7400	−	13.7400i	0.435151	−	0.435151i	0.890376	+	0.455225i	$0.150441\pi$
$998$		0			0
$999$	−7.48046	−	7.48046i	−0.236671	−	0.236671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.r.a.73.3	✓	28
3.2	odd	2		2340.2.u.i.73.9		28
5.2	odd	4		780.2.bm.a.697.7	yes	28
5.3	odd	4		3900.2.bm.b.2257.13		28
5.4	even	2		3900.2.r.b.3193.13		28
13.5	odd	4		780.2.bm.a.733.7	yes	28
15.2	even	4		2340.2.bp.i.1477.2		28
39.5	even	4		2340.2.bp.i.1513.2		28
65.18	even	4		3900.2.r.b.1357.13		28
65.44	odd	4		3900.2.bm.b.2293.13		28
65.57	even	4	inner	780.2.r.a.577.3	yes	28
195.122	odd	4		2340.2.u.i.577.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.r.a.73.3	✓	28	1.1	even	1	trivial
780.2.r.a.577.3	yes	28	65.57	even	4	inner
780.2.bm.a.697.7	yes	28	5.2	odd	4
780.2.bm.a.733.7	yes	28	13.5	odd	4
2340.2.u.i.73.9		28	3.2	odd	2
2340.2.u.i.577.9		28	195.122	odd	4
2340.2.bp.i.1477.2		28	15.2	even	4
2340.2.bp.i.1513.2		28	39.5	even	4
3900.2.r.b.1357.13		28	65.18	even	4
3900.2.r.b.3193.13		28	5.4	even	2
3900.2.bm.b.2257.13		28	5.3	odd	4
3900.2.bm.b.2293.13		28	65.44	odd	4

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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.705075 + 2.12200i) q^{5} +3.56717i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.705075 + 2.12200i) q^{5} +3.56717i q^{7} +1.00000i q^{9} +(2.90982 - 2.90982i) q^{11} +(-3.59366 - 0.292543i) q^{13} +(1.99904 - 1.00191i) q^{15} +(-2.74138 - 2.74138i) q^{17} +(-3.05307 + 3.05307i) q^{19} +(2.52237 - 2.52237i) q^{21} +(-3.58638 + 3.58638i) q^{23} +(-4.00574 - 2.99233i) q^{25} +(0.707107 - 0.707107i) q^{27} +4.28689i q^{29} +(-6.44632 - 6.44632i) q^{31} -4.11510 q^{33} +(-7.56951 - 2.51512i) q^{35} -10.5790i q^{37} +(2.33424 + 2.74796i) q^{39} +(5.79628 + 5.79628i) q^{41} +(-7.39231 + 7.39231i) q^{43} +(-2.12200 - 0.705075i) q^{45} +12.7460i q^{47} -5.72467 q^{49} +3.87689i q^{51} +(6.34720 + 6.34720i) q^{53} +(4.12298 + 8.22626i) q^{55} +4.31770 q^{57} +(-3.62177 - 3.62177i) q^{59} +0.559190 q^{61} -3.56717 q^{63} +(3.15458 - 7.41948i) q^{65} -9.61529 q^{67} +5.07190 q^{69} +(0.724767 + 0.724767i) q^{71} +3.21489 q^{73} +(0.716586 + 4.94838i) q^{75} +(10.3798 + 10.3798i) q^{77} +6.90252i q^{79} -1.00000 q^{81} -4.46117i q^{83} +(7.75007 - 3.88432i) q^{85} +(3.03129 - 3.03129i) q^{87} +(-6.82030 - 6.82030i) q^{89} +(1.04355 - 12.8192i) q^{91} +9.11647i q^{93} +(-4.32596 - 8.63125i) q^{95} -12.1805 q^{97} +(2.90982 + 2.90982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q + 8 q^{11} - 4 q^{13} - 4 q^{15} - 4 q^{17} - 16 q^{19} + 8 q^{21} - 8 q^{23} + 12 q^{25} - 8 q^{33} + 8 q^{39} + 12 q^{41} + 16 q^{43} + 4 q^{45} - 36 q^{49} + 36 q^{53} + 40 q^{55} + 16 q^{59} + 8 q^{61} - 40 q^{65} + 48 q^{67} - 8 q^{69} + 8 q^{71} + 48 q^{73} - 48 q^{77} - 28 q^{81} - 4 q^{85} - 24 q^{87} - 36 q^{89} - 24 q^{91} + 72 q^{95} - 72 q^{97} + 8 q^{99}+O(q^{100}) \) 28 * q + 8 * q^11 - 4 * q^13 - 4 * q^15 - 4 * q^17 - 16 * q^19 + 8 * q^21 - 8 * q^23 + 12 * q^25 - 8 * q^33 + 8 * q^39 + 12 * q^41 + 16 * q^43 + 4 * q^45 - 36 * q^49 + 36 * q^53 + 40 * q^55 + 16 * q^59 + 8 * q^61 - 40 * q^65 + 48 * q^67 - 8 * q^69 + 8 * q^71 + 48 * q^73 - 48 * q^77 - 28 * q^81 - 4 * q^85 - 24 * q^87 - 36 * q^89 - 24 * q^91 + 72 * q^95 - 72 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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