LMFDB - Embedded newform 672.2.bi.c.593.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 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("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.10
Character	$\chi$	$=$	672.593
Dual form			672.2.bi.c.17.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528554 + 1.64943i) q^{3} +(2.66818 + 1.54047i) q^{5} +(1.46307 + 2.20441i) q^{7} +(-2.44126 - 1.74363i) q^{9} +O(q^{10})$	\(q+(-0.528554 + 1.64943i) q^{3} +(2.66818 + 1.54047i) q^{5} +(1.46307 + 2.20441i) q^{7} +(-2.44126 - 1.74363i) q^{9} +(0.621780 + 1.07696i) q^{11} +5.98957 q^{13} +(-3.95119 + 3.58676i) q^{15} +(-0.595854 - 1.03205i) q^{17} +(0.614126 - 1.06370i) q^{19} +(-4.40934 + 1.24808i) q^{21} +(-2.56956 - 1.48354i) q^{23} +(2.24612 + 3.89040i) q^{25} +(4.16634 - 3.10509i) q^{27} -3.19900 q^{29} +(-1.33987 + 0.773574i) q^{31} +(-2.10501 + 0.456356i) q^{33} +(0.507883 + 8.13559i) q^{35} +(0.334978 + 0.193399i) q^{37} +(-3.16581 + 9.87940i) q^{39} -9.44060 q^{41} -8.29057i q^{43} +(-3.82770 - 8.41302i) q^{45} +(3.34244 - 5.78928i) q^{47} +(-2.71887 + 6.45041i) q^{49} +(2.01724 - 0.437327i) q^{51} +(5.25317 + 9.09875i) q^{53} +3.83135i q^{55} +(1.42990 + 1.57518i) q^{57} +(3.22898 - 1.86425i) q^{59} +(-3.16493 + 5.48181i) q^{61} +(0.271956 - 7.93259i) q^{63} +(15.9813 + 9.22678i) q^{65} +(-10.7324 + 6.19634i) q^{67} +(3.80515 - 3.45419i) q^{69} +6.21100i q^{71} +(-8.92963 + 5.15552i) q^{73} +(-7.60415 + 1.64854i) q^{75} +(-1.46435 + 2.94632i) q^{77} +(6.41425 - 11.1098i) q^{79} +(2.91950 + 8.51331i) q^{81} +5.22882i q^{83} -3.67159i q^{85} +(1.69085 - 5.27654i) q^{87} +(6.94090 - 12.0220i) q^{89} +(8.76314 + 13.2035i) q^{91} +(-0.567765 - 2.61890i) q^{93} +(3.27720 - 1.89209i) q^{95} -17.1489i q^{97} +(0.359884 - 3.71328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.528554	+	1.64943i	−0.305161	+	0.952301i
$3$	−0.528554	+	1.64943i	−0.305161	+	0.952301i
$4$		0			0
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.959041	−	0.283266i	$-0.0914180\pi$
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.234205	+	0.972187i	$0.424751\pi$
$6$		0			0
$7$	1.46307	+	2.20441i	0.552987	+	0.833190i
$7$	1.46307	+	2.20441i	0.552987	+	0.833190i
$8$		0			0
$9$	−2.44126	−	1.74363i	−0.813753	−	0.581210i
$10$		0			0
$11$	0.621780	+	1.07696i	0.187474	+	0.324714i	0.944407	−	0.328778i	$-0.106637\pi$
$11$	0.621780	+	1.07696i	0.187474	+	0.324714i	−0.756933	+	0.653492i	$0.773303\pi$
$12$		0			0
$13$	5.98957			1.66121			0.830604	−	0.556864i	$-0.187995\pi$
$13$	5.98957			1.66121			0.830604	+	0.556864i	$0.187995\pi$
$14$		0			0
$15$	−3.95119	+	3.58676i	−1.02019	+	0.926098i
$16$		0			0
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	0.784676	−	0.619906i	$-0.212829\pi$
$17$	−0.595854	−	1.03205i	−0.144516	−	0.250309i	−0.929192	+	0.369597i	$0.879496\pi$
$18$		0			0
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	−0.786942	−	0.617027i	$-0.788337\pi$
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	0.927832	+	0.372998i	$0.121670\pi$
$20$		0			0
$21$	−4.40934	+	1.24808i	−0.962197	+	0.272353i
$22$		0			0
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	0.207581	−	0.978218i	$-0.433441\pi$
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	−0.743371	+	0.668879i	$0.766774\pi$
$24$		0			0
$25$	2.24612	+	3.89040i	0.449225	+	0.778080i
$26$		0			0
$27$	4.16634	−	3.10509i	0.801813	−	0.597575i
$28$		0			0
$29$	−3.19900			−0.594040			−0.297020	−	0.954871i	$-0.595993\pi$
$29$	−3.19900			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$30$		0			0
$31$	−1.33987	+	0.773574i	−0.240648	+	0.138938i	−0.615474	−	0.788157i	$-0.711036\pi$
$31$	−1.33987	+	0.773574i	−0.240648	+	0.138938i	0.374827	+	0.927095i	$0.377702\pi$
$32$		0			0
$33$	−2.10501	+	0.456356i	−0.366435	+	0.0794414i
$34$		0			0
$35$	0.507883	+	8.13559i	0.0858478	+	1.37517i
$36$		0			0
$37$	0.334978	+	0.193399i	0.0550700	+	0.0317947i	0.527282	−	0.849690i	$-0.323211\pi$
$37$	0.334978	+	0.193399i	0.0550700	+	0.0317947i	−0.472212	+	0.881485i	$0.656544\pi$
$38$		0			0
$39$	−3.16581	+	9.87940i	−0.506936	+	1.58197i
$40$		0			0
$41$	−9.44060			−1.47437			−0.737187	−	0.675689i	$-0.763846\pi$
$41$	−9.44060			−1.47437			−0.737187	+	0.675689i	$0.763846\pi$
$42$		0			0
$43$		−	8.29057i		−	1.26430i	−0.774846	−	0.632150i	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$		0			0
$45$	−3.82770	−	8.41302i	−0.570600	−	1.25414i
$46$		0			0
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	−0.512352	−	0.858776i	$-0.671226\pi$
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	0.999897	+	0.0143219i	$0.00455895\pi$
$48$		0			0
$49$	−2.71887	+	6.45041i	−0.388410	+	0.921486i
$50$		0			0
$51$	2.01724	−	0.437327i	0.282470	−	0.0612380i
$52$		0			0
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	0.960367	+	0.278738i	$0.0899162\pi$
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	−0.238789	+	0.971071i	$0.576750\pi$
$54$		0			0
$55$			3.83135i			0.516619i
$56$		0			0
$57$	1.42990	+	1.57518i	0.189395	+	0.208638i
$58$		0			0
$59$	3.22898	−	1.86425i	0.420377	−	0.242705i	−0.274862	−	0.961484i	$-0.588632\pi$
$59$	3.22898	−	1.86425i	0.420377	−	0.242705i	0.695238	+	0.718779i	$0.255299\pi$
$60$		0			0
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	−0.994348	−	0.106171i	$-0.966141\pi$
$61$	−3.16493	+	5.48181i	−0.405227	+	0.701874i	0.589121	+	0.808045i	$0.299474\pi$
$62$		0			0
$63$	0.271956	−	7.93259i	0.0342632	−	0.999413i
$64$		0			0
$65$	15.9813	+	9.22678i	1.98223	+	1.14444i
$66$		0			0
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.982290	−	0.187369i	$-0.940004\pi$
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.328878	+	0.944372i	$0.606671\pi$
$68$		0			0
$69$	3.80515	−	3.45419i	0.458086	−	0.415836i
$70$		0			0
$71$			6.21100i			0.737110i	0.929606	+	0.368555i	$0.120147\pi$
$71$			6.21100i			0.737110i	−0.929606	+	0.368555i	$0.879853\pi$
$72$		0			0
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.921283	−	0.388893i	$-0.872858\pi$
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.123851	+	0.992301i	$0.539524\pi$
$74$		0			0
$75$	−7.60415	+	1.64854i	−0.878052	+	0.190357i
$76$		0			0
$77$	−1.46435	+	2.94632i	−0.166878	+	0.335764i
$78$		0			0
$79$	6.41425	−	11.1098i	0.721660	−	1.24995i	−0.238674	−	0.971100i	$-0.576713\pi$
$79$	6.41425	−	11.1098i	0.721660	−	1.24995i	0.960334	−	0.278852i	$-0.0899539\pi$
$80$		0			0
$81$	2.91950	+	8.51331i	0.324389	+	0.945924i
$82$		0			0
$83$			5.22882i			0.573938i	0.957940	+	0.286969i	$0.0926476\pi$
$83$			5.22882i			0.573938i	−0.957940	+	0.286969i	$0.907352\pi$
$84$		0			0
$85$		−	3.67159i		−	0.398240i
$86$		0			0
$87$	1.69085	−	5.27654i	0.181278	−	0.565705i
$88$		0			0
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	−0.218666	−	0.975800i	$-0.570171\pi$
$89$	6.94090	−	12.0220i	0.735734	−	1.27433i	0.954400	−	0.298529i	$-0.0964960\pi$
$90$		0			0
$91$	8.76314	+	13.2035i	0.918627	+	1.38410i
$92$		0			0
$93$	−0.567765	−	2.61890i	−0.0588745	−	0.271567i
$94$		0			0
$95$	3.27720	−	1.89209i	0.336233	−	0.194124i
$96$		0			0
$97$		−	17.1489i		−	1.74120i	−0.491989	−	0.870601i	$-0.663730\pi$
$97$		−	17.1489i		−	1.74120i	0.491989	−	0.870601i	$-0.336270\pi$
$98$		0			0
$99$	0.359884	−	3.71328i	0.0361697	−	0.373199i
$100$		0			0
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	−0.350144	−	0.936696i	$-0.613867\pi$
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	0.636130	+	0.771582i	$0.280534\pi$
$102$		0			0
$103$	−10.7667	−	6.21615i	−1.06087	−	0.612496i	−0.135200	−	0.990818i	$-0.543168\pi$
$103$	−10.7667	−	6.21615i	−1.06087	−	0.612496i	−0.925674	+	0.378322i	$0.876501\pi$
$104$		0			0
$105$	−13.6876	−	3.46238i	−1.33577	−	0.337894i
$106$		0			0
$107$	4.79031	−	8.29706i	0.463097	−	0.802107i	−0.536017	−	0.844207i	$-0.680072\pi$
$107$	4.79031	−	8.29706i	0.463097	−	0.802107i	0.999113	+	0.0421002i	$0.0134049\pi$
$108$		0			0
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	−0.475356	−	0.879794i	$-0.657681\pi$
$109$	0.510424	−	0.294693i	0.0488898	−	0.0282265i	0.524246	+	0.851567i	$0.324347\pi$
$110$		0			0
$111$	−0.496053	+	0.450301i	−0.0470833	+	0.0427407i
$112$		0			0
$113$		−	7.02041i		−	0.660425i	−0.943907	−	0.330212i	$-0.892880\pi$
$113$		−	7.02041i		−	0.660425i	0.943907	−	0.330212i	$-0.107120\pi$
$114$		0			0
$115$	−4.57070	−	7.91669i	−0.426220	−	0.738235i
$116$		0			0
$117$	−14.6221	−	10.4436i	−1.35181	−	0.965511i
$118$		0			0
$119$	1.40329	−	2.82346i	0.128639	−	0.258827i
$120$		0			0
$121$	4.72678	−	8.18702i	0.429707	−	0.744275i
$122$		0			0
$123$	4.98987	−	15.5716i	0.449921	−	1.40405i
$124$		0			0
$125$		−	1.56436i		−	0.139921i
$126$		0			0
$127$	5.88744			0.522426			0.261213	−	0.965281i	$-0.415877\pi$
$127$	5.88744			0.522426			0.261213	+	0.965281i	$0.415877\pi$
$128$		0			0
$129$	13.6747	+	4.38201i	1.20399	+	0.385815i
$130$		0			0
$131$	3.67922	+	2.12420i	0.321455	+	0.185592i	0.652041	−	0.758184i	$-0.273913\pi$
$131$	3.67922	+	2.12420i	0.321455	+	0.185592i	−0.330586	+	0.943776i	$0.607246\pi$
$132$		0			0
$133$	3.24333	−	0.202473i	0.281233	−	0.0175566i
$134$		0			0
$135$	15.8999	−	1.86680i	1.36844	−	0.160669i
$136$		0			0
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	−0.470895	−	0.882189i	$-0.656069\pi$
$137$	0.674838	−	0.389618i	0.0576553	−	0.0332873i	0.528551	+	0.848902i	$0.322736\pi$
$138$		0			0
$139$	5.54714			0.470502			0.235251	−	0.971935i	$-0.424409\pi$
$139$	5.54714			0.470502			0.235251	+	0.971935i	$0.424409\pi$
$140$		0			0
$141$	7.78237	+	8.57309i	0.655394	+	0.721984i
$142$		0			0
$143$	3.72420	+	6.45050i	0.311433	+	0.539418i
$144$		0			0
$145$	−8.53552	−	4.92798i	−0.708836	−	0.409247i
$146$		0			0
$147$	−9.20244	−	7.89399i	−0.759005	−	0.651085i
$148$		0			0
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	−0.768575	−	0.639760i	$-0.779034\pi$
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	0.938336	+	0.345726i	$0.112367\pi$
$150$		0			0
$151$	−2.16486	−	3.74965i	−0.176174	−	0.305142i	0.764393	−	0.644751i	$-0.223039\pi$
$151$	−2.16486	−	3.74965i	−0.176174	−	0.305142i	−0.940567	+	0.339608i	$0.889705\pi$
$152$		0			0
$153$	−0.344878	+	3.55845i	−0.0278817	+	0.287684i
$154$		0			0
$155$	−4.76668			−0.382869
$156$		0			0
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	0.965221	−	0.261437i	$-0.0841963\pi$
$157$	3.21017	+	5.56018i	0.256200	+	0.443751i	−0.709021	+	0.705187i	$0.750863\pi$
$158$		0			0
$159$	−17.7844	+	3.85556i	−1.41039	+	0.305766i
$160$		0			0
$161$	−0.489111	−	7.83489i	−0.0385473	−	0.617476i
$162$		0			0
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	0.0952672	−	0.995452i	$-0.469629\pi$
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	−0.814453	+	0.580230i	$0.802963\pi$
$164$		0			0
$165$	−6.31955	−	2.02508i	−0.491977	−	0.157652i
$166$		0			0
$167$	15.5718			1.20498			0.602492	−	0.798125i	$-0.294175\pi$
$167$	15.5718			1.20498			0.602492	+	0.798125i	$0.294175\pi$
$168$		0			0
$169$	22.8750			1.75961
$170$		0			0
$171$	−3.35394	+	1.52595i	−0.256482	+	0.116693i
$172$		0			0
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	0.437228	−	0.899351i	$-0.355960\pi$
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	−0.560247	+	0.828326i	$0.689294\pi$
$174$		0			0
$175$	−5.28982	+	10.6433i	−0.399873	+	0.804558i
$176$		0			0
$177$	1.36827	+	6.31134i	0.102845	+	0.474389i
$178$		0			0
$179$	7.73124	+	13.3909i	0.577860	+	1.00088i	0.995724	+	0.0923734i	$0.0294454\pi$
$179$	7.73124	+	13.3909i	0.577860	+	1.00088i	−0.417864	+	0.908509i	$0.637221\pi$
$180$		0			0
$181$	−16.6129			−1.23483			−0.617415	−	0.786638i	$-0.711820\pi$
$181$	−16.6129			−1.23483			−0.617415	+	0.786638i	$0.711820\pi$
$182$		0			0
$183$	−7.36905	−	8.11777i	−0.544736	−	0.600083i
$184$		0			0
$185$	0.595854	+	1.03205i	0.0438081	+	0.0758778i
$186$		0			0
$187$	0.740981	−	1.28342i	0.0541859	−	0.0938527i
$188$		0			0
$189$	12.9405	+	4.64138i	0.941286	+	0.337611i
$190$		0			0
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	0.514084	−	0.857740i	$-0.328132\pi$
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	−0.485783	+	0.874080i	$0.661465\pi$
$192$		0			0
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	0.895293	−	0.445477i	$-0.146966\pi$
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	−0.833441	+	0.552608i	$0.813633\pi$
$194$		0			0
$195$	−23.6659	+	21.4832i	−1.69475	+	1.53844i
$196$		0			0
$197$	16.4222			1.17003			0.585017	−	0.811021i	$-0.301088\pi$
$197$	16.4222			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$198$		0			0
$199$	−0.839396	+	0.484625i	−0.0595032	+	0.0343542i	−0.529456	−	0.848337i	$-0.677604\pi$
$199$	−0.839396	+	0.484625i	−0.0595032	+	0.0343542i	0.469953	+	0.882691i	$0.344271\pi$
$200$		0			0
$201$	−4.54780	−	20.9774i	−0.320777	−	1.47963i
$202$		0			0
$203$	−4.68036	−	7.05193i	−0.328497	−	0.494948i
$204$		0			0
$205$	−25.1892	−	14.5430i	−1.75929	−	1.01573i
$206$		0			0
$207$	3.68623	+	8.10207i	0.256211	+	0.563132i
$208$		0			0
$209$	1.52741			0.105653
$210$		0			0
$211$			9.99340i			0.687974i	0.938974	+	0.343987i	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$		0			0
$213$	−10.2446	−	3.28285i	−0.701950	−	0.224937i
$214$		0			0
$215$	12.7714	−	22.1207i	0.871003	−	1.50862i
$216$		0			0
$217$	−3.66559	−	1.82184i	−0.248837	−	0.123674i
$218$		0			0
$219$	−3.78390	−	17.4538i	−0.255692	−	1.17942i
$220$		0			0
$221$	−3.56891	−	6.18153i	−0.240071	−	0.415815i
$222$		0			0
$223$			13.7534i			0.920996i	0.887661	+	0.460498i	$0.152329\pi$
$223$			13.7534i			0.920996i	−0.887661	+	0.460498i	$0.847671\pi$
$224$		0			0
$225$	1.30005	−	13.4139i	0.0866699	−	0.894259i
$226$		0			0
$227$	−4.13075	+	2.38489i	−0.274167	+	0.158291i	−0.630780	−	0.775962i	$-0.717265\pi$
$227$	−4.13075	+	2.38489i	−0.274167	+	0.158291i	0.356613	+	0.934252i	$0.383932\pi$
$228$		0			0
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	−0.889536	−	0.456864i	$-0.848973\pi$
$229$	−0.743202	+	1.28726i	−0.0491122	+	0.0850648i	0.840424	+	0.541929i	$0.182306\pi$
$230$		0			0
$231$	−4.08577	−	3.97263i	−0.268824	−	0.261380i
$232$		0			0
$233$	2.00188	+	1.15579i	0.131148	+	0.0757182i	0.564139	−	0.825680i	$-0.309208\pi$
$233$	2.00188	+	1.15579i	0.131148	+	0.0757182i	−0.432991	+	0.901398i	$0.642542\pi$
$234$		0			0
$235$	17.8365	−	10.2979i	1.16352	−	0.671761i
$236$		0			0
$237$	14.9346	+	16.4520i	0.970108	+	1.06867i
$238$		0			0
$239$			21.6031i			1.39739i	0.715420	+	0.698695i	$0.246235\pi$
$239$			21.6031i			1.39739i	−0.715420	+	0.698695i	$0.753765\pi$
$240$		0			0
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	−0.387002	−	0.922079i	$-0.626489\pi$
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	0.605042	+	0.796193i	$0.293156\pi$
$242$		0			0
$243$	−15.5853	+	0.315780i	−0.999795	+	0.0202573i
$244$		0			0
$245$	−17.1911	+	13.0225i	−1.09830	+	0.831976i
$246$		0			0
$247$	3.67835	−	6.37109i	0.234048	−	0.405383i
$248$		0			0
$249$	−8.62459	−	2.76372i	−0.546561	−	0.175143i
$250$		0			0
$251$		−	15.6528i		−	0.987995i	−0.869463	−	0.493997i	$-0.835535\pi$
$251$		−	15.6528i		−	0.987995i	0.869463	−	0.493997i	$-0.164465\pi$
$252$		0			0
$253$		−	3.68974i		−	0.231972i
$254$		0			0
$255$	6.05604	+	1.94064i	0.379244	+	0.121527i
$256$		0			0
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	−0.994600	−	0.103782i	$-0.966906\pi$
$257$	−6.53148	+	11.3128i	−0.407422	+	0.705676i	0.587178	+	0.809458i	$0.300239\pi$
$258$		0			0
$259$	0.0637623	+	1.02139i	0.00396200	+	0.0634658i
$260$		0			0
$261$	7.80960	+	5.57788i	0.483402	+	0.345262i
$262$		0			0
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.634151	+	0.773209i	$0.718650\pi$
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.986694	+	0.162586i	$0.948016\pi$
$264$		0			0
$265$			32.3695i			1.98844i
$266$		0			0
$267$	16.1608	+	17.8028i	0.989027	+	1.08952i
$268$		0			0
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	−0.478981	−	0.877825i	$-0.658994\pi$
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	0.520729	+	0.853722i	$0.325660\pi$
$270$		0			0
$271$	4.95134	+	2.85866i	0.300773	+	0.173651i	0.642790	−	0.766043i	$-0.277777\pi$
$271$	4.95134	+	2.85866i	0.300773	+	0.173651i	−0.342017	+	0.939694i	$0.611110\pi$
$272$		0			0
$273$	−26.4101	+	7.47545i	−1.59841	+	0.452435i
$274$		0			0
$275$	−2.79319	+	4.83795i	−0.168436	+	0.291739i
$276$		0			0
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.0405619	−	0.999177i	$-0.487085\pi$
$277$	15.4143	−	8.89945i	0.926156	−	0.534716i	0.885594	+	0.464461i	$0.153752\pi$
$278$		0			0
$279$	4.61980	+	0.447742i	0.276580	+	0.0268056i
$280$		0			0
$281$			27.9140i			1.66521i	0.553866	+	0.832606i	$0.313152\pi$
$281$			27.9140i			1.66521i	−0.553866	+	0.832606i	$0.686848\pi$
$282$		0			0
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	0.914841	−	0.403815i	$-0.132316\pi$
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	−0.807134	+	0.590368i	$0.798983\pi$
$284$		0			0
$285$	1.38870	+	6.40559i	0.0822595	+	0.379434i
$286$		0			0
$287$	−13.8122	−	20.8110i	−0.815309	−	1.22843i
$288$		0			0
$289$	7.78992	−	13.4925i	0.458230	−	0.793678i
$290$		0			0
$291$	28.2859	+	9.06411i	1.65815	+	0.531347i
$292$		0			0
$293$		−	9.77037i		−	0.570791i	−0.958410	−	0.285396i	$-0.907875\pi$
$293$		−	9.77037i		−	0.570791i	0.958410	−	0.285396i	$-0.0921250\pi$
$294$		0			0
$295$	11.4873			0.668817
$296$		0			0
$297$	5.93460	+	2.55628i	0.344360	+	0.148330i
$298$		0			0
$299$	−15.3906	−	8.88575i	−0.890059	−	0.513876i
$300$		0			0
$301$	18.2758	−	12.1296i	1.05340	−	0.699141i
$302$		0			0
$303$	1.21790	+	5.61775i	0.0699666	+	0.322731i
$304$		0			0
$305$	−16.8892	+	9.75098i	−0.967072	+	0.558339i
$306$		0			0
$307$	9.56907			0.546136			0.273068	−	0.961995i	$-0.411962\pi$
$307$	9.56907			0.546136			0.273068	+	0.961995i	$0.411962\pi$
$308$		0			0
$309$	15.9439	−	14.4734i	0.907018	−	0.823361i
$310$		0			0
$311$	−8.85168	−	15.3316i	−0.501933	−	0.869373i	−0.999998	−	0.00223345i	$-0.999289\pi$
$311$	−8.85168	−	15.3316i	−0.501933	−	0.869373i	0.498065	−	0.867140i	$-0.334044\pi$
$312$		0			0
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	0.192228	−	0.981350i	$-0.438429\pi$
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	−0.753760	+	0.657150i	$0.771762\pi$
$314$		0			0
$315$	12.9456	−	20.7466i	0.729401	−	1.16894i
$316$		0			0
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	−0.831722	−	0.555193i	$-0.812645\pi$
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	0.896672	+	0.442696i	$0.145978\pi$
$318$		0			0
$319$	−1.98908	−	3.44519i	−0.111367	−	0.192893i
$320$		0			0
$321$	11.1535	+	12.2867i	0.622528	+	0.685779i
$322$		0			0
$323$	−1.46372			−0.0814434
$324$		0			0
$325$	13.4533	+	23.3018i	0.746256	+	1.29255i
$326$		0			0
$327$	0.216290	+	0.997672i	0.0119609	+	0.0551714i
$328$		0			0
$329$	17.6522	−	1.10198i	0.973197	−	0.0607540i
$330$		0			0
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.946104	−	0.323863i	$-0.104982\pi$
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.192578	+	0.981282i	$0.438315\pi$
$332$		0			0
$333$	−0.480551	−	1.05622i	−0.0263340	−	0.0578803i
$334$		0			0
$335$	−38.1812			−2.08606
$336$		0			0
$337$	−25.6463			−1.39704			−0.698522	−	0.715589i	$-0.746159\pi$
$337$	−25.6463			−1.39704			−0.698522	+	0.715589i	$0.746159\pi$
$338$		0			0
$339$	11.5797	+	3.71067i	0.628923	+	0.201536i
$340$		0			0
$341$	−1.66621	−	0.961986i	−0.0902303	−	0.0520945i
$342$		0			0
$343$	−18.1972	+	3.44385i	−0.982559	+	0.185950i
$344$		0			0
$345$	15.4739	−	3.35467i	0.833087	−	0.180609i
$346$		0			0
$347$	0.473950	+	0.820906i	0.0254430	+	0.0440686i	0.878467	−	0.477804i	$-0.158567\pi$
$347$	0.473950	+	0.820906i	0.0254430	+	0.0440686i	−0.853024	+	0.521872i	$0.825234\pi$
$348$		0			0
$349$	−14.1965			−0.759919			−0.379960	−	0.925003i	$-0.624062\pi$
$349$	−14.1965			−0.759919			−0.379960	+	0.925003i	$0.624062\pi$
$350$		0			0
$351$	24.9546	−	18.5982i	1.33198	−	0.992697i
$352$		0			0
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	0.582206	−	0.813041i	$-0.302190\pi$
$353$	−7.75978	−	13.4403i	−0.413011	−	0.715356i	−0.995217	+	0.0976847i	$0.968856\pi$
$354$		0			0
$355$	−9.56788	+	16.5721i	−0.507810	+	0.879553i
$356$		0			0
$357$	3.91540	+	3.80699i	0.207225	+	0.201487i
$358$		0			0
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	0.787602	−	0.616184i	$-0.211322\pi$
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	−0.139830	+	0.990176i	$0.544656\pi$
$360$		0			0
$361$	8.74570	+	15.1480i	0.460300	+	0.797263i
$362$		0			0
$363$	11.0056	+	12.1238i	0.577643	+	0.636334i
$364$		0			0
$365$	−31.7678			−1.66280
$366$		0			0
$367$	11.5602	−	6.67430i	0.603439	−	0.348396i	−0.166954	−	0.985965i	$-0.553393\pi$
$367$	11.5602	−	6.67430i	0.603439	−	0.348396i	0.770393	+	0.637569i	$0.220060\pi$
$368$		0			0
$369$	23.0470	+	16.4609i	1.19978	+	0.856921i
$370$		0			0
$371$	−12.3717	+	24.8922i	−0.642305	+	1.29234i
$372$		0			0
$373$	4.56967	+	2.63830i	0.236609	+	0.136606i	0.613617	−	0.789604i	$-0.289714\pi$
$373$	4.56967	+	2.63830i	0.236609	+	0.136606i	−0.377008	+	0.926210i	$0.623047\pi$
$374$		0			0
$375$	2.58031	+	0.826851i	0.133247	+	0.0426984i
$376$		0			0
$377$	−19.1607			−0.986824
$378$		0			0
$379$		−	15.3619i		−	0.789086i	−0.918877	−	0.394543i	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$		0			0
$381$	−3.11183	+	9.71094i	−0.159424	+	0.497507i
$382$		0			0
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	−0.829350	−	0.558729i	$-0.811289\pi$
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	0.898549	+	0.438874i	$0.144623\pi$
$384$		0			0
$385$	−8.44587	+	5.60552i	−0.430442	+	0.285684i
$386$		0			0
$387$	−14.4557	+	20.2394i	−0.734824	+	1.02883i
$388$		0			0
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	0.980924	−	0.194393i	$-0.0622736\pi$
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	−0.658811	+	0.752308i	$0.728940\pi$
$390$		0			0
$391$			3.53589i			0.178817i
$392$		0			0
$393$	−5.44840	+	4.94588i	−0.274835	+	0.249487i
$394$		0			0
$395$	34.2288	−	19.7620i	1.72224	−	0.994334i
$396$		0			0
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	0.392426	+	0.919784i	$0.371636\pi$
$397$	−11.9617	+	20.7184i	−0.600343	+	1.03982i	−0.992769	+	0.120041i	$0.961697\pi$
$398$		0			0
$399$	−1.38031	+	5.45668i	−0.0691021	+	0.273176i
$400$		0			0
$401$	−23.5968	−	13.6236i	−1.17837	−	0.680331i	−0.222731	−	0.974880i	$-0.571497\pi$
$401$	−23.5968	−	13.6236i	−1.17837	−	0.680331i	−0.955636	+	0.294549i	$0.904831\pi$
$402$		0			0
$403$	−8.02524	+	4.63338i	−0.399766	+	0.230805i
$404$		0			0
$405$	−5.32478	+	27.2125i	−0.264590	+	1.35220i
$406$		0			0
$407$			0.481008i			0.0238427i
$408$		0			0
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	−0.321727	−	0.946832i	$-0.604263\pi$
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	0.659117	+	0.752040i	$0.270930\pi$
$410$		0			0
$411$	0.285960	+	1.31903i	0.0141054	+	0.0650632i
$412$		0			0
$413$	8.83378	+	4.39047i	0.434682	+	0.216041i
$414$		0			0
$415$	−8.05487	+	13.9514i	−0.395398	+	0.684849i
$416$		0			0
$417$	−2.93196	+	9.14963i	−0.143579	+	0.448059i
$418$		0			0
$419$		−	19.8589i		−	0.970173i	−0.874466	−	0.485086i	$-0.838788\pi$
$419$		−	19.8589i		−	0.970173i	0.874466	−	0.485086i	$-0.161212\pi$
$420$		0			0
$421$			16.6507i			0.811505i	0.913983	+	0.405753i	$0.132991\pi$
$421$			16.6507i			0.811505i	−0.913983	+	0.405753i	$0.867009\pi$
$422$		0			0
$423$	−18.2541	+	8.30516i	−0.887547	+	0.403811i
$424$		0			0
$425$	2.67672	−	4.63622i	0.129840	−	0.224890i
$426$		0			0
$427$	−16.7147	+	1.04345i	−0.808880	+	0.0504962i
$428$		0			0
$429$	−12.6081	+	2.73338i	−0.608725	+	0.131969i
$430$		0			0
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.0612944	−	0.998120i	$-0.480477\pi$
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.895044	+	0.445977i	$0.147144\pi$
$432$		0			0
$433$		−	10.5825i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$433$		−	10.5825i		−	0.508564i	0.967130	−	0.254282i	$-0.0818392\pi$
$434$		0			0
$435$	12.6399	−	11.4741i	0.606035	−	0.550139i
$436$		0			0
$437$	−3.15607	+	1.82216i	−0.150975	+	0.0871656i
$438$		0			0
$439$	6.69332	+	3.86439i	0.319455	+	0.184437i	0.651150	−	0.758949i	$-0.274287\pi$
$439$	6.69332	+	3.86439i	0.319455	+	0.184437i	−0.331695	+	0.943387i	$0.607620\pi$
$440$		0			0
$441$	17.8846	−	11.0064i	0.851648	−	0.524115i
$442$		0			0
$443$	−2.28548	+	3.95856i	−0.108586	+	0.188077i	−0.915198	−	0.403005i	$-0.867966\pi$
$443$	−2.28548	+	3.95856i	−0.108586	+	0.188077i	0.806611	+	0.591082i	$0.201299\pi$
$444$		0			0
$445$	37.0392	−	21.3846i	1.75582	−	1.01373i
$446$		0			0
$447$	4.82478	+	5.31500i	0.228204	+	0.251391i
$448$		0			0
$449$			4.33700i			0.204676i	0.994750	+	0.102338i	$0.0326323\pi$
$449$			4.33700i			0.204676i	−0.994750	+	0.102338i	$0.967368\pi$
$450$		0			0
$451$	−5.86998	−	10.1671i	−0.276406	−	0.478750i
$452$		0			0
$453$	7.32905	−	1.58890i	0.344349	−	0.0746531i
$454$		0			0
$455$	3.04200	+	48.7287i	0.142611	+	2.28444i
$456$		0			0
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	−0.999079	−	0.0429048i	$-0.986339\pi$
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	0.536696	+	0.843776i	$0.319672\pi$
$458$		0			0
$459$	−5.68714	−	2.44969i	−0.265453	−	0.114342i
$460$		0			0
$461$		−	25.3326i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$461$		−	25.3326i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$462$		0			0
$463$	−20.9574			−0.973975			−0.486988	−	0.873409i	$-0.661904\pi$
$463$	−20.9574			−0.973975			−0.486988	+	0.873409i	$0.661904\pi$
$464$		0			0
$465$	2.51945	−	7.86233i	0.116837	−	0.364607i
$466$		0			0
$467$	26.9170	+	15.5406i	1.24557	+	0.719131i	0.970223	−	0.242214i	$-0.0778735\pi$
$467$	26.9170	+	15.5406i	1.24557	+	0.719131i	0.275348	+	0.961345i	$0.411207\pi$
$468$		0			0
$469$	−29.3615	−	14.5929i	−1.35579	−	0.673839i
$470$		0			0
$471$	−10.8679	+	2.35611i	−0.500766	+	0.108564i
$472$		0			0
$473$	8.92857	−	5.15491i	0.410536	−	0.237023i
$474$		0			0
$475$	5.51761			0.253165
$476$		0			0
$477$	3.04051	−	31.3720i	0.139216	−	1.43643i
$478$		0			0
$479$	17.0894	+	29.5997i	0.780835	+	1.35245i	0.931456	+	0.363855i	$0.118540\pi$
$479$	17.0894	+	29.5997i	0.780835	+	1.35245i	−0.150620	+	0.988592i	$0.548127\pi$
$480$		0			0
$481$	2.00637	+	1.15838i	0.0914827	+	0.0528176i
$482$		0			0
$483$	13.1816	+	3.33441i	0.599786	+	0.151721i
$484$		0			0
$485$	26.4174	−	45.7562i	1.19955	−	2.07768i
$486$		0			0
$487$	12.3371	+	21.3684i	0.559046	+	0.968296i	0.997576	+	0.0695795i	$0.0221658\pi$
$487$	12.3371	+	21.3684i	0.559046	+	0.968296i	−0.438531	+	0.898716i	$0.644501\pi$
$488$		0			0
$489$	13.5971	−	12.3430i	0.614884	−	0.558171i
$490$		0			0
$491$	−43.3064			−1.95439			−0.977196	−	0.212339i	$-0.931892\pi$
$491$	−43.3064			−1.95439			−0.977196	+	0.212339i	$0.931892\pi$
$492$		0			0
$493$	1.90614	+	3.30153i	0.0858482	+	0.148693i
$494$		0			0
$495$	6.68046	−	9.35332i	0.300264	−	0.420400i
$496$		0			0
$497$	−13.6916	+	9.08710i	−0.614152	+	0.407612i
$498$		0			0
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.448795	−	0.893635i	$-0.648147\pi$
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.998308	+	0.0581497i	$0.981480\pi$
$500$		0			0
$501$	−8.23056	+	25.6847i	−0.367714	+	1.14751i
$502$		0			0
$503$	−34.2432			−1.52683			−0.763414	−	0.645910i	$-0.776478\pi$
$503$	−34.2432			−1.52683			−0.763414	+	0.645910i	$0.776478\pi$
$504$		0			0
$505$	10.2249			0.455003
$506$		0			0
$507$	−12.0907	+	37.7307i	−0.536965	+	1.67568i
$508$		0			0
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.927758	−	0.373182i	$-0.121733\pi$
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.140694	+	0.990053i	$0.455067\pi$
$510$		0			0
$511$	−24.4295	−	12.1417i	−1.08070	−	0.537118i
$512$		0			0
$513$	−0.744220	−	6.33864i	−0.0328581	−	0.279858i
$514$		0			0
$515$	−19.1517	−	33.1716i	−0.843923	−	1.46172i
$516$		0			0
$517$	8.31307			0.365608
$518$		0			0
$519$	2.39612	−	2.17512i	0.105178	−	0.0954774i
$520$		0			0
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	0.631043	−	0.775748i	$-0.282627\pi$
$521$	−8.13261	−	14.0861i	−0.356296	−	0.617123i	−0.987339	+	0.158625i	$0.949294\pi$
$522$		0			0
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	−0.671781	−	0.740750i	$-0.734470\pi$
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	0.977399	+	0.211405i	$0.0678038\pi$
$524$		0			0
$525$	−14.7594	−	14.3508i	−0.644155	−	0.626319i
$526$		0			0
$527$	1.59673	+	0.921874i	0.0695548	+	0.0401575i
$528$		0			0
$529$	−7.09824	−	12.2945i	−0.308619	−	0.534544i
$530$		0			0
$531$	−11.1333	−	1.07902i	−0.483145	−	0.0468255i
$532$		0			0
$533$	−56.5451			−2.44924
$534$		0			0
$535$	25.5628	−	14.7587i	1.10518	−	0.638074i
$536$		0			0
$537$	−26.1738	+	5.67434i	−1.12948	+	0.244866i
$538$		0			0
$539$	−8.63734	+	1.08263i	−0.372037	+	0.0466322i
$540$		0			0
$541$	18.9287	+	10.9285i	0.813810	+	0.469853i	0.848277	−	0.529552i	$-0.177640\pi$
$541$	18.9287	+	10.9285i	0.813810	+	0.469853i	−0.0344673	+	0.999406i	$0.510973\pi$
$542$		0			0
$543$	8.78084	−	27.4019i	0.376822	−	1.17593i
$544$		0			0
$545$	1.81587			0.0777834
$546$		0			0
$547$		−	9.11111i		−	0.389563i	−0.980847	−	0.194782i	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$		0			0
$549$	17.2847	−	7.86407i	0.737692	−	0.335630i
$550$		0			0
$551$	−1.96459	+	3.40277i	−0.0836944	+	0.144963i
$552$		0			0
$553$	33.8751	−	2.11473i	1.44052	−	0.0899275i
$554$		0			0
$555$	−2.01724	+	0.437327i	−0.0856270	+	0.0185635i
$556$		0			0
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	0.817013	−	0.576619i	$-0.195628\pi$
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	−0.907873	+	0.419245i	$0.862295\pi$
$558$		0			0
$559$		−	49.6569i		−	2.10026i
$560$		0			0
$561$	1.72526	+	1.90055i	0.0728406	+	0.0802414i
$562$		0			0
$563$	−27.2512	+	15.7335i	−1.14850	+	0.663087i	−0.948521	−	0.316713i	$-0.897421\pi$
$563$	−27.2512	+	15.7335i	−1.14850	+	0.663087i	−0.199979	+	0.979800i	$0.564087\pi$
$564$		0			0
$565$	10.8148	−	18.7317i	0.454981	−	0.788049i
$566$		0			0
$567$	−14.4954	+	18.8913i	−0.608751	+	0.793362i
$568$		0			0
$569$	8.62592	+	4.98018i	0.361617	+	0.208780i	0.669790	−	0.742551i	$-0.266384\pi$
$569$	8.62592	+	4.98018i	0.361617	+	0.208780i	−0.308173	+	0.951330i	$0.599717\pi$
$570$		0			0
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.968373	−	0.249506i	$-0.919732\pi$
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.268108	+	0.963389i	$0.586399\pi$
$572$		0			0
$573$	−0.579206	+	0.525785i	−0.0241967	+	0.0219650i
$574$		0			0
$575$		−	13.3288i		−	0.555851i
$576$		0			0
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	−0.482336	−	0.875986i	$-0.660212\pi$
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	0.517458	+	0.855708i	$0.326878\pi$
$578$		0			0
$579$	−2.90905	+	0.630667i	−0.120896	+	0.0262096i
$580$		0			0
$581$	−11.5265	+	7.65011i	−0.478199	+	0.317380i
$582$		0			0
$583$	−6.53263	+	11.3149i	−0.270554	+	0.468613i
$584$		0			0
$585$	−22.9263	−	50.3904i	−0.947886	−	2.08339i
$586$		0			0
$587$		−	25.9212i		−	1.06988i	−0.844890	−	0.534940i	$-0.820334\pi$
$587$		−	25.9212i		−	1.06988i	0.844890	−	0.534940i	$-0.179666\pi$
$588$		0			0
$589$			1.90029i			0.0782999i
$590$		0			0
$591$	−8.68003	+	27.0873i	−0.357049	+	1.11422i
$592$		0			0
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.0912135	−	0.995831i	$-0.470925\pi$
$593$	22.1118	−	38.2987i	0.908022	−	1.57274i	0.816808	−	0.576909i	$-0.195741\pi$
$594$		0			0
$595$	8.09370	−	5.37178i	0.331809	−	0.220222i
$596$		0			0
$597$	−0.355691	−	1.64068i	−0.0145575	−	0.0671485i
$598$		0			0
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	−0.314222	−	0.949349i	$-0.601744\pi$
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	0.665050	+	0.746799i	$0.268410\pi$
$600$		0			0
$601$			11.8235i			0.482292i	0.970489	+	0.241146i	$0.0775233\pi$
$601$			11.8235i			0.482292i	−0.970489	+	0.241146i	$0.922477\pi$
$602$		0			0
$603$	37.0046	+	3.58642i	1.50695	+	0.146050i
$604$		0			0
$605$	25.2238	−	14.5630i	1.02549	−	0.592069i
$606$		0			0
$607$	−5.56281	−	3.21169i	−0.225788	−	0.130359i	0.382840	−	0.923815i	$-0.374946\pi$
$607$	−5.56281	−	3.21169i	−0.225788	−	0.130359i	−0.608627	+	0.793456i	$0.708279\pi$
$608$		0			0
$609$	14.1055	−	3.99261i	0.571584	−	0.161789i
$610$		0			0
$611$	20.0198	−	34.6753i	0.809915	−	1.40281i
$612$		0			0
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	−0.810989	−	0.585061i	$-0.801070\pi$
$613$	−17.5740	+	10.1463i	−0.709805	+	0.409806i	0.101184	+	0.994868i	$0.467737\pi$
$614$		0			0
$615$	37.3016	−	33.8612i	1.50414	−	1.36541i
$616$		0			0
$617$			26.7202i			1.07571i	0.843036	+	0.537856i	$0.180766\pi$
$617$			26.7202i			1.07571i	−0.843036	+	0.537856i	$0.819234\pi$
$618$		0			0
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	0.686608	−	0.727028i	$-0.259099\pi$
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	−0.972929	+	0.231106i	$0.925766\pi$
$620$		0			0
$621$	−15.3122	+	1.79780i	−0.614457	+	0.0721434i
$622$		0			0
$623$	36.6564	−	2.28836i	1.46861	−	0.0916813i
$624$		0			0
$625$	13.6405	−	23.6260i	0.545619	−	0.945040i
$626$		0			0
$627$	−0.807317	+	2.51935i	−0.0322411	+	0.100613i
$628$		0			0
$629$		−	0.460951i		−	0.0183793i
$630$		0			0
$631$	13.9775			0.556436			0.278218	−	0.960518i	$-0.410256\pi$
$631$	13.9775			0.556436			0.278218	+	0.960518i	$0.410256\pi$
$632$		0			0
$633$	−16.4834	−	5.28206i	−0.655158	−	0.209943i
$634$		0			0
$635$	15.7088	+	9.06945i	0.623383	+	0.359910i
$636$		0			0
$637$	−16.2849	+	38.6352i	−0.645231	+	1.53078i
$638$		0			0
$639$	10.8297	−	15.1627i	0.428416	−	0.599826i
$640$		0			0
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	−0.370133	−	0.928979i	$-0.620688\pi$
$641$	6.31225	−	3.64438i	0.249319	−	0.143944i	0.619452	+	0.785034i	$0.287355\pi$
$642$		0			0
$643$	25.1189			0.990594			0.495297	−	0.868724i	$-0.335059\pi$
$643$	25.1189			0.990594			0.495297	+	0.868724i	$0.335059\pi$
$644$		0			0
$645$	29.7363	+	32.7576i	1.17086	+	1.28983i
$646$		0			0
$647$	−20.2246	−	35.0301i	−0.795112	−	1.37717i	−0.922768	−	0.385355i	$-0.874079\pi$
$647$	−20.2246	−	35.0301i	−0.795112	−	1.37717i	0.127657	−	0.991818i	$-0.459254\pi$
$648$		0			0
$649$	4.01543	+	2.31831i	0.157619	+	0.0910016i
$650$		0			0
$651$	4.94246	−	5.08321i	0.193710	−	0.199227i
$652$		0			0
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	0.00767187	+	0.999971i	$0.497558\pi$
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	−0.869836	+	0.493341i	$0.835775\pi$
$654$		0			0
$655$	6.54455	+	11.3355i	0.255717	+	0.442915i
$656$		0			0
$657$	30.7889	+	2.98400i	1.20119	+	0.116417i
$658$		0			0
$659$	5.89051			0.229462			0.114731	−	0.993397i	$-0.463399\pi$
$659$	5.89051			0.229462			0.114731	+	0.993397i	$0.463399\pi$
$660$		0			0
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	−0.905186	−	0.425015i	$-0.860269\pi$
$661$	−21.0993	−	36.5450i	−0.820667	−	1.42144i	0.0845192	−	0.996422i	$-0.473065\pi$
$662$		0			0
$663$	12.0824	−	2.61940i	0.469241	−	0.101729i
$664$		0			0
$665$	8.96570	+	4.45604i	0.347675	+	0.172798i
$666$		0			0
$667$	8.22004	+	4.74584i	0.318281	+	0.183760i
$668$		0			0
$669$	−22.6853	−	7.26942i	−0.877065	−	0.281052i
$670$		0			0
$671$	−7.87156			−0.303878
$672$		0			0
$673$	−46.7729			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$673$	−46.7729			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$674$		0			0
$675$	21.4382	+	9.23431i	0.825155	+	0.355429i
$676$		0			0
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.382618	−	0.923907i	$-0.624977\pi$
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.991436	+	0.130596i	$0.958311\pi$
$678$		0			0
$679$	37.8032	−	25.0899i	1.45075	−	0.962863i
$680$		0			0
$681$	−1.75039	−	8.07394i	−0.0670751	−	0.309394i
$682$		0			0
$683$	17.1346	+	29.6781i	0.655638	+	1.13560i	0.981733	+	0.190262i	$0.0609338\pi$
$683$	17.1346	+	29.6781i	0.655638	+	1.13560i	−0.326095	+	0.945337i	$0.605733\pi$
$684$		0			0
$685$	2.40079			0.0917293
$686$		0			0
$687$	−1.73043	−	1.90625i	−0.0660201	−	0.0727280i
$688$		0			0
$689$	31.4642	+	54.4976i	1.19869	+	2.07619i
$690$		0			0
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	−0.925990	−	0.377549i	$-0.876767\pi$
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	0.789962	+	0.613156i	$0.210100\pi$
$692$		0			0
$693$	8.71215	−	4.63945i	0.330947	−	0.176238i
$694$		0			0
$695$	14.8008	+	8.54522i	0.561425	+	0.324139i
$696$		0			0
$697$	5.62522	+	9.74316i	0.213070	+	0.369048i
$698$		0			0
$699$	−2.96450	+	2.69108i	−0.112128	+	0.101786i
$700$		0			0
$701$	12.4116			0.468778			0.234389	−	0.972143i	$-0.424691\pi$
$701$	12.4116			0.468778			0.234389	+	0.972143i	$0.424691\pi$
$702$		0			0
$703$	0.411437	−	0.237543i	0.0155176	−	0.00895911i
$704$		0			0
$705$	7.55815	+	34.8631i	0.284656	+	1.31302i
$706$		0			0
$707$	7.86299	+	3.90798i	0.295718	+	0.146975i
$708$		0			0
$709$	30.5908	+	17.6616i	1.14886	+	0.663295i	0.948609	−	0.316450i	$-0.102491\pi$
$709$	30.5908	+	17.6616i	1.14886	+	0.663295i	0.200251	+	0.979745i	$0.435824\pi$
$710$		0			0
$711$	−35.0303	+	15.9379i	−1.31374	+	0.597717i
$712$		0			0
$713$	4.59050			0.171916
$714$		0			0
$715$			22.9481i			0.858211i
$716$		0			0
$717$	−35.6329	−	11.4184i	−1.33073	−	0.426429i
$718$		0			0
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	−0.998645	−	0.0520455i	$-0.983426\pi$
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	0.544395	+	0.838829i	$0.316759\pi$
$720$		0			0
$721$	−2.04942	−	32.8289i	−0.0763243	−	1.22261i
$722$		0			0
$723$	1.43434	+	6.61609i	0.0533435	+	0.246055i
$724$		0			0
$725$	−7.18536	−	12.4454i	−0.266858	−	0.462211i
$726$		0			0
$727$			5.15142i			0.191055i	0.995427	+	0.0955277i	$0.0304539\pi$
$727$			5.15142i			0.191055i	−0.995427	+	0.0955277i	$0.969546\pi$
$728$		0			0
$729$	7.71680	−	25.8738i	0.285807	−	0.958287i
$730$		0			0
$731$	−8.55627	+	4.93997i	−0.316465	+	0.182711i
$732$		0			0
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	−0.926817	−	0.375514i	$-0.877466\pi$
$733$	−3.74171	+	6.48083i	−0.138203	+	0.239375i	0.788613	+	0.614889i	$0.210799\pi$
$734$		0			0
$735$	−12.3933	−	35.2387i	−0.457133	−	1.29980i
$736$		0			0
$737$	−13.3464	−	7.70552i	−0.491619	−	0.283837i
$738$		0			0
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	−0.457788	−	0.889061i	$-0.651358\pi$
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	0.541056	+	0.840987i	$0.318025\pi$
$740$		0			0
$741$	8.56448	+	9.43466i	0.314624	+	0.346591i
$742$		0			0
$743$		−	23.6093i		−	0.866140i	−0.901360	−	0.433070i	$-0.857430\pi$
$743$		−	23.6093i		−	0.866140i	0.901360	−	0.433070i	$-0.142570\pi$
$744$		0			0
$745$	11.0580	−	6.38431i	0.405132	−	0.233903i
$746$		0			0
$747$	9.11713	−	12.7649i	0.333578	−	0.467044i
$748$		0			0
$749$	25.2987	−	1.57933i	0.924394	−	0.0577074i
$750$		0			0
$751$	−0.504993	+	0.874673i	−0.0184275	+	0.0319173i	−0.875092	−	0.483956i	$-0.839199\pi$
$751$	−0.504993	+	0.874673i	−0.0184275	+	0.0319173i	0.856665	+	0.515874i	$0.172533\pi$
$752$		0			0
$753$	25.8182	+	8.27335i	0.940868	+	0.301497i
$754$		0			0
$755$		−	13.3397i		−	0.485480i
$756$		0			0
$757$		−	11.1837i		−	0.406478i	−0.979129	−	0.203239i	$-0.934853\pi$
$757$		−	11.1837i		−	0.406478i	0.979129	−	0.203239i	$-0.0651469\pi$
$758$		0			0
$759$	6.08598	+	1.95023i	0.220907	+	0.0707888i
$760$		0			0
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	−0.929239	−	0.369480i	$-0.879536\pi$
$761$	−3.99009	+	6.91104i	−0.144641	+	0.250525i	0.784598	+	0.620005i	$0.212869\pi$
$762$		0			0
$763$	1.39641	+	0.694029i	0.0505534	+	0.0251255i
$764$		0			0
$765$	−6.40190	+	8.96331i	−0.231461	+	0.324069i
$766$		0			0
$767$	19.3402	−	11.1661i	0.698333	−	0.403183i
$768$		0			0
$769$		−	11.8900i		−	0.428766i	−0.976750	−	0.214383i	$-0.931226\pi$
$769$		−	11.8900i		−	0.428766i	0.976750	−	0.214383i	$-0.0687740\pi$
$770$		0			0
$771$	−15.2075	−	16.7527i	−0.547686	−	0.603333i
$772$		0			0
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.186809	−	0.982396i	$-0.440186\pi$
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.944185	+	0.329417i	$0.106852\pi$
$774$		0			0
$775$	−6.01902	−	3.47508i	−0.216210	−	0.124829i
$776$		0			0
$777$	−1.71841	−	0.434686i	−0.0616476	−	0.0155943i
$778$		0			0
$779$	−5.79771	+	10.0419i	−0.207725	+	0.359790i
$780$		0			0
$781$	−6.68897	+	3.86188i	−0.239350	+	0.138189i
$782$		0			0
$783$	−13.3281	+	9.93321i	−0.476309	+	0.354984i
$784$		0			0
$785$			19.7807i			0.706005i
$786$		0			0
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	0.720772	−	0.693172i	$-0.243787\pi$
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	−0.960691	+	0.277621i	$0.910454\pi$
$788$		0			0
$789$	−11.1385	−	51.3779i	−0.396540	−	1.82910i
$790$		0			0
$791$	15.4759	−	10.2713i	0.550259	−	0.365206i
$792$		0			0
$793$	−18.9565	+	32.8337i	−0.673167	+	1.16596i
$794$		0			0
$795$	−53.3913	−	17.1090i	−1.89359	−	0.606795i
$796$		0			0
$797$		−	13.9811i		−	0.495236i	−0.968858	−	0.247618i	$-0.920352\pi$
$797$		−	13.9811i		−	0.495236i	0.968858	−	0.247618i	$-0.0796479\pi$
$798$		0			0
$799$	−7.96643			−0.281832
$800$		0			0
$801$	−37.9065	+	17.2465i	−1.33936	+	0.609373i
$802$		0			0
$803$	−11.1045	−	6.41121i	−0.391871	−	0.226247i
$804$		0			0
$805$	10.7644	−	21.6584i	0.379396	−	0.763357i
$806$		0			0
$807$	0.290145	+	1.33834i	0.0102136	+	0.0471117i
$808$		0			0
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	−0.551693	−	0.834047i	$-0.686018\pi$
$809$	−2.99316	+	1.72810i	−0.105234	+	0.0607569i	0.446459	+	0.894804i	$0.352685\pi$
$810$		0			0
$811$	−45.3167			−1.59129			−0.795643	−	0.605766i	$-0.792867\pi$
$811$	−45.3167			−1.59129			−0.795643	+	0.605766i	$0.792867\pi$
$812$		0			0
$813$	−7.33222	+	6.65595i	−0.257152	+	0.233434i
$814$		0			0
$815$	−16.3327	−	28.2891i	−0.572111	−	0.990924i
$816$		0			0
$817$	−8.81865	−	5.09145i	−0.308525	−	0.178127i
$818$		0			0
$819$	1.62890	−	47.5128i	0.0569183	−	1.66023i
$820$		0			0
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	0.152490	+	0.988305i	$0.451271\pi$
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	−0.932142	+	0.362092i	$0.882063\pi$
$822$		0			0
$823$	−21.1932	−	36.7076i	−0.738747	−	1.27955i	−0.953060	−	0.302783i	$-0.902084\pi$
$823$	−21.1932	−	36.7076i	−0.738747	−	1.27955i	0.214312	−	0.976765i	$-0.431249\pi$
$824$		0			0
$825$	−6.50352	−	7.16430i	−0.226424	−	0.249429i
$826$		0			0
$827$	9.18843			0.319513			0.159757	−	0.987156i	$-0.448929\pi$
$827$	9.18843			0.319513			0.159757	+	0.987156i	$0.448929\pi$
$828$		0			0
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	0.546238	−	0.837630i	$-0.316059\pi$
$829$	−13.0225	−	22.5556i	−0.452290	−	0.783389i	−0.998528	+	0.0542413i	$0.982726\pi$
$830$		0			0
$831$	6.53175	+	30.1287i	0.226584	+	1.04515i
$832$		0			0
$833$	8.27719	−	1.03749i	0.286788	−	0.0359468i
$834$		0			0
$835$	41.5484	+	23.9880i	1.43784	+	0.830139i
$836$		0			0
$837$	−3.18033	+	7.38339i	−0.109928	+	0.255207i
$838$		0			0
$839$	31.2096			1.07748			0.538738	−	0.842473i	$-0.318901\pi$
$839$	31.2096			1.07748			0.538738	+	0.842473i	$0.318901\pi$
$840$		0			0
$841$	−18.7664			−0.647116
$842$		0			0
$843$	−46.0423	−	14.7541i	−1.58578	−	0.508158i
$844$		0			0
$845$	61.0345	+	35.2383i	2.09965	+	1.21223i
$846$		0			0
$847$	24.9632	−	1.55838i	0.857744	−	0.0535467i
$848$		0			0
$849$	−6.13410	+	1.32984i	−0.210522	+	0.0456401i
$850$		0			0
$851$	−0.573831	−	0.993904i	−0.0196707	−	0.0340706i
$852$		0			0
$853$	−4.78201			−0.163733			−0.0818665	−	0.996643i	$-0.526088\pi$
$853$	−4.78201			−0.163733			−0.0818665	+	0.996643i	$0.526088\pi$
$854$		0			0
$855$	−11.2996	−	1.09513i	−0.386438	−	0.0374528i
$856$		0			0
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	−0.999657	−	0.0262016i	$-0.991659\pi$
$857$	−15.2965	−	26.4944i	−0.522520	−	0.905031i	0.477137	−	0.878829i	$-0.341675\pi$
$858$		0			0
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	−0.577123	−	0.816657i	$-0.695825\pi$
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	0.995807	+	0.0914746i	$0.0291580\pi$
$860$		0			0
$861$	41.6268	−	11.7826i	1.41864	−	0.401550i
$862$		0			0
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.159441	−	0.987207i	$-0.550969\pi$
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.934667	+	0.355523i	$0.884303\pi$
$864$		0			0
$865$	−2.87820	−	4.98519i	−0.0978617	−	0.169501i
$866$		0			0
$867$	18.1376	+	19.9805i	0.615986	+	0.678573i
$868$		0			0
$869$	15.9530			0.541170
$870$		0			0
$871$	−64.2823	+	37.1134i	−2.17812	+	1.25754i
$872$		0			0
$873$	−29.9013	+	41.8648i	−1.01200	+	1.41691i
$874$		0			0
$875$	3.44850	−	2.28877i	0.116581	−	0.0773744i
$876$		0			0
$877$	−28.4107	−	16.4029i	−0.959360	−	0.553887i	−0.0633837	−	0.997989i	$-0.520189\pi$
$877$	−28.4107	−	16.4029i	−0.959360	−	0.553887i	−0.895976	+	0.444103i	$0.853523\pi$
$878$		0			0
$879$	16.1156	+	5.16417i	0.543565	+	0.174183i
$880$		0			0
$881$	27.1405			0.914385			0.457193	−	0.889368i	$-0.348855\pi$
$881$	27.1405			0.914385			0.457193	+	0.889368i	$0.348855\pi$
$882$		0			0
$883$			47.9537i			1.61377i	0.590709	+	0.806884i	$0.298848\pi$
$883$			47.9537i			1.61377i	−0.590709	+	0.806884i	$0.701152\pi$
$884$		0			0
$885$	−6.07167	+	18.9476i	−0.204097	+	0.636915i
$886$		0			0
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	−0.999913	−	0.0131735i	$-0.995807\pi$
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	0.511365	+	0.859364i	$0.329140\pi$
$888$		0			0
$889$	8.61372	+	12.9784i	0.288895	+	0.435280i
$890$		0			0
$891$	−7.35317	+	8.43759i	−0.246340	+	0.282670i
$892$		0			0
$893$	−4.10536	−	7.11070i	−0.137381	−	0.237950i
$894$		0			0
$895$			47.6391i			1.59240i
$896$		0			0
$897$	22.7912	−	20.6891i	0.760976	−	0.690789i
$898$		0			0
$899$	4.28625	−	2.47467i	0.142954	−	0.0825348i
$900$		0			0
$901$	6.26024	−	10.8431i	0.208559	−	0.361235i
$902$		0			0
$903$	10.3473	+	36.5559i	0.344336	+	1.21651i
$904$		0			0
$905$	−44.3263	−	25.5918i	−1.47346	−	0.850700i
$906$		0			0
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	−0.473084	−	0.881017i	$-0.656859\pi$
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	0.526441	+	0.850212i	$0.323526\pi$
$908$		0			0
$909$	−9.90984	−	0.960442i	−0.328688	−	0.0318558i
$910$		0			0
$911$			12.2209i			0.404896i	0.979293	+	0.202448i	$0.0648897\pi$
$911$			12.2209i			0.404896i	−0.979293	+	0.202448i	$0.935110\pi$
$912$		0			0
$913$	−5.63121	+	3.25118i	−0.186366	+	0.107598i
$914$		0			0
$915$	−7.15673	−	33.0115i	−0.236594	−	1.09133i
$916$		0			0
$917$	0.700333	+	11.2184i	0.0231270	+	0.370463i
$918$		0			0
$919$	−14.5126	+	25.1365i	−0.478726	+	0.829177i	−0.999702	−	0.0243939i	$-0.992234\pi$
$919$	−14.5126	+	25.1365i	−0.478726	+	0.829177i	0.520977	+	0.853571i	$0.325568\pi$
$920$		0			0
$921$	−5.05777	+	15.7835i	−0.166659	+	0.520085i
$922$		0			0
$923$			37.2012i			1.22449i
$924$		0			0
$925$			1.73760i			0.0571318i
$926$		0			0
$927$	15.4456	+	33.9484i	0.507301	+	1.11501i
$928$		0			0
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	−0.999818	−	0.0190749i	$-0.993928\pi$
$929$	−14.7335	+	25.5191i	−0.483390	+	0.837255i	0.516428	+	0.856330i	$0.327261\pi$
$930$		0			0
$931$	5.19155	+	6.85342i	0.170146	+	0.224612i
$932$		0			0
$933$	29.9670	−	6.49670i	0.981075	−	0.212692i
$934$		0			0
$935$	3.95414	−	2.28292i	0.129314	−	0.0746596i
$936$		0			0
$937$		−	23.9964i		−	0.783929i	−0.919980	−	0.391965i	$-0.871796\pi$
$937$		−	23.9964i		−	0.783929i	0.919980	−	0.391965i	$-0.128204\pi$
$938$		0			0
$939$	14.7116	−	13.3547i	0.480094	−	0.435814i
$940$		0			0
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.967839	−	0.251571i	$-0.919053\pi$
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.266052	+	0.963959i	$0.585719\pi$
$942$		0			0
$943$	24.2582	+	14.0055i	0.789955	+	0.456081i
$944$		0			0
$945$	27.3778	+	32.3186i	0.890599	+	1.05132i
$946$		0			0
$947$	−15.9345	+	27.5994i	−0.517802	+	0.896859i	0.481984	+	0.876180i	$0.339916\pi$
$947$	−15.9345	+	27.5994i	−0.517802	+	0.896859i	−0.999786	+	0.0206793i	$0.993417\pi$
$948$		0			0
$949$	−53.4846	+	30.8794i	−1.73618	+	1.00239i
$950$		0			0
$951$	2.69250	+	2.96607i	0.0873103	+	0.0961814i
$952$		0			0
$953$		−	49.4699i		−	1.60249i	−0.598338	−	0.801243i	$-0.704172\pi$
$953$		−	49.4699i		−	1.60249i	0.598338	−	0.801243i	$-0.295828\pi$
$954$		0			0
$955$	0.695736	+	1.20505i	0.0225135	+	0.0389945i
$956$		0			0
$957$	6.73394	−	1.45988i	0.217677	−	0.0471914i
$958$		0			0
$959$	1.84621	+	0.917585i	0.0596173	+	0.0296304i
$960$		0			0
$961$	−14.3032	+	24.7738i	−0.461392	+	0.799155i
$962$		0			0
$963$	−26.1614	+	11.9028i	−0.843040	+	0.383561i
$964$		0			0
$965$			5.29478i			0.170445i
$966$		0			0
$967$	−18.5748			−0.597324			−0.298662	−	0.954359i	$-0.596540\pi$
$967$	−18.5748			−0.597324			−0.298662	+	0.954359i	$0.596540\pi$
$968$		0			0
$969$	0.773654	−	2.41430i	0.0248533	−	0.0775586i
$970$		0			0
$971$	41.9333	+	24.2102i	1.34570	+	0.776943i	0.987638	−	0.156753i	$-0.0501026\pi$
$971$	41.9333	+	24.2102i	1.34570	+	0.776943i	0.358067	+	0.933696i	$0.383436\pi$
$972$		0			0
$973$	8.11583	+	12.2282i	0.260182	+	0.392018i
$974$		0			0
$975$	−45.5456	+	9.87406i	−1.45863	+	0.316223i
$976$		0			0
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.474125	−	0.880458i	$-0.342765\pi$
$977$	46.0630	−	26.5945i	1.47369	−	0.850833i	0.999561	+	0.0296250i	$0.00943130\pi$
$978$		0			0
$979$	17.2629			0.551724
$980$		0			0
$981$	−1.75991	−	0.170567i	−0.0561897	−	0.00544580i
$982$		0			0
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	0.964762	−	0.263123i	$-0.0847524\pi$
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	−0.710252	+	0.703947i	$0.751419\pi$
$984$		0			0
$985$	43.8174	+	25.2980i	1.39614	+	0.806061i
$986$		0			0
$987$	−7.51250	+	29.6986i	−0.239126	+	0.945316i
$988$		0			0
$989$	−12.2994	+	21.3031i	−0.391097	+	0.677400i
$990$		0			0
$991$	4.26387	+	7.38524i	0.135446	+	0.234600i	0.925768	−	0.378092i	$-0.123420\pi$
$991$	4.26387	+	7.38524i	0.135446	+	0.234600i	−0.790322	+	0.612692i	$0.790086\pi$
$992$		0			0
$993$	−30.6781	+	27.8486i	−0.973541	+	0.883749i
$994$		0			0
$995$	−2.98621			−0.0946693
$996$		0			0
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	0.997699	−	0.0677970i	$-0.0215970\pi$
$997$	13.8974	+	24.0710i	0.440136	+	0.762337i	−0.557564	+	0.830134i	$0.688264\pi$
$998$		0			0
$999$	1.99615	−	0.234369i	0.0631555	−	0.00741509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.593.10		48
3.2	odd	2	inner	672.2.bi.c.593.22		48
4.3	odd	2		168.2.ba.c.5.5	✓	48
7.3	odd	6	inner	672.2.bi.c.17.3		48
8.3	odd	2		168.2.ba.c.5.12	yes	48
8.5	even	2	inner	672.2.bi.c.593.15		48
12.11	even	2		168.2.ba.c.5.20	yes	48
21.17	even	6	inner	672.2.bi.c.17.15		48
24.5	odd	2	inner	672.2.bi.c.593.3		48
24.11	even	2		168.2.ba.c.5.13	yes	48
28.3	even	6		168.2.ba.c.101.13	yes	48
56.3	even	6		168.2.ba.c.101.20	yes	48
56.45	odd	6	inner	672.2.bi.c.17.22		48
84.59	odd	6		168.2.ba.c.101.12	yes	48
168.59	odd	6		168.2.ba.c.101.5	yes	48
168.101	even	6	inner	672.2.bi.c.17.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	4.3	odd	2
168.2.ba.c.5.12	yes	48	8.3	odd	2
168.2.ba.c.5.13	yes	48	24.11	even	2
168.2.ba.c.5.20	yes	48	12.11	even	2
168.2.ba.c.101.5	yes	48	168.59	odd	6
168.2.ba.c.101.12	yes	48	84.59	odd	6
168.2.ba.c.101.13	yes	48	28.3	even	6
168.2.ba.c.101.20	yes	48	56.3	even	6
672.2.bi.c.17.3		48	7.3	odd	6	inner
672.2.bi.c.17.10		48	168.101	even	6	inner
672.2.bi.c.17.15		48	21.17	even	6	inner
672.2.bi.c.17.22		48	56.45	odd	6	inner
672.2.bi.c.593.3		48	24.5	odd	2	inner
672.2.bi.c.593.10		48	1.1	even	1	trivial
672.2.bi.c.593.15		48	8.5	even	2	inner
672.2.bi.c.593.22		48	3.2	odd	2	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.528554 + 1.64943i) q^{3} +(2.66818 + 1.54047i) q^{5} +(1.46307 + 2.20441i) q^{7} +(-2.44126 - 1.74363i) q^{9} +O(q^{10})\)	\(q+(-0.528554 + 1.64943i) q^{3} +(2.66818 + 1.54047i) q^{5} +(1.46307 + 2.20441i) q^{7} +(-2.44126 - 1.74363i) q^{9} +(0.621780 + 1.07696i) q^{11} +5.98957 q^{13} +(-3.95119 + 3.58676i) q^{15} +(-0.595854 - 1.03205i) q^{17} +(0.614126 - 1.06370i) q^{19} +(-4.40934 + 1.24808i) q^{21} +(-2.56956 - 1.48354i) q^{23} +(2.24612 + 3.89040i) q^{25} +(4.16634 - 3.10509i) q^{27} -3.19900 q^{29} +(-1.33987 + 0.773574i) q^{31} +(-2.10501 + 0.456356i) q^{33} +(0.507883 + 8.13559i) q^{35} +(0.334978 + 0.193399i) q^{37} +(-3.16581 + 9.87940i) q^{39} -9.44060 q^{41} -8.29057i q^{43} +(-3.82770 - 8.41302i) q^{45} +(3.34244 - 5.78928i) q^{47} +(-2.71887 + 6.45041i) q^{49} +(2.01724 - 0.437327i) q^{51} +(5.25317 + 9.09875i) q^{53} +3.83135i q^{55} +(1.42990 + 1.57518i) q^{57} +(3.22898 - 1.86425i) q^{59} +(-3.16493 + 5.48181i) q^{61} +(0.271956 - 7.93259i) q^{63} +(15.9813 + 9.22678i) q^{65} +(-10.7324 + 6.19634i) q^{67} +(3.80515 - 3.45419i) q^{69} +6.21100i q^{71} +(-8.92963 + 5.15552i) q^{73} +(-7.60415 + 1.64854i) q^{75} +(-1.46435 + 2.94632i) q^{77} +(6.41425 - 11.1098i) q^{79} +(2.91950 + 8.51331i) q^{81} +5.22882i q^{83} -3.67159i q^{85} +(1.69085 - 5.27654i) q^{87} +(6.94090 - 12.0220i) q^{89} +(8.76314 + 13.2035i) q^{91} +(-0.567765 - 2.61890i) q^{93} +(3.27720 - 1.89209i) q^{95} -17.1489i q^{97} +(0.359884 - 3.71328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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