LMFDB - Embedded newform 672.2.bi.c.17.22

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			17.22
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69273 - 0.366975i) q^{3} +(-2.66818 + 1.54047i) q^{5} +(1.46307 - 2.20441i) q^{7} +(2.73066 - 1.24238i) q^{9} +O(q^{10})$	\(q+(1.69273 - 0.366975i) q^{3} +(-2.66818 + 1.54047i) q^{5} +(1.46307 - 2.20441i) q^{7} +(2.73066 - 1.24238i) q^{9} +(-0.621780 + 1.07696i) q^{11} +5.98957 q^{13} +(-3.95119 + 3.58676i) q^{15} +(0.595854 - 1.03205i) q^{17} +(0.614126 + 1.06370i) q^{19} +(1.66761 - 4.26838i) q^{21} +(2.56956 - 1.48354i) q^{23} +(2.24612 - 3.89040i) q^{25} +(4.16634 - 3.10509i) q^{27} +3.19900 q^{29} +(-1.33987 - 0.773574i) q^{31} +(-0.657290 + 2.05117i) q^{33} +(-0.507883 + 8.13559i) q^{35} +(0.334978 - 0.193399i) q^{37} +(10.1387 - 2.19802i) q^{39} +9.44060 q^{41} +8.29057i q^{43} +(-5.37204 + 7.52140i) q^{45} +(-3.34244 - 5.78928i) q^{47} +(-2.71887 - 6.45041i) q^{49} +(0.629882 - 1.96564i) q^{51} +(-5.25317 + 9.09875i) q^{53} -3.83135i q^{55} +(1.42990 + 1.57518i) q^{57} +(-3.22898 - 1.86425i) q^{59} +(-3.16493 - 5.48181i) q^{61} +(1.25642 - 7.83718i) q^{63} +(-15.9813 + 9.22678i) q^{65} +(-10.7324 - 6.19634i) q^{67} +(3.80515 - 3.45419i) q^{69} +6.21100i q^{71} +(-8.92963 - 5.15552i) q^{73} +(2.37440 - 7.40966i) q^{75} +(1.46435 + 2.94632i) q^{77} +(6.41425 + 11.1098i) q^{79} +(5.91299 - 6.78502i) q^{81} +5.22882i q^{83} +3.67159i q^{85} +(5.41505 - 1.17396i) q^{87} +(-6.94090 - 12.0220i) q^{89} +(8.76314 - 13.2035i) q^{91} +(-2.55192 - 0.817752i) q^{93} +(-3.27720 - 1.89209i) q^{95} +17.1489i q^{97} +(-0.359884 + 3.71328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

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

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
$3$	1.69273	−	0.366975i	0.977297	−	0.211873i
$3$	1.69273	−	0.366975i	0.977297	−	0.211873i
$4$		0			0
$5$	−2.66818	+	1.54047i	−1.19325	+	0.688921i	−0.959041	−	0.283266i	$-0.908582\pi$
$5$	−2.66818	+	1.54047i	−1.19325	+	0.688921i	−0.234205	+	0.972187i	$0.575249\pi$
$6$		0			0
$7$	1.46307	−	2.20441i	0.552987	−	0.833190i
$7$	1.46307	−	2.20441i	0.552987	−	0.833190i
$8$		0			0
$9$	2.73066	−	1.24238i	0.910220	−	0.414126i
$10$		0			0
$11$	−0.621780	+	1.07696i	−0.187474	+	0.324714i	−0.944407	−	0.328778i	$-0.893363\pi$
$11$	−0.621780	+	1.07696i	−0.187474	+	0.324714i	0.756933	+	0.653492i	$0.226697\pi$
$12$		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	$-0.787171\pi$
$17$	0.595854	−	1.03205i	0.144516	−	0.250309i	0.929192	+	0.369597i	$0.120504\pi$
$18$		0			0
$19$	0.614126	+	1.06370i	0.140890	+	0.244029i	0.927832	−	0.372998i	$-0.121670\pi$
$19$	0.614126	+	1.06370i	0.140890	+	0.244029i	−0.786942	+	0.617027i	$0.788337\pi$
$20$		0			0
$21$	1.66761	−	4.26838i	0.363902	−	0.931437i
$22$		0			0
$23$	2.56956	−	1.48354i	0.535791	−	0.309339i	−0.207581	−	0.978218i	$-0.566559\pi$
$23$	2.56956	−	1.48354i	0.535791	−	0.309339i	0.743371	+	0.668879i	$0.233226\pi$
$24$		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	$-0.404007\pi$
$29$	3.19900			0.594040			0.297020	+	0.954871i	$0.404007\pi$
$30$		0			0
$31$	−1.33987	−	0.773574i	−0.240648	−	0.138938i	0.374827	−	0.927095i	$-0.377702\pi$
$31$	−1.33987	−	0.773574i	−0.240648	−	0.138938i	−0.615474	+	0.788157i	$0.711036\pi$
$32$		0			0
$33$	−0.657290	+	2.05117i	−0.114419	+	0.357063i
$34$		0			0
$35$	−0.507883	+	8.13559i	−0.0858478	+	1.37517i
$36$		0			0
$37$	0.334978	−	0.193399i	0.0550700	−	0.0317947i	−0.472212	−	0.881485i	$-0.656544\pi$
$37$	0.334978	−	0.193399i	0.0550700	−	0.0317947i	0.527282	+	0.849690i	$0.323211\pi$
$38$		0			0
$39$	10.1387	−	2.19802i	1.62349	−	0.351965i
$40$		0			0
$41$	9.44060			1.47437			0.737187	−	0.675689i	$-0.236154\pi$
$41$	9.44060			1.47437			0.737187	+	0.675689i	$0.236154\pi$
$42$		0			0
$43$			8.29057i			1.26430i	0.774846	+	0.632150i	$0.217827\pi$
$43$			8.29057i			1.26430i	−0.774846	+	0.632150i	$0.782173\pi$
$44$		0			0
$45$	−5.37204	+	7.52140i	−0.800816	+	1.12122i
$46$		0			0
$47$	−3.34244	−	5.78928i	−0.487546	−	0.844454i	0.512352	−	0.858776i	$-0.328774\pi$
$47$	−3.34244	−	5.78928i	−0.487546	−	0.844454i	−0.999897	+	0.0143219i	$0.995441\pi$
$48$		0			0
$49$	−2.71887	−	6.45041i	−0.388410	−	0.921486i
$50$		0			0
$51$	0.629882	−	1.96564i	0.0882012	−	0.275245i
$52$		0			0
$53$	−5.25317	+	9.09875i	−0.721578	+	1.24981i	0.238789	+	0.971071i	$0.423250\pi$
$53$	−5.25317	+	9.09875i	−0.721578	+	1.24981i	−0.960367	+	0.278738i	$0.910084\pi$
$54$		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	$-0.411368\pi$
$59$	−3.22898	−	1.86425i	−0.420377	−	0.242705i	−0.695238	+	0.718779i	$0.744701\pi$
$60$		0			0
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	0.589121	−	0.808045i	$-0.299474\pi$
$61$	−3.16493	−	5.48181i	−0.405227	−	0.701874i	−0.994348	+	0.106171i	$0.966141\pi$
$62$		0			0
$63$	1.25642	−	7.83718i	0.158294	−	0.987392i
$64$		0			0
$65$	−15.9813	+	9.22678i	−1.98223	+	1.14444i
$66$		0			0
$67$	−10.7324	−	6.19634i	−1.31117	−	0.757003i	−0.328878	−	0.944372i	$-0.606671\pi$
$67$	−10.7324	−	6.19634i	−1.31117	−	0.757003i	−0.982290	+	0.187369i	$0.940004\pi$
$68$		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	−0.123851	−	0.992301i	$-0.539524\pi$
$73$	−8.92963	−	5.15552i	−1.04513	−	0.603408i	−0.921283	+	0.388893i	$0.872858\pi$
$74$		0			0
$75$	2.37440	−	7.40966i	0.274172	−	0.855594i
$76$		0			0
$77$	1.46435	+	2.94632i	0.166878	+	0.335764i
$78$		0			0
$79$	6.41425	+	11.1098i	0.721660	+	1.24995i	0.960334	+	0.278852i	$0.0899539\pi$
$79$	6.41425	+	11.1098i	0.721660	+	1.24995i	−0.238674	+	0.971100i	$0.576713\pi$
$80$		0			0
$81$	5.91299	−	6.78502i	0.656999	−	0.753891i
$82$		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
$87$	5.41505	−	1.17396i	0.580554	−	0.125861i
$88$		0			0
$89$	−6.94090	−	12.0220i	−0.735734	−	1.27433i	−0.954400	−	0.298529i	$-0.903504\pi$
$89$	−6.94090	−	12.0220i	−0.735734	−	1.27433i	0.218666	−	0.975800i	$-0.429829\pi$
$90$		0			0
$91$	8.76314	−	13.2035i	0.918627	−	1.38410i
$92$		0			0
$93$	−2.55192	−	0.817752i	−0.264621	−	0.0847969i
$94$		0			0
$95$	−3.27720	−	1.89209i	−0.336233	−	0.194124i
$96$		0			0
$97$			17.1489i			1.74120i	0.491989	+	0.870601i	$0.336270\pi$
$97$			17.1489i			1.74120i	−0.491989	+	0.870601i	$0.663730\pi$
$98$		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	$-0.386133\pi$
$101$	−2.87413	−	1.65938i	−0.285986	−	0.165114i	−0.636130	+	0.771582i	$0.719466\pi$
$102$		0			0
$103$	−10.7667	+	6.21615i	−1.06087	+	0.612496i	−0.925674	−	0.378322i	$-0.876501\pi$
$103$	−10.7667	+	6.21615i	−1.06087	+	0.612496i	−0.135200	+	0.990818i	$0.543168\pi$
$104$		0			0
$105$	2.12585	+	13.9577i	0.207462	+	1.36213i
$106$		0			0
$107$	−4.79031	−	8.29706i	−0.463097	−	0.802107i	0.536017	−	0.844207i	$-0.319928\pi$
$107$	−4.79031	−	8.29706i	−0.463097	−	0.802107i	−0.999113	+	0.0421002i	$0.986595\pi$
$108$		0			0
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	0.524246	−	0.851567i	$-0.324347\pi$
$109$	0.510424	+	0.294693i	0.0488898	+	0.0282265i	−0.475356	+	0.879794i	$0.657681\pi$
$110$		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
$117$	16.3555	−	7.44131i	1.51206	−	0.687950i
$118$		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
$123$	15.9804	−	3.46446i	1.44090	−	0.312380i
$124$		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
$129$	3.04243	+	14.0337i	0.267871	+	1.23560i
$130$		0			0
$131$	−3.67922	+	2.12420i	−0.321455	+	0.185592i	−0.652041	−	0.758184i	$-0.726087\pi$
$131$	−3.67922	+	2.12420i	−0.321455	+	0.185592i	0.330586	+	0.943776i	$0.392754\pi$
$132$		0			0
$133$	3.24333	+	0.202473i	0.281233	+	0.0175566i
$134$		0			0
$135$	−6.33323	+	14.7031i	−0.545078	+	1.26544i
$136$		0			0
$137$	−0.674838	−	0.389618i	−0.0576553	−	0.0332873i	0.470895	−	0.882189i	$-0.343931\pi$
$137$	−0.674838	−	0.389618i	−0.0576553	−	0.0332873i	−0.528551	+	0.848902i	$0.677264\pi$
$138$		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
$147$	−6.96945	−	9.92102i	−0.574831	−	0.818272i
$148$		0			0
$149$	−2.07219	−	3.58914i	−0.169761	−	0.294034i	0.768575	−	0.639760i	$-0.220966\pi$
$149$	−2.07219	−	3.58914i	−0.169761	−	0.294034i	−0.938336	+	0.345726i	$0.887633\pi$
$150$		0			0
$151$	−2.16486	+	3.74965i	−0.176174	+	0.305142i	−0.940567	−	0.339608i	$-0.889705\pi$
$151$	−2.16486	+	3.74965i	−0.176174	+	0.305142i	0.764393	+	0.644751i	$0.223039\pi$
$152$		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	−0.709021	−	0.705187i	$-0.750863\pi$
$157$	3.21017	−	5.56018i	0.256200	−	0.443751i	0.965221	+	0.261437i	$0.0841963\pi$
$158$		0			0
$159$	−5.55317	+	17.3295i	−0.440395	+	1.37432i
$160$		0			0
$161$	0.489111	−	7.83489i	0.0385473	−	0.617476i
$162$		0			0
$163$	−9.18195	+	5.30120i	−0.719186	+	0.415222i	−0.814453	−	0.580230i	$-0.802963\pi$
$163$	−9.18195	+	5.30120i	−0.719186	+	0.415222i	0.0952672	+	0.995452i	$0.469629\pi$
$164$		0			0
$165$	−1.40601	−	6.48543i	−0.109458	−	0.504890i
$166$		0			0
$167$	−15.5718			−1.20498			−0.602492	−	0.798125i	$-0.705825\pi$
$167$	−15.5718			−1.20498			−0.602492	+	0.798125i	$0.705825\pi$
$168$		0			0
$169$	22.8750			1.75961
$170$		0			0
$171$	2.99848	+	2.14162i	0.229300	+	0.163774i
$172$		0			0
$173$	1.61807	−	0.934192i	0.123019	−	0.0710253i	−0.437228	−	0.899351i	$-0.644040\pi$
$173$	1.61807	−	0.934192i	0.123019	−	0.0710253i	0.560247	+	0.828326i	$0.310706\pi$
$174$		0			0
$175$	−5.28982	−	10.6433i	−0.399873	−	0.804558i
$176$		0			0
$177$	−6.14991	−	1.97071i	−0.462256	−	0.148128i
$178$		0			0
$179$	−7.73124	+	13.3909i	−0.577860	+	1.00088i	0.417864	+	0.908509i	$0.362779\pi$
$179$	−7.73124	+	13.3909i	−0.577860	+	1.00088i	−0.995724	+	0.0923734i	$0.970555\pi$
$180$		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
$189$	−0.749273	−	13.7273i	−0.0545016	−	0.998514i
$190$		0			0
$191$	−0.391130	+	0.225819i	−0.0283012	+	0.0163397i	−0.514084	−	0.857740i	$-0.671868\pi$
$191$	−0.391130	+	0.225819i	−0.0283012	+	0.0163397i	0.485783	+	0.874080i	$0.338535\pi$
$192$		0			0
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	−0.833441	−	0.552608i	$-0.813633\pi$
$193$	0.859277	−	1.48831i	0.0618521	−	0.107131i	0.895293	+	0.445477i	$0.146966\pi$
$194$		0			0
$195$	−23.6659	+	21.4832i	−1.69475	+	1.53844i
$196$		0			0
$197$	−16.4222			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$197$	−16.4222			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$198$		0			0
$199$	−0.839396	−	0.484625i	−0.0595032	−	0.0343542i	0.469953	−	0.882691i	$-0.344271\pi$
$199$	−0.839396	−	0.484625i	−0.0595032	−	0.0343542i	−0.529456	+	0.848337i	$0.677604\pi$
$200$		0			0
$201$	−20.4409	−	6.55020i	−1.44179	−	0.462016i
$202$		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
$207$	5.17348	−	7.24340i	0.359582	−	0.503451i
$208$		0			0
$209$	−1.52741			−0.105653
$210$		0			0
$211$		−	9.99340i		−	0.687974i	−0.938974	−	0.343987i	$-0.888222\pi$
$211$		−	9.99340i		−	0.687974i	0.938974	−	0.343987i	$-0.111778\pi$
$212$		0			0
$213$	2.27928	+	10.5135i	0.156174	+	0.720375i
$214$		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
$219$	−17.0074	−	5.44995i	−1.14925	−	0.368273i
$220$		0			0
$221$	3.56891	−	6.18153i	0.240071	−	0.415815i
$222$		0			0
$223$		−	13.7534i		−	0.920996i	−0.887661	−	0.460498i	$-0.847671\pi$
$223$		−	13.7534i		−	0.920996i	0.887661	−	0.460498i	$-0.152329\pi$
$224$		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	$-0.282735\pi$
$227$	4.13075	+	2.38489i	0.274167	+	0.158291i	−0.356613	+	0.934252i	$0.616068\pi$
$228$		0			0
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	0.840424	−	0.541929i	$-0.182306\pi$
$229$	−0.743202	−	1.28726i	−0.0491122	−	0.0850648i	−0.889536	+	0.456864i	$0.848973\pi$
$230$		0			0
$231$	3.55997	+	4.44994i	0.234229	+	0.292784i
$232$		0			0
$233$	−2.00188	+	1.15579i	−0.131148	+	0.0757182i	−0.564139	−	0.825680i	$-0.690792\pi$
$233$	−2.00188	+	1.15579i	−0.131148	+	0.0757182i	0.432991	+	0.901398i	$0.357458\pi$
$234$		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	0.605042	−	0.796193i	$-0.293156\pi$
$241$	3.38489	+	1.95427i	0.218040	+	0.125885i	−0.387002	+	0.922079i	$0.626489\pi$
$242$		0			0
$243$	7.51916	−	13.6551i	0.482354	−	0.875976i
$244$		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
$249$	1.91885	+	8.85097i	0.121602	+	0.560908i
$250$		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
$255$	1.34738	+	6.21501i	0.0843764	+	0.389199i
$256$		0			0
$257$	6.53148	+	11.3128i	0.407422	+	0.705676i	0.994600	−	0.103782i	$-0.0330944\pi$
$257$	6.53148	+	11.3128i	0.407422	+	0.705676i	−0.587178	+	0.809458i	$0.699761\pi$
$258$		0			0
$259$	0.0637623	−	1.02139i	0.00396200	−	0.0634658i
$260$		0			0
$261$	8.73539	−	3.97437i	0.540707	−	0.246008i
$262$		0			0
$263$	26.2857	+	15.1761i	1.62085	+	0.935796i	0.986694	+	0.162586i	$0.0519836\pi$
$263$	26.2857	+	15.1761i	1.62085	+	0.935796i	0.634151	+	0.773209i	$0.281350\pi$
$264$		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	$-0.341006\pi$
$269$	−0.684713	−	0.395319i	−0.0417477	−	0.0241030i	−0.520729	+	0.853722i	$0.674340\pi$
$270$		0			0
$271$	4.95134	−	2.85866i	0.300773	−	0.173651i	−0.342017	−	0.939694i	$-0.611110\pi$
$271$	4.95134	−	2.85866i	0.300773	−	0.173651i	0.642790	+	0.766043i	$0.277777\pi$
$272$		0			0
$273$	9.98826	−	25.5658i	0.604517	−	1.54731i
$274$		0			0
$275$	2.79319	+	4.83795i	0.168436	+	0.291739i
$276$		0			0
$277$	15.4143	+	8.89945i	0.926156	+	0.534716i	0.885594	−	0.464461i	$-0.153752\pi$
$277$	15.4143	+	8.89945i	0.926156	+	0.534716i	0.0405619	+	0.999177i	$0.487085\pi$
$278$		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	−0.807134	−	0.590368i	$-0.798983\pi$
$283$	1.81190	−	3.13830i	0.107706	−	0.186552i	0.914841	+	0.403815i	$0.132316\pi$
$284$		0			0
$285$	−6.24175	−	2.00015i	−0.369729	−	0.118478i
$286$		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
$291$	6.29320	+	29.0284i	0.368914	+	1.70167i
$292$		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
$297$	0.753496	+	6.41765i	0.0437223	+	0.372390i
$298$		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
$303$	−5.47407	−	1.75414i	−0.314477	−	0.100773i
$304$		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	−0.498065	−	0.867140i	$-0.665956\pi$
$311$	8.85168	−	15.3316i	0.501933	−	0.869373i	0.999998	−	0.00223345i	$-0.000710930\pi$
$312$		0			0
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	−0.753760	−	0.657150i	$-0.771762\pi$
$313$	−9.93451	+	5.73569i	−0.561532	+	0.324200i	0.192228	+	0.981350i	$0.438429\pi$
$314$		0			0
$315$	8.72062	+	22.8465i	0.491351	+	1.28725i
$316$		0			0
$317$	−1.15640	−	2.00294i	−0.0649499	−	0.112497i	0.831722	−	0.555193i	$-0.187355\pi$
$317$	−1.15640	−	2.00294i	−0.0649499	−	0.112497i	−0.896672	+	0.442696i	$0.854022\pi$
$318$		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
$327$	0.972154	+	0.311523i	0.0537603	+	0.0172273i
$328$		0			0
$329$	−17.6522	−	1.10198i	−0.973197	−	0.0607540i
$330$		0			0
$331$	20.7165	−	11.9607i	1.13868	−	0.657418i	0.192578	−	0.981282i	$-0.438315\pi$
$331$	20.7165	−	11.9607i	1.13868	−	0.657418i	0.946104	+	0.323863i	$0.104982\pi$
$332$		0			0
$333$	0.674434	−	0.944277i	0.0369588	−	0.0517461i
$334$		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
$339$	−2.57632	−	11.8836i	−0.139926	−	0.645431i
$340$		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
$345$	−4.83173	+	15.0781i	−0.260132	+	0.811779i
$346$		0			0
$347$	−0.473950	+	0.820906i	−0.0254430	+	0.0440686i	−0.878467	−	0.477804i	$-0.841433\pi$
$347$	−0.473950	+	0.820906i	−0.0254430	+	0.0440686i	0.853024	+	0.521872i	$0.174766\pi$
$348$		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	$-0.697810\pi$
$353$	7.75978	−	13.4403i	0.413011	−	0.715356i	0.995217	+	0.0976847i	$0.0311437\pi$
$354$		0			0
$355$	−9.56788	−	16.5721i	−0.507810	−	0.879553i
$356$		0			0
$357$	−3.41153	−	4.26439i	−0.180557	−	0.225695i
$358$		0			0
$359$	−12.2735	+	7.08613i	−0.647772	+	0.373991i	−0.787602	−	0.616184i	$-0.788678\pi$
$359$	−12.2735	+	7.08613i	−0.647772	+	0.373991i	0.139830	+	0.990176i	$0.455344\pi$
$360$		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	0.770393	−	0.637569i	$-0.220060\pi$
$367$	11.5602	+	6.67430i	0.603439	+	0.348396i	−0.166954	+	0.985965i	$0.553393\pi$
$368$		0			0
$369$	25.7790	−	11.7288i	1.34200	−	0.610576i
$370$		0			0
$371$	12.3717	+	24.8922i	0.642305	+	1.29234i
$372$		0			0
$373$	4.56967	−	2.63830i	0.236609	−	0.136606i	−0.377008	−	0.926210i	$-0.623047\pi$
$373$	4.56967	−	2.63830i	0.236609	−	0.136606i	0.613617	+	0.789604i	$0.289714\pi$
$374$		0			0
$375$	−0.574082	−	2.64804i	−0.0296455	−	0.136744i
$376$		0			0
$377$	19.1607			0.986824
$378$		0			0
$379$			15.3619i			0.789086i	0.918877	+	0.394543i	$0.129097\pi$
$379$			15.3619i			0.789086i	−0.918877	+	0.394543i	$0.870903\pi$
$380$		0			0
$381$	9.96584	−	2.16054i	0.510565	−	0.110688i
$382$		0			0
$383$	−1.35424	−	2.34561i	−0.0691983	−	0.119855i	0.829350	−	0.558729i	$-0.188711\pi$
$383$	−1.35424	−	2.34561i	−0.0691983	−	0.119855i	−0.898549	+	0.438874i	$0.855377\pi$
$384$		0			0
$385$	−8.44587	−	5.60552i	−0.430442	−	0.285684i
$386$		0			0
$387$	10.3000	+	22.6387i	0.523579	+	1.15079i
$388$		0			0
$389$	−6.35306	+	11.0038i	−0.322113	+	0.557916i	−0.980924	−	0.194393i	$-0.937726\pi$
$389$	−6.35306	+	11.0038i	−0.322113	+	0.557916i	0.658811	+	0.752308i	$0.271060\pi$
$390$		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	−0.992769	−	0.120041i	$-0.961697\pi$
$397$	−11.9617	−	20.7184i	−0.600343	−	1.03982i	0.392426	−	0.919784i	$-0.371636\pi$
$398$		0			0
$399$	5.56439	−	0.847492i	0.278568	−	0.0424277i
$400$		0			0
$401$	23.5968	−	13.6236i	1.17837	−	0.680331i	0.222731	−	0.974880i	$-0.428503\pi$
$401$	23.5968	−	13.6236i	1.17837	−	0.680331i	0.955636	+	0.294549i	$0.0951694\pi$
$402$		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	0.659117	−	0.752040i	$-0.270930\pi$
$409$	6.82328	+	3.93942i	0.337390	+	0.194792i	−0.321727	+	0.946832i	$0.604263\pi$
$410$		0			0
$411$	−1.28530	−	0.411869i	−0.0633991	−	0.0203160i
$412$		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
$417$	9.38980	−	2.03566i	0.459820	−	0.0996868i
$418$		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	$-0.867009\pi$
$421$		−	16.6507i		−	0.811505i	0.913983	−	0.405753i	$-0.132991\pi$
$422$		0			0
$423$	−16.3196	−	11.6560i	−0.793484	−	0.566733i
$424$		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
$429$	−3.93688	+	12.2856i	−0.190074	+	0.593156i
$430$		0			0
$431$	−19.8541	−	11.4628i	−0.956339	−	0.552142i	−0.0612944	−	0.998120i	$-0.519523\pi$
$431$	−19.8541	−	11.4628i	−0.956339	−	0.552142i	−0.895044	+	0.445977i	$0.852856\pi$
$432$		0			0
$433$			10.5825i			0.508564i	0.967130	+	0.254282i	$0.0818392\pi$
$433$			10.5825i			0.508564i	−0.967130	+	0.254282i	$0.918161\pi$
$434$		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	−0.331695	−	0.943387i	$-0.607620\pi$
$439$	6.69332	−	3.86439i	0.319455	−	0.184437i	0.651150	+	0.758949i	$0.274287\pi$
$440$		0			0
$441$	−15.4382	−	14.2360i	−0.735150	−	0.677904i
$442$		0			0
$443$	2.28548	+	3.95856i	0.108586	+	0.188077i	0.915198	−	0.403005i	$-0.132034\pi$
$443$	2.28548	+	3.95856i	0.108586	+	0.188077i	−0.806611	+	0.591082i	$0.798701\pi$
$444$		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
$453$	−2.28849	+	7.14159i	−0.107523	+	0.335541i
$454$		0			0
$455$	−3.04200	+	48.7287i	−0.142611	+	2.28444i
$456$		0			0
$457$	−9.88462	−	17.1207i	−0.462383	−	0.800871i	0.536696	−	0.843776i	$-0.319672\pi$
$457$	−9.88462	−	17.1207i	−0.462383	−	0.800871i	−0.999079	+	0.0429048i	$0.986339\pi$
$458$		0			0
$459$	−0.722078	−	6.15005i	−0.0337037	−	0.287060i
$460$		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
$465$	8.06870	−	1.74925i	0.374177	−	0.0811197i
$466$		0			0
$467$	−26.9170	+	15.5406i	−1.24557	+	0.719131i	−0.970223	−	0.242214i	$-0.922127\pi$
$467$	−26.9170	+	15.5406i	−1.24557	+	0.719131i	−0.275348	+	0.961345i	$0.588793\pi$
$468$		0			0
$469$	−29.3615	+	14.5929i	−1.35579	+	0.673839i
$470$		0			0
$471$	3.39350	−	10.5899i	0.156364	−	0.487958i
$472$		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	0.150620	+	0.988592i	$0.451873\pi$
$479$	−17.0894	+	29.5997i	−0.780835	+	1.35245i	−0.931456	+	0.363855i	$0.881460\pi$
$480$		0			0
$481$	2.00637	−	1.15838i	0.0914827	−	0.0528176i
$482$		0			0
$483$	−2.04728	−	13.4418i	−0.0931543	−	0.611624i
$484$		0			0
$485$	−26.4174	−	45.7562i	−1.19955	−	2.07768i
$486$		0			0
$487$	12.3371	−	21.3684i	0.559046	−	0.968296i	−0.438531	−	0.898716i	$-0.644501\pi$
$487$	12.3371	−	21.3684i	0.559046	−	0.968296i	0.997576	−	0.0695795i	$-0.0221658\pi$
$488$		0			0
$489$	−13.5971	+	12.3430i	−0.614884	+	0.558171i
$490$		0			0
$491$	43.3064			1.95439			0.977196	−	0.212339i	$-0.0681079\pi$
$491$	43.3064			1.95439			0.977196	+	0.212339i	$0.0681079\pi$
$492$		0			0
$493$	1.90614	−	3.30153i	0.0858482	−	0.148693i
$494$		0			0
$495$	−4.75998	−	10.4621i	−0.213945	−	0.470237i
$496$		0			0
$497$	13.6916	+	9.08710i	0.614152	+	0.407612i
$498$		0			0
$499$	−32.3258	+	18.6633i	−1.44710	+	0.835485i	−0.998308	−	0.0581497i	$-0.981480\pi$
$499$	−32.3258	+	18.6633i	−1.44710	+	0.835485i	−0.448795	+	0.893635i	$0.648147\pi$
$500$		0			0
$501$	−26.3589	+	5.71447i	−1.17763	+	0.255304i
$502$		0			0
$503$	34.2432			1.52683			0.763414	−	0.645910i	$-0.223522\pi$
$503$	34.2432			1.52683			0.763414	+	0.645910i	$0.223522\pi$
$504$		0			0
$505$	10.2249			0.455003
$506$		0			0
$507$	38.7211	−	8.39454i	1.71966	−	0.372814i
$508$		0			0
$509$	−24.1054	+	13.9173i	−1.06845	+	0.616871i	−0.927758	−	0.373182i	$-0.878267\pi$
$509$	−24.1054	+	13.9173i	−1.06845	+	0.616871i	−0.140694	+	0.990053i	$0.544933\pi$
$510$		0			0
$511$	−24.4295	+	12.1417i	−1.08070	+	0.537118i
$512$		0			0
$513$	5.86153	+	2.52481i	0.258793	+	0.111473i
$514$		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	$-0.717373\pi$
$521$	8.13261	−	14.0861i	0.356296	−	0.617123i	0.987339	+	0.158625i	$0.0507061\pi$
$522$		0			0
$523$	6.98922	+	12.1057i	0.305617	+	0.529345i	0.977399	−	0.211405i	$-0.0678038\pi$
$523$	6.98922	+	12.1057i	0.305617	+	0.529345i	−0.671781	+	0.740750i	$0.734470\pi$
$524$		0			0
$525$	−12.8601	−	16.0750i	−0.561259	−	0.701570i
$526$		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
$537$	−8.17276	+	25.5043i	−0.352681	+	1.10059i
$538$		0			0
$539$	8.63734	+	1.08263i	0.372037	+	0.0466322i
$540$		0			0
$541$	18.9287	−	10.9285i	0.813810	−	0.469853i	−0.0344673	−	0.999406i	$-0.510973\pi$
$541$	18.9287	−	10.9285i	0.813810	−	0.469853i	0.848277	+	0.529552i	$0.177640\pi$
$542$		0			0
$543$	−28.1212	+	6.09653i	−1.20680	+	0.261627i
$544$		0			0
$545$	−1.81587			−0.0777834
$546$		0			0
$547$			9.11111i			0.389563i	0.980847	+	0.194782i	$0.0623998\pi$
$547$			9.11111i			0.389563i	−0.980847	+	0.194782i	$0.937600\pi$
$548$		0			0
$549$	−15.4528	−	11.0369i	−0.659510	−	0.471044i
$550$		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
$555$	−0.629882	+	1.96564i	−0.0267370	+	0.0834369i
$556$		0			0
$557$	2.14436	−	3.71415i	0.0908596	−	0.157373i	−0.817013	−	0.576619i	$-0.804372\pi$
$557$	2.14436	−	3.71415i	0.0908596	−	0.157373i	0.907873	+	0.419245i	$0.137705\pi$
$558$		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	$-0.102579\pi$
$563$	27.2512	+	15.7335i	1.14850	+	0.663087i	0.199979	+	0.979800i	$0.435913\pi$
$564$		0			0
$565$	10.8148	+	18.7317i	0.454981	+	0.788049i
$566$		0			0
$567$	−6.30589	−	22.9616i	−0.264822	−	0.964297i
$568$		0			0
$569$	−8.62592	+	4.98018i	−0.361617	+	0.208780i	−0.669790	−	0.742551i	$-0.733616\pi$
$569$	−8.62592	+	4.98018i	−0.361617	+	0.208780i	0.308173	+	0.951330i	$0.400283\pi$
$570$		0			0
$571$	−29.5465	−	17.0587i	−1.23648	−	0.713883i	−0.268108	−	0.963389i	$-0.586399\pi$
$571$	−29.5465	−	17.0587i	−1.23648	−	0.713883i	−0.968373	+	0.249506i	$0.919732\pi$
$572$		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	0.517458	−	0.855708i	$-0.326878\pi$
$577$	0.843668	+	0.487092i	0.0351224	+	0.0202779i	−0.482336	+	0.875986i	$0.660212\pi$
$578$		0			0
$579$	0.908350	−	2.83464i	0.0377497	−	0.117804i
$580$		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
$585$	−32.1762	+	45.0499i	−1.33032	+	1.86259i
$586$		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
$591$	−27.7983	+	6.02654i	−1.14347	+	0.247899i
$592$		0			0
$593$	−22.1118	−	38.2987i	−0.908022	−	1.57274i	−0.816808	−	0.576909i	$-0.804259\pi$
$593$	−22.1118	−	38.2987i	−0.908022	−	1.57274i	−0.0912135	−	0.995831i	$-0.529075\pi$
$594$		0			0
$595$	8.09370	+	5.37178i	0.331809	+	0.220222i
$596$		0			0
$597$	−1.59871	−	0.512302i	−0.0654310	−	0.0209671i
$598$		0			0
$599$	−8.58632	−	4.95731i	−0.350827	−	0.202550i	0.314222	−	0.949349i	$-0.398256\pi$
$599$	−8.58632	−	4.95731i	−0.350827	−	0.202550i	−0.665050	+	0.746799i	$0.731590\pi$
$600$		0			0
$601$		−	11.8235i		−	0.482292i	−0.970489	−	0.241146i	$-0.922477\pi$
$601$		−	11.8235i		−	0.482292i	0.970489	−	0.241146i	$-0.0775233\pi$
$602$		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	−0.608627	−	0.793456i	$-0.708279\pi$
$607$	−5.56281	+	3.21169i	−0.225788	+	0.130359i	0.382840	+	0.923815i	$0.374946\pi$
$608$		0			0
$609$	5.33469	−	13.6546i	0.216173	−	0.553311i
$610$		0			0
$611$	−20.0198	−	34.6753i	−0.809915	−	1.40281i
$612$		0			0
$613$	−17.5740	−	10.1463i	−0.709805	−	0.409806i	0.101184	−	0.994868i	$-0.467737\pi$
$613$	−17.5740	−	10.1463i	−0.709805	−	0.409806i	−0.810989	+	0.585061i	$0.801070\pi$
$614$		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	−0.972929	−	0.231106i	$-0.925766\pi$
$619$	−7.12358	+	12.3384i	−0.286321	+	0.495922i	0.686608	+	0.727028i	$0.259099\pi$
$620$		0			0
$621$	6.09915	−	14.1596i	0.244750	−	0.568207i
$622$		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
$627$	−2.58548	+	0.560520i	−0.103254	+	0.0223850i
$628$		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
$633$	−3.66733	−	16.9161i	−0.145763	−	0.672355i
$634$		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
$639$	7.71641	+	16.9601i	0.305256	+	0.670932i
$640$		0			0
$641$	−6.31225	−	3.64438i	−0.249319	−	0.143944i	0.370133	−	0.928979i	$-0.379312\pi$
$641$	−6.31225	−	3.64438i	−0.249319	−	0.143944i	−0.619452	+	0.785034i	$0.712645\pi$
$642$		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	−0.127657	−	0.991818i	$-0.540746\pi$
$647$	20.2246	−	35.0301i	0.795112	−	1.37717i	0.922768	−	0.385355i	$-0.125921\pi$
$648$		0			0
$649$	4.01543	−	2.31831i	0.157619	−	0.0910016i
$650$		0			0
$651$	−5.53629	+	4.42905i	−0.216984	+	0.173588i
$652$		0			0
$653$	22.0316	+	38.1599i	0.862164	+	1.49331i	0.869836	+	0.493341i	$0.164225\pi$
$653$	22.0316	+	38.1599i	0.862164	+	1.49331i	−0.00767187	+	0.999971i	$0.502442\pi$
$654$		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	$-0.536601\pi$
$659$	−5.89051			−0.229462			−0.114731	+	0.993397i	$0.536601\pi$
$660$		0			0
$661$	−21.0993	+	36.5450i	−0.820667	+	1.42144i	0.0845192	+	0.996422i	$0.473065\pi$
$661$	−21.0993	+	36.5450i	−0.820667	+	1.42144i	−0.905186	+	0.425015i	$0.860269\pi$
$662$		0			0
$663$	3.77273	−	11.7734i	0.146521	−	0.457239i
$664$		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
$669$	−5.04716	−	23.2808i	−0.195134	−	0.900087i
$670$		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
$675$	−2.72193	−	23.1832i	−0.104767	−	0.892320i
$676$		0			0
$677$	35.7518	−	20.6413i	1.37405	−	0.793310i	0.382618	−	0.923907i	$-0.375023\pi$
$677$	35.7518	−	20.6413i	1.37405	−	0.793310i	0.991436	+	0.130596i	$0.0416892\pi$
$678$		0			0
$679$	37.8032	+	25.0899i	1.45075	+	0.962863i
$680$		0			0
$681$	7.86743	+	2.52109i	0.301481	+	0.0966083i
$682$		0			0
$683$	−17.1346	+	29.6781i	−0.655638	+	1.13560i	0.326095	+	0.945337i	$0.394267\pi$
$683$	−17.1346	+	29.6781i	−0.655638	+	1.13560i	−0.981733	+	0.190262i	$0.939066\pi$
$684$		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	0.789962	−	0.613156i	$-0.210100\pi$
$691$	−3.57575	−	6.19338i	−0.136028	−	0.235607i	−0.925990	+	0.377549i	$0.876767\pi$
$692$		0			0
$693$	7.65908	+	6.22611i	0.290944	+	0.236511i
$694$		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	$-0.575309\pi$
$701$	−12.4116			−0.468778			−0.234389	+	0.972143i	$0.575309\pi$
$702$		0			0
$703$	0.411437	+	0.237543i	0.0155176	+	0.00895911i
$704$		0			0
$705$	33.9714	+	10.8860i	1.27944	+	0.409991i
$706$		0			0
$707$	−7.86299	+	3.90798i	−0.295718	+	0.146975i
$708$		0			0
$709$	30.5908	−	17.6616i	1.14886	−	0.663295i	0.200251	−	0.979745i	$-0.435824\pi$
$709$	30.5908	−	17.6616i	1.14886	−	0.663295i	0.948609	+	0.316450i	$0.102491\pi$
$710$		0			0
$711$	31.3177	+	22.3682i	1.17451	+	0.838872i
$712$		0			0
$713$	−4.59050			−0.171916
$714$		0			0
$715$		−	22.9481i		−	0.858211i
$716$		0			0
$717$	7.92780	+	36.5682i	0.296069	+	1.36566i
$718$		0			0
$719$	12.1803	+	21.0969i	0.454250	+	0.786783i	0.998645	−	0.0520455i	$-0.0165741\pi$
$719$	12.1803	+	21.0969i	0.454250	+	0.786783i	−0.544395	+	0.838829i	$0.683241\pi$
$720$		0			0
$721$	−2.04942	+	32.8289i	−0.0763243	+	1.22261i
$722$		0			0
$723$	6.44687	+	2.06587i	0.239762	+	0.0768307i
$724$		0			0
$725$	7.18536	−	12.4454i	0.266858	−	0.462211i
$726$		0			0
$727$		−	5.15142i		−	0.191055i	−0.995427	−	0.0955277i	$-0.969546\pi$
$727$		−	5.15142i		−	0.191055i	0.995427	−	0.0955277i	$-0.0304539\pi$
$728$		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	0.788613	−	0.614889i	$-0.210799\pi$
$733$	−3.74171	−	6.48083i	−0.138203	−	0.239375i	−0.926817	+	0.375514i	$0.877466\pi$
$734$		0			0
$735$	33.8788	+	15.7348i	1.24964	+	0.580388i
$736$		0			0
$737$	13.3464	−	7.70552i	0.491619	−	0.283837i
$738$		0			0
$739$	2.26360	+	1.30689i	0.0832679	+	0.0480747i	0.541056	−	0.840987i	$-0.318025\pi$
$739$	2.26360	+	1.30689i	0.0832679	+	0.0480747i	−0.457788	+	0.889061i	$0.651358\pi$
$740$		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
$747$	6.49617	+	14.2781i	0.237683	+	0.522409i
$748$		0			0
$749$	−25.2987	−	1.57933i	−0.924394	−	0.0577074i
$750$		0			0
$751$	−0.504993	−	0.874673i	−0.0184275	−	0.0319173i	0.856665	−	0.515874i	$-0.172533\pi$
$751$	−0.504993	−	0.874673i	−0.0184275	−	0.0319173i	−0.875092	+	0.483956i	$0.839199\pi$
$752$		0			0
$753$	−5.74418	−	26.4959i	−0.209330	−	0.965564i
$754$		0			0
$755$		−	13.3397i		−	0.485480i
$756$		0			0
$757$			11.1837i			0.406478i	0.979129	+	0.203239i	$0.0651469\pi$
$757$			11.1837i			0.406478i	−0.979129	+	0.203239i	$0.934853\pi$
$758$		0			0
$759$	1.35404	+	6.24572i	0.0491486	+	0.226705i
$760$		0			0
$761$	3.99009	+	6.91104i	0.144641	+	0.250525i	0.929239	−	0.369480i	$-0.120464\pi$
$761$	3.99009	+	6.91104i	0.144641	+	0.250525i	−0.784598	+	0.620005i	$0.787131\pi$
$762$		0			0
$763$	1.39641	−	0.694029i	0.0505534	−	0.0251255i
$764$		0			0
$765$	4.56150	+	10.0259i	0.164922	+	0.362486i
$766$		0			0
$767$	−19.3402	−	11.1661i	−0.698333	−	0.403183i
$768$		0			0
$769$			11.8900i			0.428766i	0.976750	+	0.214383i	$0.0687740\pi$
$769$			11.8900i			0.428766i	−0.976750	+	0.214383i	$0.931226\pi$
$770$		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	$-0.559814\pi$
$773$	−31.4449	−	18.1547i	−1.13099	−	0.652979i	−0.944185	+	0.329417i	$0.893148\pi$
$774$		0			0
$775$	−6.01902	+	3.47508i	−0.216210	+	0.124829i
$776$		0			0
$777$	−0.266891	−	1.75233i	−0.00957465	−	0.0628644i
$778$		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	−0.960691	−	0.277621i	$-0.910454\pi$
$787$	−6.73055	+	11.6577i	−0.239918	+	0.415551i	0.720772	+	0.693172i	$0.243787\pi$
$788$		0			0
$789$	50.0638	+	16.0427i	1.78232	+	0.571137i
$790$		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
$795$	−11.8788	−	54.7927i	−0.421297	−	1.94330i
$796$		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
$801$	−33.8891	−	24.2047i	−1.19741	−	0.855232i
$802$		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
$807$	−1.30411	−	0.417895i	−0.0459067	−	0.0147106i
$808$		0			0
$809$	2.99316	+	1.72810i	0.105234	+	0.0607569i	0.551693	−	0.834047i	$-0.313982\pi$
$809$	2.99316	+	1.72810i	0.105234	+	0.0607569i	−0.446459	+	0.894804i	$0.647315\pi$
$810$		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
$819$	7.52542	−	46.9413i	0.262959	−	1.64026i
$820$		0			0
$821$	22.3394	+	38.6931i	0.779652	+	1.35040i	0.932142	+	0.362092i	$0.117937\pi$
$821$	22.3394	+	38.6931i	0.779652	+	1.35040i	−0.152490	+	0.988305i	$0.548729\pi$
$822$		0			0
$823$	−21.1932	+	36.7076i	−0.738747	+	1.27955i	0.214312	+	0.976765i	$0.431249\pi$
$823$	−21.1932	+	36.7076i	−0.738747	+	1.27955i	−0.953060	+	0.302783i	$0.902084\pi$
$824$		0			0
$825$	6.50352	+	7.16430i	0.226424	+	0.249429i
$826$		0			0
$827$	−9.18843			−0.319513			−0.159757	−	0.987156i	$-0.551071\pi$
$827$	−9.18843			−0.319513			−0.159757	+	0.987156i	$0.551071\pi$
$828$		0			0
$829$	−13.0225	+	22.5556i	−0.452290	+	0.783389i	−0.998528	−	0.0542413i	$-0.982726\pi$
$829$	−13.0225	+	22.5556i	−0.452290	+	0.783389i	0.546238	+	0.837630i	$0.316059\pi$
$830$		0			0
$831$	29.3581	+	9.40769i	1.01842	+	0.326349i
$832$		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
$837$	−7.98437	+	0.937445i	−0.275980	+	0.0324029i
$838$		0			0
$839$	−31.2096			−1.07748			−0.538738	−	0.842473i	$-0.681099\pi$
$839$	−31.2096			−1.07748			−0.538738	+	0.842473i	$0.681099\pi$
$840$		0			0
$841$	−18.7664			−0.647116
$842$		0			0
$843$	10.2438	+	47.2509i	0.352814	+	1.62741i
$844$		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
$849$	1.91537	−	5.97721i	0.0657354	−	0.205137i
$850$		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	−0.477137	−	0.878829i	$-0.658325\pi$
$857$	15.2965	−	26.4944i	0.522520	−	0.905031i	0.999657	−	0.0262016i	$-0.00834119\pi$
$858$		0			0
$859$	12.2711	+	21.2542i	0.418684	+	0.725183i	0.995807	−	0.0914746i	$-0.0291580\pi$
$859$	12.2711	+	21.2542i	0.418684	+	0.725183i	−0.577123	+	0.816657i	$0.695825\pi$
$860$		0			0
$861$	15.7432	−	40.2961i	0.536528	−	1.37329i
$862$		0			0
$863$	32.1415	−	18.5569i	1.09411	−	0.631684i	0.159441	−	0.987207i	$-0.449031\pi$
$863$	32.1415	−	18.5569i	1.09411	−	0.631684i	0.934667	+	0.355523i	$0.115697\pi$
$864$		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
$873$	21.3054	+	46.8277i	0.721078	+	1.58488i
$874$		0			0
$875$	−3.44850	−	2.28877i	−0.116581	−	0.0773744i
$876$		0			0
$877$	−28.4107	+	16.4029i	−0.959360	+	0.553887i	−0.895976	−	0.444103i	$-0.853523\pi$
$877$	−28.4107	+	16.4029i	−0.959360	+	0.553887i	−0.0633837	+	0.997989i	$0.520189\pi$
$878$		0			0
$879$	−3.58548	−	16.5386i	−0.120935	−	0.557832i
$880$		0			0
$881$	−27.1405			−0.914385			−0.457193	−	0.889368i	$-0.651145\pi$
$881$	−27.1405			−0.914385			−0.457193	+	0.889368i	$0.651145\pi$
$882$		0			0
$883$		−	47.9537i		−	1.61377i	−0.590709	−	0.806884i	$-0.701152\pi$
$883$		−	47.9537i		−	1.61377i	0.590709	−	0.806884i	$-0.298848\pi$
$884$		0			0
$885$	19.4449	−	4.21556i	0.653633	−	0.141704i
$886$		0			0
$887$	14.5502	+	25.2017i	0.488548	+	0.846190i	0.999913	−	0.0131735i	$-0.00419338\pi$
$887$	14.5502	+	25.2017i	0.488548	+	0.846190i	−0.511365	+	0.859364i	$0.670860\pi$
$888$		0			0
$889$	8.61372	−	12.9784i	0.288895	−	0.435280i
$890$		0			0
$891$	3.63058	+	10.5868i	0.121629	+	0.354672i
$892$		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
$903$	35.3873	+	13.8254i	1.17762	+	0.460081i
$904$		0			0
$905$	44.3263	−	25.5918i	1.47346	−	0.850700i
$906$		0			0
$907$	1.60692	+	0.927757i	0.0533570	+	0.0308057i	0.526441	−	0.850212i	$-0.323526\pi$
$907$	1.60692	+	0.927757i	0.0533570	+	0.0308057i	−0.473084	+	0.881017i	$0.656859\pi$
$908$		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
$915$	32.1672	+	10.3078i	1.06341	+	0.340767i
$916$		0			0
$917$	−0.700333	+	11.2184i	−0.0231270	+	0.370463i
$918$		0			0
$919$	−14.5126	−	25.1365i	−0.478726	−	0.829177i	0.520977	−	0.853571i	$-0.325568\pi$
$919$	−14.5126	−	25.1365i	−0.478726	−	0.829177i	−0.999702	+	0.0243939i	$0.992234\pi$
$920$		0			0
$921$	16.1978	−	3.51161i	0.533737	−	0.115712i
$922$		0			0
$923$			37.2012i			1.22449i
$924$		0			0
$925$		−	1.73760i		−	0.0571318i
$926$		0			0
$927$	−21.6774	+	30.3505i	−0.711978	+	0.996841i
$928$		0			0
$929$	14.7335	+	25.5191i	0.483390	+	0.837255i	0.999818	−	0.0190749i	$-0.00607211\pi$
$929$	14.7335	+	25.5191i	0.483390	+	0.837255i	−0.516428	+	0.856330i	$0.672739\pi$
$930$		0			0
$931$	5.19155	−	6.85342i	0.170146	−	0.224612i
$932$		0			0
$933$	9.35719	−	29.2005i	0.306341	−	0.955982i
$934$		0			0
$935$	−3.95414	−	2.28292i	−0.129314	−	0.0746596i
$936$		0			0
$937$			23.9964i			0.783929i	0.919980	+	0.391965i	$0.128204\pi$
$937$			23.9964i			0.783929i	−0.919980	+	0.391965i	$0.871796\pi$
$938$		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	$-0.0809473\pi$
$941$	37.8505	+	21.8530i	1.23389	+	0.712387i	0.266052	+	0.963959i	$0.414281\pi$
$942$		0			0
$943$	24.2582	−	14.0055i	0.789955	−	0.456081i
$944$		0			0
$945$	23.1457	+	35.4727i	0.752931	+	1.15393i
$946$		0			0
$947$	15.9345	+	27.5994i	0.517802	+	0.896859i	0.999786	+	0.0206793i	$0.00658291\pi$
$947$	15.9345	+	27.5994i	0.517802	+	0.896859i	−0.481984	+	0.876180i	$0.660084\pi$
$948$		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
$957$	−2.10267	+	6.56171i	−0.0679698	+	0.212110i
$958$		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
$963$	−23.3888	−	16.7051i	−0.753693	−	0.538313i
$964$		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
$969$	2.47767	−	0.537148i	0.0795944	−	0.0172557i
$970$		0			0
$971$	−41.9333	+	24.2102i	−1.34570	+	0.776943i	−0.987638	−	0.156753i	$-0.949897\pi$
$971$	−41.9333	+	24.2102i	−1.34570	+	0.776943i	−0.358067	+	0.933696i	$0.616564\pi$
$972$		0			0
$973$	8.11583	−	12.2282i	0.260182	−	0.392018i
$974$		0			0
$975$	14.2216	−	44.3807i	0.455456	−	1.42132i
$976$		0			0
$977$	−46.0630	−	26.5945i	−1.47369	−	0.850833i	−0.474125	−	0.880458i	$-0.657235\pi$
$977$	−46.0630	−	26.5945i	−1.47369	−	0.850833i	−0.999561	+	0.0296250i	$0.990569\pi$
$978$		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	$-0.915248\pi$
$983$	−7.97962	+	13.8211i	−0.254510	+	0.440825i	0.710252	+	0.703947i	$0.248581\pi$
$984$		0			0
$985$	43.8174	−	25.2980i	1.39614	−	0.806061i
$986$		0			0
$987$	−30.2848	+	4.61256i	−0.963975	+	0.146820i
$988$		0			0
$989$	12.2994	+	21.3031i	0.391097	+	0.677400i
$990$		0			0
$991$	4.26387	−	7.38524i	0.135446	−	0.234600i	−0.790322	−	0.612692i	$-0.790086\pi$
$991$	4.26387	−	7.38524i	0.135446	−	0.234600i	0.925768	+	0.378092i	$0.123420\pi$
$992$		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	−0.557564	−	0.830134i	$-0.688264\pi$
$997$	13.8974	−	24.0710i	0.440136	−	0.762337i	0.997699	+	0.0677970i	$0.0215970\pi$
$998$		0			0
$999$	0.795108	−	1.84591i	0.0251561	−	0.0584019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.22		48
3.2	odd	2	inner	672.2.bi.c.17.10		48
4.3	odd	2		168.2.ba.c.101.20	yes	48
7.5	odd	6	inner	672.2.bi.c.593.15		48
8.3	odd	2		168.2.ba.c.101.13	yes	48
8.5	even	2	inner	672.2.bi.c.17.3		48
12.11	even	2		168.2.ba.c.101.5	yes	48
21.5	even	6	inner	672.2.bi.c.593.3		48
24.5	odd	2	inner	672.2.bi.c.17.15		48
24.11	even	2		168.2.ba.c.101.12	yes	48
28.19	even	6		168.2.ba.c.5.12	yes	48
56.5	odd	6	inner	672.2.bi.c.593.10		48
56.19	even	6		168.2.ba.c.5.5	✓	48
84.47	odd	6		168.2.ba.c.5.13	yes	48
168.5	even	6	inner	672.2.bi.c.593.22		48
168.131	odd	6		168.2.ba.c.5.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	56.19	even	6
168.2.ba.c.5.12	yes	48	28.19	even	6
168.2.ba.c.5.13	yes	48	84.47	odd	6
168.2.ba.c.5.20	yes	48	168.131	odd	6
168.2.ba.c.101.5	yes	48	12.11	even	2
168.2.ba.c.101.12	yes	48	24.11	even	2
168.2.ba.c.101.13	yes	48	8.3	odd	2
168.2.ba.c.101.20	yes	48	4.3	odd	2
672.2.bi.c.17.3		48	8.5	even	2	inner
672.2.bi.c.17.10		48	3.2	odd	2	inner
672.2.bi.c.17.15		48	24.5	odd	2	inner
672.2.bi.c.17.22		48	1.1	even	1	trivial
672.2.bi.c.593.3		48	21.5	even	6	inner
672.2.bi.c.593.10		48	56.5	odd	6	inner
672.2.bi.c.593.15		48	7.5	odd	6	inner
672.2.bi.c.593.22		48	168.5	even	6	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)

\(f(q)\)	\(=\)	\(q+(1.69273 - 0.366975i) q^{3} +(-2.66818 + 1.54047i) q^{5} +(1.46307 - 2.20441i) q^{7} +(2.73066 - 1.24238i) q^{9} +O(q^{10})\)	\(q+(1.69273 - 0.366975i) q^{3} +(-2.66818 + 1.54047i) q^{5} +(1.46307 - 2.20441i) q^{7} +(2.73066 - 1.24238i) q^{9} +(-0.621780 + 1.07696i) q^{11} +5.98957 q^{13} +(-3.95119 + 3.58676i) q^{15} +(0.595854 - 1.03205i) q^{17} +(0.614126 + 1.06370i) q^{19} +(1.66761 - 4.26838i) q^{21} +(2.56956 - 1.48354i) q^{23} +(2.24612 - 3.89040i) q^{25} +(4.16634 - 3.10509i) q^{27} +3.19900 q^{29} +(-1.33987 - 0.773574i) q^{31} +(-0.657290 + 2.05117i) q^{33} +(-0.507883 + 8.13559i) q^{35} +(0.334978 - 0.193399i) q^{37} +(10.1387 - 2.19802i) q^{39} +9.44060 q^{41} +8.29057i q^{43} +(-5.37204 + 7.52140i) q^{45} +(-3.34244 - 5.78928i) q^{47} +(-2.71887 - 6.45041i) q^{49} +(0.629882 - 1.96564i) q^{51} +(-5.25317 + 9.09875i) q^{53} -3.83135i q^{55} +(1.42990 + 1.57518i) q^{57} +(-3.22898 - 1.86425i) q^{59} +(-3.16493 - 5.48181i) q^{61} +(1.25642 - 7.83718i) q^{63} +(-15.9813 + 9.22678i) q^{65} +(-10.7324 - 6.19634i) q^{67} +(3.80515 - 3.45419i) q^{69} +6.21100i q^{71} +(-8.92963 - 5.15552i) q^{73} +(2.37440 - 7.40966i) q^{75} +(1.46435 + 2.94632i) q^{77} +(6.41425 + 11.1098i) q^{79} +(5.91299 - 6.78502i) q^{81} +5.22882i q^{83} +3.67159i q^{85} +(5.41505 - 1.17396i) q^{87} +(-6.94090 - 12.0220i) q^{89} +(8.76314 - 13.2035i) q^{91} +(-2.55192 - 0.817752i) q^{93} +(-3.27720 - 1.89209i) q^{95} +17.1489i q^{97} +(-0.359884 + 3.71328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 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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