LMFDB - Embedded newform 672.2.bi.c.17.3

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			17.3
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	0.234205	−	0.972187i	$-0.424751\pi$
$5$	2.66818	−	1.54047i	1.19325	−	0.688921i	0.959041	+	0.283266i	$0.0914180\pi$
$6$		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	−0.756933	−	0.653492i	$-0.773303\pi$
$11$	0.621780	−	1.07696i	0.187474	−	0.324714i	0.944407	+	0.328778i	$0.106637\pi$
$12$		0			0
$13$	−5.98957			−1.66121			−0.830604	−	0.556864i	$-0.812005\pi$
$13$	−5.98957			−1.66121			−0.830604	+	0.556864i	$0.812005\pi$
$14$		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	0.786942	−	0.617027i	$-0.211663\pi$
$19$	−0.614126	−	1.06370i	−0.140890	−	0.244029i	−0.927832	+	0.372998i	$0.878330\pi$
$20$		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	$-0.595993\pi$
$29$	−3.19900			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$30$		0			0
$31$	−1.33987	−	0.773574i	−0.240648	−	0.138938i	0.374827	−	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	−0.527282	−	0.849690i	$-0.676789\pi$
$37$	−0.334978	+	0.193399i	−0.0550700	+	0.0317947i	0.472212	+	0.881485i	$0.343456\pi$
$38$		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	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$		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	$-0.576750\pi$
$53$	5.25317	−	9.09875i	0.721578	−	1.24981i	0.960367	−	0.278738i	$-0.0899162\pi$
$54$		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	0.695238	−	0.718779i	$-0.255299\pi$
$59$	3.22898	+	1.86425i	0.420377	+	0.242705i	−0.274862	+	0.961484i	$0.588632\pi$
$60$		0			0
$61$	3.16493	+	5.48181i	0.405227	+	0.701874i	0.994348	−	0.106171i	$-0.0338590\pi$
$61$	3.16493	+	5.48181i	0.405227	+	0.701874i	−0.589121	+	0.808045i	$0.700526\pi$
$62$		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	0.982290	−	0.187369i	$-0.0599961\pi$
$67$	10.7324	+	6.19634i	1.31117	+	0.757003i	0.328878	+	0.944372i	$0.393329\pi$
$68$		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	$-0.907352\pi$
$83$		−	5.22882i		−	0.573938i	0.957940	−	0.286969i	$-0.0926476\pi$
$84$		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	0.636130	−	0.771582i	$-0.280534\pi$
$101$	2.87413	+	1.65938i	0.285986	+	0.165114i	−0.350144	+	0.936696i	$0.613867\pi$
$102$		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	0.999113	−	0.0421002i	$-0.0134049\pi$
$107$	4.79031	+	8.29706i	0.463097	+	0.802107i	−0.536017	+	0.844207i	$0.680072\pi$
$108$		0			0
$109$	−0.510424	−	0.294693i	−0.0488898	−	0.0282265i	0.475356	−	0.879794i	$-0.342319\pi$
$109$	−0.510424	−	0.294693i	−0.0488898	−	0.0282265i	−0.524246	+	0.851567i	$0.675653\pi$
$110$		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	−0.330586	−	0.943776i	$-0.607246\pi$
$131$	3.67922	−	2.12420i	0.321455	−	0.185592i	0.652041	+	0.758184i	$0.273913\pi$
$132$		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	$-0.575591\pi$
$139$	−5.54714			−0.470502			−0.235251	+	0.971935i	$0.575591\pi$
$140$		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	0.938336	−	0.345726i	$-0.112367\pi$
$149$	2.07219	+	3.58914i	0.169761	+	0.294034i	−0.768575	+	0.639760i	$0.779034\pi$
$150$		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	−0.965221	−	0.261437i	$-0.915804\pi$
$157$	−3.21017	+	5.56018i	−0.256200	+	0.443751i	0.709021	+	0.705187i	$0.249137\pi$
$158$		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	−0.0952672	−	0.995452i	$-0.530371\pi$
$163$	9.18195	−	5.30120i	0.719186	−	0.415222i	0.814453	+	0.580230i	$0.197037\pi$
$164$		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	−0.560247	−	0.828326i	$-0.689294\pi$
$173$	−1.61807	+	0.934192i	−0.123019	+	0.0710253i	0.437228	+	0.899351i	$0.355960\pi$
$174$		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	$-0.637221\pi$
$179$	7.73124	−	13.3909i	0.577860	−	1.00088i	0.995724	−	0.0923734i	$-0.0294454\pi$
$180$		0			0
$181$	16.6129			1.23483			0.617415	−	0.786638i	$-0.288180\pi$
$181$	16.6129			1.23483			0.617415	+	0.786638i	$0.288180\pi$
$182$		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	$-0.301088\pi$
$197$	16.4222			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$198$		0			0
$199$	−0.839396	−	0.484625i	−0.0595032	−	0.0343542i	0.469953	−	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	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$		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	0.356613	−	0.934252i	$-0.383932\pi$
$227$	−4.13075	−	2.38489i	−0.274167	−	0.158291i	−0.630780	+	0.775962i	$0.717265\pi$
$228$		0			0
$229$	0.743202	+	1.28726i	0.0491122	+	0.0850648i	0.889536	−	0.456864i	$-0.151027\pi$
$229$	0.743202	+	1.28726i	0.0491122	+	0.0850648i	−0.840424	+	0.541929i	$0.817694\pi$
$230$		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	$0.164465\pi$
$251$			15.6528i			0.987995i	−0.869463	+	0.493997i	$0.835535\pi$
$252$		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	0.520729	−	0.853722i	$-0.325660\pi$
$269$	0.684713	+	0.395319i	0.0417477	+	0.0241030i	−0.478981	+	0.877825i	$0.658994\pi$
$270$		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	−0.0405619	−	0.999177i	$-0.512915\pi$
$277$	−15.4143	−	8.89945i	−0.926156	−	0.534716i	−0.885594	+	0.464461i	$0.846248\pi$
$278$		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	$-0.867684\pi$
$283$	−1.81190	+	3.13830i	−0.107706	+	0.186552i	0.807134	+	0.590368i	$0.201017\pi$
$284$		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	$0.0921250\pi$
$293$			9.77037i			0.570791i	−0.958410	+	0.285396i	$0.907875\pi$
$294$		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	$-0.588038\pi$
$307$	−9.56907			−0.546136			−0.273068	+	0.961995i	$0.588038\pi$
$308$		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	0.896672	−	0.442696i	$-0.145978\pi$
$317$	1.15640	+	2.00294i	0.0649499	+	0.112497i	−0.831722	+	0.555193i	$0.812645\pi$
$318$		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	−0.946104	−	0.323863i	$-0.895018\pi$
$331$	−20.7165	+	11.9607i	−1.13868	+	0.657418i	−0.192578	+	0.981282i	$0.561685\pi$
$332$		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	−0.853024	−	0.521872i	$-0.825234\pi$
$347$	0.473950	−	0.820906i	0.0254430	−	0.0440686i	0.878467	+	0.477804i	$0.158567\pi$
$348$		0			0
$349$	14.1965			0.759919			0.379960	−	0.925003i	$-0.375938\pi$
$349$	14.1965			0.759919			0.379960	+	0.925003i	$0.375938\pi$
$350$		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	−0.613617	−	0.789604i	$-0.710286\pi$
$373$	−4.56967	+	2.63830i	−0.236609	+	0.136606i	0.377008	+	0.926210i	$0.376953\pi$
$374$		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	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$		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	−0.658811	−	0.752308i	$-0.728940\pi$
$389$	6.35306	−	11.0038i	0.322113	−	0.557916i	0.980924	+	0.194393i	$0.0622736\pi$
$390$		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	$0.0383026\pi$
$397$	11.9617	+	20.7184i	0.600343	+	1.03982i	−0.392426	+	0.919784i	$0.628364\pi$
$398$		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	$0.161212\pi$
$419$			19.8589i			0.970173i	−0.874466	+	0.485086i	$0.838788\pi$
$420$		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
$423$	−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	0.806611	−	0.591082i	$-0.201299\pi$
$443$	−2.28548	−	3.95856i	−0.108586	−	0.188077i	−0.915198	+	0.403005i	$0.867966\pi$
$444$		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	$0.200844\pi$
$461$			25.3326i			1.17986i	−0.807455	+	0.589929i	$0.799156\pi$
$462$		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	0.275348	−	0.961345i	$-0.411207\pi$
$467$	26.9170	−	15.5406i	1.24557	−	0.719131i	0.970223	+	0.242214i	$0.0778735\pi$
$468$		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	$-0.931892\pi$
$491$	−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
$495$	−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	0.448795	−	0.893635i	$-0.351853\pi$
$499$	32.3258	−	18.6633i	1.44710	−	0.835485i	0.998308	+	0.0581497i	$0.0185201\pi$
$500$		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	0.140694	−	0.990053i	$-0.455067\pi$
$509$	24.1054	−	13.9173i	1.06845	−	0.616871i	0.927758	+	0.373182i	$0.121733\pi$
$510$		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	0.671781	−	0.740750i	$-0.265530\pi$
$523$	−6.98922	−	12.1057i	−0.305617	−	0.529345i	−0.977399	+	0.211405i	$0.932196\pi$
$524$		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	−0.848277	−	0.529552i	$-0.822360\pi$
$541$	−18.9287	+	10.9285i	−0.813810	+	0.469853i	0.0344673	+	0.999406i	$0.489027\pi$
$542$		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	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$		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	−0.907873	−	0.419245i	$-0.862295\pi$
$557$	−2.14436	+	3.71415i	−0.0908596	+	0.157373i	0.817013	+	0.576619i	$0.195628\pi$
$558$		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	−0.199979	−	0.979800i	$-0.564087\pi$
$563$	−27.2512	−	15.7335i	−1.14850	−	0.663087i	−0.948521	+	0.316713i	$0.897421\pi$
$564$		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	0.968373	−	0.249506i	$-0.0802681\pi$
$571$	29.5465	+	17.0587i	1.23648	+	0.713883i	0.268108	+	0.963389i	$0.413601\pi$
$572$		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	$0.179666\pi$
$587$			25.9212i			1.06988i	−0.844890	+	0.534940i	$0.820334\pi$
$588$		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	0.810989	−	0.585061i	$-0.198930\pi$
$613$	17.5740	+	10.1463i	0.709805	+	0.409806i	−0.101184	+	0.994868i	$0.532263\pi$
$614$		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	$-0.740901\pi$
$619$	7.12358	−	12.3384i	0.286321	−	0.495922i	0.972929	+	0.231106i	$0.0742343\pi$
$620$		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	$-0.664941\pi$
$643$	−25.1189			−0.990594			−0.495297	+	0.868724i	$0.664941\pi$
$644$		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	$-0.835775\pi$
$653$	−22.0316	−	38.1599i	−0.862164	−	1.49331i	0.00767187	−	0.999971i	$-0.497558\pi$
$654$		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	−0.0845192	−	0.996422i	$-0.526935\pi$
$661$	21.0993	−	36.5450i	0.820667	−	1.42144i	0.905186	−	0.425015i	$-0.139731\pi$
$662$		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	−0.991436	−	0.130596i	$-0.958311\pi$
$677$	−35.7518	+	20.6413i	−1.37405	+	0.793310i	−0.382618	+	0.923907i	$0.624977\pi$
$678$		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	$-0.605733\pi$
$683$	17.1346	−	29.6781i	0.655638	−	1.13560i	0.981733	−	0.190262i	$-0.0609338\pi$
$684$		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	$-0.123233\pi$
$691$	3.57575	+	6.19338i	0.136028	+	0.235607i	−0.789962	+	0.613156i	$0.789900\pi$
$692$		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	$-0.424691\pi$
$701$	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
$705$	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	−0.948609	−	0.316450i	$-0.897509\pi$
$709$	−30.5908	+	17.6616i	−1.14886	+	0.663295i	−0.200251	+	0.979745i	$0.564176\pi$
$710$		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	0.926817	−	0.375514i	$-0.122534\pi$
$733$	3.74171	+	6.48083i	0.138203	+	0.239375i	−0.788613	+	0.614889i	$0.789201\pi$
$734$		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	0.457788	−	0.889061i	$-0.348642\pi$
$739$	−2.26360	−	1.30689i	−0.0832679	−	0.0480747i	−0.541056	+	0.840987i	$0.681975\pi$
$740$		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	$-0.934853\pi$
$757$		−	11.1837i		−	0.406478i	0.979129	−	0.203239i	$-0.0651469\pi$
$758$		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	0.944185	−	0.329417i	$-0.106852\pi$
$773$	31.4449	+	18.1547i	1.13099	+	0.652979i	0.186809	+	0.982396i	$0.440186\pi$
$774$		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	−0.720772	−	0.693172i	$-0.756213\pi$
$787$	6.73055	−	11.6577i	0.239918	−	0.415551i	0.960691	+	0.277621i	$0.0895460\pi$
$788$		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	$0.0796479\pi$
$797$			13.9811i			0.495236i	−0.968858	+	0.247618i	$0.920352\pi$
$798$		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	$-0.207133\pi$
$811$	45.3167			1.59129			0.795643	+	0.605766i	$0.207133\pi$
$812$		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	$-0.882063\pi$
$821$	−22.3394	−	38.6931i	−0.779652	−	1.35040i	0.152490	−	0.988305i	$-0.451271\pi$
$822$		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	$-0.448929\pi$
$827$	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	$-0.683941\pi$
$829$	13.0225	−	22.5556i	0.452290	−	0.783389i	0.998528	+	0.0542413i	$0.0172740\pi$
$830$		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	$-0.473912\pi$
$853$	4.78201			0.163733			0.0818665	+	0.996643i	$0.473912\pi$
$854$		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	0.577123	−	0.816657i	$-0.304175\pi$
$859$	−12.2711	−	21.2542i	−0.418684	−	0.725183i	−0.995807	+	0.0914746i	$0.970842\pi$
$860$		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	0.0633837	−	0.997989i	$-0.479811\pi$
$877$	28.4107	−	16.4029i	0.959360	−	0.553887i	0.895976	+	0.444103i	$0.146477\pi$
$878$		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	$0.298848\pi$
$883$			47.9537i			1.61377i	−0.590709	+	0.806884i	$0.701152\pi$
$884$		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	0.473084	−	0.881017i	$-0.343141\pi$
$907$	−1.60692	−	0.927757i	−0.0533570	−	0.0308057i	−0.526441	+	0.850212i	$0.676474\pi$
$908$		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	−0.266052	−	0.963959i	$-0.585719\pi$
$941$	−37.8505	−	21.8530i	−1.23389	−	0.712387i	−0.967839	+	0.251571i	$0.919053\pi$
$942$		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	$-0.993417\pi$
$947$	−15.9345	−	27.5994i	−0.517802	−	0.896859i	0.481984	−	0.876180i	$-0.339916\pi$
$948$		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	0.358067	−	0.933696i	$-0.383436\pi$
$971$	41.9333	−	24.2102i	1.34570	−	0.776943i	0.987638	+	0.156753i	$0.0501026\pi$
$972$		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	−0.997699	−	0.0677970i	$-0.978403\pi$
$997$	−13.8974	+	24.0710i	−0.440136	+	0.762337i	0.557564	+	0.830134i	$0.311736\pi$
$998$		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.17.3		48
3.2	odd	2	inner	672.2.bi.c.17.15		48
4.3	odd	2		168.2.ba.c.101.13	yes	48
7.5	odd	6	inner	672.2.bi.c.593.10		48
8.3	odd	2		168.2.ba.c.101.20	yes	48
8.5	even	2	inner	672.2.bi.c.17.22		48
12.11	even	2		168.2.ba.c.101.12	yes	48
21.5	even	6	inner	672.2.bi.c.593.22		48
24.5	odd	2	inner	672.2.bi.c.17.10		48
24.11	even	2		168.2.ba.c.101.5	yes	48
28.19	even	6		168.2.ba.c.5.5	✓	48
56.5	odd	6	inner	672.2.bi.c.593.15		48
56.19	even	6		168.2.ba.c.5.12	yes	48
84.47	odd	6		168.2.ba.c.5.20	yes	48
168.5	even	6	inner	672.2.bi.c.593.3		48
168.131	odd	6		168.2.ba.c.5.13	yes	48

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

\(f(q)\)	\(=\)	\(q+(-1.69273 + 0.366975i) q^{3} +(2.66818 - 1.54047i) q^{5} +(1.46307 - 2.20441i) q^{7} +(2.73066 - 1.24238i) q^{9} +(0.621780 - 1.07696i) q^{11} -5.98957 q^{13} +(-3.95119 + 3.58676i) q^{15} +(0.595854 - 1.03205i) q^{17} +(-0.614126 - 1.06370i) q^{19} +(-1.66761 + 4.26838i) q^{21} +(2.56956 - 1.48354i) q^{23} +(2.24612 - 3.89040i) q^{25} +(-4.16634 + 3.10509i) q^{27} -3.19900 q^{29} +(-1.33987 - 0.773574i) q^{31} +(-0.657290 + 2.05117i) q^{33} +(0.507883 - 8.13559i) q^{35} +(-0.334978 + 0.193399i) q^{37} +(10.1387 - 2.19802i) q^{39} +9.44060 q^{41} -8.29057i q^{43} +(5.37204 - 7.52140i) q^{45} +(-3.34244 - 5.78928i) q^{47} +(-2.71887 - 6.45041i) q^{49} +(-0.629882 + 1.96564i) q^{51} +(5.25317 - 9.09875i) q^{53} -3.83135i q^{55} +(1.42990 + 1.57518i) q^{57} +(3.22898 + 1.86425i) q^{59} +(3.16493 + 5.48181i) q^{61} +(1.25642 - 7.83718i) q^{63} +(-15.9813 + 9.22678i) q^{65} +(10.7324 + 6.19634i) q^{67} +(-3.80515 + 3.45419i) q^{69} +6.21100i q^{71} +(-8.92963 - 5.15552i) q^{73} +(-2.37440 + 7.40966i) q^{75} +(-1.46435 - 2.94632i) q^{77} +(6.41425 + 11.1098i) q^{79} +(5.91299 - 6.78502i) q^{81} -5.22882i q^{83} -3.67159i q^{85} +(5.41505 - 1.17396i) q^{87} +(-6.94090 - 12.0220i) q^{89} +(-8.76314 + 13.2035i) q^{91} +(2.55192 + 0.817752i) q^{93} +(-3.27720 - 1.89209i) q^{95} +17.1489i q^{97} +(0.359884 - 3.71328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 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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