LMFDB - Embedded newform 1920.2.w.i.127.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.5
Root			$-0.324536i$ of defining polynomial
Character	$\chi$	$=$	1920.127
Dual form			1920.2.w.i.1663.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(0.893756 - 2.04968i) q^{5} +(-0.804999 + 0.804999i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(0.893756 - 2.04968i) q^{5} +(-0.804999 + 0.804999i) q^{7} +1.00000i q^{9} -3.13844i q^{11} +(-3.89869 + 3.89869i) q^{13} +(2.08133 - 0.817364i) q^{15} +(-5.24962 - 5.24962i) q^{17} -7.36438 q^{19} -1.13844 q^{21} +(2.24647 + 2.24647i) q^{23} +(-3.40240 - 3.66383i) q^{25} +(-0.707107 + 0.707107i) q^{27} +0.869586i q^{29} +10.8478i q^{31} +(2.21921 - 2.21921i) q^{33} +(0.930520 + 2.36946i) q^{35} +(-6.85962 - 6.85962i) q^{37} -5.51358 q^{39} -9.93530 q^{41} +(1.35093 + 1.35093i) q^{43} +(2.04968 + 0.893756i) q^{45} +(1.96959 - 1.96959i) q^{47} +5.70395i q^{49} -7.42408i q^{51} +(3.06643 - 3.06643i) q^{53} +(-6.43281 - 2.80500i) q^{55} +(-5.20740 - 5.20740i) q^{57} +5.97822 q^{59} +3.07947 q^{61} +(-0.804999 - 0.804999i) q^{63} +(4.50660 + 11.4756i) q^{65} +(9.02716 - 9.02716i) q^{67} +3.17699i q^{69} +10.8558i q^{71} +(-0.566997 + 0.566997i) q^{73} +(0.184859 - 4.99658i) q^{75} +(2.52644 + 2.52644i) q^{77} -6.65275 q^{79} -1.00000 q^{81} +(-6.74844 - 6.74844i) q^{83} +(-15.4519 + 6.06818i) q^{85} +(-0.614890 + 0.614890i) q^{87} -1.30443i q^{89} -6.27688i q^{91} +(-7.67056 + 7.67056i) q^{93} +(-6.58195 + 15.0946i) q^{95} +(-0.0310479 - 0.0310479i) q^{97} +3.13844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	0.893756	−	2.04968i	0.399700	−	0.916646i
$5$	0.893756	−	2.04968i	0.399700	−	0.916646i
$6$		0			0
$7$	−0.804999	+	0.804999i	−0.304261	+	0.304261i	−0.842678	−	0.538417i	$-0.819022\pi$
$7$	−0.804999	+	0.804999i	−0.304261	+	0.304261i	0.538417	+	0.842678i	$0.319022\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	3.13844i		−	0.946275i	−0.880989	−	0.473138i	$-0.843121\pi$
$11$		−	3.13844i		−	0.946275i	0.880989	−	0.473138i	$-0.156879\pi$
$12$		0			0
$13$	−3.89869	+	3.89869i	−1.08130	+	1.08130i	−0.0849136	+	0.996388i	$0.527061\pi$
$13$	−3.89869	+	3.89869i	−1.08130	+	1.08130i	−0.996388	+	0.0849136i	$0.972939\pi$
$14$		0			0
$15$	2.08133	−	0.817364i	0.537396	−	0.211043i
$16$		0			0
$17$	−5.24962	−	5.24962i	−1.27322	−	1.27322i	−0.944389	−	0.328831i	$-0.893346\pi$
$17$	−5.24962	−	5.24962i	−1.27322	−	1.27322i	−0.328831	−	0.944389i	$-0.606654\pi$
$18$		0			0
$19$	−7.36438			−1.68950			−0.844752	−	0.535158i	$-0.820252\pi$
$19$	−7.36438			−1.68950			−0.844752	+	0.535158i	$0.820252\pi$
$20$		0			0
$21$	−1.13844			−0.248428
$22$		0			0
$23$	2.24647	+	2.24647i	0.468422	+	0.468422i	0.901403	−	0.432981i	$-0.142538\pi$
$23$	2.24647	+	2.24647i	0.468422	+	0.468422i	−0.432981	+	0.901403i	$0.642538\pi$
$24$		0			0
$25$	−3.40240	−	3.66383i	−0.680480	−	0.732766i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$			0.869586i			0.161478i	0.996735	+	0.0807390i	$0.0257280\pi$
$29$			0.869586i			0.161478i	−0.996735	+	0.0807390i	$0.974272\pi$
$30$		0			0
$31$			10.8478i			1.94832i	0.225852	+	0.974162i	$0.427483\pi$
$31$			10.8478i			1.94832i	−0.225852	+	0.974162i	$0.572517\pi$
$32$		0			0
$33$	2.21921	−	2.21921i	0.386315	−	0.386315i
$34$		0			0
$35$	0.930520	+	2.36946i	0.157287	+	0.400513i
$36$		0			0
$37$	−6.85962	−	6.85962i	−1.12771	−	1.12771i	−0.990548	−	0.137166i	$-0.956201\pi$
$37$	−6.85962	−	6.85962i	−1.12771	−	1.12771i	−0.137166	−	0.990548i	$-0.543799\pi$
$38$		0			0
$39$	−5.51358			−0.882879
$40$		0			0
$41$	−9.93530			−1.55163			−0.775817	−	0.630959i	$-0.782662\pi$
$41$	−9.93530			−1.55163			−0.775817	+	0.630959i	$0.782662\pi$
$42$		0			0
$43$	1.35093	+	1.35093i	0.206015	+	0.206015i	0.802571	−	0.596556i	$-0.203465\pi$
$43$	1.35093	+	1.35093i	0.206015	+	0.206015i	−0.596556	+	0.802571i	$0.703465\pi$
$44$		0			0
$45$	2.04968	+	0.893756i	0.305549	+	0.133233i
$46$		0			0
$47$	1.96959	−	1.96959i	0.287295	−	0.287295i	−0.548715	−	0.836010i	$-0.684883\pi$
$47$	1.96959	−	1.96959i	0.287295	−	0.287295i	0.836010	+	0.548715i	$0.184883\pi$
$48$		0			0
$49$			5.70395i			0.814851i
$50$		0			0
$51$		−	7.42408i		−	1.03958i
$52$		0			0
$53$	3.06643	−	3.06643i	0.421206	−	0.421206i	−0.464413	−	0.885619i	$-0.653735\pi$
$53$	3.06643	−	3.06643i	0.421206	−	0.421206i	0.885619	+	0.464413i	$0.153735\pi$
$54$		0			0
$55$	−6.43281	−	2.80500i	−0.867400	−	0.378226i
$56$		0			0
$57$	−5.20740	−	5.20740i	−0.689737	−	0.689737i
$58$		0			0
$59$	5.97822			0.778298			0.389149	−	0.921175i	$-0.372769\pi$
$59$	5.97822			0.778298			0.389149	+	0.921175i	$0.372769\pi$
$60$		0			0
$61$	3.07947			0.394286			0.197143	−	0.980375i	$-0.436834\pi$
$61$	3.07947			0.394286			0.197143	+	0.980375i	$0.436834\pi$
$62$		0			0
$63$	−0.804999	−	0.804999i	−0.101420	−	0.101420i
$64$		0			0
$65$	4.50660	+	11.4756i	0.558975	+	1.42337i
$66$		0			0
$67$	9.02716	−	9.02716i	1.10284	−	1.10284i	0.108777	−	0.994066i	$-0.465307\pi$
$67$	9.02716	−	9.02716i	1.10284	−	1.10284i	0.994066	−	0.108777i	$-0.0346934\pi$
$68$		0			0
$69$			3.17699i			0.382465i
$70$		0			0
$71$			10.8558i			1.28835i	0.764878	+	0.644175i	$0.222799\pi$
$71$			10.8558i			1.28835i	−0.764878	+	0.644175i	$0.777201\pi$
$72$		0			0
$73$	−0.566997	+	0.566997i	−0.0663620	+	0.0663620i	−0.739509	−	0.673147i	$-0.764942\pi$
$73$	−0.566997	+	0.566997i	−0.0663620	+	0.0663620i	0.673147	+	0.739509i	$0.264942\pi$
$74$		0			0
$75$	0.184859	−	4.99658i	0.0213457	−	0.576956i
$76$		0			0
$77$	2.52644	+	2.52644i	0.287915	+	0.287915i
$78$		0			0
$79$	−6.65275			−0.748493			−0.374247	−	0.927329i	$-0.622099\pi$
$79$	−6.65275			−0.748493			−0.374247	+	0.927329i	$0.622099\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−6.74844	−	6.74844i	−0.740737	−	0.740737i	0.231983	−	0.972720i	$-0.425479\pi$
$83$	−6.74844	−	6.74844i	−0.740737	−	0.740737i	−0.972720	+	0.231983i	$0.925479\pi$
$84$		0			0
$85$	−15.4519	+	6.06818i	−1.67600	+	0.658186i
$86$		0			0
$87$	−0.614890	+	0.614890i	−0.0659231	+	0.0659231i
$88$		0			0
$89$		−	1.30443i		−	0.138269i	−0.997607	−	0.0691347i	$-0.977976\pi$
$89$		−	1.30443i		−	0.138269i	0.997607	−	0.0691347i	$-0.0220238\pi$
$90$		0			0
$91$		−	6.27688i		−	0.657996i
$92$		0			0
$93$	−7.67056	+	7.67056i	−0.795400	+	0.795400i
$94$		0			0
$95$	−6.58195	+	15.0946i	−0.675294	+	1.54868i
$96$		0			0
$97$	−0.0310479	−	0.0310479i	−0.00315244	−	0.00315244i	0.705529	−	0.708681i	$-0.250710\pi$
$97$	−0.0310479	−	0.0310479i	−0.00315244	−	0.00315244i	−0.708681	+	0.705529i	$0.750710\pi$
$98$		0			0
$99$	3.13844			0.315425
$100$		0			0
$101$	−9.15521			−0.910978			−0.455489	−	0.890242i	$-0.650535\pi$
$101$	−9.15521			−0.910978			−0.455489	+	0.890242i	$0.650535\pi$
$102$		0			0
$103$	3.62800	+	3.62800i	0.357478	+	0.357478i	0.862882	−	0.505405i	$-0.168657\pi$
$103$	3.62800	+	3.62800i	0.357478	+	0.357478i	−0.505405	+	0.862882i	$0.668657\pi$
$104$		0			0
$105$	−1.01749	+	2.33344i	−0.0992966	+	0.227721i
$106$		0			0
$107$	3.88872	−	3.88872i	0.375937	−	0.375937i	−0.493697	−	0.869634i	$-0.664355\pi$
$107$	3.88872	−	3.88872i	0.375937	−	0.375937i	0.869634	+	0.493697i	$0.164355\pi$
$108$		0			0
$109$		−	4.08183i		−	0.390969i	−0.980707	−	0.195484i	$-0.937372\pi$
$109$		−	4.08183i		−	0.390969i	0.980707	−	0.195484i	$-0.0626279\pi$
$110$		0			0
$111$		−	9.70096i		−	0.920775i
$112$		0			0
$113$	−7.79359	+	7.79359i	−0.733160	+	0.733160i	−0.971244	−	0.238085i	$-0.923480\pi$
$113$	−7.79359	+	7.79359i	−0.733160	+	0.733160i	0.238085	+	0.971244i	$0.423480\pi$
$114$		0			0
$115$	6.61236	−	2.59676i	0.616606	−	0.242149i
$116$		0			0
$117$	−3.89869	−	3.89869i	−0.360434	−	0.360434i
$118$		0			0
$119$	8.45187			0.774782
$120$		0			0
$121$	1.15019			0.104563
$122$		0			0
$123$	−7.02532	−	7.02532i	−0.633452	−	0.633452i
$124$		0			0
$125$	−10.5506	+	3.69927i	−0.943675	+	0.330873i
$126$		0			0
$127$	6.58300	−	6.58300i	0.584147	−	0.584147i	−0.351893	−	0.936040i	$-0.614462\pi$
$127$	6.58300	−	6.58300i	0.584147	−	0.584147i	0.936040	+	0.351893i	$0.114462\pi$
$128$		0			0
$129$			1.91050i			0.168210i
$130$		0			0
$131$			9.81527i			0.857564i	0.903408	+	0.428782i	$0.141057\pi$
$131$			9.81527i			0.857564i	−0.903408	+	0.428782i	$0.858943\pi$
$132$		0			0
$133$	5.92831	−	5.92831i	0.514050	−	0.514050i
$134$		0			0
$135$	0.817364	+	2.08133i	0.0703475	+	0.179132i
$136$		0			0
$137$	−8.60857	−	8.60857i	−0.735480	−	0.735480i	0.236220	−	0.971700i	$-0.424092\pi$
$137$	−8.60857	−	8.60857i	−0.735480	−	0.735480i	−0.971700	+	0.236220i	$0.924092\pi$
$138$		0			0
$139$	−5.62520			−0.477124			−0.238562	−	0.971127i	$-0.576676\pi$
$139$	−5.62520			−0.477124			−0.238562	+	0.971127i	$0.576676\pi$
$140$		0			0
$141$	2.78543			0.234575
$142$		0			0
$143$	12.2358	+	12.2358i	1.02321	+	1.02321i
$144$		0			0
$145$	1.78238	+	0.777197i	0.148018	+	0.0645427i
$146$		0			0
$147$	−4.03330	+	4.03330i	−0.332661	+	0.332661i
$148$		0			0
$149$		−	15.8320i		−	1.29701i	−0.761210	−	0.648506i	$-0.775394\pi$
$149$		−	15.8320i		−	1.29701i	0.761210	−	0.648506i	$-0.224606\pi$
$150$		0			0
$151$		−	3.40196i		−	0.276847i	−0.990373	−	0.138424i	$-0.955796\pi$
$151$		−	3.40196i		−	0.276847i	0.990373	−	0.138424i	$-0.0442035\pi$
$152$		0			0
$153$	5.24962	−	5.24962i	0.424406	−	0.424406i
$154$		0			0
$155$	22.2346	+	9.69529i	1.78592	+	0.778744i
$156$		0			0
$157$	2.29411	+	2.29411i	0.183090	+	0.183090i	0.792701	−	0.609611i	$-0.208674\pi$
$157$	2.29411	+	2.29411i	0.183090	+	0.183090i	−0.609611	+	0.792701i	$0.708674\pi$
$158$		0			0
$159$	4.33659			0.343914
$160$		0			0
$161$	−3.61682			−0.285045
$162$		0			0
$163$	−8.64907	−	8.64907i	−0.677448	−	0.677448i	0.281974	−	0.959422i	$-0.409011\pi$
$163$	−8.64907	−	8.64907i	−0.677448	−	0.677448i	−0.959422	+	0.281974i	$0.909011\pi$
$164$		0			0
$165$	−2.56525	−	6.53212i	−0.199704	−	0.508524i
$166$		0			0
$167$	−2.72248	+	2.72248i	−0.210672	+	0.210672i	−0.804553	−	0.593881i	$-0.797595\pi$
$167$	−2.72248	+	2.72248i	−0.210672	+	0.210672i	0.593881	+	0.804553i	$0.297595\pi$
$168$		0			0
$169$		−	17.3996i		−	1.33843i
$170$		0			0
$171$		−	7.36438i		−	0.563168i
$172$		0			0
$173$	11.0814	−	11.0814i	0.842500	−	0.842500i	−0.146683	−	0.989183i	$-0.546860\pi$
$173$	11.0814	−	11.0814i	0.842500	−	0.842500i	0.989183	+	0.146683i	$0.0468598\pi$
$174$		0			0
$175$	5.68831	+	0.210451i	0.429996	+	0.0159086i
$176$		0			0
$177$	4.22724	+	4.22724i	0.317739	+	0.317739i
$178$		0			0
$179$	15.7174			1.17477			0.587386	−	0.809307i	$-0.300157\pi$
$179$	15.7174			1.17477			0.587386	+	0.809307i	$0.300157\pi$
$180$		0			0
$181$	−6.81058			−0.506227			−0.253113	−	0.967437i	$-0.581455\pi$
$181$	−6.81058			−0.506227			−0.253113	+	0.967437i	$0.581455\pi$
$182$		0			0
$183$	2.17751	+	2.17751i	0.160966	+	0.160966i
$184$		0			0
$185$	−20.1909	+	7.92922i	−1.48446	+	0.582968i
$186$		0			0
$187$	−16.4756	+	16.4756i	−1.20482	+	1.20482i
$188$		0			0
$189$		−	1.13844i		−	0.0828093i
$190$		0			0
$191$		−	8.98958i		−	0.650463i	−0.945634	−	0.325232i	$-0.894558\pi$
$191$		−	8.98958i		−	0.650463i	0.945634	−	0.325232i	$-0.105442\pi$
$192$		0			0
$193$	9.37180	−	9.37180i	0.674597	−	0.674597i	−0.284175	−	0.958772i	$-0.591720\pi$
$193$	9.37180	−	9.37180i	0.674597	−	0.674597i	0.958772	+	0.284175i	$0.0917198\pi$
$194$		0			0
$195$	−4.92779	+	11.3011i	−0.352887	+	0.809288i
$196$		0			0
$197$	−13.0052	−	13.0052i	−0.926584	−	0.926584i	0.0708995	−	0.997483i	$-0.477413\pi$
$197$	−13.0052	−	13.0052i	−0.926584	−	0.926584i	−0.997483	+	0.0708995i	$0.977413\pi$
$198$		0			0
$199$	−23.1478			−1.64090			−0.820452	−	0.571715i	$-0.806278\pi$
$199$	−23.1478			−1.64090			−0.820452	+	0.571715i	$0.806278\pi$
$200$		0			0
$201$	12.7663			0.900468
$202$		0			0
$203$	−0.700016	−	0.700016i	−0.0491315	−	0.0491315i
$204$		0			0
$205$	−8.87973	+	20.3642i	−0.620187	+	1.42230i
$206$		0			0
$207$	−2.24647	+	2.24647i	−0.156141	+	0.156141i
$208$		0			0
$209$			23.1127i			1.59874i
$210$		0			0
$211$		−	26.7992i		−	1.84493i	−0.386081	−	0.922465i	$-0.626171\pi$
$211$		−	26.7992i		−	1.84493i	0.386081	−	0.922465i	$-0.373829\pi$
$212$		0			0
$213$	−7.67623	+	7.67623i	−0.525967	+	0.525967i
$214$		0			0
$215$	3.97638	−	1.56158i	0.271187	−	0.106499i
$216$		0			0
$217$	−8.73247	−	8.73247i	−0.592799	−	0.592799i
$218$		0			0
$219$	−0.801855			−0.0541843
$220$		0			0
$221$	40.9333			2.75347
$222$		0			0
$223$	−6.95567	−	6.95567i	−0.465786	−	0.465786i	0.434760	−	0.900546i	$-0.356833\pi$
$223$	−6.95567	−	6.95567i	−0.465786	−	0.465786i	−0.900546	+	0.434760i	$0.856833\pi$
$224$		0			0
$225$	3.66383	−	3.40240i	0.244255	−	0.226827i
$226$		0			0
$227$	−12.8508	+	12.8508i	−0.852935	+	0.852935i	−0.990494	−	0.137558i	$-0.956075\pi$
$227$	−12.8508	+	12.8508i	−0.852935	+	0.852935i	0.137558	+	0.990494i	$0.456075\pi$
$228$		0			0
$229$			9.53535i			0.630113i	0.949073	+	0.315057i	$0.102024\pi$
$229$			9.53535i			0.630113i	−0.949073	+	0.315057i	$0.897976\pi$
$230$		0			0
$231$			3.57293i			0.235081i
$232$		0			0
$233$	3.74296	−	3.74296i	0.245209	−	0.245209i	−0.573792	−	0.819001i	$-0.694528\pi$
$233$	3.74296	−	3.74296i	0.245209	−	0.245209i	0.819001	+	0.573792i	$0.194528\pi$
$234$		0			0
$235$	−2.27671	−	5.79738i	−0.148516	−	0.378179i
$236$		0			0
$237$	−4.70421	−	4.70421i	−0.305571	−	0.305571i
$238$		0			0
$239$	−9.53499			−0.616767			−0.308383	−	0.951262i	$-0.599788\pi$
$239$	−9.53499			−0.616767			−0.308383	+	0.951262i	$0.599788\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	11.6913	+	5.09794i	0.746930	+	0.325696i
$246$		0			0
$247$	28.7114	−	28.7114i	1.82686	−	1.82686i
$248$		0			0
$249$		−	9.54373i		−	0.604809i
$250$		0			0
$251$		−	11.1224i		−	0.702039i	−0.936368	−	0.351019i	$-0.885835\pi$
$251$		−	11.1224i		−	0.702039i	0.936368	−	0.351019i	$-0.114165\pi$
$252$		0			0
$253$	7.05042	−	7.05042i	0.443256	−	0.443256i
$254$		0			0
$255$	−15.2170	−	6.63532i	−0.952926	−	0.415520i
$256$		0			0
$257$	5.53785	+	5.53785i	0.345442	+	0.345442i	0.858408	−	0.512967i	$-0.171454\pi$
$257$	5.53785	+	5.53785i	0.345442	+	0.345442i	−0.512967	+	0.858408i	$0.671454\pi$
$258$		0			0
$259$	11.0440			0.686239
$260$		0			0
$261$	−0.869586			−0.0538260
$262$		0			0
$263$	18.7941	+	18.7941i	1.15890	+	1.15890i	0.984713	+	0.174182i	$0.0557283\pi$
$263$	18.7941	+	18.7941i	1.15890	+	1.15890i	0.174182	+	0.984713i	$0.444272\pi$
$264$		0			0
$265$	−3.54457	−	9.02585i	−0.217741	−	0.554453i
$266$		0			0
$267$	0.922372	−	0.922372i	0.0564483	−	0.0564483i
$268$		0			0
$269$			4.66747i			0.284581i	0.989825	+	0.142290i	$0.0454467\pi$
$269$			4.66747i			0.284581i	−0.989825	+	0.142290i	$0.954553\pi$
$270$		0			0
$271$			21.3315i			1.29580i	0.761726	+	0.647899i	$0.224352\pi$
$271$			21.3315i			1.29580i	−0.761726	+	0.647899i	$0.775648\pi$
$272$		0			0
$273$	4.43842	−	4.43842i	0.268626	−	0.268626i
$274$		0			0
$275$	−11.4987	+	10.6782i	−0.693399	+	0.643922i
$276$		0			0
$277$	−9.32777	−	9.32777i	−0.560451	−	0.560451i	0.368984	−	0.929436i	$-0.379706\pi$
$277$	−9.32777	−	9.32777i	−0.560451	−	0.560451i	−0.929436	+	0.368984i	$0.879706\pi$
$278$		0			0
$279$	−10.8478			−0.649441
$280$		0			0
$281$	4.90448			0.292577			0.146288	−	0.989242i	$-0.453267\pi$
$281$	4.90448			0.292577			0.146288	+	0.989242i	$0.453267\pi$
$282$		0			0
$283$	2.32162	+	2.32162i	0.138006	+	0.138006i	0.772735	−	0.634729i	$-0.218888\pi$
$283$	2.32162	+	2.32162i	0.138006	+	0.138006i	−0.634729	+	0.772735i	$0.718888\pi$
$284$		0			0
$285$	−15.3277	+	6.01938i	−0.907932	+	0.356557i
$286$		0			0
$287$	7.99790	−	7.99790i	0.472101	−	0.472101i
$288$		0			0
$289$			38.1170i			2.24218i
$290$		0			0
$291$		−	0.0439083i		−	0.00257395i
$292$		0			0
$293$	0.533783	−	0.533783i	0.0311839	−	0.0311839i	−0.691343	−	0.722527i	$-0.742981\pi$
$293$	0.533783	−	0.533783i	0.0311839	−	0.0311839i	0.722527	+	0.691343i	$0.242981\pi$
$294$		0			0
$295$	5.34307	−	12.2535i	0.311085	−	0.713424i
$296$		0			0
$297$	2.21921	+	2.21921i	0.128772	+	0.128772i
$298$		0			0
$299$	−17.5166			−1.01301
$300$		0			0
$301$	−2.17499			−0.125364
$302$		0			0
$303$	−6.47371	−	6.47371i	−0.371905	−	0.371905i
$304$		0			0
$305$	2.75229	−	6.31194i	0.157596	−	0.361420i
$306$		0			0
$307$	−1.99704	+	1.99704i	−0.113977	+	0.113977i	−0.761795	−	0.647818i	$-0.775682\pi$
$307$	−1.99704	+	1.99704i	−0.113977	+	0.113977i	0.647818	+	0.761795i	$0.275682\pi$
$308$		0			0
$309$			5.13077i			0.291879i
$310$		0			0
$311$			4.50184i			0.255276i	0.991821	+	0.127638i	$0.0407396\pi$
$311$			4.50184i			0.255276i	−0.991821	+	0.127638i	$0.959260\pi$
$312$		0			0
$313$	−4.29380	+	4.29380i	−0.242700	+	0.242700i	−0.817966	−	0.575266i	$-0.804898\pi$
$313$	−4.29380	+	4.29380i	−0.242700	+	0.242700i	0.575266	+	0.817966i	$0.304898\pi$
$314$		0			0
$315$	−2.36946	+	0.930520i	−0.133504	+	0.0524289i
$316$		0			0
$317$	1.44268	+	1.44268i	0.0810287	+	0.0810287i	0.746460	−	0.665431i	$-0.231752\pi$
$317$	1.44268	+	1.44268i	0.0810287	+	0.0810287i	−0.665431	+	0.746460i	$0.731752\pi$
$318$		0			0
$319$	2.72914			0.152803
$320$		0			0
$321$	5.49948			0.306951
$322$		0			0
$323$	38.6602	+	38.6602i	2.15111	+	2.15111i
$324$		0			0
$325$	27.5491	+	1.01924i	1.52815	+	0.0565370i
$326$		0			0
$327$	2.88629	−	2.88629i	0.159612	−	0.159612i
$328$		0			0
$329$			3.17104i			0.174825i
$330$		0			0
$331$			18.8098i			1.03388i	0.856021	+	0.516941i	$0.172929\pi$
$331$			18.8098i			1.03388i	−0.856021	+	0.516941i	$0.827071\pi$
$332$		0			0
$333$	6.85962	−	6.85962i	0.375905	−	0.375905i
$334$		0			0
$335$	−10.4347	−	26.5709i	−0.570111	−	1.45172i
$336$		0			0
$337$	−17.9728	−	17.9728i	−0.979041	−	0.979041i	0.0207436	−	0.999785i	$-0.493397\pi$
$337$	−17.9728	−	17.9728i	−0.979041	−	0.979041i	−0.999785	+	0.0207436i	$0.993397\pi$
$338$		0			0
$339$	−11.0218			−0.598622
$340$		0			0
$341$	34.0452			1.84365
$342$		0			0
$343$	−10.2267	−	10.2267i	−0.552188	−	0.552188i
$344$		0			0
$345$	6.51183	+	2.83946i	0.350585	+	0.152871i
$346$		0			0
$347$	−19.4918	+	19.4918i	−1.04638	+	1.04638i	−0.0475043	+	0.998871i	$0.515127\pi$
$347$	−19.4918	+	19.4918i	−1.04638	+	1.04638i	−0.998871	+	0.0475043i	$0.984873\pi$
$348$		0			0
$349$			21.4040i			1.14573i	0.819650	+	0.572865i	$0.194168\pi$
$349$			21.4040i			1.14573i	−0.819650	+	0.572865i	$0.805832\pi$
$350$		0			0
$351$		−	5.51358i		−	0.294293i
$352$		0			0
$353$	12.4331	−	12.4331i	0.661746	−	0.661746i	−0.294046	−	0.955791i	$-0.595002\pi$
$353$	12.4331	−	12.4331i	0.661746	−	0.661746i	0.955791	+	0.294046i	$0.0950018\pi$
$354$		0			0
$355$	22.2510	+	9.70246i	1.18096	+	0.514953i
$356$		0			0
$357$	5.97638	+	5.97638i	0.316303	+	0.316303i
$358$		0			0
$359$	0.757946			0.0400029			0.0200014	−	0.999800i	$-0.493633\pi$
$359$	0.757946			0.0400029			0.0200014	+	0.999800i	$0.493633\pi$
$360$		0			0
$361$	35.2340			1.85442
$362$		0			0
$363$	0.813310	+	0.813310i	0.0426877	+	0.0426877i
$364$		0			0
$365$	0.655407	+	1.66892i	0.0343056	+	0.0873553i
$366$		0			0
$367$	−8.96265	+	8.96265i	−0.467847	+	0.467847i	−0.901216	−	0.433370i	$-0.857324\pi$
$367$	−8.96265	+	8.96265i	−0.467847	+	0.467847i	0.433370	+	0.901216i	$0.357324\pi$
$368$		0			0
$369$		−	9.93530i		−	0.517211i
$370$		0			0
$371$			4.93694i			0.256313i
$372$		0			0
$373$	13.8928	−	13.8928i	0.719340	−	0.719340i	−0.249130	−	0.968470i	$-0.580145\pi$
$373$	13.8928	−	13.8928i	0.719340	−	0.719340i	0.968470	+	0.249130i	$0.0801447\pi$
$374$		0			0
$375$	−10.0762	−	4.84463i	−0.520332	−	0.250175i
$376$		0			0
$377$	−3.39025	−	3.39025i	−0.174607	−	0.174607i
$378$		0			0
$379$	6.49469			0.333610			0.166805	−	0.985990i	$-0.446655\pi$
$379$	6.49469			0.333610			0.166805	+	0.985990i	$0.446655\pi$
$380$		0			0
$381$	9.30977			0.476954
$382$		0			0
$383$	4.50224	+	4.50224i	0.230054	+	0.230054i	0.812715	−	0.582661i	$-0.197989\pi$
$383$	4.50224	+	4.50224i	0.230054	+	0.230054i	−0.582661	+	0.812715i	$0.697989\pi$
$384$		0			0
$385$	7.43642	−	2.92038i	0.378995	−	0.148836i
$386$		0			0
$387$	−1.35093	+	1.35093i	−0.0686716	+	0.0686716i
$388$		0			0
$389$			14.0959i			0.714691i	0.933972	+	0.357346i	$0.116318\pi$
$389$			14.0959i			0.714691i	−0.933972	+	0.357346i	$0.883682\pi$
$390$		0			0
$391$		−	23.5863i		−	1.19281i
$392$		0			0
$393$	−6.94045	+	6.94045i	−0.350099	+	0.350099i
$394$		0			0
$395$	−5.94594	+	13.6360i	−0.299173	+	0.686104i
$396$		0			0
$397$	25.9999	+	25.9999i	1.30490	+	1.30490i	0.925050	+	0.379846i	$0.124023\pi$
$397$	25.9999	+	25.9999i	1.30490	+	1.30490i	0.379846	+	0.925050i	$0.375977\pi$
$398$		0			0
$399$	8.38390			0.419720
$400$		0			0
$401$	0.122354			0.00611009			0.00305504	−	0.999995i	$-0.499028\pi$
$401$	0.122354			0.00611009			0.00305504	+	0.999995i	$0.499028\pi$
$402$		0			0
$403$	−42.2922	−	42.2922i	−2.10673	−	2.10673i
$404$		0			0
$405$	−0.893756	+	2.04968i	−0.0444111	+	0.101850i
$406$		0			0
$407$	−21.5285	+	21.5285i	−1.06713	+	1.06713i
$408$		0			0
$409$			25.5615i			1.26393i	0.774996	+	0.631967i	$0.217752\pi$
$409$			25.5615i			1.26393i	−0.774996	+	0.631967i	$0.782248\pi$
$410$		0			0
$411$		−	12.1744i		−	0.600517i
$412$		0			0
$413$	−4.81246	+	4.81246i	−0.236806	+	0.236806i
$414$		0			0
$415$	−19.8636	+	7.80070i	−0.975066	+	0.382921i
$416$		0			0
$417$	−3.97762	−	3.97762i	−0.194785	−	0.194785i
$418$		0			0
$419$	15.5152			0.757965			0.378982	−	0.925404i	$-0.376274\pi$
$419$	15.5152			0.757965			0.378982	+	0.925404i	$0.376274\pi$
$420$		0			0
$421$	−8.39422			−0.409109			−0.204555	−	0.978855i	$-0.565575\pi$
$421$	−8.39422			−0.409109			−0.204555	+	0.978855i	$0.565575\pi$
$422$		0			0
$423$	1.96959	+	1.96959i	0.0957649	+	0.0957649i
$424$		0			0
$425$	−1.37241	+	37.0950i	−0.0665716	+	1.79937i
$426$		0			0
$427$	−2.47897	+	2.47897i	−0.119966	+	0.119966i
$428$		0			0
$429$			17.3040i			0.835447i
$430$		0			0
$431$			32.3248i			1.55703i	0.627626	+	0.778515i	$0.284027\pi$
$431$			32.3248i			1.55703i	−0.627626	+	0.778515i	$0.715973\pi$
$432$		0			0
$433$	23.6882	−	23.6882i	1.13838	−	1.13838i	0.149641	−	0.988740i	$-0.452188\pi$
$433$	23.6882	−	23.6882i	1.13838	−	1.13838i	0.988740	−	0.149641i	$-0.0478118\pi$
$434$		0			0
$435$	0.710768	+	1.80989i	0.0340787	+	0.0867777i
$436$		0			0
$437$	−16.5439	−	16.5439i	−0.791401	−	0.791401i
$438$		0			0
$439$	7.08623			0.338207			0.169104	−	0.985598i	$-0.445913\pi$
$439$	7.08623			0.338207			0.169104	+	0.985598i	$0.445913\pi$
$440$		0			0
$441$	−5.70395			−0.271617
$442$		0			0
$443$	15.5635	+	15.5635i	0.739443	+	0.739443i	0.972470	−	0.233027i	$-0.0748632\pi$
$443$	15.5635	+	15.5635i	0.739443	+	0.739443i	−0.233027	+	0.972470i	$0.574863\pi$
$444$		0			0
$445$	−2.67367	−	1.16584i	−0.126744	−	0.0552662i
$446$		0			0
$447$	11.1949	−	11.1949i	0.529503	−	0.529503i
$448$		0			0
$449$			10.7945i			0.509425i	0.967017	+	0.254713i	$0.0819809\pi$
$449$			10.7945i			0.509425i	−0.967017	+	0.254713i	$0.918019\pi$
$450$		0			0
$451$			31.1813i			1.46827i
$452$		0			0
$453$	2.40555	−	2.40555i	0.113022	−	0.113022i
$454$		0			0
$455$	−12.8656	−	5.61000i	−0.603149	−	0.263001i
$456$		0			0
$457$	−8.32904	−	8.32904i	−0.389616	−	0.389616i	0.484934	−	0.874551i	$-0.338843\pi$
$457$	−8.32904	−	8.32904i	−0.389616	−	0.389616i	−0.874551	+	0.484934i	$0.838843\pi$
$458$		0			0
$459$	7.42408			0.346526
$460$		0			0
$461$	3.85956			0.179758			0.0898788	−	0.995953i	$-0.471352\pi$
$461$	3.85956			0.179758			0.0898788	+	0.995953i	$0.471352\pi$
$462$		0			0
$463$	−15.8156	−	15.8156i	−0.735013	−	0.735013i	0.236595	−	0.971608i	$-0.423969\pi$
$463$	−15.8156	−	15.8156i	−0.735013	−	0.735013i	−0.971608	+	0.236595i	$0.923969\pi$
$464$		0			0
$465$	8.86661	+	22.5778i	0.411179	+	1.04702i
$466$		0			0
$467$	−2.87031	+	2.87031i	−0.132822	+	0.132822i	−0.770392	−	0.637570i	$-0.779940\pi$
$467$	−2.87031	+	2.87031i	−0.132822	+	0.132822i	0.637570	+	0.770392i	$0.279940\pi$
$468$		0			0
$469$			14.5337i			0.671104i
$470$		0			0
$471$			3.24437i			0.149493i
$472$		0			0
$473$	4.23981	−	4.23981i	0.194947	−	0.194947i
$474$		0			0
$475$	25.0566	+	26.9818i	1.14967	+	1.23801i
$476$		0			0
$477$	3.06643	+	3.06643i	0.140402	+	0.140402i
$478$		0			0
$479$	26.2860			1.20104			0.600518	−	0.799611i	$-0.294961\pi$
$479$	26.2860			1.20104			0.600518	+	0.799611i	$0.294961\pi$
$480$		0			0
$481$	53.4870			2.43880
$482$		0			0
$483$	−2.55748	−	2.55748i	−0.116369	−	0.116369i
$484$		0			0
$485$	−0.0913876	+	0.0358891i	−0.00414969	+	0.00162964i
$486$		0			0
$487$	21.1286	−	21.1286i	0.957427	−	0.957427i	−0.0417034	−	0.999130i	$-0.513278\pi$
$487$	21.1286	−	21.1286i	0.957427	−	0.957427i	0.999130	+	0.0417034i	$0.0132785\pi$
$488$		0			0
$489$		−	12.2316i		−	0.553134i
$490$		0			0
$491$		−	24.8276i		−	1.12046i	−0.828339	−	0.560228i	$-0.810714\pi$
$491$		−	24.8276i		−	1.12046i	0.828339	−	0.560228i	$-0.189286\pi$
$492$		0			0
$493$	4.56499	−	4.56499i	0.205597	−	0.205597i
$494$		0			0
$495$	2.80500	−	6.43281i	0.126075	−	0.289133i
$496$		0			0
$497$	−8.73893	−	8.73893i	−0.391995	−	0.391995i
$498$		0			0
$499$	−8.05630			−0.360650			−0.180325	−	0.983607i	$-0.557715\pi$
$499$	−8.05630			−0.360650			−0.180325	+	0.983607i	$0.557715\pi$
$500$		0			0
$501$	−3.85017			−0.172013
$502$		0			0
$503$	9.85141	+	9.85141i	0.439253	+	0.439253i	0.891760	−	0.452508i	$-0.149471\pi$
$503$	9.85141	+	9.85141i	0.439253	+	0.439253i	−0.452508	+	0.891760i	$0.649471\pi$
$504$		0			0
$505$	−8.18252	+	18.7653i	−0.364117	+	0.835044i
$506$		0			0
$507$	12.3033	−	12.3033i	0.546411	−	0.546411i
$508$		0			0
$509$		−	32.8176i		−	1.45461i	−0.686312	−	0.727307i	$-0.740771\pi$
$509$		−	32.8176i		−	1.45461i	0.686312	−	0.727307i	$-0.259229\pi$
$510$		0			0
$511$		−	0.912863i		−	0.0403827i
$512$		0			0
$513$	5.20740	−	5.20740i	0.229912	−	0.229912i
$514$		0			0
$515$	10.6788	−	4.19371i	0.470565	−	0.184797i
$516$		0			0
$517$	−6.18145	−	6.18145i	−0.271860	−	0.271860i
$518$		0			0
$519$	15.6714			0.687898
$520$		0			0
$521$	20.3968			0.893599			0.446799	−	0.894634i	$-0.352564\pi$
$521$	20.3968			0.893599			0.446799	+	0.894634i	$0.352564\pi$
$522$		0			0
$523$	−8.17711	−	8.17711i	−0.357560	−	0.357560i	0.505353	−	0.862913i	$-0.331362\pi$
$523$	−8.17711	−	8.17711i	−0.357560	−	0.357560i	−0.862913	+	0.505353i	$0.831362\pi$
$524$		0			0
$525$	3.87343	+	4.17105i	0.169050	+	0.182040i
$526$		0			0
$527$	56.9468	−	56.9468i	2.48064	−	2.48064i
$528$		0			0
$529$		−	12.9067i		−	0.561161i
$530$		0			0
$531$			5.97822i			0.259433i
$532$		0			0
$533$	38.7346	−	38.7346i	1.67778	−	1.67778i
$534$		0			0
$535$	−4.49508	−	11.4462i	−0.194339	−	0.494863i
$536$		0			0
$537$	11.1139	+	11.1139i	0.479599	+	0.479599i
$538$		0			0
$539$	17.9015			0.771073
$540$		0			0
$541$	−21.9572			−0.944012			−0.472006	−	0.881595i	$-0.656470\pi$
$541$	−21.9572			−0.944012			−0.472006	+	0.881595i	$0.656470\pi$
$542$		0			0
$543$	−4.81581	−	4.81581i	−0.206666	−	0.206666i
$544$		0			0
$545$	−8.36646	−	3.64816i	−0.358380	−	0.156270i
$546$		0			0
$547$	−21.9877	+	21.9877i	−0.940127	+	0.940127i	−0.998306	−	0.0581789i	$-0.981471\pi$
$547$	−21.9877	+	21.9877i	−0.940127	+	0.940127i	0.0581789	+	0.998306i	$0.481471\pi$
$548$		0			0
$549$			3.07947i			0.131429i
$550$		0			0
$551$		−	6.40396i		−	0.272818i
$552$		0			0
$553$	5.35546	−	5.35546i	0.227737	−	0.227737i
$554$		0			0
$555$	−19.8839	−	8.67029i	−0.844024	−	0.368033i
$556$		0			0
$557$	−6.61783	−	6.61783i	−0.280406	−	0.280406i	0.552865	−	0.833271i	$-0.313535\pi$
$557$	−6.61783	−	6.61783i	−0.280406	−	0.280406i	−0.833271	+	0.552865i	$0.813535\pi$
$558$		0			0
$559$	−10.5337			−0.445528
$560$		0			0
$561$	−23.3000			−0.983728
$562$		0			0
$563$	−26.2433	−	26.2433i	−1.10602	−	1.10602i	−0.993668	−	0.112353i	$-0.964161\pi$
$563$	−26.2433	−	26.2433i	−1.10602	−	1.10602i	−0.112353	−	0.993668i	$-0.535839\pi$
$564$		0			0
$565$	9.00883	+	22.9400i	0.379004	+	0.965092i
$566$		0			0
$567$	0.804999	−	0.804999i	0.0338068	−	0.0338068i
$568$		0			0
$569$		−	39.1193i		−	1.63997i	−0.572387	−	0.819984i	$-0.693982\pi$
$569$		−	39.1193i		−	1.63997i	0.572387	−	0.819984i	$-0.306018\pi$
$570$		0			0
$571$			39.2605i			1.64300i	0.570209	+	0.821500i	$0.306862\pi$
$571$			39.2605i			1.64300i	−0.570209	+	0.821500i	$0.693138\pi$
$572$		0			0
$573$	6.35659	−	6.35659i	0.265550	−	0.265550i
$574$		0			0
$575$	0.587297	−	15.8741i	0.0244920	−	0.661996i
$576$		0			0
$577$	−25.1538	−	25.1538i	−1.04717	−	1.04717i	−0.998831	−	0.0483372i	$-0.984608\pi$
$577$	−25.1538	−	25.1538i	−1.04717	−	1.04717i	−0.0483372	−	0.998831i	$-0.515392\pi$
$578$		0			0
$579$	13.2537			0.550806
$580$		0			0
$581$	10.8650			0.450755
$582$		0			0
$583$	−9.62380	−	9.62380i	−0.398577	−	0.398577i
$584$		0			0
$585$	−11.4756	+	4.50660i	−0.474456	+	0.186325i
$586$		0			0
$587$	−13.6858	+	13.6858i	−0.564874	+	0.564874i	−0.930688	−	0.365814i	$-0.880791\pi$
$587$	−13.6858	+	13.6858i	−0.564874	+	0.564874i	0.365814	+	0.930688i	$0.380791\pi$
$588$		0			0
$589$		−	79.8873i		−	3.29170i
$590$		0			0
$591$		−	18.3922i		−	0.756553i
$592$		0			0
$593$	0.672766	−	0.672766i	0.0276272	−	0.0276272i	−0.693158	−	0.720785i	$-0.743781\pi$
$593$	0.672766	−	0.672766i	0.0276272	−	0.0276272i	0.720785	+	0.693158i	$0.243781\pi$
$594$		0			0
$595$	7.55391	−	17.3237i	0.309680	−	0.710201i
$596$		0			0
$597$	−16.3680	−	16.3680i	−0.669896	−	0.669896i
$598$		0			0
$599$	−13.9158			−0.568586			−0.284293	−	0.958737i	$-0.591759\pi$
$599$	−13.9158			−0.568586			−0.284293	+	0.958737i	$0.591759\pi$
$600$		0			0
$601$	22.4498			0.915746			0.457873	−	0.889018i	$-0.348611\pi$
$601$	22.4498			0.915746			0.457873	+	0.889018i	$0.348611\pi$
$602$		0			0
$603$	9.02716	+	9.02716i	0.367614	+	0.367614i
$604$		0			0
$605$	1.02799	−	2.35753i	0.0417938	−	0.0958473i
$606$		0			0
$607$	−6.20871	+	6.20871i	−0.252004	+	0.252004i	−0.821792	−	0.569788i	$-0.807025\pi$
$607$	−6.20871	+	6.20871i	−0.252004	+	0.252004i	0.569788	+	0.821792i	$0.307025\pi$
$608$		0			0
$609$		−	0.989971i		−	0.0401157i
$610$		0			0
$611$			15.3577i			0.621305i
$612$		0			0
$613$	−0.912888	+	0.912888i	−0.0368712	+	0.0368712i	−0.725302	−	0.688431i	$-0.758300\pi$
$613$	−0.912888	+	0.912888i	−0.0368712	+	0.0368712i	0.688431	+	0.725302i	$0.258300\pi$
$614$		0			0
$615$	−20.6786	+	8.12076i	−0.833841	+	0.327461i
$616$		0			0
$617$	30.9629	+	30.9629i	1.24652	+	1.24652i	0.957247	+	0.289272i	$0.0934132\pi$
$617$	30.9629	+	30.9629i	1.24652	+	1.24652i	0.289272	+	0.957247i	$0.406587\pi$
$618$		0			0
$619$	−31.1418			−1.25170			−0.625848	−	0.779945i	$-0.715247\pi$
$619$	−31.1418			−1.25170			−0.625848	+	0.779945i	$0.715247\pi$
$620$		0			0
$621$	−3.17699			−0.127488
$622$		0			0
$623$	1.05007	+	1.05007i	0.0420700	+	0.0420700i
$624$		0			0
$625$	−1.84733	+	24.9317i	−0.0738931	+	0.997266i
$626$		0			0
$627$	−16.3431	+	16.3431i	−0.652681	+	0.652681i
$628$		0			0
$629$			72.0207i			2.87165i
$630$		0			0
$631$			20.7942i			0.827804i	0.910321	+	0.413902i	$0.135834\pi$
$631$			20.7942i			0.827804i	−0.910321	+	0.413902i	$0.864166\pi$
$632$		0			0
$633$	18.9499	−	18.9499i	0.753189	−	0.753189i
$634$		0			0
$635$	−7.60947	−	19.3767i	−0.301973	−	0.768939i
$636$		0			0
$637$	−22.2379	−	22.2379i	−0.881100	−	0.881100i
$638$		0			0
$639$	−10.8558			−0.429450
$640$		0			0
$641$	−34.9929			−1.38213			−0.691067	−	0.722790i	$-0.742859\pi$
$641$	−34.9929			−1.38213			−0.691067	+	0.722790i	$0.742859\pi$
$642$		0			0
$643$	8.75481	+	8.75481i	0.345256	+	0.345256i	0.858339	−	0.513083i	$-0.171497\pi$
$643$	8.75481	+	8.75481i	0.345256	+	0.345256i	−0.513083	+	0.858339i	$0.671497\pi$
$644$		0			0
$645$	3.91592	+	1.70752i	0.154189	+	0.0672336i
$646$		0			0
$647$	18.0825	−	18.0825i	0.710896	−	0.710896i	−0.255827	−	0.966723i	$-0.582348\pi$
$647$	18.0825	−	18.0825i	0.710896	−	0.710896i	0.966723	+	0.255827i	$0.0823476\pi$
$648$		0			0
$649$		−	18.7623i		−	0.736484i
$650$		0			0
$651$		−	12.3496i		−	0.484018i
$652$		0			0
$653$	−21.3378	+	21.3378i	−0.835012	+	0.835012i	−0.988197	−	0.153185i	$-0.951047\pi$
$653$	−21.3378	+	21.3378i	−0.835012	+	0.835012i	0.153185	+	0.988197i	$0.451047\pi$
$654$		0			0
$655$	20.1182	+	8.77246i	0.786083	+	0.342768i
$656$		0			0
$657$	−0.566997	−	0.566997i	−0.0221207	−	0.0221207i
$658$		0			0
$659$	−9.21723			−0.359052			−0.179526	−	0.983753i	$-0.557456\pi$
$659$	−9.21723			−0.359052			−0.179526	+	0.983753i	$0.557456\pi$
$660$		0			0
$661$	−8.83004			−0.343449			−0.171724	−	0.985145i	$-0.554934\pi$
$661$	−8.83004			−0.343449			−0.171724	+	0.985145i	$0.554934\pi$
$662$		0			0
$663$	28.9442	+	28.9442i	1.12410	+	1.12410i
$664$		0			0
$665$	−6.85270	−	17.4496i	−0.265736	−	0.676668i
$666$		0			0
$667$	−1.95350	+	1.95350i	−0.0756399	+	0.0756399i
$668$		0			0
$669$		−	9.83680i		−	0.380313i
$670$		0			0
$671$		−	9.66473i		−	0.373103i
$672$		0			0
$673$	−33.1197	+	33.1197i	−1.27667	+	1.27667i	−0.334150	+	0.942520i	$0.608449\pi$
$673$	−33.1197	+	33.1197i	−1.27667	+	1.27667i	−0.942520	+	0.334150i	$0.891551\pi$
$674$		0			0
$675$	4.99658	+	0.184859i	0.192319	+	0.00711523i
$676$		0			0
$677$	12.2803	+	12.2803i	0.471972	+	0.471972i	0.902552	−	0.430581i	$-0.141691\pi$
$677$	12.2803	+	12.2803i	0.471972	+	0.471972i	−0.430581	+	0.902552i	$0.641691\pi$
$678$		0			0
$679$	0.0499870			0.00191833
$680$		0			0
$681$	−18.1737			−0.696419
$682$		0			0
$683$	−13.0505	−	13.0505i	−0.499364	−	0.499364i	0.411876	−	0.911240i	$-0.364874\pi$
$683$	−13.0505	−	13.0505i	−0.499364	−	0.499364i	−0.911240	+	0.411876i	$0.864874\pi$
$684$		0			0
$685$	−25.3388	+	9.95089i	−0.968146	+	0.380204i
$686$		0			0
$687$	−6.74251	+	6.74251i	−0.257243	+	0.257243i
$688$		0			0
$689$			23.9101i			0.910903i
$690$		0			0
$691$		−	46.6174i		−	1.77341i	−0.462335	−	0.886705i	$-0.652988\pi$
$691$		−	46.6174i		−	1.77341i	0.462335	−	0.886705i	$-0.347012\pi$
$692$		0			0
$693$	−2.52644	+	2.52644i	−0.0959715	+	0.0959715i
$694$		0			0
$695$	−5.02756	+	11.5299i	−0.190706	+	0.437353i
$696$		0			0
$697$	52.1565	+	52.1565i	1.97557	+	1.97557i
$698$		0			0
$699$	5.29334			0.200213
$700$		0			0
$701$	29.9709			1.13199			0.565993	−	0.824410i	$-0.308493\pi$
$701$	29.9709			1.13199			0.565993	+	0.824410i	$0.308493\pi$
$702$		0			0
$703$	50.5168	+	50.5168i	1.90528	+	1.90528i
$704$		0			0
$705$	2.48949	−	5.70924i	0.0937596	−	0.215022i
$706$		0			0
$707$	7.36993	−	7.36993i	0.277175	−	0.277175i
$708$		0			0
$709$			15.0191i			0.564055i	0.959406	+	0.282028i	$0.0910070\pi$
$709$			15.0191i			0.564055i	−0.959406	+	0.282028i	$0.908993\pi$
$710$		0			0
$711$		−	6.65275i		−	0.249498i
$712$		0			0
$713$	−24.3693	+	24.3693i	−0.912638	+	0.912638i
$714$		0			0
$715$	36.0153	−	14.1437i	1.34690	−	0.528944i
$716$		0			0
$717$	−6.74225	−	6.74225i	−0.251794	−	0.251794i
$718$		0			0
$719$	−21.2457			−0.792330			−0.396165	−	0.918179i	$-0.629659\pi$
$719$	−21.2457			−0.792330			−0.396165	+	0.918179i	$0.629659\pi$
$720$		0			0
$721$	−5.84108			−0.217533
$722$		0			0
$723$	2.82843	+	2.82843i	0.105190	+	0.105190i
$724$		0			0
$725$	3.18602	−	2.95868i	0.118326	−	0.109883i
$726$		0			0
$727$	−24.6174	+	24.6174i	−0.913007	+	0.913007i	−0.996508	−	0.0835005i	$-0.973390\pi$
$727$	−24.6174	+	24.6174i	−0.913007	+	0.913007i	0.0835005	+	0.996508i	$0.473390\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	14.1837i		−	0.524604i
$732$		0			0
$733$	4.09292	−	4.09292i	0.151176	−	0.151176i	−0.627467	−	0.778643i	$-0.715908\pi$
$733$	4.09292	−	4.09292i	0.151176	−	0.151176i	0.778643	+	0.627467i	$0.215908\pi$
$734$		0			0
$735$	4.66221	+	11.8718i	0.171968	+	0.437897i
$736$		0			0
$737$	−28.3312	−	28.3312i	−1.04359	−	1.04359i
$738$		0			0
$739$	20.3695			0.749304			0.374652	−	0.927165i	$-0.377762\pi$
$739$	20.3695			0.749304			0.374652	+	0.927165i	$0.377762\pi$
$740$		0			0
$741$	40.6041			1.49163
$742$		0			0
$743$	−33.4787	−	33.4787i	−1.22821	−	1.22821i	−0.964639	−	0.263573i	$-0.915099\pi$
$743$	−33.4787	−	33.4787i	−1.22821	−	1.22821i	−0.263573	−	0.964639i	$-0.584901\pi$
$744$		0			0
$745$	−32.4507	−	14.1500i	−1.18890	−	0.518415i
$746$		0			0
$747$	6.74844	−	6.74844i	0.246912	−	0.246912i
$748$		0			0
$749$			6.26083i			0.228766i
$750$		0			0
$751$			48.6487i			1.77522i	0.460600	+	0.887608i	$0.347634\pi$
$751$			48.6487i			1.77522i	−0.460600	+	0.887608i	$0.652366\pi$
$752$		0			0
$753$	7.86472	−	7.86472i	0.286606	−	0.286606i
$754$		0			0
$755$	−6.97293	−	3.04052i	−0.253771	−	0.110656i
$756$		0			0
$757$	−3.73197	−	3.73197i	−0.135641	−	0.135641i	0.636027	−	0.771667i	$-0.280577\pi$
$757$	−3.73197	−	3.73197i	−0.135641	−	0.135641i	−0.771667	+	0.636027i	$0.780577\pi$
$758$		0			0
$759$	9.97081			0.361917
$760$		0			0
$761$	21.2244			0.769384			0.384692	−	0.923045i	$-0.374308\pi$
$761$	21.2244			0.769384			0.384692	+	0.923045i	$0.374308\pi$
$762$		0			0
$763$	3.28587	+	3.28587i	0.118956	+	0.118956i
$764$		0			0
$765$	−6.06818	−	15.4519i	−0.219395	−	0.558666i
$766$		0			0
$767$	−23.3072	+	23.3072i	−0.841575	+	0.841575i
$768$		0			0
$769$			3.54205i			0.127730i	0.997959	+	0.0638648i	$0.0203426\pi$
$769$			3.54205i			0.127730i	−0.997959	+	0.0638648i	$0.979657\pi$
$770$		0			0
$771$			7.83170i			0.282052i
$772$		0			0
$773$	−21.0079	+	21.0079i	−0.755602	+	0.755602i	−0.975519	−	0.219917i	$-0.929421\pi$
$773$	−21.0079	+	21.0079i	−0.755602	+	0.755602i	0.219917	+	0.975519i	$0.429421\pi$
$774$		0			0
$775$	39.7445	−	36.9086i	1.42767	−	1.32580i
$776$		0			0
$777$	7.80926	+	7.80926i	0.280156	+	0.280156i
$778$		0			0
$779$	73.1673			2.62149
$780$		0			0
$781$	34.0704			1.21913
$782$		0			0
$783$	−0.614890	−	0.614890i	−0.0219744	−	0.0219744i
$784$		0			0
$785$	6.75258	−	2.65183i	0.241010	−	0.0946478i
$786$		0			0
$787$	11.8769	−	11.8769i	0.423365	−	0.423365i	−0.462995	−	0.886361i	$-0.653225\pi$
$787$	11.8769	−	11.8769i	0.423365	−	0.423365i	0.886361	+	0.462995i	$0.153225\pi$
$788$		0			0
$789$			26.5789i			0.946235i
$790$		0			0
$791$		−	12.5477i		−	0.446144i
$792$		0			0
$793$	−12.0059	+	12.0059i	−0.426342	+	0.426342i
$794$		0			0
$795$	3.87585	−	8.88863i	0.137462	−	0.315247i
$796$		0			0
$797$	−26.9411	−	26.9411i	−0.954303	−	0.954303i	0.0446973	−	0.999001i	$-0.485768\pi$
$797$	−26.9411	−	26.9411i	−0.954303	−	0.954303i	−0.999001	+	0.0446973i	$0.985768\pi$
$798$		0			0
$799$	−20.6792			−0.731579
$800$		0			0
$801$	1.30443			0.0460898
$802$		0			0
$803$	1.77949	+	1.77949i	0.0627967	+	0.0627967i
$804$		0			0
$805$	−3.23255	+	7.41333i	−0.113932	+	0.261286i
$806$		0			0
$807$	−3.30040	+	3.30040i	−0.116180	+	0.116180i
$808$		0			0
$809$		−	0.966253i		−	0.0339716i	−0.999856	−	0.0169858i	$-0.994593\pi$
$809$		−	0.966253i		−	0.0339716i	0.999856	−	0.0169858i	$-0.00540701\pi$
$810$		0			0
$811$			23.6051i			0.828889i	0.910075	+	0.414444i	$0.136024\pi$
$811$			23.6051i			0.828889i	−0.910075	+	0.414444i	$0.863976\pi$
$812$		0			0
$813$	−15.0837	+	15.0837i	−0.529007	+	0.529007i
$814$		0			0
$815$	−25.4580	+	9.99770i	−0.891755	+	0.350204i
$816$		0			0
$817$	−9.94875	−	9.94875i	−0.348063	−	0.348063i
$818$		0			0
$819$	6.27688			0.219332
$820$		0			0
$821$	−35.8524			−1.25126			−0.625629	−	0.780121i	$-0.715158\pi$
$821$	−35.8524			−1.25126			−0.625629	+	0.780121i	$0.715158\pi$
$822$		0			0
$823$	−16.6066	−	16.6066i	−0.578870	−	0.578870i	0.355722	−	0.934592i	$-0.384235\pi$
$823$	−16.6066	−	16.6066i	−0.578870	−	0.578870i	−0.934592	+	0.355722i	$0.884235\pi$
$824$		0			0
$825$	−15.6815	−	0.580169i	−0.545959	−	0.0201989i
$826$		0			0
$827$	−17.9428	+	17.9428i	−0.623934	+	0.623934i	−0.946535	−	0.322601i	$-0.895443\pi$
$827$	−17.9428	+	17.9428i	−0.623934	+	0.623934i	0.322601	+	0.946535i	$0.395443\pi$
$828$		0			0
$829$		−	3.16930i		−	0.110074i	−0.998484	−	0.0550371i	$-0.982472\pi$
$829$		−	3.16930i		−	0.110074i	0.998484	−	0.0550371i	$-0.0175277\pi$
$830$		0			0
$831$		−	13.1915i		−	0.457606i
$832$		0			0
$833$	29.9436	−	29.9436i	1.03748	−	1.03748i
$834$		0			0
$835$	3.14699	+	8.01345i	0.108906	+	0.277317i
$836$		0			0
$837$	−7.67056	−	7.67056i	−0.265133	−	0.265133i
$838$		0			0
$839$	−9.22536			−0.318495			−0.159247	−	0.987239i	$-0.550907\pi$
$839$	−9.22536			−0.318495			−0.159247	+	0.987239i	$0.550907\pi$
$840$		0			0
$841$	28.2438			0.973925
$842$		0			0
$843$	3.46799	+	3.46799i	0.119444	+	0.119444i
$844$		0			0
$845$	−35.6636	−	15.5510i	−1.22686	−	0.534969i
$846$		0			0
$847$	−0.925905	+	0.925905i	−0.0318145	+	0.0318145i
$848$		0			0
$849$			3.28326i			0.112681i
$850$		0			0
$851$		−	30.8199i		−	1.05649i
$852$		0			0
$853$	5.61294	−	5.61294i	0.192183	−	0.192183i	−0.604456	−	0.796639i	$-0.706609\pi$
$853$	5.61294	−	5.61294i	0.192183	−	0.192183i	0.796639	+	0.604456i	$0.206609\pi$
$854$		0			0
$855$	−15.0946	−	6.58195i	−0.516226	−	0.225098i
$856$		0			0
$857$	4.98462	+	4.98462i	0.170271	+	0.170271i	0.787099	−	0.616827i	$-0.211582\pi$
$857$	4.98462	+	4.98462i	0.170271	+	0.170271i	−0.616827	+	0.787099i	$0.711582\pi$
$858$		0			0
$859$	−8.89245			−0.303406			−0.151703	−	0.988426i	$-0.548476\pi$
$859$	−8.89245			−0.303406			−0.151703	+	0.988426i	$0.548476\pi$
$860$		0			0
$861$	11.3107			0.385469
$862$		0			0
$863$	−4.09500	−	4.09500i	−0.139395	−	0.139395i	0.633966	−	0.773361i	$-0.281426\pi$
$863$	−4.09500	−	4.09500i	−0.139395	−	0.139395i	−0.773361	+	0.633966i	$0.781426\pi$
$864$		0			0
$865$	−12.8092	−	32.6173i	−0.435527	−	1.10902i
$866$		0			0
$867$	−26.9528	+	26.9528i	−0.915364	+	0.915364i
$868$		0			0
$869$			20.8793i			0.708281i
$870$		0			0
$871$			70.3882i			2.38501i
$872$		0			0
$873$	0.0310479	−	0.0310479i	0.00105081	−	0.00105081i
$874$		0			0
$875$	5.51532	−	11.4711i	0.186452	−	0.387795i
$876$		0			0
$877$	−5.00026	−	5.00026i	−0.168847	−	0.168847i	0.617626	−	0.786472i	$-0.288095\pi$
$877$	−5.00026	−	5.00026i	−0.168847	−	0.168847i	−0.786472	+	0.617626i	$0.788095\pi$
$878$		0			0
$879$	0.754883			0.0254616
$880$		0			0
$881$	28.6782			0.966192			0.483096	−	0.875568i	$-0.339512\pi$
$881$	28.6782			0.966192			0.483096	+	0.875568i	$0.339512\pi$
$882$		0			0
$883$	−3.79912	−	3.79912i	−0.127850	−	0.127850i	0.640286	−	0.768137i	$-0.278816\pi$
$883$	−3.79912	−	3.79912i	−0.127850	−	0.127850i	−0.768137	+	0.640286i	$0.778816\pi$
$884$		0			0
$885$	12.4426	−	4.88638i	0.418254	−	0.164254i
$886$		0			0
$887$	−20.1173	+	20.1173i	−0.675473	+	0.675473i	−0.958972	−	0.283500i	$-0.908505\pi$
$887$	−20.1173	+	20.1173i	−0.675473	+	0.675473i	0.283500	+	0.958972i	$0.408505\pi$
$888$		0			0
$889$			10.5986i			0.355466i
$890$		0			0
$891$			3.13844i			0.105142i
$892$		0			0
$893$	−14.5048	+	14.5048i	−0.485386	+	0.485386i
$894$		0			0
$895$	14.0475	−	32.2157i	0.469556	−	1.07685i
$896$		0			0
$897$	−12.3861	−	12.3861i	−0.413560	−	0.413560i
$898$		0			0
$899$	−9.43310			−0.314611
$900$		0			0
$901$	−32.1952			−1.07258
$902$		0			0
$903$	−1.53795	−	1.53795i	−0.0511798	−	0.0511798i
$904$		0			0
$905$	−6.08700	+	13.9595i	−0.202339	+	0.464031i
$906$		0			0
$907$	−3.31527	+	3.31527i	−0.110082	+	0.110082i	−0.760002	−	0.649920i	$-0.774802\pi$
$907$	−3.31527	+	3.31527i	−0.110082	+	0.110082i	0.649920	+	0.760002i	$0.274802\pi$
$908$		0			0
$909$		−	9.15521i		−	0.303659i
$910$		0			0
$911$			23.7965i			0.788414i	0.919022	+	0.394207i	$0.128981\pi$
$911$			23.7965i			0.788414i	−0.919022	+	0.394207i	$0.871019\pi$
$912$		0			0
$913$	−21.1796	+	21.1796i	−0.700941	+	0.700941i
$914$		0			0
$915$	6.40938	−	2.51705i	0.211888	−	0.0832110i
$916$		0			0
$917$	−7.90128	−	7.90128i	−0.260923	−	0.260923i
$918$		0			0
$919$	−22.0111			−0.726081			−0.363040	−	0.931773i	$-0.618261\pi$
$919$	−22.0111			−0.726081			−0.363040	+	0.931773i	$0.618261\pi$
$920$		0			0
$921$	−2.82424			−0.0930617
$922$		0			0
$923$	−42.3235	−	42.3235i	−1.39310	−	1.39310i
$924$		0			0
$925$	−1.79331	+	48.4716i	−0.0589637	+	1.59374i
$926$		0			0
$927$	−3.62800	+	3.62800i	−0.119159	+	0.119159i
$928$		0			0
$929$		−	49.1694i		−	1.61319i	−0.591101	−	0.806597i	$-0.701307\pi$
$929$		−	49.1694i		−	1.61319i	0.591101	−	0.806597i	$-0.298693\pi$
$930$		0			0
$931$		−	42.0061i		−	1.37669i
$932$		0			0
$933$	−3.18328	+	3.18328i	−0.104216	+	0.104216i
$934$		0			0
$935$	19.0446	+	48.4950i	0.622825	+	1.58595i
$936$		0			0
$937$	−39.8912	−	39.8912i	−1.30319	−	1.30319i	−0.926230	−	0.376960i	$-0.876969\pi$
$937$	−39.8912	−	39.8912i	−1.30319	−	1.30319i	−0.376960	−	0.926230i	$-0.623031\pi$
$938$		0			0
$939$	−6.07235			−0.198164
$940$		0			0
$941$	−14.5673			−0.474879			−0.237440	−	0.971402i	$-0.576308\pi$
$941$	−14.5673			−0.474879			−0.237440	+	0.971402i	$0.576308\pi$
$942$		0			0
$943$	−22.3194	−	22.3194i	−0.726819	−	0.726819i
$944$		0			0
$945$	−2.33344	−	1.01749i	−0.0759069	−	0.0330989i
$946$		0			0
$947$	8.51568	−	8.51568i	0.276722	−	0.276722i	−0.555077	−	0.831799i	$-0.687311\pi$
$947$	8.51568	−	8.51568i	0.276722	−	0.276722i	0.831799	+	0.555077i	$0.187311\pi$
$948$		0			0
$949$		−	4.42109i		−	0.143515i
$950$		0			0
$951$			2.04025i			0.0661597i
$952$		0			0
$953$	2.32920	−	2.32920i	0.0754503	−	0.0754503i	−0.668375	−	0.743825i	$-0.733010\pi$
$953$	2.32920	−	2.32920i	0.0754503	−	0.0754503i	0.743825	+	0.668375i	$0.233010\pi$
$954$		0			0
$955$	−18.4258	−	8.03449i	−0.596245	−	0.259990i
$956$		0			0
$957$	1.92980	+	1.92980i	0.0623814	+	0.0623814i
$958$		0			0
$959$	13.8598			0.447556
$960$		0			0
$961$	−86.6748			−2.79596
$962$		0			0
$963$	3.88872	+	3.88872i	0.125312	+	0.125312i
$964$		0			0
$965$	−10.8331	−	27.5853i	−0.348730	−	0.888003i
$966$		0			0
$967$	10.2799	−	10.2799i	0.330579	−	0.330579i	−0.522227	−	0.852806i	$-0.674899\pi$
$967$	10.2799	−	10.2799i	0.330579	−	0.330579i	0.852806	+	0.522227i	$0.174899\pi$
$968$		0			0
$969$			54.6737i			1.75637i
$970$		0			0
$971$		−	55.5951i		−	1.78413i	−0.451905	−	0.892066i	$-0.649255\pi$
$971$		−	55.5951i		−	1.78413i	0.451905	−	0.892066i	$-0.350745\pi$
$972$		0			0
$973$	4.52828	−	4.52828i	0.145170	−	0.145170i
$974$		0			0
$975$	18.7594	+	20.2008i	0.600782	+	0.646944i
$976$		0			0
$977$	−25.6207	−	25.6207i	−0.819680	−	0.819680i	0.166381	−	0.986061i	$-0.446792\pi$
$977$	−25.6207	−	25.6207i	−0.819680	−	0.819680i	−0.986061	+	0.166381i	$0.946792\pi$
$978$		0			0
$979$	−4.09388			−0.130841
$980$		0			0
$981$	4.08183			0.130323
$982$		0			0
$983$	10.2908	+	10.2908i	0.328227	+	0.328227i	0.851912	−	0.523685i	$-0.175443\pi$
$983$	10.2908	+	10.2908i	0.328227	+	0.328227i	−0.523685	+	0.851912i	$0.675443\pi$
$984$		0			0
$985$	−38.2801	+	15.0331i	−1.21970	+	0.478994i
$986$		0			0
$987$	−2.24226	+	2.24226i	−0.0713721	+	0.0713721i
$988$		0			0
$989$			6.06965i			0.193004i
$990$		0			0
$991$		−	5.51130i		−	0.175072i	−0.996161	−	0.0875361i	$-0.972101\pi$
$991$		−	5.51130i		−	0.175072i	0.996161	−	0.0875361i	$-0.0278993\pi$
$992$		0			0
$993$	−13.3006	+	13.3006i	−0.422081	+	0.422081i
$994$		0			0
$995$	−20.6885	+	47.4457i	−0.655869	+	1.50413i
$996$		0			0
$997$	34.6856	+	34.6856i	1.09850	+	1.09850i	0.994586	+	0.103919i	$0.0331383\pi$
$997$	34.6856	+	34.6856i	1.09850	+	1.09850i	0.103919	+	0.994586i	$0.466862\pi$
$998$		0			0
$999$	9.70096			0.306925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.127.5	✓	12
4.3	odd	2		1920.2.w.j.127.2	yes	12
5.3	odd	4		1920.2.w.j.1663.2	yes	12
8.3	odd	2		1920.2.w.l.127.5	yes	12
8.5	even	2		1920.2.w.k.127.2	yes	12
20.3	even	4	inner	1920.2.w.i.1663.5	yes	12
40.3	even	4		1920.2.w.k.1663.2	yes	12
40.13	odd	4		1920.2.w.l.1663.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.5	✓	12	1.1	even	1	trivial
1920.2.w.i.1663.5	yes	12	20.3	even	4	inner
1920.2.w.j.127.2	yes	12	4.3	odd	2
1920.2.w.j.1663.2	yes	12	5.3	odd	4
1920.2.w.k.127.2	yes	12	8.5	even	2
1920.2.w.k.1663.2	yes	12	40.3	even	4
1920.2.w.l.127.5	yes	12	8.3	odd	2
1920.2.w.l.1663.5	yes	12	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(0.893756 - 2.04968i) q^{5} +(-0.804999 + 0.804999i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(0.893756 - 2.04968i) q^{5} +(-0.804999 + 0.804999i) q^{7} +1.00000i q^{9} -3.13844i q^{11} +(-3.89869 + 3.89869i) q^{13} +(2.08133 - 0.817364i) q^{15} +(-5.24962 - 5.24962i) q^{17} -7.36438 q^{19} -1.13844 q^{21} +(2.24647 + 2.24647i) q^{23} +(-3.40240 - 3.66383i) q^{25} +(-0.707107 + 0.707107i) q^{27} +0.869586i q^{29} +10.8478i q^{31} +(2.21921 - 2.21921i) q^{33} +(0.930520 + 2.36946i) q^{35} +(-6.85962 - 6.85962i) q^{37} -5.51358 q^{39} -9.93530 q^{41} +(1.35093 + 1.35093i) q^{43} +(2.04968 + 0.893756i) q^{45} +(1.96959 - 1.96959i) q^{47} +5.70395i q^{49} -7.42408i q^{51} +(3.06643 - 3.06643i) q^{53} +(-6.43281 - 2.80500i) q^{55} +(-5.20740 - 5.20740i) q^{57} +5.97822 q^{59} +3.07947 q^{61} +(-0.804999 - 0.804999i) q^{63} +(4.50660 + 11.4756i) q^{65} +(9.02716 - 9.02716i) q^{67} +3.17699i q^{69} +10.8558i q^{71} +(-0.566997 + 0.566997i) q^{73} +(0.184859 - 4.99658i) q^{75} +(2.52644 + 2.52644i) q^{77} -6.65275 q^{79} -1.00000 q^{81} +(-6.74844 - 6.74844i) q^{83} +(-15.4519 + 6.06818i) q^{85} +(-0.614890 + 0.614890i) q^{87} -1.30443i q^{89} -6.27688i q^{91} +(-7.67056 + 7.67056i) q^{93} +(-6.58195 + 15.0946i) q^{95} +(-0.0310479 - 0.0310479i) q^{97} +3.13844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more