LMFDB - Embedded newform 1232.2.bi.b.527.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(527,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2, 3]))

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

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

chi := DirichletCharacter("1232.527");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.bi (of order $6$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.4
Character	$\chi$	$=$	1232.527
Dual form			1232.2.bi.b.879.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08822 + 1.20564i) q^{3} +(1.26539 - 2.19172i) q^{5} +(-2.64572 - 0.0128382i) q^{7} +(1.40712 - 2.43720i) q^{9} +O(q^{10})$	\(q+(-2.08822 + 1.20564i) q^{3} +(1.26539 - 2.19172i) q^{5} +(-2.64572 - 0.0128382i) q^{7} +(1.40712 - 2.43720i) q^{9} +(-2.86779 - 1.66606i) q^{11} +1.45342i q^{13} +6.10240i q^{15} +(-0.280744 + 0.162088i) q^{17} +(-0.561816 + 0.973095i) q^{19} +(5.54033 - 3.16297i) q^{21} +(1.64529 + 0.949910i) q^{23} +(-0.702430 - 1.21664i) q^{25} -0.447940i q^{27} +4.15504i q^{29} +(2.97781 - 1.71924i) q^{31} +(7.99725 + 0.0215981i) q^{33} +(-3.37601 + 5.78244i) q^{35} +(0.600067 - 1.03935i) q^{37} +(-1.75229 - 3.03506i) q^{39} +4.72055i q^{41} +11.7064 q^{43} +(-3.56110 - 6.16801i) q^{45} +(8.03611 + 4.63965i) q^{47} +(6.99967 + 0.0679325i) q^{49} +(0.390837 - 0.676950i) q^{51} +(1.66910 + 2.89097i) q^{53} +(-7.28043 + 4.17718i) q^{55} -2.70938i q^{57} +(-0.144811 + 0.0836068i) q^{59} +(-11.3970 - 6.58006i) q^{61} +(-3.75412 + 6.43007i) q^{63} +(3.18549 + 1.83914i) q^{65} +(7.96977 - 4.60135i) q^{67} -4.58098 q^{69} +14.3848i q^{71} +(-9.72727 + 5.61604i) q^{73} +(2.93366 + 1.69375i) q^{75} +(7.56599 + 4.44475i) q^{77} +(-8.66655 + 15.0109i) q^{79} +(4.76140 + 8.24698i) q^{81} +3.41648 q^{83} +0.820417i q^{85} +(-5.00947 - 8.67666i) q^{87} +(-2.73206 + 4.73207i) q^{89} +(0.0186593 - 3.84534i) q^{91} +(-4.14555 + 7.18030i) q^{93} +(1.42184 + 2.46269i) q^{95} +4.65280 q^{97} +(-8.09584 + 4.64503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 12 * q^9	$ 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) $ 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.08822	+	1.20564i	−1.20564	+	0.696074i	−0.961803	−	0.273743i	$-0.911738\pi$
$3$	−2.08822	+	1.20564i	−1.20564	+	0.696074i	−0.243833	+	0.969817i	$0.578405\pi$
$4$		0			0
$5$	1.26539	−	2.19172i	0.565900	−	0.980168i	−0.431065	−	0.902321i	$-0.641862\pi$
$5$	1.26539	−	2.19172i	0.565900	−	0.980168i	0.996965	−	0.0778470i	$-0.0248046\pi$
$6$		0			0
$7$	−2.64572	−	0.0128382i	−0.999988	−	0.00485238i
$7$	−2.64572	−	0.0128382i	−0.999988	−	0.00485238i
$8$		0			0
$9$	1.40712	−	2.43720i	0.469038	−	0.812398i
$10$		0			0
$11$	−2.86779	−	1.66606i	−0.864672	−	0.502337i
$11$	−2.86779	−	1.66606i	−0.864672	−	0.502337i
$12$		0			0
$13$			1.45342i			0.403106i	0.979478	+	0.201553i	$0.0645988\pi$
$13$			1.45342i			0.403106i	−0.979478	+	0.201553i	$0.935401\pi$
$14$		0			0
$15$			6.10240i			1.57563i
$16$		0			0
$17$	−0.280744	+	0.162088i	−0.0680905	+	0.0393120i	−0.533659	−	0.845700i	$-0.679183\pi$
$17$	−0.280744	+	0.162088i	−0.0680905	+	0.0393120i	0.465568	+	0.885012i	$0.345850\pi$
$18$		0			0
$19$	−0.561816	+	0.973095i	−0.128890	+	0.223243i	−0.923247	−	0.384208i	$-0.874475\pi$
$19$	−0.561816	+	0.973095i	−0.128890	+	0.223243i	0.794357	+	0.607451i	$0.207808\pi$
$20$		0			0
$21$	5.54033	−	3.16297i	1.20900	−	0.690216i
$22$		0			0
$23$	1.64529	+	0.949910i	0.343067	+	0.198070i	0.661627	−	0.749833i	$-0.269866\pi$
$23$	1.64529	+	0.949910i	0.343067	+	0.198070i	−0.318560	+	0.947903i	$0.603199\pi$
$24$		0			0
$25$	−0.702430	−	1.21664i	−0.140486	−	0.243329i
$26$		0			0
$27$		−	0.447940i		−	0.0862060i
$28$		0			0
$29$			4.15504i			0.771572i	0.922588	+	0.385786i	$0.126070\pi$
$29$			4.15504i			0.771572i	−0.922588	+	0.385786i	$0.873930\pi$
$30$		0			0
$31$	2.97781	−	1.71924i	0.534830	−	0.308784i	−0.208151	−	0.978097i	$-0.566745\pi$
$31$	2.97781	−	1.71924i	0.534830	−	0.308784i	0.742981	+	0.669312i	$0.233411\pi$
$32$		0			0
$33$	7.99725	+	0.0215981i	1.39214	+	0.00375974i
$34$		0			0
$35$	−3.37601	+	5.78244i	−0.570650	+	0.977410i
$36$		0			0
$37$	0.600067	−	1.03935i	0.0986504	−	0.170867i	−0.812476	−	0.582995i	$-0.801881\pi$
$37$	0.600067	−	1.03935i	0.0986504	−	0.170867i	0.911126	+	0.412127i	$0.135214\pi$
$38$		0			0
$39$	−1.75229	−	3.03506i	−0.280592	−	0.485999i
$40$		0			0
$41$			4.72055i			0.737227i	0.929583	+	0.368613i	$0.120167\pi$
$41$			4.72055i			0.737227i	−0.929583	+	0.368613i	$0.879833\pi$
$42$		0			0
$43$	11.7064			1.78520			0.892602	−	0.450846i	$-0.148878\pi$
$43$	11.7064			1.78520			0.892602	+	0.450846i	$0.148878\pi$
$44$		0			0
$45$	−3.56110	−	6.16801i	−0.530858	−	0.919473i
$46$		0			0
$47$	8.03611	+	4.63965i	1.17219	+	0.676762i	0.954194	−	0.299188i	$-0.0967158\pi$
$47$	8.03611	+	4.63965i	1.17219	+	0.676762i	0.217992	+	0.975950i	$0.430049\pi$
$48$		0			0
$49$	6.99967	+	0.0679325i	0.999953	+	0.00970465i
$50$		0			0
$51$	0.390837	−	0.676950i	0.0547282	−	0.0947920i
$52$		0			0
$53$	1.66910	+	2.89097i	0.229269	+	0.397105i	0.957592	−	0.288129i	$-0.0930332\pi$
$53$	1.66910	+	2.89097i	0.229269	+	0.397105i	−0.728323	+	0.685234i	$0.759700\pi$
$54$		0			0
$55$	−7.28043	+	4.17718i	−0.981693	+	0.563251i
$56$		0			0
$57$		−	2.70938i		−	0.358867i
$58$		0			0
$59$	−0.144811	+	0.0836068i	−0.0188528	+	0.0108847i	−0.509397	−	0.860532i	$-0.670131\pi$
$59$	−0.144811	+	0.0836068i	−0.0188528	+	0.0108847i	0.490544	+	0.871416i	$0.336798\pi$
$60$		0			0
$61$	−11.3970	−	6.58006i	−1.45924	−	0.842490i	−0.460261	−	0.887783i	$-0.652244\pi$
$61$	−11.3970	−	6.58006i	−1.45924	−	0.842490i	−0.998974	+	0.0452937i	$0.985578\pi$
$62$		0			0
$63$	−3.75412	+	6.43007i	−0.472975	+	0.810113i
$64$		0			0
$65$	3.18549	+	1.83914i	0.395111	+	0.228118i
$66$		0			0
$67$	7.96977	−	4.60135i	0.973662	−	0.562144i	0.0733113	−	0.997309i	$-0.476643\pi$
$67$	7.96977	−	4.60135i	0.973662	−	0.562144i	0.900351	+	0.435165i	$0.143310\pi$
$68$		0			0
$69$	−4.58098			−0.551485
$70$		0			0
$71$			14.3848i			1.70716i	0.520961	+	0.853581i	$0.325574\pi$
$71$			14.3848i			1.70716i	−0.520961	+	0.853581i	$0.674426\pi$
$72$		0			0
$73$	−9.72727	+	5.61604i	−1.13849	+	0.657308i	−0.946056	−	0.324002i	$-0.894972\pi$
$73$	−9.72727	+	5.61604i	−1.13849	+	0.657308i	−0.192434	+	0.981310i	$0.561638\pi$
$74$		0			0
$75$	2.93366	+	1.69375i	0.338750	+	0.195577i
$76$		0			0
$77$	7.56599	+	4.44475i	0.862224	+	0.506527i
$78$		0			0
$79$	−8.66655	+	15.0109i	−0.975063	+	1.68886i	−0.295337	+	0.955393i	$0.595432\pi$
$79$	−8.66655	+	15.0109i	−0.975063	+	1.68886i	−0.679726	+	0.733466i	$0.737901\pi$
$80$		0			0
$81$	4.76140	+	8.24698i	0.529044	+	0.916332i
$82$		0			0
$83$	3.41648			0.375008			0.187504	−	0.982264i	$-0.439960\pi$
$83$	3.41648			0.375008			0.187504	+	0.982264i	$0.439960\pi$
$84$		0			0
$85$			0.820417i			0.0889868i
$86$		0			0
$87$	−5.00947	−	8.67666i	−0.537072	−	0.930235i
$88$		0			0
$89$	−2.73206	+	4.73207i	−0.289598	+	0.501598i	−0.973714	−	0.227775i	$-0.926855\pi$
$89$	−2.73206	+	4.73207i	−0.289598	+	0.501598i	0.684116	+	0.729373i	$0.260188\pi$
$90$		0			0
$91$	0.0186593	−	3.84534i	0.00195602	−	0.403101i
$92$		0			0
$93$	−4.14555	+	7.18030i	−0.429873	+	0.744563i
$94$		0			0
$95$	1.42184	+	2.46269i	0.145877	+	0.252667i
$96$		0			0
$97$	4.65280			0.472420			0.236210	−	0.971702i	$-0.424095\pi$
$97$	4.65280			0.472420			0.236210	+	0.971702i	$0.424095\pi$
$98$		0			0
$99$	−8.09584	+	4.64503i	−0.813662	+	0.466843i
$100$		0			0
$101$	−8.51790	+	4.91781i	−0.847563	+	0.489341i	−0.859828	−	0.510584i	$-0.829429\pi$
$101$	−8.51790	+	4.91781i	−0.847563	+	0.489341i	0.0122650	+	0.999925i	$0.496096\pi$
$102$		0			0
$103$	4.95957	+	2.86341i	0.488681	+	0.282140i	0.724027	−	0.689772i	$-0.242289\pi$
$103$	4.95957	+	2.86341i	0.488681	+	0.282140i	−0.235346	+	0.971912i	$0.575622\pi$
$104$		0			0
$105$	0.0783438	−	16.1453i	0.00764558	−	1.57562i
$106$		0			0
$107$	−4.88448	+	8.46016i	−0.472200	+	0.817874i	−0.999494	−	0.0318085i	$-0.989873\pi$
$107$	−4.88448	+	8.46016i	−0.472200	+	0.817874i	0.527294	+	0.849683i	$0.323207\pi$
$108$		0			0
$109$	6.03991	−	3.48714i	0.578518	−	0.334008i	−0.182026	−	0.983294i	$-0.558266\pi$
$109$	6.03991	−	3.48714i	0.578518	−	0.334008i	0.760544	+	0.649286i	$0.224932\pi$
$110$		0			0
$111$			2.89385i			0.274672i
$112$		0			0
$113$	16.5555			1.55741			0.778706	−	0.627389i	$-0.215876\pi$
$113$	16.5555			1.55741			0.778706	+	0.627389i	$0.215876\pi$
$114$		0			0
$115$	4.16388	−	2.40401i	0.388283	−	0.224176i
$116$		0			0
$117$	3.54227	+	2.04513i	0.327483	+	0.189072i
$118$		0			0
$119$	0.744851	−	0.425234i	0.0682804	−	0.0389812i
$120$		0			0
$121$	5.44847	+	9.55585i	0.495315	+	0.868713i
$122$		0			0
$123$	−5.69127	−	9.85757i	−0.513165	−	0.888827i
$124$		0			0
$125$	9.09852			0.813796
$126$		0			0
$127$	17.9882			1.59619			0.798097	−	0.602528i	$-0.205840\pi$
$127$	17.9882			1.59619			0.798097	+	0.602528i	$0.205840\pi$
$128$		0			0
$129$	−24.4455	+	14.1136i	−2.15231	+	1.24263i
$130$		0			0
$131$	6.97649	−	12.0836i	0.609538	−	1.05575i	−0.381778	−	0.924254i	$-0.624688\pi$
$131$	6.97649	−	12.0836i	0.609538	−	1.05575i	0.991317	−	0.131498i	$-0.0419785\pi$
$132$		0			0
$133$	1.49890	−	2.56732i	0.129971	−	0.222615i
$134$		0			0
$135$	−0.981759	−	0.566819i	−0.0844964	−	0.0487840i
$136$		0			0
$137$	−0.488361	−	0.845866i	−0.0417235	−	0.0722672i	0.844410	−	0.535698i	$-0.179952\pi$
$137$	−0.488361	−	0.845866i	−0.0417235	−	0.0722672i	−0.886133	+	0.463431i	$0.846618\pi$
$138$		0			0
$139$	3.99275			0.338661			0.169330	−	0.985559i	$-0.445840\pi$
$139$	3.99275			0.338661			0.169330	+	0.985559i	$0.445840\pi$
$140$		0			0
$141$	−22.3749			−1.88431
$142$		0			0
$143$	2.42149	−	4.16810i	0.202495	−	0.348554i
$144$		0			0
$145$	9.10670	+	5.25776i	0.756270	+	0.436633i
$146$		0			0
$147$	−14.6988	+	8.29720i	−1.21233	+	0.684341i
$148$		0			0
$149$	0.154047	+	0.0889389i	0.0126200	+	0.00728616i	0.506297	−	0.862359i	$-0.331014\pi$
$149$	0.154047	+	0.0889389i	0.0126200	+	0.00728616i	−0.493677	+	0.869645i	$0.664347\pi$
$150$		0			0
$151$	1.99855	+	3.46160i	0.162640	+	0.281701i	0.935815	−	0.352492i	$-0.114666\pi$
$151$	1.99855	+	3.46160i	0.162640	+	0.281701i	−0.773175	+	0.634193i	$0.781332\pi$
$152$		0			0
$153$			0.912304i			0.0737554i
$154$		0			0
$155$		−	8.70203i		−	0.698964i
$156$		0			0
$157$	−5.35302	−	9.27170i	−0.427217	−	0.739962i	0.569407	−	0.822056i	$-0.307173\pi$
$157$	−5.35302	−	9.27170i	−0.427217	−	0.739962i	−0.996625	+	0.0820933i	$0.973839\pi$
$158$		0			0
$159$	−6.97091	−	4.02466i	−0.552829	−	0.319176i
$160$		0			0
$161$	−4.34079	−	2.53432i	−0.342102	−	0.199732i
$162$		0			0
$163$	−2.62504	−	1.51557i	−0.205609	−	0.118709i	0.393660	−	0.919256i	$-0.371209\pi$
$163$	−2.62504	−	1.51557i	−0.205609	−	0.118709i	−0.599269	+	0.800548i	$0.704542\pi$
$164$		0			0
$165$	10.1670	−	17.5004i	0.791499	−	1.36241i
$166$		0			0
$167$	−22.8877			−1.77111			−0.885553	−	0.464538i	$-0.846221\pi$
$167$	−22.8877			−1.77111			−0.885553	+	0.464538i	$0.846221\pi$
$168$		0			0
$169$	10.8876			0.837506
$170$		0			0
$171$	1.58108	+	2.73851i	0.120908	+	0.209419i
$172$		0			0
$173$	0.0929066	+	0.0536397i	0.00706356	+	0.00407815i	0.503528	−	0.863979i	$-0.332035\pi$
$173$	0.0929066	+	0.0536397i	0.00706356	+	0.00407815i	−0.496464	+	0.868057i	$0.665369\pi$
$174$		0			0
$175$	1.84281	+	3.22792i	0.139304	+	0.244008i
$176$		0			0
$177$	0.201599	−	0.349179i	0.0151531	−	0.0262459i
$178$		0			0
$179$	−11.3943	+	6.57848i	−0.851647	+	0.491699i	−0.861206	−	0.508256i	$-0.830290\pi$
$179$	−11.3943	+	6.57848i	−0.851647	+	0.491699i	0.00955935	+	0.999954i	$0.496957\pi$
$180$		0			0
$181$	−9.87838			−0.734254			−0.367127	−	0.930171i	$-0.619659\pi$
$181$	−9.87838			−0.734254			−0.367127	+	0.930171i	$0.619659\pi$
$182$		0			0
$183$	31.7326			2.34574
$184$		0			0
$185$	−1.51864	−	2.63036i	−0.111653	−	0.193388i
$186$		0			0
$187$	1.07516	+	0.00290368i	0.0786238	+	0.000212338i
$188$		0			0
$189$	−0.00575074	+	1.18512i	−0.000418304	+	0.0862050i
$190$		0			0
$191$	−13.2264	−	7.63625i	−0.957027	−	0.552540i	−0.0617702	−	0.998090i	$-0.519675\pi$
$191$	−13.2264	−	7.63625i	−0.957027	−	0.552540i	−0.895257	+	0.445551i	$0.853008\pi$
$192$		0			0
$193$	4.32819	−	2.49888i	0.311550	−	0.179873i	−0.336070	−	0.941837i	$-0.609098\pi$
$193$	4.32819	−	2.49888i	0.311550	−	0.179873i	0.647620	+	0.761964i	$0.275765\pi$
$194$		0			0
$195$	−8.86935			−0.635147
$196$		0			0
$197$		−	5.09436i		−	0.362958i	−0.983395	−	0.181479i	$-0.941912\pi$
$197$		−	5.09436i		−	0.362958i	0.983395	−	0.181479i	$-0.0580885\pi$
$198$		0			0
$199$	−4.49244	+	2.59371i	−0.318461	+	0.183863i	−0.650706	−	0.759330i	$-0.725527\pi$
$199$	−4.49244	+	2.59371i	−0.318461	+	0.183863i	0.332245	+	0.943193i	$0.392194\pi$
$200$		0			0
$201$	−11.0951	+	19.2173i	−0.782588	+	1.35548i
$202$		0			0
$203$	0.0533433	−	10.9931i	0.00374396	−	0.771563i
$204$		0			0
$205$	10.3461	+	5.97335i	0.722606	+	0.417197i
$206$		0			0
$207$	4.63023	−	2.67327i	0.321823	−	0.185805i
$208$		0			0
$209$	3.23241	−	1.85461i	0.223590	−	0.128286i
$210$		0			0
$211$	−13.3823			−0.921273			−0.460637	−	0.887589i	$-0.652379\pi$
$211$	−13.3823			−0.921273			−0.460637	+	0.887589i	$0.652379\pi$
$212$		0			0
$213$	−17.3428	−	30.0387i	−1.18831	−	2.05822i
$214$		0			0
$215$	14.8131	−	25.6571i	1.01025	−	1.74980i
$216$		0			0
$217$	−7.90052	+	4.51039i	−0.536322	+	0.306185i
$218$		0			0
$219$	13.5418	−	23.4551i	0.915070	−	1.58495i
$220$		0			0
$221$	−0.235581	−	0.408039i	−0.0158469	−	0.0274477i
$222$		0			0
$223$		−	20.9279i		−	1.40144i	−0.713439	−	0.700718i	$-0.752863\pi$
$223$		−	20.9279i		−	1.40144i	0.713439	−	0.700718i	$-0.247137\pi$
$224$		0			0
$225$	−3.95360			−0.263573
$226$		0			0
$227$	3.67729	+	6.36925i	0.244070	+	0.422742i	0.961870	−	0.273508i	$-0.0881840\pi$
$227$	3.67729	+	6.36925i	0.244070	+	0.422742i	−0.717800	+	0.696250i	$0.754851\pi$
$228$		0			0
$229$	11.1388	−	19.2930i	0.736074	−	1.27492i	−0.218176	−	0.975909i	$-0.570011\pi$
$229$	11.1388	−	19.2930i	0.736074	−	1.27492i	0.954251	−	0.299008i	$-0.0966558\pi$
$230$		0			0
$231$	−21.1582	−	0.159813i	−1.39211	−	0.0105149i
$232$		0			0
$233$	18.3314	+	10.5836i	1.20093	+	0.693356i	0.960761	−	0.277376i	$-0.0894649\pi$
$233$	18.3314	+	10.5836i	1.20093	+	0.693356i	0.240166	+	0.970732i	$0.422798\pi$
$234$		0			0
$235$	20.3376	−	11.7419i	1.32668	−	0.765960i
$236$		0			0
$237$		−	41.7948i		−	2.71487i
$238$		0			0
$239$	14.9702			0.968343			0.484171	−	0.874973i	$-0.339121\pi$
$239$	14.9702			0.968343			0.484171	+	0.874973i	$0.339121\pi$
$240$		0			0
$241$	−10.8471	+	6.26258i	−0.698724	+	0.403408i	−0.806872	−	0.590727i	$-0.798841\pi$
$241$	−10.8471	+	6.26258i	−0.698724	+	0.403408i	0.108148	+	0.994135i	$0.465508\pi$
$242$		0			0
$243$	−18.7219	−	10.8091i	−1.20101	−	0.693405i
$244$		0			0
$245$	9.00621	−	15.2554i	0.575386	−	0.974630i
$246$		0			0
$247$	−1.41431	−	0.816555i	−0.0899907	−	0.0519561i
$248$		0			0
$249$	−7.13438	+	4.11904i	−0.452123	+	0.261033i
$250$		0			0
$251$		−	12.9410i		−	0.816829i	−0.912797	−	0.408414i	$-0.866082\pi$
$251$		−	12.9410i		−	0.816829i	0.912797	−	0.408414i	$-0.133918\pi$
$252$		0			0
$253$	−3.13575	−	5.46530i	−0.197143	−	0.343601i
$254$		0			0
$255$	−0.989125	−	1.71321i	−0.0619414	−	0.107286i
$256$		0			0
$257$	−10.1710	+	17.6167i	−0.634451	+	1.09890i	0.352180	+	0.935932i	$0.385440\pi$
$257$	−10.1710	+	17.6167i	−0.634451	+	1.09890i	−0.986631	+	0.162969i	$0.947893\pi$
$258$		0			0
$259$	−1.60095	+	2.74212i	−0.0994783	+	0.170387i
$260$		0			0
$261$	10.1267	+	5.84663i	0.626824	+	0.361897i
$262$		0			0
$263$	−0.290564	−	0.503272i	−0.0179170	−	0.0310331i	0.856928	−	0.515436i	$-0.172370\pi$
$263$	−0.290564	−	0.503272i	−0.0179170	−	0.0310331i	−0.874845	+	0.484403i	$0.839037\pi$
$264$		0			0
$265$	8.44826			0.518973
$266$		0			0
$267$		−	13.1755i		−	0.806327i
$268$		0			0
$269$	1.18912	+	2.05961i	0.0725017	+	0.125577i	0.899997	−	0.435896i	$-0.143568\pi$
$269$	1.18912	+	2.05961i	0.0725017	+	0.125577i	−0.827495	+	0.561472i	$0.810235\pi$
$270$		0			0
$271$	2.18952	−	3.79235i	0.133004	−	0.230369i	−0.791829	−	0.610742i	$-0.790871\pi$
$271$	2.18952	−	3.79235i	0.133004	−	0.230369i	0.924833	+	0.380373i	$0.124204\pi$
$272$		0			0
$273$	4.59712	+	8.05242i	0.278230	+	0.487355i
$274$		0			0
$275$	−0.0125835	+	4.65938i	−0.000758814	+	0.280971i
$276$		0			0
$277$	15.2788	−	8.82120i	0.918012	−	0.530014i	0.0350116	−	0.999387i	$-0.488853\pi$
$277$	15.2788	−	8.82120i	0.918012	−	0.530014i	0.883000	+	0.469372i	$0.155520\pi$
$278$		0			0
$279$		−	9.67666i		−	0.579327i
$280$		0			0
$281$		−	30.4185i		−	1.81462i	−0.420465	−	0.907309i	$-0.638133\pi$
$281$		−	30.4185i		−	1.81462i	0.420465	−	0.907309i	$-0.361867\pi$
$282$		0			0
$283$	11.1999	+	19.3987i	0.665763	+	1.15314i	0.979078	+	0.203486i	$0.0652271\pi$
$283$	11.1999	+	19.3987i	0.665763	+	1.15314i	−0.313315	+	0.949649i	$0.601440\pi$
$284$		0			0
$285$	−5.93822	−	3.42843i	−0.351750	−	0.203083i
$286$		0			0
$287$	0.0606034	−	12.4893i	0.00357731	−	0.737218i
$288$		0			0
$289$	−8.44746	+	14.6314i	−0.496909	+	0.860672i
$290$		0			0
$291$	−9.71608	+	5.60958i	−0.569567	+	0.328839i
$292$		0			0
$293$			12.6046i			0.736367i	0.929753	+	0.368183i	$0.120020\pi$
$293$			12.6046i			0.736367i	−0.929753	+	0.368183i	$0.879980\pi$
$294$		0			0
$295$			0.423181i			0.0246386i
$296$		0			0
$297$	−0.746296	+	1.28460i	−0.0433045	+	0.0745399i
$298$		0			0
$299$	−1.38062	+	2.39130i	−0.0798431	+	0.138292i
$300$		0			0
$301$	−30.9718	−	0.150289i	−1.78518	−	0.00866249i
$302$		0			0
$303$	11.8582	−	20.5390i	0.681235	−	1.17993i
$304$		0			0
$305$	−28.8433	+	16.6527i	−1.65156	+	0.953530i
$306$		0			0
$307$	11.2605			0.642672			0.321336	−	0.946965i	$-0.395868\pi$
$307$	11.2605			0.642672			0.321336	+	0.946965i	$0.395868\pi$
$308$		0			0
$309$	−13.8089			−0.785562
$310$		0			0
$311$	−10.0467	+	5.80044i	−0.569694	+	0.328913i	−0.757027	−	0.653384i	$-0.773349\pi$
$311$	−10.0467	+	5.80044i	−0.569694	+	0.328913i	0.187333	+	0.982296i	$0.440016\pi$
$312$		0			0
$313$	12.9150	−	22.3694i	0.729998	−	1.26439i	−0.226885	−	0.973922i	$-0.572854\pi$
$313$	12.9150	−	22.3694i	0.729998	−	1.26439i	0.956883	−	0.290473i	$-0.0938125\pi$
$314$		0			0
$315$	9.34250	+	16.3646i	0.526390	+	0.922038i
$316$		0			0
$317$	−10.9371	+	18.9436i	−0.614289	+	1.06398i	0.376220	+	0.926530i	$0.377224\pi$
$317$	−10.9371	+	18.9436i	−0.614289	+	1.06398i	−0.990509	+	0.137449i	$0.956110\pi$
$318$		0			0
$319$	6.92257	−	11.9158i	0.387589	−	0.667157i
$320$		0			0
$321$		−	23.5556i		−	1.31475i
$322$		0			0
$323$		−	0.364254i		−	0.0202676i
$324$		0			0
$325$	1.76829	−	1.02093i	0.0980873	−	0.0566307i
$326$		0			0
$327$	−8.40845	+	14.5639i	−0.464988	+	0.805383i
$328$		0			0
$329$	−21.2017	−	12.3784i	−1.16889	−	0.682442i
$330$		0			0
$331$	26.1245	+	15.0830i	1.43593	+	0.829036i	0.997564	−	0.0697596i	$-0.0222232\pi$
$331$	26.1245	+	15.0830i	1.43593	+	0.829036i	0.438368	+	0.898795i	$0.355557\pi$
$332$		0			0
$333$	−1.68873	−	2.92496i	−0.0925416	−	0.160287i
$334$		0			0
$335$		−	23.2900i		−	1.27247i
$336$		0			0
$337$			16.0233i			0.872845i	0.899742	+	0.436422i	$0.143755\pi$
$337$			16.0233i			0.872845i	−0.899742	+	0.436422i	$0.856245\pi$
$338$		0			0
$339$	−34.5716	+	19.9599i	−1.87767	+	1.08407i
$340$		0			0
$341$	−11.4041	−	0.0307989i	−0.617566	−	0.00166785i
$342$		0			0
$343$	−18.5183	−	0.269594i	−0.999894	−	0.0145567i
$344$		0			0
$345$	−5.79673	+	10.0402i	−0.312086	+	0.540548i
$346$		0			0
$347$	−6.78578	−	11.7533i	−0.364280	−	0.630951i	0.624381	−	0.781120i	$-0.285351\pi$
$347$	−6.78578	−	11.7533i	−0.364280	−	0.630951i	−0.988660	+	0.150169i	$0.952018\pi$
$348$		0			0
$349$		−	8.71734i		−	0.466628i	−0.972401	−	0.233314i	$-0.925043\pi$
$349$		−	8.71734i		−	0.466628i	0.972401	−	0.233314i	$-0.0749571\pi$
$350$		0			0
$351$	0.651044			0.0347502
$352$		0			0
$353$	10.8484	+	18.7899i	0.577401	+	1.00009i	0.995776	+	0.0918137i	$0.0292664\pi$
$353$	10.8484	+	18.7899i	0.577401	+	1.00009i	−0.418375	+	0.908274i	$0.637400\pi$
$354$		0			0
$355$	31.5275	+	18.2024i	1.67330	+	0.966083i
$356$		0			0
$357$	−1.04274	+	1.78600i	−0.0551875	+	0.0945253i
$358$		0			0
$359$	8.86767	−	15.3593i	0.468018	−	0.810631i	−0.531314	−	0.847175i	$-0.678302\pi$
$359$	8.86767	−	15.3593i	0.468018	−	0.810631i	0.999332	+	0.0365443i	$0.0116350\pi$
$360$		0			0
$361$	8.86872	+	15.3611i	0.466775	+	0.808478i
$362$		0			0
$363$	−22.8985	−	13.3859i	−1.20186	−	0.702576i
$364$		0			0
$365$			28.4260i			1.48788i
$366$		0			0
$367$	7.01802	−	4.05186i	0.366338	−	0.211505i	−0.305520	−	0.952186i	$-0.598830\pi$
$367$	7.01802	−	4.05186i	0.366338	−	0.211505i	0.671857	+	0.740681i	$0.265497\pi$
$368$		0			0
$369$	11.5049	+	6.64237i	0.598922	+	0.345788i
$370$		0			0
$371$	−4.37886	−	7.67012i	−0.227339	−	0.398213i
$372$		0			0
$373$	4.88984	+	2.82315i	0.253186	+	0.146177i	0.621222	−	0.783634i	$-0.286636\pi$
$373$	4.88984	+	2.82315i	0.253186	+	0.146177i	−0.368036	+	0.929812i	$0.619970\pi$
$374$		0			0
$375$	−18.9997	+	10.9695i	−0.981142	+	0.566462i
$376$		0			0
$377$	−6.03902			−0.311025
$378$		0			0
$379$			14.5507i			0.747420i	0.927546	+	0.373710i	$0.121915\pi$
$379$			14.5507i			0.747420i	−0.927546	+	0.373710i	$0.878085\pi$
$380$		0			0
$381$	−37.5634	+	21.6872i	−1.92443	+	1.11107i
$382$		0			0
$383$	−28.9617	−	16.7210i	−1.47987	−	0.854404i	−0.480131	−	0.877197i	$-0.659411\pi$
$383$	−28.9617	−	16.7210i	−1.47987	−	0.854404i	−0.999740	+	0.0227923i	$0.992744\pi$
$384$		0			0
$385$	19.3156	−	10.9582i	0.984414	−	0.558481i
$386$		0			0
$387$	16.4722	−	28.5307i	0.837329	−	1.45030i
$388$		0			0
$389$	10.8763	+	18.8384i	0.551453	+	0.955144i	0.998170	+	0.0604691i	$0.0192597\pi$
$389$	10.8763	+	18.8384i	0.551453	+	0.955144i	−0.446717	+	0.894675i	$0.647407\pi$
$390$		0			0
$391$	−0.615875			−0.0311461
$392$		0			0
$393$			33.6444i			1.69714i
$394$		0			0
$395$	21.9332	+	37.9893i	1.10358	+	1.91145i
$396$		0			0
$397$	−13.1038	+	22.6964i	−0.657660	+	1.13910i	0.323559	+	0.946208i	$0.395120\pi$
$397$	−13.1038	+	22.6964i	−0.657660	+	1.13910i	−0.981220	+	0.192893i	$0.938213\pi$
$398$		0			0
$399$	−0.0347836	+	7.16827i	−0.00174136	+	0.358862i
$400$		0			0
$401$	−9.22893	+	15.9850i	−0.460871	+	0.798251i	−0.999005	−	0.0446079i	$-0.985796\pi$
$401$	−9.22893	+	15.9850i	−0.460871	+	0.798251i	0.538134	+	0.842859i	$0.319129\pi$
$402$		0			0
$403$	2.49877	+	4.32800i	0.124473	+	0.215593i
$404$		0			0
$405$	24.1001			1.19754
$406$		0			0
$407$	−3.45248	+	1.98088i	−0.171133	+	0.0981885i
$408$		0			0
$409$	26.8584	−	15.5067i	1.32806	−	0.766756i	0.343062	−	0.939313i	$-0.388536\pi$
$409$	26.8584	−	15.5067i	1.32806	−	0.766756i	0.985000	+	0.172556i	$0.0552027\pi$
$410$		0			0
$411$	2.03961	+	1.17757i	0.100607	+	0.0580853i
$412$		0			0
$413$	0.384203	−	0.219341i	0.0189054	−	0.0107931i
$414$		0			0
$415$	4.32319	−	7.48798i	0.212217	−	0.367571i
$416$		0			0
$417$	−8.33775	+	4.81380i	−0.408301	+	0.235733i
$418$		0			0
$419$			40.6309i			1.98495i	0.122453	+	0.992474i	$0.460924\pi$
$419$			40.6309i			1.98495i	−0.122453	+	0.992474i	$0.539076\pi$
$420$		0			0
$421$	−3.77101			−0.183788			−0.0918939	−	0.995769i	$-0.529292\pi$
$421$	−3.77101			−0.183788			−0.0918939	+	0.995769i	$0.529292\pi$
$422$		0			0
$423$	22.6155	−	13.0570i	1.09960	−	0.634855i
$424$		0			0
$425$	0.394406	+	0.227710i	0.0191315	+	0.0110456i
$426$		0			0
$427$	30.0688	+	17.5553i	1.45513	+	0.849561i
$428$		0			0
$429$	−0.0313910	+	11.6234i	−0.00151557	+	0.561181i
$430$		0			0
$431$	8.04244	+	13.9299i	0.387391	+	0.670981i	0.992098	−	0.125467i	$-0.0400431\pi$
$431$	8.04244	+	13.9299i	0.387391	+	0.670981i	−0.604707	+	0.796448i	$0.706710\pi$
$432$		0			0
$433$	14.8915			0.715640			0.357820	−	0.933791i	$-0.383520\pi$
$433$	14.8915			0.715640			0.357820	+	0.933791i	$0.383520\pi$
$434$		0			0
$435$	−25.3558			−1.21572
$436$		0			0
$437$	−1.84870	+	1.06735i	−0.0884355	+	0.0510583i
$438$		0			0
$439$	−9.25939	+	16.0377i	−0.441926	+	0.765439i	−0.997832	−	0.0658061i	$-0.979038\pi$
$439$	−9.25939	+	16.0377i	−0.441926	+	0.765439i	0.555906	+	0.831245i	$0.312371\pi$
$440$		0			0
$441$	10.0149	−	16.9640i	0.476900	−	0.807808i
$442$		0			0
$443$	−11.7235	−	6.76859i	−0.557002	−	0.321585i	0.194939	−	0.980815i	$-0.437549\pi$
$443$	−11.7235	−	6.76859i	−0.557002	−	0.321585i	−0.751941	+	0.659230i	$0.770882\pi$
$444$		0			0
$445$	6.91426	+	11.9758i	0.327767	+	0.567709i
$446$		0			0
$447$	−0.428912			−0.0202868
$448$		0			0
$449$	−26.7217			−1.26108			−0.630538	−	0.776159i	$-0.717166\pi$
$449$	−26.7217			−1.26108			−0.630538	+	0.776159i	$0.717166\pi$
$450$		0			0
$451$	7.86474	−	13.5376i	0.370336	−	0.637459i
$452$		0			0
$453$	−8.34685	−	4.81906i	−0.392169	−	0.226419i
$454$		0			0
$455$	−8.40431	−	4.90676i	−0.394000	−	0.230032i
$456$		0			0
$457$	19.4239	+	11.2144i	0.908611	+	0.524587i	0.879984	−	0.475003i	$-0.157553\pi$
$457$	19.4239	+	11.2144i	0.908611	+	0.524587i	0.0286271	+	0.999590i	$0.490886\pi$
$458$		0			0
$459$	0.0726055	+	0.125756i	0.00338893	+	0.00586981i
$460$		0			0
$461$		−	38.2426i		−	1.78113i	−0.454851	−	0.890567i	$-0.650308\pi$
$461$		−	38.2426i		−	1.78113i	0.454851	−	0.890567i	$-0.349692\pi$
$462$		0			0
$463$		−	22.1813i		−	1.03085i	−0.856934	−	0.515427i	$-0.827633\pi$
$463$		−	22.1813i		−	1.03085i	0.856934	−	0.515427i	$-0.172367\pi$
$464$		0			0
$465$	10.4915	+	18.1718i	0.486531	+	0.842696i
$466$		0			0
$467$	−5.29394	−	3.05646i	−0.244974	−	0.141436i	0.372486	−	0.928038i	$-0.378505\pi$
$467$	−5.29394	−	3.05646i	−0.244974	−	0.141436i	−0.617461	+	0.786602i	$0.711839\pi$
$468$		0			0
$469$	−21.1448	+	12.0716i	−0.976378	+	0.557413i
$470$		0			0
$471$	22.3566	+	12.9076i	1.03014	+	0.594750i
$472$		0			0
$473$	−33.5714	−	19.5035i	−1.54362	−	0.896774i
$474$		0			0
$475$	1.57855			0.0724287
$476$		0			0
$477$	9.39447			0.430143
$478$		0			0
$479$	−10.1116	−	17.5138i	−0.462011	−	0.800226i	0.537050	−	0.843550i	$-0.319538\pi$
$479$	−10.1116	−	17.5138i	−0.462011	−	0.800226i	−0.999061	+	0.0433243i	$0.986205\pi$
$480$		0			0
$481$	1.51061	+	0.872148i	0.0688777	+	0.0397665i
$482$		0			0
$483$	12.1200	+	0.0588115i	0.551479	+	0.00267602i
$484$		0			0
$485$	5.88761	−	10.1976i	0.267343	−	0.463051i
$486$		0			0
$487$	−13.2280	+	7.63720i	−0.599419	+	0.346075i	−0.768813	−	0.639474i	$-0.779152\pi$
$487$	−13.2280	+	7.63720i	−0.599419	+	0.346075i	0.169394	+	0.985548i	$0.445819\pi$
$488$		0			0
$489$	7.30890			0.330520
$490$		0			0
$491$	−23.3405			−1.05334			−0.526671	−	0.850069i	$-0.676560\pi$
$491$	−23.3405			−1.05334			−0.526671	+	0.850069i	$0.676560\pi$
$492$		0			0
$493$	−0.673482	−	1.16650i	−0.0303321	−	0.0525367i
$494$		0			0
$495$	−0.0637945	+	23.6216i	−0.00286735	+	1.06171i
$496$		0			0
$497$	0.184675	−	38.0582i	0.00828380	−	1.70714i
$498$		0			0
$499$	10.3449	+	5.97261i	0.463100	+	0.267371i	0.713347	−	0.700811i	$-0.247178\pi$
$499$	10.3449	+	5.97261i	0.463100	+	0.267371i	−0.250247	+	0.968182i	$0.580512\pi$
$500$		0			0
$501$	47.7947	−	27.5943i	2.13531	−	1.23282i
$502$		0			0
$503$	32.0270			1.42802			0.714008	−	0.700138i	$-0.246878\pi$
$503$	32.0270			1.42802			0.714008	+	0.700138i	$0.246878\pi$
$504$		0			0
$505$			24.8918i			1.10767i
$506$		0			0
$507$	−22.7357	+	13.1264i	−1.00973	+	0.582966i
$508$		0			0
$509$	−7.22822	+	12.5196i	−0.320385	+	0.554923i	−0.980567	−	0.196182i	$-0.937146\pi$
$509$	−7.22822	+	12.5196i	−0.320385	+	0.554923i	0.660182	+	0.751105i	$0.270479\pi$
$510$		0			0
$511$	25.8077	−	14.7336i	1.14167	−	0.651776i
$512$		0			0
$513$	0.435888	+	0.251660i	0.0192449	+	0.0111111i
$514$		0			0
$515$	12.5516	−	7.24666i	0.553089	−	0.319326i
$516$		0			0
$517$	−15.3159	−	26.6942i	−0.673594	−	1.17401i
$518$		0			0
$519$	−0.258680			−0.0113548
$520$		0			0
$521$	−15.8349	−	27.4268i	−0.693739	−	1.20159i	−0.970604	−	0.240683i	$-0.922629\pi$
$521$	−15.8349	−	27.4268i	−0.693739	−	1.20159i	0.276865	−	0.960909i	$-0.410705\pi$
$522$		0			0
$523$	−10.2101	+	17.6845i	−0.446458	+	0.773287i	−0.998152	−	0.0607586i	$-0.980648\pi$
$523$	−10.2101	+	17.6845i	−0.446458	+	0.773287i	0.551695	+	0.834046i	$0.313981\pi$
$524$		0			0
$525$	−7.73990	−	4.51885i	−0.337797	−	0.197219i
$526$		0			0
$527$	−0.557335	+	0.965332i	−0.0242779	+	0.0420505i
$528$		0			0
$529$	−9.69534	−	16.7928i	−0.421537	−	0.730123i
$530$		0			0
$531$			0.470578i			0.0204213i
$532$		0			0
$533$	−6.86094			−0.297181
$534$		0			0
$535$	12.3615	+	21.4108i	0.534436	+	0.925671i
$536$		0			0
$537$	15.8625	−	27.4747i	0.684517	−	1.18562i
$538$		0			0
$539$	−19.9604	−	11.8567i	−0.859756	−	0.510705i
$540$		0			0
$541$	13.0237	+	7.51926i	0.559934	+	0.323278i	0.753119	−	0.657884i	$-0.228548\pi$
$541$	13.0237	+	7.51926i	0.559934	+	0.323278i	−0.193185	+	0.981162i	$0.561882\pi$
$542$		0			0
$543$	20.6282	−	11.9097i	0.885243	−	0.511095i
$544$		0			0
$545$		−	17.6504i		−	0.756060i
$546$		0			0
$547$	−11.6564			−0.498390			−0.249195	−	0.968453i	$-0.580166\pi$
$547$	−11.6564			−0.498390			−0.249195	+	0.968453i	$0.580166\pi$
$548$		0			0
$549$	−32.0738	+	18.5178i	−1.36887	+	0.790320i
$550$		0			0
$551$	−4.04325	−	2.33437i	−0.172248	−	0.0994476i
$552$		0			0
$553$	23.1220	−	39.6034i	0.983247	−	1.68411i
$554$		0			0
$555$	6.34251	+	3.66185i	0.269225	+	0.155437i
$556$		0			0
$557$	−36.4801	+	21.0618i	−1.54571	+	0.892417i	−0.547250	+	0.836969i	$0.684325\pi$
$557$	−36.4801	+	21.0618i	−1.54571	+	0.892417i	−0.998462	+	0.0554473i	$0.982342\pi$
$558$		0			0
$559$			17.0143i			0.719626i
$560$		0			0
$561$	−2.24868	+	1.29019i	−0.0949395	+	0.0544720i
$562$		0			0
$563$	2.21272	+	3.83255i	0.0932552	+	0.161523i	0.908879	−	0.417060i	$-0.136939\pi$
$563$	2.21272	+	3.83255i	0.0932552	+	0.161523i	−0.815624	+	0.578583i	$0.803606\pi$
$564$		0			0
$565$	20.9492	−	36.2851i	0.881340	−	1.52652i
$566$		0			0
$567$	−12.4915	−	21.8803i	−0.524592	−	0.918888i
$568$		0			0
$569$	37.3836	+	21.5834i	1.56720	+	0.904824i	0.996493	+	0.0836704i	$0.0266643\pi$
$569$	37.3836	+	21.5834i	1.56720	+	0.904824i	0.570707	+	0.821153i	$0.306669\pi$
$570$		0			0
$571$	10.6770	+	18.4932i	0.446821	+	0.773916i	0.998177	−	0.0603538i	$-0.0192229\pi$
$571$	10.6770	+	18.4932i	0.446821	+	0.773916i	−0.551356	+	0.834270i	$0.685890\pi$
$572$		0			0
$573$	36.8262			1.53843
$574$		0			0
$575$		−	2.66898i		−	0.111304i
$576$		0			0
$577$	−17.5748	−	30.4404i	−0.731648	−	1.26725i	−0.956178	−	0.292785i	$-0.905418\pi$
$577$	−17.5748	−	30.4404i	−0.731648	−	1.26725i	0.224530	−	0.974467i	$-0.427915\pi$
$578$		0			0
$579$	−6.02548	+	10.4364i	−0.250410	+	0.433723i
$580$		0			0
$581$	−9.03906	−	0.0438615i	−0.375004	−	0.00181968i
$582$		0			0
$583$	0.0299007	−	11.0715i	0.00123836	−	0.458536i
$584$		0			0
$585$	8.96471	−	5.17578i	0.370645	−	0.213992i
$586$		0			0
$587$		−	18.2295i		−	0.752412i	−0.926536	−	0.376206i	$-0.877229\pi$
$587$		−	18.2295i		−	0.752412i	0.926536	−	0.376206i	$-0.122771\pi$
$588$		0			0
$589$			3.86358i			0.159196i
$590$		0			0
$591$	6.14195	+	10.6382i	0.252646	+	0.437596i
$592$		0			0
$593$	16.2804	+	9.39951i	0.668557	+	0.385992i	0.795530	−	0.605915i	$-0.207193\pi$
$593$	16.2804	+	9.39951i	0.668557	+	0.385992i	−0.126973	+	0.991906i	$0.540526\pi$
$594$		0			0
$595$	0.0105327	−	2.17059i	0.000431798	−	0.0889857i
$596$		0			0
$597$	6.25415	−	10.8325i	0.255965	−	0.443345i
$598$		0			0
$599$	−29.1754	+	16.8444i	−1.19207	+	0.688244i	−0.958776	−	0.284162i	$-0.908285\pi$
$599$	−29.1754	+	16.8444i	−1.19207	+	0.688244i	−0.233297	+	0.972406i	$0.574951\pi$
$600$		0			0
$601$			13.5530i			0.552837i	0.961037	+	0.276418i	$0.0891475\pi$
$601$			13.5530i			0.552837i	−0.961037	+	0.276418i	$0.910852\pi$
$602$		0			0
$603$		−	25.8985i		−	1.05467i
$604$		0			0
$605$	27.8382	+	0.150366i	1.13178	+	0.00611323i
$606$		0			0
$607$	−16.7014	+	28.9277i	−0.677889	+	1.17414i	0.297727	+	0.954651i	$0.403772\pi$
$607$	−16.7014	+	28.9277i	−0.677889	+	1.17414i	−0.975616	+	0.219487i	$0.929562\pi$
$608$		0			0
$609$	13.1423	+	23.0203i	0.532551	+	0.932830i
$610$		0			0
$611$	−6.74335	+	11.6798i	−0.272807	+	0.472515i
$612$		0			0
$613$	34.4374	−	19.8824i	1.39091	−	0.803043i	0.397495	−	0.917604i	$-0.369880\pi$
$613$	34.4374	−	19.8824i	1.39091	−	0.803043i	0.993416	+	0.114561i	$0.0365462\pi$
$614$		0			0
$615$	−28.8067			−1.16160
$616$		0			0
$617$	8.93997			0.359910			0.179955	−	0.983675i	$-0.442405\pi$
$617$	8.93997			0.359910			0.179955	+	0.983675i	$0.442405\pi$
$618$		0			0
$619$	−16.5529	+	9.55680i	−0.665316	+	0.384120i	−0.794299	−	0.607526i	$-0.792162\pi$
$619$	−16.5529	+	9.55680i	−0.665316	+	0.384120i	0.128984	+	0.991647i	$0.458829\pi$
$620$		0			0
$621$	0.425502	−	0.736992i	0.0170748	−	0.0295745i
$622$		0			0
$623$	7.28902	−	12.4847i	0.292029	−	0.500187i
$624$		0			0
$625$	15.0253	−	26.0246i	0.601013	−	1.04099i
$626$		0			0
$627$	−4.51401	+	7.76995i	−0.180272	+	0.310302i
$628$		0			0
$629$			0.389054i			0.0155126i
$630$		0			0
$631$			35.4165i			1.40991i	0.709252	+	0.704955i	$0.249033\pi$
$631$			35.4165i			1.40991i	−0.709252	+	0.704955i	$0.750967\pi$
$632$		0			0
$633$	27.9451	−	16.1341i	1.11072	−	0.641274i
$634$		0			0
$635$	22.7621	−	39.4251i	0.903287	−	1.56454i
$636$		0			0
$637$	−0.0987344	+	10.1735i	−0.00391200	+	0.403087i
$638$		0			0
$639$	35.0586	+	20.2411i	1.38690	+	0.800724i
$640$		0			0
$641$	−12.5274	−	21.6980i	−0.494801	−	0.857020i	0.505181	−	0.863013i	$-0.331426\pi$
$641$	−12.5274	−	21.6980i	−0.494801	−	0.857020i	−0.999982	+	0.00599312i	$0.998092\pi$
$642$		0			0
$643$			17.2549i			0.680469i	0.940341	+	0.340234i	$0.110506\pi$
$643$			17.2549i			0.680469i	−0.940341	+	0.340234i	$0.889494\pi$
$644$		0			0
$645$			71.4370i			2.81283i
$646$		0			0
$647$	−32.6402	+	18.8448i	−1.28322	+	0.740866i	−0.977435	−	0.211235i	$-0.932252\pi$
$647$	−32.6402	+	18.8448i	−1.28322	+	0.740866i	−0.305783	+	0.952101i	$0.598918\pi$
$648$		0			0
$649$	0.554583	+	0.00149775i	0.0217693	+	5.87920e-5i
$650$		0			0
$651$	11.0601	−	18.9438i	0.433481	−	0.742468i
$652$		0			0
$653$	7.98587	−	13.8319i	0.312511	−	0.541285i	−0.666394	−	0.745600i	$-0.732163\pi$
$653$	7.98587	−	13.8319i	0.312511	−	0.541285i	0.978905	+	0.204314i	$0.0654965\pi$
$654$		0			0
$655$	−17.6560	−	30.5810i	−0.689876	−	1.19490i
$656$		0			0
$657$			31.6097i			1.23321i
$658$		0			0
$659$	−28.1773			−1.09763			−0.548817	−	0.835943i	$-0.684922\pi$
$659$	−28.1773			−1.09763			−0.548817	+	0.835943i	$0.684922\pi$
$660$		0			0
$661$	−6.44116	−	11.1564i	−0.250532	−	0.433935i	0.713140	−	0.701021i	$-0.247272\pi$
$661$	−6.44116	−	11.1564i	−0.250532	−	0.433935i	−0.963672	+	0.267087i	$0.913939\pi$
$662$		0			0
$663$	0.983893	+	0.568051i	0.0382112	+	0.0220613i
$664$		0			0
$665$	−3.73016	−	6.53384i	−0.144649	−	0.253372i
$666$		0			0
$667$	−3.94692	+	6.83626i	−0.152825	+	0.264701i
$668$		0			0
$669$	25.2314	+	43.7021i	0.975503	+	1.68962i
$670$		0			0
$671$	21.7214	+	37.8583i	0.838546	+	1.46151i
$672$		0			0
$673$		−	37.7496i		−	1.45514i	−0.686032	−	0.727571i	$-0.740649\pi$
$673$		−	37.7496i		−	1.45514i	0.686032	−	0.727571i	$-0.259351\pi$
$674$		0			0
$675$	−0.544983	+	0.314646i	−0.0209764	+	0.0121107i
$676$		0			0
$677$	39.6079	+	22.8677i	1.52226	+	0.878875i	0.999654	+	0.0262989i	$0.00837216\pi$
$677$	39.6079	+	22.8677i	1.52226	+	0.878875i	0.522603	+	0.852576i	$0.324961\pi$
$678$		0			0
$679$	−12.3100	−	0.0597335i	−0.472414	−	0.00229236i
$680$		0			0
$681$	−15.3580	−	8.86694i	−0.588519	−	0.339782i
$682$		0			0
$683$	−2.97584	+	1.71810i	−0.113867	+	0.0657414i	−0.555852	−	0.831281i	$-0.687608\pi$
$683$	−2.97584	+	1.71810i	−0.113867	+	0.0657414i	0.441985	+	0.897023i	$0.354275\pi$
$684$		0			0
$685$	−2.47187			−0.0944453
$686$		0			0
$687$			53.7174i			2.04945i
$688$		0			0
$689$	−4.20179	+	2.42590i	−0.160075	+	0.0924196i
$690$		0			0
$691$	18.6638	+	10.7755i	0.710004	+	0.409921i	0.811063	−	0.584960i	$-0.198890\pi$
$691$	18.6638	+	10.7755i	0.710004	+	0.409921i	−0.101059	+	0.994880i	$0.532223\pi$
$692$		0			0
$693$	21.4790	−	12.1855i	0.815918	−	0.462889i
$694$		0			0
$695$	5.05239	−	8.75100i	0.191648	−	0.331944i
$696$		0			0
$697$	−0.765144	−	1.32527i	−0.0289819	−	0.0501981i
$698$		0			0
$699$	−51.0399			−1.93051
$700$		0			0
$701$			26.2720i			0.992281i	0.868242	+	0.496141i	$0.165250\pi$
$701$			26.2720i			0.992281i	−0.868242	+	0.496141i	$0.834750\pi$
$702$		0			0
$703$	0.674255	+	1.16784i	0.0254300	+	0.0440461i
$704$		0			0
$705$	−28.3130	+	49.0396i	−1.06633	+	1.84694i
$706$		0			0
$707$	22.5991	−	12.9018i	0.849927	−	0.485222i
$708$		0			0
$709$	1.77088	−	3.06726i	0.0665069	−	0.115193i	−0.830855	−	0.556490i	$-0.812148\pi$
$709$	1.77088	−	3.06726i	0.0665069	−	0.115193i	0.897361	+	0.441296i	$0.145481\pi$
$710$		0			0
$711$	24.3897	+	42.2442i	0.914684	+	1.58428i
$712$		0			0
$713$	6.53248			0.244643
$714$		0			0
$715$	−6.07120	−	10.5815i	−0.227050	−	0.395726i
$716$		0			0
$717$	−31.2611	+	18.0486i	−1.16747	+	0.674038i
$718$		0			0
$719$	−11.5545	−	6.67102i	−0.430912	−	0.248787i	0.268823	−	0.963190i	$-0.413365\pi$
$719$	−11.5545	−	6.67102i	−0.430912	−	0.248787i	−0.699735	+	0.714403i	$0.746699\pi$
$720$		0			0
$721$	−13.0849	−	7.63945i	−0.487306	−	0.284508i
$722$		0			0
$723$	15.1008	−	26.1553i	0.561604	−	0.972727i
$724$		0			0
$725$	5.05521	−	2.91863i	0.187746	−	0.108395i
$726$		0			0
$727$			27.3357i			1.01383i	0.861997	+	0.506913i	$0.169214\pi$
$727$			27.3357i			1.01383i	−0.861997	+	0.506913i	$0.830786\pi$
$728$		0			0
$729$	23.5590			0.872557
$730$		0			0
$731$	−3.28649	+	1.89746i	−0.121555	+	0.0701800i
$732$		0			0
$733$	−19.9303	−	11.5068i	−0.736143	−	0.425012i	0.0845226	−	0.996422i	$-0.473063\pi$
$733$	−19.9303	−	11.5068i	−0.736143	−	0.425012i	−0.820665	+	0.571409i	$0.806397\pi$
$734$		0			0
$735$	−0.414552	+	42.7148i	−0.0152910	+	1.57556i
$736$		0			0
$737$	−30.5218	−	0.0824297i	−1.12428	−	0.00303634i
$738$		0			0
$739$	−18.2380	−	31.5892i	−0.670896	−	1.16203i	−0.977650	−	0.210237i	$-0.932576\pi$
$739$	−18.2380	−	31.5892i	−0.670896	−	1.16203i	0.306754	−	0.951789i	$-0.400757\pi$
$740$		0			0
$741$	3.93787			0.144661
$742$		0			0
$743$	−35.4230			−1.29955			−0.649773	−	0.760129i	$-0.725136\pi$
$743$	−35.4230			−1.29955			−0.649773	+	0.760129i	$0.725136\pi$
$744$		0			0
$745$	0.389859	−	0.225085i	0.0142833	−	0.00824648i
$746$		0			0
$747$	4.80739	−	8.32664i	0.175893	−	0.304656i
$748$		0			0
$749$	13.0316	−	22.3205i	0.476163	−	0.815574i
$750$		0			0
$751$	32.8585	+	18.9708i	1.19902	+	0.692256i	0.960337	−	0.278841i	$-0.0899503\pi$
$751$	32.8585	+	18.9708i	1.19902	+	0.692256i	0.238685	+	0.971097i	$0.423284\pi$
$752$		0			0
$753$	15.6021	+	27.0237i	0.568573	+	0.984798i
$754$		0			0
$755$	10.1158			0.368152
$756$		0			0
$757$	−35.3553			−1.28501			−0.642505	−	0.766282i	$-0.722105\pi$
$757$	−35.3553			−1.28501			−0.642505	+	0.766282i	$0.722105\pi$
$758$		0			0
$759$	13.1373	+	7.63220i	0.476854	+	0.277031i
$760$		0			0
$761$	11.9361	+	6.89132i	0.432684	+	0.249810i	0.700489	−	0.713663i	$-0.252965\pi$
$761$	11.9361	+	6.89132i	0.432684	+	0.249810i	−0.267806	+	0.963473i	$0.586299\pi$
$762$		0			0
$763$	−16.0247	+	9.14846i	−0.580132	+	0.331196i
$764$		0			0
$765$	1.99952	+	1.15442i	0.0722927	+	0.0417382i
$766$		0			0
$767$	−0.121516	−	0.210471i	−0.00438768	−	0.00759968i
$768$		0			0
$769$			44.7028i			1.61202i	0.591899	+	0.806012i	$0.298379\pi$
$769$			44.7028i			1.61202i	−0.591899	+	0.806012i	$0.701621\pi$
$770$		0			0
$771$		−	49.0502i		−	1.76650i
$772$		0			0
$773$	4.93088	+	8.54054i	0.177351	+	0.307182i	0.940973	−	0.338483i	$-0.109914\pi$
$773$	4.93088	+	8.54054i	0.177351	+	0.307182i	−0.763621	+	0.645665i	$0.776580\pi$
$774$		0			0
$775$	−4.18340	−	2.41529i	−0.150272	−	0.0867597i
$776$		0			0
$777$	0.0371518	−	7.65631i	0.00133281	−	0.274669i
$778$		0			0
$779$	−4.59355	−	2.65209i	−0.164581	−	0.0950208i
$780$		0			0
$781$	23.9660	−	41.2526i	0.857570	−	1.47613i
$782$		0			0
$783$	1.86121			0.0665142
$784$		0			0
$785$	−27.0947			−0.967050
$786$		0			0
$787$	19.8521	+	34.3848i	0.707650	+	1.22569i	0.965726	+	0.259562i	$0.0835782\pi$
$787$	19.8521	+	34.3848i	0.707650	+	1.22569i	−0.258076	+	0.966125i	$0.583088\pi$
$788$		0			0
$789$	1.21352	+	0.700629i	0.0432026	+	0.0249431i
$790$		0			0
$791$	−43.8013	−	0.212543i	−1.55739	−	0.00755716i
$792$		0			0
$793$	9.56358	−	16.5646i	0.339613	−	0.588226i
$794$		0			0
$795$	−17.6419	+	10.1855i	−0.625692	+	0.361243i
$796$		0			0
$797$	16.3075			0.577641			0.288820	−	0.957383i	$-0.406737\pi$
$797$	16.3075			0.577641			0.288820	+	0.957383i	$0.406737\pi$
$798$		0			0
$799$	−3.00812			−0.106420
$800$		0			0
$801$	7.68865	+	13.3171i	0.271665	+	0.470538i
$802$		0			0
$803$	37.2525	+	0.100607i	1.31461	+	0.00355035i
$804$		0			0
$805$	−11.0473	+	6.30689i	−0.389367	+	0.222289i
$806$		0			0
$807$	−4.96628	−	2.86728i	−0.174821	−	0.100933i
$808$		0			0
$809$	19.2650	−	11.1226i	0.677320	−	0.391051i	−0.121524	−	0.992588i	$-0.538778\pi$
$809$	19.2650	−	11.1226i	0.677320	−	0.391051i	0.798845	+	0.601537i	$0.205445\pi$
$810$		0			0
$811$	12.8676			0.451842			0.225921	−	0.974146i	$-0.427461\pi$
$811$	12.8676			0.451842			0.225921	+	0.974146i	$0.427461\pi$
$812$		0			0
$813$			10.5590i			0.370321i
$814$		0			0
$815$	−6.64342	+	3.83558i	−0.232709	+	0.134354i
$816$		0			0
$817$	−6.57683	+	11.3914i	−0.230094	+	0.398535i
$818$		0			0
$819$	−9.34559	−	5.45631i	−0.326561	−	0.190659i
$820$		0			0
$821$	−36.7619	−	21.2245i	−1.28300	−	0.740741i	−0.305605	−	0.952158i	$-0.598859\pi$
$821$	−36.7619	−	21.2245i	−1.28300	−	0.740741i	−0.977396	+	0.211417i	$0.932192\pi$
$822$		0			0
$823$	46.0698	−	26.5984i	1.60589	−	0.927161i	0.615614	−	0.788048i	$-0.288908\pi$
$823$	46.0698	−	26.5984i	1.60589	−	0.927161i	0.990276	−	0.139114i	$-0.0444254\pi$
$824$		0			0
$825$	−5.59123	−	9.74498i	−0.194662	−	0.339277i
$826$		0			0
$827$	16.7820			0.583567			0.291784	−	0.956484i	$-0.405751\pi$
$827$	16.7820			0.583567			0.291784	+	0.956484i	$0.405751\pi$
$828$		0			0
$829$	11.7573	+	20.3642i	0.408348	+	0.707279i	0.994705	−	0.102774i	$-0.0327718\pi$
$829$	11.7573	+	20.3642i	0.408348	+	0.707279i	−0.586357	+	0.810053i	$0.699438\pi$
$830$		0			0
$831$	−21.2703	+	36.8412i	−0.737859	+	1.27801i
$832$		0			0
$833$	−1.97613	+	1.11549i	−0.0684688	+	0.0386494i
$834$		0			0
$835$	−28.9619	+	50.1636i	−1.00227	+	1.73598i
$836$		0			0
$837$	−0.770115	−	1.33388i	−0.0266191	−	0.0461056i
$838$		0			0
$839$			15.2634i			0.526953i	0.964666	+	0.263476i	$0.0848691\pi$
$839$			15.2634i			0.526953i	−0.964666	+	0.263476i	$0.915131\pi$
$840$		0			0
$841$	11.7356			0.404676
$842$		0			0
$843$	36.6737	+	63.5207i	1.26311	+	2.18777i
$844$		0			0
$845$	13.7770	−	23.8625i	0.473945	−	0.820896i
$846$		0			0
$847$	−14.2924	−	25.3520i	−0.491094	−	0.871107i
$848$		0			0
$849$	−46.7756	−	27.0059i	−1.60534	−	0.926841i
$850$		0			0
$851$	1.97457	−	1.14002i	0.0676874	−	0.0390793i
$852$		0			0
$853$			22.3639i			0.765726i	0.923805	+	0.382863i	$0.125062\pi$
$853$			22.3639i			0.765726i	−0.923805	+	0.382863i	$0.874938\pi$
$854$		0			0
$855$	8.00275			0.273688
$856$		0			0
$857$	−0.143441	+	0.0828160i	−0.00489987	+	0.00282894i	−0.502448	−	0.864607i	$-0.667567\pi$
$857$	−0.143441	+	0.0828160i	−0.00489987	+	0.00282894i	0.497548	+	0.867436i	$0.334234\pi$
$858$		0			0
$859$	−26.1958	−	15.1241i	−0.893788	−	0.516029i	−0.0186085	−	0.999827i	$-0.505924\pi$
$859$	−26.1958	−	15.1241i	−0.893788	−	0.516029i	−0.875180	+	0.483798i	$0.839257\pi$
$860$		0			0
$861$	14.9310	+	26.1534i	0.508846	+	0.891307i
$862$		0			0
$863$	−4.45074	−	2.56964i	−0.151505	−	0.0874714i	0.422331	−	0.906442i	$-0.361212\pi$
$863$	−4.45074	−	2.56964i	−0.151505	−	0.0874714i	−0.573836	+	0.818970i	$0.694545\pi$
$864$		0			0
$865$	0.235126	−	0.135750i	0.00799454	−	0.00461565i
$866$		0			0
$867$		−	40.7382i		−	1.38354i
$868$		0			0
$869$	49.8630	−	28.6091i	1.69149	−	0.970499i
$870$		0			0
$871$	6.68769	+	11.5834i	0.226604	+	0.392489i
$872$		0			0
$873$	6.54702	−	11.3398i	0.221583	−	0.383793i
$874$		0			0
$875$	−24.0721	−	0.116809i	−0.813787	−	0.00394885i
$876$		0			0
$877$	−23.2134	−	13.4023i	−0.783862	−	0.452563i	0.0539351	−	0.998544i	$-0.482824\pi$
$877$	−23.2134	−	13.4023i	−0.783862	−	0.452563i	−0.837797	+	0.545981i	$0.816157\pi$
$878$		0			0
$879$	−15.1965	−	26.3211i	−0.512566	−	0.887790i
$880$		0			0
$881$	−24.7450			−0.833682			−0.416841	−	0.908980i	$-0.636863\pi$
$881$	−24.7450			−0.833682			−0.416841	+	0.908980i	$0.636863\pi$
$882$		0			0
$883$		−	33.8722i		−	1.13989i	−0.821683	−	0.569945i	$-0.806964\pi$
$883$		−	33.8722i		−	1.13989i	0.821683	−	0.569945i	$-0.193036\pi$
$884$		0			0
$885$	−0.510202	−	0.883696i	−0.0171503	−	0.0297051i
$886$		0			0
$887$	−0.917673	+	1.58946i	−0.0308124	+	0.0533687i	−0.881020	−	0.473078i	$-0.843143\pi$
$887$	−0.917673	+	1.58946i	−0.0308124	+	0.0533687i	0.850208	+	0.526447i	$0.176476\pi$
$888$		0			0
$889$	−47.5918	−	0.230936i	−1.59618	−	0.00774535i
$890$		0			0
$891$	0.0852969	−	31.5834i	0.00285755	−	1.05808i
$892$		0			0
$893$	−9.02963	+	5.21326i	−0.302165	+	0.174455i
$894$		0			0
$895$			33.2974i			1.11301i
$896$		0			0
$897$		−	6.65809i		−	0.222307i
$898$		0			0
$899$	7.14351	+	12.3729i	0.238249	+	0.412660i
$900$		0			0
$901$	−0.937181	−	0.541081i	−0.0312220	−	0.0180260i
$902$		0			0
$903$	64.8571	−	37.0268i	2.15831	−	1.23218i
$904$		0			0
$905$	−12.5000	+	21.6507i	−0.415514	+	0.719692i
$906$		0			0
$907$	43.4434	−	25.0820i	1.44251	−	0.832835i	0.444496	−	0.895781i	$-0.353383\pi$
$907$	43.4434	−	25.0820i	1.44251	−	0.832835i	0.998017	+	0.0629457i	$0.0200495\pi$
$908$		0			0
$909$			27.6797i			0.918078i
$910$		0			0
$911$		−	41.9918i		−	1.39125i	−0.718405	−	0.695625i	$-0.755128\pi$
$911$		−	41.9918i		−	1.39125i	0.718405	−	0.695625i	$-0.244872\pi$
$912$		0			0
$913$	−9.79777	−	5.69208i	−0.324259	−	0.188380i
$914$		0			0
$915$	40.1542	−	69.5490i	1.32746	−	2.29922i
$916$		0			0
$917$	−18.6130	+	31.8803i	−0.614654	+	1.05278i
$918$		0			0
$919$	1.71946	−	2.97819i	0.0567197	−	0.0982414i	−0.836271	−	0.548316i	$-0.815269\pi$
$919$	1.71946	−	2.97819i	0.0567197	−	0.0982414i	0.892991	+	0.450074i	$0.148603\pi$
$920$		0			0
$921$	−23.5145	+	13.5761i	−0.774828	+	0.447347i
$922$		0			0
$923$	−20.9071			−0.688167
$924$		0			0
$925$	−1.68602			−0.0554360
$926$		0			0
$927$	13.9574	−	8.05829i	0.458420	−	0.264669i
$928$		0			0
$929$	−23.3381	+	40.4228i	−0.765699	+	1.32623i	0.174178	+	0.984714i	$0.444273\pi$
$929$	−23.3381	+	40.4228i	−0.765699	+	1.32623i	−0.939876	+	0.341515i	$0.889060\pi$
$930$		0			0
$931$	−3.99863	+	6.77318i	−0.131050	+	0.221982i
$932$		0			0
$933$	13.9864	−	24.2252i	0.457895	−	0.793098i
$934$		0			0
$935$	1.36687	−	2.35279i	0.0447013	−	0.0769444i
$936$		0			0
$937$		−	45.2397i		−	1.47792i	−0.673751	−	0.738959i	$-0.735318\pi$
$937$		−	45.2397i		−	1.47792i	0.673751	−	0.738959i	$-0.264682\pi$
$938$		0			0
$939$			62.2831i			2.03253i
$940$		0			0
$941$	13.8231	−	7.98074i	0.450619	−	0.260165i	−0.257473	−	0.966286i	$-0.582890\pi$
$941$	13.8231	−	7.98074i	0.450619	−	0.260165i	0.708091	+	0.706121i	$0.249556\pi$
$942$		0			0
$943$	−4.48410	+	7.76669i	−0.146022	+	0.252918i
$944$		0			0
$945$	2.59018	+	1.51225i	0.0842587	+	0.0491934i
$946$		0			0
$947$	13.6862	+	7.90173i	0.444742	+	0.256772i	0.705607	−	0.708603i	$-0.250674\pi$
$947$	13.6862	+	7.90173i	0.444742	+	0.256772i	−0.260865	+	0.965375i	$0.584008\pi$
$948$		0			0
$949$	−8.16246	−	14.1378i	−0.264965	−	0.458932i
$950$		0			0
$951$		−	52.7447i		−	1.71036i
$952$		0			0
$953$		−	29.3909i		−	0.952066i	−0.879427	−	0.476033i	$-0.842074\pi$
$953$		−	29.3909i		−	0.952066i	0.879427	−	0.476033i	$-0.157926\pi$
$954$		0			0
$955$	−33.4731	+	19.3257i	−1.08316	+	0.625365i
$956$		0			0
$957$	−0.0897409	+	33.2289i	−0.00290091	+	1.07414i
$958$		0			0
$959$	1.28121	+	2.24419i	0.0413723	+	0.0724688i
$960$		0			0
$961$	−9.58844	+	16.6077i	−0.309305	+	0.535731i
$962$		0			0
$963$	13.7460	+	23.8088i	0.442960	+	0.767229i
$964$		0			0
$965$		−	12.6482i		−	0.407161i
$966$		0			0
$967$	9.08639			0.292199			0.146099	−	0.989270i	$-0.453328\pi$
$967$	9.08639			0.292199			0.146099	+	0.989270i	$0.453328\pi$
$968$		0			0
$969$	0.439158	+	0.760644i	0.0141078	+	0.0244354i
$970$		0			0
$971$	46.8203	+	27.0317i	1.50253	+	0.867489i	0.999996	+	0.00293391i	$0.000933895\pi$
$971$	46.8203	+	27.0317i	1.50253	+	0.867489i	0.502539	+	0.864555i	$0.332399\pi$
$972$		0			0
$973$	−10.5637	−	0.0512597i	−0.338657	−	0.00164331i
$974$		0			0
$975$	−2.46173	+	4.26384i	−0.0788384	+	0.136552i
$976$		0			0
$977$	18.2561	+	31.6205i	0.584064	+	1.01163i	0.994991	+	0.0999610i	$0.0318718\pi$
$977$	18.2561	+	31.6205i	0.584064	+	1.01163i	−0.410927	+	0.911668i	$0.634795\pi$
$978$		0			0
$979$	15.7189	−	9.01881i	0.502379	−	0.288242i
$980$		0			0
$981$		−	19.6272i		−	0.626650i
$982$		0			0
$983$	19.9468	−	11.5163i	0.636203	−	0.367312i	−0.146947	−	0.989144i	$-0.546945\pi$
$983$	19.9468	−	11.5163i	0.636203	−	0.367312i	0.783150	+	0.621832i	$0.213611\pi$
$984$		0			0
$985$	−11.1654	−	6.44636i	−0.355760	−	0.205398i
$986$		0			0
$987$	59.1977	+	0.287253i	1.88428	+	0.00914337i
$988$		0			0
$989$	19.2604	+	11.1200i	0.612445	+	0.353595i
$990$		0			0
$991$	−10.0182	+	5.78403i	−0.318240	+	0.183736i	−0.650608	−	0.759414i	$-0.725486\pi$
$991$	−10.0182	+	5.78403i	−0.318240	+	0.183736i	0.332368	+	0.943150i	$0.392152\pi$
$992$		0			0
$993$	−72.7383			−2.30828
$994$		0			0
$995$			13.1282i			0.416193i
$996$		0			0
$997$	−32.0733	+	18.5175i	−1.01577	+	0.586456i	−0.912876	−	0.408237i	$-0.866144\pi$
$997$	−32.0733	+	18.5175i	−1.01577	+	0.586456i	−0.102895	+	0.994692i	$0.532810\pi$
$998$		0			0
$999$	−0.465564	−	0.268794i	−0.0147298	−	0.00850426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.bi.b.527.4	yes	32
4.3	odd	2		1232.2.bi.a.527.13	✓	32
7.4	even	3		1232.2.bi.a.879.14	yes	32
11.10	odd	2	inner	1232.2.bi.b.527.3	yes	32
28.11	odd	6	inner	1232.2.bi.b.879.3	yes	32
44.43	even	2		1232.2.bi.a.527.14	yes	32
77.32	odd	6		1232.2.bi.a.879.13	yes	32
308.263	even	6	inner	1232.2.bi.b.879.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1232.2.bi.a.527.13	✓	32	4.3	odd	2
1232.2.bi.a.527.14	yes	32	44.43	even	2
1232.2.bi.a.879.13	yes	32	77.32	odd	6
1232.2.bi.a.879.14	yes	32	7.4	even	3
1232.2.bi.b.527.3	yes	32	11.10	odd	2	inner
1232.2.bi.b.527.4	yes	32	1.1	even	1	trivial
1232.2.bi.b.879.3	yes	32	28.11	odd	6	inner
1232.2.bi.b.879.4	yes	32	308.263	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08822 + 1.20564i) q^{3} +(1.26539 - 2.19172i) q^{5} +(-2.64572 - 0.0128382i) q^{7} +(1.40712 - 2.43720i) q^{9} +O(q^{10})\)	\(q+(-2.08822 + 1.20564i) q^{3} +(1.26539 - 2.19172i) q^{5} +(-2.64572 - 0.0128382i) q^{7} +(1.40712 - 2.43720i) q^{9} +(-2.86779 - 1.66606i) q^{11} +1.45342i q^{13} +6.10240i q^{15} +(-0.280744 + 0.162088i) q^{17} +(-0.561816 + 0.973095i) q^{19} +(5.54033 - 3.16297i) q^{21} +(1.64529 + 0.949910i) q^{23} +(-0.702430 - 1.21664i) q^{25} -0.447940i q^{27} +4.15504i q^{29} +(2.97781 - 1.71924i) q^{31} +(7.99725 + 0.0215981i) q^{33} +(-3.37601 + 5.78244i) q^{35} +(0.600067 - 1.03935i) q^{37} +(-1.75229 - 3.03506i) q^{39} +4.72055i q^{41} +11.7064 q^{43} +(-3.56110 - 6.16801i) q^{45} +(8.03611 + 4.63965i) q^{47} +(6.99967 + 0.0679325i) q^{49} +(0.390837 - 0.676950i) q^{51} +(1.66910 + 2.89097i) q^{53} +(-7.28043 + 4.17718i) q^{55} -2.70938i q^{57} +(-0.144811 + 0.0836068i) q^{59} +(-11.3970 - 6.58006i) q^{61} +(-3.75412 + 6.43007i) q^{63} +(3.18549 + 1.83914i) q^{65} +(7.96977 - 4.60135i) q^{67} -4.58098 q^{69} +14.3848i q^{71} +(-9.72727 + 5.61604i) q^{73} +(2.93366 + 1.69375i) q^{75} +(7.56599 + 4.44475i) q^{77} +(-8.66655 + 15.0109i) q^{79} +(4.76140 + 8.24698i) q^{81} +3.41648 q^{83} +0.820417i q^{85} +(-5.00947 - 8.67666i) q^{87} +(-2.73206 + 4.73207i) q^{89} +(0.0186593 - 3.84534i) q^{91} +(-4.14555 + 7.18030i) q^{93} +(1.42184 + 2.46269i) q^{95} +4.65280 q^{97} +(-8.09584 + 4.64503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 12 * q^9	\( 32 q - 2 q^{5} + 12 q^{9} + 9 q^{11} + 18 q^{23} - 6 q^{25} + 5 q^{33} - 6 q^{37} - 10 q^{45} + 36 q^{47} - 32 q^{49} + 42 q^{59} + 18 q^{67} - 24 q^{69} + 78 q^{75} - 19 q^{77} - 24 q^{81} - 8 q^{89} + 18 q^{91} + 2 q^{93} + 12 q^{97}+O(q^{100}) \) 32 * q - 2 * q^5 + 12 * q^9 + 9 * q^11 + 18 * q^23 - 6 * q^25 + 5 * q^33 - 6 * q^37 - 10 * q^45 + 36 * q^47 - 32 * q^49 + 42 * q^59 + 18 * q^67 - 24 * q^69 + 78 * q^75 - 19 * q^77 - 24 * q^81 - 8 * q^89 + 18 * q^91 + 2 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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