LMFDB - Embedded newform 1120.2.bq.b.719.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(719,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("1120.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.18
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.360276 - 0.624015i) q^{3} +(1.56432 - 1.59778i) q^{5} +(1.35637 - 2.27162i) q^{7} +(1.24040 - 2.14844i) q^{9} +O(q^{10})$	\(q+(-0.360276 - 0.624015i) q^{3} +(1.56432 - 1.59778i) q^{5} +(1.35637 - 2.27162i) q^{7} +(1.24040 - 2.14844i) q^{9} +(-1.95654 - 3.38883i) q^{11} -2.55354i q^{13} +(-1.56063 - 0.400522i) q^{15} +(2.55984 + 4.43377i) q^{17} +(-3.25858 - 1.88134i) q^{19} +(-1.90619 - 0.0279831i) q^{21} +(-3.50209 + 6.06580i) q^{23} +(-0.105783 - 4.99888i) q^{25} -3.94920 q^{27} +3.39188i q^{29} +(1.59267 + 2.75858i) q^{31} +(-1.40979 + 2.44183i) q^{33} +(-1.50775 - 5.72072i) q^{35} +(-0.850773 + 1.47358i) q^{37} +(-1.59345 + 0.919977i) q^{39} -3.97345i q^{41} +0.898763i q^{43} +(-1.49234 - 5.34275i) q^{45} +(5.64460 + 3.25891i) q^{47} +(-3.32054 - 6.16230i) q^{49} +(1.84449 - 3.19476i) q^{51} +(2.92487 + 5.06602i) q^{53} +(-8.47526 - 2.17511i) q^{55} +2.71120i q^{57} +(10.2528 - 5.91946i) q^{59} +(-5.94508 + 10.2972i) q^{61} +(-3.19801 - 5.73180i) q^{63} +(-4.07998 - 3.99456i) q^{65} +(2.68095 - 1.54785i) q^{67} +5.04687 q^{69} -12.3374i q^{71} +(-2.59351 - 4.49209i) q^{73} +(-3.08127 + 1.86698i) q^{75} +(-10.3519 - 0.151968i) q^{77} +(8.84693 + 5.10778i) q^{79} +(-2.29841 - 3.98096i) q^{81} -0.786461 q^{83} +(11.0886 + 2.84580i) q^{85} +(2.11658 - 1.22201i) q^{87} +(-0.679974 - 0.392583i) q^{89} +(-5.80068 - 3.46353i) q^{91} +(1.14760 - 1.98770i) q^{93} +(-8.10344 + 2.26346i) q^{95} -16.5331 q^{97} -9.70761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{9}+O(q^{10}) $ 80 * q - 52 * q^9	$ 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) $ 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−0.360276	−	0.624015i	−0.208005	−	0.360276i	0.743081	−	0.669202i	$-0.233364\pi$
$3$	−0.360276	−	0.624015i	−0.208005	−	0.360276i	−0.951086	+	0.308926i	$0.900030\pi$
$4$		0			0
$5$	1.56432	−	1.59778i	0.699587	−	0.714548i
$5$	1.56432	−	1.59778i	0.699587	−	0.714548i
$6$		0			0
$7$	1.35637	−	2.27162i	0.512658	−	0.858593i
$7$	1.35637	−	2.27162i	0.512658	−	0.858593i
$8$		0			0
$9$	1.24040	−	2.14844i	0.413468	−	0.716147i
$10$		0			0
$11$	−1.95654	−	3.38883i	−0.589920	−	1.02177i	−0.994242	−	0.107155i	$-0.965826\pi$
$11$	−1.95654	−	3.38883i	−0.589920	−	1.02177i	0.404322	−	0.914616i	$-0.367507\pi$
$12$		0			0
$13$		−	2.55354i		−	0.708224i	−0.935203	−	0.354112i	$-0.884783\pi$
$13$		−	2.55354i		−	0.708224i	0.935203	−	0.354112i	$-0.115217\pi$
$14$		0			0
$15$	−1.56063	−	0.400522i	−0.402952	−	0.103414i
$16$		0			0
$17$	2.55984	+	4.43377i	0.620852	+	1.07535i	0.989327	+	0.145709i	$0.0465464\pi$
$17$	2.55984	+	4.43377i	0.620852	+	1.07535i	−0.368476	+	0.929637i	$0.620120\pi$
$18$		0			0
$19$	−3.25858	−	1.88134i	−0.747569	−	0.431609i	0.0772457	−	0.997012i	$-0.475387\pi$
$19$	−3.25858	−	1.88134i	−0.747569	−	0.431609i	−0.824815	+	0.565403i	$0.808721\pi$
$20$		0			0
$21$	−1.90619	−	0.0279831i	−0.415966	−	0.00610642i
$22$		0			0
$23$	−3.50209	+	6.06580i	−0.730237	+	1.26481i	0.226545	+	0.974001i	$0.427257\pi$
$23$	−3.50209	+	6.06580i	−0.730237	+	1.26481i	−0.956782	+	0.290807i	$0.906076\pi$
$24$		0			0
$25$	−0.105783	−	4.99888i	−0.0211566	−	0.999776i
$26$		0			0
$27$	−3.94920			−0.760024
$28$		0			0
$29$			3.39188i			0.629856i	0.949116	+	0.314928i	$0.101980\pi$
$29$			3.39188i			0.629856i	−0.949116	+	0.314928i	$0.898020\pi$
$30$		0			0
$31$	1.59267	+	2.75858i	0.286052	+	0.495456i	0.972864	−	0.231379i	$-0.0743237\pi$
$31$	1.59267	+	2.75858i	0.286052	+	0.495456i	−0.686812	+	0.726835i	$0.740990\pi$
$32$		0			0
$33$	−1.40979	+	2.44183i	−0.245413	+	0.425067i
$34$		0			0
$35$	−1.50775	−	5.72072i	−0.254857	−	0.966979i
$36$		0			0
$37$	−0.850773	+	1.47358i	−0.139866	+	0.242256i	−0.927446	−	0.373957i	$-0.878001\pi$
$37$	−0.850773	+	1.47358i	−0.139866	+	0.242256i	0.787580	+	0.616213i	$0.211334\pi$
$38$		0			0
$39$	−1.59345	+	0.919977i	−0.255156	+	0.147314i
$40$		0			0
$41$		−	3.97345i		−	0.620548i	−0.950647	−	0.310274i	$-0.899579\pi$
$41$		−	3.97345i		−	0.620548i	0.950647	−	0.310274i	$-0.100421\pi$
$42$		0			0
$43$			0.898763i			0.137060i	0.997649	+	0.0685300i	$0.0218309\pi$
$43$			0.898763i			0.137060i	−0.997649	+	0.0685300i	$0.978169\pi$
$44$		0			0
$45$	−1.49234	−	5.34275i	−0.222465	−	0.796449i
$46$		0			0
$47$	5.64460	+	3.25891i	0.823350	+	0.475361i	0.851570	−	0.524240i	$-0.175651\pi$
$47$	5.64460	+	3.25891i	0.823350	+	0.475361i	−0.0282202	+	0.999602i	$0.508984\pi$
$48$		0			0
$49$	−3.32054	−	6.16230i	−0.474363	−	0.880329i
$50$		0			0
$51$	1.84449	−	3.19476i	0.258281	−	0.447355i
$52$		0			0
$53$	2.92487	+	5.06602i	0.401761	+	0.695871i	0.993939	−	0.109937i	$-0.0350648\pi$
$53$	2.92487	+	5.06602i	0.401761	+	0.695871i	−0.592177	+	0.805808i	$0.701731\pi$
$54$		0			0
$55$	−8.47526	−	2.17511i	−1.14280	−	0.293292i
$56$		0			0
$57$			2.71120i			0.359108i
$58$		0			0
$59$	10.2528	−	5.91946i	1.33480	−	0.770648i	0.348771	−	0.937208i	$-0.386599\pi$
$59$	10.2528	−	5.91946i	1.33480	−	0.770648i	0.986031	+	0.166560i	$0.0532659\pi$
$60$		0			0
$61$	−5.94508	+	10.2972i	−0.761190	+	1.31842i	0.181048	+	0.983474i	$0.442051\pi$
$61$	−5.94508	+	10.2972i	−0.761190	+	1.31842i	−0.942238	+	0.334945i	$0.891282\pi$
$62$		0			0
$63$	−3.19801	−	5.73180i	−0.402911	−	0.722139i
$64$		0			0
$65$	−4.07998	−	3.99456i	−0.506060	−	0.495464i
$66$		0			0
$67$	2.68095	−	1.54785i	0.327530	−	0.189100i	−0.327214	−	0.944950i	$-0.606110\pi$
$67$	2.68095	−	1.54785i	0.327530	−	0.189100i	0.654744	+	0.755851i	$0.272776\pi$
$68$		0			0
$69$	5.04687			0.607572
$70$		0			0
$71$		−	12.3374i		−	1.46418i	−0.681207	−	0.732091i	$-0.738544\pi$
$71$		−	12.3374i		−	1.46418i	0.681207	−	0.732091i	$-0.261456\pi$
$72$		0			0
$73$	−2.59351	−	4.49209i	−0.303547	−	0.525759i	0.673390	−	0.739288i	$-0.264838\pi$
$73$	−2.59351	−	4.49209i	−0.303547	−	0.525759i	−0.976937	+	0.213529i	$0.931504\pi$
$74$		0			0
$75$	−3.08127	+	1.86698i	−0.355794	+	0.215581i
$76$		0			0
$77$	−10.3519	−	0.151968i	−1.17971	−	0.0173183i
$78$		0			0
$79$	8.84693	+	5.10778i	0.995358	+	0.574670i	0.906871	−	0.421407i	$-0.138464\pi$
$79$	8.84693	+	5.10778i	0.995358	+	0.574670i	0.0884863	+	0.996077i	$0.471797\pi$
$80$		0			0
$81$	−2.29841	−	3.98096i	−0.255379	−	0.442329i
$82$		0			0
$83$	−0.786461			−0.0863253			−0.0431626	−	0.999068i	$-0.513743\pi$
$83$	−0.786461			−0.0863253			−0.0431626	+	0.999068i	$0.513743\pi$
$84$		0			0
$85$	11.0886	+	2.84580i	1.20273	+	0.308670i
$86$		0			0
$87$	2.11658	−	1.22201i	0.226922	−	0.131013i
$88$		0			0
$89$	−0.679974	−	0.392583i	−0.0720771	−	0.0416137i	0.463528	−	0.886082i	$-0.346583\pi$
$89$	−0.679974	−	0.392583i	−0.0720771	−	0.0416137i	−0.535605	+	0.844468i	$0.679917\pi$
$90$		0			0
$91$	−5.80068	−	3.46353i	−0.608076	−	0.363077i
$92$		0			0
$93$	1.14760	−	1.98770i	0.119000	−	0.206115i
$94$		0			0
$95$	−8.10344	+	2.26346i	−0.831395	+	0.232226i
$96$		0			0
$97$	−16.5331			−1.67868			−0.839340	−	0.543607i	$-0.817058\pi$
$97$	−16.5331			−1.67868			−0.839340	+	0.543607i	$0.817058\pi$
$98$		0			0
$99$	−9.70761			−0.975651
$100$		0			0
$101$	−6.01482	−	10.4180i	−0.598497	−	1.03663i	−0.993043	−	0.117751i	$-0.962432\pi$
$101$	−6.01482	−	10.4180i	−0.598497	−	1.03663i	0.394547	−	0.918876i	$-0.370902\pi$
$102$		0			0
$103$	0.132170	+	0.0763082i	0.0130231	+	0.00751887i	0.506497	−	0.862241i	$-0.330940\pi$
$103$	0.132170	+	0.0763082i	0.0130231	+	0.00751887i	−0.493474	+	0.869760i	$0.664273\pi$
$104$		0			0
$105$	−3.02661	+	3.00190i	−0.295367	+	0.292955i
$106$		0			0
$107$	1.38413	+	0.799129i	0.133809	+	0.0772548i	0.565410	−	0.824810i	$-0.308718\pi$
$107$	1.38413	+	0.799129i	0.133809	+	0.0772548i	−0.431601	+	0.902065i	$0.642051\pi$
$108$		0			0
$109$	13.5710	−	7.83523i	1.29987	−	0.750479i	0.319486	−	0.947591i	$-0.396490\pi$
$109$	13.5710	−	7.83523i	1.29987	−	0.750479i	0.980381	+	0.197112i	$0.0631563\pi$
$110$		0			0
$111$	1.22605			0.116372
$112$		0			0
$113$		−	8.17675i		−	0.769204i	−0.923082	−	0.384602i	$-0.874339\pi$
$113$		−	8.17675i		−	0.769204i	0.923082	−	0.384602i	$-0.125661\pi$
$114$		0			0
$115$	4.21339	+	15.0844i	0.392901	+	1.40663i
$116$		0			0
$117$	−5.48613	−	3.16742i	−0.507193	−	0.292828i
$118$		0			0
$119$	13.5439	+	0.198826i	1.24157	+	0.0182264i
$120$		0			0
$121$	−2.15612	+	3.73451i	−0.196011	+	0.339501i
$122$		0			0
$123$	−2.47949	+	1.43154i	−0.223568	+	0.129077i
$124$		0			0
$125$	−8.15258	−	7.65085i	−0.729189	−	0.684313i
$126$		0			0
$127$	13.7657			1.22151			0.610756	−	0.791819i	$-0.290866\pi$
$127$	13.7657			1.22151			0.610756	+	0.791819i	$0.290866\pi$
$128$		0			0
$129$	0.560842	−	0.323802i	0.0493794	−	0.0285092i
$130$		0			0
$131$	8.10845	+	4.68141i	0.708438	+	0.409017i	0.810483	−	0.585763i	$-0.199205\pi$
$131$	8.10845	+	4.68141i	0.708438	+	0.409017i	−0.102044	+	0.994780i	$0.532538\pi$
$132$		0			0
$133$	−8.69352	+	4.85048i	−0.753824	+	0.420590i
$134$		0			0
$135$	−6.17783	+	6.30994i	−0.531703	+	0.543073i
$136$		0			0
$137$	16.1440	−	9.32074i	1.37927	−	0.796325i	0.387202	−	0.921995i	$-0.373441\pi$
$137$	16.1440	−	9.32074i	1.37927	−	0.796325i	0.992072	+	0.125670i	$0.0401081\pi$
$138$		0			0
$139$		−	4.50951i		−	0.382491i	−0.981542	−	0.191246i	$-0.938747\pi$
$139$		−	4.50951i		−	0.382491i	0.981542	−	0.191246i	$-0.0612527\pi$
$140$		0			0
$141$		−	4.69643i		−	0.395511i
$142$		0			0
$143$	−8.65351	+	4.99611i	−0.723643	+	0.417795i
$144$		0			0
$145$	5.41946	+	5.30599i	0.450062	+	0.440639i
$146$		0			0
$147$	−2.64906	+	4.29220i	−0.218491	+	0.354015i
$148$		0			0
$149$	20.1713	+	11.6459i	1.65249	+	0.954067i	0.976043	+	0.217579i	$0.0698161\pi$
$149$	20.1713	+	11.6459i	1.65249	+	0.954067i	0.676451	+	0.736488i	$0.263517\pi$
$150$		0			0
$151$	−8.61940	+	4.97642i	−0.701437	+	0.404975i	−0.807882	−	0.589344i	$-0.799386\pi$
$151$	−8.61940	+	4.97642i	−0.701437	+	0.404975i	0.106445	+	0.994319i	$0.466053\pi$
$152$		0			0
$153$	12.7009			1.02681
$154$		0			0
$155$	6.89905	+	1.77059i	0.554145	+	0.142217i
$156$		0			0
$157$	−9.97707	+	5.76026i	−0.796257	+	0.459719i	−0.842161	−	0.539227i	$-0.818717\pi$
$157$	−9.97707	+	5.76026i	−0.796257	+	0.459719i	0.0459037	+	0.998946i	$0.485383\pi$
$158$		0			0
$159$	2.10752	−	3.65033i	0.167137	−	0.289490i
$160$		0			0
$161$	9.02910	+	16.1829i	0.711593	+	1.27539i
$162$		0			0
$163$	6.80019	+	3.92609i	0.532632	+	0.307515i	0.742087	−	0.670303i	$-0.233836\pi$
$163$	6.80019	+	3.92609i	0.532632	+	0.307515i	−0.209456	+	0.977818i	$0.567169\pi$
$164$		0			0
$165$	1.69613	+	6.07233i	0.132043	+	0.472731i
$166$		0			0
$167$		−	17.7066i		−	1.37018i	−0.728459	−	0.685090i	$-0.759763\pi$
$167$		−	17.7066i		−	1.37018i	0.728459	−	0.685090i	$-0.240237\pi$
$168$		0			0
$169$	6.47944			0.498419
$170$		0			0
$171$	−8.08390	+	4.66724i	−0.618191	+	0.356913i
$172$		0			0
$173$	3.71071	+	2.14238i	0.282120	+	0.162882i	0.634383	−	0.773019i	$-0.281254\pi$
$173$	3.71071	+	2.14238i	0.282120	+	0.162882i	−0.352263	+	0.935901i	$0.614588\pi$
$174$		0			0
$175$	−11.4991	−	6.54001i	−0.869247	−	0.494378i
$176$		0			0
$177$	−7.38767	−	4.26527i	−0.555291	−	0.320598i
$178$		0			0
$179$	6.86299	+	11.8870i	0.512964	+	0.888479i	0.999887	+	0.0150343i	$0.00478576\pi$
$179$	6.86299	+	11.8870i	0.512964	+	0.888479i	−0.486923	+	0.873445i	$0.661881\pi$
$180$		0			0
$181$	−9.40055			−0.698738			−0.349369	−	0.936985i	$-0.613604\pi$
$181$	−9.40055			−0.698738			−0.349369	+	0.936985i	$0.613604\pi$
$182$		0			0
$183$	8.56747			0.633326
$184$		0			0
$185$	1.02357	+	3.66451i	0.0752545	+	0.269420i
$186$		0			0
$187$	10.0169	−	17.3497i	0.732505	−	1.26874i
$188$		0			0
$189$	−5.35656	+	8.97110i	−0.389632	+	0.652551i
$190$		0			0
$191$	−15.4640	−	8.92815i	−1.11894	−	0.646019i	−0.177808	−	0.984065i	$-0.556900\pi$
$191$	−15.4640	−	8.92815i	−1.11894	−	0.646019i	−0.941129	+	0.338047i	$0.890234\pi$
$192$		0			0
$193$	−19.8035	+	11.4335i	−1.42548	+	0.823004i	−0.996760	−	0.0804313i	$-0.974370\pi$
$193$	−19.8035	+	11.4335i	−1.42548	+	0.823004i	−0.428725	+	0.903435i	$0.641037\pi$
$194$		0			0
$195$	−1.02275	+	3.98512i	−0.0732406	+	0.285380i
$196$		0			0
$197$	13.6688			0.973859			0.486929	−	0.873441i	$-0.338117\pi$
$197$	13.6688			0.973859			0.486929	+	0.873441i	$0.338117\pi$
$198$		0			0
$199$	11.4509	+	19.8335i	0.811732	+	1.40596i	0.911651	+	0.410966i	$0.134809\pi$
$199$	11.4509	+	19.8335i	0.811732	+	1.40596i	−0.0999183	+	0.994996i	$0.531858\pi$
$200$		0			0
$201$	−1.93176	−	1.11530i	−0.136256	−	0.0786675i
$202$		0			0
$203$	7.70507	+	4.60063i	0.540790	+	0.322901i
$204$		0			0
$205$	−6.34868	−	6.21576i	−0.443411	−	0.434127i
$206$		0			0
$207$	8.68801	+	15.0481i	0.603859	+	1.04591i
$208$		0			0
$209$			14.7237i			1.01846i
$210$		0			0
$211$	3.80653			0.262052			0.131026	−	0.991379i	$-0.458173\pi$
$211$	3.80653			0.262052			0.131026	+	0.991379i	$0.458173\pi$
$212$		0			0
$213$	−7.69874	+	4.44487i	−0.527509	+	0.304558i
$214$		0			0
$215$	1.43602	+	1.40596i	0.0979359	+	0.0958854i
$216$		0			0
$217$	8.42670	+	0.123705i	0.572042	+	0.00839763i
$218$		0			0
$219$	−1.86876	+	3.23678i	−0.126279	+	0.218721i
$220$		0			0
$221$	11.3218	−	6.53664i	0.761586	−	0.439702i
$222$		0			0
$223$		−	15.1551i		−	1.01486i	−0.861693	−	0.507430i	$-0.830595\pi$
$223$		−	15.1551i		−	1.01486i	0.861693	−	0.507430i	$-0.169405\pi$
$224$		0			0
$225$	−10.8710	−	5.97336i	−0.724734	−	0.398224i
$226$		0			0
$227$	−5.92282	−	10.2586i	−0.393111	−	0.680888i	0.599747	−	0.800190i	$-0.295268\pi$
$227$	−5.92282	−	10.2586i	−0.393111	−	0.680888i	−0.992858	+	0.119301i	$0.961935\pi$
$228$		0			0
$229$	0.242540	−	0.420091i	0.0160275	−	0.0277604i	−0.857900	−	0.513816i	$-0.828231\pi$
$229$	0.242540	−	0.420091i	0.0160275	−	0.0277604i	0.873928	+	0.486056i	$0.161565\pi$
$230$		0			0
$231$	3.63472	+	6.51452i	0.239147	+	0.428624i
$232$		0			0
$233$	22.8163	+	13.1730i	1.49475	+	0.862992i	0.999982	−	0.00603553i	$-0.00192118\pi$
$233$	22.8163	+	13.1730i	1.49475	+	0.862992i	0.494764	+	0.869027i	$0.335255\pi$
$234$		0			0
$235$	14.0370	−	3.92082i	0.915673	−	0.255766i
$236$		0			0
$237$		−	7.36083i		−	0.478137i
$238$		0			0
$239$			1.78403i			0.115399i	0.998334	+	0.0576997i	$0.0183766\pi$
$239$			1.78403i			0.115399i	−0.998334	+	0.0576997i	$0.981623\pi$
$240$		0			0
$241$	−7.29829	+	4.21367i	−0.470124	+	0.271426i	−0.716292	−	0.697801i	$-0.754162\pi$
$241$	−7.29829	+	4.21367i	−0.470124	+	0.271426i	0.246167	+	0.969227i	$0.420829\pi$
$242$		0			0
$243$	−7.57992	+	13.1288i	−0.486252	+	0.842214i
$244$		0			0
$245$	−15.0404	−	4.33435i	−0.960895	−	0.276911i
$246$		0			0
$247$	−4.80408	+	8.32091i	−0.305676	+	0.529447i
$248$		0			0
$249$	0.283342	+	0.490764i	0.0179561	+	0.0311009i
$250$		0			0
$251$			19.9871i			1.26157i	0.775956	+	0.630787i	$0.217268\pi$
$251$			19.9871i			1.26157i	−0.775956	+	0.630787i	$0.782732\pi$
$252$		0			0
$253$	27.4080			1.72312
$254$		0			0
$255$	−2.21912	−	7.94472i	−0.138967	−	0.497518i
$256$		0			0
$257$	−0.516455	+	0.894526i	−0.0322156	+	0.0557990i	−0.881684	−	0.471841i	$-0.843590\pi$
$257$	−0.516455	+	0.894526i	−0.0322156	+	0.0557990i	0.849468	+	0.527640i	$0.176923\pi$
$258$		0			0
$259$	2.19346	+	3.93135i	0.136295	+	0.244282i
$260$		0			0
$261$	7.28725	+	4.20729i	0.451069	+	0.260425i
$262$		0			0
$263$	3.33070	+	5.76894i	0.205380	+	0.355728i	0.950254	−	0.311477i	$-0.100824\pi$
$263$	3.33070	+	5.76894i	0.205380	+	0.355728i	−0.744874	+	0.667205i	$0.767490\pi$
$264$		0			0
$265$	12.6698	+	3.25161i	0.778300	+	0.199745i
$266$		0			0
$267$			0.565752i			0.0346235i
$268$		0			0
$269$	3.75055	+	6.49615i	0.228675	+	0.396077i	0.957416	−	0.288713i	$-0.0932273\pi$
$269$	3.75055	+	6.49615i	0.228675	+	0.396077i	−0.728740	+	0.684790i	$0.759894\pi$
$270$		0			0
$271$	1.07782	−	1.86684i	0.0654730	−	0.113402i	−0.831431	−	0.555628i	$-0.812478\pi$
$271$	1.07782	−	1.86684i	0.0654730	−	0.113402i	0.896904	+	0.442226i	$0.145811\pi$
$272$		0			0
$273$	−0.0714560	+	4.86754i	−0.00432471	+	0.294597i
$274$		0			0
$275$	−16.7334	+	10.1390i	−1.00906	+	0.611405i
$276$		0			0
$277$	−5.98545	−	10.3671i	−0.359631	−	0.622899i	0.628268	−	0.777997i	$-0.283764\pi$
$277$	−5.98545	−	10.3671i	−0.359631	−	0.622899i	−0.987899	+	0.155098i	$0.950431\pi$
$278$		0			0
$279$	7.90220			0.473093
$280$		0			0
$281$	3.06151			0.182634			0.0913171	−	0.995822i	$-0.470892\pi$
$281$	3.06151			0.182634			0.0913171	+	0.995822i	$0.470892\pi$
$282$		0			0
$283$	−10.3523	−	17.9308i	−0.615383	−	1.06587i	−0.990317	−	0.138823i	$-0.955668\pi$
$283$	−10.3523	−	17.9308i	−0.615383	−	1.06587i	0.374934	−	0.927051i	$-0.377665\pi$
$284$		0			0
$285$	4.33190	+	4.24120i	0.256600	+	0.251227i
$286$		0			0
$287$	−9.02617	−	5.38945i	−0.532798	−	0.318129i
$288$		0			0
$289$	−4.60553	+	7.97701i	−0.270913	+	0.469236i
$290$		0			0
$291$	5.95647	+	10.3169i	0.349174	+	0.604787i
$292$		0			0
$293$		−	30.5374i		−	1.78402i	−0.452020	−	0.892008i	$-0.649296\pi$
$293$		−	30.5374i		−	1.78402i	0.452020	−	0.892008i	$-0.350704\pi$
$294$		0			0
$295$	6.58073	−	25.6417i	0.383145	−	1.49291i
$296$		0			0
$297$	7.72678	+	13.3832i	0.448353	+	0.776571i
$298$		0			0
$299$	15.4893	+	8.94273i	0.895767	+	0.517171i
$300$		0			0
$301$	2.04165	+	1.21905i	0.117679	+	0.0702649i
$302$		0			0
$303$	−4.33398	+	7.50668i	−0.248981	+	0.431247i
$304$		0			0
$305$	7.15257	+	25.6070i	0.409555	+	1.46625i
$306$		0			0
$307$	7.15470			0.408340			0.204170	−	0.978935i	$-0.434550\pi$
$307$	7.15470			0.408340			0.204170	+	0.978935i	$0.434550\pi$
$308$		0			0
$309$		−	0.109968i		−	0.00625586i
$310$		0			0
$311$	4.60675	+	7.97912i	0.261225	+	0.452454i	0.966568	−	0.256412i	$-0.0825403\pi$
$311$	4.60675	+	7.97912i	0.261225	+	0.452454i	−0.705343	+	0.708866i	$0.749207\pi$
$312$		0			0
$313$	5.15408	−	8.92713i	0.291326	−	0.504591i	−0.682798	−	0.730608i	$-0.739237\pi$
$313$	5.15408	−	8.92713i	0.291326	−	0.504591i	0.974124	+	0.226016i	$0.0725702\pi$
$314$		0			0
$315$	−14.1609	−	3.85669i	−0.797874	−	0.217300i
$316$		0			0
$317$	−16.7268	+	28.9716i	−0.939469	+	1.62721i	−0.173004	+	0.984921i	$0.555347\pi$
$317$	−16.7268	+	28.9716i	−0.939469	+	1.62721i	−0.766464	+	0.642287i	$0.777986\pi$
$318$		0			0
$319$	11.4945	−	6.63635i	0.643568	−	0.371564i
$320$		0			0
$321$		−	1.15163i		−	0.0642776i
$322$		0			0
$323$		−	19.2637i		−	1.07186i
$324$		0			0
$325$	−12.7648	+	0.270121i	−0.708066	+	0.0149836i
$326$		0			0
$327$	−9.77861	−	5.64568i	−0.540758	−	0.312207i
$328$		0			0
$329$	15.0592	−	8.40213i	0.830239	−	0.463225i
$330$		0			0
$331$	−0.130885	+	0.226700i	−0.00719411	+	0.0124606i	−0.869600	−	0.493757i	$-0.835623\pi$
$331$	−0.130885	+	0.226700i	−0.00719411	+	0.0124606i	0.862406	+	0.506217i	$0.168957\pi$
$332$		0			0
$333$	2.11060	+	3.65567i	0.115660	+	0.200330i
$334$		0			0
$335$	1.72076	−	6.70490i	0.0940152	−	0.366328i
$336$		0			0
$337$			13.7546i			0.749262i	0.927174	+	0.374631i	$0.122231\pi$
$337$			13.7546i			0.749262i	−0.927174	+	0.374631i	$0.877769\pi$
$338$		0			0
$339$	−5.10242	+	2.94588i	−0.277125	+	0.159998i
$340$		0			0
$341$	6.23225	−	10.7946i	0.337495	−	0.584559i
$342$		0			0
$343$	−18.5023	−	0.815316i	−0.999031	−	0.0440229i
$344$		0			0
$345$	7.89494	−	8.06378i	0.425049	−	0.434139i
$346$		0			0
$347$	−24.9110	+	14.3824i	−1.33729	+	0.772086i	−0.986405	−	0.164332i	$-0.947453\pi$
$347$	−24.9110	+	14.3824i	−1.33729	+	0.772086i	−0.350887	+	0.936418i	$0.614120\pi$
$348$		0			0
$349$	23.9493			1.28197			0.640987	−	0.767551i	$-0.278525\pi$
$349$	23.9493			1.28197			0.640987	+	0.767551i	$0.278525\pi$
$350$		0			0
$351$			10.0844i			0.538267i
$352$		0			0
$353$	−11.9932	−	20.7729i	−0.638336	−	1.10563i	−0.985798	−	0.167937i	$-0.946290\pi$
$353$	−11.9932	−	20.7729i	−0.638336	−	1.10563i	0.347462	−	0.937694i	$-0.387044\pi$
$354$		0			0
$355$	−19.7124	−	19.2997i	−1.04623	−	1.02432i
$356$		0			0
$357$	−4.75547	−	8.52325i	−0.251686	−	0.451098i
$358$		0			0
$359$	15.3298	+	8.85066i	0.809075	+	0.467120i	0.846635	−	0.532175i	$-0.178625\pi$
$359$	15.3298	+	8.85066i	0.809075	+	0.467120i	−0.0375594	+	0.999294i	$0.511958\pi$
$360$		0			0
$361$	−2.42111	−	4.19349i	−0.127427	−	0.220710i
$362$		0			0
$363$	3.10719			0.163085
$364$		0			0
$365$	−11.2344	−	2.88323i	−0.588038	−	0.150915i
$366$		0			0
$367$	−11.3340	+	6.54368i	−0.591629	+	0.341577i	−0.765742	−	0.643148i	$-0.777628\pi$
$367$	−11.3340	+	6.54368i	−0.591629	+	0.341577i	0.174112	+	0.984726i	$0.444294\pi$
$368$		0			0
$369$	−8.53672	−	4.92868i	−0.444404	−	0.256577i
$370$		0			0
$371$	15.4753	+	0.227179i	0.803436	+	0.0117945i
$372$		0			0
$373$	−11.0243	+	19.0947i	−0.570817	+	0.988684i	0.425665	+	0.904881i	$0.360040\pi$
$373$	−11.0243	+	19.0947i	−0.570817	+	0.988684i	−0.996482	+	0.0838033i	$0.973293\pi$
$374$		0			0
$375$	−1.83708	+	7.84375i	−0.0948662	+	0.405049i
$376$		0			0
$377$	8.66129			0.446079
$378$		0			0
$379$	−18.8729			−0.969437			−0.484719	−	0.874670i	$-0.661078\pi$
$379$	−18.8729			−0.969437			−0.484719	+	0.874670i	$0.661078\pi$
$380$		0			0
$381$	−4.95946	−	8.59004i	−0.254081	−	0.440081i
$382$		0			0
$383$	14.2851	+	8.24751i	0.729935	+	0.421428i	0.818398	−	0.574651i	$-0.194862\pi$
$383$	14.2851	+	8.24751i	0.729935	+	0.421428i	−0.0884637	+	0.996079i	$0.528196\pi$
$384$		0			0
$385$	−16.4366	+	16.3024i	−0.837686	+	0.830845i
$386$		0			0
$387$	1.93094	+	1.11483i	0.0981551	+	0.0566699i
$388$		0			0
$389$	−1.28484	+	0.741804i	−0.0651441	+	0.0376110i	−0.532218	−	0.846607i	$-0.678641\pi$
$389$	−1.28484	+	0.741804i	−0.0651441	+	0.0376110i	0.467074	+	0.884218i	$0.345308\pi$
$390$		0			0
$391$	−35.8591			−1.81347
$392$		0			0
$393$		−	6.74639i		−	0.340311i
$394$		0			0
$395$	22.0006	−	6.14521i	1.10697	−	0.309199i
$396$		0			0
$397$	23.3671	+	13.4910i	1.17276	+	0.677093i	0.954329	−	0.298759i	$-0.0965727\pi$
$397$	23.3671	+	13.4910i	1.17276	+	0.677093i	0.218431	+	0.975852i	$0.429906\pi$
$398$		0			0
$399$	6.15884	+	3.67739i	0.308327	+	0.184100i
$400$		0			0
$401$	4.72660	−	8.18671i	0.236035	−	0.408825i	−0.723538	−	0.690285i	$-0.757485\pi$
$401$	4.72660	−	8.18671i	0.236035	−	0.408825i	0.959573	+	0.281460i	$0.0908186\pi$
$402$		0			0
$403$	7.04415	−	4.06694i	0.350894	−	0.202589i
$404$		0			0
$405$	−9.95614	−	2.55517i	−0.494725	−	0.126967i
$406$		0			0
$407$	6.65830			0.330040
$408$		0			0
$409$	−18.4734	+	10.6656i	−0.913451	+	0.527381i	−0.881540	−	0.472110i	$-0.843493\pi$
$409$	−18.4734	+	10.6656i	−0.913451	+	0.527381i	−0.0319110	+	0.999491i	$0.510159\pi$
$410$		0			0
$411$	−11.6326	−	6.71607i	−0.573792	−	0.331279i
$412$		0			0
$413$	0.459773	−	31.3195i	0.0226240	−	1.54113i
$414$		0			0
$415$	−1.23028	+	1.25659i	−0.0603920	+	0.0616835i
$416$		0			0
$417$	−2.81400	+	1.62466i	−0.137802	+	0.0795602i
$418$		0			0
$419$		−	27.0871i		−	1.32329i	−0.749816	−	0.661646i	$-0.769858\pi$
$419$		−	27.0871i		−	1.32329i	0.749816	−	0.661646i	$-0.230142\pi$
$420$		0			0
$421$			10.8575i			0.529163i	0.964363	+	0.264581i	$0.0852338\pi$
$421$			10.8575i			0.529163i	−0.964363	+	0.264581i	$0.914766\pi$
$422$		0			0
$423$	14.0032	−	8.08473i	0.680857	−	0.393093i
$424$		0			0
$425$	21.8931	−	13.2653i	1.06197	−	0.643463i
$426$		0			0
$427$	15.3276	+	27.4717i	0.741755	+	1.32945i
$428$		0			0
$429$	6.23530	+	3.59995i	0.301043	+	0.173807i
$430$		0			0
$431$	1.43863	−	0.830592i	0.0692963	−	0.0400082i	−0.464952	−	0.885336i	$-0.653928\pi$
$431$	1.43863	−	0.830592i	0.0692963	−	0.0400082i	0.534248	+	0.845328i	$0.320595\pi$
$432$		0			0
$433$	−30.7666			−1.47855			−0.739274	−	0.673405i	$-0.764831\pi$
$433$	−30.7666			−1.47855			−0.739274	+	0.673405i	$0.764831\pi$
$434$		0			0
$435$	1.35852	−	5.29345i	0.0651361	−	0.253801i
$436$		0			0
$437$	22.8237	−	13.1773i	1.09181	−	0.630354i
$438$		0			0
$439$	5.33622	−	9.24260i	0.254684	−	0.441125i	−0.710126	−	0.704075i	$-0.751362\pi$
$439$	5.33622	−	9.24260i	0.254684	−	0.441125i	0.964810	+	0.262950i	$0.0846953\pi$
$440$		0			0
$441$	−17.3582	−	0.509749i	−0.826579	−	0.0242738i
$442$		0			0
$443$	10.4954	+	6.05950i	0.498650	+	0.287896i	0.728156	−	0.685412i	$-0.240378\pi$
$443$	10.4954	+	6.05950i	0.498650	+	0.287896i	−0.229506	+	0.973307i	$0.573711\pi$
$444$		0			0
$445$	−1.69096	+	0.472319i	−0.0801591	+	0.0223901i
$446$		0			0
$447$		−	16.7829i		−	0.793804i
$448$		0			0
$449$	32.0498			1.51252			0.756261	−	0.654270i	$-0.227024\pi$
$449$	32.0498			1.51252			0.756261	+	0.654270i	$0.227024\pi$
$450$		0			0
$451$	−13.4653	+	7.77422i	−0.634058	+	0.366074i
$452$		0			0
$453$	6.21072	+	3.58576i	0.291805	+	0.168474i
$454$		0			0
$455$	−14.6081	+	3.85010i	−0.684838	+	0.180496i
$456$		0			0
$457$	−5.80174	−	3.34963i	−0.271394	−	0.156689i	0.358127	−	0.933673i	$-0.383415\pi$
$457$	−5.80174	−	3.34963i	−0.271394	−	0.156689i	−0.629521	+	0.776984i	$0.716749\pi$
$458$		0			0
$459$	−10.1093	−	17.5098i	−0.471862	−	0.817289i
$460$		0			0
$461$	−15.4768			−0.720828			−0.360414	−	0.932792i	$-0.617365\pi$
$461$	−15.4768			−0.720828			−0.360414	+	0.932792i	$0.617365\pi$
$462$		0			0
$463$	14.8717			0.691145			0.345572	−	0.938392i	$-0.387685\pi$
$463$	14.8717			0.691145			0.345572	+	0.938392i	$0.387685\pi$
$464$		0			0
$465$	−1.38068	−	4.94301i	−0.0640277	−	0.229227i
$466$		0			0
$467$	−0.0443182	+	0.0767615i	−0.00205080	+	0.00355210i	−0.867049	−	0.498223i	$-0.833986\pi$
$467$	−0.0443182	+	0.0767615i	−0.00205080	+	0.00355210i	0.864998	+	0.501775i	$0.167319\pi$
$468$		0			0
$469$	0.120224	−	8.18956i	0.00555141	−	0.378159i
$470$		0			0
$471$	7.18899	+	4.15056i	0.331251	+	0.191248i
$472$		0			0
$473$	3.04576	−	1.75847i	0.140044	−	0.0808544i
$474$		0			0
$475$	−9.05990	+	16.4883i	−0.415697	+	0.756533i
$476$		0			0
$477$	14.5121			0.664462
$478$		0			0
$479$	−4.36928	−	7.56782i	−0.199638	−	0.345783i	0.748773	−	0.662826i	$-0.230643\pi$
$479$	−4.36928	−	7.56782i	−0.199638	−	0.345783i	−0.948411	+	0.317044i	$0.897310\pi$
$480$		0			0
$481$	3.76285	+	2.17248i	0.171571	+	0.0990567i
$482$		0			0
$483$	6.84541	−	11.4646i	0.311477	−	0.521657i
$484$		0			0
$485$	−25.8631	+	26.4162i	−1.17438	+	1.19950i
$486$		0			0
$487$	8.60661	+	14.9071i	0.390003	+	0.675504i	0.992449	−	0.122655i	$-0.0391408\pi$
$487$	8.60661	+	14.9071i	0.390003	+	0.675504i	−0.602447	+	0.798159i	$0.705807\pi$
$488$		0			0
$489$		−	5.65789i		−	0.255859i
$490$		0			0
$491$	15.0849			0.680770			0.340385	−	0.940286i	$-0.389443\pi$
$491$	15.0849			0.680770			0.340385	+	0.940286i	$0.389443\pi$
$492$		0			0
$493$	−15.0388	+	8.68265i	−0.677313	+	0.391047i
$494$		0			0
$495$	−15.1858	+	15.5106i	−0.682553	+	0.697149i
$496$		0			0
$497$	−28.0260	−	16.7341i	−1.25714	−	0.750625i
$498$		0			0
$499$	12.9769	−	22.4766i	0.580925	−	1.00619i	−0.414445	−	0.910074i	$-0.636024\pi$
$499$	12.9769	−	22.4766i	0.580925	−	1.00619i	0.995370	−	0.0961171i	$-0.0306423\pi$
$500$		0			0
$501$	−11.0492	+	6.37926i	−0.493642	+	0.285004i
$502$		0			0
$503$		−	6.00776i		−	0.267873i	−0.990990	−	0.133936i	$-0.957238\pi$
$503$		−	6.00776i		−	0.267873i	0.990990	−	0.133936i	$-0.0427618\pi$
$504$		0			0
$505$	−26.0547	−	6.68674i	−1.15942	−	0.297556i
$506$		0			0
$507$	−2.33438	−	4.04327i	−0.103674	−	0.179568i
$508$		0			0
$509$	−4.28454	+	7.42104i	−0.189909	+	0.328932i	−0.945220	−	0.326435i	$-0.894153\pi$
$509$	−4.28454	+	7.42104i	−0.189909	+	0.328932i	0.755311	+	0.655367i	$0.227486\pi$
$510$		0			0
$511$	−13.7221	−	0.201442i	−0.607029	−	0.00891125i
$512$		0			0
$513$	12.8688	+	7.42979i	0.568171	+	0.328033i
$514$		0			0
$515$	0.328680	−	0.0918070i	0.0144834	−	0.00404550i
$516$		0			0
$517$		−	25.5048i		−	1.12170i
$518$		0			0
$519$		−	3.08739i		−	0.135521i
$520$		0			0
$521$	16.4208	−	9.48055i	0.719408	−	0.415350i	−0.0951267	−	0.995465i	$-0.530326\pi$
$521$	16.4208	−	9.48055i	0.719408	−	0.415350i	0.814535	+	0.580115i	$0.196992\pi$
$522$		0			0
$523$	−18.0605	+	31.2816i	−0.789729	+	1.36785i	0.136404	+	0.990653i	$0.456445\pi$
$523$	−18.0605	+	31.2816i	−0.789729	+	1.36785i	−0.926133	+	0.377197i	$0.876888\pi$
$524$		0			0
$525$	0.0617588	+	9.53179i	0.00269538	+	0.416002i
$526$		0			0
$527$	−8.15394	+	14.1230i	−0.355191	+	0.615209i
$528$		0			0
$529$	−13.0293	−	22.5674i	−0.566492	−	0.981192i
$530$		0			0
$531$		−	29.3701i		−	1.27455i
$532$		0			0
$533$	−10.1463			−0.439487
$534$		0			0
$535$	3.44206	−	0.961439i	0.148813	−	0.0415666i
$536$		0			0
$537$	4.94513	−	8.56522i	0.213398	−	0.369616i
$538$		0			0
$539$	−14.3862	+	23.3096i	−0.619659	+	1.00401i
$540$		0			0
$541$	−12.3425	−	7.12594i	−0.530645	−	0.306368i	0.210634	−	0.977565i	$-0.432447\pi$
$541$	−12.3425	−	7.12594i	−0.530645	−	0.306368i	−0.741279	+	0.671197i	$0.765781\pi$
$542$		0			0
$543$	3.38679	+	5.86609i	0.145341	+	0.251738i
$544$		0			0
$545$	8.71051	−	33.9403i	0.373117	−	1.45384i
$546$		0			0
$547$			22.3957i			0.957570i	0.877932	+	0.478785i	$0.158923\pi$
$547$			22.3957i			0.957570i	−0.877932	+	0.478785i	$0.841077\pi$
$548$		0			0
$549$	14.7486	+	25.5453i	0.629455	+	1.09025i
$550$		0			0
$551$	6.38128	−	11.0527i	0.271852	−	0.470861i
$552$		0			0
$553$	23.6026	−	13.1689i	1.00369	−	0.559998i
$554$		0			0
$555$	1.91794	−	1.95896i	0.0814121	−	0.0831531i
$556$		0			0
$557$	10.3454	+	17.9188i	0.438350	+	0.759244i	0.997562	−	0.0697803i	$-0.0222298\pi$
$557$	10.3454	+	17.9188i	0.438350	+	0.759244i	−0.559213	+	0.829024i	$0.688897\pi$
$558$		0			0
$559$	2.29502			0.0970692
$560$		0			0
$561$	−14.4353			−0.609460
$562$		0			0
$563$	8.03504	+	13.9171i	0.338636	+	0.586536i	0.984177	−	0.177191i	$-0.0567010\pi$
$563$	8.03504	+	13.9171i	0.338636	+	0.586536i	−0.645540	+	0.763726i	$0.723368\pi$
$564$		0			0
$565$	−13.0646	−	12.7911i	−0.549633	−	0.538125i
$566$		0			0
$567$	−12.1607	−	0.178521i	−0.510703	−	0.00749717i
$568$		0			0
$569$	8.09523	−	14.0213i	0.339370	−	0.587805i	−0.644945	−	0.764229i	$-0.723120\pi$
$569$	8.09523	−	14.0213i	0.339370	−	0.587805i	0.984314	+	0.176424i	$0.0564530\pi$
$570$		0			0
$571$	−15.6257	−	27.0645i	−0.653914	−	1.13261i	−0.982165	−	0.188022i	$-0.939792\pi$
$571$	−15.6257	−	27.0645i	−0.653914	−	1.13261i	0.328251	−	0.944591i	$-0.393541\pi$
$572$		0			0
$573$			12.8664i			0.537501i
$574$		0			0
$575$	30.6927	+	16.8649i	1.27997	+	0.703314i
$576$		0			0
$577$	1.08399	+	1.87753i	0.0451271	+	0.0781625i	0.887707	−	0.460409i	$-0.152297\pi$
$577$	1.08399	+	1.87753i	0.0451271	+	0.0781625i	−0.842580	+	0.538572i	$0.818964\pi$
$578$		0			0
$579$	14.2694	+	8.23845i	0.593016	+	0.342378i
$580$		0			0
$581$	−1.06673	+	1.78654i	−0.0442553	+	0.0741183i
$582$		0			0
$583$	11.4453	−	19.8238i	0.474014	−	0.821017i
$584$		0			0
$585$	−13.6429	+	3.81074i	−0.564065	+	0.157555i
$586$		0			0
$587$	30.3449			1.25247			0.626235	−	0.779634i	$-0.284595\pi$
$587$	30.3449			1.25247			0.626235	+	0.779634i	$0.284595\pi$
$588$		0			0
$589$		−	11.9854i		−	0.493850i
$590$		0			0
$591$	−4.92452	−	8.52952i	−0.202568	−	0.350857i
$592$		0			0
$593$	−18.6695	+	32.3365i	−0.766664	+	1.32790i	0.172699	+	0.984975i	$0.444751\pi$
$593$	−18.6695	+	32.3365i	−0.766664	+	1.32790i	−0.939363	+	0.342926i	$0.888582\pi$
$594$		0			0
$595$	21.5048	−	21.3291i	0.881609	−	0.874410i
$596$		0			0
$597$	8.25095	−	14.2911i	0.337689	−	0.584895i
$598$		0			0
$599$	12.2174	−	7.05370i	0.499188	−	0.288206i	−0.229190	−	0.973382i	$-0.573608\pi$
$599$	12.2174	−	7.05370i	0.499188	−	0.288206i	0.728378	+	0.685175i	$0.240274\pi$
$600$		0			0
$601$		−	19.7058i		−	0.803815i	−0.915680	−	0.401907i	$-0.868347\pi$
$601$		−	19.7058i		−	0.803815i	0.915680	−	0.401907i	$-0.131653\pi$
$602$		0			0
$603$		−	7.67982i		−	0.312747i
$604$		0			0
$605$	2.59404	+	9.28698i	0.105463	+	0.377569i
$606$		0			0
$607$	−28.1585	−	16.2573i	−1.14292	−	0.659865i	−0.195768	−	0.980650i	$-0.562720\pi$
$607$	−28.1585	−	16.2573i	−1.14292	−	0.659865i	−0.947152	+	0.320785i	$0.896053\pi$
$608$		0			0
$609$	0.0949153	−	6.46557i	0.00384616	−	0.261998i
$610$		0			0
$611$	8.32176	−	14.4137i	0.336662	−	0.583116i
$612$		0			0
$613$	6.14971	+	10.6516i	0.248384	+	0.430214i	0.963078	−	0.269224i	$-0.0867671\pi$
$613$	6.14971	+	10.6516i	0.248384	+	0.430214i	−0.714693	+	0.699438i	$0.753434\pi$
$614$		0			0
$615$	−1.59145	+	6.20106i	−0.0641736	+	0.250051i
$616$		0			0
$617$		−	16.0440i		−	0.645909i	−0.946415	−	0.322954i	$-0.895324\pi$
$617$		−	16.0440i		−	0.645909i	0.946415	−	0.322954i	$-0.104676\pi$
$618$		0			0
$619$	20.5927	−	11.8892i	0.827691	−	0.477868i	−0.0253703	−	0.999678i	$-0.508076\pi$
$619$	20.5927	−	11.8892i	0.827691	−	0.477868i	0.853061	+	0.521810i	$0.174743\pi$
$620$		0			0
$621$	13.8305	−	23.9551i	0.554997	−	0.961284i
$622$		0			0
$623$	−1.81409	+	1.01216i	−0.0726801	+	0.0405512i
$624$		0			0
$625$	−24.9776	+	1.05759i	−0.999105	+	0.0423038i
$626$		0			0
$627$	9.18782	−	5.30459i	0.366926	−	0.211845i
$628$		0			0
$629$	−8.71136			−0.347345
$630$		0			0
$631$		−	20.0177i		−	0.796893i	−0.917192	−	0.398447i	$-0.869549\pi$
$631$		−	20.0177i		−	0.796893i	0.917192	−	0.398447i	$-0.130451\pi$
$632$		0			0
$633$	−1.37140	−	2.37533i	−0.0545082	−	0.0944109i
$634$		0			0
$635$	21.5341	−	21.9946i	0.854554	−	0.872829i
$636$		0			0
$637$	−15.7357	+	8.47913i	−0.623470	+	0.335956i
$638$		0			0
$639$	−26.5062	−	15.3034i	−1.04857	−	0.605392i
$640$		0			0
$641$	−0.346690	−	0.600484i	−0.0136934	−	0.0237177i	0.859097	−	0.511812i	$-0.171026\pi$
$641$	−0.346690	−	0.600484i	−0.0136934	−	0.0237177i	−0.872791	+	0.488094i	$0.837692\pi$
$642$		0			0
$643$	−42.2717			−1.66703			−0.833516	−	0.552495i	$-0.813676\pi$
$643$	−42.2717			−1.66703			−0.833516	+	0.552495i	$0.813676\pi$
$644$		0			0
$645$	0.359974	−	1.40263i	0.0141740	−	0.0552286i
$646$		0			0
$647$	−30.8701	+	17.8229i	−1.21363	+	0.700690i	−0.963548	−	0.267535i	$-0.913791\pi$
$647$	−30.8701	+	17.8229i	−1.21363	+	0.700690i	−0.250082	+	0.968225i	$0.580458\pi$
$648$		0			0
$649$	−40.1201	−	23.1634i	−1.57485	−	0.909242i
$650$		0			0
$651$	−2.95874	−	5.30296i	−0.115962	−	0.207839i
$652$		0			0
$653$	1.40762	−	2.43807i	0.0550845	−	0.0954091i	−0.837168	−	0.546945i	$-0.815791\pi$
$653$	1.40762	−	2.43807i	0.0550845	−	0.0954091i	0.892253	+	0.451536i	$0.149124\pi$
$654$		0			0
$655$	20.1641	−	5.63224i	0.787876	−	0.220070i
$656$		0			0
$657$	−12.8680			−0.502028
$658$		0			0
$659$	−8.69907			−0.338868			−0.169434	−	0.985542i	$-0.554194\pi$
$659$	−8.69907			−0.338868			−0.169434	+	0.985542i	$0.554194\pi$
$660$		0			0
$661$	13.7443	+	23.8058i	0.534591	+	0.925939i	0.999183	+	0.0404142i	$0.0128677\pi$
$661$	13.7443	+	23.8058i	0.534591	+	0.925939i	−0.464592	+	0.885525i	$0.653799\pi$
$662$		0			0
$663$	−8.15793	−	4.70998i	−0.316828	−	0.182921i
$664$		0			0
$665$	−5.84951	+	21.4780i	−0.226834	+	0.832882i
$666$		0			0
$667$	−20.5745	−	11.8787i	−0.796646	−	0.459944i
$668$		0			0
$669$	−9.45702	+	5.46001i	−0.365630	+	0.211096i
$670$		0			0
$671$	46.5272			1.79616
$672$		0			0
$673$			12.1015i			0.466480i	0.972419	+	0.233240i	$0.0749328\pi$
$673$			12.1015i			0.466480i	−0.972419	+	0.233240i	$0.925067\pi$
$674$		0			0
$675$	0.417759	+	19.7416i	0.0160795	+	0.759854i
$676$		0			0
$677$	5.13926	+	2.96715i	0.197518	+	0.114037i	0.595497	−	0.803357i	$-0.296955\pi$
$677$	5.13926	+	2.96715i	0.197518	+	0.114037i	−0.397979	+	0.917394i	$0.630288\pi$
$678$		0			0
$679$	−22.4249	+	37.5569i	−0.860589	+	1.44130i
$680$		0			0
$681$	−4.26769	+	7.39186i	−0.163538	+	0.283257i
$682$		0			0
$683$	15.2951	−	8.83063i	0.585250	−	0.337894i	−0.177967	−	0.984036i	$-0.556952\pi$
$683$	15.2951	−	8.83063i	0.585250	−	0.337894i	0.763217	+	0.646142i	$0.223619\pi$
$684$		0			0
$685$	10.3620	−	40.3752i	0.395910	−	1.54266i
$686$		0			0
$687$	−0.349524			−0.0133352
$688$		0			0
$689$	12.9363	−	7.46876i	0.492833	−	0.284537i
$690$		0			0
$691$	−11.4396	−	6.60468i	−0.435184	−	0.251254i	0.266368	−	0.963871i	$-0.414176\pi$
$691$	−11.4396	−	6.60468i	−0.435184	−	0.251254i	−0.701553	+	0.712617i	$0.747510\pi$
$692$		0			0
$693$	−13.1671	+	22.0520i	−0.500176	+	0.837687i
$694$		0			0
$695$	−7.20519	−	7.05433i	−0.273308	−	0.267586i
$696$		0			0
$697$	17.6173	−	10.1714i	0.667304	−	0.385268i
$698$		0			0
$699$		−	18.9836i		−	0.718027i
$700$		0			0
$701$		−	6.75429i		−	0.255106i	−0.991832	−	0.127553i	$-0.959288\pi$
$701$		−	6.75429i		−	0.255106i	0.991832	−	0.127553i	$-0.0407123\pi$
$702$		0			0
$703$	5.54462	−	3.20119i	0.209119	−	0.120735i
$704$		0			0
$705$	−7.50384	−	7.34673i	−0.282611	−	0.276694i
$706$		0			0
$707$	−31.8240	−	0.467180i	−1.19686	−	0.0175701i
$708$		0			0
$709$	−34.2027	−	19.7470i	−1.28451	−	0.741612i	−0.306841	−	0.951761i	$-0.599272\pi$
$709$	−34.2027	−	19.7470i	−1.28451	−	0.741612i	−0.977669	+	0.210148i	$0.932605\pi$
$710$		0			0
$711$	21.9475	−	12.6714i	0.823097	−	0.475215i
$712$		0			0
$713$	−22.3107			−0.835542
$714$		0			0
$715$	−5.55423	+	21.6419i	−0.207716	+	0.809362i
$716$		0			0
$717$	1.11326	−	0.642743i	0.0415756	−	0.0240037i
$718$		0			0
$719$	−4.16021	+	7.20569i	−0.155150	+	0.268727i	−0.933113	−	0.359582i	$-0.882919\pi$
$719$	−4.16021	+	7.20569i	−0.155150	+	0.268727i	0.777964	+	0.628309i	$0.216253\pi$
$720$		0			0
$721$	0.352614	−	0.196738i	0.0131320	−	0.00732690i
$722$		0			0
$723$	5.25879	+	3.03616i	0.195577	+	0.112916i
$724$		0			0
$725$	16.9556	−	0.358803i	0.629715	−	0.0133256i
$726$		0			0
$727$			12.2319i			0.453654i	0.973935	+	0.226827i	$0.0728353\pi$
$727$			12.2319i			0.453654i	−0.973935	+	0.226827i	$0.927165\pi$
$728$		0			0
$729$	−2.86701			−0.106186
$730$		0			0
$731$	−3.98490	+	2.30069i	−0.147387	+	0.0850939i
$732$		0			0
$733$	−18.7710	−	10.8375i	−0.693324	−	0.400291i	0.111532	−	0.993761i	$-0.464424\pi$
$733$	−18.7710	−	10.8375i	−0.693324	−	0.400291i	−0.804856	+	0.593470i	$0.797758\pi$
$734$		0			0
$735$	2.71398	+	10.9470i	0.100107	+	0.403786i
$736$		0			0
$737$	−10.4908	−	6.05686i	−0.386433	−	0.223107i
$738$		0			0
$739$	4.41640	+	7.64942i	0.162460	+	0.281389i	0.935750	−	0.352663i	$-0.114724\pi$
$739$	4.41640	+	7.64942i	0.162460	+	0.281389i	−0.773291	+	0.634052i	$0.781391\pi$
$740$		0			0
$741$	6.92316			0.254329
$742$		0			0
$743$	10.8875			0.399425			0.199712	−	0.979855i	$-0.435999\pi$
$743$	10.8875			0.399425			0.199712	+	0.979855i	$0.435999\pi$
$744$		0			0
$745$	50.1619	−	14.0112i	1.83779	−	0.513332i
$746$		0			0
$747$	−0.975528	+	1.68966i	−0.0356927	+	0.0618216i
$748$		0			0
$749$	3.69271	−	2.06032i	0.134929	−	0.0752823i
$750$		0			0
$751$	16.9728	+	9.79926i	0.619347	+	0.357580i	0.776615	−	0.629976i	$-0.216935\pi$
$751$	16.9728	+	9.79926i	0.619347	+	0.357580i	−0.157268	+	0.987556i	$0.550269\pi$
$752$		0			0
$753$	12.4723	−	7.20086i	0.454514	−	0.262414i
$754$		0			0
$755$	−5.53234	+	21.5566i	−0.201342	+	0.784525i
$756$		0			0
$757$	29.5411			1.07369			0.536845	−	0.843681i	$-0.319616\pi$
$757$	29.5411			1.07369			0.536845	+	0.843681i	$0.319616\pi$
$758$		0			0
$759$	−9.87442	−	17.1030i	−0.358419	−	0.620800i
$760$		0			0
$761$	19.6992	+	11.3734i	0.714097	+	0.412284i	0.812576	−	0.582855i	$-0.198064\pi$
$761$	19.6992	+	11.3734i	0.714097	+	0.412284i	−0.0984792	+	0.995139i	$0.531398\pi$
$762$		0			0
$763$	0.608573	−	41.4557i	0.0220318	−	1.50080i
$764$		0			0
$765$	19.8683	−	20.2932i	0.718342	−	0.733703i
$766$		0			0
$767$	−15.1156	−	26.1809i	−0.545792	−	0.945339i
$768$		0			0
$769$			49.3053i			1.77799i	0.457913	+	0.888997i	$0.348597\pi$
$769$			49.3053i			1.77799i	−0.457913	+	0.888997i	$0.651403\pi$
$770$		0			0
$771$	0.744264			0.0268040
$772$		0			0
$773$	17.7806	−	10.2656i	0.639522	−	0.369228i	−0.144908	−	0.989445i	$-0.546289\pi$
$773$	17.7806	−	10.2656i	0.639522	−	0.369228i	0.784430	+	0.620217i	$0.212955\pi$
$774$		0			0
$775$	13.6213	−	8.25337i	0.489293	−	0.296470i
$776$		0			0
$777$	1.66297	−	2.78513i	0.0596589	−	0.0999159i
$778$		0			0
$779$	−7.47541	+	12.9478i	−0.267834	+	0.463903i
$780$		0			0
$781$	−41.8094	+	24.1387i	−1.49606	+	0.863750i
$782$		0			0
$783$		−	13.3952i		−	0.478705i
$784$		0			0
$785$	−6.40375	+	24.9521i	−0.228560	+	0.890577i
$786$		0			0
$787$	−1.52258	−	2.63719i	−0.0542741	−	0.0940056i	0.837612	−	0.546266i	$-0.183951\pi$
$787$	−1.52258	−	2.63719i	−0.0542741	−	0.0940056i	−0.891886	+	0.452260i	$0.850618\pi$
$788$		0			0
$789$	2.39994	−	4.15682i	0.0854401	−	0.147987i
$790$		0			0
$791$	−18.5745	−	11.0907i	−0.660433	−	0.394339i
$792$		0			0
$793$	26.2942	+	15.1810i	0.933736	+	0.539093i
$794$		0			0
$795$	−2.53557	−	9.07763i	−0.0899273	−	0.321950i
$796$		0			0
$797$			24.2059i			0.857418i	0.903443	+	0.428709i	$0.141031\pi$
$797$			24.2059i			0.857418i	−0.903443	+	0.428709i	$0.858969\pi$
$798$		0			0
$799$			33.3692i			1.18052i
$800$		0			0
$801$	−1.68688	+	0.973922i	−0.0596031	+	0.0344118i
$802$		0			0
$803$	−10.1486	+	17.5779i	−0.358137	+	0.620312i
$804$		0			0
$805$	39.9811	+	10.8888i	1.40915	+	0.383779i
$806$		0			0
$807$	2.70246	−	4.68081i	0.0951313	−	0.164772i
$808$		0			0
$809$	7.22922	+	12.5214i	0.254166	+	0.440228i	0.964669	−	0.263466i	$-0.0848657\pi$
$809$	7.22922	+	12.5214i	0.254166	+	0.440228i	−0.710503	+	0.703694i	$0.751532\pi$
$810$		0			0
$811$			30.5466i			1.07264i	0.844016	+	0.536318i	$0.180185\pi$
$811$			30.5466i			1.07264i	−0.844016	+	0.536318i	$0.819815\pi$
$812$		0			0
$813$	−1.55325			−0.0544749
$814$		0			0
$815$	16.9107	−	4.72351i	0.592356	−	0.165457i
$816$		0			0
$817$	1.69088	−	2.92869i	0.0591564	−	0.102462i
$818$		0			0
$819$	−14.6364	+	8.16624i	−0.511436	+	0.285351i
$820$		0			0
$821$	4.87448	+	2.81428i	0.170120	+	0.0982191i	0.582643	−	0.812728i	$-0.302019\pi$
$821$	4.87448	+	2.81428i	0.170120	+	0.0982191i	−0.412522	+	0.910948i	$0.635352\pi$
$822$		0			0
$823$	−0.359886	−	0.623340i	−0.0125448	−	0.0217283i	0.859685	−	0.510825i	$-0.170660\pi$
$823$	−0.359886	−	0.623340i	−0.0125448	−	0.0217283i	−0.872230	+	0.489097i	$0.837327\pi$
$824$		0			0
$825$	12.3555	+	6.78906i	0.430164	+	0.236365i
$826$		0			0
$827$		−	54.5578i		−	1.89716i	−0.316536	−	0.948580i	$-0.602520\pi$
$827$		−	54.5578i		−	1.89716i	0.316536	−	0.948580i	$-0.397480\pi$
$828$		0			0
$829$	−7.08127	−	12.2651i	−0.245943	−	0.425985i	0.716454	−	0.697635i	$-0.245764\pi$
$829$	−7.08127	−	12.2651i	−0.245943	−	0.425985i	−0.962396	+	0.271650i	$0.912431\pi$
$830$		0			0
$831$	−4.31283	+	7.47003i	−0.149610	+	0.259133i
$832$		0			0
$833$	18.8222	−	30.4970i	0.652150	−	1.05666i
$834$		0			0
$835$	−28.2912	−	27.6989i	−0.979059	−	0.958560i
$836$		0			0
$837$	−6.28977	−	10.8942i	−0.217406	−	0.376559i
$838$		0			0
$839$	−56.3376			−1.94499			−0.972495	−	0.232923i	$-0.925171\pi$
$839$	−56.3376			−1.94499			−0.972495	+	0.232923i	$0.925171\pi$
$840$		0			0
$841$	17.4952			0.603282
$842$		0			0
$843$	−1.10299	−	1.91043i	−0.0379888	−	0.0657986i
$844$		0			0
$845$	10.1359	−	10.3527i	0.348687	−	0.356144i
$846$		0			0
$847$	5.55891	+	9.96325i	0.191006	+	0.342341i
$848$		0			0
$849$	−7.45939	+	12.9200i	−0.256006	+	0.443415i
$850$		0			0
$851$	−5.95897	−	10.3212i	−0.204271	−	0.353808i
$852$		0			0
$853$			17.4627i			0.597912i	0.954267	+	0.298956i	$0.0966384\pi$
$853$			17.4627i			0.597912i	−0.954267	+	0.298956i	$0.903362\pi$
$854$		0			0
$855$	−5.18863	+	20.2174i	−0.177447	+	0.691419i
$856$		0			0
$857$	15.2887	+	26.4809i	0.522253	+	0.904569i	0.999665	+	0.0258890i	$0.00824165\pi$
$857$	15.2887	+	26.4809i	0.522253	+	0.904569i	−0.477412	+	0.878680i	$0.658425\pi$
$858$		0			0
$859$	9.81716	+	5.66794i	0.334957	+	0.193388i	0.658040	−	0.752983i	$-0.271386\pi$
$859$	9.81716	+	5.66794i	0.334957	+	0.193388i	−0.323083	+	0.946371i	$0.604719\pi$
$860$		0			0
$861$	−0.111189	+	7.57416i	−0.00378933	+	0.258127i
$862$		0			0
$863$	−23.1411	+	40.0815i	−0.787731	+	1.36439i	0.139623	+	0.990205i	$0.455411\pi$
$863$	−23.1411	+	40.0815i	−0.787731	+	1.36439i	−0.927354	+	0.374186i	$0.877922\pi$
$864$		0			0
$865$	9.22780	−	2.57751i	0.313755	−	0.0876381i
$866$		0			0
$867$	6.63704			0.225406
$868$		0			0
$869$		−	39.9744i		−	1.35604i
$870$		0			0
$871$	−3.95249	−	6.84591i	−0.133925	−	0.231965i
$872$		0			0
$873$	−20.5077	+	35.5204i	−0.694080	+	1.20218i
$874$		0			0
$875$	−28.4377	+	8.14223i	−0.961371	+	0.275258i
$876$		0			0
$877$	6.36155	−	11.0185i	0.214814	−	0.372069i	−0.738401	−	0.674362i	$-0.764419\pi$
$877$	6.36155	−	11.0185i	0.214814	−	0.372069i	0.953215	+	0.302293i	$0.0977521\pi$
$878$		0			0
$879$	−19.0558	+	11.0019i	−0.642737	+	0.371084i
$880$		0			0
$881$			12.0552i			0.406152i	0.979163	+	0.203076i	$0.0650938\pi$
$881$			12.0552i			0.406152i	−0.979163	+	0.203076i	$0.934906\pi$
$882$		0			0
$883$			3.49917i			0.117757i	0.998265	+	0.0588783i	$0.0187524\pi$
$883$			3.49917i			0.117757i	−0.998265	+	0.0588783i	$0.981248\pi$
$884$		0			0
$885$	−18.3717	+	5.13158i	−0.617557	+	0.172496i
$886$		0			0
$887$	41.9355	+	24.2115i	1.40806	+	0.812941i	0.995201	−	0.0978559i	$-0.0311984\pi$
$887$	41.9355	+	24.2115i	1.40806	+	0.812941i	0.412855	+	0.910797i	$0.364532\pi$
$888$		0			0
$889$	18.6714	−	31.2706i	0.626218	−	1.04878i
$890$		0			0
$891$	−8.99387	+	15.5778i	−0.301306	+	0.521877i
$892$		0			0
$893$	−12.2623	−	21.2389i	−0.410341	−	0.710731i
$894$		0			0
$895$	29.7288	+	7.62966i	0.993723	+	0.255031i
$896$		0			0
$897$		−	12.8874i		−	0.430297i
$898$		0			0
$899$	−9.35677	+	5.40214i	−0.312066	+	0.180171i
$900$		0			0
$901$	−14.9744	+	25.9364i	−0.498868	+	0.864066i
$902$		0			0
$903$	0.0251502	−	1.71322i	0.000836946	−	0.0570122i
$904$		0			0
$905$	−14.7055	+	15.0200i	−0.488828	+	0.499281i
$906$		0			0
$907$	−22.7875	+	13.1563i	−0.756645	+	0.436849i	−0.828090	−	0.560595i	$-0.810572\pi$
$907$	−22.7875	+	13.1563i	−0.756645	+	0.436849i	0.0714447	+	0.997445i	$0.477239\pi$
$908$		0			0
$909$	−29.8432			−0.989836
$910$		0			0
$911$			33.1244i			1.09746i	0.836000	+	0.548730i	$0.184889\pi$
$911$			33.1244i			1.09746i	−0.836000	+	0.548730i	$0.815111\pi$
$912$		0			0
$913$	1.53874	+	2.66518i	0.0509250	+	0.0882047i
$914$		0			0
$915$	13.4023	−	13.6889i	0.443066	−	0.452541i
$916$		0			0
$917$	21.6324	−	12.0696i	0.714366	−	0.398574i
$918$		0			0
$919$	13.7579	+	7.94310i	0.453830	+	0.262019i	0.709446	−	0.704759i	$-0.248945\pi$
$919$	13.7579	+	7.94310i	0.453830	+	0.262019i	−0.255616	+	0.966778i	$0.582278\pi$
$920$		0			0
$921$	−2.57766	−	4.46464i	−0.0849368	−	0.147115i
$922$		0			0
$923$	−31.5041			−1.03697
$924$		0			0
$925$	7.45626	+	4.09703i	0.245160	+	0.134710i
$926$		0			0
$927$	0.327887	−	0.189306i	0.0107692	−	0.00621762i
$928$		0			0
$929$	11.4594	+	6.61609i	0.375971	+	0.217067i	0.676064	−	0.736843i	$-0.263684\pi$
$929$	11.4594	+	6.61609i	0.375971	+	0.217067i	−0.300093	+	0.953910i	$0.597018\pi$
$930$		0			0
$931$	−0.773145	+	26.3274i	−0.0253388	+	0.862847i
$932$		0			0
$933$	3.31940	−	5.74936i	0.108672	−	0.188226i
$934$		0			0
$935$	−12.0514	−	43.1453i	−0.394122	−	1.41100i
$936$		0			0
$937$	11.6731			0.381345			0.190672	−	0.981654i	$-0.438933\pi$
$937$	11.6731			0.381345			0.190672	+	0.981654i	$0.438933\pi$
$938$		0			0
$939$	−7.42756			−0.242389
$940$		0			0
$941$	25.6649	+	44.4529i	0.836652	+	1.44912i	0.892679	+	0.450694i	$0.148823\pi$
$941$	25.6649	+	44.4529i	0.836652	+	1.44912i	−0.0560269	+	0.998429i	$0.517843\pi$
$942$		0			0
$943$	24.1021	+	13.9154i	0.784874	+	0.453147i
$944$		0			0
$945$	5.95442	+	22.5923i	0.193697	+	0.734927i
$946$		0			0
$947$	16.0314	+	9.25574i	0.520951	+	0.300771i	0.737324	−	0.675540i	$-0.236089\pi$
$947$	16.0314	+	9.25574i	0.520951	+	0.300771i	−0.216373	+	0.976311i	$0.569423\pi$
$948$		0			0
$949$	−11.4707	+	6.62262i	−0.372355	+	0.214979i
$950$		0			0
$951$	24.1050			0.781657
$952$		0			0
$953$			3.91838i			0.126929i	0.997984	+	0.0634643i	$0.0202149\pi$
$953$			3.91838i			0.126929i	−0.997984	+	0.0634643i	$0.979785\pi$
$954$		0			0
$955$	−38.4559	+	10.7415i	−1.24440	+	0.347588i
$956$		0			0
$957$	−8.28237	−	4.78183i	−0.267731	−	0.154575i
$958$		0			0
$959$	0.723955	−	49.3154i	0.0233777	−	1.59248i
$960$		0			0
$961$	10.4268	−	18.0598i	0.336349	−	0.582573i
$962$		0			0
$963$	3.43377	−	1.98249i	0.110652	−	0.0638847i
$964$		0			0
$965$	−12.7108	+	49.5273i	−0.409175	+	1.59434i
$966$		0			0
$967$	−25.1423			−0.808522			−0.404261	−	0.914644i	$-0.632471\pi$
$967$	−25.1423			−0.808522			−0.404261	+	0.914644i	$0.632471\pi$
$968$		0			0
$969$	−12.0209	+	6.94024i	−0.386165	+	0.222953i
$970$		0			0
$971$	4.10368	+	2.36926i	0.131693	+	0.0760332i	0.564399	−	0.825502i	$-0.309108\pi$
$971$	4.10368	+	2.36926i	0.131693	+	0.0760332i	−0.432706	+	0.901535i	$0.642441\pi$
$972$		0			0
$973$	−10.2439	−	6.11654i	−0.328404	−	0.196087i
$974$		0			0
$975$	4.76742	+	7.86814i	0.152680	+	0.251982i
$976$		0			0
$977$	3.73355	−	2.15557i	0.119447	−	0.0689628i	−0.439086	−	0.898445i	$-0.644698\pi$
$977$	3.73355	−	2.15557i	0.119447	−	0.0689628i	0.558533	+	0.829482i	$0.311364\pi$
$978$		0			0
$979$			3.07242i			0.0981950i
$980$		0			0
$981$		−	38.8754i		−	1.24119i
$982$		0			0
$983$	−44.5474	+	25.7195i	−1.42084	+	0.820324i	−0.996371	−	0.0851174i	$-0.972873\pi$
$983$	−44.5474	+	25.7195i	−1.42084	+	0.820324i	−0.424472	+	0.905441i	$0.639540\pi$
$984$		0			0
$985$	21.3824	−	21.8396i	0.681299	−	0.695868i
$986$		0			0
$987$	−10.6685	−	6.37007i	−0.339583	−	0.202762i
$988$		0			0
$989$	−5.45172	−	3.14755i	−0.173355	−	0.100086i
$990$		0			0
$991$	−15.3827	+	8.88120i	−0.488647	+	0.282120i	−0.724013	−	0.689786i	$-0.757704\pi$
$991$	−15.3827	+	8.88120i	−0.488647	+	0.282120i	0.235366	+	0.971907i	$0.424371\pi$
$992$		0			0
$993$	0.188619			0.00598565
$994$		0			0
$995$	49.6025	+	12.7301i	1.57250	+	0.403571i
$996$		0			0
$997$	24.1923	−	13.9674i	0.766177	−	0.442353i	−0.0653318	−	0.997864i	$-0.520811\pi$
$997$	24.1923	−	13.9674i	0.766177	−	0.442353i	0.831509	+	0.555511i	$0.187477\pi$
$998$		0			0
$999$	3.35987	−	5.81947i	0.106302	−	0.184120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.719.18		80
4.3	odd	2		280.2.ba.b.19.10	yes	80
5.4	even	2	inner	1120.2.bq.b.719.24		80
7.3	odd	6	inner	1120.2.bq.b.1039.23		80
8.3	odd	2	inner	1120.2.bq.b.719.17		80
8.5	even	2		280.2.ba.b.19.5	✓	80
20.19	odd	2		280.2.ba.b.19.31	yes	80
28.3	even	6		280.2.ba.b.59.36	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.17		80
40.19	odd	2	inner	1120.2.bq.b.719.23		80
40.29	even	2		280.2.ba.b.19.36	yes	80
56.3	even	6	inner	1120.2.bq.b.1039.24		80
56.45	odd	6		280.2.ba.b.59.31	yes	80
140.59	even	6		280.2.ba.b.59.5	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.18		80
280.269	odd	6		280.2.ba.b.59.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.5	✓	80	8.5	even	2
280.2.ba.b.19.10	yes	80	4.3	odd	2
280.2.ba.b.19.31	yes	80	20.19	odd	2
280.2.ba.b.19.36	yes	80	40.29	even	2
280.2.ba.b.59.5	yes	80	140.59	even	6
280.2.ba.b.59.10	yes	80	280.269	odd	6
280.2.ba.b.59.31	yes	80	56.45	odd	6
280.2.ba.b.59.36	yes	80	28.3	even	6
1120.2.bq.b.719.17		80	8.3	odd	2	inner
1120.2.bq.b.719.18		80	1.1	even	1	trivial
1120.2.bq.b.719.23		80	40.19	odd	2	inner
1120.2.bq.b.719.24		80	5.4	even	2	inner
1120.2.bq.b.1039.17		80	35.24	odd	6	inner
1120.2.bq.b.1039.18		80	280.59	even	6	inner
1120.2.bq.b.1039.23		80	7.3	odd	6	inner
1120.2.bq.b.1039.24		80	56.3	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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.360276 - 0.624015i) q^{3} +(1.56432 - 1.59778i) q^{5} +(1.35637 - 2.27162i) q^{7} +(1.24040 - 2.14844i) q^{9} +O(q^{10})\)	\(q+(-0.360276 - 0.624015i) q^{3} +(1.56432 - 1.59778i) q^{5} +(1.35637 - 2.27162i) q^{7} +(1.24040 - 2.14844i) q^{9} +(-1.95654 - 3.38883i) q^{11} -2.55354i q^{13} +(-1.56063 - 0.400522i) q^{15} +(2.55984 + 4.43377i) q^{17} +(-3.25858 - 1.88134i) q^{19} +(-1.90619 - 0.0279831i) q^{21} +(-3.50209 + 6.06580i) q^{23} +(-0.105783 - 4.99888i) q^{25} -3.94920 q^{27} +3.39188i q^{29} +(1.59267 + 2.75858i) q^{31} +(-1.40979 + 2.44183i) q^{33} +(-1.50775 - 5.72072i) q^{35} +(-0.850773 + 1.47358i) q^{37} +(-1.59345 + 0.919977i) q^{39} -3.97345i q^{41} +0.898763i q^{43} +(-1.49234 - 5.34275i) q^{45} +(5.64460 + 3.25891i) q^{47} +(-3.32054 - 6.16230i) q^{49} +(1.84449 - 3.19476i) q^{51} +(2.92487 + 5.06602i) q^{53} +(-8.47526 - 2.17511i) q^{55} +2.71120i q^{57} +(10.2528 - 5.91946i) q^{59} +(-5.94508 + 10.2972i) q^{61} +(-3.19801 - 5.73180i) q^{63} +(-4.07998 - 3.99456i) q^{65} +(2.68095 - 1.54785i) q^{67} +5.04687 q^{69} -12.3374i q^{71} +(-2.59351 - 4.49209i) q^{73} +(-3.08127 + 1.86698i) q^{75} +(-10.3519 - 0.151968i) q^{77} +(8.84693 + 5.10778i) q^{79} +(-2.29841 - 3.98096i) q^{81} -0.786461 q^{83} +(11.0886 + 2.84580i) q^{85} +(2.11658 - 1.22201i) q^{87} +(-0.679974 - 0.392583i) q^{89} +(-5.80068 - 3.46353i) q^{91} +(1.14760 - 1.98770i) q^{93} +(-8.10344 + 2.26346i) q^{95} -16.5331 q^{97} -9.70761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 80 * q - 52 * q^9	\( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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