LMFDB - Embedded newform 1120.2.bq.b.719.3

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			719.3
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46528 - 2.53794i) q^{3} +(-0.852425 + 2.06721i) q^{5} +(1.45426 + 2.21023i) q^{7} +(-2.79408 + 4.83948i) q^{9} +O(q^{10})$	\(q+(-1.46528 - 2.53794i) q^{3} +(-0.852425 + 2.06721i) q^{5} +(1.45426 + 2.21023i) q^{7} +(-2.79408 + 4.83948i) q^{9} +(1.55174 + 2.68769i) q^{11} -1.62644i q^{13} +(6.49549 - 0.865643i) q^{15} +(-2.52573 - 4.37469i) q^{17} +(-6.55731 - 3.78587i) q^{19} +(3.47853 - 6.92942i) q^{21} +(1.55633 - 2.69565i) q^{23} +(-3.54674 - 3.52429i) q^{25} +7.58472 q^{27} +0.389298i q^{29} +(-3.31666 - 5.74462i) q^{31} +(4.54746 - 7.87643i) q^{33} +(-5.80867 + 1.12221i) q^{35} +(0.553818 - 0.959241i) q^{37} +(-4.12781 + 2.38319i) q^{39} -0.928523i q^{41} -3.21202i q^{43} +(-7.62250 - 9.90125i) q^{45} +(2.82412 + 1.63050i) q^{47} +(-2.77026 + 6.42850i) q^{49} +(-7.40178 + 12.8203i) q^{51} +(-5.44437 - 9.42993i) q^{53} +(-6.87877 + 0.916722i) q^{55} +22.1894i q^{57} +(5.71232 - 3.29801i) q^{59} +(-3.21046 + 5.56068i) q^{61} +(-14.7597 + 0.862304i) q^{63} +(3.36221 + 1.38642i) q^{65} +(-2.80208 + 1.61778i) q^{67} -9.12183 q^{69} -7.22771i q^{71} +(-1.58632 - 2.74759i) q^{73} +(-3.74745 + 14.1655i) q^{75} +(-3.68379 + 7.33831i) q^{77} +(6.81139 + 3.93256i) q^{79} +(-2.73150 - 4.73109i) q^{81} +10.3353 q^{83} +(11.1964 - 1.49213i) q^{85} +(0.988013 - 0.570429i) q^{87} +(-9.69972 - 5.60014i) q^{89} +(3.59482 - 2.36527i) q^{91} +(-9.71964 + 16.8349i) q^{93} +(13.4158 - 10.3282i) q^{95} -10.5782 q^{97} -17.3427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.46528	−	2.53794i	−0.845978	−	1.46528i	−0.884769	−	0.466030i	$-0.845684\pi$
$3$	−1.46528	−	2.53794i	−0.845978	−	1.46528i	0.0387905	−	0.999247i	$-0.487650\pi$
$4$		0			0
$5$	−0.852425	+	2.06721i	−0.381216	+	0.924486i
$5$	−0.852425	+	2.06721i	−0.381216	+	0.924486i
$6$		0			0
$7$	1.45426	+	2.21023i	0.549658	+	0.835389i
$7$	1.45426	+	2.21023i	0.549658	+	0.835389i
$8$		0			0
$9$	−2.79408	+	4.83948i	−0.931359	+	1.61316i
$10$		0			0
$11$	1.55174	+	2.68769i	0.467867	+	0.810369i	0.999326	−	0.0367148i	$-0.0116893\pi$
$11$	1.55174	+	2.68769i	0.467867	+	0.810369i	−0.531459	+	0.847084i	$0.678356\pi$
$12$		0			0
$13$		−	1.62644i		−	0.451094i	−0.974232	−	0.225547i	$-0.927583\pi$
$13$		−	1.62644i		−	0.451094i	0.974232	−	0.225547i	$-0.0724170\pi$
$14$		0			0
$15$	6.49549	−	0.865643i	1.67713	−	0.223508i
$16$		0			0
$17$	−2.52573	−	4.37469i	−0.612579	−	1.06102i	−0.990804	−	0.135304i	$-0.956799\pi$
$17$	−2.52573	−	4.37469i	−0.612579	−	1.06102i	0.378225	−	0.925714i	$-0.376534\pi$
$18$		0			0
$19$	−6.55731	−	3.78587i	−1.50435	−	0.868537i	−0.999987	−	0.00504564i	$-0.998394\pi$
$19$	−6.55731	−	3.78587i	−1.50435	−	0.868537i	−0.504363	−	0.863492i	$-0.668273\pi$
$20$		0			0
$21$	3.47853	−	6.92942i	0.759078	−	1.51212i
$22$		0			0
$23$	1.55633	−	2.69565i	0.324518	−	0.562081i	−0.656897	−	0.753980i	$-0.728131\pi$
$23$	1.55633	−	2.69565i	0.324518	−	0.562081i	0.981415	+	0.191899i	$0.0614647\pi$
$24$		0			0
$25$	−3.54674	−	3.52429i	−0.709349	−	0.704858i
$26$		0			0
$27$	7.58472			1.45968
$28$		0			0
$29$			0.389298i			0.0722908i	0.999347	+	0.0361454i	$0.0115079\pi$
$29$			0.389298i			0.0722908i	−0.999347	+	0.0361454i	$0.988492\pi$
$30$		0			0
$31$	−3.31666	−	5.74462i	−0.595689	−	1.03176i	−0.993449	−	0.114274i	$-0.963546\pi$
$31$	−3.31666	−	5.74462i	−0.595689	−	1.03176i	0.397760	−	0.917489i	$-0.369788\pi$
$32$		0			0
$33$	4.54746	−	7.87643i	0.791611	−	1.37111i
$34$		0			0
$35$	−5.80867	+	1.12221i	−0.981844	+	0.189688i
$36$		0			0
$37$	0.553818	−	0.959241i	0.0910471	−	0.157698i	−0.816905	−	0.576772i	$-0.804312\pi$
$37$	0.553818	−	0.959241i	0.0910471	−	0.157698i	0.907952	+	0.419074i	$0.137645\pi$
$38$		0			0
$39$	−4.12781	+	2.38319i	−0.660979	+	0.381616i
$40$		0			0
$41$		−	0.928523i		−	0.145011i	−0.997368	−	0.0725055i	$-0.976901\pi$
$41$		−	0.928523i		−	0.145011i	0.997368	−	0.0725055i	$-0.0230995\pi$
$42$		0			0
$43$		−	3.21202i		−	0.489829i	−0.969545	−	0.244914i	$-0.921240\pi$
$43$		−	3.21202i		−	0.489829i	0.969545	−	0.244914i	$-0.0787598\pi$
$44$		0			0
$45$	−7.62250	−	9.90125i	−1.13630	−	1.47599i
$46$		0			0
$47$	2.82412	+	1.63050i	0.411940	+	0.237833i	0.691623	−	0.722259i	$-0.256896\pi$
$47$	2.82412	+	1.63050i	0.411940	+	0.237833i	−0.279683	+	0.960092i	$0.590229\pi$
$48$		0			0
$49$	−2.77026	+	6.42850i	−0.395751	+	0.918358i
$50$		0			0
$51$	−7.40178	+	12.8203i	−1.03646	+	1.79520i
$52$		0			0
$53$	−5.44437	−	9.42993i	−0.747842	−	1.29530i	−0.948855	−	0.315712i	$-0.897757\pi$
$53$	−5.44437	−	9.42993i	−0.747842	−	1.29530i	0.201013	−	0.979589i	$-0.435577\pi$
$54$		0			0
$55$	−6.87877	+	0.916722i	−0.927533	+	0.123611i
$56$		0			0
$57$			22.1894i			2.93905i
$58$		0			0
$59$	5.71232	−	3.29801i	0.743681	−	0.429364i	−0.0797253	−	0.996817i	$-0.525404\pi$
$59$	5.71232	−	3.29801i	0.743681	−	0.429364i	0.823406	+	0.567453i	$0.192071\pi$
$60$		0			0
$61$	−3.21046	+	5.56068i	−0.411058	+	0.711973i	−0.995006	−	0.0998183i	$-0.968174\pi$
$61$	−3.21046	+	5.56068i	−0.411058	+	0.711973i	0.583948	+	0.811791i	$0.301507\pi$
$62$		0			0
$63$	−14.7597	+	0.862304i	−1.85955	+	0.108640i
$64$		0			0
$65$	3.36221	+	1.38642i	0.417031	+	0.171964i
$66$		0			0
$67$	−2.80208	+	1.61778i	−0.342329	+	0.197644i	−0.661301	−	0.750120i	$-0.729996\pi$
$67$	−2.80208	+	1.61778i	−0.342329	+	0.197644i	0.318973	+	0.947764i	$0.396662\pi$
$68$		0			0
$69$	−9.12183			−1.09814
$70$		0			0
$71$		−	7.22771i		−	0.857771i	−0.903359	−	0.428886i	$-0.858906\pi$
$71$		−	7.22771i		−	0.857771i	0.903359	−	0.428886i	$-0.141094\pi$
$72$		0			0
$73$	−1.58632	−	2.74759i	−0.185665	−	0.321581i	0.758136	−	0.652097i	$-0.226110\pi$
$73$	−1.58632	−	2.74759i	−0.185665	−	0.321581i	−0.943800	+	0.330516i	$0.892777\pi$
$74$		0			0
$75$	−3.74745	+	14.1655i	−0.432718	+	1.63569i
$76$		0			0
$77$	−3.68379	+	7.33831i	−0.419807	+	0.836278i
$78$		0			0
$79$	6.81139	+	3.93256i	0.766342	+	0.442448i	0.831568	−	0.555423i	$-0.187444\pi$
$79$	6.81139	+	3.93256i	0.766342	+	0.442448i	−0.0652264	+	0.997870i	$0.520777\pi$
$80$		0			0
$81$	−2.73150	−	4.73109i	−0.303500	−	0.525677i
$82$		0			0
$83$	10.3353			1.13444			0.567221	−	0.823566i	$-0.308019\pi$
$83$	10.3353			1.13444			0.567221	+	0.823566i	$0.308019\pi$
$84$		0			0
$85$	11.1964	−	1.49213i	1.21442	−	0.161844i
$86$		0			0
$87$	0.988013	−	0.570429i	0.105926	−	0.0611565i
$88$		0			0
$89$	−9.69972	−	5.60014i	−1.02817	−	0.593613i	−0.111709	−	0.993741i	$-0.535632\pi$
$89$	−9.69972	−	5.60014i	−1.02817	−	0.593613i	−0.916459	+	0.400128i	$0.868966\pi$
$90$		0			0
$91$	3.59482	−	2.36527i	0.376840	−	0.247948i
$92$		0			0
$93$	−9.71964	+	16.8349i	−1.00788	+	1.74570i
$94$		0			0
$95$	13.4158	−	10.3282i	1.37643	−	1.05965i
$96$		0			0
$97$	−10.5782			−1.07405			−0.537025	−	0.843566i	$-0.680452\pi$
$97$	−10.5782			−1.07405			−0.537025	+	0.843566i	$0.680452\pi$
$98$		0			0
$99$	−17.3427			−1.74301
$100$		0			0
$101$	2.43704	+	4.22108i	0.242495	+	0.420013i	0.961424	−	0.275070i	$-0.0887009\pi$
$101$	2.43704	+	4.22108i	0.242495	+	0.420013i	−0.718929	+	0.695083i	$0.755368\pi$
$102$		0			0
$103$	−10.9818	−	6.34034i	−1.08207	−	0.624732i	−0.150614	−	0.988593i	$-0.548125\pi$
$103$	−10.9818	−	6.34034i	−1.08207	−	0.624732i	−0.931454	+	0.363860i	$0.881459\pi$
$104$		0			0
$105$	11.3594	+	13.0977i	1.10856	+	1.27820i
$106$		0			0
$107$	−7.60939	−	4.39329i	−0.735628	−	0.424715i	0.0848496	−	0.996394i	$-0.472959\pi$
$107$	−7.60939	−	4.39329i	−0.735628	−	0.424715i	−0.820477	+	0.571679i	$0.806292\pi$
$108$		0			0
$109$	−2.69246	+	1.55449i	−0.257891	+	0.148893i	−0.623372	−	0.781925i	$-0.714238\pi$
$109$	−2.69246	+	1.55449i	−0.257891	+	0.148893i	0.365481	+	0.930819i	$0.380904\pi$
$110$		0			0
$111$	−3.24599			−0.308095
$112$		0			0
$113$		−	8.76776i		−	0.824801i	−0.911003	−	0.412401i	$-0.864690\pi$
$113$		−	8.76776i		−	0.824801i	0.911003	−	0.412401i	$-0.135310\pi$
$114$		0			0
$115$	4.24582	+	5.51511i	0.395925	+	0.514286i
$116$		0			0
$117$	7.87115	+	4.54441i	0.727688	+	0.420131i
$118$		0			0
$119$	5.99602	−	11.9444i	0.549654	−	1.09494i
$120$		0			0
$121$	0.684211	−	1.18509i	0.0622010	−	0.107735i
$122$		0			0
$123$	−2.35653	+	1.36054i	−0.212481	+	0.122676i
$124$		0			0
$125$	10.3088	−	4.32769i	0.922046	−	0.387080i
$126$		0			0
$127$	−5.82575			−0.516952			−0.258476	−	0.966018i	$-0.583220\pi$
$127$	−5.82575			−0.516952			−0.258476	+	0.966018i	$0.583220\pi$
$128$		0			0
$129$	−8.15190	+	4.70650i	−0.717735	+	0.414384i
$130$		0			0
$131$	−14.8997	−	8.60235i	−1.30179	−	0.751591i	−0.321082	−	0.947052i	$-0.604046\pi$
$131$	−14.8997	−	8.60235i	−1.30179	−	0.751591i	−0.980711	+	0.195461i	$0.937380\pi$
$132$		0			0
$133$	−1.16839	−	19.9988i	−0.101312	−	1.73412i
$134$		0			0
$135$	−6.46541	+	15.6792i	−0.556454	+	1.34945i
$136$		0			0
$137$	−4.01092	+	2.31571i	−0.342676	+	0.197844i	−0.661455	−	0.749985i	$-0.730061\pi$
$137$	−4.01092	+	2.31571i	−0.342676	+	0.197844i	0.318779	+	0.947829i	$0.396727\pi$
$138$		0			0
$139$			12.0576i			1.02271i	0.859368	+	0.511357i	$0.170857\pi$
$139$			12.0576i			1.02271i	−0.859368	+	0.511357i	$0.829143\pi$
$140$		0			0
$141$		−	9.55656i		−	0.804808i
$142$		0			0
$143$	4.37138	−	2.52382i	0.365553	−	0.211052i
$144$		0			0
$145$	−0.804762	−	0.331847i	−0.0668318	−	0.0275584i
$146$		0			0
$147$	20.3743	−	2.38881i	1.68045	−	0.197026i
$148$		0			0
$149$	15.0162	+	8.66962i	1.23018	+	0.710243i	0.967067	−	0.254523i	$-0.0819184\pi$
$149$	15.0162	+	8.66962i	1.23018	+	0.710243i	0.263110	+	0.964766i	$0.415252\pi$
$150$		0			0
$151$	−16.8208	+	9.71149i	−1.36886	+	0.790310i	−0.990782	−	0.135465i	$-0.956747\pi$
$151$	−16.8208	+	9.71149i	−1.36886	+	0.790310i	−0.378075	+	0.925775i	$0.623414\pi$
$152$		0			0
$153$	28.2283			2.28212
$154$		0			0
$155$	14.7025	−	1.95938i	1.18094	−	0.157381i
$156$		0			0
$157$	15.5317	−	8.96725i	1.23957	−	0.715665i	0.270562	−	0.962703i	$-0.412791\pi$
$157$	15.5317	−	8.96725i	1.23957	−	0.715665i	0.969006	+	0.247038i	$0.0794572\pi$
$158$		0			0
$159$	−15.9550	+	27.6349i	−1.26532	+	2.19159i
$160$		0			0
$161$	8.22132	−	0.480313i	0.647930	−	0.0378540i
$162$		0			0
$163$	−14.8747	−	8.58794i	−1.16508	−	0.672659i	−0.212564	−	0.977147i	$-0.568181\pi$
$163$	−14.8747	−	8.58794i	−1.16508	−	0.672659i	−0.952516	+	0.304488i	$0.901515\pi$
$164$		0			0
$165$	12.4059	+	16.1146i	0.965797	+	1.25452i
$166$		0			0
$167$		−	23.1940i		−	1.79481i	−0.441210	−	0.897404i	$-0.645451\pi$
$167$		−	23.1940i		−	1.79481i	0.441210	−	0.897404i	$-0.354549\pi$
$168$		0			0
$169$	10.3547			0.796514
$170$		0			0
$171$	36.6433	−	21.1560i	2.80218	−	1.61784i
$172$		0			0
$173$	13.5835	+	7.84243i	1.03273	+	0.596249i	0.917766	−	0.397121i	$-0.129991\pi$
$173$	13.5835	+	7.84243i	1.03273	+	0.596249i	0.114967	+	0.993369i	$0.463324\pi$
$174$		0			0
$175$	2.63161	−	12.9644i	0.198931	−	0.980013i
$176$		0			0
$177$	−16.7403	−	9.66500i	−1.25828	−	0.726466i
$178$		0			0
$179$	1.80380	+	3.12428i	0.134823	+	0.233520i	0.925530	−	0.378675i	$-0.123620\pi$
$179$	1.80380	+	3.12428i	0.134823	+	0.233520i	−0.790707	+	0.612195i	$0.790287\pi$
$180$		0			0
$181$	−3.98490			−0.296195			−0.148098	−	0.988973i	$-0.547315\pi$
$181$	−3.98490			−0.296195			−0.148098	+	0.988973i	$0.547315\pi$
$182$		0			0
$183$	18.8169			1.39098
$184$		0			0
$185$	1.51087	+	1.96254i	0.111081	+	0.144289i
$186$		0			0
$187$	7.83854	−	13.5767i	0.573211	−	0.992830i
$188$		0			0
$189$	11.0302	+	16.7640i	0.802326	+	1.21940i
$190$		0			0
$191$	8.00755	+	4.62316i	0.579406	+	0.334520i	0.760897	−	0.648872i	$-0.224759\pi$
$191$	8.00755	+	4.62316i	0.579406	+	0.334520i	−0.181491	+	0.983393i	$0.558092\pi$
$192$		0			0
$193$	−10.5917	+	6.11514i	−0.762410	+	0.440177i	−0.830160	−	0.557525i	$-0.811751\pi$
$193$	−10.5917	+	6.11514i	−0.762410	+	0.440177i	0.0677506	+	0.997702i	$0.478418\pi$
$194$		0			0
$195$	−1.40792	−	10.5646i	−0.100823	−	0.756544i
$196$		0			0
$197$	−7.38753			−0.526340			−0.263170	−	0.964750i	$-0.584768\pi$
$197$	−7.38753			−0.526340			−0.263170	+	0.964750i	$0.584768\pi$
$198$		0			0
$199$	2.81699	+	4.87917i	0.199691	+	0.345875i	0.948428	−	0.316992i	$-0.102673\pi$
$199$	2.81699	+	4.87917i	0.199691	+	0.345875i	−0.748737	+	0.662867i	$0.769339\pi$
$200$		0			0
$201$	8.21166	+	4.74100i	0.579206	+	0.334405i
$202$		0			0
$203$	−0.860439	+	0.566140i	−0.0603910	+	0.0397353i
$204$		0			0
$205$	1.91946	+	0.791496i	0.134061	+	0.0552805i
$206$		0			0
$207$	8.69702	+	15.0637i	0.604485	+	1.04700i
$208$		0			0
$209$		−	23.4987i		−	1.62544i
$210$		0			0
$211$	−5.14042			−0.353881			−0.176940	−	0.984222i	$-0.556620\pi$
$211$	−5.14042			−0.353881			−0.176940	+	0.984222i	$0.556620\pi$
$212$		0			0
$213$	−18.3435	+	10.5906i	−1.25687	+	0.725656i
$214$		0			0
$215$	6.63993	+	2.73801i	0.452840	+	0.186730i
$216$		0			0
$217$	7.87366	−	15.6847i	0.534499	−	1.06475i
$218$		0			0
$219$	−4.64880	+	8.05195i	−0.314137	+	0.544100i
$220$		0			0
$221$	−7.11519	+	4.10795i	−0.478619	+	0.276331i
$222$		0			0
$223$			5.70766i			0.382213i	0.981569	+	0.191106i	$0.0612076\pi$
$223$			5.70766i			0.382213i	−0.981569	+	0.191106i	$0.938792\pi$
$224$		0			0
$225$	26.9656	−	7.31728i	1.79771	−	0.487818i
$226$		0			0
$227$	−9.24524	−	16.0132i	−0.613628	−	1.06283i	−0.990624	−	0.136620i	$-0.956376\pi$
$227$	−9.24524	−	16.0132i	−0.613628	−	1.06283i	0.376996	−	0.926215i	$-0.376957\pi$
$228$		0			0
$229$	−4.79008	+	8.29666i	−0.316537	+	0.548258i	−0.979763	−	0.200161i	$-0.935854\pi$
$229$	−4.79008	+	8.29666i	−0.316537	+	0.548258i	0.663226	+	0.748419i	$0.269187\pi$
$230$		0			0
$231$	24.0219	−	1.40343i	1.58053	−	0.0923389i
$232$		0			0
$233$	−3.64278	−	2.10316i	−0.238647	−	0.137783i	0.375908	−	0.926657i	$-0.377331\pi$
$233$	−3.64278	−	2.10316i	−0.238647	−	0.137783i	−0.614555	+	0.788874i	$0.710664\pi$
$234$		0			0
$235$	−5.77794	+	4.44817i	−0.376912	+	0.290166i
$236$		0			0
$237$		−	23.0492i		−	1.49720i
$238$		0			0
$239$			21.5399i			1.39330i	0.717410	+	0.696651i	$0.245327\pi$
$239$			21.5399i			1.39330i	−0.717410	+	0.696651i	$0.754673\pi$
$240$		0			0
$241$	7.51995	−	4.34165i	0.484403	−	0.279670i	−0.237847	−	0.971303i	$-0.576442\pi$
$241$	7.51995	−	4.34165i	0.484403	−	0.279670i	0.722249	+	0.691633i	$0.243108\pi$
$242$		0			0
$243$	3.37228	−	5.84097i	0.216332	−	0.374698i
$244$		0			0
$245$	−10.9277	−	11.2065i	−0.698142	−	0.715959i
$246$		0			0
$247$	−6.15750	+	10.6651i	−0.391792	+	0.678604i
$248$		0			0
$249$	−15.1440	−	26.2302i	−0.959713	−	1.66227i
$250$		0			0
$251$		−	11.2144i		−	0.707844i	−0.935275	−	0.353922i	$-0.884848\pi$
$251$		−	11.2144i		−	0.707844i	0.935275	−	0.353922i	$-0.115152\pi$
$252$		0			0
$253$	9.66008			0.607324
$254$		0			0
$255$	−20.1928	−	26.2294i	−1.26452	−	1.64255i
$256$		0			0
$257$	−5.68553	+	9.84763i	−0.354654	+	0.614278i	−0.987059	−	0.160360i	$-0.948735\pi$
$257$	−5.68553	+	9.84763i	−0.354654	+	0.614278i	0.632405	+	0.774638i	$0.282068\pi$
$258$		0			0
$259$	2.92554	−	0.170919i	0.181784	−	0.0106204i
$260$		0			0
$261$	−1.88400	−	1.08773i	−0.116617	−	0.0673287i
$262$		0			0
$263$	9.68088	+	16.7678i	0.596949	+	1.03395i	0.993269	+	0.115833i	$0.0369537\pi$
$263$	9.68088	+	16.7678i	0.596949	+	1.03395i	−0.396320	+	0.918112i	$0.629713\pi$
$264$		0			0
$265$	24.1346	−	3.21638i	1.48258	−	0.197580i
$266$		0			0
$267$			32.8230i			2.00874i
$268$		0			0
$269$	0.761782	+	1.31945i	0.0464467	+	0.0804480i	0.888314	−	0.459236i	$-0.151877\pi$
$269$	0.761782	+	1.31945i	0.0464467	+	0.0804480i	−0.841867	+	0.539684i	$0.818544\pi$
$270$		0			0
$271$	9.32172	−	16.1457i	0.566254	−	0.980781i	−0.430677	−	0.902506i	$-0.641725\pi$
$271$	9.32172	−	16.1457i	0.566254	−	0.980781i	0.996932	−	0.0782754i	$-0.0249414\pi$
$272$		0			0
$273$	−11.2703	−	5.65764i	−0.682111	−	0.342416i
$274$		0			0
$275$	3.96858	−	15.0013i	0.239314	−	0.904614i
$276$		0			0
$277$	4.74717	+	8.22234i	0.285230	+	0.494033i	0.972665	−	0.232213i	$-0.0745967\pi$
$277$	4.74717	+	8.22234i	0.285230	+	0.494033i	−0.687435	+	0.726246i	$0.741263\pi$
$278$		0			0
$279$	37.0680			2.21920
$280$		0			0
$281$	−9.11431			−0.543714			−0.271857	−	0.962338i	$-0.587638\pi$
$281$	−9.11431			−0.543714			−0.271857	+	0.962338i	$0.587638\pi$
$282$		0			0
$283$	7.77457	+	13.4659i	0.462150	+	0.800467i	0.999068	−	0.0431671i	$-0.0137448\pi$
$283$	7.77457	+	13.4659i	0.462150	+	0.800467i	−0.536918	+	0.843635i	$0.680411\pi$
$284$		0			0
$285$	−45.8702	−	18.9148i	−2.71712	−	1.12041i
$286$		0			0
$287$	2.05225	−	1.35031i	0.121141	−	0.0797065i
$288$		0			0
$289$	−4.25859	+	7.37610i	−0.250506	+	0.433888i
$290$		0			0
$291$	15.4999	+	26.8467i	0.908623	+	1.57378i
$292$		0			0
$293$		−	8.72422i		−	0.509674i	−0.966984	−	0.254837i	$-0.917978\pi$
$293$		−	8.72422i		−	0.509674i	0.966984	−	0.254837i	$-0.0820219\pi$
$294$		0			0
$295$	1.94837	+	14.6199i	0.113438	+	0.851203i
$296$		0			0
$297$	11.7695	+	20.3854i	0.682936	+	1.18288i
$298$		0			0
$299$	−4.38432	−	2.53129i	−0.253552	−	0.146388i
$300$		0			0
$301$	7.09932	−	4.67111i	0.409198	−	0.269238i
$302$		0			0
$303$	7.14189	−	12.3701i	0.410291	−	0.710644i
$304$		0			0
$305$	−8.75845	−	11.3768i	−0.501507	−	0.651432i
$306$		0			0
$307$	−7.13157			−0.407020			−0.203510	−	0.979073i	$-0.565235\pi$
$307$	−7.13157			−0.407020			−0.203510	+	0.979073i	$0.565235\pi$
$308$		0			0
$309$			37.1614i			2.11404i
$310$		0			0
$311$	15.8284	+	27.4155i	0.897545	+	1.55459i	0.830623	+	0.556835i	$0.187984\pi$
$311$	15.8284	+	27.4155i	0.897545	+	1.55459i	0.0669214	+	0.997758i	$0.478682\pi$
$312$		0			0
$313$	−11.5185	+	19.9506i	−0.651063	+	1.12767i	0.331802	+	0.943349i	$0.392343\pi$
$313$	−11.5185	+	19.9506i	−0.651063	+	1.12767i	−0.982865	+	0.184325i	$0.940990\pi$
$314$		0			0
$315$	10.7990	−	31.2465i	0.608453	−	1.76054i
$316$		0			0
$317$	−8.93503	+	15.4759i	−0.501841	+	0.869214i	0.498157	+	0.867087i	$0.334010\pi$
$317$	−8.93503	+	15.4759i	−0.501841	+	0.869214i	−0.999998	+	0.00212719i	$0.999323\pi$
$318$		0			0
$319$	−1.04631	+	0.604089i	−0.0585823	+	0.0338225i
$320$		0			0
$321$			25.7495i			1.43720i
$322$		0			0
$323$			38.2483i			2.12819i
$324$		0			0
$325$	−5.73206	+	5.76858i	−0.317957	+	0.319983i
$326$		0			0
$327$	7.89040	+	4.55553i	0.436340	+	0.251921i
$328$		0			0
$329$	0.503204	+	8.61313i	0.0277425	+	0.474857i
$330$		0			0
$331$	−0.709904	+	1.22959i	−0.0390199	+	0.0675844i	−0.884876	−	0.465827i	$-0.845757\pi$
$331$	−0.709904	+	1.22959i	−0.0390199	+	0.0675844i	0.845856	+	0.533411i	$0.179090\pi$
$332$		0			0
$333$	3.09482	+	5.36038i	0.169595	+	0.293747i
$334$		0			0
$335$	−0.955739	−	7.17154i	−0.0522176	−	0.391823i
$336$		0			0
$337$		−	9.43095i		−	0.513737i	−0.966446	−	0.256868i	$-0.917309\pi$
$337$		−	9.43095i		−	0.513737i	0.966446	−	0.256868i	$-0.0826907\pi$
$338$		0			0
$339$	−22.2520	+	12.8472i	−1.20856	+	0.697764i
$340$		0			0
$341$	10.2932	−	17.8283i	0.557406	−	0.965456i
$342$		0			0
$343$	−18.2372	+	3.22580i	−0.984714	+	0.174177i
$344$		0			0
$345$	7.77568	−	18.8568i	0.418628	−	1.01521i
$346$		0			0
$347$	6.57622	−	3.79678i	0.353030	−	0.203822i	−0.312989	−	0.949757i	$-0.601330\pi$
$347$	6.57622	−	3.79678i	0.353030	−	0.203822i	0.666019	+	0.745935i	$0.267997\pi$
$348$		0			0
$349$	−7.65991			−0.410026			−0.205013	−	0.978759i	$-0.565724\pi$
$349$	−7.65991			−0.410026			−0.205013	+	0.978759i	$0.565724\pi$
$350$		0			0
$351$		−	12.3361i		−	0.658454i
$352$		0			0
$353$	0.293236	+	0.507900i	0.0156074	+	0.0270328i	0.873724	−	0.486423i	$-0.161698\pi$
$353$	0.293236	+	0.507900i	0.0156074	+	0.0270328i	−0.858116	+	0.513455i	$0.828365\pi$
$354$		0			0
$355$	14.9412	+	6.16108i	0.792997	+	0.326996i
$356$		0			0
$357$	−39.0999	+	2.28433i	−2.06938	+	0.120899i
$358$		0			0
$359$	−10.9912	−	6.34574i	−0.580091	−	0.334916i	0.181079	−	0.983469i	$-0.442041\pi$
$359$	−10.9912	−	6.34574i	−0.580091	−	0.334916i	−0.761169	+	0.648553i	$0.775374\pi$
$360$		0			0
$361$	19.1656	+	33.1957i	1.00871	+	1.74714i
$362$		0			0
$363$	−4.01024			−0.210483
$364$		0			0
$365$	7.03206	−	0.937151i	0.368075	−	0.0490527i
$366$		0			0
$367$	−22.8707	+	13.2044i	−1.19384	+	0.689264i	−0.959175	−	0.282812i	$-0.908733\pi$
$367$	−22.8707	+	13.2044i	−1.19384	+	0.689264i	−0.234665	+	0.972076i	$0.575399\pi$
$368$		0			0
$369$	4.49357	+	2.59436i	0.233926	+	0.135057i
$370$		0			0
$371$	12.9248	−	25.7469i	0.671023	−	1.33671i
$372$		0			0
$373$	5.88204	−	10.1880i	0.304561	−	0.527515i	−0.672603	−	0.740004i	$-0.734824\pi$
$373$	5.88204	−	10.1880i	0.304561	−	0.527515i	0.977163	+	0.212489i	$0.0681570\pi$
$374$		0			0
$375$	−26.0886	−	19.8218i	−1.34721	−	1.02359i
$376$		0			0
$377$	0.633171			0.0326100
$378$		0			0
$379$	−3.03621			−0.155960			−0.0779799	−	0.996955i	$-0.524847\pi$
$379$	−3.03621			−0.155960			−0.0779799	+	0.996955i	$0.524847\pi$
$380$		0			0
$381$	8.53634	+	14.7854i	0.437330	+	0.757478i
$382$		0			0
$383$	10.8418	+	6.25951i	0.553989	+	0.319846i	0.750729	−	0.660610i	$-0.229702\pi$
$383$	10.8418	+	6.25951i	0.553989	+	0.319846i	−0.196740	+	0.980456i	$0.563036\pi$
$384$		0			0
$385$	−12.0297	−	13.8705i	−0.613090	−	0.706908i
$386$		0			0
$387$	15.5445	+	8.97463i	0.790172	+	0.456206i
$388$		0			0
$389$	21.3594	−	12.3319i	1.08297	−	0.625251i	0.151271	−	0.988492i	$-0.451663\pi$
$389$	21.3594	−	12.3319i	1.08297	−	0.625251i	0.931695	+	0.363242i	$0.118330\pi$
$390$		0			0
$391$	−15.7235			−0.795170
$392$		0			0
$393$			50.4193i			2.54332i
$394$		0			0
$395$	−13.9356	+	10.7284i	−0.701178	+	0.539804i
$396$		0			0
$397$	−19.5980	−	11.3149i	−0.983597	−	0.567880i	−0.0802429	−	0.996775i	$-0.525570\pi$
$397$	−19.5980	−	11.3149i	−0.983597	−	0.567880i	−0.903354	+	0.428895i	$0.858903\pi$
$398$		0			0
$399$	−49.0437	+	32.2691i	−2.45526	+	1.61548i
$400$		0			0
$401$	11.9623	−	20.7194i	0.597371	−	1.03468i	−0.395837	−	0.918321i	$-0.629546\pi$
$401$	11.9623	−	20.7194i	0.597371	−	1.03468i	0.993208	−	0.116355i	$-0.0371212\pi$
$402$		0			0
$403$	−9.34330	+	5.39436i	−0.465423	+	0.268712i
$404$		0			0
$405$	12.1086	−	1.61369i	0.601680	−	0.0801848i
$406$		0			0
$407$	3.43752			0.170392
$408$		0			0
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.969605	−	0.244676i	$-0.921318\pi$
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.272907	+	0.962040i	$0.587985\pi$
$410$		0			0
$411$	11.7542	+	6.78631i	0.579794	+	0.334744i
$412$		0			0
$413$	15.5966	+	7.82940i	0.767457	+	0.385259i
$414$		0			0
$415$	−8.81003	+	21.3652i	−0.432467	+	1.04878i
$416$		0			0
$417$	30.6015	−	17.6678i	1.49856	−	0.865194i
$418$		0			0
$419$		−	18.1727i		−	0.887794i	−0.896078	−	0.443897i	$-0.853596\pi$
$419$		−	18.1727i		−	0.887794i	0.896078	−	0.443897i	$-0.146404\pi$
$420$		0			0
$421$		−	30.9941i		−	1.51056i	−0.655403	−	0.755279i	$-0.727501\pi$
$421$		−	30.9941i		−	1.51056i	0.655403	−	0.755279i	$-0.272499\pi$
$422$		0			0
$423$	−15.7816	+	9.11150i	−0.767327	+	0.443016i
$424$		0			0
$425$	−6.45955	+	24.4173i	−0.313334	+	1.18441i
$426$		0			0
$427$	−16.9593	+	0.990809i	−0.820716	+	0.0479486i
$428$		0			0
$429$	−12.8106	−	7.39619i	−0.618500	−	0.357091i
$430$		0			0
$431$	17.6956	−	10.2166i	0.852369	−	0.492115i	−0.00908058	−	0.999959i	$-0.502890\pi$
$431$	17.6956	−	10.2166i	0.852369	−	0.492115i	0.861449	+	0.507843i	$0.169557\pi$
$432$		0			0
$433$	2.57285			0.123643			0.0618216	−	0.998087i	$-0.480309\pi$
$433$	2.57285			0.123643			0.0618216	+	0.998087i	$0.480309\pi$
$434$		0			0
$435$	0.336993	+	2.52868i	0.0161576	+	0.121241i
$436$		0			0
$437$	−20.4107	+	11.7841i	−0.976377	+	0.563711i
$438$		0			0
$439$	7.66013	−	13.2677i	0.365598	−	0.633234i	−0.623274	−	0.782003i	$-0.714198\pi$
$439$	7.66013	−	13.2677i	0.365598	−	0.633234i	0.988872	+	0.148769i	$0.0475312\pi$
$440$		0			0
$441$	−23.3703	−	31.3683i	−1.11287	−	1.49373i
$442$		0			0
$443$	−5.24553	−	3.02851i	−0.249223	−	0.143889i	0.370185	−	0.928958i	$-0.379294\pi$
$443$	−5.24553	−	3.02851i	−0.249223	−	0.143889i	−0.619408	+	0.785069i	$0.712627\pi$
$444$		0			0
$445$	19.8450	−	15.2777i	0.940741	−	0.724232i
$446$		0			0
$447$		−	50.8136i		−	2.40340i
$448$		0			0
$449$	−9.93819			−0.469012			−0.234506	−	0.972115i	$-0.575347\pi$
$449$	−9.93819			−0.469012			−0.234506	+	0.972115i	$0.575347\pi$
$450$		0			0
$451$	2.49558	−	1.44083i	0.117512	−	0.0678458i
$452$		0			0
$453$	49.2943	+	28.4601i	2.31605	+	1.33717i
$454$		0			0
$455$	1.82521	+	9.44748i	0.0855671	+	0.442905i
$456$		0			0
$457$	15.9573	+	9.21295i	0.746451	+	0.430964i	0.824410	−	0.565993i	$-0.191507\pi$
$457$	15.9573	+	9.21295i	0.746451	+	0.430964i	−0.0779590	+	0.996957i	$0.524840\pi$
$458$		0			0
$459$	−19.1569	−	33.1808i	−0.894170	−	1.54875i
$460$		0			0
$461$	17.6061			0.819998			0.409999	−	0.912086i	$-0.365529\pi$
$461$	17.6061			0.819998			0.409999	+	0.912086i	$0.365529\pi$
$462$		0			0
$463$	28.5438			1.32654			0.663271	−	0.748379i	$-0.269168\pi$
$463$	28.5438			1.32654			0.663271	+	0.748379i	$0.269168\pi$
$464$		0			0
$465$	−26.5161	−	34.4431i	−1.22965	−	1.59726i
$466$		0			0
$467$	−3.09243	+	5.35625i	−0.143101	+	0.247857i	−0.928663	−	0.370925i	$-0.879041\pi$
$467$	−3.09243	+	5.35625i	−0.143101	+	0.247857i	0.785562	+	0.618783i	$0.212374\pi$
$468$		0			0
$469$	−7.65063	−	3.84058i	−0.353273	−	0.177341i
$470$		0			0
$471$	−45.5166	−	26.2790i	−2.09729	−	1.21087i
$472$		0			0
$473$	8.63292	−	4.98422i	0.396942	−	0.229175i
$474$		0			0
$475$	9.91463	+	36.5374i	0.454914	+	1.67645i
$476$		0			0
$477$	60.8480			2.78604
$478$		0			0
$479$	6.58753	+	11.4099i	0.300992	+	0.521333i	0.976361	−	0.216147i	$-0.0693490\pi$
$479$	6.58753	+	11.4099i	0.300992	+	0.521333i	−0.675369	+	0.737480i	$0.736016\pi$
$480$		0			0
$481$	−1.56015	−	0.900754i	−0.0711368	−	0.0410708i
$482$		0			0
$483$	−13.2655	−	20.1614i	−0.603602	−	0.917374i
$484$		0			0
$485$	9.01709	−	21.8673i	0.409445	−	0.992944i
$486$		0			0
$487$	−0.665258	−	1.15226i	−0.0301457	−	0.0522139i	0.850559	−	0.525880i	$-0.176264\pi$
$487$	−0.665258	−	1.15226i	−0.0301457	−	0.0522139i	−0.880705	+	0.473666i	$0.842930\pi$
$488$		0			0
$489$			50.3349i			2.27622i
$490$		0			0
$491$	−43.7619			−1.97495			−0.987474	−	0.157779i	$-0.949567\pi$
$491$	−43.7619			−1.97495			−0.987474	+	0.157779i	$0.949567\pi$
$492$		0			0
$493$	1.70306	−	0.983260i	0.0767018	−	0.0442838i
$494$		0			0
$495$	14.7834	−	35.8511i	0.664462	−	1.61139i
$496$		0			0
$497$	15.9749	−	10.5110i	0.716573	−	0.471481i
$498$		0			0
$499$	15.2053	−	26.3363i	0.680681	−	1.17897i	−0.294092	−	0.955777i	$-0.595017\pi$
$499$	15.2053	−	26.3363i	0.680681	−	1.17897i	0.974773	−	0.223197i	$-0.0716494\pi$
$500$		0			0
$501$	−58.8649	+	33.9857i	−2.62989	+	1.51837i
$502$		0			0
$503$			9.86442i			0.439833i	0.975519	+	0.219916i	$0.0705785\pi$
$503$			9.86442i			0.439833i	−0.975519	+	0.219916i	$0.929422\pi$
$504$		0			0
$505$	−10.8033	+	1.43973i	−0.480739	+	0.0640673i
$506$		0			0
$507$	−15.1725	−	26.2795i	−0.673833	−	1.16711i
$508$		0			0
$509$	7.69465	−	13.3275i	0.341059	−	0.590732i	−0.643570	−	0.765387i	$-0.722548\pi$
$509$	7.69465	−	13.3275i	0.341059	−	0.590732i	0.984630	+	0.174655i	$0.0558809\pi$
$510$		0			0
$511$	3.76588	−	7.50184i	0.166593	−	0.331862i
$512$		0			0
$513$	−49.7354	−	28.7147i	−2.19587	−	1.26779i
$514$		0			0
$515$	22.4680	−	17.2970i	0.990058	−	0.762199i
$516$		0			0
$517$			10.1205i			0.445098i
$518$		0			0
$519$		−	45.9653i		−	2.01765i
$520$		0			0
$521$	11.5108	−	6.64575i	0.504296	−	0.291156i	−0.226190	−	0.974083i	$-0.572627\pi$
$521$	11.5108	−	6.64575i	0.504296	−	0.291156i	0.730486	+	0.682928i	$0.239294\pi$
$522$		0			0
$523$	−3.96445	+	6.86663i	−0.173353	+	0.300257i	−0.939590	−	0.342301i	$-0.888794\pi$
$523$	−3.96445	+	6.86663i	−0.173353	+	0.300257i	0.766237	+	0.642558i	$0.222127\pi$
$524$		0			0
$525$	−36.7587	+	12.3175i	−1.60428	+	0.537581i
$526$		0			0
$527$	−16.7539	+	29.0187i	−0.729813	+	1.26407i
$528$		0			0
$529$	6.65566	+	11.5279i	0.289377	+	0.501215i
$530$		0			0
$531$			36.8596i			1.59957i
$532$		0			0
$533$	−1.51019			−0.0654136
$534$		0			0
$535$	15.5683	−	11.9853i	0.673076	−	0.518170i
$536$		0			0
$537$	5.28615	−	9.15588i	0.228114	−	0.395105i
$538$		0			0
$539$	−21.5766	+	2.52976i	−0.929368	+	0.108965i
$540$		0			0
$541$	−37.4487	−	21.6210i	−1.61005	−	0.929561i	−0.989358	−	0.145504i	$-0.953520\pi$
$541$	−37.4487	−	21.6210i	−1.61005	−	0.929561i	−0.620689	−	0.784057i	$-0.713147\pi$
$542$		0			0
$543$	5.83898	+	10.1134i	0.250575	+	0.434008i
$544$		0			0
$545$	−0.918349	−	6.89098i	−0.0393377	−	0.295177i
$546$		0			0
$547$		−	21.2017i		−	0.906519i	−0.891379	−	0.453260i	$-0.850261\pi$
$547$		−	21.2017i		−	0.906519i	0.891379	−	0.453260i	$-0.149739\pi$
$548$		0			0
$549$	−17.9406	−	31.0740i	−0.765684	−	1.32620i
$550$		0			0
$551$	1.47383	−	2.55275i	0.0627873	−	0.108751i
$552$		0			0
$553$	1.21366	+	20.7737i	0.0516101	+	0.883389i
$554$		0			0
$555$	2.76696	−	6.71015i	0.117451	−	0.284830i
$556$		0			0
$557$	−1.74567	−	3.02359i	−0.0739663	−	0.128113i	0.826670	−	0.562687i	$-0.190232\pi$
$557$	−1.74567	−	3.02359i	−0.0739663	−	0.128113i	−0.900636	+	0.434574i	$0.856899\pi$
$558$		0			0
$559$	−5.22417			−0.220959
$560$		0			0
$561$	−45.9425			−1.93970
$562$		0			0
$563$	7.10505	+	12.3063i	0.299442	+	0.518649i	0.976008	−	0.217733i	$-0.0698661\pi$
$563$	7.10505	+	12.3063i	0.299442	+	0.518649i	−0.676566	+	0.736382i	$0.736533\pi$
$564$		0			0
$565$	18.1248	+	7.47386i	0.762517	+	0.314427i
$566$		0			0
$567$	6.48451	−	12.9175i	0.272324	−	0.542483i
$568$		0			0
$569$	15.5447	−	26.9242i	0.651666	−	1.12872i	−0.331052	−	0.943613i	$-0.607404\pi$
$569$	15.5447	−	26.9242i	0.651666	−	1.12872i	0.982718	−	0.185107i	$-0.0592631\pi$
$570$		0			0
$571$	4.74777	+	8.22337i	0.198688	+	0.344137i	0.948103	−	0.317963i	$-0.102999\pi$
$571$	4.74777	+	8.22337i	0.198688	+	0.344137i	−0.749415	+	0.662100i	$0.769665\pi$
$572$		0			0
$573$		−	27.0969i		−	1.13199i
$574$		0			0
$575$	−15.0201	+	4.07580i	−0.626383	+	0.169973i
$576$		0			0
$577$	−16.2630	−	28.1683i	−0.677037	−	1.17266i	−0.975869	−	0.218356i	$-0.929931\pi$
$577$	−16.2630	−	28.1683i	−0.677037	−	1.17266i	0.298832	−	0.954306i	$-0.403403\pi$
$578$		0			0
$579$	31.0397	+	17.9208i	1.28996	+	0.744761i
$580$		0			0
$581$	15.0301	+	22.8433i	0.623556	+	0.947701i
$582$		0			0
$583$	16.8965	−	29.2656i	0.699781	−	1.21206i
$584$		0			0
$585$	−16.1038	+	12.3976i	−0.665811	+	0.512577i
$586$		0			0
$587$	18.4126			0.759968			0.379984	−	0.924993i	$-0.375929\pi$
$587$	18.4126			0.759968			0.379984	+	0.924993i	$0.375929\pi$
$588$		0			0
$589$			50.2256i			2.06951i
$590$		0			0
$591$	10.8248	+	18.7491i	0.445272	+	0.771234i
$592$		0			0
$593$	16.2273	−	28.1066i	0.666377	−	1.15420i	−0.312533	−	0.949907i	$-0.601177\pi$
$593$	16.2273	−	28.1066i	0.666377	−	1.15420i	0.978910	−	0.204292i	$-0.0654893\pi$
$594$		0			0
$595$	19.5804	+	22.5767i	0.802719	+	0.925556i
$596$		0			0
$597$	8.25534	−	14.2987i	0.337869	−	0.585206i
$598$		0			0
$599$	16.2697	−	9.39332i	0.664762	−	0.383801i	−0.129327	−	0.991602i	$-0.541282\pi$
$599$	16.2697	−	9.39332i	0.664762	−	0.383801i	0.794089	+	0.607801i	$0.207948\pi$
$600$		0			0
$601$		−	37.1087i		−	1.51369i	−0.653592	−	0.756847i	$-0.726739\pi$
$601$		−	37.1087i		−	1.51369i	0.653592	−	0.756847i	$-0.273261\pi$
$602$		0			0
$603$		−	18.0808i		−	0.736309i
$604$		0			0
$605$	1.86659	+	2.42461i	0.0758878	+	0.0985744i
$606$		0			0
$607$	−3.49971	−	2.02056i	−0.142049	−	0.0820119i	0.427291	−	0.904114i	$-0.359468\pi$
$607$	−3.49971	−	2.02056i	−0.142049	−	0.0820119i	−0.569340	+	0.822102i	$0.692801\pi$
$608$		0			0
$609$	2.69761	+	1.35419i	0.109313	+	0.0548744i
$610$		0			0
$611$	2.65192	−	4.59327i	0.107285	−	0.185824i
$612$		0			0
$613$	15.5447	+	26.9242i	0.627844	+	1.08746i	0.987984	+	0.154559i	$0.0493956\pi$
$613$	15.5447	+	26.9242i	0.627844	+	1.08746i	−0.360140	+	0.932898i	$0.617271\pi$
$614$		0			0
$615$	−0.803770	−	6.03122i	−0.0324111	−	0.243202i
$616$		0			0
$617$		−	15.3302i		−	0.617170i	−0.951197	−	0.308585i	$-0.900145\pi$
$617$		−	15.3302i		−	0.617170i	0.951197	−	0.308585i	$-0.0998554\pi$
$618$		0			0
$619$	−37.3373	+	21.5567i	−1.50071	+	0.866438i	−0.500715	+	0.865612i	$0.666929\pi$
$619$	−37.3373	+	21.5567i	−1.50071	+	0.866438i	−1.00000		0.000825626i	$0.999737\pi$
$620$		0			0
$621$	11.8043	−	20.4457i	0.473692	−	0.820459i
$622$		0			0
$623$	−1.72831	−	29.5827i	−0.0692431	−	1.18521i
$624$		0			0
$625$	0.158788	+	24.9995i	0.00635150	+	0.999980i
$626$		0			0
$627$	−59.6382	+	34.4321i	−2.38172	+	1.37509i
$628$		0			0
$629$	−5.59517			−0.223094
$630$		0			0
$631$			23.9995i			0.955404i	0.878522	+	0.477702i	$0.158530\pi$
$631$			23.9995i			0.955404i	−0.878522	+	0.477702i	$0.841470\pi$
$632$		0			0
$633$	7.53214	+	13.0460i	0.299376	+	0.518534i
$634$		0			0
$635$	4.96602	−	12.0431i	0.197070	−	0.477915i
$636$		0			0
$637$	10.4556	+	4.50567i	0.414266	+	0.178521i
$638$		0			0
$639$	34.9784	+	20.1948i	1.38372	+	0.798893i
$640$		0			0
$641$	12.7941	+	22.1600i	0.505336	+	0.875267i	0.999981	+	0.00617237i	$0.00196474\pi$
$641$	12.7941	+	22.1600i	0.505336	+	0.875267i	−0.494645	+	0.869095i	$0.664702\pi$
$642$		0			0
$643$	48.1544			1.89902			0.949512	−	0.313731i	$-0.101579\pi$
$643$	48.1544			1.89902			0.949512	+	0.313731i	$0.101579\pi$
$644$		0			0
$645$	−2.78046	−	20.8637i	−0.109481	−	0.821506i
$646$		0			0
$647$	−11.2431	+	6.49122i	−0.442013	+	0.255196i	−0.704451	−	0.709752i	$-0.748807\pi$
$647$	−11.2431	+	6.49122i	−0.442013	+	0.255196i	0.262438	+	0.964949i	$0.415473\pi$
$648$		0			0
$649$	17.7281	+	10.2353i	0.695887	+	0.401771i
$650$		0			0
$651$	−51.3440	+	2.99966i	−2.01233	+	0.117566i
$652$		0			0
$653$	−10.4539	+	18.1068i	−0.409094	+	0.708572i	−0.994789	−	0.101960i	$-0.967489\pi$
$653$	−10.4539	+	18.1068i	−0.409094	+	0.708572i	0.585694	+	0.810532i	$0.300822\pi$
$654$		0			0
$655$	30.4838	−	23.4680i	1.19110	−	0.916971i
$656$		0			0
$657$	17.7292			0.691682
$658$		0			0
$659$	36.6633			1.42820			0.714099	−	0.700045i	$-0.246837\pi$
$659$	36.6633			1.42820			0.714099	+	0.700045i	$0.246837\pi$
$660$		0			0
$661$	13.6519	+	23.6458i	0.530998	+	0.919715i	0.999346	+	0.0361712i	$0.0115162\pi$
$661$	13.6519	+	23.6458i	0.530998	+	0.919715i	−0.468348	+	0.883544i	$0.655151\pi$
$662$		0			0
$663$	20.8514	+	12.0386i	0.809803	+	0.467540i
$664$		0			0
$665$	42.3378	+	14.6322i	1.64179	+	0.567412i
$666$		0			0
$667$	1.04941	+	0.605877i	0.0406333	+	0.0234596i
$668$		0			0
$669$	14.4857	−	8.36330i	0.560048	−	0.323344i
$670$		0			0
$671$	−19.9272			−0.769281
$672$		0			0
$673$			4.86055i			0.187360i	0.995602	+	0.0936802i	$0.0298631\pi$
$673$			4.86055i			0.187360i	−0.995602	+	0.0936802i	$0.970137\pi$
$674$		0			0
$675$	−26.9011	−	26.7308i	−1.03542	−	1.02887i
$676$		0			0
$677$	3.37606	+	1.94917i	0.129753	+	0.0749128i	0.563471	−	0.826136i	$-0.309466\pi$
$677$	3.37606	+	1.94917i	0.129753	+	0.0749128i	−0.433719	+	0.901048i	$0.642799\pi$
$678$		0			0
$679$	−15.3834	−	23.3802i	−0.590360	−	0.897250i
$680$		0			0
$681$	−27.0937	+	46.9276i	−1.03823	+	1.79827i
$682$		0			0
$683$	15.0819	−	8.70755i	0.577094	−	0.333185i	−0.182884	−	0.983135i	$-0.558543\pi$
$683$	15.0819	−	8.70755i	0.577094	−	0.333185i	0.759978	+	0.649949i	$0.225210\pi$
$684$		0			0
$685$	−1.36805	−	10.2654i	−0.0522706	−	0.392221i
$686$		0			0
$687$	28.0752			1.07113
$688$		0			0
$689$	−15.3373	+	8.85497i	−0.584303	+	0.337347i
$690$		0			0
$691$	−12.1565	−	7.01858i	−0.462456	−	0.266999i	0.250620	−	0.968085i	$-0.419365\pi$
$691$	−12.1565	−	7.01858i	−0.462456	−	0.266999i	−0.713076	+	0.701086i	$0.752699\pi$
$692$		0			0
$693$	−25.2208	−	38.3314i	−0.958059	−	1.45609i
$694$		0			0
$695$	−24.9257	−	10.2782i	−0.945485	−	0.389875i
$696$		0			0
$697$	−4.06200	+	2.34520i	−0.153859	+	0.0888306i
$698$		0			0
$699$			12.3269i			0.466245i
$700$		0			0
$701$		−	21.7579i		−	0.821786i	−0.911684	−	0.410893i	$-0.865217\pi$
$701$		−	21.7579i		−	0.821786i	0.911684	−	0.410893i	$-0.134783\pi$
$702$		0			0
$703$	−7.26311	+	4.19336i	−0.273933	+	0.158156i
$704$		0			0
$705$	19.7555	+	8.14625i	0.744033	+	0.306805i
$706$		0			0
$707$	−5.78548	+	11.5250i	−0.217585	+	0.433442i
$708$		0			0
$709$	−26.5841	−	15.3484i	−0.998388	−	0.576420i	−0.0906173	−	0.995886i	$-0.528884\pi$
$709$	−26.5841	−	15.3484i	−0.998388	−	0.576420i	−0.907771	+	0.419466i	$0.862217\pi$
$710$		0			0
$711$	−38.0631	+	21.9757i	−1.42748	+	0.824155i
$712$		0			0
$713$	−20.6473			−0.773246
$714$		0			0
$715$	1.49100	+	11.1879i	0.0557601	+	0.418405i
$716$		0			0
$717$	54.6669	−	31.5620i	2.04157	−	1.17870i
$718$		0			0
$719$	−11.7603	+	20.3694i	−0.438585	+	0.759652i	−0.997581	−	0.0695187i	$-0.977854\pi$
$719$	−11.7603	+	20.3694i	−0.438585	+	0.759652i	0.558995	+	0.829171i	$0.311187\pi$
$720$		0			0
$721$	−1.95675	−	33.4928i	−0.0728731	−	1.24734i
$722$		0			0
$723$	−22.0376	−	12.7234i	−0.819588	−	0.473189i
$724$		0			0
$725$	1.37200	−	1.38074i	0.0509547	−	0.0512794i
$726$		0			0
$727$			29.2877i			1.08622i	0.839661	+	0.543110i	$0.182754\pi$
$727$			29.2877i			1.08622i	−0.839661	+	0.543110i	$0.817246\pi$
$728$		0			0
$729$	−36.1543			−1.33905
$730$		0			0
$731$	−14.0516	+	8.11269i	−0.519717	+	0.300059i
$732$		0			0
$733$	−39.4427	−	22.7723i	−1.45685	−	0.841113i	−0.457996	−	0.888954i	$-0.651433\pi$
$733$	−39.4427	−	22.7723i	−1.45685	−	0.841113i	−0.998855	+	0.0478408i	$0.984766\pi$
$734$		0			0
$735$	−12.4294	+	44.1544i	−0.458465	+	1.62866i
$736$		0			0
$737$	−8.69620	−	5.02076i	−0.320329	−	0.184942i
$738$		0			0
$739$	6.91988	+	11.9856i	0.254552	+	0.440897i	0.964774	−	0.263081i	$-0.0847387\pi$
$739$	6.91988	+	11.9856i	0.254552	+	0.440897i	−0.710222	+	0.703978i	$0.751405\pi$
$740$		0			0
$741$	36.0898			1.32579
$742$		0			0
$743$	−36.5334			−1.34028			−0.670141	−	0.742234i	$-0.733766\pi$
$743$	−36.5334			−1.34028			−0.670141	+	0.742234i	$0.733766\pi$
$744$		0			0
$745$	−30.7222	+	23.6515i	−1.12557	+	0.866525i
$746$		0			0
$747$	−28.8775	+	50.0173i	−1.05657	+	1.83004i
$748$		0			0
$749$	−1.35585	−	23.2075i	−0.0495417	−	0.847984i
$750$		0			0
$751$	−29.3811	−	16.9632i	−1.07213	−	0.618996i	−0.143369	−	0.989669i	$-0.545794\pi$
$751$	−29.3811	−	16.9632i	−1.07213	−	0.618996i	−0.928763	+	0.370673i	$0.879127\pi$
$752$		0			0
$753$	−28.4613	+	16.4322i	−1.03719	+	0.598821i
$754$		0			0
$755$	−5.73726	−	43.0505i	−0.208800	−	1.56677i
$756$		0			0
$757$	−31.2178			−1.13463			−0.567315	−	0.823501i	$-0.692018\pi$
$757$	−31.2178			−1.13463			−0.567315	+	0.823501i	$0.692018\pi$
$758$		0			0
$759$	−14.1547	−	24.5167i	−0.513783	−	0.889899i
$760$		0			0
$761$	−17.6688	−	10.2011i	−0.640493	−	0.369789i	0.144312	−	0.989532i	$-0.453903\pi$
$761$	−17.6688	−	10.2011i	−0.640493	−	0.369789i	−0.784804	+	0.619744i	$0.787237\pi$
$762$		0			0
$763$	−7.35133	−	3.69033i	−0.266136	−	0.133599i
$764$		0			0
$765$	−24.0625	+	58.3539i	−0.869981	+	2.10979i
$766$		0			0
$767$	−5.36403	−	9.29077i	−0.193684	−	0.335470i
$768$		0			0
$769$		−	5.57448i		−	0.201021i	−0.994936	−	0.100510i	$-0.967952\pi$
$769$		−	5.57448i		−	0.201021i	0.994936	−	0.100510i	$-0.0320476\pi$
$770$		0			0
$771$	33.3235			1.20012
$772$		0			0
$773$	−32.8342	+	18.9569i	−1.18097	+	0.681831i	−0.956238	−	0.292591i	$-0.905483\pi$
$773$	−32.8342	+	18.9569i	−1.18097	+	0.681831i	−0.224728	+	0.974422i	$0.572149\pi$
$774$		0			0
$775$	−8.48235	+	32.0635i	−0.304695	+	1.15176i
$776$		0			0
$777$	−4.72051	−	7.17439i	−0.169347	−	0.257380i
$778$		0			0
$779$	−3.51526	+	6.08862i	−0.125947	+	0.218147i
$780$		0			0
$781$	19.4258	−	11.2155i	0.695111	−	0.401323i
$782$		0			0
$783$			2.95272i			0.105522i
$784$		0			0
$785$	5.29759	+	39.7513i	0.189079	+	1.41879i
$786$		0			0
$787$	18.8744	+	32.6914i	0.672800	+	1.16532i	0.977107	+	0.212749i	$0.0682418\pi$
$787$	18.8744	+	32.6914i	0.672800	+	1.16532i	−0.304307	+	0.952574i	$0.598425\pi$
$788$		0			0
$789$	28.3703	−	49.1389i	1.01001	−	1.74939i
$790$		0			0
$791$	19.3788	−	12.7506i	0.689030	−	0.453359i
$792$		0			0
$793$	9.04414	+	5.22164i	0.321167	+	0.185426i
$794$		0			0
$795$	−43.5268	−	56.5392i	−1.54374	−	2.00524i
$796$		0			0
$797$			28.3177i			1.00306i	0.865139	+	0.501532i	$0.167230\pi$
$797$			28.3177i			1.00306i	−0.865139	+	0.501532i	$0.832770\pi$
$798$		0			0
$799$		−	16.4728i		−	0.582767i
$800$		0			0
$801$	54.2035	−	31.2944i	1.91519	−	1.10573i
$802$		0			0
$803$	4.92311	−	8.52707i	0.173733	−	0.300914i
$804$		0			0
$805$	−6.01514	+	17.4046i	−0.212006	+	0.613433i
$806$		0			0
$807$	2.23244	−	3.86671i	0.0785857	−	0.136115i
$808$		0			0
$809$	0.715781	+	1.23977i	0.0251655	+	0.0435879i	0.878334	−	0.478048i	$-0.158655\pi$
$809$	0.715781	+	1.23977i	0.0251655	+	0.0435879i	−0.853168	+	0.521636i	$0.825322\pi$
$810$		0			0
$811$		−	0.229410i		−	0.00805567i	−0.999992	−	0.00402783i	$-0.998718\pi$
$811$		−	0.229410i		−	0.00805567i	0.999992	−	0.00402783i	$-0.00128210\pi$
$812$		0			0
$813$	−54.6357			−1.91616
$814$		0			0
$815$	30.4327	−	23.4287i	1.06601	−	0.820672i
$816$		0			0
$817$	−12.1603	+	21.0622i	−0.425434	+	0.736874i
$818$		0			0
$819$	1.40249	+	24.0058i	0.0490070	+	0.838831i
$820$		0			0
$821$	2.36907	+	1.36778i	0.0826810	+	0.0477359i	0.540771	−	0.841170i	$-0.318133\pi$
$821$	2.36907	+	1.36778i	0.0826810	+	0.0477359i	−0.458089	+	0.888906i	$0.651466\pi$
$822$		0			0
$823$	1.56485	+	2.71040i	0.0545472	+	0.0944784i	0.892010	−	0.452016i	$-0.149295\pi$
$823$	1.56485	+	2.71040i	0.0545472	+	0.0944784i	−0.837462	+	0.546495i	$0.815962\pi$
$824$		0			0
$825$	−43.8875	+	11.9091i	−1.52797	+	0.414622i
$826$		0			0
$827$		−	32.3184i		−	1.12382i	−0.827198	−	0.561911i	$-0.810066\pi$
$827$		−	32.3184i		−	1.12382i	0.827198	−	0.561911i	$-0.189934\pi$
$828$		0			0
$829$	4.80290	+	8.31887i	0.166812	+	0.288926i	0.937297	−	0.348531i	$-0.113319\pi$
$829$	4.80290	+	8.31887i	0.166812	+	0.288926i	−0.770486	+	0.637457i	$0.779986\pi$
$830$		0			0
$831$	13.9118	−	24.0960i	0.482597	−	0.835882i
$832$		0			0
$833$	35.1196	−	4.11763i	1.21682	−	0.142668i
$834$		0			0
$835$	47.9470	+	19.7712i	1.65927	+	0.684209i
$836$		0			0
$837$	−25.1559	−	43.5713i	−0.869516	−	1.50605i
$838$		0			0
$839$	37.5135			1.29511			0.647555	−	0.762019i	$-0.275792\pi$
$839$	37.5135			1.29511			0.647555	+	0.762019i	$0.275792\pi$
$840$		0			0
$841$	28.8484			0.994774
$842$		0			0
$843$	13.3550	+	23.1315i	0.459970	+	0.796692i
$844$		0			0
$845$	−8.82658	+	21.4053i	−0.303644	+	0.736366i
$846$		0			0
$847$	3.61434	−	0.211160i	0.124190	−	0.00725555i
$848$		0			0
$849$	22.7838	−	39.4627i	0.781938	−	1.35436i
$850$		0			0
$851$	−1.72385	−	2.98579i	−0.0590928	−	0.102352i
$852$		0			0
$853$			38.6732i			1.32415i	0.749439	+	0.662073i	$0.230323\pi$
$853$			38.6732i			1.32415i	−0.749439	+	0.662073i	$0.769677\pi$
$854$		0			0
$855$	12.4983	+	93.7833i	0.427434	+	3.20732i
$856$		0			0
$857$	6.47602	+	11.2168i	0.221217	+	0.383158i	0.955178	−	0.296033i	$-0.0956639\pi$
$857$	6.47602	+	11.2168i	0.221217	+	0.383158i	−0.733961	+	0.679192i	$0.762331\pi$
$858$		0			0
$859$	−6.46557	−	3.73290i	−0.220603	−	0.127365i	0.385627	−	0.922655i	$-0.373985\pi$
$859$	−6.46557	−	3.73290i	−0.220603	−	0.127365i	−0.606229	+	0.795290i	$0.707319\pi$
$860$		0			0
$861$	−6.43413	−	3.22990i	−0.219275	−	0.110075i
$862$		0			0
$863$	−13.8213	+	23.9392i	−0.470482	+	0.814899i	−0.999430	−	0.0337553i	$-0.989253\pi$
$863$	−13.8213	+	23.9392i	−0.470482	+	0.814899i	0.528948	+	0.848654i	$0.322587\pi$
$864$		0			0
$865$	−27.7909	+	21.3949i	−0.944918	+	0.727448i
$866$		0			0
$867$	24.9601			0.847689
$868$		0			0
$869$			24.4092i			0.828026i
$870$		0			0
$871$	2.63123	+	4.55743i	0.0891560	+	0.154423i
$872$		0			0
$873$	29.5562	−	51.1928i	1.00033	−	1.73261i
$874$		0			0
$875$	24.5569	+	16.4912i	0.830173	+	0.557506i
$876$		0			0
$877$	−26.6238	+	46.1138i	−0.899023	+	1.55715i	−0.0702771	+	0.997528i	$0.522388\pi$
$877$	−26.6238	+	46.1138i	−0.899023	+	1.55715i	−0.828746	+	0.559625i	$0.810945\pi$
$878$		0			0
$879$	−22.1415	+	12.7834i	−0.746814	+	0.431174i
$880$		0			0
$881$			48.2909i			1.62696i	0.581592	+	0.813480i	$0.302430\pi$
$881$			48.2909i			1.62696i	−0.581592	+	0.813480i	$0.697570\pi$
$882$		0			0
$883$		−	19.1196i		−	0.643426i	−0.946837	−	0.321713i	$-0.895741\pi$
$883$		−	19.1196i		−	0.643426i	0.946837	−	0.321713i	$-0.104259\pi$
$884$		0			0
$885$	34.2494	−	26.3670i	1.15128	−	0.886318i
$886$		0			0
$887$	−29.2779	−	16.9036i	−0.983057	−	0.567568i	−0.0798654	−	0.996806i	$-0.525449\pi$
$887$	−29.2779	−	16.9036i	−0.983057	−	0.567568i	−0.903192	+	0.429237i	$0.858782\pi$
$888$		0			0
$889$	−8.47216	−	12.8763i	−0.284147	−	0.431856i
$890$		0			0
$891$	8.47714	−	14.6828i	0.283995	−	0.491894i
$892$		0			0
$893$	−12.3457	−	21.3834i	−0.413134	−	0.715570i
$894$		0			0
$895$	−7.99616	+	1.06563i	−0.267282	+	0.0356202i
$896$		0			0
$897$			14.8362i			0.495365i
$898$		0			0
$899$	2.23637	−	1.29117i	0.0745870	−	0.0430628i
$900$		0			0
$901$	−27.5020	+	47.6349i	−0.916224	+	1.58695i
$902$		0			0
$903$	−22.2574	−	11.1731i	−0.740682	−	0.371818i
$904$		0			0
$905$	3.39683	−	8.23763i	0.112914	−	0.273828i
$906$		0			0
$907$	−16.9052	+	9.76020i	−0.561327	+	0.324082i	−0.753678	−	0.657244i	$-0.771722\pi$
$907$	−16.9052	+	9.76020i	−0.561327	+	0.324082i	0.192351	+	0.981326i	$0.438389\pi$
$908$		0			0
$909$	−27.2371			−0.903399
$910$		0			0
$911$		−	47.4878i		−	1.57334i	−0.617373	−	0.786671i	$-0.711803\pi$
$911$		−	47.4878i		−	1.57334i	0.617373	−	0.786671i	$-0.288197\pi$
$912$		0			0
$913$	16.0376	+	27.7780i	0.530768	+	0.919317i
$914$		0			0
$915$	−16.0400	+	38.8985i	−0.530265	+	1.28594i
$916$		0			0
$917$	−2.65484	−	45.4419i	−0.0876707	−	1.50062i
$918$		0			0
$919$	−2.97980	−	1.72039i	−0.0982945	−	0.0567503i	0.450047	−	0.893005i	$-0.351407\pi$
$919$	−2.97980	−	1.72039i	−0.0982945	−	0.0567503i	−0.548341	+	0.836255i	$0.684741\pi$
$920$		0			0
$921$	10.4497	+	18.0995i	0.344330	+	0.596398i
$922$		0			0
$923$	−11.7555			−0.386936
$924$		0			0
$925$	−5.34489	+	1.45037i	−0.175739	+	0.0476878i
$926$		0			0
$927$	61.3679	−	35.4308i	2.01559	−	1.16370i
$928$		0			0
$929$	−14.8975	−	8.60107i	−0.488771	−	0.282192i	0.235293	−	0.971924i	$-0.424395\pi$
$929$	−14.8975	−	8.60107i	−0.488771	−	0.282192i	−0.724064	+	0.689732i	$0.757728\pi$
$930$		0			0
$931$	42.5029	−	31.6659i	1.39298	−	1.03781i
$932$		0			0
$933$	46.3859	−	80.3428i	1.51861	−	2.63030i
$934$		0			0
$935$	21.3843	+	27.7771i	0.699341	+	0.908408i
$936$		0			0
$937$	16.8939			0.551901			0.275950	−	0.961172i	$-0.411007\pi$
$937$	16.8939			0.551901			0.275950	+	0.961172i	$0.411007\pi$
$938$		0			0
$939$	67.5111			2.20314
$940$		0			0
$941$	28.6433	+	49.6117i	0.933746	+	1.61729i	0.776856	+	0.629679i	$0.216813\pi$
$941$	28.6433	+	49.6117i	0.933746	+	1.61729i	0.156890	+	0.987616i	$0.449853\pi$
$942$		0			0
$943$	−2.50297	−	1.44509i	−0.0815079	−	0.0470586i
$944$		0			0
$945$	−44.0572	+	8.51164i	−1.43318	+	0.276884i
$946$		0			0
$947$	−28.0175	−	16.1759i	−0.910447	−	0.525647i	−0.0298722	−	0.999554i	$-0.509510\pi$
$947$	−28.0175	−	16.1759i	−0.910447	−	0.525647i	−0.880575	+	0.473907i	$0.842843\pi$
$948$		0			0
$949$	−4.46880	+	2.58006i	−0.145063	+	0.0837523i
$950$		0			0
$951$	52.3692			1.69819
$952$		0			0
$953$		−	36.4296i		−	1.18007i	−0.807377	−	0.590036i	$-0.799114\pi$
$953$		−	36.4296i		−	1.18007i	0.807377	−	0.590036i	$-0.200886\pi$
$954$		0			0
$955$	−16.3829	+	12.6124i	−0.530138	+	0.408129i
$956$		0			0
$957$	3.06628	+	1.77032i	0.0991186	+	0.0572262i
$958$		0			0
$959$	−10.9512	−	5.49744i	−0.353632	−	0.177521i
$960$		0			0
$961$	−6.50040	+	11.2590i	−0.209690	+	0.363195i
$962$		0			0
$963$	42.5225	−	24.5504i	1.37027	−	0.791124i
$964$		0			0
$965$	−3.61265	−	27.1081i	−0.116295	−	0.872640i
$966$		0			0
$967$	15.8537			0.509822			0.254911	−	0.966964i	$-0.417954\pi$
$967$	15.8537			0.509822			0.254911	+	0.966964i	$0.417954\pi$
$968$		0			0
$969$	97.0716	−	56.0443i	3.11839	−	1.80040i
$970$		0			0
$971$	39.0664	+	22.5550i	1.25370	+	0.723825i	0.971843	−	0.235631i	$-0.0757155\pi$
$971$	39.0664	+	22.5550i	1.25370	+	0.723825i	0.281859	+	0.959456i	$0.409049\pi$
$972$		0			0
$973$	−26.6502	+	17.5349i	−0.854365	+	0.562144i
$974$		0			0
$975$	23.0393	+	6.09502i	0.737849	+	0.195197i
$976$		0			0
$977$	−17.5983	+	10.1604i	−0.563019	+	0.325059i	−0.754356	−	0.656465i	$-0.772051\pi$
$977$	−17.5983	+	10.1604i	−0.563019	+	0.325059i	0.191338	+	0.981524i	$0.438717\pi$
$978$		0			0
$979$		−	34.7598i		−	1.11093i
$980$		0			0
$981$		−	17.3735i		−	0.554693i
$982$		0			0
$983$	−1.38824	+	0.801501i	−0.0442780	+	0.0255639i	−0.521976	−	0.852960i	$-0.674805\pi$
$983$	−1.38824	+	0.801501i	−0.0442780	+	0.0255639i	0.477698	+	0.878524i	$0.341471\pi$
$984$		0			0
$985$	6.29731	−	15.2716i	0.200649	−	0.486594i
$986$		0			0
$987$	21.1222	−	13.8977i	0.672328	−	0.442369i
$988$		0			0
$989$	−8.65847	−	4.99897i	−0.275323	−	0.158958i
$990$		0			0
$991$	−23.9870	+	13.8489i	−0.761971	+	0.439924i	−0.830003	−	0.557759i	$-0.811661\pi$
$991$	−23.9870	+	13.8489i	−0.761971	+	0.439924i	0.0680321	+	0.997683i	$0.478328\pi$
$992$		0			0
$993$	4.16083			0.132040
$994$		0			0
$995$	−12.4876	+	1.66419i	−0.395882	+	0.0527585i
$996$		0			0
$997$	−36.4937	+	21.0697i	−1.15577	+	0.667283i	−0.950286	−	0.311378i	$-0.899210\pi$
$997$	−36.4937	+	21.0697i	−1.15577	+	0.667283i	−0.205482	+	0.978661i	$0.565876\pi$
$998$		0			0
$999$	4.20056	−	7.27558i	0.132900	−	0.230189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.719.3		80
4.3	odd	2		280.2.ba.b.19.37	yes	80
5.4	even	2	inner	1120.2.bq.b.719.37		80
7.3	odd	6	inner	1120.2.bq.b.1039.38		80
8.3	odd	2	inner	1120.2.bq.b.719.4		80
8.5	even	2		280.2.ba.b.19.24	yes	80
20.19	odd	2		280.2.ba.b.19.4	✓	80
28.3	even	6		280.2.ba.b.59.17	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.4		80
40.19	odd	2	inner	1120.2.bq.b.719.38		80
40.29	even	2		280.2.ba.b.19.17	yes	80
56.3	even	6	inner	1120.2.bq.b.1039.37		80
56.45	odd	6		280.2.ba.b.59.4	yes	80
140.59	even	6		280.2.ba.b.59.24	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.3		80
280.269	odd	6		280.2.ba.b.59.37	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.4	✓	80	20.19	odd	2
280.2.ba.b.19.17	yes	80	40.29	even	2
280.2.ba.b.19.24	yes	80	8.5	even	2
280.2.ba.b.19.37	yes	80	4.3	odd	2
280.2.ba.b.59.4	yes	80	56.45	odd	6
280.2.ba.b.59.17	yes	80	28.3	even	6
280.2.ba.b.59.24	yes	80	140.59	even	6
280.2.ba.b.59.37	yes	80	280.269	odd	6
1120.2.bq.b.719.3		80	1.1	even	1	trivial
1120.2.bq.b.719.4		80	8.3	odd	2	inner
1120.2.bq.b.719.37		80	5.4	even	2	inner
1120.2.bq.b.719.38		80	40.19	odd	2	inner
1120.2.bq.b.1039.3		80	280.59	even	6	inner
1120.2.bq.b.1039.4		80	35.24	odd	6	inner
1120.2.bq.b.1039.37		80	56.3	even	6	inner
1120.2.bq.b.1039.38		80	7.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.46528 - 2.53794i) q^{3} +(-0.852425 + 2.06721i) q^{5} +(1.45426 + 2.21023i) q^{7} +(-2.79408 + 4.83948i) q^{9} +O(q^{10})\)	\(q+(-1.46528 - 2.53794i) q^{3} +(-0.852425 + 2.06721i) q^{5} +(1.45426 + 2.21023i) q^{7} +(-2.79408 + 4.83948i) q^{9} +(1.55174 + 2.68769i) q^{11} -1.62644i q^{13} +(6.49549 - 0.865643i) q^{15} +(-2.52573 - 4.37469i) q^{17} +(-6.55731 - 3.78587i) q^{19} +(3.47853 - 6.92942i) q^{21} +(1.55633 - 2.69565i) q^{23} +(-3.54674 - 3.52429i) q^{25} +7.58472 q^{27} +0.389298i q^{29} +(-3.31666 - 5.74462i) q^{31} +(4.54746 - 7.87643i) q^{33} +(-5.80867 + 1.12221i) q^{35} +(0.553818 - 0.959241i) q^{37} +(-4.12781 + 2.38319i) q^{39} -0.928523i q^{41} -3.21202i q^{43} +(-7.62250 - 9.90125i) q^{45} +(2.82412 + 1.63050i) q^{47} +(-2.77026 + 6.42850i) q^{49} +(-7.40178 + 12.8203i) q^{51} +(-5.44437 - 9.42993i) q^{53} +(-6.87877 + 0.916722i) q^{55} +22.1894i q^{57} +(5.71232 - 3.29801i) q^{59} +(-3.21046 + 5.56068i) q^{61} +(-14.7597 + 0.862304i) q^{63} +(3.36221 + 1.38642i) q^{65} +(-2.80208 + 1.61778i) q^{67} -9.12183 q^{69} -7.22771i q^{71} +(-1.58632 - 2.74759i) q^{73} +(-3.74745 + 14.1655i) q^{75} +(-3.68379 + 7.33831i) q^{77} +(6.81139 + 3.93256i) q^{79} +(-2.73150 - 4.73109i) q^{81} +10.3353 q^{83} +(11.1964 - 1.49213i) q^{85} +(0.988013 - 0.570429i) q^{87} +(-9.69972 - 5.60014i) q^{89} +(3.59482 - 2.36527i) q^{91} +(-9.71964 + 16.8349i) q^{93} +(13.4158 - 10.3282i) q^{95} -10.5782 q^{97} -17.3427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 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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