LMFDB - Embedded newform 804.2.o.d.365.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.18
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72171 - 0.188968i) q^{3} -3.09374 q^{5} +(-1.38610 - 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +O(q^{10})$	\(q+(1.72171 - 0.188968i) q^{3} -3.09374 q^{5} +(-1.38610 - 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +(-2.72317 + 4.71667i) q^{11} +(-3.69642 + 2.13413i) q^{13} +(-5.32653 + 0.584618i) q^{15} +(-1.10628 + 0.638709i) q^{17} +(0.117880 + 0.204175i) q^{19} +(-2.53768 - 1.11589i) q^{21} +(-4.09358 + 2.36343i) q^{23} +4.57123 q^{25} +(4.91921 - 1.67372i) q^{27} +(1.17099 + 0.676069i) q^{29} +(-1.21571 - 0.701891i) q^{31} +(-3.79721 + 8.63534i) q^{33} +(4.28822 + 2.47580i) q^{35} +(3.33128 + 5.76994i) q^{37} +(-5.96089 + 4.37286i) q^{39} +(-3.91001 + 6.77233i) q^{41} -7.91208i q^{43} +(-9.06028 + 2.01309i) q^{45} +(-0.523745 - 0.302384i) q^{47} +(-2.21916 - 3.84370i) q^{49} +(-1.78399 + 1.30872i) q^{51} -8.20758 q^{53} +(8.42478 - 14.5922i) q^{55} +(0.241539 + 0.329255i) q^{57} +13.8714i q^{59} +(7.23406 - 4.17658i) q^{61} +(-4.58002 - 1.44171i) q^{63} +(11.4358 - 6.60244i) q^{65} +(6.48268 + 4.99749i) q^{67} +(-6.60135 + 4.84270i) q^{69} +(-11.3188 - 6.53491i) q^{71} +(-3.23694 - 5.60654i) q^{73} +(7.87035 - 0.863817i) q^{75} +(7.54914 - 4.35850i) q^{77} +(-8.34701 - 4.81915i) q^{79} +(8.15319 - 3.81124i) q^{81} +(12.5094 - 7.22228i) q^{83} +(3.42253 - 1.97600i) q^{85} +(2.14386 + 0.942717i) q^{87} -2.12681i q^{89} +6.83145 q^{91} +(-2.22574 - 0.978724i) q^{93} +(-0.364692 - 0.631664i) q^{95} +(2.75058 - 1.58805i) q^{97} +(-4.90590 + 15.5851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.72171	−	0.188968i	0.994031	−	0.109101i
$3$	1.72171	−	0.188968i	0.994031	−	0.109101i
$4$		0			0
$5$	−3.09374			−1.38356			−0.691782	−	0.722107i	$-0.743174\pi$
$5$	−3.09374			−1.38356			−0.691782	+	0.722107i	$0.743174\pi$
$6$		0			0
$7$	−1.38610	−	0.800262i	−0.523895	−	0.302471i	0.214632	−	0.976695i	$-0.431145\pi$
$7$	−1.38610	−	0.800262i	−0.523895	−	0.302471i	−0.738527	+	0.674224i	$0.764478\pi$
$8$		0			0
$9$	2.92858	−	0.650697i	0.976194	−	0.216899i
$10$		0			0
$11$	−2.72317	+	4.71667i	−0.821067	+	1.42213i	0.0838221	+	0.996481i	$0.473287\pi$
$11$	−2.72317	+	4.71667i	−0.821067	+	1.42213i	−0.904889	+	0.425648i	$0.860046\pi$
$12$		0			0
$13$	−3.69642	+	2.13413i	−1.02520	+	0.591901i	−0.915607	−	0.402075i	$-0.868289\pi$
$13$	−3.69642	+	2.13413i	−1.02520	+	0.591901i	−0.109596	+	0.993976i	$0.534956\pi$
$14$		0			0
$15$	−5.32653	+	0.584618i	−1.37530	+	0.150948i
$16$		0			0
$17$	−1.10628	+	0.638709i	−0.268311	+	0.154910i	−0.628120	−	0.778116i	$-0.716175\pi$
$17$	−1.10628	+	0.638709i	−0.268311	+	0.154910i	0.359809	+	0.933026i	$0.382842\pi$
$18$		0			0
$19$	0.117880	+	0.204175i	0.0270436	+	0.0468409i	0.879230	−	0.476397i	$-0.158057\pi$
$19$	0.117880	+	0.204175i	0.0270436	+	0.0468409i	−0.852187	+	0.523238i	$0.824724\pi$
$20$		0			0
$21$	−2.53768	−	1.11589i	−0.553767	−	0.243508i
$22$		0			0
$23$	−4.09358	+	2.36343i	−0.853570	+	0.492809i	−0.861854	−	0.507157i	$-0.830697\pi$
$23$	−4.09358	+	2.36343i	−0.853570	+	0.492809i	0.00828347	+	0.999966i	$0.497363\pi$
$24$		0			0
$25$	4.57123			0.914247
$26$		0			0
$27$	4.91921	−	1.67372i	0.946703	−	0.322108i
$28$		0			0
$29$	1.17099	+	0.676069i	0.217447	+	0.125543i	0.604767	−	0.796402i	$-0.293266\pi$
$29$	1.17099	+	0.676069i	0.217447	+	0.125543i	−0.387321	+	0.921945i	$0.626599\pi$
$30$		0			0
$31$	−1.21571	−	0.701891i	−0.218348	−	0.126063i	0.386837	−	0.922148i	$-0.373568\pi$
$31$	−1.21571	−	0.701891i	−0.218348	−	0.126063i	−0.605185	+	0.796085i	$0.706901\pi$
$32$		0			0
$33$	−3.79721	+	8.63534i	−0.661010	+	1.50322i
$34$		0			0
$35$	4.28822	+	2.47580i	0.724841	+	0.418487i
$36$		0			0
$37$	3.33128	+	5.76994i	0.547659	+	0.948573i	0.998434	+	0.0559354i	$0.0178141\pi$
$37$	3.33128	+	5.76994i	0.547659	+	0.948573i	−0.450776	+	0.892637i	$0.648853\pi$
$38$		0			0
$39$	−5.96089	+	4.37286i	−0.954506	+	0.700218i
$40$		0			0
$41$	−3.91001	+	6.77233i	−0.610640	+	1.05766i	0.380492	+	0.924784i	$0.375755\pi$
$41$	−3.91001	+	6.77233i	−0.610640	+	1.05766i	−0.991133	+	0.132876i	$0.957579\pi$
$42$		0			0
$43$		−	7.91208i		−	1.20658i	−0.797521	−	0.603291i	$-0.793856\pi$
$43$		−	7.91208i		−	1.20658i	0.797521	−	0.603291i	$-0.206144\pi$
$44$		0			0
$45$	−9.06028	+	2.01309i	−1.35063	+	0.300093i
$46$		0			0
$47$	−0.523745	−	0.302384i	−0.0763961	−	0.0441073i	0.461315	−	0.887236i	$-0.347378\pi$
$47$	−0.523745	−	0.302384i	−0.0763961	−	0.0441073i	−0.537711	+	0.843129i	$0.680711\pi$
$48$		0			0
$49$	−2.21916	−	3.84370i	−0.317023	−	0.549100i
$50$		0			0
$51$	−1.78399	+	1.30872i	−0.249809	+	0.183258i
$52$		0			0
$53$	−8.20758			−1.12740			−0.563699	−	0.825980i	$-0.690622\pi$
$53$	−8.20758			−1.12740			−0.563699	+	0.825980i	$0.690622\pi$
$54$		0			0
$55$	8.42478	−	14.5922i	1.13600	−	1.96761i
$56$		0			0
$57$	0.241539	+	0.329255i	0.0319926	+	0.0436109i
$58$		0			0
$59$			13.8714i			1.80590i	0.429746	+	0.902950i	$0.358603\pi$
$59$			13.8714i			1.80590i	−0.429746	+	0.902950i	$0.641397\pi$
$60$		0			0
$61$	7.23406	−	4.17658i	0.926226	−	0.534757i	0.0406100	−	0.999175i	$-0.487070\pi$
$61$	7.23406	−	4.17658i	0.926226	−	0.534757i	0.885616	+	0.464418i	$0.153737\pi$
$62$		0			0
$63$	−4.58002	−	1.44171i	−0.577028	−	0.181638i
$64$		0			0
$65$	11.4358	−	6.60244i	1.41843	−	0.818932i
$66$		0			0
$67$	6.48268	+	4.99749i	0.791985	+	0.610540i
$67$	6.48268	+	4.99749i	0.791985	+	0.610540i
$68$		0			0
$69$	−6.60135	+	4.84270i	−0.794709	+	0.582993i
$70$		0			0
$71$	−11.3188	−	6.53491i	−1.34329	−	0.775551i	−0.356004	−	0.934484i	$-0.615861\pi$
$71$	−11.3188	−	6.53491i	−1.34329	−	0.775551i	−0.987289	+	0.158933i	$0.949195\pi$
$72$		0			0
$73$	−3.23694	−	5.60654i	−0.378855	−	0.656196i	0.612041	−	0.790826i	$-0.290349\pi$
$73$	−3.23694	−	5.60654i	−0.378855	−	0.656196i	−0.990896	+	0.134630i	$0.957015\pi$
$74$		0			0
$75$	7.87035	−	0.863817i	0.908789	−	0.0997450i
$76$		0			0
$77$	7.54914	−	4.35850i	0.860305	−	0.496697i
$78$		0			0
$79$	−8.34701	−	4.81915i	−0.939112	−	0.542197i	−0.0494304	−	0.998778i	$-0.515741\pi$
$79$	−8.34701	−	4.81915i	−0.939112	−	0.542197i	−0.889682	+	0.456581i	$0.849074\pi$
$80$		0			0
$81$	8.15319	−	3.81124i	0.905910	−	0.423471i
$82$		0			0
$83$	12.5094	−	7.22228i	1.37308	−	0.792748i	0.381765	−	0.924259i	$-0.375316\pi$
$83$	12.5094	−	7.22228i	1.37308	−	0.792748i	0.991315	+	0.131511i	$0.0419829\pi$
$84$		0			0
$85$	3.42253	−	1.97600i	0.371226	−	0.214327i
$86$		0			0
$87$	2.14386	+	0.942717i	0.229845	+	0.101070i
$88$		0			0
$89$		−	2.12681i		−	0.225441i	−0.993627	−	0.112721i	$-0.964043\pi$
$89$		−	2.12681i		−	0.225441i	0.993627	−	0.112721i	$-0.0359565\pi$
$90$		0			0
$91$	6.83145			0.716131
$92$		0			0
$93$	−2.22574	−	0.978724i	−0.230798	−	0.101489i
$94$		0			0
$95$	−0.364692	−	0.631664i	−0.0374166	−	0.0648074i
$96$		0			0
$97$	2.75058	−	1.58805i	0.279280	−	0.161242i	−0.353818	−	0.935314i	$-0.615117\pi$
$97$	2.75058	−	1.58805i	0.279280	−	0.161242i	0.633097	+	0.774072i	$0.281783\pi$
$98$		0			0
$99$	−4.90590	+	15.5851i	−0.493062	+	1.56636i
$100$		0			0
$101$	−2.10535	+	3.64656i	−0.209490	+	0.362847i	−0.951554	−	0.307482i	$-0.900514\pi$
$101$	−2.10535	+	3.64656i	−0.209490	+	0.362847i	0.742064	+	0.670329i	$0.233847\pi$
$102$		0			0
$103$	−0.638994	+	1.10677i	−0.0629620	+	0.109053i	−0.895788	−	0.444481i	$-0.853388\pi$
$103$	−0.638994	+	1.10677i	−0.0629620	+	0.109053i	0.832826	+	0.553535i	$0.186721\pi$
$104$		0			0
$105$	7.85092	+	3.45229i	0.766172	+	0.336909i
$106$		0			0
$107$		−	7.73405i		−	0.747679i	−0.927493	−	0.373840i	$-0.878041\pi$
$107$		−	7.73405i		−	0.747679i	0.927493	−	0.373840i	$-0.121959\pi$
$108$		0			0
$109$			3.97936i			0.381154i	0.981672	+	0.190577i	$0.0610359\pi$
$109$			3.97936i			0.381154i	−0.981672	+	0.190577i	$0.938964\pi$
$110$		0			0
$111$	6.82583	+	9.30467i	0.647880	+	0.883160i
$112$		0			0
$113$	1.84973	−	3.20382i	0.174008	−	0.301390i	−0.765810	−	0.643067i	$-0.777662\pi$
$113$	1.84973	−	3.20382i	0.174008	−	0.301390i	0.939817	+	0.341677i	$0.110995\pi$
$114$		0			0
$115$	12.6645	−	7.31184i	1.18097	−	0.681833i
$116$		0			0
$117$	−9.43660	+	8.65522i	−0.872414	+	0.800176i
$118$		0			0
$119$	2.04454			0.187423
$120$		0			0
$121$	−9.33131	−	16.1623i	−0.848301	−	1.46930i
$122$		0			0
$123$	−5.45215	+	12.3989i	−0.491604	+	1.11797i
$124$		0			0
$125$	1.32649			0.118645
$126$		0			0
$127$	−9.10719	+	15.7741i	−0.808132	+	1.39973i	0.106024	+	0.994364i	$0.466188\pi$
$127$	−9.10719	+	15.7741i	−0.808132	+	1.39973i	−0.914156	+	0.405362i	$0.867145\pi$
$128$		0			0
$129$	−1.49513	−	13.6223i	−0.131639	−	1.19938i
$130$		0			0
$131$			3.50688i			0.306397i	0.988195	+	0.153199i	$0.0489575\pi$
$131$			3.50688i			0.306397i	−0.988195	+	0.153199i	$0.951043\pi$
$132$		0			0
$133$		−	0.377341i		−	0.0327196i
$134$		0			0
$135$	−15.2188	+	5.17806i	−1.30982	+	0.445656i
$136$		0			0
$137$	−16.4673			−1.40690			−0.703450	−	0.710745i	$-0.748358\pi$
$137$	−16.4673			−1.40690			−0.703450	+	0.710745i	$0.748358\pi$
$138$		0			0
$139$			20.9672i			1.77841i	0.457506	+	0.889207i	$0.348743\pi$
$139$			20.9672i			1.77841i	−0.457506	+	0.889207i	$0.651257\pi$
$140$		0			0
$141$	−0.958879	−	0.421648i	−0.0807522	−	0.0355091i
$142$		0			0
$143$		−	23.2464i		−	1.94396i
$144$		0			0
$145$	−3.62273	−	2.09158i	−0.300851	−	0.173697i
$146$		0			0
$147$	−4.54709	−	6.19839i	−0.375038	−	0.511235i
$148$		0			0
$149$		−	4.30917i		−	0.353021i	−0.984299	−	0.176511i	$-0.943519\pi$
$149$		−	4.30917i		−	0.353021i	0.984299	−	0.176511i	$-0.0564810\pi$
$150$		0			0
$151$	10.5111	+	18.2058i	0.855383	+	1.48157i	0.876290	+	0.481785i	$0.160011\pi$
$151$	10.5111	+	18.2058i	0.855383	+	1.48157i	−0.0209071	+	0.999781i	$0.506655\pi$
$152$		0			0
$153$	−2.82421	+	2.59036i	−0.228324	+	0.209418i
$154$		0			0
$155$	3.76110	+	2.17147i	0.302098	+	0.174417i
$156$		0			0
$157$	−9.90585	−	17.1574i	−0.790573	−	1.36931i	−0.925613	−	0.378472i	$-0.876449\pi$
$157$	−9.90585	−	17.1574i	−0.790573	−	1.36931i	0.135040	−	0.990840i	$-0.456884\pi$
$158$		0			0
$159$	−14.1311	+	1.55097i	−1.12067	+	0.123000i
$160$		0			0
$161$	7.56545			0.596241
$162$		0			0
$163$	−9.37120	+	16.2314i	−0.734009	+	1.27134i	0.221148	+	0.975240i	$0.429020\pi$
$163$	−9.37120	+	16.2314i	−0.734009	+	1.27134i	−0.955157	+	0.296101i	$0.904314\pi$
$164$		0			0
$165$	11.7476	−	26.7155i	0.914549	−	2.07980i
$166$		0			0
$167$	11.8538	+	6.84379i	0.917274	+	0.529589i	0.882764	−	0.469816i	$-0.155680\pi$
$167$	11.8538	+	6.84379i	0.917274	+	0.529589i	0.0345098	+	0.999404i	$0.489013\pi$
$168$		0			0
$169$	2.60902	−	4.51895i	0.200694	−	0.347611i
$170$		0			0
$171$	0.478079	+	0.521239i	0.0365596	+	0.0398601i
$172$		0			0
$173$	13.7355	−	7.93017i	1.04429	−	0.602920i	0.123243	−	0.992377i	$-0.460671\pi$
$173$	13.7355	−	7.93017i	1.04429	−	0.602920i	0.921045	+	0.389457i	$0.127337\pi$
$174$		0			0
$175$	−6.33616	−	3.65819i	−0.478969	−	0.276533i
$176$		0			0
$177$	2.62125	+	23.8825i	0.197025	+	1.79512i
$178$		0			0
$179$	15.9844			1.19473			0.597363	−	0.801971i	$-0.296215\pi$
$179$	15.9844			1.19473			0.597363	+	0.801971i	$0.296215\pi$
$180$		0			0
$181$	3.73838	−	6.47507i	0.277872	−	0.481288i	−0.692984	−	0.720953i	$-0.743704\pi$
$181$	3.73838	−	6.47507i	0.277872	−	0.481288i	0.970856	+	0.239665i	$0.0770376\pi$
$182$		0			0
$183$	11.6657	−	8.55788i	0.862355	−	0.632617i
$184$		0			0
$185$	−10.3061	−	17.8507i	−0.757720	−	1.31241i
$186$		0			0
$187$		−	6.95725i		−	0.508765i
$188$		0			0
$189$	−8.15791	−	1.61672i	−0.593401	−	0.117599i
$190$		0			0
$191$	−0.582685	−	1.00924i	−0.0421616	−	0.0730261i	0.844175	−	0.536068i	$-0.180091\pi$
$191$	−0.582685	−	1.00924i	−0.0421616	−	0.0730261i	−0.886336	+	0.463042i	$0.846758\pi$
$192$		0			0
$193$	20.8603			1.50156			0.750778	−	0.660554i	$-0.229679\pi$
$193$	20.8603			1.50156			0.750778	+	0.660554i	$0.229679\pi$
$194$		0			0
$195$	18.4414	−	13.5285i	1.32062	−	0.968796i
$196$		0			0
$197$	9.33029	−	16.1605i	0.664755	−	1.15139i	−0.314596	−	0.949226i	$-0.601869\pi$
$197$	9.33029	−	16.1605i	0.664755	−	1.15139i	0.979352	−	0.202165i	$-0.0647976\pi$
$198$		0			0
$199$	4.17340	+	7.22854i	0.295844	+	0.512418i	0.975181	−	0.221409i	$-0.0710657\pi$
$199$	4.17340	+	7.22854i	0.295844	+	0.512418i	−0.679337	+	0.733827i	$0.737732\pi$
$200$		0			0
$201$	12.1057	+	7.37922i	0.853868	+	0.520490i
$202$		0			0
$203$	−1.08207	−	1.87419i	−0.0759461	−	0.131543i
$204$		0			0
$205$	12.0965	−	20.9518i	0.844859	−	1.46334i
$206$		0			0
$207$	−10.4505	+	9.58518i	−0.726361	+	0.666216i
$208$		0			0
$209$	−1.28403			−0.0888185
$210$		0			0
$211$	1.30463	+	2.25969i	0.0898145	+	0.155563i	0.907433	−	0.420198i	$-0.138039\pi$
$211$	1.30463	+	2.25969i	0.0898145	+	0.155563i	−0.817618	+	0.575761i	$0.804706\pi$
$212$		0			0
$213$	−20.7226	−	9.11234i	−1.41989	−	0.624367i
$214$		0			0
$215$			24.4779i			1.66938i
$216$		0			0
$217$	1.12339	+	1.94578i	0.0762610	+	0.132088i
$218$		0			0
$219$	−6.63253	−	9.04117i	−0.448185	−	0.610946i
$220$		0			0
$221$	2.72617	−	4.72187i	0.183382	−	0.317628i
$222$		0			0
$223$	20.1726			1.35086			0.675429	−	0.737425i	$-0.263958\pi$
$223$	20.1726			1.35086			0.675429	+	0.737425i	$0.263958\pi$
$224$		0			0
$225$	13.3872	−	2.97449i	0.892482	−	0.198299i
$226$		0			0
$227$	9.98643	+	5.76567i	0.662822	+	0.382681i	0.793352	−	0.608764i	$-0.208334\pi$
$227$	9.98643	+	5.76567i	0.662822	+	0.382681i	−0.130529	+	0.991444i	$0.541668\pi$
$228$		0			0
$229$	−12.7449	+	7.35827i	−0.842207	+	0.486248i	−0.858014	−	0.513627i	$-0.828302\pi$
$229$	−12.7449	+	7.35827i	−0.842207	+	0.486248i	0.0158068	+	0.999875i	$0.494968\pi$
$230$		0			0
$231$	12.1738	−	8.93063i	0.800979	−	0.587592i
$232$		0			0
$233$	−3.97386	+	6.88293i	−0.260336	+	0.450916i	−0.966331	−	0.257301i	$-0.917167\pi$
$233$	−3.97386	+	6.88293i	−0.260336	+	0.450916i	0.705995	+	0.708217i	$0.250500\pi$
$234$		0			0
$235$	1.62033	+	0.935499i	0.105699	+	0.0610252i
$236$		0			0
$237$	−15.2818	−	6.71987i	−0.992661	−	0.436502i
$238$		0			0
$239$	−13.8741	+	24.0307i	−0.897442	+	1.55442i	−0.0666902	+	0.997774i	$0.521244\pi$
$239$	−13.8741	+	24.0307i	−0.897442	+	1.55442i	−0.830752	+	0.556642i	$0.812089\pi$
$240$		0			0
$241$	−1.22462			−0.0788850			−0.0394425	−	0.999222i	$-0.512558\pi$
$241$	−1.22462			−0.0788850			−0.0394425	+	0.999222i	$0.512558\pi$
$242$		0			0
$243$	13.3172	−	8.10255i	0.854301	−	0.519779i
$244$		0			0
$245$	6.86551	+	11.8914i	0.438621	+	0.759714i
$246$		0			0
$247$	−0.871472	−	0.503144i	−0.0554504	−	0.0320143i
$248$		0			0
$249$	20.1727	−	14.7986i	1.27839	−	0.937820i
$250$		0			0
$251$	1.29071	+	2.23557i	0.0814687	+	0.141108i	0.903881	−	0.427784i	$-0.140706\pi$
$251$	1.29071	+	2.23557i	0.0814687	+	0.141108i	−0.822412	+	0.568892i	$0.807372\pi$
$252$		0			0
$253$		−	25.7441i		−	1.61852i
$254$		0			0
$255$	5.51921	−	4.04885i	0.345627	−	0.253549i
$256$		0			0
$257$	−7.44518	−	4.29848i	−0.464418	−	0.268132i	0.249482	−	0.968379i	$-0.419740\pi$
$257$	−7.44518	−	4.29848i	−0.464418	−	0.268132i	−0.713900	+	0.700248i	$0.753073\pi$
$258$		0			0
$259$		−	10.6636i		−	0.662603i
$260$		0			0
$261$	3.86925	+	1.21797i	0.239500	+	0.0753903i
$262$		0			0
$263$		−	11.6279i		−	0.717009i	−0.933528	−	0.358505i	$-0.883287\pi$
$263$		−	11.6279i		−	0.717009i	0.933528	−	0.358505i	$-0.116713\pi$
$264$		0			0
$265$	25.3921			1.55983
$266$		0			0
$267$	−0.401899	−	3.66175i	−0.0245958	−	0.224096i
$268$		0			0
$269$		−	3.35461i		−	0.204534i	−0.994757	−	0.102267i	$-0.967390\pi$
$269$		−	3.35461i		−	0.204534i	0.994757	−	0.102267i	$-0.0326096\pi$
$270$		0			0
$271$		−	3.39129i		−	0.206006i	−0.994681	−	0.103003i	$-0.967155\pi$
$271$		−	3.39129i		−	0.206006i	0.994681	−	0.103003i	$-0.0328452\pi$
$272$		0			0
$273$	11.7618	−	1.29093i	0.711856	−	0.0781304i
$274$		0			0
$275$	−12.4482	+	21.5610i	−0.750658	+	1.30018i
$276$		0			0
$277$	−24.5468			−1.47488			−0.737438	−	0.675415i	$-0.763965\pi$
$277$	−24.5468			−1.47488			−0.737438	+	0.675415i	$0.763965\pi$
$278$		0			0
$279$	−4.01703	−	1.26449i	−0.240493	−	0.0757028i
$280$		0			0
$281$	−5.71395	−	9.89685i	−0.340865	−	0.590396i	0.643728	−	0.765254i	$-0.277387\pi$
$281$	−5.71395	−	9.89685i	−0.340865	−	0.590396i	−0.984594	+	0.174858i	$0.944053\pi$
$282$		0			0
$283$	−7.61687			−0.452776			−0.226388	−	0.974037i	$-0.572692\pi$
$283$	−7.61687			−0.452776			−0.226388	+	0.974037i	$0.572692\pi$
$284$		0			0
$285$	−0.747258	−	1.01863i	−0.0442638	−	0.0603384i
$286$		0			0
$287$	10.8393	−	6.25806i	0.639822	−	0.369402i
$288$		0			0
$289$	−7.68410	+	13.3093i	−0.452006	+	0.782897i
$290$		0			0
$291$	4.43562	−	3.25394i	0.260021	−	0.190749i
$292$		0			0
$293$			7.97510i			0.465910i	0.972487	+	0.232955i	$0.0748395\pi$
$293$			7.97510i			0.465910i	−0.972487	+	0.232955i	$0.925160\pi$
$294$		0			0
$295$		−	42.9145i		−	2.49858i
$296$		0			0
$297$	−5.50147	+	27.7601i	−0.319227	+	1.61081i
$298$		0			0
$299$	10.0877	−	17.4725i	0.583388	−	1.01046i
$300$		0			0
$301$	−6.33174	+	10.9669i	−0.364955	+	0.632121i
$302$		0			0
$303$	−2.93571	+	6.67618i	−0.168652	+	0.383536i
$304$		0			0
$305$	−22.3803	+	12.9213i	−1.28149	+	0.739870i
$306$		0			0
$307$	8.59740	+	14.8911i	0.490679	+	0.849882i	0.999942	−	0.0107293i	$-0.00341530\pi$
$307$	8.59740	+	14.8911i	0.490679	+	0.849882i	−0.509263	+	0.860611i	$0.670082\pi$
$308$		0			0
$309$	−0.891020	+	2.02629i	−0.0506883	+	0.115272i
$310$		0			0
$311$	−8.51233			−0.482690			−0.241345	−	0.970439i	$-0.577589\pi$
$311$	−8.51233			−0.482690			−0.241345	+	0.970439i	$0.577589\pi$
$312$		0			0
$313$			16.1984i			0.915589i	0.889058	+	0.457794i	$0.151360\pi$
$313$			16.1984i			0.915589i	−0.889058	+	0.457794i	$0.848640\pi$
$314$		0			0
$315$	14.1694	+	4.46027i	0.798355	+	0.251308i
$316$		0			0
$317$	−20.5239	+	11.8495i	−1.15274	+	0.665534i	−0.949553	−	0.313607i	$-0.898463\pi$
$317$	−20.5239	+	11.8495i	−1.15274	+	0.665534i	−0.203185	+	0.979140i	$0.565129\pi$
$318$		0			0
$319$	−6.37759	+	3.68210i	−0.357076	+	0.206158i
$320$		0			0
$321$	−1.46149	−	13.3158i	−0.0815723	−	0.743216i
$322$		0			0
$323$	−0.260817	−	0.150583i	−0.0145122	−	0.00837864i
$324$		0			0
$325$	−16.8972	+	9.75561i	−0.937288	+	0.541144i
$326$		0			0
$327$	0.751972	+	6.85132i	0.0415842	+	0.378879i
$328$		0			0
$329$	0.483974	+	0.838267i	0.0266823	+	0.0462152i
$330$		0			0
$331$	−20.6692	−	11.9334i	−1.13608	−	0.655917i	−0.190624	−	0.981663i	$-0.561051\pi$
$331$	−20.6692	−	11.9334i	−1.13608	−	0.655917i	−0.945457	+	0.325746i	$0.894385\pi$
$332$		0			0
$333$	13.5104	+	14.7301i	0.740366	+	0.807204i
$334$		0			0
$335$	−20.0557	−	15.4609i	−1.09576	−	0.844721i
$336$		0			0
$337$	−25.3487	+	14.6351i	−1.38083	+	0.797223i	−0.992258	−	0.124194i	$-0.960365\pi$
$337$	−25.3487	+	14.6351i	−1.38083	+	0.797223i	−0.388573	+	0.921418i	$0.627032\pi$
$338$		0			0
$339$	2.57928	−	5.86560i	0.140087	−	0.318575i
$340$		0			0
$341$	6.62117	−	3.82274i	0.358557	−	0.207013i
$342$		0			0
$343$			18.3073i			0.988502i
$344$		0			0
$345$	20.4229	−	14.9821i	1.09953	−	0.806607i
$346$		0			0
$347$	−13.6699	+	23.6770i	−0.733841	+	1.27105i	0.221389	+	0.975186i	$0.428941\pi$
$347$	−13.6699	+	23.6770i	−0.733841	+	1.27105i	−0.955230	+	0.295864i	$0.904392\pi$
$348$		0			0
$349$	23.4301			1.25418			0.627092	−	0.778945i	$-0.284245\pi$
$349$	23.4301			1.25418			0.627092	+	0.778945i	$0.284245\pi$
$350$		0			0
$351$	−14.6115	+	16.6850i	−0.779907	+	0.890580i
$352$		0			0
$353$	−2.16051	−	3.74211i	−0.114992	−	0.199172i	0.802784	−	0.596269i	$-0.203351\pi$
$353$	−2.16051	−	3.74211i	−0.114992	−	0.199172i	−0.917777	+	0.397097i	$0.870018\pi$
$354$		0			0
$355$	35.0174	+	20.2173i	1.85853	+	1.07302i
$356$		0			0
$357$	3.52011	−	0.386352i	0.186304	−	0.0204479i
$358$		0			0
$359$		−	9.88207i		−	0.521556i	−0.965399	−	0.260778i	$-0.916021\pi$
$359$		−	9.88207i		−	0.521556i	0.965399	−	0.260778i	$-0.0839790\pi$
$360$		0			0
$361$	9.47221	−	16.4063i	0.498537	−	0.863492i
$362$		0			0
$363$	−19.1200	−	26.0635i	−1.00354	−	1.36798i
$364$		0			0
$365$	10.0143	+	17.3452i	0.524170	+	0.907889i
$366$		0			0
$367$	−5.33339	−	3.07924i	−0.278401	−	0.160735i	0.354298	−	0.935132i	$-0.384720\pi$
$367$	−5.33339	−	3.07924i	−0.278401	−	0.160735i	−0.632699	+	0.774398i	$0.718053\pi$
$368$		0			0
$369$	−7.04404	+	22.3776i	−0.366698	+	1.16493i
$370$		0			0
$371$	11.3765	+	6.56822i	0.590638	+	0.341005i
$372$		0			0
$373$	14.4681	+	8.35314i	0.749128	+	0.432509i	0.825379	−	0.564580i	$-0.190962\pi$
$373$	14.4681	+	8.35314i	0.749128	+	0.432509i	−0.0762510	+	0.997089i	$0.524295\pi$
$374$		0			0
$375$	2.28383	−	0.250664i	0.117937	−	0.0129443i
$376$		0			0
$377$	−5.77128			−0.297236
$378$		0			0
$379$	−27.2027	+	15.7055i	−1.39731	+	0.806738i	−0.994110	−	0.108373i	$-0.965436\pi$
$379$	−27.2027	+	15.7055i	−1.39731	+	0.806738i	−0.403201	+	0.915111i	$0.632102\pi$
$380$		0			0
$381$	−12.6991	+	28.8794i	−0.650597	+	1.47954i
$382$		0			0
$383$	−8.06162	−	13.9631i	−0.411930	−	0.713483i	0.583171	−	0.812349i	$-0.301812\pi$
$383$	−8.06162	−	13.9631i	−0.411930	−	0.713483i	−0.995101	+	0.0988664i	$0.968478\pi$
$384$		0			0
$385$	−23.3551	+	13.4841i	−1.19029	+	0.687212i
$386$		0			0
$387$	−5.14837	−	23.1712i	−0.261706	−	1.17786i
$388$		0			0
$389$	16.5719	−	9.56781i	0.840230	−	0.485107i	−0.0171124	−	0.999854i	$-0.505447\pi$
$389$	16.5719	−	9.56781i	0.840230	−	0.485107i	0.857342	+	0.514747i	$0.172114\pi$
$390$		0			0
$391$	3.01909	−	5.22921i	0.152682	−	0.264453i
$392$		0			0
$393$	0.662688	+	6.03783i	0.0334282	+	0.304568i
$394$		0			0
$395$	25.8235	+	14.9092i	1.29932	+	0.750163i
$396$		0			0
$397$	−9.47362			−0.475467			−0.237734	−	0.971330i	$-0.576405\pi$
$397$	−9.47362			−0.475467			−0.237734	+	0.971330i	$0.576405\pi$
$398$		0			0
$399$	−0.0713054	−	0.649673i	−0.00356974	−	0.0325243i
$400$		0			0
$401$	−30.0145			−1.49885			−0.749427	−	0.662087i	$-0.769671\pi$
$401$	−30.0145			−1.49885			−0.749427	+	0.662087i	$0.769671\pi$
$402$		0			0
$403$	5.99171			0.298468
$404$		0			0
$405$	−25.2239	+	11.7910i	−1.25338	+	0.585899i
$406$		0			0
$407$	−36.2865			−1.79866
$408$		0			0
$409$	−14.5475	−	8.39898i	−0.719326	−	0.415303i	0.0951787	−	0.995460i	$-0.469658\pi$
$409$	−14.5475	−	8.39898i	−0.719326	−	0.415303i	−0.814504	+	0.580157i	$0.802991\pi$
$410$		0			0
$411$	−28.3520	+	3.11180i	−1.39850	+	0.153494i
$412$		0			0
$413$	11.1007	−	19.2270i	0.546232	−	0.946101i
$414$		0			0
$415$	−38.7007	+	22.3439i	−1.89974	+	1.09682i
$416$		0			0
$417$	3.96213	+	36.0994i	0.194026	+	1.76780i
$418$		0			0
$419$	9.38665	−	5.41939i	0.458568	−	0.264754i	−0.252874	−	0.967499i	$-0.581376\pi$
$419$	9.38665	−	5.41939i	0.458568	−	0.264754i	0.711442	+	0.702745i	$0.248042\pi$
$420$		0			0
$421$	2.61037	+	4.52130i	0.127222	+	0.220355i	0.922599	−	0.385760i	$-0.126061\pi$
$421$	2.61037	+	4.52130i	0.127222	+	0.220355i	−0.795377	+	0.606115i	$0.792727\pi$
$422$		0			0
$423$	−1.73059	−	0.544758i	−0.0841442	−	0.0264871i
$424$		0			0
$425$	−5.05705	+	2.91969i	−0.245303	+	0.141626i
$426$		0			0
$427$	−13.3695			−0.646993
$428$		0			0
$429$	−4.39282	−	40.0236i	−0.212088	−	1.93236i
$430$		0			0
$431$	19.0173	+	10.9796i	0.916031	+	0.528871i	0.882367	−	0.470562i	$-0.155949\pi$
$431$	19.0173	+	10.9796i	0.916031	+	0.528871i	0.0336644	+	0.999433i	$0.489282\pi$
$432$		0			0
$433$	22.3862	+	12.9247i	1.07581	+	0.621122i	0.929764	−	0.368156i	$-0.120011\pi$
$433$	22.3862	+	12.9247i	1.07581	+	0.621122i	0.146050	+	0.989277i	$0.453344\pi$
$434$		0			0
$435$	−6.63254	−	2.91652i	−0.318006	−	0.139837i
$436$		0			0
$437$	−0.965106	−	0.557204i	−0.0461673	−	0.0266547i
$438$		0			0
$439$	19.8324	+	34.3507i	0.946549	+	1.63947i	0.752621	+	0.658455i	$0.228790\pi$
$439$	19.8324	+	34.3507i	0.946549	+	1.63947i	0.193928	+	0.981016i	$0.437877\pi$
$440$		0			0
$441$	−9.00008	−	9.81259i	−0.428575	−	0.467266i
$442$		0			0
$443$	−8.73288	+	15.1258i	−0.414912	+	0.718648i	−0.995419	−	0.0956068i	$-0.969521\pi$
$443$	−8.73288	+	15.1258i	−0.414912	+	0.718648i	0.580508	+	0.814255i	$0.302854\pi$
$444$		0			0
$445$			6.57980i			0.311912i
$446$		0			0
$447$	−0.814296	−	7.41916i	−0.0385149	−	0.350914i
$448$		0			0
$449$	8.84785	+	5.10831i	0.417556	+	0.241076i	0.694031	−	0.719945i	$-0.255833\pi$
$449$	8.84785	+	5.10831i	0.417556	+	0.241076i	−0.276475	+	0.961021i	$0.589166\pi$
$450$		0			0
$451$	−21.2952	−	36.8844i	−1.00275	−	1.73682i
$452$		0			0
$453$	21.5374	+	29.3589i	1.01192	+	1.37940i
$454$		0			0
$455$	−21.1347			−0.990812
$456$		0			0
$457$	8.08125	−	13.9971i	0.378025	−	0.654759i	−0.612750	−	0.790277i	$-0.709937\pi$
$457$	8.08125	−	13.9971i	0.378025	−	0.654759i	0.990775	+	0.135518i	$0.0432700\pi$
$458$		0			0
$459$	−4.37299	+	4.99354i	−0.204114	+	0.233079i
$460$		0			0
$461$			31.4807i			1.46620i	0.680119	+	0.733101i	$0.261928\pi$
$461$			31.4807i			1.46620i	−0.680119	+	0.733101i	$0.738072\pi$
$462$		0			0
$463$	6.83522	−	3.94631i	0.317659	−	0.183401i	−0.332689	−	0.943036i	$-0.607956\pi$
$463$	6.83522	−	3.94631i	0.317659	−	0.183401i	0.650349	+	0.759636i	$0.274623\pi$
$464$		0			0
$465$	6.88586	+	3.02792i	0.319324	+	0.140416i
$466$		0			0
$467$	−9.30098	+	5.36992i	−0.430398	+	0.248490i	−0.699516	−	0.714617i	$-0.746601\pi$
$467$	−9.30098	+	5.36992i	−0.430398	+	0.248490i	0.269118	+	0.963107i	$0.413268\pi$
$468$		0			0
$469$	−4.98631	−	12.1148i	−0.230246	−	0.559411i
$470$		0			0
$471$	−20.2972	−	27.6683i	−0.935247	−	1.27489i
$472$		0			0
$473$	37.3187	+	21.5459i	1.71591	+	0.990683i
$474$		0			0
$475$	0.538859	+	0.933332i	0.0247246	+	0.0428242i
$476$		0			0
$477$	−24.0366	+	5.34065i	−1.10056	+	0.244531i
$478$		0			0
$479$	−10.1713	+	5.87238i	−0.464737	+	0.268316i	−0.714034	−	0.700111i	$-0.753134\pi$
$479$	−10.1713	+	5.87238i	−0.464737	+	0.268316i	0.249297	+	0.968427i	$0.419800\pi$
$480$		0			0
$481$	−24.6276	−	14.2188i	−1.12292	−	0.648319i
$482$		0			0
$483$	13.0255	−	1.42963i	0.592682	−	0.0650504i
$484$		0			0
$485$	−8.50960	+	4.91302i	−0.386401	+	0.223089i
$486$		0			0
$487$	33.9794	−	19.6180i	1.53975	−	0.888977i	0.540901	−	0.841087i	$-0.318083\pi$
$487$	33.9794	−	19.6180i	1.53975	−	0.888977i	0.998853	−	0.0478904i	$-0.0152498\pi$
$488$		0			0
$489$	−13.0673	+	29.7166i	−0.590923	+	1.34383i
$490$		0			0
$491$		−	13.0134i		−	0.587285i	−0.955915	−	0.293643i	$-0.905132\pi$
$491$		−	13.0134i		−	0.587285i	0.955915	−	0.293643i	$-0.0948675\pi$
$492$		0			0
$493$	−1.72725			−0.0777912
$494$		0			0
$495$	15.1776	−	48.2163i	0.682182	−	2.16716i
$496$		0			0
$497$	10.4593	+	18.1160i	0.469163	+	0.812614i
$498$		0			0
$499$	−24.1351	+	13.9344i	−1.08043	+	0.623789i	−0.931014	−	0.364985i	$-0.881074\pi$
$499$	−24.1351	+	13.9344i	−1.08043	+	0.623789i	−0.149421	+	0.988774i	$0.547741\pi$
$500$		0			0
$501$	21.7021	+	9.54305i	0.969577	+	0.426352i
$502$		0			0
$503$	2.68521	−	4.65092i	0.119728	−	0.207374i	−0.799932	−	0.600091i	$-0.795131\pi$
$503$	2.68521	−	4.65092i	0.119728	−	0.207374i	0.919660	+	0.392716i	$0.128465\pi$
$504$		0			0
$505$	6.51339	−	11.2815i	0.289842	−	0.502021i
$506$		0			0
$507$	3.63804	−	8.27335i	0.161571	−	0.367432i
$508$		0			0
$509$		−	36.8498i		−	1.63334i	−0.577106	−	0.816669i	$-0.695818\pi$
$509$		−	36.8498i		−	1.63334i	0.577106	−	0.816669i	$-0.304182\pi$
$510$		0			0
$511$			10.3616i			0.458370i
$512$		0			0
$513$	0.921611	+	0.807081i	0.0406901	+	0.0356335i
$514$		0			0
$515$	1.97688	−	3.42406i	0.0871119	−	0.150882i
$516$		0			0
$517$	2.85249	−	1.64689i	0.125453	−	0.0724301i
$518$		0			0
$519$	22.1500	−	16.2490i	0.972275	−	0.713253i
$520$		0			0
$521$	23.8720			1.04585			0.522927	−	0.852378i	$-0.324840\pi$
$521$	23.8720			1.04585			0.522927	+	0.852378i	$0.324840\pi$
$522$		0			0
$523$	0.409211	+	0.708774i	0.0178936	+	0.0309925i	0.874834	−	0.484424i	$-0.160971\pi$
$523$	0.409211	+	0.708774i	0.0178936	+	0.0309925i	−0.856940	+	0.515416i	$0.827637\pi$
$524$		0			0
$525$	−11.6003	−	5.10101i	−0.506280	−	0.222626i
$526$		0			0
$527$	1.79322			0.0781137
$528$		0			0
$529$	−0.328401	+	0.568806i	−0.0142783	+	0.0247307i
$530$		0			0
$531$	9.02606	+	40.6235i	0.391698	+	1.76291i
$532$		0			0
$533$		−	33.3778i		−	1.44575i
$534$		0			0
$535$			23.9272i			1.03446i
$536$		0			0
$537$	27.5204	−	3.02053i	1.18759	−	0.130346i
$538$		0			0
$539$	24.1726			1.04119
$540$		0			0
$541$			29.2068i			1.25570i	0.778335	+	0.627849i	$0.216065\pi$
$541$			29.2068i			1.25570i	−0.778335	+	0.627849i	$0.783935\pi$
$542$		0			0
$543$	5.21284	−	11.8546i	0.223704	−	0.508731i
$544$		0			0
$545$		−	12.3111i		−	0.527350i
$546$		0			0
$547$	−6.11997	−	3.53337i	−0.261671	−	0.151076i	0.363425	−	0.931623i	$-0.381607\pi$
$547$	−6.11997	−	3.53337i	−0.261671	−	0.151076i	−0.625097	+	0.780547i	$0.714940\pi$
$548$		0			0
$549$	18.4678	−	16.9386i	0.788188	−	0.722924i
$550$		0			0
$551$			0.318781i			0.0135805i
$552$		0			0
$553$	7.71317	+	13.3596i	0.327997	+	0.568108i
$554$		0			0
$555$	−21.1174	−	28.7862i	−0.896382	−	1.22191i
$556$		0			0
$557$	12.3055	+	7.10459i	0.521401	+	0.301031i	0.737508	−	0.675339i	$-0.236003\pi$
$557$	12.3055	+	7.10459i	0.521401	+	0.301031i	−0.216107	+	0.976370i	$0.569336\pi$
$558$		0			0
$559$	16.8854	+	29.2464i	0.714177	+	1.23699i
$560$		0			0
$561$	−1.31470	−	11.9784i	−0.0555066	−	0.505728i
$562$		0			0
$563$	17.0228			0.717424			0.358712	−	0.933448i	$-0.383216\pi$
$563$	17.0228			0.717424			0.358712	+	0.933448i	$0.383216\pi$
$564$		0			0
$565$	−5.72258	+	9.91179i	−0.240751	+	0.416992i
$566$		0			0
$567$	−14.3511	−	1.24195i	−0.602689	−	0.0521570i
$568$		0			0
$569$	−24.1597	−	13.9486i	−1.01283	−	0.584755i	−0.100808	−	0.994906i	$-0.532143\pi$
$569$	−24.1597	−	13.9486i	−1.01283	−	0.584755i	−0.912018	+	0.410151i	$0.865476\pi$
$570$		0			0
$571$	1.48575	−	2.57339i	0.0621766	−	0.107693i	−0.833261	−	0.552879i	$-0.813529\pi$
$571$	1.48575	−	2.57339i	0.0621766	−	0.107693i	0.895438	+	0.445186i	$0.146862\pi$
$572$		0			0
$573$	−1.19393	−	1.62751i	−0.0498772	−	0.0679903i
$574$		0			0
$575$	−18.7127	+	10.8038i	−0.780374	+	0.450549i
$576$		0			0
$577$	−29.0883	−	16.7941i	−1.21096	−	0.699149i	−0.247992	−	0.968762i	$-0.579771\pi$
$577$	−29.0883	−	16.7941i	−1.21096	−	0.699149i	−0.962969	+	0.269614i	$0.913104\pi$
$578$		0			0
$579$	35.9154	−	3.94193i	1.49259	−	0.163821i
$580$		0			0
$581$	−23.1189			−0.959132
$582$		0			0
$583$	22.3506	−	38.7124i	0.925668	−	1.60330i
$584$		0			0
$585$	29.1944	−	26.7770i	1.20704	−	1.10709i
$586$		0			0
$587$	−13.3898	−	23.1918i	−0.552656	−	0.957227i	−0.998082	−	0.0619088i	$-0.980281\pi$
$587$	−13.3898	−	23.1918i	−0.552656	−	0.957227i	0.445426	−	0.895319i	$-0.353052\pi$
$588$		0			0
$589$		−	0.330957i		−	0.0136368i
$590$		0			0
$591$	13.0102	−	29.5869i	0.535170	−	1.21704i
$592$		0			0
$593$	−14.1727	−	24.5478i	−0.582002	−	1.00806i	−0.995242	−	0.0974354i	$-0.968936\pi$
$593$	−14.1727	−	24.5478i	−0.582002	−	1.00806i	0.413239	−	0.910622i	$-0.364397\pi$
$594$		0			0
$595$	−6.32527			−0.259311
$596$		0			0
$597$	8.55135	+	11.6568i	0.349984	+	0.477082i
$598$		0			0
$599$	−16.7747	+	29.0546i	−0.685394	+	1.18714i	0.287918	+	0.957655i	$0.407037\pi$
$599$	−16.7747	+	29.0546i	−0.685394	+	1.18714i	−0.973313	+	0.229483i	$0.926297\pi$
$600$		0			0
$601$	3.71989	+	6.44303i	0.151737	+	0.262817i	0.931866	−	0.362802i	$-0.118180\pi$
$601$	3.71989	+	6.44303i	0.151737	+	0.262817i	−0.780129	+	0.625619i	$0.784847\pi$
$602$		0			0
$603$	22.2369	+	10.4173i	0.905557	+	0.424225i
$604$		0			0
$605$	28.8687	+	50.0020i	1.17368	+	2.03287i
$606$		0			0
$607$	−17.2851	+	29.9386i	−0.701579	+	1.21517i	0.266332	+	0.963881i	$0.414188\pi$
$607$	−17.2851	+	29.9386i	−0.701579	+	1.21517i	−0.967912	+	0.251290i	$0.919145\pi$
$608$		0			0
$609$	−2.21717	−	3.02234i	−0.0898441	−	0.122472i
$610$		0			0
$611$	2.58131			0.104429
$612$		0			0
$613$	3.10205	+	5.37290i	0.125290	+	0.217009i	0.921846	−	0.387555i	$-0.126680\pi$
$613$	3.10205	+	5.37290i	0.125290	+	0.217009i	−0.796556	+	0.604565i	$0.793347\pi$
$614$		0			0
$615$	16.8675	−	38.3589i	0.680165	−	1.54678i
$616$		0			0
$617$		−	5.72944i		−	0.230659i	−0.993327	−	0.115329i	$-0.963208\pi$
$617$		−	5.72944i		−	0.230659i	0.993327	−	0.115329i	$-0.0367923\pi$
$618$		0			0
$619$	23.1159	+	40.0379i	0.929105	+	1.60926i	0.784822	+	0.619721i	$0.212754\pi$
$619$	23.1159	+	40.0379i	0.929105	+	1.60926i	0.144283	+	0.989537i	$0.453913\pi$
$620$		0			0
$621$	−16.1815	+	18.4777i	−0.649340	+	0.741486i
$622$		0			0
$623$	−1.70201	+	2.94796i	−0.0681894	+	0.118108i
$624$		0			0
$625$	−26.9600			−1.07840
$626$		0			0
$627$	−2.21074	+	0.242641i	−0.0882883	+	0.00969016i
$628$		0			0
$629$	−7.37063	−	4.25543i	−0.293886	−	0.169675i
$630$		0			0
$631$	−0.0252987	+	0.0146062i	−0.00100712	+	0.000581464i	−0.500503	−	0.865735i	$-0.666852\pi$
$631$	−0.0252987	+	0.0146062i	−0.00100712	+	0.000581464i	0.499496	+	0.866316i	$0.333518\pi$
$632$		0			0
$633$	2.67321	+	3.64400i	0.106250	+	0.144836i
$634$		0			0
$635$	28.1753	−	48.8010i	1.11810	−	1.93661i
$636$		0			0
$637$	16.4059	+	9.47195i	0.650025	+	0.375292i
$638$		0			0
$639$	−37.4003	−	11.7729i	−1.47953	−	0.465729i
$640$		0			0
$641$	−9.49914	+	16.4530i	−0.375193	+	0.649854i	−0.990356	−	0.138546i	$-0.955757\pi$
$641$	−9.49914	+	16.4530i	−0.375193	+	0.649854i	0.615163	+	0.788400i	$0.289090\pi$
$642$		0			0
$643$	−38.4133			−1.51487			−0.757437	−	0.652908i	$-0.773549\pi$
$643$	−38.4133			−1.51487			−0.757437	+	0.652908i	$0.773549\pi$
$644$		0			0
$645$	4.62555	+	42.1439i	0.182131	+	1.65942i
$646$		0			0
$647$	9.84720	+	17.0558i	0.387133	+	0.670534i	0.992063	−	0.125745i	$-0.0401320\pi$
$647$	9.84720	+	17.0558i	0.387133	+	0.670534i	−0.604929	+	0.796279i	$0.706799\pi$
$648$		0			0
$649$	−65.4267	−	37.7741i	−2.56822	−	1.48276i
$650$		0			0
$651$	2.30185	+	3.13778i	0.0902166	+	0.122979i
$652$		0			0
$653$	−19.8292	−	34.3452i	−0.775976	−	1.34403i	−0.934244	−	0.356634i	$-0.883924\pi$
$653$	−19.8292	−	34.3452i	−0.775976	−	1.34403i	0.158268	−	0.987396i	$-0.449409\pi$
$654$		0			0
$655$		−	10.8494i		−	0.423920i
$656$		0			0
$657$	−13.1278	−	14.3130i	−0.512164	−	0.558402i
$658$		0			0
$659$	8.48654	+	4.89970i	0.330588	+	0.190865i	0.656102	−	0.754672i	$-0.272204\pi$
$659$	8.48654	+	4.89970i	0.330588	+	0.190865i	−0.325514	+	0.945537i	$0.605537\pi$
$660$		0			0
$661$			22.0111i			0.856133i	0.903747	+	0.428067i	$0.140805\pi$
$661$			22.0111i			0.856133i	−0.903747	+	0.428067i	$0.859195\pi$
$662$		0			0
$663$	3.80140	−	8.64486i	0.147634	−	0.335739i
$664$		0			0
$665$			1.16740i			0.0452697i
$666$		0			0
$667$	−6.39137			−0.247475
$668$		0			0
$669$	34.7314	−	3.81198i	1.34279	−	0.147380i
$670$		0			0
$671$			45.4942i			1.75628i
$672$		0			0
$673$		−	27.2693i		−	1.05116i	−0.850745	−	0.525578i	$-0.823849\pi$
$673$		−	27.2693i		−	1.05116i	0.850745	−	0.525578i	$-0.176151\pi$
$674$		0			0
$675$	22.4869	−	7.65097i	0.865520	−	0.294486i
$676$		0			0
$677$	−12.5178	+	21.6815i	−0.481099	+	0.833288i	−0.999765	−	0.0216892i	$-0.993096\pi$
$677$	−12.5178	+	21.6815i	−0.481099	+	0.833288i	0.518666	+	0.854977i	$0.326429\pi$
$678$		0			0
$679$	−5.08343			−0.195084
$680$		0			0
$681$	18.2833	+	8.03970i	0.700617	+	0.308082i
$682$		0			0
$683$	−3.36151	−	5.82230i	−0.128625	−	0.222784i	0.794519	−	0.607239i	$-0.207723\pi$
$683$	−3.36151	−	5.82230i	−0.128625	−	0.222784i	−0.923144	+	0.384455i	$0.874390\pi$
$684$		0			0
$685$	50.9457			1.94654
$686$		0			0
$687$	−20.5526	+	15.0772i	−0.784130	+	0.575231i
$688$		0			0
$689$	30.3387	−	17.5160i	1.15581	−	0.667308i
$690$		0			0
$691$	15.8629	−	27.4753i	0.603453	−	1.04521i	−0.388841	−	0.921305i	$-0.627124\pi$
$691$	15.8629	−	27.4753i	0.603453	−	1.04521i	0.992294	−	0.123907i	$-0.0395423\pi$
$692$		0			0
$693$	19.2722	−	17.6764i	0.732091	−	0.671472i
$694$		0			0
$695$		−	64.8670i		−	2.46055i
$696$		0			0
$697$		−	9.98942i		−	0.378376i
$698$		0			0
$699$	−5.54119	+	12.6013i	−0.209587	+	0.476627i
$700$		0			0
$701$	−18.3857	+	31.8450i	−0.694418	+	1.20277i	0.275958	+	0.961170i	$0.411005\pi$
$701$	−18.3857	+	31.8450i	−0.694418	+	1.20277i	−0.970376	+	0.241598i	$0.922329\pi$
$702$		0			0
$703$	−0.785385	+	1.36033i	−0.0296214	+	0.0513057i
$704$		0			0
$705$	2.96652	+	1.30447i	0.111726	+	0.0491291i
$706$		0			0
$707$	5.83642	−	3.36966i	0.219501	−	0.126729i
$708$		0			0
$709$	−13.8280	−	23.9508i	−0.519321	−	0.899490i	−0.999748	−	0.0224551i	$-0.992852\pi$
$709$	−13.8280	−	23.9508i	−0.519321	−	0.899490i	0.480427	−	0.877035i	$-0.340482\pi$
$710$		0			0
$711$	−27.5807	−	8.68190i	−1.03436	−	0.325597i
$712$		0			0
$713$	6.63548			0.248501
$714$		0			0
$715$			71.9183i			2.68959i
$716$		0			0
$717$	−19.3462	+	43.9957i	−0.722497	+	1.64305i
$718$		0			0
$719$	−11.5718	+	6.68101i	−0.431557	+	0.249160i	−0.700010	−	0.714133i	$-0.746821\pi$
$719$	−11.5718	+	6.68101i	−0.431557	+	0.249160i	0.268453	+	0.963293i	$0.413488\pi$
$720$		0			0
$721$	1.77141	−	1.02273i	0.0659709	−	0.0380883i
$722$		0			0
$723$	−2.10845	+	0.231415i	−0.0784141	+	0.00860641i
$724$		0			0
$725$	5.35285	+	3.09047i	0.198800	+	0.114777i
$726$		0			0
$727$	14.1810	−	8.18741i	0.525944	−	0.303654i	−0.213419	−	0.976961i	$-0.568460\pi$
$727$	14.1810	−	8.18741i	0.525944	−	0.303654i	0.739363	+	0.673307i	$0.235127\pi$
$728$		0			0
$729$	21.3973	−	16.4668i	0.792493	−	0.609881i
$730$		0			0
$731$	5.05352	+	8.75295i	0.186911	+	0.323739i
$732$		0			0
$733$	−42.1025	−	24.3079i	−1.55509	−	0.897831i	−0.997714	−	0.0675706i	$-0.978475\pi$
$733$	−42.1025	−	24.3079i	−1.55509	−	0.897831i	−0.557375	−	0.830261i	$-0.688191\pi$
$734$		0			0
$735$	14.0675	+	19.1762i	0.518888	+	0.707325i
$736$		0			0
$737$	−41.2249	+	16.9676i	−1.51854	+	0.625011i
$738$		0			0
$739$	−6.15543	+	3.55384i	−0.226431	+	0.130730i	−0.608925	−	0.793228i	$-0.708399\pi$
$739$	−6.15543	+	3.55384i	−0.226431	+	0.130730i	0.382493	+	0.923958i	$0.375065\pi$
$740$		0			0
$741$	−1.59550	−	0.701589i	−0.0586122	−	0.0257735i
$742$		0			0
$743$	22.9252	−	13.2359i	0.841046	−	0.485578i	−0.0165740	−	0.999863i	$-0.505276\pi$
$743$	22.9252	−	13.2359i	0.841046	−	0.485578i	0.857619	+	0.514285i	$0.171943\pi$
$744$		0			0
$745$			13.3315i			0.488427i
$746$		0			0
$747$	31.9352	−	29.2908i	1.16845	−	1.07170i
$748$		0			0
$749$	−6.18927	+	10.7201i	−0.226151	+	0.391705i
$750$		0			0
$751$	43.9009			1.60197			0.800984	−	0.598686i	$-0.204310\pi$
$751$	43.9009			1.60197			0.800984	+	0.598686i	$0.204310\pi$
$752$		0			0
$753$	2.64468	+	3.60510i	0.0963773	+	0.131377i
$754$		0			0
$755$	−32.5187	−	56.3240i	−1.18348	−	2.04984i
$756$		0			0
$757$	44.1206	+	25.4731i	1.60359	+	0.925834i	0.990761	+	0.135620i	$0.0433025\pi$
$757$	44.1206	+	25.4731i	1.60359	+	0.925834i	0.612831	+	0.790214i	$0.290031\pi$
$758$		0			0
$759$	−4.86481	−	44.3239i	−0.176581	−	1.60886i
$760$		0			0
$761$		−	13.1323i		−	0.476046i	−0.971260	−	0.238023i	$-0.923501\pi$
$761$		−	13.1323i		−	0.476046i	0.971260	−	0.238023i	$-0.0764993\pi$
$762$		0			0
$763$	3.18453	−	5.51577i	0.115288	−	0.199684i
$764$		0			0
$765$	8.73739	−	8.01391i	0.315901	−	0.289744i
$766$		0			0
$767$	−29.6033	−	51.2744i	−1.06891	−	1.85141i
$768$		0			0
$769$	20.9102	+	12.0725i	0.754042	+	0.435347i	0.827153	−	0.561977i	$-0.189959\pi$
$769$	20.9102	+	12.0725i	0.754042	+	0.435347i	−0.0731103	+	0.997324i	$0.523293\pi$
$770$		0			0
$771$	−13.6307	−	5.99384i	−0.490899	−	0.215863i
$772$		0			0
$773$	38.4914	+	22.2230i	1.38444	+	0.799306i	0.992681	−	0.120762i	$-0.0385338\pi$
$773$	38.4914	+	22.2230i	1.38444	+	0.799306i	0.391758	+	0.920068i	$0.371867\pi$
$774$		0			0
$775$	−5.55730	−	3.20851i	−0.199624	−	0.115253i
$776$		0			0
$777$	−2.01508	−	18.3596i	−0.0722905	−	0.658648i
$778$		0			0
$779$	−1.84365			−0.0660557
$780$		0			0
$781$	61.6460	−	35.5913i	2.20587	−	1.27356i
$782$		0			0
$783$	6.89188	+	1.36582i	0.246296	+	0.0488106i
$784$		0			0
$785$	30.6461	+	53.0807i	1.09381	+	1.89453i
$786$		0			0
$787$	9.97228	−	5.75750i	0.355473	−	0.205233i	−0.311620	−	0.950207i	$-0.600872\pi$
$787$	9.97228	−	5.75750i	0.355473	−	0.205233i	0.667093	+	0.744974i	$0.267538\pi$
$788$		0			0
$789$	−2.19731	−	20.0200i	−0.0782263	−	0.712729i
$790$		0			0
$791$	−5.12779	+	2.96053i	−0.182323	+	0.105264i
$792$		0			0
$793$	−17.8267	+	30.8768i	−0.633046	+	1.09647i
$794$		0			0
$795$	43.7179	−	4.79830i	1.55051	−	0.170178i
$796$		0			0
$797$	42.2817	+	24.4114i	1.49769	+	0.864695i	0.999996	−	0.00265569i	$-0.000845333\pi$
$797$	42.2817	+	24.4114i	1.49769	+	0.864695i	0.497698	+	0.867350i	$0.334179\pi$
$798$		0			0
$799$	0.772543			0.0273306
$800$		0			0
$801$	−1.38391	−	6.22854i	−0.0488980	−	0.220075i
$802$		0			0
$803$	35.2589			1.24426
$804$		0			0
$805$	−23.4056			−0.824938
$806$		0			0
$807$	−0.633913	−	5.77566i	−0.0223148	−	0.203313i
$808$		0			0
$809$	−19.8060			−0.696343			−0.348171	−	0.937431i	$-0.613197\pi$
$809$	−19.8060			−0.696343			−0.348171	+	0.937431i	$0.613197\pi$
$810$		0			0
$811$	42.7352	+	24.6732i	1.50063	+	0.866392i	1.00000		0.000733561i	$0.000233500\pi$
$811$	42.7352	+	24.6732i	1.50063	+	0.866392i	0.500635	+	0.865658i	$0.333100\pi$
$812$		0			0
$813$	−0.640846	−	5.83883i	−0.0224754	−	0.204777i
$814$		0			0
$815$	28.9921	−	50.2157i	1.01555	−	1.75898i
$816$		0			0
$817$	1.61545	−	0.932680i	0.0565174	−	0.0326303i
$818$		0			0
$819$	20.0065	−	4.44521i	0.699083	−	0.155328i
$820$		0			0
$821$	3.00276	−	1.73364i	0.104797	−	0.0605046i	−0.446685	−	0.894691i	$-0.647396\pi$
$821$	3.00276	−	1.73364i	0.104797	−	0.0605046i	0.551482	+	0.834186i	$0.314062\pi$
$822$		0			0
$823$	−2.25869	−	3.91216i	−0.0787329	−	0.136369i	0.823971	−	0.566633i	$-0.191754\pi$
$823$	−2.25869	−	3.91216i	−0.0787329	−	0.136369i	−0.902703	+	0.430263i	$0.858421\pi$
$824$		0			0
$825$	−17.3580	+	39.4741i	−0.604326	+	1.37431i
$826$		0			0
$827$	29.4294	−	16.9911i	1.02336	−	0.590837i	0.108284	−	0.994120i	$-0.465464\pi$
$827$	29.4294	−	16.9911i	1.02336	−	0.590837i	0.915075	+	0.403283i	$0.132131\pi$
$828$		0			0
$829$	−32.1140			−1.11537			−0.557683	−	0.830054i	$-0.688309\pi$
$829$	−32.1140			−1.11537			−0.557683	+	0.830054i	$0.688309\pi$
$830$		0			0
$831$	−42.2626	+	4.63856i	−1.46607	+	0.160910i
$832$		0			0
$833$	4.91001	+	2.83479i	0.170122	+	0.0982198i
$834$		0			0
$835$	−36.6726	−	21.1729i	−1.26911	−	0.732719i
$836$		0			0
$837$	−7.15511	−	1.41799i	−0.247317	−	0.0490129i
$838$		0			0
$839$	−38.5481	−	22.2558i	−1.33083	−	0.768354i	−0.345402	−	0.938455i	$-0.612257\pi$
$839$	−38.5481	−	22.2558i	−1.33083	−	0.768354i	−0.985427	+	0.170101i	$0.945591\pi$
$840$		0			0
$841$	−13.5859	−	23.5314i	−0.468478	−	0.811428i
$842$		0			0
$843$	−11.7080	−	15.9598i	−0.403243	−	0.549683i
$844$		0			0
$845$	−8.07162	+	13.9805i	−0.277672	+	0.480942i
$846$		0			0
$847$			29.8700i			1.02634i
$848$		0			0
$849$	−13.1141	+	1.43934i	−0.450073	+	0.0493982i
$850$		0			0
$851$	−27.2737	−	15.7465i	−0.934931	−	0.539782i
$852$		0			0
$853$	−13.4918	−	23.3684i	−0.461950	−	0.800120i	0.537108	−	0.843513i	$-0.319517\pi$
$853$	−13.4918	−	23.3684i	−0.461950	−	0.800120i	−0.999058	+	0.0433929i	$0.986183\pi$
$854$		0			0
$855$	−1.47905	−	1.61258i	−0.0505825	−	0.0551490i
$856$		0			0
$857$	56.1494			1.91803			0.959013	−	0.283361i	$-0.0914495\pi$
$857$	56.1494			1.91803			0.959013	+	0.283361i	$0.0914495\pi$
$858$		0			0
$859$	11.5654	−	20.0318i	0.394606	−	0.683478i	−0.598445	−	0.801164i	$-0.704214\pi$
$859$	11.5654	−	20.0318i	0.394606	−	0.683478i	0.993051	+	0.117686i	$0.0375478\pi$
$860$		0			0
$861$	17.4795	−	12.8229i	0.595701	−	0.437002i
$862$		0			0
$863$			1.39823i			0.0475965i	0.999717	+	0.0237982i	$0.00757593\pi$
$863$			1.39823i			0.0475965i	−0.999717	+	0.0237982i	$0.992424\pi$
$864$		0			0
$865$	−42.4940	+	24.5339i	−1.44484	+	0.834178i
$866$		0			0
$867$	−10.7148	+	24.3667i	−0.363893	+	0.827538i
$868$		0			0
$869$	45.4607	−	26.2467i	1.54215	−	0.890359i
$870$		0			0
$871$	−34.6280	−	4.63795i	−1.17332	−	0.157151i
$872$		0			0
$873$	7.02197	−	6.44053i	0.237658	−	0.217979i
$874$		0			0
$875$	−1.83864	−	1.06154i	−0.0621574	−	0.0358866i
$876$		0			0
$877$	−3.53778	−	6.12762i	−0.119462	−	0.206915i	0.800092	−	0.599877i	$-0.204784\pi$
$877$	−3.53778	−	6.12762i	−0.119462	−	0.206915i	−0.919555	+	0.392962i	$0.871450\pi$
$878$		0			0
$879$	1.50704	+	13.7308i	0.0508312	+	0.463129i
$880$		0			0
$881$	−39.3763	+	22.7339i	−1.32662	+	0.765925i	−0.984775	−	0.173831i	$-0.944385\pi$
$881$	−39.3763	+	22.7339i	−1.32662	+	0.765925i	−0.341845	+	0.939756i	$0.611052\pi$
$882$		0			0
$883$	−5.92073	−	3.41833i	−0.199248	−	0.115036i	0.397056	−	0.917794i	$-0.370032\pi$
$883$	−5.92073	−	3.41833i	−0.199248	−	0.115036i	−0.596305	+	0.802758i	$0.703365\pi$
$884$		0			0
$885$	−8.10946	−	73.8863i	−0.272596	−	2.48366i
$886$		0			0
$887$	−12.3293	+	7.11832i	−0.413977	+	0.239010i	−0.692497	−	0.721421i	$-0.743489\pi$
$887$	−12.3293	+	7.11832i	−0.413977	+	0.239010i	0.278520	+	0.960430i	$0.410156\pi$
$888$		0			0
$889$	25.2469	−	14.5763i	0.846752	−	0.488873i
$890$		0			0
$891$	−4.22616	+	48.8345i	−0.141582	+	1.63602i
$892$		0			0
$893$		−	0.142581i		−	0.00477129i
$894$		0			0
$895$	−49.4514			−1.65298
$896$		0			0
$897$	14.0664	−	31.9888i	0.469664	−	1.06807i
$898$		0			0
$899$	−0.949054	−	1.64381i	−0.0316527	−	0.0548241i
$900$		0			0
$901$	9.07985	−	5.24225i	0.302494	−	0.174645i
$902$		0			0
$903$	−8.82904	+	20.0783i	−0.293812	+	0.668165i
$904$		0			0
$905$	−11.5656	+	20.0322i	−0.384453	+	0.665892i
$906$		0			0
$907$	−6.39971	+	11.0846i	−0.212499	+	0.368059i	−0.952496	−	0.304551i	$-0.901494\pi$
$907$	−6.39971	+	11.0846i	−0.212499	+	0.368059i	0.739997	+	0.672610i	$0.234827\pi$
$908$		0			0
$909$	−3.79287	+	12.0492i	−0.125801	+	0.399647i
$910$		0			0
$911$		−	23.0571i		−	0.763917i	−0.924180	−	0.381958i	$-0.875250\pi$
$911$		−	23.0571i		−	0.763917i	0.924180	−	0.381958i	$-0.124750\pi$
$912$		0			0
$913$			78.6700i			2.60360i
$914$		0			0
$915$	−36.0907	+	26.4759i	−1.19312	+	0.875265i
$916$		0			0
$917$	2.80642	−	4.86087i	0.0926762	−	0.160520i
$918$		0			0
$919$	22.8421	−	13.1879i	0.753491	−	0.435028i	−0.0734629	−	0.997298i	$-0.523405\pi$
$919$	22.8421	−	13.1879i	0.753491	−	0.435028i	0.826954	+	0.562270i	$0.190072\pi$
$920$		0			0
$921$	17.6162	+	24.0136i	0.580473	+	0.791275i
$922$		0			0
$923$	55.7854			1.83620
$924$		0			0
$925$	15.2281	+	26.3758i	0.500695	+	0.867230i
$926$		0			0
$927$	−1.15118	+	3.65706i	−0.0378096	+	0.120114i
$928$		0			0
$929$	42.6683			1.39990			0.699951	−	0.714190i	$-0.253205\pi$
$929$	42.6683			1.39990			0.699951	+	0.714190i	$0.253205\pi$
$930$		0			0
$931$	0.523191	−	0.906194i	0.0171469	−	0.0296993i
$932$		0			0
$933$	−14.6558	+	1.60856i	−0.479809	+	0.0526618i
$934$		0			0
$935$			21.5239i			0.703908i
$936$		0			0
$937$		−	60.7057i		−	1.98317i	−0.129465	−	0.991584i	$-0.541326\pi$
$937$		−	60.7057i		−	1.98317i	0.129465	−	0.991584i	$-0.458674\pi$
$938$		0			0
$939$	3.06098	+	27.8890i	0.0998914	+	0.910123i
$940$		0			0
$941$	−6.18642			−0.201671			−0.100836	−	0.994903i	$-0.532152\pi$
$941$	−6.18642			−0.201671			−0.100836	+	0.994903i	$0.532152\pi$
$942$		0			0
$943$		−	36.9641i		−	1.20372i
$944$		0			0
$945$	25.2385	+	5.00173i	0.821007	+	0.162706i
$946$		0			0
$947$			9.92974i			0.322673i	0.986899	+	0.161337i	$0.0515805\pi$
$947$			9.92974i			0.322673i	−0.986899	+	0.161337i	$0.948420\pi$
$948$		0			0
$949$	23.9302	+	13.8161i	0.776806	+	0.448489i
$950$		0			0
$951$	−33.0971	+	24.2798i	−1.07325	+	0.787325i
$952$		0			0
$953$		−	52.6077i		−	1.70413i	−0.523435	−	0.852066i	$-0.675350\pi$
$953$		−	52.6077i		−	1.70413i	0.523435	−	0.852066i	$-0.324650\pi$
$954$		0			0
$955$	1.80268	+	3.12233i	0.0583333	+	0.101036i
$956$		0			0
$957$	−10.2846	+	7.54468i	−0.332453	+	0.243885i
$958$		0			0
$959$	22.8253	+	13.1782i	0.737068	+	0.425546i
$960$		0			0
$961$	−14.5147	−	25.1402i	−0.468216	−	0.810974i
$962$		0			0
$963$	−5.03252	−	22.6498i	−0.162171	−	0.729880i
$964$		0			0
$965$	−64.5363			−2.07750
$966$		0			0
$967$	0.472680	−	0.818705i	0.0152004	−	0.0263278i	−0.858325	−	0.513106i	$-0.828495\pi$
$967$	0.472680	−	0.818705i	0.0152004	−	0.0263278i	0.873526	+	0.486778i	$0.161828\pi$
$968$		0			0
$969$	−0.477506	−	0.209974i	−0.0153397	−	0.00674533i
$970$		0			0
$971$	−50.0989	−	28.9246i	−1.60775	−	0.928235i	−0.989872	−	0.141960i	$-0.954660\pi$
$971$	−50.0989	−	28.9246i	−1.60775	−	0.928235i	−0.617877	−	0.786275i	$-0.712007\pi$
$972$		0			0
$973$	16.7792	−	29.0625i	0.537918	−	0.931701i
$974$		0			0
$975$	−27.2486	+	19.9894i	−0.872654	+	0.640172i
$976$		0			0
$977$	33.8510	−	19.5439i	1.08299	−	0.625264i	0.151288	−	0.988490i	$-0.451658\pi$
$977$	33.8510	−	19.5439i	1.08299	−	0.625264i	0.931701	+	0.363225i	$0.118324\pi$
$978$		0			0
$979$	10.0315	+	5.79166i	0.320607	+	0.185102i
$980$		0			0
$981$	2.58936	+	11.6539i	0.0826719	+	0.372080i
$982$		0			0
$983$	16.2145			0.517164			0.258582	−	0.965989i	$-0.416745\pi$
$983$	16.2145			0.517164			0.258582	+	0.965989i	$0.416745\pi$
$984$		0			0
$985$	−28.8655	+	49.9965i	−0.919731	+	1.59302i
$986$		0			0
$987$	0.991669	+	1.35180i	0.0315652	+	0.0430282i
$988$		0			0
$989$	18.6996	+	32.3887i	0.594614	+	1.02990i
$990$		0			0
$991$			29.7836i			0.946107i	0.881034	+	0.473053i	$0.156848\pi$
$991$			29.7836i			0.946107i	−0.881034	+	0.473053i	$0.843152\pi$
$992$		0			0
$993$	−37.8414	−	16.6400i	−1.20086	−	0.528054i
$994$		0			0
$995$	−12.9114	−	22.3632i	−0.409319	−	0.708962i
$996$		0			0
$997$	24.2248			0.767207			0.383604	−	0.923498i	$-0.374683\pi$
$997$	24.2248			0.767207			0.383604	+	0.923498i	$0.374683\pi$
$998$		0			0
$999$	26.0445	+	22.8079i	0.824013	+	0.721612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.18	yes	36
3.2	odd	2	inner	804.2.o.d.365.1	✓	36
67.38	odd	6	inner	804.2.o.d.641.1	yes	36
201.38	even	6	inner	804.2.o.d.641.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.1	✓	36	3.2	odd	2	inner
804.2.o.d.365.18	yes	36	1.1	even	1	trivial
804.2.o.d.641.1	yes	36	67.38	odd	6	inner
804.2.o.d.641.18	yes	36	201.38	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72171 - 0.188968i) q^{3} -3.09374 q^{5} +(-1.38610 - 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +O(q^{10})\)	\(q+(1.72171 - 0.188968i) q^{3} -3.09374 q^{5} +(-1.38610 - 0.800262i) q^{7} +(2.92858 - 0.650697i) q^{9} +(-2.72317 + 4.71667i) q^{11} +(-3.69642 + 2.13413i) q^{13} +(-5.32653 + 0.584618i) q^{15} +(-1.10628 + 0.638709i) q^{17} +(0.117880 + 0.204175i) q^{19} +(-2.53768 - 1.11589i) q^{21} +(-4.09358 + 2.36343i) q^{23} +4.57123 q^{25} +(4.91921 - 1.67372i) q^{27} +(1.17099 + 0.676069i) q^{29} +(-1.21571 - 0.701891i) q^{31} +(-3.79721 + 8.63534i) q^{33} +(4.28822 + 2.47580i) q^{35} +(3.33128 + 5.76994i) q^{37} +(-5.96089 + 4.37286i) q^{39} +(-3.91001 + 6.77233i) q^{41} -7.91208i q^{43} +(-9.06028 + 2.01309i) q^{45} +(-0.523745 - 0.302384i) q^{47} +(-2.21916 - 3.84370i) q^{49} +(-1.78399 + 1.30872i) q^{51} -8.20758 q^{53} +(8.42478 - 14.5922i) q^{55} +(0.241539 + 0.329255i) q^{57} +13.8714i q^{59} +(7.23406 - 4.17658i) q^{61} +(-4.58002 - 1.44171i) q^{63} +(11.4358 - 6.60244i) q^{65} +(6.48268 + 4.99749i) q^{67} +(-6.60135 + 4.84270i) q^{69} +(-11.3188 - 6.53491i) q^{71} +(-3.23694 - 5.60654i) q^{73} +(7.87035 - 0.863817i) q^{75} +(7.54914 - 4.35850i) q^{77} +(-8.34701 - 4.81915i) q^{79} +(8.15319 - 3.81124i) q^{81} +(12.5094 - 7.22228i) q^{83} +(3.42253 - 1.97600i) q^{85} +(2.14386 + 0.942717i) q^{87} -2.12681i q^{89} +6.83145 q^{91} +(-2.22574 - 0.978724i) q^{93} +(-0.364692 - 0.631664i) q^{95} +(2.75058 - 1.58805i) q^{97} +(-4.90590 + 15.5851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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