LMFDB - Embedded newform 232.2.q.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(9,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("232.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.q (of order $14$, degree $6$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	232.9
Dual form			232.2.q.a.129.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884679 - 0.705508i) q^{3} +(0.449269 - 0.216356i) q^{5} +(2.01029 + 2.52083i) q^{7} +(-0.382647 + 1.67649i) q^{9} +O(q^{10})$	\(q+(0.884679 - 0.705508i) q^{3} +(0.449269 - 0.216356i) q^{5} +(2.01029 + 2.52083i) q^{7} +(-0.382647 + 1.67649i) q^{9} +(2.96468 - 0.676669i) q^{11} +(-1.36941 - 5.99976i) q^{13} +(0.244817 - 0.508369i) q^{15} -2.56896i q^{17} +(1.46765 + 1.17041i) q^{19} +(3.55693 + 0.811847i) q^{21} +(-3.94699 - 1.90077i) q^{23} +(-2.96242 + 3.71475i) q^{25} +(2.31714 + 4.81158i) q^{27} +(-5.30871 - 0.904210i) q^{29} +(2.42714 + 5.04001i) q^{31} +(2.14540 - 2.69024i) q^{33} +(1.44856 + 0.697590i) q^{35} +(-2.36573 - 0.539963i) q^{37} +(-5.44437 - 4.34174i) q^{39} -6.10666i q^{41} +(-2.83073 + 5.87807i) q^{43} +(0.190807 + 0.835981i) q^{45} +(-6.57220 + 1.50006i) q^{47} +(-0.755652 + 3.31073i) q^{49} +(-1.81243 - 2.27271i) q^{51} +(-0.169193 + 0.0814792i) q^{53} +(1.18554 - 0.945434i) q^{55} +2.12414 q^{57} +6.11377 q^{59} +(-8.61388 + 6.86934i) q^{61} +(-4.99537 + 2.40564i) q^{63} +(-1.91332 - 2.39922i) q^{65} +(2.07788 - 9.10378i) q^{67} +(-4.83283 + 1.10306i) q^{69} +(-1.82023 - 7.97497i) q^{71} +(-2.47425 + 5.13783i) q^{73} +5.37638i q^{75} +(7.66565 + 6.11315i) q^{77} +(-14.1195 - 3.22268i) q^{79} +(0.796613 + 0.383629i) q^{81} +(4.09672 - 5.13713i) q^{83} +(-0.555812 - 1.15416i) q^{85} +(-5.33443 + 2.94540i) q^{87} +(2.74003 + 5.68973i) q^{89} +(12.3715 - 15.5133i) q^{91} +(5.70301 + 2.74643i) q^{93} +(0.912596 + 0.208294i) q^{95} +(6.19837 + 4.94303i) q^{97} +5.22917i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	$ 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) $ 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.884679	−	0.705508i	0.510770	−	0.407325i	−0.333904	−	0.942607i	$-0.608366\pi$
$3$	0.884679	−	0.705508i	0.510770	−	0.407325i	0.844674	+	0.535282i	$0.179795\pi$
$4$		0			0
$5$	0.449269	−	0.216356i	0.200919	−	0.0967575i	−0.330719	−	0.943729i	$-0.607291\pi$
$5$	0.449269	−	0.216356i	0.200919	−	0.0967575i	0.531638	+	0.846972i	$0.321577\pi$
$6$		0			0
$7$	2.01029	+	2.52083i	0.759820	+	0.952784i	0.999838	−	0.0179842i	$-0.00572486\pi$
$7$	2.01029	+	2.52083i	0.759820	+	0.952784i	−0.240018	+	0.970768i	$0.577153\pi$
$8$		0			0
$9$	−0.382647	+	1.67649i	−0.127549	+	0.558829i
$10$		0			0
$11$	2.96468	−	0.676669i	0.893885	−	0.204023i	0.249182	−	0.968457i	$-0.419838\pi$
$11$	2.96468	−	0.676669i	0.893885	−	0.204023i	0.644703	+	0.764433i	$0.276981\pi$
$12$		0			0
$13$	−1.36941	−	5.99976i	−0.379805	−	1.66403i	−0.698068	−	0.716032i	$-0.745957\pi$
$13$	−1.36941	−	5.99976i	−0.379805	−	1.66403i	0.318263	−	0.948002i	$-0.396900\pi$
$14$		0			0
$15$	0.244817	−	0.508369i	0.0632116	−	0.131260i
$16$		0			0
$17$		−	2.56896i		−	0.623065i	−0.950235	−	0.311533i	$-0.899158\pi$
$17$		−	2.56896i		−	0.623065i	0.950235	−	0.311533i	$-0.100842\pi$
$18$		0			0
$19$	1.46765	+	1.17041i	0.336702	+	0.268511i	0.777215	−	0.629235i	$-0.216632\pi$
$19$	1.46765	+	1.17041i	0.336702	+	0.268511i	−0.440512	+	0.897746i	$0.645203\pi$
$20$		0			0
$21$	3.55693	+	0.811847i	0.776186	+	0.177159i
$22$		0			0
$23$	−3.94699	−	1.90077i	−0.823005	−	0.396338i	−0.0255178	−	0.999674i	$-0.508123\pi$
$23$	−3.94699	−	1.90077i	−0.823005	−	0.396338i	−0.797487	+	0.603336i	$0.793838\pi$
$24$		0			0
$25$	−2.96242	+	3.71475i	−0.592483	+	0.742951i
$26$		0			0
$27$	2.31714	+	4.81158i	0.445933	+	0.925989i
$28$		0			0
$29$	−5.30871	−	0.904210i	−0.985803	−	0.167908i
$29$	−5.30871	−	0.904210i	−0.985803	−	0.167908i
$30$		0			0
$31$	2.42714	+	5.04001i	0.435928	+	0.905213i	0.996997	+	0.0774441i	$0.0246759\pi$
$31$	2.42714	+	5.04001i	0.435928	+	0.905213i	−0.561069	+	0.827769i	$0.689610\pi$
$32$		0			0
$33$	2.14540	−	2.69024i	0.373466	−	0.468311i
$34$		0			0
$35$	1.44856	+	0.697590i	0.244851	+	0.117914i
$36$		0			0
$37$	−2.36573	−	0.539963i	−0.388924	−	0.0887694i	0.0235874	−	0.999722i	$-0.492491\pi$
$37$	−2.36573	−	0.539963i	−0.388924	−	0.0887694i	−0.412511	+	0.910952i	$0.635348\pi$
$38$		0			0
$39$	−5.44437	−	4.34174i	−0.871796	−	0.695234i
$40$		0			0
$41$		−	6.10666i		−	0.953700i	−0.878985	−	0.476850i	$-0.841779\pi$
$41$		−	6.10666i		−	0.953700i	0.878985	−	0.476850i	$-0.158221\pi$
$42$		0			0
$43$	−2.83073	+	5.87807i	−0.431682	+	0.896398i	0.565736	+	0.824586i	$0.308592\pi$
$43$	−2.83073	+	5.87807i	−0.431682	+	0.896398i	−0.997418	+	0.0718111i	$0.977122\pi$
$44$		0			0
$45$	0.190807	+	0.835981i	0.0284438	+	0.124621i
$46$		0			0
$47$	−6.57220	+	1.50006i	−0.958654	+	0.218806i	−0.673096	−	0.739555i	$-0.735036\pi$
$47$	−6.57220	+	1.50006i	−0.958654	+	0.218806i	−0.285558	+	0.958362i	$0.592179\pi$
$48$		0			0
$49$	−0.755652	+	3.31073i	−0.107950	+	0.472961i
$50$		0			0
$51$	−1.81243	−	2.27271i	−0.253790	−	0.318243i
$52$		0			0
$53$	−0.169193	+	0.0814792i	−0.0232405	+	0.0111920i	−0.445468	−	0.895298i	$-0.646963\pi$
$53$	−0.169193	+	0.0814792i	−0.0232405	+	0.0111920i	0.422227	+	0.906490i	$0.361248\pi$
$54$		0			0
$55$	1.18554	−	0.945434i	0.159858	−	0.127482i
$56$		0			0
$57$	2.12414			0.281349
$58$		0			0
$59$	6.11377			0.795945			0.397973	−	0.917397i	$-0.369714\pi$
$59$	6.11377			0.795945			0.397973	+	0.917397i	$0.369714\pi$
$60$		0			0
$61$	−8.61388	+	6.86934i	−1.10289	+	0.879529i	−0.993428	−	0.114461i	$-0.963486\pi$
$61$	−8.61388	+	6.86934i	−1.10289	+	0.879529i	−0.109467	+	0.993990i	$0.534914\pi$
$62$		0			0
$63$	−4.99537	+	2.40564i	−0.629358	+	0.303083i
$64$		0			0
$65$	−1.91332	−	2.39922i	−0.237318	−	0.297587i
$66$		0			0
$67$	2.07788	−	9.10378i	0.253853	−	1.11220i	−0.673845	−	0.738873i	$-0.735358\pi$
$67$	2.07788	−	9.10378i	0.253853	−	1.11220i	0.927698	−	0.373331i	$-0.121784\pi$
$68$		0			0
$69$	−4.83283	+	1.10306i	−0.581805	+	0.132793i
$70$		0			0
$71$	−1.82023	−	7.97497i	−0.216022	−	0.946454i	−0.960384	−	0.278678i	$-0.910104\pi$
$71$	−1.82023	−	7.97497i	−0.216022	−	0.946454i	0.744362	−	0.667776i	$-0.232754\pi$
$72$		0			0
$73$	−2.47425	+	5.13783i	−0.289589	+	0.601337i	−0.994114	−	0.108342i	$-0.965446\pi$
$73$	−2.47425	+	5.13783i	−0.289589	+	0.601337i	0.704525	+	0.709679i	$0.251160\pi$
$74$		0			0
$75$			5.37638i			0.620810i
$76$		0			0
$77$	7.66565	+	6.11315i	0.873582	+	0.696659i
$78$		0			0
$79$	−14.1195	−	3.22268i	−1.58856	−	0.362579i	−0.665249	−	0.746622i	$-0.731675\pi$
$79$	−14.1195	−	3.22268i	−1.58856	−	0.362579i	−0.923316	+	0.384042i	$0.874532\pi$
$80$		0			0
$81$	0.796613	+	0.383629i	0.0885126	+	0.0426254i
$82$		0			0
$83$	4.09672	−	5.13713i	0.449674	−	0.563873i	−0.504390	−	0.863476i	$-0.668283\pi$
$83$	4.09672	−	5.13713i	0.449674	−	0.563873i	0.954064	+	0.299603i	$0.0968542\pi$
$84$		0			0
$85$	−0.555812	−	1.15416i	−0.0602863	−	0.125186i
$86$		0			0
$87$	−5.33443	+	2.94540i	−0.571911	+	0.315780i
$88$		0			0
$89$	2.74003	+	5.68973i	0.290442	+	0.603110i	0.994226	−	0.107304i	$-0.0342219\pi$
$89$	2.74003	+	5.68973i	0.290442	+	0.603110i	−0.703784	+	0.710414i	$0.748508\pi$
$90$		0			0
$91$	12.3715	−	15.5133i	1.29688	−	1.62624i
$92$		0			0
$93$	5.70301	+	2.74643i	0.591375	+	0.284791i
$94$		0			0
$95$	0.912596	+	0.208294i	0.0936304	+	0.0213705i
$96$		0			0
$97$	6.19837	+	4.94303i	0.629349	+	0.501889i	0.885434	−	0.464765i	$-0.153861\pi$
$97$	6.19837	+	4.94303i	0.629349	+	0.501889i	−0.256085	+	0.966654i	$0.582433\pi$
$98$		0			0
$99$			5.22917i			0.525552i
$100$		0			0
$101$	6.53540	−	13.5709i	0.650297	−	1.35036i	−0.271408	−	0.962464i	$-0.587489\pi$
$101$	6.53540	−	13.5709i	0.650297	−	1.35036i	0.921705	−	0.387891i	$-0.126796\pi$
$102$		0			0
$103$	0.725283	+	3.17767i	0.0714643	+	0.313105i	0.998008	−	0.0630806i	$-0.0200925\pi$
$103$	0.725283	+	3.17767i	0.0714643	+	0.313105i	−0.926544	+	0.376186i	$0.877235\pi$
$104$		0			0
$105$	1.77367	−	0.404828i	0.173092	−	0.0395071i
$106$		0			0
$107$	0.776551	−	3.40229i	0.0750720	−	0.328912i	−0.923421	−	0.383788i	$-0.874619\pi$
$107$	0.776551	−	3.40229i	0.0750720	−	0.328912i	0.998493	+	0.0548762i	$0.0174764\pi$
$108$		0			0
$109$	8.12398	+	10.1871i	0.778136	+	0.975751i	1.00000		0.000673747i	$0.000214461\pi$
$109$	8.12398	+	10.1871i	0.778136	+	0.975751i	−0.221864	+	0.975078i	$0.571214\pi$
$110$		0			0
$111$	−2.47386	+	1.19135i	−0.234809	+	0.113078i
$112$		0			0
$113$	11.4963	−	9.16801i	1.08148	−	0.862453i	0.0904269	−	0.995903i	$-0.471177\pi$
$113$	11.4963	−	9.16801i	1.08148	−	0.862453i	0.991056	+	0.133450i	$0.0426054\pi$
$114$		0			0
$115$	−2.18450			−0.203706
$116$		0			0
$117$	10.5825			0.978354
$118$		0			0
$119$	6.47592	−	5.16438i	0.593647	−	0.473418i
$120$		0			0
$121$	−1.57920	+	0.760503i	−0.143564	+	0.0691366i
$122$		0			0
$123$	−4.30830	−	5.40243i	−0.388466	−	0.487121i
$124$		0			0
$125$	−1.08201	+	4.74060i	−0.0967780	+	0.424012i
$126$		0			0
$127$	6.83891	−	1.56094i	0.606855	−	0.138511i	0.0919582	−	0.995763i	$-0.470687\pi$
$127$	6.83891	−	1.56094i	0.606855	−	0.138511i	0.514897	+	0.857252i	$0.327830\pi$
$128$		0			0
$129$	1.64274	+	7.19731i	0.144635	+	0.633688i
$130$		0			0
$131$	−5.60098	+	11.6306i	−0.489360	+	1.01617i	0.499361	+	0.866394i	$0.333568\pi$
$131$	−5.60098	+	11.6306i	−0.489360	+	1.01617i	−0.988721	+	0.149772i	$0.952146\pi$
$132$		0			0
$133$			6.05258i			0.524825i
$134$		0			0
$135$	2.08203	+	1.66037i	0.179193	+	0.142901i
$136$		0			0
$137$	−16.8440	−	3.84453i	−1.43908	−	0.328461i	−0.569394	−	0.822065i	$-0.692822\pi$
$137$	−16.8440	−	3.84453i	−1.43908	−	0.328461i	−0.869687	+	0.493604i	$0.835679\pi$
$138$		0			0
$139$	17.2905	+	8.32666i	1.46656	+	0.706258i	0.985381	−	0.170364i	$-0.0544943\pi$
$139$	17.2905	+	8.32666i	1.46656	+	0.706258i	0.481179	+	0.876622i	$0.340209\pi$
$140$		0			0
$141$	−4.75598	+	5.96381i	−0.400526	+	0.502244i
$142$		0			0
$143$	−8.11971	−	16.8607i	−0.679004	−	1.40997i
$144$		0			0
$145$	−2.58067	+	0.742340i	−0.214313	+	0.0616480i
$146$		0			0
$147$	1.66724	+	3.46205i	0.137511	+	0.285545i
$148$		0			0
$149$	8.42867	−	10.5692i	0.690503	−	0.865864i	−0.305771	−	0.952105i	$-0.598914\pi$
$149$	8.42867	−	10.5692i	0.690503	−	0.865864i	0.996274	+	0.0862414i	$0.0274856\pi$
$150$		0			0
$151$	16.0846	+	7.74595i	1.30895	+	0.630356i	0.952665	−	0.304022i	$-0.0983295\pi$
$151$	16.0846	+	7.74595i	1.30895	+	0.630356i	0.356283	+	0.934378i	$0.384044\pi$
$152$		0			0
$153$	4.30683	+	0.983007i	0.348187	+	0.0794714i
$154$		0			0
$155$	2.18088	+	1.73919i	0.175172	+	0.139695i
$156$		0			0
$157$		−	19.3561i		−	1.54479i	−0.635145	−	0.772393i	$-0.719059\pi$
$157$		−	19.3561i		−	1.54479i	0.635145	−	0.772393i	$-0.280941\pi$
$158$		0			0
$159$	−0.0921976	+	0.191450i	−0.00731174	+	0.0151830i
$160$		0			0
$161$	−3.14310	−	13.7708i	−0.247711	−	1.08529i
$162$		0			0
$163$	10.1995	−	2.32796i	0.798883	−	0.182340i	0.196455	−	0.980513i	$-0.437057\pi$
$163$	10.1995	−	2.32796i	0.798883	−	0.182340i	0.602428	+	0.798173i	$0.294200\pi$
$164$		0			0
$165$	0.381808	−	1.67281i	0.0297237	−	0.130228i
$166$		0			0
$167$	−10.5074	−	13.1758i	−0.813085	−	1.01958i	−0.999313	−	0.0370695i	$-0.988198\pi$
$167$	−10.5074	−	13.1758i	−0.813085	−	1.01958i	0.186228	−	0.982507i	$-0.440374\pi$
$168$		0			0
$169$	−22.4093	+	10.7917i	−1.72379	+	0.830133i
$170$		0			0
$171$	−2.52377	+	2.01264i	−0.192998	+	0.153911i
$172$		0			0
$173$	9.74382			0.740809			0.370404	−	0.928871i	$-0.379219\pi$
$173$	9.74382			0.740809			0.370404	+	0.928871i	$0.379219\pi$
$174$		0			0
$175$	−15.3196			−1.15805
$176$		0			0
$177$	5.40873	−	4.31332i	0.406545	−	0.324209i
$178$		0			0
$179$	−19.4501	+	9.36669i	−1.45377	+	0.700099i	−0.983245	−	0.182287i	$-0.941650\pi$
$179$	−19.4501	+	9.36669i	−1.45377	+	0.700099i	−0.470526	+	0.882386i	$0.655936\pi$
$180$		0			0
$181$	−0.00986916	−	0.0123755i	−0.000733569	−	0.000919866i	0.781465	−	0.623950i	$-0.214473\pi$
$181$	−0.00986916	−	0.0123755i	−0.000733569	−	0.000919866i	−0.782198	+	0.623030i	$0.785902\pi$
$182$		0			0
$183$	−2.77415	+	12.1543i	−0.205071	+	0.898474i
$184$		0			0
$185$	−1.17967	+	0.269253i	−0.0867313	+	0.0197959i
$186$		0			0
$187$	−1.73834	−	7.61616i	−0.127120	−	0.556949i
$188$		0			0
$189$	−7.47105	+	15.5138i	−0.543439	+	1.12846i
$190$		0			0
$191$			13.8382i			1.00129i	0.865651	+	0.500647i	$0.166905\pi$
$191$			13.8382i			1.00129i	−0.865651	+	0.500647i	$0.833095\pi$
$192$		0			0
$193$	−2.45404	−	1.95703i	−0.176646	−	0.140870i	0.531176	−	0.847262i	$-0.321750\pi$
$193$	−2.45404	−	1.95703i	−0.176646	−	0.140870i	−0.707821	+	0.706391i	$0.750322\pi$
$194$		0			0
$195$	−3.38534	−	0.772683i	−0.242430	−	0.0553330i
$196$		0			0
$197$	0.549977	+	0.264855i	0.0391842	+	0.0188701i	0.453373	−	0.891321i	$-0.350220\pi$
$197$	0.549977	+	0.264855i	0.0391842	+	0.0188701i	−0.414189	+	0.910191i	$0.635935\pi$
$198$		0			0
$199$	−7.78476	+	9.76178i	−0.551847	+	0.691994i	−0.977027	−	0.213115i	$-0.931639\pi$
$199$	−7.78476	+	9.76178i	−0.551847	+	0.691994i	0.425180	+	0.905109i	$0.360211\pi$
$200$		0			0
$201$	−4.58454	−	9.51989i	−0.323368	−	0.671481i
$202$		0			0
$203$	−8.39271	−	15.2001i	−0.589053	−	1.06684i
$204$		0			0
$205$	−1.32121	−	2.74353i	−0.0922776	−	0.191616i
$206$		0			0
$207$	4.69692	−	5.88975i	0.326459	−	0.409366i
$208$		0			0
$209$	5.14310	+	2.47679i	0.355756	+	0.171323i
$210$		0			0
$211$	13.7015	+	3.12728i	0.943250	+	0.215291i	0.666376	−	0.745616i	$-0.267845\pi$
$211$	13.7015	+	3.12728i	0.943250	+	0.215291i	0.276874	+	0.960906i	$0.410702\pi$
$212$		0			0
$213$	−7.23673	−	5.77110i	−0.495852	−	0.395429i
$214$		0			0
$215$			3.25328i			0.221872i
$216$		0			0
$217$	−7.82574	+	16.2503i	−0.531246	+	1.10314i
$218$		0			0
$219$	1.43586	+	6.29093i	0.0970267	+	0.425102i
$220$		0			0
$221$	−15.4132	+	3.51796i	−1.03680	+	0.236643i
$222$		0			0
$223$	0.433198	−	1.89796i	0.0290091	−	0.127097i	−0.958350	−	0.285596i	$-0.907808\pi$
$223$	0.433198	−	1.89796i	0.0290091	−	0.127097i	0.987359	+	0.158499i	$0.0506655\pi$
$224$		0			0
$225$	−5.09417	−	6.38789i	−0.339612	−	0.425859i
$226$		0			0
$227$	5.13778	−	2.47422i	0.341007	−	0.164220i	−0.255540	−	0.966798i	$-0.582253\pi$
$227$	5.13778	−	2.47422i	0.341007	−	0.164220i	0.596547	+	0.802578i	$0.296539\pi$
$228$		0			0
$229$	−12.5753	+	10.0285i	−0.830999	+	0.662700i	−0.943654	−	0.330934i	$-0.892636\pi$
$229$	−12.5753	+	10.0285i	−0.830999	+	0.662700i	0.112654	+	0.993634i	$0.464065\pi$
$230$		0			0
$231$	11.0945			0.729966
$232$		0			0
$233$	30.3854			1.99061			0.995305	−	0.0967850i	$-0.0308559\pi$
$233$	30.3854			1.99061			0.995305	+	0.0967850i	$0.0308559\pi$
$234$		0			0
$235$	−2.62813	+	2.09587i	−0.171441	+	0.136719i
$236$		0			0
$237$	−14.7648	+	7.11037i	−0.959079	+	0.461868i
$238$		0			0
$239$	15.6603	+	19.6374i	1.01298	+	1.27024i	0.962433	+	0.271519i	$0.0875261\pi$
$239$	15.6603	+	19.6374i	1.01298	+	1.27024i	0.0505504	+	0.998722i	$0.483902\pi$
$240$		0			0
$241$	6.10459	−	26.7460i	0.393231	−	1.72286i	−0.259919	−	0.965631i	$-0.583696\pi$
$241$	6.10459	−	26.7460i	0.393231	−	1.72286i	0.653150	−	0.757229i	$-0.273447\pi$
$242$		0			0
$243$	−14.6443	+	3.34246i	−0.939430	+	0.214419i
$244$		0			0
$245$	0.376806	+	1.65090i	0.0240733	+	0.105472i
$246$		0			0
$247$	5.01239	−	10.4083i	0.318931	−	0.662266i
$248$		0			0
$249$		−	7.43498i		−	0.471173i
$250$		0			0
$251$	−2.52803	−	2.01603i	−0.159568	−	0.127251i	0.540451	−	0.841375i	$-0.318254\pi$
$251$	−2.52803	−	2.01603i	−0.159568	−	0.127251i	−0.700019	+	0.714124i	$0.746825\pi$
$252$		0			0
$253$	−12.9878	−	2.96437i	−0.816534	−	0.186369i
$254$		0			0
$255$	−1.30598	−	0.628927i	−0.0817837	−	0.0393850i
$256$		0			0
$257$	−18.7866	+	23.5576i	−1.17187	+	1.46948i	−0.318703	+	0.947855i	$0.603247\pi$
$257$	−18.7866	+	23.5576i	−1.17187	+	1.46948i	−0.853172	+	0.521630i	$0.825324\pi$
$258$		0			0
$259$	−3.39466	−	7.04909i	−0.210934	−	0.438009i
$260$		0			0
$261$	3.54726	−	8.55399i	0.219570	−	0.529478i
$262$		0			0
$263$	5.01350	+	10.4106i	0.309146	+	0.641947i	0.996428	−	0.0844426i	$-0.0269110\pi$
$263$	5.01350	+	10.4106i	0.309146	+	0.641947i	−0.687283	+	0.726390i	$0.741197\pi$
$264$		0			0
$265$	−0.0583847	+	0.0732121i	−0.00358654	+	0.00449738i
$266$		0			0
$267$	6.43820	+	3.10047i	0.394011	+	0.189746i
$268$		0			0
$269$	−3.61113	−	0.824216i	−0.220174	−	0.0502533i	0.111011	−	0.993819i	$-0.464591\pi$
$269$	−3.61113	−	0.824216i	−0.220174	−	0.0502533i	−0.331185	+	0.943566i	$0.607448\pi$
$270$		0			0
$271$	6.96690	+	5.55592i	0.423209	+	0.337498i	0.811824	−	0.583902i	$-0.198475\pi$
$271$	6.96690	+	5.55592i	0.423209	+	0.337498i	−0.388615	+	0.921400i	$0.627046\pi$
$272$		0			0
$273$		−	22.4525i		−	1.35889i
$274$		0			0
$275$	−6.26896	+	13.0176i	−0.378033	+	0.784993i
$276$		0			0
$277$	−5.47276	−	23.9777i	−0.328826	−	1.44068i	−0.821371	−	0.570394i	$-0.806790\pi$
$277$	−5.47276	−	23.9777i	−0.328826	−	1.44068i	0.492545	−	0.870287i	$-0.336067\pi$
$278$		0			0
$279$	−9.37825	+	2.14053i	−0.561461	+	0.128150i
$280$		0			0
$281$	−2.92059	+	12.7960i	−0.174228	+	0.763342i	0.809999	+	0.586431i	$0.199468\pi$
$281$	−2.92059	+	12.7960i	−0.174228	+	0.763342i	−0.984227	+	0.176911i	$0.943390\pi$
$282$		0			0
$283$	−12.8043	−	16.0561i	−0.761138	−	0.954437i	0.238723	−	0.971088i	$-0.423271\pi$
$283$	−12.8043	−	16.0561i	−0.761138	−	0.954437i	−0.999861	+	0.0166504i	$0.994700\pi$
$284$		0			0
$285$	0.954308	−	0.459571i	0.0565283	−	0.0272226i
$286$		0			0
$287$	15.3938	−	12.2762i	0.908670	−	0.724640i
$288$		0			0
$289$	10.4004			0.611789
$290$		0			0
$291$	8.97092			0.525885
$292$		0			0
$293$	15.6075	−	12.4466i	0.911799	−	0.727136i	−0.0506158	−	0.998718i	$-0.516118\pi$
$293$	15.6075	−	12.4466i	0.911799	−	0.727136i	0.962415	+	0.271583i	$0.0875470\pi$
$294$		0			0
$295$	2.74672	−	1.32275i	0.159921	−	0.0770137i
$296$		0			0
$297$	10.1254	+	12.6969i	0.587536	+	0.736747i
$298$		0			0
$299$	−5.99914	+	26.2839i	−0.346939	+	1.52004i
$300$		0			0
$301$	−20.5082	+	4.68087i	−1.18207	+	0.269801i
$302$		0			0
$303$	−3.79265	−	16.6167i	−0.217882	−	0.954604i
$304$		0			0
$305$	−2.38372	+	4.94985i	−0.136491	+	0.283427i
$306$		0			0
$307$			23.2931i			1.32941i	0.747107	+	0.664704i	$0.231442\pi$
$307$			23.2931i			1.32941i	−0.747107	+	0.664704i	$0.768558\pi$
$308$		0			0
$309$	2.88352	+	2.29953i	0.164038	+	0.130816i
$310$		0			0
$311$	13.9338	+	3.18030i	0.790113	+	0.180338i	0.598490	−	0.801131i	$-0.295768\pi$
$311$	13.9338	+	3.18030i	0.790113	+	0.180338i	0.191623	+	0.981469i	$0.438625\pi$
$312$		0			0
$313$	9.70690	+	4.67460i	0.548666	+	0.264224i	0.687615	−	0.726076i	$-0.258658\pi$
$313$	9.70690	+	4.67460i	0.548666	+	0.264224i	−0.138948	+	0.990300i	$0.544372\pi$
$314$		0			0
$315$	−1.72379	+	2.16156i	−0.0971244	+	0.121790i
$316$		0			0
$317$	−3.09045	−	6.41738i	−0.173577	−	0.360436i	0.795972	−	0.605333i	$-0.206960\pi$
$317$	−3.09045	−	6.41738i	−0.173577	−	0.360436i	−0.969549	+	0.244897i	$0.921246\pi$
$318$		0			0
$319$	−16.3505	+	0.911545i	−0.915452	+	0.0510367i
$320$		0			0
$321$	−1.71335	−	3.55780i	−0.0956297	−	0.198577i
$322$		0			0
$323$	3.00675	−	3.77035i	0.167300	−	0.209788i
$324$		0			0
$325$	26.3444	+	12.6868i	1.46132	+	0.703736i
$326$		0			0
$327$	14.3742	+	3.28082i	0.794897	+	0.181430i
$328$		0			0
$329$	−16.9935	−	13.5518i	−0.936879	−	0.747136i
$330$		0			0
$331$		−	15.7331i		−	0.864769i	−0.901689	−	0.432385i	$-0.857672\pi$
$331$		−	15.7331i		−	0.864769i	0.901689	−	0.432385i	$-0.142328\pi$
$332$		0			0
$333$	1.81048	−	3.75950i	0.0992138	−	0.206019i
$334$		0			0
$335$	−1.03614	−	4.53960i	−0.0566101	−	0.248025i
$336$		0			0
$337$	14.6927	−	3.35351i	0.800362	−	0.182677i	0.197270	−	0.980349i	$-0.436792\pi$
$337$	14.6927	−	3.35351i	0.800362	−	0.182677i	0.603092	+	0.797672i	$0.293935\pi$
$338$		0			0
$339$	3.70245	−	16.2215i	0.201089	−	0.881031i
$340$		0			0
$341$	10.6061	+	13.2997i	0.574354	+	0.720217i
$342$		0			0
$343$	10.4699	−	5.04202i	0.565319	−	0.272243i
$344$		0			0
$345$	−1.93259	+	1.54119i	−0.104047	+	0.0829746i
$346$		0			0
$347$	−15.1733			−0.814548			−0.407274	−	0.913306i	$-0.633521\pi$
$347$	−15.1733			−0.814548			−0.407274	+	0.913306i	$0.633521\pi$
$348$		0			0
$349$	16.5059			0.883540			0.441770	−	0.897128i	$-0.354351\pi$
$349$	16.5059			0.883540			0.441770	+	0.897128i	$0.354351\pi$
$350$		0			0
$351$	25.6952	−	20.4913i	1.37151	−	1.09374i
$352$		0			0
$353$	21.5048	−	10.3562i	1.14459	−	0.551204i	0.237184	−	0.971465i	$-0.423776\pi$
$353$	21.5048	−	10.3562i	1.14459	−	0.551204i	0.907404	+	0.420260i	$0.138061\pi$
$354$		0			0
$355$	−2.54321	−	3.18908i	−0.134979	−	0.169259i
$356$		0			0
$357$	2.08561	−	9.13764i	0.110382	−	0.483615i
$358$		0			0
$359$	−24.4200	+	5.57371i	−1.28884	+	0.294169i	−0.811398	−	0.584494i	$-0.801293\pi$
$359$	−24.4200	+	5.57371i	−1.28884	+	0.294169i	−0.477442	+	0.878663i	$0.658436\pi$
$360$		0			0
$361$	−3.44376	−	15.0881i	−0.181251	−	0.794111i
$362$		0			0
$363$	−0.860545	+	1.78694i	−0.0451669	+	0.0937900i
$364$		0			0
$365$			2.84358i			0.148840i
$366$		0			0
$367$	18.1136	+	14.4451i	0.945523	+	0.754030i	0.969349	−	0.245686i	$-0.0790133\pi$
$367$	18.1136	+	14.4451i	0.945523	+	0.754030i	−0.0238259	+	0.999716i	$0.507585\pi$
$368$		0			0
$369$	10.2377	+	2.33669i	0.532955	+	0.121643i
$370$		0			0
$371$	−0.545524	−	0.262710i	−0.0283222	−	0.0136392i
$372$		0			0
$373$	9.49553	−	11.9070i	0.491660	−	0.616522i	−0.472666	−	0.881242i	$-0.656708\pi$
$373$	9.49553	−	11.9070i	0.491660	−	0.616522i	0.964325	+	0.264720i	$0.0852796\pi$
$374$		0			0
$375$	2.38730	+	4.95728i	0.123280	+	0.255993i
$376$		0			0
$377$	1.84473	+	33.0892i	0.0950087	+	1.70418i
$378$		0			0
$379$	3.10982	+	6.45761i	0.159741	+	0.331705i	0.965442	−	0.260616i	$-0.0839258\pi$
$379$	3.10982	+	6.45761i	0.159741	+	0.331705i	−0.805702	+	0.592322i	$0.798212\pi$
$380$		0			0
$381$	4.94899	−	6.20583i	0.253544	−	0.317935i
$382$		0			0
$383$	22.9725	+	11.0630i	1.17384	+	0.565292i	0.916111	−	0.400924i	$-0.131311\pi$
$383$	22.9725	+	11.0630i	1.17384	+	0.565292i	0.257731	+	0.966217i	$0.417025\pi$
$384$		0			0
$385$	4.76656	+	1.08794i	0.242926	+	0.0554463i
$386$		0			0
$387$	−8.77134	−	6.99491i	−0.445872	−	0.355571i
$388$		0			0
$389$		−	8.78365i		−	0.445349i	−0.974893	−	0.222674i	$-0.928521\pi$
$389$		−	8.78365i		−	0.445349i	0.974893	−	0.222674i	$-0.0714787\pi$
$390$		0			0
$391$	−4.88301	+	10.1397i	−0.246945	+	0.512786i
$392$		0			0
$393$	3.25038	+	14.2409i	0.163960	+	0.718356i
$394$		0			0
$395$	−7.04068	+	1.60699i	−0.354255	+	0.0808564i
$396$		0			0
$397$	−1.47770	+	6.47421i	−0.0741635	+	0.324931i	−0.998377	−	0.0569437i	$-0.981864\pi$
$397$	−1.47770	+	6.47421i	−0.0741635	+	0.324931i	0.924214	+	0.381875i	$0.124722\pi$
$398$		0			0
$399$	4.27014	+	5.35459i	0.213774	+	0.268065i
$400$		0			0
$401$	−31.4070	+	15.1248i	−1.56839	+	0.755298i	−0.997823	−	0.0659520i	$-0.978992\pi$
$401$	−31.4070	+	15.1248i	−1.56839	+	0.755298i	−0.570569	+	0.821250i	$0.693277\pi$
$402$		0			0
$403$	26.9151	−	21.4641i	1.34074	−	1.06920i
$404$		0			0
$405$	0.440894			0.0219082
$406$		0			0
$407$	−7.37902			−0.365764
$408$		0			0
$409$	−26.1095	+	20.8216i	−1.29103	+	1.02956i	−0.293749	+	0.955883i	$0.594903\pi$
$409$	−26.1095	+	20.8216i	−1.29103	+	1.02956i	−0.997282	+	0.0736798i	$0.976526\pi$
$410$		0			0
$411$	−17.6139	+	8.48240i	−0.868829	+	0.418406i
$412$		0			0
$413$	12.2905	+	15.4118i	0.604775	+	0.758364i
$414$		0			0
$415$	0.729078	−	3.19430i	0.0357890	−	0.156802i
$416$		0			0
$417$	21.1711	−	4.83216i	1.03675	−	0.236632i
$418$		0			0
$419$	−4.92977	−	21.5987i	−0.240835	−	1.05517i	−0.940259	−	0.340460i	$-0.889417\pi$
$419$	−4.92977	−	21.5987i	−0.240835	−	1.05517i	0.699424	−	0.714707i	$-0.253440\pi$
$420$		0			0
$421$	−10.7328	+	22.2868i	−0.523083	+	1.08619i	0.457340	+	0.889292i	$0.348802\pi$
$421$	−10.7328	+	22.2868i	−0.523083	+	1.08619i	−0.980423	+	0.196902i	$0.936912\pi$
$422$		0			0
$423$		−	11.5922i		−	0.563632i
$424$		0			0
$425$	9.54307	+	7.61034i	0.462907	+	0.369156i
$426$		0			0
$427$	−34.6329	−	7.90473i	−1.67600	−	0.382537i
$428$		0			0
$429$	−19.0787	−	9.18783i	−0.921130	−	0.443593i
$430$		0			0
$431$	15.0340	−	18.8521i	0.724164	−	0.908073i	−0.274402	−	0.961615i	$-0.588480\pi$
$431$	15.0340	−	18.8521i	0.724164	−	0.908073i	0.998566	+	0.0535422i	$0.0170512\pi$
$432$		0			0
$433$	1.71721	+	3.56582i	0.0825238	+	0.171362i	0.938147	−	0.346236i	$-0.112540\pi$
$433$	1.71721	+	3.56582i	0.0825238	+	0.171362i	−0.855624	+	0.517598i	$0.826826\pi$
$434$		0			0
$435$	−1.75934	+	2.47742i	−0.0843538	+	0.118783i
$436$		0			0
$437$	−3.56812	−	7.40928i	−0.170686	−	0.354434i
$438$		0			0
$439$	1.06081	−	1.33021i	0.0506297	−	0.0634877i	−0.755872	−	0.654720i	$-0.772787\pi$
$439$	1.06081	−	1.33021i	0.0506297	−	0.0634877i	0.806502	+	0.591232i	$0.201358\pi$
$440$		0			0
$441$	−5.26124	−	2.53368i	−0.250535	−	0.120651i
$442$		0			0
$443$	10.0108	+	2.28491i	0.475629	+	0.108559i	0.453614	−	0.891198i	$-0.350135\pi$
$443$	10.0108	+	2.28491i	0.475629	+	0.108559i	0.0220155	+	0.999758i	$0.492992\pi$
$444$		0			0
$445$	2.46202	+	1.96339i	0.116711	+	0.0930738i
$446$		0			0
$447$		−	15.2969i		−	0.723517i
$448$		0			0
$449$	−0.781405	+	1.62260i	−0.0368768	+	0.0765755i	−0.918593	−	0.395204i	$-0.870674\pi$
$449$	−0.781405	+	1.62260i	−0.0368768	+	0.0765755i	0.881717	+	0.471780i	$0.156388\pi$
$450$		0			0
$451$	−4.13219	−	18.1043i	−0.194577	−	0.852498i
$452$		0			0
$453$	19.6946	−	4.49516i	0.925332	−	0.211201i
$454$		0			0
$455$	2.20170	−	9.64629i	0.103217	−	0.452225i
$456$		0			0
$457$	−19.9146	−	24.9722i	−0.931567	−	1.16815i	−0.985512	−	0.169604i	$-0.945751\pi$
$457$	−19.9146	−	24.9722i	−0.931567	−	1.16815i	0.0539450	−	0.998544i	$-0.482820\pi$
$458$		0			0
$459$	12.3608	−	5.95264i	0.576952	−	0.277845i
$460$		0			0
$461$	−18.0616	+	14.4037i	−0.841214	+	0.670846i	−0.946184	−	0.323630i	$-0.895097\pi$
$461$	−18.0616	+	14.4037i	−0.841214	+	0.670846i	0.104970	+	0.994475i	$0.466525\pi$
$462$		0			0
$463$	−32.1958			−1.49626			−0.748132	−	0.663550i	$-0.769049\pi$
$463$	−32.1958			−1.49626			−0.748132	+	0.663550i	$0.769049\pi$
$464$		0			0
$465$	3.15639			0.146374
$466$		0			0
$467$	−29.6432	+	23.6396i	−1.37172	+	1.09391i	−0.386563	+	0.922263i	$0.626338\pi$
$467$	−29.6432	+	23.6396i	−1.37172	+	1.09391i	−0.985158	+	0.171649i	$0.945091\pi$
$468$		0			0
$469$	27.1262	−	13.0633i	1.25257	−	0.603207i
$470$		0			0
$471$	−13.6559	−	17.1240i	−0.629231	−	0.789031i
$472$		0			0
$473$	−4.41470	+	19.3421i	−0.202988	+	0.889350i
$474$		0			0
$475$	−8.69559	+	1.98471i	−0.398981	+	0.0910648i
$476$		0			0
$477$	−0.0718574	−	0.314828i	−0.00329013	−	0.0144150i
$478$		0			0
$479$	−14.8601	+	30.8572i	−0.678974	+	1.40990i	0.221573	+	0.975144i	$0.428881\pi$
$479$	−14.8601	+	30.8572i	−0.678974	+	1.40990i	−0.900547	+	0.434759i	$0.856833\pi$
$480$		0			0
$481$			14.9333i			0.680898i
$482$		0			0
$483$	−12.4961	−	9.96527i	−0.568590	−	0.453435i
$484$		0			0
$485$	3.85419	+	0.879693i	0.175010	+	0.0399448i
$486$		0			0
$487$	25.3197	+	12.1933i	1.14735	+	0.552533i	0.908236	−	0.418459i	$-0.137430\pi$
$487$	25.3197	+	12.1933i	1.14735	+	0.552533i	0.239111	+	0.970992i	$0.423144\pi$
$488$		0			0
$489$	7.38085	−	9.25529i	0.333774	−	0.418539i
$490$		0			0
$491$	−2.93180	−	6.08795i	−0.132310	−	0.274745i	0.824279	−	0.566183i	$-0.191581\pi$
$491$	−2.93180	−	6.08795i	−0.132310	−	0.274745i	−0.956590	+	0.291438i	$0.905866\pi$
$492$		0			0
$493$	−2.32288	+	13.6379i	−0.104617	+	0.614220i
$494$		0			0
$495$	1.13136	+	2.34930i	0.0508511	+	0.105593i
$496$		0			0
$497$	16.4443	−	20.6205i	0.737629	−	0.924957i
$498$		0			0
$499$	−19.7715	−	9.52144i	−0.885092	−	0.426238i	−0.0646105	−	0.997911i	$-0.520580\pi$
$499$	−19.7715	−	9.52144i	−0.885092	−	0.426238i	−0.820482	+	0.571673i	$0.806295\pi$
$500$		0			0
$501$	−18.5913	−	4.24335i	−0.830599	−	0.189579i
$502$		0			0
$503$	−15.9422	−	12.7134i	−0.710826	−	0.566865i	0.199930	−	0.979810i	$-0.435929\pi$
$503$	−15.9422	−	12.7134i	−0.710826	−	0.566865i	−0.910756	+	0.412946i	$0.864500\pi$
$504$		0			0
$505$		−	7.51096i		−	0.334233i
$506$		0			0
$507$	−12.2114	+	25.3571i	−0.542325	+	1.12615i
$508$		0			0
$509$	3.82202	+	16.7453i	0.169408	+	0.742225i	0.986236	+	0.165343i	$0.0528733\pi$
$509$	3.82202	+	16.7453i	0.169408	+	0.742225i	−0.816828	+	0.576881i	$0.804270\pi$
$510$		0			0
$511$	−17.9256	+	4.09139i	−0.792980	+	0.180993i
$512$		0			0
$513$	−2.23079	+	9.77373i	−0.0984918	+	0.431521i
$514$		0			0
$515$	1.01336	+	1.27071i	0.0446538	+	0.0559941i
$516$		0			0
$517$	−18.4694	+	8.89441i	−0.812285	+	0.391176i
$518$		0			0
$519$	8.62015	−	6.87434i	0.378383	−	0.301750i
$520$		0			0
$521$	8.50737			0.372715			0.186357	−	0.982482i	$-0.440332\pi$
$521$	8.50737			0.372715			0.186357	+	0.982482i	$0.440332\pi$
$522$		0			0
$523$	−9.75899			−0.426731			−0.213365	−	0.976972i	$-0.568442\pi$
$523$	−9.75899			−0.426731			−0.213365	+	0.976972i	$0.568442\pi$
$524$		0			0
$525$	−13.5529	+	10.8081i	−0.591498	+	0.471704i
$526$		0			0
$527$	12.9476	−	6.23524i	0.564007	−	0.271611i
$528$		0			0
$529$	−2.37445	−	2.97746i	−0.103237	−	0.129455i
$530$		0			0
$531$	−2.33942	+	10.2497i	−0.101522	+	0.444797i
$532$		0			0
$533$	−36.6385	+	8.36249i	−1.58699	+	0.362220i
$534$		0			0
$535$	−0.387228	−	1.69656i	−0.0167413	−	0.0733485i
$536$		0			0
$537$	−10.5989	+	22.0088i	−0.457374	+	0.949748i
$538$		0			0
$539$			10.3266i			0.444797i
$540$		0			0
$541$	19.9775	+	15.9315i	0.858901	+	0.684950i	0.950459	−	0.310849i	$-0.100613\pi$
$541$	19.9775	+	15.9315i	0.858901	+	0.684950i	−0.0915587	+	0.995800i	$0.529185\pi$
$542$		0			0
$543$	−0.0174621	−	0.00398561i	−0.000749369	−	0.000171039i
$544$		0			0
$545$	5.85390	+	2.81909i	0.250754	+	0.120757i
$546$		0			0
$547$	9.96032	−	12.4898i	0.425873	−	0.534027i	−0.521886	−	0.853015i	$-0.674771\pi$
$547$	9.96032	−	12.4898i	0.425873	−	0.534027i	0.947759	+	0.318988i	$0.103343\pi$
$548$		0			0
$549$	−8.22028	−	17.0696i	−0.350833	−	0.728512i
$550$		0			0
$551$	−6.73304	−	7.54045i	−0.286837	−	0.321234i
$552$		0			0
$553$	−20.2605	−	42.0713i	−0.861563	−	1.78905i
$554$		0			0
$555$	−0.853673	+	1.07047i	−0.0362364	+	0.0454390i
$556$		0			0
$557$	−13.5258	−	6.51370i	−0.573108	−	0.275994i	0.124800	−	0.992182i	$-0.460171\pi$
$557$	−13.5258	−	6.51370i	−0.573108	−	0.275994i	−0.697908	+	0.716188i	$0.745885\pi$
$558$		0			0
$559$	39.1434	+	8.93423i	1.65559	+	0.377878i
$560$		0			0
$561$	−6.91114	−	5.51145i	−0.291789	−	0.232694i
$562$		0			0
$563$			22.8811i			0.964324i	0.876082	+	0.482162i	$0.160148\pi$
$563$			22.8811i			0.964324i	−0.876082	+	0.482162i	$0.839852\pi$
$564$		0			0
$565$	3.18138	−	6.60620i	0.133842	−	0.277925i
$566$		0			0
$567$	0.634365	+	2.77933i	0.0266408	+	0.116721i
$568$		0			0
$569$	6.17874	−	1.41026i	0.259026	−	0.0591211i	−0.0910355	−	0.995848i	$-0.529018\pi$
$569$	6.17874	−	1.41026i	0.259026	−	0.0591211i	0.350062	+	0.936727i	$0.386161\pi$
$570$		0			0
$571$	6.34309	−	27.7909i	0.265450	−	1.16301i	−0.649793	−	0.760111i	$-0.725144\pi$
$571$	6.34309	−	27.7909i	0.265450	−	1.16301i	0.915243	−	0.402902i	$-0.131998\pi$
$572$		0			0
$573$	9.76295	+	12.2423i	0.407853	+	0.511431i
$574$		0			0
$575$	18.7535	−	9.03123i	0.782076	−	0.376628i
$576$		0			0
$577$	17.3981	−	13.8745i	0.724291	−	0.577602i	−0.190425	−	0.981702i	$-0.560986\pi$
$577$	17.3981	−	13.8745i	0.724291	−	0.577602i	0.914715	+	0.404099i	$0.132415\pi$
$578$		0			0
$579$	−3.55175			−0.147606
$580$		0			0
$581$	21.1854			0.878920
$582$		0			0
$583$	−0.446470	+	0.356048i	−0.0184909	+	0.0147460i
$584$		0			0
$585$	4.75439	−	2.28959i	0.196570	−	0.0946631i
$586$		0			0
$587$	8.20045	+	10.2830i	0.338469	+	0.424426i	0.921714	−	0.387870i	$-0.126789\pi$
$587$	8.20045	+	10.2830i	0.338469	+	0.424426i	−0.583246	+	0.812296i	$0.698217\pi$
$588$		0			0
$589$	−2.33670	+	10.2377i	−0.0962820	+	0.421839i
$590$		0			0
$591$	0.673411	−	0.153702i	0.0277004	−	0.00632244i
$592$		0			0
$593$	2.90152	+	12.7124i	0.119151	+	0.522036i	0.998913	+	0.0466202i	$0.0148451\pi$
$593$	2.90152	+	12.7124i	0.119151	+	0.522036i	−0.879761	+	0.475415i	$0.842298\pi$
$594$		0			0
$595$	1.79208	−	3.72130i	0.0734682	−	0.152558i
$596$		0			0
$597$			14.1283i			0.578231i
$598$		0			0
$599$	1.36327	+	1.08718i	0.0557019	+	0.0444208i	0.650945	−	0.759125i	$-0.274373\pi$
$599$	1.36327	+	1.08718i	0.0557019	+	0.0444208i	−0.595243	+	0.803546i	$0.702944\pi$
$600$		0			0
$601$	−10.6144	−	2.42266i	−0.432970	−	0.0988225i	0.000480812	−	1.00000i	$-0.499847\pi$
$601$	−10.6144	−	2.42266i	−0.432970	−	0.0988225i	−0.433450	+	0.901177i	$0.642704\pi$
$602$		0			0
$603$	14.4673	+	6.96707i	0.589153	+	0.283721i
$604$		0			0
$605$	−0.544945	+	0.683340i	−0.0221552	+	0.0277817i
$606$		0			0
$607$	12.0667	+	25.0567i	0.489771	+	1.01702i	0.988634	+	0.150339i	$0.0480365\pi$
$607$	12.0667	+	25.0567i	0.489771	+	1.01702i	−0.498864	+	0.866680i	$0.666249\pi$
$608$		0			0
$609$	−18.1486	−	7.52607i	−0.735420	−	0.304972i
$610$		0			0
$611$	18.0000	+	37.3774i	0.728203	+	1.51213i
$612$		0			0
$613$	19.4057	−	24.3340i	0.783790	−	0.982842i	−0.216189	−	0.976352i	$-0.569363\pi$
$613$	19.4057	−	24.3340i	0.783790	−	0.982842i	0.999979	−	0.00649029i	$-0.00206594\pi$
$614$		0			0
$615$	−3.10443	−	1.49502i	−0.125183	−	0.0602849i
$616$		0			0
$617$	−29.9695	−	6.84034i	−1.20653	−	0.275382i	−0.428458	−	0.903561i	$-0.640943\pi$
$617$	−29.9695	−	6.84034i	−1.20653	−	0.275382i	−0.778068	+	0.628180i	$0.783800\pi$
$618$		0			0
$619$	−27.9819	−	22.3148i	−1.12469	−	0.896908i	−0.129182	−	0.991621i	$-0.541235\pi$
$619$	−27.9819	−	22.3148i	−1.12469	−	0.896908i	−0.995505	+	0.0947131i	$0.969807\pi$
$620$		0			0
$621$		−	23.3956i		−	0.938834i
$622$		0			0
$623$	−8.83457	+	18.3452i	−0.353950	+	0.734984i
$624$		0			0
$625$	−4.74683	−	20.7972i	−0.189873	−	0.831888i
$626$		0			0
$627$	6.29739	−	1.43734i	0.251494	−	0.0574018i
$628$		0			0
$629$	−1.38715	+	6.07748i	−0.0553091	+	0.242325i
$630$		0			0
$631$	−0.807873	−	1.01304i	−0.0321609	−	0.0403285i	0.765491	−	0.643447i	$-0.222496\pi$
$631$	−0.807873	−	1.01304i	−0.0321609	−	0.0403285i	−0.797652	+	0.603118i	$0.793925\pi$
$632$		0			0
$633$	14.3277	−	6.89988i	0.569477	−	0.274246i
$634$		0			0
$635$	2.73479	−	2.18092i	0.108527	−	0.0865472i
$636$		0			0
$637$	20.8984			0.828023
$638$		0			0
$639$	14.0664			0.556459
$640$		0			0
$641$	7.79784	−	6.21857i	0.307996	−	0.245619i	−0.457277	−	0.889324i	$-0.651175\pi$
$641$	7.79784	−	6.21857i	0.307996	−	0.245619i	0.765273	+	0.643705i	$0.222604\pi$
$642$		0			0
$643$	4.80963	−	2.31619i	0.189673	−	0.0913418i	−0.336637	−	0.941635i	$-0.609289\pi$
$643$	4.80963	−	2.31619i	0.189673	−	0.0913418i	0.526310	+	0.850293i	$0.323575\pi$
$644$		0			0
$645$	2.29522	+	2.87811i	0.0903740	+	0.113325i
$646$		0			0
$647$	5.69886	−	24.9683i	0.224045	−	0.981607i	−0.730353	−	0.683070i	$-0.760644\pi$
$647$	5.69886	−	24.9683i	0.224045	−	0.981607i	0.954398	−	0.298537i	$-0.0964985\pi$
$648$		0			0
$649$	18.1254	−	4.13700i	0.711484	−	0.162392i
$650$		0			0
$651$	4.54146	+	19.8975i	0.177994	+	0.779843i
$652$		0			0
$653$	14.0437	−	29.1620i	0.549571	−	1.14120i	−0.422468	−	0.906378i	$-0.638836\pi$
$653$	14.0437	−	29.1620i	0.549571	−	1.14120i	0.972039	−	0.234819i	$-0.0754496\pi$
$654$		0			0
$655$			6.43705i			0.251516i
$656$		0			0
$657$	−7.66673	−	6.11402i	−0.299108	−	0.238531i
$658$		0			0
$659$	7.94198	+	1.81271i	0.309376	+	0.0706130i	0.374390	−	0.927271i	$-0.377852\pi$
$659$	7.94198	+	1.81271i	0.309376	+	0.0706130i	−0.0650143	+	0.997884i	$0.520709\pi$
$660$		0			0
$661$	3.79092	+	1.82561i	0.147450	+	0.0710080i	0.506153	−	0.862443i	$-0.331067\pi$
$661$	3.79092	+	1.82561i	0.147450	+	0.0710080i	−0.358704	+	0.933451i	$0.616781\pi$
$662$		0			0
$663$	−11.1538	+	13.9864i	−0.433177	+	0.543186i
$664$		0			0
$665$	1.30951	+	2.71923i	0.0507807	+	0.105447i
$666$		0			0
$667$	19.2347	+	13.6596i	0.744772	+	0.528900i
$668$		0			0
$669$	−0.955788	−	1.98471i	−0.0369529	−	0.0767335i
$670$		0			0
$671$	−20.8892	+	26.1942i	−0.806417	+	1.01121i
$672$		0			0
$673$	13.2946	+	6.40233i	0.512468	+	0.246792i	0.672201	−	0.740369i	$-0.265349\pi$
$673$	13.2946	+	6.40233i	0.512468	+	0.246792i	−0.159733	+	0.987160i	$0.551063\pi$
$674$		0			0
$675$	−24.7382	−	5.64632i	−0.952172	−	0.217327i
$676$		0			0
$677$	−6.88854	−	5.49343i	−0.264748	−	0.211130i	0.482114	−	0.876108i	$-0.339869\pi$
$677$	−6.88854	−	5.49343i	−0.264748	−	0.211130i	−0.746862	+	0.664979i	$0.768441\pi$
$678$		0			0
$679$			25.5620i			0.980979i
$680$		0			0
$681$	2.79970	−	5.81364i	0.107285	−	0.222779i
$682$		0			0
$683$	−0.165355	−	0.724467i	−0.00632713	−	0.0277210i	0.971666	−	0.236359i	$-0.0759541\pi$
$683$	−0.165355	−	0.724467i	−0.00632713	−	0.0277210i	−0.977993	+	0.208638i	$0.933097\pi$
$684$		0			0
$685$	−8.39927	+	1.91708i	−0.320920	+	0.0732478i
$686$		0			0
$687$	−4.04994	+	17.7440i	−0.154515	+	0.676974i
$688$		0			0
$689$	0.720550	+	0.903541i	0.0274508	+	0.0344222i
$690$		0			0
$691$	18.9866	−	9.14344i	0.722283	−	0.347833i	−0.0363611	−	0.999339i	$-0.511577\pi$
$691$	18.9866	−	9.14344i	0.722283	−	0.347833i	0.758644	+	0.651506i	$0.225862\pi$
$692$		0			0
$693$	−13.1819	+	10.5122i	−0.500737	+	0.399325i
$694$		0			0
$695$	9.56960			0.362996
$696$		0			0
$697$	−15.6878			−0.594217
$698$		0			0
$699$	26.8813	−	21.4371i	1.01674	−	0.810826i
$700$		0			0
$701$	−14.5359	+	7.00011i	−0.549013	+	0.264391i	−0.687761	−	0.725937i	$-0.741406\pi$
$701$	−14.5359	+	7.00011i	−0.549013	+	0.264391i	0.138748	+	0.990328i	$0.455692\pi$
$702$		0			0
$703$	−2.84009	−	3.56136i	−0.107116	−	0.134319i
$704$		0			0
$705$	−0.846405	+	3.70834i	−0.0318774	+	0.139664i
$706$		0			0
$707$	47.3480	−	10.8069i	1.78071	−	0.406435i
$708$		0			0
$709$	3.21880	+	14.1025i	0.120884	+	0.529629i	0.998716	+	0.0506598i	$0.0161324\pi$
$709$	3.21880	+	14.1025i	0.120884	+	0.529629i	−0.877832	+	0.478970i	$0.841010\pi$
$710$		0			0
$711$	10.8055	−	22.4380i	0.405240	−	0.841489i
$712$		0			0
$713$		−	24.5063i		−	0.917770i
$714$		0			0
$715$	−7.29586	−	5.81825i	−0.272850	−	0.217590i
$716$		0			0
$717$	27.7088	+	6.32435i	1.03480	+	0.236187i
$718$		0			0
$719$	0.597255	+	0.287623i	0.0222738	+	0.0107265i	0.444988	−	0.895537i	$-0.353208\pi$
$719$	0.597255	+	0.287623i	0.0222738	+	0.0107265i	−0.422714	+	0.906263i	$0.638922\pi$
$720$		0			0
$721$	−6.55234	+	8.21637i	−0.244022	+	0.305994i
$722$		0			0
$723$	−13.4689	−	27.9684i	−0.500914	−	1.04016i
$724$		0			0
$725$	19.0855	−	17.0419i	0.708819	−	0.632920i
$726$		0			0
$727$	1.74191	+	3.61711i	0.0646038	+	0.134151i	0.930770	−	0.365604i	$-0.119138\pi$
$727$	1.74191	+	3.61711i	0.0646038	+	0.134151i	−0.866167	+	0.499755i	$0.833423\pi$
$728$		0			0
$729$	−12.2512	+	15.3625i	−0.453747	+	0.568981i
$730$		0			0
$731$	15.1006	+	7.27205i	0.558514	+	0.268966i
$732$		0			0
$733$	−20.8873	−	4.76739i	−0.771491	−	0.176088i	−0.181383	−	0.983412i	$-0.558057\pi$
$733$	−20.8873	−	4.76739i	−0.771491	−	0.176088i	−0.590107	+	0.807325i	$0.700915\pi$
$734$		0			0
$735$	1.49807	+	1.19467i	0.0552573	+	0.0440662i
$736$		0			0
$737$		−	28.3959i		−	1.04597i
$738$		0			0
$739$	21.0121	−	43.6320i	0.772942	−	1.60503i	−0.0230587	−	0.999734i	$-0.507340\pi$
$739$	21.0121	−	43.6320i	0.772942	−	1.60503i	0.796000	−	0.605296i	$-0.206945\pi$
$740$		0			0
$741$	−2.90881	−	12.7443i	−0.106858	−	0.468174i
$742$		0			0
$743$	6.44747	−	1.47159i	0.236535	−	0.0539875i	−0.102610	−	0.994722i	$-0.532719\pi$
$743$	6.44747	−	1.47159i	0.236535	−	0.0539875i	0.339145	+	0.940734i	$0.389862\pi$
$744$		0			0
$745$	1.50002	−	6.57201i	0.0549564	−	0.240780i
$746$		0			0
$747$	7.04472	+	8.83380i	0.257753	+	0.323212i
$748$		0			0
$749$	10.1377	−	4.88206i	0.370423	−	0.178387i
$750$		0			0
$751$	−8.07046	+	6.43598i	−0.294495	+	0.234852i	−0.759580	−	0.650414i	$-0.774595\pi$
$751$	−8.07046	+	6.43598i	−0.294495	+	0.234852i	0.465084	+	0.885266i	$0.346024\pi$
$752$		0			0
$753$	−3.65882			−0.133335
$754$		0			0
$755$	8.90220			0.323984
$756$		0			0
$757$	11.0238	−	8.79118i	0.400667	−	0.319521i	−0.402341	−	0.915490i	$-0.631803\pi$
$757$	11.0238	−	8.79118i	0.400667	−	0.319521i	0.803007	+	0.595969i	$0.203232\pi$
$758$		0			0
$759$	−13.5814	+	6.54046i	−0.492974	+	0.237404i
$760$		0			0
$761$	16.6023	+	20.8186i	0.601833	+	0.754675i	0.985662	−	0.168729i	$-0.0539664\pi$
$761$	16.6023	+	20.8186i	0.601833	+	0.754675i	−0.383829	+	0.923404i	$0.625395\pi$
$762$		0			0
$763$	−9.34847	+	40.9583i	−0.338437	+	1.48279i
$764$		0			0
$765$	2.14761	−	0.490177i	0.0776468	−	0.0177224i
$766$		0			0
$767$	−8.37224	−	36.6812i	−0.302304	−	1.32448i
$768$		0			0
$769$	−8.54732	+	17.7487i	−0.308224	+	0.640034i	−0.996332	−	0.0855747i	$-0.972727\pi$
$769$	−8.54732	+	17.7487i	−0.308224	+	0.640034i	0.688108	+	0.725609i	$0.258442\pi$
$770$		0			0
$771$			34.0950i			1.22790i
$772$		0			0
$773$	−4.66892	−	3.72334i	−0.167929	−	0.133919i	0.535919	−	0.844269i	$-0.319965\pi$
$773$	−4.66892	−	3.72334i	−0.167929	−	0.133919i	−0.703849	+	0.710350i	$0.748537\pi$
$774$		0			0
$775$	−25.9126	−	5.91439i	−0.930809	−	0.212451i
$776$		0			0
$777$	−7.97638	−	3.84122i	−0.286151	−	0.137803i
$778$		0			0
$779$	7.14731	−	8.96245i	0.256079	−	0.321113i
$780$		0			0
$781$	−10.7928	−	22.4115i	−0.386198	−	0.801948i
$782$		0			0
$783$	−7.95032	−	27.6385i	−0.284121	−	0.987718i
$784$		0			0
$785$	−4.18782	−	8.69610i	−0.149470	−	0.310377i
$786$		0			0
$787$	−19.5200	+	24.4773i	−0.695812	+	0.872520i	−0.996703	−	0.0811382i	$-0.974144\pi$
$787$	−19.5200	+	24.4773i	−0.695812	+	0.872520i	0.300891	+	0.953658i	$0.402716\pi$
$788$		0			0
$789$	11.7801	+	5.67301i	0.419384	+	0.201965i
$790$		0			0
$791$	46.2220	+	10.5499i	1.64346	+	0.375110i
$792$		0			0
$793$	53.0103	+	42.2743i	1.88245	+	1.50120i
$794$		0			0
$795$			0.105960i			0.00375802i
$796$		0			0
$797$	−10.0149	+	20.7962i	−0.354747	+	0.736640i	−0.999618	−	0.0276518i	$-0.991197\pi$
$797$	−10.0149	+	20.7962i	−0.354747	+	0.736640i	0.644870	+	0.764292i	$0.276911\pi$
$798$		0			0
$799$	3.85360	+	16.8837i	0.136331	+	0.597304i
$800$		0			0
$801$	−10.5872	+	2.41646i	−0.374081	+	0.0853815i
$802$		0			0
$803$	−3.85875	+	16.9063i	−0.136172	+	0.596609i
$804$		0			0
$805$	−4.39150	−	5.50676i	−0.154780	−	0.194088i
$806$		0			0
$807$	−3.77618	+	1.81851i	−0.132928	+	0.0640147i
$808$		0			0
$809$	−36.0373	+	28.7388i	−1.26700	+	1.01040i	−0.268111	+	0.963388i	$0.586399\pi$
$809$	−36.0373	+	28.7388i	−1.26700	+	1.01040i	−0.998894	+	0.0470146i	$0.985029\pi$
$810$		0			0
$811$	14.2865			0.501668			0.250834	−	0.968030i	$-0.419295\pi$
$811$	14.2865			0.501668			0.250834	+	0.968030i	$0.419295\pi$
$812$		0			0
$813$	10.0832			0.353634
$814$		0			0
$815$	4.07862	−	3.25259i	0.142868	−	0.113933i
$816$		0			0
$817$	−11.0343	+	5.31384i	−0.386041	+	0.185908i
$818$		0			0
$819$	21.2740	+	26.6767i	0.743373	+	0.932160i
$820$		0			0
$821$	1.49751	−	6.56103i	0.0522635	−	0.228981i	−0.942050	−	0.335472i	$-0.891104\pi$
$821$	1.49751	−	6.56103i	0.0522635	−	0.228981i	0.994314	+	0.106490i	$0.0339614\pi$
$822$		0			0
$823$	−28.6239	+	6.53321i	−0.997766	+	0.227734i	−0.690063	−	0.723749i	$-0.742417\pi$
$823$	−28.6239	+	6.53321i	−0.997766	+	0.227734i	−0.307703	+	0.951483i	$0.599560\pi$
$824$		0			0
$825$	3.63803	+	15.9392i	0.126660	+	0.554933i
$826$		0			0
$827$	11.2870	−	23.4377i	0.392488	−	0.815010i	−0.607301	−	0.794472i	$-0.707748\pi$
$827$	11.2870	−	23.4377i	0.392488	−	0.815010i	0.999789	−	0.0205381i	$-0.00653793\pi$
$828$		0			0
$829$		−	40.0544i		−	1.39115i	−0.718456	−	0.695573i	$-0.755151\pi$
$829$		−	40.0544i		−	1.39115i	0.718456	−	0.695573i	$-0.244849\pi$
$830$		0			0
$831$	−21.7581	−	17.3515i	−0.754781	−	0.601917i
$832$		0			0
$833$	8.50514	+	1.94124i	0.294686	+	0.0672601i
$834$		0			0
$835$	−7.57130	−	3.64615i	−0.262016	−	0.126180i
$836$		0			0
$837$	−18.6264	+	23.3568i	−0.643823	+	0.807329i
$838$		0			0
$839$	10.0150	+	20.7964i	0.345757	+	0.717972i	0.999240	−	0.0389691i	$-0.0124074\pi$
$839$	10.0150	+	20.7964i	0.345757	+	0.717972i	−0.653483	+	0.756941i	$0.726693\pi$
$840$		0			0
$841$	27.3648	+	9.60038i	0.943614	+	0.331048i
$842$		0			0
$843$	6.44386	+	13.3808i	0.221938	+	0.460860i
$844$		0			0
$845$	−7.73291	+	9.69677i	−0.266020	+	0.333579i
$846$		0			0
$847$	−5.09176	−	2.45206i	−0.174955	−	0.0842538i
$848$		0			0
$849$	−22.6555	−	5.17096i	−0.777533	−	0.177467i
$850$		0			0
$851$	8.31118	+	6.62795i	0.284904	+	0.227203i
$852$		0			0
$853$			21.5499i			0.737853i	0.929459	+	0.368926i	$0.120275\pi$
$853$			21.5499i			0.737853i	−0.929459	+	0.368926i	$0.879725\pi$
$854$		0			0
$855$	−0.698404	+	1.45025i	−0.0238849	+	0.0495976i
$856$		0			0
$857$	−9.07097	−	39.7425i	−0.309859	−	1.35758i	−0.854736	−	0.519063i	$-0.826281\pi$
$857$	−9.07097	−	39.7425i	−0.309859	−	1.35758i	0.544877	−	0.838516i	$-0.316576\pi$
$858$		0			0
$859$	5.06981	−	1.15715i	0.172980	−	0.0394815i	−0.135154	−	0.990825i	$-0.543153\pi$
$859$	5.06981	−	1.15715i	0.172980	−	0.0394815i	0.308133	+	0.951343i	$0.400296\pi$
$860$		0			0
$861$	4.95767	−	21.7210i	0.168957	−	0.740249i
$862$		0			0
$863$	−33.8937	−	42.5013i	−1.15375	−	1.44676i	−0.873493	−	0.486837i	$-0.838151\pi$
$863$	−33.8937	−	42.5013i	−1.15375	−	1.44676i	−0.280261	−	0.959924i	$-0.590421\pi$
$864$		0			0
$865$	4.37759	−	2.10814i	0.148843	−	0.0716788i
$866$		0			0
$867$	9.20104	−	7.33758i	0.312484	−	0.249197i
$868$		0			0
$869$	−44.0404			−1.49397
$870$		0			0
$871$	−57.4660			−1.94716
$872$		0			0
$873$	−10.6587	+	8.50004i	−0.360743	+	0.287683i
$874$		0			0
$875$	−14.1254	+	6.80244i	−0.477526	+	0.229964i
$876$		0			0
$877$	−27.0111	−	33.8709i	−0.912101	−	1.14374i	−0.989179	−	0.146713i	$-0.953130\pi$
$877$	−27.0111	−	33.8709i	−0.912101	−	1.14374i	0.0770781	−	0.997025i	$-0.475441\pi$
$878$		0			0
$879$	5.02648	−	22.0224i	0.169539	−	0.742798i
$880$		0			0
$881$	−3.94111	+	0.899532i	−0.132779	+	0.0303060i	−0.288394	−	0.957512i	$-0.593121\pi$
$881$	−3.94111	+	0.899532i	−0.132779	+	0.0303060i	0.155615	+	0.987818i	$0.450264\pi$
$882$		0			0
$883$	3.70910	+	16.2506i	0.124821	+	0.546877i	0.998207	+	0.0598490i	$0.0190619\pi$
$883$	3.70910	+	16.2506i	0.124821	+	0.546877i	−0.873386	+	0.487028i	$0.838081\pi$
$884$		0			0
$885$	1.49676	−	3.10805i	0.0503130	−	0.104476i
$886$		0			0
$887$		−	47.3352i		−	1.58936i	−0.607029	−	0.794680i	$-0.707639\pi$
$887$		−	47.3352i		−	1.58936i	0.607029	−	0.794680i	$-0.292361\pi$
$888$		0			0
$889$	17.6831	+	14.1018i	0.593071	+	0.472959i
$890$		0			0
$891$	2.62129	+	0.598293i	0.0878167	+	0.0200436i
$892$		0			0
$893$	−11.4014	−	5.49062i	−0.381533	−	0.183737i
$894$		0			0
$895$	−6.71179	+	8.41632i	−0.224350	+	0.281327i
$896$		0			0
$897$	13.2362	+	27.4853i	0.441945	+	0.917707i
$898$		0			0
$899$	−8.32776	−	28.9506i	−0.277746	−	0.965557i
$900$		0			0
$901$	0.209317	+	0.434652i	0.00697337	+	0.0144803i
$902$		0			0
$903$	−14.8408	+	18.6098i	−0.493871	+	0.619295i
$904$		0			0
$905$	−0.00711143	−	0.00342468i	−0.000236392	−	0.000113840i
$906$		0			0
$907$	5.49972	+	1.25527i	0.182615	+	0.0416807i	0.312850	−	0.949802i	$-0.398716\pi$
$907$	5.49972	+	1.25527i	0.182615	+	0.0416807i	−0.130235	+	0.991483i	$0.541573\pi$
$908$		0			0
$909$	20.2507	+	16.1494i	0.671673	+	0.535641i
$910$		0			0
$911$		−	0.641362i		−	0.0212493i	−0.999944	−	0.0106246i	$-0.996618\pi$
$911$		−	0.641362i		−	0.0212493i	0.999944	−	0.0106246i	$-0.00338199\pi$
$912$		0			0
$913$	8.66934	−	18.0021i	0.286913	−	0.595782i
$914$		0			0
$915$	1.38333	+	6.06076i	0.0457315	+	0.200363i
$916$		0			0
$917$	−40.5783	+	9.26173i	−1.34001	+	0.305849i
$918$		0			0
$919$	−6.24537	+	27.3627i	−0.206016	+	0.902613i	0.761172	+	0.648550i	$0.224624\pi$
$919$	−6.24537	+	27.3627i	−0.206016	+	0.902613i	−0.967188	+	0.254063i	$0.918233\pi$
$920$		0			0
$921$	16.4335	+	20.6069i	0.541502	+	0.679022i
$922$		0			0
$923$	−45.3552	+	21.8419i	−1.49289	+	0.718936i
$924$		0			0
$925$	9.01411	−	7.18852i	0.296382	−	0.236357i
$926$		0			0
$927$	−5.60485			−0.184087
$928$		0			0
$929$	−10.5246			−0.345302			−0.172651	−	0.984983i	$-0.555233\pi$
$929$	−10.5246			−0.345302			−0.172651	+	0.984983i	$0.555233\pi$
$930$		0			0
$931$	−4.98395	+	3.97457i	−0.163342	+	0.130261i
$932$		0			0
$933$	14.5707	−	7.01686i	0.477022	−	0.229722i
$934$		0			0
$935$	−2.42879	−	3.04560i	−0.0794298	−	0.0996018i
$936$		0			0
$937$	9.93731	−	43.5382i	0.324638	−	1.42233i	−0.504560	−	0.863376i	$-0.668345\pi$
$937$	9.93731	−	43.5382i	0.324638	−	1.42233i	0.829198	−	0.558955i	$-0.188797\pi$
$938$		0			0
$939$	11.8855	−	2.71278i	0.387867	−	0.0885282i
$940$		0			0
$941$	5.22072	+	22.8735i	0.170191	+	0.745654i	0.985920	+	0.167220i	$0.0534790\pi$
$941$	5.22072	+	22.8735i	0.170191	+	0.745654i	−0.815729	+	0.578434i	$0.803664\pi$
$942$		0			0
$943$	−11.6074	+	24.1029i	−0.377988	+	0.784899i
$944$		0			0
$945$			8.58627i			0.279311i
$946$		0			0
$947$	−47.2705	−	37.6970i	−1.53609	−	1.22499i	−0.884622	−	0.466308i	$-0.845584\pi$
$947$	−47.2705	−	37.6970i	−1.53609	−	1.22499i	−0.651464	−	0.758680i	$-0.725845\pi$
$948$		0			0
$949$	34.2140	+	7.80912i	1.11063	+	0.253495i
$950$		0			0
$951$	−7.26157	−	3.49699i	−0.235473	−	0.113398i
$952$		0			0
$953$	−28.3109	+	35.5007i	−0.917079	+	1.14998i	0.0712208	+	0.997461i	$0.477310\pi$
$953$	−28.3109	+	35.5007i	−0.917079	+	1.14998i	−0.988300	+	0.152521i	$0.951261\pi$
$954$		0			0
$955$	2.99398	+	6.21706i	0.0968828	+	0.201179i
$956$		0			0
$957$	−13.8218	+	12.3418i	−0.446797	+	0.398955i
$958$		0			0
$959$	−24.1700	−	50.1895i	−0.780490	−	1.62070i
$960$		0			0
$961$	−0.182532	+	0.228887i	−0.00588811	+	0.00738346i
$962$		0			0
$963$	5.40675	+	2.60376i	0.174230	+	0.0839048i
$964$		0			0
$965$	−1.52594	−	0.348286i	−0.0491218	−	0.0112117i
$966$		0			0
$967$	0.268035	+	0.213751i	0.00861942	+	0.00687375i	0.627790	−	0.778383i	$-0.283960\pi$
$967$	0.268035	+	0.213751i	0.00861942	+	0.00687375i	−0.619171	+	0.785256i	$0.712531\pi$
$968$		0			0
$969$		−	5.45683i		−	0.175299i
$970$		0			0
$971$	25.6584	−	53.2803i	0.823418	−	1.70984i	0.127363	−	0.991856i	$-0.459349\pi$
$971$	25.6584	−	53.2803i	0.823418	−	1.70984i	0.696055	−	0.717988i	$-0.254937\pi$
$972$		0			0
$973$	13.7689	+	60.3254i	0.441410	+	1.93394i
$974$		0			0
$975$	32.2570	−	7.36244i	1.03305	−	0.235787i
$976$		0			0
$977$	3.95732	−	17.3382i	0.126606	−	0.554697i	−0.871343	−	0.490675i	$-0.836750\pi$
$977$	3.95732	−	17.3382i	0.126606	−	0.554697i	0.997949	−	0.0640217i	$-0.0203927\pi$
$978$		0			0
$979$	11.9734	+	15.0141i	0.382671	+	0.479854i
$980$		0			0
$981$	−20.1872	+	9.72165i	−0.644528	+	0.310389i
$982$		0			0
$983$	−46.9498	+	37.4412i	−1.49747	+	1.19419i	−0.569243	+	0.822169i	$0.692764\pi$
$983$	−46.9498	+	37.4412i	−1.49747	+	1.19419i	−0.928224	+	0.372021i	$0.878665\pi$
$984$		0			0
$985$	0.304390			0.00969868
$986$		0			0
$987$	−24.5947			−0.782857
$988$		0			0
$989$	22.3457	−	17.8201i	0.710553	−	0.566647i
$990$		0			0
$991$	−47.5554	+	22.9015i	−1.51065	+	0.727490i	−0.991851	−	0.127407i	$-0.959335\pi$
$991$	−47.5554	+	22.9015i	−1.51065	+	0.727490i	−0.518798	+	0.854897i	$0.673620\pi$
$992$		0			0
$993$	−11.0998	−	13.9187i	−0.352242	−	0.441698i
$994$		0			0
$995$	−1.38542	+	6.06994i	−0.0439209	+	0.192430i
$996$		0			0
$997$	4.20871	−	0.960611i	0.133291	−	0.0304228i	−0.155355	−	0.987859i	$-0.549652\pi$
$997$	4.20871	−	0.960611i	0.133291	−	0.0304228i	0.288646	+	0.957436i	$0.406795\pi$
$998$		0			0
$999$	−2.88365	−	12.6341i	−0.0912345	−	0.399725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.q.a.9.6	✓	48
4.3	odd	2		464.2.y.e.241.3		48
29.10	odd	28		6728.2.a.be.1.16		24
29.13	even	14	inner	232.2.q.a.129.6	yes	48
29.19	odd	28		6728.2.a.bf.1.9		24
116.71	odd	14		464.2.y.e.129.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.q.a.9.6	✓	48	1.1	even	1	trivial
232.2.q.a.129.6	yes	48	29.13	even	14	inner
464.2.y.e.129.3		48	116.71	odd	14
464.2.y.e.241.3		48	4.3	odd	2
6728.2.a.be.1.16		24	29.10	odd	28
6728.2.a.bf.1.9		24	29.19	odd	28

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.q (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.884679 - 0.705508i) q^{3} +(0.449269 - 0.216356i) q^{5} +(2.01029 + 2.52083i) q^{7} +(-0.382647 + 1.67649i) q^{9} +O(q^{10})\)	\(q+(0.884679 - 0.705508i) q^{3} +(0.449269 - 0.216356i) q^{5} +(2.01029 + 2.52083i) q^{7} +(-0.382647 + 1.67649i) q^{9} +(2.96468 - 0.676669i) q^{11} +(-1.36941 - 5.99976i) q^{13} +(0.244817 - 0.508369i) q^{15} -2.56896i q^{17} +(1.46765 + 1.17041i) q^{19} +(3.55693 + 0.811847i) q^{21} +(-3.94699 - 1.90077i) q^{23} +(-2.96242 + 3.71475i) q^{25} +(2.31714 + 4.81158i) q^{27} +(-5.30871 - 0.904210i) q^{29} +(2.42714 + 5.04001i) q^{31} +(2.14540 - 2.69024i) q^{33} +(1.44856 + 0.697590i) q^{35} +(-2.36573 - 0.539963i) q^{37} +(-5.44437 - 4.34174i) q^{39} -6.10666i q^{41} +(-2.83073 + 5.87807i) q^{43} +(0.190807 + 0.835981i) q^{45} +(-6.57220 + 1.50006i) q^{47} +(-0.755652 + 3.31073i) q^{49} +(-1.81243 - 2.27271i) q^{51} +(-0.169193 + 0.0814792i) q^{53} +(1.18554 - 0.945434i) q^{55} +2.12414 q^{57} +6.11377 q^{59} +(-8.61388 + 6.86934i) q^{61} +(-4.99537 + 2.40564i) q^{63} +(-1.91332 - 2.39922i) q^{65} +(2.07788 - 9.10378i) q^{67} +(-4.83283 + 1.10306i) q^{69} +(-1.82023 - 7.97497i) q^{71} +(-2.47425 + 5.13783i) q^{73} +5.37638i q^{75} +(7.66565 + 6.11315i) q^{77} +(-14.1195 - 3.22268i) q^{79} +(0.796613 + 0.383629i) q^{81} +(4.09672 - 5.13713i) q^{83} +(-0.555812 - 1.15416i) q^{85} +(-5.33443 + 2.94540i) q^{87} +(2.74003 + 5.68973i) q^{89} +(12.3715 - 15.5133i) q^{91} +(5.70301 + 2.74643i) q^{93} +(0.912596 + 0.208294i) q^{95} +(6.19837 + 4.94303i) q^{97} +5.22917i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9	\( 48 q - 2 q^{5} - 4 q^{7} + 6 q^{9} + 10 q^{13} + 14 q^{15} + 14 q^{21} + 4 q^{23} - 48 q^{25} - 4 q^{29} + 10 q^{33} + 8 q^{35} - 38 q^{45} - 14 q^{47} - 18 q^{49} - 56 q^{51} - 48 q^{53} - 28 q^{55} - 12 q^{57} - 128 q^{59} - 28 q^{61} + 42 q^{63} - 28 q^{65} - 4 q^{67} + 28 q^{69} - 14 q^{71} - 28 q^{73} + 14 q^{77} - 32 q^{81} + 80 q^{83} - 112 q^{87} + 42 q^{89} - 28 q^{91} + 6 q^{93} + 70 q^{97}+O(q^{100}) \) 48 * q - 2 * q^5 - 4 * q^7 + 6 * q^9 + 10 * q^13 + 14 * q^15 + 14 * q^21 + 4 * q^23 - 48 * q^25 - 4 * q^29 + 10 * q^33 + 8 * q^35 - 38 * q^45 - 14 * q^47 - 18 * q^49 - 56 * q^51 - 48 * q^53 - 28 * q^55 - 12 * q^57 - 128 * q^59 - 28 * q^61 + 42 * q^63 - 28 * q^65 - 4 * q^67 + 28 * q^69 - 14 * q^71 - 28 * q^73 + 14 * q^77 - 32 * q^81 + 80 * q^83 - 112 * q^87 + 42 * q^89 - 28 * q^91 + 6 * q^93 + 70 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more