LMFDB - Embedded newform 405.2.r.a.197.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			197.13
Character	$\chi$	$=$	405.197
Dual form			405.2.r.a.368.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75676 - 0.153697i) q^{2} +(1.09297 - 0.192720i) q^{4} +(-0.131866 - 2.23218i) q^{5} +(2.75943 - 1.93217i) q^{7} +(-1.51630 + 0.406292i) q^{8} +O(q^{10})$	\(q+(1.75676 - 0.153697i) q^{2} +(1.09297 - 0.192720i) q^{4} +(-0.131866 - 2.23218i) q^{5} +(2.75943 - 1.93217i) q^{7} +(-1.51630 + 0.406292i) q^{8} +(-0.574736 - 3.90113i) q^{10} +(1.11880 + 3.07388i) q^{11} +(0.506571 - 5.79013i) q^{13} +(4.55068 - 3.81848i) q^{14} +(-4.68713 + 1.70598i) q^{16} +(-1.11325 - 0.298295i) q^{17} +(6.40749 + 3.69937i) q^{19} +(-0.574311 - 2.41429i) q^{20} +(2.43791 + 5.22812i) q^{22} +(-1.09807 + 1.56820i) q^{23} +(-4.96522 + 0.588699i) q^{25} -10.2497i q^{26} +(2.64360 - 2.64360i) q^{28} +(-0.381851 - 0.320411i) q^{29} +(0.573116 + 3.25030i) q^{31} +(-5.12653 + 2.39054i) q^{32} +(-2.00157 - 0.352930i) q^{34} +(-4.67682 - 5.90474i) q^{35} +(-1.17991 + 4.40348i) q^{37} +(11.8250 + 5.51409i) q^{38} +(1.10686 + 3.33107i) q^{40} +(1.39279 + 1.65986i) q^{41} +(-1.68889 + 3.62184i) q^{43} +(1.81521 + 3.14404i) q^{44} +(-1.68801 + 2.92372i) q^{46} +(2.84791 + 4.06724i) q^{47} +(1.48701 - 4.08553i) q^{49} +(-8.63222 + 1.79734i) q^{50} +(-0.562207 - 6.42605i) q^{52} +(-1.25033 - 1.25033i) q^{53} +(6.71392 - 2.90271i) q^{55} +(-3.39910 + 4.05089i) q^{56} +(-0.720066 - 0.504196i) q^{58} +(-9.92422 - 3.61212i) q^{59} +(-1.82504 + 10.3503i) q^{61} +(1.50639 + 5.62192i) q^{62} +(0.000691655 - 0.000399327i) q^{64} +(-12.9914 - 0.367231i) q^{65} +(-5.82623 - 0.509729i) q^{67} +(-1.27424 - 0.111481i) q^{68} +(-9.12360 - 9.65440i) q^{70} +(6.62671 - 3.82593i) q^{71} +(-1.84806 - 6.89704i) q^{73} +(-1.39602 + 7.91721i) q^{74} +(7.71612 + 2.80844i) q^{76} +(9.02653 + 6.32044i) q^{77} +(-5.08874 + 6.06452i) q^{79} +(4.42611 + 10.2375i) q^{80} +(2.70191 + 2.70191i) q^{82} +(-0.544416 - 6.22270i) q^{83} +(-0.519047 + 2.52431i) q^{85} +(-2.41031 + 6.62228i) q^{86} +(-2.94533 - 4.20637i) q^{88} +(-0.260380 + 0.450992i) q^{89} +(-9.78968 - 16.9562i) q^{91} +(-0.897929 + 1.92562i) q^{92} +(5.62822 + 6.70745i) q^{94} +(7.41270 - 14.7905i) q^{95} +(4.27963 + 1.99563i) q^{97} +(1.98439 - 7.40585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.75676	−	0.153697i	1.24222	−	0.108680i	0.552967	−	0.833203i	$-0.313496\pi$
$2$	1.75676	−	0.153697i	1.24222	−	0.108680i	0.689250	+	0.724523i	$0.257940\pi$
$3$		0			0
$3$		0			0
$4$	1.09297	−	0.192720i	0.546484	−	0.0963599i
$5$	−0.131866	−	2.23218i	−0.0589725	−	0.998260i
$5$	−0.131866	−	2.23218i	−0.0589725	−	0.998260i
$6$		0			0
$7$	2.75943	−	1.93217i	1.04297	−	0.730292i	0.0791502	−	0.996863i	$-0.474779\pi$
$7$	2.75943	−	1.93217i	1.04297	−	0.730292i	0.963815	+	0.266570i	$0.0858904\pi$
$8$	−1.51630	+	0.406292i	−0.536093	+	0.143646i
$9$		0			0
$10$	−0.574736	−	3.90113i	−0.181747	−	1.23365i
$11$	1.11880	+	3.07388i	0.337332	+	0.926811i	0.986148	+	0.165866i	$0.0530420\pi$
$11$	1.11880	+	3.07388i	0.337332	+	0.926811i	−0.648817	+	0.760945i	$0.724736\pi$
$12$		0			0
$13$	0.506571	−	5.79013i	0.140497	−	1.60589i	−0.519396	−	0.854534i	$-0.673843\pi$
$13$	0.506571	−	5.79013i	0.140497	−	1.60589i	0.659893	−	0.751359i	$-0.270601\pi$
$14$	4.55068	−	3.81848i	1.21622	−	1.02053i
$15$		0			0
$16$	−4.68713	+	1.70598i	−1.17178	+	0.426494i
$17$	−1.11325	−	0.298295i	−0.270003	−	0.0723472i	0.121277	−	0.992619i	$-0.461301\pi$
$17$	−1.11325	−	0.298295i	−0.270003	−	0.0723472i	−0.391280	+	0.920271i	$0.627968\pi$
$18$		0			0
$19$	6.40749	+	3.69937i	1.46998	+	0.848693i	0.999433	−	0.0336827i	$-0.0107236\pi$
$19$	6.40749	+	3.69937i	1.46998	+	0.848693i	0.470546	+	0.882375i	$0.344057\pi$
$20$	−0.574311	−	2.41429i	−0.128420	−	0.539851i
$21$		0			0
$22$	2.43791	+	5.22812i	0.519765	+	1.11464i
$23$	−1.09807	+	1.56820i	−0.228963	+	0.326993i	−0.917151	−	0.398539i	$-0.869517\pi$
$23$	−1.09807	+	1.56820i	−0.228963	+	0.326993i	0.688189	+	0.725532i	$0.258406\pi$
$24$		0			0
$25$	−4.96522	+	0.588699i	−0.993044	+	0.117740i
$26$		−	10.2497i		−	2.01014i
$27$		0			0
$28$	2.64360	−	2.64360i	0.499593	−	0.499593i
$29$	−0.381851	−	0.320411i	−0.0709079	−	0.0594988i	0.606645	−	0.794973i	$-0.292515\pi$
$29$	−0.381851	−	0.320411i	−0.0709079	−	0.0594988i	−0.677553	+	0.735474i	$0.736959\pi$
$30$		0			0
$31$	0.573116	+	3.25030i	0.102935	+	0.583772i	0.992025	+	0.126040i	$0.0402269\pi$
$31$	0.573116	+	3.25030i	0.102935	+	0.583772i	−0.889090	+	0.457732i	$0.848662\pi$
$32$	−5.12653	+	2.39054i	−0.906251	+	0.422592i
$33$		0			0
$34$	−2.00157	−	0.352930i	−0.343266	−	0.0605270i
$35$	−4.67682	−	5.90474i	−0.790528	−	0.998083i
$36$		0			0
$37$	−1.17991	+	4.40348i	−0.193976	+	0.723928i	0.798554	+	0.601924i	$0.205599\pi$
$37$	−1.17991	+	4.40348i	−0.193976	+	0.723928i	−0.992530	+	0.122004i	$0.961068\pi$
$38$	11.8250	+	5.51409i	1.91827	+	0.894503i
$39$		0			0
$40$	1.10686	+	3.33107i	0.175011	+	0.526689i
$41$	1.39279	+	1.65986i	0.217517	+	0.259226i	0.863758	−	0.503907i	$-0.168105\pi$
$41$	1.39279	+	1.65986i	0.217517	+	0.259226i	−0.646241	+	0.763133i	$0.723660\pi$
$42$		0			0
$43$	−1.68889	+	3.62184i	−0.257554	+	0.552325i	−0.991985	−	0.126358i	$-0.959671\pi$
$43$	−1.68889	+	3.62184i	−0.257554	+	0.552325i	0.734431	+	0.678683i	$0.237449\pi$
$44$	1.81521	+	3.14404i	0.273654	+	0.473982i
$45$		0			0
$46$	−1.68801	+	2.92372i	−0.248884	+	0.431080i
$47$	2.84791	+	4.06724i	0.415410	+	0.593268i	0.971262	−	0.238014i	$-0.0764965\pi$
$47$	2.84791	+	4.06724i	0.415410	+	0.593268i	−0.555851	+	0.831282i	$0.687608\pi$
$48$		0			0
$49$	1.48701	−	4.08553i	0.212430	−	0.583647i
$50$	−8.63222	+	1.79734i	−1.22078	+	0.254182i
$51$		0			0
$52$	−0.562207	−	6.42605i	−0.0779641	−	0.891133i
$53$	−1.25033	−	1.25033i	−0.171746	−	0.171746i	0.616000	−	0.787746i	$-0.288752\pi$
$53$	−1.25033	−	1.25033i	−0.171746	−	0.171746i	−0.787746	+	0.616000i	$0.788752\pi$
$54$		0			0
$55$	6.71392	−	2.90271i	0.905305	−	0.391401i
$56$	−3.39910	+	4.05089i	−0.454223	+	0.541322i
$57$		0			0
$58$	−0.720066	−	0.504196i	−0.0945493	−	0.0662041i
$59$	−9.92422	−	3.61212i	−1.29202	−	0.470258i	−0.397633	−	0.917545i	$-0.630168\pi$
$59$	−9.92422	−	3.61212i	−1.29202	−	0.470258i	−0.894391	+	0.447286i	$0.852391\pi$
$60$		0			0
$61$	−1.82504	+	10.3503i	−0.233672	+	1.32522i	0.611720	+	0.791074i	$0.290478\pi$
$61$	−1.82504	+	10.3503i	−0.233672	+	1.32522i	−0.845392	+	0.534146i	$0.820633\pi$
$62$	1.50639	+	5.62192i	0.191312	+	0.713985i
$63$		0			0
$64$	0.000691655	0	0.000399327i	8.64569e−5	0	4.99159e-5i
$65$	−12.9914	−	0.367231i	−1.61138	−	0.0455494i
$66$		0			0
$67$	−5.82623	−	0.509729i	−0.711787	−	0.0622733i	−0.274490	−	0.961590i	$-0.588509\pi$
$67$	−5.82623	−	0.509729i	−0.711787	−	0.0622733i	−0.437298	+	0.899317i	$0.644064\pi$
$68$	−1.27424	−	0.111481i	−0.154524	−	0.0135191i
$69$		0			0
$70$	−9.12360	−	9.65440i	−1.09048	−	1.15392i
$71$	6.62671	−	3.82593i	0.786446	−	0.454055i	−0.0522640	−	0.998633i	$-0.516644\pi$
$71$	6.62671	−	3.82593i	0.786446	−	0.454055i	0.838710	+	0.544579i	$0.183310\pi$
$72$		0			0
$73$	−1.84806	−	6.89704i	−0.216299	−	0.807238i	−0.985705	−	0.168478i	$-0.946115\pi$
$73$	−1.84806	−	6.89704i	−0.216299	−	0.807238i	0.769407	−	0.638759i	$-0.220552\pi$
$74$	−1.39602	+	7.91721i	−0.162284	+	0.920357i
$75$		0			0
$76$	7.71612	+	2.80844i	0.885100	+	0.322150i
$77$	9.02653	+	6.32044i	1.02867	+	0.720281i
$78$		0			0
$79$	−5.08874	+	6.06452i	−0.572528	+	0.682312i	−0.972148	−	0.234369i	$-0.924698\pi$
$79$	−5.08874	+	6.06452i	−0.572528	+	0.682312i	0.399620	+	0.916681i	$0.369142\pi$
$80$	4.42611	+	10.2375i	0.494854	+	1.14459i
$81$		0			0
$82$	2.70191	+	2.70191i	0.298375	+	0.298375i
$83$	−0.544416	−	6.22270i	−0.0597574	−	0.683031i	−0.965705	−	0.259641i	$-0.916396\pi$
$83$	−0.544416	−	6.22270i	−0.0597574	−	0.683031i	0.905948	−	0.423389i	$-0.139160\pi$
$84$		0			0
$85$	−0.519047	+	2.52431i	−0.0562985	+	0.273800i
$86$	−2.41031	+	6.62228i	−0.259911	+	0.714099i
$87$		0			0
$88$	−2.94533	−	4.20637i	−0.313974	−	0.448401i
$89$	−0.260380	+	0.450992i	−0.0276002	+	0.0478050i	−0.879496	−	0.475907i	$-0.842120\pi$
$89$	−0.260380	+	0.450992i	−0.0276002	+	0.0478050i	0.851895	+	0.523712i	$0.175453\pi$
$90$		0			0
$91$	−9.78968	−	16.9562i	−1.02624	−	1.77750i
$92$	−0.897929	+	1.92562i	−0.0936156	+	0.200759i
$93$		0			0
$94$	5.62822	+	6.70745i	0.580506	+	0.691820i
$95$	7.41270	−	14.7905i	0.760527	−	1.51747i
$96$		0			0
$97$	4.27963	+	1.99563i	0.434531	+	0.202625i	0.627560	−	0.778568i	$-0.284054\pi$
$97$	4.27963	+	1.99563i	0.434531	+	0.202625i	−0.193029	+	0.981193i	$0.561831\pi$
$98$	1.98439	−	7.40585i	0.200454	−	0.748103i
$99$		0			0
$100$	−5.31338	+	1.60033i	−0.531338	+	0.160033i
$101$	6.92843	+	1.22167i	0.689404	+	0.121561i	0.507366	−	0.861731i	$-0.330619\pi$
$101$	6.92843	+	1.22167i	0.689404	+	0.121561i	0.182038	+	0.983291i	$0.441730\pi$
$102$		0			0
$103$	6.34471	−	2.95859i	0.625163	−	0.291518i	−0.0841052	−	0.996457i	$-0.526803\pi$
$103$	6.34471	−	2.95859i	0.625163	−	0.291518i	0.709268	+	0.704938i	$0.249025\pi$
$104$	1.58437	+	8.98539i	0.155360	+	0.881090i
$105$		0			0
$106$	−2.38870	−	2.00436i	−0.232011	−	0.194680i
$107$	3.17818	−	3.17818i	0.307247	−	0.307247i	−0.536594	−	0.843841i	$-0.680289\pi$
$107$	3.17818	−	3.17818i	0.307247	−	0.307247i	0.843841	+	0.536594i	$0.180289\pi$
$108$		0			0
$109$		−	3.14715i		−	0.301442i	−0.988576	−	0.150721i	$-0.951840\pi$
$109$		−	3.14715i		−	0.301442i	0.988576	−	0.150721i	$-0.0481595\pi$
$110$	11.3486	−	6.13127i	1.08205	−	0.584593i
$111$		0			0
$112$	−9.63755	+	13.7639i	−0.910663	+	1.30056i
$113$	−0.190621	−	0.408788i	−0.0179321	−	0.0384556i	0.897138	−	0.441751i	$-0.145643\pi$
$113$	−0.190621	−	0.408788i	−0.0179321	−	0.0384556i	−0.915070	+	0.403295i	$0.867865\pi$
$114$		0			0
$115$	3.64530	+	2.24429i	0.339926	+	0.209281i
$116$	−0.479100	−	0.276609i	−0.0444833	−	0.0256825i
$117$		0			0
$118$	−17.9897	−	4.82031i	−1.65608	−	0.443746i
$119$	−3.64830	+	1.32787i	−0.334439	+	0.121726i
$120$		0			0
$121$	0.229444	−	0.192526i	0.0208585	−	0.0175024i
$122$	−1.61535	+	18.4635i	−0.146247	+	1.67161i
$123$		0			0
$124$	1.25280	+	3.44203i	0.112504	+	0.309103i
$125$	1.96883	+	11.0056i	0.176097	+	0.984373i
$126$		0			0
$127$	0.534026	−	0.143092i	0.0473871	−	0.0126973i	−0.235048	−	0.971984i	$-0.575525\pi$
$127$	0.534026	−	0.143092i	0.0473871	−	0.0126973i	0.282435	+	0.959287i	$0.408858\pi$
$128$	9.26822	−	6.48968i	0.819203	−	0.573612i
$129$		0			0
$130$	−22.8792	+	1.35160i	−2.00664	+	0.118543i
$131$	−14.1236	+	2.49037i	−1.23398	+	0.217585i	−0.752336	−	0.658780i	$-0.771073\pi$
$131$	−14.1236	+	2.49037i	−1.23398	+	0.217585i	−0.481648	+	0.876365i	$0.659962\pi$
$132$		0			0
$133$	24.8288	−	2.17224i	2.15293	−	0.188357i
$134$	−10.3136			−0.890962
$135$		0			0
$136$	1.80922			0.155139
$137$	−3.37255	+	0.295060i	−0.288136	+	0.0252087i	−0.230308	−	0.973118i	$-0.573973\pi$
$137$	−3.37255	+	0.295060i	−0.288136	+	0.0252087i	−0.0578286	+	0.998327i	$0.518418\pi$
$138$		0			0
$139$	5.42140	−	0.955940i	0.459837	−	0.0810818i	0.0610693	−	0.998134i	$-0.480549\pi$
$139$	5.42140	−	0.955940i	0.459837	−	0.0810818i	0.398768	+	0.917052i	$0.369438\pi$
$140$	−6.24958	−	5.55238i	−0.528186	−	0.469262i
$141$		0			0
$142$	11.0535	−	7.73975i	0.927590	−	0.649505i
$143$	18.3649	−	4.92087i	1.53575	−	0.411504i
$144$		0			0
$145$	−0.664860	+	0.894609i	−0.0552136	+	0.0742933i
$146$	−4.30665	−	11.8324i	−0.356420	−	0.979257i
$147$		0			0
$148$	−0.440966	+	5.04026i	−0.0362472	+	0.414307i
$149$	10.1897	−	8.55016i	0.834771	−	0.700456i	−0.121610	−	0.992578i	$-0.538806\pi$
$149$	10.1897	−	8.55016i	0.834771	−	0.700456i	0.956381	+	0.292122i	$0.0943613\pi$
$150$		0			0
$151$	13.7660	−	5.01040i	1.12026	−	0.407741i	0.285512	−	0.958375i	$-0.407836\pi$
$151$	13.7660	−	5.01040i	1.12026	−	0.407741i	0.834747	+	0.550634i	$0.185614\pi$
$152$	−11.2187	−	3.00604i	−0.909957	−	0.243822i
$153$		0			0
$154$	16.8289	+	9.71616i	1.35611	+	0.782950i
$155$	7.17968	−	1.70790i	0.576686	−	0.137182i
$156$		0			0
$157$	−2.34570	−	5.03036i	−0.187207	−	0.401467i	0.790195	−	0.612855i	$-0.209979\pi$
$157$	−2.34570	−	5.03036i	−0.187207	−	0.401467i	−0.977402	+	0.211389i	$0.932201\pi$
$158$	−8.00759	+	11.4360i	−0.637050	+	0.909802i
$159$		0			0
$160$	6.01213	+	11.1281i	0.475300	+	0.879753i
$161$			6.44900i			0.508252i
$162$		0			0
$163$	5.06235	−	5.06235i	0.396514	−	0.396514i	−0.480488	−	0.877002i	$-0.659540\pi$
$163$	5.06235	−	5.06235i	0.396514	−	0.396514i	0.877002	+	0.480488i	$0.159540\pi$
$164$	1.84216	+	1.54575i	0.143848	+	0.120703i
$165$		0			0
$166$	−1.91282	−	10.8481i	−0.148463	−	0.841978i
$167$	12.7047	−	5.92432i	0.983123	−	0.458438i	0.136505	−	0.990639i	$-0.456413\pi$
$167$	12.7047	−	5.92432i	0.983123	−	0.458438i	0.846618	+	0.532202i	$0.178635\pi$
$168$		0			0
$169$	−20.4665	−	3.60879i	−1.57434	−	0.277599i
$170$	−0.523863	+	4.51439i	−0.0401784	+	0.346238i
$171$		0			0
$172$	−1.14791	+	4.28404i	−0.0875269	+	0.326655i
$173$	−8.87248	−	4.13731i	−0.674563	−	0.314554i	0.0549816	−	0.998487i	$-0.482490\pi$
$173$	−8.87248	−	4.13731i	−0.674563	−	0.314554i	−0.729544	+	0.683934i	$0.760268\pi$
$174$		0			0
$175$	−12.5637	+	11.2181i	−0.949727	+	0.848011i
$176$	−10.4879	−	12.4990i	−0.790558	−	0.942151i
$177$		0			0
$178$	−0.388110	+	0.832304i	−0.0290900	+	0.0623838i
$179$	−5.82103	−	10.0823i	−0.435084	−	0.753588i	0.562218	−	0.826989i	$-0.309948\pi$
$179$	−5.82103	−	10.0823i	−0.435084	−	0.753588i	−0.997303	+	0.0734009i	$0.976615\pi$
$180$		0			0
$181$	−10.5182	+	18.2180i	−0.781810	+	1.35413i	0.149076	+	0.988826i	$0.452370\pi$
$181$	−10.5182	+	18.2180i	−0.781810	+	1.35413i	−0.930886	+	0.365309i	$0.880963\pi$
$182$	−19.8042	−	28.2834i	−1.46799	−	2.09650i
$183$		0			0
$184$	1.02785	−	2.82400i	0.0757743	−	0.208188i
$185$	9.98494	+	2.05309i	0.734108	+	0.150947i
$186$		0			0
$187$	−0.328585	−	3.75574i	−0.0240285	−	0.274647i
$188$	3.89651	+	3.89651i	0.284182	+	0.284182i
$189$		0			0
$190$	10.7491	−	27.1226i	0.779822	−	1.96768i
$191$	−16.1454	+	19.2414i	−1.16824	+	1.39226i	−0.264388	+	0.964416i	$0.585170\pi$
$191$	−16.1454	+	19.2414i	−1.16824	+	1.39226i	−0.903854	+	0.427841i	$0.859274\pi$
$192$		0			0
$193$	−3.27354	−	2.29216i	−0.235635	−	0.164993i	0.449795	−	0.893132i	$-0.351497\pi$
$193$	−3.27354	−	2.29216i	−0.235635	−	0.164993i	−0.685430	+	0.728138i	$0.740386\pi$
$194$	7.82501	+	2.84807i	0.561803	+	0.204480i
$195$		0			0
$196$	0.837894	−	4.75193i	0.0598496	−	0.339424i
$197$	−2.68314	−	10.0136i	−0.191166	−	0.713441i	−0.993226	−	0.116198i	$-0.962929\pi$
$197$	−2.68314	−	10.0136i	−0.191166	−	0.713441i	0.802060	−	0.597243i	$-0.203737\pi$
$198$		0			0
$199$	−10.6933	+	6.17378i	−0.758027	+	0.437647i	−0.828587	−	0.559860i	$-0.810855\pi$
$199$	−10.6933	+	6.17378i	−0.758027	+	0.437647i	0.0705597	+	0.997508i	$0.477521\pi$
$200$	7.28959	−	2.90997i	0.515452	−	0.205766i
$201$		0			0
$202$	12.3593	+	1.08130i	0.869601	+	0.0760802i
$203$	−1.67278	−	0.146349i	−0.117406	−	0.0102717i
$204$		0			0
$205$	3.52143	−	3.32782i	0.245948	−	0.232425i
$206$	10.6914	−	6.17269i	0.744906	−	0.430072i
$207$		0			0
$208$	7.50345	+	28.0033i	0.520271	+	1.94168i
$209$	−4.20271	+	23.8347i	−0.290707	+	1.64868i
$210$		0			0
$211$	8.83540	+	3.21582i	0.608254	+	0.221386i	0.627739	−	0.778424i	$-0.283980\pi$
$211$	8.83540	+	3.21582i	0.608254	+	0.221386i	−0.0194850	+	0.999810i	$0.506203\pi$
$212$	−1.60753	−	1.12561i	−0.110406	−	0.0773070i
$213$		0			0
$214$	5.09483	−	6.07178i	0.348275	−	0.415058i
$215$	8.30729	+	3.29230i	0.566553	+	0.224533i
$216$		0			0
$217$	7.86162	+	7.86162i	0.533682	+	0.533682i
$218$	−0.483706	−	5.52878i	−0.0327607	−	0.374456i
$219$		0			0
$220$	6.77869	−	4.46647i	0.457019	−	0.301129i
$221$	−2.29111	+	6.29477i	−0.154117	+	0.423432i
$222$		0			0
$223$	8.07893	+	11.5379i	0.541005	+	0.772635i	0.992838	−	0.119467i	$-0.0381186\pi$
$223$	8.07893	+	11.5379i	0.541005	+	0.772635i	−0.451833	+	0.892102i	$0.649230\pi$
$224$	−9.52736	+	16.5019i	−0.636573	+	1.10258i
$225$		0			0
$226$	−0.397705	−	0.688845i	−0.0264549	−	0.0458213i
$227$	11.1767	−	23.9686i	0.741825	−	1.59085i	−0.0634761	−	0.997983i	$-0.520219\pi$
$227$	11.1767	−	23.9686i	0.741825	−	1.59085i	0.805301	−	0.592866i	$-0.202004\pi$
$228$		0			0
$229$	−6.42008	−	7.65115i	−0.424251	−	0.505602i	0.511004	−	0.859579i	$-0.329274\pi$
$229$	−6.42008	−	7.65115i	−0.424251	−	0.505602i	−0.935254	+	0.353976i	$0.884829\pi$
$230$	6.74886	+	3.38240i	0.445007	+	0.223029i
$231$		0			0
$232$	0.709181	+	0.330696i	0.0465600	+	0.0217113i
$233$	−7.01401	+	26.1766i	−0.459503	+	1.71489i	0.214997	+	0.976615i	$0.431026\pi$
$233$	−7.01401	+	26.1766i	−0.459503	+	1.71489i	−0.674500	+	0.738274i	$0.735641\pi$
$234$		0			0
$235$	8.70325	−	6.89337i	0.567737	−	0.449674i
$236$	−11.5430	−	2.03534i	−0.751385	−	0.132489i
$237$		0			0
$238$	−6.20510	+	2.89348i	−0.402217	+	0.187557i
$239$	−4.31982	−	24.4989i	−0.279426	−	1.58470i	−0.724543	−	0.689230i	$-0.757949\pi$
$239$	−4.31982	−	24.4989i	−0.279426	−	1.58470i	0.445117	−	0.895472i	$-0.353162\pi$
$240$		0			0
$241$	−21.8499	−	18.3342i	−1.40747	−	1.18101i	−0.957665	−	0.287885i	$-0.907048\pi$
$241$	−21.8499	−	18.3342i	−1.40747	−	1.18101i	−0.449808	−	0.893125i	$-0.648508\pi$
$242$	0.373487	−	0.373487i	0.0240087	−	0.0240087i
$243$		0			0
$244$			11.6643i			0.746728i
$245$	−9.31571	−	2.78053i	−0.595159	−	0.177641i
$246$		0			0
$247$	24.6656	−	35.2262i	1.56944	−	2.24139i
$248$	−2.18959	−	4.69559i	−0.139039	−	0.298170i
$249$		0			0
$250$	5.15028	+	19.0316i	0.325732	+	1.20367i
$251$	−9.61601	−	5.55181i	−0.606957	−	0.350427i	0.164816	−	0.986324i	$-0.447297\pi$
$251$	−9.61601	−	5.55181i	−0.606957	−	0.350427i	−0.771774	+	0.635897i	$0.780630\pi$
$252$		0			0
$253$	−6.04899	−	1.62082i	−0.380297	−	0.101900i
$254$	0.916163	−	0.333456i	0.0574852	−	0.0209229i
$255$		0			0
$256$	15.2834	−	12.8243i	0.955211	−	0.801518i
$257$	−2.45897	+	28.1062i	−0.153386	+	1.75321i	0.396555	+	0.918011i	$0.370206\pi$
$257$	−2.45897	+	28.1062i	−0.153386	+	1.75321i	−0.549941	+	0.835203i	$0.685350\pi$
$258$		0			0
$259$	5.25241	+	14.4309i	0.326369	+	0.896691i
$260$	−14.2700	+	2.10233i	−0.884985	+	0.130381i
$261$		0			0
$262$	−24.4290	+	6.54573i	−1.50923	+	0.404397i
$263$	−2.02429	+	1.41742i	−0.124823	+	0.0874019i	−0.634321	−	0.773070i	$-0.718720\pi$
$263$	−2.02429	+	1.41742i	−0.124823	+	0.0874019i	0.509498	+	0.860472i	$0.329831\pi$
$264$		0			0
$265$	−2.62608	+	2.95583i	−0.161319	+	0.181575i
$266$	43.2844	−	7.63221i	2.65394	−	0.467961i
$267$		0			0
$268$	−6.46612	+	0.565712i	−0.394981	+	0.0345564i
$269$	−2.07465			−0.126494			−0.0632468	−	0.997998i	$-0.520146\pi$
$269$	−2.07465			−0.126494			−0.0632468	+	0.997998i	$0.520146\pi$
$270$		0			0
$271$	−18.0921			−1.09901			−0.549507	−	0.835489i	$-0.685184\pi$
$271$	−18.0921			−1.09901			−0.549507	+	0.835489i	$0.685184\pi$
$272$	5.72684	−	0.501034i	0.347241	−	0.0303796i
$273$		0			0
$274$	−5.87941	+	1.03670i	−0.355188	+	0.0626293i
$275$	−7.36469	−	14.6039i	−0.444108	−	0.880647i
$276$		0			0
$277$	21.0713	−	14.7543i	1.26605	−	0.886497i	0.268991	−	0.963143i	$-0.413310\pi$
$277$	21.0713	−	14.7543i	1.26605	−	0.886497i	0.997058	+	0.0766456i	$0.0244210\pi$
$278$	9.37718	−	2.51261i	0.562406	−	0.150696i
$279$		0			0
$280$	9.49052	+	7.05321i	0.567167	+	0.421510i
$281$	−0.952631	−	2.61733i	−0.0568292	−	0.156137i	0.908029	−	0.418906i	$-0.137586\pi$
$281$	−0.952631	−	2.61733i	−0.0568292	−	0.156137i	−0.964859	+	0.262769i	$0.915364\pi$
$282$		0			0
$283$	1.78620	−	20.4164i	0.106179	−	1.21363i	−0.736962	−	0.675935i	$-0.763740\pi$
$283$	1.78620	−	20.4164i	0.106179	−	1.21363i	0.843140	−	0.537694i	$-0.180704\pi$
$284$	6.50545	−	5.45872i	0.386028	−	0.323916i
$285$		0			0
$286$	31.5065	−	11.4674i	1.86302	−	0.678083i
$287$	7.05042	+	1.88915i	0.416173	+	0.111513i
$288$		0			0
$289$	−13.5721	−	7.83584i	−0.798358	−	0.460932i
$290$	−1.03050	+	1.67380i	−0.0605131	+	0.0982890i
$291$		0			0
$292$	−3.34907	−	7.18209i	−0.195989	−	0.420300i
$293$	17.9864	−	25.6873i	1.05078	−	1.50067i	0.196743	−	0.980455i	$-0.436964\pi$
$293$	17.9864	−	25.6873i	1.05078	−	1.50067i	0.854036	−	0.520213i	$-0.174148\pi$
$294$		0			0
$295$	−6.75422	+	22.6289i	−0.393246	+	1.31751i
$296$		−	7.15639i		−	0.415957i
$297$		0			0
$298$	16.5867	−	16.5867i	0.960842	−	0.960842i
$299$	8.52385	+	7.15236i	0.492947	+	0.413631i
$300$		0			0
$301$	2.33764	+	13.2574i	0.134740	+	0.764146i
$302$	23.4134	−	10.9179i	1.34729	−	0.628252i
$303$		0			0
$304$	−36.3437	−	6.40838i	−2.08446	−	0.367546i
$305$	23.3444	+	2.70895i	1.33669	+	0.155114i
$306$		0			0
$307$	2.49145	−	9.29823i	0.142195	−	0.530678i	−0.857669	−	0.514201i	$-0.828088\pi$
$307$	2.49145	−	9.29823i	0.142195	−	0.530678i	0.999864	−	0.0164767i	$-0.00524495\pi$
$308$	11.0838	+	5.16845i	0.631557	+	0.294500i
$309$		0			0
$310$	12.3505	−	4.10387i	0.701460	−	0.233084i
$311$	0.00272616	+	0.00324891i	0.000154586	+	0.000184229i	0.766122	−	0.642695i	$-0.222184\pi$
$311$	0.00272616	+	0.00324891i	0.000154586	+	0.000184229i	−0.765967	+	0.642880i	$0.777740\pi$
$312$		0			0
$313$	−10.0379	+	21.5265i	−0.567378	+	1.21675i	0.388081	+	0.921625i	$0.373138\pi$
$313$	−10.0379	+	21.5265i	−0.567378	+	1.21675i	−0.955460	+	0.295122i	$0.904640\pi$
$314$	−4.89398	−	8.47662i	−0.276183	−	0.478363i
$315$		0			0
$316$	−4.39308	+	7.60903i	−0.247130	+	0.428041i
$317$	−0.455273	−	0.650197i	−0.0255707	−	0.0365187i	0.806163	−	0.591693i	$-0.201540\pi$
$317$	−0.455273	−	0.650197i	−0.0255707	−	0.0365187i	−0.831734	+	0.555175i	$0.812651\pi$
$318$		0			0
$319$	0.557690	−	1.53224i	0.0312246	−	0.0857890i
$320$	−0.000982575	−	0.00149124i	−5.49276e−5	−	8.33628e-5i
$321$		0			0
$322$	0.991189	+	11.3293i	0.0552368	+	0.631359i
$323$	−6.02965	−	6.02965i	−0.335499	−	0.335499i
$324$		0			0
$325$	0.893405	+	29.0475i	0.0495572	+	1.61127i
$326$	8.11527	−	9.67140i	0.449463	−	0.535649i
$327$		0			0
$328$	−2.78627	−	1.95097i	−0.153846	−	0.107724i
$329$	15.7172	+	5.72060i	0.866518	+	0.315387i
$330$		0			0
$331$	−0.994980	+	5.64281i	−0.0546891	+	0.310157i	−0.999865	−	0.0164031i	$-0.994778\pi$
$331$	−0.994980	+	5.64281i	−0.0546891	+	0.310157i	0.945176	+	0.326560i	$0.105890\pi$
$332$	−1.79427	−	6.69630i	−0.0984733	−	0.367507i
$333$		0			0
$334$	21.4086	−	12.3603i	1.17143	−	0.676325i
$335$	−0.369521	+	13.0724i	−0.0201891	+	0.714221i
$336$		0			0
$337$	−25.4396	−	2.22568i	−1.38578	−	0.121240i	−0.630271	−	0.776375i	$-0.717056\pi$
$337$	−25.4396	−	2.22568i	−1.38578	−	0.121240i	−0.755512	+	0.655135i	$0.772612\pi$
$338$	−36.5094	−	3.19415i	−1.98585	−	0.173739i
$339$		0			0
$340$	−0.0808168	+	2.85902i	−0.00438291	+	0.155052i
$341$	−9.34986	+	5.39814i	−0.506323	+	0.292326i
$342$		0			0
$343$	2.31243	+	8.63010i	0.124859	+	0.465982i
$344$	1.08934	−	6.17798i	0.0587335	−	0.333094i
$345$		0			0
$346$	−16.2227	−	5.90459i	−0.872139	−	0.317433i
$347$	−9.96940	−	6.98065i	−0.535185	−	0.374741i	0.274516	−	0.961582i	$-0.411482\pi$
$347$	−9.96940	−	6.98065i	−0.535185	−	0.374741i	−0.809702	+	0.586842i	$0.800371\pi$
$348$		0			0
$349$	−0.0762364	+	0.0908550i	−0.00408084	+	0.00486336i	−0.768081	−	0.640353i	$-0.778788\pi$
$349$	−0.0762364	+	0.0908550i	−0.00408084	+	0.00486336i	0.764000	+	0.645216i	$0.223233\pi$
$350$	−20.3472	+	21.6386i	−1.08761	+	1.15663i
$351$		0			0
$352$	−13.0838	−	13.0838i	−0.697370	−	0.697370i
$353$	1.88537	+	21.5499i	0.100348	+	1.14699i	0.864735	+	0.502228i	$0.167486\pi$
$353$	1.88537	+	21.5499i	0.100348	+	1.14699i	−0.764387	+	0.644758i	$0.776958\pi$
$354$		0			0
$355$	−9.41400	−	14.2875i	−0.499643	−	0.758300i
$356$	−0.197672	+	0.543100i	−0.0104766	+	0.0287842i
$357$		0			0
$358$	−11.7758	−	16.8175i	−0.622369	−	0.888835i
$359$	−15.2804	+	26.4664i	−0.806468	+	1.39684i	0.108828	+	0.994061i	$0.465290\pi$
$359$	−15.2804	+	26.4664i	−0.806468	+	1.39684i	−0.915296	+	0.402782i	$0.868043\pi$
$360$		0			0
$361$	17.8706	+	30.9528i	0.940558	+	1.62910i
$362$	−15.6779	+	33.6213i	−0.824011	+	1.76710i
$363$		0			0
$364$	−13.9676	−	16.6460i	−0.732102	−	0.872485i
$365$	−15.1517	+	5.03468i	−0.793077	+	0.263527i
$366$		0			0
$367$	−13.9364	−	6.49863i	−0.727472	−	0.339226i	0.0233530	−	0.999727i	$-0.492566\pi$
$367$	−13.9364	−	6.49863i	−0.727472	−	0.339226i	−0.750825	+	0.660502i	$0.770344\pi$
$368$	2.47147	−	9.22364i	0.128834	−	0.480816i
$369$		0			0
$370$	17.8567	+	2.07214i	0.928326	+	0.107726i
$371$	−5.86604	−	1.03434i	−0.304550	−	0.0537003i
$372$		0			0
$373$	−25.2501	+	11.7743i	−1.30740	+	0.609651i	−0.946425	−	0.322924i	$-0.895334\pi$
$373$	−25.2501	+	11.7743i	−1.30740	+	0.609651i	−0.360976	+	0.932575i	$0.617556\pi$
$374$	−1.15449	−	6.54744i	−0.0596973	−	0.338560i
$375$		0			0
$376$	−5.97077	−	5.01007i	−0.307919	−	0.258375i
$377$	−2.04865	+	2.04865i	−0.105511	+	0.105511i
$378$		0			0
$379$		−	16.6622i		−	0.855880i	−0.903807	−	0.427940i	$-0.859240\pi$
$379$		−	16.6622i		−	0.855880i	0.903807	−	0.427940i	$-0.140760\pi$
$380$	5.25143	−	17.5941i	0.269393	−	0.902558i
$381$		0			0
$382$	−25.4063	+	36.2840i	−1.29990	+	1.85645i
$383$	13.4360	+	28.8135i	0.686546	+	1.47230i	0.871927	+	0.489636i	$0.162870\pi$
$383$	13.4360	+	28.8135i	0.686546	+	1.47230i	−0.185381	+	0.982667i	$0.559352\pi$
$384$		0			0
$385$	12.9180	−	20.9823i	0.658365	−	1.06935i
$386$	−6.10313	−	3.52364i	−0.310641	−	0.179349i
$387$		0			0
$388$	5.06210	+	1.35639i	0.256989	+	0.0688601i
$389$	10.3645	−	3.77237i	0.525501	−	0.191267i	−0.0656273	−	0.997844i	$-0.520905\pi$
$389$	10.3645	−	3.77237i	0.525501	−	0.191267i	0.591128	+	0.806577i	$0.298683\pi$
$390$		0			0
$391$	1.69021	−	1.41826i	0.0854778	−	0.0717244i
$392$	−0.594840	+	6.79905i	−0.0300440	+	0.343404i
$393$		0			0
$394$	−6.25270	−	17.1791i	−0.315006	−	0.865473i
$395$	14.2081	+	10.5593i	0.714888	+	0.531294i
$396$		0			0
$397$	−15.3279	+	4.10710i	−0.769286	+	0.206129i	−0.622056	−	0.782973i	$-0.713702\pi$
$397$	−15.3279	+	4.10710i	−0.769286	+	0.206129i	−0.147230	+	0.989102i	$0.547036\pi$
$398$	−17.8367	+	12.4894i	−0.894071	+	0.626035i
$399$		0			0
$400$	22.2683	−	11.2299i	1.11342	−	0.561493i
$401$	18.2547	−	3.21880i	0.911598	−	0.160739i	0.301869	−	0.953349i	$-0.402389\pi$
$401$	18.2547	−	3.21880i	0.911598	−	0.160739i	0.609729	+	0.792610i	$0.291278\pi$
$402$		0			0
$403$	19.1100	−	1.67191i	0.951937	−	0.0832837i
$404$	7.80799			0.388462
$405$		0			0
$406$	−2.96116			−0.146960
$407$	−14.8559	+	1.29972i	−0.736379	+	0.0644248i
$408$		0			0
$409$	15.3828	−	2.71240i	0.760628	−	0.134119i	0.220137	−	0.975469i	$-0.429350\pi$
$409$	15.3828	−	2.71240i	0.760628	−	0.134119i	0.540491	+	0.841350i	$0.318238\pi$
$410$	5.67484	−	6.38742i	0.280260	−	0.315452i
$411$		0			0
$412$	6.36439	−	4.45640i	0.313551	−	0.219551i
$413$	−34.3644	+	9.20792i	−1.69096	+	0.453092i
$414$		0			0
$415$	−13.8184	+	2.03580i	−0.678318	+	0.0999334i
$416$	11.2446	+	30.8943i	0.551311	+	1.51472i
$417$		0			0
$418$	−3.71983	+	42.5179i	−0.181943	+	2.07962i
$419$	−8.40402	+	7.05181i	−0.410563	+	0.344503i	−0.824560	−	0.565775i	$-0.808577\pi$
$419$	−8.40402	+	7.05181i	−0.410563	+	0.344503i	0.413996	+	0.910279i	$0.364133\pi$
$420$		0			0
$421$	−4.13716	+	1.50580i	−0.201633	+	0.0733884i	−0.440863	−	0.897575i	$-0.645327\pi$
$421$	−4.13716	+	1.50580i	−0.201633	+	0.0733884i	0.239230	+	0.970963i	$0.423105\pi$
$422$	16.0159	+	4.29146i	0.779644	+	0.208905i
$423$		0			0
$424$	2.40387	+	1.38788i	0.116742	+	0.0674012i
$425$	5.70315	+	0.825732i	0.276644	+	0.0400539i
$426$		0			0
$427$	14.9625	+	32.0872i	0.724086	+	1.55281i
$428$	2.86115	−	4.08615i	0.138299	−	0.197512i
$429$		0			0
$430$	15.0999	+	4.50699i	0.728184	+	0.217346i
$431$			22.9617i			1.10603i	0.833173	+	0.553013i	$0.186522\pi$
$431$			22.9617i			1.10603i	−0.833173	+	0.553013i	$0.813478\pi$
$432$		0			0
$433$	−11.8168	+	11.8168i	−0.567878	+	0.567878i	−0.931534	−	0.363655i	$-0.881529\pi$
$433$	−11.8168	+	11.8168i	−0.567878	+	0.567878i	0.363655	+	0.931534i	$0.381529\pi$
$434$	15.0193	+	12.6027i	0.720949	+	0.604948i
$435$		0			0
$436$	−0.606518	−	3.43973i	−0.0290469	−	0.164733i
$437$	−12.8372	+	5.98609i	−0.614087	+	0.286353i
$438$		0			0
$439$	15.4676	+	2.72735i	0.738226	+	0.130169i	0.530103	−	0.847933i	$-0.322153\pi$
$439$	15.4676	+	2.72735i	0.738226	+	0.130169i	0.208124	+	0.978103i	$0.433264\pi$
$440$	−9.00098	+	7.12918i	−0.429105	+	0.339871i
$441$		0			0
$442$	−3.05744	+	11.4105i	−0.145428	+	0.542744i
$443$	−21.0959	−	9.83716i	−1.00229	−	0.467378i	−0.149017	−	0.988835i	$-0.547611\pi$
$443$	−21.0959	−	9.83716i	−1.00229	−	0.467378i	−0.853278	+	0.521457i	$0.825389\pi$
$444$		0			0
$445$	1.04103	+	0.521744i	0.0493495	+	0.0247330i
$446$	15.9661	+	19.0276i	0.756016	+	0.900984i
$447$		0			0
$448$	0.00113700	−	0.00243831i	5.37184e−5	−	0.000115199i
$449$	−15.4027	−	26.6783i	−0.726900	−	1.25903i	−0.958187	−	0.286142i	$-0.907627\pi$
$449$	−15.4027	−	26.6783i	−0.726900	−	1.25903i	0.231288	−	0.972885i	$-0.425706\pi$
$450$		0			0
$451$	−3.54396	+	6.13831i	−0.166878	+	0.289042i
$452$	−0.287125	−	0.410056i	−0.0135052	−	0.0192874i
$453$		0			0
$454$	15.9509	−	43.8248i	0.748615	−	2.05680i
$455$	−36.5584	+	24.0883i	−1.71388	+	1.12927i
$456$		0			0
$457$	2.28713	+	26.1420i	0.106988	+	1.22287i	0.839973	+	0.542629i	$0.182571\pi$
$457$	2.28713	+	26.1420i	0.106988	+	1.22287i	−0.732985	+	0.680245i	$0.761874\pi$
$458$	−12.4545	−	12.4545i	−0.581961	−	0.581961i
$459$		0			0
$460$	4.41672	+	1.75041i	0.205931	+	0.0816134i
$461$	12.6198	−	15.0397i	0.587761	−	0.700467i	−0.387413	−	0.921906i	$-0.626631\pi$
$461$	12.6198	−	15.0397i	0.587761	−	0.700467i	0.975174	+	0.221440i	$0.0710756\pi$
$462$		0			0
$463$	−6.86273	−	4.80533i	−0.318938	−	0.223323i	0.403134	−	0.915141i	$-0.367921\pi$
$463$	−6.86273	−	4.80533i	−0.318938	−	0.223323i	−0.722072	+	0.691818i	$0.756810\pi$
$464$	2.33640	+	0.850378i	0.108464	+	0.0394778i
$465$		0			0
$466$	−8.29867	+	47.0641i	−0.384429	+	2.18020i
$467$	0.507459	+	1.89386i	0.0234824	+	0.0876375i	0.976673	−	0.214734i	$-0.0688884\pi$
$467$	0.507459	+	1.89386i	0.0234824	+	0.0876375i	−0.953190	+	0.302371i	$0.902222\pi$
$468$		0			0
$469$	−17.0619	+	9.85072i	−0.787847	+	0.454864i
$470$	14.2300	−	13.4477i	0.656382	−	0.620294i
$471$		0			0
$472$	16.5157	+	1.44494i	0.760196	+	0.0665085i
$473$	−13.0227	−	1.13933i	−0.598782	−	0.0523867i
$474$		0			0
$475$	−33.9924	−	14.5961i	−1.55968	−	0.669715i
$476$	−3.73157	+	2.15442i	−0.171036	+	0.0987478i
$477$		0			0
$478$	−11.3543	−	42.3747i	−0.519333	−	1.93818i
$479$	3.17060	−	17.9814i	0.144868	−	0.821589i	−0.822604	−	0.568614i	$-0.807480\pi$
$479$	3.17060	−	17.9814i	0.144868	−	0.821589i	0.967473	−	0.252975i	$-0.0814091\pi$
$480$		0			0
$481$	24.8990	+	9.06251i	1.13530	+	0.413215i
$482$	−41.2029	−	28.8506i	−1.87674	−	1.31411i
$483$		0			0
$484$	0.213671	−	0.254643i	0.00971233	−	0.0115747i
$485$	3.89025	−	9.81605i	0.176647	−	0.445724i
$486$		0			0
$487$	−23.0616	−	23.0616i	−1.04502	−	1.04502i	−0.998938	−	0.0460835i	$-0.985326\pi$
$487$	−23.0616	−	23.0616i	−1.04502	−	1.04502i	−0.0460835	−	0.998938i	$-0.514674\pi$
$488$	−1.43793	−	16.4357i	−0.0650922	−	0.744008i
$489$		0			0
$490$	−16.7928	−	3.45293i	−0.758623	−	0.155987i
$491$	−1.13497	+	3.11830i	−0.0512204	+	0.140727i	−0.962665	−	0.270697i	$-0.912746\pi$
$491$	−1.13497	+	3.11830i	−0.0512204	+	0.140727i	0.911444	+	0.411423i	$0.134968\pi$
$492$		0			0
$493$	0.329519	+	0.470602i	0.0148408	+	0.0211949i
$494$	37.9175	−	65.6750i	1.70599	−	2.95486i
$495$		0			0
$496$	−8.23121	−	14.2569i	−0.369592	−	0.640153i
$497$	10.8936	−	23.3613i	0.488643	−	1.04790i
$498$		0			0
$499$	4.13042	+	4.92245i	0.184903	+	0.220359i	0.850531	−	0.525925i	$-0.176281\pi$
$499$	4.13042	+	4.92245i	0.184903	+	0.220359i	−0.665628	+	0.746284i	$0.731836\pi$
$500$	4.27287	+	11.6494i	0.191088	+	0.520976i
$501$		0			0
$502$	−17.7463	−	8.27524i	−0.792057	−	0.369342i
$503$	−1.67013	+	6.23303i	−0.0744676	+	0.277917i	−0.993112	−	0.117168i	$-0.962618\pi$
$503$	−1.67013	+	6.23303i	−0.0744676	+	0.277917i	0.918644	+	0.395085i	$0.129285\pi$
$504$		0			0
$505$	1.81335	−	15.6266i	0.0806931	−	0.695373i
$506$	−10.8757	−	1.91769i	−0.483486	−	0.0852516i
$507$		0			0
$508$	0.556097	−	0.259312i	0.0246728	−	0.0115051i
$509$	2.35893	+	13.3781i	0.104558	+	0.592976i	0.991396	+	0.130896i	$0.0417854\pi$
$509$	2.35893	+	13.3781i	0.104558	+	0.592976i	−0.886838	+	0.462080i	$0.847103\pi$
$510$		0			0
$511$	−18.4259	−	15.4611i	−0.815112	−	0.683960i
$512$	8.87720	−	8.87720i	0.392320	−	0.392320i
$513$		0			0
$514$			49.7537i			2.19454i
$515$	−7.44075	−	13.7724i	−0.327878	−	0.606884i
$516$		0			0
$517$	−9.31597	+	13.3046i	−0.409716	+	0.585135i
$518$	11.4452	+	24.5443i	0.502874	+	1.07842i
$519$		0			0
$520$	19.8481	−	4.72146i	0.870395	−	0.207050i
$521$	26.9126	+	15.5380i	1.17906	+	0.680731i	0.955797	−	0.294027i	$-0.0949957\pi$
$521$	26.9126	+	15.5380i	1.17906	+	0.680731i	0.223263	+	0.974758i	$0.428329\pi$
$522$		0			0
$523$	3.82198	+	1.02410i	0.167124	+	0.0447807i	0.341411	−	0.939914i	$-0.389095\pi$
$523$	3.82198	+	1.02410i	0.167124	+	0.0447807i	−0.174287	+	0.984695i	$0.555762\pi$
$524$	−14.9567	+	5.44379i	−0.653386	+	0.237813i
$525$		0			0
$526$	−3.33833	+	2.80120i	−0.145558	+	0.122138i
$527$	0.331527	−	3.78937i	0.0144415	−	0.165068i
$528$		0			0
$529$	6.61296	+	18.1689i	0.287520	+	0.789954i
$530$	−4.15909	+	5.59630i	−0.180659	+	0.243088i
$531$		0			0
$532$	26.7185	−	7.15919i	1.15839	−	0.310390i
$533$	10.3163	−	7.22357i	0.446850	−	0.312888i
$534$		0			0
$535$	−7.51336	−	6.67517i	−0.324831	−	0.288593i
$536$	9.04142	−	1.59425i	0.390530	−	0.0688609i
$537$		0			0
$538$	−3.64466	+	0.318866i	−0.157132	+	0.0137473i
$539$	14.2221			0.612590
$540$		0			0
$541$	43.8935			1.88713			0.943565	−	0.331186i	$-0.107449\pi$
$541$	43.8935			1.88713			0.943565	+	0.331186i	$0.107449\pi$
$542$	−31.7834	+	2.78069i	−1.36521	+	0.119441i
$543$		0			0
$544$	6.42021	−	1.13206i	0.275264	−	0.0485365i
$545$	−7.02499	+	0.415003i	−0.300917	+	0.0177768i
$546$		0			0
$547$	−19.7055	+	13.7979i	−0.842546	+	0.589957i	−0.913185	−	0.407545i	$-0.866385\pi$
$547$	−19.7055	+	13.7979i	−0.842546	+	0.589957i	0.0706388	+	0.997502i	$0.477496\pi$
$548$	−3.62923	+	0.972448i	−0.155033	+	0.0415409i
$549$		0			0
$550$	−15.1826	−	24.5236i	−0.647387	−	1.04569i
$551$	−1.26139	−	3.46563i	−0.0537369	−	0.147641i
$552$		0			0
$553$	−2.32430	+	26.5669i	−0.0988395	+	1.12974i
$554$	34.7495	−	29.1583i	1.47636	−	1.23882i
$555$		0			0
$556$	5.74120	−	2.08962i	0.243481	−	0.0886198i
$557$	25.5871	+	6.85604i	1.08416	+	0.290500i	0.756299	−	0.654226i	$-0.227006\pi$
$557$	25.5871	+	6.85604i	1.08416	+	0.290500i	0.327861	+	0.944726i	$0.393672\pi$
$558$		0			0
$559$	20.1154	+	11.6136i	0.850790	+	0.491204i
$560$	31.9942	+	19.6977i	1.35200	+	0.832381i
$561$		0			0
$562$	−2.07582	−	4.45161i	−0.0875632	−	0.187780i
$563$	12.3664	−	17.6610i	0.521181	−	0.744323i	−0.469140	−	0.883124i	$-0.655436\pi$
$563$	12.3664	−	17.6610i	0.521181	−	0.744323i	0.990320	+	0.138801i	$0.0443248\pi$
$564$		0			0
$565$	−0.887351	+	0.479406i	−0.0373311	+	0.0201687i
$566$		−	36.1412i		−	1.51913i
$567$		0			0
$568$	−8.49364	+	8.49364i	−0.356385	+	0.356385i
$569$	−8.77990	−	7.36721i	−0.368073	−	0.308850i	0.439926	−	0.898034i	$-0.355005\pi$
$569$	−8.77990	−	7.36721i	−0.368073	−	0.308850i	−0.807999	+	0.589184i	$0.799449\pi$
$570$		0			0
$571$	1.87072	+	10.6094i	0.0782872	+	0.443989i	0.998604	+	0.0528155i	$0.0168195\pi$
$571$	1.87072	+	10.6094i	0.0782872	+	0.443989i	−0.920317	+	0.391173i	$0.872069\pi$
$572$	19.1239	−	8.91764i	0.799612	−	0.372865i
$573$		0			0
$574$	12.6763	+	2.23517i	0.529097	+	0.0932940i
$575$	4.52895	−	8.43290i	0.188870	−	0.351676i
$576$		0			0
$577$	6.65499	−	24.8368i	0.277051	−	1.03397i	−0.677403	−	0.735612i	$-0.736895\pi$
$577$	6.65499	−	24.8368i	0.277051	−	1.03397i	0.954454	−	0.298357i	$-0.0964385\pi$
$578$	−25.0472	−	11.6797i	−1.04183	−	0.485812i
$579$		0			0
$580$	−0.554262	+	1.10591i	−0.0230145	+	0.0459205i
$581$	−13.5256	−	16.1192i	−0.561137	−	0.668737i
$582$		0			0
$583$	2.44449	−	5.24223i	0.101241	−	0.217111i
$584$	5.60442	+	9.70714i	0.231913	+	0.401684i
$585$		0			0
$586$	27.6498	−	47.8909i	1.14220	−	1.97835i
$587$	21.1711	+	30.2354i	0.873824	+	1.24795i	0.967633	+	0.252360i	$0.0812067\pi$
$587$	21.1711	+	30.2354i	0.873824	+	1.24795i	−0.0938095	+	0.995590i	$0.529904\pi$
$588$		0			0
$589$	−8.35183	+	22.9465i	−0.344131	+	0.945492i
$590$	−8.38756	+	40.7917i	−0.345310	+	1.67937i
$591$		0			0
$592$	−1.98184	−	22.6526i	−0.0814533	−	0.931016i
$593$	21.8217	+	21.8217i	0.896109	+	0.896109i	0.995089	−	0.0989808i	$-0.0315582\pi$
$593$	21.8217	+	21.8217i	0.896109	+	0.896109i	−0.0989808	+	0.995089i	$0.531558\pi$
$594$		0			0
$595$	3.44513	+	7.96854i	0.141237	+	0.326678i
$596$	9.48922	−	11.3088i	0.388693	−	0.463227i
$597$		0			0
$598$	16.0736	+	11.2549i	0.657300	+	0.460247i
$599$	−16.2128	−	5.90099i	−0.662438	−	0.241108i	−0.0111496	−	0.999938i	$-0.503549\pi$
$599$	−16.2128	−	5.90099i	−0.662438	−	0.241108i	−0.651289	+	0.758830i	$0.725771\pi$
$600$		0			0
$601$	7.91812	−	44.9059i	0.322987	−	1.83175i	−0.200473	−	0.979699i	$-0.564248\pi$
$601$	7.91812	−	44.9059i	0.322987	−	1.83175i	0.523460	−	0.852050i	$-0.324641\pi$
$602$	6.14430	+	22.9308i	0.250423	+	0.934592i
$603$		0			0
$604$	14.0802	−	8.12919i	0.572914	−	0.330772i
$605$	−0.460008	−	0.486771i	−0.0187020	−	0.0197901i
$606$		0			0
$607$	47.7085	+	4.17395i	1.93643	+	0.169416i	0.988726	−	0.149737i	$-0.0478428\pi$
$607$	47.7085	+	4.17395i	1.93643	+	0.169416i	0.947703	+	0.319153i	$0.103398\pi$
$608$	−41.6917	−	3.64755i	−1.69082	−	0.147928i
$609$		0			0
$610$	41.4268	+	1.17102i	1.67732	+	0.0474133i
$611$	24.9925	−	14.4294i	1.01109	−	0.583752i
$612$		0			0
$613$	−4.15240	−	15.4970i	−0.167714	−	0.625916i	−0.997678	−	0.0681004i	$-0.978306\pi$
$613$	−4.15240	−	15.4970i	−0.167714	−	0.625916i	0.829965	−	0.557816i	$-0.188360\pi$
$614$	2.94778	−	16.7177i	0.118963	−	0.674671i
$615$		0			0
$616$	−16.2549	−	5.91629i	−0.654927	−	0.238374i
$617$	−20.9035	−	14.6368i	−0.841541	−	0.589254i	0.0713522	−	0.997451i	$-0.477269\pi$
$617$	−20.9035	−	14.6368i	−0.841541	−	0.589254i	−0.912894	+	0.408198i	$0.866157\pi$
$618$		0			0
$619$	27.5321	−	32.8114i	1.10661	−	1.31880i	0.163414	−	0.986558i	$-0.447749\pi$
$619$	27.5321	−	32.8114i	1.10661	−	1.31880i	0.943193	−	0.332245i	$-0.107806\pi$
$620$	7.51802	−	3.25035i	0.301931	−	0.130537i
$621$		0			0
$622$	0.00528856	+	0.00528856i	0.000212052	+	0.000212052i
$623$	0.152893	+	1.74758i	0.00612554	+	0.0700152i
$624$		0			0
$625$	24.3069	−	5.84604i	0.972275	−	0.233842i
$626$	−14.3257	+	39.3596i	−0.572571	+	1.57313i
$627$		0			0
$628$	−3.53322	−	5.04597i	−0.140991	−	0.201356i
$629$	2.62708	−	4.55023i	0.104748	−	0.181430i
$630$		0			0
$631$	−6.58555	−	11.4065i	−0.262167	−	0.454086i	0.704651	−	0.709554i	$-0.251104\pi$
$631$	−6.58555	−	11.4065i	−0.262167	−	0.454086i	−0.966817	+	0.255468i	$0.917770\pi$
$632$	5.25209	−	11.2631i	0.208917	−	0.448024i
$633$		0			0
$634$	−0.899738	−	1.07227i	−0.0357332	−	0.0425851i
$635$	−0.389826	−	1.17317i	−0.0154698	−	0.0465559i
$636$		0			0
$637$	−22.9025	−	10.6796i	−0.907429	−	0.423141i
$638$	0.744227	−	2.77749i	0.0294642	−	0.109962i
$639$		0			0
$640$	−15.7083	−	19.8325i	−0.620924	−	0.783950i
$641$	−2.12742	−	0.375121i	−0.0840278	−	0.0148164i	0.131476	−	0.991319i	$-0.458028\pi$
$641$	−2.12742	−	0.375121i	−0.0840278	−	0.0148164i	−0.215504	+	0.976503i	$0.569139\pi$
$642$		0			0
$643$	4.05710	−	1.89186i	0.159996	−	0.0746075i	−0.340970	−	0.940074i	$-0.610756\pi$
$643$	4.05710	−	1.89186i	0.159996	−	0.0746075i	0.500967	+	0.865466i	$0.332978\pi$
$644$	1.24285	+	7.04855i	0.0489751	+	0.277752i
$645$		0			0
$646$	−11.5194	−	9.66592i	−0.453224	−	0.380300i
$647$	35.0743	−	35.0743i	1.37891	−	1.37891i	0.532451	−	0.846461i	$-0.321271\pi$
$647$	35.0743	−	35.0743i	1.37891	−	1.37891i	0.846461	−	0.532451i	$-0.178729\pi$
$648$		0			0
$649$		−	34.5472i		−	1.35609i
$650$	6.03400	+	50.8922i	0.236673	+	1.99616i
$651$		0			0
$652$	4.55737	−	6.50860i	0.178481	−	0.254897i
$653$	−1.35569	−	2.90729i	−0.0530523	−	0.113771i	0.877995	−	0.478670i	$-0.158881\pi$
$653$	−1.35569	−	2.90729i	−0.0530523	−	0.113771i	−0.931047	+	0.364899i	$0.881103\pi$
$654$		0			0
$655$	7.42137	+	31.1979i	0.289977	+	1.21900i
$656$	−9.35984	−	5.40391i	−0.365440	−	0.210987i
$657$		0			0
$658$	28.4906	+	7.63403i	1.11068	+	0.297606i
$659$	16.5503	−	6.02381i	0.644708	−	0.234654i	0.00108739	−	0.999999i	$-0.499654\pi$
$659$	16.5503	−	6.02381i	0.644708	−	0.234654i	0.643620	+	0.765345i	$0.277432\pi$
$660$		0			0
$661$	−31.9596	+	26.8173i	−1.24309	+	1.04307i	−0.245809	+	0.969318i	$0.579054\pi$
$661$	−31.9596	+	26.8173i	−1.24309	+	1.04307i	−0.997276	+	0.0737542i	$0.976502\pi$
$662$	−0.880660	+	10.0660i	−0.0342278	+	0.391226i
$663$		0			0
$664$	3.35373	+	9.21430i	0.130150	+	0.357584i
$665$	−8.12291	−	55.1358i	−0.314993	−	2.13808i
$666$		0			0
$667$	0.921766	−	0.246987i	0.0356909	−	0.00956336i
$668$	12.7441	−	8.92355i	0.493086	−	0.345263i
$669$		0			0
$670$	1.36002	+	23.0218i	0.0525423	+	0.889412i
$671$	−33.8575	+	5.96999i	−1.30705	+	0.230469i
$672$		0			0
$673$	−7.51557	+	0.657527i	−0.289704	+	0.0253458i	−0.231081	−	0.972934i	$-0.574226\pi$
$673$	−7.51557	+	0.657527i	−0.289704	+	0.0253458i	−0.0586226	+	0.998280i	$0.518671\pi$
$674$	−45.0333			−1.73462
$675$		0			0
$676$	−23.0647			−0.887104
$677$	20.9561	−	1.83342i	0.805407	−	0.0704639i	0.322986	−	0.946404i	$-0.395313\pi$
$677$	20.9561	−	1.83342i	0.805407	−	0.0704639i	0.482420	+	0.875940i	$0.339758\pi$
$678$		0			0
$679$	15.6652	−	2.76220i	0.601177	−	0.106004i
$680$	−0.238576	−	4.03850i	−0.00914896	−	0.154869i
$681$		0			0
$682$	−15.5958	+	10.9203i	−0.597193	+	0.418159i
$683$	−4.72063	+	1.26489i	−0.180630	+	0.0483997i	−0.348000	−	0.937494i	$-0.613139\pi$
$683$	−4.72063	+	1.26489i	−0.180630	+	0.0483997i	0.167370	+	0.985894i	$0.446472\pi$
$684$		0			0
$685$	1.10335	+	7.48922i	0.0421569	+	0.286148i
$686$	5.38880	+	14.8056i	0.205745	+	0.565281i
$687$		0			0
$688$	1.73728	−	19.8572i	0.0662333	−	0.757050i
$689$	−7.87294	+	6.60618i	−0.299935	+	0.251676i
$690$		0			0
$691$	39.6616	−	14.4357i	1.50880	−	0.549158i	0.550478	−	0.834850i	$-0.314445\pi$
$691$	39.6616	−	14.4357i	1.50880	−	0.549158i	0.958322	+	0.285692i	$0.0922233\pi$
$692$	−10.4947	−	2.81204i	−0.398948	−	0.106898i
$693$		0			0
$694$	−18.5867	−	10.7311i	−0.705543	−	0.407346i
$695$	−2.84873	−	11.9755i	−0.108058	−	0.454256i
$696$		0			0
$697$	−1.05540	−	2.26330i	−0.0399759	−	0.0857287i
$698$	−0.119965	+	0.171328i	−0.00454074	+	0.00648485i
$699$		0			0
$700$	−11.5698	+	14.6823i	−0.437296	+	0.554940i
$701$			3.71261i			0.140223i	0.997539	+	0.0701117i	$0.0223356\pi$
$701$			3.71261i			0.140223i	−0.997539	+	0.0701117i	$0.977664\pi$
$702$		0			0
$703$	−23.8504	+	23.8504i	−0.899533	+	0.899533i
$704$	0.00200131	+	0.00167930i	7.54273e−5	+	6.32910e-5i
$705$		0			0
$706$	6.62429	+	37.5682i	0.249309	+	1.41390i
$707$	21.4790	−	10.0158i	0.807800	−	0.376683i
$708$		0			0
$709$	−18.4462	−	3.25257i	−0.692763	−	0.122153i	−0.183829	−	0.982958i	$-0.558849\pi$
$709$	−18.4462	−	3.25257i	−0.692763	−	0.122153i	−0.508934	+	0.860805i	$0.669960\pi$
$710$	−18.7341	−	23.6528i	−0.703077	−	0.887673i
$711$		0			0
$712$	0.211580	−	0.789629i	0.00792931	−	0.0295926i
$713$	−5.72646	−	2.67029i	−0.214457	−	0.100003i
$714$		0			0
$715$	−13.4060	−	40.3449i	−0.501355	−	1.50881i
$716$	−8.30527	−	9.89783i	−0.310382	−	0.369899i
$717$		0			0
$718$	−22.7762	+	48.8436i	−0.849999	+	1.82283i
$719$	7.23920	+	12.5387i	0.269977	+	0.467613i	0.968856	−	0.247627i	$-0.0796506\pi$
$719$	7.23920	+	12.5387i	0.269977	+	0.467613i	−0.698879	+	0.715240i	$0.746317\pi$
$720$		0			0
$721$	11.7913	−	20.4231i	0.439130	−	0.760596i
$722$	36.1517	+	51.6300i	1.34543	+	1.92147i
$723$		0			0
$724$	−7.98507	+	21.9388i	−0.296763	+	0.815349i
$725$	2.08460	+	1.36612i	0.0774200	+	0.0507363i
$726$		0			0
$727$	0.355020	+	4.05790i	0.0131670	+	0.150499i	0.999932	−	0.0116572i	$-0.00371069\pi$
$727$	0.355020	+	4.05790i	0.0131670	+	0.150499i	−0.986765	+	0.162156i	$0.948155\pi$
$728$	21.7333	+	21.7333i	0.805489	+	0.805489i
$729$		0			0
$730$	−25.8441	+	11.1735i	−0.956534	+	0.413549i
$731$	2.96054	−	3.52824i	0.109500	−	0.130497i
$732$		0			0
$733$	−0.238710	−	0.167146i	−0.00881695	−	0.00617370i	0.569160	−	0.822227i	$-0.307269\pi$
$733$	−0.238710	−	0.167146i	−0.00881695	−	0.00617370i	−0.577977	+	0.816053i	$0.696158\pi$
$734$	−25.4816	−	9.27456i	−0.940545	−	0.342330i
$735$		0			0
$736$	1.88042	−	10.6644i	0.0693133	−	0.393096i
$737$	−4.95155	−	18.4794i	−0.182393	−	0.680699i
$738$		0			0
$739$	0.493834	−	0.285115i	0.0181660	−	0.0104881i	−0.490890	−	0.871222i	$-0.663328\pi$
$739$	0.493834	−	0.285115i	0.0181660	−	0.0104881i	0.509055	+	0.860734i	$0.329995\pi$
$740$	11.3089	+	0.319672i	0.415723	+	0.0117514i
$741$		0			0
$742$	−10.4642	−	0.915499i	−0.384153	−	0.0336090i
$743$	45.2865	+	3.96205i	1.66140	+	0.145354i	0.878806	−	0.477179i	$-0.158341\pi$
$743$	45.2865	+	3.96205i	1.66140	+	0.145354i	0.782594	+	0.622533i	$0.213896\pi$
$744$		0			0
$745$	−20.4291	−	21.6177i	−0.748466	−	0.792011i
$746$	−42.5487	+	24.5655i	−1.55782	+	0.899407i
$747$		0			0
$748$	−1.08294	−	4.04158i	−0.0395962	−	0.147775i
$749$	2.62917	−	14.9108i	0.0960678	−	0.544827i
$750$		0			0
$751$	21.7741	+	7.92512i	0.794547	+	0.289192i	0.707225	−	0.706988i	$-0.249947\pi$
$751$	21.7741	+	7.92512i	0.794547	+	0.289192i	0.0873224	+	0.996180i	$0.472169\pi$
$752$	−20.2871	−	14.2052i	−0.739795	−	0.518010i
$753$		0			0
$754$	−3.28412	+	3.91386i	−0.119601	+	0.142535i
$755$	−12.9994	−	30.0674i	−0.473096	−	1.09426i
$756$		0			0
$757$	−8.24491	−	8.24491i	−0.299666	−	0.299666i	0.541217	−	0.840883i	$-0.317964\pi$
$757$	−8.24491	−	8.24491i	−0.299666	−	0.299666i	−0.840883	+	0.541217i	$0.817964\pi$
$758$	−2.56092	−	29.2715i	−0.0930169	−	1.06319i
$759$		0			0
$760$	−5.23065	+	25.4385i	−0.189735	+	0.922752i
$761$	−13.7885	+	37.8835i	−0.499832	+	1.37328i	0.391605	+	0.920133i	$0.371920\pi$
$761$	−13.7885	+	37.8835i	−0.499832	+	1.37328i	−0.891437	+	0.453144i	$0.850302\pi$
$762$		0			0
$763$	−6.08083	−	8.68433i	−0.220141	−	0.314394i
$764$	−13.9383	+	24.1418i	−0.504268	+	0.873418i
$765$		0			0
$766$	28.0323	+	48.5534i	1.01285	+	1.75431i
$767$	−25.9420	+	55.6327i	−0.936710	+	2.00878i
$768$		0			0
$769$	−13.5646	−	16.1656i	−0.489151	−	0.582947i	0.463850	−	0.885914i	$-0.346468\pi$
$769$	−13.5646	−	16.1656i	−0.489151	−	0.582947i	−0.953001	+	0.302966i	$0.902023\pi$
$770$	19.4690	−	38.8463i	0.701614	−	1.39992i
$771$		0			0
$772$	−4.01963	−	1.87438i	−0.144669	−	0.0674605i
$773$	−6.07695	+	22.6795i	−0.218573	+	0.815724i	0.766306	+	0.642476i	$0.222093\pi$
$773$	−6.07695	+	22.6795i	−0.218573	+	0.815724i	−0.984878	+	0.173248i	$0.944574\pi$
$774$		0			0
$775$	−4.75910	−	15.8011i	−0.170952	−	0.567592i
$776$	−7.30002	−	1.28719i	−0.262055	−	0.0462074i
$777$		0			0
$778$	17.6281	−	8.22014i	0.632000	−	0.294706i
$779$	2.78384	+	15.7879i	0.0997414	+	0.565662i
$780$		0			0
$781$	19.1745	+	16.0893i	0.686116	+	0.575720i
$782$	2.75132	−	2.75132i	0.0983870	−	0.0983870i
$783$		0			0
$784$			21.6862i			0.774507i
$785$	−10.9193	+	5.89934i	−0.389728	+	0.210557i
$786$		0			0
$787$	4.65344	−	6.64580i	0.165877	−	0.236897i	−0.727604	−	0.685997i	$-0.759366\pi$
$787$	4.65344	−	6.64580i	0.165877	−	0.236897i	0.893482	+	0.449100i	$0.148255\pi$
$788$	−4.86241	−	10.4275i	−0.173216	−	0.371464i
$789$		0			0
$790$	26.5832	+	16.3663i	0.945787	+	0.582288i
$791$	−1.31585	−	0.759709i	−0.0467864	−	0.0270121i
$792$		0			0
$793$	59.0051	+	15.8104i	2.09533	+	0.561442i
$794$	−26.2962	+	9.57104i	−0.933218	+	0.339663i
$795$		0			0
$796$	−10.4976	+	8.80855i	−0.372078	+	0.312211i
$797$	1.11177	−	12.7075i	0.0393807	−	0.450124i	−0.950748	−	0.309964i	$-0.899683\pi$
$797$	1.11177	−	12.7075i	0.0393807	−	0.450124i	0.990129	−	0.140160i	$-0.0447616\pi$
$798$		0			0
$799$	−1.95721	−	5.37738i	−0.0692410	−	0.190238i
$800$	24.0471	−	14.8876i	0.850192	−	0.526354i
$801$		0			0
$802$	31.5745	−	8.46035i	1.11493	−	0.298745i
$803$	19.1331	−	13.3971i	0.675192	−	0.472775i
$804$		0			0
$805$	14.3953	−	0.850406i	0.507368	−	0.0299729i
$806$	33.3147	−	5.87429i	1.17346	−	0.206913i
$807$		0			0
$808$	−11.0019	+	0.962544i	−0.387047	+	0.0338622i
$809$	−37.1510			−1.30616			−0.653080	−	0.757289i	$-0.726523\pi$
$809$	−37.1510			−1.30616			−0.653080	+	0.757289i	$0.726523\pi$
$810$		0			0
$811$	−4.94368			−0.173596			−0.0867981	−	0.996226i	$-0.527664\pi$
$811$	−4.94368			−0.173596			−0.0867981	+	0.996226i	$0.527664\pi$
$812$	−1.85650	+	0.162423i	−0.0651503	+	0.00569991i
$813$		0			0
$814$	−25.8985	+	4.56660i	−0.907741	+	0.160059i
$815$	−11.9676	−	10.6325i	−0.419207	−	0.372440i
$816$		0			0
$817$	−24.2201	+	16.9591i	−0.847353	+	0.593323i
$818$	26.6069	−	7.12931i	0.930290	−	0.249270i
$819$		0			0
$820$	3.20748	−	4.31586i	0.112010	−	0.150716i
$821$	−11.5751	−	31.8023i	−0.403973	−	1.10991i	−0.960306	−	0.278948i	$-0.910014\pi$
$821$	−11.5751	−	31.8023i	−0.403973	−	1.10991i	0.556333	−	0.830959i	$-0.312208\pi$
$822$		0			0
$823$	1.42916	−	16.3354i	0.0498174	−	0.569416i	−0.929735	−	0.368229i	$-0.879964\pi$
$823$	1.42916	−	16.3354i	0.0498174	−	0.569416i	0.979553	−	0.201187i	$-0.0644800\pi$
$824$	−8.41844	+	7.06391i	−0.293270	+	0.246083i
$825$		0			0
$826$	−58.9548	+	21.4578i	−2.05130	+	0.746612i
$827$	−30.9381	−	8.28983i	−1.07582	−	0.288266i	−0.322939	−	0.946420i	$-0.604671\pi$
$827$	−30.9381	−	8.28983i	−1.07582	−	0.288266i	−0.752883	+	0.658154i	$0.771338\pi$
$828$		0			0
$829$	−2.18006	−	1.25866i	−0.0757168	−	0.0437151i	0.461664	−	0.887055i	$-0.347253\pi$
$829$	−2.18006	−	1.25866i	−0.0757168	−	0.0437151i	−0.537380	+	0.843340i	$0.680586\pi$
$830$	−23.9627	+	5.70025i	−0.831757	+	0.197859i
$831$		0			0
$832$	−0.00196178	−	0.00420706i	−6.80126e−5	−	0.000145854i
$833$	−2.87411	+	4.10466i	−0.0995821	+	0.142218i
$834$		0			0
$835$	−14.8995	−	27.5780i	−0.515617	−	0.954376i
$836$			26.8606i			0.928992i
$837$		0			0
$838$	−13.6800	+	13.6800i	−0.472568	+	0.472568i
$839$	37.2023	+	31.2164i	1.28437	+	1.07771i	0.992627	+	0.121213i	$0.0386784\pi$
$839$	37.2023	+	31.2164i	1.28437	+	1.07771i	0.291739	+	0.956498i	$0.405766\pi$
$840$		0			0
$841$	−4.99265	−	28.3147i	−0.172160	−	0.976370i
$842$	−7.03657	+	3.28121i	−0.242496	+	0.113078i
$843$		0			0
$844$	10.2766	+	1.81204i	0.353734	+	0.0623729i
$845$	−5.35662	+	46.1607i	−0.184273	+	1.58798i
$846$		0			0
$847$	0.261140	−	0.974587i	0.00897287	−	0.0334872i
$848$	7.99348	+	3.72742i	0.274497	+	0.128000i
$849$		0			0
$850$	10.1460	+	0.574057i	0.348004	+	0.0196900i
$851$	−5.60993	−	6.68566i	−0.192306	−	0.229181i
$852$		0			0
$853$	3.95780	−	8.48753i	0.135512	−	0.290607i	−0.826828	−	0.562455i	$-0.809857\pi$
$853$	3.95780	−	8.48753i	0.135512	−	0.290607i	0.962340	+	0.271848i	$0.0876347\pi$
$854$	31.2172	+	54.0698i	1.06823	+	1.85023i
$855$		0			0
$856$	−3.52781	+	6.11035i	−0.120578	+	0.208847i
$857$	−31.1992	−	44.5570i	−1.06574	−	1.52204i	−0.835955	−	0.548798i	$-0.815086\pi$
$857$	−31.1992	−	44.5570i	−1.06574	−	1.52204i	−0.229788	−	0.973241i	$-0.573803\pi$
$858$		0			0
$859$	−10.1859	+	27.9855i	−0.347538	+	0.954853i	0.635605	+	0.772015i	$0.280751\pi$
$859$	−10.1859	+	27.9855i	−0.347538	+	0.954853i	−0.983143	+	0.182839i	$0.941471\pi$
$860$	9.71410	+	1.99741i	0.331248	+	0.0681110i
$861$		0			0
$862$	3.52913	+	40.3382i	0.120203	+	1.37392i
$863$	−19.0658	−	19.0658i	−0.649007	−	0.649007i	0.303746	−	0.952753i	$-0.401763\pi$
$863$	−19.0658	−	19.0658i	−0.649007	−	0.649007i	−0.952753	+	0.303746i	$0.901763\pi$
$864$		0			0
$865$	−8.06522	+	20.3505i	−0.274226	+	0.691939i
$866$	−18.9430	+	22.5754i	−0.643711	+	0.767145i
$867$		0			0
$868$	10.1076	+	7.07741i	0.343074	+	0.240223i
$869$	−24.3349	−	8.85719i	−0.825506	−	0.300460i
$870$		0			0
$871$	−5.90279	+	33.4764i	−0.200009	+	1.13430i
$872$	1.27866	+	4.77202i	0.0433009	+	0.161601i
$873$		0			0
$874$	−21.6319	+	12.4892i	−0.731708	+	0.422452i
$875$	26.6976	+	26.5651i	0.902543	+	0.898065i
$876$		0			0
$877$	−3.95512	−	0.346028i	−0.133555	−	0.0116845i	0.0201823	−	0.999796i	$-0.493575\pi$
$877$	−3.95512	−	0.346028i	−0.133555	−	0.0116845i	−0.153737	+	0.988112i	$0.549131\pi$
$878$	27.5920	+	2.41399i	0.931184	+	0.0814681i
$879$		0			0
$880$	−26.5171	+	25.0591i	−0.893890	+	0.844743i
$881$	−11.0930	+	6.40454i	−0.373732	+	0.215774i	−0.675088	−	0.737737i	$-0.735894\pi$
$881$	−11.0930	+	6.40454i	−0.373732	+	0.215774i	0.301355	+	0.953512i	$0.402561\pi$
$882$		0			0
$883$	−8.03874	−	30.0010i	−0.270525	−	1.00961i	−0.958781	−	0.284146i	$-0.908290\pi$
$883$	−8.03874	−	30.0010i	−0.270525	−	1.00961i	0.688256	−	0.725468i	$-0.258377\pi$
$884$	−1.29098	+	7.32153i	−0.0434205	+	0.246250i
$885$		0			0
$886$	−38.5723	−	14.0392i	−1.29586	−	0.471655i
$887$	28.2142	+	19.7558i	0.947341	+	0.663335i	0.941630	−	0.336649i	$-0.109293\pi$
$887$	28.2142	+	19.7558i	0.947341	+	0.663335i	0.00571031	+	0.999984i	$0.498182\pi$
$888$		0			0
$889$	1.19713	−	1.42668i	0.0401504	−	0.0478493i
$890$	1.90903	+	0.756576i	0.0639907	+	0.0253605i
$891$		0			0
$892$	11.0536	+	11.0536i	0.370102	+	0.370102i
$893$	3.20176	+	36.5962i	0.107143	+	1.22465i
$894$		0			0
$895$	−21.7379	+	14.3231i	−0.726618	+	0.478768i
$896$	13.0358	−	35.8156i	0.435496	−	1.19652i
$897$		0			0
$898$	−31.1593	−	44.5000i	−1.03980	−	1.48499i
$899$	0.822588	−	1.42476i	0.0274348	−	0.0475185i
$900$		0			0
$901$	1.01896	+	1.76490i	0.0339466	+	0.0587973i
$902$	−5.28245	+	11.3282i	−0.175886	+	0.377189i
$903$		0			0
$904$	0.455126	+	0.542398i	0.0151373	+	0.0180399i
$905$	42.0528	+	21.0761i	1.39788	+	0.700593i
$906$		0			0
$907$	28.3482	+	13.2190i	0.941287	+	0.438929i	0.831810	−	0.555060i	$-0.187305\pi$
$907$	28.3482	+	13.2190i	0.941287	+	0.438929i	0.109477	+	0.993989i	$0.465083\pi$
$908$	7.59659	−	28.3509i	0.252102	−	0.940856i
$909$		0			0
$910$	−60.5220	+	47.9362i	−2.00628	+	1.58907i
$911$	14.8888	+	2.62530i	0.493288	+	0.0869800i	0.414758	−	0.909932i	$-0.363866\pi$
$911$	14.8888	+	2.62530i	0.493288	+	0.0869800i	0.0785299	+	0.996912i	$0.474977\pi$
$912$		0			0
$913$	18.5188	−	8.63545i	0.612882	−	0.285792i
$914$	8.03589	+	45.5738i	0.265804	+	1.50745i
$915$		0			0
$916$	−8.49147	−	7.12519i	−0.280566	−	0.235423i
$917$	−34.1612	+	34.1612i	−1.12810	+	1.12810i
$918$		0			0
$919$			1.84099i			0.0607286i	0.999539	+	0.0303643i	$0.00966675\pi$
$919$			1.84099i			0.0607286i	−0.999539	+	0.0303643i	$0.990333\pi$
$920$	−6.43921	−	1.92196i	−0.212294	−	0.0633650i
$921$		0			0
$922$	19.8584	−	28.3607i	0.654001	−	0.934010i
$923$	−18.7957	−	40.3076i	−0.618670	−	1.32674i
$924$		0			0
$925$	3.26619	−	22.5589i	0.107392	−	0.741732i
$926$	−12.7947	−	7.38704i	−0.420461	−	0.242753i
$927$		0			0
$928$	2.72352	+	0.729766i	0.0894041	+	0.0239557i
$929$	43.8338	−	15.9542i	1.43814	−	0.523441i	0.498888	−	0.866666i	$-0.333742\pi$
$929$	43.8338	−	15.9542i	1.43814	−	0.523441i	0.939253	+	0.343226i	$0.111520\pi$
$930$		0			0
$931$	24.6419	−	20.6770i	0.807605	−	0.677661i
$932$	−2.62133	+	29.9620i	−0.0858647	+	0.981438i
$933$		0			0
$934$	1.18256	+	3.24907i	0.0386947	+	0.106313i
$935$	−8.34015	+	1.22872i	−0.272752	+	0.0401833i
$936$		0			0
$937$	−6.41697	+	1.71942i	−0.209633	+	0.0561711i	−0.362107	−	0.932136i	$-0.617943\pi$
$937$	−6.41697	+	1.71942i	−0.209633	+	0.0561711i	0.152474	+	0.988307i	$0.451276\pi$
$938$	−28.4597	+	19.9277i	−0.929243	+	0.650663i
$939$		0			0
$940$	8.18389	−	9.21153i	0.266929	−	0.300447i
$941$	42.6827	−	7.52611i	1.39142	−	0.245344i	0.572805	−	0.819692i	$-0.305855\pi$
$941$	42.6827	−	7.52611i	1.39142	−	0.245344i	0.818612	+	0.574347i	$0.194744\pi$
$942$		0			0
$943$	−4.13236	+	0.361535i	−0.134568	+	0.0117732i
$944$	52.6783			1.71453
$945$		0			0
$946$	−23.0528			−0.749511
$947$	−50.2480	+	4.39613i	−1.63284	+	0.142855i	−0.866363	−	0.499415i	$-0.833548\pi$
$947$	−50.2480	+	4.39613i	−1.63284	+	0.142855i	−0.766478	+	0.642270i	$0.777993\pi$
$948$		0			0
$949$	−40.8709	+	7.20665i	−1.32673	+	0.233938i
$950$	−61.9599	−	20.4173i	−2.01024	−	0.662425i
$951$		0			0
$952$	4.99241	−	3.49573i	0.161805	−	0.113297i
$953$	−30.3800	+	8.14030i	−0.984105	+	0.263690i	−0.714773	−	0.699357i	$-0.753470\pi$
$953$	−30.3800	+	8.14030i	−0.984105	+	0.263690i	−0.269333	+	0.963047i	$0.586803\pi$
$954$		0			0
$955$	45.0792	+	33.5022i	1.45873	+	1.08410i
$956$	−9.44285	−	25.9440i	−0.305404	−	0.839089i
$957$		0			0
$958$	2.80631	−	32.0762i	0.0906677	−	1.03634i
$959$	−8.73620	+	7.33054i	−0.282107	+	0.236716i
$960$		0			0
$961$	18.8945	−	6.87702i	0.609498	−	0.221839i
$962$	45.1345	+	12.0938i	1.45519	+	0.389918i
$963$		0			0
$964$	−27.4146	−	15.8278i	−0.882964	−	0.509780i
$965$	−4.68483	+	7.60939i	−0.150810	+	0.244955i
$966$		0			0
$967$	3.62934	+	7.78315i	0.116712	+	0.250289i	0.955982	−	0.293425i	$-0.0947952\pi$
$967$	3.62934	+	7.78315i	0.116712	+	0.250289i	−0.839270	+	0.543715i	$0.817017\pi$
$968$	−0.269684	+	0.385149i	−0.00866797	+	0.0123791i
$969$		0			0
$970$	5.32554	−	17.8424i	0.170993	−	0.572884i
$971$		−	29.8892i		−	0.959189i	−0.877490	−	0.479595i	$-0.840784\pi$
$971$		−	29.8892i		−	0.959189i	0.877490	−	0.479595i	$-0.159216\pi$
$972$		0			0
$973$	13.1129	−	13.1129i	0.420381	−	0.420381i
$974$	−44.0582	−	36.9692i	−1.41172	−	1.18457i
$975$		0			0
$976$	−9.10317	−	51.6266i	−0.291385	−	1.65253i
$977$	32.5668	−	15.1861i	1.04190	−	0.485848i	0.175128	−	0.984546i	$-0.443966\pi$
$977$	32.5668	−	15.1861i	1.04190	−	0.485848i	0.866776	+	0.498698i	$0.166188\pi$
$978$		0			0
$979$	−1.67761	−	0.295808i	−0.0536166	−	0.00945406i
$980$	−10.7176	−	1.24371i	−0.342362	−	0.0397287i
$981$		0			0
$982$	−1.51459	+	5.65254i	−0.0483327	+	0.180380i
$983$	33.2165	+	15.4891i	1.05944	+	0.494026i	0.872636	−	0.488371i	$-0.162409\pi$
$983$	33.2165	+	15.4891i	1.05944	+	0.494026i	0.186806	+	0.982397i	$0.440186\pi$
$984$		0			0
$985$	−21.9984	+	7.30971i	−0.700926	+	0.232907i
$986$	0.651216	+	0.776090i	0.0207390	+	0.0247157i
$987$		0			0
$988$	20.1700	−	43.2547i	0.641693	−	1.37611i
$989$	−3.82526	−	6.62555i	−0.121636	−	0.210680i
$990$		0			0
$991$	−19.5180	+	33.8061i	−0.620009	+	1.07389i	0.369474	+	0.929241i	$0.379538\pi$
$991$	−19.5180	+	33.8061i	−0.620009	+	1.07389i	−0.989483	+	0.144647i	$0.953795\pi$
$992$	−10.7081	−	15.2927i	−0.339982	−	0.485545i
$993$		0			0
$994$	15.5468	−	42.7146i	0.493115	−	1.35482i
$995$	15.1910	+	23.0552i	0.481588	+	0.730899i
$996$		0			0
$997$	−3.41553	−	39.0397i	−0.108171	−	1.23640i	−0.835259	−	0.549856i	$-0.814683\pi$
$997$	−3.41553	−	39.0397i	−0.108171	−	1.23640i	0.727088	−	0.686544i	$-0.240873\pi$
$998$	8.01273	+	8.01273i	0.253638	+	0.253638i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.197.13		192
3.2	odd	2		135.2.q.a.92.4	yes	192
5.3	odd	4	inner	405.2.r.a.278.4		192
15.2	even	4		675.2.ba.b.443.4		192
15.8	even	4		135.2.q.a.38.13	yes	192
15.14	odd	2		675.2.ba.b.632.13		192
27.5	odd	18	inner	405.2.r.a.287.4		192
27.22	even	9		135.2.q.a.32.13	✓	192
135.22	odd	36		675.2.ba.b.518.13		192
135.49	even	18		675.2.ba.b.32.4		192
135.103	odd	36		135.2.q.a.113.4	yes	192
135.113	even	36	inner	405.2.r.a.368.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.13	✓	192	27.22	even	9
135.2.q.a.38.13	yes	192	15.8	even	4
135.2.q.a.92.4	yes	192	3.2	odd	2
135.2.q.a.113.4	yes	192	135.103	odd	36
405.2.r.a.197.13		192	1.1	even	1	trivial
405.2.r.a.278.4		192	5.3	odd	4	inner
405.2.r.a.287.4		192	27.5	odd	18	inner
405.2.r.a.368.13		192	135.113	even	36	inner
675.2.ba.b.32.4		192	135.49	even	18
675.2.ba.b.443.4		192	15.2	even	4
675.2.ba.b.518.13		192	135.22	odd	36
675.2.ba.b.632.13		192	15.14	odd	2

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75676 - 0.153697i) q^{2} +(1.09297 - 0.192720i) q^{4} +(-0.131866 - 2.23218i) q^{5} +(2.75943 - 1.93217i) q^{7} +(-1.51630 + 0.406292i) q^{8} +O(q^{10})\)	\(q+(1.75676 - 0.153697i) q^{2} +(1.09297 - 0.192720i) q^{4} +(-0.131866 - 2.23218i) q^{5} +(2.75943 - 1.93217i) q^{7} +(-1.51630 + 0.406292i) q^{8} +(-0.574736 - 3.90113i) q^{10} +(1.11880 + 3.07388i) q^{11} +(0.506571 - 5.79013i) q^{13} +(4.55068 - 3.81848i) q^{14} +(-4.68713 + 1.70598i) q^{16} +(-1.11325 - 0.298295i) q^{17} +(6.40749 + 3.69937i) q^{19} +(-0.574311 - 2.41429i) q^{20} +(2.43791 + 5.22812i) q^{22} +(-1.09807 + 1.56820i) q^{23} +(-4.96522 + 0.588699i) q^{25} -10.2497i q^{26} +(2.64360 - 2.64360i) q^{28} +(-0.381851 - 0.320411i) q^{29} +(0.573116 + 3.25030i) q^{31} +(-5.12653 + 2.39054i) q^{32} +(-2.00157 - 0.352930i) q^{34} +(-4.67682 - 5.90474i) q^{35} +(-1.17991 + 4.40348i) q^{37} +(11.8250 + 5.51409i) q^{38} +(1.10686 + 3.33107i) q^{40} +(1.39279 + 1.65986i) q^{41} +(-1.68889 + 3.62184i) q^{43} +(1.81521 + 3.14404i) q^{44} +(-1.68801 + 2.92372i) q^{46} +(2.84791 + 4.06724i) q^{47} +(1.48701 - 4.08553i) q^{49} +(-8.63222 + 1.79734i) q^{50} +(-0.562207 - 6.42605i) q^{52} +(-1.25033 - 1.25033i) q^{53} +(6.71392 - 2.90271i) q^{55} +(-3.39910 + 4.05089i) q^{56} +(-0.720066 - 0.504196i) q^{58} +(-9.92422 - 3.61212i) q^{59} +(-1.82504 + 10.3503i) q^{61} +(1.50639 + 5.62192i) q^{62} +(0.000691655 - 0.000399327i) q^{64} +(-12.9914 - 0.367231i) q^{65} +(-5.82623 - 0.509729i) q^{67} +(-1.27424 - 0.111481i) q^{68} +(-9.12360 - 9.65440i) q^{70} +(6.62671 - 3.82593i) q^{71} +(-1.84806 - 6.89704i) q^{73} +(-1.39602 + 7.91721i) q^{74} +(7.71612 + 2.80844i) q^{76} +(9.02653 + 6.32044i) q^{77} +(-5.08874 + 6.06452i) q^{79} +(4.42611 + 10.2375i) q^{80} +(2.70191 + 2.70191i) q^{82} +(-0.544416 - 6.22270i) q^{83} +(-0.519047 + 2.52431i) q^{85} +(-2.41031 + 6.62228i) q^{86} +(-2.94533 - 4.20637i) q^{88} +(-0.260380 + 0.450992i) q^{89} +(-9.78968 - 16.9562i) q^{91} +(-0.897929 + 1.92562i) q^{92} +(5.62822 + 6.70745i) q^{94} +(7.41270 - 14.7905i) q^{95} +(4.27963 + 1.99563i) q^{97} +(1.98439 - 7.40585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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