LMFDB - Embedded newform 675.2.r.a.46.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.17
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.251657 + 0.279494i) q^{2} +(0.194272 - 1.84837i) q^{4} +(0.102616 - 2.23371i) q^{5} +(1.17975 - 2.04339i) q^{7} +(1.17403 - 0.852985i) q^{8} +O(q^{10})$	\(q+(0.251657 + 0.279494i) q^{2} +(0.194272 - 1.84837i) q^{4} +(0.102616 - 2.23371i) q^{5} +(1.17975 - 2.04339i) q^{7} +(1.17403 - 0.852985i) q^{8} +(0.650132 - 0.533449i) q^{10} +(-0.251022 - 0.278789i) q^{11} +(0.237736 - 0.264032i) q^{13} +(0.868006 - 0.184500i) q^{14} +(-3.10202 - 0.659354i) q^{16} +(-3.45606 + 2.51098i) q^{17} +(-3.26679 + 2.37346i) q^{19} +(-4.10879 - 0.623618i) q^{20} +(0.0147481 - 0.140318i) q^{22} +(4.49630 - 0.955717i) q^{23} +(-4.97894 - 0.458427i) q^{25} +0.133623 q^{26} +(-3.54774 - 2.57759i) q^{28} +(0.336493 - 0.149816i) q^{29} +(5.37131 + 2.39146i) q^{31} +(-2.04755 - 3.54645i) q^{32} +(-1.57154 - 0.334042i) q^{34} +(-4.44328 - 2.84490i) q^{35} +(-3.03352 - 9.33621i) q^{37} +(-1.48548 - 0.315748i) q^{38} +(-1.78485 - 2.70998i) q^{40} +(5.77601 - 6.41491i) q^{41} +(-3.86472 + 6.69390i) q^{43} +(-0.564071 + 0.409822i) q^{44} +(1.39864 + 1.01617i) q^{46} +(0.611825 - 0.272402i) q^{47} +(0.716381 + 1.24081i) q^{49} +(-1.12486 - 1.50695i) q^{50} +(-0.441844 - 0.490718i) q^{52} +(8.98419 + 6.52740i) q^{53} +(-0.648493 + 0.532104i) q^{55} +(-0.357913 - 3.40531i) q^{56} +(0.126554 + 0.0563453i) q^{58} +(7.75940 - 8.61768i) q^{59} +(4.33263 + 4.81187i) q^{61} +(0.683331 + 2.10308i) q^{62} +(-1.48405 + 4.56744i) q^{64} +(-0.565377 - 0.558127i) q^{65} +(-11.6258 - 5.17613i) q^{67} +(3.96980 + 6.87589i) q^{68} +(-0.323050 - 1.95781i) q^{70} +(1.67206 + 1.21482i) q^{71} +(1.94846 - 5.99673i) q^{73} +(1.84600 - 3.19737i) q^{74} +(3.75239 + 6.49933i) q^{76} +(-0.865817 + 0.184035i) q^{77} +(10.8685 - 4.83898i) q^{79} +(-1.79112 + 6.86136i) q^{80} +3.24650 q^{82} +(-0.919146 - 8.74509i) q^{83} +(5.25415 + 7.97751i) q^{85} +(-2.84349 + 0.604402i) q^{86} +(-0.532511 - 0.113189i) q^{88} +(0.603343 - 1.85690i) q^{89} +(-0.259051 - 0.797278i) q^{91} +(-0.893017 - 8.49649i) q^{92} +(0.230105 + 0.102449i) q^{94} +(4.96640 + 7.54061i) q^{95} +(10.2797 - 4.57681i) q^{97} +(-0.166516 + 0.512483i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.251657	+	0.279494i	0.177949	+	0.197632i	0.825520	−	0.564373i	$-0.190882\pi$
$2$	0.251657	+	0.279494i	0.177949	+	0.197632i	−0.647571	+	0.762005i	$0.724215\pi$
$3$		0			0
$3$		0			0
$4$	0.194272	−	1.84837i	0.0971358	−	0.924185i
$5$	0.102616	−	2.23371i	0.0458911	−	0.998946i
$5$	0.102616	−	2.23371i	0.0458911	−	0.998946i
$6$		0			0
$7$	1.17975	−	2.04339i	0.445903	−	0.772327i	−0.552211	−	0.833704i	$-0.686216\pi$
$7$	1.17975	−	2.04339i	0.445903	−	0.772327i	0.998115	+	0.0613768i	$0.0195491\pi$
$8$	1.17403	−	0.852985i	0.415084	−	0.301576i
$9$		0			0
$10$	0.650132	−	0.533449i	0.205590	−	0.168692i
$11$	−0.251022	−	0.278789i	−0.0756861	−	0.0840580i	0.704112	−	0.710089i	$-0.251345\pi$
$11$	−0.251022	−	0.278789i	−0.0756861	−	0.0840580i	−0.779798	+	0.626031i	$0.784678\pi$
$12$		0			0
$13$	0.237736	−	0.264032i	0.0659360	−	0.0732294i	−0.709274	−	0.704933i	$-0.750977\pi$
$13$	0.237736	−	0.264032i	0.0659360	−	0.0732294i	0.775210	+	0.631703i	$0.217644\pi$
$14$	0.868006	−	0.184500i	0.231984	−	0.0493098i
$15$		0			0
$16$	−3.10202	−	0.659354i	−0.775505	−	0.164839i
$17$	−3.45606	+	2.51098i	−0.838218	+	0.609001i	−0.921872	−	0.387494i	$-0.873341\pi$
$17$	−3.45606	+	2.51098i	−0.838218	+	0.609001i	0.0836542	+	0.996495i	$0.473341\pi$
$18$		0			0
$19$	−3.26679	+	2.37346i	−0.749452	+	0.544509i	−0.895657	−	0.444746i	$-0.853294\pi$
$19$	−3.26679	+	2.37346i	−0.749452	+	0.544509i	0.146205	+	0.989254i	$0.453294\pi$
$20$	−4.10879	−	0.623618i	−0.918754	−	0.139445i
$21$		0			0
$22$	0.0147481	−	0.140318i	0.00314430	−	0.0299160i
$23$	4.49630	−	0.955717i	0.937543	−	0.199281i	0.286291	−	0.958143i	$-0.407578\pi$
$23$	4.49630	−	0.955717i	0.937543	−	0.199281i	0.651252	+	0.758862i	$0.274244\pi$
$24$		0			0
$25$	−4.97894	−	0.458427i	−0.995788	−	0.0916855i
$26$	0.133623			0.0262057
$27$		0			0
$28$	−3.54774	−	2.57759i	−0.670460	−	0.487118i
$29$	0.336493	−	0.149816i	0.0624852	−	0.0278202i	−0.375256	−	0.926921i	$-0.622445\pi$
$29$	0.336493	−	0.149816i	0.0624852	−	0.0278202i	0.437741	+	0.899101i	$0.355779\pi$
$30$		0			0
$31$	5.37131	+	2.39146i	0.964716	+	0.429519i	0.827775	−	0.561060i	$-0.189606\pi$
$31$	5.37131	+	2.39146i	0.964716	+	0.429519i	0.136941	+	0.990579i	$0.456273\pi$
$32$	−2.04755	−	3.54645i	−0.361958	−	0.626930i
$33$		0			0
$34$	−1.57154	−	0.334042i	−0.269518	−	0.0572878i
$35$	−4.44328	−	2.84490i	−0.751051	−	0.480877i
$36$		0			0
$37$	−3.03352	−	9.33621i	−0.498707	−	1.53486i	−0.811099	−	0.584910i	$-0.801130\pi$
$37$	−3.03352	−	9.33621i	−0.498707	−	1.53486i	0.312391	−	0.949953i	$-0.398870\pi$
$38$	−1.48548	−	0.315748i	−0.240976	−	0.0512211i
$39$		0			0
$40$	−1.78485	−	2.70998i	−0.282209	−	0.428486i
$41$	5.77601	−	6.41491i	0.902061	−	1.00184i	−0.0979168	−	0.995195i	$-0.531218\pi$
$41$	5.77601	−	6.41491i	0.902061	−	1.00184i	0.999978	−	0.00664576i	$-0.00211543\pi$
$42$		0			0
$43$	−3.86472	+	6.69390i	−0.589365	+	1.02081i	0.404951	+	0.914338i	$0.367289\pi$
$43$	−3.86472	+	6.69390i	−0.589365	+	1.02081i	−0.994316	+	0.106471i	$0.966045\pi$
$44$	−0.564071	+	0.409822i	−0.0850370	+	0.0617830i
$45$		0			0
$46$	1.39864	+	1.01617i	0.206219	+	0.149827i
$47$	0.611825	−	0.272402i	0.0892438	−	0.0397339i	−0.361629	−	0.932322i	$-0.617779\pi$
$47$	0.611825	−	0.272402i	0.0892438	−	0.0397339i	0.450873	+	0.892588i	$0.351113\pi$
$48$		0			0
$49$	0.716381	+	1.24081i	0.102340	+	0.177258i
$50$	−1.12486	−	1.50695i	−0.159079	−	0.213115i
$51$		0			0
$52$	−0.441844	−	0.490718i	−0.0612728	−	0.0680503i
$53$	8.98419	+	6.52740i	1.23407	+	0.896607i	0.997189	−	0.0749310i	$-0.0238736\pi$
$53$	8.98419	+	6.52740i	1.23407	+	0.896607i	0.236885	+	0.971538i	$0.423874\pi$
$54$		0			0
$55$	−0.648493	+	0.532104i	−0.0874427	+	0.0717489i
$56$	−0.357913	−	3.40531i	−0.0478281	−	0.455054i
$57$		0			0
$58$	0.126554	+	0.0563453i	0.0166173	+	0.00739850i
$59$	7.75940	−	8.61768i	1.01019	−	1.12193i	0.0176673	−	0.999844i	$-0.494376\pi$
$59$	7.75940	−	8.61768i	1.01019	−	1.12193i	0.992520	−	0.122083i	$-0.0389573\pi$
$60$		0			0
$61$	4.33263	+	4.81187i	0.554736	+	0.616097i	0.953660	−	0.300887i	$-0.0972829\pi$
$61$	4.33263	+	4.81187i	0.554736	+	0.616097i	−0.398924	+	0.916984i	$0.630616\pi$
$62$	0.683331	+	2.10308i	0.0867831	+	0.267091i
$63$		0			0
$64$	−1.48405	+	4.56744i	−0.185506	+	0.570930i
$65$	−0.565377	−	0.558127i	−0.0701264	−	0.0692272i
$66$		0			0
$67$	−11.6258	−	5.17613i	−1.42032	−	0.632365i	−0.454300	−	0.890849i	$-0.650111\pi$
$67$	−11.6258	−	5.17613i	−1.42032	−	0.632365i	−0.966016	+	0.258484i	$0.916777\pi$
$68$	3.96980	+	6.87589i	0.481409	+	0.833825i
$69$		0			0
$70$	−0.323050	−	1.95781i	−0.0386118	−	0.234003i
$71$	1.67206	+	1.21482i	0.198437	+	0.144173i	0.682567	−	0.730823i	$-0.260864\pi$
$71$	1.67206	+	1.21482i	0.198437	+	0.144173i	−0.484129	+	0.874996i	$0.660864\pi$
$72$		0			0
$73$	1.94846	−	5.99673i	0.228050	−	0.701864i	−0.769918	−	0.638143i	$-0.779703\pi$
$73$	1.94846	−	5.99673i	0.228050	−	0.701864i	0.997968	−	0.0637218i	$-0.0202970\pi$
$74$	1.84600	−	3.19737i	0.214594	−	0.371687i
$75$		0			0
$76$	3.75239	+	6.49933i	0.430428	+	0.745524i
$77$	−0.865817	+	0.184035i	−0.0986690	+	0.0209727i
$78$		0			0
$79$	10.8685	−	4.83898i	1.22281	−	0.544428i	0.309187	−	0.951001i	$-0.399943\pi$
$79$	10.8685	−	4.83898i	1.22281	−	0.544428i	0.913618	+	0.406573i	$0.133276\pi$
$80$	−1.79112	+	6.86136i	−0.200254	+	0.767123i
$81$		0			0
$82$	3.24650			0.358516
$83$	−0.919146	−	8.74509i	−0.100889	−	0.959899i	−0.921491	−	0.388399i	$-0.873028\pi$
$83$	−0.919146	−	8.74509i	−0.100889	−	0.959899i	0.820602	−	0.571500i	$-0.193638\pi$
$84$		0			0
$85$	5.25415	+	7.97751i	0.569893	+	0.865283i
$86$	−2.84349	+	0.604402i	−0.306621	+	0.0651743i
$87$		0			0
$88$	−0.532511	−	0.113189i	−0.0567659	−	0.0120660i
$89$	0.603343	−	1.85690i	0.0639542	−	0.196831i	−0.913974	−	0.405774i	$-0.867002\pi$
$89$	0.603343	−	1.85690i	0.0639542	−	0.196831i	0.977928	+	0.208943i	$0.0670022\pi$
$90$		0			0
$91$	−0.259051	−	0.797278i	−0.0271560	−	0.0835775i
$92$	−0.893017	−	8.49649i	−0.0931035	−	0.885821i
$93$		0			0
$94$	0.230105	+	0.102449i	0.0237335	+	0.0105668i
$95$	4.96640	+	7.54061i	0.509542	+	0.773650i
$96$		0			0
$97$	10.2797	−	4.57681i	1.04374	−	0.464704i	0.188034	−	0.982162i	$-0.439788\pi$
$97$	10.2797	−	4.57681i	1.04374	−	0.464704i	0.855708	+	0.517458i	$0.173122\pi$
$98$	−0.166516	+	0.512483i	−0.0168206	+	0.0517686i
$99$		0			0
$100$	−1.81461	+	9.11387i	−0.181461	+	0.911387i
$101$	−7.92712	+	13.7302i	−0.788778	+	1.36620i	0.137938	+	0.990441i	$0.455952\pi$
$101$	−7.92712	+	13.7302i	−0.788778	+	1.36620i	−0.926716	+	0.375762i	$0.877381\pi$
$102$		0			0
$103$	0.147980	−	1.40793i	0.0145809	−	0.138728i	−0.984810	−	0.173638i	$-0.944448\pi$
$103$	0.147980	−	1.40793i	0.0145809	−	0.138728i	0.999390	+	0.0349100i	$0.0111144\pi$
$104$	0.0538941	−	0.512768i	0.00528475	−	0.0502810i
$105$		0			0
$106$	0.436570	+	4.15369i	0.0424035	+	0.403442i
$107$	−7.97644			−0.771112			−0.385556	−	0.922684i	$-0.625990\pi$
$107$	−7.97644			−0.771112			−0.385556	+	0.922684i	$0.625990\pi$
$108$		0			0
$109$	2.73023	+	8.40279i	0.261509	+	0.804841i	0.992477	+	0.122430i	$0.0390687\pi$
$109$	2.73023	+	8.40279i	0.261509	+	0.804841i	−0.730968	+	0.682411i	$0.760931\pi$
$110$	−0.311917	−	0.0473418i	−0.0297402	−	0.00451386i
$111$		0			0
$112$	−5.00692	+	5.56075i	−0.473110	+	0.525441i
$113$	−11.1422	+	12.3746i	−1.04817	+	1.16411i	−0.0620474	+	0.998073i	$0.519763\pi$
$113$	−11.1422	+	12.3746i	−1.04817	+	1.16411i	−0.986120	+	0.166035i	$0.946904\pi$
$114$		0			0
$115$	−1.67341	−	10.1415i	−0.156046	−	0.945700i
$116$	−0.211545	−	0.651069i	−0.0196415	−	0.0604503i
$117$		0			0
$118$	4.36130			0.401490
$119$	1.05361	+	10.0244i	0.0965839	+	0.918935i
$120$		0			0
$121$	1.13510	−	10.7998i	0.103191	−	0.981798i
$122$	−0.254550	+	2.42188i	−0.0230459	+	0.219267i
$123$		0			0
$124$	5.46380	−	9.46358i	0.490664	−	0.849855i
$125$	−1.53491	+	11.0745i	−0.137287	+	0.990531i
$126$		0			0
$127$	2.85948	−	8.80056i	0.253738	−	0.780924i	−0.740338	−	0.672235i	$-0.765335\pi$
$127$	2.85948	−	8.80056i	0.253738	−	0.780924i	0.994076	−	0.108689i	$-0.0346653\pi$
$128$	−9.13215	+	4.06589i	−0.807175	+	0.359378i
$129$		0			0
$130$	0.0137118	−	0.298476i	0.00120261	−	0.0261781i
$131$	14.5226	+	6.46590i	1.26885	+	0.564928i	0.927083	−	0.374857i	$-0.122308\pi$
$131$	14.5226	+	6.46590i	1.26885	+	0.564928i	0.341766	+	0.939785i	$0.388975\pi$
$132$		0			0
$133$	0.995904	+	9.47539i	0.0863558	+	0.821621i
$134$	−1.47902	−	4.55194i	−0.127768	−	0.393228i
$135$		0			0
$136$	−1.91571	+	5.89594i	−0.164271	+	0.505573i
$137$	−6.85368	−	1.45679i	−0.585550	−	0.124462i	−0.0943950	−	0.995535i	$-0.530092\pi$
$137$	−6.85368	−	1.45679i	−0.585550	−	0.124462i	−0.491155	+	0.871072i	$0.663425\pi$
$138$		0			0
$139$	15.6703	−	3.33083i	1.32914	−	0.282517i	0.512013	−	0.858978i	$-0.328900\pi$
$139$	15.6703	−	3.33083i	1.32914	−	0.282517i	0.817125	+	0.576461i	$0.195567\pi$
$140$	−6.12164	+	7.66014i	−0.517373	+	0.647400i
$141$		0			0
$142$	0.0812508	+	0.773050i	0.00681842	+	0.0648729i
$143$	−0.133286			−0.0111460
$144$		0			0
$145$	−0.300117	−	0.767002i	−0.0249234	−	0.0636961i
$146$	2.16639	−	0.964540i	0.179292	−	0.0798259i
$147$		0			0
$148$	−17.8461	+	3.79331i	−1.46694	+	0.311808i
$149$	−5.59996	−	9.69941i	−0.458766	−	0.794606i	0.540130	−	0.841582i	$-0.318375\pi$
$149$	−5.59996	−	9.69941i	−0.458766	−	0.794606i	−0.998896	+	0.0469753i	$0.985042\pi$
$150$		0			0
$151$	−1.72821	+	2.99334i	−0.140640	+	0.243595i	−0.927738	−	0.373233i	$-0.878249\pi$
$151$	−1.72821	+	2.99334i	−0.140640	+	0.243595i	0.787098	+	0.616828i	$0.211583\pi$
$152$	−1.81079	+	5.57304i	−0.146874	+	0.452033i
$153$		0			0
$154$	−0.269326	−	0.195677i	−0.0217029	−	0.0157681i
$155$	5.89302	−	11.7526i	0.473339	−	0.943989i
$156$		0			0
$157$	−0.881657	−	1.52708i	−0.0703639	−	0.121874i	0.828697	−	0.559698i	$-0.189083\pi$
$157$	−0.881657	−	1.52708i	−0.0703639	−	0.121874i	−0.899061	+	0.437824i	$0.855749\pi$
$158$	4.08761	+	1.81992i	0.325193	+	0.144785i
$159$		0			0
$160$	−8.13186	+	4.20971i	−0.642880	+	0.332806i
$161$	3.35161	−	10.3152i	0.264143	−	0.812950i
$162$		0			0
$163$	2.57870	+	7.93644i	0.201980	+	0.621630i	0.999824	+	0.0187660i	$0.00597376\pi$
$163$	2.57870	+	7.93644i	0.201980	+	0.621630i	−0.797844	+	0.602864i	$0.794026\pi$
$164$	−10.7350	−	11.9224i	−0.838264	−	0.930986i
$165$		0			0
$166$	2.21289	−	2.45766i	0.171753	−	0.190752i
$167$	−10.5124	−	4.68040i	−0.813471	−	0.362181i	−0.0425362	−	0.999095i	$-0.513544\pi$
$167$	−10.5124	−	4.68040i	−0.813471	−	0.362181i	−0.770935	+	0.636914i	$0.780210\pi$
$168$		0			0
$169$	1.34568	+	12.8032i	0.103513	+	0.984865i
$170$	−0.907419	+	3.47610i	−0.0695959	+	0.266605i
$171$		0			0
$172$	11.6220	+	8.44387i	0.886169	+	0.643839i
$173$	12.1226	+	13.4635i	0.921664	+	1.02361i	0.999645	+	0.0266567i	$0.00848611\pi$
$173$	12.1226	+	13.4635i	0.921664	+	1.02361i	−0.0779806	+	0.996955i	$0.524847\pi$
$174$		0			0
$175$	−6.81065	+	9.63307i	−0.514837	+	0.728192i
$176$	0.594856	+	1.03032i	0.0448389	+	0.0776633i
$177$		0			0
$178$	0.670827	−	0.298672i	0.0502806	−	0.0223864i
$179$	5.91468	+	4.29726i	0.442084	+	0.321193i	0.786462	−	0.617638i	$-0.211910\pi$
$179$	5.91468	+	4.29726i	0.442084	+	0.321193i	−0.344379	+	0.938831i	$0.611910\pi$
$180$		0			0
$181$	−7.81043	+	5.67461i	−0.580544	+	0.421790i	−0.838920	−	0.544254i	$-0.816813\pi$
$181$	−7.81043	+	5.67461i	−0.580544	+	0.421790i	0.258376	+	0.966044i	$0.416813\pi$
$182$	0.157642	−	0.273044i	0.0116852	−	0.0202394i
$183$		0			0
$184$	4.46359	−	4.95732i	0.329060	−	0.365458i
$185$	−21.1657	+	5.81796i	−1.55613	+	0.427745i
$186$		0			0
$187$	1.56758	+	0.333200i	0.114633	+	0.0243660i
$188$	−0.384640	−	1.18380i	−0.0280527	−	0.0863374i
$189$		0			0
$190$	−0.857723	+	3.28573i	−0.0622258	+	0.238372i
$191$	12.8257	+	2.72619i	0.928036	+	0.197260i	0.647046	−	0.762451i	$-0.276004\pi$
$191$	12.8257	+	2.72619i	0.928036	+	0.197260i	0.280990	+	0.959711i	$0.409337\pi$
$192$		0			0
$193$	8.40007	+	14.5494i	0.604650	+	1.04729i	0.992107	+	0.125397i	$0.0400205\pi$
$193$	8.40007	+	14.5494i	0.604650	+	1.04729i	−0.387456	+	0.921888i	$0.626646\pi$
$194$	3.86614	+	1.72132i	0.277573	+	0.123583i
$195$		0			0
$196$	2.43265	−	1.08308i	0.173761	−	0.0773632i
$197$	9.40465	+	6.83288i	0.670054	+	0.486823i	0.870043	−	0.492976i	$-0.164091\pi$
$197$	9.40465	+	6.83288i	0.670054	+	0.486823i	−0.199989	+	0.979798i	$0.564091\pi$
$198$		0			0
$199$	7.37976			0.523137			0.261568	−	0.965185i	$-0.415760\pi$
$199$	7.37976			0.523137			0.261568	+	0.965185i	$0.415760\pi$
$200$	−6.23647	+	3.70875i	−0.440985	+	0.262248i
$201$		0			0
$202$	−5.83241	+	1.23972i	−0.410367	+	0.0872262i
$203$	0.0908449	−	0.864331i	0.00637606	−	0.0606642i
$204$		0			0
$205$	−13.7364	−	13.5602i	−0.959388	−	0.947086i
$206$	0.430749	−	0.312957i	0.0300117	−	0.0218048i
$207$		0			0
$208$	−0.911552	+	0.662281i	−0.0632047	+	0.0459209i
$209$	1.48173	+	0.314951i	0.102493	+	0.0217856i
$210$		0			0
$211$	−10.8684	+	2.31014i	−0.748209	+	0.159037i	−0.566209	−	0.824262i	$-0.691590\pi$
$211$	−10.8684	+	2.31014i	−0.748209	+	0.159037i	−0.182000	+	0.983299i	$0.558257\pi$
$212$	13.8104	−	15.3380i	0.948504	−	1.05342i
$213$		0			0
$214$	−2.00733	−	2.22936i	−0.137218	−	0.152396i
$215$	14.5557	+	9.31958i	0.992687	+	0.635590i
$216$		0			0
$217$	11.2235	−	8.15434i	0.761900	−	0.553553i
$218$	−1.66144	+	2.87771i	−0.112527	+	0.194903i
$219$		0			0
$220$	0.857541	+	1.30203i	0.0578154	+	0.0877827i
$221$	−0.158651	+	1.50946i	−0.0106720	+	0.101537i
$222$		0			0
$223$	−2.02383	−	2.24769i	−0.135525	−	0.150516i	0.671562	−	0.740949i	$-0.265624\pi$
$223$	−2.02383	−	2.24769i	−0.135525	−	0.150516i	−0.807087	+	0.590433i	$0.798957\pi$
$224$	−9.66236			−0.645594
$225$		0			0
$226$	−6.26264			−0.416585
$227$	−6.12150	−	6.79861i	−0.406298	−	0.451240i	0.504919	−	0.863167i	$-0.331522\pi$
$227$	−6.12150	−	6.79861i	−0.406298	−	0.451240i	−0.911217	+	0.411927i	$0.864856\pi$
$228$		0			0
$229$	3.08084	−	29.3122i	0.203588	−	1.93701i	−0.124206	−	0.992256i	$-0.539638\pi$
$229$	3.08084	−	29.3122i	0.203588	−	1.93701i	0.327794	−	0.944749i	$-0.393695\pi$
$230$	2.41336	−	3.01989i	0.159132	−	0.199126i
$231$		0			0
$232$	0.267263	−	0.462913i	0.0175467	−	0.0303917i
$233$	−6.59518	+	4.79168i	−0.432064	+	0.313913i	−0.782474	−	0.622683i	$-0.786042\pi$
$233$	−6.59518	+	4.79168i	−0.432064	+	0.313913i	0.350409	+	0.936597i	$0.386042\pi$
$234$		0			0
$235$	−0.545685	−	1.39459i	−0.0355965	−	0.0909732i
$236$	−14.4212	−	16.0164i	−0.938743	−	1.04258i
$237$		0			0
$238$	−2.53661	+	2.81719i	−0.164424	+	0.182611i
$239$	4.63943	−	0.986142i	0.300100	−	0.0637882i	−0.0554008	−	0.998464i	$-0.517644\pi$
$239$	4.63943	−	0.986142i	0.300100	−	0.0637882i	0.355501	+	0.934676i	$0.384310\pi$
$240$		0			0
$241$	24.4782	+	5.20301i	1.57678	+	0.335155i	0.911455	−	0.411399i	$-0.134960\pi$
$241$	24.4782	+	5.20301i	1.57678	+	0.335155i	0.665325	+	0.746554i	$0.268293\pi$
$242$	3.30413	−	2.40059i	0.212397	−	0.154316i
$243$		0			0
$244$	9.73582	−	7.07349i	0.623272	−	0.452834i
$245$	2.84512	−	1.47286i	0.181768	−	0.0940978i
$246$		0			0
$247$	−0.149962	+	1.42679i	−0.00954185	+	0.0907847i
$248$	8.34598	−	1.77399i	0.529970	−	0.112649i
$249$		0			0
$250$	−3.48152	+	2.35797i	−0.220191	+	0.149131i
$251$	20.6780			1.30518			0.652591	−	0.757710i	$-0.273682\pi$
$251$	20.6780			1.30518			0.652591	+	0.757710i	$0.273682\pi$
$252$		0			0
$253$	−1.39511	−	1.01361i	−0.0877101	−	0.0637251i
$254$	3.17931	−	1.41552i	0.199488	−	0.0888176i
$255$		0			0
$256$	5.34003	+	2.37753i	0.333752	+	0.148596i
$257$	−0.199971	−	0.346359i	−0.0124738	−	0.0216053i	0.859721	−	0.510764i	$-0.170637\pi$
$257$	−0.199971	−	0.346359i	−0.0124738	−	0.0216053i	−0.872195	+	0.489158i	$0.837304\pi$
$258$		0			0
$259$	−22.6563	−	4.81574i	−1.40779	−	0.299235i
$260$	−1.14146	+	0.936598i	−0.0707905	+	0.0580853i
$261$		0			0
$262$	1.84755	+	5.68618i	0.114142	+	0.351293i
$263$	2.61206	+	0.555211i	0.161067	+	0.0342357i	0.287739	−	0.957709i	$-0.407096\pi$
$263$	2.61206	+	0.555211i	0.161067	+	0.0342357i	−0.126673	+	0.991945i	$0.540430\pi$
$264$		0			0
$265$	15.5022	−	19.3983i	0.952295	−	1.19163i
$266$	−2.39769	+	2.66290i	−0.147012	+	0.163273i
$267$		0			0
$268$	−11.8260	+	20.4832i	−0.722386	+	1.25121i
$269$	−15.1805	+	11.0293i	−0.925574	+	0.672469i	−0.944905	−	0.327344i	$-0.893846\pi$
$269$	−15.1805	+	11.0293i	−0.925574	+	0.672469i	0.0193308	+	0.999813i	$0.493846\pi$
$270$		0			0
$271$	−10.8085	−	7.85283i	−0.656569	−	0.477025i	0.208934	−	0.977930i	$-0.433001\pi$
$271$	−10.8085	−	7.85283i	−0.656569	−	0.477025i	−0.865503	+	0.500905i	$0.833001\pi$
$272$	12.3764	−	5.51032i	0.750429	−	0.334112i
$273$		0			0
$274$	−1.31761	−	2.28217i	−0.0795999	−	0.137871i
$275$	1.12202	+	1.50315i	0.0676604	+	0.0906432i
$276$		0			0
$277$	15.2370	+	16.9224i	0.915502	+	1.01677i	0.999793	+	0.0203270i	$0.00647072\pi$
$277$	15.2370	+	16.9224i	0.915502	+	1.01677i	−0.0842913	+	0.996441i	$0.526863\pi$
$278$	4.87449	+	3.54153i	0.292353	+	0.212407i
$279$		0			0
$280$	−7.64322	+	0.450036i	−0.456770	+	0.0268948i
$281$	0.938013	+	8.92460i	0.0559572	+	0.532397i	0.986212	+	0.165484i	$0.0529186\pi$
$281$	0.938013	+	8.92460i	0.0559572	+	0.532397i	−0.930255	+	0.366913i	$0.880415\pi$
$282$		0			0
$283$	−5.94030	−	2.64479i	−0.353114	−	0.157216i	0.222511	−	0.974930i	$-0.428575\pi$
$283$	−5.94030	−	2.64479i	−0.353114	−	0.157216i	−0.575625	+	0.817714i	$0.695241\pi$
$284$	2.57028	−	2.85458i	0.152518	−	0.169388i
$285$		0			0
$286$	−0.0335424	−	0.0372527i	−0.00198341	−	0.00220280i
$287$	−6.29389	−	19.3706i	−0.371517	−	1.14341i
$288$		0			0
$289$	0.386075	−	1.18822i	0.0227103	−	0.0698951i
$290$	0.138846	−	0.276903i	0.00815330	−	0.0162603i
$291$		0			0
$292$	−10.7057	−	4.76646i	−0.626501	−	0.278936i
$293$	−8.56935	−	14.8426i	−0.500627	−	0.867111i	−1.00000		0.000723948i	$-0.999770\pi$
$293$	−8.56935	−	14.8426i	−0.500627	−	0.867111i	0.499373	−	0.866387i	$-0.333564\pi$
$294$		0			0
$295$	−18.4532	−	18.2166i	−1.07439	−	1.06061i
$296$	−11.5251	−	8.37347i	−0.669883	−	0.486698i
$297$		0			0
$298$	1.30165	−	4.00608i	0.0754028	−	0.232066i
$299$	0.816590	−	1.41438i	0.0472246	−	0.0817955i
$300$		0			0
$301$	9.11881	+	15.7942i	0.525599	+	0.910365i
$302$	−1.27154	+	0.270273i	−0.0731687	+	0.0155525i
$303$		0			0
$304$	11.6986	−	5.20854i	0.670959	−	0.298730i
$305$	11.1929	−	9.18407i	0.640905	−	0.525878i
$306$		0			0
$307$	−22.7466			−1.29822			−0.649109	−	0.760695i	$-0.724858\pi$
$307$	−22.7466			−1.29822			−0.649109	+	0.760695i	$0.724858\pi$
$308$	0.171961	+	1.63610i	0.00979841	+	0.0932256i
$309$		0			0
$310$	4.76779	−	1.31056i	0.270792	−	0.0744346i
$311$	14.0711	−	2.99091i	0.797902	−	0.169599i	0.209118	−	0.977890i	$-0.432941\pi$
$311$	14.0711	−	2.99091i	0.797902	−	0.169599i	0.588783	+	0.808291i	$0.299607\pi$
$312$		0			0
$313$	−2.52983	−	0.537731i	−0.142994	−	0.0303944i	0.135858	−	0.990728i	$-0.456621\pi$
$313$	−2.52983	−	0.537731i	−0.142994	−	0.0303944i	−0.278853	+	0.960334i	$0.589954\pi$
$314$	0.204932	−	0.630717i	0.0115650	−	0.0355934i
$315$		0			0
$316$	−6.83279	−	21.0292i	−0.384374	−	1.18298i
$317$	1.62161	+	15.4286i	0.0910786	+	0.866555i	0.940718	+	0.339190i	$0.110153\pi$
$317$	1.62161	+	15.4286i	0.0910786	+	0.866555i	−0.849639	+	0.527364i	$0.823180\pi$
$318$		0			0
$319$	−0.126234	−	0.0562032i	−0.00706777	−	0.00314678i
$320$	10.0501	+	3.78363i	0.561816	+	0.211512i
$321$		0			0
$322$	3.72648	−	1.65914i	0.207669	−	0.0924601i
$323$	5.33052	−	16.4056i	0.296598	−	0.912834i
$324$		0			0
$325$	−1.30471	+	1.20562i	−0.0723724	+	0.0668756i
$326$	−1.56923	+	2.71799i	−0.0869119	+	0.150536i
$327$		0			0
$328$	1.30941	−	12.4582i	0.0722999	−	0.687887i
$329$	0.165178	−	1.57156i	0.00910654	−	0.0866429i
$330$		0			0
$331$	−0.905650	−	8.61669i	−0.0497790	−	0.473616i	−0.990807	−	0.135286i	$-0.956805\pi$
$331$	−0.905650	−	8.61669i	−0.0497790	−	0.473616i	0.941028	−	0.338330i	$-0.109862\pi$
$332$	−16.3427			−0.896924
$333$		0			0
$334$	−1.33737	−	4.11600i	−0.0731775	−	0.225217i
$335$	−12.7550	+	25.4375i	−0.696879	+	1.38980i
$336$		0			0
$337$	−11.0484	+	12.2705i	−0.601845	+	0.668417i	−0.964676	−	0.263438i	$-0.915144\pi$
$337$	−11.0484	+	12.2705i	−0.601845	+	0.668417i	0.362831	+	0.931855i	$0.381810\pi$
$338$	−3.23978	+	3.59814i	−0.176221	+	0.195713i
$339$		0			0
$340$	15.7661	−	8.16182i	0.855039	−	0.442637i
$341$	−0.681607	−	2.09777i	−0.0369111	−	0.113601i
$342$		0			0
$343$	19.8971			1.07434
$344$	1.17248	+	11.1554i	0.0632159	+	0.601459i
$345$		0			0
$346$	−0.712226	+	6.77638i	−0.0382895	+	0.364300i
$347$	0.0586871	−	0.558370i	0.00315049	−	0.0299749i	−0.992834	−	0.119504i	$-0.961870\pi$
$347$	0.0586871	−	0.558370i	0.00315049	−	0.0299749i	0.995984	+	0.0895292i	$0.0285362\pi$
$348$		0			0
$349$	−17.9910	+	31.1614i	−0.963037	+	1.66803i	−0.248239	+	0.968699i	$0.579852\pi$
$349$	−17.9910	+	31.1614i	−0.963037	+	1.66803i	−0.714798	+	0.699331i	$0.753481\pi$
$350$	−4.40633	+	0.520699i	−0.235528	+	0.0278325i
$351$		0			0
$352$	−0.474731	+	1.46107i	−0.0253032	+	0.0778754i
$353$	−12.0310	+	5.35653i	−0.640343	+	0.285099i	−0.701110	−	0.713053i	$-0.747312\pi$
$353$	−12.0310	+	5.35653i	−0.640343	+	0.285099i	0.0607671	+	0.998152i	$0.480645\pi$
$354$		0			0
$355$	2.88515	−	3.61025i	0.153128	−	0.191612i
$356$	−3.31503	−	1.47594i	−0.175696	−	0.0782249i
$357$		0			0
$358$	0.287413	+	2.73455i	0.0151903	+	0.144526i
$359$	−11.4732	−	35.3108i	−0.605532	−	1.86364i	−0.493093	−	0.869976i	$-0.664134\pi$
$359$	−11.4732	−	35.3108i	−0.605532	−	1.86364i	−0.112438	−	0.993659i	$-0.535866\pi$
$360$		0			0
$361$	−0.832742	+	2.56292i	−0.0438285	+	0.134890i
$362$	−3.55157	−	0.754909i	−0.186666	−	0.0396771i
$363$		0			0
$364$	−1.52399	+	0.323934i	−0.0798789	+	0.0169788i
$365$	−13.1950	−	4.96765i	−0.690660	−	0.260019i
$366$		0			0
$367$	−2.68728	−	25.5678i	−0.140275	−	1.33463i	−0.807543	−	0.589809i	$-0.799203\pi$
$367$	−2.68728	−	25.5678i	−0.140275	−	1.33463i	0.667268	−	0.744818i	$-0.267464\pi$
$368$	−14.5778			−0.759918
$369$		0			0
$370$	−6.95258	−	4.45154i	−0.361448	−	0.231425i
$371$	23.9371	−	10.6575i	1.24275	−	0.553309i
$372$		0			0
$373$	4.55272	−	0.967710i	0.235731	−	0.0501061i	−0.0885313	−	0.996073i	$-0.528217\pi$
$373$	4.55272	−	0.967710i	0.235731	−	0.0501061i	0.324262	+	0.945967i	$0.394884\pi$
$374$	0.301366	+	0.521981i	0.0155833	+	0.0269910i
$375$		0			0
$376$	0.485948	−	0.841686i	0.0250609	−	0.0434067i
$377$	0.0404401	−	0.124462i	0.00208277	−	0.00641011i
$378$		0			0
$379$	20.4895	+	14.8865i	1.05247	+	0.764666i	0.972681	−	0.232145i	$-0.0745745\pi$
$379$	20.4895	+	14.8865i	1.05247	+	0.764666i	0.0797917	+	0.996812i	$0.474574\pi$
$380$	14.9027	−	7.71482i	0.764491	−	0.395762i
$381$		0			0
$382$	2.46573	+	4.27077i	0.126158	+	0.218512i
$383$	−6.22916	−	2.77340i	−0.318295	−	0.141714i	0.241370	−	0.970433i	$-0.422403\pi$
$383$	−6.22916	−	2.77340i	−0.318295	−	0.141714i	−0.559665	+	0.828719i	$0.689070\pi$
$384$		0			0
$385$	0.322235	+	1.95287i	0.0164226	+	0.0995275i
$386$	−1.95251	+	6.00922i	−0.0993803	+	0.305861i
$387$		0			0
$388$	−6.46258	−	19.8898i	−0.328088	−	1.00975i
$389$	1.48640	+	1.65081i	0.0753635	+	0.0836996i	0.779647	−	0.626219i	$-0.215398\pi$
$389$	1.48640	+	1.65081i	0.0753635	+	0.0836996i	−0.704284	+	0.709919i	$0.748732\pi$
$390$		0			0
$391$	−13.1397	+	14.5931i	−0.664503	+	0.738005i
$392$	1.89945	+	0.845689i	0.0959366	+	0.0427137i
$393$		0			0
$394$	0.457002	+	4.34808i	0.0230234	+	0.219053i
$395$	−9.69362	−	24.7737i	−0.487739	−	1.24650i
$396$		0			0
$397$	−18.7858	−	13.6487i	−0.942831	−	0.685007i	0.00626974	−	0.999980i	$-0.498004\pi$
$397$	−18.7858	−	13.6487i	−0.942831	−	0.685007i	−0.949100	+	0.314974i	$0.898004\pi$
$398$	1.85717	+	2.06259i	0.0930915	+	0.103389i
$399$		0			0
$400$	15.1425	+	4.70494i	0.757125	+	0.235247i
$401$	−7.72116	−	13.3734i	−0.385576	−	0.667837i	0.606273	−	0.795257i	$-0.292664\pi$
$401$	−7.72116	−	13.3734i	−0.385576	−	0.667837i	−0.991849	+	0.127419i	$0.959331\pi$
$402$		0			0
$403$	1.90838	−	0.849664i	0.0950630	−	0.0423248i
$404$	23.8384	+	17.3196i	1.18601	+	0.861684i
$405$		0			0
$406$	0.264437	−	0.192125i	0.0131238	−	0.00953499i
$407$	−1.84135	+	3.18931i	−0.0912722	+	0.158088i
$408$		0			0
$409$	−18.1304	+	20.1359i	−0.896491	+	0.995655i	0.103508	+	0.994629i	$0.466993\pi$
$409$	−18.1304	+	20.1359i	−0.896491	+	0.995655i	−0.999999	+	0.00102597i	$0.999673\pi$
$410$	0.333142	−	7.25175i	0.0164527	−	0.358138i
$411$		0			0
$412$	−2.57364	−	0.547043i	−0.126794	−	0.0269509i
$413$	−8.45511	−	26.0221i	−0.416049	−	1.28047i
$414$		0			0
$415$	−19.6283	+	1.15573i	−0.963517	+	0.0567323i
$416$	−1.42315	−	0.302500i	−0.0697758	−	0.0148313i
$417$		0			0
$418$	0.284861	+	0.493394i	0.0139330	+	0.0241327i
$419$	−14.7146	−	6.55134i	−0.718853	−	0.320054i	0.0145068	−	0.999895i	$-0.495382\pi$
$419$	−14.7146	−	6.55134i	−0.718853	−	0.320054i	−0.733360	+	0.679841i	$0.762049\pi$
$420$		0			0
$421$	15.5870	−	6.93978i	0.759664	−	0.338224i	0.00991855	−	0.999951i	$-0.496843\pi$
$421$	15.5870	−	6.93978i	0.759664	−	0.338224i	0.749745	+	0.661727i	$0.230176\pi$
$422$	−3.38077	−	2.45627i	−0.164573	−	0.119570i
$423$		0			0
$424$	16.1155			0.782639
$425$	18.3586	−	10.9176i	0.890524	−	0.529584i
$426$		0			0
$427$	14.9439	−	3.17643i	0.723187	−	0.153718i
$428$	−1.54960	+	14.7434i	−0.0749025	+	0.712650i
$429$		0			0
$430$	1.05827	+	6.41355i	0.0510345	+	0.309289i
$431$	−8.91750	+	6.47894i	−0.429541	+	0.312080i	−0.781465	−	0.623949i	$-0.785527\pi$
$431$	−8.91750	+	6.47894i	−0.429541	+	0.312080i	0.351925	+	0.936028i	$0.385527\pi$
$432$		0			0
$433$	14.8065	−	10.7575i	0.711555	−	0.516975i	−0.172120	−	0.985076i	$-0.555062\pi$
$433$	14.8065	−	10.7575i	0.711555	−	0.516975i	0.883675	+	0.468101i	$0.155062\pi$
$434$	5.10356	+	1.08479i	0.244979	+	0.0520718i
$435$		0			0
$436$	16.0619	−	3.41406i	0.769224	−	0.163504i
$437$	−12.4201	+	13.7939i	−0.594133	+	0.659852i
$438$		0			0
$439$	−14.1066	−	15.6670i	−0.673271	−	0.747743i	0.305614	−	0.952156i	$-0.401138\pi$
$439$	−14.1066	−	15.6670i	−0.673271	−	0.747743i	−0.978885	+	0.204412i	$0.934472\pi$
$440$	−0.307475	+	1.17786i	−0.0146583	+	0.0561524i
$441$		0			0
$442$	−0.461810	+	0.335525i	−0.0219661	+	0.0159593i
$443$	15.9033	−	27.5452i	0.755586	−	1.30871i	−0.189496	−	0.981882i	$-0.560685\pi$
$443$	15.9033	−	27.5452i	0.755586	−	1.30871i	0.945082	−	0.326833i	$-0.105981\pi$
$444$		0			0
$445$	−4.08587	−	1.53824i	−0.193689	−	0.0729197i
$446$	0.118904	−	1.13129i	0.00563025	−	0.0535683i
$447$		0			0
$448$	7.58224	+	8.42093i	0.358227	+	0.397851i
$449$	14.3360			0.676559			0.338280	−	0.941046i	$-0.390155\pi$
$449$	14.3360			0.676559			0.338280	+	0.941046i	$0.390155\pi$
$450$		0			0
$451$	−3.23831			−0.152486
$452$	20.7083	+	22.9989i	0.974037	+	1.08178i
$453$		0			0
$454$	0.359650	−	3.42184i	0.0168792	−	0.160595i
$455$	−1.80747	+	0.496833i	−0.0847356	+	0.0232919i
$456$		0			0
$457$	−11.2914	+	19.5574i	−0.528191	+	0.914854i	0.471268	+	0.881990i	$0.343796\pi$
$457$	−11.2914	+	19.5574i	−0.528191	+	0.914854i	−0.999460	+	0.0328645i	$0.989537\pi$
$458$	8.96789	−	6.51556i	0.419042	−	0.304452i
$459$		0			0
$460$	−19.0704	+	1.12287i	−0.889160	+	0.0523541i
$461$	17.7130	+	19.6723i	0.824978	+	0.916231i	0.997634	−	0.0687512i	$-0.0219014\pi$
$461$	17.7130	+	19.6723i	0.824978	+	0.916231i	−0.172656	+	0.984982i	$0.555235\pi$
$462$		0			0
$463$	3.84446	−	4.26971i	0.178667	−	0.198430i	−0.647158	−	0.762356i	$-0.724043\pi$
$463$	3.84446	−	4.26971i	0.178667	−	0.198430i	0.825826	+	0.563925i	$0.190709\pi$
$464$	−1.14259	+	0.242865i	−0.0530434	+	0.0112747i
$465$		0			0
$466$	−2.99897	−	0.637450i	−0.138924	−	0.0295293i
$467$	14.6975	−	10.6783i	0.680118	−	0.494135i	−0.193279	−	0.981144i	$-0.561912\pi$
$467$	14.6975	−	10.6783i	0.680118	−	0.494135i	0.873397	+	0.487009i	$0.161912\pi$
$468$		0			0
$469$	−24.2924	+	17.6494i	−1.12172	+	0.814975i
$470$	0.252454	−	0.503475i	0.0116449	−	0.0232236i
$471$		0			0
$472$	1.75903	−	16.7361i	0.0809661	−	0.770341i
$473$	2.83631	−	0.602877i	0.130414	−	0.0277203i
$474$		0			0
$475$	17.3532	−	10.3197i	0.796219	−	0.473501i
$476$	18.7335			0.858648
$477$		0			0
$478$	1.44317	+	1.04852i	0.0660090	+	0.0479583i
$479$	0.302630	−	0.134740i	0.0138275	−	0.00615641i	−0.399811	−	0.916597i	$-0.630924\pi$
$479$	0.302630	−	0.134740i	0.0138275	−	0.00615641i	0.413639	+	0.910441i	$0.364258\pi$
$480$		0			0
$481$	−3.18624	−	1.41860i	−0.145280	−	0.0646828i
$482$	4.70591	+	8.15088i	0.214348	+	0.371262i
$483$		0			0
$484$	−19.7415	−	4.19618i	−0.897340	−	0.190735i
$485$	−9.16841	−	23.4315i	−0.416316	−	1.06397i
$486$		0			0
$487$	−6.16698	−	18.9800i	−0.279452	−	0.860066i	−0.988007	−	0.154410i	$-0.950652\pi$
$487$	−6.16698	−	18.9800i	−0.279452	−	0.860066i	0.708555	−	0.705656i	$-0.249348\pi$
$488$	9.19110	+	1.95363i	0.416062	+	0.0884366i
$489$		0			0
$490$	1.12765	+	0.424537i	0.0509421	+	0.0191786i
$491$	−24.1735	+	26.8474i	−1.09094	+	1.21161i	−0.115043	+	0.993361i	$0.536701\pi$
$491$	−24.1735	+	26.8474i	−1.09094	+	1.21161i	−0.975894	+	0.218247i	$0.929966\pi$
$492$		0			0
$493$	−0.786756	+	1.36270i	−0.0354337	+	0.0613730i
$494$	−0.436519	+	0.317149i	−0.0196399	+	0.0142692i
$495$		0			0
$496$	−15.0851	−	10.9600i	−0.677340	−	0.492117i
$497$	4.45497	−	1.98348i	0.199833	−	0.0889713i
$498$		0			0
$499$	−13.7067	−	23.7407i	−0.613596	−	1.06278i	−0.990629	−	0.136579i	$-0.956389\pi$
$499$	−13.7067	−	23.7407i	−0.613596	−	1.06278i	0.377033	−	0.926200i	$-0.376944\pi$
$500$	20.1715	+	4.98854i	0.902099	+	0.223094i
$501$		0			0
$502$	5.20376	+	5.77936i	0.232255	+	0.257946i
$503$	1.33405	+	0.969242i	0.0594822	+	0.0432164i	0.617129	−	0.786862i	$-0.288296\pi$
$503$	1.33405	+	0.969242i	0.0594822	+	0.0432164i	−0.557647	+	0.830078i	$0.688296\pi$
$504$		0			0
$505$	29.8558	+	19.1158i	1.32857	+	0.850643i
$506$	−0.0677931	−	0.645008i	−0.00301377	−	0.0286741i
$507$		0			0
$508$	−15.7112	−	6.99507i	−0.697071	−	0.310356i
$509$	−16.5374	+	18.3667i	−0.733009	+	0.814089i	−0.988259	−	0.152786i	$-0.951176\pi$
$509$	−16.5374	+	18.3667i	−0.733009	+	0.814089i	0.255250	+	0.966875i	$0.417842\pi$
$510$		0			0
$511$	−9.95495	−	11.0561i	−0.440381	−	0.489093i
$512$	6.85745	+	21.1051i	0.303059	+	0.932721i
$513$		0			0
$514$	0.0464812	−	0.143054i	0.00205020	−	0.00630986i
$515$	−3.12974	−	0.475021i	−0.137913	−	0.0209319i
$516$		0			0
$517$	−0.229524	−	0.102191i	−0.0100945	−	0.00449435i
$518$	−4.35565	−	7.54420i	−0.191376	−	0.331473i
$519$		0			0
$520$	−1.13985	−	0.173002i	−0.0499855	−	0.00758663i
$521$	−0.868044	−	0.630671i	−0.0380297	−	0.0276302i	0.568608	−	0.822609i	$-0.307482\pi$
$521$	−0.868044	−	0.630671i	−0.0380297	−	0.0276302i	−0.606638	+	0.794978i	$0.707482\pi$
$522$		0			0
$523$	−4.86221	+	14.9643i	−0.212610	+	0.654345i	0.786705	+	0.617329i	$0.211785\pi$
$523$	−4.86221	+	14.9643i	−0.212610	+	0.654345i	−0.999315	+	0.0370160i	$0.988215\pi$
$524$	14.7727	−	25.5871i	0.645349	−	1.11778i
$525$		0			0
$526$	0.502166	+	0.869777i	0.0218955	+	0.0379241i
$527$	−24.5685	+	5.22219i	−1.07022	+	0.227482i
$528$		0			0
$529$	−1.70825	+	0.760563i	−0.0742718	+	0.0330679i
$530$	9.32295	−	0.548939i	0.404963	−	0.0238444i
$531$		0			0
$532$	17.7075			0.767718
$533$	−0.320579	−	3.05011i	−0.0138858	−	0.132115i
$534$		0			0
$535$	−0.818507	+	17.8171i	−0.0353872	+	0.770299i
$536$	−18.0642	+	3.83967i	−0.780256	+	0.165848i
$537$		0			0
$538$	−6.90292	−	1.46726i	−0.297606	−	0.0632581i
$539$	0.166096	−	0.511190i	0.00715425	−	0.0220185i
$540$		0			0
$541$	5.82440	+	17.9257i	0.250410	+	0.770684i	0.994699	+	0.102826i	$0.0327886\pi$
$541$	5.82440	+	17.9257i	0.250410	+	0.770684i	−0.744289	+	0.667858i	$0.767211\pi$
$542$	−0.525219	−	4.99713i	−0.0225601	−	0.214645i
$543$		0			0
$544$	15.9815	+	7.11542i	0.685201	+	0.305071i
$545$	19.0496	−	5.23630i	0.815994	−	0.224298i
$546$		0			0
$547$	−2.09671	+	0.933517i	−0.0896490	+	0.0399143i	−0.451071	−	0.892488i	$-0.648958\pi$
$547$	−2.09671	+	0.933517i	−0.0896490	+	0.0399143i	0.361422	+	0.932402i	$0.382291\pi$
$548$	−4.02417	+	12.3851i	−0.171904	+	0.529067i
$549$		0			0
$550$	−0.137755	+	0.691876i	−0.00587391	+	0.0295017i
$551$	−0.743668	+	1.28807i	−0.0316813	+	0.0548737i
$552$		0			0
$553$	2.93424	−	27.9174i	0.124776	−	1.18717i
$554$	−0.895203	+	8.51729i	−0.0380335	+	0.361865i
$555$		0			0
$556$	−3.11231	−	29.6116i	−0.131991	−	1.25581i
$557$	−26.8111			−1.13602			−0.568012	−	0.823020i	$-0.692287\pi$
$557$	−26.8111			−1.13602			−0.568012	+	0.823020i	$0.692287\pi$
$558$		0			0
$559$	0.848622	+	2.61179i	0.0358929	+	0.110467i
$560$	11.9073	+	11.7546i	0.503176	+	0.496724i
$561$		0			0
$562$	−2.25831	+	2.50811i	−0.0952611	+	0.105798i
$563$	−14.2112	+	15.7832i	−0.598932	+	0.665181i	−0.964032	−	0.265787i	$-0.914368\pi$
$563$	−14.2112	+	15.7832i	−0.598932	+	0.665181i	0.365100	+	0.930968i	$0.381035\pi$
$564$		0			0
$565$	26.4980	+	26.1582i	1.11478	+	1.10049i
$566$	−0.755716	−	2.32586i	−0.0317651	−	0.0977630i
$567$		0			0
$568$	2.99928			0.125847
$569$	4.28476	+	40.7668i	0.179627	+	1.70903i	0.598612	+	0.801039i	$0.295719\pi$
$569$	4.28476	+	40.7668i	0.179627	+	1.70903i	−0.418985	+	0.907993i	$0.637614\pi$
$570$		0			0
$571$	−4.61545	+	43.9131i	−0.193151	+	1.83771i	0.283929	+	0.958845i	$0.408362\pi$
$571$	−4.61545	+	43.9131i	−0.193151	+	1.83771i	−0.477079	+	0.878860i	$0.658305\pi$
$572$	−0.0258937	+	0.246362i	−0.00108267	+	0.0103009i
$573$		0			0
$574$	3.83006	−	6.63386i	0.159864	−	0.276892i
$575$	−22.8249	+	2.69723i	−0.951865	+	0.112482i
$576$		0			0
$577$	−1.18692	+	3.65297i	−0.0494122	+	0.152075i	−0.972718	−	0.231990i	$-0.925476\pi$
$577$	−1.18692	+	3.65297i	−0.0494122	+	0.152075i	0.923306	+	0.384065i	$0.125476\pi$
$578$	0.429257	−	0.191118i	0.0178548	−	0.00794945i
$579$		0			0
$580$	−1.47601	+	0.405721i	−0.0612879	+	0.0168467i
$581$	−18.9540	−	8.43885i	−0.786343	−	0.350102i
$582$		0			0
$583$	−0.435469	−	4.14321i	−0.0180353	−	0.171594i
$584$	−2.82757	−	8.70237i	−0.117006	−	0.360107i
$585$		0			0
$586$	1.99186	−	6.13031i	0.0822830	−	0.253241i
$587$	−38.7560	−	8.23783i	−1.59963	−	0.340012i	−0.680126	−	0.733095i	$-0.738075\pi$
$587$	−38.7560	−	8.23783i	−1.59963	−	0.340012i	−0.919503	+	0.393083i	$0.871408\pi$
$588$		0			0
$589$	−23.2230	+	4.93619i	−0.956885	+	0.203392i
$590$	0.447537	−	9.74188i	0.0184248	−	0.401067i
$591$		0			0
$592$	3.25416	+	30.9612i	0.133745	+	1.27250i
$593$	23.7687			0.976065			0.488033	−	0.872825i	$-0.337715\pi$
$593$	23.7687			0.976065			0.488033	+	0.872825i	$0.337715\pi$
$594$		0			0
$595$	22.4997	−	1.32479i	0.922399	−	0.0543113i
$596$	−19.0160	+	8.46647i	−0.778926	+	0.346800i
$597$		0			0
$598$	0.600810	−	0.127706i	0.0245690	−	0.00522229i
$599$	21.3498	+	36.9790i	0.872330	+	1.51092i	0.859580	+	0.511001i	$0.170725\pi$
$599$	21.3498	+	36.9790i	0.872330	+	1.51092i	0.0127494	+	0.999919i	$0.495942\pi$
$600$		0			0
$601$	15.2463	−	26.4074i	0.621910	−	1.07718i	−0.367220	−	0.930134i	$-0.619690\pi$
$601$	15.2463	−	26.4074i	0.621910	−	1.07718i	0.989130	−	0.147045i	$-0.0469764\pi$
$602$	−2.11958	+	6.52338i	−0.0863875	+	0.265873i
$603$		0			0
$604$	5.19707	+	3.77589i	0.211466	+	0.153639i
$605$	−24.0071	−	3.64372i	−0.976028	−	0.148138i
$606$		0			0
$607$	13.5546	+	23.4772i	0.550163	+	0.952910i	0.998262	+	0.0589263i	$0.0187677\pi$
$607$	13.5546	+	23.4772i	0.550163	+	0.952910i	−0.448099	+	0.893984i	$0.647899\pi$
$608$	15.1062	+	6.72574i	0.612639	+	0.272765i
$609$		0			0
$610$	5.38367	+	0.817115i	0.217978	+	0.0330840i
$611$	0.0735297	−	0.226301i	0.00297469	−	0.00915517i
$612$		0			0
$613$	6.76831	+	20.8307i	0.273370	+	0.841345i	0.989646	+	0.143529i	$0.0458449\pi$
$613$	6.76831	+	20.8307i	0.273370	+	0.841345i	−0.716277	+	0.697816i	$0.754155\pi$
$614$	−5.72435	−	6.35754i	−0.231016	−	0.256569i
$615$		0			0
$616$	−0.859519	+	0.954592i	−0.0346310	+	0.0384616i
$617$	25.7012	+	11.4429i	1.03469	+	0.460674i	0.852576	−	0.522604i	$-0.175039\pi$
$617$	25.7012	+	11.4429i	1.03469	+	0.460674i	0.182114	+	0.983277i	$0.441706\pi$
$618$		0			0
$619$	3.83468	+	36.4846i	0.154129	+	1.46644i	0.748975	+	0.662599i	$0.230546\pi$
$619$	3.83468	+	36.4846i	0.154129	+	1.46644i	−0.594846	+	0.803840i	$0.702787\pi$
$620$	−20.5782	−	13.1757i	−0.826442	−	0.529148i
$621$		0			0
$622$	4.37705	+	3.18011i	0.175504	+	0.127511i
$623$	−3.08257	−	3.42354i	−0.123501	−	0.137161i
$624$		0			0
$625$	24.5797	+	4.56496i	0.983188	+	0.182599i
$626$	−0.486357	−	0.842395i	−0.0194387	−	0.0336689i
$627$		0			0
$628$	−2.99388	+	1.33296i	−0.119469	+	0.0531910i
$629$	33.9270	+	24.6494i	1.35276	+	0.982837i
$630$		0			0
$631$	−9.47939	+	6.88718i	−0.377369	+	0.274174i	−0.760260	−	0.649619i	$-0.774928\pi$
$631$	−9.47939	+	6.88718i	−0.377369	+	0.274174i	0.382891	+	0.923793i	$0.374928\pi$
$632$	8.63244	−	14.9518i	0.343380	−	0.594752i
$633$		0			0
$634$	−3.90410	+	4.33594i	−0.155052	+	0.172202i
$635$	−19.3645	−	7.29032i	−0.768457	−	0.289308i
$636$		0			0
$637$	0.497923	+	0.105837i	0.0197284	+	0.00419341i
$638$	−0.0160594	−	0.0494257i	−0.000635797	−	0.00195678i
$639$		0			0
$640$	8.14493	+	20.8158i	0.321957	+	0.822817i
$641$	−27.6619	−	5.87971i	−1.09258	−	0.232235i	−0.373824	−	0.927500i	$-0.621954\pi$
$641$	−27.6619	−	5.87971i	−1.09258	−	0.232235i	−0.718753	+	0.695265i	$0.755287\pi$
$642$		0			0
$643$	−24.9228	−	43.1676i	−0.982861	−	1.70237i	−0.651081	−	0.759009i	$-0.725684\pi$
$643$	−24.9228	−	43.1676i	−0.982861	−	1.70237i	−0.331780	−	0.943357i	$-0.607649\pi$
$644$	−18.4152	−	8.19895i	−0.725659	−	0.323084i
$645$		0			0
$646$	5.92673	−	2.63875i	0.233184	−	0.103820i
$647$	36.4560	+	26.4868i	1.43323	+	1.04131i	0.989403	+	0.145194i	$0.0463808\pi$
$647$	36.4560	+	26.4868i	1.43323	+	1.04131i	0.443830	+	0.896111i	$0.353619\pi$
$648$		0			0
$649$	−4.35029			−0.170764
$650$	−0.665302	−	0.0612566i	−0.0260953	−	0.00240268i
$651$		0			0
$652$	15.1704	−	3.22458i	0.594121	−	0.126284i
$653$	4.51995	−	43.0045i	0.176879	−	1.68290i	−0.441692	−	0.897167i	$-0.645622\pi$
$653$	4.51995	−	43.0045i	0.176879	−	1.68290i	0.618572	−	0.785728i	$-0.287712\pi$
$654$		0			0
$655$	15.9332	−	31.7759i	0.622562	−	1.24159i
$656$	−22.1470	+	16.0907i	−0.864694	+	0.628237i
$657$		0			0
$658$	0.480809	−	0.349328i	0.0187439	−	0.0136182i
$659$	−33.2873	−	7.07544i	−1.29669	−	0.275620i	−0.492667	−	0.870218i	$-0.663978\pi$
$659$	−33.2873	−	7.07544i	−1.29669	−	0.275620i	−0.804023	+	0.594598i	$0.797311\pi$
$660$		0			0
$661$	2.92574	−	0.621885i	0.113798	−	0.0241885i	−0.150661	−	0.988586i	$-0.548140\pi$
$661$	2.92574	−	0.621885i	0.113798	−	0.0241885i	0.264459	+	0.964397i	$0.414807\pi$
$662$	2.18040	−	2.42157i	0.0847435	−	0.0941172i
$663$		0			0
$664$	−8.53854	−	9.48301i	−0.331360	−	0.368012i
$665$	21.2675	−	1.25224i	0.824718	−	0.0485598i
$666$		0			0
$667$	1.36979	−	0.995212i	0.0530385	−	0.0385347i
$668$	−10.6934	+	18.5215i	−0.413739	+	0.716617i
$669$		0			0
$670$	−10.3195	+	2.83660i	−0.398677	+	0.109587i
$671$	0.253908	−	2.41577i	0.00980201	−	0.0932599i
$672$		0			0
$673$	−4.74148	−	5.26595i	−0.182771	−	0.202987i	0.644796	−	0.764355i	$-0.276942\pi$
$673$	−4.74148	−	5.26595i	−0.182771	−	0.202987i	−0.827567	+	0.561367i	$0.810276\pi$
$674$	−6.20994			−0.239198
$675$		0			0
$676$	23.9266			0.920253
$677$	24.1204	+	26.7884i	0.927021	+	1.02956i	0.999482	+	0.0321899i	$0.0102481\pi$
$677$	24.1204	+	26.7884i	0.927021	+	1.02956i	−0.0724607	+	0.997371i	$0.523085\pi$
$678$		0			0
$679$	2.77526	−	26.4048i	0.106505	−	1.01332i
$680$	12.9733	+	4.88415i	0.497501	+	0.187299i
$681$		0			0
$682$	0.414783	−	0.718424i	0.0158828	−	0.0275099i
$683$	−21.8805	+	15.8971i	−0.837236	+	0.608287i	−0.921597	−	0.388148i	$-0.873115\pi$
$683$	−21.8805	+	15.8971i	−0.837236	+	0.608287i	0.0843615	+	0.996435i	$0.473115\pi$
$684$		0			0
$685$	−3.95736	+	15.1597i	−0.151203	+	0.579221i
$686$	5.00725	+	5.56111i	0.191178	+	0.212324i
$687$		0			0
$688$	16.4021	−	18.2164i	0.625324	−	0.694492i
$689$	3.85931	−	0.820321i	0.147028	−	0.0312517i
$690$		0			0
$691$	12.3850	+	2.63252i	0.471148	+	0.100146i	0.437366	−	0.899284i	$-0.355911\pi$
$691$	12.3850	+	2.63252i	0.471148	+	0.100146i	0.0337821	+	0.999429i	$0.489245\pi$
$692$	27.2406	−	19.7915i	1.03553	−	0.752359i
$693$		0			0
$694$	0.170830	−	0.124115i	0.00648462	−	0.00471135i
$695$	−5.83209	−	35.3448i	−0.221224	−	1.34070i
$696$		0			0
$697$	−3.85457	+	36.6737i	−0.146002	+	1.38912i
$698$	−13.2370	+	2.81361i	−0.501027	+	0.106497i
$699$		0			0
$700$	16.4824	+	14.4600i	0.622975	+	0.546538i
$701$	−38.2015			−1.44285			−0.721426	−	0.692492i	$-0.756513\pi$
$701$	−38.2015			−1.44285			−0.721426	+	0.692492i	$0.756513\pi$
$702$		0			0
$703$	32.0690	+	23.2995i	1.20950	+	0.878756i
$704$	1.64588	−	0.732794i	0.0620315	−	0.0276182i
$705$		0			0
$706$	−4.52479	−	2.01457i	−0.170293	−	0.0758192i
$707$	18.7040	+	32.3963i	0.703437	+	1.21839i
$708$		0			0
$709$	−38.6194	−	8.20880i	−1.45038	−	0.308288i	−0.585666	−	0.810552i	$-0.699167\pi$
$709$	−38.6194	−	8.20880i	−1.45038	−	0.308288i	−0.864714	+	0.502264i	$0.832500\pi$
$710$	1.73511	−	0.102164i	0.0651175	−	0.00383415i
$711$		0			0
$712$	−0.875563	−	2.69470i	−0.0328131	−	0.100988i
$713$	26.4366	+	5.61927i	0.990058	+	0.210443i
$714$		0			0
$715$	−0.0136772	+	0.297723i	−0.000511500	+	0.0111342i
$716$	9.09199	−	10.0977i	0.339784	−	0.377368i
$717$		0			0
$718$	6.98185	−	12.0929i	0.260560	−	0.451304i
$719$	−8.24606	+	5.99111i	−0.307526	+	0.223431i	−0.730834	−	0.682555i	$-0.760869\pi$
$719$	−8.24606	+	5.99111i	−0.307526	+	0.223431i	0.423308	+	0.905986i	$0.360869\pi$
$720$		0			0
$721$	−2.70238	−	1.96339i	−0.100642	−	0.0731205i
$722$	−0.925884	+	0.412230i	−0.0344578	+	0.0153416i
$723$		0			0
$724$	8.97143	+	15.5390i	0.333421	+	0.577501i
$725$	−1.74406	+	0.591669i	−0.0647727	+	0.0219740i
$726$		0			0
$727$	18.4337	+	20.4727i	0.683668	+	0.759290i	0.980688	−	0.195581i	$-0.0626593\pi$
$727$	18.4337	+	20.4727i	0.683668	+	0.759290i	−0.297019	+	0.954871i	$0.595993\pi$
$728$	−0.984202	−	0.715064i	−0.0364769	−	0.0265020i
$729$		0			0
$730$	−1.93220	−	4.93807i	−0.0715139	−	0.182766i
$731$	−3.45149	−	32.8387i	−0.127658	−	1.21458i
$732$		0			0
$733$	3.46741	+	1.54379i	0.128072	+	0.0570211i	0.469772	−	0.882788i	$-0.344336\pi$
$733$	3.46741	+	1.54379i	0.128072	+	0.0570211i	−0.341700	+	0.939809i	$0.611003\pi$
$734$	6.46976	−	7.18539i	0.238803	−	0.265218i
$735$		0			0
$736$	−12.5958	−	13.9890i	−0.464287	−	0.515642i
$737$	1.47529	+	4.54046i	0.0543428	+	0.167250i
$738$		0			0
$739$	−6.92487	+	21.3125i	−0.254735	+	0.783995i	0.739146	+	0.673545i	$0.235229\pi$
$739$	−6.92487	+	21.3125i	−0.254735	+	0.783995i	−0.993882	+	0.110450i	$0.964771\pi$
$740$	6.64186	+	40.2523i	0.244160	+	1.47970i
$741$		0			0
$742$	9.00264	+	4.00823i	0.330497	+	0.147147i
$743$	−0.543224	−	0.940891i	−0.0199289	−	0.0345179i	0.855889	−	0.517160i	$-0.173011\pi$
$743$	−0.543224	−	0.940891i	−0.0199289	−	0.0345179i	−0.875818	+	0.482642i	$0.839677\pi$
$744$		0			0
$745$	−22.2403	+	11.5134i	−0.814823	+	0.421818i
$746$	1.41619	+	1.02892i	0.0518505	+	0.0376716i
$747$		0			0
$748$	0.920413	−	2.83274i	0.0336536	−	0.103575i
$749$	−9.41020	+	16.2990i	−0.343841	+	0.595551i
$750$		0			0
$751$	−7.82702	−	13.5568i	−0.285612	−	0.494694i	0.687145	−	0.726520i	$-0.258863\pi$
$751$	−7.82702	−	13.5568i	−0.285612	−	0.494694i	−0.972757	+	0.231826i	$0.925530\pi$
$752$	−2.07750	+	0.441586i	−0.0757587	+	0.0161030i
$753$		0			0
$754$	0.0449633	−	0.0200190i	0.00163747	−	0.000729048i
$755$	6.50893	+	4.16748i	0.236884	+	0.151670i
$756$		0			0
$757$	−8.77489			−0.318929			−0.159464	−	0.987204i	$-0.550977\pi$
$757$	−8.77489			−0.318929			−0.159464	+	0.987204i	$0.550977\pi$
$758$	0.995648	+	9.47296i	0.0361636	+	0.344073i
$759$		0			0
$760$	12.2628	+	4.61667i	0.444817	+	0.167464i
$761$	−18.6323	+	3.96042i	−0.675421	+	0.143565i	−0.532837	−	0.846218i	$-0.678874\pi$
$761$	−18.6323	+	3.96042i	−0.675421	+	0.143565i	−0.142583	+	0.989783i	$0.545541\pi$
$762$		0			0
$763$	20.3911	+	4.33427i	0.738209	+	0.156911i
$764$	7.53068	−	23.1771i	0.272450	−	0.838516i
$765$		0			0
$766$	−0.792465	−	2.43896i	−0.0286329	−	0.0881231i
$767$	−0.430661	−	4.09746i	−0.0155503	−	0.147951i
$768$		0			0
$769$	25.2970	+	11.2630i	0.912234	+	0.406153i	0.808530	−	0.588456i	$-0.200264\pi$
$769$	25.2970	+	11.2630i	0.912234	+	0.406153i	0.103704	+	0.994608i	$0.466930\pi$
$770$	−0.464722	+	0.581517i	−0.0167474	+	0.0209564i
$771$		0			0
$772$	28.5245	−	12.6999i	1.02662	−	0.457080i
$773$	−4.15971	+	12.8023i	−0.149615	+	0.460466i	−0.997576	−	0.0695925i	$-0.977830\pi$
$773$	−4.15971	+	12.8023i	−0.149615	+	0.460466i	0.847961	+	0.530059i	$0.177830\pi$
$774$		0			0
$775$	−25.6471	−	14.3693i	−0.921272	−	0.516161i
$776$	8.16473	−	14.1417i	0.293097	−	0.507659i
$777$		0			0
$778$	−0.0873289	+	0.830879i	−0.00313089	+	0.0297884i
$779$	−3.64346	+	34.6652i	−0.130541	+	1.24201i
$780$		0			0
$781$	−0.0810459	−	0.771100i	−0.00290005	−	0.0275921i
$782$	−7.38538			−0.264101
$783$		0			0
$784$	−1.40410	−	4.32136i	−0.0501463	−	0.154334i
$785$	−3.50152	+	1.81267i	−0.124975	+	0.0646968i
$786$		0			0
$787$	−7.57983	+	8.41826i	−0.270192	+	0.300078i	−0.862937	−	0.505312i	$-0.831378\pi$
$787$	−7.57983	+	8.41826i	−0.270192	+	0.300078i	0.592745	+	0.805390i	$0.298044\pi$
$788$	14.4568	−	16.0558i	0.515000	−	0.571966i
$789$		0			0
$790$	4.48463	−	8.94379i	0.159556	−	0.318206i
$791$	12.1412	+	37.3667i	0.431691	+	1.32861i
$792$		0			0
$793$	2.30051			0.0816935
$794$	−0.912860	−	8.68529i	−0.0323962	−	0.308229i
$795$		0			0
$796$	1.43368	−	13.6405i	0.0508153	−	0.483476i
$797$	−0.423937	+	4.03349i	−0.0150166	+	0.142873i	−0.999461	−	0.0328217i	$-0.989551\pi$
$797$	−0.423937	+	4.03349i	−0.0150166	+	0.142873i	0.984445	+	0.175695i	$0.0562173\pi$
$798$		0			0
$799$	−1.43051	+	2.47772i	−0.0506078	+	0.0876553i
$800$	8.56881	+	18.5962i	0.302953	+	0.657476i
$801$		0			0
$802$	1.79471	−	5.52354i	0.0633733	−	0.195043i
$803$	−2.16093	+	0.962107i	−0.0762575	+	0.0339520i
$804$		0			0
$805$	−22.6972	−	8.54502i	−0.799972	−	0.301172i
$806$	0.717733	+	0.319555i	0.0252810	+	0.0112558i
$807$		0			0
$808$	2.40493	+	22.8814i	0.0846052	+	0.804965i
$809$	−1.08629	−	3.34324i	−0.0381918	−	0.117542i	0.930143	−	0.367198i	$-0.119683\pi$
$809$	−1.08629	−	3.34324i	−0.0381918	−	0.117542i	−0.968335	+	0.249655i	$0.919683\pi$
$810$		0			0
$811$	13.6058	−	41.8744i	0.477765	−	1.47041i	−0.364428	−	0.931232i	$-0.618735\pi$
$811$	13.6058	−	41.8744i	0.477765	−	1.47041i	0.842193	−	0.539177i	$-0.181265\pi$
$812$	−1.57996	−	0.335830i	−0.0554456	−	0.0117853i
$813$		0			0
$814$	−1.35478	+	0.287967i	−0.0474850	+	0.0100933i
$815$	17.9923	−	4.94568i	0.630244	−	0.173240i
$816$		0			0
$817$	−3.26246	−	31.0403i	−0.114139	−	1.08596i
$818$	−10.1905			−0.356302
$819$		0			0
$820$	−27.7329	+	22.7555i	−0.968474	+	0.794657i
$821$	−16.1456	+	7.18849i	−0.563485	+	0.250880i	−0.668653	−	0.743575i	$-0.733129\pi$
$821$	−16.1456	+	7.18849i	−0.563485	+	0.250880i	0.105167	+	0.994455i	$0.466462\pi$
$822$		0			0
$823$	−31.3810	+	6.67023i	−1.09387	+	0.232510i	−0.719308	−	0.694691i	$-0.755541\pi$
$823$	−31.3810	+	6.67023i	−1.09387	+	0.232510i	−0.374564	+	0.927201i	$0.622208\pi$
$824$	−1.02721	−	1.77919i	−0.0357847	−	0.0619809i
$825$		0			0
$826$	5.14524	−	8.91181i	0.179026	−	0.310082i
$827$	14.6544	−	45.1017i	0.509584	−	1.56834i	−0.283341	−	0.959019i	$-0.591443\pi$
$827$	14.6544	−	45.1017i	0.509584	−	1.56834i	0.792925	−	0.609320i	$-0.208557\pi$
$828$		0			0
$829$	−1.12381	−	0.816496i	−0.0390315	−	0.0283581i	0.568098	−	0.822961i	$-0.307679\pi$
$829$	−1.12381	−	0.816496i	−0.0390315	−	0.0283581i	−0.607130	+	0.794603i	$0.707679\pi$
$830$	−5.26263	−	5.19515i	−0.182669	−	0.180326i
$831$		0			0
$832$	0.853140	+	1.47768i	0.0295773	+	0.0512294i
$833$	−5.59150	−	2.48950i	−0.193734	−	0.0862559i
$834$		0			0
$835$	−11.5334	+	23.0013i	−0.399130	+	0.795993i
$836$	0.870005	−	2.67760i	0.0300897	−	0.0926067i
$837$		0			0
$838$	−1.87197	−	5.76132i	−0.0646660	−	0.199021i
$839$	−18.3941	−	20.4287i	−0.635036	−	0.705279i	0.336630	−	0.941637i	$-0.390713\pi$
$839$	−18.3941	−	20.4287i	−0.635036	−	0.705279i	−0.971666	+	0.236358i	$0.924046\pi$
$840$		0			0
$841$	−19.3140	+	21.4504i	−0.666000	+	0.739668i
$842$	5.86220	+	2.61002i	0.202025	+	0.0899473i
$843$		0			0
$844$	2.15858	+	20.5375i	0.0743015	+	0.706932i
$845$	28.7369	−	1.69204i	0.988578	−	0.0582079i
$846$		0			0
$847$	−20.7290	−	15.0605i	−0.712256	−	0.517484i
$848$	−23.5653	−	26.1719i	−0.809234	−	0.898746i
$849$		0			0
$850$	7.67149	+	2.38362i	0.263130	+	0.0817573i
$851$	−22.5624	−	39.0792i	−0.773428	−	1.33962i
$852$		0			0
$853$	−6.53467	+	2.90942i	−0.223743	+	0.0996168i	−0.515547	−	0.856861i	$-0.672411\pi$
$853$	−6.53467	+	2.90942i	−0.223743	+	0.0996168i	0.291804	+	0.956478i	$0.405745\pi$
$854$	4.64854	+	3.37736i	0.159070	+	0.115571i
$855$		0			0
$856$	−9.36461	+	6.80379i	−0.320076	+	0.232549i
$857$	−4.13554	+	7.16297i	−0.141267	+	0.244682i	−0.927974	−	0.372645i	$-0.878451\pi$
$857$	−4.13554	+	7.16297i	−0.141267	+	0.244682i	0.786707	+	0.617327i	$0.211784\pi$
$858$		0			0
$859$	15.2287	−	16.9132i	0.519596	−	0.577070i	−0.425046	−	0.905172i	$-0.639742\pi$
$859$	15.2287	−	16.9132i	0.519596	−	0.577070i	0.944642	+	0.328102i	$0.106409\pi$
$860$	20.0538	−	25.0937i	0.683828	−	0.855689i
$861$		0			0
$862$	−4.05498	−	0.861912i	−0.138113	−	0.0293568i
$863$	6.39640	+	19.6861i	0.217736	+	0.670123i	0.998948	+	0.0458569i	$0.0146018\pi$
$863$	6.39640	+	19.6861i	0.217736	+	0.670123i	−0.781212	+	0.624266i	$0.785398\pi$
$864$		0			0
$865$	31.3176	−	25.6968i	1.06483	−	0.873718i
$866$	6.73283	+	1.43111i	0.228791	+	0.0486310i
$867$		0			0
$868$	−12.8918	−	22.3293i	−0.437577	−	0.757906i
$869$	−4.07730	−	1.81533i	−0.138313	−	0.0615809i
$870$		0			0
$871$	−4.13053	+	1.83903i	−0.139958	+	0.0623132i
$872$	10.3728	+	7.53631i	0.351269	+	0.255212i
$873$		0			0
$874$	−6.98091			−0.236133
$875$	20.8186	+	16.2015i	0.703798	+	0.547712i
$876$		0			0
$877$	−11.5921	+	2.46399i	−0.391439	+	0.0832029i	−0.399427	−	0.916765i	$-0.630791\pi$
$877$	−11.5921	+	2.46399i	−0.391439	+	0.0832029i	0.00798764	+	0.999968i	$0.497457\pi$
$878$	0.828790	−	7.88541i	0.0279703	−	0.266120i
$879$		0			0
$880$	2.36248	−	1.22301i	0.0796392	−	0.0412276i
$881$	−0.952966	+	0.692370i	−0.0321062	+	0.0233265i	−0.603723	−	0.797194i	$-0.706317\pi$
$881$	−0.952966	+	0.692370i	−0.0321062	+	0.0233265i	0.571616	+	0.820521i	$0.306317\pi$
$882$		0			0
$883$	−5.30098	+	3.85139i	−0.178392	+	0.129609i	−0.673398	−	0.739280i	$-0.735166\pi$
$883$	−5.30098	+	3.85139i	−0.178392	+	0.129609i	0.495006	+	0.868890i	$0.335166\pi$
$884$	2.75922	+	0.586491i	0.0928027	+	0.0197258i
$885$		0			0
$886$	11.7009	−	2.48710i	0.393099	−	0.0835558i
$887$	35.6845	−	39.6316i	1.19817	−	1.33070i	0.268063	−	0.963401i	$-0.413616\pi$
$887$	35.6845	−	39.6316i	1.19817	−	1.33070i	0.930103	−	0.367298i	$-0.119717\pi$
$888$		0			0
$889$	−14.6095	−	16.2255i	−0.489986	−	0.544185i
$890$	−0.598309	−	1.52908i	−0.0200554	−	0.0512550i
$891$		0			0
$892$	−4.54773	+	3.30412i	−0.152269	+	0.110630i
$893$	−1.35217	+	2.34202i	−0.0452485	+	0.0783727i
$894$		0			0
$895$	10.2058	−	12.7707i	0.341142	−	0.426878i
$896$	−2.46546	+	23.4572i	−0.0823651	+	0.783651i
$897$		0			0
$898$	3.60777	+	4.00683i	0.120393	+	0.133710i
$899$	2.16569			0.0722298
$900$		0			0
$901$	−47.4401			−1.58046
$902$	−0.814945	−	0.905088i	−0.0271347	−	0.0301361i
$903$		0			0
$904$	−2.52590	+	24.0323i	−0.0840102	+	0.799304i
$905$	11.8740	+	18.0285i	0.394704	+	0.599289i
$906$		0			0
$907$	−23.7125	+	41.0712i	−0.787360	+	1.36375i	0.140220	+	0.990120i	$0.455219\pi$
$907$	−23.7125	+	41.0712i	−0.787360	+	1.36375i	−0.927579	+	0.373626i	$0.878114\pi$
$908$	−13.7556	+	9.99402i	−0.456495	+	0.331663i
$909$		0			0
$910$	−0.593725	−	0.380146i	−0.0196818	−	0.0126017i
$911$	6.75939	+	7.50706i	0.223949	+	0.248720i	0.844640	−	0.535335i	$-0.179815\pi$
$911$	6.75939	+	7.50706i	0.223949	+	0.248720i	−0.620691	+	0.784055i	$0.713148\pi$
$912$		0			0
$913$	−2.20731	+	2.45146i	−0.0730512	+	0.0811316i
$914$	−8.30773	+	1.76586i	−0.274795	+	0.0584095i
$915$		0			0
$916$	−53.5813	−	11.3891i	−1.77038	−	0.376305i
$917$	30.3454	−	22.0472i	1.00209	−	0.728064i
$918$		0			0
$919$	16.4085	−	11.9215i	0.541266	−	0.393253i	−0.283289	−	0.959035i	$-0.591426\pi$
$919$	16.4085	−	11.9215i	0.541266	−	0.393253i	0.824555	+	0.565782i	$0.191426\pi$
$920$	−10.6152	−	10.4791i	−0.349973	−	0.345485i
$921$		0			0
$922$	−1.04067	+	9.90136i	−0.0342728	+	0.326084i
$923$	0.718262	−	0.152671i	0.0236419	−	0.00502524i
$924$		0			0
$925$	10.8237	+	47.8751i	0.355882	+	1.57412i
$926$	2.16084			0.0710097
$927$		0			0
$928$	−1.22030	−	0.886601i	−0.0400584	−	0.0291041i
$929$	32.9758	−	14.6818i	1.08190	−	0.481693i	0.213189	−	0.977011i	$-0.431615\pi$
$929$	32.9758	−	14.6818i	1.08190	−	0.481693i	0.868712	+	0.495318i	$0.164948\pi$
$930$		0			0
$931$	−5.28527	−	2.35316i	−0.173218	−	0.0771215i
$932$	7.57554	+	13.1212i	0.248145	+	0.429800i
$933$		0			0
$934$	6.68325	+	1.42057i	0.218683	+	0.0464824i
$935$	0.905130	−	3.46733i	0.0296009	−	0.113394i
$936$		0			0
$937$	−2.52174	−	7.76113i	−0.0823818	−	0.253545i	0.901379	−	0.433032i	$-0.142556\pi$
$937$	−2.52174	−	7.76113i	−0.0823818	−	0.253545i	−0.983760	+	0.179487i	$0.942556\pi$
$938$	−11.0462	−	2.34795i	−0.360673	−	0.0766634i
$939$		0			0
$940$	−2.68374	+	0.737698i	−0.0875338	+	0.0240610i
$941$	33.3049	−	36.9888i	1.08571	−	1.20580i	0.108371	−	0.994111i	$-0.465437\pi$
$941$	33.3049	−	36.9888i	1.08571	−	1.20580i	0.977337	−	0.211690i	$-0.0678968\pi$
$942$		0			0
$943$	19.8398	−	34.3636i	0.646073	−	1.11903i
$944$	−29.7519	+	21.6160i	−0.968342	+	0.703541i
$945$		0			0
$946$	0.882279	+	0.641013i	0.0286854	+	0.0208411i
$947$	7.02616	−	3.12825i	0.228319	−	0.101654i	−0.289389	−	0.957212i	$-0.593452\pi$
$947$	7.02616	−	3.12825i	0.228319	−	0.101654i	0.517708	+	0.855557i	$0.326785\pi$
$948$		0			0
$949$	−1.12011	−	1.94009i	−0.0363604	−	0.0629781i
$950$	7.25135	+	2.25307i	0.235265	+	0.0730993i
$951$		0			0
$952$	9.78763	+	10.8703i	0.317219	+	0.352307i
$953$	−8.32277	−	6.04685i	−0.269601	−	0.195877i	0.444768	−	0.895646i	$-0.353286\pi$
$953$	−8.32277	−	6.04685i	−0.269601	−	0.195877i	−0.714369	+	0.699769i	$0.753286\pi$
$954$		0			0
$955$	7.40564	−	28.3692i	0.239641	−	0.918006i
$956$	−0.921446	−	8.76697i	−0.0298017	−	0.283544i
$957$		0			0
$958$	0.113818	+	0.0506750i	0.00367729	+	0.00163723i
$959$	−11.0624	+	12.2861i	−0.357224	+	0.396738i
$960$		0			0
$961$	2.38886	+	2.65309i	0.0770599	+	0.0855837i
$962$	−0.405349	−	1.24753i	−0.0130690	−	0.0402221i
$963$		0			0
$964$	14.3725	−	44.2340i	0.462907	−	1.42468i
$965$	33.3610	−	17.2704i	1.07393	−	0.555952i
$966$		0			0
$967$	−16.4716	−	7.33365i	−0.529692	−	0.235834i	0.124423	−	0.992229i	$-0.460292\pi$
$967$	−16.4716	−	7.33365i	−0.529692	−	0.235834i	−0.654115	+	0.756395i	$0.726959\pi$
$968$	−7.87940	−	13.6475i	−0.253254	−	0.438648i
$969$		0			0
$970$	4.24165	−	8.45922i	0.136191	−	0.271609i
$971$	−21.6172	−	15.7058i	−0.693730	−	0.504025i	0.184154	−	0.982897i	$-0.441046\pi$
$971$	−21.6172	−	15.7058i	−0.693730	−	0.504025i	−0.877884	+	0.478873i	$0.841046\pi$
$972$		0			0
$973$	11.6809	−	35.9500i	0.374472	−	1.15251i
$974$	3.75283	−	6.50008i	0.120248	−	0.208276i
$975$		0			0
$976$	−10.2672	−	17.7832i	−0.328644	−	0.569228i
$977$	−24.3316	+	5.17184i	−0.778437	+	0.165462i	−0.579962	−	0.814644i	$-0.696932\pi$
$977$	−24.3316	+	5.17184i	−0.778437	+	0.165462i	−0.198476	+	0.980106i	$0.563599\pi$
$978$		0			0
$979$	−0.669135	+	0.297918i	−0.0213857	+	0.00952151i
$980$	−2.16967	−	5.54498i	−0.0693076	−	0.177128i
$981$		0			0
$982$	−13.5871			−0.433583
$983$	−3.60482	−	34.2976i	−0.114976	−	1.09392i	−0.888094	−	0.459662i	$-0.847971\pi$
$983$	−3.60482	−	34.2976i	−0.114976	−	1.09392i	0.773118	−	0.634262i	$-0.218696\pi$
$984$		0			0
$985$	16.2278	−	20.3061i	0.517059	−	0.647007i
$986$	−0.578859	+	0.123040i	−0.0184346	+	0.00391840i
$987$		0			0
$988$	2.60811	+	0.554371i	0.0829750	+	0.0176369i
$989$	−10.9795	+	33.7913i	−0.349127	+	1.07450i
$990$		0			0
$991$	−1.92211	−	5.91566i	−0.0610580	−	0.187917i	0.915875	−	0.401464i	$-0.131498\pi$
$991$	−1.92211	−	5.91566i	−0.0610580	−	0.187917i	−0.976933	+	0.213547i	$0.931498\pi$
$992$	−2.51680	−	23.9457i	−0.0799084	−	0.760278i
$993$		0			0
$994$	1.67550	+	0.745979i	0.0531435	+	0.0236610i
$995$	0.757278	−	16.4842i	0.0240073	−	0.522586i
$996$		0			0
$997$	−7.41814	+	3.30277i	−0.234935	+	0.104600i	−0.520828	−	0.853662i	$-0.674377\pi$
$997$	−7.41814	+	3.30277i	−0.234935	+	0.104600i	0.285893	+	0.958262i	$0.407710\pi$
$998$	3.18598	−	9.80545i	0.100851	−	0.310386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.17		224
3.2	odd	2		225.2.q.a.196.12	yes	224
9.4	even	3	inner	675.2.r.a.496.12		224
9.5	odd	6		225.2.q.a.121.17	yes	224
25.6	even	5	inner	675.2.r.a.181.12		224
75.56	odd	10		225.2.q.a.106.17	yes	224
225.31	even	15	inner	675.2.r.a.631.17		224
225.131	odd	30		225.2.q.a.31.12	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.12	✓	224	225.131	odd	30
225.2.q.a.106.17	yes	224	75.56	odd	10
225.2.q.a.121.17	yes	224	9.5	odd	6
225.2.q.a.196.12	yes	224	3.2	odd	2
675.2.r.a.46.17		224	1.1	even	1	trivial
675.2.r.a.181.12		224	25.6	even	5	inner
675.2.r.a.496.12		224	9.4	even	3	inner
675.2.r.a.631.17		224	225.31	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.251657 + 0.279494i) q^{2} +(0.194272 - 1.84837i) q^{4} +(0.102616 - 2.23371i) q^{5} +(1.17975 - 2.04339i) q^{7} +(1.17403 - 0.852985i) q^{8} +O(q^{10})\)	\(q+(0.251657 + 0.279494i) q^{2} +(0.194272 - 1.84837i) q^{4} +(0.102616 - 2.23371i) q^{5} +(1.17975 - 2.04339i) q^{7} +(1.17403 - 0.852985i) q^{8} +(0.650132 - 0.533449i) q^{10} +(-0.251022 - 0.278789i) q^{11} +(0.237736 - 0.264032i) q^{13} +(0.868006 - 0.184500i) q^{14} +(-3.10202 - 0.659354i) q^{16} +(-3.45606 + 2.51098i) q^{17} +(-3.26679 + 2.37346i) q^{19} +(-4.10879 - 0.623618i) q^{20} +(0.0147481 - 0.140318i) q^{22} +(4.49630 - 0.955717i) q^{23} +(-4.97894 - 0.458427i) q^{25} +0.133623 q^{26} +(-3.54774 - 2.57759i) q^{28} +(0.336493 - 0.149816i) q^{29} +(5.37131 + 2.39146i) q^{31} +(-2.04755 - 3.54645i) q^{32} +(-1.57154 - 0.334042i) q^{34} +(-4.44328 - 2.84490i) q^{35} +(-3.03352 - 9.33621i) q^{37} +(-1.48548 - 0.315748i) q^{38} +(-1.78485 - 2.70998i) q^{40} +(5.77601 - 6.41491i) q^{41} +(-3.86472 + 6.69390i) q^{43} +(-0.564071 + 0.409822i) q^{44} +(1.39864 + 1.01617i) q^{46} +(0.611825 - 0.272402i) q^{47} +(0.716381 + 1.24081i) q^{49} +(-1.12486 - 1.50695i) q^{50} +(-0.441844 - 0.490718i) q^{52} +(8.98419 + 6.52740i) q^{53} +(-0.648493 + 0.532104i) q^{55} +(-0.357913 - 3.40531i) q^{56} +(0.126554 + 0.0563453i) q^{58} +(7.75940 - 8.61768i) q^{59} +(4.33263 + 4.81187i) q^{61} +(0.683331 + 2.10308i) q^{62} +(-1.48405 + 4.56744i) q^{64} +(-0.565377 - 0.558127i) q^{65} +(-11.6258 - 5.17613i) q^{67} +(3.96980 + 6.87589i) q^{68} +(-0.323050 - 1.95781i) q^{70} +(1.67206 + 1.21482i) q^{71} +(1.94846 - 5.99673i) q^{73} +(1.84600 - 3.19737i) q^{74} +(3.75239 + 6.49933i) q^{76} +(-0.865817 + 0.184035i) q^{77} +(10.8685 - 4.83898i) q^{79} +(-1.79112 + 6.86136i) q^{80} +3.24650 q^{82} +(-0.919146 - 8.74509i) q^{83} +(5.25415 + 7.97751i) q^{85} +(-2.84349 + 0.604402i) q^{86} +(-0.532511 - 0.113189i) q^{88} +(0.603343 - 1.85690i) q^{89} +(-0.259051 - 0.797278i) q^{91} +(-0.893017 - 8.49649i) q^{92} +(0.230105 + 0.102449i) q^{94} +(4.96640 + 7.54061i) q^{95} +(10.2797 - 4.57681i) q^{97} +(-0.166516 + 0.512483i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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