LMFDB - Embedded newform 891.2.u.c.701.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			701.1
Character	$\chi$	$=$	891.701
Dual form			891.2.u.c.755.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22569 - 0.990940i) q^{2} +(2.63346 + 2.92476i) q^{4} +(-1.54387 - 3.46760i) q^{5} +(0.0764681 + 0.359754i) q^{7} +(-1.45728 - 4.48505i) q^{8} +O(q^{10})$	\(q+(-2.22569 - 0.990940i) q^{2} +(2.63346 + 2.92476i) q^{4} +(-1.54387 - 3.46760i) q^{5} +(0.0764681 + 0.359754i) q^{7} +(-1.45728 - 4.48505i) q^{8} +9.24768i q^{10} +(0.223636 + 3.30908i) q^{11} +(0.943068 - 0.0991205i) q^{13} +(0.186301 - 0.876476i) q^{14} +(-0.378188 + 3.59821i) q^{16} +(2.77873 + 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(6.07615 - 13.6472i) q^{20} +(2.78135 - 7.58658i) q^{22} +(4.30242 + 2.48400i) q^{23} +(-6.29504 + 6.99135i) q^{25} +(-2.19720 - 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(2.42915 - 0.516332i) q^{29} +(-0.367304 - 3.49466i) q^{31} +(-0.308515 + 0.534364i) q^{32} +(-4.18401 - 7.24691i) q^{34} +(1.12943 - 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(-10.3274 - 1.08546i) q^{38} +(-13.3025 + 11.9776i) q^{40} +(2.65968 + 0.565333i) q^{41} +(1.63461 - 0.943743i) q^{43} +(-9.08931 + 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(-0.0153145 - 0.0137893i) q^{47} +(6.27124 - 2.79214i) q^{49} +(20.9388 - 9.32255i) q^{50} +(2.77344 + 2.49722i) q^{52} +(-3.25941 - 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +(1.50208 - 0.867226i) q^{56} +(-5.91818 - 1.25795i) q^{58} +(-4.92273 + 4.43245i) q^{59} +(9.69908 + 1.01941i) q^{61} +(-2.64550 + 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +(-1.79969 - 3.11715i) q^{65} +(-2.23176 + 3.86552i) q^{67} +(1.41299 + 13.4437i) q^{68} +(-3.32689 + 0.707153i) q^{70} +(6.06985 - 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(11.7088 - 13.0039i) q^{74} +(14.5275 + 8.38745i) q^{76} +(-1.17335 + 0.333493i) q^{77} +(4.44852 - 9.99155i) q^{79} +(13.0610 - 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(0.959910 - 9.13294i) q^{83} +(2.71060 - 12.7524i) q^{85} +(-4.57333 + 0.480676i) q^{86} +(14.5155 - 5.82527i) q^{88} +3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(4.06516 + 19.1251i) q^{92} +(0.0204210 + 0.0458663i) q^{94} +(-10.8256 - 12.0231i) q^{95} +(-13.7825 - 6.13637i) q^{97} -16.7247 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4}+O(q^{10}) $ 32 * q + 4 * q^4	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.22569	−	0.990940i	−1.57380	−	0.700700i	−0.580285	−	0.814413i	$-0.697059\pi$
$2$	−2.22569	−	0.990940i	−1.57380	−	0.700700i	−0.993514	+	0.113713i	$0.963726\pi$
$3$		0			0
$3$		0			0
$4$	2.63346	+	2.92476i	1.31673	+	1.46238i
$5$	−1.54387	−	3.46760i	−0.690442	−	1.55076i	−0.828287	−	0.560303i	$-0.810685\pi$
$5$	−1.54387	−	3.46760i	−0.690442	−	1.55076i	0.137846	−	0.990454i	$-0.455982\pi$
$6$		0			0
$7$	0.0764681	+	0.359754i	0.0289022	+	0.135974i	0.990233	−	0.139422i	$-0.0445244\pi$
$7$	0.0764681	+	0.359754i	0.0289022	+	0.135974i	−0.961331	+	0.275396i	$0.911191\pi$
$8$	−1.45728	−	4.48505i	−0.515226	−	1.58570i
$9$		0			0
$10$			9.24768i			2.92437i
$11$	0.223636	+	3.30908i	0.0674289	+	0.997724i
$11$	0.223636	+	3.30908i	0.0674289	+	0.997724i
$12$		0			0
$13$	0.943068	−	0.0991205i	0.261560	−	0.0274911i	0.0271593	−	0.999631i	$-0.491354\pi$
$13$	0.943068	−	0.0991205i	0.261560	−	0.0274911i	0.234401	+	0.972140i	$0.424687\pi$
$14$	0.186301	−	0.876476i	0.0497910	−	0.234248i
$15$		0			0
$16$	−0.378188	+	3.59821i	−0.0945469	+	0.899554i
$17$	2.77873	+	2.01886i	0.673940	+	0.489646i	0.871342	−	0.490676i	$-0.163250\pi$
$17$	2.77873	+	2.01886i	0.673940	+	0.489646i	−0.197402	+	0.980323i	$0.563250\pi$
$18$		0			0
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.195425	−	0.980719i	$-0.437391\pi$
$19$	4.05368	−	1.31712i	0.929979	−	0.302168i	0.734554	+	0.678550i	$0.237391\pi$
$20$	6.07615	−	13.6472i	1.35867	−	3.05162i
$21$		0			0
$22$	2.78135	−	7.58658i	0.592986	−	1.61746i
$23$	4.30242	+	2.48400i	0.897116	+	0.517950i	0.876263	−	0.481832i	$-0.160029\pi$
$23$	4.30242	+	2.48400i	0.897116	+	0.517950i	0.0208527	+	0.999783i	$0.493362\pi$
$24$		0			0
$25$	−6.29504	+	6.99135i	−1.25901	+	1.39827i
$26$	−2.19720	−	0.713913i	−0.430906	−	0.140010i
$27$		0			0
$28$	−0.850818	+	1.17105i	−0.160789	+	0.221308i
$29$	2.42915	−	0.516332i	0.451082	−	0.0958804i	0.0232317	−	0.999730i	$-0.492604\pi$
$29$	2.42915	−	0.516332i	0.451082	−	0.0958804i	0.427850	+	0.903850i	$0.359271\pi$
$30$		0			0
$31$	−0.367304	−	3.49466i	−0.0659697	−	0.627660i	−0.976693	−	0.214642i	$-0.931141\pi$
$31$	−0.367304	−	3.49466i	−0.0659697	−	0.627660i	0.910723	−	0.413018i	$-0.135525\pi$
$32$	−0.308515	+	0.534364i	−0.0545383	+	0.0944632i
$33$		0			0
$34$	−4.18401	−	7.24691i	−0.717551	−	1.24284i
$35$	1.12943	−	0.820576i	0.190908	−	0.138703i
$36$		0			0
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	0.585179	+	0.810904i	$0.301024\pi$
$37$	−2.21947	+	6.83082i	−0.364878	+	1.12298i	−0.950057	+	0.312075i	$0.898976\pi$
$38$	−10.3274	−	1.08546i	−1.67533	−	0.176084i
$39$		0			0
$40$	−13.3025	+	11.9776i	−2.10331	+	1.89383i
$41$	2.65968	+	0.565333i	0.415373	+	0.0882902i	0.410858	−	0.911700i	$-0.365229\pi$
$41$	2.65968	+	0.565333i	0.415373	+	0.0882902i	0.00451539	+	0.999990i	$0.498563\pi$
$42$		0			0
$43$	1.63461	−	0.943743i	0.249276	−	0.143919i	−0.370157	−	0.928969i	$-0.620696\pi$
$43$	1.63461	−	0.943743i	0.249276	−	0.143919i	0.619433	+	0.785050i	$0.287363\pi$
$44$	−9.08931	+	9.36841i	−1.37026	+	1.41234i
$45$		0			0
$46$	−7.11434	−	9.79205i	−1.04895	−	1.44376i
$47$	−0.0153145	−	0.0137893i	−0.00223385	−	0.00201137i	0.668013	−	0.744150i	$-0.267145\pi$
$47$	−0.0153145	−	0.0137893i	−0.00223385	−	0.00201137i	−0.670247	+	0.742138i	$0.733812\pi$
$48$		0			0
$49$	6.27124	−	2.79214i	0.895892	−	0.398877i
$50$	20.9388	−	9.32255i	2.96119	−	1.31841i
$51$		0			0
$52$	2.77344	+	2.49722i	0.384607	+	0.346301i
$53$	−3.25941	−	4.48619i	−0.447714	−	0.616226i	0.524190	−	0.851601i	$-0.324368\pi$
$53$	−3.25941	−	4.48619i	−0.447714	−	0.616226i	−0.971905	+	0.235375i	$0.924368\pi$
$54$		0			0
$55$	11.1293	−	5.88428i	1.50067	−	0.793436i
$56$	1.50208	−	0.867226i	0.200724	−	0.115888i
$57$		0			0
$58$	−5.91818	−	1.25795i	−0.777095	−	0.165177i
$59$	−4.92273	+	4.43245i	−0.640885	+	0.577055i	−0.924170	−	0.381980i	$-0.875242\pi$
$59$	−4.92273	+	4.43245i	−0.640885	+	0.577055i	0.283286	+	0.959036i	$0.408576\pi$
$60$		0			0
$61$	9.69908	+	1.01941i	1.24184	+	0.130523i	0.702572	−	0.711612i	$-0.252035\pi$
$61$	9.69908	+	1.01941i	1.24184	+	0.130523i	0.539267	+	0.842135i	$0.318701\pi$
$62$	−2.64550	+	8.14200i	−0.335978	+	1.03404i
$63$		0			0
$64$	7.07028	−	5.13686i	0.883786	−	0.642108i
$65$	−1.79969	−	3.11715i	−0.223224	−	0.386635i
$66$		0			0
$67$	−2.23176	+	3.86552i	−0.272652	+	0.472248i	−0.969540	−	0.244932i	$-0.921234\pi$
$67$	−2.23176	+	3.86552i	−0.272652	+	0.472248i	0.696888	+	0.717180i	$0.254568\pi$
$68$	1.41299	+	13.4437i	0.171350	+	1.63029i
$69$		0			0
$70$	−3.32689	+	0.707153i	−0.397640	+	0.0845209i
$71$	6.06985	−	8.35443i	0.720359	−	0.991489i	−0.279153	−	0.960247i	$-0.590054\pi$
$71$	6.06985	−	8.35443i	0.720359	−	0.991489i	0.999512	−	0.0312420i	$-0.00994626\pi$
$72$		0			0
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	0.0539588	−	0.998543i	$-0.482816\pi$
$73$	−4.18072	−	1.35840i	−0.489317	−	0.158989i	−0.543275	+	0.839555i	$0.682816\pi$
$74$	11.7088	−	13.0039i	1.36112	−	1.51167i
$75$		0			0
$76$	14.5275	+	8.38745i	1.66642	+	0.962106i
$77$	−1.17335	+	0.333493i	−0.133716	+	0.0380051i
$78$		0			0
$79$	4.44852	−	9.99155i	0.500498	−	1.12414i	−0.469921	−	0.882709i	$-0.655717\pi$
$79$	4.44852	−	9.99155i	0.500498	−	1.12414i	0.970419	−	0.241428i	$-0.0776159\pi$
$80$	13.0610	−	4.24379i	1.46027	−	0.474470i
$81$		0			0
$82$	−5.35942	−	3.89384i	−0.591848	−	0.430003i
$83$	0.959910	−	9.13294i	0.105364	−	1.00247i	−0.806293	−	0.591517i	$-0.798529\pi$
$83$	0.959910	−	9.13294i	0.105364	−	1.00247i	0.911656	−	0.410953i	$-0.134804\pi$
$84$		0			0
$85$	2.71060	−	12.7524i	0.294006	−	1.38319i
$86$	−4.57333	+	0.480676i	−0.493154	+	0.0518326i
$87$		0			0
$88$	14.5155	−	5.82527i	1.54735	−	0.620976i
$89$			3.04837i			0.323127i	0.986862	+	0.161563i	$0.0516536\pi$
$89$			3.04837i			0.323127i	−0.986862	+	0.161563i	$0.948346\pi$
$90$		0			0
$91$	0.107774	+	0.331693i	0.0112978	+	0.0347709i
$92$	4.06516	+	19.1251i	0.423822	+	1.99392i
$93$		0			0
$94$	0.0204210	+	0.0458663i	0.00210627	+	0.00473075i
$95$	−10.8256	−	12.0231i	−1.11069	−	1.23354i
$96$		0			0
$97$	−13.7825	−	6.13637i	−1.39940	−	0.623054i	−0.438195	−	0.898880i	$-0.644382\pi$
$97$	−13.7825	−	6.13637i	−1.39940	−	0.623054i	−0.961208	+	0.275826i	$0.911049\pi$
$98$	−16.7247			−1.68945
$99$		0			0
$100$	−37.0257			−3.70257
$101$	15.9503	+	7.10154i	1.58712	+	0.706630i	0.995061	−	0.0992672i	$-0.0316499\pi$
$101$	15.9503	+	7.10154i	1.58712	+	0.706630i	0.592056	+	0.805897i	$0.298317\pi$
$102$		0			0
$103$	−6.23336	−	6.92285i	−0.614191	−	0.682128i	0.353161	−	0.935562i	$-0.385107\pi$
$103$	−6.23336	−	6.92285i	−0.614191	−	0.682128i	−0.967353	+	0.253434i	$0.918440\pi$
$104$	−1.81887	−	4.08526i	−0.178355	−	0.400593i
$105$		0			0
$106$	2.80888	+	13.2147i	0.272823	+	1.28353i
$107$	−4.76675	−	14.6705i	−0.460819	−	1.41825i	−0.864166	−	0.503207i	$-0.832153\pi$
$107$	−4.76675	−	14.6705i	−0.460819	−	1.41825i	0.403347	−	0.915047i	$-0.367847\pi$
$108$		0			0
$109$			10.6286i			1.01803i	0.860757	+	0.509016i	$0.169991\pi$
$109$			10.6286i			1.01803i	−0.860757	+	0.509016i	$0.830009\pi$
$110$	−30.6013	+	2.06812i	−2.91772	+	0.197187i
$111$		0			0
$112$	−1.32339	+	0.139094i	−0.125049	+	0.0131432i
$113$	0.217688	−	1.02414i	0.0204783	−	0.0963429i	−0.966722	−	0.255831i	$-0.917651\pi$
$113$	0.217688	−	1.02414i	0.0204783	−	0.0963429i	0.987200	+	0.159488i	$0.0509843\pi$
$114$		0			0
$115$	1.97113	−	18.7540i	0.183809	−	1.74882i
$116$	7.90722	+	5.74493i	0.734167	+	0.533404i
$117$		0			0
$118$	15.3487	−	4.98711i	1.41297	−	0.459101i
$119$	−0.513811	+	1.15404i	−0.0471010	+	0.105790i
$120$		0			0
$121$	−10.9000	+	1.48006i	−0.990907	+	0.134551i
$122$	−20.5769	−	11.8801i	−1.86295	−	1.07557i
$123$		0			0
$124$	9.25376	−	10.2773i	0.831012	−	0.922932i
$125$	15.9120	+	5.17013i	1.42321	+	0.462430i
$126$		0			0
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	−0.0502930	−	0.998735i	$-0.516016\pi$
$127$	10.3127	−	14.1942i	0.915101	−	1.25953i	0.965394	−	0.260794i	$-0.0839845\pi$
$128$	−19.6195	+	4.17025i	−1.73413	+	0.368601i
$129$		0			0
$130$	0.916634	+	8.72119i	0.0803941	+	0.764899i
$131$	6.94451	−	12.0282i	0.606744	−	1.05091i	−0.385029	−	0.922905i	$-0.625808\pi$
$131$	6.94451	−	12.0282i	0.606744	−	1.05091i	0.991773	−	0.128008i	$-0.0408582\pi$
$132$		0			0
$133$	0.783818	+	1.35761i	0.0679656	+	0.117720i
$134$	8.79769	−	6.39189i	0.760004	−	0.552176i
$135$		0			0
$136$	5.00531	−	15.4048i	0.429202	−	1.32095i
$137$	1.03205	+	0.108472i	0.0881736	+	0.00926742i	0.148513	−	0.988911i	$-0.452551\pi$
$137$	1.03205	+	0.108472i	0.0881736	+	0.00926742i	−0.0603389	+	0.998178i	$0.519218\pi$
$138$		0			0
$139$	14.7403	−	13.2723i	1.25026	−	1.12574i	0.263309	−	0.964712i	$-0.415186\pi$
$139$	14.7403	−	13.2723i	1.25026	−	1.12574i	0.986950	−	0.161027i	$-0.0514805\pi$
$140$	5.37429	+	1.14234i	0.454210	+	0.0965454i
$141$		0			0
$142$	−21.7883	+	12.5795i	−1.82844	+	1.05565i
$143$	0.538902	+	3.09852i	0.0450652	+	0.259111i
$144$		0			0
$145$	−5.54073	−	7.62616i	−0.460133	−	0.633318i
$146$	7.95889	+	7.16622i	0.658683	+	0.593080i
$147$		0			0
$148$	−25.8234	+	11.4973i	−2.12267	+	0.945072i
$149$	−7.34124	+	3.26853i	−0.601418	+	0.267769i	−0.684779	−	0.728751i	$-0.740101\pi$
$149$	−7.34124	+	3.26853i	−0.601418	+	0.267769i	0.0833609	+	0.996519i	$0.473435\pi$
$150$		0			0
$151$	7.48610	+	6.74051i	0.609210	+	0.548535i	0.914943	−	0.403582i	$-0.132235\pi$
$151$	7.48610	+	6.74051i	0.609210	+	0.548535i	−0.305734	+	0.952117i	$0.598902\pi$
$152$	−11.8147	−	16.2615i	−0.958299	−	1.31899i
$153$		0			0
$154$	2.94199	+	0.420471i	0.237072	+	0.0338826i
$155$	−11.5510	+	6.66898i	−0.927800	+	0.535665i
$156$		0			0
$157$	15.8287	+	3.36450i	1.26327	+	0.268516i	0.790386	−	0.612609i	$-0.209880\pi$
$157$	15.8287	+	3.36450i	1.26327	+	0.268516i	0.472883	+	0.881125i	$0.343213\pi$
$158$	−19.8021	+	17.8298i	−1.57537	+	1.41847i
$159$		0			0
$160$	2.32927	+	0.244816i	0.184145	+	0.0193544i
$161$	−0.564633	+	1.73776i	−0.0444993	+	0.136955i
$162$		0			0
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	−0.714959	−	0.699166i	$-0.753555\pi$
$163$	−3.45923	+	2.51328i	−0.270948	+	0.196855i	0.444012	+	0.896021i	$0.353555\pi$
$164$	5.35072	+	9.26772i	0.417821	+	0.723687i
$165$		0			0
$166$	−11.1867	+	19.3759i	−0.868253	+	1.50386i
$167$	1.91840	+	18.2523i	0.148450	+	1.41241i	0.774475	+	0.632604i	$0.218014\pi$
$167$	1.91840	+	18.2523i	0.148450	+	1.41241i	−0.626025	+	0.779803i	$0.715319\pi$
$168$		0			0
$169$	−11.8364	+	2.51590i	−0.910490	+	0.193531i
$170$	−18.6698	+	25.6968i	−1.43191	+	1.97085i
$171$		0			0
$172$	7.06490	+	2.29553i	0.538694	+	0.175032i
$173$	4.13682	−	4.59441i	0.314517	−	0.349306i	−0.565071	−	0.825042i	$-0.691151\pi$
$173$	4.13682	−	4.59441i	0.314517	−	0.349306i	0.879588	+	0.475736i	$0.157818\pi$
$174$		0			0
$175$	−2.99654	−	1.73005i	−0.226517	−	0.130780i
$176$	−11.9913	−	0.446760i	−0.903881	−	0.0336758i
$177$		0			0
$178$	3.02075	−	6.78472i	0.226415	−	0.508536i
$179$	8.77414	−	2.85089i	0.655810	−	0.213086i	0.0378357	−	0.999284i	$-0.487954\pi$
$179$	8.77414	−	2.85089i	0.655810	−	0.213086i	0.617974	+	0.786198i	$0.287954\pi$
$180$		0			0
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	0.706533	−	0.707680i	$-0.250258\pi$
$181$	3.38790	+	2.46145i	0.251821	+	0.182958i	−0.454713	+	0.890638i	$0.650258\pi$
$182$	0.0888176	−	0.845043i	0.00658360	−	0.0626388i
$183$		0			0
$184$	4.87104	−	22.9164i	0.359098	−	1.68942i
$185$	27.1131	−	2.84970i	1.99339	−	0.209514i
$186$		0			0
$187$	−6.05915	+	9.64651i	−0.443089	+	0.705423i
$188$		−	0.0811047i		−	0.00591517i
$189$		0			0
$190$	12.1803	+	37.4872i	0.883653	+	2.71960i
$191$	4.19627	+	19.7419i	0.303632	+	1.42848i	0.820125	+	0.572184i	$0.193904\pi$
$191$	4.19627	+	19.7419i	0.303632	+	1.42848i	−0.516493	+	0.856291i	$0.672763\pi$
$192$		0			0
$193$	3.25957	+	7.32111i	0.234629	+	0.526985i	0.992036	−	0.125958i	$-0.0402005\pi$
$193$	3.25957	+	7.32111i	0.234629	+	0.526985i	−0.757407	+	0.652944i	$0.773534\pi$
$194$	24.5948	+	27.3153i	1.76580	+	1.96112i
$195$		0			0
$196$	24.6814	+	10.9889i	1.76296	+	0.784919i
$197$	21.1710			1.50837			0.754187	−	0.656659i	$-0.228031\pi$
$197$	21.1710			1.50837			0.754187	+	0.656659i	$0.228031\pi$
$198$		0			0
$199$	−10.5160			−0.745457			−0.372729	−	0.927940i	$-0.621578\pi$
$199$	−10.5160			−0.745457			−0.372729	+	0.927940i	$0.621578\pi$
$200$	40.5301	+	18.0452i	2.86591	+	1.27599i
$201$		0			0
$202$	−28.4632	−	31.6116i	−2.00267	−	2.22419i
$203$	0.371505	+	0.834414i	0.0260745	+	0.0585644i
$204$		0			0
$205$	−2.14587	−	10.0955i	−0.149874	−	0.705102i
$206$	7.01339	+	21.5850i	0.488646	+	1.50390i
$207$		0			0
$208$			3.43085i			0.237886i
$209$	5.26501	+	13.1194i	0.364188	+	0.907487i
$210$		0			0
$211$	3.67797	−	0.386570i	0.253202	−	0.0266126i	0.0229227	−	0.999737i	$-0.492703\pi$
$211$	3.67797	−	0.386570i	0.253202	−	0.0266126i	0.230279	+	0.973125i	$0.426036\pi$
$212$	4.53749	−	21.3472i	0.311636	−	1.46613i
$213$		0			0
$214$	−3.92833	+	37.3756i	−0.268535	+	2.55494i
$215$	−5.79615	−	4.21115i	−0.395294	−	0.287198i
$216$		0			0
$217$	1.22913	−	0.399369i	0.0834390	−	0.0271110i
$218$	10.5323	−	23.6559i	0.713336	−	1.60218i
$219$		0			0
$220$	46.5186	+	17.0544i	3.13629	+	1.14981i
$221$	2.82064	+	1.62850i	0.189737	+	0.109545i
$222$		0			0
$223$	−11.9755	+	13.3001i	−0.801939	+	0.890644i	−0.995909	−	0.0903637i	$-0.971197\pi$
$223$	−11.9755	+	13.3001i	−0.801939	+	0.890644i	0.193969	+	0.981008i	$0.437864\pi$
$224$	−0.215832	−	0.0701279i	−0.0144209	−	0.00468562i
$225$		0			0
$226$	−1.49936	+	2.06370i	−0.0997363	+	0.137275i
$227$	16.9986	−	3.61317i	1.12824	−	0.239815i	0.394268	−	0.918996i	$-0.370998\pi$
$227$	16.9986	−	3.61317i	1.12824	−	0.239815i	0.733971	+	0.679181i	$0.237665\pi$
$228$		0			0
$229$	−0.447032	−	4.25323i	−0.0295407	−	0.281061i	−0.999313	−	0.0370509i	$-0.988204\pi$
$229$	−0.447032	−	4.25323i	−0.0295407	−	0.281061i	0.969773	−	0.244010i	$-0.0784630\pi$
$230$	−22.9713	+	39.7874i	−1.51468	+	2.62350i
$231$		0			0
$232$	−5.85572	−	10.1424i	−0.384447	−	0.665882i
$233$	−18.9171	+	13.7441i	−1.23930	+	0.900404i	−0.997552	−	0.0699355i	$-0.977721\pi$
$233$	−18.9171	+	13.7441i	−1.23930	+	0.900404i	−0.241748	+	0.970339i	$0.577721\pi$
$234$		0			0
$235$	−0.0241719	+	0.0743935i	−0.00157680	+	0.00485289i
$236$	−25.9277	−	2.72511i	−1.68775	−	0.177389i
$237$		0			0
$238$	2.28716	−	2.05937i	0.148255	−	0.133489i
$239$	−19.5588	−	4.15734i	−1.26515	−	0.268916i	−0.473993	−	0.880528i	$-0.657188\pi$
$239$	−19.5588	−	4.15734i	−1.26515	−	0.268916i	−0.791158	+	0.611612i	$0.790521\pi$
$240$		0			0
$241$	2.01411	−	1.16285i	0.129740	−	0.0749057i	−0.433725	−	0.901045i	$-0.642801\pi$
$241$	2.01411	−	1.16285i	0.129740	−	0.0749057i	0.563466	+	0.826140i	$0.309468\pi$
$242$	25.7266	+	7.50707i	1.65377	+	0.482573i
$243$		0			0
$244$	22.5606	+	31.0520i	1.44430	+	1.98790i
$245$	−19.3640	−	17.4354i	−1.23712	−	1.11391i
$246$		0			0
$247$	3.69235	−	1.64394i	0.234938	−	0.104601i
$248$	−15.1385	+	6.74008i	−0.961293	+	0.427995i
$249$		0			0
$250$	−30.2919	−	27.2750i	−1.91583	−	1.72502i
$251$	1.88681	+	2.59698i	0.119095	+	0.163920i	0.864402	−	0.502801i	$-0.167697\pi$
$251$	1.88681	+	2.59698i	0.119095	+	0.163920i	−0.745307	+	0.666721i	$0.767697\pi$
$252$		0			0
$253$	−7.25758	+	14.7925i	−0.456280	+	0.929999i
$254$	−37.0184	+	21.3726i	−2.32274	+	1.34103i
$255$		0			0
$256$	30.7025	+	6.52603i	1.91891	+	0.407877i
$257$	13.4084	−	12.0730i	0.836393	−	0.753091i	−0.134930	−	0.990855i	$-0.543081\pi$
$257$	13.4084	−	12.0730i	0.836393	−	0.753091i	0.971323	+	0.237764i	$0.0764144\pi$
$258$		0			0
$259$	−2.62713	−	0.276123i	−0.163242	−	0.0171574i
$260$	4.37750	−	13.4726i	0.271481	−	0.835533i
$261$		0			0
$262$	−27.3756	+	19.8895i	−1.69127	+	1.22878i
$263$	−1.02983	−	1.78372i	−0.0635019	−	0.109989i	0.832527	−	0.553985i	$-0.186894\pi$
$263$	−1.02983	−	1.78372i	−0.0635019	−	0.109989i	−0.896028	+	0.443997i	$0.853560\pi$
$264$		0			0
$265$	−10.5242	+	18.2284i	−0.646496	+	1.11976i
$266$	−0.399221	−	3.79834i	−0.0244778	−	0.232891i
$267$		0			0
$268$	−17.1829	+	3.65235i	−1.04962	+	0.223103i
$269$	1.69280	−	2.32994i	0.103212	−	0.142059i	−0.754287	−	0.656545i	$-0.772017\pi$
$269$	1.69280	−	2.32994i	0.103212	−	0.142059i	0.857499	+	0.514486i	$0.172017\pi$
$270$		0			0
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	0.587692	−	0.809085i	$-0.300037\pi$
$271$	9.67272	+	3.14286i	0.587576	+	0.190915i	−0.000115761		1.00000i	$0.500037\pi$
$272$	−8.31518	+	9.23495i	−0.504182	+	0.559951i
$273$		0			0
$274$	−2.18952	−	1.26412i	−0.132274	−	0.0763683i
$275$	−24.5427	−	19.2672i	−1.47998	−	1.16186i
$276$		0			0
$277$	2.97354	−	6.67868i	0.178663	−	0.401283i	−0.801908	−	0.597447i	$-0.796182\pi$
$277$	2.97354	−	6.67868i	0.178663	−	0.401283i	0.980571	+	0.196164i	$0.0628485\pi$
$278$	−45.9594	+	14.9331i	−2.75646	+	0.895629i
$279$		0			0
$280$	−5.32621	−	3.86972i	−0.318302	−	0.231260i
$281$	−0.240983	+	2.29280i	−0.0143758	+	0.136777i	−0.999356	−	0.0358925i	$-0.988573\pi$
$281$	−0.240983	+	2.29280i	−0.0143758	+	0.136777i	0.984980	+	0.172670i	$0.0552393\pi$
$282$		0			0
$283$	−5.07987	+	23.8989i	−0.301967	+	1.42064i	0.521487	+	0.853259i	$0.325377\pi$
$283$	−5.07987	+	23.8989i	−0.301967	+	1.42064i	−0.823454	+	0.567383i	$0.807956\pi$
$284$	40.4194	−	4.24825i	2.39845	−	0.252087i
$285$		0			0
$286$	1.87102	−	7.43035i	0.110636	−	0.439366i
$287$			1.00006i			0.0590318i
$288$		0			0
$289$	−1.60777	−	4.94822i	−0.0945749	−	0.291072i
$290$	4.77487	+	22.4640i	0.280390	+	1.31913i
$291$		0			0
$292$	−7.03679	−	15.8049i	−0.411797	−	0.924911i
$293$	7.13388	+	7.92298i	0.416766	+	0.462865i	0.914572	−	0.404423i	$-0.132528\pi$
$293$	7.13388	+	7.92298i	0.416766	+	0.462865i	−0.497806	+	0.867288i	$0.665861\pi$
$294$		0			0
$295$	22.9700	+	10.2269i	1.33737	+	0.595434i
$296$	33.8709			1.96871
$297$		0			0
$298$	19.5782			1.13414
$299$	4.30369	+	1.91613i	0.248889	+	0.110812i
$300$		0			0
$301$	0.464511	+	0.515892i	0.0267740	+	0.0297355i
$302$	−9.98227	−	22.4206i	−0.574415	−	1.29016i
$303$		0			0
$304$	3.20623	+	15.0841i	0.183890	+	0.865135i
$305$	−11.4392	−	35.2063i	−0.655009	−	2.01591i
$306$		0			0
$307$			4.56848i			0.260737i	0.991466	+	0.130369i	$0.0416160\pi$
$307$			4.56848i			0.260737i	−0.991466	+	0.130369i	$0.958384\pi$
$308$	−4.06537	−	2.55353i	−0.231646	−	0.145501i
$309$		0			0
$310$	32.3175	−	3.39671i	1.83551	−	0.192920i
$311$	1.95067	−	9.17719i	0.110612	−	0.520391i	−0.887599	−	0.460616i	$-0.847628\pi$
$311$	1.95067	−	9.17719i	0.110612	−	0.520391i	0.998212	−	0.0597746i	$-0.0190382\pi$
$312$		0			0
$313$	0.524316	−	4.98853i	0.0296361	−	0.281968i	−0.969660	−	0.244457i	$-0.921390\pi$
$313$	0.524316	−	4.98853i	0.0296361	−	0.281968i	0.999296	−	0.0375113i	$-0.0119430\pi$
$314$	−31.8958	−	23.1736i	−1.79998	−	1.30776i
$315$		0			0
$316$	40.9379	−	13.3015i	2.30294	−	0.748269i
$317$	4.74914	−	10.6667i	0.266738	−	0.599104i	−0.729669	−	0.683801i	$-0.760326\pi$
$317$	4.74914	−	10.6667i	0.266738	−	0.599104i	0.996407	+	0.0846972i	$0.0269923\pi$
$318$		0			0
$319$	2.25183	+	7.92277i	0.126078	+	0.443590i
$320$	−28.7282	−	16.5862i	−1.60596	−	0.927199i
$321$		0			0
$322$	2.97871	−	3.30819i	0.165997	−	0.184358i
$323$	13.9232	+	4.52391i	0.774706	+	0.251717i
$324$		0			0
$325$	−5.24366	+	7.21728i	−0.290866	+	0.400343i
$326$	10.1897	−	2.16588i	0.564353	−	0.119957i
$327$		0			0
$328$	−1.34036	−	12.7527i	−0.0740089	−	0.704148i
$329$	0.00378967	−	0.00656390i	0.000208931	−	0.000361880i
$330$		0			0
$331$	14.5258	+	25.1595i	0.798411	+	1.38289i	0.920650	+	0.390388i	$0.127659\pi$
$331$	14.5258	+	25.1595i	0.798411	+	1.38289i	−0.122239	+	0.992501i	$0.539007\pi$
$332$	29.2395	−	21.2438i	1.60473	−	1.16590i
$333$		0			0
$334$	13.8172	−	42.5250i	0.756044	−	2.32686i
$335$	16.8496	+	1.77096i	0.920592	+	0.0967582i
$336$		0			0
$337$	−21.4623	+	19.3247i	−1.16912	+	1.05268i	−0.171403	+	0.985201i	$0.554830\pi$
$337$	−21.4623	+	19.3247i	−1.16912	+	1.05268i	−0.997720	+	0.0674824i	$0.978503\pi$
$338$	28.8372	+	6.12953i	1.56853	+	0.333402i
$339$		0			0
$340$	44.4359	−	25.6551i	2.40987	−	1.39134i
$341$	11.4820	−	1.99697i	0.621783	−	0.108142i
$342$		0			0
$343$	2.99731	+	4.12544i	0.161840	+	0.222753i
$344$	−6.61482	−	5.95601i	−0.356647	−	0.321126i
$345$		0			0
$346$	−13.7601	+	6.12638i	−0.739746	+	0.329356i
$347$	−20.2286	+	9.00637i	−1.08593	+	0.483488i	−0.870066	−	0.492936i	$-0.835924\pi$
$347$	−20.2286	+	9.00637i	−1.08593	+	0.483488i	−0.215865	+	0.976423i	$0.569257\pi$
$348$		0			0
$349$	11.6395	+	10.4802i	0.623048	+	0.560995i	0.919024	−	0.394201i	$-0.128978\pi$
$349$	11.6395	+	10.4802i	0.623048	+	0.560995i	−0.295977	+	0.955195i	$0.595645\pi$
$350$	4.95498	+	6.81994i	0.264855	+	0.364541i
$351$		0			0
$352$	−1.83725	−	0.901398i	−0.0979257	−	0.0480447i
$353$	9.66798	−	5.58181i	0.514575	−	0.297090i	−0.220137	−	0.975469i	$-0.570651\pi$
$353$	9.66798	−	5.58181i	0.514575	−	0.297090i	0.734712	+	0.678379i	$0.237317\pi$
$354$		0			0
$355$	−38.3409	−	8.14961i	−2.03492	−	0.432536i
$356$	−8.91574	+	8.02777i	−0.472533	+	0.425471i
$357$		0			0
$358$	−22.3536	−	2.34945i	−1.18142	−	0.124172i
$359$	5.11867	−	15.7536i	0.270153	−	0.831445i	−0.720308	−	0.693654i	$-0.756000\pi$
$359$	5.11867	−	15.7536i	0.270153	−	0.831445i	0.990461	−	0.137791i	$-0.0440002\pi$
$360$		0			0
$361$	−0.673787	+	0.489535i	−0.0354625	+	0.0257650i
$362$	−5.10125	−	8.83563i	−0.268116	−	0.464390i
$363$		0			0
$364$	−0.686304	+	1.18871i	−0.0359721	+	0.0623055i
$365$	1.74413	+	16.5943i	0.0912918	+	0.868583i
$366$		0			0
$367$	−9.59589	+	2.03967i	−0.500902	+	0.106470i	−0.451432	−	0.892306i	$-0.649087\pi$
$367$	−9.59589	+	2.03967i	−0.500902	+	0.106470i	−0.0494699	+	0.998776i	$0.515753\pi$
$368$	−10.5651	+	14.5416i	−0.550743	+	0.758033i
$369$		0			0
$370$	−63.1692	−	20.5249i	−3.28401	−	1.06704i
$371$	1.36469	−	1.51564i	0.0708510	−	0.0786880i
$372$		0			0
$373$	10.9422	+	6.31750i	0.566567	+	0.327108i	0.755777	−	0.654829i	$-0.227259\pi$
$373$	10.9422	+	6.31750i	0.566567	+	0.327108i	−0.189210	+	0.981937i	$0.560593\pi$
$374$	23.0449	−	15.4659i	1.19162	−	0.799721i
$375$		0			0
$376$	−0.0395279	+	0.0887811i	−0.00203850	+	0.00457854i
$377$	2.23967	−	0.727714i	0.115349	−	0.0374792i
$378$		0			0
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.983695	−	0.179843i	$-0.942441\pi$
$379$	−28.3981	−	20.6325i	−1.45871	−	1.05982i	−0.475019	−	0.879975i	$-0.657559\pi$
$380$	6.65569	−	63.3246i	0.341430	−	3.24849i
$381$		0			0
$382$	10.2235	−	48.0976i	0.523078	−	2.46089i
$383$	−22.4628	+	2.36094i	−1.14780	+	0.120638i	−0.659267	−	0.751909i	$-0.729133\pi$
$383$	−22.4628	+	2.36094i	−1.14780	+	0.120638i	−0.488529	+	0.872548i	$0.662466\pi$
$384$		0			0
$385$	2.96793	+	3.55385i	0.151260	+	0.181121i
$386$		−	19.5246i		−	0.993774i
$387$		0			0
$388$	−18.3484	−	56.4704i	−0.931497	−	2.86685i
$389$	−1.52999	−	7.19803i	−0.0775735	−	0.364955i	0.922189	−	0.386739i	$-0.126399\pi$
$389$	−1.52999	−	7.19803i	−0.0775735	−	0.364955i	−0.999763	+	0.0217844i	$0.993065\pi$
$390$		0			0
$391$	6.94038	+	15.5884i	0.350990	+	0.788337i
$392$	−21.6618	−	24.0579i	−1.09409	−	1.21511i
$393$		0			0
$394$	−47.1201	−	20.9792i	−2.37388	−	1.05692i
$395$	−41.5146			−2.08883
$396$		0			0
$397$	16.7327			0.839790			0.419895	−	0.907573i	$-0.362067\pi$
$397$	16.7327			0.839790			0.419895	+	0.907573i	$0.362067\pi$
$398$	23.4053	+	10.4207i	1.17320	+	0.522342i
$399$		0			0
$400$	−22.7757	−	25.2949i	−1.13878	−	1.26475i
$401$	−2.06355	−	4.63481i	−0.103049	−	0.231451i	0.854662	−	0.519186i	$-0.173765\pi$
$401$	−2.06355	−	4.63481i	−0.103049	−	0.231451i	−0.957710	+	0.287734i	$0.907098\pi$
$402$		0			0
$403$	−0.692785	−	3.25930i	−0.0345101	−	0.162357i
$404$	21.2343	+	65.3525i	1.05645	+	3.25141i
$405$		0			0
$406$		−	2.22528i		−	0.110439i
$407$	−23.1000	−	5.81676i	−1.14503	−	0.288326i
$408$		0			0
$409$	−32.1705	+	3.38125i	−1.59073	+	0.167192i	−0.858116	−	0.513455i	$-0.828365\pi$
$409$	−32.1705	+	3.38125i	−1.59073	+	0.167192i	−0.732611	+	0.680647i	$0.761699\pi$
$410$	−5.22802	+	24.5959i	−0.258194	+	1.21471i
$411$		0			0
$412$	3.83232	−	36.4621i	0.188805	−	1.79636i
$413$	−1.97102	−	1.43203i	−0.0969877	−	0.0704657i
$414$		0			0
$415$	−33.1513	+	10.7715i	−1.62734	+	0.528753i
$416$	−0.237985	+	0.534522i	−0.0116682	+	0.0262071i
$417$		0			0
$418$	1.28227	−	34.4170i	0.0627178	−	1.68339i
$419$	24.1686	+	13.9538i	1.18071	+	0.681686i	0.956180	−	0.292781i	$-0.0945806\pi$
$419$	24.1686	+	13.9538i	1.18071	+	0.681686i	0.224534	+	0.974466i	$0.427914\pi$
$420$		0			0
$421$	17.8850	−	19.8633i	0.871659	−	0.968076i	−0.128060	−	0.991766i	$-0.540875\pi$
$421$	17.8850	−	19.8633i	0.871659	−	0.968076i	0.999719	+	0.0236907i	$0.00754169\pi$
$422$	−8.56907	−	2.78426i	−0.417136	−	0.135536i
$423$		0			0
$424$	−15.3709	+	21.1562i	−0.746478	+	1.02744i
$425$	−31.6068	+	6.71823i	−1.53315	+	0.325882i
$426$		0			0
$427$	0.374932	+	3.56724i	0.0181442	+	0.172631i
$428$	30.3547	−	52.5759i	1.46725	−	2.54135i
$429$		0			0
$430$	8.72743	+	15.1164i	0.420874	+	0.728975i
$431$	−0.579760	+	0.421220i	−0.0279260	+	0.0202895i	−0.601661	−	0.798752i	$-0.705494\pi$
$431$	−0.579760	+	0.421220i	−0.0279260	+	0.0202895i	0.573735	+	0.819041i	$0.305494\pi$
$432$		0			0
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	−0.829580	−	0.558387i	$-0.811420\pi$
$433$	3.53281	−	10.8729i	0.169776	−	0.522517i	0.999356	+	0.0358703i	$0.0114203\pi$
$434$	−3.13142	−	0.329125i	−0.150313	−	0.0157985i
$435$		0			0
$436$	−31.0860	+	27.9899i	−1.48875	+	1.34047i
$437$	20.7124	+	4.40255i	0.990807	+	0.210603i
$438$		0			0
$439$	7.42639	−	4.28763i	0.354442	−	0.204637i	−0.312198	−	0.950017i	$-0.601065\pi$
$439$	7.42639	−	4.28763i	0.354442	−	0.204637i	0.666640	+	0.745380i	$0.267732\pi$
$440$	−42.6097	−	41.3403i	−2.03134	−	1.97082i
$441$		0			0
$442$	−4.66412	−	6.41961i	−0.221850	−	0.305350i
$443$	−10.3869	−	9.35237i	−0.493495	−	0.444345i	0.384422	−	0.923157i	$-0.374401\pi$
$443$	−10.3869	−	9.35237i	−0.493495	−	0.444345i	−0.877917	+	0.478813i	$0.841067\pi$
$444$		0			0
$445$	10.5705	−	4.70630i	0.501091	−	0.223100i
$446$	39.8334	−	17.7350i	1.88617	−	0.839775i
$447$		0			0
$448$	2.38866	+	2.15076i	0.112854	+	0.101614i
$449$	12.7008	+	17.4811i	0.599388	+	0.824986i	0.995652	−	0.0931501i	$-0.0296936\pi$
$449$	12.7008	+	17.4811i	0.599388	+	0.824986i	−0.396264	+	0.918136i	$0.629694\pi$
$450$		0			0
$451$	−1.27593	+	8.92753i	−0.0600811	+	0.420381i
$452$	3.56863	−	2.06035i	0.167854	−	0.0969107i
$453$		0			0
$454$	−41.4141	−	8.80283i	−1.94366	−	0.413137i
$455$	0.983790	−	0.885809i	0.0461208	−	0.0415273i
$456$		0			0
$457$	−9.75135	−	1.02491i	−0.456149	−	0.0479432i	−0.126332	−	0.991988i	$-0.540320\pi$
$457$	−9.75135	−	1.02491i	−0.456149	−	0.0479432i	−0.329817	+	0.944045i	$0.606987\pi$
$458$	−3.21974	+	9.90934i	−0.150449	+	0.463033i
$459$		0			0
$460$	60.0419	−	43.6230i	2.79947	−	2.03393i
$461$	6.17927	+	10.7028i	0.287797	+	0.498479i	0.973284	−	0.229606i	$-0.0737437\pi$
$461$	6.17927	+	10.7028i	0.287797	+	0.498479i	−0.685486	+	0.728085i	$0.740410\pi$
$462$		0			0
$463$	16.9359	−	29.3338i	0.787076	−	1.36326i	−0.140675	−	0.990056i	$-0.544927\pi$
$463$	16.9359	−	29.3338i	0.787076	−	1.36326i	0.927751	−	0.373200i	$-0.121739\pi$
$464$	0.939198	+	8.93587i	0.0436012	+	0.414837i
$465$		0			0
$466$	55.7231	−	11.8443i	2.58132	−	0.548677i
$467$	9.24994	−	12.7315i	0.428036	−	0.589142i	−0.539465	−	0.842008i	$-0.681373\pi$
$467$	9.24994	−	12.7315i	0.428036	−	0.589142i	0.967501	+	0.252867i	$0.0813734\pi$
$468$		0			0
$469$	−1.56129	−	0.507295i	−0.0720939	−	0.0234247i
$470$	0.127519	−	0.141624i	0.00588199	−	0.00653261i
$471$		0			0
$472$	27.0535	+	15.6194i	1.24524	+	0.718939i
$473$	3.48848	+	5.19800i	0.160400	+	0.239004i
$474$		0			0
$475$	−16.3096	+	36.6320i	−0.748337	+	1.68079i
$476$	−4.72838	+	1.53634i	−0.216725	+	0.0704182i
$477$		0			0
$478$	39.4120	+	28.6345i	1.80266	+	1.30971i
$479$	1.30337	−	12.4008i	0.0595526	−	0.566605i	−0.923541	−	0.383500i	$-0.874719\pi$
$479$	1.30337	−	12.4008i	0.0595526	−	0.566605i	0.983093	−	0.183105i	$-0.0586148\pi$
$480$		0			0
$481$	−1.41603	+	6.66192i	−0.0645656	+	0.303757i
$482$	−5.63510	+	0.592273i	−0.256672	+	0.0269773i
$483$		0			0
$484$	−33.0335	−	27.9821i	−1.50152	−	1.27191i
$485$			57.2660i			2.60032i
$486$		0			0
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	0.890468	−	0.455046i	$-0.150377\pi$
$487$	−2.14955	−	6.61563i	−0.0974054	−	0.299783i	−0.987873	+	0.155263i	$0.950377\pi$
$488$	−9.56215	−	44.9864i	−0.432858	−	2.03644i
$489$		0			0
$490$	25.8208	+	57.9944i	1.16646	+	2.61992i
$491$	0.202024	+	0.224370i	0.00911721	+	0.0101257i	0.747686	−	0.664052i	$-0.231165\pi$
$491$	0.202024	+	0.224370i	0.00911721	+	0.0101257i	−0.738569	+	0.674178i	$0.764498\pi$
$492$		0			0
$493$	7.79235	+	3.46938i	0.350950	+	0.156253i
$494$	−9.84705			−0.443040
$495$		0			0
$496$	12.7135			0.570851
$497$	3.46969	+	1.54481i	0.155637	+	0.0692940i
$498$		0			0
$499$	4.42745	+	4.91718i	0.198200	+	0.220123i	0.834049	−	0.551690i	$-0.186017\pi$
$499$	4.42745	+	4.91718i	0.198200	+	0.220123i	−0.635850	+	0.771813i	$0.719350\pi$
$500$	26.7823	+	60.1541i	1.19774	+	2.69017i
$501$		0			0
$502$	−1.62601	−	7.64978i	−0.0725724	−	0.341426i
$503$	−3.19188	−	9.82361i	−0.142319	−	0.438013i	0.854337	−	0.519719i	$-0.173963\pi$
$503$	−3.19188	−	9.82361i	−0.142319	−	0.438013i	−0.996657	+	0.0817056i	$0.973963\pi$
$504$		0			0
$505$		−	66.2732i		−	2.94912i
$506$	30.8116	−	25.7318i	1.36974	−	1.14392i
$507$		0			0
$508$	68.6725	−	7.21777i	3.04685	−	0.320237i
$509$	−4.22581	+	19.8809i	−0.187306	+	0.881204i	0.779641	+	0.626226i	$0.215401\pi$
$509$	−4.22581	+	19.8809i	−0.187306	+	0.881204i	−0.966947	+	0.254978i	$0.917932\pi$
$510$		0			0
$511$	0.168998	−	1.60791i	0.00747602	−	0.0711296i
$512$	−29.4132	−	21.3699i	−1.29989	−	0.944427i
$513$		0			0
$514$	−41.8065	+	13.5838i	−1.84401	+	0.599154i
$515$	−14.3821	+	32.3028i	−0.633752	+	1.42343i
$516$		0			0
$517$	0.0422048	−	0.0537607i	0.00185617	−	0.00236439i
$518$	5.57356	+	3.21790i	0.244888	+	0.141386i
$519$		0			0
$520$	−11.3579	+	12.6143i	−0.498078	+	0.553172i
$521$	11.4110	+	3.70764i	0.499923	+	0.162435i	0.548115	−	0.836403i	$-0.315346\pi$
$521$	11.4110	+	3.70764i	0.499923	+	0.162435i	−0.0481915	+	0.998838i	$0.515346\pi$
$522$		0			0
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.0316743	+	0.999498i	$0.510084\pi$
$523$	−22.2395	+	30.6101i	−0.972466	+	1.33848i	−0.940791	+	0.338986i	$0.889916\pi$
$524$	53.4678	−	11.3649i	2.33575	−	0.496479i
$525$		0			0
$526$	0.524522	+	4.99049i	0.0228702	+	0.217596i
$527$	6.03461	−	10.4522i	0.262872	−	0.455307i
$528$		0			0
$529$	0.840532	+	1.45584i	0.0365449	+	0.0632976i
$530$	41.4869	−	30.1420i	1.80207	−	1.30928i
$531$		0			0
$532$	−1.90653	+	5.86770i	−0.0826586	+	0.254397i
$533$	2.56430	+	0.269519i	0.111072	+	0.0116742i
$534$		0			0
$535$	−43.5123	+	39.1786i	−1.88120	+	1.69384i
$536$	20.5893	+	4.37639i	0.889323	+	0.189031i
$537$		0			0
$538$	−6.07649	+	3.50826i	−0.261976	+	0.151252i
$539$	10.6419	+	20.1276i	0.458378	+	0.866957i
$540$		0			0
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	0.959559	+	0.281508i	$0.0908345\pi$
$541$	21.6491	+	29.7975i	0.930769	+	1.28109i	−0.0287904	+	0.999585i	$0.509166\pi$
$542$	−18.4141	−	16.5801i	−0.790952	−	0.712176i
$543$		0			0
$544$	−1.93609	+	0.862003i	−0.0830091	+	0.0369581i
$545$	36.8556	−	16.4092i	1.57872	−	0.702892i
$546$		0			0
$547$	−27.2544	−	24.5400i	−1.16532	−	1.04925i	−0.997991	−	0.0633524i	$-0.979821\pi$
$547$	−27.2544	−	24.5400i	−1.16532	−	1.04925i	−0.167324	−	0.985902i	$-0.553513\pi$
$548$	2.40060	+	3.30414i	0.102548	+	0.141146i
$549$		0			0
$550$	35.5317	+	67.2032i	1.51508	+	2.86555i
$551$	9.16693	−	5.29253i	0.390524	−	0.225469i
$552$		0			0
$553$	3.93467	+	0.836340i	0.167319	+	0.0355648i
$554$	−13.2363	+	11.9181i	−0.562358	+	0.506350i
$555$		0			0
$556$	77.6363	+	8.15990i	3.29251	+	0.346057i
$557$	−2.30765	+	7.10223i	−0.0977784	+	0.300931i	−0.987968	−	0.154660i	$-0.950572\pi$
$557$	−2.30765	+	7.10223i	−0.0977784	+	0.300931i	0.890189	+	0.455591i	$0.150572\pi$
$558$		0			0
$559$	1.44800	−	1.05204i	0.0612441	−	0.0444964i
$560$	2.52547	+	4.37425i	0.106721	+	0.184846i
$561$		0			0
$562$	2.80838	−	4.86426i	0.118464	−	0.205186i
$563$	0.409209	+	3.89336i	0.0172461	+	0.164086i	0.999755	−	0.0221293i	$-0.00704455\pi$
$563$	0.409209	+	3.89336i	0.0172461	+	0.164086i	−0.982509	+	0.186215i	$0.940378\pi$
$564$		0			0
$565$	−3.88739	+	0.826289i	−0.163544	+	0.0347622i
$566$	34.9886	−	48.1576i	1.47068	−	2.02422i
$567$		0			0
$568$	−46.3155	−	15.0488i	−1.94335	−	0.631434i
$569$	25.2069	−	27.9951i	1.05673	−	1.17362i	0.0723817	−	0.997377i	$-0.476940\pi$
$569$	25.2069	−	27.9951i	1.05673	−	1.17362i	0.984347	−	0.176240i	$-0.0563933\pi$
$570$		0			0
$571$	26.2762	+	15.1706i	1.09962	+	0.634868i	0.936122	−	0.351675i	$-0.114388\pi$
$571$	26.2762	+	15.1706i	1.09962	+	0.634868i	0.163502	+	0.986543i	$0.447721\pi$
$572$	−7.64323	+	9.73599i	−0.319580	+	0.407082i
$573$		0			0
$574$	0.991002	−	2.22583i	0.0413636	−	0.0929043i
$575$	−44.4504	+	14.4428i	−1.85371	+	0.602307i
$576$		0			0
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	0.642282	−	0.766468i	$-0.277988\pi$
$577$	2.68563	+	1.95122i	0.111804	+	0.0812305i	−0.530478	+	0.847699i	$0.677988\pi$
$578$	−1.32499	+	12.6064i	−0.0551121	+	0.524357i
$579$		0			0
$580$	7.71336	−	36.2885i	0.320280	−	1.50680i
$581$	3.35902	−	0.353047i	0.139355	−	0.0146469i
$582$		0			0
$583$	14.1162	−	11.7889i	0.584635	−	0.488247i
$584$			20.7303i			0.857826i
$585$		0			0
$586$	−8.02659	−	24.7033i	−0.331576	−	1.02048i
$587$	8.50514	+	40.0135i	0.351045	+	1.65154i	0.699813	+	0.714326i	$0.253267\pi$
$587$	8.50514	+	40.0135i	0.351045	+	1.65154i	−0.348768	+	0.937209i	$0.613400\pi$
$588$		0			0
$589$	−6.09183	−	13.6825i	−0.251009	−	0.563776i
$590$	−40.9898	−	45.5238i	−1.68752	−	1.87419i
$591$		0			0
$592$	−23.7394	−	10.5694i	−0.975682	−	0.434401i
$593$	4.62924			0.190100			0.0950500	−	0.995472i	$-0.469699\pi$
$593$	4.62924			0.190100			0.0950500	+	0.995472i	$0.469699\pi$
$594$		0			0
$595$	4.79500			0.196576
$596$	−28.8925	−	12.8638i	−1.18348	−	0.526921i
$597$		0			0
$598$	−7.67990	−	8.52940i	−0.314055	−	0.348793i
$599$	−12.4375	−	27.9352i	−0.508184	−	1.14140i	−0.967441	−	0.253097i	$-0.918551\pi$
$599$	−12.4375	−	27.9352i	−0.508184	−	1.14140i	0.459257	−	0.888304i	$-0.348116\pi$
$600$		0			0
$601$	6.49309	+	30.5476i	0.264859	+	1.24606i	0.886488	+	0.462751i	$0.153138\pi$
$601$	6.49309	+	30.5476i	0.264859	+	1.24606i	−0.621630	+	0.783311i	$0.713529\pi$
$602$	−0.522639	−	1.60852i	−0.0213012	−	0.0655583i
$603$		0			0
$604$			39.6459i			1.61317i
$605$	21.9604	+	35.5117i	0.892819	+	1.44376i
$606$		0			0
$607$	30.5982	−	3.21600i	1.24194	−	0.130533i	0.539322	−	0.842100i	$-0.318681\pi$
$607$	30.5982	−	3.21600i	1.24194	−	0.130533i	0.702619	+	0.711566i	$0.252014\pi$
$608$	−0.546801	+	2.57250i	−0.0221757	+	0.104329i
$609$		0			0
$610$	−9.42721	+	89.6939i	−0.381697	+	3.63160i
$611$	−0.0158094	−	0.0114862i	−0.000639581	−	0.000464683i
$612$		0			0
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.224205	−	0.974542i	$-0.428021\pi$
$613$	24.2244	−	7.87097i	0.978413	−	0.317906i	0.754207	+	0.656636i	$0.228021\pi$
$614$	4.52709	−	10.1680i	0.182699	−	0.410348i
$615$		0			0
$616$	3.20564	+	4.77655i	0.129159	+	0.192453i
$617$	3.64536	+	2.10465i	0.146757	+	0.0847300i	0.571580	−	0.820546i	$-0.306331\pi$
$617$	3.64536	+	2.10465i	0.146757	+	0.0847300i	−0.424824	+	0.905276i	$0.639664\pi$
$618$		0			0
$619$	25.7637	−	28.6135i	1.03553	−	1.15007i	0.0470228	−	0.998894i	$-0.485027\pi$
$619$	25.7637	−	28.6135i	1.03553	−	1.15007i	0.988507	−	0.151178i	$-0.0483067\pi$
$620$	−49.9243	−	16.2214i	−2.00501	−	0.651467i
$621$		0			0
$622$	−13.4356	+	18.4926i	−0.538720	+	0.741484i
$623$	−1.09666	+	0.233103i	−0.0439369	+	0.00933908i
$624$		0			0
$625$	−1.72132	−	16.3773i	−0.0688529	−	0.655091i
$626$	−6.11030	+	10.5833i	−0.244217	+	0.422995i
$627$		0			0
$628$	31.8440	+	55.1554i	1.27071	+	2.20094i
$629$	−19.9578	+	14.5002i	−0.795769	+	0.578160i
$630$		0			0
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	−0.997083	−	0.0763220i	$-0.975682\pi$
$631$	−3.65655	+	11.2537i	−0.145565	+	0.448003i	0.851518	+	0.524325i	$0.175682\pi$
$632$	−51.2953	−	5.39135i	−2.04042	−	0.214457i
$633$		0			0
$634$	−21.1402	+	19.0347i	−0.839585	+	0.755965i
$635$	−65.1411	−	13.8462i	−2.58505	−	0.549469i
$636$		0			0
$637$	5.63745	−	3.25478i	0.223364	−	0.128959i
$638$	2.83913	−	19.8650i	0.112402	−	0.786465i
$639$		0			0
$640$	44.7507	+	61.5941i	1.76893	+	2.43472i
$641$	−26.7087	−	24.0486i	−1.05493	−	0.949863i	−0.0561091	−	0.998425i	$-0.517869\pi$
$641$	−26.7087	−	24.0486i	−1.05493	−	0.949863i	−0.998820	+	0.0485621i	$0.984536\pi$
$642$		0			0
$643$	2.97384	−	1.32404i	0.117277	−	0.0522149i	−0.347260	−	0.937769i	$-0.612888\pi$
$643$	2.97384	−	1.32404i	0.117277	−	0.0522149i	0.464536	+	0.885554i	$0.346221\pi$
$644$	−6.56947	+	2.92491i	−0.258873	+	0.115258i
$645$		0			0
$646$	−26.5057	−	23.8658i	−1.04285	−	0.938989i
$647$	7.14454	+	9.83361i	0.280881	+	0.386599i	0.926025	−	0.377461i	$-0.123203\pi$
$647$	7.14454	+	9.83361i	0.280881	+	0.386599i	−0.645145	+	0.764060i	$0.723203\pi$
$648$		0			0
$649$	−15.7682	−	15.2984i	−0.618956	−	0.600516i
$650$	18.8227	−	10.8673i	0.738285	−	0.426249i
$651$		0			0
$652$	−16.4605	−	3.49878i	−0.644642	−	0.137023i
$653$	18.9653	−	17.0765i	0.742171	−	0.668254i	−0.208651	−	0.977990i	$-0.566907\pi$
$653$	18.9653	−	17.0765i	0.742171	−	0.668254i	0.950823	+	0.309736i	$0.100241\pi$
$654$		0			0
$655$	−52.4305	−	5.51067i	−2.04863	−	0.215320i
$656$	−3.04005	+	9.35631i	−0.118694	+	0.365303i
$657$		0			0
$658$	−0.0149391	+	0.0108539i	−0.000582385	+	0.000423127i
$659$	−13.9720	−	24.2003i	−0.544273	−	0.942708i	−0.998652	−	0.0519000i	$-0.983472\pi$
$659$	−13.9720	−	24.2003i	−0.544273	−	0.942708i	0.454379	−	0.890808i	$-0.349861\pi$
$660$		0			0
$661$	13.6899	−	23.7116i	0.532475	−	0.922274i	−0.466806	−	0.884360i	$-0.654595\pi$
$661$	13.6899	−	23.7116i	0.532475	−	0.922274i	0.999281	−	0.0379144i	$-0.0120714\pi$
$662$	−7.39843	−	70.3913i	−0.287548	−	2.73584i
$663$		0			0
$664$	−42.3605	+	9.00401i	−1.64391	+	0.349423i
$665$	3.49754	−	4.81395i	0.135629	−	0.186677i
$666$		0			0
$667$	11.7338	+	3.81254i	0.454334	+	0.147622i
$668$	−48.3316	+	53.6777i	−1.87001	+	2.07685i
$669$		0			0
$670$	−35.7470	−	20.6386i	−1.38103	−	0.797337i
$671$	−1.20425	+	32.3230i	−0.0464896	+	1.24781i
$672$		0			0
$673$	−5.51079	+	12.3774i	−0.212425	+	0.477115i	−0.988060	−	0.154067i	$-0.950763\pi$
$673$	−5.51079	+	12.3774i	−0.212425	+	0.477115i	0.775635	+	0.631181i	$0.217430\pi$
$674$	66.9179	−	21.7429i	2.57758	−	0.837507i
$675$		0			0
$676$	−38.5290	−	27.9930i	−1.48189	−	1.07665i
$677$	−3.83588	+	36.4960i	−0.147425	+	1.40265i	0.631422	+	0.775440i	$0.282472\pi$
$677$	−3.83588	+	36.4960i	−0.147425	+	1.40265i	−0.778847	+	0.627214i	$0.784195\pi$
$678$		0			0
$679$	1.15366	−	5.42756i	0.0442735	−	0.208291i
$680$	−61.1451	+	6.42661i	−2.34481	+	0.246449i
$681$		0			0
$682$	−27.5341	−	6.93330i	−1.05434	−	0.265490i
$683$		−	30.8347i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$683$		−	30.8347i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$684$		0			0
$685$	−1.21721	−	3.74619i	−0.0465072	−	0.143134i
$686$	−2.58301	−	12.1521i	−0.0986198	−	0.463969i
$687$		0			0
$688$	2.77760	+	6.23859i	0.105895	+	0.237844i
$689$	−3.51852	−	3.90771i	−0.134045	−	0.148872i
$690$		0			0
$691$	−43.5943	−	19.4094i	−1.65841	−	0.738370i	−0.658507	−	0.752574i	$-0.728812\pi$
$691$	−43.5943	−	19.4094i	−1.65841	−	0.738370i	−0.999899	+	0.0142040i	$0.995479\pi$
$692$	24.3317			0.924953
$693$		0			0
$694$	53.9474			2.04782
$695$	−68.7801	−	30.6229i	−2.60898	−	1.16159i
$696$		0			0
$697$	6.24921	+	6.94045i	0.236706	+	0.262888i
$698$	−15.5206	−	34.8598i	−0.587463	−	1.31946i
$699$		0			0
$700$	−2.83129	−	13.3202i	−0.107013	−	0.503455i
$701$	−4.34678	−	13.3780i	−0.164176	−	0.505281i	0.834799	−	0.550555i	$-0.185584\pi$
$701$	−4.34678	−	13.3780i	−0.164176	−	0.505281i	−0.998975	+	0.0452742i	$0.985584\pi$
$702$		0			0
$703$			30.6133i			1.15460i
$704$	18.5794	+	22.2473i	0.700239	+	0.838477i
$705$		0			0
$706$	−27.0491	+	2.84298i	−1.01801	+	0.106997i
$707$	−1.33512	+	6.28124i	−0.0502123	+	0.236230i
$708$		0			0
$709$	0.948508	−	9.02445i	0.0356220	−	0.338920i	−0.962167	−	0.272460i	$-0.912163\pi$
$709$	0.948508	−	9.02445i	0.0356220	−	0.338920i	0.997789	−	0.0664604i	$-0.0211706\pi$
$710$	77.2591	+	56.1320i	2.89948	+	2.10660i
$711$		0			0
$712$	13.6721	−	4.44233i	0.512383	−	0.166483i
$713$	7.10045	−	15.9479i	0.265914	−	0.597253i
$714$		0			0
$715$	9.91242	−	6.65242i	0.370703	−	0.248786i
$716$	31.4445	+	18.1545i	1.17514	+	0.678466i
$717$		0			0
$718$	−27.0035	+	29.9904i	−1.00776	+	1.11923i
$719$	−32.2802	−	10.4885i	−1.20385	−	0.391155i	−0.362674	−	0.931916i	$-0.618136\pi$
$719$	−32.2802	−	10.4885i	−1.20385	−	0.391155i	−0.841176	+	0.540761i	$0.818136\pi$
$720$		0			0
$721$	2.01387	−	2.77186i	0.0750005	−	0.103229i
$722$	1.98474	−	0.421870i	0.0738644	−	0.0157004i
$723$		0			0
$724$	1.72276	+	16.3909i	0.0640257	+	0.609164i
$725$	−11.6817	+	20.2334i	−0.433849	+	0.751448i
$726$		0			0
$727$	−15.4496	−	26.7595i	−0.572993	−	0.992454i	−0.996256	−	0.0864469i	$-0.972449\pi$
$727$	−15.4496	−	26.7595i	−0.572993	−	0.992454i	0.423263	−	0.906007i	$-0.360885\pi$
$728$	1.33060	−	0.966740i	0.0493154	−	0.0358298i
$729$		0			0
$730$	12.5620	−	38.6620i	0.464942	−	1.43094i
$731$	6.44742	+	0.677652i	0.238467	+	0.0250638i
$732$		0			0
$733$	30.9155	−	27.8365i	1.14189	−	1.02816i	0.142628	−	0.989776i	$-0.454445\pi$
$733$	30.9155	−	27.8365i	1.14189	−	1.02816i	0.999263	−	0.0383869i	$-0.0122219\pi$
$734$	23.3787	+	4.96929i	0.862922	+	0.183420i
$735$		0			0
$736$	−2.65472	+	1.53271i	−0.0978545	+	0.0564963i
$737$	−13.2904	−	6.52058i	−0.489558	−	0.240189i
$738$		0			0
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	0.624883	−	0.780718i	$-0.285146\pi$
$739$	−8.44687	−	11.6261i	−0.310723	−	0.427674i	−0.935607	+	0.353044i	$0.885146\pi$
$740$	79.7360	+	71.7946i	2.93115	+	2.63922i
$741$		0			0
$742$	−4.53927	+	2.02101i	−0.166642	+	0.0741938i
$743$	−12.2687	+	5.46239i	−0.450096	+	0.200396i	−0.619250	−	0.785194i	$-0.712563\pi$
$743$	−12.2687	+	5.46239i	−0.450096	+	0.200396i	0.169154	+	0.985590i	$0.445897\pi$
$744$		0			0
$745$	22.6679	+	20.4103i	0.830488	+	0.747775i
$746$	−18.0937	−	24.9039i	−0.662459	−	0.911796i
$747$		0			0
$748$	−44.1703	+	7.68220i	−1.61502	+	0.280889i
$749$	4.91328	−	2.83669i	0.179528	−	0.103650i
$750$		0			0
$751$	35.5699	+	7.56062i	1.29796	+	0.275891i	0.804540	−	0.593898i	$-0.202412\pi$
$751$	35.5699	+	7.56062i	1.29796	+	0.275891i	0.493424	+	0.869789i	$0.335745\pi$
$752$	0.0554084	−	0.0498900i	0.00202054	−	0.00181930i
$753$		0			0
$754$	−5.70594	−	0.599718i	−0.207798	−	0.0218405i
$755$	11.8158	−	36.3653i	0.430021	−	1.32347i
$756$		0			0
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.991397	−	0.130887i	$-0.958218\pi$
$757$	−32.2811	+	23.4536i	−1.17328	+	0.852435i	−0.181878	+	0.983321i	$0.558218\pi$
$758$	42.7599	+	74.0623i	1.55311	+	2.69006i
$759$		0			0
$760$	−38.1481	+	66.0744i	−1.38378	+	2.39677i
$761$	0.356458	+	3.39147i	0.0129216	+	0.122941i	0.999081	−	0.0428583i	$-0.0136464\pi$
$761$	0.356458	+	3.39147i	0.0129216	+	0.122941i	−0.986160	+	0.165799i	$0.946980\pi$
$762$		0			0
$763$	−3.82367	+	0.812747i	−0.138426	+	0.0294234i
$764$	−46.6896	+	64.2627i	−1.68917	+	2.32494i
$765$		0			0
$766$	52.3347	+	17.0046i	1.89093	+	0.614401i
$767$	−4.20312	+	4.66804i	−0.151766	+	0.168553i
$768$		0			0
$769$	−18.5463	−	10.7077i	−0.668796	−	0.386130i	0.126824	−	0.991925i	$-0.459522\pi$
$769$	−18.5463	−	10.7077i	−0.668796	−	0.386130i	−0.795620	+	0.605795i	$0.792855\pi$
$770$	−3.08404	−	10.8508i	−0.111141	−	0.391035i
$771$		0			0
$772$	−12.8285	+	28.8133i	−0.461709	+	1.03701i
$773$	−34.1302	+	11.0896i	−1.22758	+	0.398864i	−0.849836	−	0.527048i	$-0.823299\pi$
$773$	−34.1302	+	11.0896i	−1.22758	+	0.398864i	−0.377741	+	0.925911i	$0.623299\pi$
$774$		0			0
$775$	26.7446	+	19.4311i	0.960694	+	0.697985i
$776$	−7.43693	+	70.7577i	−0.266970	+	2.54005i
$777$		0			0
$778$	−3.72754	+	17.5367i	−0.133639	+	0.628721i
$779$	11.5261	−	1.21145i	0.412966	−	0.0434045i
$780$		0			0
$781$	29.0029	+	18.2172i	1.03781	+	0.651864i
$782$		−	41.5723i		−	1.48662i
$783$		0			0
$784$	7.67500	+	23.6212i	0.274107	+	0.843615i
$785$	−12.7708	−	60.0820i	−0.455810	−	2.14442i
$786$		0			0
$787$	−19.5492	−	43.9082i	−0.696853	−	1.56516i	−0.819740	−	0.572736i	$-0.805882\pi$
$787$	−19.5492	−	43.9082i	−0.696853	−	1.56516i	0.122887	−	0.992421i	$-0.460785\pi$
$788$	55.7532	+	61.9202i	1.98612	+	2.20581i
$789$		0			0
$790$	92.3986	+	41.1385i	3.28740	+	1.46364i
$791$	0.385085			0.0136920
$792$		0			0
$793$	9.24793			0.328404
$794$	−37.2418	−	16.5811i	−1.32166	−	0.588441i
$795$		0			0
$796$	−27.6934	−	30.7566i	−0.981567	−	1.09014i
$797$	2.45905	+	5.52311i	0.0871039	+	0.195639i	0.951845	−	0.306579i	$-0.0991843\pi$
$797$	2.45905	+	5.52311i	0.0871039	+	0.195639i	−0.864741	+	0.502218i	$0.832518\pi$
$798$		0			0
$799$	−0.0147162	−	0.0692345i	−0.000520623	−	0.00244934i
$800$	−1.79381	−	5.52078i	−0.0634208	−	0.195189i
$801$		0			0
$802$			12.3605i			0.436464i
$803$	3.56008	−	14.1381i	0.125633	−	0.498923i
$804$		0			0
$805$	6.89758	−	0.724964i	0.243108	−	0.0255516i
$806$	−1.68785	+	7.94069i	−0.0594518	+	0.279699i
$807$		0			0
$808$	8.60666	−	81.8869i	0.302781	−	2.88077i
$809$	−6.01444	−	4.36974i	−0.211456	−	0.153632i	0.477016	−	0.878895i	$-0.341718\pi$
$809$	−6.01444	−	4.36974i	−0.211456	−	0.153632i	−0.688472	+	0.725263i	$0.741718\pi$
$810$		0			0
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.221530	−	0.975154i	$-0.428895\pi$
$811$	27.7357	−	9.01188i	0.973933	−	0.316450i	0.752402	+	0.658704i	$0.228895\pi$
$812$	−1.46211	+	3.28396i	−0.0513101	+	0.115244i
$813$		0			0
$814$	45.6494	+	35.8371i	1.60001	+	1.25609i
$815$	14.0556	+	8.11503i	0.492348	+	0.284257i
$816$		0			0
$817$	5.38317	−	5.97861i	0.188333	−	0.209165i
$818$	74.9521	+	24.3534i	2.62064	+	0.851497i
$819$		0			0
$820$	23.8759	−	32.8623i	0.833782	−	1.14760i
$821$	1.04896	−	0.222964i	0.0366091	−	0.00778150i	−0.189571	−	0.981867i	$-0.560710\pi$
$821$	1.04896	−	0.222964i	0.0366091	−	0.00778150i	0.226180	+	0.974086i	$0.427376\pi$
$822$		0			0
$823$	0.935132	+	8.89719i	0.0325967	+	0.310136i	0.998657	+	0.0518182i	$0.0165016\pi$
$823$	0.935132	+	8.89719i	0.0325967	+	0.310136i	−0.966060	+	0.258318i	$0.916832\pi$
$824$	−21.9655	+	38.0454i	−0.765206	+	1.32538i
$825$		0			0
$826$	2.96782	+	5.14042i	0.103264	+	0.178858i
$827$	−28.5608	+	20.7507i	−0.993157	+	0.721571i	−0.960610	−	0.277899i	$-0.910362\pi$
$827$	−28.5608	+	20.7507i	−0.993157	+	0.721571i	−0.0325471	+	0.999470i	$0.510362\pi$
$828$		0			0
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	−0.694106	−	0.719873i	$-0.744200\pi$
$829$	8.36614	−	25.7483i	0.290568	−	0.894276i	0.984674	−	0.174404i	$-0.0557998\pi$
$830$	84.4585	+	8.87694i	2.93160	+	0.308123i
$831$		0			0
$832$	6.15859	−	5.54522i	0.213511	−	0.192246i
$833$	23.0630	+	4.90220i	0.799086	+	0.169851i
$834$		0			0
$835$	60.3300	−	34.8315i	2.08780	−	1.20539i
$836$	−24.5058	+	49.9483i	−0.847552	+	1.72750i
$837$		0			0
$838$	−39.9645	−	55.0064i	−1.38055	−	1.90016i
$839$	27.6695	+	24.9137i	0.955256	+	0.860116i	0.990254	−	0.139271i	$-0.0444759\pi$
$839$	27.6695	+	24.9137i	0.955256	+	0.860116i	−0.0349983	+	0.999387i	$0.511143\pi$
$840$		0			0
$841$	−20.8586	+	9.28687i	−0.719264	+	0.320237i
$842$	−59.4896	+	26.4865i	−2.05015	+	0.912785i
$843$		0			0
$844$	10.8164	+	9.73914i	0.372316	+	0.335235i
$845$	26.9980	+	37.1595i	0.928759	+	1.27833i
$846$		0			0
$847$	−1.36596	−	3.80813i	−0.0469349	−	0.130849i
$848$	17.3750	−	10.0314i	0.596658	−	0.344481i
$849$		0			0
$850$	77.0042	+	16.3677i	2.64122	+	0.561409i
$851$	−26.5168	+	23.8759i	−0.908985	+	0.818454i
$852$		0			0
$853$	−34.9266	−	3.67093i	−1.19586	−	0.125690i	−0.514405	−	0.857547i	$-0.671987\pi$
$853$	−34.9266	−	3.67093i	−1.19586	−	0.125690i	−0.681458	+	0.731857i	$0.738654\pi$
$854$	2.70044	−	8.31109i	0.0924070	−	0.284400i
$855$		0			0
$856$	−58.8516	+	42.7582i	−2.01151	+	1.46144i
$857$	−14.9819	−	25.9493i	−0.511770	−	0.886412i	−0.999907	−	0.0136449i	$-0.995657\pi$
$857$	−14.9819	−	25.9493i	−0.511770	−	0.886412i	0.488137	−	0.872767i	$-0.337677\pi$
$858$		0			0
$859$	−8.63419	+	14.9548i	−0.294595	+	0.510253i	−0.974891	−	0.222685i	$-0.928518\pi$
$859$	−8.63419	+	14.9548i	−0.294595	+	0.510253i	0.680296	+	0.732938i	$0.261851\pi$
$860$	−2.94736	−	28.0423i	−0.100504	−	0.956233i
$861$		0			0
$862$	1.70777	−	0.362997i	0.0581668	−	0.0123637i
$863$	20.4637	−	28.1659i	0.696593	−	0.958778i	−0.303389	−	0.952867i	$-0.598118\pi$
$863$	20.4637	−	28.1659i	0.696593	−	0.958778i	0.999983	−	0.00591175i	$-0.00188178\pi$
$864$		0			0
$865$	−22.3183	−	7.25166i	−0.758845	−	0.246564i
$866$	−18.6373	+	20.6988i	−0.633321	+	0.703374i
$867$		0			0
$868$	4.40493	+	2.54319i	0.149513	+	0.0863215i
$869$	34.0576	+	12.4860i	1.15533	+	0.423560i
$870$		0			0
$871$	−1.72155	+	3.86666i	−0.0583324	+	0.131017i
$872$	47.6696	−	15.4888i	1.61430	−	0.524517i
$873$		0			0
$874$	−41.7366	−	30.3234i	−1.41176	−	1.02570i
$875$	−0.643213	+	6.11977i	−0.0217446	+	0.206886i
$876$		0			0
$877$	0.412267	−	1.93956i	0.0139213	−	0.0654944i	−0.970639	−	0.240542i	$-0.922675\pi$
$877$	0.412267	−	1.93956i	0.0139213	−	0.0654944i	0.984560	+	0.175048i	$0.0560080\pi$
$878$	−20.7776	+	2.18381i	−0.701210	+	0.0737001i
$879$		0			0
$880$	16.9639	+	42.2709i	0.571854	+	1.42495i
$881$			48.9571i			1.64941i	0.565566	+	0.824703i	$0.308658\pi$
$881$			48.9571i			1.64941i	−0.565566	+	0.824703i	$0.691342\pi$
$882$		0			0
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	0.952187	+	0.305515i	$0.0988286\pi$
$883$	10.7400	+	33.0542i	0.361429	+	1.11236i	−0.590758	+	0.806848i	$0.701171\pi$
$884$	2.66509	+	12.5383i	0.0896368	+	0.421708i
$885$		0			0
$886$	13.8503	+	31.1082i	0.465309	+	1.04510i
$887$	9.69775	+	10.7704i	0.325618	+	0.361636i	0.883621	−	0.468204i	$-0.155099\pi$
$887$	9.69775	+	10.7704i	0.325618	+	0.361636i	−0.558002	+	0.829839i	$0.688432\pi$
$888$		0			0
$889$	5.89500	+	2.62462i	0.197712	+	0.0880271i
$890$	−28.1903			−0.944943
$891$		0			0
$892$	−70.4368			−2.35840
$893$	−0.0802423	−	0.0357262i	−0.00268521	−	0.00119553i
$894$		0			0
$895$	−23.4319	−	26.0238i	−0.783242	−	0.869879i
$896$	−3.00053	−	6.73930i	−0.100241	−	0.225144i
$897$		0			0
$898$	−10.9452	−	51.4933i	−0.365247	−	1.71835i
$899$	−2.69664	−	8.29941i	−0.0899380	−	0.276801i
$900$		0			0
$901$		−	19.0462i		−	0.634521i
$902$	11.6865	−	18.6055i	0.389117	−	0.619496i
$903$		0			0
$904$	−4.91054	+	0.516119i	−0.163322	+	0.0171659i
$905$	3.30484	−	15.5480i	0.109857	−	0.516835i
$906$		0			0
$907$	−2.38002	+	22.6444i	−0.0790274	+	0.751896i	0.881213	+	0.472720i	$0.156728\pi$
$907$	−2.38002	+	22.6444i	−0.0790274	+	0.751896i	−0.960240	+	0.279176i	$0.909939\pi$
$908$	55.3329	+	40.2017i	1.83629	+	1.33414i
$909$		0			0
$910$	−3.06739	+	0.996656i	−0.101683	+	0.0330388i
$911$	−9.23066	+	20.7324i	−0.305825	+	0.686895i	−0.999440	−	0.0334508i	$-0.989350\pi$
$911$	−9.23066	+	20.7324i	−0.305825	+	0.686895i	0.693615	+	0.720346i	$0.256017\pi$
$912$		0			0
$913$	30.4363	+	1.13396i	1.00729	+	0.0375286i
$914$	20.6878	+	11.9441i	0.684293	+	0.395077i
$915$		0			0
$916$	11.2624	−	12.5082i	0.372121	−	0.413282i
$917$	4.85824	+	1.57854i	0.160433	+	0.0521280i
$918$		0			0
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	−0.821012	−	0.570911i	$-0.806590\pi$
$919$	−0.737746	+	1.01542i	−0.0243360	+	0.0334956i	0.796676	+	0.604407i	$0.206590\pi$
$920$	−86.9852	+	18.4893i	−2.86782	+	0.609574i
$921$		0			0
$922$	−3.14728	−	29.9444i	−0.103650	−	0.986166i
$923$	4.89619	−	8.48045i	0.161160	−	0.279137i
$924$		0			0
$925$	−33.7850	−	58.5173i	−1.11084	−	1.92404i
$926$	−66.7619	+	48.5054i	−2.19393	+	1.59399i
$927$		0			0
$928$	−0.473521	+	1.45735i	−0.0155441	+	0.0478398i
$929$	2.85937	+	0.300532i	0.0938129	+	0.00986013i	0.151319	−	0.988485i	$-0.451648\pi$
$929$	2.85937	+	0.300532i	0.0938129	+	0.00986013i	−0.0575057	+	0.998345i	$0.518315\pi$
$930$		0			0
$931$	21.7440	−	19.5784i	0.712632	−	0.641657i
$932$	−90.0155	−	19.1334i	−2.94856	−	0.626735i
$933$		0			0
$934$	−33.2036	+	19.1701i	−1.08645	+	0.627265i
$935$	42.8048	+	6.11769i	1.39987	+	0.200070i
$936$		0			0
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	0.994975	−	0.100120i	$-0.0319227\pi$
$937$	18.1303	+	24.9542i	0.592291	+	0.815219i	−0.402684	+	0.915339i	$0.631923\pi$
$938$	2.97225	+	2.67623i	0.0970475	+	0.0873820i
$939$		0			0
$940$	−0.281239	+	0.125215i	−0.00917299	+	0.00408408i
$941$	−5.97537	+	2.66041i	−0.194792	+	0.0867268i	−0.501814	−	0.864975i	$-0.667334\pi$
$941$	−5.97537	+	2.66041i	−0.194792	+	0.0867268i	0.307023	+	0.951702i	$0.400667\pi$
$942$		0			0
$943$	10.0388	+	9.03896i	0.326908	+	0.294349i
$944$	−14.0872	−	19.3893i	−0.458498	−	0.631069i
$945$		0			0
$946$	−2.61336	−	15.0260i	−0.0849675	−	0.488537i
$947$	−28.8021	+	16.6289i	−0.935944	+	0.540368i	−0.888687	−	0.458515i	$-0.848381\pi$
$947$	−28.8021	+	16.6289i	−0.935944	+	0.540368i	−0.0472574	+	0.998883i	$0.515048\pi$
$948$		0			0
$949$	−4.07735	−	0.866668i	−0.132356	−	0.0281332i
$950$	72.6003	−	65.3696i	2.35546	−	2.12087i
$951$		0			0
$952$	5.92468	+	0.622709i	0.192020	+	0.0201821i
$953$	−16.9820	+	52.2651i	−0.550100	+	1.69303i	0.158445	+	0.987368i	$0.449352\pi$
$953$	−16.9820	+	52.2651i	−0.550100	+	1.69303i	−0.708545	+	0.705666i	$0.750648\pi$
$954$		0			0
$955$	61.9785	−	45.0300i	2.00558	−	1.45714i
$956$	−39.3481	−	68.1528i	−1.27261	−	2.20422i
$957$		0			0
$958$	−15.1893	+	26.3086i	−0.490744	+	0.849994i
$959$	0.0398952	+	0.379577i	0.00128828	+	0.0122572i
$960$		0			0
$961$	18.2448	−	3.87806i	0.588543	−	0.125099i
$962$	9.75321	−	13.4241i	0.314456	−	0.432812i
$963$		0			0
$964$	8.70515	+	2.82847i	0.280374	+	0.0910990i
$965$	20.3543	−	22.6058i	0.655229	−	0.727705i
$966$		0			0
$967$	−29.4790	−	17.0197i	−0.947982	−	0.547318i	−0.0555286	−	0.998457i	$-0.517684\pi$
$967$	−29.4790	−	17.0197i	−0.947982	−	0.547318i	−0.892454	+	0.451139i	$0.851018\pi$
$968$	22.5225	+	46.7300i	0.723899	+	1.50196i
$969$		0			0
$970$	56.7472	−	127.456i	1.82204	−	4.09238i
$971$	−36.2008	+	11.7624i	−1.16174	+	0.377472i	−0.825554	−	0.564323i	$-0.809137\pi$
$971$	−36.2008	+	11.7624i	−1.16174	+	0.377472i	−0.336186	+	0.941796i	$0.609137\pi$
$972$		0			0
$973$	5.90192	+	4.28799i	0.189207	+	0.137467i
$974$	−1.77147	+	16.8544i	−0.0567615	+	0.540050i
$975$		0			0
$976$	−7.33614	+	34.5138i	−0.234824	+	1.10476i
$977$	−31.9247	+	3.35542i	−1.02136	+	0.107349i	−0.600376	−	0.799718i	$-0.704982\pi$
$977$	−31.9247	+	3.35542i	−1.02136	+	0.107349i	−0.420985	+	0.907068i	$0.638316\pi$
$978$		0			0
$979$	−10.0873	+	0.681727i	−0.322391	+	0.0217881i
$980$		−	102.551i		−	3.27586i
$981$		0			0
$982$	−0.227305	−	0.699572i	−0.00725358	−	0.0223242i
$983$	4.45564	+	20.9622i	0.142113	+	0.668589i	0.990306	+	0.138902i	$0.0443573\pi$
$983$	4.45564	+	20.9622i	0.142113	+	0.668589i	−0.848193	+	0.529687i	$0.822309\pi$
$984$		0			0
$985$	−32.6854	−	73.4127i	−1.04144	−	2.33912i
$986$	−13.9054	−	15.4435i	−0.442838	−	0.491821i
$987$		0			0
$988$	14.5318	+	6.46996i	0.462317	+	0.205837i
$989$	9.37704			0.298172
$990$		0			0
$991$	−29.3068			−0.930962			−0.465481	−	0.885058i	$-0.654119\pi$
$991$	−29.3068			−0.930962			−0.465481	+	0.885058i	$0.654119\pi$
$992$	1.98074	+	0.881883i	0.0628886	+	0.0279998i
$993$		0			0
$994$	−6.19164	−	6.87651i	−0.196387	−	0.218110i
$995$	16.2353	+	36.4651i	0.514695	+	1.15602i
$996$		0			0
$997$	6.81165	+	32.0463i	0.215727	+	1.01492i	0.944081	+	0.329715i	$0.106953\pi$
$997$	6.81165	+	32.0463i	0.215727	+	1.01492i	−0.728354	+	0.685202i	$0.759714\pi$
$998$	−4.98148	−	15.3314i	−0.157686	−	0.485308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.701.1		32
3.2	odd	2	inner	891.2.u.c.701.4		32
9.2	odd	6	inner	891.2.u.c.107.1		32
9.4	even	3		99.2.j.a.8.4	yes	16
9.5	odd	6		99.2.j.a.8.1	✓	16
9.7	even	3	inner	891.2.u.c.107.4		32
11.7	odd	10	inner	891.2.u.c.458.1		32
33.29	even	10	inner	891.2.u.c.458.4		32
36.23	even	6		1584.2.cd.c.305.4		16
36.31	odd	6		1584.2.cd.c.305.1		16
99.7	odd	30	inner	891.2.u.c.755.4		32
99.13	odd	30		1089.2.d.g.1088.15		16
99.29	even	30	inner	891.2.u.c.755.1		32
99.31	even	15		1089.2.d.g.1088.1		16
99.40	odd	30		99.2.j.a.62.1	yes	16
99.68	even	30		1089.2.d.g.1088.2		16
99.86	odd	30		1089.2.d.g.1088.16		16
99.95	even	30		99.2.j.a.62.4	yes	16
396.95	odd	30		1584.2.cd.c.161.1		16
396.139	even	30		1584.2.cd.c.161.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.1	✓	16	9.5	odd	6
99.2.j.a.8.4	yes	16	9.4	even	3
99.2.j.a.62.1	yes	16	99.40	odd	30
99.2.j.a.62.4	yes	16	99.95	even	30
891.2.u.c.107.1		32	9.2	odd	6	inner
891.2.u.c.107.4		32	9.7	even	3	inner
891.2.u.c.458.1		32	11.7	odd	10	inner
891.2.u.c.458.4		32	33.29	even	10	inner
891.2.u.c.701.1		32	1.1	even	1	trivial
891.2.u.c.701.4		32	3.2	odd	2	inner
891.2.u.c.755.1		32	99.29	even	30	inner
891.2.u.c.755.4		32	99.7	odd	30	inner
1089.2.d.g.1088.1		16	99.31	even	15
1089.2.d.g.1088.2		16	99.68	even	30
1089.2.d.g.1088.15		16	99.13	odd	30
1089.2.d.g.1088.16		16	99.86	odd	30
1584.2.cd.c.161.1		16	396.95	odd	30
1584.2.cd.c.161.4		16	396.139	even	30
1584.2.cd.c.305.1		16	36.31	odd	6
1584.2.cd.c.305.4		16	36.23	even	6

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22569 - 0.990940i) q^{2} +(2.63346 + 2.92476i) q^{4} +(-1.54387 - 3.46760i) q^{5} +(0.0764681 + 0.359754i) q^{7} +(-1.45728 - 4.48505i) q^{8} +O(q^{10})\)	\(q+(-2.22569 - 0.990940i) q^{2} +(2.63346 + 2.92476i) q^{4} +(-1.54387 - 3.46760i) q^{5} +(0.0764681 + 0.359754i) q^{7} +(-1.45728 - 4.48505i) q^{8} +9.24768i q^{10} +(0.223636 + 3.30908i) q^{11} +(0.943068 - 0.0991205i) q^{13} +(0.186301 - 0.876476i) q^{14} +(-0.378188 + 3.59821i) q^{16} +(2.77873 + 2.01886i) q^{17} +(4.05368 - 1.31712i) q^{19} +(6.07615 - 13.6472i) q^{20} +(2.78135 - 7.58658i) q^{22} +(4.30242 + 2.48400i) q^{23} +(-6.29504 + 6.99135i) q^{25} +(-2.19720 - 0.713913i) q^{26} +(-0.850818 + 1.17105i) q^{28} +(2.42915 - 0.516332i) q^{29} +(-0.367304 - 3.49466i) q^{31} +(-0.308515 + 0.534364i) q^{32} +(-4.18401 - 7.24691i) q^{34} +(1.12943 - 0.820576i) q^{35} +(-2.21947 + 6.83082i) q^{37} +(-10.3274 - 1.08546i) q^{38} +(-13.3025 + 11.9776i) q^{40} +(2.65968 + 0.565333i) q^{41} +(1.63461 - 0.943743i) q^{43} +(-9.08931 + 9.36841i) q^{44} +(-7.11434 - 9.79205i) q^{46} +(-0.0153145 - 0.0137893i) q^{47} +(6.27124 - 2.79214i) q^{49} +(20.9388 - 9.32255i) q^{50} +(2.77344 + 2.49722i) q^{52} +(-3.25941 - 4.48619i) q^{53} +(11.1293 - 5.88428i) q^{55} +(1.50208 - 0.867226i) q^{56} +(-5.91818 - 1.25795i) q^{58} +(-4.92273 + 4.43245i) q^{59} +(9.69908 + 1.01941i) q^{61} +(-2.64550 + 8.14200i) q^{62} +(7.07028 - 5.13686i) q^{64} +(-1.79969 - 3.11715i) q^{65} +(-2.23176 + 3.86552i) q^{67} +(1.41299 + 13.4437i) q^{68} +(-3.32689 + 0.707153i) q^{70} +(6.06985 - 8.35443i) q^{71} +(-4.18072 - 1.35840i) q^{73} +(11.7088 - 13.0039i) q^{74} +(14.5275 + 8.38745i) q^{76} +(-1.17335 + 0.333493i) q^{77} +(4.44852 - 9.99155i) q^{79} +(13.0610 - 4.24379i) q^{80} +(-5.35942 - 3.89384i) q^{82} +(0.959910 - 9.13294i) q^{83} +(2.71060 - 12.7524i) q^{85} +(-4.57333 + 0.480676i) q^{86} +(14.5155 - 5.82527i) q^{88} +3.04837i q^{89} +(0.107774 + 0.331693i) q^{91} +(4.06516 + 19.1251i) q^{92} +(0.0204210 + 0.0458663i) q^{94} +(-10.8256 - 12.0231i) q^{95} +(-13.7825 - 6.13637i) q^{97} -16.7247 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4}+O(q^{10}) \) 32 * q + 4 * q^4	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

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