LMFDB - Embedded newform 325.2.e.c.276.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 8x^{8} - 2x^{7} + 52x^{6} - 5x^{5} + 97x^{4} + 60x^{3} + 141x^{2} + 36x + 9 $ x^10 + 8x^8 - 2x^7 + 52x^6 - 5x^5 + 97x^4 + 60x^3 + 141x^2 + 36x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			276.1
Root			$-1.30241 - 2.25583i$ of defining polynomial
Character	$\chi$	$=$	325.276
Dual form			325.2.e.c.126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30241 - 2.25583i) q^{2} +(-0.0676602 - 0.117191i) q^{3} +(-2.39253 + 4.14398i) q^{4} +(-0.176242 + 0.305261i) q^{6} +(1.62616 - 2.81660i) q^{7} +7.25455 q^{8} +(1.49084 - 2.58222i) q^{9} +O(q^{10})$	\(q+(-1.30241 - 2.25583i) q^{2} +(-0.0676602 - 0.117191i) q^{3} +(-2.39253 + 4.14398i) q^{4} +(-0.176242 + 0.305261i) q^{6} +(1.62616 - 2.81660i) q^{7} +7.25455 q^{8} +(1.49084 - 2.58222i) q^{9} +(-0.176242 - 0.305261i) q^{11} +0.647516 q^{12} +(-0.400724 - 3.58321i) q^{13} -8.47171 q^{14} +(-4.66332 - 8.07710i) q^{16} +(-3.37118 + 5.83905i) q^{17} -7.76674 q^{18} +(-1.39253 + 2.41193i) q^{19} -0.440107 q^{21} +(-0.459078 + 0.795147i) q^{22} +(-3.55031 - 6.14931i) q^{23} +(-0.490844 - 0.850167i) q^{24} +(-7.56123 + 5.57077i) q^{26} -0.809445 q^{27} +(7.78129 + 13.4776i) q^{28} +(-4.06500 - 7.04079i) q^{29} +7.11923 q^{31} +(-4.89253 + 8.47411i) q^{32} +(-0.0238492 + 0.0413080i) q^{33} +17.5626 q^{34} +(7.13377 + 12.3561i) q^{36} +(-2.04092 - 3.53498i) q^{37} +7.25455 q^{38} +(-0.392807 + 0.289402i) q^{39} +(0.202022 + 0.349912i) q^{41} +(0.573198 + 0.992808i) q^{42} +(-0.877834 + 1.52045i) q^{43} +1.68666 q^{44} +(-9.24789 + 16.0178i) q^{46} -3.75653 q^{47} +(-0.631042 + 1.09300i) q^{48} +(-1.78882 - 3.09833i) q^{49} +0.912378 q^{51} +(15.8075 + 6.91234i) q^{52} -3.44334 q^{53} +(1.05423 + 1.82597i) q^{54} +(11.7971 - 20.4332i) q^{56} +0.376875 q^{57} +(-10.5886 + 18.3399i) q^{58} +(1.12712 - 1.95224i) q^{59} +(3.05961 - 5.29941i) q^{61} +(-9.27213 - 16.0598i) q^{62} +(-4.84872 - 8.39822i) q^{63} +6.83497 q^{64} +0.124245 q^{66} +(5.85663 + 10.1440i) q^{67} +(-16.1313 - 27.9402i) q^{68} +(-0.480429 + 0.832128i) q^{69} +(0.857592 - 1.48539i) q^{71} +(10.8154 - 18.7328i) q^{72} +10.5626 q^{73} +(-5.31622 + 9.20797i) q^{74} +(-6.66332 - 11.5412i) q^{76} -1.14640 q^{77} +(1.16444 + 0.509188i) q^{78} +8.62003 q^{79} +(-4.41777 - 7.65179i) q^{81} +(0.526228 - 0.911454i) q^{82} +7.81830 q^{83} +(1.05297 - 1.82379i) q^{84} +4.57319 q^{86} +(-0.550078 + 0.952762i) q^{87} +(-1.27856 - 2.21453i) q^{88} +(3.59455 + 6.22594i) q^{89} +(-10.7441 - 4.69822i) q^{91} +33.9768 q^{92} +(-0.481688 - 0.834309i) q^{93} +(4.89253 + 8.47411i) q^{94} +1.32412 q^{96} +(3.43618 - 5.95163i) q^{97} +(-4.65955 + 8.07058i) q^{98} -1.05100 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9	$ 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) $ 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 16 * q^14 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 16 * q^21 - 8 * q^22 - 15 * q^23 + 14 * q^24 - 9 * q^26 + 42 * q^27 + 17 * q^28 + q^29 - 31 * q^32 + 2 * q^33 + 54 * q^34 + 13 * q^36 - 17 * q^37 + 6 * q^38 - 10 * q^39 - 6 * q^41 - 32 * q^42 - 12 * q^43 - 16 * q^44 + 7 * q^46 - 24 * q^47 + 2 * q^48 - 7 * q^49 + 23 * q^52 + 16 * q^53 - 19 * q^54 + 17 * q^56 - 8 * q^57 - 38 * q^58 + 12 * q^59 - 5 * q^61 - 13 * q^62 - 26 * q^63 - 10 * q^64 + 86 * q^66 + 16 * q^67 - 25 * q^68 - 20 * q^69 - 19 * q^71 + 45 * q^72 - 16 * q^73 - 2 * q^74 - 24 * q^76 + 64 * q^77 + 42 * q^78 - 28 * q^79 - 29 * q^81 + 23 * q^82 - 14 * q^83 + 34 * q^84 - 84 * q^86 - 21 * q^87 - 2 * q^88 + 10 * q^89 + 17 * q^91 + 142 * q^92 + 33 * q^93 + 31 * q^94 + 34 * q^96 - 37 * q^97 + 21 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.30241	−	2.25583i	−0.920941	−	1.59512i	−0.797963	−	0.602707i	$-0.794089\pi$
$2$	−1.30241	−	2.25583i	−0.920941	−	1.59512i	−0.122978	−	0.992409i	$-0.539244\pi$
$3$	−0.0676602	−	0.117191i	−0.0390636	−	0.0676602i	0.845833	−	0.533448i	$-0.179104\pi$
$3$	−0.0676602	−	0.117191i	−0.0390636	−	0.0676602i	−0.884896	+	0.465788i	$0.845771\pi$
$4$	−2.39253	+	4.14398i	−1.19626	+	2.07199i
$5$		0			0
$5$		0			0
$6$	−0.176242	+	0.305261i	−0.0719506	+	0.124622i
$7$	1.62616	−	2.81660i	0.614632	−	1.06457i	−0.375816	−	0.926694i	$-0.622638\pi$
$7$	1.62616	−	2.81660i	0.614632	−	1.06457i	0.990449	−	0.137880i	$-0.0440290\pi$
$8$	7.25455			2.56487
$9$	1.49084	−	2.58222i	0.496948	−	0.860739i
$10$		0			0
$11$	−0.176242	−	0.305261i	−0.0531390	−	0.0920395i	0.838232	−	0.545313i	$-0.183589\pi$
$11$	−0.176242	−	0.305261i	−0.0531390	−	0.0920395i	−0.891371	+	0.453274i	$0.850256\pi$
$12$	0.647516			0.186922
$13$	−0.400724	−	3.58321i	−0.111141	−	0.993805i
$13$	−0.400724	−	3.58321i	−0.111141	−	0.993805i
$14$	−8.47171			−2.26416
$15$		0			0
$16$	−4.66332	−	8.07710i	−1.16583	−	2.01928i
$17$	−3.37118	+	5.83905i	−0.817630	+	1.41618i	0.0897934	+	0.995960i	$0.471379\pi$
$17$	−3.37118	+	5.83905i	−0.817630	+	1.41618i	−0.907424	+	0.420217i	$0.861954\pi$
$18$	−7.76674			−1.83064
$19$	−1.39253	+	2.41193i	−0.319468	+	0.553334i	−0.980377	−	0.197132i	$-0.936837\pi$
$19$	−1.39253	+	2.41193i	−0.319468	+	0.553334i	0.660909	+	0.750466i	$0.270171\pi$
$20$		0			0
$21$	−0.440107			−0.0960391
$22$	−0.459078	+	0.795147i	−0.0978758	+	0.169526i
$23$	−3.55031	−	6.14931i	−0.740290	−	1.28222i	−0.952363	−	0.304967i	$-0.901355\pi$
$23$	−3.55031	−	6.14931i	−0.740290	−	1.28222i	0.212073	−	0.977254i	$-0.431979\pi$
$24$	−0.490844	−	0.850167i	−0.100193	−	0.173540i
$25$		0			0
$26$	−7.56123	+	5.57077i	−1.48288	+	1.09252i
$27$	−0.809445			−0.155778
$28$	7.78129	+	13.4776i	1.47052	+	2.54702i
$29$	−4.06500	−	7.04079i	−0.754852	−	1.30744i	−0.945448	−	0.325773i	$-0.894375\pi$
$29$	−4.06500	−	7.04079i	−0.754852	−	1.30744i	0.190596	−	0.981669i	$-0.438958\pi$
$30$		0			0
$31$	7.11923			1.27865			0.639325	−	0.768936i	$-0.279214\pi$
$31$	7.11923			1.27865			0.639325	+	0.768936i	$0.279214\pi$
$32$	−4.89253	+	8.47411i	−0.864885	+	1.49802i
$33$	−0.0238492	+	0.0413080i	−0.00415161	+	0.00719080i
$34$	17.5626			3.01196
$35$		0			0
$36$	7.13377	+	12.3561i	1.18896	+	2.05934i
$37$	−2.04092	−	3.53498i	−0.335525	−	0.581147i	0.648060	−	0.761589i	$-0.275581\pi$
$37$	−2.04092	−	3.53498i	−0.335525	−	0.581147i	−0.983586	+	0.180442i	$0.942247\pi$
$38$	7.25455			1.17684
$39$	−0.392807	+	0.289402i	−0.0628995	+	0.0463414i
$40$		0			0
$41$	0.202022	+	0.349912i	0.0315505	+	0.0546470i	0.881369	−	0.472428i	$-0.156622\pi$
$41$	0.202022	+	0.349912i	0.0315505	+	0.0546470i	−0.849819	+	0.527075i	$0.823289\pi$
$42$	0.573198	+	0.992808i	0.0884463	+	0.153194i
$43$	−0.877834	+	1.52045i	−0.133868	+	0.231867i	−0.925165	−	0.379566i	$-0.876073\pi$
$43$	−0.877834	+	1.52045i	−0.133868	+	0.231867i	0.791296	+	0.611433i	$0.209407\pi$
$44$	1.68666			0.254273
$45$		0			0
$46$	−9.24789	+	16.0178i	−1.36353	+	2.36170i
$47$	−3.75653			−0.547946			−0.273973	−	0.961737i	$-0.588338\pi$
$47$	−3.75653			−0.547946			−0.273973	+	0.961737i	$0.588338\pi$
$48$	−0.631042	+	1.09300i	−0.0910831	+	0.157761i
$49$	−1.78882	−	3.09833i	−0.255546	−	0.442619i
$50$		0			0
$51$	0.912378			0.127758
$52$	15.8075	+	6.91234i	2.19211	+	0.958570i
$53$	−3.44334			−0.472980			−0.236490	−	0.971634i	$-0.575997\pi$
$53$	−3.44334			−0.472980			−0.236490	+	0.971634i	$0.575997\pi$
$54$	1.05423	+	1.82597i	0.143462	+	0.248483i
$55$		0			0
$56$	11.7971	−	20.4332i	1.57645	−	2.73050i
$57$	0.376875			0.0499183
$58$	−10.5886	+	18.3399i	−1.39035	+	2.40815i
$59$	1.12712	−	1.95224i	0.146739	−	0.254159i	−0.783281	−	0.621667i	$-0.786456\pi$
$59$	1.12712	−	1.95224i	0.146739	−	0.254159i	0.930020	+	0.367508i	$0.119789\pi$
$60$		0			0
$61$	3.05961	−	5.29941i	0.391743	−	0.678519i	−0.600936	−	0.799297i	$-0.705205\pi$
$61$	3.05961	−	5.29941i	0.391743	−	0.678519i	0.992680	+	0.120778i	$0.0385388\pi$
$62$	−9.27213	−	16.0598i	−1.17756	−	2.03960i
$63$	−4.84872	−	8.39822i	−0.610881	−	1.05808i
$64$	6.83497			0.854371
$65$		0			0
$66$	0.124245			0.0152935
$67$	5.85663	+	10.1440i	0.715502	+	1.23929i	0.962766	+	0.270337i	$0.0871351\pi$
$67$	5.85663	+	10.1440i	0.715502	+	1.23929i	−0.247264	+	0.968948i	$0.579532\pi$
$68$	−16.1313	−	27.9402i	−1.95620	−	3.38824i
$69$	−0.480429	+	0.832128i	−0.0578369	+	0.100176i
$70$		0			0
$71$	0.857592	−	1.48539i	0.101777	−	0.176284i	−0.810640	−	0.585545i	$-0.800880\pi$
$71$	0.857592	−	1.48539i	0.101777	−	0.176284i	0.912417	+	0.409262i	$0.134214\pi$
$72$	10.8154	−	18.7328i	1.27461	−	2.20768i
$73$	10.5626			1.23626			0.618128	−	0.786078i	$-0.287891\pi$
$73$	10.5626			1.23626			0.618128	+	0.786078i	$0.287891\pi$
$74$	−5.31622	+	9.20797i	−0.617998	+	1.07040i
$75$		0			0
$76$	−6.66332	−	11.5412i	−0.764335	−	1.32387i
$77$	−1.14640			−0.130644
$78$	1.16444	+	0.509188i	0.131847	+	0.0576542i
$79$	8.62003			0.969829			0.484914	−	0.874562i	$-0.338851\pi$
$79$	8.62003			0.969829			0.484914	+	0.874562i	$0.338851\pi$
$80$		0			0
$81$	−4.41777	−	7.65179i	−0.490863	−	0.850199i
$82$	0.526228	−	0.911454i	0.0581122	−	0.100653i
$83$	7.81830			0.858170			0.429085	−	0.903264i	$-0.358836\pi$
$83$	7.81830			0.858170			0.429085	+	0.903264i	$0.358836\pi$
$84$	1.05297	−	1.82379i	0.114888	−	0.198992i
$85$		0			0
$86$	4.57319			0.493139
$87$	−0.550078	+	0.952762i	−0.0589745	+	0.102147i
$88$	−1.27856	−	2.21453i	−0.136295	−	0.236069i
$89$	3.59455	+	6.22594i	0.381021	+	0.659948i	0.991209	−	0.132309i	$-0.0422391\pi$
$89$	3.59455	+	6.22594i	0.381021	+	0.659948i	−0.610187	+	0.792257i	$0.708906\pi$
$90$		0			0
$91$	−10.7441	−	4.69822i	−1.12629	−	0.492507i
$92$	33.9768			3.54233
$93$	−0.481688	−	0.834309i	−0.0499488	−	0.0865138i
$94$	4.89253	+	8.47411i	0.504626	+	0.874037i
$95$		0			0
$96$	1.32412			0.135142
$97$	3.43618	−	5.95163i	0.348891	−	0.604297i	−0.637162	−	0.770730i	$-0.719892\pi$
$97$	3.43618	−	5.95163i	0.348891	−	0.604297i	0.986053	+	0.166433i	$0.0532250\pi$
$98$	−4.65955	+	8.07058i	−0.470686	+	0.815251i
$99$	−1.05100			−0.105629
$100$		0			0
$101$	2.76164	+	4.78329i	0.274793	+	0.475955i	0.970083	−	0.242774i	$-0.0780574\pi$
$101$	2.76164	+	4.78329i	0.274793	+	0.475955i	−0.695290	+	0.718729i	$0.744724\pi$
$102$	−1.18829	−	2.05817i	−0.117658	−	0.203790i
$103$	10.2573			1.01068			0.505342	−	0.862919i	$-0.331366\pi$
$103$	10.2573			1.01068			0.505342	+	0.862919i	$0.331366\pi$
$104$	−2.90707	−	25.9946i	−0.285062	−	2.54898i
$105$		0			0
$106$	4.48464	+	7.76762i	0.435586	+	0.754458i
$107$	0.507606	+	0.879199i	0.0490721	+	0.0849954i	0.889518	−	0.456900i	$-0.151040\pi$
$107$	0.507606	+	0.879199i	0.0490721	+	0.0849954i	−0.840446	+	0.541895i	$0.817707\pi$
$108$	1.93662	−	3.35432i	0.186351	−	0.322770i
$109$	−13.6200			−1.30456			−0.652281	−	0.757977i	$-0.726188\pi$
$109$	−13.6200			−1.30456			−0.652281	+	0.757977i	$0.726188\pi$
$110$		0			0
$111$	−0.276178	+	0.478355i	−0.0262137	+	0.0454034i
$112$	−30.3333			−2.86623
$113$	−6.01773	+	10.4230i	−0.566101	+	0.980515i	0.430846	+	0.902426i	$0.358215\pi$
$113$	−6.01773	+	10.4230i	−0.566101	+	0.980515i	−0.996946	+	0.0780895i	$0.975118\pi$
$114$	−0.490844	−	0.850167i	−0.0459718	−	0.0796254i
$115$		0			0
$116$	38.9025			3.61201
$117$	−9.85006	−	4.30726i	−0.910638	−	0.398206i
$118$	−5.87189			−0.540552
$119$	10.9642	+	18.9905i	1.00508	+	1.74086i
$120$		0			0
$121$	5.43788	−	9.41868i	0.494352	−	0.856244i
$122$	−15.9394			−1.44309
$123$	0.0273376	−	0.0473502i	0.00246495	−	0.00426942i
$124$	−17.0329	+	29.5019i	−1.52960	+	2.64935i
$125$		0			0
$126$	−12.6300	+	21.8758i	−1.12517	+	1.94885i
$127$	4.62639	+	8.01315i	0.410526	+	0.711052i	0.994947	−	0.100398i	$-0.0320117\pi$
$127$	4.62639	+	8.01315i	0.410526	+	0.711052i	−0.584421	+	0.811450i	$0.698678\pi$
$128$	0.883141	+	1.52965i	0.0780594	+	0.135203i
$129$	0.237578			0.0209175
$130$		0			0
$131$	−1.50080			−0.131125			−0.0655627	−	0.997848i	$-0.520884\pi$
$131$	−1.50080			−0.131125			−0.0655627	+	0.997848i	$0.520884\pi$
$132$	−0.114120	−	0.197661i	−0.00993283	−	0.0172042i
$133$	4.52896	+	7.84438i	0.392710	+	0.680194i
$134$	15.2554	−	26.4232i	1.31787	−	2.28262i
$135$		0			0
$136$	−24.4564	+	42.3597i	−2.09712	+	3.63231i
$137$	−0.585922	+	1.01485i	−0.0500587	+	0.0867042i	−0.889969	−	0.456021i	$-0.849274\pi$
$137$	−0.585922	+	1.01485i	−0.0500587	+	0.0867042i	0.839910	+	0.542725i	$0.182608\pi$
$138$	2.50286			0.213057
$139$	6.26702	−	10.8548i	0.531562	−	0.920692i	−0.467759	−	0.883856i	$-0.654939\pi$
$139$	6.26702	−	10.8548i	0.531562	−	0.920692i	0.999321	−	0.0368364i	$-0.0117280\pi$
$140$		0			0
$141$	0.254167	+	0.440231i	0.0214048	+	0.0370741i
$142$	−4.46774			−0.374924
$143$	−1.02319	+	0.753839i	−0.0855634	+	0.0630392i
$144$	−27.8091			−2.31743
$145$		0			0
$146$	−13.7568	−	23.8274i	−1.13852	−	1.97197i
$147$	−0.242064	+	0.419268i	−0.0199651	+	0.0345806i
$148$	19.5318			1.60551
$149$	9.78121	−	16.9415i	0.801308	−	1.38791i	−0.117448	−	0.993079i	$-0.537471\pi$
$149$	9.78121	−	16.9415i	0.801308	−	1.38791i	0.918756	−	0.394826i	$-0.129195\pi$
$150$		0			0
$151$	9.94414			0.809243			0.404621	−	0.914484i	$-0.367403\pi$
$151$	9.94414			0.809243			0.404621	+	0.914484i	$0.367403\pi$
$152$	−10.1022	+	17.4974i	−0.819393	+	1.41923i
$153$	10.0518	+	17.4102i	0.812640	+	1.40753i
$154$	1.49307	+	2.58608i	0.120315	+	0.208392i
$155$		0			0
$156$	−0.259475	−	2.32019i	−0.0207746	−	0.185764i
$157$	6.60923			0.527474			0.263737	−	0.964595i	$-0.415045\pi$
$157$	6.60923			0.527474			0.263737	+	0.964595i	$0.415045\pi$
$158$	−11.2268	−	19.4454i	−0.893155	−	1.54699i
$159$	0.232977	+	0.403529i	0.0184763	+	0.0320019i
$160$		0			0
$161$	−23.0935			−1.82003
$162$	−11.5075	+	19.9315i	−0.904111	+	1.56597i
$163$	−3.81571	+	6.60901i	−0.298870	+	0.517657i	−0.975878	−	0.218318i	$-0.929943\pi$
$163$	−3.81571	+	6.60901i	−0.298870	+	0.517657i	0.677008	+	0.735976i	$0.263276\pi$
$164$	−1.93337			−0.150971
$165$		0			0
$166$	−10.1826	−	17.6368i	−0.790324	−	1.36888i
$167$	9.81762	+	17.0046i	0.759710	+	1.31586i	0.942998	+	0.332797i	$0.107993\pi$
$167$	9.81762	+	17.0046i	0.759710	+	1.31586i	−0.183288	+	0.983059i	$0.558674\pi$
$168$	−3.19277			−0.246328
$169$	−12.6788	+	2.87176i	−0.975295	+	0.220905i
$170$		0			0
$171$	4.15208	+	7.19162i	0.317518	+	0.549957i
$172$	−4.20048	−	7.27545i	−0.320284	−	0.554748i
$173$	3.63865	−	6.30232i	0.276641	−	0.479157i	−0.693907	−	0.720065i	$-0.744112\pi$
$173$	3.63865	−	6.30232i	0.276641	−	0.479157i	0.970548	+	0.240908i	$0.0774453\pi$
$174$	2.86570			0.217248
$175$		0			0
$176$	−1.64375	+	2.84705i	−0.123902	+	0.214605i
$177$	−0.305046			−0.0229286
$178$	9.36313	−	16.2174i	0.701796	−	1.21555i
$179$	7.42636	+	12.8628i	0.555072	+	0.961413i	0.997898	+	0.0648057i	$0.0206428\pi$
$179$	7.42636	+	12.8628i	0.555072	+	0.961413i	−0.442826	+	0.896608i	$0.646024\pi$
$180$		0			0
$181$	−12.2959			−0.913948			−0.456974	−	0.889480i	$-0.651067\pi$
$181$	−12.2959			−0.913948			−0.456974	+	0.889480i	$0.651067\pi$
$182$	3.39482	+	30.3560i	0.251641	+	2.25013i
$183$	−0.828056			−0.0612117
$184$	−25.7559	−	44.6105i	−1.89875	−	3.28873i
$185$		0			0
$186$	−1.25471	+	2.17322i	−0.0919997	+	0.159348i
$187$	2.37657			0.173792
$188$	8.98759	−	15.5670i	0.655488	−	1.13534i
$189$	−1.31629	+	2.27988i	−0.0957460	+	0.165837i
$190$		0			0
$191$	0.838301	−	1.45198i	0.0606573	−	0.105062i	−0.834102	−	0.551610i	$-0.814014\pi$
$191$	0.838301	−	1.45198i	0.0606573	−	0.105062i	0.894759	+	0.446549i	$0.147347\pi$
$192$	−0.462456	−	0.800997i	−0.0333749	−	0.0578069i
$193$	−1.44232	−	2.49817i	−0.103820	−	0.179822i	0.809435	−	0.587209i	$-0.199773\pi$
$193$	−1.44232	−	2.49817i	−0.103820	−	0.179822i	−0.913256	+	0.407387i	$0.866440\pi$
$194$	−17.9012			−1.28523
$195$		0			0
$196$	17.1192			1.22280
$197$	−2.49152	−	4.31545i	−0.177514	−	0.307463i	0.763515	−	0.645791i	$-0.223472\pi$
$197$	−2.49152	−	4.31545i	−0.177514	−	0.307463i	−0.941028	+	0.338328i	$0.890139\pi$
$198$	1.36883	+	2.37088i	0.0972784	+	0.168491i
$199$	−11.4591	+	19.8477i	−0.812312	+	1.40697i	0.0989305	+	0.995094i	$0.468458\pi$
$199$	−11.4591	+	19.8477i	−0.812312	+	1.40697i	−0.911242	+	0.411871i	$0.864875\pi$
$200$		0			0
$201$	0.792522	−	1.37269i	0.0559002	−	0.0968220i
$202$	7.19354	−	12.4596i	0.506136	−	0.876653i
$203$	−26.4414			−1.85583
$204$	−2.18289	+	3.78087i	−0.152833	+	0.264714i
$205$		0			0
$206$	−13.3592	−	23.1388i	−0.930780	−	1.61216i
$207$	−21.1718			−1.47154
$208$	−27.0733	+	19.9464i	−1.87719	+	1.38303i
$209$	0.981688			0.0679048
$210$		0			0
$211$	−0.627865	−	1.08749i	−0.0432240	−	0.0748661i	0.843604	−	0.536966i	$-0.180430\pi$
$211$	−0.627865	−	1.08749i	−0.0432240	−	0.0748661i	−0.886828	+	0.462100i	$0.847096\pi$
$212$	8.23830	−	14.2691i	0.565808	−	0.980009i
$213$	−0.232099			−0.0159032
$214$	1.32222	−	2.29015i	0.0903850	−	0.156551i
$215$		0			0
$216$	−5.87215			−0.399549
$217$	11.5770	−	20.0520i	0.785900	−	1.36122i
$218$	17.7388	+	30.7245i	1.20142	+	2.08093i
$219$	−0.714666	−	1.23784i	−0.0482926	−	0.0836453i
$220$		0			0
$221$	22.2735	+	9.73980i	1.49828	+	0.655170i
$222$	1.43879			0.0965650
$223$	−2.12446	−	3.67968i	−0.142265	−	0.246410i	0.786084	−	0.618119i	$-0.212105\pi$
$223$	−2.12446	−	3.67968i	−0.142265	−	0.246410i	−0.928349	+	0.371710i	$0.878772\pi$
$224$	15.9121	+	27.5606i	1.06317	+	1.84147i
$225$		0			0
$226$	31.3501			2.08538
$227$	7.50392	−	12.9972i	0.498052	−	0.862652i	−0.501945	−	0.864900i	$-0.667382\pi$
$227$	7.50392	−	12.9972i	0.498052	−	0.862652i	0.999997	+	0.00224733i	$0.000715348\pi$
$228$	−0.901683	+	1.56176i	−0.0597154	+	0.103430i
$229$	−1.86852			−0.123475			−0.0617375	−	0.998092i	$-0.519664\pi$
$229$	−1.86852			−0.123475			−0.0617375	+	0.998092i	$0.519664\pi$
$230$		0			0
$231$	0.0775654	+	0.134347i	0.00510343	+	0.00883939i
$232$	−29.4897	−	51.0777i	−1.93610	−	3.35342i
$233$	15.0743			0.987551			0.493775	−	0.869590i	$-0.335617\pi$
$233$	15.0743			0.987551			0.493775	+	0.869590i	$0.335617\pi$
$234$	3.11232	+	27.8299i	0.203459	+	1.81930i
$235$		0			0
$236$	5.39335	+	9.34155i	0.351077	+	0.608083i
$237$	−0.583233	−	1.01019i	−0.0378850	−	0.0656188i
$238$	28.5596	−	49.4667i	1.85125	−	3.20645i
$239$	22.2262			1.43769			0.718847	−	0.695169i	$-0.244670\pi$
$239$	22.2262			1.43769			0.718847	+	0.695169i	$0.244670\pi$
$240$		0			0
$241$	2.66206	−	4.61082i	0.171478	−	0.297009i	−0.767459	−	0.641098i	$-0.778479\pi$
$241$	2.66206	−	4.61082i	0.171478	−	0.297009i	0.938937	+	0.344089i	$0.111812\pi$
$242$	−28.3293			−1.82108
$243$	−1.81198	+	3.13844i	−0.116239	+	0.201331i
$244$	14.6404	+	25.3579i	0.937257	+	1.62338i
$245$		0			0
$246$	−0.142419			−0.00908030
$247$	9.20047	+	4.02321i	0.585412	+	0.255990i
$248$	51.6468			3.27957
$249$	−0.528988	−	0.916234i	−0.0335232	−	0.0580640i
$250$		0			0
$251$	−10.4151	+	18.0394i	−0.657393	+	1.13864i	0.323896	+	0.946093i	$0.395007\pi$
$251$	−10.4151	+	18.0394i	−0.657393	+	1.13864i	−0.981288	+	0.192544i	$0.938326\pi$
$252$	46.4027			2.92310
$253$	−1.25143	+	2.16754i	−0.0786766	+	0.136272i
$254$	12.0509	−	20.8728i	0.756140	−	1.30967i
$255$		0			0
$256$	9.13539	−	15.8230i	0.570962	−	0.988935i
$257$	−7.96972	−	13.8040i	−0.497138	−	0.861068i	0.502857	−	0.864370i	$-0.332282\pi$
$257$	−7.96972	−	13.8040i	−0.497138	−	0.861068i	−0.999995	+	0.00330197i	$0.998949\pi$
$258$	−0.309423	−	0.535936i	−0.0192638	−	0.0333659i
$259$	−13.2755			−0.824899
$260$		0			0
$261$	−24.2411			−1.50049
$262$	1.95465	+	3.38555i	0.120759	+	0.209160i
$263$	8.85021	+	15.3290i	0.545727	+	0.945227i	0.998561	+	0.0536320i	$0.0170798\pi$
$263$	8.85021	+	15.3290i	0.545727	+	0.945227i	−0.452834	+	0.891595i	$0.649587\pi$
$264$	−0.173015	+	0.299671i	−0.0106483	+	0.0184435i
$265$		0			0
$266$	11.7971	−	20.4332i	0.723326	−	1.25284i
$267$	0.486416	−	0.842497i	0.0297682	−	0.0515600i
$268$	−56.0486			−3.42371
$269$	0.755787	−	1.30906i	0.0460811	−	0.0798148i	−0.842065	−	0.539376i	$-0.818660\pi$
$269$	0.755787	−	1.30906i	0.0460811	−	0.0798148i	0.888146	+	0.459561i	$0.151993\pi$
$270$		0			0
$271$	13.6501	+	23.6427i	0.829185	+	1.43619i	0.898678	+	0.438609i	$0.144529\pi$
$271$	13.6501	+	23.6427i	0.829185	+	1.43619i	−0.0694927	+	0.997582i	$0.522138\pi$
$272$	62.8835			3.81287
$273$	0.176361	+	1.57700i	0.0106739	+	0.0954441i
$274$	3.05244			0.184404
$275$		0			0
$276$	−2.29888	−	3.98178i	−0.138376	−	0.239675i
$277$	−1.31171	+	2.27195i	−0.0788132	+	0.136508i	−0.902738	−	0.430190i	$-0.858446\pi$
$277$	−1.31171	+	2.27195i	−0.0788132	+	0.136508i	0.823925	+	0.566699i	$0.191780\pi$
$278$	−32.6489			−1.95815
$279$	10.6137	−	18.3834i	0.635423	−	1.10059i
$280$		0			0
$281$	8.98774			0.536164			0.268082	−	0.963396i	$-0.413610\pi$
$281$	8.98774			0.536164			0.268082	+	0.963396i	$0.413610\pi$
$282$	0.662059	−	1.14672i	0.0394250	−	0.0682862i
$283$	−11.7196	−	20.2989i	−0.696658	−	1.20665i	−0.969619	−	0.244621i	$-0.921336\pi$
$283$	−11.7196	−	20.2989i	−0.696658	−	1.20665i	0.272961	−	0.962025i	$-0.411997\pi$
$284$	4.10362	+	7.10769i	0.243505	+	0.421764i
$285$		0			0
$286$	3.03314	+	1.32634i	0.179354	+	0.0784282i
$287$	1.31408			0.0775678
$288$	14.5880	+	25.2671i	0.859606	+	1.48888i
$289$	−14.2297	−	24.6465i	−0.837039	−	1.44979i
$290$		0			0
$291$	−0.929970			−0.0545158
$292$	−25.2712	+	43.7711i	−1.47889	+	2.56151i
$293$	0.588332	−	1.01902i	0.0343707	−	0.0595318i	−0.848328	−	0.529470i	$-0.822391\pi$
$293$	0.588332	−	1.01902i	0.0343707	−	0.0595318i	0.882699	+	0.469939i	$0.155724\pi$
$294$	1.26106			0.0735468
$295$		0			0
$296$	−14.8060	−	25.6447i	−0.860579	−	1.49057i
$297$	0.142658	+	0.247091i	0.00827788	+	0.0143377i
$298$	−50.9564			−2.95183
$299$	−20.6116	+	15.1857i	−1.19200	+	0.878211i
$300$		0			0
$301$	2.85500	+	4.94501i	0.164560	+	0.285026i
$302$	−12.9513	−	22.4323i	−0.745265	−	1.29084i
$303$	0.373706	−	0.647277i	0.0214688	−	0.0371851i
$304$	25.9752			1.48978
$305$		0			0
$306$	26.1831	−	45.3504i	1.49679	−	2.59251i
$307$	16.6150			0.948269			0.474134	−	0.880453i	$-0.342761\pi$
$307$	16.6150			0.948269			0.474134	+	0.880453i	$0.342761\pi$
$308$	2.74278	−	4.75064i	0.156285	−	0.270693i
$309$	−0.694013	−	1.20207i	−0.0394810	−	0.0683831i
$310$		0			0
$311$	−14.7129			−0.834294			−0.417147	−	0.908839i	$-0.636970\pi$
$311$	−14.7129			−0.834294			−0.417147	+	0.908839i	$0.636970\pi$
$312$	−2.84964	+	2.09948i	−0.161329	+	0.118860i
$313$	1.86190			0.105241			0.0526204	−	0.998615i	$-0.483243\pi$
$313$	1.86190			0.105241			0.0526204	+	0.998615i	$0.483243\pi$
$314$	−8.60791	−	14.9093i	−0.485773	−	0.841383i
$315$		0			0
$316$	−20.6236	+	35.7212i	−1.16017	+	2.00947i
$317$	−13.9811			−0.785258			−0.392629	−	0.919697i	$-0.628434\pi$
$317$	−13.9811			−0.785258			−0.392629	+	0.919697i	$0.628434\pi$
$318$	0.606863	−	1.05112i	0.0340312	−	0.0589437i
$319$	−1.43285	+	2.48177i	−0.0802242	+	0.138952i
$320$		0			0
$321$	0.0686894	−	0.118974i	0.00383387	−	0.00664046i
$322$	30.0772	+	52.0952i	1.67614	+	2.90315i
$323$	−9.38891	−	16.2621i	−0.522413	−	0.904846i
$324$	42.2785			2.34881
$325$		0			0
$326$	19.8784			1.10096
$327$	0.921534	+	1.59614i	0.0509609	+	0.0882669i
$328$	1.46557	+	2.53845i	0.0809228	+	0.140162i
$329$	−6.10873	+	10.5806i	−0.336785	+	0.583329i
$330$		0			0
$331$	−7.15262	+	12.3887i	−0.393144	+	0.680945i	−0.992862	−	0.119266i	$-0.961946\pi$
$331$	−7.15262	+	12.3887i	−0.393144	+	0.680945i	0.599719	+	0.800211i	$0.295279\pi$
$332$	−18.7055	+	32.3989i	−1.02660	+	1.77812i
$333$	−12.1708			−0.666955
$334$	25.5731	−	44.2939i	1.39930	−	2.42365i
$335$		0			0
$336$	2.05236	+	3.55479i	0.111965	+	0.193929i
$337$	−9.24507			−0.503611			−0.251805	−	0.967778i	$-0.581024\pi$
$337$	−9.24507			−0.503611			−0.251805	+	0.967778i	$0.581024\pi$
$338$	22.9912	+	24.8612i	1.25056	+	1.35227i
$339$	1.62864			0.0884558
$340$		0			0
$341$	−1.25471	−	2.17322i	−0.0679463	−	0.117686i
$342$	10.8154	−	18.7328i	0.584830	−	1.01296i
$343$	11.1306			0.600997
$344$	−6.36829	+	11.0302i	−0.343355	+	0.594708i
$345$		0			0
$346$	−18.9560			−1.01908
$347$	2.27065	−	3.93288i	0.121895	−	0.211128i	−0.798620	−	0.601836i	$-0.794436\pi$
$347$	2.27065	−	3.93288i	0.121895	−	0.211128i	0.920515	+	0.390707i	$0.127770\pi$
$348$	−2.63215	−	4.55902i	−0.141098	−	0.244389i
$349$	−10.6508	−	18.4476i	−0.570122	−	0.987480i	−0.996553	−	0.0829598i	$-0.973563\pi$
$349$	−10.6508	−	18.4476i	−0.570122	−	0.987480i	0.426431	−	0.904520i	$-0.359771\pi$
$350$		0			0
$351$	0.324364	+	2.90041i	0.0173133	+	0.154813i
$352$	3.44908			0.183837
$353$	−12.0176	−	20.8150i	−0.639631	−	1.10787i	−0.985514	−	0.169595i	$-0.945754\pi$
$353$	−12.0176	−	20.8150i	−0.639631	−	1.10787i	0.345883	−	0.938278i	$-0.387579\pi$
$354$	0.397294	+	0.688133i	0.0211159	+	0.0365738i
$355$		0			0
$356$	−34.4002			−1.82321
$357$	1.48368	−	2.56980i	0.0785245	−	0.136008i
$358$	19.3443	−	33.5053i	1.02238	−	1.77081i
$359$	3.56759			0.188290			0.0941451	−	0.995558i	$-0.469988\pi$
$359$	3.56759			0.188290			0.0941451	+	0.995558i	$0.469988\pi$
$360$		0			0
$361$	5.62174	+	9.73713i	0.295881	+	0.512481i
$362$	16.0143	+	27.7375i	0.841692	+	1.45785i
$363$	−1.47171			−0.0772448
$364$	45.1749	−	33.2828i	2.36781	−	1.74449i
$365$		0			0
$366$	1.07847	+	1.86796i	0.0563723	+	0.0976397i
$367$	−13.2523	−	22.9537i	−0.691765	−	1.19817i	−0.971259	−	0.238025i	$-0.923500\pi$
$367$	−13.2523	−	22.9537i	−0.691765	−	1.19817i	0.279494	−	0.960148i	$-0.409833\pi$
$368$	−33.1124	+	57.3524i	−1.72610	+	2.98970i
$369$	1.20473			0.0627158
$370$		0			0
$371$	−5.59945	+	9.69852i	−0.290709	+	0.503522i
$372$	4.60981			0.239008
$373$	−12.4356	+	21.5391i	−0.643891	+	1.11525i	0.340666	+	0.940185i	$0.389348\pi$
$373$	−12.4356	+	21.5391i	−0.643891	+	1.11525i	−0.984556	+	0.175067i	$0.943986\pi$
$374$	−3.09527	−	5.36116i	−0.160052	−	0.277219i
$375$		0			0
$376$	−27.2519			−1.40541
$377$	−23.5997	+	17.3872i	−1.21545	+	0.895485i
$378$	6.85738			0.352706
$379$	16.1404	+	27.9560i	0.829078	+	1.43600i	0.898763	+	0.438435i	$0.144467\pi$
$379$	16.1404	+	27.9560i	0.829078	+	1.43600i	−0.0696852	+	0.997569i	$0.522199\pi$
$380$		0			0
$381$	0.626046	−	1.08434i	0.0320733	−	0.0555526i
$382$	−4.36724			−0.223447
$383$	0.416177	−	0.720840i	0.0212657	−	0.0368332i	−0.855197	−	0.518304i	$-0.826564\pi$
$383$	0.416177	−	0.720840i	0.0212657	−	0.0368332i	0.876462	+	0.481470i	$0.159897\pi$
$384$	0.119507	−	0.206992i	0.00609857	−	0.0105630i
$385$		0			0
$386$	−3.75697	+	6.50726i	−0.191225	+	0.331211i
$387$	2.61743	+	4.53352i	0.133051	+	0.230452i
$388$	16.4423	+	28.4789i	0.834731	+	1.44580i
$389$	−36.0627			−1.82845			−0.914225	−	0.405207i	$-0.867200\pi$
$389$	−36.0627			−1.82845			−0.914225	+	0.405207i	$0.867200\pi$
$390$		0			0
$391$	47.8749			2.42114
$392$	−12.9771	−	22.4770i	−0.655442	−	1.13526i
$393$	0.101544	+	0.175880i	0.00512223	+	0.00887197i
$394$	−6.48995	+	11.2409i	−0.326959	+	0.566310i
$395$		0			0
$396$	2.51454	−	4.35532i	0.126361	−	0.218863i
$397$	3.80059	−	6.58281i	0.190746	−	0.330382i	−0.754752	−	0.656011i	$-0.772243\pi$
$397$	3.80059	−	6.58281i	0.190746	−	0.330382i	0.945498	+	0.325629i	$0.105576\pi$
$398$	59.6975			2.99236
$399$	0.612860	−	1.06151i	0.0306814	−	0.0531417i
$400$		0			0
$401$	9.66466	+	16.7397i	0.482630	+	0.835940i	0.999801	−	0.0199424i	$-0.00634828\pi$
$401$	9.66466	+	16.7397i	0.482630	+	0.835940i	−0.517171	+	0.855882i	$0.673015\pi$
$402$	−4.12874			−0.205923
$403$	−2.85284	−	25.5097i	−0.142110	−	1.27073i
$404$	−26.4291			−1.31490
$405$		0			0
$406$	34.4375	+	59.6475i	1.70911	+	2.96026i
$407$	−0.719393	+	1.24603i	−0.0356590	+	0.0617632i
$408$	6.61889			0.327684
$409$	7.79244	−	13.4969i	0.385311	−	0.667379i	−0.606501	−	0.795083i	$-0.707427\pi$
$409$	7.79244	−	13.4969i	0.385311	−	0.667379i	0.991812	+	0.127704i	$0.0407607\pi$
$410$		0			0
$411$	0.158574			0.00782190
$412$	−24.5409	+	42.5061i	−1.20904	+	2.09413i
$413$	−3.66578	−	6.34931i	−0.180381	−	0.312429i
$414$	27.5743	+	47.7601i	1.35520	+	2.34728i
$415$		0			0
$416$	32.3251	+	14.1352i	1.58487	+	0.693035i
$417$	−1.69611			−0.0830590
$418$	−1.27856	−	2.21453i	−0.0625363	−	0.108316i
$419$	12.6596	+	21.9271i	0.618463	+	1.07121i	0.989766	+	0.142698i	$0.0455778\pi$
$419$	12.6596	+	21.9271i	0.618463	+	1.07121i	−0.371303	+	0.928512i	$0.621089\pi$
$420$		0			0
$421$	−8.65115			−0.421631			−0.210816	−	0.977526i	$-0.567612\pi$
$421$	−8.65115			−0.421631			−0.210816	+	0.977526i	$0.567612\pi$
$422$	−1.63547	+	2.83272i	−0.0796135	+	0.137895i
$423$	−5.60040	+	9.70017i	−0.272301	+	0.471639i
$424$	−24.9799			−1.21313
$425$		0			0
$426$	0.302288	+	0.523578i	0.0146459	+	0.0253674i
$427$	−9.95087	−	17.2354i	−0.481556	−	0.834080i
$428$	−4.85784			−0.234813
$429$	0.157572	+	0.0689036i	0.00760766	+	0.00332670i
$430$		0			0
$431$	−6.70929	−	11.6208i	−0.323175	−	0.559756i	0.657966	−	0.753047i	$-0.271417\pi$
$431$	−6.70929	−	11.6208i	−0.323175	−	0.559756i	−0.981141	+	0.193292i	$0.938084\pi$
$432$	3.77470	+	6.53797i	0.181610	+	0.314558i
$433$	−18.0854	+	31.3248i	−0.869129	+	1.50538i	−0.00624076	+	0.999981i	$0.501987\pi$
$433$	−18.0854	+	31.3248i	−0.869129	+	1.50538i	−0.862888	+	0.505395i	$0.831347\pi$
$434$	−60.3120			−2.89507
$435$		0			0
$436$	32.5863	−	56.4411i	1.56060	−	2.70304i
$437$	19.7756			0.945995
$438$	−1.86157	+	3.22434i	−0.0889493	+	0.154065i
$439$	−16.5319	−	28.6342i	−0.789027	−	1.36663i	−0.926564	−	0.376138i	$-0.877252\pi$
$439$	−16.5319	−	28.6342i	−0.789027	−	1.36663i	0.137537	−	0.990497i	$-0.456081\pi$
$440$		0			0
$441$	−10.6674			−0.507973
$442$	−7.03774	−	62.9304i	−0.334751	−	2.99330i
$443$	−17.7778			−0.844650			−0.422325	−	0.906444i	$-0.638786\pi$
$443$	−17.7778			−0.844650			−0.422325	+	0.906444i	$0.638786\pi$
$444$	−1.32153	−	2.28895i	−0.0627170	−	0.108629i
$445$		0			0
$446$	−5.53383	+	9.58488i	−0.262035	+	0.453857i
$447$	−2.64719			−0.125208
$448$	11.1148	−	19.2514i	0.525124	−	0.909542i
$449$	15.9153	−	27.5662i	0.751091	−	1.30093i	−0.196203	−	0.980563i	$-0.562861\pi$
$449$	15.9153	−	27.5662i	0.751091	−	1.30093i	0.947294	−	0.320365i	$-0.103805\pi$
$450$		0			0
$451$	0.0712095	−	0.123338i	0.00335312	−	0.00580778i
$452$	−28.7952	−	49.8747i	−1.35441	−	2.34591i
$453$	−0.672823	−	1.16536i	−0.0316120	−	0.0547535i
$454$	−39.0926			−1.83471
$455$		0			0
$456$	2.73406			0.128034
$457$	10.9985	+	19.0500i	0.514490	+	0.891122i	0.999859	+	0.0168127i	$0.00535189\pi$
$457$	10.9985	+	19.0500i	0.514490	+	0.891122i	−0.485369	+	0.874309i	$0.661315\pi$
$458$	2.43357	+	4.21506i	0.113713	+	0.196957i
$459$	2.72878	−	4.72639i	0.127369	−	0.220609i
$460$		0			0
$461$	6.86668	−	11.8934i	0.319813	−	0.553933i	−0.660636	−	0.750707i	$-0.729713\pi$
$461$	6.86668	−	11.8934i	0.319813	−	0.553933i	0.980449	+	0.196774i	$0.0630465\pi$
$462$	0.202043	−	0.349949i	0.00939991	−	0.0162811i
$463$	7.26980			0.337856			0.168928	−	0.985628i	$-0.445969\pi$
$463$	7.26980			0.337856			0.168928	+	0.985628i	$0.445969\pi$
$464$	−37.9128	+	65.6669i	−1.76006	+	3.04851i
$465$		0			0
$466$	−19.6329	−	34.0051i	−0.909476	−	1.57526i
$467$	30.9639			1.43284			0.716418	−	0.697671i	$-0.245780\pi$
$467$	30.9639			1.43284			0.716418	+	0.697671i	$0.245780\pi$
$468$	41.4157	−	30.5132i	1.91444	−	1.41047i
$469$	38.0954			1.75908
$470$		0			0
$471$	−0.447182	−	0.774542i	−0.0206051	−	0.0356890i
$472$	8.17677	−	14.1626i	0.376366	−	0.651886i
$473$	0.618846			0.0284545
$474$	−1.51921	+	2.63135i	−0.0697797	+	0.120862i
$475$		0			0
$476$	−104.928			−4.80938
$477$	−5.13349	+	8.89147i	−0.235046	+	0.407112i
$478$	−28.9476	−	50.1386i	−1.32403	−	2.29329i
$479$	4.12407	+	7.14310i	0.188434	+	0.326377i	0.944728	−	0.327855i	$-0.106326\pi$
$479$	4.12407	+	7.14310i	0.188434	+	0.326377i	−0.756294	+	0.654231i	$0.772992\pi$
$480$		0			0
$481$	−11.8487	+	8.72961i	−0.540256	+	0.398036i
$482$	−13.8683			−0.631685
$483$	1.56251	+	2.70635i	0.0710968	+	0.123143i
$484$	26.0205	+	45.0689i	1.18275	+	2.04859i
$485$		0			0
$486$	9.43974			0.428195
$487$	14.8995	−	25.8068i	0.675163	−	1.16942i	−0.301258	−	0.953543i	$-0.597407\pi$
$487$	14.8995	−	25.8068i	0.675163	−	1.16942i	0.976421	−	0.215874i	$-0.0692600\pi$
$488$	22.1961	−	38.4448i	1.00477	−	1.74031i
$489$	1.03269			0.0466997
$490$		0			0
$491$	−19.1828	−	33.2256i	−0.865709	−	1.49945i	−0.866342	−	0.499451i	$-0.833535\pi$
$491$	−19.1828	−	33.2256i	−0.865709	−	1.49945i	0.000633368	−	1.00000i	$-0.499798\pi$
$492$	0.130812	+	0.226573i	0.00589746	+	0.0102147i
$493$	54.8153			2.46876
$494$	−2.90707	−	25.9946i	−0.130795	−	1.16955i
$495$		0			0
$496$	−33.1992	−	57.5027i	−1.49069	−	2.58195i
$497$	−2.78917	−	4.83099i	−0.125111	−	0.216699i
$498$	−1.37791	+	2.38662i	−0.0617458	+	0.106947i
$499$	−29.9843			−1.34228			−0.671141	−	0.741329i	$-0.734196\pi$
$499$	−29.9843			−1.34228			−0.671141	+	0.741329i	$0.734196\pi$
$500$		0			0
$501$	1.32852	−	2.30107i	0.0593541	−	0.102804i
$502$	54.2586			2.42168
$503$	14.0174	−	24.2788i	0.625003	−	1.08254i	−0.363537	−	0.931580i	$-0.618431\pi$
$503$	14.0174	−	24.2788i	0.625003	−	1.08254i	0.988540	−	0.150958i	$-0.0482357\pi$
$504$	−35.1752	−	60.9253i	−1.56683	−	2.71383i
$505$		0			0
$506$	6.51948			0.289826
$507$	1.19440	+	1.29154i	0.0530450	+	0.0573594i
$508$	−44.2751			−1.96439
$509$	19.2106	+	33.2737i	0.851495	+	1.47483i	0.879859	+	0.475235i	$0.157637\pi$
$509$	19.2106	+	33.2737i	0.851495	+	1.47483i	−0.0283637	+	0.999598i	$0.509030\pi$
$510$		0			0
$511$	17.1765	−	29.7505i	0.759843	−	1.31609i
$512$	−44.0594			−1.94717
$513$	1.12717	−	1.95232i	0.0497659	−	0.0861971i
$514$	−20.7596	+	35.9568i	−0.915669	+	1.58598i
$515$		0			0
$516$	−0.568411	+	0.984517i	−0.0250229	+	0.0433409i
$517$	0.662059	+	1.14672i	0.0291173	+	0.0504327i
$518$	17.2901	+	29.9473i	0.759683	+	1.31581i
$519$	−0.984767			−0.0432265
$520$		0			0
$521$	−0.893030			−0.0391243			−0.0195622	−	0.999809i	$-0.506227\pi$
$521$	−0.893030			−0.0391243			−0.0195622	+	0.999809i	$0.506227\pi$
$522$	31.5718	+	54.6840i	1.38186	+	2.39345i
$523$	5.11256	+	8.85522i	0.223557	+	0.387212i	0.955885	−	0.293740i	$-0.0948999\pi$
$523$	5.11256	+	8.85522i	0.223557	+	0.387212i	−0.732329	+	0.680951i	$0.761567\pi$
$524$	3.59070	−	6.21928i	0.156860	−	0.271690i
$525$		0			0
$526$	23.0531	−	39.9292i	1.00516	−	1.74100i
$527$	−24.0002	+	41.5695i	−1.04546	+	1.81080i
$528$	0.444865			0.0193603
$529$	−13.7094	+	23.7453i	−0.596060	+	1.03241i
$530$		0			0
$531$	−3.36073	−	5.82096i	−0.145843	−	0.252608i
$532$	−43.3426			−1.87914
$533$	1.17285	−	0.864104i	0.0508019	−	0.0374285i
$534$	−2.53405			−0.109659
$535$		0			0
$536$	42.4872	+	73.5900i	1.83517	+	3.17861i
$537$	1.00494	−	1.74060i	0.0433663	−	0.0751126i
$538$	−3.93737			−0.169752
$539$	−0.630532	+	1.09211i	−0.0271589	+	0.0470407i
$540$		0			0
$541$	−15.4261			−0.663219			−0.331609	−	0.943417i	$-0.607592\pi$
$541$	−15.4261			−0.663219			−0.331609	+	0.943417i	$0.607592\pi$
$542$	35.5560	−	61.5848i	1.52726	−	2.64529i
$543$	0.831944	+	1.44097i	0.0357021	+	0.0618379i
$544$	−32.9871	−	57.1354i	−1.41431	−	2.44966i
$545$		0			0
$546$	3.32775	−	2.45173i	0.142414	−	0.104924i
$547$	10.7393			0.459177			0.229589	−	0.973288i	$-0.426262\pi$
$547$	10.7393			0.459177			0.229589	+	0.973288i	$0.426262\pi$
$548$	−2.80367	−	4.85610i	−0.119767	−	0.207442i
$549$	−9.12281	−	15.8012i	−0.389352	−	0.674378i
$550$		0			0
$551$	22.6425			0.964603
$552$	−3.48530	+	6.03671i	−0.148344	+	0.256939i
$553$	14.0176	−	24.2792i	0.596088	−	1.03245i
$554$	6.83353			0.290329
$555$		0			0
$556$	29.9880	+	51.9408i	1.27178	+	2.20278i
$557$	−9.25021	−	16.0218i	−0.391944	−	0.678867i	0.600762	−	0.799428i	$-0.294864\pi$
$557$	−9.25021	−	16.0218i	−0.391944	−	0.678867i	−0.992706	+	0.120561i	$0.961531\pi$
$558$	−55.2932			−2.34075
$559$	5.79988	+	2.53618i	0.245309	+	0.107269i
$560$		0			0
$561$	−0.160800	−	0.278513i	−0.00678896	−	0.0117588i
$562$	−11.7057	−	20.2749i	−0.493775	−	0.855244i
$563$	−19.9411	+	34.5389i	−0.840415	+	1.45564i	0.0491288	+	0.998792i	$0.484356\pi$
$563$	−19.9411	+	34.5389i	−0.840415	+	1.45564i	−0.889544	+	0.456849i	$0.848978\pi$
$564$	−2.43241			−0.102423
$565$		0			0
$566$	−30.5274	+	52.8749i	−1.28316	+	2.22250i
$567$	−28.7361			−1.20680
$568$	6.22144	−	10.7759i	0.261046	−	0.452145i
$569$	−0.385811	−	0.668245i	−0.0161741	−	0.0280143i	0.857825	−	0.513942i	$-0.171815\pi$
$569$	−0.385811	−	0.668245i	−0.0161741	−	0.0280143i	−0.873999	+	0.485927i	$0.838482\pi$
$570$		0			0
$571$	−30.1208			−1.26052			−0.630259	−	0.776385i	$-0.717051\pi$
$571$	−30.1208			−1.26052			−0.630259	+	0.776385i	$0.717051\pi$
$572$	−0.675884	−	6.04365i	−0.0282601	−	0.252698i
$573$	−0.226878			−0.00947798
$574$	−1.71147	−	2.96435i	−0.0714353	−	0.123730i
$575$		0			0
$576$	10.1899	−	17.6494i	0.424578	−	0.735391i
$577$	15.2295			0.634014			0.317007	−	0.948423i	$-0.397322\pi$
$577$	15.2295			0.634014			0.317007	+	0.948423i	$0.397322\pi$
$578$	−37.0656	+	64.1995i	−1.54173	+	2.67035i
$579$	−0.195175	+	0.338053i	−0.00811119	+	0.0140490i
$580$		0			0
$581$	12.7138	−	22.0210i	0.527459	−	0.913586i
$582$	1.21120	+	2.09786i	0.0502058	+	0.0869590i
$583$	0.606863	+	1.05112i	0.0251337	+	0.0435328i
$584$	76.6267			3.17083
$585$		0			0
$586$	−3.06499			−0.126614
$587$	19.9117	+	34.4881i	0.821845	+	1.42348i	0.904307	+	0.426884i	$0.140389\pi$
$587$	19.9117	+	34.4881i	0.821845	+	1.42348i	−0.0824611	+	0.996594i	$0.526278\pi$
$588$	−1.15829	−	2.00622i	−0.0477671	−	0.0827350i
$589$	−9.91372	+	17.1711i	−0.408488	+	0.707521i
$590$		0			0
$591$	−0.337154	+	0.583968i	−0.0138687	+	0.0240212i
$592$	−19.0349	+	32.9695i	−0.782331	+	1.35504i
$593$	−7.45086			−0.305970			−0.152985	−	0.988229i	$-0.548889\pi$
$593$	−7.45086			−0.305970			−0.152985	+	0.988229i	$0.548889\pi$
$594$	0.371598	−	0.643627i	0.0152469	−	0.0264083i
$595$		0			0
$596$	46.8036	+	81.0662i	1.91715	+	3.32060i
$597$	3.10129			0.126927
$598$	61.1011	+	26.7184i	2.49861	+	1.09260i
$599$	9.61411			0.392822			0.196411	−	0.980522i	$-0.437071\pi$
$599$	9.61411			0.392822			0.196411	+	0.980522i	$0.437071\pi$
$600$		0			0
$601$	2.75437	+	4.77070i	0.112353	+	0.194601i	0.916719	−	0.399534i	$-0.130828\pi$
$601$	2.75437	+	4.77070i	0.112353	+	0.194601i	−0.804366	+	0.594135i	$0.797495\pi$
$602$	7.43675	−	12.8808i	0.303099	−	0.524984i
$603$	34.9253			1.42227
$604$	−23.7916	+	41.2083i	−0.968068	+	1.67674i
$605$		0			0
$606$	−1.94687			−0.0790861
$607$	−15.1939	+	26.3166i	−0.616702	+	1.06816i	0.373381	+	0.927678i	$0.378198\pi$
$607$	−15.1939	+	26.3166i	−0.616702	+	1.06816i	−0.990083	+	0.140481i	$0.955135\pi$
$608$	−13.6260	−	23.6008i	−0.552605	−	0.957141i
$609$	1.78903	+	3.09870i	0.0724953	+	0.125566i
$610$		0			0
$611$	1.50533	+	13.4604i	0.0608991	+	0.544551i
$612$	−96.1968			−3.88852
$613$	16.2506	+	28.1469i	0.656357	+	1.13684i	0.981552	+	0.191196i	$0.0612367\pi$
$613$	16.2506	+	28.1469i	0.656357	+	1.13684i	−0.325195	+	0.945647i	$0.605430\pi$
$614$	−21.6395	−	37.4807i	−0.873299	−	1.51260i
$615$		0			0
$616$	−8.31658			−0.335085
$617$	−3.79833	+	6.57890i	−0.152915	+	0.264856i	−0.932298	−	0.361691i	$-0.882199\pi$
$617$	−3.79833	+	6.57890i	−0.152915	+	0.264856i	0.779383	+	0.626548i	$0.215533\pi$
$618$	−1.80777	+	3.13116i	−0.0727193	+	0.125954i
$619$	35.4509			1.42489			0.712445	−	0.701728i	$-0.247588\pi$
$619$	35.4509			1.42489			0.712445	+	0.701728i	$0.247588\pi$
$620$		0			0
$621$	2.87378	+	4.97753i	0.115321	+	0.199741i
$622$	19.1622	+	33.1899i	0.768335	+	1.33080i
$623$	23.3813			0.936752
$624$	4.16932	+	1.82317i	0.166906	+	0.0729852i
$625$		0			0
$626$	−2.42495	−	4.20014i	−0.0969206	−	0.167871i
$627$	−0.0664212	−	0.115045i	−0.00265261	−	0.00459445i
$628$	−15.8128	+	27.3885i	−0.630998	+	1.09292i
$629$	27.5212			1.09734
$630$		0			0
$631$	3.20395	−	5.54940i	0.127547	−	0.220918i	−0.795179	−	0.606375i	$-0.792623\pi$
$631$	3.20395	−	5.54940i	0.127547	−	0.220918i	0.922726	+	0.385457i	$0.125956\pi$
$632$	62.5344			2.48748
$633$	−0.0849629	+	0.147160i	−0.00337697	+	0.00584909i
$634$	18.2091	+	31.5391i	0.723176	+	1.25258i
$635$		0			0
$636$	−2.22962			−0.0884102
$637$	−10.3852	+	7.65131i	−0.411475	+	0.303156i
$638$	7.46461			0.295527
$639$	−2.55707	−	4.42898i	−0.101156	−	0.175208i
$640$		0			0
$641$	−2.63046	+	4.55610i	−0.103897	+	0.179955i	−0.913287	−	0.407317i	$-0.866465\pi$
$641$	−2.63046	+	4.55610i	−0.103897	+	0.179955i	0.809390	+	0.587272i	$0.199798\pi$
$642$	−0.357846			−0.0141231
$643$	−3.77459	+	6.53778i	−0.148855	+	0.257825i	−0.930805	−	0.365517i	$-0.880892\pi$
$643$	−3.77459	+	6.53778i	−0.148855	+	0.257825i	0.781949	+	0.623342i	$0.214226\pi$
$644$	55.2519	−	95.6991i	2.17723	−	3.77107i
$645$		0			0
$646$	−24.4564	+	42.3597i	−0.962223	+	1.66662i
$647$	−5.77316	−	9.99940i	−0.226966	−	0.393117i	0.729941	−	0.683510i	$-0.239547\pi$
$647$	−5.77316	−	9.99940i	−0.226966	−	0.393117i	−0.956908	+	0.290393i	$0.906214\pi$
$648$	−32.0489	−	55.5103i	−1.25900	−	2.18065i
$649$	−0.794587			−0.0311903
$650$		0			0
$651$	−3.13322			−0.122801
$652$	−18.2584	−	31.6245i	−0.715054	−	1.23851i
$653$	10.9418	+	18.9517i	0.428185	+	0.741639i	0.996712	−	0.0810263i	$-0.0258198\pi$
$653$	10.9418	+	18.9517i	0.428185	+	0.741639i	−0.568527	+	0.822665i	$0.692486\pi$
$654$	2.40042	−	4.15766i	0.0938640	−	0.162577i
$655$		0			0
$656$	1.88418	−	3.26350i	0.0735649	−	0.127418i
$657$	15.7471	−	27.2749i	0.614355	−	1.06409i
$658$	31.8242			1.24064
$659$	16.8561	−	29.1957i	0.656622	−	1.13730i	−0.324862	−	0.945761i	$-0.605318\pi$
$659$	16.8561	−	29.1957i	0.656622	−	1.13730i	0.981485	−	0.191542i	$-0.0613487\pi$
$660$		0			0
$661$	−22.3781	−	38.7599i	−0.870405	−	1.50759i	−0.861578	−	0.507625i	$-0.830523\pi$
$661$	−22.3781	−	38.7599i	−0.870405	−	1.50759i	−0.00882737	−	0.999961i	$-0.502810\pi$
$662$	37.2625			1.44825
$663$	−0.365612	−	3.26925i	−0.0141992	−	0.126967i
$664$	56.7182			2.20109
$665$		0			0
$666$	15.8513	+	27.4553i	0.614226	+	1.06387i
$667$	−28.8640	+	49.9939i	−1.11762	+	1.93577i
$668$	−93.9557			−3.63525
$669$	−0.287483	+	0.497936i	−0.0111148	+	0.0192513i
$670$		0			0
$671$	−2.15693			−0.0832675
$672$	2.15323	−	3.72951i	0.0830628	−	0.143869i
$673$	−6.04859	−	10.4765i	−0.233156	−	0.403838i	0.725579	−	0.688139i	$-0.241572\pi$
$673$	−6.04859	−	10.4765i	−0.233156	−	0.403838i	−0.958735	+	0.284301i	$0.908239\pi$
$674$	12.0408	+	20.8553i	0.463796	+	0.803318i
$675$		0			0
$676$	18.4340	−	59.4116i	0.708999	−	2.28506i
$677$	23.3796			0.898549			0.449275	−	0.893394i	$-0.351682\pi$
$677$	23.3796			0.898549			0.449275	+	0.893394i	$0.351682\pi$
$678$	−2.12116	−	3.67395i	−0.0814626	−	0.141097i
$679$	−11.1756	−	19.3567i	−0.428879	−	0.742841i
$680$		0			0
$681$	−2.03087			−0.0778230
$682$	−3.26828	+	5.66083i	−0.125149	+	0.216764i
$683$	−3.81319	+	6.60464i	−0.145908	+	0.252719i	−0.929711	−	0.368289i	$-0.879944\pi$
$683$	−3.81319	+	6.60464i	−0.145908	+	0.252719i	0.783804	+	0.621009i	$0.213277\pi$
$684$	−39.7359			−1.51934
$685$		0			0
$686$	−14.4966	−	25.1088i	−0.553483	−	0.958660i
$687$	0.126424	+	0.218973i	0.00482338	+	0.00835434i
$688$	16.3745			0.624271
$689$	1.37983	+	12.3382i	0.0525674	+	0.470050i
$690$		0			0
$691$	−10.8125	−	18.7278i	−0.411328	−	0.712440i	0.583707	−	0.811964i	$-0.301601\pi$
$691$	−10.8125	−	18.7278i	−0.411328	−	0.712440i	−0.995035	+	0.0995235i	$0.968268\pi$
$692$	17.4111	+	30.1570i	0.661872	+	1.14640i
$693$	−1.70910	+	2.96024i	−0.0649232	+	0.112450i
$694$	−11.8292			−0.449032
$695$		0			0
$696$	−3.99056	+	6.91186i	−0.151262	+	0.261993i
$697$	−2.72420			−0.103186
$698$	−27.7432	+	48.0527i	−1.05010	+	1.81882i
$699$	−1.01993	−	1.76657i	−0.0385773	−	0.0668179i
$700$		0			0
$701$	15.9225			0.601386			0.300693	−	0.953721i	$-0.402782\pi$
$701$	15.9225			0.601386			0.300693	+	0.953721i	$0.402782\pi$
$702$	6.12040	−	4.50923i	0.231000	−	0.170190i
$703$	11.3682			0.428758
$704$	−1.20461	−	2.08645i	−0.0454005	−	0.0786359i
$705$		0			0
$706$	−31.3035	+	54.2193i	−1.17812	+	2.04057i
$707$	17.9635			0.675587
$708$	0.729830	−	1.26410i	0.0274287	−	0.0475079i
$709$	−8.24352	+	14.2782i	−0.309592	+	0.536229i	−0.978273	−	0.207320i	$-0.933526\pi$
$709$	−8.24352	+	14.2782i	−0.309592	+	0.536229i	0.668681	+	0.743549i	$0.266859\pi$
$710$		0			0
$711$	12.8511	−	22.2588i	0.481954	−	0.834770i
$712$	26.0768	+	45.1664i	0.977270	+	1.69268i
$713$	−25.2754	−	43.7784i	−0.946573	−	1.63951i
$714$	−7.72940			−0.289266
$715$		0			0
$716$	−71.0711			−2.65605
$717$	−1.50383	−	2.60471i	−0.0561615	−	0.0972746i
$718$	−4.64645	−	8.04789i	−0.173404	−	0.300345i
$719$	−3.59455	+	6.22594i	−0.134054	+	0.232188i	−0.925236	−	0.379393i	$-0.876133\pi$
$719$	−3.59455	+	6.22594i	−0.134054	+	0.232188i	0.791182	+	0.611581i	$0.209466\pi$
$720$		0			0
$721$	16.6801	−	28.8908i	0.621199	−	1.07595i
$722$	14.6436	−	25.3634i	0.544977	−	0.943929i
$723$	−0.720462			−0.0267943
$724$	29.4183	−	50.9540i	1.09332	−	1.89369i
$725$		0			0
$726$	1.91677	+	3.31994i	0.0711379	+	0.123214i
$727$	−23.2523			−0.862380			−0.431190	−	0.902261i	$-0.641906\pi$
$727$	−23.2523			−0.862380			−0.431190	+	0.902261i	$0.641906\pi$
$728$	−77.9437	−	34.0834i	−2.88879	−	1.26322i
$729$	−26.0162			−0.963563
$730$		0			0
$731$	−5.91866	−	10.2514i	−0.218910	−	0.379163i
$732$	1.98115	−	3.43145i	0.0732253	−	0.126830i
$733$	−14.5437			−0.537184			−0.268592	−	0.963254i	$-0.586558\pi$
$733$	−14.5437			−0.537184			−0.268592	+	0.963254i	$0.586558\pi$
$734$	−34.5198	+	59.7901i	−1.27415	+	2.20689i
$735$		0			0
$736$	69.4799			2.56106
$737$	2.06437	−	3.57560i	0.0760421	−	0.131709i
$738$	−1.56905	−	2.71767i	−0.0577575	−	0.100039i
$739$	−14.2972	−	24.7635i	−0.525931	−	0.910940i	−0.999544	−	0.0302064i	$-0.990384\pi$
$739$	−14.2972	−	24.7635i	−0.525931	−	0.910940i	0.473612	−	0.880733i	$-0.342950\pi$
$740$		0			0
$741$	−0.151023	−	1.35042i	−0.00554796	−	0.0496090i
$742$	29.1710			1.07090
$743$	1.10527	+	1.91439i	0.0405486	+	0.0702322i	0.885587	−	0.464473i	$-0.153756\pi$
$743$	1.10527	+	1.91439i	0.0405486	+	0.0702322i	−0.845039	+	0.534705i	$0.820423\pi$
$744$	−3.49443	−	6.05253i	−0.128112	−	0.221897i
$745$		0			0
$746$	64.7848			2.37194
$747$	11.6559	−	20.1886i	0.426466	−	0.738661i
$748$	−5.68602	+	9.84847i	−0.207901	+	0.360096i
$749$	3.30180			0.120645
$750$		0			0
$751$	10.1966	+	17.6610i	0.372078	+	0.644458i	0.989885	−	0.141872i	$-0.0453121\pi$
$751$	10.1966	+	17.6610i	0.372078	+	0.644458i	−0.617807	+	0.786330i	$0.711979\pi$
$752$	17.5179	+	30.3419i	0.638811	+	1.10645i
$753$	2.81874			0.102721
$754$	69.9590	+	30.5919i	2.54776	+	1.11409i
$755$		0			0
$756$	−6.29852	−	10.9094i	−0.229075	−	0.396769i
$757$	17.4224	+	30.1764i	0.633227	+	1.09678i	0.986888	+	0.161408i	$0.0516034\pi$
$757$	17.4224	+	30.1764i	0.633227	+	1.09678i	−0.353661	+	0.935374i	$0.615063\pi$
$758$	42.0428	−	72.8202i	1.52706	−	2.64495i
$759$	0.338688			0.0122936
$760$		0			0
$761$	23.0535	−	39.9298i	0.835689	−	1.44746i	−0.0577800	−	0.998329i	$-0.518402\pi$
$761$	23.0535	−	39.9298i	0.835689	−	1.44746i	0.893469	−	0.449126i	$-0.148264\pi$
$762$	−3.26146			−0.118150
$763$	−22.1484	+	38.3622i	−0.801826	+	1.38880i
$764$	4.01132	+	6.94780i	0.145124	+	0.251363i
$765$		0			0
$766$	−2.16813			−0.0783377
$767$	−7.44694	−	3.25642i	−0.268894	−	0.117582i
$768$	−2.47241			−0.0892154
$769$	1.02903	+	1.78233i	0.0371077	+	0.0642725i	0.883983	−	0.467519i	$-0.154852\pi$
$769$	1.02903	+	1.78233i	0.0371077	+	0.0642725i	−0.846875	+	0.531792i	$0.821519\pi$
$770$		0			0
$771$	−1.07847	+	1.86796i	−0.0388400	+	0.0672729i
$772$	13.8031			0.496785
$773$	17.7036	−	30.6635i	0.636754	−	1.10289i	−0.349387	−	0.936979i	$-0.613610\pi$
$773$	17.7036	−	30.6635i	0.636754	−	1.10289i	0.986141	−	0.165912i	$-0.0530566\pi$
$774$	6.81791	−	11.8090i	0.245065	−	0.424464i
$775$		0			0
$776$	24.9279	−	43.1764i	0.894860	−	1.54994i
$777$	0.898223	+	1.55577i	0.0322236	+	0.0558129i
$778$	46.9683	+	81.3514i	1.68389	+	2.91659i
$779$	−1.12528			−0.0403174
$780$		0			0
$781$	−0.604576			−0.0216334
$782$	−62.3525	−	107.998i	−2.22972	−	3.86199i
$783$	3.29039	+	5.69913i	0.117589	+	0.203670i
$784$	−16.6837	+	28.8970i	−0.595846	+	1.03204i
$785$		0			0
$786$	0.264504	−	0.458134i	0.00943455	−	0.0163411i
$787$	9.46456	−	16.3931i	0.337375	−	0.584351i	−0.646563	−	0.762860i	$-0.723794\pi$
$787$	9.46456	−	16.3931i	0.337375	−	0.584351i	0.983938	+	0.178510i	$0.0571277\pi$
$788$	23.8441			0.849413
$789$	1.19761	−	2.07433i	0.0426362	−	0.0738480i
$790$		0			0
$791$	19.5716	+	33.8991i	0.695888	+	1.20531i
$792$	−7.62452			−0.270926
$793$	−20.2150	−	8.83965i	−0.717854	−	0.313905i
$794$	−19.7996			−0.702663
$795$		0			0
$796$	−54.8323	−	94.9723i	−1.94348	−	3.36620i
$797$	−8.07586	+	13.9878i	−0.286062	+	0.495473i	−0.972866	−	0.231369i	$-0.925680\pi$
$797$	−8.07586	+	13.9878i	−0.286062	+	0.495473i	0.686805	+	0.726842i	$0.259013\pi$
$798$	−3.19277			−0.113023
$799$	12.6639	−	21.9345i	0.448017	−	0.775988i
$800$		0			0
$801$	21.4356			0.757391
$802$	25.1746	−	43.6037i	0.888947	−	1.53970i
$803$	−1.86157	−	3.22434i	−0.0656934	−	0.113784i
$804$	3.79226	+	6.56839i	0.133743	+	0.231649i
$805$		0			0
$806$	−53.8301	+	39.6596i	−1.89609	+	1.39695i
$807$	−0.204547			−0.00720038
$808$	20.0344	+	34.7006i	0.704808	+	1.22076i
$809$	11.4370	+	19.8095i	0.402104	+	0.696465i	0.993980	−	0.109565i	$-0.0349457\pi$
$809$	11.4370	+	19.8095i	0.402104	+	0.696465i	−0.591876	+	0.806029i	$0.701612\pi$
$810$		0			0
$811$	−53.7279			−1.88664			−0.943321	−	0.331882i	$-0.892316\pi$
$811$	−53.7279			−1.88664			−0.943321	+	0.331882i	$0.892316\pi$
$812$	63.2619	−	109.573i	2.22006	−	3.84525i
$813$	1.84714	−	3.19934i	0.0647820	−	0.112206i
$814$	3.74777			0.131359
$815$		0			0
$816$	−4.25471	−	7.36937i	−0.148945	−	0.257980i
$817$	−2.44481	−	4.23454i	−0.0855332	−	0.148148i
$818$	−40.5957			−1.41940
$819$	−28.1496	+	20.7394i	−0.983628	+	0.724692i
$820$		0			0
$821$	14.4717	+	25.0657i	0.505066	+	0.874800i	0.999983	+	0.00585988i	$0.00186527\pi$
$821$	14.4717	+	25.0657i	0.505066	+	0.874800i	−0.494917	+	0.868940i	$0.664801\pi$
$822$	−0.206528	−	0.357718i	−0.00720351	−	0.0124768i
$823$	20.8724	−	36.1520i	0.727565	−	1.26018i	−0.230345	−	0.973109i	$-0.573986\pi$
$823$	20.8724	−	36.1520i	0.727565	−	1.26018i	0.957910	−	0.287070i	$-0.0926811\pi$
$824$	74.4123			2.59227
$825$		0			0
$826$	−9.54867	+	16.5388i	−0.332241	+	0.575458i
$827$	11.5286			0.400888			0.200444	−	0.979705i	$-0.435761\pi$
$827$	11.5286			0.400888			0.200444	+	0.979705i	$0.435761\pi$
$828$	50.6542	−	87.7356i	1.76035	−	3.04902i
$829$	14.4032	+	24.9471i	0.500244	+	0.866448i	1.00000		0.000281967i	$8.97530e-5\pi$
$829$	14.4032	+	24.9471i	0.500244	+	0.866448i	−0.499756	+	0.866166i	$0.666577\pi$
$830$		0			0
$831$	0.355003			0.0123149
$832$	−2.73894	−	24.4912i	−0.0949555	−	0.849078i
$833$	24.1217			0.835769
$834$	2.20903	+	3.82615i	0.0764924	+	0.132489i
$835$		0			0
$836$	−2.34872	+	4.06810i	−0.0812320	+	0.140698i
$837$	−5.76262			−0.199185
$838$	32.9760	−	57.1161i	1.13914	−	1.97304i
$839$	−9.38900	+	16.2622i	−0.324144	+	0.561434i	−0.981339	−	0.192287i	$-0.938410\pi$
$839$	−9.38900	+	16.2622i	−0.324144	+	0.561434i	0.657195	+	0.753721i	$0.271743\pi$
$840$		0			0
$841$	−18.5485	+	32.1269i	−0.639602	+	1.10782i
$842$	11.2673	+	19.5156i	0.388298	+	0.672551i
$843$	−0.608113	−	1.05328i	−0.0209445	−	0.0362770i
$844$	6.00873			0.206829
$845$		0			0
$846$	29.1760			1.00309
$847$	−17.6858	−	30.6326i	−0.607690	−	1.05255i
$848$	16.0574	+	27.8123i	0.551414	+	0.955077i
$849$	−1.58590	+	2.74686i	−0.0544280	+	0.0942720i
$850$		0			0
$851$	−14.4918	+	25.1005i	−0.496773	+	0.860435i
$852$	0.555304	−	0.961815i	0.0190244	−	0.0329512i
$853$	−26.7981			−0.917550			−0.458775	−	0.888553i	$-0.651712\pi$
$853$	−26.7981			−0.917550			−0.458775	+	0.888553i	$0.651712\pi$
$854$	−25.9202	+	44.8950i	−0.886970	+	1.53628i
$855$		0			0
$856$	3.68245	+	6.37819i	0.125864	+	0.218002i
$857$	−5.34675			−0.182641			−0.0913207	−	0.995822i	$-0.529109\pi$
$857$	−5.34675			−0.182641			−0.0913207	+	0.995822i	$0.529109\pi$
$858$	−0.0497881	−	0.445197i	−0.00169974	−	0.0151988i
$859$	−28.4574			−0.970954			−0.485477	−	0.874249i	$-0.661354\pi$
$859$	−28.4574			−0.970954			−0.485477	+	0.874249i	$0.661354\pi$
$860$		0			0
$861$	−0.0889110	−	0.153998i	−0.00303008	−	0.00524825i
$862$	−17.4764	+	30.2701i	−0.595250	+	1.03100i
$863$	12.2695			0.417659			0.208830	−	0.977952i	$-0.433035\pi$
$863$	12.2695			0.417659			0.208830	+	0.977952i	$0.433035\pi$
$864$	3.96023	−	6.85932i	0.134730	−	0.233359i
$865$		0			0
$866$	94.2182			3.20166
$867$	−1.92556	+	3.33517i	−0.0653956	+	0.113268i
$868$	55.3967	+	95.9500i	1.88029	+	3.25675i
$869$	−1.51921	−	2.63135i	−0.0515358	−	0.0892625i
$870$		0			0
$871$	34.0012	−	25.0505i	1.15209	−	0.848804i
$872$	−98.8071			−3.34603
$873$	−10.2456	−	17.7459i	−0.346761	−	0.600608i
$874$	−25.7559	−	44.6105i	−0.871206	−	1.50897i
$875$		0			0
$876$	6.83943			0.231083
$877$	−23.5508	+	40.7912i	−0.795255	+	1.37742i	0.127422	+	0.991849i	$0.459330\pi$
$877$	−23.5508	+	40.7912i	−0.795255	+	1.37742i	−0.922677	+	0.385573i	$0.874004\pi$
$878$	−43.0626	+	74.5867i	−1.45329	+	2.51718i
$879$	−0.159227			−0.00537058
$880$		0			0
$881$	7.11197	+	12.3183i	0.239608	+	0.415014i	0.960602	−	0.277928i	$-0.0896476\pi$
$881$	7.11197	+	12.3183i	0.239608	+	0.415014i	−0.720994	+	0.692942i	$0.756314\pi$
$882$	13.8933	+	24.0639i	0.467813	+	0.810275i
$883$	−8.05745			−0.271155			−0.135577	−	0.990767i	$-0.543289\pi$
$883$	−8.05745			−0.271155			−0.135577	+	0.990767i	$0.543289\pi$
$884$	−93.6514	+	68.9980i	−3.14984	+	2.32066i
$885$		0			0
$886$	23.1540	+	40.1039i	0.777873	+	1.34732i
$887$	−14.3419	−	24.8408i	−0.481552	−	0.834073i	0.518223	−	0.855245i	$-0.326594\pi$
$887$	−14.3419	−	24.8408i	−0.481552	−	0.834073i	−0.999776	+	0.0211719i	$0.993260\pi$
$888$	−2.00355	+	3.47025i	−0.0672347	+	0.116454i
$889$	30.0931			1.00929
$890$		0			0
$891$	−1.55719	+	2.69714i	−0.0521680	+	0.0903575i
$892$	20.3314			0.680744
$893$	5.23107	−	9.06047i	0.175051	−	0.303197i
$894$	3.44772	+	5.97163i	0.115309	+	0.199721i
$895$		0			0
$896$	5.74453			0.191911
$897$	3.17421	+	1.38803i	0.105984	+	0.0463449i
$898$	−82.9130			−2.76684
$899$	−28.9397	−	50.1250i	−0.965192	−	1.67176i
$900$		0			0
$901$	11.6081	−	20.1059i	0.386723	−	0.669823i
$902$	−0.370975			−0.0123521
$903$	0.386340	−	0.669161i	0.0128566	−	0.0222683i
$904$	−43.6559	+	75.6143i	−1.45197	+	2.51489i
$905$		0			0
$906$	−1.75258	+	3.03555i	−0.0582255	+	0.100850i
$907$	−14.4414	−	25.0133i	−0.479520	−	0.830553i	0.520204	−	0.854042i	$-0.325856\pi$
$907$	−14.4414	−	25.0133i	−0.479520	−	0.830553i	−0.999724	+	0.0234890i	$0.992523\pi$
$908$	35.9067	+	62.1921i	1.19160	+	2.06392i
$909$	16.4687			0.546231
$910$		0			0
$911$	−24.3270			−0.805991			−0.402995	−	0.915202i	$-0.632031\pi$
$911$	−24.3270			−0.805991			−0.402995	+	0.915202i	$0.632031\pi$
$912$	−1.75749	−	3.04406i	−0.0581962	−	0.100799i
$913$	−1.37791	−	2.38662i	−0.0456023	−	0.0789855i
$914$	28.6491	−	49.6217i	0.947629	−	1.64134i
$915$		0			0
$916$	4.47048	−	7.74309i	0.147709	−	0.255839i
$917$	−2.44054	+	4.22715i	−0.0805939	+	0.139593i
$918$	−14.2159			−0.469196
$919$	5.86947	−	10.1662i	0.193616	−	0.335353i	−0.752830	−	0.658215i	$-0.771312\pi$
$919$	5.86947	−	10.1662i	0.193616	−	0.335353i	0.946446	+	0.322862i	$0.104645\pi$
$920$		0			0
$921$	−1.12417	−	1.94713i	−0.0370428	−	0.0641600i
$922$	−35.7728			−1.17812
$923$	−5.66614	−	2.47770i	−0.186503	−	0.0815546i
$924$	−0.742309			−0.0244202
$925$		0			0
$926$	−9.46823	−	16.3995i	−0.311145	−	0.538920i
$927$	15.2921	−	26.4866i	0.502258	−	0.869936i
$928$	79.5525			2.61144
$929$	21.6632	−	37.5218i	0.710746	−	1.23105i	−0.253831	−	0.967249i	$-0.581691\pi$
$929$	21.6632	−	37.5218i	0.710746	−	1.23105i	0.964577	−	0.263800i	$-0.0849760\pi$
$930$		0			0
$931$	9.96394			0.326555
$932$	−36.0657	+	62.4676i	−1.18137	+	2.04619i
$933$	0.995480	+	1.72422i	0.0325905	+	0.0564485i
$934$	−40.3275	−	69.8493i	−1.31956	−	2.28554i
$935$		0			0
$936$	−71.4577	−	31.2472i	−2.33567	−	1.02135i
$937$	−29.8349			−0.974663			−0.487331	−	0.873217i	$-0.662030\pi$
$937$	−29.8349			−0.974663			−0.487331	+	0.873217i	$0.662030\pi$
$938$	−49.6157	−	85.9369i	−1.62001	−	2.80594i
$939$	−0.125977	−	0.218198i	−0.00411109	−	0.00712062i
$940$		0			0
$941$	−7.53619			−0.245673			−0.122836	−	0.992427i	$-0.539199\pi$
$941$	−7.53619			−0.245673			−0.122836	+	0.992427i	$0.539199\pi$
$942$	−1.16483	+	2.01754i	−0.0379521	+	0.0657349i
$943$	1.43448	−	2.48459i	0.0467130	−	0.0809093i
$944$	−21.0245			−0.684291
$945$		0			0
$946$	−0.805989	−	1.39601i	−0.0262050	−	0.0453883i
$947$	0.953323	+	1.65120i	0.0309788	+	0.0536569i	0.881099	−	0.472932i	$-0.156804\pi$
$947$	0.953323	+	1.65120i	0.0309788	+	0.0536569i	−0.850120	+	0.526588i	$0.823471\pi$
$948$	5.58160			0.181282
$949$	−4.23267	−	37.8480i	−0.137398	−	1.22860i
$950$		0			0
$951$	0.945966	+	1.63846i	0.0306751	+	0.0531307i
$952$	79.5401	+	137.768i	2.57791	+	4.46507i
$953$	−8.40543	+	14.5586i	−0.272279	+	0.471600i	−0.969445	−	0.245309i	$-0.921111\pi$
$953$	−8.40543	+	14.5586i	−0.272279	+	0.471600i	0.697166	+	0.716909i	$0.254444\pi$
$954$	26.7436			0.865855
$955$		0			0
$956$	−53.1768	+	92.1049i	−1.71986	+	2.97888i
$957$	0.387788			0.0125354
$958$	10.7424	−	18.6065i	0.347073	−	0.601147i
$959$	1.90561	+	3.30062i	0.0615354	+	0.106582i
$960$		0			0
$961$	19.6834			0.634948
$962$	35.1244	+	15.3593i	1.13246	+	0.495204i
$963$	3.02704			0.0975452
$964$	12.7381	+	22.0630i	0.410266	+	0.710602i
$965$		0			0
$966$	4.07006	−	7.04955i	0.130952	−	0.226815i
$967$	36.1265			1.16175			0.580874	−	0.813993i	$-0.302711\pi$
$967$	36.1265			1.16175			0.580874	+	0.813993i	$0.302711\pi$
$968$	39.4493	−	68.3283i	1.26795	−	2.19615i
$969$	−1.27051	+	2.20059i	−0.0408147	+	0.0706931i
$970$		0			0
$971$	−9.42596	+	16.3262i	−0.302494	+	0.523934i	−0.976700	−	0.214609i	$-0.931152\pi$
$971$	−9.42596	+	16.3262i	−0.302494	+	0.523934i	0.674207	+	0.738543i	$0.264486\pi$
$972$	−8.67043	−	15.0176i	−0.278104	−	0.481690i
$973$	−20.3824	−	35.3034i	−0.653430	−	1.13177i
$974$	−77.6211			−2.48714
$975$		0			0
$976$	−57.0718			−1.82682
$977$	16.1888	+	28.0399i	0.517926	+	0.897074i	0.999783	+	0.0208245i	$0.00662913\pi$
$977$	16.1888	+	28.0399i	0.517926	+	0.897074i	−0.481857	+	0.876250i	$0.660038\pi$
$978$	−1.34498	−	2.32957i	−0.0430077	−	0.0744915i
$979$	1.26702	−	2.19455i	0.0404942	−	0.0701380i
$980$		0			0
$981$	−20.3053	+	35.1699i	−0.648299	+	1.12289i
$982$	−49.9677	+	86.5465i	−1.59453	+	2.76181i
$983$	−19.3591			−0.617459			−0.308729	−	0.951150i	$-0.599904\pi$
$983$	−19.3591			−0.617459			−0.308729	+	0.951150i	$0.599904\pi$
$984$	0.198322	−	0.343504i	0.00632228	−	0.0109505i
$985$		0			0
$986$	−71.3919	−	123.654i	−2.27358	−	3.93796i
$987$	1.65327			0.0526242
$988$	−38.6845	+	28.5009i	−1.23072	+	0.906735i
$989$	12.4663			0.396406
$990$		0			0
$991$	−19.4005	−	33.6027i	−0.616278	−	1.06742i	−0.990159	−	0.139948i	$-0.955307\pi$
$991$	−19.4005	−	33.6027i	−0.616278	−	1.06742i	0.373881	−	0.927477i	$-0.378027\pi$
$992$	−34.8310	+	60.3291i	−1.10589	+	1.91545i
$993$	1.93579			0.0614305
$994$	−7.26527	+	12.5838i	−0.230440	+	0.399135i
$995$		0			0
$996$	5.06247			0.160411
$997$	26.3337	−	45.6114i	0.833998	−	1.44453i	−0.0608463	−	0.998147i	$-0.519380\pi$
$997$	26.3337	−	45.6114i	0.833998	−	1.44453i	0.894844	−	0.446379i	$-0.147287\pi$
$998$	39.0518	+	67.6397i	1.23616	+	2.14110i
$999$	1.65201	+	2.86137i	0.0522674	+	0.0905298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.c.276.1	yes	10
5.2	odd	4		325.2.o.c.224.10		20
5.3	odd	4		325.2.o.c.224.1		20
5.4	even	2		325.2.e.d.276.5	yes	10
13.3	even	3		4225.2.a.bp.1.5		5
13.9	even	3	inner	325.2.e.c.126.1	✓	10
13.10	even	6		4225.2.a.bo.1.1		5
65.9	even	6		325.2.e.d.126.5	yes	10
65.22	odd	12		325.2.o.c.74.1		20
65.29	even	6		4225.2.a.bn.1.1		5
65.48	odd	12		325.2.o.c.74.10		20
65.49	even	6		4225.2.a.bm.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.e.c.126.1	✓	10	13.9	even	3	inner
325.2.e.c.276.1	yes	10	1.1	even	1	trivial
325.2.e.d.126.5	yes	10	65.9	even	6
325.2.e.d.276.5	yes	10	5.4	even	2
325.2.o.c.74.1		20	65.22	odd	12
325.2.o.c.74.10		20	65.48	odd	12
325.2.o.c.224.1		20	5.3	odd	4
325.2.o.c.224.10		20	5.2	odd	4
4225.2.a.bm.1.5		5	65.49	even	6
4225.2.a.bn.1.1		5	65.29	even	6
4225.2.a.bo.1.1		5	13.10	even	6
4225.2.a.bp.1.5		5	13.3	even	3

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30241 - 2.25583i) q^{2} +(-0.0676602 - 0.117191i) q^{3} +(-2.39253 + 4.14398i) q^{4} +(-0.176242 + 0.305261i) q^{6} +(1.62616 - 2.81660i) q^{7} +7.25455 q^{8} +(1.49084 - 2.58222i) q^{9} +O(q^{10})\)	\(q+(-1.30241 - 2.25583i) q^{2} +(-0.0676602 - 0.117191i) q^{3} +(-2.39253 + 4.14398i) q^{4} +(-0.176242 + 0.305261i) q^{6} +(1.62616 - 2.81660i) q^{7} +7.25455 q^{8} +(1.49084 - 2.58222i) q^{9} +(-0.176242 - 0.305261i) q^{11} +0.647516 q^{12} +(-0.400724 - 3.58321i) q^{13} -8.47171 q^{14} +(-4.66332 - 8.07710i) q^{16} +(-3.37118 + 5.83905i) q^{17} -7.76674 q^{18} +(-1.39253 + 2.41193i) q^{19} -0.440107 q^{21} +(-0.459078 + 0.795147i) q^{22} +(-3.55031 - 6.14931i) q^{23} +(-0.490844 - 0.850167i) q^{24} +(-7.56123 + 5.57077i) q^{26} -0.809445 q^{27} +(7.78129 + 13.4776i) q^{28} +(-4.06500 - 7.04079i) q^{29} +7.11923 q^{31} +(-4.89253 + 8.47411i) q^{32} +(-0.0238492 + 0.0413080i) q^{33} +17.5626 q^{34} +(7.13377 + 12.3561i) q^{36} +(-2.04092 - 3.53498i) q^{37} +7.25455 q^{38} +(-0.392807 + 0.289402i) q^{39} +(0.202022 + 0.349912i) q^{41} +(0.573198 + 0.992808i) q^{42} +(-0.877834 + 1.52045i) q^{43} +1.68666 q^{44} +(-9.24789 + 16.0178i) q^{46} -3.75653 q^{47} +(-0.631042 + 1.09300i) q^{48} +(-1.78882 - 3.09833i) q^{49} +0.912378 q^{51} +(15.8075 + 6.91234i) q^{52} -3.44334 q^{53} +(1.05423 + 1.82597i) q^{54} +(11.7971 - 20.4332i) q^{56} +0.376875 q^{57} +(-10.5886 + 18.3399i) q^{58} +(1.12712 - 1.95224i) q^{59} +(3.05961 - 5.29941i) q^{61} +(-9.27213 - 16.0598i) q^{62} +(-4.84872 - 8.39822i) q^{63} +6.83497 q^{64} +0.124245 q^{66} +(5.85663 + 10.1440i) q^{67} +(-16.1313 - 27.9402i) q^{68} +(-0.480429 + 0.832128i) q^{69} +(0.857592 - 1.48539i) q^{71} +(10.8154 - 18.7328i) q^{72} +10.5626 q^{73} +(-5.31622 + 9.20797i) q^{74} +(-6.66332 - 11.5412i) q^{76} -1.14640 q^{77} +(1.16444 + 0.509188i) q^{78} +8.62003 q^{79} +(-4.41777 - 7.65179i) q^{81} +(0.526228 - 0.911454i) q^{82} +7.81830 q^{83} +(1.05297 - 1.82379i) q^{84} +4.57319 q^{86} +(-0.550078 + 0.952762i) q^{87} +(-1.27856 - 2.21453i) q^{88} +(3.59455 + 6.22594i) q^{89} +(-10.7441 - 4.69822i) q^{91} +33.9768 q^{92} +(-0.481688 - 0.834309i) q^{93} +(4.89253 + 8.47411i) q^{94} +1.32412 q^{96} +(3.43618 - 5.95163i) q^{97} +(-4.65955 + 8.07058i) q^{98} -1.05100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9	\( 10 q - 3 q^{3} - 6 q^{4} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 4 q^{9} - 3 q^{11} + 4 q^{12} + 10 q^{13} - 16 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{18} + 4 q^{19} - 16 q^{21} - 8 q^{22} - 15 q^{23} + 14 q^{24} - 9 q^{26} + 42 q^{27} + 17 q^{28} + q^{29} - 31 q^{32} + 2 q^{33} + 54 q^{34} + 13 q^{36} - 17 q^{37} + 6 q^{38} - 10 q^{39} - 6 q^{41} - 32 q^{42} - 12 q^{43} - 16 q^{44} + 7 q^{46} - 24 q^{47} + 2 q^{48} - 7 q^{49} + 23 q^{52} + 16 q^{53} - 19 q^{54} + 17 q^{56} - 8 q^{57} - 38 q^{58} + 12 q^{59} - 5 q^{61} - 13 q^{62} - 26 q^{63} - 10 q^{64} + 86 q^{66} + 16 q^{67} - 25 q^{68} - 20 q^{69} - 19 q^{71} + 45 q^{72} - 16 q^{73} - 2 q^{74} - 24 q^{76} + 64 q^{77} + 42 q^{78} - 28 q^{79} - 29 q^{81} + 23 q^{82} - 14 q^{83} + 34 q^{84} - 84 q^{86} - 21 q^{87} - 2 q^{88} + 10 q^{89} + 17 q^{91} + 142 q^{92} + 33 q^{93} + 31 q^{94} + 34 q^{96} - 37 q^{97} + 21 q^{98} + 56 q^{99}+O(q^{100}) \) 10 * q - 3 * q^3 - 6 * q^4 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 4 * q^9 - 3 * q^11 + 4 * q^12 + 10 * q^13 - 16 * q^14 - 4 * q^16 - 4 * q^17 - 4 * q^18 + 4 * q^19 - 16 * q^21 - 8 * q^22 - 15 * q^23 + 14 * q^24 - 9 * q^26 + 42 * q^27 + 17 * q^28 + q^29 - 31 * q^32 + 2 * q^33 + 54 * q^34 + 13 * q^36 - 17 * q^37 + 6 * q^38 - 10 * q^39 - 6 * q^41 - 32 * q^42 - 12 * q^43 - 16 * q^44 + 7 * q^46 - 24 * q^47 + 2 * q^48 - 7 * q^49 + 23 * q^52 + 16 * q^53 - 19 * q^54 + 17 * q^56 - 8 * q^57 - 38 * q^58 + 12 * q^59 - 5 * q^61 - 13 * q^62 - 26 * q^63 - 10 * q^64 + 86 * q^66 + 16 * q^67 - 25 * q^68 - 20 * q^69 - 19 * q^71 + 45 * q^72 - 16 * q^73 - 2 * q^74 - 24 * q^76 + 64 * q^77 + 42 * q^78 - 28 * q^79 - 29 * q^81 + 23 * q^82 - 14 * q^83 + 34 * q^84 - 84 * q^86 - 21 * q^87 - 2 * q^88 + 10 * q^89 + 17 * q^91 + 142 * q^92 + 33 * q^93 + 31 * q^94 + 34 * q^96 - 37 * q^97 + 21 * q^98 + 56 * q^99

Introduction

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