LMFDB - Embedded newform 950.2.e.h.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.h.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +1.00000 q^{11} +2.56155 q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.219224 - 0.379706i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} +3.56155 q^{18} +(-2.50000 - 3.57071i) q^{19} +(0.561553 - 0.972638i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-1.28078 + 2.21837i) q^{24} +2.00000 q^{26} +1.43845 q^{27} +(0.219224 + 0.379706i) q^{28} +(-1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 + 2.21837i) q^{33} +(2.56155 + 4.43674i) q^{34} +(-1.78078 + 3.08440i) q^{36} +4.68466 q^{37} +(4.34233 - 0.379706i) q^{38} +5.12311 q^{39} +(3.06155 - 5.30277i) q^{41} +(0.561553 + 0.972638i) q^{42} +(1.56155 - 2.70469i) q^{43} +(-0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(1.43845 + 2.49146i) q^{47} +(-1.28078 - 2.21837i) q^{48} -6.80776 q^{49} +(6.56155 + 11.3649i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.78078 - 6.54850i) q^{53} +(-0.719224 + 1.24573i) q^{54} -0.438447 q^{56} +(11.1231 - 0.972638i) q^{57} +2.00000 q^{58} +(-7.28078 + 12.6107i) q^{59} +(-2.56155 - 4.43674i) q^{61} +(-5.12311 + 8.87348i) q^{62} +(0.780776 + 1.35234i) q^{63} +1.00000 q^{64} +(-1.28078 - 2.21837i) q^{66} +(4.71922 + 8.17394i) q^{67} -5.12311 q^{68} +12.0000 q^{69} +(-8.12311 + 14.0696i) q^{71} +(-1.78078 - 3.08440i) q^{72} +(-0.842329 + 1.45896i) q^{73} +(-2.34233 + 4.05703i) q^{74} +(-1.84233 + 3.95042i) q^{76} -0.438447 q^{77} +(-2.56155 + 4.43674i) q^{78} +(5.56155 - 9.63289i) q^{79} +(3.50000 - 6.06218i) q^{81} +(3.06155 + 5.30277i) q^{82} +10.8078 q^{83} -1.12311 q^{84} +(1.56155 + 2.70469i) q^{86} +5.12311 q^{87} +1.00000 q^{88} +(1.34233 + 2.32498i) q^{89} +(0.438447 + 0.759413i) q^{91} +(-2.34233 + 4.05703i) q^{92} +(-13.1231 + 22.7299i) q^{93} -2.87689 q^{94} +2.56155 q^{96} +(0.842329 - 1.45896i) q^{97} +(3.40388 - 5.89570i) q^{98} +(-1.78078 - 3.08440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 6 q^{21} - 2 q^{22} + 3 q^{23} - q^{24} + 8 q^{26} + 14 q^{27} + 5 q^{28} - 4 q^{29} + 8 q^{31} - 2 q^{32} - q^{33} + 2 q^{34} - 3 q^{36} - 6 q^{37} + 5 q^{38} + 4 q^{39} + 4 q^{41} - 6 q^{42} - 2 q^{43} - 2 q^{44} - 6 q^{46} + 14 q^{47} - q^{48} + 14 q^{49} + 18 q^{51} - 4 q^{52} - 11 q^{53} - 7 q^{54} - 10 q^{56} + 28 q^{57} + 8 q^{58} - 25 q^{59} - 2 q^{61} - 4 q^{62} - q^{63} + 4 q^{64} - q^{66} + 23 q^{67} - 4 q^{68} + 48 q^{69} - 16 q^{71} - 3 q^{72} + 9 q^{73} + 3 q^{74} + 5 q^{76} - 10 q^{77} - 2 q^{78} + 14 q^{79} + 14 q^{81} + 4 q^{82} + 2 q^{83} + 12 q^{84} - 2 q^{86} + 4 q^{87} + 4 q^{88} - 7 q^{89} + 10 q^{91} + 3 q^{92} - 36 q^{93} - 28 q^{94} + 2 q^{96} - 9 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9 + 4 * q^11 + 2 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 6 * q^21 - 2 * q^22 + 3 * q^23 - q^24 + 8 * q^26 + 14 * q^27 + 5 * q^28 - 4 * q^29 + 8 * q^31 - 2 * q^32 - q^33 + 2 * q^34 - 3 * q^36 - 6 * q^37 + 5 * q^38 + 4 * q^39 + 4 * q^41 - 6 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^46 + 14 * q^47 - q^48 + 14 * q^49 + 18 * q^51 - 4 * q^52 - 11 * q^53 - 7 * q^54 - 10 * q^56 + 28 * q^57 + 8 * q^58 - 25 * q^59 - 2 * q^61 - 4 * q^62 - q^63 + 4 * q^64 - q^66 + 23 * q^67 - 4 * q^68 + 48 * q^69 - 16 * q^71 - 3 * q^72 + 9 * q^73 + 3 * q^74 + 5 * q^76 - 10 * q^77 - 2 * q^78 + 14 * q^79 + 14 * q^81 + 4 * q^82 + 2 * q^83 + 12 * q^84 - 2 * q^86 + 4 * q^87 + 4 * q^88 - 7 * q^89 + 10 * q^91 + 3 * q^92 - 36 * q^93 - 28 * q^94 + 2 * q^96 - 9 * q^97 - 7 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.28078	+	2.21837i	−0.739457	+	1.28078i	0.213284	+	0.976990i	$0.431584\pi$
$3$	−1.28078	+	2.21837i	−0.739457	+	1.28078i	−0.952740	+	0.303786i	$0.901749\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.28078	−	2.21837i	−0.522875	−	0.905646i
$7$	−0.438447			−0.165717			−0.0828587	−	0.996561i	$-0.526405\pi$
$7$	−0.438447			−0.165717			−0.0828587	+	0.996561i	$0.526405\pi$
$8$	1.00000			0.353553
$9$	−1.78078	−	3.08440i	−0.593592	−	1.02813i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$	2.56155			0.739457
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.219224	−	0.379706i	0.0585900	−	0.101481i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.56155	−	4.43674i	0.621268	−	1.07607i	−0.367982	−	0.929833i	$-0.619951\pi$
$17$	2.56155	−	4.43674i	0.621268	−	1.07607i	0.989250	−	0.146235i	$-0.0467154\pi$
$18$	3.56155			0.839466
$19$	−2.50000	−	3.57071i	−0.573539	−	0.819178i
$19$	−2.50000	−	3.57071i	−0.573539	−	0.819178i
$20$		0			0
$21$	0.561553	−	0.972638i	0.122541	−	0.212247i
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−2.34233	−	4.05703i	−0.488409	−	0.845950i	0.511502	−	0.859282i	$-0.329089\pi$
$23$	−2.34233	−	4.05703i	−0.488409	−	0.845950i	−0.999911	+	0.0133324i	$0.995756\pi$
$24$	−1.28078	+	2.21837i	−0.261437	+	0.452823i
$25$		0			0
$26$	2.00000			0.392232
$27$	1.43845			0.276829
$28$	0.219224	+	0.379706i	0.0414294	+	0.0717578i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$		0			0
$31$	10.2462			1.84027			0.920137	−	0.391597i	$-0.128077\pi$
$31$	10.2462			1.84027			0.920137	+	0.391597i	$0.128077\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.28078	+	2.21837i	−0.222955	+	0.386169i
$34$	2.56155	+	4.43674i	0.439303	+	0.760895i
$35$		0			0
$36$	−1.78078	+	3.08440i	−0.296796	+	0.514066i
$37$	4.68466			0.770153			0.385077	−	0.922885i	$-0.374175\pi$
$37$	4.68466			0.770153			0.385077	+	0.922885i	$0.374175\pi$
$38$	4.34233	−	0.379706i	0.704419	−	0.0615965i
$39$	5.12311			0.820353
$40$		0			0
$41$	3.06155	−	5.30277i	0.478134	−	0.828153i	−0.521552	−	0.853220i	$-0.674647\pi$
$41$	3.06155	−	5.30277i	0.478134	−	0.828153i	0.999686	+	0.0250670i	$0.00797991\pi$
$42$	0.561553	+	0.972638i	0.0866495	+	0.150081i
$43$	1.56155	−	2.70469i	0.238135	−	0.412461i	−0.722044	−	0.691847i	$-0.756797\pi$
$43$	1.56155	−	2.70469i	0.238135	−	0.412461i	0.960179	+	0.279385i	$0.0901307\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	4.68466			0.690715
$47$	1.43845	+	2.49146i	0.209819	+	0.363417i	0.951657	−	0.307161i	$-0.0993792\pi$
$47$	1.43845	+	2.49146i	0.209819	+	0.363417i	−0.741838	+	0.670579i	$0.766046\pi$
$48$	−1.28078	−	2.21837i	−0.184864	−	0.320194i
$49$	−6.80776			−0.972538
$50$		0			0
$51$	6.56155	+	11.3649i	0.918801	+	1.59141i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−3.78078	−	6.54850i	−0.519330	−	0.899505i	−0.999748	−	0.0224656i	$-0.992848\pi$
$53$	−3.78078	−	6.54850i	−0.519330	−	0.899505i	0.480418	−	0.877040i	$-0.340485\pi$
$54$	−0.719224	+	1.24573i	−0.0978739	+	0.169523i
$55$		0			0
$56$	−0.438447			−0.0585900
$57$	11.1231	−	0.972638i	1.47329	−	0.128829i
$58$	2.00000			0.262613
$59$	−7.28078	+	12.6107i	−0.947876	+	1.64177i	−0.197989	+	0.980204i	$0.563441\pi$
$59$	−7.28078	+	12.6107i	−0.947876	+	1.64177i	−0.749887	+	0.661566i	$0.769892\pi$
$60$		0			0
$61$	−2.56155	−	4.43674i	−0.327973	−	0.568066i	0.654136	−	0.756377i	$-0.273032\pi$
$61$	−2.56155	−	4.43674i	−0.327973	−	0.568066i	−0.982110	+	0.188310i	$0.939699\pi$
$62$	−5.12311	+	8.87348i	−0.650635	+	1.12693i
$63$	0.780776	+	1.35234i	0.0983686	+	0.170379i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.28078	−	2.21837i	−0.157653	−	0.273062i
$67$	4.71922	+	8.17394i	0.576545	+	0.998605i	0.995872	+	0.0907698i	$0.0289328\pi$
$67$	4.71922	+	8.17394i	0.576545	+	0.998605i	−0.419327	+	0.907835i	$0.637734\pi$
$68$	−5.12311			−0.621268
$69$	12.0000			1.44463
$70$		0			0
$71$	−8.12311	+	14.0696i	−0.964035	+	1.66976i	−0.251850	+	0.967766i	$0.581039\pi$
$71$	−8.12311	+	14.0696i	−0.964035	+	1.66976i	−0.712185	+	0.701992i	$0.752294\pi$
$72$	−1.78078	−	3.08440i	−0.209867	−	0.363499i
$73$	−0.842329	+	1.45896i	−0.0985872	+	0.170758i	−0.911100	−	0.412185i	$-0.864766\pi$
$73$	−0.842329	+	1.45896i	−0.0985872	+	0.170758i	0.812513	+	0.582943i	$0.198099\pi$
$74$	−2.34233	+	4.05703i	−0.272290	+	0.471621i
$75$		0			0
$76$	−1.84233	+	3.95042i	−0.211330	+	0.453144i
$77$	−0.438447			−0.0499657
$78$	−2.56155	+	4.43674i	−0.290039	+	0.502362i
$79$	5.56155	−	9.63289i	0.625724	−	1.08379i	−0.362677	−	0.931915i	$-0.618137\pi$
$79$	5.56155	−	9.63289i	0.625724	−	1.08379i	0.988400	−	0.151870i	$-0.0485295\pi$
$80$		0			0
$81$	3.50000	−	6.06218i	0.388889	−	0.673575i
$82$	3.06155	+	5.30277i	0.338092	+	0.585592i
$83$	10.8078			1.18631			0.593153	−	0.805090i	$-0.297883\pi$
$83$	10.8078			1.18631			0.593153	+	0.805090i	$0.297883\pi$
$84$	−1.12311			−0.122541
$85$		0			0
$86$	1.56155	+	2.70469i	0.168387	+	0.291654i
$87$	5.12311			0.549255
$88$	1.00000			0.106600
$89$	1.34233	+	2.32498i	0.142287	+	0.246448i	0.928357	−	0.371689i	$-0.121221\pi$
$89$	1.34233	+	2.32498i	0.142287	+	0.246448i	−0.786071	+	0.618137i	$0.787888\pi$
$90$		0			0
$91$	0.438447	+	0.759413i	0.0459618	+	0.0796081i
$92$	−2.34233	+	4.05703i	−0.244205	+	0.422975i
$93$	−13.1231	+	22.7299i	−1.36080	+	2.35698i
$94$	−2.87689			−0.296729
$95$		0			0
$96$	2.56155			0.261437
$97$	0.842329	−	1.45896i	0.0855256	−	0.148135i	−0.820089	−	0.572235i	$-0.806076\pi$
$97$	0.842329	−	1.45896i	0.0855256	−	0.148135i	0.905615	+	0.424101i	$0.139410\pi$
$98$	3.40388	−	5.89570i	0.343844	−	0.595555i
$99$	−1.78078	−	3.08440i	−0.178975	−	0.309993i
$100$		0			0
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$	−13.1231			−1.29938
$103$	5.80776			0.572256			0.286128	−	0.958191i	$-0.407632\pi$
$103$	5.80776			0.572256			0.286128	+	0.958191i	$0.407632\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	7.56155			0.734443
$107$	−2.24621			−0.217149			−0.108575	−	0.994088i	$-0.534629\pi$
$107$	−2.24621			−0.217149			−0.108575	+	0.994088i	$0.534629\pi$
$108$	−0.719224	−	1.24573i	−0.0692073	−	0.119871i
$109$	7.12311	−	12.3376i	0.682270	−	1.18173i	−0.292017	−	0.956413i	$-0.594326\pi$
$109$	7.12311	−	12.3376i	0.682270	−	1.18173i	0.974286	−	0.225313i	$-0.0723404\pi$
$110$		0			0
$111$	−6.00000	+	10.3923i	−0.569495	+	0.986394i
$112$	0.219224	−	0.379706i	0.0207147	−	0.0358789i
$113$	16.8078			1.58114			0.790571	−	0.612371i	$-0.209784\pi$
$113$	16.8078			1.58114			0.790571	+	0.612371i	$0.209784\pi$
$114$	−4.71922	+	10.1192i	−0.441996	+	0.947751i
$115$		0			0
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$	−3.56155	+	6.16879i	−0.329266	+	0.570305i
$118$	−7.28078	−	12.6107i	−0.670250	−	1.16091i
$119$	−1.12311	+	1.94528i	−0.102955	+	0.178323i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	5.12311			0.463824
$123$	7.84233	+	13.5833i	0.707119	+	1.22477i
$124$	−5.12311	−	8.87348i	−0.460068	−	0.796862i
$125$		0			0
$126$	−1.56155			−0.139114
$127$	−7.78078	−	13.4767i	−0.690432	−	1.19586i	−0.971696	−	0.236233i	$-0.924087\pi$
$127$	−7.78078	−	13.4767i	−0.690432	−	1.19586i	0.281264	−	0.959630i	$-0.409246\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	8.06155	−	13.9630i	0.704341	−	1.21995i	−0.262588	−	0.964908i	$-0.584576\pi$
$131$	8.06155	−	13.9630i	0.704341	−	1.21995i	0.966929	−	0.255046i	$-0.0820908\pi$
$132$	2.56155			0.222955
$133$	1.09612	+	1.56557i	0.0950455	+	0.135752i
$134$	−9.43845			−0.815358
$135$		0			0
$136$	2.56155	−	4.43674i	0.219651	−	0.380447i
$137$	−2.71922	−	4.70983i	−0.232319	−	0.402388i	0.726171	−	0.687514i	$-0.241298\pi$
$137$	−2.71922	−	4.70983i	−0.232319	−	0.402388i	−0.958490	+	0.285126i	$0.907965\pi$
$138$	−6.00000	+	10.3923i	−0.510754	+	0.884652i
$139$	−4.40388	−	7.62775i	−0.373532	−	0.646977i	0.616574	−	0.787297i	$-0.288520\pi$
$139$	−4.40388	−	7.62775i	−0.373532	−	0.646977i	−0.990106	+	0.140320i	$0.955187\pi$
$140$		0			0
$141$	−7.36932			−0.620608
$142$	−8.12311	−	14.0696i	−0.681676	−	1.18070i
$143$	−1.00000	−	1.73205i	−0.0836242	−	0.144841i
$144$	3.56155			0.296796
$145$		0			0
$146$	−0.842329	−	1.45896i	−0.0697117	−	0.120744i
$147$	8.71922	−	15.1021i	0.719149	−	1.24560i
$148$	−2.34233	−	4.05703i	−0.192538	−	0.333486i
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	0.326411	+	0.945228i	$0.394160\pi$
$149$	−8.00000	+	13.8564i	−0.655386	+	1.13516i	−0.981797	+	0.189933i	$0.939173\pi$
$150$		0			0
$151$	20.4924			1.66765			0.833825	−	0.552029i	$-0.186146\pi$
$151$	20.4924			1.66765			0.833825	+	0.552029i	$0.186146\pi$
$152$	−2.50000	−	3.57071i	−0.202777	−	0.289623i
$153$	−18.2462			−1.47512
$154$	0.219224	−	0.379706i	0.0176655	−	0.0305976i
$155$		0			0
$156$	−2.56155	−	4.43674i	−0.205088	−	0.355223i
$157$	1.21922	−	2.11176i	0.0973046	−	0.168537i	−0.813263	−	0.581896i	$-0.802311\pi$
$157$	1.21922	−	2.11176i	0.0973046	−	0.168537i	0.910568	+	0.413359i	$0.135645\pi$
$158$	5.56155	+	9.63289i	0.442453	+	0.766352i
$159$	19.3693			1.53609
$160$		0			0
$161$	1.02699	+	1.77879i	0.0809380	+	0.140189i
$162$	3.50000	+	6.06218i	0.274986	+	0.476290i
$163$	−17.0540			−1.33577			−0.667885	−	0.744264i	$-0.732800\pi$
$163$	−17.0540			−1.33577			−0.667885	+	0.744264i	$0.732800\pi$
$164$	−6.12311			−0.478134
$165$		0			0
$166$	−5.40388	+	9.35980i	−0.419423	+	0.726461i
$167$	0.342329	+	0.592932i	0.0264902	+	0.0458824i	0.878967	−	0.476883i	$-0.158234\pi$
$167$	0.342329	+	0.592932i	0.0264902	+	0.0458824i	−0.852476	+	0.522766i	$0.824900\pi$
$168$	0.561553	−	0.972638i	0.0433247	−	0.0750407i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	−6.56155	+	14.0696i	−0.501774	+	1.07593i
$172$	−3.12311			−0.238135
$173$	−2.90388	+	5.02967i	−0.220778	+	0.382399i	−0.955044	−	0.296463i	$-0.904193\pi$
$173$	−2.90388	+	5.02967i	−0.220778	+	0.382399i	0.734266	+	0.678861i	$0.237526\pi$
$174$	−2.56155	+	4.43674i	−0.194191	+	0.336348i
$175$		0			0
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	−18.6501	−	32.3029i	−1.40183	−	2.42804i
$178$	−2.68466			−0.201224
$179$	11.4924			0.858984			0.429492	−	0.903071i	$-0.358693\pi$
$179$	11.4924			0.858984			0.429492	+	0.903071i	$0.358693\pi$
$180$		0			0
$181$	−10.6847	−	18.5064i	−0.794184	−	1.37557i	−0.923356	−	0.383945i	$-0.874565\pi$
$181$	−10.6847	−	18.5064i	−0.794184	−	1.37557i	0.129171	−	0.991622i	$-0.458768\pi$
$182$	−0.876894			−0.0649997
$183$	13.1231			0.970088
$184$	−2.34233	−	4.05703i	−0.172679	−	0.299088i
$185$		0			0
$186$	−13.1231	−	22.7299i	−0.962233	−	1.66664i
$187$	2.56155	−	4.43674i	0.187319	−	0.324447i
$188$	1.43845	−	2.49146i	0.104910	−	0.181709i
$189$	−0.630683			−0.0458754
$190$		0			0
$191$	−5.36932			−0.388510			−0.194255	−	0.980951i	$-0.562229\pi$
$191$	−5.36932			−0.388510			−0.194255	+	0.980951i	$0.562229\pi$
$192$	−1.28078	+	2.21837i	−0.0924321	+	0.160097i
$193$	12.8078	−	22.1837i	0.921923	−	1.59682i	0.125487	−	0.992095i	$-0.459951\pi$
$193$	12.8078	−	22.1837i	0.921923	−	1.59682i	0.796436	−	0.604722i	$-0.206716\pi$
$194$	0.842329	+	1.45896i	0.0604757	+	0.104747i
$195$		0			0
$196$	3.40388	+	5.89570i	0.243134	+	0.421121i
$197$	−14.4384			−1.02870			−0.514348	−	0.857581i	$-0.671966\pi$
$197$	−14.4384			−1.02870			−0.514348	+	0.857581i	$0.671966\pi$
$198$	3.56155			0.253109
$199$	1.43845	+	2.49146i	0.101969	+	0.176615i	0.912496	−	0.409086i	$-0.134152\pi$
$199$	1.43845	+	2.49146i	0.101969	+	0.176615i	−0.810527	+	0.585701i	$0.800819\pi$
$200$		0			0
$201$	−24.1771			−1.70532
$202$	10.0000			0.703598
$203$	0.438447	+	0.759413i	0.0307730	+	0.0533003i
$204$	6.56155	−	11.3649i	0.459401	−	0.795705i
$205$		0			0
$206$	−2.90388	+	5.02967i	−0.202323	+	0.350434i
$207$	−8.34233	+	14.4493i	−0.579832	+	1.00430i
$208$	2.00000			0.138675
$209$	−2.50000	−	3.57071i	−0.172929	−	0.246991i
$210$		0			0
$211$	1.65767	−	2.87117i	0.114119	−	0.197659i	−0.803308	−	0.595563i	$-0.796929\pi$
$211$	1.65767	−	2.87117i	0.114119	−	0.197659i	0.917427	+	0.397904i	$0.130262\pi$
$212$	−3.78078	+	6.54850i	−0.259665	+	0.449753i
$213$	−20.8078	−	36.0401i	−1.42572	−	2.46943i
$214$	1.12311	−	1.94528i	0.0767739	−	0.132976i
$215$		0			0
$216$	1.43845			0.0978739
$217$	−4.49242			−0.304966
$218$	7.12311	+	12.3376i	0.482438	+	0.835606i
$219$	−2.15767	−	3.73720i	−0.145802	−	0.252536i
$220$		0			0
$221$	−10.2462			−0.689235
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	5.65767	−	9.79937i	0.378866	−	0.656215i	−0.612032	−	0.790833i	$-0.709648\pi$
$223$	5.65767	−	9.79937i	0.378866	−	0.656215i	0.990897	+	0.134619i	$0.0429809\pi$
$224$	0.219224	+	0.379706i	0.0146475	+	0.0253702i
$225$		0			0
$226$	−8.40388	+	14.5560i	−0.559018	+	0.968247i
$227$	−19.9309			−1.32286			−0.661429	−	0.750008i	$-0.730050\pi$
$227$	−19.9309			−1.32286			−0.661429	+	0.750008i	$0.730050\pi$
$228$	−6.40388	−	9.14657i	−0.424107	−	0.605747i
$229$	12.8769			0.850929			0.425465	−	0.904975i	$-0.360111\pi$
$229$	12.8769			0.850929			0.425465	+	0.904975i	$0.360111\pi$
$230$		0			0
$231$	0.561553	−	0.972638i	0.0369475	−	0.0639949i
$232$	−1.00000	−	1.73205i	−0.0656532	−	0.113715i
$233$	1.15767	−	2.00514i	0.0758415	−	0.131361i	−0.825610	−	0.564241i	$-0.809169\pi$
$233$	1.15767	−	2.00514i	0.0758415	−	0.131361i	0.901452	+	0.432879i	$0.142502\pi$
$234$	−3.56155	−	6.16879i	−0.232826	−	0.403266i
$235$		0			0
$236$	14.5616			0.947876
$237$	14.2462	+	24.6752i	0.925391	+	1.60282i
$238$	−1.12311	−	1.94528i	−0.0728001	−	0.126094i
$239$	18.2462			1.18025			0.590125	−	0.807312i	$-0.299079\pi$
$239$	18.2462			1.18025			0.590125	+	0.807312i	$0.299079\pi$
$240$		0			0
$241$	4.28078	+	7.41452i	0.275749	+	0.477611i	0.970324	−	0.241809i	$-0.0777408\pi$
$241$	4.28078	+	7.41452i	0.275749	+	0.477611i	−0.694575	+	0.719421i	$0.744407\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	11.1231	+	19.2658i	0.713548	+	1.23590i
$244$	−2.56155	+	4.43674i	−0.163987	+	0.284033i
$245$		0			0
$246$	−15.6847			−1.00002
$247$	−3.68466	+	7.90084i	−0.234449	+	0.502718i
$248$	10.2462			0.650635
$249$	−13.8423	+	23.9756i	−0.877222	+	1.51939i
$250$		0			0
$251$	−12.9654	−	22.4568i	−0.818371	−	1.41746i	−0.906882	−	0.421385i	$-0.861544\pi$
$251$	−12.9654	−	22.4568i	−0.818371	−	1.41746i	0.0885109	−	0.996075i	$-0.471789\pi$
$252$	0.780776	−	1.35234i	0.0491843	−	0.0851897i
$253$	−2.34233	−	4.05703i	−0.147261	−	0.255063i
$254$	15.5616			0.976419
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.52699	+	11.3051i	0.407142	+	0.705191i	0.994568	−	0.104087i	$-0.0331920\pi$
$257$	6.52699	+	11.3051i	0.407142	+	0.705191i	−0.587426	+	0.809278i	$0.699859\pi$
$258$	−8.00000			−0.498058
$259$	−2.05398			−0.127628
$260$		0			0
$261$	−3.56155	+	6.16879i	−0.220455	+	0.381839i
$262$	8.06155	+	13.9630i	0.498044	+	0.862638i
$263$	−1.09612	+	1.89853i	−0.0675895	+	0.117068i	−0.897840	−	0.440322i	$-0.854864\pi$
$263$	−1.09612	+	1.89853i	−0.0675895	+	0.117068i	0.830250	+	0.557391i	$0.188197\pi$
$264$	−1.28078	+	2.21837i	−0.0788263	+	0.136531i
$265$		0			0
$266$	−1.90388	+	0.166481i	−0.116734	+	0.0102076i
$267$	−6.87689			−0.420859
$268$	4.71922	−	8.17394i	0.288272	−	0.499303i
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	4.12311	−	7.14143i	0.250461	−	0.433811i	−0.713192	−	0.700969i	$-0.752751\pi$
$271$	4.12311	−	7.14143i	0.250461	−	0.433811i	0.963653	+	0.267158i	$0.0860845\pi$
$272$	2.56155	+	4.43674i	0.155317	+	0.269017i
$273$	−2.24621			−0.135947
$274$	5.43845			0.328549
$275$		0			0
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−4.24621			−0.255130			−0.127565	−	0.991830i	$-0.540716\pi$
$277$	−4.24621			−0.255130			−0.127565	+	0.991830i	$0.540716\pi$
$278$	8.80776			0.528255
$279$	−18.2462	−	31.6034i	−1.09237	−	1.89204i
$280$		0			0
$281$	−4.18466	−	7.24804i	−0.249636	−	0.432382i	0.713789	−	0.700361i	$-0.246978\pi$
$281$	−4.18466	−	7.24804i	−0.249636	−	0.432382i	−0.963425	+	0.267979i	$0.913644\pi$
$282$	3.68466	−	6.38202i	0.219418	−	0.380043i
$283$	−9.71922	+	16.8342i	−0.577748	+	1.00069i	0.417989	+	0.908452i	$0.362735\pi$
$283$	−9.71922	+	16.8342i	−0.577748	+	1.00069i	−0.995737	+	0.0922367i	$0.970598\pi$
$284$	16.2462			0.964035
$285$		0			0
$286$	2.00000			0.118262
$287$	−1.34233	+	2.32498i	−0.0792352	+	0.137239i
$288$	−1.78078	+	3.08440i	−0.104933	+	0.181750i
$289$	−4.62311	−	8.00745i	−0.271947	−	0.471027i
$290$		0			0
$291$	2.15767	+	3.73720i	0.126485	+	0.219078i
$292$	1.68466			0.0985872
$293$	−23.5616			−1.37648			−0.688240	−	0.725483i	$-0.741617\pi$
$293$	−23.5616			−1.37648			−0.688240	+	0.725483i	$0.741617\pi$
$294$	8.71922	+	15.1021i	0.508515	+	0.880775i
$295$		0			0
$296$	4.68466			0.272290
$297$	1.43845			0.0834672
$298$	−8.00000	−	13.8564i	−0.463428	−	0.802680i
$299$	−4.68466	+	8.11407i	−0.270921	+	0.469249i
$300$		0			0
$301$	−0.684658	+	1.18586i	−0.0394631	+	0.0683520i
$302$	−10.2462	+	17.7470i	−0.589603	+	1.02122i
$303$	25.6155			1.47157
$304$	4.34233	−	0.379706i	0.249050	−	0.0217777i
$305$		0			0
$306$	9.12311	−	15.8017i	0.521533	−	0.903322i
$307$	−11.9654	+	20.7247i	−0.682903	+	1.18282i	0.291187	+	0.956666i	$0.405950\pi$
$307$	−11.9654	+	20.7247i	−0.682903	+	1.18282i	−0.974091	+	0.226157i	$0.927384\pi$
$308$	0.219224	+	0.379706i	0.0124914	+	0.0216358i
$309$	−7.43845	+	12.8838i	−0.423158	+	0.732932i
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$	5.12311			0.290039
$313$	2.15767	+	3.73720i	0.121959	+	0.211239i	0.920540	−	0.390648i	$-0.127749\pi$
$313$	2.15767	+	3.73720i	0.121959	+	0.211239i	−0.798581	+	0.601887i	$0.794416\pi$
$314$	1.21922	+	2.11176i	0.0688048	+	0.119173i
$315$		0			0
$316$	−11.1231			−0.625724
$317$	9.34233	+	16.1814i	0.524717	+	0.908837i	0.999586	+	0.0287805i	$0.00916237\pi$
$317$	9.34233	+	16.1814i	0.524717	+	0.908837i	−0.474868	+	0.880057i	$0.657504\pi$
$318$	−9.68466	+	16.7743i	−0.543089	+	0.940657i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$		0			0
$321$	2.87689	−	4.98293i	0.160573	−	0.278120i
$322$	−2.05398			−0.114464
$323$	−22.2462	+	1.94528i	−1.23781	+	0.108238i
$324$	−7.00000			−0.388889
$325$		0			0
$326$	8.52699	−	14.7692i	0.472266	−	0.817989i
$327$	18.2462	+	31.6034i	1.00902	+	1.74767i
$328$	3.06155	−	5.30277i	0.169046	−	0.292796i
$329$	−0.630683	−	1.09238i	−0.0347707	−	0.0602246i
$330$		0			0
$331$	23.4924			1.29126			0.645630	−	0.763650i	$-0.276595\pi$
$331$	23.4924			1.29126			0.645630	+	0.763650i	$0.276595\pi$
$332$	−5.40388	−	9.35980i	−0.296577	−	0.513686i
$333$	−8.34233	−	14.4493i	−0.457157	−	0.791819i
$334$	−0.684658			−0.0374628
$335$		0			0
$336$	0.561553	+	0.972638i	0.0306352	+	0.0530618i
$337$	10.5270	−	18.2333i	0.573442	−	0.993230i	−0.422767	−	0.906238i	$-0.638941\pi$
$337$	10.5270	−	18.2333i	0.573442	−	0.993230i	0.996209	−	0.0869917i	$-0.0277254\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	−21.5270	+	37.2858i	−1.16919	+	2.02509i
$340$		0			0
$341$	10.2462			0.554863
$342$	−8.90388	−	12.7173i	−0.481467	−	0.687672i
$343$	6.05398			0.326884
$344$	1.56155	−	2.70469i	0.0841933	−	0.145827i
$345$		0			0
$346$	−2.90388	−	5.02967i	−0.156114	−	0.270397i
$347$	0.842329	−	1.45896i	0.0452186	−	0.0783209i	−0.842530	−	0.538649i	$-0.818935\pi$
$347$	0.842329	−	1.45896i	0.0452186	−	0.0783209i	0.887749	+	0.460328i	$0.152268\pi$
$348$	−2.56155	−	4.43674i	−0.137314	−	0.237834i
$349$	−14.2462			−0.762582			−0.381291	−	0.924455i	$-0.624520\pi$
$349$	−14.2462			−0.762582			−0.381291	+	0.924455i	$0.624520\pi$
$350$		0			0
$351$	−1.43845	−	2.49146i	−0.0767786	−	0.132984i
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−24.1771			−1.28682			−0.643408	−	0.765523i	$-0.722480\pi$
$353$	−24.1771			−1.28682			−0.643408	+	0.765523i	$0.722480\pi$
$354$	37.3002			1.98248
$355$		0			0
$356$	1.34233	−	2.32498i	0.0711433	−	0.123224i
$357$	−2.87689	−	4.98293i	−0.152261	−	0.263724i
$358$	−5.74621	+	9.95273i	−0.303697	+	0.526018i
$359$	−7.56155	+	13.0970i	−0.399083	+	0.691233i	−0.993613	−	0.112841i	$-0.964005\pi$
$359$	−7.56155	+	13.0970i	−0.399083	+	0.691233i	0.594530	+	0.804074i	$0.297338\pi$
$360$		0			0
$361$	−6.50000	+	17.8536i	−0.342105	+	0.939662i
$362$	21.3693			1.12315
$363$	12.8078	−	22.1837i	0.672233	−	1.16434i
$364$	0.438447	−	0.759413i	0.0229809	−	0.0398040i
$365$		0			0
$366$	−6.56155	+	11.3649i	−0.342978	+	0.594055i
$367$	−8.87689	−	15.3752i	−0.463370	−	0.802581i	0.535756	−	0.844373i	$-0.320027\pi$
$367$	−8.87689	−	15.3752i	−0.463370	−	0.802581i	−0.999126	+	0.0417921i	$0.986693\pi$
$368$	4.68466			0.244205
$369$	−21.8078			−1.13527
$370$		0			0
$371$	1.65767	+	2.87117i	0.0860620	+	0.149064i
$372$	26.2462			1.36080
$373$	35.8078			1.85406			0.927028	−	0.374992i	$-0.122355\pi$
$373$	35.8078			1.85406			0.927028	+	0.374992i	$0.122355\pi$
$374$	2.56155	+	4.43674i	0.132455	+	0.229418i
$375$		0			0
$376$	1.43845	+	2.49146i	0.0741822	+	0.128487i
$377$	−2.00000	+	3.46410i	−0.103005	+	0.178410i
$378$	0.315342	−	0.546188i	0.0162194	−	0.0280929i
$379$	−0.492423			−0.0252940			−0.0126470	−	0.999920i	$-0.504026\pi$
$379$	−0.492423			−0.0252940			−0.0126470	+	0.999920i	$0.504026\pi$
$380$		0			0
$381$	39.8617			2.04218
$382$	2.68466	−	4.64996i	0.137359	−	0.237913i
$383$	2.56155	−	4.43674i	0.130889	−	0.226707i	−0.793130	−	0.609052i	$-0.791550\pi$
$383$	2.56155	−	4.43674i	0.130889	−	0.226707i	0.924020	+	0.382345i	$0.124883\pi$
$384$	−1.28078	−	2.21837i	−0.0653593	−	0.113206i
$385$		0			0
$386$	12.8078	+	22.1837i	0.651898	+	1.12912i
$387$	−11.1231			−0.565419
$388$	−1.68466			−0.0855256
$389$	9.56155	+	16.5611i	0.484790	+	0.839681i	0.999847	−	0.0174749i	$-0.00556271\pi$
$389$	9.56155	+	16.5611i	0.484790	+	0.839681i	−0.515057	+	0.857156i	$0.672229\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	−6.80776			−0.343844
$393$	20.6501	+	35.7670i	1.04166	+	1.80421i
$394$	7.21922	−	12.5041i	0.363699	−	0.629946i
$395$		0			0
$396$	−1.78078	+	3.08440i	−0.0894874	+	0.154997i
$397$	14.1501	−	24.5087i	0.710173	−	1.23006i	−0.254619	−	0.967041i	$-0.581950\pi$
$397$	14.1501	−	24.5087i	0.710173	−	1.23006i	0.964792	−	0.263014i	$-0.0847165\pi$
$398$	−2.87689			−0.144206
$399$	−4.87689	+	0.426450i	−0.244150	+	0.0213492i
$400$		0			0
$401$	−13.9654	+	24.1888i	−0.697401	+	1.20793i	0.271964	+	0.962307i	$0.412327\pi$
$401$	−13.9654	+	24.1888i	−0.697401	+	1.20793i	−0.969365	+	0.245626i	$0.921007\pi$
$402$	12.0885	−	20.9380i	0.602922	−	1.04429i
$403$	−10.2462	−	17.7470i	−0.510400	−	0.884039i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$		0			0
$406$	−0.876894			−0.0435195
$407$	4.68466			0.232210
$408$	6.56155	+	11.3649i	0.324845	+	0.562649i
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	−0.999751	−	0.0223042i	$-0.992900\pi$
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	0.480560	−	0.876962i	$-0.340434\pi$
$410$		0			0
$411$	13.9309			0.687159
$412$	−2.90388	−	5.02967i	−0.143064	−	0.247794i
$413$	3.19224	−	5.52911i	0.157080	−	0.272070i
$414$	−8.34233	−	14.4493i	−0.410003	−	0.710146i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$	22.5616			1.10484
$418$	4.34233	−	0.379706i	0.212390	−	0.0185720i
$419$	−17.5616			−0.857938			−0.428969	−	0.903319i	$-0.641123\pi$
$419$	−17.5616			−0.857938			−0.428969	+	0.903319i	$0.641123\pi$
$420$		0			0
$421$	−16.2462	+	28.1393i	−0.791792	+	1.37142i	0.133065	+	0.991107i	$0.457518\pi$
$421$	−16.2462	+	28.1393i	−0.791792	+	1.37142i	−0.924856	+	0.380316i	$0.875815\pi$
$422$	1.65767	+	2.87117i	0.0806942	+	0.139766i
$423$	5.12311	−	8.87348i	0.249094	−	0.431443i
$424$	−3.78078	−	6.54850i	−0.183611	−	0.318023i
$425$		0			0
$426$	41.6155			2.01628
$427$	1.12311	+	1.94528i	0.0543509	+	0.0941385i
$428$	1.12311	+	1.94528i	0.0542874	+	0.0940285i
$429$	5.12311			0.247346
$430$		0			0
$431$	3.68466	+	6.38202i	0.177484	+	0.307411i	0.941018	−	0.338356i	$-0.109871\pi$
$431$	3.68466	+	6.38202i	0.177484	+	0.307411i	−0.763534	+	0.645767i	$0.776538\pi$
$432$	−0.719224	+	1.24573i	−0.0346037	+	0.0599353i
$433$	−18.3693	−	31.8166i	−0.882773	−	1.52901i	−0.848245	−	0.529604i	$-0.822341\pi$
$433$	−18.3693	−	31.8166i	−0.882773	−	1.52901i	−0.0345280	−	0.999404i	$-0.510993\pi$
$434$	2.24621	−	3.89055i	0.107822	−	0.186752i
$435$		0			0
$436$	−14.2462			−0.682270
$437$	−8.63068	+	18.5064i	−0.412862	+	0.885280i
$438$	4.31534			0.206195
$439$	8.24621	−	14.2829i	0.393570	−	0.681684i	−0.599347	−	0.800489i	$-0.704573\pi$
$439$	8.24621	−	14.2829i	0.393570	−	0.681684i	0.992918	+	0.118806i	$0.0379065\pi$
$440$		0			0
$441$	12.1231	+	20.9978i	0.577291	+	0.999897i
$442$	5.12311	−	8.87348i	0.243681	−	0.422068i
$443$	16.9654	+	29.3850i	0.806052	+	1.39612i	0.915578	+	0.402139i	$0.131733\pi$
$443$	16.9654	+	29.3850i	0.806052	+	1.39612i	−0.109526	+	0.993984i	$0.534933\pi$
$444$	12.0000			0.569495
$445$		0			0
$446$	5.65767	+	9.79937i	0.267898	+	0.464014i
$447$	−20.4924	−	35.4939i	−0.969258	−	1.67880i
$448$	−0.438447			−0.0207147
$449$	29.0000			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$450$		0			0
$451$	3.06155	−	5.30277i	0.144163	−	0.249697i
$452$	−8.40388	−	14.5560i	−0.395285	−	0.684654i
$453$	−26.2462	+	45.4598i	−1.23315	+	2.13589i
$454$	9.96543	−	17.2606i	0.467701	−	0.810082i
$455$		0			0
$456$	11.1231	−	0.972638i	0.520887	−	0.0455479i
$457$	−7.05398			−0.329971			−0.164986	−	0.986296i	$-0.552758\pi$
$457$	−7.05398			−0.329971			−0.164986	+	0.986296i	$0.552758\pi$
$458$	−6.43845	+	11.1517i	−0.300849	+	0.521086i
$459$	3.68466	−	6.38202i	0.171985	−	0.297887i
$460$		0			0
$461$	19.4924	−	33.7619i	0.907853	−	1.57245i	0.0908110	−	0.995868i	$-0.471054\pi$
$461$	19.4924	−	33.7619i	0.907853	−	1.57245i	0.817042	−	0.576579i	$-0.195613\pi$
$462$	0.561553	+	0.972638i	0.0261258	+	0.0452512i
$463$	19.5616			0.909102			0.454551	−	0.890721i	$-0.349800\pi$
$463$	19.5616			0.909102			0.454551	+	0.890721i	$0.349800\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	1.15767	+	2.00514i	0.0536281	+	0.0928865i
$467$	−16.5616			−0.766377			−0.383189	−	0.923670i	$-0.625174\pi$
$467$	−16.5616			−0.766377			−0.383189	+	0.923670i	$0.625174\pi$
$468$	7.12311			0.329266
$469$	−2.06913	−	3.58384i	−0.0955436	−	0.165486i
$470$		0			0
$471$	3.12311	+	5.40938i	0.143905	+	0.249251i
$472$	−7.28078	+	12.6107i	−0.335125	+	0.580453i
$473$	1.56155	−	2.70469i	0.0718003	−	0.124362i
$474$	−28.4924			−1.30870
$475$		0			0
$476$	2.24621			0.102955
$477$	−13.4654	+	23.3228i	−0.616540	+	1.06788i
$478$	−9.12311	+	15.8017i	−0.417281	+	0.722752i
$479$	−14.6847	−	25.4346i	−0.670959	−	1.16214i	−0.977632	−	0.210321i	$-0.932549\pi$
$479$	−14.6847	−	25.4346i	−0.670959	−	1.16214i	0.306673	−	0.951815i	$-0.400784\pi$
$480$		0			0
$481$	−4.68466	−	8.11407i	−0.213602	−	0.369970i
$482$	−8.56155			−0.389968
$483$	−5.26137			−0.239400
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$		0			0
$486$	−22.2462			−1.00911
$487$	6.93087			0.314068			0.157034	−	0.987593i	$-0.449807\pi$
$487$	6.93087			0.314068			0.157034	+	0.987593i	$0.449807\pi$
$488$	−2.56155	−	4.43674i	−0.115956	−	0.200842i
$489$	21.8423	−	37.8320i	0.987744	−	1.71082i
$490$		0			0
$491$	4.58854	−	7.94759i	0.207078	−	0.358670i	−0.743715	−	0.668497i	$-0.766938\pi$
$491$	4.58854	−	7.94759i	0.207078	−	0.358670i	0.950793	+	0.309827i	$0.100271\pi$
$492$	7.84233	−	13.5833i	0.353560	−	0.612383i
$493$	−10.2462			−0.461466
$494$	−5.00000	−	7.14143i	−0.224961	−	0.321308i
$495$		0			0
$496$	−5.12311	+	8.87348i	−0.230034	+	0.398431i
$497$	3.56155	−	6.16879i	0.159757	−	0.276708i
$498$	−13.8423	−	23.9756i	−0.620290	−	1.07437i
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$		0			0
$501$	−1.75379			−0.0783535
$502$	25.9309			1.15735
$503$	13.7116	+	23.7493i	0.611372	+	1.05893i	0.991009	+	0.133792i	$0.0427154\pi$
$503$	13.7116	+	23.7493i	0.611372	+	1.05893i	−0.379637	+	0.925135i	$0.623951\pi$
$504$	0.780776	+	1.35234i	0.0347785	+	0.0602382i
$505$		0			0
$506$	4.68466			0.208258
$507$	11.5270	+	19.9653i	0.511931	+	0.886691i
$508$	−7.78078	+	13.4767i	−0.345216	+	0.597932i
$509$	0.438447	+	0.759413i	0.0194338	+	0.0336604i	0.875579	−	0.483075i	$-0.160480\pi$
$509$	0.438447	+	0.759413i	0.0194338	+	0.0336604i	−0.856145	+	0.516736i	$0.827147\pi$
$510$		0			0
$511$	0.369317	−	0.639676i	0.0163376	−	0.0282976i
$512$	1.00000			0.0441942
$513$	−3.59612	−	5.13628i	−0.158772	−	0.226772i
$514$	−13.0540			−0.575786
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	1.43845	+	2.49146i	0.0632628	+	0.109574i
$518$	1.02699	−	1.77879i	0.0451232	−	0.0781558i
$519$	−7.43845	−	12.8838i	−0.326512	−	0.565535i
$520$		0			0
$521$	−22.8078			−0.999226			−0.499613	−	0.866249i	$-0.666524\pi$
$521$	−22.8078			−0.999226			−0.499613	+	0.866249i	$0.666524\pi$
$522$	−3.56155	−	6.16879i	−0.155885	−	0.270001i
$523$	7.31534	+	12.6705i	0.319878	+	0.554044i	0.980462	−	0.196707i	$-0.0630249\pi$
$523$	7.31534	+	12.6705i	0.319878	+	0.554044i	−0.660585	+	0.750752i	$0.729692\pi$
$524$	−16.1231			−0.704341
$525$		0			0
$526$	−1.09612	−	1.89853i	−0.0477930	−	0.0827799i
$527$	26.2462	−	45.4598i	1.14330	−	1.98026i
$528$	−1.28078	−	2.21837i	−0.0557386	−	0.0965422i
$529$	0.526988	−	0.912769i	0.0229125	−	0.0396856i
$530$		0			0
$531$	51.8617			2.25061
$532$	0.807764	−	1.73205i	0.0350210	−	0.0750939i
$533$	−12.2462			−0.530442
$534$	3.43845	−	5.95557i	0.148796	−	0.257723i
$535$		0			0
$536$	4.71922	+	8.17394i	0.203839	+	0.353060i
$537$	−14.7192	+	25.4944i	−0.635181	+	1.10017i
$538$	−2.00000	−	3.46410i	−0.0862261	−	0.149348i
$539$	−6.80776			−0.293231
$540$		0			0
$541$	14.2462	+	24.6752i	0.612492	+	1.06087i	0.990819	+	0.135196i	$0.0431664\pi$
$541$	14.2462	+	24.6752i	0.612492	+	1.06087i	−0.378326	+	0.925672i	$0.623500\pi$
$542$	4.12311	+	7.14143i	0.177103	+	0.306751i
$543$	54.7386			2.34906
$544$	−5.12311			−0.219651
$545$		0			0
$546$	1.12311	−	1.94528i	0.0480645	−	0.0832501i
$547$	−2.43845	−	4.22351i	−0.104260	−	0.180584i	0.809175	−	0.587567i	$-0.199914\pi$
$547$	−2.43845	−	4.22351i	−0.104260	−	0.180584i	−0.913436	+	0.406983i	$0.866581\pi$
$548$	−2.71922	+	4.70983i	−0.116159	+	0.201194i
$549$	−9.12311	+	15.8017i	−0.389365	+	0.674399i
$550$		0			0
$551$	−3.68466	+	7.90084i	−0.156972	+	0.336587i
$552$	12.0000			0.510754
$553$	−2.43845	+	4.22351i	−0.103693	+	0.179602i
$554$	2.12311	−	3.67733i	0.0902021	−	0.156235i
$555$		0			0
$556$	−4.40388	+	7.62775i	−0.186766	+	0.323489i
$557$	20.8348	+	36.0868i	0.882797	+	1.52905i	0.848218	+	0.529647i	$0.177676\pi$
$557$	20.8348	+	36.0868i	0.882797	+	1.52905i	0.0345785	+	0.999402i	$0.488991\pi$
$558$	36.4924			1.54485
$559$	−6.24621			−0.264187
$560$		0			0
$561$	6.56155	+	11.3649i	0.277029	+	0.479828i
$562$	8.36932			0.353038
$563$	−21.3002			−0.897696			−0.448848	−	0.893608i	$-0.648166\pi$
$563$	−21.3002			−0.897696			−0.448848	+	0.893608i	$0.648166\pi$
$564$	3.68466	+	6.38202i	0.155152	+	0.268731i
$565$		0			0
$566$	−9.71922	−	16.8342i	−0.408529	−	0.707594i
$567$	−1.53457	+	2.65794i	−0.0644457	+	0.111623i
$568$	−8.12311	+	14.0696i	−0.340838	+	0.590349i
$569$	−11.1771			−0.468568			−0.234284	−	0.972168i	$-0.575274\pi$
$569$	−11.1771			−0.468568			−0.234284	+	0.972168i	$0.575274\pi$
$570$		0			0
$571$	−4.80776			−0.201199			−0.100599	−	0.994927i	$-0.532076\pi$
$571$	−4.80776			−0.201199			−0.100599	+	0.994927i	$0.532076\pi$
$572$	−1.00000	+	1.73205i	−0.0418121	+	0.0724207i
$573$	6.87689	−	11.9111i	0.287286	−	0.497595i
$574$	−1.34233	−	2.32498i	−0.0560277	−	0.0970429i
$575$		0			0
$576$	−1.78078	−	3.08440i	−0.0741990	−	0.128516i
$577$	16.3153			0.679217			0.339608	−	0.940567i	$-0.389705\pi$
$577$	16.3153			0.679217			0.339608	+	0.940567i	$0.389705\pi$
$578$	9.24621			0.384592
$579$	32.8078	+	56.8247i	1.36344	+	2.36155i
$580$		0			0
$581$	−4.73863			−0.196592
$582$	−4.31534			−0.178877
$583$	−3.78078	−	6.54850i	−0.156584	−	0.271211i
$584$	−0.842329	+	1.45896i	−0.0348558	+	0.0603721i
$585$		0			0
$586$	11.7808	−	20.4049i	0.486659	−	0.842919i
$587$	13.3693	−	23.1563i	0.551811	−	0.955764i	−0.446333	−	0.894867i	$-0.647270\pi$
$587$	13.3693	−	23.1563i	0.551811	−	0.955764i	0.998144	−	0.0608975i	$-0.0193963\pi$
$588$	−17.4384			−0.719149
$589$	−25.6155	−	36.5863i	−1.05547	−	1.50751i
$590$		0			0
$591$	18.4924	−	32.0298i	0.760677	−	1.31753i
$592$	−2.34233	+	4.05703i	−0.0962691	+	0.166743i
$593$	12.7732	+	22.1238i	0.524532	+	0.908517i	0.999592	+	0.0285632i	$0.00909317\pi$
$593$	12.7732	+	22.1238i	0.524532	+	0.908517i	−0.475060	+	0.879954i	$0.657573\pi$
$594$	−0.719224	+	1.24573i	−0.0295101	+	0.0511130i
$595$		0			0
$596$	16.0000			0.655386
$597$	−7.36932			−0.301606
$598$	−4.68466	−	8.11407i	−0.191570	−	0.331809i
$599$	16.2462	+	28.1393i	0.663802	+	1.14974i	0.979609	+	0.200915i	$0.0643917\pi$
$599$	16.2462	+	28.1393i	0.663802	+	1.14974i	−0.315806	+	0.948824i	$0.602275\pi$
$600$		0			0
$601$	−11.6307			−0.474425			−0.237213	−	0.971458i	$-0.576234\pi$
$601$	−11.6307			−0.474425			−0.237213	+	0.971458i	$0.576234\pi$
$602$	−0.684658	−	1.18586i	−0.0279046	−	0.0483322i
$603$	16.8078	−	29.1119i	0.684465	−	1.18553i
$604$	−10.2462	−	17.7470i	−0.416912	−	0.722113i
$605$		0			0
$606$	−12.8078	+	22.1837i	−0.520280	+	0.901151i
$607$	−10.1922			−0.413690			−0.206845	−	0.978374i	$-0.566320\pi$
$607$	−10.1922			−0.413690			−0.206845	+	0.978374i	$0.566320\pi$
$608$	−1.84233	+	3.95042i	−0.0747163	+	0.160211i
$609$	−2.24621			−0.0910211
$610$		0			0
$611$	2.87689	−	4.98293i	0.116387	−	0.201588i
$612$	9.12311	+	15.8017i	0.368780	+	0.638745i
$613$	15.3423	−	26.5737i	0.619671	−	1.07330i	−0.369875	−	0.929082i	$-0.620599\pi$
$613$	15.3423	−	26.5737i	0.619671	−	1.07330i	0.989546	−	0.144220i	$-0.0460672\pi$
$614$	−11.9654	−	20.7247i	−0.482886	−	0.836382i
$615$		0			0
$616$	−0.438447			−0.0176655
$617$	3.59612	+	6.22866i	0.144774	+	0.250756i	0.929289	−	0.369354i	$-0.120421\pi$
$617$	3.59612	+	6.22866i	0.144774	+	0.250756i	−0.784514	+	0.620111i	$0.787088\pi$
$618$	−7.43845	−	12.8838i	−0.299218	−	0.518261i
$619$	26.0540			1.04720			0.523599	−	0.851965i	$-0.324589\pi$
$619$	26.0540			1.04720			0.523599	+	0.851965i	$0.324589\pi$
$620$		0			0
$621$	−3.36932	−	5.83583i	−0.135206	−	0.234184i
$622$	−2.00000	+	3.46410i	−0.0801927	+	0.138898i
$623$	−0.588540	−	1.01938i	−0.0235794	−	0.0408407i
$624$	−2.56155	+	4.43674i	−0.102544	+	0.177612i
$625$		0			0
$626$	−4.31534			−0.172476
$627$	11.1231	−	0.972638i	0.444214	−	0.0388434i
$628$	−2.43845			−0.0973046
$629$	12.0000	−	20.7846i	0.478471	−	0.828737i
$630$		0			0
$631$	−2.12311	−	3.67733i	−0.0845195	−	0.146392i	0.820667	−	0.571407i	$-0.193602\pi$
$631$	−2.12311	−	3.67733i	−0.0845195	−	0.146392i	−0.905186	+	0.425015i	$0.860269\pi$
$632$	5.56155	−	9.63289i	0.221227	−	0.383176i
$633$	4.24621	+	7.35465i	0.168772	+	0.292321i
$634$	−18.6847			−0.742063
$635$		0			0
$636$	−9.68466	−	16.7743i	−0.384022	−	0.665145i
$637$	6.80776	+	11.7914i	0.269733	+	0.467192i
$638$	2.00000			0.0791808
$639$	57.8617			2.28898
$640$		0			0
$641$	−3.71922	+	6.44188i	−0.146900	+	0.254439i	−0.930080	−	0.367356i	$-0.880263\pi$
$641$	−3.71922	+	6.44188i	−0.146900	+	0.254439i	0.783180	+	0.621795i	$0.213596\pi$
$642$	2.87689	+	4.98293i	0.113542	+	0.196660i
$643$	−11.2808	+	19.5389i	−0.444870	+	0.770538i	−0.998043	−	0.0625284i	$-0.980084\pi$
$643$	−11.2808	+	19.5389i	−0.444870	+	0.770538i	0.553173	+	0.833067i	$0.313417\pi$
$644$	1.02699	−	1.77879i	0.0404690	−	0.0700943i
$645$		0			0
$646$	9.43845	−	20.2384i	0.371351	−	0.796270i
$647$	−3.17708			−0.124904			−0.0624520	−	0.998048i	$-0.519892\pi$
$647$	−3.17708			−0.124904			−0.0624520	+	0.998048i	$0.519892\pi$
$648$	3.50000	−	6.06218i	0.137493	−	0.238145i
$649$	−7.28078	+	12.6107i	−0.285795	+	0.495012i
$650$		0			0
$651$	5.75379	−	9.96585i	0.225509	−	0.390593i
$652$	8.52699	+	14.7692i	0.333943	+	0.578406i
$653$	5.06913			0.198370			0.0991852	−	0.995069i	$-0.468376\pi$
$653$	5.06913			0.198370			0.0991852	+	0.995069i	$0.468376\pi$
$654$	−36.4924			−1.42697
$655$		0			0
$656$	3.06155	+	5.30277i	0.119534	+	0.207038i
$657$	6.00000			0.234082
$658$	1.26137			0.0491732
$659$	−9.46543	−	16.3946i	−0.368721	−	0.638643i	0.620645	−	0.784092i	$-0.286871\pi$
$659$	−9.46543	−	16.3946i	−0.368721	−	0.638643i	−0.989366	+	0.145448i	$0.953538\pi$
$660$		0			0
$661$	19.9309	+	34.5213i	0.775221	+	1.34272i	0.934670	+	0.355516i	$0.115695\pi$
$661$	19.9309	+	34.5213i	0.775221	+	1.34272i	−0.159449	+	0.987206i	$0.550972\pi$
$662$	−11.7462	+	20.3450i	−0.456529	+	0.790732i
$663$	13.1231	−	22.7299i	0.509659	−	0.882756i
$664$	10.8078			0.419423
$665$		0			0
$666$	16.6847			0.646517
$667$	−4.68466	+	8.11407i	−0.181391	+	0.314178i
$668$	0.342329	−	0.592932i	0.0132451	−	0.0229412i
$669$	14.4924	+	25.1016i	0.560309	+	0.970484i
$670$		0			0
$671$	−2.56155	−	4.43674i	−0.0988876	−	0.171278i
$672$	−1.12311			−0.0433247
$673$	−46.1080			−1.77733			−0.888665	−	0.458556i	$-0.848367\pi$
$673$	−46.1080			−1.77733			−0.888665	+	0.458556i	$0.848367\pi$
$674$	10.5270	+	18.2333i	0.405484	+	0.702320i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	23.1771			0.890768			0.445384	−	0.895340i	$-0.353067\pi$
$677$	23.1771			0.890768			0.445384	+	0.895340i	$0.353067\pi$
$678$	−21.5270	−	37.2858i	−0.826739	−	1.43195i
$679$	−0.369317	+	0.639676i	−0.0141731	+	0.0245485i
$680$		0			0
$681$	25.5270	−	44.2140i	0.978196	−	1.69429i
$682$	−5.12311	+	8.87348i	−0.196174	+	0.339783i
$683$	−28.0000			−1.07139			−0.535695	−	0.844411i	$-0.679950\pi$
$683$	−28.0000			−1.07139			−0.535695	+	0.844411i	$0.679950\pi$
$684$	15.4654	−	1.35234i	0.591336	−	0.0517082i
$685$		0			0
$686$	−3.02699	+	5.24290i	−0.115571	+	0.200175i
$687$	−16.4924	+	28.5657i	−0.629225	+	1.08985i
$688$	1.56155	+	2.70469i	0.0595336	+	0.103115i
$689$	−7.56155	+	13.0970i	−0.288072	+	0.498956i
$690$		0			0
$691$	−21.0691			−0.801507			−0.400754	−	0.916186i	$-0.631252\pi$
$691$	−21.0691			−0.801507			−0.400754	+	0.916186i	$0.631252\pi$
$692$	5.80776			0.220778
$693$	0.780776	+	1.35234i	0.0296592	+	0.0513713i
$694$	0.842329	+	1.45896i	0.0319744	+	0.0553813i
$695$		0			0
$696$	5.12311			0.194191
$697$	−15.6847	−	27.1666i	−0.594099	−	1.02901i
$698$	7.12311	−	12.3376i	0.269614	−	0.466984i
$699$	2.96543	+	5.13628i	0.112163	+	0.194272i
$700$		0			0
$701$	−3.24621	+	5.62260i	−0.122608	+	0.212363i	−0.920795	−	0.390046i	$-0.872459\pi$
$701$	−3.24621	+	5.62260i	−0.122608	+	0.212363i	0.798188	+	0.602409i	$0.205792\pi$
$702$	2.87689			0.108581
$703$	−11.7116	−	16.7276i	−0.441713	−	0.630892i
$704$	1.00000			0.0376889
$705$		0			0
$706$	12.0885	−	20.9380i	0.454958	−	0.788011i
$707$	2.19224	+	3.79706i	0.0824475	+	0.142803i
$708$	−18.6501	+	32.3029i	−0.700913	+	1.21402i
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	0.947282	+	0.320400i	$0.103817\pi$
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	−0.196167	+	0.980571i	$0.562849\pi$
$710$		0			0
$711$	−39.6155			−1.48570
$712$	1.34233	+	2.32498i	0.0503059	+	0.0871324i
$713$	−24.0000	−	41.5692i	−0.898807	−	1.55678i
$714$	5.75379			0.215330
$715$		0			0
$716$	−5.74621	−	9.95273i	−0.214746	−	0.371951i
$717$	−23.3693	+	40.4768i	−0.872743	+	1.51164i
$718$	−7.56155	−	13.0970i	−0.282195	−	0.488775i
$719$	−7.43845	+	12.8838i	−0.277407	+	0.480483i	−0.970740	−	0.240134i	$-0.922808\pi$
$719$	−7.43845	+	12.8838i	−0.277407	+	0.480483i	0.693332	+	0.720618i	$0.256142\pi$
$720$		0			0
$721$	−2.54640			−0.0948328
$722$	−12.2116	−	14.5560i	−0.454470	−	0.541716i
$723$	−21.9309			−0.815618
$724$	−10.6847	+	18.5064i	−0.397092	+	0.687784i
$725$		0			0
$726$	12.8078	+	22.1837i	0.475341	+	0.823314i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	0.438447	+	0.759413i	0.0162499	+	0.0281457i
$729$	−35.9848			−1.33277
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	−6.56155	−	11.3649i	−0.242522	−	0.420060i
$733$	26.9309			0.994714			0.497357	−	0.867546i	$-0.334304\pi$
$733$	26.9309			0.994714			0.497357	+	0.867546i	$0.334304\pi$
$734$	17.7538			0.655304
$735$		0			0
$736$	−2.34233	+	4.05703i	−0.0863394	+	0.149544i
$737$	4.71922	+	8.17394i	0.173835	+	0.301091i
$738$	10.9039	−	18.8861i	0.401377	−	0.695206i
$739$	−9.37689	+	16.2413i	−0.344935	+	0.597444i	−0.985342	−	0.170591i	$-0.945432\pi$
$739$	−9.37689	+	16.2413i	−0.344935	+	0.597444i	0.640407	+	0.768036i	$0.278766\pi$
$740$		0			0
$741$	−12.8078	−	18.2931i	−0.470505	−	0.672016i
$742$	−3.31534			−0.121710
$743$	−9.21922	+	15.9682i	−0.338221	+	0.585815i	−0.984098	−	0.177626i	$-0.943158\pi$
$743$	−9.21922	+	15.9682i	−0.338221	+	0.585815i	0.645878	+	0.763441i	$0.276492\pi$
$744$	−13.1231	+	22.7299i	−0.481116	+	0.833318i
$745$		0			0
$746$	−17.9039	+	31.0104i	−0.655508	+	1.13537i
$747$	−19.2462	−	33.3354i	−0.704182	−	1.21968i
$748$	−5.12311			−0.187319
$749$	0.984845			0.0359855
$750$		0			0
$751$	17.4384	+	30.2043i	0.636338	+	1.10217i	0.986230	+	0.165380i	$0.0528849\pi$
$751$	17.4384	+	30.2043i	0.636338	+	1.10217i	−0.349892	+	0.936790i	$0.613782\pi$
$752$	−2.87689			−0.104910
$753$	66.4233			2.42060
$754$	−2.00000	−	3.46410i	−0.0728357	−	0.126155i
$755$		0			0
$756$	0.315342	+	0.546188i	0.0114689	+	0.0198647i
$757$	−9.78078	+	16.9408i	−0.355488	+	0.615724i	−0.987201	−	0.159478i	$-0.949019\pi$
$757$	−9.78078	+	16.9408i	−0.355488	+	0.615724i	0.631713	+	0.775202i	$0.282352\pi$
$758$	0.246211	−	0.426450i	0.00894280	−	0.0154894i
$759$	12.0000			0.435572
$760$		0			0
$761$	−51.9848			−1.88445			−0.942225	−	0.334982i	$-0.891270\pi$
$761$	−51.9848			−1.88445			−0.942225	+	0.334982i	$0.891270\pi$
$762$	−19.9309	+	34.5213i	−0.722019	+	1.25057i
$763$	−3.12311	+	5.40938i	−0.113064	+	0.195833i
$764$	2.68466	+	4.64996i	0.0971275	+	0.168230i
$765$		0			0
$766$	2.56155	+	4.43674i	0.0925527	+	0.160306i
$767$	29.1231			1.05157
$768$	2.56155			0.0924321
$769$	−13.2462	−	22.9431i	−0.477671	−	0.827350i	0.522002	−	0.852944i	$-0.325185\pi$
$769$	−13.2462	−	22.9431i	−0.477671	−	0.827350i	−0.999672	+	0.0255946i	$0.991852\pi$
$770$		0			0
$771$	−33.4384			−1.20426
$772$	−25.6155			−0.921923
$773$	−7.15009	−	12.3843i	−0.257171	−	0.445433i	0.708312	−	0.705900i	$-0.249457\pi$
$773$	−7.15009	−	12.3843i	−0.257171	−	0.445433i	−0.965483	+	0.260466i	$0.916124\pi$
$774$	5.56155	−	9.63289i	0.199906	−	0.346247i
$775$		0			0
$776$	0.842329	−	1.45896i	0.0302379	−	0.0523735i
$777$	2.63068	−	4.55648i	0.0943752	−	0.163463i
$778$	−19.1231			−0.685597
$779$	−26.5885	+	2.32498i	−0.952633	+	0.0833011i
$780$		0			0
$781$	−8.12311	+	14.0696i	−0.290668	+	0.503451i
$782$	12.0000	−	20.7846i	0.429119	−	0.743256i
$783$	−1.43845	−	2.49146i	−0.0514059	−	0.0890376i
$784$	3.40388	−	5.89570i	0.121567	−	0.210561i
$785$		0			0
$786$	−41.3002			−1.47313
$787$	−8.56155			−0.305186			−0.152593	−	0.988289i	$-0.548762\pi$
$787$	−8.56155			−0.305186			−0.152593	+	0.988289i	$0.548762\pi$
$788$	7.21922	+	12.5041i	0.257174	+	0.445439i
$789$	−2.80776	−	4.86319i	−0.0999590	−	0.173134i
$790$		0			0
$791$	−7.36932			−0.262023
$792$	−1.78078	−	3.08440i	−0.0632771	−	0.109599i
$793$	−5.12311	+	8.87348i	−0.181927	+	0.315106i
$794$	14.1501	+	24.5087i	0.502168	+	0.869781i
$795$		0			0
$796$	1.43845	−	2.49146i	0.0509844	−	0.0883076i
$797$	4.19224			0.148497			0.0742483	−	0.997240i	$-0.476344\pi$
$797$	4.19224			0.148497			0.0742483	+	0.997240i	$0.476344\pi$
$798$	2.06913	−	4.43674i	0.0732464	−	0.157059i
$799$	14.7386			0.521415
$800$		0			0
$801$	4.78078	−	8.28055i	0.168920	−	0.292579i
$802$	−13.9654	−	24.1888i	−0.493137	−	0.854138i
$803$	−0.842329	+	1.45896i	−0.0297252	+	0.0514855i
$804$	12.0885	+	20.9380i	0.426330	+	0.738425i
$805$		0			0
$806$	20.4924			0.721815
$807$	−5.12311	−	8.87348i	−0.180342	−	0.312361i
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	23.4384			0.824052			0.412026	−	0.911172i	$-0.364821\pi$
$809$	23.4384			0.824052			0.412026	+	0.911172i	$0.364821\pi$
$810$		0			0
$811$	4.58854	+	7.94759i	0.161125	+	0.279077i	0.935273	−	0.353928i	$-0.115154\pi$
$811$	4.58854	+	7.94759i	0.161125	+	0.279077i	−0.774147	+	0.633006i	$0.781821\pi$
$812$	0.438447	−	0.759413i	0.0153865	−	0.0266502i
$813$	10.5616	+	18.2931i	0.370410	+	0.641569i
$814$	−2.34233	+	4.05703i	−0.0820986	+	0.142199i
$815$		0			0
$816$	−13.1231			−0.459401
$817$	−13.5616	+	1.18586i	−0.474459	+	0.0414881i
$818$	21.0000			0.734248
$819$	1.56155	−	2.70469i	0.0545651	−	0.0945095i
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	−6.96543	+	12.0645i	−0.242947	+	0.420797i
$823$	−13.5885	−	23.5360i	−0.473667	−	0.820415i	0.525879	−	0.850560i	$-0.323737\pi$
$823$	−13.5885	−	23.5360i	−0.473667	−	0.820415i	−0.999546	+	0.0301446i	$0.990403\pi$
$824$	5.80776			0.202323
$825$		0			0
$826$	3.19224	+	5.52911i	0.111072	+	0.192383i
$827$	−15.9654	−	27.6529i	−0.555173	−	0.961587i	−0.997890	−	0.0649260i	$-0.979319\pi$
$827$	−15.9654	−	27.6529i	−0.555173	−	0.961587i	0.442718	−	0.896661i	$-0.354014\pi$
$828$	16.6847			0.579832
$829$	26.7386			0.928671			0.464336	−	0.885659i	$-0.346293\pi$
$829$	26.7386			0.928671			0.464336	+	0.885659i	$0.346293\pi$
$830$		0			0
$831$	5.43845	−	9.41967i	0.188658	−	0.326765i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−17.4384	+	30.2043i	−0.604206	+	1.04652i
$834$	−11.2808	+	19.5389i	−0.390621	+	0.676576i
$835$		0			0
$836$	−1.84233	+	3.95042i	−0.0637183	+	0.136628i
$837$	14.7386			0.509442
$838$	8.78078	−	15.2088i	0.303327	−	0.525378i
$839$	−1.24621	+	2.15850i	−0.0430240	+	0.0745197i	−0.886735	−	0.462277i	$-0.847033\pi$
$839$	−1.24621	+	2.15850i	−0.0430240	+	0.0745197i	0.843712	+	0.536797i	$0.180366\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−16.2462	−	28.1393i	−0.559881	−	0.969743i
$843$	21.4384			0.738379
$844$	−3.31534			−0.114119
$845$		0			0
$846$	5.12311	+	8.87348i	0.176136	+	0.305077i
$847$	4.38447			0.150652
$848$	7.56155			0.259665
$849$	−24.8963	−	43.1217i	−0.854439	−	1.47993i
$850$		0			0
$851$	−10.9730	−	19.0058i	−0.376150	−	0.651511i
$852$	−20.8078	+	36.0401i	−0.712862	+	1.23471i
$853$	0.369317	−	0.639676i	0.0126452	−	0.0219021i	−0.859634	−	0.510911i	$-0.829308\pi$
$853$	0.369317	−	0.639676i	0.0126452	−	0.0219021i	0.872279	+	0.489009i	$0.162641\pi$
$854$	−2.24621			−0.0768638
$855$		0			0
$856$	−2.24621			−0.0767739
$857$	14.8963	−	25.8012i	0.508848	−	0.881351i	−0.491099	−	0.871104i	$-0.663405\pi$
$857$	14.8963	−	25.8012i	0.508848	−	0.881351i	0.999947	−	0.0102472i	$-0.00326184\pi$
$858$	−2.56155	+	4.43674i	−0.0874500	+	0.151468i
$859$	−23.7462	−	41.1296i	−0.810210	−	1.40333i	−0.912717	−	0.408593i	$-0.866020\pi$
$859$	−23.7462	−	41.1296i	−0.810210	−	1.40333i	0.102506	−	0.994732i	$-0.467314\pi$
$860$		0			0
$861$	−3.43845	−	5.95557i	−0.117182	−	0.202965i
$862$	−7.36932			−0.251000
$863$	−52.3002			−1.78032			−0.890160	−	0.455649i	$-0.849407\pi$
$863$	−52.3002			−1.78032			−0.890160	+	0.455649i	$0.849407\pi$
$864$	−0.719224	−	1.24573i	−0.0244685	−	0.0423807i
$865$		0			0
$866$	36.7386			1.24843
$867$	23.6847			0.804373
$868$	2.24621	+	3.89055i	0.0762414	+	0.132054i
$869$	5.56155	−	9.63289i	0.188663	−	0.326773i
$870$		0			0
$871$	9.43845	−	16.3479i	0.319810	−	0.553926i
$872$	7.12311	−	12.3376i	0.241219	−	0.417803i
$873$	−6.00000			−0.203069
$874$	−11.7116	−	16.7276i	−0.396152	−	0.565819i
$875$		0			0
$876$	−2.15767	+	3.73720i	−0.0729009	+	0.126268i
$877$	8.90388	−	15.4220i	0.300663	−	0.520763i	−0.675623	−	0.737247i	$-0.736125\pi$
$877$	8.90388	−	15.4220i	0.300663	−	0.520763i	0.976286	+	0.216484i	$0.0694588\pi$
$878$	8.24621	+	14.2829i	0.278296	+	0.482023i
$879$	30.1771	−	52.2682i	1.01785	−	1.76296i
$880$		0			0
$881$	−24.1231			−0.812728			−0.406364	−	0.913711i	$-0.633204\pi$
$881$	−24.1231			−0.812728			−0.406364	+	0.913711i	$0.633204\pi$
$882$	−24.2462			−0.816412
$883$	−4.40388	−	7.62775i	−0.148202	−	0.256694i	0.782361	−	0.622826i	$-0.214015\pi$
$883$	−4.40388	−	7.62775i	−0.148202	−	0.256694i	−0.930563	+	0.366131i	$0.880682\pi$
$884$	5.12311	+	8.87348i	0.172309	+	0.298447i
$885$		0			0
$886$	−33.9309			−1.13993
$887$	−13.1231	−	22.7299i	−0.440631	−	0.763195i	0.557106	−	0.830442i	$-0.311912\pi$
$887$	−13.1231	−	22.7299i	−0.440631	−	0.763195i	−0.997736	+	0.0672468i	$0.978579\pi$
$888$	−6.00000	+	10.3923i	−0.201347	+	0.348743i
$889$	3.41146	+	5.90882i	0.114417	+	0.198176i
$890$		0			0
$891$	3.50000	−	6.06218i	0.117254	−	0.203091i
$892$	−11.3153			−0.378866
$893$	5.30019	−	11.3649i	0.177364	−	0.380313i
$894$	40.9848			1.37074
$895$		0			0
$896$	0.219224	−	0.379706i	0.00732375	−	0.0126851i
$897$	−12.0000	−	20.7846i	−0.400668	−	0.693978i
$898$	−14.5000	+	25.1147i	−0.483871	+	0.838090i
$899$	−10.2462	−	17.7470i	−0.341730	−	0.591894i
$900$		0			0
$901$	−38.7386			−1.29057
$902$	3.06155	+	5.30277i	0.101939	+	0.176563i
$903$	−1.75379	−	3.03765i	−0.0583624	−	0.101087i
$904$	16.8078			0.559018
$905$		0			0
$906$	−26.2462	−	45.4598i	−0.871972	−	1.51030i
$907$	−25.0885	+	43.4546i	−0.833051	+	1.44289i	0.0625559	+	0.998041i	$0.480075\pi$
$907$	−25.0885	+	43.4546i	−0.833051	+	1.44289i	−0.895607	+	0.444846i	$0.853259\pi$
$908$	9.96543	+	17.2606i	0.330715	+	0.572814i
$909$	−17.8078	+	30.8440i	−0.590646	+	1.02303i
$910$		0			0
$911$	12.3845			0.410316			0.205158	−	0.978729i	$-0.434229\pi$
$911$	12.3845			0.410316			0.205158	+	0.978729i	$0.434229\pi$
$912$	−4.71922	+	10.1192i	−0.156269	+	0.335081i
$913$	10.8078			0.357685
$914$	3.52699	−	6.10892i	0.116662	−	0.202065i
$915$		0			0
$916$	−6.43845	−	11.1517i	−0.212732	−	0.368463i
$917$	−3.53457	+	6.12205i	−0.116722	+	0.202168i
$918$	3.68466	+	6.38202i	0.121612	+	0.210638i
$919$	20.2462			0.667861			0.333930	−	0.942598i	$-0.391625\pi$
$919$	20.2462			0.667861			0.333930	+	0.942598i	$0.391625\pi$
$920$		0			0
$921$	−30.6501	−	53.0875i	−1.00995	−	1.74929i
$922$	19.4924	+	33.7619i	0.641949	+	1.11189i
$923$	32.4924			1.06950
$924$	−1.12311			−0.0369475
$925$		0			0
$926$	−9.78078	+	16.9408i	−0.321416	+	0.556709i
$927$	−10.3423	−	17.9134i	−0.339687	−	0.588355i
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	17.9924	−	31.1638i	0.590312	−	1.02245i	−0.403878	−	0.914813i	$-0.632338\pi$
$929$	17.9924	−	31.1638i	0.590312	−	1.02245i	0.994190	−	0.107638i	$-0.0343287\pi$
$930$		0			0
$931$	17.0194	+	24.3086i	0.557789	+	0.796682i
$932$	−2.31534			−0.0758415
$933$	−5.12311	+	8.87348i	−0.167723	+	0.290505i
$934$	8.28078	−	14.3427i	0.270955	−	0.469308i
$935$		0			0
$936$	−3.56155	+	6.16879i	−0.116413	+	0.201633i
$937$	−25.0885	−	43.4546i	−0.819607	−	1.41960i	−0.905972	−	0.423337i	$-0.860859\pi$
$937$	−25.0885	−	43.4546i	−0.819607	−	1.41960i	0.0863653	−	0.996264i	$-0.472475\pi$
$938$	4.13826			0.135119
$939$	−11.0540			−0.360733
$940$		0			0
$941$	8.12311	+	14.0696i	0.264806	+	0.458657i	0.967513	−	0.252822i	$-0.0813589\pi$
$941$	8.12311	+	14.0696i	0.264806	+	0.458657i	−0.702707	+	0.711479i	$0.748026\pi$
$942$	−6.24621			−0.203513
$943$	−28.6847			−0.934101
$944$	−7.28078	−	12.6107i	−0.236969	−	0.410442i
$945$		0			0
$946$	1.56155	+	2.70469i	0.0507705	+	0.0879370i
$947$	28.2462	−	48.9239i	0.917879	−	1.58981i	0.115247	−	0.993337i	$-0.463234\pi$
$947$	28.2462	−	48.9239i	0.917879	−	1.58981i	0.802631	−	0.596475i	$-0.203433\pi$
$948$	14.2462	−	24.6752i	0.462695	−	0.801412i
$949$	3.36932			0.109373
$950$		0			0
$951$	−47.8617			−1.55202
$952$	−1.12311	+	1.94528i	−0.0364001	+	0.0630468i
$953$	−7.84233	+	13.5833i	−0.254038	+	0.440007i	−0.964634	−	0.263594i	$-0.915092\pi$
$953$	−7.84233	+	13.5833i	−0.254038	+	0.440007i	0.710596	+	0.703600i	$0.248425\pi$
$954$	−13.4654	−	23.3228i	−0.435960	−	0.755104i
$955$		0			0
$956$	−9.12311	−	15.8017i	−0.295062	−	0.511063i
$957$	5.12311			0.165606
$958$	29.3693			0.948880
$959$	1.19224	+	2.06501i	0.0384993	+	0.0666828i
$960$		0			0
$961$	73.9848			2.38661
$962$	9.36932			0.302079
$963$	4.00000	+	6.92820i	0.128898	+	0.223258i
$964$	4.28078	−	7.41452i	0.137875	−	0.238806i
$965$		0			0
$966$	2.63068	−	4.55648i	0.0846408	−	0.146602i
$967$	14.5616	−	25.2213i	0.468268	−	0.811064i	−0.531074	−	0.847325i	$-0.678212\pi$
$967$	14.5616	−	25.2213i	0.468268	−	0.811064i	0.999342	+	0.0362613i	$0.0115449\pi$
$968$	−10.0000			−0.321412
$969$	24.1771	−	51.8418i	0.776680	−	1.66540i
$970$		0			0
$971$	−8.96543	+	15.5286i	−0.287714	+	0.498336i	−0.973264	−	0.229690i	$-0.926229\pi$
$971$	−8.96543	+	15.5286i	−0.287714	+	0.498336i	0.685549	+	0.728026i	$0.259562\pi$
$972$	11.1231	−	19.2658i	0.356774	−	0.617950i
$973$	1.93087	+	3.34436i	0.0619008	+	0.107215i
$974$	−3.46543	+	6.00231i	−0.111040	+	0.192326i
$975$		0			0
$976$	5.12311			0.163987
$977$	30.3153			0.969874			0.484937	−	0.874549i	$-0.338843\pi$
$977$	30.3153			0.969874			0.484937	+	0.874549i	$0.338843\pi$
$978$	21.8423	+	37.8320i	0.698441	+	1.20973i
$979$	1.34233	+	2.32498i	0.0429010	+	0.0743068i
$980$		0			0
$981$	−50.7386			−1.61996
$982$	4.58854	+	7.94759i	0.146426	+	0.253618i
$983$	20.7808	−	35.9934i	0.662804	−	1.14801i	−0.317072	−	0.948401i	$-0.602700\pi$
$983$	20.7808	−	35.9934i	0.662804	−	1.14801i	0.979876	−	0.199608i	$-0.0639670\pi$
$984$	7.84233	+	13.5833i	0.250004	+	0.433020i
$985$		0			0
$986$	5.12311	−	8.87348i	0.163153	−	0.282589i
$987$	3.23106			0.102846
$988$	8.68466	−	0.759413i	0.276296	−	0.0241601i
$989$	−14.6307			−0.465229
$990$		0			0
$991$	4.19224	−	7.26117i	0.133171	−	0.230659i	−0.791726	−	0.610876i	$-0.790817\pi$
$991$	4.19224	−	7.26117i	0.133171	−	0.230659i	0.924897	+	0.380217i	$0.124151\pi$
$992$	−5.12311	−	8.87348i	−0.162659	−	0.281733i
$993$	−30.0885	+	52.1149i	−0.954831	+	1.65382i
$994$	3.56155	+	6.16879i	0.112966	+	0.195662i
$995$		0			0
$996$	27.6847			0.877222
$997$	−1.34233	−	2.32498i	−0.0425120	−	0.0736329i	0.843986	−	0.536364i	$-0.180203\pi$
$997$	−1.34233	−	2.32498i	−0.0425120	−	0.0736329i	−0.886498	+	0.462732i	$0.846869\pi$
$998$	−14.5000	−	25.1147i	−0.458989	−	0.794993i
$999$	6.73863			0.213201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.h.201.1		4
5.2	odd	4		950.2.j.f.49.2		8
5.3	odd	4		950.2.j.f.49.3		8
5.4	even	2		190.2.e.c.11.2	✓	4
15.14	odd	2		1710.2.l.m.1531.1		4
19.7	even	3	inner	950.2.e.h.501.1		4
20.19	odd	2		1520.2.q.h.961.1		4
95.7	odd	12		950.2.j.f.349.3		8
95.49	even	6		3610.2.a.k.1.1		2
95.64	even	6		190.2.e.c.121.2	yes	4
95.83	odd	12		950.2.j.f.349.2		8
95.84	odd	6		3610.2.a.u.1.2		2
285.254	odd	6		1710.2.l.m.1261.1		4
380.159	odd	6		1520.2.q.h.881.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.c.11.2	✓	4	5.4	even	2
190.2.e.c.121.2	yes	4	95.64	even	6
950.2.e.h.201.1		4	1.1	even	1	trivial
950.2.e.h.501.1		4	19.7	even	3	inner
950.2.j.f.49.2		8	5.2	odd	4
950.2.j.f.49.3		8	5.3	odd	4
950.2.j.f.349.2		8	95.83	odd	12
950.2.j.f.349.3		8	95.7	odd	12
1520.2.q.h.881.1		4	380.159	odd	6
1520.2.q.h.961.1		4	20.19	odd	2
1710.2.l.m.1261.1		4	285.254	odd	6
1710.2.l.m.1531.1		4	15.14	odd	2
3610.2.a.k.1.1		2	95.49	even	6
3610.2.a.u.1.2		2	95.84	odd	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.28078 + 2.21837i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.28078 - 2.21837i) q^{6} -0.438447 q^{7} +1.00000 q^{8} +(-1.78078 - 3.08440i) q^{9} +1.00000 q^{11} +2.56155 q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.219224 - 0.379706i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.56155 - 4.43674i) q^{17} +3.56155 q^{18} +(-2.50000 - 3.57071i) q^{19} +(0.561553 - 0.972638i) q^{21} +(-0.500000 + 0.866025i) q^{22} +(-2.34233 - 4.05703i) q^{23} +(-1.28078 + 2.21837i) q^{24} +2.00000 q^{26} +1.43845 q^{27} +(0.219224 + 0.379706i) q^{28} +(-1.00000 - 1.73205i) q^{29} +10.2462 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 + 2.21837i) q^{33} +(2.56155 + 4.43674i) q^{34} +(-1.78078 + 3.08440i) q^{36} +4.68466 q^{37} +(4.34233 - 0.379706i) q^{38} +5.12311 q^{39} +(3.06155 - 5.30277i) q^{41} +(0.561553 + 0.972638i) q^{42} +(1.56155 - 2.70469i) q^{43} +(-0.500000 - 0.866025i) q^{44} +4.68466 q^{46} +(1.43845 + 2.49146i) q^{47} +(-1.28078 - 2.21837i) q^{48} -6.80776 q^{49} +(6.56155 + 11.3649i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.78078 - 6.54850i) q^{53} +(-0.719224 + 1.24573i) q^{54} -0.438447 q^{56} +(11.1231 - 0.972638i) q^{57} +2.00000 q^{58} +(-7.28078 + 12.6107i) q^{59} +(-2.56155 - 4.43674i) q^{61} +(-5.12311 + 8.87348i) q^{62} +(0.780776 + 1.35234i) q^{63} +1.00000 q^{64} +(-1.28078 - 2.21837i) q^{66} +(4.71922 + 8.17394i) q^{67} -5.12311 q^{68} +12.0000 q^{69} +(-8.12311 + 14.0696i) q^{71} +(-1.78078 - 3.08440i) q^{72} +(-0.842329 + 1.45896i) q^{73} +(-2.34233 + 4.05703i) q^{74} +(-1.84233 + 3.95042i) q^{76} -0.438447 q^{77} +(-2.56155 + 4.43674i) q^{78} +(5.56155 - 9.63289i) q^{79} +(3.50000 - 6.06218i) q^{81} +(3.06155 + 5.30277i) q^{82} +10.8078 q^{83} -1.12311 q^{84} +(1.56155 + 2.70469i) q^{86} +5.12311 q^{87} +1.00000 q^{88} +(1.34233 + 2.32498i) q^{89} +(0.438447 + 0.759413i) q^{91} +(-2.34233 + 4.05703i) q^{92} +(-13.1231 + 22.7299i) q^{93} -2.87689 q^{94} +2.56155 q^{96} +(0.842329 - 1.45896i) q^{97} +(3.40388 - 5.89570i) q^{98} +(-1.78078 - 3.08440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - q^{6} - 10 q^{7} + 4 q^{8} - 3 q^{9} + 4 q^{11} + 2 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{16} + 2 q^{17} + 6 q^{18} - 10 q^{19} - 6 q^{21} - 2 q^{22} + 3 q^{23} - q^{24} + 8 q^{26} + 14 q^{27} + 5 q^{28} - 4 q^{29} + 8 q^{31} - 2 q^{32} - q^{33} + 2 q^{34} - 3 q^{36} - 6 q^{37} + 5 q^{38} + 4 q^{39} + 4 q^{41} - 6 q^{42} - 2 q^{43} - 2 q^{44} - 6 q^{46} + 14 q^{47} - q^{48} + 14 q^{49} + 18 q^{51} - 4 q^{52} - 11 q^{53} - 7 q^{54} - 10 q^{56} + 28 q^{57} + 8 q^{58} - 25 q^{59} - 2 q^{61} - 4 q^{62} - q^{63} + 4 q^{64} - q^{66} + 23 q^{67} - 4 q^{68} + 48 q^{69} - 16 q^{71} - 3 q^{72} + 9 q^{73} + 3 q^{74} + 5 q^{76} - 10 q^{77} - 2 q^{78} + 14 q^{79} + 14 q^{81} + 4 q^{82} + 2 q^{83} + 12 q^{84} - 2 q^{86} + 4 q^{87} + 4 q^{88} - 7 q^{89} + 10 q^{91} + 3 q^{92} - 36 q^{93} - 28 q^{94} + 2 q^{96} - 9 q^{97} - 7 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - q^6 - 10 * q^7 + 4 * q^8 - 3 * q^9 + 4 * q^11 + 2 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^16 + 2 * q^17 + 6 * q^18 - 10 * q^19 - 6 * q^21 - 2 * q^22 + 3 * q^23 - q^24 + 8 * q^26 + 14 * q^27 + 5 * q^28 - 4 * q^29 + 8 * q^31 - 2 * q^32 - q^33 + 2 * q^34 - 3 * q^36 - 6 * q^37 + 5 * q^38 + 4 * q^39 + 4 * q^41 - 6 * q^42 - 2 * q^43 - 2 * q^44 - 6 * q^46 + 14 * q^47 - q^48 + 14 * q^49 + 18 * q^51 - 4 * q^52 - 11 * q^53 - 7 * q^54 - 10 * q^56 + 28 * q^57 + 8 * q^58 - 25 * q^59 - 2 * q^61 - 4 * q^62 - q^63 + 4 * q^64 - q^66 + 23 * q^67 - 4 * q^68 + 48 * q^69 - 16 * q^71 - 3 * q^72 + 9 * q^73 + 3 * q^74 + 5 * q^76 - 10 * q^77 - 2 * q^78 + 14 * q^79 + 14 * q^81 + 4 * q^82 + 2 * q^83 + 12 * q^84 - 2 * q^86 + 4 * q^87 + 4 * q^88 - 7 * q^89 + 10 * q^91 + 3 * q^92 - 36 * q^93 - 28 * q^94 + 2 * q^96 - 9 * q^97 - 7 * q^98 - 3 * q^99

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