LMFDB - Embedded newform 475.2.e.f.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 17 x^{10} - 18 x^{9} + 109 x^{8} - 93 x^{7} + 484 x^{6} - 147 x^{5} + 1009 x^{4} - 552 x^{3} + 1107 x^{2} + 33 x + 1 $ x^12 - 3x^11 + 17x^10 - 18x^9 + 109x^8 - 93x^7 + 484x^6 - 147x^5 + 1009x^4 - 552x^3 + 1107x^2 + 33*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$-0.975939 + 1.69038i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.f.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +O(q^{10})$	\(q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 + 5.94669i) q^{13} +(-0.641933 - 1.11186i) q^{14} +(1.03919 + 1.79993i) q^{16} +(2.61787 + 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 - 3.72468i) q^{19} +(-0.873195 - 1.51242i) q^{21} +(-2.79990 - 4.84957i) q^{22} +(-1.45072 + 2.51271i) q^{23} +(-2.27175 - 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 + 1.38812i) q^{28} +(-3.52494 + 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 - 6.57195i) q^{32} +(-3.80859 - 6.59667i) q^{33} +(5.68101 - 9.83980i) q^{34} +(-7.73984 - 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 + 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 - 5.39393i) q^{41} +(-1.89491 + 3.28208i) q^{42} +(-2.18013 - 3.77609i) q^{43} +(-3.49558 + 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 + 2.21600i) q^{47} +(3.06756 - 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 - 13.3847i) q^{51} +(-9.30181 - 16.1112i) q^{52} +(4.79573 - 8.30645i) q^{53} +(-8.69138 - 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 + 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 + 2.53263i) q^{59} +(-1.16586 + 2.01932i) q^{61} +(7.39371 + 12.8063i) q^{62} +(-1.69013 + 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 + 14.3153i) q^{66} +(-2.15122 + 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 + 11.6852i) q^{71} +(-4.39714 + 7.61607i) q^{72} +(4.21337 + 7.29777i) q^{73} +(5.23574 + 9.06858i) q^{74} +(11.8064 - 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 - 38.0935i) q^{78} +(-2.93630 - 5.08583i) q^{79} +(-3.25215 - 5.63288i) q^{81} +(-6.75806 + 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 + 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 + 3.21855i) q^{89} +(-2.03122 + 3.51818i) q^{91} +(-3.93039 - 6.80764i) q^{92} +(10.0574 + 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 - 2.18732i) q^{97} +(7.21552 + 12.4977i) q^{98} +(-7.37182 + 12.7684i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	$ 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.08504	−	1.87935i	−0.767241	−	1.32890i	−0.939053	−	0.343771i	$-0.888295\pi$
$2$	−1.08504	−	1.87935i	−0.767241	−	1.32890i	0.171812	−	0.985130i	$-0.445038\pi$
$3$	−1.47594	−	2.55640i	−0.852134	−	1.47594i	−0.879279	−	0.476308i	$-0.841975\pi$
$3$	−1.47594	−	2.55640i	−0.852134	−	1.47594i	0.0271449	−	0.999632i	$-0.491358\pi$
$4$	−1.35464	+	2.34630i	−0.677319	+	1.17315i
$5$		0			0
$5$		0			0
$6$	−3.20292	+	5.54761i	−1.30758	+	2.26480i
$7$	0.591620			0.223611			0.111806	−	0.993730i	$-0.464337\pi$
$7$	0.591620			0.223611			0.111806	+	0.993730i	$0.464337\pi$
$8$	1.53919			0.544185
$9$	−2.85679	+	4.94811i	−0.952264	+	1.64937i
$10$		0			0
$11$	2.58045			0.778036			0.389018	−	0.921230i	$-0.372814\pi$
$11$	2.58045			0.778036			0.389018	+	0.921230i	$0.372814\pi$
$12$	7.99745			2.30867
$13$	−3.43332	+	5.94669i	−0.952232	+	1.64931i	−0.211653	+	0.977345i	$0.567885\pi$
$13$	−3.43332	+	5.94669i	−0.952232	+	1.64931i	−0.740579	+	0.671969i	$0.765449\pi$
$14$	−0.641933	−	1.11186i	−0.171564	−	0.297157i
$15$		0			0
$16$	1.03919	+	1.79993i	0.259797	+	0.449982i
$17$	2.61787	+	4.53429i	0.634927	+	1.09973i	0.986531	+	0.163577i	$0.0523033\pi$
$17$	2.61787	+	4.53429i	0.634927	+	1.09973i	−0.351603	+	0.936149i	$0.614363\pi$
$18$	12.3990			2.92247
$19$	−2.26423	−	3.72468i	−0.519449	−	0.854501i
$19$	−2.26423	−	3.72468i	−0.519449	−	0.854501i
$20$		0			0
$21$	−0.873195	−	1.51242i	−0.190547	−	0.330037i
$22$	−2.79990	−	4.84957i	−0.596941	−	1.03393i
$23$	−1.45072	+	2.51271i	−0.302495	+	0.523937i	−0.976701	−	0.214607i	$-0.931153\pi$
$23$	−1.45072	+	2.51271i	−0.302495	+	0.523937i	0.674205	+	0.738544i	$0.264486\pi$
$24$	−2.27175	−	3.93478i	−0.463719	−	0.803185i
$25$		0			0
$26$	14.9012			2.92237
$27$	8.01017			1.54156
$28$	−0.801431	+	1.38812i	−0.151456	+	0.262330i
$29$	−3.52494	+	6.10538i	−0.654565	+	1.13374i	0.327438	+	0.944873i	$0.393815\pi$
$29$	−3.52494	+	6.10538i	−0.654565	+	1.13374i	−0.982003	+	0.188867i	$0.939518\pi$
$30$		0			0
$31$	−6.81421			−1.22387			−0.611934	−	0.790909i	$-0.709608\pi$
$31$	−6.81421			−1.22387			−0.611934	+	0.790909i	$0.709608\pi$
$32$	3.79432	−	6.57195i	0.670747	−	1.16177i
$33$	−3.80859	−	6.59667i	−0.662990	−	1.14833i
$34$	5.68101	−	9.83980i	0.974285	−	1.68751i
$35$		0			0
$36$	−7.73984	−	13.4058i	−1.28997	−	2.23430i
$37$	−4.82538			−0.793287			−0.396644	−	0.917973i	$-0.629825\pi$
$37$	−4.82538			−0.793287			−0.396644	+	0.917973i	$0.629825\pi$
$38$	−4.54320	+	8.29672i	−0.737005	+	1.34591i
$39$	20.2695			3.24572
$40$		0			0
$41$	−3.11419	−	5.39393i	−0.486355	−	0.842391i	0.513522	−	0.858076i	$-0.328340\pi$
$41$	−3.11419	−	5.39393i	−0.486355	−	0.842391i	−0.999877	+	0.0156852i	$0.995007\pi$
$42$	−1.89491	+	3.28208i	−0.292391	+	0.506436i
$43$	−2.18013	−	3.77609i	−0.332467	−	0.575849i	0.650528	−	0.759482i	$-0.274548\pi$
$43$	−2.18013	−	3.77609i	−0.332467	−	0.575849i	−0.982995	+	0.183633i	$0.941214\pi$
$44$	−3.49558	+	6.05452i	−0.526978	+	0.912753i
$45$		0			0
$46$	6.29636			0.928348
$47$	−1.27941	+	2.21600i	−0.186621	+	0.323237i	−0.944121	−	0.329598i	$-0.893087\pi$
$47$	−1.27941	+	2.21600i	−0.186621	+	0.323237i	0.757501	+	0.652834i	$0.226420\pi$
$48$	3.06756	−	5.31317i	0.442764	−	0.766890i
$49$	−6.64999			−0.949998
$50$		0			0
$51$	7.72764	−	13.3847i	1.08209	−	1.87423i
$52$	−9.30181	−	16.1112i	−1.28993	−	2.23422i
$53$	4.79573	−	8.30645i	0.658745	−	1.14098i	−0.322196	−	0.946673i	$-0.604421\pi$
$53$	4.79573	−	8.30645i	0.658745	−	1.14098i	0.980941	−	0.194306i	$-0.0622456\pi$
$54$	−8.69138	−	15.0539i	−1.18275	−	2.04858i
$55$		0			0
$56$	0.910615			0.121686
$57$	−6.17993	+	11.2857i	−0.818551	+	1.49483i
$58$	15.2989			2.00884
$59$	1.46221	+	2.53263i	0.190364	+	0.329720i	0.945371	−	0.325997i	$-0.105700\pi$
$59$	1.46221	+	2.53263i	0.190364	+	0.329720i	−0.755007	+	0.655717i	$0.772367\pi$
$60$		0			0
$61$	−1.16586	+	2.01932i	−0.149273	+	0.258548i	−0.930959	−	0.365124i	$-0.881027\pi$
$61$	−1.16586	+	2.01932i	−0.149273	+	0.258548i	0.781686	+	0.623672i	$0.214360\pi$
$62$	7.39371	+	12.8063i	0.939003	+	1.62640i
$63$	−1.69013	+	2.92740i	−0.212937	+	0.368818i
$64$	−12.3112			−1.53891
$65$		0			0
$66$	−8.26497	+	14.3153i	−1.01735	+	1.76210i
$67$	−2.15122	+	3.72603i	−0.262814	+	0.455207i	−0.966989	−	0.254820i	$-0.917984\pi$
$67$	−2.15122	+	3.72603i	−0.262814	+	0.455207i	0.704175	+	0.710027i	$0.251317\pi$
$68$	−14.1851			−1.72019
$69$	8.56468			1.03107
$70$		0			0
$71$	6.74645	+	11.6852i	0.800656	+	1.38678i	0.919185	+	0.393827i	$0.128849\pi$
$71$	6.74645	+	11.6852i	0.800656	+	1.38678i	−0.118528	+	0.992951i	$0.537818\pi$
$72$	−4.39714	+	7.61607i	−0.518208	+	0.897563i
$73$	4.21337	+	7.29777i	0.493137	+	0.854139i	0.999969	−	0.00790620i	$-0.00251665\pi$
$73$	4.21337	+	7.29777i	0.493137	+	0.854139i	−0.506831	+	0.862045i	$0.669183\pi$
$74$	5.23574	+	9.06858i	0.608643	+	1.05420i
$75$		0			0
$76$	11.8064	−	0.266962i	1.35429	−	0.0306226i
$77$	1.52665			0.173978
$78$	−21.9933	−	38.0935i	−2.49025	−	4.31324i
$79$	−2.93630	−	5.08583i	−0.330360	−	0.572200i	0.652222	−	0.758028i	$-0.273837\pi$
$79$	−2.93630	−	5.08583i	−0.330360	−	0.572200i	−0.982582	+	0.185827i	$0.940503\pi$
$80$		0			0
$81$	−3.25215	−	5.63288i	−0.361350	−	0.625876i
$82$	−6.75806	+	11.7053i	−0.746303	+	1.29263i
$83$	−4.02036			−0.441292			−0.220646	−	0.975354i	$-0.570816\pi$
$83$	−4.02036			−0.441292			−0.220646	+	0.975354i	$0.570816\pi$
$84$	4.73145			0.516244
$85$		0			0
$86$	−4.73107	+	8.19445i	−0.510164	+	0.883630i
$87$	20.8104			2.23111
$88$	3.97180			0.423396
$89$	−1.85823	+	3.21855i	−0.196972	+	0.341166i	−0.947545	−	0.319622i	$-0.896444\pi$
$89$	−1.85823	+	3.21855i	−0.196972	+	0.341166i	0.750573	+	0.660787i	$0.229778\pi$
$90$		0			0
$91$	−2.03122	+	3.51818i	−0.212930	+	0.368805i
$92$	−3.93039	−	6.80764i	−0.409772	−	0.709745i
$93$	10.0574	+	17.4199i	1.04290	+	1.80636i
$94$	5.55285			0.572733
$95$		0			0
$96$	−22.4007			−2.28627
$97$	−1.26285	−	2.18732i	−0.128223	−	0.222089i	0.794765	−	0.606917i	$-0.207594\pi$
$97$	−1.26285	−	2.18732i	−0.128223	−	0.222089i	−0.922988	+	0.384828i	$0.874261\pi$
$98$	7.21552	+	12.4977i	0.728878	+	1.26245i
$99$	−7.37182	+	12.7684i	−0.740895	+	1.28327i
$100$		0			0
$101$	−0.692736	+	1.19985i	−0.0689298	+	0.119390i	−0.898430	−	0.439116i	$-0.855292\pi$
$101$	−0.692736	+	1.19985i	−0.0689298	+	0.119390i	0.829501	+	0.558506i	$0.188625\pi$
$102$	−33.5393			−3.32088
$103$	0.166774			0.0164328			0.00821638	−	0.999966i	$-0.497385\pi$
$103$	0.166774			0.0164328			0.00821638	+	0.999966i	$0.497385\pi$
$104$	−5.28453	+	9.15307i	−0.518191	+	0.897533i
$105$		0			0
$106$	−20.8143			−2.02166
$107$	−4.51729			−0.436703			−0.218351	−	0.975870i	$-0.570068\pi$
$107$	−4.51729			−0.436703			−0.218351	+	0.975870i	$0.570068\pi$
$108$	−10.8509	+	18.7943i	−1.04413	+	1.80848i
$109$	5.35464	+	9.27450i	0.512881	+	0.888336i	0.999888	+	0.0149384i	$0.00475523\pi$
$109$	5.35464	+	9.27450i	0.512881	+	0.888336i	−0.487007	+	0.873398i	$0.661911\pi$
$110$		0			0
$111$	7.12196	+	12.3356i	0.675987	+	1.17084i
$112$	0.614805	+	1.06487i	0.0580936	+	0.100621i
$113$	13.2065			1.24237			0.621183	−	0.783665i	$-0.286652\pi$
$113$	13.2065			1.24237			0.621183	+	0.783665i	$0.286652\pi$
$114$	27.9152	−	0.631206i	2.61450	−	0.0591178i
$115$		0			0
$116$	−9.55004	−	16.5411i	−0.886699	−	1.53581i
$117$	−19.6166	−	33.9769i	−1.81355	−	3.14117i
$118$	3.17313	−	5.49602i	0.292110	−	0.505950i
$119$	1.54879	+	2.68257i	0.141977	+	0.245911i
$120$		0			0
$121$	−4.34127			−0.394661
$122$	5.06002			0.458113
$123$	−9.19271	+	15.9222i	−0.828879	+	1.43566i
$124$	9.23079	−	15.9882i	0.828949	−	1.43578i
$125$		0			0
$126$	7.33548			0.653496
$127$	−0.860805	+	1.49096i	−0.0763841	+	0.132301i	−0.901687	−	0.432389i	$-0.857671\pi$
$127$	−0.860805	+	1.49096i	−0.0763841	+	0.132301i	0.825303	+	0.564690i	$0.191004\pi$
$128$	5.76959	+	9.99323i	0.509965	+	0.883285i
$129$	−6.43548	+	11.1466i	−0.566612	+	0.981401i
$130$		0			0
$131$	−1.64201	−	2.84405i	−0.143463	−	0.248486i	0.785335	−	0.619071i	$-0.212491\pi$
$131$	−1.64201	−	2.84405i	−0.143463	−	0.248486i	−0.928799	+	0.370585i	$0.879157\pi$
$132$	20.6370			1.79622
$133$	−1.33956	−	2.20360i	−0.116155	−	0.191076i
$134$	9.33668			0.806567
$135$		0			0
$136$	4.02940	+	6.97913i	0.345518	+	0.598455i
$137$	−4.07541	+	7.05882i	−0.348186	+	0.603075i	−0.985927	−	0.167175i	$-0.946536\pi$
$137$	−4.07541	+	7.05882i	−0.348186	+	0.603075i	0.637741	+	0.770251i	$0.279869\pi$
$138$	−9.29304	−	16.0960i	−0.791076	−	1.37018i
$139$	7.81401	−	13.5343i	0.662776	−	1.14796i	−0.317108	−	0.948390i	$-0.602712\pi$
$139$	7.81401	−	13.5343i	0.662776	−	1.14796i	0.979883	−	0.199571i	$-0.0639550\pi$
$140$		0			0
$141$	7.55331			0.636103
$142$	14.6404	−	25.3579i	1.22859	−	2.12799i
$143$	−8.85952	+	15.3451i	−0.740870	+	1.28323i
$144$	−11.8750			−0.989582
$145$		0			0
$146$	9.14337	−	15.8368i	0.756711	−	1.31066i
$147$	9.81497	+	17.0000i	0.809525	+	1.40214i
$148$	6.53664	−	11.3218i	0.537308	−	0.930646i
$149$	−1.61005	−	2.78869i	−0.131900	−	0.228458i	0.792509	−	0.609861i	$-0.208775\pi$
$149$	−1.61005	−	2.78869i	−0.131900	−	0.228458i	−0.924409	+	0.381402i	$0.875441\pi$
$150$		0			0
$151$	−11.1226			−0.905142			−0.452571	−	0.891728i	$-0.649493\pi$
$151$	−11.1226			−0.905142			−0.452571	+	0.891728i	$0.649493\pi$
$152$	−3.48507	−	5.73299i	−0.282677	−	0.465007i
$153$	−29.9149			−2.41847
$154$	−1.65648	−	2.86910i	−0.133483	−	0.231199i
$155$		0			0
$156$	−27.4578	+	47.5583i	−2.19838	+	3.80771i
$157$	−10.7157	−	18.5602i	−0.855209	−	1.48127i	−0.876451	−	0.481491i	$-0.840095\pi$
$157$	−10.7157	−	18.5602i	−0.855209	−	1.48127i	0.0212418	−	0.999774i	$-0.493238\pi$
$158$	−6.37203	+	11.0367i	−0.506932	+	0.878032i
$159$	−28.3128			−2.24535
$160$		0			0
$161$	−0.858273	+	1.48657i	−0.0676414	+	0.117158i
$162$	−7.05744	+	12.2238i	−0.554485	+	0.960396i
$163$	10.3129			0.807768			0.403884	−	0.914810i	$-0.367660\pi$
$163$	10.3129			0.807768			0.403884	+	0.914810i	$0.367660\pi$
$164$	16.8744			1.31767
$165$		0			0
$166$	4.36226	+	7.55566i	0.338577	+	0.586433i
$167$	−3.25342	+	5.63509i	−0.251757	+	0.436056i	−0.964010	−	0.265867i	$-0.914342\pi$
$167$	−3.25342	+	5.63509i	−0.251757	+	0.436056i	0.712252	+	0.701923i	$0.247675\pi$
$168$	−1.34401	−	2.32790i	−0.103693	−	0.179601i
$169$	−17.0754	−	29.5754i	−1.31349	−	2.27503i
$170$		0			0
$171$	24.8986	−	0.562995i	1.90404	−	0.0430533i
$172$	11.8131			0.900744
$173$	−3.13027	−	5.42179i	−0.237990	−	0.412211i	0.722147	−	0.691739i	$-0.243155\pi$
$173$	−3.13027	−	5.42179i	−0.237990	−	0.412211i	−0.960137	+	0.279528i	$0.909822\pi$
$174$	−22.5802	−	39.1100i	−1.71180	−	2.96492i
$175$		0			0
$176$	2.68158	+	4.64463i	0.202131	+	0.350102i
$177$	4.31628	−	7.47601i	0.324431	−	0.561931i
$178$	8.06505			0.604501
$179$	23.1893			1.73325			0.866624	−	0.498961i	$-0.166285\pi$
$179$	23.1893			1.73325			0.866624	+	0.498961i	$0.166285\pi$
$180$		0			0
$181$	1.59948	−	2.77039i	0.118889	−	0.205921i	−0.800439	−	0.599414i	$-0.795400\pi$
$181$	1.59948	−	2.77039i	0.118889	−	0.205921i	0.919328	+	0.393493i	$0.128733\pi$
$182$	8.81585			0.653474
$183$	6.88294			0.508801
$184$	−2.23293	+	3.86754i	−0.164614	+	0.285119i
$185$		0			0
$186$	21.8253	−	37.8026i	1.60031	−	2.77182i
$187$	6.75529	+	11.7005i	0.493996	+	0.855626i
$188$	−3.46627	−	6.00375i	−0.252803	−	0.437868i
$189$	4.73898			0.344710
$190$		0			0
$191$	18.9443			1.37076			0.685382	−	0.728184i	$-0.259635\pi$
$191$	18.9443			1.37076			0.685382	+	0.728184i	$0.259635\pi$
$192$	18.1706	+	31.4725i	1.31135	+	2.27133i
$193$	0.515269	+	0.892472i	0.0370899	+	0.0642415i	0.883974	−	0.467535i	$-0.154858\pi$
$193$	0.515269	+	0.892472i	0.0370899	+	0.0642415i	−0.846885	+	0.531777i	$0.821525\pi$
$194$	−2.74049	+	4.74667i	−0.196756	+	0.340791i
$195$		0			0
$196$	9.00832	−	15.6029i	0.643452	−	1.11449i
$197$	−18.5515			−1.32174			−0.660868	−	0.750502i	$-0.729812\pi$
$197$	−18.5515			−1.32174			−0.660868	+	0.750502i	$0.729812\pi$
$198$	31.9950			2.27378
$199$	−11.3166	+	19.6010i	−0.802215	+	1.38948i	0.115940	+	0.993256i	$0.463012\pi$
$199$	−11.3166	+	19.6010i	−0.802215	+	1.38948i	−0.918155	+	0.396221i	$0.870321\pi$
$200$		0			0
$201$	12.7003			0.895810
$202$	3.00659			0.211543
$203$	−2.08542	+	3.61206i	−0.146368	+	0.253517i
$204$	20.9363	+	36.2627i	1.46583	+	2.53890i
$205$		0			0
$206$	−0.180957	−	0.313427i	−0.0126079	−	0.0218375i
$207$	−8.28879	−	14.3566i	−0.576111	−	0.997853i
$208$	−14.2715			−0.989549
$209$	−5.84273	−	9.61137i	−0.404150	−	0.664832i
$210$		0			0
$211$	−6.21978	−	10.7730i	−0.428187	−	0.741642i	0.568525	−	0.822666i	$-0.307514\pi$
$211$	−6.21978	−	10.7730i	−0.428187	−	0.741642i	−0.996712	+	0.0810240i	$0.974181\pi$
$212$	12.9930	+	22.5045i	0.892360	+	1.54561i
$213$	19.9147	−	34.4933i	1.36453	−	2.36344i
$214$	4.90145	+	8.48956i	0.335056	+	0.580335i
$215$		0			0
$216$	12.3292			0.838893
$217$	−4.03142			−0.273671
$218$	11.6200	−	20.1265i	0.787008	−	1.36314i
$219$	12.4373	−	21.5421i	0.840438	−	1.45568i
$220$		0			0
$221$	−35.9520			−2.41839
$222$	15.4553	−	26.7693i	1.03729	−	1.79664i
$223$	9.58654	+	16.6044i	0.641962	+	1.11191i	0.984994	+	0.172588i	$0.0552128\pi$
$223$	9.58654	+	16.6044i	0.641962	+	1.11191i	−0.343032	+	0.939324i	$0.611454\pi$
$224$	2.24479	−	3.88810i	0.149987	−	0.259784i
$225$		0			0
$226$	−14.3297	−	24.8197i	−0.953195	−	1.65098i
$227$	−26.5208			−1.76025			−0.880123	−	0.474745i	$-0.842540\pi$
$227$	−26.5208			−1.76025			−0.880123	+	0.474745i	$0.842540\pi$
$228$	−18.1080	−	29.7880i	−1.19923	−	1.97276i
$229$	−8.81023			−0.582196			−0.291098	−	0.956693i	$-0.594021\pi$
$229$	−8.81023			−0.582196			−0.291098	+	0.956693i	$0.594021\pi$
$230$		0			0
$231$	−2.25324	−	3.90272i	−0.148252	−	0.256780i
$232$	−5.42555	+	9.39733i	−0.356205	+	0.616965i
$233$	2.25616	+	3.90778i	0.147806	+	0.256007i	0.930416	−	0.366505i	$-0.119446\pi$
$233$	2.25616	+	3.90778i	0.147806	+	0.256007i	−0.782610	+	0.622512i	$0.786112\pi$
$234$	−42.5697	+	73.7328i	−2.78287	+	4.82006i
$235$		0			0
$236$	−7.92308			−0.515749
$237$	−8.66761	+	15.0127i	−0.563022	+	0.975182i
$238$	3.36100	−	5.82142i	0.217861	−	0.377347i
$239$	−7.82431			−0.506112			−0.253056	−	0.967452i	$-0.581436\pi$
$239$	−7.82431			−0.506112			−0.253056	+	0.967452i	$0.581436\pi$
$240$		0			0
$241$	−13.6697	+	23.6766i	−0.880541	+	1.52514i	−0.0298010	+	0.999556i	$0.509487\pi$
$241$	−13.6697	+	23.6766i	−0.880541	+	1.52514i	−0.850740	+	0.525586i	$0.823846\pi$
$242$	4.71046	+	8.15876i	0.302800	+	0.524465i
$243$	2.41531	−	4.18345i	0.154942	−	0.268368i
$244$	−3.15863	−	5.47091i	−0.202210	−	0.350239i
$245$		0			0
$246$	39.8979			2.54380
$247$	29.9233	−	0.676612i	1.90398	−	0.0430518i
$248$	−10.4884			−0.666011
$249$	5.93380	+	10.2777i	0.376040	+	0.651320i
$250$		0			0
$251$	8.11886	−	14.0623i	0.512458	−	0.887603i	−0.487438	−	0.873158i	$-0.662068\pi$
$251$	8.11886	−	14.0623i	0.512458	−	0.887603i	0.999896	−	0.0144451i	$-0.00459818\pi$
$252$	−4.57904	−	7.93113i	−0.288452	−	0.499614i
$253$	−3.74350	+	6.48394i	−0.235352	+	0.407642i
$254$	3.73604			0.234420
$255$		0			0
$256$	0.209275	−	0.362476i	0.0130797	−	0.0226547i
$257$	4.57174	−	7.91848i	0.285177	−	0.493941i	−0.687475	−	0.726208i	$-0.741281\pi$
$257$	4.57174	−	7.91848i	0.285177	−	0.493941i	0.972652	+	0.232267i	$0.0746143\pi$
$258$	27.9311			1.73891
$259$	−2.85479			−0.177388
$260$		0			0
$261$	−20.1400	−	34.8836i	−1.24664	−	2.15924i
$262$	−3.56331	+	6.17183i	−0.220142	+	0.381297i
$263$	7.64861	+	13.2478i	0.471634	+	0.816894i	0.999473	−	0.0324505i	$-0.0103311\pi$
$263$	7.64861	+	13.2478i	0.471634	+	0.816894i	−0.527840	+	0.849344i	$0.676998\pi$
$264$	−5.86214	−	10.1535i	−0.360790	−	0.624906i
$265$		0			0
$266$	−2.68785	+	4.90850i	−0.164803	+	0.300960i
$267$	10.9705			0.671386
$268$	−5.82826	−	10.0948i	−0.356017	−	0.616640i
$269$	7.07334	+	12.2514i	0.431269	+	0.746981i	0.996983	−	0.0776213i	$-0.0247325\pi$
$269$	7.07334	+	12.2514i	0.431269	+	0.746981i	−0.565714	+	0.824602i	$0.691399\pi$
$270$		0			0
$271$	5.68158	+	9.84078i	0.345131	+	0.597785i	0.985378	−	0.170385i	$-0.0545010\pi$
$271$	5.68158	+	9.84078i	0.345131	+	0.597785i	−0.640246	+	0.768170i	$0.721168\pi$
$272$	−5.44093	+	9.42396i	−0.329905	+	0.571412i
$273$	11.9918			0.725779
$274$	17.6880			1.06857
$275$		0			0
$276$	−11.6020	+	20.0953i	−0.698360	+	1.20960i
$277$	18.9102			1.13620			0.568101	−	0.822959i	$-0.307678\pi$
$277$	18.9102			1.13620			0.568101	+	0.822959i	$0.307678\pi$
$278$	−33.9142			−2.03404
$279$	19.4668	−	33.7175i	1.16545	−	2.01861i
$280$		0			0
$281$	13.9438	−	24.1513i	0.831816	−	1.44075i	−0.0647802	−	0.997900i	$-0.520635\pi$
$281$	13.9438	−	24.1513i	0.831816	−	1.44075i	0.896596	−	0.442849i	$-0.146032\pi$
$282$	−8.19567	−	14.1953i	−0.488045	−	0.845318i
$283$	−7.19798	−	12.4673i	−0.427876	−	0.741102i	0.568809	−	0.822470i	$-0.307405\pi$
$283$	−7.19798	−	12.4673i	−0.427876	−	0.741102i	−0.996684	+	0.0813677i	$0.974071\pi$
$284$	−36.5560			−2.16920
$285$		0			0
$286$	38.4519			2.27371
$287$	−1.84242	−	3.19116i	−0.108754	−	0.188368i
$288$	21.6792	+	37.5494i	1.27746	+	2.21262i
$289$	−5.20651	+	9.01794i	−0.306265	+	0.530467i
$290$		0			0
$291$	−3.72778	+	6.45670i	−0.218526	+	0.378498i
$292$	−22.8303			−1.33605
$293$	2.63178			0.153750			0.0768752	−	0.997041i	$-0.475506\pi$
$293$	2.63178			0.153750			0.0768752	+	0.997041i	$0.475506\pi$
$294$	21.2993	−	36.8915i	1.24220	−	2.15156i
$295$		0			0
$296$	−7.42717			−0.431695
$297$	20.6699			1.19939
$298$	−3.49395	+	6.05169i	−0.202399	+	0.350565i
$299$	−9.96155	−	17.2539i	−0.576091	−	0.997819i
$300$		0			0
$301$	−1.28981	−	2.23401i	−0.0743433	−	0.128766i
$302$	12.0685	+	20.9032i	0.694463	+	1.20284i
$303$	4.08974			0.234950
$304$	4.35120	−	7.94610i	0.249559	−	0.455740i
$305$		0			0
$306$	32.4589	+	56.2205i	1.85555	+	3.21391i
$307$	8.41257	+	14.5710i	0.480131	+	0.831611i	0.999740	−	0.0227929i	$-0.00725584\pi$
$307$	8.41257	+	14.5710i	0.480131	+	0.831611i	−0.519609	+	0.854404i	$0.673923\pi$
$308$	−2.06805	+	3.58197i	−0.117838	+	0.204102i
$309$	−0.246149	−	0.426342i	−0.0140029	−	0.0242538i
$310$		0			0
$311$	−18.3273			−1.03924			−0.519622	−	0.854396i	$-0.673927\pi$
$311$	−18.3273			−1.03924			−0.519622	+	0.854396i	$0.673927\pi$
$312$	31.1986			1.76627
$313$	11.7527	−	20.3562i	0.664299	−	1.15060i	−0.315176	−	0.949033i	$-0.602063\pi$
$313$	11.7527	−	20.3562i	0.664299	−	1.15060i	0.979475	−	0.201567i	$-0.0646033\pi$
$314$	−23.2541	+	40.2772i	−1.31230	+	2.27298i
$315$		0			0
$316$	15.9105			0.895036
$317$	1.94177	−	3.36324i	0.109061	−	0.188899i	−0.806329	−	0.591467i	$-0.798549\pi$
$317$	1.94177	−	3.36324i	0.109061	−	0.188899i	0.915390	+	0.402568i	$0.131882\pi$
$318$	30.7207	+	53.2097i	1.72273	+	2.98385i
$319$	−9.09594	+	15.7546i	−0.509275	+	0.882090i
$320$		0			0
$321$	6.66724	+	11.5480i	0.372129	+	0.644546i
$322$	3.72505			0.207589
$323$	10.9613	−	20.0174i	0.609905	−	1.11380i
$324$	17.6219			0.978996
$325$		0			0
$326$	−11.1899	−	19.3815i	−0.619753	−	1.07344i
$327$	15.8062	−	27.3772i	0.874087	−	1.51396i
$328$	−4.79333	−	8.30228i	−0.264667	−	0.458417i
$329$	−0.756923	+	1.31103i	−0.0417305	+	0.0722793i
$330$		0			0
$331$	3.25821			0.179087			0.0895437	−	0.995983i	$-0.471459\pi$
$331$	3.25821			0.179087			0.0895437	+	0.995983i	$0.471459\pi$
$332$	5.44613	−	9.43297i	0.298895	−	0.517702i
$333$	13.7851	−	23.8765i	0.755419	−	1.30842i
$334$	14.1204			0.772635
$335$		0			0
$336$	1.81483	−	3.14338i	0.0990070	−	0.171485i
$337$	11.0987	+	19.2234i	0.604582	+	1.04717i	0.992117	+	0.125312i	$0.0399933\pi$
$337$	11.0987	+	19.2234i	0.604582	+	1.04717i	−0.387535	+	0.921855i	$0.626673\pi$
$338$	−37.0551	+	64.1813i	−2.01553	+	3.49100i
$339$	−19.4921	−	33.7612i	−1.05866	−	1.83366i
$340$		0			0
$341$	−17.5837			−0.952213
$342$	−28.0741	−	46.1823i	−1.51807	−	2.49725i
$343$	−8.07560			−0.436042
$344$	−3.35563	−	5.81212i	−0.180923	−	0.313369i
$345$		0			0
$346$	−6.79296	+	11.7658i	−0.365192	+	0.632531i
$347$	1.49728	+	2.59336i	0.0803780	+	0.139219i	0.903412	−	0.428773i	$-0.141054\pi$
$347$	1.49728	+	2.59336i	0.0803780	+	0.139219i	−0.823034	+	0.567992i	$0.807721\pi$
$348$	−28.1905	+	48.8274i	−1.51117	+	2.61743i
$349$	15.1407			0.810461			0.405230	−	0.914215i	$-0.367191\pi$
$349$	15.1407			0.810461			0.405230	+	0.914215i	$0.367191\pi$
$350$		0			0
$351$	−27.5015	+	47.6340i	−1.46792	+	2.54251i
$352$	9.79106	−	16.9586i	0.521865	−	0.903897i
$353$	−34.4369			−1.83289			−0.916446	−	0.400159i	$-0.868955\pi$
$353$	−34.4369			−1.83289			−0.916446	+	0.400159i	$0.868955\pi$
$354$	−18.7334			−0.995668
$355$		0			0
$356$	−5.03446	−	8.71994i	−0.266826	−	0.462156i
$357$	4.57182	−	7.91863i	0.241967	−	0.419098i
$358$	−25.1614	−	43.5808i	−1.32982	−	2.30332i
$359$	−1.58165	−	2.73950i	−0.0834763	−	0.144585i	0.821265	−	0.570548i	$-0.193269\pi$
$359$	−1.58165	−	2.73950i	−0.0834763	−	0.144585i	−0.904741	+	0.425962i	$0.859936\pi$
$360$		0			0
$361$	−8.74655	+	16.8671i	−0.460345	+	0.887740i
$362$	−6.94204			−0.364865
$363$	6.40744	+	11.0980i	0.336304	+	0.582495i
$364$	−5.50314	−	9.53171i	−0.288443	−	0.499597i
$365$		0			0
$366$	−7.46829	−	12.9354i	−0.390374	−	0.676147i
$367$	−10.7270	+	18.5797i	−0.559945	+	0.969853i	0.437556	+	0.899191i	$0.355844\pi$
$367$	−10.7270	+	18.5797i	−0.559945	+	0.969853i	−0.997500	+	0.0706615i	$0.977489\pi$
$368$	−6.03027			−0.314350
$369$	35.5864			1.85255
$370$		0			0
$371$	2.83725	−	4.91426i	0.147303	−	0.255136i
$372$	−54.4963			−2.82550
$373$	−33.1587			−1.71689			−0.858446	−	0.512904i	$-0.828570\pi$
$373$	−33.1587			−1.71689			−0.858446	+	0.512904i	$0.828570\pi$
$374$	14.6596	−	25.3911i	0.758028	−	1.31294i
$375$		0			0
$376$	−1.96925	+	3.41084i	−0.101556	+	0.175901i
$377$	−24.2045	−	41.9234i	−1.24660	−	2.15917i
$378$	−5.14199	−	8.90619i	−0.264476	−	0.458085i
$379$	−14.1646			−0.727589			−0.363795	−	0.931479i	$-0.618519\pi$
$379$	−14.1646			−0.727589			−0.363795	+	0.931479i	$0.618519\pi$
$380$		0			0
$381$	5.08198			0.260358
$382$	−20.5554	−	35.6030i	−1.05171	−	1.82161i
$383$	−5.41036	−	9.37102i	−0.276457	−	0.478837i	0.694045	−	0.719932i	$-0.255827\pi$
$383$	−5.41036	−	9.37102i	−0.276457	−	0.478837i	−0.970502	+	0.241095i	$0.922494\pi$
$384$	17.0311	−	29.4988i	0.869117	−	1.50535i
$385$		0			0
$386$	1.11818	−	1.93674i	0.0569138	−	0.0985775i
$387$	24.9127			1.26638
$388$	6.84281			0.347391
$389$	−5.38703	+	9.33061i	−0.273133	+	0.473081i	−0.969662	−	0.244448i	$-0.921393\pi$
$389$	−5.38703	+	9.33061i	−0.273133	+	0.473081i	0.696529	+	0.717529i	$0.254727\pi$
$390$		0			0
$391$	−15.1912			−0.768250
$392$	−10.2356			−0.516975
$393$	−4.84702	+	8.39529i	−0.244500	+	0.423486i
$394$	20.1291	+	34.8647i	1.01409	+	1.75646i
$395$		0			0
$396$	−19.9723	−	34.5930i	−1.00364	−	1.73836i
$397$	1.55107	+	2.68653i	0.0778461	+	0.134833i	0.902320	−	0.431066i	$-0.141862\pi$
$397$	1.55107	+	2.68653i	0.0778461	+	0.134833i	−0.824474	+	0.565899i	$0.808529\pi$
$398$	49.1162			2.46197
$399$	−3.65617	+	6.67683i	−0.183037	+	0.334260i
$400$		0			0
$401$	5.65671	+	9.79771i	0.282483	+	0.489274i	0.971996	−	0.234999i	$-0.0755088\pi$
$401$	5.65671	+	9.79771i	0.282483	+	0.489274i	−0.689513	+	0.724273i	$0.742175\pi$
$402$	−13.7804	−	23.8683i	−0.687303	−	1.19044i
$403$	23.3954	−	40.5220i	1.16541	−	2.01854i
$404$	−1.87681	−	3.25074i	−0.0933749	−	0.161730i
$405$		0			0
$406$	9.05110			0.449199
$407$	−12.4517			−0.617206
$408$	11.8943	−	20.6015i	0.588855	−	1.01993i
$409$	−7.11186	+	12.3181i	−0.351659	+	0.609091i	−0.986540	−	0.163519i	$-0.947716\pi$
$409$	−7.11186	+	12.3181i	−0.351659	+	0.609091i	0.634882	+	0.772609i	$0.281049\pi$
$410$		0			0
$411$	24.0602			1.18680
$412$	−0.225919	+	0.391303i	−0.0111302	+	0.0192781i
$413$	0.865075	+	1.49835i	0.0425675	+	0.0737291i
$414$	−17.9874	+	31.1551i	−0.884032	+	1.53119i
$415$		0			0
$416$	26.0542	+	45.1272i	1.27741	+	2.21255i
$417$	−46.1320			−2.25909
$418$	−11.7235	+	21.4093i	−0.573416	+	1.04716i
$419$	−11.0053			−0.537643			−0.268821	−	0.963190i	$-0.586634\pi$
$419$	−11.0053			−0.537643			−0.268821	+	0.963190i	$0.586634\pi$
$420$		0			0
$421$	11.4625	+	19.8536i	0.558646	+	0.967604i	0.997610	+	0.0690991i	$0.0220125\pi$
$421$	11.4625	+	19.8536i	0.558646	+	0.967604i	−0.438963	+	0.898505i	$0.644654\pi$
$422$	−13.4975	+	23.3783i	−0.657046	+	1.13804i
$423$	−7.31000	−	12.6613i	−0.355424	−	0.615613i
$424$	7.38154	−	12.7852i	0.358479	−	0.620904i
$425$		0			0
$426$	−86.4332			−4.18770
$427$	−0.689744	+	1.19467i	−0.0333791	+	0.0578142i
$428$	6.11929	−	10.5989i	0.295787	−	0.512318i
$429$	52.3045			2.52528
$430$		0			0
$431$	8.49811	−	14.7192i	0.409340	−	0.708997i	−0.585476	−	0.810690i	$-0.699092\pi$
$431$	8.49811	−	14.7192i	0.409340	−	0.708997i	0.994816	+	0.101693i	$0.0324258\pi$
$432$	8.32408	+	14.4177i	0.400492	+	0.693673i
$433$	−15.7493	+	27.2786i	−0.756863	+	1.31093i	0.187580	+	0.982249i	$0.439936\pi$
$433$	−15.7493	+	27.2786i	−0.756863	+	1.31093i	−0.944443	+	0.328676i	$0.893398\pi$
$434$	4.37427	+	7.57645i	0.209972	+	0.363681i
$435$		0			0
$436$	−29.0144			−1.38954
$437$	12.6438	−	0.285896i	0.604836	−	0.0136763i
$438$	−53.9802			−2.57928
$439$	−1.57963	−	2.73600i	−0.0753916	−	0.130582i	0.825865	−	0.563868i	$-0.190687\pi$
$439$	−1.57963	−	2.73600i	−0.0753916	−	0.130582i	−0.901256	+	0.433286i	$0.857354\pi$
$440$		0			0
$441$	18.9976	−	32.9049i	0.904649	−	1.56690i
$442$	39.0095	+	67.5664i	1.85549	+	3.21380i
$443$	5.94720	−	10.3008i	0.282560	−	0.489408i	−0.689455	−	0.724329i	$-0.742150\pi$
$443$	5.94720	−	10.3008i	0.282560	−	0.489408i	0.972015	+	0.234921i	$0.0754831\pi$
$444$	−38.5907			−1.83143
$445$		0			0
$446$	20.8036	−	36.0329i	0.985080	−	1.70621i
$447$	−4.75267	+	8.23186i	−0.224794	+	0.389354i
$448$	−7.28358			−0.344117
$449$	21.2175			1.00132			0.500659	−	0.865645i	$-0.333091\pi$
$449$	21.2175			1.00132			0.500659	+	0.865645i	$0.333091\pi$
$450$		0			0
$451$	−8.03602	−	13.9188i	−0.378401	−	0.655410i
$452$	−17.8901	+	30.9865i	−0.841479	+	1.45748i
$453$	16.4162	+	28.4338i	0.771302	+	1.33593i
$454$	28.7762	+	49.8418i	1.35053	+	2.33919i
$455$		0			0
$456$	−9.51208	+	17.3708i	−0.445444	+	0.813462i
$457$	−9.41670			−0.440495			−0.220247	−	0.975444i	$-0.570686\pi$
$457$	−9.41670			−0.440495			−0.220247	+	0.975444i	$0.570686\pi$
$458$	9.55948	+	16.5575i	0.446685	+	0.773682i
$459$	20.9696	+	36.3204i	0.978777	+	1.69529i
$460$		0			0
$461$	−1.16004	−	2.00924i	−0.0540282	−	0.0935797i	0.837746	−	0.546060i	$-0.183873\pi$
$461$	−1.16004	−	2.00924i	−0.0540282	−	0.0935797i	−0.891775	+	0.452480i	$0.850539\pi$
$462$	−4.88972	+	8.46924i	−0.227490	+	0.394025i
$463$	−14.7160			−0.683909			−0.341955	−	0.939716i	$-0.611089\pi$
$463$	−14.7160			−0.683909			−0.341955	+	0.939716i	$0.611089\pi$
$464$	−14.6523			−0.680217
$465$		0			0
$466$	4.89606	−	8.48023i	0.226806	−	0.392839i
$467$	11.7747			0.544867			0.272434	−	0.962175i	$-0.412172\pi$
$467$	11.7747			0.544867			0.272434	+	0.962175i	$0.412172\pi$
$468$	106.293			4.91341
$469$	−1.27271	+	2.20439i	−0.0587681	+	0.101789i
$470$		0			0
$471$	−31.6316	+	54.7875i	−1.45751	+	2.52447i
$472$	2.25062	+	3.89819i	0.103593	+	0.179429i
$473$	−5.62572	−	9.74403i	−0.258671	−	0.448031i
$474$	37.6189			1.72789
$475$		0			0
$476$	−8.39217			−0.384655
$477$	27.4008	+	47.4596i	1.25460	+	2.17303i
$478$	8.48971	+	14.7046i	0.388310	+	0.672573i
$479$	−5.69219	+	9.85915i	−0.260083	+	0.450476i	−0.966264	−	0.257555i	$-0.917083\pi$
$479$	−5.69219	+	9.85915i	−0.260083	+	0.450476i	0.706181	+	0.708031i	$0.250416\pi$
$480$		0			0
$481$	16.5671	−	28.6950i	0.755394	−	1.30838i
$482$	59.3288			2.70235
$483$	5.06703			0.230558
$484$	5.88084	−	10.1859i	0.267311	−	0.462996i
$485$		0			0
$486$	−10.4829			−0.475513
$487$	4.77063			0.216178			0.108089	−	0.994141i	$-0.465527\pi$
$487$	4.77063			0.216178			0.108089	+	0.994141i	$0.465527\pi$
$488$	−1.79447	+	3.10812i	−0.0812321	+	0.140698i
$489$	−15.2212	−	26.3639i	−0.688326	−	1.19222i
$490$		0			0
$491$	2.50665	+	4.34165i	0.113124	+	0.195936i	0.917028	−	0.398822i	$-0.130581\pi$
$491$	2.50665	+	4.34165i	0.113124	+	0.195936i	−0.803904	+	0.594758i	$0.797248\pi$
$492$	−24.9056	−	43.1377i	−1.12283	−	1.94480i
$493$	−36.9114			−1.66240
$494$	−33.7397	−	55.5023i	−1.51802	−	2.49717i
$495$		0			0
$496$	−7.08125	−	12.2651i	−0.317958	−	0.550719i
$497$	3.99133	+	6.91319i	0.179036	+	0.310099i
$498$	12.8769	−	22.3034i	0.577026	−	0.999439i
$499$	−10.9112	−	18.8987i	−0.488450	−	0.846021i	0.511461	−	0.859306i	$-0.329104\pi$
$499$	−10.9112	−	18.8987i	−0.488450	−	0.846021i	−0.999912	+	0.0132853i	$0.995771\pi$
$500$		0			0
$501$	19.2074			0.858124
$502$	−35.2372			−1.57272
$503$	7.58583	−	13.1391i	0.338236	−	0.585841i	−0.645865	−	0.763451i	$-0.723503\pi$
$503$	7.58583	−	13.1391i	0.338236	−	0.585841i	0.984101	+	0.177610i	$0.0568366\pi$
$504$	−2.60144	+	4.50582i	−0.115877	+	0.200705i
$505$		0			0
$506$	16.2475			0.722288
$507$	−50.4045	+	87.3031i	−2.23854	+	3.87727i
$508$	−2.33216	−	4.03941i	−0.103473	−	0.179220i
$509$	−2.59122	+	4.48812i	−0.114854	+	0.198933i	−0.917721	−	0.397225i	$-0.869973\pi$
$509$	−2.59122	+	4.48812i	−0.114854	+	0.198933i	0.802868	+	0.596157i	$0.203307\pi$
$510$		0			0
$511$	2.49271	+	4.31750i	0.110271	+	0.190995i
$512$	22.1701			0.979789
$513$	−18.1368	−	29.8354i	−0.800761	−	1.31726i
$514$	−19.8421			−0.875199
$515$		0			0
$516$	−17.4355	−	30.1991i	−0.767554	−	1.32944i
$517$	−3.30145	+	5.71828i	−0.145198	+	0.251490i
$518$	3.09757	+	5.36515i	0.136099	+	0.235731i
$519$	−9.24018	+	16.0045i	−0.405599	+	0.702518i
$520$		0			0
$521$	11.2091			0.491079			0.245540	−	0.969387i	$-0.421035\pi$
$521$	11.2091			0.491079			0.245540	+	0.969387i	$0.421035\pi$
$522$	−43.7056	+	75.7004i	−1.91294	+	3.31332i
$523$	−2.71940	+	4.71014i	−0.118911	+	0.205960i	−0.919336	−	0.393472i	$-0.871274\pi$
$523$	−2.71940	+	4.71014i	−0.118911	+	0.205960i	0.800425	+	0.599433i	$0.204607\pi$
$524$	8.89733			0.388682
$525$		0			0
$526$	16.5982	−	28.7488i	0.723714	−	1.25351i
$527$	−17.8387	−	30.8976i	−0.777067	−	1.34592i
$528$	7.91569	−	13.7104i	0.344486	−	0.596668i
$529$	7.29084	+	12.6281i	0.316993	+	0.549048i
$530$		0			0
$531$	−16.7090			−0.725107
$532$	6.98492	−	0.157940i	0.302835	−	0.00684756i
$533$	42.7680			1.85249
$534$	−11.9035	−	20.6175i	−0.515116	−	0.892206i
$535$		0			0
$536$	−3.31114	+	5.73506i	−0.143019	+	0.247717i
$537$	−34.2260	−	59.2811i	−1.47696	−	2.55817i
$538$	15.3498	−	26.5866i	0.661776	−	1.14623i
$539$	−17.1600			−0.739132
$540$		0			0
$541$	−7.14111	+	12.3688i	−0.307020	+	0.531775i	−0.977709	−	0.209964i	$-0.932665\pi$
$541$	−7.14111	+	12.3688i	−0.307020	+	0.531775i	0.670689	+	0.741739i	$0.265999\pi$
$542$	12.3295	−	21.3554i	0.529598	−	0.917291i
$543$	−9.44296			−0.405236
$544$	39.7322			1.70350
$545$		0			0
$546$	−13.0117	−	22.5369i	−0.556848	−	0.964488i
$547$	12.5122	−	21.6717i	0.534982	−	0.926616i	−0.464182	−	0.885740i	$-0.653652\pi$
$547$	12.5122	−	21.6717i	0.534982	−	0.926616i	0.999164	−	0.0408766i	$-0.0130151\pi$
$548$	−11.0414	−	19.1243i	−0.471666	−	0.816949i
$549$	−6.66122	−	11.5376i	−0.284294	−	0.492412i
$550$		0			0
$551$	30.7219	−	0.694668i	1.30880	−	0.0295939i
$552$	13.1827			0.561091
$553$	−1.73718	−	3.00888i	−0.0738722	−	0.127950i
$554$	−20.5184	−	35.5388i	−0.871741	−	1.50990i
$555$		0			0
$556$	21.1703	+	36.6680i	0.897821	+	1.55507i
$557$	3.57846	−	6.19807i	0.151624	−	0.262621i	−0.780201	−	0.625529i	$-0.784883\pi$
$557$	3.57846	−	6.19807i	0.151624	−	0.262621i	0.931825	+	0.362909i	$0.118216\pi$
$558$	−84.4892			−3.57671
$559$	29.9403			1.26634
$560$		0			0
$561$	19.9408	−	34.5385i	0.841901	−	1.45822i
$562$	−60.5184			−2.55282
$563$	28.9386			1.21962			0.609809	−	0.792548i	$-0.291246\pi$
$563$	28.9386			1.21962			0.609809	+	0.792548i	$0.291246\pi$
$564$	−10.2320	+	17.7223i	−0.430845	+	0.746245i
$565$		0			0
$566$	−15.6202	+	27.0551i	−0.656568	+	1.13721i
$567$	−1.92403	−	3.33253i	−0.0808019	−	0.139953i
$568$	10.3841	+	17.9857i	0.435706	+	0.754664i
$569$	38.8864			1.63020			0.815100	−	0.579320i	$-0.196682\pi$
$569$	38.8864			1.63020			0.815100	+	0.579320i	$0.196682\pi$
$570$		0			0
$571$	15.1613			0.634480			0.317240	−	0.948345i	$-0.397244\pi$
$571$	15.1613			0.634480			0.317240	+	0.948345i	$0.397244\pi$
$572$	−24.0029	−	41.5742i	−1.00361	−	1.73831i
$573$	−27.9607	−	48.4293i	−1.16807	−	2.02316i
$574$	−3.99820	+	6.92509i	−0.166882	+	0.289048i
$575$		0			0
$576$	35.1707	−	60.9174i	1.46544	−	2.53822i
$577$	20.6412			0.859303			0.429651	−	0.902995i	$-0.358636\pi$
$577$	20.6412			0.859303			0.429651	+	0.902995i	$0.358636\pi$
$578$	22.5972			0.939918
$579$	1.52101	−	2.63447i	0.0632111	−	0.109485i
$580$		0			0
$581$	−2.37852			−0.0986778
$582$	16.1792			0.670649
$583$	12.3752	−	21.4344i	0.512527	−	0.887723i
$584$	6.48517	+	11.2326i	0.268358	+	0.464810i
$585$		0			0
$586$	−2.85560	−	4.94604i	−0.117964	−	0.204319i
$587$	−3.58942	−	6.21706i	−0.148151	−	0.256606i	0.782393	−	0.622785i	$-0.213999\pi$
$587$	−3.58942	−	6.21706i	−0.148151	−	0.256606i	−0.930544	+	0.366180i	$0.880666\pi$
$588$	−53.1829			−2.19323
$589$	15.4289	+	25.3808i	0.635738	+	1.04580i
$590$		0			0
$591$	27.3808	+	47.4250i	1.12630	+	1.95080i
$592$	−5.01448	−	8.68533i	−0.206094	−	0.356965i
$593$	−18.3743	+	31.8253i	−0.754543	+	1.30691i	0.191058	+	0.981579i	$0.438808\pi$
$593$	−18.3743	+	31.8253i	−0.754543	+	1.30691i	−0.945601	+	0.325328i	$0.894525\pi$
$594$	−22.4277	−	38.8459i	−0.920219	−	1.59387i
$595$		0			0
$596$	8.72413			0.357354
$597$	66.8107			2.73438
$598$	−21.6174	+	37.4425i	−0.884002	+	1.53114i
$599$	0.926876	−	1.60540i	0.0378711	−	0.0655947i	−0.846469	−	0.532439i	$-0.821276\pi$
$599$	0.926876	−	1.60540i	0.0378711	−	0.0655947i	0.884340	+	0.466844i	$0.154609\pi$
$600$		0			0
$601$	−38.1633			−1.55671			−0.778356	−	0.627823i	$-0.783946\pi$
$601$	−38.1633			−1.55671			−0.778356	+	0.627823i	$0.783946\pi$
$602$	−2.79899	+	4.84800i	−0.114078	+	0.197590i
$603$	−12.2912	−	21.2890i	−0.500536	−	0.866954i
$604$	15.0671	−	26.0969i	0.613070	−	1.06187i
$605$		0			0
$606$	−4.43755	−	7.68606i	−0.180263	−	0.312225i
$607$	7.44914			0.302351			0.151176	−	0.988507i	$-0.451694\pi$
$607$	7.44914			0.302351			0.151176	+	0.988507i	$0.451694\pi$
$608$	−33.0696	+	0.747755i	−1.34115	+	0.0303255i
$609$	12.3118			0.498901
$610$		0			0
$611$	−8.78523	−	15.2165i	−0.355412	−	0.615592i
$612$	40.5238	−	70.1893i	1.63808	−	2.83723i
$613$	10.6049	+	18.3682i	0.428326	+	0.741883i	0.996725	−	0.0808706i	$-0.0257700\pi$
$613$	10.6049	+	18.3682i	0.428326	+	0.741883i	−0.568398	+	0.822754i	$0.692437\pi$
$614$	18.2560	−	31.6203i	0.736753	−	1.27609i
$615$		0			0
$616$	2.34980			0.0946760
$617$	15.4076	−	26.6868i	0.620287	−	1.07437i	−0.369145	−	0.929372i	$-0.620349\pi$
$617$	15.4076	−	26.6868i	0.620287	−	1.07437i	0.989432	−	0.144997i	$-0.0463172\pi$
$618$	−0.534164	+	0.925199i	−0.0214872	+	0.0372170i
$619$	7.32036			0.294230			0.147115	−	0.989119i	$-0.453001\pi$
$619$	7.32036			0.294230			0.147115	+	0.989119i	$0.453001\pi$
$620$		0			0
$621$	−11.6205	+	20.1273i	−0.466314	+	0.807680i
$622$	19.8859	+	34.4434i	0.797352	+	1.38105i
$623$	−1.09937	+	1.90416i	−0.0440452	+	0.0762885i
$624$	21.0638	+	36.4836i	0.843228	+	1.46051i
$625$		0			0
$626$	−51.0086			−2.03871
$627$	−15.9470	+	29.1222i	−0.636862	+	1.16303i
$628$	58.0638			2.31700
$629$	−12.6322	−	21.8797i	−0.503680	−	0.872399i
$630$		0			0
$631$	−2.25414	+	3.90429i	−0.0897360	+	0.155427i	−0.907399	−	0.420269i	$-0.861936\pi$
$631$	−2.25414	+	3.90429i	−0.0897360	+	0.155427i	0.817664	+	0.575696i	$0.195269\pi$
$632$	−4.51953	−	7.82805i	−0.179777	−	0.311383i
$633$	−18.3600	+	31.8005i	−0.729746	+	1.26396i
$634$	−8.42762			−0.334704
$635$		0			0
$636$	38.3536	−	66.4305i	1.52082	−	2.63414i
$637$	22.8315	−	39.5454i	0.904618	−	1.56685i
$638$	39.4780			1.56295
$639$	−77.0928			−3.04975
$640$		0			0
$641$	8.48158	+	14.6905i	0.335002	+	0.580241i	0.983485	−	0.180988i	$-0.0579296\pi$
$641$	8.48158	+	14.6905i	0.335002	+	0.580241i	−0.648483	+	0.761229i	$0.724596\pi$
$642$	14.4685	−	25.0602i	0.571026	−	0.989046i
$643$	−4.64306	−	8.04202i	−0.183104	−	0.317146i	0.759832	−	0.650120i	$-0.225281\pi$
$643$	−4.64306	−	8.04202i	−0.183104	−	0.317146i	−0.942936	+	0.332974i	$0.891948\pi$
$644$	−2.32530	−	4.02753i	−0.0916295	−	0.158707i
$645$		0			0
$646$	−49.5132	+	1.11957i	−1.94807	+	0.0440489i
$647$	39.2779			1.54418			0.772088	−	0.635516i	$-0.219213\pi$
$647$	39.2779			1.54418			0.772088	+	0.635516i	$0.219213\pi$
$648$	−5.00567	−	8.67007i	−0.196641	−	0.340593i
$649$	3.77317	+	6.53533i	0.148110	+	0.256534i
$650$		0			0
$651$	5.95013	+	10.3059i	0.233204	+	0.403921i
$652$	−13.9702	+	24.1972i	−0.547116	+	0.947634i
$653$	26.5513			1.03903			0.519517	−	0.854460i	$-0.326112\pi$
$653$	26.5513			1.03903			0.519517	+	0.854460i	$0.326112\pi$
$654$	−68.6018			−2.68254
$655$		0			0
$656$	6.47246	−	11.2106i	0.252707	−	0.437702i
$657$	−48.1469			−1.87839
$658$	3.28518			0.128069
$659$	−16.3143	+	28.2573i	−0.635517	+	1.10075i	0.350889	+	0.936417i	$0.385880\pi$
$659$	−16.3143	+	28.2573i	−0.635517	+	1.10075i	−0.986405	+	0.164330i	$0.947454\pi$
$660$		0			0
$661$	−3.13332	+	5.42707i	−0.121872	+	0.211088i	−0.920506	−	0.390729i	$-0.872223\pi$
$661$	−3.13332	+	5.42707i	−0.121872	+	0.211088i	0.798634	+	0.601817i	$0.205556\pi$
$662$	−3.53530	−	6.12332i	−0.137403	−	0.237989i
$663$	53.0629	+	91.9077i	2.06079	+	3.56940i
$664$	−6.18809			−0.240145
$665$		0			0
$666$	−59.8297			−2.31836
$667$	−10.2274	−	17.7143i	−0.396006	−	0.685902i
$668$	−8.81442	−	15.2670i	−0.341040	−	0.590699i
$669$	28.2983	−	49.0141i	1.09408	−	1.89499i
$670$		0			0
$671$	−3.00844	+	5.21077i	−0.116140	+	0.201160i
$672$	−13.2527			−0.511235
$673$	−7.39044			−0.284881			−0.142440	−	0.989803i	$-0.545495\pi$
$673$	−7.39044			−0.284881			−0.142440	+	0.989803i	$0.545495\pi$
$674$	24.0850	−	41.7165i	0.927721	−	1.60686i
$675$		0			0
$676$	92.5238			3.55861
$677$	−20.2751			−0.779234			−0.389617	−	0.920977i	$-0.627393\pi$
$677$	−20.2751			−0.779234			−0.389617	+	0.920977i	$0.627393\pi$
$678$	−42.2994	+	73.2648i	−1.62450	+	2.81372i
$679$	−0.747127	−	1.29406i	−0.0286721	−	0.0496615i
$680$		0			0
$681$	39.1431	+	67.7978i	1.49997	+	2.59802i
$682$	19.0791	+	33.0460i	0.730577	+	1.26540i
$683$	24.6563			0.943448			0.471724	−	0.881746i	$-0.343632\pi$
$683$	24.6563			0.943448			0.471724	+	0.881746i	$0.343632\pi$
$684$	−32.4076	+	59.1822i	−1.23914	+	2.26289i
$685$		0			0
$686$	8.76238	+	15.1769i	0.334549	+	0.579456i
$687$	13.0034	+	22.5225i	0.496109	+	0.859286i
$688$	4.53113	−	7.84815i	0.172748	−	0.299208i
$689$	32.9306	+	57.0374i	1.25456	+	2.17295i
$690$		0			0
$691$	−41.7299			−1.58748			−0.793739	−	0.608258i	$-0.791869\pi$
$691$	−41.7299			−1.58748			−0.793739	+	0.608258i	$0.791869\pi$
$692$	16.9615			0.644781
$693$	−4.36131	+	7.55402i	−0.165673	+	0.286953i
$694$	3.24922	−	5.62782i	0.123339	−	0.213629i
$695$		0			0
$696$	32.0311			1.21414
$697$	16.3051	−	28.2413i	0.617600	−	1.06971i
$698$	−16.4283	−	28.4546i	−0.621819	−	1.07702i
$699$	6.65991	−	11.5353i	0.251901	−	0.436305i
$700$		0			0
$701$	3.60840	+	6.24993i	0.136287	+	0.236057i	0.926089	−	0.377306i	$-0.123150\pi$
$701$	3.60840	+	6.24993i	0.136287	+	0.236057i	−0.789801	+	0.613363i	$0.789816\pi$
$702$	119.361			4.50500
$703$	10.9258	+	17.9730i	0.412073	+	0.677865i
$704$	−31.7686			−1.19732
$705$		0			0
$706$	37.3655	+	64.7190i	1.40627	+	2.43573i
$707$	−0.409836	+	0.709857i	−0.0154135	+	0.0266969i
$708$	11.6940	+	20.2546i	0.439487	+	0.761213i
$709$	10.3172	−	17.8700i	0.387472	−	0.671122i	−0.604636	−	0.796502i	$-0.706682\pi$
$709$	10.3172	−	17.8700i	0.387472	−	0.671122i	0.992109	+	0.125380i	$0.0400149\pi$
$710$		0			0
$711$	33.5536			1.25836
$712$	−2.86017	+	4.95396i	−0.107189	+	0.185657i
$713$	9.88549	−	17.1222i	0.370214	−	0.641230i
$714$	−19.8425			−0.742587
$715$		0			0
$716$	−31.4131	+	54.4091i	−1.17396	+	2.03336i
$717$	11.5482	+	20.0021i	0.431275	+	0.746991i
$718$	−3.43232	+	5.94495i	−0.128093	+	0.221864i
$719$	−0.748958	−	1.29723i	−0.0279314	−	0.0483787i	0.851722	−	0.523994i	$-0.175559\pi$
$719$	−0.748958	−	1.29723i	−0.0279314	−	0.0483787i	−0.879653	+	0.475616i	$0.842225\pi$
$720$		0			0
$721$	0.0986670			0.00367455
$722$	41.1895	−	1.86367i	1.53291	−	0.0693585i
$723$	80.7024			3.00136
$724$	4.33344	+	7.50574i	0.161051	+	0.278949i
$725$		0			0
$726$	13.9047	−	24.0837i	0.516052	−	0.893828i
$727$	5.68222	+	9.84190i	0.210742	+	0.365016i	0.951947	−	0.306263i	$-0.0990787\pi$
$727$	5.68222	+	9.84190i	0.210742	+	0.365016i	−0.741205	+	0.671279i	$0.765745\pi$
$728$	−3.12643	+	5.41514i	−0.115873	+	0.200698i
$729$	−33.7723			−1.25083
$730$		0			0
$731$	11.4146	−	19.7707i	0.422184	−	0.731244i
$732$	−9.32389	+	16.1494i	−0.344621	+	0.596901i
$733$	45.6910			1.68764			0.843818	−	0.536630i	$-0.180303\pi$
$733$	45.6910			1.68764			0.843818	+	0.536630i	$0.180303\pi$
$734$	46.5570			1.71845
$735$		0			0
$736$	11.0090	+	19.0681i	0.405796	+	0.702859i
$737$	−5.55113	+	9.61484i	−0.204479	+	0.354167i
$738$	−38.6127	−	66.8792i	−1.42135	−	2.46186i
$739$	1.78276	+	3.08783i	0.0655799	+	0.113588i	0.896951	−	0.442130i	$-0.145777\pi$
$739$	1.78276	+	3.08783i	0.0655799	+	0.113588i	−0.831371	+	0.555718i	$0.812444\pi$
$740$		0			0
$741$	−45.8947	−	75.4975i	−1.68599	−	2.77347i
$742$	−12.3142			−0.452067
$743$	−21.2482	−	36.8030i	−0.779522	−	1.35017i	−0.932218	−	0.361898i	$-0.882129\pi$
$743$	−21.2482	−	36.8030i	−0.779522	−	1.35017i	0.152696	−	0.988273i	$-0.451205\pi$
$744$	15.4802	+	26.8125i	0.567531	+	0.982992i
$745$		0			0
$746$	35.9786	+	62.3168i	1.31727	+	2.28158i
$747$	11.4853	−	19.8932i	0.420226	−	0.727853i
$748$	−36.6039			−1.33837
$749$	−2.67252			−0.0976516
$750$		0			0
$751$	6.38588	−	11.0607i	0.233024	−	0.403610i	−0.725672	−	0.688040i	$-0.758471\pi$
$751$	6.38588	−	11.0607i	0.233024	−	0.403610i	0.958697	+	0.284431i	$0.0918045\pi$
$752$	−5.31818			−0.193934
$753$	−47.9317			−1.74673
$754$	−52.5259	+	90.9775i	−1.91288	+	3.31320i
$755$		0			0
$756$	−6.41960	+	11.1191i	−0.233478	+	0.404396i
$757$	5.67306	+	9.82603i	0.206191	+	0.357133i	0.950512	−	0.310689i	$-0.100560\pi$
$757$	5.67306	+	9.82603i	0.206191	+	0.357133i	−0.744321	+	0.667822i	$0.767227\pi$
$758$	15.3693	+	26.6203i	0.558237	+	0.966894i
$759$	22.1007			0.802206
$760$		0			0
$761$	−36.9214			−1.33840			−0.669199	−	0.743083i	$-0.733363\pi$
$761$	−36.9214			−1.33840			−0.669199	+	0.743083i	$0.733363\pi$
$762$	−5.51417	−	9.55082i	−0.199757	−	0.345990i
$763$	3.16791	+	5.48698i	0.114686	+	0.198642i
$764$	−25.6627	+	44.4491i	−0.928444	+	1.60811i
$765$		0			0
$766$	−11.7410	+	20.3359i	−0.424218	+	0.734767i
$767$	−20.0810			−0.725083
$768$	−1.23551			−0.0445827
$769$	−14.2528	+	24.6866i	−0.513971	+	0.890223i	0.485898	+	0.874015i	$0.338493\pi$
$769$	−14.2528	+	24.6866i	−0.513971	+	0.890223i	−0.999869	+	0.0162076i	$0.994841\pi$
$770$		0			0
$771$	−26.9904			−0.972036
$772$	−2.79201			−0.100487
$773$	7.60956	−	13.1801i	0.273697	−	0.474057i	−0.696109	−	0.717936i	$-0.745087\pi$
$773$	7.60956	−	13.1801i	0.273697	−	0.474057i	0.969805	+	0.243880i	$0.0784202\pi$
$774$	−27.0314	−	46.8197i	−0.971622	−	1.68290i
$775$		0			0
$776$	−1.94376	−	3.36670i	−0.0697770	−	0.120857i
$777$	4.21350	+	7.29799i	0.151158	+	0.261814i
$778$	23.3807

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +O(q^{10})\)	\(q+(-1.08504 - 1.87935i) q^{2} +(-1.47594 - 2.55640i) q^{3} +(-1.35464 + 2.34630i) q^{4} +(-3.20292 + 5.54761i) q^{6} +0.591620 q^{7} +1.53919 q^{8} +(-2.85679 + 4.94811i) q^{9} +2.58045 q^{11} +7.99745 q^{12} +(-3.43332 + 5.94669i) q^{13} +(-0.641933 - 1.11186i) q^{14} +(1.03919 + 1.79993i) q^{16} +(2.61787 + 4.53429i) q^{17} +12.3990 q^{18} +(-2.26423 - 3.72468i) q^{19} +(-0.873195 - 1.51242i) q^{21} +(-2.79990 - 4.84957i) q^{22} +(-1.45072 + 2.51271i) q^{23} +(-2.27175 - 3.93478i) q^{24} +14.9012 q^{26} +8.01017 q^{27} +(-0.801431 + 1.38812i) q^{28} +(-3.52494 + 6.10538i) q^{29} -6.81421 q^{31} +(3.79432 - 6.57195i) q^{32} +(-3.80859 - 6.59667i) q^{33} +(5.68101 - 9.83980i) q^{34} +(-7.73984 - 13.4058i) q^{36} -4.82538 q^{37} +(-4.54320 + 8.29672i) q^{38} +20.2695 q^{39} +(-3.11419 - 5.39393i) q^{41} +(-1.89491 + 3.28208i) q^{42} +(-2.18013 - 3.77609i) q^{43} +(-3.49558 + 6.05452i) q^{44} +6.29636 q^{46} +(-1.27941 + 2.21600i) q^{47} +(3.06756 - 5.31317i) q^{48} -6.64999 q^{49} +(7.72764 - 13.3847i) q^{51} +(-9.30181 - 16.1112i) q^{52} +(4.79573 - 8.30645i) q^{53} +(-8.69138 - 15.0539i) q^{54} +0.910615 q^{56} +(-6.17993 + 11.2857i) q^{57} +15.2989 q^{58} +(1.46221 + 2.53263i) q^{59} +(-1.16586 + 2.01932i) q^{61} +(7.39371 + 12.8063i) q^{62} +(-1.69013 + 2.92740i) q^{63} -12.3112 q^{64} +(-8.26497 + 14.3153i) q^{66} +(-2.15122 + 3.72603i) q^{67} -14.1851 q^{68} +8.56468 q^{69} +(6.74645 + 11.6852i) q^{71} +(-4.39714 + 7.61607i) q^{72} +(4.21337 + 7.29777i) q^{73} +(5.23574 + 9.06858i) q^{74} +(11.8064 - 0.266962i) q^{76} +1.52665 q^{77} +(-21.9933 - 38.0935i) q^{78} +(-2.93630 - 5.08583i) q^{79} +(-3.25215 - 5.63288i) q^{81} +(-6.75806 + 11.7053i) q^{82} -4.02036 q^{83} +4.73145 q^{84} +(-4.73107 + 8.19445i) q^{86} +20.8104 q^{87} +3.97180 q^{88} +(-1.85823 + 3.21855i) q^{89} +(-2.03122 + 3.51818i) q^{91} +(-3.93039 - 6.80764i) q^{92} +(10.0574 + 17.4199i) q^{93} +5.55285 q^{94} -22.4007 q^{96} +(-1.26285 - 2.18732i) q^{97} +(7.21552 + 12.4977i) q^{98} +(-7.37182 + 12.7684i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9	\( 12 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{6} + 4 q^{7} + 12 q^{8} - 7 q^{9} - 2 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{14} + 6 q^{16} + 3 q^{17} + 14 q^{18} - 6 q^{19} - 3 q^{21} - 9 q^{22} + 6 q^{23} - 11 q^{24} + 38 q^{26} + 36 q^{27} + 4 q^{28} - 3 q^{29} - 6 q^{31} + 6 q^{32} + 18 q^{33} + q^{34} - 13 q^{36} - 12 q^{37} - 18 q^{38} + 16 q^{39} - 11 q^{41} + 11 q^{42} - 13 q^{43} - 21 q^{44} - 24 q^{46} + 6 q^{47} + 19 q^{48} + 8 q^{49} + 17 q^{51} + q^{52} - 18 q^{53} - 18 q^{54} + 8 q^{56} - 20 q^{57} + 10 q^{58} - 4 q^{59} - 25 q^{61} + 21 q^{62} - 43 q^{63} - 44 q^{64} - 34 q^{66} - 6 q^{67} - 2 q^{68} + 26 q^{69} - 18 q^{71} - 13 q^{72} - q^{73} + 6 q^{74} + 24 q^{76} - 22 q^{77} - 72 q^{78} - 3 q^{79} - 2 q^{81} - 31 q^{82} - 46 q^{83} + 74 q^{84} - 9 q^{86} + 22 q^{87} + 22 q^{88} - 12 q^{89} + 11 q^{91} - 28 q^{92} + 13 q^{93} + 16 q^{94} - 26 q^{96} - 3 q^{97} + 22 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^6 + 4 * q^7 + 12 * q^8 - 7 * q^9 - 2 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^14 + 6 * q^16 + 3 * q^17 + 14 * q^18 - 6 * q^19 - 3 * q^21 - 9 * q^22 + 6 * q^23 - 11 * q^24 + 38 * q^26 + 36 * q^27 + 4 * q^28 - 3 * q^29 - 6 * q^31 + 6 * q^32 + 18 * q^33 + q^34 - 13 * q^36 - 12 * q^37 - 18 * q^38 + 16 * q^39 - 11 * q^41 + 11 * q^42 - 13 * q^43 - 21 * q^44 - 24 * q^46 + 6 * q^47 + 19 * q^48 + 8 * q^49 + 17 * q^51 + q^52 - 18 * q^53 - 18 * q^54 + 8 * q^56 - 20 * q^57 + 10 * q^58 - 4 * q^59 - 25 * q^61 + 21 * q^62 - 43 * q^63 - 44 * q^64 - 34 * q^66 - 6 * q^67 - 2 * q^68 + 26 * q^69 - 18 * q^71 - 13 * q^72 - q^73 + 6 * q^74 + 24 * q^76 - 22 * q^77 - 72 * q^78 - 3 * q^79 - 2 * q^81 - 31 * q^82 - 46 * q^83 + 74 * q^84 - 9 * q^86 + 22 * q^87 + 22 * q^88 - 12 * q^89 + 11 * q^91 - 28 * q^92 + 13 * q^93 + 16 * q^94 - 26 * q^96 - 3 * q^97 + 22 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more