LMFDB - Embedded newform 605.2.j.f.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			269.1
Root			$-1.13551 + 1.56290i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.f.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.83730 + 0.596975i) q^{2} +(0.304260 - 0.418778i) q^{3} +(1.40126 - 1.01807i) q^{4} +(0.809764 + 2.08429i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.526994 - 0.725345i) q^{7} +(0.304260 - 0.418778i) q^{8} +(0.844250 + 2.59833i) q^{9} +O(q^{10})$	\(q+(-1.83730 + 0.596975i) q^{2} +(0.304260 - 0.418778i) q^{3} +(1.40126 - 1.01807i) q^{4} +(0.809764 + 2.08429i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.526994 - 0.725345i) q^{7} +(0.304260 - 0.418778i) q^{8} +(0.844250 + 2.59833i) q^{9} +(-2.73205 - 3.34607i) q^{10} -0.896575i q^{12} +(-4.03499 + 1.31105i) q^{13} +(1.40126 + 1.01807i) q^{14} +(1.11924 + 0.295056i) q^{15} +(-1.37948 + 4.24561i) q^{16} +(0.984606 + 0.319918i) q^{17} +(-3.10228 - 4.26992i) q^{18} +(5.01279 + 3.64201i) q^{19} +(3.25665 + 2.09624i) q^{20} -0.464102 q^{21} -6.31319i q^{23} +(-0.0828009 - 0.254835i) q^{24} +(-3.68856 + 3.37557i) q^{25} +(6.63083 - 4.81758i) q^{26} +(2.82191 + 0.916893i) q^{27} +(-1.47691 - 0.479877i) q^{28} +(-5.60503 + 4.07230i) q^{29} +(-2.23251 + 0.126049i) q^{30} +(-1.62789 - 5.01012i) q^{31} -7.58871i q^{32} -2.00000 q^{34} +(1.08509 - 1.68577i) q^{35} +(3.82831 + 2.78143i) q^{36} +(3.93354 + 5.41405i) q^{37} +(-11.3842 - 3.69895i) q^{38} +(-0.678648 + 2.08867i) q^{39} +(1.11924 + 0.295056i) q^{40} +(1.40126 + 1.01807i) q^{41} +(0.852694 - 0.277057i) q^{42} +10.6945i q^{43} +(-4.73205 + 3.86370i) q^{45} +(3.76882 + 11.5992i) q^{46} +(-2.41224 + 3.32016i) q^{47} +(1.35825 + 1.86947i) q^{48} +(1.91472 - 5.89289i) q^{49} +(4.76187 - 8.40392i) q^{50} +(0.433551 - 0.314993i) q^{51} +(-4.31932 + 5.94504i) q^{52} +(-11.3842 + 3.69895i) q^{53} -5.73205 q^{54} -0.464102 q^{56} +(3.05038 - 0.991130i) q^{57} +(7.86707 - 10.8281i) q^{58} +(-3.82831 + 2.78143i) q^{59} +(1.86873 - 0.726014i) q^{60} +(-2.55494 + 7.86329i) q^{61} +(5.98183 + 8.23328i) q^{62} +(1.43977 - 1.98168i) q^{63} +(1.77130 + 5.45150i) q^{64} +(-6.00000 - 7.34847i) q^{65} +14.9372i q^{67} +(1.70539 - 0.554114i) q^{68} +(-2.64383 - 1.92085i) q^{69} +(-0.987277 + 3.74503i) q^{70} +(0.678648 - 2.08867i) q^{71} +(1.34500 + 0.437016i) q^{72} +(-2.87955 - 3.96336i) q^{73} +(-10.4591 - 7.59901i) q^{74} +(0.291333 + 2.57174i) q^{75} +10.7321 q^{76} -4.24264i q^{78} +(1.68850 + 5.19667i) q^{79} +(-9.96616 + 0.562695i) q^{80} +(-5.38826 + 3.91480i) q^{81} +(-3.18230 - 1.03399i) q^{82} +(-9.41498 - 3.05911i) q^{83} +(-0.650326 + 0.472490i) q^{84} +(0.130495 + 2.31127i) q^{85} +(-6.38437 - 19.6491i) q^{86} +3.58630i q^{87} +6.46410 q^{89} +(6.38766 - 9.92370i) q^{90} +(3.07738 + 2.23585i) q^{91} +(-6.42730 - 8.84642i) q^{92} +(-2.59343 - 0.842656i) q^{93} +(2.44995 - 7.54017i) q^{94} +(-3.53184 + 13.3973i) q^{95} +(-3.17798 - 2.30894i) q^{96} +(0.624215 - 0.202820i) q^{97} +11.9700i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^6 - 4 * q^9	$ 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) $ 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−1.83730	+	0.596975i	−1.29917	+	0.422125i	−0.875292	−	0.483595i	$-0.839331\pi$
$2$	−1.83730	+	0.596975i	−1.29917	+	0.422125i	−0.423876	+	0.905720i	$0.639331\pi$
$3$	0.304260	−	0.418778i	0.175665	−	0.241782i	−0.712101	−	0.702077i	$-0.752256\pi$
$3$	0.304260	−	0.418778i	0.175665	−	0.241782i	0.887766	+	0.460295i	$0.152256\pi$
$4$	1.40126	−	1.01807i	0.700629	−	0.509037i
$5$	0.809764	+	2.08429i	0.362137	+	0.932125i
$5$	0.809764	+	2.08429i	0.362137	+	0.932125i
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−0.526994	−	0.725345i	−0.199185	−	0.274155i	0.697727	−	0.716364i	$-0.254195\pi$
$7$	−0.526994	−	0.725345i	−0.199185	−	0.274155i	−0.896912	+	0.442209i	$0.854195\pi$
$8$	0.304260	−	0.418778i	0.107572	−	0.148060i
$9$	0.844250	+	2.59833i	0.281417	+	0.866112i
$10$	−2.73205	−	3.34607i	−0.863950	−	1.05812i
$11$		0			0
$11$		0			0
$12$		−	0.896575i		−	0.258819i
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.809426	−	0.587222i	$-0.800222\pi$
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.309679	+	0.950841i	$0.600222\pi$
$14$	1.40126	+	1.01807i	0.374502	+	0.272092i
$15$	1.11924	+	0.295056i	0.288985	+	0.0761832i
$16$	−1.37948	+	4.24561i	−0.344871	+	1.06140i
$17$	0.984606	+	0.319918i	0.238802	+	0.0775915i	0.425973	−	0.904736i	$-0.359932\pi$
$17$	0.984606	+	0.319918i	0.238802	+	0.0775915i	−0.187171	+	0.982327i	$0.559932\pi$
$18$	−3.10228	−	4.26992i	−0.731215	−	1.00643i
$19$	5.01279	+	3.64201i	1.15001	+	0.835534i	0.988483	−	0.151334i	$-0.0483569\pi$
$19$	5.01279	+	3.64201i	1.15001	+	0.835534i	0.161531	+	0.986868i	$0.448357\pi$
$20$	3.25665	+	2.09624i	0.728210	+	0.468733i
$21$	−0.464102			−0.101275
$22$		0			0
$23$		−	6.31319i		−	1.31639i	−0.752847	−	0.658196i	$-0.771320\pi$
$23$		−	6.31319i		−	1.31639i	0.752847	−	0.658196i	$-0.228680\pi$
$24$	−0.0828009	−	0.254835i	−0.0169017	−	0.0520179i
$25$	−3.68856	+	3.37557i	−0.737713	+	0.675114i
$26$	6.63083	−	4.81758i	1.30041	−	0.944805i
$27$	2.82191	+	0.916893i	0.543076	+	0.176456i
$28$	−1.47691	−	0.479877i	−0.279110	−	0.0906882i
$29$	−5.60503	+	4.07230i	−1.04083	+	0.756206i	−0.970447	−	0.241314i	$-0.922422\pi$
$29$	−5.60503	+	4.07230i	−1.04083	+	0.756206i	−0.0703816	+	0.997520i	$0.522422\pi$
$30$	−2.23251	+	0.126049i	−0.407599	+	0.0230133i
$31$	−1.62789	−	5.01012i	−0.292377	−	0.899844i	−0.984090	−	0.177671i	$-0.943144\pi$
$31$	−1.62789	−	5.01012i	−0.292377	−	0.899844i	0.691713	−	0.722173i	$-0.256856\pi$
$32$		−	7.58871i		−	1.34151i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	1.08509	−	1.68577i	0.183414	−	0.284947i
$36$	3.82831	+	2.78143i	0.638052	+	0.463572i
$37$	3.93354	+	5.41405i	0.646669	+	0.890064i	0.998949	−	0.0458308i	$-0.0145935\pi$
$37$	3.93354	+	5.41405i	0.646669	+	0.890064i	−0.352280	+	0.935895i	$0.614594\pi$
$38$	−11.3842	−	3.69895i	−1.84676	−	0.600049i
$39$	−0.678648	+	2.08867i	−0.108671	+	0.334454i
$40$	1.11924	+	0.295056i	0.176967	+	0.0466525i
$41$	1.40126	+	1.01807i	0.218840	+	0.158996i	0.691804	−	0.722085i	$-0.256816\pi$
$41$	1.40126	+	1.01807i	0.218840	+	0.158996i	−0.472964	+	0.881082i	$0.656816\pi$
$42$	0.852694	−	0.277057i	0.131574	−	0.0427508i
$43$			10.6945i			1.63090i	0.578827	+	0.815451i	$0.303511\pi$
$43$			10.6945i			1.63090i	−0.578827	+	0.815451i	$0.696489\pi$
$44$		0			0
$45$	−4.73205	+	3.86370i	−0.705412	+	0.575967i
$46$	3.76882	+	11.5992i	0.555682	+	1.71021i
$47$	−2.41224	+	3.32016i	−0.351861	+	0.484295i	−0.947859	−	0.318691i	$-0.896757\pi$
$47$	−2.41224	+	3.32016i	−0.351861	+	0.484295i	0.595998	+	0.802986i	$0.296757\pi$
$48$	1.35825	+	1.86947i	0.196046	+	0.269834i
$49$	1.91472	−	5.89289i	0.273531	−	0.841842i
$50$	4.76187	−	8.40392i	0.673430	−	1.18849i
$51$	0.433551	−	0.314993i	0.0607093	−	0.0441079i
$52$	−4.31932	+	5.94504i	−0.598982	+	0.824428i
$53$	−11.3842	+	3.69895i	−1.56374	+	0.508090i	−0.957803	−	0.287424i	$-0.907201\pi$
$53$	−11.3842	+	3.69895i	−1.56374	+	0.508090i	−0.605936	+	0.795514i	$0.707201\pi$
$54$	−5.73205			−0.780033
$55$		0			0
$56$	−0.464102			−0.0620182
$57$	3.05038	−	0.991130i	0.404033	−	0.131278i
$58$	7.86707	−	10.8281i	1.03300	−	1.42180i
$59$	−3.82831	+	2.78143i	−0.498403	+	0.362111i	−0.808407	−	0.588624i	$-0.799670\pi$
$59$	−3.82831	+	2.78143i	−0.498403	+	0.362111i	0.310003	+	0.950735i	$0.399670\pi$
$60$	1.86873	−	0.726014i	0.241252	−	0.0937281i
$61$	−2.55494	+	7.86329i	−0.327126	+	1.00679i	0.643346	+	0.765576i	$0.277546\pi$
$61$	−2.55494	+	7.86329i	−0.327126	+	1.00679i	−0.970472	+	0.241215i	$0.922454\pi$
$62$	5.98183	+	8.23328i	0.759693	+	1.04563i
$63$	1.43977	−	1.98168i	0.181394	−	0.249668i
$64$	1.77130	+	5.45150i	0.221413	+	0.681438i
$65$	−6.00000	−	7.34847i	−0.744208	−	0.911465i
$66$		0			0
$67$			14.9372i			1.82487i	0.409226	+	0.912433i	$0.365799\pi$
$67$			14.9372i			1.82487i	−0.409226	+	0.912433i	$0.634201\pi$
$68$	1.70539	−	0.554114i	0.206809	−	0.0671962i
$69$	−2.64383	−	1.92085i	−0.318279	−	0.231243i
$70$	−0.987277	+	3.74503i	−0.118002	+	0.447617i
$71$	0.678648	−	2.08867i	0.0805407	−	0.247879i	−0.902676	−	0.430321i	$-0.858400\pi$
$71$	0.678648	−	2.08867i	0.0805407	−	0.247879i	0.983217	+	0.182442i	$0.0584003\pi$
$72$	1.34500	+	0.437016i	0.158509	+	0.0515028i
$73$	−2.87955	−	3.96336i	−0.337026	−	0.463876i	0.606544	−	0.795050i	$-0.292555\pi$
$73$	−2.87955	−	3.96336i	−0.337026	−	0.463876i	−0.943570	+	0.331174i	$0.892555\pi$
$74$	−10.4591	−	7.59901i	−1.21585	−	0.883367i
$75$	0.291333	+	2.57174i	0.0336402	+	0.296959i
$76$	10.7321			1.23105
$77$		0			0
$78$		−	4.24264i		−	0.480384i
$79$	1.68850	+	5.19667i	0.189971	+	0.584671i	0.999999	−	0.00172104i	$-0.000547824\pi$
$79$	1.68850	+	5.19667i	0.189971	+	0.584671i	−0.810027	+	0.586392i	$0.800548\pi$
$80$	−9.96616	+	0.562695i	−1.11425	+	0.0629112i
$81$	−5.38826	+	3.91480i	−0.598695	+	0.434978i
$82$	−3.18230	−	1.03399i	−0.351426	−	0.114185i
$83$	−9.41498	−	3.05911i	−1.03343	−	0.335781i	−0.257283	−	0.966336i	$-0.582827\pi$
$83$	−9.41498	−	3.05911i	−1.03343	−	0.335781i	−0.776145	+	0.630555i	$0.782827\pi$
$84$	−0.650326	+	0.472490i	−0.0709564	+	0.0515529i
$85$	0.130495	+	2.31127i	0.0141542	+	0.250692i
$86$	−6.38437	−	19.6491i	−0.688444	−	2.11881i
$87$			3.58630i			0.384492i
$88$		0			0
$89$	6.46410			0.685193			0.342597	−	0.939483i	$-0.388694\pi$
$89$	6.46410			0.685193			0.342597	+	0.939483i	$0.388694\pi$
$90$	6.38766	−	9.92370i	0.673319	−	1.04605i
$91$	3.07738	+	2.23585i	0.322597	+	0.234380i
$92$	−6.42730	−	8.84642i	−0.670092	−	0.922303i
$93$	−2.59343	−	0.842656i	−0.268926	−	0.0873793i
$94$	2.44995	−	7.54017i	0.252693	−	0.777709i
$95$	−3.53184	+	13.3973i	−0.362359	+	1.37453i
$96$	−3.17798	−	2.30894i	−0.324352	−	0.235655i
$97$	0.624215	−	0.202820i	0.0633795	−	0.0205932i	−0.277156	−	0.960825i	$-0.589392\pi$
$97$	0.624215	−	0.202820i	0.0633795	−	0.0205932i	0.340535	+	0.940232i	$0.389392\pi$
$98$			11.9700i			1.20916i
$99$		0			0
$100$	−1.73205	+	8.48528i	−0.173205	+	0.848528i
$101$	−0.430246	−	1.32416i	−0.0428111	−	0.131759i	0.927367	−	0.374154i	$-0.122067\pi$
$101$	−0.430246	−	1.32416i	−0.0428111	−	0.131759i	−0.970178	+	0.242395i	$0.922067\pi$
$102$	−0.608520	+	0.837556i	−0.0602525	+	0.0829304i
$103$	−2.49376	−	3.43237i	−0.245718	−	0.338201i	0.668288	−	0.743903i	$-0.267027\pi$
$103$	−2.49376	−	3.43237i	−0.245718	−	0.338201i	−0.914006	+	0.405701i	$0.867027\pi$
$104$	−0.678648	+	2.08867i	−0.0665470	+	0.204810i
$105$	−0.375813	−	0.967324i	−0.0366756	−	0.0944012i
$106$	18.7080	−	13.5922i	1.81708	−	1.32019i
$107$	2.57529	−	3.54458i	0.248962	−	0.342667i	−0.666185	−	0.745786i	$-0.732074\pi$
$107$	2.57529	−	3.54458i	0.248962	−	0.342667i	0.915148	+	0.403119i	$0.132074\pi$
$108$	4.88769	−	1.58811i	0.470318	−	0.152815i
$109$	1.19615			0.114571			0.0572853	−	0.998358i	$-0.481756\pi$
$109$	1.19615			0.114571			0.0572853	+	0.998358i	$0.481756\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$	3.80651	−	1.23681i	0.359682	−	0.116868i
$113$	1.66251	−	2.28825i	0.156396	−	0.215260i	−0.723628	−	0.690190i	$-0.757527\pi$
$113$	1.66251	−	2.28825i	0.156396	−	0.215260i	0.880023	+	0.474930i	$0.157527\pi$
$114$	−5.01279	+	3.64201i	−0.469491	+	0.341105i
$115$	13.1586	−	5.11220i	1.22704	−	0.476715i
$116$	−3.70820	+	11.4127i	−0.344298	+	1.05964i
$117$	−6.81308	−	9.37740i	−0.629870	−	0.866941i
$118$	5.37331	−	7.39573i	0.494653	−	0.680832i
$119$	−0.286831	−	0.882774i	−0.0262937	−	0.0809237i
$120$	0.464102	−	0.378937i	0.0423665	−	0.0345921i
$121$		0			0
$122$		−	15.9725i		−	1.44608i
$123$	0.852694	−	0.277057i	0.0768848	−	0.0249814i
$124$	−7.38176	−	5.36316i	−0.662902	−	0.481626i
$125$	−10.0226	−	4.95464i	−0.896444	−	0.443156i
$126$	−1.46228	+	4.50045i	−0.130271	+	0.400932i
$127$	3.18230	+	1.03399i	0.282383	+	0.0917519i	0.446784	−	0.894642i	$-0.352569\pi$
$127$	3.18230	+	1.03399i	0.282383	+	0.0917519i	−0.164401	+	0.986394i	$0.552569\pi$
$128$	2.41224	+	3.32016i	0.213214	+	0.293463i
$129$	4.47864	+	3.25392i	0.394322	+	0.286492i
$130$	15.4107	+	9.91949i	1.35160	+	0.869997i
$131$	21.1244			1.84564			0.922822	−	0.385227i	$-0.125877\pi$
$131$	21.1244			1.84564			0.922822	+	0.385227i	$0.125877\pi$
$132$		0			0
$133$		−	5.55532i		−	0.481707i
$134$	−8.91712	−	27.4441i	−0.770322	−	2.37081i
$135$	0.374003	+	6.62415i	0.0321891	+	0.570116i
$136$	0.433551	−	0.314993i	0.0371767	−	0.0270104i
$137$	13.0896	+	4.25306i	1.11832	+	0.363364i	0.809126	−	0.587636i	$-0.199941\pi$
$137$	13.0896	+	4.25306i	1.11832	+	0.363364i	0.309193	+	0.950999i	$0.399941\pi$
$138$	6.00420	+	1.95088i	0.511112	+	0.166070i
$139$	13.4203	−	9.75045i	1.13830	−	0.827022i	0.151417	−	0.988470i	$-0.451616\pi$
$139$	13.4203	−	9.75045i	1.13830	−	0.827022i	0.986881	+	0.161447i	$0.0516162\pi$
$140$	−0.195743	−	3.46690i	−0.0165433	−	0.293007i
$141$	0.656462	+	2.02038i	0.0552841	+	0.170147i
$142$			4.24264i			0.356034i
$143$		0			0
$144$	−12.1962			−1.01635
$145$	−13.0266	−	8.38494i	−1.08180	−	0.696332i
$146$	7.65662	+	5.56286i	0.633666	+	0.460386i
$147$	−1.88524	−	2.59481i	−0.155492	−	0.214017i
$148$	11.0238	+	3.58185i	0.906151	+	0.294426i
$149$	4.24344	−	13.0600i	0.347636	−	1.06991i	−0.612522	−	0.790454i	$-0.709845\pi$
$149$	4.24344	−	13.0600i	0.347636	−	1.06991i	0.960157	−	0.279459i	$-0.0901553\pi$
$150$	−2.07053	−	4.55114i	−0.169058	−	0.371599i
$151$	5.01279	+	3.64201i	0.407935	+	0.296382i	0.772765	−	0.634692i	$-0.218873\pi$
$151$	5.01279	+	3.64201i	0.407935	+	0.296382i	−0.364830	+	0.931074i	$0.618873\pi$
$152$	3.05038	−	0.991130i	0.247419	−	0.0803913i
$153$			2.82843i			0.228665i
$154$		0			0
$155$	9.12436	−	7.45001i	0.732886	−	0.598399i
$156$	1.17545	+	3.61767i	0.0941116	+	0.289646i
$157$	7.09550	−	9.76612i	0.566282	−	0.779421i	−0.425826	−	0.904805i	$-0.640016\pi$
$157$	7.09550	−	9.76612i	0.566282	−	0.779421i	0.992108	+	0.125384i	$0.0400164\pi$
$158$	−6.20456	−	8.53985i	−0.493609	−	0.679394i
$159$	−1.91472	+	5.89289i	−0.151847	+	0.467337i
$160$	15.8171	−	6.14506i	1.25045	−	0.485810i
$161$	−4.57924	+	3.32701i	−0.360895	+	0.262205i
$162$	7.56281	−	10.4093i	0.594191	−	0.817833i
$163$	7.21729	−	2.34504i	0.565302	−	0.183678i	−0.0124036	−	0.999923i	$-0.503948\pi$
$163$	7.21729	−	2.34504i	0.565302	−	0.183678i	0.577705	+	0.816245i	$0.303948\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	19.1244			1.48434
$167$	−1.83730	+	0.596975i	−0.142175	+	0.0461953i	−0.379240	−	0.925298i	$-0.623814\pi$
$167$	−1.83730	+	0.596975i	−0.142175	+	0.0461953i	0.237065	+	0.971494i	$0.423814\pi$
$168$	−0.141208	+	0.194356i	−0.0108944	+	0.0149949i
$169$	4.04508	−	2.93893i	0.311160	−	0.226071i
$170$	−1.61953	−	4.16859i	−0.124212	−	0.319716i
$171$	−5.23110	+	16.0997i	−0.400032	+	1.23117i
$172$	10.8878	+	14.9858i	0.830189	+	1.14266i
$173$	−4.48237	+	6.16946i	−0.340789	+	0.469055i	−0.944672	−	0.328018i	$-0.893619\pi$
$173$	−4.48237	+	6.16946i	−0.340789	+	0.469055i	0.603883	+	0.797073i	$0.293619\pi$
$174$	−2.14093	−	6.58911i	−0.162304	−	0.499519i
$175$	4.39230	+	0.896575i	0.332027	+	0.0677747i
$176$		0			0
$177$			2.44949i			0.184115i
$178$	−11.8765	+	3.85891i	−0.890181	+	0.289237i
$179$	−6.90569	−	5.01728i	−0.516155	−	0.375009i	0.298998	−	0.954254i	$-0.403348\pi$
$179$	−6.90569	−	5.01728i	−0.516155	−	0.375009i	−0.815154	+	0.579245i	$0.803348\pi$
$180$	−2.69729	+	10.2316i	−0.201044	+	0.762620i
$181$	1.04828	−	3.22627i	0.0779180	−	0.239807i	−0.904509	−	0.426455i	$-0.859762\pi$
$181$	1.04828	−	3.22627i	0.0779180	−	0.239807i	0.982427	+	0.186648i	$0.0597623\pi$
$182$	−6.98881	−	2.27080i	−0.518045	−	0.168323i
$183$	2.51561	+	3.46244i	0.185959	+	0.255951i
$184$	−2.64383	−	1.92085i	−0.194905	−	0.141607i
$185$	−8.09923	+	12.5827i	−0.595467	+	0.925102i
$186$	5.26795			0.386265
$187$		0			0
$188$			7.10823i			0.518421i
$189$	−0.822064	−	2.53005i	−0.0597963	−	0.184034i
$190$	−1.50881	−	26.7233i	−0.109461	−	1.93871i
$191$	8.68241	−	6.30814i	0.628237	−	0.456441i	−0.227552	−	0.973766i	$-0.573072\pi$
$191$	8.68241	−	6.30814i	0.628237	−	0.456441i	0.855789	+	0.517325i	$0.173072\pi$
$192$	2.82191	+	0.916893i	0.203654	+	0.0661710i
$193$	9.77537	+	3.17621i	0.703647	+	0.228629i	0.638919	−	0.769274i	$-0.279382\pi$
$193$	9.77537	+	3.17621i	0.703647	+	0.228629i	0.0647279	+	0.997903i	$0.479382\pi$
$194$	−1.02579	+	0.745282i	−0.0736476	+	0.0535081i
$195$	−4.90294	+	0.276823i	−0.351107	+	0.0198237i
$196$	−3.31639	−	10.2068i	−0.236885	−	0.729056i
$197$		−	2.55103i		−	0.181753i	−0.995862	−	0.0908765i	$-0.971033\pi$
$197$		−	2.55103i		−	0.181753i	0.995862	−	0.0908765i	$-0.0289669\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	0.291333	+	2.57174i	0.0206003	+	0.181850i
$201$	6.25536	+	4.54479i	0.441219	+	0.320564i
$202$	1.58098	+	2.17603i	0.111237	+	0.153105i
$203$	5.90764	+	1.91951i	0.414635	+	0.134723i
$204$	0.286831	−	0.882774i	0.0200822	−	0.0618065i
$205$	−0.987277	+	3.74503i	−0.0689544	+	0.261565i
$206$	6.63083	+	4.81758i	0.461992	+	0.335657i
$207$	16.4038	−	5.32991i	1.14014	−	0.370455i
$208$		−	18.9396i		−	1.31322i
$209$		0			0
$210$	1.26795	+	1.55291i	0.0874968	+	0.107161i
$211$	3.43761	+	10.5799i	0.236655	+	0.728350i	0.996898	+	0.0787102i	$0.0250802\pi$
$211$	3.43761	+	10.5799i	0.236655	+	0.728350i	−0.760242	+	0.649640i	$0.774920\pi$
$212$	−12.1864	+	16.7731i	−0.836965	+	1.15198i
$213$	−0.668201	−	0.919700i	−0.0457844	−	0.0630168i
$214$	−2.61555	+	8.04984i	−0.178795	+	0.550276i
$215$	−22.2906	+	8.66005i	−1.52020	+	0.590610i
$216$	1.24257	−	0.902778i	0.0845460	−	0.0614263i
$217$	−2.77618	+	3.82108i	−0.188459	+	0.259392i
$218$	−2.19769	+	0.714073i	−0.148846	+	0.0483631i
$219$	−2.53590			−0.171360
$220$		0			0
$221$	−4.39230			−0.295458
$222$	−6.36459	+	2.06798i	−0.427164	+	0.138794i
$223$	−3.40654	+	4.68870i	−0.228119	+	0.313979i	−0.907698	−	0.419623i	$-0.862162\pi$
$223$	−3.40654	+	4.68870i	−0.228119	+	0.313979i	0.679580	+	0.733602i	$0.262162\pi$
$224$	−5.50443	+	3.99920i	−0.367780	+	0.267208i
$225$	−11.8849	−	6.73430i	−0.792329	−	0.448953i
$226$	−1.68850	+	5.19667i	−0.112317	+	0.345677i
$227$	−12.6537	−	17.4163i	−0.839856	−	1.15596i	−0.986008	−	0.166700i	$-0.946689\pi$
$227$	−12.6537	−	17.4163i	−0.839856	−	1.15596i	0.146152	−	0.989262i	$-0.453311\pi$
$228$	3.26533	−	4.49435i	0.216252	−	0.297645i
$229$	5.54012	+	17.0507i	0.366101	+	1.12674i	0.949288	+	0.314406i	$0.101805\pi$
$229$	5.54012	+	17.0507i	0.366101	+	1.12674i	−0.583187	+	0.812338i	$0.698195\pi$
$230$	−21.1244	+	17.2480i	−1.39290	+	1.13730i
$231$		0			0
$232$			3.58630i			0.235452i
$233$	12.3688	−	4.01887i	0.810307	−	0.263285i	0.125579	−	0.992084i	$-0.459921\pi$
$233$	12.3688	−	4.01887i	0.810307	−	0.263285i	0.684728	+	0.728799i	$0.259921\pi$
$234$	18.1158	+	13.1619i	1.18426	+	0.860418i
$235$	−8.87353	−	2.33926i	−0.578845	−	0.152597i
$236$	−2.53275	+	7.79500i	−0.164868	+	0.507412i
$237$	2.68999	+	0.874032i	0.174734	+	0.0567745i
$238$	1.05399	+	1.45069i	0.0683199	+	0.0940342i
$239$	−9.43334	−	6.85373i	−0.610192	−	0.443331i	0.239290	−	0.970948i	$-0.423085\pi$
$239$	−9.43334	−	6.85373i	−0.610192	−	0.443331i	−0.849482	+	0.527618i	$0.823085\pi$
$240$	−2.79666	+	4.34482i	−0.180524	+	0.280457i
$241$	−10.1244			−0.652167			−0.326084	−	0.945341i	$-0.605729\pi$
$241$	−10.1244			−0.652167			−0.326084	+	0.945341i	$0.605729\pi$
$242$		0			0
$243$			12.3490i			0.792188i
$244$	4.42528	+	13.6196i	0.283300	+	0.871906i
$245$	13.8330	−	0.781018i	0.883757	−	0.0498974i
$246$	−1.40126	+	1.01807i	−0.0893410	+	0.0649100i
$247$	−25.0014	−	8.12345i	−1.59080	−	0.516883i
$248$	−2.59343	−	0.842656i	−0.164683	−	0.0535087i
$249$	−4.14569	+	3.01202i	−0.262722	+	0.190879i
$250$	21.3722	+	3.11994i	1.35170	+	0.197323i
$251$	−4.38685	−	13.5013i	−0.276896	−	0.852197i	−0.988712	−	0.149831i	$-0.952127\pi$
$251$	−4.38685	−	13.5013i	−0.276896	−	0.852197i	0.711816	−	0.702366i	$-0.247873\pi$
$252$		−	4.24264i		−	0.267261i
$253$		0			0
$254$	−6.46410			−0.405594
$255$	1.00761	+	0.648578i	0.0630991	+	0.0406155i
$256$	−15.6887	−	11.3985i	−0.980544	−	0.712407i
$257$	2.93923	+	4.04550i	0.183344	+	0.252351i	0.890789	−	0.454417i	$-0.150152\pi$
$257$	2.93923	+	4.04550i	0.183344	+	0.252351i	−0.707445	+	0.706768i	$0.750152\pi$
$258$	−10.1711	−	3.30479i	−0.633225	−	0.205747i
$259$	1.85410	−	5.70634i	0.115208	−	0.354575i
$260$	−15.8888	−	4.18866i	−0.985384	−	0.259770i
$261$	−15.3132	−	11.1257i	−0.947866	−	0.688665i
$262$	−38.8118	+	12.6107i	−2.39780	+	0.779092i
$263$		−	21.4906i		−	1.32517i	−0.748988	−	0.662584i	$-0.769460\pi$
$263$		−	21.4906i		−	1.32517i	0.748988	−	0.662584i	$-0.230540\pi$
$264$		0			0
$265$	−16.9282	−	20.7327i	−1.03989	−	1.27360i
$266$	3.31639	+	10.2068i	0.203341	+	0.625818i
$267$	1.96677	−	2.70702i	0.120364	−	0.165667i
$268$	15.2071	+	20.9308i	0.928924	+	1.27855i
$269$	6.09754	−	18.7663i	0.371774	−	1.14420i	−0.573856	−	0.818956i	$-0.694553\pi$
$269$	6.09754	−	18.7663i	0.371774	−	1.14420i	0.945630	−	0.325245i	$-0.105447\pi$
$270$	−4.64161	−	11.9473i	−0.282479	−	0.727088i
$271$	−3.66962	+	2.66613i	−0.222913	+	0.161956i	−0.693637	−	0.720325i	$-0.743993\pi$
$271$	−3.66962	+	2.66613i	−0.222913	+	0.161956i	0.470724	+	0.882281i	$0.343993\pi$
$272$	−2.71650	+	3.73894i	−0.164712	+	0.226706i
$273$	1.87265	−	0.608460i	0.113338	−	0.0368256i
$274$	−26.5885			−1.60627
$275$		0			0
$276$	−5.66025			−0.340707
$277$	21.5906	−	7.01523i	1.29726	−	0.421504i	0.422630	−	0.906302i	$-0.361107\pi$
$277$	21.5906	−	7.01523i	1.29726	−	0.421504i	0.874626	+	0.484798i	$0.161107\pi$
$278$	−18.8364	+	25.9261i	−1.12973	+	1.55494i
$279$	11.6436	−	8.45958i	0.697085	−	0.506462i
$280$	−0.375813	−	0.967324i	−0.0224591	−	0.0578087i
$281$	5.35233	−	16.4728i	0.319293	−	0.982684i	−0.654658	−	0.755925i	$-0.727187\pi$
$281$	5.35233	−	16.4728i	0.319293	−	0.982684i	0.973951	−	0.226758i	$-0.0728128\pi$
$282$	−2.41224	−	3.32016i	−0.143647	−	0.197712i
$283$	−17.7009	+	24.3632i	−1.05221	+	1.44824i	−0.165332	+	0.986238i	$0.552870\pi$
$283$	−17.7009	+	24.3632i	−1.05221	+	1.44824i	−0.886877	+	0.462005i	$0.847130\pi$
$284$	−1.17545	−	3.61767i	−0.0697503	−	0.214669i
$285$	4.53590	+	5.55532i	0.268683	+	0.329069i
$286$		0			0
$287$		−	1.55291i		−	0.0916656i
$288$	19.7180	−	6.40677i	1.16189	−	0.377522i
$289$	−12.8862	−	9.36236i	−0.758011	−	0.550727i
$290$	28.9394	+	7.62909i	1.69938	+	0.447996i
$291$	0.104987	−	0.323118i	0.00615446	−	0.0189415i
$292$	−8.06998	−	2.62210i	−0.472260	−	0.153447i
$293$	5.53636	+	7.62015i	0.323438	+	0.445174i	0.939513	−	0.342514i	$-0.111278\pi$
$293$	5.53636	+	7.62015i	0.323438	+	0.445174i	−0.616075	+	0.787687i	$0.711278\pi$
$294$	5.01279	+	3.64201i	0.292352	+	0.212406i
$295$	−8.89734	−	5.72702i	−0.518023	−	0.333440i
$296$	3.46410			0.201347
$297$		0			0
$298$			26.5283i			1.53674i
$299$	8.27690	+	25.4737i	0.478665	+	1.47318i
$300$	3.02646	+	3.30708i	0.174732	+	0.190934i
$301$	7.75722	−	5.63595i	0.447119	−	0.324851i
$302$	−11.3842	−	3.69895i	−0.655087	−	0.212851i
$303$	−0.685436	−	0.222712i	−0.0393773	−	0.0127944i
$304$	−22.3776	+	16.2583i	−1.28344	+	0.932477i
$305$	−18.4583	+	1.04217i	−1.05692	+	0.0596742i
$306$	−1.68850	−	5.19667i	−0.0965251	−	0.297074i
$307$			17.6269i			1.00602i	0.864280	+	0.503010i	$0.167774\pi$
$307$			17.6269i			1.00602i	−0.864280	+	0.503010i	$0.832226\pi$
$308$		0			0
$309$	−2.19615			−0.124935
$310$	−12.3167	+	19.1349i	−0.699542	+	1.08679i
$311$	22.6950	+	16.4889i	1.28692	+	0.934999i	0.999738	−	0.0228789i	$-0.00728322\pi$
$311$	22.6950	+	16.4889i	1.28692	+	0.934999i	0.287177	+	0.957878i	$0.407283\pi$
$312$	0.668201	+	0.919700i	0.0378295	+	0.0520678i
$313$	16.3072	+	5.29854i	0.921739	+	0.299491i	0.731180	−	0.682185i	$-0.238970\pi$
$313$	16.3072	+	5.29854i	0.921739	+	0.299491i	0.190559	+	0.981676i	$0.438970\pi$
$314$	−7.20643	+	22.1791i	−0.406683	+	1.25164i
$315$	5.29628	+	1.39622i	0.298411	+	0.0786681i
$316$	7.65662	+	5.56286i	0.430718	+	0.312935i
$317$	6.62842	−	2.15370i	0.372289	−	0.120964i	−0.116896	−	0.993144i	$-0.537294\pi$
$317$	6.62842	−	2.15370i	0.372289	−	0.120964i	0.489185	+	0.872180i	$0.337294\pi$
$318$		−	11.9700i		−	0.671247i
$319$		0			0
$320$	−9.92820	+	8.10634i	−0.555003	+	0.453158i
$321$	−0.700835	−	2.15695i	−0.0391168	−	0.120389i
$322$	6.42730	−	8.84642i	0.358179	−	0.492991i
$323$	3.77048	+	5.18962i	0.209795	+	0.288758i
$324$	−3.56479	+	10.9713i	−0.198044	+	0.609516i
$325$	10.4578	−	18.4563i	0.580094	−	1.02377i
$326$	−11.8604	+	8.61708i	−0.656887	+	0.477256i
$327$	0.363941	−	0.500922i	0.0201260	−	0.0277011i
$328$	0.852694	−	0.277057i	0.0470821	−	0.0152979i
$329$	3.67949			0.202857
$330$		0			0
$331$	−7.80385			−0.428938			−0.214469	−	0.976731i	$-0.568802\pi$
$331$	−7.80385			−0.428938			−0.214469	+	0.976731i	$0.568802\pi$
$332$	−16.3072	+	5.29854i	−0.894975	+	0.290795i
$333$	−10.7466	+	14.7915i	−0.588911	+	0.810567i
$334$	3.01929	−	2.19364i	0.165208	−	0.120031i
$335$	−31.1335	+	12.0956i	−1.70100	+	0.660852i
$336$	0.640220	−	1.97040i	0.0349269	−	0.107494i
$337$	−4.60174	−	6.33375i	−0.250673	−	0.345021i	0.665074	−	0.746777i	$-0.268400\pi$
$337$	−4.60174	−	6.33375i	−0.250673	−	0.345021i	−0.915747	+	0.401756i	$0.868400\pi$
$338$	−5.67757	+	7.81450i	−0.308819	+	0.425053i
$339$	−0.452432	−	1.39244i	−0.0245727	−	0.0756271i
$340$	2.53590	+	3.10583i	0.137528	+	0.168437i
$341$		0			0
$342$		−	32.7028i		−	1.76836i
$343$	−11.2523	+	3.65609i	−0.607566	+	0.197410i
$344$	4.47864	+	3.25392i	0.241472	+	0.175440i
$345$	1.86275	−	7.06595i	0.100287	−	0.380418i
$346$	4.55245	−	14.0110i	0.244741	−	0.753237i
$347$	−2.82191	−	0.916893i	−0.151488	−	0.0492214i	0.232291	−	0.972646i	$-0.425378\pi$
$347$	−2.82191	−	0.916893i	−0.151488	−	0.0492214i	−0.383779	+	0.923425i	$0.625378\pi$
$348$	3.65112	+	5.02534i	0.195721	+	0.269386i
$349$	22.1028	+	16.0586i	1.18313	+	0.859597i	0.992522	−	0.122069i	$-0.0389529\pi$
$349$	22.1028	+	16.0586i	1.18313	+	0.859597i	0.190612	+	0.981666i	$0.438953\pi$
$350$	−8.60522	+	0.974818i	−0.459968	+	0.0521062i
$351$	−12.5885			−0.671922
$352$		0			0
$353$			1.69161i			0.0900356i	0.998986	+	0.0450178i	$0.0143345\pi$
$353$			1.69161i			0.0900356i	−0.998986	+	0.0450178i	$0.985666\pi$
$354$	−1.46228	−	4.50045i	−0.0777195	−	0.239196i
$355$	4.90294	−	0.276823i	0.260221	−	0.0146922i
$356$	9.05788	−	6.58093i	0.480067	−	0.348789i
$357$	−0.456957	−	0.148474i	−0.0241847	−	0.00785810i
$358$	15.6830	+	5.09572i	0.828873	+	0.269317i
$359$	14.8372	−	10.7798i	0.783076	−	0.568938i	−0.122825	−	0.992428i	$-0.539195\pi$
$359$	14.8372	−	10.7798i	0.783076	−	0.568938i	0.905901	+	0.423491i	$0.139195\pi$
$360$	0.178260	+	3.15725i	0.00939513	+	0.166402i
$361$	5.99255	+	18.4432i	0.315397	+	0.970694i
$362$			6.55343i			0.344441i
$363$		0			0
$364$	6.58846			0.345329
$365$	5.92905	−	9.21121i	0.310341	−	0.482137i
$366$	−6.68891	−	4.85978i	−0.349635	−	0.254025i
$367$	17.4185	+	23.9745i	0.909238	+	1.25146i	0.967426	+	0.253153i	$0.0814677\pi$
$367$	17.4185	+	23.9745i	0.909238	+	1.25146i	−0.0581882	+	0.998306i	$0.518532\pi$
$368$	26.8034	+	8.70894i	1.39722	+	0.453985i
$369$	−1.46228	+	4.50045i	−0.0761235	+	0.234284i
$370$	7.36914	−	27.9533i	0.383103	−	1.45322i
$371$	8.68241	+	6.30814i	0.450768	+	0.327502i
$372$	−4.49195	+	1.45952i	−0.232897	+	0.0756727i
$373$		−	34.1170i		−	1.76651i	−0.468892	−	0.883255i	$-0.655347\pi$
$373$		−	34.1170i		−	1.76651i	0.468892	−	0.883255i	$-0.344653\pi$
$374$		0			0
$375$	−5.12436	+	2.68973i	−0.264621	+	0.138897i
$376$	0.656462	+	2.02038i	0.0338544	+	0.104193i
$377$	17.2773	−	23.7801i	0.889826	−	1.22474i
$378$	3.02076	+	4.15771i	0.155371	+	0.213850i
$379$	1.68850	−	5.19667i	0.0867324	−	0.266935i	−0.898279	−	0.439426i	$-0.855182\pi$
$379$	1.68850	−	5.19667i	0.0867324	−	0.266935i	0.985011	+	0.172491i	$0.0551817\pi$
$380$	8.69043	+	22.3688i	0.445810	+	1.14749i
$381$	1.40126	−	1.01807i	0.0717886	−	0.0521575i
$382$	−12.1864	+	16.7731i	−0.623510	+	0.858188i
$383$	22.6011	−	7.34355i	1.15486	−	0.375238i	0.331890	−	0.943318i	$-0.392314\pi$
$383$	22.6011	−	7.34355i	1.15486	−	0.375238i	0.822973	+	0.568080i	$0.192314\pi$
$384$	2.12436			0.108408
$385$		0			0
$386$	−19.8564			−1.01066
$387$	−27.7880	+	9.02886i	−1.41254	+	0.458963i
$388$	0.668201	−	0.919700i	0.0339228	−	0.0466907i
$389$	−14.6629	+	10.6532i	−0.743439	+	0.540140i	−0.893786	−	0.448493i	$-0.851961\pi$
$389$	−14.6629	+	10.6532i	−0.743439	+	0.540140i	0.150347	+	0.988633i	$0.451961\pi$
$390$	8.84291	−	3.43554i	0.447778	−	0.173965i
$391$	2.01970	−	6.21601i	0.102141	−	0.314357i
$392$	−1.88524	−	2.59481i	−0.0952191	−	0.131058i
$393$	6.42730	−	8.84642i	0.324214	−	0.446243i
$394$	1.52290	+	4.68700i	0.0767225	+	0.236128i
$395$	−9.46410	+	7.72741i	−0.476191	+	0.388808i
$396$		0			0
$397$			16.0096i			0.803500i	0.915749	+	0.401750i	$0.131598\pi$
$397$			16.0096i			0.803500i	−0.915749	+	0.401750i	$0.868402\pi$
$398$	−3.67460	+	1.19395i	−0.184191	+	0.0598473i
$399$	−2.32645	−	1.69026i	−0.116468	−	0.0846189i
$400$	−9.24306	−	20.3168i	−0.462153	−	1.01584i
$401$	−9.98759	+	30.7386i	−0.498756	+	1.53501i	0.312264	+	0.949995i	$0.398913\pi$
$401$	−9.98759	+	30.7386i	−0.498756	+	1.53501i	−0.811020	+	0.585018i	$0.801087\pi$
$402$	−14.2061	−	4.61584i	−0.708536	−	0.230217i
$403$	13.1370	+	18.0815i	0.654401	+	0.900706i
$404$	−1.95098	−	1.41747i	−0.0970648	−	0.0705217i
$405$	−12.5228	−	8.06065i	−0.622263	−	0.400537i
$406$	−12.0000			−0.595550
$407$		0			0
$408$		−	0.277401i		−	0.0137334i
$409$	0.579606	+	1.78384i	0.0286597	+	0.0882054i	0.964363	−	0.264582i	$-0.0852339\pi$
$409$	0.579606	+	1.78384i	0.0286597	+	0.0882054i	−0.935704	+	0.352787i	$0.885234\pi$
$410$	−0.421768	−	7.47013i	−0.0208296	−	0.368924i
$411$	5.76372	−	4.18759i	0.284304	−	0.206559i
$412$	−6.98881	−	2.27080i	−0.344314	−	0.111874i
$413$	4.03499	+	1.31105i	0.198549	+	0.0645125i
$414$	−26.9569	+	19.5853i	−1.32486	+	0.962565i
$415$	−1.24782	−	22.1007i	−0.0612531	−	1.08488i
$416$	9.94916	+	30.6204i	0.487798	+	1.50129i
$417$		−	8.58682i		−	0.420498i
$418$		0			0
$419$	29.6603			1.44900			0.724499	−	0.689276i	$-0.242071\pi$
$419$	29.6603			1.44900			0.724499	+	0.689276i	$0.242071\pi$
$420$	−1.51142	−	0.972866i	−0.0737497	−	0.0474710i
$421$	−17.0319	−	12.3744i	−0.830083	−	0.603091i	0.0894999	−	0.995987i	$-0.471473\pi$
$421$	−17.0319	−	12.3744i	−0.830083	−	0.603091i	−0.919583	+	0.392896i	$0.871473\pi$
$422$	−12.6319	−	17.3863i	−0.614909	−	0.846350i
$423$	−10.6634	−	3.46475i	−0.518473	−	0.168462i
$424$	−1.91472	+	5.89289i	−0.0929868	+	0.286184i
$425$	−4.71169	+	2.14357i	−0.228551	+	0.103978i
$426$	1.77672	+	1.29087i	0.0860826	+	0.0625427i
$427$	7.05003	−	2.29069i	0.341175	−	0.110854i
$428$		−	7.58871i		−	0.366814i
$429$		0			0
$430$	35.7846	−	29.2180i	1.72569	−	1.40902i
$431$	−5.84914	−	18.0018i	−0.281743	−	0.867116i	−0.987356	−	0.158518i	$-0.949328\pi$
$431$	−5.84914	−	18.0018i	−0.281743	−	0.867116i	0.705613	−	0.708597i	$-0.250672\pi$
$432$	−7.78554	+	10.7159i	−0.374582	+	0.515568i
$433$	−11.9040	−	16.3844i	−0.572069	−	0.787385i	0.420729	−	0.907186i	$-0.361774\pi$
$433$	−11.9040	−	16.3844i	−0.572069	−	0.787385i	−0.992798	+	0.119801i	$0.961774\pi$
$434$	2.81958	−	8.67778i	0.135344	−	0.416547i
$435$	−7.47491	+	2.90406i	−0.358394	+	0.139239i
$436$	1.67612	−	1.21777i	0.0802715	−	0.0583207i
$437$	22.9927	−	31.6467i	1.09989	−	1.51387i
$438$	4.65921	−	1.51387i	0.222625	−	0.0723354i
$439$	20.2487			0.966418			0.483209	−	0.875505i	$-0.339471\pi$
$439$	20.2487			0.966418			0.483209	+	0.875505i	$0.339471\pi$
$440$		0			0
$441$	16.9282			0.806105
$442$	8.06998	−	2.62210i	0.383850	−	0.124720i
$443$	−5.39515	+	7.42579i	−0.256332	+	0.352810i	−0.917716	−	0.397237i	$-0.869969\pi$
$443$	−5.39515	+	7.42579i	−0.256332	+	0.352810i	0.661385	+	0.750047i	$0.269969\pi$
$444$	4.85410	−	3.52671i	0.230365	−	0.167370i
$445$	5.23440	+	13.4731i	0.248134	+	0.638686i
$446$	3.45980	−	10.6482i	0.163826	−	0.504206i
$447$	−4.17811	−	5.75068i	−0.197618	−	0.271998i
$448$	3.02076	−	4.15771i	0.142717	−	0.196433i
$449$	3.24983	+	10.0019i	0.153369	+	0.472021i	0.997992	−	0.0633406i	$-0.0201755\pi$
$449$	3.24983	+	10.0019i	0.153369	+	0.472021i	−0.844623	+	0.535361i	$0.820175\pi$
$450$	25.8564	+	5.27792i	1.21888	+	0.248803i
$451$		0			0
$452$		−	4.89898i		−	0.230429i
$453$	3.05038	−	0.991130i	0.143320	−	0.0465674i
$454$	33.6458	+	24.4451i	1.57907	+	1.14726i
$455$	−2.16821	+	8.22467i	−0.101647	+	0.385578i
$456$	0.513047	−	1.57900i	0.0240256	−	0.0739432i
$457$	20.1750	+	6.55524i	0.943745	+	0.306641i	0.740171	−	0.672418i	$-0.234744\pi$
$457$	20.1750	+	6.55524i	0.943745	+	0.306641i	0.203573	+	0.979060i	$0.434744\pi$
$458$	−20.3577	−	28.0200i	−0.951254	−	1.30929i
$459$	2.48514	+	1.80556i	0.115996	+	0.0842762i
$460$	13.2339	−	20.5599i	0.617036	−	0.958610i
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$		−	17.8671i		−	0.830356i	−0.909740	−	0.415178i	$-0.863719\pi$
$463$		−	17.8671i		−	0.830356i	0.909740	−	0.415178i	$-0.136281\pi$
$464$	−9.55734	−	29.4145i	−0.443688	−	1.36553i
$465$	−0.343722	−	6.08782i	−0.0159397	−	0.282316i
$466$	−20.3260	+	14.7677i	−0.941585	+	0.684102i
$467$	16.8961	+	5.48987i	0.781858	+	0.254041i	0.672633	−	0.739976i	$-0.265163\pi$
$467$	16.8961	+	5.48987i	0.781858	+	0.254041i	0.109225	+	0.994017i	$0.465163\pi$
$468$	−19.0938	−	6.20395i	−0.882610	−	0.286778i
$469$	10.8346	−	7.87180i	0.500295	−	0.363486i
$470$	17.6998	−	0.999341i	0.816431	−	0.0460962i
$471$	−1.93096	−	5.94288i	−0.0889738	−	0.273833i
$472$			2.44949i			0.112747i
$473$		0			0
$474$	−5.46410			−0.250974
$475$	−30.7839	+	3.48727i	−1.41246	+	0.160007i
$476$	−1.30065	−	0.944980i	−0.0596153	−	0.0433131i
$477$	−19.2222	−	26.4571i	−0.880125	−	1.21139i
$478$	21.4234	+	6.96088i	0.979883	+	0.318383i
$479$	−2.92457	+	9.00090i	−0.133627	+	0.411261i	−0.995374	−	0.0960769i	$-0.969371\pi$
$479$	−2.92457	+	9.00090i	−0.133627	+	0.411261i	0.861747	+	0.507338i	$0.169371\pi$
$480$	2.23909	−	8.49355i	0.102200	−	0.387676i
$481$	−22.9699	−	16.6886i	−1.04734	−	0.760934i
$482$	18.6015	−	6.04399i	0.847274	−	0.275296i
$483$			2.92996i			0.133318i
$484$		0			0
$485$	0.928203	+	1.13681i	0.0421475	+	0.0516200i
$486$	−7.37204	−	22.6888i	−0.334402	−	1.02918i
$487$	−7.48128	+	10.2971i	−0.339009	+	0.466606i	−0.944152	−	0.329511i	$-0.893116\pi$
$487$	−7.48128	+	10.2971i	−0.339009	+	0.466606i	0.605142	+	0.796117i	$0.293116\pi$
$488$	2.51561	+	3.46244i	0.113876	+	0.156737i
$489$	1.21388	−	3.73594i	0.0548936	−	0.168945i
$490$	−24.9491	+	9.69291i	−1.12709	+	0.437881i
$491$	12.7119	−	9.23576i	0.573681	−	0.416804i	−0.262759	−	0.964861i	$-0.584632\pi$
$491$	12.7119	−	9.23576i	0.573681	−	0.416804i	0.836441	+	0.548057i	$0.184632\pi$
$492$	0.912780	−	1.25633i	0.0411513	−	0.0566399i
$493$	−6.82155	+	2.21646i	−0.307227	+	0.0998242i
$494$	50.7846			2.28491
$495$		0			0
$496$	23.5167			1.05593
$497$	−1.87265	+	0.608460i	−0.0839996	+	0.0272931i
$498$	5.81878	−	8.00886i	0.260746	−	0.358886i
$499$	31.0600	−	22.5664i	1.39044	−	1.01021i	0.394621	−	0.918844i	$-0.370876\pi$
$499$	31.0600	−	22.5664i	1.39044	−	1.01021i	0.995817	−	0.0913680i	$-0.0291240\pi$
$500$	−19.0884	+	3.26097i	−0.853658	+	0.145835i
$501$	−0.309017	+	0.951057i	−0.0138059	+	0.0424901i
$502$	16.1199	+	22.1872i	0.719468	+	0.990262i
$503$	20.1350	−	27.7134i	0.897775	−	1.23568i	−0.0733975	−	0.997303i	$-0.523384\pi$
$503$	20.1350	−	27.7134i	0.897775	−	1.23568i	0.971172	−	0.238378i	$-0.0766158\pi$
$504$	−0.391818	−	1.20589i	−0.0174530	−	0.0537147i
$505$	2.41154	−	1.96902i	0.107312	−	0.0876201i
$506$		0			0
$507$		−	2.58819i		−	0.114946i
$508$	5.51190	−	1.79092i	0.244551	−	0.0794594i
$509$	−17.7403	−	12.8891i	−0.786324	−	0.571298i	0.120546	−	0.992708i	$-0.461535\pi$
$509$	−17.7403	−	12.8891i	−0.786324	−	0.571298i	−0.906870	+	0.421410i	$0.861535\pi$
$510$	−2.23847	−	0.590112i	−0.0991212	−	0.0261306i
$511$	−1.35730	+	4.17733i	−0.0600433	+	0.184794i
$512$	27.8233	+	9.04035i	1.22963	+	0.399531i
$513$	10.8063	+	14.8736i	0.477110	+	0.656685i
$514$	−7.81531	−	5.67815i	−0.344719	−	0.250453i
$515$	5.13471	−	7.97714i	0.226262	−	0.351515i
$516$	9.58846			0.422108
$517$		0			0
$518$			11.5911i			0.509284i
$519$	1.21983	+	3.75424i	0.0535444	+	0.164793i
$520$	−4.90294	+	0.276823i	−0.215008	+	0.0121395i
$521$	−31.7529	+	23.0698i	−1.39112	+	1.01071i	−0.395377	+	0.918519i	$0.629386\pi$
$521$	−31.7529	+	23.0698i	−1.39112	+	1.01071i	−0.995742	+	0.0921880i	$0.970614\pi$
$522$	34.7768	+	11.2997i	1.52214	+	0.494573i
$523$	−8.23724	−	2.67644i	−0.360189	−	0.117033i	0.123331	−	0.992366i	$-0.460642\pi$
$523$	−8.23724	−	2.67644i	−0.360189	−	0.117033i	−0.483521	+	0.875333i	$0.660642\pi$
$524$	29.6007	−	21.5062i	1.29311	−	0.939501i
$525$	1.71187	−	1.56661i	0.0747121	−	0.0683724i
$526$	12.8294	+	39.4847i	0.559386	+	1.72161i
$527$		−	5.45378i		−	0.237570i
$528$		0			0
$529$	−16.8564			−0.732887
$530$	43.4791	+	27.9865i	1.88861	+	1.21566i
$531$	−10.4591	−	7.59901i	−0.453888	−	0.329769i
$532$	−5.65572	−	7.78444i	−0.245207	−	0.337498i
$533$	−6.98881	−	2.27080i	−0.302719	−	0.0983593i
$534$	−1.99752	+	6.14773i	−0.0864410	+	0.266038i
$535$	9.47332	+	2.49739i	0.409567	+	0.107971i
$536$	6.25536	+	4.54479i	0.270190	+	0.196305i
$537$	−4.20225	+	1.36539i	−0.181340	+	0.0589211i
$538$			38.1194i			1.64344i
$539$		0			0
$540$	7.26795	+	8.90138i	0.312763	+	0.383055i
$541$	−7.22862	−	22.2474i	−0.310783	−	0.956491i	−0.977456	−	0.211140i	$-0.932282\pi$
$541$	−7.22862	−	22.2474i	−0.310783	−	0.956491i	0.666673	−	0.745350i	$-0.267718\pi$
$542$	5.15058	−	7.08916i	0.221236	−	0.304505i
$543$	−1.03214	−	1.42062i	−0.0442935	−	0.0609648i
$544$	2.42776	−	7.47189i	0.104089	−	0.320354i
$545$	0.968601	+	2.49313i	0.0414903	+	0.106794i
$546$	−3.07738	+	2.23585i	−0.131700	+	0.0956854i
$547$	−11.9040	+	16.3844i	−0.508977	+	0.700547i	−0.983746	−	0.179563i	$-0.942532\pi$
$547$	−11.9040	+	16.3844i	−0.508977	+	0.700547i	0.474769	+	0.880110i	$0.342532\pi$
$548$	22.6718	−	7.36652i	0.968492	−	0.314682i
$549$	−22.5885			−0.964052
$550$		0			0
$551$	−42.9282			−1.82880
$552$	−1.60882	+	0.522738i	−0.0684760	+	0.0222492i
$553$	2.87955	−	3.96336i	0.122451	−	0.168539i
$554$	−35.4806	+	25.7781i	−1.50743	+	1.09521i
$555$	2.80510	+	7.22021i	0.119070	+	0.306481i
$556$	8.87869	−	27.3258i	0.376540	−	1.15887i
$557$	3.81417	+	5.24976i	0.161612	+	0.222439i	0.882141	−	0.470985i	$-0.156101\pi$
$557$	3.81417	+	5.24976i	0.161612	+	0.222439i	−0.720530	+	0.693424i	$0.756101\pi$
$558$	−16.3427	+	22.4937i	−0.691840	+	0.952236i
$559$	−14.0210	−	43.1524i	−0.593027	−	1.82515i
$560$	5.66025	+	6.93237i	0.239189	+	0.292946i
$561$		0			0
$562$			33.4607i			1.41145i
$563$	5.77572	−	1.87665i	0.243418	−	0.0790912i	−0.184767	−	0.982782i	$-0.559153\pi$
$563$	5.77572	−	1.87665i	0.243418	−	0.0790912i	0.428185	+	0.903691i	$0.359153\pi$
$564$	2.97677	+	2.16275i	0.125345	+	0.0910682i
$565$	6.11562	+	1.61222i	0.257286	+	0.0678265i
$566$	17.9777	−	55.3295i	0.755657	−	2.32567i
$567$	5.67916	+	1.84527i	0.238502	+	0.0774941i
$568$	−0.668201	−	0.919700i	−0.0280371	−	0.0385898i
$569$	4.75350	+	3.45362i	0.199277	+	0.144783i	0.682949	−	0.730466i	$-0.260697\pi$
$569$	4.75350	+	3.45362i	0.199277	+	0.144783i	−0.483672	+	0.875249i	$0.660697\pi$
$570$	−11.6502	−	7.49897i	−0.487973	−	0.314097i
$571$	35.7128			1.49453			0.747267	−	0.664524i	$-0.231365\pi$
$571$	35.7128			1.49453			0.747267	+	0.664524i	$0.231365\pi$
$572$		0			0
$573$		−	5.55532i		−	0.232077i
$574$	0.927051	+	2.85317i	0.0386944	+	0.119089i
$575$	21.3106	+	23.2866i	0.888715	+	0.971119i
$576$	−12.6694	+	9.20487i	−0.527892	+	0.383536i
$577$	−19.7180	−	6.40677i	−0.820871	−	0.266717i	−0.131676	−	0.991293i	$-0.542036\pi$
$577$	−19.7180	−	6.40677i	−0.820871	−	0.266717i	−0.689195	+	0.724576i	$0.742036\pi$
$578$	29.2649	+	9.50874i	1.21726	+	0.395511i
$579$	4.30438	−	3.12732i	0.178884	−	0.129967i
$580$	−26.7901	+	1.51259i	−1.11240	+	0.0628067i
$581$	2.74272	+	8.44124i	0.113787	+	0.350202i
$582$			0.656339i			0.0272061i
$583$		0			0
$584$	−2.53590			−0.104936
$585$	14.0283	−	21.7940i	0.579998	−	0.901069i
$586$	−14.7210	−	10.6954i	−0.608119	−	0.441824i
$587$	21.1293	+	29.0820i	0.872099	+	1.20034i	0.978547	+	0.206024i	$0.0660523\pi$
$587$	21.1293	+	29.0820i	0.872099	+	1.20034i	−0.106448	+	0.994318i	$0.533948\pi$
$588$	−5.28342	−	1.71669i	−0.217885	−	0.0707950i
$589$	10.0866	−	31.0435i	0.415612	−	1.27912i
$590$	19.7660	+	5.21077i	0.813753	+	0.214524i
$591$	−1.06831	−	0.776175i	−0.0439445	−	0.0319276i
$592$	−28.4122	+	9.23168i	−1.16773	+	0.379420i
$593$			30.2533i			1.24235i	0.783670	+	0.621177i	$0.213345\pi$
$593$			30.2533i			1.24235i	−0.783670	+	0.621177i	$0.786655\pi$
$594$		0			0
$595$	1.60770	−	1.31268i	0.0659091	−	0.0538145i
$596$	−7.34985	−	22.6205i	−0.301062	−	0.926572i
$597$	0.608520	−	0.837556i	0.0249051	−	0.0342789i
$598$	−30.4143	−	41.8617i	−1.24373	−	1.71185i
$599$	−6.31781	+	19.4442i	−0.258139	+	0.794469i	0.735056	+	0.678006i	$0.237156\pi$
$599$	−6.31781	+	19.4442i	−0.258139	+	0.794469i	−0.993195	+	0.116463i	$0.962844\pi$
$600$	1.16563	+	0.660475i	0.0475866	+	0.0269638i
$601$	−16.1803	+	11.7557i	−0.660010	+	0.479525i	−0.866666	−	0.498888i	$-0.833742\pi$
$601$	−16.1803	+	11.7557i	−0.660010	+	0.479525i	0.206656	+	0.978414i	$0.433742\pi$
$602$	−10.8878	+	14.9858i	−0.443755	+	0.610776i
$603$	−38.8118	+	12.6107i	−1.58054	+	0.513548i
$604$	10.7321			0.436681
$605$		0			0
$606$	1.39230			0.0565585
$607$	29.9503	−	9.73145i	1.21565	−	0.394987i	0.370152	−	0.928971i	$-0.379306\pi$
$607$	29.9503	−	9.73145i	1.21565	−	0.394987i	0.845495	+	0.533984i	$0.179306\pi$
$608$	27.6381	−	38.0406i	1.12087	−	1.54275i
$609$	2.60131	−	1.88996i	0.105410	−	0.0765850i
$610$	33.2913	−	12.9339i	1.34792	−	0.523679i
$611$	5.38046	−	16.5594i	0.217670	−	0.669920i
$612$	2.87955	+	3.96336i	0.116399	+	0.160209i
$613$	3.93354	−	5.41405i	0.158874	−	0.218671i	−0.722158	−	0.691728i	$-0.756850\pi$
$613$	3.93354	−	5.41405i	0.158874	−	0.218671i	0.881032	+	0.473057i	$0.156850\pi$
$614$	−10.5228	−	32.3859i	−0.424666	−	1.30699i
$615$	1.26795	+	1.55291i	0.0511286	+	0.0626195i
$616$		0			0
$617$			1.69161i			0.0681019i	0.999420	+	0.0340509i	$0.0108408\pi$
$617$			1.69161i			0.0681019i	−0.999420	+	0.0340509i	$0.989159\pi$
$618$	4.03499	−	1.31105i	0.162311	−	0.0527381i
$619$	−23.2872	−	16.9192i	−0.935993	−	0.680039i	0.0114597	−	0.999934i	$-0.496352\pi$
$619$	−23.2872	−	16.9192i	−0.935993	−	0.680039i	−0.947453	+	0.319896i	$0.896352\pi$
$620$	5.20093	−	19.7287i	0.208874	−	0.792322i
$621$	5.78852	−	17.8152i	0.232285	−	0.714901i
$622$	−51.5410	−	16.7467i	−2.06660	−	0.671481i
$623$	−3.40654	−	4.68870i	−0.136480	−	0.187849i
$624$	−7.93148	−	5.76256i	−0.317513	−	0.230687i
$625$	2.21102	−	24.9020i	0.0884409	−	0.996081i
$626$	−33.1244			−1.32392
$627$		0			0
$628$		−	20.9086i		−	0.834344i
$629$	2.14093	+	6.58911i	0.0853646	+	0.262725i
$630$	−10.5644	+	0.596470i	−0.420894	+	0.0237639i
$631$	−15.6306	+	11.3563i	−0.622245	+	0.452088i	−0.853705	−	0.520757i	$-0.825650\pi$
$631$	−15.6306	+	11.3563i	−0.622245	+	0.452088i	0.231460	+	0.972844i	$0.425650\pi$
$632$	2.68999	+	0.874032i	0.107002	+	0.0347671i
$633$	5.47655	+	1.77944i	0.217674	+	0.0707264i
$634$	−10.8927	+	7.91400i	−0.432604	+	0.314305i
$635$	0.421768	+	7.47013i	0.0167373	+	0.296443i
$636$	3.31639	+	10.2068i	0.131503	+	0.404725i
$637$			26.2880i			1.04157i
$638$		0			0
$639$	6.00000			0.237356
$640$	−4.96684	+	7.71635i	−0.196332	+	0.305016i
$641$	−16.0642	−	11.6713i	−0.634497	−	0.460989i	0.223459	−	0.974713i	$-0.428265\pi$
$641$	−16.0642	−	11.6713i	−0.634497	−	0.460989i	−0.857955	+	0.513725i	$0.828265\pi$
$642$	2.57529	+	3.54458i	0.101639	+	0.139893i
$643$	−26.3111	−	8.54899i	−1.03761	−	0.337139i	−0.259814	−	0.965659i	$-0.583661\pi$
$643$	−26.3111	−	8.54899i	−1.03761	−	0.337139i	−0.777794	+	0.628520i	$0.783661\pi$
$644$	−3.02956	+	9.32401i	−0.119381	+	0.367418i
$645$	−3.15549	+	11.9697i	−0.124247	+	0.471307i
$646$	−10.0256	−	7.28401i	−0.394451	−	0.286586i
$647$	18.0480	−	5.86414i	0.709538	−	0.230543i	0.0680568	−	0.997681i	$-0.478320\pi$
$647$	18.0480	−	5.86414i	0.709538	−	0.230543i	0.641482	+	0.767138i	$0.278320\pi$
$648$			3.44760i			0.135435i
$649$		0			0
$650$	−8.19615	+	40.1528i	−0.321480	+	1.57492i
$651$	0.755504	+	2.32520i	0.0296106	+	0.0911319i
$652$	7.72586	−	10.6337i	0.302568	−	0.416449i
$653$	18.7767	+	25.8440i	0.734791	+	1.01135i	0.998901	+	0.0468603i	$0.0149216\pi$
$653$	18.7767	+	25.8440i	0.734791	+	1.01135i	−0.264111	+	0.964492i	$0.585078\pi$
$654$	−0.369631	+	1.13761i	−0.0144537	+	0.0444840i
$655$	17.1057	+	44.0294i	0.668377	+	1.72037i
$656$	−6.25536	+	4.54479i	−0.244231	+	0.177444i
$657$	7.86707	−	10.8281i	0.306924	−	0.422444i
$658$	−6.76033	+	2.19656i	−0.263545	+	0.0856310i
$659$	−11.3205			−0.440984			−0.220492	−	0.975389i	$-0.570766\pi$
$659$	−11.3205			−0.440984			−0.220492	+	0.975389i	$0.570766\pi$
$660$		0			0
$661$	−1.58846			−0.0617838			−0.0308919	−	0.999523i	$-0.509835\pi$
$661$	−1.58846			−0.0617838			−0.0308919	+	0.999523i	$0.509835\pi$
$662$	14.3380	−	4.65870i	0.557263	−	0.181066i
$663$	−1.33640	+	1.83940i	−0.0519016	+	0.0714364i
$664$	−4.14569	+	3.01202i	−0.160884	+	0.116889i
$665$	11.5789	−	4.49850i	0.449011	−	0.174444i
$666$	10.9146	−	33.5918i	0.422934	−	1.30166i
$667$	25.7092	+	35.3857i	0.995464	+	1.37014i
$668$	−1.96677	+	2.70702i	−0.0760965	+	0.104738i
$669$	0.927051	+	2.85317i	0.0358419	+	0.110310i
$670$	49.9808	−	40.8091i	1.93093	−	1.57659i
$671$		0			0
$672$			3.52193i			0.135861i
$673$	1.53813	−	0.499769i	0.0592906	−	0.0192647i	−0.279222	−	0.960227i	$-0.590076\pi$
$673$	1.53813	−	0.499769i	0.0592906	−	0.0192647i	0.338512	+	0.940962i	$0.390076\pi$
$674$	12.2359	+	8.88987i	0.471308	+	0.342425i
$675$	−13.5038	+	6.14353i	−0.519762	+	0.236465i
$676$	2.67617	−	8.23639i	0.102929	−	0.316784i
$677$	8.59763	+	2.79354i	0.330434	+	0.107364i	0.469535	−	0.882914i	$-0.344421\pi$
$677$	8.59763	+	2.79354i	0.330434	+	0.107364i	−0.139102	+	0.990278i	$0.544421\pi$
$678$	1.66251	+	2.28825i	0.0638482	+	0.0878795i
$679$	−0.476072	−	0.345887i	−0.0182700	−	0.0132739i
$680$	1.00761	+	0.648578i	0.0386402	+	0.0248718i
$681$	−11.1436			−0.427023
$682$		0			0
$683$			22.4887i			0.860507i	0.902708	+	0.430253i	$0.141576\pi$
$683$			22.4887i			0.860507i	−0.902708	+	0.430253i	$0.858424\pi$
$684$	9.06054	+	27.8855i	0.346438	+	1.06623i
$685$	1.73484	+	30.7265i	0.0662847	+	1.17400i
$686$	18.4912	−	13.4347i	0.705998	−	0.512938i
$687$	8.82611	+	2.86778i	0.336737	+	0.109413i
$688$	−45.4049	−	14.7529i	−1.73104	−	0.562450i
$689$	41.0856	−	29.8504i	1.56524	−	1.13721i
$690$	0.795771	+	14.0943i	0.0302945	+	0.536560i
$691$	−8.62434	−	26.5430i	−0.328086	−	1.00974i	−0.970029	−	0.242991i	$-0.921871\pi$
$691$	−8.62434	−	26.5430i	−0.328086	−	1.00974i	0.641943	−	0.766752i	$-0.278129\pi$
$692$			13.2084i			0.502108i
$693$		0			0
$694$	5.73205			0.217586
$695$	31.1901	+	20.0764i	1.18311	+	0.761541i
$696$	1.50186	+	1.09117i	0.0569280	+	0.0413606i
$697$	1.05399	+	1.45069i	0.0399226	+	0.0549488i
$698$	−50.1960	−	16.3097i	−1.89995	−	0.617330i
$699$	2.08032	−	6.40256i	0.0786849	−	0.242167i
$700$	7.06753	−	3.21536i	0.267128	−	0.121529i
$701$	−8.20634	−	5.96225i	−0.309949	−	0.225191i	0.421926	−	0.906630i	$-0.361354\pi$
$701$	−8.20634	−	5.96225i	−0.309949	−	0.225191i	−0.731875	+	0.681439i	$0.761354\pi$
$702$	23.1288	−	7.51499i	0.872939	−	0.283635i
$703$			41.4655i			1.56390i
$704$		0			0
$705$	−3.67949	+	3.00429i	−0.138578	+	0.113148i
$706$	−1.00985	−	3.10800i	−0.0380063	−	0.116971i
$707$	−0.733736	+	1.00990i	−0.0275950	+	0.0379812i
$708$	2.49376	+	3.43237i	0.0937213	+	0.128996i
$709$	−7.22862	+	22.2474i	−0.271477	+	0.835519i	0.718654	+	0.695368i	$0.244759\pi$
$709$	−7.22862	+	22.2474i	−0.271477	+	0.835519i	−0.990130	+	0.140151i	$0.955241\pi$
$710$	−8.84291	+	3.43554i	−0.331869	+	0.128933i
$711$	−12.0772	+	8.77458i	−0.452929	+	0.329072i
$712$	1.96677	−	2.70702i	0.0737077	−	0.101450i
$713$	−31.6298	+	10.2772i	−1.18455	+	0.384883i
$714$	0.928203			0.0347371
$715$		0			0
$716$	−14.7846			−0.552527
$717$	−5.74038	+	1.86516i	−0.214378	+	0.0696558i
$718$	−20.8250	+	28.6632i	−0.777183	+	1.06970i
$719$	−32.2020	+	23.3961i	−1.20093	+	0.872528i	−0.994376	−	0.105907i	$-0.966225\pi$
$719$	−32.2020	+	23.3961i	−1.20093	+	0.872528i	−0.206556	+	0.978435i	$0.566225\pi$
$720$	−9.87600	−	25.4204i	−0.368057	−	0.947361i
$721$	−1.17545	+	3.61767i	−0.0437762	+	0.134729i
$722$	−22.0202	−	30.3082i	−0.819508	−	1.12796i
$723$	−3.08044	+	4.23986i	−0.114563	+	0.157682i
$724$	−1.81567	−	5.58807i	−0.0674790	−	0.207679i
$725$	6.92820	−	33.9411i	0.257307	−	1.26054i
$726$		0			0
$727$		−	4.00240i		−	0.148441i	−0.997242	−	0.0742205i	$-0.976353\pi$
$727$		−	4.00240i		−	0.148441i	0.997242	−	0.0742205i	$-0.0236469\pi$
$728$	1.87265	−	0.608460i	0.0694049	−	0.0225510i
$729$	−10.9933	−	7.98709i	−0.407159	−	0.295818i
$730$	−5.39458	+	20.4632i	−0.199662	+	0.757379i
$731$	−3.42137	+	10.5299i	−0.126544	+	0.389463i
$732$	7.05003	+	2.29069i	0.260577	+	0.0846665i
$733$	−20.4393	−	28.1322i	−0.754941	−	1.03909i	−0.997618	−	0.0689799i	$-0.978026\pi$
$733$	−20.4393	−	28.1322i	−0.754941	−	1.03909i	0.242677	−	0.970107i	$-0.421974\pi$
$734$	−46.3152	−	33.6499i	−1.70952	−	1.24204i
$735$	3.88175	−	6.03058i	0.143181	−	0.222441i
$736$	−47.9090			−1.76595
$737$		0			0
$738$		−	9.14162i		−	0.336508i
$739$	7.74761	+	23.8447i	0.285000	+	0.877141i	0.986399	+	0.164371i	$0.0525596\pi$
$739$	7.74761	+	23.8447i	0.285000	+	0.877141i	−0.701398	+	0.712770i	$0.747440\pi$
$740$	1.46105	+	25.8773i	0.0537091	+	0.951268i
$741$	−11.0089	+	7.99840i	−0.404420	+	0.293829i
$742$	−19.7180	−	6.40677i	−0.723870	−	0.235200i
$743$	−7.64837	−	2.48511i	−0.280592	−	0.0911697i	0.165341	−	0.986237i	$-0.447128\pi$
$743$	−7.64837	−	2.48511i	−0.280592	−	0.0911697i	−0.445932	+	0.895067i	$0.647128\pi$
$744$	−1.14196	+	0.829684i	−0.0418664	+	0.0304177i
$745$	30.6570	−	1.73091i	1.12318	−	0.0634156i
$746$	20.3670	+	62.6832i	0.745688	+	2.29499i
$747$		−	27.0459i		−	0.989559i
$748$		0			0
$749$	−3.92820			−0.143533
$750$	7.80928	−	8.00095i	0.285155	−	0.292153i
$751$	16.6989	+	12.1325i	0.609353	+	0.442721i	0.849186	−	0.528093i	$-0.177093\pi$
$751$	16.6989	+	12.1325i	0.609353	+	0.442721i	−0.239834	+	0.970814i	$0.577093\pi$
$752$	−10.7685	−	14.8215i	−0.392685	−	0.540485i
$753$	−6.98881	−	2.27080i	−0.254686	−	0.0827526i
$754$	−17.5474	+	54.0054i	−0.639039	+	1.96676i
$755$	−3.53184	+	13.3973i	−0.128537	+	0.487578i
$756$	−3.72770	−	2.70834i	−0.135575	−	0.0985012i
$757$	−33.3611	+	10.8397i	−1.21253	+	0.393975i	−0.844356	−	0.535782i	$-0.820017\pi$
$757$	−33.3611	+	10.8397i	−1.21253	+	0.393975i	−0.368174	+	0.929757i	$0.620017\pi$
$758$			10.5558i			0.383405i
$759$		0			0
$760$	4.53590	+	5.55532i	0.164534	+	0.201513i
$761$	2.42776	+	7.47189i	0.0880063	+	0.270856i	0.985368	−	0.170440i	$-0.0545190\pi$
$761$	2.42776	+	7.47189i	0.0880063	+	0.270856i	−0.897362	+	0.441296i	$0.854519\pi$
$762$	−1.96677	+	2.70702i	−0.0712485	+	0.0980651i
$763$	−0.630365	−	0.867623i	−0.0228207	−	0.0314101i
$764$	5.74415	−	17.6787i	0.207816	−	0.639592i
$765$	−5.89527	+	2.29036i	−0.213144	+	0.0828081i
$766$	−37.1411	+	26.9846i	−1.34196	+	0.974994i
$767$	11.8006	−	16.2421i	0.426095	−	0.586470i
$768$	−9.54689	+	3.10197i	−0.344494	+	0.111933i
$769$	−17.8564			−0.643918			−0.321959	−	0.946754i	$-0.604341\pi$
$769$	−17.8564			−0.643918			−0.321959	+	0.946754i	$0.604341\pi$
$770$		0			0
$771$	2.58846			0.0932210
$772$	16.9314	−	5.50136i	0.609376	−	0.197998i
$773$	30.3546	−	41.7795i	1.09178	−	1.50271i	0.245928	−	0.969288i	$-0.420907\pi$
$773$	30.3546	−	41.7795i	1.09178	−	1.50271i	0.845852	−	0.533418i	$-0.179093\pi$
$774$	45.6649	−	33.1775i	1.64139	−	1.19254i
$775$	22.9166	+	12.9851i	0.823188	+	0.466438i
$776$	0.104987	−	0.323118i	0.00376882	−	0.0115992i
$777$	−1.82556	−	2.51267i	−0.0654916	−	0.0901415i
$778$	20.5805	−	28.3266i	0.737845	−	1.01556i
$779$	3.31639	+	10.2068i	0.118822	+	0.365696i
$780$	−6.58846	+	5.37945i	−0.235905	+	0.192615i
$781$		0			0
$782$			12.6264i			0.451519i
$783$	−19.5507	+	6.35242i	−0.698686	+	0.227017i
$784$	22.3776	+	16.2583i	0.799201	+	0.580653i
$785$	26.1011	+	6.88086i	0.931590	+	0.245588i
$786$	−6.52778	+	20.0905i	−0.232838	+	0.716603i
$787$	−4.43073	−	1.43963i	−0.157938	−	0.0513173i	0.228981	−	0.973431i	$-0.426461\pi$
$787$	−4.43073	−	1.43963i	−0.157938	−	0.0513173i	−0.386919	+	0.922114i	$0.626461\pi$
$788$	−2.59713	−	3.57465i	−0.0925190	−	0.127342i
$789$	−8.99979	−	6.53873i	−0.320401	−	0.232785i
$790$	12.7753	−	19.8474i	0.454526	−	0.706139i
$791$	−2.53590			−0.0901662
$792$		0			0
$793$		−	35.0779i		−	1.24565i
$794$	−9.55734	−	29.4145i	−0.339177	−	1.04388i
$795$	−13.8330	+	0.781018i	−0.490605	+	0.0276999i
$796$	2.80252	−	2.03615i	0.0993326	−	0.0721693i
$797$	7.51646	+	2.44225i	0.266247	+	0.0865088i	0.439098	−	0.898439i	$-0.355298\pi$
$797$	7.51646	+	2.44225i	0.266247	+	0.0865088i	−0.172851	+	0.984948i	$0.555298\pi$
$798$	5.28342	+	1.71669i	0.187031	+	0.0607701i
$799$	−3.43728	+	2.49733i	−0.121602	+	0.0883492i
$800$	25.6162	+	27.9914i	0.905670	+	0.989647i
$801$	5.45732	+	16.7959i	0.192825	+	0.593454i
$802$		−	62.4384i		−	2.20478i
$803$		0			0
$804$	13.3923			0.472310
$805$	−10.6426	−	6.85039i	−0.375102	−	0.241445i
$806$	−34.9309	−	25.3788i	−1.23039	−	0.893928i
$807$	−6.00367	−	8.26335i	−0.211339	−	0.290884i
$808$	−0.685436	−	0.222712i	−0.0241136	−	0.00783497i
$809$	6.63277	−	20.4136i	0.233196	−	0.717703i	−0.764160	−	0.645027i	$-0.776846\pi$
$809$	6.63277	−	20.4136i	0.233196	−	0.717703i	0.997356	−	0.0726760i	$-0.0231539\pi$
$810$	27.8202	+	7.33403i	0.977501	+	0.257692i
$811$	26.6820	+	19.3856i	0.936932	+	0.680721i	0.947680	−	0.319222i	$-0.103421\pi$
$811$	26.6820	+	19.3856i	0.936932	+	0.680721i	−0.0107485	+	0.999942i	$0.503421\pi$
$812$	10.2323	−	3.32468i	0.359084	−	0.116674i
$813$			2.34795i			0.0823463i
$814$		0			0
$815$	10.7321	+	13.1440i	0.375927	+	0.460415i
$816$	0.739263	+	2.27522i	0.0258794	+	0.0796485i
$817$	−38.9496	+	53.6095i	−1.36267	+	1.87556i
$818$	−2.12982	−	2.93145i	−0.0744674	−	0.102496i
$819$	−3.21140	+	9.88367i	−0.112215	+	0.345363i
$820$	2.42929	+	6.25288i	0.0848345	+	0.218360i
$821$	−15.2126	+	11.0526i	−0.530925	+	0.385739i	−0.820703	−	0.571354i	$-0.806418\pi$
$821$	−15.2126	+	11.0526i	−0.530925	+	0.385739i	0.289779	+	0.957094i	$0.406418\pi$
$822$	−8.08980	+	11.1347i	−0.282164	+	0.388366i
$823$	46.0291	−	14.9558i	1.60447	−	0.521325i	0.636264	−	0.771471i	$-0.280479\pi$
$823$	46.0291	−	14.9558i	1.60447	−	0.521325i	0.968208	+	0.250146i	$0.0804787\pi$
$824$	−2.19615			−0.0765066
$825$		0			0
$826$	−8.19615			−0.285181
$827$	−25.4230	+	8.26044i	−0.884045	+	0.287244i	−0.715636	−	0.698473i	$-0.753863\pi$
$827$	−25.4230	+	8.26044i	−0.884045	+	0.287244i	−0.168409	+	0.985717i	$0.553863\pi$
$828$	17.5597	−	24.1689i	0.610242	−	0.839926i
$829$	33.9631	−	24.6757i	1.17959	−	0.857022i	0.187464	−	0.982272i	$-0.439973\pi$
$829$	33.9631	−	24.6757i	1.17959	−	0.857022i	0.992125	+	0.125250i	$0.0399733\pi$
$830$	15.4862	+	39.8608i	0.537534	+	1.38359i
$831$	3.63135	−	11.1761i	0.125970	−	0.387696i
$832$	−14.2944	−	19.6745i	−0.495568	−	0.682091i
$833$	3.77048	−	5.18962i	0.130639	−	0.179810i
$834$	5.12612	+	15.7766i	0.177503	+	0.546298i
$835$	−2.73205	−	3.34607i	−0.0945465	−	0.115795i
$836$		0			0
$837$		−	15.6307i		−	0.540275i
$838$	−54.4948	+	17.7064i	−1.88249	+	0.611658i
$839$	2.25280	+	1.63675i	0.0777752	+	0.0565070i	0.625993	−	0.779828i	$-0.284694\pi$
$839$	2.25280	+	1.63675i	0.0777752	+	0.0565070i	−0.548218	+	0.836335i	$0.684694\pi$
$840$	−0.519439	−	0.136936i	−0.0179223	−	0.00472474i
$841$	5.87132	−	18.0701i	0.202459	−	0.623106i
$842$	38.6799	+	12.5679i	1.33300	+	0.433117i
$843$	−5.26994	−	7.25345i	−0.181506	−	0.249822i
$844$	15.5881	+	11.3254i	0.536564	+	0.389837i
$845$	9.40115	+	6.05131i	0.323409	+	0.208171i
$846$	21.6603			0.744695
$847$		0			0
$848$		−	53.4355i		−	1.83498i
$849$	4.81710	+	14.8255i	0.165322	+	0.508810i
$850$	7.37713	−	6.75114i	0.253033	−	0.231562i
$851$	34.1799	−	24.8332i	1.17167	−	0.851270i
$852$	−1.87265	−	0.608460i	−0.0641558	−	0.0208455i
$853$	11.8153	+	3.83902i	0.404547	+	0.131445i	0.504221	−	0.863575i	$-0.331780\pi$
$853$	11.8153	+	3.83902i	0.404547	+	0.131445i	−0.0996734	+	0.995020i	$0.531780\pi$
$854$	−11.5855	+	8.41738i	−0.396449	+	0.288037i
$855$	−37.7924	+	2.13378i	−1.29247	+	0.0729738i
$856$	−0.700835	−	2.15695i	−0.0239540	−	0.0737230i
$857$		−	24.4206i		−	0.834191i	−0.908863	−	0.417095i	$-0.863048\pi$
$857$		−	24.4206i		−	0.834191i	0.908863	−	0.417095i	$-0.136952\pi$
$858$		0			0
$859$	11.8038			0.402742			0.201371	−	0.979515i	$-0.435460\pi$
$859$	11.8038			0.402742			0.201371	+	0.979515i	$0.435460\pi$
$860$	−22.4183	+	34.8284i	−0.764456	+	1.18764i
$861$	−0.650326	−	0.472490i	−0.0221631	−	0.0161024i
$862$	21.4932	+	29.5829i	0.732063	+	1.00760i
$863$	9.28307	+	3.01625i	0.315999	+	0.102674i	0.462722	−	0.886503i	$-0.346873\pi$
$863$	9.28307	+	3.01625i	0.315999	+	0.102674i	−0.146723	+	0.989178i	$0.546873\pi$
$864$	6.95803	−	21.4146i	0.236717	−	0.728540i
$865$	−16.4886	−	4.34678i	−0.560630	−	0.147795i
$866$	31.6523	+	22.9967i	1.07559	+	0.781460i
$867$	−7.84150	+	2.54786i	−0.266311	+	0.0865298i
$868$			8.18067i			0.277670i
$869$		0			0
$870$	12.0000	−	9.79796i	0.406838	−	0.332182i
$871$	−19.5834	−	60.2714i	−0.663557	−	2.04222i
$872$	0.363941	−	0.500922i	0.0123246	−	0.0169634i
$873$	1.05399	+	1.45069i	0.0356721	+	0.0490984i
$874$	−23.3522	+	71.8706i	−0.789899	+	2.43106i
$875$	1.68800	+	9.88087i	0.0570649	+	0.334034i
$876$	−3.55345	+	2.58173i	−0.120060	+	0.0872286i
$877$	−32.9081	+	45.2941i	−1.11123	+	1.52947i	−0.291629	+	0.956532i	$0.594197\pi$
$877$	−32.9081	+	45.2941i	−1.11123	+	1.52947i	−0.819597	+	0.572940i	$0.805803\pi$
$878$	−37.2030	+	12.0880i	−1.25554	+	0.407949i
$879$	4.87564			0.164451
$880$		0			0
$881$	38.9090			1.31088			0.655438	−	0.755249i	$-0.272484\pi$
$881$	38.9090			1.31088			0.655438	+	0.755249i	$0.272484\pi$
$882$	−31.1022	+	10.1057i	−1.04727	+	0.340277i
$883$	27.6381	−	38.0406i	0.930097	−	1.28017i	−0.0297250	−	0.999558i	$-0.509463\pi$
$883$	27.6381	−	38.0406i	0.930097	−	1.28017i	0.959822	−	0.280610i	$-0.0905368\pi$
$884$	−6.15475	+	4.47169i	−0.207007	+	0.150399i
$885$	−5.10546	+	1.98351i	−0.171618	+	0.0666749i
$886$	5.47951	−	16.8642i	0.184088	−	0.566563i
$887$	4.90600	+	6.75253i	0.164727	+	0.226728i	0.883399	−	0.468622i	$-0.155249\pi$
$887$	4.90600	+	6.75253i	0.164727	+	0.226728i	−0.718671	+	0.695350i	$0.755249\pi$
$888$	1.05399	−	1.45069i	0.0353695	−	0.0486820i
$889$	−0.927051	−	2.85317i	−0.0310923	−	0.0956922i
$890$	−17.6603	−	21.6293i	−0.591973	−	0.725016i
$891$		0			0
$892$			10.0382i			0.336104i
$893$	−24.1841	+	7.85788i	−0.809289	+	0.262954i
$894$	11.1095	+	8.07150i	0.371556	+	0.269951i
$895$	4.86550	−	18.4563i	0.162636	−	0.616926i
$896$	1.13703	−	3.49940i	0.0379854	−	0.116907i
$897$	13.1861	+	4.28444i	0.440273	+	0.143053i
$898$	−11.9418	−	16.4365i	−0.398504	−	0.548493i
$899$	29.5270	+	21.4526i	0.984782	+	0.715486i
$900$	−23.5099	+	2.66325i	−0.783663	+	0.0887751i
$901$	−12.3923			−0.412848
$902$		0			0
$903$		−	4.96335i		−	0.165170i
$904$	−0.452432	−	1.39244i	−0.0150477	−	0.0463120i
$905$	7.57336	−	0.427596i	0.251747	−	0.0142138i
$906$	−5.01279	+	3.64201i	−0.166539	+	0.120998i
$907$	7.67425	+	2.49351i	0.254819	+	0.0827958i	0.433641	−	0.901086i	$-0.357229\pi$
$907$	7.67425	+	2.49351i	0.254819	+	0.0827958i	−0.178822	+	0.983881i	$0.557229\pi$
$908$	−35.4622	−	11.5224i	−1.17686	−	0.382383i
$909$	3.07738	−	2.23585i	0.102070	−	0.0741583i
$910$	−0.926266	−	16.4055i	−0.0307054	−	0.543839i
$911$	5.63916	+	17.3556i	0.186834	+	0.575015i	0.999975	−	0.00705102i	$-0.00224443\pi$
$911$	5.63916	+	17.3556i	0.186834	+	0.575015i	−0.813141	+	0.582066i	$0.802244\pi$
$912$			14.3180i			0.474116i
$913$		0			0
$914$	−40.9808			−1.35552
$915$	−5.17969	+	8.04702i	−0.171235	+	0.266026i
$916$	25.1220	+	18.2522i	0.830056	+	0.603071i
$917$	−11.1324	−	15.3224i	−0.367624	−	0.505992i
$918$	−5.64381	−	1.83379i	−0.186274	−	0.0605240i
$919$	−10.1916	+	31.3666i	−0.336190	+	1.03469i	0.629942	+	0.776642i	$0.283079\pi$
$919$	−10.1916	+	31.3666i	−0.336190	+	1.03469i	−0.966133	+	0.258046i	$0.916921\pi$
$920$	1.86275	−	7.06595i	0.0614129	−	0.232957i
$921$	7.38176	+	5.36316i	0.243237	+	0.176722i
$922$	60.6309	−	19.7002i	1.99677	−	0.648791i
$923$			9.31749i			0.306689i
$924$		0			0
$925$	−32.7846	−	6.69213i	−1.07795	−	0.220036i
$926$	10.6662	+	32.8273i	0.350514	+	1.07877i
$927$	6.81308	−	9.37740i	0.223771	−	0.307994i
$928$	30.9035	+	42.5350i	1.01446	+	1.39628i
$929$	4.98864	−	15.3535i	0.163672	−	0.503731i	−0.835264	−	0.549849i	$-0.814685\pi$
$929$	4.98864	−	15.3535i	0.163672	−	0.503731i	0.998936	+	0.0461183i	$0.0146851\pi$
$930$	4.26580	+	10.9800i	0.139881	+	0.360047i
$931$	31.0600	−	22.5664i	1.01795	−	0.739585i
$932$	13.2404	−	18.2238i	0.433703	−	0.596941i
$933$	13.8104	−	4.48726i	0.452131	−	0.146906i
$934$	−34.3205			−1.12300
$935$		0			0
$936$	−6.00000			−0.196116
$937$	21.5906	−	7.01523i	0.705336	−	0.229177i	0.0656819	−	0.997841i	$-0.479078\pi$
$937$	21.5906	−	7.01523i	0.705336	−	0.229177i	0.639654	+	0.768663i	$0.279078\pi$
$938$	−15.2071	+	20.9308i	−0.496531	+	0.683416i
$939$	7.18055	−	5.21697i	0.234328	−	0.170249i
$940$	−14.8156	+	5.75599i	−0.483233	+	0.187740i
$941$	−8.34346	+	25.6785i	−0.271989	+	0.837096i	0.718011	+	0.696031i	$0.245053\pi$
$941$	−8.34346	+	25.6785i	−0.271989	+	0.837096i	−0.990000	+	0.141065i	$0.954947\pi$
$942$	7.09550	+	9.76612i	0.231184	+	0.318197i
$943$	6.42730	−	8.84642i	0.209302	−	0.288079i
$944$	−6.52778	−	20.0905i	−0.212461	−	0.653889i
$945$	4.60770	−	3.76217i	0.149888	−	0.122383i
$946$		0			0
$947$		−	14.3180i		−	0.465273i	−0.972564	−	0.232636i	$-0.925265\pi$
$947$		−	14.3180i		−	0.465273i	0.972564	−	0.232636i	$-0.0747352\pi$
$948$	4.65921	−	1.51387i	0.151324	−	0.0491681i
$949$	16.8151	+	12.2169i	0.545841	+	0.396577i
$950$	54.4774	−	24.7844i	1.76748	−	0.804111i
$951$	1.11484	−	3.43112i	0.0361511	−	0.111262i
$952$	−0.456957	−	0.148474i	−0.0148101	−	0.00481208i
$953$	−18.4506	−	25.3951i	−0.597675	−	0.822629i	0.397818	−	0.917464i	$-0.369767\pi$
$953$	−18.4506	−	25.3951i	−0.597675	−	0.822629i	−0.995493	+	0.0948355i	$0.969767\pi$
$954$	51.1112	+	37.1345i	1.65479	+	1.20227i
$955$	20.1787	+	12.9886i	0.652968	+	0.420301i
$956$	−20.1962			−0.653190
$957$		0			0
$958$		−	18.2832i		−	0.590705i
$959$	−3.81319	−	11.7358i	−0.123134	−	0.378969i
$960$	0.374003	+	6.62415i	0.0120709	+	0.213794i
$961$	2.62826	−	1.90954i	0.0847827	−	0.0615982i
$962$	52.1652	+	16.9495i	1.68187	+	0.546474i
$963$	11.3842	+	3.69895i	0.366850	+	0.119197i
$964$	−14.1868	+	10.3073i	−0.456927	+	0.331977i
$965$	1.29558	+	22.9467i	0.0417064	+	0.738681i
$966$	−1.74911	−	5.38322i	−0.0562768	−	0.173202i
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		0			0
$969$	3.32051			0.106670
$970$	−2.38404	−	1.53455i	−0.0765468	−	0.0492715i
$971$	8.95727	+	6.50784i	0.287453	+	0.208846i	0.722161	−	0.691725i	$-0.243149\pi$
$971$	8.95727	+	6.50784i	0.287453	+	0.208846i	−0.434709	+	0.900571i	$0.643149\pi$
$972$	12.5722	+	17.3041i	0.403253	+	0.555030i
$973$	−14.1449	−	4.59595i	−0.453464	−	0.147339i
$974$	7.59825	−	23.3850i	0.243464	−	0.749304i
$975$	−4.54720	−	9.99500i	−0.145627	−	0.320096i
$976$	−29.8600	−	21.6945i	−0.955795	−	0.694425i
$977$	14.2414	−	4.62733i	0.455624	−	0.148041i	−0.0722087	−	0.997390i	$-0.523005\pi$
$977$	14.2414	−	4.62733i	0.455624	−	0.148041i	0.527833	+	0.849348i	$0.323005\pi$
$978$			7.58871i			0.242660i
$979$		0			0
$980$	18.5885	−	15.1774i	0.593786	−	0.484825i
$981$	1.00985	+	3.10800i	0.0322421	+	0.0992309i
$982$	−17.8421	+	24.5576i	−0.569365	+	0.783663i
$983$	−8.82354	−	12.1446i	−0.281427	−	0.387351i	0.644779	−	0.764369i	$-0.276950\pi$
$983$	−8.82354	−	12.1446i	−0.281427	−	0.387351i	−0.926206	+	0.377018i	$0.876950\pi$
$984$	0.143415	−	0.441387i	0.00457191	−	0.0140709i
$985$	5.31709	−	2.06573i	0.169417	−	0.0658196i
$986$	11.2101	−	8.14459i	0.357001	−	0.259377i
$987$	1.11952	−	1.54089i	0.0356348	−	0.0490471i
$988$	−43.3037	+	14.0702i	−1.37768	+	0.447634i
$989$	67.5167			2.14690
$990$		0			0
$991$	−45.9090			−1.45835			−0.729173	−	0.684329i	$-0.760095\pi$
$991$	−45.9090			−1.45835			−0.729173	+	0.684329i	$0.760095\pi$
$992$	−38.0203	+	12.3535i	−1.20715	+	0.392226i
$993$	−2.37440	+	3.26808i	−0.0753493	+	0.103709i
$994$	3.07738	−	2.23585i	0.0976085	−	0.0709167i
$995$	1.61953	+	4.16859i	0.0513425	+	0.132153i
$996$	−2.74272	+	8.44124i	−0.0869066	+	0.267471i
$997$	0.103371	+	0.142278i	0.00327380	+	0.00450599i	0.810651	−	0.585530i	$-0.199114\pi$
$997$	0.103371	+	0.142278i	0.00327380	+	0.00450599i	−0.807377	+	0.590036i	$0.799114\pi$
$998$	−43.5950	+	60.0034i	−1.37998	+	1.89937i
$999$	6.13597	+	18.8846i	0.194133	+	0.597481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.f.269.1		16
5.4	even	2	inner	605.2.j.f.269.4		16
11.2	odd	10		605.2.j.e.9.1		16
11.3	even	5		605.2.b.d.364.4	yes	4
11.4	even	5	inner	605.2.j.f.124.1		16
11.5	even	5	inner	605.2.j.f.444.4		16
11.6	odd	10		605.2.j.e.444.1		16
11.7	odd	10		605.2.j.e.124.4		16
11.8	odd	10		605.2.b.e.364.1	yes	4
11.9	even	5	inner	605.2.j.f.9.4		16
11.10	odd	2		605.2.j.e.269.4		16
55.3	odd	20		3025.2.a.y.1.4		4
55.4	even	10	inner	605.2.j.f.124.4		16
55.8	even	20		3025.2.a.z.1.1		4
55.9	even	10	inner	605.2.j.f.9.1		16
55.14	even	10		605.2.b.d.364.1	✓	4
55.19	odd	10		605.2.b.e.364.4	yes	4
55.24	odd	10		605.2.j.e.9.4		16
55.29	odd	10		605.2.j.e.124.1		16
55.39	odd	10		605.2.j.e.444.4		16
55.47	odd	20		3025.2.a.y.1.1		4
55.49	even	10	inner	605.2.j.f.444.1		16
55.52	even	20		3025.2.a.z.1.4		4
55.54	odd	2		605.2.j.e.269.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.1	✓	4	55.14	even	10
605.2.b.d.364.4	yes	4	11.3	even	5
605.2.b.e.364.1	yes	4	11.8	odd	10
605.2.b.e.364.4	yes	4	55.19	odd	10
605.2.j.e.9.1		16	11.2	odd	10
605.2.j.e.9.4		16	55.24	odd	10
605.2.j.e.124.1		16	55.29	odd	10
605.2.j.e.124.4		16	11.7	odd	10
605.2.j.e.269.1		16	55.54	odd	2
605.2.j.e.269.4		16	11.10	odd	2
605.2.j.e.444.1		16	11.6	odd	10
605.2.j.e.444.4		16	55.39	odd	10
605.2.j.f.9.1		16	55.9	even	10	inner
605.2.j.f.9.4		16	11.9	even	5	inner
605.2.j.f.124.1		16	11.4	even	5	inner
605.2.j.f.124.4		16	55.4	even	10	inner
605.2.j.f.269.1		16	1.1	even	1	trivial
605.2.j.f.269.4		16	5.4	even	2	inner
605.2.j.f.444.1		16	55.49	even	10	inner
605.2.j.f.444.4		16	11.5	even	5	inner
3025.2.a.y.1.1		4	55.47	odd	20
3025.2.a.y.1.4		4	55.3	odd	20
3025.2.a.z.1.1		4	55.8	even	20
3025.2.a.z.1.4		4	55.52	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.83730 + 0.596975i) q^{2} +(0.304260 - 0.418778i) q^{3} +(1.40126 - 1.01807i) q^{4} +(0.809764 + 2.08429i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.526994 - 0.725345i) q^{7} +(0.304260 - 0.418778i) q^{8} +(0.844250 + 2.59833i) q^{9} +O(q^{10})\)	\(q+(-1.83730 + 0.596975i) q^{2} +(0.304260 - 0.418778i) q^{3} +(1.40126 - 1.01807i) q^{4} +(0.809764 + 2.08429i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-0.526994 - 0.725345i) q^{7} +(0.304260 - 0.418778i) q^{8} +(0.844250 + 2.59833i) q^{9} +(-2.73205 - 3.34607i) q^{10} -0.896575i q^{12} +(-4.03499 + 1.31105i) q^{13} +(1.40126 + 1.01807i) q^{14} +(1.11924 + 0.295056i) q^{15} +(-1.37948 + 4.24561i) q^{16} +(0.984606 + 0.319918i) q^{17} +(-3.10228 - 4.26992i) q^{18} +(5.01279 + 3.64201i) q^{19} +(3.25665 + 2.09624i) q^{20} -0.464102 q^{21} -6.31319i q^{23} +(-0.0828009 - 0.254835i) q^{24} +(-3.68856 + 3.37557i) q^{25} +(6.63083 - 4.81758i) q^{26} +(2.82191 + 0.916893i) q^{27} +(-1.47691 - 0.479877i) q^{28} +(-5.60503 + 4.07230i) q^{29} +(-2.23251 + 0.126049i) q^{30} +(-1.62789 - 5.01012i) q^{31} -7.58871i q^{32} -2.00000 q^{34} +(1.08509 - 1.68577i) q^{35} +(3.82831 + 2.78143i) q^{36} +(3.93354 + 5.41405i) q^{37} +(-11.3842 - 3.69895i) q^{38} +(-0.678648 + 2.08867i) q^{39} +(1.11924 + 0.295056i) q^{40} +(1.40126 + 1.01807i) q^{41} +(0.852694 - 0.277057i) q^{42} +10.6945i q^{43} +(-4.73205 + 3.86370i) q^{45} +(3.76882 + 11.5992i) q^{46} +(-2.41224 + 3.32016i) q^{47} +(1.35825 + 1.86947i) q^{48} +(1.91472 - 5.89289i) q^{49} +(4.76187 - 8.40392i) q^{50} +(0.433551 - 0.314993i) q^{51} +(-4.31932 + 5.94504i) q^{52} +(-11.3842 + 3.69895i) q^{53} -5.73205 q^{54} -0.464102 q^{56} +(3.05038 - 0.991130i) q^{57} +(7.86707 - 10.8281i) q^{58} +(-3.82831 + 2.78143i) q^{59} +(1.86873 - 0.726014i) q^{60} +(-2.55494 + 7.86329i) q^{61} +(5.98183 + 8.23328i) q^{62} +(1.43977 - 1.98168i) q^{63} +(1.77130 + 5.45150i) q^{64} +(-6.00000 - 7.34847i) q^{65} +14.9372i q^{67} +(1.70539 - 0.554114i) q^{68} +(-2.64383 - 1.92085i) q^{69} +(-0.987277 + 3.74503i) q^{70} +(0.678648 - 2.08867i) q^{71} +(1.34500 + 0.437016i) q^{72} +(-2.87955 - 3.96336i) q^{73} +(-10.4591 - 7.59901i) q^{74} +(0.291333 + 2.57174i) q^{75} +10.7321 q^{76} -4.24264i q^{78} +(1.68850 + 5.19667i) q^{79} +(-9.96616 + 0.562695i) q^{80} +(-5.38826 + 3.91480i) q^{81} +(-3.18230 - 1.03399i) q^{82} +(-9.41498 - 3.05911i) q^{83} +(-0.650326 + 0.472490i) q^{84} +(0.130495 + 2.31127i) q^{85} +(-6.38437 - 19.6491i) q^{86} +3.58630i q^{87} +6.46410 q^{89} +(6.38766 - 9.92370i) q^{90} +(3.07738 + 2.23585i) q^{91} +(-6.42730 - 8.84642i) q^{92} +(-2.59343 - 0.842656i) q^{93} +(2.44995 - 7.54017i) q^{94} +(-3.53184 + 13.3973i) q^{95} +(-3.17798 - 2.30894i) q^{96} +(0.624215 - 0.202820i) q^{97} +11.9700i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^6 - 4 * q^9	\( 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) \) 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

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