LMFDB - Embedded newform 605.2.j.e.9.4

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			9.4
Root			$1.13551 + 1.56290i$ of defining polynomial
Character	$\chi$	$=$	605.9
Dual form			605.2.j.e.269.4

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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	$-0.160669\pi$
$2$	1.83730	+	0.596975i	1.29917	+	0.422125i	0.423876	+	0.905720i	$0.360669\pi$
$3$	0.304260	+	0.418778i	0.175665	+	0.241782i	0.887766	−	0.460295i	$-0.152256\pi$
$3$	0.304260	+	0.418778i	0.175665	+	0.241782i	−0.712101	+	0.702077i	$0.752256\pi$
$4$	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	$-0.745805\pi$
$7$	0.526994	−	0.725345i	0.199185	−	0.274155i	0.896912	+	0.442209i	$0.145805\pi$
$8$	−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	$-0.199778\pi$
$13$	4.03499	+	1.31105i	1.11911	+	0.363619i	0.309679	+	0.950841i	$0.399778\pi$
$14$	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	$-0.640068\pi$
$17$	−0.984606	+	0.319918i	−0.238802	+	0.0775915i	0.187171	+	0.982327i	$0.440068\pi$
$18$	3.10228	−	4.26992i	0.731215	−	1.00643i
$19$	−5.01279	+	3.64201i	−1.15001	+	0.835534i	−0.988483	−	0.151334i	$-0.951643\pi$
$19$	−5.01279	+	3.64201i	−1.15001	+	0.835534i	−0.161531	+	0.986868i	$0.551643\pi$
$20$	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	$0.228680\pi$
$23$			6.31319i			1.31639i	−0.752847	+	0.658196i	$0.771320\pi$
$24$	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	$-0.0775783\pi$
$29$	5.60503	+	4.07230i	1.04083	+	0.756206i	0.0703816	+	0.997520i	$0.477578\pi$
$30$	2.23251	+	0.126049i	0.407599	+	0.0230133i
$31$	−1.62789	+	5.01012i	−0.292377	+	0.899844i	0.691713	+	0.722173i	$0.256856\pi$
$31$	−1.62789	+	5.01012i	−0.292377	+	0.899844i	−0.984090	+	0.177671i	$0.943144\pi$
$32$		−	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	−0.352280	−	0.935895i	$-0.614594\pi$
$37$	3.93354	−	5.41405i	0.646669	−	0.890064i	0.998949	+	0.0458308i	$0.0145935\pi$
$38$	−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	$-0.743184\pi$
$41$	−1.40126	+	1.01807i	−0.218840	+	0.158996i	0.472964	+	0.881082i	$0.343184\pi$
$42$	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	0.595998	−	0.802986i	$-0.296757\pi$
$47$	−2.41224	−	3.32016i	−0.351861	−	0.484295i	−0.947859	+	0.318691i	$0.896757\pi$
$48$	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	−0.605936	−	0.795514i	$-0.707201\pi$
$53$	−11.3842	−	3.69895i	−1.56374	−	0.508090i	−0.957803	+	0.287424i	$0.907201\pi$
$54$	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	0.310003	−	0.950735i	$-0.399670\pi$
$59$	−3.82831	−	2.78143i	−0.498403	−	0.362111i	−0.808407	+	0.588624i	$0.799670\pi$
$60$	1.86873	+	0.726014i	0.241252	+	0.0937281i
$61$	2.55494	+	7.86329i	0.327126	+	1.00679i	0.970472	+	0.241215i	$0.0775458\pi$
$61$	2.55494	+	7.86329i	0.327126	+	1.00679i	−0.643346	+	0.765576i	$0.722454\pi$
$62$	−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	$-0.634201\pi$
$67$		−	14.9372i		−	1.82487i	0.409226	−	0.912433i	$-0.365799\pi$
$68$	−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	0.983217	−	0.182442i	$-0.0584003\pi$
$71$	0.678648	+	2.08867i	0.0805407	+	0.247879i	−0.902676	+	0.430321i	$0.858400\pi$
$72$	−1.34500	+	0.437016i	−0.158509	+	0.0515028i
$73$	2.87955	−	3.96336i	0.337026	−	0.463876i	−0.606544	−	0.795050i	$-0.707445\pi$
$73$	2.87955	−	3.96336i	0.337026	−	0.463876i	0.943570	+	0.331174i	$0.107445\pi$
$74$	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	$-0.999452\pi$
$79$	−1.68850	+	5.19667i	−0.189971	+	0.584671i	0.810027	+	0.586392i	$0.199452\pi$
$80$	−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	$-0.417173\pi$
$83$	9.41498	−	3.05911i	1.03343	−	0.335781i	0.776145	+	0.630555i	$0.217173\pi$
$84$	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	0.340535	−	0.940232i	$-0.389392\pi$
$97$	0.624215	+	0.202820i	0.0633795	+	0.0205932i	−0.277156	+	0.960825i	$0.589392\pi$
$98$			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	$-0.877933\pi$
$101$	0.430246	−	1.32416i	0.0428111	−	0.131759i	0.970178	+	0.242395i	$0.0779331\pi$
$102$	−0.608520	−	0.837556i	−0.0602525	−	0.0829304i
$103$	−2.49376	+	3.43237i	−0.245718	+	0.338201i	−0.914006	−	0.405701i	$-0.867027\pi$
$103$	−2.49376	+	3.43237i	−0.245718	+	0.338201i	0.668288	+	0.743903i	$0.267027\pi$
$104$	−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	$-0.267926\pi$
$107$	−2.57529	−	3.54458i	−0.248962	−	0.342667i	−0.915148	+	0.403119i	$0.867926\pi$
$108$	4.88769	+	1.58811i	0.470318	+	0.152815i
$109$	−1.19615			−0.114571			−0.0572853	−	0.998358i	$-0.518244\pi$
$109$	−1.19615			−0.114571			−0.0572853	+	0.998358i	$0.518244\pi$
$110$		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	0.880023	−	0.474930i	$-0.157527\pi$
$113$	1.66251	+	2.28825i	0.156396	+	0.215260i	−0.723628	+	0.690190i	$0.757527\pi$
$114$	−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	$-0.647431\pi$
$127$	−3.18230	+	1.03399i	−0.282383	+	0.0917519i	0.164401	+	0.986394i	$0.447431\pi$
$128$	−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	$-0.874123\pi$
$131$	−21.1244			−1.84564			−0.922822	+	0.385227i	$0.874123\pi$
$132$		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	0.309193	−	0.950999i	$-0.399941\pi$
$137$	13.0896	−	4.25306i	1.11832	−	0.363364i	0.809126	+	0.587636i	$0.199941\pi$
$138$	−6.00420	+	1.95088i	−0.511112	+	0.166070i
$139$	−13.4203	−	9.75045i	−1.13830	−	0.827022i	−0.151417	−	0.988470i	$-0.548384\pi$
$139$	−13.4203	−	9.75045i	−1.13830	−	0.827022i	−0.986881	+	0.161447i	$0.948384\pi$
$140$	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	−0.960157	−	0.279459i	$-0.909845\pi$
$149$	−4.24344	−	13.0600i	−0.347636	−	1.06991i	0.612522	−	0.790454i	$-0.290155\pi$
$150$	2.07053	−	4.55114i	0.169058	−	0.371599i
$151$	−5.01279	+	3.64201i	−0.407935	+	0.296382i	−0.772765	−	0.634692i	$-0.781127\pi$
$151$	−5.01279	+	3.64201i	−0.407935	+	0.296382i	0.364830	+	0.931074i	$0.381127\pi$
$152$	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	0.992108	−	0.125384i	$-0.0400164\pi$
$157$	7.09550	+	9.76612i	0.566282	+	0.779421i	−0.425826	+	0.904805i	$0.640016\pi$
$158$	−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	0.577705	−	0.816245i	$-0.303948\pi$
$163$	7.21729	+	2.34504i	0.565302	+	0.183678i	−0.0124036	+	0.999923i	$0.503948\pi$
$164$	−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	$-0.376186\pi$
$167$	1.83730	+	0.596975i	0.142175	+	0.0461953i	−0.237065	+	0.971494i	$0.576186\pi$
$168$	−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	$-0.106381\pi$
$173$	4.48237	+	6.16946i	0.340789	+	0.469055i	−0.603883	+	0.797073i	$0.706381\pi$
$174$	−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	−0.815154	−	0.579245i	$-0.803348\pi$
$179$	−6.90569	+	5.01728i	−0.516155	+	0.375009i	0.298998	+	0.954254i	$0.403348\pi$
$180$	−2.69729	−	10.2316i	−0.201044	−	0.762620i
$181$	1.04828	+	3.22627i	0.0779180	+	0.239807i	0.982427	−	0.186648i	$-0.0597623\pi$
$181$	1.04828	+	3.22627i	0.0779180	+	0.239807i	−0.904509	+	0.426455i	$0.859762\pi$
$182$	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	0.855789	−	0.517325i	$-0.173072\pi$
$191$	8.68241	+	6.30814i	0.628237	+	0.456441i	−0.227552	+	0.973766i	$0.573072\pi$
$192$	2.82191	−	0.916893i	0.203654	−	0.0661710i
$193$	−9.77537	+	3.17621i	−0.703647	+	0.228629i	−0.638919	−	0.769274i	$-0.720618\pi$
$193$	−9.77537	+	3.17621i	−0.703647	+	0.228629i	−0.0647279	+	0.997903i	$0.520618\pi$
$194$	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	0.760242	+	0.649640i	$0.225080\pi$
$211$	−3.43761	+	10.5799i	−0.236655	+	0.728350i	−0.996898	+	0.0787102i	$0.974920\pi$
$212$	−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	0.679580	−	0.733602i	$-0.262162\pi$
$223$	−3.40654	−	4.68870i	−0.228119	−	0.313979i	−0.907698	+	0.419623i	$0.862162\pi$
$224$	−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	−0.146152	−	0.989262i	$-0.546689\pi$
$227$	12.6537	−	17.4163i	0.839856	−	1.15596i	0.986008	−	0.166700i	$-0.0533112\pi$
$228$	−3.26533	−	4.49435i	−0.216252	−	0.297645i
$229$	5.54012	−	17.0507i	0.366101	−	1.12674i	−0.583187	−	0.812338i	$-0.698195\pi$
$229$	5.54012	−	17.0507i	0.366101	−	1.12674i	0.949288	−	0.314406i	$-0.101805\pi$
$230$	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	$-0.540079\pi$
$233$	−12.3688	−	4.01887i	−0.810307	−	0.263285i	−0.684728	+	0.728799i	$0.740079\pi$
$234$	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	$-0.576915\pi$
$239$	9.43334	−	6.85373i	0.610192	−	0.443331i	0.849482	+	0.527618i	$0.176915\pi$
$240$	−2.79666	−	4.34482i	−0.180524	−	0.280457i
$241$	10.1244			0.652167			0.326084	−	0.945341i	$-0.394271\pi$
$241$	10.1244			0.652167			0.326084	+	0.945341i	$0.394271\pi$
$242$		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	0.711816	+	0.702366i	$0.247873\pi$
$251$	−4.38685	+	13.5013i	−0.276896	+	0.852197i	−0.988712	+	0.149831i	$0.952127\pi$
$252$		−	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	−0.707445	−	0.706768i	$-0.750152\pi$
$257$	2.93923	−	4.04550i	0.183344	−	0.252351i	0.890789	+	0.454417i	$0.150152\pi$
$258$	−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	0.945630	+	0.325245i	$0.105447\pi$
$269$	6.09754	+	18.7663i	0.371774	+	1.14420i	−0.573856	+	0.818956i	$0.694553\pi$
$270$	4.64161	−	11.9473i	0.282479	−	0.727088i
$271$	3.66962	+	2.66613i	0.222913	+	0.161956i	0.693637	−	0.720325i	$-0.256007\pi$
$271$	3.66962	+	2.66613i	0.222913	+	0.161956i	−0.470724	+	0.882281i	$0.656007\pi$
$272$	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	$-0.638893\pi$
$277$	−21.5906	−	7.01523i	−1.29726	−	0.421504i	−0.874626	+	0.484798i	$0.838893\pi$
$278$	−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	−0.973951	−	0.226758i	$-0.927187\pi$
$281$	−5.35233	−	16.4728i	−0.319293	−	0.982684i	0.654658	−	0.755925i	$-0.272813\pi$
$282$	2.41224	−	3.32016i	0.143647	−	0.197712i
$283$	17.7009	+	24.3632i	1.05221	+	1.44824i	0.886877	+	0.462005i	$0.152870\pi$
$283$	17.7009	+	24.3632i	1.05221	+	1.44824i	0.165332	+	0.986238i	$0.447130\pi$
$284$	−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	$-0.888722\pi$
$293$	−5.53636	+	7.62015i	−0.323438	+	0.445174i	0.616075	+	0.787687i	$0.288722\pi$
$294$	−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	0.287177	−	0.957878i	$-0.407283\pi$
$311$	22.6950	−	16.4889i	1.28692	−	0.934999i	0.999738	+	0.0228789i	$0.00728322\pi$
$312$	0.668201	−	0.919700i	0.0378295	−	0.0520678i
$313$	16.3072	−	5.29854i	0.921739	−	0.299491i	0.190559	−	0.981676i	$-0.438970\pi$
$313$	16.3072	−	5.29854i	0.921739	−	0.299491i	0.731180	+	0.682185i	$0.238970\pi$
$314$	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	0.489185	−	0.872180i	$-0.337294\pi$
$317$	6.62842	+	2.15370i	0.372289	+	0.120964i	−0.116896	+	0.993144i	$0.537294\pi$
$318$		−	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	$-0.731600\pi$
$337$	4.60174	−	6.33375i	0.250673	−	0.345021i	0.915747	+	0.401756i	$0.131600\pi$
$338$	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	$-0.574622\pi$
$347$	2.82191	−	0.916893i	0.151488	−	0.0492214i	0.383779	+	0.923425i	$0.374622\pi$
$348$	−3.65112	+	5.02534i	−0.195721	+	0.269386i
$349$	−22.1028	+	16.0586i	−1.18313	+	0.859597i	−0.992522	−	0.122069i	$-0.961047\pi$
$349$	−22.1028	+	16.0586i	−1.18313	+	0.859597i	−0.190612	+	0.981666i	$0.561047\pi$
$350$	−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	$-0.985666\pi$
$353$		−	1.69161i		−	0.0900356i	0.998986	−	0.0450178i	$-0.0143345\pi$
$354$	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	$-0.460805\pi$
$359$	−14.8372	−	10.7798i	−0.783076	−	0.568938i	−0.905901	+	0.423491i	$0.860805\pi$
$360$	−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	−0.0581882	−	0.998306i	$-0.518532\pi$
$367$	17.4185	−	23.9745i	0.909238	−	1.25146i	0.967426	−	0.253153i	$-0.0814677\pi$
$368$	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	0.985011	−	0.172491i	$-0.0551817\pi$
$379$	1.68850	+	5.19667i	0.0867324	+	0.266935i	−0.898279	+	0.439426i	$0.855182\pi$
$380$	−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	0.822973	−	0.568080i	$-0.192314\pi$
$383$	22.6011	+	7.34355i	1.15486	+	0.375238i	0.331890	+	0.943318i	$0.392314\pi$
$384$	−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	0.150347	−	0.988633i	$-0.451961\pi$
$389$	−14.6629	−	10.6532i	−0.743439	−	0.540140i	−0.893786	+	0.448493i	$0.851961\pi$
$390$	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	$-0.868402\pi$
$397$		−	16.0096i		−	0.803500i	0.915749	−	0.401750i	$-0.131598\pi$
$398$	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	−0.811020	−	0.585018i	$-0.801087\pi$
$401$	−9.98759	−	30.7386i	−0.498756	−	1.53501i	0.312264	−	0.949995i	$-0.398913\pi$
$402$	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	$-0.914766\pi$
$409$	−0.579606	+	1.78384i	−0.0286597	+	0.0882054i	0.935704	+	0.352787i	$0.114766\pi$
$410$	−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	−0.919583	−	0.392896i	$-0.871473\pi$
$421$	−17.0319	+	12.3744i	−0.830083	+	0.603091i	0.0894999	+	0.995987i	$0.471473\pi$
$422$	−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	−0.705613	−	0.708597i	$-0.749328\pi$
$431$	5.84914	−	18.0018i	0.281743	−	0.867116i	0.987356	−	0.158518i	$-0.0506717\pi$
$432$	−7.78554	−	10.7159i	−0.374582	−	0.515568i
$433$	−11.9040	+	16.3844i	−0.572069	+	0.787385i	−0.992798	−	0.119801i	$-0.961774\pi$
$433$	−11.9040	+	16.3844i	−0.572069	+	0.787385i	0.420729	+	0.907186i	$0.361774\pi$
$434$	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	$-0.660529\pi$
$439$	−20.2487			−0.966418			−0.483209	+	0.875505i	$0.660529\pi$
$440$		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	0.661385	−	0.750047i	$-0.269969\pi$
$443$	−5.39515	−	7.42579i	−0.256332	−	0.352810i	−0.917716	+	0.397237i	$0.869969\pi$
$444$	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	−0.844623	−	0.535361i	$-0.820175\pi$
$449$	3.24983	−	10.0019i	0.153369	−	0.472021i	0.997992	+	0.0633406i	$0.0201755\pi$
$450$	−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	$-0.765256\pi$
$457$	−20.1750	+	6.55524i	−0.943745	+	0.306641i	−0.203573	+	0.979060i	$0.565256\pi$
$458$	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	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$			17.8671i			0.830356i	0.909740	+	0.415178i	$0.136281\pi$
$463$			17.8671i			0.830356i	−0.909740	+	0.415178i	$0.863719\pi$
$464$	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	0.109225	−	0.994017i	$-0.465163\pi$
$467$	16.8961	−	5.48987i	0.781858	−	0.254041i	0.672633	+	0.739976i	$0.265163\pi$
$468$	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	$-0.0306295\pi$
$479$	2.92457	+	9.00090i	0.133627	+	0.411261i	−0.861747	+	0.507338i	$0.830629\pi$
$480$	−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	0.605142	−	0.796117i	$-0.293116\pi$
$487$	−7.48128	−	10.2971i	−0.339009	−	0.466606i	−0.944152	+	0.329511i	$0.893116\pi$
$488$	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	$-0.415368\pi$
$491$	−12.7119	−	9.23576i	−0.573681	−	0.416804i	−0.836441	+	0.548057i	$0.815368\pi$
$492$	−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	0.995817	+	0.0913680i	$0.0291240\pi$
$499$	31.0600	+	22.5664i	1.39044	+	1.01021i	0.394621	+	0.918844i	$0.370876\pi$
$500$	−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	−0.971172	−	0.238378i	$-0.923384\pi$
$503$	−20.1350	−	27.7134i	−0.897775	−	1.23568i	0.0733975	−	0.997303i	$-0.476616\pi$
$504$	−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	−0.906870	−	0.421410i	$-0.861535\pi$
$509$	−17.7403	+	12.8891i	−0.786324	+	0.571298i	0.120546	+	0.992708i	$0.461535\pi$
$510$	−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	−0.995742	−	0.0921880i	$-0.970614\pi$
$521$	−31.7529	−	23.0698i	−1.39112	−	1.01071i	−0.395377	−	0.918519i	$-0.629386\pi$
$522$	34.7768	−	11.2997i	1.52214	−	0.494573i
$523$	8.23724	−	2.67644i	0.360189	−	0.117033i	−0.123331	−	0.992366i	$-0.539358\pi$
$523$	8.23724	−	2.67644i	0.360189	−	0.117033i	0.483521	+	0.875333i	$0.339358\pi$
$524$	−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	−0.666673	−	0.745350i	$-0.732282\pi$
$541$	7.22862	−	22.2474i	0.310783	−	0.956491i	0.977456	−	0.211140i	$-0.0677177\pi$
$542$	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	$-0.0574684\pi$
$547$	11.9040	+	16.3844i	0.508977	+	0.700547i	−0.474769	+	0.880110i	$0.657468\pi$
$548$	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	$-0.843899\pi$
$557$	−3.81417	+	5.24976i	−0.161612	+	0.222439i	0.720530	+	0.693424i	$0.243899\pi$
$558$	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	$-0.440847\pi$
$563$	−5.77572	−	1.87665i	−0.243418	−	0.0790912i	−0.428185	+	0.903691i	$0.640847\pi$
$564$	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	$-0.739303\pi$
$569$	−4.75350	+	3.45362i	−0.199277	+	0.144783i	0.483672	+	0.875249i	$0.339303\pi$
$570$	−11.6502	+	7.49897i	−0.487973	+	0.314097i
$571$	−35.7128			−1.49453			−0.747267	−	0.664524i	$-0.768635\pi$
$571$	−35.7128			−1.49453			−0.747267	+	0.664524i	$0.768635\pi$
$572$		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	−0.689195	−	0.724576i	$-0.742036\pi$
$577$	−19.7180	+	6.40677i	−0.820871	+	0.266717i	−0.131676	+	0.991293i	$0.542036\pi$
$578$	−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	−0.106448	−	0.994318i	$-0.533948\pi$
$587$	21.1293	−	29.0820i	0.872099	−	1.20034i	0.978547	−	0.206024i	$-0.0660523\pi$
$588$	−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	−0.993195	−	0.116463i	$-0.962844\pi$
$599$	−6.31781	−	19.4442i	−0.258139	−	0.794469i	0.735056	−	0.678006i	$-0.237156\pi$
$600$	−1.16563	+	0.660475i	−0.0475866	+	0.0269638i
$601$	16.1803	+	11.7557i	0.660010	+	0.479525i	0.866666	−	0.498888i	$-0.166258\pi$
$601$	16.1803	+	11.7557i	0.660010	+	0.479525i	−0.206656	+	0.978414i	$0.566258\pi$
$602$	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	$-0.620694\pi$
$607$	−29.9503	−	9.73145i	−1.21565	−	0.394987i	−0.845495	+	0.533984i	$0.820694\pi$
$608$	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	$-0.243150\pi$
$613$	−3.93354	−	5.41405i	−0.158874	−	0.218671i	−0.881032	+	0.473057i	$0.843150\pi$
$614$	−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	$-0.989159\pi$
$617$		−	1.69161i		−	0.0681019i	0.999420	−	0.0340509i	$-0.0108408\pi$
$618$	−4.03499	−	1.31105i	−0.162311	−	0.0527381i
$619$	−23.2872	+	16.9192i	−0.935993	+	0.680039i	−0.947453	−	0.319896i	$-0.896352\pi$
$619$	−23.2872	+	16.9192i	−0.935993	+	0.680039i	0.0114597	+	0.999934i	$0.496352\pi$
$620$	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	0.231460	−	0.972844i	$-0.425650\pi$
$631$	−15.6306	−	11.3563i	−0.622245	−	0.452088i	−0.853705	+	0.520757i	$0.825650\pi$
$632$	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	−0.857955	−	0.513725i	$-0.828265\pi$
$641$	−16.0642	+	11.6713i	−0.634497	+	0.460989i	0.223459	+	0.974713i	$0.428265\pi$
$642$	2.57529	−	3.54458i	0.101639	−	0.139893i
$643$	−26.3111	+	8.54899i	−1.03761	+	0.337139i	−0.777794	−	0.628520i	$-0.783661\pi$
$643$	−26.3111	+	8.54899i	−1.03761	+	0.337139i	−0.259814	+	0.965659i	$0.583661\pi$
$644$	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	0.641482	−	0.767138i	$-0.278320\pi$
$647$	18.0480	+	5.86414i	0.709538	+	0.230543i	0.0680568	+	0.997681i	$0.478320\pi$
$648$			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	−0.264111	−	0.964492i	$-0.585078\pi$
$653$	18.7767	−	25.8440i	0.734791	−	1.01135i	0.998901	−	0.0468603i	$-0.0149216\pi$
$654$	−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	$-0.429234\pi$
$659$	11.3205			0.440984			0.220492	+	0.975389i	$0.429234\pi$
$660$		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	$-0.409924\pi$
$673$	−1.53813	−	0.499769i	−0.0592906	−	0.0192647i	−0.338512	+	0.940962i	$0.609924\pi$
$674$	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	$-0.655579\pi$
$677$	−8.59763	+	2.79354i	−0.330434	+	0.107364i	0.139102	+	0.990278i	$0.455579\pi$
$678$	−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	$-0.858424\pi$
$683$		−	22.4887i		−	0.860507i	0.902708	−	0.430253i	$-0.141576\pi$
$684$	−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	0.641943	+	0.766752i	$0.278129\pi$
$691$	−8.62434	+	26.5430i	−0.328086	+	1.00974i	−0.970029	+	0.242991i	$0.921871\pi$
$692$			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	$-0.638646\pi$
$701$	8.20634	−	5.96225i	0.309949	−	0.225191i	0.731875	+	0.681439i	$0.238646\pi$
$702$	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	−0.990130	−	0.140151i	$-0.955241\pi$
$709$	−7.22862	−	22.2474i	−0.271477	−	0.835519i	0.718654	−	0.695368i	$-0.244759\pi$
$710$	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	−0.206556	−	0.978435i	$-0.566225\pi$
$719$	−32.2020	−	23.3961i	−1.20093	−	0.872528i	−0.994376	+	0.105907i	$0.966225\pi$
$720$	−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	$0.0236469\pi$
$727$			4.00240i			0.148441i	−0.997242	+	0.0742205i	$0.976353\pi$
$728$	−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	−0.242677	−	0.970107i	$-0.578026\pi$
$733$	20.4393	−	28.1322i	0.754941	−	1.03909i	0.997618	−	0.0689799i	$-0.0219744\pi$
$734$	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	0.701398	+	0.712770i	$0.252560\pi$
$739$	−7.74761	+	23.8447i	−0.285000	+	0.877141i	−0.986399	+	0.164371i	$0.947440\pi$
$740$	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	$-0.552872\pi$
$743$	7.64837	−	2.48511i	0.280592	−	0.0911697i	0.445932	+	0.895067i	$0.352872\pi$
$744$	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	−0.239834	−	0.970814i	$-0.577093\pi$
$751$	16.6989	−	12.1325i	0.609353	−	0.442721i	0.849186	+	0.528093i	$0.177093\pi$
$752$	−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	−0.368174	−	0.929757i	$-0.620017\pi$
$757$	−33.3611	−	10.8397i	−1.21253	−	0.393975i	−0.844356	+	0.535782i	$0.820017\pi$
$758$			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	$-0.945481\pi$
$761$	−2.42776	+	7.47189i	−0.0880063	+	0.270856i	0.897362	+	0.441296i	$0.145481\pi$
$762$	−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	$-0.395659\pi$
$769$	17.8564			0.643918			0.321959	+	0.946754i	$0.395659\pi$
$770$		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	0.845852	+	0.533418i	$0.179093\pi$
$773$	30.3546	+	41.7795i	1.09178	+	1.50271i	0.245928	+	0.969288i	$0.420907\pi$
$774$	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	$-0.573539\pi$
$787$	4.43073	−	1.43963i	0.157938	−	0.0513173i	0.386919	+	0.922114i	$0.373539\pi$
$788$	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	−0.172851	−	0.984948i	$-0.555298\pi$
$797$	7.51646	−	2.44225i	0.266247	−	0.0865088i	0.439098	+	0.898439i	$0.355298\pi$
$798$	−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	−0.997356	−	0.0726760i	$-0.976846\pi$
$809$	−6.63277	−	20.4136i	−0.233196	−	0.717703i	0.764160	−	0.645027i	$-0.223154\pi$
$810$	−27.8202	+	7.33403i	−0.977501	+	0.257692i
$811$	−26.6820	+	19.3856i	−0.936932	+	0.680721i	−0.947680	−	0.319222i	$-0.896579\pi$
$811$	−26.6820	+	19.3856i	−0.936932	+	0.680721i	0.0107485	+	0.999942i	$0.496579\pi$
$812$	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	$-0.193582\pi$
$821$	15.2126	+	11.0526i	0.530925	+	0.385739i	−0.289779	+	0.957094i	$0.593582\pi$
$822$	8.08980	+	11.1347i	0.282164	+	0.388366i
$823$	46.0291	+	14.9558i	1.60447	+	0.521325i	0.968208	−	0.250146i	$-0.0804787\pi$
$823$	46.0291	+	14.9558i	1.60447	+	0.521325i	0.636264	+	0.771471i	$0.280479\pi$
$824$	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	$-0.246137\pi$
$827$	25.4230	+	8.26044i	0.884045	+	0.287244i	0.168409	+	0.985717i	$0.446137\pi$
$828$	17.5597	+	24.1689i	0.610242	+	0.839926i
$829$	33.9631	+	24.6757i	1.17959	+	0.857022i	0.992125	−	0.125250i	$-0.0399733\pi$
$829$	33.9631	+	24.6757i	1.17959	+	0.857022i	0.187464	+	0.982272i	$0.439973\pi$
$830$	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	−0.548218	−	0.836335i	$-0.684694\pi$
$839$	2.25280	−	1.63675i	0.0777752	−	0.0565070i	0.625993	+	0.779828i	$0.284694\pi$
$840$	−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	$-0.668220\pi$
$853$	−11.8153	+	3.83902i	−0.404547	+	0.131445i	0.0996734	+	0.995020i	$0.468220\pi$
$854$	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	−0.146723	−	0.989178i	$-0.546873\pi$
$863$	9.28307	−	3.01625i	0.315999	−	0.102674i	0.462722	+	0.886503i	$0.346873\pi$
$864$	−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	0.819597	+	0.572940i	$0.194197\pi$
$877$	32.9081	+	45.2941i	1.11123	+	1.52947i	0.291629	+	0.956532i	$0.405803\pi$
$878$	−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	0.959822	+	0.280610i	$0.0905368\pi$
$883$	27.6381	+	38.0406i	0.930097	+	1.28017i	−0.0297250	+	0.999558i	$0.509463\pi$
$884$	−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	$-0.844751\pi$
$887$	−4.90600	+	6.75253i	−0.164727	+	0.226728i	0.718671	+	0.695350i	$0.244751\pi$
$888$	−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	−0.178822	−	0.983881i	$-0.557229\pi$
$907$	7.67425	−	2.49351i	0.254819	−	0.0827958i	0.433641	+	0.901086i	$0.357229\pi$
$908$	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	−0.813141	−	0.582066i	$-0.802244\pi$
$911$	5.63916	−	17.3556i	0.186834	−	0.575015i	0.999975	+	0.00705102i	$0.00224443\pi$
$912$			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	0.966133	+	0.258046i	$0.0830785\pi$
$919$	10.1916	+	31.3666i	0.336190	+	1.03469i	−0.629942	+	0.776642i	$0.716921\pi$
$920$	−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	0.998936	−	0.0461183i	$-0.0146851\pi$
$929$	4.98864	+	15.3535i	0.163672	+	0.503731i	−0.835264	+	0.549849i	$0.814685\pi$
$930$	−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	$-0.520922\pi$
$937$	−21.5906	−	7.01523i	−0.705336	−	0.229177i	−0.639654	+	0.768663i	$0.720922\pi$
$938$	−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	0.990000	+	0.141065i	$0.0450526\pi$
$941$	8.34346	+	25.6785i	0.271989	+	0.837096i	−0.718011	+	0.696031i	$0.754947\pi$
$942$	−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	$0.0747352\pi$
$947$			14.3180i			0.465273i	−0.972564	+	0.232636i	$0.925265\pi$
$948$	−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	$-0.630233\pi$
$953$	18.4506	−	25.3951i	0.597675	−	0.822629i	0.995493	+	0.0948355i	$0.0302325\pi$
$954$	−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	−0.434709	−	0.900571i	$-0.643149\pi$
$971$	8.95727	−	6.50784i	0.287453	−	0.208846i	0.722161	+	0.691725i	$0.243149\pi$
$972$	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	0.527833	−	0.849348i	$-0.323005\pi$
$977$	14.2414	+	4.62733i	0.455624	+	0.148041i	−0.0722087	+	0.997390i	$0.523005\pi$
$978$			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	−0.926206	−	0.377018i	$-0.876950\pi$
$983$	−8.82354	+	12.1446i	−0.281427	+	0.387351i	0.644779	+	0.764369i	$0.276950\pi$
$984$	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	$-0.800886\pi$
$997$	−0.103371	+	0.142278i	−0.00327380	+	0.00450599i	0.807377	+	0.590036i	$0.200886\pi$
$998$	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.e.9.4		16
5.4	even	2	inner	605.2.j.e.9.1		16
11.2	odd	10		605.2.j.f.124.4		16
11.3	even	5	inner	605.2.j.e.444.4		16
11.4	even	5		605.2.b.e.364.4	yes	4
11.5	even	5	inner	605.2.j.e.269.1		16
11.6	odd	10		605.2.j.f.269.4		16
11.7	odd	10		605.2.b.d.364.1	✓	4
11.8	odd	10		605.2.j.f.444.1		16
11.9	even	5	inner	605.2.j.e.124.1		16
11.10	odd	2		605.2.j.f.9.1		16
55.4	even	10		605.2.b.e.364.1	yes	4
55.7	even	20		3025.2.a.y.1.4		4
55.9	even	10	inner	605.2.j.e.124.4		16
55.14	even	10	inner	605.2.j.e.444.1		16
55.18	even	20		3025.2.a.y.1.1		4
55.19	odd	10		605.2.j.f.444.4		16
55.24	odd	10		605.2.j.f.124.1		16
55.29	odd	10		605.2.b.d.364.4	yes	4
55.37	odd	20		3025.2.a.z.1.1		4
55.39	odd	10		605.2.j.f.269.1		16
55.48	odd	20		3025.2.a.z.1.4		4
55.49	even	10	inner	605.2.j.e.269.4		16
55.54	odd	2		605.2.j.f.9.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.1	✓	4	11.7	odd	10
605.2.b.d.364.4	yes	4	55.29	odd	10
605.2.b.e.364.1	yes	4	55.4	even	10
605.2.b.e.364.4	yes	4	11.4	even	5
605.2.j.e.9.1		16	5.4	even	2	inner
605.2.j.e.9.4		16	1.1	even	1	trivial
605.2.j.e.124.1		16	11.9	even	5	inner
605.2.j.e.124.4		16	55.9	even	10	inner
605.2.j.e.269.1		16	11.5	even	5	inner
605.2.j.e.269.4		16	55.49	even	10	inner
605.2.j.e.444.1		16	55.14	even	10	inner
605.2.j.e.444.4		16	11.3	even	5	inner
605.2.j.f.9.1		16	11.10	odd	2
605.2.j.f.9.4		16	55.54	odd	2
605.2.j.f.124.1		16	55.24	odd	10
605.2.j.f.124.4		16	11.2	odd	10
605.2.j.f.269.1		16	55.39	odd	10
605.2.j.f.269.4		16	11.6	odd	10
605.2.j.f.444.1		16	11.8	odd	10
605.2.j.f.444.4		16	55.19	odd	10
3025.2.a.y.1.1		4	55.18	even	20
3025.2.a.y.1.4		4	55.7	even	20
3025.2.a.z.1.1		4	55.37	odd	20
3025.2.a.z.1.4		4	55.48	odd	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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