LMFDB - Embedded newform 605.2.j.f.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.f.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83730 + 0.596975i) q^{2} +(-0.304260 - 0.418778i) q^{3} +(1.40126 + 1.01807i) q^{4} +(-1.88023 - 1.21026i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.526994 - 0.725345i) q^{7} +(-0.304260 - 0.418778i) q^{8} +(0.844250 - 2.59833i) q^{9} +O(q^{10})$	\(q+(1.83730 + 0.596975i) q^{2} +(-0.304260 - 0.418778i) q^{3} +(1.40126 + 1.01807i) q^{4} +(-1.88023 - 1.21026i) 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} +(0.0652477 + 1.15563i) 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} +(-1.40255 - 3.61010i) q^{20} -0.464102 q^{21} -6.31319i q^{23} +(-0.0828009 + 0.254835i) q^{24} +(2.07053 + 4.55114i) 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} +(-0.570005 + 2.16220i) q^{30} +(-1.62789 + 5.01012i) q^{31} -7.58871i q^{32} -2.00000 q^{34} +(-1.86873 + 0.726014i) 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} +(0.0652477 + 1.15563i) 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} +(1.08727 + 9.59787i) 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} +(-1.08509 + 1.68577i) 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} +(-3.86682 + 0.218323i) 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} +(1.27594 - 2.25182i) q^{75} +10.7321 q^{76} -4.24264i q^{78} +(1.68850 - 5.19667i) q^{79} +(-2.54456 + 9.65227i) 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} +(2.23847 + 0.590112i) q^{85} +(-6.38437 + 19.6491i) q^{86} +3.58630i q^{87} +6.46410 q^{89} +(-11.0007 + 4.27387i) 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} +(-13.8330 + 0.781018i) 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	0.712101	−	0.702077i	$-0.247744\pi$
$3$	−0.304260	−	0.418778i	−0.175665	−	0.241782i	−0.887766	+	0.460295i	$0.847744\pi$
$4$	1.40126	+	1.01807i	0.700629	+	0.509037i
$5$	−1.88023	−	1.21026i	−0.840864	−	0.541246i
$5$	−1.88023	−	1.21026i	−0.840864	−	0.541246i
$6$	−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
$15$	0.0652477	+	1.15563i	0.0168469	+	0.298383i
$16$	−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	0.161531	−	0.986868i	$-0.448357\pi$
$19$	5.01279	−	3.64201i	1.15001	−	0.835534i	0.988483	+	0.151334i	$0.0483569\pi$
$20$	−1.40255	−	3.61010i	−0.313620	−	0.807244i
$21$	−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
$25$	2.07053	+	4.55114i	0.414106	+	0.910229i
$26$	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	−0.0703816	−	0.997520i	$-0.522422\pi$
$29$	−5.60503	−	4.07230i	−1.04083	−	0.756206i	−0.970447	+	0.241314i	$0.922422\pi$
$30$	−0.570005	+	2.16220i	−0.104068	+	0.394761i
$31$	−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
$35$	−1.86873	+	0.726014i	−0.315873	+	0.122719i
$36$	3.82831	−	2.78143i	0.638052	−	0.463572i
$37$	−3.93354	+	5.41405i	−0.646669	+	0.890064i	−0.998949	−	0.0458308i	$-0.985406\pi$
$37$	−3.93354	+	5.41405i	−0.646669	+	0.890064i	0.352280	+	0.935895i	$0.385406\pi$
$38$	11.3842	−	3.69895i	1.84676	−	0.600049i
$39$	−0.678648	−	2.08867i	−0.108671	−	0.334454i
$40$	0.0652477	+	1.15563i	0.0103166	+	0.182722i
$41$	1.40126	−	1.01807i	0.218840	−	0.158996i	−0.472964	−	0.881082i	$-0.656816\pi$
$41$	1.40126	−	1.01807i	0.218840	−	0.158996i	0.691804	+	0.722085i	$0.256816\pi$
$42$	−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	$-0.103243\pi$
$47$	2.41224	+	3.32016i	0.351861	+	0.484295i	−0.595998	+	0.802986i	$0.703243\pi$
$48$	−1.35825	+	1.86947i	−0.196046	+	0.269834i
$49$	1.91472	+	5.89289i	0.273531	+	0.841842i
$50$	1.08727	+	9.59787i	0.153763	+	1.35734i
$51$	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	$-0.0927989\pi$
$53$	11.3842	+	3.69895i	1.56374	+	0.508090i	0.605936	+	0.795514i	$0.292799\pi$
$54$	−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	$0.799670\pi$
$60$	−1.08509	+	1.68577i	−0.140085	+	0.217632i
$61$	−2.55494	−	7.86329i	−0.327126	−	1.00679i	−0.970472	−	0.241215i	$-0.922454\pi$
$61$	−2.55494	−	7.86329i	−0.327126	−	1.00679i	0.643346	−	0.765576i	$-0.277546\pi$
$62$	−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
$70$	−3.86682	+	0.218323i	−0.462174	+	0.0260946i
$71$	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
$75$	1.27594	−	2.25182i	0.147333	−	0.260018i
$76$	10.7321			1.23105
$77$		0			0
$78$		−	4.24264i		−	0.480384i
$79$	1.68850	−	5.19667i	0.189971	−	0.584671i	−0.810027	−	0.586392i	$-0.800548\pi$
$79$	1.68850	−	5.19667i	0.189971	−	0.584671i	0.999999	+	0.00172104i	$0.000547824\pi$
$80$	−2.54456	+	9.65227i	−0.284490	+	1.07916i
$81$	−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
$85$	2.23847	+	0.590112i	0.242796	+	0.0640067i
$86$	−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	$0.388694\pi$
$90$	−11.0007	+	4.27387i	−1.15958	+	0.450505i
$91$	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
$95$	−13.8330	+	0.781018i	−1.41923	+	0.0801308i
$96$	−3.17798	+	2.30894i	−0.324352	+	0.235655i
$97$	−0.624215	−	0.202820i	−0.0633795	−	0.0205932i	0.277156	−	0.960825i	$-0.410608\pi$
$97$	−0.624215	−	0.202820i	−0.0633795	−	0.0205932i	−0.340535	+	0.940232i	$0.610608\pi$
$98$			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	−0.970178	−	0.242395i	$-0.922067\pi$
$101$	−0.430246	+	1.32416i	−0.0428111	+	0.131759i	0.927367	+	0.374154i	$0.122067\pi$
$102$	0.608520	+	0.837556i	0.0602525	+	0.0829304i
$103$	2.49376	−	3.43237i	0.245718	−	0.338201i	−0.668288	−	0.743903i	$-0.732973\pi$
$103$	2.49376	−	3.43237i	0.245718	−	0.338201i	0.914006	+	0.405701i	$0.132973\pi$
$104$	−0.678648	−	2.08867i	−0.0665470	−	0.204810i
$105$	0.872618	+	0.561685i	0.0851588	+	0.0548148i
$106$	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	$-0.481756\pi$
$109$	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	$-0.242473\pi$
$113$	−1.66251	−	2.28825i	−0.156396	−	0.215260i	−0.880023	+	0.474930i	$0.842473\pi$
$114$	−5.01279	−	3.64201i	−0.469491	−	0.341105i
$115$	−7.64062	+	11.8703i	−0.712491	+	1.10691i
$116$	−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
$125$	1.61500	−	11.0631i	0.144450	−	0.989512i
$126$	−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
$130$	−6.63695	−	17.0832i	−0.582099	−	1.49830i
$131$	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
$135$	6.41551	+	1.69128i	0.552160	+	0.145562i
$136$	0.433551	+	0.314993i	0.0371767	+	0.0270104i
$137$	−13.0896	+	4.25306i	−1.11832	+	0.363364i	−0.809126	−	0.587636i	$-0.800059\pi$
$137$	−13.0896	+	4.25306i	−1.11832	+	0.363364i	−0.309193	+	0.950999i	$0.600059\pi$
$138$	−6.00420	+	1.95088i	−0.511112	+	0.166070i
$139$	13.4203	+	9.75045i	1.13830	+	0.827022i	0.986881	−	0.161447i	$-0.0516162\pi$
$139$	13.4203	+	9.75045i	1.13830	+	0.827022i	0.151417	+	0.988470i	$0.451616\pi$
$140$	−3.35771	−	0.885168i	−0.283778	−	0.0748104i
$141$	0.656462	−	2.02038i	0.0552841	−	0.170147i
$142$			4.24264i			0.356034i
$143$		0			0
$144$	−12.1962			−1.01635
$145$	5.61021	+	14.4404i	0.465902	+	1.19921i
$146$	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	$0.0901553\pi$
$149$	4.24344	+	13.0600i	0.347636	+	1.06991i	−0.612522	+	0.790454i	$0.709845\pi$
$150$	3.68856	−	3.37557i	0.301170	−	0.275614i
$151$	5.01279	−	3.64201i	0.407935	−	0.296382i	−0.364830	−	0.931074i	$-0.618873\pi$
$151$	5.01279	−	3.64201i	0.407935	−	0.296382i	0.772765	+	0.634692i	$0.218873\pi$
$152$	−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	$-0.359984\pi$
$157$	−7.09550	−	9.76612i	−0.566282	−	0.779421i	−0.992108	+	0.125384i	$0.959984\pi$
$158$	6.20456	−	8.53985i	0.493609	−	0.679394i
$159$	−1.91472	−	5.89289i	−0.151847	−	0.467337i
$160$	−9.18432	+	14.2685i	−0.726085	+	1.12803i
$161$	−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	$-0.496052\pi$
$163$	−7.21729	−	2.34504i	−0.565302	−	0.183678i	−0.577705	+	0.816245i	$0.696052\pi$
$164$	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
$170$	3.76046	+	2.42052i	0.288414	+	0.185646i
$171$	−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	$0.403348\pi$
$180$	−10.5644	+	0.596470i	−0.787421	+	0.0444582i
$181$	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
$185$	13.9484	−	5.41905i	1.02550	−	0.398416i
$186$	5.26795			0.386265
$187$		0			0
$188$			7.10823i			0.518421i
$189$	−0.822064	+	2.53005i	−0.0597963	+	0.184034i
$190$	−25.8816	−	6.82298i	−1.87765	−	0.494991i
$191$	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
$195$	−1.25182	+	4.74851i	−0.0896445	+	0.340048i
$196$	−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	$0.477417\pi$
$200$	1.27594	−	2.25182i	0.0902225	−	0.159228i
$201$	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
$205$	−3.86682	+	0.218323i	−0.270071	+	0.0152483i
$206$	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	$-0.774920\pi$
$211$	3.43761	−	10.5799i	0.236655	−	0.728350i	0.996898	−	0.0787102i	$-0.0250802\pi$
$212$	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
$215$	12.9432	−	20.1082i	0.882718	−	1.37137i
$216$	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	$-0.137838\pi$
$223$	3.40654	+	4.68870i	0.228119	+	0.313979i	−0.679580	+	0.733602i	$0.737838\pi$
$224$	−5.50443	−	3.99920i	−0.367780	−	0.267208i
$225$	13.5734	−	1.53763i	0.904896	−	0.102509i
$226$	−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
$235$	−0.517297	−	9.16210i	−0.0337447	−	0.597669i
$236$	−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	−0.849482	−	0.527618i	$-0.823085\pi$
$239$	−9.43334	+	6.85373i	−0.610192	+	0.443331i	0.239290	+	0.970948i	$0.423085\pi$
$240$	4.81636	−	1.87119i	0.310895	−	0.120785i
$241$	−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
$245$	3.53184	−	13.3973i	0.225641	−	0.855922i
$246$	−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
$250$	9.57163	−	19.3621i	0.605363	−	1.22457i
$251$	−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
$255$	−0.433951	−	1.11697i	−0.0271751	−	0.0699474i
$256$	−15.6887	+	11.3985i	−0.980544	+	0.712407i
$257$	−2.93923	+	4.04550i	−0.183344	+	0.252351i	−0.890789	−	0.454417i	$-0.849848\pi$
$257$	−2.93923	+	4.04550i	−0.183344	+	0.252351i	0.707445	+	0.706768i	$0.249848\pi$
$258$	10.1711	−	3.30479i	0.633225	−	0.205747i
$259$	1.85410	+	5.70634i	0.115208	+	0.354575i
$260$	−0.926266	−	16.4055i	−0.0574446	−	1.01743i
$261$	−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	$0.694553\pi$
$270$	10.7776	+	6.93728i	0.655902	+	0.422190i
$271$	−3.66962	−	2.66613i	−0.222913	−	0.161956i	0.470724	−	0.882281i	$-0.343993\pi$
$271$	−3.66962	−	2.66613i	−0.222913	−	0.161956i	−0.693637	+	0.720325i	$0.743993\pi$
$272$	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
$280$	0.872618	+	0.561685i	0.0521489	+	0.0335671i
$281$	5.35233	+	16.4728i	0.319293	+	0.982684i	0.973951	+	0.226758i	$0.0728128\pi$
$281$	5.35233	+	16.4728i	0.319293	+	0.982684i	−0.654658	+	0.755925i	$0.727187\pi$
$282$	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
$290$	1.68707	+	29.8805i	0.0990682	+	1.75465i
$291$	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
$295$	3.83184	+	9.86299i	0.223099	+	0.574245i
$296$	3.46410			0.201347
$297$		0			0
$298$			26.5283i			1.53674i
$299$	8.27690	−	25.4737i	0.478665	−	1.47318i
$300$	4.08044	−	1.85639i	0.235584	−	0.107179i
$301$	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
$305$	−4.71277	+	17.8769i	−0.269852	+	1.02363i
$306$	−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
$310$	21.2116	−	8.24088i	1.20474	−	0.468051i
$311$	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	−0.731180	−	0.682185i	$-0.761030\pi$
$313$	−16.3072	+	5.29854i	−0.921739	+	0.299491i	−0.190559	+	0.981676i	$0.561030\pi$
$314$	−7.20643	−	22.1791i	−0.406683	−	1.25164i
$315$	0.308755	+	5.46852i	0.0173964	+	0.308116i
$316$	7.65662	−	5.56286i	0.430718	−	0.312935i
$317$	−6.62842	−	2.15370i	−0.372289	−	0.120964i	0.116896	−	0.993144i	$-0.462706\pi$
$317$	−6.62842	−	2.15370i	−0.372289	−	0.120964i	−0.489185	+	0.872180i	$0.662706\pi$
$318$		−	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
$325$	2.38781	+	21.0784i	0.132452	+	1.16922i
$326$	−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
$335$	18.0779	−	28.0853i	0.987701	−	1.53447i
$336$	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
$345$	7.29574	−	0.411921i	0.392789	−	0.0221771i
$346$	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	0.190612	−	0.981666i	$-0.438953\pi$
$349$	22.1028	−	16.0586i	1.18313	−	0.859597i	0.992522	+	0.122069i	$0.0389529\pi$
$350$	7.53475	+	4.26937i	0.402749	+	0.228208i
$351$	−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
$355$	1.25182	−	4.74851i	0.0664396	−	0.252025i
$356$	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	0.905901	−	0.423491i	$-0.139195\pi$
$359$	14.8372	+	10.7798i	0.783076	+	0.568938i	−0.122825	+	0.992428i	$0.539195\pi$
$360$	3.05781	+	0.806108i	0.161161	+	0.0424856i
$361$	5.99255	−	18.4432i	0.315397	−	0.970694i
$362$			6.55343i			0.344441i
$363$		0			0
$364$	6.58846			0.345329
$365$	−10.2109	+	3.96702i	−0.534464	+	0.207643i
$366$	−6.68891	+	4.85978i	−0.349635	+	0.254025i
$367$	−17.4185	+	23.9745i	−0.909238	+	1.25146i	0.0581882	+	0.998306i	$0.481468\pi$
$367$	−17.4185	+	23.9745i	−0.909238	+	1.25146i	−0.967426	+	0.253153i	$0.918532\pi$
$368$	−26.8034	+	8.70894i	−1.39722	+	0.453985i
$369$	−1.46228	−	4.50045i	−0.0761235	−	0.234284i
$370$	28.8624	−	1.62959i	1.50048	−	0.0847181i
$371$	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	$0.855182\pi$
$380$	−20.1787	−	12.9886i	−1.03515	−	0.666301i
$381$	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	$-0.607686\pi$
$383$	−22.6011	−	7.34355i	−1.15486	−	0.375238i	−0.822973	+	0.568080i	$0.807686\pi$
$384$	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	$0.851961\pi$
$390$	−5.13471	+	7.97714i	−0.260006	+	0.403938i
$391$	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
$400$	16.4661	−	15.0689i	0.823306	−	0.753445i
$401$	−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
$405$	5.39323	+	13.8819i	0.267992	+	0.689799i
$406$	−12.0000			−0.595550
$407$		0			0
$408$		−	0.277401i		−	0.0137334i
$409$	0.579606	−	1.78384i	0.0286597	−	0.0882054i	−0.935704	−	0.352787i	$-0.885234\pi$
$409$	0.579606	−	1.78384i	0.0286597	−	0.0882054i	0.964363	+	0.264582i	$0.0852339\pi$
$410$	−7.23485	−	1.90727i	−0.357304	−	0.0941935i
$411$	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
$415$	−21.4047	−	5.64276i	−1.05071	−	0.276992i
$416$	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	$0.242071\pi$
$420$	0.650927	+	1.67545i	0.0317620	+	0.0817538i
$421$	−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
$425$	−3.49465	−	3.81868i	−0.169515	−	0.185233i
$426$	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	$0.250672\pi$
$431$	−5.84914	+	18.0018i	−0.281743	+	0.867116i	−0.987356	+	0.158518i	$0.949328\pi$
$432$	7.78554	+	10.7159i	0.374582	+	0.515568i
$433$	11.9040	−	16.3844i	0.572069	−	0.787385i	−0.420729	−	0.907186i	$-0.638226\pi$
$433$	11.9040	−	16.3844i	0.572069	−	0.787385i	0.992798	+	0.119801i	$0.0382257\pi$
$434$	2.81958	+	8.67778i	0.135344	+	0.416547i
$435$	4.34037	−	6.74307i	0.208105	−	0.323306i
$436$	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	$-0.130031\pi$
$443$	5.39515	+	7.42579i	0.256332	+	0.352810i	−0.661385	+	0.750047i	$0.730031\pi$
$444$	4.85410	+	3.52671i	0.230365	+	0.167370i
$445$	−12.1540	−	7.82326i	−0.576155	−	0.370858i
$446$	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
$455$	−8.49214	+	0.479471i	−0.398118	+	0.0224779i
$456$	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
$460$	−22.7913	+	8.85458i	−1.06265	+	0.412847i
$461$	−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
$465$	−5.89608	−	1.55434i	−0.273424	−	0.0720808i
$466$	−20.3260	−	14.7677i	−0.941585	−	0.684102i
$467$	−16.8961	+	5.48987i	−0.781858	+	0.254041i	−0.672633	−	0.739976i	$-0.734837\pi$
$467$	−16.8961	+	5.48987i	−0.781858	+	0.254041i	−0.109225	+	0.994017i	$0.534837\pi$
$468$	19.0938	−	6.20395i	0.882610	−	0.286778i
$469$	10.8346	+	7.87180i	0.500295	+	0.363486i
$470$	4.51911	−	17.1423i	0.208451	−	0.790717i
$471$	−1.93096	+	5.94288i	−0.0889738	+	0.273833i
$472$			2.44949i			0.112747i
$473$		0			0
$474$	−5.46410			−0.250974
$475$	26.9544	+	15.2730i	1.23675	+	0.700775i
$476$	−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	0.861747	−	0.507338i	$-0.169371\pi$
$479$	−2.92457	−	9.00090i	−0.133627	−	0.411261i	−0.995374	+	0.0960769i	$0.969371\pi$
$480$	8.76976	−	0.495146i	0.400283	−	0.0226002i
$481$	−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	$-0.106884\pi$
$487$	7.48128	+	10.2971i	0.339009	+	0.466606i	−0.605142	+	0.796117i	$0.706884\pi$
$488$	−2.51561	+	3.46244i	−0.113876	+	0.156737i
$489$	1.21388	+	3.73594i	0.0548936	+	0.168945i
$490$	14.4869	−	22.5064i	0.654451	−	1.01674i
$491$	12.7119	+	9.23576i	0.573681	+	0.416804i	0.836441	−	0.548057i	$-0.184632\pi$
$491$	12.7119	+	9.23576i	0.573681	+	0.416804i	−0.262759	+	0.964861i	$0.584632\pi$
$492$	−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	$0.370876\pi$
$500$	13.5261	−	13.8580i	0.604904	−	0.619751i
$501$	−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	$0.461535\pi$
$510$	−0.130495	−	2.31127i	−0.00577843	−	0.102345i
$511$	−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
$515$	−8.84291	+	3.43554i	−0.389665	+	0.151388i
$516$	9.58846			0.422108
$517$		0			0
$518$			11.5911i			0.509284i
$519$	1.21983	−	3.75424i	0.0535444	−	0.164793i
$520$	−1.25182	+	4.74851i	−0.0548958	+	0.208236i
$521$	−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
$525$	−0.960937	−	2.11219i	−0.0419387	−	0.0921837i
$526$	12.8294	−	39.4847i	0.559386	−	1.72161i
$527$		−	5.45378i		−	0.237570i
$528$		0			0
$529$	−16.8564			−0.732887
$530$	−18.7253	−	48.1980i	−0.813374	−	2.09359i
$531$	−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
$535$	0.552263	+	9.78140i	0.0238764	+	0.422887i
$536$	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	$0.267718\pi$
$541$	−7.22862	+	22.2474i	−0.310783	+	0.956491i	−0.977456	+	0.211140i	$0.932282\pi$
$542$	−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
$545$	−2.24904	−	1.44766i	−0.0963384	−	0.0620109i
$546$	−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
$555$	−6.51331	−	4.19247i	−0.276475	−	0.177960i
$556$	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
$565$	0.356520	+	6.31450i	0.0149989	+	0.265653i
$566$	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	−0.483672	−	0.875249i	$-0.660697\pi$
$569$	4.75350	−	3.45362i	0.199277	−	0.144783i	0.682949	+	0.730466i	$0.260697\pi$
$570$	5.01742	+	12.9146i	0.210157	+	0.540933i
$571$	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
$575$	28.7322	−	13.0717i	1.19822	−	0.545126i
$576$	−12.6694	−	9.20487i	−0.527892	−	0.383536i
$577$	19.7180	−	6.40677i	0.820871	−	0.266717i	0.131676	−	0.991293i	$-0.457964\pi$
$577$	19.7180	−	6.40677i	0.820871	−	0.266717i	0.689195	+	0.724576i	$0.257964\pi$
$578$	−29.2649	+	9.50874i	−1.21726	+	0.395511i
$579$	4.30438	+	3.12732i	0.178884	+	0.129967i
$580$	−6.84006	+	25.9464i	−0.284018	+	1.07736i
$581$	2.74272	−	8.44124i	0.113787	−	0.350202i
$582$			0.656339i			0.0272061i
$583$		0			0
$584$	−2.53590			−0.104936
$585$	−24.1593	+	9.38606i	−0.998863	+	0.388066i
$586$	−14.7210	+	10.6954i	−0.608119	+	0.441824i
$587$	−21.1293	+	29.0820i	−0.872099	+	1.20034i	0.106448	+	0.994318i	$0.466052\pi$
$587$	−21.1293	+	29.0820i	−0.872099	+	1.20034i	−0.978547	+	0.206024i	$0.933948\pi$
$588$	5.28342	−	1.71669i	0.217885	−	0.0707950i
$589$	10.0866	+	31.0435i	0.415612	+	1.27912i
$590$	1.15229	+	20.4088i	0.0474391	+	0.840216i
$591$	−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	$-0.237156\pi$
$600$	−1.33123	+	0.150805i	−0.0543473	+	0.00615658i
$601$	−16.1803	−	11.7557i	−0.660010	−	0.479525i	0.206656	−	0.978414i	$-0.433742\pi$
$601$	−16.1803	−	11.7557i	−0.660010	−	0.479525i	−0.866666	+	0.498888i	$0.833742\pi$
$602$	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
$610$	−19.3309	+	30.0319i	−0.782683	+	1.21596i
$611$	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	$0.0108408\pi$
$617$			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	−0.947453	−	0.319896i	$-0.896352\pi$
$619$	−23.2872	+	16.9192i	−0.935993	+	0.680039i	0.0114597	+	0.999934i	$0.496352\pi$
$620$	20.3702	−	1.15011i	0.818088	−	0.0461897i
$621$	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
$625$	−16.4258	+	18.8466i	−0.657032	+	0.753863i
$626$	−33.1244			−1.32392
$627$		0			0
$628$		−	20.9086i		−	0.834344i
$629$	2.14093	−	6.58911i	0.0853646	−	0.262725i
$630$	−2.69729	+	10.2316i	−0.107463	+	0.407638i
$631$	−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
$635$	7.23485	+	1.90727i	0.287106	+	0.0756878i
$636$	3.31639	−	10.2068i	0.131503	−	0.404725i
$637$			26.2880i			1.04157i
$638$		0			0
$639$	6.00000			0.237356
$640$	8.55382	−	3.32322i	0.338119	−	0.131362i
$641$	−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	0.259814	−	0.965659i	$-0.416339\pi$
$643$	26.3111	−	8.54899i	1.03761	−	0.337139i	0.777794	+	0.628520i	$0.216339\pi$
$644$	−3.02956	−	9.32401i	−0.119381	−	0.367418i
$645$	−12.3590	+	0.697794i	−0.486634	+	0.0274756i
$646$	−10.0256	+	7.28401i	−0.394451	+	0.286586i
$647$	−18.0480	−	5.86414i	−0.709538	−	0.230543i	−0.0680568	−	0.997681i	$-0.521680\pi$
$647$	−18.0480	−	5.86414i	−0.709538	−	0.230543i	−0.641482	+	0.767138i	$0.721680\pi$
$648$			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	$0.414922\pi$
$653$	−18.7767	+	25.8440i	−0.734791	+	1.01135i	−0.998901	+	0.0468603i	$0.985078\pi$
$654$	−0.369631	−	1.13761i	−0.0144537	−	0.0444840i
$655$	−39.7187	−	25.5660i	−1.55194	−	0.998947i
$656$	−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
$665$	−6.72339	+	10.4453i	−0.260722	+	0.405050i
$666$	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
$675$	−10.0158	−	10.9444i	−0.385507	−	0.421252i
$676$	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
$680$	−0.433951	−	1.11697i	−0.0166413	−	0.0428338i
$681$	−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
$685$	29.7587	+	7.84509i	1.13702	+	0.299745i
$686$	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
$690$	13.6504	+	3.59855i	0.519661	+	0.136994i
$691$	−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
$695$	−13.4327	−	34.5752i	−0.509533	−	1.31151i
$696$	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
$700$	5.24197	+	5.72803i	0.198128	+	0.216499i
$701$	−8.20634	+	5.96225i	−0.309949	+	0.225191i	−0.731875	−	0.681439i	$-0.761354\pi$
$701$	−8.20634	+	5.96225i	−0.309949	+	0.225191i	0.421926	+	0.906630i	$0.361354\pi$
$702$	−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	$-0.244759\pi$
$710$	5.13471	−	7.97714i	0.192702	−	0.299377i
$711$	−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	$0.966225\pi$
$720$	22.9316	+	14.7605i	0.854609	+	0.550093i
$721$	−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
$730$	−21.1287	+	1.19294i	−0.782009	+	0.0441527i
$731$	−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
$735$	−6.68509	+	2.59721i	−0.246583	+	0.0957995i
$736$	−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	$-0.747440\pi$
$739$	7.74761	−	23.8447i	0.285000	−	0.877141i	0.986399	−	0.164371i	$-0.0525596\pi$
$740$	25.0623	+	6.60699i	0.921307	+	0.242878i
$741$	−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
$745$	7.82733	−	29.6914i	0.286771	−	1.08781i
$746$	20.3670	−	62.6832i	0.745688	−	2.29499i
$747$		−	27.0459i		−	0.989559i
$748$		0			0
$749$	−3.92820			−0.143533
$750$	−11.0207	+	1.88272i	−0.402418	+	0.0687473i
$751$	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
$755$	−13.8330	+	0.781018i	−0.503434	+	0.0284242i
$756$	−3.72770	+	2.70834i	−0.135575	+	0.0985012i
$757$	33.3611	+	10.8397i	1.21253	+	0.393975i	0.844356	−	0.535782i	$-0.179983\pi$
$757$	33.3611	+	10.8397i	1.21253	+	0.393975i	0.368174	+	0.929757i	$0.379983\pi$
$758$			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	−0.897362	−	0.441296i	$-0.854519\pi$
$761$	2.42776	−	7.47189i	0.0880063	−	0.270856i	0.985368	+	0.170440i	$0.0545190\pi$
$762$	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
$765$	3.42314	−	5.31809i	0.123764	−	0.192276i
$766$	−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	−0.845852	−	0.533418i	$-0.820907\pi$
$773$	−30.3546	−	41.7795i	−1.09178	−	1.50271i	−0.245928	−	0.969288i	$-0.579093\pi$
$774$	45.6649	+	33.1775i	1.64139	+	1.19254i
$775$	−26.1723	+	2.96486i	−0.940139	+	0.106501i
$776$	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
$785$	1.52161	+	26.9500i	0.0543086	+	0.961885i
$786$	−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
$790$	−22.0015	+	8.54773i	−0.782777	+	0.304115i
$791$	−2.53590			−0.0901662
$792$		0			0
$793$		−	35.0779i		−	1.24565i
$794$	−9.55734	+	29.4145i	−0.339177	+	1.04388i
$795$	−3.53184	+	13.3973i	−0.125261	+	0.475153i
$796$	2.80252	+	2.03615i	0.0993326	+	0.0721693i
$797$	−7.51646	+	2.44225i	−0.266247	+	0.0865088i	−0.439098	−	0.898439i	$-0.644702\pi$
$797$	−7.51646	+	2.44225i	−0.266247	+	0.0865088i	0.172851	+	0.984948i	$0.444702\pi$
$798$	−5.28342	+	1.71669i	−0.187031	+	0.0607701i
$799$	−3.43728	−	2.49733i	−0.121602	−	0.0883492i
$800$	34.5373	−	15.7127i	1.22108	−	0.555526i
$801$	5.45732	−	16.7959i	0.192825	−	0.593454i
$802$		−	62.4384i		−	2.20478i
$803$		0			0
$804$	13.3923			0.472310
$805$	4.58347	+	11.7976i	0.161546	+	0.415812i
$806$	−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	$0.0231539\pi$
$809$	6.63277	+	20.4136i	0.233196	+	0.717703i	−0.764160	+	0.645027i	$0.776846\pi$
$810$	1.62182	+	28.7249i	0.0569851	+	1.00929i
$811$	26.6820	−	19.3856i	0.936932	−	0.680721i	−0.0107485	−	0.999942i	$-0.503421\pi$
$811$	26.6820	−	19.3856i	0.936932	−	0.680721i	0.947680	+	0.319222i	$0.103421\pi$
$812$	−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
$820$	−5.64069	−	3.63079i	−0.196981	−	0.126793i
$821$	−15.2126	−	11.0526i	−0.530925	−	0.385739i	0.289779	−	0.957094i	$-0.406418\pi$
$821$	−15.2126	−	11.0526i	−0.530925	−	0.385739i	−0.820703	+	0.571354i	$0.806418\pi$
$822$	8.08980	+	11.1347i	0.282164	+	0.388366i
$823$	−46.0291	−	14.9558i	−1.60447	−	0.521325i	−0.636264	−	0.771471i	$-0.719521\pi$
$823$	−46.0291	−	14.9558i	−1.60447	−	0.521325i	−0.968208	+	0.250146i	$0.919521\pi$
$824$	−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	$0.439973\pi$
$830$	−35.9582	−	23.1455i	−1.24813	−	0.803391i
$831$	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	$0.284694\pi$
$840$	−0.0302816	−	0.536331i	−0.00104481	−	0.0185052i
$841$	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
$845$	−4.04882	−	10.4215i	−0.139284	−	0.358510i
$846$	21.6603			0.744695
$847$		0			0
$848$		−	53.4355i		−	1.83498i
$849$	4.81710	−	14.8255i	0.165322	−	0.508810i
$850$	−4.14106	−	9.10229i	−0.142037	−	0.312206i
$851$	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
$855$	−9.64915	+	36.6021i	−0.329994	+	1.25177i
$856$	−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	$0.435460\pi$
$860$	38.6084	−	14.9996i	1.31653	−	0.511484i
$861$	−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	$-0.653127\pi$
$863$	−9.28307	+	3.01625i	−0.315999	+	0.102674i	0.146723	+	0.989178i	$0.453127\pi$
$864$	6.95803	+	21.4146i	0.236717	+	0.728540i
$865$	−0.961232	−	17.0249i	−0.0326829	−	0.578862i
$866$	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
$875$	−7.17345	−	7.00161i	−0.242507	−	0.236698i
$876$	−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	$-0.909463\pi$
$883$	−27.6381	−	38.0406i	−0.930097	−	1.28017i	0.0297250	−	0.999558i	$-0.490537\pi$
$884$	−6.15475	−	4.47169i	−0.207007	−	0.150399i
$885$	2.96452	−	4.60560i	0.0996514	−	0.154816i
$886$	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
$895$	19.0565	−	1.07594i	0.636989	−	0.0359647i
$896$	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
$900$	20.5853	+	11.6641i	0.686177	+	0.388805i
$901$	−12.3923			−0.412848
$902$		0			0
$903$		−	4.96335i		−	0.165170i
$904$	−0.452432	+	1.39244i	−0.0150477	+	0.0463120i
$905$	1.93363	−	7.33483i	0.0642760	−	0.243818i
$906$	−5.01279	−	3.64201i	−0.166539	−	0.120998i
$907$	−7.67425	+	2.49351i	−0.254819	+	0.0827958i	−0.433641	−	0.901086i	$-0.642771\pi$
$907$	−7.67425	+	2.49351i	−0.254819	+	0.0827958i	0.178822	+	0.983881i	$0.442771\pi$
$908$	35.4622	−	11.5224i	1.17686	−	0.382383i
$909$	3.07738	+	2.23585i	0.102070	+	0.0741583i
$910$	−15.8888	−	4.18866i	−0.526710	−	0.138853i
$911$	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
$915$	8.92037	−	3.46563i	0.294898	−	0.114570i
$916$	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	$-0.916921\pi$
$919$	−10.1916	−	31.3666i	−0.336190	−	1.03469i	0.629942	−	0.776642i	$-0.283079\pi$
$920$	7.29574	−	0.411921i	0.240533	−	0.0135806i
$921$	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	$0.814685\pi$
$930$	−9.90496	−	6.37560i	−0.324796	−	0.209064i
$931$	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
$940$	8.60283	−	13.3651i	0.280593	−	0.435922i
$941$	−8.34346	−	25.6785i	−0.271989	−	0.837096i	−0.990000	−	0.141065i	$-0.954947\pi$
$941$	−8.34346	−	25.6785i	−0.271989	−	0.837096i	0.718011	−	0.696031i	$-0.245053\pi$
$942$	−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
$950$	40.4058	+	44.1523i	1.31094	+	1.43249i
$951$	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
$955$	−8.69043	−	22.3688i	−0.281216	−	0.723836i
$956$	−20.1962			−0.653190
$957$		0			0
$958$		−	18.2832i		−	0.590705i
$959$	−3.81319	+	11.7358i	−0.123134	+	0.378969i
$960$	6.41551	+	1.69128i	0.207060	+	0.0545857i
$961$	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
$965$	22.2240	+	5.85875i	0.715416	+	0.188600i
$966$	−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
$970$	1.02674	+	2.64278i	0.0329666	+	0.0848545i
$971$	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
$975$	8.10065	−	7.41327i	0.259428	−	0.237415i
$976$	−29.8600	+	21.6945i	−0.955795	+	0.694425i
$977$	−14.2414	−	4.62733i	−0.455624	−	0.148041i	0.0722087	−	0.997390i	$-0.476995\pi$
$977$	−14.2414	−	4.62733i	−0.455624	−	0.148041i	−0.527833	+	0.849348i	$0.676995\pi$
$978$			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	$-0.723050\pi$
$983$	8.82354	−	12.1446i	0.281427	−	0.387351i	0.926206	+	0.377018i	$0.123050\pi$
$984$	0.143415	+	0.441387i	0.00457191	+	0.0140709i
$985$	−3.08741	+	4.79652i	−0.0983731	+	0.152830i
$986$	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
$995$	−3.76046	−	2.42052i	−0.119215	−	0.0767358i
$996$	−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.f.9.4		16
5.4	even	2	inner	605.2.j.f.9.1		16
11.2	odd	10		605.2.j.e.124.4		16
11.3	even	5	inner	605.2.j.f.444.4		16
11.4	even	5		605.2.b.d.364.4	yes	4
11.5	even	5	inner	605.2.j.f.269.1		16
11.6	odd	10		605.2.j.e.269.4		16
11.7	odd	10		605.2.b.e.364.1	yes	4
11.8	odd	10		605.2.j.e.444.1		16
11.9	even	5	inner	605.2.j.f.124.1		16
11.10	odd	2		605.2.j.e.9.1		16
55.4	even	10		605.2.b.d.364.1	✓	4
55.7	even	20		3025.2.a.z.1.4		4
55.9	even	10	inner	605.2.j.f.124.4		16
55.14	even	10	inner	605.2.j.f.444.1		16
55.18	even	20		3025.2.a.z.1.1		4
55.19	odd	10		605.2.j.e.444.4		16
55.24	odd	10		605.2.j.e.124.1		16
55.29	odd	10		605.2.b.e.364.4	yes	4
55.37	odd	20		3025.2.a.y.1.1		4
55.39	odd	10		605.2.j.e.269.1		16
55.48	odd	20		3025.2.a.y.1.4		4
55.49	even	10	inner	605.2.j.f.269.4		16
55.54	odd	2		605.2.j.e.9.4		16

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

\(f(q)\)	\(=\)	\(q+(1.83730 + 0.596975i) q^{2} +(-0.304260 - 0.418778i) q^{3} +(1.40126 + 1.01807i) q^{4} +(-1.88023 - 1.21026i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(0.526994 - 0.725345i) q^{7} +(-0.304260 - 0.418778i) q^{8} +(0.844250 - 2.59833i) q^{9} +O(q^{10})\)	\(q+(1.83730 + 0.596975i) q^{2} +(-0.304260 - 0.418778i) q^{3} +(1.40126 + 1.01807i) q^{4} +(-1.88023 - 1.21026i) 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} +(0.0652477 + 1.15563i) 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} +(-1.40255 - 3.61010i) q^{20} -0.464102 q^{21} -6.31319i q^{23} +(-0.0828009 + 0.254835i) q^{24} +(2.07053 + 4.55114i) 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} +(-0.570005 + 2.16220i) q^{30} +(-1.62789 + 5.01012i) q^{31} -7.58871i q^{32} -2.00000 q^{34} +(-1.86873 + 0.726014i) 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} +(0.0652477 + 1.15563i) 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} +(1.08727 + 9.59787i) 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} +(-1.08509 + 1.68577i) 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} +(-3.86682 + 0.218323i) 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} +(1.27594 - 2.25182i) q^{75} +10.7321 q^{76} -4.24264i q^{78} +(1.68850 - 5.19667i) q^{79} +(-2.54456 + 9.65227i) 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} +(2.23847 + 0.590112i) q^{85} +(-6.38437 + 19.6491i) q^{86} +3.58630i q^{87} +6.46410 q^{89} +(-11.0007 + 4.27387i) 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} +(-13.8330 + 0.781018i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more