LMFDB - Embedded newform 1890.2.bk.a.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(341,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 5]))

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

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

chi := DirichletCharacter("1890.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bk (of order $6$, degree $2$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1890.521
Dual form			1890.2.bk.a.341.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +(-1.09808 + 0.633975i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(4.09808 - 2.36603i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.633975 + 1.09808i) q^{22} +(8.19615 + 4.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} +(2.50000 - 0.866025i) q^{28} +(0.401924 + 0.232051i) q^{29} -2.19615i q^{31} -1.00000i q^{32} +(-0.500000 + 2.59808i) q^{35} +(2.09808 + 3.63397i) q^{37} +(-2.36603 - 4.09808i) q^{38} +(0.866025 + 0.500000i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(3.59808 - 6.23205i) q^{43} +(1.09808 - 0.633975i) q^{44} +(4.73205 - 8.19615i) q^{46} +9.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(9.29423 + 5.36603i) q^{53} +1.26795i q^{55} +(-0.866025 - 2.50000i) q^{56} +(0.232051 - 0.401924i) q^{58} +8.19615 q^{59} -0.928203i q^{61} -2.19615 q^{62} -1.00000 q^{64} +3.46410i q^{65} -4.00000 q^{67} +(2.59808 + 0.500000i) q^{70} +1.26795i q^{71} +(6.00000 + 3.46410i) q^{73} +(3.63397 - 2.09808i) q^{74} +(-4.09808 + 2.36603i) q^{76} +(2.19615 - 2.53590i) q^{77} -16.5885 q^{79} +(0.500000 - 0.866025i) q^{80} +(-7.79423 + 4.50000i) q^{82} +(0.401924 - 0.696152i) q^{83} +(-6.23205 - 3.59808i) q^{86} +(-0.633975 - 1.09808i) q^{88} +(8.19615 + 14.1962i) q^{89} +(6.00000 - 6.92820i) q^{91} +(-8.19615 - 4.73205i) q^{92} -9.00000i q^{94} -4.73205i q^{95} +(13.3923 + 7.73205i) q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7	$ 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7} + 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 10 q^{28} + 12 q^{29} - 2 q^{35} - 2 q^{37} - 6 q^{38} - 18 q^{41} + 4 q^{43} - 6 q^{44} + 12 q^{46} + 36 q^{47} + 22 q^{49} + 12 q^{52} + 6 q^{53} - 6 q^{58} + 12 q^{59} + 12 q^{62} - 4 q^{64} - 16 q^{67} + 24 q^{73} + 18 q^{74} - 6 q^{76} - 12 q^{77} - 4 q^{79} + 2 q^{80} + 12 q^{83} - 18 q^{86} - 6 q^{88} + 12 q^{89} + 24 q^{91} - 12 q^{92} + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7 + 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 10 * q^28 + 12 * q^29 - 2 * q^35 - 2 * q^37 - 6 * q^38 - 18 * q^41 + 4 * q^43 - 6 * q^44 + 12 * q^46 + 36 * q^47 + 22 * q^49 + 12 * q^52 + 6 * q^53 - 6 * q^58 + 12 * q^59 + 12 * q^62 - 4 * q^64 - 16 * q^67 + 24 * q^73 + 18 * q^74 - 6 * q^76 - 12 * q^77 - 4 * q^79 + 2 * q^80 + 12 * q^83 - 18 * q^86 - 6 * q^88 + 12 * q^89 + 24 * q^91 - 12 * q^92 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	−0.656322	−	0.754481i	$-0.727889\pi$
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	0.325239	+	0.945632i	$0.394555\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	0.866025	+	2.50000i	0.231455	+	0.668153i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	0.633975	+	1.09808i	0.135164	+	0.234111i
$23$	8.19615	+	4.73205i	1.70902	+	0.986701i	0.935781	+	0.352581i	$0.114696\pi$
$23$	8.19615	+	4.73205i	1.70902	+	0.986701i	0.773234	+	0.634120i	$0.218638\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.73205	+	3.00000i	0.339683	+	0.588348i
$27$		0			0
$28$	2.50000	−	0.866025i	0.472456	−	0.163663i
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	0.536853	−	0.843676i	$-0.319613\pi$
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	−0.462218	+	0.886766i	$0.652946\pi$
$30$		0			0
$31$		−	2.19615i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$31$		−	2.19615i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		0			0
$35$	−0.500000	+	2.59808i	−0.0845154	+	0.439155i
$36$		0			0
$37$	2.09808	+	3.63397i	0.344922	+	0.597422i	0.985340	−	0.170605i	$-0.0545722\pi$
$37$	2.09808	+	3.63397i	0.344922	+	0.597422i	−0.640418	+	0.768027i	$0.721239\pi$
$38$	−2.36603	−	4.09808i	−0.383820	−	0.664796i
$39$		0			0
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	−0.449662	−	0.893199i	$-0.648456\pi$
$43$	3.59808	−	6.23205i	0.548701	−	0.950379i	0.998364	−	0.0571802i	$-0.0182110\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$		0			0
$46$	4.73205	−	8.19615i	0.697703	−	1.20846i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$	9.29423	+	5.36603i	1.27666	+	0.737080i	0.976233	−	0.216724i	$-0.0695373\pi$
$53$	9.29423	+	5.36603i	1.27666	+	0.737080i	0.300428	+	0.953805i	$0.402871\pi$
$54$		0			0
$55$			1.26795i			0.170970i
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$		0			0
$58$	0.232051	−	0.401924i	0.0304698	−	0.0527752i
$59$	8.19615			1.06705			0.533524	−	0.845785i	$-0.320867\pi$
$59$	8.19615			1.06705			0.533524	+	0.845785i	$0.320867\pi$
$60$		0			0
$61$		−	0.928203i		−	0.118844i	−0.998233	−	0.0594221i	$-0.981074\pi$
$61$		−	0.928203i		−	0.118844i	0.998233	−	0.0594221i	$-0.0189258\pi$
$62$	−2.19615			−0.278912
$63$		0			0
$64$	−1.00000			−0.125000
$65$			3.46410i			0.429669i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$		0			0
$70$	2.59808	+	0.500000i	0.310530	+	0.0597614i
$71$			1.26795i			0.150478i	0.997166	+	0.0752389i	$0.0239720\pi$
$71$			1.26795i			0.150478i	−0.997166	+	0.0752389i	$0.976028\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$	3.63397	−	2.09808i	0.422441	−	0.243896i
$75$		0			0
$76$	−4.09808	+	2.36603i	−0.470082	+	0.271402i
$77$	2.19615	−	2.53590i	0.250275	−	0.288992i
$78$		0			0
$79$	−16.5885			−1.86635			−0.933174	−	0.359426i	$-0.882973\pi$
$79$	−16.5885			−1.86635			−0.933174	+	0.359426i	$0.882973\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−7.79423	+	4.50000i	−0.860729	+	0.496942i
$83$	0.401924	−	0.696152i	0.0441169	−	0.0764127i	−0.843124	−	0.537720i	$-0.819286\pi$
$83$	0.401924	−	0.696152i	0.0441169	−	0.0764127i	0.887241	+	0.461307i	$0.152619\pi$
$84$		0			0
$85$		0			0
$86$	−6.23205	−	3.59808i	−0.672019	−	0.387991i
$87$		0			0
$88$	−0.633975	−	1.09808i	−0.0675819	−	0.117055i
$89$	8.19615	+	14.1962i	0.868790	+	1.50479i	0.863234	+	0.504805i	$0.168435\pi$
$89$	8.19615	+	14.1962i	0.868790	+	1.50479i	0.00555677	+	0.999985i	$0.498231\pi$
$90$		0			0
$91$	6.00000	−	6.92820i	0.628971	−	0.726273i
$92$	−8.19615	−	4.73205i	−0.854508	−	0.493350i
$93$		0			0
$94$		−	9.00000i		−	0.928279i
$95$		−	4.73205i		−	0.485498i
$96$		0			0
$97$	13.3923	+	7.73205i	1.35978	+	0.785071i	0.989594	−	0.143886i	$-0.0459598\pi$
$97$	13.3923	+	7.73205i	1.35978	+	0.785071i	0.370188	+	0.928957i	$0.379293\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	0.885329	−	0.464965i	$-0.153933\pi$
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	−0.845336	+	0.534235i	$0.820600\pi$
$102$		0			0
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.116298	−	0.993214i	$-0.537103\pi$
$103$	−10.5000	−	6.06218i	−1.03460	−	0.597324i	−0.918298	+	0.395890i	$0.870436\pi$
$104$	−1.73205	−	3.00000i	−0.169842	−	0.294174i
$105$		0			0
$106$	5.36603	−	9.29423i	0.521194	−	0.902735i
$107$	−1.79423	+	1.03590i	−0.173455	+	0.100144i	−0.584214	−	0.811600i	$-0.698597\pi$
$107$	−1.79423	+	1.03590i	−0.173455	+	0.100144i	0.410759	+	0.911744i	$0.365264\pi$
$108$		0			0
$109$	−1.59808	+	2.76795i	−0.153068	+	0.265121i	−0.932354	−	0.361547i	$-0.882249\pi$
$109$	−1.59808	+	2.76795i	−0.153068	+	0.265121i	0.779286	+	0.626669i	$0.215582\pi$
$110$	1.26795			0.120894
$111$		0			0
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	16.0981	−	9.29423i	1.51438	−	0.874327i	0.514522	−	0.857477i	$-0.327970\pi$
$113$	16.0981	−	9.29423i	1.51438	−	0.874327i	0.999858	−	0.0168501i	$-0.00536380\pi$
$114$		0			0
$115$	8.19615	−	4.73205i	0.764295	−	0.441266i
$116$	−0.401924	−	0.232051i	−0.0373177	−	0.0215454i
$117$		0			0
$118$		−	8.19615i		−	0.754517i
$119$		0			0
$120$		0			0
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$	−0.928203			−0.0840356
$123$		0			0
$124$			2.19615i			0.197220i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.39230			0.833432			0.416716	−	0.909037i	$-0.363181\pi$
$127$	9.39230			0.833432			0.416716	+	0.909037i	$0.363181\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	3.46410			0.303822
$131$	8.19615	−	14.1962i	0.716101	−	1.24032i	−0.246432	−	0.969160i	$-0.579258\pi$
$131$	8.19615	−	14.1962i	0.716101	−	1.24032i	0.962533	−	0.271164i	$-0.0874084\pi$
$132$		0			0
$133$	−8.19615	+	9.46410i	−0.710697	+	0.820642i
$134$			4.00000i			0.345547i
$135$		0			0
$136$		0			0
$137$	9.29423	−	5.36603i	0.794060	−	0.458450i	−0.0473302	−	0.998879i	$-0.515071\pi$
$137$	9.29423	−	5.36603i	0.794060	−	0.458450i	0.841390	+	0.540429i	$0.181738\pi$
$138$		0			0
$139$	−13.9019	+	8.02628i	−1.17915	+	0.680780i	−0.955817	−	0.293963i	$-0.905026\pi$
$139$	−13.9019	+	8.02628i	−1.17915	+	0.680780i	−0.223329	+	0.974743i	$0.571692\pi$
$140$	0.500000	−	2.59808i	0.0422577	−	0.219578i
$141$		0			0
$142$	1.26795			0.106404
$143$	2.19615	−	3.80385i	0.183651	−	0.318094i
$144$		0			0
$145$	0.401924	−	0.232051i	0.0333780	−	0.0192708i
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$		0			0
$148$	−2.09808	−	3.63397i	−0.172461	−	0.298711i
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	0.861113	−	0.508413i	$-0.169768\pi$
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	−0.00974235	+	0.999953i	$0.503101\pi$
$150$		0			0
$151$	−3.09808	−	5.36603i	−0.252118	−	0.436681i	0.711991	−	0.702189i	$-0.247794\pi$
$151$	−3.09808	−	5.36603i	−0.252118	−	0.436681i	−0.964109	+	0.265508i	$0.914460\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$		0			0
$154$	−2.53590	−	2.19615i	−0.204349	−	0.176971i
$155$	−1.90192	−	1.09808i	−0.152766	−	0.0881996i
$156$		0			0
$157$			0.339746i			0.0271147i	0.999908	+	0.0135573i	$0.00431557\pi$
$157$			0.339746i			0.0271147i	−0.999908	+	0.0135573i	$0.995684\pi$
$158$			16.5885i			1.31971i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−24.5885	−	4.73205i	−1.93784	−	0.372938i
$162$		0			0
$163$	−6.19615	−	10.7321i	−0.485320	−	0.840599i	0.514538	−	0.857468i	$-0.327964\pi$
$163$	−6.19615	−	10.7321i	−0.485320	−	0.840599i	−0.999858	+	0.0168687i	$0.994630\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−0.696152	−	0.401924i	−0.0540319	−	0.0311953i
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	0.591888	−	0.806020i	$-0.298383\pi$
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	−0.993978	+	0.109580i	$0.965050\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$	−3.59808	+	6.23205i	−0.274351	+	0.475189i
$173$	2.19615			0.166970			0.0834852	−	0.996509i	$-0.473395\pi$
$173$	2.19615			0.166970			0.0834852	+	0.996509i	$0.473395\pi$
$174$		0			0
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$	−1.09808	+	0.633975i	−0.0827706	+	0.0477876i
$177$		0			0
$178$	14.1962	−	8.19615i	1.06405	−	0.614328i
$179$	5.70577	+	3.29423i	0.426469	+	0.246222i	0.697841	−	0.716252i	$-0.254144\pi$
$179$	5.70577	+	3.29423i	0.426469	+	0.246222i	−0.271372	+	0.962475i	$0.587477\pi$
$180$		0			0
$181$		−	7.39230i		−	0.549466i	−0.961521	−	0.274733i	$-0.911411\pi$
$181$		−	7.39230i		−	0.549466i	0.961521	−	0.274733i	$-0.0885894\pi$
$182$	−6.92820	−	6.00000i	−0.513553	−	0.444750i
$183$		0			0
$184$	−4.73205	+	8.19615i	−0.348851	+	0.604228i
$185$	4.19615			0.308507
$186$		0			0
$187$		0			0
$188$	−9.00000			−0.656392
$189$		0			0
$190$	−4.73205			−0.343299
$191$		−	3.46410i		−	0.250654i	−0.992116	−	0.125327i	$-0.960002\pi$
$191$		−	3.46410i		−	0.250654i	0.992116	−	0.125327i	$-0.0399979\pi$
$192$		0			0
$193$	24.1962			1.74168			0.870839	−	0.491569i	$-0.163576\pi$
$193$	24.1962			1.74168			0.870839	+	0.491569i	$0.163576\pi$
$194$	7.73205	−	13.3923i	0.555129	−	0.961511i
$195$		0			0
$196$	−5.50000	+	4.33013i	−0.392857	+	0.309295i
$197$			6.33975i			0.451688i	0.974163	+	0.225844i	$0.0725140\pi$
$197$			6.33975i			0.451688i	−0.974163	+	0.225844i	$0.927486\pi$
$198$		0			0
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	0.697355	−	0.716726i	$-0.254360\pi$
$199$	6.00000	+	3.46410i	0.425329	+	0.245564i	−0.272026	+	0.962290i	$0.587694\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$		0			0
$202$	0.696152	−	0.401924i	0.0489811	−	0.0282793i
$203$	−1.20577	−	0.232051i	−0.0846286	−	0.0162868i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	−6.06218	+	10.5000i	−0.422372	+	0.731570i
$207$		0			0
$208$	−3.00000	+	1.73205i	−0.208013	+	0.120096i
$209$	−3.00000	+	5.19615i	−0.207514	+	0.359425i
$210$		0			0
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	0.624221	−	0.781248i	$-0.285416\pi$
$211$	−5.29423	−	9.16987i	−0.364470	−	0.631280i	−0.988691	+	0.149968i	$0.952083\pi$
$212$	−9.29423	−	5.36603i	−0.638330	−	0.368540i
$213$		0			0
$214$	1.03590	+	1.79423i	0.0708126	+	0.122651i
$215$	−3.59808	−	6.23205i	−0.245387	−	0.425022i
$216$		0			0
$217$	1.90192	+	5.49038i	0.129111	+	0.372711i
$218$	2.76795	+	1.59808i	0.187469	+	0.108235i
$219$		0			0
$220$		−	1.26795i		−	0.0854851i
$221$		0			0
$222$		0			0
$223$	8.89230	+	5.13397i	0.595473	+	0.343796i	0.767259	−	0.641338i	$-0.221620\pi$
$223$	8.89230	+	5.13397i	0.595473	+	0.343796i	−0.171786	+	0.985134i	$0.554954\pi$
$224$	0.866025	+	2.50000i	0.0578638	+	0.167038i
$225$		0			0
$226$	−9.29423	−	16.0981i	−0.618243	−	1.07083i
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	0.783894	−	0.620895i	$-0.213231\pi$
$227$	−2.19615	−	3.80385i	−0.145764	−	0.252470i	−0.929658	+	0.368425i	$0.879897\pi$
$228$		0			0
$229$	24.1865	+	13.9641i	1.59829	+	0.922774i	0.991817	+	0.127671i	$0.0407501\pi$
$229$	24.1865	+	13.9641i	1.59829	+	0.922774i	0.606475	+	0.795103i	$0.292583\pi$
$230$	−4.73205	−	8.19615i	−0.312022	−	0.540438i
$231$		0			0
$232$	−0.232051	+	0.401924i	−0.0152349	+	0.0263876i
$233$	−4.09808	+	2.36603i	−0.268474	+	0.155003i	−0.628194	−	0.778057i	$-0.716206\pi$
$233$	−4.09808	+	2.36603i	−0.268474	+	0.155003i	0.359720	+	0.933060i	$0.382872\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$	−8.19615			−0.533524
$237$		0			0
$238$		0			0
$239$	−18.2942	+	10.5622i	−1.18336	+	0.683210i	−0.956788	−	0.290785i	$-0.906084\pi$
$239$	−18.2942	+	10.5622i	−1.18336	+	0.683210i	−0.226567	+	0.973996i	$0.572750\pi$
$240$		0			0
$241$	−17.8923	+	10.3301i	−1.15254	+	0.665422i	−0.949506	−	0.313749i	$-0.898415\pi$
$241$	−17.8923	+	10.3301i	−1.15254	+	0.665422i	−0.203039	+	0.979171i	$0.565082\pi$
$242$	8.13397	+	4.69615i	0.522872	+	0.301880i
$243$		0			0
$244$			0.928203i			0.0594221i
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$		0			0
$247$	−8.19615	+	14.1962i	−0.521509	+	0.903280i
$248$	2.19615			0.139456
$249$		0			0
$250$			1.00000i			0.0632456i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$		−	9.39230i		−	0.589326i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.80385	+	6.58846i	−0.237277	+	0.410977i	−0.959932	−	0.280233i	$-0.909588\pi$
$257$	−3.80385	+	6.58846i	−0.237277	+	0.410977i	0.722655	+	0.691209i	$0.242922\pi$
$258$		0			0
$259$	−8.39230	−	7.26795i	−0.521472	−	0.451608i
$260$		−	3.46410i		−	0.214834i
$261$		0			0
$262$	−14.1962	−	8.19615i	−0.877041	−	0.506360i
$263$	−8.89230	+	5.13397i	−0.548323	+	0.316574i	−0.748445	−	0.663196i	$-0.769199\pi$
$263$	−8.89230	+	5.13397i	−0.548323	+	0.316574i	0.200122	+	0.979771i	$0.435866\pi$
$264$		0			0
$265$	9.29423	−	5.36603i	0.570940	−	0.329632i
$266$	9.46410	+	8.19615i	0.580281	+	0.502538i
$267$		0			0
$268$	4.00000			0.244339
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	21.2942	−	12.2942i	1.29353	−	0.746821i	0.314254	−	0.949339i	$-0.398246\pi$
$271$	21.2942	−	12.2942i	1.29353	−	0.746821i	0.979279	+	0.202518i	$0.0649124\pi$
$272$		0			0
$273$		0			0
$274$	−5.36603	−	9.29423i	−0.324173	−	0.561485i
$275$	1.09808	+	0.633975i	0.0662165	+	0.0382301i
$276$		0			0
$277$	6.90192	+	11.9545i	0.414696	+	0.718275i	0.995397	−	0.0958423i	$-0.0305544\pi$
$277$	6.90192	+	11.9545i	0.414696	+	0.718275i	−0.580700	+	0.814118i	$0.697221\pi$
$278$	8.02628	+	13.9019i	0.481384	+	0.833782i
$279$		0			0
$280$	−2.59808	−	0.500000i	−0.155265	−	0.0298807i
$281$	−2.30385	−	1.33013i	−0.137436	−	0.0793487i	0.429705	−	0.902969i	$-0.358617\pi$
$281$	−2.30385	−	1.33013i	−0.137436	−	0.0793487i	−0.567141	+	0.823620i	$0.691951\pi$
$282$		0			0
$283$		−	10.8564i		−	0.645346i	−0.946510	−	0.322673i	$-0.895419\pi$
$283$		−	10.8564i		−	0.645346i	0.946510	−	0.322673i	$-0.104581\pi$
$284$		−	1.26795i		−	0.0752389i
$285$		0			0
$286$	−3.80385	−	2.19615i	−0.224926	−	0.129861i
$287$	18.0000	+	15.5885i	1.06251	+	0.920158i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−0.232051	−	0.401924i	−0.0136265	−	0.0236018i
$291$		0			0
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$	2.19615	+	3.80385i	0.128301	+	0.222223i	0.923018	−	0.384756i	$-0.125714\pi$
$293$	2.19615	+	3.80385i	0.128301	+	0.222223i	−0.794718	+	0.606979i	$0.792381\pi$
$294$		0			0
$295$	4.09808	−	7.09808i	0.238599	−	0.413266i
$296$	−3.63397	+	2.09808i	−0.211220	+	0.121948i
$297$		0			0
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	−32.7846			−1.89598
$300$		0			0
$301$	−3.59808	+	18.6962i	−0.207390	+	1.07763i
$302$	−5.36603	+	3.09808i	−0.308780	+	0.178274i
$303$		0			0
$304$	4.09808	−	2.36603i	0.235041	−	0.135701i
$305$	−0.803848	−	0.464102i	−0.0460282	−	0.0265744i
$306$		0			0
$307$			17.7846i			1.01502i	0.861645	+	0.507511i	$0.169434\pi$
$307$			17.7846i			1.01502i	−0.861645	+	0.507511i	$0.830566\pi$
$308$	−2.19615	+	2.53590i	−0.125137	+	0.144496i
$309$		0			0
$310$	−1.09808	+	1.90192i	−0.0623665	+	0.108022i
$311$	26.1962			1.48545			0.742724	−	0.669598i	$-0.233534\pi$
$311$	26.1962			1.48545			0.742724	+	0.669598i	$0.233534\pi$
$312$		0			0
$313$		−	9.80385i		−	0.554146i	−0.960849	−	0.277073i	$-0.910636\pi$
$313$		−	9.80385i		−	0.554146i	0.960849	−	0.277073i	$-0.0893644\pi$
$314$	0.339746			0.0191730
$315$		0			0
$316$	16.5885			0.933174
$317$			27.4641i			1.54254i	0.636510	+	0.771269i	$0.280378\pi$
$317$			27.4641i			1.54254i	−0.636510	+	0.771269i	$0.719622\pi$
$318$		0			0
$319$	−0.588457			−0.0329473
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−4.73205	+	24.5885i	−0.263707	+	1.37026i
$323$		0			0
$324$		0			0
$325$	3.00000	+	1.73205i	0.166410	+	0.0960769i
$326$	−10.7321	+	6.19615i	−0.594393	+	0.343173i
$327$		0			0
$328$	7.79423	−	4.50000i	0.430364	−	0.248471i
$329$	−22.5000	+	7.79423i	−1.24047	+	0.429710i
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	−0.401924	+	0.696152i	−0.0220584	+	0.0382063i
$333$		0			0
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$	−2.00000	+	3.46410i	−0.109272	+	0.189264i
$336$		0			0
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	0.697100	−	0.716974i	$-0.254473\pi$
$337$	−5.00000	−	8.66025i	−0.272367	−	0.471754i	−0.969468	+	0.245220i	$0.921140\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$		0			0
$340$		0			0
$341$	1.39230	+	2.41154i	0.0753975	+	0.130592i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	6.23205	+	3.59808i	0.336010	+	0.193995i
$345$		0			0
$346$		−	2.19615i		−	0.118066i
$347$			27.2487i			1.46279i	0.681955	+	0.731394i	$0.261130\pi$
$347$			27.2487i			1.46279i	−0.681955	+	0.731394i	$0.738870\pi$
$348$		0			0
$349$	−3.80385	−	2.19615i	−0.203615	−	0.117557i	0.394725	−	0.918799i	$-0.370840\pi$
$349$	−3.80385	−	2.19615i	−0.203615	−	0.117557i	−0.598341	+	0.801242i	$0.704173\pi$
$350$	1.73205	−	2.00000i	0.0925820	−	0.106904i
$351$		0			0
$352$	0.633975	+	1.09808i	0.0337910	+	0.0585277i
$353$	−15.2942	−	26.4904i	−0.814030	−	1.40994i	−0.910023	−	0.414559i	$-0.863936\pi$
$353$	−15.2942	−	26.4904i	−0.814030	−	1.40994i	0.0959929	−	0.995382i	$-0.469397\pi$
$354$		0			0
$355$	1.09808	+	0.633975i	0.0582798	+	0.0336479i
$356$	−8.19615	−	14.1962i	−0.434395	−	0.752395i
$357$		0			0
$358$	3.29423	−	5.70577i	0.174105	−	0.301559i
$359$	22.6865	−	13.0981i	1.19735	−	0.691290i	0.237386	−	0.971415i	$-0.423709\pi$
$359$	22.6865	−	13.0981i	1.19735	−	0.691290i	0.959963	+	0.280125i	$0.0903760\pi$
$360$		0			0
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	−7.39230			−0.388531
$363$		0			0
$364$	−6.00000	+	6.92820i	−0.314485	+	0.363137i
$365$	6.00000	−	3.46410i	0.314054	−	0.181319i
$366$		0			0
$367$	16.2846	−	9.40192i	0.850050	−	0.490776i	−0.0106179	−	0.999944i	$-0.503380\pi$
$367$	16.2846	−	9.40192i	0.850050	−	0.490776i	0.860668	+	0.509167i	$0.170047\pi$
$368$	8.19615	+	4.73205i	0.427254	+	0.246675i
$369$		0			0
$370$		−	4.19615i		−	0.218148i
$371$	−27.8827	−	5.36603i	−1.44760	−	0.278590i
$372$		0			0
$373$	0.0980762	−	0.169873i	0.00507819	−	0.00879569i	−0.863475	−	0.504391i	$-0.831717\pi$
$373$	0.0980762	−	0.169873i	0.00507819	−	0.00879569i	0.868553	+	0.495596i	$0.165050\pi$
$374$		0			0
$375$		0			0
$376$			9.00000i			0.464140i
$377$	−1.60770			−0.0828005
$378$		0			0
$379$	−30.3923			−1.56115			−0.780574	−	0.625063i	$-0.785073\pi$
$379$	−30.3923			−1.56115			−0.780574	+	0.625063i	$0.785073\pi$
$380$			4.73205i			0.242749i
$381$		0			0
$382$	−3.46410			−0.177239
$383$	0.696152	−	1.20577i	0.0355717	−	0.0616120i	−0.847691	−	0.530490i	$-0.822008\pi$
$383$	0.696152	−	1.20577i	0.0355717	−	0.0616120i	0.883263	+	0.468878i	$0.155341\pi$
$384$		0			0
$385$	−1.09808	−	3.16987i	−0.0559631	−	0.161552i
$386$		−	24.1962i		−	1.23155i
$387$		0			0
$388$	−13.3923	−	7.73205i	−0.679891	−	0.392535i
$389$	−26.5981	+	15.3564i	−1.34858	+	0.778601i	−0.988048	−	0.154148i	$-0.950737\pi$
$389$	−26.5981	+	15.3564i	−1.34858	+	0.778601i	−0.360528	+	0.932748i	$0.617404\pi$
$390$		0			0
$391$		0			0
$392$	4.33013	+	5.50000i	0.218704	+	0.277792i
$393$		0			0
$394$	6.33975			0.319392
$395$	−8.29423	+	14.3660i	−0.417328	+	0.722833i
$396$		0			0
$397$	−0.509619	+	0.294229i	−0.0255770	+	0.0147669i	−0.512734	−	0.858548i	$-0.671367\pi$
$397$	−0.509619	+	0.294229i	−0.0255770	+	0.0147669i	0.487157	+	0.873314i	$0.338034\pi$
$398$	3.46410	−	6.00000i	0.173640	−	0.300753i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−23.8923	−	13.7942i	−1.19312	−	0.688851i	−0.234111	−	0.972210i	$-0.575218\pi$
$401$	−23.8923	−	13.7942i	−1.19312	−	0.688851i	−0.959014	+	0.283359i	$0.908551\pi$
$402$		0			0
$403$	3.80385	+	6.58846i	0.189483	+	0.328194i
$404$	−0.401924	−	0.696152i	−0.0199965	−	0.0346349i
$405$		0			0
$406$	−0.232051	+	1.20577i	−0.0115165	+	0.0598414i
$407$	−4.60770	−	2.66025i	−0.228395	−	0.131864i
$408$		0			0
$409$		−	34.5167i		−	1.70674i	−0.521307	−	0.853370i	$-0.674555\pi$
$409$		−	34.5167i		−	1.70674i	0.521307	−	0.853370i	$-0.325445\pi$
$410$			9.00000i			0.444478i
$411$		0			0
$412$	10.5000	+	6.06218i	0.517298	+	0.298662i
$413$	−20.4904	+	7.09808i	−1.00827	+	0.349273i
$414$		0			0
$415$	−0.401924	−	0.696152i	−0.0197297	−	0.0341728i
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$		0			0
$418$	5.19615	+	3.00000i	0.254152	+	0.146735i
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	0.710734	−	0.703461i	$-0.248363\pi$
$419$	−5.19615	−	9.00000i	−0.253849	−	0.439679i	−0.964582	+	0.263783i	$0.915030\pi$
$420$		0			0
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	0.463494	+	0.886100i	$0.346596\pi$
$421$	−10.9904	+	19.0359i	−0.535638	+	0.927753i	−0.999132	+	0.0416527i	$0.986738\pi$
$422$	−9.16987	+	5.29423i	−0.446382	+	0.257719i
$423$		0			0
$424$	−5.36603	+	9.29423i	−0.260597	+	0.451368i
$425$		0			0
$426$		0			0
$427$	0.803848	+	2.32051i	0.0389009	+	0.112297i
$428$	1.79423	−	1.03590i	0.0867273	−	0.0500720i
$429$		0			0
$430$	−6.23205	+	3.59808i	−0.300536	+	0.173515i
$431$	−2.41154	−	1.39230i	−0.116160	−	0.0670650i	0.440794	−	0.897608i	$-0.354697\pi$
$431$	−2.41154	−	1.39230i	−0.116160	−	0.0670650i	−0.556954	+	0.830543i	$0.688030\pi$
$432$		0			0
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	5.49038	−	1.90192i	0.263547	−	0.0912953i
$435$		0			0
$436$	1.59808	−	2.76795i	0.0765340	−	0.132561i
$437$	44.7846			2.14234
$438$		0			0
$439$			12.3397i			0.588944i	0.955660	+	0.294472i	$0.0951438\pi$
$439$			12.3397i			0.588944i	−0.955660	+	0.294472i	$0.904856\pi$
$440$	−1.26795			−0.0604471
$441$		0			0
$442$		0			0
$443$			9.00000i			0.427603i	0.976877	+	0.213801i	$0.0685846\pi$
$443$			9.00000i			0.427603i	−0.976877	+	0.213801i	$0.931415\pi$
$444$		0			0
$445$	16.3923			0.777070
$446$	5.13397	−	8.89230i	0.243101	−	0.421063i
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$			21.5885i			1.01882i	0.860523	+	0.509411i	$0.170137\pi$
$449$			21.5885i			1.01882i	−0.860523	+	0.509411i	$0.829863\pi$
$450$		0			0
$451$	9.88269	+	5.70577i	0.465358	+	0.268674i
$452$	−16.0981	+	9.29423i	−0.757190	+	0.437164i
$453$		0			0
$454$	−3.80385	+	2.19615i	−0.178523	+	0.103071i
$455$	−3.00000	−	8.66025i	−0.140642	−	0.405999i
$456$		0			0
$457$	−18.3923			−0.860356			−0.430178	−	0.902744i	$-0.641549\pi$
$457$	−18.3923			−0.860356			−0.430178	+	0.902744i	$0.641549\pi$
$458$	13.9641	−	24.1865i	0.652500	−	1.13016i
$459$		0			0
$460$	−8.19615	+	4.73205i	−0.382148	+	0.220633i
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	−0.799160	−	0.601119i	$-0.794722\pi$
$461$	2.59808	−	4.50000i	0.121004	−	0.209586i	0.920164	+	0.391533i	$0.128055\pi$
$462$		0			0
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	0.998696	+	0.0510591i	$0.0162597\pi$
$463$	11.6962	+	20.2583i	0.543566	+	0.941484i	−0.455129	+	0.890425i	$0.650407\pi$
$464$	0.401924	+	0.232051i	0.0186588	+	0.0107727i
$465$		0			0
$466$	2.36603	+	4.09808i	0.109604	+	0.189840i
$467$	8.59808	+	14.8923i	0.397872	+	0.689134i	0.993463	−	0.114154i	$-0.0364156\pi$
$467$	8.59808	+	14.8923i	0.397872	+	0.689134i	−0.595592	+	0.803287i	$0.703082\pi$
$468$		0			0
$469$	10.0000	−	3.46410i	0.461757	−	0.159957i
$470$	−7.79423	−	4.50000i	−0.359521	−	0.207570i
$471$		0			0
$472$			8.19615i			0.377258i
$473$			9.12436i			0.419538i
$474$		0			0
$475$	−4.09808	−	2.36603i	−0.188033	−	0.108561i
$476$		0			0
$477$		0			0
$478$	10.5622	+	18.2942i	0.483103	+	0.836759i
$479$	−5.19615	−	9.00000i	−0.237418	−	0.411220i	0.722554	−	0.691314i	$-0.242968\pi$
$479$	−5.19615	−	9.00000i	−0.237418	−	0.411220i	−0.959973	+	0.280094i	$0.909635\pi$
$480$		0			0
$481$	−12.5885	−	7.26795i	−0.573984	−	0.331390i
$482$	10.3301	+	17.8923i	0.470524	+	0.814972i
$483$		0			0
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	13.3923	−	7.73205i	0.608113	−	0.351094i
$486$		0			0
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	0.167031	+	0.985952i	$0.446582\pi$
$487$	−17.0000	+	29.4449i	−0.770344	+	1.33427i	−0.937375	+	0.348323i	$0.886751\pi$
$488$	0.928203			0.0420178
$489$		0			0
$490$	−6.92820	+	1.00000i	−0.312984	+	0.0451754i
$491$	−2.49038	+	1.43782i	−0.112389	+	0.0648880i	−0.555141	−	0.831756i	$-0.687336\pi$
$491$	−2.49038	+	1.43782i	−0.112389	+	0.0648880i	0.442752	+	0.896644i	$0.354002\pi$
$492$		0			0
$493$		0			0
$494$	14.1962	+	8.19615i	0.638715	+	0.368762i
$495$		0			0
$496$		−	2.19615i		−	0.0986102i
$497$	−1.09808	−	3.16987i	−0.0492554	−	0.142188i
$498$		0			0
$499$	2.90192	−	5.02628i	0.129908	−	0.225007i	−0.793733	−	0.608267i	$-0.791865\pi$
$499$	2.90192	−	5.02628i	0.129908	−	0.225007i	0.923641	+	0.383259i	$0.125198\pi$
$500$	1.00000			0.0447214
$501$		0			0
$502$			18.0000i			0.803379i
$503$	13.3923			0.597133			0.298567	−	0.954389i	$-0.403491\pi$
$503$	13.3923			0.597133			0.298567	+	0.954389i	$0.403491\pi$
$504$		0			0
$505$	0.803848			0.0357707
$506$			12.0000i			0.533465i
$507$		0			0
$508$	−9.39230			−0.416716
$509$	10.7942	−	18.6962i	0.478446	−	0.828692i	−0.521249	−	0.853405i	$-0.674534\pi$
$509$	10.7942	−	18.6962i	0.478446	−	0.828692i	0.999695	+	0.0247124i	$0.00786699\pi$
$510$		0			0
$511$	−18.0000	−	3.46410i	−0.796273	−	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	6.58846	+	3.80385i	0.290604	+	0.167781i
$515$	−10.5000	+	6.06218i	−0.462685	+	0.267131i
$516$		0			0
$517$	−9.88269	+	5.70577i	−0.434640	+	0.250940i
$518$	−7.26795	+	8.39230i	−0.319335	+	0.368737i
$519$		0			0
$520$	−3.46410			−0.151911
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	−0.538948	−	0.842339i	$-0.681178\pi$
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	0.998961	+	0.0455727i	$0.0145113\pi$
$522$		0			0
$523$	−28.5788	+	16.5000i	−1.24967	+	0.721495i	−0.971043	−	0.238906i	$-0.923211\pi$
$523$	−28.5788	+	16.5000i	−1.24967	+	0.721495i	−0.278623	+	0.960401i	$0.589878\pi$
$524$	−8.19615	+	14.1962i	−0.358051	+	0.620162i
$525$		0			0
$526$	5.13397	+	8.89230i	0.223852	+	0.387723i
$527$		0			0
$528$		0			0
$529$	33.2846	+	57.6506i	1.44716	+	2.50655i
$530$	−5.36603	−	9.29423i	−0.233085	−	0.403715i
$531$		0			0
$532$	8.19615	−	9.46410i	0.355348	−	0.410321i
$533$	27.0000	+	15.5885i	1.16950	+	0.675211i
$534$		0			0
$535$			2.07180i			0.0895716i
$536$		−	4.00000i		−	0.172774i
$537$		0			0
$538$	−15.5885	−	9.00000i	−0.672066	−	0.388018i
$539$	−3.29423	+	8.24167i	−0.141892	+	0.354994i
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−12.2942	−	21.2942i	−0.528082	−	0.914665i
$543$		0			0
$544$		0			0
$545$	1.59808	+	2.76795i	0.0684541	+	0.118566i
$546$		0			0
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	−0.451434	−	0.892305i	$-0.649087\pi$
$547$	12.7942	−	22.1603i	0.547042	−	0.947504i	0.998475	−	0.0551993i	$-0.0175794\pi$
$548$	−9.29423	+	5.36603i	−0.397030	+	0.229225i
$549$		0			0
$550$	0.633975	−	1.09808i	0.0270328	−	0.0468221i
$551$	2.19615			0.0935592
$552$		0			0
$553$	41.4711	−	14.3660i	1.76353	−	0.610906i
$554$	11.9545	−	6.90192i	0.507897	−	0.293235i
$555$		0			0
$556$	13.9019	−	8.02628i	0.589573	−	0.340390i
$557$	7.60770	+	4.39230i	0.322348	+	0.186108i	0.652439	−	0.757841i	$-0.273746\pi$
$557$	7.60770	+	4.39230i	0.322348	+	0.186108i	−0.330090	+	0.943949i	$0.607079\pi$
$558$		0			0
$559$			24.9282i			1.05435i
$560$	−0.500000	+	2.59808i	−0.0211289	+	0.109789i
$561$		0			0
$562$	−1.33013	+	2.30385i	−0.0561080	+	0.0971819i
$563$	34.3923			1.44946			0.724731	−	0.689031i	$-0.241964\pi$
$563$	34.3923			1.44946			0.724731	+	0.689031i	$0.241964\pi$
$564$		0			0
$565$		−	18.5885i		−	0.782022i
$566$	−10.8564			−0.456329
$567$		0			0
$568$	−1.26795			−0.0532020
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$		0			0
$571$	42.3923			1.77406			0.887031	−	0.461709i	$-0.152764\pi$
$571$	42.3923			1.77406			0.887031	+	0.461709i	$0.152764\pi$
$572$	−2.19615	+	3.80385i	−0.0918257	+	0.159047i
$573$		0			0
$574$	15.5885	−	18.0000i	0.650650	−	0.751305i
$575$		−	9.46410i		−	0.394680i
$576$		0			0
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	0.000500448	−	1.00000i	$-0.499841\pi$
$577$	−20.7846	−	12.0000i	−0.865275	−	0.499567i	−0.865775	+	0.500433i	$0.833174\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$		0			0
$580$	−0.401924	+	0.232051i	−0.0166890	+	0.00963539i
$581$	−0.401924	+	2.08846i	−0.0166746	+	0.0866438i
$582$		0			0
$583$	−13.6077			−0.563573
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$		0			0
$586$	3.80385	−	2.19615i	0.157135	−	0.0907222i
$587$	20.5981	−	35.6769i	0.850174	−	1.47254i	−0.0308777	−	0.999523i	$-0.509830\pi$
$587$	20.5981	−	35.6769i	0.850174	−	1.47254i	0.881051	−	0.473021i	$-0.156836\pi$
$588$		0			0
$589$	−5.19615	−	9.00000i	−0.214104	−	0.370839i
$590$	−7.09808	−	4.09808i	−0.292223	−	0.168715i
$591$		0			0
$592$	2.09808	+	3.63397i	0.0862304	+	0.149355i
$593$	7.39230	+	12.8038i	0.303566	+	0.525791i	0.976941	−	0.213510i	$-0.0684895\pi$
$593$	7.39230	+	12.8038i	0.303566	+	0.525791i	−0.673375	+	0.739301i	$0.735156\pi$
$594$		0			0
$595$		0			0
$596$	−10.3923	−	6.00000i	−0.425685	−	0.245770i
$597$		0			0
$598$			32.7846i			1.34066i
$599$			16.3923i			0.669771i	0.942259	+	0.334886i	$0.108698\pi$
$599$			16.3923i			0.669771i	−0.942259	+	0.334886i	$0.891302\pi$
$600$		0			0
$601$	3.58846	+	2.07180i	0.146376	+	0.0845104i	0.571399	−	0.820672i	$-0.306401\pi$
$601$	3.58846	+	2.07180i	0.146376	+	0.0845104i	−0.425023	+	0.905182i	$0.639734\pi$
$602$	18.6962	+	3.59808i	0.761998	+	0.146647i
$603$		0			0
$604$	3.09808	+	5.36603i	0.126059	+	0.218340i
$605$	4.69615	+	8.13397i	0.190926	+	0.330693i
$606$		0			0
$607$	−15.6962	−	9.06218i	−0.637087	−	0.367822i	0.146404	−	0.989225i	$-0.453230\pi$
$607$	−15.6962	−	9.06218i	−0.637087	−	0.367822i	−0.783492	+	0.621402i	$0.786563\pi$
$608$	−2.36603	−	4.09808i	−0.0959550	−	0.166199i
$609$		0			0
$610$	−0.464102	+	0.803848i	−0.0187909	+	0.0325468i
$611$	−27.0000	+	15.5885i	−1.09230	+	0.630641i
$612$		0			0
$613$	−17.3923	+	30.1244i	−0.702469	+	1.21671i	0.265129	+	0.964213i	$0.414586\pi$
$613$	−17.3923	+	30.1244i	−0.702469	+	1.21671i	−0.967597	+	0.252498i	$0.918748\pi$
$614$	17.7846			0.717728
$615$		0			0
$616$	2.53590	+	2.19615i	0.102174	+	0.0884855i
$617$	−26.1962	+	15.1244i	−1.05462	+	0.608884i	−0.923938	−	0.382541i	$-0.875049\pi$
$617$	−26.1962	+	15.1244i	−1.05462	+	0.608884i	−0.130679	+	0.991425i	$0.541716\pi$
$618$		0			0
$619$	3.80385	−	2.19615i	0.152890	−	0.0882708i	−0.421603	−	0.906780i	$-0.638533\pi$
$619$	3.80385	−	2.19615i	0.152890	−	0.0882708i	0.574493	+	0.818509i	$0.305199\pi$
$620$	1.90192	+	1.09808i	0.0763831	+	0.0440998i
$621$		0			0
$622$		−	26.1962i		−	1.05037i
$623$	−32.7846	−	28.3923i	−1.31349	−	1.13751i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.80385			−0.391841
$627$		0			0
$628$		−	0.339746i		−	0.0135573i
$629$		0			0
$630$		0			0
$631$	−8.39230			−0.334092			−0.167046	−	0.985949i	$-0.553423\pi$
$631$	−8.39230			−0.334092			−0.167046	+	0.985949i	$0.553423\pi$
$632$		−	16.5885i		−	0.659853i
$633$		0			0
$634$	27.4641			1.09074
$635$	4.69615	−	8.13397i	0.186361	−	0.322787i
$636$		0			0
$637$	−9.00000	+	22.5167i	−0.356593	+	0.892143i
$638$			0.588457i			0.0232972i
$639$		0			0
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	38.7846	−	22.3923i	1.53190	−	0.884443i	0.532626	−	0.846351i	$-0.321205\pi$
$641$	38.7846	−	22.3923i	1.53190	−	0.884443i	0.999274	−	0.0380920i	$-0.0121280\pi$
$642$		0			0
$643$	−31.7942	+	18.3564i	−1.25384	+	0.723906i	−0.971870	−	0.235517i	$-0.924322\pi$
$643$	−31.7942	+	18.3564i	−1.25384	+	0.723906i	−0.281972	+	0.959423i	$0.590988\pi$
$644$	24.5885	+	4.73205i	0.968921	+	0.186469i
$645$		0			0
$646$		0			0
$647$	12.6962	−	21.9904i	0.499137	−	0.864531i	−0.500862	−	0.865527i	$-0.666984\pi$
$647$	12.6962	−	21.9904i	0.499137	−	0.864531i	1.00000		0.000995924i	$0.000317013\pi$
$648$		0			0
$649$	−9.00000	+	5.19615i	−0.353281	+	0.203967i
$650$	1.73205	−	3.00000i	0.0679366	−	0.117670i
$651$		0			0
$652$	6.19615	+	10.7321i	0.242660	+	0.420300i
$653$	−19.1769	−	11.0718i	−0.750451	−	0.433273i	0.0754061	−	0.997153i	$-0.475975\pi$
$653$	−19.1769	−	11.0718i	−0.750451	−	0.433273i	−0.825857	+	0.563880i	$0.809308\pi$
$654$		0			0
$655$	−8.19615	−	14.1962i	−0.320250	−	0.554690i
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$		0			0
$658$	7.79423	+	22.5000i	0.303851	+	0.877141i
$659$	17.7058	+	10.2224i	0.689719	+	0.398209i	0.803507	−	0.595296i	$-0.202965\pi$
$659$	17.7058	+	10.2224i	0.689719	+	0.398209i	−0.113788	+	0.993505i	$0.536298\pi$
$660$		0			0
$661$		−	40.8564i		−	1.58913i	−0.607179	−	0.794565i	$-0.707699\pi$
$661$		−	40.8564i		−	1.58913i	0.607179	−	0.794565i	$-0.292301\pi$
$662$			8.00000i			0.310929i
$663$		0			0
$664$	0.696152	+	0.401924i	0.0270160	+	0.0155977i
$665$	4.09808	+	11.8301i	0.158917	+	0.458753i
$666$		0			0
$667$	2.19615	+	3.80385i	0.0850354	+	0.147286i
$668$	5.19615	+	9.00000i	0.201045	+	0.348220i
$669$		0			0
$670$	3.46410	+	2.00000i	0.133830	+	0.0772667i
$671$	0.588457	+	1.01924i	0.0227171	+	0.0393472i
$672$		0			0
$673$	−13.4904	+	23.3660i	−0.520016	+	0.900694i	0.479713	+	0.877425i	$0.340741\pi$
$673$	−13.4904	+	23.3660i	−0.520016	+	0.900694i	−0.999729	+	0.0232688i	$0.992593\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	28.9808			1.11382			0.556911	−	0.830572i	$-0.311987\pi$
$677$	28.9808			1.11382			0.556911	+	0.830572i	$0.311987\pi$
$678$		0			0
$679$	−40.1769	−	7.73205i	−1.54185	−	0.296729i
$680$		0			0
$681$		0			0
$682$	2.41154	−	1.39230i	0.0923427	−	0.0533141i
$683$	−36.7750	−	21.2321i	−1.40716	−	0.812422i	−0.412043	−	0.911164i	$-0.635185\pi$
$683$	−36.7750	−	21.2321i	−1.40716	−	0.812422i	−0.995113	+	0.0987426i	$0.968518\pi$
$684$		0			0
$685$		−	10.7321i		−	0.410051i
$686$	15.5885	+	10.0000i	0.595170	+	0.381802i
$687$		0			0
$688$	3.59808	−	6.23205i	0.137175	−	0.237595i
$689$	−37.1769			−1.41633
$690$		0			0
$691$		−	18.9282i		−	0.720063i	−0.932940	−	0.360031i	$-0.882766\pi$
$691$		−	18.9282i		−	0.720063i	0.932940	−	0.360031i	$-0.117234\pi$
$692$	−2.19615			−0.0834852
$693$		0			0
$694$	27.2487			1.03435
$695$			16.0526i			0.608908i
$696$		0			0
$697$		0			0
$698$	−2.19615	+	3.80385i	−0.0831256	+	0.143978i
$699$		0			0
$700$	−2.00000	−	1.73205i	−0.0755929	−	0.0654654i
$701$		−	9.67949i		−	0.365589i	−0.983151	−	0.182795i	$-0.941486\pi$
$701$		−	9.67949i		−	0.365589i	0.983151	−	0.182795i	$-0.0585144\pi$
$702$		0			0
$703$	17.1962	+	9.92820i	0.648565	+	0.374449i
$704$	1.09808	−	0.633975i	0.0413853	−	0.0238938i
$705$		0			0
$706$	−26.4904	+	15.2942i	−0.996979	+	0.575606i
$707$	−1.60770	−	1.39230i	−0.0604636	−	0.0523630i
$708$		0			0
$709$	−5.21539			−0.195868			−0.0979340	−	0.995193i	$-0.531223\pi$
$709$	−5.21539			−0.195868			−0.0979340	+	0.995193i	$0.531223\pi$
$710$	0.633975	−	1.09808i	0.0237926	−	0.0412101i
$711$		0			0
$712$	−14.1962	+	8.19615i	−0.532023	+	0.307164i
$713$	10.3923	−	18.0000i	0.389195	−	0.674105i
$714$		0			0
$715$	−2.19615	−	3.80385i	−0.0821314	−	0.142256i
$716$	−5.70577	−	3.29423i	−0.213235	−	0.123111i
$717$		0			0
$718$	−13.0981	−	22.6865i	−0.488816	−	0.846654i
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	−0.934718	−	0.355389i	$-0.884348\pi$
$719$	−20.7846	−	36.0000i	−0.775135	−	1.34257i	0.159583	−	0.987184i	$-0.448985\pi$
$720$		0			0
$721$	31.5000	+	6.06218i	1.17312	+	0.225767i
$722$	−2.93782	−	1.69615i	−0.109334	−	0.0631243i
$723$		0			0
$724$			7.39230i			0.274733i
$725$		−	0.464102i		−	0.0172363i
$726$		0			0
$727$	0.215390	+	0.124356i	0.00798838	+	0.00461210i	0.503989	−	0.863710i	$-0.331865\pi$
$727$	0.215390	+	0.124356i	0.00798838	+	0.00461210i	−0.496000	+	0.868322i	$0.665199\pi$
$728$	6.92820	+	6.00000i	0.256776	+	0.222375i
$729$		0			0
$730$	−3.46410	−	6.00000i	−0.128212	−	0.222070i
$731$		0			0
$732$		0			0
$733$	−3.50962	−	2.02628i	−0.129631	−	0.0748423i	0.433782	−	0.901018i	$-0.357179\pi$
$733$	−3.50962	−	2.02628i	−0.129631	−	0.0748423i	−0.563413	+	0.826175i	$0.690512\pi$
$734$	−9.40192	−	16.2846i	−0.347031	−	0.601076i
$735$		0			0
$736$	4.73205	−	8.19615i	0.174426	−	0.302114i
$737$	4.39230	−	2.53590i	0.161793	−	0.0934110i
$738$		0			0
$739$	14.5885	−	25.2679i	0.536645	−	0.929497i	−0.462437	−	0.886652i	$-0.653025\pi$
$739$	14.5885	−	25.2679i	0.536645	−	0.929497i	0.999082	−	0.0428442i	$-0.0136419\pi$
$740$	−4.19615			−0.154254
$741$		0			0
$742$	−5.36603	+	27.8827i	−0.196993	+	1.02361i
$743$	−38.6769	+	22.3301i	−1.41892	+	0.819213i	−0.996204	−	0.0870500i	$-0.972256\pi$
$743$	−38.6769	+	22.3301i	−1.41892	+	0.819213i	−0.422714	+	0.906263i	$0.638923\pi$
$744$		0			0
$745$	10.3923	−	6.00000i	0.380745	−	0.219823i
$746$	−0.169873	−	0.0980762i	−0.00621949	−	0.00359083i
$747$		0			0
$748$		0			0
$749$	3.58846	−	4.14359i	0.131119	−	0.151404i
$750$		0			0
$751$	21.1962	−	36.7128i	0.773459	−	1.33967i	−0.162198	−	0.986758i	$-0.551858\pi$
$751$	21.1962	−	36.7128i	0.773459	−	1.33967i	0.935657	−	0.352911i	$-0.114808\pi$
$752$	9.00000			0.328196
$753$		0			0
$754$			1.60770i			0.0585488i
$755$	−6.19615			−0.225501
$756$		0			0
$757$	22.5885			0.820991			0.410496	−	0.911863i	$-0.365356\pi$
$757$	22.5885			0.820991			0.410496	+	0.911863i	$0.365356\pi$
$758$			30.3923i			1.10390i
$759$		0			0
$760$	4.73205			0.171650
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	−0.394973	−	0.918693i	$-0.629246\pi$
$761$	16.5000	−	28.5788i	0.598125	−	1.03598i	0.993098	−	0.117289i	$-0.0374205\pi$
$762$		0			0
$763$	1.59808	−	8.30385i	0.0578542	−	0.300619i
$764$			3.46410i			0.125327i
$765$		0			0
$766$	−1.20577	−	0.696152i	−0.0435663	−	0.0251530i
$767$	−24.5885	+	14.1962i	−0.887838	+	0.512593i
$768$		0			0
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	−0.723255	−	0.690581i	$-0.757355\pi$
$769$	−13.5000	+	7.79423i	−0.486822	+	0.281067i	0.236433	+	0.971648i	$0.424022\pi$
$770$	−3.16987	+	1.09808i	−0.114234	+	0.0395719i
$771$		0			0
$772$	−24.1962			−0.870839
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$		0			0
$775$	−1.90192	+	1.09808i	−0.0683191	+	0.0394441i
$776$	−7.73205	+	13.3923i	−0.277564	+	0.480756i
$777$		0			0
$778$	15.3564	+	26.5981i	0.550554	+	0.953587i
$779$	−36.8827	−	21.2942i	−1.32146	−	0.762945i
$780$		0			0
$781$	−0.803848	−	1.39230i	−0.0287639	−	0.0498206i
$782$		0			0
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	0.294229	+	0.169873i	0.0105015	+	0.00606303i
$786$		0			0
$787$		−	39.2487i		−	1.39907i	−0.714601	−	0.699533i	$-0.753392\pi$
$787$		−	39.2487i		−	1.39907i	0.714601	−	0.699533i	$-0.246608\pi$
$788$		−	6.33975i		−	0.225844i
$789$		0			0
$790$	14.3660	+	8.29423i	0.511120	+	0.295095i
$791$	−32.1962	+	37.1769i	−1.14476	+	1.32186i
$792$		0			0
$793$	1.60770	+	2.78461i	0.0570909	+	0.0988844i
$794$	0.294229	+	0.509619i	0.0104418	+	0.0180857i
$795$		0			0
$796$	−6.00000	−	3.46410i	−0.212664	−	0.122782i
$797$	21.5885	+	37.3923i	0.764702	+	1.32450i	0.940404	+	0.340060i	$0.110447\pi$
$797$	21.5885	+	37.3923i	0.764702	+	1.32450i	−0.175701	+	0.984444i	$0.556219\pi$
$798$		0			0
$799$		0			0
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$		0			0
$802$	−13.7942	+	23.8923i	−0.487091	+	0.843667i
$803$	−8.78461			−0.310002
$804$		0			0
$805$	−16.3923	+	18.9282i	−0.577753	+	0.667132i
$806$	6.58846	−	3.80385i	0.232069	−	0.133985i
$807$		0			0
$808$	−0.696152	+	0.401924i	−0.0244906	+	0.0141396i
$809$	−6.48076	−	3.74167i	−0.227851	−	0.131550i	0.381729	−	0.924274i	$-0.375329\pi$
$809$	−6.48076	−	3.74167i	−0.227851	−	0.131550i	−0.609580	+	0.792724i	$0.708662\pi$
$810$		0			0
$811$		−	51.4641i		−	1.80715i	−0.428431	−	0.903575i	$-0.640933\pi$
$811$		−	51.4641i		−	1.80715i	0.428431	−	0.903575i	$-0.359067\pi$
$812$	1.20577	+	0.232051i	0.0423143	+	0.00814339i
$813$		0			0
$814$	−2.66025	+	4.60770i	−0.0932419	+	0.161500i
$815$	−12.3923			−0.434084
$816$		0			0
$817$		−	34.0526i		−	1.19135i
$818$	−34.5167			−1.20685
$819$		0			0
$820$	9.00000			0.314294
$821$		−	18.7128i		−	0.653082i	−0.945183	−	0.326541i	$-0.894117\pi$
$821$		−	18.7128i		−	0.653082i	0.945183	−	0.326541i	$-0.105883\pi$
$822$		0			0
$823$	51.3923			1.79142			0.895712	−	0.444636i	$-0.146667\pi$
$823$	51.3923			1.79142			0.895712	+	0.444636i	$0.146667\pi$
$824$	6.06218	−	10.5000i	0.211186	−	0.365785i
$825$		0			0
$826$	7.09808	+	20.4904i	0.246974	+	0.712952i
$827$		−	37.6410i		−	1.30891i	−0.756103	−	0.654453i	$-0.772899\pi$
$827$		−	37.6410i		−	1.30891i	0.756103	−	0.654453i	$-0.227101\pi$
$828$		0			0
$829$	−6.18653	−	3.57180i	−0.214867	−	0.124054i	0.388704	−	0.921363i	$-0.372923\pi$
$829$	−6.18653	−	3.57180i	−0.214867	−	0.124054i	−0.603571	+	0.797309i	$0.706256\pi$
$830$	−0.696152	+	0.401924i	−0.0241638	+	0.0139510i
$831$		0			0
$832$	3.00000	−	1.73205i	0.104006	−	0.0600481i
$833$		0			0
$834$		0			0
$835$	−10.3923			−0.359641
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$		0			0
$838$	−9.00000	+	5.19615i	−0.310900	+	0.179498i
$839$	7.09808	−	12.2942i	0.245053	−	0.424444i	−0.717094	−	0.696977i	$-0.754528\pi$
$839$	7.09808	−	12.2942i	0.245053	−	0.424444i	0.962146	+	0.272533i	$0.0878614\pi$
$840$		0			0
$841$	−14.3923	−	24.9282i	−0.496286	−	0.859593i
$842$	19.0359	+	10.9904i	0.656020	+	0.378754i
$843$		0			0
$844$	5.29423	+	9.16987i	0.182235	+	0.315640i
$845$	0.500000	+	0.866025i	0.0172005	+	0.0297922i
$846$		0			0
$847$	4.69615	−	24.4019i	0.161362	−	0.838460i
$848$	9.29423	+	5.36603i	0.319165	+	0.184270i
$849$		0			0
$850$		0			0
$851$			39.7128i			1.36134i
$852$		0			0
$853$	−38.7846	−	22.3923i	−1.32796	−	0.766698i	−0.342976	−	0.939344i	$-0.611435\pi$
$853$	−38.7846	−	22.3923i	−1.32796	−	0.766698i	−0.984984	+	0.172646i	$0.944768\pi$
$854$	2.32051	−	0.803848i	0.0794062	−	0.0275071i
$855$		0			0
$856$	−1.03590	−	1.79423i	−0.0354063	−	0.0613255i
$857$	24.2942	+	42.0788i	0.829875	+	1.43739i	0.898136	+	0.439718i	$0.144922\pi$
$857$	24.2942	+	42.0788i	0.829875	+	1.43739i	−0.0682607	+	0.997668i	$0.521745\pi$
$858$		0			0
$859$	22.6865	+	13.0981i	0.774055	+	0.446901i	0.834319	−	0.551282i	$-0.185861\pi$
$859$	22.6865	+	13.0981i	0.774055	+	0.446901i	−0.0602645	+	0.998182i	$0.519194\pi$
$860$	3.59808	+	6.23205i	0.122693	+	0.212511i
$861$		0			0
$862$	−1.39230	+	2.41154i	−0.0474221	+	0.0821375i
$863$	4.60770	−	2.66025i	0.156848	−	0.0905561i	−0.419522	−	0.907745i	$-0.637802\pi$
$863$	4.60770	−	2.66025i	0.156848	−	0.0905561i	0.576370	+	0.817189i	$0.304469\pi$
$864$		0			0
$865$	1.09808	−	1.90192i	0.0373357	−	0.0646673i
$866$	18.0000			0.611665
$867$		0			0
$868$	−1.90192	−	5.49038i	−0.0645555	−	0.186356i
$869$	18.2154	−	10.5167i	0.617915	−	0.356753i
$870$		0			0
$871$	12.0000	−	6.92820i	0.406604	−	0.234753i
$872$	−2.76795	−	1.59808i	−0.0937346	−	0.0541177i
$873$		0			0
$874$		−	44.7846i		−	1.51486i
$875$	2.50000	−	0.866025i	0.0845154	−	0.0292770i
$876$		0			0
$877$	20.8827	−	36.1699i	0.705158	−	1.22137i	−0.261476	−	0.965210i	$-0.584209\pi$
$877$	20.8827	−	36.1699i	0.705158	−	1.22137i	0.966634	−	0.256160i	$-0.0824574\pi$
$878$	12.3397			0.416446
$879$		0			0
$880$			1.26795i			0.0427426i
$881$	4.39230			0.147981			0.0739903	−	0.997259i	$-0.476427\pi$
$881$	4.39230			0.147981			0.0739903	+	0.997259i	$0.476427\pi$
$882$		0			0
$883$	−44.3731			−1.49327			−0.746636	−	0.665232i	$-0.768332\pi$
$883$	−44.3731			−1.49327			−0.746636	+	0.665232i	$0.768332\pi$
$884$		0			0
$885$		0			0
$886$	9.00000			0.302361
$887$	14.3038	−	24.7750i	0.480276	−	0.831863i	−0.519468	−	0.854490i	$-0.673870\pi$
$887$	14.3038	−	24.7750i	0.480276	−	0.831863i	0.999744	+	0.0226273i	$0.00720310\pi$
$888$		0			0
$889$	−23.4808	+	8.13397i	−0.787519	+	0.272805i
$890$		−	16.3923i		−	0.549471i
$891$		0			0
$892$	−8.89230	−	5.13397i	−0.297736	−	0.171898i
$893$	36.8827	−	21.2942i	1.23423	−	0.712584i
$894$		0			0
$895$	5.70577	−	3.29423i	0.190723	−	0.110114i
$896$	−0.866025	−	2.50000i	−0.0289319	−	0.0835191i
$897$		0			0
$898$	21.5885			0.720416
$899$	0.509619	−	0.882686i	0.0169967	−	0.0294392i
$900$		0			0
$901$		0			0
$902$	5.70577	−	9.88269i	0.189981	−	0.329057i
$903$		0			0
$904$	9.29423	+	16.0981i	0.309121	+	0.535414i
$905$	−6.40192	−	3.69615i	−0.212807	−	0.122864i
$906$		0			0
$907$	−16.5981	−	28.7487i	−0.551130	−	0.954585i	−0.998193	−	0.0600830i	$-0.980863\pi$
$907$	−16.5981	−	28.7487i	−0.551130	−	0.954585i	0.447063	−	0.894502i	$-0.352470\pi$
$908$	2.19615	+	3.80385i	0.0728819	+	0.126235i
$909$		0			0
$910$	−8.66025	+	3.00000i	−0.287085	+	0.0994490i
$911$	−4.90192	−	2.83013i	−0.162408	−	0.0937663i	0.416593	−	0.909093i	$-0.363224\pi$
$911$	−4.90192	−	2.83013i	−0.162408	−	0.0937663i	−0.579001	+	0.815327i	$0.696557\pi$
$912$		0			0
$913$			1.01924i			0.0337319i
$914$			18.3923i			0.608363i
$915$		0			0
$916$	−24.1865	−	13.9641i	−0.799146	−	0.461387i
$917$	−8.19615	+	42.5885i	−0.270661	+	1.40639i
$918$		0			0
$919$	13.2942	+	23.0263i	0.438536	+	0.759567i	0.997577	−	0.0695733i	$-0.0221638\pi$
$919$	13.2942	+	23.0263i	0.438536	+	0.759567i	−0.559041	+	0.829140i	$0.688830\pi$
$920$	4.73205	+	8.19615i	0.156011	+	0.270219i
$921$		0			0
$922$	−4.50000	−	2.59808i	−0.148200	−	0.0855631i
$923$	−2.19615	−	3.80385i	−0.0722872	−	0.125205i
$924$		0			0
$925$	2.09808	−	3.63397i	0.0689843	−	0.119484i
$926$	20.2583	−	11.6962i	0.665730	−	0.384359i
$927$		0			0
$928$	0.232051	−	0.401924i	0.00761744	−	0.0131938i
$929$	−32.5692			−1.06856			−0.534281	−	0.845307i	$-0.679417\pi$
$929$	−32.5692			−1.06856			−0.534281	+	0.845307i	$0.679417\pi$
$930$		0			0
$931$	12.2942	−	30.7583i	0.402927	−	1.00806i
$932$	4.09808	−	2.36603i	0.134237	−	0.0775017i
$933$		0			0
$934$	14.8923	−	8.59808i	0.487291	−	0.281338i
$935$		0			0
$936$		0			0
$937$			11.4115i			0.372799i	0.982474	+	0.186399i	$0.0596818\pi$
$937$			11.4115i			0.372799i	−0.982474	+	0.186399i	$0.940318\pi$
$938$	−3.46410	−	10.0000i	−0.113107	−	0.326512i
$939$		0			0
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	−25.9808			−0.846949			−0.423474	−	0.905908i	$-0.639190\pi$
$941$	−25.9808			−0.846949			−0.423474	+	0.905908i	$0.639190\pi$
$942$		0			0
$943$		−	85.1769i		−	2.77374i
$944$	8.19615			0.266762
$945$		0			0
$946$	9.12436			0.296658
$947$			59.5692i			1.93574i	0.251452	+	0.967870i	$0.419092\pi$
$947$			59.5692i			1.93574i	−0.251452	+	0.967870i	$0.580908\pi$
$948$		0			0
$949$	−24.0000			−0.779073
$950$	−2.36603	+	4.09808i	−0.0767640	+	0.132959i
$951$		0			0
$952$		0			0
$953$			4.73205i			0.153286i	0.997059	+	0.0766431i	$0.0244202\pi$
$953$			4.73205i			0.153286i	−0.997059	+	0.0766431i	$0.975580\pi$
$954$		0			0
$955$	−3.00000	−	1.73205i	−0.0970777	−	0.0560478i
$956$	18.2942	−	10.5622i	0.591678	−	0.341605i
$957$		0			0
$958$	−9.00000	+	5.19615i	−0.290777	+	0.167880i
$959$	−18.5885	+	21.4641i	−0.600253	+	0.693112i
$960$		0			0
$961$	26.1769			0.844417
$962$	−7.26795	+	12.5885i	−0.234328	+	0.405868i
$963$		0			0
$964$	17.8923	−	10.3301i	0.576272	−	0.332711i
$965$	12.0981	−	20.9545i	0.389451	−	0.674549i
$966$		0			0
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	0.965508	−	0.260375i	$-0.0838461\pi$
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	−0.708245	+	0.705967i	$0.750513\pi$
$968$	−8.13397	−	4.69615i	−0.261436	−	0.150940i
$969$		0			0
$970$	−7.73205	−	13.3923i	−0.248261	−	0.430001i
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	0.567074	−	0.823667i	$-0.308075\pi$
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	−0.996853	+	0.0792670i	$0.974742\pi$
$972$		0			0
$973$	27.8038	−	32.1051i	0.891350	−	1.02924i
$974$	29.4449	+	17.0000i	0.943474	+	0.544715i
$975$		0			0
$976$		−	0.928203i		−	0.0297111i
$977$		−	18.9282i		−	0.605567i	−0.953059	−	0.302783i	$-0.902084\pi$
$977$		−	18.9282i		−	0.605567i	0.953059	−	0.302783i	$-0.0979159\pi$
$978$		0			0
$979$	−18.0000	−	10.3923i	−0.575282	−	0.332140i
$980$	1.00000	+	6.92820i	0.0319438	+	0.221313i
$981$		0			0
$982$	1.43782	+	2.49038i	0.0458827	+	0.0794713i
$983$	5.30385	+	9.18653i	0.169166	+	0.293005i	0.938127	−	0.346291i	$-0.112559\pi$
$983$	5.30385	+	9.18653i	0.169166	+	0.293005i	−0.768961	+	0.639296i	$0.779226\pi$
$984$		0			0
$985$	5.49038	+	3.16987i	0.174938	+	0.101001i
$986$		0			0
$987$		0			0
$988$	8.19615	−	14.1962i	0.260754	−	0.451640i
$989$	58.9808	−	34.0526i	1.87548	−	1.08281i
$990$		0			0
$991$	22.2942	−	38.6147i	0.708200	−	1.22664i	−0.257325	−	0.966325i	$-0.582841\pi$
$991$	22.2942	−	38.6147i	0.708200	−	1.22664i	0.965524	−	0.260313i	$-0.0838256\pi$
$992$	−2.19615			−0.0697279
$993$		0			0
$994$	−3.16987	+	1.09808i	−0.100542	+	0.0348289i
$995$	6.00000	−	3.46410i	0.190213	−	0.109819i
$996$		0			0
$997$	−11.7058	+	6.75833i	−0.370725	+	0.214038i	−0.673775	−	0.738936i	$-0.735328\pi$
$997$	−11.7058	+	6.75833i	−0.370725	+	0.214038i	0.303050	+	0.952975i	$0.401995\pi$
$998$	−5.02628	−	2.90192i	−0.159104	−	0.0918588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bk.a.521.1		4
3.2	odd	2		630.2.bk.a.101.2	yes	4
7.5	odd	6		1890.2.t.a.1601.1		4
9.4	even	3		630.2.t.a.311.2	✓	4
9.5	odd	6		1890.2.t.a.1151.1		4
21.5	even	6		630.2.t.a.551.2	yes	4
63.5	even	6	inner	1890.2.bk.a.341.2		4
63.40	odd	6		630.2.bk.a.131.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.a.311.2	✓	4	9.4	even	3
630.2.t.a.551.2	yes	4	21.5	even	6
630.2.bk.a.101.2	yes	4	3.2	odd	2
630.2.bk.a.131.1	yes	4	63.40	odd	6
1890.2.t.a.1151.1		4	9.5	odd	6
1890.2.t.a.1601.1		4	7.5	odd	6
1890.2.bk.a.341.2		4	63.5	even	6	inner
1890.2.bk.a.521.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{10} +(-1.09808 + 0.633975i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(0.866025 + 2.50000i) q^{14} +1.00000 q^{16} +(4.09808 - 2.36603i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.633975 + 1.09808i) q^{22} +(8.19615 + 4.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.73205 + 3.00000i) q^{26} +(2.50000 - 0.866025i) q^{28} +(0.401924 + 0.232051i) q^{29} -2.19615i q^{31} -1.00000i q^{32} +(-0.500000 + 2.59808i) q^{35} +(2.09808 + 3.63397i) q^{37} +(-2.36603 - 4.09808i) q^{38} +(0.866025 + 0.500000i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(3.59808 - 6.23205i) q^{43} +(1.09808 - 0.633975i) q^{44} +(4.73205 - 8.19615i) q^{46} +9.00000 q^{47} +(5.50000 - 4.33013i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(3.00000 - 1.73205i) q^{52} +(9.29423 + 5.36603i) q^{53} +1.26795i q^{55} +(-0.866025 - 2.50000i) q^{56} +(0.232051 - 0.401924i) q^{58} +8.19615 q^{59} -0.928203i q^{61} -2.19615 q^{62} -1.00000 q^{64} +3.46410i q^{65} -4.00000 q^{67} +(2.59808 + 0.500000i) q^{70} +1.26795i q^{71} +(6.00000 + 3.46410i) q^{73} +(3.63397 - 2.09808i) q^{74} +(-4.09808 + 2.36603i) q^{76} +(2.19615 - 2.53590i) q^{77} -16.5885 q^{79} +(0.500000 - 0.866025i) q^{80} +(-7.79423 + 4.50000i) q^{82} +(0.401924 - 0.696152i) q^{83} +(-6.23205 - 3.59808i) q^{86} +(-0.633975 - 1.09808i) q^{88} +(8.19615 + 14.1962i) q^{89} +(6.00000 - 6.92820i) q^{91} +(-8.19615 - 4.73205i) q^{92} -9.00000i q^{94} -4.73205i q^{95} +(13.3923 + 7.73205i) q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7	\( 4 q - 4 q^{4} + 2 q^{5} - 10 q^{7} + 6 q^{11} - 12 q^{13} + 4 q^{16} + 6 q^{19} - 2 q^{20} + 6 q^{22} + 12 q^{23} - 2 q^{25} + 10 q^{28} + 12 q^{29} - 2 q^{35} - 2 q^{37} - 6 q^{38} - 18 q^{41} + 4 q^{43} - 6 q^{44} + 12 q^{46} + 36 q^{47} + 22 q^{49} + 12 q^{52} + 6 q^{53} - 6 q^{58} + 12 q^{59} + 12 q^{62} - 4 q^{64} - 16 q^{67} + 24 q^{73} + 18 q^{74} - 6 q^{76} - 12 q^{77} - 4 q^{79} + 2 q^{80} + 12 q^{83} - 18 q^{86} - 6 q^{88} + 12 q^{89} + 24 q^{91} - 12 q^{92} + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^5 - 10 * q^7 + 6 * q^11 - 12 * q^13 + 4 * q^16 + 6 * q^19 - 2 * q^20 + 6 * q^22 + 12 * q^23 - 2 * q^25 + 10 * q^28 + 12 * q^29 - 2 * q^35 - 2 * q^37 - 6 * q^38 - 18 * q^41 + 4 * q^43 - 6 * q^44 + 12 * q^46 + 36 * q^47 + 22 * q^49 + 12 * q^52 + 6 * q^53 - 6 * q^58 + 12 * q^59 + 12 * q^62 - 4 * q^64 - 16 * q^67 + 24 * q^73 + 18 * q^74 - 6 * q^76 - 12 * q^77 - 4 * q^79 + 2 * q^80 + 12 * q^83 - 18 * q^86 - 6 * q^88 + 12 * q^89 + 24 * q^91 - 12 * q^92 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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