LMFDB - Embedded newform 170.2.c.b.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(69,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("170.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.c (of order $2$, degree $1$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 4x^{3} + 25x^{2} - 20x + 8 $ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.6
Root			$0.432320 - 0.432320i$ of defining polynomial
Character	$\chi$	$=$	170.69
Dual form			170.2.c.b.69.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.62620i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} -2.62620 q^{6} +0.864641i q^{7} -1.00000i q^{8} -3.89692 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.62620i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} -2.62620 q^{6} +0.864641i q^{7} -1.00000i q^{8} -3.89692 q^{9} +(0.432320 - 2.19388i) q^{10} +2.00000 q^{11} -2.62620i q^{12} +2.62620i q^{13} -0.864641 q^{14} +(1.13536 - 5.76156i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -3.89692i q^{18} +0.896916 q^{19} +(2.19388 + 0.432320i) q^{20} -2.27072 q^{21} +2.00000i q^{22} +3.13536i q^{23} +2.62620 q^{24} +(4.62620 + 1.89692i) q^{25} -2.62620 q^{26} -2.35548i q^{27} -0.864641i q^{28} -9.49084 q^{29} +(5.76156 + 1.13536i) q^{30} +9.01395 q^{31} +1.00000i q^{32} +5.25240i q^{33} -1.00000 q^{34} +(0.373802 - 1.89692i) q^{35} +3.89692 q^{36} +10.1816i q^{37} +0.896916i q^{38} -6.89692 q^{39} +(-0.432320 + 2.19388i) q^{40} +9.52311 q^{41} -2.27072i q^{42} -7.25240i q^{43} -2.00000 q^{44} +(8.54936 + 1.68472i) q^{45} -3.13536 q^{46} -10.4200i q^{47} +2.62620i q^{48} +6.25240 q^{49} +(-1.89692 + 4.62620i) q^{50} -2.62620 q^{51} -2.62620i q^{52} -11.4017i q^{53} +2.35548 q^{54} +(-4.38776 - 0.864641i) q^{55} +0.864641 q^{56} +2.35548i q^{57} -9.49084i q^{58} +4.14931 q^{59} +(-1.13536 + 5.76156i) q^{60} +3.28467 q^{61} +9.01395i q^{62} -3.36943i q^{63} -1.00000 q^{64} +(1.13536 - 5.76156i) q^{65} -5.25240 q^{66} +1.25240i q^{67} -1.00000i q^{68} -8.23407 q^{69} +(1.89692 + 0.373802i) q^{70} -12.5371 q^{71} +3.89692i q^{72} +2.62620i q^{73} -10.1816 q^{74} +(-4.98168 + 12.1493i) q^{75} -0.896916 q^{76} +1.72928i q^{77} -6.89692i q^{78} +7.91087 q^{79} +(-2.19388 - 0.432320i) q^{80} -5.50479 q^{81} +9.52311i q^{82} +4.20617i q^{83} +2.27072 q^{84} +(0.432320 - 2.19388i) q^{85} +7.25240 q^{86} -24.9248i q^{87} -2.00000i q^{88} -4.14931 q^{89} +(-1.68472 + 8.54936i) q^{90} -2.27072 q^{91} -3.13536i q^{92} +23.6724i q^{93} +10.4200 q^{94} +(-1.96772 - 0.387755i) q^{95} -2.62620 q^{96} -6.14931i q^{97} +6.25240i q^{98} -7.79383 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9} + 12 q^{11} + 12 q^{15} + 6 q^{16} - 2 q^{19} - 2 q^{20} - 24 q^{21} - 2 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{29} + 22 q^{30} + 6 q^{31} - 6 q^{34} + 20 q^{35} + 16 q^{36} - 34 q^{39} + 32 q^{41} - 12 q^{44} + 8 q^{45} - 24 q^{46} + 2 q^{49} - 4 q^{50} + 2 q^{51} - 14 q^{54} + 4 q^{55} - 18 q^{59} - 12 q^{60} - 18 q^{61} - 6 q^{64} + 12 q^{65} + 4 q^{66} + 32 q^{69} + 4 q^{70} - 2 q^{71} - 16 q^{74} + 16 q^{75} + 2 q^{76} - 8 q^{79} + 2 q^{80} + 38 q^{81} + 24 q^{84} + 8 q^{86} + 18 q^{89} + 28 q^{90} - 24 q^{91} + 30 q^{94} - 14 q^{95} + 2 q^{96} - 32 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^9 + 12 * q^11 + 12 * q^15 + 6 * q^16 - 2 * q^19 - 2 * q^20 - 24 * q^21 - 2 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^29 + 22 * q^30 + 6 * q^31 - 6 * q^34 + 20 * q^35 + 16 * q^36 - 34 * q^39 + 32 * q^41 - 12 * q^44 + 8 * q^45 - 24 * q^46 + 2 * q^49 - 4 * q^50 + 2 * q^51 - 14 * q^54 + 4 * q^55 - 18 * q^59 - 12 * q^60 - 18 * q^61 - 6 * q^64 + 12 * q^65 + 4 * q^66 + 32 * q^69 + 4 * q^70 - 2 * q^71 - 16 * q^74 + 16 * q^75 + 2 * q^76 - 8 * q^79 + 2 * q^80 + 38 * q^81 + 24 * q^84 + 8 * q^86 + 18 * q^89 + 28 * q^90 - 24 * q^91 + 30 * q^94 - 14 * q^95 + 2 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$1$	$-1$

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
$3$			2.62620i			1.51624i	0.652117	+	0.758118i	$0.273881\pi$
$3$			2.62620i			1.51624i	−0.652117	+	0.758118i	$0.726119\pi$
$4$	−1.00000			−0.500000
$5$	−2.19388	−	0.432320i	−0.981132	−	0.193340i
$5$	−2.19388	−	0.432320i	−0.981132	−	0.193340i
$6$	−2.62620			−1.07214
$7$			0.864641i			0.326804i	0.986560	+	0.163402i	$0.0522467\pi$
$7$			0.864641i			0.326804i	−0.986560	+	0.163402i	$0.947753\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−3.89692			−1.29897
$10$	0.432320	−	2.19388i	0.136712	−	0.693765i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		−	2.62620i		−	0.758118i
$13$			2.62620i			0.728376i	0.931325	+	0.364188i	$0.118653\pi$
$13$			2.62620i			0.728376i	−0.931325	+	0.364188i	$0.881347\pi$
$14$	−0.864641			−0.231085
$15$	1.13536	−	5.76156i	0.293148	−	1.48763i
$16$	1.00000			0.250000
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$		−	3.89692i		−	0.918512i
$19$	0.896916			0.205767			0.102883	−	0.994693i	$-0.467193\pi$
$19$	0.896916			0.205767			0.102883	+	0.994693i	$0.467193\pi$
$20$	2.19388	+	0.432320i	0.490566	+	0.0966698i
$21$	−2.27072			−0.495511
$22$			2.00000i			0.426401i
$23$			3.13536i			0.653768i	0.945065	+	0.326884i	$0.105999\pi$
$23$			3.13536i			0.653768i	−0.945065	+	0.326884i	$0.894001\pi$
$24$	2.62620			0.536070
$25$	4.62620	+	1.89692i	0.925240	+	0.379383i
$26$	−2.62620			−0.515040
$27$		−	2.35548i		−	0.453312i
$28$		−	0.864641i		−	0.163402i
$29$	−9.49084			−1.76240			−0.881202	−	0.472739i	$-0.843265\pi$
$29$	−9.49084			−1.76240			−0.881202	+	0.472739i	$0.843265\pi$
$30$	5.76156	+	1.13536i	1.05191	+	0.207287i
$31$	9.01395			1.61895			0.809477	−	0.587152i	$-0.199751\pi$
$31$	9.01395			1.61895			0.809477	+	0.587152i	$0.199751\pi$
$32$			1.00000i			0.176777i
$33$			5.25240i			0.914325i
$34$	−1.00000			−0.171499
$35$	0.373802	−	1.89692i	0.0631841	−	0.320637i
$36$	3.89692			0.649486
$37$			10.1816i			1.67384i	0.547323	+	0.836921i	$0.315647\pi$
$37$			10.1816i			1.67384i	−0.547323	+	0.836921i	$0.684353\pi$
$38$			0.896916i			0.145499i
$39$	−6.89692			−1.10439
$40$	−0.432320	+	2.19388i	−0.0683559	+	0.346883i
$41$	9.52311			1.48726			0.743630	−	0.668591i	$-0.233102\pi$
$41$	9.52311			1.48726			0.743630	+	0.668591i	$0.233102\pi$
$42$		−	2.27072i		−	0.350379i
$43$		−	7.25240i		−	1.10598i	−0.833188	−	0.552990i	$-0.813487\pi$
$43$		−	7.25240i		−	1.10598i	0.833188	−	0.552990i	$-0.186513\pi$
$44$	−2.00000			−0.301511
$45$	8.54936	+	1.68472i	1.27446	+	0.251143i
$46$	−3.13536			−0.462283
$47$		−	10.4200i		−	1.51992i	−0.649971	−	0.759959i	$-0.725219\pi$
$47$		−	10.4200i		−	1.51992i	0.649971	−	0.759959i	$-0.274781\pi$
$48$			2.62620i			0.379059i
$49$	6.25240			0.893199
$50$	−1.89692	+	4.62620i	−0.268264	+	0.654243i
$51$	−2.62620			−0.367741
$52$		−	2.62620i		−	0.364188i
$53$		−	11.4017i		−	1.56615i	−0.621930	−	0.783073i	$-0.713651\pi$
$53$		−	11.4017i		−	1.56615i	0.621930	−	0.783073i	$-0.286349\pi$
$54$	2.35548			0.320540
$55$	−4.38776	−	0.864641i	−0.591645	−	0.116588i
$56$	0.864641			0.115542
$57$			2.35548i			0.311991i
$58$		−	9.49084i		−	1.24621i
$59$	4.14931			0.540194			0.270097	−	0.962833i	$-0.412944\pi$
$59$	4.14931			0.540194			0.270097	+	0.962833i	$0.412944\pi$
$60$	−1.13536	+	5.76156i	−0.146574	+	0.743814i
$61$	3.28467			0.420559			0.210280	−	0.977641i	$-0.432563\pi$
$61$	3.28467			0.420559			0.210280	+	0.977641i	$0.432563\pi$
$62$			9.01395i			1.14477i
$63$		−	3.36943i		−	0.424509i
$64$	−1.00000			−0.125000
$65$	1.13536	−	5.76156i	0.140824	−	0.714633i
$66$	−5.25240			−0.646525
$67$			1.25240i			0.153005i	0.997069	+	0.0765023i	$0.0243752\pi$
$67$			1.25240i			0.153005i	−0.997069	+	0.0765023i	$0.975625\pi$
$68$		−	1.00000i		−	0.121268i
$69$	−8.23407			−0.991266
$70$	1.89692	+	0.373802i	0.226725	+	0.0446779i
$71$	−12.5371			−1.48788			−0.743938	−	0.668249i	$-0.767044\pi$
$71$	−12.5371			−1.48788			−0.743938	+	0.668249i	$0.767044\pi$
$72$			3.89692i			0.459256i
$73$			2.62620i			0.307373i	0.988120	+	0.153687i	$0.0491146\pi$
$73$			2.62620i			0.307373i	−0.988120	+	0.153687i	$0.950885\pi$
$74$	−10.1816			−1.18359
$75$	−4.98168	+	12.1493i	−0.575235	+	1.40288i
$76$	−0.896916			−0.102883
$77$			1.72928i			0.197070i
$78$		−	6.89692i		−	0.780922i
$79$	7.91087			0.890042			0.445021	−	0.895520i	$-0.353196\pi$
$79$	7.91087			0.890042			0.445021	+	0.895520i	$0.353196\pi$
$80$	−2.19388	−	0.432320i	−0.245283	−	0.0483349i
$81$	−5.50479			−0.611644
$82$			9.52311i			1.05165i
$83$			4.20617i			0.461687i	0.972991	+	0.230843i	$0.0741485\pi$
$83$			4.20617i			0.461687i	−0.972991	+	0.230843i	$0.925851\pi$
$84$	2.27072			0.247756
$85$	0.432320	−	2.19388i	0.0468917	−	0.237959i
$86$	7.25240			0.782046
$87$		−	24.9248i		−	2.67222i
$88$		−	2.00000i		−	0.213201i
$89$	−4.14931			−0.439826			−0.219913	−	0.975519i	$-0.570577\pi$
$89$	−4.14931			−0.439826			−0.219913	+	0.975519i	$0.570577\pi$
$90$	−1.68472	+	8.54936i	−0.177585	+	0.901181i
$91$	−2.27072			−0.238036
$92$		−	3.13536i		−	0.326884i
$93$			23.6724i			2.45472i
$94$	10.4200			1.07474
$95$	−1.96772	−	0.387755i	−0.201884	−	0.0397828i
$96$	−2.62620			−0.268035
$97$		−	6.14931i		−	0.624368i	−0.950022	−	0.312184i	$-0.898939\pi$
$97$		−	6.14931i		−	0.624368i	0.950022	−	0.312184i	$-0.101061\pi$
$98$			6.25240i			0.631587i
$99$	−7.79383			−0.783310
$100$	−4.62620	−	1.89692i	−0.462620	−	0.189692i
$101$	0.206167			0.0205144			0.0102572	−	0.999947i	$-0.496735\pi$
$101$	0.206167			0.0205144			0.0102572	+	0.999947i	$0.496735\pi$
$102$		−	2.62620i		−	0.260032i
$103$		−	4.77551i		−	0.470545i	−0.971929	−	0.235273i	$-0.924402\pi$
$103$		−	4.77551i		−	0.470545i	0.971929	−	0.235273i	$-0.0755983\pi$
$104$	2.62620			0.257520
$105$	4.98168	+	0.981678i	0.486162	+	0.0958020i
$106$	11.4017			1.10743
$107$			6.29862i			0.608911i	0.952527	+	0.304456i	$0.0984745\pi$
$107$			6.29862i			0.608911i	−0.952527	+	0.304456i	$0.901526\pi$
$108$			2.35548i			0.226656i
$109$	−5.55539			−0.532110			−0.266055	−	0.963958i	$-0.585720\pi$
$109$	−5.55539			−0.532110			−0.266055	+	0.963958i	$0.585720\pi$
$110$	0.864641	−	4.38776i	0.0824403	−	0.418356i
$111$	−26.7389			−2.53794
$112$			0.864641i			0.0817009i
$113$		−	10.6262i		−	0.999629i	−0.866133	−	0.499814i	$-0.833402\pi$
$113$		−	10.6262i		−	0.999629i	0.866133	−	0.499814i	$-0.166598\pi$
$114$	−2.35548			−0.220611
$115$	1.35548	−	6.87859i	0.126399	−	0.641432i
$116$	9.49084			0.881202
$117$		−	10.2341i		−	0.946140i
$118$			4.14931i			0.381975i
$119$	−0.864641			−0.0792615
$120$	−5.76156	−	1.13536i	−0.525956	−	0.103644i
$121$	−7.00000			−0.636364
$122$			3.28467i			0.297380i
$123$			25.0096i			2.25504i
$124$	−9.01395			−0.809477
$125$	−9.32924	−	6.16160i	−0.834432	−	0.551110i
$126$	3.36943			0.300173
$127$		−	14.3555i		−	1.27384i	−0.770929	−	0.636921i	$-0.780208\pi$
$127$		−	14.3555i		−	1.27384i	0.770929	−	0.636921i	$-0.219792\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	19.0462			1.67693
$130$	5.76156	+	1.13536i	0.505322	+	0.0995776i
$131$	17.0462			1.48934			0.744668	−	0.667435i	$-0.232608\pi$
$131$	17.0462			1.48934			0.744668	+	0.667435i	$0.232608\pi$
$132$		−	5.25240i		−	0.457162i
$133$			0.775511i			0.0672453i
$134$	−1.25240			−0.108191
$135$	−1.01832	+	5.16763i	−0.0876432	+	0.444759i
$136$	1.00000			0.0857493
$137$			14.5048i			1.23923i	0.784907	+	0.619614i	$0.212711\pi$
$137$			14.5048i			1.23923i	−0.784907	+	0.619614i	$0.787289\pi$
$138$		−	8.23407i		−	0.700931i
$139$	14.7110			1.24777			0.623884	−	0.781517i	$-0.285554\pi$
$139$	14.7110			1.24777			0.623884	+	0.781517i	$0.285554\pi$
$140$	−0.373802	+	1.89692i	−0.0315920	+	0.160319i
$141$	27.3651			2.30455
$142$		−	12.5371i		−	1.05209i
$143$			5.25240i			0.439227i
$144$	−3.89692			−0.324743
$145$	20.8217	+	4.10308i	1.72915	+	0.340743i
$146$	−2.62620			−0.217346
$147$			16.4200i			1.35430i
$148$		−	10.1816i		−	0.836921i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	−12.1493	−	4.98168i	−0.991987	−	0.406752i
$151$	−5.18785			−0.422181			−0.211090	−	0.977467i	$-0.567701\pi$
$151$	−5.18785			−0.422181			−0.211090	+	0.977467i	$0.567701\pi$
$152$		−	0.896916i		−	0.0727495i
$153$		−	3.89692i		−	0.315047i
$154$	−1.72928			−0.139349
$155$	−19.7755	−	3.89692i	−1.58841	−	0.313008i
$156$	6.89692			0.552195
$157$			10.2341i			0.816768i	0.912810	+	0.408384i	$0.133908\pi$
$157$			10.2341i			0.816768i	−0.912810	+	0.408384i	$0.866092\pi$
$158$			7.91087i			0.629355i
$159$	29.9431			2.37465
$160$	0.432320	−	2.19388i	0.0341779	−	0.173441i
$161$	−2.71096			−0.213654
$162$		−	5.50479i		−	0.432497i
$163$		−	6.47689i		−	0.507309i	−0.967295	−	0.253654i	$-0.918367\pi$
$163$		−	6.47689i		−	0.507309i	0.967295	−	0.253654i	$-0.0816326\pi$
$164$	−9.52311			−0.743630
$165$	2.27072	−	11.5231i	0.176775	−	0.897073i
$166$	−4.20617			−0.326462
$167$		−	3.84632i		−	0.297637i	−0.988865	−	0.148819i	$-0.952453\pi$
$167$		−	3.84632i		−	0.297637i	0.988865	−	0.148819i	$-0.0475470\pi$
$168$			2.27072i			0.175190i
$169$	6.10308			0.469468
$170$	2.19388	+	0.432320i	0.168263	+	0.0331575i
$171$	−3.49521			−0.267285
$172$			7.25240i			0.552990i
$173$			23.9109i			1.81791i	0.416895	+	0.908955i	$0.363118\pi$
$173$			23.9109i			1.81791i	−0.416895	+	0.908955i	$0.636882\pi$
$174$	24.9248			1.88955
$175$	−1.64015	+	4.00000i	−0.123984	+	0.302372i
$176$	2.00000			0.150756
$177$			10.8969i			0.819062i
$178$		−	4.14931i		−	0.311004i
$179$	14.7110			1.09955			0.549774	−	0.835313i	$-0.314714\pi$
$179$	14.7110			1.09955			0.549774	+	0.835313i	$0.314714\pi$
$180$	−8.54936	−	1.68472i	−0.637231	−	0.125571i
$181$	−23.4340			−1.74183			−0.870917	−	0.491430i	$-0.836474\pi$
$181$	−23.4340			−1.74183			−0.870917	+	0.491430i	$0.836474\pi$
$182$		−	2.27072i		−	0.168317i
$183$			8.62620i			0.637667i
$184$	3.13536			0.231142
$185$	4.40171	−	22.3372i	0.323620	−	1.64226i
$186$	−23.6724			−1.73575
$187$			2.00000i			0.146254i
$188$			10.4200i			0.759959i
$189$	2.03664			0.148144
$190$	0.387755	−	1.96772i	0.0281307	−	0.142754i
$191$	18.5048			1.33896			0.669480	−	0.742830i	$-0.266517\pi$
$191$	18.5048			1.33896			0.669480	+	0.742830i	$0.266517\pi$
$192$		−	2.62620i		−	0.189530i
$193$		−	5.45856i		−	0.392916i	−0.980512	−	0.196458i	$-0.937056\pi$
$193$		−	5.45856i		−	0.392916i	0.980512	−	0.196458i	$-0.0629439\pi$
$194$	6.14931			0.441495
$195$	15.1310	+	2.98168i	1.08355	+	0.213522i
$196$	−6.25240			−0.446600
$197$		−	13.9388i		−	0.993097i	−0.868009	−	0.496548i	$-0.834601\pi$
$197$		−	13.9388i		−	0.993097i	0.868009	−	0.496548i	$-0.165399\pi$
$198$		−	7.79383i		−	0.553884i
$199$	11.2847			0.799949			0.399975	−	0.916526i	$-0.369019\pi$
$199$	11.2847			0.799949			0.399975	+	0.916526i	$0.369019\pi$
$200$	1.89692	−	4.62620i	0.134132	−	0.327122i
$201$	−3.28904			−0.231991
$202$			0.206167i			0.0145059i
$203$		−	8.20617i		−	0.575960i
$204$	2.62620			0.183871
$205$	−20.8925	−	4.11704i	−1.45920	−	0.287546i
$206$	4.77551			0.332726
$207$		−	12.2182i		−	0.849226i
$208$			2.62620i			0.182094i
$209$	1.79383			0.124082
$210$	−0.981678	+	4.98168i	−0.0677422	+	0.343768i
$211$	−14.8401			−1.02163			−0.510816	−	0.859690i	$-0.670657\pi$
$211$	−14.8401			−1.02163			−0.510816	+	0.859690i	$0.670657\pi$
$212$			11.4017i			0.783073i
$213$		−	32.9248i		−	2.25597i
$214$	−6.29862			−0.430565
$215$	−3.13536	+	15.9109i	−0.213830	+	1.08511i
$216$	−2.35548			−0.160270
$217$			7.79383i			0.529080i
$218$		−	5.55539i		−	0.376258i
$219$	−6.89692			−0.466050
$220$	4.38776	+	0.864641i	0.295822	+	0.0582941i
$221$	−2.62620			−0.176657
$222$		−	26.7389i		−	1.79460i
$223$			3.30925i			0.221604i	0.993843	+	0.110802i	$0.0353419\pi$
$223$			3.30925i			0.221604i	−0.993843	+	0.110802i	$0.964658\pi$
$224$	−0.864641			−0.0577712
$225$	−18.0279	−	7.39212i	−1.20186	−	0.492808i
$226$	10.6262			0.706844
$227$			24.7187i			1.64063i	0.571909	+	0.820317i	$0.306203\pi$
$227$			24.7187i			1.64063i	−0.571909	+	0.820317i	$0.693797\pi$
$228$		−	2.35548i		−	0.155995i
$229$	−4.27072			−0.282217			−0.141109	−	0.989994i	$-0.545067\pi$
$229$	−4.27072			−0.282217			−0.141109	+	0.989994i	$0.545067\pi$
$230$	6.87859	+	1.35548i	0.453561	+	0.0893777i
$231$	−4.54144			−0.298805
$232$			9.49084i			0.623104i
$233$			0.832365i			0.0545301i	0.999628	+	0.0272650i	$0.00867981\pi$
$233$			0.832365i			0.0545301i	−0.999628	+	0.0272650i	$0.991320\pi$
$234$	10.2341			0.669022
$235$	−4.50479	+	22.8603i	−0.293860	+	1.49124i
$236$	−4.14931			−0.270097
$237$			20.7755i			1.34951i
$238$		−	0.864641i		−	0.0560463i
$239$	4.71096			0.304727			0.152363	−	0.988325i	$-0.451312\pi$
$239$	4.71096			0.304727			0.152363	+	0.988325i	$0.451312\pi$
$240$	1.13536	−	5.76156i	0.0732871	−	0.371907i
$241$	−23.4865			−1.51290			−0.756448	−	0.654054i	$-0.773067\pi$
$241$	−23.4865			−1.51290			−0.756448	+	0.654054i	$0.773067\pi$
$242$		−	7.00000i		−	0.449977i
$243$		−	21.5231i		−	1.38071i
$244$	−3.28467			−0.210280
$245$	−13.7170	−	2.70304i	−0.876346	−	0.172691i
$246$	−25.0096			−1.59455
$247$			2.35548i			0.149876i
$248$		−	9.01395i		−	0.572387i
$249$	−11.0462			−0.700026
$250$	6.16160	−	9.32924i	0.389694	−	0.590033i
$251$	−6.29862			−0.397566			−0.198783	−	0.980044i	$-0.563699\pi$
$251$	−6.29862			−0.397566			−0.198783	+	0.980044i	$0.563699\pi$
$252$			3.36943i			0.212254i
$253$			6.27072i			0.394237i
$254$	14.3555			0.900743
$255$	5.76156	+	1.13536i	0.360803	+	0.0710989i
$256$	1.00000			0.0625000
$257$			1.49521i			0.0932685i	0.998912	+	0.0466342i	$0.0148495\pi$
$257$			1.49521i			0.0932685i	−0.998912	+	0.0466342i	$0.985150\pi$
$258$			19.0462i			1.18577i
$259$	−8.80342			−0.547018
$260$	−1.13536	+	5.76156i	−0.0704120	+	0.357317i
$261$	36.9850			2.28931
$262$			17.0462i			1.05312i
$263$		−	9.94315i		−	0.613121i	−0.951851	−	0.306560i	$-0.900822\pi$
$263$		−	9.94315i		−	0.613121i	0.951851	−	0.306560i	$-0.0991781\pi$
$264$	5.25240			0.323263
$265$	−4.92919	+	25.0140i	−0.302798	+	1.53659i
$266$	−0.775511			−0.0475496
$267$		−	10.8969i		−	0.666880i
$268$		−	1.25240i		−	0.0765023i
$269$	−1.96772			−0.119974			−0.0599871	−	0.998199i	$-0.519106\pi$
$269$	−1.96772			−0.119974			−0.0599871	+	0.998199i	$0.519106\pi$
$270$	−5.16763	−	1.01832i	−0.314492	−	0.0619731i
$271$	8.84006			0.536995			0.268498	−	0.963280i	$-0.413473\pi$
$271$	8.84006			0.536995			0.268498	+	0.963280i	$0.413473\pi$
$272$			1.00000i			0.0606339i
$273$		−	5.96336i		−	0.360919i
$274$	−14.5048			−0.876267
$275$	9.25240	+	3.79383i	0.557940	+	0.228777i
$276$	8.23407			0.495633
$277$			19.8463i			1.19245i	0.802817	+	0.596225i	$0.203333\pi$
$277$			19.8463i			1.19245i	−0.802817	+	0.596225i	$0.796667\pi$
$278$			14.7110i			0.882305i
$279$	−35.1266			−2.10298
$280$	−1.89692	−	0.373802i	−0.113362	−	0.0223389i
$281$	−11.9065			−0.710282			−0.355141	−	0.934813i	$-0.615567\pi$
$281$	−11.9065			−0.710282			−0.355141	+	0.934813i	$0.615567\pi$
$282$			27.3651i			1.62957i
$283$			13.7370i			0.816579i	0.912853	+	0.408289i	$0.133875\pi$
$283$			13.7370i			0.816579i	−0.912853	+	0.408289i	$0.866125\pi$
$284$	12.5371			0.743938
$285$	1.01832	−	5.16763i	0.0603202	−	0.306104i
$286$	−5.25240			−0.310581
$287$			8.23407i			0.486042i
$288$		−	3.89692i		−	0.229628i
$289$	−1.00000			−0.0588235
$290$	−4.10308	+	20.8217i	−0.240941	+	1.22269i
$291$	16.1493			0.946689
$292$		−	2.62620i		−	0.153687i
$293$		−	12.1772i		−	0.711401i	−0.934600	−	0.355700i	$-0.884242\pi$
$293$		−	12.1772i		−	0.711401i	0.934600	−	0.355700i	$-0.115758\pi$
$294$	−16.4200			−0.957636
$295$	−9.10308	−	1.79383i	−0.530002	−	0.104441i
$296$	10.1816			0.591793
$297$		−	4.71096i		−	0.273358i
$298$		−	10.0000i		−	0.579284i
$299$	−8.23407			−0.476189
$300$	4.98168	−	12.1493i	0.287617	−	0.701441i
$301$	6.27072			0.361438
$302$		−	5.18785i		−	0.298527i
$303$			0.541436i			0.0311047i
$304$	0.896916			0.0514417
$305$	−7.20617	−	1.42003i	−0.412624	−	0.0813107i
$306$	3.89692			0.222772
$307$		−	23.7938i		−	1.35799i	−0.734145	−	0.678993i	$-0.762417\pi$
$307$		−	23.7938i		−	1.35799i	0.734145	−	0.678993i	$-0.237583\pi$
$308$		−	1.72928i		−	0.0985350i
$309$	12.5414			0.713457
$310$	3.89692	−	19.7755i	0.221330	−	1.12317i
$311$	32.9205			1.86675			0.933374	−	0.358906i	$-0.116850\pi$
$311$	32.9205			1.86675			0.933374	+	0.358906i	$0.116850\pi$
$312$			6.89692i			0.390461i
$313$		−	29.0462i		−	1.64179i	−0.571079	−	0.820895i	$-0.693475\pi$
$313$		−	29.0462i		−	1.64179i	0.571079	−	0.820895i	$-0.306525\pi$
$314$	−10.2341			−0.577542
$315$	−1.45667	+	7.39212i	−0.0820743	+	0.416499i
$316$	−7.91087			−0.445021
$317$		−	20.6864i		−	1.16186i	−0.813953	−	0.580931i	$-0.802688\pi$
$317$		−	20.6864i		−	1.16186i	0.813953	−	0.580931i	$-0.197312\pi$
$318$			29.9431i			1.67913i
$319$	−18.9817			−1.06277
$320$	2.19388	+	0.432320i	0.122641	+	0.0241674i
$321$	−16.5414			−0.923253
$322$		−	2.71096i		−	0.151076i
$323$			0.896916i			0.0499058i
$324$	5.50479			0.305822
$325$	−4.98168	+	12.1493i	−0.276334	+	0.673923i
$326$	6.47689			0.358722
$327$		−	14.5896i		−	0.806804i
$328$		−	9.52311i		−	0.525826i
$329$	9.00958			0.496714
$330$	11.5231	+	2.27072i	0.634327	+	0.124999i
$331$	4.02021			0.220971			0.110485	−	0.993878i	$-0.464759\pi$
$331$	4.02021			0.220971			0.110485	+	0.993878i	$0.464759\pi$
$332$		−	4.20617i		−	0.230843i
$333$		−	39.6768i		−	2.17428i
$334$	3.84632			0.210461
$335$	0.541436	−	2.74760i	0.0295818	−	0.150118i
$336$	−2.27072			−0.123878
$337$		−	2.21386i		−	0.120597i	−0.998180	−	0.0602984i	$-0.980795\pi$
$337$		−	2.21386i		−	0.120597i	0.998180	−	0.0602984i	$-0.0192052\pi$
$338$			6.10308i			0.331964i
$339$	27.9065			1.51567
$340$	−0.432320	+	2.19388i	−0.0234459	+	0.118980i
$341$	18.0279			0.976266
$342$		−	3.49521i		−	0.188999i
$343$			11.4586i			0.618704i
$344$	−7.25240			−0.391023
$345$	18.0646	+	3.55976i	0.972563	+	0.191651i
$346$	−23.9109			−1.28546
$347$			1.37380i			0.0737496i	0.999320	+	0.0368748i	$0.0117403\pi$
$347$			1.37380i			0.0737496i	−0.999320	+	0.0368748i	$0.988260\pi$
$348$			24.9248i			1.33611i
$349$	20.8680			1.11704			0.558518	−	0.829492i	$-0.311370\pi$
$349$	20.8680			1.11704			0.558518	+	0.829492i	$0.311370\pi$
$350$	−4.00000	−	1.64015i	−0.213809	−	0.0876698i
$351$	6.18596			0.330182
$352$			2.00000i			0.106600i
$353$		−	13.7572i		−	0.732221i	−0.930571	−	0.366111i	$-0.880689\pi$
$353$		−	13.7572i		−	0.732221i	0.930571	−	0.366111i	$-0.119311\pi$
$354$	−10.8969			−0.579165
$355$	27.5048	+	5.42003i	1.45980	+	0.287665i
$356$	4.14931			0.219913
$357$		−	2.27072i		−	0.120179i
$358$			14.7110i			0.777498i
$359$	−9.31695			−0.491730			−0.245865	−	0.969304i	$-0.579072\pi$
$359$	−9.31695			−0.491730			−0.245865	+	0.969304i	$0.579072\pi$
$360$	1.68472	−	8.54936i	0.0887924	−	0.450591i
$361$	−18.1955			−0.957660
$362$		−	23.4340i		−	1.23166i
$363$		−	18.3834i		−	0.964878i
$364$	2.27072			0.119018
$365$	1.13536	−	5.76156i	0.0594274	−	0.301574i
$366$	−8.62620			−0.450899
$367$		−	12.3878i		−	0.646636i	−0.946290	−	0.323318i	$-0.895202\pi$
$367$		−	12.3878i		−	0.646636i	0.946290	−	0.323318i	$-0.104798\pi$
$368$			3.13536i			0.163442i
$369$	−37.1108			−1.93191
$370$	22.3372	+	4.40171i	1.16125	+	0.228834i
$371$	9.85838			0.511822
$372$		−	23.6724i		−	1.22736i
$373$		−	23.3169i		−	1.20731i	−0.797247	−	0.603653i	$-0.793711\pi$
$373$		−	23.3169i		−	1.20731i	0.797247	−	0.603653i	$-0.206289\pi$
$374$	−2.00000			−0.103418
$375$	16.1816	−	24.5004i	0.835614	−	1.26520i
$376$	−10.4200			−0.537372
$377$		−	24.9248i		−	1.28369i
$378$			2.03664i			0.104754i
$379$	−28.9817			−1.48869			−0.744344	−	0.667796i	$-0.767238\pi$
$379$	−28.9817			−1.48869			−0.744344	+	0.667796i	$0.767238\pi$
$380$	1.96772	+	0.387755i	0.100942	+	0.0198914i
$381$	37.7003			1.93145
$382$			18.5048i			0.946788i
$383$			14.9527i			0.764049i	0.924152	+	0.382024i	$0.124773\pi$
$383$			14.9527i			0.764049i	−0.924152	+	0.382024i	$0.875227\pi$
$384$	2.62620			0.134018
$385$	0.747604	−	3.79383i	0.0381014	−	0.193352i
$386$	5.45856			0.277834
$387$			28.2620i			1.43664i
$388$			6.14931i			0.312184i
$389$	19.3169			0.979408			0.489704	−	0.871889i	$-0.337105\pi$
$389$	19.3169			0.979408			0.489704	+	0.871889i	$0.337105\pi$
$390$	−2.98168	+	15.1310i	−0.150983	+	0.766187i
$391$	−3.13536			−0.158562
$392$		−	6.25240i		−	0.315794i
$393$			44.7668i			2.25818i
$394$	13.9388			0.702225
$395$	−17.3555	−	3.42003i	−0.873249	−	0.172080i
$396$	7.79383			0.391655
$397$		−	9.57560i		−	0.480586i	−0.970700	−	0.240293i	$-0.922757\pi$
$397$		−	9.57560i		−	0.480586i	0.970700	−	0.240293i	$-0.0772435\pi$
$398$			11.2847i			0.565649i
$399$	−2.03664			−0.101960
$400$	4.62620	+	1.89692i	0.231310	+	0.0948458i
$401$	11.3169			0.565141			0.282571	−	0.959246i	$-0.408813\pi$
$401$	11.3169			0.565141			0.282571	+	0.959246i	$0.408813\pi$
$402$		−	3.28904i		−	0.164042i
$403$			23.6724i			1.17921i
$404$	−0.206167			−0.0102572
$405$	12.0768	+	2.37983i	0.600103	+	0.118255i
$406$	8.20617			0.407265
$407$			20.3632i			1.00937i
$408$			2.62620i			0.130016i
$409$	9.10308			0.450119			0.225059	−	0.974345i	$-0.427742\pi$
$409$	9.10308			0.450119			0.225059	+	0.974345i	$0.427742\pi$
$410$	4.11704	−	20.8925i	0.203326	−	1.03181i
$411$	−38.0925			−1.87896
$412$			4.77551i			0.235273i
$413$			3.58767i			0.176537i
$414$	12.2182			0.600493
$415$	1.81841	−	9.22782i	0.0892623	−	0.452976i
$416$	−2.62620			−0.128760
$417$			38.6339i			1.89191i
$418$			1.79383i			0.0877392i
$419$	4.02791			0.196776			0.0983881	−	0.995148i	$-0.468631\pi$
$419$	4.02791			0.196776			0.0983881	+	0.995148i	$0.468631\pi$
$420$	−4.98168	−	0.981678i	−0.243081	−	0.0479010i
$421$	15.2524			0.743356			0.371678	−	0.928362i	$-0.378782\pi$
$421$	15.2524			0.743356			0.371678	+	0.928362i	$0.378782\pi$
$422$		−	14.8401i		−	0.722403i
$423$			40.6060i			1.97433i
$424$	−11.4017			−0.553716
$425$	−1.89692	+	4.62620i	−0.0920140	+	0.224404i
$426$	32.9248			1.59521
$427$			2.84006i			0.137440i
$428$		−	6.29862i		−	0.304456i
$429$	−13.7938			−0.665973
$430$	−15.9109	−	3.13536i	−0.767290	−	0.151200i
$431$	−4.45231			−0.214460			−0.107230	−	0.994234i	$-0.534198\pi$
$431$	−4.45231			−0.214460			−0.107230	+	0.994234i	$0.534198\pi$
$432$		−	2.35548i		−	0.113328i
$433$			10.7110i			0.514736i	0.966313	+	0.257368i	$0.0828552\pi$
$433$			10.7110i			0.514736i	−0.966313	+	0.257368i	$0.917145\pi$
$434$	−7.79383			−0.374116
$435$	−10.7755	+	54.6820i	−0.516646	+	2.62180i
$436$	5.55539			0.266055
$437$			2.81215i			0.134524i
$438$		−	6.89692i		−	0.329547i
$439$	−5.09871			−0.243348			−0.121674	−	0.992570i	$-0.538826\pi$
$439$	−5.09871			−0.243348			−0.121674	+	0.992570i	$0.538826\pi$
$440$	−0.864641	+	4.38776i	−0.0412201	+	0.209178i
$441$	−24.3651			−1.16024
$442$		−	2.62620i		−	0.124916i
$443$			10.8034i			0.513286i	0.966506	+	0.256643i	$0.0826164\pi$
$443$			10.8034i			0.513286i	−0.966506	+	0.256643i	$0.917384\pi$
$444$	26.7389			1.26897
$445$	9.10308	+	1.79383i	0.431528	+	0.0850358i
$446$	−3.30925			−0.156698
$447$		−	26.2620i		−	1.24215i
$448$		−	0.864641i		−	0.0408504i
$449$	5.82174			0.274745			0.137372	−	0.990519i	$-0.456134\pi$
$449$	5.82174			0.274745			0.137372	+	0.990519i	$0.456134\pi$
$450$	7.39212	−	18.0279i	0.348468	−	0.849844i
$451$	19.0462			0.896852
$452$			10.6262i			0.499814i
$453$		−	13.6243i		−	0.640126i
$454$	−24.7187			−1.16010
$455$	4.98168	+	0.981678i	0.233545	+	0.0460218i
$456$	2.35548			0.110305
$457$		−	13.7014i		−	0.640923i	−0.947261	−	0.320462i	$-0.896162\pi$
$457$		−	13.7014i		−	0.640923i	0.947261	−	0.320462i	$-0.103838\pi$
$458$		−	4.27072i		−	0.199558i
$459$	2.35548			0.109944
$460$	−1.35548	+	6.87859i	−0.0631996	+	0.320716i
$461$	−27.0741			−1.26097			−0.630484	−	0.776202i	$-0.717144\pi$
$461$	−27.0741			−1.26097			−0.630484	+	0.776202i	$0.717144\pi$
$462$		−	4.54144i		−	0.211287i
$463$			37.3372i			1.73520i	0.497258	+	0.867602i	$0.334340\pi$
$463$			37.3372i			1.73520i	−0.497258	+	0.867602i	$0.665660\pi$
$464$	−9.49084			−0.440601
$465$	10.2341	−	51.9344i	0.474594	−	2.40840i
$466$	−0.832365			−0.0385586
$467$		−	35.3449i		−	1.63556i	−0.575528	−	0.817782i	$-0.695203\pi$
$467$		−	35.3449i		−	1.63556i	0.575528	−	0.817782i	$-0.304797\pi$
$468$			10.2341i			0.473070i
$469$	−1.08287			−0.0500024
$470$	−22.8603	−	4.50479i	−1.05447	−	0.207791i
$471$	−26.8767			−1.23841
$472$		−	4.14931i		−	0.190988i
$473$		−	14.5048i		−	0.666931i
$474$	−20.7755			−0.954251
$475$	4.14931	+	1.70138i	0.190384	+	0.0780644i
$476$	0.864641			0.0396308
$477$			44.4315i			2.03438i
$478$			4.71096i			0.215474i
$479$	−31.0419			−1.41834			−0.709169	−	0.705038i	$-0.750930\pi$
$479$	−31.0419			−1.41834			−0.709169	+	0.705038i	$0.750930\pi$
$480$	5.76156	+	1.13536i	0.262978	+	0.0518218i
$481$	−26.7389			−1.21919
$482$		−	23.4865i		−	1.06978i
$483$		−	7.11952i		−	0.323949i
$484$	7.00000			0.318182
$485$	−2.65847	+	13.4908i	−0.120715	+	0.612587i
$486$	21.5231			0.976308
$487$		−	13.1633i		−	0.596485i	−0.954490	−	0.298242i	$-0.903600\pi$
$487$		−	13.1633i		−	0.596485i	0.954490	−	0.298242i	$-0.0964003\pi$
$488$		−	3.28467i		−	0.148690i
$489$	17.0096			0.769200
$490$	2.70304	−	13.7170i	0.122111	−	0.619671i
$491$	24.3555			1.09915			0.549574	−	0.835445i	$-0.314790\pi$
$491$	24.3555			1.09915			0.549574	+	0.835445i	$0.314790\pi$
$492$		−	25.0096i		−	1.12752i
$493$		−	9.49084i		−	0.427446i
$494$	−2.35548			−0.105978
$495$	17.0987	+	3.36943i	0.768530	+	0.151445i
$496$	9.01395			0.404738
$497$		−	10.8401i		−	0.486243i
$498$		−	11.0462i		−	0.494993i
$499$	−36.2620			−1.62331			−0.811655	−	0.584138i	$-0.801433\pi$
$499$	−36.2620			−1.62331			−0.811655	+	0.584138i	$0.801433\pi$
$500$	9.32924	+	6.16160i	0.417216	+	0.275555i
$501$	10.1012			0.451288
$502$		−	6.29862i		−	0.281121i
$503$		−	42.3511i		−	1.88834i	−0.329455	−	0.944171i	$-0.606865\pi$
$503$		−	42.3511i		−	1.88834i	0.329455	−	0.944171i	$-0.393135\pi$
$504$	−3.36943			−0.150086
$505$	−0.452306	−	0.0891304i	−0.0201274	−	0.00396625i
$506$	−6.27072			−0.278767
$507$			16.0279i			0.711824i
$508$			14.3555i			0.636921i
$509$	1.70138			0.0754121			0.0377061	−	0.999289i	$-0.487995\pi$
$509$	1.70138			0.0754121			0.0377061	+	0.999289i	$0.487995\pi$
$510$	−1.13536	+	5.76156i	−0.0502745	+	0.255126i
$511$	−2.27072			−0.100451
$512$			1.00000i			0.0441942i
$513$		−	2.11267i		−	0.0932766i
$514$	−1.49521			−0.0659508
$515$	−2.06455	+	10.4769i	−0.0909750	+	0.461667i
$516$	−19.0462			−0.838463
$517$		−	20.8401i		−	0.916545i
$518$		−	8.80342i		−	0.386800i
$519$	−62.7947			−2.75638
$520$	−5.76156	−	1.13536i	−0.252661	−	0.0497888i
$521$	3.01832			0.132235			0.0661175	−	0.997812i	$-0.478939\pi$
$521$	3.01832			0.132235			0.0661175	+	0.997812i	$0.478939\pi$
$522$			36.9850i			1.61879i
$523$		−	5.79383i		−	0.253347i	−0.991944	−	0.126673i	$-0.959570\pi$
$523$		−	5.79383i		−	0.253347i	0.991944	−	0.126673i	$-0.0404300\pi$
$524$	−17.0462			−0.744668
$525$	−10.5048	−	4.30736i	−0.458467	−	0.187989i
$526$	9.94315			0.433542
$527$			9.01395i			0.392654i
$528$			5.25240i			0.228581i
$529$	13.1695			0.572588
$530$	−25.0140	−	4.92919i	−1.08654	−	0.214110i
$531$	−16.1695			−0.701698
$532$		−	0.775511i		−	0.0336226i
$533$			25.0096i			1.08329i
$534$	10.8969			0.471556
$535$	2.72302	−	13.8184i	0.117727	−	0.597422i
$536$	1.25240			0.0540953
$537$			38.6339i			1.66718i
$538$		−	1.96772i		−	0.0848346i
$539$	12.5048			0.538620
$540$	1.01832	−	5.16763i	0.0438216	−	0.222380i
$541$	0.258654			0.0111204			0.00556019	−	0.999985i	$-0.498230\pi$
$541$	0.258654			0.0111204			0.00556019	+	0.999985i	$0.498230\pi$
$542$			8.84006i			0.379713i
$543$		−	61.5423i		−	2.64103i
$544$	−1.00000			−0.0428746
$545$	12.1878	+	2.40171i	0.522070	+	0.102878i
$546$	5.96336			0.255208
$547$		−	32.4113i		−	1.38581i	−0.721030	−	0.692903i	$-0.756331\pi$
$547$		−	32.4113i		−	1.38581i	0.721030	−	0.692903i	$-0.243669\pi$
$548$		−	14.5048i		−	0.619614i
$549$	−12.8001			−0.546295
$550$	−3.79383	+	9.25240i	−0.161770	+	0.394523i
$551$	−8.51249			−0.362644
$552$			8.23407i			0.350465i
$553$			6.84006i			0.290869i
$554$	−19.8463			−0.843189
$555$	58.6618	+	11.5598i	2.49005	+	0.490684i
$556$	−14.7110			−0.623884
$557$			22.9248i			0.971356i	0.874138	+	0.485678i	$0.161427\pi$
$557$			22.9248i			0.971356i	−0.874138	+	0.485678i	$0.838573\pi$
$558$		−	35.1266i		−	1.48703i
$559$	19.0462			0.805570
$560$	0.373802	−	1.89692i	0.0157960	−	0.0801593i
$561$	−5.25240			−0.221756
$562$		−	11.9065i		−	0.502245i
$563$			17.8863i			0.753817i	0.926250	+	0.376909i	$0.123013\pi$
$563$			17.8863i			0.753817i	−0.926250	+	0.376909i	$0.876987\pi$
$564$	−27.3651			−1.15228
$565$	−4.59392	+	23.3126i	−0.193268	+	0.980768i
$566$	−13.7370			−0.577408
$567$		−	4.75967i		−	0.199887i
$568$			12.5371i			0.526044i
$569$	−12.3555			−0.517969			−0.258984	−	0.965882i	$-0.583388\pi$
$569$	−12.3555			−0.517969			−0.258984	+	0.965882i	$0.583388\pi$
$570$	5.16763	+	1.01832i	0.216448	+	0.0426528i
$571$	−27.3169			−1.14318			−0.571589	−	0.820540i	$-0.693673\pi$
$571$	−27.3169			−1.14318			−0.571589	+	0.820540i	$0.693673\pi$
$572$		−	5.25240i		−	0.219614i
$573$			48.5972i			2.03018i
$574$	−8.23407			−0.343684
$575$	−5.94751	+	14.5048i	−0.248028	+	0.604892i
$576$	3.89692			0.162372
$577$		−	10.6339i		−	0.442695i	−0.975195	−	0.221347i	$-0.928955\pi$
$577$		−	10.6339i		−	0.442695i	0.975195	−	0.221347i	$-0.0710455\pi$
$578$		−	1.00000i		−	0.0415945i
$579$	14.3353			0.595753
$580$	−20.8217	−	4.10308i	−0.864576	−	0.170371i
$581$	−3.63682			−0.150881
$582$			16.1493i			0.669411i
$583$		−	22.8034i		−	0.944421i
$584$	2.62620			0.108673
$585$	−4.42440	+	22.4523i	−0.182926	+	0.928289i
$586$	12.1772			0.503036
$587$			22.3757i			0.923544i	0.886999	+	0.461772i	$0.152786\pi$
$587$			22.3757i			0.923544i	−0.886999	+	0.461772i	$0.847214\pi$
$588$		−	16.4200i		−	0.677151i
$589$	8.08476			0.333127
$590$	1.79383	−	9.10308i	0.0738509	−	0.374768i
$591$	36.6060			1.50577
$592$			10.1816i			0.418461i
$593$			12.1695i			0.499742i	0.968279	+	0.249871i	$0.0803883\pi$
$593$			12.1695i			0.499742i	−0.968279	+	0.249871i	$0.919612\pi$
$594$	4.71096			0.193293
$595$	1.89692	+	0.373802i	0.0777660	+	0.0153244i
$596$	10.0000			0.409616
$597$			29.6358i			1.21291i
$598$		−	8.23407i		−	0.336716i
$599$	25.1387			1.02714			0.513569	−	0.858048i	$-0.328323\pi$
$599$	25.1387			1.02714			0.513569	+	0.858048i	$0.328323\pi$
$600$	12.1493	+	4.98168i	0.495994	+	0.203376i
$601$	−4.50479			−0.183754			−0.0918772	−	0.995770i	$-0.529287\pi$
$601$	−4.50479			−0.183754			−0.0918772	+	0.995770i	$0.529287\pi$
$602$			6.27072i			0.255575i
$603$		−	4.88048i		−	0.198749i
$604$	5.18785			0.211090
$605$	15.3571	+	3.02624i	0.624357	+	0.123034i
$606$	−0.541436			−0.0219944
$607$		−	7.00626i		−	0.284375i	−0.989840	−	0.142188i	$-0.954586\pi$
$607$		−	7.00626i		−	0.284375i	0.989840	−	0.142188i	$-0.0454136\pi$
$608$			0.896916i			0.0363748i
$609$	21.5510			0.873291
$610$	1.42003	−	7.20617i	0.0574954	−	0.291769i
$611$	27.3651			1.10707
$612$			3.89692i			0.157524i
$613$		−	7.46626i		−	0.301559i	−0.988567	−	0.150780i	$-0.951822\pi$
$613$		−	7.46626i		−	0.301559i	0.988567	−	0.150780i	$-0.0481784\pi$
$614$	23.7938			0.960241
$615$	10.8122	−	54.8680i	0.435988	−	2.21249i
$616$	1.72928			0.0696747
$617$			36.1772i			1.45644i	0.685343	+	0.728220i	$0.259652\pi$
$617$			36.1772i			1.45644i	−0.685343	+	0.728220i	$0.740348\pi$
$618$			12.5414i			0.504491i
$619$	4.27072			0.171655			0.0858273	−	0.996310i	$-0.472647\pi$
$619$	4.27072			0.171655			0.0858273	+	0.996310i	$0.472647\pi$
$620$	19.7755	+	3.89692i	0.794204	+	0.156504i
$621$	7.38528			0.296361
$622$			32.9205i			1.31999i
$623$		−	3.58767i		−	0.143737i
$624$	−6.89692			−0.276098
$625$	17.8034	+	17.5510i	0.712137	+	0.702041i
$626$	29.0462			1.16092
$627$			4.71096i			0.188138i
$628$		−	10.2341i		−	0.408384i
$629$	−10.1816			−0.405966
$630$	−7.39212	−	1.45667i	−0.294509	−	0.0580353i
$631$	26.0279			1.03615			0.518077	−	0.855334i	$-0.326648\pi$
$631$	26.0279			1.03615			0.518077	+	0.855334i	$0.326648\pi$
$632$		−	7.91087i		−	0.314677i
$633$		−	38.9729i		−	1.54904i
$634$	20.6864			0.821561
$635$	−6.20617	+	31.4942i	−0.246284	+	1.24981i
$636$	−29.9431			−1.18732
$637$			16.4200i			0.650585i
$638$		−	18.9817i		−	0.751492i
$639$	48.8559			1.93271
$640$	−0.432320	+	2.19388i	−0.0170890	+	0.0867206i
$641$	12.6831			0.500950			0.250475	−	0.968123i	$-0.419413\pi$
$641$	12.6831			0.500950			0.250475	+	0.968123i	$0.419413\pi$
$642$		−	16.5414i		−	0.652838i
$643$		−	25.1108i		−	0.990272i	−0.868815	−	0.495136i	$-0.835118\pi$
$643$		−	25.1108i		−	0.990272i	0.868815	−	0.495136i	$-0.164882\pi$
$644$	2.71096			0.106827
$645$	−41.7851	−	8.23407i	−1.64529	−	0.324216i
$646$	−0.896916			−0.0352887
$647$			38.0635i			1.49643i	0.663456	+	0.748215i	$0.269089\pi$
$647$			38.0635i			1.49643i	−0.663456	+	0.748215i	$0.730911\pi$
$648$			5.50479i			0.216249i
$649$	8.29862			0.325750
$650$	−12.1493	−	4.98168i	−0.476535	−	0.195397i
$651$	−20.4681			−0.802210
$652$			6.47689i			0.253654i
$653$		−	45.2682i		−	1.77148i	−0.464179	−	0.885742i	$-0.653650\pi$
$653$		−	45.2682i		−	1.77148i	0.464179	−	0.885742i	$-0.346350\pi$
$654$	14.5896			0.570497
$655$	−37.3973	−	7.36943i	−1.46123	−	0.287948i
$656$	9.52311			0.371815
$657$		−	10.2341i		−	0.399269i
$658$			9.00958i			0.351230i
$659$	−40.7466			−1.58726			−0.793630	−	0.608400i	$-0.791812\pi$
$659$	−40.7466			−1.58726			−0.793630	+	0.608400i	$0.791812\pi$
$660$	−2.27072	+	11.5231i	−0.0883876	+	0.448537i
$661$	2.53270			0.0985106			0.0492553	−	0.998786i	$-0.484315\pi$
$661$	2.53270			0.0985106			0.0492553	+	0.998786i	$0.484315\pi$
$662$			4.02021i			0.156250i
$663$		−	6.89692i		−	0.267854i
$664$	4.20617			0.163231
$665$	0.335269	−	1.70138i	0.0130012	−	0.0659765i
$666$	39.6768			1.53744
$667$		−	29.7572i		−	1.15220i
$668$			3.84632i			0.148819i
$669$	−8.69075			−0.336004
$670$	2.74760	+	0.541436i	0.106149	+	0.0209175i
$671$	6.56934			0.253607
$672$		−	2.27072i		−	0.0875949i
$673$			37.0818i			1.42940i	0.699431	+	0.714700i	$0.253437\pi$
$673$			37.0818i			1.42940i	−0.699431	+	0.714700i	$0.746563\pi$
$674$	2.21386			0.0852748
$675$	4.46815	−	10.8969i	0.171979	−	0.419423i
$676$	−6.10308			−0.234734
$677$		−	44.3790i		−	1.70562i	−0.522218	−	0.852812i	$-0.674895\pi$
$677$		−	44.3790i		−	1.70562i	0.522218	−	0.852812i	$-0.325105\pi$
$678$			27.9065i			1.07174i
$679$	5.31695			0.204046
$680$	−2.19388	−	0.432320i	−0.0841314	−	0.0165787i
$681$	−64.9161			−2.48759
$682$			18.0279i			0.690324i
$683$		−	7.46626i		−	0.285688i	−0.989745	−	0.142844i	$-0.954375\pi$
$683$		−	7.46626i		−	0.285688i	0.989745	−	0.142844i	$-0.0456248\pi$
$684$	3.49521			0.133643
$685$	6.27072	−	31.8217i	0.239592	−	1.21585i
$686$	−11.4586			−0.437490
$687$		−	11.2158i		−	0.427908i
$688$		−	7.25240i		−	0.276495i
$689$	29.9431			1.14074
$690$	−3.55976	+	18.0646i	−0.135518	+	0.687706i
$691$	26.8959			1.02317			0.511584	−	0.859233i	$-0.329059\pi$
$691$	26.8959			1.02317			0.511584	+	0.859233i	$0.329059\pi$
$692$		−	23.9109i		−	0.908955i
$693$		−	6.73887i		−	0.255988i
$694$	−1.37380			−0.0521488
$695$	−32.2740	−	6.35985i	−1.22422	−	0.241243i
$696$	−24.9248			−0.944773
$697$			9.52311i			0.360714i
$698$			20.8680i			0.789864i
$699$	−2.18596			−0.0826805
$700$	1.64015	−	4.00000i	0.0619919	−	0.151186i
$701$	23.7938			0.898681			0.449340	−	0.893361i	$-0.351659\pi$
$701$	23.7938			0.898681			0.449340	+	0.893361i	$0.351659\pi$
$702$			6.18596i			0.233474i
$703$			9.13203i			0.344421i
$704$	−2.00000			−0.0753778
$705$	−60.0356	−	11.8305i	−2.26107	−	0.445562i
$706$	13.7572			0.517759
$707$			0.178261i			0.00670419i
$708$		−	10.8969i		−	0.409531i
$709$	17.0140			0.638972			0.319486	−	0.947591i	$-0.396490\pi$
$709$	17.0140			0.638972			0.319486	+	0.947591i	$0.396490\pi$
$710$	−5.42003	+	27.5048i	−0.203410	+	1.03224i
$711$	−30.8280			−1.15614
$712$			4.14931i			0.155502i
$713$			28.2620i			1.05842i
$714$	2.27072			0.0849795
$715$	2.27072	−	11.5231i	0.0849200	−	0.430940i
$716$	−14.7110			−0.549774
$717$			12.3719i			0.462038i
$718$		−	9.31695i		−	0.347705i
$719$	23.8665			0.890071			0.445036	−	0.895513i	$-0.353191\pi$
$719$	23.8665			0.890071			0.445036	+	0.895513i	$0.353191\pi$
$720$	8.54936	+	1.68472i	0.318616	+	0.0627857i
$721$	4.12910			0.153776
$722$		−	18.1955i		−	0.677168i
$723$		−	61.6801i		−	2.29391i
$724$	23.4340			0.870917
$725$	−43.9065	−	18.0033i	−1.63065	−	0.668627i
$726$	18.3834			0.682271
$727$		−	28.3834i		−	1.05268i	−0.850274	−	0.526341i	$-0.823564\pi$
$727$		−	28.3834i		−	1.05268i	0.850274	−	0.526341i	$-0.176436\pi$
$728$			2.27072i			0.0841584i
$729$	40.0096			1.48184
$730$	5.76156	+	1.13536i	0.213245	+	0.0420215i
$731$	7.25240			0.268240
$732$		−	8.62620i		−	0.318833i
$733$			28.2216i			1.04239i	0.853439	+	0.521194i	$0.174513\pi$
$733$			28.2216i			1.04239i	−0.853439	+	0.521194i	$0.825487\pi$
$734$	12.3878			0.457240
$735$	7.09871	−	36.0235i	0.261840	−	1.32875i
$736$	−3.13536			−0.115571
$737$			2.50479i			0.0922652i
$738$		−	37.1108i		−	1.36607i
$739$	−0.226378			−0.00832746			−0.00416373	−	0.999991i	$-0.501325\pi$
$739$	−0.226378			−0.00832746			−0.00416373	+	0.999991i	$0.501325\pi$
$740$	−4.40171	+	22.3372i	−0.161810	+	0.821130i
$741$	−6.18596			−0.227247
$742$			9.85838i			0.361913i
$743$			47.6035i			1.74640i	0.487359	+	0.873202i	$0.337960\pi$
$743$			47.6035i			1.74640i	−0.487359	+	0.873202i	$0.662040\pi$
$744$	23.6724			0.867873
$745$	21.9388	+	4.32320i	0.803775	+	0.158390i
$746$	23.3169			0.853694
$747$		−	16.3911i		−	0.599718i
$748$		−	2.00000i		−	0.0731272i
$749$	−5.44605			−0.198994
$750$	24.5004	+	16.1816i	0.894629	+	0.590868i
$751$	0.124733			0.00455157			0.00227578	−	0.999997i	$-0.499276\pi$
$751$	0.124733			0.00455157			0.00227578	+	0.999997i	$0.499276\pi$
$752$		−	10.4200i		−	0.379979i
$753$		−	16.5414i		−	0.602803i
$754$	24.9248			0.907709
$755$	11.3815	+	2.24281i	0.414215	+	0.0816243i
$756$	−2.03664			−0.0740720
$757$		−	33.7774i		−	1.22766i	−0.789438	−	0.613830i	$-0.789628\pi$
$757$		−	33.7774i		−	1.22766i	0.789438	−	0.613830i	$-0.210372\pi$
$758$		−	28.9817i		−	1.05266i
$759$	−16.4681			−0.597756
$760$	−0.387755	+	1.96772i	−0.0140654	+	0.0713769i
$761$	11.4219			0.414044			0.207022	−	0.978336i	$-0.433623\pi$
$761$	11.4219			0.414044			0.207022	+	0.978336i	$0.433623\pi$
$762$			37.7003i			1.36574i
$763$		−	4.80342i		−	0.173895i
$764$	−18.5048			−0.669480
$765$	−1.68472	+	8.54936i	−0.0609111	+	0.309103i
$766$	−14.9527			−0.540264
$767$			10.8969i			0.393465i
$768$			2.62620i			0.0947648i
$769$	−12.1127			−0.436794			−0.218397	−	0.975860i	$-0.570083\pi$
$769$	−12.1127			−0.436794			−0.218397	+	0.975860i	$0.570083\pi$
$770$	3.79383	+	0.747604i	0.136720	+	0.0269418i
$771$	−3.92671			−0.141417
$772$			5.45856i			0.196458i
$773$			37.4586i			1.34729i	0.739055	+	0.673645i	$0.235272\pi$
$773$			37.4586i			1.34729i	−0.739055	+	0.673645i	$0.764728\pi$
$774$	−28.2620			−1.01586
$775$	41.7003	+	17.0987i	1.49792	+	0.614204i
$776$	−6.14931			−0.220747
$777$		−	23.1195i		−	0.829408i
$778$			19.3169i			0.692546i
$779$	8.54144			0.306029
$780$	−15.1310	−	2.98168i	−0.541776	−	0.106761i
$781$	−25.0741			−0.897223
$782$		−	3.13536i		−	0.112120i
$783$			22.3555i			0.798920i
$784$	6.25240			0.223300
$785$	4.42440	−	22.4523i	0.157914	−	0.801357i
$786$	−44.7668			−1.59678
$787$			25.0664i			0.893522i	0.894653	+	0.446761i	$0.147423\pi$
$787$			25.0664i			0.893522i	−0.894653	+	0.446761i	$0.852577\pi$
$788$			13.9388i			0.496548i
$789$	26.1127			0.929636
$790$	3.42003	−	17.3555i	0.121679	−	0.617480i
$791$	9.18785			0.326682
$792$			7.79383i			0.276942i
$793$			8.62620i			0.306325i
$794$	9.57560			0.339825
$795$	−65.6916	−	12.9450i	−2.32984	−	0.459113i
$796$	−11.2847			−0.399975
$797$			19.5510i			0.692533i	0.938136	+	0.346266i	$0.112551\pi$
$797$			19.5510i			0.692533i	−0.938136	+	0.346266i	$0.887449\pi$
$798$		−	2.03664i		−	0.0720964i
$799$	10.4200			0.368634
$800$	−1.89692	+	4.62620i	−0.0670661	+	0.163561i
$801$	16.1695			0.571322
$802$			11.3169i			0.399615i
$803$			5.25240i			0.185353i
$804$	3.28904			0.115996
$805$	5.94751	+	1.17200i	0.209622	+	0.0413077i
$806$	−23.6724			−0.833826
$807$		−	5.16763i		−	0.181909i
$808$		−	0.206167i		−	0.00725294i
$809$	−20.1974			−0.710104			−0.355052	−	0.934847i	$-0.615537\pi$
$809$	−20.1974			−0.710104			−0.355052	+	0.934847i	$0.615537\pi$
$810$	−2.37983	+	12.0768i	−0.0836189	+	0.424337i
$811$	28.1570			0.988726			0.494363	−	0.869255i	$-0.335401\pi$
$811$	28.1570			0.988726			0.494363	+	0.869255i	$0.335401\pi$
$812$			8.20617i			0.287980i
$813$			23.2158i			0.814212i
$814$	−20.3632			−0.713729
$815$	−2.80009	+	14.2095i	−0.0980829	+	0.497737i
$816$	−2.62620			−0.0919353
$817$		−	6.50479i		−	0.227574i
$818$			9.10308i			0.318282i
$819$	8.84880			0.309202
$820$	20.8925	+	4.11704i	0.729599	+	0.143773i
$821$	−51.2759			−1.78954			−0.894771	−	0.446525i	$-0.852661\pi$
$821$	−51.2759			−1.78954			−0.894771	+	0.446525i	$0.852661\pi$
$822$		−	38.0925i		−	1.32863i
$823$			52.9850i			1.84694i	0.383669	+	0.923471i	$0.374660\pi$
$823$			52.9850i			1.84694i	−0.383669	+	0.923471i	$0.625340\pi$
$824$	−4.77551			−0.166363
$825$	−9.96336	+	24.2986i	−0.346880	+	0.845970i
$826$	−3.58767			−0.124831
$827$		−	39.7205i		−	1.38122i	−0.723228	−	0.690609i	$-0.757342\pi$
$827$		−	39.7205i		−	1.38122i	0.723228	−	0.690609i	$-0.242658\pi$
$828$			12.2182i			0.424613i
$829$	−23.0096			−0.799156			−0.399578	−	0.916699i	$-0.630843\pi$
$829$	−23.0096			−0.799156			−0.399578	+	0.916699i	$0.630843\pi$
$830$	9.22782	+	1.81841i	0.320302	+	0.0631180i
$831$	−52.1204			−1.80804
$832$		−	2.62620i		−	0.0910470i
$833$			6.25240i			0.216633i
$834$	−38.6339			−1.33778
$835$	−1.66284	+	8.43835i	−0.0575450	+	0.292021i
$836$	−1.79383			−0.0620410
$837$		−	21.2322i		−	0.733892i
$838$			4.02791i			0.139142i
$839$	−2.39545			−0.0827002			−0.0413501	−	0.999145i	$-0.513166\pi$
$839$	−2.39545			−0.0827002			−0.0413501	+	0.999145i	$0.513166\pi$
$840$	0.981678	−	4.98168i	0.0338711	−	0.171884i
$841$	61.0760			2.10607
$842$			15.2524i			0.525632i
$843$		−	31.2688i		−	1.07696i
$844$	14.8401			0.510816
$845$	−13.3894	−	2.63849i	−0.460610	−	0.0907667i
$846$	−40.6060			−1.39606
$847$		−	6.05249i		−	0.207966i
$848$		−	11.4017i		−	0.391536i
$849$	−36.0760			−1.23813
$850$	−4.62620	−	1.89692i	−0.158677	−	0.0650637i
$851$	−31.9229			−1.09430
$852$			32.9248i			1.12799i
$853$		−	2.24614i		−	0.0769063i	−0.999260	−	0.0384532i	$-0.987757\pi$
$853$		−	2.24614i		−	0.0769063i	0.999260	−	0.0384532i	$-0.0122430\pi$
$854$	−2.84006			−0.0971849
$855$	7.66806	+	1.51105i	0.262242	+	0.0516768i
$856$	6.29862			0.215283
$857$			18.3188i			0.625760i	0.949793	+	0.312880i	$0.101294\pi$
$857$			18.3188i			0.625760i	−0.949793	+	0.312880i	$0.898706\pi$
$858$		−	13.7938i		−	0.470914i
$859$	42.1127			1.43687			0.718433	−	0.695596i	$-0.244860\pi$
$859$	42.1127			1.43687			0.718433	+	0.695596i	$0.244860\pi$
$860$	3.13536	−	15.9109i	0.106915	−	0.542556i
$861$	−21.6243			−0.736954
$862$		−	4.45231i		−	0.151646i
$863$			44.8313i			1.52608i	0.646354	+	0.763038i	$0.276293\pi$
$863$			44.8313i			1.52608i	−0.646354	+	0.763038i	$0.723707\pi$
$864$	2.35548			0.0801351
$865$	10.3372	−	52.4575i	0.351474	−	1.78361i
$866$	−10.7110			−0.363973
$867$		−	2.62620i		−	0.0891904i
$868$		−	7.79383i		−	0.264540i
$869$	15.8217			0.536716
$870$	−54.6820	−	10.7755i	−1.85389	−	0.365324i
$871$	−3.28904			−0.111445
$872$			5.55539i			0.188129i
$873$			23.9634i			0.811037i
$874$	−2.81215			−0.0951226
$875$	5.32757	−	8.06644i	0.180105	−	0.272695i
$876$	6.89692			0.233025
$877$		−	2.29530i		−	0.0775067i	−0.999249	−	0.0387533i	$-0.987661\pi$
$877$		−	2.29530i		−	0.0775067i	0.999249	−	0.0387533i	$-0.0123387\pi$
$878$		−	5.09871i		−	0.172073i
$879$	31.9798			1.07865
$880$	−4.38776	−	0.864641i	−0.147911	−	0.0291470i
$881$	−20.9171			−0.704716			−0.352358	−	0.935865i	$-0.614620\pi$
$881$	−20.9171			−0.704716			−0.352358	+	0.935865i	$0.614620\pi$
$882$		−	24.3651i		−	0.820414i
$883$		−	26.6743i		−	0.897662i	−0.893617	−	0.448831i	$-0.851840\pi$
$883$		−	26.6743i		−	0.897662i	0.893617	−	0.448831i	$-0.148160\pi$
$884$	2.62620			0.0883286
$885$	4.71096	−	23.9065i	0.158357	−	0.803608i
$886$	−10.8034			−0.362948
$887$			29.1633i			0.979207i	0.871945	+	0.489603i	$0.162858\pi$
$887$			29.1633i			0.979207i	−0.871945	+	0.489603i	$0.837142\pi$
$888$			26.7389i			0.897298i
$889$	12.4123			0.416296
$890$	−1.79383	+	9.10308i	−0.0601294	+	0.305136i
$891$	−11.0096			−0.368835
$892$		−	3.30925i		−	0.110802i
$893$		−	9.34590i		−	0.312748i
$894$	26.2620			0.878332
$895$	−32.2740	−	6.35985i	−1.07880	−	0.212586i
$896$	0.864641			0.0288856
$897$		−	21.6243i		−	0.722015i
$898$			5.82174i			0.194274i
$899$	−85.5500			−2.85325
$900$	18.0279	+	7.39212i	0.600930	+	0.246404i
$901$	11.4017			0.379846
$902$			19.0462i			0.634170i
$903$			16.4681i			0.548026i
$904$	−10.6262			−0.353422
$905$	51.4113	+	10.1310i	1.70897	+	0.336766i
$906$	13.6243			0.452637
$907$		−	23.2322i		−	0.771412i	−0.922622	−	0.385706i	$-0.873958\pi$
$907$		−	23.2322i		−	0.771412i	0.922622	−	0.385706i	$-0.126042\pi$
$908$		−	24.7187i		−	0.820317i
$909$	−0.803417			−0.0266477
$910$	−0.981678	+	4.98168i	−0.0325423	+	0.165141i
$911$	−20.8646			−0.691276			−0.345638	−	0.938368i	$-0.612338\pi$
$911$	−20.8646			−0.691276			−0.345638	+	0.938368i	$0.612338\pi$
$912$			2.35548i			0.0779977i
$913$			8.41233i			0.278408i
$914$	13.7014			0.453201
$915$	3.72928	−	18.9248i	0.123286	−	0.625635i
$916$	4.27072			0.141109
$917$			14.7389i			0.486720i
$918$			2.35548i			0.0777424i
$919$	−18.2062			−0.600566			−0.300283	−	0.953850i	$-0.597081\pi$
$919$	−18.2062			−0.600566			−0.300283	+	0.953850i	$0.597081\pi$
$920$	−6.87859	−	1.35548i	−0.226781	−	0.0446888i
$921$	62.4873			2.05903
$922$		−	27.0741i		−	0.891639i
$923$		−	32.9248i		−	1.08373i
$924$	4.54144			0.149402
$925$	−19.3136	+	47.1020i	−0.635028	+	1.54871i
$926$	−37.3372			−1.22698
$927$			18.6098i			0.611225i
$928$		−	9.49084i		−	0.311552i
$929$	−17.2803			−0.566948			−0.283474	−	0.958980i	$-0.591487\pi$
$929$	−17.2803			−0.566948			−0.283474	+	0.958980i	$0.591487\pi$
$930$	51.9344	+	10.2341i	1.70300	+	0.335589i
$931$	5.60788			0.183791
$932$		−	0.832365i		−	0.0272650i
$933$			86.4556i			2.83043i
$934$	35.3449			1.15652
$935$	0.864641	−	4.38776i	0.0282768	−	0.143495i
$936$	−10.2341			−0.334511
$937$		−	50.2986i		−	1.64318i	−0.570076	−	0.821592i	$-0.693086\pi$
$937$		−	50.2986i		−	1.64318i	0.570076	−	0.821592i	$-0.306914\pi$
$938$		−	1.08287i		−	0.0353571i
$939$	76.2811			2.48934
$940$	4.50479	−	22.8603i	0.146930	−	0.745620i
$941$	20.7153			0.675300			0.337650	−	0.941272i	$-0.390368\pi$
$941$	20.7153			0.675300			0.337650	+	0.941272i	$0.390368\pi$
$942$		−	26.8767i		−	0.875690i
$943$			29.8584i			0.972323i
$944$	4.14931			0.135049
$945$	−4.46815	−	0.880483i	−0.145349	−	0.0286421i
$946$	14.5048			0.471591
$947$			8.89692i			0.289111i	0.989497	+	0.144555i	$0.0461752\pi$
$947$			8.89692i			0.289111i	−0.989497	+	0.144555i	$0.953825\pi$
$948$		−	20.7755i		−	0.674757i
$949$	−6.89692			−0.223883
$950$	−1.70138	+	4.14931i	−0.0551999	+	0.134621i
$951$	54.3265			1.76166
$952$			0.864641i			0.0280232i
$953$			17.2158i			0.557673i	0.960339	+	0.278836i	$0.0899487\pi$
$953$			17.2158i			0.557673i	−0.960339	+	0.278836i	$0.910051\pi$
$954$	−44.4315			−1.43852
$955$	−40.5972	−	8.00000i	−1.31370	−	0.258874i
$956$	−4.71096			−0.152363
$957$		−	49.8496i		−	1.61141i
$958$		−	31.0419i		−	1.00292i
$959$	−12.5414			−0.404984
$960$	−1.13536	+	5.76156i	−0.0366436	+	0.185953i
$961$	50.2514			1.62101
$962$		−	26.7389i		−	0.862096i
$963$		−	24.5452i		−	0.790958i
$964$	23.4865			0.756448
$965$	−2.35985	+	11.9754i	−0.0759662	+	0.385502i
$966$	7.11952			0.229067
$967$		−	1.90754i		−	0.0613424i	−0.999530	−	0.0306712i	$-0.990236\pi$
$967$		−	1.90754i		−	0.0613424i	0.999530	−	0.0306712i	$-0.00976448\pi$
$968$			7.00000i			0.224989i
$969$	−2.35548			−0.0756689
$970$	−13.4908	−	2.65847i	−0.433165	−	0.0853584i
$971$	−4.97398			−0.159623			−0.0798113	−	0.996810i	$-0.525432\pi$
$971$	−4.97398			−0.159623			−0.0798113	+	0.996810i	$0.525432\pi$
$972$			21.5231i			0.690354i
$973$			12.7197i			0.407775i
$974$	13.1633			0.421778
$975$	−31.9065	−	13.0829i	−1.02183	−	0.418987i
$976$	3.28467			0.105140
$977$		−	51.2716i		−	1.64032i	−0.572132	−	0.820161i	$-0.693884\pi$
$977$		−	51.2716i		−	1.64032i	0.572132	−	0.820161i	$-0.306116\pi$
$978$			17.0096i			0.543907i
$979$	−8.29862			−0.265225
$980$	13.7170	+	2.70304i	0.438173	+	0.0863454i
$981$	21.6489			0.691196
$982$			24.3555i			0.777215i
$983$			9.88296i			0.315218i	0.987502	+	0.157609i	$0.0503785\pi$
$983$			9.88296i			0.315218i	−0.987502	+	0.157609i	$0.949622\pi$
$984$	25.0096			0.797276
$985$	−6.02602	+	30.5800i	−0.192005	+	0.974359i
$986$	9.49084			0.302250
$987$			23.6610i			0.753136i
$988$		−	2.35548i		−	0.0749378i
$989$	22.7389			0.723054
$990$	−3.36943	+	17.0987i	−0.107088	+	0.543433i
$991$	−37.7807			−1.20014			−0.600072	−	0.799946i	$-0.704861\pi$
$991$	−37.7807			−1.20014			−0.600072	+	0.799946i	$0.704861\pi$
$992$			9.01395i			0.286193i
$993$			10.5579i			0.335044i
$994$	10.8401			0.343826
$995$	−24.7572	−	4.87859i	−0.784856	−	0.154662i
$996$	11.0462			0.350013
$997$			8.14494i			0.257953i	0.991648	+	0.128976i	$0.0411692\pi$
$997$			8.14494i			0.257953i	−0.991648	+	0.128976i	$0.958831\pi$
$998$		−	36.2620i		−	1.14785i
$999$	23.9825			0.758774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.c.b.69.6	yes	6
3.2	odd	2		1530.2.d.g.919.3		6
4.3	odd	2		1360.2.e.c.1089.2		6
5.2	odd	4		850.2.a.p.1.3		3
5.3	odd	4		850.2.a.q.1.1		3
5.4	even	2	inner	170.2.c.b.69.1	✓	6
15.2	even	4		7650.2.a.do.1.2		3
15.8	even	4		7650.2.a.dj.1.2		3
15.14	odd	2		1530.2.d.g.919.6		6
20.3	even	4		6800.2.a.bk.1.3		3
20.7	even	4		6800.2.a.bp.1.1		3
20.19	odd	2		1360.2.e.c.1089.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.c.b.69.1	✓	6	5.4	even	2	inner
170.2.c.b.69.6	yes	6	1.1	even	1	trivial
850.2.a.p.1.3		3	5.2	odd	4
850.2.a.q.1.1		3	5.3	odd	4
1360.2.e.c.1089.2		6	4.3	odd	2
1360.2.e.c.1089.5		6	20.19	odd	2
1530.2.d.g.919.3		6	3.2	odd	2
1530.2.d.g.919.6		6	15.14	odd	2
6800.2.a.bk.1.3		3	20.3	even	4
6800.2.a.bp.1.1		3	20.7	even	4
7650.2.a.dj.1.2		3	15.8	even	4
7650.2.a.do.1.2		3	15.2	even	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.62620i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} -2.62620 q^{6} +0.864641i q^{7} -1.00000i q^{8} -3.89692 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.62620i q^{3} -1.00000 q^{4} +(-2.19388 - 0.432320i) q^{5} -2.62620 q^{6} +0.864641i q^{7} -1.00000i q^{8} -3.89692 q^{9} +(0.432320 - 2.19388i) q^{10} +2.00000 q^{11} -2.62620i q^{12} +2.62620i q^{13} -0.864641 q^{14} +(1.13536 - 5.76156i) q^{15} +1.00000 q^{16} +1.00000i q^{17} -3.89692i q^{18} +0.896916 q^{19} +(2.19388 + 0.432320i) q^{20} -2.27072 q^{21} +2.00000i q^{22} +3.13536i q^{23} +2.62620 q^{24} +(4.62620 + 1.89692i) q^{25} -2.62620 q^{26} -2.35548i q^{27} -0.864641i q^{28} -9.49084 q^{29} +(5.76156 + 1.13536i) q^{30} +9.01395 q^{31} +1.00000i q^{32} +5.25240i q^{33} -1.00000 q^{34} +(0.373802 - 1.89692i) q^{35} +3.89692 q^{36} +10.1816i q^{37} +0.896916i q^{38} -6.89692 q^{39} +(-0.432320 + 2.19388i) q^{40} +9.52311 q^{41} -2.27072i q^{42} -7.25240i q^{43} -2.00000 q^{44} +(8.54936 + 1.68472i) q^{45} -3.13536 q^{46} -10.4200i q^{47} +2.62620i q^{48} +6.25240 q^{49} +(-1.89692 + 4.62620i) q^{50} -2.62620 q^{51} -2.62620i q^{52} -11.4017i q^{53} +2.35548 q^{54} +(-4.38776 - 0.864641i) q^{55} +0.864641 q^{56} +2.35548i q^{57} -9.49084i q^{58} +4.14931 q^{59} +(-1.13536 + 5.76156i) q^{60} +3.28467 q^{61} +9.01395i q^{62} -3.36943i q^{63} -1.00000 q^{64} +(1.13536 - 5.76156i) q^{65} -5.25240 q^{66} +1.25240i q^{67} -1.00000i q^{68} -8.23407 q^{69} +(1.89692 + 0.373802i) q^{70} -12.5371 q^{71} +3.89692i q^{72} +2.62620i q^{73} -10.1816 q^{74} +(-4.98168 + 12.1493i) q^{75} -0.896916 q^{76} +1.72928i q^{77} -6.89692i q^{78} +7.91087 q^{79} +(-2.19388 - 0.432320i) q^{80} -5.50479 q^{81} +9.52311i q^{82} +4.20617i q^{83} +2.27072 q^{84} +(0.432320 - 2.19388i) q^{85} +7.25240 q^{86} -24.9248i q^{87} -2.00000i q^{88} -4.14931 q^{89} +(-1.68472 + 8.54936i) q^{90} -2.27072 q^{91} -3.13536i q^{92} +23.6724i q^{93} +10.4200 q^{94} +(-1.96772 - 0.387755i) q^{95} -2.62620 q^{96} -6.14931i q^{97} +6.25240i q^{98} -7.79383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} + 2 q^{6} - 16 q^{9} + 12 q^{11} + 12 q^{15} + 6 q^{16} - 2 q^{19} - 2 q^{20} - 24 q^{21} - 2 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{29} + 22 q^{30} + 6 q^{31} - 6 q^{34} + 20 q^{35} + 16 q^{36} - 34 q^{39} + 32 q^{41} - 12 q^{44} + 8 q^{45} - 24 q^{46} + 2 q^{49} - 4 q^{50} + 2 q^{51} - 14 q^{54} + 4 q^{55} - 18 q^{59} - 12 q^{60} - 18 q^{61} - 6 q^{64} + 12 q^{65} + 4 q^{66} + 32 q^{69} + 4 q^{70} - 2 q^{71} - 16 q^{74} + 16 q^{75} + 2 q^{76} - 8 q^{79} + 2 q^{80} + 38 q^{81} + 24 q^{84} + 8 q^{86} + 18 q^{89} + 28 q^{90} - 24 q^{91} + 30 q^{94} - 14 q^{95} + 2 q^{96} - 32 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 + 2 * q^6 - 16 * q^9 + 12 * q^11 + 12 * q^15 + 6 * q^16 - 2 * q^19 - 2 * q^20 - 24 * q^21 - 2 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^29 + 22 * q^30 + 6 * q^31 - 6 * q^34 + 20 * q^35 + 16 * q^36 - 34 * q^39 + 32 * q^41 - 12 * q^44 + 8 * q^45 - 24 * q^46 + 2 * q^49 - 4 * q^50 + 2 * q^51 - 14 * q^54 + 4 * q^55 - 18 * q^59 - 12 * q^60 - 18 * q^61 - 6 * q^64 + 12 * q^65 + 4 * q^66 + 32 * q^69 + 4 * q^70 - 2 * q^71 - 16 * q^74 + 16 * q^75 + 2 * q^76 - 8 * q^79 + 2 * q^80 + 38 * q^81 + 24 * q^84 + 8 * q^86 + 18 * q^89 + 28 * q^90 - 24 * q^91 + 30 * q^94 - 14 * q^95 + 2 * q^96 - 32 * q^99

Introduction

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