LMFDB - Embedded newform 525.2.t.i.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$1.71408 - 0.248842i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.i.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780577 + 0.450666i) q^{2} +(0.641538 + 1.60886i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(-1.22583 - 0.966719i) q^{6} +(-0.105498 - 2.64365i) q^{7} -2.87309i q^{8} +(-2.17686 + 2.06429i) q^{9} +O(q^{10})$	\(q+(-0.780577 + 0.450666i) q^{2} +(0.641538 + 1.60886i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(-1.22583 - 0.966719i) q^{6} +(-0.105498 - 2.64365i) q^{7} -2.87309i q^{8} +(-2.17686 + 2.06429i) q^{9} +(-5.46176 - 3.15335i) q^{11} +(-2.03564 - 0.295524i) q^{12} -3.77183i q^{13} +(1.27375 + 2.01603i) q^{14} +(0.107205 + 0.185685i) q^{16} +(1.88963 - 3.27294i) q^{17} +(0.768900 - 2.59237i) q^{18} +(-4.57893 + 2.64365i) q^{19} +(4.18558 - 1.86573i) q^{21} +5.68443 q^{22} +(-5.87050 + 3.38933i) q^{23} +(4.62239 - 1.84320i) q^{24} +(1.69984 + 2.94420i) q^{26} +(-4.71769 - 2.17794i) q^{27} +(2.78161 + 1.46129i) q^{28} +3.06327i q^{29} +(0.349819 + 0.201968i) q^{31} +(4.80897 + 2.77646i) q^{32} +(1.56937 - 10.8102i) q^{33} +3.40637i q^{34} +(-0.830485 - 3.46465i) q^{36} +(0.668021 + 1.15705i) q^{37} +(2.38281 - 4.12714i) q^{38} +(6.06834 - 2.41977i) q^{39} +6.53749 q^{41} +(-2.42634 + 3.34265i) q^{42} -4.84564 q^{43} +(6.48638 - 3.74491i) q^{44} +(3.05492 - 5.29127i) q^{46} +(-0.970371 - 1.68073i) q^{47} +(-0.229964 + 0.291602i) q^{48} +(-6.97774 + 0.557800i) q^{49} +(6.47796 + 0.940437i) q^{51} +(3.87929 + 2.23971i) q^{52} +(1.24774 + 0.720381i) q^{53} +(4.66404 - 0.426055i) q^{54} +(-7.59543 + 0.303106i) q^{56} +(-7.19082 - 5.67086i) q^{57} +(-1.38051 - 2.39112i) q^{58} +(1.60223 - 2.77514i) q^{59} +(-11.3644 + 6.56124i) q^{61} -0.364081 q^{62} +(5.68691 + 5.53707i) q^{63} -5.43385 q^{64} +(3.64678 + 9.14545i) q^{66} +(1.55082 - 2.68611i) q^{67} +(2.24412 + 3.88694i) q^{68} +(-9.21911 - 7.27042i) q^{69} -2.21562i q^{71} +(5.93088 + 6.25430i) q^{72} +(-2.18121 - 1.25932i) q^{73} +(-1.04288 - 0.602109i) q^{74} -6.27919i q^{76} +(-7.76013 + 14.7716i) q^{77} +(-3.64630 + 4.62362i) q^{78} +(-3.05960 - 5.29938i) q^{79} +(0.477421 - 8.98733i) q^{81} +(-5.10301 + 2.94623i) q^{82} +8.53654 q^{83} +(-0.566504 + 5.41270i) q^{84} +(3.78240 - 2.18377i) q^{86} +(-4.92836 + 1.96520i) q^{87} +(-9.05984 + 15.6921i) q^{88} +(0.590783 + 1.02327i) q^{89} +(-9.97138 + 0.397921i) q^{91} -8.05034i q^{92} +(-0.100516 + 0.692381i) q^{93} +(1.51490 + 0.874627i) q^{94} +(-1.38180 + 9.51816i) q^{96} -9.10556i q^{97} +(5.19528 - 3.58004i) q^{98} +(18.3989 - 4.41026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.780577	+	0.450666i	−0.551951	+	0.318669i	−0.749909	−	0.661541i	$-0.769903\pi$
$2$	−0.780577	+	0.450666i	−0.551951	+	0.318669i	0.197957	+	0.980211i	$0.436569\pi$
$3$	0.641538	+	1.60886i	0.370392	+	0.928875i
$3$	0.641538	+	1.60886i	0.370392	+	0.928875i
$4$	−0.593800	+	1.02849i	−0.296900	+	0.514245i
$5$		0			0
$5$		0			0
$6$	−1.22583	−	0.966719i	−0.500443	−	0.394662i
$7$	−0.105498	−	2.64365i	−0.0398746	−	0.999205i
$7$	−0.105498	−	2.64365i	−0.0398746	−	0.999205i
$8$		−	2.87309i		−	1.01579i
$9$	−2.17686	+	2.06429i	−0.725619	+	0.688096i
$10$		0			0
$11$	−5.46176	−	3.15335i	−1.64678	−	0.950770i	−0.978340	−	0.207005i	$-0.933628\pi$
$11$	−5.46176	−	3.15335i	−1.64678	−	0.950770i	−0.668442	−	0.743765i	$-0.733038\pi$
$12$	−2.03564	−	0.295524i	−0.587639	−	0.0853104i
$13$		−	3.77183i		−	1.04612i	−0.852297	−	0.523059i	$-0.824791\pi$
$13$		−	3.77183i		−	1.04612i	0.852297	−	0.523059i	$-0.175209\pi$
$14$	1.27375	+	2.01603i	0.340425	+	0.538806i
$15$		0			0
$16$	0.107205	+	0.185685i	0.0268013	+	0.0464212i
$17$	1.88963	−	3.27294i	0.458303	−	0.793804i	−0.540569	−	0.841300i	$-0.681791\pi$
$17$	1.88963	−	3.27294i	0.458303	−	0.793804i	0.998871	+	0.0474963i	$0.0151242\pi$
$18$	0.768900	−	2.59237i	0.181231	−	0.611028i
$19$	−4.57893	+	2.64365i	−1.05048	+	0.606494i	−0.922783	−	0.385319i	$-0.874091\pi$
$19$	−4.57893	+	2.64365i	−1.05048	+	0.606494i	−0.127695	+	0.991813i	$0.540758\pi$
$20$		0			0
$21$	4.18558	−	1.86573i	0.913367	−	0.407136i
$22$	5.68443			1.21192
$23$	−5.87050	+	3.38933i	−1.22408	+	0.706725i	−0.965786	−	0.259340i	$-0.916495\pi$
$23$	−5.87050	+	3.38933i	−1.22408	+	0.706725i	−0.258298	+	0.966065i	$0.583162\pi$
$24$	4.62239	−	1.84320i	0.943542	−	0.376241i
$25$		0			0
$26$	1.69984	+	2.94420i	0.333365	+	0.577406i
$27$	−4.71769	−	2.17794i	−0.907920	−	0.419144i
$28$	2.78161	+	1.46129i	0.525675	+	0.276158i
$29$			3.06327i			0.568834i	0.958701	+	0.284417i	$0.0918000\pi$
$29$			3.06327i			0.568834i	−0.958701	+	0.284417i	$0.908200\pi$
$30$		0			0
$31$	0.349819	+	0.201968i	0.0628294	+	0.0362746i	0.531086	−	0.847318i	$-0.321784\pi$
$31$	0.349819	+	0.201968i	0.0628294	+	0.0362746i	−0.468256	+	0.883593i	$0.655118\pi$
$32$	4.80897	+	2.77646i	0.850114	+	0.490813i
$33$	1.56937	−	10.8102i	0.273192	−	1.88181i
$34$			3.40637i			0.584188i
$35$		0			0
$36$	−0.830485	−	3.46465i	−0.138414	−	0.577442i
$37$	0.668021	+	1.15705i	0.109822	+	0.190217i	0.915698	−	0.401867i	$-0.131639\pi$
$37$	0.668021	+	1.15705i	0.109822	+	0.190217i	−0.805876	+	0.592084i	$0.798305\pi$
$38$	2.38281	−	4.12714i	0.386542	−	0.669511i
$39$	6.06834	−	2.41977i	0.971713	−	0.387474i
$40$		0			0
$41$	6.53749			1.02098			0.510492	−	0.859882i	$-0.329463\pi$
$41$	6.53749			1.02098			0.510492	+	0.859882i	$0.329463\pi$
$42$	−2.42634	+	3.34265i	−0.374393	+	0.515782i
$43$	−4.84564			−0.738954			−0.369477	−	0.929240i	$-0.620463\pi$
$43$	−4.84564			−0.738954			−0.369477	+	0.929240i	$0.620463\pi$
$44$	6.48638	−	3.74491i	0.977858	−	0.564567i
$45$		0			0
$46$	3.05492	−	5.29127i	0.450423	−	0.780156i
$47$	−0.970371	−	1.68073i	−0.141543	−	0.245160i	0.786535	−	0.617546i	$-0.211873\pi$
$47$	−0.970371	−	1.68073i	−0.141543	−	0.245160i	−0.928078	+	0.372386i	$0.878540\pi$
$48$	−0.229964	+	0.291602i	−0.0331925	+	0.0420891i
$49$	−6.97774	+	0.557800i	−0.996820	+	0.0796858i
$50$		0			0
$51$	6.47796	+	0.940437i	0.907096	+	0.131688i
$52$	3.87929	+	2.23971i	0.537961	+	0.310592i
$53$	1.24774	+	0.720381i	0.171390	+	0.0989519i	0.583241	−	0.812299i	$-0.301784\pi$
$53$	1.24774	+	0.720381i	0.171390	+	0.0989519i	−0.411851	+	0.911251i	$0.635118\pi$
$54$	4.66404	−	0.426055i	0.634696	−	0.0579787i
$55$		0			0
$56$	−7.59543	+	0.303106i	−1.01498	+	0.0405042i
$57$	−7.19082	−	5.67086i	−0.952447	−	0.751123i
$58$	−1.38051	−	2.39112i	−0.181270	−	0.313969i
$59$	1.60223	−	2.77514i	0.208592	−	0.361293i	−0.742679	−	0.669648i	$-0.766445\pi$
$59$	1.60223	−	2.77514i	0.208592	−	0.361293i	0.951271	+	0.308355i	$0.0997785\pi$
$60$		0			0
$61$	−11.3644	+	6.56124i	−1.45506	+	0.840080i	−0.998762	−	0.0497461i	$-0.984159\pi$
$61$	−11.3644	+	6.56124i	−1.45506	+	0.840080i	−0.456300	+	0.889826i	$0.650825\pi$
$62$	−0.364081			−0.0462384
$63$	5.68691	+	5.53707i	0.716483	+	0.697605i
$64$	−5.43385			−0.679231
$65$		0			0
$66$	3.64678	+	9.14545i	0.448887	+	1.12573i
$67$	1.55082	−	2.68611i	0.189463	−	0.328160i	−0.755608	−	0.655024i	$-0.772659\pi$
$67$	1.55082	−	2.68611i	0.189463	−	0.328160i	0.945071	+	0.326864i	$0.105992\pi$
$68$	2.24412	+	3.88694i	0.272140	+	0.471360i
$69$	−9.21911	−	7.27042i	−1.10985	−	0.875256i
$70$		0			0
$71$		−	2.21562i		−	0.262946i	−0.991320	−	0.131473i	$-0.958029\pi$
$71$		−	2.21562i		−	0.262946i	0.991320	−	0.131473i	$-0.0419707\pi$
$72$	5.93088	+	6.25430i	0.698961	+	0.737077i
$73$	−2.18121	−	1.25932i	−0.255292	−	0.147393i	0.366893	−	0.930263i	$-0.380421\pi$
$73$	−2.18121	−	1.25932i	−0.255292	−	0.147393i	−0.622185	+	0.782870i	$0.713755\pi$
$74$	−1.04288	−	0.602109i	−0.121233	−	0.0699938i
$75$		0			0
$76$		−	6.27919i		−	0.720272i
$77$	−7.76013	+	14.7716i	−0.884349	+	1.68338i
$78$	−3.64630	+	4.62362i	−0.412862	+	0.523522i
$79$	−3.05960	−	5.29938i	−0.344232	−	0.596227i	0.640982	−	0.767556i	$-0.278527\pi$
$79$	−3.05960	−	5.29938i	−0.344232	−	0.596227i	−0.985214	+	0.171329i	$0.945194\pi$
$80$		0			0
$81$	0.477421	−	8.98733i	0.0530468	−	0.998592i
$82$	−5.10301	+	2.94623i	−0.563534	+	0.325356i
$83$	8.53654			0.937007			0.468503	−	0.883462i	$-0.344793\pi$
$83$	8.53654			0.937007			0.468503	+	0.883462i	$0.344793\pi$
$84$	−0.566504	+	5.41270i	−0.0618107	+	0.590574i
$85$		0			0
$86$	3.78240	−	2.18377i	0.407867	−	0.235482i
$87$	−4.92836	+	1.96520i	−0.528376	+	0.210692i
$88$	−9.05984	+	15.6921i	−0.965782	+	1.67278i
$89$	0.590783	+	1.02327i	0.0626229	+	0.108466i	0.895637	−	0.444786i	$-0.146720\pi$
$89$	0.590783	+	1.02327i	0.0626229	+	0.108466i	−0.833014	+	0.553252i	$0.813387\pi$
$90$		0			0
$91$	−9.97138	+	0.397921i	−1.04529	+	0.0417135i
$92$		−	8.05034i		−	0.839306i
$93$	−0.100516	+	0.692381i	−0.0104230	+	0.0717965i
$94$	1.51490	+	0.874627i	0.156250	+	0.0902109i
$95$		0			0
$96$	−1.38180	+	9.51816i	−0.141029	+	0.971443i
$97$		−	9.10556i		−	0.924530i	−0.886742	−	0.462265i	$-0.847037\pi$
$97$		−	9.10556i		−	0.924530i	0.886742	−	0.462265i	$-0.152963\pi$
$98$	5.19528	−	3.58004i	0.524803	−	0.361639i
$99$	18.3989	−	4.41026i	1.84916	−	0.443247i
$100$		0			0
$101$	−1.15241	+	1.99604i	−0.114669	+	0.198613i	−0.917647	−	0.397395i	$-0.869914\pi$
$101$	−1.15241	+	1.99604i	−0.114669	+	0.198613i	0.802978	+	0.596008i	$0.203247\pi$
$102$	−5.48037	+	2.18532i	−0.542638	+	0.216379i
$103$	−6.74347	+	3.89335i	−0.664454	+	0.383623i	−0.793972	−	0.607954i	$-0.791990\pi$
$103$	−6.74347	+	3.89335i	−0.664454	+	0.383623i	0.129518	+	0.991577i	$0.458657\pi$
$104$	−10.8368			−1.06264
$105$		0			0
$106$	−1.29861			−0.126132
$107$	4.72768	−	2.72952i	0.457042	−	0.263873i	−0.253758	−	0.967268i	$-0.581667\pi$
$107$	4.72768	−	2.72952i	0.457042	−	0.263873i	0.710800	+	0.703395i	$0.248333\pi$
$108$	5.04135	−	3.55884i	0.485104	−	0.342450i
$109$	3.29331	−	5.70418i	0.315442	−	0.546362i	−0.664089	−	0.747653i	$-0.731181\pi$
$109$	3.29331	−	5.70418i	0.315442	−	0.546362i	0.979531	+	0.201292i	$0.0645139\pi$
$110$		0			0
$111$	−1.43296	+	1.81704i	−0.136011	+	0.172466i
$112$	0.479575	−	0.303002i	0.0453156	−	0.0286310i
$113$		−	0.214344i		−	0.0201638i	−0.999949	−	0.0100819i	$-0.996791\pi$
$113$		−	0.214344i		−	0.0201638i	0.999949	−	0.0100819i	$-0.00320922\pi$
$114$	8.16865	+	1.18588i	0.765064	+	0.111068i
$115$		0			0
$116$	−3.15054	−	1.81897i	−0.292520	−	0.168887i
$117$	7.78615	+	8.21074i	0.719829	+	0.759083i
$118$			2.88828i			0.265888i
$119$	−8.85184	−	4.65023i	−0.811447	−	0.426286i
$120$		0			0
$121$	14.3872	+	24.9193i	1.30793	+	2.26539i
$122$	5.91386	−	10.2431i	0.535415	−	0.927367i
$123$	4.19405	+	10.5179i	0.378165	+	0.948367i
$124$	−0.415445	+	0.239857i	−0.0373081	+	0.0215398i
$125$		0			0
$126$	−6.93444	−	1.75921i	−0.617769	−	0.156723i
$127$	1.05320			0.0934560			0.0467280	−	0.998908i	$-0.485121\pi$
$127$	1.05320			0.0934560			0.0467280	+	0.998908i	$0.485121\pi$
$128$	−5.37640	+	3.10407i	−0.475211	+	0.274363i
$129$	−3.10867	−	7.79596i	−0.273703	−	0.686396i
$130$		0			0
$131$	5.22860	+	9.05621i	0.456825	+	0.791245i	0.998791	−	0.0491560i	$-0.0156531\pi$
$131$	5.22860	+	9.05621i	0.456825	+	0.791245i	−0.541966	+	0.840401i	$0.682320\pi$
$132$	10.1863	+	8.03317i	0.886603	+	0.699197i
$133$	7.47194	+	11.8262i	0.647899	+	1.02546i
$134$			2.79562i			0.241505i
$135$		0			0
$136$	−9.40343	−	5.42907i	−0.806338	−	0.465539i
$137$	−6.31673	−	3.64697i	−0.539675	−	0.311581i	0.205272	−	0.978705i	$-0.434192\pi$
$137$	−6.31673	−	3.64697i	−0.539675	−	0.311581i	−0.744947	+	0.667124i	$0.767525\pi$
$138$	10.4728	+	1.52038i	0.891501	+	0.129423i
$139$			10.8548i			0.920693i	0.887739	+	0.460347i	$0.152275\pi$
$139$			10.8548i			0.920693i	−0.887739	+	0.460347i	$0.847725\pi$
$140$		0			0
$141$	2.08153	−	2.63944i	0.175297	−	0.222281i
$142$	0.998507	+	1.72946i	0.0837928	+	0.145133i
$143$	−11.8939	+	20.6008i	−0.994617	+	1.72273i
$144$	−0.616677	−	0.182907i	−0.0513898	−	0.0152422i
$145$		0			0
$146$	2.27014			0.187878
$147$	−5.37391	−	10.8684i	−0.443232	−	0.896407i
$148$	−1.58668			−0.130425
$149$	−2.54658	+	1.47027i	−0.208624	+	0.120449i	−0.600672	−	0.799496i	$-0.705100\pi$
$149$	−2.54658	+	1.47027i	−0.208624	+	0.120449i	0.392048	+	0.919945i	$0.371767\pi$
$150$		0			0
$151$	−2.49298	+	4.31797i	−0.202876	+	0.351391i	−0.949454	−	0.313907i	$-0.898362\pi$
$151$	−2.49298	+	4.31797i	−0.202876	+	0.351391i	0.746578	+	0.665298i	$0.231695\pi$
$152$	7.59543	+	13.1557i	0.616071	+	1.06707i
$153$	2.64283	+	11.0255i	0.213660	+	0.891356i
$154$	−0.599698	−	15.0276i	−0.0483250	−	1.21096i
$155$		0			0
$156$	−1.11467	+	7.67810i	−0.0892447	+	0.614740i
$157$	6.14808	+	3.54960i	0.490671	+	0.283289i	0.724853	−	0.688904i	$-0.241908\pi$
$157$	6.14808	+	3.54960i	0.490671	+	0.283289i	−0.234182	+	0.972193i	$0.575241\pi$
$158$	4.77650	+	2.75772i	0.379998	+	0.219392i
$159$	−0.358521	+	2.46958i	−0.0284326	+	0.195851i
$160$		0			0
$161$	9.57953	+	15.1620i	0.754973	+	1.19493i
$162$	3.67762	+	7.23046i	0.288941	+	0.568079i
$163$	−8.84246	−	15.3156i	−0.692595	−	1.19961i	−0.970985	−	0.239141i	$-0.923134\pi$
$163$	−8.84246	−	15.3156i	−0.692595	−	1.19961i	0.278390	−	0.960468i	$-0.410199\pi$
$164$	−3.88196	+	6.72375i	−0.303130	+	0.525036i
$165$		0			0
$166$	−6.66343	+	3.84713i	−0.517182	+	0.298595i
$167$	−10.9235			−0.845287			−0.422643	−	0.906296i	$-0.638898\pi$
$167$	−10.9235			−0.845287			−0.422643	+	0.906296i	$0.638898\pi$
$168$	−5.36041	−	12.0255i	−0.413565	−	0.927790i
$169$	−1.22669			−0.0943611
$170$		0			0
$171$	4.51043	−	15.2071i	0.344921	−	1.16291i
$172$	2.87734	−	4.98370i	0.219395	−	0.380004i
$173$	−11.5554	−	20.0145i	−0.878539	−	1.52167i	−0.852945	−	0.522001i	$-0.825186\pi$
$173$	−11.5554	−	20.0145i	−0.878539	−	1.52167i	−0.0255936	−	0.999672i	$-0.508148\pi$
$174$	2.96132	−	3.75504i	0.224497	−	0.284669i
$175$		0			0
$176$		−	1.35222i		−	0.101927i
$177$	5.49270	+	0.797402i	0.412857	+	0.0599364i
$178$	−0.922304	−	0.532492i	−0.0691296	−	0.0399120i
$179$	−15.2776	−	8.82051i	−1.14190	−	0.659276i	−0.194999	−	0.980803i	$-0.562470\pi$
$179$	−15.2776	−	8.82051i	−1.14190	−	0.659276i	−0.946900	+	0.321527i	$0.895804\pi$
$180$		0			0
$181$		−	14.8545i		−	1.10413i	−0.833802	−	0.552064i	$-0.813840\pi$
$181$		−	14.8545i		−	1.10413i	0.833802	−	0.552064i	$-0.186160\pi$
$182$	7.60411	−	4.80438i	0.563654	−	0.356124i
$183$	−17.8468	−	14.0744i	−1.31927	−	1.04041i
$184$	9.73785	+	16.8665i	0.717884	+	1.24341i
$185$		0			0
$186$	−0.233572	−	0.585756i	−0.0171263	−	0.0429497i
$187$	−20.6414	+	11.9173i	−1.50945	+	0.871481i
$188$	2.30482			0.168097
$189$	−5.25999	+	12.7017i	−0.382608	+	0.923911i
$190$		0			0
$191$	16.1877	−	9.34599i	1.17130	−	0.676252i	0.217316	−	0.976101i	$-0.430270\pi$
$191$	16.1877	−	9.34599i	1.17130	−	0.676252i	0.953987	+	0.299850i	$0.0969365\pi$
$192$	−3.48602	−	8.74230i	−0.251582	−	0.630921i
$193$	1.29778	−	2.24781i	0.0934160	−	0.161801i	−0.815530	−	0.578714i	$-0.803555\pi$
$193$	1.29778	−	2.24781i	0.0934160	−	0.161801i	0.908946	+	0.416913i	$0.136888\pi$
$194$	4.10357	+	7.10759i	0.294619	+	0.510295i
$195$		0			0
$196$	3.56969	−	7.50776i	0.254978	−	0.536269i
$197$			7.83600i			0.558292i	0.960249	+	0.279146i	$0.0900513\pi$
$197$			7.83600i			0.558292i	−0.960249	+	0.279146i	$0.909949\pi$
$198$	−12.3742	+	11.7343i	−0.879396	+	0.833921i
$199$	3.06915	+	1.77198i	0.217566	+	0.125612i	0.604823	−	0.796360i	$-0.293244\pi$
$199$	3.06915	+	1.77198i	0.217566	+	0.125612i	−0.387256	+	0.921972i	$0.626577\pi$
$200$		0			0
$201$	5.31648	+	0.771819i	0.374996	+	0.0544399i
$202$		−	2.07741i		−	0.146166i
$203$	8.09819	−	0.323169i	0.568382	−	0.0226820i
$204$	−4.81384	+	6.10410i	−0.337036	+	0.427372i
$205$		0			0
$206$	3.50920	−	6.07811i	0.244498	−	0.423482i
$207$	5.78268	−	19.4965i	0.401924	−	1.35510i
$208$	0.700371	−	0.404359i	0.0485620	−	0.0280373i
$209$	33.3453			2.30655
$210$		0			0
$211$	23.9742			1.65045			0.825225	−	0.564804i	$-0.191048\pi$
$211$	23.9742			1.65045			0.825225	+	0.564804i	$0.191048\pi$
$212$	−1.48181	+	0.855523i	−0.101771	+	0.0587576i
$213$	3.56463	−	1.42141i	0.244244	−	0.0973931i
$214$	−2.46021	+	4.26121i	−0.168177	+	0.291290i
$215$		0			0
$216$	−6.25741	+	13.5543i	−0.425763	+	0.922256i
$217$	0.497028	−	0.946107i	0.0337404	−	0.0642259i
$218$			5.93674i			0.402087i
$219$	0.626744	−	4.31717i	0.0423515	−	0.291727i
$220$		0			0
$221$	−12.3450	−	7.12736i	−0.830412	−	0.479438i
$222$	0.299660	−	2.06413i	0.0201118	−	0.138535i
$223$		−	16.9380i		−	1.13425i	−0.823632	−	0.567125i	$-0.808056\pi$
$223$		−	16.9380i		−	1.13425i	0.823632	−	0.567125i	$-0.191944\pi$
$224$	6.83264	−	13.0061i	0.456525	−	0.869009i
$225$		0			0
$226$	0.0965976	+	0.167312i	0.00642557	+	0.0111294i
$227$	−10.9486	+	18.9635i	−0.726685	+	1.25865i	0.231592	+	0.972813i	$0.425606\pi$
$227$	−10.9486	+	18.9635i	−0.726685	+	1.25865i	−0.958277	+	0.285842i	$0.907727\pi$
$228$	10.1023	−	4.02834i	0.669043	−	0.266783i
$229$	−0.218276	+	0.126022i	−0.0144241	+	0.00832775i	−0.507195	−	0.861831i	$-0.669318\pi$
$229$	−0.218276	+	0.126022i	−0.0144241	+	0.00832775i	0.492771	+	0.870159i	$0.335984\pi$
$230$		0			0
$231$	−28.7439	−	3.00840i	−1.89121	−	0.197938i
$232$	8.80103			0.577816
$233$	12.9405	−	7.47118i	0.847758	−	0.489453i	−0.0121359	−	0.999926i	$-0.503863\pi$
$233$	12.9405	−	7.47118i	0.847758	−	0.489453i	0.859894	+	0.510473i	$0.170530\pi$
$234$	−9.77799	−	2.90016i	−0.639207	−	0.189589i
$235$		0			0
$236$	1.90281	+	3.29576i	0.123862	+	0.214535i
$237$	6.56311	−	8.32221i	0.426320	−	0.540586i
$238$	9.00525	−	0.359366i	0.583723	−	0.0232943i
$239$		−	19.5021i		−	1.26149i	−0.775991	−	0.630744i	$-0.782750\pi$
$239$		−	19.5021i		−	1.26149i	0.775991	−	0.630744i	$-0.217250\pi$
$240$		0			0
$241$	8.54154	+	4.93146i	0.550209	+	0.317663i	0.749206	−	0.662337i	$-0.230435\pi$
$241$	8.54154	+	4.93146i	0.550209	+	0.317663i	−0.198997	+	0.980000i	$0.563768\pi$
$242$	−22.4606	−	12.9676i	−1.44382	−	0.833592i
$243$	14.7656	−	4.99761i	0.947216	−	0.320597i
$244$		−	15.5842i		−	0.997678i
$245$		0			0
$246$	−8.01384	−	6.31992i	−0.510944	−	0.402943i
$247$	9.97138	+	17.2709i	0.634464	+	1.09892i
$248$	0.580273	−	1.00506i	0.0368474	−	0.0638215i
$249$	5.47651	+	13.7341i	0.347060	+	0.870363i
$250$		0			0
$251$	−26.5460			−1.67557			−0.837784	−	0.546002i	$-0.816149\pi$
$251$	−26.5460			−1.67557			−0.837784	+	0.546002i	$0.816149\pi$
$252$	−9.07170	+	2.56103i	−0.571464	+	0.161329i
$253$	42.7510			2.68773
$254$	−0.822100	+	0.474640i	−0.0515832	+	0.0297815i
$255$		0			0
$256$	8.23165	−	14.2576i	0.514478	−	0.891102i
$257$	−7.66481	−	13.2758i	−0.478117	−	0.828124i	0.521568	−	0.853210i	$-0.325347\pi$
$257$	−7.66481	−	13.2758i	−0.478117	−	0.828124i	−0.999685	+	0.0250861i	$0.992014\pi$
$258$	5.93993	+	4.68438i	0.369804	+	0.291637i
$259$	2.98835	−	1.88808i	0.185687	−	0.117319i
$260$		0			0
$261$	−6.32347	−	6.66829i	−0.391413	−	0.412757i
$262$	−8.16266	−	4.71271i	−0.504291	−	0.291152i
$263$	−19.0437	−	10.9949i	−1.17428	−	0.677972i	−0.219598	−	0.975591i	$-0.570474\pi$
$263$	−19.0437	−	10.9949i	−1.17428	−	0.677972i	−0.954685	+	0.297618i	$0.903808\pi$
$264$	−31.0586	−	4.50893i	−1.91153	−	0.277505i
$265$		0			0
$266$	−11.1621	−	5.86389i	−0.684391	−	0.359538i
$267$	−1.26728	+	1.60695i	−0.0775564	+	0.0983438i
$268$	1.84176	+	3.19002i	0.112503	+	0.194861i
$269$	−14.9395	+	25.8760i	−0.910878	+	1.57769i	−0.0980517	+	0.995181i	$0.531261\pi$
$269$	−14.9395	+	25.8760i	−0.910878	+	1.57769i	−0.812826	+	0.582506i	$0.802072\pi$
$270$		0			0
$271$	−10.7412	+	6.20142i	−0.652480	+	0.376710i	−0.789406	−	0.613872i	$-0.789611\pi$
$271$	−10.7412	+	6.20142i	−0.652480	+	0.376710i	0.136926	+	0.990581i	$0.456278\pi$
$272$	0.810312			0.0491324
$273$	−7.03722	−	15.7873i	−0.425912	−	0.955489i
$274$	6.57426			0.397166
$275$		0			0
$276$	12.9519	−	5.16460i	0.779611	−	0.310872i
$277$	4.03409	−	6.98725i	0.242385	−	0.419823i	−0.719008	−	0.695002i	$-0.755404\pi$
$277$	4.03409	−	6.98725i	0.242385	−	0.419823i	0.961393	+	0.275178i	$0.0887370\pi$
$278$	−4.89190	−	8.47302i	−0.293397	−	0.508178i
$279$	−1.17843	+	0.282472i	−0.0705507	+	0.0169112i
$280$		0			0
$281$		−	17.6732i		−	1.05430i	−0.849773	−	0.527149i	$-0.823261\pi$
$281$		−	17.6732i		−	1.05430i	0.849773	−	0.527149i	$-0.176739\pi$
$282$	−0.435287	+	2.99837i	−0.0259210	+	0.178550i
$283$	−20.5021	−	11.8369i	−1.21872	−	0.703629i	−0.254077	−	0.967184i	$-0.581772\pi$
$283$	−20.5021	−	11.8369i	−1.21872	−	0.703629i	−0.964644	+	0.263555i	$0.915105\pi$
$284$	2.27875	+	1.31564i	0.135219	+	0.0780686i
$285$		0			0
$286$		−	21.4407i		−	1.26781i
$287$	−0.689694	−	17.2828i	−0.0407113	−	1.02017i
$288$	−16.1999	+	3.88315i	−0.954586	+	0.228817i
$289$	1.35859	+	2.35315i	0.0799172	+	0.138421i
$290$		0			0
$291$	14.6496	−	5.84156i	0.858773	−	0.342439i
$292$	2.59041	−	1.49557i	0.151592	−	0.0875217i
$293$	−2.70804			−0.158205			−0.0791026	−	0.996866i	$-0.525205\pi$
$293$	−2.70804			−0.158205			−0.0791026	+	0.996866i	$0.525205\pi$
$294$	9.09275	+	6.06175i	0.530300	+	0.353528i
$295$		0			0
$296$	3.32430	−	1.91928i	0.193221	−	0.111556i
$297$	18.8991	+	26.7719i	1.09664	+	1.55346i
$298$	1.32520	−	2.29532i	0.0767670	−	0.132964i
$299$	12.7840	+	22.1425i	0.739317	+	1.28053i
$300$		0			0
$301$	0.511207	+	12.8102i	0.0294655	+	0.738366i
$302$		−	4.49401i		−	0.258601i
$303$	−3.95066	−	0.573536i	−0.226959	−	0.0329488i
$304$	−0.981769	−	0.566825i	−0.0563083	−	0.0325096i
$305$		0			0
$306$	−7.03174	−	7.41519i	−0.401978	−	0.423898i
$307$			5.49592i			0.313669i	0.987625	+	0.156834i	$0.0501289\pi$
$307$			5.49592i			0.313669i	−0.987625	+	0.156834i	$0.949871\pi$
$308$	−10.5845	−	16.7526i	−0.603109	−	0.954569i
$309$	−10.5900	−	8.35157i	−0.602446	−	0.475104i
$310$		0			0
$311$	−10.9235	+	18.9201i	−0.619416	+	1.07286i	0.370177	+	0.928961i	$0.379297\pi$
$311$	−10.9235	+	18.9201i	−0.619416	+	1.07286i	−0.989593	+	0.143898i	$0.954036\pi$
$312$	−6.95222	−	17.4349i	−0.393592	−	0.987056i
$313$	21.2964	−	12.2955i	1.20375	−	0.694983i	0.242360	−	0.970186i	$-0.422079\pi$
$313$	21.2964	−	12.2955i	1.20375	−	0.694983i	0.961386	+	0.275203i	$0.0887452\pi$
$314$	−6.39874			−0.361102
$315$		0			0
$316$	7.26715			0.408809
$317$	20.7457	−	11.9775i	1.16520	−	0.672726i	0.212652	−	0.977128i	$-0.431790\pi$
$317$	20.7457	−	11.9775i	1.16520	−	0.672726i	0.952544	+	0.304402i	$0.0984565\pi$
$318$	−0.833105	−	2.08927i	−0.0467182	−	0.117161i
$319$	9.65954	−	16.7308i	0.540830	−	0.936746i
$320$		0			0
$321$	7.42441	+	5.85507i	0.414390	+	0.326798i
$322$	−14.3105	−	7.51791i	−0.797496	−	0.418956i
$323$			19.9821i			1.11183i
$324$	8.95989	+	5.82769i	0.497772	+	0.323761i
$325$		0			0
$326$	13.8044	+	7.97000i	0.764557	+	0.441417i
$327$	11.2900	+	1.63903i	0.624339	+	0.0906383i
$328$		−	18.7828i		−	1.03711i
$329$	−4.34089	+	2.74263i	−0.239321	+	0.151206i
$330$		0			0
$331$	−13.5511	−	23.4712i	−0.744837	−	1.29009i	−0.950271	−	0.311424i	$-0.899194\pi$
$331$	−13.5511	−	23.4712i	−0.744837	−	1.29009i	0.205434	−	0.978671i	$-0.434139\pi$
$332$	−5.06899	+	8.77975i	−0.278197	+	0.481852i
$333$	−3.84267	−	1.13974i	−0.210577	−	0.0624572i
$334$	8.52664	−	4.92286i	0.466557	−	0.269367i
$335$		0			0
$336$	0.795153	+	0.577181i	0.0433791	+	0.0314878i
$337$	−3.19846			−0.174231			−0.0871155	−	0.996198i	$-0.527765\pi$
$337$	−3.19846			−0.174231			−0.0871155	+	0.996198i	$0.527765\pi$
$338$	0.957529	−	0.552830i	0.0520827	−	0.0300700i
$339$	0.344849	−	0.137510i	0.0187296	−	0.00746850i
$340$		0			0
$341$	−1.27375	−	2.20620i	−0.0689776	−	0.119473i
$342$	3.33258	+	13.9030i	0.180205	+	0.751788i
$343$	2.21077	+	18.3878i	0.119370	+	0.992850i
$344$			13.9220i			0.750622i
$345$		0			0
$346$	18.0397	+	10.4152i	0.969821	+	0.559926i
$347$	28.2567	+	16.3140i	1.51690	+	0.875783i	0.999803	+	0.0198563i	$0.00632087\pi$
$347$	28.2567	+	16.3140i	1.51690	+	0.875783i	0.517097	+	0.855927i	$0.327012\pi$
$348$	0.905269	−	6.23571i	0.0485275	−	0.334269i
$349$			32.4849i			1.73888i	0.494041	+	0.869439i	$0.335519\pi$
$349$			32.4849i			1.73888i	−0.494041	+	0.869439i	$0.664481\pi$
$350$		0			0
$351$	−8.21481	+	17.7943i	−0.438474	+	0.949790i
$352$	−17.5103	−	30.3287i	−0.933301	−	1.61653i
$353$	3.33584	−	5.77784i	0.177549	−	0.307523i	−0.763492	−	0.645818i	$-0.776517\pi$
$353$	3.33584	−	5.77784i	0.177549	−	0.307523i	0.941040	+	0.338294i	$0.109850\pi$
$354$	−4.64684	+	1.85294i	−0.246977	+	0.0984828i
$355$		0			0
$356$	−1.40323			−0.0743709
$357$	1.80277	−	17.2247i	0.0954127	−	0.911626i
$358$	15.9004			0.840364
$359$	14.0322	−	8.10148i	0.740590	−	0.427580i	−0.0816940	−	0.996657i	$-0.526033\pi$
$359$	14.0322	−	8.10148i	0.740590	−	0.427580i	0.822284	+	0.569078i	$0.192700\pi$
$360$		0			0
$361$	4.47774	−	7.75567i	0.235671	−	0.408193i
$362$	6.69443	+	11.5951i	0.351852	+	0.609425i
$363$	−30.8618	+	39.1337i	−1.61982	+	2.05398i
$364$	5.51175	−	10.4918i	0.288894	−	0.549918i
$365$		0			0
$366$	20.2737	+	2.94323i	1.05972	+	0.153845i
$367$	−14.9080	−	8.60716i	−0.778193	−	0.449290i	0.0575965	−	0.998340i	$-0.481656\pi$
$367$	−14.9080	−	8.60716i	−0.778193	−	0.449290i	−0.835789	+	0.549050i	$0.814990\pi$
$368$	−1.25869	−	0.726708i	−0.0656140	−	0.0378823i
$369$	−14.2312	+	13.4953i	−0.740846	+	0.702535i
$370$		0			0
$371$	1.77280	−	3.37457i	0.0920391	−	0.175199i
$372$	−0.652421	−	0.514515i	−0.0338264	−	0.0266764i
$373$	−6.16568	−	10.6793i	−0.319247	−	0.552952i	0.661084	−	0.750312i	$-0.270097\pi$
$373$	−6.16568	−	10.6793i	−0.319247	−	0.552952i	−0.980331	+	0.197360i	$0.936763\pi$
$374$	10.7415	−	18.6048i	0.555428	−	0.962030i
$375$		0			0
$376$	−4.82889	+	2.78796i	−0.249031	+	0.143778i
$377$	11.5541			0.595067
$378$	−1.61839	−	12.2851i	−0.0832408	−	0.631879i
$379$	−3.57576			−0.183675			−0.0918373	−	0.995774i	$-0.529274\pi$
$379$	−3.57576			−0.183675			−0.0918373	+	0.995774i	$0.529274\pi$
$380$		0			0
$381$	0.675665	+	1.69444i	0.0346154	+	0.0868090i
$382$	−8.42384	+	14.5905i	−0.431001	+	0.746516i
$383$	11.5654	+	20.0319i	0.590965	+	1.02358i	0.994103	+	0.108442i	$0.0345861\pi$
$383$	11.5654	+	20.0319i	0.590965	+	1.02358i	−0.403138	+	0.915139i	$0.632081\pi$
$384$	−8.44317	−	6.65850i	−0.430864	−	0.339790i
$385$		0			0
$386$			2.33946i			0.119075i
$387$	10.5483	−	10.0028i	0.536199	−	0.508471i
$388$	9.36499	+	5.40688i	0.475435	+	0.274493i
$389$	−14.7169	−	8.49679i	−0.746175	−	0.430804i	0.0781352	−	0.996943i	$-0.475103\pi$
$389$	−14.7169	−	8.49679i	−0.746175	−	0.430804i	−0.824310	+	0.566138i	$0.808437\pi$
$390$		0			0
$391$			25.6184i			1.29558i
$392$	1.60261	+	20.0477i	0.0809440	+	1.01256i
$393$	−11.2158	+	14.2220i	−0.565763	+	0.717405i
$394$	−3.53142	−	6.11660i	−0.177910	−	0.308150i
$395$		0			0
$396$	−6.38934	+	21.5419i	−0.321076	+	1.08252i
$397$	−18.7837	+	10.8448i	−0.942726	+	0.544283i	−0.890814	−	0.454368i	$-0.849865\pi$
$397$	−18.7837	+	10.8448i	−0.942726	+	0.544283i	−0.0519125	+	0.998652i	$0.516532\pi$
$398$	−3.19428			−0.160115
$399$	−14.2331	+	19.6082i	−0.712548	+	0.981640i
$400$		0			0
$401$	0.425230	−	0.245507i	0.0212350	−	0.0122600i	−0.489345	−	0.872090i	$-0.662764\pi$
$401$	0.425230	−	0.245507i	0.0212350	−	0.0122600i	0.510580	+	0.859830i	$0.329431\pi$
$402$	−4.49776	+	1.79349i	−0.224328	+	0.0894514i
$403$	0.761790	−	1.31946i	0.0379475	−	0.0657270i
$404$	−1.36860	−	2.37049i	−0.0680906	−	0.117936i
$405$		0			0
$406$	−6.17562	+	3.90184i	−0.306491	+	0.193645i
$407$		−	8.42601i		−	0.417662i
$408$	2.70196	−	18.6118i	0.133767	−	0.921419i
$409$	24.2867	+	14.0219i	1.20090	+	0.693339i	0.960755	−	0.277399i	$-0.0894723\pi$
$409$	24.2867	+	14.0219i	1.20090	+	0.693339i	0.240143	+	0.970738i	$0.422806\pi$
$410$		0			0
$411$	1.81503	−	12.5024i	0.0895290	−	0.616698i
$412$		−	9.24747i		−	0.455590i
$413$	−7.50553	−	3.94295i	−0.369323	−	0.194020i
$414$	4.27260	+	17.8246i	0.209987	+	0.876031i
$415$		0			0
$416$	10.4723	−	18.1386i	0.513448	−	0.889319i
$417$	−17.4639	+	6.96378i	−0.855210	+	0.341018i
$418$	−26.0286	+	15.0276i	−1.27310	+	0.735025i
$419$	3.44153			0.168130			0.0840649	−	0.996460i	$-0.473210\pi$
$419$	3.44153			0.168130			0.0840649	+	0.996460i	$0.473210\pi$
$420$		0			0
$421$	18.7964			0.916078			0.458039	−	0.888932i	$-0.348552\pi$
$421$	18.7964			0.916078			0.458039	+	0.888932i	$0.348552\pi$
$422$	−18.7137	+	10.8044i	−0.910968	+	0.525948i
$423$	5.58188	+	1.65559i	0.271400	+	0.0804975i
$424$	2.06972	−	3.58485i	0.100514	−	0.174096i
$425$		0			0
$426$	−2.14188	+	2.71597i	−0.103775	+	0.131589i
$427$	18.5445	+	29.3512i	0.897432	+	1.42041i
$428$			6.48316i			0.313375i
$429$	−40.7742	−	5.91938i	−1.96860	−	0.285791i
$430$		0			0
$431$	5.95390	+	3.43749i	0.286789	+	0.165578i	0.636493	−	0.771282i	$-0.280384\pi$
$431$	5.95390	+	3.43749i	0.286789	+	0.165578i	−0.349704	+	0.936860i	$0.613718\pi$
$432$	−0.101350	−	1.10949i	−0.00487622	−	0.0533803i
$433$			15.2776i			0.734193i	0.930183	+	0.367096i	$0.119648\pi$
$433$			15.2776i			0.734193i	−0.930183	+	0.367096i	$0.880352\pi$
$434$	0.0384100	+	0.962503i	0.00184374	+	0.0462016i
$435$		0			0
$436$	3.91113	+	6.77428i	0.187309	+	0.324429i
$437$	17.9204	−	31.0391i	0.857249	−	1.48480i
$438$	1.45638	+	3.65234i	0.0695886	+	0.174515i
$439$	33.3367	−	19.2469i	1.59107	−	0.918606i	0.597948	−	0.801535i	$-0.295983\pi$
$439$	33.3367	−	19.2469i	1.59107	−	0.918606i	0.993124	−	0.117071i	$-0.0373505\pi$
$440$		0			0
$441$	14.0381	−	15.6183i	0.668480	−	0.743730i
$442$	12.8483			0.611129
$443$	3.33990	−	1.92829i	0.158683	−	0.0916158i	−0.418556	−	0.908191i	$-0.637464\pi$
$443$	3.33990	−	1.92829i	0.158683	−	0.0916158i	0.577239	+	0.816575i	$0.304130\pi$
$444$	−1.01792	−	2.55275i	−0.0483082	−	0.121148i
$445$		0			0
$446$	7.63337	+	13.2214i	0.361450	+	0.626050i
$447$	−3.99919	−	3.15386i	−0.189155	−	0.149172i
$448$	0.573262	+	14.3652i	0.0270841	+	0.678691i
$449$		−	2.52159i		−	0.119001i	−0.998228	−	0.0595005i	$-0.981049\pi$
$449$		−	2.52159i		−	0.119001i	0.998228	−	0.0595005i	$-0.0189508\pi$
$450$		0			0
$451$	−35.7062	−	20.6150i	−1.68134	−	0.970721i
$452$	0.220451	+	0.127277i	0.0103691	+	0.00598662i
$453$	−8.54635	−	1.24071i	−0.401542	−	0.0582938i
$454$		−	19.7367i		−	0.926288i
$455$		0			0
$456$	−16.2929	+	20.6598i	−0.762984	+	0.967486i
$457$	4.65226	+	8.05795i	0.217623	+	0.376935i	0.954081	−	0.299549i	$-0.0968362\pi$
$457$	4.65226	+	8.05795i	0.217623	+	0.376935i	−0.736457	+	0.676484i	$0.763503\pi$
$458$	0.113588	−	0.196739i	0.00530760	−	0.00919303i
$459$	−16.0429	+	11.3252i	−0.748820	+	0.528615i
$460$		0			0
$461$	−11.3898			−0.530477			−0.265238	−	0.964183i	$-0.585451\pi$
$461$	−11.3898			−0.530477			−0.265238	+	0.964183i	$0.585451\pi$
$462$	23.7926	−	10.6056i	1.10693	−	0.493418i
$463$	−0.322319			−0.0149795			−0.00748973	−	0.999972i	$-0.502384\pi$
$463$	−0.322319			−0.0149795			−0.00748973	+	0.999972i	$0.502384\pi$
$464$	−0.568801	+	0.328398i	−0.0264059	+	0.0152455i
$465$		0			0
$466$	−6.73402	+	11.6637i	−0.311947	+	0.540309i
$467$	11.6576	+	20.1915i	0.539449	+	0.934353i	0.998934	+	0.0461675i	$0.0147008\pi$
$467$	11.6576	+	20.1915i	0.539449	+	0.934353i	−0.459485	+	0.888186i	$0.651966\pi$
$468$	−13.0681	+	3.13245i	−0.604072	+	0.144798i
$469$	−7.26473	−	3.81645i	−0.335454	−	0.176227i
$470$		0			0
$471$	−1.76657	+	12.1686i	−0.0813995	+	0.560700i
$472$	−7.97323	−	4.60334i	−0.366997	−	0.211886i
$473$	26.4657	+	15.2800i	1.21690	+	0.702575i
$474$	−1.37247	+	9.45390i	−0.0630396	+	0.434232i
$475$		0			0
$476$	10.0389	−	6.34274i	0.460134	−	0.290719i
$477$	−4.20322	+	1.00752i	−0.192452	+	0.0461312i
$478$	8.78895	+	15.2229i	0.401997	+	0.696280i
$479$	−0.316556	+	0.548292i	−0.0144638	+	0.0250521i	−0.873167	−	0.487422i	$-0.837937\pi$
$479$	−0.316556	+	0.548292i	−0.0144638	+	0.0250521i	0.858703	+	0.512474i	$0.171271\pi$
$480$		0			0
$481$	4.36418	−	2.51966i	0.198990	−	0.114887i
$482$	−8.88978			−0.404918
$483$	−18.2478	+	25.1391i	−0.830305	+	1.14387i
$484$	−34.1724			−1.55329
$485$		0			0
$486$	−9.27346	+	10.5554i	−0.420653	+	0.478802i
$487$	−10.8253	+	18.7500i	−0.490541	+	0.849642i	−0.999941	−	0.0108880i	$-0.996534\pi$
$487$	−10.8253	+	18.7500i	−0.490541	+	0.849642i	0.509400	+	0.860530i	$0.329868\pi$
$488$	18.8510	+	32.6509i	0.853345	+	1.47804i
$489$	18.9679	−	24.0518i	0.857756	−	1.08766i
$490$		0			0
$491$			36.1608i			1.63191i	0.578112	+	0.815957i	$0.303789\pi$
$491$			36.1608i			1.63191i	−0.578112	+	0.815957i	$0.696211\pi$
$492$	−13.3080	−	1.93198i	−0.599970	−	0.0871006i
$493$	10.0259	+	5.78844i	0.451543	+	0.260698i
$494$	−15.5669	−	8.98754i	−0.700387	−	0.404368i
$495$		0			0
$496$			0.0866082i			0.00388882i
$497$	−5.85732	+	0.233744i	−0.262737	+	0.0104849i
$498$	−10.4643	−	8.25244i	−0.468918	−	0.369801i
$499$	4.50676	+	7.80593i	0.201750	+	0.349442i	0.949092	−	0.314998i	$-0.102004\pi$
$499$	4.50676	+	7.80593i	0.201750	+	0.349442i	−0.747342	+	0.664439i	$0.768670\pi$
$500$		0			0
$501$	−7.00785	−	17.5744i	−0.313088	−	0.785166i
$502$	20.7212	−	11.9634i	0.924832	−	0.533952i
$503$	18.9044			0.842907			0.421453	−	0.906850i	$-0.361520\pi$
$503$	18.9044			0.842907			0.421453	+	0.906850i	$0.361520\pi$
$504$	15.9085	−	16.3390i	0.708620	−	0.727796i
$505$		0			0
$506$	−33.3704	+	19.2664i	−1.48350	+	0.856497i
$507$	−0.786971	−	1.97358i	−0.0349506	−	0.0876497i
$508$	−0.625387	+	1.08320i	−0.0277471	+	0.0480593i
$509$	−19.6636	−	34.0584i	−0.871574	−	1.50961i	−0.860368	−	0.509673i	$-0.829766\pi$
$509$	−19.6636	−	34.0584i	−0.871574	−	1.50961i	−0.0112055	−	0.999937i	$-0.503567\pi$
$510$		0			0
$511$	−3.09909	+	5.89921i	−0.137096	+	0.260966i
$512$			2.42264i			0.107067i
$513$	27.3597	−	2.49927i	1.20796	−	0.110346i
$514$	11.9659	+	6.90854i	0.527795	+	0.304723i
$515$		0			0
$516$	9.86400	+	1.43200i	0.434238	+	0.0630405i
$517$			12.2397i			0.538300i
$518$	−1.48174	+	2.82054i	−0.0651040	+	0.123927i
$519$	24.7873	−	31.4310i	1.08804	−	1.37967i
$520$		0			0
$521$	8.61869	−	14.9280i	0.377592	−	0.654008i	−0.613120	−	0.789990i	$-0.710086\pi$
$521$	8.61869	−	14.9280i	0.377592	−	0.654008i	0.990711	+	0.135982i	$0.0434190\pi$
$522$	7.94113	+	2.35534i	0.347574	+	0.103091i
$523$	−32.7149	+	18.8880i	−1.43052	+	0.825914i	−0.997161	−	0.0753051i	$-0.976007\pi$
$523$	−32.7149	+	18.8880i	−1.43052	+	0.825914i	−0.433364	+	0.901219i	$0.642674\pi$
$524$	−12.4190			−0.542525
$525$		0			0
$526$	19.8201			0.864196
$527$	1.32206	−	0.763291i	0.0575898	−	0.0332495i
$528$	2.17553	−	0.867500i	0.0946778	−	0.0377531i
$529$	11.4752	−	19.8756i	0.498920	−	0.864156i
$530$		0			0
$531$	2.24087	+	9.34855i	0.0972455	+	0.405693i
$532$	−16.6000	+	0.662443i	−0.719699	+	0.0287206i
$533$		−	24.6583i		−	1.06807i
$534$	0.265012	−	1.82547i	0.0114682	−	0.0789959i
$535$		0			0
$536$	−7.71742	−	4.45565i	−0.333342	−	0.192455i
$537$	4.38982	−	30.2382i	0.189435	−	1.30487i
$538$		−	26.9309i		−	1.16108i
$539$	39.8697	+	18.9567i	1.71731	+	0.816521i
$540$		0			0
$541$	−9.89533	−	17.1392i	−0.425433	−	0.736872i	0.571027	−	0.820931i	$-0.306545\pi$
$541$	−9.89533	−	17.1392i	−0.425433	−	0.736872i	−0.996461	+	0.0840587i	$0.973212\pi$
$542$	5.58955	−	9.68138i	0.240092	−	0.415851i
$543$	23.8988	−	9.52974i	1.02560	−	0.408960i
$544$	18.1744	−	10.4930i	0.779219	−	0.449882i
$545$		0			0
$546$	12.6079	+	9.15175i	0.539568	+	0.391659i
$547$	−8.91454			−0.381158			−0.190579	−	0.981672i	$-0.561037\pi$
$547$	−8.91454			−0.381158			−0.190579	+	0.981672i	$0.561037\pi$
$548$	7.50174	−	4.33113i	0.320459	−	0.185017i
$549$	11.1944	−	37.7423i	0.477765	−	1.61080i
$550$		0			0
$551$	−8.09819	−	14.0265i	−0.344995	−	0.597548i
$552$	−20.8886	+	26.4873i	−0.889076	+	1.12737i
$553$	−13.6869	+	8.64757i	−0.582026	+	0.367732i
$554$			7.27212i			0.308963i
$555$		0			0
$556$	−11.1641	−	6.44558i	−0.473462	−	0.273354i
$557$	18.1599	+	10.4847i	0.769462	+	0.444249i	0.832683	−	0.553751i	$-0.186804\pi$
$557$	18.1599	+	10.4847i	0.769462	+	0.444249i	−0.0632208	+	0.998000i	$0.520137\pi$
$558$	0.792554	−	0.751569i	0.0335515	−	0.0318165i
$559$			18.2769i			0.773032i
$560$		0			0
$561$	−32.4155	−	25.5637i	−1.36859	−	1.07930i
$562$	7.96474	+	13.7953i	0.335972	+	0.581921i
$563$	9.04347	−	15.6638i	0.381137	−	0.660148i	−0.610088	−	0.792333i	$-0.708866\pi$
$563$	9.04347	−	15.6638i	0.381137	−	0.660148i	0.991225	+	0.132185i	$0.0421993\pi$
$564$	1.47863	+	3.70814i	0.0622616	+	0.156141i
$565$		0			0
$566$	21.3379			0.896900
$567$	−23.8097	−	0.313985i	−0.999913	−	0.0131861i
$568$	−6.36568			−0.267098
$569$	−22.0888	+	12.7530i	−0.926010	+	0.534632i	−0.885547	−	0.464549i	$-0.846216\pi$
$569$	−22.0888	+	12.7530i	−0.926010	+	0.534632i	−0.0404626	+	0.999181i	$0.512883\pi$
$570$		0			0
$571$	−19.8853	+	34.4424i	−0.832175	+	1.44137i	0.0641352	+	0.997941i	$0.479571\pi$
$571$	−19.8853	+	34.4424i	−0.832175	+	1.44137i	−0.896310	+	0.443428i	$0.853762\pi$
$572$	−14.1252	−	24.4655i	−0.590603	−	1.02295i
$573$	25.4214	+	20.0480i	1.06199	+	0.837516i
$574$	8.32714	+	13.1797i	0.347568	+	0.550112i
$575$		0			0
$576$	11.8287	−	11.2170i	0.492863	−	0.467377i
$577$	−1.72826	−	0.997811i	−0.0719484	−	0.0415394i	0.463594	−	0.886048i	$-0.346560\pi$
$577$	−1.72826	−	0.997811i	−0.0719484	−	0.0415394i	−0.535543	+	0.844508i	$0.679893\pi$
$578$	−2.12097	−	1.22454i	−0.0882208	−	0.0509343i
$579$	4.44899	+	0.645881i	0.184894	+	0.0268419i
$580$		0			0
$581$	−0.900590	−	22.5676i	−0.0373628	−	0.936262i
$582$	−8.80252	+	11.1619i	−0.364876	+	0.462674i
$583$	−4.54322	−	7.86909i	−0.188161	−	0.325904i
$584$	−3.61815	+	6.26682i	−0.149720	+	0.259323i
$585$		0			0
$586$	2.11383	−	1.22042i	0.0873216	−	0.0504152i
$587$	−27.4257			−1.13198			−0.565989	−	0.824413i	$-0.691506\pi$
$587$	−27.4257			−1.13198			−0.565989	+	0.824413i	$0.691506\pi$
$588$	14.3690	+	0.926607i	0.592569	+	0.0382126i
$589$	−2.13573			−0.0880013
$590$		0			0
$591$	−12.6070	+	5.02709i	−0.518583	+	0.206787i
$592$	−0.143231	+	0.248083i	−0.00588674	+	0.0101961i
$593$	0.606763	+	1.05094i	0.0249168	+	0.0431571i	0.878215	−	0.478266i	$-0.158735\pi$
$593$	0.606763	+	1.05094i	0.0249168	+	0.0431571i	−0.853298	+	0.521423i	$0.825401\pi$
$594$	−26.8174	−	12.3803i	−1.10033	−	0.507971i
$595$		0			0
$596$		−	3.49218i		−	0.143045i
$597$	−0.881883	+	6.07463i	−0.0360930	+	0.248618i
$598$	−19.9578	−	11.5226i	−0.816134	−	0.471195i
$599$	32.9617	+	19.0304i	1.34678	+	0.777563i	0.987792	−	0.155780i	$-0.0497891\pi$
$599$	32.9617	+	19.0304i	1.34678	+	0.777563i	0.358986	+	0.933343i	$0.383122\pi$
$600$		0			0
$601$		−	8.32414i		−	0.339549i	−0.985483	−	0.169774i	$-0.945696\pi$
$601$		−	8.32414i		−	0.339549i	0.985483	−	0.169774i	$-0.0543039\pi$
$602$	−6.17215	−	9.76894i	−0.251558	−	0.398152i
$603$	2.16898	+	9.04862i	0.0883275	+	0.368488i
$604$	−2.96066	−	5.12802i	−0.120468	−	0.208656i
$605$		0			0
$606$	3.34227	−	1.33274i	0.135770	−	0.0541388i
$607$	26.1996	−	15.1263i	1.06341	−	0.613959i	0.137036	−	0.990566i	$-0.456242\pi$
$607$	26.1996	−	15.1263i	1.06341	−	0.613959i	0.926373	+	0.376607i	$0.122909\pi$
$608$	−29.3599			−1.19070
$609$	5.71523	+	12.8215i	0.231593	+	0.519555i
$610$		0			0
$611$	−6.33943	+	3.66007i	−0.256466	+	0.148071i
$612$	−12.9089	−	3.82879i	−0.521811	−	0.154770i
$613$	1.41851	−	2.45694i	0.0572933	−	0.0992349i	−0.835956	−	0.548796i	$-0.815086\pi$
$613$	1.41851	−	2.45694i	0.0572933	−	0.0992349i	0.893249	+	0.449561i	$0.148420\pi$
$614$	−2.47683	−	4.28999i	−0.0999566	−	0.173130i
$615$		0			0
$616$	42.4402	+	22.2955i	1.70996	+	0.898313i
$617$			23.3983i			0.941979i	0.882139	+	0.470990i	$0.156103\pi$
$617$			23.3983i			0.941979i	−0.882139	+	0.470990i	$0.843897\pi$
$618$	12.0301	+	1.74647i	0.483922	+	0.0702533i
$619$	−34.7980	−	20.0907i	−1.39865	−	0.807511i	−0.404400	−	0.914582i	$-0.632519\pi$
$619$	−34.7980	−	20.0907i	−1.39865	−	0.807511i	−0.994251	+	0.107071i	$0.965853\pi$
$620$		0			0
$621$	35.0769	−	3.20424i	1.40759	−	0.128582i
$622$		−	19.6914i		−	0.789555i
$623$	2.64283	−	1.66978i	0.105883	−	0.0668981i
$624$	1.09987	+	0.867386i	0.0440301	+	0.0347232i
$625$		0			0
$626$	−11.0823	+	19.1952i	−0.442939	+	0.767194i
$627$	21.3923	+	53.6480i	0.854326	+	2.14249i
$628$	−7.30146	+	4.21550i	−0.291360	+	0.168217i
$629$	5.04925			0.201327
$630$		0			0
$631$	−22.9329			−0.912945			−0.456473	−	0.889737i	$-0.650887\pi$
$631$	−22.9329			−0.912945			−0.456473	+	0.889737i	$0.650887\pi$
$632$	−15.2256	+	8.79049i	−0.605641	+	0.349667i
$633$	15.3803	+	38.5711i	0.611314	+	1.53306i
$634$	−10.7958	+	18.6988i	−0.428754	+	0.742624i
$635$		0			0
$636$	−2.32705	−	1.83517i	−0.0922737	−	0.0727694i
$637$	2.10393	+	26.3188i	0.0833607	+	1.04279i
$638$			17.4129i			0.689384i
$639$	4.57369	+	4.82310i	0.180932	+	0.190799i
$640$		0			0
$641$	1.70493	+	0.984339i	0.0673405	+	0.0388791i	0.533292	−	0.845931i	$-0.320955\pi$
$641$	1.70493	+	0.984339i	0.0673405	+	0.0388791i	−0.465952	+	0.884810i	$0.654288\pi$
$642$	−8.43401	−	1.22441i	−0.332864	−	0.0483234i
$643$		−	18.9036i		−	0.745483i	−0.927935	−	0.372742i	$-0.878418\pi$
$643$		−	18.9036i		−	0.745483i	0.927935	−	0.372742i	$-0.121582\pi$
$644$	−21.2823	+	0.849297i	−0.838638	+	0.0334670i
$645$		0			0
$646$	−9.00525	−	15.5975i	−0.354307	−	0.613677i
$647$	−3.33350	+	5.77380i	−0.131054	+	0.226991i	−0.924083	−	0.382192i	$-0.875169\pi$
$647$	−3.33350	+	5.77380i	−0.131054	+	0.226991i	0.793029	+	0.609183i	$0.208503\pi$
$648$	−25.8214	−	1.37167i	−1.01436	−	0.0538844i
$649$	−17.5020	+	10.1048i	−0.687012	+	0.396647i
$650$		0			0
$651$	1.84101	+	0.192684i	0.0721551	+	0.00755190i
$652$	21.0026			0.822525
$653$	−29.3074	+	16.9206i	−1.14689	+	0.662156i	−0.948127	−	0.317892i	$-0.897025\pi$
$653$	−29.3074	+	16.9206i	−1.14689	+	0.662156i	−0.198761	+	0.980048i	$0.563692\pi$
$654$	−9.55138	+	3.80864i	−0.373488	+	0.148930i
$655$		0			0
$656$	0.700852	+	1.21391i	0.0273637	+	0.0473953i
$657$	7.34780	−	1.76129i	0.286665	−	0.0687143i
$658$	2.15239	−	4.09713i	0.0839088	−	0.159723i
$659$		−	22.0797i		−	0.860101i	−0.902805	−	0.430051i	$-0.858496\pi$
$659$		−	22.0797i		−	0.860101i	0.902805	−	0.430051i	$-0.141504\pi$
$660$		0			0
$661$	27.1770	+	15.6907i	1.05706	+	0.610296i	0.924619	−	0.380894i	$-0.124384\pi$
$661$	27.1770	+	15.6907i	1.05706	+	0.610296i	0.132445	+	0.991190i	$0.457717\pi$
$662$	21.1554	+	12.2141i	0.822227	+	0.474713i
$663$	3.54717	−	24.4338i	0.137761	−	0.948929i
$664$		−	24.5262i		−	0.951802i
$665$		0			0
$666$	3.51314	−	0.842108i	0.136131	−	0.0326310i
$667$	−10.3824	−	17.9829i	−0.402009	−	0.696301i
$668$	6.48638	−	11.2347i	0.250965	−	0.434685i
$669$	27.2508	−	10.8663i	1.05358	−	0.420117i
$670$		0			0
$671$	82.7594			3.19489
$672$	25.3084	+	2.64883i	0.976294	+	0.102181i
$673$	40.5686			1.56380			0.781902	−	0.623401i	$-0.214249\pi$
$673$	40.5686			1.56380			0.781902	+	0.623401i	$0.214249\pi$
$674$	2.49664	−	1.44144i	0.0961671	−	0.0555221i
$675$		0			0
$676$	0.728410	−	1.26164i	0.0280158	−	0.0485248i
$677$	−19.9031	−	34.4733i	−0.764940	−	1.32491i	−0.940278	−	0.340407i	$-0.889435\pi$
$677$	−19.9031	−	34.4733i	−0.764940	−	1.32491i	0.175338	−	0.984508i	$-0.443898\pi$
$678$	−0.207210	+	0.262749i	−0.00795786	+	0.0100908i
$679$	−24.0719	+	0.960621i	−0.923794	+	0.0368653i
$680$		0			0
$681$	−37.5336	−	5.44894i	−1.43829	−	0.208804i
$682$	1.98852	+	1.14808i	0.0761445	+	0.0439621i
$683$	−19.9121	−	11.4962i	−0.761915	−	0.439892i	0.0680680	−	0.997681i	$-0.478317\pi$
$683$	−19.9121	−	11.4962i	−0.761915	−	0.439892i	−0.829983	+	0.557789i	$0.811650\pi$
$684$	12.9621	+	13.6689i	0.495617	+	0.522643i
$685$		0			0
$686$	−10.0125	−	13.3568i	−0.382277	−	0.509965i
$687$	−0.342784	−	0.270328i	−0.0130780	−	0.0103137i
$688$	−0.519478	−	0.899762i	−0.0198049	−	0.0343031i
$689$	2.71715	−	4.70625i	0.103515	−	0.179294i
$690$		0			0
$691$	20.7325	−	11.9699i	0.788702	−	0.455358i	−0.0508031	−	0.998709i	$-0.516178\pi$
$691$	20.7325	−	11.9699i	0.788702	−	0.455358i	0.839506	+	0.543351i	$0.182845\pi$
$692$	27.4463			1.04335
$693$	−13.6002	−	48.1749i	−0.516629	−	1.83001i
$694$	−29.4087			−1.11634
$695$		0			0
$696$	5.64620	+	14.1596i	0.214019	+	0.536719i
$697$	12.3534	−	21.3968i	0.467920	−	0.810461i
$698$	−14.6399	−	25.3570i	−0.554127	−	0.959776i
$699$	20.3219	+	16.0263i	0.768644	+	0.606172i
$700$		0			0
$701$			7.70996i			0.291201i	0.989343	+	0.145601i	$0.0465115\pi$
$701$			7.70996i			0.291201i	−0.989343	+	0.145601i	$0.953489\pi$
$702$	−1.60700	−	17.5920i	−0.0606525	−	0.663966i
$703$	−6.11765	−	3.53202i	−0.230731	−	0.133213i
$704$	29.6784	+	17.1348i	1.11855	+	0.645793i
$705$		0			0
$706$			6.01340i			0.226317i
$707$	5.39839	+	2.83599i	0.203027	+	0.106658i
$708$	−4.08169	+	5.17570i	−0.153399	+	0.194515i
$709$	1.62353	+	2.81203i	0.0609729	+	0.105608i	0.894901	−	0.446266i	$-0.147246\pi$
$709$	1.62353	+	2.81203i	0.0609729	+	0.105608i	−0.833928	+	0.551874i	$0.813913\pi$
$710$		0			0
$711$	17.5998	+	5.22010i	0.660042	+	0.195769i
$712$	2.93993	−	1.69737i	0.110179	−	0.0636117i
$713$	−2.73815			−0.102545
$714$	6.35538	+	14.2576i	0.237844	+	0.533578i
$715$		0			0
$716$	18.1436	−	10.4752i	0.678060	−	0.391478i
$717$	31.3762	−	12.5114i	1.17176	−	0.467245i
$718$	−7.30213	+	12.6477i	−0.272513	+	0.472006i
$719$	−17.8697	−	30.9513i	−0.666429	−	1.15429i	−0.978896	−	0.204360i	$-0.934489\pi$
$719$	−17.8697	−	30.9513i	−0.666429	−	1.15429i	0.312467	−	0.949929i	$-0.398845\pi$
$720$		0			0
$721$	11.0041	+	17.4166i	0.409813	+	0.648629i
$722$			8.07187i			0.300404i
$723$	−2.45431	+	16.9059i	−0.0912766	+	0.628736i
$724$	15.2777	+	8.82061i	0.567793	+	0.327815i
$725$		0			0
$726$	6.45378	−	44.4552i	0.239522	−	1.64989i
$727$		−	33.2693i		−	1.23389i	−0.787006	−	0.616945i	$-0.788370\pi$
$727$		−	33.2693i		−	1.23389i	0.787006	−	0.616945i	$-0.211630\pi$
$728$	1.14326	+	28.6487i	0.0423722	+	1.06179i
$729$	17.5132	+	20.5497i	0.648636	+	0.761099i
$730$		0			0
$731$	−9.15648	+	15.8595i	−0.338665	+	0.586584i
$732$	25.0728	−	9.99788i	0.926719	−	0.369532i
$733$	−14.5521	+	8.40163i	−0.537492	+	0.310321i	−0.744062	−	0.668111i	$-0.767103\pi$
$733$	−14.5521	+	8.40163i	−0.537492	+	0.310321i	0.206570	+	0.978432i	$0.433770\pi$
$734$	15.5158			0.572700
$735$		0			0
$736$	−37.6414			−1.38748
$737$	−16.9404	+	9.78057i	−0.624009	+	0.360272i
$738$	5.02667	−	16.9476i	0.185034	−	0.623850i
$739$	−18.4120	+	31.8906i	−0.677297	+	1.17311i	0.298494	+	0.954411i	$0.403516\pi$
$739$	−18.4120	+	31.8906i	−0.677297	+	1.17311i	−0.975792	+	0.218702i	$0.929818\pi$
$740$		0			0
$741$	−21.3895	+	27.1225i	−0.785763	+	0.996371i
$742$	0.137001	+	3.43305i	0.00502945	+	0.126031i
$743$		−	45.3970i		−	1.66545i	−0.553684	−	0.832727i	$-0.686779\pi$
$743$		−	45.3970i		−	1.66545i	0.553684	−	0.832727i	$-0.313221\pi$
$744$	1.98927	+	0.288792i	0.0729302	+	0.0105876i
$745$		0			0
$746$	9.62558	+	5.55733i	0.352417	+	0.203468i
$747$	−18.5828	+	17.6219i	−0.679910	+	0.644751i
$748$		−	28.3060i		−	1.03497i
$749$	−7.71466	−	12.2103i	−0.281888	−	0.446156i
$750$		0			0
$751$	−9.49215	−	16.4409i	−0.346374	−	0.599937i	0.639229	−	0.769017i	$-0.279254\pi$
$751$	−9.49215	−	16.4409i	−0.346374	−	0.599937i	−0.985602	+	0.169080i	$0.945920\pi$
$752$	0.208057	−	0.360366i	0.00758707	−	0.0131412i
$753$	−17.0303	−	42.7088i	−0.620617	−	1.55639i
$754$	−9.01888	+	5.20705i	−0.328448	+	0.189630i
$755$		0			0
$756$	−9.94017	−	12.9521i	−0.361521	−	0.471063i
$757$	−24.7352			−0.899017			−0.449508	−	0.893276i	$-0.648401\pi$
$757$	−24.7352			−0.899017			−0.449508	+	0.893276i	$0.648401\pi$
$758$	2.79116	−	1.61148i	0.101379	−	0.0585315i
$759$	27.4264	+	68.7803i	0.995514	+	2.49657i
$760$		0			0
$761$	−23.8401	−	41.2923i	−0.864204	−	1.49685i	−0.867835	−	0.496852i	$-0.834489\pi$
$761$	−23.8401	−	41.2923i	−0.864204	−	1.49685i	0.00363106	−	0.999993i	$-0.498844\pi$
$762$	−1.29104	−	1.01814i	−0.0467693	−	0.0368835i
$763$	−15.4273	−	8.10457i	−0.558505	−	0.293405i
$764$			22.1986i			0.803116i
$765$		0			0
$766$	−18.0554	−	10.4243i	−0.652368	−	0.376645i
$767$	−10.4674	−	6.04333i	−0.377954	−	0.218212i
$768$	28.2194	+	4.09675i	1.01828	+	0.147829i
$769$			48.8811i			1.76270i	0.472467	+	0.881349i	$0.343364\pi$
$769$			48.8811i			1.76270i	−0.472467	+	0.881349i	$0.656636\pi$
$770$		0			0
$771$	16.4417	−	20.8485i	0.592133	−	0.750842i
$772$	1.54124	+	2.66950i	0.0554704	+	0.0960775i
$773$	5.51932	−	9.55974i	0.198516	−	0.343840i	−0.749531	−	0.661969i	$-0.769721\pi$
$773$	5.51932	−	9.55974i	0.198516	−	0.343840i	0.948047	+	0.318129i	$0.103054\pi$
$774$	−3.72581	+	12.5617i	−0.133922	+	0.451522i
$775$		0			0
$776$	−26.1611			−0.939128
$777$	4.95479	+	3.59656i	0.177752	+	0.129026i
$778$	15.3169			0.549136
$779$	−29.9347	+	17.2828i	−1.07252	+	0.619221i
$780$		0			0
$781$	−6.98662	+	12.1012i	−0.250001	+	0.433015i
$782$	−11.5453	−	19.9971i	−0.412860	−	0.715095i
$783$	6.67161	−	14.4515i	0.238424	−	0.516456i
$784$	−0.851624	−	1.23586i	−0.0304152	−	0.0441379i
$785$		0			0
$786$	2.34544	−	16.1560i	0.0836590	−	0.576264i
$787$	14.6934	+	8.48325i	0.523764	+	0.302395i	0.738473	−	0.674283i	$-0.235547\pi$
$787$	14.6934	+	8.48325i	0.523764	+	0.302395i	−0.214709	+	0.976678i	$0.568880\pi$
$788$	−8.05925	−	4.65301i	−0.287099	−	0.165757i
$789$	5.47196	−	37.6922i	0.194807	−	1.34188i
$790$		0			0
$791$	−0.566649	+	0.0226129i	−0.0201477	+	0.000804022i
$792$	−12.6711	−	52.8616i	−0.450246	−	1.87836i
$793$	24.7479	+	42.8645i	0.878822	+	1.52216i
$794$	9.77475	−	16.9304i	0.346893	−	0.600836i
$795$		0			0
$796$	−3.64492	+	2.10440i	−0.129191	+	0.0745884i
$797$	−11.9116			−0.421930			−0.210965	−	0.977494i	$-0.567661\pi$
$797$	−11.9116			−0.421930			−0.210965	+	0.977494i	$0.567661\pi$
$798$	2.27328	−	21.7201i	0.0804731	−	0.768885i
$799$	−7.33457			−0.259478
$800$		0			0
$801$	−3.39837	−	1.00796i	−0.120075	−	0.0356145i
$802$	−0.221283	+	0.383274i	−0.00781378	+	0.0135339i
$803$	7.94217	+	13.7562i	0.280273	+	0.485447i
$804$	−3.95073	+	5.00965i	−0.139332	+	0.176677i
$805$		0			0
$806$			1.37325i			0.0483708i
$807$	−51.2151	−	7.43514i	−1.80286	−	0.261729i
$808$	5.73479	+	3.31098i	0.201749	+	0.116480i
$809$	8.58544	+	4.95680i	0.301848	+	0.174272i	0.643273	−	0.765637i	$-0.277576\pi$
$809$	8.58544	+	4.95680i	0.301848	+	0.174272i	−0.341425	+	0.939909i	$0.610909\pi$
$810$		0			0
$811$		−	40.3504i		−	1.41689i	−0.705765	−	0.708446i	$-0.749396\pi$
$811$		−	40.3504i		−	1.41689i	0.705765	−	0.708446i	$-0.250604\pi$
$812$	−4.47633	+	8.52082i	−0.157088	+	0.299022i
$813$	−16.8681	−	13.3026i	−0.591590	−	0.466543i
$814$	3.79732	+	6.57715i	0.133096	+	0.230529i
$815$		0			0
$816$	0.519846	+	1.30368i	0.0181982	+	0.0456379i
$817$	22.1879	−	12.8102i	0.776255	−	0.448171i
$818$	−25.2768			−0.883783
$819$	20.8849	−	21.4500i	0.729776	−	0.749525i
$820$		0			0
$821$	−21.2757	+	12.2835i	−0.742527	+	0.428698i	−0.822987	−	0.568060i	$-0.807694\pi$
$821$	−21.2757	+	12.2835i	−0.742527	+	0.428698i	0.0804605	+	0.996758i	$0.474361\pi$
$822$	4.21764	+	10.5771i	0.147107	+	0.368917i
$823$	16.6942	−	28.9152i	0.581924	−	1.00792i	−0.413327	−	0.910583i	$-0.635633\pi$
$823$	16.6942	−	28.9152i	0.581924	−	1.00792i	0.995251	−	0.0973396i	$-0.0310333\pi$
$824$	11.1859	+	19.3746i	0.389680	+	0.674946i
$825$		0			0
$826$	7.63560	−	0.304709i	0.265677	−	0.0106022i
$827$		−	35.0677i		−	1.21942i	−0.792623	−	0.609712i	$-0.791285\pi$
$827$		−	35.0677i		−	1.21942i	0.792623	−	0.609712i	$-0.208715\pi$
$828$	16.6182	+	17.5244i	0.577523	+	0.609017i
$829$	−20.7299	−	11.9684i	−0.719979	−	0.415680i	0.0947660	−	0.995500i	$-0.469790\pi$
$829$	−20.7299	−	11.9684i	−0.719979	−	0.415680i	−0.814745	+	0.579820i	$0.803123\pi$
$830$		0			0
$831$	13.8295	+	2.00770i	0.479741	+	0.0696463i
$832$			20.4956i			0.710555i
$833$	−11.3597	+	23.8917i	−0.393590	+	0.827800i
$834$	10.4936	−	13.3061i	0.363362	−	0.460754i
$835$		0			0
$836$	−19.8004	+	34.2954i	−0.684813	+	1.18613i
$837$	−1.21046	−	1.71471i	−0.0418398	−	0.0592690i
$838$	−2.68638	+	1.55098i	−0.0927994	+	0.0535778i
$839$	−44.6267			−1.54068			−0.770342	−	0.637631i	$-0.779914\pi$
$839$	−44.6267			−1.54068			−0.770342	+	0.637631i	$0.779914\pi$
$840$		0			0
$841$	19.6164			0.676428
$842$	−14.6720	+	8.47088i	−0.505631	+	0.291926i
$843$	28.4338	−	11.3381i	0.979311	−	0.390503i
$844$	−14.2358	+	24.6572i	−0.490018	+	0.848736i
$845$		0			0
$846$	−5.10320	+	1.22325i	−0.175452	+	0.0420562i
$847$	64.3601	−	40.6636i	2.21144	−	1.39722i
$848$			0.308914i			0.0106081i
$849$	5.89101	−	40.5787i	0.202179	−	1.39266i
$850$		0			0
$851$	−7.84323	−	4.52829i	−0.268863	−	0.155228i
$852$	−0.654770	+	4.51022i	−0.0224320	+	0.154517i
$853$		−	1.24909i		−	0.0427680i	−0.999771	−	0.0213840i	$-0.993193\pi$
$853$		−	1.24909i		−	0.0427680i	0.999771	−	0.0213840i	$-0.00680726\pi$
$854$	−27.7030	−	14.5535i	−0.947979	−	0.498011i
$855$		0			0
$856$	−7.84216	−	13.5830i	−0.268040	−	0.464258i
$857$	−4.60678	+	7.97918i	−0.157365	+	0.272564i	−0.933918	−	0.357488i	$-0.883633\pi$
$857$	−4.60678	+	7.97918i	−0.157365	+	0.272564i	0.776553	+	0.630052i	$0.216966\pi$
$858$	34.4951	−	13.7550i	1.17764	−	0.469589i
$859$	0.860775	−	0.496969i	0.0293693	−	0.0169564i	−0.485243	−	0.874379i	$-0.661269\pi$
$859$	0.860775	−	0.496969i	0.0293693	−	0.0169564i	0.514613	+	0.857423i	$0.327936\pi$
$860$		0			0
$861$	27.3632	−	12.1972i	0.932534	−	0.415680i
$862$	−6.19664			−0.211058
$863$	3.54799	−	2.04843i	0.120775	−	0.0697295i	−0.438395	−	0.898782i	$-0.644453\pi$
$863$	3.54799	−	2.04843i	0.120775	−	0.0697295i	0.559170	+	0.829053i	$0.311120\pi$
$864$	−16.6403	−	23.5721i	−0.566113	−	0.801940i
$865$		0			0
$866$	−6.88508	−	11.9253i	−0.233965	−	0.405239i
$867$	−2.91430	+	3.69542i	−0.0989749	+	0.125503i
$868$	0.677927	+	1.07299i	0.0230104	+	0.0364195i
$869$			38.5919i			1.30914i
$870$		0			0
$871$	−10.1315	−	5.84944i	−0.343294	−	0.198201i
$872$	−16.3886	−	9.46197i	−0.554989	−	0.320423i
$873$	18.7965	+	19.8215i	0.636166	+	0.670857i
$874$			32.3045i			1.09272i
$875$		0			0
$876$	4.06801	+	3.20813i	0.137445	+	0.108393i
$877$	−5.03871	−	8.72731i	−0.170145	−	0.294700i	0.768325	−	0.640060i	$-0.221090\pi$
$877$	−5.03871	−	8.72731i	−0.170145	−	0.294700i	−0.938471	+	0.345359i	$0.887757\pi$
$878$	−17.3479	+	30.0474i	−0.585463	+	1.01405i
$879$	−1.73731	−	4.35685i	−0.0585980	−	0.146953i
$880$		0			0
$881$	−30.3645			−1.02301			−0.511503	−	0.859281i	$-0.670911\pi$
$881$	−30.3645			−1.02301			−0.511503	+	0.859281i	$0.670911\pi$
$882$	−3.91916	+	18.5178i	−0.131965	+	0.623527i
$883$	16.1748			0.544326			0.272163	−	0.962251i	$-0.412261\pi$
$883$	16.1748			0.544326			0.272163	+	0.962251i	$0.412261\pi$
$884$	14.6609	−	8.46445i	0.493098	−	0.284690i
$885$		0			0
$886$	−1.73803	+	3.01036i	−0.0583903	+	0.101135i
$887$	2.29479	+	3.97469i	0.0770514	+	0.133457i	0.901977	−	0.431785i	$-0.142116\pi$
$887$	2.29479	+	3.97469i	0.0770514	+	0.133457i	−0.824925	+	0.565242i	$0.808783\pi$
$888$	5.22052	+	4.11703i	0.175189	+	0.138159i
$889$	−0.111110	−	2.78428i	−0.00372652	−	0.0933816i
$890$		0			0
$891$	−30.9477	+	47.5811i	−1.03679	+	1.59403i
$892$	17.4205	+	10.0577i	0.583283	+	0.336758i
$893$	8.88652	+	5.13064i	0.297376	+	0.171690i
$894$	4.54301	+	0.659531i	0.151941	+	0.0220580i
$895$		0			0
$896$	8.77326	+	13.8858i	0.293094	+	0.463893i
$897$	−27.4228	+	34.7729i	−0.915620	+	1.16103i
$898$	1.13639	+	1.96829i	0.0379220	+	0.0656827i
$899$	−0.618683	+	1.07159i	−0.0206342	+	0.0357395i
$900$		0			0
$901$	4.71552	−	2.72251i	0.157097	−	0.0906998i
$902$	37.1619			1.23736
$903$	−20.2818	+	9.04067i	−0.674936	+	0.300855i
$904$	−0.615829			−0.0204822
$905$		0			0
$906$	7.23023	−	2.88308i	0.240208	−	0.0957839i
$907$	−15.6580	+	27.1205i	−0.519916	+	0.900521i	0.479816	+	0.877369i	$0.340703\pi$
$907$	−15.6580	+	27.1205i	−0.519916	+	0.900521i	−0.999732	+	0.0231520i	$0.992630\pi$
$908$	−13.0026	−	22.5211i	−0.431505	−	0.747389i
$909$	−1.61176	−	6.72400i	−0.0534586	−	0.223021i
$910$		0			0
$911$		−	2.78118i		−	0.0921447i	−0.998938	−	0.0460724i	$-0.985330\pi$
$911$		−	2.78118i		−	0.0921447i	0.998938	−	0.0460724i	$-0.0146705\pi$
$912$	0.282099	−	1.94317i	0.00934124	−	0.0643447i
$913$	−46.6245	−	26.9187i	−1.54305	−	0.890878i
$914$	−7.26289	−	4.19323i	−0.240235	−	0.138700i
$915$		0			0
$916$		−	0.299327i		−	0.00989003i
$917$	23.3898	−	14.7780i	0.772400	−	0.488012i
$918$	7.41887	−	16.0702i	0.244859	−	0.530396i
$919$	−29.0225	−	50.2685i	−0.957365	−	1.65821i	−0.728860	−	0.684663i	$-0.759949\pi$
$919$	−29.0225	−	50.2685i	−0.957365	−	1.65821i	−0.228506	−	0.973543i	$-0.573384\pi$
$920$		0			0
$921$	−8.84217	+	3.52584i	−0.291359	+	0.116180i
$922$	8.89063	−	5.13301i	0.292797	−	0.169047i
$923$	−8.35695			−0.275072
$924$	20.1622	−	27.7765i	0.663288	−	0.913778i
$925$		0			0
$926$	0.251595	−	0.145259i	0.00826793	−	0.00477349i
$927$	6.64259	−	22.3957i	0.218171	−	0.735573i
$928$	−8.50504	+	14.7312i	−0.279191	+	0.483574i
$929$	20.7329	+	35.9104i	0.680224	+	1.17818i	0.974912	+	0.222589i	$0.0714508\pi$
$929$	20.7329	+	35.9104i	0.680224	+	1.17818i	−0.294689	+	0.955593i	$0.595216\pi$
$930$		0			0
$931$	30.4760	−	21.0008i	0.998809	−	0.688274i
$932$			17.7455i			0.581274i
$933$	−37.4476	−	5.43645i	−1.22598	−	0.177981i
$934$	−18.1993	−	10.5074i	−0.595499	−	0.343812i
$935$		0			0
$936$	23.5902	−	22.3703i	0.771069	−	0.731195i
$937$		−	15.3201i		−	0.500486i	−0.968183	−	0.250243i	$-0.919489\pi$
$937$		−	15.3201i		−	0.500486i	0.968183	−	0.250243i	$-0.0805105\pi$
$938$	7.39063	−	0.294933i	0.241312	−	0.00962990i
$939$	33.4442	+	26.3749i	1.09141	+	0.860714i
$940$		0			0
$941$	25.5592	−	44.2698i	0.833206	−	1.44316i	−0.0622769	−	0.998059i	$-0.519836\pi$
$941$	25.5592	−	44.2698i	0.833206	−	1.44316i	0.895483	−	0.445096i	$-0.146830\pi$
$942$	−4.10503	−	10.2947i	−0.133749	−	0.335419i
$943$	−38.3783	+	22.1577i	−1.24977	+	0.721555i
$944$	0.687068			0.0223622
$945$		0			0
$946$	−27.5447			−0.895556
$947$	6.95988	−	4.01829i	0.226166	−	0.130577i	−0.382636	−	0.923899i	$-0.624984\pi$
$947$	6.95988	−	4.01829i	0.226166	−	0.130577i	0.608802	+	0.793322i	$0.291650\pi$
$948$	4.66215	+	11.6918i	0.151420	+	0.379733i
$949$	−4.74996	+	8.22716i	−0.154190	+	0.267065i
$950$		0			0
$951$	32.5794	+	25.6929i	1.05646	+	0.833149i
$952$	−13.3605	+	25.4321i	−0.433017	+	0.824260i
$953$		−	43.7448i		−	1.41703i	−0.705695	−	0.708516i	$-0.749365\pi$
$953$		−	43.7448i		−	1.41703i	0.705695	−	0.708516i	$-0.250635\pi$
$954$	2.82688	−	2.68070i	0.0915236	−	0.0867908i
$955$		0			0
$956$	20.0578	+	11.5804i	0.648714	+	0.374535i
$957$	33.1145	+	4.80739i	1.07044	+	0.155401i
$958$		−	0.570645i		−	0.0184367i
$959$	−8.97489	+	17.0840i	−0.289814	+	0.551670i
$960$		0			0
$961$	−15.4184	−	26.7055i	−0.497368	−	0.861467i
$962$	−2.27105	+	3.93358i	−0.0732217	+	0.126824i
$963$	−4.65695	+	15.7011i	−0.150068	+	0.505960i
$964$	−10.1439	+	5.85660i	−0.326714	+	0.188628i
$965$		0			0
$966$	2.91449	−	27.8467i	0.0937723	−	0.895952i
$967$	28.3067			0.910281			0.455140	−	0.890420i	$-0.349589\pi$
$967$	28.3067			0.910281			0.455140	+	0.890420i	$0.349589\pi$
$968$	71.5954	−	41.3357i	2.30116	−	1.32858i
$969$	−32.1483	+	12.8193i	−1.03275	+	0.411814i
$970$		0			0
$971$	−16.4304	−	28.4583i	−0.527277	−	0.913270i	−0.999495	−	0.0317882i	$-0.989880\pi$
$971$	−16.4304	−	28.4583i	−0.527277	−	0.913270i	0.472218	−	0.881482i	$-0.343454\pi$
$972$	−3.62783	+	18.1539i	−0.116363	+	0.582287i
$973$	28.6963	−	1.14516i	0.919961	−	0.0367123i
$974$		−	19.5144i		−	0.625282i
$975$		0			0
$976$	−2.43664	−	1.40680i	−0.0779950	−	0.0450304i
$977$	−44.2178	−	25.5291i	−1.41465	−	0.816750i	−0.418830	−	0.908065i	$-0.637560\pi$
$977$	−44.2178	−	25.5291i	−1.41465	−	0.816750i	−0.995822	+	0.0913150i	$0.970893\pi$
$978$	−3.96653	+	27.3225i	−0.126836	+	0.873676i
$979$		−	7.45178i		−	0.238160i
$980$		0			0
$981$	4.60601	+	19.2155i	0.147059	+	0.613505i
$982$	−16.2965	−	28.2263i	−0.520041	−	0.900737i
$983$	−15.0732	+	26.1076i	−0.480762	+	0.832704i	−0.999756	−	0.0220736i	$-0.992973\pi$
$983$	−15.0732	+	26.1076i	−0.480762	+	0.832704i	0.518994	+	0.854778i	$0.326307\pi$
$984$	30.2189	−	12.0499i	0.963342	−	0.384136i
$985$		0			0
$986$	−10.4346			−0.332306
$987$	−7.19736	−	5.22438i	−0.229094	−	0.166294i
$988$	−23.6840			−0.753489
$989$	28.4463	−	16.4235i	0.904541	−	0.522237i
$990$		0			0
$991$	−25.9382	+	44.9263i	−0.823955	+	1.42713i	0.0787606	+	0.996894i	$0.474904\pi$
$991$	−25.9382	+	44.9263i	−0.823955	+	1.42713i	−0.902715	+	0.430238i	$0.858430\pi$
$992$	1.12151	+	1.94252i	0.0356081	+	0.0616751i
$993$	29.0683	−	36.8595i	0.922456	−	1.16970i
$994$	4.46675	−	2.82215i	0.141677	−	0.0895133i
$995$		0			0
$996$	−17.3773	−	2.52275i	−0.550622	−	0.0799365i
$997$	−43.8884	−	25.3390i	−1.38996	−	0.802494i	−0.396649	−	0.917970i	$-0.629827\pi$
$997$	−43.8884	−	25.3390i	−1.38996	−	0.802494i	−0.993310	+	0.115477i	$0.963160\pi$
$998$	−7.03574	−	4.06209i	−0.222713	−	0.128583i
$999$	−0.631539	−	6.91349i	−0.0199810	−	0.218733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.i.101.4	yes	20
3.2	odd	2	inner	525.2.t.i.101.7	yes	20
5.2	odd	4		525.2.q.g.374.8		40
5.3	odd	4		525.2.q.g.374.13		40
5.4	even	2		525.2.t.h.101.7	yes	20
7.5	odd	6	inner	525.2.t.i.26.7	yes	20
15.2	even	4		525.2.q.g.374.14		40
15.8	even	4		525.2.q.g.374.7		40
15.14	odd	2		525.2.t.h.101.4	yes	20
21.5	even	6	inner	525.2.t.i.26.4	yes	20
35.12	even	12		525.2.q.g.299.7		40
35.19	odd	6		525.2.t.h.26.4	✓	20
35.33	even	12		525.2.q.g.299.14		40
105.47	odd	12		525.2.q.g.299.13		40
105.68	odd	12		525.2.q.g.299.8		40
105.89	even	6		525.2.t.h.26.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.7		40	35.12	even	12
525.2.q.g.299.8		40	105.68	odd	12
525.2.q.g.299.13		40	105.47	odd	12
525.2.q.g.299.14		40	35.33	even	12
525.2.q.g.374.7		40	15.8	even	4
525.2.q.g.374.8		40	5.2	odd	4
525.2.q.g.374.13		40	5.3	odd	4
525.2.q.g.374.14		40	15.2	even	4
525.2.t.h.26.4	✓	20	35.19	odd	6
525.2.t.h.26.7	yes	20	105.89	even	6
525.2.t.h.101.4	yes	20	15.14	odd	2
525.2.t.h.101.7	yes	20	5.4	even	2
525.2.t.i.26.4	yes	20	21.5	even	6	inner
525.2.t.i.26.7	yes	20	7.5	odd	6	inner
525.2.t.i.101.4	yes	20	1.1	even	1	trivial
525.2.t.i.101.7	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780577 + 0.450666i) q^{2} +(0.641538 + 1.60886i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(-1.22583 - 0.966719i) q^{6} +(-0.105498 - 2.64365i) q^{7} -2.87309i q^{8} +(-2.17686 + 2.06429i) q^{9} +O(q^{10})\)	\(q+(-0.780577 + 0.450666i) q^{2} +(0.641538 + 1.60886i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(-1.22583 - 0.966719i) q^{6} +(-0.105498 - 2.64365i) q^{7} -2.87309i q^{8} +(-2.17686 + 2.06429i) q^{9} +(-5.46176 - 3.15335i) q^{11} +(-2.03564 - 0.295524i) q^{12} -3.77183i q^{13} +(1.27375 + 2.01603i) q^{14} +(0.107205 + 0.185685i) q^{16} +(1.88963 - 3.27294i) q^{17} +(0.768900 - 2.59237i) q^{18} +(-4.57893 + 2.64365i) q^{19} +(4.18558 - 1.86573i) q^{21} +5.68443 q^{22} +(-5.87050 + 3.38933i) q^{23} +(4.62239 - 1.84320i) q^{24} +(1.69984 + 2.94420i) q^{26} +(-4.71769 - 2.17794i) q^{27} +(2.78161 + 1.46129i) q^{28} +3.06327i q^{29} +(0.349819 + 0.201968i) q^{31} +(4.80897 + 2.77646i) q^{32} +(1.56937 - 10.8102i) q^{33} +3.40637i q^{34} +(-0.830485 - 3.46465i) q^{36} +(0.668021 + 1.15705i) q^{37} +(2.38281 - 4.12714i) q^{38} +(6.06834 - 2.41977i) q^{39} +6.53749 q^{41} +(-2.42634 + 3.34265i) q^{42} -4.84564 q^{43} +(6.48638 - 3.74491i) q^{44} +(3.05492 - 5.29127i) q^{46} +(-0.970371 - 1.68073i) q^{47} +(-0.229964 + 0.291602i) q^{48} +(-6.97774 + 0.557800i) q^{49} +(6.47796 + 0.940437i) q^{51} +(3.87929 + 2.23971i) q^{52} +(1.24774 + 0.720381i) q^{53} +(4.66404 - 0.426055i) q^{54} +(-7.59543 + 0.303106i) q^{56} +(-7.19082 - 5.67086i) q^{57} +(-1.38051 - 2.39112i) q^{58} +(1.60223 - 2.77514i) q^{59} +(-11.3644 + 6.56124i) q^{61} -0.364081 q^{62} +(5.68691 + 5.53707i) q^{63} -5.43385 q^{64} +(3.64678 + 9.14545i) q^{66} +(1.55082 - 2.68611i) q^{67} +(2.24412 + 3.88694i) q^{68} +(-9.21911 - 7.27042i) q^{69} -2.21562i q^{71} +(5.93088 + 6.25430i) q^{72} +(-2.18121 - 1.25932i) q^{73} +(-1.04288 - 0.602109i) q^{74} -6.27919i q^{76} +(-7.76013 + 14.7716i) q^{77} +(-3.64630 + 4.62362i) q^{78} +(-3.05960 - 5.29938i) q^{79} +(0.477421 - 8.98733i) q^{81} +(-5.10301 + 2.94623i) q^{82} +8.53654 q^{83} +(-0.566504 + 5.41270i) q^{84} +(3.78240 - 2.18377i) q^{86} +(-4.92836 + 1.96520i) q^{87} +(-9.05984 + 15.6921i) q^{88} +(0.590783 + 1.02327i) q^{89} +(-9.97138 + 0.397921i) q^{91} -8.05034i q^{92} +(-0.100516 + 0.692381i) q^{93} +(1.51490 + 0.874627i) q^{94} +(-1.38180 + 9.51816i) q^{96} -9.10556i q^{97} +(5.19528 - 3.58004i) q^{98} +(18.3989 - 4.41026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q + 3 q^{3} + 14 q^{4} - 7 q^{9} - 21 q^{12} - 18 q^{16} + 14 q^{18} - 9 q^{21} + 20 q^{22} + 18 q^{24} - 10 q^{28} + 42 q^{31} + 12 q^{33} - 36 q^{36} + 24 q^{37} + 33 q^{42} + 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} - 84 q^{52} - 75 q^{54} + 6 q^{57} - 4 q^{58} - 90 q^{61} - 5 q^{63} - 120 q^{64} + 6 q^{66} + 20 q^{67} - 35 q^{72} - 48 q^{73} - 108 q^{78} + 46 q^{79} + 29 q^{81} + 36 q^{82} + 75 q^{84} + 69 q^{87} + 4 q^{88} - 30 q^{91} - 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q + 3 * q^3 + 14 * q^4 - 7 * q^9 - 21 * q^12 - 18 * q^16 + 14 * q^18 - 9 * q^21 + 20 * q^22 + 18 * q^24 - 10 * q^28 + 42 * q^31 + 12 * q^33 - 36 * q^36 + 24 * q^37 + 33 * q^42 + 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 - 84 * q^52 - 75 * q^54 + 6 * q^57 - 4 * q^58 - 90 * q^61 - 5 * q^63 - 120 * q^64 + 6 * q^66 + 20 * q^67 - 35 * q^72 - 48 * q^73 - 108 * q^78 + 46 * q^79 + 29 * q^81 + 36 * q^82 + 75 * q^84 + 69 * q^87 + 4 * q^88 - 30 * q^91 - 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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