LMFDB - Embedded newform 525.2.t.i.26.4

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			26.4
Root			$1.71408 + 0.248842i$ of defining polynomial
Character	$\chi$	$=$	525.26
Dual form			525.2.t.i.101.4

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.197957	−	0.980211i	$-0.436569\pi$
$2$	−0.780577	−	0.450666i	−0.551951	−	0.318669i	−0.749909	+	0.661541i	$0.769903\pi$
$3$	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	−0.668442	+	0.743765i	$0.733038\pi$
$11$	−5.46176	+	3.15335i	−1.64678	+	0.950770i	−0.978340	+	0.207005i	$0.933628\pi$
$12$	−2.03564	+	0.295524i	−0.587639	+	0.0853104i
$13$			3.77183i			1.04612i	0.852297	+	0.523059i	$0.175209\pi$
$13$			3.77183i			1.04612i	−0.852297	+	0.523059i	$0.824791\pi$
$14$	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	0.998871	−	0.0474963i	$-0.0151242\pi$
$17$	1.88963	+	3.27294i	0.458303	+	0.793804i	−0.540569	+	0.841300i	$0.681791\pi$
$18$	0.768900	+	2.59237i	0.181231	+	0.611028i
$19$	−4.57893	−	2.64365i	−1.05048	−	0.606494i	−0.127695	−	0.991813i	$-0.540758\pi$
$19$	−4.57893	−	2.64365i	−1.05048	−	0.606494i	−0.922783	+	0.385319i	$0.874091\pi$
$20$		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	−0.258298	−	0.966065i	$-0.583162\pi$
$23$	−5.87050	−	3.38933i	−1.22408	−	0.706725i	−0.965786	+	0.259340i	$0.916495\pi$
$24$	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	$-0.908200\pi$
$29$		−	3.06327i		−	0.568834i	0.958701	−	0.284417i	$-0.0918000\pi$
$30$		0			0
$31$	0.349819	−	0.201968i	0.0628294	−	0.0362746i	−0.468256	−	0.883593i	$-0.655118\pi$
$31$	0.349819	−	0.201968i	0.0628294	−	0.0362746i	0.531086	+	0.847318i	$0.321784\pi$
$32$	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	−0.805876	−	0.592084i	$-0.798305\pi$
$37$	0.668021	−	1.15705i	0.109822	−	0.190217i	0.915698	+	0.401867i	$0.131639\pi$
$38$	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	−0.928078	−	0.372386i	$-0.878540\pi$
$47$	−0.970371	+	1.68073i	−0.141543	+	0.245160i	0.786535	+	0.617546i	$0.211873\pi$
$48$	−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	−0.411851	−	0.911251i	$-0.635118\pi$
$53$	1.24774	−	0.720381i	0.171390	−	0.0989519i	0.583241	+	0.812299i	$0.301784\pi$
$54$	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	0.951271	−	0.308355i	$-0.0997785\pi$
$59$	1.60223	+	2.77514i	0.208592	+	0.361293i	−0.742679	+	0.669648i	$0.766445\pi$
$60$		0			0
$61$	−11.3644	−	6.56124i	−1.45506	−	0.840080i	−0.456300	−	0.889826i	$-0.650825\pi$
$61$	−11.3644	−	6.56124i	−1.45506	−	0.840080i	−0.998762	+	0.0497461i	$0.984159\pi$
$62$	−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	0.945071	−	0.326864i	$-0.105992\pi$
$67$	1.55082	+	2.68611i	0.189463	+	0.328160i	−0.755608	+	0.655024i	$0.772659\pi$
$68$	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	$0.0419707\pi$
$71$			2.21562i			0.262946i	−0.991320	+	0.131473i	$0.958029\pi$
$72$	5.93088	−	6.25430i	0.698961	−	0.737077i
$73$	−2.18121	+	1.25932i	−0.255292	+	0.147393i	−0.622185	−	0.782870i	$-0.713755\pi$
$73$	−2.18121	+	1.25932i	−0.255292	+	0.147393i	0.366893	+	0.930263i	$0.380421\pi$
$74$	−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	−0.985214	−	0.171329i	$-0.945194\pi$
$79$	−3.05960	+	5.29938i	−0.344232	+	0.596227i	0.640982	+	0.767556i	$0.278527\pi$
$80$		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	−0.833014	−	0.553252i	$-0.813387\pi$
$89$	0.590783	−	1.02327i	0.0626229	−	0.108466i	0.895637	+	0.444786i	$0.146720\pi$
$90$		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	$0.152963\pi$
$97$			9.10556i			0.924530i	−0.886742	+	0.462265i	$0.847037\pi$
$98$	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	0.802978	−	0.596008i	$-0.203247\pi$
$101$	−1.15241	−	1.99604i	−0.114669	−	0.198613i	−0.917647	+	0.397395i	$0.869914\pi$
$102$	−5.48037	−	2.18532i	−0.542638	−	0.216379i
$103$	−6.74347	−	3.89335i	−0.664454	−	0.383623i	0.129518	−	0.991577i	$-0.458657\pi$
$103$	−6.74347	−	3.89335i	−0.664454	−	0.383623i	−0.793972	+	0.607954i	$0.791990\pi$
$104$	−10.8368			−1.06264
$105$		0			0
$106$	−1.29861			−0.126132
$107$	4.72768	+	2.72952i	0.457042	+	0.263873i	0.710800	−	0.703395i	$-0.248333\pi$
$107$	4.72768	+	2.72952i	0.457042	+	0.263873i	−0.253758	+	0.967268i	$0.581667\pi$
$108$	5.04135	+	3.55884i	0.485104	+	0.342450i
$109$	3.29331	+	5.70418i	0.315442	+	0.546362i	0.979531	−	0.201292i	$-0.0645139\pi$
$109$	3.29331	+	5.70418i	0.315442	+	0.546362i	−0.664089	+	0.747653i	$0.731181\pi$
$110$		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	$0.00320922\pi$
$113$			0.214344i			0.0201638i	−0.999949	+	0.0100819i	$0.996791\pi$
$114$	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	−0.541966	−	0.840401i	$-0.682320\pi$
$131$	5.22860	−	9.05621i	0.456825	−	0.791245i	0.998791	+	0.0491560i	$0.0156531\pi$
$132$	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	−0.744947	−	0.667124i	$-0.767525\pi$
$137$	−6.31673	+	3.64697i	−0.539675	+	0.311581i	0.205272	+	0.978705i	$0.434192\pi$
$138$	10.4728	−	1.52038i	0.891501	−	0.129423i
$139$		−	10.8548i		−	0.920693i	−0.887739	−	0.460347i	$-0.847725\pi$
$139$		−	10.8548i		−	0.920693i	0.887739	−	0.460347i	$-0.152275\pi$
$140$		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	0.392048	−	0.919945i	$-0.371767\pi$
$149$	−2.54658	−	1.47027i	−0.208624	−	0.120449i	−0.600672	+	0.799496i	$0.705100\pi$
$150$		0			0
$151$	−2.49298	−	4.31797i	−0.202876	−	0.351391i	0.746578	−	0.665298i	$-0.231695\pi$
$151$	−2.49298	−	4.31797i	−0.202876	−	0.351391i	−0.949454	+	0.313907i	$0.898362\pi$
$152$	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	−0.234182	−	0.972193i	$-0.575241\pi$
$157$	6.14808	−	3.54960i	0.490671	−	0.283289i	0.724853	+	0.688904i	$0.241908\pi$
$158$	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	0.278390	+	0.960468i	$0.410199\pi$
$163$	−8.84246	+	15.3156i	−0.692595	+	1.19961i	−0.970985	+	0.239141i	$0.923134\pi$
$164$	−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	−0.0255936	+	0.999672i	$0.508148\pi$
$173$	−11.5554	+	20.0145i	−0.878539	+	1.52167i	−0.852945	+	0.522001i	$0.825186\pi$
$174$	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	−0.946900	−	0.321527i	$-0.895804\pi$
$179$	−15.2776	+	8.82051i	−1.14190	+	0.659276i	−0.194999	+	0.980803i	$0.562470\pi$
$180$		0			0
$181$			14.8545i			1.10413i	0.833802	+	0.552064i	$0.186160\pi$
$181$			14.8545i			1.10413i	−0.833802	+	0.552064i	$0.813840\pi$
$182$	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	0.953987	−	0.299850i	$-0.0969365\pi$
$191$	16.1877	+	9.34599i	1.17130	+	0.676252i	0.217316	+	0.976101i	$0.430270\pi$
$192$	−3.48602	+	8.74230i	−0.251582	+	0.630921i
$193$	1.29778	+	2.24781i	0.0934160	+	0.161801i	0.908946	−	0.416913i	$-0.136888\pi$
$193$	1.29778	+	2.24781i	0.0934160	+	0.161801i	−0.815530	+	0.578714i	$0.803555\pi$
$194$	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	$-0.909949\pi$
$197$		−	7.83600i		−	0.558292i	0.960249	−	0.279146i	$-0.0900513\pi$
$198$	−12.3742	−	11.7343i	−0.879396	−	0.833921i
$199$	3.06915	−	1.77198i	0.217566	−	0.125612i	−0.387256	−	0.921972i	$-0.626577\pi$
$199$	3.06915	−	1.77198i	0.217566	−	0.125612i	0.604823	+	0.796360i	$0.293244\pi$
$200$		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	$0.191944\pi$
$223$			16.9380i			1.13425i	−0.823632	+	0.567125i	$0.808056\pi$
$224$	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	−0.958277	−	0.285842i	$-0.907727\pi$
$227$	−10.9486	−	18.9635i	−0.726685	−	1.25865i	0.231592	−	0.972813i	$-0.425606\pi$
$228$	10.1023	+	4.02834i	0.669043	+	0.266783i
$229$	−0.218276	−	0.126022i	−0.0144241	−	0.00832775i	0.492771	−	0.870159i	$-0.335984\pi$
$229$	−0.218276	−	0.126022i	−0.0144241	−	0.00832775i	−0.507195	+	0.861831i	$0.669318\pi$
$230$		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	0.859894	−	0.510473i	$-0.170530\pi$
$233$	12.9405	+	7.47118i	0.847758	+	0.489453i	−0.0121359	+	0.999926i	$0.503863\pi$
$234$	−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	$0.217250\pi$
$239$			19.5021i			1.26149i	−0.775991	+	0.630744i	$0.782750\pi$
$240$		0			0
$241$	8.54154	−	4.93146i	0.550209	−	0.317663i	−0.198997	−	0.980000i	$-0.563768\pi$
$241$	8.54154	−	4.93146i	0.550209	−	0.317663i	0.749206	+	0.662337i	$0.230435\pi$
$242$	−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	−0.999685	−	0.0250861i	$-0.992014\pi$
$257$	−7.66481	+	13.2758i	−0.478117	+	0.828124i	0.521568	+	0.853210i	$0.325347\pi$
$258$	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	−0.954685	−	0.297618i	$-0.903808\pi$
$263$	−19.0437	+	10.9949i	−1.17428	+	0.677972i	−0.219598	+	0.975591i	$0.570474\pi$
$264$	−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	−0.812826	−	0.582506i	$-0.802072\pi$
$269$	−14.9395	−	25.8760i	−0.910878	−	1.57769i	−0.0980517	−	0.995181i	$-0.531261\pi$
$270$		0			0
$271$	−10.7412	−	6.20142i	−0.652480	−	0.376710i	0.136926	−	0.990581i	$-0.456278\pi$
$271$	−10.7412	−	6.20142i	−0.652480	−	0.376710i	−0.789406	+	0.613872i	$0.789611\pi$
$272$	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	0.961393	−	0.275178i	$-0.0887370\pi$
$277$	4.03409	+	6.98725i	0.242385	+	0.419823i	−0.719008	+	0.695002i	$0.755404\pi$
$278$	−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	$0.176739\pi$
$281$			17.6732i			1.05430i	−0.849773	+	0.527149i	$0.823261\pi$
$282$	−0.435287	−	2.99837i	−0.0259210	−	0.178550i
$283$	−20.5021	+	11.8369i	−1.21872	+	0.703629i	−0.964644	−	0.263555i	$-0.915105\pi$
$283$	−20.5021	+	11.8369i	−1.21872	+	0.703629i	−0.254077	+	0.967184i	$0.581772\pi$
$284$	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	$-0.949871\pi$
$307$		−	5.49592i		−	0.313669i	0.987625	−	0.156834i	$-0.0501289\pi$
$308$	−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	−0.989593	−	0.143898i	$-0.954036\pi$
$311$	−10.9235	−	18.9201i	−0.619416	−	1.07286i	0.370177	−	0.928961i	$-0.379297\pi$
$312$	−6.95222	+	17.4349i	−0.393592	+	0.987056i
$313$	21.2964	+	12.2955i	1.20375	+	0.694983i	0.961386	−	0.275203i	$-0.0887452\pi$
$313$	21.2964	+	12.2955i	1.20375	+	0.694983i	0.242360	+	0.970186i	$0.422079\pi$
$314$	−6.39874			−0.361102
$315$		0			0
$316$	7.26715			0.408809
$317$	20.7457	+	11.9775i	1.16520	+	0.672726i	0.952544	−	0.304402i	$-0.0984565\pi$
$317$	20.7457	+	11.9775i	1.16520	+	0.672726i	0.212652	+	0.977128i	$0.431790\pi$
$318$	−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	0.205434	+	0.978671i	$0.434139\pi$
$331$	−13.5511	+	23.4712i	−0.744837	+	1.29009i	−0.950271	+	0.311424i	$0.899194\pi$
$332$	−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	0.517097	−	0.855927i	$-0.327012\pi$
$347$	28.2567	−	16.3140i	1.51690	−	0.875783i	0.999803	−	0.0198563i	$-0.00632087\pi$
$348$	0.905269	+	6.23571i	0.0485275	+	0.334269i
$349$		−	32.4849i		−	1.73888i	−0.494041	−	0.869439i	$-0.664481\pi$
$349$		−	32.4849i		−	1.73888i	0.494041	−	0.869439i	$-0.335519\pi$
$350$		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	0.941040	−	0.338294i	$-0.109850\pi$
$353$	3.33584	+	5.77784i	0.177549	+	0.307523i	−0.763492	+	0.645818i	$0.776517\pi$
$354$	−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	0.822284	−	0.569078i	$-0.192700\pi$
$359$	14.0322	+	8.10148i	0.740590	+	0.427580i	−0.0816940	+	0.996657i	$0.526033\pi$
$360$		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	−0.835789	−	0.549050i	$-0.814990\pi$
$367$	−14.9080	+	8.60716i	−0.778193	+	0.449290i	0.0575965	+	0.998340i	$0.481656\pi$
$368$	−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	−0.980331	−	0.197360i	$-0.936763\pi$
$373$	−6.16568	+	10.6793i	−0.319247	+	0.552952i	0.661084	+	0.750312i	$0.270097\pi$
$374$	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	−0.403138	−	0.915139i	$-0.632081\pi$
$383$	11.5654	−	20.0319i	0.590965	−	1.02358i	0.994103	−	0.108442i	$-0.0345861\pi$
$384$	−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	−0.824310	−	0.566138i	$-0.808437\pi$
$389$	−14.7169	+	8.49679i	−0.746175	+	0.430804i	0.0781352	+	0.996943i	$0.475103\pi$
$390$		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	−0.0519125	−	0.998652i	$-0.516532\pi$
$397$	−18.7837	−	10.8448i	−0.942726	−	0.544283i	−0.890814	+	0.454368i	$0.849865\pi$
$398$	−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	0.510580	−	0.859830i	$-0.329431\pi$
$401$	0.425230	+	0.245507i	0.0212350	+	0.0122600i	−0.489345	+	0.872090i	$0.662764\pi$
$402$	−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	0.240143	−	0.970738i	$-0.422806\pi$
$409$	24.2867	−	14.0219i	1.20090	−	0.693339i	0.960755	+	0.277399i	$0.0894723\pi$
$410$		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	−0.349704	−	0.936860i	$-0.613718\pi$
$431$	5.95390	−	3.43749i	0.286789	−	0.165578i	0.636493	+	0.771282i	$0.280384\pi$
$432$	−0.101350	+	1.10949i	−0.00487622	+	0.0533803i
$433$		−	15.2776i		−	0.734193i	−0.930183	−	0.367096i	$-0.880352\pi$
$433$		−	15.2776i		−	0.734193i	0.930183	−	0.367096i	$-0.119648\pi$
$434$	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	0.993124	+	0.117071i	$0.0373505\pi$
$439$	33.3367	+	19.2469i	1.59107	+	0.918606i	0.597948	+	0.801535i	$0.295983\pi$
$440$		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	0.577239	−	0.816575i	$-0.304130\pi$
$443$	3.33990	+	1.92829i	0.158683	+	0.0916158i	−0.418556	+	0.908191i	$0.637464\pi$
$444$	−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	$0.0189508\pi$
$449$			2.52159i			0.119001i	−0.998228	+	0.0595005i	$0.981049\pi$
$450$		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	−0.736457	−	0.676484i	$-0.763503\pi$
$457$	4.65226	−	8.05795i	0.217623	−	0.376935i	0.954081	+	0.299549i	$0.0968362\pi$
$458$	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	−0.459485	−	0.888186i	$-0.651966\pi$
$467$	11.6576	−	20.1915i	0.539449	−	0.934353i	0.998934	−	0.0461675i	$-0.0147008\pi$
$468$	−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	0.858703	−	0.512474i	$-0.171271\pi$
$479$	−0.316556	−	0.548292i	−0.0144638	−	0.0250521i	−0.873167	+	0.487422i	$0.837937\pi$
$480$		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	0.509400	−	0.860530i	$-0.329868\pi$
$487$	−10.8253	−	18.7500i	−0.490541	−	0.849642i	−0.999941	+	0.0108880i	$0.996534\pi$
$488$	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	$-0.696211\pi$
$491$		−	36.1608i		−	1.63191i	0.578112	−	0.815957i	$-0.303789\pi$
$492$	−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	−0.747342	−	0.664439i	$-0.768670\pi$
$499$	4.50676	−	7.80593i	0.201750	−	0.349442i	0.949092	+	0.314998i	$0.102004\pi$
$500$		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	−0.0112055	+	0.999937i	$0.503567\pi$
$509$	−19.6636	+	34.0584i	−0.871574	+	1.50961i	−0.860368	+	0.509673i	$0.829766\pi$
$510$		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	0.990711	−	0.135982i	$-0.0434190\pi$
$521$	8.61869	+	14.9280i	0.377592	+	0.654008i	−0.613120	+	0.789990i	$0.710086\pi$
$522$	7.94113	−	2.35534i	0.347574	−	0.103091i
$523$	−32.7149	−	18.8880i	−1.43052	−	0.825914i	−0.433364	−	0.901219i	$-0.642674\pi$
$523$	−32.7149	−	18.8880i	−1.43052	−	0.825914i	−0.997161	+	0.0753051i	$0.976007\pi$
$524$	−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	−0.996461	−	0.0840587i	$-0.973212\pi$
$541$	−9.89533	+	17.1392i	−0.425433	+	0.736872i	0.571027	+	0.820931i	$0.306545\pi$
$542$	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	−0.0632208	−	0.998000i	$-0.520137\pi$
$557$	18.1599	−	10.4847i	0.769462	−	0.444249i	0.832683	+	0.553751i	$0.186804\pi$
$558$	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	0.991225	−	0.132185i	$-0.0421993\pi$
$563$	9.04347	+	15.6638i	0.381137	+	0.660148i	−0.610088	+	0.792333i	$0.708866\pi$
$564$	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	−0.0404626	−	0.999181i	$-0.512883\pi$
$569$	−22.0888	−	12.7530i	−0.926010	−	0.534632i	−0.885547	+	0.464549i	$0.846216\pi$
$570$		0			0
$571$	−19.8853	−	34.4424i	−0.832175	−	1.44137i	−0.896310	−	0.443428i	$-0.853762\pi$
$571$	−19.8853	−	34.4424i	−0.832175	−	1.44137i	0.0641352	−	0.997941i	$-0.479571\pi$
$572$	−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	−0.535543	−	0.844508i	$-0.679893\pi$
$577$	−1.72826	+	0.997811i	−0.0719484	+	0.0415394i	0.463594	+	0.886048i	$0.346560\pi$
$578$	−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	−0.853298	−	0.521423i	$-0.825401\pi$
$593$	0.606763	−	1.05094i	0.0249168	−	0.0431571i	0.878215	+	0.478266i	$0.158735\pi$
$594$	−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	0.358986	−	0.933343i	$-0.383122\pi$
$599$	32.9617	−	19.0304i	1.34678	−	0.777563i	0.987792	+	0.155780i	$0.0497891\pi$
$600$		0			0
$601$			8.32414i			0.339549i	0.985483	+	0.169774i	$0.0543039\pi$
$601$			8.32414i			0.339549i	−0.985483	+	0.169774i	$0.945696\pi$
$602$	−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	0.926373	−	0.376607i	$-0.122909\pi$
$607$	26.1996	+	15.1263i	1.06341	+	0.613959i	0.137036	+	0.990566i	$0.456242\pi$
$608$	−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	0.893249	−	0.449561i	$-0.148420\pi$
$613$	1.41851	+	2.45694i	0.0572933	+	0.0992349i	−0.835956	+	0.548796i	$0.815086\pi$
$614$	−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	$-0.843897\pi$
$617$		−	23.3983i		−	0.941979i	0.882139	−	0.470990i	$-0.156103\pi$
$618$	12.0301	−	1.74647i	0.483922	−	0.0702533i
$619$	−34.7980	+	20.0907i	−1.39865	+	0.807511i	−0.994251	−	0.107071i	$-0.965853\pi$
$619$	−34.7980	+	20.0907i	−1.39865	+	0.807511i	−0.404400	+	0.914582i	$0.632519\pi$
$620$		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	−0.465952	−	0.884810i	$-0.654288\pi$
$641$	1.70493	−	0.984339i	0.0673405	−	0.0388791i	0.533292	+	0.845931i	$0.320955\pi$
$642$	−8.43401	+	1.22441i	−0.332864	+	0.0483234i
$643$			18.9036i			0.745483i	0.927935	+	0.372742i	$0.121582\pi$
$643$			18.9036i			0.745483i	−0.927935	+	0.372742i	$0.878418\pi$
$644$	−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	0.793029	−	0.609183i	$-0.208503\pi$
$647$	−3.33350	−	5.77380i	−0.131054	−	0.226991i	−0.924083	+	0.382192i	$0.875169\pi$
$648$	−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	−0.198761	−	0.980048i	$-0.563692\pi$
$653$	−29.3074	−	16.9206i	−1.14689	−	0.662156i	−0.948127	+	0.317892i	$0.897025\pi$
$654$	−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	$0.141504\pi$
$659$			22.0797i			0.860101i	−0.902805	+	0.430051i	$0.858496\pi$
$660$		0			0
$661$	27.1770	−	15.6907i	1.05706	−	0.610296i	0.132445	−	0.991190i	$-0.457717\pi$
$661$	27.1770	−	15.6907i	1.05706	−	0.610296i	0.924619	+	0.380894i	$0.124384\pi$
$662$	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	0.175338	+	0.984508i	$0.443898\pi$
$677$	−19.9031	+	34.4733i	−0.764940	+	1.32491i	−0.940278	+	0.340407i	$0.889435\pi$
$678$	−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	−0.829983	−	0.557789i	$-0.811650\pi$
$683$	−19.9121	+	11.4962i	−0.761915	+	0.439892i	0.0680680	+	0.997681i	$0.478317\pi$
$684$	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	0.839506	−	0.543351i	$-0.182845\pi$
$691$	20.7325	+	11.9699i	0.788702	+	0.455358i	−0.0508031	+	0.998709i	$0.516178\pi$
$692$	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	$-0.953489\pi$
$701$		−	7.70996i		−	0.291201i	0.989343	−	0.145601i	$-0.0465115\pi$
$702$	−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	−0.833928	−	0.551874i	$-0.813913\pi$
$709$	1.62353	−	2.81203i	0.0609729	−	0.105608i	0.894901	+	0.446266i	$0.147246\pi$
$710$		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	0.312467	+	0.949929i	$0.398845\pi$
$719$	−17.8697	+	30.9513i	−0.666429	+	1.15429i	−0.978896	+	0.204360i	$0.934489\pi$
$720$		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	$0.211630\pi$
$727$			33.2693i			1.23389i	−0.787006	+	0.616945i	$0.788370\pi$
$728$	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	0.206570	−	0.978432i	$-0.433770\pi$
$733$	−14.5521	−	8.40163i	−0.537492	−	0.310321i	−0.744062	+	0.668111i	$0.767103\pi$
$734$	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	−0.975792	−	0.218702i	$-0.929818\pi$
$739$	−18.4120	−	31.8906i	−0.677297	−	1.17311i	0.298494	−	0.954411i	$-0.403516\pi$
$740$		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	$0.313221\pi$
$743$			45.3970i			1.66545i	−0.553684	+	0.832727i	$0.686779\pi$
$744$	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	−0.985602	−	0.169080i	$-0.945920\pi$
$751$	−9.49215	+	16.4409i	−0.346374	+	0.599937i	0.639229	+	0.769017i	$0.279254\pi$
$752$	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	0.00363106	+	0.999993i	$0.498844\pi$
$761$	−23.8401	+	41.2923i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$762$	−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	$-0.656636\pi$
$769$		−	48.8811i		−	1.76270i	0.472467	−	0.881349i	$-0.343364\pi$
$770$		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	0.948047	−	0.318129i	$-0.103054\pi$
$773$	5.51932	+	9.55974i	0.198516	+	0.343840i	−0.749531	+	0.661969i	$0.769721\pi$
$774$	−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	−0.214709	−	0.976678i	$-0.568880\pi$
$787$	14.6934	−	8.48325i	0.523764	−	0.302395i	0.738473	+	0.674283i	$0.235547\pi$
$788$	−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	−0.341425	−	0.939909i	$-0.610909\pi$
$809$	8.58544	−	4.95680i	0.301848	−	0.174272i	0.643273	+	0.765637i	$0.277576\pi$
$810$		0			0
$811$			40.3504i			1.41689i	0.705765	+	0.708446i	$0.250604\pi$
$811$			40.3504i			1.41689i	−0.705765	+	0.708446i	$0.749396\pi$
$812$	−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	0.0804605	−	0.996758i	$-0.474361\pi$
$821$	−21.2757	−	12.2835i	−0.742527	−	0.428698i	−0.822987	+	0.568060i	$0.807694\pi$
$822$	4.21764	−	10.5771i	0.147107	−	0.368917i
$823$	16.6942	+	28.9152i	0.581924	+	1.00792i	0.995251	+	0.0973396i	$0.0310333\pi$
$823$	16.6942	+	28.9152i	0.581924	+	1.00792i	−0.413327	+	0.910583i	$0.635633\pi$
$824$	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	$0.208715\pi$
$827$			35.0677i			1.21942i	−0.792623	+	0.609712i	$0.791285\pi$
$828$	16.6182	−	17.5244i	0.577523	−	0.609017i
$829$	−20.7299	+	11.9684i	−0.719979	+	0.415680i	−0.814745	−	0.579820i	$-0.803123\pi$
$829$	−20.7299	+	11.9684i	−0.719979	+	0.415680i	0.0947660	+	0.995500i	$0.469790\pi$
$830$		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	$0.00680726\pi$
$853$			1.24909i			0.0427680i	−0.999771	+	0.0213840i	$0.993193\pi$
$854$	−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	0.776553	−	0.630052i	$-0.216966\pi$
$857$	−4.60678	−	7.97918i	−0.157365	−	0.272564i	−0.933918	+	0.357488i	$0.883633\pi$
$858$	34.4951	+	13.7550i	1.17764	+	0.469589i
$859$	0.860775	+	0.496969i	0.0293693	+	0.0169564i	0.514613	−	0.857423i	$-0.327936\pi$
$859$	0.860775	+	0.496969i	0.0293693	+	0.0169564i	−0.485243	+	0.874379i	$0.661269\pi$
$860$		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	0.559170	−	0.829053i	$-0.311120\pi$
$863$	3.54799	+	2.04843i	0.120775	+	0.0697295i	−0.438395	+	0.898782i	$0.644453\pi$
$864$	−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	−0.938471	−	0.345359i	$-0.887757\pi$
$877$	−5.03871	+	8.72731i	−0.170145	+	0.294700i	0.768325	+	0.640060i	$0.221090\pi$
$878$	−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	−0.824925	−	0.565242i	$-0.808783\pi$
$887$	2.29479	−	3.97469i	0.0770514	−	0.133457i	0.901977	+	0.431785i	$0.142116\pi$
$888$	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	−0.999732	−	0.0231520i	$-0.992630\pi$
$907$	−15.6580	−	27.1205i	−0.519916	−	0.900521i	0.479816	−	0.877369i	$-0.340703\pi$
$908$	−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	$0.0146705\pi$
$911$			2.78118i			0.0921447i	−0.998938	+	0.0460724i	$0.985330\pi$
$912$	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	−0.228506	+	0.973543i	$0.573384\pi$
$919$	−29.0225	+	50.2685i	−0.957365	+	1.65821i	−0.728860	+	0.684663i	$0.759949\pi$
$920$		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	−0.294689	−	0.955593i	$-0.595216\pi$
$929$	20.7329	−	35.9104i	0.680224	−	1.17818i	0.974912	−	0.222589i	$-0.0714508\pi$
$930$		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	$0.0805105\pi$
$937$			15.3201i			0.500486i	−0.968183	+	0.250243i	$0.919489\pi$
$938$	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	0.895483	+	0.445096i	$0.146830\pi$
$941$	25.5592	+	44.2698i	0.833206	+	1.44316i	−0.0622769	+	0.998059i	$0.519836\pi$
$942$	−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	0.608802	−	0.793322i	$-0.291650\pi$
$947$	6.95988	+	4.01829i	0.226166	+	0.130577i	−0.382636	+	0.923899i	$0.624984\pi$
$948$	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	$0.250635\pi$
$953$			43.7448i			1.41703i	−0.705695	+	0.708516i	$0.749365\pi$
$954$	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	0.472218	+	0.881482i	$0.343454\pi$
$971$	−16.4304	+	28.4583i	−0.527277	+	0.913270i	−0.999495	+	0.0317882i	$0.989880\pi$
$972$	−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	−0.995822	−	0.0913150i	$-0.970893\pi$
$977$	−44.2178	+	25.5291i	−1.41465	+	0.816750i	−0.418830	+	0.908065i	$0.637560\pi$
$978$	−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	0.518994	−	0.854778i	$-0.326307\pi$
$983$	−15.0732	−	26.1076i	−0.480762	−	0.832704i	−0.999756	+	0.0220736i	$0.992973\pi$
$984$	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	−0.902715	−	0.430238i	$-0.858430\pi$
$991$	−25.9382	−	44.9263i	−0.823955	−	1.42713i	0.0787606	−	0.996894i	$-0.474904\pi$
$992$	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	−0.993310	−	0.115477i	$-0.963160\pi$
$997$	−43.8884	+	25.3390i	−1.38996	+	0.802494i	−0.396649	+	0.917970i	$0.629827\pi$
$998$	−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.26.4	yes	20
3.2	odd	2	inner	525.2.t.i.26.7	yes	20
5.2	odd	4		525.2.q.g.299.13		40
5.3	odd	4		525.2.q.g.299.8		40
5.4	even	2		525.2.t.h.26.7	yes	20
7.3	odd	6	inner	525.2.t.i.101.7	yes	20
15.2	even	4		525.2.q.g.299.7		40
15.8	even	4		525.2.q.g.299.14		40
15.14	odd	2		525.2.t.h.26.4	✓	20
21.17	even	6	inner	525.2.t.i.101.4	yes	20
35.3	even	12		525.2.q.g.374.7		40
35.17	even	12		525.2.q.g.374.14		40
35.24	odd	6		525.2.t.h.101.4	yes	20
105.17	odd	12		525.2.q.g.374.8		40
105.38	odd	12		525.2.q.g.374.13		40
105.59	even	6		525.2.t.h.101.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.7		40	15.2	even	4
525.2.q.g.299.8		40	5.3	odd	4
525.2.q.g.299.13		40	5.2	odd	4
525.2.q.g.299.14		40	15.8	even	4
525.2.q.g.374.7		40	35.3	even	12
525.2.q.g.374.8		40	105.17	odd	12
525.2.q.g.374.13		40	105.38	odd	12
525.2.q.g.374.14		40	35.17	even	12
525.2.t.h.26.4	✓	20	15.14	odd	2
525.2.t.h.26.7	yes	20	5.4	even	2
525.2.t.h.101.4	yes	20	35.24	odd	6
525.2.t.h.101.7	yes	20	105.59	even	6
525.2.t.i.26.4	yes	20	1.1	even	1	trivial
525.2.t.i.26.7	yes	20	3.2	odd	2	inner
525.2.t.i.101.4	yes	20	21.17	even	6	inner
525.2.t.i.101.7	yes	20	7.3	odd	6	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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Representations

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Database

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