LMFDB - Embedded newform 1445.2.b.f.579.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(579,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1445.579");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 9x^{8} + 228x^{6} - 225x^{4} - 1250x^{2} + 15625 $ x^12 - 2x^10 - 9x^8 + 228x^6 - 225x^4 - 1250*x^2 + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			579.3
Root			$0.178191 + 2.22896i$ of defining polynomial
Character	$\chi$	$=$	1445.579
Dual form			1445.2.b.f.579.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80333i q^{2} -0.561698i q^{3} -1.25200 q^{4} +(-0.178191 - 2.22896i) q^{5} -1.01293 q^{6} +3.11199i q^{7} -1.34889i q^{8} +2.68450 q^{9} +(-4.01955 + 0.321338i) q^{10} -5.61195 q^{11} +0.703246i q^{12} +1.24880i q^{13} +5.61195 q^{14} +(-1.25200 + 0.100090i) q^{15} -4.93650 q^{16} -4.84103i q^{18} -4.00000 q^{19} +(0.223095 + 2.79065i) q^{20} +1.74800 q^{21} +10.1202i q^{22} -2.32777i q^{23} -0.757669 q^{24} +(-4.93650 + 0.794361i) q^{25} +2.25200 q^{26} -3.19297i q^{27} -3.89622i q^{28} -6.62488 q^{29} +(0.180495 + 2.25777i) q^{30} -4.55412 q^{31} +6.20435i q^{32} +3.15222i q^{33} +(6.93650 - 0.554530i) q^{35} -3.36099 q^{36} +1.90762i q^{37} +7.21332i q^{38} +0.701449 q^{39} +(-3.00662 + 0.240360i) q^{40} -5.92343 q^{41} -3.15222i q^{42} +2.04316i q^{43} +7.02616 q^{44} +(-0.478353 - 5.98362i) q^{45} -4.19774 q^{46} -4.85546i q^{47} +2.77282i q^{48} -2.68450 q^{49} +(1.43250 + 8.90213i) q^{50} -1.56350i q^{52} -9.11674i q^{53} -5.75798 q^{54} +(1.00000 + 12.5088i) q^{55} +4.19774 q^{56} +2.24679i q^{57} +11.9468i q^{58} -6.00000 q^{59} +(1.56750 - 0.125312i) q^{60} -5.65685 q^{61} +8.21258i q^{62} +8.35413i q^{63} +1.31550 q^{64} +(2.78352 - 0.222525i) q^{65} +5.68450 q^{66} -8.46212i q^{67} -1.30750 q^{69} +(-1.00000 - 12.5088i) q^{70} +8.79676 q^{71} -3.62109i q^{72} +1.56845i q^{73} +3.44007 q^{74} +(0.446191 + 2.77282i) q^{75} +5.00800 q^{76} -17.4643i q^{77} -1.26494i q^{78} +4.91050 q^{79} +(0.879640 + 11.0032i) q^{80} +6.26000 q^{81} +10.6819i q^{82} +3.94658i q^{83} -2.18850 q^{84} +3.68450 q^{86} +3.72118i q^{87} +7.56991i q^{88} +10.6130 q^{89} +(-10.7905 + 0.862629i) q^{90} -3.88626 q^{91} +2.91437i q^{92} +2.55804i q^{93} -8.75600 q^{94} +(0.712765 + 8.91583i) q^{95} +3.48497 q^{96} -12.3919i q^{97} +4.84103i q^{98} -15.0653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 28 q^{9} - 12 q^{15} + 4 q^{16} - 48 q^{19} + 24 q^{21} + 4 q^{25} + 24 q^{26} - 52 q^{30} + 20 q^{35} + 68 q^{36} + 28 q^{49} - 40 q^{50} + 12 q^{55} - 72 q^{59} + 76 q^{60} + 76 q^{64}+ \cdots - 96 q^{94}+O(q^{100}) $ 12 * q - 12 * q^4 - 28 * q^9 - 12 * q^15 + 4 * q^16 - 48 * q^19 + 24 * q^21 + 4 * q^25 + 24 * q^26 - 52 * q^30 + 20 * q^35 + 68 * q^36 + 28 * q^49 - 40 * q^50 + 12 * q^55 - 72 * q^59 + 76 * q^60 + 76 * q^64 + 8 * q^66 - 88 * q^69 - 12 * q^70 + 48 * q^76 + 60 * q^81 + 40 * q^84 - 16 * q^86 + 16 * q^89 - 96 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.80333i		−	1.27515i	−0.770389	−	0.637574i	$-0.779938\pi$
$2$		−	1.80333i		−	1.27515i	0.770389	−	0.637574i	$-0.220062\pi$
$3$		−	0.561698i		−	0.324296i	−0.986766	−	0.162148i	$-0.948158\pi$
$3$		−	0.561698i		−	0.324296i	0.986766	−	0.162148i	$-0.0518423\pi$
$4$	−1.25200			−0.626000
$5$	−0.178191	−	2.22896i	−0.0796895	−	0.996820i
$5$	−0.178191	−	2.22896i	−0.0796895	−	0.996820i
$6$	−1.01293			−0.413526
$7$			3.11199i			1.17622i	0.808780	+	0.588111i	$0.200128\pi$
$7$			3.11199i			1.17622i	−0.808780	+	0.588111i	$0.799872\pi$
$8$		−	1.34889i		−	0.476905i
$9$	2.68450			0.894832
$10$	−4.01955	+	0.321338i	−1.27109	+	0.101616i
$11$	−5.61195			−1.69207			−0.846033	−	0.533130i	$-0.821016\pi$
$11$	−5.61195			−1.69207			−0.846033	+	0.533130i	$0.821016\pi$
$12$			0.703246i			0.203010i
$13$			1.24880i			0.346355i	0.984891	+	0.173178i	$0.0554034\pi$
$13$			1.24880i			0.346355i	−0.984891	+	0.173178i	$0.944597\pi$
$14$	5.61195			1.49986
$15$	−1.25200	+	0.100090i	−0.323265	+	0.0258430i
$16$	−4.93650			−1.23412
$17$		0			0
$17$		0			0
$18$		−	4.84103i		−	1.14104i
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	0.223095	+	2.79065i	0.0498857	+	0.624009i
$21$	1.74800			0.381445
$22$			10.1202i			2.15763i
$23$		−	2.32777i		−	0.485373i	−0.970105	−	0.242687i	$-0.921971\pi$
$23$		−	2.32777i		−	0.485373i	0.970105	−	0.242687i	$-0.0780287\pi$
$24$	−0.757669			−0.154659
$25$	−4.93650	+	0.794361i	−0.987299	+	0.158872i
$26$	2.25200			0.441654
$27$		−	3.19297i		−	0.614487i
$28$		−	3.89622i		−	0.736316i
$29$	−6.62488			−1.23021			−0.615104	−	0.788446i	$-0.710886\pi$
$29$	−6.62488			−1.23021			−0.615104	+	0.788446i	$0.710886\pi$
$30$	0.180495	+	2.25777i	0.0329537	+	0.412211i
$31$	−4.55412			−0.817944			−0.408972	−	0.912547i	$-0.634113\pi$
$31$	−4.55412			−0.817944			−0.408972	+	0.912547i	$0.634113\pi$
$32$			6.20435i			1.09678i
$33$			3.15222i			0.548731i
$34$		0			0
$35$	6.93650	−	0.554530i	1.17248	−	0.0937326i
$36$	−3.36099			−0.560165
$37$			1.90762i			0.313611i	0.987630	+	0.156805i	$0.0501195\pi$
$37$			1.90762i			0.313611i	−0.987630	+	0.156805i	$0.949880\pi$
$38$			7.21332i			1.17016i
$39$	0.701449			0.112322
$40$	−3.00662	+	0.240360i	−0.475388	+	0.0380043i
$41$	−5.92343			−0.925084			−0.462542	−	0.886597i	$-0.653063\pi$
$41$	−5.92343			−0.925084			−0.462542	+	0.886597i	$0.653063\pi$
$42$		−	3.15222i		−	0.486398i
$43$			2.04316i			0.311579i	0.987790	+	0.155790i	$0.0497922\pi$
$43$			2.04316i			0.311579i	−0.987790	+	0.155790i	$0.950208\pi$
$44$	7.02616			1.05923
$45$	−0.478353	−	5.98362i	−0.0713087	−	0.891986i
$46$	−4.19774			−0.618922
$47$		−	4.85546i		−	0.708242i	−0.935200	−	0.354121i	$-0.884780\pi$
$47$		−	4.85546i		−	0.708242i	0.935200	−	0.354121i	$-0.115220\pi$
$48$			2.77282i			0.400222i
$49$	−2.68450			−0.383499
$50$	1.43250	+	8.90213i	0.202585	+	1.25895i
$51$		0			0
$52$		−	1.56350i		−	0.216818i
$53$		−	9.11674i		−	1.25228i	−0.779710	−	0.626140i	$-0.784634\pi$
$53$		−	9.11674i		−	1.25228i	0.779710	−	0.626140i	$-0.215366\pi$
$54$	−5.75798			−0.783562
$55$	1.00000	+	12.5088i	0.134840	+	1.68669i
$56$	4.19774			0.560946
$57$			2.24679i			0.297595i
$58$			11.9468i			1.56870i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$	1.56750	−	0.125312i	0.202364	−	0.0161777i
$61$	−5.65685			−0.724286			−0.362143	−	0.932123i	$-0.617955\pi$
$61$	−5.65685			−0.724286			−0.362143	+	0.932123i	$0.617955\pi$
$62$			8.21258i			1.04300i
$63$			8.35413i			1.05252i
$64$	1.31550			0.164438
$65$	2.78352	−	0.222525i	0.345254	−	0.0276009i
$66$	5.68450			0.699713
$67$		−	8.46212i		−	1.03381i	−0.856042	−	0.516906i	$-0.827084\pi$
$67$		−	8.46212i		−	1.03381i	0.856042	−	0.516906i	$-0.172916\pi$
$68$		0			0
$69$	−1.30750			−0.157405
$70$	−1.00000	−	12.5088i	−0.119523	−	1.49509i
$71$	8.79676			1.04398			0.521992	−	0.852951i	$-0.325189\pi$
$71$	8.79676			1.04398			0.521992	+	0.852951i	$0.325189\pi$
$72$		−	3.62109i		−	0.426750i
$73$			1.56845i			0.183573i	0.995779	+	0.0917864i	$0.0292577\pi$
$73$			1.56845i			0.183573i	−0.995779	+	0.0917864i	$0.970742\pi$
$74$	3.44007			0.399900
$75$	0.446191	+	2.77282i	0.0515217	+	0.320178i
$76$	5.00800			0.574457
$77$		−	17.4643i		−	1.99025i
$78$		−	1.26494i		−	0.143227i
$79$	4.91050			0.552475			0.276237	−	0.961089i	$-0.410912\pi$
$79$	4.91050			0.552475			0.276237	+	0.961089i	$0.410912\pi$
$80$	0.879640	+	11.0032i	0.0983467	+	1.23020i
$81$	6.26000			0.695556
$82$			10.6819i			1.17962i
$83$			3.94658i			0.433194i	0.976261	+	0.216597i	$0.0694957\pi$
$83$			3.94658i			0.433194i	−0.976261	+	0.216597i	$0.930504\pi$
$84$	−2.18850			−0.238785
$85$		0			0
$86$	3.68450			0.397309
$87$			3.72118i			0.398952i
$88$			7.56991i			0.806955i
$89$	10.6130			1.12497			0.562487	−	0.826806i	$-0.309845\pi$
$89$	10.6130			1.12497			0.562487	+	0.826806i	$0.309845\pi$
$90$	−10.7905	+	0.862629i	−1.13741	+	0.0909291i
$91$	−3.88626			−0.407391
$92$			2.91437i			0.303844i
$93$			2.55804i			0.265256i
$94$	−8.75600			−0.903113
$95$	0.712765	+	8.91583i	0.0731281	+	0.914745i
$96$	3.48497			0.355683
$97$		−	12.3919i		−	1.25821i	−0.777322	−	0.629103i	$-0.783422\pi$
$97$		−	12.3919i		−	1.25821i	0.777322	−	0.629103i	$-0.216578\pi$
$98$			4.84103i			0.489018i
$99$	−15.0653			−1.51412
$100$	6.18049	−	0.994540i	0.618049	−	0.0994540i
$101$	9.62099			0.957324			0.478662	−	0.877999i	$-0.341122\pi$
$101$	9.62099			0.957324			0.478662	+	0.877999i	$0.341122\pi$
$102$		0			0
$103$		−	1.84298i		−	0.181594i	−0.995869	−	0.0907972i	$-0.971058\pi$
$103$		−	1.84298i		−	0.181594i	0.995869	−	0.0907972i	$-0.0289415\pi$
$104$	1.68450			0.165178
$105$	−0.311478	−	3.89622i	−0.0303972	−	0.380232i
$106$	−16.4405			−1.59684
$107$			16.9869i			1.64218i	0.570798	+	0.821091i	$0.306634\pi$
$107$			16.9869i			1.64218i	−0.570798	+	0.821091i	$0.693366\pi$
$108$			3.99760i			0.384669i
$109$	−0.446191			−0.0427373			−0.0213687	−	0.999772i	$-0.506802\pi$
$109$	−0.446191			−0.0427373			−0.0213687	+	0.999772i	$0.506802\pi$
$110$	22.5575	−	1.80333i	2.15077	−	0.171941i
$111$	1.07151			0.101703
$112$		−	15.3623i		−	1.45160i
$113$		−	11.3246i		−	1.06533i	−0.846327	−	0.532663i	$-0.821191\pi$
$113$		−	11.3246i		−	1.06533i	0.846327	−	0.532663i	$-0.178809\pi$
$114$	4.05171			0.379477
$115$	−5.18850	+	0.414788i	−0.483830	+	0.0386792i
$116$	8.29435			0.770111
$117$			3.35240i			0.309929i
$118$			10.8200i			0.996060i
$119$		0			0
$120$	0.135010	+	1.68881i	0.0123247	+	0.154167i
$121$	20.4940			1.86309
$122$			10.2012i			0.923571i
$123$			3.32718i			0.300001i
$124$	5.70176			0.512033
$125$	2.65024	+	10.8617i	0.237044	+	0.971499i
$126$	15.0653			1.34212
$127$			5.85000i			0.519104i	0.965729	+	0.259552i	$0.0835748\pi$
$127$			5.85000i			0.519104i	−0.965729	+	0.259552i	$0.916425\pi$
$128$			10.0364i			0.887102i
$129$	1.14764			0.101044
$130$	−0.401287	−	5.01961i	−0.0351952	−	0.440249i
$131$	19.5632			1.70924			0.854620	−	0.519253i	$-0.173790\pi$
$131$	19.5632			1.70924			0.854620	+	0.519253i	$0.173790\pi$
$132$		−	3.94658i		−	0.343506i
$133$		−	12.4480i		−	1.07938i
$134$	−15.2600			−1.31826
$135$	−7.11699	+	0.568959i	−0.612533	+	0.0489682i
$136$		0			0
$137$		−	13.8577i		−	1.18394i	−0.805959	−	0.591971i	$-0.798350\pi$
$137$		−	13.8577i		−	1.18394i	0.805959	−	0.591971i	$-0.201650\pi$
$138$			2.35786i			0.200714i
$139$	−10.1997			−0.865124			−0.432562	−	0.901604i	$-0.642390\pi$
$139$	−10.1997			−0.865124			−0.432562	+	0.901604i	$0.642390\pi$
$140$	−8.68450	+	0.694271i	−0.733974	+	0.0586766i
$141$	−2.72730			−0.229680
$142$		−	15.8635i		−	1.33123i
$143$		−	7.00821i		−	0.586056i
$144$	−13.2520			−1.10433
$145$	1.18049	+	14.7666i	0.0980347	+	1.22630i
$146$	2.82843			0.234082
$147$			1.50788i			0.124367i
$148$		−	2.38834i		−	0.196320i
$149$	−15.9365			−1.30557			−0.652784	−	0.757544i	$-0.726399\pi$
$149$	−15.9365			−1.30557			−0.652784	+	0.757544i	$0.726399\pi$
$150$	5.00031	−	0.804630i	0.408274	−	0.0656977i
$151$	−3.36899			−0.274165			−0.137082	−	0.990560i	$-0.543772\pi$
$151$	−3.36899			−0.274165			−0.137082	+	0.990560i	$0.543772\pi$
$152$			5.39556i			0.437638i
$153$		0			0
$154$	−31.4940			−2.53786
$155$	0.811504	+	10.1509i	0.0651816	+	0.815343i
$156$	−0.878214			−0.0703134
$157$		−	3.92136i		−	0.312959i	−0.987681	−	0.156479i	$-0.949986\pi$
$157$		−	3.92136i		−	0.312959i	0.987681	−	0.156479i	$-0.0500144\pi$
$158$		−	8.85526i		−	0.704486i
$159$	−5.12085			−0.406110
$160$	13.8292	−	1.10556i	1.09330	−	0.0874023i
$161$	7.24400			0.570907
$162$		−	11.2889i		−	0.886936i
$163$			14.7197i			1.15293i	0.817121	+	0.576466i	$0.195569\pi$
$163$			14.7197i			1.15293i	−0.817121	+	0.576466i	$0.804431\pi$
$164$	7.41613			0.579103
$165$	7.02616	−	0.561698i	0.546986	−	0.0437281i
$166$	7.11699			0.552386
$167$			0.420150i			0.0325122i	0.999868	+	0.0162561i	$0.00517470\pi$
$167$			0.420150i			0.0325122i	−0.999868	+	0.0162561i	$0.994825\pi$
$168$		−	2.35786i		−	0.181913i
$169$	11.4405			0.880038
$170$		0			0
$171$	−10.7380			−0.821154
$172$		−	2.55804i		−	0.195049i
$173$		−	16.6024i		−	1.26226i	−0.775679	−	0.631128i	$-0.782592\pi$
$173$		−	16.6024i		−	1.26226i	0.775679	−	0.631128i	$-0.217408\pi$
$174$	6.71052			0.508723
$175$	−2.47204	−	15.3623i	−0.186869	−	1.16128i
$176$	27.7034			2.08822
$177$			3.37019i			0.253319i
$178$		−	19.1387i		−	1.43451i
$179$	−19.7935			−1.47943			−0.739717	−	0.672918i	$-0.765041\pi$
$179$	−19.7935			−1.47943			−0.739717	+	0.672918i	$0.765041\pi$
$180$	0.598899	+	7.49150i	0.0446393	+	0.558383i
$181$	9.36350			0.695983			0.347992	−	0.937498i	$-0.386864\pi$
$181$	9.36350			0.695983			0.347992	+	0.937498i	$0.386864\pi$
$182$			7.00821i			0.519483i
$183$			3.17744i			0.234883i
$184$	−3.13991			−0.231477
$185$	4.25200	−	0.339921i	0.312613	−	0.0249915i
$186$	4.61299			0.338241
$187$		0			0
$188$			6.07904i			0.443360i
$189$	9.93650			0.722774
$190$	16.0782	−	1.28535i	1.16643	−	0.0932491i
$191$	13.9365			1.00841			0.504205	−	0.863584i	$-0.331786\pi$
$191$	13.9365			1.00841			0.504205	+	0.863584i	$0.331786\pi$
$192$		−	0.738916i		−	0.0533267i
$193$		−	4.17482i		−	0.300510i	−0.988647	−	0.150255i	$-0.951991\pi$
$193$		−	4.17482i		−	0.300510i	0.988647	−	0.150255i	$-0.0480095\pi$
$194$	−22.3467			−1.60440
$195$	−0.124992	−	1.56350i	−0.00895086	−	0.111964i
$196$	3.36099			0.240071
$197$		−	17.6901i		−	1.26037i	−0.776446	−	0.630184i	$-0.782979\pi$
$197$		−	17.6901i		−	1.26037i	0.776446	−	0.630184i	$-0.217021\pi$
$198$			27.1676i			1.93072i
$199$	−5.60063			−0.397018			−0.198509	−	0.980099i	$-0.563610\pi$
$199$	−5.60063			−0.397018			−0.198509	+	0.980099i	$0.563610\pi$
$200$	1.07151	+	6.65879i	0.0757669	+	0.470848i
$201$	−4.75316			−0.335262
$202$		−	17.3498i		−	1.22073i
$203$		−	20.6166i		−	1.44700i
$204$		0			0
$205$	1.05550	+	13.2031i	0.0737195	+	0.922142i
$206$	−3.32351			−0.231560
$207$		−	6.24889i		−	0.434328i
$208$		−	6.16470i		−	0.427445i
$209$	22.4478			1.55275
$210$	−7.02616	+	0.561698i	−0.484851	+	0.0387608i
$211$	0.923118			0.0635501			0.0317750	−	0.999495i	$-0.489884\pi$
$211$	0.923118			0.0635501			0.0317750	+	0.999495i	$0.489884\pi$
$212$			11.4142i			0.783928i
$213$		−	4.94112i		−	0.338560i
$214$	30.6329			2.09402
$215$	4.55412	−	0.364073i	0.310588	−	0.0248296i
$216$	−4.30697			−0.293052
$217$		−	14.1724i		−	0.962084i
$218$			0.804630i			0.0544964i
$219$	0.880993			0.0595320
$220$	−1.25200	−	15.6610i	−0.0844098	−	1.05587i
$221$		0			0
$222$		−	1.93228i		−	0.129686i
$223$			1.24880i			0.0836259i	0.999125	+	0.0418129i	$0.0133134\pi$
$223$			1.24880i			0.0836259i	−0.999125	+	0.0418129i	$0.986687\pi$
$224$	−19.3079			−1.29006
$225$	−13.2520	+	2.13246i	−0.883467	+	0.142164i
$226$	−20.4219			−1.35845
$227$		−	11.5828i		−	0.768775i	−0.923172	−	0.384388i	$-0.874413\pi$
$227$		−	11.5828i		−	0.768775i	0.923172	−	0.384388i	$-0.125587\pi$
$228$		−	2.81298i		−	0.186294i
$229$	−11.7480			−0.776330			−0.388165	−	0.921590i	$-0.626891\pi$
$229$	−11.7480			−0.776330			−0.388165	+	0.921590i	$0.626891\pi$
$230$	0.748000	+	9.35657i	0.0493216	+	0.616954i
$231$	−9.80969			−0.645430
$232$			8.93623i			0.586692i
$233$		−	11.3042i		−	0.740561i	−0.928920	−	0.370280i	$-0.879262\pi$
$233$		−	11.3042i		−	0.740561i	0.928920	−	0.370280i	$-0.120738\pi$
$234$	6.04548			0.395206
$235$	−10.8226	+	0.865200i	−0.705989	+	0.0564395i
$236$	7.51200			0.488990
$237$		−	2.75822i		−	0.179166i
$238$		0			0
$239$	−5.13501			−0.332156			−0.166078	−	0.986113i	$-0.553110\pi$
$239$	−5.13501			−0.332156			−0.166078	+	0.986113i	$0.553110\pi$
$240$	6.18049	−	0.494092i	0.398949	−	0.0318935i
$241$	−8.48528			−0.546585			−0.273293	−	0.961931i	$-0.588113\pi$
$241$	−8.48528			−0.546585			−0.273293	+	0.961931i	$0.588113\pi$
$242$		−	36.9574i		−	2.37571i
$243$		−	13.0951i		−	0.840054i
$244$	7.08238			0.453403
$245$	0.478353	+	5.98362i	0.0305609	+	0.382280i
$246$	6.00000			0.382546
$247$		−	4.99520i		−	0.317837i
$248$			6.14301i			0.390081i
$249$	2.21679			0.140483
$250$	19.5872	−	4.77925i	1.23880	−	0.302266i
$251$	−19.8095			−1.25036			−0.625182	−	0.780479i	$-0.714975\pi$
$251$	−19.8095			−1.25036			−0.625182	+	0.780479i	$0.714975\pi$
$252$		−	10.4594i		−	0.658879i
$253$			13.0633i			0.821284i
$254$	10.5495			0.661934
$255$		0			0
$256$	20.7300			1.29562
$257$			24.3982i			1.52192i	0.648801	+	0.760958i	$0.275271\pi$
$257$			24.3982i			1.52192i	−0.648801	+	0.760958i	$0.724729\pi$
$258$		−	2.06957i		−	0.128846i
$259$	−5.93650			−0.368876
$260$	−3.48497	+	0.278602i	−0.216129	+	0.0172781i
$261$	−17.7845			−1.10083
$262$		−	35.2788i		−	2.17953i
$263$			18.0585i			1.11354i	0.830668	+	0.556768i	$0.187959\pi$
$263$			18.0585i			1.11354i	−0.830668	+	0.556768i	$0.812041\pi$
$264$	4.25200			0.261693
$265$	−20.3208	+	1.62452i	−1.24830	+	0.0997936i
$266$	−22.4478			−1.37636
$267$		−	5.96129i		−	0.364825i
$268$			10.5946i			0.647167i
$269$	17.8601			1.08895			0.544475	−	0.838777i	$-0.316729\pi$
$269$	17.8601			1.08895			0.544475	+	0.838777i	$0.316729\pi$
$270$	1.02602	+	12.8343i	0.0624417	+	0.781070i
$271$	−15.8570			−0.963243			−0.481622	−	0.876379i	$-0.659952\pi$
$271$	−15.8570			−0.963243			−0.481622	+	0.876379i	$0.659952\pi$
$272$		0			0
$273$			2.18290i			0.132115i
$274$	−24.9900			−1.50970
$275$	27.7034	−	4.45791i	1.67058	−	0.268822i
$276$	1.63699			0.0985355
$277$		−	14.1784i		−	0.851896i	−0.904748	−	0.425948i	$-0.859941\pi$
$277$		−	14.1784i		−	0.851896i	0.904748	−	0.425948i	$-0.140059\pi$
$278$			18.3934i			1.10316i
$279$	−12.2255			−0.731922
$280$	−0.748000	−	9.35657i	−0.0447015	−	0.559162i
$281$	−7.80949			−0.465875			−0.232937	−	0.972492i	$-0.574834\pi$
$281$	−7.80949			−0.465875			−0.232937	+	0.972492i	$0.574834\pi$
$282$			4.91823i			0.292876i
$283$		−	20.9080i		−	1.24285i	−0.783474	−	0.621425i	$-0.786554\pi$
$283$		−	20.9080i		−	1.24285i	0.783474	−	0.621425i	$-0.213446\pi$
$284$	−11.0135			−0.653534
$285$	5.00800	−	0.400358i	0.296648	−	0.0237152i
$286$	−12.6381			−0.747307
$287$		−	18.4337i		−	1.08810i
$288$			16.6556i			0.981438i
$289$		0			0
$290$	26.6290	−	2.12882i	1.56371	−	0.125009i
$291$	−6.96050			−0.408032
$292$		−	1.96370i		−	0.114917i
$293$			4.79502i			0.280128i	0.990142	+	0.140064i	$0.0447309\pi$
$293$			4.79502i			0.280128i	−0.990142	+	0.140064i	$0.955269\pi$
$294$	2.71920			0.158587
$295$	1.06915	+	13.3737i	0.0622482	+	0.778649i
$296$	2.57317			0.149562
$297$			17.9188i			1.03975i
$298$			28.7388i			1.66479i
$299$	2.90692			0.168112
$300$	−0.558631	−	3.47157i	−0.0322526	−	0.200431i
$301$	−6.35830			−0.366486
$302$			6.07540i			0.349600i
$303$		−	5.40409i		−	0.310457i
$304$	19.7460			1.13251
$305$	1.00800	+	12.6089i	0.0577180	+	0.721983i
$306$		0			0
$307$			24.9924i			1.42639i	0.700966	+	0.713195i	$0.252753\pi$
$307$			24.9924i			1.42639i	−0.700966	+	0.713195i	$0.747247\pi$
$308$			21.8654i			1.24589i
$309$	−1.03520			−0.0588904
$310$	18.3055	−	1.46341i	1.03968	−	0.0831161i
$311$	−4.03229			−0.228650			−0.114325	−	0.993443i	$-0.536471\pi$
$311$	−4.03229			−0.228650			−0.114325	+	0.993443i	$0.536471\pi$
$312$		−	0.946178i		−	0.0535668i
$313$		−	22.6491i		−	1.28021i	−0.768289	−	0.640103i	$-0.778892\pi$
$313$		−	22.6491i		−	1.28021i	0.768289	−	0.640103i	$-0.221108\pi$
$314$	−7.07151			−0.399068
$315$	18.6210	−	1.48863i	1.04917	−	0.0838749i
$316$	−6.14795			−0.345849
$317$			8.27315i			0.464666i	0.972636	+	0.232333i	$0.0746360\pi$
$317$			8.27315i			0.464666i	−0.972636	+	0.232333i	$0.925364\pi$
$318$			9.23459i			0.517850i
$319$	37.1785			2.08160
$320$	−0.234411	−	2.93220i	−0.0131040	−	0.163915i
$321$	9.54148			0.532554
$322$		−	13.0633i		−	0.727991i
$323$		0			0
$324$	−7.83752			−0.435418
$325$	−0.991998	−	6.16470i	−0.0550262	−	0.341956i
$326$	26.5444			1.47016
$327$			0.250624i			0.0138596i
$328$			7.99006i			0.441177i
$329$	15.1102			0.833050
$330$	−1.01293	−	12.6705i	−0.0557598	−	0.697488i
$331$	−5.51200			−0.302967			−0.151484	−	0.988460i	$-0.548405\pi$
$331$	−5.51200			−0.302967			−0.151484	+	0.988460i	$0.548405\pi$
$332$		−	4.94112i		−	0.271179i
$333$			5.12099i			0.280629i
$334$	0.757669			0.0414578
$335$	−18.8617	+	1.50788i	−1.03052	+	0.0823840i
$336$	−8.62899			−0.470750
$337$			9.53810i			0.519573i	0.965666	+	0.259787i	$0.0836522\pi$
$337$			9.53810i			0.519573i	−0.965666	+	0.259787i	$0.916348\pi$
$338$		−	20.6310i		−	1.12218i
$339$	−6.36099			−0.345482
$340$		0			0
$341$	25.5575			1.38402
$342$			19.3641i			1.04709i
$343$			13.4298i			0.725142i
$344$	2.75600			0.148594
$345$	0.232986	+	2.91437i	0.0125435	+	0.156904i
$346$	−29.9396			−1.60956
$347$		−	11.5471i		−	0.619881i	−0.950756	−	0.309940i	$-0.899691\pi$
$347$		−	11.5471i		−	0.619881i	0.950756	−	0.309940i	$-0.100309\pi$
$348$		−	4.65892i		−	0.249744i
$349$	11.4325			0.611967			0.305984	−	0.952037i	$-0.401015\pi$
$349$	11.4325			0.611967			0.305984	+	0.952037i	$0.401015\pi$
$350$	−27.7034	+	4.45791i	−1.48081	+	0.238285i
$351$	3.98738			0.212831
$352$		−	34.8185i		−	1.85583i
$353$		−	31.8017i		−	1.69263i	−0.532680	−	0.846317i	$-0.678815\pi$
$353$		−	31.8017i		−	1.69263i	0.532680	−	0.846317i	$-0.321185\pi$
$354$	6.07756			0.323019
$355$	−1.56750	−	19.6076i	−0.0831945	−	1.04066i
$356$	−13.2875			−0.704234
$357$		0			0
$358$			35.6942i			1.88650i
$359$	−25.1785			−1.32887			−0.664435	−	0.747346i	$-0.731328\pi$
$359$	−25.1785			−1.32887			−0.664435	+	0.747346i	$0.731328\pi$
$360$	−8.07125	+	0.645246i	−0.425392	+	0.0340075i
$361$	−3.00000			−0.157895
$362$		−	16.8855i		−	0.887481i
$363$		−	11.5114i		−	0.604193i
$364$	4.86560			0.255027
$365$	3.49600	−	0.279483i	0.182989	−	0.0146288i
$366$	5.72998			0.299511
$367$			6.08693i			0.317735i	0.987300	+	0.158868i	$0.0507843\pi$
$367$			6.08693i			0.317735i	−0.987300	+	0.158868i	$0.949216\pi$
$368$			11.4910i			0.599011i
$369$	−15.9014			−0.827795
$370$	−0.612990	−	7.66776i	−0.0318678	−	0.398628i
$371$	28.3712			1.47296
$372$		−	3.20267i		−	0.166050i
$373$		−	30.0732i		−	1.55713i	−0.627562	−	0.778566i	$-0.715947\pi$
$373$		−	30.0732i		−	1.55713i	0.627562	−	0.778566i	$-0.284053\pi$
$374$		0			0
$375$	6.10099	−	1.48863i	0.315054	−	0.0768726i
$376$	−6.54949			−0.337764
$377$		−	8.27315i		−	0.426089i
$378$		−	17.9188i		−	0.921643i
$379$	1.01293			0.0520306			0.0260153	−	0.999662i	$-0.491718\pi$
$379$	1.01293			0.0520306			0.0260153	+	0.999662i	$0.491718\pi$
$380$	−0.892382	−	11.1626i	−0.0457782	−	0.572630i
$381$	3.28593			0.168343
$382$		−	25.1321i		−	1.28587i
$383$		−	25.8660i		−	1.32169i	−0.750521	−	0.660846i	$-0.770198\pi$
$383$		−	25.8660i		−	1.32169i	0.750521	−	0.660846i	$-0.229802\pi$
$384$	5.63743			0.287684
$385$	−38.9273	+	3.11199i	−1.98392	+	0.158602i
$386$	−7.52857			−0.383194
$387$			5.48486i			0.278811i
$388$			15.5147i			0.787637i
$389$	−33.0695			−1.67669			−0.838345	−	0.545140i	$-0.816476\pi$
$389$	−33.0695			−1.67669			−0.838345	+	0.545140i	$0.816476\pi$
$390$	−2.81951	+	0.225402i	−0.142771	+	0.0114137i
$391$		0			0
$392$			3.62109i			0.182893i
$393$		−	10.9886i		−	0.554301i
$394$	−31.9011			−1.60715
$395$	−0.875008	−	10.9453i	−0.0440264	−	0.550718i
$396$	18.8617			0.947836
$397$			8.15201i			0.409138i	0.978852	+	0.204569i	$0.0655792\pi$
$397$			8.15201i			0.409138i	−0.978852	+	0.204569i	$0.934421\pi$
$398$			10.0998i			0.506257i
$399$	−6.99200			−0.350038
$400$	24.3690	−	3.92136i	1.21845	−	0.196068i
$401$	0.165449			0.00826215			0.00413108	−	0.999991i	$-0.498685\pi$
$401$	0.165449			0.00826215			0.00413108	+	0.999991i	$0.498685\pi$
$402$			8.57151i			0.427508i
$403$		−	5.68719i		−	0.283299i
$404$	−12.0455			−0.599285
$405$	−1.11548	−	13.9533i	−0.0554285	−	0.693344i
$406$	−37.1785			−1.84514
$407$		−	10.7055i		−	0.530650i
$408$		0			0
$409$	−13.3690			−0.661054			−0.330527	−	0.943797i	$-0.607226\pi$
$409$	−13.3690			−0.661054			−0.330527	+	0.943797i	$0.607226\pi$
$410$	23.8095	−	1.90342i	1.17587	−	0.0940032i
$411$	−7.78383			−0.383948
$412$			2.30741i			0.113678i
$413$		−	18.6720i		−	0.918787i
$414$	−11.2688			−0.553832
$415$	8.79676	−	0.703246i	0.431816	−	0.0345210i
$416$	−7.74800			−0.379877
$417$			5.72913i			0.280557i
$418$		−	40.4808i		−	1.97998i
$419$	−23.5732			−1.15162			−0.575812	−	0.817582i	$-0.695314\pi$
$419$	−23.5732			−1.15162			−0.575812	+	0.817582i	$0.695314\pi$
$420$	0.389971	+	4.87806i	0.0190286	+	0.238025i
$421$	−5.82751			−0.284015			−0.142008	−	0.989866i	$-0.545356\pi$
$421$	−5.82751			−0.284015			−0.142008	+	0.989866i	$0.545356\pi$
$422$		−	1.66469i		−	0.0810357i
$423$		−	13.0345i		−	0.633757i
$424$	−12.2975			−0.597219
$425$		0			0
$426$	−8.91047			−0.431714
$427$		−	17.6041i		−	0.851921i
$428$		−	21.2676i		−	1.02801i
$429$	−3.93650			−0.190056
$430$	−0.656545	−	8.21258i	−0.0316614	−	0.396046i
$431$	−6.93636			−0.334112			−0.167056	−	0.985947i	$-0.553426\pi$
$431$	−6.93636			−0.334112			−0.167056	+	0.985947i	$0.553426\pi$
$432$			15.7621i			0.758353i
$433$			15.4464i			0.742307i	0.928572	+	0.371153i	$0.121038\pi$
$433$			15.4464i			0.742307i	−0.928572	+	0.371153i	$0.878962\pi$
$434$	−25.5575			−1.22680
$435$	8.29435	−	0.663081i	0.397684	−	0.0317923i
$436$	0.558631			0.0267536
$437$			9.31108i			0.445409i
$438$		−	1.58872i		−	0.0759121i
$439$	−1.47043			−0.0701800			−0.0350900	−	0.999384i	$-0.511172\pi$
$439$	−1.47043			−0.0701800			−0.0350900	+	0.999384i	$0.511172\pi$
$440$	16.8730	−	1.34889i	0.804388	−	0.0643058i
$441$	−7.20652			−0.343167
$442$		0			0
$443$		−	12.7838i		−	0.607379i	−0.952771	−	0.303689i	$-0.901782\pi$
$443$		−	12.7838i		−	0.607379i	0.952771	−	0.303689i	$-0.0982185\pi$
$444$	−1.34153			−0.0636660
$445$	−1.89114	−	23.6559i	−0.0896487	−	1.12140i
$446$	2.25200			0.106635
$447$			8.95150i			0.423391i
$448$			4.09384i			0.193416i
$449$	9.73119			0.459243			0.229622	−	0.973280i	$-0.426251\pi$
$449$	9.73119			0.459243			0.229622	+	0.973280i	$0.426251\pi$
$450$	3.84553	+	23.8977i	0.181280	+	1.12655i
$451$	33.2420			1.56530
$452$			14.1784i			0.666894i
$453$			1.89236i			0.0889106i
$454$	−20.8876			−0.980302
$455$	0.692497	+	8.66230i	0.0324648	+	0.406095i
$456$	3.03068			0.141924
$457$			36.2279i			1.69467i	0.531058	+	0.847336i	$0.321795\pi$
$457$			36.2279i			1.69467i	−0.531058	+	0.847336i	$0.678205\pi$
$458$			21.1855i			0.989935i
$459$		0			0
$460$	6.49600	−	0.519315i	0.302878	−	0.0242132i
$461$	−40.0595			−1.86576			−0.932878	−	0.360193i	$-0.882711\pi$
$461$	−40.0595			−1.86576			−0.932878	+	0.360193i	$0.882711\pi$
$462$			17.6901i			0.823018i
$463$		−	15.3607i		−	0.713874i	−0.934128	−	0.356937i	$-0.883821\pi$
$463$		−	15.3607i		−	0.713874i	0.934128	−	0.356937i	$-0.116179\pi$
$464$	32.7037			1.51823
$465$	5.70176	−	0.455820i	0.264413	−	0.0211381i
$466$	−20.3851			−0.944324
$467$		−	19.4471i		−	0.899903i	−0.893053	−	0.449952i	$-0.851441\pi$
$467$		−	19.4471i		−	0.899903i	0.893053	−	0.449952i	$-0.148559\pi$
$468$		−	4.19721i		−	0.194016i
$469$	26.3341			1.21599
$470$	1.56024	+	19.5167i	0.0719686	+	0.900240i
$471$	−2.20262			−0.101491
$472$			8.09334i			0.372526i
$473$		−	11.4661i		−	0.527213i
$474$	−4.97398			−0.228462
$475$	19.7460	−	3.17744i	0.906008	−	0.145791i
$476$		0			0
$477$		−	24.4739i		−	1.12058i
$478$			9.26012i			0.423548i
$479$	−14.5547			−0.665023			−0.332511	−	0.943099i	$-0.607896\pi$
$479$	−14.5547			−0.665023			−0.332511	+	0.943099i	$0.607896\pi$
$480$	−0.620991	−	7.76785i	−0.0283442	−	0.354552i
$481$	−2.38224			−0.108621
$482$			15.3018i			0.696976i
$483$		−	4.06894i		−	0.185143i
$484$	−25.6585			−1.16629
$485$	−27.6210	+	2.20813i	−1.25420	+	0.100266i
$486$	−23.6149			−1.07119
$487$		−	29.6975i		−	1.34572i	−0.739768	−	0.672861i	$-0.765065\pi$
$487$		−	29.6975i		−	1.34572i	0.739768	−	0.672861i	$-0.234935\pi$
$488$			7.63048i			0.345415i
$489$	8.26800			0.373892
$490$	10.7905	−	0.862629i	0.487463	−	0.0389696i
$491$	21.0715			0.950944			0.475472	−	0.879731i	$-0.342277\pi$
$491$	21.0715			0.950944			0.475472	+	0.879731i	$0.342277\pi$
$492$		−	4.16563i		−	0.187801i
$493$		0			0
$494$	−9.00800			−0.405289
$495$	2.68450	+	33.5798i	0.120659	+	1.50930i
$496$	22.4814			1.00944
$497$			27.3754i			1.22796i
$498$		−	3.99760i		−	0.179137i
$499$	9.40840			0.421178			0.210589	−	0.977575i	$-0.432462\pi$
$499$	9.40840			0.421178			0.210589	+	0.977575i	$0.432462\pi$
$500$	−3.31810	−	13.5988i	−0.148390	−	0.608158i
$501$	0.235997			0.0105436
$502$			35.7231i			1.59440i
$503$			29.3788i			1.30993i	0.755658	+	0.654967i	$0.227317\pi$
$503$			29.3788i			1.30993i	−0.755658	+	0.654967i	$0.772683\pi$
$504$	11.2688			0.501952
$505$	−1.71438	−	21.4448i	−0.0762887	−	0.954280i
$506$	23.5575			1.04726
$507$		−	6.42610i		−	0.285393i
$508$		−	7.32420i		−	0.324959i
$509$	−14.3930			−0.637958			−0.318979	−	0.947762i	$-0.603340\pi$
$509$	−14.3930			−0.637958			−0.318979	+	0.947762i	$0.603340\pi$
$510$		0			0
$511$	−4.88099			−0.215922
$512$		−	17.3102i		−	0.765009i
$513$			12.7719i			0.563892i
$514$	43.9980			1.94067
$515$	−4.10793	+	0.328403i	−0.181017	+	0.0144712i
$516$	−1.43685			−0.0632536
$517$			27.2486i			1.19839i
$518$			10.7055i			0.470371i
$519$	−9.32552			−0.409345
$520$	−0.300162	−	3.75467i	−0.0131630	−	0.164653i
$521$	27.6698			1.21224			0.606118	−	0.795375i	$-0.292726\pi$
$521$	27.6698			1.21224			0.606118	+	0.795375i	$0.292726\pi$
$522$			32.0712i			1.40372i
$523$			37.4867i			1.63918i	0.572950	+	0.819590i	$0.305799\pi$
$523$			37.4867i			1.63918i	−0.572950	+	0.819590i	$0.694201\pi$
$524$	−24.4931			−1.06998
$525$	−8.62899	+	1.38854i	−0.376600	+	0.0606010i
$526$	32.5655			1.41992
$527$		0			0
$528$		−	15.5609i		−	0.677202i
$529$	17.5815			0.764413
$530$	2.92955	+	36.6452i	0.127252	+	1.59176i
$531$	−16.1070			−0.698983
$532$			15.5849i			0.675689i
$533$		−	7.39718i		−	0.320408i
$534$	−10.7502			−0.465206
$535$	37.8630	−	3.02691i	1.63696	−	0.130865i
$536$	−11.4145			−0.493030
$537$			11.1180i			0.479775i
$538$		−	32.2076i		−	1.38857i
$539$	15.0653			0.648906
$540$	8.91047	−	0.712337i	0.383446	−	0.0306541i
$541$	12.7279			0.547216			0.273608	−	0.961841i	$-0.411783\pi$
$541$	12.7279			0.547216			0.273608	+	0.961841i	$0.411783\pi$
$542$			28.5954i			1.22828i
$543$		−	5.25946i		−	0.225705i
$544$		0			0
$545$	0.0795073	+	0.994540i	0.00340572	+	0.0426014i
$546$	3.93650			0.168466
$547$		−	28.7922i		−	1.23106i	−0.788112	−	0.615532i	$-0.788941\pi$
$547$		−	28.7922i		−	1.23106i	0.788112	−	0.615532i	$-0.211059\pi$
$548$			17.3498i			0.741148i
$549$	−15.1858			−0.648114
$550$	−8.03909	−	49.9583i	−0.342788	−	2.13023i
$551$	26.4995			1.12892
$552$			1.76368i			0.0750671i
$553$			15.2814i			0.649833i
$554$	−25.5683			−1.08629
$555$	−0.190933	−	2.38834i	−0.00810465	−	0.101379i
$556$	12.7700			0.541568
$557$			4.93477i			0.209093i	0.994520	+	0.104546i	$0.0333391\pi$
$557$			4.93477i			0.209093i	−0.994520	+	0.104546i	$0.966661\pi$
$558$			22.0466i			0.933308i
$559$	−2.55150			−0.107917
$560$	−34.2420	+	2.73743i	−1.44699	+	0.115678i
$561$		0			0
$562$			14.0831i			0.594059i
$563$		−	3.97544i		−	0.167545i	−0.996485	−	0.0837724i	$-0.973303\pi$
$563$		−	3.97544i		−	0.167545i	0.996485	−	0.0837724i	$-0.0266969\pi$
$564$	3.41458			0.143780
$565$	−25.2420	+	2.01794i	−1.06194	+	0.0848953i
$566$	−37.7040			−1.58482
$567$			19.4811i			0.818128i
$568$		−	11.8659i		−	0.497881i
$569$	5.49600			0.230404			0.115202	−	0.993342i	$-0.463248\pi$
$569$	5.49600			0.230404			0.115202	+	0.993342i	$0.463248\pi$
$570$	−0.721979	−	9.03108i	−0.0302404	−	0.378270i
$571$	17.4475			0.730155			0.365077	−	0.930977i	$-0.381043\pi$
$571$	17.4475			0.730155			0.365077	+	0.930977i	$0.381043\pi$
$572$			8.77428i			0.366871i
$573$		−	7.82810i		−	0.327024i
$574$	−33.2420			−1.38749
$575$	1.84909	+	11.4910i	0.0771123	+	0.479209i
$576$	3.53147			0.147144
$577$			32.3418i			1.34641i	0.739458	+	0.673203i	$0.235082\pi$
$577$			32.3418i			1.34641i	−0.739458	+	0.673203i	$0.764918\pi$
$578$		0			0
$579$	−2.34499			−0.0974543
$580$	−1.47798	−	18.4877i	−0.0613698	−	0.767662i
$581$	−12.2817			−0.509532
$582$			12.5521i			0.520301i
$583$			51.1627i			2.11894i
$584$	2.11566			0.0875467
$585$	7.47235	−	0.597368i	0.308944	−	0.0246981i
$586$	8.64701			0.357205
$587$			28.6847i			1.18394i	0.805959	+	0.591972i	$0.201650\pi$
$587$			28.6847i			1.18394i	−0.805959	+	0.591972i	$0.798350\pi$
$588$		−	1.88786i		−	0.0778541i
$589$	18.2165			0.750597
$590$	24.1173	−	1.92803i	0.992892	−	0.0793755i
$591$	−9.93650			−0.408733
$592$		−	9.41695i		−	0.387034i
$593$			9.74614i			0.400226i	0.979773	+	0.200113i	$0.0641309\pi$
$593$			9.74614i			0.400226i	−0.979773	+	0.200113i	$0.935869\pi$
$594$	32.3135			1.32584
$595$		0			0
$596$	19.9525			0.817286
$597$			3.14586i			0.128752i
$598$		−	5.24214i		−	0.214367i
$599$	−8.07951			−0.330120			−0.165060	−	0.986284i	$-0.552782\pi$
$599$	−8.07951			−0.330120			−0.165060	+	0.986284i	$0.552782\pi$
$600$	3.74023	−	0.601863i	0.152694	−	0.0245709i
$601$	18.2165			0.743066			0.371533	−	0.928420i	$-0.378832\pi$
$601$	18.2165			0.743066			0.371533	+	0.928420i	$0.378832\pi$
$602$			11.4661i			0.467324i
$603$		−	22.7165i		−	0.925089i
$604$	4.21798			0.171627
$605$	−3.65185	−	45.6802i	−0.148469	−	1.85716i
$606$	−9.74536			−0.395878
$607$			11.8506i			0.481001i	0.970649	+	0.240501i	$0.0773116\pi$
$607$			11.8506i			0.481001i	−0.970649	+	0.240501i	$0.922688\pi$
$608$		−	24.8174i		−	1.00648i
$609$	−11.5803			−0.469257
$610$	22.7380	−	1.81776i	0.920634	−	0.0735989i
$611$	6.06350			0.245303
$612$		0			0
$613$		−	23.1494i		−	0.934995i	−0.883994	−	0.467497i	$-0.845156\pi$
$613$		−	23.1494i		−	0.934995i	0.883994	−	0.467497i	$-0.154844\pi$
$614$	45.0695			1.81886
$615$	7.41613	−	0.592874i	0.299047	−	0.0239070i
$616$	−23.5575			−0.949158
$617$		−	10.4843i		−	0.422081i	−0.977477	−	0.211040i	$-0.932315\pi$
$617$		−	10.4843i		−	0.422081i	0.977477	−	0.211040i	$-0.0676852\pi$
$618$			1.86681i			0.0750940i
$619$	−23.2924			−0.936202			−0.468101	−	0.883675i	$-0.655062\pi$
$619$	−23.2924			−0.936202			−0.468101	+	0.883675i	$0.655062\pi$
$620$	−1.01600	−	12.7090i	−0.0408037	−	0.510405i
$621$	−7.43250			−0.298256
$622$			7.27155i			0.291562i
$623$			33.0275i			1.32322i
$624$	−3.46270			−0.138619
$625$	23.7380	−	7.84272i	0.949519	−	0.313709i
$626$	−40.8439			−1.63245
$627$		−	12.6089i		−	0.503550i
$628$			4.90954i			0.195912i
$629$		0			0
$630$	−2.68450	−	33.5798i	−0.106953	−	1.33785i
$631$	41.1310			1.63740			0.818699	−	0.574223i	$-0.194696\pi$
$631$	41.1310			1.63740			0.818699	+	0.574223i	$0.194696\pi$
$632$		−	6.62373i		−	0.263478i
$633$		−	0.518514i		−	0.0206091i
$634$	14.9192			0.592518
$635$	13.0394	−	1.04242i	0.517453	−	0.0413671i
$636$	6.41131			0.254225
$637$		−	3.35240i		−	0.132827i
$638$		−	67.0451i		−	2.65434i
$639$	23.6149			0.934189
$640$	22.3707	−	1.78840i	0.884281	−	0.0706927i
$641$	47.2807			1.86747			0.933737	−	0.357959i	$-0.116527\pi$
$641$	47.2807			1.86747			0.933737	+	0.357959i	$0.116527\pi$
$642$		−	17.2064i		−	0.679084i
$643$			7.06878i			0.278765i	0.990239	+	0.139383i	$0.0445118\pi$
$643$			7.06878i			0.278765i	−0.990239	+	0.139383i	$0.955488\pi$
$644$	−9.06949			−0.357388
$645$	−0.204499	−	2.55804i	−0.00805215	−	0.100723i
$646$		0			0
$647$			26.9462i			1.05937i	0.848196	+	0.529683i	$0.177689\pi$
$647$			26.9462i			1.05937i	−0.848196	+	0.529683i	$0.822311\pi$
$648$		−	8.44406i		−	0.331714i
$649$	33.6717			1.32173
$650$	−11.1170	+	1.78890i	−0.436044	+	0.0701665i
$651$	−7.96060			−0.312000
$652$		−	18.4290i		−	0.721736i
$653$			28.2509i			1.10554i	0.833333	+	0.552771i	$0.186430\pi$
$653$			28.2509i			1.10554i	−0.833333	+	0.552771i	$0.813570\pi$
$654$	0.451959			0.0176730
$655$	−3.48598	−	43.6054i	−0.136209	−	1.70380i
$656$	29.2410			1.14167
$657$			4.21049i			0.164267i
$658$		−	27.2486i		−	1.06226i
$659$	−14.1230			−0.550153			−0.275077	−	0.961422i	$-0.588703\pi$
$659$	−14.1230			−0.550153			−0.275077	+	0.961422i	$0.588703\pi$
$660$	−8.79676	+	0.703246i	−0.342413	+	0.0273738i
$661$	49.0355			1.90726			0.953629	−	0.300984i	$-0.0973150\pi$
$661$	49.0355			1.90726			0.953629	+	0.300984i	$0.0973150\pi$
$662$			9.93996i			0.386328i
$663$		0			0
$664$	5.32351			0.206592
$665$	−27.7460	+	2.21812i	−1.07594	+	0.0860149i
$666$	9.23485			0.357843
$667$			15.4212i			0.597111i
$668$		−	0.526028i		−	0.0203526i
$669$	0.701449			0.0271196
$670$	2.71920	+	34.0139i	0.105052	+	1.31407i
$671$	31.7460			1.22554
$672$			10.8452i			0.418363i
$673$		−	31.4528i		−	1.21242i	−0.795306	−	0.606209i	$-0.792690\pi$
$673$		−	31.4528i		−	1.21242i	0.795306	−	0.606209i	$-0.207310\pi$
$674$	17.2003			0.662532
$675$	2.53637	+	15.7621i	0.0976249	+	0.606683i
$676$	−14.3235			−0.550904
$677$		−	30.2796i		−	1.16374i	−0.813282	−	0.581870i	$-0.802321\pi$
$677$		−	30.2796i		−	1.16374i	0.813282	−	0.581870i	$-0.197679\pi$
$678$			11.4710i			0.440540i
$679$	38.5635			1.47993
$680$		0			0
$681$	−6.50602			−0.249311
$682$		−	46.0886i		−	1.76482i
$683$			46.1788i			1.76698i	0.468449	+	0.883490i	$0.344813\pi$
$683$			46.1788i			1.76698i	−0.468449	+	0.883490i	$0.655187\pi$
$684$	13.4440			0.514043
$685$	−30.8882	+	2.46932i	−1.18018	+	0.0943478i
$686$	24.2184			0.924663
$687$			6.59883i			0.251761i
$688$		−	10.0861i		−	0.384527i
$689$	11.3850			0.433734
$690$	5.25557	−	0.420150i	0.200076	−	0.0159948i
$691$	10.6458			0.404987			0.202494	−	0.979284i	$-0.435095\pi$
$691$	10.6458			0.404987			0.202494	+	0.979284i	$0.435095\pi$
$692$			20.7862i			0.790172i
$693$		−	46.8830i		−	1.78094i
$694$	−20.8232			−0.790439
$695$	1.81749	+	22.7346i	0.0689413	+	0.862372i
$696$	5.01946			0.190262
$697$		0			0
$698$		−	20.6166i		−	0.780349i
$699$	−6.34953			−0.240161
$700$	3.09500	+	19.2337i	0.116980	+	0.726964i
$701$	39.4145			1.48866			0.744332	−	0.667810i	$-0.232768\pi$
$701$	39.4145			1.48866			0.744332	+	0.667810i	$0.232768\pi$
$702$		−	7.19057i		−	0.271391i
$703$		−	7.63048i		−	0.287789i
$704$	−7.38255			−0.278240
$705$	0.485981	+	6.07904i	0.0183031	+	0.228950i
$706$	−57.3490			−2.15836
$707$			29.9404i			1.12603i
$708$		−	4.21948i		−	0.158578i
$709$	15.1971			0.570740			0.285370	−	0.958417i	$-0.407884\pi$
$709$	15.1971			0.570740			0.285370	+	0.958417i	$0.407884\pi$
$710$	−35.3590	+	2.82673i	−1.32700	+	0.106085i
$711$	13.1822			0.494372
$712$		−	14.3158i		−	0.536506i
$713$			10.6009i			0.397008i
$714$		0			0
$715$	−15.6210	+	1.24880i	−0.584192	+	0.0467025i
$716$	24.7815			0.926126
$717$			2.88432i			0.107717i
$718$			45.4051i			1.69450i
$719$	−6.85786			−0.255755			−0.127878	−	0.991790i	$-0.540816\pi$
$719$	−6.85786			−0.255755			−0.127878	+	0.991790i	$0.540816\pi$
$720$	2.36139	+	29.5381i	0.0880038	+	1.10082i
$721$	5.73535			0.213595
$722$			5.40999i			0.201339i
$723$			4.76617i			0.177256i
$724$	−11.7231			−0.435686
$725$	32.7037	−	5.26254i	1.21458	−	0.195446i
$726$	−20.7589			−0.770435
$727$			38.5606i			1.43013i	0.699057	+	0.715066i	$0.253603\pi$
$727$			38.5606i			1.43013i	−0.699057	+	0.715066i	$0.746397\pi$
$728$			5.24214i			0.194287i
$729$	11.4245			0.423129
$730$	−0.504001	−	6.30444i	−0.0186539	−	0.233338i
$731$		0			0
$732$		−	3.97816i		−	0.147037i
$733$		−	42.7425i		−	1.57873i	−0.613923	−	0.789366i	$-0.710409\pi$
$733$		−	42.7425i		−	1.57873i	0.613923	−	0.789366i	$-0.289591\pi$
$734$	10.9767			0.405159
$735$	3.36099	−	0.268690i	0.123972	−	0.00991078i
$736$	14.4423			0.532350
$737$			47.4890i			1.74928i
$738$			28.6755i			1.05556i
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$	−5.32351	+	0.425581i	−0.195696	+	0.0156447i
$741$	−2.80580			−0.103073
$742$		−	51.1627i		−	1.87824i
$743$			52.2906i			1.91836i	0.282804	+	0.959178i	$0.408735\pi$
$743$			52.2906i			1.91836i	−0.282804	+	0.959178i	$0.591265\pi$
$744$	3.45051			0.126502
$745$	2.83974	+	35.5218i	0.104040	+	1.30142i
$746$	−54.2320			−1.98557
$747$			10.5946i			0.387635i
$748$		0			0
$749$	−52.8630			−1.93157
$750$	−2.68450	−	11.0021i	−0.0980239	−	0.401740i
$751$	−39.4604			−1.43993			−0.719966	−	0.694010i	$-0.755842\pi$
$751$	−39.4604			−1.43993			−0.719966	+	0.694010i	$0.755842\pi$
$752$			23.9690i			0.874058i
$753$			11.1269i			0.405489i
$754$	−14.9192			−0.543326
$755$	0.600324	+	7.50933i	0.0218480	+	0.273293i
$756$	−12.4405			−0.452456
$757$			8.61186i			0.313003i	0.987678	+	0.156502i	$0.0500216\pi$
$757$			8.61186i			0.313003i	−0.987678	+	0.156502i	$0.949978\pi$
$758$		−	1.82664i		−	0.0663466i
$759$	7.33764			0.266340
$760$	12.0265	−	0.961442i	0.436246	−	0.0348751i
$761$	41.2400			1.49495			0.747474	−	0.664291i	$-0.231267\pi$
$761$	41.2400			1.49495			0.747474	+	0.664291i	$0.231267\pi$
$762$		−	5.92562i		−	0.214663i
$763$		−	1.38854i		−	0.0502686i
$764$	−17.4485			−0.631265
$765$		0			0
$766$	−46.6450			−1.68535
$767$		−	7.49280i		−	0.270549i
$768$		−	11.6440i		−	0.420166i
$769$	−17.3510			−0.625692			−0.312846	−	0.949804i	$-0.601282\pi$
$769$	−17.3510			−0.625692			−0.312846	+	0.949804i	$0.601282\pi$
$770$	5.61195	+	70.1987i	0.202241	+	2.52979i
$771$	13.7044			0.493552
$772$			5.22687i			0.188119i
$773$			20.0124i			0.719796i	0.932992	+	0.359898i	$0.117188\pi$
$773$			20.0124i			0.719796i	−0.932992	+	0.359898i	$0.882812\pi$
$774$	9.89101			0.355525
$775$	22.4814	−	3.61761i	0.807555	−	0.129949i
$776$	−16.7153			−0.600044
$777$			3.33452i			0.119625i
$778$			59.6352i			2.13803i
$779$	23.6937			0.848915
$780$	0.156490	+	1.95750i	0.00560324	+	0.0700898i
$781$	−49.3670			−1.76649
$782$		0			0
$783$			21.1530i			0.755948i
$784$	13.2520			0.473286
$785$	−8.74054	+	0.698752i	−0.311963	+	0.0249395i
$786$	−19.8160			−0.706815
$787$		−	33.9131i		−	1.20887i	−0.796653	−	0.604437i	$-0.793398\pi$
$787$		−	33.9131i		−	1.20887i	0.796653	−	0.604437i	$-0.206602\pi$
$788$			22.1480i			0.788990i
$789$	10.1434			0.361116
$790$	−19.7380	+	1.57793i	−0.702246	+	0.0561402i
$791$	35.2420			1.25306
$792$			20.3214i			0.722089i
$793$		−	7.06428i		−	0.250860i
$794$	14.7008			0.521711
$795$	0.912491	+	11.4142i	0.0323627	+	0.404819i
$796$	7.01200			0.248534
$797$		−	0.730287i		−	0.0258681i	−0.999916	−	0.0129340i	$-0.995883\pi$
$797$		−	0.730287i		−	0.0258681i	0.999916	−	0.0129340i	$-0.00411715\pi$
$798$			12.6089i			0.446350i
$799$		0			0
$800$	−4.92849	−	30.6278i	−0.174249	−	1.08285i
$801$	28.4905			1.00666
$802$		−	0.298360i		−	0.0105355i
$803$		−	8.80204i		−	0.310617i
$804$	5.95095			0.209874
$805$	−1.29082	−	16.1466i	−0.0454953	−	0.569091i
$806$	−10.2559			−0.361248
$807$		−	10.0320i		−	0.353142i
$808$		−	12.9777i		−	0.456553i
$809$	20.4333			0.718395			0.359198	−	0.933262i	$-0.383050\pi$
$809$	20.4333			0.718395			0.359198	+	0.933262i	$0.383050\pi$
$810$	−25.1624	+	2.01157i	−0.884115	+	0.0706795i
$811$	−2.51695			−0.0883820			−0.0441910	−	0.999023i	$-0.514071\pi$
$811$	−2.51695			−0.0883820			−0.0441910	+	0.999023i	$0.514071\pi$
$812$			25.8119i			0.905822i
$813$			8.90684i			0.312376i
$814$	−19.3055			−0.676657
$815$	32.8095	−	2.62291i	1.14927	−	0.0918767i
$816$		0			0
$817$		−	8.17265i		−	0.285925i
$818$			24.1087i			0.842941i
$819$	−10.4326			−0.364546
$820$	−1.32149	−	16.5302i	−0.0461484	−	0.577261i
$821$	15.2982			0.533912			0.266956	−	0.963709i	$-0.413982\pi$
$821$	15.2982			0.533912			0.266956	+	0.963709i	$0.413982\pi$
$822$			14.0368i			0.489590i
$823$		−	14.3448i		−	0.500029i	−0.968242	−	0.250014i	$-0.919565\pi$
$823$		−	14.3448i		−	0.500029i	0.968242	−	0.250014i	$-0.0804354\pi$
$824$	−2.48598			−0.0866033
$825$	−2.50400	−	15.5609i	−0.0871781	−	0.541762i
$826$	−33.6717			−1.17159
$827$		−	40.3144i		−	1.40187i	−0.713226	−	0.700934i	$-0.752767\pi$
$827$		−	40.3144i		−	1.40187i	0.713226	−	0.700934i	$-0.247233\pi$
$828$			7.82361i			0.271889i
$829$	−37.1150			−1.28906			−0.644528	−	0.764581i	$-0.722946\pi$
$829$	−37.1150			−1.28906			−0.644528	+	0.764581i	$0.722946\pi$
$830$	−1.26818	−	15.8635i	−0.0440193	−	0.550629i
$831$	−7.96396			−0.276267
$832$			1.64280i			0.0569540i
$833$		0			0
$834$	10.3315			0.357751
$835$	0.936496	−	0.0748670i	0.0324088	−	0.00259088i
$836$	−28.1047			−0.972020
$837$			14.5412i			0.502616i
$838$			42.5102i			1.46849i
$839$	7.10180			0.245182			0.122591	−	0.992457i	$-0.460880\pi$
$839$	7.10180			0.245182			0.122591	+	0.992457i	$0.460880\pi$
$840$	−5.25557	+	0.420150i	−0.181334	+	0.0144965i
$841$	14.8890			0.513414
$842$			10.5089i			0.362161i
$843$			4.38657i			0.151082i
$844$	−1.15574			−0.0397824
$845$	−2.03860	−	25.5004i	−0.0701298	−	0.877239i
$846$	−23.5054			−0.808134
$847$			63.7771i			2.19141i
$848$			45.0048i			1.54547i
$849$	−11.7440			−0.403052
$850$		0			0
$851$	4.44050			0.152218
$852$			6.18629i			0.211939i
$853$			38.3399i			1.31273i	0.754442	+	0.656366i	$0.227907\pi$
$853$			38.3399i			1.31273i	−0.754442	+	0.656366i	$0.772093\pi$
$854$	−31.7460			−1.08633
$855$	1.91341	+	23.9345i	0.0654374	+	0.818542i
$856$	22.9134			0.783164
$857$			1.73040i			0.0591094i	0.999563	+	0.0295547i	$0.00940892\pi$
$857$			1.73040i			0.0591094i	−0.999563	+	0.0295547i	$0.990591\pi$
$858$			7.09880i			0.242349i
$859$	−30.9245			−1.05513			−0.527565	−	0.849515i	$-0.676895\pi$
$859$	−30.9245			−1.05513			−0.527565	+	0.849515i	$0.676895\pi$
$860$	−5.70176	+	0.455820i	−0.194428	+	0.0155433i
$861$	−10.3542			−0.352868
$862$			12.5085i			0.426043i
$863$		−	40.2134i		−	1.36888i	−0.729070	−	0.684439i	$-0.760047\pi$
$863$		−	40.2134i		−	1.36888i	0.729070	−	0.684439i	$-0.239953\pi$
$864$	19.8103			0.673960
$865$	−37.0060	+	2.95840i	−1.25824	+	0.100589i
$866$	27.8550			0.946550
$867$		0			0
$868$			17.7438i			0.602265i
$869$	−27.5575			−0.934824
$870$	−1.19575	−	14.9575i	−0.0405399	−	0.507105i
$871$	10.5675			0.358066
$872$			0.601863i			0.0203816i
$873$		−	33.2660i		−	1.12588i
$874$	16.7909			0.567962
$875$	−33.8015	+	8.24751i	−1.14270	+	0.278817i
$876$	−1.10300			−0.0372670
$877$			1.01124i			0.0341472i	0.999854	+	0.0170736i	$0.00543497\pi$
$877$			1.01124i			0.0341472i	−0.999854	+	0.0170736i	$0.994565\pi$
$878$			2.65168i			0.0894898i
$879$	2.69336			0.0908446
$880$	−4.93650	−	61.7496i	−0.166409	−	2.08158i
$881$	−19.5296			−0.657968			−0.328984	−	0.944336i	$-0.606706\pi$
$881$	−19.5296			−0.657968			−0.328984	+	0.944336i	$0.606706\pi$
$882$			12.9957i			0.437589i
$883$		−	12.6125i		−	0.424445i	−0.977221	−	0.212223i	$-0.931930\pi$
$883$		−	12.6125i		−	0.424445i	0.977221	−	0.212223i	$-0.0680702\pi$
$884$		0			0
$885$	7.51200	−	0.600538i	0.252513	−	0.0201869i
$886$	−23.0535			−0.774497
$887$			37.1151i			1.24620i	0.782141	+	0.623102i	$0.214128\pi$
$887$			37.1151i			1.24620i	−0.782141	+	0.623102i	$0.785872\pi$
$888$		−	1.44534i		−	0.0485026i
$889$	−18.2052			−0.610581
$890$	−42.6594	+	3.41035i	−1.42995	+	0.114315i
$891$	−35.1308			−1.17693
$892$		−	1.56350i		−	0.0523498i
$893$			19.4218i			0.649927i
$894$	16.1425			0.539886
$895$	3.52702	+	44.1188i	0.117895	+	1.47473i
$896$	−31.2332			−1.04343
$897$		−	1.63281i		−	0.0545180i
$898$		−	17.5486i		−	0.585603i
$899$	30.1705			1.00624
$900$	16.5915	−	2.66984i	0.553050	−	0.0889946i
$901$		0			0
$902$		−	59.9463i		−	1.99599i
$903$			3.57145i			0.118850i
$904$	−15.2756			−0.508059
$905$	−1.66849	−	20.8708i	−0.0554626	−	0.693770i
$906$	3.41254			0.113374
$907$		−	34.4437i		−	1.14368i	−0.820364	−	0.571842i	$-0.806229\pi$
$907$		−	34.4437i		−	1.14368i	0.820364	−	0.571842i	$-0.193771\pi$
$908$			14.5016i			0.481254i
$909$	25.8275			0.856644
$910$	15.6210	−	1.24880i	0.517831	−	0.0413973i
$911$	−10.1968			−0.337835			−0.168918	−	0.985630i	$-0.554027\pi$
$911$	−10.1968			−0.337835			−0.168918	+	0.985630i	$0.554027\pi$
$912$		−	11.0913i		−	0.367269i
$913$		−	22.1480i		−	0.732992i
$914$	65.3309			2.16096
$915$	7.08238	−	0.566192i	0.234136	−	0.0187177i
$916$	14.7085			0.485983
$917$			60.8804i			2.01045i
$918$		0			0
$919$	50.5315			1.66688			0.833440	−	0.552611i	$-0.186368\pi$
$919$	50.5315			1.66688			0.833440	+	0.552611i	$0.186368\pi$
$920$	0.559503	+	6.99871i	0.0184463	+	0.230741i
$921$	14.0382			0.462573
$922$			72.2405i			2.37911i
$923$			10.9854i			0.361589i
$924$	12.2817			0.404039
$925$	−1.51534	−	9.41695i	−0.0498240	−	0.309628i
$926$	−27.7005			−0.910295
$927$		−	4.94748i		−	0.162496i
$928$		−	41.1031i		−	1.34927i
$929$	−28.3712			−0.930830			−0.465415	−	0.885093i	$-0.654095\pi$
$929$	−28.3712			−0.930830			−0.465415	+	0.885093i	$0.654095\pi$
$930$	−0.821994	−	10.2822i	−0.0269542	−	0.337165i
$931$	10.7380			0.351923
$932$			14.1528i			0.463591i
$933$			2.26493i			0.0741504i
$934$	−35.0695			−1.14751
$935$		0			0
$936$	4.52202			0.147807
$937$		−	47.5024i		−	1.55183i	−0.630835	−	0.775917i	$-0.717287\pi$
$937$		−	47.5024i		−	1.55183i	0.630835	−	0.775917i	$-0.282713\pi$
$938$		−	47.4890i		−	1.55057i
$939$	−12.7220			−0.415166
$940$	13.5499	−	1.08323i	0.441950	−	0.0353311i
$941$	−46.0404			−1.50087			−0.750437	−	0.660942i	$-0.770157\pi$
$941$	−46.0404			−1.50087			−0.750437	+	0.660942i	$0.770157\pi$
$942$			3.97205i			0.129416i
$943$			13.7884i			0.449011i
$944$	29.6190			0.964016
$945$	−1.77060	−	22.1480i	−0.0575975	−	0.720475i
$946$	−20.6772			−0.672274
$947$			29.7383i			0.966366i	0.875519	+	0.483183i	$0.160519\pi$
$947$			29.7383i			0.966366i	−0.875519	+	0.483183i	$0.839481\pi$
$948$			3.45329i			0.112158i
$949$	−1.95868			−0.0635814
$950$	−5.72998	−	35.6085i	−0.185905	−	1.15529i
$951$	4.64701			0.150690
$952$		0			0
$953$		−	9.02109i		−	0.292222i	−0.989268	−	0.146111i	$-0.953324\pi$
$953$		−	9.02109i		−	0.292222i	0.989268	−	0.146111i	$-0.0466756\pi$
$954$	−44.1344			−1.42891
$955$	−2.48336	−	31.0638i	−0.0803597	−	1.00520i
$956$	6.42903			0.207930
$957$		−	20.8831i		−	0.675054i
$958$			26.2470i			0.848002i
$959$	43.1250			1.39258
$960$	−1.64701	+	0.131668i	−0.0531571	+	0.00424958i
$961$	−10.2600			−0.330968
$962$			4.29596i			0.138507i
$963$			45.6011i			1.46948i
$964$	10.6236			0.342162
$965$	−9.30549	+	0.743916i	−0.299554	+	0.0239475i
$966$	−7.33764			−0.236085
$967$		−	11.7541i		−	0.377986i	−0.981978	−	0.188993i	$-0.939478\pi$
$967$		−	11.7541i		−	0.377986i	0.981978	−	0.188993i	$-0.0605223\pi$
$968$		−	27.6441i		−	0.888516i
$969$		0			0
$970$	3.98198	+	49.8098i	0.127854	+	1.59930i
$971$	19.9525			0.640306			0.320153	−	0.947366i	$-0.396266\pi$
$971$	19.9525			0.640306			0.320153	+	0.947366i	$0.396266\pi$
$972$			16.3951i			0.525874i
$973$		−	31.7413i		−	1.01758i
$974$	−53.5544			−1.71599
$975$	−3.46270	+	0.557203i	−0.110895	+	0.0178448i
$976$	27.9250			0.893859
$977$		−	27.2005i		−	0.870221i	−0.900377	−	0.435110i	$-0.856709\pi$
$977$		−	27.2005i		−	0.870221i	0.900377	−	0.435110i	$-0.143291\pi$
$978$		−	14.9099i		−	0.476767i
$979$	−59.5596			−1.90353
$980$	−0.598899	−	7.49150i	−0.0191311	−	0.239307i
$981$	−1.19780			−0.0382427
$982$		−	37.9989i		−	1.21259i
$983$		−	7.12485i		−	0.227248i	−0.993524	−	0.113624i	$-0.963754\pi$
$983$		−	7.12485i		−	0.227248i	0.993524	−	0.113624i	$-0.0362459\pi$
$984$	4.48800			0.143072
$985$	−39.4305	+	3.15222i	−1.25636	+	0.100438i
$986$		0			0
$987$		−	8.48734i		−	0.270155i
$988$			6.25400i			0.198966i
$989$	4.75601			0.151232
$990$	60.5555	−	4.84103i	1.92458	−	0.153858i
$991$	56.9670			1.80962			0.904808	−	0.425820i	$-0.140014\pi$
$991$	56.9670			1.80962			0.904808	+	0.425820i	$0.140014\pi$
$992$		−	28.2554i		−	0.897108i
$993$			3.09608i			0.0982511i
$994$	49.3670			1.56583
$995$	0.997984	+	12.4836i	0.0316382	+	0.395756i
$996$	−2.77542			−0.0879425
$997$			5.04451i			0.159761i	0.996804	+	0.0798806i	$0.0254539\pi$
$997$			5.04451i			0.159761i	−0.996804	+	0.0798806i	$0.974546\pi$
$998$		−	16.9665i		−	0.537064i
$999$	6.09097			0.192710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.b.f.579.3		12
5.2	odd	4		7225.2.a.bp.1.9		12
5.3	odd	4		7225.2.a.bp.1.4		12
5.4	even	2	inner	1445.2.b.f.579.10		12
17.8	even	8		85.2.j.c.64.2	yes	12
17.15	even	8		85.2.j.c.4.5	yes	12
17.16	even	2	inner	1445.2.b.f.579.4		12
51.8	odd	8		765.2.t.e.64.5		12
51.32	odd	8		765.2.t.e.514.2		12
85.8	odd	8		425.2.e.d.251.5		12
85.32	odd	8		425.2.e.d.276.5		12
85.33	odd	4		7225.2.a.bp.1.3		12
85.42	odd	8		425.2.e.d.251.2		12
85.49	even	8		85.2.j.c.4.2	✓	12
85.59	even	8		85.2.j.c.64.5	yes	12
85.67	odd	4		7225.2.a.bp.1.10		12
85.83	odd	8		425.2.e.d.276.2		12
85.84	even	2	inner	1445.2.b.f.579.9		12
255.59	odd	8		765.2.t.e.64.2		12
255.134	odd	8		765.2.t.e.514.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.2	✓	12	85.49	even	8
85.2.j.c.4.5	yes	12	17.15	even	8
85.2.j.c.64.2	yes	12	17.8	even	8
85.2.j.c.64.5	yes	12	85.59	even	8
425.2.e.d.251.2		12	85.42	odd	8
425.2.e.d.251.5		12	85.8	odd	8
425.2.e.d.276.2		12	85.83	odd	8
425.2.e.d.276.5		12	85.32	odd	8
765.2.t.e.64.2		12	255.59	odd	8
765.2.t.e.64.5		12	51.8	odd	8
765.2.t.e.514.2		12	51.32	odd	8
765.2.t.e.514.5		12	255.134	odd	8
1445.2.b.f.579.3		12	1.1	even	1	trivial
1445.2.b.f.579.4		12	17.16	even	2	inner
1445.2.b.f.579.9		12	85.84	even	2	inner
1445.2.b.f.579.10		12	5.4	even	2	inner
7225.2.a.bp.1.3		12	85.33	odd	4
7225.2.a.bp.1.4		12	5.3	odd	4
7225.2.a.bp.1.9		12	5.2	odd	4
7225.2.a.bp.1.10		12	85.67	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.80333i q^{2} -0.561698i q^{3} -1.25200 q^{4} +(-0.178191 - 2.22896i) q^{5} -1.01293 q^{6} +3.11199i q^{7} -1.34889i q^{8} +2.68450 q^{9} +(-4.01955 + 0.321338i) q^{10} -5.61195 q^{11} +0.703246i q^{12} +1.24880i q^{13} +5.61195 q^{14} +(-1.25200 + 0.100090i) q^{15} -4.93650 q^{16} -4.84103i q^{18} -4.00000 q^{19} +(0.223095 + 2.79065i) q^{20} +1.74800 q^{21} +10.1202i q^{22} -2.32777i q^{23} -0.757669 q^{24} +(-4.93650 + 0.794361i) q^{25} +2.25200 q^{26} -3.19297i q^{27} -3.89622i q^{28} -6.62488 q^{29} +(0.180495 + 2.25777i) q^{30} -4.55412 q^{31} +6.20435i q^{32} +3.15222i q^{33} +(6.93650 - 0.554530i) q^{35} -3.36099 q^{36} +1.90762i q^{37} +7.21332i q^{38} +0.701449 q^{39} +(-3.00662 + 0.240360i) q^{40} -5.92343 q^{41} -3.15222i q^{42} +2.04316i q^{43} +7.02616 q^{44} +(-0.478353 - 5.98362i) q^{45} -4.19774 q^{46} -4.85546i q^{47} +2.77282i q^{48} -2.68450 q^{49} +(1.43250 + 8.90213i) q^{50} -1.56350i q^{52} -9.11674i q^{53} -5.75798 q^{54} +(1.00000 + 12.5088i) q^{55} +4.19774 q^{56} +2.24679i q^{57} +11.9468i q^{58} -6.00000 q^{59} +(1.56750 - 0.125312i) q^{60} -5.65685 q^{61} +8.21258i q^{62} +8.35413i q^{63} +1.31550 q^{64} +(2.78352 - 0.222525i) q^{65} +5.68450 q^{66} -8.46212i q^{67} -1.30750 q^{69} +(-1.00000 - 12.5088i) q^{70} +8.79676 q^{71} -3.62109i q^{72} +1.56845i q^{73} +3.44007 q^{74} +(0.446191 + 2.77282i) q^{75} +5.00800 q^{76} -17.4643i q^{77} -1.26494i q^{78} +4.91050 q^{79} +(0.879640 + 11.0032i) q^{80} +6.26000 q^{81} +10.6819i q^{82} +3.94658i q^{83} -2.18850 q^{84} +3.68450 q^{86} +3.72118i q^{87} +7.56991i q^{88} +10.6130 q^{89} +(-10.7905 + 0.862629i) q^{90} -3.88626 q^{91} +2.91437i q^{92} +2.55804i q^{93} -8.75600 q^{94} +(0.712765 + 8.91583i) q^{95} +3.48497 q^{96} -12.3919i q^{97} +4.84103i q^{98} -15.0653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 28 q^{9} - 12 q^{15} + 4 q^{16} - 48 q^{19} + 24 q^{21} + 4 q^{25} + 24 q^{26} - 52 q^{30} + 20 q^{35} + 68 q^{36} + 28 q^{49} - 40 q^{50} + 12 q^{55} - 72 q^{59} + 76 q^{60} + 76 q^{64}+ \cdots - 96 q^{94}+O(q^{100}) \) 12 * q - 12 * q^4 - 28 * q^9 - 12 * q^15 + 4 * q^16 - 48 * q^19 + 24 * q^21 + 4 * q^25 + 24 * q^26 - 52 * q^30 + 20 * q^35 + 68 * q^36 + 28 * q^49 - 40 * q^50 + 12 * q^55 - 72 * q^59 + 76 * q^60 + 76 * q^64 + 8 * q^66 - 88 * q^69 - 12 * q^70 + 48 * q^76 + 60 * q^81 + 40 * q^84 - 16 * q^86 + 16 * q^89 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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