LMFDB - Embedded newform 845.2.d.a.844.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.1
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.a.844.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.67513 q^{2} -0.481194i q^{3} +5.15633 q^{4} +(1.48119 - 1.67513i) q^{5} +1.28726i q^{6} +0.806063 q^{7} -8.44358 q^{8} +2.76845 q^{9} +(-3.96239 + 4.48119i) q^{10} -3.67513i q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.806063 - 0.712742i) q^{15} +12.2750 q^{16} -1.35026i q^{17} -7.40597 q^{18} -1.67513i q^{19} +(7.63752 - 8.63752i) q^{20} -0.387873i q^{21} +9.83146i q^{22} -6.48119i q^{23} +4.06300i q^{24} +(-0.612127 - 4.96239i) q^{25} -2.77575i q^{27} +4.15633 q^{28} -2.41819 q^{29} +(2.15633 + 1.90668i) q^{30} +5.28726i q^{31} -15.9502 q^{32} -1.76845 q^{33} +3.61213i q^{34} +(1.19394 - 1.35026i) q^{35} +14.2750 q^{36} +3.76845 q^{37} +4.48119i q^{38} +(-12.5066 + 14.1441i) q^{40} +8.31265i q^{41} +1.03761i q^{42} +6.79384i q^{43} -18.9502i q^{44} +(4.10062 - 4.63752i) q^{45} +17.3380i q^{46} +3.19394 q^{47} -5.90668i q^{48} -6.35026 q^{49} +(1.63752 + 13.2750i) q^{50} -0.649738 q^{51} +5.73813i q^{53} +7.42548i q^{54} +(-6.15633 - 5.44358i) q^{55} -6.80606 q^{56} -0.806063 q^{57} +6.46898 q^{58} -5.98778i q^{59} +(-4.15633 - 3.67513i) q^{60} -1.76845 q^{61} -14.1441i q^{62} +2.23155 q^{63} +18.1187 q^{64} +4.73084 q^{66} -9.89446 q^{67} -6.96239i q^{68} -3.11871 q^{69} +(-3.19394 + 3.61213i) q^{70} -8.56230i q^{71} -23.3757 q^{72} +11.7685 q^{73} -10.0811 q^{74} +(-2.38787 + 0.294552i) q^{75} -8.63752i q^{76} -2.96239i q^{77} +2.26187 q^{79} +(18.1817 - 20.5623i) q^{80} +6.96968 q^{81} -22.2374i q^{82} +3.84367 q^{83} -2.00000i q^{84} +(-2.26187 - 2.00000i) q^{85} -18.1744i q^{86} +1.16362i q^{87} +31.0313i q^{88} -2.77575i q^{89} +(-10.9697 + 12.4060i) q^{90} -33.4191i q^{92} +2.54420 q^{93} -8.54420 q^{94} +(-2.80606 - 2.48119i) q^{95} +7.67513i q^{96} +1.87399 q^{97} +16.9878 q^{98} -10.1744i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.67513			−1.89160			−0.945802	−	0.324745i	$-0.894721\pi$
$2$	−2.67513			−1.89160			−0.945802	+	0.324745i	$0.894721\pi$
$3$		−	0.481194i		−	0.277818i	−0.990305	−	0.138909i	$-0.955641\pi$
$3$		−	0.481194i		−	0.277818i	0.990305	−	0.138909i	$-0.0443595\pi$
$4$	5.15633			2.57816
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$5$	1.48119	−	1.67513i	0.662410	−	0.749141i
$6$			1.28726i			0.525521i
$7$	0.806063			0.304663			0.152332	−	0.988329i	$-0.451322\pi$
$7$	0.806063			0.304663			0.152332	+	0.988329i	$0.451322\pi$
$8$	−8.44358			−2.98526
$9$	2.76845			0.922817
$10$	−3.96239	+	4.48119i	−1.25302	+	1.41708i
$11$		−	3.67513i		−	1.10809i	−0.832486	−	0.554047i	$-0.813083\pi$
$11$		−	3.67513i		−	1.10809i	0.832486	−	0.554047i	$-0.186917\pi$
$12$		−	2.48119i		−	0.716259i
$13$		0			0
$13$		0			0
$14$	−2.15633			−0.576302
$15$	−0.806063	−	0.712742i	−0.208125	−	0.184029i
$16$	12.2750			3.06876
$17$		−	1.35026i		−	0.327487i	−0.986503	−	0.163743i	$-0.947643\pi$
$17$		−	1.35026i		−	0.327487i	0.986503	−	0.163743i	$-0.0523569\pi$
$18$	−7.40597			−1.74560
$19$		−	1.67513i		−	0.384301i	−0.981365	−	0.192151i	$-0.938454\pi$
$19$		−	1.67513i		−	0.384301i	0.981365	−	0.192151i	$-0.0615462\pi$
$20$	7.63752	−	8.63752i	1.70780	−	1.93141i
$21$		−	0.387873i		−	0.0846409i
$22$			9.83146i			2.09607i
$23$		−	6.48119i		−	1.35142i	−0.737166	−	0.675711i	$-0.763837\pi$
$23$		−	6.48119i		−	1.35142i	0.737166	−	0.675711i	$-0.236163\pi$
$24$			4.06300i			0.829357i
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$		0			0
$27$		−	2.77575i		−	0.534193i
$28$	4.15633			0.785472
$29$	−2.41819			−0.449047			−0.224523	−	0.974469i	$-0.572083\pi$
$29$	−2.41819			−0.449047			−0.224523	+	0.974469i	$0.572083\pi$
$30$	2.15633	+	1.90668i	0.393689	+	0.348110i
$31$			5.28726i			0.949620i	0.880088	+	0.474810i	$0.157483\pi$
$31$			5.28726i			0.949620i	−0.880088	+	0.474810i	$0.842517\pi$
$32$	−15.9502			−2.81962
$33$	−1.76845			−0.307848
$34$			3.61213i			0.619475i
$35$	1.19394	−	1.35026i	0.201812	−	0.228236i
$36$	14.2750			2.37917
$37$	3.76845			0.619530			0.309765	−	0.950813i	$-0.399750\pi$
$37$	3.76845			0.619530			0.309765	+	0.950813i	$0.399750\pi$
$38$			4.48119i			0.726946i
$39$		0			0
$40$	−12.5066	+	14.1441i	−1.97747	+	2.23638i
$41$			8.31265i			1.29822i	0.760695	+	0.649109i	$0.224858\pi$
$41$			8.31265i			1.29822i	−0.760695	+	0.649109i	$0.775142\pi$
$42$			1.03761i			0.160107i
$43$			6.79384i			1.03605i	0.855365	+	0.518026i	$0.173333\pi$
$43$			6.79384i			1.03605i	−0.855365	+	0.518026i	$0.826667\pi$
$44$		−	18.9502i		−	2.85685i
$45$	4.10062	−	4.63752i	0.611284	−	0.691321i
$46$			17.3380i			2.55635i
$47$	3.19394			0.465884			0.232942	−	0.972491i	$-0.425165\pi$
$47$	3.19394			0.465884			0.232942	+	0.972491i	$0.425165\pi$
$48$		−	5.90668i		−	0.852556i
$49$	−6.35026			−0.907180
$50$	1.63752	+	13.2750i	0.231580	+	1.87737i
$51$	−0.649738			−0.0909816
$52$		0			0
$53$			5.73813i			0.788193i	0.919069	+	0.394097i	$0.128943\pi$
$53$			5.73813i			0.788193i	−0.919069	+	0.394097i	$0.871057\pi$
$54$			7.42548i			1.01048i
$55$	−6.15633	−	5.44358i	−0.830119	−	0.734013i
$56$	−6.80606			−0.909498
$57$	−0.806063			−0.106766
$58$	6.46898			0.849418
$59$		−	5.98778i		−	0.779543i	−0.920912	−	0.389771i	$-0.872554\pi$
$59$		−	5.98778i		−	0.779543i	0.920912	−	0.389771i	$-0.127446\pi$
$60$	−4.15633	−	3.67513i	−0.536579	−	0.474457i
$61$	−1.76845			−0.226427			−0.113214	−	0.993571i	$-0.536114\pi$
$61$	−1.76845			−0.226427			−0.113214	+	0.993571i	$0.536114\pi$
$62$		−	14.1441i		−	1.79630i
$63$	2.23155			0.281149
$64$	18.1187			2.26484
$65$		0			0
$66$	4.73084			0.582326
$67$	−9.89446			−1.20880			−0.604400	−	0.796681i	$-0.706587\pi$
$67$	−9.89446			−1.20880			−0.604400	+	0.796681i	$0.706587\pi$
$68$		−	6.96239i		−	0.844314i
$69$	−3.11871			−0.375449
$70$	−3.19394	+	3.61213i	−0.381748	+	0.431732i
$71$		−	8.56230i		−	1.01616i	−0.861311	−	0.508079i	$-0.830356\pi$
$71$		−	8.56230i		−	1.01616i	0.861311	−	0.508079i	$-0.169644\pi$
$72$	−23.3757			−2.75485
$73$	11.7685			1.37739			0.688697	−	0.725050i	$-0.258183\pi$
$73$	11.7685			1.37739			0.688697	+	0.725050i	$0.258183\pi$
$74$	−10.0811			−1.17190
$75$	−2.38787	+	0.294552i	−0.275728	+	0.0340119i
$76$		−	8.63752i		−	0.990791i
$77$		−	2.96239i		−	0.337596i
$78$		0			0
$79$	2.26187			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$79$	2.26187			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$80$	18.1817	−	20.5623i	2.03278	−	2.29893i
$81$	6.96968			0.774409
$82$		−	22.2374i		−	2.45571i
$83$	3.84367			0.421898			0.210949	−	0.977497i	$-0.432345\pi$
$83$	3.84367			0.421898			0.210949	+	0.977497i	$0.432345\pi$
$84$		−	2.00000i		−	0.218218i
$85$	−2.26187	−	2.00000i	−0.245334	−	0.216930i
$86$		−	18.1744i		−	1.95980i
$87$			1.16362i			0.124753i
$88$			31.0313i			3.30794i
$89$		−	2.77575i		−	0.294229i	−0.989120	−	0.147114i	$-0.953001\pi$
$89$		−	2.77575i		−	0.294229i	0.989120	−	0.147114i	$-0.0469985\pi$
$90$	−10.9697	+	12.4060i	−1.15631	+	1.30770i
$91$		0			0
$92$		−	33.4191i		−	3.48419i
$93$	2.54420			0.263821
$94$	−8.54420			−0.881267
$95$	−2.80606	−	2.48119i	−0.287896	−	0.254565i
$96$			7.67513i			0.783340i
$97$	1.87399			0.190275			0.0951375	−	0.995464i	$-0.469671\pi$
$97$	1.87399			0.190275			0.0951375	+	0.995464i	$0.469671\pi$
$98$	16.9878			1.71603
$99$		−	10.1744i		−	1.02257i
$100$	−3.15633	−	25.5877i	−0.315633	−	2.55877i
$101$	−10.4993			−1.04472			−0.522359	−	0.852725i	$-0.674948\pi$
$101$	−10.4993			−1.04472			−0.522359	+	0.852725i	$0.674948\pi$
$102$	1.73813			0.172101
$103$		−	15.3684i		−	1.51429i	−0.653247	−	0.757145i	$-0.726594\pi$
$103$		−	15.3684i		−	1.51429i	0.653247	−	0.757145i	$-0.273406\pi$
$104$		0			0
$105$	−0.649738	−	0.574515i	−0.0634080	−	0.0560670i
$106$		−	15.3503i		−	1.49095i
$107$		−	11.1309i		−	1.07607i	−0.842923	−	0.538034i	$-0.819167\pi$
$107$		−	11.1309i		−	1.07607i	0.842923	−	0.538034i	$-0.180833\pi$
$108$		−	14.3127i		−	1.37724i
$109$			9.58769i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$109$			9.58769i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$110$	16.4690	+	14.5623i	1.57026	+	1.38846i
$111$		−	1.81336i		−	0.172116i
$112$	9.89446			0.934939
$113$			0.574515i			0.0540459i	0.999635	+	0.0270229i	$0.00860271\pi$
$113$			0.574515i			0.0540459i	−0.999635	+	0.0270229i	$0.991397\pi$
$114$	2.15633			0.201958
$115$	−10.8568	−	9.59991i	−1.01241	−	0.895196i
$116$	−12.4690			−1.15772
$117$		0			0
$118$			16.0181i			1.47459i
$119$		−	1.08840i		−	0.0997732i
$120$	6.80606	+	6.01810i	0.621306	+	0.549375i
$121$	−2.50659			−0.227872
$122$	4.73084			0.428310
$123$	4.00000			0.360668
$124$			27.2628i			2.44827i
$125$	−9.21933	−	6.32487i	−0.824602	−	0.565713i
$126$	−5.96968			−0.531822
$127$		−	4.29455i		−	0.381080i	−0.981679	−	0.190540i	$-0.938976\pi$
$127$		−	4.29455i		−	0.381080i	0.981679	−	0.190540i	$-0.0610239\pi$
$128$	−16.5696			−1.46456
$129$	3.26916			0.287833
$130$		0			0
$131$	−0.836381			−0.0730749			−0.0365375	−	0.999332i	$-0.511633\pi$
$131$	−0.836381			−0.0730749			−0.0365375	+	0.999332i	$0.511633\pi$
$132$	−9.11871			−0.793682
$133$		−	1.35026i		−	0.117083i
$134$	26.4690			2.28657
$135$	−4.64974	−	4.11142i	−0.400186	−	0.353855i
$136$			11.4010i			0.977632i
$137$	−14.9380			−1.27624			−0.638118	−	0.769939i	$-0.720287\pi$
$137$	−14.9380			−1.27624			−0.638118	+	0.769939i	$0.720287\pi$
$138$	8.34297			0.710201
$139$	8.43866			0.715758			0.357879	−	0.933768i	$-0.383500\pi$
$139$	8.43866			0.715758			0.357879	+	0.933768i	$0.383500\pi$
$140$	6.15633	−	6.96239i	0.520304	−	0.588429i
$141$		−	1.53690i		−	0.129431i
$142$			22.9053i			1.92217i
$143$		0			0
$144$	33.9829			2.83190
$145$	−3.58181	+	4.05079i	−0.297453	+	0.336399i
$146$	−31.4821			−2.60548
$147$			3.05571i			0.252031i
$148$	19.4314			1.59725
$149$		−	11.3503i		−	0.929850i	−0.885350	−	0.464925i	$-0.846081\pi$
$149$		−	11.3503i		−	0.929850i	0.885350	−	0.464925i	$-0.153919\pi$
$150$	6.38787	−	0.787965i	0.521568	−	0.0643371i
$151$			13.9878i			1.13831i	0.822230	+	0.569155i	$0.192729\pi$
$151$			13.9878i			1.13831i	−0.822230	+	0.569155i	$0.807271\pi$
$152$			14.1441i			1.14724i
$153$		−	3.73813i		−	0.302210i
$154$			7.92478i			0.638597i
$155$	8.85685	+	7.83146i	0.711399	+	0.629038i
$156$		0			0
$157$		−	2.77575i		−	0.221529i	−0.993847	−	0.110764i	$-0.964670\pi$
$157$		−	2.77575i		−	0.221529i	0.993847	−	0.110764i	$-0.0353299\pi$
$158$	−6.05079			−0.481375
$159$	2.76116			0.218974
$160$	−23.6253	+	26.7186i	−1.86774	+	2.11229i
$161$		−	5.22425i		−	0.411729i
$162$	−18.6448			−1.46487
$163$	−2.23155			−0.174788			−0.0873942	−	0.996174i	$-0.527854\pi$
$163$	−2.23155			−0.174788			−0.0873942	+	0.996174i	$0.527854\pi$
$164$			42.8627i			3.34702i
$165$	−2.61942	+	2.96239i	−0.203922	+	0.230622i
$166$	−10.2823			−0.798064
$167$	−15.6932			−1.21438			−0.607189	−	0.794557i	$-0.707703\pi$
$167$	−15.6932			−1.21438			−0.607189	+	0.794557i	$0.707703\pi$
$168$			3.27504i			0.252675i
$169$		0			0
$170$	6.05079	+	5.35026i	0.464074	+	0.410346i
$171$		−	4.63752i		−	0.354640i
$172$			35.0313i			2.67111i
$173$			25.5877i			1.94540i	0.232075	+	0.972698i	$0.425449\pi$
$173$			25.5877i			1.94540i	−0.232075	+	0.972698i	$0.574551\pi$
$174$		−	3.11283i		−	0.235983i
$175$	−0.493413	−	4.00000i	−0.0372985	−	0.302372i
$176$		−	45.1124i		−	3.40047i
$177$	−2.88129			−0.216571
$178$			7.42548i			0.556564i
$179$	12.1260			0.906340			0.453170	−	0.891424i	$-0.350293\pi$
$179$	12.1260			0.906340			0.453170	+	0.891424i	$0.350293\pi$
$180$	21.1441	−	23.9126i	1.57599	−	1.78234i
$181$	2.73084			0.202982			0.101491	−	0.994836i	$-0.467639\pi$
$181$	2.73084			0.202982			0.101491	+	0.994836i	$0.467639\pi$
$182$		0			0
$183$			0.850969i			0.0629054i
$184$			54.7245i			4.03434i
$185$	5.58181	−	6.31265i	0.410383	−	0.464115i
$186$	−6.80606			−0.499045
$187$	−4.96239			−0.362886
$188$	16.4690			1.20112
$189$		−	2.23743i		−	0.162749i
$190$	7.50659	+	6.63752i	0.544585	+	0.481536i
$191$	20.6253			1.49239			0.746197	−	0.665725i	$-0.231878\pi$
$191$	20.6253			1.49239			0.746197	+	0.665725i	$0.231878\pi$
$192$		−	8.71862i		−	0.629212i
$193$	21.7889			1.56840			0.784200	−	0.620508i	$-0.213073\pi$
$193$	21.7889			1.56840			0.784200	+	0.620508i	$0.213073\pi$
$194$	−5.01317			−0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$			27.2179i			1.93429i
$199$	−16.7513			−1.18747			−0.593734	−	0.804661i	$-0.702347\pi$
$199$	−16.7513			−1.18747			−0.593734	+	0.804661i	$0.702347\pi$
$200$	5.16854	+	41.9003i	0.365471	+	2.96280i
$201$			4.76116i			0.335826i
$202$	28.0870			1.97619
$203$	−1.94921			−0.136808
$204$	−3.35026			−0.234565
$205$	13.9248	+	12.3127i	0.972549	+	0.859953i
$206$			41.1124i			2.86443i
$207$		−	17.9429i		−	1.24712i
$208$		0			0
$209$	−6.15633			−0.425842
$210$	1.73813	+	1.53690i	0.119943	+	0.106056i
$211$	−4.90175			−0.337451			−0.168725	−	0.985663i	$-0.553965\pi$
$211$	−4.90175			−0.337451			−0.168725	+	0.985663i	$0.553965\pi$
$212$			29.5877i			2.03209i
$213$	−4.12013			−0.282307
$214$			29.7767i			2.03549i
$215$	11.3806	+	10.0630i	0.776149	+	0.686291i
$216$			23.4372i			1.59470i
$217$			4.26187i			0.289314i
$218$		−	25.6483i		−	1.73712i
$219$		−	5.66291i		−	0.382664i
$220$	−31.7440	−	28.0689i	−2.14018	−	1.89240i
$221$		0			0
$222$			4.85097i			0.325576i
$223$	24.9076			1.66794			0.833969	−	0.551811i	$-0.186063\pi$
$223$	24.9076			1.66794			0.833969	+	0.551811i	$0.186063\pi$
$224$	−12.8568			−0.859034
$225$	−1.69464	−	13.7381i	−0.112976	−	0.915876i
$226$		−	1.53690i		−	0.102233i
$227$	−9.95509			−0.660743			−0.330371	−	0.943851i	$-0.607174\pi$
$227$	−9.95509			−0.660743			−0.330371	+	0.943851i	$0.607174\pi$
$228$	−4.15633			−0.275259
$229$		−	5.35026i		−	0.353555i	−0.984251	−	0.176778i	$-0.943433\pi$
$229$		−	5.35026i		−	0.353555i	0.984251	−	0.176778i	$-0.0565673\pi$
$230$	29.0435	+	25.6810i	1.91507	+	1.69336i
$231$	−1.42548			−0.0937900
$232$	20.4182			1.34052
$233$			10.7612i			0.704987i	0.935814	+	0.352493i	$0.114666\pi$
$233$			10.7612i			0.704987i	−0.935814	+	0.352493i	$0.885334\pi$
$234$		0			0
$235$	4.73084	−	5.35026i	0.308606	−	0.349013i
$236$		−	30.8749i		−	2.00979i
$237$		−	1.08840i		−	0.0706990i
$238$			2.91160i			0.188731i
$239$		−	11.8618i		−	0.767274i	−0.923484	−	0.383637i	$-0.874671\pi$
$239$		−	11.8618i		−	0.767274i	0.923484	−	0.383637i	$-0.125329\pi$
$240$	−9.89446	−	8.74894i	−0.638685	−	0.564742i
$241$		−	28.6253i		−	1.84392i	−0.387288	−	0.921959i	$-0.626588\pi$
$241$		−	28.6253i		−	1.84392i	0.387288	−	0.921959i	$-0.373412\pi$
$242$	6.70545			0.431043
$243$		−	11.6810i		−	0.749337i
$244$	−9.11871			−0.583766
$245$	−9.40597	+	10.6375i	−0.600925	+	0.679606i
$246$	−10.7005			−0.682240
$247$		0			0
$248$		−	44.6434i		−	2.83486i
$249$		−	1.84955i		−	0.117211i
$250$	24.6629	+	16.9199i	1.55982	+	1.07011i
$251$	19.3865			1.22366			0.611831	−	0.790988i	$-0.290433\pi$
$251$	19.3865			1.22366			0.611831	+	0.790988i	$0.290433\pi$
$252$	11.5066			0.724847
$253$	−23.8192			−1.49750
$254$			11.4885i			0.720852i
$255$	−0.962389	+	1.08840i	−0.0602671	+	0.0681580i
$256$	8.08840			0.505525
$257$			22.8627i			1.42614i	0.701094	+	0.713069i	$0.252695\pi$
$257$			22.8627i			1.42614i	−0.701094	+	0.713069i	$0.747305\pi$
$258$	−8.74543			−0.544467
$259$	3.03761			0.188748
$260$		0			0
$261$	−6.69464			−0.414388
$262$	2.23743			0.138229
$263$			21.8822i			1.34932i	0.738130	+	0.674658i	$0.235709\pi$
$263$			21.8822i			1.34932i	−0.738130	+	0.674658i	$0.764291\pi$
$264$	14.9321			0.919005
$265$	9.61213	+	8.49929i	0.590468	+	0.522107i
$266$			3.61213i			0.221474i
$267$	−1.33567			−0.0817419
$268$	−51.0191			−3.11648
$269$	−22.7513			−1.38717			−0.693586	−	0.720374i	$-0.743970\pi$
$269$	−22.7513			−1.38717			−0.693586	+	0.720374i	$0.743970\pi$
$270$	12.4387	+	10.9986i	0.756993	+	0.669353i
$271$			0.123638i			0.00751049i	0.999993	+	0.00375525i	$0.00119534\pi$
$271$			0.123638i			0.00751049i	−0.999993	+	0.00375525i	$0.998805\pi$
$272$		−	16.5745i		−	1.00498i
$273$		0			0
$274$	39.9610			2.41413
$275$	−18.2374	+	2.24965i	−1.09976	+	0.135659i
$276$	−16.0811			−0.967969
$277$		−	15.3503i		−	0.922308i	−0.887320	−	0.461154i	$-0.847436\pi$
$277$		−	15.3503i		−	0.922308i	0.887320	−	0.461154i	$-0.152564\pi$
$278$	−22.5745			−1.35393
$279$			14.6375i			0.876325i
$280$	−10.0811	+	11.4010i	−0.602461	+	0.681343i
$281$			13.9248i			0.830683i	0.909666	+	0.415341i	$0.136338\pi$
$281$			13.9248i			0.830683i	−0.909666	+	0.415341i	$0.863662\pi$
$282$			4.11142i			0.244831i
$283$		−	20.3815i		−	1.21156i	−0.795634	−	0.605778i	$-0.792862\pi$
$283$		−	20.3815i		−	1.21156i	0.795634	−	0.605778i	$-0.207138\pi$
$284$		−	44.1500i		−	2.61982i
$285$	−1.19394	+	1.35026i	−0.0707227	+	0.0799826i
$286$		0			0
$287$			6.70052i			0.395519i
$288$	−44.1573			−2.60199
$289$	15.1768			0.892753
$290$	9.58181	−	10.8364i	0.562663	−	0.636334i
$291$		−	0.901754i		−	0.0528618i
$292$	60.6820			3.55114
$293$	−5.38058			−0.314337			−0.157168	−	0.987572i	$-0.550237\pi$
$293$	−5.38058			−0.314337			−0.157168	+	0.987572i	$0.550237\pi$
$294$		−	8.17442i		−	0.476742i
$295$	−10.0303	−	8.86907i	−0.583988	−	0.516377i
$296$	−31.8192			−1.84946
$297$	−10.2012			−0.591935
$298$			30.3634i			1.75891i
$299$		0			0
$300$	−12.3127	+	1.51881i	−0.710871	+	0.0876883i
$301$			5.47627i			0.315647i
$302$		−	37.4191i		−	2.15323i
$303$			5.05220i			0.290241i
$304$		−	20.5623i		−	1.17933i
$305$	−2.61942	+	2.96239i	−0.149988	+	0.169626i
$306$			10.0000i			0.571662i
$307$	−19.1695			−1.09406			−0.547031	−	0.837113i	$-0.684242\pi$
$307$	−19.1695			−1.09406			−0.547031	+	0.837113i	$0.684242\pi$
$308$		−	15.2750i		−	0.870376i
$309$	−7.39517			−0.420696
$310$	−23.6932	−	20.9502i	−1.34568	−	1.18989i
$311$	25.2506			1.43183			0.715915	−	0.698187i	$-0.246010\pi$
$311$	25.2506			1.43183			0.715915	+	0.698187i	$0.246010\pi$
$312$		0			0
$313$			2.81194i			0.158940i	0.996837	+	0.0794702i	$0.0253229\pi$
$313$			2.81194i			0.158940i	−0.996837	+	0.0794702i	$0.974677\pi$
$314$			7.42548i			0.419044i
$315$	3.30536	−	3.73813i	0.186236	−	0.210620i
$316$	11.6629			0.656090
$317$	23.7685			1.33497			0.667485	−	0.744624i	$-0.267371\pi$
$317$	23.7685			1.33497			0.667485	+	0.744624i	$0.267371\pi$
$318$	−7.38646			−0.414212
$319$			8.88717i			0.497586i
$320$	26.8373	−	30.3512i	1.50025	−	1.69668i
$321$	−5.35614			−0.298951
$322$			13.9756i			0.778828i
$323$	−2.26187			−0.125854
$324$	35.9380			1.99655
$325$		0			0
$326$	5.96968			0.330630
$327$	4.61354			0.255129
$328$		−	70.1886i		−	3.87551i
$329$	2.57452			0.141938
$330$	7.00729	−	7.92478i	0.385739	−	0.436245i
$331$			11.8011i			0.648649i	0.945946	+	0.324325i	$0.105137\pi$
$331$			11.8011i			0.648649i	−0.945946	+	0.324325i	$0.894863\pi$
$332$	19.8192			1.08772
$333$	10.4328			0.571713
$334$	41.9814			2.29712
$335$	−14.6556	+	16.5745i	−0.800722	+	0.905563i
$336$		−	4.76116i		−	0.259742i
$337$			16.1114i			0.877645i	0.898574	+	0.438822i	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$		0			0
$339$	0.276454			0.0150149
$340$	−11.6629	−	10.3127i	−0.632510	−	0.559282i
$341$	19.4314			1.05227
$342$			12.4060i			0.670838i
$343$	−10.7612			−0.581048
$344$		−	57.3644i		−	3.09288i
$345$	−4.61942	+	5.22425i	−0.248701	+	0.281264i
$346$		−	68.4504i		−	3.67992i
$347$		−	27.4944i		−	1.47598i	−0.674814	−	0.737988i	$-0.735776\pi$
$347$		−	27.4944i		−	1.47598i	0.674814	−	0.737988i	$-0.264224\pi$
$348$			6.00000i			0.321634i
$349$			17.6023i			0.942228i	0.882072	+	0.471114i	$0.156148\pi$
$349$			17.6023i			0.942228i	−0.882072	+	0.471114i	$0.843852\pi$
$350$	1.31994	+	10.7005i	0.0705540	+	0.571967i
$351$		0			0
$352$			58.6190i			3.12440i
$353$	15.7685			0.839270			0.419635	−	0.907693i	$-0.362158\pi$
$353$	15.7685			0.839270			0.419635	+	0.907693i	$0.362158\pi$
$354$	7.70782			0.409666
$355$	−14.3430	−	12.6824i	−0.761246	−	0.673113i
$356$		−	14.3127i		−	0.758569i
$357$	−0.523730			−0.0277187
$358$	−32.4387			−1.71444
$359$			14.8242i			0.782389i	0.920308	+	0.391195i	$0.127938\pi$
$359$			14.8242i			0.782389i	−0.920308	+	0.391195i	$0.872062\pi$
$360$	−34.6239	+	39.1573i	−1.82484	+	2.06377i
$361$	16.1939			0.852312
$362$	−7.30536			−0.383961
$363$			1.20616i			0.0633067i
$364$		0			0
$365$	17.4314	−	19.7137i	0.912399	−	1.03186i
$366$		−	2.27645i		−	0.118992i
$367$			27.0313i			1.41102i	0.708700	+	0.705510i	$0.249282\pi$
$367$			27.0313i			1.41102i	−0.708700	+	0.705510i	$0.750718\pi$
$368$		−	79.5569i		−	4.14719i
$369$			23.0132i			1.19802i
$370$	−14.9321	+	16.8872i	−0.776281	+	0.877922i
$371$			4.62530i			0.240134i
$372$	13.1187			0.680174
$373$			12.9525i			0.670657i	0.942101	+	0.335329i	$0.108847\pi$
$373$			12.9525i			0.670657i	−0.942101	+	0.335329i	$0.891153\pi$
$374$	13.2750			0.686436
$375$	−3.04349	+	4.43629i	−0.157165	+	0.229089i
$376$	−26.9683			−1.39078
$377$		0			0
$378$			5.98541i			0.307856i
$379$		−	30.2858i		−	1.55568i	−0.628463	−	0.777840i	$-0.716316\pi$
$379$		−	30.2858i		−	1.55568i	0.628463	−	0.777840i	$-0.283684\pi$
$380$	−14.4690	−	12.7938i	−0.742243	−	0.656310i
$381$	−2.06651			−0.105871
$382$	−55.1754			−2.82302
$383$	−21.0943			−1.07787			−0.538934	−	0.842348i	$-0.681173\pi$
$383$	−21.0943			−1.07787			−0.538934	+	0.842348i	$0.681173\pi$
$384$			7.97319i			0.406880i
$385$	−4.96239	−	4.38787i	−0.252907	−	0.223627i
$386$	−58.2882			−2.96679
$387$			18.8084i			0.956086i
$388$	9.66291			0.490560
$389$	−6.77575			−0.343544			−0.171772	−	0.985137i	$-0.554949\pi$
$389$	−6.77575			−0.343544			−0.171772	+	0.985137i	$0.554949\pi$
$390$		0			0
$391$	−8.75131			−0.442573
$392$	53.6190			2.70817
$393$			0.402462i			0.0203015i
$394$	5.35026			0.269542
$395$	3.35026	−	3.78892i	0.168570	−	0.190641i
$396$		−	52.4626i		−	2.63635i
$397$	10.4690			0.525423			0.262711	−	0.964874i	$-0.415383\pi$
$397$	10.4690			0.525423			0.262711	+	0.964874i	$0.415383\pi$
$398$	44.8119			2.24622
$399$	−0.649738			−0.0325276
$400$	−7.51388	−	60.9135i	−0.375694	−	3.04568i
$401$			5.01317i			0.250346i	0.992135	+	0.125173i	$0.0399486\pi$
$401$			5.01317i			0.250346i	−0.992135	+	0.125173i	$0.960051\pi$
$402$		−	12.7367i		−	0.635250i
$403$		0			0
$404$	−54.1378			−2.69345
$405$	10.3235	−	11.6751i	0.512977	−	0.580142i
$406$	5.21440			0.258787
$407$		−	13.8496i		−	0.686497i
$408$	5.48612			0.271603
$409$		−	14.3879i		−	0.711435i	−0.934594	−	0.355717i	$-0.884237\pi$
$409$		−	14.3879i		−	0.711435i	0.934594	−	0.355717i	$-0.115763\pi$
$410$	−37.2506	−	32.9380i	−1.83968	−	1.62669i
$411$			7.18806i			0.354561i
$412$		−	79.2443i		−	3.90408i
$413$		−	4.82653i		−	0.237498i
$414$			47.9995i			2.35905i
$415$	5.69323	−	6.43866i	0.279470	−	0.316061i
$416$		0			0
$417$		−	4.06063i		−	0.198850i
$418$	16.4690			0.805524
$419$	−17.4617			−0.853059			−0.426529	−	0.904474i	$-0.640264\pi$
$419$	−17.4617			−0.853059			−0.426529	+	0.904474i	$0.640264\pi$
$420$	−3.35026	−	2.96239i	−0.163476	−	0.144550i
$421$		−	2.88717i		−	0.140712i	−0.997522	−	0.0703559i	$-0.977586\pi$
$421$		−	2.88717i		−	0.140712i	0.997522	−	0.0703559i	$-0.0224135\pi$
$422$	13.1128			0.638323
$423$	8.84226			0.429925
$424$		−	48.4504i		−	2.35296i
$425$	−6.70052	+	0.826531i	−0.325023	+	0.0400927i
$426$	11.0219			0.534012
$427$	−1.42548			−0.0689840
$428$		−	57.3947i		−	2.77428i
$429$		0			0
$430$	−30.4445	−	26.9199i	−1.46817	−	1.29819i
$431$		−	0.889535i		−	0.0428474i	−0.999770	−	0.0214237i	$-0.993180\pi$
$431$		−	0.889535i		−	0.0428474i	0.999770	−	0.0214237i	$-0.00681990\pi$
$432$		−	34.0724i		−	1.63931i
$433$			25.2506i			1.21347i	0.794906	+	0.606733i	$0.207520\pi$
$433$			25.2506i			1.21347i	−0.794906	+	0.606733i	$0.792480\pi$
$434$		−	11.4010i		−	0.547268i
$435$	1.94921	+	1.72355i	0.0934577	+	0.0826377i
$436$			49.4372i			2.36761i
$437$	−10.8568			−0.519354
$438$			15.1490i			0.723849i
$439$	28.8119			1.37512			0.687560	−	0.726128i	$-0.258682\pi$
$439$	28.8119			1.37512			0.687560	+	0.726128i	$0.258682\pi$
$440$	51.9814	+	45.9633i	2.47812	+	2.19122i
$441$	−17.5804			−0.837162
$442$		0			0
$443$			36.9805i			1.75700i	0.477746	+	0.878498i	$0.341454\pi$
$443$			36.9805i			1.75700i	−0.477746	+	0.878498i	$0.658546\pi$
$444$		−	9.35026i		−	0.443744i
$445$	−4.64974	−	4.11142i	−0.220419	−	0.194900i
$446$	−66.6312			−3.15508
$447$	−5.46168			−0.258329
$448$	14.6048			0.690013
$449$			12.6859i			0.598686i	0.954146	+	0.299343i	$0.0967675\pi$
$449$			12.6859i			0.598686i	−0.954146	+	0.299343i	$0.903232\pi$
$450$	4.53339	+	36.7513i	0.213706	+	1.73247i
$451$	30.5501			1.43855
$452$			2.96239i			0.139339i
$453$	6.73084			0.316242
$454$	26.6312			1.24986
$455$		0			0
$456$	6.80606			0.318723
$457$	25.0494			1.17176			0.585880	−	0.810398i	$-0.300749\pi$
$457$	25.0494			1.17176			0.585880	+	0.810398i	$0.300749\pi$
$458$			14.3127i			0.668786i
$459$	−3.74798			−0.174941
$460$	−55.9814	−	49.5002i	−2.61015	−	2.30796i
$461$			36.8872i			1.71801i	0.511970	+	0.859003i	$0.328916\pi$
$461$			36.8872i			1.71801i	−0.511970	+	0.859003i	$0.671084\pi$
$462$	3.81336			0.177413
$463$	39.0191			1.81337			0.906685	−	0.421809i	$-0.138605\pi$
$463$	39.0191			1.81337			0.906685	+	0.421809i	$0.138605\pi$
$464$	−29.6834			−1.37802
$465$	3.76845	−	4.26187i	0.174758	−	0.197639i
$466$		−	28.7875i		−	1.33356i
$467$			32.7694i			1.51639i	0.652029	+	0.758194i	$0.273918\pi$
$467$			32.7694i			1.51639i	−0.652029	+	0.758194i	$0.726082\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	−12.6556	+	14.3127i	−0.583760	+	0.660193i
$471$	−1.33567			−0.0615446
$472$			50.5583i			2.32714i
$473$	24.9683			1.14804
$474$			2.91160i			0.133734i
$475$	−8.31265	+	1.02539i	−0.381411	+	0.0470482i
$476$		−	5.61213i		−	0.257231i
$477$			15.8858i			0.727359i
$478$			31.7318i			1.45138i
$479$		−	16.8749i		−	0.771036i	−0.922700	−	0.385518i	$-0.874023\pi$
$479$		−	16.8749i		−	0.771036i	0.922700	−	0.385518i	$-0.125977\pi$
$480$	12.8568	+	11.3684i	0.586832	+	0.518892i
$481$		0			0
$482$			76.5764i			3.48796i
$483$	−2.51388			−0.114386
$484$	−12.9248			−0.587490
$485$	2.77575	−	3.13918i	0.126040	−	0.142543i
$486$			31.2482i			1.41745i
$487$	9.24472			0.418918			0.209459	−	0.977817i	$-0.432830\pi$
$487$	9.24472			0.418918			0.209459	+	0.977817i	$0.432830\pi$
$488$	14.9321			0.675943
$489$			1.07381i			0.0485593i
$490$	25.1622	−	28.4568i	1.13671	−	1.28555i
$491$	25.7499			1.16208			0.581038	−	0.813876i	$-0.302647\pi$
$491$	25.7499			1.16208			0.581038	+	0.813876i	$0.302647\pi$
$492$	20.6253			0.929860
$493$			3.26519i			0.147057i
$494$		0			0
$495$	−17.0435	−	15.0703i	−0.766048	−	0.677360i
$496$			64.9013i			2.91415i
$497$		−	6.90175i		−	0.309586i
$498$			4.94780i			0.221716i
$499$		−	27.7015i		−	1.24009i	−0.784567	−	0.620044i	$-0.787115\pi$
$499$		−	27.7015i		−	1.24009i	0.784567	−	0.620044i	$-0.212885\pi$
$500$	−47.5379	−	32.6131i	−2.12596	−	1.45850i
$501$			7.55149i			0.337376i
$502$	−51.8613			−2.31468
$503$			2.35519i			0.105013i	0.998621	+	0.0525063i	$0.0167210\pi$
$503$			2.35519i			0.105013i	−0.998621	+	0.0525063i	$0.983279\pi$
$504$	−18.8423			−0.839301
$505$	−15.5515	+	17.5877i	−0.692032	+	0.782642i
$506$	63.7196			2.83268
$507$		0			0
$508$		−	22.1441i		−	0.982486i
$509$			21.5125i			0.953523i	0.879033	+	0.476762i	$0.158190\pi$
$509$			21.5125i			0.953523i	−0.879033	+	0.476762i	$0.841810\pi$
$510$	2.57452	−	2.91160i	0.114001	−	0.128928i
$511$	9.48612			0.419641
$512$	11.5017			0.508306
$513$	−4.64974			−0.205291
$514$		−	61.1608i		−	2.69769i
$515$	−25.7440	−	22.7635i	−1.13442	−	1.00308i
$516$	16.8568			0.742081
$517$		−	11.7381i		−	0.516243i
$518$	−8.12601			−0.357036
$519$	12.3127			0.540465
$520$		0			0
$521$	37.7440			1.65360			0.826798	−	0.562499i	$-0.190160\pi$
$521$	37.7440			1.65360			0.826798	+	0.562499i	$0.190160\pi$
$522$	17.9090			0.783858
$523$			23.7416i			1.03815i	0.854729	+	0.519075i	$0.173723\pi$
$523$			23.7416i			1.03815i	−0.854729	+	0.519075i	$0.826277\pi$
$524$	−4.31265			−0.188399
$525$	−1.92478	+	0.237428i	−0.0840042	+	0.0103622i
$526$		−	58.5379i		−	2.55237i
$527$	7.13918			0.310988
$528$	−21.7078			−0.944712
$529$	−19.0059			−0.826343
$530$	−25.7137	−	22.7367i	−1.11693	−	0.987620i
$531$		−	16.5769i		−	0.719376i
$532$		−	6.96239i		−	0.301858i
$533$		0			0
$534$	3.57310			0.154623
$535$	−18.6458	−	16.4871i	−0.806127	−	0.712798i
$536$	83.5447			3.60858
$537$		−	5.83497i		−	0.251797i
$538$	60.8627			2.62398
$539$			23.3380i			1.00524i
$540$	−23.9756	−	21.1998i	−1.03174	−	0.912295i
$541$			13.0376i			0.560531i	0.959923	+	0.280265i	$0.0904225\pi$
$541$			13.0376i			0.560531i	−0.959923	+	0.280265i	$0.909578\pi$
$542$		−	0.330749i		−	0.0142069i
$543$		−	1.31406i		−	0.0563919i
$544$			21.5369i			0.923387i
$545$	16.0606	+	14.2012i	0.687962	+	0.608314i
$546$		0			0
$547$		−	8.43041i		−	0.360458i	−0.983625	−	0.180229i	$-0.942316\pi$
$547$		−	8.43041i		−	0.360458i	0.983625	−	0.180229i	$-0.0576839\pi$
$548$	−77.0249			−3.29034
$549$	−4.89587			−0.208951
$550$	48.7875	−	6.01810i	2.08031	−	0.256613i
$551$			4.05079i			0.172569i
$552$	26.3331			1.12081
$553$	1.82321			0.0775306
$554$			41.0640i			1.74464i
$555$	−3.03761	−	2.68594i	−0.128939	−	0.114012i
$556$	43.5125			1.84534
$557$	13.6932			0.580201			0.290100	−	0.956996i	$-0.406311\pi$
$557$	13.6932			0.580201			0.290100	+	0.956996i	$0.406311\pi$
$558$		−	39.1573i		−	1.65766i
$559$		0			0
$560$	14.6556	−	16.5745i	0.619313	−	0.700401i
$561$			2.38787i			0.100816i
$562$		−	37.2506i		−	1.57132i
$563$			8.86907i			0.373787i	0.982380	+	0.186893i	$0.0598419\pi$
$563$			8.86907i			0.373787i	−0.982380	+	0.186893i	$0.940158\pi$
$564$		−	7.92478i		−	0.333693i
$565$	0.962389	+	0.850969i	0.0404880	+	0.0358005i
$566$			54.5233i			2.29178i
$567$	5.61801			0.235934
$568$			72.2965i			3.03349i
$569$	−32.7816			−1.37428			−0.687139	−	0.726526i	$-0.741134\pi$
$569$	−32.7816			−1.37428			−0.687139	+	0.726526i	$0.741134\pi$
$570$	3.19394	−	3.61213i	0.133779	−	0.151295i
$571$	−40.2882			−1.68601			−0.843005	−	0.537906i	$-0.819215\pi$
$571$	−40.2882			−1.68601			−0.843005	+	0.537906i	$0.819215\pi$
$572$		0			0
$573$		−	9.92478i		−	0.414614i
$574$		−	17.9248i		−	0.748166i
$575$	−32.1622	+	3.96731i	−1.34126	+	0.165448i
$576$	50.1608			2.09003
$577$	−28.8568			−1.20133			−0.600663	−	0.799502i	$-0.705097\pi$
$577$	−28.8568			−1.20133			−0.600663	+	0.799502i	$0.705097\pi$
$578$	−40.5999			−1.68873
$579$		−	10.4847i		−	0.435729i
$580$	−18.4690	+	20.8872i	−0.766882	+	0.867292i
$581$	3.09825			0.128537
$582$			2.41231i			0.0999935i
$583$	21.0884			0.873392
$584$	−99.3679			−4.11187
$585$		0			0
$586$	14.3938			0.594600
$587$	−41.6786			−1.72026			−0.860131	−	0.510074i	$-0.829618\pi$
$587$	−41.6786			−1.72026			−0.860131	+	0.510074i	$0.829618\pi$
$588$			15.7562i			0.649776i
$589$	8.85685			0.364940
$590$	26.8324	+	23.7259i	1.10467	+	0.976781i
$591$			0.962389i			0.0395874i
$592$	46.2579			1.90119
$593$	−22.4993			−0.923935			−0.461968	−	0.886897i	$-0.652856\pi$
$593$	−22.4993			−0.923935			−0.461968	+	0.886897i	$0.652856\pi$
$594$	27.2896			1.11971
$595$	−1.82321	−	1.61213i	−0.0747442	−	0.0660908i
$596$		−	58.5256i		−	2.39730i
$597$			8.06063i			0.329900i
$598$		0			0
$599$	−4.15045			−0.169583			−0.0847913	−	0.996399i	$-0.527022\pi$
$599$	−4.15045			−0.169583			−0.0847913	+	0.996399i	$0.527022\pi$
$600$	20.1622	−	2.48707i	0.823119	−	0.101534i
$601$	27.9248			1.13908			0.569538	−	0.821965i	$-0.307122\pi$
$601$	27.9248			1.13908			0.569538	+	0.821965i	$0.307122\pi$
$602$		−	14.6497i		−	0.597079i
$603$	−27.3923			−1.11550
$604$			72.1255i			2.93475i
$605$	−3.71274	+	4.19886i	−0.150944	+	0.170708i
$606$		−	13.5153i		−	0.549021i
$607$		−	8.19489i		−	0.332620i	−0.986073	−	0.166310i	$-0.946815\pi$
$607$		−	8.19489i		−	0.332620i	0.986073	−	0.166310i	$-0.0531853\pi$
$608$			26.7186i			1.08358i
$609$			0.937951i			0.0380077i
$610$	7.00729	−	7.92478i	0.283717	−	0.320865i
$611$		0			0
$612$		−	19.2750i		−	0.779147i
$613$	33.1392			1.33848			0.669239	−	0.743047i	$-0.266620\pi$
$613$	33.1392			1.33848			0.669239	+	0.743047i	$0.266620\pi$
$614$	51.2809			2.06953
$615$	5.92478	−	6.70052i	0.238910	−	0.270191i
$616$			25.0132i			1.00781i
$617$	29.0132			1.16803			0.584013	−	0.811744i	$-0.301482\pi$
$617$	29.0132			1.16803			0.584013	+	0.811744i	$0.301482\pi$
$618$	19.7830			0.795791
$619$		−	12.2134i		−	0.490900i	−0.969409	−	0.245450i	$-0.921064\pi$
$619$		−	12.2134i		−	0.490900i	0.969409	−	0.245450i	$-0.0789357\pi$
$620$	45.6688	+	40.3815i	1.83410	+	1.62176i
$621$	−17.9902			−0.721920
$622$	−67.5487			−2.70845
$623$		−	2.23743i		−	0.0896406i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$		−	7.52232i		−	0.300652i
$627$			2.96239i			0.118306i
$628$		−	14.3127i		−	0.571137i
$629$		−	5.08840i		−	0.202888i
$630$	−8.84226	+	10.0000i	−0.352284	+	0.398410i
$631$		−	1.22188i		−	0.0486424i	−0.999704	−	0.0243212i	$-0.992258\pi$
$631$		−	1.22188i		−	0.0486424i	0.999704	−	0.0243212i	$-0.00774245\pi$
$632$	−19.0982			−0.759687
$633$			2.35870i			0.0937498i
$634$	−63.5837			−2.52523
$635$	−7.19394	−	6.36107i	−0.285483	−	0.252431i
$636$	14.2374			0.564551
$637$		0			0
$638$		−	23.7743i		−	0.941235i
$639$		−	23.7043i		−	0.937728i
$640$	−24.5428	+	27.7562i	−0.970139	+	1.09716i
$641$	22.1016			0.872960			0.436480	−	0.899714i	$-0.356225\pi$
$641$	22.1016			0.872960			0.436480	+	0.899714i	$0.356225\pi$
$642$	14.3284			0.565496
$643$	11.6688			0.460172			0.230086	−	0.973170i	$-0.426099\pi$
$643$	11.6688			0.460172			0.230086	+	0.973170i	$0.426099\pi$
$644$		−	26.9380i		−	1.06150i
$645$	4.84226	−	5.47627i	0.190664	−	0.215628i
$646$	6.05079			0.238065
$647$			11.9575i			0.470096i	0.971984	+	0.235048i	$0.0755248\pi$
$647$			11.9575i			0.470096i	−0.971984	+	0.235048i	$0.924475\pi$
$648$	−58.8491			−2.31181
$649$	−22.0059			−0.863806
$650$		0			0
$651$	2.05079			0.0803766
$652$	−11.5066			−0.450633
$653$		−	10.9986i		−	0.430408i	−0.976569	−	0.215204i	$-0.930958\pi$
$653$		−	10.9986i		−	0.430408i	0.976569	−	0.215204i	$-0.0690416\pi$
$654$	−12.3418			−0.482604
$655$	−1.23884	+	1.40105i	−0.0484056	+	0.0547434i
$656$			102.038i			3.98392i
$657$	32.5804			1.27108
$658$	−6.88717			−0.268490
$659$	2.63989			0.102835			0.0514177	−	0.998677i	$-0.483626\pi$
$659$	2.63989			0.102835			0.0514177	+	0.998677i	$0.483626\pi$
$660$	−13.5066	+	15.2750i	−0.525743	+	0.594580i
$661$			18.3028i			0.711896i	0.934506	+	0.355948i	$0.115842\pi$
$661$			18.3028i			0.711896i	−0.934506	+	0.355948i	$0.884158\pi$
$662$		−	31.5696i		−	1.22699i
$663$		0			0
$664$	−32.4544			−1.25947
$665$	−2.26187	−	2.00000i	−0.0877114	−	0.0775567i
$666$	−27.9090			−1.08145
$667$			15.6728i			0.606852i
$668$	−80.9194			−3.13087
$669$		−	11.9854i		−	0.463383i
$670$	39.2057	−	44.3390i	1.51465	−	1.71296i
$671$			6.49929i			0.250902i
$672$			6.18664i			0.238655i
$673$		−	6.71037i		−	0.258666i	−0.991601	−	0.129333i	$-0.958716\pi$
$673$		−	6.71037i		−	0.258666i	0.991601	−	0.129333i	$-0.0412836\pi$
$674$		−	43.1002i		−	1.66016i
$675$	−13.7743	+	1.69911i	−0.530174	+	0.0653987i
$676$		0			0
$677$			1.57593i			0.0605679i	0.999541	+	0.0302840i	$0.00964116\pi$
$677$			1.57593i			0.0605679i	−0.999541	+	0.0302840i	$0.990359\pi$
$678$	−0.739549			−0.0284022
$679$	1.51056			0.0579698
$680$	19.0982	+	16.8872i	0.732384	+	0.647593i
$681$			4.79033i			0.183566i
$682$	−51.9814			−1.99047
$683$	−15.1939			−0.581380			−0.290690	−	0.956817i	$-0.593885\pi$
$683$	−15.1939			−0.581380			−0.290690	+	0.956817i	$0.593885\pi$
$684$		−	23.9126i		−	0.914320i
$685$	−22.1260	+	25.0230i	−0.845391	+	0.956081i
$686$	28.7875			1.09911
$687$	−2.57452			−0.0982239
$688$			83.3947i			3.17939i
$689$		0			0
$690$	12.3576	−	13.9756i	0.470444	−	0.532041i
$691$			18.7127i			0.711866i	0.934511	+	0.355933i	$0.115837\pi$
$691$			18.7127i			0.711866i	−0.934511	+	0.355933i	$0.884163\pi$
$692$			131.938i			5.01555i
$693$		−	8.20123i		−	0.311539i
$694$			73.5510i			2.79196i
$695$	12.4993	−	14.1359i	0.474125	−	0.536204i
$696$		−	9.82512i		−	0.372420i
$697$	11.2243			0.425149
$698$		−	47.0884i		−	1.78232i
$699$	5.17821			0.195858
$700$	−2.54420	−	20.6253i	−0.0961617	−	0.779563i
$701$	−24.3028			−0.917904			−0.458952	−	0.888461i	$-0.651775\pi$
$701$	−24.3028			−0.917904			−0.458952	+	0.888461i	$0.651775\pi$
$702$		0			0
$703$		−	6.31265i		−	0.238086i
$704$		−	66.5886i		−	2.50965i
$705$	−2.57452	−	2.27645i	−0.0969619	−	0.0857362i
$706$	−42.1827			−1.58757
$707$	−8.46310			−0.318287
$708$	−14.8568			−0.558355
$709$			9.66291i			0.362898i	0.983400	+	0.181449i	$0.0580788\pi$
$709$			9.66291i			0.362898i	−0.983400	+	0.181449i	$0.941921\pi$
$710$	38.3693	+	33.9271i	1.43997	+	1.27326i
$711$	6.26187			0.234838
$712$			23.4372i			0.878348i
$713$	34.2677			1.28334
$714$	1.40105			0.0524329
$715$		0			0
$716$	62.5256			2.33669
$717$	−5.70782			−0.213162
$718$		−	39.6566i		−	1.47997i
$719$	28.4142			1.05967			0.529836	−	0.848100i	$-0.322254\pi$
$719$	28.4142			1.05967			0.529836	+	0.848100i	$0.322254\pi$
$720$	50.3352	−	56.9257i	1.87588	−	2.12150i
$721$		−	12.3879i		−	0.461349i
$722$	−43.3209			−1.61224
$723$	−13.7743			−0.512273
$724$	14.0811			0.523320
$725$	1.48024	+	12.0000i	0.0549747	+	0.445669i
$726$		−	3.22662i		−	0.119751i
$727$		−	34.8545i		−	1.29268i	−0.763049	−	0.646341i	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		0			0
$729$	15.2882			0.566230
$730$	−46.6312	+	52.7367i	−1.72590	+	1.95187i
$731$	9.17347			0.339293
$732$			4.38787i			0.162180i
$733$	6.25202			0.230923			0.115462	−	0.993312i	$-0.463165\pi$
$733$	6.25202			0.230923			0.115462	+	0.993312i	$0.463165\pi$
$734$		−	72.3122i		−	2.66909i
$735$	5.11871	+	4.52610i	0.188807	+	0.166948i
$736$			103.376i			3.81050i
$737$			36.3634i			1.33946i
$738$		−	61.5633i		−	2.26617i
$739$			32.0846i			1.18025i	0.807311	+	0.590126i	$0.200922\pi$
$739$			32.0846i			1.18025i	−0.807311	+	0.590126i	$0.799078\pi$
$740$	28.7816	−	32.5501i	1.05803	−	1.19656i
$741$		0			0
$742$		−	12.3733i		−	0.454238i
$743$	−30.5442			−1.12056			−0.560279	−	0.828304i	$-0.689306\pi$
$743$	−30.5442			−1.12056			−0.560279	+	0.828304i	$0.689306\pi$
$744$	−21.4821			−0.787574
$745$	−19.0132	−	16.8119i	−0.696589	−	0.615942i
$746$		−	34.6497i		−	1.26862i
$747$	10.6410			0.389335
$748$	−25.5877			−0.935579
$749$		−	8.97224i		−	0.327838i
$750$	8.14174	−	11.8677i	0.297294	−	0.433345i
$751$	−28.1622			−1.02765			−0.513827	−	0.857894i	$-0.671773\pi$
$751$	−28.1622			−1.02765			−0.513827	+	0.857894i	$0.671773\pi$
$752$	39.2057			1.42968
$753$		−	9.32865i		−	0.339955i
$754$		0			0
$755$	23.4314	+	20.7186i	0.852755	+	0.754028i
$756$		−	11.5369i		−	0.419593i
$757$		−	35.4109i		−	1.28703i	−0.765433	−	0.643515i	$-0.777475\pi$
$757$		−	35.4109i		−	1.28703i	0.765433	−	0.643515i	$-0.222525\pi$
$758$			81.0186i			2.94273i
$759$			11.4617i			0.416033i
$760$	23.6932	+	20.9502i	0.859444	+	0.759943i
$761$		−	19.2388i		−	0.697407i	−0.937233	−	0.348704i	$-0.886622\pi$
$761$		−	19.2388i		−	0.697407i	0.937233	−	0.348704i	$-0.113378\pi$
$762$	5.52820			0.200265
$763$			7.72829i			0.279783i
$764$	106.351			3.84764
$765$	−6.26187	−	5.53690i	−0.226398	−	0.200187i
$766$	56.4299			2.03890
$767$		0			0
$768$		−	3.89209i		−	0.140444i
$769$			48.9643i			1.76570i	0.469657	+	0.882849i	$0.344378\pi$
$769$			48.9643i			1.76570i	−0.469657	+	0.882849i	$0.655622\pi$
$770$	13.2750	+	11.7381i	0.478399	+	0.423013i
$771$	11.0014			0.396206
$772$	112.351			4.04359
$773$	46.1681			1.66055			0.830275	−	0.557354i	$-0.188183\pi$
$773$	46.1681			1.66055			0.830275	+	0.557354i	$0.188183\pi$
$774$		−	50.3150i		−	1.80854i
$775$	26.2374	−	3.23647i	0.942476	−	0.116258i
$776$	−15.8232			−0.568020
$777$		−	1.46168i		−	0.0524375i
$778$	18.1260			0.649849
$779$	13.9248			0.498907
$780$		0			0
$781$	−31.4676			−1.12600
$782$	23.4109			0.837172
$783$			6.71228i			0.239877i
$784$	−77.9497			−2.78392
$785$	−4.64974	−	4.11142i	−0.165956	−	0.146743i
$786$		−	1.07664i		−	0.0384024i
$787$	−22.6458			−0.807234			−0.403617	−	0.914928i	$-0.632247\pi$
$787$	−22.6458			−0.807234			−0.403617	+	0.914928i	$0.632247\pi$
$788$	−10.3127			−0.367373
$789$	10.5296			0.374864
$790$	−8.96239	+	10.1359i	−0.318867	+	0.360618i
$791$			0.463096i			0.0164658i
$792$			85.9086i			3.05263i
$793$		0			0
$794$	−28.0059			−0.993891
$795$	4.08981	−	4.62530i	0.145051	−	0.164043i
$796$	−86.3752			−3.06149
$797$			8.23743i			0.291785i	0.989300	+	0.145892i	$0.0466053\pi$
$797$			8.23743i			0.291785i	−0.989300	+	0.145892i	$0.953395\pi$
$798$	1.73813			0.0615293
$799$		−	4.31265i		−	0.152571i
$800$	9.76353	+	79.1509i	0.345193	+	2.79841i
$801$		−	7.68452i		−	0.271519i
$802$		−	13.4109i		−	0.473555i
$803$		−	43.2506i		−	1.52628i
$804$			24.5501i			0.865814i
$805$	−8.75131	−	7.73813i	−0.308443	−	0.272733i
$806$		0			0
$807$			10.9478i			0.385381i
$808$	88.6516			3.11875
$809$	−44.1319			−1.55159			−0.775797	−	0.630982i	$-0.782652\pi$
$809$	−44.1319			−1.55159			−0.775797	+	0.630982i	$0.782652\pi$
$810$	−27.6166	+	31.2325i	−0.970348	+	1.09740i
$811$		−	22.6883i		−	0.796694i	−0.917235	−	0.398347i	$-0.869584\pi$
$811$		−	22.6883i		−	0.796694i	0.917235	−	0.398347i	$-0.130416\pi$
$812$	−10.0508			−0.352713
$813$	0.0594941			0.00208655
$814$			37.0494i			1.29858i
$815$	−3.30536	+	3.73813i	−0.115782	+	0.130941i
$816$	−7.97556			−0.279201
$817$	11.3806			0.398156
$818$			38.4894i			1.34575i
$819$		0			0
$820$	71.8007	+	63.4880i	2.50739	+	2.21710i
$821$			50.2736i			1.75456i	0.479978	+	0.877281i	$0.340645\pi$
$821$			50.2736i			1.75456i	−0.479978	+	0.877281i	$0.659355\pi$
$822$		−	19.2290i		−	0.670688i
$823$		−	5.13093i		−	0.178853i	−0.995993	−	0.0894265i	$-0.971497\pi$
$823$		−	5.13093i		−	0.178853i	0.995993	−	0.0894265i	$-0.0285034\pi$
$824$			129.764i			4.52054i
$825$	1.08252	+	8.77575i	0.0376884	+	0.305532i
$826$			12.9116i			0.449252i
$827$	18.6946			0.650076			0.325038	−	0.945701i	$-0.394623\pi$
$827$	18.6946			0.650076			0.325038	+	0.945701i	$0.394623\pi$
$828$		−	92.5193i		−	3.21527i
$829$	−3.44121			−0.119518			−0.0597591	−	0.998213i	$-0.519033\pi$
$829$	−3.44121			−0.119518			−0.0597591	+	0.998213i	$0.519033\pi$
$830$	−15.2301	+	17.2243i	−0.528646	+	0.597863i
$831$	−7.38646			−0.256233
$832$		0			0
$833$			8.57452i			0.297089i
$834$			10.8627i			0.376146i
$835$	−23.2447	+	26.2882i	−0.804417	+	0.909741i
$836$	−31.7440			−1.09789
$837$	14.6761			0.507280
$838$	46.7123			1.61365
$839$			52.6248i			1.81681i	0.418090	+	0.908406i	$0.362700\pi$
$839$			52.6248i			1.81681i	−0.418090	+	0.908406i	$0.637300\pi$
$840$	5.48612	+	4.85097i	0.189289	+	0.167374i
$841$	−23.1524			−0.798357
$842$			7.72355i			0.266171i
$843$	6.70052			0.230778
$844$	−25.2750			−0.870003
$845$		0			0
$846$	−23.6542			−0.813248
$847$	−2.02047			−0.0694241
$848$			70.4358i			2.41878i
$849$	−9.80748			−0.336592
$850$	17.9248	−	2.21108i	0.614815	−	0.0758394i
$851$		−	24.4241i		−	0.837246i
$852$	−21.2447			−0.727832
$853$	6.31853			0.216342			0.108171	−	0.994132i	$-0.465501\pi$
$853$	6.31853			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$854$	3.81336			0.130490
$855$	−7.76845	−	6.86907i	−0.265675	−	0.234917i
$856$			93.9850i			3.21234i
$857$		−	0.775746i		−	0.0264990i	−0.999912	−	0.0132495i	$-0.995782\pi$
$857$		−	0.775746i		−	0.0264990i	0.999912	−	0.0132495i	$-0.00421757\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	58.6820	+	51.8881i	2.00104	+	1.76937i
$861$	3.22425			0.109882
$862$			2.37962i			0.0810503i
$863$	−19.9208			−0.678112			−0.339056	−	0.940766i	$-0.610108\pi$
$863$	−19.9208			−0.678112			−0.339056	+	0.940766i	$0.610108\pi$
$864$			44.2736i			1.50622i
$865$	42.8627	+	37.9003i	1.45738	+	1.28865i
$866$		−	67.5487i		−	2.29540i
$867$		−	7.30299i		−	0.248022i
$868$			21.9756i			0.745899i
$869$		−	8.31265i		−	0.281987i
$870$	−5.21440	−	4.61071i	−0.176785	−	0.156318i
$871$		0			0
$872$		−	80.9544i		−	2.74146i
$873$	5.18806			0.175589
$874$	29.0435			0.982411
$875$	−7.43136	−	5.09825i	−0.251226	−	0.172352i
$876$		−	29.1998i		−	0.986570i
$877$	−22.1378			−0.747539			−0.373770	−	0.927522i	$-0.621935\pi$
$877$	−22.1378			−0.747539			−0.373770	+	0.927522i	$0.621935\pi$
$878$	−77.0757			−2.60118
$879$			2.58910i			0.0873283i
$880$	−75.5691	−	66.8202i	−2.54743	−	2.25251i
$881$	−2.23155			−0.0751828			−0.0375914	−	0.999293i	$-0.511969\pi$
$881$	−2.23155			−0.0751828			−0.0375914	+	0.999293i	$0.511969\pi$
$882$	47.0299			1.58358
$883$			4.30440i			0.144855i	0.997374	+	0.0724273i	$0.0230745\pi$
$883$			4.30440i			0.144855i	−0.997374	+	0.0724273i	$0.976925\pi$
$884$		0			0
$885$	−4.26774	+	4.82653i	−0.143459	+	0.162242i
$886$		−	98.9276i		−	3.32354i
$887$		−	15.9330i		−	0.534979i	−0.963561	−	0.267489i	$-0.913806\pi$
$887$		−	15.9330i		−	0.534979i	0.963561	−	0.267489i	$-0.0861940\pi$
$888$			15.3112i			0.513811i
$889$		−	3.46168i		−	0.116101i
$890$	12.4387	+	10.9986i	0.416945	+	0.368673i
$891$		−	25.6145i		−	0.858118i
$892$	128.432			4.30022
$893$		−	5.35026i		−	0.179040i
$894$	14.6107			0.488655
$895$	17.9610	−	20.3127i	0.600369	−	0.678977i
$896$	−13.3561			−0.446197
$897$		0			0
$898$		−	33.9365i		−	1.13248i
$899$		−	12.7856i		−	0.426423i
$900$	−8.73813	−	70.8383i	−0.291271	−	2.36128i
$901$	7.74798			0.258123
$902$	−81.7255			−2.72116
$903$	2.63515			0.0876923
$904$		−	4.85097i		−	0.161341i
$905$	4.04491	−	4.57452i	0.134457	−	0.152062i
$906$	−18.0059			−0.598205
$907$		−	51.9086i		−	1.72360i	−0.507251	−	0.861798i	$-0.669338\pi$
$907$		−	51.9086i		−	1.72360i	0.507251	−	0.861798i	$-0.330662\pi$
$908$	−51.3317			−1.70350
$909$	−29.0668			−0.964085
$910$		0			0
$911$	−9.67750			−0.320630			−0.160315	−	0.987066i	$-0.551251\pi$
$911$	−9.67750			−0.320630			−0.160315	+	0.987066i	$0.551251\pi$
$912$	−9.89446			−0.327638
$913$		−	14.1260i		−	0.467503i
$914$	−67.0103			−2.21651
$915$	1.42548	+	1.26045i	0.0471251	+	0.0416692i
$916$		−	27.5877i		−	0.911523i
$917$	−0.674176			−0.0222632
$918$	10.0263			0.330919
$919$	−13.5515			−0.447022			−0.223511	−	0.974701i	$-0.571752\pi$
$919$	−13.5515			−0.447022			−0.223511	+	0.974701i	$0.571752\pi$
$920$	91.6707	+	81.0576i	3.02229	+	2.67239i
$921$			9.22425i			0.303949i
$922$		−	98.6780i		−	3.24979i
$923$		0			0
$924$	−7.35026			−0.241806
$925$	−2.30677	−	18.7005i	−0.0758462	−	0.614869i
$926$	−104.381			−3.43017
$927$		−	42.5466i		−	1.39741i
$928$	38.5705			1.26614
$929$		−	9.44992i		−	0.310042i	−0.987911	−	0.155021i	$-0.950455\pi$
$929$		−	9.44992i		−	0.310042i	0.987911	−	0.155021i	$-0.0495445\pi$
$930$	−10.0811	+	11.4010i	−0.330572	+	0.373855i
$931$			10.6375i			0.348631i
$932$			55.4880i			1.81757i
$933$		−	12.1504i		−	0.397788i
$934$		−	87.6625i		−	2.86840i
$935$	−7.35026	+	8.31265i	−0.240379	+	0.271853i
$936$		0			0
$937$		−	16.0409i		−	0.524035i	−0.965063	−	0.262017i	$-0.915612\pi$
$937$		−	16.0409i		−	0.524035i	0.965063	−	0.262017i	$-0.0843877\pi$
$938$	21.3357			0.696634
$939$	1.35309			0.0441565
$940$	24.3938	−	27.5877i	0.795636	−	0.899811i
$941$			21.6747i			0.706574i	0.935515	+	0.353287i	$0.114936\pi$
$941$			21.6747i			0.706574i	−0.935515	+	0.353287i	$0.885064\pi$
$942$	3.57310			0.116418
$943$	53.8759			1.75444
$944$		−	73.5002i		−	2.39223i
$945$	−3.74798	−	3.31406i	−0.121922	−	0.107807i
$946$	−66.7934			−2.17164
$947$	−4.63118			−0.150493			−0.0752466	−	0.997165i	$-0.523974\pi$
$947$	−4.63118			−0.150493			−0.0752466	+	0.997165i	$0.523974\pi$
$948$		−	5.61213i		−	0.182273i
$949$		0			0
$950$	22.2374	−	2.74306i	0.721477	−	0.0889966i
$951$		−	11.4372i		−	0.370878i
$952$			9.18997i			0.297849i
$953$		−	26.2981i		−	0.851878i	−0.904752	−	0.425939i	$-0.859944\pi$
$953$		−	26.2981i		−	0.851878i	0.904752	−	0.425939i	$-0.140056\pi$
$954$		−	42.4965i		−	1.37587i
$955$	30.5501	−	34.5501i	0.988577	−	1.11801i
$956$		−	61.1632i		−	1.97816i
$957$	4.27645			0.138238
$958$			45.1427i			1.45849i
$959$	−12.0409			−0.388822
$960$	−14.6048	−	12.9140i	−0.471369	−	0.416797i
$961$	3.04491			0.0982228
$962$		0			0
$963$		−	30.8155i		−	0.993014i
$964$		−	147.601i		−	4.75392i
$965$	32.2736	−	36.4993i	1.03892	−	1.17495i
$966$	6.72496			0.216372
$967$	11.9405			0.383981			0.191990	−	0.981397i	$-0.438506\pi$
$967$	11.9405			0.383981			0.191990	+	0.981397i	$0.438506\pi$
$968$	21.1646			0.680255
$969$			1.08840i			0.0349643i
$970$	−7.42548	+	8.39772i	−0.238418	+	0.269635i
$971$	30.1524			0.967635			0.483818	−	0.875169i	$-0.339250\pi$
$971$	30.1524			0.967635			0.483818	+	0.875169i	$0.339250\pi$
$972$		−	60.2311i		−	1.93191i
$973$	6.80209			0.218065
$974$	−24.7308			−0.792427
$975$		0			0
$976$	−21.7078			−0.694850
$977$	−26.9321			−0.861633			−0.430817	−	0.902439i	$-0.641774\pi$
$977$	−26.9321			−0.861633			−0.430817	+	0.902439i	$0.641774\pi$
$978$		−	2.87258i		−	0.0918549i
$979$	−10.2012			−0.326033
$980$	−48.5002	+	54.8505i	−1.54928	+	1.75214i
$981$			26.5431i			0.847455i
$982$	−68.8843			−2.19819
$983$	20.5902			0.656727			0.328363	−	0.944551i	$-0.393503\pi$
$983$	20.5902			0.656727			0.328363	+	0.944551i	$0.393503\pi$
$984$	−33.7743			−1.07669
$985$	−2.96239	+	3.35026i	−0.0943895	+	0.106748i
$986$		−	8.73481i		−	0.278173i
$987$		−	1.23884i		−	0.0394328i
$988$		0			0
$989$	44.0322			1.40014
$990$	45.5936	+	40.3150i	1.44906	+	1.28130i
$991$	−48.1378			−1.52915			−0.764573	−	0.644537i	$-0.777050\pi$
$991$	−48.1378			−1.52915			−0.764573	+	0.644537i	$0.777050\pi$
$992$		−	84.3327i		−	2.67756i
$993$	5.67864			0.180206
$994$			18.4631i			0.585614i
$995$	−24.8119	+	28.0606i	−0.786591	+	0.889582i
$996$		−	9.53690i		−	0.302188i
$997$		−	33.4255i		−	1.05860i	−0.848436	−	0.529298i	$-0.822455\pi$
$997$		−	33.4255i		−	1.05860i	0.848436	−	0.529298i	$-0.177545\pi$
$998$			74.1051i			2.34576i
$999$		−	10.4603i		−	0.330948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.a.844.1		6
5.4	even	2		845.2.d.b.844.6		6
13.2	odd	12		845.2.n.g.529.1		12
13.3	even	3		845.2.l.e.654.6		12
13.4	even	6		845.2.l.d.699.1		12
13.5	odd	4		845.2.b.c.339.6		6
13.6	odd	12		845.2.n.g.484.6		12
13.7	odd	12		845.2.n.f.484.1		12
13.8	odd	4		65.2.b.a.14.1	✓	6
13.9	even	3		845.2.l.e.699.5		12
13.10	even	6		845.2.l.d.654.2		12
13.11	odd	12		845.2.n.f.529.6		12
13.12	even	2		845.2.d.b.844.5		6
39.8	even	4		585.2.c.b.469.6		6
52.47	even	4		1040.2.d.c.209.4		6
65.4	even	6		845.2.l.e.699.6		12
65.8	even	4		325.2.a.j.1.1		3
65.9	even	6		845.2.l.d.699.2		12
65.18	even	4		4225.2.a.bh.1.3		3
65.19	odd	12		845.2.n.g.484.1		12
65.24	odd	12		845.2.n.f.529.1		12
65.29	even	6		845.2.l.d.654.1		12
65.34	odd	4		65.2.b.a.14.6	yes	6
65.44	odd	4		845.2.b.c.339.1		6
65.47	even	4		325.2.a.k.1.3		3
65.49	even	6		845.2.l.e.654.5		12
65.54	odd	12		845.2.n.g.529.6		12
65.57	even	4		4225.2.a.ba.1.1		3
65.59	odd	12		845.2.n.f.484.6		12
65.64	even	2	inner	845.2.d.a.844.2		6
195.8	odd	4		2925.2.a.bj.1.3		3
195.47	odd	4		2925.2.a.bf.1.1		3
195.164	even	4		585.2.c.b.469.1		6
260.47	odd	4		5200.2.a.cb.1.3		3
260.99	even	4		1040.2.d.c.209.3		6
260.203	odd	4		5200.2.a.cj.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	13.8	odd	4
65.2.b.a.14.6	yes	6	65.34	odd	4
325.2.a.j.1.1		3	65.8	even	4
325.2.a.k.1.3		3	65.47	even	4
585.2.c.b.469.1		6	195.164	even	4
585.2.c.b.469.6		6	39.8	even	4
845.2.b.c.339.1		6	65.44	odd	4
845.2.b.c.339.6		6	13.5	odd	4
845.2.d.a.844.1		6	1.1	even	1	trivial
845.2.d.a.844.2		6	65.64	even	2	inner
845.2.d.b.844.5		6	13.12	even	2
845.2.d.b.844.6		6	5.4	even	2
845.2.l.d.654.1		12	65.29	even	6
845.2.l.d.654.2		12	13.10	even	6
845.2.l.d.699.1		12	13.4	even	6
845.2.l.d.699.2		12	65.9	even	6
845.2.l.e.654.5		12	65.49	even	6
845.2.l.e.654.6		12	13.3	even	3
845.2.l.e.699.5		12	13.9	even	3
845.2.l.e.699.6		12	65.4	even	6
845.2.n.f.484.1		12	13.7	odd	12
845.2.n.f.484.6		12	65.59	odd	12
845.2.n.f.529.1		12	65.24	odd	12
845.2.n.f.529.6		12	13.11	odd	12
845.2.n.g.484.1		12	65.19	odd	12
845.2.n.g.484.6		12	13.6	odd	12
845.2.n.g.529.1		12	13.2	odd	12
845.2.n.g.529.6		12	65.54	odd	12
1040.2.d.c.209.3		6	260.99	even	4
1040.2.d.c.209.4		6	52.47	even	4
2925.2.a.bf.1.1		3	195.47	odd	4
2925.2.a.bj.1.3		3	195.8	odd	4
4225.2.a.ba.1.1		3	65.57	even	4
4225.2.a.bh.1.3		3	65.18	even	4
5200.2.a.cb.1.3		3	260.47	odd	4
5200.2.a.cj.1.1		3	260.203	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.67513 q^{2} -0.481194i q^{3} +5.15633 q^{4} +(1.48119 - 1.67513i) q^{5} +1.28726i q^{6} +0.806063 q^{7} -8.44358 q^{8} +2.76845 q^{9} +(-3.96239 + 4.48119i) q^{10} -3.67513i q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.806063 - 0.712742i) q^{15} +12.2750 q^{16} -1.35026i q^{17} -7.40597 q^{18} -1.67513i q^{19} +(7.63752 - 8.63752i) q^{20} -0.387873i q^{21} +9.83146i q^{22} -6.48119i q^{23} +4.06300i q^{24} +(-0.612127 - 4.96239i) q^{25} -2.77575i q^{27} +4.15633 q^{28} -2.41819 q^{29} +(2.15633 + 1.90668i) q^{30} +5.28726i q^{31} -15.9502 q^{32} -1.76845 q^{33} +3.61213i q^{34} +(1.19394 - 1.35026i) q^{35} +14.2750 q^{36} +3.76845 q^{37} +4.48119i q^{38} +(-12.5066 + 14.1441i) q^{40} +8.31265i q^{41} +1.03761i q^{42} +6.79384i q^{43} -18.9502i q^{44} +(4.10062 - 4.63752i) q^{45} +17.3380i q^{46} +3.19394 q^{47} -5.90668i q^{48} -6.35026 q^{49} +(1.63752 + 13.2750i) q^{50} -0.649738 q^{51} +5.73813i q^{53} +7.42548i q^{54} +(-6.15633 - 5.44358i) q^{55} -6.80606 q^{56} -0.806063 q^{57} +6.46898 q^{58} -5.98778i q^{59} +(-4.15633 - 3.67513i) q^{60} -1.76845 q^{61} -14.1441i q^{62} +2.23155 q^{63} +18.1187 q^{64} +4.73084 q^{66} -9.89446 q^{67} -6.96239i q^{68} -3.11871 q^{69} +(-3.19394 + 3.61213i) q^{70} -8.56230i q^{71} -23.3757 q^{72} +11.7685 q^{73} -10.0811 q^{74} +(-2.38787 + 0.294552i) q^{75} -8.63752i q^{76} -2.96239i q^{77} +2.26187 q^{79} +(18.1817 - 20.5623i) q^{80} +6.96968 q^{81} -22.2374i q^{82} +3.84367 q^{83} -2.00000i q^{84} +(-2.26187 - 2.00000i) q^{85} -18.1744i q^{86} +1.16362i q^{87} +31.0313i q^{88} -2.77575i q^{89} +(-10.9697 + 12.4060i) q^{90} -33.4191i q^{92} +2.54420 q^{93} -8.54420 q^{94} +(-2.80606 - 2.48119i) q^{95} +7.67513i q^{96} +1.87399 q^{97} +16.9878 q^{98} -10.1744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 10 q^{4} - 2 q^{5} + 4 q^{7} - 18 q^{8} - 6 q^{9} - 2 q^{10} + 8 q^{14} - 4 q^{15} + 10 q^{16} + 10 q^{18} + 14 q^{20} - 2 q^{25} + 4 q^{28} - 12 q^{29} - 8 q^{30} - 22 q^{32} + 12 q^{33}+ \cdots + 50 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 10 * q^4 - 2 * q^5 + 4 * q^7 - 18 * q^8 - 6 * q^9 - 2 * q^10 + 8 * q^14 - 4 * q^15 + 10 * q^16 + 10 * q^18 + 14 * q^20 - 2 * q^25 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 22 * q^32 + 12 * q^33 + 8 * q^35 + 22 * q^36 - 34 * q^40 + 38 * q^45 + 20 * q^47 - 18 * q^49 - 22 * q^50 - 24 * q^51 - 16 * q^55 - 40 * q^56 - 4 * q^57 - 24 * q^58 - 4 * q^60 + 12 * q^61 + 36 * q^63 + 66 * q^64 - 16 * q^66 - 20 * q^67 + 24 * q^69 - 20 * q^70 - 90 * q^72 + 48 * q^73 + 4 * q^74 - 16 * q^75 + 32 * q^79 + 58 * q^80 + 46 * q^81 + 44 * q^83 - 32 * q^85 - 70 * q^90 - 4 * q^93 - 32 * q^94 - 16 * q^95 + 28 * q^97 + 50 * q^98

Introduction

L-functions

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