LMFDB - Embedded newform 287.2.c.a.204.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 60x^{6} + 118x^{4} + 96x^{2} + 25 $ x^10 + 13x^8 + 60x^6 + 118x^4 + 96x^2 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.4
Root			$2.10917i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.a.204.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44859 q^{2} +3.10917i q^{3} +0.0984241 q^{4} -3.65619 q^{5} -4.50392i q^{6} +1.00000i q^{7} +2.75461 q^{8} -6.66693 q^{9} +O(q^{10})$	\(q-1.44859 q^{2} +3.10917i q^{3} +0.0984241 q^{4} -3.65619 q^{5} -4.50392i q^{6} +1.00000i q^{7} +2.75461 q^{8} -6.66693 q^{9} +5.29633 q^{10} -3.49318i q^{11} +0.306017i q^{12} +5.95691i q^{13} -1.44859i q^{14} -11.3677i q^{15} -4.18716 q^{16} -1.79241i q^{17} +9.65768 q^{18} -2.37060i q^{19} -0.359857 q^{20} -3.10917 q^{21} +5.06020i q^{22} +5.32751 q^{23} +8.56455i q^{24} +8.36770 q^{25} -8.62914i q^{26} -11.4011i q^{27} +0.0984241i q^{28} -4.93103i q^{29} +16.4672i q^{30} -0.651320 q^{31} +0.556273 q^{32} +10.8609 q^{33} +2.59647i q^{34} -3.65619i q^{35} -0.656187 q^{36} -9.06699 q^{37} +3.43404i q^{38} -18.5210 q^{39} -10.0714 q^{40} +(-6.39037 - 0.404009i) q^{41} +4.50392 q^{42} -7.41229 q^{43} -0.343813i q^{44} +24.3755 q^{45} -7.71739 q^{46} +2.96808i q^{47} -13.0186i q^{48} -1.00000 q^{49} -12.1214 q^{50} +5.57290 q^{51} +0.586303i q^{52} -4.25762i q^{53} +16.5156i q^{54} +12.7717i q^{55} +2.75461i q^{56} +7.37060 q^{57} +7.14306i q^{58} -11.4623 q^{59} -1.11886i q^{60} +4.80555 q^{61} +0.943498 q^{62} -6.66693i q^{63} +7.56851 q^{64} -21.7796i q^{65} -15.7330 q^{66} +4.03929i q^{67} -0.176416i q^{68} +16.5641i q^{69} +5.29633i q^{70} +8.10435i q^{71} -18.3648 q^{72} +0.0731247 q^{73} +13.1344 q^{74} +26.0166i q^{75} -0.233324i q^{76} +3.49318 q^{77} +26.8294 q^{78} -12.7121i q^{79} +15.3090 q^{80} +15.4472 q^{81} +(9.25704 + 0.585246i) q^{82} -9.42550 q^{83} -0.306017 q^{84} +6.55337i q^{85} +10.7374 q^{86} +15.3314 q^{87} -9.62235i q^{88} +5.09356i q^{89} -35.3103 q^{90} -5.95691 q^{91} +0.524355 q^{92} -2.02506i q^{93} -4.29955i q^{94} +8.66736i q^{95} +1.72955i q^{96} +6.72905i q^{97} +1.44859 q^{98} +23.2888i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	$ 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.44859			−1.02431			−0.512155	−	0.858893i	$-0.671153\pi$
$2$	−1.44859			−1.02431			−0.512155	+	0.858893i	$0.671153\pi$
$3$			3.10917i			1.79508i	0.440933	+	0.897540i	$0.354647\pi$
$3$			3.10917i			1.79508i	−0.440933	+	0.897540i	$0.645353\pi$
$4$	0.0984241			0.0492121
$5$	−3.65619			−1.63510			−0.817548	−	0.575860i	$-0.804667\pi$
$5$	−3.65619			−1.63510			−0.817548	+	0.575860i	$0.804667\pi$
$6$		−	4.50392i		−	1.83872i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.75461			0.973902
$9$	−6.66693			−2.22231
$10$	5.29633			1.67485
$11$		−	3.49318i		−	1.05323i	−0.850103	−	0.526616i	$-0.823460\pi$
$11$		−	3.49318i		−	1.05323i	0.850103	−	0.526616i	$-0.176540\pi$
$12$			0.306017i			0.0883396i
$13$			5.95691i			1.65215i	0.563562	+	0.826074i	$0.309431\pi$
$13$			5.95691i			1.65215i	−0.563562	+	0.826074i	$0.690569\pi$
$14$		−	1.44859i		−	0.387153i
$15$		−	11.3677i		−	2.93513i
$16$	−4.18716			−1.04679
$17$		−	1.79241i		−	0.434723i	−0.976091	−	0.217361i	$-0.930255\pi$
$17$		−	1.79241i		−	0.434723i	0.976091	−	0.217361i	$-0.0697450\pi$
$18$	9.65768			2.27634
$19$		−	2.37060i		−	0.543853i	−0.962318	−	0.271927i	$-0.912339\pi$
$19$		−	2.37060i		−	0.543853i	0.962318	−	0.271927i	$-0.0876608\pi$
$20$	−0.359857			−0.0804665
$21$	−3.10917			−0.678476
$22$			5.06020i			1.07884i
$23$	5.32751			1.11086			0.555431	−	0.831563i	$-0.312553\pi$
$23$	5.32751			1.11086			0.555431	+	0.831563i	$0.312553\pi$
$24$			8.56455i			1.74823i
$25$	8.36770			1.67354
$26$		−	8.62914i		−	1.69231i
$27$		−	11.4011i		−	2.19414i
$28$			0.0984241i			0.0186004i
$29$		−	4.93103i		−	0.915669i	−0.889038	−	0.457834i	$-0.848625\pi$
$29$		−	4.93103i		−	0.915669i	0.889038	−	0.457834i	$-0.151375\pi$
$30$			16.4672i			3.00648i
$31$	−0.651320			−0.116980			−0.0584902	−	0.998288i	$-0.518629\pi$
$31$	−0.651320			−0.116980			−0.0584902	+	0.998288i	$0.518629\pi$
$32$	0.556273			0.0983362
$33$	10.8609			1.89064
$34$			2.59647i			0.445291i
$35$		−	3.65619i		−	0.618008i
$36$	−0.656187			−0.109364
$37$	−9.06699			−1.49060			−0.745302	−	0.666727i	$-0.767694\pi$
$37$	−9.06699			−1.49060			−0.745302	+	0.666727i	$0.767694\pi$
$38$			3.43404i			0.557075i
$39$	−18.5210			−2.96574
$40$	−10.0714			−1.59242
$41$	−6.39037	−	0.404009i	−0.998007	−	0.0630957i
$41$	−6.39037	−	0.404009i	−0.998007	−	0.0630957i
$42$	4.50392			0.694970
$43$	−7.41229			−1.13036			−0.565182	−	0.824967i	$-0.691194\pi$
$43$	−7.41229			−1.13036			−0.565182	+	0.824967i	$0.691194\pi$
$44$		−	0.343813i		−	0.0518318i
$45$	24.3755			3.63369
$46$	−7.71739			−1.13787
$47$			2.96808i			0.432939i	0.976289	+	0.216470i	$0.0694542\pi$
$47$			2.96808i			0.432939i	−0.976289	+	0.216470i	$0.930546\pi$
$48$		−	13.0186i		−	1.87907i
$49$	−1.00000			−0.142857
$50$	−12.1214			−1.71423
$51$	5.57290			0.780362
$52$			0.586303i			0.0813056i
$53$		−	4.25762i		−	0.584830i	−0.956292	−	0.292415i	$-0.905541\pi$
$53$		−	4.25762i		−	0.584830i	0.956292	−	0.292415i	$-0.0944588\pi$
$54$			16.5156i			2.24749i
$55$			12.7717i			1.72214i
$56$			2.75461i			0.368100i
$57$	7.37060			0.976260
$58$			7.14306i			0.937929i
$59$	−11.4623			−1.49227			−0.746133	−	0.665797i	$-0.768092\pi$
$59$	−11.4623			−1.49227			−0.746133	+	0.665797i	$0.768092\pi$
$60$		−	1.11886i		−	0.144444i
$61$	4.80555			0.615288			0.307644	−	0.951502i	$-0.400459\pi$
$61$	4.80555			0.615288			0.307644	+	0.951502i	$0.400459\pi$
$62$	0.943498			0.119824
$63$		−	6.66693i		−	0.839954i
$64$	7.56851			0.946063
$65$		−	21.7796i		−	2.70142i
$66$	−15.7330			−1.93660
$67$			4.03929i			0.493477i	0.969082	+	0.246739i	$0.0793589\pi$
$67$			4.03929i			0.493477i	−0.969082	+	0.246739i	$0.920641\pi$
$68$		−	0.176416i		−	0.0213936i
$69$			16.5641i			1.99409i
$70$			5.29633i			0.633033i
$71$			8.10435i			0.961809i	0.876773	+	0.480905i	$0.159692\pi$
$71$			8.10435i			0.961809i	−0.876773	+	0.480905i	$0.840308\pi$
$72$	−18.3648			−2.16431
$73$	0.0731247			0.00855860			0.00427930	−	0.999991i	$-0.498638\pi$
$73$	0.0731247			0.00855860			0.00427930	+	0.999991i	$0.498638\pi$
$74$	13.1344			1.52684
$75$			26.0166i			3.00414i
$76$		−	0.233324i		−	0.0267641i
$77$	3.49318			0.398085
$78$	26.8294			3.03784
$79$		−	12.7121i		−	1.43022i	−0.699011	−	0.715111i	$-0.746376\pi$
$79$		−	12.7121i		−	1.43022i	0.699011	−	0.715111i	$-0.253624\pi$
$80$	15.3090			1.71160
$81$	15.4472			1.71635
$82$	9.25704	+	0.585246i	1.02227	+	0.0646296i
$83$	−9.42550			−1.03458			−0.517291	−	0.855809i	$-0.673060\pi$
$83$	−9.42550			−1.03458			−0.517291	+	0.855809i	$0.673060\pi$
$84$	−0.306017			−0.0333892
$85$			6.55337i			0.710813i
$86$	10.7374			1.15784
$87$	15.3314			1.64370
$88$		−	9.62235i		−	1.02575i
$89$			5.09356i			0.539916i	0.962872	+	0.269958i	$0.0870098\pi$
$89$			5.09356i			0.539916i	−0.962872	+	0.269958i	$0.912990\pi$
$90$	−35.3103			−3.72203
$91$	−5.95691			−0.624453
$92$	0.524355			0.0546678
$93$		−	2.02506i		−	0.209989i
$94$		−	4.29955i		−	0.443464i
$95$			8.66736i			0.889253i
$96$			1.72955i			0.176521i
$97$			6.72905i			0.683231i	0.939840	+	0.341616i	$0.110974\pi$
$97$			6.72905i			0.683231i	−0.939840	+	0.341616i	$0.889026\pi$
$98$	1.44859			0.146330
$99$			23.2888i			2.34061i
$100$	0.823584			0.0823584
$101$		−	3.94129i		−	0.392173i	−0.980587	−	0.196087i	$-0.937177\pi$
$101$		−	3.94129i		−	0.392173i	0.980587	−	0.196087i	$-0.0628234\pi$
$102$	−8.07286			−0.799333
$103$	7.33562			0.722800			0.361400	−	0.932411i	$-0.382299\pi$
$103$	7.33562			0.722800			0.361400	+	0.932411i	$0.382299\pi$
$104$			16.4090i			1.60903i
$105$	11.3677			1.10937
$106$			6.16757i			0.599047i
$107$	−12.2451			−1.18378			−0.591891	−	0.806018i	$-0.701618\pi$
$107$	−12.2451			−1.18378			−0.591891	+	0.806018i	$0.701618\pi$
$108$		−	1.12214i		−	0.107978i
$109$		−	0.611171i		−	0.0585395i	−0.999572	−	0.0292698i	$-0.990682\pi$
$109$		−	0.611171i		−	0.0585395i	0.999572	−	0.0292698i	$-0.00931819\pi$
$110$		−	18.5010i		−	1.76400i
$111$		−	28.1908i		−	2.67575i
$112$		−	4.18716i		−	0.395650i
$113$	−4.75905			−0.447693			−0.223847	−	0.974624i	$-0.571862\pi$
$113$	−4.75905			−0.447693			−0.223847	+	0.974624i	$0.571862\pi$
$114$	−10.6770			−0.999993
$115$	−19.4784			−1.81637
$116$		−	0.485332i		−	0.0450620i
$117$		−	39.7143i		−	3.67159i
$118$	16.6042			1.52854
$119$	1.79241			0.164310
$120$		−	31.3136i		−	2.85853i
$121$	−1.20229			−0.109299
$122$	−6.96129			−0.630246
$123$	1.25613	−	19.8687i	0.113262	−	1.79150i
$124$	−0.0641056			−0.00575685
$125$	−12.3130			−1.10130
$126$			9.65768i			0.860374i
$127$	5.37696			0.477128			0.238564	−	0.971127i	$-0.423323\pi$
$127$	5.37696			0.477128			0.238564	+	0.971127i	$0.423323\pi$
$128$	−12.0762			−1.06740
$129$		−	23.0461i		−	2.02909i
$130$			31.5497i			2.76709i
$131$	−10.3789			−0.906807			−0.453403	−	0.891305i	$-0.649790\pi$
$131$	−10.3789			−0.906807			−0.453403	+	0.891305i	$0.649790\pi$
$132$	1.06897			0.0930421
$133$	2.37060			0.205557
$134$		−	5.85128i		−	0.505474i
$135$			41.6846i			3.58764i
$136$		−	4.93738i		−	0.423377i
$137$		−	20.0538i		−	1.71331i	−0.515887	−	0.856657i	$-0.672537\pi$
$137$		−	20.0538i		−	1.71331i	0.515887	−	0.856657i	$-0.327463\pi$
$138$		−	23.9947i		−	2.04256i
$139$	14.5283			1.23228			0.616138	−	0.787638i	$-0.288696\pi$
$139$	14.5283			1.23228			0.616138	+	0.787638i	$0.288696\pi$
$140$		−	0.359857i		−	0.0304135i
$141$	−9.22827			−0.777160
$142$		−	11.7399i		−	0.985191i
$143$	20.8085			1.74010
$144$	27.9155			2.32629
$145$			18.0288i			1.49721i
$146$	−0.105928			−0.00876667
$147$		−	3.10917i		−	0.256440i
$148$	−0.892410			−0.0733557
$149$			5.49565i			0.450221i	0.974333	+	0.225110i	$0.0722743\pi$
$149$			5.49565i			0.450221i	−0.974333	+	0.225110i	$0.927726\pi$
$150$		−	37.6875i		−	3.07717i
$151$			5.15838i			0.419783i	0.977725	+	0.209892i	$0.0673111\pi$
$151$			5.15838i			0.419783i	−0.977725	+	0.209892i	$0.932689\pi$
$152$		−	6.53009i		−	0.529660i
$153$			11.9499i			0.966088i
$154$	−5.06020			−0.407762
$155$	2.38135			0.191274
$156$	−1.82292			−0.145950
$157$			0.182773i			0.0145869i	0.999973	+	0.00729343i	$0.00232159\pi$
$157$			0.182773i			0.0145869i	−0.999973	+	0.00729343i	$0.997678\pi$
$158$			18.4147i			1.46499i
$159$	13.2377			1.04982
$160$	−2.03384			−0.160789
$161$			5.32751i			0.419866i
$162$	−22.3767			−1.75808
$163$	−13.7411			−1.07629			−0.538144	−	0.842853i	$-0.680874\pi$
$163$	−13.7411			−1.07629			−0.538144	+	0.842853i	$0.680874\pi$
$164$	−0.628966	−	0.0397643i	−0.0491140	−	0.00310507i
$165$	−39.7094			−3.09137
$166$	13.6537			1.05973
$167$		−	4.71986i		−	0.365234i	−0.983184	−	0.182617i	$-0.941543\pi$
$167$		−	4.71986i		−	0.365234i	0.983184	−	0.182617i	$-0.0584568\pi$
$168$	−8.56455			−0.660769
$169$	−22.4847			−1.72959
$170$		−	9.49318i		−	0.728094i
$171$			15.8046i			1.20861i
$172$	−0.729548			−0.0556275
$173$	−4.74665			−0.360881			−0.180441	−	0.983586i	$-0.557752\pi$
$173$	−4.74665			−0.360881			−0.180441	+	0.983586i	$0.557752\pi$
$174$	−22.2090			−1.68366
$175$			8.36770i			0.632539i
$176$			14.6265i			1.10251i
$177$		−	35.6383i		−	2.67874i
$178$		−	7.37850i		−	0.553042i
$179$			23.9628i			1.79107i	0.444995	+	0.895533i	$0.353205\pi$
$179$			23.9628i			1.79107i	−0.444995	+	0.895533i	$0.646795\pi$
$180$	2.39914			0.178822
$181$		−	9.98760i		−	0.742373i	−0.928558	−	0.371186i	$-0.878951\pi$
$181$		−	9.98760i		−	0.742373i	0.928558	−	0.371186i	$-0.121049\pi$
$182$	8.62914			0.639634
$183$			14.9413i			1.10449i
$184$	14.6752			1.08187
$185$	33.1506			2.43728
$186$			2.93349i			0.215094i
$187$	−6.26120			−0.457864
$188$			0.292131i			0.0213058i
$189$	11.4011			0.829309
$190$		−	12.5555i		−	0.910871i
$191$			12.9089i			0.934058i	0.884242	+	0.467029i	$0.154676\pi$
$191$			12.9089i			0.934058i	−0.884242	+	0.467029i	$0.845324\pi$
$192$			23.5318i			1.69826i
$193$			24.6438i			1.77390i	0.461868	+	0.886949i	$0.347179\pi$
$193$			24.6438i			1.77390i	−0.461868	+	0.886949i	$0.652821\pi$
$194$		−	9.74766i		−	0.699841i
$195$	67.7163			4.84927
$196$	−0.0984241			−0.00703030
$197$	−2.21908			−0.158103			−0.0790514	−	0.996871i	$-0.525189\pi$
$197$	−2.21908			−0.158103			−0.0790514	+	0.996871i	$0.525189\pi$
$198$		−	33.7360i		−	2.39751i
$199$		−	5.54172i		−	0.392842i	−0.980520	−	0.196421i	$-0.937068\pi$
$199$		−	5.54172i		−	0.392842i	0.980520	−	0.196421i	$-0.0629319\pi$
$200$	23.0498			1.62986
$201$	−12.5588			−0.885831
$202$			5.70933i			0.401707i
$203$	4.93103			0.346090
$204$	0.548507			0.0384032
$205$	23.3644	+	1.47713i	1.63184	+	0.103168i
$206$	−10.6263			−0.740371
$207$	−35.5181			−2.46868
$208$		−	24.9425i		−	1.72945i
$209$	−8.28093			−0.572804
$210$	−16.4672			−1.13634
$211$			2.35804i			0.162334i	0.996701	+	0.0811669i	$0.0258647\pi$
$211$			2.35804i			0.162334i	−0.996701	+	0.0811669i	$0.974135\pi$
$212$		−	0.419053i		−	0.0287807i
$213$	−25.1978			−1.72652
$214$	17.7382			1.21256
$215$	27.1007			1.84825
$216$		−	31.4056i		−	2.13688i
$217$		−	0.651320i		−	0.0442145i
$218$			0.885338i			0.0599627i
$219$			0.227357i			0.0153634i
$220$			1.25704i			0.0847499i
$221$	10.6772			0.718226
$222$			40.8370i			2.74080i
$223$	−0.977337			−0.0654473			−0.0327237	−	0.999464i	$-0.510418\pi$
$223$	−0.977337			−0.0654473			−0.0327237	+	0.999464i	$0.510418\pi$
$224$			0.556273i			0.0371676i
$225$	−55.7869			−3.71913
$226$	6.89393			0.458577
$227$		−	21.9737i		−	1.45845i	−0.684276	−	0.729223i	$-0.739882\pi$
$227$		−	21.9737i		−	1.45845i	0.684276	−	0.729223i	$-0.260118\pi$
$228$	0.725445			0.0480438
$229$			4.55000i			0.300672i	0.988635	+	0.150336i	$0.0480356\pi$
$229$			4.55000i			0.300672i	−0.988635	+	0.150336i	$0.951964\pi$
$230$	28.2162			1.86052
$231$			10.8609i			0.714594i
$232$		−	13.5831i		−	0.891772i
$233$		−	3.86146i		−	0.252973i	−0.991968	−	0.126486i	$-0.959630\pi$
$233$		−	3.86146i		−	0.252973i	0.991968	−	0.126486i	$-0.0403700\pi$
$234$			57.5299i			3.76084i
$235$		−	10.8519i		−	0.707897i
$236$	−1.12817			−0.0734375
$237$	39.5241			2.56736
$238$	−2.59647			−0.168304
$239$			2.03480i			0.131620i	0.997832	+	0.0658101i	$0.0209631\pi$
$239$			2.03480i			0.131620i	−0.997832	+	0.0658101i	$0.979037\pi$
$240$			47.5984i			3.07246i
$241$	−19.0453			−1.22681			−0.613406	−	0.789767i	$-0.710201\pi$
$241$	−19.0453			−1.22681			−0.613406	+	0.789767i	$0.710201\pi$
$242$	1.74164			0.111957
$243$			13.8246i			0.886847i
$244$	0.472982			0.0302796
$245$	3.65619			0.233585
$246$	−1.81963	+	28.7817i	−0.116015	+	1.83506i
$247$	14.1215			0.898526
$248$	−1.79413			−0.113928
$249$		−	29.3055i		−	1.85716i
$250$	17.8365			1.12808
$251$	−12.9250			−0.815818			−0.407909	−	0.913023i	$-0.633742\pi$
$251$	−12.9250			−0.815818			−0.407909	+	0.913023i	$0.633742\pi$
$252$		−	0.656187i		−	0.0413359i
$253$		−	18.6099i		−	1.17000i
$254$	−7.78903			−0.488727
$255$	−20.3755			−1.27597
$256$	2.35655			0.147285
$257$			15.2181i			0.949277i	0.880181	+	0.474639i	$0.157421\pi$
$257$			15.2181i			0.949277i	−0.880181	+	0.474639i	$0.842579\pi$
$258$			33.3844i			2.07842i
$259$		−	9.06699i		−	0.563395i
$260$		−	2.14363i		−	0.132943i
$261$			32.8748i			2.03490i
$262$	15.0348			0.928852
$263$			12.5864i			0.776108i	0.921637	+	0.388054i	$0.126853\pi$
$263$			12.5864i			0.776108i	−0.921637	+	0.388054i	$0.873147\pi$
$264$	29.9175			1.84130
$265$			15.5667i			0.956253i
$266$	−3.43404			−0.210554
$267$	−15.8367			−0.969192
$268$			0.397563i			0.0242850i
$269$	6.55584			0.399717			0.199858	−	0.979825i	$-0.435952\pi$
$269$	6.55584			0.399717			0.199858	+	0.979825i	$0.435952\pi$
$270$		−	60.3840i		−	3.67486i
$271$	−23.0436			−1.39980			−0.699898	−	0.714243i	$-0.746771\pi$
$271$	−23.0436			−1.39980			−0.699898	+	0.714243i	$0.746771\pi$
$272$			7.50510i			0.455063i
$273$		−	18.5210i		−	1.12094i
$274$			29.0498i			1.75497i
$275$		−	29.2299i		−	1.76263i
$276$			1.63031i			0.0981331i
$277$	7.77567			0.467195			0.233597	−	0.972333i	$-0.424950\pi$
$277$	7.77567			0.467195			0.233597	+	0.972333i	$0.424950\pi$
$278$	−21.0456			−1.26223
$279$	4.34230			0.259967
$280$		−	10.0714i		−	0.601880i
$281$		−	27.3573i		−	1.63200i	−0.578050	−	0.816001i	$-0.696186\pi$
$281$		−	27.3573i		−	1.63200i	0.578050	−	0.816001i	$-0.303814\pi$
$282$	13.3680			0.796054
$283$	−10.2675			−0.610340			−0.305170	−	0.952298i	$-0.598713\pi$
$283$	−10.2675			−0.610340			−0.305170	+	0.952298i	$0.598713\pi$
$284$			0.797663i			0.0473326i
$285$	−26.9483			−1.59628
$286$	−30.1431			−1.78240
$287$	0.404009	−	6.39037i	0.0238479	−	0.377211i
$288$	−3.70864			−0.218534
$289$	13.7873			0.811016
$290$		−	26.1163i		−	1.53360i
$291$	−20.9218			−1.22645
$292$	0.00719724			0.000421186
$293$			28.0523i			1.63883i	0.573200	+	0.819415i	$0.305702\pi$
$293$			28.0523i			1.63883i	−0.573200	+	0.819415i	$0.694298\pi$
$294$			4.50392i			0.262674i
$295$	41.9084			2.44000
$296$	−24.9760			−1.45170
$297$	−39.8261			−2.31095
$298$		−	7.96096i		−	0.461166i
$299$			31.7355i			1.83531i
$300$			2.56066i			0.147840i
$301$		−	7.41229i		−	0.427237i
$302$		−	7.47240i		−	0.429989i
$303$	12.2541			0.703982
$304$			9.92609i			0.569300i
$305$	−17.5700			−1.00606
$306$		−	17.3105i		−	0.989575i
$307$	−4.76174			−0.271767			−0.135883	−	0.990725i	$-0.543387\pi$
$307$	−4.76174			−0.271767			−0.135883	+	0.990725i	$0.543387\pi$
$308$	0.343813			0.0195906
$309$			22.8077i			1.29748i
$310$	−3.44960			−0.195924
$311$			1.32240i			0.0749866i	0.999297	+	0.0374933i	$0.0119373\pi$
$311$			1.32240i			0.0749866i	−0.999297	+	0.0374933i	$0.988063\pi$
$312$	−51.0182			−2.88834
$313$		−	14.3503i		−	0.811129i	−0.914066	−	0.405565i	$-0.867075\pi$
$313$		−	14.3503i		−	0.811129i	0.914066	−	0.405565i	$-0.132925\pi$
$314$		−	0.264764i		−	0.0149415i
$315$			24.3755i			1.37341i
$316$		−	1.25118i		−	0.0703842i
$317$			34.2992i			1.92644i	0.268719	+	0.963219i	$0.413400\pi$
$317$			34.2992i			1.92644i	−0.268719	+	0.963219i	$0.586600\pi$
$318$	−19.1760			−1.07534
$319$	−17.2250			−0.964412
$320$	−27.6719			−1.54691
$321$		−	38.0722i		−	2.12498i
$322$		−	7.71739i		−	0.430074i
$323$	−4.24908			−0.236425
$324$	1.52038			0.0844653
$325$			49.8456i			2.76494i
$326$	19.9053			1.10245
$327$	1.90023			0.105083
$328$	−17.6030	−	1.11289i	−0.971962	−	0.0614490i
$329$	−2.96808			−0.163636
$330$	57.5228			3.16653
$331$			26.6434i			1.46445i	0.681060	+	0.732227i	$0.261519\pi$
$331$			26.6434i			1.46445i	−0.681060	+	0.732227i	$0.738481\pi$
$332$	−0.927697			−0.0509140
$333$	60.4490			3.31258
$334$			6.83716i			0.374113i
$335$		−	14.7684i		−	0.806883i
$336$	13.0186			0.710222
$337$	20.1902			1.09983			0.549915	−	0.835220i	$-0.314660\pi$
$337$	20.1902			1.09983			0.549915	+	0.835220i	$0.314660\pi$
$338$	32.5712			1.77164
$339$		−	14.7967i		−	0.803645i
$340$			0.645010i			0.0349806i
$341$			2.27518i			0.123208i
$342$		−	22.8945i		−	1.23799i
$343$		−	1.00000i		−	0.0539949i
$344$	−20.4180			−1.10086
$345$		−	60.5615i		−	3.26052i
$346$	6.87597			0.369654
$347$		−	11.5192i		−	0.618381i	−0.951000	−	0.309190i	$-0.899942\pi$
$347$		−	11.5192i		−	0.618381i	0.951000	−	0.309190i	$-0.100058\pi$
$348$	1.50898			0.0808898
$349$	22.0234			1.17889			0.589444	−	0.807809i	$-0.299347\pi$
$349$	22.0234			1.17889			0.589444	+	0.807809i	$0.299347\pi$
$350$		−	12.1214i		−	0.647916i
$351$	67.9153			3.62505
$352$		−	1.94316i		−	0.103571i
$353$	11.1116			0.591410			0.295705	−	0.955279i	$-0.404445\pi$
$353$	11.1116			0.591410			0.295705	+	0.955279i	$0.404445\pi$
$354$			51.6254i			2.74386i
$355$		−	29.6310i		−	1.57265i
$356$			0.501329i			0.0265704i
$357$			5.57290i			0.294949i
$358$		−	34.7124i		−	1.83461i
$359$	−30.5753			−1.61370			−0.806852	−	0.590753i	$-0.798831\pi$
$359$	−30.5753			−1.61370			−0.806852	+	0.590753i	$0.798831\pi$
$360$	67.1452			3.53886
$361$	13.3802			0.704224
$362$			14.4680i			0.760420i
$363$		−	3.73814i		−	0.196201i
$364$	−0.586303			−0.0307306
$365$	−0.267358			−0.0139941
$366$		−	21.6438i		−	1.13134i
$367$	−11.1376			−0.581379			−0.290689	−	0.956818i	$-0.593885\pi$
$367$	−11.1376			−0.581379			−0.290689	+	0.956818i	$0.593885\pi$
$368$	−22.3071			−1.16284
$369$	42.6041	+	2.69350i	2.21788	+	0.140218i
$370$	−48.0217			−2.49653
$371$	4.25762			0.221045
$372$		−	0.199315i		−	0.0103340i
$373$	−19.0374			−0.985718			−0.492859	−	0.870109i	$-0.664048\pi$
$373$	−19.0374			−0.985718			−0.492859	+	0.870109i	$0.664048\pi$
$374$	9.06993			0.468995
$375$		−	38.2830i		−	1.97693i
$376$			8.17591i			0.421640i
$377$	29.3737			1.51282
$378$	−16.5156			−0.849470
$379$	−3.89892			−0.200274			−0.100137	−	0.994974i	$-0.531928\pi$
$379$	−3.89892			−0.200274			−0.100137	+	0.994974i	$0.531928\pi$
$380$			0.853078i			0.0437620i
$381$			16.7179i			0.856483i
$382$		−	18.6998i		−	0.956766i
$383$			2.33115i			0.119116i	0.998225	+	0.0595580i	$0.0189691\pi$
$383$			2.33115i			0.119116i	−0.998225	+	0.0595580i	$0.981031\pi$
$384$		−	37.5471i		−	1.91607i
$385$	−12.7717			−0.650907
$386$		−	35.6988i		−	1.81702i
$387$	49.4172			2.51202
$388$			0.662301i			0.0336232i
$389$	1.96592			0.0996763			0.0498382	−	0.998757i	$-0.484129\pi$
$389$	1.96592			0.0996763			0.0498382	+	0.998757i	$0.484129\pi$
$390$	−98.0935			−4.96716
$391$		−	9.54906i		−	0.482917i
$392$	−2.75461			−0.139129
$393$		−	32.2697i		−	1.62779i
$394$	3.21454			0.161946
$395$			46.4778i			2.33855i
$396$			2.29218i			0.115186i
$397$			38.6495i			1.93976i	0.243582	+	0.969880i	$0.421678\pi$
$397$			38.6495i			1.93976i	−0.243582	+	0.969880i	$0.578322\pi$
$398$			8.02770i			0.402392i
$399$			7.37060i			0.368992i
$400$	−35.0369			−1.75185
$401$	−0.0758278			−0.00378666			−0.00189333	−	0.999998i	$-0.500603\pi$
$401$	−0.0758278			−0.00378666			−0.00189333	+	0.999998i	$0.500603\pi$
$402$	18.1926			0.907366
$403$		−	3.87985i		−	0.193269i
$404$		−	0.387918i		−	0.0192997i
$405$	−56.4778			−2.80640
$406$	−7.14306			−0.354504
$407$			31.6726i			1.56995i
$408$	15.3512			0.759996
$409$	−23.2549			−1.14988			−0.574941	−	0.818195i	$-0.694975\pi$
$409$	−23.2549			−1.14988			−0.574941	+	0.818195i	$0.694975\pi$
$410$	−33.8455	−	2.13977i	−1.67151	−	0.105676i
$411$	62.3507			3.07553
$412$	0.722002			0.0355705
$413$		−	11.4623i		−	0.564024i
$414$	51.4513			2.52870
$415$	34.4614			1.69164
$416$			3.31367i			0.162466i
$417$			45.1710i			2.21203i
$418$	11.9957			0.586729
$419$	−6.32873			−0.309179			−0.154589	−	0.987979i	$-0.549405\pi$
$419$	−6.32873			−0.309179			−0.154589	+	0.987979i	$0.549405\pi$
$420$	1.11886			0.0545946
$421$		−	36.1487i		−	1.76178i	−0.473321	−	0.880890i	$-0.656945\pi$
$421$		−	36.1487i		−	1.76178i	0.473321	−	0.880890i	$-0.343055\pi$
$422$		−	3.41584i		−	0.166280i
$423$		−	19.7880i		−	0.962125i
$424$		−	11.7281i		−	0.569567i
$425$		−	14.9983i		−	0.727526i
$426$	36.5014			1.76850
$427$			4.80555i			0.232557i
$428$	−1.20522			−0.0582563
$429$			64.6972i			3.12361i
$430$	−39.2579			−1.89319
$431$	−5.88108			−0.283282			−0.141641	−	0.989918i	$-0.545238\pi$
$431$	−5.88108			−0.283282			−0.141641	+	0.989918i	$0.545238\pi$
$432$			47.7383i			2.29681i
$433$	−29.0349			−1.39533			−0.697663	−	0.716426i	$-0.745777\pi$
$433$	−29.0349			−1.39533			−0.697663	+	0.716426i	$0.745777\pi$
$434$			0.943498i			0.0452893i
$435$	−56.0545			−2.68761
$436$		−	0.0601539i		−	0.00288085i
$437$		−	12.6294i		−	0.604146i
$438$		−	0.329348i		−	0.0157369i
$439$		−	2.40621i		−	0.114842i	−0.998350	−	0.0574212i	$-0.981712\pi$
$439$		−	2.40621i		−	0.114842i	0.998350	−	0.0574212i	$-0.0182878\pi$
$440$			35.1811i			1.67719i
$441$	6.66693			0.317473
$442$	−15.4669			−0.735686
$443$	−36.5170			−1.73498			−0.867488	−	0.497458i	$-0.834267\pi$
$443$	−36.5170			−1.73498			−0.867488	+	0.497458i	$0.834267\pi$
$444$		−	2.77465i		−	0.131679i
$445$		−	18.6230i		−	0.882815i
$446$	1.41576			0.0670384
$447$	−17.0869			−0.808182
$448$			7.56851i			0.357578i
$449$	−8.29905			−0.391656			−0.195828	−	0.980638i	$-0.562739\pi$
$449$	−8.29905			−0.391656			−0.195828	+	0.980638i	$0.562739\pi$
$450$	80.8126			3.80954
$451$	−1.41128	+	22.3227i	−0.0664544	+	1.05113i
$452$	−0.468405			−0.0220319
$453$	−16.0383			−0.753545
$454$			31.8310i			1.49390i
$455$	21.7796			1.02104
$456$	20.3031			0.950782
$457$		−	38.9329i		−	1.82120i	−0.413286	−	0.910601i	$-0.635619\pi$
$457$		−	38.9329i		−	1.82120i	0.413286	−	0.910601i	$-0.364381\pi$
$458$		−	6.59110i		−	0.307982i
$459$	−20.4354			−0.953844
$460$	−1.91714			−0.0893872
$461$	−4.96105			−0.231059			−0.115530	−	0.993304i	$-0.536857\pi$
$461$	−4.96105			−0.231059			−0.115530	+	0.993304i	$0.536857\pi$
$462$		−	15.7330i		−	0.731966i
$463$		−	5.47011i		−	0.254218i	−0.991889	−	0.127109i	$-0.959430\pi$
$463$		−	5.47011i		−	0.254218i	0.991889	−	0.127109i	$-0.0405697\pi$
$464$			20.6470i			0.958513i
$465$			7.40401i			0.343353i
$466$			5.59369i			0.259123i
$467$	29.3644			1.35882			0.679412	−	0.733757i	$-0.262235\pi$
$467$	29.3644			1.35882			0.679412	+	0.733757i	$0.262235\pi$
$468$		−	3.90884i		−	0.180686i
$469$	−4.03929			−0.186517
$470$			15.7199i			0.725107i
$471$	−0.568271			−0.0261846
$472$	−31.5742			−1.45332
$473$			25.8924i			1.19054i
$474$	−57.2543			−2.62978
$475$		−	19.8365i		−	0.910161i
$476$	0.176416			0.00808602
$477$			28.3853i			1.29967i
$478$		−	2.94760i		−	0.134820i
$479$			25.5665i			1.16816i	0.811695	+	0.584081i	$0.198545\pi$
$479$			25.5665i			1.16816i	−0.811695	+	0.584081i	$0.801455\pi$
$480$		−	6.32355i		−	0.288629i
$481$		−	54.0112i		−	2.46270i
$482$	27.5888			1.25664
$483$	−16.5641			−0.753694
$484$	−0.118335			−0.00537885
$485$		−	24.6027i		−	1.11715i
$486$		−	20.0262i		−	0.908407i
$487$	26.7578			1.21251			0.606256	−	0.795270i	$-0.292671\pi$
$487$	26.7578			1.21251			0.606256	+	0.795270i	$0.292671\pi$
$488$	13.2374			0.599230
$489$		−	42.7234i		−	1.93202i
$490$	−5.29633			−0.239264
$491$	−22.9309			−1.03486			−0.517428	−	0.855727i	$-0.673110\pi$
$491$	−22.9309			−1.03486			−0.517428	+	0.855727i	$0.673110\pi$
$492$	0.123634	−	1.95556i	0.00557385	−	0.0881636i
$493$	−8.83841			−0.398062
$494$	−20.4562			−0.920370
$495$		−	85.1481i		−	3.82712i
$496$	2.72718			0.122454
$497$	−8.10435			−0.363530
$498$			42.4517i			1.90231i
$499$		−	14.5180i		−	0.649916i	−0.945728	−	0.324958i	$-0.894650\pi$
$499$		−	14.5180i		−	0.649916i	0.945728	−	0.324958i	$-0.105350\pi$
$500$	−1.21189			−0.0541974
$501$	14.6748			0.655624
$502$	18.7231			0.835651
$503$			34.3782i			1.53285i	0.642335	+	0.766424i	$0.277966\pi$
$503$			34.3782i			1.53285i	−0.642335	+	0.766424i	$0.722034\pi$
$504$		−	18.3648i		−	0.818033i
$505$			14.4101i			0.641241i
$506$			26.9582i			1.19844i
$507$		−	69.9088i		−	3.10476i
$508$	0.529222			0.0234805
$509$			2.39171i			0.106011i	0.998594	+	0.0530053i	$0.0168800\pi$
$509$			2.39171i			0.106011i	−0.998594	+	0.0530053i	$0.983120\pi$
$510$	29.5159			1.30699
$511$			0.0731247i			0.00323485i
$512$	20.7388			0.916534
$513$	−27.0275			−1.19329
$514$		−	22.0448i		−	0.972355i
$515$	−26.8204			−1.18185
$516$		−	2.26829i		−	0.0998558i
$517$	10.3680			0.455986
$518$			13.1344i			0.577091i
$519$		−	14.7581i		−	0.647810i
$520$		−	59.9942i		−	2.63092i
$521$		−	12.0488i		−	0.527867i	−0.964541	−	0.263933i	$-0.914980\pi$
$521$		−	12.0488i		−	0.527867i	0.964541	−	0.263933i	$-0.0850199\pi$
$522$		−	47.6223i		−	2.08437i
$523$	2.42150			0.105885			0.0529423	−	0.998598i	$-0.483140\pi$
$523$	2.42150			0.105885			0.0529423	+	0.998598i	$0.483140\pi$
$524$	−1.02153			−0.0446258
$525$	−26.0166			−1.13546
$526$		−	18.2325i		−	0.794975i
$527$			1.16743i			0.0508540i
$528$	−45.4763			−1.97910
$529$	5.38233			0.234014
$530$		−	22.5498i		−	0.979500i
$531$	76.4185			3.31628
$532$	0.233324			0.0101159
$533$	2.40665	−	38.0668i	0.104243	−	1.64886i
$534$	22.9410			0.992754
$535$	44.7705			1.93560
$536$			11.1267i			0.480599i
$537$	−74.5045			−3.21511
$538$	−9.49675			−0.409434
$539$			3.49318i			0.150462i
$540$			4.10277i			0.176555i
$541$	27.1055			1.16536			0.582679	−	0.812702i	$-0.302004\pi$
$541$	27.1055			1.16536			0.582679	+	0.812702i	$0.302004\pi$
$542$	33.3808			1.43383
$543$	31.0531			1.33262
$544$		−	0.997068i		−	0.0427489i
$545$			2.23455i			0.0957178i
$546$			26.8294i			1.14819i
$547$			34.1454i			1.45995i	0.683473	+	0.729975i	$0.260468\pi$
$547$			34.1454i			1.45995i	−0.683473	+	0.729975i	$0.739532\pi$
$548$		−	1.97378i		−	0.0843157i
$549$	−32.0383			−1.36736
$550$			42.3422i			1.80548i
$551$	−11.6895			−0.497990
$552$			45.6277i			1.94204i
$553$	12.7121			0.540573
$554$	−11.2638			−0.478552
$555$			103.071i			4.37511i
$556$	1.42994			0.0606428
$557$		−	3.80010i		−	0.161016i	−0.996754	−	0.0805078i	$-0.974346\pi$
$557$		−	3.80010i		−	0.161016i	0.996754	−	0.0805078i	$-0.0256542\pi$
$558$	−6.29024			−0.266287
$559$		−	44.1543i		−	1.86753i
$560$			15.3090i			0.646925i
$561$		−	19.4671i		−	0.821902i
$562$			39.6297i			1.67168i
$563$			43.4788i			1.83241i	0.400705	+	0.916207i	$0.368765\pi$
$563$			43.4788i			1.83241i	−0.400705	+	0.916207i	$0.631235\pi$
$564$	−0.908284			−0.0382457
$565$	17.4000			0.732022
$566$	14.8734			0.625178
$567$			15.4472i			0.648721i
$568$			22.3243i			0.936708i
$569$	34.8405			1.46059			0.730295	−	0.683132i	$-0.239383\pi$
$569$	34.8405			1.46059			0.730295	+	0.683132i	$0.239383\pi$
$570$	39.0371			1.63509
$571$		−	38.7433i		−	1.62136i	−0.585491	−	0.810679i	$-0.699098\pi$
$571$		−	38.7433i		−	1.62136i	0.585491	−	0.810679i	$-0.300902\pi$
$572$	2.04806			0.0856338
$573$	−40.1361			−1.67671
$574$	−0.585246	+	9.25704i	−0.0244277	+	0.386382i
$575$	44.5790			1.85907
$576$	−50.4587			−2.10245
$577$			1.20066i			0.0499840i	0.999688	+	0.0249920i	$0.00795602\pi$
$577$			1.20066i			0.0499840i	−0.999688	+	0.0249920i	$0.992044\pi$
$578$	−19.9722			−0.830733
$579$	−76.6216			−3.18429
$580$			1.77446i			0.0736806i
$581$		−	9.42550i		−	0.391036i
$582$	30.3071			1.25627
$583$	−14.8726			−0.615962
$584$	0.201430			0.00833524
$585$			145.203i			6.00340i
$586$		−	40.6363i		−	1.67867i
$587$		−	25.8520i		−	1.06703i	−0.845791	−	0.533514i	$-0.820871\pi$
$587$		−	25.8520i		−	1.06703i	0.845791	−	0.533514i	$-0.179129\pi$
$588$		−	0.306017i		−	0.0126199i
$589$			1.54402i			0.0636202i
$590$	−60.7082			−2.49932
$591$		−	6.89949i		−	0.283807i
$592$	37.9649			1.56035
$593$		−	9.19966i		−	0.377785i	−0.981998	−	0.188892i	$-0.939510\pi$
$593$		−	9.19966i		−	0.377785i	0.981998	−	0.188892i	$-0.0604897\pi$
$594$	57.6919			2.36713
$595$	−6.55337			−0.268662
$596$			0.540904i			0.0221563i
$597$	17.2301			0.705183
$598$		−	45.9718i		−	1.87993i
$599$	5.56121			0.227225			0.113613	−	0.993525i	$-0.463758\pi$
$599$	5.56121			0.227225			0.113613	+	0.993525i	$0.463758\pi$
$600$			71.6656i			2.92574i
$601$			12.7969i			0.521996i	0.965339	+	0.260998i	$0.0840517\pi$
$601$			12.7969i			0.521996i	−0.965339	+	0.260998i	$0.915948\pi$
$602$			10.7374i			0.437624i
$603$		−	26.9296i		−	1.09666i
$604$			0.507709i			0.0206584i
$605$	4.39581			0.178715
$606$	−17.7513			−0.721096
$607$	−23.1522			−0.939719			−0.469859	−	0.882741i	$-0.655695\pi$
$607$	−23.1522			−0.939719			−0.469859	+	0.882741i	$0.655695\pi$
$608$		−	1.31870i		−	0.0534805i
$609$			15.3314i			0.621260i
$610$	25.4518			1.03051
$611$	−17.6806			−0.715280
$612$			1.17615i			0.0475432i
$613$	−7.42757			−0.299997			−0.149998	−	0.988686i	$-0.547927\pi$
$613$	−7.42757			−0.299997			−0.149998	+	0.988686i	$0.547927\pi$
$614$	6.89782			0.278373
$615$	−4.59266	+	72.6438i	−0.185194	+	2.92928i
$616$	9.62235			0.387695
$617$	42.9977			1.73102			0.865512	−	0.500889i	$-0.166993\pi$
$617$	42.9977			1.73102			0.865512	+	0.500889i	$0.166993\pi$
$618$		−	33.0390i		−	1.32903i
$619$	−41.9224			−1.68500			−0.842502	−	0.538693i	$-0.818918\pi$
$619$	−41.9224			−1.68500			−0.842502	+	0.538693i	$0.818918\pi$
$620$	0.234382			0.00941301
$621$		−	60.7395i		−	2.43739i
$622$		−	1.91563i		−	0.0768096i
$623$	−5.09356			−0.204069
$624$	77.5505			3.10451
$625$	3.17994			0.127198
$626$			20.7878i			0.830848i
$627$		−	25.7468i		−	1.02823i
$628$			0.0179893i			0.000717849i
$629$			16.2517i			0.647999i
$630$		−	35.3103i		−	1.40679i
$631$	−25.4520			−1.01323			−0.506615	−	0.862173i	$-0.669103\pi$
$631$	−25.4520			−1.01323			−0.506615	+	0.862173i	$0.669103\pi$
$632$		−	35.0169i		−	1.39290i
$633$	−7.33153			−0.291402
$634$		−	49.6857i		−	1.97327i
$635$	−19.6592			−0.780150
$636$	1.30291			0.0516636
$637$		−	5.95691i		−	0.236021i
$638$	24.9520			0.987858
$639$		−	54.0311i		−	2.13744i
$640$	44.1530			1.74530
$641$			14.0713i			0.555782i	0.960613	+	0.277891i	$0.0896353\pi$
$641$			14.0713i			0.555782i	−0.960613	+	0.277891i	$0.910365\pi$
$642$			55.1511i			2.17664i
$643$			8.47751i			0.334320i	0.985930	+	0.167160i	$0.0534597\pi$
$643$			8.47751i			0.334320i	−0.985930	+	0.167160i	$0.946540\pi$
$644$			0.524355i			0.0206625i
$645$			84.2607i			3.31776i
$646$	6.15520			0.242173
$647$	−34.8150			−1.36872			−0.684359	−	0.729146i	$-0.739918\pi$
$647$	−34.8150			−1.36872			−0.684359	+	0.729146i	$0.739918\pi$
$648$	42.5510			1.67156
$649$			40.0399i			1.57170i
$650$		−	72.2060i		−	2.83215i
$651$	2.02506			0.0793685
$652$	−1.35246			−0.0529663
$653$		−	17.9764i		−	0.703471i	−0.936099	−	0.351736i	$-0.885592\pi$
$653$		−	17.9764i		−	0.703471i	0.936099	−	0.351736i	$-0.114408\pi$
$654$	−2.75267			−0.107638
$655$	37.9471			1.48272
$656$	26.7575	+	1.69165i	1.04470	+	0.0660479i
$657$	−0.487518			−0.0190199
$658$	4.29955			0.167614
$659$		−	4.75959i		−	0.185407i	−0.995694	−	0.0927037i	$-0.970449\pi$
$659$		−	4.75959i		−	0.185407i	0.995694	−	0.0927037i	$-0.0295509\pi$
$660$	−3.90836			−0.152133
$661$	0.113246			0.00440476			0.00220238	−	0.999998i	$-0.499299\pi$
$661$	0.113246			0.00440476			0.00220238	+	0.999998i	$0.499299\pi$
$662$		−	38.5955i		−	1.50006i
$663$			33.1972i			1.28927i
$664$	−25.9636			−1.00758
$665$	−8.66736			−0.336106
$666$	−87.5660			−3.39311
$667$		−	26.2701i		−	1.01718i
$668$		−	0.464548i		−	0.0179739i
$669$		−	3.03871i		−	0.117483i
$670$			21.3934i			0.826499i
$671$		−	16.7867i		−	0.648041i
$672$	−1.72955			−0.0667188
$673$		−	1.49845i		−	0.0577611i	−0.999583	−	0.0288805i	$-0.990806\pi$
$673$		−	1.49845i		−	0.0577611i	0.999583	−	0.0288805i	$-0.00919424\pi$
$674$	−29.2474			−1.12657
$675$		−	95.4011i		−	3.67199i
$676$	−2.21304			−0.0851169
$677$	29.5597			1.13607			0.568037	−	0.823003i	$-0.307703\pi$
$677$	29.5597			1.13607			0.568037	+	0.823003i	$0.307703\pi$
$678$			21.4344i			0.823182i
$679$	−6.72905			−0.258237
$680$			18.0520i			0.692263i
$681$	68.3199			2.61803
$682$		−	3.29581i		−	0.126203i
$683$			19.8463i			0.759396i	0.925111	+	0.379698i	$0.123972\pi$
$683$			19.8463i			0.759396i	−0.925111	+	0.379698i	$0.876028\pi$
$684$			1.55556i			0.0594782i
$685$			73.3205i			2.80143i
$686$			1.44859i			0.0553076i
$687$	−14.1467			−0.539731
$688$	31.0364			1.18325
$689$	25.3623			0.966225
$690$			87.7290i			3.33979i
$691$			31.2162i			1.18752i	0.804642	+	0.593760i	$0.202357\pi$
$691$			31.2162i			1.18752i	−0.804642	+	0.593760i	$0.797643\pi$
$692$	−0.467185			−0.0177597
$693$	−23.2888			−0.884668
$694$			16.6866i			0.633414i
$695$	−53.1182			−2.01489
$696$	42.2320			1.60080
$697$	−0.724149	+	11.4541i	−0.0274291	+	0.433856i
$698$	−31.9030			−1.20755
$699$	12.0059			0.454106
$700$			0.823584i			0.0311285i
$701$	6.70562			0.253268			0.126634	−	0.991950i	$-0.459583\pi$
$701$	6.70562			0.253268			0.126634	+	0.991950i	$0.459583\pi$
$702$	−98.3817			−3.71318
$703$			21.4942i			0.810670i
$704$		−	26.4381i		−	0.996425i
$705$	33.7403			1.27073
$706$	−16.0962			−0.605788
$707$	3.94129			0.148228
$708$		−	3.50767i		−	0.131826i
$709$			19.4202i			0.729341i	0.931137	+	0.364671i	$0.118818\pi$
$709$			19.4202i			0.729341i	−0.931137	+	0.364671i	$0.881182\pi$
$710$			42.9233i			1.61088i
$711$			84.7507i			3.17840i
$712$			14.0308i			0.525825i
$713$	−3.46991			−0.129949
$714$		−	8.07286i		−	0.302119i
$715$	−76.0799			−2.84523
$716$			2.35852i			0.0881421i
$717$	−6.32653			−0.236269
$718$	44.2913			1.65293
$719$		−	41.8569i		−	1.56100i	−0.625157	−	0.780499i	$-0.714965\pi$
$719$		−	41.8569i		−	1.56100i	0.625157	−	0.780499i	$-0.285035\pi$
$720$	−102.064			−3.80371
$721$			7.33562i			0.273193i
$722$	−19.3825			−0.721344
$723$		−	59.2149i		−	2.20223i
$724$		−	0.983021i		−	0.0365337i
$725$		−	41.2614i		−	1.53241i
$726$			5.41504i			0.200971i
$727$		−	26.4987i		−	0.982784i	−0.870938	−	0.491392i	$-0.836488\pi$
$727$		−	26.4987i		−	0.982784i	0.870938	−	0.491392i	$-0.163512\pi$
$728$	−16.4090			−0.608156
$729$	3.35861			0.124393
$730$	0.387293			0.0143343
$731$			13.2858i			0.491394i
$732$			1.47058i			0.0543543i
$733$	20.8948			0.771768			0.385884	−	0.922547i	$-0.373897\pi$
$733$	20.8948			0.771768			0.385884	+	0.922547i	$0.373897\pi$
$734$	16.1339			0.595512
$735$			11.3677i			0.419304i
$736$	2.96355			0.109238
$737$	14.1099			0.519746
$738$	−61.7161	−	3.90179i	−2.27180	−	0.143627i
$739$	−29.7510			−1.09441			−0.547204	−	0.836999i	$-0.684308\pi$
$739$	−29.7510			−1.09441			−0.547204	+	0.836999i	$0.684308\pi$
$740$	3.26282			0.119944
$741$			43.9060i			1.61293i
$742$	−6.16757			−0.226418
$743$	48.6602			1.78517			0.892585	−	0.450879i	$-0.148890\pi$
$743$	48.6602			1.78517			0.892585	+	0.450879i	$0.148890\pi$
$744$		−	5.57826i		−	0.204509i
$745$		−	20.0931i		−	0.736154i
$746$	27.5774			1.00968
$747$	62.8392			2.29916
$748$	−0.616253			−0.0225324
$749$		−	12.2451i		−	0.447427i
$750$			55.4566i			2.02499i
$751$			40.1059i			1.46349i	0.681580	+	0.731743i	$0.261293\pi$
$751$			40.1059i			1.46349i	−0.681580	+	0.731743i	$0.738707\pi$
$752$		−	12.4278i		−	0.453197i
$753$		−	40.1860i		−	1.46446i
$754$	−42.5505			−1.54960
$755$		−	18.8600i		−	0.686386i
$756$	1.12214			0.0408120
$757$		−	8.79547i		−	0.319677i	−0.987143	−	0.159838i	$-0.948903\pi$
$757$		−	8.79547i		−	0.319677i	0.987143	−	0.159838i	$-0.0510973\pi$
$758$	5.64795			0.205143
$759$	57.8614			2.10024
$760$			23.8752i			0.866045i
$761$	−11.0545			−0.400726			−0.200363	−	0.979722i	$-0.564212\pi$
$761$	−11.0545			−0.400726			−0.200363	+	0.979722i	$0.564212\pi$
$762$		−	24.2174i		−	0.877304i
$763$	0.611171			0.0221259
$764$			1.27055i			0.0459669i
$765$		−	43.6909i		−	1.57965i
$766$		−	3.37688i		−	0.122012i
$767$		−	68.2799i		−	2.46545i
$768$			7.32692i			0.264387i
$769$	35.0642			1.26445			0.632224	−	0.774786i	$-0.282142\pi$
$769$	35.0642			1.26445			0.632224	+	0.774786i	$0.282142\pi$
$770$	18.5010			0.666731
$771$	−47.3156			−1.70403
$772$			2.42554i			0.0872972i
$773$		−	27.5621i		−	0.991339i	−0.868511	−	0.495670i	$-0.834923\pi$
$773$		−	27.5621i		−	0.991339i	0.868511	−	0.495670i	$-0.165077\pi$
$774$	−71.5855			−2.57309
$775$	−5.45005			−0.195772
$776$			18.5359i			0.665401i
$777$	28.1908			1.01134
$778$	−2.84783			−0.102100
$779$	−0.957746	+	15.1490i	−0.0343148	+	0.542770i
$780$	6.66492			0.238642
$781$	28.3099			1.01301
$782$			13.8327i			0.494657i
$783$	−56.2192			−2.00911
$784$	4.18716			0.149541
$785$		−	0.668251i		−	0.0238509i
$786$			46.7457i			1.66736i
$787$	23.3250			0.831446			0.415723	−	0.909491i	$-0.363529\pi$
$787$	23.3250			0.831446			0.415723	+	0.909491i	$0.363529\pi$
$788$	−0.218411			−0.00778057
$789$	−39.1331			−1.39317
$790$		−	67.3274i		−	2.39540i
$791$		−	4.75905i		−	0.169212i
$792$			64.1515i			2.27953i
$793$			28.6262i			1.01655i
$794$		−	55.9874i		−	1.98692i
$795$	−48.3994			−1.71655
$796$		−	0.545439i		−	0.0193326i
$797$	−46.1121			−1.63338			−0.816688	−	0.577080i	$-0.804192\pi$
$797$	−46.1121			−1.63338			−0.816688	+	0.577080i	$0.804192\pi$
$798$		−	10.6770i		−	0.377962i
$799$	5.32001			0.188208
$800$	4.65473			0.164570
$801$		−	33.9584i		−	1.19986i
$802$	0.109844			0.00387872
$803$		−	0.255438i		−	0.00901420i
$804$	−1.23609			−0.0435936
$805$		−	19.4784i		−	0.686522i
$806$			5.62033i			0.197968i
$807$			20.3832i			0.717523i
$808$		−	10.8567i		−	0.381938i
$809$		−	29.9838i		−	1.05417i	−0.849811	−	0.527087i	$-0.823284\pi$
$809$		−	29.9838i		−	1.05417i	0.849811	−	0.527087i	$-0.176716\pi$
$810$	81.8134			2.87463
$811$	−14.6477			−0.514352			−0.257176	−	0.966365i	$-0.582792\pi$
$811$	−14.6477			−0.514352			−0.257176	+	0.966365i	$0.582792\pi$
$812$	0.485332			0.0170318
$813$		−	71.6463i		−	2.51275i
$814$		−	45.8807i		−	1.60812i
$815$	50.2401			1.75983
$816$	−23.3346			−0.816875
$817$			17.5716i			0.614752i
$818$	33.6870			1.17784
$819$	39.7143			1.38773
$820$	2.29962	+	0.145386i	0.0803061	+	0.00507709i
$821$	20.4475			0.713623			0.356812	−	0.934176i	$-0.383864\pi$
$821$	20.4475			0.713623			0.356812	+	0.934176i	$0.383864\pi$
$822$	−90.3209			−3.15030
$823$		−	27.9735i		−	0.975093i	−0.873097	−	0.487547i	$-0.837892\pi$
$823$		−	27.9735i		−	0.975093i	0.873097	−	0.487547i	$-0.162108\pi$
$824$	20.2068			0.703936
$825$	90.8806			3.16406
$826$			16.6042i			0.577735i
$827$		−	25.7497i		−	0.895403i	−0.894183	−	0.447702i	$-0.852243\pi$
$827$		−	25.7497i		−	0.895403i	0.894183	−	0.447702i	$-0.147757\pi$
$828$	−3.49584			−0.121489
$829$	−3.28640			−0.114141			−0.0570706	−	0.998370i	$-0.518176\pi$
$829$	−3.28640			−0.114141			−0.0570706	+	0.998370i	$0.518176\pi$
$830$	−49.9206			−1.73277
$831$			24.1759i			0.838652i
$832$			45.0849i			1.56304i
$833$			1.79241i			0.0621032i
$834$		−	65.4344i		−	2.26581i
$835$			17.2567i			0.597192i
$836$	−0.815044			−0.0281889
$837$			7.42577i			0.256672i
$838$	9.16776			0.316695
$839$			15.5175i			0.535722i	0.963458	+	0.267861i	$0.0863168\pi$
$839$			15.5175i			0.535722i	−0.963458	+	0.267861i	$0.913683\pi$
$840$	31.3136			1.08042
$841$	4.68497			0.161551
$842$			52.3648i			1.80461i
$843$	85.0586			2.92957
$844$			0.232088i			0.00798878i
$845$	82.2083			2.82805
$846$			28.6648i			0.985515i
$847$		−	1.20229i		−	0.0413113i
$848$			17.8274i			0.612194i
$849$		−	31.9234i		−	1.09561i
$850$			21.7265i			0.745212i
$851$	−48.3044			−1.65585
$852$	−2.48007			−0.0849658
$853$	43.2555			1.48104			0.740521	−	0.672033i	$-0.234579\pi$
$853$	43.2555			1.48104			0.740521	+	0.672033i	$0.234579\pi$
$854$		−	6.96129i		−	0.238211i
$855$		−	57.7847i		−	1.97620i
$856$	−33.7306			−1.15289
$857$	18.0652			0.617096			0.308548	−	0.951209i	$-0.400157\pi$
$857$	18.0652			0.617096			0.308548	+	0.951209i	$0.400157\pi$
$858$		−	93.7200i		−	3.19955i
$859$	5.77705			0.197110			0.0985552	−	0.995132i	$-0.468578\pi$
$859$	5.77705			0.197110			0.0985552	+	0.995132i	$0.468578\pi$
$860$	2.66736			0.0909563
$861$	19.8687	+	1.25613i	0.677124	+	0.0428089i
$862$	8.51929			0.290168
$863$	17.9411			0.610723			0.305361	−	0.952237i	$-0.401223\pi$
$863$	17.9411			0.610723			0.305361	+	0.952237i	$0.401223\pi$
$864$		−	6.34213i		−	0.215764i
$865$	17.3546			0.590075
$866$	42.0597			1.42925
$867$			42.8670i			1.45584i
$868$		−	0.0641056i		−	0.00217589i
$869$	−44.4056			−1.50636
$870$	81.2001			2.75294
$871$	−24.0616			−0.815298
$872$		−	1.68354i		−	0.0570118i
$873$		−	44.8621i		−	1.51835i
$874$			18.2949i			0.618833i
$875$		−	12.3130i		−	0.416254i
$876$			0.0223774i			0.000756063i
$877$	30.1765			1.01899			0.509494	−	0.860474i	$-0.329832\pi$
$877$	30.1765			1.01899			0.509494	+	0.860474i	$0.329832\pi$
$878$			3.48563i			0.117634i
$879$	−87.2192			−2.94183
$880$		−	53.4772i		−	1.80272i
$881$	−31.1999			−1.05115			−0.525576	−	0.850747i	$-0.676150\pi$
$881$	−31.1999			−1.05115			−0.525576	+	0.850747i	$0.676150\pi$
$882$	−9.65768			−0.325191
$883$			29.4676i			0.991665i	0.868418	+	0.495833i	$0.165137\pi$
$883$			29.4676i			0.991665i	−0.868418	+	0.495833i	$0.834863\pi$
$884$	1.05089			0.0353454
$885$			130.300i			4.37999i
$886$	52.8983			1.77715
$887$			6.30588i			0.211731i	0.994380	+	0.105865i	$0.0337613\pi$
$887$			6.30588i			0.211731i	−0.994380	+	0.105865i	$0.966239\pi$
$888$		−	77.6547i		−	2.60592i
$889$			5.37696i			0.180337i
$890$			26.9772i			0.904276i
$891$		−	53.9598i		−	1.80772i
$892$	−0.0961936			−0.00322080
$893$	7.03614			0.235455
$894$	24.7520			0.827829
$895$		−	87.6126i		−	2.92857i
$896$		−	12.0762i		−	0.403439i
$897$	−98.6709			−3.29453
$898$	12.0219			0.401178
$899$			3.21168i			0.107115i
$900$	−5.49078			−0.183026
$901$	−7.63139			−0.254239
$902$	2.04437	−	32.3365i	0.0680700	−	1.07669i
$903$	23.0461			0.766925
$904$	−13.1093			−0.436010
$905$			36.5165i			1.21385i
$906$	23.2330			0.771864
$907$	47.1719			1.56632			0.783159	−	0.621822i	$-0.213607\pi$
$907$	47.1719			1.56632			0.783159	+	0.621822i	$0.213607\pi$
$908$		−	2.16274i		−	0.0717731i
$909$			26.2763i			0.871531i
$910$	−31.5497			−1.04586
$911$	6.03039			0.199796			0.0998978	−	0.994998i	$-0.468148\pi$
$911$	6.03039			0.199796			0.0998978	+	0.994998i	$0.468148\pi$
$912$	−30.8619			−1.02194
$913$			32.9249i			1.08966i
$914$			56.3979i			1.86548i
$915$		−	54.6281i		−	1.80595i
$916$			0.447829i			0.0147967i
$917$		−	10.3789i		−	0.342741i
$918$	29.6026			0.977033
$919$			28.2161i			0.930762i	0.885110	+	0.465381i	$0.154083\pi$
$919$			28.2161i			0.930762i	−0.885110	+	0.465381i	$0.845917\pi$
$920$	−53.6553			−1.76896
$921$		−	14.8050i		−	0.487843i
$922$	7.18655			0.236676
$923$	−48.2768			−1.58905
$924$			1.06897i			0.0351666i
$925$	−75.8698			−2.49458
$926$			7.92397i			0.260398i
$927$	−48.9060			−1.60629
$928$		−	2.74300i		−	0.0900434i
$929$		−	38.7373i		−	1.27093i	−0.772130	−	0.635464i	$-0.780809\pi$
$929$		−	38.7373i		−	1.27093i	0.772130	−	0.635464i	$-0.219191\pi$
$930$		−	10.7254i		−	0.351700i
$931$			2.37060i			0.0776933i
$932$		−	0.380061i		−	0.0124493i
$933$	−4.11158			−0.134607
$934$	−42.5372			−1.39186
$935$	22.8921			0.748652
$936$		−	109.397i		−	3.57577i
$937$			38.0104i			1.24175i	0.783911	+	0.620874i	$0.213222\pi$
$937$			38.0104i			1.24175i	−0.783911	+	0.620874i	$0.786778\pi$
$938$	5.85128			0.191051
$939$	44.6176			1.45604
$940$		−	1.06809i		−	0.0348371i
$941$	−4.54897			−0.148292			−0.0741460	−	0.997247i	$-0.523623\pi$
$941$	−4.54897			−0.148292			−0.0741460	+	0.997247i	$0.523623\pi$
$942$	0.823195			0.0268211
$943$	−34.0447	−	2.15236i	−1.10865	−	0.0700906i
$944$	47.9946			1.56209
$945$	−41.6846			−1.35600
$946$		−	37.5076i		−	1.21948i
$947$	41.4432			1.34672			0.673362	−	0.739313i	$-0.264850\pi$
$947$	41.4432			1.34672			0.673362	+	0.739313i	$0.264850\pi$
$948$	3.89012			0.126345
$949$			0.435597i			0.0141401i
$950$			28.7350i			0.932287i
$951$	−106.642			−3.45811
$952$	4.93738			0.160022
$953$	7.28118			0.235861			0.117930	−	0.993022i	$-0.462374\pi$
$953$	7.28118			0.235861			0.117930	+	0.993022i	$0.462374\pi$
$954$		−	41.1187i		−	1.33127i
$955$		−	47.1975i		−	1.52728i
$956$			0.200273i			0.00647730i
$957$		−	53.5553i		−	1.73120i
$958$		−	37.0354i		−	1.19656i
$959$	20.0538			0.647572
$960$		−	86.0365i		−	2.77682i
$961$	−30.5758			−0.986316
$962$			78.2402i			2.52257i
$963$	81.6374			2.63073
$964$	−1.87451			−0.0603740
$965$		−	90.1022i		−	2.90049i
$966$	23.9947			0.772016
$967$		−	42.8174i		−	1.37692i	−0.725276	−	0.688458i	$-0.758288\pi$
$967$		−	42.8174i		−	1.37692i	0.725276	−	0.688458i	$-0.241712\pi$
$968$	−3.31185			−0.106447
$969$		−	13.2111i		−	0.424402i
$970$			35.6393i			1.14431i
$971$			11.6707i			0.374530i	0.982309	+	0.187265i	$0.0599623\pi$
$971$			11.6707i			0.374530i	−0.982309	+	0.187265i	$0.940038\pi$
$972$			1.36067i			0.0436436i
$973$			14.5283i			0.465756i
$974$	−38.7612			−1.24199
$975$	−154.978			−4.96328
$976$	−20.1216			−0.644077
$977$		−	0.476799i		−	0.0152541i	−0.999971	−	0.00762707i	$-0.997572\pi$
$977$		−	0.476799i		−	0.0152541i	0.999971	−	0.00762707i	$-0.00242779\pi$
$978$			61.8889i			1.97899i
$979$	17.7927			0.568657
$980$	0.359857			0.0114952
$981$			4.07463i			0.130093i
$982$	33.2175			1.06001
$983$	−6.86224			−0.218872			−0.109436	−	0.993994i	$-0.534904\pi$
$983$	−6.86224			−0.218872			−0.109436	+	0.993994i	$0.534904\pi$
$984$	3.46016	−	54.7306i	0.110306	−	1.74475i
$985$	8.11337			0.258513
$986$	12.8033			0.407739
$987$		−	9.22827i		−	0.293739i
$988$	1.38989			0.0442183
$989$	−39.4890			−1.25568
$990$			123.345i			3.92016i
$991$			33.7935i			1.07349i	0.843745	+	0.536744i	$0.180346\pi$
$991$			33.7935i			1.07349i	−0.843745	+	0.536744i	$0.819654\pi$
$992$	−0.362312			−0.0115034
$993$	−82.8389			−2.62881
$994$	11.7399			0.372367
$995$			20.2616i			0.642335i
$996$		−	2.88437i		−	0.0913946i
$997$			40.6639i			1.28784i	0.765094	+	0.643919i	$0.222692\pi$
$997$			40.6639i			1.28784i	−0.765094	+	0.643919i	$0.777308\pi$
$998$			21.0307i			0.665716i
$999$			103.374i			3.27060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.a.204.4	yes	10
41.40	even	2	inner	287.2.c.a.204.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.a.204.3	✓	10	41.40	even	2	inner
287.2.c.a.204.4	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.44859 q^{2} +3.10917i q^{3} +0.0984241 q^{4} -3.65619 q^{5} -4.50392i q^{6} +1.00000i q^{7} +2.75461 q^{8} -6.66693 q^{9} +O(q^{10})\)	\(q-1.44859 q^{2} +3.10917i q^{3} +0.0984241 q^{4} -3.65619 q^{5} -4.50392i q^{6} +1.00000i q^{7} +2.75461 q^{8} -6.66693 q^{9} +5.29633 q^{10} -3.49318i q^{11} +0.306017i q^{12} +5.95691i q^{13} -1.44859i q^{14} -11.3677i q^{15} -4.18716 q^{16} -1.79241i q^{17} +9.65768 q^{18} -2.37060i q^{19} -0.359857 q^{20} -3.10917 q^{21} +5.06020i q^{22} +5.32751 q^{23} +8.56455i q^{24} +8.36770 q^{25} -8.62914i q^{26} -11.4011i q^{27} +0.0984241i q^{28} -4.93103i q^{29} +16.4672i q^{30} -0.651320 q^{31} +0.556273 q^{32} +10.8609 q^{33} +2.59647i q^{34} -3.65619i q^{35} -0.656187 q^{36} -9.06699 q^{37} +3.43404i q^{38} -18.5210 q^{39} -10.0714 q^{40} +(-6.39037 - 0.404009i) q^{41} +4.50392 q^{42} -7.41229 q^{43} -0.343813i q^{44} +24.3755 q^{45} -7.71739 q^{46} +2.96808i q^{47} -13.0186i q^{48} -1.00000 q^{49} -12.1214 q^{50} +5.57290 q^{51} +0.586303i q^{52} -4.25762i q^{53} +16.5156i q^{54} +12.7717i q^{55} +2.75461i q^{56} +7.37060 q^{57} +7.14306i q^{58} -11.4623 q^{59} -1.11886i q^{60} +4.80555 q^{61} +0.943498 q^{62} -6.66693i q^{63} +7.56851 q^{64} -21.7796i q^{65} -15.7330 q^{66} +4.03929i q^{67} -0.176416i q^{68} +16.5641i q^{69} +5.29633i q^{70} +8.10435i q^{71} -18.3648 q^{72} +0.0731247 q^{73} +13.1344 q^{74} +26.0166i q^{75} -0.233324i q^{76} +3.49318 q^{77} +26.8294 q^{78} -12.7121i q^{79} +15.3090 q^{80} +15.4472 q^{81} +(9.25704 + 0.585246i) q^{82} -9.42550 q^{83} -0.306017 q^{84} +6.55337i q^{85} +10.7374 q^{86} +15.3314 q^{87} -9.62235i q^{88} +5.09356i q^{89} -35.3103 q^{90} -5.95691 q^{91} +0.524355 q^{92} -2.02506i q^{93} -4.29955i q^{94} +8.66736i q^{95} +1.72955i q^{96} +6.72905i q^{97} +1.44859 q^{98} +23.2888i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9	\( 10 q + 4 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{8} - 10 q^{9} + 8 q^{10} - 16 q^{16} + 20 q^{18} - 22 q^{20} - 12 q^{21} - 4 q^{23} - 4 q^{25} + 14 q^{31} + 18 q^{32} - 2 q^{33} + 20 q^{36} - 22 q^{37} - 46 q^{39} - 58 q^{40} - 4 q^{41} - 8 q^{42} + 18 q^{43} + 50 q^{45} + 8 q^{46} - 10 q^{49} - 22 q^{50} + 14 q^{51} + 62 q^{57} + 34 q^{59} - 28 q^{61} - 44 q^{62} + 8 q^{64} - 36 q^{66} - 20 q^{72} + 12 q^{74} + 12 q^{77} + 78 q^{78} - 4 q^{80} + 10 q^{81} + 74 q^{82} - 20 q^{83} - 6 q^{84} + 12 q^{86} - 8 q^{87} - 54 q^{90} - 14 q^{91} - 30 q^{92} - 4 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 12 * q^4 - 10 * q^5 + 12 * q^8 - 10 * q^9 + 8 * q^10 - 16 * q^16 + 20 * q^18 - 22 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^25 + 14 * q^31 + 18 * q^32 - 2 * q^33 + 20 * q^36 - 22 * q^37 - 46 * q^39 - 58 * q^40 - 4 * q^41 - 8 * q^42 + 18 * q^43 + 50 * q^45 + 8 * q^46 - 10 * q^49 - 22 * q^50 + 14 * q^51 + 62 * q^57 + 34 * q^59 - 28 * q^61 - 44 * q^62 + 8 * q^64 - 36 * q^66 - 20 * q^72 + 12 * q^74 + 12 * q^77 + 78 * q^78 - 4 * q^80 + 10 * q^81 + 74 * q^82 - 20 * q^83 - 6 * q^84 + 12 * q^86 - 8 * q^87 - 54 * q^90 - 14 * q^91 - 30 * q^92 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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