LMFDB - Embedded newform 230.3.d.a.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.d (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$-2.98291i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} -3.16228i q^{10} +7.57553i q^{11} -0.557045 q^{12} -2.64076 q^{13} +12.0387i q^{14} -0.622795i q^{15} +4.00000 q^{16} -7.56057i q^{17} +12.6182 q^{18} -24.2676i q^{19} +4.47214i q^{20} +2.37096i q^{21} -10.7134i q^{22} +(-15.7366 - 16.7738i) q^{23} +0.787781 q^{24} -5.00000 q^{25} +3.73460 q^{26} +4.99180 q^{27} -17.0252i q^{28} -31.8513 q^{29} +0.880766i q^{30} -56.5071 q^{31} -5.65685 q^{32} -2.10995i q^{33} +10.6923i q^{34} +19.0348 q^{35} -17.8449 q^{36} -39.9378i q^{37} +34.3195i q^{38} +0.735511 q^{39} -6.32456i q^{40} -42.5710 q^{41} -3.35304i q^{42} -20.5721i q^{43} +15.1511i q^{44} -19.9511i q^{45} +(22.2549 + 23.7217i) q^{46} +84.3049 q^{47} -1.11409 q^{48} -23.4647 q^{49} +7.07107 q^{50} +2.10579i q^{51} -5.28152 q^{52} -11.9189i q^{53} -7.05947 q^{54} -16.9394 q^{55} +24.0773i q^{56} +6.75907i q^{57} +45.0446 q^{58} +67.6561 q^{59} -1.24559i q^{60} +35.1621i q^{61} +79.9131 q^{62} +75.9532i q^{63} +8.00000 q^{64} -5.90492i q^{65} +2.98393i q^{66} -44.0660i q^{67} -15.1211i q^{68} +(4.38299 + 4.67188i) q^{69} -26.9193 q^{70} +8.86597 q^{71} +25.2364 q^{72} -87.4150 q^{73} +56.4805i q^{74} +1.39261 q^{75} -48.5352i q^{76} +64.4876 q^{77} -1.04017 q^{78} +154.217i q^{79} +8.94427i q^{80} +78.9115 q^{81} +60.2046 q^{82} +141.642i q^{83} +4.74191i q^{84} +16.9059 q^{85} +29.0933i q^{86} +8.87131 q^{87} -21.4268i q^{88} +63.7252i q^{89} +28.2152i q^{90} +22.4798i q^{91} +(-31.4732 - 33.5476i) q^{92} +15.7385 q^{93} -119.225 q^{94} +54.2639 q^{95} +1.57556 q^{96} -143.322i q^{97} +33.1841 q^{98} -67.5921i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−0.278523			−0.0928408			−0.0464204	−	0.998922i	$-0.514781\pi$
$3$	−0.278523			−0.0928408			−0.0464204	+	0.998922i	$0.514781\pi$
$4$	2.00000			0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	0.393890			0.0656484
$7$		−	8.51262i		−	1.21609i	−0.793903	−	0.608044i	$-0.791954\pi$
$7$		−	8.51262i		−	1.21609i	0.793903	−	0.608044i	$-0.208046\pi$
$8$	−2.82843			−0.353553
$9$	−8.92243			−0.991381
$10$		−	3.16228i		−	0.316228i
$11$			7.57553i			0.688684i	0.938844	+	0.344342i	$0.111898\pi$
$11$			7.57553i			0.688684i	−0.938844	+	0.344342i	$0.888102\pi$
$12$	−0.557045			−0.0464204
$13$	−2.64076			−0.203135			−0.101568	−	0.994829i	$-0.532386\pi$
$13$	−2.64076			−0.203135			−0.101568	+	0.994829i	$0.532386\pi$
$14$			12.0387i			0.859904i
$15$		−	0.622795i		−	0.0415197i
$16$	4.00000			0.250000
$17$		−	7.56057i		−	0.444739i	−0.974962	−	0.222370i	$-0.928621\pi$
$17$		−	7.56057i		−	0.444739i	0.974962	−	0.222370i	$-0.0713792\pi$
$18$	12.6182			0.701012
$19$		−	24.2676i		−	1.27724i	−0.769522	−	0.638620i	$-0.779505\pi$
$19$		−	24.2676i		−	1.27724i	0.769522	−	0.638620i	$-0.220495\pi$
$20$			4.47214i			0.223607i
$21$			2.37096i			0.112903i
$22$		−	10.7134i		−	0.486973i
$23$	−15.7366	−	16.7738i	−0.684199	−	0.729295i
$23$	−15.7366	−	16.7738i	−0.684199	−	0.729295i
$24$	0.787781			0.0328242
$25$	−5.00000			−0.200000
$26$	3.73460			0.143638
$27$	4.99180			0.184881
$28$		−	17.0252i		−	0.608044i
$29$	−31.8513			−1.09832			−0.549161	−	0.835717i	$-0.685053\pi$
$29$	−31.8513			−1.09832			−0.549161	+	0.835717i	$0.685053\pi$
$30$			0.880766i			0.0293589i
$31$	−56.5071			−1.82281			−0.911405	−	0.411511i	$-0.865001\pi$
$31$	−56.5071			−1.82281			−0.911405	+	0.411511i	$0.865001\pi$
$32$	−5.65685			−0.176777
$33$		−	2.10995i		−	0.0639380i
$34$			10.6923i			0.314478i
$35$	19.0348			0.543851
$36$	−17.8449			−0.495690
$37$		−	39.9378i		−	1.07940i	−0.841858	−	0.539700i	$-0.818538\pi$
$37$		−	39.9378i		−	1.07940i	0.841858	−	0.539700i	$-0.181462\pi$
$38$			34.3195i			0.903146i
$39$	0.735511			0.0188593
$40$		−	6.32456i		−	0.158114i
$41$	−42.5710			−1.03832			−0.519159	−	0.854678i	$-0.673755\pi$
$41$	−42.5710			−1.03832			−0.519159	+	0.854678i	$0.673755\pi$
$42$		−	3.35304i		−	0.0798342i
$43$		−	20.5721i		−	0.478420i	−0.970968	−	0.239210i	$-0.923112\pi$
$43$		−	20.5721i		−	0.478420i	0.970968	−	0.239210i	$-0.0768884\pi$
$44$			15.1511i			0.344342i
$45$		−	19.9511i		−	0.443359i
$46$	22.2549	+	23.7217i	0.483802	+	0.515690i
$47$	84.3049			1.79372			0.896860	−	0.442314i	$-0.145842\pi$
$47$	84.3049			1.79372			0.896860	+	0.442314i	$0.145842\pi$
$48$	−1.11409			−0.0232102
$49$	−23.4647			−0.478871
$50$	7.07107			0.141421
$51$			2.10579i			0.0412900i
$52$	−5.28152			−0.101568
$53$		−	11.9189i		−	0.224885i	−0.993658	−	0.112443i	$-0.964133\pi$
$53$		−	11.9189i		−	0.224885i	0.993658	−	0.112443i	$-0.0358674\pi$
$54$	−7.05947			−0.130731
$55$	−16.9394			−0.307989
$56$			24.0773i			0.429952i
$57$			6.75907i			0.118580i
$58$	45.0446			0.776631
$59$	67.6561			1.14671			0.573357	−	0.819306i	$-0.305641\pi$
$59$	67.6561			1.14671			0.573357	+	0.819306i	$0.305641\pi$
$60$		−	1.24559i		−	0.0207598i
$61$			35.1621i			0.576428i	0.957566	+	0.288214i	$0.0930614\pi$
$61$			35.1621i			0.576428i	−0.957566	+	0.288214i	$0.906939\pi$
$62$	79.9131			1.28892
$63$			75.9532i			1.20561i
$64$	8.00000			0.125000
$65$		−	5.90492i		−	0.0908449i
$66$			2.98393i			0.0452110i
$67$		−	44.0660i		−	0.657701i	−0.944382	−	0.328850i	$-0.893339\pi$
$67$		−	44.0660i		−	0.657701i	0.944382	−	0.328850i	$-0.106661\pi$
$68$		−	15.1211i		−	0.222370i
$69$	4.38299	+	4.67188i	0.0635216	+	0.0677084i
$70$	−26.9193			−0.384561
$71$	8.86597			0.124873			0.0624364	−	0.998049i	$-0.480113\pi$
$71$	8.86597			0.124873			0.0624364	+	0.998049i	$0.480113\pi$
$72$	25.2364			0.350506
$73$	−87.4150			−1.19747			−0.598733	−	0.800949i	$-0.704329\pi$
$73$	−87.4150			−1.19747			−0.598733	+	0.800949i	$0.704329\pi$
$74$			56.4805i			0.763250i
$75$	1.39261			0.0185682
$76$		−	48.5352i		−	0.638620i
$77$	64.4876			0.837501
$78$	−1.04017			−0.0133355
$79$			154.217i			1.95211i	0.217517	+	0.976057i	$0.430204\pi$
$79$			154.217i			1.95211i	−0.217517	+	0.976057i	$0.569796\pi$
$80$			8.94427i			0.111803i
$81$	78.9115			0.974216
$82$	60.2046			0.734202
$83$			141.642i			1.70653i	0.521476	+	0.853266i	$0.325382\pi$
$83$			141.642i			1.70653i	−0.521476	+	0.853266i	$0.674618\pi$
$84$			4.74191i			0.0564513i
$85$	16.9059			0.198893
$86$			29.0933i			0.338294i
$87$	8.87131			0.101969
$88$		−	21.4268i		−	0.243487i
$89$			63.7252i			0.716013i	0.933719	+	0.358007i	$0.116543\pi$
$89$			63.7252i			0.716013i	−0.933719	+	0.358007i	$0.883457\pi$
$90$			28.2152i			0.313502i
$91$			22.4798i			0.247030i
$92$	−31.4732	−	33.5476i	−0.342100	−	0.364648i
$93$	15.7385			0.169231
$94$	−119.225			−1.26835
$95$	54.2639			0.571199
$96$	1.57556			0.0164121
$97$		−	143.322i		−	1.47755i	−0.673952	−	0.738775i	$-0.735404\pi$
$97$		−	143.322i		−	1.47755i	0.673952	−	0.738775i	$-0.264596\pi$
$98$	33.1841			0.338613
$99$		−	67.5921i		−	0.682748i
$100$	−10.0000			−0.100000
$101$	27.7102			0.274359			0.137179	−	0.990546i	$-0.456196\pi$
$101$	27.7102			0.274359			0.137179	+	0.990546i	$0.456196\pi$
$102$		−	2.97803i		−	0.0291964i
$103$			133.542i			1.29652i	0.761418	+	0.648261i	$0.224503\pi$
$103$			133.542i			1.29652i	−0.761418	+	0.648261i	$0.775497\pi$
$104$	7.46919			0.0718192
$105$	−5.30162			−0.0504916
$106$			16.8559i			0.159018i
$107$		−	50.3091i		−	0.470179i	−0.971974	−	0.235089i	$-0.924462\pi$
$107$		−	50.3091i		−	0.470179i	0.971974	−	0.235089i	$-0.0755383\pi$
$108$	9.98360			0.0924407
$109$		−	128.819i		−	1.18182i	−0.806737	−	0.590911i	$-0.798768\pi$
$109$		−	128.819i		−	1.18182i	0.806737	−	0.590911i	$-0.201232\pi$
$110$	23.9559			0.217781
$111$			11.1236i			0.100212i
$112$		−	34.0505i		−	0.304022i
$113$		−	86.3028i		−	0.763742i	−0.924216	−	0.381871i	$-0.875280\pi$
$113$		−	86.3028i		−	0.763742i	0.924216	−	0.381871i	$-0.124720\pi$
$114$		−	9.55876i		−	0.0838488i
$115$	37.5073	−	35.1881i	0.326151	−	0.305983i
$116$	−63.7027			−0.549161
$117$	23.5620			0.201384
$118$	−95.6802			−0.810849
$119$	−64.3602			−0.540842
$120$			1.76153i			0.0146794i
$121$	63.6114			0.525714
$122$		−	49.7267i		−	0.407596i
$123$	11.8570			0.0963983
$124$	−113.014			−0.911405
$125$		−	11.1803i		−	0.0894427i
$126$		−	107.414i		−	0.852492i
$127$	−11.0135			−0.0867206			−0.0433603	−	0.999059i	$-0.513806\pi$
$127$	−11.0135			−0.0867206			−0.0433603	+	0.999059i	$0.513806\pi$
$128$	−11.3137			−0.0883883
$129$			5.72978i			0.0444169i
$130$			8.35081i			0.0642370i
$131$	3.63941			0.0277818			0.0138909	−	0.999904i	$-0.495578\pi$
$131$	3.63941			0.0277818			0.0138909	+	0.999904i	$0.495578\pi$
$132$		−	4.21991i		−	0.0319690i
$133$	−206.581			−1.55324
$134$			62.3187i			0.465065i
$135$			11.1620i			0.0826815i
$136$			21.3845i			0.157239i
$137$			9.69785i			0.0707873i	0.999373	+	0.0353936i	$0.0112685\pi$
$137$			9.69785i			0.0707873i	−0.999373	+	0.0353936i	$0.988732\pi$
$138$	−6.19849	−	6.60703i	−0.0449166	−	0.0478771i
$139$	8.05485			0.0579486			0.0289743	−	0.999580i	$-0.490776\pi$
$139$	8.05485			0.0579486			0.0289743	+	0.999580i	$0.490776\pi$
$140$	38.0696			0.271926
$141$	−23.4808			−0.166531
$142$	−12.5384			−0.0882984
$143$		−	20.0051i		−	0.139896i
$144$	−35.6897			−0.247845
$145$		−	71.2217i		−	0.491184i
$146$	123.624			0.846737
$147$	6.53544			0.0444588
$148$		−	79.8755i		−	0.539700i
$149$			144.062i			0.966859i	0.875383	+	0.483430i	$0.160609\pi$
$149$			144.062i			0.966859i	−0.875383	+	0.483430i	$0.839391\pi$
$150$	−1.96945			−0.0131297
$151$	−109.956			−0.728188			−0.364094	−	0.931362i	$-0.618621\pi$
$151$	−109.956			−0.728188			−0.364094	+	0.931362i	$0.618621\pi$
$152$			68.6391i			0.451573i
$153$			67.4586i			0.440906i
$154$	−91.1992			−0.592202
$155$		−	126.354i		−	0.815185i
$156$	1.47102			0.00942963
$157$		−	24.8208i		−	0.158094i	−0.996871	−	0.0790471i	$-0.974812\pi$
$157$		−	24.8208i		−	0.158094i	0.996871	−	0.0790471i	$-0.0251877\pi$
$158$		−	218.096i		−	1.38035i
$159$			3.31969i			0.0208785i
$160$		−	12.6491i		−	0.0790569i
$161$	−142.789	+	133.960i	−0.886887	+	0.832047i
$162$	−111.598			−0.688875
$163$	108.964			0.668489			0.334244	−	0.942486i	$-0.391519\pi$
$163$	108.964			0.668489			0.334244	+	0.942486i	$0.391519\pi$
$164$	−85.1421			−0.519159
$165$	4.71800			0.0285940
$166$		−	200.312i		−	1.20670i
$167$	72.1383			0.431966			0.215983	−	0.976397i	$-0.430704\pi$
$167$	72.1383			0.431966			0.215983	+	0.976397i	$0.430704\pi$
$168$		−	6.70608i		−	0.0399171i
$169$	−162.026			−0.958736
$170$	−23.9086			−0.140639
$171$			216.526i			1.26623i
$172$		−	41.1441i		−	0.239210i
$173$	−150.077			−0.867497			−0.433748	−	0.901034i	$-0.642809\pi$
$173$	−150.077			−0.867497			−0.433748	+	0.901034i	$0.642809\pi$
$174$	−12.5459			−0.0721031
$175$			42.5631i			0.243218i
$176$			30.3021i			0.172171i
$177$	−18.8437			−0.106462
$178$		−	90.1210i		−	0.506298i
$179$	207.058			1.15675			0.578375	−	0.815771i	$-0.303687\pi$
$179$	207.058			1.15675			0.578375	+	0.815771i	$0.303687\pi$
$180$		−	39.9023i		−	0.221679i
$181$		−	331.138i		−	1.82949i	−0.404031	−	0.914746i	$-0.632391\pi$
$181$		−	331.138i		−	1.82949i	0.404031	−	0.914746i	$-0.367609\pi$
$182$		−	31.7912i		−	0.174677i
$183$		−	9.79343i		−	0.0535160i
$184$	44.5098	+	47.4434i	0.241901	+	0.257845i
$185$	89.3036			0.482722
$186$	−22.2576			−0.119665
$187$	57.2753			0.306285
$188$	168.610			0.896860
$189$		−	42.4933i		−	0.224832i
$190$	−76.7408			−0.403899
$191$		−	172.749i		−	0.904447i	−0.891905	−	0.452223i	$-0.850631\pi$
$191$		−	172.749i		−	0.904447i	0.891905	−	0.452223i	$-0.149369\pi$
$192$	−2.22818			−0.0116051
$193$	136.450			0.706996			0.353498	−	0.935435i	$-0.384992\pi$
$193$	136.450			0.706996			0.353498	+	0.935435i	$0.384992\pi$
$194$			202.689i			1.04479i
$195$			1.64465i			0.00843412i
$196$	−46.9293			−0.239435
$197$	−271.090			−1.37609			−0.688046	−	0.725667i	$-0.741531\pi$
$197$	−271.090			−1.37609			−0.688046	+	0.725667i	$0.741531\pi$
$198$			95.5896i			0.482776i
$199$		−	257.292i		−	1.29292i	−0.762946	−	0.646462i	$-0.776248\pi$
$199$		−	257.292i		−	1.29292i	0.762946	−	0.646462i	$-0.223752\pi$
$200$	14.1421			0.0707107
$201$			12.2734i			0.0610615i
$202$	−39.1882			−0.194001
$203$			271.138i			1.33566i
$204$			4.21158i			0.0206450i
$205$		−	95.1918i		−	0.464350i
$206$		−	188.857i		−	0.916780i
$207$	140.408	+	149.663i	0.678302	+	0.723009i
$208$	−10.5630			−0.0507838
$209$	183.840			0.879615
$210$	7.49762			0.0357030
$211$	54.1944			0.256846			0.128423	−	0.991720i	$-0.459009\pi$
$211$	54.1944			0.256846			0.128423	+	0.991720i	$0.459009\pi$
$212$		−	23.8378i		−	0.112443i
$213$	−2.46937			−0.0115933
$214$			71.1478i			0.332467i
$215$	46.0005			0.213956
$216$	−14.1189			−0.0653655
$217$			481.023i			2.21670i
$218$			182.177i			0.835674i
$219$	24.3471			0.111174
$220$	−33.8788			−0.153994
$221$			19.9656i			0.0903423i
$222$		−	15.7311i		−	0.0708608i
$223$	104.611			0.469105			0.234553	−	0.972103i	$-0.424637\pi$
$223$	104.611			0.469105			0.234553	+	0.972103i	$0.424637\pi$
$224$			48.1546i			0.214976i
$225$	44.6121			0.198276
$226$			122.051i			0.540047i
$227$		−	200.484i		−	0.883190i	−0.897215	−	0.441595i	$-0.854413\pi$
$227$		−	200.484i		−	0.883190i	0.897215	−	0.441595i	$-0.145587\pi$
$228$			13.5181i			0.0592901i
$229$		−	22.0718i		−	0.0963834i	−0.998838	−	0.0481917i	$-0.984654\pi$
$229$		−	22.0718i		−	0.0963834i	0.998838	−	0.0481917i	$-0.0153458\pi$
$230$	−53.0434	+	49.7634i	−0.230623	+	0.216363i
$231$	−17.9612			−0.0777543
$232$	90.0892			0.388315
$233$	−338.632			−1.45335			−0.726677	−	0.686979i	$-0.758936\pi$
$233$	−338.632			−1.45335			−0.726677	+	0.686979i	$0.758936\pi$
$234$	−33.3217			−0.142400
$235$			188.511i			0.802176i
$236$	135.312			0.573357
$237$		−	42.9529i		−	0.181236i
$238$	91.0191			0.382433
$239$	149.374			0.624997			0.312499	−	0.949918i	$-0.398834\pi$
$239$	149.374			0.624997			0.312499	+	0.949918i	$0.398834\pi$
$240$		−	2.49118i		−	0.0103799i
$241$		−	133.030i		−	0.551991i	−0.961159	−	0.275995i	$-0.910993\pi$
$241$		−	133.030i		−	0.551991i	0.961159	−	0.275995i	$-0.0890074\pi$
$242$	−89.9601			−0.371736
$243$	−66.9048			−0.275328
$244$			70.3242i			0.288214i
$245$		−	52.4686i		−	0.214158i
$246$	−16.7683			−0.0681639
$247$			64.0848i			0.259453i
$248$	159.826			0.644461
$249$		−	39.4505i		−	0.158436i
$250$			15.8114i			0.0632456i
$251$			376.920i			1.50167i	0.660489	+	0.750836i	$0.270349\pi$
$251$			376.920i			1.50167i	−0.660489	+	0.750836i	$0.729651\pi$
$252$			151.906i			0.602803i
$253$	127.070	−	119.213i	0.502254	−	0.471197i
$254$	15.5755			0.0613208
$255$	−4.70869			−0.0184654
$256$	16.0000			0.0625000
$257$	226.085			0.879708			0.439854	−	0.898069i	$-0.355030\pi$
$257$	226.085			0.879708			0.439854	+	0.898069i	$0.355030\pi$
$258$		−	8.10314i		−	0.0314075i
$259$	−339.975			−1.31264
$260$		−	11.8098i		−	0.0454224i
$261$	284.191			1.08885
$262$	−5.14690			−0.0196447
$263$			2.43654i			0.00926441i	0.999989	+	0.00463221i	$0.00147448\pi$
$263$			2.43654i			0.00926441i	−0.999989	+	0.00463221i	$0.998526\pi$
$264$			5.96785i			0.0226055i
$265$	26.6515			0.100572
$266$	292.149			1.09830
$267$		−	17.7489i		−	0.0664753i
$268$		−	88.1319i		−	0.328850i
$269$	−311.337			−1.15739			−0.578694	−	0.815545i	$-0.696437\pi$
$269$	−311.337			−1.15739			−0.578694	+	0.815545i	$0.696437\pi$
$270$		−	15.7855i		−	0.0584647i
$271$	260.751			0.962182			0.481091	−	0.876671i	$-0.340241\pi$
$271$	260.751			0.962182			0.481091	+	0.876671i	$0.340241\pi$
$272$		−	30.2423i		−	0.111185i
$273$		−	6.26112i		−	0.0229345i
$274$		−	13.7148i		−	0.0500541i
$275$		−	37.8776i		−	0.137737i
$276$	8.76599	+	9.34376i	0.0317608	+	0.0338542i
$277$	−182.267			−0.658004			−0.329002	−	0.944329i	$-0.606712\pi$
$277$	−182.267			−0.658004			−0.329002	+	0.944329i	$0.606712\pi$
$278$	−11.3913			−0.0409758
$279$	504.180			1.80710
$280$	−53.8385			−0.192280
$281$		−	4.60502i		−	0.0163880i	−0.999966	−	0.00819398i	$-0.997392\pi$
$281$		−	4.60502i		−	0.0163880i	0.999966	−	0.00819398i	$-0.00260825\pi$
$282$	33.2069			0.117755
$283$		−	332.897i		−	1.17631i	−0.808747	−	0.588157i	$-0.799854\pi$
$283$		−	332.897i		−	1.17631i	0.808747	−	0.588157i	$-0.200146\pi$
$284$	17.7319			0.0624364
$285$	−15.1137			−0.0530306
$286$			28.2915i			0.0989215i
$287$			362.391i			1.26269i
$288$	50.4729			0.175253
$289$	231.838			0.802207
$290$			100.723i			0.347320i
$291$			39.9185i			0.137177i
$292$	−174.830			−0.598733
$293$		−	336.114i		−	1.14715i	−0.819154	−	0.573574i	$-0.805557\pi$
$293$		−	336.114i		−	1.14715i	0.819154	−	0.573574i	$-0.194443\pi$
$294$	−9.24251			−0.0314371
$295$			151.284i			0.512826i
$296$			112.961i			0.381625i
$297$			37.8155i			0.127325i
$298$		−	203.734i		−	0.683673i
$299$	41.5565	+	44.2955i	0.138985	+	0.148146i
$300$	2.78523			0.00928408
$301$	−175.122			−0.581801
$302$	155.502			0.514907
$303$	−7.71792			−0.0254717
$304$		−	97.0703i		−	0.319310i
$305$	−78.6248			−0.257786
$306$		−	95.4009i		−	0.311768i
$307$	−457.934			−1.49164			−0.745821	−	0.666147i	$-0.767943\pi$
$307$	−457.934			−1.49164			−0.745821	+	0.666147i	$0.767943\pi$
$308$	128.975			0.418750
$309$		−	37.1944i		−	0.120370i
$310$			178.691i			0.576423i
$311$	−455.620			−1.46502			−0.732508	−	0.680758i	$-0.761650\pi$
$311$	−455.620			−1.46502			−0.732508	+	0.680758i	$0.761650\pi$
$312$	−2.08034			−0.00666775
$313$			589.353i			1.88292i	0.337130	+	0.941458i	$0.390544\pi$
$313$			589.353i			1.88292i	−0.337130	+	0.941458i	$0.609456\pi$
$314$			35.1019i			0.111789i
$315$	−169.837			−0.539164
$316$			308.434i			0.976057i
$317$	−386.251			−1.21846			−0.609229	−	0.792994i	$-0.708521\pi$
$317$	−386.251			−1.21846			−0.609229	+	0.792994i	$0.708521\pi$
$318$		−	4.69475i		−	0.0147634i
$319$		−	241.291i		−	0.756397i
$320$			17.8885i			0.0559017i
$321$			14.0122i			0.0436518i
$322$	201.934	−	189.447i	0.627124	−	0.588346i
$323$	−183.477			−0.568039
$324$	157.823			0.487108
$325$	13.2038			0.0406271
$326$	−154.098			−0.472693
$327$			35.8789i			0.109721i
$328$	120.409			0.367101
$329$		−	717.655i		−	2.18132i
$330$	−6.67226			−0.0202190
$331$	220.712			0.666803			0.333402	−	0.942785i	$-0.391804\pi$
$331$	220.712			0.666803			0.333402	+	0.942785i	$0.391804\pi$
$332$			283.284i			0.853266i
$333$			356.342i			1.07010i
$334$	−102.019			−0.305446
$335$	98.5345			0.294133
$336$			9.48382i			0.0282257i
$337$		−	193.563i		−	0.574371i	−0.957875	−	0.287185i	$-0.907280\pi$
$337$		−	193.563i		−	0.574371i	0.957875	−	0.287185i	$-0.0927196\pi$
$338$	229.140			0.677929
$339$			24.0373i			0.0709064i
$340$	33.8119			0.0994467
$341$		−	428.071i		−	1.25534i
$342$		−	306.213i		−	0.895361i
$343$		−	217.373i		−	0.633739i
$344$			58.1866i			0.169147i
$345$	−10.4466	+	9.80067i	−0.0302801	+	0.0284077i
$346$	212.241			0.613413
$347$	−262.429			−0.756278			−0.378139	−	0.925749i	$-0.623436\pi$
$347$	−262.429			−0.756278			−0.378139	+	0.925749i	$0.623436\pi$
$348$	17.7426			0.0509846
$349$	229.831			0.658543			0.329271	−	0.944235i	$-0.393197\pi$
$349$	229.831			0.658543			0.329271	+	0.944235i	$0.393197\pi$
$350$		−	60.1933i		−	0.171981i
$351$	−13.1821			−0.0375560
$352$		−	42.8536i		−	0.121743i
$353$	367.482			1.04103			0.520513	−	0.853854i	$-0.325741\pi$
$353$	367.482			1.04103			0.520513	+	0.853854i	$0.325741\pi$
$354$	26.6491			0.0752799
$355$			19.8249i			0.0558448i
$356$			127.450i			0.358007i
$357$	17.9258			0.0502123
$358$	−292.824			−0.817945
$359$		−	239.971i		−	0.668442i	−0.942495	−	0.334221i	$-0.891527\pi$
$359$		−	239.971i		−	0.668442i	0.942495	−	0.334221i	$-0.108473\pi$
$360$			56.4304i			0.156751i
$361$	−227.915			−0.631344
$362$			468.300i			1.29365i
$363$	−17.7172			−0.0488077
$364$			44.9595i			0.123515i
$365$		−	195.466i		−	0.535523i
$366$			13.8500i			0.0378416i
$367$		−	389.113i		−	1.06025i	−0.847918	−	0.530127i	$-0.822144\pi$
$367$		−	389.113i		−	1.06025i	0.847918	−	0.530127i	$-0.177856\pi$
$368$	−62.9463	−	67.0952i	−0.171050	−	0.182324i
$369$	379.837			1.02937
$370$	−126.294			−0.341336
$371$	−101.461			−0.273480
$372$	31.4770			0.0846156
$373$			546.309i			1.46463i	0.680964	+	0.732317i	$0.261561\pi$
$373$			546.309i			1.46463i	−0.680964	+	0.732317i	$0.738439\pi$
$374$	−80.9995			−0.216576
$375$			3.11398i			0.00830394i
$376$	−238.450			−0.634176
$377$	84.1117			0.223108
$378$			60.0946i			0.158980i
$379$			295.837i			0.780573i	0.920693	+	0.390287i	$0.127624\pi$
$379$			295.837i			0.780573i	−0.920693	+	0.390287i	$0.872376\pi$
$380$	108.528			0.285600
$381$	3.06751			0.00805122
$382$			244.304i			0.639541i
$383$		−	566.033i		−	1.47789i	−0.673765	−	0.738946i	$-0.735324\pi$
$383$		−	566.033i		−	1.47789i	0.673765	−	0.738946i	$-0.264676\pi$
$384$	3.15112			0.00820605
$385$			144.199i			0.374542i
$386$	−192.970			−0.499921
$387$			183.553i			0.474296i
$388$		−	286.645i		−	0.738775i
$389$		−	196.043i		−	0.503966i	−0.967732	−	0.251983i	$-0.918917\pi$
$389$		−	196.043i		−	0.503966i	0.967732	−	0.251983i	$-0.0810826\pi$
$390$		−	2.32589i		−	0.00596382i
$391$	−126.819	+	118.978i	−0.324346	+	0.304290i
$392$	66.3681			0.169306
$393$	−1.01366			−0.00257928
$394$	383.380			0.973045
$395$	−344.840			−0.873012
$396$		−	135.184i		−	0.341374i
$397$	−298.788			−0.752616			−0.376308	−	0.926495i	$-0.622806\pi$
$397$	−298.788			−0.752616			−0.376308	+	0.926495i	$0.622806\pi$
$398$			363.866i			0.914236i
$399$	57.5374			0.144204
$400$	−20.0000			−0.0500000
$401$			785.114i			1.95789i	0.204121	+	0.978946i	$0.434567\pi$
$401$			785.114i			1.95789i	−0.204121	+	0.978946i	$0.565433\pi$
$402$		−	17.3572i		−	0.0431770i
$403$	149.222			0.370277
$404$	55.4204			0.137179
$405$			176.451i			0.435683i
$406$		−	383.447i		−	0.944452i
$407$	302.550			0.743365
$408$		−	5.95607i		−	0.0145982i
$409$	358.186			0.875761			0.437881	−	0.899033i	$-0.355729\pi$
$409$	358.186			0.875761			0.437881	+	0.899033i	$0.355729\pi$
$410$			134.621i			0.328345i
$411$		−	2.70107i		−	0.00657195i
$412$			267.084i			0.648261i
$413$		−	575.930i		−	1.39450i
$414$	−198.568	−	211.655i	−0.479632	−	0.511245i
$415$	−316.722			−0.763184
$416$	14.9384			0.0359096
$417$	−2.24346			−0.00537999
$418$	−259.988			−0.621982
$419$		−	195.271i		−	0.466042i	−0.972472	−	0.233021i	$-0.925139\pi$
$419$		−	195.271i		−	0.466042i	0.972472	−	0.233021i	$-0.0748610\pi$
$420$	−10.6032			−0.0252458
$421$		−	768.042i		−	1.82433i	−0.409826	−	0.912164i	$-0.634410\pi$
$421$		−	768.042i		−	1.82433i	0.409826	−	0.912164i	$-0.365590\pi$
$422$	−76.6425			−0.181617
$423$	−752.204			−1.77826
$424$			33.7118i			0.0795089i
$425$			37.8028i			0.0889479i
$426$	3.49222			0.00819770
$427$	299.321			0.700987
$428$		−	100.618i		−	0.235089i
$429$			5.57188i			0.0129881i
$430$	−65.0546			−0.151290
$431$			333.122i			0.772905i	0.922309	+	0.386453i	$0.126300\pi$
$431$			333.122i			0.772905i	−0.922309	+	0.386453i	$0.873700\pi$
$432$	19.9672			0.0462204
$433$		−	7.49741i		−	0.0173150i	−0.999963	−	0.00865752i	$-0.997244\pi$
$433$		−	7.49741i		−	0.0173150i	0.999963	−	0.00865752i	$-0.00275581\pi$
$434$		−	680.270i		−	1.56744i
$435$			19.8369i			0.0456020i
$436$		−	257.637i		−	0.590911i
$437$	−407.059	+	381.889i	−0.931485	+	0.873887i
$438$	−34.4319			−0.0786117
$439$	−303.939			−0.692344			−0.346172	−	0.938171i	$-0.612519\pi$
$439$	−303.939			−0.692344			−0.346172	+	0.938171i	$0.612519\pi$
$440$	47.9118			0.108891
$441$	209.362			0.474743
$442$		−	28.2357i		−	0.0638816i
$443$	637.145			1.43825			0.719125	−	0.694881i	$-0.244543\pi$
$443$	637.145			1.43825			0.719125	+	0.694881i	$0.244543\pi$
$444$			22.2471i			0.0501062i
$445$	−142.494			−0.320211
$446$	−147.942			−0.331708
$447$		−	40.1245i		−	0.0897640i
$448$		−	68.1009i		−	0.152011i
$449$	88.9331			0.198069			0.0990346	−	0.995084i	$-0.468425\pi$
$449$	88.9331			0.198069			0.0990346	+	0.995084i	$0.468425\pi$
$450$	−63.0911			−0.140202
$451$		−	322.498i		−	0.715073i
$452$		−	172.606i		−	0.381871i
$453$	30.6253			0.0676056
$454$			283.527i			0.624509i
$455$	−50.2663			−0.110475
$456$		−	19.1175i		−	0.0419244i
$457$			377.669i			0.826410i	0.910638	+	0.413205i	$0.135591\pi$
$457$			377.669i			0.826410i	−0.910638	+	0.413205i	$0.864409\pi$
$458$			31.2142i			0.0681534i
$459$		−	37.7408i		−	0.0822240i
$460$	75.0147	−	70.3761i	0.163075	−	0.152992i
$461$	−585.070			−1.26913			−0.634566	−	0.772869i	$-0.718821\pi$
$461$	−585.070			−1.26913			−0.634566	+	0.772869i	$0.718821\pi$
$462$	25.4010			0.0549806
$463$	−225.877			−0.487854			−0.243927	−	0.969794i	$-0.578436\pi$
$463$	−225.877			−0.487854			−0.243927	+	0.969794i	$0.578436\pi$
$464$	−127.405			−0.274580
$465$			35.1924i			0.0756825i
$466$	478.897			1.02768
$467$		−	702.984i		−	1.50532i	−0.658410	−	0.752659i	$-0.728771\pi$
$467$		−	702.984i		−	1.50532i	0.658410	−	0.752659i	$-0.271229\pi$
$468$	47.1240			0.100692
$469$	−375.117			−0.799822
$470$		−	266.595i		−	0.567224i
$471$			6.91315i			0.0146776i
$472$	−191.360			−0.405424
$473$	155.844			0.329480
$474$			60.7446i			0.128153i
$475$			121.338i			0.255448i
$476$	−128.720			−0.270421
$477$			106.346i			0.222947i
$478$	−211.247			−0.441940
$479$		−	291.706i		−	0.608989i	−0.952514	−	0.304494i	$-0.901512\pi$
$479$		−	291.706i		−	0.608989i	0.952514	−	0.304494i	$-0.0984875\pi$
$480$			3.52306i			0.00733971i
$481$			105.466i			0.219264i
$482$			188.132i			0.390316i
$483$	39.7699	−	37.3107i	0.0823394	−	0.0772479i
$484$	127.223			0.262857
$485$	320.479			0.660781
$486$	94.6177			0.194687
$487$	205.957			0.422909			0.211454	−	0.977388i	$-0.432180\pi$
$487$	205.957			0.422909			0.211454	+	0.977388i	$0.432180\pi$
$488$		−	99.4534i		−	0.203798i
$489$	−30.3488			−0.0620630
$490$			74.2018i			0.151432i
$491$	−192.478			−0.392012			−0.196006	−	0.980603i	$-0.562797\pi$
$491$	−192.478			−0.392012			−0.196006	+	0.980603i	$0.562797\pi$
$492$	23.7140			0.0481992
$493$			240.814i			0.488467i
$494$		−	90.6296i		−	0.183461i
$495$	151.140			0.305334
$496$	−226.028			−0.455703
$497$		−	75.4726i		−	0.151856i
$498$			55.7915i			0.112031i
$499$	887.386			1.77833			0.889164	−	0.457589i	$-0.151287\pi$
$499$	887.386			1.77833			0.889164	+	0.457589i	$0.151287\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	−20.0921			−0.0401041
$502$		−	533.045i		−	1.06184i
$503$		−	330.810i		−	0.657673i	−0.944387	−	0.328837i	$-0.893343\pi$
$503$		−	330.810i		−	0.657673i	0.944387	−	0.328837i	$-0.106657\pi$
$504$		−	214.828i		−	0.426246i
$505$			61.9619i			0.122697i
$506$	−179.704	+	168.592i	−0.355147	+	0.333187i
$507$	45.1280			0.0890099
$508$	−22.0270			−0.0433603
$509$	−407.928			−0.801430			−0.400715	−	0.916203i	$-0.631238\pi$
$509$	−407.928			−0.801430			−0.400715	+	0.916203i	$0.631238\pi$
$510$	6.65909			0.0130570
$511$			744.131i			1.45622i
$512$	−22.6274			−0.0441942
$513$		−	121.139i		−	0.236138i
$514$	−319.733			−0.622048
$515$	−298.609			−0.579822
$516$			11.4596i			0.0222085i
$517$			638.654i			1.23531i
$518$	480.797			0.928180
$519$	41.7998			0.0805391
$520$			16.7016i			0.0321185i
$521$		−	458.780i		−	0.880576i	−0.897857	−	0.440288i	$-0.854876\pi$
$521$		−	458.780i		−	0.880576i	0.897857	−	0.440288i	$-0.145124\pi$
$522$	−401.907			−0.769937
$523$		−	404.987i		−	0.774354i	−0.922005	−	0.387177i	$-0.873450\pi$
$523$		−	404.987i		−	0.774354i	0.922005	−	0.387177i	$-0.126550\pi$
$524$	7.27882			0.0138909
$525$		−	11.8548i		−	0.0225805i
$526$		−	3.44579i		−	0.00655093i
$527$			427.226i			0.810675i
$528$		−	8.43982i		−	0.0159845i
$529$	−33.7199	+	527.924i	−0.0637427	+	0.997966i
$530$	−37.6909			−0.0711149
$531$	−603.656			−1.13683
$532$	−413.161			−0.776619
$533$	112.420			0.210919
$534$			25.1007i			0.0470051i
$535$	112.495			0.210270
$536$			124.637i			0.232532i
$537$	−57.6703			−0.107394
$538$	440.298			0.818397
$539$		−	177.757i		−	0.329791i
$540$			22.3240i			0.0413408i
$541$	1047.51			1.93625			0.968123	−	0.250477i	$-0.0805875\pi$
$541$	1047.51			1.93625			0.968123	+	0.250477i	$0.0805875\pi$
$542$	−368.758			−0.680366
$543$			92.2294i			0.169851i
$544$			42.7690i			0.0786195i
$545$	288.047			0.528527
$546$			8.85457i			0.0162172i
$547$	123.784			0.226296			0.113148	−	0.993578i	$-0.463907\pi$
$547$	123.784			0.226296			0.113148	+	0.993578i	$0.463907\pi$
$548$			19.3957i			0.0353936i
$549$		−	313.731i		−	0.571459i
$550$			53.5671i			0.0973946i
$551$			772.955i			1.40282i
$552$	−12.3970	−	13.2141i	−0.0224583	−	0.0239385i
$553$	1312.79			2.37394
$554$	257.765			0.465279
$555$	−24.8731			−0.0448163
$556$	16.1097			0.0289743
$557$			246.292i			0.442176i	0.975254	+	0.221088i	$0.0709608\pi$
$557$			246.292i			0.442176i	−0.975254	+	0.221088i	$0.929039\pi$
$558$	−713.019			−1.27781
$559$			54.3259i			0.0971840i
$560$	76.1392			0.135963
$561$	−15.9525			−0.0284357
$562$			6.51248i			0.0115880i
$563$			574.776i			1.02092i	0.859902	+	0.510458i	$0.170524\pi$
$563$			574.776i			1.02092i	−0.859902	+	0.510458i	$0.829476\pi$
$564$	−46.9616			−0.0832653
$565$	192.979			0.341556
$566$			470.787i			0.831780i
$567$		−	671.743i		−	1.18473i
$568$	−25.0768			−0.0441492
$569$			794.332i			1.39601i	0.716091	+	0.698007i	$0.245930\pi$
$569$			794.332i			1.39601i	−0.716091	+	0.698007i	$0.754070\pi$
$570$	21.3740			0.0374983
$571$		−	416.688i		−	0.729751i	−0.931056	−	0.364876i	$-0.881111\pi$
$571$		−	416.688i		−	0.729751i	0.931056	−	0.364876i	$-0.118889\pi$
$572$		−	40.0103i		−	0.0699480i
$573$			48.1146i			0.0839696i
$574$		−	512.498i		−	0.892854i
$575$	78.6829	+	83.8689i	0.136840	+	0.145859i
$576$	−71.3794			−0.123923
$577$	−282.647			−0.489856			−0.244928	−	0.969541i	$-0.578764\pi$
$577$	−282.647			−0.489856			−0.244928	+	0.969541i	$0.578764\pi$
$578$	−327.868			−0.567246
$579$	−38.0044			−0.0656381
$580$		−	142.443i		−	0.245592i
$581$	1205.75			2.07529
$582$		−	56.4533i		−	0.0969988i
$583$	90.2920			0.154875
$584$	247.247			0.423368
$585$			52.6862i			0.0900618i
$586$			475.337i			0.811156i
$587$	−168.123			−0.286410			−0.143205	−	0.989693i	$-0.545741\pi$
$587$	−168.123			−0.286410			−0.143205	+	0.989693i	$0.545741\pi$
$588$	13.0709			0.0222294
$589$			1371.29i			2.32817i
$590$		−	213.947i		−	0.362623i
$591$	75.5048			0.127758
$592$		−	159.751i		−	0.269850i
$593$	−419.364			−0.707191			−0.353595	−	0.935398i	$-0.615041\pi$
$593$	−419.364			−0.707191			−0.353595	+	0.935398i	$0.615041\pi$
$594$		−	53.4792i		−	0.0900323i
$595$		−	143.914i		−	0.241872i
$596$			288.124i			0.483430i
$597$			71.6616i			0.120036i
$598$	−58.7698	−	62.6433i	−0.0982773	−	0.104755i
$599$	−519.774			−0.867736			−0.433868	−	0.900977i	$-0.642852\pi$
$599$	−519.774			−0.867736			−0.433868	+	0.900977i	$0.642852\pi$
$600$	−3.93890			−0.00656484
$601$	1089.19			1.81230			0.906151	−	0.422955i	$-0.139007\pi$
$601$	1089.19			1.81230			0.906151	+	0.422955i	$0.139007\pi$
$602$	247.660			0.411395
$603$			393.175i			0.652032i
$604$	−219.913			−0.364094
$605$			142.239i			0.235107i
$606$	10.9148			0.0180112
$607$	890.673			1.46734			0.733668	−	0.679508i	$-0.237807\pi$
$607$	890.673			1.46734			0.733668	+	0.679508i	$0.237807\pi$
$608$			137.278i			0.225786i
$609$		−	75.5181i		−	0.124003i
$610$	111.192			0.182282
$611$	−222.629			−0.364368
$612$			134.917i			0.220453i
$613$		−	629.354i		−	1.02668i	−0.858186	−	0.513339i	$-0.828408\pi$
$613$		−	629.354i		−	1.02668i	0.858186	−	0.513339i	$-0.171592\pi$
$614$	647.616			1.05475
$615$			26.5131i			0.0431107i
$616$	−182.398			−0.296101
$617$			157.187i			0.254760i	0.991854	+	0.127380i	$0.0406568\pi$
$617$			157.187i			0.254760i	−0.991854	+	0.127380i	$0.959343\pi$
$618$			52.6008i			0.0851146i
$619$			462.293i			0.746838i	0.927663	+	0.373419i	$0.121815\pi$
$619$			462.293i			0.746838i	−0.927663	+	0.373419i	$0.878185\pi$
$620$		−	252.707i		−	0.407593i
$621$	−78.5539	−	83.7314i	−0.126496	−	0.134833i
$622$	644.344			1.03592
$623$	542.468			0.870735
$624$	2.94204			0.00471481
$625$	25.0000			0.0400000
$626$		−	833.471i		−	1.33142i
$627$	−51.2035			−0.0816642
$628$		−	49.6416i		−	0.0790471i
$629$	−301.952			−0.480051
$630$	240.185			0.381246
$631$			411.630i			0.652345i	0.945310	+	0.326173i	$0.105759\pi$
$631$			411.630i			0.652345i	−0.945310	+	0.326173i	$0.894241\pi$
$632$		−	436.191i		−	0.690176i
$633$	−15.0944			−0.0238458
$634$	546.242			0.861581
$635$		−	24.6270i		−	0.0387827i
$636$			6.63937i			0.0104393i
$637$	61.9645			0.0972756
$638$			341.236i			0.534853i
$639$	−79.1060			−0.123797
$640$		−	25.2982i		−	0.0395285i
$641$		−	251.089i		−	0.391715i	−0.980632	−	0.195857i	$-0.937251\pi$
$641$		−	251.089i		−	0.391715i	0.980632	−	0.195857i	$-0.0627490\pi$
$642$		−	19.8163i		−	0.0308665i
$643$			102.907i			0.160042i	0.996793	+	0.0800211i	$0.0254988\pi$
$643$			102.907i			0.160042i	−0.996793	+	0.0800211i	$0.974501\pi$
$644$	−285.578	+	267.919i	−0.443444	+	0.416023i
$645$	−12.8122			−0.0198639
$646$	259.475			0.401664
$647$	−437.368			−0.675993			−0.337997	−	0.941147i	$-0.609749\pi$
$647$	−437.368			−0.675993			−0.337997	+	0.941147i	$0.609749\pi$
$648$	−223.195			−0.344437
$649$			512.530i			0.789723i
$650$	−18.6730			−0.0287277
$651$		−	133.976i		−	0.205800i
$652$	217.927			0.334244
$653$	−94.4001			−0.144564			−0.0722819	−	0.997384i	$-0.523028\pi$
$653$	−94.4001			−0.144564			−0.0722819	+	0.997384i	$0.523028\pi$
$654$		−	50.7404i		−	0.0775847i
$655$			8.13797i			0.0124244i
$656$	−170.284			−0.259580
$657$	779.954			1.18714
$658$			1014.92i			1.54243i
$659$		−	759.727i		−	1.15285i	−0.817151	−	0.576424i	$-0.804448\pi$
$659$		−	759.727i		−	1.15285i	0.817151	−	0.576424i	$-0.195552\pi$
$660$	9.43600			0.0142970
$661$		−	581.754i		−	0.880112i	−0.897970	−	0.440056i	$-0.854959\pi$
$661$		−	581.754i		−	0.880112i	0.897970	−	0.440056i	$-0.145041\pi$
$662$	−312.134			−0.471501
$663$		−	5.56088i		−	0.00838745i
$664$		−	400.625i		−	0.603350i
$665$		−	461.928i		−	0.694629i
$666$		−	503.943i		−	0.756672i
$667$	501.231	+	534.267i	0.751471	+	0.801001i
$668$	144.277			0.215983
$669$	−29.1364			−0.0435521
$670$	−139.349			−0.207983
$671$	−266.371			−0.396977
$672$		−	13.4122i		−	0.0199586i
$673$	−831.173			−1.23503			−0.617513	−	0.786560i	$-0.711860\pi$
$673$	−831.173			−1.23503			−0.617513	+	0.786560i	$0.711860\pi$
$674$			273.739i			0.406142i
$675$	−24.9590			−0.0369763
$676$	−324.053			−0.479368
$677$		−	106.706i		−	0.157616i	−0.996890	−	0.0788079i	$-0.974889\pi$
$677$		−	106.706i		−	0.157616i	0.996890	−	0.0788079i	$-0.0251114\pi$
$678$		−	33.9938i		−	0.0501384i
$679$	−1220.05			−1.79683
$680$	−47.8172			−0.0703195
$681$			55.8393i			0.0819961i
$682$			605.384i			0.887660i
$683$	380.675			0.557357			0.278678	−	0.960385i	$-0.410104\pi$
$683$	380.675			0.557357			0.278678	+	0.960385i	$0.410104\pi$
$684$			433.051i			0.633116i
$685$	−21.6851			−0.0316570
$686$			307.411i			0.448121i
$687$			6.14749i			0.00894832i
$688$		−	82.2883i		−	0.119605i
$689$			31.4750i			0.0456821i
$690$	14.7738	−	13.8602i	0.0214113	−	0.0200873i
$691$	−318.845			−0.461425			−0.230713	−	0.973022i	$-0.574106\pi$
$691$	−318.845			−0.461425			−0.230713	+	0.973022i	$0.574106\pi$
$692$	−300.154			−0.433748
$693$	−575.385			−0.830282
$694$	371.130			0.534769
$695$			18.0112i			0.0259154i
$696$	−25.0919			−0.0360515
$697$			321.861i			0.461781i
$698$	−325.031			−0.465660
$699$	94.3165			0.134931
$700$			85.1262i			0.121609i
$701$		−	112.754i		−	0.160848i	−0.996761	−	0.0804239i	$-0.974373\pi$
$701$		−	112.754i		−	0.160848i	0.996761	−	0.0804239i	$-0.0256274\pi$
$702$	18.6424			0.0265561
$703$	−969.193			−1.37865
$704$			60.6042i			0.0860855i
$705$		−	52.5047i		−	0.0744747i
$706$	−519.698			−0.736116
$707$		−	235.887i		−	0.333644i
$708$	−37.6875			−0.0532309
$709$			465.481i			0.656531i	0.944585	+	0.328266i	$0.106464\pi$
$709$			465.481i			0.656531i	−0.944585	+	0.328266i	$0.893536\pi$
$710$		−	28.0367i		−	0.0394883i
$711$		−	1375.99i		−	1.93529i
$712$		−	180.242i		−	0.253149i
$713$	889.229	+	947.838i	1.24717	+	1.32937i
$714$	−25.3509			−0.0355054
$715$	44.7328			0.0625634
$716$	414.116			0.578375
$717$	−41.6041			−0.0580253
$718$			339.370i			0.472660i
$719$	−347.913			−0.483885			−0.241943	−	0.970291i	$-0.577785\pi$
$719$	−347.913			−0.483885			−0.241943	+	0.970291i	$0.577785\pi$
$720$		−	79.8046i		−	0.110840i
$721$	1136.79			1.57669
$722$	322.321			0.446428
$723$			37.0518i			0.0512473i
$724$		−	662.276i		−	0.914746i
$725$	159.257			0.219664
$726$	25.0559			0.0345123
$727$		−	88.3077i		−	0.121469i	−0.998154	−	0.0607343i	$-0.980656\pi$
$727$		−	88.3077i		−	0.121469i	0.998154	−	0.0607343i	$-0.0193442\pi$
$728$		−	63.5824i		−	0.0873385i
$729$	−691.569			−0.948654
$730$			276.431i			0.378672i
$731$	−155.536			−0.212772
$732$		−	19.5869i		−	0.0267580i
$733$			510.848i			0.696928i	0.937322	+	0.348464i	$0.113297\pi$
$733$			510.848i			0.696928i	−0.937322	+	0.348464i	$0.886703\pi$
$734$			550.289i			0.749712i
$735$			14.6137i			0.0198826i
$736$	89.0196	+	94.8869i	0.120950	+	0.128922i
$737$	333.823			0.452948
$738$	−537.171			−0.727873
$739$	−416.763			−0.563955			−0.281978	−	0.959421i	$-0.590990\pi$
$739$	−416.763			−0.563955			−0.281978	+	0.959421i	$0.590990\pi$
$740$	178.607			0.241361
$741$		−	17.8491i		−	0.0240878i
$742$	143.488			0.193380
$743$		−	633.469i		−	0.852583i	−0.904586	−	0.426291i	$-0.859820\pi$
$743$		−	633.469i		−	0.852583i	0.904586	−	0.426291i	$-0.140180\pi$
$744$	−44.5152			−0.0598323
$745$	−322.132			−0.432393
$746$		−	772.597i		−	1.03565i
$747$		−	1263.79i		−	1.69182i
$748$	114.551			0.153142
$749$	−428.262			−0.571779
$750$		−	4.40383i		−	0.00587177i
$751$		−	1282.52i		−	1.70775i	−0.520475	−	0.853877i	$-0.674245\pi$
$751$		−	1282.52i		−	1.70775i	0.520475	−	0.853877i	$-0.325755\pi$
$752$	337.219			0.448430
$753$		−	104.981i		−	0.139416i
$754$	−118.952			−0.157761
$755$		−	245.870i		−	0.325655i
$756$		−	84.9866i		−	0.112416i
$757$		−	1233.64i		−	1.62964i	−0.579716	−	0.814819i	$-0.696836\pi$
$757$		−	1233.64i		−	1.62964i	0.579716	−	0.814819i	$-0.303164\pi$
$758$		−	418.377i		−	0.551949i
$759$	−35.3919	+	33.2035i	−0.0466297	+	0.0437463i
$760$	−153.482			−0.201950
$761$	−262.559			−0.345018			−0.172509	−	0.985008i	$-0.555187\pi$
$761$	−262.559			−0.345018			−0.172509	+	0.985008i	$0.555187\pi$
$762$	−4.33812			−0.00569307
$763$	−1096.58			−1.43720
$764$		−	345.499i		−	0.452223i
$765$	−150.842			−0.197179
$766$			800.491i			1.04503i
$767$	−178.663			−0.232938
$768$	−4.45636			−0.00580255
$769$			801.510i			1.04228i	0.853473	+	0.521138i	$0.174492\pi$
$769$			801.510i			1.04228i	−0.853473	+	0.521138i	$0.825508\pi$
$770$		−	203.928i		−	0.264841i
$771$	−62.9698			−0.0816729
$772$	272.900			0.353498
$773$		−	1143.79i		−	1.47967i	−0.672786	−	0.739837i	$-0.734903\pi$
$773$		−	1143.79i		−	1.47967i	0.672786	−	0.739837i	$-0.265097\pi$
$774$		−	259.583i		−	0.335378i
$775$	282.536			0.364562
$776$			405.377i			0.522393i
$777$	94.6907			0.121867
$778$			277.246i			0.356357i
$779$			1033.10i			1.32618i
$780$			3.28930i			0.00421706i
$781$			67.1644i			0.0859979i
$782$	179.350	−	168.260i	0.229347	−	0.215166i
$783$	−158.995			−0.203059
$784$	−93.8587			−0.119718
$785$	55.5010			0.0707019
$786$	1.43353			0.00182383
$787$		−	111.467i		−	0.141635i	−0.997489	−	0.0708175i	$-0.977439\pi$
$787$		−	111.467i		−	0.141635i	0.997489	−	0.0708175i	$-0.0225608\pi$
$788$	−542.181			−0.688046
$789$		−	0.678632i		−	0.000860116i
$790$	487.677			0.617312
$791$	−734.663			−0.928777
$792$			191.179i			0.241388i
$793$		−	92.8546i		−	0.117093i
$794$	422.551			0.532180
$795$	−7.42304			−0.00933716
$796$		−	514.584i		−	0.646462i
$797$		−	231.014i		−	0.289855i	−0.989442	−	0.144927i	$-0.953705\pi$
$797$		−	231.014i		−	0.289855i	0.989442	−	0.144927i	$-0.0462949\pi$
$798$	−81.3701			−0.101968
$799$		−	637.393i		−	0.797738i
$800$	28.2843			0.0353553
$801$		−	568.583i		−	0.709842i
$802$		−	1110.32i		−	1.38444i
$803$		−	662.215i		−	0.824676i
$804$			24.5467i			0.0305307i
$805$	−299.543	−	319.286i	−0.372103	−	0.396628i
$806$	−211.031			−0.261825
$807$	86.7145			0.107453
$808$	−78.3763			−0.0970004
$809$	−165.201			−0.204204			−0.102102	−	0.994774i	$-0.532557\pi$
$809$	−165.201			−0.204204			−0.102102	+	0.994774i	$0.532557\pi$
$810$		−	249.540i		−	0.308074i
$811$	317.322			0.391273			0.195636	−	0.980677i	$-0.437323\pi$
$811$	317.322			0.391273			0.195636	+	0.980677i	$0.437323\pi$
$812$			542.276i			0.667828i
$813$	−72.6251			−0.0893298
$814$	−427.870			−0.525638
$815$			243.650i			0.298957i
$816$			8.42315i			0.0103225i
$817$	−499.234			−0.611058
$818$	−506.552			−0.619257
$819$		−	200.574i		−	0.244901i
$820$		−	190.384i		−	0.232175i
$821$	−1389.82			−1.69284			−0.846421	−	0.532514i	$-0.821247\pi$
$821$	−1389.82			−1.69284			−0.846421	+	0.532514i	$0.821247\pi$
$822$			3.81989i			0.00464707i
$823$	948.001			1.15188			0.575942	−	0.817490i	$-0.304635\pi$
$823$	948.001			1.15188			0.575942	+	0.817490i	$0.304635\pi$
$824$		−	377.713i		−	0.458390i
$825$			10.5498i			0.0127876i
$826$			814.489i			0.986064i
$827$		−	1177.54i		−	1.42387i	−0.702245	−	0.711935i	$-0.747819\pi$
$827$		−	1177.54i		−	1.42387i	0.702245	−	0.711935i	$-0.252181\pi$
$828$	280.817	+	299.326i	0.339151	+	0.361505i
$829$	−1278.78			−1.54256			−0.771279	−	0.636497i	$-0.780383\pi$
$829$	−1278.78			−1.54256			−0.771279	+	0.636497i	$0.780383\pi$
$830$	447.912			0.539653
$831$	50.7655			0.0610897
$832$	−21.1261			−0.0253919
$833$			177.406i			0.212973i
$834$	3.17273			0.00380423
$835$			161.306i			0.193181i
$836$	367.679			0.439808
$837$	−282.072			−0.337004
$838$			276.156i			0.329541i
$839$			1435.77i			1.71128i	0.517570	+	0.855641i	$0.326837\pi$
$839$			1435.77i			1.71128i	−0.517570	+	0.855641i	$0.673163\pi$
$840$	14.9952			0.0178515
$841$	173.507			0.206311
$842$			1086.18i			1.28999i
$843$			1.28260i			0.00152147i
$844$	108.389			0.128423
$845$		−	362.302i		−	0.428760i
$846$	1063.78			1.25742
$847$		−	541.500i		−	0.639315i
$848$		−	47.6757i		−	0.0562213i
$849$			92.7193i			0.109210i
$850$		−	53.4613i		−	0.0628956i
$851$	−669.908	+	628.484i	−0.787201	+	0.738524i
$852$	−4.93875			−0.00579665
$853$	812.996			0.953102			0.476551	−	0.879147i	$-0.341887\pi$
$853$	812.996			0.953102			0.476551	+	0.879147i	$0.341887\pi$
$854$	−423.304			−0.495673
$855$	−484.166			−0.566276
$856$			142.296i			0.166233i
$857$	−958.841			−1.11883			−0.559417	−	0.828886i	$-0.688975\pi$
$857$	−958.841			−1.11883			−0.559417	+	0.828886i	$0.688975\pi$
$858$		−	7.87983i		−	0.00918395i
$859$	−383.654			−0.446628			−0.223314	−	0.974747i	$-0.571688\pi$
$859$	−383.654			−0.446628			−0.223314	+	0.974747i	$0.571688\pi$
$860$	92.0011			0.106978
$861$		−	100.934i		−	0.117229i
$862$		−	471.106i		−	0.546526i
$863$	1017.48			1.17900			0.589502	−	0.807767i	$-0.299324\pi$
$863$	1017.48			1.17900			0.589502	+	0.807767i	$0.299324\pi$
$864$	−28.2379			−0.0326827
$865$		−	335.582i		−	0.387956i
$866$			10.6029i			0.0122436i
$867$	−64.5721			−0.0744776
$868$			962.047i			1.10835i
$869$	−1168.27			−1.34439
$870$		−	28.0536i		−	0.0322455i
$871$			116.368i			0.133602i
$872$			364.354i			0.417837i
$873$			1278.78i			1.46482i
$874$	575.669	−	540.072i	0.658660	−	0.617932i
$875$	−95.1740			−0.108770
$876$	48.6941			0.0555869
$877$	1443.83			1.64633			0.823163	−	0.567806i	$-0.192207\pi$
$877$	1443.83			1.64633			0.823163	+	0.567806i	$0.192207\pi$
$878$	429.835			0.489561
$879$			93.6154i			0.106502i
$880$	−67.7576			−0.0769972
$881$			894.988i			1.01588i	0.861393	+	0.507939i	$0.169592\pi$
$881$			894.988i			1.01588i	−0.861393	+	0.507939i	$0.830408\pi$
$882$	−296.082			−0.335694
$883$	−870.115			−0.985407			−0.492704	−	0.870197i	$-0.663991\pi$
$883$	−870.115			−0.985407			−0.492704	+	0.870197i	$0.663991\pi$
$884$			39.9313i			0.0451711i
$885$		−	42.1359i		−	0.0476112i
$886$	−901.058			−1.01700
$887$	−529.330			−0.596764			−0.298382	−	0.954446i	$-0.596447\pi$
$887$	−529.330			−0.596764			−0.298382	+	0.954446i	$0.596447\pi$
$888$		−	31.4622i		−	0.0354304i
$889$			93.7539i			0.105460i
$890$	201.517			0.226423
$891$			597.796i			0.670927i
$892$	209.221			0.234553
$893$		−	2045.87i		−	2.29101i
$894$			56.7446i			0.0634728i
$895$			462.996i			0.517314i
$896$			96.3093i			0.107488i
$897$	−11.5744	−	12.3373i	−0.0129035	−	0.0137540i
$898$	−125.770			−0.140056
$899$	1799.83			2.00203
$900$	89.2243			0.0991381
$901$	−90.1138			−0.100015
$902$			456.081i			0.505633i
$903$	48.7755			0.0540149
$904$			244.101i			0.270023i
$905$	740.447			0.818173
$906$	−43.3107			−0.0478044
$907$		−	691.482i		−	0.762384i	−0.924496	−	0.381192i	$-0.875514\pi$
$907$		−	691.482i		−	0.762384i	0.924496	−	0.381192i	$-0.124486\pi$
$908$		−	400.968i		−	0.441595i
$909$	−247.242			−0.271994
$910$	71.0873			0.0781179
$911$			1794.49i			1.96980i	0.173115	+	0.984902i	$0.444617\pi$
$911$			1794.49i			1.96980i	−0.173115	+	0.984902i	$0.555383\pi$
$912$			27.0363i			0.0296450i
$913$	−1073.01			−1.17526
$914$		−	534.105i		−	0.584360i
$915$	21.8988			0.0239331
$916$		−	44.1436i		−	0.0481917i
$917$		−	30.9809i		−	0.0337851i
$918$			53.3736i			0.0581412i
$919$		−	428.705i		−	0.466491i	−0.972418	−	0.233245i	$-0.925065\pi$
$919$		−	428.705i		−	0.466491i	0.972418	−	0.233245i	$-0.0749345\pi$
$920$	−106.087	+	99.5269i	−0.115312	+	0.108181i
$921$	127.545			0.138485
$922$	827.413			0.897411
$923$	−23.4129			−0.0253661
$924$	−35.9225			−0.0388771
$925$			199.689i			0.215880i
$926$	319.438			0.344965
$927$		−	1191.52i		−	1.28535i
$928$	180.178			0.194158
$929$	1577.01			1.69754			0.848768	−	0.528766i	$-0.177345\pi$
$929$	1577.01			1.69754			0.848768	+	0.528766i	$0.177345\pi$
$930$		−	49.7695i		−	0.0535156i
$931$			569.431i			0.611633i
$932$	−677.263			−0.726677
$933$	126.900			0.136013
$934$			994.169i			1.06442i
$935$			128.071i			0.136975i
$936$	−66.6433			−0.0712001
$937$		−	141.317i		−	0.150818i	−0.997153	−	0.0754091i	$-0.975974\pi$
$937$		−	141.317i		−	0.150818i	0.997153	−	0.0754091i	$-0.0240263\pi$
$938$	530.495			0.565560
$939$		−	164.148i		−	0.174812i
$940$			377.023i			0.401088i
$941$		−	1506.21i		−	1.60065i	−0.599566	−	0.800325i	$-0.704660\pi$
$941$		−	1506.21i		−	1.60065i	0.599566	−	0.800325i	$-0.295340\pi$
$942$		−	9.77667i		−	0.0103786i
$943$	669.923	+	714.078i	0.710417	+	0.757240i
$944$	270.624			0.286678
$945$	95.0179			0.100548
$946$	−220.397			−0.232978
$947$	1689.84			1.78441			0.892205	−	0.451632i	$-0.149158\pi$
$947$	1689.84			1.78441			0.892205	+	0.451632i	$0.149158\pi$
$948$		−	85.9058i		−	0.0906179i
$949$	230.842			0.243248
$950$		−	171.598i		−	0.180629i
$951$	107.580			0.113123
$952$	182.038			0.191217
$953$		−	990.482i		−	1.03933i	−0.854370	−	0.519665i	$-0.826057\pi$
$953$		−	990.482i		−	1.03933i	0.854370	−	0.519665i	$-0.173943\pi$
$954$		−	150.395i		−	0.157647i
$955$	386.279			0.404481
$956$	298.749			0.312499
$957$			67.2049i			0.0702245i
$958$			412.534i			0.430620i
$959$	82.5541			0.0860836
$960$		−	4.98236i		−	0.00518996i
$961$	2232.05			2.32264
$962$		−	149.151i		−	0.155043i
$963$			448.879i			0.466126i
$964$		−	266.059i		−	0.275995i
$965$			305.112i			0.316178i
$966$	−56.2432	+	52.7654i	−0.0582227	+	0.0546225i
$967$	1528.09			1.58024			0.790118	−	0.612954i	$-0.210019\pi$
$967$	1528.09			1.58024			0.790118	+	0.612954i	$0.210019\pi$
$968$	−179.920			−0.185868
$969$	51.1024			0.0527372
$970$	−453.225			−0.467243
$971$			616.239i			0.634643i	0.948318	+	0.317322i	$0.102783\pi$
$971$			616.239i			0.634643i	−0.948318	+	0.317322i	$0.897217\pi$
$972$	−133.810			−0.137664
$973$		−	68.5679i		−	0.0704706i
$974$	−291.267			−0.299042
$975$	−3.67755			−0.00377185
$976$			140.648i			0.144107i
$977$			1393.79i			1.42660i	0.700859	+	0.713299i	$0.252800\pi$
$977$			1393.79i			1.42660i	−0.700859	+	0.713299i	$0.747200\pi$
$978$	42.9197			0.0438852
$979$	−482.752			−0.493107
$980$		−	104.937i		−	0.107079i
$981$			1149.37i			1.17164i
$982$	272.205			0.277195
$983$			1033.22i			1.05109i	0.850767	+	0.525543i	$0.176138\pi$
$983$			1033.22i			1.05109i	−0.850767	+	0.525543i	$0.823862\pi$
$984$	−33.5367			−0.0340820
$985$		−	606.176i		−	0.615407i
$986$		−	340.563i		−	0.345398i
$987$			199.883i			0.202516i
$988$			128.170i			0.129726i
$989$	−345.071	+	323.734i	−0.348909	+	0.327335i
$990$	−213.745			−0.215904
$991$	−1122.80			−1.13300			−0.566501	−	0.824061i	$-0.691703\pi$
$991$	−1122.80			−1.13300			−0.566501	+	0.824061i	$0.691703\pi$
$992$	319.652			0.322230
$993$	−61.4732			−0.0619066
$994$			106.734i			0.107379i
$995$	575.323			0.578214
$996$		−	78.9011i		−	0.0792179i
$997$	−718.650			−0.720812			−0.360406	−	0.932795i	$-0.617362\pi$
$997$	−718.650			−0.720812			−0.360406	+	0.932795i	$0.617362\pi$
$998$	−1254.95			−1.25747
$999$		−	199.361i		−	0.199561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.d.a.91.4	yes	16
3.2	odd	2		2070.3.c.a.91.9		16
4.3	odd	2		1840.3.k.d.321.10		16
5.2	odd	4		1150.3.c.c.1149.7		32
5.3	odd	4		1150.3.c.c.1149.26		32
5.4	even	2		1150.3.d.b.551.14		16
23.22	odd	2	inner	230.3.d.a.91.3	✓	16
69.68	even	2		2070.3.c.a.91.16		16
92.91	even	2		1840.3.k.d.321.9		16
115.22	even	4		1150.3.c.c.1149.25		32
115.68	even	4		1150.3.c.c.1149.8		32
115.114	odd	2		1150.3.d.b.551.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.3	✓	16	23.22	odd	2	inner
230.3.d.a.91.4	yes	16	1.1	even	1	trivial
1150.3.c.c.1149.7		32	5.2	odd	4
1150.3.c.c.1149.8		32	115.68	even	4
1150.3.c.c.1149.25		32	115.22	even	4
1150.3.c.c.1149.26		32	5.3	odd	4
1150.3.d.b.551.13		16	115.114	odd	2
1150.3.d.b.551.14		16	5.4	even	2
1840.3.k.d.321.9		16	92.91	even	2
1840.3.k.d.321.10		16	4.3	odd	2
2070.3.c.a.91.9		16	3.2	odd	2
2070.3.c.a.91.16		16	69.68	even	2

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} -3.16228i q^{10} +7.57553i q^{11} -0.557045 q^{12} -2.64076 q^{13} +12.0387i q^{14} -0.622795i q^{15} +4.00000 q^{16} -7.56057i q^{17} +12.6182 q^{18} -24.2676i q^{19} +4.47214i q^{20} +2.37096i q^{21} -10.7134i q^{22} +(-15.7366 - 16.7738i) q^{23} +0.787781 q^{24} -5.00000 q^{25} +3.73460 q^{26} +4.99180 q^{27} -17.0252i q^{28} -31.8513 q^{29} +0.880766i q^{30} -56.5071 q^{31} -5.65685 q^{32} -2.10995i q^{33} +10.6923i q^{34} +19.0348 q^{35} -17.8449 q^{36} -39.9378i q^{37} +34.3195i q^{38} +0.735511 q^{39} -6.32456i q^{40} -42.5710 q^{41} -3.35304i q^{42} -20.5721i q^{43} +15.1511i q^{44} -19.9511i q^{45} +(22.2549 + 23.7217i) q^{46} +84.3049 q^{47} -1.11409 q^{48} -23.4647 q^{49} +7.07107 q^{50} +2.10579i q^{51} -5.28152 q^{52} -11.9189i q^{53} -7.05947 q^{54} -16.9394 q^{55} +24.0773i q^{56} +6.75907i q^{57} +45.0446 q^{58} +67.6561 q^{59} -1.24559i q^{60} +35.1621i q^{61} +79.9131 q^{62} +75.9532i q^{63} +8.00000 q^{64} -5.90492i q^{65} +2.98393i q^{66} -44.0660i q^{67} -15.1211i q^{68} +(4.38299 + 4.67188i) q^{69} -26.9193 q^{70} +8.86597 q^{71} +25.2364 q^{72} -87.4150 q^{73} +56.4805i q^{74} +1.39261 q^{75} -48.5352i q^{76} +64.4876 q^{77} -1.04017 q^{78} +154.217i q^{79} +8.94427i q^{80} +78.9115 q^{81} +60.2046 q^{82} +141.642i q^{83} +4.74191i q^{84} +16.9059 q^{85} +29.0933i q^{86} +8.87131 q^{87} -21.4268i q^{88} +63.7252i q^{89} +28.2152i q^{90} +22.4798i q^{91} +(-31.4732 - 33.5476i) q^{92} +15.7385 q^{93} -119.225 q^{94} +54.2639 q^{95} +1.57556 q^{96} -143.322i q^{97} +33.1841 q^{98} -67.5921i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Introduction

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