LMFDB - Embedded newform 110.3.c.b.109.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,3,Mod(109,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.109"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.130897030168576.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 169x^{4} - 112x^{2} + 1936 $ x^8 + 18x^6 + 169x^4 - 112*x^2 + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.2
Root			$-1.41421 - 1.08854i$ of defining polynomial
Character	$\chi$	$=$	110.109
Dual form			110.3.c.b.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421 q^{2} -1.08854i q^{3} +2.00000 q^{4} +(1.40754 + 4.79780i) q^{5} +1.53943i q^{6} -2.82843 q^{7} -2.82843 q^{8} +7.81507 q^{9} +(-1.99056 - 6.78511i) q^{10} +(2.81507 + 10.6337i) q^{11} -2.17709i q^{12} +11.0522 q^{13} +4.00000 q^{14} +(5.22261 - 1.53216i) q^{15} +4.00000 q^{16} +21.8428 q^{17} -11.0522 q^{18} +5.87305i q^{19} +(2.81507 + 9.59559i) q^{20} +3.07887i q^{21} +(-3.98111 - 15.0383i) q^{22} +22.4568i q^{23} +3.07887i q^{24} +(-21.0377 + 13.5061i) q^{25} -15.6301 q^{26} -18.3039i q^{27} -5.65685 q^{28} -36.3770i q^{29} +(-7.38588 + 2.16681i) q^{30} -37.7055 q^{31} -5.65685 q^{32} +(11.5752 - 3.06433i) q^{33} -30.8904 q^{34} +(-3.98111 - 13.5702i) q^{35} +15.6301 q^{36} -52.3321i q^{37} -8.30575i q^{38} -12.0308i q^{39} +(-3.98111 - 13.5702i) q^{40} +51.2020i q^{41} -4.35417i q^{42} -26.7151 q^{43} +(5.63015 + 21.2674i) q^{44} +(11.0000 + 37.4951i) q^{45} -31.7587i q^{46} -49.4691i q^{47} -4.35417i q^{48} -41.0000 q^{49} +(29.7518 - 19.1006i) q^{50} -23.7769i q^{51} +22.1044 q^{52} +42.7365i q^{53} +25.8857i q^{54} +(-47.0560 + 28.4735i) q^{55} +8.00000 q^{56} +6.39307 q^{57} +51.4449i q^{58} +29.7055 q^{59} +(10.4452 - 3.06433i) q^{60} -12.3155i q^{61} +53.3236 q^{62} -22.1044 q^{63} +8.00000 q^{64} +(15.5563 + 53.0261i) q^{65} +(-16.3699 + 4.33362i) q^{66} -5.84532i q^{67} +43.6857 q^{68} +24.4452 q^{69} +(5.63015 + 19.1912i) q^{70} +86.4452 q^{71} -22.1044 q^{72} +49.0810 q^{73} +74.0088i q^{74} +(14.7020 + 22.9004i) q^{75} +11.7461i q^{76} +(-7.96223 - 30.0766i) q^{77} +17.0141i q^{78} -147.733i q^{79} +(5.63015 + 19.1912i) q^{80} +50.4110 q^{81} -72.4106i q^{82} -105.911 q^{83} +6.15773i q^{84} +(30.7446 + 104.797i) q^{85} +37.7809 q^{86} -39.5980 q^{87} +(-7.96223 - 30.0766i) q^{88} +45.7055 q^{89} +(-15.5563 - 53.0261i) q^{90} -31.2603 q^{91} +44.9136i q^{92} +41.0441i q^{93} +69.9599i q^{94} +(-28.1777 + 8.26653i) q^{95} +6.15773i q^{96} +35.7206i q^{97} +57.9828 q^{98} +(22.0000 + 83.1031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 10 q^{5} + 20 q^{9} - 20 q^{11} + 32 q^{14} - 22 q^{15} + 32 q^{16} - 20 q^{20} - 62 q^{25} - 40 q^{26} - 4 q^{31} + 8 q^{34} + 40 q^{36} - 40 q^{44} + 88 q^{45} - 328 q^{49} + 138 q^{55}+ \cdots + 176 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 10 * q^5 + 20 * q^9 - 20 * q^11 + 32 * q^14 - 22 * q^15 + 32 * q^16 - 20 * q^20 - 62 * q^25 - 40 * q^26 - 4 * q^31 + 8 * q^34 + 40 * q^36 - 40 * q^44 + 88 * q^45 - 328 * q^49 + 138 * q^55 + 64 * q^56 - 60 * q^59 - 44 * q^60 + 64 * q^64 - 216 * q^66 + 68 * q^69 - 40 * q^70 + 564 * q^71 + 394 * q^75 - 40 * q^80 - 192 * q^81 - 208 * q^86 + 68 * q^89 - 80 * q^91 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$-1$	$-1$

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
$3$		−	1.08854i		−	0.362848i	−0.983405	−	0.181424i	$-0.941929\pi$
$3$		−	1.08854i		−	0.362848i	0.983405	−	0.181424i	$-0.0580706\pi$
$4$	2.00000			0.500000
$5$	1.40754	+	4.79780i	0.281507	+	0.959559i
$5$	1.40754	+	4.79780i	0.281507	+	0.959559i
$6$			1.53943i			0.256572i
$7$	−2.82843			−0.404061			−0.202031	−	0.979379i	$-0.564754\pi$
$7$	−2.82843			−0.404061			−0.202031	+	0.979379i	$0.564754\pi$
$8$	−2.82843			−0.353553
$9$	7.81507			0.868341
$10$	−1.99056	−	6.78511i	−0.199056	−	0.678511i
$11$	2.81507	+	10.6337i	0.255916	+	0.966699i
$11$	2.81507	+	10.6337i	0.255916	+	0.966699i
$12$		−	2.17709i		−	0.181424i
$13$	11.0522			0.850168			0.425084	−	0.905154i	$-0.360245\pi$
$13$	11.0522			0.850168			0.425084	+	0.905154i	$0.360245\pi$
$14$	4.00000			0.285714
$15$	5.22261	−	1.53216i	0.348174	−	0.102144i
$16$	4.00000			0.250000
$17$	21.8428			1.28487			0.642436	−	0.766339i	$-0.277924\pi$
$17$	21.8428			1.28487			0.642436	+	0.766339i	$0.277924\pi$
$18$	−11.0522			−0.614010
$19$			5.87305i			0.309108i	0.987984	+	0.154554i	$0.0493940\pi$
$19$			5.87305i			0.309108i	−0.987984	+	0.154554i	$0.950606\pi$
$20$	2.81507	+	9.59559i	0.140754	+	0.479780i
$21$			3.07887i			0.146613i
$22$	−3.98111	−	15.0383i	−0.180960	−	0.683559i
$23$			22.4568i			0.976383i	0.872736	+	0.488192i	$0.162343\pi$
$23$			22.4568i			0.976383i	−0.872736	+	0.488192i	$0.837657\pi$
$24$			3.07887i			0.128286i
$25$	−21.0377	+	13.5061i	−0.841507	+	0.540246i
$26$	−15.6301			−0.601159
$27$		−	18.3039i		−	0.677924i
$28$	−5.65685			−0.202031
$29$		−	36.3770i		−	1.25438i	−0.778866	−	0.627190i	$-0.784205\pi$
$29$		−	36.3770i		−	1.25438i	0.778866	−	0.627190i	$-0.215795\pi$
$30$	−7.38588	+	2.16681i	−0.246196	+	0.0722269i
$31$	−37.7055			−1.21631			−0.608153	−	0.793820i	$-0.708089\pi$
$31$	−37.7055			−1.21631			−0.608153	+	0.793820i	$0.708089\pi$
$32$	−5.65685			−0.176777
$33$	11.5752	−	3.06433i	0.350765	−	0.0928585i
$34$	−30.8904			−0.908542
$35$	−3.98111	−	13.5702i	−0.113746	−	0.387720i
$36$	15.6301			0.434171
$37$		−	52.3321i		−	1.41438i	−0.707023	−	0.707191i	$-0.749962\pi$
$37$		−	52.3321i		−	1.41438i	0.707023	−	0.707191i	$-0.250038\pi$
$38$		−	8.30575i		−	0.218572i
$39$		−	12.0308i		−	0.308482i
$40$	−3.98111	−	13.5702i	−0.0995279	−	0.339255i
$41$			51.2020i			1.24883i	0.781093	+	0.624415i	$0.214662\pi$
$41$			51.2020i			1.24883i	−0.781093	+	0.624415i	$0.785338\pi$
$42$		−	4.35417i		−	0.103671i
$43$	−26.7151			−0.621282			−0.310641	−	0.950527i	$-0.600544\pi$
$43$	−26.7151			−0.621282			−0.310641	+	0.950527i	$0.600544\pi$
$44$	5.63015	+	21.2674i	0.127958	+	0.483350i
$45$	11.0000	+	37.4951i	0.244444	+	0.833225i
$46$		−	31.7587i		−	0.690407i
$47$		−	49.4691i		−	1.05253i	−0.850319	−	0.526267i	$-0.823591\pi$
$47$		−	49.4691i		−	1.05253i	0.850319	−	0.526267i	$-0.176409\pi$
$48$		−	4.35417i		−	0.0907120i
$49$	−41.0000			−0.836735
$50$	29.7518	−	19.1006i	0.595036	−	0.382011i
$51$		−	23.7769i		−	0.466213i
$52$	22.1044			0.425084
$53$			42.7365i			0.806350i	0.915123	+	0.403175i	$0.132093\pi$
$53$			42.7365i			0.806350i	−0.915123	+	0.403175i	$0.867907\pi$
$54$			25.8857i			0.479364i
$55$	−47.0560	+	28.4735i	−0.855563	+	0.517699i
$56$	8.00000			0.142857
$57$	6.39307			0.112159
$58$			51.4449i			0.886981i
$59$	29.7055			0.503483			0.251742	−	0.967794i	$-0.418997\pi$
$59$	29.7055			0.503483			0.251742	+	0.967794i	$0.418997\pi$
$60$	10.4452	−	3.06433i	0.174087	−	0.0510722i
$61$		−	12.3155i		−	0.201893i	−0.994892	−	0.100946i	$-0.967813\pi$
$61$		−	12.3155i		−	0.201893i	0.994892	−	0.100946i	$-0.0321871\pi$
$62$	53.3236			0.860059
$63$	−22.1044			−0.350863
$64$	8.00000			0.125000
$65$	15.5563	+	53.0261i	0.239328	+	0.815786i
$66$	−16.3699	+	4.33362i	−0.248028	+	0.0656609i
$67$		−	5.84532i		−	0.0872436i	−0.999048	−	0.0436218i	$-0.986110\pi$
$67$		−	5.84532i		−	0.0872436i	0.999048	−	0.0436218i	$-0.0138897\pi$
$68$	43.6857			0.642436
$69$	24.4452			0.354279
$70$	5.63015	+	19.1912i	0.0804307	+	0.274160i
$71$	86.4452			1.21754			0.608769	−	0.793347i	$-0.291664\pi$
$71$	86.4452			1.21754			0.608769	+	0.793347i	$0.291664\pi$
$72$	−22.1044			−0.307005
$73$	49.0810			0.672343			0.336171	−	0.941801i	$-0.390868\pi$
$73$	49.0810			0.672343			0.336171	+	0.941801i	$0.390868\pi$
$74$			74.0088i			1.00012i
$75$	14.7020	+	22.9004i	0.196027	+	0.305339i
$76$			11.7461i			0.154554i
$77$	−7.96223	−	30.0766i	−0.103406	−	0.390605i
$78$			17.0141i			0.218129i
$79$		−	147.733i		−	1.87004i	−0.354599	−	0.935019i	$-0.615383\pi$
$79$		−	147.733i		−	1.87004i	0.354599	−	0.935019i	$-0.384617\pi$
$80$	5.63015	+	19.1912i	0.0703768	+	0.239890i
$81$	50.4110			0.622358
$82$		−	72.4106i		−	0.883056i
$83$	−105.911			−1.27604			−0.638019	−	0.770021i	$-0.720246\pi$
$83$	−105.911			−1.27604			−0.638019	+	0.770021i	$0.720246\pi$
$84$			6.15773i			0.0733063i
$85$	30.7446	+	104.797i	0.361701	+	1.23291i
$86$	37.7809			0.439312
$87$	−39.5980			−0.455149
$88$	−7.96223	−	30.0766i	−0.0904799	−	0.341780i
$89$	45.7055			0.513545			0.256773	−	0.966472i	$-0.417341\pi$
$89$	45.7055			0.513545			0.256773	+	0.966472i	$0.417341\pi$
$90$	−15.5563	−	53.0261i	−0.172848	−	0.589179i
$91$	−31.2603			−0.343520
$92$			44.9136i			0.488192i
$93$			41.0441i			0.441334i
$94$			69.9599i			0.744254i
$95$	−28.1777	+	8.26653i	−0.296607	+	0.0870161i
$96$			6.15773i			0.0641430i
$97$			35.7206i			0.368254i	0.982902	+	0.184127i	$0.0589458\pi$
$97$			35.7206i			0.368254i	−0.982902	+	0.184127i	$0.941054\pi$
$98$	57.9828			0.591661
$99$	22.0000	+	83.1031i	0.222222	+	0.839425i
$100$	−42.0754	+	27.0123i	−0.420754	+	0.270123i
$101$		−	172.079i		−	1.70375i	−0.523742	−	0.851877i	$-0.675464\pi$
$101$		−	172.079i		−	1.70375i	0.523742	−	0.851877i	$-0.324536\pi$
$102$			33.6256i			0.329663i
$103$		−	91.4004i		−	0.887383i	−0.896180	−	0.443691i	$-0.853669\pi$
$103$		−	91.4004i		−	0.887383i	0.896180	−	0.443691i	$-0.146331\pi$
$104$	−31.2603			−0.300580
$105$	−14.7718	+	4.33362i	−0.140684	+	0.0412725i
$106$		−	60.4386i		−	0.570175i
$107$	−83.4968			−0.780344			−0.390172	−	0.920742i	$-0.627584\pi$
$107$	−83.4968			−0.780344			−0.390172	+	0.920742i	$0.627584\pi$
$108$		−	36.6079i		−	0.338962i
$109$			11.1767i			0.102539i	0.998685	+	0.0512694i	$0.0163267\pi$
$109$			11.1767i			0.102539i	−0.998685	+	0.0512694i	$0.983673\pi$
$110$	66.5472	−	40.2675i	0.604974	−	0.366069i
$111$	−56.9658			−0.513205
$112$	−11.3137			−0.101015
$113$		−	77.6520i		−	0.687186i	−0.939119	−	0.343593i	$-0.888356\pi$
$113$		−	77.6520i		−	0.687186i	0.939119	−	0.343593i	$-0.111644\pi$
$114$	−9.04117			−0.0793085
$115$	−107.743	+	31.6088i	−0.936897	+	0.274859i
$116$		−	72.7541i		−	0.627190i
$117$	86.3736			0.738236
$118$	−42.0099			−0.356016
$119$	−61.7809			−0.519167
$120$	−14.7718	+	4.33362i	−0.123098	+	0.0361135i
$121$	−105.151	+	59.8692i	−0.869014	+	0.494787i
$122$			17.4167i			0.142760i
$123$	55.7356			0.453135
$124$	−75.4110			−0.608153
$125$	−94.4110	−	81.9241i	−0.755288	−	0.655393i
$126$	31.2603			0.248098
$127$	132.936			1.04674			0.523370	−	0.852105i	$-0.324674\pi$
$127$	132.936			1.04674			0.523370	+	0.852105i	$0.324674\pi$
$128$	−11.3137			−0.0883883
$129$			29.0806i			0.225431i
$130$	−22.0000	−	74.9902i	−0.169231	−	0.576848i
$131$			148.018i			1.12991i	0.825123	+	0.564953i	$0.191106\pi$
$131$			148.018i			1.12991i	−0.825123	+	0.564953i	$0.808894\pi$
$132$	23.1505	−	6.12866i	0.175382	−	0.0464292i
$133$		−	16.6115i		−	0.124898i
$134$			8.26653i			0.0616905i
$135$	87.8186	−	25.7635i	0.650508	−	0.190840i
$136$	−61.7809			−0.454271
$137$			212.795i			1.55325i	0.629962	+	0.776626i	$0.283070\pi$
$137$			212.795i			1.55325i	−0.629962	+	0.776626i	$0.716930\pi$
$138$	−34.5708			−0.250513
$139$		−	246.541i		−	1.77368i	−0.462078	−	0.886839i	$-0.652896\pi$
$139$		−	246.541i		−	1.77368i	0.462078	−	0.886839i	$-0.347104\pi$
$140$	−7.96223	−	27.1404i	−0.0568731	−	0.193860i
$141$	−53.8493			−0.381910
$142$	−122.252			−0.860930
$143$	31.1127	+	117.525i	0.217571	+	0.821856i
$144$	31.2603			0.217085
$145$	174.530	−	51.2020i	1.20365	−	0.353117i
$146$	−69.4110			−0.475418
$147$			44.6303i			0.303607i
$148$		−	104.664i		−	0.707191i
$149$		−	13.6862i		−	0.0918539i	−0.998945	−	0.0459270i	$-0.985376\pi$
$149$		−	13.6862i		−	0.0918539i	0.998945	−	0.0459270i	$-0.0146241\pi$
$150$	−20.7918	−	32.3861i	−0.138612	−	0.215907i
$151$			170.139i			1.12675i	0.826202	+	0.563374i	$0.190497\pi$
$151$			170.139i			1.12675i	−0.826202	+	0.563374i	$0.809503\pi$
$152$		−	16.6115i		−	0.109286i
$153$	170.703			1.11571
$154$	11.2603	+	42.5348i	0.0731188	+	0.276200i
$155$	−53.0719	−	180.903i	−0.342399	−	1.16712i
$156$		−	24.0616i		−	0.154241i
$157$			36.5258i			0.232649i	0.993211	+	0.116324i	$0.0371112\pi$
$157$			36.5258i			0.232649i	−0.993211	+	0.116324i	$0.962889\pi$
$158$			208.926i			1.32232i
$159$	46.5206			0.292582
$160$	−7.96223	−	27.1404i	−0.0497639	−	0.169628i
$161$		−	63.5175i		−	0.394518i
$162$	−71.2919			−0.440074
$163$		−	100.914i		−	0.619104i	−0.950882	−	0.309552i	$-0.899821\pi$
$163$		−	100.914i		−	0.619104i	0.950882	−	0.309552i	$-0.100179\pi$
$164$			102.404i			0.624415i
$165$	30.9946	+	51.2225i	0.187846	+	0.310439i
$166$	149.781			0.902294
$167$	−104.652			−0.626658			−0.313329	−	0.949645i	$-0.601444\pi$
$167$	−104.652			−0.626658			−0.313329	+	0.949645i	$0.601444\pi$
$168$		−	8.70835i		−	0.0518354i
$169$	−46.8493			−0.277215
$170$	−43.4794	−	148.206i	−0.255761	−	0.871800i
$171$			45.8983i			0.268411i
$172$	−53.4302			−0.310641
$173$	−206.640			−1.19445			−0.597225	−	0.802073i	$-0.703730\pi$
$173$	−206.640			−1.19445			−0.597225	+	0.802073i	$0.703730\pi$
$174$	56.0000			0.321839
$175$	59.5036	−	38.2011i	0.340020	−	0.218292i
$176$	11.2603	+	42.5348i	0.0639789	+	0.241675i
$177$		−	32.3357i		−	0.182688i
$178$	−64.6374			−0.363131
$179$	125.117			0.698975			0.349488	−	0.936941i	$-0.386356\pi$
$179$	125.117			0.698975			0.349488	+	0.936941i	$0.386356\pi$
$180$	22.0000	+	74.9902i	0.122222	+	0.416612i
$181$	91.6232			0.506205			0.253103	−	0.967439i	$-0.418549\pi$
$181$	91.6232			0.506205			0.253103	+	0.967439i	$0.418549\pi$
$182$	44.2087			0.242905
$183$	−13.4059			−0.0732564
$184$		−	63.5175i		−	0.345204i
$185$	251.079	−	73.6594i	1.35718	−	0.398159i
$186$		−	58.0451i		−	0.312070i
$187$	61.4892	+	232.270i	0.328819	+	1.24209i
$188$		−	98.9382i		−	0.526267i
$189$			51.7714i			0.273923i
$190$	39.8493	−	11.6906i	0.209733	−	0.0615297i
$191$	90.2945			0.472746			0.236373	−	0.971662i	$-0.424041\pi$
$191$	90.2945			0.472746			0.236373	+	0.971662i	$0.424041\pi$
$192$		−	8.70835i		−	0.0453560i
$193$	153.113			0.793332			0.396666	−	0.917963i	$-0.370167\pi$
$193$	153.113			0.793332			0.396666	+	0.917963i	$0.370167\pi$
$194$		−	50.5166i		−	0.260395i
$195$	57.7212	−	16.9338i	0.296006	−	0.0868398i
$196$	−82.0000			−0.418367
$197$	−321.869			−1.63385			−0.816927	−	0.576741i	$-0.804324\pi$
$197$	−321.869			−1.63385			−0.816927	+	0.576741i	$0.804324\pi$
$198$	−31.1127	−	117.525i	−0.157135	−	0.593563i
$199$	−48.5890			−0.244166			−0.122083	−	0.992520i	$-0.538957\pi$
$199$	−48.5890			−0.244166			−0.122083	+	0.992520i	$0.538957\pi$
$200$	59.5036	−	38.2011i	0.297518	−	0.191006i
$201$	−6.36289			−0.0316561
$202$			243.357i			1.20474i
$203$			102.890i			0.506846i
$204$		−	47.5538i		−	0.233107i
$205$	−245.657	+	72.0687i	−1.19833	+	0.351554i
$206$			129.260i			0.627474i
$207$			175.502i			0.847834i
$208$	44.2087			0.212542
$209$	−62.4522	+	16.5331i	−0.298814	+	0.0791056i
$210$	20.8904	−	6.12866i	0.0994783	−	0.0291841i
$211$			145.508i			0.689612i	0.938674	+	0.344806i	$0.112055\pi$
$211$			145.508i			0.689612i	−0.938674	+	0.344806i	$0.887945\pi$
$212$			85.4731i			0.403175i
$213$		−	94.0994i		−	0.441781i
$214$	118.082			0.551787
$215$	−37.6025	−	128.174i	−0.174895	−	0.596156i
$216$			51.7714i			0.239682i
$217$	106.647			0.491462
$218$		−	15.8063i		−	0.0725059i
$219$		−	53.4268i		−	0.243958i
$220$	−94.1119	+	56.9469i	−0.427781	+	0.258850i
$221$	241.411			1.09236
$222$	80.5618			0.362891
$223$		−	78.0918i		−	0.350187i	−0.984552	−	0.175094i	$-0.943977\pi$
$223$		−	78.0918i		−	0.350187i	0.984552	−	0.175094i	$-0.0560228\pi$
$224$	16.0000			0.0714286
$225$	−164.411	+	105.551i	−0.730716	+	0.469118i
$226$			109.816i			0.485914i
$227$	268.701			1.18370			0.591851	−	0.806047i	$-0.298397\pi$
$227$	268.701			1.18370			0.591851	+	0.806047i	$0.298397\pi$
$228$	12.7861			0.0560796
$229$	166.528			0.727195			0.363597	−	0.931556i	$-0.381548\pi$
$229$	166.528			0.727195			0.363597	+	0.931556i	$0.381548\pi$
$230$	152.372	−	44.7016i	0.662486	−	0.194355i
$231$	−32.7397	+	8.66723i	−0.141730	+	0.0375205i
$232$			102.890i			0.443490i
$233$	−42.0682			−0.180550			−0.0902750	−	0.995917i	$-0.528775\pi$
$233$	−42.0682			−0.180550			−0.0902750	+	0.995917i	$0.528775\pi$
$234$	−122.151			−0.522012
$235$	237.343	−	69.6296i	1.00997	−	0.296296i
$236$	59.4110			0.251742
$237$	−160.814			−0.678539
$238$	87.3714			0.367107
$239$		−	10.0906i		−	0.0422203i	−0.999777	−	0.0211101i	$-0.993280\pi$
$239$		−	10.0906i		−	0.0422203i	0.999777	−	0.0211101i	$-0.00672007\pi$
$240$	20.8904	−	6.12866i	0.0870435	−	0.0255361i
$241$		−	157.254i		−	0.652507i	−0.945282	−	0.326254i	$-0.894214\pi$
$241$		−	157.254i		−	0.652507i	0.945282	−	0.326254i	$-0.105786\pi$
$242$	148.706	−	84.6679i	0.614486	−	0.349867i
$243$		−	219.610i		−	0.903745i
$244$		−	24.6309i		−	0.100946i
$245$	−57.7090	−	196.710i	−0.235547	−	0.802896i
$246$	−78.8220			−0.320415
$247$			64.9100i			0.262794i
$248$	106.647			0.430029
$249$			115.289i			0.463007i
$250$	133.517	+	115.858i	0.534069	+	0.463433i
$251$	−415.939			−1.65713			−0.828563	−	0.559896i	$-0.810841\pi$
$251$	−415.939			−1.65713			−0.828563	+	0.559896i	$0.810841\pi$
$252$	−44.2087			−0.175431
$253$	−238.799	+	63.2176i	−0.943869	+	0.249872i
$254$	−188.000			−0.740157
$255$	114.077	−	33.4668i	0.447359	−	0.131242i
$256$	16.0000			0.0625000
$257$		−	129.015i		−	0.502003i	−0.967987	−	0.251002i	$-0.919240\pi$
$257$		−	129.015i		−	0.502003i	0.967987	−	0.251002i	$-0.0807599\pi$
$258$		−	41.1261i		−	0.159404i
$259$			148.018i			0.571497i
$260$	31.1127	+	106.052i	0.119664	+	0.407893i
$261$		−	284.289i		−	1.08923i
$262$		−	209.329i		−	0.798964i
$263$	229.103			0.871113			0.435556	−	0.900162i	$-0.356552\pi$
$263$	229.103			0.871113			0.435556	+	0.900162i	$0.356552\pi$
$264$	−32.7397	+	8.66723i	−0.124014	+	0.0328304i
$265$	−205.041	+	60.1532i	−0.773740	+	0.226993i
$266$			23.4922i			0.0883165i
$267$		−	49.7524i		−	0.186339i
$268$		−	11.6906i		−	0.0436218i
$269$	−370.836			−1.37857			−0.689286	−	0.724489i	$-0.742076\pi$
$269$	−370.836			−1.37857			−0.689286	+	0.724489i	$0.742076\pi$
$270$	−124.194	+	36.4350i	−0.459978	+	0.134945i
$271$			234.226i			0.864302i	0.901801	+	0.432151i	$0.142245\pi$
$271$			234.226i			0.864302i	−0.901801	+	0.432151i	$0.857755\pi$
$272$	87.3714			0.321218
$273$			34.0282i			0.124645i
$274$		−	300.938i		−	1.09831i
$275$	−202.843	−	185.687i	−0.737610	−	0.675227i
$276$	48.8904			0.177139
$277$	−478.169			−1.72624			−0.863121	−	0.504997i	$-0.831493\pi$
$277$	−478.169			−1.72624			−0.863121	+	0.504997i	$0.831493\pi$
$278$			348.662i			1.25418i
$279$	−294.671			−1.05617
$280$	11.2603	+	38.3824i	0.0402153	+	0.137080i
$281$		−	340.847i		−	1.21298i	−0.795091	−	0.606490i	$-0.792577\pi$
$281$		−	340.847i		−	1.21298i	0.795091	−	0.606490i	$-0.207423\pi$
$282$	76.1544			0.270051
$283$	289.875			1.02429			0.512147	−	0.858898i	$-0.328850\pi$
$283$	289.875			1.02429			0.512147	+	0.858898i	$0.328850\pi$
$284$	172.890			0.608769
$285$	8.99848	+	30.6726i	0.0315736	+	0.107623i
$286$	−44.0000	−	166.206i	−0.153846	−	0.581140i
$287$		−	144.821i		−	0.504603i
$288$	−44.2087			−0.153503
$289$	188.110			0.650898
$290$	−246.822	+	72.4106i	−0.851110	+	0.249692i
$291$	38.8835			0.133620
$292$	98.1620			0.336171
$293$	−373.944			−1.27626			−0.638129	−	0.769930i	$-0.720291\pi$
$293$	−373.944			−1.27626			−0.638129	+	0.769930i	$0.720291\pi$
$294$		−	63.1168i		−	0.214683i
$295$	41.8116	+	142.521i	0.141734	+	0.483122i
$296$			148.018i			0.500060i
$297$	194.638	−	51.5269i	0.655348	−	0.173491i
$298$			19.3553i			0.0649505i
$299$			248.197i			0.830090i
$300$	29.4041	+	45.8009i	0.0980135	+	0.152670i
$301$	75.5617			0.251036
$302$		−	240.613i		−	0.796732i
$303$	−187.316			−0.618204
$304$			23.4922i			0.0772770i
$305$	59.0871	−	17.3345i	0.193728	−	0.0568343i
$306$	−241.411			−0.788925
$307$	−366.959			−1.19531			−0.597654	−	0.801754i	$-0.703900\pi$
$307$	−366.959			−1.19531			−0.597654	+	0.801754i	$0.703900\pi$
$308$	−15.9245	−	60.1532i	−0.0517028	−	0.195303i
$309$	−99.4934			−0.321985
$310$	75.0550	+	255.836i	0.242113	+	0.825277i
$311$	−272.589			−0.876492			−0.438246	−	0.898855i	$-0.644400\pi$
$311$	−272.589			−0.876492			−0.438246	+	0.898855i	$0.644400\pi$
$312$			34.0282i			0.109065i
$313$			83.9447i			0.268194i	0.990968	+	0.134097i	$0.0428134\pi$
$313$			83.9447i			0.268194i	−0.990968	+	0.134097i	$0.957187\pi$
$314$		−	51.6553i		−	0.164507i
$315$	−31.1127	−	106.052i	−0.0987705	−	0.336674i
$316$		−	295.466i		−	0.935019i
$317$		−	276.170i		−	0.871197i	−0.900141	−	0.435599i	$-0.856537\pi$
$317$		−	276.170i		−	0.871197i	0.900141	−	0.435599i	$-0.143463\pi$
$318$	−65.7900			−0.206887
$319$	386.822	−	102.404i	1.21261	−	0.321016i
$320$	11.2603	+	38.3824i	0.0351884	+	0.119945i
$321$			90.8899i			0.283146i
$322$			89.8272i			0.278967i
$323$			128.284i			0.397164i
$324$	100.822			0.311179
$325$	−232.512	+	149.272i	−0.715422	+	0.459300i
$326$			142.714i			0.437773i
$327$	12.1664			0.0372060
$328$		−	144.821i		−	0.441528i
$329$			139.920i			0.425288i
$330$	−43.8330	−	72.4395i	−0.132827	−	0.219514i
$331$	421.117			1.27226			0.636128	−	0.771584i	$-0.280535\pi$
$331$	421.117			1.27226			0.636128	+	0.771584i	$0.280535\pi$
$332$	−211.822			−0.638019
$333$		−	408.979i		−	1.22817i
$334$	148.000			0.443114
$335$	28.0447	−	8.22750i	0.0837154	−	0.0245597i
$336$			12.3155i			0.0366532i
$337$	601.361			1.78445			0.892226	−	0.451589i	$-0.149143\pi$
$337$	601.361			1.78445			0.892226	+	0.451589i	$0.149143\pi$
$338$	66.2549			0.196020
$339$	−84.5276			−0.249344
$340$	61.4892	+	209.595i	0.180851	+	0.616456i
$341$	−106.144	−	400.949i	−0.311272	−	1.17580i
$342$		−	64.9100i		−	0.189795i
$343$	254.558			0.742153
$344$	75.5617			0.219656
$345$	34.4075	+	117.283i	0.0997320	+	0.339951i
$346$	292.233			0.844604
$347$	531.241			1.53095			0.765477	−	0.643463i	$-0.222503\pi$
$347$	531.241			1.53095			0.765477	+	0.643463i	$0.222503\pi$
$348$	−79.1960			−0.227575
$349$		−	242.556i		−	0.695002i	−0.937680	−	0.347501i	$-0.887030\pi$
$349$		−	242.556i		−	0.695002i	0.937680	−	0.347501i	$-0.112970\pi$
$350$	−84.1507	+	54.0246i	−0.240431	+	0.154356i
$351$		−	202.298i		−	0.576349i
$352$	−15.9245	−	60.1532i	−0.0452399	−	0.170890i
$353$			643.382i			1.82261i	0.411731	+	0.911305i	$0.364924\pi$
$353$			643.382i			1.82261i	−0.411731	+	0.911305i	$0.635076\pi$
$354$			45.7296i			0.129180i
$355$	121.675	+	414.746i	0.342746	+	1.16830i
$356$	91.4110			0.256773
$357$			67.2512i			0.188379i
$358$	−176.941			−0.494250
$359$			597.374i			1.66399i	0.554780	+	0.831997i	$0.312803\pi$
$359$			597.374i			1.66399i	−0.554780	+	0.831997i	$0.687197\pi$
$360$	−31.1127	−	106.052i	−0.0864242	−	0.294589i
$361$	326.507			0.904452
$362$	−129.575			−0.357941
$363$	65.1703	+	114.461i	0.179532	+	0.315320i
$364$	−62.5206			−0.171760
$365$	69.0833	+	235.481i	0.189269	+	0.645152i
$366$	18.9588			0.0518001
$367$		−	680.355i		−	1.85383i	−0.375274	−	0.926914i	$-0.622451\pi$
$367$		−	680.355i		−	1.85383i	0.375274	−	0.926914i	$-0.377549\pi$
$368$			89.8272i			0.244096i
$369$			400.147i			1.08441i
$370$	−355.079	+	104.170i	−0.959673	+	0.281541i
$371$		−	120.877i		−	0.325815i
$372$			82.0882i			0.220667i
$373$	79.3608			0.212763			0.106382	−	0.994325i	$-0.466073\pi$
$373$	79.3608			0.212763			0.106382	+	0.994325i	$0.466073\pi$
$374$	−86.9588	−	328.479i	−0.232510	−	0.878287i
$375$	−89.1780	+	102.771i	−0.237808	+	0.274055i
$376$			139.920i			0.372127i
$377$		−	402.046i		−	1.06643i
$378$		−	73.2158i		−	0.193692i
$379$	−86.7327			−0.228846			−0.114423	−	0.993432i	$-0.536502\pi$
$379$	−86.7327			−0.228846			−0.114423	+	0.993432i	$0.536502\pi$
$380$	−56.3554	+	16.5331i	−0.148304	+	0.0435081i
$381$		−	144.707i		−	0.379808i
$382$	−127.696			−0.334282
$383$			734.141i			1.91682i	0.285400	+	0.958409i	$0.407874\pi$
$383$			734.141i			1.91682i	−0.285400	+	0.958409i	$0.592126\pi$
$384$			12.3155i			0.0320715i
$385$	133.094	−	80.5351i	0.345700	−	0.209182i
$386$	−216.535			−0.560970
$387$	−208.781			−0.539485
$388$			71.4413i			0.184127i
$389$	287.939			0.740202			0.370101	−	0.928992i	$-0.379323\pi$
$389$	287.939			0.740202			0.370101	+	0.928992i	$0.379323\pi$
$390$	−81.6301	+	23.9480i	−0.209308	+	0.0614050i
$391$			490.521i			1.25453i
$392$	115.966			0.295830
$393$	161.124			0.409984
$394$	455.192			1.15531
$395$	708.792	−	207.939i	1.79441	−	0.526429i
$396$	44.0000	+	166.206i	0.111111	+	0.419712i
$397$			193.045i			0.486260i	0.969994	+	0.243130i	$0.0781741\pi$
$397$			193.045i			0.486260i	−0.969994	+	0.243130i	$0.921826\pi$
$398$	68.7152			0.172651
$399$	−18.0823			−0.0453191
$400$	−84.1507	+	54.0246i	−0.210377	+	0.135061i
$401$	354.233			0.883374			0.441687	−	0.897169i	$-0.354380\pi$
$401$	354.233			0.883374			0.441687	+	0.897169i	$0.354380\pi$
$402$	8.99848			0.0223843
$403$	−416.728			−1.03406
$404$		−	344.158i		−	0.851877i
$405$	70.9553	+	241.862i	0.175198	+	0.597190i
$406$		−	145.508i		−	0.358394i
$407$	556.484	−	147.319i	1.36728	−	0.361963i
$408$			67.2512i			0.164831i
$409$			586.482i			1.43394i	0.697103	+	0.716971i	$0.254472\pi$
$409$			586.482i			1.43394i	−0.697103	+	0.716971i	$0.745528\pi$
$410$	347.411	−	101.920i	0.847344	−	0.248587i
$411$	231.637			0.563594
$412$		−	182.801i		−	0.443691i
$413$	−84.0199			−0.203438
$414$		−	248.197i		−	0.599509i
$415$	−149.074	−	508.140i	−0.359214	−	1.22443i
$416$	−62.5206			−0.150290
$417$	−268.371			−0.643575
$418$	88.3207	−	23.3813i	0.211294	−	0.0559361i
$419$	36.1507			0.0862786			0.0431393	−	0.999069i	$-0.486264\pi$
$419$	36.1507			0.0862786			0.0431393	+	0.999069i	$0.486264\pi$
$420$	−29.5435	+	8.66723i	−0.0703418	+	0.0206363i
$421$	−295.644			−0.702242			−0.351121	−	0.936330i	$-0.614200\pi$
$421$	−295.644			−0.702242			−0.351121	+	0.936330i	$0.614200\pi$
$422$		−	205.780i		−	0.487629i
$423$		−	386.605i		−	0.913959i
$424$		−	120.877i		−	0.285088i
$425$	−459.523	+	295.013i	−1.08123	+	0.694147i
$426$			133.077i			0.312386i
$427$			34.8334i			0.0815770i
$428$	−166.994			−0.390172
$429$	127.932	−	33.8675i	0.298209	−	0.0789453i
$430$	53.1780	+	181.265i	0.123670	+	0.421546i
$431$			290.732i			0.674551i	0.941406	+	0.337276i	$0.109505\pi$
$431$			290.732i			0.674551i	−0.941406	+	0.337276i	$0.890495\pi$
$432$		−	73.2158i		−	0.169481i
$433$		−	212.960i		−	0.491823i	−0.969292	−	0.245912i	$-0.920913\pi$
$433$		−	212.960i		−	0.491823i	0.969292	−	0.245912i	$-0.0790873\pi$
$434$	−150.822			−0.347516
$435$	−55.7356	−	189.983i	−0.128128	−	0.436743i
$436$			22.3535i			0.0512694i
$437$	−131.890			−0.301808
$438$			75.5569i			0.172504i
$439$		−	157.824i		−	0.359507i	−0.983712	−	0.179754i	$-0.942470\pi$
$439$		−	157.824i		−	0.359507i	0.983712	−	0.179754i	$-0.0575300\pi$
$440$	133.094	−	80.5351i	0.302487	−	0.183034i
$441$	−320.418			−0.726571
$442$	−341.407			−0.772413
$443$			218.723i			0.493731i	0.969050	+	0.246865i	$0.0794006\pi$
$443$			218.723i			0.493731i	−0.969050	+	0.246865i	$0.920599\pi$
$444$	−113.932			−0.256603
$445$	64.3322	+	219.286i	0.144567	+	0.492777i
$446$			110.438i			0.247620i
$447$	−14.8981			−0.0333290
$448$	−22.6274			−0.0505076
$449$	−824.610			−1.83655			−0.918274	−	0.395946i	$-0.870417\pi$
$449$	−824.610			−1.83655			−0.918274	+	0.395946i	$0.870417\pi$
$450$	232.512	−	149.272i	0.516694	−	0.331716i
$451$	−544.466	+	144.137i	−1.20724	+	0.319595i
$452$		−	155.304i		−	0.343593i
$453$	185.204			0.408838
$454$	−380.000			−0.837004
$455$	−44.0000	−	149.980i	−0.0967033	−	0.329627i
$456$	−18.0823			−0.0396542
$457$	304.472			0.666242			0.333121	−	0.942884i	$-0.391898\pi$
$457$	304.472			0.666242			0.333121	+	0.942884i	$0.391898\pi$
$458$	−235.506			−0.514204
$459$		−	399.810i		−	0.871046i
$460$	−215.486	+	63.2176i	−0.468449	+	0.137429i
$461$		−	254.639i		−	0.552363i	−0.961106	−	0.276181i	$-0.910931\pi$
$461$		−	254.639i		−	0.552363i	0.961106	−	0.276181i	$-0.0890690\pi$
$462$	46.3009	−	12.2573i	0.100218	−	0.0265310i
$463$		−	151.472i		−	0.327153i	−0.986531	−	0.163576i	$-0.947697\pi$
$463$		−	151.472i		−	0.327153i	0.986531	−	0.163576i	$-0.0523030\pi$
$464$		−	145.508i		−	0.313595i
$465$	−196.921	+	57.7711i	−0.423486	+	0.124239i
$466$	59.4934			0.127668
$467$		−	719.707i		−	1.54113i	−0.637363	−	0.770564i	$-0.719975\pi$
$467$		−	719.707i		−	1.54113i	0.637363	−	0.770564i	$-0.280025\pi$
$468$	172.747			0.369118
$469$			16.5331i			0.0352517i
$470$	−335.653	+	98.4711i	−0.714156	+	0.209513i
$471$	39.7600			0.0844161
$472$	−84.0199			−0.178008
$473$	−75.2050	−	284.080i	−0.158996	−	0.600592i
$474$	227.425			0.479799
$475$	−79.3223	−	123.555i	−0.166994	−	0.260117i
$476$	−123.562			−0.259584
$477$			333.989i			0.700187i
$478$			14.2703i			0.0298542i
$479$		−	525.759i		−	1.09762i	−0.835948	−	0.548809i	$-0.815082\pi$
$479$		−	525.759i		−	1.09762i	0.835948	−	0.548809i	$-0.184918\pi$
$480$	−29.5435	+	8.66723i	−0.0615490	+	0.0180567i
$481$		−	578.384i		−	1.20246i
$482$			222.391i			0.461392i
$483$	−69.1415			−0.143150
$484$	−210.301	+	119.738i	−0.434507	+	0.247393i
$485$	−171.380	+	50.2781i	−0.353361	+	0.103666i
$486$			310.576i			0.639044i
$487$			638.185i			1.31044i	0.755437	+	0.655221i	$0.227424\pi$
$487$			638.185i			1.31044i	−0.755437	+	0.655221i	$0.772576\pi$
$488$			34.8334i			0.0713799i
$489$	−109.849			−0.224641
$490$	81.6128	+	278.189i	0.166557	+	0.567733i
$491$			697.269i			1.42010i	0.704152	+	0.710050i	$0.251327\pi$
$491$			697.269i			1.42010i	−0.704152	+	0.710050i	$0.748673\pi$
$492$	111.471			0.226567
$493$		−	794.578i		−	1.61172i
$494$		−	91.7966i		−	0.185823i
$495$	−367.746	+	222.522i	−0.742921	+	0.449540i
$496$	−150.822			−0.304077
$497$	−244.504			−0.491960
$498$		−	163.043i		−	0.327396i
$499$	−363.411			−0.728279			−0.364139	−	0.931344i	$-0.618637\pi$
$499$	−363.411			−0.728279			−0.364139	+	0.931344i	$0.618637\pi$
$500$	−188.822	−	163.848i	−0.377644	−	0.327696i
$501$			113.918i			0.227381i
$502$	588.226			1.17176
$503$	336.989			0.669959			0.334980	−	0.942225i	$-0.391271\pi$
$503$	336.989			0.669959			0.334980	+	0.942225i	$0.391271\pi$
$504$	62.5206			0.124049
$505$	825.601	−	242.208i	1.63485	−	0.479619i
$506$	337.712	−	89.4031i	0.667416	−	0.176686i
$507$			50.9975i			0.100587i
$508$	265.872			0.523370
$509$	502.528			0.987284			0.493642	−	0.869665i	$-0.335665\pi$
$509$	502.528			0.987284			0.493642	+	0.869665i	$0.335665\pi$
$510$	−161.329	+	47.3292i	−0.316331	+	0.0928024i
$511$	−138.822			−0.271667
$512$	−22.6274			−0.0441942
$513$	107.500			0.209552
$514$			182.455i			0.354970i
$515$	438.521	−	128.649i	0.851496	−	0.249805i
$516$			58.1611i			0.112715i
$517$	526.039	−	139.259i	1.01748	−	0.269360i
$518$		−	209.329i		−	0.404109i
$519$			224.937i			0.433404i
$520$	−44.0000	−	149.980i	−0.0846154	−	0.288424i
$521$	−351.939			−0.675506			−0.337753	−	0.941235i	$-0.609667\pi$
$521$	−351.939			−0.675506			−0.337753	+	0.941235i	$0.609667\pi$
$522$			402.046i			0.770202i
$523$	−402.799			−0.770171			−0.385085	−	0.922881i	$-0.625828\pi$
$523$	−402.799			−0.770171			−0.385085	+	0.922881i	$0.625828\pi$
$524$			296.035i			0.564953i
$525$	−41.5836	−	64.7722i	−0.0792069	−	0.123376i
$526$	−324.000			−0.615970
$527$	−823.595			−1.56280
$528$	46.3009	−	12.2573i	0.0876912	−	0.0232146i
$529$	24.6916			0.0466759
$530$	289.972	−	85.0695i	0.547117	−	0.160509i
$531$	232.151			0.437195
$532$		−	33.2230i		−	0.0624492i
$533$			565.894i			1.06171i
$534$			70.3606i			0.131761i
$535$	−117.525	−	400.601i	−0.219673	−	0.748786i
$536$			16.5331i			0.0308453i
$537$		−	136.195i		−	0.253622i
$538$	524.441			0.974798
$539$	−115.418	−	435.981i	−0.214134	−	0.808871i
$540$	175.637	−	51.5269i	0.325254	−	0.0954202i
$541$			227.499i			0.420515i	0.977646	+	0.210258i	$0.0674303\pi$
$541$			227.499i			0.420515i	−0.977646	+	0.210258i	$0.932570\pi$
$542$		−	331.245i		−	0.611154i
$543$		−	99.7358i		−	0.183676i
$544$	−123.562			−0.227136
$545$	−53.6237	+	15.7317i	−0.0983921	+	0.0288654i
$546$		−	48.1231i		−	0.0881376i
$547$	−724.833			−1.32511			−0.662553	−	0.749015i	$-0.730527\pi$
$547$	−724.833			−1.32511			−0.662553	+	0.749015i	$0.730527\pi$
$548$			425.591i			0.776626i
$549$		−	96.2463i		−	0.175312i
$550$	286.863	+	262.602i	0.521569	+	0.477458i
$551$	213.644			0.387739
$552$	−69.1415			−0.125256
$553$			417.852i			0.755609i
$554$	676.233			1.22064
$555$	−80.1814	−	273.310i	−0.144471	−	0.492451i
$556$		−	493.083i		−	0.886839i
$557$	583.537			1.04764			0.523822	−	0.851828i	$-0.324506\pi$
$557$	583.537			1.04764			0.523822	+	0.851828i	$0.324506\pi$
$558$	416.728			0.746825
$559$	−295.260			−0.528194
$560$	−15.9245	−	54.2809i	−0.0284365	−	0.0969301i
$561$	252.836	−	66.9337i	0.450688	−	0.119311i
$562$			482.031i			0.857707i
$563$	−262.211			−0.465739			−0.232869	−	0.972508i	$-0.574811\pi$
$563$	−262.211			−0.465739			−0.232869	+	0.972508i	$0.574811\pi$
$564$	−107.699			−0.190955
$565$	372.558	−	109.298i	0.659395	−	0.193448i
$566$	−409.946			−0.724285
$567$	−142.584			−0.251471
$568$	−244.504			−0.430465
$569$			867.460i			1.52453i	0.647262	+	0.762267i	$0.275914\pi$
$569$			867.460i			1.52453i	−0.647262	+	0.762267i	$0.724086\pi$
$570$	−12.7258	−	43.3777i	−0.0223259	−	0.0761012i
$571$			630.208i			1.10369i	0.833946	+	0.551846i	$0.186076\pi$
$571$			630.208i			1.10369i	−0.833946	+	0.551846i	$0.813924\pi$
$572$	62.2254	+	235.051i	0.108786	+	0.410928i
$573$		−	98.2895i		−	0.171535i
$574$			204.808i			0.356808i
$575$	−303.305	−	472.439i	−0.527487	−	0.821634i
$576$	62.5206			0.108543
$577$			769.176i			1.33306i	0.745478	+	0.666530i	$0.232221\pi$
$577$			769.176i			1.33306i	−0.745478	+	0.666530i	$0.767779\pi$
$578$	−266.027			−0.460254
$579$		−	166.670i		−	0.287859i
$580$	349.059	−	102.404i	0.601826	−	0.176559i
$581$	299.562			0.515597
$582$	−54.9895			−0.0944837
$583$	−454.447	+	120.306i	−0.779498	+	0.206358i
$584$	−138.822			−0.237709
$585$	121.574	+	414.403i	0.207819	+	0.708381i
$586$	528.836			0.902450
$587$			523.523i			0.891861i	0.895068	+	0.445931i	$0.147127\pi$
$587$			523.523i			0.891861i	−0.895068	+	0.445931i	$0.852873\pi$
$588$			89.2606i			0.151804i
$589$		−	221.446i		−	0.375970i
$590$	−59.1305	−	201.555i	−0.100221	−	0.341619i
$591$			350.369i			0.592840i
$592$		−	209.329i		−	0.353595i
$593$	−8.65008			−0.0145870			−0.00729349	−	0.999973i	$-0.502322\pi$
$593$	−8.65008			−0.0145870			−0.00729349	+	0.999973i	$0.502322\pi$
$594$	−275.260	+	72.8701i	−0.463401	+	0.122677i
$595$	−86.9588	−	296.412i	−0.146149	−	0.498171i
$596$		−	27.3725i		−	0.0459270i
$597$			52.8912i			0.0885950i
$598$		−	351.003i		−	0.586962i
$599$	1124.34			1.87703			0.938517	−	0.345233i	$-0.112200\pi$
$599$	1124.34			1.87703			0.938517	+	0.345233i	$0.112200\pi$
$600$	−41.5836	−	64.7722i	−0.0693060	−	0.107954i
$601$		−	533.572i		−	0.887807i	−0.896075	−	0.443903i	$-0.853593\pi$
$601$		−	533.572i		−	0.887807i	0.896075	−	0.443903i	$-0.146407\pi$
$602$	−106.860			−0.177509
$603$		−	45.6816i		−	0.0757572i
$604$			340.278i			0.563374i
$605$	−435.244	−	420.224i	−0.719411	−	0.694584i
$606$	264.904			0.437136
$607$	−933.711			−1.53824			−0.769119	−	0.639106i	$-0.779305\pi$
$607$	−933.711			−1.53824			−0.769119	+	0.639106i	$0.779305\pi$
$608$		−	33.2230i		−	0.0546431i
$609$	112.000			0.183908
$610$	−83.5617	+	24.5146i	−0.136986	+	0.0401879i
$611$		−	546.742i		−	0.894831i
$612$	341.407			0.557854
$613$	216.288			0.352835			0.176417	−	0.984315i	$-0.443549\pi$
$613$	216.288			0.352835			0.176417	+	0.984315i	$0.443549\pi$
$614$	518.959			0.845210
$615$	78.4499	+	267.408i	0.127561	+	0.434810i
$616$	22.5206	+	85.0695i	0.0365594	+	0.138100i
$617$		−	5.63643i		−	0.00913522i	−0.999990	−	0.00456761i	$-0.998546\pi$
$617$		−	5.63643i		−	0.00913522i	0.999990	−	0.00456761i	$-0.00145392\pi$
$618$	140.705			0.227678
$619$	278.870			0.450516			0.225258	−	0.974299i	$-0.427677\pi$
$619$	278.870			0.450516			0.225258	+	0.974299i	$0.427677\pi$
$620$	−106.144	−	361.807i	−0.171200	−	0.583559i
$621$	411.048			0.661913
$622$	385.499			0.619773
$623$	−129.275			−0.207504
$624$		−	48.1231i		−	0.0771204i
$625$	260.168	−	568.276i	0.416269	−	0.909241i
$626$		−	118.716i		−	0.189642i
$627$	17.9970	+	67.9819i	0.0287033	+	0.108424i
$628$			73.0517i			0.116324i
$629$		−	1143.08i		−	1.81730i
$630$	44.0000	+	149.980i	0.0698413	+	0.238064i
$631$	−452.843			−0.717659			−0.358830	−	0.933403i	$-0.616824\pi$
$631$	−452.843			−0.717659			−0.358830	+	0.933403i	$0.616824\pi$
$632$			417.852i			0.661158i
$633$	158.392			0.250224
$634$			390.563i			0.616029i
$635$	187.112	+	637.800i	0.294665	+	1.00441i
$636$	93.0412			0.146291
$637$	−453.139			−0.711365
$638$	−547.049	+	144.821i	−0.857444	+	0.226992i
$639$	675.576			1.05724
$640$	−15.9245	−	54.2809i	−0.0248820	−	0.0848138i
$641$	457.802			0.714199			0.357100	−	0.934066i	$-0.383766\pi$
$641$	457.802			0.714199			0.357100	+	0.934066i	$0.383766\pi$
$642$		−	128.538i		−	0.200215i
$643$		−	1242.30i		−	1.93203i	−0.258481	−	0.966016i	$-0.583222\pi$
$643$		−	1242.30i		−	1.93203i	0.258481	−	0.966016i	$-0.416778\pi$
$644$		−	127.035i		−	0.197259i
$645$	−139.523	+	40.9320i	−0.216314	+	0.0634604i
$646$		−	181.421i		−	0.280838i
$647$			1045.87i			1.61649i	0.588848	+	0.808243i	$0.299581\pi$
$647$			1045.87i			1.61649i	−0.588848	+	0.808243i	$0.700419\pi$
$648$	−142.584			−0.220037
$649$	83.6232	+	315.879i	0.128849	+	0.486717i
$650$	328.822	−	211.103i	0.505880	−	0.324774i
$651$		−	116.090i		−	0.178326i
$652$		−	201.828i		−	0.309552i
$653$			1051.88i			1.61085i	0.592699	+	0.805424i	$0.298062\pi$
$653$			1051.88i			1.61085i	−0.592699	+	0.805424i	$0.701938\pi$
$654$	−17.2058			−0.0263086
$655$	−710.158	+	208.340i	−1.08421	+	0.318077i
$656$			204.808i			0.312207i
$657$	383.572			0.583823
$658$		−	197.876i		−	0.300724i
$659$		−	86.2083i		−	0.130817i	−0.997859	−	0.0654084i	$-0.979165\pi$
$659$		−	86.2083i		−	0.130817i	0.997859	−	0.0654084i	$-0.0208350\pi$
$660$	61.9892	+	102.445i	0.0939230	+	0.155220i
$661$	−688.664			−1.04185			−0.520926	−	0.853602i	$-0.674413\pi$
$661$	−688.664			−1.04185			−0.520926	+	0.853602i	$0.674413\pi$
$662$	−595.549			−0.899620
$663$		−	262.786i		−	0.396360i
$664$	299.562			0.451147
$665$	79.6985	−	23.3813i	0.119847	−	0.0351598i
$666$			578.384i			0.868445i
$667$	816.912			1.22476
$668$	−209.304			−0.313329
$669$	−85.0063			−0.127065
$670$	−39.6611	+	11.6354i	−0.0591957	+	0.0173663i
$671$	130.959	−	34.6689i	0.195170	−	0.0516676i
$672$		−	17.4167i		−	0.0259177i
$673$	811.827			1.20628			0.603140	−	0.797635i	$-0.293916\pi$
$673$	811.827			1.20628			0.603140	+	0.797635i	$0.293916\pi$
$674$	−850.452			−1.26180
$675$	247.216	+	385.072i	0.366245	+	0.570478i
$676$	−93.6985			−0.138607
$677$	236.610			0.349498			0.174749	−	0.984613i	$-0.444089\pi$
$677$	236.610			0.349498			0.174749	+	0.984613i	$0.444089\pi$
$678$	119.540			0.176313
$679$		−	101.033i		−	0.148797i
$680$	−86.9588	−	296.412i	−0.127881	−	0.435900i
$681$		−	292.492i		−	0.429504i
$682$	150.110	+	567.027i	0.220103	+	0.831418i
$683$		−	101.645i		−	0.148821i	−0.997228	−	0.0744105i	$-0.976292\pi$
$683$		−	101.645i		−	0.148821i	0.997228	−	0.0744105i	$-0.0237075\pi$
$684$			91.7966i			0.134206i
$685$	−1020.95	+	299.517i	−1.49044	+	0.437252i
$686$	−360.000			−0.524781
$687$		−	181.272i		−	0.263861i
$688$	−106.860			−0.155320
$689$			472.332i			0.685533i
$690$	−48.6596	−	165.863i	−0.0705212	−	0.240382i
$691$	150.582			0.217919			0.108959	−	0.994046i	$-0.465248\pi$
$691$	150.582			0.217919			0.108959	+	0.994046i	$0.465248\pi$
$692$	−413.280			−0.597225
$693$	−62.2254	−	235.051i	−0.0897913	−	0.339179i
$694$	−751.288			−1.08255
$695$	1182.85	−	347.016i	1.70195	−	0.499303i
$696$	112.000			0.160920
$697$			1118.40i			1.60459i
$698$			343.026i			0.491441i
$699$			45.7930i			0.0655122i
$700$	119.007	−	76.4023i	0.170010	−	0.109146i
$701$			704.744i			1.00534i	0.864478	+	0.502671i	$0.167649\pi$
$701$			704.744i			1.00534i	−0.864478	+	0.502671i	$0.832351\pi$
$702$			286.093i			0.407540i
$703$	307.349			0.437197
$704$	22.5206	+	85.0695i	0.0319895	+	0.120837i
$705$	−75.7948	−	258.358i	−0.107510	−	0.366465i
$706$		−	909.879i		−	1.28878i
$707$			486.713i			0.688421i
$708$		−	64.6715i		−	0.0913439i
$709$	−885.583			−1.24906			−0.624529	−	0.781001i	$-0.714709\pi$
$709$	−885.583			−1.24906			−0.624529	+	0.781001i	$0.714709\pi$
$710$	−172.074	−	586.540i	−0.242358	−	0.826113i
$711$		−	1154.54i		−	1.62383i
$712$	−129.275			−0.181566
$713$		−	846.746i		−	1.18758i
$714$		−	95.1075i		−	0.133204i
$715$	−520.071	+	314.694i	−0.727372	+	0.440131i
$716$	250.233			0.349488
$717$	−10.9841			−0.0153195
$718$		−	844.815i		−	1.17662i
$719$	−1128.12			−1.56901			−0.784504	−	0.620123i	$-0.787083\pi$
$719$	−1128.12			−1.56901			−0.784504	+	0.620123i	$0.787083\pi$
$720$	44.0000	+	149.980i	0.0611111	+	0.208306i
$721$			258.519i			0.358557i
$722$	−461.751			−0.639544
$723$	−171.178			−0.236761
$724$	183.246			0.253103
$725$	491.313	+	765.288i	0.677674	+	1.05557i
$726$	−92.1647	−	161.873i	−0.126949	−	0.222965i
$727$		−	626.987i		−	0.862430i	−0.902249	−	0.431215i	$-0.858085\pi$
$727$		−	626.987i		−	0.862430i	0.902249	−	0.431215i	$-0.141915\pi$
$728$	88.4175			0.121453
$729$	214.644			0.294436
$730$	−97.6985	−	333.020i	−0.133834	−	0.456192i
$731$	−583.534			−0.798268
$732$	−26.8118			−0.0366282
$733$	141.276			0.192737			0.0963685	−	0.995346i	$-0.469277\pi$
$733$	141.276			0.192737			0.0963685	+	0.995346i	$0.469277\pi$
$734$			962.167i			1.31085i
$735$	−214.127	+	62.8188i	−0.291329	+	0.0854677i
$736$		−	127.035i		−	0.172602i
$737$	62.1573	−	16.4550i	0.0843383	−	0.0223270i
$738$		−	565.894i		−	0.766794i
$739$		−	848.418i		−	1.14806i	−0.818834	−	0.574031i	$-0.805379\pi$
$739$		−	848.418i		−	1.14806i	0.818834	−	0.574031i	$-0.194621\pi$
$740$	502.158	−	147.319i	0.678591	−	0.199079i
$741$	70.6574			0.0953541
$742$			170.946i			0.230386i
$743$	1315.28			1.77023			0.885113	−	0.465376i	$-0.154081\pi$
$743$	1315.28			1.77023			0.885113	+	0.465376i	$0.154081\pi$
$744$		−	116.090i		−	0.156035i
$745$	65.6637	−	19.2639i	0.0881393	−	0.0258575i
$746$	−112.233			−0.150446
$747$	−827.703			−1.10804
$748$	122.978	+	464.540i	0.164410	+	0.621043i
$749$	236.165			0.315307
$750$	126.117	−	145.339i	0.168156	−	0.193786i
$751$	−544.405			−0.724906			−0.362453	−	0.932002i	$-0.618061\pi$
$751$	−544.405			−0.724906			−0.362453	+	0.932002i	$0.618061\pi$
$752$		−	197.876i		−	0.263134i
$753$			452.767i			0.601285i
$754$			568.578i			0.754083i
$755$	−816.292	+	239.477i	−1.08118	+	0.317188i
$756$			103.543i			0.136961i
$757$		−	1065.19i		−	1.40712i	−0.710634	−	0.703562i	$-0.751592\pi$
$757$		−	1065.19i		−	1.40712i	0.710634	−	0.703562i	$-0.248408\pi$
$758$	122.659			0.161819
$759$	68.8151	+	259.943i	0.0906654	+	0.342481i
$760$	79.6985	−	23.3813i	0.104867	−	0.0307648i
$761$		−	1137.39i		−	1.49460i	−0.664488	−	0.747299i	$-0.731350\pi$
$761$		−	1137.39i		−	1.49460i	0.664488	−	0.747299i	$-0.268650\pi$
$762$			204.646i			0.268565i
$763$		−	31.6126i		−	0.0414319i
$764$	180.589			0.236373
$765$	240.271	+	819.000i	0.314080	+	1.07059i
$766$		−	1038.23i		−	1.35539i
$767$	328.311			0.428045
$768$		−	17.4167i		−	0.0226780i
$769$			375.854i			0.488756i	0.969680	+	0.244378i	$0.0785838\pi$
$769$			375.854i			0.488756i	−0.969680	+	0.244378i	$0.921416\pi$
$770$	−188.224	+	113.894i	−0.244447	+	0.147914i
$771$	−140.438			−0.182151
$772$	306.226			0.396666
$773$		−	176.434i		−	0.228245i	−0.993467	−	0.114123i	$-0.963594\pi$
$773$		−	176.434i		−	0.228245i	0.993467	−	0.114123i	$-0.0364057\pi$
$774$	295.260			0.381473
$775$	793.237	−	509.256i	1.02353	−	0.657105i
$776$		−	101.033i		−	0.130197i
$777$	161.124			0.207366
$778$	−407.207			−0.523402
$779$	−300.712			−0.386023
$780$	115.442	−	33.8675i	0.148003	−	0.0434199i
$781$	243.350	+	919.232i	0.311587	+	1.17699i
$782$		−	693.701i		−	0.887085i
$783$	−665.843			−0.850374
$784$	−164.000			−0.209184
$785$	−175.244	+	51.4115i	−0.223240	+	0.0654923i
$786$	−227.863			−0.289902
$787$	−81.8506			−0.104003			−0.0520017	−	0.998647i	$-0.516560\pi$
$787$	−81.8506			−0.104003			−0.0520017	+	0.998647i	$0.516560\pi$
$788$	−643.739			−0.816927
$789$		−	249.388i		−	0.316081i
$790$	−1002.38	+	294.071i	−1.26884	+	0.372242i
$791$			219.633i			0.277665i
$792$	−62.2254	−	235.051i	−0.0785674	−	0.296782i
$793$		−	136.113i		−	0.171643i
$794$		−	273.007i		−	0.343838i
$795$	65.4794	+	223.196i	0.0823640	+	0.280750i
$796$	−97.1780			−0.122083
$797$			115.706i			0.145177i	0.997362	+	0.0725886i	$0.0231260\pi$
$797$			115.706i			0.145177i	−0.997362	+	0.0725886i	$0.976874\pi$
$798$	25.5723			0.0320455
$799$		−	1080.55i		−	1.35237i
$800$	119.007	−	76.4023i	0.148759	−	0.0955029i
$801$	357.192			0.445932
$802$	−500.961			−0.624640
$803$	138.167	+	521.912i	0.172063	+	0.649953i
$804$	−12.7258			−0.0158281
$805$	304.744	−	89.4031i	0.378564	−	0.111060i
$806$	589.343			0.731194
$807$			403.671i			0.500212i
$808$			486.713i			0.602368i
$809$		−	793.230i		−	0.980507i	−0.871580	−	0.490254i	$-0.836904\pi$
$809$		−	793.230i		−	0.980507i	0.871580	−	0.490254i	$-0.163096\pi$
$810$	−100.346	−	342.044i	−0.123884	−	0.422277i
$811$			290.394i			0.358069i	0.983843	+	0.179035i	$0.0572974\pi$
$811$			290.394i			0.358069i	−0.983843	+	0.179035i	$0.942703\pi$
$812$			205.780i			0.253423i
$813$	254.965			0.313610
$814$	−786.987	+	208.340i	−0.966814	+	0.255946i
$815$	484.165	−	142.040i	0.594067	−	0.174282i
$816$		−	95.1075i		−	0.116553i
$817$		−	156.899i		−	0.192043i
$818$		−	829.411i		−	1.01395i
$819$	−244.301			−0.298292
$820$	−491.313	+	144.137i	−0.599163	+	0.175777i
$821$			850.021i			1.03535i	0.855578	+	0.517674i	$0.173202\pi$
$821$			850.021i			1.03535i	−0.855578	+	0.517674i	$0.826798\pi$
$822$	−327.584			−0.398521
$823$			446.765i			0.542850i	0.962460	+	0.271425i	$0.0874949\pi$
$823$			446.765i			0.542850i	−0.962460	+	0.271425i	$0.912505\pi$
$824$			258.519i			0.313737i
$825$	−202.129	+	220.803i	−0.245005	+	0.267640i
$826$	118.822			0.143852
$827$	1078.95			1.30465			0.652327	−	0.757938i	$-0.273793\pi$
$827$	1078.95			1.30465			0.652327	+	0.757938i	$0.273793\pi$
$828$			351.003i			0.423917i
$829$	−560.883			−0.676578			−0.338289	−	0.941042i	$-0.609848\pi$
$829$	−560.883			−0.676578			−0.338289	+	0.941042i	$0.609848\pi$
$830$	210.822	+	718.618i	0.254002	+	0.865805i
$831$			520.508i			0.626363i
$832$	88.4175			0.106271
$833$	−895.556			−1.07510
$834$	379.534			0.455077
$835$	−147.301	−	502.098i	−0.176409	−	0.601315i
$836$	−124.904	+	33.0661i	−0.149407	+	0.0395528i
$837$			690.159i			0.824563i
$838$	−51.1249			−0.0610082
$839$	82.8835			0.0987884			0.0493942	−	0.998779i	$-0.484271\pi$
$839$	82.8835			0.0987884			0.0493942	+	0.998779i	$0.484271\pi$
$840$	41.7809	−	12.2573i	0.0497391	−	0.0145920i
$841$	−482.288			−0.573470
$842$	418.104			0.496560
$843$	−371.027			−0.440127
$844$			291.016i			0.344806i
$845$	−65.9421	−	224.773i	−0.0780379	−	0.266004i
$846$			546.742i			0.646267i
$847$	297.411	−	169.336i	0.351135	−	0.199924i
$848$			170.946i			0.201587i
$849$		−	315.542i		−	0.371663i
$850$	649.863	−	417.211i	0.764545	−	0.490836i
$851$	1175.21			1.38098
$852$		−	188.199i		−	0.220891i
$853$	−412.282			−0.483332			−0.241666	−	0.970359i	$-0.577694\pi$
$853$	−412.282			−0.483332			−0.241666	+	0.970359i	$0.577694\pi$
$854$		−	49.2619i		−	0.0576837i
$855$	−220.211	+	64.6035i	−0.257556	+	0.0755597i
$856$	236.165			0.275893
$857$	−1108.08			−1.29297			−0.646485	−	0.762927i	$-0.723762\pi$
$857$	−1108.08			−1.29297			−0.646485	+	0.762927i	$0.723762\pi$
$858$	−180.923	+	47.8959i	−0.210866	+	0.0558227i
$859$	785.281			0.914181			0.457090	−	0.889420i	$-0.348892\pi$
$859$	785.281			0.914181			0.457090	+	0.889420i	$0.348892\pi$
$860$	−75.2050	−	256.347i	−0.0874477	−	0.298078i
$861$	−157.644			−0.183094
$862$		−	411.156i		−	0.476980i
$863$		−	749.791i		−	0.868819i	−0.900716	−	0.434409i	$-0.856957\pi$
$863$		−	749.791i		−	0.868819i	0.900716	−	0.434409i	$-0.143043\pi$
$864$			103.543i			0.119841i
$865$	−290.853	−	991.416i	−0.336247	−	1.14615i
$866$			301.170i			0.347772i
$867$		−	204.765i		−	0.236177i
$868$	213.295			0.245731
$869$	1570.95	−	415.879i	1.80776	−	0.478572i
$870$	78.8220	+	268.677i	0.0906000	+	0.308824i
$871$		−	64.6035i		−	0.0741717i
$872$		−	31.6126i		−	0.0362530i
$873$			279.159i			0.319770i
$874$	186.521			0.213410
$875$	267.035	+	231.716i	0.305183	+	0.264819i
$876$		−	106.854i		−	0.121979i
$877$	−273.360			−0.311699			−0.155849	−	0.987781i	$-0.549811\pi$
$877$	−273.360			−0.311699			−0.155849	+	0.987781i	$0.549811\pi$
$878$			223.196i			0.254210i
$879$			407.054i			0.463087i
$880$	−188.224	+	113.894i	−0.213891	+	0.129425i
$881$	−795.076			−0.902470			−0.451235	−	0.892405i	$-0.649016\pi$
$881$	−795.076			−0.902470			−0.451235	+	0.892405i	$0.649016\pi$
$882$	453.139			0.513764
$883$			1552.42i			1.75812i	0.476711	+	0.879060i	$0.341829\pi$
$883$			1552.42i			1.75812i	−0.476711	+	0.879060i	$0.658171\pi$
$884$	482.822			0.546179
$885$	155.140	−	45.5137i	0.175300	−	0.0514280i
$886$		−	309.321i		−	0.349120i
$887$	865.828			0.976131			0.488066	−	0.872807i	$-0.337703\pi$
$887$	865.828			0.976131			0.488066	+	0.872807i	$0.337703\pi$
$888$	161.124			0.181446
$889$	−376.000			−0.422947
$890$	−90.9794	−	310.117i	−0.102224	−	0.348446i
$891$	141.911	+	536.055i	0.159271	+	0.601633i
$892$		−	156.184i		−	0.175094i
$893$	290.534			0.325347
$894$	21.0690			0.0235672
$895$	176.106	+	600.284i	0.196767	+	0.670708i
$896$	32.0000			0.0357143
$897$	270.173			0.301196
$898$	1166.17			1.29864
$899$			1371.61i			1.52571i
$900$	−328.822	+	211.103i	−0.365358	+	0.234559i
$901$			933.487i			1.03606i
$902$	769.991	−	203.841i	0.853649	−	0.225988i
$903$		−	82.2523i		−	0.0910878i
$904$			219.633i			0.242957i
$905$	128.963	+	439.589i	0.142501	+	0.485734i
$906$	−261.918			−0.289092
$907$		−	1393.40i		−	1.53628i	−0.640284	−	0.768139i	$-0.721183\pi$
$907$		−	1393.40i		−	1.53628i	0.640284	−	0.768139i	$-0.278817\pi$
$908$	537.401			0.591851
$909$		−	1344.81i		−	1.47944i
$910$	62.2254	+	212.104i	0.0683796	+	0.233082i
$911$	1578.26			1.73245			0.866224	−	0.499655i	$-0.166540\pi$
$911$	1578.26			1.73245			0.866224	+	0.499655i	$0.166540\pi$
$912$	25.5723			0.0280398
$913$	−298.147	−	1126.23i	−0.326558	−	1.23354i
$914$	−430.589			−0.471104
$915$	−18.8693	−	64.3189i	−0.0206222	−	0.0702938i
$916$	333.055			0.363597
$917$		−	418.657i		−	0.456551i
$918$			565.417i			0.615922i
$919$			249.051i			0.271002i	0.990777	+	0.135501i	$0.0432644\pi$
$919$			249.051i			0.271002i	−0.990777	+	0.135501i	$0.956736\pi$
$920$	304.744	−	89.4031i	0.331243	−	0.0971773i
$921$			399.451i			0.433715i
$922$			360.114i			0.390579i
$923$	955.408			1.03511
$924$	−65.4794	+	17.3345i	−0.0708652	+	0.0187602i
$925$	706.805	+	1100.95i	0.764114	+	1.19021i
$926$			214.213i			0.231332i
$927$		−	714.301i		−	0.770551i
$928$			205.780i			0.221745i
$929$	604.288			0.650471			0.325235	−	0.945633i	$-0.394556\pi$
$929$	604.288			0.650471			0.325235	+	0.945633i	$0.394556\pi$
$930$	278.489	−	81.7006i	0.299450	−	0.0878501i
$931$		−	240.795i		−	0.258641i
$932$	−84.1363			−0.0902750
$933$			296.725i			0.318033i
$934$			1017.82i			1.08974i
$935$	−1027.84	+	621.941i	−1.09929	+	0.665177i
$936$	−244.301			−0.261006
$937$	−1248.76			−1.33272			−0.666361	−	0.745629i	$-0.732149\pi$
$937$	−1248.76			−1.33272			−0.666361	+	0.745629i	$0.732149\pi$
$938$		−	23.3813i		−	0.0249267i
$939$	91.3775			0.0973136
$940$	474.685	−	139.259i	0.504984	−	0.148148i
$941$		−	615.457i		−	0.654046i	−0.945016	−	0.327023i	$-0.893955\pi$
$941$		−	615.457i		−	0.654046i	0.945016	−	0.327023i	$-0.106045\pi$
$942$	−56.2291			−0.0596912
$943$	−1149.83			−1.21934
$944$	118.822			0.125871
$945$	−248.388	+	72.8701i	−0.262845	+	0.0771112i
$946$	106.356	+	401.750i	0.112427	+	0.424683i
$947$			262.503i			0.277194i	0.990349	+	0.138597i	$0.0442593\pi$
$947$			262.503i			0.277194i	−0.990349	+	0.138597i	$0.955741\pi$
$948$	−321.627			−0.339269
$949$	542.452			0.571604
$950$	112.179	+	174.734i	0.118083	+	0.183930i
$951$	−300.623			−0.316112
$952$	174.743			0.183553
$953$	−528.907			−0.554992			−0.277496	−	0.960727i	$-0.589504\pi$
$953$	−528.907			−0.554992			−0.277496	+	0.960727i	$0.589504\pi$
$954$		−	472.332i		−	0.495107i
$955$	127.093	+	433.214i	0.133081	+	0.453628i
$956$		−	20.1813i		−	0.0211101i
$957$	−111.471	−	421.073i	−0.116480	−	0.439992i
$958$			743.535i			0.776133i
$959$		−	601.876i		−	0.627608i
$960$	41.7809	−	12.2573i	0.0435217	−	0.0127680i
$961$	460.706			0.479402
$962$			817.959i			0.850269i
$963$	−652.534			−0.677605
$964$		−	314.508i		−	0.326254i
$965$	215.512	+	734.605i	0.223329	+	0.761249i
$966$	97.7809			0.101222
$967$	735.954			0.761069			0.380534	−	0.924767i	$-0.375740\pi$
$967$	735.954			0.761069			0.380534	+	0.924767i	$0.375740\pi$
$968$	297.411	−	169.336i	0.307243	−	0.174934i
$969$	139.643			0.144110
$970$	242.368	−	71.1040i	0.249864	−	0.0733031i
$971$	−1451.82			−1.49518			−0.747588	−	0.664163i	$-0.768788\pi$
$971$	−1451.82			−1.49518			−0.747588	+	0.664163i	$0.768788\pi$
$972$		−	439.220i		−	0.451873i
$973$			697.324i			0.716674i
$974$		−	902.530i		−	0.926622i
$975$	162.489	+	253.100i	0.166656	+	0.259590i
$976$		−	49.2619i		−	0.0504732i
$977$		−	1340.06i		−	1.37161i	−0.727785	−	0.685806i	$-0.759450\pi$
$977$		−	1340.06i		−	1.37161i	0.727785	−	0.685806i	$-0.240550\pi$
$978$	155.350			0.158845
$979$	128.664	+	486.018i	0.131424	+	0.496444i
$980$	−115.418	−	393.419i	−0.117773	−	0.401448i
$981$			87.3470i			0.0890387i
$982$		−	986.087i		−	1.00416i
$983$			662.938i			0.674403i	0.941432	+	0.337202i	$0.109480\pi$
$983$			662.938i			0.674403i	−0.941432	+	0.337202i	$0.890520\pi$
$984$	−157.644			−0.160207
$985$	−453.043	−	1544.26i	−0.459942	−	1.56778i
$986$			1123.70i			1.13966i
$987$	152.309			0.154315
$988$			129.820i			0.131397i
$989$		−	599.936i		−	0.606609i
$990$	520.071	−	314.694i	0.525324	−	0.317872i
$991$	−650.836			−0.656747			−0.328373	−	0.944548i	$-0.606500\pi$
$991$	−650.836			−0.656747			−0.328373	+	0.944548i	$0.606500\pi$
$992$	213.295			0.215015
$993$		−	458.404i		−	0.461635i
$994$	345.781			0.347868
$995$	−68.3908	−	233.120i	−0.0687344	−	0.234291i
$996$			230.578i			0.231504i
$997$	189.166			0.189735			0.0948676	−	0.995490i	$-0.469757\pi$
$997$	189.166			0.189735			0.0948676	+	0.995490i	$0.469757\pi$
$998$	513.941			0.514971
$999$	−957.884			−0.958843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.c.b.109.2	✓	8
3.2	odd	2		990.3.h.b.109.5		8
4.3	odd	2		880.3.i.g.769.6		8
5.2	odd	4		550.3.d.d.351.2		8
5.3	odd	4		550.3.d.d.351.7		8
5.4	even	2	inner	110.3.c.b.109.7	yes	8
11.10	odd	2	inner	110.3.c.b.109.6	yes	8
15.14	odd	2		990.3.h.b.109.2		8
20.19	odd	2		880.3.i.g.769.3		8
33.32	even	2		990.3.h.b.109.1		8
44.43	even	2		880.3.i.g.769.5		8
55.32	even	4		550.3.d.d.351.6		8
55.43	even	4		550.3.d.d.351.3		8
55.54	odd	2	inner	110.3.c.b.109.3	yes	8
165.164	even	2		990.3.h.b.109.6		8
220.219	even	2		880.3.i.g.769.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.c.b.109.2	✓	8	1.1	even	1	trivial
110.3.c.b.109.3	yes	8	55.54	odd	2	inner
110.3.c.b.109.6	yes	8	11.10	odd	2	inner
110.3.c.b.109.7	yes	8	5.4	even	2	inner
550.3.d.d.351.2		8	5.2	odd	4
550.3.d.d.351.3		8	55.43	even	4
550.3.d.d.351.6		8	55.32	even	4
550.3.d.d.351.7		8	5.3	odd	4
880.3.i.g.769.3		8	20.19	odd	2
880.3.i.g.769.4		8	220.219	even	2
880.3.i.g.769.5		8	44.43	even	2
880.3.i.g.769.6		8	4.3	odd	2
990.3.h.b.109.1		8	33.32	even	2
990.3.h.b.109.2		8	15.14	odd	2
990.3.h.b.109.5		8	3.2	odd	2
990.3.h.b.109.6		8	165.164	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -1.08854i q^{3} +2.00000 q^{4} +(1.40754 + 4.79780i) q^{5} +1.53943i q^{6} -2.82843 q^{7} -2.82843 q^{8} +7.81507 q^{9} +(-1.99056 - 6.78511i) q^{10} +(2.81507 + 10.6337i) q^{11} -2.17709i q^{12} +11.0522 q^{13} +4.00000 q^{14} +(5.22261 - 1.53216i) q^{15} +4.00000 q^{16} +21.8428 q^{17} -11.0522 q^{18} +5.87305i q^{19} +(2.81507 + 9.59559i) q^{20} +3.07887i q^{21} +(-3.98111 - 15.0383i) q^{22} +22.4568i q^{23} +3.07887i q^{24} +(-21.0377 + 13.5061i) q^{25} -15.6301 q^{26} -18.3039i q^{27} -5.65685 q^{28} -36.3770i q^{29} +(-7.38588 + 2.16681i) q^{30} -37.7055 q^{31} -5.65685 q^{32} +(11.5752 - 3.06433i) q^{33} -30.8904 q^{34} +(-3.98111 - 13.5702i) q^{35} +15.6301 q^{36} -52.3321i q^{37} -8.30575i q^{38} -12.0308i q^{39} +(-3.98111 - 13.5702i) q^{40} +51.2020i q^{41} -4.35417i q^{42} -26.7151 q^{43} +(5.63015 + 21.2674i) q^{44} +(11.0000 + 37.4951i) q^{45} -31.7587i q^{46} -49.4691i q^{47} -4.35417i q^{48} -41.0000 q^{49} +(29.7518 - 19.1006i) q^{50} -23.7769i q^{51} +22.1044 q^{52} +42.7365i q^{53} +25.8857i q^{54} +(-47.0560 + 28.4735i) q^{55} +8.00000 q^{56} +6.39307 q^{57} +51.4449i q^{58} +29.7055 q^{59} +(10.4452 - 3.06433i) q^{60} -12.3155i q^{61} +53.3236 q^{62} -22.1044 q^{63} +8.00000 q^{64} +(15.5563 + 53.0261i) q^{65} +(-16.3699 + 4.33362i) q^{66} -5.84532i q^{67} +43.6857 q^{68} +24.4452 q^{69} +(5.63015 + 19.1912i) q^{70} +86.4452 q^{71} -22.1044 q^{72} +49.0810 q^{73} +74.0088i q^{74} +(14.7020 + 22.9004i) q^{75} +11.7461i q^{76} +(-7.96223 - 30.0766i) q^{77} +17.0141i q^{78} -147.733i q^{79} +(5.63015 + 19.1912i) q^{80} +50.4110 q^{81} -72.4106i q^{82} -105.911 q^{83} +6.15773i q^{84} +(30.7446 + 104.797i) q^{85} +37.7809 q^{86} -39.5980 q^{87} +(-7.96223 - 30.0766i) q^{88} +45.7055 q^{89} +(-15.5563 - 53.0261i) q^{90} -31.2603 q^{91} +44.9136i q^{92} +41.0441i q^{93} +69.9599i q^{94} +(-28.1777 + 8.26653i) q^{95} +6.15773i q^{96} +35.7206i q^{97} +57.9828 q^{98} +(22.0000 + 83.1031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 10 q^{5} + 20 q^{9} - 20 q^{11} + 32 q^{14} - 22 q^{15} + 32 q^{16} - 20 q^{20} - 62 q^{25} - 40 q^{26} - 4 q^{31} + 8 q^{34} + 40 q^{36} - 40 q^{44} + 88 q^{45} - 328 q^{49} + 138 q^{55}+ \cdots + 176 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 10 * q^5 + 20 * q^9 - 20 * q^11 + 32 * q^14 - 22 * q^15 + 32 * q^16 - 20 * q^20 - 62 * q^25 - 40 * q^26 - 4 * q^31 + 8 * q^34 + 40 * q^36 - 40 * q^44 + 88 * q^45 - 328 * q^49 + 138 * q^55 + 64 * q^56 - 60 * q^59 - 44 * q^60 + 64 * q^64 - 216 * q^66 + 68 * q^69 - 40 * q^70 + 564 * q^71 + 394 * q^75 - 40 * q^80 - 192 * q^81 - 208 * q^86 + 68 * q^89 - 80 * q^91 + 176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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