LMFDB - Embedded newform 230.3.c.a.229.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(229,230)]

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([1, 1]))

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.5
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -0.894518i q^{3} -2.00000 q^{4} +(-3.14390 + 3.88792i) q^{5} -1.26504 q^{6} -4.24317 q^{7} +2.82843i q^{8} +8.19984 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -0.894518i q^{3} -2.00000 q^{4} +(-3.14390 + 3.88792i) q^{5} -1.26504 q^{6} -4.24317 q^{7} +2.82843i q^{8} +8.19984 q^{9} +(5.49835 + 4.44614i) q^{10} +9.15214i q^{11} +1.78904i q^{12} +6.01633i q^{13} +6.00075i q^{14} +(3.47782 + 2.81227i) q^{15} +4.00000 q^{16} +19.3074 q^{17} -11.5963i q^{18} +31.0808i q^{19} +(6.28779 - 7.77584i) q^{20} +3.79559i q^{21} +12.9431 q^{22} +(-5.12985 + 22.4206i) q^{23} +2.53008 q^{24} +(-5.23184 - 24.4464i) q^{25} +8.50838 q^{26} -15.3856i q^{27} +8.48634 q^{28} -45.5926 q^{29} +(3.97715 - 4.91837i) q^{30} +33.3338 q^{31} -5.65685i q^{32} +8.18675 q^{33} -27.3048i q^{34} +(13.3401 - 16.4971i) q^{35} -16.3997 q^{36} -21.2063 q^{37} +43.9548 q^{38} +5.38172 q^{39} +(-10.9967 - 8.89228i) q^{40} +33.7460 q^{41} +5.36778 q^{42} +5.50332 q^{43} -18.3043i q^{44} +(-25.7794 + 31.8803i) q^{45} +(31.7076 + 7.25471i) q^{46} +71.8467i q^{47} -3.57807i q^{48} -30.9955 q^{49} +(-34.5725 + 7.39893i) q^{50} -17.2708i q^{51} -12.0327i q^{52} -3.73758 q^{53} -21.7585 q^{54} +(-35.5828 - 28.7734i) q^{55} -12.0015i q^{56} +27.8023 q^{57} +64.4777i q^{58} -4.90558 q^{59} +(-6.95563 - 5.62455i) q^{60} -42.5481i q^{61} -47.1411i q^{62} -34.7933 q^{63} -8.00000 q^{64} +(-23.3910 - 18.9147i) q^{65} -11.5778i q^{66} -118.039 q^{67} -38.6147 q^{68} +(20.0557 + 4.58875i) q^{69} +(-23.3304 - 18.8657i) q^{70} +92.6322 q^{71} +23.1926i q^{72} +43.2716i q^{73} +29.9903i q^{74} +(-21.8678 + 4.67997i) q^{75} -62.1615i q^{76} -38.8341i q^{77} -7.61090i q^{78} +58.6070i q^{79} +(-12.5756 + 15.5517i) q^{80} +60.0359 q^{81} -47.7241i q^{82} -18.2625 q^{83} -7.59119i q^{84} +(-60.7004 + 75.0655i) q^{85} -7.78287i q^{86} +40.7834i q^{87} -25.8861 q^{88} -164.528i q^{89} +(45.0856 + 36.4576i) q^{90} -25.5283i q^{91} +(10.2597 - 44.8413i) q^{92} -29.8177i q^{93} +101.607 q^{94} +(-120.840 - 97.7147i) q^{95} -5.06016 q^{96} -91.9716 q^{97} +43.8343i q^{98} +75.0460i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	0.894518i		−	0.298173i	−0.988824	−	0.149086i	$-0.952367\pi$
$3$		−	0.894518i		−	0.298173i	0.988824	−	0.149086i	$-0.0476333\pi$
$4$	−2.00000			−0.500000
$5$	−3.14390	+	3.88792i	−0.628779	+	0.777584i
$5$	−3.14390	+	3.88792i	−0.628779	+	0.777584i
$6$	−1.26504			−0.210840
$7$	−4.24317			−0.606167			−0.303084	−	0.952964i	$-0.598016\pi$
$7$	−4.24317			−0.606167			−0.303084	+	0.952964i	$0.598016\pi$
$8$			2.82843i			0.353553i
$9$	8.19984			0.911093
$10$	5.49835	+	4.44614i	0.549835	+	0.444614i
$11$			9.15214i			0.832012i	0.909362	+	0.416006i	$0.136571\pi$
$11$			9.15214i			0.832012i	−0.909362	+	0.416006i	$0.863429\pi$
$12$			1.78904i			0.149086i
$13$			6.01633i			0.462795i	0.972859	+	0.231397i	$0.0743297\pi$
$13$			6.01633i			0.462795i	−0.972859	+	0.231397i	$0.925670\pi$
$14$			6.00075i			0.428625i
$15$	3.47782	+	2.81227i	0.231854	+	0.187485i
$16$	4.00000			0.250000
$17$	19.3074			1.13573			0.567864	−	0.823122i	$-0.307770\pi$
$17$	19.3074			1.13573			0.567864	+	0.823122i	$0.307770\pi$
$18$		−	11.5963i		−	0.644240i
$19$			31.0808i			1.63583i	0.575339	+	0.817915i	$0.304870\pi$
$19$			31.0808i			1.63583i	−0.575339	+	0.817915i	$0.695130\pi$
$20$	6.28779	−	7.77584i	0.314390	−	0.388792i
$21$			3.79559i			0.180743i
$22$	12.9431			0.588322
$23$	−5.12985	+	22.4206i	−0.223037	+	0.974810i
$23$	−5.12985	+	22.4206i	−0.223037	+	0.974810i
$24$	2.53008			0.105420
$25$	−5.23184	−	24.4464i	−0.209273	−	0.977857i
$26$	8.50838			0.327245
$27$		−	15.3856i		−	0.569836i
$28$	8.48634			0.303084
$29$	−45.5926			−1.57216			−0.786079	−	0.618125i	$-0.787892\pi$
$29$	−45.5926			−1.57216			−0.786079	+	0.618125i	$0.787892\pi$
$30$	3.97715	−	4.91837i	0.132572	−	0.163946i
$31$	33.3338			1.07528			0.537642	−	0.843173i	$-0.319315\pi$
$31$	33.3338			1.07528			0.537642	+	0.843173i	$0.319315\pi$
$32$		−	5.65685i		−	0.176777i
$33$	8.18675			0.248083
$34$		−	27.3048i		−	0.803081i
$35$	13.3401	−	16.4971i	0.381145	−	0.471346i
$36$	−16.3997			−0.455546
$37$	−21.2063			−0.573144			−0.286572	−	0.958059i	$-0.592516\pi$
$37$	−21.2063			−0.573144			−0.286572	+	0.958059i	$0.592516\pi$
$38$	43.9548			1.15671
$39$	5.38172			0.137993
$40$	−10.9967	−	8.89228i	−0.274917	−	0.222307i
$41$	33.7460			0.823074			0.411537	−	0.911393i	$-0.364992\pi$
$41$	33.7460			0.823074			0.411537	+	0.911393i	$0.364992\pi$
$42$	5.36778			0.127804
$43$	5.50332			0.127984			0.0639921	−	0.997950i	$-0.479617\pi$
$43$	5.50332			0.127984			0.0639921	+	0.997950i	$0.479617\pi$
$44$		−	18.3043i		−	0.416006i
$45$	−25.7794	+	31.8803i	−0.572876	+	0.708451i
$46$	31.7076	+	7.25471i	0.689295	+	0.157711i
$47$			71.8467i			1.52865i	0.644829	+	0.764327i	$0.276929\pi$
$47$			71.8467i			1.52865i	−0.644829	+	0.764327i	$0.723071\pi$
$48$		−	3.57807i		−	0.0745432i
$49$	−30.9955			−0.632561
$50$	−34.5725	+	7.39893i	−0.691449	+	0.147979i
$51$		−	17.2708i		−	0.338643i
$52$		−	12.0327i		−	0.231397i
$53$	−3.73758			−0.0705204			−0.0352602	−	0.999378i	$-0.511226\pi$
$53$	−3.73758			−0.0705204			−0.0352602	+	0.999378i	$0.511226\pi$
$54$	−21.7585			−0.402935
$55$	−35.5828	−	28.7734i	−0.646959	−	0.523152i
$56$		−	12.0015i		−	0.214312i
$57$	27.8023			0.487760
$58$			64.4777i			1.11168i
$59$	−4.90558			−0.0831453			−0.0415727	−	0.999135i	$-0.513237\pi$
$59$	−4.90558			−0.0831453			−0.0415727	+	0.999135i	$0.513237\pi$
$60$	−6.95563	−	5.62455i	−0.115927	−	0.0937424i
$61$		−	42.5481i		−	0.697510i	−0.937214	−	0.348755i	$-0.886605\pi$
$61$		−	42.5481i		−	0.697510i	0.937214	−	0.348755i	$-0.113395\pi$
$62$		−	47.1411i		−	0.760341i
$63$	−34.7933			−0.552275
$64$	−8.00000			−0.125000
$65$	−23.3910	−	18.9147i	−0.359862	−	0.290996i
$66$		−	11.5778i		−	0.175421i
$67$	−118.039			−1.76178			−0.880888	−	0.473325i	$-0.843054\pi$
$67$	−118.039			−1.76178			−0.880888	+	0.473325i	$0.843054\pi$
$68$	−38.6147			−0.567864
$69$	20.0557	+	4.58875i	0.290662	+	0.0665036i
$70$	−23.3304	−	18.8657i	−0.333292	−	0.269510i
$71$	92.6322			1.30468			0.652339	−	0.757927i	$-0.273788\pi$
$71$	92.6322			1.30468			0.652339	+	0.757927i	$0.273788\pi$
$72$			23.1926i			0.322120i
$73$			43.2716i			0.592762i	0.955070	+	0.296381i	$0.0957797\pi$
$73$			43.2716i			0.592762i	−0.955070	+	0.296381i	$0.904220\pi$
$74$			29.9903i			0.405274i
$75$	−21.8678	+	4.67997i	−0.291570	+	0.0623997i
$76$		−	62.1615i		−	0.817915i
$77$		−	38.8341i		−	0.504339i
$78$		−	7.61090i		−	0.0975756i
$79$			58.6070i			0.741861i	0.928661	+	0.370931i	$0.120961\pi$
$79$			58.6070i			0.741861i	−0.928661	+	0.370931i	$0.879039\pi$
$80$	−12.5756	+	15.5517i	−0.157195	+	0.194396i
$81$	60.0359			0.741183
$82$		−	47.7241i		−	0.582001i
$83$	−18.2625			−0.220030			−0.110015	−	0.993930i	$-0.535090\pi$
$83$	−18.2625			−0.220030			−0.110015	+	0.993930i	$0.535090\pi$
$84$		−	7.59119i		−	0.0903713i
$85$	−60.7004	+	75.0655i	−0.714122	+	0.883124i
$86$		−	7.78287i		−	0.0904985i
$87$			40.7834i			0.468775i
$88$	−25.8861			−0.294161
$89$		−	164.528i		−	1.84863i	−0.381626	−	0.924317i	$-0.624636\pi$
$89$		−	164.528i		−	1.84863i	0.381626	−	0.924317i	$-0.375364\pi$
$90$	45.0856	+	36.4576i	0.500951	+	0.405085i
$91$		−	25.5283i		−	0.280531i
$92$	10.2597	−	44.8413i	0.111519	−	0.487405i
$93$		−	29.8177i		−	0.320621i
$94$	101.607			1.08092
$95$	−120.840	−	97.7147i	−1.27199	−	1.02858i
$96$	−5.06016			−0.0527100
$97$	−91.9716			−0.948161			−0.474081	−	0.880481i	$-0.657219\pi$
$97$	−91.9716			−0.948161			−0.474081	+	0.880481i	$0.657219\pi$
$98$			43.8343i			0.447288i
$99$			75.0460i			0.758041i
$100$	10.4637	+	48.8929i	0.104637	+	0.488929i
$101$	−45.8103			−0.453568			−0.226784	−	0.973945i	$-0.572821\pi$
$101$	−45.8103			−0.453568			−0.226784	+	0.973945i	$0.572821\pi$
$102$	−24.4246			−0.239457
$103$	−92.4920			−0.897980			−0.448990	−	0.893537i	$-0.648216\pi$
$103$	−92.4920			−0.897980			−0.448990	+	0.893537i	$0.648216\pi$
$104$	−17.0168			−0.163623
$105$	−14.7570	−	11.9330i	−0.140543	−	0.113647i
$106$			5.28574i			0.0498654i
$107$	167.883			1.56900			0.784501	−	0.620128i	$-0.212919\pi$
$107$	167.883			1.56900			0.784501	+	0.620128i	$0.212919\pi$
$108$			30.7711i			0.284918i
$109$		−	97.1728i		−	0.891493i	−0.895159	−	0.445747i	$-0.852938\pi$
$109$		−	97.1728i		−	0.891493i	0.895159	−	0.445747i	$-0.147062\pi$
$110$	−40.6917	+	50.3216i	−0.369924	+	0.457469i
$111$			18.9695i			0.170896i
$112$	−16.9727			−0.151542
$113$	138.661			1.22709			0.613546	−	0.789659i	$-0.289742\pi$
$113$	138.661			1.22709			0.613546	+	0.789659i	$0.289742\pi$
$114$		−	39.3184i		−	0.344898i
$115$	−71.0419	−	90.4326i	−0.617755	−	0.786370i
$116$	91.1852			0.786079
$117$			49.3329i			0.421649i
$118$			6.93753i			0.0587926i
$119$	−81.9245			−0.688441
$120$	−7.95431	+	9.83675i	−0.0662859	+	0.0819729i
$121$	37.2384			0.307755
$122$	−60.1721			−0.493214
$123$		−	30.1864i		−	0.245418i
$124$	−66.6676			−0.537642
$125$	111.494	+	56.5161i	0.891953	+	0.452129i
$126$			49.2052i			0.390517i
$127$			83.8308i			0.660085i	0.943966	+	0.330043i	$0.107063\pi$
$127$			83.8308i			0.660085i	−0.943966	+	0.330043i	$0.892937\pi$
$128$			11.3137i			0.0883883i
$129$		−	4.92282i		−	0.0381614i
$130$	−26.7494	+	33.0799i	−0.205765	+	0.254461i
$131$	225.405			1.72065			0.860323	−	0.509749i	$-0.170262\pi$
$131$	225.405			1.72065			0.860323	+	0.509749i	$0.170262\pi$
$132$	−16.3735			−0.124042
$133$		−	131.881i		−	0.991586i
$134$			166.932i			1.24576i
$135$	59.8179	+	48.3706i	0.443095	+	0.358301i
$136$			54.6095i			0.401540i
$137$	250.554			1.82886			0.914429	−	0.404746i	$-0.132640\pi$
$137$	250.554			1.82886			0.914429	+	0.404746i	$0.132640\pi$
$138$	6.48947	−	28.3630i	0.0470251	−	0.205529i
$139$	−117.008			−0.841785			−0.420893	−	0.907110i	$-0.638283\pi$
$139$	−117.008			−0.841785			−0.420893	+	0.907110i	$0.638283\pi$
$140$	−26.6802	+	32.9942i	−0.190573	+	0.235673i
$141$	64.2682			0.455803
$142$		−	131.002i		−	0.922547i
$143$	−55.0623			−0.385051
$144$	32.7993			0.227773
$145$	143.338	−	177.260i	0.988541	−	1.22249i
$146$	61.1953			0.419146
$147$			27.7261i			0.188613i
$148$	42.4127			0.286572
$149$			182.213i			1.22291i	0.791280	+	0.611454i	$0.209415\pi$
$149$			182.213i			1.22291i	−0.791280	+	0.611454i	$0.790585\pi$
$150$	6.61848	+	30.9257i	0.0441232	+	0.206171i
$151$	−66.0235			−0.437242			−0.218621	−	0.975810i	$-0.570156\pi$
$151$	−66.0235			−0.437242			−0.218621	+	0.975810i	$0.570156\pi$
$152$	−87.9097			−0.578353
$153$	158.317			1.03475
$154$	−54.9197			−0.356621
$155$	−104.798	+	129.599i	−0.676116	+	0.836124i
$156$	−10.7634			−0.0689964
$157$	120.019			0.764450			0.382225	−	0.924069i	$-0.375158\pi$
$157$	120.019			0.764450			0.382225	+	0.924069i	$0.375158\pi$
$158$	82.8829			0.524575
$159$			3.34333i			0.0210273i
$160$	21.9934	+	17.7846i	0.137459	+	0.111154i
$161$	21.7668	−	95.1345i	0.135198	−	0.590898i
$162$		−	84.9035i		−	0.524096i
$163$			47.4060i			0.290835i	0.989370	+	0.145417i	$0.0464525\pi$
$163$			47.4060i			0.290835i	−0.989370	+	0.145417i	$0.953548\pi$
$164$	−67.4920			−0.411537
$165$	−25.7383	+	31.8294i	−0.155990	+	0.192906i
$166$			25.8271i			0.155585i
$167$		−	186.382i		−	1.11606i	−0.829821	−	0.558029i	$-0.811558\pi$
$167$		−	186.382i		−	1.11606i	0.829821	−	0.558029i	$-0.188442\pi$
$168$	−10.7356			−0.0639022
$169$	132.804			0.785821
$170$	106.159	+	85.8433i	0.624463	+	0.504961i
$171$			254.857i			1.49039i
$172$	−11.0066			−0.0639921
$173$		−	254.580i		−	1.47156i	−0.677220	−	0.735781i	$-0.736815\pi$
$173$		−	254.580i		−	1.47156i	0.677220	−	0.735781i	$-0.263185\pi$
$174$	57.6765			0.331474
$175$	22.1996	+	103.730i	0.126855	+	0.592745i
$176$			36.6085i			0.208003i
$177$			4.38813i			0.0247917i
$178$	−232.678			−1.30718
$179$	4.80936			0.0268679			0.0134340	−	0.999910i	$-0.495724\pi$
$179$	4.80936			0.0268679			0.0134340	+	0.999910i	$0.495724\pi$
$180$	51.5589	−	63.7606i	0.286438	−	0.354226i
$181$		−	217.170i		−	1.19984i	−0.800062	−	0.599918i	$-0.795200\pi$
$181$		−	217.170i		−	1.19984i	0.800062	−	0.599918i	$-0.204800\pi$
$182$	−36.1025			−0.198365
$183$	−38.0601			−0.207979
$184$	−63.4151	−	14.5094i	−0.344647	−	0.0788555i
$185$	66.6705	−	82.4485i	0.360381	−	0.445668i
$186$	−42.1686			−0.226713
$187$			176.704i			0.944940i
$188$		−	143.693i		−	0.764327i
$189$			65.2836i			0.345416i
$190$	−138.189	+	170.893i	−0.727313	+	0.899436i
$191$		−	209.557i		−	1.09716i	−0.836099	−	0.548578i	$-0.815169\pi$
$191$		−	209.557i		−	1.09716i	0.836099	−	0.548578i	$-0.184831\pi$
$192$			7.15615i			0.0372716i
$193$			69.2800i			0.358964i	0.983761	+	0.179482i	$0.0574422\pi$
$193$			69.2800i			0.358964i	−0.983761	+	0.179482i	$0.942558\pi$
$194$			130.068i			0.670451i
$195$	−16.9196	+	20.9237i	−0.0867670	+	0.107301i
$196$	61.9910			0.316281
$197$			261.497i			1.32740i	0.748000	+	0.663698i	$0.231014\pi$
$197$			261.497i			1.32740i	−0.748000	+	0.663698i	$0.768986\pi$
$198$	106.131			0.536016
$199$			8.23431i			0.0413784i	0.999786	+	0.0206892i	$0.00658605\pi$
$199$			8.23431i			0.0413784i	−0.999786	+	0.0206892i	$0.993414\pi$
$200$	69.1449	−	14.7979i	0.345725	−	0.0739893i
$201$			105.588i			0.525314i
$202$			64.7856i			0.320721i
$203$	193.457			0.952991
$204$			34.5416i			0.169322i
$205$	−106.094	+	131.202i	−0.517531	+	0.640009i
$206$			130.803i			0.634968i
$207$	−42.0640	+	183.845i	−0.203208	+	0.888143i
$208$			24.0653i			0.115699i
$209$	−284.455			−1.36103
$210$	−16.8757	+	20.8695i	−0.0803607	+	0.0993786i
$211$	32.5997			0.154501			0.0772505	−	0.997012i	$-0.475386\pi$
$211$	32.5997			0.154501			0.0772505	+	0.997012i	$0.475386\pi$
$212$	7.47516			0.0352602
$213$		−	82.8612i		−	0.389020i
$214$		−	237.423i		−	1.10945i
$215$	−17.3019	+	21.3965i	−0.0804738	+	0.0995184i
$216$	43.5170			0.201467
$217$	−141.441			−0.651802
$218$	−137.423			−0.630381
$219$	38.7072			0.176745
$220$	71.1655	+	57.5467i	0.323480	+	0.261576i
$221$			116.160i			0.525609i
$222$	26.8269			0.120842
$223$			53.1764i			0.238459i	0.992867	+	0.119230i	$0.0380425\pi$
$223$			53.1764i			0.238459i	−0.992867	+	0.119230i	$0.961958\pi$
$224$			24.0030i			0.107156i
$225$	−42.9002	−	200.457i	−0.190668	−	0.890919i
$226$		−	196.097i		−	0.867686i
$227$	34.4014			0.151548			0.0757741	−	0.997125i	$-0.475857\pi$
$227$	34.4014			0.151548			0.0757741	+	0.997125i	$0.475857\pi$
$228$	−55.6046			−0.243880
$229$		−	211.661i		−	0.924284i	−0.886806	−	0.462142i	$-0.847081\pi$
$229$		−	211.661i		−	0.924284i	0.886806	−	0.462142i	$-0.152919\pi$
$230$	−127.891	+	100.468i	−0.556048	+	0.436819i
$231$	−34.7378			−0.150380
$232$		−	128.955i		−	0.555842i
$233$		−	139.212i		−	0.597474i	−0.954335	−	0.298737i	$-0.903435\pi$
$233$		−	139.212i		−	0.597474i	0.954335	−	0.298737i	$-0.0965654\pi$
$234$	69.7673			0.298151
$235$	−279.334	−	225.879i	−1.18866	−	0.961185i
$236$	9.81115			0.0415727
$237$	52.4251			0.221203
$238$			115.859i			0.486801i
$239$	218.136			0.912704			0.456352	−	0.889799i	$-0.349156\pi$
$239$	218.136			0.912704			0.456352	+	0.889799i	$0.349156\pi$
$240$	13.9113	+	11.2491i	0.0579636	+	0.0468712i
$241$		−	28.9044i		−	0.119935i	−0.998200	−	0.0599676i	$-0.980900\pi$
$241$		−	28.9044i		−	0.119935i	0.998200	−	0.0599676i	$-0.0190997\pi$
$242$		−	52.6631i		−	0.217616i
$243$		−	192.173i		−	0.790837i
$244$			85.0962i			0.348755i
$245$	97.4466	−	120.508i	0.397741	−	0.491870i
$246$	−42.6901			−0.173537
$247$	−186.992			−0.757053
$248$			94.2823i			0.380170i
$249$			16.3362i			0.0656071i
$250$	79.9258	−	157.676i	0.319703	−	0.630706i
$251$			41.4490i			0.165136i	0.996585	+	0.0825678i	$0.0263121\pi$
$251$			41.4490i			0.165136i	−0.996585	+	0.0825678i	$0.973688\pi$
$252$	69.5866			0.276137
$253$	−205.197	−	46.9491i	−0.811054	−	0.185570i
$254$	118.555			0.466751
$255$	67.1475	+	54.2976i	0.263323	+	0.212932i
$256$	16.0000			0.0625000
$257$			329.627i			1.28260i	0.767292	+	0.641298i	$0.221604\pi$
$257$			329.627i			1.28260i	−0.767292	+	0.641298i	$0.778396\pi$
$258$	−6.96192			−0.0269842
$259$	89.9821			0.347421
$260$	46.7820	+	37.8294i	0.179931	+	0.145498i
$261$	−373.852			−1.43238
$262$		−	318.770i		−	1.21668i
$263$	−329.569			−1.25311			−0.626556	−	0.779376i	$-0.715536\pi$
$263$	−329.569			−1.25311			−0.626556	+	0.779376i	$0.715536\pi$
$264$			23.1556i			0.0877107i
$265$	11.7506	−	14.5314i	0.0443417	−	0.0548355i
$266$	−186.508			−0.701157
$267$	−147.174			−0.551212
$268$	236.078			0.880888
$269$	−156.347			−0.581215			−0.290608	−	0.956842i	$-0.593857\pi$
$269$	−156.347			−0.581215			−0.290608	+	0.956842i	$0.593857\pi$
$270$	68.4064	−	84.5952i	0.253357	−	0.313316i
$271$	−85.7303			−0.316348			−0.158174	−	0.987411i	$-0.550561\pi$
$271$	−85.7303			−0.316348			−0.158174	+	0.987411i	$0.550561\pi$
$272$	77.2295			0.283932
$273$	−22.8355			−0.0836467
$274$		−	354.336i		−	1.29320i
$275$	223.737	−	47.8825i	0.813589	−	0.174118i
$276$	−40.1113	−	9.17750i	−0.145331	−	0.0332518i
$277$		−	158.369i		−	0.571731i	−0.958270	−	0.285865i	$-0.907719\pi$
$277$		−	158.369i		−	0.571731i	0.958270	−	0.285865i	$-0.0922810\pi$
$278$			165.475i			0.595232i
$279$	273.332			0.979684
$280$	46.6609	+	37.7315i	0.166646	+	0.134755i
$281$		−	124.956i		−	0.444682i	−0.974969	−	0.222341i	$-0.928630\pi$
$281$		−	124.956i		−	0.444682i	0.974969	−	0.222341i	$-0.0713698\pi$
$282$		−	90.8890i		−	0.322301i
$283$	−44.5033			−0.157255			−0.0786277	−	0.996904i	$-0.525054\pi$
$283$	−44.5033			−0.157255			−0.0786277	+	0.996904i	$0.525054\pi$
$284$	−185.264			−0.652339
$285$	−87.4076	+	108.093i	−0.306693	+	0.379274i
$286$			77.8698i			0.272272i
$287$	−143.190			−0.498920
$288$		−	46.3853i		−	0.161060i
$289$	83.7747			0.289878
$290$	−250.684	−	202.711i	−0.864428	−	0.699004i
$291$			82.2703i			0.282716i
$292$		−	86.5432i		−	0.296381i
$293$	−24.2355			−0.0827152			−0.0413576	−	0.999144i	$-0.513168\pi$
$293$	−24.2355			−0.0827152			−0.0413576	+	0.999144i	$0.513168\pi$
$294$	39.2106			0.133369
$295$	15.4226	−	19.0725i	0.0522801	−	0.0646525i
$296$		−	59.9806i		−	0.202637i
$297$	140.811			0.474111
$298$	257.688			0.864726
$299$	−134.890	−	30.8629i	−0.451137	−	0.103220i
$300$	43.7356	−	9.35995i	0.145785	−	0.0311998i
$301$	−23.3515			−0.0775798
$302$			93.3714i			0.309177i
$303$			40.9782i			0.135242i
$304$			124.323i			0.408957i
$305$	165.424	+	133.767i	0.542373	+	0.438580i
$306$		−	223.894i		−	0.731681i
$307$		−	110.763i		−	0.360792i	−0.983594	−	0.180396i	$-0.942262\pi$
$307$		−	110.763i		−	0.360792i	0.983594	−	0.180396i	$-0.0577379\pi$
$308$			77.6681i			0.252169i
$309$			82.7358i			0.267753i
$310$	183.281	+	148.207i	0.591229	+	0.478087i
$311$	−232.496			−0.747577			−0.373789	−	0.927514i	$-0.621941\pi$
$311$	−232.496			−0.747577			−0.373789	+	0.927514i	$0.621941\pi$
$312$			15.2218i			0.0487878i
$313$	−421.714			−1.34733			−0.673664	−	0.739038i	$-0.735281\pi$
$313$	−421.714			−1.34733			−0.673664	+	0.739038i	$0.735281\pi$
$314$		−	169.732i		−	0.540548i
$315$	109.387	−	135.274i	0.347259	−	0.429440i
$316$		−	117.214i		−	0.370931i
$317$			541.909i			1.70949i	0.519046	+	0.854747i	$0.326287\pi$
$317$			541.909i			1.70949i	−0.519046	+	0.854747i	$0.673713\pi$
$318$	4.72819			0.0148685
$319$		−	417.270i		−	1.30806i
$320$	25.1512	−	31.1034i	0.0785974	−	0.0971980i
$321$		−	150.175i		−	0.467834i
$322$	−134.541	−	30.7830i	−0.417828	−	0.0955993i
$323$			600.088i			1.85786i
$324$	−120.072			−0.370592
$325$	147.078	−	31.4765i	0.452547	−	0.0968506i
$326$	67.0422			0.205651
$327$	−86.9228			−0.265819
$328$			95.4481i			0.291000i
$329$		−	304.858i		−	0.926620i
$330$	45.0136	+	36.3995i	0.136405	+	0.110301i
$331$	−338.422			−1.02242			−0.511211	−	0.859455i	$-0.670803\pi$
$331$	−338.422			−1.02242			−0.511211	+	0.859455i	$0.670803\pi$
$332$	36.5251			0.110015
$333$	−173.888			−0.522188
$334$	−263.583			−0.789172
$335$	371.102	−	458.926i	1.10777	−	1.36993i
$336$			15.1824i			0.0451856i
$337$	436.048			1.29391			0.646955	−	0.762528i	$-0.276042\pi$
$337$	436.048			1.29391			0.646955	+	0.762528i	$0.276042\pi$
$338$		−	187.813i		−	0.555659i
$339$		−	124.035i		−	0.365886i
$340$	121.401	−	150.131i	0.357061	−	0.441562i
$341$			305.076i			0.894650i
$342$	360.423			1.05387
$343$	339.435			0.989605
$344$			15.5657i			0.0452492i
$345$	−80.8936	+	63.5483i	−0.234474	+	0.184198i
$346$	−360.031			−1.04055
$347$		−	152.139i		−	0.438440i	−0.975675	−	0.219220i	$-0.929649\pi$
$347$		−	152.139i		−	0.438440i	0.975675	−	0.219220i	$-0.0703513\pi$
$348$		−	81.5669i		−	0.234388i
$349$	638.916			1.83070			0.915352	−	0.402653i	$-0.131912\pi$
$349$	638.916			1.83070			0.915352	+	0.402653i	$0.131912\pi$
$350$	146.697	−	31.3949i	0.419134	−	0.0896998i
$351$	92.5647			0.263717
$352$	51.7723			0.147080
$353$		−	253.586i		−	0.718374i	−0.933266	−	0.359187i	$-0.883054\pi$
$353$		−	253.586i		−	0.718374i	0.933266	−	0.359187i	$-0.116946\pi$
$354$	6.20575			0.0175304
$355$	−291.226	+	360.146i	−0.820355	+	1.01450i
$356$			329.057i			0.924317i
$357$			73.2830i			0.205274i
$358$		−	6.80146i		−	0.0189985i
$359$			677.588i			1.88743i	0.330758	+	0.943716i	$0.392696\pi$
$359$			677.588i			1.88743i	−0.330758	+	0.943716i	$0.607304\pi$
$360$	−90.1711	−	72.9152i	−0.250475	−	0.202542i
$361$	−605.014			−1.67594
$362$	−307.125			−0.848412
$363$		−	33.3104i		−	0.0917643i
$364$			51.0566i			0.140265i
$365$	−168.236	−	136.041i	−0.460922	−	0.372716i
$366$			53.8251i			0.147063i
$367$	−237.490			−0.647112			−0.323556	−	0.946209i	$-0.604878\pi$
$367$	−237.490			−0.647112			−0.323556	+	0.946209i	$0.604878\pi$
$368$	−20.5194	+	89.6825i	−0.0557593	+	0.243702i
$369$	276.712			0.749896
$370$	−116.600	−	94.2863i	−0.315135	−	0.254828i
$371$	15.8592			0.0427471
$372$			59.6354i			0.160310i
$373$	48.9215			0.131157			0.0655784	−	0.997847i	$-0.479111\pi$
$373$	48.9215			0.131157			0.0655784	+	0.997847i	$0.479111\pi$
$374$	249.897			0.668173
$375$	50.5547	−	99.7335i	0.134812	−	0.265956i
$376$	−203.213			−0.540461
$377$		−	274.300i		−	0.727587i
$378$	92.3250			0.244246
$379$			601.308i			1.58656i	0.608855	+	0.793282i	$0.291629\pi$
$379$			601.308i			1.58656i	−0.608855	+	0.793282i	$0.708371\pi$
$380$	241.679	+	195.429i	0.635997	+	0.514288i
$381$	74.9882			0.196819
$382$	−296.358			−0.775807
$383$	523.642			1.36721			0.683605	−	0.729852i	$-0.260411\pi$
$383$	523.642			1.36721			0.683605	+	0.729852i	$0.260411\pi$
$384$	10.1203			0.0263550
$385$	150.984	+	122.090i	0.392166	+	0.317118i
$386$	97.9768			0.253826
$387$	45.1263			0.116605
$388$	183.943			0.474081
$389$			428.599i			1.10180i	0.834572	+	0.550899i	$0.185715\pi$
$389$			428.599i			1.10180i	−0.834572	+	0.550899i	$0.814285\pi$
$390$	29.5906	+	23.9279i	0.0758732	+	0.0613535i
$391$	−99.0440	+	432.883i	−0.253309	+	1.10712i
$392$		−	87.6685i		−	0.223644i
$393$		−	201.629i		−	0.513050i
$394$	369.813			0.938611
$395$	−227.859	−	184.254i	−0.576859	−	0.466467i
$396$		−	150.092i		−	0.379020i
$397$		−	174.671i		−	0.439977i	−0.975503	−	0.219988i	$-0.929398\pi$
$397$		−	174.671i		−	0.439977i	0.975503	−	0.219988i	$-0.0706019\pi$
$398$	11.6451			0.0292590
$399$	−117.970			−0.295664
$400$	−20.9273	−	97.7857i	−0.0523184	−	0.244464i
$401$			563.043i			1.40410i	0.712129	+	0.702048i	$0.247731\pi$
$401$			563.043i			1.40410i	−0.712129	+	0.702048i	$0.752269\pi$
$402$	149.324			0.371453
$403$			200.547i			0.497636i
$404$	91.6207			0.226784
$405$	−188.746	+	233.415i	−0.466041	+	0.576332i
$406$		−	273.590i		−	0.673867i
$407$		−	194.083i		−	0.476863i
$408$	48.8492			0.119728
$409$	107.219			0.262149			0.131074	−	0.991373i	$-0.458157\pi$
$409$	107.219			0.262149			0.131074	+	0.991373i	$0.458157\pi$
$410$	185.547	+	150.040i	0.452555	+	0.365950i
$411$		−	224.125i		−	0.545316i
$412$	184.984			0.448990
$413$	20.8152			0.0504000
$414$	259.997	+	59.4874i	0.628012	+	0.143689i
$415$	57.4155	−	71.0032i	0.138351	−	0.171092i
$416$	34.0335			0.0818113
$417$			104.666i			0.250998i
$418$			402.281i			0.962394i
$419$		−	324.472i		−	0.774396i	−0.921997	−	0.387198i	$-0.873443\pi$
$419$		−	324.472i		−	0.774396i	0.921997	−	0.387198i	$-0.126557\pi$
$420$	29.5139	+	23.8659i	0.0702713	+	0.0568236i
$421$			282.258i			0.670446i	0.942139	+	0.335223i	$0.108812\pi$
$421$			282.258i			0.670446i	−0.942139	+	0.335223i	$0.891188\pi$
$422$		−	46.1030i		−	0.109249i
$423$			589.131i			1.39275i
$424$		−	10.5715i		−	0.0249327i
$425$	−101.013	−	471.996i	−0.237678	−	1.11058i
$426$	−117.183			−0.275078
$427$			180.539i			0.422808i
$428$	−335.766			−0.784501
$429$			49.2542i			0.114812i
$430$	30.2592	+	24.4685i	0.0703702	+	0.0569036i
$431$			109.495i			0.254048i	0.991900	+	0.127024i	$0.0405426\pi$
$431$			109.495i			0.254048i	−0.991900	+	0.127024i	$0.959457\pi$
$432$		−	61.5423i		−	0.142459i
$433$	644.151			1.48765			0.743823	−	0.668377i	$-0.233011\pi$
$433$	644.151			1.48765			0.743823	+	0.668377i	$0.233011\pi$
$434$			200.028i			0.460894i
$435$	−158.563	−	128.219i	−0.364512	−	0.294756i
$436$			194.346i			0.445747i
$437$	−696.850	−	159.440i	−1.59462	−	0.364851i
$438$		−	54.7403i		−	0.124978i
$439$	−108.832			−0.247908			−0.123954	−	0.992288i	$-0.539558\pi$
$439$	−108.832			−0.247908			−0.123954	+	0.992288i	$0.539558\pi$
$440$	81.3834	−	100.643i	0.184962	−	0.228735i
$441$	−254.158			−0.576322
$442$	164.274			0.371662
$443$			190.460i			0.429933i	0.976621	+	0.214966i	$0.0689642\pi$
$443$			190.460i			0.429933i	−0.976621	+	0.214966i	$0.931036\pi$
$444$		−	37.9389i		−	0.0854480i
$445$	639.673	+	517.260i	1.43747	+	1.16238i
$446$	75.2028			0.168616
$447$	162.993			0.364638
$448$	33.9454			0.0757709
$449$	−562.296			−1.25233			−0.626165	−	0.779691i	$-0.715376\pi$
$449$	−562.296			−1.25233			−0.626165	+	0.779691i	$0.715376\pi$
$450$	−283.489	+	60.6701i	−0.629975	+	0.134822i
$451$			308.848i			0.684807i
$452$	−277.323			−0.613546
$453$			59.0593i			0.130374i
$454$		−	48.6510i		−	0.107161i
$455$	99.2520	+	80.2584i	0.218136	+	0.176392i
$456$			78.6368i			0.172449i
$457$	487.235			1.06616			0.533080	−	0.846065i	$-0.321034\pi$
$457$	487.235			1.06616			0.533080	+	0.846065i	$0.321034\pi$
$458$	−299.334			−0.653567
$459$		−	297.055i		−	0.647179i
$460$	142.084	+	180.865i	0.308878	+	0.393185i
$461$	−150.086			−0.325566			−0.162783	−	0.986662i	$-0.552047\pi$
$461$	−150.086			−0.325566			−0.162783	+	0.986662i	$0.552047\pi$
$462$			49.1267i			0.106335i
$463$			64.9580i			0.140298i	0.997537	+	0.0701490i	$0.0223475\pi$
$463$			64.9580i			0.140298i	−0.997537	+	0.0701490i	$0.977653\pi$
$464$	−182.370			−0.393040
$465$	115.929	+	93.7438i	0.249309	+	0.201600i
$466$	−196.875			−0.422478
$467$	816.931			1.74932			0.874659	−	0.484740i	$-0.161086\pi$
$467$	816.931			1.74932			0.874659	+	0.484740i	$0.161086\pi$
$468$		−	98.6659i		−	0.210824i
$469$	500.860			1.06793
$470$	−319.441	+	395.038i	−0.679661	+	0.840507i
$471$		−	107.359i		−	0.227938i
$472$		−	13.8751i		−	0.0293963i
$473$			50.3671i			0.106484i
$474$		−	74.1402i		−	0.156414i
$475$	759.814	−	162.609i	1.59961	−	0.342336i
$476$	163.849			0.344220
$477$	−30.6475			−0.0642506
$478$		−	308.491i		−	0.645379i
$479$		−	656.029i		−	1.36958i	−0.728740	−	0.684790i	$-0.759894\pi$
$479$		−	656.029i		−	1.36958i	0.728740	−	0.684790i	$-0.240106\pi$
$480$	15.9086	−	19.6735i	0.0331430	−	0.0409865i
$481$		−	127.584i		−	0.265248i
$482$	−40.8770			−0.0848070
$483$	−85.0996	−	19.4708i	−0.176190	−	0.0403123i
$484$	−74.4768			−0.153878
$485$	289.149	−	357.578i	0.596184	−	0.737275i
$486$	−271.774			−0.559206
$487$		−	961.208i		−	1.97373i	−0.161537	−	0.986867i	$-0.551645\pi$
$487$		−	961.208i		−	1.97373i	0.161537	−	0.986867i	$-0.448355\pi$
$488$	120.344			0.246607
$489$	42.4056			0.0867190
$490$	−170.424	−	137.810i	−0.347804	−	0.281246i
$491$	−20.8751			−0.0425155			−0.0212578	−	0.999774i	$-0.506767\pi$
$491$	−20.8751			−0.0425155			−0.0212578	+	0.999774i	$0.506767\pi$
$492$			60.3729i			0.122709i
$493$	−880.274			−1.78554
$494$			264.447i			0.535317i
$495$	−291.773	−	235.937i	−0.589440	−	0.476640i
$496$	133.335			0.268821
$497$	−393.054			−0.790853
$498$	23.1028			0.0463912
$499$	−134.862			−0.270265			−0.135132	−	0.990828i	$-0.543146\pi$
$499$	−134.862			−0.270265			−0.135132	+	0.990828i	$0.543146\pi$
$500$	−222.988	−	113.032i	−0.445976	−	0.226064i
$501$	−166.722			−0.332778
$502$	58.6178			0.116768
$503$	462.560			0.919603			0.459802	−	0.888022i	$-0.347921\pi$
$503$	462.560			0.919603			0.459802	+	0.888022i	$0.347921\pi$
$504$		−	98.4103i		−	0.195259i
$505$	144.023	−	178.107i	0.285194	−	0.352687i
$506$	−66.3961	+	290.192i	−0.131218	+	0.573502i
$507$		−	118.795i		−	0.234311i
$508$		−	167.662i		−	0.330043i
$509$	71.5492			0.140568			0.0702841	−	0.997527i	$-0.477609\pi$
$509$	71.5492			0.140568			0.0702841	+	0.997527i	$0.477609\pi$
$510$	76.7884	−	94.9609i	0.150566	−	0.186198i
$511$		−	183.609i		−	0.359313i
$512$		−	22.6274i		−	0.0441942i
$513$	478.195			0.932155
$514$	466.163			0.906932
$515$	290.785	−	359.601i	0.564631	−	0.698255i
$516$			9.84564i			0.0190807i
$517$	−657.551			−1.27186
$518$		−	127.254i		−	0.245664i
$519$	−227.727			−0.438780
$520$	53.4989	−	66.1598i	0.102882	−	0.127230i
$521$		−	703.098i		−	1.34952i	−0.738039	−	0.674758i	$-0.764248\pi$
$521$		−	703.098i		−	1.34952i	0.738039	−	0.674758i	$-0.235752\pi$
$522$			528.706i			1.01285i
$523$	316.308			0.604796			0.302398	−	0.953182i	$-0.402213\pi$
$523$	316.308			0.604796			0.302398	+	0.953182i	$0.402213\pi$
$524$	−450.809			−0.860323
$525$	92.7887	−	19.8579i	0.176740	−	0.0378246i
$526$			466.080i			0.886084i
$527$	643.588			1.22123
$528$	32.7470			0.0620209
$529$	−476.369	−	230.029i	−0.900509	−	0.434838i
$530$	−20.5505	−	16.6178i	−0.0387746	−	0.0313543i
$531$	−40.2249			−0.0757531
$532$			263.762i			0.495793i
$533$			203.027i			0.380914i
$534$			208.135i			0.389766i
$535$	−527.807	+	652.716i	−0.986556	+	1.22003i
$536$		−	333.865i		−	0.622882i
$537$		−	4.30206i		−	0.00801129i
$538$			221.108i			0.410981i
$539$		−	283.675i		−	0.526299i
$540$	−119.636	−	96.7413i	−0.221548	−	0.179151i
$541$	835.702			1.54474			0.772368	−	0.635175i	$-0.219072\pi$
$541$	835.702			1.54474			0.772368	+	0.635175i	$0.219072\pi$
$542$			121.241i			0.223692i
$543$	−194.263			−0.357758
$544$		−	109.219i		−	0.200770i
$545$	377.800	+	305.501i	0.693211	+	0.560552i
$546$			32.2943i			0.0591471i
$547$		−	548.384i		−	1.00253i	−0.865294	−	0.501266i	$-0.832868\pi$
$547$		−	548.384i		−	1.00253i	0.865294	−	0.501266i	$-0.167132\pi$
$548$	−501.107			−0.914429
$549$		−	348.888i		−	0.635496i
$550$	−67.7160	−	316.412i	−0.123120	−	0.575294i
$551$		−	1417.05i		−	2.57178i
$552$	−12.9789	+	56.7260i	−0.0235126	+	0.102764i
$553$		−	248.680i		−	0.449692i
$554$	−223.968			−0.404275
$555$	−73.7517	−	59.6380i	−0.132886	−	0.107456i
$556$	234.016			0.420893
$557$	−205.109			−0.368238			−0.184119	−	0.982904i	$-0.558943\pi$
$557$	−205.109			−0.368238			−0.184119	+	0.982904i	$0.558943\pi$
$558$		−	386.550i		−	0.692741i
$559$			33.1098i			0.0592304i
$560$	53.3603	−	65.9884i	0.0952863	−	0.117836i
$561$	158.065			0.281755
$562$	−176.714			−0.314438
$563$	−95.5701			−0.169752			−0.0848758	−	0.996392i	$-0.527049\pi$
$563$	−95.5701			−0.169752			−0.0848758	+	0.996392i	$0.527049\pi$
$564$	−128.536			−0.227901
$565$	−435.937	+	539.105i	−0.771570	+	0.954168i
$566$			62.9371i			0.111196i
$567$	−254.742			−0.449281
$568$			262.003i			0.461273i
$569$			539.366i			0.947919i	0.880547	+	0.473960i	$0.157176\pi$
$569$			539.366i			0.947919i	−0.880547	+	0.473960i	$0.842824\pi$
$570$	152.867	+	123.613i	0.268187	+	0.216865i
$571$		−	8.33423i		−	0.0145958i	−0.999973	−	0.00729792i	$-0.997677\pi$
$571$		−	8.33423i		−	0.0145958i	0.999973	−	0.00729792i	$-0.00232302\pi$
$572$	110.125			0.192525
$573$	−187.453			−0.327142
$574$			202.501i			0.352790i
$575$	574.943	+	8.10552i	0.999901	+	0.0140966i
$576$	−65.5987			−0.113887
$577$			647.549i			1.12227i	0.827725	+	0.561134i	$0.189635\pi$
$577$			647.549i			1.12227i	−0.827725	+	0.561134i	$0.810365\pi$
$578$		−	118.475i		−	0.204975i
$579$	61.9723			0.107033
$580$	−286.677	+	354.521i	−0.494270	+	0.611243i
$581$	77.4910			0.133375
$582$	116.348			0.199910
$583$		−	34.2068i		−	0.0586738i
$584$	−122.391			−0.209573
$585$	−191.802	−	155.098i	−0.327867	−	0.265124i
$586$			34.2742i			0.0584885i
$587$			117.713i			0.200534i	0.994961	+	0.100267i	$0.0319696\pi$
$587$			117.713i			0.200534i	−0.994961	+	0.100267i	$0.968030\pi$
$588$		−	55.4521i		−	0.0943063i
$589$			1036.04i			1.75898i
$590$	−26.9726	−	21.8109i	−0.0457162	−	0.0369676i
$591$	233.914			0.395794
$592$	−84.8253			−0.143286
$593$		−	650.635i		−	1.09719i	−0.836088	−	0.548596i	$-0.815163\pi$
$593$		−	650.635i		−	1.09719i	0.836088	−	0.548596i	$-0.184837\pi$
$594$		−	199.137i		−	0.335247i
$595$	257.562	−	318.516i	0.432877	−	0.535321i
$596$		−	364.426i		−	0.611454i
$597$	7.36574			0.0123379
$598$	−43.6467	+	190.763i	−0.0729878	+	0.319002i
$599$	−893.478			−1.49162			−0.745808	−	0.666161i	$-0.767937\pi$
$599$	−893.478			−1.49162			−0.745808	+	0.666161i	$0.767937\pi$
$600$	−13.2370	−	61.8514i	−0.0220616	−	0.103086i
$601$	−896.626			−1.49189			−0.745945	−	0.666008i	$-0.768002\pi$
$601$	−896.626			−1.49189			−0.745945	+	0.666008i	$0.768002\pi$
$602$			33.0240i			0.0548572i
$603$	−967.901			−1.60514
$604$	132.047			0.218621
$605$	−117.074	+	144.780i	−0.193510	+	0.239306i
$606$	57.9519			0.0956302
$607$			308.410i			0.508089i	0.967192	+	0.254045i	$0.0817610\pi$
$607$			308.410i			0.508089i	−0.967192	+	0.254045i	$0.918239\pi$
$608$	175.819			0.289177
$609$		−	173.051i		−	0.284156i
$610$	189.175	−	233.944i	0.310123	−	0.383515i
$611$	−432.254			−0.707453
$612$	−316.635			−0.517377
$613$	−446.968			−0.729149			−0.364575	−	0.931174i	$-0.618786\pi$
$613$	−446.968			−0.729149			−0.364575	+	0.931174i	$0.618786\pi$
$614$	−156.643			−0.255118
$615$	117.362	+	94.9030i	0.190833	+	0.154314i
$616$	109.839			0.178311
$617$	−81.9662			−0.132846			−0.0664232	−	0.997792i	$-0.521159\pi$
$617$	−81.9662			−0.132846			−0.0664232	+	0.997792i	$0.521159\pi$
$618$	117.006			0.189330
$619$		−	299.873i		−	0.484447i	−0.970220	−	0.242224i	$-0.922123\pi$
$619$		−	299.873i		−	0.484447i	0.970220	−	0.242224i	$-0.0778767\pi$
$620$	209.596	−	259.198i	0.338058	−	0.418062i
$621$	344.954	+	78.9257i	0.555482	+	0.127095i
$622$			328.800i			0.528617i
$623$			698.122i			1.12058i
$624$	21.5269			0.0344982
$625$	−570.256	+	255.799i	−0.912409	+	0.409279i
$626$			596.393i			0.952705i
$627$			254.451i			0.405822i
$628$	−240.037			−0.382225
$629$	−409.439			−0.650936
$630$	−191.306	−	154.696i	−0.303660	−	0.245549i
$631$		−	317.603i		−	0.503332i	−0.967814	−	0.251666i	$-0.919021\pi$
$631$		−	317.603i		−	0.503332i	0.967814	−	0.251666i	$-0.0809785\pi$
$632$	−165.766			−0.262288
$633$		−	29.1611i		−	0.0460680i
$634$	766.375			1.20879
$635$	−325.928	−	263.555i	−0.513272	−	0.415048i
$636$		−	6.68667i		−	0.0105136i
$637$		−	186.479i		−	0.292746i
$638$	−590.109			−0.924935
$639$	759.569			1.18868
$640$	−43.9868	−	35.5691i	−0.0687294	−	0.0555768i
$641$		−	673.108i		−	1.05009i	−0.851074	−	0.525045i	$-0.824048\pi$
$641$		−	673.108i		−	1.05009i	0.851074	−	0.525045i	$-0.175952\pi$
$642$	−212.379			−0.330808
$643$	544.385			0.846633			0.423316	−	0.905982i	$-0.360866\pi$
$643$	544.385			0.846633			0.423316	+	0.905982i	$0.360866\pi$
$644$	−43.5337	+	190.269i	−0.0675989	+	0.295449i
$645$	19.1395	+	15.4768i	0.0296737	+	0.0239951i
$646$	848.653			1.31370
$647$			336.042i			0.519385i	0.965691	+	0.259692i	$0.0836212\pi$
$647$			336.042i			0.519385i	−0.965691	+	0.259692i	$0.916379\pi$
$648$			169.807i			0.262048i
$649$		−	44.8965i		−	0.0691779i
$650$	−44.5144	−	207.999i	−0.0684837	−	0.319999i
$651$			126.522i			0.194350i
$652$		−	94.8121i		−	0.145417i
$653$		−	882.240i		−	1.35106i	−0.737334	−	0.675528i	$-0.763916\pi$
$653$		−	882.240i		−	1.35106i	0.737334	−	0.675528i	$-0.236084\pi$
$654$			122.927i			0.187962i
$655$	−708.649	+	876.355i	−1.08191	+	1.33795i
$656$	134.984			0.205768
$657$			354.820i			0.540061i
$658$	−431.134			−0.655219
$659$		−	940.687i		−	1.42745i	−0.700428	−	0.713723i	$-0.747008\pi$
$659$		−	940.687i		−	1.42745i	0.700428	−	0.713723i	$-0.252992\pi$
$660$	51.4766	−	63.6589i	0.0779949	−	0.0964529i
$661$			789.812i			1.19487i	0.801916	+	0.597437i	$0.203814\pi$
$661$			789.812i			1.19487i	−0.801916	+	0.597437i	$0.796186\pi$
$662$			478.600i			0.722961i
$663$	103.907			0.156722
$664$		−	51.6542i		−	0.0777925i
$665$	512.743	+	414.620i	0.771042	+	0.623489i
$666$			245.915i			0.369242i
$667$	233.883	−	1022.21i	0.350650	−	1.53256i
$668$			372.763i			0.558029i
$669$	47.5673			0.0711021
$670$	−649.020	−	524.818i	−0.968686	−	0.783310i
$671$	389.406			0.580337
$672$	21.4711			0.0319511
$673$		−	993.337i		−	1.47598i	−0.674809	−	0.737992i	$-0.735774\pi$
$673$		−	993.337i		−	1.47598i	0.674809	−	0.737992i	$-0.264226\pi$
$674$		−	616.664i		−	0.914932i
$675$	−376.122	+	80.4948i	−0.557218	+	0.119252i
$676$	−265.608			−0.392911
$677$	−810.859			−1.19772			−0.598862	−	0.800852i	$-0.704380\pi$
$677$	−810.859			−1.19772			−0.598862	+	0.800852i	$0.704380\pi$
$678$	−175.412			−0.258720
$679$	390.251			0.574744
$680$	−212.317	−	171.687i	−0.312231	−	0.252480i
$681$		−	30.7727i		−	0.0451875i
$682$	431.442			0.632613
$683$			224.729i			0.329032i	0.986374	+	0.164516i	$0.0526063\pi$
$683$			224.729i			0.329032i	−0.986374	+	0.164516i	$0.947394\pi$
$684$		−	509.714i		−	0.745197i
$685$	−787.714	+	974.132i	−1.14995	+	1.42209i
$686$		−	480.033i		−	0.699756i
$687$	−189.335			−0.275596
$688$	22.0133			0.0319960
$689$		−	22.4865i		−	0.0326365i
$690$	89.8708	+	114.401i	0.130248	+	0.165798i
$691$	1234.62			1.78672			0.893360	−	0.449341i	$-0.148341\pi$
$691$	1234.62			1.78672			0.893360	+	0.449341i	$0.148341\pi$
$692$			509.160i			0.735781i
$693$		−	318.433i		−	0.459499i
$694$	−215.157			−0.310024
$695$	367.861	−	454.918i	0.529297	−	0.654559i
$696$	−115.353			−0.165737
$697$	651.547			0.934788
$698$		−	903.564i		−	1.29450i
$699$	−124.527			−0.178151
$700$	−44.3991	−	207.461i	−0.0634274	−	0.296372i
$701$			660.380i			0.942054i	0.882119	+	0.471027i	$0.156117\pi$
$701$			660.380i			0.942054i	−0.882119	+	0.471027i	$0.843883\pi$
$702$		−	130.906i		−	0.186476i
$703$		−	659.109i		−	0.937566i
$704$		−	73.2171i		−	0.104002i
$705$	−202.053	+	249.870i	−0.286599	+	0.354425i
$706$	−358.625			−0.507967
$707$	194.381			0.274938
$708$		−	8.77625i		−	0.0123958i
$709$			407.367i			0.574565i	0.957846	+	0.287282i	$0.0927518\pi$
$709$			407.367i			0.574565i	−0.957846	+	0.287282i	$0.907248\pi$
$710$	509.324	+	411.856i	0.717358	+	0.580078i
$711$			480.568i			0.675904i
$712$	465.357			0.653591
$713$	−170.998	+	747.365i	−0.239828	+	1.04820i
$714$	103.638			0.145151
$715$	173.110	−	214.078i	0.242112	−	0.299409i
$716$	−9.61872			−0.0134340
$717$		−	195.127i		−	0.272143i
$718$	958.254			1.33462
$719$	91.0091			0.126577			0.0632887	−	0.997995i	$-0.479841\pi$
$719$	91.0091			0.126577			0.0632887	+	0.997995i	$0.479841\pi$
$720$	−103.118	+	127.521i	−0.143219	+	0.177113i
$721$	392.459			0.544326
$722$			855.619i			1.18507i
$723$	−25.8555			−0.0357614
$724$			434.341i			0.599918i
$725$	238.533	+	1114.58i	0.329011	+	1.53735i
$726$	−47.1081			−0.0648872
$727$	663.513			0.912672			0.456336	−	0.889807i	$-0.349161\pi$
$727$	663.513			0.912672			0.456336	+	0.889807i	$0.349161\pi$
$728$	72.2050			0.0991827
$729$	368.420			0.505377
$730$	−192.392	+	237.922i	−0.263550	+	0.325921i
$731$	106.255			0.145355
$732$	76.1201			0.103989
$733$	184.588			0.251825			0.125912	−	0.992041i	$-0.459814\pi$
$733$	184.588			0.251825			0.125912	+	0.992041i	$0.459814\pi$
$734$			335.862i			0.457577i
$735$	−107.797	−	87.1678i	−0.146662	−	0.118596i
$736$	126.830	+	29.0188i	0.172324	+	0.0394278i
$737$		−	1080.31i		−	1.46582i
$738$		−	391.330i		−	0.530257i
$739$	524.664			0.709965			0.354983	−	0.934873i	$-0.384487\pi$
$739$	524.664			0.709965			0.354983	+	0.934873i	$0.384487\pi$
$740$	−133.341	+	164.897i	−0.180191	+	0.222834i
$741$			167.268i			0.225733i
$742$		−	22.4283i		−	0.0302268i
$743$	1432.63			1.92818			0.964088	−	0.265583i	$-0.0855646\pi$
$743$	1432.63			1.92818			0.964088	+	0.265583i	$0.0855646\pi$
$744$	84.3372			0.113356
$745$	−708.430	−	572.859i	−0.950913	−	0.768939i
$746$		−	69.1854i		−	0.0927419i
$747$	−149.750			−0.200468
$748$		−	353.407i		−	0.472470i
$749$	−712.357			−0.951077
$750$	−141.045	−	71.4951i	−0.188059	−	0.0953268i
$751$			450.467i			0.599823i	0.953967	+	0.299911i	$0.0969571\pi$
$751$			450.467i			0.599823i	−0.953967	+	0.299911i	$0.903043\pi$
$752$			287.387i			0.382163i
$753$	37.0769			0.0492389
$754$	−387.919			−0.514481
$755$	207.571	−	256.694i	0.274929	−	0.339992i
$756$		−	130.567i		−	0.172708i
$757$	−498.016			−0.657882			−0.328941	−	0.944351i	$-0.606692\pi$
$757$	−498.016			−0.657882			−0.328941	+	0.944351i	$0.606692\pi$
$758$	850.377			1.12187
$759$	−41.9968	+	183.552i	−0.0553318	+	0.241834i
$760$	276.379	−	341.786i	0.363656	−	0.449718i
$761$	1212.30			1.59303			0.796515	−	0.604619i	$-0.206675\pi$
$761$	1212.30			1.59303			0.796515	+	0.604619i	$0.206675\pi$
$762$		−	106.049i		−	0.139172i
$763$			412.321i			0.540394i
$764$			419.114i			0.548578i
$765$	−497.733	+	615.525i	−0.650632	+	0.804608i
$766$		−	740.541i		−	0.966764i
$767$		−	29.5136i		−	0.0384792i
$768$		−	14.3123i		−	0.0186358i
$769$		−	26.1169i		−	0.0339622i	−0.999856	−	0.0169811i	$-0.994594\pi$
$769$		−	26.1169i		−	0.0339622i	0.999856	−	0.0169811i	$-0.00540551\pi$
$770$	172.662	−	213.523i	0.224236	−	0.277303i
$771$	294.858			0.382435
$772$		−	138.560i		−	0.179482i
$773$	159.160			0.205899			0.102949	−	0.994687i	$-0.467172\pi$
$773$	159.160			0.205899			0.102949	+	0.994687i	$0.467172\pi$
$774$		−	63.8183i		−	0.0824525i
$775$	−174.397	−	814.893i	−0.225028	−	1.05147i
$776$		−	260.135i		−	0.335226i
$777$		−	80.4906i		−	0.103592i
$778$	606.131			0.779089
$779$			1048.85i			1.34641i
$780$	33.8391	−	41.8474i	0.0433835	−	0.0536505i
$781$			847.782i			1.08551i
$782$	612.190	+	140.069i	0.782851	+	0.179117i
$783$			701.468i			0.895873i
$784$	−123.982			−0.158140
$785$	−377.326	+	466.623i	−0.480670	+	0.594424i
$786$	−285.146			−0.362781
$787$	−682.346			−0.867022			−0.433511	−	0.901148i	$-0.642725\pi$
$787$	−682.346			−0.867022			−0.433511	+	0.901148i	$0.642725\pi$
$788$		−	522.994i		−	0.663698i
$789$			294.805i			0.373644i
$790$	−260.575	+	322.242i	−0.329842	+	0.407901i
$791$	−588.364			−0.743823
$792$	−212.262			−0.268008
$793$	255.983			0.322804
$794$	−247.022			−0.311110
$795$	−12.9986	−	10.5111i	−0.0163505	−	0.0132215i
$796$		−	16.4686i		−	0.0206892i
$797$	1154.78			1.44891			0.724455	−	0.689322i	$-0.242091\pi$
$797$	1154.78			1.44891			0.724455	+	0.689322i	$0.242091\pi$
$798$			166.835i			0.209066i
$799$			1387.17i			1.73613i
$800$	−138.290	+	29.5957i	−0.172862	+	0.0369947i
$801$		−	1349.11i		−	1.68428i
$802$	796.263			0.992846
$803$	−396.027			−0.493185
$804$		−	211.176i		−	0.262657i
$805$	301.443	+	383.721i	0.374463	+	0.476672i
$806$	283.617			0.351882
$807$			139.855i			0.173303i
$808$		−	129.571i		−	0.160360i
$809$	−107.567			−0.132962			−0.0664812	−	0.997788i	$-0.521177\pi$
$809$	−107.567			−0.132962			−0.0664812	+	0.997788i	$0.521177\pi$
$810$	330.098	+	266.928i	0.407528	+	0.329541i
$811$	−262.024			−0.323087			−0.161544	−	0.986866i	$-0.551647\pi$
$811$	−262.024			−0.323087			−0.161544	+	0.986866i	$0.551647\pi$
$812$	−386.914			−0.476496
$813$			76.6873i			0.0943263i
$814$	−274.475			−0.337193
$815$	−184.311	−	149.040i	−0.226148	−	0.182871i
$816$		−	69.0832i		−	0.0846608i
$817$			171.047i			0.209360i
$818$		−	151.630i		−	0.185367i
$819$		−	209.328i		−	0.255590i
$820$	212.188	−	262.404i	0.258766	−	0.320004i
$821$	1163.19			1.41679			0.708396	−	0.705815i	$-0.249419\pi$
$821$	1163.19			1.41679			0.708396	+	0.705815i	$0.249419\pi$
$822$	−316.960			−0.385597
$823$			614.581i			0.746757i	0.927679	+	0.373378i	$0.121801\pi$
$823$			614.581i			0.746757i	−0.927679	+	0.373378i	$0.878199\pi$
$824$		−	261.607i		−	0.317484i
$825$	−42.8318	−	200.137i	−0.0519173	−	0.242590i
$826$		−	29.4371i		−	0.0356382i
$827$	−11.4556			−0.0138520			−0.00692599	−	0.999976i	$-0.502205\pi$
$827$	−11.4556			−0.0138520			−0.00692599	+	0.999976i	$0.502205\pi$
$828$	84.1279	−	367.691i	0.101604	−	0.444071i
$829$	383.752			0.462910			0.231455	−	0.972846i	$-0.425651\pi$
$829$	383.752			0.462910			0.231455	+	0.972846i	$0.425651\pi$
$830$	−100.414	−	81.1978i	−0.120980	−	0.0978286i
$831$	−141.664			−0.170475
$832$		−	48.1306i		−	0.0578493i
$833$	−598.442			−0.718418
$834$	148.020			0.177482
$835$	724.637	+	585.965i	0.867829	+	0.701754i
$836$	568.911			0.680515
$837$		−	512.860i		−	0.612736i
$838$	−458.872			−0.547581
$839$		−	824.028i		−	0.982155i	−0.871116	−	0.491078i	$-0.836603\pi$
$839$		−	824.028i		−	0.982155i	0.871116	−	0.491078i	$-0.163397\pi$
$840$	33.7515	−	41.7390i	0.0401803	−	0.0496893i
$841$	1237.69			1.47168
$842$	399.173			0.474077
$843$	−111.775			−0.132592
$844$	−65.1995			−0.0772505
$845$	−417.521	+	516.330i	−0.494108	+	0.611042i
$846$	833.157			0.984820
$847$	−158.009			−0.186551
$848$	−14.9503			−0.0176301
$849$			39.8090i			0.0468893i
$850$	−667.504	+	142.854i	−0.785298	+	0.168064i
$851$	108.785	−	475.459i	0.127832	−	0.558707i
$852$			165.722i			0.194510i
$853$		−	750.060i		−	0.879320i	−0.898164	−	0.439660i	$-0.855099\pi$
$853$		−	750.060i		−	0.879320i	0.898164	−	0.439660i	$-0.144901\pi$
$854$	255.321			0.298970
$855$	−990.864	−	801.245i	−1.15891	−	0.937128i
$856$			474.845i			0.554726i
$857$			112.618i			0.131410i	0.997839	+	0.0657048i	$0.0209296\pi$
$857$			112.618i			0.131410i	−0.997839	+	0.0657048i	$0.979070\pi$
$858$	69.6560			0.0811841
$859$	−556.523			−0.647873			−0.323936	−	0.946079i	$-0.605006\pi$
$859$	−556.523			−0.647873			−0.323936	+	0.946079i	$0.605006\pi$
$860$	34.6037	−	42.7929i	0.0402369	−	0.0497592i
$861$			128.086i			0.148764i
$862$	154.849			0.179639
$863$		−	710.644i		−	0.823457i	−0.911307	−	0.411729i	$-0.864925\pi$
$863$		−	710.644i		−	0.823457i	0.911307	−	0.411729i	$-0.135075\pi$
$864$	−87.0339			−0.100734
$865$	989.787	+	800.373i	1.14426	+	0.925287i
$866$		−	910.967i		−	1.05192i
$867$		−	74.9380i		−	0.0864337i
$868$	282.882			0.325901
$869$	−536.379			−0.617238
$870$	−181.329	+	224.242i	−0.208424	+	0.257749i
$871$		−	710.162i		−	0.815341i
$872$	274.846			0.315190
$873$	−754.152			−0.863863
$874$	−225.482	+	985.495i	−0.257988	+	1.12757i
$875$	−473.088	−	239.807i	−0.540673	−	0.274065i
$876$	−77.4145			−0.0883727
$877$		−	786.054i		−	0.896299i	−0.893959	−	0.448149i	$-0.852083\pi$
$877$		−	786.054i		−	0.896299i	0.893959	−	0.448149i	$-0.147917\pi$
$878$			153.911i			0.175297i
$879$			21.6791i			0.0246634i
$880$	−142.331	−	115.093i	−0.161740	−	0.130788i
$881$			1128.95i			1.28144i	0.767773	+	0.640722i	$0.221365\pi$
$881$			1128.95i			1.28144i	−0.767773	+	0.640722i	$0.778635\pi$
$882$			359.434i			0.407521i
$883$			1645.38i			1.86340i	0.363226	+	0.931701i	$0.381675\pi$
$883$			1645.38i			1.86340i	−0.363226	+	0.931701i	$0.618325\pi$
$884$		−	232.319i		−	0.262804i
$885$	−17.0607	−	13.7958i	−0.0192776	−	0.0155885i
$886$	269.351			0.304008
$887$		−	327.792i		−	0.369551i	−0.982781	−	0.184775i	$-0.940844\pi$
$887$		−	327.792i		−	0.369551i	0.982781	−	0.184775i	$-0.0591558\pi$
$888$	−53.6537			−0.0604209
$889$		−	355.708i		−	0.400122i
$890$	731.516	−	904.635i	0.821929	−	1.01644i
$891$			549.456i			0.616674i
$892$		−	106.353i		−	0.119230i
$893$	−2233.05			−2.50062
$894$		−	230.507i		−	0.257838i
$895$	−15.1201	+	18.6984i	−0.0168940	+	0.0208921i
$896$		−	48.0060i		−	0.0535781i
$897$	−27.6074	+	120.662i	−0.0307775	+	0.134517i
$898$			795.206i			0.885531i
$899$	−1519.78			−1.69052
$900$	85.8004	+	400.913i	0.0953338	+	0.445459i
$901$	−72.1629			−0.0800920
$902$	436.777			0.484232
$903$			20.8884i			0.0231322i
$904$			392.194i			0.433843i
$905$	844.341	+	682.761i	0.932973	+	0.754432i
$906$	83.5224			0.0921881
$907$	−1239.75			−1.36687			−0.683436	−	0.730011i	$-0.739515\pi$
$907$	−1239.75			−1.36687			−0.683436	+	0.730011i	$0.739515\pi$
$908$	−68.8028			−0.0757741
$909$	−375.637			−0.413242
$910$	113.502	−	140.364i	0.124728	−	0.154246i
$911$			998.723i			1.09629i	0.836382	+	0.548146i	$0.184666\pi$
$911$			998.723i			1.09629i	−0.836382	+	0.548146i	$0.815334\pi$
$912$	111.209			0.121940
$913$		−	167.141i		−	0.183068i
$914$		−	689.055i		−	0.753889i
$915$	119.657	−	147.974i	0.130773	−	0.161721i
$916$			423.322i			0.462142i
$917$	−956.430			−1.04300
$918$	−420.099			−0.457624
$919$		−	165.882i		−	0.180502i	−0.995919	−	0.0902512i	$-0.971233\pi$
$919$		−	165.882i		−	0.180502i	0.995919	−	0.0902512i	$-0.0287670\pi$
$920$	255.782	−	200.937i	0.278024	−	0.218410i
$921$	−99.0796			−0.107578
$922$			212.253i			0.230210i
$923$			557.306i			0.603798i
$924$	69.4756			0.0751900
$925$	110.948	+	518.419i	0.119944	+	0.560453i
$926$	91.8645			0.0992057
$927$	−758.419			−0.818144
$928$			257.911i			0.277921i
$929$	613.100			0.659957			0.329978	−	0.943988i	$-0.392959\pi$
$929$	613.100			0.659957			0.329978	+	0.943988i	$0.392959\pi$
$930$	132.574	−	163.948i	0.142552	−	0.176288i
$931$		−	963.364i		−	1.03476i
$932$			278.423i			0.298737i
$933$			207.972i			0.222907i
$934$		−	1155.31i		−	1.23695i
$935$	−687.010	−	555.538i	−0.734770	−	0.594158i
$936$	−139.535			−0.149075
$937$	1135.07			1.21139			0.605696	−	0.795696i	$-0.292895\pi$
$937$	1135.07			1.21139			0.605696	+	0.795696i	$0.292895\pi$
$938$		−	708.322i		−	0.755141i
$939$			377.231i			0.401737i
$940$	558.668	+	451.757i	0.594328	+	0.480593i
$941$		−	872.481i		−	0.927185i	−0.886049	−	0.463592i	$-0.846560\pi$
$941$		−	872.481i		−	0.927185i	0.886049	−	0.463592i	$-0.153440\pi$
$942$	−151.828			−0.161177
$943$	−173.112	+	756.607i	−0.183576	+	0.802340i
$944$	−19.6223			−0.0207863
$945$	−253.817	−	205.245i	−0.268590	−	0.217190i
$946$	71.2299			0.0752959
$947$		−	245.896i		−	0.259658i	−0.991536	−	0.129829i	$-0.958557\pi$
$947$		−	245.896i		−	0.259658i	0.991536	−	0.129829i	$-0.0414428\pi$
$948$	−104.850			−0.110601
$949$	−260.336			−0.274327
$950$	−229.965	−	1074.54i	−0.242068	−	1.13109i
$951$	484.748			0.509724
$952$		−	231.717i		−	0.243401i
$953$	1181.64			1.23992			0.619960	−	0.784633i	$-0.287149\pi$
$953$	1181.64			1.23992			0.619960	+	0.784633i	$0.287149\pi$
$954$			43.3422i			0.0454320i
$955$	814.740	+	658.825i	0.853131	+	0.689869i
$956$	−436.272			−0.456352
$957$	−373.255			−0.390027
$958$	−927.765			−0.968439
$959$	−1063.14			−1.10859
$960$	−27.8225	−	22.4982i	−0.0289818	−	0.0234356i
$961$	150.143			0.156236
$962$	−180.431			−0.187559
$963$	1376.61			1.42951
$964$			57.8088i			0.0599676i
$965$	−269.355	−	217.809i	−0.279125	−	0.225709i
$966$	−27.5359	+	120.349i	−0.0285051	+	0.124585i
$967$		−	1044.35i		−	1.07999i	−0.841668	−	0.539995i	$-0.818426\pi$
$967$		−	1044.35i		−	1.07999i	0.841668	−	0.539995i	$-0.181574\pi$
$968$			105.326i			0.108808i
$969$	536.790			0.553963
$970$	−505.692	−	408.919i	−0.521332	−	0.421566i
$971$			35.8617i			0.0369327i	0.999829	+	0.0184664i	$0.00587836\pi$
$971$			35.8617i			0.0369327i	−0.999829	+	0.0184664i	$0.994122\pi$
$972$			384.347i			0.395418i
$973$	496.486			0.510263
$974$	−1359.35			−1.39564
$975$	−28.1563	−	131.564i	−0.0288782	−	0.134937i
$976$		−	170.192i		−	0.174378i
$977$	−1150.09			−1.17716			−0.588581	−	0.808439i	$-0.700313\pi$
$977$	−1150.09			−1.17716			−0.588581	+	0.808439i	$0.700313\pi$
$978$		−	59.9705i		−	0.0613196i
$979$	1505.79			1.53809
$980$	−194.893	+	241.016i	−0.198871	+	0.245935i
$981$		−	796.801i		−	0.812233i
$982$			29.5219i			0.0300630i
$983$	−44.3858			−0.0451534			−0.0225767	−	0.999745i	$-0.507187\pi$
$983$	−44.3858			−0.0451534			−0.0225767	+	0.999745i	$0.507187\pi$
$984$	85.3801			0.0867684
$985$	−1016.68	−	822.120i	−1.03216	−	0.834639i
$986$			1244.89i			1.26257i
$987$	−272.701			−0.276293
$988$	373.984			0.378527
$989$	−28.2312	+	123.388i	−0.0285452	+	0.124760i
$990$	−333.665	+	412.629i	−0.337035	+	0.416797i
$991$	−416.486			−0.420269			−0.210134	−	0.977673i	$-0.567390\pi$
$991$	−416.486			−0.420269			−0.210134	+	0.977673i	$0.567390\pi$
$992$		−	188.565i		−	0.190085i
$993$			302.724i			0.304858i
$994$			555.862i			0.559218i
$995$	−32.0143	−	25.8878i	−0.0321752	−	0.0260179i
$996$		−	32.6723i		−	0.0328036i
$997$			1202.35i			1.20597i	0.797754	+	0.602983i	$0.206021\pi$
$997$			1202.35i			1.20597i	−0.797754	+	0.602983i	$0.793979\pi$
$998$			190.724i			0.191106i
$999$			326.272i			0.326598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.5	✓	24
5.2	odd	4		1150.3.d.e.551.20		24
5.3	odd	4		1150.3.d.e.551.5		24
5.4	even	2	inner	230.3.c.a.229.20	yes	24
23.22	odd	2	inner	230.3.c.a.229.6	yes	24
115.22	even	4		1150.3.d.e.551.17		24
115.68	even	4		1150.3.d.e.551.8		24
115.114	odd	2	inner	230.3.c.a.229.19	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.5	✓	24	1.1	even	1	trivial
230.3.c.a.229.6	yes	24	23.22	odd	2	inner
230.3.c.a.229.19	yes	24	115.114	odd	2	inner
230.3.c.a.229.20	yes	24	5.4	even	2	inner
1150.3.d.e.551.5		24	5.3	odd	4
1150.3.d.e.551.8		24	115.68	even	4
1150.3.d.e.551.17		24	115.22	even	4
1150.3.d.e.551.20		24	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -0.894518i q^{3} -2.00000 q^{4} +(-3.14390 + 3.88792i) q^{5} -1.26504 q^{6} -4.24317 q^{7} +2.82843i q^{8} +8.19984 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -0.894518i q^{3} -2.00000 q^{4} +(-3.14390 + 3.88792i) q^{5} -1.26504 q^{6} -4.24317 q^{7} +2.82843i q^{8} +8.19984 q^{9} +(5.49835 + 4.44614i) q^{10} +9.15214i q^{11} +1.78904i q^{12} +6.01633i q^{13} +6.00075i q^{14} +(3.47782 + 2.81227i) q^{15} +4.00000 q^{16} +19.3074 q^{17} -11.5963i q^{18} +31.0808i q^{19} +(6.28779 - 7.77584i) q^{20} +3.79559i q^{21} +12.9431 q^{22} +(-5.12985 + 22.4206i) q^{23} +2.53008 q^{24} +(-5.23184 - 24.4464i) q^{25} +8.50838 q^{26} -15.3856i q^{27} +8.48634 q^{28} -45.5926 q^{29} +(3.97715 - 4.91837i) q^{30} +33.3338 q^{31} -5.65685i q^{32} +8.18675 q^{33} -27.3048i q^{34} +(13.3401 - 16.4971i) q^{35} -16.3997 q^{36} -21.2063 q^{37} +43.9548 q^{38} +5.38172 q^{39} +(-10.9967 - 8.89228i) q^{40} +33.7460 q^{41} +5.36778 q^{42} +5.50332 q^{43} -18.3043i q^{44} +(-25.7794 + 31.8803i) q^{45} +(31.7076 + 7.25471i) q^{46} +71.8467i q^{47} -3.57807i q^{48} -30.9955 q^{49} +(-34.5725 + 7.39893i) q^{50} -17.2708i q^{51} -12.0327i q^{52} -3.73758 q^{53} -21.7585 q^{54} +(-35.5828 - 28.7734i) q^{55} -12.0015i q^{56} +27.8023 q^{57} +64.4777i q^{58} -4.90558 q^{59} +(-6.95563 - 5.62455i) q^{60} -42.5481i q^{61} -47.1411i q^{62} -34.7933 q^{63} -8.00000 q^{64} +(-23.3910 - 18.9147i) q^{65} -11.5778i q^{66} -118.039 q^{67} -38.6147 q^{68} +(20.0557 + 4.58875i) q^{69} +(-23.3304 - 18.8657i) q^{70} +92.6322 q^{71} +23.1926i q^{72} +43.2716i q^{73} +29.9903i q^{74} +(-21.8678 + 4.67997i) q^{75} -62.1615i q^{76} -38.8341i q^{77} -7.61090i q^{78} +58.6070i q^{79} +(-12.5756 + 15.5517i) q^{80} +60.0359 q^{81} -47.7241i q^{82} -18.2625 q^{83} -7.59119i q^{84} +(-60.7004 + 75.0655i) q^{85} -7.78287i q^{86} +40.7834i q^{87} -25.8861 q^{88} -164.528i q^{89} +(45.0856 + 36.4576i) q^{90} -25.5283i q^{91} +(10.2597 - 44.8413i) q^{92} -29.8177i q^{93} +101.607 q^{94} +(-120.840 - 97.7147i) q^{95} -5.06016 q^{96} -91.9716 q^{97} +43.8343i q^{98} +75.0460i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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