LMFDB - Embedded newform 24.4.f.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,4,Mod(11,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("24.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	24.f (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:	$1.41604584014$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 10x^{6} + 120x^{4} - 640x^{2} + 4096 $ x^8 - 10x^6 + 120x^4 - 640*x^2 + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$1.95291 - 2.04601i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.4.f.b.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95291 - 2.04601i) q^{2} +(-4.37228 - 2.80770i) q^{3} +(-0.372281 - 7.99133i) q^{4} +13.1715 q^{5} +(-14.2832 + 3.46254i) q^{6} +26.9490i q^{7} +(-17.0773 - 14.8447i) q^{8} +(11.2337 + 24.5521i) q^{9} +O(q^{10})$	\(q+(1.95291 - 2.04601i) q^{2} +(-4.37228 - 2.80770i) q^{3} +(-0.372281 - 7.99133i) q^{4} +13.1715 q^{5} +(-14.2832 + 3.46254i) q^{6} +26.9490i q^{7} +(-17.0773 - 14.8447i) q^{8} +(11.2337 + 24.5521i) q^{9} +(25.7228 - 26.9490i) q^{10} -21.9834i q^{11} +(-20.8095 + 35.9856i) q^{12} +10.0326i q^{13} +(55.1379 + 52.6290i) q^{14} +(-57.5896 - 36.9816i) q^{15} +(-63.7228 + 5.95005i) q^{16} +6.09352i q^{17} +(72.1721 + 24.9638i) q^{18} -40.1902 q^{19} +(-4.90351 - 105.258i) q^{20} +(75.6647 - 117.829i) q^{21} +(-44.9783 - 42.9317i) q^{22} +9.80703 q^{23} +(32.9877 + 112.853i) q^{24} +48.4891 q^{25} +(20.5268 + 19.5928i) q^{26} +(19.8179 - 138.889i) q^{27} +(215.359 - 10.0326i) q^{28} -164.501 q^{29} +(-188.132 + 45.6069i) q^{30} +47.0143i q^{31} +(-112.271 + 141.997i) q^{32} +(-61.7228 + 96.1178i) q^{33} +(12.4674 + 11.9001i) q^{34} +354.960i q^{35} +(192.022 - 98.9124i) q^{36} +205.560i q^{37} +(-78.4878 + 82.2294i) q^{38} +(28.1685 - 43.8654i) q^{39} +(-224.935 - 195.527i) q^{40} -419.120i q^{41} +(-93.3119 - 384.919i) q^{42} +205.038 q^{43} +(-175.677 + 8.18402i) q^{44} +(147.965 + 323.388i) q^{45} +(19.1522 - 20.0652i) q^{46} +566.089 q^{47} +(295.320 + 152.899i) q^{48} -383.250 q^{49} +(94.6949 - 99.2090i) q^{50} +(17.1087 - 26.6426i) q^{51} +(80.1740 - 3.73496i) q^{52} -342.173 q^{53} +(-245.466 - 311.786i) q^{54} -289.555i q^{55} +(400.049 - 460.218i) q^{56} +(175.723 + 112.842i) q^{57} +(-321.255 + 336.570i) q^{58} -3.70288i q^{59} +(-274.093 + 473.985i) q^{60} -717.005i q^{61} +(96.1915 + 91.8146i) q^{62} +(-661.654 + 302.737i) q^{63} +(71.2716 + 507.015i) q^{64} +132.145i q^{65} +(76.1184 + 313.995i) q^{66} -238.701 q^{67} +(48.6953 - 2.26850i) q^{68} +(-42.8791 - 27.5351i) q^{69} +(726.250 + 693.205i) q^{70} -517.054 q^{71} +(172.626 - 586.045i) q^{72} +984.195 q^{73} +(420.576 + 401.439i) q^{74} +(-212.008 - 136.143i) q^{75} +(14.9621 + 321.173i) q^{76} +592.432 q^{77} +(-34.7383 - 143.298i) q^{78} -329.100i q^{79} +(-839.327 + 78.3712i) q^{80} +(-476.609 + 551.621i) q^{81} +(-857.522 - 818.503i) q^{82} -625.333i q^{83} +(-969.777 - 560.796i) q^{84} +80.2609i q^{85} +(400.421 - 419.509i) q^{86} +(719.244 + 461.868i) q^{87} +(-326.337 + 375.419i) q^{88} +238.583i q^{89} +(950.616 + 328.811i) q^{90} -270.369 q^{91} +(-3.65097 - 78.3712i) q^{92} +(132.002 - 205.560i) q^{93} +(1105.52 - 1158.22i) q^{94} -529.366 q^{95} +(889.566 - 305.628i) q^{96} -1001.01 q^{97} +(-748.453 + 784.132i) q^{98} +(539.739 - 246.955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9	$ 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9} - 24 q^{10} + 36 q^{12} - 280 q^{16} + 264 q^{18} + 184 q^{19} - 176 q^{22} + 264 q^{24} + 296 q^{25} - 324 q^{27} + 528 q^{28} - 624 q^{30} - 264 q^{33} - 176 q^{34} - 516 q^{36} - 1248 q^{40} + 1320 q^{42} - 152 q^{43} + 1440 q^{46} + 1080 q^{48} - 952 q^{49} + 1056 q^{51} + 2112 q^{52} - 1584 q^{54} + 1176 q^{57} - 2616 q^{58} - 2640 q^{60} - 1360 q^{64} + 792 q^{66} - 1496 q^{67} + 3696 q^{70} + 2640 q^{72} + 1072 q^{73} - 708 q^{75} + 1912 q^{76} - 3696 q^{78} - 504 q^{81} - 2816 q^{82} - 4224 q^{84} - 1232 q^{88} + 4104 q^{90} + 3168 q^{91} + 4800 q^{94} + 4752 q^{96} - 3872 q^{97} + 2112 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9 - 24 * q^10 + 36 * q^12 - 280 * q^16 + 264 * q^18 + 184 * q^19 - 176 * q^22 + 264 * q^24 + 296 * q^25 - 324 * q^27 + 528 * q^28 - 624 * q^30 - 264 * q^33 - 176 * q^34 - 516 * q^36 - 1248 * q^40 + 1320 * q^42 - 152 * q^43 + 1440 * q^46 + 1080 * q^48 - 952 * q^49 + 1056 * q^51 + 2112 * q^52 - 1584 * q^54 + 1176 * q^57 - 2616 * q^58 - 2640 * q^60 - 1360 * q^64 + 792 * q^66 - 1496 * q^67 + 3696 * q^70 + 2640 * q^72 + 1072 * q^73 - 708 * q^75 + 1912 * q^76 - 3696 * q^78 - 504 * q^81 - 2816 * q^82 - 4224 * q^84 - 1232 * q^88 + 4104 * q^90 + 3168 * q^91 + 4800 * q^94 + 4752 * q^96 - 3872 * q^97 + 2112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.95291	−	2.04601i	0.690458	−	0.723372i
$2$	1.95291	−	2.04601i	0.690458	−	0.723372i
$3$	−4.37228	−	2.80770i	−0.841446	−	0.540341i
$3$	−4.37228	−	2.80770i	−0.841446	−	0.540341i
$4$	−0.372281	−	7.99133i	−0.0465352	−	0.998917i
$5$	13.1715			1.17810			0.589049	−	0.808098i	$-0.299503\pi$
$5$	13.1715			1.17810			0.589049	+	0.808098i	$0.299503\pi$
$6$	−14.2832	+	3.46254i	−0.971851	+	0.235596i
$7$			26.9490i			1.45511i	0.686049	+	0.727555i	$0.259344\pi$
$7$			26.9490i			1.45511i	−0.686049	+	0.727555i	$0.740656\pi$
$8$	−17.0773	−	14.8447i	−0.754719	−	0.656048i
$9$	11.2337	+	24.5521i	0.416063	+	0.909336i
$10$	25.7228	−	26.9490i	0.813427	−	0.852203i
$11$		−	21.9834i		−	0.602569i	−0.953534	−	0.301284i	$-0.902585\pi$
$11$		−	21.9834i		−	0.602569i	0.953534	−	0.301284i	$-0.0974153\pi$
$12$	−20.8095	+	35.9856i	−0.500599	+	0.865679i
$13$			10.0326i			0.214042i	0.994257	+	0.107021i	$0.0341312\pi$
$13$			10.0326i			0.214042i	−0.994257	+	0.107021i	$0.965869\pi$
$14$	55.1379	+	52.6290i	1.05259	+	1.00469i
$15$	−57.5896	−	36.9816i	−0.991305	−	0.636575i
$16$	−63.7228	+	5.95005i	−0.995669	+	0.0929695i
$17$			6.09352i			0.0869350i	0.999055	+	0.0434675i	$0.0138405\pi$
$17$			6.09352i			0.0869350i	−0.999055	+	0.0434675i	$0.986160\pi$
$18$	72.1721	+	24.9638i	0.945062	+	0.326890i
$19$	−40.1902			−0.485277			−0.242638	−	0.970117i	$-0.578013\pi$
$19$	−40.1902			−0.485277			−0.242638	+	0.970117i	$0.578013\pi$
$20$	−4.90351	−	105.258i	−0.0548229	−	1.17682i
$21$	75.6647	−	117.829i	0.786256	−	1.22440i
$22$	−44.9783	−	42.9317i	−0.435882	−	0.416049i
$23$	9.80703			0.0889090			0.0444545	−	0.999011i	$-0.485845\pi$
$23$	9.80703			0.0889090			0.0444545	+	0.999011i	$0.485845\pi$
$24$	32.9877	+	112.853i	0.280566	+	0.959835i
$25$	48.4891			0.387913
$26$	20.5268	+	19.5928i	0.154832	+	0.147787i
$27$	19.8179	−	138.889i	0.141258	−	0.989973i
$28$	215.359	−	10.0326i	1.45353	−	0.0677138i
$29$	−164.501			−1.05335			−0.526673	−	0.850068i	$-0.676561\pi$
$29$	−164.501			−1.05335			−0.526673	+	0.850068i	$0.676561\pi$
$30$	−188.132	+	45.6069i	−1.14494	+	0.277555i
$31$			47.0143i			0.272387i	0.990682	+	0.136194i	$0.0434870\pi$
$31$			47.0143i			0.272387i	−0.990682	+	0.136194i	$0.956513\pi$
$32$	−112.271	+	141.997i	−0.620216	+	0.784431i
$33$	−61.7228	+	96.1178i	−0.325593	+	0.507029i
$34$	12.4674	+	11.9001i	0.0628864	+	0.0600250i
$35$			354.960i			1.71426i
$36$	192.022	−	98.9124i	0.888989	−	0.457928i
$37$			205.560i			0.913346i	0.889635	+	0.456673i	$0.150959\pi$
$37$			205.560i			0.913346i	−0.889635	+	0.456673i	$0.849041\pi$
$38$	−78.4878	+	82.2294i	−0.335063	+	0.351036i
$39$	28.1685	−	43.8654i	0.115656	−	0.180105i
$40$	−224.935	−	195.527i	−0.889133	−	0.772888i
$41$		−	419.120i		−	1.59648i	−0.602342	−	0.798238i	$-0.705766\pi$
$41$		−	419.120i		−	1.59648i	0.602342	−	0.798238i	$-0.294234\pi$
$42$	−93.3119	−	384.919i	−0.342818	−	1.41415i
$43$	205.038			0.727163			0.363581	−	0.931562i	$-0.381554\pi$
$43$	205.038			0.727163			0.363581	+	0.931562i	$0.381554\pi$
$44$	−175.677	+	8.18402i	−0.601916	+	0.0280406i
$45$	147.965	+	323.388i	0.490162	+	1.07129i
$46$	19.1522	−	20.0652i	0.0613879	−	0.0643143i
$47$	566.089			1.75686			0.878432	−	0.477868i	$-0.158590\pi$
$47$	566.089			1.75686			0.878432	+	0.477868i	$0.158590\pi$
$48$	295.320	+	152.899i	0.888037	+	0.459772i
$49$	−383.250			−1.11735
$50$	94.6949	−	99.2090i	0.267838	−	0.280606i
$51$	17.1087	−	26.6426i	0.0469746	−	0.0731511i
$52$	80.1740	−	3.73496i	0.213810	−	0.00996049i
$53$	−342.173			−0.886813			−0.443407	−	0.896321i	$-0.646230\pi$
$53$	−342.173			−0.886813			−0.443407	+	0.896321i	$0.646230\pi$
$54$	−245.466	−	311.786i	−0.618586	−	0.785717i
$55$		−	289.555i		−	0.709885i
$56$	400.049	−	460.218i	0.954622	−	1.09820i
$57$	175.723	+	112.842i	0.408334	+	0.262215i
$58$	−321.255	+	336.570i	−0.727291	+	0.761962i
$59$		−	3.70288i		−	0.00817075i	−0.999992	−	0.00408538i	$-0.998700\pi$
$59$		−	3.70288i		−	0.00817075i	0.999992	−	0.00408538i	$-0.00130042\pi$
$60$	−274.093	+	473.985i	−0.589754	+	1.01985i
$61$		−	717.005i		−	1.50497i	−0.658610	−	0.752484i	$-0.728855\pi$
$61$		−	717.005i		−	1.50497i	0.658610	−	0.752484i	$-0.271145\pi$
$62$	96.1915	+	91.8146i	0.197038	+	0.188072i
$63$	−661.654	+	302.737i	−1.32318	+	0.605417i
$64$	71.2716	+	507.015i	0.139202	+	0.990264i
$65$			132.145i			0.252162i
$66$	76.1184	+	313.995i	0.141963	+	0.585607i
$67$	−238.701			−0.435253			−0.217627	−	0.976032i	$-0.569832\pi$
$67$	−238.701			−0.435253			−0.217627	+	0.976032i	$0.569832\pi$
$68$	48.6953	−	2.26850i	0.0868408	−	0.00404554i
$69$	−42.8791	−	27.5351i	−0.0748121	−	0.0480412i
$70$	726.250	+	693.205i	1.24005	+	1.18363i
$71$	−517.054			−0.864268			−0.432134	−	0.901809i	$-0.642239\pi$
$71$	−517.054			−0.864268			−0.432134	+	0.901809i	$0.642239\pi$
$72$	172.626	−	586.045i	0.282558	−	0.959250i
$73$	984.195			1.57796			0.788982	−	0.614417i	$-0.210609\pi$
$73$	984.195			1.57796			0.788982	+	0.614417i	$0.210609\pi$
$74$	420.576	+	401.439i	0.660689	+	0.630627i
$75$	−212.008	−	136.143i	−0.326408	−	0.209605i
$76$	14.9621	+	321.173i	0.0225824	+	0.484751i
$77$	592.432			0.876804
$78$	−34.7383	−	143.298i	−0.0504274	−	0.208017i
$79$		−	329.100i		−	0.468691i	−0.972153	−	0.234346i	$-0.924705\pi$
$79$		−	329.100i		−	0.468691i	0.972153	−	0.234346i	$-0.0752948\pi$
$80$	−839.327	+	78.3712i	−1.17299	+	0.109527i
$81$	−476.609	+	551.621i	−0.653784	+	0.756681i
$82$	−857.522	−	818.503i	−1.15485	−	1.10230i
$83$		−	625.333i		−	0.826978i	−0.910509	−	0.413489i	$-0.864310\pi$
$83$		−	625.333i		−	0.826978i	0.910509	−	0.413489i	$-0.135690\pi$
$84$	−969.777	−	560.796i	−1.25966	−	0.728427i
$85$			80.2609i			0.102418i
$86$	400.421	−	419.509i	0.502075	−	0.526009i
$87$	719.244	+	461.868i	0.886334	+	0.569167i
$88$	−326.337	+	375.419i	−0.395314	+	0.454770i
$89$			238.583i			0.284154i	0.989856	+	0.142077i	$0.0453781\pi$
$89$			238.583i			0.284154i	−0.989856	+	0.142077i	$0.954622\pi$
$90$	950.616	+	328.811i	1.11338	+	0.385109i
$91$	−270.369			−0.311455
$92$	−3.65097	−	78.3712i	−0.00413739	−	0.0888127i
$93$	132.002	−	205.560i	0.147182	−	0.229199i
$94$	1105.52	−	1158.22i	1.21304	−	1.27087i
$95$	−529.366			−0.571703
$96$	889.566	−	305.628i	0.945739	−	0.324928i
$97$	−1001.01			−1.04781			−0.523903	−	0.851778i	$-0.675525\pi$
$97$	−1001.01			−1.04781			−0.523903	+	0.851778i	$0.675525\pi$
$98$	−748.453	+	784.132i	−0.771481	+	0.808258i
$99$	539.739	−	246.955i	0.547937	−	0.250706i
$100$	−18.0516	−	387.493i	−0.0180516	−	0.387493i
$101$	598.875			0.590003			0.295001	−	0.955497i	$-0.404680\pi$
$101$	598.875			0.590003			0.295001	+	0.955497i	$0.404680\pi$
$102$	−21.0990	−	87.0352i	−0.0204815	−	0.0844879i
$103$			1225.30i			1.17216i	0.810253	+	0.586080i	$0.199330\pi$
$103$			1225.30i			1.17216i	−0.810253	+	0.586080i	$0.800670\pi$
$104$	148.931	−	171.331i	0.140422	−	0.161542i
$105$	996.619	−	1551.98i	0.926286	−	1.44246i
$106$	−668.234	+	700.088i	−0.612307	+	0.641496i
$107$			324.370i			0.293066i	0.989206	+	0.146533i	$0.0468114\pi$
$107$			324.370i			0.293066i	−0.989206	+	0.146533i	$0.953189\pi$
$108$	−1117.29	−	106.666i	−0.995474	−	0.0950361i
$109$			1208.38i			1.06186i	0.847417	+	0.530928i	$0.178157\pi$
$109$			1208.38i			1.06186i	−0.847417	+	0.530928i	$0.821843\pi$
$110$	−592.432	−	565.476i	−0.513511	−	0.490146i
$111$	577.149	−	898.764i	0.493518	−	0.768531i
$112$	−160.348	−	1717.27i	−0.135281	−	1.44881i
$113$			1823.44i			1.51800i	0.651089	+	0.759002i	$0.274313\pi$
$113$			1823.44i			1.51800i	−0.651089	+	0.759002i	$0.725687\pi$
$114$	574.046	−	139.160i	0.471617	−	0.114329i
$115$	129.174			0.104743
$116$	61.2406	+	1314.58i	0.0490176	+	1.05221i
$117$	−246.322	+	112.703i	−0.194636	+	0.0890549i
$118$	−7.57612	−	7.23140i	−0.00591050	−	0.00564156i
$119$	−164.214			−0.126500
$120$	434.498	+	1486.45i	0.330534	+	1.13078i
$121$	847.728			0.636911
$122$	−1467.00	−	1400.25i	−1.08865	−	1.03912i
$123$	−1176.76	+	1832.51i	−0.862642	+	1.34335i
$124$	375.707	−	17.5025i	0.272092	−	0.0126756i
$125$	−1007.77			−0.721098
$126$	−672.750	+	1944.97i	−0.475662	+	1.37517i
$127$			543.520i			0.379760i	0.981807	+	0.189880i	$0.0608100\pi$
$127$			543.520i			0.379760i	−0.981807	+	0.189880i	$0.939190\pi$
$128$	1176.54	+	844.333i	0.812443	+	0.583041i
$129$	−896.484	−	575.684i	−0.611868	−	0.392916i
$130$	270.369	+	258.067i	0.182407	+	0.174108i
$131$		−	1246.47i		−	0.831335i	−0.909517	−	0.415668i	$-0.863548\pi$
$131$		−	1246.47i		−	0.831335i	0.909517	−	0.415668i	$-0.136452\pi$
$132$	791.087	+	457.465i	0.521631	+	0.301645i
$133$		−	1083.09i		−	0.706132i
$134$	−466.162	+	488.384i	−0.300524	+	0.314850i
$135$	261.032	−	1829.38i	0.166415	−	1.16628i
$136$	90.4563	−	104.061i	0.0570335	−	0.0656115i
$137$		−	2246.38i		−	1.40088i	−0.713709	−	0.700442i	$-0.752986\pi$
$137$		−	2246.38i		−	1.40088i	0.713709	−	0.700442i	$-0.247014\pi$
$138$	−140.076	+	33.9572i	−0.0864063	+	0.0209466i
$139$	1733.77			1.05796			0.528979	−	0.848635i	$-0.322575\pi$
$139$	1733.77			1.05796			0.528979	+	0.848635i	$0.322575\pi$
$140$	2836.60	−	132.145i	1.71240	−	0.0797734i
$141$	−2475.10	−	1589.41i	−1.47831	−	0.949306i
$142$	−1009.76	+	1057.90i	−0.596741	+	0.625188i
$143$	220.551			0.128975
$144$	−861.928	−	1497.69i	−0.498801	−	0.866717i
$145$	−2166.73			−1.24094
$146$	1922.05	−	2013.67i	1.08952	−	1.14146i
$147$	1675.68	+	1076.05i	0.940187	+	0.603749i
$148$	1642.70	−	76.5260i	0.912356	−	0.0425027i
$149$	1196.89			0.658074			0.329037	−	0.944317i	$-0.393276\pi$
$149$	1196.89			0.658074			0.329037	+	0.944317i	$0.393276\pi$
$150$	−692.582	+	167.895i	−0.376994	+	0.0913906i
$151$		−	2505.09i		−	1.35007i	−0.737784	−	0.675037i	$-0.764128\pi$
$151$		−	2505.09i		−	1.35007i	0.737784	−	0.675037i	$-0.235872\pi$
$152$	686.342	+	596.610i	0.366248	+	0.318365i
$153$	−149.609	+	68.4527i	−0.0790531	+	0.0361704i
$154$	1156.97	−	1212.12i	0.605397	−	0.634256i
$155$			619.250i			0.320899i
$156$	−361.030	−	208.774i	−0.185292	−	0.107149i
$157$			2717.53i			1.38142i	0.723133	+	0.690709i	$0.242701\pi$
$157$			2717.53i			1.38142i	−0.723133	+	0.690709i	$0.757299\pi$
$158$	−673.340	−	642.702i	−0.339038	−	0.323612i
$159$	1496.08	+	960.718i	0.746205	+	0.479182i
$160$	−1478.78	+	1870.32i	−0.730675	+	0.924136i
$161$			264.290i			0.129372i
$162$	197.845	+	2052.41i	0.0959519	+	0.995386i
$163$	−2009.71			−0.965723			−0.482861	−	0.875697i	$-0.660402\pi$
$163$	−2009.71			−0.965723			−0.482861	+	0.875697i	$0.660402\pi$
$164$	−3349.33	+	156.030i	−1.59475	+	0.0742923i
$165$	−812.984	+	1266.02i	−0.383580	+	0.597329i
$166$	−1279.43	−	1221.22i	−0.598213	−	0.570994i
$167$	4.79686			0.00222271			0.00111135	−	0.999999i	$-0.499646\pi$
$167$	4.79686			0.00222271			0.00111135	+	0.999999i	$0.499646\pi$
$168$	−3041.28	+	888.985i	−1.39667	+	0.408254i
$169$	2096.35			0.954186
$170$	164.214	+	156.742i	0.0740863	+	0.0707153i
$171$	−451.484	−	986.752i	−0.201906	−	0.441280i
$172$	−76.3318	−	1638.53i	−0.0338386	−	0.726375i
$173$	1501.84			0.660016			0.330008	−	0.943978i	$-0.392948\pi$
$173$	1501.84			0.660016			0.330008	+	0.943978i	$0.392948\pi$
$174$	2349.60	−	569.590i	1.02370	−	0.248164i
$175$			1306.73i			0.564456i
$176$	130.803	+	1400.85i	0.0560205	+	0.599959i
$177$	−10.3966	+	16.1901i	−0.00441500	+	0.00687525i
$178$	488.142	+	465.931i	0.205549	+	0.196196i
$179$			360.443i			0.150507i	0.997164	+	0.0752535i	$0.0239766\pi$
$179$			360.443i			0.150507i	−0.997164	+	0.0752535i	$0.976023\pi$
$180$	2529.22	−	1302.83i	1.04732	−	0.539484i
$181$		−	1143.06i		−	0.469410i	−0.972067	−	0.234705i	$-0.924588\pi$
$181$		−	1143.06i		−	0.469410i	0.972067	−	0.234705i	$-0.0754125\pi$
$182$	−528.007	+	553.177i	−0.215047	+	0.225298i
$183$	−2013.13	+	3134.95i	−0.813197	+	1.26635i
$184$	−167.478	−	145.582i	−0.0671013	−	0.0583285i
$185$			2707.53i			1.07601i
$186$	−162.789	−	671.516i	−0.0641733	−	0.264720i
$187$	133.957			0.0523843
$188$	−210.744	−	4523.81i	−0.0817559	−	1.75496i
$189$	3742.93	+	534.073i	1.44052	+	0.205546i
$190$	−1033.80	+	1083.09i	−0.394737	+	0.413554i
$191$	−1904.00			−0.721302			−0.360651	−	0.932701i	$-0.617446\pi$
$191$	−1904.00			−0.721302			−0.360651	+	0.932701i	$0.617446\pi$
$192$	1111.92	−	2416.92i	0.417949	−	0.908470i
$193$	934.152			0.348403			0.174201	−	0.984710i	$-0.444266\pi$
$193$	934.152			0.348403			0.174201	+	0.984710i	$0.444266\pi$
$194$	−1954.88	+	2048.07i	−0.723467	+	0.757954i
$195$	371.023	−	577.775i	0.136254	−	0.212181i
$196$	142.677	+	3062.68i	0.0519959	+	1.11614i
$197$	−1268.62			−0.458808			−0.229404	−	0.973331i	$-0.573678\pi$
$197$	−1268.62			−0.458808			−0.229404	+	0.973331i	$0.573678\pi$
$198$	548.790	−	1586.59i	0.196974	−	0.569465i
$199$			2293.01i			0.816820i	0.912798	+	0.408410i	$0.133917\pi$
$199$			2293.01i			0.816820i	−0.912798	+	0.408410i	$0.866083\pi$
$200$	−828.066	−	719.805i	−0.292765	−	0.254489i
$201$	1043.67	+	670.200i	0.366242	+	0.235185i
$202$	1169.55	−	1225.30i	0.407372	−	0.426792i
$203$		−	4433.14i		−	1.53274i
$204$	−219.279	−	126.803i	−0.0752578	−	0.0435196i
$205$		−	5520.45i		−	1.88080i
$206$	2506.97	+	2392.90i	0.847909	+	0.809328i
$207$	110.169	+	240.783i	0.0369917	+	0.0808481i
$208$	−59.6946	−	639.307i	−0.0198994	−	0.213115i
$209$			883.519i			0.292413i
$210$	−1229.06	−	5069.97i	−0.403873	−	1.66601i
$211$	−2663.70			−0.869084			−0.434542	−	0.900652i	$-0.643090\pi$
$211$	−2663.70			−0.869084			−0.434542	+	0.900652i	$0.643090\pi$
$212$	127.385	+	2734.42i	0.0412680	+	0.885853i
$213$	2260.71	+	1451.73i	0.727235	+	0.467000i
$214$	663.663	+	633.466i	0.211996	+	0.202350i
$215$	2700.66			0.856668
$216$	−2400.20	+	2077.67i	−0.756079	+	0.654480i
$217$	−1266.99			−0.396354
$218$	2472.36	+	2359.87i	0.768117	+	0.733167i
$219$	−4303.18	−	2763.32i	−1.32777	−	0.852639i
$220$	−2313.93	+	107.796i	−0.709116	+	0.0330346i
$221$	−61.1339			−0.0186078
$222$	−711.757	−	2936.06i	−0.215180	−	0.887636i
$223$		−	5227.96i		−	1.56991i	−0.619552	−	0.784956i	$-0.712686\pi$
$223$		−	5227.96i		−	1.56991i	0.619552	−	0.784956i	$-0.287314\pi$
$224$	−3826.69	−	3025.60i	−1.14143	−	0.902483i
$225$	544.712	+	1190.51i	0.161396	+	0.352743i
$226$	3730.76	+	3561.01i	1.09808	+	1.04812i
$227$			5531.45i			1.61734i	0.588265	+	0.808669i	$0.299811\pi$
$227$			5531.45i			1.61734i	−0.588265	+	0.808669i	$0.700189\pi$
$228$	836.338	−	1446.27i	0.242929	−	0.420094i
$229$			782.326i			0.225754i	0.993609	+	0.112877i	$0.0360065\pi$
$229$			782.326i			0.225754i	−0.993609	+	0.112877i	$0.963993\pi$
$230$	252.264	−	264.290i	0.0723209	−	0.0757685i
$231$	−2590.28	−	1663.37i	−0.737783	−	0.473774i
$232$	2809.24	+	2441.96i	0.794981	+	0.691046i
$233$		−	3918.64i		−	1.10180i	−0.834573	−	0.550898i	$-0.814285\pi$
$233$		−	3918.64i		−	1.10180i	0.834573	−	0.550898i	$-0.185715\pi$
$234$	−250.452	+	724.075i	−0.0699683	+	0.202283i
$235$	7456.26			2.06976
$236$	−29.5910	+	1.37851i	−0.00816190	+	0.000380227i
$237$	−924.012	+	1438.92i	−0.253253	+	0.394378i
$238$	−320.696	+	335.984i	−0.0873430	+	0.0915066i
$239$	−4134.14			−1.11889			−0.559446	−	0.828867i	$-0.688986\pi$
$239$	−4134.14			−1.11889			−0.559446	+	0.828867i	$0.688986\pi$
$240$	3889.82	+	2013.91i	1.04619	+	0.541656i
$241$	1221.11			0.326384			0.163192	−	0.986594i	$-0.447821\pi$
$241$	1221.11			0.326384			0.163192	+	0.986594i	$0.447821\pi$
$242$	1655.54	−	1734.46i	0.439760	−	0.460724i
$243$	3632.65	−	1073.67i	0.958990	−	0.283440i
$244$	−5729.83	+	266.928i	−1.50334	+	0.0700340i
$245$	−5047.99			−1.31634
$246$	1451.22	+	5986.39i	0.376123	+	1.55154i
$247$		−	403.213i		−	0.103870i
$248$	697.911	−	802.879i	0.178699	−	0.205576i
$249$	−1755.74	+	2734.13i	−0.446850	+	0.695857i
$250$	−1968.07	+	2061.89i	−0.497888	+	0.521622i
$251$			4399.34i			1.10631i	0.833078	+	0.553156i	$0.186577\pi$
$251$			4399.34i			1.10631i	−0.833078	+	0.553156i	$0.813423\pi$
$252$	2665.59	+	5174.80i	0.666336	+	1.29358i
$253$		−	215.592i		−	0.0535738i
$254$	1112.04	+	1061.45i	0.274708	+	0.262209i
$255$	225.348	−	350.923i	0.0553406	−	0.0861791i
$256$	4025.19	−	758.308i	0.982713	−	0.185134i
$257$		−	3796.23i		−	0.921409i	−0.887553	−	0.460705i	$-0.847597\pi$
$257$		−	3796.23i		−	0.921409i	0.887553	−	0.460705i	$-0.152403\pi$
$258$	−2928.61	+	709.951i	−0.706694	+	0.171316i
$259$	−5539.63			−1.32902
$260$	1056.01	−	49.1951i	0.251889	−	0.0117344i
$261$	−1847.95	−	4038.84i	−0.438258	−	0.957846i
$262$	−2550.29	−	2434.25i	−0.601365	−	0.574002i
$263$	6525.99			1.53007			0.765037	−	0.643986i	$-0.222720\pi$
$263$	6525.99			1.53007			0.765037	+	0.643986i	$0.222720\pi$
$264$	2480.90	−	725.182i	0.578366	−	0.169060i
$265$	−4506.94			−1.04475
$266$	−2216.00	−	2115.17i	−0.510796	−	0.487554i
$267$	669.868	−	1043.15i	0.153540	−	0.239100i
$268$	88.8639	+	1907.54i	0.0202546	+	0.434782i
$269$	−772.537			−0.175102			−0.0875509	−	0.996160i	$-0.527904\pi$
$269$	−772.537			−0.175102			−0.0875509	+	0.996160i	$0.527904\pi$
$270$	−3233.16	−	4106.70i	−0.728755	−	0.925651i
$271$			3732.58i			0.836673i	0.908292	+	0.418336i	$0.137387\pi$
$271$			3732.58i			0.836673i	−0.908292	+	0.418336i	$0.862613\pi$
$272$	−36.2567	−	388.296i	−0.00808231	−	0.0865585i
$273$	1182.13	+	759.115i	0.262072	+	0.168292i
$274$	−4596.11	−	4386.98i	−1.01336	−	0.967252i
$275$		−	1065.96i		−	0.233744i
$276$	−204.079	+	352.912i	−0.0445078	+	0.0769667i
$277$			6502.55i			1.41047i	0.708973	+	0.705236i	$0.249159\pi$
$277$			6502.55i			1.41047i	−0.708973	+	0.705236i	$0.750841\pi$
$278$	3385.89	−	3547.30i	0.730476	−	0.765297i
$279$	−1154.30	+	528.144i	−0.247692	+	0.113330i
$280$	5269.26	−	6061.77i	1.12464	−	1.29379i
$281$		−	548.243i		−	0.116389i	−0.998305	−	0.0581947i	$-0.981466\pi$
$281$		−	548.243i		−	0.116389i	0.998305	−	0.0581947i	$-0.0185344\pi$
$282$	−8085.59	+	1960.10i	−1.70741	+	0.413910i
$283$	−664.623			−0.139603			−0.0698017	−	0.997561i	$-0.522237\pi$
$283$	−664.623			−0.139603			−0.0698017	+	0.997561i	$0.522237\pi$
$284$	192.490	+	4131.95i	0.0402189	+	0.863332i
$285$	2314.54	+	1486.30i	0.481057	+	0.308915i
$286$	430.717	−	451.250i	0.0890519	−	0.0932970i
$287$	11294.9			2.32305
$288$	−4747.54	−	1161.34i	−0.971360	−	0.237613i
$289$	4875.87			0.992442
$290$	−4231.42	+	4433.14i	−0.856820	+	0.897665i
$291$	4376.70	+	2810.53i	0.881673	+	0.566173i
$292$	−366.398	−	7865.03i	−0.0734308	−	1.57625i
$293$	5112.98			1.01947			0.509733	−	0.860332i	$-0.329744\pi$
$293$	5112.98			1.01947			0.509733	+	0.860332i	$0.329744\pi$
$294$	5474.05	−	1327.02i	1.08589	−	0.263242i
$295$		−	48.7726i		−	0.00962594i
$296$	3051.46	−	3510.41i	0.599198	−	0.689320i
$297$	−3053.27	−	435.666i	−0.596527	−	0.0851175i
$298$	2337.42	−	2448.84i	0.454373	−	0.476033i
$299$			98.3902i			0.0190303i
$300$	−1009.04	+	1744.91i	−0.194189	+	0.335808i
$301$			5525.57i			1.05810i
$302$	−5125.42	−	4892.21i	−0.976606	−	0.932169i
$303$	−2618.45	−	1681.46i	−0.496455	−	0.318803i
$304$	2561.03	−	239.134i	0.483175	−	0.0451160i
$305$		−	9444.05i		−	1.77300i
$306$	−152.117	+	439.782i	−0.0284182	+	0.0821590i
$307$	594.602			0.110540			0.0552699	−	0.998471i	$-0.482398\pi$
$307$	594.602			0.110540			0.0552699	+	0.998471i	$0.482398\pi$
$308$	−220.551	−	4734.32i	−0.0408022	−	0.875854i
$309$	3440.27	−	5357.36i	0.633367	−	0.986310i
$310$	1266.99	+	1209.34i	0.232129	+	0.221567i
$311$	−7168.24			−1.30699			−0.653495	−	0.756931i	$-0.726698\pi$
$311$	−7168.24			−1.30699			−0.653495	+	0.756931i	$0.726698\pi$
$312$	−1132.21	+	330.953i	−0.205445	+	0.0600529i
$313$	−3774.51			−0.681623			−0.340811	−	0.940132i	$-0.610702\pi$
$313$	−3774.51			−0.681623			−0.340811	+	0.940132i	$0.610702\pi$
$314$	5560.08	+	5307.09i	0.999279	+	0.953811i
$315$	−8715.00	+	3987.51i	−1.55884	+	0.713240i
$316$	−2629.95	+	122.518i	−0.468184	+	0.0218106i
$317$	−9400.75			−1.66561			−0.832805	−	0.553566i	$-0.813267\pi$
$317$	−9400.75			−1.66561			−0.832805	+	0.553566i	$0.813267\pi$
$318$	4887.34	−	1184.79i	0.861851	−	0.208929i
$319$			3616.29i			0.634714i
$320$	938.756	+	6678.16i	0.163994	+	1.16663i
$321$	910.733	−	1418.24i	0.158356	−	0.246599i
$322$	540.739	+	516.134i	0.0935844	+	0.0893262i
$323$		−	244.900i		−	0.0421876i
$324$	4585.62	+	3603.38i	0.786285	+	0.617863i
$325$			486.473i			0.0830297i
$326$	−3924.79	+	4111.88i	−0.666791	+	0.698577i
$327$	3392.78	−	5283.40i	0.573765	−	0.893494i
$328$	−6221.69	+	7157.45i	−1.04736	+	1.20489i
$329$			15255.6i			2.55643i
$330$	1002.60	+	4135.79i	0.167246	+	0.689902i
$331$	9218.16			1.53074			0.765371	−	0.643589i	$-0.222555\pi$
$331$	9218.16			1.53074			0.765371	+	0.643589i	$0.222555\pi$
$332$	−4997.24	+	232.800i	−0.826082	+	0.0384836i
$333$	−5046.91	+	2309.19i	−0.830538	+	0.380009i
$334$	9.36785	−	9.81441i	0.00153469	−	0.00160785i
$335$	−3144.06			−0.512771
$336$	−4120.48	+	7958.59i	−0.669019	+	1.29219i
$337$	2977.58			0.481302			0.240651	−	0.970612i	$-0.422639\pi$
$337$	2977.58			0.481302			0.240651	+	0.970612i	$0.422639\pi$
$338$	4093.98	−	4289.14i	0.658825	−	0.690232i
$339$	5119.65	−	7972.57i	0.820240	−	1.27732i
$340$	641.392	−	29.8797i	0.102307	−	0.00476603i
$341$	1033.54			0.164132
$342$	−2900.61	−	1003.30i	−0.458617	−	0.158632i
$343$		−	1084.70i		−	0.170752i
$344$	−3501.50	−	3043.72i	−0.548804	−	0.477053i
$345$	−564.783	−	362.680i	−0.0881359	−	0.0565972i
$346$	2932.96	−	3072.77i	0.455714	−	0.477438i
$347$			2497.80i			0.386424i	0.981157	+	0.193212i	$0.0618905\pi$
$347$			2497.80i			0.386424i	−0.981157	+	0.193212i	$0.938110\pi$
$348$	3423.18	−	5919.66i	0.527304	−	0.911860i
$349$		−	8874.07i		−	1.36108i	−0.732710	−	0.680541i	$-0.761745\pi$
$349$		−	8874.07i		−	1.36108i	0.732710	−	0.680541i	$-0.238255\pi$
$350$	2673.59	+	2551.94i	0.408312	+	0.389733i
$351$	1393.42	+	198.826i	0.211896	+	0.0302351i
$352$	3121.59	+	2468.11i	0.472674	+	0.373723i
$353$			2525.66i			0.380814i	0.981705	+	0.190407i	$0.0609808\pi$
$353$			2525.66i			0.380814i	−0.981705	+	0.190407i	$0.939019\pi$
$354$	12.8214	+	52.8892i	0.00192499	+	0.00794076i
$355$	−6810.39			−1.01819
$356$	1906.59	−	88.8199i	0.283846	−	0.0132232i
$357$	717.991	+	461.064i	0.106443	+	0.0683532i
$358$	737.468	+	703.912i	0.108873	+	0.103919i
$359$	−9422.15			−1.38519			−0.692594	−	0.721328i	$-0.743532\pi$
$359$	−9422.15			−1.38519			−0.692594	+	0.721328i	$0.743532\pi$
$360$	2273.75	−	7719.10i	0.332880	−	1.13009i
$361$	−5243.75			−0.764506
$362$	−2338.72	−	2232.30i	−0.339558	−	0.324108i
$363$	−3706.51	−	2380.16i	−0.535926	−	0.344149i
$364$	100.653	+	2160.61i	0.0144936	+	0.311118i
$365$	12963.4			1.85899
$366$	2482.65	+	10241.2i	0.354564	+	1.46261i
$367$			613.530i			0.0872643i	0.999048	+	0.0436322i	$0.0138930\pi$
$367$			613.530i			0.0872643i	−0.999048	+	0.0436322i	$0.986107\pi$
$368$	−624.931	+	58.3523i	−0.0885239	+	0.00826582i
$369$	10290.3	−	4708.26i	1.45173	−	0.664234i
$370$	5539.63	+	5287.57i	0.778356	+	0.742940i
$371$		−	9221.23i		−	1.29041i
$372$	−1691.84	−	978.344i	−0.235800	−	0.136357i
$373$		−	10759.8i		−	1.49362i	−0.665039	−	0.746809i	$-0.731585\pi$
$373$		−	10759.8i		−	1.49362i	0.665039	−	0.746809i	$-0.268415\pi$
$374$	261.605	−	274.076i	0.0361692	−	0.0378934i
$375$	4406.23	+	2829.50i	0.606765	+	0.389639i
$376$	−9667.30	−	8403.41i	−1.32594	−	1.15259i
$377$		−	1650.37i		−	0.225460i
$378$	8402.33	−	6615.06i	1.14330	−	0.900112i
$379$	−10132.1			−1.37322			−0.686610	−	0.727026i	$-0.740902\pi$
$379$	−10132.1			−1.37322			−0.686610	+	0.727026i	$0.740902\pi$
$380$	197.073	+	4230.34i	0.0266043	+	0.571084i
$381$	1526.04	−	2376.42i	0.205200	−	0.319548i
$382$	−3718.35	+	3895.60i	−0.498029	+	0.521770i
$383$	−9452.43			−1.26109			−0.630544	−	0.776154i	$-0.717168\pi$
$383$	−9452.43			−1.26109			−0.630544	+	0.776154i	$0.717168\pi$
$384$	−2773.55	−	6995.04i	−0.368586	−	0.929594i
$385$	7803.24			1.03296
$386$	1824.31	−	1911.28i	0.240557	−	0.252025i
$387$	2303.33	+	5034.11i	0.302545	+	0.661235i
$388$	372.658	+	7999.41i	0.0487598	+	1.04667i
$389$	3385.08			0.441209			0.220605	−	0.975363i	$-0.429197\pi$
$389$	3385.08			0.441209			0.220605	+	0.975363i	$0.429197\pi$
$390$	−457.556	−	1887.46i	−0.0594084	−	0.245064i
$391$			59.7593i			0.00772930i
$392$	6544.89	+	5689.22i	0.843283	+	0.733033i
$393$	−3499.72	+	5449.94i	−0.449205	+	0.699524i
$394$	−2477.50	+	2595.60i	−0.316788	+	0.331889i
$395$		−	4334.75i		−	0.552164i
$396$	−2174.44	−	4221.30i	−0.275933	−	0.535677i
$397$			4125.91i			0.521596i	0.965393	+	0.260798i	$0.0839857\pi$
$397$			4125.91i			0.521596i	−0.965393	+	0.260798i	$0.916014\pi$
$398$	4691.52	+	4478.05i	0.590865	+	0.563980i
$399$	−3040.98	+	4735.56i	−0.381552	+	0.594172i
$400$	−3089.86	+	288.513i	−0.386233	+	0.0360641i
$401$			8829.27i			1.09953i	0.835318	+	0.549767i	$0.185283\pi$
$401$			8829.27i			1.09953i	−0.835318	+	0.549767i	$0.814717\pi$
$402$	3409.42	−	826.511i	0.423001	−	0.102544i
$403$	−471.676			−0.0583024
$404$	−222.950	−	4785.81i	−0.0274559	−	0.589363i
$405$	−6277.66	+	7265.69i	−0.770221	+	0.891444i
$406$	−9070.23	−	8657.52i	−1.10874	−	1.05829i
$407$	4518.91			0.550354
$408$	−687.672	+	201.011i	−0.0834433	+	0.0243910i
$409$	1648.22			0.199264			0.0996320	−	0.995024i	$-0.468233\pi$
$409$	1648.22			0.199264			0.0996320	+	0.995024i	$0.468233\pi$
$410$	−11294.9	−	10780.9i	−1.36052	−	1.29862i
$411$	−6307.15	+	9821.81i	−0.756956	+	1.17877i
$412$	9791.79	−	456.157i	1.17089	−	0.0545467i
$413$	99.7891			0.0118893
$414$	707.793	+	244.821i	0.0840245	+	0.0290635i
$415$		−	8236.59i		−	0.974261i
$416$	−1424.60	−	1126.37i	−0.167901	−	0.132752i
$417$	−7580.51	−	4867.89i	−0.890214	−	0.571658i
$418$	1807.68	+	1725.43i	0.211523	+	0.201899i
$419$		−	11553.7i		−	1.34710i	−0.739143	−	0.673549i	$-0.764769\pi$
$419$		−	11553.7i		−	1.34710i	0.739143	−	0.673549i	$-0.235231\pi$
$420$	−12773.4	−	7386.54i	−1.48400	−	0.858158i
$421$			7651.40i			0.885763i	0.896580	+	0.442882i	$0.146044\pi$
$421$			7651.40i			0.885763i	−0.896580	+	0.442882i	$0.853956\pi$
$422$	−5201.97	+	5449.95i	−0.600066	+	0.628671i
$423$	6359.27	+	13898.7i	0.730965	+	1.59758i
$424$	5843.41	+	5079.45i	0.669295	+	0.581792i
$425$			295.469i			0.0337232i
$426$	7385.21	−	1790.32i	0.839940	−	0.203618i
$427$	19322.6			2.18990
$428$	2592.15	−	120.757i	0.292748	−	0.0136379i
$429$	−964.313	−	619.241i	−0.108526	−	0.0696906i
$430$	5274.15	−	5525.57i	0.591494	−	0.619690i
$431$	14803.7			1.65445			0.827224	−	0.561873i	$-0.189919\pi$
$431$	14803.7			1.65445			0.827224	+	0.561873i	$0.189919\pi$
$432$	−436.455	+	8968.34i	−0.0486086	+	0.998818i
$433$	1938.03			0.215094			0.107547	−	0.994200i	$-0.465700\pi$
$433$	1938.03			0.215094			0.107547	+	0.994200i	$0.465700\pi$
$434$	−2474.31	+	2592.27i	−0.273666	+	0.286711i
$435$	9473.54	+	6083.51i	1.04419	+	0.670533i
$436$	9656.61	−	449.859i	1.06071	−	0.0494136i
$437$	−394.146			−0.0431455
$438$	−14057.5	+	3407.81i	−1.53355	+	0.371761i
$439$			5276.73i			0.573678i	0.957979	+	0.286839i	$0.0926045\pi$
$439$			5276.73i			0.573678i	−0.957979	+	0.286839i	$0.907395\pi$
$440$	−4298.36	+	4944.84i	−0.465718	+	0.535764i
$441$	−4305.31	−	9409.58i	−0.464886	−	1.01604i
$442$	−119.389	+	125.080i	−0.0128479	+	0.0134603i
$443$			9203.98i			0.987121i	0.869712	+	0.493560i	$0.164305\pi$
$443$			9203.98i			0.987121i	−0.869712	+	0.493560i	$0.835695\pi$
$444$	−7397.19	−	4277.59i	−0.790664	−	0.457220i
$445$			3142.50i			0.334761i
$446$	−10696.4	−	10209.7i	−1.13563	−	1.08396i
$447$	−5233.14	−	3360.50i	−0.553734	−	0.355585i
$448$	−13663.6	+	1920.70i	−1.44094	+	0.202555i
$449$		−	3221.17i		−	0.338567i	−0.985567	−	0.169283i	$-0.945855\pi$
$449$		−	3221.17i		−	0.338567i	0.985567	−	0.169283i	$-0.0541453\pi$
$450$	3499.56	+	1210.47i	0.366602	+	0.126805i
$451$	−9213.69			−0.961986
$452$	14571.7	−	678.831i	1.51636	−	0.0706405i
$453$	−7033.52	+	10952.9i	−0.729500	+	1.13601i
$454$	11317.4	+	10802.4i	1.16994	+	1.11670i
$455$	−3561.18			−0.366924
$456$	−1325.78	−	4535.59i	−0.136152	−	0.465786i
$457$	−12015.1			−1.22985			−0.614925	−	0.788585i	$-0.710814\pi$
$457$	−12015.1			−1.22985			−0.614925	+	0.788585i	$0.710814\pi$
$458$	1600.64	+	1527.81i	0.163304	+	0.155873i
$459$	846.325	+	120.761i	0.0860633	+	0.0122802i
$460$	−48.0889	−	1032.27i	−0.00487425	−	0.104630i
$461$	4758.79			0.480778			0.240389	−	0.970677i	$-0.422725\pi$
$461$	4758.79			0.480778			0.240389	+	0.970677i	$0.422725\pi$
$462$	−8461.85	+	2051.32i	−0.852123	+	0.206571i
$463$		−	12568.3i		−	1.26156i	−0.775963	−	0.630778i	$-0.782736\pi$
$463$		−	12568.3i		−	1.26156i	0.775963	−	0.630778i	$-0.217264\pi$
$464$	10482.5	−	978.788i	1.04878	−	0.0979291i
$465$	1738.66	−	2707.53i	0.173395	−	0.270019i
$466$	−8017.55	−	7652.75i	−0.797009	−	0.760744i
$467$			15360.6i			1.52207i	0.648712	+	0.761034i	$0.275308\pi$
$467$			15360.6i			1.52207i	−0.648712	+	0.761034i	$0.724692\pi$
$468$	992.351	+	1926.48i	0.0980159	+	0.190281i
$469$		−	6432.76i		−	0.633342i
$470$	14561.4	−	15255.6i	1.42908	−	1.49720i
$471$	7630.00	−	11881.8i	0.746437	−	1.16239i
$472$	−54.9681	+	63.2354i	−0.00536041	+	0.00616662i
$473$		−	4507.44i		−	0.438165i
$474$	1139.52	+	4700.61i	0.110422	+	0.455498i
$475$	−1948.79			−0.188245
$476$	61.1339	+	1312.29i	0.00588670	+	0.126363i
$477$	−3843.87	−	8401.06i	−0.368970	−	0.806411i
$478$	−8073.61	+	8458.48i	−0.772548	+	0.809376i
$479$	−2268.94			−0.216431			−0.108216	−	0.994127i	$-0.534514\pi$
$479$	−2268.94			−0.216431			−0.108216	+	0.994127i	$0.534514\pi$
$480$	11716.9	−	4025.59i	1.11417	−	0.382797i
$481$	−2062.30			−0.195494
$482$	2384.71	−	2498.39i	0.225354	−	0.236097i
$483$	742.045	−	1155.55i	0.0699052	−	0.108860i
$484$	−315.593	−	6774.48i	−0.0296388	−	0.636221i
$485$	−13184.8			−1.23442
$486$	4897.51	−	9529.20i	0.457110	−	0.889410i
$487$		−	11478.8i		−	1.06808i	−0.845459	−	0.534040i	$-0.820673\pi$
$487$		−	11478.8i		−	1.06808i	0.845459	−	0.534040i	$-0.179327\pi$
$488$	−10643.7	+	12244.5i	−0.987331	+	1.13583i
$489$	8787.02	+	5642.66i	0.812603	+	0.521820i
$490$	−9858.27	+	10328.2i	−0.908880	+	0.952206i
$491$		−	20306.4i		−	1.86642i	−0.359325	−	0.933212i	$-0.616993\pi$
$491$		−	20306.4i		−	1.86642i	0.359325	−	0.933212i	$-0.383007\pi$
$492$	15082.3	+	8721.68i	1.38204	+	0.799194i
$493$		−	1002.39i		−	0.0915727i
$494$	−824.976	−	787.439i	−0.0751365	−	0.0717177i
$495$	7109.19	−	3252.78i	0.645524	−	0.295356i
$496$	−279.737	−	2995.88i	−0.0253237	−	0.271208i
$497$		−	13934.1i		−	1.25761i
$498$	2165.24	+	8931.78i	0.194832	+	0.803700i
$499$	1024.04			0.0918681			0.0459340	−	0.998944i	$-0.485374\pi$
$499$	1024.04			0.0918681			0.0459340	+	0.998944i	$0.485374\pi$
$500$	375.172	+	8053.39i	0.0335564	+	0.720317i
$501$	−20.9732	−	13.4681i	−0.00187029	−	0.00120102i
$502$	9001.08	+	8591.52i	0.800275	+	0.763862i
$503$	−7799.62			−0.691388			−0.345694	−	0.938347i	$-0.612356\pi$
$503$	−7799.62			−0.691388			−0.345694	+	0.938347i	$0.612356\pi$
$504$	15793.3	+	4652.10i	1.39582	+	0.411152i
$505$	7888.10			0.695080
$506$	−441.103	−	421.032i	−0.0387538	−	0.0369904i
$507$	−9165.82	−	5885.90i	−0.802896	−	0.515586i
$508$	4343.45	−	202.342i	0.379349	−	0.0176722i
$509$	298.935			0.0260315			0.0130158	−	0.999915i	$-0.495857\pi$
$509$	298.935			0.0260315			0.0130158	+	0.999915i	$0.495857\pi$
$510$	−277.906	−	1146.39i	−0.0241292	−	0.0995350i
$511$			26523.1i			2.29611i
$512$	6309.34	−	9716.48i	0.544602	−	0.838695i
$513$	−796.485	+	5581.99i	−0.0685491	+	0.480411i
$514$	−7767.11	−	7413.69i	−0.666522	−	0.636195i
$515$			16139.1i			1.38092i
$516$	−4266.74	+	7378.42i	−0.364017	+	0.629490i
$517$		−	12444.6i		−	1.05863i
$518$	−10818.4	+	11334.1i	−0.917632	+	0.961375i
$519$	−6566.47	−	4216.71i	−0.555368	−	0.356634i
$520$	1961.65	−	2256.68i	0.165431	−	0.190312i
$521$			9553.38i			0.803342i	0.915784	+	0.401671i	$0.131571\pi$
$521$			9553.38i			0.803342i	−0.915784	+	0.401671i	$0.868429\pi$
$522$	−11872.4	−	4106.57i	−0.995478	−	0.344329i
$523$	13485.0			1.12745			0.563726	−	0.825962i	$-0.309367\pi$
$523$	13485.0			1.12745			0.563726	+	0.825962i	$0.309367\pi$
$524$	−9960.99	+	464.039i	−0.830435	+	0.0386863i
$525$	3668.91	−	5713.41i	0.304999	−	0.474959i
$526$	12744.7	−	13352.2i	1.05645	−	1.10681i
$527$	−286.482			−0.0236800
$528$	3361.25	−	6492.15i	0.277044	−	0.535103i
$529$	−12070.8			−0.992095
$530$	−8801.66	+	9221.23i	−0.721358	+	0.755745i
$531$	90.9135	−	41.5970i	0.00742996	−	0.00339954i
$532$	−8655.30	+	403.213i	−0.705367	+	0.0328599i
$533$	4204.87			0.341713
$534$	−826.101	−	3407.73i	−0.0669455	−	0.276155i
$535$			4272.45i			0.345260i
$536$	4076.38	+	3543.44i	0.328494	+	0.285547i
$537$	1012.01	−	1575.96i	0.0813251	−	0.126643i
$538$	−1508.69	+	1580.61i	−0.120900	+	0.126664i
$539$			8425.15i			0.673278i
$540$	−14716.4	−	1404.95i	−1.17276	−	0.111962i
$541$			14897.0i			1.18387i	0.805986	+	0.591934i	$0.201635\pi$
$541$			14897.0i			1.18387i	−0.805986	+	0.591934i	$0.798365\pi$
$542$	7636.89	+	7289.40i	0.605226	+	0.577687i
$543$	−3209.38	+	4997.80i	−0.253642	+	0.394983i
$544$	−865.262	−	684.126i	−0.0681945	−	0.0539185i
$545$			15916.3i			1.25097i
$546$	3861.75	−	936.163i	0.302688	−	0.0733774i
$547$	−8674.79			−0.678076			−0.339038	−	0.940773i	$-0.610101\pi$
$547$	−8674.79			−0.678076			−0.339038	+	0.940773i	$0.610101\pi$
$548$	−17951.6	+	836.285i	−1.39937	+	0.0651904i
$549$	17604.0	−	8054.61i	1.36852	−	0.626161i
$550$	−2180.96	−	2081.72i	−0.169084	−	0.161391i
$551$	6611.32			0.511165
$552$	323.511	+	1106.75i	0.0249448	+	0.0853379i
$553$	8868.92			0.681998
$554$	13304.3	+	12698.9i	1.02030	+	0.973871i
$555$	7601.93	−	11838.1i	0.581413	−	0.905404i
$556$	−645.449	−	13855.1i	−0.0492322	−	1.05681i
$557$	−22222.8			−1.69050			−0.845251	−	0.534369i	$-0.820549\pi$
$557$	−22222.8			−1.69050			−0.845251	+	0.534369i	$0.820549\pi$
$558$	−1173.65	+	3393.12i	−0.0890408	+	0.257423i
$559$			2057.07i			0.155643i
$560$	−2112.03	−	22619.0i	−0.159374	−	1.70684i
$561$	−585.696	−	376.109i	−0.0440786	−	0.0283054i
$562$	−1121.71	−	1070.67i	−0.0841928	−	0.0803620i
$563$		−	8321.78i		−	0.622950i	−0.950254	−	0.311475i	$-0.899177\pi$
$563$		−	8321.78i		−	0.622950i	0.950254	−	0.311475i	$-0.100823\pi$
$564$	−11780.0	+	20371.1i	−0.879484	+	1.52088i
$565$			24017.4i			1.78836i
$566$	−1297.95	+	1359.82i	−0.0963903	+	0.100985i
$567$	−14865.6	−	12844.1i	−1.10105	−	0.951328i
$568$	8829.91	+	7675.50i	0.652280	+	0.567001i
$569$		−	12051.5i		−	0.887915i	−0.896048	−	0.443957i	$-0.853574\pi$
$569$		−	12051.5i		−	0.887915i	0.896048	−	0.443957i	$-0.146426\pi$
$570$	7561.06	−	1832.95i	0.555611	−	0.134691i
$571$	−11319.5			−0.829608			−0.414804	−	0.909911i	$-0.636150\pi$
$571$	−11319.5			−0.829608			−0.414804	+	0.909911i	$0.636150\pi$
$572$	−82.1072	−	1762.50i	−0.00600188	−	0.128835i
$573$	8324.83	+	5345.86i	0.606937	+	0.389749i
$574$	22057.9	−	23109.4i	1.60397	−	1.68043i
$575$	475.534			0.0344889
$576$	−11647.6	+	7445.52i	−0.842566	+	0.538593i
$577$	3145.14			0.226922			0.113461	−	0.993542i	$-0.463806\pi$
$577$	3145.14			0.226922			0.113461	+	0.993542i	$0.463806\pi$
$578$	9522.14	−	9976.06i	0.685240	−	0.717905i
$579$	−4084.37	−	2622.81i	−0.293162	−	0.188256i
$580$	806.632	+	17315.0i	0.0577475	+	1.23960i
$581$	16852.1			1.20334
$582$	14297.7	−	3466.03i	1.01831	−	0.246859i
$583$			7522.14i			0.534366i
$584$	−16807.4	−	14610.1i	−1.19092	−	1.03522i
$585$	−3244.43	+	1484.47i	−0.229300	+	0.104915i
$586$	9985.20	−	10461.2i	0.703899	−	0.737454i
$587$		−	8484.84i		−	0.596604i	−0.954472	−	0.298302i	$-0.903580\pi$
$587$		−	8484.84i		−	0.596604i	0.954472	−	0.298302i	$-0.0964203\pi$
$588$	7975.24	−	13791.5i	0.559343	−	0.967264i
$589$		−	1889.51i		−	0.132183i
$590$	−99.7891	−	95.2486i	−0.00696314	−	0.00664631i
$591$	5546.75	+	3561.89i	0.386062	+	0.247913i
$592$	−1223.09	−	13098.8i	−0.0849133	−	0.909390i
$593$			6571.68i			0.455087i	0.973768	+	0.227543i	$0.0730693\pi$
$593$			6571.68i			0.455087i	−0.973768	+	0.227543i	$0.926931\pi$
$594$	−6854.13	+	5396.18i	−0.473448	+	0.372741i
$595$	−2162.95			−0.149029
$596$	−445.580	−	9564.75i	−0.0306236	−	0.657361i
$597$	6438.08	−	10025.7i	0.441362	−	0.687310i
$598$	201.307	+	192.147i	0.0137660	+	0.0131396i
$599$	17732.4			1.20956			0.604779	−	0.796393i	$-0.293261\pi$
$599$	17732.4			1.20956			0.604779	+	0.796393i	$0.293261\pi$
$600$	1599.54	+	5472.15i	0.108835	+	0.372332i
$601$	22182.6			1.50557			0.752785	−	0.658266i	$-0.228710\pi$
$601$	22182.6			1.50557			0.752785	+	0.658266i	$0.228710\pi$
$602$	11305.4	+	10790.9i	0.765402	+	0.730575i
$603$	−2681.49	−	5860.61i	−0.181093	−	0.395792i
$604$	−20019.0	+	932.597i	−1.34861	+	0.0628259i
$605$	11165.9			0.750343
$606$	−8553.87	+	2073.63i	−0.573395	+	0.139002i
$607$		−	4360.03i		−	0.291546i	−0.989318	−	0.145773i	$-0.953433\pi$
$607$		−	4360.03i		−	0.291546i	0.989318	−	0.145773i	$-0.0465668\pi$
$608$	4512.20	−	5706.89i	0.300977	−	0.380666i
$609$	−12446.9	+	19382.9i	−0.828200	+	1.28971i
$610$	−19322.6	−	18443.4i	−1.28254	−	1.22418i
$611$			5679.36i			0.376043i
$612$	602.725	+	1170.09i	0.0398100	+	0.0772843i
$613$		−	14917.5i		−	0.982892i	−0.870908	−	0.491446i	$-0.836468\pi$
$613$		−	14917.5i		−	0.982892i	0.870908	−	0.491446i	$-0.163532\pi$
$614$	1161.20	−	1216.56i	0.0763231	−	0.0799615i
$615$	−15499.7	+	24136.9i	−1.01628	+	1.58259i
$616$	−10117.2	−	8794.46i	−0.661741	−	0.575225i
$617$		−	16400.2i		−	1.07010i	−0.844822	−	0.535048i	$-0.820294\pi$
$617$		−	16400.2i		−	1.07010i	0.844822	−	0.535048i	$-0.179706\pi$
$618$	−4242.65	−	17501.3i	−0.276156	−	1.13917i
$619$	3457.20			0.224486			0.112243	−	0.993681i	$-0.464197\pi$
$619$	3457.20			0.224486			0.112243	+	0.993681i	$0.464197\pi$
$620$	4948.63	−	230.535i	0.320551	−	0.0149331i
$621$	194.355	−	1362.09i	0.0125591	−	0.0880175i
$622$	−13998.9	+	14666.3i	−0.902422	+	0.945440i
$623$	−6429.57			−0.413476
$624$	−1533.98	+	2962.83i	−0.0984106	+	0.190077i
$625$	−19334.9			−1.23744
$626$	−7371.28	+	7722.67i	−0.470632	+	0.493067i
$627$	2480.65	−	3862.99i	0.158003	−	0.246050i
$628$	21716.7	−	1011.69i	1.37992	−	0.0642845i
$629$	−1252.58			−0.0794017
$630$	−8861.15	+	25618.2i	−0.560376	+	1.62008i
$631$			10766.4i			0.679247i	0.940562	+	0.339623i	$0.110300\pi$
$631$			10766.4i			0.679247i	−0.940562	+	0.339623i	$0.889700\pi$
$632$	−4885.38	+	5620.15i	−0.307484	+	0.353730i
$633$	11646.4	+	7478.86i	0.731287	+	0.469602i
$634$	−18358.8	+	19234.0i	−1.15003	+	1.20486i
$635$			7158.99i			0.447395i
$636$	7120.46	−	12313.3i	0.443938	−	0.767696i
$637$		−	3845.00i		−	0.239159i
$638$	7398.96	+	7062.30i	0.459134	+	0.438243i
$639$	−5808.42	−	12694.7i	−0.359590	−	0.785910i
$640$	15496.9	+	11121.2i	0.957137	+	0.686879i
$641$		−	4116.88i		−	0.253677i	−0.991923	−	0.126839i	$-0.959517\pi$
$641$		−	4116.88i		−	0.253677i	0.991923	−	0.126839i	$-0.0404830\pi$
$642$	−1123.14	−	4633.05i	−0.0690450	−	0.284816i
$643$	−7733.58			−0.474312			−0.237156	−	0.971472i	$-0.576215\pi$
$643$	−7733.58			−0.474312			−0.237156	+	0.971472i	$0.576215\pi$
$644$	2112.03	−	98.3902i	0.129232	−	0.00602037i
$645$	−11808.1	−	7582.64i	−0.720840	−	0.462893i
$646$	−501.066	−	478.267i	−0.0305173	−	0.0291287i
$647$	2769.95			0.168312			0.0841561	−	0.996453i	$-0.473181\pi$
$647$	2769.95			0.168312			0.0841561	+	0.996453i	$0.473181\pi$
$648$	16327.8	−	2345.12i	0.989842	−	0.142168i
$649$	−81.4021			−0.00492344
$650$	995.326	+	950.038i	0.0600614	+	0.0573285i
$651$	5539.63	+	3557.32i	0.333510	+	0.214166i
$652$	748.178	+	16060.3i	0.0449401	+	0.964676i
$653$	−13463.7			−0.806855			−0.403428	−	0.915012i	$-0.632181\pi$
$653$	−13463.7			−0.806855			−0.403428	+	0.915012i	$0.632181\pi$
$654$	−4184.08	−	17259.6i	−0.250169	−	1.03197i
$655$		−	16418.0i		−	0.979394i
$656$	2493.78	+	26707.5i	0.148424	+	1.58956i
$657$	11056.1	+	24164.0i	0.656532	+	1.43490i
$658$	31212.9	+	29792.7i	1.84925	+	1.76511i
$659$		−	5523.87i		−	0.326524i	−0.986583	−	0.163262i	$-0.947798\pi$
$659$		−	5523.87i		−	0.326524i	0.986583	−	0.163262i	$-0.0522017\pi$
$660$	10419.8	+	6025.51i	0.614532	+	0.355368i
$661$		−	5189.81i		−	0.305386i	−0.988274	−	0.152693i	$-0.951205\pi$
$661$		−	5189.81i		−	0.305386i	0.988274	−	0.152693i	$-0.0487946\pi$
$662$	18002.2	−	18860.4i	1.05691	−	1.10730i
$663$	267.295	+	171.646i	0.0156574	+	0.0100545i
$664$	−9282.86	+	10679.0i	−0.542537	+	0.624136i
$665$		−	14265.9i		−	0.831892i
$666$	−5131.55	+	14835.7i	−0.298564	+	0.863168i
$667$	−1613.26			−0.0936519
$668$	−1.78578	−	38.3333i	−0.000103434	−	0.00222030i
$669$	−14678.5	+	22858.1i	−0.848288	+	1.32100i
$670$	−6140.06	+	6432.76i	−0.354047	+	0.370924i
$671$	−15762.2			−0.906847
$672$	8236.39	+	23972.9i	0.472806	+	1.37615i
$673$	−3878.74			−0.222161			−0.111081	−	0.993811i	$-0.535431\pi$
$673$	−3878.74			−0.222161			−0.111081	+	0.993811i	$0.535431\pi$
$674$	5814.94	−	6092.14i	0.332319	−	0.348161i
$675$	960.953	−	6734.62i	0.0547957	−	0.384023i
$676$	−780.431	−	16752.6i	−0.0444032	−	0.953152i
$677$	−24431.3			−1.38696			−0.693480	−	0.720476i	$-0.743923\pi$
$677$	−24431.3			−1.38696			−0.693480	+	0.720476i	$0.743923\pi$
$678$	−6313.71	−	26044.6i	−0.357635	−	1.47527i
$679$		−	26976.3i		−	1.52467i
$680$	1191.45	−	1370.64i	0.0671910	−	0.0772968i
$681$	15530.6	−	24185.1i	0.873914	−	1.36090i
$682$	2018.40	−	2114.62i	0.113326	−	0.118729i
$683$			18958.5i			1.06212i	0.847335	+	0.531058i	$0.178205\pi$
$683$			18958.5i			1.06212i	−0.847335	+	0.531058i	$0.821795\pi$
$684$	−7717.39	+	3975.31i	−0.431406	+	0.222222i
$685$		−	29588.3i		−	1.65038i
$686$	−2219.29	−	2118.31i	−0.123517	−	0.117897i
$687$	2196.53	−	3420.55i	0.121984	−	0.189959i
$688$	−13065.6	+	1219.99i	−0.724013	+	0.0676039i
$689$		−	3432.89i		−	0.189815i
$690$	−1845.02	+	447.268i	−0.101795	+	0.0246771i
$691$	25328.5			1.39442			0.697209	−	0.716868i	$-0.254425\pi$
$691$	25328.5			1.39442			0.697209	+	0.716868i	$0.254425\pi$
$692$	−559.107	−	12001.7i	−0.0307140	−	0.659301i
$693$	6655.20	+	14545.4i	0.364805	+	0.797310i
$694$	5110.52	+	4877.98i	0.279528	+	0.266809i
$695$	22836.3			1.24638
$696$	−5426.50	−	18564.4i	−0.295533	−	1.01104i
$697$	2553.91			0.138790
$698$	−18156.4	−	17330.3i	−0.984570	−	0.939771i
$699$	−11002.3	+	17133.4i	−0.595346	+	0.927102i
$700$	10442.6	−	486.473i	0.563845	−	0.0262671i
$701$	11295.0			0.608569			0.304284	−	0.952581i	$-0.401583\pi$
$701$	11295.0			0.608569			0.304284	+	0.952581i	$0.401583\pi$
$702$	3128.03	−	2462.67i	0.168176	−	0.132404i
$703$		−	8261.48i		−	0.443226i
$704$	11145.9	−	1566.80i	0.596702	−	0.0838790i
$705$	−32600.9	−	20934.9i	−1.74159	−	1.11837i
$706$	5167.52	+	4932.39i	0.275471	+	0.262936i
$707$			16139.1i			0.858519i
$708$	133.251	+	77.0552i	0.00707325	+	0.00409027i
$709$			29445.8i			1.55975i	0.625936	+	0.779874i	$0.284717\pi$
$709$			29445.8i			1.55975i	−0.625936	+	0.779874i	$0.715283\pi$
$710$	−13300.1	+	13934.1i	−0.703019	+	0.736532i
$711$	8080.08	−	3697.00i	0.426198	−	0.195005i
$712$	3541.68	−	4074.36i	0.186419	−	0.214457i
$713$			461.070i			0.0242177i
$714$	2345.51	−	568.598i	0.122939	−	0.0298029i
$715$	2905.00			0.151945
$716$	2880.42	−	134.186i	0.150344	−	0.00700387i
$717$	18075.6	+	11607.4i	0.941488	+	0.604584i
$718$	−18400.6	+	19277.8i	−0.956414	+	1.00201i
$719$	12404.3			0.643396			0.321698	−	0.946842i	$-0.395746\pi$
$719$	12404.3			0.643396			0.321698	+	0.946842i	$0.395746\pi$
$720$	−11352.9	−	19726.8i	−0.587636	−	1.02108i
$721$	−33020.7			−1.70562
$722$	−10240.6	+	10728.7i	−0.527860	+	0.553023i
$723$	−5339.03	−	3428.50i	−0.274634	−	0.176359i
$724$	−9134.60	+	425.541i	−0.468902	+	0.0218441i
$725$	−7976.50			−0.408607
$726$	−12108.3	+	2935.29i	−0.618983	+	0.150053i
$727$			7076.17i			0.360991i	0.983576	+	0.180496i	$0.0577702\pi$
$727$			7076.17i			0.360991i	−0.983576	+	0.180496i	$0.942230\pi$
$728$	4617.19	+	4013.54i	0.235061	+	0.204329i
$729$	−18897.5	−	5504.99i	−0.960093	−	0.279683i
$730$	25316.3	−	26523.1i	1.28356	−	1.34475i
$731$			1249.40i			0.0632159i
$732$	25801.9	+	14920.5i	1.30282	+	0.753386i
$733$		−	10430.6i		−	0.525600i	−0.964850	−	0.262800i	$-0.915354\pi$
$733$		−	10430.6i		−	0.525600i	0.964850	−	0.262800i	$-0.0846460\pi$
$734$	1255.29	+	1198.17i	0.0631246	+	0.0602523i
$735$	22071.2	+	14173.2i	1.10763	+	0.711274i
$736$	−1101.05	+	1392.57i	−0.0551428	+	0.0697430i
$737$			5247.47i			0.262270i
$738$	10462.8	−	30248.7i	0.521872	−	1.50877i
$739$	30256.6			1.50610			0.753050	−	0.657963i	$-0.228582\pi$
$739$	30256.6			1.50610			0.753050	+	0.657963i	$0.228582\pi$
$740$	21636.8	−	1007.96i	1.07484	−	0.0500723i
$741$	−1132.10	+	1762.96i	−0.0561251	+	0.0874007i
$742$	−18866.7	−	18008.2i	−0.933448	−	0.890975i
$743$	5577.21			0.275381			0.137690	−	0.990475i	$-0.456032\pi$
$743$	5577.21			0.275381			0.137690	+	0.990475i	$0.456032\pi$
$744$	−5305.70	+	1550.89i	−0.261447	+	0.0764226i
$745$	15764.9			0.775275
$746$	−22014.5	−	21012.9i	−1.08044	−	1.03128i
$747$	15353.2	−	7024.79i	0.752001	−	0.344075i
$748$	−49.8695	−	1070.49i	−0.00243771	−	0.0523276i
$749$	−8741.46			−0.426443
$750$	14394.1	−	3489.42i	0.700800	−	0.169888i
$751$			10687.5i			0.519296i	0.965703	+	0.259648i	$0.0836066\pi$
$751$			10687.5i			0.519296i	−0.965703	+	0.259648i	$0.916393\pi$
$752$	−36072.8	+	3368.26i	−1.74925	+	0.163335i
$753$	12352.0	−	19235.2i	0.597786	−	0.930901i
$754$	−3376.68	−	3223.03i	−0.163092	−	0.155671i
$755$		−	32995.8i		−	1.59052i
$756$	2874.53	−	30109.8i	0.138288	−	1.44852i
$757$			9377.01i			0.450215i	0.974334	+	0.225108i	$0.0722734\pi$
$757$			9377.01i			0.450215i	−0.974334	+	0.225108i	$0.927727\pi$
$758$	−19787.1	+	20730.3i	−0.948151	+	0.993349i
$759$	−605.317	+	942.630i	−0.0289481	+	0.0450794i
$760$	9040.17	+	7858.27i	0.431476	+	0.375065i
$761$			15663.5i			0.746124i	0.927806	+	0.373062i	$0.121692\pi$
$761$			15663.5i			0.746124i	−0.927806	+	0.373062i	$0.878308\pi$
$762$	−1881.96	−	7763.22i	−0.0894699	−	0.369071i
$763$	−32564.8			−1.54512
$764$	708.824	+	15215.5i	0.0335659	+	0.720521i
$765$	−1970.57	+	901.626i	−0.0931323	+	0.0426123i
$766$	−18459.7	+	19339.7i	−0.870728	+	0.912236i
$767$	37.1496			0.00174889
$768$	−19728.4	−	7985.99i	−0.926936	−	0.375221i
$769$	18293.6			0.857848			0.428924	−	0.903341i	$-0.358893\pi$
$769$	18293.6			0.857848			0.428924	+	0.903341i	$0.358893\pi$
$770$	15239.0	−	15965.5i	0.713216	−	0.747215i
$771$	−10658.7	+	16598.2i	−0.497876	+	0.775316i
$772$	−347.767	−	7465.12i	−0.0162130	−	0.348025i
$773$	7495.03			0.348742			0.174371	−	0.984680i	$-0.444211\pi$
$773$	7495.03			0.348742			0.174371	+	0.984680i	$0.444211\pi$
$774$	14798.0	+	5118.53i	0.687214	+	0.237702i
$775$			2279.68i			0.105663i
$776$	17094.6	+	14859.7i	0.790800	+	0.687411i
$777$	24220.8	+	15553.6i	1.11830	+	0.718124i
$778$	6610.76	−	6925.90i	0.304637	−	0.319159i
$779$			16844.5i			0.774733i
$780$	−4755.31	−	2749.87i	−0.218292	−	0.126232i
$781$			11366.6i			0.520781i
$782$	122.268	+	116.705i	0.00559116	+	0.00533676i
$783$	−3260.06	+	22847.4i	−0.148793	+	1.04278i
$784$	24421.8	−	2280.36i	1.11251	−	0.103879i
$785$			35794.0i			1.62744i
$786$	4315.96	+	17803.7i	0.195859	+	0.807934i
$787$	−16884.3			−0.764753			−0.382377	−	0.924007i	$-0.624894\pi$
$787$	−16884.3			−0.764753			−0.382377	+	0.924007i	$0.624894\pi$
$788$	472.283	+	10137.9i	0.0213507	+	0.458311i
$789$	−28533.5	−	18323.0i	−1.28748	−	0.826763i
$790$	−8868.92	−	8465.37i	−0.399420	−	0.381246i
$791$	−49139.8			−2.20886
$792$	−12883.3	−	3794.91i	−0.578014	−	0.170260i
$793$	7193.44			0.322127
$794$	8441.64	+	8057.54i	0.377308	+	0.360140i
$795$	19705.6	+	12654.1i	0.879103	+	0.564523i
$796$	18324.2	−	853.645i	0.815936	−	0.0380109i
$797$	29212.0			1.29830			0.649148	−	0.760662i	$-0.275125\pi$
$797$	29212.0			1.29830			0.649148	+	0.760662i	$0.275125\pi$
$798$	3750.22	+	15470.0i	0.166362	+	0.686255i
$799$			3449.48i			0.152733i
$800$	−5443.93	+	6885.32i	−0.240590	+	0.304291i
$801$	−5857.70	+	2680.16i	−0.258392	+	0.118226i
$802$	18064.7	+	17242.8i	0.795372	+	0.759182i
$803$		−	21636.0i		−	0.950832i
$804$	4967.25	−	8589.80i	0.217887	−	0.376790i
$805$			3481.10i			0.152413i
$806$	−921.141	+	965.052i	−0.0402554	+	0.0421743i
$807$	3377.75	+	2169.05i	0.147339	+	0.0946147i
$808$	−10227.2	−	8890.10i	−0.445286	−	0.387070i
$809$		−	28157.8i		−	1.22370i	−0.790973	−	0.611851i	$-0.790425\pi$
$809$		−	28157.8i		−	1.22370i	0.790973	−	0.611851i	$-0.209575\pi$
$810$	2605.93	+	27033.4i	0.113041	+	1.17266i
$811$	−24658.2			−1.06765			−0.533827	−	0.845594i	$-0.679247\pi$
$811$	−24658.2			−1.06765			−0.533827	+	0.845594i	$0.679247\pi$
$812$	−35426.7	+	1650.37i	−1.53107	+	0.0713261i
$813$	10480.0	−	16319.9i	0.452089	−	0.704015i
$814$	8825.02	−	9245.71i	0.379996	−	0.398111i
$815$	−26471.0			−1.13771
$816$	−931.693	+	1799.54i	−0.0399703	+	0.0772015i
$817$	−8240.51			−0.352875
$818$	3218.82	−	3372.26i	0.137584	−	0.144142i
$819$	−3037.24	−	6638.13i	−0.129585	−	0.283217i
$820$	−44115.7	+	2055.16i	−1.87877	+	0.0875235i
$821$	23980.9			1.01941			0.509707	−	0.860348i	$-0.329754\pi$
$821$	23980.9			1.01941			0.509707	+	0.860348i	$0.329754\pi$
$822$	7778.17	+	32085.6i	0.330042	+	1.36145i
$823$		−	7533.72i		−	0.319087i	−0.987191	−	0.159544i	$-0.948998\pi$
$823$		−	7533.72i		−	0.319087i	0.987191	−	0.159544i	$-0.0510023\pi$
$824$	18189.2	−	20924.9i	0.768993	−	0.884652i
$825$	−2992.89	+	4660.67i	−0.126302	+	0.196683i
$826$	194.879	−	204.169i	0.00820910	−	0.00860043i
$827$		−	25167.2i		−	1.05822i	−0.848553	−	0.529110i	$-0.822526\pi$
$827$		−	25167.2i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$828$	1883.16	−	970.037i	0.0790391	−	0.0407139i
$829$		−	4440.96i		−	0.186057i	−0.995663	−	0.0930283i	$-0.970345\pi$
$829$		−	4440.96i		−	0.186057i	0.995663	−	0.0930283i	$-0.0296547\pi$
$830$	−16852.1	−	16085.3i	−0.704753	−	0.672686i
$831$	18257.2	−	28431.0i	0.762136	−	1.18684i
$832$	−5086.69	+	715.041i	−0.211958	+	0.0297952i
$833$		−	2335.34i		−	0.0971365i
$834$	−24763.8	+	6003.23i	−1.02818	+	0.249250i
$835$	63.1820			0.00261857
$836$	7060.49	−	328.917i	0.292096	−	0.0136075i
$837$	6529.78	+	931.724i	0.269656	+	0.0384768i
$838$	−23638.9	−	22563.3i	−0.974453	−	0.930115i
$839$	−8795.36			−0.361918			−0.180959	−	0.983491i	$-0.557920\pi$
$839$	−8795.36			−0.361918			−0.180959	+	0.983491i	$0.557920\pi$
$840$	−40058.3	+	11709.3i	−1.64541	+	0.480963i
$841$	2671.53			0.109538
$842$	15654.8	+	14942.5i	0.640737	+	0.611582i
$843$	−1539.30	+	2397.07i	−0.0628900	+	0.0979353i
$844$	991.646	+	21286.5i	0.0404430	+	0.868142i
$845$	27612.1			1.12412
$846$	40855.8	+	14131.7i	1.66035	+	0.574302i
$847$			22845.5i			0.926776i
$848$	21804.2	−	2035.95i	0.882973	−	0.0824466i
$849$	2905.92	+	1866.06i	0.117469	+	0.0754335i
$850$	604.532	+	577.025i	0.0243944	+	0.0232845i
$851$			2015.93i			0.0812046i
$852$	10759.6	−	18606.5i	0.432652	−	0.748179i
$853$		−	35919.6i		−	1.44181i	−0.693034	−	0.720905i	$-0.743726\pi$
$853$		−	35919.6i		−	1.44181i	0.693034	−	0.720905i	$-0.256274\pi$
$854$	37735.3	−	39534.1i	1.51203	−	1.58411i
$855$	−5946.73	−	12997.0i	−0.237864	−	0.519870i
$856$	4815.17	−	5539.38i	0.192265	−	0.221182i
$857$			35984.3i			1.43431i	0.696916	+	0.717153i	$0.254555\pi$
$857$			35984.3i			1.43431i	−0.696916	+	0.717153i	$0.745445\pi$
$858$	−3150.19	+	763.667i	−0.125345	+	0.0303860i
$859$	19362.0			0.769060			0.384530	−	0.923112i	$-0.374364\pi$
$859$	19362.0			0.769060			0.384530	+	0.923112i	$0.374364\pi$
$860$	−1005.41	−	21581.9i	−0.0398652	−	0.855740i
$861$	−49384.3	−	31712.6i	−1.95472	−	1.25524i
$862$	28910.2	−	30288.4i	1.14233	−	1.19678i
$863$	25590.4			1.00940			0.504698	−	0.863296i	$-0.331604\pi$
$863$	25590.4			1.00940			0.504698	+	0.863296i	$0.331604\pi$
$864$	17496.9	+	18407.3i	0.688955	+	0.724804i
$865$	19781.5			0.777563
$866$	3784.80	−	3965.22i	0.148513	−	0.155593i
$867$	−21318.7	−	13690.0i	−0.835087	−	0.536258i
$868$	471.676	+	10124.9i	0.0184444	+	0.395924i
$869$	−7234.75			−0.282419
$870$	30947.9	−	7502.37i	1.20601	−	0.292361i
$871$		−	2394.80i		−	0.0931626i
$872$	17938.1	−	20636.0i	0.696628	−	0.801403i
$873$	−11245.0	−	24576.9i	−0.435953	−	0.952808i
$874$	−769.732	+	806.426i	−0.0297901	+	0.0312102i
$875$		−	27158.3i		−	1.04928i
$876$	−20480.6	+	35416.9i	−0.789927	+	1.36601i
$877$			28481.1i			1.09662i	0.836275	+	0.548311i	$0.184729\pi$
$877$			28481.1i			1.09662i	−0.836275	+	0.548311i	$0.815271\pi$
$878$	10796.2	+	10305.0i	0.414983	+	0.396101i
$879$	−22355.4	−	14355.7i	−0.857826	−	0.550860i
$880$	1722.87	+	18451.3i	0.0659976	+	0.706810i
$881$			24952.4i			0.954219i	0.878844	+	0.477109i	$0.158315\pi$
$881$			24952.4i			0.954219i	−0.878844	+	0.477109i	$0.841685\pi$
$882$	−27659.9	−	9567.38i	−1.05596	−	0.365250i
$883$	28650.5			1.09192			0.545961	−	0.837811i	$-0.316165\pi$
$883$	28650.5			1.09192			0.545961	+	0.837811i	$0.316165\pi$
$884$	22.7590	+	488.542i	0.000865915	+	0.0185876i
$885$	−136.939	+	213.248i	−0.00520129	+	0.00809971i
$886$	18831.4	+	17974.6i	0.714056	+	0.681565i
$887$	542.531			0.0205371			0.0102686	−	0.999947i	$-0.496731\pi$
$887$	542.531			0.0205371			0.0102686	+	0.999947i	$0.496731\pi$
$888$	−23198.0	+	6780.93i	−0.876661	+	0.256253i
$889$	−14647.3			−0.552593
$890$	6429.57	+	6137.02i	0.242157	+	0.231139i
$891$	12126.5	+	10477.5i	0.455952	+	0.393950i
$892$	−41778.4	+	1946.27i	−1.56821	+	0.0730561i
$893$	−22751.2			−0.852565
$894$	−17095.5	+	4144.27i	−0.639550	+	0.155039i
$895$			4747.58i			0.177312i
$896$	−22754.0	+	31706.7i	−0.848389	+	1.18219i
$897$	276.250	−	430.189i	0.0102828	−	0.0160129i
$898$	−6590.53	−	6290.65i	−0.244910	−	0.233766i
$899$		−	7733.89i		−	0.286918i
$900$	9310.96	−	4796.18i	0.344851	−	0.177636i
$901$		−	2085.04i		−	0.0770951i
$902$	−17993.5	+	18851.3i	−0.664211	+	0.695874i
$903$	15514.1	−	24159.4i	0.571736	−	0.890336i
$904$	27068.3	−	31139.4i	0.995883	−	1.14567i
$905$		−	15055.9i		−	0.553011i
$906$	8673.95	+	35780.7i	0.318071	+	1.31207i
$907$	−17915.8			−0.655880			−0.327940	−	0.944699i	$-0.606354\pi$
$907$	−17915.8			−0.655880			−0.327940	+	0.944699i	$0.606354\pi$
$908$	44203.7	−	2059.26i	1.61558	−	0.0752631i
$909$	6727.57	+	14703.6i	0.245478	+	0.536511i
$910$	−6954.66	+	7286.19i	−0.253346	+	0.265423i
$911$	−30577.4			−1.11205			−0.556023	−	0.831167i	$-0.687673\pi$
$911$	−30577.4			−1.11205			−0.556023	+	0.831167i	$0.687673\pi$
$912$	−11869.0	−	6145.04i	−0.430944	−	0.223117i
$913$	−13747.0			−0.498311
$914$	−23464.4	+	24582.9i	−0.849160	+	0.889640i
$915$	−26516.0	+	41292.0i	−0.958025	+	1.49188i
$916$	6251.83	−	291.245i	0.225509	−	0.0105055i
$917$	33591.3			1.20968
$918$	1899.87	−	1495.75i	0.0683063	−	0.0537768i
$919$			21519.6i			0.772435i	0.922408	+	0.386217i	$0.126219\pi$
$919$			21519.6i			0.772435i	−0.922408	+	0.386217i	$0.873781\pi$
$920$	−2205.94	−	1917.54i	−0.0790519	−	0.0687167i
$921$	−2599.77	−	1669.46i	−0.0930133	−	0.0597292i
$922$	9293.48	−	9736.50i	0.331957	−	0.347782i
$923$		−	5187.41i		−	0.184990i
$924$	−12328.2	+	21319.0i	−0.438927	+	0.759031i
$925$			9967.40i			0.354299i
$926$	−25714.9	−	24544.9i	−0.912575	−	0.871052i
$927$	−30083.7	+	13764.7i	−1.06589	+	0.487692i
$928$	18468.7	−	23358.7i	0.653302	−	0.826277i
$929$		−	23763.7i		−	0.839247i	−0.907698	−	0.419624i	$-0.862162\pi$
$929$		−	23763.7i		−	0.839247i	0.907698	−	0.419624i	$-0.137838\pi$
$930$	−2144.17	−	8844.89i	−0.0756024	−	0.311866i
$931$	15402.9			0.542223
$932$	−31315.1	+	1458.84i	−1.10060	+	0.0512722i
$933$	31341.6	+	20126.2i	1.09976	+	0.706220i
$934$	31428.0	+	29998.0i	1.10102	+	1.05092i
$935$	1764.41			0.0617138
$936$	5879.56	+	1731.89i	0.205320	+	0.0604792i
$937$	−11835.5			−0.412644			−0.206322	−	0.978484i	$-0.566149\pi$
$937$	−11835.5			−0.412644			−0.206322	+	0.978484i	$0.566149\pi$
$938$	−13161.5	−	12562.6i	−0.458142	−	0.437296i
$939$	16503.2	+	10597.7i	0.573549	+	0.368309i
$940$	−2775.83	−	59585.5i	−0.0963164	−	2.06751i
$941$	−41547.4			−1.43933			−0.719664	−	0.694323i	$-0.755704\pi$
$941$	−41547.4			−1.43933			−0.719664	+	0.694323i	$0.755704\pi$
$942$	−9409.54	−	38815.1i	−0.325456	−	1.34253i
$943$		−	4110.32i		−	0.141941i
$944$	22.0323	+	235.958i	0.000759631	+	0.00813537i
$945$	49300.1	+	7034.56i	1.69707	+	0.242153i
$946$	−9222.25	−	8802.63i	−0.316957	−	0.302535i
$947$			41519.6i			1.42472i	0.701816	+	0.712358i	$0.252373\pi$
$947$			41519.6i			1.42472i	−0.701816	+	0.712358i	$0.747627\pi$
$948$	11842.9	+	6848.41i	0.405736	+	0.234627i
$949$			9874.06i			0.337751i
$950$	−3805.81	+	3987.23i	−0.129975	+	0.136171i
$951$	41102.7	+	26394.4i	1.40152	+	0.899998i
$952$	2804.35	+	2437.71i	0.0954720	+	0.0829901i
$953$			31542.2i			1.07214i	0.844173	+	0.536071i	$0.180092\pi$
$953$			31542.2i			1.07214i	−0.844173	+	0.536071i	$0.819908\pi$
$954$	−24695.4	−	8541.95i	−0.838094	−	0.289891i
$955$	−25078.6			−0.849764
$956$	1539.06	+	33037.3i	0.0520679	+	1.11768i
$957$	10153.5	−	15811.5i	0.342962	−	0.534077i
$958$	−4431.04	+	4642.27i	−0.149437	+	0.156560i
$959$	60537.8			2.03844
$960$	14645.7	−	31834.6i	0.492385	−	1.07027i
$961$	27580.7			0.925805
$962$	−4027.49	+	4219.48i	−0.134981	+	0.141415i
$963$	−7963.96	+	3643.87i	−0.266495	+	0.121934i
$964$	−454.596	−	9758.28i	−0.0151883	−	0.326030i
$965$	12304.2			0.410452
$966$	−915.113	−	3774.91i	−0.0304796	−	0.125731i
$967$			51845.5i			1.72414i	0.506793	+	0.862068i	$0.330831\pi$
$967$			51845.5i			1.72414i	−0.506793	+	0.862068i	$0.669169\pi$
$968$	−14477.0	−	12584.2i	−0.480689	−	0.417844i
$969$	−687.604	+	1070.77i	−0.0227957	+	0.0354986i
$970$	−25748.8	+	26976.3i	−0.852314	+	0.892944i
$971$		−	16303.5i		−	0.538830i	−0.963024	−	0.269415i	$-0.913170\pi$
$971$		−	16303.5i		−	0.538830i	0.963024	−	0.269415i	$-0.0868304\pi$
$972$	−9932.41	−	28630.0i	−0.327760	−	0.944761i
$973$			46723.3i			1.53945i
$974$	−23485.7	−	22417.1i	−0.772620	−	0.737465i
$975$	1365.87	−	2127.00i	0.0448644	−	0.0698650i
$976$	4266.21	+	45689.6i	0.139916	+	1.49845i
$977$		−	46997.0i		−	1.53896i	−0.638668	−	0.769482i	$-0.720514\pi$
$977$		−	46997.0i		−	1.53896i	0.638668	−	0.769482i	$-0.279486\pi$
$978$	28705.2	−	6958.70i	0.938539	−	0.227520i
$979$	5244.87			0.171222
$980$	1879.27	+	40340.1i	0.0612562	+	1.31492i
$981$	−29668.4	+	13574.6i	−0.965584	+	0.441798i
$982$	−41547.0	−	39656.6i	−1.35012	−	1.28869i
$983$	−10730.9			−0.348180			−0.174090	−	0.984730i	$-0.555698\pi$
$983$	−10730.9			−0.348180			−0.174090	+	0.984730i	$0.555698\pi$
$984$	47298.9	−	13825.8i	1.53235	−	0.447916i
$985$	−16709.6			−0.540521
$986$	−2050.89	−	1957.58i	−0.0662411	−	0.0632271i
$987$	42832.9	−	66701.6i	1.38135	−	2.15110i
$988$	−3222.21	+	150.109i	−0.103757	+	0.00483359i
$989$	2010.81			0.0646513
$990$	7228.41	−	20897.8i	0.232054	−	0.670885i
$991$		−	53985.5i		−	1.73048i	−0.501358	−	0.865240i	$-0.667166\pi$
$991$		−	53985.5i		−	1.73048i	0.501358	−	0.865240i	$-0.332834\pi$
$992$	−6675.89	−	5278.34i	−0.213669	−	0.168939i
$993$	−40304.4	−	25881.8i	−1.28804	−	0.827123i
$994$	−28509.3	−	27212.1i	−0.909717	−	0.868324i
$995$			30202.5i			0.962294i
$996$	22503.0	+	13012.9i	0.715898	+	0.413985i
$997$		−	49281.6i		−	1.56546i	−0.622361	−	0.782731i	$-0.713826\pi$
$997$		−	49281.6i		−	1.56546i	0.622361	−	0.782731i	$-0.286174\pi$
$998$	1999.85	−	2095.18i	0.0634311	−	0.0664548i
$999$	28550.0	+	4073.76i	0.904187	+	0.129017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.4.f.b.11.5	yes	8
3.2	odd	2	inner	24.4.f.b.11.4	yes	8
4.3	odd	2		96.4.f.b.47.8		8
8.3	odd	2	inner	24.4.f.b.11.3	✓	8
8.5	even	2		96.4.f.b.47.7		8
12.11	even	2		96.4.f.b.47.5		8
16.3	odd	4		768.4.c.v.767.7		16
16.5	even	4		768.4.c.v.767.8		16
16.11	odd	4		768.4.c.v.767.10		16
16.13	even	4		768.4.c.v.767.9		16
24.5	odd	2		96.4.f.b.47.6		8
24.11	even	2	inner	24.4.f.b.11.6	yes	8
48.5	odd	4		768.4.c.v.767.11		16
48.11	even	4		768.4.c.v.767.5		16
48.29	odd	4		768.4.c.v.767.6		16
48.35	even	4		768.4.c.v.767.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.f.b.11.3	✓	8	8.3	odd	2	inner
24.4.f.b.11.4	yes	8	3.2	odd	2	inner
24.4.f.b.11.5	yes	8	1.1	even	1	trivial
24.4.f.b.11.6	yes	8	24.11	even	2	inner
96.4.f.b.47.5		8	12.11	even	2
96.4.f.b.47.6		8	24.5	odd	2
96.4.f.b.47.7		8	8.5	even	2
96.4.f.b.47.8		8	4.3	odd	2
768.4.c.v.767.5		16	48.11	even	4
768.4.c.v.767.6		16	48.29	odd	4
768.4.c.v.767.7		16	16.3	odd	4
768.4.c.v.767.8		16	16.5	even	4
768.4.c.v.767.9		16	16.13	even	4
768.4.c.v.767.10		16	16.11	odd	4
768.4.c.v.767.11		16	48.5	odd	4
768.4.c.v.767.12		16	48.35	even	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:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.95291 - 2.04601i) q^{2} +(-4.37228 - 2.80770i) q^{3} +(-0.372281 - 7.99133i) q^{4} +13.1715 q^{5} +(-14.2832 + 3.46254i) q^{6} +26.9490i q^{7} +(-17.0773 - 14.8447i) q^{8} +(11.2337 + 24.5521i) q^{9} +O(q^{10})\)	\(q+(1.95291 - 2.04601i) q^{2} +(-4.37228 - 2.80770i) q^{3} +(-0.372281 - 7.99133i) q^{4} +13.1715 q^{5} +(-14.2832 + 3.46254i) q^{6} +26.9490i q^{7} +(-17.0773 - 14.8447i) q^{8} +(11.2337 + 24.5521i) q^{9} +(25.7228 - 26.9490i) q^{10} -21.9834i q^{11} +(-20.8095 + 35.9856i) q^{12} +10.0326i q^{13} +(55.1379 + 52.6290i) q^{14} +(-57.5896 - 36.9816i) q^{15} +(-63.7228 + 5.95005i) q^{16} +6.09352i q^{17} +(72.1721 + 24.9638i) q^{18} -40.1902 q^{19} +(-4.90351 - 105.258i) q^{20} +(75.6647 - 117.829i) q^{21} +(-44.9783 - 42.9317i) q^{22} +9.80703 q^{23} +(32.9877 + 112.853i) q^{24} +48.4891 q^{25} +(20.5268 + 19.5928i) q^{26} +(19.8179 - 138.889i) q^{27} +(215.359 - 10.0326i) q^{28} -164.501 q^{29} +(-188.132 + 45.6069i) q^{30} +47.0143i q^{31} +(-112.271 + 141.997i) q^{32} +(-61.7228 + 96.1178i) q^{33} +(12.4674 + 11.9001i) q^{34} +354.960i q^{35} +(192.022 - 98.9124i) q^{36} +205.560i q^{37} +(-78.4878 + 82.2294i) q^{38} +(28.1685 - 43.8654i) q^{39} +(-224.935 - 195.527i) q^{40} -419.120i q^{41} +(-93.3119 - 384.919i) q^{42} +205.038 q^{43} +(-175.677 + 8.18402i) q^{44} +(147.965 + 323.388i) q^{45} +(19.1522 - 20.0652i) q^{46} +566.089 q^{47} +(295.320 + 152.899i) q^{48} -383.250 q^{49} +(94.6949 - 99.2090i) q^{50} +(17.1087 - 26.6426i) q^{51} +(80.1740 - 3.73496i) q^{52} -342.173 q^{53} +(-245.466 - 311.786i) q^{54} -289.555i q^{55} +(400.049 - 460.218i) q^{56} +(175.723 + 112.842i) q^{57} +(-321.255 + 336.570i) q^{58} -3.70288i q^{59} +(-274.093 + 473.985i) q^{60} -717.005i q^{61} +(96.1915 + 91.8146i) q^{62} +(-661.654 + 302.737i) q^{63} +(71.2716 + 507.015i) q^{64} +132.145i q^{65} +(76.1184 + 313.995i) q^{66} -238.701 q^{67} +(48.6953 - 2.26850i) q^{68} +(-42.8791 - 27.5351i) q^{69} +(726.250 + 693.205i) q^{70} -517.054 q^{71} +(172.626 - 586.045i) q^{72} +984.195 q^{73} +(420.576 + 401.439i) q^{74} +(-212.008 - 136.143i) q^{75} +(14.9621 + 321.173i) q^{76} +592.432 q^{77} +(-34.7383 - 143.298i) q^{78} -329.100i q^{79} +(-839.327 + 78.3712i) q^{80} +(-476.609 + 551.621i) q^{81} +(-857.522 - 818.503i) q^{82} -625.333i q^{83} +(-969.777 - 560.796i) q^{84} +80.2609i q^{85} +(400.421 - 419.509i) q^{86} +(719.244 + 461.868i) q^{87} +(-326.337 + 375.419i) q^{88} +238.583i q^{89} +(950.616 + 328.811i) q^{90} -270.369 q^{91} +(-3.65097 - 78.3712i) q^{92} +(132.002 - 205.560i) q^{93} +(1105.52 - 1158.22i) q^{94} -529.366 q^{95} +(889.566 - 305.628i) q^{96} -1001.01 q^{97} +(-748.453 + 784.132i) q^{98} +(539.739 - 246.955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9	\( 8 q - 12 q^{3} + 20 q^{4} - 48 q^{9} - 24 q^{10} + 36 q^{12} - 280 q^{16} + 264 q^{18} + 184 q^{19} - 176 q^{22} + 264 q^{24} + 296 q^{25} - 324 q^{27} + 528 q^{28} - 624 q^{30} - 264 q^{33} - 176 q^{34} - 516 q^{36} - 1248 q^{40} + 1320 q^{42} - 152 q^{43} + 1440 q^{46} + 1080 q^{48} - 952 q^{49} + 1056 q^{51} + 2112 q^{52} - 1584 q^{54} + 1176 q^{57} - 2616 q^{58} - 2640 q^{60} - 1360 q^{64} + 792 q^{66} - 1496 q^{67} + 3696 q^{70} + 2640 q^{72} + 1072 q^{73} - 708 q^{75} + 1912 q^{76} - 3696 q^{78} - 504 q^{81} - 2816 q^{82} - 4224 q^{84} - 1232 q^{88} + 4104 q^{90} + 3168 q^{91} + 4800 q^{94} + 4752 q^{96} - 3872 q^{97} + 2112 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 20 * q^4 - 48 * q^9 - 24 * q^10 + 36 * q^12 - 280 * q^16 + 264 * q^18 + 184 * q^19 - 176 * q^22 + 264 * q^24 + 296 * q^25 - 324 * q^27 + 528 * q^28 - 624 * q^30 - 264 * q^33 - 176 * q^34 - 516 * q^36 - 1248 * q^40 + 1320 * q^42 - 152 * q^43 + 1440 * q^46 + 1080 * q^48 - 952 * q^49 + 1056 * q^51 + 2112 * q^52 - 1584 * q^54 + 1176 * q^57 - 2616 * q^58 - 2640 * q^60 - 1360 * q^64 + 792 * q^66 - 1496 * q^67 + 3696 * q^70 + 2640 * q^72 + 1072 * q^73 - 708 * q^75 + 1912 * q^76 - 3696 * q^78 - 504 * q^81 - 2816 * q^82 - 4224 * q^84 - 1232 * q^88 + 4104 * q^90 + 3168 * q^91 + 4800 * q^94 + 4752 * q^96 - 3872 * q^97 + 2112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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