LMFDB - Embedded newform 24.4.f.b.11.6

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

$q$-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	$-0.740656\pi$
$7$		−	26.9490i		−	1.45511i	0.686049	−	0.727555i	$-0.259344\pi$
$8$	−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	$0.0974153\pi$
$11$			21.9834i			0.602569i	−0.953534	+	0.301284i	$0.902585\pi$
$12$	−20.8095	−	35.9856i	−0.500599	−	0.865679i
$13$		−	10.0326i		−	0.214042i	−0.994257	−	0.107021i	$-0.965869\pi$
$13$		−	10.0326i		−	0.214042i	0.994257	−	0.107021i	$-0.0341312\pi$
$14$	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	$-0.986160\pi$
$17$		−	6.09352i		−	0.0869350i	0.999055	−	0.0434675i	$-0.0138405\pi$
$18$	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	$-0.956513\pi$
$31$		−	47.0143i		−	0.272387i	0.990682	−	0.136194i	$-0.0434870\pi$
$32$	−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	$-0.849041\pi$
$37$		−	205.560i		−	0.913346i	0.889635	−	0.456673i	$-0.150959\pi$
$38$	−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	$0.294234\pi$
$41$			419.120i			1.59648i	−0.602342	+	0.798238i	$0.705766\pi$
$42$	−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	$0.00130042\pi$
$59$			3.70288i			0.00817075i	−0.999992	+	0.00408538i	$0.998700\pi$
$60$	−274.093	−	473.985i	−0.589754	−	1.01985i
$61$			717.005i			1.50497i	0.658610	+	0.752484i	$0.271145\pi$
$61$			717.005i			1.50497i	−0.658610	+	0.752484i	$0.728855\pi$
$62$	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	$0.0752948\pi$
$79$			329.100i			0.468691i	−0.972153	+	0.234346i	$0.924705\pi$
$80$	−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	$0.135690\pi$
$83$			625.333i			0.826978i	−0.910509	+	0.413489i	$0.864310\pi$
$84$	−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	$-0.954622\pi$
$89$		−	238.583i		−	0.284154i	0.989856	−	0.142077i	$-0.0453781\pi$
$90$	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	$-0.800670\pi$
$103$		−	1225.30i		−	1.17216i	0.810253	−	0.586080i	$-0.199330\pi$
$104$	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	$-0.953189\pi$
$107$		−	324.370i		−	0.293066i	0.989206	−	0.146533i	$-0.0468114\pi$
$108$	−1117.29	+	106.666i	−0.995474	+	0.0950361i
$109$		−	1208.38i		−	1.06186i	−0.847417	−	0.530928i	$-0.821843\pi$
$109$		−	1208.38i		−	1.06186i	0.847417	−	0.530928i	$-0.178157\pi$
$110$	−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	$-0.725687\pi$
$113$		−	1823.44i		−	1.51800i	0.651089	−	0.759002i	$-0.274313\pi$
$114$	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	$-0.939190\pi$
$127$		−	543.520i		−	0.379760i	0.981807	−	0.189880i	$-0.0608100\pi$
$128$	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	$0.136452\pi$
$131$			1246.47i			0.831335i	−0.909517	+	0.415668i	$0.863548\pi$
$132$	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	$0.247014\pi$
$137$			2246.38i			1.40088i	−0.713709	+	0.700442i	$0.752986\pi$
$138$	−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	$0.235872\pi$
$151$			2505.09i			1.35007i	−0.737784	+	0.675037i	$0.764128\pi$
$152$	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	$-0.757299\pi$
$157$		−	2717.53i		−	1.38142i	0.723133	−	0.690709i	$-0.242701\pi$
$158$	−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	$-0.976023\pi$
$179$		−	360.443i		−	0.150507i	0.997164	−	0.0752535i	$-0.0239766\pi$
$180$	2529.22	+	1302.83i	1.04732	+	0.539484i
$181$			1143.06i			0.469410i	0.972067	+	0.234705i	$0.0754125\pi$
$181$			1143.06i			0.469410i	−0.972067	+	0.234705i	$0.924588\pi$
$182$	−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	$-0.866083\pi$
$199$		−	2293.01i		−	0.816820i	0.912798	−	0.408410i	$-0.133917\pi$
$200$	−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	$0.287314\pi$
$223$			5227.96i			1.56991i	−0.619552	+	0.784956i	$0.712686\pi$
$224$	−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	$-0.700189\pi$
$227$		−	5531.45i		−	1.61734i	0.588265	−	0.808669i	$-0.299811\pi$
$228$	836.338	+	1446.27i	0.242929	+	0.420094i
$229$		−	782.326i		−	0.225754i	−0.993609	−	0.112877i	$-0.963993\pi$
$229$		−	782.326i		−	0.225754i	0.993609	−	0.112877i	$-0.0360065\pi$
$230$	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	$0.185715\pi$
$233$			3918.64i			1.10180i	−0.834573	+	0.550898i	$0.814285\pi$
$234$	−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	$-0.813423\pi$
$251$		−	4399.34i		−	1.10631i	0.833078	−	0.553156i	$-0.186577\pi$
$252$	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	$0.152403\pi$
$257$			3796.23i			0.921409i	−0.887553	+	0.460705i	$0.847597\pi$
$258$	−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	$-0.862613\pi$
$271$		−	3732.58i		−	0.836673i	0.908292	−	0.418336i	$-0.137387\pi$
$272$	−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	$-0.750841\pi$
$277$		−	6502.55i		−	1.41047i	0.708973	−	0.705236i	$-0.249159\pi$
$278$	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	$0.0185344\pi$
$281$			548.243i			0.116389i	−0.998305	+	0.0581947i	$0.981466\pi$
$282$	−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	$-0.938110\pi$
$347$		−	2497.80i		−	0.386424i	0.981157	−	0.193212i	$-0.0618905\pi$
$348$	3423.18	+	5919.66i	0.527304	+	0.911860i
$349$			8874.07i			1.36108i	0.732710	+	0.680541i	$0.238255\pi$
$349$			8874.07i			1.36108i	−0.732710	+	0.680541i	$0.761745\pi$
$350$	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	$-0.939019\pi$
$353$		−	2525.66i		−	0.380814i	0.981705	−	0.190407i	$-0.0609808\pi$
$354$	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	$-0.986107\pi$
$367$		−	613.530i		−	0.0872643i	0.999048	−	0.0436322i	$-0.0138930\pi$
$368$	−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	$0.268415\pi$
$373$			10759.8i			1.49362i	−0.665039	+	0.746809i	$0.731585\pi$
$374$	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	$-0.916014\pi$
$397$		−	4125.91i		−	0.521596i	0.965393	−	0.260798i	$-0.0839857\pi$
$398$	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	$-0.814717\pi$
$401$		−	8829.27i		−	1.09953i	0.835318	−	0.549767i	$-0.185283\pi$
$402$	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	$0.235231\pi$
$419$			11553.7i			1.34710i	−0.739143	+	0.673549i	$0.764769\pi$
$420$	−12773.4	+	7386.54i	−1.48400	+	0.858158i
$421$		−	7651.40i		−	0.885763i	−0.896580	−	0.442882i	$-0.853956\pi$
$421$		−	7651.40i		−	0.885763i	0.896580	−	0.442882i	$-0.146044\pi$
$422$	−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	$-0.907395\pi$
$439$		−	5276.73i		−	0.573678i	0.957979	−	0.286839i	$-0.0926045\pi$
$440$	−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	$-0.835695\pi$
$443$		−	9203.98i		−	0.987121i	0.869712	−	0.493560i	$-0.164305\pi$
$444$	−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	$0.0541453\pi$
$449$			3221.17i			0.338567i	−0.985567	+	0.169283i	$0.945855\pi$
$450$	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	$0.217264\pi$
$463$			12568.3i			1.26156i	−0.775963	+	0.630778i	$0.782736\pi$
$464$	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	$-0.724692\pi$
$467$		−	15360.6i		−	1.52207i	0.648712	−	0.761034i	$-0.275308\pi$
$468$	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	$0.179327\pi$
$487$			11478.8i			1.06808i	−0.845459	+	0.534040i	$0.820673\pi$
$488$	−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	$0.383007\pi$
$491$			20306.4i			1.86642i	−0.359325	+	0.933212i	$0.616993\pi$
$492$	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	$-0.868429\pi$
$521$		−	9553.38i		−	0.803342i	0.915784	−	0.401671i	$-0.131571\pi$
$522$	−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	$-0.798365\pi$
$541$		−	14897.0i		−	1.18387i	0.805986	−	0.591934i	$-0.201635\pi$
$542$	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	$0.100823\pi$
$563$			8321.78i			0.622950i	−0.950254	+	0.311475i	$0.899177\pi$
$564$	−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	$0.146426\pi$
$569$			12051.5i			0.887915i	−0.896048	+	0.443957i	$0.853574\pi$
$570$	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	$0.0964203\pi$
$587$			8484.84i			0.596604i	−0.954472	+	0.298302i	$0.903580\pi$
$588$	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	$-0.926931\pi$
$593$		−	6571.68i		−	0.455087i	0.973768	−	0.227543i	$-0.0730693\pi$
$594$	−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	$0.0465668\pi$
$607$			4360.03i			0.291546i	−0.989318	+	0.145773i	$0.953433\pi$
$608$	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	$0.163532\pi$
$613$			14917.5i			0.982892i	−0.870908	+	0.491446i	$0.836468\pi$
$614$	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	$0.179706\pi$
$617$			16400.2i			1.07010i	−0.844822	+	0.535048i	$0.820294\pi$
$618$	−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	$-0.889700\pi$
$631$		−	10766.4i		−	0.679247i	0.940562	−	0.339623i	$-0.110300\pi$
$632$	−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	$0.0404830\pi$
$641$			4116.88i			0.253677i	−0.991923	+	0.126839i	$0.959517\pi$
$642$	−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	$0.0522017\pi$
$659$			5523.87i			0.326524i	−0.986583	+	0.163262i	$0.947798\pi$
$660$	10419.8	−	6025.51i	0.614532	−	0.355368i
$661$			5189.81i			0.305386i	0.988274	+	0.152693i	$0.0487946\pi$
$661$			5189.81i			0.305386i	−0.988274	+	0.152693i	$0.951205\pi$
$662$	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	$-0.821795\pi$
$683$		−	18958.5i		−	1.06212i	0.847335	−	0.531058i	$-0.178205\pi$
$684$	−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	$-0.715283\pi$
$709$		−	29445.8i		−	1.55975i	0.625936	−	0.779874i	$-0.284717\pi$
$710$	−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	$-0.942230\pi$
$727$		−	7076.17i		−	0.360991i	0.983576	−	0.180496i	$-0.0577702\pi$
$728$	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	$0.0846460\pi$
$733$			10430.6i			0.525600i	−0.964850	+	0.262800i	$0.915354\pi$
$734$	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	$-0.916393\pi$
$751$		−	10687.5i		−	0.519296i	0.965703	−	0.259648i	$-0.0836066\pi$
$752$	−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	$-0.927727\pi$
$757$		−	9377.01i		−	0.450215i	0.974334	−	0.225108i	$-0.0722734\pi$
$758$	−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	$-0.878308\pi$
$761$		−	15663.5i		−	0.746124i	0.927806	−	0.373062i	$-0.121692\pi$
$762$	−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	$0.209575\pi$
$809$			28157.8i			1.22370i	−0.790973	+	0.611851i	$0.790425\pi$
$810$	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	$0.0510023\pi$
$823$			7533.72i			0.319087i	−0.987191	+	0.159544i	$0.948998\pi$
$824$	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	$0.177474\pi$
$827$			25167.2i			1.05822i	−0.848553	+	0.529110i	$0.822526\pi$
$828$	1883.16	+	970.037i	0.0790391	+	0.0407139i
$829$			4440.96i			0.186057i	0.995663	+	0.0930283i	$0.0296547\pi$
$829$			4440.96i			0.186057i	−0.995663	+	0.0930283i	$0.970345\pi$
$830$	−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	$0.256274\pi$
$853$			35919.6i			1.44181i	−0.693034	+	0.720905i	$0.743726\pi$
$854$	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	$-0.745445\pi$
$857$		−	35984.3i		−	1.43431i	0.696916	−	0.717153i	$-0.254555\pi$
$858$	−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	$-0.815271\pi$
$877$		−	28481.1i		−	1.09662i	0.836275	−	0.548311i	$-0.184729\pi$
$878$	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	$-0.841685\pi$
$881$		−	24952.4i		−	0.954219i	0.878844	−	0.477109i	$-0.158315\pi$
$882$	−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	$-0.873781\pi$
$919$		−	21519.6i		−	0.772435i	0.922408	−	0.386217i	$-0.126219\pi$
$920$	−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	$0.137838\pi$
$929$			23763.7i			0.839247i	−0.907698	+	0.419624i	$0.862162\pi$
$930$	−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	$-0.747627\pi$
$947$		−	41519.6i		−	1.42472i	0.701816	−	0.712358i	$-0.252373\pi$
$948$	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	$-0.819908\pi$
$953$		−	31542.2i		−	1.07214i	0.844173	−	0.536071i	$-0.180092\pi$
$954$	−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	$-0.669169\pi$
$967$		−	51845.5i		−	1.72414i	0.506793	−	0.862068i	$-0.330831\pi$
$968$	−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	$0.0868304\pi$
$971$			16303.5i			0.538830i	−0.963024	+	0.269415i	$0.913170\pi$
$972$	−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	$0.279486\pi$
$977$			46997.0i			1.53896i	−0.638668	+	0.769482i	$0.720514\pi$
$978$	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	$0.332834\pi$
$991$			53985.5i			1.73048i	−0.501358	+	0.865240i	$0.667166\pi$
$992$	−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	$0.286174\pi$
$997$			49281.6i			1.56546i	−0.622361	+	0.782731i	$0.713826\pi$
$998$	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.11.6	yes	8
3.2	odd	2	inner	24.4.f.b.11.3	✓	8
4.3	odd	2		96.4.f.b.47.6		8
8.3	odd	2	inner	24.4.f.b.11.4	yes	8
8.5	even	2		96.4.f.b.47.5		8
12.11	even	2		96.4.f.b.47.7		8
16.3	odd	4		768.4.c.v.767.11		16
16.5	even	4		768.4.c.v.767.12		16
16.11	odd	4		768.4.c.v.767.6		16
16.13	even	4		768.4.c.v.767.5		16
24.5	odd	2		96.4.f.b.47.8		8
24.11	even	2	inner	24.4.f.b.11.5	yes	8
48.5	odd	4		768.4.c.v.767.7		16
48.11	even	4		768.4.c.v.767.9		16
48.29	odd	4		768.4.c.v.767.10		16
48.35	even	4		768.4.c.v.767.8		16

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