LMFDB - Embedded newform 220.3.i.a.43.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.i (of order $4$, degree $2$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.3
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97731 - 0.300385i) q^{2} +(3.24619 - 3.24619i) q^{3} +(3.81954 + 1.18791i) q^{4} +(1.98058 - 4.59100i) q^{5} +(-7.39385 + 5.44363i) q^{6} +(7.61337 - 7.61337i) q^{7} +(-7.19559 - 3.49620i) q^{8} -12.0755i q^{9} +(-5.29530 + 8.48291i) q^{10} +(-6.09319 + 9.15823i) q^{11} +(16.2551 - 8.54277i) q^{12} +(4.80206 - 4.80206i) q^{13} +(-17.3410 + 12.7671i) q^{14} +(-8.47392 - 21.3326i) q^{15} +(13.1777 + 9.07454i) q^{16} +(14.5907 + 14.5907i) q^{17} +(-3.62731 + 23.8771i) q^{18} +20.7331i q^{19} +(13.0186 - 15.1827i) q^{20} -49.4289i q^{21} +(14.7991 - 16.2784i) q^{22} +(-29.0675 + 29.0675i) q^{23} +(-34.7076 + 12.0089i) q^{24} +(-17.1546 - 18.1857i) q^{25} +(-10.9376 + 8.05270i) q^{26} +(-9.98374 - 9.98374i) q^{27} +(38.1236 - 20.0356i) q^{28} +1.92818 q^{29} +(10.3476 + 44.7267i) q^{30} -8.59885i q^{31} +(-23.3307 - 21.9016i) q^{32} +(9.94971 + 49.5090i) q^{33} +(-24.4675 - 33.2331i) q^{34} +(-19.8741 - 50.0319i) q^{35} +(14.3446 - 46.1229i) q^{36} +(17.6719 - 17.6719i) q^{37} +(6.22791 - 40.9959i) q^{38} -31.1768i q^{39} +(-30.3025 + 26.1105i) q^{40} -5.50642i q^{41} +(-14.8477 + 97.7365i) q^{42} +(-45.1761 - 45.1761i) q^{43} +(-34.1523 + 27.7420i) q^{44} +(-55.4387 - 23.9166i) q^{45} +(66.2070 - 48.7441i) q^{46} +(16.6738 + 16.6738i) q^{47} +(72.2352 - 13.3198i) q^{48} -66.9268i q^{49} +(28.4573 + 41.1118i) q^{50} +94.7281 q^{51} +(24.0460 - 12.6372i) q^{52} +(31.2455 + 31.2455i) q^{53} +(16.7420 + 22.7399i) q^{54} +(29.9774 + 46.1124i) q^{55} +(-81.4006 + 28.1648i) q^{56} +(67.3036 + 67.3036i) q^{57} +(-3.81261 - 0.579196i) q^{58} -70.3798 q^{59} +(-7.02523 - 91.5470i) q^{60} +27.2372i q^{61} +(-2.58296 + 17.0026i) q^{62} +(-91.9354 - 91.9354i) q^{63} +(39.5531 + 50.3145i) q^{64} +(-12.5354 - 31.5571i) q^{65} +(-4.80193 - 100.884i) q^{66} +(40.1755 + 40.1755i) q^{67} +(38.3972 + 73.0620i) q^{68} +188.717i q^{69} +(24.2685 + 104.899i) q^{70} -18.0249i q^{71} +(-42.2185 + 86.8906i) q^{72} +(-20.1988 + 20.1988i) q^{73} +(-40.2513 + 29.6345i) q^{74} +(-114.721 - 3.34721i) q^{75} +(-24.6291 + 79.1909i) q^{76} +(23.3353 + 116.115i) q^{77} +(-9.36504 + 61.6463i) q^{78} +63.7129i q^{79} +(67.7608 - 42.5261i) q^{80} +43.8614 q^{81} +(-1.65405 + 10.8879i) q^{82} +(60.3034 + 60.3034i) q^{83} +(58.7171 - 188.796i) q^{84} +(95.8837 - 38.0877i) q^{85} +(75.7572 + 102.898i) q^{86} +(6.25923 - 6.25923i) q^{87} +(75.8631 - 44.5958i) q^{88} -158.122i q^{89} +(102.436 + 63.9435i) q^{90} -73.1197i q^{91} +(-145.554 + 76.4948i) q^{92} +(-27.9135 - 27.9135i) q^{93} +(-27.9608 - 37.9780i) q^{94} +(95.1857 + 41.0636i) q^{95} +(-146.833 + 4.63901i) q^{96} +(-42.2823 + 42.2823i) q^{97} +(-20.1038 + 132.335i) q^{98} +(110.590 + 73.5784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.97731	−	0.300385i	−0.988657	−	0.150192i
$2$	−1.97731	−	0.300385i	−0.988657	−	0.150192i
$3$	3.24619	−	3.24619i	1.08206	−	1.08206i	0.0857470	−	0.996317i	$-0.472672\pi$
$3$	3.24619	−	3.24619i	1.08206	−	1.08206i	0.996317	−	0.0857470i	$-0.0273277\pi$
$4$	3.81954	+	1.18791i	0.954884	+	0.296978i
$5$	1.98058	−	4.59100i	0.396116	−	0.918200i
$5$	1.98058	−	4.59100i	0.396116	−	0.918200i
$6$	−7.39385	+	5.44363i	−1.23231	+	0.907272i
$7$	7.61337	−	7.61337i	1.08762	−	1.08762i	0.0918517	−	0.995773i	$-0.470721\pi$
$7$	7.61337	−	7.61337i	1.08762	−	1.08762i	0.995773	−	0.0918517i	$-0.0292786\pi$
$8$	−7.19559	−	3.49620i	−0.899449	−	0.437025i
$9$		−	12.0755i		−	1.34172i
$10$	−5.29530	+	8.48291i	−0.529530	+	0.848291i
$11$	−6.09319	+	9.15823i	−0.553926	+	0.832566i
$11$	−6.09319	+	9.15823i	−0.553926	+	0.832566i
$12$	16.2551	−	8.54277i	1.35459	−	0.711897i
$13$	4.80206	−	4.80206i	0.369389	−	0.369389i	−0.497865	−	0.867254i	$-0.665883\pi$
$13$	4.80206	−	4.80206i	0.369389	−	0.369389i	0.867254	+	0.497865i	$0.165883\pi$
$14$	−17.3410	+	12.7671i	−1.23864	+	0.911934i
$15$	−8.47392	−	21.3326i	−0.564928	−	1.42217i
$16$	13.1777	+	9.07454i	0.823609	+	0.567159i
$17$	14.5907	+	14.5907i	0.858274	+	0.858274i	0.991135	−	0.132861i	$-0.0424163\pi$
$17$	14.5907	+	14.5907i	0.858274	+	0.858274i	−0.132861	+	0.991135i	$0.542416\pi$
$18$	−3.62731	+	23.8771i	−0.201517	+	1.32651i
$19$			20.7331i			1.09122i	0.838040	+	0.545608i	$0.183701\pi$
$19$			20.7331i			1.09122i	−0.838040	+	0.545608i	$0.816299\pi$
$20$	13.0186	−	15.1827i	0.650930	−	0.759137i
$21$		−	49.4289i		−	2.35376i
$22$	14.7991	−	16.2784i	0.672688	−	0.739926i
$23$	−29.0675	+	29.0675i	−1.26380	+	1.26380i	−0.314569	+	0.949234i	$0.601860\pi$
$23$	−29.0675	+	29.0675i	−1.26380	+	1.26380i	−0.949234	+	0.314569i	$0.898140\pi$
$24$	−34.7076	+	12.0089i	−1.44615	+	0.500372i
$25$	−17.1546	−	18.1857i	−0.686184	−	0.727428i
$26$	−10.9376	+	8.05270i	−0.420678	+	0.309719i
$27$	−9.98374	−	9.98374i	−0.369768	−	0.369768i
$28$	38.1236	−	20.0356i	1.36156	−	0.715555i
$29$	1.92818			0.0664889			0.0332444	−	0.999447i	$-0.489416\pi$
$29$	1.92818			0.0664889			0.0332444	+	0.999447i	$0.489416\pi$
$30$	10.3476	+	44.7267i	0.344920	+	1.49089i
$31$		−	8.59885i		−	0.277382i	−0.990336	−	0.138691i	$-0.955710\pi$
$31$		−	8.59885i		−	0.277382i	0.990336	−	0.138691i	$-0.0442895\pi$
$32$	−23.3307	−	21.9016i	−0.729083	−	0.684425i
$33$	9.94971	+	49.5090i	0.301506	+	1.50027i
$34$	−24.4675	−	33.2331i	−0.719632	−	0.977445i
$35$	−19.8741	−	50.0319i	−0.567831	−	1.42948i
$36$	14.3446	−	46.1229i	0.398462	−	1.28119i
$37$	17.6719	−	17.6719i	0.477619	−	0.477619i	−0.426750	−	0.904369i	$-0.640342\pi$
$37$	17.6719	−	17.6719i	0.477619	−	0.477619i	0.904369	+	0.426750i	$0.140342\pi$
$38$	6.22791	−	40.9959i	0.163892	−	1.07884i
$39$		−	31.1768i		−	0.799405i
$40$	−30.3025	+	26.1105i	−0.757563	+	0.652762i
$41$		−	5.50642i		−	0.134303i	−0.997743	−	0.0671515i	$-0.978609\pi$
$41$		−	5.50642i		−	0.134303i	0.997743	−	0.0671515i	$-0.0213911\pi$
$42$	−14.8477	+	97.7365i	−0.353517	+	2.32706i
$43$	−45.1761	−	45.1761i	−1.05061	−	1.05061i	−0.998649	−	0.0519587i	$-0.983454\pi$
$43$	−45.1761	−	45.1761i	−1.05061	−	1.05061i	−0.0519587	−	0.998649i	$-0.516546\pi$
$44$	−34.1523	+	27.7420i	−0.776189	+	0.630501i
$45$	−55.4387	−	23.9166i	−1.23197	−	0.531479i
$46$	66.2070	−	48.7441i	1.43928	−	1.05965i
$47$	16.6738	+	16.6738i	0.354763	+	0.354763i	0.861878	−	0.507116i	$-0.169288\pi$
$47$	16.6738	+	16.6738i	0.354763	+	0.354763i	−0.507116	+	0.861878i	$0.669288\pi$
$48$	72.2352	−	13.3198i	1.50490	−	0.277495i
$49$		−	66.9268i		−	1.36585i
$50$	28.4573	+	41.1118i	0.569146	+	0.822237i
$51$	94.7281			1.85741
$52$	24.0460	−	12.6372i	0.462424	−	0.243023i
$53$	31.2455	+	31.2455i	0.589538	+	0.589538i	0.937506	−	0.347968i	$-0.113128\pi$
$53$	31.2455	+	31.2455i	0.589538	+	0.589538i	−0.347968	+	0.937506i	$0.613128\pi$
$54$	16.7420	+	22.7399i	0.310037	+	0.421110i
$55$	29.9774	+	46.1124i	0.545043	+	0.838408i
$56$	−81.4006	+	28.1648i	−1.45358	+	0.502943i
$57$	67.3036	+	67.3036i	1.18077	+	1.18077i
$58$	−3.81261	−	0.579196i	−0.0657347	−	0.00998613i
$59$	−70.3798			−1.19288			−0.596439	−	0.802658i	$-0.703418\pi$
$59$	−70.3798			−1.19288			−0.596439	+	0.802658i	$0.703418\pi$
$60$	−7.02523	−	91.5470i	−0.117087	−	1.52578i
$61$			27.2372i			0.446511i	0.974760	+	0.223256i	$0.0716685\pi$
$61$			27.2372i			0.446511i	−0.974760	+	0.223256i	$0.928331\pi$
$62$	−2.58296	+	17.0026i	−0.0416607	+	0.274236i
$63$	−91.9354	−	91.9354i	−1.45929	−	1.45929i
$64$	39.5531	+	50.3145i	0.618018	+	0.786164i
$65$	−12.5354	−	31.5571i	−0.192852	−	0.485494i
$66$	−4.80193	−	100.884i	−0.0727565	−	1.52854i
$67$	40.1755	+	40.1755i	0.599634	+	0.599634i	0.940215	−	0.340581i	$-0.110624\pi$
$67$	40.1755	+	40.1755i	0.599634	+	0.599634i	−0.340581	+	0.940215i	$0.610624\pi$
$68$	38.3972	+	73.0620i	0.564664	+	1.07444i
$69$			188.717i			2.73503i
$70$	24.2685	+	104.899i	0.346693	+	1.49855i
$71$		−	18.0249i		−	0.253872i	−0.991911	−	0.126936i	$-0.959486\pi$
$71$		−	18.0249i		−	0.253872i	0.991911	−	0.126936i	$-0.0405144\pi$
$72$	−42.2185	+	86.8906i	−0.586368	+	1.20681i
$73$	−20.1988	+	20.1988i	−0.276695	+	0.276695i	−0.831788	−	0.555093i	$-0.812683\pi$
$73$	−20.1988	+	20.1988i	−0.276695	+	0.276695i	0.555093	+	0.831788i	$0.312683\pi$
$74$	−40.2513	+	29.6345i	−0.543936	+	0.400467i
$75$	−114.721	−	3.34721i	−1.52962	−	0.0446294i
$76$	−24.6291	+	79.1909i	−0.324067	+	1.04199i
$77$	23.3353	+	116.115i	0.303056	+	1.50798i
$78$	−9.36504	+	61.6463i	−0.120065	+	0.790337i
$79$			63.7129i			0.806493i	0.915091	+	0.403246i	$0.132118\pi$
$79$			63.7129i			0.806493i	−0.915091	+	0.403246i	$0.867882\pi$
$80$	67.7608	−	42.5261i	0.847010	−	0.531577i
$81$	43.8614			0.541499
$82$	−1.65405	+	10.8879i	−0.0201713	+	0.132780i
$83$	60.3034	+	60.3034i	0.726547	+	0.726547i	0.969930	−	0.243383i	$-0.0782572\pi$
$83$	60.3034	+	60.3034i	0.726547	+	0.726547i	−0.243383	+	0.969930i	$0.578257\pi$
$84$	58.7171	−	188.796i	0.699014	−	2.24757i
$85$	95.8837	−	38.0877i	1.12804	−	0.448091i
$86$	75.7572	+	102.898i	0.880897	+	1.19648i
$87$	6.25923	−	6.25923i	0.0719452	−	0.0719452i
$88$	75.8631	−	44.5958i	0.862081	−	0.506771i
$89$		−	158.122i		−	1.77665i	−0.459211	−	0.888327i	$-0.651868\pi$
$89$		−	158.122i		−	1.77665i	0.459211	−	0.888327i	$-0.348132\pi$
$90$	102.436	+	63.9435i	1.13817	+	0.710483i
$91$		−	73.1197i		−	0.803513i
$92$	−145.554	+	76.4948i	−1.58211	+	0.831465i
$93$	−27.9135	−	27.9135i	−0.300145	−	0.300145i
$94$	−27.9608	−	37.9780i	−0.297456	−	0.404021i
$95$	95.1857	+	41.0636i	1.00195	+	0.432249i
$96$	−146.833	+	4.63901i	−1.52951	+	0.0483230i
$97$	−42.2823	+	42.2823i	−0.435899	+	0.435899i	−0.890629	−	0.454730i	$-0.849736\pi$
$97$	−42.2823	+	42.2823i	−0.435899	+	0.435899i	0.454730	+	0.890629i	$0.349736\pi$
$98$	−20.1038	+	132.335i	−0.205141	+	1.35036i
$99$	110.590	+	73.5784i	1.11707	+	0.743216i
$100$	−43.9196	−	89.8391i	−0.439196	−	0.898391i
$101$		−	29.8413i		−	0.295459i	−0.989028	−	0.147729i	$-0.952804\pi$
$101$		−	29.8413i		−	0.295459i	0.989028	−	0.147729i	$-0.0471965\pi$
$102$	−187.307	−	28.4549i	−1.83635	−	0.278970i
$103$	19.5770	−	19.5770i	0.190068	−	0.190068i	−0.605658	−	0.795725i	$-0.707090\pi$
$103$	19.5770	−	19.5770i	0.190068	−	0.190068i	0.795725	+	0.605658i	$0.207090\pi$
$104$	−51.3426	+	17.7647i	−0.493679	+	0.170814i
$105$	−226.928	−	97.8980i	−2.16122	−	0.932362i
$106$	−52.3965	−	71.1679i	−0.494307	−	0.671395i
$107$	−35.0360	+	35.0360i	−0.327439	+	0.327439i	−0.851612	−	0.524173i	$-0.824375\pi$
$107$	−35.0360	+	35.0360i	−0.327439	+	0.327439i	0.524173	+	0.851612i	$0.324375\pi$
$108$	−26.2735	−	49.9931i	−0.243273	−	0.462899i
$109$	158.734			1.45628			0.728140	−	0.685429i	$-0.240385\pi$
$109$	158.734			1.45628			0.728140	+	0.685429i	$0.240385\pi$
$110$	−45.4232	−	100.184i	−0.412938	−	0.910759i
$111$		−	114.733i		−	1.03363i
$112$	169.415	−	31.2392i	1.51263	−	0.278921i
$113$	−75.0963	−	75.0963i	−0.664569	−	0.664569i	0.291885	−	0.956453i	$-0.405718\pi$
$113$	−75.0963	−	75.0963i	−0.664569	−	0.664569i	−0.956453	+	0.291885i	$0.905718\pi$
$114$	−112.863	−	153.297i	−0.990030	−	1.34471i
$115$	75.8783	+	191.019i	0.659812	+	1.66104i
$116$	7.36475	+	2.29050i	0.0634892	+	0.0197457i
$117$	−57.9873	−	57.9873i	−0.495618	−	0.495618i
$118$	139.163	+	21.1410i	1.17935	+	0.179161i
$119$	222.168			1.86696
$120$	−13.6083	+	183.127i	−0.113402	+	1.52606i
$121$	−46.7462	−	111.606i	−0.386332	−	0.922360i
$122$	8.18165	−	53.8565i	0.0670627	−	0.441447i
$123$	−17.8749	−	17.8749i	−0.145324	−	0.145324i
$124$	10.2147	−	32.8436i	0.0823763	−	0.264868i
$125$	−117.467	+	42.7385i	−0.939734	+	0.341908i
$126$	154.169	+	209.401i	1.22356	+	1.66191i
$127$	90.0794	−	90.0794i	0.709286	−	0.709286i	−0.257099	−	0.966385i	$-0.582767\pi$
$127$	90.0794	−	90.0794i	0.709286	−	0.709286i	0.966385	+	0.257099i	$0.0827666\pi$
$128$	−63.0952	−	111.369i	−0.492931	−	0.870068i
$129$	−293.301			−2.27365
$130$	15.3071	+	66.1637i	0.117747	+	0.508952i
$131$	−134.972			−1.03032			−0.515161	−	0.857093i	$-0.672268\pi$
$131$	−134.972			−1.03032			−0.515161	+	0.857093i	$0.672268\pi$
$132$	−20.8090	+	200.921i	−0.157644	+	1.52213i
$133$	157.849	+	157.849i	1.18683	+	1.18683i
$134$	−67.3714	−	91.5076i	−0.502772	−	0.682893i
$135$	−65.6090	+	26.0617i	−0.485992	+	0.193050i
$136$	−53.9765	−	156.000i	−0.396886	−	1.14706i
$137$	96.1568	−	96.1568i	0.701874	−	0.701874i	−0.262938	−	0.964813i	$-0.584692\pi$
$137$	96.1568	−	96.1568i	0.701874	−	0.701874i	0.964813	+	0.262938i	$0.0846916\pi$
$138$	56.6878	−	373.153i	0.410781	−	2.70401i
$139$			265.052i			1.90685i	0.301628	+	0.953426i	$0.402470\pi$
$139$			265.052i			1.90685i	−0.301628	+	0.953426i	$0.597530\pi$
$140$	−16.4764	−	214.707i	−0.117689	−	1.53362i
$141$	108.253			0.767752
$142$	−5.41442	+	35.6410i	−0.0381297	+	0.250993i
$143$	14.7185	+	73.2381i	0.102927	+	0.512155i
$144$	109.580	−	159.128i	0.760971	−	1.10506i
$145$	3.81891	−	8.85227i	0.0263373	−	0.0610501i
$146$	46.0067	−	33.8719i	0.315114	−	0.231999i
$147$	−217.257	−	217.257i	−1.47794	−	1.47794i
$148$	88.4912	−	46.5059i	0.597913	−	0.314229i
$149$	−176.929			−1.18744			−0.593721	−	0.804671i	$-0.702342\pi$
$149$	−176.929			−1.18744			−0.593721	+	0.804671i	$0.702342\pi$
$150$	225.835	+	41.0791i	1.50556	+	0.273860i
$151$	−25.9429			−0.171807			−0.0859037	−	0.996303i	$-0.527378\pi$
$151$	−25.9429			−0.171807			−0.0859037	+	0.996303i	$0.527378\pi$
$152$	72.4872	−	149.187i	0.476889	−	0.981493i
$153$	176.190	−	176.190i	1.15157	−	1.15157i
$154$	−11.2621	−	236.605i	−0.0731304	−	1.53639i
$155$	−39.4773	−	17.0307i	−0.254692	−	0.109876i
$156$	37.0352	−	119.081i	0.237405	−	0.763339i
$157$	87.1246	−	87.1246i	0.554934	−	0.554934i	−0.372927	−	0.927861i	$-0.621646\pi$
$157$	87.1246	−	87.1246i	0.554934	−	0.554934i	0.927861	+	0.372927i	$0.121646\pi$
$158$	19.1384	−	125.980i	0.121129	−	0.797345i
$159$	202.858			1.27584
$160$	−146.759	+	63.7332i	−0.917241	+	0.398332i
$161$			442.603i			2.74909i
$162$	−86.7278	−	13.1753i	−0.535357	−	0.0813291i
$163$	−3.98479	+	3.98479i	−0.0244466	+	0.0244466i	−0.719224	−	0.694778i	$-0.755503\pi$
$163$	−3.98479	+	3.98479i	−0.0244466	+	0.0244466i	0.694778	+	0.719224i	$0.255503\pi$
$164$	6.54114	−	21.0320i	0.0398850	−	0.128244i
$165$	247.002	+	52.3775i	1.49698	+	0.317440i
$166$	−101.125	−	137.353i	−0.609184	−	0.827428i
$167$	138.416	−	138.416i	0.828841	−	0.828841i	−0.158515	−	0.987357i	$-0.550671\pi$
$167$	138.416	−	138.416i	0.828841	−	0.828841i	0.987357	+	0.158515i	$0.0506707\pi$
$168$	−172.814	+	355.670i	−1.02865	+	2.11709i
$169$			122.881i			0.727104i
$170$	−201.033	+	46.5094i	−1.18255	+	0.273585i
$171$	250.363			1.46411
$172$	−118.887	−	226.217i	−0.691202	−	1.31522i
$173$	−142.650	+	142.650i	−0.824567	+	0.824567i	−0.986759	−	0.162193i	$-0.948143\pi$
$173$	−142.650	+	142.650i	−0.824567	+	0.824567i	0.162193	+	0.986759i	$0.448143\pi$
$174$	−14.2566	+	10.4963i	−0.0819348	+	0.0603235i
$175$	−269.059	−	7.85028i	−1.53748	−	0.0448588i
$176$	−163.401	+	65.3918i	−0.928415	+	0.371545i
$177$	−228.466	+	228.466i	−1.29077	+	1.29077i
$178$	−47.4975	+	312.657i	−0.266840	+	1.75650i
$179$	−128.414			−0.717396			−0.358698	−	0.933454i	$-0.616779\pi$
$179$	−128.414			−0.717396			−0.358698	+	0.933454i	$0.616779\pi$
$180$	−183.340	−	157.206i	−1.01855	−	0.873369i
$181$	63.5332			0.351012			0.175506	−	0.984478i	$-0.443844\pi$
$181$	63.5332			0.351012			0.175506	+	0.984478i	$0.443844\pi$
$182$	−21.9640	+	144.580i	−0.120682	+	0.794398i
$183$	88.4172	+	88.4172i	0.483154	+	0.483154i
$184$	310.784	−	107.532i	1.68904	−	0.584413i
$185$	−46.1311	−	116.132i	−0.249357	−	0.627743i
$186$	46.8090	+	63.5786i	0.251661	+	0.341820i
$187$	−222.528	+	44.7209i	−1.18999	+	0.239149i
$188$	43.8793	+	83.4934i	0.233401	+	0.444114i
$189$	−152.020			−0.804338
$190$	−175.877	−	109.788i	−0.925669	−	0.577832i
$191$			73.4358i			0.384481i	0.981348	+	0.192240i	$0.0615753\pi$
$191$			73.4358i			0.384481i	−0.981348	+	0.192240i	$0.938425\pi$
$192$	291.728	+	34.9335i	1.51941	+	0.181945i
$193$	53.3222	−	53.3222i	0.276281	−	0.276281i	−0.555342	−	0.831622i	$-0.687413\pi$
$193$	53.3222	−	53.3222i	0.276281	−	0.276281i	0.831622	+	0.555342i	$0.187413\pi$
$194$	96.3062	−	70.9043i	0.496424	−	0.365486i
$195$	−143.133	−	61.7482i	−0.734014	−	0.316657i
$196$	79.5031	−	255.630i	0.405628	−	1.30423i
$197$	12.4442	+	12.4442i	0.0631683	+	0.0631683i	0.737985	−	0.674817i	$-0.235777\pi$
$197$	12.4442	+	12.4442i	0.0631683	+	0.0631683i	−0.674817	+	0.737985i	$0.735777\pi$
$198$	−196.570	−	178.707i	−0.992778	−	0.902562i
$199$	−134.542			−0.676092			−0.338046	−	0.941130i	$-0.609766\pi$
$199$	−134.542			−0.676092			−0.338046	+	0.941130i	$0.609766\pi$
$200$	59.8565	+	190.833i	0.299283	+	0.954165i
$201$	260.835			1.29768
$202$	−8.96389	+	59.0057i	−0.0443757	+	0.292107i
$203$	14.6799	−	14.6799i	0.0723149	−	0.0723149i
$204$	361.818	+	112.529i	1.77362	+	0.551611i
$205$	−25.2800	−	10.9059i	−0.123317	−	0.0531996i
$206$	−44.5905	+	32.8292i	−0.216459	+	0.159365i
$207$	351.005	+	351.005i	1.69568	+	1.69568i
$208$	106.857	−	19.7038i	0.513734	−	0.0947298i
$209$	−189.878	−	126.331i	−0.908509	−	0.604453i
$210$	419.301	+	261.741i	1.99667	+	1.24639i
$211$	−325.918			−1.54464			−0.772318	−	0.635236i	$-0.780903\pi$
$211$	−325.918			−1.54464			−0.772318	+	0.635236i	$0.780903\pi$
$212$	82.2266	+	156.460i	0.387861	+	0.738021i
$213$	−58.5124	−	58.5124i	−0.274706	−	0.274706i
$214$	79.8014	−	58.7529i	0.372904	−	0.274546i
$215$	−296.879	+	117.929i	−1.38083	+	0.548506i
$216$	36.9337	+	106.744i	0.170990	+	0.494186i
$217$	−65.4662	−	65.4662i	−0.301688	−	0.301688i
$218$	−313.868	−	47.6814i	−1.43976	−	0.218722i
$219$			131.138i			0.598804i
$220$	59.7223	+	211.739i	0.271465	+	0.962448i
$221$	140.130			0.634074
$222$	−34.4640	+	226.863i	−0.155243	+	1.02190i
$223$	−83.7285	+	83.7285i	−0.375464	+	0.375464i	−0.869463	−	0.493998i	$-0.835535\pi$
$223$	−83.7285	+	83.7285i	−0.375464	+	0.375464i	0.493998	+	0.869463i	$0.335535\pi$
$224$	−344.370	+	10.8800i	−1.53737	+	0.0485714i
$225$	−219.602	+	207.151i	−0.976009	+	0.920670i
$226$	125.931	+	171.047i	0.557217	+	0.756843i
$227$	201.535	−	201.535i	0.887819	−	0.887819i	−0.106494	−	0.994313i	$-0.533963\pi$
$227$	201.535	−	201.535i	0.887819	−	0.887819i	0.994313	+	0.106494i	$0.0339626\pi$
$228$	177.118	+	337.020i	0.776834	+	1.47816i
$229$			146.104i			0.638011i	0.947753	+	0.319005i	$0.103349\pi$
$229$			146.104i			0.638011i	−0.947753	+	0.319005i	$0.896651\pi$
$230$	−92.6559	−	400.498i	−0.402852	−	1.74130i
$231$	452.681	+	301.180i	1.95966	+	1.30381i
$232$	−13.8744	−	6.74130i	−0.0598034	−	0.0290573i
$233$	296.687	−	296.687i	1.27334	−	1.27334i	0.329009	−	0.944327i	$-0.393286\pi$
$233$	296.687	−	296.687i	1.27334	−	1.27334i	0.944327	−	0.329009i	$-0.106714\pi$
$234$	97.2406	+	132.078i	0.415558	+	0.564434i
$235$	109.574	−	43.5257i	0.466270	−	0.185216i
$236$	−268.818	−	83.6050i	−1.13906	−	0.354258i
$237$	206.824	+	206.824i	0.872677	+	0.872677i
$238$	−439.296	−	66.7360i	−1.84578	−	0.280403i
$239$		−	102.318i		−	0.428107i	−0.976822	−	0.214053i	$-0.931333\pi$
$239$		−	102.318i		−	0.428107i	0.976822	−	0.214053i	$-0.0686667\pi$
$240$	81.9165	−	358.013i	0.341319	−	1.49172i
$241$		−	124.284i		−	0.515702i	−0.966185	−	0.257851i	$-0.916986\pi$
$241$		−	124.284i		−	0.515702i	0.966185	−	0.257851i	$-0.0830143\pi$
$242$	58.9072	+	234.721i	0.243418	+	0.969921i
$243$	232.236	−	232.236i	0.955705	−	0.955705i
$244$	−32.3554	+	104.034i	−0.132604	+	0.426367i
$245$	−307.261	−	132.554i	−1.25413	−	0.541037i
$246$	29.9749	+	40.7137i	0.121849	+	0.165503i
$247$	99.5615	+	99.5615i	0.403083	+	0.403083i
$248$	−30.0633	+	61.8738i	−0.121223	+	0.249491i
$249$	391.513			1.57234
$250$	245.106	−	49.2221i	0.980426	−	0.196889i
$251$		−	312.241i		−	1.24399i	−0.783021	−	0.621995i	$-0.786323\pi$
$251$		−	312.241i		−	1.24399i	0.783021	−	0.621995i	$-0.213677\pi$
$252$	−241.940	−	460.362i	−0.960079	−	1.82683i
$253$	−89.0930	−	443.320i	−0.352146	−	1.75225i
$254$	−205.174	+	151.057i	−0.807770	+	0.594711i
$255$	187.617	−	434.897i	0.735752	−	1.70548i
$256$	91.3055	+	239.164i	0.356662	+	0.934233i
$257$	−58.8883	+	58.8883i	−0.229137	+	0.229137i	−0.812332	−	0.583195i	$-0.801802\pi$
$257$	−58.8883	+	58.8883i	−0.229137	+	0.229137i	0.583195	+	0.812332i	$0.301802\pi$
$258$	579.948	+	88.1032i	2.24786	+	0.341485i
$259$		−	269.086i		−	1.03894i
$260$	−10.3923	−	135.424i	−0.0399705	−	0.520863i
$261$		−	23.2838i		−	0.0892098i
$262$	266.882	+	40.5436i	1.01863	+	0.154747i
$263$	199.015	+	199.015i	0.756711	+	0.756711i	0.975722	−	0.219012i	$-0.0702832\pi$
$263$	199.015	+	199.015i	0.756711	+	0.756711i	−0.219012	+	0.975722i	$0.570283\pi$
$264$	101.500	−	391.033i	0.384468	−	1.48119i
$265$	205.333	−	81.5639i	0.774840	−	0.307788i
$266$	−264.701	−	359.532i	−0.995117	−	1.35162i
$267$	−513.295	−	513.295i	−1.92245	−	1.92245i
$268$	105.727	+	201.177i	0.394503	+	0.750659i
$269$			498.105i			1.85169i	0.377900	+	0.925846i	$0.376646\pi$
$269$			498.105i			1.85169i	−0.377900	+	0.925846i	$0.623354\pi$
$270$	137.558	−	31.8243i	0.509474	−	0.117868i
$271$	95.3382			0.351802			0.175901	−	0.984408i	$-0.443716\pi$
$271$	95.3382			0.351802			0.175901	+	0.984408i	$0.443716\pi$
$272$	59.8684	+	324.675i	0.220104	+	1.19366i
$273$	−237.360	−	237.360i	−0.869452	−	0.869452i
$274$	−219.016	+	161.248i	−0.799329	+	0.588497i
$275$	271.075	−	46.2967i	0.985727	−	0.168352i
$276$	−224.179	+	720.813i	−0.812244	+	2.61164i
$277$	−230.570	−	230.570i	−0.832384	−	0.832384i	0.155458	−	0.987842i	$-0.450315\pi$
$277$	−230.570	−	230.570i	−0.832384	−	0.832384i	−0.987842	+	0.155458i	$0.950315\pi$
$278$	79.6177	−	524.092i	0.286395	−	1.88522i
$279$	−103.836			−0.372171
$280$	−31.9158	+	429.493i	−0.113985	+	1.53390i
$281$			379.926i			1.35205i	0.736878	+	0.676025i	$0.236299\pi$
$281$			379.926i			1.35205i	−0.736878	+	0.676025i	$0.763701\pi$
$282$	−214.050	−	32.5176i	−0.759043	−	0.115311i
$283$	−226.175	−	226.175i	−0.799204	−	0.799204i	0.183766	−	0.982970i	$-0.441171\pi$
$283$	−226.175	−	226.175i	−0.799204	−	0.799204i	−0.982970	+	0.183766i	$0.941171\pi$
$284$	21.4120	−	68.8470i	0.0753944	−	0.242419i
$285$	442.291	−	175.691i	1.55190	−	0.616459i
$286$	−7.10344	−	149.236i	−0.0248372	−	0.521804i
$287$	−41.9224	−	41.9224i	−0.146071	−	0.146071i
$288$	−264.473	+	281.730i	−0.918310	+	0.978229i
$289$			136.775i			0.473268i
$290$	−10.2103	+	16.3566i	−0.0352079	+	0.0564019i
$291$			274.513i			0.943342i
$292$	−101.144	+	53.1556i	−0.346384	+	0.182040i
$293$	90.9722	−	90.9722i	0.310485	−	0.310485i	−0.534612	−	0.845097i	$-0.679542\pi$
$293$	90.9722	−	90.9722i	0.310485	−	0.310485i	0.845097	+	0.534612i	$0.179542\pi$
$294$	364.325	+	494.847i	1.23920	+	1.68315i
$295$	−139.393	+	323.114i	−0.472519	+	1.09530i
$296$	−188.944	+	65.3753i	−0.638326	+	0.220862i
$297$	152.266	−	30.6006i	0.512680	−	0.103032i
$298$	349.844	+	53.1468i	1.17397	+	0.178345i
$299$			279.167i			0.933670i
$300$	−434.207	−	149.064i	−1.44736	−	0.496878i
$301$	−687.885			−2.28533
$302$	51.2973	+	7.79286i	0.169858	+	0.0258042i
$303$	−96.8707	−	96.8707i	−0.319705	−	0.319705i
$304$	−188.143	+	273.215i	−0.618893	+	0.898735i
$305$	125.046	+	53.9455i	0.409987	+	0.176871i
$306$	−401.307	+	295.458i	−1.31146	+	0.965548i
$307$	108.441	−	108.441i	0.353229	−	0.353229i	−0.508081	−	0.861310i	$-0.669645\pi$
$307$	108.441	−	108.441i	0.353229	−	0.353229i	0.861310	+	0.508081i	$0.169645\pi$
$308$	−48.8038	+	471.224i	−0.158454	+	1.52995i
$309$		−	127.101i		−	0.411331i
$310$	72.9433	+	45.5335i	0.235301	+	0.146882i
$311$		−	183.814i		−	0.591041i	−0.955336	−	0.295521i	$-0.904507\pi$
$311$		−	183.814i		−	0.591041i	0.955336	−	0.295521i	$-0.0954931\pi$
$312$	−109.000	+	224.335i	−0.349360	+	0.719024i
$313$	75.3895	+	75.3895i	0.240861	+	0.240861i	0.817206	−	0.576345i	$-0.195522\pi$
$313$	75.3895	+	75.3895i	0.240861	+	0.240861i	−0.576345	+	0.817206i	$0.695522\pi$
$314$	−198.444	+	146.102i	−0.631986	+	0.465292i
$315$	−604.161	+	239.990i	−1.91797	+	0.761873i
$316$	−75.6853	+	243.354i	−0.239510	+	0.770107i
$317$	173.507	−	173.507i	0.547342	−	0.547342i	−0.378329	−	0.925671i	$-0.623501\pi$
$317$	173.507	−	173.507i	0.547342	−	0.547342i	0.925671	+	0.378329i	$0.123501\pi$
$318$	−401.114	−	60.9355i	−1.26136	−	0.191621i
$319$	−11.7487	+	17.6587i	−0.0368299	+	0.0553564i
$320$	309.332	−	81.9365i	0.966663	−	0.256051i
$321$			227.467i			0.708620i
$322$	132.951	−	875.165i	0.412892	−	2.71790i
$323$	−302.510	+	302.510i	−0.936562	+	0.936562i
$324$	167.530	+	52.1035i	0.517069	+	0.160813i
$325$	−169.706	−	4.95149i	−0.522173	−	0.0152353i
$326$	9.07615	−	6.68220i	0.0278409	−	0.0204976i
$327$	515.282	−	515.282i	1.57579	−	1.57579i
$328$	−19.2516	+	39.6220i	−0.0586938	+	0.120799i
$329$	253.888			0.771697
$330$	−472.667	−	177.763i	−1.43232	−	0.538674i
$331$			163.386i			0.493612i	0.969065	+	0.246806i	$0.0793811\pi$
$331$			163.386i			0.493612i	−0.969065	+	0.246806i	$0.920619\pi$
$332$	158.696	+	301.966i	0.478000	+	0.909537i
$333$	−213.398	−	213.398i	−0.640833	−	0.640833i
$334$	−315.271	+	232.115i	−0.943925	+	0.694954i
$335$	264.016	−	104.875i	0.788109	−	0.313059i
$336$	448.545	−	651.361i	1.33495	−	1.93858i
$337$	−206.708	−	206.708i	−0.613377	−	0.613377i	0.330447	−	0.943824i	$-0.392800\pi$
$337$	−206.708	−	206.708i	−0.613377	−	0.613377i	−0.943824	+	0.330447i	$0.892800\pi$
$338$	36.9115	−	242.973i	0.109206	−	0.718856i
$339$	−487.554			−1.43821
$340$	411.476	−	31.5763i	1.21022	−	0.0928714i
$341$	78.7502	+	52.3944i	0.230939	+	0.153649i
$342$	−495.046	−	75.2053i	−1.44750	−	0.219899i
$343$	−136.484	−	136.484i	−0.397911	−	0.397911i
$344$	167.124	+	483.014i	0.485826	+	1.40411i
$345$	866.401	+	373.770i	2.51131	+	1.08339i
$346$	324.914	−	239.214i	0.939057	−	0.691370i
$347$	−21.7171	+	21.7171i	−0.0625853	+	0.0625853i	−0.737707	−	0.675121i	$-0.764091\pi$
$347$	−21.7171	+	21.7171i	−0.0625853	+	0.0625853i	0.675121	+	0.737707i	$0.264091\pi$
$348$	31.3428	−	16.4720i	0.0900655	−	0.0473332i
$349$	−315.410			−0.903753			−0.451876	−	0.892081i	$-0.649245\pi$
$349$	−315.410			−0.903753			−0.451876	+	0.892081i	$0.649245\pi$
$350$	529.656	+	96.3437i	1.51330	+	0.275268i
$351$	−95.8849			−0.273176
$352$	342.738	−	80.2170i	0.973687	−	0.227889i
$353$	92.8687	+	92.8687i	0.263084	+	0.263084i	0.826306	−	0.563222i	$-0.190438\pi$
$353$	92.8687	+	92.8687i	0.263084	+	0.263084i	−0.563222	+	0.826306i	$0.690438\pi$
$354$	520.378	−	383.122i	1.46999	−	1.08227i
$355$	−82.7526	−	35.6999i	−0.233106	−	0.100563i
$356$	187.835	−	603.954i	0.527627	−	1.69650i
$357$	721.201	−	721.201i	2.02017	−	2.02017i
$358$	253.915	+	38.5736i	0.709259	+	0.107748i
$359$		−	265.398i		−	0.739271i	−0.929177	−	0.369635i	$-0.879483\pi$
$359$		−	265.398i		−	0.739271i	0.929177	−	0.369635i	$-0.120517\pi$
$360$	315.298	+	365.919i	0.875826	+	1.01644i
$361$	−68.8617			−0.190753
$362$	−125.625	−	19.0844i	−0.347031	−	0.0527194i
$363$	−514.040	−	210.546i	−1.41609	−	0.580016i
$364$	86.8596	−	279.283i	0.238625	−	0.767262i
$365$	52.7272	+	132.738i	0.144458	+	0.363665i
$366$	−148.269	−	201.388i	−0.405107	−	0.550240i
$367$	−130.264	−	130.264i	−0.354943	−	0.354943i	0.507002	−	0.861945i	$-0.330754\pi$
$367$	−130.264	−	130.264i	−0.354943	−	0.354943i	−0.861945	+	0.507002i	$0.830754\pi$
$368$	−646.818	+	119.270i	−1.75766	+	0.324102i
$369$	−66.4930			−0.180198
$370$	56.3312	+	243.487i	0.152247	+	0.658074i
$371$	475.768			1.28239
$372$	−73.4579	−	139.775i	−0.197468	−	0.375740i
$373$	−408.820	+	408.820i	−1.09603	+	1.09603i	−0.101163	+	0.994870i	$0.532256\pi$
$373$	−408.820	+	408.820i	−1.09603	+	1.09603i	−0.994870	+	0.101163i	$0.967744\pi$
$374$	453.441	−	21.5832i	1.21241	−	0.0577092i
$375$	−242.582	+	520.057i	−0.646886	+	1.38682i
$376$	−61.6830	−	178.273i	−0.164051	−	0.474131i
$377$	9.25922	−	9.25922i	0.0245603	−	0.0245603i
$378$	300.591	+	45.6645i	0.795214	+	0.120805i
$379$	114.598			0.302368			0.151184	−	0.988506i	$-0.451691\pi$
$379$	114.598			0.302368			0.151184	+	0.988506i	$0.451691\pi$
$380$	314.786	+	269.916i	0.828383	+	0.710306i
$381$		−	584.830i		−	1.53499i
$382$	22.0590	−	145.206i	0.0577461	−	0.380119i
$383$	107.027	−	107.027i	0.279443	−	0.279443i	−0.553443	−	0.832887i	$-0.686686\pi$
$383$	107.027	−	107.027i	0.279443	−	0.279443i	0.832887	+	0.553443i	$0.186686\pi$
$384$	−566.343	−	156.705i	−1.47485	−	0.408086i
$385$	579.300	+	122.842i	1.50468	+	0.319071i
$386$	−121.452	+	89.4175i	−0.314642	+	0.231651i
$387$	−545.526	+	545.526i	−1.40963	+	1.40963i
$388$	−211.726	+	111.271i	−0.545686	+	0.286781i
$389$		−	397.311i		−	1.02136i	−0.859770	−	0.510682i	$-0.829393\pi$
$389$		−	397.311i		−	1.02136i	0.859770	−	0.510682i	$-0.170607\pi$
$390$	264.470	+	165.090i	0.678128	+	0.423309i
$391$	−848.228			−2.16938
$392$	−233.990	+	481.578i	−0.596913	+	1.22852i
$393$	−438.146	+	438.146i	−1.11487	+	1.11487i
$394$	−20.8680	−	28.3441i	−0.0529644	−	0.0719392i
$395$	292.506	+	126.189i	0.740522	+	0.319465i
$396$	334.999	+	412.407i	0.845958	+	1.04143i
$397$	−142.656	+	142.656i	−0.359335	+	0.359335i	−0.863568	−	0.504233i	$-0.831775\pi$
$397$	−142.656	+	142.656i	−0.359335	+	0.359335i	0.504233	+	0.863568i	$0.331775\pi$
$398$	266.032	+	40.4145i	0.668423	+	0.101544i
$399$	1024.82			2.56846
$400$	−61.0318	−	395.316i	−0.152579	−	0.988291i
$401$	−101.697			−0.253608			−0.126804	−	0.991928i	$-0.540472\pi$
$401$	−101.697			−0.253608			−0.126804	+	0.991928i	$0.540472\pi$
$402$	−515.752	−	78.3508i	−1.28296	−	0.194902i
$403$	−41.2921	−	41.2921i	−0.102462	−	0.102462i
$404$	35.4488	−	113.980i	0.0877446	−	0.282129i
$405$	86.8712	−	201.368i	0.214497	−	0.497205i
$406$	−33.4365	+	24.6172i	−0.0823558	+	0.0606335i
$407$	54.1651	+	269.522i	0.133084	+	0.662215i
$408$	−681.625	−	331.189i	−1.67065	−	0.811737i
$409$	−555.544			−1.35830			−0.679149	−	0.734000i	$-0.737651\pi$
$409$	−555.544			−1.35830			−0.679149	+	0.734000i	$0.737651\pi$
$410$	46.7105	+	29.1582i	0.113928	+	0.0711175i
$411$		−	624.287i		−	1.51895i
$412$	98.0308	−	51.5194i	0.237939	−	0.125047i
$413$	−535.828	+	535.828i	−1.29740	+	1.29740i
$414$	−588.611	−	799.484i	−1.42176	−	1.93112i
$415$	396.289	−	157.417i	0.954913	−	0.379319i
$416$	−217.208	+	6.86244i	−0.522134	+	0.0164962i
$417$	860.411	+	860.411i	2.06334	+	2.06334i
$418$	337.501	+	306.832i	0.807420	+	0.734048i
$419$	−282.912			−0.675208			−0.337604	−	0.941288i	$-0.609617\pi$
$419$	−282.912			−0.675208			−0.337604	+	0.941288i	$0.609617\pi$
$420$	−750.467	−	643.496i	−1.78683	−	1.53213i
$421$	183.454			0.435759			0.217879	−	0.975976i	$-0.430086\pi$
$421$	183.454			0.435759			0.217879	+	0.975976i	$0.430086\pi$
$422$	644.442	+	97.9009i	1.52711	+	0.231993i
$423$	201.345	−	201.345i	0.475994	−	0.475994i
$424$	−115.589	−	334.071i	−0.272617	−	0.787903i
$425$	15.0447	−	515.638i	0.0353993	−	1.21327i
$426$	98.1212	+	133.274i	0.230331	+	0.312849i
$427$	207.367	+	207.367i	0.485637	+	0.485637i
$428$	−175.441	+	92.2017i	−0.409909	+	0.215424i
$429$	285.524	+	189.966i	0.665557	+	0.442811i
$430$	622.446	−	144.004i	1.44755	−	0.334893i
$431$	379.287			0.880016			0.440008	−	0.897994i	$-0.354976\pi$
$431$	379.287			0.880016			0.440008	+	0.897994i	$0.354976\pi$
$432$	−40.9653	−	222.161i	−0.0948270	−	0.514261i
$433$	258.366	+	258.366i	0.596689	+	0.596689i	0.939430	−	0.342741i	$-0.111355\pi$
$433$	258.366	+	258.366i	0.596689	+	0.596689i	−0.342741	+	0.939430i	$0.611355\pi$
$434$	109.782	+	149.112i	0.252954	+	0.343577i
$435$	−16.3392	−	41.1331i	−0.0375614	−	0.0945588i
$436$	606.292	+	188.562i	1.39058	+	0.432482i
$437$	−602.659	−	602.659i	−1.37908	−	1.37908i
$438$	39.3919	−	259.301i	0.0899359	−	0.592012i
$439$			504.134i			1.14837i	0.818726	+	0.574184i	$0.194681\pi$
$439$			504.134i			1.14837i	−0.818726	+	0.574184i	$0.805319\pi$
$440$	−54.4865	−	436.613i	−0.123833	−	0.992303i
$441$	−808.176			−1.83260
$442$	−277.082	−	42.0930i	−0.626881	−	0.0952331i
$443$	−457.618	+	457.618i	−1.03300	+	1.03300i	−0.0335621	+	0.999437i	$0.510685\pi$
$443$	−457.618	+	457.618i	−1.03300	+	1.03300i	−0.999437	+	0.0335621i	$0.989315\pi$
$444$	136.292	−	438.226i	0.306965	−	0.986996i
$445$	−725.939	−	313.174i	−1.63132	−	0.703762i
$446$	190.708	−	140.407i	0.427597	−	0.314813i
$447$	−574.345	+	574.345i	−1.28489	+	1.28489i
$448$	684.196	+	81.9304i	1.52722	+	0.182880i
$449$			54.8759i			0.122218i	0.998131	+	0.0611090i	$0.0194637\pi$
$449$			54.8759i			0.122218i	−0.998131	+	0.0611090i	$0.980536\pi$
$450$	496.447	−	343.637i	1.10322	−	0.763637i
$451$	50.4291	+	33.5517i	0.111816	+	0.0743939i
$452$	−197.625	−	376.041i	−0.437224	−	0.831948i
$453$	−84.2157	+	84.2157i	−0.185907	+	0.185907i
$454$	−459.036	+	337.960i	−1.01109	+	0.744405i
$455$	−335.692	−	144.819i	−0.737786	−	0.318285i
$456$	−248.982	−	719.597i	−0.546014	−	1.57806i
$457$	−309.442	−	309.442i	−0.677116	−	0.677116i	0.282230	−	0.959347i	$-0.408926\pi$
$457$	−309.442	−	309.442i	−0.677116	−	0.677116i	−0.959347	+	0.282230i	$0.908926\pi$
$458$	43.8876	−	288.894i	0.0958244	−	0.630774i
$459$		−	291.339i		−	0.634725i
$460$	62.9062	+	819.743i	0.136753	+	1.78205i
$461$		−	59.6963i		−	0.129493i	−0.997902	−	0.0647466i	$-0.979376\pi$
$461$		−	59.6963i		−	0.129493i	0.997902	−	0.0647466i	$-0.0206239\pi$
$462$	−804.623	−	731.505i	−1.74161	−	1.58334i
$463$	203.614	−	203.614i	0.439770	−	0.439770i	−0.452164	−	0.891935i	$-0.649348\pi$
$463$	203.614	−	203.614i	0.439770	−	0.439770i	0.891935	+	0.452164i	$0.149348\pi$
$464$	25.4090	+	17.4973i	0.0547608	+	0.0377097i
$465$	−183.436	+	72.8660i	−0.394486	+	0.156701i
$466$	−675.764	+	497.523i	−1.45014	+	1.06765i
$467$	−518.064	−	518.064i	−1.10934	−	1.10934i	−0.993237	−	0.116108i	$-0.962958\pi$
$467$	−518.064	−	518.064i	−1.10934	−	1.10934i	−0.116108	−	0.993237i	$-0.537042\pi$
$468$	−152.601	−	290.369i	−0.326071	−	0.620446i
$469$	611.741			1.30435
$470$	−229.736	+	53.1498i	−0.488799	+	0.113085i
$471$		−	565.647i		−	1.20095i
$472$	506.425	+	246.062i	1.07293	+	0.521318i
$473$	689.000	−	138.467i	1.45666	−	0.292741i
$474$	−346.830	−	471.084i	−0.731708	−	0.993847i
$475$	377.046	−	355.668i	0.793782	−	0.748775i
$476$	848.580	+	263.916i	1.78273	+	0.554445i
$477$	377.306	−	377.306i	0.790998	−	0.790998i
$478$	−30.7347	+	202.314i	−0.0642984	+	0.423251i
$479$		−	874.586i		−	1.82586i	−0.408118	−	0.912929i	$-0.633815\pi$
$479$		−	874.586i		−	1.82586i	0.408118	−	0.912929i	$-0.366185\pi$
$480$	−269.516	+	683.297i	−0.561492	+	1.42353i
$481$		−	169.723i		−	0.352854i
$482$	−37.3331	+	245.749i	−0.0774545	+	0.509852i
$483$	1436.77	+	1436.77i	2.97469	+	2.97469i
$484$	−45.9714	−	481.812i	−0.0949823	−	0.995479i
$485$	110.374	+	277.861i	0.227576	+	0.572910i
$486$	−528.964	+	389.444i	−1.08840	+	0.801325i
$487$	218.183	+	218.183i	0.448013	+	0.448013i	0.894694	−	0.446680i	$-0.147394\pi$
$487$	218.183	+	218.183i	0.448013	+	0.448013i	−0.446680	+	0.894694i	$0.647394\pi$
$488$	95.2268	−	195.988i	0.195137	−	0.401614i
$489$			25.8708i			0.0529055i
$490$	567.734	+	354.398i	1.15864	+	0.723260i
$491$	−22.4882			−0.0458009			−0.0229004	−	0.999738i	$-0.507290\pi$
$491$	−22.4882			−0.0458009			−0.0229004	+	0.999738i	$0.507290\pi$
$492$	−47.0401	−	89.5077i	−0.0956100	−	0.181926i
$493$	28.1334	+	28.1334i	0.0570657	+	0.0570657i
$494$	−166.958	−	226.771i	−0.337971	−	0.459051i
$495$	556.832	−	361.992i	1.12491	−	0.731298i
$496$	78.0306	−	113.313i	0.157320	−	0.228454i
$497$	−137.231	−	137.231i	−0.276118	−	0.276118i
$498$	−774.144	−	117.605i	−1.55451	−	0.236154i
$499$	544.283			1.09075			0.545374	−	0.838193i	$-0.316388\pi$
$499$	544.283			1.09075			0.545374	+	0.838193i	$0.316388\pi$
$500$	−499.438	+	23.7013i	−0.998876	+	0.0474026i
$501$		−	898.653i		−	1.79372i
$502$	−93.7926	+	617.399i	−0.186838	+	1.22988i
$503$	−243.400	−	243.400i	−0.483898	−	0.483898i	0.422476	−	0.906374i	$-0.361161\pi$
$503$	−243.400	−	243.400i	−0.483898	−	0.483898i	−0.906374	+	0.422476i	$0.861161\pi$
$504$	340.105	+	982.955i	0.674812	+	1.95031i
$505$	−137.002	−	59.1032i	−0.271290	−	0.117036i
$506$	42.9981	+	903.345i	0.0849765	+	1.78527i
$507$	398.894	+	398.894i	0.786773	+	0.786773i
$508$	451.068	−	237.055i	0.887929	−	0.466644i
$509$			613.385i			1.20508i	0.798089	+	0.602539i	$0.205844\pi$
$509$			613.385i			1.20508i	−0.798089	+	0.602539i	$0.794156\pi$
$510$	−501.614	+	803.571i	−0.983557	+	1.57563i
$511$			307.561i			0.601881i
$512$	−108.698	−	500.329i	−0.212302	−	0.977204i
$513$	206.994	−	206.994i	0.403497	−	0.403497i
$514$	134.130	−	98.7514i	0.260953	−	0.192123i
$515$	−51.1042	−	128.652i	−0.0992314	−	0.249809i
$516$	−1120.27	−	348.415i	−2.17107	−	0.675223i
$517$	−254.300	+	51.1060i	−0.491875	+	0.0988510i
$518$	−80.8293	+	532.067i	−0.156041	+	1.02716i
$519$			926.139i			1.78447i
$520$	−20.1306	+	270.898i	−0.0387126	+	0.520958i
$521$	−70.3446			−0.135018			−0.0675092	−	0.997719i	$-0.521505\pi$
$521$	−70.3446			−0.135018			−0.0675092	+	0.997719i	$0.521505\pi$
$522$	−6.99409	+	46.0393i	−0.0133986	+	0.0881978i
$523$	232.623	+	232.623i	0.444785	+	0.444785i	0.893616	−	0.448831i	$-0.148160\pi$
$523$	232.623	+	232.623i	0.444785	+	0.444785i	−0.448831	+	0.893616i	$0.648160\pi$
$524$	−515.531	−	160.335i	−0.983839	−	0.305983i
$525$	−898.900	+	847.933i	−1.71219	+	1.61511i
$526$	−333.734	−	453.296i	−0.634475	−	0.861779i
$527$	125.463	−	125.463i	0.238070	−	0.238070i
$528$	−318.157	+	742.706i	−0.602570	+	1.40664i
$529$		−	1160.84i		−	2.19440i
$530$	−430.508	+	99.5987i	−0.812278	+	0.187922i
$531$			849.873i			1.60052i
$532$	415.399	+	790.420i	0.780826	+	1.48575i
$533$	−26.4422	−	26.4422i	−0.0496100	−	0.0496100i
$534$	860.759	+	1169.13i	1.61191	+	2.18938i
$535$	91.4586	+	230.242i	0.170951	+	0.430359i
$536$	−148.625	−	429.548i	−0.277285	−	0.801395i
$537$	−416.856	+	416.856i	−0.776269	+	0.776269i
$538$	149.623	−	984.910i	0.278110	−	1.83069i
$539$	612.931	+	407.798i	1.13716	+	0.756582i
$540$	−281.555	+	21.6062i	−0.521398	+	0.0400116i
$541$			710.769i			1.31381i	0.753975	+	0.656903i	$0.228134\pi$
$541$			710.769i			1.31381i	−0.753975	+	0.656903i	$0.771866\pi$
$542$	−188.514	−	28.6382i	−0.347811	−	0.0528379i
$543$	206.241	−	206.241i	0.379818	−	0.379818i
$544$	−20.8510	−	659.969i	−0.0383290	−	1.21318i
$545$	314.387	−	728.750i	0.576856	−	1.33716i
$546$	398.036	+	540.636i	0.729005	+	0.990175i
$547$	−585.075	+	585.075i	−1.06961	+	1.06961i	−0.0722178	+	0.997389i	$0.523008\pi$
$547$	−585.075	+	585.075i	−1.06961	+	1.06961i	−0.997389	+	0.0722178i	$0.976992\pi$
$548$	481.500	−	253.049i	0.878650	−	0.461768i
$549$	328.903			0.599096
$550$	−549.907	+	10.1163i	−0.999831	+	0.0183932i
$551$			39.9771i			0.0725537i
$552$	659.794	−	1357.93i	1.19528	−	2.46002i
$553$	485.070	+	485.070i	0.877161	+	0.877161i
$554$	386.650	+	525.170i	0.697924	+	0.947960i
$555$	−526.739	−	227.238i	−0.949078	−	0.409437i
$556$	−314.858	+	1012.38i	−0.566292	+	1.82082i
$557$	783.137	+	783.137i	1.40599	+	1.40599i	0.779137	+	0.626853i	$0.215657\pi$
$557$	783.137	+	783.137i	1.40599	+	1.40599i	0.626853	+	0.779137i	$0.284343\pi$
$558$	205.315	+	31.1906i	0.367949	+	0.0558972i
$559$	−433.877			−0.776166
$560$	192.121	−	839.655i	0.343073	−	1.49938i
$561$	−577.196	+	867.542i	−1.02887	+	1.54642i
$562$	114.124	−	751.233i	0.203068	−	1.33671i
$563$	−166.677	−	166.677i	−0.296052	−	0.296052i	0.543414	−	0.839465i	$-0.317132\pi$
$563$	−166.677	−	166.677i	−0.296052	−	0.296052i	−0.839465	+	0.543414i	$0.817132\pi$
$564$	413.476	+	128.595i	0.733114	+	0.228005i
$565$	−493.501	+	196.033i	−0.873454	+	0.346961i
$566$	379.279	+	515.158i	0.670104	+	0.910173i
$567$	333.933	−	333.933i	0.588948	−	0.588948i
$568$	−63.0189	+	129.700i	−0.110949	+	0.228345i
$569$	−207.863			−0.365313			−0.182656	−	0.983177i	$-0.558470\pi$
$569$	−207.863			−0.365313			−0.182656	+	0.983177i	$0.558470\pi$
$570$	−927.324	+	214.538i	−1.62688	+	0.376382i
$571$	−281.714			−0.493370			−0.246685	−	0.969096i	$-0.579341\pi$
$571$	−281.714			−0.493370			−0.246685	+	0.969096i	$0.579341\pi$
$572$	−30.7825	+	297.220i	−0.0538156	+	0.519615i
$573$	238.387	+	238.387i	0.416033	+	0.416033i
$574$	70.3010	+	95.4867i	0.122476	+	0.166353i
$575$	1027.25	+	29.9720i	1.78653	+	0.0521252i
$576$	607.574	−	477.625i	1.05482	−	0.829210i
$577$	−592.720	+	592.720i	−1.02724	+	1.02724i	−0.0276261	+	0.999618i	$0.508795\pi$
$577$	−592.720	+	592.720i	−1.02724	+	1.02724i	−0.999618	+	0.0276261i	$0.991205\pi$
$578$	41.0850	−	270.446i	0.0710814	−	0.467900i
$579$		−	346.188i		−	0.597907i
$580$	25.1022	−	29.2750i	0.0432796	−	0.0504742i
$581$	918.225			1.58042
$582$	82.4595	−	542.797i	0.141683	−	0.932642i
$583$	−476.538	+	95.7688i	−0.817390	+	0.164269i
$584$	215.961	−	74.7231i	0.369796	−	0.127951i
$585$	−381.069	+	151.371i	−0.651399	+	0.258754i
$586$	−207.207	+	152.554i	−0.353596	+	0.260331i
$587$	685.616	+	685.616i	1.16800	+	1.16800i	0.982678	+	0.185323i	$0.0593332\pi$
$587$	685.616	+	685.616i	1.16800	+	1.16800i	0.185323	+	0.982678i	$0.440667\pi$
$588$	−571.740	−	1087.90i	−0.972347	−	1.85018i
$589$	178.281			0.302684
$590$	372.682	−	597.026i	0.631665	−	1.01191i
$591$	80.7923			0.136704
$592$	393.240	−	72.5114i	0.664257	−	0.122485i
$593$	−292.276	+	292.276i	−0.492877	+	0.492877i	−0.909212	−	0.416334i	$-0.863315\pi$
$593$	−292.276	+	292.276i	−0.492877	+	0.492877i	0.416334	+	0.909212i	$0.363315\pi$
$594$	−310.270	+	14.7684i	−0.522340	+	0.0248627i
$595$	440.022	−	1019.97i	0.739533	−	1.71424i
$596$	−675.787	−	210.176i	−1.13387	−	0.352644i
$597$	−436.750	+	436.750i	−0.731575	+	0.731575i
$598$	83.8577	−	552.001i	0.140230	−	0.923079i
$599$	−279.936			−0.467340			−0.233670	−	0.972316i	$-0.575073\pi$
$599$	−279.936			−0.467340			−0.233670	+	0.972316i	$0.575073\pi$
$600$	813.786	+	425.174i	1.35631	+	0.708624i
$601$		−	426.259i		−	0.709249i	−0.935009	−	0.354625i	$-0.884609\pi$
$601$		−	426.259i		−	0.709249i	0.935009	−	0.354625i	$-0.115391\pi$
$602$	1360.17	+	206.630i	2.25941	+	0.343240i
$603$	485.140	−	485.140i	0.804544	−	0.804544i
$604$	−99.0899	−	30.8179i	−0.164056	−	0.0510229i
$605$	−604.966	−	6.43211i	−0.999943	−	0.0106316i
$606$	162.445	+	220.642i	0.268061	+	0.364096i
$607$	366.659	−	366.659i	0.604051	−	0.604051i	−0.337334	−	0.941385i	$-0.609525\pi$
$607$	366.659	−	366.659i	0.604051	−	0.604051i	0.941385	+	0.337334i	$0.109525\pi$
$608$	454.088	−	483.717i	0.746856	−	0.795587i
$609$		−	95.3077i		−	0.156499i
$610$	−231.051	−	144.229i	−0.378772	−	0.236441i
$611$	160.137			0.262091
$612$	882.261	−	463.666i	1.44160	−	0.757624i
$613$	139.096	−	139.096i	0.226911	−	0.226911i	−0.584490	−	0.811401i	$-0.698705\pi$
$613$	139.096	−	139.096i	0.226911	−	0.226911i	0.811401	+	0.584490i	$0.198705\pi$
$614$	−246.997	+	181.848i	−0.402275	+	0.296170i
$615$	−117.466	+	46.6610i	−0.191002	+	0.0758716i
$616$	238.049	−	917.099i	0.386443	−	1.48880i
$617$	−0.408616	+	0.408616i	−0.000662262	+	0.000662262i	−0.707438	−	0.706776i	$-0.750149\pi$
$617$	−0.408616	+	0.408616i	−0.000662262	+	0.000662262i	0.706776	+	0.707438i	$0.250149\pi$
$618$	−38.1793	+	251.319i	−0.0617789	+	0.406666i
$619$	−716.332			−1.15724			−0.578621	−	0.815597i	$-0.696409\pi$
$619$	−716.332			−1.15724			−0.578621	+	0.815597i	$0.696409\pi$
$620$	−130.554	−	111.945i	−0.210571	−	0.180556i
$621$	580.404			0.934629
$622$	−55.2149	+	363.458i	−0.0887700	+	0.584337i
$623$	−1203.84	−	1203.84i	−1.93233	−	1.93233i
$624$	282.915	−	410.840i	0.453389	−	0.658397i
$625$	−36.4400	+	623.937i	−0.0583040	+	0.998299i
$626$	−126.423	−	171.715i	−0.201953	−	0.274305i
$627$	−1026.48	+	206.288i	−1.63712	+	0.329008i
$628$	436.272	−	229.280i	0.694701	−	0.365095i
$629$	515.690			0.819856
$630$	1266.71	−	293.055i	2.01064	−	0.465166i
$631$			713.848i			1.13130i	0.824647	+	0.565648i	$0.191374\pi$
$631$			713.848i			1.13130i	−0.824647	+	0.565648i	$0.808626\pi$
$632$	222.753	−	458.452i	0.352458	−	0.725399i
$633$	−1057.99	+	1057.99i	−1.67139	+	1.67139i
$634$	−395.197	+	290.959i	−0.623340	+	0.458927i
$635$	−235.145	−	591.964i	−0.370307	−	0.932227i
$636$	774.824	+	240.977i	1.21828	+	0.378895i
$637$	−321.386	−	321.386i	−0.504531	−	0.504531i
$638$	28.5354	−	31.3876i	0.0447263	−	0.0491969i
$639$	−217.661			−0.340627
$640$	−636.259	+	69.0953i	−0.994155	+	0.107961i
$641$	485.650			0.757644			0.378822	−	0.925469i	$-0.376329\pi$
$641$	485.650			0.757644			0.378822	+	0.925469i	$0.376329\pi$
$642$	68.3277	−	449.774i	0.106429	−	0.700582i
$643$	−846.612	+	846.612i	−1.31666	+	1.31666i	−0.400257	+	0.916403i	$0.631079\pi$
$643$	−846.612	+	846.612i	−1.31666	+	1.31666i	−0.916403	+	0.400257i	$0.868921\pi$
$644$	−525.773	+	1690.54i	−0.816418	+	2.62506i
$645$	−580.906	+	1346.54i	−0.900630	+	2.08767i
$646$	689.026	−	507.287i	1.06660	−	0.785274i
$647$	102.117	+	102.117i	0.157831	+	0.157831i	0.781605	−	0.623774i	$-0.214401\pi$
$647$	102.117	+	102.117i	0.157831	+	0.157831i	−0.623774	+	0.781605i	$0.714401\pi$
$648$	−315.609	−	153.349i	−0.487051	−	0.236649i
$649$	428.837	−	644.554i	0.660767	−	0.993150i
$650$	334.075	+	60.7678i	0.513961	+	0.0934889i
$651$	−425.032			−0.652891
$652$	−19.9536	+	10.4865i	−0.0306037	+	0.0160836i
$653$	−728.793	−	728.793i	−1.11607	−	1.11607i	−0.992313	−	0.123756i	$-0.960506\pi$
$653$	−728.793	−	728.793i	−1.11607	−	1.11607i	−0.123756	−	0.992313i	$-0.539494\pi$
$654$	−1173.66	+	864.092i	−1.79458	+	1.32124i
$655$	−267.323	+	619.658i	−0.408127	+	0.946042i
$656$	49.9683	−	72.5622i	0.0761711	−	0.110613i
$657$	243.911	+	243.911i	0.371249	+	0.371249i
$658$	−502.017	−	76.2642i	−0.762943	−	0.115903i
$659$			280.987i			0.426384i	0.977010	+	0.213192i	$0.0683860\pi$
$659$			280.987i			0.426384i	−0.977010	+	0.213192i	$0.931614\pi$
$660$	881.214	+	493.474i	1.33517	+	0.747688i
$661$	284.789			0.430846			0.215423	−	0.976521i	$-0.430887\pi$
$661$	284.789			0.430846			0.215423	+	0.976521i	$0.430887\pi$
$662$	49.0786	−	323.065i	0.0741368	−	0.488013i
$663$	454.890	−	454.890i	0.686108	−	0.686108i
$664$	−223.086	−	644.752i	−0.335973	−	0.971012i
$665$	1037.32	−	412.052i	1.55987	−	0.619627i
$666$	357.852	+	486.055i	0.537316	+	0.729813i
$667$	−56.0473	+	56.0473i	−0.0840289	+	0.0840289i
$668$	693.113	−	364.261i	1.03759	−	0.545300i
$669$			543.598i			0.812553i
$670$	−553.546	+	128.064i	−0.826188	+	0.191140i
$671$	−249.444	−	165.961i	−0.371750	−	0.247334i
$672$	−1082.57	+	1153.21i	−1.61097	+	1.71609i
$673$	185.497	−	185.497i	0.275627	−	0.275627i	−0.555733	−	0.831361i	$-0.687562\pi$
$673$	185.497	−	185.497i	0.275627	−	0.275627i	0.831361	+	0.555733i	$0.187562\pi$
$674$	346.635	+	470.819i	0.514295	+	0.698544i
$675$	−10.2944	+	352.828i	−0.0152510	+	0.522709i
$676$	−145.971	+	469.347i	−0.215934	+	0.694300i
$677$	54.6688	+	54.6688i	0.0807516	+	0.0807516i	0.746329	−	0.665577i	$-0.231815\pi$
$677$	54.6688	+	54.6688i	0.0807516	+	0.0807516i	−0.665577	+	0.746329i	$0.731815\pi$
$678$	964.047	+	146.454i	1.42190	+	0.216009i
$679$			643.821i			0.948190i
$680$	−823.103	−	61.1651i	−1.21045	−	0.0899487i
$681$		−	1308.44i		−	1.92135i
$682$	−139.975	−	127.255i	−0.205242	−	0.186592i
$683$	−9.87009	+	9.87009i	−0.0144511	+	0.0144511i	−0.714295	−	0.699844i	$-0.753253\pi$
$683$	−9.87009	+	9.87009i	−0.0144511	+	0.0144511i	0.699844	+	0.714295i	$0.253253\pi$
$684$	956.271	+	297.409i	1.39806	+	0.434808i
$685$	−251.010	−	631.902i	−0.366437	−	0.922485i
$686$	228.873	+	310.868i	0.333634	+	0.453161i
$687$	474.283	+	474.283i	0.690369	+	0.690369i
$688$	−185.367	−	1005.27i	−0.269428	−	1.46115i
$689$	300.086			0.435538
$690$	−1600.87	−	999.315i	−2.32010	−	1.44828i
$691$			500.999i			0.725034i	0.931977	+	0.362517i	$0.118083\pi$
$691$			500.999i			0.725034i	−0.931977	+	0.362517i	$0.881917\pi$
$692$	−714.313	+	375.402i	−1.03224	+	0.542488i
$693$	1402.15	−	281.786i	2.02330	−	0.406617i
$694$	49.4650	−	36.4180i	0.0712753	−	0.0524756i
$695$	1216.86	+	524.958i	1.75087	+	0.755335i
$696$	−66.9225	+	23.1553i	−0.0961530	+	0.0332692i
$697$	80.3424	−	80.3424i	0.115269	−	0.115269i
$698$	623.664	+	94.7443i	0.893501	+	0.135737i
$699$		−	1926.21i		−	2.75566i
$700$	−1018.35	−	349.602i	−1.45479	−	0.499432i
$701$			588.564i			0.839606i	0.907615	+	0.419803i	$0.137901\pi$
$701$			588.564i			0.839606i	−0.907615	+	0.419803i	$0.862099\pi$
$702$	189.595	+	28.8024i	0.270078	+	0.0410290i
$703$	366.394	+	366.394i	0.521186	+	0.521186i
$704$	−701.796	+	55.6608i	−0.996870	+	0.0790636i
$705$	214.404	−	496.990i	0.304119	−	0.704950i
$706$	−155.734	−	211.527i	−0.220587	−	0.299613i
$707$	−227.193	−	227.193i	−0.321348	−	0.321348i
$708$	−1144.03	+	601.239i	−1.61587	+	0.849207i
$709$		−	656.320i		−	0.925698i	−0.886437	−	0.462849i	$-0.846827\pi$
$709$		−	656.320i		−	0.925698i	0.886437	−	0.462849i	$-0.153173\pi$
$710$	152.904	+	95.4475i	0.215358	+	0.134433i
$711$	769.367			1.08209
$712$	−552.827	+	1137.78i	−0.776443	+	1.59801i
$713$	249.947	+	249.947i	0.350557	+	0.350557i
$714$	−1642.68	+	1209.40i	−2.30067	+	1.69384i
$715$	365.388	+	77.4815i	0.511031	+	0.108366i
$716$	−490.482	−	152.544i	−0.685031	−	0.213051i
$717$	−332.142	−	332.142i	−0.463239	−	0.463239i
$718$	−79.7216	+	524.776i	−0.111033	+	0.730885i
$719$	−1219.17			−1.69565			−0.847827	−	0.530274i	$-0.822089\pi$
$719$	−1219.17			−1.69565			−0.847827	+	0.530274i	$0.822089\pi$
$720$	−513.525	−	818.247i	−0.713230	−	1.13645i
$721$		−	298.094i		−	0.413445i
$722$	136.161	+	20.6850i	0.188589	+	0.0286496i
$723$	−403.450	−	403.450i	−0.558022	−	0.558022i
$724$	242.668	+	75.4718i	0.335176	+	0.104243i
$725$	−33.0771	−	35.0653i	−0.0456236	−	0.0483659i
$726$	953.173	+	570.725i	1.31291	+	0.786123i
$727$	−451.881	−	451.881i	−0.621570	−	0.621570i	0.324363	−	0.945933i	$-0.394850\pi$
$727$	−451.881	−	451.881i	−0.621570	−	0.621570i	−0.945933	+	0.324363i	$0.894850\pi$
$728$	−255.641	+	526.139i	−0.351155	+	0.722719i
$729$		−	1113.01i		−	1.52677i
$730$	−64.3858	−	278.303i	−0.0881998	−	0.381237i
$731$		−	1318.30i		−	1.80342i
$732$	232.681	+	442.744i	0.317870	+	0.604842i
$733$	529.659	−	529.659i	0.722591	−	0.722591i	−0.246541	−	0.969132i	$-0.579294\pi$
$733$	529.659	−	529.659i	0.722591	−	0.722591i	0.969132	+	0.246541i	$0.0792942\pi$
$734$	218.443	+	296.702i	0.297607	+	0.404226i
$735$	−1427.72	+	567.133i	−1.94248	+	0.771609i
$736$	1314.79	−	41.5393i	1.78640	−	0.0564392i
$737$	−612.733	+	123.139i	−0.831388	+	0.167082i
$738$	131.477	+	19.9735i	0.178154	+	0.0270643i
$739$		−	515.272i		−	0.697255i	−0.937261	−	0.348628i	$-0.886648\pi$
$739$		−	515.272i		−	0.697255i	0.937261	−	0.348628i	$-0.113352\pi$
$740$	−38.2446	−	498.372i	−0.0516818	−	0.673475i
$741$	646.392			0.872323
$742$	−940.742	−	142.913i	−1.26785	−	0.192606i
$743$	944.478	+	944.478i	1.27117	+	1.27117i	0.945476	+	0.325692i	$0.105597\pi$
$743$	944.478	+	944.478i	1.27117	+	1.27117i	0.325692	+	0.945476i	$0.394403\pi$
$744$	103.263	+	298.446i	0.138794	+	0.401136i
$745$	−350.422	+	812.281i	−0.470365	+	1.09031i
$746$	931.169	−	685.562i	1.24822	−	0.918984i
$747$	728.195	−	728.195i	0.974827	−	0.974827i
$748$	−903.079	−	93.5302i	−1.20732	−	0.125040i
$749$			533.484i			0.712262i
$750$	635.878	−	955.447i	0.847838	−	1.27393i
$751$		−	26.2915i		−	0.0350086i	−0.999847	−	0.0175043i	$-0.994428\pi$
$751$		−	26.2915i		−	0.0350086i	0.999847	−	0.0175043i	$-0.00557208\pi$
$752$	68.4161	+	371.031i	0.0909788	+	0.493392i
$753$	−1013.60	−	1013.60i	−1.34608	−	1.34608i
$754$	−21.0897	+	15.5270i	−0.0279704	+	0.0205929i
$755$	−51.3821	+	119.104i	−0.0680557	+	0.157754i
$756$	−580.645	−	180.586i	−0.768049	−	0.238870i
$757$	222.887	−	222.887i	0.294434	−	0.294434i	−0.544395	−	0.838829i	$-0.683241\pi$
$757$	222.887	−	222.887i	0.294434	−	0.294434i	0.838829	+	0.544395i	$0.183241\pi$
$758$	−226.595	−	34.4234i	−0.298939	−	0.0454135i
$759$	−1728.32	−	1149.89i	−2.27710	−	1.51501i
$760$	−541.351	−	628.266i	−0.712304	−	0.826665i
$761$			290.544i			0.381793i	0.981610	+	0.190897i	$0.0611395\pi$
$761$			290.544i			0.381793i	−0.981610	+	0.190897i	$0.938861\pi$
$762$	−175.674	+	1156.39i	−0.230543	+	1.51757i
$763$	1208.50	−	1208.50i	1.58388	−	1.58388i
$764$	−87.2352	+	280.491i	−0.114182	+	0.367135i
$765$	−459.929	−	1157.85i	−0.601215	−	1.51352i
$766$	−243.775	+	179.476i	−0.318244	+	0.234303i
$767$	−337.968	+	337.968i	−0.440636	+	0.440636i
$768$	1072.77	+	479.976i	1.39683	+	0.624969i
$769$	−342.290			−0.445111			−0.222555	−	0.974920i	$-0.571440\pi$
$769$	−342.290			−0.445111			−0.222555	+	0.974920i	$0.571440\pi$
$770$	−1108.56	−	416.911i	−1.43969	−	0.541442i
$771$			382.325i			0.495882i
$772$	267.008	−	140.324i	0.345865	−	0.181767i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97731 - 0.300385i) q^{2} +(3.24619 - 3.24619i) q^{3} +(3.81954 + 1.18791i) q^{4} +(1.98058 - 4.59100i) q^{5} +(-7.39385 + 5.44363i) q^{6} +(7.61337 - 7.61337i) q^{7} +(-7.19559 - 3.49620i) q^{8} -12.0755i q^{9} +(-5.29530 + 8.48291i) q^{10} +(-6.09319 + 9.15823i) q^{11} +(16.2551 - 8.54277i) q^{12} +(4.80206 - 4.80206i) q^{13} +(-17.3410 + 12.7671i) q^{14} +(-8.47392 - 21.3326i) q^{15} +(13.1777 + 9.07454i) q^{16} +(14.5907 + 14.5907i) q^{17} +(-3.62731 + 23.8771i) q^{18} +20.7331i q^{19} +(13.0186 - 15.1827i) q^{20} -49.4289i q^{21} +(14.7991 - 16.2784i) q^{22} +(-29.0675 + 29.0675i) q^{23} +(-34.7076 + 12.0089i) q^{24} +(-17.1546 - 18.1857i) q^{25} +(-10.9376 + 8.05270i) q^{26} +(-9.98374 - 9.98374i) q^{27} +(38.1236 - 20.0356i) q^{28} +1.92818 q^{29} +(10.3476 + 44.7267i) q^{30} -8.59885i q^{31} +(-23.3307 - 21.9016i) q^{32} +(9.94971 + 49.5090i) q^{33} +(-24.4675 - 33.2331i) q^{34} +(-19.8741 - 50.0319i) q^{35} +(14.3446 - 46.1229i) q^{36} +(17.6719 - 17.6719i) q^{37} +(6.22791 - 40.9959i) q^{38} -31.1768i q^{39} +(-30.3025 + 26.1105i) q^{40} -5.50642i q^{41} +(-14.8477 + 97.7365i) q^{42} +(-45.1761 - 45.1761i) q^{43} +(-34.1523 + 27.7420i) q^{44} +(-55.4387 - 23.9166i) q^{45} +(66.2070 - 48.7441i) q^{46} +(16.6738 + 16.6738i) q^{47} +(72.2352 - 13.3198i) q^{48} -66.9268i q^{49} +(28.4573 + 41.1118i) q^{50} +94.7281 q^{51} +(24.0460 - 12.6372i) q^{52} +(31.2455 + 31.2455i) q^{53} +(16.7420 + 22.7399i) q^{54} +(29.9774 + 46.1124i) q^{55} +(-81.4006 + 28.1648i) q^{56} +(67.3036 + 67.3036i) q^{57} +(-3.81261 - 0.579196i) q^{58} -70.3798 q^{59} +(-7.02523 - 91.5470i) q^{60} +27.2372i q^{61} +(-2.58296 + 17.0026i) q^{62} +(-91.9354 - 91.9354i) q^{63} +(39.5531 + 50.3145i) q^{64} +(-12.5354 - 31.5571i) q^{65} +(-4.80193 - 100.884i) q^{66} +(40.1755 + 40.1755i) q^{67} +(38.3972 + 73.0620i) q^{68} +188.717i q^{69} +(24.2685 + 104.899i) q^{70} -18.0249i q^{71} +(-42.2185 + 86.8906i) q^{72} +(-20.1988 + 20.1988i) q^{73} +(-40.2513 + 29.6345i) q^{74} +(-114.721 - 3.34721i) q^{75} +(-24.6291 + 79.1909i) q^{76} +(23.3353 + 116.115i) q^{77} +(-9.36504 + 61.6463i) q^{78} +63.7129i q^{79} +(67.7608 - 42.5261i) q^{80} +43.8614 q^{81} +(-1.65405 + 10.8879i) q^{82} +(60.3034 + 60.3034i) q^{83} +(58.7171 - 188.796i) q^{84} +(95.8837 - 38.0877i) q^{85} +(75.7572 + 102.898i) q^{86} +(6.25923 - 6.25923i) q^{87} +(75.8631 - 44.5958i) q^{88} -158.122i q^{89} +(102.436 + 63.9435i) q^{90} -73.1197i q^{91} +(-145.554 + 76.4948i) q^{92} +(-27.9135 - 27.9135i) q^{93} +(-27.9608 - 37.9780i) q^{94} +(95.1857 + 41.0636i) q^{95} +(-146.833 + 4.63901i) q^{96} +(-42.2823 + 42.2823i) q^{97} +(-20.1038 + 132.335i) q^{98} +(110.590 + 73.5784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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