LMFDB - Embedded newform 35.3.c.c.34.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,3,Mod(34,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.34"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.3
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	35.34
Dual form			35.3.c.c.34.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.00000i q^{2} -3.16228 q^{3} -5.00000 q^{4} +(1.58114 + 4.74342i) q^{5} -9.48683i q^{6} +(6.32456 - 3.00000i) q^{7} -3.00000i q^{8} +1.00000 q^{9} +(-14.2302 + 4.74342i) q^{10} +14.0000 q^{11} +15.8114 q^{12} +3.16228 q^{13} +(9.00000 + 18.9737i) q^{14} +(-5.00000 - 15.0000i) q^{15} -11.0000 q^{16} -6.32456 q^{17} +3.00000i q^{18} -28.4605i q^{19} +(-7.90569 - 23.7171i) q^{20} +(-20.0000 + 9.48683i) q^{21} +42.0000i q^{22} -12.0000i q^{23} +9.48683i q^{24} +(-20.0000 + 15.0000i) q^{25} +9.48683i q^{26} +25.2982 q^{27} +(-31.6228 + 15.0000i) q^{28} +14.0000 q^{29} +(45.0000 - 15.0000i) q^{30} +37.9473i q^{31} -45.0000i q^{32} -44.2719 q^{33} -18.9737i q^{34} +(24.2302 + 25.2566i) q^{35} -5.00000 q^{36} +18.0000i q^{37} +85.3815 q^{38} -10.0000 q^{39} +(14.2302 - 4.74342i) q^{40} -18.9737i q^{41} +(-28.4605 - 60.0000i) q^{42} -42.0000i q^{43} -70.0000 q^{44} +(1.58114 + 4.74342i) q^{45} +36.0000 q^{46} -44.2719 q^{47} +34.7851 q^{48} +(31.0000 - 37.9473i) q^{49} +(-45.0000 - 60.0000i) q^{50} +20.0000 q^{51} -15.8114 q^{52} +54.0000i q^{53} +75.8947i q^{54} +(22.1359 + 66.4078i) q^{55} +(-9.00000 - 18.9737i) q^{56} +90.0000i q^{57} +42.0000i q^{58} +9.48683i q^{59} +(25.0000 + 75.0000i) q^{60} -66.4078i q^{61} -113.842 q^{62} +(6.32456 - 3.00000i) q^{63} +91.0000 q^{64} +(5.00000 + 15.0000i) q^{65} -132.816i q^{66} -102.000i q^{67} +31.6228 q^{68} +37.9473i q^{69} +(-75.7698 + 72.6907i) q^{70} -16.0000 q^{71} -3.00000i q^{72} -63.2456 q^{73} -54.0000 q^{74} +(63.2456 - 47.4342i) q^{75} +142.302i q^{76} +(88.5438 - 42.0000i) q^{77} -30.0000i q^{78} -76.0000 q^{79} +(-17.3925 - 52.1776i) q^{80} -89.0000 q^{81} +56.9210 q^{82} -72.7324 q^{83} +(100.000 - 47.4342i) q^{84} +(-10.0000 - 30.0000i) q^{85} +126.000 q^{86} -44.2719 q^{87} -42.0000i q^{88} +56.9210i q^{89} +(-14.2302 + 4.74342i) q^{90} +(20.0000 - 9.48683i) q^{91} +60.0000i q^{92} -120.000i q^{93} -132.816i q^{94} +(135.000 - 45.0000i) q^{95} +142.302i q^{96} +69.5701 q^{97} +(113.842 + 93.0000i) q^{98} +14.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 20 q^{4} + 4 q^{9} + 56 q^{11} + 36 q^{14} - 20 q^{15} - 44 q^{16} - 80 q^{21} - 80 q^{25} + 56 q^{29} + 180 q^{30} + 40 q^{35} - 20 q^{36} - 40 q^{39} - 280 q^{44} + 144 q^{46} + 124 q^{49} - 180 q^{50}+ \cdots + 56 q^{99}+O(q^{100}) $ 4 * q - 20 * q^4 + 4 * q^9 + 56 * q^11 + 36 * q^14 - 20 * q^15 - 44 * q^16 - 80 * q^21 - 80 * q^25 + 56 * q^29 + 180 * q^30 + 40 * q^35 - 20 * q^36 - 40 * q^39 - 280 * q^44 + 144 * q^46 + 124 * q^49 - 180 * q^50 + 80 * q^51 - 36 * q^56 + 100 * q^60 + 364 * q^64 + 20 * q^65 - 360 * q^70 - 64 * q^71 - 216 * q^74 - 304 * q^79 - 356 * q^81 + 400 * q^84 - 40 * q^85 + 504 * q^86 + 80 * q^91 + 540 * q^95 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			3.00000i			1.50000i	0.661438	+	0.750000i	$0.269947\pi$
$2$			3.00000i			1.50000i	−0.661438	+	0.750000i	$0.730053\pi$
$3$	−3.16228			−1.05409			−0.527046	−	0.849837i	$-0.676701\pi$
$3$	−3.16228			−1.05409			−0.527046	+	0.849837i	$0.676701\pi$
$4$	−5.00000			−1.25000
$5$	1.58114	+	4.74342i	0.316228	+	0.948683i
$5$	1.58114	+	4.74342i	0.316228	+	0.948683i
$6$		−	9.48683i		−	1.58114i
$7$	6.32456	−	3.00000i	0.903508	−	0.428571i
$7$	6.32456	−	3.00000i	0.903508	−	0.428571i
$8$		−	3.00000i		−	0.375000i
$9$	1.00000			0.111111
$10$	−14.2302	+	4.74342i	−1.42302	+	0.474342i
$11$	14.0000			1.27273			0.636364	−	0.771389i	$-0.280438\pi$
$11$	14.0000			1.27273			0.636364	+	0.771389i	$0.280438\pi$
$12$	15.8114			1.31762
$13$	3.16228			0.243252			0.121626	−	0.992576i	$-0.461189\pi$
$13$	3.16228			0.243252			0.121626	+	0.992576i	$0.461189\pi$
$14$	9.00000	+	18.9737i	0.642857	+	1.35526i
$15$	−5.00000	−	15.0000i	−0.333333	−	1.00000i
$16$	−11.0000			−0.687500
$17$	−6.32456			−0.372033			−0.186016	−	0.982547i	$-0.559558\pi$
$17$	−6.32456			−0.372033			−0.186016	+	0.982547i	$0.559558\pi$
$18$			3.00000i			0.166667i
$19$		−	28.4605i		−	1.49792i	−0.662615	−	0.748960i	$-0.730553\pi$
$19$		−	28.4605i		−	1.49792i	0.662615	−	0.748960i	$-0.269447\pi$
$20$	−7.90569	−	23.7171i	−0.395285	−	1.18585i
$21$	−20.0000	+	9.48683i	−0.952381	+	0.451754i
$22$			42.0000i			1.90909i
$23$		−	12.0000i		−	0.521739i	−0.965374	−	0.260870i	$-0.915991\pi$
$23$		−	12.0000i		−	0.521739i	0.965374	−	0.260870i	$-0.0840093\pi$
$24$			9.48683i			0.395285i
$25$	−20.0000	+	15.0000i	−0.800000	+	0.600000i
$26$			9.48683i			0.364878i
$27$	25.2982			0.936971
$28$	−31.6228	+	15.0000i	−1.12938	+	0.535714i
$29$	14.0000			0.482759			0.241379	−	0.970431i	$-0.422400\pi$
$29$	14.0000			0.482759			0.241379	+	0.970431i	$0.422400\pi$
$30$	45.0000	−	15.0000i	1.50000	−	0.500000i
$31$			37.9473i			1.22411i	0.790816	+	0.612054i	$0.209656\pi$
$31$			37.9473i			1.22411i	−0.790816	+	0.612054i	$0.790344\pi$
$32$		−	45.0000i		−	1.40625i
$33$	−44.2719			−1.34157
$34$		−	18.9737i		−	0.558049i
$35$	24.2302	+	25.2566i	0.692293	+	0.721617i
$36$	−5.00000			−0.138889
$37$			18.0000i			0.486486i	0.969965	+	0.243243i	$0.0782113\pi$
$37$			18.0000i			0.486486i	−0.969965	+	0.243243i	$0.921789\pi$
$38$	85.3815			2.24688
$39$	−10.0000			−0.256410
$40$	14.2302	−	4.74342i	0.355756	−	0.118585i
$41$		−	18.9737i		−	0.462772i	−0.972862	−	0.231386i	$-0.925674\pi$
$41$		−	18.9737i		−	0.462772i	0.972862	−	0.231386i	$-0.0743261\pi$
$42$	−28.4605	−	60.0000i	−0.677631	−	1.42857i
$43$		−	42.0000i		−	0.976744i	−0.872635	−	0.488372i	$-0.837591\pi$
$43$		−	42.0000i		−	0.976744i	0.872635	−	0.488372i	$-0.162409\pi$
$44$	−70.0000			−1.59091
$45$	1.58114	+	4.74342i	0.0351364	+	0.105409i
$46$	36.0000			0.782609
$47$	−44.2719			−0.941955			−0.470978	−	0.882145i	$-0.656099\pi$
$47$	−44.2719			−0.941955			−0.470978	+	0.882145i	$0.656099\pi$
$48$	34.7851			0.724689
$49$	31.0000	−	37.9473i	0.632653	−	0.774435i
$50$	−45.0000	−	60.0000i	−0.900000	−	1.20000i
$51$	20.0000			0.392157
$52$	−15.8114			−0.304065
$53$			54.0000i			1.01887i	0.860510	+	0.509434i	$0.170145\pi$
$53$			54.0000i			1.01887i	−0.860510	+	0.509434i	$0.829855\pi$
$54$			75.8947i			1.40546i
$55$	22.1359	+	66.4078i	0.402472	+	1.20742i
$56$	−9.00000	−	18.9737i	−0.160714	−	0.338815i
$57$			90.0000i			1.57895i
$58$			42.0000i			0.724138i
$59$			9.48683i			0.160794i	0.996763	+	0.0803969i	$0.0256188\pi$
$59$			9.48683i			0.160794i	−0.996763	+	0.0803969i	$0.974381\pi$
$60$	25.0000	+	75.0000i	0.416667	+	1.25000i
$61$		−	66.4078i		−	1.08865i	−0.838873	−	0.544326i	$-0.816785\pi$
$61$		−	66.4078i		−	1.08865i	0.838873	−	0.544326i	$-0.183215\pi$
$62$	−113.842			−1.83616
$63$	6.32456	−	3.00000i	0.100390	−	0.0476190i
$64$	91.0000			1.42188
$65$	5.00000	+	15.0000i	0.0769231	+	0.230769i
$66$		−	132.816i		−	2.01236i
$67$		−	102.000i		−	1.52239i	−0.648524	−	0.761194i	$-0.724613\pi$
$67$		−	102.000i		−	1.52239i	0.648524	−	0.761194i	$-0.275387\pi$
$68$	31.6228			0.465041
$69$			37.9473i			0.549961i
$70$	−75.7698	+	72.6907i	−1.08243	+	1.03844i
$71$	−16.0000			−0.225352			−0.112676	−	0.993632i	$-0.535942\pi$
$71$	−16.0000			−0.225352			−0.112676	+	0.993632i	$0.535942\pi$
$72$		−	3.00000i		−	0.0416667i
$73$	−63.2456			−0.866377			−0.433189	−	0.901303i	$-0.642612\pi$
$73$	−63.2456			−0.866377			−0.433189	+	0.901303i	$0.642612\pi$
$74$	−54.0000			−0.729730
$75$	63.2456	−	47.4342i	0.843274	−	0.632456i
$76$			142.302i			1.87240i
$77$	88.5438	−	42.0000i	1.14992	−	0.545455i
$78$		−	30.0000i		−	0.384615i
$79$	−76.0000			−0.962025			−0.481013	−	0.876714i	$-0.659731\pi$
$79$	−76.0000			−0.962025			−0.481013	+	0.876714i	$0.659731\pi$
$80$	−17.3925	−	52.1776i	−0.217407	−	0.652220i
$81$	−89.0000			−1.09877
$82$	56.9210			0.694159
$83$	−72.7324			−0.876294			−0.438147	−	0.898903i	$-0.644365\pi$
$83$	−72.7324			−0.876294			−0.438147	+	0.898903i	$0.644365\pi$
$84$	100.000	−	47.4342i	1.19048	−	0.564692i
$85$	−10.0000	−	30.0000i	−0.117647	−	0.352941i
$86$	126.000			1.46512
$87$	−44.2719			−0.508872
$88$		−	42.0000i		−	0.477273i
$89$			56.9210i			0.639562i	0.947492	+	0.319781i	$0.103609\pi$
$89$			56.9210i			0.639562i	−0.947492	+	0.319781i	$0.896391\pi$
$90$	−14.2302	+	4.74342i	−0.158114	+	0.0527046i
$91$	20.0000	−	9.48683i	0.219780	−	0.104251i
$92$			60.0000i			0.652174i
$93$		−	120.000i		−	1.29032i
$94$		−	132.816i		−	1.41293i
$95$	135.000	−	45.0000i	1.42105	−	0.473684i
$96$			142.302i			1.48232i
$97$	69.5701			0.717218			0.358609	−	0.933488i	$-0.383251\pi$
$97$	69.5701			0.717218			0.358609	+	0.933488i	$0.383251\pi$
$98$	113.842	+	93.0000i	1.16165	+	0.948980i
$99$	14.0000			0.141414
$100$	100.000	−	75.0000i	1.00000	−	0.750000i
$101$			104.355i			1.03322i	0.856221	+	0.516610i	$0.172806\pi$
$101$			104.355i			1.03322i	−0.856221	+	0.516610i	$0.827194\pi$
$102$			60.0000i			0.588235i
$103$	88.5438			0.859648			0.429824	−	0.902913i	$-0.358576\pi$
$103$	88.5438			0.859648			0.429824	+	0.902913i	$0.358576\pi$
$104$		−	9.48683i		−	0.0912195i
$105$	−76.6228	−	79.8683i	−0.729741	−	0.760651i
$106$	−162.000			−1.52830
$107$			54.0000i			0.504673i	0.967640	+	0.252336i	$0.0811990\pi$
$107$			54.0000i			0.504673i	−0.967640	+	0.252336i	$0.918801\pi$
$108$	−126.491			−1.17121
$109$	74.0000			0.678899			0.339450	−	0.940624i	$-0.389759\pi$
$109$	74.0000			0.678899			0.339450	+	0.940624i	$0.389759\pi$
$110$	−199.223	+	66.4078i	−1.81112	+	0.603708i
$111$		−	56.9210i		−	0.512802i
$112$	−69.5701	+	33.0000i	−0.621162	+	0.294643i
$113$			78.0000i			0.690265i	0.938554	+	0.345133i	$0.112166\pi$
$113$			78.0000i			0.690265i	−0.938554	+	0.345133i	$0.887834\pi$
$114$	−270.000			−2.36842
$115$	56.9210	−	18.9737i	0.494965	−	0.164988i
$116$	−70.0000			−0.603448
$117$	3.16228			0.0270280
$118$	−28.4605			−0.241191
$119$	−40.0000	+	18.9737i	−0.336134	+	0.159443i
$120$	−45.0000	+	15.0000i	−0.375000	+	0.125000i
$121$	75.0000			0.619835
$122$	199.223			1.63298
$123$			60.0000i			0.487805i
$124$		−	189.737i		−	1.53013i
$125$	−102.774	−	71.1512i	−0.822192	−	0.569210i
$126$	9.00000	+	18.9737i	0.0714286	+	0.150585i
$127$		−	72.0000i		−	0.566929i	−0.958983	−	0.283465i	$-0.908516\pi$
$127$		−	72.0000i		−	0.566929i	0.958983	−	0.283465i	$-0.0914838\pi$
$128$			93.0000i			0.726562i
$129$			132.816i			1.02958i
$130$	−45.0000	+	15.0000i	−0.346154	+	0.115385i
$131$		−	47.4342i		−	0.362093i	−0.983475	−	0.181046i	$-0.942052\pi$
$131$		−	47.4342i		−	0.362093i	0.983475	−	0.181046i	$-0.0579484\pi$
$132$	221.359			1.67697
$133$	−85.3815	−	180.000i	−0.641966	−	1.35338i
$134$	306.000			2.28358
$135$	40.0000	+	120.000i	0.296296	+	0.888889i
$136$			18.9737i			0.139512i
$137$			84.0000i			0.613139i	0.951848	+	0.306569i	$0.0991811\pi$
$137$			84.0000i			0.613139i	−0.951848	+	0.306569i	$0.900819\pi$
$138$	−113.842			−0.824942
$139$			123.329i			0.887258i	0.896211	+	0.443629i	$0.146309\pi$
$139$			123.329i			0.887258i	−0.896211	+	0.443629i	$0.853691\pi$
$140$	−121.151	−	126.283i	−0.865366	−	0.902021i
$141$	140.000			0.992908
$142$		−	48.0000i		−	0.338028i
$143$	44.2719			0.309594
$144$	−11.0000			−0.0763889
$145$	22.1359	+	66.4078i	0.152662	+	0.457985i
$146$		−	189.737i		−	1.29957i
$147$	−98.0306	+	120.000i	−0.666875	+	0.816327i
$148$		−	90.0000i		−	0.608108i
$149$	−46.0000			−0.308725			−0.154362	−	0.988014i	$-0.549332\pi$
$149$	−46.0000			−0.308725			−0.154362	+	0.988014i	$0.549332\pi$
$150$	142.302	+	189.737i	0.948683	+	1.26491i
$151$	14.0000			0.0927152			0.0463576	−	0.998925i	$-0.485239\pi$
$151$	14.0000			0.0927152			0.0463576	+	0.998925i	$0.485239\pi$
$152$	−85.3815			−0.561720
$153$	−6.32456			−0.0413370
$154$	126.000	+	265.631i	0.818182	+	1.72488i
$155$	−180.000	+	60.0000i	−1.16129	+	0.387097i
$156$	50.0000			0.320513
$157$	117.004			0.745250			0.372625	−	0.927982i	$-0.378458\pi$
$157$	117.004			0.745250			0.372625	+	0.927982i	$0.378458\pi$
$158$		−	228.000i		−	1.44304i
$159$		−	170.763i		−	1.07398i
$160$	213.454	−	71.1512i	1.33409	−	0.444695i
$161$	−36.0000	−	75.8947i	−0.223602	−	0.471395i
$162$		−	267.000i		−	1.64815i
$163$			54.0000i			0.331288i	0.986186	+	0.165644i	$0.0529703\pi$
$163$			54.0000i			0.331288i	−0.986186	+	0.165644i	$0.947030\pi$
$164$			94.8683i			0.578465i
$165$	−70.0000	−	210.000i	−0.424242	−	1.27273i
$166$		−	218.197i		−	1.31444i
$167$	−139.140			−0.833175			−0.416587	−	0.909096i	$-0.636774\pi$
$167$	−139.140			−0.833175			−0.416587	+	0.909096i	$0.636774\pi$
$168$	28.4605	+	60.0000i	0.169408	+	0.357143i
$169$	−159.000			−0.940828
$170$	90.0000	−	30.0000i	0.529412	−	0.176471i
$171$		−	28.4605i		−	0.166436i
$172$			210.000i			1.22093i
$173$	211.873			1.22470			0.612349	−	0.790588i	$-0.290225\pi$
$173$	211.873			1.22470			0.612349	+	0.790588i	$0.290225\pi$
$174$		−	132.816i		−	0.763308i
$175$	−81.4911	+	154.868i	−0.465663	+	0.884962i
$176$	−154.000			−0.875000
$177$		−	30.0000i		−	0.169492i
$178$	−170.763			−0.959343
$179$	−178.000			−0.994413			−0.497207	−	0.867632i	$-0.665641\pi$
$179$	−178.000			−0.994413			−0.497207	+	0.867632i	$0.665641\pi$
$180$	−7.90569	−	23.7171i	−0.0439205	−	0.131762i
$181$		−	28.4605i		−	0.157240i	−0.996905	−	0.0786202i	$-0.974949\pi$
$181$		−	28.4605i		−	0.157240i	0.996905	−	0.0786202i	$-0.0250514\pi$
$182$	28.4605	+	60.0000i	0.156376	+	0.329670i
$183$			210.000i			1.14754i
$184$	−36.0000			−0.195652
$185$	−85.3815	+	28.4605i	−0.461522	+	0.153841i
$186$	360.000			1.93548
$187$	−88.5438			−0.473496
$188$	221.359			1.17744
$189$	160.000	−	75.8947i	0.846561	−	0.401559i
$190$	135.000	+	405.000i	0.710526	+	2.13158i
$191$	−148.000			−0.774869			−0.387435	−	0.921897i	$-0.626639\pi$
$191$	−148.000			−0.774869			−0.387435	+	0.921897i	$0.626639\pi$
$192$	−287.767			−1.49879
$193$			258.000i			1.33679i	0.743808	+	0.668394i	$0.233018\pi$
$193$			258.000i			1.33679i	−0.743808	+	0.668394i	$0.766982\pi$
$194$			208.710i			1.07583i
$195$	−15.8114	−	47.4342i	−0.0810840	−	0.243252i
$196$	−155.000	+	189.737i	−0.790816	+	0.968044i
$197$		−	342.000i		−	1.73604i	−0.496529	−	0.868020i	$-0.665392\pi$
$197$		−	342.000i		−	1.73604i	0.496529	−	0.868020i	$-0.334608\pi$
$198$			42.0000i			0.212121i
$199$		−	56.9210i		−	0.286035i	−0.989720	−	0.143018i	$-0.954319\pi$
$199$		−	56.9210i		−	0.286035i	0.989720	−	0.143018i	$-0.0456805\pi$
$200$	45.0000	+	60.0000i	0.225000	+	0.300000i
$201$			322.552i			1.60474i
$202$	−313.065			−1.54983
$203$	88.5438	−	42.0000i	0.436176	−	0.206897i
$204$	−100.000			−0.490196
$205$	90.0000	−	30.0000i	0.439024	−	0.146341i
$206$			265.631i			1.28947i
$207$		−	12.0000i		−	0.0579710i
$208$	−34.7851			−0.167236
$209$		−	398.447i		−	1.90644i
$210$	239.605	−	229.868i	1.14098	−	1.09461i
$211$	242.000			1.14692			0.573460	−	0.819234i	$-0.305601\pi$
$211$	242.000			1.14692			0.573460	+	0.819234i	$0.305601\pi$
$212$		−	270.000i		−	1.27358i
$213$	50.5964			0.237542
$214$	−162.000			−0.757009
$215$	199.223	−	66.4078i	0.926621	−	0.308874i
$216$		−	75.8947i		−	0.351364i
$217$	113.842	+	240.000i	0.524617	+	1.10599i
$218$			222.000i			1.01835i
$219$	200.000			0.913242
$220$	−110.680	−	332.039i	−0.503090	−	1.50927i
$221$	−20.0000			−0.0904977
$222$	170.763			0.769203
$223$	−44.2719			−0.198529			−0.0992643	−	0.995061i	$-0.531649\pi$
$223$	−44.2719			−0.198529			−0.0992643	+	0.995061i	$0.531649\pi$
$224$	−135.000	−	284.605i	−0.602679	−	1.27056i
$225$	−20.0000	+	15.0000i	−0.0888889	+	0.0666667i
$226$	−234.000			−1.03540
$227$	−357.337			−1.57417			−0.787087	−	0.616842i	$-0.788412\pi$
$227$	−357.337			−1.57417			−0.787087	+	0.616842i	$0.788412\pi$
$228$		−	450.000i		−	1.97368i
$229$			237.171i			1.03568i	0.855477	+	0.517840i	$0.173264\pi$
$229$			237.171i			1.03568i	−0.855477	+	0.517840i	$0.826736\pi$
$230$	56.9210	+	170.763i	0.247483	+	0.742448i
$231$	−280.000	+	132.816i	−1.21212	+	0.574960i
$232$		−	42.0000i		−	0.181034i
$233$		−	252.000i		−	1.08155i	−0.841169	−	0.540773i	$-0.818132\pi$
$233$		−	252.000i		−	1.08155i	0.841169	−	0.540773i	$-0.181868\pi$
$234$			9.48683i			0.0405420i
$235$	−70.0000	−	210.000i	−0.297872	−	0.893617i
$236$		−	47.4342i		−	0.200992i
$237$	240.333			1.01406
$238$	−56.9210	−	120.000i	−0.239164	−	0.504202i
$239$	242.000			1.01255			0.506276	−	0.862371i	$-0.331022\pi$
$239$	242.000			1.01255			0.506276	+	0.862371i	$0.331022\pi$
$240$	55.0000	+	165.000i	0.229167	+	0.687500i
$241$		−	265.631i		−	1.10220i	−0.834438	−	0.551102i	$-0.814207\pi$
$241$		−	265.631i		−	1.10220i	0.834438	−	0.551102i	$-0.185793\pi$
$242$			225.000i			0.929752i
$243$	53.7587			0.221229
$244$			332.039i			1.36082i
$245$	229.015	+	87.0459i	0.934756	+	0.355289i
$246$	−180.000			−0.731707
$247$		−	90.0000i		−	0.364372i
$248$	113.842			0.459040
$249$	230.000			0.923695
$250$	213.454	−	308.322i	0.853815	−	1.23329i
$251$			483.828i			1.92760i	0.266620	+	0.963802i	$0.414093\pi$
$251$			483.828i			1.92760i	−0.266620	+	0.963802i	$0.585907\pi$
$252$	−31.6228	+	15.0000i	−0.125487	+	0.0595238i
$253$		−	168.000i		−	0.664032i
$254$	216.000			0.850394
$255$	31.6228	+	94.8683i	0.124011	+	0.372033i
$256$	85.0000			0.332031
$257$	−82.2192			−0.319919			−0.159960	−	0.987124i	$-0.551136\pi$
$257$	−82.2192			−0.319919			−0.159960	+	0.987124i	$0.551136\pi$
$258$	−398.447			−1.54437
$259$	54.0000	+	113.842i	0.208494	+	0.439544i
$260$	−25.0000	−	75.0000i	−0.0961538	−	0.288462i
$261$	14.0000			0.0536398
$262$	142.302			0.543139
$263$			318.000i			1.20913i	0.796558	+	0.604563i	$0.206652\pi$
$263$			318.000i			1.20913i	−0.796558	+	0.604563i	$0.793348\pi$
$264$			132.816i			0.503090i
$265$	−256.144	+	85.3815i	−0.966583	+	0.322194i
$266$	540.000	−	256.144i	2.03008	−	0.962949i
$267$		−	180.000i		−	0.674157i
$268$			510.000i			1.90299i
$269$		−	256.144i		−	0.952210i	−0.879388	−	0.476105i	$-0.842048\pi$
$269$		−	256.144i		−	0.952210i	0.879388	−	0.476105i	$-0.157952\pi$
$270$	−360.000	+	120.000i	−1.33333	+	0.444444i
$271$		−	341.526i		−	1.26024i	−0.776496	−	0.630122i	$-0.783005\pi$
$271$		−	341.526i		−	1.26024i	0.776496	−	0.630122i	$-0.216995\pi$
$272$	69.5701			0.255772
$273$	−63.2456	+	30.0000i	−0.231669	+	0.109890i
$274$	−252.000			−0.919708
$275$	−280.000	+	210.000i	−1.01818	+	0.763636i
$276$		−	189.737i		−	0.687452i
$277$		−	6.00000i		−	0.0216606i	−0.999941	−	0.0108303i	$-0.996553\pi$
$277$		−	6.00000i		−	0.0216606i	0.999941	−	0.0108303i	$-0.00344747\pi$
$278$	−369.986			−1.33089
$279$			37.9473i			0.136012i
$280$	75.7698	−	72.6907i	0.270606	−	0.259610i
$281$	14.0000			0.0498221			0.0249110	−	0.999690i	$-0.492070\pi$
$281$	14.0000			0.0498221			0.0249110	+	0.999690i	$0.492070\pi$
$282$			420.000i			1.48936i
$283$	515.451			1.82138			0.910691	−	0.413088i	$-0.135550\pi$
$283$	515.451			1.82138			0.910691	+	0.413088i	$0.135550\pi$
$284$	80.0000			0.281690
$285$	−426.907	+	142.302i	−1.49792	+	0.499307i
$286$			132.816i			0.464390i
$287$	−56.9210	−	120.000i	−0.198331	−	0.418118i
$288$		−	45.0000i		−	0.156250i
$289$	−249.000			−0.861592
$290$	−199.223	+	66.4078i	−0.686978	+	0.228993i
$291$	−220.000			−0.756014
$292$	316.228			1.08297
$293$	458.530			1.56495			0.782475	−	0.622682i	$-0.213957\pi$
$293$	458.530			1.56495			0.782475	+	0.622682i	$0.213957\pi$
$294$	−360.000	−	294.092i	−1.22449	−	1.00031i
$295$	−45.0000	+	15.0000i	−0.152542	+	0.0508475i
$296$	54.0000			0.182432
$297$	354.175			1.19251
$298$		−	138.000i		−	0.463087i
$299$		−	37.9473i		−	0.126914i
$300$	−316.228	+	237.171i	−1.05409	+	0.790569i
$301$	−126.000	−	265.631i	−0.418605	−	0.882496i
$302$			42.0000i			0.139073i
$303$		−	330.000i		−	1.08911i
$304$			313.065i			1.02982i
$305$	315.000	−	105.000i	1.03279	−	0.344262i
$306$		−	18.9737i		−	0.0620054i
$307$	−91.7061			−0.298717			−0.149358	−	0.988783i	$-0.547721\pi$
$307$	−91.7061			−0.298717			−0.149358	+	0.988783i	$0.547721\pi$
$308$	−442.719	+	210.000i	−1.43740	+	0.681818i
$309$	−280.000			−0.906149
$310$	−180.000	−	540.000i	−0.580645	−	1.74194i
$311$		−	360.500i		−	1.15916i	−0.814914	−	0.579581i	$-0.803216\pi$
$311$		−	360.500i		−	1.15916i	0.814914	−	0.579581i	$-0.196784\pi$
$312$			30.0000i			0.0961538i
$313$	−556.561			−1.77815			−0.889075	−	0.457762i	$-0.848651\pi$
$313$	−556.561			−1.77815			−0.889075	+	0.457762i	$0.848651\pi$
$314$			351.013i			1.11788i
$315$	24.2302	+	25.2566i	0.0769214	+	0.0801796i
$316$	380.000			1.20253
$317$			318.000i			1.00315i	0.865113	+	0.501577i	$0.167247\pi$
$317$			318.000i			1.00315i	−0.865113	+	0.501577i	$0.832753\pi$
$318$	512.289			1.61097
$319$	196.000			0.614420
$320$	143.884	+	431.651i	0.449636	+	1.34891i
$321$		−	170.763i		−	0.531972i
$322$	227.684	−	108.000i	0.707093	−	0.335404i
$323$			180.000i			0.557276i
$324$	445.000			1.37346
$325$	−63.2456	+	47.4342i	−0.194602	+	0.145951i
$326$	−162.000			−0.496933
$327$	−234.009			−0.715622
$328$	−56.9210			−0.173540
$329$	−280.000	+	132.816i	−0.851064	+	0.403695i
$330$	630.000	−	210.000i	1.90909	−	0.636364i
$331$	374.000			1.12991			0.564955	−	0.825122i	$-0.308894\pi$
$331$	374.000			1.12991			0.564955	+	0.825122i	$0.308894\pi$
$332$	363.662			1.09537
$333$			18.0000i			0.0540541i
$334$		−	417.421i		−	1.24976i
$335$	483.828	−	161.276i	1.44426	−	0.481421i
$336$	220.000	−	104.355i	0.654762	−	0.310581i
$337$			654.000i			1.94065i	0.241799	+	0.970326i	$0.422263\pi$
$337$			654.000i			1.94065i	−0.241799	+	0.970326i	$0.577737\pi$
$338$		−	477.000i		−	1.41124i
$339$		−	246.658i		−	0.727604i
$340$	50.0000	+	150.000i	0.147059	+	0.441176i
$341$			531.263i			1.55795i
$342$	85.3815			0.249653
$343$	82.2192	−	333.000i	0.239706	−	0.970845i
$344$	−126.000			−0.366279
$345$	−180.000	+	60.0000i	−0.521739	+	0.173913i
$346$			635.618i			1.83705i
$347$		−	282.000i		−	0.812680i	−0.913722	−	0.406340i	$-0.866805\pi$
$347$		−	282.000i		−	0.812680i	0.913722	−	0.406340i	$-0.133195\pi$
$348$	221.359			0.636090
$349$			161.276i			0.462109i	0.972941	+	0.231055i	$0.0742176\pi$
$349$			161.276i			0.462109i	−0.972941	+	0.231055i	$0.925782\pi$
$350$	−464.605	−	244.473i	−1.32744	−	0.698495i
$351$	80.0000			0.227920
$352$		−	630.000i		−	1.78977i
$353$	−613.482			−1.73791			−0.868954	−	0.494892i	$-0.835208\pi$
$353$	−613.482			−1.73791			−0.868954	+	0.494892i	$0.835208\pi$
$354$	90.0000			0.254237
$355$	−25.2982	−	75.8947i	−0.0712626	−	0.213788i
$356$		−	284.605i		−	0.799452i
$357$	126.491	−	60.0000i	0.354317	−	0.168067i
$358$		−	534.000i		−	1.49162i
$359$	254.000			0.707521			0.353760	−	0.935336i	$-0.384903\pi$
$359$	254.000			0.707521			0.353760	+	0.935336i	$0.384903\pi$
$360$	14.2302	−	4.74342i	0.0395285	−	0.0131762i
$361$	−449.000			−1.24377
$362$	85.3815			0.235860
$363$	−237.171			−0.653363
$364$	−100.000	+	47.4342i	−0.274725	+	0.130314i
$365$	−100.000	−	300.000i	−0.273973	−	0.821918i
$366$	−630.000			−1.72131
$367$	69.5701			0.189564			0.0947822	−	0.995498i	$-0.469785\pi$
$367$	69.5701			0.189564			0.0947822	+	0.995498i	$0.469785\pi$
$368$			132.000i			0.358696i
$369$		−	18.9737i		−	0.0514191i
$370$	−85.3815	−	256.144i	−0.230761	−	0.692282i
$371$	162.000	+	341.526i	0.436658	+	0.920555i
$372$			600.000i			1.61290i
$373$			618.000i			1.65684i	0.560110	+	0.828418i	$0.310759\pi$
$373$			618.000i			1.65684i	−0.560110	+	0.828418i	$0.689241\pi$
$374$		−	265.631i		−	0.710244i
$375$	325.000	+	225.000i	0.866667	+	0.600000i
$376$			132.816i			0.353233i
$377$	44.2719			0.117432
$378$	227.684	+	480.000i	0.602339	+	1.26984i
$379$	−466.000			−1.22955			−0.614776	−	0.788702i	$-0.710753\pi$
$379$	−466.000			−1.22955			−0.614776	+	0.788702i	$0.710753\pi$
$380$	−675.000	+	225.000i	−1.77632	+	0.592105i
$381$			227.684i			0.597596i
$382$		−	444.000i		−	1.16230i
$383$	31.6228			0.0825660			0.0412830	−	0.999147i	$-0.486855\pi$
$383$	31.6228			0.0825660			0.0412830	+	0.999147i	$0.486855\pi$
$384$		−	294.092i		−	0.765864i
$385$	339.223	+	353.592i	0.881100	+	0.918421i
$386$	−774.000			−2.00518
$387$		−	42.0000i		−	0.108527i
$388$	−347.851			−0.896522
$389$	14.0000			0.0359897			0.0179949	−	0.999838i	$-0.494272\pi$
$389$	14.0000			0.0359897			0.0179949	+	0.999838i	$0.494272\pi$
$390$	142.302	−	47.4342i	0.364878	−	0.121626i
$391$			75.8947i			0.194104i
$392$	−113.842	−	93.0000i	−0.290413	−	0.237245i
$393$			150.000i			0.381679i
$394$	1026.00			2.60406
$395$	−120.167	−	360.500i	−0.304219	−	0.912657i
$396$	−70.0000			−0.176768
$397$	79.0569			0.199136			0.0995679	−	0.995031i	$-0.468254\pi$
$397$	79.0569			0.199136			0.0995679	+	0.995031i	$0.468254\pi$
$398$	170.763			0.429053
$399$	270.000	+	569.210i	0.676692	+	1.42659i
$400$	220.000	−	165.000i	0.550000	−	0.412500i
$401$	404.000			1.00748			0.503741	−	0.863855i	$-0.331957\pi$
$401$	404.000			1.00748			0.503741	+	0.863855i	$0.331957\pi$
$402$	−967.657			−2.40711
$403$			120.000i			0.297767i
$404$		−	521.776i		−	1.29152i
$405$	−140.721	−	422.164i	−0.347460	−	1.04238i
$406$	126.000	+	265.631i	0.310345	+	0.654264i
$407$			252.000i			0.619165i
$408$		−	60.0000i		−	0.147059i
$409$			208.710i			0.510294i	0.966902	+	0.255147i	$0.0821239\pi$
$409$			208.710i			0.510294i	−0.966902	+	0.255147i	$0.917876\pi$
$410$	90.0000	+	270.000i	0.219512	+	0.658537i
$411$		−	265.631i		−	0.646305i
$412$	−442.719			−1.07456
$413$	28.4605	+	60.0000i	0.0689116	+	0.145278i
$414$	36.0000			0.0869565
$415$	−115.000	−	345.000i	−0.277108	−	0.831325i
$416$		−	142.302i		−	0.342073i
$417$		−	390.000i		−	0.935252i
$418$	1195.34			2.85967
$419$			237.171i			0.566040i	0.959114	+	0.283020i	$0.0913363\pi$
$419$			237.171i			0.566040i	−0.959114	+	0.283020i	$0.908664\pi$
$420$	383.114	+	399.342i	0.912176	+	0.950813i
$421$	554.000			1.31591			0.657957	−	0.753055i	$-0.271421\pi$
$421$	554.000			1.31591			0.657957	+	0.753055i	$0.271421\pi$
$422$			726.000i			1.72038i
$423$	−44.2719			−0.104662
$424$	162.000			0.382075
$425$	126.491	−	94.8683i	0.297626	−	0.223220i
$426$			151.789i			0.356313i
$427$	−199.223	−	420.000i	−0.466566	−	0.983607i
$428$		−	270.000i		−	0.630841i
$429$	−140.000			−0.326340
$430$	199.223	+	597.670i	0.463310	+	1.38993i
$431$	−358.000			−0.830626			−0.415313	−	0.909678i	$-0.636328\pi$
$431$	−358.000			−0.830626			−0.415313	+	0.909678i	$0.636328\pi$
$432$	−278.280			−0.644168
$433$	107.517			0.248308			0.124154	−	0.992263i	$-0.460378\pi$
$433$	107.517			0.248308			0.124154	+	0.992263i	$0.460378\pi$
$434$	−720.000	+	341.526i	−1.65899	+	0.786926i
$435$	−70.0000	−	210.000i	−0.160920	−	0.482759i
$436$	−370.000			−0.848624
$437$	−341.526			−0.781524
$438$			600.000i			1.36986i
$439$			18.9737i			0.0432202i	0.999766	+	0.0216101i	$0.00687924\pi$
$439$			18.9737i			0.0432202i	−0.999766	+	0.0216101i	$0.993121\pi$
$440$	199.223	−	66.4078i	0.452781	−	0.150927i
$441$	31.0000	−	37.9473i	0.0702948	−	0.0860484i
$442$		−	60.0000i		−	0.135747i
$443$		−	366.000i		−	0.826185i	−0.910689	−	0.413093i	$-0.864449\pi$
$443$		−	366.000i		−	0.826185i	0.910689	−	0.413093i	$-0.135551\pi$
$444$			284.605i			0.641002i
$445$	−270.000	+	90.0000i	−0.606742	+	0.202247i
$446$		−	132.816i		−	0.297793i
$447$	145.465			0.325425
$448$	575.535	−	273.000i	1.28468	−	0.609375i
$449$	74.0000			0.164811			0.0824053	−	0.996599i	$-0.473740\pi$
$449$	74.0000			0.164811			0.0824053	+	0.996599i	$0.473740\pi$
$450$	−45.0000	−	60.0000i	−0.100000	−	0.133333i
$451$		−	265.631i		−	0.588983i
$452$		−	390.000i		−	0.862832i
$453$	−44.2719			−0.0977304
$454$		−	1072.01i		−	2.36126i
$455$	76.6228	+	79.8683i	0.168402	+	0.175535i
$456$	270.000			0.592105
$457$			138.000i			0.301969i	0.988536	+	0.150985i	$0.0482444\pi$
$457$			138.000i			0.301969i	−0.988536	+	0.150985i	$0.951756\pi$
$458$	−711.512			−1.55352
$459$	−160.000			−0.348584
$460$	−284.605	+	94.8683i	−0.618706	+	0.206235i
$461$		−	692.539i		−	1.50225i	−0.660158	−	0.751127i	$-0.729511\pi$
$461$		−	692.539i		−	1.50225i	0.660158	−	0.751127i	$-0.270489\pi$
$462$	−398.447	−	840.000i	−0.862439	−	1.81818i
$463$		−	606.000i		−	1.30886i	−0.756125	−	0.654428i	$-0.772910\pi$
$463$		−	606.000i		−	1.30886i	0.756125	−	0.654428i	$-0.227090\pi$
$464$	−154.000			−0.331897
$465$	569.210	−	189.737i	1.22411	−	0.408036i
$466$	756.000			1.62232
$467$	534.425			1.14438			0.572189	−	0.820121i	$-0.306094\pi$
$467$	534.425			1.14438			0.572189	+	0.820121i	$0.306094\pi$
$468$	−15.8114			−0.0337850
$469$	−306.000	−	645.105i	−0.652452	−	1.37549i
$470$	630.000	−	210.000i	1.34043	−	0.446809i
$471$	−370.000			−0.785563
$472$	28.4605			0.0602977
$473$		−	588.000i		−	1.24313i
$474$			720.999i			1.52110i
$475$	426.907	+	569.210i	0.898753	+	1.19834i
$476$	200.000	−	94.8683i	0.420168	−	0.199303i
$477$			54.0000i			0.113208i
$478$			726.000i			1.51883i
$479$			531.263i			1.10911i	0.832148	+	0.554554i	$0.187111\pi$
$479$			531.263i			1.10911i	−0.832148	+	0.554554i	$0.812889\pi$
$480$	−675.000	+	225.000i	−1.40625	+	0.468750i
$481$			56.9210i			0.118339i
$482$	796.894			1.65331
$483$	113.842	+	240.000i	0.235698	+	0.496894i
$484$	−375.000			−0.774793
$485$	110.000	+	330.000i	0.226804	+	0.680412i
$486$			161.276i			0.331844i
$487$			108.000i			0.221766i	0.993833	+	0.110883i	$0.0353679\pi$
$487$			108.000i			0.221766i	−0.993833	+	0.110883i	$0.964632\pi$
$488$	−199.223			−0.408245
$489$		−	170.763i		−	0.349209i
$490$	−261.138	+	687.046i	−0.532934	+	1.40213i
$491$	674.000			1.37271			0.686354	−	0.727267i	$-0.259210\pi$
$491$	674.000			1.37271			0.686354	+	0.727267i	$0.259210\pi$
$492$		−	300.000i		−	0.609756i
$493$	−88.5438			−0.179602
$494$	270.000			0.546559
$495$	22.1359	+	66.4078i	0.0447191	+	0.134157i
$496$		−	417.421i		−	0.841574i
$497$	−101.193	+	48.0000i	−0.203607	+	0.0965795i
$498$			690.000i			1.38554i
$499$	62.0000			0.124248			0.0621242	−	0.998068i	$-0.480212\pi$
$499$	62.0000			0.124248			0.0621242	+	0.998068i	$0.480212\pi$
$500$	513.870	+	355.756i	1.02774	+	0.711512i
$501$	440.000			0.878244
$502$	−1451.49			−2.89141
$503$	−632.456			−1.25737			−0.628683	−	0.777661i	$-0.716406\pi$
$503$	−632.456			−1.25737			−0.628683	+	0.777661i	$0.716406\pi$
$504$	−9.00000	−	18.9737i	−0.0178571	−	0.0376462i
$505$	−495.000	+	165.000i	−0.980198	+	0.326733i
$506$	504.000			0.996047
$507$	502.802			0.991720
$508$			360.000i			0.708661i
$509$			635.618i			1.24876i	0.781122	+	0.624379i	$0.214648\pi$
$509$			635.618i			1.24876i	−0.781122	+	0.624379i	$0.785352\pi$
$510$	−284.605	+	94.8683i	−0.558049	+	0.186016i
$511$	−400.000	+	189.737i	−0.782779	+	0.371305i
$512$			627.000i			1.22461i
$513$		−	720.000i		−	1.40351i
$514$		−	246.658i		−	0.479879i
$515$	140.000	+	420.000i	0.271845	+	0.815534i
$516$		−	664.078i		−	1.28697i
$517$	−619.806			−1.19885
$518$	−341.526	+	162.000i	−0.659317	+	0.312741i
$519$	−670.000			−1.29094
$520$	45.0000	−	15.0000i	0.0865385	−	0.0288462i
$521$			398.447i			0.764773i	0.924002	+	0.382387i	$0.124898\pi$
$521$			398.447i			0.764773i	−0.924002	+	0.382387i	$0.875102\pi$
$522$			42.0000i			0.0804598i
$523$	−262.469			−0.501853			−0.250926	−	0.968006i	$-0.580735\pi$
$523$	−262.469			−0.501853			−0.250926	+	0.968006i	$0.580735\pi$
$524$			237.171i			0.452616i
$525$	257.698	−	489.737i	0.490852	−	0.932832i
$526$	−954.000			−1.81369
$527$		−	240.000i		−	0.455408i
$528$	486.991			0.922331
$529$	385.000			0.727788
$530$	−256.144	−	768.433i	−0.483291	−	1.44987i
$531$			9.48683i			0.0178660i
$532$	426.907	+	900.000i	0.802458	+	1.69173i
$533$		−	60.0000i		−	0.112570i
$534$	540.000			1.01124
$535$	−256.144	+	85.3815i	−0.478775	+	0.159592i
$536$	−306.000			−0.570896
$537$	562.885			1.04820
$538$	768.433			1.42832
$539$	434.000	−	531.263i	0.805195	−	0.985645i
$540$	−200.000	−	600.000i	−0.370370	−	1.11111i
$541$	−1006.00			−1.85952			−0.929760	−	0.368167i	$-0.879985\pi$
$541$	−1006.00			−1.85952			−0.929760	+	0.368167i	$0.879985\pi$
$542$	1024.58			1.89037
$543$			90.0000i			0.165746i
$544$			284.605i			0.523171i
$545$	117.004	+	351.013i	0.214687	+	0.644060i
$546$	−90.0000	−	189.737i	−0.164835	−	0.347503i
$547$			318.000i			0.581353i	0.956821	+	0.290676i	$0.0938803\pi$
$547$			318.000i			0.581353i	−0.956821	+	0.290676i	$0.906120\pi$
$548$		−	420.000i		−	0.766423i
$549$		−	66.4078i		−	0.120961i
$550$	−630.000	−	840.000i	−1.14545	−	1.52727i
$551$		−	398.447i		−	0.723134i
$552$	113.842			0.206235
$553$	−480.666	+	228.000i	−0.869197	+	0.412297i
$554$	18.0000			0.0324910
$555$	270.000	−	90.0000i	0.486486	−	0.162162i
$556$		−	616.644i		−	1.10907i
$557$			18.0000i			0.0323160i	0.999869	+	0.0161580i	$0.00514347\pi$
$557$			18.0000i			0.0323160i	−0.999869	+	0.0161580i	$0.994857\pi$
$558$	−113.842			−0.204018
$559$		−	132.816i		−	0.237595i
$560$	−266.533	−	277.822i	−0.475951	−	0.496111i
$561$	280.000			0.499109
$562$			42.0000i			0.0747331i
$563$	60.0833			0.106720			0.0533599	−	0.998575i	$-0.483007\pi$
$563$	60.0833			0.106720			0.0533599	+	0.998575i	$0.483007\pi$
$564$	−700.000			−1.24113
$565$	−369.986	+	123.329i	−0.654843	+	0.218281i
$566$			1546.35i			2.73207i
$567$	−562.885	+	267.000i	−0.992743	+	0.470899i
$568$			48.0000i			0.0845070i
$569$	464.000			0.815466			0.407733	−	0.913101i	$-0.366319\pi$
$569$	464.000			0.815466			0.407733	+	0.913101i	$0.366319\pi$
$570$	−426.907	−	1280.72i	−0.748960	−	2.24688i
$571$	314.000			0.549912			0.274956	−	0.961457i	$-0.411337\pi$
$571$	314.000			0.549912			0.274956	+	0.961457i	$0.411337\pi$
$572$	−221.359			−0.386992
$573$	468.017			0.816784
$574$	360.000	−	170.763i	0.627178	−	0.297497i
$575$	180.000	+	240.000i	0.313043	+	0.417391i
$576$	91.0000			0.157986
$577$	676.727			1.17284			0.586419	−	0.810008i	$-0.300537\pi$
$577$	676.727			1.17284			0.586419	+	0.810008i	$0.300537\pi$
$578$		−	747.000i		−	1.29239i
$579$		−	815.868i		−	1.40910i
$580$	−110.680	−	332.039i	−0.190827	−	0.572481i
$581$	−460.000	+	218.197i	−0.791738	+	0.375554i
$582$		−	660.000i		−	1.13402i
$583$			756.000i			1.29674i
$584$			189.737i			0.324892i
$585$	5.00000	+	15.0000i	0.00854701	+	0.0256410i
$586$			1375.59i			2.34742i
$587$	−585.021			−0.996629			−0.498315	−	0.866996i	$-0.666048\pi$
$587$	−585.021			−0.996629			−0.498315	+	0.866996i	$0.666048\pi$
$588$	490.153	−	600.000i	0.833594	−	1.02041i
$589$	1080.00			1.83362
$590$	−45.0000	−	135.000i	−0.0762712	−	0.228814i
$591$			1081.50i			1.82995i
$592$		−	198.000i		−	0.334459i
$593$	449.043			0.757240			0.378620	−	0.925552i	$-0.376399\pi$
$593$	449.043			0.757240			0.378620	+	0.925552i	$0.376399\pi$
$594$			1062.53i			1.78876i
$595$	−153.246	−	159.737i	−0.257556	−	0.268465i
$596$	230.000			0.385906
$597$			180.000i			0.301508i
$598$	113.842			0.190371
$599$	−136.000			−0.227045			−0.113523	−	0.993535i	$-0.536213\pi$
$599$	−136.000			−0.227045			−0.113523	+	0.993535i	$0.536213\pi$
$600$	−142.302	−	189.737i	−0.237171	−	0.316228i
$601$			360.500i			0.599833i	0.953965	+	0.299917i	$0.0969588\pi$
$601$			360.500i			0.599833i	−0.953965	+	0.299917i	$0.903041\pi$
$602$	796.894	−	378.000i	1.32374	−	0.627907i
$603$		−	102.000i		−	0.169154i
$604$	−70.0000			−0.115894
$605$	118.585	+	355.756i	0.196009	+	0.588027i
$606$	990.000			1.63366
$607$	828.517			1.36494			0.682468	−	0.730915i	$-0.260906\pi$
$607$	828.517			1.36494			0.682468	+	0.730915i	$0.260906\pi$
$608$	−1280.72			−2.10645
$609$	−280.000	+	132.816i	−0.459770	+	0.218088i
$610$	315.000	+	945.000i	0.516393	+	1.54918i
$611$	−140.000			−0.229133
$612$	31.6228			0.0516712
$613$			198.000i			0.323002i	0.986873	+	0.161501i	$0.0516334\pi$
$613$			198.000i			0.323002i	−0.986873	+	0.161501i	$0.948367\pi$
$614$		−	275.118i		−	0.448075i
$615$	−284.605	+	94.8683i	−0.462772	+	0.154257i
$616$	−126.000	−	265.631i	−0.204545	−	0.431220i
$617$		−	822.000i		−	1.33225i	−0.745839	−	0.666126i	$-0.767951\pi$
$617$		−	822.000i		−	1.33225i	0.745839	−	0.666126i	$-0.232049\pi$
$618$		−	840.000i		−	1.35922i
$619$		−	863.302i		−	1.39467i	−0.716745	−	0.697336i	$-0.754369\pi$
$619$		−	863.302i		−	1.39467i	0.716745	−	0.697336i	$-0.245631\pi$
$620$	900.000	−	300.000i	1.45161	−	0.483871i
$621$		−	303.579i		−	0.488855i
$622$	1081.50			1.73874
$623$	170.763	+	360.000i	0.274098	+	0.577849i
$624$	110.000			0.176282
$625$	175.000	−	600.000i	0.280000	−	0.960000i
$626$		−	1669.68i		−	2.66722i
$627$			1260.00i			2.00957i
$628$	−585.021			−0.931563
$629$		−	113.842i		−	0.180989i
$630$	−75.7698	+	72.6907i	−0.120269	+	0.115382i
$631$	−16.0000			−0.0253566			−0.0126783	−	0.999920i	$-0.504036\pi$
$631$	−16.0000			−0.0253566			−0.0126783	+	0.999920i	$0.504036\pi$
$632$			228.000i			0.360759i
$633$	−765.271			−1.20896
$634$	−954.000			−1.50473
$635$	341.526	−	113.842i	0.537836	−	0.179279i
$636$			853.815i			1.34248i
$637$	98.0306	−	120.000i	0.153894	−	0.188383i
$638$			588.000i			0.921630i
$639$	−16.0000			−0.0250391
$640$	−441.138	+	147.046i	−0.689278	+	0.229759i
$641$	−1156.00			−1.80343			−0.901716	−	0.432329i	$-0.857692\pi$
$641$	−1156.00			−1.80343			−0.901716	+	0.432329i	$0.857692\pi$
$642$	512.289			0.797958
$643$	−736.811			−1.14590			−0.572948	−	0.819592i	$-0.694200\pi$
$643$	−736.811			−1.14590			−0.572948	+	0.819592i	$0.694200\pi$
$644$	180.000	+	379.473i	0.279503	+	0.589244i
$645$	−630.000	+	210.000i	−0.976744	+	0.325581i
$646$	−540.000			−0.835913
$647$	−746.298			−1.15347			−0.576737	−	0.816930i	$-0.695674\pi$
$647$	−746.298			−1.15347			−0.576737	+	0.816930i	$0.695674\pi$
$648$			267.000i			0.412037i
$649$			132.816i			0.204647i
$650$	−142.302	−	189.737i	−0.218927	−	0.291903i
$651$	−360.000	−	758.947i	−0.552995	−	1.16582i
$652$		−	270.000i		−	0.414110i
$653$			834.000i			1.27718i	0.769546	+	0.638591i	$0.220482\pi$
$653$			834.000i			1.27718i	−0.769546	+	0.638591i	$0.779518\pi$
$654$		−	702.026i		−	1.07343i
$655$	225.000	−	75.0000i	0.343511	−	0.114504i
$656$			208.710i			0.318156i
$657$	−63.2456			−0.0962642
$658$	−398.447	−	840.000i	−0.605543	−	1.27660i
$659$	−958.000			−1.45372			−0.726859	−	0.686787i	$-0.759021\pi$
$659$	−958.000			−1.45372			−0.726859	+	0.686787i	$0.759021\pi$
$660$	350.000	+	1050.00i	0.530303	+	1.59091i
$661$		−	104.355i		−	0.157875i	−0.996880	−	0.0789373i	$-0.974847\pi$
$661$		−	104.355i		−	0.157875i	0.996880	−	0.0789373i	$-0.0251527\pi$
$662$			1122.00i			1.69486i
$663$	63.2456			0.0953930
$664$			218.197i			0.328610i
$665$	718.815	−	689.605i	1.08092	−	1.03700i
$666$	−54.0000			−0.0810811
$667$		−	168.000i		−	0.251874i
$668$	695.701			1.04147
$669$	140.000			0.209268
$670$	483.828	+	1451.49i	0.722132	+	2.16640i
$671$		−	929.710i		−	1.38556i
$672$	426.907	+	900.000i	0.635279	+	1.33929i
$673$		−	456.000i		−	0.677563i	−0.940865	−	0.338782i	$-0.889985\pi$
$673$		−	456.000i		−	0.677563i	0.940865	−	0.338782i	$-0.110015\pi$
$674$	−1962.00			−2.91098
$675$	−505.964	+	379.473i	−0.749577	+	0.562183i
$676$	795.000			1.17604
$677$	−243.495			−0.359668			−0.179834	−	0.983697i	$-0.557556\pi$
$677$	−243.495			−0.359668			−0.179834	+	0.983697i	$0.557556\pi$
$678$	739.973			1.09141
$679$	440.000	−	208.710i	0.648012	−	0.307379i
$680$	−90.0000	+	30.0000i	−0.132353	+	0.0441176i
$681$	1130.00			1.65932
$682$	−1593.79			−2.33693
$683$		−	882.000i		−	1.29136i	−0.763607	−	0.645681i	$-0.776574\pi$
$683$		−	882.000i		−	1.29136i	0.763607	−	0.645681i	$-0.223426\pi$
$684$			142.302i			0.208045i
$685$	−398.447	+	132.816i	−0.581674	+	0.193891i
$686$	999.000	+	246.658i	1.45627	+	0.359559i
$687$		−	750.000i		−	1.09170i
$688$			462.000i			0.671512i
$689$			170.763i			0.247842i
$690$	−180.000	−	540.000i	−0.260870	−	0.782609i
$691$			901.249i			1.30427i	0.758104	+	0.652134i	$0.226126\pi$
$691$			901.249i			1.30427i	−0.758104	+	0.652134i	$0.773874\pi$
$692$	−1059.36			−1.53087
$693$	88.5438	−	42.0000i	0.127769	−	0.0606061i
$694$	846.000			1.21902
$695$	−585.000	+	195.000i	−0.841727	+	0.280576i
$696$			132.816i			0.190827i
$697$			120.000i			0.172166i
$698$	−483.828			−0.693164
$699$			796.894i			1.14005i
$700$	407.456	−	774.342i	0.582079	−	1.10620i
$701$	−358.000			−0.510699			−0.255350	−	0.966849i	$-0.582191\pi$
$701$	−358.000			−0.510699			−0.255350	+	0.966849i	$0.582191\pi$
$702$			240.000i			0.341880i
$703$	512.289			0.728718
$704$	1274.00			1.80966
$705$	221.359	+	664.078i	0.313985	+	0.941955i
$706$		−	1840.45i		−	2.60686i
$707$	313.065	+	660.000i	0.442808	+	0.933522i
$708$			150.000i			0.211864i
$709$	−238.000			−0.335684			−0.167842	−	0.985814i	$-0.553680\pi$
$709$	−238.000			−0.335684			−0.167842	+	0.985814i	$0.553680\pi$
$710$	227.684	−	75.8947i	0.320682	−	0.106894i
$711$	−76.0000			−0.106892
$712$	170.763			0.239836
$713$	455.368			0.638665
$714$	180.000	+	379.473i	0.252101	+	0.531475i
$715$	70.0000	+	210.000i	0.0979021	+	0.293706i
$716$	890.000			1.24302
$717$	−765.271			−1.06732
$718$			762.000i			1.06128i
$719$		−	569.210i		−	0.791669i	−0.918322	−	0.395834i	$-0.870455\pi$
$719$		−	569.210i		−	0.791669i	0.918322	−	0.395834i	$-0.129545\pi$
$720$	−17.3925	−	52.1776i	−0.0241563	−	0.0724689i
$721$	560.000	−	265.631i	0.776699	−	0.368421i
$722$		−	1347.00i		−	1.86565i
$723$			840.000i			1.16183i
$724$			142.302i			0.196550i
$725$	−280.000	+	210.000i	−0.386207	+	0.289655i
$726$		−	711.512i		−	0.980045i
$727$	1037.23			1.42672			0.713361	−	0.700797i	$-0.247172\pi$
$727$	1037.23			1.42672			0.713361	+	0.700797i	$0.247172\pi$
$728$	−28.4605	−	60.0000i	−0.0390941	−	0.0824176i
$729$	631.000			0.865569
$730$	900.000	−	300.000i	1.23288	−	0.410959i
$731$			265.631i			0.363381i
$732$		−	1050.00i		−	1.43443i
$733$	629.293			0.858517			0.429259	−	0.903182i	$-0.358775\pi$
$733$	629.293			0.858517			0.429259	+	0.903182i	$0.358775\pi$
$734$			208.710i			0.284346i
$735$	−724.210	−	275.263i	−0.985320	−	0.374508i
$736$	−540.000			−0.733696
$737$		−	1428.00i		−	1.93758i
$738$	56.9210			0.0771287
$739$	−466.000			−0.630582			−0.315291	−	0.948995i	$-0.602102\pi$
$739$	−466.000			−0.630582			−0.315291	+	0.948995i	$0.602102\pi$
$740$	426.907	−	142.302i	0.576902	−	0.192301i
$741$			284.605i			0.384082i
$742$	−1024.58	+	486.000i	−1.38083	+	0.654987i
$743$			924.000i			1.24361i	0.783173	+	0.621803i	$0.213600\pi$
$743$			924.000i			1.24361i	−0.783173	+	0.621803i	$0.786400\pi$
$744$	−360.000			−0.483871
$745$	−72.7324	−	218.197i	−0.0976274	−	0.292882i
$746$	−1854.00			−2.48525
$747$	−72.7324			−0.0973660
$748$	442.719			0.591870
$749$	162.000	+	341.526i	0.216288	+	0.455976i
$750$	−675.000	+	975.000i	−0.900000	+	1.30000i
$751$	1142.00			1.52064			0.760320	−	0.649549i	$-0.225042\pi$
$751$	1142.00			1.52064			0.760320	+	0.649549i	$0.225042\pi$
$752$	486.991			0.647594
$753$		−	1530.00i		−	2.03187i
$754$			132.816i			0.176148i
$755$	22.1359	+	66.4078i	0.0293191	+	0.0879574i
$756$	−800.000	+	379.473i	−1.05820	+	0.501949i
$757$		−	162.000i		−	0.214003i	−0.994259	−	0.107001i	$-0.965875\pi$
$757$		−	162.000i		−	0.214003i	0.994259	−	0.107001i	$-0.0341249\pi$
$758$		−	1398.00i		−	1.84433i
$759$			531.263i			0.699951i
$760$	−135.000	−	405.000i	−0.177632	−	0.532895i
$761$		−	929.710i		−	1.22169i	−0.791748	−	0.610847i	$-0.790829\pi$
$761$		−	929.710i		−	1.22169i	0.791748	−	0.610847i	$-0.209171\pi$
$762$	−683.052			−0.896394
$763$	468.017	−	222.000i	0.613391	−	0.290957i
$764$	740.000			0.968586
$765$	−10.0000	−	30.0000i	−0.0130719	−	0.0392157i
$766$			94.8683i			0.123849i
$767$			30.0000i			0.0391134i
$768$	−268.794			−0.349992
$769$			151.789i			0.197385i	0.995118	+	0.0986927i	$0.0314661\pi$
$769$			151.789i			0.197385i	−0.995118	+	0.0986927i	$0.968534\pi$
$770$	−1060.78	+	1017.67i	−1.37763	+	1.32165i
$771$	260.000			0.337224
$772$		−	1290.00i		−	1.67098i
$773$	1274.40			1.64864			0.824319	−	0.566125i	$-0.191558\pi$
$773$	1274.40			1.64864			0.824319	+	0.566125i	$0.191558\pi$
$774$	126.000			0.162791
$775$	−569.210	−	758.947i	−0.734464	−	0.979286i
$776$		−	208.710i		−	0.268957i
$777$	−170.763	−	360.000i	−0.219772	−	0.463320i
$778$			42.0000i			0.0539846i
$779$	−540.000			−0.693196
$780$	79.0569	+	237.171i	0.101355	+	0.304065i
$781$	−224.000			−0.286812
$782$	−227.684			−0.291156
$783$	354.175			0.452331
$784$	−341.000	+	417.421i	−0.434949	+	0.532424i
$785$	185.000	+	555.000i	0.235669	+	0.707006i
$786$	−450.000			−0.572519
$787$	230.846			0.293324			0.146662	−	0.989187i	$-0.453147\pi$
$787$	230.846			0.293324			0.146662	+	0.989187i	$0.453147\pi$
$788$			1710.00i			2.17005i
$789$		−	1005.60i		−	1.27453i
$790$	1081.50	−	360.500i	1.36899	−	0.456329i
$791$	234.000	+	493.315i	0.295828	+	0.623660i
$792$		−	42.0000i		−	0.0530303i
$793$		−	210.000i		−	0.264817i
$794$			237.171i			0.298704i
$795$	810.000	−	270.000i	1.01887	−	0.339623i
$796$			284.605i			0.357544i
$797$	−1192.18			−1.49583			−0.747916	−	0.663793i	$-0.768946\pi$
$797$	−1192.18			−1.49583			−0.747916	+	0.663793i	$0.768946\pi$
$798$	−1707.63	+	810.000i	−2.13989	+	1.01504i
$799$	280.000			0.350438
$800$	675.000	+	900.000i	0.843750	+	1.12500i
$801$			56.9210i			0.0710624i
$802$			1212.00i			1.51122i
$803$	−885.438			−1.10266
$804$		−	1612.76i		−	2.00592i
$805$	303.079	−	290.763i	0.376496	−	0.361196i
$806$	−360.000			−0.446650
$807$			810.000i			1.00372i
$808$	313.065			0.387457
$809$	1424.00			1.76020			0.880099	−	0.474790i	$-0.157476\pi$
$809$	1424.00			1.76020			0.880099	+	0.474790i	$0.157476\pi$
$810$	1266.49	−	422.164i	1.56357	−	0.521190i
$811$			1109.96i			1.36863i	0.729186	+	0.684315i	$0.239899\pi$
$811$			1109.96i			1.36863i	−0.729186	+	0.684315i	$0.760101\pi$
$812$	−442.719	+	210.000i	−0.545220	+	0.258621i
$813$			1080.00i			1.32841i
$814$	−756.000			−0.928747
$815$	−256.144	+	85.3815i	−0.314288	+	0.104763i
$816$	−220.000			−0.269608
$817$	−1195.34			−1.46309
$818$	−626.131			−0.765441
$819$	20.0000	−	9.48683i	0.0244200	−	0.0115834i
$820$	−450.000	+	150.000i	−0.548780	+	0.182927i
$821$	662.000			0.806334			0.403167	−	0.915126i	$-0.367909\pi$
$821$	662.000			0.806334			0.403167	+	0.915126i	$0.367909\pi$
$822$	796.894			0.969457
$823$		−	1182.00i		−	1.43621i	−0.695935	−	0.718104i	$-0.745010\pi$
$823$		−	1182.00i		−	1.43621i	0.695935	−	0.718104i	$-0.254990\pi$
$824$		−	265.631i		−	0.322368i
$825$	885.438	−	664.078i	1.07326	−	0.804943i
$826$	−180.000	+	85.3815i	−0.217918	+	0.103367i
$827$			18.0000i			0.0217654i	0.999941	+	0.0108827i	$0.00346414\pi$
$827$			18.0000i			0.0217654i	−0.999941	+	0.0108827i	$0.996536\pi$
$828$			60.0000i			0.0724638i
$829$			1166.88i			1.40758i	0.710410	+	0.703788i	$0.248509\pi$
$829$			1166.88i			1.40758i	−0.710410	+	0.703788i	$0.751491\pi$
$830$	1035.00	−	345.000i	1.24699	−	0.415663i
$831$			18.9737i			0.0228323i
$832$	287.767			0.345874
$833$	−196.061	+	240.000i	−0.235368	+	0.288115i
$834$	1170.00			1.40288
$835$	−220.000	−	660.000i	−0.263473	−	0.790419i
$836$			1992.23i			2.38306i
$837$			960.000i			1.14695i
$838$	−711.512			−0.849060
$839$		−	1119.45i		−	1.33426i	−0.744940	−	0.667131i	$-0.767522\pi$
$839$		−	1119.45i		−	1.33426i	0.744940	−	0.667131i	$-0.232478\pi$
$840$	−239.605	+	229.868i	−0.285244	+	0.273653i
$841$	−645.000			−0.766944
$842$			1662.00i			1.97387i
$843$	−44.2719			−0.0525171
$844$	−1210.00			−1.43365
$845$	−251.401	−	754.203i	−0.297516	−	0.892548i
$846$		−	132.816i		−	0.156993i
$847$	474.342	−	225.000i	0.560026	−	0.265643i
$848$		−	594.000i		−	0.700472i
$849$	−1630.00			−1.91991
$850$	284.605	+	379.473i	0.334829	+	0.446439i
$851$	216.000			0.253819
$852$	−252.982			−0.296927
$853$	1407.21			1.64972			0.824861	−	0.565335i	$-0.191253\pi$
$853$	1407.21			1.64972			0.824861	+	0.565335i	$0.191253\pi$
$854$	1260.00	−	597.670i	1.47541	−	0.699848i
$855$	135.000	−	45.0000i	0.157895	−	0.0526316i
$856$	162.000			0.189252
$857$	126.491			0.147598			0.0737988	−	0.997273i	$-0.476488\pi$
$857$	126.491			0.147598			0.0737988	+	0.997273i	$0.476488\pi$
$858$		−	420.000i		−	0.489510i
$859$			1546.35i			1.80018i	0.435705	+	0.900090i	$0.356499\pi$
$859$			1546.35i			1.80018i	−0.435705	+	0.900090i	$0.643501\pi$
$860$	−996.117	+	332.039i	−1.15828	+	0.386092i
$861$	180.000	+	379.473i	0.209059	+	0.440736i
$862$		−	1074.00i		−	1.24594i
$863$		−	162.000i		−	0.187717i	−0.995586	−	0.0938586i	$-0.970080\pi$
$863$		−	162.000i		−	0.187717i	0.995586	−	0.0938586i	$-0.0299202\pi$
$864$		−	1138.42i		−	1.31762i
$865$	335.000	+	1005.00i	0.387283	+	1.16185i
$866$			322.552i			0.372462i
$867$	787.407			0.908197
$868$	−569.210	−	1200.00i	−0.655772	−	1.38249i
$869$	−1064.00			−1.22440
$870$	630.000	−	210.000i	0.724138	−	0.241379i
$871$		−	322.552i		−	0.370324i
$872$		−	222.000i		−	0.254587i
$873$	69.5701			0.0796908
$874$		−	1024.58i		−	1.17229i
$875$	−863.454	−	141.678i	−0.986804	−	0.161918i
$876$	−1000.00			−1.14155
$877$		−	426.000i		−	0.485747i	−0.970058	−	0.242873i	$-0.921910\pi$
$877$		−	426.000i		−	0.485747i	0.970058	−	0.242873i	$-0.0780900\pi$
$878$	−56.9210			−0.0648303
$879$	−1450.00			−1.64960
$880$	−243.495	−	730.486i	−0.276699	−	0.830098i
$881$			455.368i			0.516876i	0.966028	+	0.258438i	$0.0832078\pi$
$881$			455.368i			0.516876i	−0.966028	+	0.258438i	$0.916792\pi$
$882$	113.842	+	93.0000i	0.129073	+	0.105442i
$883$		−	342.000i		−	0.387316i	−0.981069	−	0.193658i	$-0.937965\pi$
$883$		−	342.000i		−	0.387316i	0.981069	−	0.193658i	$-0.0620352\pi$
$884$	100.000			0.113122
$885$	142.302	−	47.4342i	0.160794	−	0.0535979i
$886$	1098.00			1.23928
$887$	−139.140			−0.156866			−0.0784330	−	0.996919i	$-0.524992\pi$
$887$	−139.140			−0.156866			−0.0784330	+	0.996919i	$0.524992\pi$
$888$	−170.763			−0.192301
$889$	−216.000	−	455.368i	−0.242970	−	0.512225i
$890$	−270.000	−	810.000i	−0.303371	−	0.910112i
$891$	−1246.00			−1.39843
$892$	221.359			0.248161
$893$			1260.00i			1.41097i
$894$			436.394i			0.488137i
$895$	−281.443	−	844.328i	−0.314461	−	0.943383i
$896$	279.000	+	588.184i	0.311384	+	0.656455i
$897$			120.000i			0.133779i
$898$			222.000i			0.247216i
$899$			531.263i			0.590948i
$900$	100.000	−	75.0000i	0.111111	−	0.0833333i
$901$		−	341.526i		−	0.379052i
$902$	796.894			0.883474
$903$	398.447	+	840.000i	0.441248	+	0.930233i
$904$	234.000			0.258850
$905$	135.000	−	45.0000i	0.149171	−	0.0497238i
$906$		−	132.816i		−	0.146596i
$907$		−	1446.00i		−	1.59427i	−0.603803	−	0.797133i	$-0.706349\pi$
$907$		−	1446.00i		−	1.59427i	0.603803	−	0.797133i	$-0.293651\pi$
$908$	1786.69			1.96772
$909$			104.355i			0.114802i
$910$	−239.605	+	229.868i	−0.263302	+	0.252603i
$911$	374.000			0.410538			0.205269	−	0.978706i	$-0.434193\pi$
$911$	374.000			0.410538			0.205269	+	0.978706i	$0.434193\pi$
$912$		−	990.000i		−	1.08553i
$913$	−1018.25			−1.11528
$914$	−414.000			−0.452954
$915$	−996.117	+	332.039i	−1.08865	+	0.362884i
$916$		−	1185.85i		−	1.29460i
$917$	−142.302	−	300.000i	−0.155183	−	0.327154i
$918$		−	480.000i		−	0.522876i
$919$	704.000			0.766050			0.383025	−	0.923738i	$-0.374882\pi$
$919$	704.000			0.766050			0.383025	+	0.923738i	$0.374882\pi$
$920$	−56.9210	−	170.763i	−0.0618706	−	0.185612i
$921$	290.000			0.314875
$922$	2077.62			2.25338
$923$	−50.5964			−0.0548174
$924$	1400.00	−	664.078i	1.51515	−	0.718699i
$925$	−270.000	−	360.000i	−0.291892	−	0.389189i
$926$	1818.00			1.96328
$927$	88.5438			0.0955165
$928$		−	630.000i		−	0.678879i
$929$			303.579i			0.326780i	0.986562	+	0.163390i	$0.0522429\pi$
$929$			303.579i			0.326780i	−0.986562	+	0.163390i	$0.947757\pi$
$930$	569.210	+	1707.63i	0.612054	+	1.83616i
$931$	−1080.00	−	882.275i	−1.16004	−	0.947664i
$932$			1260.00i			1.35193i
$933$			1140.00i			1.22186i
$934$			1603.27i			1.71657i
$935$	−140.000	−	420.000i	−0.149733	−	0.449198i
$936$		−	9.48683i		−	0.0101355i
$937$	278.280			0.296991			0.148495	−	0.988913i	$-0.452557\pi$
$937$	278.280			0.296991			0.148495	+	0.988913i	$0.452557\pi$
$938$	1935.31	−	918.000i	2.06323	−	0.978678i
$939$	1760.00			1.87433
$940$	350.000	+	1050.00i	0.372340	+	1.11702i
$941$		−	1072.01i		−	1.13923i	−0.821913	−	0.569613i	$-0.807093\pi$
$941$		−	1072.01i		−	1.13923i	0.821913	−	0.569613i	$-0.192907\pi$
$942$		−	1110.00i		−	1.17834i
$943$	−227.684			−0.241446
$944$		−	104.355i		−	0.110546i
$945$	612.982	+	638.947i	0.648658	+	0.676134i
$946$	1764.00			1.86469
$947$			354.000i			0.373812i	0.982378	+	0.186906i	$0.0598460\pi$
$947$			354.000i			0.373812i	−0.982378	+	0.186906i	$0.940154\pi$
$948$	−1201.67			−1.26758
$949$	−200.000			−0.210748
$950$	−1707.63	+	1280.72i	−1.79751	+	1.34813i
$951$		−	1005.60i		−	1.05742i
$952$	56.9210	+	120.000i	0.0597910	+	0.126050i
$953$		−	612.000i		−	0.642183i	−0.947048	−	0.321091i	$-0.895950\pi$
$953$		−	612.000i		−	0.642183i	0.947048	−	0.321091i	$-0.104050\pi$
$954$	−162.000			−0.169811
$955$	−234.009	−	702.026i	−0.245035	−	0.735105i
$956$	−1210.00			−1.26569
$957$	−619.806			−0.647656
$958$	−1593.79			−1.66366
$959$	252.000	+	531.263i	0.262774	+	0.553976i
$960$	−455.000	−	1365.00i	−0.473958	−	1.42188i
$961$	−479.000			−0.498439
$962$	−170.763			−0.177508
$963$			54.0000i			0.0560748i
$964$			1328.16i			1.37776i
$965$	−1223.80	+	407.934i	−1.26819	+	0.422729i
$966$	−720.000	+	341.526i	−0.745342	+	0.353547i
$967$			1644.00i			1.70010i	0.526699	+	0.850052i	$0.323429\pi$
$967$			1644.00i			1.70010i	−0.526699	+	0.850052i	$0.676571\pi$
$968$		−	225.000i		−	0.232438i
$969$		−	569.210i		−	0.587420i
$970$	−990.000	+	330.000i	−1.02062	+	0.340206i
$971$		−	85.3815i		−	0.0879315i	−0.999033	−	0.0439658i	$-0.986001\pi$
$971$		−	85.3815i		−	0.0879315i	0.999033	−	0.0439658i	$-0.0139992\pi$
$972$	−268.794			−0.276537
$973$	369.986	+	780.000i	0.380253	+	0.801644i
$974$	−324.000			−0.332649
$975$	200.000	−	150.000i	0.205128	−	0.153846i
$976$			730.486i			0.748449i
$977$			888.000i			0.908905i	0.890771	+	0.454452i	$0.150165\pi$
$977$			888.000i			0.908905i	−0.890771	+	0.454452i	$0.849835\pi$
$978$	512.289			0.523813
$979$			796.894i			0.813988i
$980$	−1145.08	−	435.230i	−1.16845	−	0.444112i
$981$	74.0000			0.0754332
$982$			2022.00i			2.05906i
$983$	−101.193			−0.102943			−0.0514715	−	0.998674i	$-0.516391\pi$
$983$	−101.193			−0.102943			−0.0514715	+	0.998674i	$0.516391\pi$
$984$	180.000			0.182927
$985$	1622.25	−	540.749i	1.64695	−	0.548984i
$986$		−	265.631i		−	0.269403i
$987$	885.438	−	420.000i	0.897100	−	0.425532i
$988$			450.000i			0.455466i
$989$	−504.000			−0.509606
$990$	−199.223	+	66.4078i	−0.201236	+	0.0670786i
$991$	1244.00			1.25530			0.627649	−	0.778497i	$-0.284017\pi$
$991$	1244.00			1.25530			0.627649	+	0.778497i	$0.284017\pi$
$992$	1707.63			1.72140
$993$	−1182.69			−1.19103
$994$	−144.000	−	303.579i	−0.144869	−	0.305411i
$995$	270.000	−	90.0000i	0.271357	−	0.0904523i
$996$	−1150.00			−1.15462
$997$	−1211.15			−1.21480			−0.607398	−	0.794397i	$-0.707787\pi$
$997$	−1211.15			−1.21480			−0.607398	+	0.794397i	$0.707787\pi$
$998$			186.000i			0.186373i
$999$			455.368i			0.455824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.c.c.34.3	yes	4
3.2	odd	2		315.3.e.c.244.1		4
4.3	odd	2		560.3.p.f.209.4		4
5.2	odd	4		175.3.d.b.76.2		2
5.3	odd	4		175.3.d.h.76.1		2
5.4	even	2	inner	35.3.c.c.34.2	yes	4
7.2	even	3		245.3.i.c.129.4		8
7.3	odd	6		245.3.i.c.19.1		8
7.4	even	3		245.3.i.c.19.2		8
7.5	odd	6		245.3.i.c.129.3		8
7.6	odd	2	inner	35.3.c.c.34.4	yes	4
15.14	odd	2		315.3.e.c.244.4		4
20.19	odd	2		560.3.p.f.209.2		4
21.20	even	2		315.3.e.c.244.2		4
28.27	even	2		560.3.p.f.209.1		4
35.4	even	6		245.3.i.c.19.3		8
35.9	even	6		245.3.i.c.129.1		8
35.13	even	4		175.3.d.h.76.2		2
35.19	odd	6		245.3.i.c.129.2		8
35.24	odd	6		245.3.i.c.19.4		8
35.27	even	4		175.3.d.b.76.1		2
35.34	odd	2	inner	35.3.c.c.34.1	✓	4
105.104	even	2		315.3.e.c.244.3		4
140.139	even	2		560.3.p.f.209.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.c.c.34.1	✓	4	35.34	odd	2	inner
35.3.c.c.34.2	yes	4	5.4	even	2	inner
35.3.c.c.34.3	yes	4	1.1	even	1	trivial
35.3.c.c.34.4	yes	4	7.6	odd	2	inner
175.3.d.b.76.1		2	35.27	even	4
175.3.d.b.76.2		2	5.2	odd	4
175.3.d.h.76.1		2	5.3	odd	4
175.3.d.h.76.2		2	35.13	even	4
245.3.i.c.19.1		8	7.3	odd	6
245.3.i.c.19.2		8	7.4	even	3
245.3.i.c.19.3		8	35.4	even	6
245.3.i.c.19.4		8	35.24	odd	6
245.3.i.c.129.1		8	35.9	even	6
245.3.i.c.129.2		8	35.19	odd	6
245.3.i.c.129.3		8	7.5	odd	6
245.3.i.c.129.4		8	7.2	even	3
315.3.e.c.244.1		4	3.2	odd	2
315.3.e.c.244.2		4	21.20	even	2
315.3.e.c.244.3		4	105.104	even	2
315.3.e.c.244.4		4	15.14	odd	2
560.3.p.f.209.1		4	28.27	even	2
560.3.p.f.209.2		4	20.19	odd	2
560.3.p.f.209.3		4	140.139	even	2
560.3.p.f.209.4		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.00000i q^{2} -3.16228 q^{3} -5.00000 q^{4} +(1.58114 + 4.74342i) q^{5} -9.48683i q^{6} +(6.32456 - 3.00000i) q^{7} -3.00000i q^{8} +1.00000 q^{9} +(-14.2302 + 4.74342i) q^{10} +14.0000 q^{11} +15.8114 q^{12} +3.16228 q^{13} +(9.00000 + 18.9737i) q^{14} +(-5.00000 - 15.0000i) q^{15} -11.0000 q^{16} -6.32456 q^{17} +3.00000i q^{18} -28.4605i q^{19} +(-7.90569 - 23.7171i) q^{20} +(-20.0000 + 9.48683i) q^{21} +42.0000i q^{22} -12.0000i q^{23} +9.48683i q^{24} +(-20.0000 + 15.0000i) q^{25} +9.48683i q^{26} +25.2982 q^{27} +(-31.6228 + 15.0000i) q^{28} +14.0000 q^{29} +(45.0000 - 15.0000i) q^{30} +37.9473i q^{31} -45.0000i q^{32} -44.2719 q^{33} -18.9737i q^{34} +(24.2302 + 25.2566i) q^{35} -5.00000 q^{36} +18.0000i q^{37} +85.3815 q^{38} -10.0000 q^{39} +(14.2302 - 4.74342i) q^{40} -18.9737i q^{41} +(-28.4605 - 60.0000i) q^{42} -42.0000i q^{43} -70.0000 q^{44} +(1.58114 + 4.74342i) q^{45} +36.0000 q^{46} -44.2719 q^{47} +34.7851 q^{48} +(31.0000 - 37.9473i) q^{49} +(-45.0000 - 60.0000i) q^{50} +20.0000 q^{51} -15.8114 q^{52} +54.0000i q^{53} +75.8947i q^{54} +(22.1359 + 66.4078i) q^{55} +(-9.00000 - 18.9737i) q^{56} +90.0000i q^{57} +42.0000i q^{58} +9.48683i q^{59} +(25.0000 + 75.0000i) q^{60} -66.4078i q^{61} -113.842 q^{62} +(6.32456 - 3.00000i) q^{63} +91.0000 q^{64} +(5.00000 + 15.0000i) q^{65} -132.816i q^{66} -102.000i q^{67} +31.6228 q^{68} +37.9473i q^{69} +(-75.7698 + 72.6907i) q^{70} -16.0000 q^{71} -3.00000i q^{72} -63.2456 q^{73} -54.0000 q^{74} +(63.2456 - 47.4342i) q^{75} +142.302i q^{76} +(88.5438 - 42.0000i) q^{77} -30.0000i q^{78} -76.0000 q^{79} +(-17.3925 - 52.1776i) q^{80} -89.0000 q^{81} +56.9210 q^{82} -72.7324 q^{83} +(100.000 - 47.4342i) q^{84} +(-10.0000 - 30.0000i) q^{85} +126.000 q^{86} -44.2719 q^{87} -42.0000i q^{88} +56.9210i q^{89} +(-14.2302 + 4.74342i) q^{90} +(20.0000 - 9.48683i) q^{91} +60.0000i q^{92} -120.000i q^{93} -132.816i q^{94} +(135.000 - 45.0000i) q^{95} +142.302i q^{96} +69.5701 q^{97} +(113.842 + 93.0000i) q^{98} +14.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 20 q^{4} + 4 q^{9} + 56 q^{11} + 36 q^{14} - 20 q^{15} - 44 q^{16} - 80 q^{21} - 80 q^{25} + 56 q^{29} + 180 q^{30} + 40 q^{35} - 20 q^{36} - 40 q^{39} - 280 q^{44} + 144 q^{46} + 124 q^{49} - 180 q^{50}+ \cdots + 56 q^{99}+O(q^{100}) \) 4 * q - 20 * q^4 + 4 * q^9 + 56 * q^11 + 36 * q^14 - 20 * q^15 - 44 * q^16 - 80 * q^21 - 80 * q^25 + 56 * q^29 + 180 * q^30 + 40 * q^35 - 20 * q^36 - 40 * q^39 - 280 * q^44 + 144 * q^46 + 124 * q^49 - 180 * q^50 + 80 * q^51 - 36 * q^56 + 100 * q^60 + 364 * q^64 + 20 * q^65 - 360 * q^70 - 64 * q^71 - 216 * q^74 - 304 * q^79 - 356 * q^81 + 400 * q^84 - 40 * q^85 + 504 * q^86 + 80 * q^91 + 540 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more