LMFDB - Embedded newform 675.2.u.e.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(49,675)] 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("675.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [132] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	675.49
Dual form			675.2.u.e.124.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70577 - 2.03285i) q^{2} +(0.184133 + 1.72224i) q^{3} +(-0.875557 + 4.96553i) q^{4} +(3.18696 - 3.31205i) q^{6} +(4.87417 - 0.859447i) q^{7} +(6.99134 - 4.03645i) q^{8} +(-2.93219 + 0.634241i) q^{9} +(-0.580782 - 0.211388i) q^{11} +(-8.71303 - 0.593596i) q^{12} +(2.57283 - 3.06618i) q^{13} +(-10.0613 - 8.44245i) q^{14} +(-10.6550 - 3.87811i) q^{16} +(0.580760 + 0.335302i) q^{17} +(6.29095 + 4.87884i) q^{18} +(2.35070 + 4.07153i) q^{19} +(2.37767 + 8.23621i) q^{21} +(0.560959 + 1.54122i) q^{22} +(-4.03047 - 0.710681i) q^{23} +(8.23906 + 11.2975i) q^{24} -10.6217 q^{26} +(-1.63223 - 4.93314i) q^{27} +24.9553i q^{28} +(3.99400 - 3.35136i) q^{29} +(-0.409029 + 2.31972i) q^{31} +(4.76914 + 13.1031i) q^{32} +(0.257118 - 1.03917i) q^{33} +(-0.309021 - 1.75255i) q^{34} +(-0.582045 - 15.1152i) q^{36} +(0.508066 + 0.293332i) q^{37} +(4.26708 - 11.7237i) q^{38} +(5.75442 + 3.86643i) q^{39} +(3.38756 + 2.84250i) q^{41} +(12.6873 - 18.8825i) q^{42} +(0.578526 - 1.58949i) q^{43} +(1.55816 - 2.69881i) q^{44} +(5.43034 + 9.40562i) q^{46} +(9.95611 - 1.75553i) q^{47} +(4.71707 - 19.0645i) q^{48} +(16.4410 - 5.98403i) q^{49} +(-0.470532 + 1.06195i) q^{51} +(12.9725 + 15.4601i) q^{52} +3.46376i q^{53} +(-7.24415 + 11.7329i) q^{54} +(30.6078 - 25.6830i) q^{56} +(-6.57930 + 4.79817i) q^{57} +(-13.6256 - 2.40257i) q^{58} +(-1.39010 + 0.505956i) q^{59} +(-1.08461 - 6.15113i) q^{61} +(5.41336 - 3.12540i) q^{62} +(-13.7469 + 5.61146i) q^{63} +(7.16284 - 12.4064i) q^{64} +(-2.55106 + 1.24989i) q^{66} +(-2.83572 + 3.37947i) q^{67} +(-2.17344 + 2.59021i) q^{68} +(0.481817 - 7.07228i) q^{69} +(-1.91695 + 3.32025i) q^{71} +(-17.9399 + 16.2698i) q^{72} +(1.59610 - 0.921510i) q^{73} +(-0.270341 - 1.53318i) q^{74} +(-22.2755 + 8.10762i) q^{76} +(-3.01251 - 0.531186i) q^{77} +(-1.95581 - 18.2931i) q^{78} +(-8.36705 + 7.02079i) q^{79} +(8.19548 - 3.71943i) q^{81} -11.7350i q^{82} +(9.07001 + 10.8092i) q^{83} +(-42.9789 + 4.59510i) q^{84} +(-4.21802 + 1.53523i) q^{86} +(6.50726 + 6.26150i) q^{87} +(-4.91371 + 0.866419i) q^{88} +(8.12267 + 14.0689i) q^{89} +(9.90517 - 17.1563i) q^{91} +(7.05782 - 19.3912i) q^{92} +(-4.07042 - 0.277307i) q^{93} +(-20.5515 - 17.2448i) q^{94} +(-21.6885 + 10.6263i) q^{96} +(3.06640 - 8.42485i) q^{97} +(-40.2091 - 23.2148i) q^{98} +(1.83704 + 0.251472i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.70577	−	2.03285i	−1.20616	−	1.43744i	−0.868150	−	0.496301i	$-0.834691\pi$
$2$	−1.70577	−	2.03285i	−1.20616	−	1.43744i	−0.338009	−	0.941143i	$-0.609753\pi$
$3$	0.184133	+	1.72224i	0.106309	+	0.994333i
$3$	0.184133	+	1.72224i	0.106309	+	0.994333i
$4$	−0.875557	+	4.96553i	−0.437778	+	2.48276i
$5$		0			0
$5$		0			0
$6$	3.18696	−	3.31205i	1.30107	−	1.35214i
$7$	4.87417	−	0.859447i	1.84226	−	0.324840i	0.859703	−	0.510795i	$-0.170649\pi$
$7$	4.87417	−	0.859447i	1.84226	−	0.324840i	0.982558	+	0.185954i	$0.0595376\pi$
$8$	6.99134	−	4.03645i	2.47181	−	1.42710i
$9$	−2.93219	+	0.634241i	−0.977397	+	0.211414i
$10$		0			0
$11$	−0.580782	−	0.211388i	−0.175113	−	0.0637357i	0.252976	−	0.967473i	$-0.418591\pi$
$11$	−0.580782	−	0.211388i	−0.175113	−	0.0637357i	−0.428089	+	0.903737i	$0.640813\pi$
$12$	−8.71303	−	0.593596i	−2.51524	−	0.171357i
$13$	2.57283	−	3.06618i	0.713574	−	0.850404i	−0.280416	−	0.959879i	$-0.590472\pi$
$13$	2.57283	−	3.06618i	0.713574	−	0.850404i	0.993990	+	0.109475i	$0.0349168\pi$
$14$	−10.0613	−	8.44245i	−2.68900	−	2.25634i
$15$		0			0
$16$	−10.6550	−	3.87811i	−2.66375	−	0.969527i
$17$	0.580760	+	0.335302i	0.140855	+	0.0813227i	0.568771	−	0.822496i	$-0.307419\pi$
$17$	0.580760	+	0.335302i	0.140855	+	0.0813227i	−0.427916	+	0.903818i	$0.640752\pi$
$18$	6.29095	+	4.87884i	1.48279	+	1.14995i
$19$	2.35070	+	4.07153i	0.539288	+	0.934074i	0.998943	+	0.0459762i	$0.0146398\pi$
$19$	2.35070	+	4.07153i	0.539288	+	0.934074i	−0.459655	+	0.888098i	$0.652027\pi$
$20$		0			0
$21$	2.37767	+	8.23621i	0.518849	+	1.79729i
$22$	0.560959	+	1.54122i	0.119597	+	0.328590i
$23$	−4.03047	−	0.710681i	−0.840412	−	0.148187i	−0.263159	−	0.964753i	$-0.584764\pi$
$23$	−4.03047	−	0.710681i	−0.840412	−	0.148187i	−0.577253	+	0.816565i	$0.695875\pi$
$24$	8.23906	+	11.2975i	1.68179	+	2.30609i
$25$		0			0
$26$	−10.6217			−2.08309
$27$	−1.63223	−	4.93314i	−0.314122	−	0.949383i
$28$			24.9553i			4.71611i
$29$	3.99400	−	3.35136i	0.741666	−	0.622332i	−0.191618	−	0.981470i	$-0.561374\pi$
$29$	3.99400	−	3.35136i	0.741666	−	0.622332i	0.933285	+	0.359138i	$0.116929\pi$
$30$		0			0
$31$	−0.409029	+	2.31972i	−0.0734638	+	0.416634i	0.925791	+	0.378036i	$0.123400\pi$
$31$	−0.409029	+	2.31972i	−0.0734638	+	0.416634i	−0.999255	+	0.0385982i	$0.987711\pi$
$32$	4.76914	+	13.1031i	0.843073	+	2.31632i
$33$	0.257118	−	1.03917i	0.0447585	−	0.180896i
$34$	−0.309021	−	1.75255i	−0.0529967	−	0.300559i
$35$		0			0
$36$	−0.582045	−	15.1152i	−0.0970075	−	2.51920i
$37$	0.508066	+	0.293332i	0.0835255	+	0.0482235i	0.541181	−	0.840906i	$-0.317977\pi$
$37$	0.508066	+	0.293332i	0.0835255	+	0.0482235i	−0.457656	+	0.889130i	$0.651311\pi$
$38$	4.26708	−	11.7237i	0.692212	−	1.90184i
$39$	5.75442	+	3.86643i	0.921444	+	0.619124i
$40$		0			0
$41$	3.38756	+	2.84250i	0.529048	+	0.443924i	0.867772	−	0.496962i	$-0.165551\pi$
$41$	3.38756	+	2.84250i	0.529048	+	0.443924i	−0.338725	+	0.940886i	$0.609996\pi$
$42$	12.6873	−	18.8825i	1.95769	−	2.91363i
$43$	0.578526	−	1.58949i	0.0882243	−	0.242394i	−0.887732	−	0.460361i	$-0.847720\pi$
$43$	0.578526	−	1.58949i	0.0882243	−	0.242394i	0.975956	+	0.217966i	$0.0699423\pi$
$44$	1.55816	−	2.69881i	0.234901	−	0.406861i
$45$		0			0
$46$	5.43034	+	9.40562i	0.800659	+	1.38678i
$47$	9.95611	−	1.75553i	1.45225	−	0.256070i	0.608818	−	0.793310i	$-0.291644\pi$
$47$	9.95611	−	1.75553i	1.45225	−	0.256070i	0.843430	+	0.537240i	$0.180533\pi$
$48$	4.71707	−	19.0645i	0.680851	−	2.75173i
$49$	16.4410	−	5.98403i	2.34871	−	0.854861i
$50$		0			0
$51$	−0.470532	+	1.06195i	−0.0658876	+	0.148702i
$52$	12.9725	+	15.4601i	1.79897	+	2.14392i
$53$			3.46376i			0.475784i	0.971292	+	0.237892i	$0.0764565\pi$
$53$			3.46376i			0.475784i	−0.971292	+	0.237892i	$0.923543\pi$
$54$	−7.24415	+	11.7329i	−0.985803	+	1.59664i
$55$		0			0
$56$	30.6078	−	25.6830i	4.09015	−	3.43204i
$57$	−6.57930	+	4.79817i	−0.871449	+	0.635533i
$58$	−13.6256	−	2.40257i	−1.78914	−	0.315473i
$59$	−1.39010	+	0.505956i	−0.180976	+	0.0658698i	−0.430919	−	0.902391i	$-0.641810\pi$
$59$	−1.39010	+	0.505956i	−0.180976	+	0.0658698i	0.249943	+	0.968261i	$0.419588\pi$
$60$		0			0
$61$	−1.08461	−	6.15113i	−0.138870	−	0.787571i	−0.972086	−	0.234624i	$-0.924614\pi$
$61$	−1.08461	−	6.15113i	−0.138870	−	0.787571i	0.833216	−	0.552947i	$-0.186497\pi$
$62$	5.41336	−	3.12540i	0.687497	−	0.396927i
$63$	−13.7469	+	5.61146i	−1.73194	+	0.706977i
$64$	7.16284	−	12.4064i	0.895354	−	1.55080i
$65$		0			0
$66$	−2.55106	+	1.24989i	−0.314014	+	0.153851i
$67$	−2.83572	+	3.37947i	−0.346438	+	0.412868i	−0.910924	−	0.412574i	$-0.864630\pi$
$67$	−2.83572	+	3.37947i	−0.346438	+	0.412868i	0.564486	+	0.825442i	$0.309074\pi$
$68$	−2.17344	+	2.59021i	−0.263568	+	0.314109i
$69$	0.481817	−	7.07228i	0.0580039	−	0.851403i
$70$		0			0
$71$	−1.91695	+	3.32025i	−0.227500	+	0.394041i	−0.957066	−	0.289869i	$-0.906388\pi$
$71$	−1.91695	+	3.32025i	−0.227500	+	0.394041i	0.729567	+	0.683910i	$0.239722\pi$
$72$	−17.9399	+	16.2698i	−2.11423	+	1.91742i
$73$	1.59610	−	0.921510i	0.186810	−	0.107855i	−0.403679	−	0.914901i	$-0.632269\pi$
$73$	1.59610	−	0.921510i	0.186810	−	0.107855i	0.590488	+	0.807046i	$0.298935\pi$
$74$	−0.270341	−	1.53318i	−0.0314265	−	0.178228i
$75$		0			0
$76$	−22.2755	+	8.10762i	−2.55517	+	0.930007i
$77$	−3.01251	−	0.531186i	−0.343307	−	0.0605343i
$78$	−1.95581	−	18.2931i	−0.221452	−	2.07129i
$79$	−8.36705	+	7.02079i	−0.941367	+	0.789901i	−0.977823	−	0.209435i	$-0.932838\pi$
$79$	−8.36705	+	7.02079i	−0.941367	+	0.789901i	0.0364556	+	0.999335i	$0.488393\pi$
$80$		0			0
$81$	8.19548	−	3.71943i	0.910608	−	0.413270i
$82$		−	11.7350i		−	1.29592i
$83$	9.07001	+	10.8092i	0.995563	+	1.18647i	0.982445	+	0.186552i	$0.0597313\pi$
$83$	9.07001	+	10.8092i	0.995563	+	1.18647i	0.0131182	+	0.999914i	$0.495824\pi$
$84$	−42.9789	+	4.59510i	−4.68938	+	0.501366i
$85$		0			0
$86$	−4.21802	+	1.53523i	−0.454841	+	0.165549i
$87$	6.50726	+	6.26150i	0.697651	+	0.671304i
$88$	−4.91371	+	0.866419i	−0.523803	+	0.0923606i
$89$	8.12267	+	14.0689i	0.861002	+	1.49130i	0.870963	+	0.491348i	$0.163496\pi$
$89$	8.12267	+	14.0689i	0.861002	+	1.49130i	−0.00996172	+	0.999950i	$0.503171\pi$
$90$		0			0
$91$	9.90517	−	17.1563i	1.03834	−	1.79846i
$92$	7.05782	−	19.3912i	0.735828	−	2.02167i
$93$	−4.07042	−	0.277307i	−0.422083	−	0.0287554i
$94$	−20.5515	−	17.2448i	−2.11973	−	1.77866i
$95$		0			0
$96$	−21.6885	+	10.6263i	−2.21357	+	1.08454i
$97$	3.06640	−	8.42485i	0.311345	−	0.855414i	−0.681041	−	0.732246i	$-0.738472\pi$
$97$	3.06640	−	8.42485i	0.311345	−	0.855414i	0.992386	−	0.123168i	$-0.0393055\pi$
$98$	−40.2091	−	23.2148i	−4.06174	−	2.34504i
$99$	1.83704	+	0.251472i	0.184629	+	0.0252739i
$100$		0			0
$101$	0.390529	+	2.21480i	0.0388591	+	0.220381i	0.998053	−	0.0623673i	$-0.0198650\pi$
$101$	0.390529	+	2.21480i	0.0388591	+	0.220381i	−0.959194	+	0.282748i	$0.908754\pi$
$102$	2.96140	−	0.854909i	0.293222	−	0.0846486i
$103$	4.03048	+	11.0736i	0.397135	+	1.09112i	0.963673	+	0.267084i	$0.0860600\pi$
$103$	4.03048	+	11.0736i	0.397135	+	1.09112i	−0.566539	+	0.824035i	$0.691718\pi$
$104$	5.61104	−	31.8218i	0.550208	−	3.12038i
$105$		0			0
$106$	7.04132	−	5.90837i	0.683914	−	0.573872i
$107$		−	13.2113i		−	1.27718i	−0.769546	−	0.638591i	$-0.779518\pi$
$107$		−	13.2113i		−	1.27718i	0.769546	−	0.638591i	$-0.220482\pi$
$108$	25.9247	−	3.78563i	2.49461	−	0.364272i
$109$	8.55216			0.819148			0.409574	−	0.912277i	$-0.365677\pi$
$109$	8.55216			0.819148			0.409574	+	0.912277i	$0.365677\pi$
$110$		0			0
$111$	−0.411635	+	0.929021i	−0.0390707	+	0.0881788i
$112$	−55.2673	−	9.74512i	−5.22227	−	0.920827i
$113$	−6.09175	−	16.7369i	−0.573064	−	1.57448i	−0.799636	−	0.600485i	$-0.794974\pi$
$113$	−6.09175	−	16.7369i	−0.573064	−	1.57448i	0.226572	−	0.973994i	$-0.427248\pi$
$114$	20.9767	+	5.19020i	1.96465	+	0.486107i
$115$		0			0
$116$	13.1443	+	22.7666i	1.22042	+	2.11383i
$117$	−5.59932	+	10.6224i	−0.517657	+	0.982041i
$118$	3.39972	+	1.96283i	0.312970	+	0.180693i
$119$	3.11889	+	1.13518i	0.285909	+	0.104062i
$120$		0			0
$121$	−8.13387	−	6.82512i	−0.739442	−	0.620466i
$122$	−10.6543	+	12.6972i	−0.964591	+	1.14955i
$123$	−4.27169	+	6.35757i	−0.385165	+	0.573243i
$124$	−11.1605	−	4.06209i	−1.00224	−	0.364787i
$125$		0			0
$126$	34.8562	+	18.3736i	3.10524	+	1.63685i
$127$	−1.95521	+	1.12884i	−0.173497	+	0.100168i	−0.584234	−	0.811586i	$-0.698605\pi$
$127$	−1.95521	+	1.12884i	−0.173497	+	0.100168i	0.410737	+	0.911754i	$0.365271\pi$
$128$	−9.97410	+	1.75870i	−0.881595	+	0.155449i
$129$	2.84399	+	0.703680i	0.250400	+	0.0619556i
$130$		0			0
$131$	−2.09609	+	11.8875i	−0.183136	+	1.03862i	0.745190	+	0.666852i	$0.232359\pi$
$131$	−2.09609	+	11.8875i	−0.183136	+	1.03862i	−0.928327	+	0.371766i	$0.878752\pi$
$132$	4.93490	+	2.18658i	0.429528	+	0.190317i
$133$	14.9570	+	17.8250i	1.29693	+	1.54563i
$134$	11.7070			1.01133
$135$		0			0
$136$	5.41372			0.464223
$137$	−7.30892	−	8.71044i	−0.624443	−	0.744183i	0.357384	−	0.933957i	$-0.383669\pi$
$137$	−7.30892	−	8.71044i	−0.624443	−	0.744183i	−0.981828	+	0.189775i	$0.939224\pi$
$138$	−15.1988	+	11.0842i	−1.29381	+	0.943550i
$139$	−0.969841	+	5.50024i	−0.0822608	+	0.466524i	0.915653	+	0.401969i	$0.131674\pi$
$139$	−0.969841	+	5.50024i	−0.0822608	+	0.466524i	−0.997914	+	0.0645554i	$0.979437\pi$
$140$		0			0
$141$	4.85669	+	16.8235i	0.409007	+	1.41680i
$142$	10.0194	−	1.76670i	0.840813	−	0.148258i
$143$	−2.14240	+	1.23692i	−0.179157	+	0.103436i
$144$	33.7022	+	4.61350i	2.80851	+	0.384458i
$145$		0			0
$146$	−4.59587	−	1.67276i	−0.380357	−	0.138439i
$147$	13.3332	+	27.2134i	1.09971	+	2.24452i
$148$	−1.90139	+	2.26599i	−0.156293	+	0.186263i
$149$	12.3042	+	10.3245i	1.00800	+	0.845814i	0.988073	−	0.153988i	$-0.0492116\pi$
$149$	12.3042	+	10.3245i	1.00800	+	0.845814i	0.0199287	+	0.999801i	$0.493656\pi$
$150$		0			0
$151$	−17.6953	−	6.44056i	−1.44002	−	0.524125i	−0.500237	−	0.865889i	$-0.666754\pi$
$151$	−17.6953	−	6.44056i	−1.44002	−	0.524125i	−0.939786	+	0.341763i	$0.888976\pi$
$152$	32.8691	+	18.9770i	2.66604	+	1.53924i
$153$	−1.91556	−	0.614827i	−0.154864	−	0.0497058i
$154$	4.05881	+	7.03006i	0.327068	+	0.566499i
$155$		0			0
$156$	−24.2372	+	25.1885i	−1.94053	+	2.01669i
$157$	−1.80950	−	4.97156i	−0.144414	−	0.396774i	0.846305	−	0.532698i	$-0.178822\pi$
$157$	−1.80950	−	4.97156i	−0.144414	−	0.396774i	−0.990719	+	0.135924i	$0.956600\pi$
$158$	28.5445	+	5.03316i	2.27088	+	0.400417i
$159$	−5.96542	+	0.637794i	−0.473088	+	0.0505803i
$160$		0			0
$161$	−20.2560			−1.59640
$162$	−21.5406	−	10.3157i	−1.69239	−	0.810479i
$163$		−	7.25998i		−	0.568646i	−0.958729	−	0.284323i	$-0.908231\pi$
$163$		−	7.25998i		−	0.568646i	0.958729	−	0.284323i	$-0.0917688\pi$
$164$	−17.0805	+	14.3323i	−1.33376	+	1.11916i
$165$		0			0
$166$	6.50224	−	36.8760i	0.504671	−	2.86213i
$167$	0.585998	+	1.61002i	0.0453459	+	0.124587i	0.960299	−	0.278974i	$-0.0899945\pi$
$167$	0.585998	+	1.61002i	0.0453459	+	0.124587i	−0.914953	+	0.403561i	$0.867772\pi$
$168$	49.8681	+	47.9848i	3.84741	+	3.70211i
$169$	−0.524568	−	2.97497i	−0.0403514	−	0.228844i
$170$		0			0
$171$	−9.47504	−	10.4476i	−0.724574	−	0.798948i
$172$	7.38611	+	4.26437i	0.563185	+	0.325155i
$173$	−5.59776	+	15.3797i	−0.425590	+	1.16930i	0.522873	+	0.852411i	$0.324860\pi$
$173$	−5.59776	+	15.3797i	−0.425590	+	1.16930i	−0.948463	+	0.316888i	$0.897362\pi$
$174$	1.62886	−	23.9090i	0.123483	−	1.81253i
$175$		0			0
$176$	5.36846	+	4.50467i	0.404663	+	0.339553i
$177$	−1.12734	−	2.30092i	−0.0847360	−	0.172948i
$178$	14.7446	−	40.5104i	1.10515	−	3.03638i
$179$	8.67440	−	15.0245i	0.648355	−	1.12298i	−0.335161	−	0.942161i	$-0.608791\pi$
$179$	8.67440	−	15.0245i	0.648355	−	1.12298i	0.983516	−	0.180823i	$-0.0578760\pi$
$180$		0			0
$181$	2.30173	+	3.98671i	0.171086	+	0.296330i	0.938800	−	0.344463i	$-0.111939\pi$
$181$	2.30173	+	3.98671i	0.171086	+	0.296330i	−0.767714	+	0.640793i	$0.778606\pi$
$182$	−51.7720	+	9.12881i	−3.83760	+	0.676672i
$183$	10.3940	−	3.00058i	0.768345	−	0.221809i
$184$	−31.0471	+	11.3002i	−2.28882	+	0.833062i
$185$		0			0
$186$	6.37946	+	8.74758i	0.467765	+	0.641404i
$187$	−0.266417	−	0.317503i	−0.0194823	−	0.0232181i
$188$			50.9744i			3.71769i
$189$	−12.1955	−	22.6421i	−0.887093	−	1.64697i
$190$		0			0
$191$	−16.1562	+	13.5567i	−1.16902	+	0.980926i	−0.999989	−	0.00468455i	$-0.998509\pi$
$191$	−16.1562	+	13.5567i	−1.16902	+	0.980926i	−0.169033	+	0.985610i	$0.554064\pi$
$192$	22.6856	+	10.0517i	1.63720	+	0.725416i
$193$	−7.43293	−	1.31063i	−0.535034	−	0.0943410i	−0.100399	−	0.994947i	$-0.532012\pi$
$193$	−7.43293	−	1.31063i	−0.535034	−	0.0943410i	−0.434636	+	0.900606i	$0.643123\pi$
$194$	−22.3570	+	8.13730i	−1.60514	+	0.584224i
$195$		0			0
$196$	15.3189	+	86.8776i	1.09420	+	6.20554i
$197$	1.67324	−	0.966046i	0.119213	−	0.0688279i	−0.439208	−	0.898386i	$-0.644741\pi$
$197$	1.67324	−	0.966046i	0.119213	−	0.0688279i	0.558421	+	0.829558i	$0.311407\pi$
$198$	−2.62235	−	4.16338i	−0.186362	−	0.295878i
$199$	−3.52096	+	6.09848i	−0.249594	+	0.432310i	−0.963413	−	0.268020i	$-0.913631\pi$
$199$	−3.52096	+	6.09848i	−0.249594	+	0.432310i	0.713819	+	0.700330i	$0.246964\pi$
$200$		0			0
$201$	−6.34240	−	4.26150i	−0.447358	−	0.300583i
$202$	3.83621	−	4.57182i	0.269915	−	0.321672i
$203$	16.5871	−	19.7677i	1.16418	−	1.38742i
$204$	−4.86115	−	3.26623i	−0.340348	−	0.228682i
$205$		0			0
$206$	15.6360	−	27.0824i	1.08941	−	1.88692i
$207$	12.2689	−	0.472441i	0.852745	−	0.0328369i
$208$	−39.3044	+	22.6924i	−2.72527	+	1.57344i
$209$	−0.504575	−	2.86158i	−0.0349022	−	0.197940i
$210$		0			0
$211$	25.7199	−	9.36128i	1.77063	−	0.644457i	0.770658	−	0.637249i	$-0.219928\pi$
$211$	25.7199	−	9.36128i	1.77063	−	0.644457i	0.999974	−	0.00720786i	$-0.00229435\pi$
$212$	−17.1994	−	3.03272i	−1.18126	−	0.208288i
$213$	−6.07122	−	2.69006i	−0.415993	−	0.184320i
$214$	−26.8566	+	22.5353i	−1.83588	+	1.54048i
$215$		0			0
$216$	−31.3238	−	27.9008i	−2.13132	−	1.89841i
$217$			11.6582i			0.791412i
$218$	−14.5880	−	17.3853i	−0.988023	−	1.17748i
$219$	1.88095	+	2.57918i	0.127103	+	0.174285i
$220$		0			0
$221$	2.52229	−	0.918038i	0.169668	−	0.0617539i
$222$	2.59072	−	0.747900i	0.173878	−	0.0501957i
$223$	−3.57665	+	0.630661i	−0.239511	+	0.0422322i	−0.292115	−	0.956383i	$-0.594359\pi$
$223$	−3.57665	+	0.630661i	−0.239511	+	0.0422322i	0.0526043	+	0.998615i	$0.483248\pi$
$224$	34.5070	+	59.7679i	2.30560	+	3.99341i
$225$		0			0
$226$	−23.6327	+	40.9330i	−1.57202	+	2.72282i
$227$	2.68055	−	7.36474i	0.177914	−	0.488815i	−0.818395	−	0.574657i	$-0.805136\pi$
$227$	2.68055	−	7.36474i	0.177914	−	0.488815i	0.996309	+	0.0858415i	$0.0273579\pi$
$228$	−18.0649	−	36.8708i	−1.19638	−	2.44183i
$229$	−17.1140	−	14.3603i	−1.13092	−	0.948957i	−0.131819	−	0.991274i	$-0.542082\pi$
$229$	−17.1140	−	14.3603i	−1.13092	−	0.948957i	−0.999104	+	0.0423169i	$0.986526\pi$
$230$		0			0
$231$	0.360125	−	5.28605i	0.0236945	−	0.347797i
$232$	14.3958	−	39.5521i	0.945130	−	2.59672i
$233$	−12.3653	−	7.13909i	−0.810076	−	0.467697i	0.0369064	−	0.999319i	$-0.488250\pi$
$233$	−12.3653	−	7.13909i	−0.810076	−	0.467697i	−0.846982	+	0.531621i	$0.821583\pi$
$234$	31.1449	−	6.73674i	2.03601	−	0.440394i
$235$		0			0
$236$	−1.29522	−	7.34559i	−0.0843120	−	0.478157i
$237$	−13.6321	−	13.1173i	−0.885501	−	0.852059i
$238$	−3.01244	−	8.27661i	−0.195268	−	0.536493i
$239$	0.515978	−	2.92626i	0.0333759	−	0.189284i	−0.963562	−	0.267486i	$-0.913807\pi$
$239$	0.515978	−	2.92626i	0.0333759	−	0.189284i	0.996937	+	0.0782025i	$0.0249181\pi$
$240$		0			0
$241$	−2.94886	+	2.47439i	−0.189953	+	0.159389i	−0.732804	−	0.680439i	$-0.761789\pi$
$241$	−2.94886	+	2.47439i	−0.189953	+	0.159389i	0.542852	+	0.839829i	$0.317345\pi$
$242$			28.1770i			1.81129i
$243$	7.91480	+	13.4297i	0.507734	+	0.861514i
$244$	31.4933			2.01615
$245$		0			0
$246$	20.2105	−	2.16081i	1.28858	−	0.137768i
$247$	18.5320	+	3.26769i	1.17916	+	0.207918i
$248$	6.50378	+	17.8690i	0.412990	+	1.13468i
$249$	−16.9459	+	17.6110i	−1.07390	+	1.11605i
$250$		0			0
$251$	−3.39241	−	5.87583i	−0.214127	−	0.370879i	0.738875	−	0.673842i	$-0.235357\pi$
$251$	−3.39241	−	5.87583i	−0.214127	−	0.370879i	−0.953002	+	0.302963i	$0.902024\pi$
$252$	−15.8277	−	73.1737i	−0.997051	−	4.60951i
$253$	2.19060	+	1.26474i	0.137722	+	0.0795137i
$254$	5.62990	+	2.04911i	0.353251	+	0.128573i
$255$		0			0
$256$	−1.35952	−	1.14078i	−0.0849702	−	0.0712985i
$257$	−2.35335	+	2.80462i	−0.146798	+	0.174947i	−0.834433	−	0.551110i	$-0.814205\pi$
$257$	−2.35335	+	2.80462i	−0.146798	+	0.174947i	0.687635	+	0.726057i	$0.258649\pi$
$258$	−3.42071	−	6.98174i	−0.212964	−	0.434664i
$259$	2.72850	+	0.993093i	0.169541	+	0.0617078i
$260$		0			0
$261$	−9.58558	+	12.3600i	−0.593333	+	0.765064i
$262$	27.7410	−	16.0163i	1.71385	−	0.989490i
$263$	−11.1697	+	1.96952i	−0.688752	+	0.121446i	−0.507061	−	0.861910i	$-0.669268\pi$
$263$	−11.1697	+	1.96952i	−0.688752	+	0.121446i	−0.181691	+	0.983356i	$0.558157\pi$
$264$	−2.39695	−	8.30302i	−0.147522	−	0.511016i
$265$		0			0
$266$	10.7226	−	60.8107i	0.657442	−	3.72854i
$267$	−22.7343	+	16.5797i	−1.39131	+	1.01466i
$268$	−14.2980	−	17.0397i	−0.873392	−	1.04087i
$269$	−28.4015			−1.73167			−0.865833	−	0.500332i	$-0.833211\pi$
$269$	−28.4015			−1.73167			−0.865833	+	0.500332i	$0.833211\pi$
$270$		0			0
$271$	19.8799			1.20762			0.603810	−	0.797128i	$-0.293649\pi$
$271$	19.8799			1.20762			0.603810	+	0.797128i	$0.293649\pi$
$272$	−4.88767	−	5.82489i	−0.296358	−	0.353186i
$273$	31.3710	+	13.9000i	1.89866	+	0.841266i
$274$	−5.23972	+	29.7159i	−0.316543	+	1.79521i
$275$		0			0
$276$	34.6958	+	8.58466i	2.08844	+	0.516736i
$277$	−12.9566	+	2.28460i	−0.778488	+	0.137269i	−0.548753	−	0.835985i	$-0.684897\pi$
$277$	−12.9566	+	2.28460i	−0.778488	+	0.137269i	−0.229736	+	0.973253i	$0.573786\pi$
$278$	12.8355	−	7.41058i	0.769822	−	0.444457i
$279$	−0.271911	−	7.06128i	−0.0162789	−	0.422748i
$280$		0			0
$281$	−3.46507	−	1.26118i	−0.206709	−	0.0752359i	0.236591	−	0.971609i	$-0.423970\pi$
$281$	−3.46507	−	1.26118i	−0.206709	−	0.0752359i	−0.443300	+	0.896374i	$0.646192\pi$
$282$	25.9154	−	38.5699i	1.54324	−	2.29680i
$283$	11.3541	−	13.5313i	0.674932	−	0.804352i	−0.314515	−	0.949253i	$-0.601842\pi$
$283$	11.3541	−	13.5313i	0.674932	−	0.804352i	0.989446	+	0.144900i	$0.0462862\pi$
$284$	−14.8084	−	12.4257i	−0.878717	−	0.737331i
$285$		0			0
$286$	6.16891	+	2.24530i	0.364775	+	0.132767i
$287$	18.9545	+	10.9434i	1.11885	+	0.645967i
$288$	−22.2946	−	35.3960i	−1.31372	−	2.08573i
$289$	−8.27515	−	14.3330i	−0.486773	−	0.843116i
$290$		0			0
$291$	15.0742	+	3.72976i	0.883665	+	0.218642i
$292$	3.17831	+	8.73233i	0.185996	+	0.511021i
$293$	−21.8891	−	3.85963i	−1.27877	−	0.225482i	−0.507314	−	0.861761i	$-0.669362\pi$
$293$	−21.8891	−	3.85963i	−1.27877	−	0.225482i	−0.771459	+	0.636279i	$0.780473\pi$
$294$	32.5774	−	73.5242i	1.89995	−	4.28802i
$295$		0			0
$296$	4.73608			0.275279
$297$	−0.0948351	+	3.21011i	−0.00550289	+	0.186270i
$298$		−	42.6238i		−	2.46913i
$299$	−12.5488	+	10.5297i	−0.725715	+	0.608947i
$300$		0			0
$301$	1.45375	−	8.24463i	0.0837928	−	0.475212i
$302$	17.0913	+	46.9580i	0.983495	+	2.70213i
$303$	−3.74250	+	1.08040i	−0.215001	+	0.0620675i
$304$	−9.25690	−	52.4985i	−0.530920	−	3.01100i
$305$		0			0
$306$	2.01765	+	4.94281i	0.115341	+	0.282561i
$307$	−17.0120	−	9.82186i	−0.970924	−	0.560563i	−0.0714059	−	0.997447i	$-0.522749\pi$
$307$	−17.0120	−	9.82186i	−0.970924	−	0.560563i	−0.899518	+	0.436884i	$0.856082\pi$
$308$	5.27524	−	14.4936i	0.300585	−	0.825850i
$309$	−18.3293	+	8.98046i	−1.04272	+	0.510880i
$310$		0			0
$311$	−22.0191	−	18.4762i	−1.24859	−	1.04769i	−0.996802	−	0.0799057i	$-0.974538\pi$
$311$	−22.0191	−	18.4762i	−1.24859	−	1.04769i	−0.251785	−	0.967783i	$-0.581017\pi$
$312$	55.8378	+	3.80408i	3.16119	+	0.215364i
$313$	−8.87155	+	24.3744i	−0.501450	+	1.37772i	0.388410	+	0.921487i	$0.373024\pi$
$313$	−8.87155	+	24.3744i	−0.501450	+	1.37772i	−0.889860	+	0.456235i	$0.849198\pi$
$314$	−7.01987	+	12.1588i	−0.396154	+	0.686159i
$315$		0			0
$316$	−27.5361	−	47.6940i	−1.54903	−	2.68299i
$317$	−21.3889	+	3.77144i	−1.20132	+	0.211825i	−0.738269	−	0.674506i	$-0.764357\pi$
$317$	−21.3889	+	3.77144i	−1.20132	+	0.211825i	−0.463052	+	0.886331i	$0.653246\pi$
$318$	11.4721	+	11.0389i	0.643326	+	0.619030i
$319$	−3.02808	+	1.10213i	−0.169540	+	0.0617075i
$320$		0			0
$321$	22.7529	−	2.43263i	1.26994	−	0.135776i
$322$	34.5520	+	41.1774i	1.92551	+	2.29473i
$323$			3.15278i			0.175425i
$324$	11.2933	+	43.9515i	0.627408	+	2.44175i
$325$		0			0
$326$	−14.7585	+	12.3838i	−0.817397	+	0.685877i
$327$	1.57474	+	14.7288i	0.0870831	+	0.814506i
$328$	35.1572	+	6.19916i	1.94123	+	0.342291i
$329$	47.0189	−	17.1135i	2.59224	−	0.943497i
$330$		0			0
$331$	−2.33358	−	13.2344i	−0.128265	−	0.727427i	−0.979315	−	0.202342i	$-0.935145\pi$
$331$	−2.33358	−	13.2344i	−0.128265	−	0.727427i	0.851050	−	0.525085i	$-0.175966\pi$
$332$	−61.6148	+	35.5733i	−3.38155	+	1.95234i
$333$	−1.67579	−	0.537869i	−0.0918327	−	0.0294750i
$334$	2.27335	−	3.93756i	0.124392	−	0.215454i
$335$		0			0
$336$	6.60684	−	96.9777i	0.360433	−	5.29057i
$337$	−23.5823	+	28.1043i	−1.28461	+	1.53094i	−0.612649	+	0.790355i	$0.709896\pi$
$337$	−23.5823	+	28.1043i	−1.28461	+	1.53094i	−0.671962	+	0.740586i	$0.734548\pi$
$338$	−5.15289	+	6.14097i	−0.280280	+	0.334025i
$339$	27.7033	−	13.5733i	1.50464	−	0.737198i
$340$		0			0
$341$	0.727917	−	1.26079i	0.0394189	−	0.0682755i
$342$	−5.07623	+	37.0825i	−0.274491	+	2.00519i
$343$	44.9892	−	25.9746i	2.42919	−	1.40249i
$344$	−2.37122	−	13.4478i	−0.127847	−	0.725059i
$345$		0			0
$346$	40.8132	−	14.8548i	2.19413	−	0.798599i
$347$	0.846961	+	0.149342i	0.0454673	+	0.00801711i	0.196336	−	0.980537i	$-0.437096\pi$
$347$	0.846961	+	0.149342i	0.0454673	+	0.00801711i	−0.150868	+	0.988554i	$0.548207\pi$
$348$	−36.7892	+	26.8297i	−1.97211	+	1.43822i
$349$	5.98623	−	5.02304i	0.320435	−	0.268877i	−0.468354	−	0.883541i	$-0.655153\pi$
$349$	5.98623	−	5.02304i	0.320435	−	0.268877i	0.788789	+	0.614664i	$0.210708\pi$
$350$		0			0
$351$	−19.3253	−	7.68741i	−1.03151	−	0.410324i
$352$		−	8.61820i		−	0.459351i
$353$	−5.90324	−	7.03521i	−0.314198	−	0.374447i	0.585714	−	0.810518i	$-0.300814\pi$
$353$	−5.90324	−	7.03521i	−0.314198	−	0.374447i	−0.899912	+	0.436071i	$0.856370\pi$
$354$	−2.75446	+	6.21655i	−0.146398	+	0.330406i
$355$		0			0
$356$	−76.9713	+	28.0153i	−4.07947	+	1.48481i
$357$	−1.38076	+	5.58050i	−0.0730777	+	0.295351i
$358$	−45.3391	+	7.99450i	−2.39624	+	0.422523i
$359$	−3.70396	−	6.41544i	−0.195487	−	0.338594i	0.751573	−	0.659650i	$-0.229296\pi$
$359$	−3.70396	−	6.41544i	−0.195487	−	0.338594i	−0.947060	+	0.321056i	$0.895962\pi$
$360$		0			0
$361$	−1.55159	+	2.68744i	−0.0816627	+	0.141444i
$362$	4.17819	−	11.4795i	0.219601	−	0.603348i
$363$	10.2568	−	15.2652i	0.538340	−	0.801213i
$364$	76.5173	+	64.2057i	4.01060	+	3.36529i
$365$		0			0
$366$	−23.8294	−	16.0111i	−1.24559	−	0.836916i
$367$	−3.86916	+	10.6304i	−0.201968	+	0.554904i	−0.998783	−	0.0493202i	$-0.984295\pi$
$367$	−3.86916	+	10.6304i	−0.201968	+	0.554904i	0.796815	+	0.604224i	$0.206517\pi$
$368$	40.1886	+	23.2029i	2.09498	+	1.20954i
$369$	−11.7358	−	6.18622i	−0.610941	−	0.322042i
$370$		0			0
$371$	2.97692	+	16.8830i	0.154554	+	0.876519i
$372$	4.94086	−	19.9690i	0.256172	−	1.03534i
$373$	−8.78719	−	24.1426i	−0.454984	−	1.25006i	−0.929177	−	0.369636i	$-0.879482\pi$
$373$	−8.78719	−	24.1426i	−0.454984	−	1.25006i	0.474193	−	0.880421i	$-0.342740\pi$
$374$	−0.190992	+	1.08317i	−0.00987598	+	0.0560095i
$375$		0			0
$376$	62.5205	−	52.4609i	3.22425	−	2.70546i
$377$		−	20.8688i		−	1.07480i
$378$	−25.2254	+	63.4138i	−1.29745	+	3.26166i
$379$	20.0575			1.03029			0.515143	−	0.857104i	$-0.327739\pi$
$379$	20.0575			1.03029			0.515143	+	0.857104i	$0.327739\pi$
$380$		0			0
$381$	−2.30415	−	3.15947i	−0.118045	−	0.161865i
$382$	55.1174	+	9.71869i	2.82005	+	0.497251i
$383$	0.0207118	+	0.0569053i	0.00105833	+	0.00290773i	0.940221	−	0.340566i	$-0.110619\pi$
$383$	0.0207118	+	0.0569053i	0.00105833	+	0.00290773i	−0.939162	+	0.343474i	$0.888396\pi$
$384$	−4.86546	−	16.8539i	−0.248290	−	0.860073i
$385$		0			0
$386$	10.0145	+	17.3457i	0.509727	+	0.882872i
$387$	−0.688229	+	5.02760i	−0.0349847	+	0.255567i
$388$	39.1490	+	22.6027i	1.98749	+	1.14748i
$389$	−5.61420	−	2.04340i	−0.284651	−	0.103605i	0.195749	−	0.980654i	$-0.437286\pi$
$389$	−5.61420	−	2.04340i	−0.284651	−	0.103605i	−0.480400	+	0.877050i	$0.659508\pi$
$390$		0			0
$391$	−2.10245	−	1.76416i	−0.106325	−	0.0892175i
$392$	90.7903	−	108.200i	4.58560	−	5.46491i
$393$	−20.8591	−	1.42108i	−1.05220	−	0.0716838i
$394$	−4.81799	−	1.75360i	−0.242727	−	0.0883453i
$395$		0			0
$396$	−2.85712	+	8.90168i	−0.143576	+	0.447326i
$397$	18.7049	−	10.7993i	0.938770	−	0.541999i	0.0491952	−	0.998789i	$-0.484334\pi$
$397$	18.7049	−	10.7993i	0.938770	−	0.541999i	0.889574	+	0.456790i	$0.151001\pi$
$398$	18.4033	−	3.24499i	0.922472	−	0.162657i
$399$	−27.9448	+	29.0416i	−1.39899	+	1.45390i
$400$		0			0
$401$	−3.79031	+	21.4959i	−0.189279	+	1.07346i	0.731054	+	0.682320i	$0.239029\pi$
$401$	−3.79031	+	21.4959i	−0.189279	+	1.07346i	−0.920333	+	0.391136i	$0.872082\pi$
$402$	2.15565	+	20.1623i	0.107514	+	1.00560i
$403$	6.06030	+	7.22239i	0.301885	+	0.359773i
$404$	−11.3396			−0.564166
$405$		0			0
$406$	−68.4785			−3.39853
$407$	−0.233069	−	0.277761i	−0.0115528	−	0.0137681i
$408$	0.996846	+	9.32371i	0.0493512	+	0.461592i
$409$	4.25615	−	24.1378i	0.210453	−	1.19354i	−0.678171	−	0.734904i	$-0.737227\pi$
$409$	4.25615	−	24.1378i	0.210453	−	1.19354i	0.888624	−	0.458635i	$-0.151662\pi$
$410$		0			0
$411$	13.6556	−	14.1916i	0.673581	−	0.700018i
$412$	−58.5154	+	10.3179i	−2.88285	+	0.508324i
$413$	−6.34074	+	3.66083i	−0.312008	+	0.180138i
$414$	−21.8882	−	24.1349i	−1.07575	−	1.18617i
$415$		0			0
$416$	52.4466	+	19.0890i	2.57141	+	0.935916i
$417$	−9.65129	−	0.657518i	−0.472626	−	0.0321988i
$418$	−4.95649	+	5.90692i	−0.242430	+	0.288917i
$419$	5.67118	+	4.75869i	0.277055	+	0.232477i	0.770718	−	0.637177i	$-0.219898\pi$
$419$	5.67118	+	4.75869i	0.277055	+	0.232477i	−0.493663	+	0.869654i	$0.664342\pi$
$420$		0			0
$421$	−20.8889	−	7.60293i	−1.01806	−	0.370544i	−0.221538	−	0.975152i	$-0.571108\pi$
$421$	−20.8889	−	7.60293i	−1.01806	−	0.370544i	−0.796523	+	0.604608i	$0.793330\pi$
$422$	−62.9023	−	36.3166i	−3.06203	−	1.76787i
$423$	−28.0798	+	11.4621i	−1.36529	+	0.557308i
$424$	13.9813	+	24.2164i	0.678993	+	1.17605i
$425$		0			0
$426$	4.88758	+	16.9305i	0.236804	+	0.820287i
$427$	−10.5731	−	29.0495i	−0.511670	−	1.40580i
$428$	65.6010	+	11.5672i	3.17094	+	0.559123i
$429$	−2.52475	−	3.46197i	−0.121896	−	0.167145i
$430$		0			0
$431$	26.0455			1.25457			0.627283	−	0.778792i	$-0.284167\pi$
$431$	26.0455			1.25457			0.627283	+	0.778792i	$0.284167\pi$
$432$	−1.73984	+	58.8926i	−0.0837082	+	2.83347i
$433$			21.4654i			1.03156i	0.856720	+	0.515781i	$0.172498\pi$
$433$			21.4654i			1.03156i	−0.856720	+	0.515781i	$0.827502\pi$
$434$	23.6995	−	19.8862i	1.13761	−	0.954569i
$435$		0			0
$436$	−7.48790	+	42.4660i	−0.358606	+	2.03375i
$437$	−6.58088	−	18.0808i	−0.314806	−	0.864922i
$438$	2.03463	−	8.22318i	0.0972186	−	0.392919i
$439$	1.07788	+	6.11299i	0.0514446	+	0.291757i	0.999666	−	0.0258540i	$-0.00823050\pi$
$439$	1.07788	+	6.11299i	0.0514446	+	0.291757i	−0.948221	+	0.317611i	$0.897119\pi$
$440$		0			0
$441$	−44.4128	+	27.9739i	−2.11489	+	1.33209i
$442$	−6.16867	−	3.56148i	−0.293414	−	0.169403i
$443$	4.76605	−	13.0946i	0.226442	−	0.622143i	−0.773490	−	0.633808i	$-0.781491\pi$
$443$	4.76605	−	13.0946i	0.226442	−	0.622143i	0.999932	+	0.0116648i	$0.00371311\pi$
$444$	−4.25267	−	2.85740i	−0.201823	−	0.135606i
$445$		0			0
$446$	7.38298	+	6.19505i	0.349594	+	0.293344i
$447$	−15.5156	+	23.0919i	−0.733861	+	1.09221i
$448$	24.2502	−	66.6269i	1.14571	−	3.14782i
$449$	7.15441	−	12.3918i	0.337637	−	0.584805i	−0.646350	−	0.763041i	$-0.723706\pi$
$449$	7.15441	−	12.3918i	0.337637	−	0.584805i	0.983988	+	0.178236i	$0.0570389\pi$
$450$		0			0
$451$	−1.36657	−	2.36696i	−0.0643491	−	0.111456i
$452$	88.4415	−	15.5946i	4.15994	−	0.733509i
$453$	7.83387	−	31.6614i	0.368067	−	1.48758i
$454$	−19.5438	+	7.11337i	−0.917237	+	0.333847i
$455$		0			0
$456$	−26.6306	+	60.1027i	−1.24709	+	2.81456i
$457$	−19.1449	−	22.8161i	−0.895563	−	1.06729i	−0.997369	−	0.0724858i	$-0.976907\pi$
$457$	−19.1449	−	22.8161i	−0.895563	−	1.06729i	0.101807	−	0.994804i	$-0.467538\pi$
$458$			59.2855i			2.77023i
$459$	0.706159	−	3.41226i	0.0329607	−	0.159271i
$460$		0			0
$461$	10.2376	−	8.59034i	0.476811	−	0.400092i	−0.372461	−	0.928048i	$-0.621486\pi$
$461$	10.2376	−	8.59034i	0.476811	−	0.400092i	0.849272	+	0.527956i	$0.177041\pi$
$462$	−11.3601	+	8.28469i	−0.528518	+	0.385439i
$463$	−25.4473	−	4.48705i	−1.18264	−	0.208531i	−0.452457	−	0.891786i	$-0.649453\pi$
$463$	−25.4473	−	4.48705i	−1.18264	−	0.208531i	−0.730180	+	0.683255i	$0.760564\pi$
$464$	−55.5530	+	20.2196i	−2.57898	+	0.938673i
$465$		0			0
$466$	6.57954	+	37.3144i	0.304791	+	1.72856i
$467$	25.9567	−	14.9861i	1.20114	−	0.693476i	0.240328	−	0.970692i	$-0.422745\pi$
$467$	25.9567	−	14.9861i	1.20114	−	0.693476i	0.960808	+	0.277216i	$0.0894118\pi$
$468$	−47.8433	−	37.1041i	−2.21156	−	1.71514i
$469$	−10.9173	+	18.9093i	−0.504112	+	0.873148i
$470$		0			0
$471$	8.22901	−	4.03181i	0.379173	−	0.185776i
$472$	−7.67641	+	9.14839i	−0.353336	+	0.421089i
$473$	−0.671995	+	0.800853i	−0.0308984	+	0.0368232i
$474$	−3.41230	+	50.0871i	−0.156732	+	2.30058i
$475$		0			0
$476$	−8.36756	+	14.4930i	−0.383527	+	0.664288i
$477$	−2.19686	−	10.1564i	−0.100587	−	0.465030i
$478$	−6.82879	+	3.94261i	−0.312342	+	0.180331i
$479$	7.24624	+	41.0955i	0.331089	+	1.87770i	0.462876	+	0.886423i	$0.346817\pi$
$479$	7.24624	+	41.0955i	0.331089	+	1.87770i	−0.131787	+	0.991278i	$0.542072\pi$
$480$		0			0
$481$	2.20657	−	0.803127i	0.100611	−	0.0366194i
$482$	10.0601	+	1.77387i	0.458227	+	0.0807977i
$483$	−3.72980	−	34.8856i	−0.169712	−	1.58735i
$484$	41.0120	−	34.4132i	1.86418	−	1.56423i
$485$		0			0
$486$	13.7998	−	38.9975i	0.625969	−	1.76896i
$487$			10.6705i			0.483528i	0.970335	+	0.241764i	$0.0777260\pi$
$487$			10.6705i			0.483528i	−0.970335	+	0.241764i	$0.922274\pi$
$488$	−32.4116	−	38.6267i	−1.46721	−	1.74855i
$489$	12.5034	−	1.33680i	0.565423	−	0.0604524i
$490$		0			0
$491$	21.6015	−	7.86231i	0.974863	−	0.354821i	0.195022	−	0.980799i	$-0.437522\pi$
$491$	21.6015	−	7.86231i	0.974863	−	0.354821i	0.779841	+	0.625978i	$0.215300\pi$
$492$	−27.8286	−	26.7776i	−1.25461	−	1.20723i
$493$	3.44327	−	0.607141i	0.155077	−	0.0273443i
$494$	−24.9685	−	43.2467i	−1.12339	−	1.94576i
$495$		0			0
$496$	13.3543	−	23.1304i	0.599627	−	1.03858i
$497$	−6.48994	+	17.8309i	−0.291113	+	0.799827i
$498$	64.7064	+	4.40828i	2.89957	+	0.197540i
$499$	4.74279	+	3.97967i	0.212316	+	0.178155i	0.742744	−	0.669576i	$-0.233524\pi$
$499$	4.74279	+	3.97967i	0.212316	+	0.178155i	−0.530427	+	0.847730i	$0.677969\pi$
$500$		0			0
$501$	−2.66493	+	1.30568i	−0.119060	+	0.0583337i
$502$	−6.15804	+	16.9191i	−0.274847	+	0.755135i
$503$	19.6513	+	11.3457i	0.876209	+	0.505879i	0.869406	−	0.494098i	$-0.164501\pi$
$503$	19.6513	+	11.3457i	0.876209	+	0.505879i	0.00680220	+	0.999977i	$0.497835\pi$
$504$	−73.4588	+	94.7203i	−3.27211	+	4.21918i
$505$		0			0
$506$	−1.16561	−	6.61052i	−0.0518178	−	0.293874i
$507$	5.02701	−	1.45122i	0.223257	−	0.0644509i
$508$	−3.89339	−	10.6970i	−0.172741	−	0.474603i
$509$	−1.12200	+	6.36316i	−0.0497316	+	0.282042i	−0.999524	−	0.0308376i	$-0.990183\pi$
$509$	−1.12200	+	6.36316i	−0.0497316	+	0.282042i	0.949793	+	0.312880i	$0.101294\pi$
$510$		0			0
$511$	6.98768	−	5.86336i	0.309117	−	0.259380i
$512$			24.9655i			1.10333i
$513$	16.2486	−	18.2420i	0.717391	−	0.805404i
$514$	9.71564			0.428539
$515$		0			0
$516$	−5.98422	+	13.5058i	−0.263441	+	0.594561i
$517$	−6.15343	−	1.08502i	−0.270628	−	0.0477189i
$518$	−2.63537	−	7.24063i	−0.115792	−	0.318135i
$519$	−27.5183	−	6.80875i	−1.20792	−	0.298871i
$520$		0			0
$521$	−6.47331	−	11.2121i	−0.283601	−	0.491211i	0.688668	−	0.725077i	$-0.258196\pi$
$521$	−6.47331	−	11.2121i	−0.283601	−	0.491211i	−0.972269	+	0.233866i	$0.924862\pi$
$522$	41.4768	−	1.59716i	1.81539	−	0.0699058i
$523$	9.01756	+	5.20629i	0.394310	+	0.227655i	0.684026	−	0.729458i	$-0.260227\pi$
$523$	9.01756	+	5.20629i	0.394310	+	0.227655i	−0.289716	+	0.957113i	$0.593561\pi$
$524$	−57.1926	−	20.8164i	−2.49847	−	0.909369i
$525$		0			0
$526$	23.0566	+	19.3468i	1.00532	+	0.843560i
$527$	−1.01535	+	1.21005i	−0.0442295	+	0.0527107i
$528$	−6.76960	+	10.0752i	−0.294609	+	0.438467i
$529$	−5.87328	−	2.13770i	−0.255360	−	0.0929434i
$530$		0			0
$531$	3.75514	−	2.36522i	0.162959	−	0.102642i
$532$	−101.606	+	58.6625i	−4.40520	+	2.54334i
$533$	17.4312	−	3.07359i	0.755029	−	0.133132i
$534$	72.4835	+	17.9343i	3.13667	+	0.776095i
$535$		0			0
$536$	−6.18437	+	35.0733i	−0.267124	+	1.51494i
$537$	27.4730	+	12.1728i	1.18555	+	0.525297i
$538$	48.4462	+	57.7360i	2.08867	+	2.48917i
$539$	−10.8136			−0.465774
$540$		0			0
$541$	−5.27984			−0.226998			−0.113499	−	0.993538i	$-0.536206\pi$
$541$	−5.27984			−0.226998			−0.113499	+	0.993538i	$0.536206\pi$
$542$	−33.9105	−	40.4130i	−1.45658	−	1.73589i
$543$	−6.44223	+	4.69820i	−0.276463	+	0.201619i
$544$	−1.62377	+	9.20887i	−0.0696186	+	0.394827i
$545$		0			0
$546$	−25.2549	−	87.4827i	−1.08081	−	3.74391i
$547$	−16.4534	+	2.90118i	−0.703497	+	0.124045i	−0.513942	−	0.857825i	$-0.671815\pi$
$547$	−16.4534	+	2.90118i	−0.703497	+	0.124045i	−0.189555	+	0.981870i	$0.560704\pi$
$548$	49.6513	−	28.6662i	2.12100	−	1.22456i
$549$	7.08158	+	17.3484i	0.302235	+	0.740411i
$550$		0			0
$551$	23.0339	+	8.38364i	0.981276	+	0.357155i
$552$	−25.1784	−	51.3896i	−1.07166	−	2.18729i
$553$	−34.7484	+	41.4115i	−1.47765	+	1.76100i
$554$	26.7452	+	22.4419i	1.13630	+	0.953466i
$555$		0			0
$556$	−26.4625	−	9.63155i	−1.12226	−	0.408469i
$557$	33.9311	+	19.5901i	1.43770	+	0.830059i	0.997690	−	0.0679311i	$-0.0216398\pi$
$557$	33.9311	+	19.5901i	1.43770	+	0.830059i	0.440015	+	0.897990i	$0.354973\pi$
$558$	−13.8907	+	12.5976i	−0.588041	+	0.533301i
$559$	−3.38520	−	5.86333i	−0.143179	−	0.247993i
$560$		0			0
$561$	0.497759	−	0.517295i	0.0210154	−	0.0218402i
$562$	3.34680	+	9.19527i	0.141176	+	0.387879i
$563$	8.69060	+	1.53239i	0.366265	+	0.0645824i	0.353752	−	0.935339i	$-0.384906\pi$
$563$	8.69060	+	1.53239i	0.366265	+	0.0645824i	0.0125132	+	0.999922i	$0.496017\pi$
$564$	−87.7900	+	9.38608i	−3.69662	+	0.395225i
$565$		0			0
$566$	−46.8746			−1.97029
$567$	36.7494	−	25.1727i	1.54333	−	1.05715i
$568$			30.9507i			1.29866i
$569$	−23.1035	+	19.3862i	−0.968550	+	0.812710i	−0.982323	−	0.187195i	$-0.940060\pi$
$569$	−23.1035	+	19.3862i	−0.968550	+	0.812710i	0.0137724	+	0.999905i	$0.495616\pi$
$570$		0			0
$571$	−1.93833	+	10.9928i	−0.0811164	+	0.460034i	0.917011	+	0.398862i	$0.130595\pi$
$571$	−1.93833	+	10.9928i	−0.0811164	+	0.460034i	−0.998127	+	0.0611717i	$0.980516\pi$
$572$	−4.26615	−	11.7212i	−0.178377	−	0.490086i
$573$	−26.3227	−	25.3286i	−1.09964	−	1.05812i
$574$	−10.0856	−	57.1986i	−0.420967	−	2.38742i
$575$		0			0
$576$	−13.1341	+	40.9209i	−0.547256	+	1.70504i
$577$	10.0309	+	5.79136i	0.417593	+	0.241098i	0.694047	−	0.719930i	$-0.255826\pi$
$577$	10.0309	+	5.79136i	0.417593	+	0.241098i	−0.276454	+	0.961027i	$0.589159\pi$
$578$	−15.0214	+	41.2709i	−0.624806	+	1.71664i
$579$	0.888558	−	13.0426i	0.0369272	−	0.542032i
$580$		0			0
$581$	53.4987	+	44.8907i	2.21950	+	1.86238i
$582$	−18.1310	−	37.0057i	−0.751555	−	1.53394i
$583$	0.732196	−	2.01169i	0.0303245	−	0.0833158i
$584$	7.43926	−	12.8852i	0.307839	−	0.533193i
$585$		0			0
$586$	29.4916	+	51.0809i	1.21829	+	2.11013i
$587$	17.5375	−	3.09233i	0.723849	−	0.127634i	0.200428	−	0.979708i	$-0.435767\pi$
$587$	17.5375	−	3.09233i	0.723849	−	0.127634i	0.523421	+	0.852074i	$0.324656\pi$
$588$	−146.803	+	42.3797i	−6.05405	+	1.74771i
$589$	−10.4063	+	3.78759i	−0.428785	+	0.156065i
$590$		0			0
$591$	1.97186	+	2.70383i	0.0811114	+	0.111221i
$592$	−4.27588	−	5.09579i	−0.175737	−	0.209436i
$593$		−	31.6202i		−	1.29849i	−0.760581	−	0.649243i	$-0.775086\pi$
$593$		−	31.6202i		−	1.29849i	0.760581	−	0.649243i	$-0.224914\pi$
$594$	6.68745	−	5.28291i	0.274390	−	0.216761i
$595$		0			0
$596$	−62.0395	+	52.0573i	−2.54124	+	2.13235i
$597$	−11.1514	−	4.94099i	−0.456394	−	0.202221i
$598$	42.8106	+	7.54866i	1.75065	+	0.308688i
$599$	−32.9090	+	11.9779i	−1.34463	+	0.489404i	−0.911266	−	0.411818i	$-0.864894\pi$
$599$	−32.9090	+	11.9779i	−1.34463	+	0.489404i	−0.433359	+	0.901221i	$0.642672\pi$
$600$		0			0
$601$	3.46045	+	19.6252i	0.141155	+	0.800528i	0.970375	+	0.241606i	$0.0776740\pi$
$601$	3.46045	+	19.6252i	0.141155	+	0.800528i	−0.829220	+	0.558923i	$0.811215\pi$
$602$	−19.2399	+	11.1081i	−0.784159	+	0.452734i
$603$	6.17145	−	11.7078i	0.251321	−	0.476778i
$604$	47.4740	−	82.2275i	1.93169	−	3.34579i
$605$		0			0
$606$	8.58013	+	5.76504i	0.348544	+	0.234189i
$607$	22.6583	−	27.0031i	0.919670	−	1.09602i	−0.0754300	−	0.997151i	$-0.524033\pi$
$607$	22.6583	−	27.0031i	0.919670	−	1.09602i	0.995100	−	0.0988695i	$-0.0315226\pi$
$608$	−42.1389	+	50.2192i	−1.70896	+	2.03666i
$609$	37.0989	+	24.9270i	1.50332	+	1.01009i
$610$		0			0
$611$	20.2326	−	35.0438i	0.818522	−	1.41772i
$612$	4.73012	−	8.97346i	0.191204	−	0.362731i
$613$	16.7845	−	9.69056i	0.677921	−	0.391398i	−0.121150	−	0.992634i	$-0.538658\pi$
$613$	16.7845	−	9.69056i	0.677921	−	0.391398i	0.799071	+	0.601236i	$0.205325\pi$
$614$	9.05203	+	51.3366i	0.365310	+	2.07178i
$615$		0			0
$616$	−23.2056	+	8.44614i	−0.934979	+	0.340305i
$617$	23.3249	+	4.11280i	0.939024	+	0.165575i	0.622155	−	0.782894i	$-0.286257\pi$
$617$	23.3249	+	4.11280i	0.939024	+	0.165575i	0.316869	+	0.948469i	$0.397369\pi$
$618$	49.5214	+	21.9422i	1.99204	+	0.882644i
$619$	−4.09803	+	3.43865i	−0.164714	+	0.138211i	−0.721419	−	0.692499i	$-0.756510\pi$
$619$	−4.09803	+	3.43865i	−0.164714	+	0.138211i	0.556705	+	0.830710i	$0.312065\pi$
$620$		0			0
$621$	3.07276	+	21.0429i	0.123306	+	0.844421i
$622$			76.2776i			3.05845i
$623$	51.6827	+	61.5930i	2.07062	+	2.46767i
$624$	−46.3190	−	63.5131i	−1.85424	−	2.54256i
$625$		0			0
$626$	64.6823	−	23.5424i	2.58523	−	0.940945i
$627$	4.83541	−	1.39591i	0.193108	−	0.0557472i
$628$	26.2707	−	4.63224i	1.04832	−	0.184847i
$629$	0.196710	+	0.340711i	0.00784332	+	0.0135850i
$630$		0			0
$631$	6.85767	−	11.8778i	0.273000	−	0.472849i	−0.696629	−	0.717432i	$-0.745318\pi$
$631$	6.85767	−	11.8778i	0.273000	−	0.472849i	0.969628	+	0.244583i	$0.0786509\pi$
$632$	−30.1578	+	82.8580i	−1.19961	+	3.29591i
$633$	20.8582	+	42.5720i	0.829040	+	1.69209i
$634$	44.1513	+	37.0473i	1.75347	+	1.47134i
$635$		0			0
$636$	2.05608	−	30.1799i	0.0815288	−	1.19671i
$637$	23.9517	−	65.8068i	0.949002	−	2.60736i
$638$	7.40566	+	4.27566i	0.293193	+	0.169275i
$639$	3.51501	−	10.9514i	0.139052	−	0.433231i
$640$		0			0
$641$	2.65860	+	15.0777i	0.105008	+	0.595533i	0.991217	+	0.132246i	$0.0422189\pi$
$641$	2.65860	+	15.0777i	0.105008	+	0.595533i	−0.886208	+	0.463287i	$0.846670\pi$
$642$	−43.7564	−	42.1038i	−1.72693	−	1.66171i
$643$	−7.77795	−	21.3698i	−0.306733	−	0.842741i	−0.993288	−	0.115664i	$-0.963101\pi$
$643$	−7.77795	−	21.3698i	−0.306733	−	0.842741i	0.686556	−	0.727077i	$-0.259122\pi$
$644$	17.7353	−	100.582i	0.698868	−	3.96347i
$645$		0			0
$646$	6.40914	−	5.37790i	0.252164	−	0.211591i
$647$		−	28.4897i		−	1.12005i	−0.828477	−	0.560024i	$-0.810792\pi$
$647$		−	28.4897i		−	1.12005i	0.828477	−	0.560024i	$-0.189208\pi$
$648$	42.2841	−	59.0845i	1.66108	−	2.32106i
$649$	0.914300			0.0358894
$650$		0			0
$651$	−20.0782	+	2.14667i	−0.786928	+	0.0841345i
$652$	36.0497	+	6.35653i	1.41181	+	0.248941i
$653$	−9.00437	−	24.7393i	−0.352368	−	0.968124i	−0.981607	−	0.190912i	$-0.938856\pi$
$653$	−9.00437	−	24.7393i	−0.352368	−	0.968124i	0.629239	−	0.777212i	$-0.283367\pi$
$654$	27.2554	−	28.3252i	1.06577	−	1.10760i
$655$		0			0
$656$	−25.0710	−	43.4242i	−0.978856	−	1.69543i
$657$	−4.09561	+	3.71436i	−0.159785	+	0.144911i
$658$	−114.993	−	66.3910i	−4.48288	−	2.58819i
$659$	−9.78162	−	3.56022i	−0.381038	−	0.138686i	0.144398	−	0.989520i	$-0.453875\pi$
$659$	−9.78162	−	3.56022i	−0.381038	−	0.138686i	−0.525436	+	0.850833i	$0.676098\pi$
$660$		0			0
$661$	−3.49397	−	2.93179i	−0.135900	−	0.114033i	0.572304	−	0.820042i	$-0.306050\pi$
$661$	−3.49397	−	2.93179i	−0.135900	−	0.114033i	−0.708204	+	0.706008i	$0.750494\pi$
$662$	−22.9230	+	27.3186i	−0.890928	+	1.06177i
$663$	2.04551	+	4.17493i	0.0794412	+	0.162141i
$664$	107.042	+	38.9603i	4.15405	+	1.51195i
$665$		0			0
$666$	1.76510	+	4.32411i	0.0683961	+	0.167556i
$667$	−18.4794	+	10.6691i	−0.715527	+	0.413110i
$668$	−8.50766	+	1.50013i	−0.329171	+	0.0580418i
$669$	−1.74473	−	6.04372i	−0.0674550	−	0.233664i
$670$		0			0
$671$	−0.670350	+	3.80174i	−0.0258786	+	0.146765i
$672$	−96.5805	+	70.4345i	−3.72567	+	2.71707i
$673$	−3.42911	−	4.08665i	−0.132182	−	0.157529i	0.695893	−	0.718145i	$-0.255009\pi$
$673$	−3.42911	−	4.08665i	−0.132182	−	0.157529i	−0.828076	+	0.560616i	$0.810564\pi$
$674$	97.3579			3.75009
$675$		0			0
$676$	15.2316			0.585831
$677$	4.41607	+	5.26287i	0.169724	+	0.202269i	0.844201	−	0.536027i	$-0.180075\pi$
$677$	4.41607	+	5.26287i	0.169724	+	0.202269i	−0.674477	+	0.738295i	$0.735631\pi$
$678$	−74.8477	−	33.1639i	−2.87451	−	1.27365i
$679$	7.70540	−	43.6995i	0.295706	−	1.67703i
$680$		0			0
$681$	13.1774	+	3.26044i	0.504959	+	0.124940i
$682$	−3.80465	+	0.670863i	−0.145688	+	0.0256887i
$683$	−43.6372	+	25.1940i	−1.66973	+	0.964020i	−0.701951	+	0.712225i	$0.747688\pi$
$683$	−43.6372	+	25.1940i	−1.66973	+	0.964020i	−0.967781	+	0.251795i	$0.918979\pi$
$684$	60.1738	−	37.9011i	2.30080	−	1.44919i
$685$		0			0
$686$	−129.544	−	47.1500i	−4.94600	−	1.80020i
$687$	21.5806	−	32.1185i	0.823352	−	1.22540i
$688$	−12.3284	+	14.6924i	−0.470016	+	0.560143i
$689$	10.6205	+	8.91166i	0.404609	+	0.339507i
$690$		0			0
$691$	−33.7131	−	12.2706i	−1.28251	−	0.466794i	−0.391246	−	0.920286i	$-0.627956\pi$
$691$	−33.7131	−	12.2706i	−1.28251	−	0.466794i	−0.891260	+	0.453492i	$0.850178\pi$
$692$	−71.4674	−	41.2617i	−2.71678	−	1.56853i
$693$	9.17014	−	0.353117i	0.348345	−	0.0134138i
$694$	−1.14113	−	1.97649i	−0.0433166	−	0.0750266i
$695$		0			0
$696$	70.7688	+	17.5101i	2.68248	+	0.663718i
$697$	1.01426	+	2.78666i	0.0384179	+	0.105552i
$698$	−20.4222	−	3.60099i	−0.772992	−	0.136299i
$699$	10.0183	−	22.6105i	0.378928	−	0.855206i
$700$		0			0
$701$	21.7709			0.822275			0.411138	−	0.911573i	$-0.365132\pi$
$701$	21.7709			0.822275			0.411138	+	0.911573i	$0.365132\pi$
$702$	17.3371	+	52.3984i	0.654345	+	1.97765i
$703$			2.75814i			0.104025i
$704$	−6.78261	+	5.69128i	−0.255629	+	0.214498i
$705$		0			0
$706$	−4.23200	+	24.0009i	−0.159273	+	0.903284i
$707$	3.80701	+	10.4597i	0.143177	+	0.393376i
$708$	12.4123	−	3.58325i	0.466484	−	0.134667i
$709$	0.344678	+	1.95477i	0.0129447	+	0.0734128i	0.990596	−	0.136821i	$-0.0436885\pi$
$709$	0.344678	+	1.95477i	0.0129447	+	0.0734128i	−0.977651	+	0.210234i	$0.932577\pi$
$710$		0			0
$711$	20.0809	−	25.8930i	0.753093	−	0.971064i
$712$	113.577	+	65.5736i	4.25647	+	2.45747i
$713$	3.29716	−	9.05888i	0.123480	−	0.339258i
$714$	13.6996	−	6.71213i	0.512694	−	0.251195i
$715$		0			0
$716$	67.0096	+	56.2278i	2.50427	+	2.10133i
$717$	5.13471	+	0.349815i	0.191759	+	0.0130641i
$718$	−6.72357	+	18.4729i	−0.250921	+	0.689401i
$719$	6.62793	−	11.4799i	0.247180	−	0.428128i	−0.715562	−	0.698549i	$-0.753829\pi$
$719$	6.62793	−	11.4799i	0.247180	−	0.428128i	0.962742	+	0.270421i	$0.0871628\pi$
$720$		0			0
$721$	29.1624	+	50.5108i	1.08607	+	1.88112i
$722$	8.10981	−	1.42998i	0.301816	−	0.0532183i
$723$	−4.80446	−	4.62301i	−0.178680	−	0.171932i
$724$	−21.8114	+	7.93871i	−0.810615	+	0.295040i
$725$		0			0
$726$	−48.5275	+	5.18832i	−1.80102	+	0.192557i
$727$	9.07640	+	10.8168i	0.336625	+	0.401174i	0.907629	−	0.419773i	$-0.137890\pi$
$727$	9.07640	+	10.8168i	0.336625	+	0.401174i	−0.571004	+	0.820947i	$0.693446\pi$
$728$		−	159.927i		−	5.92729i
$729$	−21.6717	+	16.1040i	−0.802655	+	0.596444i
$730$		0			0
$731$	0.868942	−	0.729129i	0.0321390	−	0.0269678i
$732$	5.79895	+	54.2388i	0.214335	+	2.00472i
$733$	−41.5177	−	7.32069i	−1.53349	−	0.270396i	−0.657772	−	0.753217i	$-0.728501\pi$
$733$	−41.5177	−	7.32069i	−1.53349	−	0.270396i	−0.875719	+	0.482821i	$0.839612\pi$
$734$	28.2100	−	10.2676i	1.04125	−	0.378984i
$735$		0			0
$736$	−9.90977	−	56.2011i	−0.365279	−	2.07160i
$737$	2.36131	−	1.36330i	0.0869801	−	0.0502180i
$738$	7.44285	+	34.4094i	0.273975	+	1.26663i
$739$	−18.7703	+	32.5111i	−0.690477	+	1.19594i	0.281205	+	0.959648i	$0.409266\pi$
$739$	−18.7703	+	32.5111i	−0.690477	+	1.19594i	−0.971682	+	0.236294i	$0.924067\pi$
$740$		0			0
$741$	−2.21538	+	32.5181i	−0.0813839	+	1.19458i
$742$	29.2426	−	34.8500i	1.07353	−	1.27938i
$743$	−8.38025	+	9.98719i	−0.307442	+	0.366395i	−0.897537	−	0.440939i	$-0.854646\pi$
$743$	−8.38025	+	9.98719i	−0.307442	+	0.366395i	0.590096	+	0.807333i	$0.299090\pi$
$744$	−29.5770	+	14.4913i	−1.08435	+	0.531277i
$745$		0			0
$746$	−34.0895	+	59.0447i	−1.24811	+	2.16178i
$747$	−33.4507	−	25.9421i	−1.22390	−	0.949172i
$748$	1.80983	−	1.04491i	0.0661741	−	0.0382056i
$749$	−11.3544	−	64.3939i	−0.414880	−	2.35290i
$750$		0			0
$751$	−31.6810	+	11.5309i	−1.15606	+	0.420770i	−0.847687	−	0.530497i	$-0.822005\pi$
$751$	−31.6810	+	11.5309i	−1.15606	+	0.420770i	−0.308368	+	0.951267i	$0.599783\pi$
$752$	−112.891	−	19.9057i	−4.11670	−	0.725885i
$753$	9.49491	−	6.92447i	0.346014	−	0.252342i
$754$	−42.4231	+	35.5972i	−1.54496	+	1.29637i
$755$		0			0
$756$	123.108	−	40.7327i	4.47739	−	1.48143i
$757$			11.5115i			0.418391i	0.977874	+	0.209196i	$0.0670845\pi$
$757$			11.5115i			0.418391i	−0.977874	+	0.209196i	$0.932915\pi$
$758$	−34.2135	−	40.7740i	−1.24269	−	1.48098i
$759$	−1.77482	+	4.00561i	−0.0644220	+	0.145394i
$760$		0			0
$761$	−18.3980	+	6.69633i	−0.666927	+	0.242742i	−0.653224	−	0.757164i	$-0.726584\pi$
$761$	−18.3980	+	6.69633i	−0.666927	+	0.242742i	−0.0137030	+	0.999906i	$0.504362\pi$
$762$	−2.49241	+	10.0733i	−0.0902904	+	0.364918i
$763$	41.6846	−	7.35013i	1.50909	−	0.266092i
$764$	−53.1704	−	92.0937i	−1.92364	−	3.33183i
$765$		0			0
$766$	0.0803506	−	0.139171i	0.00290319	−	0.00502846i
$767$	−2.02514	+	5.56403i	−0.0731236	+	0.200906i
$768$	1.71435	−	2.55147i	0.0618613	−	0.0920684i
$769$	3.17999	+	2.66833i	0.114674	+	0.0962225i	0.698321	−	0.715784i	$-0.253931\pi$
$769$	3.17999	+	2.66833i	0.114674	+	0.0962225i	−0.583648	+	0.812007i	$0.698375\pi$
$770$		0			0
$771$	−5.26354	−	3.53660i	−0.189562	−	0.127368i
$772$	13.0159	−	35.7609i	0.468453	−	1.28706i
$773$	−37.0181	−	21.3724i	−1.33145	−	0.768712i	−0.345927	−	0.938262i	$-0.612435\pi$
$773$	−37.0181	−	21.3724i	−1.33145	−	0.768712i	−0.985522	+	0.169550i	$0.945769\pi$
$774$	11.3943	−	7.17684i	0.409561	−	0.257966i
$775$		0			0
$776$	−12.5683	−	71.2784i	−0.451176	−	2.55875i
$777$	−1.20793	+	4.88198i	−0.0433343	+	0.175140i
$778$	5.42257	+	14.8984i	0.194409	+	0.534134i
$779$	−3.61019	+	20.4744i	−0.129349	+	0.733572i
$780$		0			0
$781$	1.81519	−	1.52312i	0.0649525	−	0.0545016i
$782$			7.28321i			0.260447i
$783$	−23.0518	−	14.2327i	−0.823805	−	0.508637i
$784$	−198.386			−7.08520
$785$		0			0
$786$	32.6919	+	44.8275i	1.16608	+	1.59894i
$787$	3.51939	+	0.620563i	0.125453	+	0.0221207i	0.236022	−	0.971748i	$-0.424156\pi$
$787$	3.51939	+	0.620563i	0.125453	+	0.0221207i	−0.110569	+	0.993868i	$0.535267\pi$
$788$	3.33191	+	9.15435i	0.118694	+	0.326110i
$789$	−5.44868	−	18.8742i	−0.193978	−	0.671938i
$790$		0			0
$791$	−44.0767	−	76.3431i	−1.56719	−	2.71445i
$792$	13.8584	−	5.65698i	0.492437	−	0.201012i
$793$	−21.6510	−	12.5002i	−0.768848	−	0.443895i
$794$	−53.8594	−	19.6032i	−1.91140	−	0.695692i
$795$		0			0
$796$	−27.1994	−	22.8230i	−0.964057	−	0.808940i
$797$	8.32897	−	9.92608i	0.295027	−	0.351600i	−0.598086	−	0.801432i	$-0.704072\pi$
$797$	8.32897	−	9.92608i	0.295027	−	0.351600i	0.893113	+	0.449832i	$0.148516\pi$
$798$	106.705	+	7.26951i	3.77730	+	0.257338i
$799$	6.37074	+	2.31876i	0.225381	+	0.0820319i
$800$		0			0
$801$	−32.7403	−	36.1009i	−1.15682	−	1.27556i
$802$	50.1635	−	28.9619i	1.77133	−	1.02268i
$803$	−1.12178	+	0.197801i	−0.0395869	+	0.00698024i
$804$	26.7137	−	27.7622i	0.942120	−	0.979097i
$805$		0			0
$806$	4.34459	−	24.6394i	0.153032	−	0.867886i
$807$	−5.22965	−	48.9140i	−0.184092	−	1.72185i
$808$	11.6703	+	13.9081i	0.410559	+	0.489285i
$809$	−1.24985			−0.0439423			−0.0219711	−	0.999759i	$-0.506994\pi$
$809$	−1.24985			−0.0439423			−0.0219711	+	0.999759i	$0.506994\pi$
$810$		0			0
$811$	33.8303			1.18794			0.593972	−	0.804486i	$-0.297559\pi$
$811$	33.8303			1.18794			0.593972	+	0.804486i	$0.297559\pi$
$812$	83.6342	+	99.6714i	2.93499	+	3.49778i
$813$	3.66056	+	34.2379i	0.128381	+	1.20078i
$814$	−0.167086	+	0.947590i	−0.00585635	+	0.0332130i
$815$		0			0
$816$	9.13186	−	9.49027i	0.319679	−	0.332226i
$817$	7.83159	−	1.38092i	0.273993	−	0.0483123i
$818$	−56.3287	+	32.5214i	−1.96949	+	1.13708i
$819$	−18.1626	+	56.5877i	−0.634653	+	1.97733i
$820$		0			0
$821$	52.8205	+	19.2251i	1.84345	+	0.670960i	0.988289	+	0.152595i	$0.0487629\pi$
$821$	52.8205	+	19.2251i	1.84345	+	0.670960i	0.855159	+	0.518366i	$0.173459\pi$
$822$	−52.1426	−	3.55234i	−1.81868	−	0.123902i
$823$	−20.2270	+	24.1056i	−0.705068	+	0.840267i	−0.993090	−	0.117357i	$-0.962558\pi$
$823$	−20.2270	+	24.1056i	−0.705068	+	0.840267i	0.288022	+	0.957624i	$0.407002\pi$
$824$	72.8767	+	61.1508i	2.53878	+	2.13029i
$825$		0			0
$826$	18.2578	+	6.64528i	0.635269	+	0.231219i
$827$	−30.8151	−	17.7911i	−1.07155	−	0.618658i	−0.142943	−	0.989731i	$-0.545657\pi$
$827$	−30.8151	−	17.7911i	−1.07155	−	0.618658i	−0.928604	+	0.371073i	$0.878990\pi$
$828$	−8.39617	+	61.3350i	−0.291787	+	2.13154i
$829$	−4.30490	−	7.45631i	−0.149515	−	0.258968i	0.781533	−	0.623864i	$-0.214438\pi$
$829$	−4.30490	−	7.45631i	−0.149515	−	0.258968i	−0.931048	+	0.364895i	$0.881105\pi$
$830$		0			0
$831$	−6.32037	−	21.8937i	−0.219251	−	0.759484i
$832$	−19.6114	−	53.8820i	−0.679905	−	1.86802i
$833$	11.5547	+	2.03741i	0.400347	+	0.0705921i
$834$	15.1262	+	20.7412i	0.523778	+	0.718210i
$835$		0			0
$836$	14.6511			0.506718
$837$	12.1111	−	1.76851i	0.418622	−	0.0611287i
$838$		−	19.6459i		−	0.678656i
$839$	−22.3100	+	18.7203i	−0.770227	+	0.646298i	−0.940767	−	0.339053i	$-0.889893\pi$
$839$	−22.3100	+	18.7203i	−0.770227	+	0.646298i	0.170540	+	0.985351i	$0.445449\pi$
$840$		0			0
$841$	−0.315412	+	1.78879i	−0.0108763	+	0.0616824i
$842$	20.1759	+	55.4328i	0.695307	+	1.91034i
$843$	1.53402	−	6.19990i	0.0528344	−	0.213536i
$844$	23.9645	+	135.909i	0.824891	+	4.67819i
$845$		0			0
$846$	71.1983	+	37.5303i	2.44785	+	1.29032i
$847$	−45.5116	−	26.2762i	−1.56380	−	0.902859i
$848$	13.4328	−	36.9064i	0.461286	−	1.26737i
$849$	25.3948	+	17.0629i	0.871546	+	0.585597i
$850$		0			0
$851$	−1.83928	−	1.54334i	−0.0630497	−	0.0529050i
$852$	18.6733	−	27.7915i	0.639737	−	0.952122i
$853$	15.0542	−	41.3611i	0.515447	−	1.41618i	−0.360040	−	0.932937i	$-0.617237\pi$
$853$	15.0542	−	41.3611i	0.515447	−	1.41618i	0.875487	−	0.483242i	$-0.160541\pi$
$854$	−41.0180	+	71.0452i	−1.40361	+	2.43112i
$855$		0			0
$856$	−53.3267	−	92.3645i	−1.82267	−	3.15695i
$857$	28.6812	−	5.05727i	0.979731	−	0.172753i	0.339224	−	0.940706i	$-0.389836\pi$
$857$	28.6812	−	5.05727i	0.979731	−	0.172753i	0.640507	+	0.767953i	$0.278724\pi$
$858$	−2.73103	+	11.0378i	−0.0932360	+	0.376823i
$859$	50.8120	−	18.4940i	1.73368	−	0.631009i	0.734800	−	0.678283i	$-0.237276\pi$
$859$	50.8120	−	18.4940i	1.73368	−	0.631009i	0.998882	+	0.0472747i	$0.0150536\pi$
$860$		0			0
$861$	−15.3569	+	34.6591i	−0.523363	+	1.18118i
$862$	−44.4275	−	52.9466i	−1.51321	−	1.80337i
$863$			8.54878i			0.291004i	0.989358	+	0.145502i	$0.0464797\pi$
$863$			8.54878i			0.291004i	−0.989358	+	0.145502i	$0.953520\pi$
$864$	56.8551	−	44.9141i	1.93425	−	1.52801i
$865$		0			0
$866$	43.6361	−	36.6150i	1.48281	−	1.24423i
$867$	23.1610	−	16.8909i	0.786590	−	0.573646i
$868$	−57.8893	−	10.2074i	−1.96489	−	0.346463i
$869$	6.34355	−	2.30886i	0.215190	−	0.0783228i
$870$		0			0
$871$	3.06626	+	17.3896i	0.103896	+	0.589224i
$872$	59.7911	−	34.5204i	2.02478	−	1.16901i
$873$	−3.64786	+	26.6481i	−0.123461	+	0.901901i
$874$	−25.5302	+	44.2196i	−0.863572	+	1.49575i
$875$		0			0
$876$	−14.4539	+	7.08170i	−0.488352	+	0.239269i
$877$	11.7741	−	14.0318i	0.397582	−	0.473820i	−0.529699	−	0.848186i	$-0.677695\pi$
$877$	11.7741	−	14.0318i	0.397582	−	0.473820i	0.927281	+	0.374366i	$0.122140\pi$
$878$	10.5882	−	12.6185i	0.357334	−	0.425854i
$879$	2.61669	−	38.4088i	0.0882589	−	1.29550i
$880$		0			0
$881$	3.34854	−	5.79984i	0.112815	−	0.195402i	−0.804089	−	0.594509i	$-0.797347\pi$
$881$	3.34854	−	5.79984i	0.112815	−	0.195402i	0.916904	+	0.399107i	$0.130680\pi$
$882$	132.625	+	42.5678i	4.46570	+	1.43333i
$883$	10.0585	−	5.80730i	0.338497	−	0.195431i	−0.321110	−	0.947042i	$-0.604056\pi$
$883$	10.0585	−	5.80730i	0.338497	−	0.195431i	0.659607	+	0.751611i	$0.270723\pi$
$884$	2.35014	+	13.3283i	0.0790437	+	0.448279i
$885$		0			0
$886$	−34.7492	+	12.6477i	−1.16742	+	0.424906i
$887$	−55.8670	−	9.85087i	−1.87583	−	0.330760i	−0.884971	−	0.465646i	$-0.845822\pi$
$887$	−55.8670	−	9.85087i	−1.87583	−	0.330760i	−0.990861	+	0.134887i	$0.956933\pi$
$888$	0.872070	+	8.15665i	0.0292648	+	0.273719i
$889$	−8.55983	+	7.18255i	−0.287088	+	0.240895i
$890$		0			0
$891$	−5.54603	+	0.427760i	−0.185799	+	0.0143305i
$892$		−	18.3122i		−	0.613137i
$893$	30.5515	+	36.4099i	1.02237	+	1.21841i
$894$	73.4083	−	7.84846i	2.45514	−	0.262492i
$895$		0			0
$896$	−47.1039	+	17.1444i	−1.57363	+	0.572755i
$897$	−20.4452	−	19.6731i	−0.682646	−	0.656866i
$898$	−37.3945	+	6.59365i	−1.24787	+	0.220033i
$899$	6.14055	+	10.6358i	0.204799	+	0.354722i
$900$		0			0
$901$	−1.16141	+	2.01162i	−0.0386921	+	0.0670166i
$902$	−2.48064	+	6.81551i	−0.0825964	+	0.226932i
$903$	14.4669	+	0.985591i	0.481427	+	0.0327984i
$904$	−110.147	−	92.4247i	−3.66345	−	3.07400i
$905$		0			0
$906$	−77.7257	+	38.0818i	−2.58226	+	1.26518i
$907$	−2.72027	+	7.47387i	−0.0903249	+	0.248166i	−0.976627	−	0.214942i	$-0.931044\pi$
$907$	−2.72027	+	7.47387i	−0.0903249	+	0.248166i	0.886302	+	0.463108i	$0.153266\pi$
$908$	34.2229	+	19.7586i	1.13573	+	0.655712i
$909$	−2.54982	−	6.24653i	−0.0845723	−	0.207184i
$910$		0			0
$911$	−2.88348	−	16.3530i	−0.0955339	−	0.541800i	−0.994582	−	0.103951i	$-0.966852\pi$
$911$	−2.88348	−	16.3530i	−0.0955339	−	0.541800i	0.899049	−	0.437849i	$-0.144260\pi$
$912$	88.7103	−	25.6093i	2.93749	−	0.848008i
$913$	−2.98277	−	8.19509i	−0.0987153	−	0.271218i
$914$	−13.7249	+	77.8377i	−0.453979	+	2.57464i
$915$		0			0
$916$	86.2909	−	72.4066i	2.85113	−	2.39238i
$917$			59.7432i			1.97290i
$918$	−8.14116	+	4.38500i	−0.268698	+	0.144726i
$919$	29.5872			0.975992			0.487996	−	0.872846i	$-0.337728\pi$
$919$	29.5872			0.975992			0.487996	+	0.872846i	$0.337728\pi$
$920$		0			0
$921$	13.7831	−	31.1071i	0.454168	−	1.02501i
$922$	−34.9258	−	6.15836i	−1.15022	−	0.202815i
$923$	5.24849	+	14.4201i	0.172756	+	0.474644i
$924$	25.9327	+	6.41645i	0.853125	+	0.211086i
$925$		0			0
$926$	34.2857	+	59.3845i	1.12670	+	1.95150i
$927$	−18.8415	−	29.9137i	−0.618836	−	0.982496i
$928$	62.9612	+	36.3507i	2.06680	+	1.19327i
$929$	43.5356	+	15.8456i	1.42836	+	0.519879i	0.936460	−	0.350775i	$-0.114082\pi$
$929$	43.5356	+	15.8456i	1.42836	+	0.519879i	0.491896	+	0.870654i	$0.336304\pi$
$930$		0			0
$931$	63.0120	+	52.8734i	2.06514	+	1.73285i
$932$	46.2759	−	55.1494i	1.51582	−	1.80648i
$933$	27.7659	−	41.3241i	0.909015	−	1.35289i
$934$	−74.7408	−	27.2034i	−2.44559	−	0.890123i
$935$		0			0
$936$	3.73006	+	96.8663i	0.121921	+	3.16617i
$937$	−22.0608	+	12.7368i	−0.720694	+	0.416093i	−0.815008	−	0.579450i	$-0.803267\pi$
$937$	−22.0608	+	12.7368i	−0.720694	+	0.416093i	0.0943143	+	0.995542i	$0.469934\pi$
$938$	57.0621	−	10.0616i	1.86314	−	0.328522i
$939$	−43.6120	−	10.7908i	−1.42322	−	0.352143i
$940$		0			0
$941$	5.04981	−	28.6389i	0.164619	−	0.933602i	−0.784837	−	0.619702i	$-0.787253\pi$
$941$	5.04981	−	28.6389i	0.164619	−	0.933602i	0.949456	−	0.313899i	$-0.101635\pi$
$942$	−22.2329	−	9.85103i	−0.724385	−	0.320964i
$943$	−11.6334	−	13.8641i	−0.378834	−	0.451477i
$944$	16.7737			0.545937
$945$		0			0
$946$	2.77428			0.0901997
$947$	31.5248	+	37.5697i	1.02442	+	1.22085i	0.975030	+	0.222073i	$0.0712822\pi$
$947$	31.5248	+	37.5697i	1.02442	+	1.22085i	0.0493867	+	0.998780i	$0.484273\pi$
$948$	77.0699	−	56.2057i	2.50311	−	1.82548i
$949$	1.28098	−	7.26481i	0.0415825	−	0.235826i
$950$		0			0
$951$	−10.4337	−	36.1423i	−0.338337	−	1.17199i
$952$	26.3874	−	4.65281i	0.855220	−	0.150798i
$953$	−39.4900	+	22.7996i	−1.27921	+	0.738550i	−0.976702	−	0.214598i	$-0.931156\pi$
$953$	−39.4900	+	22.7996i	−1.27921	+	0.738550i	−0.302504	+	0.953148i	$0.597822\pi$
$954$	−16.8992	+	21.7904i	−0.547131	+	0.705489i
$955$		0			0
$956$	14.0787	+	5.12421i	0.455336	+	0.165729i
$957$	−2.45570	−	5.01213i	−0.0793814	−	0.162019i
$958$	71.1807	−	84.8299i	2.29974	−	2.74073i
$959$	−43.1111	−	36.1745i	−1.39213	−	1.16813i
$960$		0			0
$961$	23.9167	+	8.70496i	0.771506	+	0.280805i
$962$	−5.39654	−	3.11569i	−0.173991	−	0.100454i
$963$	8.37913	+	38.7380i	0.270014	+	1.24831i
$964$	−9.70475	−	16.8091i	−0.312569	−	0.541385i
$965$		0			0
$966$	−64.5551	+	67.0888i	−2.07703	+	2.15855i
$967$	18.9103	+	51.9555i	0.608113	+	1.67078i	0.734345	+	0.678776i	$0.237489\pi$
$967$	18.9103	+	51.9555i	0.608113	+	1.67078i	−0.126232	+	0.992001i	$0.540288\pi$
$968$	−84.4159	−	14.8848i	−2.71323	−	0.478416i
$969$	−5.42983	+	0.580531i	−0.174431	+	0.0186493i
$970$		0			0
$971$	−38.0240			−1.22025			−0.610124	−	0.792306i	$-0.708880\pi$
$971$	−38.0240			−1.22025			−0.610124	+	0.792306i	$0.708880\pi$
$972$	−73.6153	+	27.5427i	−2.36121	+	0.883433i
$973$			27.6426i			0.886181i
$974$	21.6916	−	18.2015i	0.695045	−	0.583212i
$975$		0			0
$976$	−12.2982	+	69.7466i	−0.393656	+	2.23253i
$977$	−8.64447	−	23.7505i	−0.276561	−	0.759845i	−0.997746	−	0.0671026i	$-0.978625\pi$
$977$	−8.64447	−	23.7505i	−0.276561	−	0.759845i	0.721185	−	0.692742i	$-0.243598\pi$
$978$	−24.0454	−	23.1373i	−0.768887	−	0.739849i
$979$	−1.74352	−	9.88799i	−0.0557231	−	0.316022i
$980$		0			0
$981$	−25.0766	+	5.42413i	−0.800633	+	0.173179i
$982$	−52.8301	−	30.5015i	−1.68588	−	0.973341i
$983$	−18.3781	+	50.4934i	−0.586170	+	1.61049i	0.191275	+	0.981537i	$0.438738\pi$
$983$	−18.3781	+	50.4934i	−0.586170	+	1.61049i	−0.777445	+	0.628951i	$0.783484\pi$
$984$	−4.20281	+	61.6904i	−0.133981	+	1.96662i
$985$		0			0
$986$	−7.10764	−	5.96402i	−0.226354	−	0.189933i
$987$	38.1312	+	77.8265i	1.21373	+	2.47725i
$988$	−32.4516	+	89.1601i	−1.03242	+	2.83656i
$989$	−3.46135	+	5.99523i	−0.110065	+	0.190637i
$990$		0			0
$991$	17.5824	+	30.4537i	0.558525	+	0.967393i	0.997620	+	0.0689524i	$0.0219657\pi$
$991$	17.5824	+	30.4537i	0.558525	+	0.967393i	−0.439095	+	0.898440i	$0.644701\pi$
$992$	−32.3463	+	5.70352i	−1.02699	+	0.181087i
$993$	22.3630	−	6.45586i	0.709669	−	0.204871i
$994$	47.3180	−	17.2223i	1.50084	−	0.546260i
$995$		0			0
$996$	−72.6110	−	99.5650i	−2.30077	−	3.15484i
$997$	−19.5094	−	23.2504i	−0.617868	−	0.736347i	0.362834	−	0.931854i	$-0.381809\pi$
$997$	−19.5094	−	23.2504i	−0.617868	−	0.736347i	−0.980702	+	0.195507i	$0.937365\pi$
$998$		−	16.4298i		−	0.520076i
$999$	0.617768	−	2.98514i	0.0195453	−	0.0944457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.e.49.1		132
5.2	odd	4		675.2.l.f.76.11	✓	66
5.3	odd	4		675.2.l.g.76.1	yes	66
5.4	even	2	inner	675.2.u.e.49.22		132
27.16	even	9	inner	675.2.u.e.124.22		132
135.43	odd	36		675.2.l.g.151.1	yes	66
135.97	odd	36		675.2.l.f.151.11	yes	66
135.124	even	18	inner	675.2.u.e.124.1		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.11	✓	66	5.2	odd	4
675.2.l.f.151.11	yes	66	135.97	odd	36
675.2.l.g.76.1	yes	66	5.3	odd	4
675.2.l.g.151.1	yes	66	135.43	odd	36
675.2.u.e.49.1		132	1.1	even	1	trivial
675.2.u.e.49.22		132	5.4	even	2	inner
675.2.u.e.124.1		132	135.124	even	18	inner
675.2.u.e.124.22		132	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70577 - 2.03285i) q^{2} +(0.184133 + 1.72224i) q^{3} +(-0.875557 + 4.96553i) q^{4} +(3.18696 - 3.31205i) q^{6} +(4.87417 - 0.859447i) q^{7} +(6.99134 - 4.03645i) q^{8} +(-2.93219 + 0.634241i) q^{9} +(-0.580782 - 0.211388i) q^{11} +(-8.71303 - 0.593596i) q^{12} +(2.57283 - 3.06618i) q^{13} +(-10.0613 - 8.44245i) q^{14} +(-10.6550 - 3.87811i) q^{16} +(0.580760 + 0.335302i) q^{17} +(6.29095 + 4.87884i) q^{18} +(2.35070 + 4.07153i) q^{19} +(2.37767 + 8.23621i) q^{21} +(0.560959 + 1.54122i) q^{22} +(-4.03047 - 0.710681i) q^{23} +(8.23906 + 11.2975i) q^{24} -10.6217 q^{26} +(-1.63223 - 4.93314i) q^{27} +24.9553i q^{28} +(3.99400 - 3.35136i) q^{29} +(-0.409029 + 2.31972i) q^{31} +(4.76914 + 13.1031i) q^{32} +(0.257118 - 1.03917i) q^{33} +(-0.309021 - 1.75255i) q^{34} +(-0.582045 - 15.1152i) q^{36} +(0.508066 + 0.293332i) q^{37} +(4.26708 - 11.7237i) q^{38} +(5.75442 + 3.86643i) q^{39} +(3.38756 + 2.84250i) q^{41} +(12.6873 - 18.8825i) q^{42} +(0.578526 - 1.58949i) q^{43} +(1.55816 - 2.69881i) q^{44} +(5.43034 + 9.40562i) q^{46} +(9.95611 - 1.75553i) q^{47} +(4.71707 - 19.0645i) q^{48} +(16.4410 - 5.98403i) q^{49} +(-0.470532 + 1.06195i) q^{51} +(12.9725 + 15.4601i) q^{52} +3.46376i q^{53} +(-7.24415 + 11.7329i) q^{54} +(30.6078 - 25.6830i) q^{56} +(-6.57930 + 4.79817i) q^{57} +(-13.6256 - 2.40257i) q^{58} +(-1.39010 + 0.505956i) q^{59} +(-1.08461 - 6.15113i) q^{61} +(5.41336 - 3.12540i) q^{62} +(-13.7469 + 5.61146i) q^{63} +(7.16284 - 12.4064i) q^{64} +(-2.55106 + 1.24989i) q^{66} +(-2.83572 + 3.37947i) q^{67} +(-2.17344 + 2.59021i) q^{68} +(0.481817 - 7.07228i) q^{69} +(-1.91695 + 3.32025i) q^{71} +(-17.9399 + 16.2698i) q^{72} +(1.59610 - 0.921510i) q^{73} +(-0.270341 - 1.53318i) q^{74} +(-22.2755 + 8.10762i) q^{76} +(-3.01251 - 0.531186i) q^{77} +(-1.95581 - 18.2931i) q^{78} +(-8.36705 + 7.02079i) q^{79} +(8.19548 - 3.71943i) q^{81} -11.7350i q^{82} +(9.07001 + 10.8092i) q^{83} +(-42.9789 + 4.59510i) q^{84} +(-4.21802 + 1.53523i) q^{86} +(6.50726 + 6.26150i) q^{87} +(-4.91371 + 0.866419i) q^{88} +(8.12267 + 14.0689i) q^{89} +(9.90517 - 17.1563i) q^{91} +(7.05782 - 19.3912i) q^{92} +(-4.07042 - 0.277307i) q^{93} +(-20.5515 - 17.2448i) q^{94} +(-21.6885 + 10.6263i) q^{96} +(3.06640 - 8.42485i) q^{97} +(-40.2091 - 23.2148i) q^{98} +(1.83704 + 0.251472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{6} + 12 q^{9} + 30 q^{11} - 30 q^{14} + 36 q^{16} - 24 q^{19} + 24 q^{21} + 78 q^{24} + 12 q^{26} + 30 q^{29} + 6 q^{31} + 60 q^{36} + 30 q^{39} + 78 q^{41} - 102 q^{44} + 18 q^{46} + 12 q^{49}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 12 * q^6 + 12 * q^9 + 30 * q^11 - 30 * q^14 + 36 * q^16 - 24 * q^19 + 24 * q^21 + 78 * q^24 + 12 * q^26 + 30 * q^29 + 6 * q^31 + 60 * q^36 + 30 * q^39 + 78 * q^41 - 102 * q^44 + 18 * q^46 + 12 * q^49 - 150 * q^54 + 288 * q^56 - 90 * q^59 - 108 * q^61 + 48 * q^64 + 96 * q^66 - 102 * q^69 - 30 * q^71 - 192 * q^74 - 96 * q^76 - 96 * q^79 - 108 * q^81 - 114 * q^84 - 222 * q^86 + 24 * q^89 + 18 * q^91 - 72 * q^94 - 498 * q^96 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more