LMFDB - Embedded newform 150.4.g.b.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.85028650086$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 66 x^{14} + 116 x^{13} - 15174 x^{12} + 66830 x^{11} - 253085 x^{10} + \cdots + 48733788520125 $ x^16 - 4x^15 + 66x^14 + 116x^13 - 15174x^12 + 66830x^11 - 253085x^10 - 2763760x^9 + 83790040x^8 - 245751650x^7 + 550471825x^6 + 10129042700x^5 - 118334390050x^4 + 286942998000x^3 + 664960189500x^2 - 7593598503000*x + 48733788520125
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.2
Root			$0.147988 - 7.05156i$ of defining polynomial
Character	$\chi$	$=$	150.61
Dual form			150.4.g.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61803 + 1.17557i) q^{2} +(0.927051 - 2.85317i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-3.72153 + 10.5428i) q^{5} +(1.85410 + 5.70634i) q^{6} +7.73387 q^{7} +(2.47214 + 7.60845i) q^{8} +(-7.28115 - 5.29007i) q^{9} +(-6.37221 - 21.4335i) q^{10} +(-8.25866 + 6.00027i) q^{11} +(-9.70820 - 7.05342i) q^{12} +(-32.3623 - 23.5126i) q^{13} +(-12.5137 + 9.09171i) q^{14} +(26.6303 + 20.3919i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(37.6583 + 115.900i) q^{17} +18.0000 q^{18} +(36.2669 + 111.618i) q^{19} +(35.5070 + 27.1891i) q^{20} +(7.16969 - 22.0660i) q^{21} +(6.30906 - 19.4173i) q^{22} +(-69.9088 + 50.7917i) q^{23} +24.0000 q^{24} +(-97.3004 - 78.4706i) q^{25} +80.0041 q^{26} +(-21.8435 + 15.8702i) q^{27} +(9.55959 - 29.4214i) q^{28} +(-44.9977 + 138.489i) q^{29} +(-67.0608 - 1.68894i) q^{30} +(73.3462 + 225.736i) q^{31} +32.0000 q^{32} +(9.46358 + 29.1259i) q^{33} +(-197.181 - 143.261i) q^{34} +(-28.7818 + 81.5365i) q^{35} +(-29.1246 + 21.1603i) q^{36} +(-105.537 - 76.6773i) q^{37} +(-189.896 - 137.968i) q^{38} +(-97.0870 + 70.5378i) q^{39} +(-89.4144 - 2.25192i) q^{40} +(157.273 + 114.266i) q^{41} +(14.3394 + 44.1321i) q^{42} -193.886 q^{43} +(12.6181 + 38.8346i) q^{44} +(82.8691 - 57.0764i) q^{45} +(53.4055 - 164.365i) q^{46} +(-15.6058 + 48.0298i) q^{47} +(-38.8328 + 28.2137i) q^{48} -283.187 q^{49} +(249.683 + 12.5846i) q^{50} +365.594 q^{51} +(-129.449 + 94.0505i) q^{52} +(127.551 - 392.560i) q^{53} +(16.6869 - 51.3571i) q^{54} +(-32.5246 - 109.399i) q^{55} +(19.1192 + 58.8428i) q^{56} +352.087 q^{57} +(-89.9953 - 276.977i) q^{58} +(413.130 + 300.156i) q^{59} +(110.492 - 76.1019i) q^{60} +(639.479 - 464.608i) q^{61} +(-384.046 - 279.026i) q^{62} +(-56.3115 - 40.9127i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(368.326 - 253.686i) q^{65} +(-49.5520 - 36.0016i) q^{66} +(-172.725 - 531.591i) q^{67} +487.459 q^{68} +(80.1083 + 246.548i) q^{69} +(-49.2819 - 165.764i) q^{70} +(-16.6518 + 51.2491i) q^{71} +(22.2492 - 68.4761i) q^{72} +(358.865 - 260.731i) q^{73} +260.903 q^{74} +(-314.092 + 204.868i) q^{75} +469.449 q^{76} +(-63.8714 + 46.4053i) q^{77} +(74.1679 - 228.265i) q^{78} +(36.2394 - 111.533i) q^{79} +(147.323 - 101.469i) q^{80} +(25.0304 + 77.0356i) q^{81} -388.801 q^{82} +(-93.1727 - 286.756i) q^{83} +(-75.0820 - 54.5502i) q^{84} +(-1362.06 - 34.3037i) q^{85} +(313.714 - 227.926i) q^{86} +(353.416 + 256.772i) q^{87} +(-66.0693 - 48.0022i) q^{88} +(-959.843 + 697.367i) q^{89} +(-66.9876 + 189.770i) q^{90} +(-250.286 - 181.843i) q^{91} +(106.811 + 328.731i) q^{92} +712.060 q^{93} +(-31.2117 - 96.0597i) q^{94} +(-1311.73 - 33.0363i) q^{95} +(29.6656 - 91.3014i) q^{96} +(65.7524 - 202.365i) q^{97} +(458.207 - 332.907i) q^{98} +91.8744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	−3.72153	+	10.5428i	−0.332864	+	0.942975i
$5$	−3.72153	+	10.5428i	−0.332864	+	0.942975i
$6$	1.85410	+	5.70634i	0.126156	+	0.388267i
$7$	7.73387			0.417590			0.208795	−	0.977959i	$-0.433046\pi$
$7$	7.73387			0.417590			0.208795	+	0.977959i	$0.433046\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$	−6.37221	−	21.4335i	−0.201507	−	0.677787i
$11$	−8.25866	+	6.00027i	−0.226371	+	0.164468i	−0.695190	−	0.718826i	$-0.744680\pi$
$11$	−8.25866	+	6.00027i	−0.226371	+	0.164468i	0.468819	+	0.883294i	$0.344680\pi$
$12$	−9.70820	−	7.05342i	−0.233543	−	0.169679i
$13$	−32.3623	−	23.5126i	−0.690438	−	0.501633i	0.186366	−	0.982480i	$-0.440329\pi$
$13$	−32.3623	−	23.5126i	−0.690438	−	0.501633i	−0.876804	+	0.480848i	$0.840329\pi$
$14$	−12.5137	+	9.09171i	−0.238887	+	0.173562i
$15$	26.6303	+	20.3919i	0.458394	+	0.351010i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	37.6583	+	115.900i	0.537263	+	1.65353i	0.738707	+	0.674027i	$0.235437\pi$
$17$	37.6583	+	115.900i	0.537263	+	1.65353i	−0.201443	+	0.979500i	$0.564563\pi$
$18$	18.0000			0.235702
$19$	36.2669	+	111.618i	0.437905	+	1.34773i	0.890080	+	0.455804i	$0.150648\pi$
$19$	36.2669	+	111.618i	0.437905	+	1.34773i	−0.452175	+	0.891929i	$0.649352\pi$
$20$	35.5070	+	27.1891i	0.396981	+	0.303984i
$21$	7.16969	−	22.0660i	0.0745026	−	0.229295i
$22$	6.30906	−	19.4173i	0.0611407	−	0.188172i
$23$	−69.9088	+	50.7917i	−0.633782	+	0.460470i	−0.857708	−	0.514136i	$-0.828112\pi$
$23$	−69.9088	+	50.7917i	−0.633782	+	0.460470i	0.223926	+	0.974606i	$0.428112\pi$
$24$	24.0000			0.204124
$25$	−97.3004	−	78.4706i	−0.778403	−	0.627765i
$26$	80.0041			0.603465
$27$	−21.8435	+	15.8702i	−0.155695	+	0.113119i
$28$	9.55959	−	29.4214i	0.0645212	−	0.198576i
$29$	−44.9977	+	138.489i	−0.288133	+	0.886782i	0.697309	+	0.716771i	$0.254381\pi$
$29$	−44.9977	+	138.489i	−0.288133	+	0.886782i	−0.985442	+	0.170012i	$0.945619\pi$
$30$	−67.0608	−	1.68894i	−0.408119	−	0.0102786i
$31$	73.3462	+	225.736i	0.424947	+	1.30785i	0.903045	+	0.429547i	$0.141327\pi$
$31$	73.3462	+	225.736i	0.424947	+	1.30785i	−0.478097	+	0.878307i	$0.658673\pi$
$32$	32.0000			0.176777
$33$	9.46358	+	29.1259i	0.0499212	+	0.153642i
$34$	−197.181	−	143.261i	−0.994598	−	0.722618i
$35$	−28.7818	+	81.5365i	−0.139001	+	0.393777i
$36$	−29.1246	+	21.1603i	−0.134836	+	0.0979642i
$37$	−105.537	−	76.6773i	−0.468925	−	0.340694i	0.328097	−	0.944644i	$-0.393593\pi$
$37$	−105.537	−	76.6773i	−0.468925	−	0.340694i	−0.797022	+	0.603950i	$0.793593\pi$
$38$	−189.896	−	137.968i	−0.810663	−	0.588981i
$39$	−97.0870	+	70.5378i	−0.398625	+	0.289618i
$40$	−89.4144	−	2.25192i	−0.353441	−	0.00890150i
$41$	157.273	+	114.266i	0.599073	+	0.435252i	0.845550	−	0.533897i	$-0.179273\pi$
$41$	157.273	+	114.266i	0.599073	+	0.435252i	−0.246477	+	0.969149i	$0.579273\pi$
$42$	14.3394	+	44.1321i	0.0526813	+	0.162136i
$43$	−193.886			−0.687612			−0.343806	−	0.939041i	$-0.611716\pi$
$43$	−193.886			−0.687612			−0.343806	+	0.939041i	$0.611716\pi$
$44$	12.6181	+	38.8346i	0.0432330	+	0.133057i
$45$	82.8691	−	57.0764i	0.274520	−	0.189077i
$46$	53.4055	−	164.365i	0.171179	−	0.526834i
$47$	−15.6058	+	48.0298i	−0.0484329	+	0.149061i	−0.972348	−	0.233536i	$-0.924970\pi$
$47$	−15.6058	+	48.0298i	−0.0484329	+	0.149061i	0.923915	+	0.382597i	$0.124970\pi$
$48$	−38.8328	+	28.2137i	−0.116772	+	0.0848395i
$49$	−283.187			−0.825619
$50$	249.683	+	12.5846i	0.706210	+	0.0355947i
$51$	365.594			1.00379
$52$	−129.449	+	94.0505i	−0.345219	+	0.250816i
$53$	127.551	−	392.560i	0.330574	−	1.01740i	−0.638288	−	0.769798i	$-0.720357\pi$
$53$	127.551	−	392.560i	0.330574	−	1.01740i	0.968861	−	0.247604i	$-0.0796431\pi$
$54$	16.6869	−	51.3571i	0.0420519	−	0.129422i
$55$	−32.5246	−	109.399i	−0.0797385	−	0.268208i
$56$	19.1192	+	58.8428i	0.0456233	+	0.140414i
$57$	352.087			0.818158
$58$	−89.9953	−	276.977i	−0.203741	−	0.627050i
$59$	413.130	+	300.156i	0.911609	+	0.662323i	0.941421	−	0.337233i	$-0.109491\pi$
$59$	413.130	+	300.156i	0.911609	+	0.662323i	−0.0298123	+	0.999556i	$0.509491\pi$
$60$	110.492	−	76.1019i	0.237741	−	0.163745i
$61$	639.479	−	464.608i	1.34224	−	0.975197i	0.342885	−	0.939377i	$-0.388596\pi$
$61$	639.479	−	464.608i	1.34224	−	0.975197i	0.999358	−	0.0358196i	$-0.0114042\pi$
$62$	−384.046	−	279.026i	−0.786675	−	0.571553i
$63$	−56.3115	−	40.9127i	−0.112612	−	0.0818177i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	368.326	−	253.686i	0.702849	−	0.484090i
$66$	−49.5520	−	36.0016i	−0.0924155	−	0.0671438i
$67$	−172.725	−	531.591i	−0.314950	−	0.969317i	−0.975775	−	0.218777i	$-0.929793\pi$
$67$	−172.725	−	531.591i	−0.314950	−	0.969317i	0.660825	−	0.750540i	$-0.270207\pi$
$68$	487.459			0.869311
$69$	80.1083	+	246.548i	0.139767	+	0.430158i
$70$	−49.2819	−	165.764i	−0.0841473	−	0.283037i
$71$	−16.6518	+	51.2491i	−0.0278339	+	0.0856640i	−0.964008	−	0.265871i	$-0.914340\pi$
$71$	−16.6518	+	51.2491i	−0.0278339	+	0.0856640i	0.936175	+	0.351535i	$0.114340\pi$
$72$	22.2492	−	68.4761i	0.0364180	−	0.112083i
$73$	358.865	−	260.731i	0.575370	−	0.418030i	−0.261682	−	0.965154i	$-0.584277\pi$
$73$	358.865	−	260.731i	0.575370	−	0.418030i	0.837052	+	0.547124i	$0.184277\pi$
$74$	260.903			0.409855
$75$	−314.092	+	204.868i	−0.483577	+	0.315415i
$76$	469.449			0.708546
$77$	−63.8714	+	46.4053i	−0.0945302	+	0.0686802i
$78$	74.1679	−	228.265i	0.107665	−	0.331358i
$79$	36.2394	−	111.533i	0.0516108	−	0.158842i	−0.921929	−	0.387358i	$-0.873388\pi$
$79$	36.2394	−	111.533i	0.0516108	−	0.158842i	0.973540	+	0.228517i	$0.0733876\pi$
$80$	147.323	−	101.469i	0.205890	−	0.141808i
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$	−388.801			−0.523609
$83$	−93.1727	−	286.756i	−0.123217	−	0.379224i	0.870355	−	0.492425i	$-0.163889\pi$
$83$	−93.1727	−	286.756i	−0.123217	−	0.379224i	−0.993572	+	0.113201i	$0.963889\pi$
$84$	−75.0820	−	54.5502i	−0.0975252	−	0.0708562i
$85$	−1362.06	−	34.3037i	−1.73807	−	0.0437737i
$86$	313.714	−	227.926i	0.393356	−	0.285790i
$87$	353.416	+	256.772i	0.435520	+	0.316423i
$88$	−66.0693	−	48.0022i	−0.0800342	−	0.0581483i
$89$	−959.843	+	697.367i	−1.14318	+	0.830570i	−0.987559	−	0.157247i	$-0.949738\pi$
$89$	−959.843	+	697.367i	−1.14318	+	0.830570i	−0.155622	+	0.987817i	$0.549738\pi$
$90$	−66.9876	+	189.770i	−0.0784568	+	0.222261i
$91$	−250.286	−	181.843i	−0.288320	−	0.209477i
$92$	106.811	+	328.731i	0.121042	+	0.372528i
$93$	712.060			0.793948
$94$	−31.2117	−	96.0597i	−0.0342472	−	0.105402i
$95$	−1311.73	−	33.0363i	−1.41664	−	0.0356784i
$96$	29.6656	−	91.3014i	0.0315389	−	0.0970668i
$97$	65.7524	−	202.365i	0.0688262	−	0.211825i	−0.910728	−	0.413007i	$-0.864478\pi$
$97$	65.7524	−	202.365i	0.0688262	−	0.211825i	0.979554	+	0.201182i	$0.0644783\pi$
$98$	458.207	−	332.907i	0.472305	−	0.343149i
$99$	91.8744			0.0932699
$100$	−418.790	+	273.158i	−0.418790	+	0.273158i
$101$	701.772			0.691376			0.345688	−	0.938350i	$-0.387646\pi$
$101$	701.772			0.691376			0.345688	+	0.938350i	$0.387646\pi$
$102$	−591.544	+	429.782i	−0.574231	+	0.417204i
$103$	221.496	−	681.693i	0.211889	−	0.652129i	−0.787470	−	0.616352i	$-0.788610\pi$
$103$	221.496	−	681.693i	0.211889	−	0.652129i	0.999360	−	0.0357761i	$-0.0113903\pi$
$104$	98.8905	−	304.354i	0.0932405	−	0.286965i
$105$	205.955	+	157.708i	0.191421	+	0.146578i
$106$	255.101	+	785.120i	0.233751	+	0.719412i
$107$	−1510.38			−1.36461			−0.682306	−	0.731066i	$-0.739023\pi$
$107$	−1510.38			−1.36461			−0.682306	+	0.731066i	$0.739023\pi$
$108$	33.3738	+	102.714i	0.0297352	+	0.0915155i
$109$	1534.02	+	1114.53i	1.34800	+	0.979381i	0.999108	+	0.0422183i	$0.0134425\pi$
$109$	1534.02	+	1114.53i	1.34800	+	0.979381i	0.348893	+	0.937162i	$0.386558\pi$
$110$	181.233	+	138.777i	0.157090	+	0.120290i
$111$	−316.612	+	230.032i	−0.270734	+	0.196700i
$112$	−100.109	−	72.7337i	−0.0844593	−	0.0613633i
$113$	−276.771	−	201.086i	−0.230411	−	0.167403i	0.466590	−	0.884474i	$-0.345483\pi$
$113$	−276.771	−	201.086i	−0.230411	−	0.167403i	−0.697001	+	0.717071i	$0.745483\pi$
$114$	−569.688	+	413.903i	−0.468037	+	0.340048i
$115$	−275.318	−	926.056i	−0.223248	−	0.750914i
$116$	471.222	+	342.363i	0.377171	+	0.274031i
$117$	111.252	+	342.398i	0.0879080	+	0.270553i
$118$	−1021.31			−0.796775
$119$	291.244	+	896.358i	0.224356	+	0.690496i
$120$	−89.3168	+	253.027i	−0.0679456	+	0.192484i
$121$	−379.099	+	1166.75i	−0.284823	+	0.876595i
$122$	−488.518	+	1503.50i	−0.362528	+	1.11575i
$123$	471.820	−	342.798i	0.345875	−	0.251293i
$124$	949.414			0.687579
$125$	1189.40	−	733.786i	0.851069	−	0.525054i
$126$	139.210			0.0984268
$127$	−966.637	+	702.303i	−0.675395	+	0.490703i	−0.871827	−	0.489814i	$-0.837065\pi$
$127$	−966.637	+	702.303i	−0.675395	+	0.490703i	0.196432	+	0.980517i	$0.437065\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	−179.742	+	553.189i	−0.122678	+	0.377563i
$130$	−297.738	+	843.466i	−0.200872	+	0.569052i
$131$	−856.655	−	2636.51i	−0.571346	−	1.75842i	−0.648297	−	0.761387i	$-0.724519\pi$
$131$	−856.655	−	2636.51i	−0.571346	−	1.75842i	0.0769514	−	0.997035i	$-0.475481\pi$
$132$	122.499			0.0807741
$133$	280.484	+	863.240i	0.182865	+	0.562800i
$134$	904.397	+	657.083i	0.583045	+	0.423607i
$135$	−86.0249	−	289.352i	−0.0548433	−	0.184470i
$136$	−788.726	+	573.043i	−0.497299	+	0.361309i
$137$	−1460.05	−	1060.78i	−0.910511	−	0.661525i	0.0306327	−	0.999531i	$-0.490248\pi$
$137$	−1460.05	−	1060.78i	−0.910511	−	0.661525i	−0.941144	+	0.338005i	$0.890248\pi$
$138$	−419.453	−	304.750i	−0.258740	−	0.187986i
$139$	−1250.78	+	908.745i	−0.763236	+	0.554523i	−0.899901	−	0.436094i	$-0.856361\pi$
$139$	−1250.78	+	908.745i	−0.763236	+	0.554523i	0.136665	+	0.990617i	$0.456361\pi$
$140$	274.607	+	210.277i	0.165775	+	0.126941i
$141$	122.570	+	89.0522i	0.0732074	+	0.0531883i
$142$	−33.3037	−	102.498i	−0.0196816	−	0.0605736i
$143$	408.352			0.238798
$144$	44.4984	+	136.952i	0.0257514	+	0.0792547i
$145$	−1292.59	−	989.790i	−0.740304	−	0.566880i
$146$	−274.149	+	843.742i	−0.155402	+	0.478278i
$147$	−262.529	+	807.981i	−0.147300	+	0.453341i
$148$	−422.149	+	306.709i	−0.234462	+	0.170347i
$149$	2284.75			1.25620			0.628100	−	0.778133i	$-0.283833\pi$
$149$	2284.75			1.25620			0.628100	+	0.778133i	$0.283833\pi$
$150$	267.375	−	700.721i	0.145541	−	0.381424i
$151$	2800.59			1.50933			0.754664	−	0.656111i	$-0.227800\pi$
$151$	2800.59			1.50933			0.754664	+	0.656111i	$0.227800\pi$
$152$	−759.584	+	551.870i	−0.405332	+	0.294491i
$153$	338.925	−	1043.10i	0.179088	−	0.551176i
$154$	48.7934	−	150.171i	0.0255317	−	0.0785786i
$155$	−2652.85	−	66.8126i	−1.37472	−	0.0346227i
$156$	148.336	+	456.531i	0.0761305	+	0.234306i
$157$	2975.35			1.51247			0.756237	−	0.654298i	$-0.227036\pi$
$157$	2975.35			1.51247			0.756237	+	0.654298i	$0.227036\pi$
$158$	72.4788	+	223.067i	0.0364943	+	0.112318i
$159$	−1001.80	−	727.847i	−0.499670	−	0.363031i
$160$	−119.089	+	337.369i	−0.0588426	+	0.166696i
$161$	−540.665	+	392.816i	−0.264661	+	0.192287i
$162$	−131.061	−	95.2212i	−0.0635624	−	0.0461808i
$163$	2215.24	+	1609.47i	1.06449	+	0.773395i	0.974913	−	0.222585i	$-0.0714495\pi$
$163$	2215.24	+	1609.47i	1.06449	+	0.773395i	0.0895737	+	0.995980i	$0.471450\pi$
$164$	629.094	−	457.063i	0.299536	−	0.217626i
$165$	−342.287	−	8.62058i	−0.161497	−	0.00406734i
$166$	487.858	+	354.450i	0.228103	+	0.165727i
$167$	255.373	+	785.958i	0.118332	+	0.364187i	0.992627	−	0.121206i	$-0.0386763\pi$
$167$	255.373	+	785.958i	0.118332	+	0.364187i	−0.874296	+	0.485394i	$0.838676\pi$
$168$	185.613			0.0852401
$169$	−184.433	−	567.625i	−0.0839474	−	0.258364i
$170$	2244.18	−	1545.69i	1.01248	−	0.697347i
$171$	326.402	−	1004.56i	0.145968	−	0.449245i
$172$	−239.656	+	737.585i	−0.106242	+	0.326979i
$173$	−432.673	+	314.355i	−0.190147	+	0.138150i	−0.678786	−	0.734336i	$-0.737494\pi$
$173$	−432.673	+	314.355i	−0.190147	+	0.138150i	0.488639	+	0.872486i	$0.337494\pi$
$174$	−873.693			−0.380658
$175$	−752.508	−	606.881i	−0.325053	−	0.262148i
$176$	163.332			0.0699525
$177$	1239.39	−	900.469i	0.526318	−	0.382392i
$178$	733.255	−	2256.73i	0.308763	−	0.950274i
$179$	−930.760	+	2864.58i	−0.388649	+	1.19614i	0.545149	+	0.838339i	$0.316473\pi$
$179$	−930.760	+	2864.58i	−0.388649	+	1.19614i	−0.933798	+	0.357801i	$0.883527\pi$
$180$	−114.700	−	385.803i	−0.0474957	−	0.159756i
$181$	136.701	+	420.721i	0.0561375	+	0.172773i	0.975194	−	0.221353i	$-0.0710473\pi$
$181$	136.701	+	420.721i	0.0561375	+	0.172773i	−0.919056	+	0.394126i	$0.871047\pi$
$182$	618.741			0.252001
$183$	−732.777	−	2255.26i	−0.296002	−	0.911002i
$184$	−559.270	−	406.334i	−0.224076	−	0.162801i
$185$	1201.15	−	827.299i	0.477354	−	0.328780i
$186$	−1152.14	+	837.077i	−0.454187	+	0.329986i
$187$	−1006.44	−	731.222i	−0.393573	−	0.285948i
$188$	163.427	+	118.736i	0.0633995	+	0.0460624i
$189$	−168.934	+	122.738i	−0.0650168	+	0.0472375i
$190$	2161.27	−	1488.58i	0.825235	−	0.568384i
$191$	−3342.20	−	2428.25i	−1.26614	−	0.919905i	−0.267099	−	0.963669i	$-0.586065\pi$
$191$	−3342.20	−	2428.25i	−1.26614	−	0.919905i	−0.999042	+	0.0437636i	$0.986065\pi$
$192$	59.3313	+	182.603i	0.0223014	+	0.0686366i
$193$	2340.37			0.872869			0.436434	−	0.899736i	$-0.356241\pi$
$193$	2340.37			0.872869			0.436434	+	0.899736i	$0.356241\pi$
$194$	131.505	+	404.730i	0.0486675	+	0.149783i
$195$	−382.352	−	1286.08i	−0.140414	−	0.472296i
$196$	−350.039	+	1077.31i	−0.127565	+	0.392605i
$197$	−324.169	+	997.691i	−0.117239	+	0.360825i	−0.992407	−	0.122994i	$-0.960751\pi$
$197$	−324.169	+	997.691i	−0.117239	+	0.360825i	0.875168	+	0.483819i	$0.160751\pi$
$198$	−148.656	+	108.005i	−0.0533561	+	0.0387655i
$199$	1844.85			0.657177			0.328589	−	0.944473i	$-0.393427\pi$
$199$	1844.85			0.657177			0.328589	+	0.944473i	$0.393427\pi$
$200$	356.500	−	934.295i	0.126042	−	0.330323i
$201$	−1676.84			−0.588435
$202$	−1135.49	+	824.983i	−0.395509	+	0.287354i
$203$	−348.006	+	1071.05i	−0.120321	+	0.370311i
$204$	451.900	−	1390.80i	0.155095	−	0.477332i
$205$	−1789.98	+	1232.86i	−0.609841	+	0.420031i
$206$	442.991	+	1363.39i	0.149828	+	0.461124i
$207$	777.708			0.261133
$208$	197.781	+	608.707i	0.0659310	+	0.202915i
$209$	−969.255	−	704.205i	−0.320788	−	0.233066i
$210$	−518.639	−	13.0620i	−0.170426	−	0.00429222i
$211$	725.823	−	527.341i	0.236814	−	0.172055i	−0.463049	−	0.886333i	$-0.653245\pi$
$211$	725.823	−	527.341i	0.236814	−	0.172055i	0.699863	+	0.714277i	$0.253245\pi$
$212$	−1335.73	−	970.462i	−0.432727	−	0.314394i
$213$	130.785	+	95.0210i	0.0420716	+	0.0305668i
$214$	2443.84	−	1775.55i	0.780642	−	0.567170i
$215$	721.552	−	2044.09i	0.228881	−	0.648401i
$216$	−174.748	−	126.962i	−0.0550466	−	0.0399937i
$217$	567.250	+	1745.82i	0.177454	+	0.546146i
$218$	−3792.30			−1.17820
$219$	−411.223	−	1265.61i	−0.126885	−	0.390513i
$220$	−456.383	−	11.4941i	−0.139861	−	0.00352242i
$221$	1506.41	−	4636.25i	0.458516	−	1.41117i
$222$	241.870	−	744.399i	0.0731227	−	0.225049i
$223$	−1354.46	+	984.070i	−0.406731	+	0.295508i	−0.772277	−	0.635286i	$-0.780882\pi$
$223$	−1354.46	+	984.070i	−0.406731	+	0.295508i	0.365546	+	0.930793i	$0.380882\pi$
$224$	247.484			0.0738201
$225$	293.344	+	1086.08i	0.0869168	+	0.321802i
$226$	684.216			0.201387
$227$	−3129.02	+	2273.37i	−0.914892	+	0.664708i	−0.942247	−	0.334918i	$-0.891291\pi$
$227$	−3129.02	+	2273.37i	−0.914892	+	0.664708i	0.0273553	+	0.999626i	$0.491291\pi$
$228$	435.203	−	1339.42i	0.126412	−	0.389057i
$229$	976.323	−	3004.81i	0.281735	−	0.867090i	−0.705624	−	0.708587i	$-0.749333\pi$
$229$	976.323	−	3004.81i	0.281735	−	0.867090i	0.987358	−	0.158503i	$-0.0506669\pi$
$230$	1534.12	+	1174.73i	0.439812	+	0.336781i
$231$	73.1901	+	225.256i	0.0208466	+	0.0641591i
$232$	−1164.92			−0.329660
$233$	1832.69	+	5640.45i	0.515295	+	1.58592i	0.782744	+	0.622344i	$0.213820\pi$
$233$	1832.69	+	5640.45i	0.515295	+	1.58592i	−0.267448	+	0.963572i	$0.586180\pi$
$234$	−582.522	−	423.227i	−0.162738	−	0.118236i
$235$	−448.290	−	343.274i	−0.124439	−	0.0952881i
$236$	1652.52	−	1200.63i	0.455805	−	0.331161i
$237$	−284.628	−	206.794i	−0.0780109	−	0.0566782i
$238$	−1524.98	−	1107.96i	−0.415334	−	0.301758i
$239$	−2084.21	+	1514.26i	−0.564084	+	0.409831i	−0.832951	−	0.553346i	$-0.813351\pi$
$239$	−2084.21	+	1514.26i	−0.564084	+	0.409831i	0.268868	+	0.963177i	$0.413351\pi$
$240$	−152.933	−	514.404i	−0.0411325	−	0.138353i
$241$	3155.45	+	2292.57i	0.843404	+	0.612769i	0.923320	−	0.384033i	$-0.125465\pi$
$241$	3155.45	+	2292.57i	0.843404	+	0.612769i	−0.0799152	+	0.996802i	$0.525465\pi$
$242$	−758.199	−	2333.50i	−0.201400	−	0.619846i
$243$	243.000			0.0641500
$244$	−977.036	−	3007.01i	−0.256346	−	0.788951i
$245$	1053.89	−	2985.58i	0.274819	−	0.778538i
$246$	−360.439	+	1109.32i	−0.0934176	+	0.287510i
$247$	1450.75	−	4464.95i	0.373721	−	1.15019i
$248$	−1536.18	+	1116.10i	−0.393338	+	0.285777i
$249$	−904.539			−0.230212
$250$	−1061.88	+	2585.52i	−0.268637	+	0.654090i
$251$	−559.400			−0.140673			−0.0703366	−	0.997523i	$-0.522407\pi$
$251$	−559.400			−0.140673			−0.0703366	+	0.997523i	$0.522407\pi$
$252$	−225.246	+	163.651i	−0.0563062	+	0.0409088i
$253$	272.589	−	838.943i	0.0677373	−	0.208474i
$254$	738.445	−	2272.70i	0.182418	−	0.561424i
$255$	−1360.57	+	3854.38i	−0.334127	+	0.946552i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	4671.04			1.13374			0.566871	−	0.823807i	$-0.308154\pi$
$257$	4671.04			1.13374			0.566871	+	0.823807i	$0.308154\pi$
$258$	−359.484	−	1106.38i	−0.0867461	−	0.266977i
$259$	−816.212	−	593.012i	−0.195818	−	0.142270i
$260$	−509.803	−	1714.77i	−0.121603	−	0.409021i
$261$	1060.25	−	770.316i	0.251447	−	0.182687i
$262$	4485.51	+	3258.91i	1.05769	+	0.768459i
$263$	4235.64	+	3077.37i	0.993083	+	0.721517i	0.960594	−	0.277955i	$-0.0896567\pi$
$263$	4235.64	+	3077.37i	0.993083	+	0.721517i	0.0324887	+	0.999472i	$0.489657\pi$
$264$	−198.208	+	144.006i	−0.0462078	+	0.0335719i
$265$	3663.99	+	2805.66i	0.849348	+	0.650379i
$266$	−1468.63	−	1067.02i	−0.338525	−	0.245952i
$267$	1099.88	+	3385.09i	0.252104	+	0.775895i
$268$	−2235.79			−0.509600
$269$	−134.824	−	414.946i	−0.0305590	−	0.0940510i	0.934614	−	0.355665i	$-0.115745\pi$
$269$	−134.824	−	414.946i	−0.0305590	−	0.0940510i	−0.965173	+	0.261613i	$0.915745\pi$
$270$	479.345	+	367.053i	0.108045	+	0.0827339i
$271$	−1912.79	+	5886.95i	−0.428758	+	1.31958i	0.470591	+	0.882351i	$0.344041\pi$
$271$	−1912.79	+	5886.95i	−0.428758	+	1.31958i	−0.899349	+	0.437231i	$0.855959\pi$
$272$	602.533	−	1854.41i	0.134316	−	0.413382i
$273$	−750.858	+	545.530i	−0.166462	+	0.120941i
$274$	3609.43			0.795816
$275$	1274.42	+	64.2336i	0.279455	+	0.0140852i
$276$	1036.94			0.226147
$277$	6220.49	−	4519.45i	1.34929	−	0.980316i	0.350243	−	0.936659i	$-0.386099\pi$
$277$	6220.49	−	4519.45i	1.34929	−	0.980316i	0.999047	−	0.0436570i	$-0.0139009\pi$
$278$	955.511	−	2940.76i	0.206143	−	0.634443i
$279$	660.116	−	2031.63i	0.141649	−	0.435951i
$280$	−691.519	−	17.4161i	−0.147593	−	0.00371717i
$281$	−2226.60	−	6852.77i	−0.472697	−	1.45481i	−0.849039	−	0.528330i	$-0.822818\pi$
$281$	−2226.60	−	6852.77i	−0.472697	−	1.45481i	0.376342	−	0.926481i	$-0.377182\pi$
$282$	−303.009			−0.0639856
$283$	−268.223	−	825.504i	−0.0563398	−	0.173396i	0.918927	−	0.394428i	$-0.129057\pi$
$283$	−268.223	−	825.504i	−0.0563398	−	0.173396i	−0.975267	+	0.221032i	$0.929057\pi$
$284$	174.380	+	126.695i	0.0364351	+	0.0264716i
$285$	−1310.30	+	3711.97i	−0.272335	+	0.771502i
$286$	−660.727	+	480.046i	−0.136607	+	0.0992508i
$287$	1216.33	+	883.717i	0.250167	+	0.181757i
$288$	−232.997	−	169.282i	−0.0476718	−	0.0346356i
$289$	−8040.04	+	5841.43i	−1.63648	+	1.18897i
$290$	3255.03	+	81.9786i	0.659110	+	0.0165998i
$291$	−516.426	−	375.205i	−0.104032	−	0.0755839i
$292$	−548.297	−	1687.48i	−0.109886	−	0.338194i
$293$	−4510.54			−0.899347			−0.449673	−	0.893193i	$-0.648460\pi$
$293$	−4510.54			−0.899347			−0.449673	+	0.893193i	$0.648460\pi$
$294$	−525.058	−	1615.96i	−0.104156	−	0.320561i
$295$	−4701.96	+	3238.50i	−0.927995	+	0.639161i
$296$	322.493	−	992.532i	0.0633262	−	0.194898i
$297$	85.1723	−	262.133i	0.0166404	−	0.0512139i
$298$	−3696.80	+	2685.88i	−0.718623	+	0.522110i
$299$	3456.66			0.668574
$300$	391.126	+	1448.11i	0.0752722	+	0.278689i
$301$	−1499.49			−0.287140
$302$	−4531.45	+	3292.29i	−0.863428	+	0.627317i
$303$	650.579	−	2002.28i	0.123349	−	0.379629i
$304$	580.271	−	1785.89i	0.109476	−	0.336933i
$305$	2518.42	+	8470.94i	0.472802	+	1.59031i
$306$	677.849	+	2086.21i	0.126634	+	0.389740i
$307$	−2858.84			−0.531474			−0.265737	−	0.964046i	$-0.585615\pi$
$307$	−2858.84			−0.531474			−0.265737	+	0.964046i	$0.585615\pi$
$308$	97.5868	+	300.341i	0.0180537	+	0.0555634i
$309$	−1739.65	−	1263.93i	−0.320276	−	0.232694i
$310$	4370.94	−	3010.51i	0.800816	−	0.551566i
$311$	239.491	−	174.000i	0.0436665	−	0.0317256i	−0.565738	−	0.824585i	$-0.691409\pi$
$311$	239.491	−	174.000i	0.0436665	−	0.0317256i	0.609404	+	0.792860i	$0.291409\pi$
$312$	−776.696	−	564.303i	−0.140935	−	0.102395i
$313$	6022.90	+	4375.89i	1.08765	+	0.790224i	0.979001	−	0.203857i	$-0.0653476\pi$
$313$	6022.90	+	4375.89i	1.08765	+	0.790224i	0.108649	+	0.994080i	$0.465348\pi$
$314$	−4814.21	+	3497.73i	−0.865228	+	0.628625i
$315$	640.898	−	441.422i	0.114637	−	0.0789565i
$316$	−379.504	−	275.726i	−0.0675594	−	0.0490848i
$317$	−1928.98	−	5936.80i	−0.341775	−	1.05187i	−0.963288	−	0.268471i	$-0.913482\pi$
$317$	−1928.98	−	5936.80i	−0.341775	−	1.05187i	0.621513	−	0.783404i	$-0.286518\pi$
$318$	2476.57			0.436728
$319$	−459.348	−	1413.73i	−0.0806225	−	0.248130i
$320$	−203.911	−	685.872i	−0.0356218	−	0.119817i
$321$	−1400.20	+	4309.36i	−0.243462	+	0.749299i
$322$	413.032	−	1271.18i	0.0714824	−	0.220000i
$323$	−11570.8	+	8406.69i	−1.99324	+	1.44818i
$324$	324.000			0.0555556
$325$	1303.82	+	4827.28i	0.222532	+	0.823905i
$326$	−5476.39			−0.930396
$327$	4602.05	−	3343.59i	0.778269	−	0.565446i
$328$	−480.585	+	1479.09i	−0.0809020	+	0.248991i
$329$	−120.694	+	371.457i	−0.0202251	+	0.0622464i
$330$	563.966	−	388.434i	0.0940767	−	0.0647958i
$331$	−1093.01	−	3363.93i	−0.181502	−	0.558606i	0.818369	−	0.574694i	$-0.194879\pi$
$331$	−1093.01	−	3363.93i	−0.181502	−	0.558606i	−0.999871	+	0.0160879i	$0.994879\pi$
$332$	−1206.05			−0.199370
$333$	362.805	+	1116.60i	0.0597045	+	0.183751i
$334$	−1337.15	−	971.497i	−0.219059	−	0.159156i
$335$	6247.25	+	157.338i	1.01888	+	0.0256606i
$336$	−300.328	+	218.201i	−0.0487626	+	0.0354281i
$337$	−1208.52	−	878.042i	−0.195348	−	0.141929i	0.485812	−	0.874064i	$-0.338524\pi$
$337$	−1208.52	−	878.042i	−0.195348	−	0.141929i	−0.681160	+	0.732135i	$0.738524\pi$
$338$	965.701	+	701.623i	0.155406	+	0.112909i
$339$	−830.314	+	603.258i	−0.133028	+	0.0966504i
$340$	−1814.10	+	5139.18i	−0.289362	+	0.819738i
$341$	−1960.22	−	1424.18i	−0.311296	−	0.226170i
$342$	652.804	+	2009.13i	0.103215	+	0.317664i
$343$	−4842.85			−0.762360
$344$	−479.312	−	1475.17i	−0.0751243	−	0.231209i
$345$	−2897.43	−	72.9724i	−0.452151	−	0.0113875i
$346$	330.533	−	1017.27i	0.0513571	−	0.158061i
$347$	1713.06	−	5272.24i	0.265019	−	0.815645i	−0.726670	−	0.686987i	$-0.758933\pi$
$347$	1713.06	−	5272.24i	0.265019	−	0.815645i	0.991689	−	0.128658i	$-0.0410671\pi$
$348$	1413.67	−	1027.09i	0.217760	−	0.158212i
$349$	−7125.07			−1.09283			−0.546413	−	0.837516i	$-0.684007\pi$
$349$	−7125.07			−1.09283			−0.546413	+	0.837516i	$0.684007\pi$
$350$	1931.02	+	97.3279i	0.294906	+	0.0148640i
$351$	1080.06			0.164242
$352$	−264.277	+	192.009i	−0.0400171	+	0.0290741i
$353$	640.562	−	1971.45i	0.0965826	−	0.297251i	−0.891080	−	0.453846i	$-0.850052\pi$
$353$	640.562	−	1971.45i	0.0965826	−	0.297251i	0.987663	+	0.156595i	$0.0500517\pi$
$354$	−946.809	+	2913.98i	−0.142154	+	0.437504i
$355$	−478.337	−	366.282i	−0.0715141	−	0.0547612i
$356$	1466.51	+	4513.45i	0.218328	+	0.671945i
$357$	2827.46			0.419174
$358$	−1861.52	−	5729.17i	−0.274817	−	0.845799i
$359$	8541.69	+	6205.90i	1.25575	+	0.912353i	0.998541	−	0.0540034i	$-0.0171982\pi$
$359$	8541.69	+	6205.90i	1.25575	+	0.912353i	0.257206	+	0.966357i	$0.417198\pi$
$360$	639.127	+	489.405i	0.0935693	+	0.0716497i
$361$	−5594.26	+	4064.47i	−0.815608	+	0.592574i
$362$	−715.774	−	520.040i	−0.103923	−	0.0755047i
$363$	2977.48	+	2163.27i	0.430516	+	0.312788i
$364$	−1001.14	+	727.374i	−0.144160	+	0.104738i
$365$	1413.30	+	4753.75i	0.202672	+	0.681706i
$366$	3836.87	+	2787.65i	0.547969	+	0.398122i
$367$	1031.53	+	3174.71i	0.146717	+	0.451549i	0.997228	−	0.0744088i	$-0.0237070\pi$
$367$	1031.53	+	3174.71i	0.146717	+	0.451549i	−0.850511	+	0.525958i	$0.823707\pi$
$368$	1382.59			0.195849
$369$	−540.658	−	1663.97i	−0.0762752	−	0.234751i
$370$	−970.957	+	2750.64i	−0.136426	+	0.386483i
$371$	986.459	−	3036.01i	0.138044	−	0.424856i
$372$	880.155	−	2708.84i	0.122672	−	0.377545i
$373$	2521.78	−	1832.18i	0.350062	−	0.254335i	−0.398833	−	0.917024i	$-0.630585\pi$
$373$	2521.78	−	1832.18i	0.350062	−	0.254335i	0.748895	+	0.662689i	$0.230585\pi$
$374$	2488.06			0.343996
$375$	−990.976	−	4073.83i	−0.136463	−	0.560991i
$376$	−404.013			−0.0554132
$377$	4712.46	−	3423.80i	0.643777	−	0.467731i
$378$	129.054	−	397.189i	0.0175604	−	0.0540455i
$379$	2085.17	−	6417.51i	0.282607	−	0.869776i	−0.704498	−	0.709706i	$-0.748828\pi$
$379$	2085.17	−	6417.51i	0.282607	−	0.869776i	0.987106	−	0.160070i	$-0.0511721\pi$
$380$	−1747.07	+	4949.29i	−0.235849	+	0.668141i
$381$	1107.67	+	3409.05i	0.148944	+	0.458401i
$382$	8262.37			1.10665
$383$	1763.72	+	5428.17i	0.235305	+	0.724194i	0.997081	+	0.0763534i	$0.0243277\pi$
$383$	1763.72	+	5428.17i	0.235305	+	0.724194i	−0.761776	+	0.647841i	$0.775672\pi$
$384$	−310.663	−	225.710i	−0.0412850	−	0.0299953i
$385$	−251.541	−	846.081i	−0.0332980	−	0.112001i
$386$	−3786.80	+	2751.27i	−0.499334	+	0.362788i
$387$	1411.71	+	1025.67i	0.185430	+	0.134723i
$388$	−688.568	−	500.274i	−0.0900947	−	0.0654576i
$389$	3495.69	−	2539.77i	0.455626	−	0.331032i	−0.336187	−	0.941795i	$-0.609137\pi$
$389$	3495.69	−	2539.77i	0.455626	−	0.331032i	0.791813	+	0.610763i	$0.209137\pi$
$390$	2130.53	+	1631.43i	0.276625	+	0.211823i
$391$	−8519.42	−	6189.72i	−1.10191	−	0.800582i
$392$	−700.077	−	2154.62i	−0.0902022	−	0.277614i
$393$	−8316.58			−1.06747
$394$	−648.339	−	1995.38i	−0.0829006	−	0.255142i
$395$	1041.01	+	797.140i	0.132604	+	0.101540i
$396$	113.563	−	349.511i	0.0144110	−	0.0443525i
$397$	2544.79	−	7832.06i	0.321711	−	0.990126i	−0.651192	−	0.758913i	$-0.725731\pi$
$397$	2544.79	−	7832.06i	0.321711	−	0.990126i	0.972903	−	0.231213i	$-0.0742693\pi$
$398$	−2985.04	+	2168.76i	−0.375946	+	0.273141i
$399$	2722.99			0.341654
$400$	521.501	+	1930.81i	0.0651876	+	0.241352i
$401$	−3509.00			−0.436986			−0.218493	−	0.975839i	$-0.570114\pi$
$401$	−3509.00			−0.436986			−0.218493	+	0.975839i	$0.570114\pi$
$402$	2713.19	−	1971.25i	0.336621	−	0.244570i
$403$	2934.00	−	9029.92i	0.362662	−	1.11616i
$404$	867.438	−	2669.70i	0.106823	−	0.328769i
$405$	−905.320	−	22.8007i	−0.111076	−	0.00279747i
$406$	−696.012	−	2142.11i	−0.0850801	−	0.261849i
$407$	1331.68			0.162184
$408$	903.799	+	2781.61i	0.109668	+	0.337525i
$409$	−12275.9	−	8918.95i	−1.48412	−	1.07827i	−0.976201	−	0.216866i	$-0.930417\pi$
$409$	−12275.9	−	8918.95i	−1.48412	−	1.07827i	−0.507914	−	0.861407i	$-0.669583\pi$
$410$	1446.94	−	4099.05i	0.174291	−	0.493750i
$411$	−4380.14	+	3182.35i	−0.525684	+	0.381932i
$412$	−2319.53	−	1685.24i	−0.277367	−	0.201519i
$413$	3195.09	+	2321.37i	0.380679	+	0.276579i
$414$	−1258.36	+	914.251i	−0.149384	+	0.108534i
$415$	3369.95	+	84.8729i	0.398613	+	0.0100392i
$416$	−1035.59	−	752.404i	−0.122053	−	0.0886770i
$417$	1433.27	+	4411.14i	0.168315	+	0.518020i
$418$	2396.13			0.280379
$419$	2205.93	+	6789.17i	0.257200	+	0.791581i	0.993388	+	0.114804i	$0.0366240\pi$
$419$	2205.93	+	6789.17i	0.257200	+	0.791581i	−0.736188	+	0.676777i	$0.763376\pi$
$420$	854.531	−	588.562i	0.0992782	−	0.0683783i
$421$	−1743.21	+	5365.06i	−0.201803	+	0.621086i	0.798026	+	0.602622i	$0.205877\pi$
$421$	−1743.21	+	5365.06i	−0.201803	+	0.621086i	−0.999830	+	0.0184635i	$0.994123\pi$
$422$	−554.480	+	1706.51i	−0.0639612	+	0.196852i
$423$	367.710	−	267.157i	0.0422663	−	0.0307083i
$424$	3302.10			0.378217
$425$	5430.60	−	14232.2i	0.619818	−	1.62439i
$426$	−323.319			−0.0367719
$427$	4945.64	−	3593.22i	0.560507	−	0.407232i
$428$	−1866.93	+	5745.81i	−0.210844	+	0.648912i
$429$	378.563	−	1165.10i	0.0426042	−	0.131122i
$430$	1235.48	+	4155.65i	0.138559	+	0.466054i
$431$	−3270.85	−	10066.6i	−0.365548	−	1.12504i	−0.949637	−	0.313351i	$-0.898548\pi$
$431$	−3270.85	−	10066.6i	−0.365548	−	1.12504i	0.584089	−	0.811689i	$-0.301452\pi$
$432$	432.000			0.0481125
$433$	−2467.74	−	7594.92i	−0.273885	−	0.842930i	−0.989512	−	0.144448i	$-0.953859\pi$
$433$	−2467.74	−	7594.92i	−0.273885	−	0.842930i	0.715628	−	0.698482i	$-0.246141\pi$
$434$	−2970.16	−	2157.95i	−0.328507	−	0.238675i
$435$	−4022.34	+	2770.40i	−0.443348	+	0.305358i
$436$	6136.07	−	4458.11i	0.674001	−	0.489690i
$437$	−8204.65	−	5961.02i	−0.898127	−	0.652527i
$438$	2153.19	+	1564.38i	0.234894	+	0.170660i
$439$	−8383.66	+	6091.09i	−0.911459	+	0.662214i	−0.941383	−	0.337338i	$-0.890473\pi$
$439$	−8383.66	+	6091.09i	−0.911459	+	0.662214i	0.0299245	+	0.999552i	$0.490473\pi$
$440$	751.955	−	517.912i	0.0814728	−	0.0561148i
$441$	2061.93	+	1498.08i	0.222647	+	0.161762i
$442$	3012.82	+	9272.50i	0.324220	+	0.997846i
$443$	−7569.69			−0.811844			−0.405922	−	0.913908i	$-0.633050\pi$
$443$	−7569.69			−0.811844			−0.405922	+	0.913908i	$0.633050\pi$
$444$	483.740	+	1488.80i	0.0517056	+	0.159133i
$445$	−3780.10	−	12714.7i	−0.402683	−	1.35446i
$446$	1034.71	−	3184.52i	0.109854	−	0.338097i
$447$	2118.08	−	6518.77i	0.224120	−	0.689770i
$448$	−400.437	+	290.935i	−0.0422296	+	0.0306816i
$449$	14728.9			1.54811			0.774056	−	0.633118i	$-0.218225\pi$
$449$	14728.9			1.54811			0.774056	+	0.633118i	$0.218225\pi$
$450$	−1751.41	−	1412.47i	−0.183471	−	0.147966i
$451$	−1984.49			−0.207198
$452$	−1107.09	+	804.344i	−0.115206	+	0.0837017i
$453$	2596.29	−	7990.55i	0.269281	−	0.828761i
$454$	2390.36	−	7356.77i	0.247104	−	0.760508i
$455$	2848.58	−	1961.97i	0.293503	−	0.202151i
$456$	870.406	+	2678.83i	0.0893870	+	0.275105i
$457$	−4253.69			−0.435403			−0.217701	−	0.976015i	$-0.569856\pi$
$457$	−4253.69			−0.435403			−0.217701	+	0.976015i	$0.569856\pi$
$458$	1952.65	+	6009.63i	0.199216	+	0.613125i
$459$	−2661.95	−	1934.02i	−0.270695	−	0.196672i
$460$	−3863.24	−	97.2965i	−0.391575	−	0.00986189i
$461$	7676.86	−	5577.57i	0.775590	−	0.563499i	−0.128062	−	0.991766i	$-0.540876\pi$
$461$	7676.86	−	5577.57i	0.775590	−	0.563499i	0.903652	+	0.428267i	$0.140876\pi$
$462$	−383.228	−	278.432i	−0.0385918	−	0.0280386i
$463$	6287.68	+	4568.26i	0.631130	+	0.458543i	0.856791	−	0.515663i	$-0.172454\pi$
$463$	6287.68	+	4568.26i	0.631130	+	0.458543i	−0.225662	+	0.974206i	$0.572454\pi$
$464$	1884.89	−	1369.45i	0.188586	−	0.137015i
$465$	−2649.96	+	7507.09i	−0.264277	+	0.748673i
$466$	−9596.11	−	6971.99i	−0.953930	−	0.693071i
$467$	3599.56	+	11078.3i	0.356676	+	1.09774i	0.955031	+	0.296505i	$0.0958212\pi$
$467$	3599.56	+	11078.3i	0.356676	+	1.09774i	−0.598355	+	0.801231i	$0.704179\pi$
$468$	1440.07			0.142238
$469$	−1335.83	−	4111.26i	−0.131520	−	0.404777i
$470$	1128.89	+	28.4314i	0.110791	+	0.00279030i
$471$	2758.30	−	8489.17i	0.269842	−	0.830489i
$472$	−1262.41	+	3885.31i	−0.123109	+	0.378889i
$473$	1601.24	−	1163.37i	0.155655	−	0.113090i
$474$	703.639			0.0681840
$475$	5229.95	−	13706.4i	0.505193	−	1.32398i
$476$	3769.95			0.363015
$477$	−3005.39	+	2183.54i	−0.288485	+	0.209596i
$478$	1592.19	−	4900.26i	0.152354	−	0.468897i
$479$	4163.91	−	12815.2i	0.397189	−	1.22242i	−0.530054	−	0.847964i	$-0.677828\pi$
$479$	4163.91	−	12815.2i	0.397189	−	1.22242i	0.927243	−	0.374459i	$-0.122172\pi$
$480$	852.169	+	652.539i	0.0810334	+	0.0620504i
$481$	1612.55	+	4962.92i	0.152861	+	0.470456i
$482$	−7800.70			−0.737162
$483$	619.547	+	1906.77i	0.0583652	+	0.179630i
$484$	3969.98	+	2884.36i	0.372838	+	0.270883i
$485$	1888.79	+	1446.32i	0.176836	+	0.135410i
$486$	−393.182	+	285.664i	−0.0366978	+	0.0266625i
$487$	5757.98	+	4183.42i	0.535768	+	0.389258i	0.822511	−	0.568749i	$-0.192573\pi$
$487$	5757.98	+	4183.42i	0.535768	+	0.389258i	−0.286743	+	0.958008i	$0.592573\pi$
$488$	5115.83	+	3716.87i	0.474555	+	0.344784i
$489$	6645.73	−	4828.41i	0.614582	−	0.446520i
$490$	1804.53	+	6069.69i	0.166368	+	0.559594i
$491$	16642.5	+	12091.5i	1.52966	+	1.11137i	0.956425	+	0.291977i	$0.0943132\pi$
$491$	16642.5	+	12091.5i	1.52966	+	1.11137i	0.573239	+	0.819388i	$0.305687\pi$
$492$	−720.877	−	2218.63i	−0.0660562	−	0.203300i
$493$	−17745.4			−1.62112
$494$	2901.50	+	8929.90i	0.264261	+	0.813310i
$495$	−341.914	+	968.612i	−0.0310462	+	0.0879512i
$496$	1173.54	−	3611.78i	0.106237	−	0.326963i
$497$	−128.783	+	396.353i	−0.0116232	+	0.0357724i
$498$	1463.58	−	1063.35i	0.131696	−	0.0956824i
$499$	11276.5			1.01163			0.505815	−	0.862642i	$-0.331192\pi$
$499$	11276.5			1.01163			0.505815	+	0.862642i	$0.331192\pi$
$500$	−1321.30	−	5431.77i	−0.118181	−	0.485833i
$501$	2479.22			0.221084
$502$	905.127	−	657.614i	0.0804737	−	0.0584676i
$503$	−1239.12	+	3813.62i	−0.109840	+	0.338053i	−0.990836	−	0.135071i	$-0.956874\pi$
$503$	−1239.12	+	3813.62i	−0.109840	+	0.338053i	0.880996	+	0.473124i	$0.156874\pi$
$504$	172.073	−	529.585i	0.0152078	−	0.0468047i
$505$	−2611.67	+	7398.63i	−0.230134	+	0.651950i
$506$	545.178	+	1677.89i	0.0478975	+	0.147413i
$507$	−1790.51			−0.156843
$508$	1476.89	+	4545.40i	0.128989	+	0.396987i
$509$	−8454.42	−	6142.49i	−0.736219	−	0.534894i	0.155306	−	0.987866i	$-0.450364\pi$
$509$	−8454.42	−	6142.49i	−0.736219	−	0.534894i	−0.891525	+	0.452972i	$0.850364\pi$
$510$	−2329.65	−	7835.97i	−0.202271	−	0.680358i
$511$	2775.42	−	2016.46i	0.240268	−	0.174565i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	−2563.60	−	1862.56i	−0.220635	−	0.160300i
$514$	−7557.91	+	5491.14i	−0.648570	+	0.471214i
$515$	6362.64	+	4872.12i	0.544410	+	0.416876i
$516$	1882.28	+	1367.56i	0.160587	+	0.116673i
$517$	−159.309	−	490.301i	−0.0135520	−	0.0417088i
$518$	2017.79			0.171151
$519$	495.799	+	1525.91i	0.0419329	+	0.129056i
$520$	2840.71	+	2175.24i	0.239564	+	0.183444i
$521$	−4177.39	+	12856.7i	−0.351276	+	1.08112i	0.606861	+	0.794808i	$0.292428\pi$
$521$	−4177.39	+	12856.7i	−0.351276	+	1.08112i	−0.958137	+	0.286309i	$0.907572\pi$
$522$	−809.958	+	2492.79i	−0.0679136	+	0.209017i
$523$	11142.8	−	8095.73i	0.931628	−	0.676867i	−0.0147630	−	0.999891i	$-0.504699\pi$
$523$	11142.8	−	8095.73i	0.931628	−	0.676867i	0.946391	+	0.323024i	$0.104699\pi$
$524$	−11088.8			−0.924457
$525$	−2429.15	+	1584.42i	−0.201937	+	0.131714i
$526$	−10471.1			−0.867986
$527$	−23400.8	+	17001.7i	−1.93426	+	1.40532i
$528$	151.417	−	466.015i	0.0124803	−	0.0384104i
$529$	−1452.37	+	4469.93i	−0.119370	+	0.367382i
$530$	−9226.72	−	232.377i	−0.756194	−	0.0190449i
$531$	−1420.21	−	4370.97i	−0.116068	−	0.357220i
$532$	3630.65			0.295881
$533$	−2403.05	−	7395.82i	−0.195286	−	0.601029i
$534$	−5759.06	−	4184.20i	−0.466702	−	0.339079i
$535$	5620.91	−	15923.6i	0.454231	−	1.28680i
$536$	3617.59	−	2628.33i	0.291522	−	0.211803i
$537$	7310.28	+	5311.23i	0.587452	+	0.426809i
$538$	705.949	+	512.902i	0.0565718	+	0.0411018i
$539$	2338.75	−	1699.20i	0.186896	−	0.135788i
$540$	−1207.09	−	30.4009i	−0.0961945	−	0.00242268i
$541$	5143.65	+	3737.08i	0.408766	+	0.296986i	0.773102	−	0.634282i	$-0.218704\pi$
$541$	5143.65	+	3737.08i	0.408766	+	0.296986i	−0.364336	+	0.931268i	$0.618704\pi$
$542$	−3825.57	−	11773.9i	−0.303178	−	0.933086i
$543$	1327.12			0.104884
$544$	1205.07	+	3708.81i	0.0949757	+	0.292305i
$545$	−17459.1	+	12025.0i	−1.37223	+	0.945131i
$546$	573.605	−	1765.37i	0.0449597	−	0.138372i
$547$	−5345.14	+	16450.6i	−0.417809	+	1.28588i	0.491905	+	0.870649i	$0.336301\pi$
$547$	−5345.14	+	16450.6i	−0.417809	+	1.28588i	−0.909714	+	0.415235i	$0.863699\pi$
$548$	−5840.18	+	4243.14i	−0.455256	+	0.330763i
$549$	−7113.95			−0.553035
$550$	−2137.56	+	1394.23i	−0.165720	+	0.108091i
$551$	−17089.8			−1.32132
$552$	−1677.81	+	1219.00i	−0.129370	+	0.0939930i
$553$	280.271	−	862.585i	0.0215521	−	0.0663307i
$554$	−4752.03	+	14625.3i	−0.364431	+	1.12160i
$555$	−1246.90	−	4194.04i	−0.0953653	−	0.320770i
$556$	1911.02	+	5881.52i	0.145765	+	0.448619i
$557$	4163.35			0.316709			0.158355	−	0.987382i	$-0.449381\pi$
$557$	4163.35			0.316709			0.158355	+	0.987382i	$0.449381\pi$
$558$	1320.23	+	4063.26i	0.100161	+	0.308264i
$559$	6274.60	+	4558.76i	0.474753	+	0.344929i
$560$	1139.38	−	784.750i	0.0859775	−	0.0592174i
$561$	−3019.32	+	2193.66i	−0.227230	+	0.165092i
$562$	11658.6	+	8470.49i	0.875070	+	0.635776i
$563$	16316.5	+	11854.6i	1.22142	+	0.887413i	0.996217	−	0.0868992i	$-0.0276958\pi$
$563$	16316.5	+	11854.6i	1.22142	+	0.887413i	0.225202	+	0.974312i	$0.427696\pi$
$564$	490.280	−	356.209i	0.0366037	−	0.0265942i
$565$	3150.02	−	2169.59i	0.234553	−	0.161549i
$566$	1404.43	+	1020.38i	0.104298	+	0.0757769i
$567$	193.582	+	595.783i	0.0143380	+	0.0441279i
$568$	−431.092			−0.0318454
$569$	3467.86	+	10673.0i	0.255501	+	0.786351i	0.993731	+	0.111802i	$0.0356621\pi$
$569$	3467.86	+	10673.0i	0.255501	+	0.786351i	−0.738230	+	0.674550i	$0.764338\pi$
$570$	−2243.57	−	7546.45i	−0.164865	−	0.554537i
$571$	−1121.61	+	3451.95i	−0.0822027	+	0.252994i	−0.983708	−	0.179774i	$-0.942463\pi$
$571$	−1121.61	+	3451.95i	−0.0822027	+	0.252994i	0.901505	+	0.432768i	$0.142463\pi$
$572$	504.750	−	1553.46i	0.0368963	−	0.113555i
$573$	−10026.6	+	7284.75i	−0.731007	+	0.531108i
$574$	−3006.94			−0.218654
$575$	10787.8	+	543.731i	0.782404	+	0.0394351i
$576$	576.000			0.0416667
$577$	−17209.2	+	12503.2i	−1.24164	+	0.902106i	−0.997707	−	0.0676850i	$-0.978439\pi$
$577$	−17209.2	+	12503.2i	−1.24164	+	0.902106i	−0.243936	+	0.969791i	$0.578439\pi$
$578$	6142.04	−	18903.3i	0.441999	−	1.36033i
$579$	2169.64	−	6677.48i	0.155729	−	0.479286i
$580$	−5363.12	+	3693.87i	−0.383951	+	0.264448i
$581$	−720.585	−	2217.73i	−0.0514542	−	0.158360i
$582$	1276.68			0.0909276
$583$	1302.07	+	4007.36i	0.0924978	+	0.284679i
$584$	2870.92	+	2085.85i	0.203424	+	0.147796i
$585$	−4023.85	−	101.342i	−0.284386	−	0.00716232i
$586$	7298.21	−	5302.46i	0.514481	−	0.373793i
$587$	−12273.0	−	8916.85i	−0.862965	−	0.626981i	0.0657249	−	0.997838i	$-0.479064\pi$
$587$	−12273.0	−	8916.85i	−0.862965	−	0.626981i	−0.928690	+	0.370857i	$0.879064\pi$
$588$	2749.24	+	1997.44i	0.192818	+	0.140090i
$589$	−22536.2	+	16373.5i	−1.57655	+	1.14543i
$590$	3800.85	−	10767.5i	0.265218	−	0.751339i
$591$	2546.06	+	1849.82i	0.177210	+	0.128750i
$592$	644.987	+	1985.06i	0.0447784	+	0.137814i
$593$	−18119.0			−1.25473			−0.627367	−	0.778723i	$-0.715868\pi$
$593$	−18119.0			−1.25473			−0.627367	+	0.778723i	$0.715868\pi$
$594$	170.345	+	524.266i	0.0117665	+	0.0362137i
$595$	−10534.0	−	265.301i	−0.725800	−	0.0182794i
$596$	2824.10	−	8691.69i	0.194093	−	0.597358i
$597$	1710.27	−	5263.68i	0.117248	−	0.360851i
$598$	−5592.99	+	4063.54i	−0.382465	+	0.277877i
$599$	22328.8			1.52309			0.761546	−	0.648111i	$-0.224441\pi$
$599$	22328.8			1.52309			0.761546	+	0.648111i	$0.224441\pi$
$600$	−2335.21	−	1883.29i	−0.158891	−	0.128142i
$601$	19237.3			1.30567			0.652833	−	0.757502i	$-0.273580\pi$
$601$	19237.3			1.30567			0.652833	+	0.757502i	$0.273580\pi$
$602$	2426.22	−	1762.75i	0.164261	−	0.119343i
$603$	−1554.52	+	4784.32i	−0.104983	+	0.323106i
$604$	3461.72	−	10654.1i	0.233204	−	0.717728i
$605$	−10889.9	−	8338.85i	−0.731800	−	0.560368i
$606$	1301.16	+	4004.55i	0.0872210	+	0.268439i
$607$	−27794.5			−1.85856			−0.929280	−	0.369377i	$-0.879571\pi$
$607$	−27794.5			−1.85856			−0.929280	+	0.369377i	$0.879571\pi$
$608$	1160.54	+	3571.78i	0.0774114	+	0.238248i
$609$	2733.28	+	1985.84i	0.181868	+	0.132135i
$610$	−14033.1	−	10745.7i	−0.931447	−	0.713246i
$611$	1634.35	−	1187.42i	0.108214	−	0.0786220i
$612$	−3549.27	−	2578.69i	−0.234429	−	0.170323i
$613$	21367.3	+	15524.3i	1.40786	+	1.02287i	0.993629	+	0.112697i	$0.0359490\pi$
$613$	21367.3	+	15524.3i	1.40786	+	1.02287i	0.414230	+	0.910172i	$0.364051\pi$
$614$	4625.70	−	3360.77i	0.304036	−	0.220895i
$615$	1858.14	+	6250.03i	0.121833	+	0.409798i
$616$	−510.971	−	371.242i	−0.0334215	−	0.0242821i
$617$	−435.914	−	1341.61i	−0.0284428	−	0.0875381i	0.935827	−	0.352459i	$-0.114654\pi$
$617$	−435.914	−	1341.61i	−0.0284428	−	0.0875381i	−0.964270	+	0.264921i	$0.914654\pi$
$618$	4300.65			0.279931
$619$	5249.80	+	16157.2i	0.340884	+	1.04913i	0.963750	+	0.266806i	$0.0859682\pi$
$619$	5249.80	+	16157.2i	0.340884	+	1.04913i	−0.622866	+	0.782329i	$0.714032\pi$
$620$	−3533.27	+	10009.5i	−0.228870	+	0.648370i
$621$	720.975	−	2218.93i	0.0465889	−	0.143386i
$622$	−182.955	+	563.077i	−0.0117939	+	0.0362979i
$623$	−7423.30	+	5393.34i	−0.477381	+	0.346837i
$624$	1920.10			0.123182
$625$	3309.73	+	15270.4i	0.211823	+	0.977308i
$626$	−14889.4			−0.950641
$627$	−2907.76	+	2112.61i	−0.185207	+	0.134561i
$628$	3677.73	−	11318.9i	0.233690	−	0.719224i
$629$	4912.57	−	15119.3i	0.311410	−	0.958423i
$630$	−518.073	+	1467.66i	−0.0327627	+	0.0928140i
$631$	5889.28	+	18125.3i	0.371551	+	1.14352i	0.945776	+	0.324818i	$0.105303\pi$
$631$	5889.28	+	18125.3i	0.371551	+	1.14352i	−0.574226	+	0.818697i	$0.694697\pi$
$632$	938.186			0.0590491
$633$	−831.719	−	2559.77i	−0.0522241	−	0.160729i
$634$	10100.3	+	7338.29i	0.632703	+	0.459686i
$635$	−3806.85	−	12804.7i	−0.237906	−	0.800218i
$636$	−4007.18	+	2911.39i	−0.249835	+	0.181516i
$637$	9164.60	+	6658.47i	0.570039	+	0.414157i
$638$	2405.18	+	1747.46i	0.149251	+	0.108437i
$639$	392.355	−	285.063i	0.0242901	−	0.0176478i
$640$	1136.23	+	870.053i	0.0701770	+	0.0537373i
$641$	6378.64	+	4634.36i	0.393044	+	0.285563i	0.766702	−	0.642003i	$-0.221897\pi$
$641$	6378.64	+	4634.36i	0.393044	+	0.285563i	−0.373658	+	0.927567i	$0.621897\pi$
$642$	−2800.39	−	8618.72i	−0.172154	−	0.529834i
$643$	18479.5			1.13338			0.566689	−	0.823932i	$-0.308224\pi$
$643$	18479.5			1.13338			0.566689	+	0.823932i	$0.308224\pi$
$644$	826.063	+	2542.36i	0.0505457	+	0.155564i
$645$	−5163.23	−	3953.69i	−0.315197	−	0.241359i
$646$	8839.32	−	27204.6i	0.538357	−	1.65689i
$647$	−8302.19	+	25551.5i	−0.504471	+	1.55260i	0.297188	+	0.954819i	$0.403951\pi$
$647$	−8302.19	+	25551.5i	−0.504471	+	1.55260i	−0.801659	+	0.597782i	$0.796049\pi$
$648$	−524.243	+	380.885i	−0.0317812	+	0.0230904i
$649$	−5212.92			−0.315293
$650$	−7784.43	−	6277.97i	−0.469739	−	0.378834i
$651$	5506.98			0.331545
$652$	8860.98	−	6437.88i	0.532243	−	0.386698i
$653$	8641.40	−	26595.5i	0.517862	−	1.59382i	−0.260151	−	0.965568i	$-0.583772\pi$
$653$	8641.40	−	26595.5i	0.517862	−	1.59382i	0.778013	−	0.628248i	$-0.216228\pi$
$654$	−3515.65	+	10820.1i	−0.210203	+	0.646939i
$655$	30984.3	+	780.345i	1.84833	+	0.0465506i
$656$	−961.170	−	2958.18i	−0.0572064	−	0.176063i
$657$	−3992.23			−0.237065
$658$	−241.387	−	742.913i	−0.0143013	−	0.0440148i
$659$	−16701.3	−	12134.2i	−0.987238	−	0.717270i	−0.0279234	−	0.999610i	$-0.508889\pi$
$659$	−16701.3	−	12134.2i	−0.987238	−	0.717270i	−0.959314	+	0.282340i	$0.908889\pi$
$660$	−455.885	+	1291.48i	−0.0268868	+	0.0761680i
$661$	−10767.3	+	7822.91i	−0.633586	+	0.460327i	−0.857641	−	0.514250i	$-0.828070\pi$
$661$	−10767.3	+	7822.91i	−0.633586	+	0.460327i	0.224055	+	0.974577i	$0.428070\pi$
$662$	5723.07	+	4158.05i	0.336002	+	0.244120i
$663$	−11831.5	−	8596.08i	−0.693057	−	0.503536i
$664$	1951.43	−	1417.80i	0.114052	−	0.0828634i
$665$	−10144.8	−	255.498i	−0.591575	−	0.0148989i
$666$	−1899.67	−	1380.19i	−0.110527	−	0.0803023i
$667$	−3888.34	−	11967.1i	−0.225723	−	0.694703i
$668$	3305.62			0.191465
$669$	1552.07	+	4776.78i	0.0896957	+	0.276055i
$670$	−10293.2	+	7089.50i	−0.593525	+	0.408793i
$671$	−2493.46	+	7674.09i	−0.143456	+	0.441512i
$672$	229.430	−	706.113i	0.0131703	−	0.0405341i
$673$	17136.4	−	12450.4i	0.981518	−	0.713114i	0.0234703	−	0.999725i	$-0.492528\pi$
$673$	17136.4	−	12450.4i	0.981518	−	0.713114i	0.958047	+	0.286610i	$0.0925285\pi$
$674$	2987.63			0.170741
$675$	3370.72	+	169.892i	0.192206	+	0.00968765i
$676$	−2387.34			−0.135830
$677$	13868.7	−	10076.2i	0.787323	−	0.572023i	−0.119845	−	0.992793i	$-0.538240\pi$
$677$	13868.7	−	10076.2i	0.787323	−	0.572023i	0.907168	+	0.420769i	$0.138240\pi$
$678$	634.303	−	1952.19i	0.0359296	−	0.110580i
$679$	508.520	−	1565.06i	0.0287411	−	0.0884561i
$680$	−3106.19	−	10448.0i	−0.175172	−	0.589207i
$681$	3585.54	+	11035.2i	0.201759	+	0.620952i
$682$	4845.93			0.272083
$683$	−8055.15	−	24791.2i	−0.451276	−	1.38889i	−0.875452	−	0.483306i	$-0.839436\pi$
$683$	−8055.15	−	24791.2i	−0.451276	−	1.38889i	0.424175	−	0.905580i	$-0.360564\pi$
$684$	−3418.13	−	2483.42i	−0.191075	−	0.138824i
$685$	16617.2	−	11445.2i	0.926878	−	0.638391i
$686$	7835.90	−	5693.11i	0.436116	−	0.316857i
$687$	−7668.14	−	5571.23i	−0.425848	−	0.309397i
$688$	2509.71	+	1823.41i	0.139072	+	0.101042i
$689$	−13358.0	+	9705.12i	−0.738603	+	0.536626i
$690$	4773.92	−	3288.06i	0.263391	−	0.181412i
$691$	13937.5	+	10126.2i	0.767304	+	0.557479i	0.901142	−	0.433524i	$-0.142730\pi$
$691$	13937.5	+	10126.2i	0.767304	+	0.557479i	−0.133838	+	0.991003i	$0.542730\pi$
$692$	661.065	+	2034.55i	0.0363149	+	0.111766i
$693$	710.545			0.0389486
$694$	3426.11	+	10544.5i	0.187397	+	0.576748i
$695$	−4925.88	−	16568.6i	−0.268848	−	0.904293i
$696$	−1079.94	+	3323.73i	−0.0588149	+	0.181014i
$697$	−7320.80	+	22531.1i	−0.397841	+	1.22443i
$698$	11528.6	−	8376.02i	0.625163	−	0.454208i
$699$	17792.2			0.962749
$700$	−3238.87	+	2112.57i	−0.174882	+	0.114068i
$701$	22740.5			1.22524			0.612622	−	0.790376i	$-0.290115\pi$
$701$	22740.5			1.22524			0.612622	+	0.790376i	$0.290115\pi$
$702$	−1747.57	+	1269.68i	−0.0939567	+	0.0682636i
$703$	4731.06	−	14560.7i	0.253820	−	0.781178i
$704$	201.890	−	621.353i	0.0108082	−	0.0332644i
$705$	−1395.01	+	960.816i	−0.0745233	+	0.0513283i
$706$	1281.12	+	3942.89i	0.0682942	+	0.210188i
$707$	5427.42			0.288711
$708$	−1893.62	−	5827.96i	−0.100518	−	0.309362i
$709$	6139.76	+	4460.80i	0.325224	+	0.236289i	0.738401	−	0.674362i	$-0.235581\pi$
$709$	6139.76	+	4460.80i	0.325224	+	0.236289i	−0.413177	+	0.910651i	$0.635581\pi$
$710$	1204.56	+	30.3370i	0.0636707	+	0.00160356i
$711$	−853.884	+	620.383i	−0.0450396	+	0.0327232i
$712$	−7678.74	−	5578.93i	−0.404176	−	0.293651i
$713$	−16593.1	−	12055.6i	−0.871551	−	0.633219i
$714$	−4574.93	+	3323.88i	−0.239793	+	0.174220i
$715$	−1519.69	+	4305.16i	−0.0794872	+	0.225180i
$716$	9747.04	+	7081.64i	0.508749	+	0.369628i
$717$	2388.29	+	7350.39i	0.124396	+	0.382853i
$718$	−21116.2			−1.09756
$719$	6120.18	+	18836.0i	0.317447	+	0.977000i	0.974736	+	0.223362i	$0.0717031\pi$
$719$	6120.18	+	18836.0i	0.317447	+	0.977000i	−0.657289	+	0.753639i	$0.728297\pi$
$720$	−1609.46	−	40.5346i	−0.0833069	−	0.00209810i
$721$	1713.02	−	5272.13i	0.0884828	−	0.272322i
$722$	4273.63	−	13152.9i	0.220288	−	0.677978i
$723$	9466.35	−	6877.71i	0.486940	−	0.353782i
$724$	1769.49			0.0908323
$725$	15245.6	−	9944.00i	0.780974	−	0.509394i
$726$	−7360.75			−0.376285
$727$	23631.1	−	17169.0i	1.20554	−	0.875877i	0.210723	−	0.977546i	$-0.432418\pi$
$727$	23631.1	−	17169.0i	1.20554	−	0.875877i	0.994818	+	0.101669i	$0.0324183\pi$
$728$	764.806	−	2353.83i	0.0389363	−	0.119834i
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$	−7875.14	−	6030.30i	−0.399277	−	0.305742i
$731$	−7301.41	−	22471.4i	−0.369429	−	1.13698i
$732$	−9485.27			−0.478942
$733$	−9455.20	−	29100.1i	−0.476447	−	1.46635i	−0.843996	−	0.536349i	$-0.819803\pi$
$733$	−9455.20	−	29100.1i	−0.476447	−	1.46635i	0.367549	−	0.930004i	$-0.380197\pi$
$734$	−5401.14	−	3924.16i	−0.271607	−	0.197334i
$735$	−7541.36	−	5774.71i	−0.378459	−	0.289801i
$736$	−2237.08	+	1625.33i	−0.112038	+	0.0814003i
$737$	4616.16	+	3353.84i	0.230717	+	0.167626i
$738$	2830.92	+	2056.79i	0.141203	+	0.102590i
$739$	24027.4	−	17456.9i	1.19602	−	0.868962i	0.202136	−	0.979357i	$-0.435212\pi$
$739$	24027.4	−	17456.9i	1.19602	−	0.868962i	0.993888	+	0.110395i	$0.0352117\pi$
$740$	−1662.53	−	5592.05i	−0.0825888	−	0.277795i
$741$	−11394.3	−	8278.48i	−0.564888	−	0.410415i
$742$	1972.92	+	6072.02i	0.0976120	+	0.300419i
$743$	−11076.7			−0.546922			−0.273461	−	0.961883i	$-0.588168\pi$
$743$	−11076.7			−0.546922			−0.273461	+	0.961883i	$0.588168\pi$
$744$	1760.31	+	5417.68i	0.0867420	+	0.266965i
$745$	−8502.76	+	24087.6i	−0.418144	+	1.18456i
$746$	−1926.47	+	5929.07i	−0.0945485	+	0.290990i
$747$	−838.554	+	2580.80i	−0.0410724	+	0.126408i
$748$	−4025.76	+	2924.89i	−0.196787	+	0.142974i
$749$	−11681.1			−0.569848
$750$	6392.51	+	5426.63i	0.311228	+	0.264204i
$751$	13613.7			0.661480			0.330740	−	0.943722i	$-0.392702\pi$
$751$	13613.7			0.661480			0.330740	+	0.943722i	$0.392702\pi$
$752$	653.706	−	474.945i	0.0316997	−	0.0230312i
$753$	−518.592	+	1596.06i	−0.0250977	+	0.0772427i
$754$	−3600.00	+	11079.7i	−0.173878	+	0.535142i
$755$	−10422.5	+	29526.0i	−0.502401	+	1.42326i
$756$	258.109	+	794.377i	0.0124171	+	0.0382159i
$757$	−23665.9			−1.13626			−0.568131	−	0.822938i	$-0.692333\pi$
$757$	−23665.9			−1.13626			−0.568131	+	0.822938i	$0.692333\pi$
$758$	4170.35	+	12835.0i	0.199834	+	0.615025i
$759$	−2140.94	−	1555.49i	−0.102386	−	0.0743881i
$760$	−2991.43	−	10061.9i	−0.142777	−	0.480243i
$761$	8697.59	−	6319.17i	0.414307	−	0.301011i	−0.361036	−	0.932552i	$-0.617577\pi$
$761$	8697.59	−	6319.17i	0.414307	−	0.301011i	0.775343	+	0.631540i	$0.217577\pi$
$762$	−5799.82	−	4213.82i	−0.275729	−	0.200329i
$763$	11863.9	+	8619.62i	0.562912	+	0.408979i
$764$	−13368.8	+	9713.00i	−0.633071	+	0.459953i
$765$	9735.88	+	7455.15i	0.460133	+	0.352342i
$766$	−9234.95	−	6709.58i	−0.435603	−	0.316484i
$767$	−6312.39	−	19427.5i	−0.297167	−	0.914586i
$768$	768.000			0.0360844
$769$	5858.85	+	18031.7i	0.274741	+	0.845565i	0.989288	+	0.145978i	$0.0466328\pi$
$769$	5858.85	+	18031.7i	0.274741	+	0.845565i	−0.714547	+	0.699587i	$0.753367\pi$
$770$	1401.63	+	1073.28i	0.0655990	+	0.0502317i
$771$	4330.30	−	13327.3i	0.202272	−	0.622530i
$772$	2892.86	−	8903.30i	0.134866	−	0.415074i
$773$	11287.0	−	8200.50i	0.525182	−	0.381567i	−0.293370	−	0.955999i	$-0.594777\pi$
$773$	11287.0	−	8200.50i	0.525182	−	0.381567i	0.818553	+	0.574432i	$0.194777\pi$
$774$	−3489.94			−0.162072
$775$	10577.1	−	27719.8i	0.490244	−	1.28480i
$776$	1702.23			0.0787456
$777$	−2448.63	+	1779.04i	−0.113056	+	0.0821398i
$778$	−2670.47	+	8218.86i	−0.123060	+	0.378741i
$779$	−7050.31	+	21698.6i	−0.324267	+	0.997990i
$780$	−5365.14	−	135.122i	−0.246286	−	0.00620276i
$781$	−169.986	−	523.164i	−0.00778821	−	0.0239696i
$782$	21061.2			0.963102
$783$	−1214.94	−	3739.19i	−0.0554512	−	0.170661i
$784$	3665.65	+	2663.25i	0.166985	+	0.121322i
$785$	−11072.8	+	31368.4i	−0.503448	+	1.42623i
$786$	13456.5	−	9776.73i	0.610659	−	0.443670i
$787$	−23265.8	−	16903.6i	−1.05379	−	0.765625i	−0.0808630	−	0.996725i	$-0.525768\pi$
$787$	−23265.8	−	16903.6i	−1.05379	−	0.765625i	−0.972930	+	0.231100i	$0.925768\pi$
$788$	3394.75	+	2466.43i	0.153468	+	0.111501i
$789$	12706.9	−	9232.12i	0.573357	−	0.416568i
$790$	−2621.48	−	66.0225i	−0.118061	−	0.00297339i
$791$	−2140.51	−	1555.17i	−0.0962173	−	0.0699060i
$792$	227.126	+	699.022i	0.0101901	+	0.0313620i
$793$	−31619.2			−1.41593
$794$	5089.58	+	15664.1i	0.227484	+	0.700125i
$795$	11401.7	−	7853.00i	0.508652	−	0.350336i
$796$	2280.37	−	7018.24i	0.101539	−	0.312506i
$797$	−1597.77	+	4917.42i	−0.0710110	+	0.218549i	−0.980263	−	0.197696i	$-0.936654\pi$
$797$	−1597.77	+	4917.42i	−0.0710110	+	0.218549i	0.909252	+	0.416245i	$0.136654\pi$
$798$	−4405.89	+	3201.07i	−0.195447	+	0.142001i
$799$	−6154.36			−0.272498
$800$	−3113.61	−	2511.06i	−0.137604	−	0.110974i
$801$	10677.9			0.471017
$802$	5677.69	−	4125.08i	0.249983	−	0.181623i
$803$	−1399.29	+	4306.57i	−0.0614943	+	0.189260i
$804$	−2072.69	+	6379.10i	−0.0909183	+	0.279818i
$805$	−2129.27	−	7161.99i	−0.0932261	−	0.313574i
$806$	5868.00	+	18059.8i	0.256441	+	0.789244i
$807$	−1308.90			−0.0570948
$808$	1734.88	+	5339.40i	0.0755356	+	0.232475i
$809$	−31470.6	−	22864.7i	−1.36767	−	0.993673i	−0.997915	−	0.0645452i	$-0.979440\pi$
$809$	−31470.6	−	22864.7i	−1.36767	−	0.993673i	−0.369759	−	0.929128i	$-0.620560\pi$
$810$	1491.64	−	1027.38i	0.0647049	−	0.0445658i
$811$	−13162.8	+	9563.34i	−0.569924	+	0.414074i	−0.835078	−	0.550132i	$-0.814577\pi$
$811$	−13162.8	+	9563.34i	−0.569924	+	0.414074i	0.265153	+	0.964206i	$0.414577\pi$
$812$	3644.37	+	2647.79i	0.157503	+	0.114432i
$813$	15023.2	+	10915.0i	0.648078	+	0.470856i
$814$	−2154.71	+	1565.49i	−0.0927794	+	0.0674081i
$815$	−25212.4	+	17365.1i	−1.08362	+	0.746349i
$816$	−4732.35	−	3438.26i	−0.203021	−	0.147504i
$817$	−7031.64	−	21641.2i	−0.301109	−	0.926717i
$818$	30347.7			1.29716
$819$	860.407	+	2648.06i	0.0367095	+	0.112980i
$820$	2477.53	+	8333.37i	0.105511	+	0.354895i
$821$	−410.554	+	1263.55i	−0.0174524	+	0.0537130i	−0.959403	−	0.282037i	$-0.908990\pi$
$821$	−410.554	+	1263.55i	−0.0174524	+	0.0537130i	0.941951	+	0.335750i	$0.108990\pi$
$822$	3346.13	−	10298.3i	0.141982	−	0.436977i
$823$	−35639.1	+	25893.3i	−1.50948	+	1.09670i	−0.543072	+	0.839686i	$0.682739\pi$
$823$	−35639.1	+	25893.3i	−1.50948	+	1.09670i	−0.966407	+	0.257015i	$0.917261\pi$
$824$	5734.20			0.242427
$825$	1364.72	−	3576.58i	0.0575920	−	0.150934i
$826$	−7898.70			−0.332725
$827$	−18787.8	+	13650.2i	−0.789984	+	0.573957i	−0.907959	−	0.419059i	$-0.862360\pi$
$827$	−18787.8	+	13650.2i	−0.789984	+	0.573957i	0.117975	+	0.993017i	$0.462360\pi$
$828$	961.300	−	2958.58i	0.0403472	−	0.124176i
$829$	3358.16	−	10335.4i	0.140692	−	0.433006i	−0.855740	−	0.517406i	$-0.826898\pi$
$829$	3358.16	−	10335.4i	0.140692	−	0.433006i	0.996432	+	0.0844006i	$0.0268975\pi$
$830$	−5552.47	+	3824.29i	−0.232204	+	0.159931i
$831$	−7128.05	−	21937.9i	−0.297556	−	0.915784i
$832$	2560.13			0.106679
$833$	−10664.4	−	32821.5i	−0.443575	−	1.36518i
$834$	−7504.68	−	5452.47i	−0.311590	−	0.226383i
$835$	−9236.56	−	232.625i	−0.382808	−	0.00964109i
$836$	−3877.02	+	2816.82i	−0.160394	+	0.116533i
$837$	−5184.62	−	3766.85i	−0.214106	−	0.155557i
$838$	−11550.4	−	8391.87i	−0.476137	−	0.345934i
$839$	16649.8	−	12096.8i	0.685117	−	0.497767i	−0.189934	−	0.981797i	$-0.560827\pi$
$839$	16649.8	−	12096.8i	0.685117	−	0.497767i	0.875051	+	0.484030i	$0.160827\pi$
$840$	−690.764	+	1956.88i	−0.0283734	+	0.0803793i
$841$	2576.82	+	1872.17i	0.105655	+	0.0767628i
$842$	−3486.43	−	10730.1i	−0.142696	−	0.439174i
$843$	−21616.3			−0.883160
$844$	−1108.96	−	3413.03i	−0.0452274	−	0.139196i
$845$	6670.72	+	168.003i	0.271573	+	0.00683964i
$846$	−280.905	+	864.537i	−0.0114157	+	0.0351340i
$847$	−2931.90	+	9023.47i	−0.118939	+	0.366057i
$848$	−5342.91	+	3881.85i	−0.216363	+	0.157197i
$849$	−2603.96			−0.105262
$850$	7944.08	+	29412.3i	0.320564	+	1.18686i
$851$	11272.6			0.454075
$852$	523.141	−	380.084i	0.0210358	−	0.0152834i
$853$	14852.2	−	45710.4i	0.596166	−	1.83481i	0.0473314	−	0.998879i	$-0.484928\pi$
$853$	14852.2	−	45710.4i	0.596166	−	1.83481i	0.548835	−	0.835931i	$-0.315072\pi$
$854$	−3778.14	+	11627.9i	−0.151388	+	0.465924i
$855$	9376.17	+	7179.70i	0.375039	+	0.287182i
$856$	−3733.86	−	11491.6i	−0.149089	−	0.458850i
$857$	27949.0			1.11402			0.557012	−	0.830505i	$-0.311948\pi$
$857$	27949.0			1.11402			0.557012	+	0.830505i	$0.311948\pi$
$858$	757.125	+	2330.19i	0.0301257	+	0.0927173i
$859$	1968.02	+	1429.85i	0.0781701	+	0.0567939i	0.626184	−	0.779675i	$-0.284616\pi$
$859$	1968.02	+	1429.85i	0.0781701	+	0.0567939i	−0.548014	+	0.836469i	$0.684616\pi$
$860$	−6884.31	−	5271.59i	−0.272969	−	0.209023i
$861$	3649.00	−	2651.15i	0.144434	−	0.104937i
$862$	17126.4	+	12443.0i	0.676713	+	0.491661i
$863$	33236.8	+	24148.0i	1.31100	+	0.952499i	0.999998	+	0.00209113i	$0.000665628\pi$
$863$	33236.8	+	24148.0i	1.31100	+	0.952499i	0.311005	+	0.950408i	$0.399334\pi$
$864$	−698.991	+	507.846i	−0.0275233	+	0.0199969i
$865$	−1703.97	−	5731.46i	−0.0669789	−	0.225290i
$866$	12921.3	+	9387.84i	0.507023	+	0.368374i
$867$	9213.06	+	28354.9i	0.360890	+	1.11071i
$868$	7342.64			0.287126
$869$	369.942	+	1138.56i	0.0144412	+	0.0444455i
$870$	3251.48	−	9211.15i	0.126707	−	0.358951i
$871$	−6909.33	+	21264.7i	−0.268787	+	0.827243i
$872$	−4687.54	+	14426.8i	−0.182041	+	0.560266i
$873$	−1549.28	+	1125.62i	−0.0600631	+	0.0436384i
$874$	20283.0			0.784992
$875$	9198.70	−	5675.00i	0.355398	−	0.219257i
$876$	−5322.98			−0.205305
$877$	27561.1	−	20024.3i	1.06120	−	0.771006i	0.0868893	−	0.996218i	$-0.472307\pi$
$877$	27561.1	−	20024.3i	1.06120	−	0.771006i	0.974310	+	0.225212i	$0.0723073\pi$
$878$	6404.55	−	19711.2i	0.246177	−	0.757654i
$879$	−4181.50	+	12869.3i	−0.160453	+	0.493825i
$880$	−607.846	+	1721.98i	−0.0232847	+	0.0659634i
$881$	13767.6	+	42372.2i	0.526494	+	1.62038i	0.761342	+	0.648350i	$0.224541\pi$
$881$	13767.6	+	42372.2i	0.526494	+	1.62038i	−0.234848	+	0.972032i	$0.575459\pi$
$882$	−5097.37			−0.194600
$883$	14348.4	+	44159.9i	0.546844	+	1.68301i	0.716565	+	0.697520i	$0.245713\pi$
$883$	14348.4	+	44159.9i	0.546844	+	1.68301i	−0.169721	+	0.985492i	$0.554287\pi$
$884$	−15775.3	−	11461.4i	−0.600205	−	0.436075i
$885$	4881.02	+	16417.7i	0.185394	+	0.623589i
$886$	12248.0	−	8898.70i	0.464425	−	0.337424i
$887$	30403.8	+	22089.7i	1.15091	+	0.836187i	0.988602	−	0.150553i	$-0.0481053\pi$
$887$	30403.8	+	22089.7i	1.15091	+	0.836187i	0.162311	+	0.986740i	$0.448105\pi$
$888$	−2532.90	−	1840.26i	−0.0957189	−	0.0695439i
$889$	−7475.84	+	5431.52i	−0.282038	+	0.204913i
$890$	21063.3	+	16129.0i	0.793308	+	0.607467i
$891$	−668.952	−	486.022i	−0.0251523	−	0.0182742i
$892$	2069.43	+	6369.04i	0.0776788	+	0.239071i
$893$	−5926.97			−0.222104
$894$	4236.15	+	13037.5i	0.158477	+	0.487741i
$895$	−26736.8	−	20473.4i	−0.998563	−	0.764639i
$896$	305.907	−	941.484i	0.0114058	−	0.0351036i
$897$	3204.50	−	9862.43i	0.119281	−	0.367109i
$898$	−23831.9	+	17314.9i	−0.885615	+	0.643437i
$899$	−34562.3			−1.28222
$900$	4494.29	+	226.523i	0.166455	+	0.00838975i
$901$	50301.2			1.85991
$902$	3210.98	−	2332.91i	0.118530	−	0.0861170i
$903$	−1390.10	+	4278.29i	−0.0512289	+	0.157666i
$904$	845.738	−	2602.91i	0.0311160	−	0.0957651i
$905$	−4944.31	−	124.524i	−0.181607	−	0.00457381i
$906$	5192.57	+	15981.1i	0.190410	+	0.586023i
$907$	−33154.3			−1.21375			−0.606875	−	0.794797i	$-0.707577\pi$
$907$	−33154.3			−1.21375			−0.606875	+	0.794797i	$0.707577\pi$
$908$	4780.72	+	14713.5i	0.174729	+	0.537760i
$909$	−5109.71	−	3712.42i	−0.186445	−	0.135460i
$910$	−2302.67	+	6523.25i	−0.0838820	+	0.237630i
$911$	−32179.5	+	23379.8i	−1.17031	+	0.850281i	−0.991046	−	0.133519i	$-0.957372\pi$
$911$	−32179.5	+	23379.8i	−1.17031	+	0.850281i	−0.179266	+	0.983801i	$0.557372\pi$
$912$	−4557.50	−	3311.22i	−0.165476	−	0.120225i
$913$	2490.09	+	1809.16i	0.0902630	+	0.0655799i
$914$	6882.61	−	5000.51i	0.249077	−	0.180965i
$915$	26503.7	+	667.502i	0.957581	+	0.0241169i
$916$	−10224.2	−	7428.31i	−0.368795	−	0.267946i
$917$	−6625.26	−	20390.5i	−0.238588	−	0.734299i
$918$	6580.70			0.236596
$919$	−14128.3	−	43482.3i	−0.507126	−	1.56077i	−0.797167	−	0.603759i	$-0.793669\pi$
$919$	−14128.3	−	43482.3i	−0.507126	−	1.56077i	0.290041	−	0.957014i	$-0.406331\pi$
$920$	6365.23	−	4384.08i	0.228104	−	0.157107i
$921$	−2650.29	+	8156.75i	−0.0948208	+	0.291829i
$922$	−5864.60	+	18049.4i	−0.209480	+	0.644712i
$923$	1743.89	−	1267.01i	0.0621895	−	0.0451833i
$924$	947.393			0.0337304
$925$	4251.90	+	15742.3i	0.151137	+	0.559572i
$926$	−15544.0			−0.551628
$927$	−5218.95	+	3791.79i	−0.184911	+	0.134346i
$928$	−1439.93	+	4431.63i	−0.0509352	+	0.156762i
$929$	10879.4	−	33483.3i	0.384220	−	1.18251i	−0.552824	−	0.833298i	$-0.686450\pi$
$929$	10879.4	−	33483.3i	0.384220	−	1.18251i	0.937044	−	0.349210i	$-0.113550\pi$
$930$	−4537.40	−	15261.9i	−0.159986	−	0.538128i
$931$	−10270.3	−	31608.8i	−0.361543	−	1.11271i
$932$	23722.9			0.833766
$933$	−274.432	−	844.615i	−0.00962969	−	0.0296371i
$934$	−18847.5	−	13693.5i	−0.660289	−	0.479728i
$935$	11454.6	−	7889.41i	0.400648	−	0.275948i
$936$	−2330.09	+	1692.91i	−0.0813689	+	0.0591180i
$937$	−8814.56	−	6404.15i	−0.307320	−	0.223281i	0.423426	−	0.905931i	$-0.360827\pi$
$937$	−8814.56	−	6404.15i	−0.307320	−	0.223281i	−0.730746	+	0.682650i	$0.760827\pi$
$938$	6994.49	+	5081.79i	0.243474	+	0.176894i
$939$	18068.7	−	13127.7i	0.627955	−	0.456236i
$940$	−1860.01	+	1281.09i	−0.0645391	+	0.0444516i
$941$	4345.11	+	3156.90i	0.150528	+	0.109365i	0.660500	−	0.750826i	$-0.270344\pi$
$941$	4345.11	+	3156.90i	0.150528	+	0.109365i	−0.509972	+	0.860191i	$0.670344\pi$
$942$	5516.60	+	16978.3i	0.190807	+	0.587244i
$943$	−16798.6			−0.580102
$944$	−2524.83	−	7770.61i	−0.0870509	−	0.267915i
$945$	−665.305	−	2237.81i	−0.0229020	−	0.0770328i
$946$	−1223.24	+	3764.73i	−0.0420411	+	0.129389i
$947$	−605.914	+	1864.81i	−0.0207915	+	0.0639897i	−0.960914	−	0.276847i	$-0.910710\pi$
$947$	−605.914	+	1864.81i	−0.0207915	+	0.0639897i	0.940122	+	0.340837i	$0.110710\pi$
$948$	−1138.51	+	827.178i	−0.0390054	+	0.0283391i
$949$	−17744.2			−0.606955
$950$	7650.56	+	28325.5i	0.261281	+	0.967371i
$951$	−18727.0			−0.638553
$952$	−6099.90	+	4431.84i	−0.207667	+	0.150879i
$953$	−5551.92	+	17087.0i	−0.188714	+	0.580801i	−0.999993	−	0.00385829i	$-0.998772\pi$
$953$	−5551.92	+	17087.0i	−0.188714	+	0.580801i	0.811279	+	0.584659i	$0.198772\pi$
$954$	2295.91	−	7066.08i	0.0779170	−	0.239804i
$955$	38038.6	−	26199.2i	1.28890	−	0.887736i
$956$	3184.38	+	9800.52i	0.107730	+	0.331560i
$957$	−4459.45			−0.150631
$958$	8327.81	+	25630.4i	0.280855	+	0.864384i
$959$	−11291.8	−	8203.97i	−0.380220	−	0.276246i
$960$	−2145.94	−	54.0461i	−0.0721459	−	0.00181701i
$961$	−21475.9	+	15603.1i	−0.720884	+	0.523753i
$962$	−8443.42	−	6134.50i	−0.282980	−	0.205597i
$963$	10997.3	+	7989.99i	0.367998	+	0.267366i
$964$	12621.8	−	9170.28i	0.421702	−	0.306385i
$965$	−8709.77	+	24674.0i	−0.290547	+	0.823093i
$966$	−3243.99	−	2356.90i	−0.108047	−	0.0785010i
$967$	−7592.72	−	23368.0i	−0.252498	−	0.777108i	−0.994312	−	0.106503i	$-0.966035\pi$
$967$	−7592.72	−	23368.0i	−0.252498	−	0.777108i	0.741815	−	0.670605i	$-0.233965\pi$
$968$	−9814.33			−0.325872
$969$	13259.0	+	40806.9i	0.439566	+	1.35285i
$970$	−4756.38	−	119.790i	−0.157441	−	0.00396520i
$971$	−4129.75	+	12710.1i	−0.136488	+	0.420067i	−0.995819	−	0.0913536i	$-0.970881\pi$
$971$	−4129.75	+	12710.1i	−0.136488	+	0.420067i	0.859330	+	0.511421i	$0.170881\pi$
$972$	300.365	−	924.427i	0.00991172	−	0.0305052i
$973$	−9673.37	+	7028.11i	−0.318719	+	0.231563i
$974$	−14234.5			−0.468278
$975$	14981.8	+	755.116i	0.492103	+	0.0248032i
$976$	−12647.0			−0.414776
$977$	−16404.4	+	11918.5i	−0.537179	+	0.390283i	−0.823036	−	0.567989i	$-0.807722\pi$
$977$	−16404.4	+	11918.5i	−0.537179	+	0.390283i	0.285857	+	0.958272i	$0.407722\pi$
$978$	−5076.89	+	15625.1i	−0.165993	+	0.510874i
$979$	3742.63	−	11518.6i	0.122181	−	0.376034i
$980$	−10055.1	−	7699.62i	−0.327755	−	0.250975i
$981$	−5273.48	−	16230.1i	−0.171630	−	0.528224i
$982$	−41142.5			−1.33698
$983$	691.148	+	2127.13i	0.0224254	+	0.0690183i	0.961643	−	0.274304i	$-0.0884476\pi$
$983$	691.148	+	2127.13i	0.0224254	+	0.0690183i	−0.939218	+	0.343323i	$0.888448\pi$
$984$	3774.56	+	2742.38i	0.122285	+	0.0888454i
$985$	−9312.03	−	7130.59i	−0.301224	−	0.230659i
$986$	28712.7	−	20861.0i	0.927381	−	0.673782i
$987$	947.939	+	688.718i	0.0305707	+	0.0222109i
$988$	−15192.5	−	11038.0i	−0.489207	−	0.355430i
$989$	13554.3	−	9847.79i	0.435796	−	0.316624i
$990$	−585.443	−	1969.19i	−0.0187946	−	0.0632171i
$991$	−30991.0	−	22516.3i	−0.993402	−	0.721749i	−0.0327387	−	0.999464i	$-0.510423\pi$
$991$	−30991.0	−	22516.3i	−0.993402	−	0.721749i	−0.960664	+	0.277715i	$0.910423\pi$
$992$	2347.08	+	7223.57i	0.0751208	+	0.231198i
$993$	−10611.2			−0.339108
$994$	−257.566	−	792.707i	−0.00821881	−	0.0252949i
$995$	−6865.69	+	19449.9i	−0.218751	+	0.619702i
$996$	−1118.07	+	3441.07i	−0.0355697	+	0.109472i
$997$	7363.29	−	22661.9i	0.233900	−	0.719869i	−0.763366	−	0.645966i	$-0.776455\pi$
$997$	7363.29	−	22661.9i	0.233900	−	0.719869i	0.997265	−	0.0739025i	$-0.0235454\pi$
$998$	−18245.7	+	13256.3i	−0.578714	+	0.420461i
$999$	3522.18			0.111549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.g.b.61.2	✓	16
25.16	even	5	inner	150.4.g.b.91.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.4.g.b.61.2	✓	16	1.1	even	1	trivial
150.4.g.b.91.2	yes	16	25.16	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(0.927051 - 2.85317i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-3.72153 + 10.5428i) q^{5} +(1.85410 + 5.70634i) q^{6} +7.73387 q^{7} +(2.47214 + 7.60845i) q^{8} +(-7.28115 - 5.29007i) q^{9} +(-6.37221 - 21.4335i) q^{10} +(-8.25866 + 6.00027i) q^{11} +(-9.70820 - 7.05342i) q^{12} +(-32.3623 - 23.5126i) q^{13} +(-12.5137 + 9.09171i) q^{14} +(26.6303 + 20.3919i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(37.6583 + 115.900i) q^{17} +18.0000 q^{18} +(36.2669 + 111.618i) q^{19} +(35.5070 + 27.1891i) q^{20} +(7.16969 - 22.0660i) q^{21} +(6.30906 - 19.4173i) q^{22} +(-69.9088 + 50.7917i) q^{23} +24.0000 q^{24} +(-97.3004 - 78.4706i) q^{25} +80.0041 q^{26} +(-21.8435 + 15.8702i) q^{27} +(9.55959 - 29.4214i) q^{28} +(-44.9977 + 138.489i) q^{29} +(-67.0608 - 1.68894i) q^{30} +(73.3462 + 225.736i) q^{31} +32.0000 q^{32} +(9.46358 + 29.1259i) q^{33} +(-197.181 - 143.261i) q^{34} +(-28.7818 + 81.5365i) q^{35} +(-29.1246 + 21.1603i) q^{36} +(-105.537 - 76.6773i) q^{37} +(-189.896 - 137.968i) q^{38} +(-97.0870 + 70.5378i) q^{39} +(-89.4144 - 2.25192i) q^{40} +(157.273 + 114.266i) q^{41} +(14.3394 + 44.1321i) q^{42} -193.886 q^{43} +(12.6181 + 38.8346i) q^{44} +(82.8691 - 57.0764i) q^{45} +(53.4055 - 164.365i) q^{46} +(-15.6058 + 48.0298i) q^{47} +(-38.8328 + 28.2137i) q^{48} -283.187 q^{49} +(249.683 + 12.5846i) q^{50} +365.594 q^{51} +(-129.449 + 94.0505i) q^{52} +(127.551 - 392.560i) q^{53} +(16.6869 - 51.3571i) q^{54} +(-32.5246 - 109.399i) q^{55} +(19.1192 + 58.8428i) q^{56} +352.087 q^{57} +(-89.9953 - 276.977i) q^{58} +(413.130 + 300.156i) q^{59} +(110.492 - 76.1019i) q^{60} +(639.479 - 464.608i) q^{61} +(-384.046 - 279.026i) q^{62} +(-56.3115 - 40.9127i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(368.326 - 253.686i) q^{65} +(-49.5520 - 36.0016i) q^{66} +(-172.725 - 531.591i) q^{67} +487.459 q^{68} +(80.1083 + 246.548i) q^{69} +(-49.2819 - 165.764i) q^{70} +(-16.6518 + 51.2491i) q^{71} +(22.2492 - 68.4761i) q^{72} +(358.865 - 260.731i) q^{73} +260.903 q^{74} +(-314.092 + 204.868i) q^{75} +469.449 q^{76} +(-63.8714 + 46.4053i) q^{77} +(74.1679 - 228.265i) q^{78} +(36.2394 - 111.533i) q^{79} +(147.323 - 101.469i) q^{80} +(25.0304 + 77.0356i) q^{81} -388.801 q^{82} +(-93.1727 - 286.756i) q^{83} +(-75.0820 - 54.5502i) q^{84} +(-1362.06 - 34.3037i) q^{85} +(313.714 - 227.926i) q^{86} +(353.416 + 256.772i) q^{87} +(-66.0693 - 48.0022i) q^{88} +(-959.843 + 697.367i) q^{89} +(-66.9876 + 189.770i) q^{90} +(-250.286 - 181.843i) q^{91} +(106.811 + 328.731i) q^{92} +712.060 q^{93} +(-31.2117 - 96.0597i) q^{94} +(-1311.73 - 33.0363i) q^{95} +(29.6656 - 91.3014i) q^{96} +(65.7524 - 202.365i) q^{97} +(458.207 - 332.907i) q^{98} +91.8744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Introduction

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