LMFDB - Embedded newform 25.4.d.a.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.d (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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.2
Character	$\chi$	$=$	25.16
Dual form			25.4.d.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81638 - 2.04622i) q^{2} +(2.63646 + 8.11420i) q^{3} +(1.27284 + 3.91740i) q^{4} +(9.28856 + 6.22275i) q^{5} +(9.17815 - 28.2474i) q^{6} +12.5082 q^{7} +(-4.17503 + 12.8494i) q^{8} +(-37.0458 + 26.9153i) q^{9} +O(q^{10})$	\(q+(-2.81638 - 2.04622i) q^{2} +(2.63646 + 8.11420i) q^{3} +(1.27284 + 3.91740i) q^{4} +(9.28856 + 6.22275i) q^{5} +(9.17815 - 28.2474i) q^{6} +12.5082 q^{7} +(-4.17503 + 12.8494i) q^{8} +(-37.0458 + 26.9153i) q^{9} +(-13.4270 - 36.5321i) q^{10} +(-30.5650 - 22.2068i) q^{11} +(-28.4308 + 20.6562i) q^{12} +(25.8465 - 18.7786i) q^{13} +(-35.2278 - 25.5945i) q^{14} +(-26.0037 + 91.7752i) q^{15} +(64.7099 - 47.0145i) q^{16} +(-5.81584 + 17.8993i) q^{17} +159.410 q^{18} +(49.5522 - 152.506i) q^{19} +(-12.5542 + 44.3076i) q^{20} +(32.9774 + 101.494i) q^{21} +(40.6427 + 125.085i) q^{22} +(-86.4266 - 62.7926i) q^{23} -115.270 q^{24} +(47.5547 + 115.601i) q^{25} -111.218 q^{26} +(-129.703 - 94.2345i) q^{27} +(15.9210 + 48.9997i) q^{28} +(33.1890 + 102.145i) q^{29} +(261.028 - 205.265i) q^{30} +(-2.18936 + 6.73816i) q^{31} -170.364 q^{32} +(99.6067 - 306.558i) q^{33} +(53.0055 - 38.5108i) q^{34} +(116.183 + 77.8354i) q^{35} +(-152.592 - 110.864i) q^{36} +(-52.3230 + 38.0149i) q^{37} +(-451.619 + 328.120i) q^{38} +(220.516 + 160.214i) q^{39} +(-118.739 + 93.3724i) q^{40} +(305.782 - 222.164i) q^{41} +(114.802 - 353.324i) q^{42} -234.897 q^{43} +(48.0885 - 148.001i) q^{44} +(-511.589 + 19.4780i) q^{45} +(114.923 + 353.696i) q^{46} +(32.9933 + 101.543i) q^{47} +(552.090 + 401.117i) q^{48} -186.545 q^{49} +(102.612 - 422.883i) q^{50} -160.572 q^{51} +(106.462 + 77.3489i) q^{52} +(-64.0024 - 196.979i) q^{53} +(172.467 + 530.800i) q^{54} +(-145.718 - 396.467i) q^{55} +(-52.2221 + 160.723i) q^{56} +1368.11 q^{57} +(115.539 - 355.591i) q^{58} +(-261.882 + 190.269i) q^{59} +(-392.619 + 14.9484i) q^{60} +(221.781 + 161.134i) q^{61} +(19.9538 - 14.4973i) q^{62} +(-463.376 + 336.662i) q^{63} +(-37.8690 - 27.5134i) q^{64} +(356.931 - 13.5896i) q^{65} +(-907.814 + 659.566i) q^{66} +(-43.7313 + 134.591i) q^{67} -77.5215 q^{68} +(281.651 - 866.833i) q^{69} +(-167.948 - 456.950i) q^{70} +(-185.509 - 570.937i) q^{71} +(-191.179 - 588.388i) q^{72} +(116.952 + 84.9707i) q^{73} +225.148 q^{74} +(-812.631 + 690.645i) q^{75} +660.500 q^{76} +(-382.313 - 277.767i) q^{77} +(-293.223 - 902.448i) q^{78} +(98.8328 + 304.176i) q^{79} +(893.621 - 34.0233i) q^{80} +(40.6249 - 125.030i) q^{81} -1315.80 q^{82} +(-344.182 + 1059.28i) q^{83} +(-355.618 + 258.372i) q^{84} +(-165.404 + 130.068i) q^{85} +(661.558 + 480.650i) q^{86} +(-741.324 + 538.604i) q^{87} +(412.954 - 300.028i) q^{88} +(43.7671 + 31.7986i) q^{89} +(1480.69 + 991.966i) q^{90} +(323.293 - 234.886i) q^{91} +(135.977 - 418.493i) q^{92} -60.4469 q^{93} +(114.857 - 353.495i) q^{94} +(1409.28 - 1108.21i) q^{95} +(-449.159 - 1382.37i) q^{96} +(406.468 + 1250.98i) q^{97} +(525.381 + 381.712i) q^{98} +1730.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) $ 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.81638	−	2.04622i	−0.995740	−	0.723448i	−0.0345696	−	0.999402i	$-0.511006\pi$
$2$	−2.81638	−	2.04622i	−0.995740	−	0.723448i	−0.961171	+	0.275955i	$0.911006\pi$
$3$	2.63646	+	8.11420i	0.507387	+	1.56158i	0.796720	+	0.604349i	$0.206567\pi$
$3$	2.63646	+	8.11420i	0.507387	+	1.56158i	−0.289332	+	0.957229i	$0.593433\pi$
$4$	1.27284	+	3.91740i	0.159105	+	0.489676i
$5$	9.28856	+	6.22275i	0.830794	+	0.556580i
$5$	9.28856	+	6.22275i	0.830794	+	0.556580i
$6$	9.17815	−	28.2474i	0.624494	−	1.92199i
$7$	12.5082			0.675379			0.337690	−	0.941258i	$-0.390355\pi$
$7$	12.5082			0.675379			0.337690	+	0.941258i	$0.390355\pi$
$8$	−4.17503	+	12.8494i	−0.184512	+	0.567869i
$9$	−37.0458	+	26.9153i	−1.37207	+	0.996864i
$10$	−13.4270	−	36.5321i	−0.424599	−	1.15525i
$11$	−30.5650	−	22.2068i	−0.837791	−	0.608691i	0.0839620	−	0.996469i	$-0.473243\pi$
$11$	−30.5650	−	22.2068i	−0.837791	−	0.608691i	−0.921753	+	0.387778i	$0.873243\pi$
$12$	−28.4308	+	20.6562i	−0.683938	+	0.496910i
$13$	25.8465	−	18.7786i	0.551424	−	0.400633i	−0.276886	−	0.960903i	$-0.589302\pi$
$13$	25.8465	−	18.7786i	0.551424	−	0.400633i	0.828310	+	0.560269i	$0.189302\pi$
$14$	−35.2278	−	25.5945i	−0.672502	−	0.488602i
$15$	−26.0037	+	91.7752i	−0.447608	+	1.57975i
$16$	64.7099	−	47.0145i	1.01109	−	0.734602i
$17$	−5.81584	+	17.8993i	−0.0829735	+	0.255366i	−0.983933	−	0.178536i	$-0.942864\pi$
$17$	−5.81584	+	17.8993i	−0.0829735	+	0.255366i	0.900960	+	0.433902i	$0.142864\pi$
$18$	159.410			2.08740
$19$	49.5522	−	152.506i	0.598319	−	1.84144i	0.0608593	−	0.998146i	$-0.480616\pi$
$19$	49.5522	−	152.506i	0.598319	−	1.84144i	0.537459	−	0.843290i	$-0.319384\pi$
$20$	−12.5542	+	44.3076i	−0.140360	+	0.495374i
$21$	32.9774	+	101.494i	0.342679	+	1.05466i
$22$	40.6427	+	125.085i	0.393866	+	1.21220i
$23$	−86.4266	−	62.7926i	−0.783530	−	0.569268i	0.122506	−	0.992468i	$-0.460907\pi$
$23$	−86.4266	−	62.7926i	−0.783530	−	0.569268i	−0.906036	+	0.423200i	$0.860907\pi$
$24$	−115.270			−0.980390
$25$	47.5547	+	115.601i	0.380438	+	0.924807i
$26$	−111.218			−0.838913
$27$	−129.703	−	94.2345i	−0.924492	−	0.671683i
$28$	15.9210	+	48.9997i	0.107456	+	0.330717i
$29$	33.1890	+	102.145i	0.212519	+	0.654065i	0.999320	+	0.0368592i	$0.0117353\pi$
$29$	33.1890	+	102.145i	0.212519	+	0.654065i	−0.786802	+	0.617206i	$0.788265\pi$
$30$	261.028	−	205.265i	1.58857	−	1.24920i
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	−0.957198	−	0.289432i	$-0.906533\pi$
$31$	−2.18936	+	6.73816i	−0.0126845	+	0.0390390i	0.944514	+	0.328471i	$0.106533\pi$
$32$	−170.364			−0.941138
$33$	99.6067	−	306.558i	0.525433	−	1.61712i
$34$	53.0055	−	38.5108i	0.267364	−	0.194251i
$35$	116.183	+	77.8354i	0.561101	+	0.375903i
$36$	−152.592	−	110.864i	−0.706443	−	0.513261i
$37$	−52.3230	+	38.0149i	−0.232482	+	0.168908i	−0.697928	−	0.716168i	$-0.745894\pi$
$37$	−52.3230	+	38.0149i	−0.232482	+	0.168908i	0.465445	+	0.885077i	$0.345894\pi$
$38$	−451.619	+	328.120i	−1.92795	+	1.40074i
$39$	220.516	+	160.214i	0.905406	+	0.657816i
$40$	−118.739	+	93.3724i	−0.469356	+	0.369087i
$41$	305.782	−	222.164i	1.16476	−	0.846248i	0.174388	−	0.984677i	$-0.444205\pi$
$41$	305.782	−	222.164i	1.16476	−	0.846248i	0.990372	+	0.138429i	$0.0442052\pi$
$42$	114.802	−	353.324i	0.421770	−	1.29807i
$43$	−234.897			−0.833056			−0.416528	−	0.909123i	$-0.636753\pi$
$43$	−234.897			−0.833056			−0.416528	+	0.909123i	$0.636753\pi$
$44$	48.0885	−	148.001i	0.164764	−	0.507091i
$45$	−511.589	+	19.4780i	−1.69474	+	0.0645247i
$46$	114.923	+	353.696i	0.368357	+	1.13369i
$47$	32.9933	+	101.543i	0.102395	+	0.315139i	0.989110	−	0.147177i	$-0.0470186\pi$
$47$	32.9933	+	101.543i	0.102395	+	0.315139i	−0.886715	+	0.462316i	$0.847019\pi$
$48$	552.090	+	401.117i	1.66015	+	1.20617i
$49$	−186.545			−0.543863
$50$	102.612	−	422.883i	0.290232	−	1.19609i
$51$	−160.572			−0.440874
$52$	106.462	+	77.3489i	0.283915	+	0.206276i
$53$	−64.0024	−	196.979i	−0.165876	−	0.510512i	0.833224	−	0.552935i	$-0.186492\pi$
$53$	−64.0024	−	196.979i	−0.165876	−	0.510512i	−0.999100	+	0.0424228i	$0.986492\pi$
$54$	172.467	+	530.800i	0.434627	+	1.33764i
$55$	−145.718	−	396.467i	−0.357247	−	0.971994i
$56$	−52.2221	+	160.723i	−0.124615	+	0.383527i
$57$	1368.11			3.17912
$58$	115.539	−	355.591i	0.261568	−	0.805025i
$59$	−261.882	+	190.269i	−0.577868	+	0.419845i	−0.837955	−	0.545740i	$-0.816249\pi$
$59$	−261.882	+	190.269i	−0.577868	+	0.419845i	0.260087	+	0.965585i	$0.416249\pi$
$60$	−392.619	+	14.9484i	−0.844782	+	0.0321639i
$61$	221.781	+	161.134i	0.465511	+	0.338214i	0.795689	−	0.605705i	$-0.207109\pi$
$61$	221.781	+	161.134i	0.465511	+	0.338214i	−0.330178	+	0.943919i	$0.607109\pi$
$62$	19.9538	−	14.4973i	0.0408732	−	0.0296961i
$63$	−463.376	+	336.662i	−0.926665	+	0.673261i
$64$	−37.8690	−	27.5134i	−0.0739629	−	0.0537372i
$65$	356.931	−	13.5896i	0.681105	−	0.0259321i
$66$	−907.814	+	659.566i	−1.69309	+	1.23011i
$67$	−43.7313	+	134.591i	−0.0797407	+	0.245417i	−0.982978	−	0.183726i	$-0.941184\pi$
$67$	−43.7313	+	134.591i	−0.0797407	+	0.245417i	0.903237	+	0.429142i	$0.141184\pi$
$68$	−77.5215			−0.138248
$69$	281.651	−	866.833i	0.491403	−	1.51238i
$70$	−167.948	−	456.950i	−0.286765	−	0.780229i
$71$	−185.509	−	570.937i	−0.310082	−	0.954334i	−0.977732	−	0.209859i	$-0.932700\pi$
$71$	−185.509	−	570.937i	−0.310082	−	0.954334i	0.667650	−	0.744475i	$-0.267300\pi$
$72$	−191.179	−	588.388i	−0.312926	−	0.963087i
$73$	116.952	+	84.9707i	0.187510	+	0.136234i	0.677580	−	0.735449i	$-0.263029\pi$
$73$	116.952	+	84.9707i	0.187510	+	0.136234i	−0.490070	+	0.871683i	$0.663029\pi$
$74$	225.148			0.353688
$75$	−812.631	+	690.645i	−1.25113	+	1.06332i
$76$	660.500			0.996902
$77$	−382.313	−	277.767i	−0.565826	−	0.411097i
$78$	−293.223	−	902.448i	−0.425654	−	1.31003i
$79$	98.8328	+	304.176i	0.140754	+	0.433196i	0.996441	−	0.0842982i	$-0.0268648\pi$
$79$	98.8328	+	304.176i	0.140754	+	0.433196i	−0.855687	+	0.517494i	$0.826865\pi$
$80$	893.621	−	34.0233i	1.24887	−	0.0475491i
$81$	40.6249	−	125.030i	0.0557268	−	0.171510i
$82$	−1315.80			−1.77202
$83$	−344.182	+	1059.28i	−0.455167	+	1.40086i	0.415773	+	0.909469i	$0.363511\pi$
$83$	−344.182	+	1059.28i	−0.455167	+	1.40086i	−0.870939	+	0.491390i	$0.836489\pi$
$84$	−355.618	+	258.372i	−0.461918	+	0.335603i
$85$	−165.404	+	130.068i	−0.211065	+	0.165975i
$86$	661.558	+	480.650i	0.829507	+	0.602672i
$87$	−741.324	+	538.604i	−0.913544	+	0.663728i
$88$	412.954	−	300.028i	0.500239	−	0.363445i
$89$	43.7671	+	31.7986i	0.0521270	+	0.0378725i	0.613544	−	0.789661i	$-0.289743\pi$
$89$	43.7671	+	31.7986i	0.0521270	+	0.0378725i	−0.561417	+	0.827533i	$0.689743\pi$
$90$	1480.69	+	991.966i	1.73420	+	1.16180i
$91$	323.293	−	234.886i	0.372421	−	0.270579i
$92$	135.977	−	418.493i	0.154093	−	0.474249i
$93$	−60.4469			−0.0673984
$94$	114.857	−	353.495i	0.126028	−	0.387874i
$95$	1409.28	−	1108.21i	1.52199	−	1.19684i
$96$	−449.159	−	1382.37i	−0.477522	−	1.46966i
$97$	406.468	+	1250.98i	0.425470	+	1.30946i	0.902543	+	0.430599i	$0.141698\pi$
$97$	406.468	+	1250.98i	0.425470	+	1.30946i	−0.477073	+	0.878863i	$0.658302\pi$
$98$	525.381	+	381.712i	0.541546	+	0.393456i
$99$	1730.01			1.75629
$100$	−392.325	+	333.433i	−0.392325	+	0.333433i
$101$	−345.232			−0.340117			−0.170059	−	0.985434i	$-0.554396\pi$
$101$	−345.232			−0.340117			−0.170059	+	0.985434i	$0.554396\pi$
$102$	452.231	+	328.565i	0.438996	+	0.318949i
$103$	−450.899	−	1387.73i	−0.431344	−	1.32754i	−0.896787	−	0.442463i	$-0.854105\pi$
$103$	−450.899	−	1387.73i	−0.431344	−	1.32754i	0.465443	−	0.885078i	$-0.345895\pi$
$104$	133.384	+	410.513i	0.125763	+	0.387058i
$105$	−325.259	+	1147.94i	−0.302305	+	1.06693i
$106$	−222.807	+	685.731i	−0.204160	+	0.628340i
$107$	−1081.01			−0.976683			−0.488342	−	0.872653i	$-0.662398\pi$
$107$	−1081.01			−0.976683			−0.488342	+	0.872653i	$0.662398\pi$
$108$	204.064	−	628.043i	0.181815	−	0.559569i
$109$	−1031.20	+	749.212i	−0.906158	+	0.658362i	−0.940040	−	0.341064i	$-0.889213\pi$
$109$	−1031.20	+	749.212i	−0.906158	+	0.658362i	0.0338823	+	0.999426i	$0.489213\pi$
$110$	−400.863	+	1414.77i	−0.347462	+	1.22630i
$111$	−446.408	−	324.334i	−0.381722	−	0.277337i
$112$	809.404	−	588.067i	0.682871	−	0.496135i
$113$	227.388	−	165.207i	0.189300	−	0.137535i	−0.489099	−	0.872228i	$-0.662674\pi$
$113$	227.388	−	165.207i	0.189300	−	0.137535i	0.678399	+	0.734694i	$0.262674\pi$
$114$	−3853.11	−	2799.44i	−3.16558	−	2.29993i
$115$	−412.036	−	1121.06i	−0.334109	−	0.909042i
$116$	−357.900	+	260.029i	−0.286467	+	0.208130i
$117$	−452.071	+	1391.33i	−0.357214	+	1.09939i
$118$	1126.89			0.879142
$119$	−72.7457	+	223.888i	−0.0560386	+	0.172469i
$120$	−1070.69	−	717.296i	−0.814503	−	0.545666i
$121$	29.7771	+	91.6445i	0.0223720	+	0.0688539i
$122$	−294.906	−	907.627i	−0.218848	−	0.673546i
$123$	2608.87	+	1895.45i	1.91247	+	1.38949i
$124$	−29.1828			−0.0211346
$125$	−277.640	+	1369.69i	−0.198663	+	0.980068i
$126$	1993.93			1.40979
$127$	157.590	+	114.496i	0.110109	+	0.0799990i	0.641477	−	0.767142i	$-0.278322\pi$
$127$	157.590	+	114.496i	0.110109	+	0.0799990i	−0.531368	+	0.847141i	$0.678322\pi$
$128$	471.518	+	1451.18i	0.325600	+	1.00209i
$129$	−619.296	−	1906.00i	−0.422682	−	1.30088i
$130$	−1033.06	−	692.085i	−0.696964	−	0.466922i
$131$	766.106	−	2357.83i	0.510954	−	1.57256i	−0.279570	−	0.960125i	$-0.590192\pi$
$131$	766.106	−	2357.83i	0.510954	−	1.57256i	0.790524	−	0.612431i	$-0.209808\pi$
$132$	1327.69			0.875462
$133$	619.809	−	1907.58i	0.404092	−	1.24367i
$134$	398.567	−	289.576i	0.256947	−	0.186683i
$135$	−618.353	−	1682.41i	−0.394218	−	1.07258i
$136$	−205.714	−	149.460i	−0.129705	−	0.0942361i
$137$	1428.80	−	1038.08i	0.891027	−	0.647369i	−0.0451188	−	0.998982i	$-0.514367\pi$
$137$	1428.80	−	1038.08i	0.891027	−	0.647369i	0.936145	+	0.351613i	$0.114367\pi$
$138$	−2566.97	+	1865.01i	−1.58344	+	1.15044i
$139$	1897.81	+	1378.84i	1.15806	+	0.841379i	0.989531	−	0.144318i	$-0.0460987\pi$
$139$	1897.81	+	1378.84i	1.15806	+	0.841379i	0.168528	+	0.985697i	$0.446099\pi$
$140$	−157.030	+	554.209i	−0.0947961	+	0.334566i
$141$	−736.953	+	535.428i	−0.440160	+	0.319795i
$142$	−645.799	+	1987.56i	−0.381650	+	1.17460i
$143$	−1207.01			−0.705840
$144$	−1131.82	+	3483.38i	−0.654987	+	2.01584i
$145$	−327.346	+	1155.31i	−0.187480	+	0.661677i
$146$	−155.513	−	478.620i	−0.0881530	−	0.271307i
$147$	−491.819	−	1513.66i	−0.275949	−	0.849284i
$148$	−215.519	−	156.583i	−0.119699	−	0.0869667i
$149$	222.823			0.122513			0.0612563	−	0.998122i	$-0.480489\pi$
$149$	222.823			0.122513			0.0612563	+	0.998122i	$0.480489\pi$
$150$	3701.89	−	282.297i	2.01505	−	0.153663i
$151$	−1320.15			−0.711471			−0.355735	−	0.934587i	$-0.615770\pi$
$151$	−1320.15			−0.711471			−0.355735	+	0.934587i	$0.615770\pi$
$152$	1752.73	+	1273.43i	0.935297	+	0.679533i
$153$	−266.314	−	819.629i	−0.140720	−	0.433092i
$154$	508.367	+	1564.59i	0.266009	+	0.818692i
$155$	−62.2659	+	48.9640i	−0.0322666	+	0.0253734i
$156$	−346.942	+	1067.78i	−0.178062	+	0.548017i
$157$	−1708.75			−0.868620			−0.434310	−	0.900763i	$-0.643008\pi$
$157$	−1708.75			−0.868620			−0.434310	+	0.900763i	$0.643008\pi$
$158$	344.060	−	1058.91i	0.173240	−	0.533179i
$159$	1429.59	−	1038.66i	0.713042	−	0.518055i
$160$	−1582.44	−	1060.13i	−0.781892	−	0.523819i
$161$	−1081.04	−	785.423i	−0.529180	−	0.384472i
$162$	−370.255	+	269.006i	−0.179568	+	0.130464i
$163$	−1100.74	+	799.735i	−0.528937	+	0.384295i	−0.819960	−	0.572421i	$-0.806004\pi$
$163$	−1100.74	+	799.735i	−0.528937	+	0.384295i	0.291023	+	0.956716i	$0.406004\pi$
$164$	1259.52	+	915.094i	0.599707	+	0.435712i
$165$	2832.84	−	2227.65i	1.33658	−	1.05105i
$166$	3136.87	−	2279.07i	1.46668	−	1.06560i
$167$	901.420	−	2774.28i	0.417688	−	1.28551i	−0.492136	−	0.870518i	$-0.663784\pi$
$167$	901.420	−	2774.28i	0.417688	−	1.28551i	0.909824	−	0.414994i	$-0.136216\pi$
$168$	−1441.82			−0.662135
$169$	−363.505	+	1118.75i	−0.165455	+	0.509218i
$170$	731.988	−	27.8694i	0.330241	−	0.0125734i
$171$	2269.05	+	6983.42i	1.01473	+	3.12301i
$172$	−298.986	−	920.185i	−0.132544	−	0.407927i
$173$	−1432.40	−	1040.70i	−0.629499	−	0.457357i	0.226728	−	0.973958i	$-0.427197\pi$
$173$	−1432.40	−	1040.70i	−0.629499	−	0.457357i	−0.856226	+	0.516601i	$0.827197\pi$
$174$	3189.95			1.38982
$175$	594.824	+	1445.96i	0.256940	+	0.624595i
$176$	−3021.90			−1.29423
$177$	−2234.32	−	1623.33i	−0.948824	−	0.689361i
$178$	−58.1977	−	179.114i	−0.0245062	−	0.0754223i
$179$	−644.168	−	1982.55i	−0.268980	−	0.827835i	−0.990750	−	0.135702i	$-0.956671\pi$
$179$	−644.168	−	1982.55i	−0.268980	−	0.827835i	0.721770	−	0.692133i	$-0.243329\pi$
$180$	−727.476	−	1979.31i	−0.301238	−	0.819606i
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	−0.978906	−	0.204310i	$-0.934505\pi$
$181$	−162.821	+	501.111i	−0.0668639	+	0.205786i	0.912042	+	0.410096i	$0.134505\pi$
$182$	−1391.14			−0.566584
$183$	−722.751	+	2224.40i	−0.291953	+	0.898538i
$184$	1167.68	−	848.370i	0.467840	−	0.339906i
$185$	−722.562	+	27.5105i	−0.287156	+	0.0109330i
$186$	170.241	+	123.688i	0.0671113	+	0.0487592i
$187$	575.247	−	417.942i	0.224953	−	0.163438i
$188$	−355.789	+	258.496i	−0.138024	+	0.100281i
$189$	−1622.35	−	1178.70i	−0.624383	−	0.453641i
$190$	−6236.70	+	237.453i	−2.38136	+	0.0906667i
$191$	−1872.83	+	1360.69i	−0.709494	+	0.515478i	−0.883011	−	0.469353i	$-0.844487\pi$
$191$	−1872.83	+	1360.69i	−0.709494	+	0.515478i	0.173516	+	0.984831i	$0.444487\pi$
$192$	123.409	−	379.815i	0.0463870	−	0.142764i
$193$	2028.97			0.756727			0.378363	−	0.925657i	$-0.376487\pi$
$193$	2028.97			0.756727			0.378363	+	0.925657i	$0.376487\pi$
$194$	1415.01	−	4354.96i	0.523670	−	1.61169i
$195$	1051.30	+	2860.38i	0.386079	+	1.05044i
$196$	−237.442	−	730.772i	−0.0865314	−	0.266316i
$197$	815.098	+	2508.61i	0.294788	+	0.907265i	0.983292	+	0.182033i	$0.0582677\pi$
$197$	815.098	+	2508.61i	0.294788	+	0.907265i	−0.688504	+	0.725232i	$0.741732\pi$
$198$	−4872.36	−	3539.97i	−1.74880	−	1.27058i
$199$	594.340			0.211717			0.105858	−	0.994381i	$-0.466241\pi$
$199$	594.340			0.211717			0.105858	+	0.994381i	$0.466241\pi$
$200$	−1683.94	+	128.414i	−0.595364	+	0.0454011i
$201$	−1207.39			−0.423697
$202$	972.304	+	706.420i	0.338669	+	0.246057i
$203$	415.134	+	1277.65i	0.143531	+	0.441742i
$204$	−204.383	−	629.025i	−0.0701453	−	0.215885i
$205$	4222.75	−	160.775i	1.43868	−	0.0547757i
$206$	−1569.69	+	4831.00i	−0.530899	+	1.63394i
$207$	4891.82			1.64254
$208$	789.658	−	2430.32i	0.263235	−	0.810154i
$209$	−4901.23	+	3560.95i	−1.62213	+	1.17855i
$210$	3265.00	−	2567.49i	1.07289	−	0.843684i
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	0.808461	−	0.588550i	$-0.200301\pi$
$211$	1528.02	+	1110.17i	0.498545	+	0.362214i	−0.309916	+	0.950764i	$0.600301\pi$
$212$	690.182	−	501.446i	0.223594	−	0.162450i
$213$	4143.60	−	3010.51i	1.33293	−	0.968434i
$214$	3044.53	+	2211.98i	0.972523	+	0.706579i
$215$	−2181.85	−	1461.70i	−0.692098	−	0.463662i
$216$	1752.37	−	1273.17i	0.552008	−	0.401057i
$217$	−27.3850	+	84.2823i	−0.00856688	+	0.0263661i
$218$	4437.31			1.37859
$219$	−381.129	+	1173.00i	−0.117600	+	0.361935i
$220$	1367.65	−	1075.48i	0.419122	−	0.329584i
$221$	185.804	+	571.847i	0.0565546	+	0.174057i
$222$	593.594	+	1826.90i	0.179457	+	0.552312i
$223$	−1810.08	−	1315.10i	−0.543553	−	0.394914i	0.281850	−	0.959458i	$-0.409052\pi$
$223$	−1810.08	−	1315.10i	−0.543553	−	0.394914i	−0.825403	+	0.564544i	$0.809052\pi$
$224$	−2130.95			−0.635625
$225$	−4873.14	−	3002.57i	−1.44389	−	0.889651i
$226$	−978.462			−0.287993
$227$	1359.84	+	987.983i	0.397603	+	0.288875i	0.768564	−	0.639773i	$-0.220972\pi$
$227$	1359.84	+	987.983i	0.397603	+	0.288875i	−0.370961	+	0.928648i	$0.620972\pi$
$228$	1741.38	+	5359.43i	0.505815	+	1.55674i
$229$	1280.57	+	3941.19i	0.369531	+	1.13730i	0.947095	+	0.320953i	$0.104003\pi$
$229$	1280.57	+	3941.19i	0.369531	+	1.13730i	−0.577564	+	0.816345i	$0.695997\pi$
$230$	−1133.49	+	4000.46i	−0.324958	+	1.14688i
$231$	1245.90	−	3834.49i	0.354867	−	1.09217i
$232$	−1451.07			−0.410635
$233$	−1435.29	+	4417.38i	−0.403559	+	1.24203i	0.518534	+	0.855057i	$0.326478\pi$
$233$	−1435.29	+	4417.38i	−0.403559	+	1.24203i	−0.922093	+	0.386969i	$0.873522\pi$
$234$	4120.17	−	2993.48i	1.15104	−	0.836282i
$235$	−325.416	+	1148.50i	−0.0903310	+	0.318807i
$236$	−1078.69	−	783.717i	−0.297530	−	0.216168i
$237$	−2207.58	+	1603.90i	−0.605053	+	0.439596i
$238$	663.004	−	481.701i	0.180572	−	0.131193i
$239$	−2707.72	−	1967.27i	−0.732835	−	0.532436i	0.157624	−	0.987499i	$-0.449617\pi$
$239$	−2707.72	−	1967.27i	−0.732835	−	0.532436i	−0.890459	+	0.455063i	$0.849617\pi$
$240$	2632.07	+	7161.32i	0.707914	+	1.92609i
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.629222	−	0.777226i	$-0.283374\pi$
$241$	5847.12	−	4248.18i	1.56285	−	1.13548i	0.933626	−	0.358250i	$-0.116626\pi$
$242$	103.661	−	319.036i	0.0275355	−	0.0847455i
$243$	−3207.05			−0.846635
$244$	−348.933	+	1073.90i	−0.0915497	+	0.281761i
$245$	−1732.73	−	1160.82i	−0.451838	−	0.302703i
$246$	−3469.04	−	10676.6i	−0.899098	−	2.76714i
$247$	−1583.09	−	4872.26i	−0.407813	−	1.25512i
$248$	−77.4408	−	56.2640i	−0.0198286	−	0.0144063i
$249$	−9502.64			−2.41850
$250$	3584.62	−	3289.44i	0.906845	−	0.832171i
$251$	5546.43			1.39477			0.697386	−	0.716696i	$-0.254346\pi$
$251$	5546.43			1.39477			0.697386	+	0.716696i	$0.254346\pi$
$252$	−1908.65	−	1386.71i	−0.477117	−	0.346646i
$253$	1247.21	+	3838.51i	0.309926	+	0.953855i
$254$	−209.550	−	644.928i	−0.0517651	−	0.159317i
$255$	−1491.48	−	999.199i	−0.366275	−	0.245381i
$256$	1525.75	−	4695.77i	0.372497	−	1.14643i
$257$	−56.6174			−0.0137420			−0.00687100	−	0.999976i	$-0.502187\pi$
$257$	−56.6174			−0.0137420			−0.00687100	+	0.999976i	$0.502187\pi$
$258$	−2155.92	+	6635.23i	−0.520238	+	1.60113i
$259$	−654.466	+	475.498i	−0.157014	+	0.114077i
$260$	507.552	+	1380.94i	0.121066	+	0.329394i
$261$	−3978.78	−	2890.75i	−0.943603	−	0.685568i
$262$	−6982.29	+	5072.93i	−1.64644	+	1.19621i
$263$	5389.55	−	3915.74i	1.26363	−	0.918079i	0.264697	−	0.964332i	$-0.414728\pi$
$263$	5389.55	−	3915.74i	1.26363	−	0.918079i	0.998930	+	0.0462529i	$0.0147280\pi$
$264$	3523.23	+	2559.77i	0.821362	+	0.596754i
$265$	631.262	−	2227.92i	0.146333	−	0.516454i
$266$	−5648.94	+	4104.19i	−1.30210	+	0.946031i
$267$	−142.630	+	438.971i	−0.0326922	+	0.100616i
$268$	−582.911			−0.132862
$269$	1574.21	−	4844.92i	0.356807	−	1.09814i	−0.598147	−	0.801387i	$-0.704096\pi$
$269$	1574.21	−	4844.92i	0.356807	−	1.09814i	0.954954	−	0.296754i	$-0.0959040\pi$
$270$	−1701.06	+	6003.59i	−0.383420	+	1.35321i
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	0.961994	+	0.273072i	$0.0880396\pi$
$271$	1535.70	+	4726.39i	0.344232	+	1.05944i	−0.617762	+	0.786365i	$0.711960\pi$
$272$	465.185	+	1431.69i	0.103698	+	0.319151i
$273$	2758.26	+	2003.99i	0.611492	+	0.444275i
$274$	−6148.19			−1.35557
$275$	1113.61	−	4589.38i	0.244194	−	1.00636i
$276$	3754.23			0.818762
$277$	−4137.40	−	3006.00i	−0.897445	−	0.652032i	0.0403637	−	0.999185i	$-0.487148\pi$
$277$	−4137.40	−	3006.00i	−0.897445	−	0.652032i	−0.937808	+	0.347153i	$0.887148\pi$
$278$	−2523.55	−	7766.67i	−0.544432	−	1.67559i
$279$	−100.253	−	308.548i	−0.0215126	−	0.0662089i
$280$	−1485.21	+	1167.92i	−0.316993	+	0.249273i
$281$	208.142	−	640.597i	0.0441877	−	0.135996i	−0.926529	−	0.376224i	$-0.877222\pi$
$281$	208.142	−	640.597i	0.0441877	−	0.135996i	0.970716	+	0.240228i	$0.0772223\pi$
$282$	3171.14			0.669641
$283$	879.284	−	2706.16i	0.184693	−	0.568425i	−0.815250	−	0.579109i	$-0.803401\pi$
$283$	879.284	−	2706.16i	0.184693	−	0.568425i	0.999943	+	0.0106833i	$0.00340066\pi$
$284$	2000.47	−	1453.42i	0.417978	−	0.303679i
$285$	12707.7	+	8513.39i	2.64120	+	1.76944i
$286$	3399.39	+	2469.80i	0.702833	+	0.510638i
$287$	3824.79	−	2778.87i	0.786655	−	0.571538i
$288$	6311.27	−	4585.41i	1.29130	−	0.938187i
$289$	3688.14	+	2679.59i	0.750690	+	0.545408i
$290$	3285.94	−	2583.96i	0.665370	−	0.523226i
$291$	−9079.06	+	6596.32i	−1.82895	+	1.32881i
$292$	−184.003	+	566.303i	−0.0368766	+	0.113495i
$293$	208.321			0.0415367			0.0207684	−	0.999784i	$-0.493389\pi$
$293$	208.321			0.0415367			0.0207684	+	0.999784i	$0.493389\pi$
$294$	−1712.14	+	5269.41i	−0.339639	+	1.04530i
$295$	−3616.51	+	137.693i	−0.713766	+	0.0271756i
$296$	−270.019	−	831.032i	−0.0530220	−	0.163185i
$297$	1871.72	+	5760.56i	0.365684	+	1.12546i
$298$	−627.554	−	455.945i	−0.121991	−	0.0886314i
$299$	−3412.98			−0.660126
$300$	−3739.89	−	2304.32i	−0.719742	−	0.443467i
$301$	−2938.13			−0.562629
$302$	3718.04	+	2701.31i	0.708440	+	0.514712i
$303$	−910.191	−	2801.28i	−0.172571	−	0.531120i
$304$	−3963.48	−	12198.3i	−0.747766	−	2.30139i
$305$	1057.34	+	2876.79i	0.198501	+	0.540080i
$306$	−927.101	+	2853.32i	−0.173199	+	0.533051i
$307$	661.860			0.123044			0.0615218	−	0.998106i	$-0.480405\pi$
$307$	661.860			0.123044			0.0615218	+	0.998106i	$0.480405\pi$
$308$	601.501	−	1851.23i	0.111278	−	0.342479i
$309$	10071.5	−	7317.37i	1.85420	−	1.34715i
$310$	275.555	−	10.4914i	0.0504855	−	0.00192216i
$311$	7024.85	+	5103.86i	1.28085	+	0.930589i	0.999578	−	0.0290408i	$-0.00924527\pi$
$311$	7024.85	+	5103.86i	1.28085	+	0.930589i	0.281267	+	0.959629i	$0.409245\pi$
$312$	−2979.32	+	2164.60i	−0.540611	+	0.392777i
$313$	−3033.40	+	2203.89i	−0.547788	+	0.397992i	−0.826969	−	0.562247i	$-0.809937\pi$
$313$	−3033.40	+	2203.89i	−0.547788	+	0.397992i	0.279181	+	0.960238i	$0.409937\pi$
$314$	4812.50	+	3496.48i	0.864920	+	0.628401i
$315$	−6399.06	+	243.635i	−1.14459	+	0.0435787i
$316$	−1065.78	+	774.336i	−0.189731	+	0.137848i
$317$	−1932.02	+	5946.15i	−0.342313	+	1.05353i	0.620694	+	0.784053i	$0.286851\pi$
$317$	−1932.02	+	5946.15i	−0.342313	+	1.05353i	−0.963007	+	0.269477i	$0.913149\pi$
$318$	−6151.58			−1.08479
$319$	1253.89	−	3859.09i	0.220077	−	0.677327i
$320$	−180.539	−	491.210i	−0.0315389	−	0.0858108i
$321$	−2850.04	−	8771.52i	−0.495557	−	1.52517i
$322$	1437.48	+	4424.10i	0.248781	+	0.765668i
$323$	2441.57	+	1773.90i	0.420596	+	0.305581i
$324$	541.504			0.0928505
$325$	3399.94	+	2094.86i	0.580291	+	0.357545i
$326$	4736.54			0.804701
$327$	−8797.98	−	6392.10i	−1.48786	−	1.08099i
$328$	1578.03	+	4856.66i	0.265646	+	0.817574i
$329$	412.686	+	1270.12i	0.0691554	+	0.212839i
$330$	−12536.6	+	477.313i	−2.09126	+	0.0796219i
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	0.730553	+	0.682856i	$0.239262\pi$
$331$	−1576.86	+	4853.08i	−0.261849	+	0.805890i	−0.992402	+	0.123034i	$0.960738\pi$
$332$	−4587.72			−0.758386
$333$	915.163	−	2816.58i	0.150602	−	0.463507i
$334$	−8215.53	+	5968.93i	−1.34591	+	0.977861i
$335$	−1243.73	+	978.028i	−0.202842	+	0.159509i
$336$	6905.65	+	5017.25i	1.12123	+	0.814623i
$337$	4227.20	−	3071.24i	0.683294	−	0.496442i	−0.191155	−	0.981560i	$-0.561223\pi$
$337$	4227.20	−	3071.24i	0.683294	−	0.496442i	0.874449	+	0.485118i	$0.161223\pi$
$338$	3312.98	−	2407.02i	0.533143	−	0.387351i
$339$	1940.03	+	1409.51i	0.310819	+	0.225823i
$340$	−720.063	−	482.397i	−0.114856	−	0.0769461i
$341$	216.551	−	157.333i	0.0343897	−	0.0249856i
$342$	7899.10	−	24310.9i	1.24893	−	3.84381i
$343$	−6623.65			−1.04269
$344$	980.700	−	3018.28i	0.153709	−	0.473067i
$345$	8010.22	−	6298.98i	1.25002	−	0.982974i
$346$	1904.68	+	5862.00i	0.295943	+	0.910818i
$347$	−243.163	−	748.379i	−0.0376187	−	0.115778i	0.930484	−	0.366333i	$-0.119387\pi$
$347$	−243.163	−	748.379i	−0.0376187	−	0.115778i	−0.968102	+	0.250555i	$0.919387\pi$
$348$	−3053.52	−	2218.51i	−0.470361	−	0.341737i
$349$	4031.08			0.618277			0.309138	−	0.951017i	$-0.399959\pi$
$349$	4031.08			0.618277			0.309138	+	0.951017i	$0.399959\pi$
$350$	1283.50	−	5289.51i	0.196017	−	0.807817i
$351$	−5121.94			−0.778886
$352$	5207.18	+	3783.24i	0.788477	+	0.572862i
$353$	730.568	+	2248.46i	0.110154	+	0.339018i	0.990905	−	0.134560i	$-0.0429621\pi$
$353$	730.568	+	2248.46i	0.110154	+	0.339018i	−0.880752	+	0.473578i	$0.842962\pi$
$354$	2971.01	+	9143.82i	0.446066	+	1.37285i
$355$	1829.69	−	6457.55i	0.273549	−	0.965440i
$356$	−68.8596	+	211.928i	−0.0102515	+	0.0315510i
$357$	−2008.46			−0.297757
$358$	−2242.50	+	6901.71i	−0.331061	+	1.01890i
$359$	3962.13	−	2878.66i	0.582488	−	0.423202i	−0.257132	−	0.966376i	$-0.582778\pi$
$359$	3962.13	−	2878.66i	0.582488	−	0.423202i	0.839620	+	0.543174i	$0.182778\pi$
$360$	1885.62	−	6654.94i	0.276058	−	0.974295i
$361$	−15253.6	−	11082.4i	−2.22388	−	1.61575i
$362$	1483.95	−	1078.15i	0.215455	−	0.156537i
$363$	−665.115	+	483.234i	−0.0961694	+	0.0698711i
$364$	1331.64	+	967.496i	0.191750	+	0.139315i
$365$	557.566	+	1517.02i	0.0799571	+	0.217547i
$366$	6587.15	−	4785.85i	0.940754	−	0.683498i
$367$	−3638.89	+	11199.3i	−0.517570	+	1.59292i	0.260986	+	0.965343i	$0.415952\pi$
$367$	−3638.89	+	11199.3i	−0.517570	+	1.59292i	−0.778556	+	0.627575i	$0.784048\pi$
$368$	−8544.82			−1.21041
$369$	−5348.33	+	16460.5i	−0.754534	+	2.32222i
$370$	2091.30	+	1401.04i	0.293842	+	0.196856i
$371$	−800.555	−	2463.85i	−0.112029	−	0.344790i
$372$	−76.9394	−	236.795i	−0.0107234	−	0.0330034i
$373$	−10144.8	−	7370.66i	−1.40826	−	1.02316i	−0.993573	−	0.113193i	$-0.963892\pi$
$373$	−10144.8	−	7370.66i	−1.40826	−	1.02316i	−0.414684	−	0.909966i	$-0.636108\pi$
$374$	−2475.32			−0.342234
$375$	−11845.9	+	1358.30i	−1.63125	+	0.187046i
$376$	−1442.51			−0.197851
$377$	2775.96	+	2016.85i	0.379228	+	0.275525i
$378$	2157.26	+	6639.35i	0.293538	+	0.903417i
$379$	1673.08	+	5149.21i	0.226755	+	0.697881i	0.998109	+	0.0614740i	$0.0195801\pi$
$379$	1673.08	+	5149.21i	0.226755	+	0.697881i	−0.771353	+	0.636407i	$0.780420\pi$
$380$	6135.09	+	4110.13i	0.828220	+	0.554855i
$381$	−513.562	+	1580.58i	−0.0690567	+	0.212535i
$382$	8058.88			1.07939
$383$	−4385.52	+	13497.2i	−0.585090	+	1.80072i	0.0138191	+	0.999905i	$0.495601\pi$
$383$	−4385.52	+	13497.2i	−0.585090	+	1.80072i	−0.598909	+	0.800817i	$0.704399\pi$
$384$	−10532.1	+	7651.99i	−1.39964	+	1.01690i
$385$	−1822.67	−	4959.09i	−0.241277	−	0.656465i
$386$	−5714.34	−	4151.71i	−0.753503	−	0.547452i
$387$	8701.93	−	6322.32i	1.14301	−	0.830443i
$388$	−4383.23	+	3184.60i	−0.573517	+	0.416685i
$389$	−191.659	−	139.248i	−0.0249807	−	0.0181495i	0.575225	−	0.817995i	$-0.304915\pi$
$389$	−191.659	−	139.248i	−0.0249807	−	0.0181495i	−0.600206	+	0.799846i	$0.704915\pi$
$390$	2892.09	−	10207.1i	0.375504	−	1.32527i
$391$	1626.59	−	1181.79i	0.210384	−	0.152853i
$392$	778.830	−	2396.99i	0.100349	−	0.308843i
$393$	21151.7			2.71492
$394$	2837.55	−	8733.07i	0.362826	−	1.11666i
$395$	−974.798	+	3440.37i	−0.124171	+	0.438238i
$396$	2202.03	+	6777.14i	0.279434	+	0.860010i
$397$	−3538.88	−	10891.6i	−0.447384	−	1.37691i	−0.879848	−	0.475255i	$-0.842356\pi$
$397$	−3538.88	−	10891.6i	−0.447384	−	1.37691i	0.432464	−	0.901651i	$-0.357644\pi$
$398$	−1673.89	−	1216.15i	−0.210815	−	0.153166i
$399$	17112.5			2.14711
$400$	8512.18	+	5244.76i	1.06402	+	0.655595i
$401$	13344.5			1.66183			0.830915	−	0.556399i	$-0.187818\pi$
$401$	13344.5			1.66183			0.830915	+	0.556399i	$0.187818\pi$
$402$	3400.48	+	2470.59i	0.421892	+	0.306522i
$403$	69.9457	+	215.271i	0.00864576	+	0.0266089i
$404$	−439.426	−	1352.41i	−0.0541145	−	0.166547i
$405$	1155.38	−	908.555i	0.141756	−	0.111473i
$406$	1445.18	−	4447.81i	0.176658	−	0.543697i
$407$	2443.44			0.297584
$408$	670.392	−	2063.25i	0.0813464	−	0.250358i
$409$	6080.01	−	4417.39i	0.735055	−	0.534048i	−0.156104	−	0.987741i	$-0.549893\pi$
$409$	6080.01	−	4417.39i	0.735055	−	0.534048i	0.891158	+	0.453692i	$0.149893\pi$
$410$	−12221.8	−	8187.87i	−1.47218	−	0.986268i
$411$	12190.2	+	8856.70i	1.46301	+	1.06294i
$412$	4862.36	−	3532.71i	0.581435	−	0.422437i
$413$	−3275.68	+	2379.92i	−0.390280	+	0.283555i
$414$	−13777.2	−	10009.7i	−1.63554	−	1.18829i
$415$	−9788.60	+	7697.45i	−1.15784	+	0.910489i
$416$	−4403.31	+	3199.19i	−0.518967	+	0.377051i
$417$	−6184.67	+	19034.5i	−0.726294	+	2.23530i
$418$	21090.2			2.46784
$419$	−1980.00	+	6093.82i	−0.230858	+	0.710507i	0.766786	+	0.641903i	$0.221855\pi$
$419$	−1980.00	+	6093.82i	−0.230858	+	0.710507i	−0.997644	+	0.0686047i	$0.978145\pi$
$420$	−4910.96	+	186.978i	−0.570548	+	0.0217228i
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	0.728924	+	0.684594i	$0.240021\pi$
$421$	4678.50	+	14399.0i	0.541607	+	1.66689i	−0.187318	+	0.982299i	$0.559979\pi$
$422$	−2031.83	−	6253.32i	−0.234378	−	0.721343i
$423$	−3955.32	−	2873.71i	−0.454644	−	0.330318i
$424$	2798.28			0.320510
$425$	−2345.75	+	178.881i	−0.267730	+	0.0204165i
$426$	−17830.1			−2.02787
$427$	2774.09	+	2015.49i	0.314397	+	0.228423i
$428$	−1375.95	−	4234.75i	−0.155395	−	0.478258i
$429$	−3182.23	−	9793.90i	−0.358134	−	1.10222i
$430$	3153.96	+	8581.26i	0.353715	+	0.962384i
$431$	3787.43	−	11656.5i	0.423281	−	1.30272i	−0.481350	−	0.876528i	$-0.659853\pi$
$431$	3787.43	−	11656.5i	0.423281	−	1.30272i	0.904631	−	0.426196i	$-0.140147\pi$
$432$	−12823.4			−1.42817
$433$	3856.48	−	11869.0i	0.428016	−	1.31730i	−0.472061	−	0.881566i	$-0.656490\pi$
$433$	3856.48	−	11869.0i	0.428016	−	1.31730i	0.900077	−	0.435731i	$-0.143510\pi$
$434$	249.586	−	181.335i	0.0276049	−	0.0200561i
$435$	−10237.4	+	389.775i	−1.12838	+	0.0429616i
$436$	−4247.52	−	3086.01i	−0.466558	−	0.338974i
$437$	−13858.9	+	10069.1i	−1.51707	+	1.10222i
$438$	3473.61	−	2523.72i	0.378939	−	0.275316i
$439$	−13041.9	−	9475.47i	−1.41789	−	1.03016i	−0.992115	−	0.125330i	$-0.960001\pi$
$439$	−13041.9	−	9475.47i	−1.41789	−	1.03016i	−0.425776	−	0.904828i	$-0.639999\pi$
$440$	5702.75	−	217.124i	0.617881	−	0.0235249i
$441$	6910.70	−	5020.92i	0.746215	−	0.542157i
$442$	646.829	−	1990.73i	0.0696075	−	0.214230i
$443$	−11988.6			−1.28577			−0.642885	−	0.765963i	$-0.722263\pi$
$443$	−11988.6			−1.28577			−0.642885	+	0.765963i	$0.722263\pi$
$444$	702.342	−	2161.59i	0.0750713	−	0.231046i
$445$	208.658	+	567.715i	0.0222277	+	0.0604770i
$446$	2406.89	+	7407.66i	0.255538	+	0.786464i
$447$	587.464	+	1808.03i	0.0621613	+	0.191313i
$448$	−473.673	−	344.144i	−0.0499530	−	0.0362930i
$449$	768.211			0.0807442			0.0403721	−	0.999185i	$-0.487146\pi$
$449$	768.211			0.0807442			0.0403721	+	0.999185i	$0.487146\pi$
$450$	7580.68	+	18427.9i	0.794126	+	1.93044i
$451$	−14279.8			−1.49093
$452$	936.613	+	680.490i	0.0974659	+	0.0708131i
$453$	−3480.52	−	10711.9i	−0.360991	−	1.11102i
$454$	−1808.20	−	5565.07i	−0.186923	−	0.575290i
$455$	4464.56	−	169.982i	0.460004	−	0.0175140i
$456$	−5711.88	+	17579.4i	−0.586586	+	1.80533i
$457$	13017.8			1.33249			0.666246	−	0.745732i	$-0.267900\pi$
$457$	13017.8			1.33249			0.666246	+	0.745732i	$0.267900\pi$
$458$	4457.97	−	13720.2i	0.454819	−	1.39979i
$459$	2441.06	−	1773.54i	0.248233	−	0.180352i
$460$	3867.21	−	3041.05i	0.391977	−	0.308238i
$461$	−12600.2	−	9154.58i	−1.27299	−	0.924883i	−0.273675	−	0.961822i	$-0.588239\pi$
$461$	−12600.2	−	9154.58i	−1.27299	−	0.924883i	−0.999318	+	0.0369393i	$0.988239\pi$
$462$	−11355.1	+	8249.98i	−1.14348	+	0.830788i
$463$	−3292.54	+	2392.17i	−0.330491	+	0.240116i	−0.740639	−	0.671903i	$-0.765477\pi$
$463$	−3292.54	+	2392.17i	−0.330491	+	0.240116i	0.410148	+	0.912019i	$0.365477\pi$
$464$	6949.96	+	5049.44i	0.695353	+	0.505203i
$465$	−561.465	−	376.146i	−0.0559942	−	0.0375126i
$466$	13081.3	−	9504.09i	1.30038	−	0.944782i
$467$	153.591	−	472.706i	0.0152192	−	0.0468399i	−0.943159	−	0.332343i	$-0.892161\pi$
$467$	153.591	−	472.706i	0.0152192	−	0.0468399i	0.958378	+	0.285503i	$0.0921608\pi$
$468$	−6025.82			−0.595179
$469$	−547.000	+	1683.49i	−0.0538552	+	0.165749i
$470$	3266.57	−	2568.73i	0.320586	−	0.252099i
$471$	−4505.06	−	13865.2i	−0.440727	−	1.35642i
$472$	−1351.47	−	4159.41i	−0.131794	−	0.405619i
$473$	7179.62	+	5216.30i	0.697926	+	0.507073i
$474$	9499.30			0.920500
$475$	19986.3	−	1524.11i	1.93060	−	0.147223i
$476$	−969.655			−0.0933698
$477$	7672.78	+	5574.60i	0.736504	+	0.535101i
$478$	3600.49	+	11081.2i	0.344524	+	1.06034i
$479$	1404.36	+	4322.18i	0.133960	+	0.412287i	0.995427	−	0.0955270i	$-0.0304536\pi$
$479$	1404.36	+	4322.18i	0.133960	+	0.412287i	−0.861467	+	0.507814i	$0.830454\pi$
$480$	4430.10	−	15635.2i	0.421261	−	1.48676i
$481$	−638.500	+	1965.10i	−0.0605261	+	0.186280i
$482$	−25160.4			−2.37765
$483$	3522.95	−	10842.5i	0.331883	−	1.02143i
$484$	−321.107	+	233.298i	−0.0301566	+	0.0219100i
$485$	−4009.04	+	14149.2i	−0.375342	+	1.32470i
$486$	9032.26	+	6562.32i	0.843028	+	0.612496i
$487$	13359.2	−	9706.02i	1.24304	−	0.903125i	0.245247	−	0.969461i	$-0.421131\pi$
$487$	13359.2	−	9706.02i	1.24304	−	0.903125i	0.997797	+	0.0663359i	$0.0211309\pi$
$488$	−2996.41	+	2177.02i	−0.277954	+	0.201945i
$489$	−9391.27	−	6823.15i	−0.868482	−	0.630989i
$490$	2504.74	+	6814.87i	0.230923	+	0.628295i
$491$	1292.08	−	938.748i	0.118759	−	0.0862833i	−0.526821	−	0.849977i	$-0.676616\pi$
$491$	1292.08	−	938.748i	0.118759	−	0.0862833i	0.645579	+	0.763693i	$0.276616\pi$
$492$	−4104.58	+	12632.6i	−0.376115	+	1.15756i
$493$	−2021.35			−0.184659
$494$	−5511.12	+	16961.5i	−0.501937	+	1.54480i
$495$	16069.3	+	10765.4i	1.45911	+	0.977513i
$496$	175.118	+	538.958i	0.0158529	+	0.0487901i
$497$	−2320.38	−	7141.39i	−0.209423	−	0.644537i
$498$	26763.0	+	19444.5i	2.40819	+	1.74966i
$499$	−3319.59			−0.297806			−0.148903	−	0.988852i	$-0.547574\pi$
$499$	−3319.59			−0.297806			−0.148903	+	0.988852i	$0.547574\pi$
$500$	−5719.01	+	655.765i	−0.511524	+	0.0586534i
$501$	24887.6			2.21936
$502$	−15620.9	−	11349.2i	−1.38883	−	1.00904i
$503$	2028.57	+	6243.29i	0.179820	+	0.553429i	0.999821	−	0.0189337i	$-0.00602714\pi$
$503$	2028.57	+	6243.29i	0.179820	+	0.553429i	−0.820001	+	0.572362i	$0.806027\pi$
$504$	−2391.31	−	7359.68i	−0.211344	−	0.650449i
$505$	−3206.71	−	2148.29i	−0.282568	−	0.189302i
$506$	4341.83	−	13362.8i	0.381458	−	1.17401i
$507$	−10036.1			−0.879134
$508$	−247.940	+	763.080i	−0.0216546	+	0.0666461i
$509$	−12497.0	+	9079.59i	−1.08825	+	0.790660i	−0.979103	−	0.203366i	$-0.934812\pi$
$509$	−12497.0	+	9079.59i	−1.08825	+	0.790660i	−0.109147	+	0.994026i	$0.534812\pi$
$510$	2156.00	+	5866.02i	0.187194	+	0.509317i
$511$	1462.86	+	1062.83i	0.126640	+	0.0920095i
$512$	−4030.06	+	2928.01i	−0.347862	+	0.252736i
$513$	−20798.4	+	15110.9i	−1.79000	+	1.30051i
$514$	159.456	+	115.852i	0.0136835	+	0.00994162i
$515$	4447.27	−	15695.8i	0.380524	−	1.34299i
$516$	6678.30	−	4852.07i	0.569759	−	0.413954i
$517$	1246.50	−	3836.33i	0.106037	−	0.326348i
$518$	2816.20			0.238874
$519$	4667.97	−	14366.5i	0.394800	−	1.21507i
$520$	−1315.58	+	4643.08i	−0.110946	+	0.391563i
$521$	−2533.05	−	7795.93i	−0.213004	−	0.655559i	−0.999289	−	0.0376951i	$-0.987998\pi$
$521$	−2533.05	−	7795.93i	−0.213004	−	0.655559i	0.786285	−	0.617863i	$-0.212002\pi$
$522$	5290.64	+	16282.9i	0.443611	+	1.36529i
$523$	13281.5	+	9649.57i	1.11044	+	0.806781i	0.982733	−	0.185031i	$-0.0592387\pi$
$523$	13281.5	+	9649.57i	1.11044	+	0.806781i	0.127706	+	0.991812i	$0.459239\pi$
$524$	10211.7			0.851338
$525$	−10164.6	+	8638.73i	−0.844986	+	0.718143i
$526$	−23191.5			−1.92243
$527$	−107.876	−	78.3762i	−0.00891676	−	0.00647841i
$528$	−7967.12	−	24520.3i	−0.656675	−	2.02104i
$529$	−233.162	−	717.598i	−0.0191635	−	0.0589790i
$530$	−6336.69	+	4982.98i	−0.519336	+	0.408390i
$531$	4580.49	−	14097.3i	0.374343	−	1.15211i
$532$	8261.66			0.673287
$533$	3731.48	−	11484.3i	0.303242	−	0.933284i
$534$	1299.93	−	944.455i	0.105344	−	0.0765366i
$535$	−10041.0	−	6726.85i	−0.811423	−	0.543602i
$536$	−1546.84	−	1123.84i	−0.124651	−	0.0905646i
$537$	14388.4	−	10453.8i	1.15625	−	0.840066i
$538$	−14347.3	+	10423.9i	−1.14973	+	0.835331i
$539$	5701.75	+	4142.56i	0.455643	+	0.331044i
$540$	5803.62	−	4563.78i	0.462496	−	0.363692i
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.994468	−	0.105043i	$-0.966502\pi$
$541$	−15123.6	+	10987.9i	−1.20187	+	0.873212i	−0.207406	+	0.978255i	$0.566502\pi$
$542$	5346.12	−	16453.7i	0.423682	−	1.30396i
$543$	−4495.38			−0.355277
$544$	990.811	−	3049.40i	0.0780895	−	0.240335i
$545$	−14240.5	+	542.188i	−1.11926	+	0.0426143i
$546$	−3667.69	−	11288.0i	−0.287478	−	0.884765i
$547$	3698.27	+	11382.1i	0.289080	+	0.889695i	0.985146	+	0.171718i	$0.0549319\pi$
$547$	3698.27	+	11382.1i	0.289080	+	0.889695i	−0.696067	+	0.717977i	$0.745068\pi$
$548$	5885.23	+	4275.87i	0.458768	+	0.333314i
$549$	−12553.0			−0.975865
$550$	−12527.2	+	10646.7i	−0.971205	+	0.825415i
$551$	17222.3			1.33157
$552$	9962.39	+	7238.10i	0.768166	+	0.558105i
$553$	1236.22	+	3804.70i	0.0950623	+	0.292572i
$554$	5501.56	+	16932.0i	0.421911	+	1.29851i
$555$	−2128.23	−	5790.48i	−0.162772	−	0.442869i
$556$	−2985.86	+	9189.54i	−0.227750	+	0.700941i
$557$	−1182.53			−0.0899558			−0.0449779	−	0.998988i	$-0.514322\pi$
$557$	−1182.53			−0.0899558			−0.0449779	+	0.998988i	$0.514322\pi$
$558$	−349.005	+	1074.13i	−0.0264777	+	0.0814901i
$559$	−6071.25	+	4411.02i	−0.459367	+	0.333750i
$560$	11177.6	−	425.571i	0.843464	−	0.0321137i
$561$	4907.88	+	3565.78i	0.369360	+	0.268356i
$562$	−1897.01	+	1378.26i	−0.142385	+	0.103449i
$563$	6830.40	−	4962.58i	0.511310	−	0.371488i	−0.302011	−	0.953305i	$-0.597658\pi$
$563$	6830.40	−	4962.58i	0.511310	−	0.371488i	0.813320	+	0.581816i	$0.197658\pi$
$564$	−3035.51	−	2205.43i	−0.226628	−	0.164655i
$565$	3140.16	−	119.557i	0.233818	−	0.00890229i
$566$	−8013.79	+	5822.36i	−0.595132	+	0.432389i
$567$	508.144	−	1563.91i	0.0376368	−	0.115834i
$568$	8110.70			0.599150
$569$	1206.03	−	3711.79i	0.0888568	−	0.273473i	−0.896747	−	0.442543i	$-0.854076\pi$
$569$	1206.03	−	3711.79i	0.0888568	−	0.273473i	0.985604	+	0.169070i	$0.0540764\pi$
$570$	−18369.6	−	49979.7i	−1.34985	−	3.67267i
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	0.971880	−	0.235478i	$-0.0756656\pi$
$571$	644.040	+	1982.15i	0.0472018	+	0.145272i	−0.924678	+	0.380751i	$0.875666\pi$
$572$	−1536.33	−	4728.34i	−0.112303	−	0.345633i
$573$	−15978.6	−	11609.1i	−1.16495	−	0.846384i
$574$	−16458.2			−1.19678
$575$	3148.88	−	12977.1i	0.228378	−	0.941185i
$576$	2143.42			0.155051
$577$	5851.58	+	4251.42i	0.422192	+	0.306740i	0.778519	−	0.627621i	$-0.215971\pi$
$577$	5851.58	+	4251.42i	0.422192	+	0.306740i	−0.356327	+	0.934361i	$0.615971\pi$
$578$	−4904.17	−	15093.5i	−0.352918	−	1.08617i
$579$	5349.29	+	16463.4i	0.383954	+	1.18169i
$580$	−4942.47	+	188.177i	−0.353836	+	0.0134718i
$581$	−4305.09	+	13249.7i	−0.307410	+	0.946111i
$582$	39067.6			2.78248
$583$	−2418.04	+	7441.95i	−0.171775	+	0.528669i
$584$	−1580.10	+	1148.01i	−0.111961	+	0.0813443i
$585$	−12857.0	+	10110.3i	−0.908670	+	0.714549i
$586$	−586.712	−	426.271i	−0.0413598	−	0.0300497i
$587$	−8558.36	+	6218.01i	−0.601774	+	0.437214i	−0.846508	−	0.532376i	$-0.821299\pi$
$587$	−8558.36	+	6218.01i	−0.601774	+	0.437214i	0.244734	+	0.969590i	$0.421299\pi$
$588$	5303.62	−	3853.30i	0.371969	−	0.270251i
$589$	919.123	+	667.782i	0.0642985	+	0.0467156i
$590$	10467.2	+	7012.37i	0.730386	+	0.489313i
$591$	−18206.4	+	13227.7i	−1.26719	+	0.920670i
$592$	−1598.57	+	4919.88i	−0.110981	+	0.341564i
$593$	7485.02			0.518335			0.259168	−	0.965832i	$-0.416552\pi$
$593$	7485.02			0.518335			0.259168	+	0.965832i	$0.416552\pi$
$594$	6515.89	−	20053.9i	0.450085	−	1.38522i
$595$	−2068.90	+	1626.92i	−0.142549	+	0.112096i
$596$	283.618	+	872.888i	0.0194924	+	0.0599914i
$597$	1566.95	+	4822.59i	0.107422	+	0.330612i
$598$	9612.24	+	6983.70i	0.657314	+	0.477566i
$599$	16860.4			1.15008			0.575039	−	0.818126i	$-0.304987\pi$
$599$	16860.4			1.15008			0.575039	+	0.818126i	$0.304987\pi$
$600$	−5481.63	−	13325.3i	−0.372978	−	0.906671i
$601$	11032.4			0.748788			0.374394	−	0.927270i	$-0.377851\pi$
$601$	11032.4			0.748788			0.374394	+	0.927270i	$0.377851\pi$
$602$	8274.90	+	6012.07i	0.560232	+	0.407032i
$603$	−2002.50	−	6163.07i	−0.135238	−	0.416218i
$604$	−1680.34	−	5171.55i	−0.113199	−	0.348390i
$605$	−293.694	+	1036.54i	−0.0197362	+	0.0696552i
$606$	−3168.59	+	9751.91i	−0.212401	+	0.653704i
$607$	937.076			0.0626602			0.0313301	−	0.999509i	$-0.490026\pi$
$607$	937.076			0.0626602			0.0313301	+	0.999509i	$0.490026\pi$
$608$	−8441.92	+	25981.6i	−0.563101	+	1.73305i
$609$	−9272.63	+	6736.96i	−0.616988	+	0.448268i
$610$	2908.68	−	10265.7i	0.193064	−	0.681385i
$611$	2759.59	+	2004.96i	0.182718	+	0.132753i
$612$	2871.84	−	2086.52i	0.189685	−	0.137814i
$613$	17272.2	−	12549.0i	1.13804	−	0.826835i	0.151196	−	0.988504i	$-0.451688\pi$
$613$	17272.2	−	12549.0i	1.13804	−	0.826835i	0.986845	+	0.161669i	$0.0516876\pi$
$614$	−1864.05	−	1354.31i	−0.122519	−	0.0890156i
$615$	12437.7	+	33840.3i	0.815505	+	2.21882i
$616$	5165.31	−	3752.82i	0.337851	−	0.245463i
$617$	8530.27	−	26253.5i	0.556590	−	1.71301i	−0.135119	−	0.990829i	$-0.543142\pi$
$617$	8530.27	−	26253.5i	0.556590	−	1.71301i	0.691708	−	0.722177i	$-0.256858\pi$
$618$	−43338.1			−2.82090
$619$	3030.03	−	9325.47i	0.196748	−	0.605529i	−0.803204	−	0.595705i	$-0.796873\pi$
$619$	3030.03	−	9325.47i	0.196748	−	0.605529i	0.999952	−	0.00982399i	$-0.00312712\pi$
$620$	−271.066	−	181.597i	−0.0175585	−	0.0117631i
$621$	5292.53	+	16288.7i	0.342000	+	1.05257i
$622$	−9341.05	−	28748.8i	−0.602157	−	1.85325i
$623$	547.447	+	397.744i	0.0352055	+	0.0255783i
$624$	21802.0			1.39868
$625$	−11102.1	+	10994.7i	−0.710534	+	0.703663i
$626$	13052.8			0.833381
$627$	−41816.2	−	30381.2i	−2.66344	−	1.93510i
$628$	−2174.97	−	6693.88i	−0.138202	−	0.425342i
$629$	−376.138	−	1157.63i	−0.0238436	−	0.0733830i
$630$	18520.7	+	12407.7i	1.17124	+	0.784659i
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	−1.00000		0.000497352i	$-0.999842\pi$
$631$	−3022.55	+	9302.45i	−0.190691	+	0.586885i	0.809309	+	0.587383i	$0.199842\pi$
$632$	−4321.11			−0.271969
$633$	−4979.57	+	15325.5i	−0.312670	+	0.962300i
$634$	17608.4	−	12793.3i	1.10303	−	0.801397i
$635$	751.306	+	2044.15i	0.0469523	+	0.127747i
$636$	5888.47	+	4278.23i	0.367128	+	0.266734i
$637$	−4821.53	+	3503.04i	−0.299899	+	0.217890i
$638$	−11428.0	+	8302.91i	−0.709150	+	0.515228i
$639$	22239.3	+	16157.8i	1.37679	+	1.00030i
$640$	−4650.63	+	16413.6i	−0.287238	+	1.01375i
$641$	−18210.1	+	13230.4i	−1.12208	+	0.815242i	−0.984524	−	0.175251i	$-0.943926\pi$
$641$	−18210.1	+	13230.4i	−1.12208	+	0.815242i	−0.137561	+	0.990493i	$0.543926\pi$
$642$	−9921.66	+	30535.7i	−0.609932	+	1.87718i
$643$	−649.245			−0.0398192			−0.0199096	−	0.999802i	$-0.506338\pi$
$643$	−649.245			−0.0398192			−0.0199096	+	0.999802i	$0.506338\pi$
$644$	1700.82	−	5234.59i	0.104071	−	0.320298i
$645$	6108.18	−	21557.7i	0.372883	−	1.31602i
$646$	−3246.58	−	9991.96i	−0.197732	−	0.608558i
$647$	9808.83	+	30188.5i	0.596020	+	1.83436i	0.549584	+	0.835439i	$0.314786\pi$
$647$	9808.83	+	30188.5i	0.596020	+	1.83436i	0.0464360	+	0.998921i	$0.485214\pi$
$648$	1436.96	+	1044.01i	0.0871127	+	0.0632911i
$649$	12229.7			0.739688
$650$	−5288.96	−	12856.9i	−0.319154	−	0.775832i
$651$	−756.082			−0.0455195
$652$	−4533.95	−	3294.11i	−0.272336	−	0.197864i
$653$	−1670.26	−	5140.54i	−0.100096	−	0.308062i	0.888453	−	0.458968i	$-0.151781\pi$
$653$	−1670.26	−	5140.54i	−0.100096	−	0.308062i	−0.988548	+	0.150906i	$0.951781\pi$
$654$	11698.8	+	36005.2i	0.699478	+	2.15277i
$655$	21788.2	−	17133.6i	1.29975	−	1.02208i
$656$	9342.22	−	28752.4i	0.556025	−	1.71127i
$657$	−6619.60			−0.393083
$658$	1436.66	−	4421.58i	0.0851167	−	0.261962i
$659$	−2971.87	+	2159.19i	−0.175671	+	0.127633i	−0.672146	−	0.740418i	$-0.734627\pi$
$659$	−2971.87	+	2159.19i	−0.175671	+	0.127633i	0.496475	+	0.868051i	$0.334627\pi$
$660$	12332.4	+	8261.91i	0.727328	+	0.487264i
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	0.343698	−	0.939080i	$-0.388320\pi$
$661$	−7532.06	−	5472.36i	−0.443212	−	0.322012i	−0.786910	+	0.617068i	$0.788320\pi$
$662$	14371.5	−	10441.5i	0.843753	−	0.613023i
$663$	−4150.21	+	3015.31i	−0.243108	+	0.176629i
$664$	−12174.2	−	8845.06i	−0.711521	−	0.516950i
$665$	17627.5	−	13861.7i	1.02792	−	0.808322i
$666$	−8340.79	+	6059.94i	−0.485284	+	0.352579i
$667$	3545.55	−	10912.1i	0.205823	−	0.633460i
$668$	12015.4			0.695940
$669$	5898.79	−	18154.6i	0.340897	−	1.04917i
$670$	5504.07	−	209.559i	0.317374	−	0.0120836i
$671$	−3200.49	−	9850.10i	−0.184134	−	0.566705i
$672$	−5618.17	−	17290.9i	−0.322508	−	0.992578i
$673$	−25425.2	−	18472.5i	−1.45627	−	1.05804i	−0.984315	−	0.176422i	$-0.943548\pi$
$673$	−25425.2	−	18472.5i	−1.45627	−	1.05804i	−0.471958	−	0.881621i	$-0.656452\pi$
$674$	−18189.8			−1.03953
$675$	4725.61	−	19475.0i	0.269465	−	1.11051i
$676$	−4845.29			−0.275677
$677$	−6007.13	−	4364.44i	−0.341023	−	0.247768i	0.404070	−	0.914728i	$-0.367595\pi$
$677$	−6007.13	−	4364.44i	−0.341023	−	0.247768i	−0.745094	+	0.666960i	$0.767595\pi$
$678$	−2579.68	−	7939.43i	−0.146124	−	0.449723i
$679$	5084.19	+	15647.5i	0.287354	+	0.884384i
$680$	−980.737	−	2668.38i	−0.0553081	−	0.150482i
$681$	−4431.51	+	13638.8i	−0.249363	+	0.767459i
$682$	−931.827			−0.0523189
$683$	6948.13	−	21384.1i	0.389257	−	1.19801i	−0.544087	−	0.839029i	$-0.683124\pi$
$683$	6948.13	−	21384.1i	0.389257	−	1.19801i	0.933344	−	0.358982i	$-0.116876\pi$
$684$	−24468.7	+	17777.6i	−1.36781	+	0.993776i
$685$	19731.2	−	751.238i	1.10057	−	0.0419027i
$686$	18654.7	+	13553.4i	1.03825	+	0.754334i
$687$	−28603.4	+	20781.6i	−1.58848	+	1.15410i
$688$	−15200.1	+	11043.5i	−0.842296	+	0.611964i
$689$	−5353.22	−	3889.34i	−0.295996	−	0.215054i
$690$	−35448.9	+	1349.67i	−1.95582	+	0.0744651i
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	−0.497794	−	0.867295i	$-0.665857\pi$
$691$	3146.51	−	2286.07i	0.173225	−	0.125856i	0.671020	+	0.741439i	$0.265857\pi$
$692$	2253.62	−	6935.93i	0.123800	−	0.381018i
$693$	21639.3			1.18616
$694$	−846.508	+	2605.28i	−0.0463012	+	0.142500i
$695$	9047.75	+	24617.0i	0.493814	+	1.34357i
$696$	−3825.69	−	11774.3i	−0.208351	−	0.641239i
$697$	2198.20	+	6765.37i	0.119459	+	0.367656i
$698$	−11353.0	−	8248.47i	−0.615643	−	0.447291i
$699$	−39627.6			−2.14428
$700$	−4907.29	+	4170.64i	−0.264969	+	0.225193i
$701$	−12744.3			−0.686655			−0.343327	−	0.939216i	$-0.611554\pi$
$701$	−12744.3			−0.686655			−0.343327	+	0.939216i	$0.611554\pi$
$702$	14425.3	+	10480.6i	0.775568	+	0.563483i
$703$	3204.78	+	9863.29i	0.171935	+	0.529162i
$704$	546.482	+	1681.90i	0.0292561	+	0.0900410i
$705$	−10177.1	+	387.477i	−0.543674	+	0.0206996i
$706$	2543.28	−	7827.41i	0.135577	−	0.417264i
$707$	−4318.23			−0.229708
$708$	3515.30	−	10819.0i	0.186600	−	0.574297i
$709$	12309.4	−	8943.33i	0.652032	−	0.473729i	−0.211931	−	0.977285i	$-0.567975\pi$
$709$	12309.4	−	8943.33i	0.652032	−	0.473729i	0.863963	+	0.503556i	$0.167975\pi$
$710$	−18366.7	+	14443.0i	−0.970829	+	0.763430i
$711$	−11848.3	−	8608.32i	−0.624961	−	0.454061i
$712$	−591.322	+	429.621i	−0.0311246	+	0.0226134i
$713$	612.326	−	444.881i	0.0321624	−	0.0233673i
$714$	5656.60	+	4109.76i	0.296489	+	0.215412i
$715$	−11211.4	−	7510.91i	−0.586408	−	0.392856i
$716$	6946.51	−	5046.93i	0.362574	−	0.263426i
$717$	8824.03	−	27157.6i	0.459609	−	1.41453i
$718$	−17049.2			−0.886172
$719$	4155.65	−	12789.8i	0.215549	−	0.663392i	−0.783565	−	0.621310i	$-0.786601\pi$
$719$	4155.65	−	12789.8i	0.215549	−	0.663392i	0.999114	−	0.0420821i	$-0.0133991\pi$
$720$	−32189.1	+	25312.5i	−1.66614	+	1.31020i
$721$	−5639.94	−	17358.0i	−0.291321	−	0.896593i
$722$	20282.9	+	62424.5i	1.04550	+	3.21773i
$723$	49886.3	+	36244.5i	2.56610	+	1.86438i
$724$	−2170.30			−0.111407
$725$	−10229.8	+	8694.16i	−0.524033	+	0.445369i
$726$	2862.02			0.146308
$727$	23307.2	+	16933.7i	1.18902	+	0.863871i	0.993160	−	0.116761i	$-0.0372513\pi$
$727$	23307.2	+	16933.7i	1.18902	+	0.863871i	0.195857	+	0.980633i	$0.437251\pi$
$728$	1668.39	+	5134.77i	0.0849377	+	0.261411i
$729$	−9552.13	−	29398.4i	−0.485298	−	1.49360i
$730$	1533.84	−	5413.41i	0.0777671	−	0.274465i
$731$	1366.12	−	4204.49i	0.0691215	−	0.212734i
$732$	−9633.82			−0.486443
$733$	−4508.60	+	13876.0i	−0.227188	+	0.699213i	0.770874	+	0.636988i	$0.219820\pi$
$733$	−4508.60	+	13876.0i	−0.227188	+	0.699213i	−0.998062	+	0.0622256i	$0.980180\pi$
$734$	33164.8	−	24095.6i	1.66776	−	1.21170i
$735$	4850.86	−	17120.2i	0.243437	−	0.859168i
$736$	14724.0	+	10697.6i	0.737410	+	0.535760i
$737$	4325.48	−	3142.65i	0.216189	−	0.157070i
$738$	48744.6	−	35415.1i	2.43132	−	1.76646i
$739$	−836.136	−	607.488i	−0.0416208	−	0.0302393i	0.566780	−	0.823869i	$-0.308189\pi$
$739$	−836.136	−	607.488i	−0.0416208	−	0.0302393i	−0.608401	+	0.793630i	$0.708189\pi$
$740$	−1027.48	−	2795.55i	−0.0510416	−	0.138874i
$741$	35360.7	−	25691.1i	1.75305	−	1.27366i
$742$	−2786.92	+	8577.26i	−0.137885	+	0.424368i
$743$	−3409.57			−0.168351			−0.0841756	−	0.996451i	$-0.526826\pi$
$743$	−3409.57			−0.168351			−0.0841756	+	0.996451i	$0.526826\pi$
$744$	252.367	−	776.707i	0.0124358	−	0.0382735i
$745$	2069.71	+	1386.57i	0.101783	+	0.0681880i
$746$	13489.7	+	41517.1i	0.662056	+	2.03760i
$747$	−15760.5	−	48505.7i	−0.771947	−	2.37581i
$748$	2369.45	+	1721.50i	0.115823	+	0.0841503i
$749$	−13521.5			−0.659632
$750$	36141.9	+	20413.8i	1.75962	+	0.993876i
$751$	−19553.4			−0.950087			−0.475043	−	0.879962i	$-0.657568\pi$
$751$	−19553.4			−0.950087			−0.475043	+	0.879962i	$0.657568\pi$
$752$	6908.98	+	5019.66i	0.335032	+	0.243415i
$753$	14623.0	+	45004.9i	0.707690	+	2.17805i
$754$	−3691.23	−	11360.4i	−0.178285	−	0.548703i
$755$	−12262.3	−	8214.95i	−0.591086	−	0.395990i
$756$	2552.47	−	7855.69i	0.122794	−	0.377922i
$757$	12295.8			0.590353			0.295176	−	0.955443i	$-0.404622\pi$
$757$	12295.8			0.590353			0.295176	+	0.955443i	$0.404622\pi$
$758$	5824.38	−	17925.6i	0.279091	−	0.858954i
$759$	−27858.2	+	20240.2i	−1.33227	+	0.967948i
$760$	8356.08	+	22735.2i	0.398825	+	1.08512i
$761$	1950.66	+	1417.24i	0.0929190	+	0.0675096i	0.633275	−	0.773927i	$-0.281710\pi$
$761$	1950.66	+	1417.24i	0.0929190	+	0.0675096i	−0.540356	+	0.841437i	$0.681710\pi$
$762$	4680.60	−	3400.66i	0.222520	−	0.161670i
$763$	−12898.5	+	9371.29i	−0.612000	+	0.444644i
$764$	−7714.20	−	5604.70i	−0.365301	−	0.265407i
$765$	2626.68	−	9270.38i	0.124141	−	0.438133i
$766$	39969.6	−	29039.6i	1.88533	−	1.36977i
$767$	−3195.76	+	9835.54i	−0.150446	+	0.463026i
$768$	42125.0			1.97924
$769$	−8608.70	+	26494.8i	−0.403690	+	1.24243i	0.518294	+	0.855202i	$0.326567\pi$
$769$	−8608.70	+	26494.8i	−0.403690	+	1.24243i	−0.921984	+	0.387227i	$0.873433\pi$
$770$	−5014.08	+	17696.3i	−0.234669	+	0.828219i
$771$	−149.270	−	459.404i	−0.00697252	−	0.0214592i
$772$	2582.55	+	7948.28i	0.120399	+	0.370551i
$773$	20165.3	+	14651.0i	0.938287	+	0.681705i	0.948008	−	0.318247i	$-0.103094\pi$
$773$	20165.3	+	14651.0i	0.938287	+	0.681705i	−0.00972064	+	0.999953i	$0.503094\pi$
$774$	−37444.8			−1.73892
$775$	−883.051	+	67.3394i	−0.0409292	+	0.00312117i
$776$	−17771.4			−0.822107
$777$	−5583.76	−	4056.84i	−0.257807	−	0.187308i
$778$	254.851	+	784.352i	0.0117440	+	0.0361444i
$779$	−18729.1	−	57642.4i	−0.861414	−	2.65116i
$780$	−9867.11	+	7759.19i	−0.452948	+	0.356184i
$781$	−7008.59	+	21570.2i	−0.321110	+	0.988276i
$782$	−6999.28			−0.320069
$783$	5320.90	−	16376.0i	0.242852	−	0.747423i
$784$	−12071.3	+	8770.32i	−0.549895	+	0.399522i
$785$	−15871.9	−	10633.1i	−0.721644	−	0.483456i
$786$	−59571.3	−	43281.1i	−2.70336	−	1.96410i
$787$	−10460.2	+	7599.80i	−0.473782	+	0.344223i	−0.798913	−	0.601446i	$-0.794592\pi$
$787$	−10460.2	+	7599.80i	−0.473782	+	0.344223i	0.325131	+	0.945669i	$0.394592\pi$
$788$	−8789.76	+	6386.13i	−0.397363	+	0.288701i
$789$	45982.4	+	33408.2i	2.07480	+	1.50743i
$790$	9785.15	−	7694.74i	0.440684	−	0.346540i
$791$	2844.22	−	2066.45i	0.127849	−	0.0928880i
$792$	−7222.82	+	22229.6i	−0.324055	+	0.997340i
$793$	8758.12			0.392194
$794$	−12319.7	+	37916.1i	−0.550641	+	1.69470i
$795$	19742.1	−	751.652i	0.880730	−	0.0335325i
$796$	756.501	+	2328.27i	0.0336852	+	0.103673i
$797$	4001.08	+	12314.1i	0.177824	+	0.547285i	0.999751	−	0.0223070i	$-0.00710112\pi$
$797$	4001.08	+	12314.1i	0.177824	+	0.547285i	−0.821927	+	0.569592i	$0.807101\pi$
$798$	−48195.4	−	35016.0i	−2.13797	−	1.55333i
$799$	−2009.43			−0.0889719
$800$	−8101.62	−	19694.2i	−0.358045	−	0.870371i
$801$	−2477.26			−0.109275
$802$	−37583.2	−	27305.8i	−1.65475	−	1.20225i
$803$	−1687.72	−	5194.26i	−0.0741697	−	0.228271i
$804$	−1536.82	−	4729.85i	−0.0674123	−	0.207474i
$805$	−5153.83	−	14022.5i	−0.225650	−	0.613948i
$806$	243.497	−	749.408i	0.0106412	−	0.0327503i
$807$	43462.9			1.89587
$808$	1441.35	−	4436.03i	0.0627557	−	0.193142i
$809$	7492.76	−	5443.81i	0.325626	−	0.236581i	−0.412946	−	0.910755i	$-0.635500\pi$
$809$	7492.76	−	5443.81i	0.325626	−	0.236581i	0.738572	+	0.674174i	$0.235500\pi$
$810$	−5113.09	+	194.674i	−0.221797	+	0.00844461i
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	0.645545	−	0.763722i	$-0.276630\pi$
$811$	2741.13	+	1991.55i	0.118686	+	0.0862303i	−0.526859	+	0.849953i	$0.676630\pi$
$812$	−4476.68	+	3252.50i	−0.193474	+	0.140567i
$813$	−34302.0	+	24921.9i	−1.47973	+	1.07509i
$814$	−6881.65	−	4999.81i	−0.296317	−	0.215287i
$815$	−15200.8	+	578.750i	−0.653328	+	0.0248745i
$816$	−10390.6	+	7549.20i	−0.445764	+	0.323866i
$817$	−11639.6	+	35823.2i	−0.498433	+	1.53402i
$818$	−26162.6			−1.11828
$819$	−5654.60	+	17403.1i	−0.241255	+	0.742506i
$820$	6004.71	+	16337.6i	0.255724	+	0.695772i
$821$	3816.58	+	11746.2i	0.162241	+	0.499325i	0.998822	−	0.0485169i	$-0.0154495\pi$
$821$	3816.58	+	11746.2i	0.162241	+	0.499325i	−0.836582	+	0.547842i	$0.815449\pi$
$822$	−16209.5	−	49887.6i	−0.687798	−	2.11683i
$823$	−23545.0	−	17106.4i	−0.997239	−	0.724536i	−0.0357442	−	0.999361i	$-0.511380\pi$
$823$	−23545.0	−	17106.4i	−0.997239	−	0.724536i	−0.961494	+	0.274825i	$0.911380\pi$
$824$	19714.0			0.833457
$825$	40175.1	−	3063.66i	1.69541	−	0.129288i
$826$	14095.4			0.593754
$827$	6507.78	+	4728.18i	0.273637	+	0.198809i	0.716137	−	0.697959i	$-0.245908\pi$
$827$	6507.78	+	4728.18i	0.273637	+	0.198809i	−0.442500	+	0.896768i	$0.645908\pi$
$828$	6226.52	+	19163.3i	0.261336	+	0.804311i
$829$	7849.09	+	24157.0i	0.328842	+	1.01207i	0.969676	+	0.244393i	$0.0785886\pi$
$829$	7849.09	+	24157.0i	0.328842	+	1.01207i	−0.640834	+	0.767679i	$0.721411\pi$
$830$	43319.1	−	1649.31i	1.81160	−	0.0689740i
$831$	13483.1	−	41496.9i	0.562846	−	1.73226i
$832$	−1495.44			−0.0623139
$833$	1084.92	−	3339.03i	0.0451262	−	0.138884i
$834$	56367.1	−	40953.1i	2.34033	−	1.70035i
$835$	25636.6	−	20159.8i	1.06250	−	0.835519i
$836$	−20188.2	−	14667.6i	−0.835195	−	0.606805i
$837$	918.933	−	667.644i	0.0379486	−	0.0275713i
$838$	18045.7	−	13111.0i	0.743889	−	0.540467i
$839$	−26598.5	−	19324.9i	−1.09450	−	0.795198i	−0.114343	−	0.993441i	$-0.536476\pi$
$839$	−26598.5	−	19324.9i	−1.09450	−	0.795198i	−0.980153	+	0.198243i	$0.936476\pi$
$840$	−13392.4	−	8972.08i	−0.550098	−	0.368531i
$841$	10399.0	−	7555.31i	0.426380	−	0.309784i
$842$	16287.0	−	50126.2i	0.666611	−	2.05162i
$843$	5746.69			0.234788
$844$	−2404.06	+	7398.93i	−0.0980463	+	0.301756i
$845$	−10338.2	+	8129.60i	−0.420880	+	0.330967i
$846$	5259.44	+	16186.9i	0.213739	+	0.657822i
$847$	372.458	+	1146.31i	0.0151096	+	0.0465025i
$848$	−13402.5	−	9737.46i	−0.542739	−	0.394323i
$849$	24276.5			0.981351
$850$	6972.54	+	4296.11i	0.281360	+	0.173359i
$851$	6909.15			0.278311
$852$	17067.5	+	12400.3i	0.686295	+	0.498623i
$853$	−2870.65	−	8834.96i	−0.115228	−	0.354635i	0.876767	−	0.480916i	$-0.159696\pi$
$853$	−2870.65	−	8834.96i	−0.115228	−	0.354635i	−0.991994	+	0.126281i	$0.959696\pi$
$854$	−3688.74	−	11352.8i	−0.147806	−	0.454899i
$855$	−22379.9	+	78985.6i	−0.895176	+	3.15936i
$856$	4513.24	−	13890.3i	0.180210	−	0.554628i
$857$	−39874.7			−1.58937			−0.794687	−	0.607019i	$-0.792365\pi$
$857$	−39874.7			−1.58937			−0.794687	+	0.607019i	$0.792365\pi$
$858$	−11078.1	+	34094.9i	−0.440793	+	1.35662i
$859$	−22161.6	+	16101.3i	−0.880261	+	0.639547i	−0.933321	−	0.359044i	$-0.883103\pi$
$859$	−22161.6	+	16101.3i	−0.880261	+	0.639547i	0.0530595	+	0.998591i	$0.483103\pi$
$860$	2948.93	−	10407.7i	0.116928	−	0.412674i
$861$	32632.2	+	23708.7i	1.29164	+	0.938432i
$862$	−34518.6	+	25079.2i	−1.36393	+	0.990953i
$863$	26794.6	−	19467.4i	1.05689	−	0.767879i	0.0833829	−	0.996518i	$-0.473428\pi$
$863$	26794.6	−	19467.4i	1.05689	−	0.767879i	0.973511	+	0.228639i	$0.0734276\pi$
$864$	22096.7	+	16054.2i	0.870075	+	0.632146i
$865$	−6828.91	−	18580.1i	−0.268428	−	0.730336i
$866$	−35148.0	+	25536.5i	−1.37919	+	1.00204i
$867$	−12019.1	+	36990.9i	−0.470807	+	1.44899i
$868$	−365.024			−0.0142739
$869$	3733.95	−	11491.9i	0.145760	−	0.448603i
$870$	29630.1	+	19850.3i	1.15466	+	0.773549i
$871$	1397.13	+	4299.91i	0.0543511	+	0.167276i
$872$	−5321.64	−	16378.3i	−0.206667	−	0.636055i
$873$	−48728.5	−	35403.3i	−1.88913	−	1.37253i
$874$	59635.4			2.30801
$875$	−3472.78	+	17132.3i	−0.134173	+	0.661918i
$876$	−5080.21			−0.195941
$877$	−25574.8	−	18581.1i	−0.984719	−	0.715440i	−0.0259603	−	0.999663i	$-0.508264\pi$
$877$	−25574.8	−	18581.1i	−0.984719	−	0.715440i	−0.958758	+	0.284223i	$0.908264\pi$
$878$	17342.0	+	53373.0i	0.666586	+	2.05154i
$879$	549.231	+	1690.36i	0.0210752	+	0.0648629i
$880$	−28069.1	−	18804.5i	−1.07524	−	0.720342i
$881$	−13273.0	+	40850.2i	−0.507583	+	1.56218i	0.288803	+	0.957389i	$0.406743\pi$
$881$	−13273.0	+	40850.2i	−0.507583	+	1.56218i	−0.796385	+	0.604790i	$0.793257\pi$
$882$	−29737.1			−1.13526
$883$	−633.110	+	1948.51i	−0.0241289	+	0.0742612i	−0.962396	−	0.271651i	$-0.912430\pi$
$883$	−633.110	+	1948.51i	−0.0241289	+	0.0742612i	0.938267	+	0.345912i	$0.112430\pi$
$884$	−2003.66	+	1455.74i	−0.0762333	+	0.0553868i
$885$	−10652.0	−	28982.0i	−0.404593	−	1.10081i
$886$	33764.5	+	24531.3i	1.28029	+	0.930187i
$887$	9661.40	−	7019.42i	0.365725	−	0.265715i	−0.389711	−	0.920937i	$-0.627425\pi$
$887$	9661.40	−	7019.42i	0.365725	−	0.265715i	0.755436	+	0.655222i	$0.227425\pi$
$888$	6031.27	−	4381.97i	0.227923	−	0.165596i
$889$	1971.17	+	1432.14i	0.0743655	+	0.0540297i
$890$	574.010	−	2025.86i	0.0216189	−	0.0763000i
$891$	−4018.22	+	2919.41i	−0.151084	+	0.109769i
$892$	2847.84	−	8764.75i	0.106898	−	0.328997i
$893$	17120.8			0.641574
$894$	2045.10	−	6294.18i	0.0765083	−	0.235468i
$895$	6353.49	−	22423.5i	0.237289	−	0.837469i
$896$	5897.85	+	18151.7i	0.219903	+	0.676792i
$897$	−8998.18	−	27693.6i	−0.334939	−	1.03084i
$898$	−2163.57	−	1571.93i	−0.0804002	−	0.0584142i
$899$	−760.933			−0.0282297
$900$	5559.55	−	22911.8i	0.205909	−	0.848587i
$901$	3898.02			0.144131
$902$	40217.3	+	29219.6i	1.48458	+	1.07861i
$903$	−7746.28	−	23840.6i	−0.285471	−	0.878588i
$904$	1173.46	+	3611.55i	0.0431735	+	0.132874i
$905$	−4630.66	+	3641.40i	−0.170087	+	0.133751i
$906$	−12116.5	+	37290.8i	−0.444309	+	1.36744i
$907$	2447.01			0.0895827			0.0447913	−	0.998996i	$-0.485738\pi$
$907$	2447.01			0.0895827			0.0447913	+	0.998996i	$0.485738\pi$
$908$	−2139.46	+	6584.59i	−0.0781945	+	0.240658i
$909$	12789.4	−	9292.03i	0.466663	−	0.339051i
$910$	−12921.7	−	8656.74i	−0.470715	−	0.315349i
$911$	−19395.7	−	14091.8i	−0.705387	−	0.512493i	0.176296	−	0.984337i	$-0.443589\pi$
$911$	−19395.7	−	14091.8i	−0.705387	−	0.512493i	−0.881682	+	0.471844i	$0.843589\pi$
$912$	88530.0	−	64320.8i	3.21439	−	2.33539i
$913$	34043.2	−	24733.8i	1.23402	−	0.896571i
$914$	−36663.2	−	26637.3i	−1.32682	−	0.963988i
$915$	−20555.2	+	16164.0i	−0.742660	+	0.584005i
$916$	−13809.3	+	10033.0i	−0.498113	+	0.361900i
$917$	9582.61	−	29492.2i	0.345088	−	1.06207i
$918$	−10504.0			−0.377651
$919$	−6201.28	+	19085.6i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$919$	−6201.28	+	19085.6i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$920$	16125.3	−	613.947i	0.577864	−	0.0220013i
$921$	1744.97	+	5370.46i	0.0624307	+	0.192142i
$922$	16754.6	+	51565.5i	0.598465	+	1.84189i
$923$	−15516.1	−	11273.1i	−0.553325	−	0.402014i
$924$	16607.1			0.591269
$925$	−6882.76	−	4240.79i	−0.244653	−	0.150742i
$926$	14167.9			0.502794
$927$	54055.0	+	39273.3i	1.91521	+	1.39148i
$928$	−5654.21	−	17401.9i	−0.200009	−	0.615565i
$929$	4458.92	+	13723.2i	0.157473	+	0.484653i	0.998403	−	0.0564915i	$-0.0179914\pi$
$929$	4458.92	+	13723.2i	0.157473	+	0.484653i	−0.840930	+	0.541144i	$0.817991\pi$
$930$	811.621	+	2208.25i	0.0286173	+	0.0778617i
$931$	−9243.71	+	28449.2i	−0.325403	+	1.00149i
$932$	−19131.6			−0.672398
$933$	−22892.9	+	70457.2i	−0.803302	+	2.47231i
$934$	−1399.83	+	1017.04i	−0.0490406	+	0.0356301i
$935$	7943.97	−	302.455i	0.277856	−	0.0105790i
$936$	−15990.4	−	11617.7i	−0.558400	−	0.405701i
$937$	30964.9	−	22497.3i	1.07959	−	0.784371i	0.101981	−	0.994786i	$-0.467482\pi$
$937$	30964.9	−	22497.3i	1.07959	−	0.784371i	0.977612	+	0.210416i	$0.0674818\pi$
$938$	4985.35	−	3622.07i	0.173537	−	0.126082i
$939$	−25880.2	−	18803.1i	−0.899435	−	0.653478i
$940$	−4913.32	+	187.068i	−0.170484	+	0.00649093i
$941$	13900.7	−	10099.5i	0.481563	−	0.349876i	−0.320368	−	0.947293i	$-0.603806\pi$
$941$	13900.7	−	10099.5i	0.481563	−	0.349876i	0.801930	+	0.597417i	$0.203806\pi$
$942$	−15683.2	+	48267.9i	−0.542448	+	1.66948i
$943$	−40378.0			−1.39437
$944$	−8001.00	+	24624.5i	−0.275858	+	0.849005i
$945$	−7734.48	−	21043.9i	−0.266246	−	0.724401i
$946$	−9546.84	−	29382.1i	−0.328113	−	1.00983i
$947$	5191.85	+	15978.9i	0.178155	+	0.548304i	0.999763	−	0.0217480i	$-0.00692315\pi$
$947$	5191.85	+	15978.9i	0.178155	+	0.548304i	−0.821609	+	0.570052i	$0.806923\pi$
$948$	−9093.01	−	6606.46i	−0.311527	−	0.226337i
$949$	4618.43			0.157977
$950$	−59407.5	−	36603.8i	−2.02888	−	1.25009i
$951$	−53341.9			−1.81885
$952$	−2573.12	−	1869.48i	−0.0876000	−	0.0636451i
$953$	−5977.19	−	18395.9i	−0.203169	−	0.625290i	−0.999784	−	0.0208023i	$-0.993378\pi$
$953$	−5977.19	−	18395.9i	−0.203169	−	0.625290i	0.796615	−	0.604487i	$-0.206622\pi$
$954$	−10202.6	−	31400.4i	−0.346249	−	1.06564i
$955$	−25863.2	+	984.703i	−0.876348	+	0.0333657i
$956$	4260.10	−	13111.2i	0.144123	−	0.443565i
$957$	34619.2			1.16936
$958$	4888.92	−	15046.5i	0.164879	−	0.507444i
$959$	17871.7	−	12984.6i	0.601781	−	0.437219i
$960$	3509.79	−	2759.99i	0.117998	−	0.0927898i
$961$	24060.8	+	17481.2i	0.807654	+	0.586795i
$962$	5819.28	−	4227.96i	0.195032	−	0.141699i
$963$	40046.8	−	29095.7i	1.34007	−	0.973620i
$964$	24084.3	+	17498.3i	0.804672	+	0.584628i
$965$	18846.2	+	12625.8i	0.628684	+	0.421179i
$966$	−32108.1	+	23327.9i	−1.06942	+	0.776981i
$967$	12275.5	−	37780.0i	0.408224	−	1.25638i	−0.509950	−	0.860204i	$-0.670336\pi$
$967$	12275.5	−	37780.0i	0.408224	−	1.25638i	0.918173	−	0.396179i	$-0.129664\pi$
$968$	−1301.90			−0.0432279
$969$	−7956.69	+	24488.2i	−0.263783	+	0.811840i
$970$	40243.2	−	31646.0i	1.33210	−	1.04752i
$971$	3924.88	+	12079.5i	0.129717	+	0.399229i	0.994731	−	0.102520i	$-0.0326904\pi$
$971$	3924.88	+	12079.5i	0.129717	+	0.399229i	−0.865014	+	0.501748i	$0.832690\pi$
$972$	−4082.06	−	12563.3i	−0.134704	−	0.414576i
$973$	23738.2	+	17246.8i	0.782129	+	0.568250i
$974$	−57485.2			−1.89111
$975$	−8034.32	+	33110.8i	−0.263902	+	1.08758i
$976$	21927.1			0.719127
$977$	−11761.8	−	8545.44i	−0.385152	−	0.279829i	0.378314	−	0.925677i	$-0.376504\pi$
$977$	−11761.8	−	8545.44i	−0.385152	−	0.279829i	−0.763466	+	0.645848i	$0.776504\pi$
$978$	12487.7	+	38433.2i	0.408295	+	1.25660i
$979$	−631.596	−	1943.85i	−0.0206189	−	0.0634584i
$980$	2341.92	−	8265.36i	0.0763365	−	0.269416i
$981$	18036.4	−	55510.3i	0.587011	−	1.80663i
$982$	−5559.86			−0.180674
$983$	−6980.26	+	21483.0i	−0.226486	+	0.697053i	0.771651	+	0.636046i	$0.219431\pi$
$983$	−6980.26	+	21483.0i	−0.226486	+	0.697053i	−0.998137	+	0.0610068i	$0.980569\pi$
$984$	−35247.5	+	25608.8i	−1.14192	+	0.829654i
$985$	−8039.39	+	28373.5i	−0.260057	+	0.917824i
$986$	5692.89	+	4136.13i	0.183873	+	0.133591i
$987$	−9217.95	+	6697.24i	−0.297275	+	0.215983i
$988$	17071.6	−	12403.2i	0.549716	−	0.399392i
$989$	20301.3	+	14749.8i	0.652724	+	0.474232i
$990$	−23228.8	−	63200.7i	−0.745717	−	2.02894i
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	−0.593791	−	0.804619i	$-0.702369\pi$
$991$	−375.742	+	272.992i	−0.0120442	+	0.00875064i	0.581747	+	0.813370i	$0.302369\pi$
$992$	372.989	−	1147.94i	0.0119379	−	0.0367411i
$993$	−43536.2			−1.39132
$994$	−8077.78	+	24860.9i	−0.257758	+	0.793298i
$995$	5520.56	+	3698.43i	0.175893	+	0.117837i
$996$	−12095.4	−	37225.7i	−0.384795	−	1.18428i
$997$	−6307.66	−	19413.0i	−0.200367	−	0.616666i	−0.999872	−	0.0160063i	$-0.994905\pi$
$997$	−6307.66	−	19413.0i	−0.200367	−	0.616666i	0.799505	−	0.600659i	$-0.205095\pi$
$998$	9349.23	+	6792.62i	0.296538	+	0.215447i
$999$	10368.7			0.328381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.d.a.16.2	yes	28
3.2	odd	2		225.4.h.b.91.6		28
5.2	odd	4		125.4.e.b.49.12		56
5.3	odd	4		125.4.e.b.49.3		56
5.4	even	2		125.4.d.a.76.6		28
25.2	odd	20		125.4.e.b.74.3		56
25.6	even	5		625.4.a.c.1.12		14
25.11	even	5	inner	25.4.d.a.11.2	✓	28
25.14	even	10		125.4.d.a.51.6		28
25.19	even	10		625.4.a.d.1.3		14
25.23	odd	20		125.4.e.b.74.12		56
75.11	odd	10		225.4.h.b.136.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.2	✓	28	25.11	even	5	inner
25.4.d.a.16.2	yes	28	1.1	even	1	trivial
125.4.d.a.51.6		28	25.14	even	10
125.4.d.a.76.6		28	5.4	even	2
125.4.e.b.49.3		56	5.3	odd	4
125.4.e.b.49.12		56	5.2	odd	4
125.4.e.b.74.3		56	25.2	odd	20
125.4.e.b.74.12		56	25.23	odd	20
225.4.h.b.91.6		28	3.2	odd	2
225.4.h.b.136.6		28	75.11	odd	10
625.4.a.c.1.12		14	25.6	even	5
625.4.a.d.1.3		14	25.19	even	10

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81638 - 2.04622i) q^{2} +(2.63646 + 8.11420i) q^{3} +(1.27284 + 3.91740i) q^{4} +(9.28856 + 6.22275i) q^{5} +(9.17815 - 28.2474i) q^{6} +12.5082 q^{7} +(-4.17503 + 12.8494i) q^{8} +(-37.0458 + 26.9153i) q^{9} +O(q^{10})\)	\(q+(-2.81638 - 2.04622i) q^{2} +(2.63646 + 8.11420i) q^{3} +(1.27284 + 3.91740i) q^{4} +(9.28856 + 6.22275i) q^{5} +(9.17815 - 28.2474i) q^{6} +12.5082 q^{7} +(-4.17503 + 12.8494i) q^{8} +(-37.0458 + 26.9153i) q^{9} +(-13.4270 - 36.5321i) q^{10} +(-30.5650 - 22.2068i) q^{11} +(-28.4308 + 20.6562i) q^{12} +(25.8465 - 18.7786i) q^{13} +(-35.2278 - 25.5945i) q^{14} +(-26.0037 + 91.7752i) q^{15} +(64.7099 - 47.0145i) q^{16} +(-5.81584 + 17.8993i) q^{17} +159.410 q^{18} +(49.5522 - 152.506i) q^{19} +(-12.5542 + 44.3076i) q^{20} +(32.9774 + 101.494i) q^{21} +(40.6427 + 125.085i) q^{22} +(-86.4266 - 62.7926i) q^{23} -115.270 q^{24} +(47.5547 + 115.601i) q^{25} -111.218 q^{26} +(-129.703 - 94.2345i) q^{27} +(15.9210 + 48.9997i) q^{28} +(33.1890 + 102.145i) q^{29} +(261.028 - 205.265i) q^{30} +(-2.18936 + 6.73816i) q^{31} -170.364 q^{32} +(99.6067 - 306.558i) q^{33} +(53.0055 - 38.5108i) q^{34} +(116.183 + 77.8354i) q^{35} +(-152.592 - 110.864i) q^{36} +(-52.3230 + 38.0149i) q^{37} +(-451.619 + 328.120i) q^{38} +(220.516 + 160.214i) q^{39} +(-118.739 + 93.3724i) q^{40} +(305.782 - 222.164i) q^{41} +(114.802 - 353.324i) q^{42} -234.897 q^{43} +(48.0885 - 148.001i) q^{44} +(-511.589 + 19.4780i) q^{45} +(114.923 + 353.696i) q^{46} +(32.9933 + 101.543i) q^{47} +(552.090 + 401.117i) q^{48} -186.545 q^{49} +(102.612 - 422.883i) q^{50} -160.572 q^{51} +(106.462 + 77.3489i) q^{52} +(-64.0024 - 196.979i) q^{53} +(172.467 + 530.800i) q^{54} +(-145.718 - 396.467i) q^{55} +(-52.2221 + 160.723i) q^{56} +1368.11 q^{57} +(115.539 - 355.591i) q^{58} +(-261.882 + 190.269i) q^{59} +(-392.619 + 14.9484i) q^{60} +(221.781 + 161.134i) q^{61} +(19.9538 - 14.4973i) q^{62} +(-463.376 + 336.662i) q^{63} +(-37.8690 - 27.5134i) q^{64} +(356.931 - 13.5896i) q^{65} +(-907.814 + 659.566i) q^{66} +(-43.7313 + 134.591i) q^{67} -77.5215 q^{68} +(281.651 - 866.833i) q^{69} +(-167.948 - 456.950i) q^{70} +(-185.509 - 570.937i) q^{71} +(-191.179 - 588.388i) q^{72} +(116.952 + 84.9707i) q^{73} +225.148 q^{74} +(-812.631 + 690.645i) q^{75} +660.500 q^{76} +(-382.313 - 277.767i) q^{77} +(-293.223 - 902.448i) q^{78} +(98.8328 + 304.176i) q^{79} +(893.621 - 34.0233i) q^{80} +(40.6249 - 125.030i) q^{81} -1315.80 q^{82} +(-344.182 + 1059.28i) q^{83} +(-355.618 + 258.372i) q^{84} +(-165.404 + 130.068i) q^{85} +(661.558 + 480.650i) q^{86} +(-741.324 + 538.604i) q^{87} +(412.954 - 300.028i) q^{88} +(43.7671 + 31.7986i) q^{89} +(1480.69 + 991.966i) q^{90} +(323.293 - 234.886i) q^{91} +(135.977 - 418.493i) q^{92} -60.4469 q^{93} +(114.857 - 353.495i) q^{94} +(1409.28 - 1108.21i) q^{95} +(-449.159 - 1382.37i) q^{96} +(406.468 + 1250.98i) q^{97} +(525.381 + 381.712i) q^{98} +1730.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9}+O(q^{10}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9	\( 28 q - q^{2} - 7 q^{3} - 31 q^{4} - 20 q^{5} + q^{6} - 16 q^{7} + 100 q^{8} - 34 q^{9} - 25 q^{10} - 89 q^{11} + 139 q^{12} + 33 q^{13} - 17 q^{14} + 225 q^{15} - 207 q^{16} - 191 q^{17} - 552 q^{18} - 115 q^{19} - 225 q^{20} - 144 q^{21} + 808 q^{22} + 433 q^{23} + 780 q^{24} + 90 q^{25} + 586 q^{26} + 35 q^{27} - 13 q^{28} - 5 q^{29} + 675 q^{30} - 639 q^{31} - 1386 q^{32} + 251 q^{33} - 777 q^{34} - 1030 q^{35} + 673 q^{36} + 699 q^{37} - 2355 q^{38} - 1133 q^{39} + 410 q^{40} + 341 q^{41} - 2407 q^{42} - 172 q^{43} + 548 q^{44} + 470 q^{45} - 1239 q^{46} + 2319 q^{47} + 4738 q^{48} + 1344 q^{49} + 2335 q^{50} + 2006 q^{51} + 2344 q^{52} - 927 q^{53} + 1615 q^{54} + 1225 q^{55} - 2910 q^{56} - 770 q^{57} + 2410 q^{58} - 1905 q^{59} - 12030 q^{60} + 1391 q^{61} - 3832 q^{62} - 6142 q^{63} - 3596 q^{64} + 1215 q^{65} + 3632 q^{66} - 3611 q^{67} + 3622 q^{68} + 2687 q^{69} + 560 q^{70} - 3719 q^{71} + 9025 q^{72} + 4593 q^{73} + 4848 q^{74} + 3815 q^{75} + 3520 q^{76} + 1368 q^{77} - 3679 q^{78} + 775 q^{79} + 9500 q^{80} - 3712 q^{81} - 6762 q^{82} - 2447 q^{83} - 7612 q^{84} - 8185 q^{85} + 3891 q^{86} - 85 q^{87} - 10960 q^{88} - 5075 q^{89} + 685 q^{90} + 376 q^{91} - 8456 q^{92} + 4366 q^{93} + 3573 q^{94} + 3265 q^{95} - 7754 q^{96} + 7439 q^{97} + 7082 q^{98} + 6572 q^{99}+O(q^{100}) \) 28 * q - q^2 - 7 * q^3 - 31 * q^4 - 20 * q^5 + q^6 - 16 * q^7 + 100 * q^8 - 34 * q^9 - 25 * q^10 - 89 * q^11 + 139 * q^12 + 33 * q^13 - 17 * q^14 + 225 * q^15 - 207 * q^16 - 191 * q^17 - 552 * q^18 - 115 * q^19 - 225 * q^20 - 144 * q^21 + 808 * q^22 + 433 * q^23 + 780 * q^24 + 90 * q^25 + 586 * q^26 + 35 * q^27 - 13 * q^28 - 5 * q^29 + 675 * q^30 - 639 * q^31 - 1386 * q^32 + 251 * q^33 - 777 * q^34 - 1030 * q^35 + 673 * q^36 + 699 * q^37 - 2355 * q^38 - 1133 * q^39 + 410 * q^40 + 341 * q^41 - 2407 * q^42 - 172 * q^43 + 548 * q^44 + 470 * q^45 - 1239 * q^46 + 2319 * q^47 + 4738 * q^48 + 1344 * q^49 + 2335 * q^50 + 2006 * q^51 + 2344 * q^52 - 927 * q^53 + 1615 * q^54 + 1225 * q^55 - 2910 * q^56 - 770 * q^57 + 2410 * q^58 - 1905 * q^59 - 12030 * q^60 + 1391 * q^61 - 3832 * q^62 - 6142 * q^63 - 3596 * q^64 + 1215 * q^65 + 3632 * q^66 - 3611 * q^67 + 3622 * q^68 + 2687 * q^69 + 560 * q^70 - 3719 * q^71 + 9025 * q^72 + 4593 * q^73 + 4848 * q^74 + 3815 * q^75 + 3520 * q^76 + 1368 * q^77 - 3679 * q^78 + 775 * q^79 + 9500 * q^80 - 3712 * q^81 - 6762 * q^82 - 2447 * q^83 - 7612 * q^84 - 8185 * q^85 + 3891 * q^86 - 85 * q^87 - 10960 * q^88 - 5075 * q^89 + 685 * q^90 + 376 * q^91 - 8456 * q^92 + 4366 * q^93 + 3573 * q^94 + 3265 * q^95 - 7754 * q^96 + 7439 * q^97 + 7082 * q^98 + 6572 * q^99

Introduction

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