LMFDB - Embedded newform 25.4.d.a.11.2

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			11.2
Character	$\chi$	$=$	25.11
Dual form			25.4.d.a.16.2

$q$-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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.81638	+	2.04622i	−0.995740	+	0.723448i	−0.961171	−	0.275955i	$-0.911006\pi$
$2$	−2.81638	+	2.04622i	−0.995740	+	0.723448i	−0.0345696	+	0.999402i	$0.511006\pi$
$3$	2.63646	−	8.11420i	0.507387	−	1.56158i	−0.289332	−	0.957229i	$-0.593433\pi$
$3$	2.63646	−	8.11420i	0.507387	−	1.56158i	0.796720	−	0.604349i	$-0.206567\pi$
$4$	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	−0.921753	−	0.387778i	$-0.873243\pi$
$11$	−30.5650	+	22.2068i	−0.837791	+	0.608691i	0.0839620	+	0.996469i	$0.473243\pi$
$12$	−28.4308	−	20.6562i	−0.683938	−	0.496910i
$13$	25.8465	+	18.7786i	0.551424	+	0.400633i	0.828310	−	0.560269i	$-0.189302\pi$
$13$	25.8465	+	18.7786i	0.551424	+	0.400633i	−0.276886	+	0.960903i	$0.589302\pi$
$14$	−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	0.900960	−	0.433902i	$-0.142864\pi$
$17$	−5.81584	−	17.8993i	−0.0829735	−	0.255366i	−0.983933	+	0.178536i	$0.942864\pi$
$18$	159.410			2.08740
$19$	49.5522	+	152.506i	0.598319	+	1.84144i	0.537459	+	0.843290i	$0.319384\pi$
$19$	49.5522	+	152.506i	0.598319	+	1.84144i	0.0608593	+	0.998146i	$0.480616\pi$
$20$	−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	−0.906036	−	0.423200i	$-0.860907\pi$
$23$	−86.4266	+	62.7926i	−0.783530	+	0.569268i	0.122506	+	0.992468i	$0.460907\pi$
$24$	−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	−0.786802	−	0.617206i	$-0.788265\pi$
$29$	33.1890	−	102.145i	0.212519	−	0.654065i	0.999320	−	0.0368592i	$-0.0117353\pi$
$30$	261.028	+	205.265i	1.58857	+	1.24920i
$31$	−2.18936	−	6.73816i	−0.0126845	−	0.0390390i	0.944514	−	0.328471i	$-0.106533\pi$
$31$	−2.18936	−	6.73816i	−0.0126845	−	0.0390390i	−0.957198	+	0.289432i	$0.906533\pi$
$32$	−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	0.465445	−	0.885077i	$-0.345894\pi$
$37$	−52.3230	−	38.0149i	−0.232482	−	0.168908i	−0.697928	+	0.716168i	$0.745894\pi$
$38$	−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	0.990372	−	0.138429i	$-0.0442052\pi$
$41$	305.782	+	222.164i	1.16476	+	0.846248i	0.174388	+	0.984677i	$0.444205\pi$
$42$	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	−0.886715	−	0.462316i	$-0.847019\pi$
$47$	32.9933	−	101.543i	0.102395	−	0.315139i	0.989110	+	0.147177i	$0.0470186\pi$
$48$	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	−0.999100	−	0.0424228i	$-0.986492\pi$
$53$	−64.0024	+	196.979i	−0.165876	+	0.510512i	0.833224	+	0.552935i	$0.186492\pi$
$54$	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	0.260087	−	0.965585i	$-0.416249\pi$
$59$	−261.882	−	190.269i	−0.577868	−	0.419845i	−0.837955	+	0.545740i	$0.816249\pi$
$60$	−392.619	−	14.9484i	−0.844782	−	0.0321639i
$61$	221.781	−	161.134i	0.465511	−	0.338214i	−0.330178	−	0.943919i	$-0.607109\pi$
$61$	221.781	−	161.134i	0.465511	−	0.338214i	0.795689	+	0.605705i	$0.207109\pi$
$62$	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	0.903237	−	0.429142i	$-0.141184\pi$
$67$	−43.7313	−	134.591i	−0.0797407	−	0.245417i	−0.982978	+	0.183726i	$0.941184\pi$
$68$	−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	0.667650	+	0.744475i	$0.267300\pi$
$71$	−185.509	+	570.937i	−0.310082	+	0.954334i	−0.977732	+	0.209859i	$0.932700\pi$
$72$	−191.179	+	588.388i	−0.312926	+	0.963087i
$73$	116.952	−	84.9707i	0.187510	−	0.136234i	−0.490070	−	0.871683i	$-0.663029\pi$
$73$	116.952	−	84.9707i	0.187510	−	0.136234i	0.677580	+	0.735449i	$0.263029\pi$
$74$	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	−0.855687	−	0.517494i	$-0.826865\pi$
$79$	98.8328	−	304.176i	0.140754	−	0.433196i	0.996441	+	0.0842982i	$0.0268648\pi$
$80$	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	−0.870939	−	0.491390i	$-0.836489\pi$
$83$	−344.182	−	1059.28i	−0.455167	−	1.40086i	0.415773	−	0.909469i	$-0.363511\pi$
$84$	−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	−0.561417	−	0.827533i	$-0.689743\pi$
$89$	43.7671	−	31.7986i	0.0521270	−	0.0378725i	0.613544	+	0.789661i	$0.289743\pi$
$90$	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	−0.477073	−	0.878863i	$-0.658302\pi$
$97$	406.468	−	1250.98i	0.425470	−	1.30946i	0.902543	−	0.430599i	$-0.141698\pi$
$98$	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	0.465443	+	0.885078i	$0.345895\pi$
$103$	−450.899	+	1387.73i	−0.431344	+	1.32754i	−0.896787	+	0.442463i	$0.854105\pi$
$104$	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	0.0338823	−	0.999426i	$-0.489213\pi$
$109$	−1031.20	−	749.212i	−0.906158	−	0.658362i	−0.940040	+	0.341064i	$0.889213\pi$
$110$	−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	0.678399	−	0.734694i	$-0.262674\pi$
$113$	227.388	+	165.207i	0.189300	+	0.137535i	−0.489099	+	0.872228i	$0.662674\pi$
$114$	−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	−0.531368	−	0.847141i	$-0.678322\pi$
$127$	157.590	−	114.496i	0.110109	−	0.0799990i	0.641477	+	0.767142i	$0.278322\pi$
$128$	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	0.790524	+	0.612431i	$0.209808\pi$
$131$	766.106	+	2357.83i	0.510954	+	1.57256i	−0.279570	+	0.960125i	$0.590192\pi$
$132$	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	0.936145	−	0.351613i	$-0.114367\pi$
$137$	1428.80	+	1038.08i	0.891027	+	0.647369i	−0.0451188	+	0.998982i	$0.514367\pi$
$138$	−2566.97	−	1865.01i	−1.58344	−	1.15044i
$139$	1897.81	−	1378.84i	1.15806	−	0.841379i	0.168528	−	0.985697i	$-0.446099\pi$
$139$	1897.81	−	1378.84i	1.15806	−	0.841379i	0.989531	+	0.144318i	$0.0460987\pi$
$140$	−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	0.291023	−	0.956716i	$-0.406004\pi$
$163$	−1100.74	−	799.735i	−0.528937	−	0.384295i	−0.819960	+	0.572421i	$0.806004\pi$
$164$	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	0.909824	+	0.414994i	$0.136216\pi$
$167$	901.420	+	2774.28i	0.417688	+	1.28551i	−0.492136	+	0.870518i	$0.663784\pi$
$168$	−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	−0.856226	−	0.516601i	$-0.827197\pi$
$173$	−1432.40	+	1040.70i	−0.629499	+	0.457357i	0.226728	+	0.973958i	$0.427197\pi$
$174$	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	0.721770	+	0.692133i	$0.243329\pi$
$179$	−644.168	+	1982.55i	−0.268980	+	0.827835i	−0.990750	+	0.135702i	$0.956671\pi$
$180$	−727.476	+	1979.31i	−0.301238	+	0.819606i
$181$	−162.821	−	501.111i	−0.0668639	−	0.205786i	0.912042	−	0.410096i	$-0.134505\pi$
$181$	−162.821	−	501.111i	−0.0668639	−	0.205786i	−0.978906	+	0.204310i	$0.934505\pi$
$182$	−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	0.173516	−	0.984831i	$-0.444487\pi$
$191$	−1872.83	−	1360.69i	−0.709494	−	0.515478i	−0.883011	+	0.469353i	$0.844487\pi$
$192$	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	−0.688504	−	0.725232i	$-0.741732\pi$
$197$	815.098	−	2508.61i	0.294788	−	0.907265i	0.983292	−	0.182033i	$-0.0582677\pi$
$198$	−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	−0.309916	−	0.950764i	$-0.600301\pi$
$211$	1528.02	−	1110.17i	0.498545	−	0.362214i	0.808461	+	0.588550i	$0.200301\pi$
$212$	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	−0.825403	−	0.564544i	$-0.809052\pi$
$223$	−1810.08	+	1315.10i	−0.543553	+	0.394914i	0.281850	+	0.959458i	$0.409052\pi$
$224$	−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	−0.370961	−	0.928648i	$-0.620972\pi$
$227$	1359.84	−	987.983i	0.397603	−	0.288875i	0.768564	+	0.639773i	$0.220972\pi$
$228$	1741.38	−	5359.43i	0.505815	−	1.55674i
$229$	1280.57	−	3941.19i	0.369531	−	1.13730i	−0.577564	−	0.816345i	$-0.695997\pi$
$229$	1280.57	−	3941.19i	0.369531	−	1.13730i	0.947095	−	0.320953i	$-0.104003\pi$
$230$	−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	−0.922093	−	0.386969i	$-0.873522\pi$
$233$	−1435.29	−	4417.38i	−0.403559	−	1.24203i	0.518534	−	0.855057i	$-0.326478\pi$
$234$	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	−0.890459	−	0.455063i	$-0.849617\pi$
$239$	−2707.72	+	1967.27i	−0.732835	+	0.532436i	0.157624	+	0.987499i	$0.449617\pi$
$240$	2632.07	−	7161.32i	0.707914	−	1.92609i
$241$	5847.12	+	4248.18i	1.56285	+	1.13548i	0.933626	+	0.358250i	$0.116626\pi$
$241$	5847.12	+	4248.18i	1.56285	+	1.13548i	0.629222	+	0.777226i	$0.283374\pi$
$242$	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	0.998930	−	0.0462529i	$-0.0147280\pi$
$263$	5389.55	+	3915.74i	1.26363	+	0.918079i	0.264697	+	0.964332i	$0.414728\pi$
$264$	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	0.954954	+	0.296754i	$0.0959040\pi$
$269$	1574.21	+	4844.92i	0.356807	+	1.09814i	−0.598147	+	0.801387i	$0.704096\pi$
$270$	−1701.06	−	6003.59i	−0.383420	−	1.35321i
$271$	1535.70	−	4726.39i	0.344232	−	1.05944i	−0.617762	−	0.786365i	$-0.711960\pi$
$271$	1535.70	−	4726.39i	0.344232	−	1.05944i	0.961994	−	0.273072i	$-0.0880396\pi$
$272$	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	−0.937808	−	0.347153i	$-0.887148\pi$
$277$	−4137.40	+	3006.00i	−0.897445	+	0.652032i	0.0403637	+	0.999185i	$0.487148\pi$
$278$	−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	0.970716	−	0.240228i	$-0.0772223\pi$
$281$	208.142	+	640.597i	0.0441877	+	0.135996i	−0.926529	+	0.376224i	$0.877222\pi$
$282$	3171.14			0.669641
$283$	879.284	+	2706.16i	0.184693	+	0.568425i	0.999943	−	0.0106833i	$-0.00340066\pi$
$283$	879.284	+	2706.16i	0.184693	+	0.568425i	−0.815250	+	0.579109i	$0.803401\pi$
$284$	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	0.281267	−	0.959629i	$-0.409245\pi$
$311$	7024.85	−	5103.86i	1.28085	−	0.930589i	0.999578	+	0.0290408i	$0.00924527\pi$
$312$	−2979.32	−	2164.60i	−0.540611	−	0.392777i
$313$	−3033.40	−	2203.89i	−0.547788	−	0.397992i	0.279181	−	0.960238i	$-0.409937\pi$
$313$	−3033.40	−	2203.89i	−0.547788	−	0.397992i	−0.826969	+	0.562247i	$0.809937\pi$
$314$	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	−0.963007	−	0.269477i	$-0.913149\pi$
$317$	−1932.02	−	5946.15i	−0.342313	−	1.05353i	0.620694	−	0.784053i	$-0.286851\pi$
$318$	−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	−0.992402	−	0.123034i	$-0.960738\pi$
$331$	−1576.86	−	4853.08i	−0.261849	−	0.805890i	0.730553	−	0.682856i	$-0.239262\pi$
$332$	−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	0.874449	−	0.485118i	$-0.161223\pi$
$337$	4227.20	+	3071.24i	0.683294	+	0.496442i	−0.191155	+	0.981560i	$0.561223\pi$
$338$	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	−0.968102	−	0.250555i	$-0.919387\pi$
$347$	−243.163	+	748.379i	−0.0376187	+	0.115778i	0.930484	+	0.366333i	$0.119387\pi$
$348$	−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	−0.880752	−	0.473578i	$-0.842962\pi$
$353$	730.568	−	2248.46i	0.110154	−	0.339018i	0.990905	+	0.134560i	$0.0429621\pi$
$354$	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	0.839620	−	0.543174i	$-0.182778\pi$
$359$	3962.13	+	2878.66i	0.582488	+	0.423202i	−0.257132	+	0.966376i	$0.582778\pi$
$360$	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	−0.778556	−	0.627575i	$-0.784048\pi$
$367$	−3638.89	−	11199.3i	−0.517570	−	1.59292i	0.260986	−	0.965343i	$-0.415952\pi$
$368$	−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	−0.414684	+	0.909966i	$0.636108\pi$
$373$	−10144.8	+	7370.66i	−1.40826	+	1.02316i	−0.993573	+	0.113193i	$0.963892\pi$
$374$	−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	−0.771353	−	0.636407i	$-0.780420\pi$
$379$	1673.08	−	5149.21i	0.226755	−	0.697881i	0.998109	−	0.0614740i	$-0.0195801\pi$
$380$	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	−0.598909	−	0.800817i	$-0.704399\pi$
$383$	−4385.52	−	13497.2i	−0.585090	−	1.80072i	0.0138191	−	0.999905i	$-0.495601\pi$
$384$	−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	−0.600206	−	0.799846i	$-0.704915\pi$
$389$	−191.659	+	139.248i	−0.0249807	+	0.0181495i	0.575225	+	0.817995i	$0.304915\pi$
$390$	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	0.432464	+	0.901651i	$0.357644\pi$
$397$	−3538.88	+	10891.6i	−0.447384	+	1.37691i	−0.879848	+	0.475255i	$0.842356\pi$
$398$	−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	0.891158	−	0.453692i	$-0.149893\pi$
$409$	6080.01	+	4417.39i	0.735055	+	0.534048i	−0.156104	+	0.987741i	$0.549893\pi$
$410$	−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	−0.997644	−	0.0686047i	$-0.978145\pi$
$419$	−1980.00	−	6093.82i	−0.230858	−	0.710507i	0.766786	−	0.641903i	$-0.221855\pi$
$420$	−4910.96	−	186.978i	−0.570548	−	0.0217228i
$421$	4678.50	−	14399.0i	0.541607	−	1.66689i	−0.187318	−	0.982299i	$-0.559979\pi$
$421$	4678.50	−	14399.0i	0.541607	−	1.66689i	0.728924	−	0.684594i	$-0.240021\pi$
$422$	−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	0.904631	+	0.426196i	$0.140147\pi$
$431$	3787.43	+	11656.5i	0.423281	+	1.30272i	−0.481350	+	0.876528i	$0.659853\pi$
$432$	−12823.4			−1.42817
$433$	3856.48	+	11869.0i	0.428016	+	1.31730i	0.900077	+	0.435731i	$0.143510\pi$
$433$	3856.48	+	11869.0i	0.428016	+	1.31730i	−0.472061	+	0.881566i	$0.656490\pi$
$434$	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	−0.425776	+	0.904828i	$0.639999\pi$
$439$	−13041.9	+	9475.47i	−1.41789	+	1.03016i	−0.992115	+	0.125330i	$0.960001\pi$
$440$	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	−0.999318	−	0.0369393i	$-0.988239\pi$
$461$	−12600.2	+	9154.58i	−1.27299	+	0.924883i	−0.273675	+	0.961822i	$0.588239\pi$
$462$	−11355.1	−	8249.98i	−1.14348	−	0.830788i
$463$	−3292.54	−	2392.17i	−0.330491	−	0.240116i	0.410148	−	0.912019i	$-0.365477\pi$
$463$	−3292.54	−	2392.17i	−0.330491	−	0.240116i	−0.740639	+	0.671903i	$0.765477\pi$
$464$	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	0.958378	−	0.285503i	$-0.0921608\pi$
$467$	153.591	+	472.706i	0.0152192	+	0.0468399i	−0.943159	+	0.332343i	$0.892161\pi$
$468$	−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	−0.861467	−	0.507814i	$-0.830454\pi$
$479$	1404.36	−	4322.18i	0.133960	−	0.412287i	0.995427	+	0.0955270i	$0.0304536\pi$
$480$	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	0.997797	−	0.0663359i	$-0.0211309\pi$
$487$	13359.2	+	9706.02i	1.24304	+	0.903125i	0.245247	+	0.969461i	$0.421131\pi$
$488$	−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	0.645579	−	0.763693i	$-0.276616\pi$
$491$	1292.08	+	938.748i	0.118759	+	0.0862833i	−0.526821	+	0.849977i	$0.676616\pi$
$492$	−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	−0.820001	−	0.572362i	$-0.806027\pi$
$503$	2028.57	−	6243.29i	0.179820	−	0.553429i	0.999821	+	0.0189337i	$0.00602714\pi$
$504$	−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	−0.109147	−	0.994026i	$-0.534812\pi$
$509$	−12497.0	−	9079.59i	−1.08825	−	0.790660i	−0.979103	+	0.203366i	$0.934812\pi$
$510$	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	0.786285	+	0.617863i	$0.212002\pi$
$521$	−2533.05	+	7795.93i	−0.213004	+	0.655559i	−0.999289	+	0.0376951i	$0.987998\pi$
$522$	5290.64	−	16282.9i	0.443611	−	1.36529i
$523$	13281.5	−	9649.57i	1.11044	−	0.806781i	0.127706	−	0.991812i	$-0.459239\pi$
$523$	13281.5	−	9649.57i	1.11044	−	0.806781i	0.982733	+	0.185031i	$0.0592387\pi$
$524$	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	−0.207406	−	0.978255i	$-0.566502\pi$
$541$	−15123.6	−	10987.9i	−1.20187	−	0.873212i	−0.994468	+	0.105043i	$0.966502\pi$
$542$	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	−0.696067	−	0.717977i	$-0.745068\pi$
$547$	3698.27	−	11382.1i	0.289080	−	0.889695i	0.985146	−	0.171718i	$-0.0549319\pi$
$548$	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	0.813320	−	0.581816i	$-0.197658\pi$
$563$	6830.40	+	4962.58i	0.511310	+	0.371488i	−0.302011	+	0.953305i	$0.597658\pi$
$564$	−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	0.985604	−	0.169070i	$-0.0540764\pi$
$569$	1206.03	+	3711.79i	0.0888568	+	0.273473i	−0.896747	+	0.442543i	$0.854076\pi$
$570$	−18369.6	+	49979.7i	−1.34985	+	3.67267i
$571$	644.040	−	1982.15i	0.0472018	−	0.145272i	−0.924678	−	0.380751i	$-0.875666\pi$
$571$	644.040	−	1982.15i	0.0472018	−	0.145272i	0.971880	+	0.235478i	$0.0756656\pi$
$572$	−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	−0.356327	−	0.934361i	$-0.615971\pi$
$577$	5851.58	−	4251.42i	0.422192	−	0.306740i	0.778519	+	0.627621i	$0.215971\pi$
$578$	−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	0.244734	−	0.969590i	$-0.421299\pi$
$587$	−8558.36	−	6218.01i	−0.601774	−	0.437214i	−0.846508	+	0.532376i	$0.821299\pi$
$588$	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	0.986845	−	0.161669i	$-0.0516876\pi$
$613$	17272.2	+	12549.0i	1.13804	+	0.826835i	0.151196	+	0.988504i	$0.451688\pi$
$614$	−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	0.691708	+	0.722177i	$0.256858\pi$
$617$	8530.27	+	26253.5i	0.556590	+	1.71301i	−0.135119	+	0.990829i	$0.543142\pi$
$618$	−43338.1			−2.82090
$619$	3030.03	+	9325.47i	0.196748	+	0.605529i	0.999952	+	0.00982399i	$0.00312712\pi$
$619$	3030.03	+	9325.47i	0.196748	+	0.605529i	−0.803204	+	0.595705i	$0.796873\pi$
$620$	−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	0.809309	−	0.587383i	$-0.199842\pi$
$631$	−3022.55	−	9302.45i	−0.190691	−	0.586885i	−1.00000		0.000497352i	$0.999842\pi$
$632$	−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	−0.137561	−	0.990493i	$-0.543926\pi$
$641$	−18210.1	−	13230.4i	−1.12208	−	0.815242i	−0.984524	+	0.175251i	$0.943926\pi$
$642$	−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	0.0464360	−	0.998921i	$-0.485214\pi$
$647$	9808.83	−	30188.5i	0.596020	−	1.83436i	0.549584	−	0.835439i	$-0.314786\pi$
$648$	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	−0.988548	−	0.150906i	$-0.951781\pi$
$653$	−1670.26	+	5140.54i	−0.100096	+	0.308062i	0.888453	+	0.458968i	$0.151781\pi$
$654$	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	0.496475	−	0.868051i	$-0.334627\pi$
$659$	−2971.87	−	2159.19i	−0.175671	−	0.127633i	−0.672146	+	0.740418i	$0.734627\pi$
$660$	12332.4	−	8261.91i	0.727328	−	0.487264i
$661$	−7532.06	+	5472.36i	−0.443212	+	0.322012i	−0.786910	−	0.617068i	$-0.788320\pi$
$661$	−7532.06	+	5472.36i	−0.443212	+	0.322012i	0.343698	+	0.939080i	$0.388320\pi$
$662$	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	−0.471958	+	0.881621i	$0.656452\pi$
$673$	−25425.2	+	18472.5i	−1.45627	+	1.05804i	−0.984315	+	0.176422i	$0.943548\pi$
$674$	−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	−0.745094	−	0.666960i	$-0.767595\pi$
$677$	−6007.13	+	4364.44i	−0.341023	+	0.247768i	0.404070	+	0.914728i	$0.367595\pi$
$678$	−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	0.933344	+	0.358982i	$0.116876\pi$
$683$	6948.13	+	21384.1i	0.389257	+	1.19801i	−0.544087	+	0.839029i	$0.683124\pi$
$684$	−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	0.671020	−	0.741439i	$-0.265857\pi$
$691$	3146.51	+	2286.07i	0.173225	+	0.125856i	−0.497794	+	0.867295i	$0.665857\pi$
$692$	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	0.863963	−	0.503556i	$-0.167975\pi$
$709$	12309.4	+	8943.33i	0.652032	+	0.473729i	−0.211931	+	0.977285i	$0.567975\pi$
$710$	−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	0.999114	+	0.0420821i	$0.0133991\pi$
$719$	4155.65	+	12789.8i	0.215549	+	0.663392i	−0.783565	+	0.621310i	$0.786601\pi$
$720$	−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	0.195857	−	0.980633i	$-0.437251\pi$
$727$	23307.2	−	16933.7i	1.18902	−	0.863871i	0.993160	+	0.116761i	$0.0372513\pi$
$728$	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	−0.998062	−	0.0622256i	$-0.980180\pi$
$733$	−4508.60	−	13876.0i	−0.227188	−	0.699213i	0.770874	−	0.636988i	$-0.219820\pi$
$734$	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	−0.608401	−	0.793630i	$-0.708189\pi$
$739$	−836.136	+	607.488i	−0.0416208	+	0.0302393i	0.566780	+	0.823869i	$0.308189\pi$
$740$	−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	−0.540356	−	0.841437i	$-0.681710\pi$
$761$	1950.66	−	1417.24i	0.0929190	−	0.0675096i	0.633275	+	0.773927i	$0.281710\pi$
$762$	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	−0.921984	−	0.387227i	$-0.873433\pi$
$769$	−8608.70	−	26494.8i	−0.403690	−	1.24243i	0.518294	−	0.855202i	$-0.326567\pi$
$770$	−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	−0.00972064	−	0.999953i	$-0.503094\pi$
$773$	20165.3	−	14651.0i	0.938287	−	0.681705i	0.948008	+	0.318247i	$0.103094\pi$
$774$	−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	0.325131	−	0.945669i	$-0.394592\pi$
$787$	−10460.2	−	7599.80i	−0.473782	−	0.344223i	−0.798913	+	0.601446i	$0.794592\pi$
$788$	−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	−0.821927	−	0.569592i	$-0.807101\pi$
$797$	4001.08	−	12314.1i	0.177824	−	0.547285i	0.999751	+	0.0223070i	$0.00710112\pi$
$798$	−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	0.738572	−	0.674174i	$-0.235500\pi$
$809$	7492.76	+	5443.81i	0.325626	+	0.236581i	−0.412946	+	0.910755i	$0.635500\pi$
$810$	−5113.09	−	194.674i	−0.221797	−	0.00844461i
$811$	2741.13	−	1991.55i	0.118686	−	0.0862303i	−0.526859	−	0.849953i	$-0.676630\pi$
$811$	2741.13	−	1991.55i	0.118686	−	0.0862303i	0.645545	+	0.763722i	$0.276630\pi$
$812$	−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	−0.836582	−	0.547842i	$-0.815449\pi$
$821$	3816.58	−	11746.2i	0.162241	−	0.499325i	0.998822	+	0.0485169i	$0.0154495\pi$
$822$	−16209.5	+	49887.6i	−0.687798	+	2.11683i
$823$	−23545.0	+	17106.4i	−0.997239	+	0.724536i	−0.961494	−	0.274825i	$-0.911380\pi$
$823$	−23545.0	+	17106.4i	−0.997239	+	0.724536i	−0.0357442	+	0.999361i	$0.511380\pi$
$824$	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	−0.442500	−	0.896768i	$-0.645908\pi$
$827$	6507.78	−	4728.18i	0.273637	−	0.198809i	0.716137	+	0.697959i	$0.245908\pi$
$828$	6226.52	−	19163.3i	0.261336	−	0.804311i
$829$	7849.09	−	24157.0i	0.328842	−	1.01207i	−0.640834	−	0.767679i	$-0.721411\pi$
$829$	7849.09	−	24157.0i	0.328842	−	1.01207i	0.969676	−	0.244393i	$-0.0785886\pi$
$830$	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	−0.980153	−	0.198243i	$-0.936476\pi$
$839$	−26598.5	+	19324.9i	−1.09450	+	0.795198i	−0.114343	+	0.993441i	$0.536476\pi$
$840$	−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	−0.991994	−	0.126281i	$-0.959696\pi$
$853$	−2870.65	+	8834.96i	−0.115228	+	0.354635i	0.876767	+	0.480916i	$0.159696\pi$
$854$	−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	0.0530595	−	0.998591i	$-0.483103\pi$
$859$	−22161.6	−	16101.3i	−0.880261	−	0.639547i	−0.933321	+	0.359044i	$0.883103\pi$
$860$	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	0.973511	−	0.228639i	$-0.0734276\pi$
$863$	26794.6	+	19467.4i	1.05689	+	0.767879i	0.0833829	+	0.996518i	$0.473428\pi$
$864$	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	−0.958758	−	0.284223i	$-0.908264\pi$
$877$	−25574.8	+	18581.1i	−0.984719	+	0.715440i	−0.0259603	+	0.999663i	$0.508264\pi$
$878$	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	−0.796385	−	0.604790i	$-0.793257\pi$
$881$	−13273.0	−	40850.2i	−0.507583	−	1.56218i	0.288803	−	0.957389i	$-0.406743\pi$
$882$	−29737.1			−1.13526
$883$	−633.110	−	1948.51i	−0.0241289	−	0.0742612i	0.938267	−	0.345912i	$-0.112430\pi$
$883$	−633.110	−	1948.51i	−0.0241289	−	0.0742612i	−0.962396	+	0.271651i	$0.912430\pi$
$884$	−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	0.755436	−	0.655222i	$-0.227425\pi$
$887$	9661.40	+	7019.42i	0.365725	+	0.265715i	−0.389711	+	0.920937i	$0.627425\pi$
$888$	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	−0.881682	−	0.471844i	$-0.843589\pi$
$911$	−19395.7	+	14091.8i	−0.705387	+	0.512493i	0.176296	+	0.984337i	$0.443589\pi$
$912$	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	−0.998527	−	0.0542539i	$-0.982722\pi$
$919$	−6201.28	−	19085.6i	−0.222591	−	0.685066i	0.775936	−	0.630812i	$-0.217278\pi$
$920$	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	−0.840930	−	0.541144i	$-0.817991\pi$
$929$	4458.92	−	13723.2i	0.157473	−	0.484653i	0.998403	+	0.0564915i	$0.0179914\pi$
$930$	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	0.977612	−	0.210416i	$-0.0674818\pi$
$937$	30964.9	+	22497.3i	1.07959	+	0.784371i	0.101981	+	0.994786i	$0.467482\pi$
$938$	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	0.801930	−	0.597417i	$-0.203806\pi$
$941$	13900.7	+	10099.5i	0.481563	+	0.349876i	−0.320368	+	0.947293i	$0.603806\pi$
$942$	−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	−0.821609	−	0.570052i	$-0.806923\pi$
$947$	5191.85	−	15978.9i	0.178155	−	0.548304i	0.999763	+	0.0217480i	$0.00692315\pi$
$948$	−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	0.796615	+	0.604487i	$0.206622\pi$
$953$	−5977.19	+	18395.9i	−0.203169	+	0.625290i	−0.999784	+	0.0208023i	$0.993378\pi$
$954$	−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	0.918173	+	0.396179i	$0.129664\pi$
$967$	12275.5	+	37780.0i	0.408224	+	1.25638i	−0.509950	+	0.860204i	$0.670336\pi$
$968$	−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	−0.865014	−	0.501748i	$-0.832690\pi$
$971$	3924.88	−	12079.5i	0.129717	−	0.399229i	0.994731	+	0.102520i	$0.0326904\pi$
$972$	−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	−0.763466	−	0.645848i	$-0.776504\pi$
$977$	−11761.8	+	8545.44i	−0.385152	+	0.279829i	0.378314	+	0.925677i	$0.376504\pi$
$978$	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	−0.998137	−	0.0610068i	$-0.980569\pi$
$983$	−6980.26	−	21483.0i	−0.226486	−	0.697053i	0.771651	−	0.636046i	$-0.219431\pi$
$984$	−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	0.581747	−	0.813370i	$-0.302369\pi$
$991$	−375.742	−	272.992i	−0.0120442	−	0.00875064i	−0.593791	+	0.804619i	$0.702369\pi$
$992$	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	0.799505	+	0.600659i	$0.205095\pi$
$997$	−6307.66	+	19413.0i	−0.200367	+	0.616666i	−0.999872	+	0.0160063i	$0.994905\pi$
$998$	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.11.2	✓	28
3.2	odd	2		225.4.h.b.136.6		28
5.2	odd	4		125.4.e.b.74.3		56
5.3	odd	4		125.4.e.b.74.12		56
5.4	even	2		125.4.d.a.51.6		28
25.4	even	10		625.4.a.d.1.3		14
25.9	even	10		125.4.d.a.76.6		28
25.12	odd	20		125.4.e.b.49.12		56
25.13	odd	20		125.4.e.b.49.3		56
25.16	even	5	inner	25.4.d.a.16.2	yes	28
25.21	even	5		625.4.a.c.1.12		14
75.41	odd	10		225.4.h.b.91.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.d.a.11.2	✓	28	1.1	even	1	trivial
25.4.d.a.16.2	yes	28	25.16	even	5	inner
125.4.d.a.51.6		28	5.4	even	2
125.4.d.a.76.6		28	25.9	even	10
125.4.e.b.49.3		56	25.13	odd	20
125.4.e.b.49.12		56	25.12	odd	20
125.4.e.b.74.3		56	5.2	odd	4
125.4.e.b.74.12		56	5.3	odd	4
225.4.h.b.91.6		28	75.41	odd	10
225.4.h.b.136.6		28	3.2	odd	2
625.4.a.c.1.12		14	25.21	even	5
625.4.a.d.1.3		14	25.4	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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