LMFDB - Embedded newform 11.4.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,4,Mod(3,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("11.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	11.c (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:	$0.649021010063$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.1
Root			$-2.05602 + 1.49379i$ of defining polynomial
Character	$\chi$	$=$	11.3
Dual form			11.4.c.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.17405 + 3.03263i) q^{2} +(1.40336 + 4.31911i) q^{3} +(5.75376 - 17.7083i) q^{4} +(6.98613 + 5.07572i) q^{5} +(-18.9560 - 13.7723i) q^{6} +(0.513765 - 1.58121i) q^{7} +(16.9313 + 52.1091i) q^{8} +(5.15818 - 3.74763i) q^{9} -44.5532 q^{10} +(-26.2401 - 25.3467i) q^{11} +84.5585 q^{12} +(23.1570 - 16.8245i) q^{13} +(2.65073 + 8.15810i) q^{14} +(-12.1185 + 37.2969i) q^{15} +(-108.191 - 78.6055i) q^{16} +(-6.36020 - 4.62095i) q^{17} +(-10.1653 + 31.2857i) q^{18} +(14.8350 + 45.6575i) q^{19} +(130.079 - 94.5077i) q^{20} +7.55040 q^{21} +(186.395 + 26.2219i) q^{22} -153.265 q^{23} +(-201.304 + 146.256i) q^{24} +(-15.5841 - 47.9628i) q^{25} +(-45.6359 + 140.453i) q^{26} +(122.625 + 89.0921i) q^{27} +(-25.0443 - 18.1958i) q^{28} +(74.9153 - 230.566i) q^{29} +(-62.5244 - 192.430i) q^{30} +(-134.251 + 97.5391i) q^{31} +251.651 q^{32} +(72.6507 - 148.905i) q^{33} +40.5614 q^{34} +(11.6150 - 8.43878i) q^{35} +(-36.6852 - 112.905i) q^{36} +(-21.2522 + 65.4077i) q^{37} +(-200.384 - 145.588i) q^{38} +(105.165 + 76.4065i) q^{39} +(-146.207 + 449.979i) q^{40} +(95.0373 + 292.495i) q^{41} +(-31.5158 + 22.8976i) q^{42} -52.9746 q^{43} +(-599.825 + 318.828i) q^{44} +55.0576 q^{45} +(639.737 - 464.796i) q^{46} +(-16.8521 - 51.8654i) q^{47} +(187.674 - 577.602i) q^{48} +(275.257 + 199.986i) q^{49} +(210.502 + 152.939i) q^{50} +(11.0327 - 33.9553i) q^{51} +(-164.693 - 506.874i) q^{52} +(-202.450 + 147.088i) q^{53} -782.025 q^{54} +(-54.6643 - 310.263i) q^{55} +91.0939 q^{56} +(-176.381 + 128.148i) q^{57} +(386.519 + 1189.58i) q^{58} +(117.153 - 360.561i) q^{59} +(590.737 + 429.195i) q^{60} +(-565.131 - 410.592i) q^{61} +(264.571 - 814.267i) q^{62} +(-3.27569 - 10.0815i) q^{63} +(-184.877 + 134.321i) q^{64} +247.174 q^{65} +(148.325 + 841.859i) q^{66} -278.021 q^{67} +(-118.424 + 86.0402i) q^{68} +(-215.087 - 661.969i) q^{69} +(-22.8899 + 70.4479i) q^{70} +(125.156 + 90.9311i) q^{71} +(282.620 + 205.336i) q^{72} +(-293.936 + 904.642i) q^{73} +(-109.649 - 337.465i) q^{74} +(185.287 - 134.619i) q^{75} +893.872 q^{76} +(-53.5596 + 28.4688i) q^{77} -670.675 q^{78} +(-1.79641 + 1.30517i) q^{79} +(-356.858 - 1098.30i) q^{80} +(-159.515 + 490.936i) q^{81} +(-1283.72 - 932.676i) q^{82} +(614.553 + 446.499i) q^{83} +(43.4432 - 133.704i) q^{84} +(-20.9785 - 64.5651i) q^{85} +(221.119 - 160.652i) q^{86} +1100.97 q^{87} +(876.514 - 1796.50i) q^{88} +1157.64 q^{89} +(-229.813 + 166.969i) q^{90} +(-14.7058 - 45.2598i) q^{91} +(-881.852 + 2714.06i) q^{92} +(-609.685 - 442.962i) q^{93} +(227.630 + 165.383i) q^{94} +(-128.105 + 394.267i) q^{95} +(353.159 + 1086.91i) q^{96} +(-598.393 + 434.758i) q^{97} -1755.42 q^{98} +(-230.341 - 32.4042i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19}+ \cdots + 2099 q^{99}+O(q^{100}) $ 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9 + 40 * q^10 + 67 * q^11 + 190 * q^12 - 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 - 31 * q^17 - 102 * q^18 + 148 * q^19 + 342 * q^20 + 334 * q^21 + 647 * q^22 - 12 * q^23 - 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 - 42 * q^28 - 199 * q^29 - 114 * q^30 - 361 * q^31 + 324 * q^32 - 232 * q^33 - 298 * q^34 + 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 + 365 * q^39 + 532 * q^40 - 31 * q^41 + 170 * q^42 - 650 * q^43 - 1208 * q^44 + 452 * q^45 + 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 - 147 * q^50 - 246 * q^51 - 590 * q^52 - 1493 * q^53 - 3100 * q^54 - 1583 * q^55 - 1560 * q^56 + 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 - 525 * q^61 + 2456 * q^62 - 68 * q^63 + 471 * q^64 + 1790 * q^65 + 1014 * q^66 + 86 * q^67 + 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 + 919 * q^72 - 2155 * q^73 - 1476 * q^74 - 160 * q^75 - 242 * q^76 - 2015 * q^77 - 1340 * q^78 - 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 + 52 * q^83 - 84 * q^84 + 2383 * q^85 + 1061 * q^86 + 2310 * q^87 + 4543 * q^88 + 3782 * q^89 - 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 + 702 * q^94 - 1317 * q^95 + 1252 * q^96 - 1344 * q^97 + 2740 * q^98 + 2099 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

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

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 $

$2$	−4.17405	+	3.03263i	−1.47575	+	1.07220i	−0.496856	+	0.867833i	$0.665512\pi$
$2$	−4.17405	+	3.03263i	−1.47575	+	1.07220i	−0.978895	+	0.204363i	$0.934488\pi$
$3$	1.40336	+	4.31911i	0.270078	+	0.831213i	0.990480	+	0.137657i	$0.0439571\pi$
$3$	1.40336	+	4.31911i	0.270078	+	0.831213i	−0.720402	+	0.693556i	$0.756043\pi$
$4$	5.75376	−	17.7083i	0.719220	−	2.21353i
$5$	6.98613	+	5.07572i	0.624858	+	0.453986i	0.854615	−	0.519262i	$-0.173793\pi$
$5$	6.98613	+	5.07572i	0.624858	+	0.453986i	−0.229757	+	0.973248i	$0.573793\pi$
$6$	−18.9560	−	13.7723i	−1.28979	−	0.937088i
$7$	0.513765	−	1.58121i	0.0277407	−	0.0853771i	−0.936228	−	0.351394i	$-0.885708\pi$
$7$	0.513765	−	1.58121i	0.0277407	−	0.0853771i	0.963968	+	0.266017i	$0.0857077\pi$
$8$	16.9313	+	52.1091i	0.748264	+	2.30292i
$9$	5.15818	−	3.74763i	0.191044	−	0.138801i
$10$	−44.5532			−1.40890
$11$	−26.2401	−	25.3467i	−0.719246	−	0.694756i
$11$	−26.2401	−	25.3467i	−0.719246	−	0.694756i
$12$	84.5585			2.03416
$13$	23.1570	−	16.8245i	0.494045	−	0.358945i	−0.312693	−	0.949854i	$-0.601231\pi$
$13$	23.1570	−	16.8245i	0.494045	−	0.358945i	0.806738	+	0.590910i	$0.201231\pi$
$14$	2.65073	+	8.15810i	0.0506026	+	0.155739i
$15$	−12.1185	+	37.2969i	−0.208599	+	0.642002i
$16$	−108.191	−	78.6055i	−1.69049	−	1.22821i
$17$	−6.36020	−	4.62095i	−0.0907397	−	0.0659262i	0.541490	−	0.840707i	$-0.317860\pi$
$17$	−6.36020	−	4.62095i	−0.0907397	−	0.0659262i	−0.632230	+	0.774781i	$0.717860\pi$
$18$	−10.1653	+	31.2857i	−0.133111	+	0.409672i
$19$	14.8350	+	45.6575i	0.179126	+	0.551292i	0.999798	−	0.0201074i	$-0.00640081\pi$
$19$	14.8350	+	45.6575i	0.179126	+	0.551292i	−0.820672	+	0.571399i	$0.806401\pi$
$20$	130.079	−	94.5077i	1.45432	−	1.05663i
$21$	7.55040			0.0784587
$22$	186.395	+	26.2219i	1.80634	+	0.254115i
$23$	−153.265			−1.38948			−0.694739	−	0.719262i	$-0.744480\pi$
$23$	−153.265			−1.38948			−0.694739	+	0.719262i	$0.744480\pi$
$24$	−201.304	+	146.256i	−1.71213	+	1.24393i
$25$	−15.5841	−	47.9628i	−0.124673	−	0.383703i
$26$	−45.6359	+	140.453i	−0.344228	+	1.05943i
$27$	122.625	+	89.0921i	0.874042	+	0.635029i
$28$	−25.0443	−	18.1958i	−0.169033	−	0.122810i
$29$	74.9153	−	230.566i	0.479704	−	1.47638i	−0.359802	−	0.933029i	$-0.617156\pi$
$29$	74.9153	−	230.566i	0.479704	−	1.47638i	0.839507	−	0.543350i	$-0.182844\pi$
$30$	−62.5244	−	192.430i	−0.380511	−	1.17109i
$31$	−134.251	+	97.5391i	−0.777813	+	0.565114i	−0.904322	−	0.426851i	$-0.859623\pi$
$31$	−134.251	+	97.5391i	−0.777813	+	0.565114i	0.126509	+	0.991965i	$0.459623\pi$
$32$	251.651			1.39019
$33$	72.6507	−	148.905i	0.383238	−	0.785484i
$34$	40.5614			0.204595
$35$	11.6150	−	8.43878i	0.0560940	−	0.0407547i
$36$	−36.6852	−	112.905i	−0.169839	−	0.522710i
$37$	−21.2522	+	65.4077i	−0.0944283	+	0.290620i	−0.987104	−	0.160079i	$-0.948825\pi$
$37$	−21.2522	+	65.4077i	−0.0944283	+	0.290620i	0.892676	+	0.450699i	$0.148825\pi$
$38$	−200.384	−	145.588i	−0.855438	−	0.621512i
$39$	105.165	+	76.4065i	0.431790	+	0.313714i
$40$	−146.207	+	449.979i	−0.577934	+	1.77870i
$41$	95.0373	+	292.495i	0.362008	+	1.11415i	0.951833	+	0.306616i	$0.0991966\pi$
$41$	95.0373	+	292.495i	0.362008	+	1.11415i	−0.589825	+	0.807531i	$0.700803\pi$
$42$	−31.5158	+	22.8976i	−0.115786	+	0.0841231i
$43$	−52.9746			−0.187873			−0.0939367	−	0.995578i	$-0.529945\pi$
$43$	−52.9746			−0.187873			−0.0939367	+	0.995578i	$0.529945\pi$
$44$	−599.825	+	318.828i	−2.05516	+	1.09239i
$45$	55.0576			0.182389
$46$	639.737	−	464.796i	2.05052	−	1.48979i
$47$	−16.8521	−	51.8654i	−0.0523007	−	0.160965i	0.921495	−	0.388391i	$-0.126969\pi$
$47$	−16.8521	−	51.8654i	−0.0523007	−	0.160965i	−0.973795	+	0.227426i	$0.926969\pi$
$48$	187.674	−	577.602i	0.564343	−	1.73687i
$49$	275.257	+	199.986i	0.802497	+	0.583048i
$50$	210.502	+	152.939i	0.595390	+	0.432576i
$51$	11.0327	−	33.9553i	0.0302920	−	0.0932292i
$52$	−164.693	−	506.874i	−0.439209	−	1.35174i
$53$	−202.450	+	147.088i	−0.524691	+	0.381210i	−0.818368	−	0.574694i	$-0.805121\pi$
$53$	−202.450	+	147.088i	−0.524691	+	0.381210i	0.293677	+	0.955905i	$0.405121\pi$
$54$	−782.025			−1.97074
$55$	−54.6643	−	310.263i	−0.134017	−	0.760651i
$56$	91.0939			0.217374
$57$	−176.381	+	128.148i	−0.409863	+	0.297783i
$58$	386.519	+	1189.58i	0.875042	+	2.69310i
$59$	117.153	−	360.561i	0.258509	−	0.795610i	−0.734609	−	0.678491i	$-0.762634\pi$
$59$	117.153	−	360.561i	0.258509	−	0.795610i	0.993118	−	0.117119i	$-0.0373658\pi$
$60$	590.737	+	429.195i	1.27106	+	0.923481i
$61$	−565.131	−	410.592i	−1.18619	−	0.861818i	−0.193334	−	0.981133i	$-0.561930\pi$
$61$	−565.131	−	410.592i	−1.18619	−	0.861818i	−0.992856	+	0.119315i	$0.961930\pi$
$62$	264.571	−	814.267i	0.541945	−	1.66794i
$63$	−3.27569	−	10.0815i	−0.00655077	−	0.0201612i
$64$	−184.877	+	134.321i	−0.361088	+	0.262346i
$65$	247.174			0.471664
$66$	148.325	+	841.859i	0.276629	+	1.57009i
$67$	−278.021			−0.506949			−0.253475	−	0.967342i	$-0.581573\pi$
$67$	−278.021			−0.506949			−0.253475	+	0.967342i	$0.581573\pi$
$68$	−118.424	+	86.0402i	−0.211192	+	0.153440i
$69$	−215.087	−	661.969i	−0.375267	−	1.15495i
$70$	−22.8899	+	70.4479i	−0.0390838	+	0.120288i
$71$	125.156	+	90.9311i	0.209201	+	0.151993i	0.687452	−	0.726230i	$-0.258729\pi$
$71$	125.156	+	90.9311i	0.209201	+	0.151993i	−0.478251	+	0.878223i	$0.658729\pi$
$72$	282.620	+	205.336i	0.462599	+	0.336098i
$73$	−293.936	+	904.642i	−0.471268	+	1.45042i	0.379656	+	0.925128i	$0.376042\pi$
$73$	−293.936	+	904.642i	−0.471268	+	1.45042i	−0.850925	+	0.525288i	$0.823958\pi$
$74$	−109.649	−	337.465i	−0.172249	−	0.530129i
$75$	185.287	−	134.619i	0.285268	−	0.207259i
$76$	893.872			1.34913
$77$	−53.5596	+	28.4688i	−0.0792686	+	0.0421341i
$78$	−670.675			−0.973577
$79$	−1.79641	+	1.30517i	−0.00255838	+	0.00185877i	−0.589064	−	0.808087i	$-0.700503\pi$
$79$	−1.79641	+	1.30517i	−0.00255838	+	0.00185877i	0.586505	+	0.809945i	$0.300503\pi$
$80$	−356.858	−	1098.30i	−0.498724	−	1.53492i
$81$	−159.515	+	490.936i	−0.218813	+	0.673437i
$82$	−1283.72	−	932.676i	−1.72882	−	1.25606i
$83$	614.553	+	446.499i	0.812722	+	0.590477i	0.914618	−	0.404318i	$-0.132491\pi$
$83$	614.553	+	446.499i	0.812722	+	0.590477i	−0.101897	+	0.994795i	$0.532491\pi$
$84$	43.4432	−	133.704i	0.0564291	−	0.173671i
$85$	−20.9785	−	64.5651i	−0.0267698	−	0.0823891i
$86$	221.119	−	160.652i	0.277254	−	0.201437i
$87$	1100.97			1.35674
$88$	876.514	−	1796.50i	1.06178	−	2.17622i
$89$	1157.64			1.37876			0.689382	−	0.724398i	$-0.257882\pi$
$89$	1157.64			1.37876			0.689382	+	0.724398i	$0.257882\pi$
$90$	−229.813	+	166.969i	−0.269161	+	0.195557i
$91$	−14.7058	−	45.2598i	−0.0169405	−	0.0521375i
$92$	−881.852	+	2714.06i	−0.999341	+	3.07566i
$93$	−609.685	−	442.962i	−0.679800	−	0.493904i
$94$	227.630	+	165.383i	0.249769	+	0.181468i
$95$	−128.105	+	394.267i	−0.138351	+	0.425800i
$96$	353.159	+	1086.91i	0.375459	+	1.15554i
$97$	−598.393	+	434.758i	−0.626368	+	0.455083i	−0.855140	−	0.518397i	$-0.826529\pi$
$97$	−598.393	+	434.758i	−0.626368	+	0.455083i	0.228772	+	0.973480i	$0.426529\pi$
$98$	−1755.42			−1.80943
$99$	−230.341	−	32.4042i	−0.233840	−	0.0328964i
$100$	−939.006			−0.939006
$101$	−498.530	+	362.203i	−0.491144	+	0.356837i	−0.805624	−	0.592427i	$-0.798170\pi$
$101$	−498.530	+	362.203i	−0.491144	+	0.356837i	0.314480	+	0.949264i	$0.398170\pi$
$102$	56.9225	+	175.189i	0.0552565	+	0.170062i
$103$	472.029	−	1452.76i	0.451558	−	1.38975i	−0.423572	−	0.905862i	$-0.639224\pi$
$103$	472.029	−	1452.76i	0.451558	−	1.38975i	0.875129	−	0.483889i	$-0.160776\pi$
$104$	1268.79	+	921.828i	1.19630	+	0.869160i
$105$	52.7481	+	38.3237i	0.0490256	+	0.0356192i
$106$	398.972	−	1227.91i	0.365581	−	1.12514i
$107$	−23.0481	−	70.9348i	−0.0208238	−	0.0640890i	0.940105	−	0.340886i	$-0.110727\pi$
$107$	−23.0481	−	70.9348i	−0.0208238	−	0.0640890i	−0.960928	+	0.276797i	$0.910727\pi$
$108$	2283.22	−	1658.86i	2.03429	−	1.47800i
$109$	583.022			0.512325			0.256162	−	0.966634i	$-0.417542\pi$
$109$	583.022			0.512325			0.256162	+	0.966634i	$0.417542\pi$
$110$	1169.08	+	1129.28i	1.01334	+	0.978840i
$111$	−312.328			−0.267070
$112$	−179.876	+	130.688i	−0.151756	+	0.110258i
$113$	−56.3647	−	173.473i	−0.0469234	−	0.144415i	0.924850	−	0.380333i	$-0.124191\pi$
$113$	−56.3647	−	173.473i	−0.0469234	−	0.144415i	−0.971773	+	0.235917i	$0.924191\pi$
$114$	347.597	−	1069.79i	0.285574	−	0.878907i
$115$	−1070.73	−	777.931i	−0.868227	−	0.630804i
$116$	−3651.87	−	2653.24i	−2.92300	−	2.12368i
$117$	56.3955	−	173.568i	0.0445621	−	0.137148i
$118$	604.442	+	1860.28i	0.471554	+	1.45130i
$119$	−10.5743	+	7.68270i	−0.00814577	+	0.00591825i
$120$	−2148.69			−1.63456
$121$	46.0904	+	1330.20i	0.0346284	+	0.999400i
$122$	3604.06			2.67456
$123$	−1129.95	+	820.953i	−0.828323	+	0.601812i
$124$	954.799	+	2938.57i	0.691480	+	2.12816i
$125$	468.131	−	1440.76i	0.334968	−	1.03092i
$126$	44.2465	+	32.1470i	0.0312841	+	0.0227292i
$127$	117.331	+	85.2459i	0.0819798	+	0.0595618i	0.628020	−	0.778197i	$-0.283866\pi$
$127$	117.331	+	85.2459i	0.0819798	+	0.0595618i	−0.546040	+	0.837759i	$0.683866\pi$
$128$	−257.776	+	793.352i	−0.178003	+	0.547836i
$129$	−74.3427	−	228.803i	−0.0507404	−	0.156163i
$130$	−1031.72	+	749.587i	−0.696059	+	0.505716i
$131$	−2.12942			−0.00142022			−0.000710109	−	1.00000i	$-0.500226\pi$
$131$	−2.12942			−0.00142022			−0.000710109		1.00000i	$0.500226\pi$
$132$	−2218.83	−	2143.28i	−1.46306	−	1.41325i
$133$	79.8156			0.0520368
$134$	1160.47	−	843.133i	0.748131	−	0.543549i
$135$	404.466	+	1244.82i	0.257858	+	0.793606i
$136$	133.108	−	409.663i	0.0839256	−	0.258296i
$137$	321.914	+	233.884i	0.200752	+	0.145855i	0.683619	−	0.729839i	$-0.260405\pi$
$137$	321.914	+	233.884i	0.200752	+	0.145855i	−0.482868	+	0.875693i	$0.660405\pi$
$138$	2905.29	+	2110.82i	1.79214	+	1.30206i
$139$	80.7202	−	248.431i	0.0492561	−	0.151595i	−0.923403	−	0.383831i	$-0.874604\pi$
$139$	80.7202	−	248.431i	0.0492561	−	0.151595i	0.972659	+	0.232237i	$0.0746044\pi$
$140$	−82.6062	−	254.236i	−0.0498679	−	0.153478i
$141$	200.363	−	145.572i	0.119671	−	0.0869460i
$142$	−798.168			−0.471695
$143$	−1034.09	−	145.475i	−0.604719	−	0.0850713i
$144$	−852.654			−0.493434
$145$	1693.65	−	1230.51i	0.970002	−	0.704748i
$146$	−1516.54	−	4667.42i	−0.859654	−	2.64574i
$147$	−477.475	+	1469.52i	−0.267901	+	0.824515i
$148$	1035.98	+	752.680i	0.575383	+	0.418040i
$149$	−766.961	−	557.230i	−0.421691	−	0.306376i	0.356627	−	0.934247i	$-0.383927\pi$
$149$	−766.961	−	557.230i	−0.421691	−	0.306376i	−0.778318	+	0.627871i	$0.783927\pi$
$150$	−365.148	+	1123.81i	−0.198762	+	0.611725i
$151$	560.925	+	1726.35i	0.302301	+	0.930386i	0.980671	+	0.195666i	$0.0626868\pi$
$151$	560.925	+	1726.35i	0.302301	+	0.930386i	−0.678370	+	0.734721i	$0.737313\pi$
$152$	−2127.99	+	1546.08i	−1.13555	+	0.825023i
$153$	−50.1247			−0.0264859
$154$	137.225	−	281.257i	0.0718048	−	0.147171i
$155$	−1432.98			−0.742577
$156$	1958.12	−	1422.66i	1.00497	−	0.730152i
$157$	−285.706	−	879.314i	−0.145235	−	0.446986i	0.851806	−	0.523857i	$-0.175507\pi$
$157$	−285.706	−	879.314i	−0.145235	−	0.446986i	−0.997041	+	0.0768703i	$0.975507\pi$
$158$	3.54023	−	10.8957i	0.00178257	−	0.00548617i
$159$	−919.402	−	667.985i	−0.458574	−	0.333174i
$160$	1758.07	+	1277.31i	0.868672	+	0.631127i
$161$	−78.7423	+	242.344i	−0.0385451	+	0.118630i
$162$	−823.002	−	2532.94i	−0.399143	−	1.22844i
$163$	2372.06	−	1723.40i	1.13984	−	0.828143i	0.152744	−	0.988266i	$-0.451189\pi$
$163$	2372.06	−	1723.40i	1.13984	−	0.828143i	0.987097	+	0.160123i	$0.0511891\pi$
$164$	5726.40			2.72656
$165$	1263.35	−	671.513i	0.596068	−	0.316832i
$166$	−3919.24			−1.83248
$167$	−890.503	+	646.988i	−0.412630	+	0.299793i	−0.774666	−	0.632371i	$-0.782082\pi$
$167$	−890.503	+	646.988i	−0.412630	+	0.299793i	0.362036	+	0.932164i	$0.382082\pi$
$168$	127.838	+	393.445i	0.0587078	+	0.180684i
$169$	−425.730	+	1310.26i	−0.193778	+	0.596387i
$170$	283.367	+	205.878i	0.127843	+	0.0928833i
$171$	247.629	+	179.913i	0.110741	+	0.0804579i
$172$	−304.803	+	938.088i	−0.135122	+	0.415864i
$173$	−1115.66	−	3433.65i	−0.490301	−	1.50899i	−0.824153	−	0.566367i	$-0.808349\pi$
$173$	−1115.66	−	3433.65i	−0.490301	−	1.50899i	0.333852	−	0.942626i	$-0.391651\pi$
$174$	−4595.52	+	3338.84i	−2.00221	+	1.45469i
$175$	−83.8457			−0.0362179
$176$	846.563	+	4804.91i	0.362569	+	2.05786i
$177$	1721.71			0.731139
$178$	−4832.07	+	3510.70i	−2.03471	+	1.47831i
$179$	1060.08	+	3262.59i	0.442648	+	1.36233i	0.885043	+	0.465510i	$0.154129\pi$
$179$	1060.08	+	3262.59i	0.442648	+	1.36233i	−0.442395	+	0.896821i	$0.645871\pi$
$180$	316.788	−	974.974i	0.131178	−	0.403724i
$181$	2997.81	+	2178.04i	1.23108	+	0.894433i	0.996971	−	0.0777766i	$-0.0247821\pi$
$181$	2997.81	+	2178.04i	1.23108	+	0.894433i	0.234111	+	0.972210i	$0.424782\pi$
$182$	198.639	+	144.320i	0.0809016	+	0.0587785i
$183$	980.307	−	3017.07i	0.395991	−	1.21873i
$184$	−2594.98	−	7986.51i	−1.03970	−	3.19986i
$185$	−480.462	+	349.076i	−0.190942	+	0.138727i
$186$	3888.20			1.53278
$187$	49.7666	+	282.464i	0.0194615	+	0.110459i
$188$	−1015.41			−0.393917
$189$	203.873	−	148.123i	0.0784635	−	0.0570070i
$190$	−660.948	−	2034.19i	−0.252370	−	0.776713i
$191$	−939.172	+	2890.48i	−0.355791	+	1.09501i	0.599758	+	0.800181i	$0.295264\pi$
$191$	−939.172	+	2890.48i	−0.355791	+	1.09501i	−0.955549	+	0.294831i	$0.904736\pi$
$192$	−839.596	−	610.003i	−0.315587	−	0.229287i
$193$	565.820	+	411.092i	0.211029	+	0.153322i	0.688279	−	0.725446i	$-0.258366\pi$
$193$	565.820	+	411.092i	0.211029	+	0.153322i	−0.477250	+	0.878768i	$0.658366\pi$
$194$	1179.27	−	3629.41i	0.436425	−	1.34318i
$195$	346.875	+	1067.57i	0.127386	+	0.392053i
$196$	5125.16	−	3723.65i	1.86777	−	1.35701i
$197$	−4239.08			−1.53311			−0.766553	−	0.642181i	$-0.778030\pi$
$197$	−4239.08			−1.53311			−0.766553	+	0.642181i	$0.778030\pi$
$198$	1059.73	−	563.283i	0.380361	−	0.202176i
$199$	−2020.32			−0.719680			−0.359840	−	0.933014i	$-0.617169\pi$
$199$	−2020.32			−0.719680			−0.359840	+	0.933014i	$0.617169\pi$
$200$	2235.44	−	1624.14i	0.790348	−	0.574222i
$201$	−390.164	−	1200.80i	−0.136916	−	0.421383i
$202$	982.464	−	3023.71i	0.342207	−	1.05321i
$203$	−326.083	−	236.913i	−0.112742	−	0.0819115i
$204$	−537.809	−	390.741i	−0.184579	−	0.134105i
$205$	−820.678	+	2525.79i	−0.279603	+	0.860530i
$206$	2435.40	+	7495.38i	0.823699	+	2.53509i
$207$	−790.569	+	574.382i	−0.265451	+	0.192861i
$208$	−3827.88			−1.27604
$209$	767.993	−	1574.08i	0.254178	−	0.520963i
$210$	−336.395			−0.110540
$211$	4472.00	−	3249.10i	1.45908	−	1.06008i	0.475473	−	0.879730i	$-0.342277\pi$
$211$	4472.00	−	3249.10i	1.45908	−	1.06008i	0.983602	−	0.180350i	$-0.0577231\pi$
$212$	1439.83	+	4431.35i	0.466453	+	1.43559i
$213$	−217.102	+	668.171i	−0.0698384	+	0.214941i
$214$	311.323	+	226.189i	0.0994467	+	0.0722523i
$215$	−370.087	−	268.884i	−0.117394	−	0.0852919i
$216$	−2566.32	+	7898.31i	−0.808406	+	2.48802i
$217$	85.2560	+	262.391i	0.0266707	+	0.0820841i
$218$	−2433.57	+	1768.09i	−0.756064	+	0.549312i
$219$	−4319.75			−1.33288
$220$	−5808.74	−	817.168i	−1.78011	−	0.250425i
$221$	−225.028			−0.0684934
$222$	1303.67	−	947.173i	0.394130	−	0.286352i
$223$	−1011.25	−	3112.31i	−0.303670	−	0.934600i	−0.980170	−	0.198157i	$-0.936504\pi$
$223$	−1011.25	−	3112.31i	−0.303670	−	0.934600i	0.676500	−	0.736442i	$-0.263496\pi$
$224$	129.290	−	397.913i	0.0385649	−	0.118690i
$225$	−260.133	−	188.997i	−0.0770763	−	0.0559992i
$226$	761.347	+	553.151i	0.224089	+	0.162810i
$227$	1742.88	−	5364.04i	0.509600	−	1.56839i	−0.283298	−	0.959032i	$-0.591428\pi$
$227$	1742.88	−	5364.04i	0.509600	−	1.56839i	0.792897	−	0.609355i	$-0.208572\pi$
$228$	1254.43	+	3860.73i	0.364371	+	1.12142i
$229$	−883.468	+	641.877i	−0.254940	+	0.185225i	−0.707913	−	0.706299i	$-0.750363\pi$
$229$	−883.468	+	641.877i	−0.254940	+	0.185225i	0.452973	+	0.891524i	$0.350363\pi$
$230$	6828.46			1.95763
$231$	−198.124	−	191.378i	−0.0564311	−	0.0545097i
$232$	13283.0			3.75892
$233$	1331.44	−	967.350i	0.374359	−	0.271988i	−0.384657	−	0.923060i	$-0.625680\pi$
$233$	1331.44	−	967.350i	0.374359	−	0.271988i	0.759016	+	0.651072i	$0.225680\pi$
$234$	290.968	+	895.507i	0.0812871	+	0.250176i
$235$	145.523	−	447.875i	0.0403953	−	0.124324i
$236$	−5710.83	−	4149.16i	−1.57518	−	1.14444i
$237$	−8.15819	−	5.92727i	−0.00223600	−	0.00162455i
$238$	20.8391	−	64.1360i	0.00567561	−	0.0174677i
$239$	251.820	+	775.023i	0.0681544	+	0.209758i	0.979333	−	0.202253i	$-0.0648265\pi$
$239$	251.820	+	775.023i	0.0681544	+	0.209758i	−0.911179	+	0.412011i	$0.864826\pi$
$240$	4242.86	−	3082.62i	1.14115	−	0.829092i
$241$	−6368.48			−1.70220			−0.851100	−	0.525004i	$-0.824064\pi$
$241$	−6368.48			−1.70220			−0.851100	+	0.525004i	$0.824064\pi$
$242$	−4226.39	−	5412.56i	−1.12266	−	1.43774i
$243$	1748.19			0.461509
$244$	−10522.5	+	7645.04i	−2.76079	+	2.00583i
$245$	907.907	+	2794.25i	0.236751	+	0.728645i
$246$	2226.81	−	6853.41i	0.577138	−	1.77625i
$247$	1111.70	+	807.697i	0.286379	+	0.208067i
$248$	−7355.72	−	5344.24i	−1.88342	−	1.36839i
$249$	−1066.04	+	3280.92i	−0.271314	+	0.835020i
$250$	2415.28	+	7433.48i	0.611024	+	1.88054i
$251$	512.385	−	372.269i	0.128850	−	0.0936153i	−0.521493	−	0.853255i	$-0.674625\pi$
$251$	512.385	−	372.269i	0.128850	−	0.0936153i	0.650344	+	0.759640i	$0.274625\pi$
$252$	−197.374			−0.0493389
$253$	4021.70	+	3884.77i	0.999376	+	0.965348i
$254$	−748.264			−0.184844
$255$	249.424	−	181.217i	0.0612530	−	0.0445029i
$256$	−1894.91	−	5831.92i	−0.462623	−	1.42381i
$257$	141.266	−	434.772i	0.0342877	−	0.105527i	−0.932448	−	0.361304i	$-0.882332\pi$
$257$	141.266	−	434.772i	0.0342877	−	0.105527i	0.966736	+	0.255778i	$0.0823315\pi$
$258$	1004.19	+	729.583i	0.242317	+	0.176054i
$259$	92.5044	+	67.2083i	0.0221928	+	0.0161240i
$260$	1422.18	−	4377.02i	0.339230	−	1.04404i
$261$	−477.649	−	1470.05i	−0.113279	−	0.348636i
$262$	8.88832	−	6.45774i	0.00209589	−	0.00152275i
$263$	6954.78			1.63061			0.815305	−	0.579032i	$-0.196570\pi$
$263$	6954.78			1.63061			0.815305	+	0.579032i	$0.196570\pi$
$264$	8989.36	+	1264.62i	2.09567	+	0.294817i
$265$	−2160.92			−0.500922
$266$	−333.155	+	242.051i	−0.0767933	+	0.0557936i
$267$	1624.60	+	4999.99i	0.372373	+	1.14605i
$268$	−1599.66	+	4923.26i	−0.364608	+	1.12215i
$269$	3576.88	+	2598.76i	0.810730	+	0.589030i	0.914042	−	0.405619i	$-0.132944\pi$
$269$	3576.88	+	2598.76i	0.810730	+	0.589030i	−0.103312	+	0.994649i	$0.532944\pi$
$270$	−5463.33	−	3969.34i	−1.23144	−	0.894690i
$271$	1080.12	−	3324.28i	0.242114	−	0.745151i	−0.753984	−	0.656893i	$-0.771870\pi$
$271$	1080.12	−	3324.28i	0.242114	−	0.745151i	0.996098	−	0.0882573i	$-0.0281298\pi$
$272$	324.885	+	999.893i	0.0724230	+	0.222895i
$273$	174.844	−	127.032i	0.0387621	−	0.0281623i
$274$	−2052.97			−0.452644
$275$	−806.771	+	1653.56i	−0.176910	+	0.362594i
$276$	−12959.9			−2.82643
$277$	−2219.84	+	1612.80i	−0.481505	+	0.349834i	−0.801908	−	0.597447i	$-0.796182\pi$
$277$	−2219.84	+	1612.80i	−0.481505	+	0.349834i	0.320403	+	0.947281i	$0.396182\pi$
$278$	416.469	+	1281.76i	0.0898495	+	0.276528i
$279$	−326.950	+	1006.25i	−0.0701576	+	0.215923i
$280$	636.394	+	462.367i	0.135828	+	0.0986847i
$281$	1415.40	+	1028.35i	0.300483	+	0.218313i	0.727802	−	0.685787i	$-0.240542\pi$
$281$	1415.40	+	1028.35i	0.300483	+	0.218313i	−0.427319	+	0.904101i	$0.640542\pi$
$282$	−394.859	+	1215.25i	−0.0833813	+	0.256621i
$283$	−640.941	−	1972.61i	−0.134629	−	0.414345i	0.860903	−	0.508769i	$-0.169899\pi$
$283$	−640.941	−	1972.61i	−0.134629	−	0.414345i	−0.995532	+	0.0944237i	$0.969899\pi$
$284$	2330.35	−	1693.10i	0.486904	−	0.353756i
$285$	−1882.66			−0.391296
$286$	4757.51	−	2528.78i	0.983627	−	0.522833i
$287$	511.321			0.105165
$288$	1298.06	−	943.097i	0.265587	−	0.192960i
$289$	−1499.10	−	4613.76i	−0.305130	−	0.939092i
$290$	−3337.72	+	10272.4i	−0.675854	+	2.08006i
$291$	−2717.53	−	1974.40i	−0.547438	−	0.397737i
$292$	14328.4	+	10410.2i	2.87160	+	2.08634i
$293$	−1088.24	+	3349.25i	−0.216981	+	0.667799i	0.782026	+	0.623246i	$0.214186\pi$
$293$	−1088.24	+	3349.25i	−0.216981	+	0.667799i	−0.999007	+	0.0445534i	$0.985814\pi$
$294$	−2463.49	−	7581.84i	−0.488686	−	1.50402i
$295$	2648.55	−	1924.29i	0.522727	−	0.379784i
$296$	−3768.16			−0.739932
$297$	−959.501	−	5445.92i	−0.187461	−	1.06399i
$298$	4891.21			0.950806
$299$	−3549.16	+	2578.61i	−0.686465	+	0.498746i
$300$	−1317.77	−	4055.67i	−0.253604	−	0.780514i
$301$	−27.2165	+	83.7638i	−0.00521174	+	0.0160401i
$302$	−7576.71	−	5504.80i	−1.44368	−	1.04889i
$303$	−2264.01	−	1644.90i	−0.429255	−	0.311872i
$304$	1983.91	−	6105.85i	0.374293	−	1.15196i
$305$	−1864.03	−	5736.89i	−0.349948	−	1.07703i
$306$	209.223	−	152.009i	0.0390866	−	0.0283981i
$307$	6944.40			1.29100			0.645501	−	0.763759i	$-0.276648\pi$
$307$	6944.40			1.29100			0.645501	+	0.763759i	$0.276648\pi$
$308$	195.964	+	1112.25i	0.0362536	+	0.205767i
$309$	6937.05			1.27714
$310$	5981.32	−	4345.68i	1.09586	−	0.796188i
$311$	707.667	+	2177.98i	0.129029	+	0.397111i	0.994614	−	0.103652i	$-0.0330527\pi$
$311$	707.667	+	2177.98i	0.129029	+	0.397111i	−0.865584	+	0.500763i	$0.833053\pi$
$312$	−2200.91	+	6773.69i	−0.399365	+	1.22912i
$313$	−6406.71	−	4654.75i	−1.15696	−	0.840581i	−0.167570	−	0.985860i	$-0.553592\pi$
$313$	−6406.71	−	4654.75i	−1.15696	−	0.840581i	−0.989391	+	0.145279i	$0.953592\pi$
$314$	3859.19	+	2803.86i	0.693587	+	0.503921i
$315$	28.2867	−	87.0574i	0.00505960	−	0.0155718i
$316$	12.7762	+	39.3210i	0.00227441	+	0.00699993i
$317$	1122.42	−	815.485i	0.198869	−	0.144486i	−0.483894	−	0.875126i	$-0.660778\pi$
$317$	1122.42	−	815.485i	0.198869	−	0.144486i	0.682763	+	0.730640i	$0.260778\pi$
$318$	5863.38			1.03397
$319$	−7809.87	+	4151.22i	−1.37075	+	0.728601i
$320$	−1973.35			−0.344730
$321$	274.030	−	199.095i	0.0476476	−	0.0346180i
$322$	−406.264	−	1250.35i	−0.0703112	−	0.216396i
$323$	116.628	−	358.943i	0.0200908	−	0.0618331i
$324$	7775.81	+	5649.45i	1.33330	+	0.968699i
$325$	−1167.83	−	848.479i	−0.199322	−	0.144816i
$326$	−4674.67	+	14387.1i	−0.794190	+	2.44427i
$327$	818.192	+	2518.14i	0.138367	+	0.425851i
$328$	−13632.5	+	9904.62i	−2.29491	+	1.66735i
$329$	−90.6680			−0.0151936
$330$	−3236.82	+	6634.19i	−0.539943	+	1.10667i
$331$	−11641.4			−1.93315			−0.966574	−	0.256389i	$-0.917467\pi$
$331$	−11641.4			−1.93315			−0.966574	+	0.256389i	$0.917467\pi$
$332$	11442.7	−	8313.61i	1.89157	−	1.37430i
$333$	135.501	+	417.030i	0.0222986	+	0.0686279i
$334$	1754.93	−	5401.13i	0.287502	−	0.884840i
$335$	−1942.29	−	1411.15i	−0.316772	−	0.230148i
$336$	−816.887	−	593.503i	−0.132634	−	0.0963639i
$337$	−2619.63	+	8062.40i	−0.423444	+	1.30323i	0.481033	+	0.876702i	$0.340262\pi$
$337$	−2619.63	+	8062.40i	−0.423444	+	1.30323i	−0.904477	+	0.426523i	$0.859738\pi$
$338$	−2196.52	−	6760.19i	−0.353476	−	1.08789i
$339$	670.147	−	486.890i	0.107367	−	0.0780066i
$340$	−1264.04			−0.201624
$341$	5995.06	+	843.380i	0.952055	+	0.133934i
$342$	−1579.23			−0.249692
$343$	918.989	−	667.685i	0.144667	−	0.105107i
$344$	−896.928	−	2760.46i	−0.140579	−	0.432657i
$345$	1857.35	−	5716.32i	0.289844	−	0.892048i
$346$	15069.8	+	10948.9i	2.34150	+	1.70120i
$347$	1546.04	+	1123.27i	0.239181	+	0.173775i	0.700918	−	0.713241i	$-0.252774\pi$
$347$	1546.04	+	1123.27i	0.239181	+	0.173775i	−0.461737	+	0.887017i	$0.652774\pi$
$348$	6334.73	−	19496.3i	0.975797	−	3.00319i
$349$	2665.62	+	8203.92i	0.408846	+	1.25830i	0.917641	+	0.397410i	$0.130091\pi$
$349$	2665.62	+	8203.92i	0.408846	+	1.25830i	−0.508796	+	0.860887i	$0.669909\pi$
$350$	349.977	−	254.273i	0.0534487	−	0.0388327i
$351$	4338.55			0.659756
$352$	−6603.37	−	6378.53i	−0.999889	−	0.965843i
$353$	6345.10			0.956702			0.478351	−	0.878169i	$-0.341235\pi$
$353$	6345.10			0.956702			0.478351	+	0.878169i	$0.341235\pi$
$354$	−7186.51	+	5221.30i	−1.07898	+	0.783924i
$355$	412.814	+	1270.51i	0.0617181	+	0.189949i
$356$	6660.81	−	20499.9i	0.991635	−	3.05194i
$357$	−48.0221	−	34.8901i	−0.00711932	−	0.00517249i
$358$	−14319.0	−	10403.4i	−2.11392	−	1.53586i
$359$	1412.92	−	4348.52i	0.207719	−	0.639292i	−0.791872	−	0.610687i	$-0.790893\pi$
$359$	1412.92	−	4348.52i	0.207719	−	0.639292i	0.999591	−	0.0286053i	$-0.00910660\pi$
$360$	932.195	+	2869.00i	0.136475	+	0.420027i
$361$	3684.52	−	2676.96i	0.537180	−	0.390284i
$362$	−19118.2			−2.77578
$363$	−5680.61	+	2065.83i	−0.821362	+	0.298699i
$364$	−886.085			−0.127592
$365$	−6645.18	+	4828.01i	−0.952944	+	0.692354i
$366$	5057.81	+	15566.3i	0.722338	+	2.22313i
$367$	440.465	−	1355.61i	0.0626487	−	0.192813i	−0.914833	−	0.403832i	$-0.867678\pi$
$367$	440.465	−	1355.61i	0.0626487	−	0.192813i	0.977482	+	0.211019i	$0.0676781\pi$
$368$	16582.0	+	12047.5i	2.34890	+	1.70657i
$369$	1586.38	+	1152.57i	0.223804	+	0.162603i
$370$	946.856	−	2914.12i	0.133040	−	0.409454i
$371$	128.565	+	395.684i	0.0179913	+	0.0553716i
$372$	−11352.1	+	8247.77i	−1.58220	+	1.14953i
$373$	8121.64			1.12741			0.563703	−	0.825977i	$-0.309376\pi$
$373$	8121.64			1.12741			0.563703	+	0.825977i	$0.309376\pi$
$374$	−1064.34	−	1028.10i	−0.147154	−	0.142144i
$375$	6879.76			0.947385
$376$	2417.33	−	1756.30i	0.331554	−	0.240888i
$377$	−2144.34	−	6599.61i	−0.292943	−	0.901585i
$378$	−401.777	+	1236.54i	−0.0546698	+	0.168256i
$379$	−4285.43	−	3113.54i	−0.580811	−	0.421984i	0.258205	−	0.966090i	$-0.416869\pi$
$379$	−4285.43	−	3113.54i	−0.580811	−	0.421984i	−0.839017	+	0.544106i	$0.816869\pi$
$380$	6244.70	+	4537.04i	0.843017	+	0.612488i
$381$	−203.528	+	626.396i	−0.0273676	+	0.0842290i
$382$	−4845.58	−	14913.2i	−0.649009	−	1.99744i
$383$	−8929.36	+	6487.56i	−1.19130	+	0.865532i	−0.993401	−	0.114690i	$-0.963412\pi$
$383$	−8929.36	+	6487.56i	−1.19130	+	0.865532i	−0.197901	+	0.980222i	$0.563412\pi$
$384$	−3788.33			−0.503443
$385$	−518.674	−	72.9666i	−0.0686599	−	0.00965902i
$386$	−3608.45			−0.475817
$387$	−273.252	+	198.529i	−0.0358920	+	0.0260771i
$388$	4255.80	+	13098.0i	0.556844	+	1.71379i
$389$	3436.44	−	10576.3i	0.447903	−	1.37851i	−0.431365	−	0.902178i	$-0.641968\pi$
$389$	3436.44	−	10576.3i	0.447903	−	1.37851i	0.879268	−	0.476327i	$-0.158032\pi$
$390$	−4685.42	−	3404.16i	−0.608348	−	0.441990i
$391$	974.797	+	708.232i	0.126081	+	0.0916031i
$392$	−5760.63	+	17729.4i	−0.742234	+	2.28436i
$393$	−2.98835	−	9.19721i	−0.000383569	−	0.00118050i
$394$	17694.1	−	12855.6i	2.26248	−	1.64379i
$395$	−19.1746			−0.00244248
$396$	−1899.15	+	3892.50i	−0.241000	+	0.493953i
$397$	−2320.56			−0.293364			−0.146682	−	0.989184i	$-0.546859\pi$
$397$	−2320.56			−0.293364			−0.146682	+	0.989184i	$0.546859\pi$
$398$	8432.91	−	6126.86i	1.06207	−	0.771638i
$399$	112.010	+	344.732i	0.0140540	+	0.0432537i
$400$	−2084.08	+	6414.15i	−0.260511	+	0.801769i
$401$	−394.560	−	286.665i	−0.0491357	−	0.0356992i	0.562946	−	0.826493i	$-0.309668\pi$
$401$	−394.560	−	286.665i	−0.0491357	−	0.0356992i	−0.612082	+	0.790794i	$0.709668\pi$
$402$	5270.15	+	3828.99i	0.653859	+	0.475056i
$403$	−1467.80	+	4517.42i	−0.181430	+	0.558384i
$404$	3545.57	+	10912.1i	0.436630	+	1.34381i
$405$	−3606.24	+	2620.09i	−0.442458	+	0.321465i
$406$	2079.56			0.254204
$407$	2215.53	−	1177.63i	0.269827	−	0.143423i
$408$	1956.18			0.237366
$409$	8135.14	−	5910.52i	0.983513	−	0.714564i	0.0250218	−	0.999687i	$-0.492034\pi$
$409$	8135.14	−	5910.52i	0.983513	−	0.714564i	0.958491	+	0.285123i	$0.0920345\pi$
$410$	−4234.22	−	13031.6i	−0.510032	−	1.56972i
$411$	−558.409	+	1718.61i	−0.0670177	+	0.206259i
$412$	−23009.8	−	16717.6i	−2.75149	−	1.99907i
$413$	−509.931	−	370.487i	−0.0607556	−	0.0441416i
$414$	1557.99	−	4795.00i	0.184954	−	0.569231i
$415$	2027.04	+	6238.59i	0.239768	+	0.737929i
$416$	5827.48	−	4233.91i	0.686817	−	0.499002i
$417$	1186.28			0.139310
$418$	1567.95	+	8899.32i	0.183471	+	1.04134i
$419$	1237.92			0.144335			0.0721675	−	0.997393i	$-0.477008\pi$
$419$	1237.92			0.144335			0.0721675	+	0.997393i	$0.477008\pi$
$420$	982.146	−	713.571i	0.114104	−	0.0829017i
$421$	−1224.17	−	3767.59i	−0.141715	−	0.436155i	0.854859	−	0.518861i	$-0.173644\pi$
$421$	−1224.17	−	3767.59i	−0.141715	−	0.436155i	−0.996574	+	0.0827059i	$0.973644\pi$
$422$	−8813.06	+	27123.8i	−1.01662	+	3.12883i
$423$	−281.299	−	204.376i	−0.0323338	−	0.0234919i
$424$	−11092.4	−	8059.08i	−1.27050	−	0.923075i
$425$	−122.516	+	377.066i	−0.0139833	+	0.0430363i
$426$	−1120.12	−	3447.37i	−0.127394	−	0.392079i
$427$	−939.575	+	682.641i	−0.106485	+	0.0773661i
$428$	−1388.74			−0.156840
$429$	−822.881	−	4670.49i	−0.0926085	−	0.525626i
$430$	2360.19			0.264694
$431$	−6886.78	+	5003.54i	−0.769662	+	0.559192i	−0.901859	−	0.432031i	$-0.857797\pi$
$431$	−6886.78	+	5003.54i	−0.769662	+	0.559192i	0.132197	+	0.991224i	$0.457797\pi$
$432$	−6263.79	−	19278.0i	−0.697608	−	2.14702i
$433$	−3339.00	+	10276.4i	−0.370582	+	1.14053i	0.575829	+	0.817570i	$0.304679\pi$
$433$	−3339.00	+	10276.4i	−0.370582	+	1.14053i	−0.946411	+	0.322964i	$0.895321\pi$
$434$	−1151.60	−	836.684i	−0.127370	−	0.0925395i
$435$	7691.53	+	5588.22i	0.847771	+	0.615942i
$436$	3354.57	−	10324.3i	0.368474	−	1.13405i
$437$	−2273.69	−	6997.70i	−0.248891	−	0.766008i
$438$	18030.9	−	13100.2i	1.96700	−	1.42911i
$439$	3175.21			0.345204			0.172602	−	0.984992i	$-0.444783\pi$
$439$	3175.21			0.345204			0.172602	+	0.984992i	$0.444783\pi$
$440$	15242.0	−	8101.65i	1.65144	−	0.877798i
$441$	2169.29			0.234240
$442$	939.280	−	682.427i	0.101079	−	0.0734383i
$443$	−733.995	−	2259.00i	−0.0787204	−	0.242276i	0.903950	−	0.427638i	$-0.140654\pi$
$443$	−733.995	−	2259.00i	−0.0787204	−	0.242276i	−0.982670	+	0.185362i	$0.940654\pi$
$444$	−1797.06	+	5530.78i	−0.192082	+	0.591169i
$445$	8087.45	+	5875.87i	0.861532	+	0.625940i
$446$	13659.5	+	9924.21i	1.45022	+	1.05364i
$447$	1330.41	−	4094.59i	0.140775	−	0.433260i
$448$	117.406	+	361.338i	0.0123815	+	0.0381063i
$449$	−6609.71	+	4802.23i	−0.694725	+	0.504747i	−0.878210	−	0.478275i	$-0.841262\pi$
$449$	−6609.71	+	4802.23i	−0.694725	+	0.504747i	0.183485	+	0.983022i	$0.441262\pi$
$450$	1658.97			0.173788
$451$	4919.98	−	10084.0i	0.513687	−	1.05285i
$452$	−3396.21			−0.353416
$453$	−6669.11	+	4845.39i	−0.691705	+	0.502553i
$454$	8992.25	+	27675.3i	0.929576	+	2.86094i
$455$	126.989	−	390.833i	0.0130843	−	0.0402693i
$456$	−9664.03	−	7021.33i	−0.992456	−	0.721061i
$457$	−7454.30	−	5415.86i	−0.763014	−	0.554362i	0.136819	−	0.990596i	$-0.456312\pi$
$457$	−7454.30	−	5415.86i	−0.763014	−	0.554362i	−0.899833	+	0.436234i	$0.856312\pi$
$458$	1741.07	−	5358.46i	0.177631	−	0.546691i
$459$	−368.227	−	1133.29i	−0.0374452	−	0.115245i
$460$	−19936.5	+	14484.7i	−2.02075	+	1.46816i
$461$	−4588.84			−0.463609			−0.231804	−	0.972762i	$-0.574463\pi$
$461$	−4588.84			−0.463609			−0.231804	+	0.972762i	$0.574463\pi$
$462$	1407.36	+	197.986i	0.141723	+	0.0199375i
$463$	−11230.6			−1.12728			−0.563639	−	0.826021i	$-0.690599\pi$
$463$	−11230.6			−1.12728			−0.563639	+	0.826021i	$0.690599\pi$
$464$	−26228.9	+	19056.4i	−2.62424	+	1.90662i
$465$	−2010.99	−	6189.18i	−0.200553	−	0.617240i
$466$	−2623.90	+	8075.54i	−0.260837	+	0.802773i
$467$	10566.7	+	7677.17i	1.04704	+	0.760722i	0.971648	−	0.236432i	$-0.0759781\pi$
$467$	10566.7	+	7677.17i	1.04704	+	0.760722i	0.0753954	+	0.997154i	$0.475978\pi$
$468$	−2749.09	−	1997.33i	−0.271532	−	0.197279i
$469$	−142.837	+	439.608i	−0.0140631	+	0.0432819i
$470$	750.816	+	2310.77i	0.0736863	+	0.226783i
$471$	3396.90	−	2467.99i	0.332316	−	0.241442i
$472$	20772.0			2.02566
$473$	1390.06	+	1342.73i	0.135127	+	0.130526i
$474$	52.0280			0.00504161
$475$	1958.67	−	1423.06i	0.189200	−	0.137462i
$476$	75.2051	+	231.457i	0.00724164	+	0.0222875i
$477$	−493.038	+	1517.42i	−0.0473264	+	0.145656i
$478$	−3401.47	−	2471.31i	−0.325480	−	0.236475i
$479$	−12911.7	−	9380.93i	−1.23163	−	0.894835i	−0.234623	−	0.972087i	$-0.575385\pi$
$479$	−12911.7	−	9380.93i	−1.23163	−	0.894835i	−0.997012	+	0.0772519i	$0.975385\pi$
$480$	−3049.64	+	9385.82i	−0.289992	+	0.892505i
$481$	608.315	+	1872.20i	0.0576648	+	0.177474i
$482$	26582.4	−	19313.2i	2.51202	−	1.82509i
$483$	−1157.21			−0.109017
$484$	23820.8	+	6837.48i	2.23711	+	0.642138i
$485$	−6387.16			−0.597992
$486$	−7297.06	+	5301.62i	−0.681073	+	0.494828i
$487$	−1342.84	−	4132.82i	−0.124948	−	0.384550i	0.868944	−	0.494911i	$-0.164799\pi$
$487$	−1342.84	−	4132.82i	−0.124948	−	0.384550i	−0.993892	+	0.110361i	$0.964799\pi$
$488$	11827.2	−	36400.3i	1.09711	−	3.37657i
$489$	10772.4	+	7826.63i	0.996208	+	0.723788i
$490$	−12263.6	−	8910.01i	−1.13064	−	0.821455i
$491$	898.493	−	2765.28i	0.0825834	−	0.254165i	−0.901236	−	0.433329i	$-0.857339\pi$
$491$	898.493	−	2765.28i	0.0825834	−	0.254165i	0.983819	+	0.179163i	$0.0573390\pi$
$492$	8036.22	+	24732.9i	0.736383	+	2.26636i
$493$	−1541.91	+	1120.26i	−0.140860	+	0.102341i
$494$	−7089.74			−0.645713
$495$	−1444.72	−	1395.53i	−0.131182	−	0.126716i
$496$	22191.9			2.00896
$497$	208.081	−	151.180i	0.0187801	−	0.0136446i
$498$	−5500.12	−	16927.6i	−0.494912	−	1.52318i
$499$	4900.21	−	15081.3i	0.439606	−	1.35297i	−0.448686	−	0.893690i	$-0.648108\pi$
$499$	4900.21	−	15081.3i	0.439606	−	1.35297i	0.888292	−	0.459279i	$-0.151892\pi$
$500$	−22819.8	−	16579.6i	−2.04107	−	1.48292i
$501$	−4044.11	−	2938.22i	−0.360634	−	0.262016i
$502$	−1009.77	+	3107.75i	−0.0897772	+	0.276306i
$503$	592.264	+	1822.80i	0.0525005	+	0.161580i	0.973869	−	0.227110i	$-0.0729277\pi$
$503$	592.264	+	1822.80i	0.0525005	+	0.161580i	−0.921369	+	0.388690i	$0.872928\pi$
$504$	469.879	−	341.387i	0.0415279	−	0.0301718i
$505$	−5321.24			−0.468895
$506$	−28567.9	−	4018.90i	−2.50987	−	0.353087i
$507$	−6256.62			−0.548060
$508$	2184.65	−	1587.24i	0.190803	−	0.138627i
$509$	2745.05	+	8448.39i	0.239041	+	0.735694i	0.996560	+	0.0828798i	$0.0264118\pi$
$509$	2745.05	+	8448.39i	0.239041	+	0.735694i	−0.757518	+	0.652814i	$0.773588\pi$
$510$	−491.544	+	1512.82i	−0.0426783	+	0.131350i
$511$	1279.41	+	929.547i	0.110759	+	0.0804711i
$512$	20196.6	+	14673.7i	1.74330	+	1.26658i
$513$	−2248.58	+	6920.42i	−0.193523	+	0.595602i
$514$	728.850	+	2243.17i	0.0625451	+	0.192494i
$515$	10671.4	−	7753.26i	0.913087	−	0.663397i
$516$	−4479.46			−0.382165
$517$	−872.416	+	1788.10i	−0.0742143	+	0.152110i
$518$	−589.936			−0.0500392
$519$	13264.6	−	9637.33i	1.12187	−	0.815090i
$520$	4184.97	+	12880.0i	0.352929	+	1.08620i
$521$	−4332.81	+	13335.0i	−0.364346	+	1.12134i	0.586044	+	0.810279i	$0.300684\pi$
$521$	−4332.81	+	13335.0i	−0.364346	+	1.12134i	−0.950390	+	0.311061i	$0.899316\pi$
$522$	6451.86	+	4687.55i	0.540977	+	0.393043i
$523$	12238.5	+	8891.81i	1.02324	+	0.743425i	0.966944	−	0.254989i	$-0.0820718\pi$
$523$	12238.5	+	8891.81i	1.02324	+	0.743425i	0.0562933	+	0.998414i	$0.482072\pi$
$524$	−12.2522	+	37.7084i	−0.00102145	+	0.00314370i
$525$	−117.666	−	362.139i	−0.00978165	−	0.0301048i
$526$	−29029.6	+	21091.3i	−2.40637	+	1.74833i
$527$	1304.59			0.107834
$528$	−19564.9	+	10399.4i	−1.61260	+	0.857154i
$529$	11323.2			0.930650
$530$	9019.80	−	6553.27i	0.739236	−	0.537086i
$531$	−746.952	−	2298.88i	−0.0610451	−	0.187878i
$532$	459.240	−	1413.40i	0.0374259	−	0.115185i
$533$	7121.86	+	5174.33i	0.578765	+	0.420498i
$534$	−21944.3	−	15943.4i	−1.77832	−	1.29202i
$535$	199.028	−	612.545i	0.0160836	−	0.0495002i
$536$	−4707.24	−	14487.4i	−0.379332	−	1.16746i
$537$	−12603.8	+	9157.19i	−1.01284	+	0.735870i
$538$	−22811.2			−1.82799
$539$	−2153.80	−	12224.5i	−0.172116	−	0.976895i
$540$	24370.7			1.94213
$541$	9680.26	−	7033.12i	0.769292	−	0.558923i	−0.132455	−	0.991189i	$-0.542286\pi$
$541$	9680.26	−	7033.12i	0.769292	−	0.558923i	0.901746	+	0.432266i	$0.142286\pi$
$542$	5572.81	+	17151.4i	0.441647	+	1.35925i
$543$	−5200.17	+	16004.5i	−0.410977	+	1.26486i
$544$	−1600.55	−	1162.87i	−0.126145	−	0.0916500i
$545$	4073.07	+	2959.26i	0.320130	+	0.232588i
$546$	−344.570	+	1060.48i	−0.0270077	+	0.0831212i
$547$	4819.71	+	14833.5i	0.376738	+	1.15948i	0.942299	+	0.334774i	$0.108660\pi$
$547$	4819.71	+	14833.5i	0.376738	+	1.15948i	−0.565560	+	0.824707i	$0.691340\pi$
$548$	5993.90	−	4354.82i	0.467238	−	0.339469i
$549$	−4453.79			−0.346235
$550$	−1647.12	−	9348.67i	−0.127697	−	0.724780i
$551$	11638.4			0.899843
$552$	30852.9	−	22416.0i	2.37896	−	1.72842i
$553$	1.14081	+	3.51105i	8.77254e−5	+	0.000269991i
$554$	4374.68	−	13463.9i	0.335491	−	1.03254i
$555$	−2181.96	−	1585.29i	−0.166881	−	0.121246i
$556$	−3934.84	−	2858.83i	−0.300134	−	0.218060i
$557$	5765.73	−	17745.1i	0.438603	−	1.34988i	−0.450747	−	0.892652i	$-0.648842\pi$
$557$	5765.73	−	17745.1i	0.438603	−	1.34988i	0.889349	−	0.457228i	$-0.151158\pi$
$558$	−1686.87	−	5191.65i	−0.127976	−	0.393871i
$559$	−1226.73	+	891.272i	−0.0928179	+	0.0674361i
$560$	−1919.97			−0.144882
$561$	−1150.15	+	611.348i	−0.0865589	+	0.0460091i
$562$	−9026.55			−0.677512
$563$	−12107.4	+	8796.55i	−0.906335	+	0.658491i	−0.940085	−	0.340940i	$-0.889255\pi$
$563$	−12107.4	+	8796.55i	−0.906335	+	0.658491i	0.0337505	+	0.999430i	$0.489255\pi$
$564$	−1424.99	−	4385.67i	−0.106388	−	0.327429i
$565$	486.727	−	1497.99i	0.0362421	−	0.111542i
$566$	8657.52	+	6290.06i	0.642938	+	0.467122i
$567$	694.318	+	504.451i	0.0514261	+	0.0373632i
$568$	−2619.29	+	8061.34i	−0.193491	+	0.595504i
$569$	4038.36	+	12428.8i	0.297534	+	0.915715i	0.982359	+	0.187007i	$0.0598788\pi$
$569$	4038.36	+	12428.8i	0.297534	+	0.915715i	−0.684825	+	0.728708i	$0.740121\pi$
$570$	7858.33	−	5709.41i	0.577455	−	0.419546i
$571$	−13852.7			−1.01527			−0.507633	−	0.861573i	$-0.669480\pi$
$571$	−13852.7			−1.01527			−0.507633	+	0.861573i	$0.669480\pi$
$572$	−8526.00	+	17474.9i	−0.623234	+	1.27738i
$573$	−13802.3			−1.00628
$574$	−2134.28	+	1550.65i	−0.155197	+	0.112757i
$575$	2388.50	+	7351.04i	0.173230	+	0.533147i
$576$	−450.242	+	1385.70i	−0.0325696	+	0.100239i
$577$	−10358.9	−	7526.18i	−0.747395	−	0.543014i	0.147624	−	0.989044i	$-0.452838\pi$
$577$	−10358.9	−	7526.18i	−0.747395	−	0.543014i	−0.895018	+	0.446030i	$0.852838\pi$
$578$	20249.2	+	14711.9i	1.45719	+	1.05871i
$579$	−981.501	+	3020.75i	−0.0704487	+	0.216819i
$580$	−12045.3	−	37071.7i	−0.862337	−	2.65400i
$581$	1021.74	−	742.339i	0.0729587	−	0.0530076i
$582$	17330.8			1.23434
$583$	9040.52	+	1271.81i	0.642230	+	0.0903483i
$584$	−52116.8			−3.69282
$585$	1274.97	−	926.318i	0.0901084	−	0.0654676i
$586$	−5614.67	−	17280.2i	−0.395802	−	1.21815i
$587$	3729.16	−	11477.2i	0.262213	−	0.807008i	−0.730109	−	0.683330i	$-0.760531\pi$
$587$	3729.16	−	11477.2i	0.262213	−	0.807008i	0.992322	−	0.123678i	$-0.0394691\pi$
$588$	23275.3	+	16910.5i	1.63241	+	1.18602i
$589$	−6445.01	−	4682.57i	−0.450869	−	0.327576i
$590$	−5219.56	+	16064.1i	−0.364213	+	1.12093i
$591$	−5948.97	−	18309.1i	−0.414058	−	1.27434i
$592$	7440.71	−	5405.99i	0.516573	−	0.375312i
$593$	10537.6			0.729729			0.364864	−	0.931061i	$-0.381115\pi$
$593$	10537.6			0.729729			0.364864	+	0.931061i	$0.381115\pi$
$594$	20520.5	+	19821.8i	1.41745	+	1.36919i
$595$	−112.869			−0.00777676
$596$	−14280.5	+	10375.4i	−0.981462	+	0.713074i
$597$	−2835.24	−	8725.96i	−0.194369	−	0.598208i
$598$	6994.40	−	21526.5i	0.478298	−	1.47205i
$599$	−4430.23	−	3218.75i	−0.302194	−	0.219557i	0.426346	−	0.904560i	$-0.359801\pi$
$599$	−4430.23	−	3218.75i	−0.302194	−	0.219557i	−0.728540	+	0.685003i	$0.759801\pi$
$600$	10152.0	+	7375.86i	0.690756	+	0.501864i
$601$	5285.43	−	16266.9i	0.358731	−	1.10406i	−0.595083	−	0.803664i	$-0.702881\pi$
$601$	5285.43	−	16266.9i	0.358731	−	1.10406i	0.953814	−	0.300396i	$-0.0971190\pi$
$602$	−140.421	−	432.172i	−0.00950688	−	0.0292592i
$603$	−1434.08	+	1041.92i	−0.0968494	+	0.0703652i
$604$	33798.1			2.27686
$605$	−6429.74	+	9526.90i	−0.432076	+	0.640204i
$606$	14438.5			0.967861
$607$	−1317.77	+	957.418i	−0.0881165	+	0.0640204i	−0.630971	−	0.775806i	$-0.717343\pi$
$607$	−1317.77	+	957.418i	−0.0881165	+	0.0640204i	0.542855	+	0.839827i	$0.317343\pi$
$608$	3733.25	+	11489.8i	0.249019	+	0.766401i
$609$	565.641	−	1740.86i	0.0376370	−	0.115835i
$610$	25178.4	+	18293.2i	1.67122	+	1.21421i
$611$	−1262.85	−	917.517i	−0.0836164	−	0.0607509i
$612$	−288.405	+	887.621i	−0.0190492	+	0.0586273i
$613$	−4887.80	−	15043.1i	−0.322049	−	0.991166i	−0.972755	−	0.231836i	$-0.925527\pi$
$613$	−4887.80	−	15043.1i	−0.322049	−	0.991166i	0.650706	−	0.759330i	$-0.274473\pi$
$614$	−28986.3	+	21059.8i	−1.90520	+	1.38421i
$615$	−12060.9			−0.790799
$616$	−2390.32	−	2308.93i	−0.156345	−	0.151022i
$617$	−9377.02			−0.611839			−0.305919	−	0.952057i	$-0.598964\pi$
$617$	−9377.02			−0.611839			−0.305919	+	0.952057i	$0.598964\pi$
$618$	−28955.6	+	21037.5i	−1.88473	+	1.36934i
$619$	1974.65	+	6077.36i	0.128220	+	0.394620i	0.994474	−	0.104984i	$-0.0334790\pi$
$619$	1974.65	+	6077.36i	0.128220	+	0.394620i	−0.866254	+	0.499604i	$0.833479\pi$
$620$	−8245.00	+	25375.5i	−0.534076	+	1.64372i
$621$	−18794.1	−	13654.7i	−1.21446	−	0.882359i
$622$	−9558.83	−	6944.90i	−0.616197	−	0.447693i
$623$	594.757	−	1830.47i	0.0382479	−	0.117715i
$624$	−5371.91	−	16533.0i	−0.344629	−	1.06066i
$625$	5483.36	−	3983.90i	0.350935	−	0.254969i
$626$	40858.1			2.60865
$627$	7876.39	+	1108.04i	0.501679	+	0.0705757i
$628$	−17215.0			−1.09387
$629$	437.414	−	317.800i	0.0277279	−	0.0201455i
$630$	145.943	+	449.165i	0.00922936	+	0.0284050i
$631$	−5471.23	+	16838.7i	−0.345176	+	1.06234i	0.616313	+	0.787501i	$0.288626\pi$
$631$	−5471.23	+	16838.7i	−0.345176	+	1.06234i	−0.961489	+	0.274842i	$0.911374\pi$
$632$	−98.4268	−	71.5112i	−0.00619495	−	0.00450089i
$633$	20309.0	+	14755.4i	1.27522	+	0.926499i
$634$	−2211.97	+	6807.76i	−0.138563	+	0.426452i
$635$	387.004	+	1191.08i	0.0241855	+	0.0744353i
$636$	−17118.9	+	12437.6i	−1.06731	+	0.775444i
$637$	9738.77			0.605752
$638$	20009.7	−	41011.8i	1.24168	−	2.54494i
$639$	986.352			0.0610634
$640$	−5827.68	+	4234.06i	−0.359937	+	0.261509i
$641$	5615.05	+	17281.3i	0.345992	+	1.06485i	0.961051	+	0.276373i	$0.0891324\pi$
$641$	5615.05	+	17281.3i	0.345992	+	1.06485i	−0.615058	+	0.788482i	$0.710868\pi$
$642$	−540.037	+	1662.06i	−0.0331987	+	0.102175i
$643$	−4417.63	−	3209.60i	−0.270940	−	0.196849i	0.444016	−	0.896019i	$-0.353553\pi$
$643$	−4417.63	−	3209.60i	−0.270940	−	0.196849i	−0.714956	+	0.699169i	$0.753553\pi$
$644$	3838.42	+	2788.78i	0.234868	+	0.170642i
$645$	641.973	−	1975.79i	0.0391902	−	0.120615i
$646$	601.730	+	1851.93i	0.0366482	+	0.112792i
$647$	9107.65	−	6617.09i	0.553414	−	0.402079i	−0.275629	−	0.961264i	$-0.588886\pi$
$647$	9107.65	−	6617.09i	0.553414	−	0.402079i	0.829043	+	0.559186i	$0.188886\pi$
$648$	−28283.0			−1.71460
$649$	−12213.1	+	6491.72i	−0.738686	+	0.392638i
$650$	7447.71			0.449421
$651$	−1013.65	+	736.460i	−0.0610262	+	0.0443381i
$652$	−16870.2	−	51921.1i	−1.01332	−	3.11869i
$653$	710.830	−	2187.71i	0.0425986	−	0.131105i	−0.927495	−	0.373835i	$-0.878043\pi$
$653$	710.830	−	2187.71i	0.0425986	−	0.131105i	0.970094	+	0.242730i	$0.0780427\pi$
$654$	−11051.8	−	8029.57i	−0.660791	−	0.480093i
$655$	−14.8764	−	10.8083i	−0.000887434	−	0.000644759i
$656$	12709.5	−	39115.8i	0.756437	−	2.32807i
$657$	1874.09	+	5767.87i	0.111287	+	0.342505i
$658$	378.453	−	274.962i	0.0224219	−	0.0162905i
$659$	−8719.26			−0.515408			−0.257704	−	0.966224i	$-0.582966\pi$
$659$	−8719.26			−0.515408			−0.257704	+	0.966224i	$0.582966\pi$
$660$	−4622.34	−	26235.4i	−0.272612	−	1.54729i
$661$	22031.4			1.29640			0.648201	−	0.761469i	$-0.275522\pi$
$661$	22031.4			1.29640			0.648201	+	0.761469i	$0.275522\pi$
$662$	48592.0	−	35304.2i	2.85284	−	2.07271i
$663$	−315.796	−	971.921i	−0.0184985	−	0.0569326i
$664$	−12861.5	+	39583.6i	−0.751690	+	2.31346i
$665$	557.602	+	405.122i	0.0325156	+	0.0236240i
$666$	−1830.29	−	1329.78i	−0.106490	−	0.0773693i
$667$	−11481.9	+	35337.7i	−0.666539	+	2.05140i
$668$	6333.29	+	19491.9i	0.366830	+	1.12899i
$669$	12023.3	−	8735.41i	0.694837	−	0.504829i
$670$	12386.7			0.714240
$671$	4421.98	+	25098.2i	0.254409	+	1.44397i
$672$	1900.07			0.109073
$673$	7198.75	−	5230.20i	0.412320	−	0.299568i	−0.362220	−	0.932092i	$-0.617981\pi$
$673$	7198.75	−	5230.20i	0.412320	−	0.299568i	0.774540	+	0.632525i	$0.217981\pi$
$674$	−13515.8	−	41597.3i	−0.772416	−	2.37725i
$675$	2362.12	−	7269.85i	0.134693	−	0.414543i
$676$	20752.9	+	15077.9i	1.18075	+	0.857867i
$677$	−14765.0	−	10727.4i	−0.838207	−	0.608993i	0.0836624	−	0.996494i	$-0.473338\pi$
$677$	−14765.0	−	10727.4i	−0.838207	−	0.608993i	−0.921869	+	0.387501i	$0.873338\pi$
$678$	−1320.67	+	4064.61i	−0.0748085	+	0.230237i
$679$	380.009	+	1169.55i	0.0214778	+	0.0661018i
$680$	3009.24	−	2186.34i	0.169704	−	0.123298i
$681$	25613.8			1.44130
$682$	−27581.4	+	14660.5i	−1.54860	+	0.823136i
$683$	−17118.2			−0.959018			−0.479509	−	0.877537i	$-0.659185\pi$
$683$	−17118.2			−0.959018			−0.479509	+	0.877537i	$0.659185\pi$
$684$	4610.75	−	3349.90i	0.257743	−	0.187261i
$685$	1061.80	+	3267.89i	0.0592253	+	0.182277i
$686$	−1811.07	+	5573.91i	−0.100797	+	0.310223i
$687$	−4012.17	−	2915.01i	−0.222815	−	0.161884i
$688$	5731.39	+	4164.10i	0.317598	+	0.230748i
$689$	−2213.43	+	6812.24i	−0.122388	+	0.376670i
$690$	9582.82	+	29492.9i	0.528712	+	1.62721i
$691$	3859.56	−	2804.13i	0.212481	−	0.154377i	−0.476454	−	0.879199i	$-0.658078\pi$
$691$	3859.56	−	2804.13i	0.212481	−	0.154377i	0.688936	+	0.724823i	$0.258078\pi$
$692$	−67223.2			−3.69284
$693$	−169.579	+	347.569i	−0.00929550	+	0.0190520i
$694$	−9859.71			−0.539293
$695$	1824.89	−	1325.86i	0.0995999	−	0.0723636i
$696$	18640.9	+	57370.7i	1.01520	+	3.12447i
$697$	747.149	−	2299.49i	0.0406030	−	0.124963i
$698$	−36005.9	−	26159.8i	−1.95250	−	1.41857i
$699$	6046.59	+	4393.10i	0.327186	+	0.237715i
$700$	−482.428	+	1484.76i	−0.0260487	+	0.0801696i
$701$	−3565.64	−	10973.9i	−0.192114	−	0.591267i	−0.999998	−	0.00192549i	$-0.999387\pi$
$701$	−3565.64	−	10973.9i	−0.192114	−	0.591267i	0.807884	−	0.589342i	$-0.200613\pi$
$702$	−18109.3	+	13157.2i	−0.973636	+	0.707388i
$703$	−3301.63			−0.177131
$704$	8255.79	+	1161.42i	0.441977	+	0.0621769i
$705$	2138.64			0.114250
$706$	−26484.8	+	19242.3i	−1.41185	+	1.02577i
$707$	316.591	+	974.366i	0.0168410	+	0.0518314i
$708$	9906.31	−	30488.5i	0.525850	−	1.61840i
$709$	−4649.09	−	3377.76i	−0.246263	−	0.178920i	0.457806	−	0.889052i	$-0.348635\pi$
$709$	−4649.09	−	3377.76i	−0.246263	−	0.178920i	−0.704069	+	0.710132i	$0.748635\pi$
$710$	−5576.10	−	4051.27i	−0.294743	−	0.214143i
$711$	−4.37491	+	13.4646i	−0.000230762	+	0.000710213i
$712$	19600.4	+	60323.8i	1.03168	+	3.17518i
$713$	20576.0	−	14949.4i	1.08075	−	0.785214i
$714$	306.255			0.0160523
$715$	−6485.88	−	6265.04i	−0.339242	−	0.327691i
$716$	63874.2			3.33392
$717$	−2994.01	+	2175.28i	−0.155946	+	0.113302i
$718$	7289.83	+	22435.8i	0.378906	+	1.16615i
$719$	5927.94	−	18244.3i	0.307475	−	0.946312i	−0.671267	−	0.741216i	$-0.734249\pi$
$719$	5927.94	−	18244.3i	0.307475	−	0.946312i	0.978742	−	0.205096i	$-0.0657506\pi$
$720$	−5956.75	−	4327.83i	−0.308326	−	0.224012i
$721$	−2054.60	−	1492.75i	−0.106126	−	0.0771054i
$722$	−7261.16	+	22347.6i	−0.374283	+	1.15193i
$723$	−8937.30	−	27506.2i	−0.459726	−	1.41489i
$724$	55818.0	−	40554.2i	2.86528	−	2.08174i
$725$	−12226.1			−0.626296
$726$	17446.3	−	25850.0i	0.891862	−	1.32147i
$727$	35335.6			1.80265			0.901323	−	0.433148i	$-0.142597\pi$
$727$	35335.6			1.80265			0.901323	+	0.433148i	$0.142597\pi$
$728$	2109.46	−	1532.61i	0.107392	−	0.0780252i
$729$	6760.25	+	20805.9i	0.343456	+	1.05705i
$730$	13095.8	−	40304.7i	0.663969	−	2.04349i
$731$	336.929	+	244.793i	0.0170476	+	0.0123858i
$732$	−47786.7	−	34719.0i	−2.41290	−	1.75308i
$733$	4628.65	−	14245.5i	0.233238	−	0.717831i	−0.764113	−	0.645083i	$-0.776823\pi$
$733$	4628.65	−	14245.5i	0.233238	−	0.717831i	0.997350	−	0.0727486i	$-0.0231771\pi$
$734$	2272.54	+	6994.16i	0.114279	+	0.351716i
$735$	−10794.5	+	7842.70i	−0.541718	+	0.393581i
$736$	−38569.4			−1.93164
$737$	7295.30	+	7046.90i	0.364621	+	0.352206i
$738$	−10117.0			−0.504622
$739$	−17366.5	+	12617.5i	−0.864463	+	0.628069i	−0.929095	−	0.369840i	$-0.879413\pi$
$739$	−17366.5	+	12617.5i	−0.864463	+	0.628069i	0.0646324	+	0.997909i	$0.479413\pi$
$740$	3417.06	+	10516.6i	0.169748	+	0.522432i
$741$	−1928.41	+	5935.04i	−0.0956032	+	0.294236i
$742$	−1736.60	−	1261.71i	−0.0859200	−	0.0624245i
$743$	−20729.2	−	15060.6i	−1.02353	−	0.743636i	−0.0565237	−	0.998401i	$-0.518002\pi$
$743$	−20729.2	−	15060.6i	−1.02353	−	0.743636i	−0.967003	+	0.254766i	$0.918002\pi$
$744$	12759.6	−	39270.1i	0.628750	−	1.93509i
$745$	−2529.75	−	7785.76i	−0.124406	−	0.382883i
$746$	−33900.2	+	24629.9i	−1.66377	+	1.20880i
$747$	4843.28			0.237224
$748$	5288.30	+	743.953i	0.258502	+	0.0363658i
$749$	−124.004			−0.00604940
$750$	−28716.5	+	20863.8i	−1.39810	+	1.01578i
$751$	−313.521	−	964.918i	−0.0152337	−	0.0468846i	0.943151	−	0.332365i	$-0.107847\pi$
$751$	−313.521	−	964.918i	−0.0152337	−	0.0468846i	−0.958384	+	0.285481i	$0.907847\pi$
$752$	−2253.66	+	6936.05i	−0.109285	+	0.336346i
$753$	2326.94	+	1690.62i	0.112614	+	0.0818188i
$754$	28964.8	+	21044.1i	1.39899	+	1.01642i
$755$	−4843.77	+	14907.6i	−0.233487	+	0.718600i
$756$	−1449.95	−	4462.50i	−0.0697544	−	0.214682i
$757$	3918.89	−	2847.24i	0.188156	−	0.136704i	−0.489719	−	0.871880i	$-0.662901\pi$
$757$	3918.89	−	2847.24i	0.188156	−	0.136704i	0.677876	+	0.735177i	$0.262901\pi$
$758$	27329.8			1.30958
$759$	−11134.8	+	22821.9i	−0.532501	+	1.09141i
$760$	−22713.9			−1.08410
$761$	−16023.6	+	11641.9i	−0.763280	+	0.554556i	−0.899915	−	0.436066i	$-0.856371\pi$
$761$	−16023.6	+	11641.9i	−0.763280	+	0.554556i	0.136634	+	0.990622i	$0.456371\pi$
$762$	−1050.09	−	3231.84i	−0.0499221	−	0.153644i
$763$	299.536	−	921.878i	0.0142122	−	0.0437408i
$764$	45781.5	+	33262.2i	2.16795	+	1.57511i
$765$	−350.177	−	254.419i	−0.0165499	−	0.0120242i
$766$	17597.3	−	54158.8i	0.830046	−	2.55462i
$767$	−3353.34	−	10320.5i	−0.157865	−	0.485858i
$768$	22529.5	−	16368.6i	1.05854	−	0.769077i
$769$	−30538.7			−1.43206			−0.716030	−	0.698069i	$-0.754043\pi$
$769$	−30538.7			−1.43206			−0.716030	+	0.698069i	$0.754043\pi$
$770$	2386.25	−	1268.38i	0.111681	−	0.0593626i
$771$	2076.08			0.0969754
$772$	10535.3	−	7654.36i	0.491159	−	0.356848i
$773$	728.385	+	2241.74i	0.0338916	+	0.104308i	0.966571	−	0.256398i	$-0.0825359\pi$
$773$	728.385	+	2241.74i	0.0338916	+	0.104308i	−0.932680	+	0.360706i	$0.882536\pi$
$774$	538.504	−	1657.35i	0.0250079	−	0.0769665i
$775$	6770.43	+	4919.01i	0.313808	+	0.227995i
$776$	−32786.4	−	23820.7i	−1.51671	−	1.10195i
$777$	−160.463	+	493.854i	−0.00740872	+	0.0228017i
$778$	17730.0	+	54567.4i	0.817034	+	2.51457i
$779$	−11944.7	+	8678.33i	−0.549375	+	0.399144i
$780$	20900.7			0.959441
$781$	−979.307	−	5558.33i	−0.0448686	−	0.254664i
$782$	−6216.66			−0.284280
$783$	29728.0	−	21598.7i	1.35682	−	0.985791i
$784$	−14060.4	−	43273.4i	−0.640505	−	1.97127i
$785$	2467.17	−	7593.16i	0.112175	−	0.345238i
$786$	40.3653	+	29.3271i	0.00183178	+	0.00133087i
$787$	21210.6	+	15410.4i	0.960705	+	0.697993i	0.953314	−	0.301980i	$-0.0976475\pi$
$787$	21210.6	+	15410.4i	0.960705	+	0.697993i	0.00739057	+	0.999973i	$0.497647\pi$
$788$	−24390.7	+	75066.7i	−1.10264	+	3.39358i
$789$	9760.09	+	30038.5i	0.440391	+	1.35538i
$790$	80.0360	−	58.1495i	0.00360450	−	0.00261882i
$791$	−303.254			−0.0136314
$792$	−2211.42	−	12551.5i	−0.0992163	−	0.563130i
$793$	−19994.7			−0.895376
$794$	9686.15	−	7037.40i	0.432933	−	0.314544i
$795$	−3032.56	−	9333.25i	−0.135288	−	0.416373i
$796$	−11624.4	+	35776.3i	−0.517609	+	1.59304i
$797$	−14698.5	−	10679.1i	−0.653260	−	0.474621i	0.211120	−	0.977460i	$-0.432289\pi$
$797$	−14698.5	−	10679.1i	−0.653260	−	0.474621i	−0.864380	+	0.502839i	$0.832289\pi$
$798$	−1512.98	−	1099.25i	−0.0671165	−	0.0487630i
$799$	−132.485	+	407.747i	−0.00586606	+	0.0180539i
$800$	−3921.75	−	12069.9i	−0.173319	−	0.533420i
$801$	5971.33	−	4338.43i	0.263404	−	0.191374i
$802$	2516.27			0.110789
$803$	30642.6	−	16287.6i	1.34664	−	0.715788i
$804$	−23509.0			−1.03122
$805$	−1780.17	+	1293.37i	−0.0779414	+	0.0566278i
$806$	−7572.98	−	23307.2i	−0.330951	−	1.01856i
$807$	−6204.65	+	19096.0i	−0.270650	+	0.832974i
$808$	−27314.8	−	19845.4i	−1.18927	−	0.864057i
$809$	2514.96	+	1827.23i	0.109297	+	0.0794091i	0.641091	−	0.767465i	$-0.278482\pi$
$809$	2514.96	+	1827.23i	0.109297	+	0.0794091i	−0.531794	+	0.846874i	$0.678482\pi$
$810$	7106.90	−	21872.8i	0.308285	−	0.948804i
$811$	−6414.12	−	19740.6i	−0.277719	−	0.854731i	−0.988487	−	0.151305i	$-0.951652\pi$
$811$	−6414.12	−	19740.6i	−0.277719	−	0.854731i	0.710768	−	0.703426i	$-0.248348\pi$
$812$	−6071.52	+	4411.22i	−0.262400	+	0.190645i
$813$	15873.8			0.684769
$814$	−5676.42	+	11634.4i	−0.244421	+	0.500964i
$815$	25319.0			1.08820
$816$	−3862.72	+	2806.43i	−0.165713	+	0.120398i
$817$	−785.879	−	2418.69i	−0.0336529	−	0.103573i
$818$	−16032.1	+	49341.7i	−0.685268	+	2.10904i
$819$	−245.472	−	178.346i	−0.0104731	−	0.00760917i
$820$	40005.3	+	29065.6i	1.70372	+	1.23782i
$821$	−2446.51	+	7529.59i	−0.104000	+	0.320079i	−0.989494	−	0.144571i	$-0.953820\pi$
$821$	−2446.51	+	7529.59i	−0.104000	+	0.320079i	0.885495	+	0.464650i	$0.153820\pi$
$822$	−2881.06	−	8867.00i	−0.122249	−	0.376244i
$823$	−23678.5	+	17203.4i	−1.00289	+	0.728643i	−0.962706	−	0.270550i	$-0.912795\pi$
$823$	−23678.5	+	17203.4i	−1.00289	+	0.728643i	−0.0401845	+	0.999192i	$0.512795\pi$
$824$	83693.9			3.53837
$825$	−8274.09	−	1163.99i	−0.349172	−	0.0491212i
$826$	3252.03			0.136989
$827$	11248.1	−	8172.24i	0.472957	−	0.343624i	−0.325635	−	0.945495i	$-0.605578\pi$
$827$	11248.1	−	8172.24i	0.472957	−	0.343624i	0.798593	+	0.601872i	$0.205578\pi$
$828$	5622.56	+	17304.5i	0.235987	+	0.726294i
$829$	−2924.52	+	9000.74i	−0.122524	+	0.377091i	−0.993442	−	0.114338i	$-0.963525\pi$
$829$	−2924.52	+	9000.74i	−0.122524	+	0.377091i	0.870918	+	0.491429i	$0.163525\pi$
$830$	−27380.3	−	19893.0i	−1.14504	−	0.831921i
$831$	−10081.1	−	7324.36i	−0.420830	−	0.305751i
$832$	−2021.30	+	6220.93i	−0.0842260	+	0.259221i
$833$	−826.562	−	2543.90i	−0.0343802	−	0.105811i
$834$	−4951.60	+	3597.55i	−0.205588	+	0.149368i
$835$	−9505.10			−0.393937
$836$	−23455.3	−	22656.7i	−0.970358	−	0.937318i
$837$	−25152.5			−1.03871
$838$	−5167.15	+	3754.15i	−0.213003	+	0.154755i
$839$	−11790.8	−	36288.4i	−0.485178	−	1.49323i	−0.831723	−	0.555191i	$-0.812645\pi$
$839$	−11790.8	−	36288.4i	−0.485178	−	1.49323i	0.346544	−	0.938034i	$-0.387355\pi$
$840$	−1103.92	+	3397.52i	−0.0453440	+	0.139554i
$841$	−27817.1	−	20210.3i	−1.14056	−	0.828665i
$842$	16535.4	+	12013.7i	0.676780	+	0.491710i
$843$	−2455.23	+	7556.41i	−0.100311	+	0.308727i
$844$	−31805.0	−	97885.8i	−1.29713	−	3.99214i
$845$	−9624.72	+	6992.77i	−0.391835	+	0.284685i
$846$	1793.95			0.0729046
$847$	2127.00	+	610.533i	0.0862865	+	0.0247676i
$848$	33465.3			1.35519
$849$	7620.46	−	5536.59i	0.308049	−	0.223811i
$850$	−632.113	−	1945.44i	−0.0255074	−	0.0785037i
$851$	3257.23	−	10024.7i	0.131206	−	0.403811i
$852$	10583.0	+	7689.00i	0.425549	+	0.309179i
$853$	33219.9	+	24135.6i	1.33344	+	0.968802i	0.999658	+	0.0261527i	$0.00832562\pi$
$853$	33219.9	+	24135.6i	1.33344	+	0.968802i	0.333784	+	0.942650i	$0.391674\pi$
$854$	1851.64	−	5698.76i	0.0741942	−	0.228346i
$855$	816.780	+	2513.79i	0.0326705	+	0.100550i
$856$	3306.11	−	2402.03i	0.132010	−	0.0959110i
$857$	2923.27			0.116519			0.0582596	−	0.998301i	$-0.481445\pi$
$857$	2923.27			0.116519			0.0582596	+	0.998301i	$0.481445\pi$
$858$	17598.6	+	16999.4i	0.700241	+	0.676399i
$859$	18049.4			0.716924			0.358462	−	0.933544i	$-0.383301\pi$
$859$	18049.4			0.716924			0.358462	+	0.933544i	$0.383301\pi$
$860$	−6890.87	+	5006.51i	−0.273229	+	0.198512i
$861$	717.570	+	2208.45i	0.0284027	+	0.0874145i
$862$	13571.9	−	41770.1i	0.536266	−	1.65046i
$863$	28309.1	+	20567.8i	1.11663	+	0.811280i	0.983695	−	0.179844i	$-0.0575594\pi$
$863$	28309.1	+	20567.8i	1.11663	+	0.811280i	0.132937	+	0.991125i	$0.457559\pi$
$864$	30858.7	+	22420.1i	1.21509	+	0.882811i
$865$	9634.10	−	29650.7i	0.378693	−	1.16550i
$866$	−17227.3	−	53020.1i	−0.675989	−	2.08048i
$867$	17823.6	−	12949.6i	0.698177	−	0.507255i
$868$	5137.03			0.200878
$869$	80.2199	+	11.2853i	0.00313150	+	0.000440536i
$870$	−49051.9			−1.91151
$871$	−6438.11	+	4677.56i	−0.250456	+	0.181967i
$872$	9871.30	+	30380.8i	0.383354	+	1.17984i
$873$	−1457.30	+	4485.12i	−0.0564974	+	0.173881i
$874$	30711.9	+	22313.5i	1.18861	+	0.863577i
$875$	−2037.63	−	1480.42i	−0.0787251	−	0.0571971i
$876$	−24854.8	+	76495.2i	−0.958637	+	2.95038i
$877$	9368.87	+	28834.4i	0.360734	+	1.11023i	0.952609	+	0.304197i	$0.0983880\pi$
$877$	9368.87	+	28834.4i	0.360734	+	1.11023i	−0.591875	+	0.806030i	$0.701612\pi$
$878$	−13253.5	+	9629.24i	−0.509435	+	0.370126i
$879$	−15993.0			−0.613685
$880$	−18474.2	+	37864.6i	−0.707686	+	1.45047i
$881$	−33005.5			−1.26218			−0.631092	−	0.775708i	$-0.717393\pi$
$881$	−33005.5			−1.26218			−0.631092	+	0.775708i	$0.717393\pi$
$882$	−9054.75	+	6578.66i	−0.345680	+	0.251151i
$883$	−4268.92	−	13138.4i	−0.162696	−	0.500727i	0.836163	−	0.548481i	$-0.184794\pi$
$883$	−4268.92	−	13138.4i	−0.162696	−	0.500727i	−0.998859	+	0.0477542i	$0.984794\pi$
$884$	−1294.76	+	3984.86i	−0.0492618	+	0.151612i
$885$	12028.1	+	8738.91i	0.456858	+	0.331927i
$886$	9914.45	+	7203.27i	0.375940	+	0.273136i
$887$	6507.03	−	20026.6i	0.246319	−	0.758091i	−0.749098	−	0.662459i	$-0.769513\pi$
$887$	6507.03	−	20026.6i	0.246319	−	0.758091i	0.995417	−	0.0956319i	$-0.0304872\pi$
$888$	−5288.10	−	16275.1i	−0.199839	−	0.615041i
$889$	195.072	−	141.728i	0.00735939	−	0.00534691i
$890$	−51576.8			−1.94254
$891$	16629.3	−	8839.05i	0.625255	−	0.332345i
$892$	−60932.1			−2.28717
$893$	2118.04	−	1538.85i	0.0793703	−	0.0576659i
$894$	6864.15	+	21125.7i	0.256791	+	0.790323i
$895$	−9154.13	+	28173.5i	−0.341887	+	1.05222i
$896$	1122.02	+	815.193i	0.0418348	+	0.0303947i
$897$	−16118.1	−	11710.5i	−0.599963	−	0.435899i
$898$	13025.9	−	40089.6i	0.484053	−	1.48976i
$899$	12431.7	+	38260.9i	0.461202	+	1.41943i
$900$	−4843.56	+	3519.05i	−0.179391	+	0.130335i
$901$	1967.31			0.0727421
$902$	10044.7	+	57011.6i	0.370790	+	2.10452i
$903$	−399.980			−0.0147403
$904$	8085.17	−	5874.22i	0.297466	−	0.216121i
$905$	9888.00	+	30432.1i	0.363191	+	1.11779i
$906$	13143.0	−	40449.9i	0.481949	−	1.48329i
$907$	30830.3	+	22399.5i	1.12867	+	0.820026i	0.985501	−	0.169672i	$-0.0542708\pi$
$907$	30830.3	+	22399.5i	1.12867	+	0.820026i	0.143169	+	0.989698i	$0.454271\pi$
$908$	−84959.7	−	61726.8i	−3.10516	−	2.25603i
$909$	−1214.10	+	3736.62i	−0.0443005	+	0.136343i
$910$	655.191	+	2016.47i	0.0238674	+	0.0734564i
$911$	507.339	−	368.603i	0.0184510	−	0.0134055i	−0.578522	−	0.815667i	$-0.696370\pi$
$911$	507.339	−	368.603i	0.0184510	−	0.0134055i	0.596973	+	0.802262i	$0.296370\pi$
$912$	29156.0			1.05861
$913$	−4808.69	−	27293.1i	−0.174309	−	0.989341i
$914$	47538.9			1.72040
$915$	22162.4	−	16101.9i	0.800727	−	0.581762i
$916$	6283.26	+	19337.9i	0.226643	+	0.697535i
$917$	−1.09402	+	3.36706i	−3.93978e−5	+	0.000121254i
$918$	4973.84	+	3613.70i	0.178825	+	0.129924i
$919$	−39549.3	−	28734.2i	−1.41960	−	1.03140i	−0.991838	−	0.127506i	$-0.959303\pi$
$919$	−39549.3	−	28734.2i	−1.41960	−	1.03140i	−0.427760	−	0.903892i	$-0.640697\pi$
$920$	22408.5	−	68966.1i	0.803027	−	2.47146i
$921$	9745.52	+	29993.6i	0.348671	+	1.07310i
$922$	19154.1	−	13916.3i	0.684171	−	0.497080i
$923$	4428.10			0.157912
$924$	−4528.92	+	2407.28i	−0.161245	+	0.0857076i
$925$	3468.33			0.123284
$926$	46877.1	−	34058.2i	1.66358	−	1.20866i
$927$	−3009.59	−	9262.57i	−0.106632	−	0.328180i
$928$	18852.5	−	58022.2i	0.666880	−	2.05245i
$929$	26061.9	+	18935.1i	0.920412	+	0.668719i	0.943627	−	0.331012i	$-0.107390\pi$
$929$	26061.9	+	18935.1i	0.920412	+	0.668719i	−0.0232142	+	0.999731i	$0.507390\pi$
$930$	27163.5	+	19735.4i	0.957769	+	0.695860i
$931$	−5047.40	+	15534.3i	−0.177682	+	0.546849i
$932$	−9469.28	−	29143.4i	−0.332807	−	1.02428i
$933$	−8413.80	+	6112.99i	−0.295236	+	0.214502i
$934$	−67388.0			−2.36082
$935$	−1086.03	+	2225.93i	−0.0379862	+	0.0778565i
$936$	9999.30			0.349185
$937$	−36759.1	+	26707.0i	−1.28161	+	0.931143i	−0.999600	−	0.0282695i	$-0.991000\pi$
$937$	−36759.1	+	26707.0i	−1.28161	+	0.931143i	−0.282008	+	0.959412i	$0.591000\pi$
$938$	−736.957	−	2268.12i	−0.0256530	−	0.0789517i
$939$	11113.4	−	34203.6i	0.386233	−	1.18870i
$940$	−7093.78	−	5153.93i	−0.246142	−	0.178833i
$941$	33853.3	+	24595.9i	1.17278	+	0.852076i	0.991339	−	0.131326i	$-0.0419234\pi$
$941$	33853.3	+	24595.9i	1.17278	+	0.852076i	0.181442	+	0.983402i	$0.441923\pi$
$942$	−6694.35	+	20603.1i	−0.231543	+	0.712617i
$943$	−14565.9	−	44829.3i	−0.503003	−	1.54808i
$944$	−41017.0	+	29800.6i	−1.41418	+	1.02746i
$945$	2176.11			0.0749089
$946$	−9874.20	−	1389.09i	−0.339364	−	0.0477414i
$947$	−24265.2			−0.832644			−0.416322	−	0.909217i	$-0.636681\pi$
$947$	−24265.2			−0.832644			−0.416322	+	0.909217i	$0.636681\pi$
$948$	−151.902	+	110.363i	−0.00520416	+	0.00378105i
$949$	8413.50	+	25894.1i	0.287791	+	0.885730i
$950$	−3860.00	+	11879.9i	−0.131826	+	0.405719i
$951$	5097.33	+	3703.43i	0.173809	+	0.126280i
$952$	−579.375	−	420.941i	−0.0197244	−	0.0143306i
$953$	14016.6	−	43138.8i	0.476436	−	1.46632i	−0.367575	−	0.929994i	$-0.619812\pi$
$953$	14016.6	−	43138.8i	0.476436	−	1.46632i	0.844011	−	0.536326i	$-0.180188\pi$
$954$	−2543.79	−	7828.98i	−0.0863294	−	0.265694i
$955$	−21232.4	+	15426.3i	−0.719440	+	0.522703i
$956$	15173.2			0.513323
$957$	−28889.7	−	27906.0i	−0.975831	−	0.942605i
$958$	82343.2			2.77702
$959$	535.207	−	388.851i	0.0180216	−	0.0130935i
$960$	−2769.33	−	8523.11i	−0.0931038	−	0.286544i
$961$	−696.452	+	2143.46i	−0.0233779	+	0.0719499i
$962$	−8216.83	−	5969.88i	−0.275386	−	0.200080i
$963$	−384.724	−	279.518i	−0.0128739	−	0.00935343i
$964$	−36642.7	+	112775.i	−1.22426	+	3.76787i
$965$	1866.30	+	5743.88i	0.0622574	+	0.191608i
$966$	4830.28	−	3509.40i	0.160882	−	0.116887i
$967$	22874.2			0.760687			0.380343	−	0.924845i	$-0.375806\pi$
$967$	22874.2			0.760687			0.380343	+	0.924845i	$0.375806\pi$
$968$	−68535.2	+	24923.7i	−2.27563	+	0.827561i
$969$	1713.98			0.0568226
$970$	26660.4	−	19369.9i	0.882487	−	0.641165i
$971$	28.7466	+	88.4729i	0.000950074	+	0.00292403i	0.951530	−	0.307555i	$-0.0995107\pi$
$971$	28.7466	+	88.4729i	0.000950074	+	0.00292403i	−0.950580	+	0.310479i	$0.899511\pi$
$972$	10058.7	−	30957.5i	0.331927	−	1.02157i
$973$	−351.350	−	255.271i	−0.0115763	−	0.00841069i
$974$	18138.4	+	13178.3i	0.596705	+	0.433532i
$975$	2025.78	−	6234.72i	0.0665405	−	0.204791i
$976$	28867.4	+	88844.9i	0.946746	+	2.91379i
$977$	4207.13	−	3056.66i	0.137767	−	0.100093i	−0.516767	−	0.856126i	$-0.672865\pi$
$977$	4207.13	−	3056.66i	0.137767	−	0.100093i	0.654534	+	0.756032i	$0.272865\pi$
$978$	−68699.9			−2.24620
$979$	−30376.7	−	29342.4i	−0.991670	−	0.957904i
$980$	54705.2			1.78316
$981$	3007.33	−	2184.95i	0.0978763	−	0.0711113i
$982$	4635.70	+	14267.2i	0.150643	+	0.463631i
$983$	−14199.5	+	43701.7i	−0.460727	+	1.41797i	0.403551	+	0.914957i	$0.367776\pi$
$983$	−14199.5	+	43701.7i	−0.460727	+	1.41797i	−0.864278	+	0.503015i	$0.832224\pi$
$984$	−61910.5	−	44980.6i	−2.00573	−	1.45725i
$985$	−29614.7	−	21516.4i	−0.957974	−	0.696009i
$986$	3038.67	−	9352.08i	0.0981451	−	0.302060i
$987$	−127.240	−	391.605i	−0.00410344	−	0.0126291i
$988$	20699.4	−	15039.0i	0.666532	−	0.484264i
$989$	8119.17			0.261046
$990$	10262.5	+	1443.71i	0.329457	+	0.0463477i
$991$	22935.6			0.735191			0.367595	−	0.929986i	$-0.380181\pi$
$991$	22935.6			0.735191			0.367595	+	0.929986i	$0.380181\pi$
$992$	−33784.5	+	24545.9i	−1.08131	+	0.785617i
$993$	−16337.2	−	50280.7i	−0.522100	−	1.60686i
$994$	−410.071	+	1262.07i	−0.0130852	+	0.0402720i
$995$	−14114.2	−	10254.6i	−0.449698	−	0.326725i
$996$	51965.7	+	37755.3i	1.65321	+	1.20113i
$997$	−1240.92	+	3819.17i	−0.0394187	+	0.121318i	−0.968829	−	0.247729i	$-0.920316\pi$
$997$	−1240.92	+	3819.17i	−0.0394187	+	0.121318i	0.929411	+	0.369047i	$0.120316\pi$
$998$	25282.2	+	77810.7i	0.801899	+	2.46799i
$999$	−8433.35	+	6127.19i	−0.267087	+	0.194050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.4.c.a.3.1	✓	8
3.2	odd	2		99.4.f.c.91.2		8
4.3	odd	2		176.4.m.c.113.1		8
11.2	odd	10		121.4.a.f.1.1		4
11.3	even	5		121.4.c.h.27.2		8
11.4	even	5	inner	11.4.c.a.4.1	yes	8
11.5	even	5		121.4.c.h.9.2		8
11.6	odd	10		121.4.c.b.9.1		8
11.7	odd	10		121.4.c.i.81.2		8
11.8	odd	10		121.4.c.b.27.1		8
11.9	even	5		121.4.a.g.1.4		4
11.10	odd	2		121.4.c.i.3.2		8
33.2	even	10		1089.4.a.bh.1.4		4
33.20	odd	10		1089.4.a.y.1.1		4
33.26	odd	10		99.4.f.c.37.2		8
44.15	odd	10		176.4.m.c.81.1		8
44.31	odd	10		1936.4.a.bk.1.1		4
44.35	even	10		1936.4.a.bl.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.1	✓	8	1.1	even	1	trivial
11.4.c.a.4.1	yes	8	11.4	even	5	inner
99.4.f.c.37.2		8	33.26	odd	10
99.4.f.c.91.2		8	3.2	odd	2
121.4.a.f.1.1		4	11.2	odd	10
121.4.a.g.1.4		4	11.9	even	5
121.4.c.b.9.1		8	11.6	odd	10
121.4.c.b.27.1		8	11.8	odd	10
121.4.c.h.9.2		8	11.5	even	5
121.4.c.h.27.2		8	11.3	even	5
121.4.c.i.3.2		8	11.10	odd	2
121.4.c.i.81.2		8	11.7	odd	10
176.4.m.c.81.1		8	44.15	odd	10
176.4.m.c.113.1		8	4.3	odd	2
1089.4.a.y.1.1		4	33.20	odd	10
1089.4.a.bh.1.4		4	33.2	even	10
1936.4.a.bk.1.1		4	44.31	odd	10
1936.4.a.bl.1.1		4	44.35	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.17405 + 3.03263i) q^{2} +(1.40336 + 4.31911i) q^{3} +(5.75376 - 17.7083i) q^{4} +(6.98613 + 5.07572i) q^{5} +(-18.9560 - 13.7723i) q^{6} +(0.513765 - 1.58121i) q^{7} +(16.9313 + 52.1091i) q^{8} +(5.15818 - 3.74763i) q^{9} -44.5532 q^{10} +(-26.2401 - 25.3467i) q^{11} +84.5585 q^{12} +(23.1570 - 16.8245i) q^{13} +(2.65073 + 8.15810i) q^{14} +(-12.1185 + 37.2969i) q^{15} +(-108.191 - 78.6055i) q^{16} +(-6.36020 - 4.62095i) q^{17} +(-10.1653 + 31.2857i) q^{18} +(14.8350 + 45.6575i) q^{19} +(130.079 - 94.5077i) q^{20} +7.55040 q^{21} +(186.395 + 26.2219i) q^{22} -153.265 q^{23} +(-201.304 + 146.256i) q^{24} +(-15.5841 - 47.9628i) q^{25} +(-45.6359 + 140.453i) q^{26} +(122.625 + 89.0921i) q^{27} +(-25.0443 - 18.1958i) q^{28} +(74.9153 - 230.566i) q^{29} +(-62.5244 - 192.430i) q^{30} +(-134.251 + 97.5391i) q^{31} +251.651 q^{32} +(72.6507 - 148.905i) q^{33} +40.5614 q^{34} +(11.6150 - 8.43878i) q^{35} +(-36.6852 - 112.905i) q^{36} +(-21.2522 + 65.4077i) q^{37} +(-200.384 - 145.588i) q^{38} +(105.165 + 76.4065i) q^{39} +(-146.207 + 449.979i) q^{40} +(95.0373 + 292.495i) q^{41} +(-31.5158 + 22.8976i) q^{42} -52.9746 q^{43} +(-599.825 + 318.828i) q^{44} +55.0576 q^{45} +(639.737 - 464.796i) q^{46} +(-16.8521 - 51.8654i) q^{47} +(187.674 - 577.602i) q^{48} +(275.257 + 199.986i) q^{49} +(210.502 + 152.939i) q^{50} +(11.0327 - 33.9553i) q^{51} +(-164.693 - 506.874i) q^{52} +(-202.450 + 147.088i) q^{53} -782.025 q^{54} +(-54.6643 - 310.263i) q^{55} +91.0939 q^{56} +(-176.381 + 128.148i) q^{57} +(386.519 + 1189.58i) q^{58} +(117.153 - 360.561i) q^{59} +(590.737 + 429.195i) q^{60} +(-565.131 - 410.592i) q^{61} +(264.571 - 814.267i) q^{62} +(-3.27569 - 10.0815i) q^{63} +(-184.877 + 134.321i) q^{64} +247.174 q^{65} +(148.325 + 841.859i) q^{66} -278.021 q^{67} +(-118.424 + 86.0402i) q^{68} +(-215.087 - 661.969i) q^{69} +(-22.8899 + 70.4479i) q^{70} +(125.156 + 90.9311i) q^{71} +(282.620 + 205.336i) q^{72} +(-293.936 + 904.642i) q^{73} +(-109.649 - 337.465i) q^{74} +(185.287 - 134.619i) q^{75} +893.872 q^{76} +(-53.5596 + 28.4688i) q^{77} -670.675 q^{78} +(-1.79641 + 1.30517i) q^{79} +(-356.858 - 1098.30i) q^{80} +(-159.515 + 490.936i) q^{81} +(-1283.72 - 932.676i) q^{82} +(614.553 + 446.499i) q^{83} +(43.4432 - 133.704i) q^{84} +(-20.9785 - 64.5651i) q^{85} +(221.119 - 160.652i) q^{86} +1100.97 q^{87} +(876.514 - 1796.50i) q^{88} +1157.64 q^{89} +(-229.813 + 166.969i) q^{90} +(-14.7058 - 45.2598i) q^{91} +(-881.852 + 2714.06i) q^{92} +(-609.685 - 442.962i) q^{93} +(227.630 + 165.383i) q^{94} +(-128.105 + 394.267i) q^{95} +(353.159 + 1086.91i) q^{96} +(-598.393 + 434.758i) q^{97} -1755.42 q^{98} +(-230.341 - 32.4042i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19}+ \cdots + 2099 q^{99}+O(q^{100}) \) 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9 + 40 * q^10 + 67 * q^11 + 190 * q^12 - 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 - 31 * q^17 - 102 * q^18 + 148 * q^19 + 342 * q^20 + 334 * q^21 + 647 * q^22 - 12 * q^23 - 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 - 42 * q^28 - 199 * q^29 - 114 * q^30 - 361 * q^31 + 324 * q^32 - 232 * q^33 - 298 * q^34 + 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 + 365 * q^39 + 532 * q^40 - 31 * q^41 + 170 * q^42 - 650 * q^43 - 1208 * q^44 + 452 * q^45 + 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 - 147 * q^50 - 246 * q^51 - 590 * q^52 - 1493 * q^53 - 3100 * q^54 - 1583 * q^55 - 1560 * q^56 + 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 - 525 * q^61 + 2456 * q^62 - 68 * q^63 + 471 * q^64 + 1790 * q^65 + 1014 * q^66 + 86 * q^67 + 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 + 919 * q^72 - 2155 * q^73 - 1476 * q^74 - 160 * q^75 - 242 * q^76 - 2015 * q^77 - 1340 * q^78 - 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 + 52 * q^83 - 84 * q^84 + 2383 * q^85 + 1061 * q^86 + 2310 * q^87 + 4543 * q^88 + 3782 * q^89 - 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 + 702 * q^94 - 1317 * q^95 + 1252 * q^96 - 1344 * q^97 + 2740 * q^98 + 2099 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more