LMFDB - Embedded newform 21.4.g.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,4,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, 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:	$1.23904011012$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Root			$2.85284 + 0.928053i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.4.g.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65310 - 0.954416i) q^{2} +(1.60743 - 4.94127i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(-0.623706 - 1.08029i) q^{5} +(-2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} +23.5862i q^{8} +(-21.8323 - 15.8855i) q^{9} +O(q^{10})$	\(q+(1.65310 - 0.954416i) q^{2} +(1.60743 - 4.94127i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(-0.623706 - 1.08029i) q^{5} +(-2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} +23.5862i q^{8} +(-21.8323 - 15.8855i) q^{9} +(-2.06209 - 1.19055i) q^{10} +(-35.2392 - 20.3453i) q^{11} +(15.1408 + 16.8274i) q^{12} +19.5973i q^{13} +(31.4927 + 16.0617i) q^{14} +(-6.34057 + 1.34540i) q^{15} +(5.08559 + 8.80850i) q^{16} +(52.3592 - 90.6889i) q^{17} +(-51.2523 - 5.42323i) q^{18} +(35.0345 - 20.2272i) q^{19} +5.43418 q^{20} +(92.9734 - 24.8386i) q^{21} -77.6716 q^{22} +(-69.6324 + 40.2023i) q^{23} +(116.546 + 37.9133i) q^{24} +(61.7220 - 106.906i) q^{25} +(18.7040 + 32.3962i) q^{26} +(-113.589 + 82.3444i) q^{27} +(-80.5720 + 4.19132i) q^{28} +211.712i q^{29} +(-9.19750 + 8.27562i) q^{30} +(-86.6242 - 50.0125i) q^{31} +(-146.596 - 84.6373i) q^{32} +(-157.176 + 141.422i) q^{33} -199.890i q^{34} +(10.4962 - 20.5803i) q^{35} +(107.486 - 47.7656i) q^{36} +(94.9875 + 164.523i) q^{37} +(38.6103 - 66.8750i) q^{38} +(96.8355 + 31.5014i) q^{39} +(25.4799 - 14.7109i) q^{40} +186.753 q^{41} +(129.988 - 129.796i) q^{42} +158.618 q^{43} +(153.515 - 88.6317i) q^{44} +(-3.54405 + 33.4931i) q^{45} +(-76.7393 + 132.916i) q^{46} +(-179.034 - 310.097i) q^{47} +(51.6999 - 10.9702i) q^{48} +(-139.753 + 313.238i) q^{49} -235.634i q^{50} +(-363.954 - 404.498i) q^{51} +(-73.9351 - 42.6865i) q^{52} +(366.460 + 211.576i) q^{53} +(-109.182 + 244.534i) q^{54} +50.7580i q^{55} +(-366.442 + 237.769i) q^{56} +(-43.6323 - 205.629i) q^{57} +(202.061 + 349.980i) q^{58} +(-312.781 + 541.753i) q^{59} +(8.73508 - 26.8517i) q^{60} +(699.575 - 403.900i) q^{61} -190.931 q^{62} +(26.7144 - 499.333i) q^{63} -404.486 q^{64} +(21.1708 - 12.2229i) q^{65} +(-124.852 + 383.797i) q^{66} +(-149.272 + 258.547i) q^{67} +(228.096 + 395.074i) q^{68} +(86.7208 + 408.695i) q^{69} +(-2.29089 - 44.0390i) q^{70} -455.386i q^{71} +(374.680 - 514.941i) q^{72} +(-434.467 - 250.840i) q^{73} +(314.047 + 181.315i) q^{74} +(-429.035 - 476.829i) q^{75} +176.234i q^{76} +(-39.1491 - 752.584i) q^{77} +(190.144 - 40.3465i) q^{78} +(30.9561 + 53.6176i) q^{79} +(6.34382 - 10.9878i) q^{80} +(224.299 + 693.636i) q^{81} +(308.720 - 178.240i) q^{82} +73.1180 q^{83} +(-108.804 + 404.866i) q^{84} -130.627 q^{85} +(262.211 - 151.388i) q^{86} +(1046.13 + 340.313i) q^{87} +(479.870 - 831.158i) q^{88} +(-57.3723 - 99.3717i) q^{89} +(26.1077 + 58.7498i) q^{90} +(-304.469 + 197.557i) q^{91} -350.271i q^{92} +(-386.368 + 347.642i) q^{93} +(-591.922 - 341.746i) q^{94} +(-43.7025 - 25.2316i) q^{95} +(-653.860 + 588.322i) q^{96} -1416.51i q^{97} +(67.9336 + 651.195i) q^{98} +(446.156 + 1003.98i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 1479 * q^93 - 1356 * q^94 - 4410 * q^96 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.65310	−	0.954416i	0.584458	−	0.337437i	−0.178445	−	0.983950i	$-0.557107\pi$
$2$	1.65310	−	0.954416i	0.584458	−	0.337437i	0.762903	+	0.646513i	$0.223773\pi$
$3$	1.60743	−	4.94127i	0.309351	−	0.950948i
$3$	1.60743	−	4.94127i	0.309351	−	0.950948i
$4$	−2.17818	+	3.77272i	−0.272273	+	0.471590i
$5$	−0.623706	−	1.08029i	−0.0557859	−	0.0966240i	0.836784	−	0.547533i	$-0.184433\pi$
$5$	−0.623706	−	1.08029i	−0.0557859	−	0.0966240i	−0.892570	+	0.450909i	$0.851100\pi$
$6$	−2.05878	−	9.70256i	−0.140082	−	0.660175i
$7$	10.0808	+	15.5363i	0.544314	+	0.838881i
$7$	10.0808	+	15.5363i	0.544314	+	0.838881i
$8$			23.5862i			1.04237i
$9$	−21.8323	−	15.8855i	−0.808604	−	0.588353i
$10$	−2.06209	−	1.19055i	−0.0652090	−	0.0376484i
$11$	−35.2392	−	20.3453i	−0.965910	−	0.557668i	−0.0679230	−	0.997691i	$-0.521637\pi$
$11$	−35.2392	−	20.3453i	−0.965910	−	0.557668i	−0.897987	+	0.440022i	$0.854971\pi$
$12$	15.1408	+	16.8274i	0.364230	+	0.404804i
$13$			19.5973i			0.418101i	0.977905	+	0.209050i	$0.0670373\pi$
$13$			19.5973i			0.418101i	−0.977905	+	0.209050i	$0.932963\pi$
$14$	31.4927	+	16.0617i	0.601198	+	0.306619i
$15$	−6.34057	+	1.34540i	−0.109142	+	0.0231588i
$16$	5.08559	+	8.80850i	0.0794623	+	0.137633i
$17$	52.3592	−	90.6889i	0.746999	−	1.29384i	−0.202256	−	0.979333i	$-0.564827\pi$
$17$	52.3592	−	90.6889i	0.746999	−	1.29384i	0.949255	−	0.314507i	$-0.101839\pi$
$18$	−51.2523	−	5.42323i	−0.671127	−	0.0710148i
$19$	35.0345	−	20.2272i	0.423025	−	0.244234i	−0.273346	−	0.961916i	$-0.588130\pi$
$19$	35.0345	−	20.2272i	0.423025	−	0.244234i	0.696371	+	0.717682i	$0.254797\pi$
$20$	5.43418			0.0607559
$21$	92.9734	−	24.8386i	0.966117	−	0.258106i
$22$	−77.6716			−0.752711
$23$	−69.6324	+	40.2023i	−0.631276	+	0.364467i	−0.781246	−	0.624223i	$-0.785416\pi$
$23$	−69.6324	+	40.2023i	−0.631276	+	0.364467i	0.149970	+	0.988691i	$0.452082\pi$
$24$	116.546	+	37.9133i	0.991243	+	0.322459i
$25$	61.7220	−	106.906i	0.493776	−	0.855245i
$26$	18.7040	+	32.3962i	0.141083	+	0.244362i
$27$	−113.589	+	82.3444i	−0.809636	+	0.586933i
$28$	−80.5720	+	4.19132i	−0.543810	+	0.0282888i
$29$			211.712i			1.35565i	0.735222	+	0.677827i	$0.237078\pi$
$29$			211.712i			1.35565i	−0.735222	+	0.677827i	$0.762922\pi$
$30$	−9.19750	+	8.27562i	−0.0559742	+	0.0503638i
$31$	−86.6242	−	50.0125i	−0.501876	−	0.289758i	0.227612	−	0.973752i	$-0.426908\pi$
$31$	−86.6242	−	50.0125i	−0.501876	−	0.289758i	−0.729488	+	0.683994i	$0.760242\pi$
$32$	−146.596	−	84.6373i	−0.809837	−	0.467560i
$33$	−157.176	+	141.422i	−0.829119	+	0.746015i
$34$		−	199.890i		−	1.00826i
$35$	10.4962	−	20.5803i	0.0506910	−	0.0993916i
$36$	107.486	−	47.7656i	0.497622	−	0.221137i
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	0.996140	−	0.0877801i	$-0.0279773\pi$
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	−0.574090	+	0.818792i	$0.694644\pi$
$38$	38.6103	−	66.8750i	0.164827	−	0.285488i
$39$	96.8355	+	31.5014i	0.397592	+	0.129340i
$40$	25.4799	−	14.7109i	0.100718	−	0.0581497i
$41$	186.753			0.711362			0.355681	−	0.934607i	$-0.384249\pi$
$41$	186.753			0.711362			0.355681	+	0.934607i	$0.384249\pi$
$42$	129.988	−	129.796i	0.477560	−	0.476855i
$43$	158.618			0.562536			0.281268	−	0.959629i	$-0.409245\pi$
$43$	158.618			0.562536			0.281268	+	0.959629i	$0.409245\pi$
$44$	153.515	−	88.6317i	0.525982	−	0.303676i
$45$	−3.54405	+	33.4931i	−0.0117404	+	0.110952i
$46$	−76.7393	+	132.916i	−0.245969	+	0.426032i
$47$	−179.034	−	310.097i	−0.555635	−	0.962388i	−0.997854	−	0.0654808i	$-0.979142\pi$
$47$	−179.034	−	310.097i	−0.555635	−	0.962388i	0.442219	−	0.896907i	$-0.354191\pi$
$48$	51.6999	−	10.9702i	0.155463	−	0.0329877i
$49$	−139.753	+	313.238i	−0.407444	+	0.913230i
$50$		−	235.634i		−	0.666473i
$51$	−363.954	−	404.498i	−0.999290	−	1.11061i
$52$	−73.9351	−	42.6865i	−0.197172	−	0.113837i
$53$	366.460	+	211.576i	0.949758	+	0.548343i	0.893006	−	0.450045i	$-0.148592\pi$
$53$	366.460	+	211.576i	0.949758	+	0.548343i	0.0567521	+	0.998388i	$0.481926\pi$
$54$	−109.182	+	244.534i	−0.275145	+	0.616238i
$55$			50.7580i			0.124440i
$56$	−366.442	+	237.769i	−0.874427	+	0.567379i
$57$	−43.6323	−	205.629i	−0.101390	−	0.477829i
$58$	202.061	+	349.980i	0.457447	+	0.792322i
$59$	−312.781	+	541.753i	−0.690180	+	1.19543i	0.281599	+	0.959532i	$0.409135\pi$
$59$	−312.781	+	541.753i	−0.690180	+	1.19543i	−0.971779	+	0.235895i	$0.924198\pi$
$60$	8.73508	−	26.8517i	0.0187949	−	0.0577757i
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.469011	−	0.883192i	$-0.344611\pi$
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.999372	+	0.0354209i	$0.0112772\pi$
$62$	−190.931			−0.391101
$63$	26.7144	−	499.333i	0.0534239	−	0.998572i
$64$	−404.486			−0.790012
$65$	21.1708	−	12.2229i	0.0403986	−	0.0233241i
$66$	−124.852	+	383.797i	−0.232852	+	0.715789i
$67$	−149.272	+	258.547i	−0.272187	+	0.471441i	−0.969421	−	0.245402i	$-0.921080\pi$
$67$	−149.272	+	258.547i	−0.272187	+	0.471441i	0.697235	+	0.716843i	$0.254413\pi$
$68$	228.096	+	395.074i	0.406775	+	0.704555i
$69$	86.7208	+	408.695i	0.151304	+	0.713059i
$70$	−2.29089	−	44.0390i	−0.00391162	−	0.0751952i
$71$		−	455.386i		−	0.761189i	−0.924742	−	0.380594i	$-0.875719\pi$
$71$		−	455.386i		−	0.761189i	0.924742	−	0.380594i	$-0.124281\pi$
$72$	374.680	−	514.941i	0.613284	−	0.842867i
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	0.109491	−	0.993988i	$-0.465078\pi$
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	−0.806073	+	0.591816i	$0.798411\pi$
$74$	314.047	+	181.315i	0.493341	+	0.284831i
$75$	−429.035	−	476.829i	−0.660543	−	0.734126i
$76$			176.234i			0.265993i
$77$	−39.1491	−	752.584i	−0.0579410	−	1.11383i
$78$	190.144	−	40.3465i	0.276020	−	0.0585685i
$79$	30.9561	+	53.6176i	0.0440865	+	0.0763601i	0.887227	−	0.461334i	$-0.152629\pi$
$79$	30.9561	+	53.6176i	0.0440865	+	0.0763601i	−0.843140	+	0.537694i	$0.819296\pi$
$80$	6.34382	−	10.9878i	0.00886576	−	0.0153559i
$81$	224.299	+	693.636i	0.307681	+	0.951490i
$82$	308.720	−	178.240i	0.415761	−	0.240040i
$83$	73.1180			0.0966957			0.0483478	−	0.998831i	$-0.484604\pi$
$83$	73.1180			0.0966957			0.0483478	+	0.998831i	$0.484604\pi$
$84$	−108.804	+	404.866i	−0.141327	+	0.525886i
$85$	−130.627			−0.166688
$86$	262.211	−	151.388i	0.328779	−	0.189820i
$87$	1046.13	+	340.313i	1.28916	+	0.419373i
$88$	479.870	−	831.158i	0.581298	−	1.00684i
$89$	−57.3723	−	99.3717i	−0.0683309	−	0.118353i	0.829836	−	0.558008i	$-0.188434\pi$
$89$	−57.3723	−	99.3717i	−0.0683309	−	0.118353i	−0.898167	+	0.439655i	$0.855101\pi$
$90$	26.1077	+	58.7498i	0.0305777	+	0.0688086i
$91$	−304.469	+	197.557i	−0.350737	+	0.227578i
$92$		−	350.271i		−	0.396938i
$93$	−386.368	+	347.642i	−0.430801	+	0.387621i
$94$	−591.922	−	341.746i	−0.649490	−	0.374983i
$95$	−43.7025	−	25.2316i	−0.0471977	−	0.0272496i
$96$	−653.860	+	588.322i	−0.695149	+	0.625473i
$97$		−	1416.51i		−	1.48273i	−0.671101	−	0.741366i	$-0.734178\pi$
$97$		−	1416.51i		−	1.48273i	0.671101	−	0.741366i	$-0.265822\pi$
$98$	67.9336	+	651.195i	0.0700238	+	0.671231i
$99$	446.156	+	1003.98i	0.452933	+	1.01923i
$100$	268.883	+	465.720i	0.268883	+	0.465720i
$101$	−120.406	+	208.549i	−0.118622	+	0.205459i	−0.919222	−	0.393740i	$-0.871181\pi$
$101$	−120.406	+	208.549i	−0.118622	+	0.205459i	0.800600	+	0.599199i	$0.204514\pi$
$102$	−987.710	−	321.310i	−0.958802	−	0.311906i
$103$	−960.453	+	554.518i	−0.918799	+	0.530469i	−0.883252	−	0.468899i	$-0.844651\pi$
$103$	−960.453	+	554.518i	−0.918799	+	0.530469i	−0.0355471	+	0.999368i	$0.511317\pi$
$104$	−462.226			−0.435817
$105$	−84.8209	−	84.9462i	−0.0788349	−	0.0789514i
$106$	807.725			0.740124
$107$	−924.644	+	533.843i	−0.835408	+	0.482323i	−0.855701	−	0.517471i	$-0.826874\pi$
$107$	−924.644	+	533.843i	−0.835408	+	0.482323i	0.0202926	+	0.999794i	$0.493540\pi$
$108$	−63.2455	−	607.900i	−0.0563500	−	0.541622i
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	−0.868233	−	0.496157i	$-0.834744\pi$
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	0.863801	+	0.503833i	$0.168077\pi$
$110$	48.4442	+	83.9079i	0.0419907	+	0.0727300i
$111$	965.640	−	204.899i	0.825716	−	0.175208i
$112$	−85.5845	+	167.808i	−0.0722051	+	0.141575i
$113$			884.294i			0.736171i	0.929792	+	0.368086i	$0.119987\pi$
$113$			884.294i			0.736171i	−0.929792	+	0.368086i	$0.880013\pi$
$114$	−268.384	−	298.281i	−0.220495	−	0.245058i
$115$	86.8602	+	50.1487i	0.0704326	+	0.0406643i
$116$	−798.731	−	461.148i	−0.639313	−	0.369108i
$117$	311.314	−	427.854i	0.245991	−	0.338078i
$118$			1194.09i			0.931569i
$119$	1936.79	−	100.751i	1.49198	−	0.0776122i
$120$	−31.7330	−	149.550i	−0.0241401	−	0.113767i
$121$	162.366	+	281.226i	0.121988	+	0.211289i
$122$	770.976	−	1335.37i	0.572139	−	0.990973i
$123$	300.192	−	922.795i	0.220061	−	0.676468i
$124$	377.366	−	217.873i	0.273294	−	0.157787i
$125$	−309.912			−0.221755
$126$	−432.410	−	850.942i	−0.305731	−	0.601650i
$127$	−840.132			−0.587005			−0.293503	−	0.955958i	$-0.594821\pi$
$127$	−840.132			−0.587005			−0.293503	+	0.955958i	$0.594821\pi$
$128$	504.115	−	291.051i	0.348108	−	0.200980i
$129$	254.968	−	783.776i	0.174021	−	0.534943i
$130$	23.3315	−	40.4114i	0.0157408	−	0.0272639i
$131$	258.951	+	448.517i	0.172707	+	0.299138i	0.939366	−	0.342918i	$-0.111415\pi$
$131$	258.951	+	448.517i	0.172707	+	0.299138i	−0.766658	+	0.642056i	$0.778082\pi$
$132$	−191.189	−	901.027i	−0.126067	−	0.594124i
$133$	667.434	+	340.400i	0.435142	+	0.221928i
$134$			569.871i			0.367383i
$135$	159.802	+	71.3501i	0.101878	+	0.0454877i
$136$	2139.01	+	1234.96i	1.34866	+	0.778651i
$137$	−950.957	−	549.035i	−0.593034	−	0.342389i	0.173262	−	0.984876i	$-0.444569\pi$
$137$	−950.957	−	549.035i	−0.593034	−	0.342389i	−0.766296	+	0.642487i	$0.777903\pi$
$138$	533.423	+	592.844i	0.329043	+	0.365697i
$139$			828.268i			0.505416i	0.967543	+	0.252708i	$0.0813212\pi$
$139$			828.268i			0.505416i	−0.967543	+	0.252708i	$0.918679\pi$
$140$	54.7811	+	84.4270i	0.0330703	+	0.0509670i
$141$	−1820.06	+	386.197i	−1.08707	+	0.230664i
$142$	−434.628	−	752.797i	−0.256853	−	0.444883i
$143$	398.714	−	690.592i	0.233162	−	0.403848i
$144$	28.8976	−	273.097i	0.0167231	−	0.158042i
$145$	228.710	−	132.046i	0.130989	−	0.0756264i
$146$	−957.621			−0.542830
$147$	1323.15	+	1194.07i	0.742391	+	0.669967i
$148$	−827.601			−0.459651
$149$	−773.007	+	446.296i	−0.425015	+	0.245382i	−0.697221	−	0.716857i	$-0.745580\pi$
$149$	−773.007	+	446.296i	−0.425015	+	0.245382i	0.272206	+	0.962239i	$0.412247\pi$
$150$	−1164.33	−	378.766i	−0.633781	−	0.206174i
$151$	−712.518	+	1234.12i	−0.383999	+	0.665106i	−0.991630	−	0.129113i	$-0.958787\pi$
$151$	−712.518	+	1234.12i	−0.383999	+	0.665106i	0.607630	+	0.794220i	$0.292120\pi$
$152$	477.083	+	826.332i	0.254583	+	0.440950i
$153$	−2583.76	+	1148.19i	−1.36526	+	0.606705i
$154$	−782.996	−	1206.73i	−0.409712	−	0.631436i
$155$			124.772i			0.0646577i
$156$	−329.771	+	296.718i	−0.169249	+	0.152285i
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	0.436468	−	0.899720i	$-0.356229\pi$
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	−0.560946	+	0.827853i	$0.689562\pi$
$158$	102.347	+	59.0900i	0.0515334	+	0.0297528i
$159$	1634.51	−	1470.68i	0.815254	−	0.733540i
$160$			211.155i			0.104333i
$161$	−1326.55	−	676.557i	−0.649358	−	0.331181i
$162$	1032.81	+	932.572i	0.500894	+	0.452283i
$163$	−1158.07	−	2005.83i	−0.556484	−	0.963858i	−0.997786	−	0.0664997i	$-0.978817\pi$
$163$	−1158.07	−	2005.83i	−0.556484	−	0.963858i	0.441303	−	0.897358i	$-0.354516\pi$
$164$	−406.781	+	704.565i	−0.193685	+	0.335471i
$165$	250.809	+	81.5902i	0.118336	+	0.0384957i
$166$	120.871	−	69.7849i	0.0565145	−	0.0326287i
$167$	2344.70			1.08646			0.543229	−	0.839585i	$-0.317202\pi$
$167$	2344.70			1.08646			0.543229	+	0.839585i	$0.317202\pi$
$168$	585.848	+	2192.89i	0.269043	+	1.00705i
$169$	1812.95			0.825192
$170$	−215.939	+	124.672i	−0.0974221	+	0.0562467i
$171$	−1086.21	−	114.936i	−0.485755	−	0.0513999i
$172$	−345.499	+	598.423i	−0.153163	+	0.265287i
$173$	−516.901	−	895.298i	−0.227163	−	0.393458i	0.729803	−	0.683657i	$-0.239612\pi$
$173$	−516.901	−	895.298i	−0.227163	−	0.393458i	−0.956966	+	0.290199i	$0.906278\pi$
$174$	2054.15	−	435.869i	0.894969	−	0.189903i
$175$	2283.13	−	118.767i	0.986218	−	0.0513026i
$176$		−	413.872i		−	0.177255i
$177$	2174.17	+	2416.37i	0.923281	+	1.02613i
$178$	−189.684	−	109.514i	−0.0798730	−	0.0461147i
$179$	125.472	+	72.4412i	0.0523922	+	0.0302486i	0.525967	−	0.850505i	$-0.323703\pi$
$179$	125.472	+	72.4412i	0.0523922	+	0.0302486i	−0.473575	+	0.880753i	$0.657037\pi$
$180$	−118.641	−	86.3248i	−0.0491275	−	0.0357460i
$181$		−	2057.17i		−	0.844797i	−0.906410	−	0.422398i	$-0.861188\pi$
$181$		−	2057.17i		−	0.844797i	0.906410	−	0.422398i	$-0.138812\pi$
$182$	−314.766	+	617.171i	−0.128198	+	0.251361i
$183$	−871.257	−	4106.03i	−0.351941	−	1.65862i
$184$	−948.219	−	1642.36i	−0.379911	−	0.658025i
$185$	118.489	−	205.228i	0.0470889	−	0.0815604i
$186$	−306.909	+	943.441i	−0.120987	+	0.371916i
$187$	−3690.19	+	2130.53i	−1.44307	+	0.833155i
$188$	1559.88			0.605137
$189$	−2424.40	−	934.648i	−0.933063	−	0.359712i
$190$	−96.3259			−0.0367801
$191$	2553.66	−	1474.36i	0.967417	−	0.558538i	0.0689690	−	0.997619i	$-0.478029\pi$
$191$	2553.66	−	1474.36i	0.967417	−	0.558538i	0.898448	+	0.439080i	$0.144696\pi$
$192$	−650.185	+	1998.68i	−0.244391	+	0.751260i
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	−0.572815	−	0.819685i	$-0.694149\pi$
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	0.996275	+	0.0862300i	$0.0274820\pi$
$194$	−1351.94	−	2341.63i	−0.500329	−	0.866594i
$195$	−26.3662	−	124.258i	−0.00968270	−	0.0456323i
$196$	−877.352	−	1209.54i	−0.319735	−	0.440794i
$197$			495.849i			0.179329i	0.995972	+	0.0896645i	$0.0285795\pi$
$197$			495.849i			0.179329i	−0.995972	+	0.0896645i	$0.971421\pi$
$198$	1695.75	+	1233.86i	0.608645	+	0.442860i
$199$	727.207	+	419.853i	0.259047	+	0.149561i	0.623900	−	0.781504i	$-0.285547\pi$
$199$	727.207	+	419.853i	0.259047	+	0.149561i	−0.364853	+	0.931065i	$0.618881\pi$
$200$	2521.50	+	1455.79i	0.891484	+	0.514699i
$201$	1037.61	+	1153.19i	0.364115	+	0.404676i
$202$			459.668i			0.160109i
$203$	−3289.22	+	2134.24i	−1.13723	+	0.737902i
$204$	2318.81	−	492.028i	0.795831	−	0.168867i
$205$	−116.479	−	201.747i	−0.0396840	−	0.0687347i
$206$	−1058.48	+	1833.34i	−0.357999	+	0.620073i
$207$	2158.87	+	228.439i	0.724888	+	0.0767035i
$208$	−172.623	+	99.6638i	−0.0575444	+	0.0332233i
$209$	−1646.12			−0.544805
$210$	−221.291	−	59.4699i	−0.0727168	−	0.0195420i
$211$	4001.71			1.30564			0.652818	−	0.757514i	$-0.273586\pi$
$211$	4001.71			1.30564			0.652818	+	0.757514i	$0.273586\pi$
$212$	−1596.43	+	921.701i	−0.517186	+	0.298598i
$213$	−2250.19	−	732.004i	−0.723851	−	0.235474i
$214$	−1019.02	+	1764.99i	−0.325507	+	0.563795i
$215$	−98.9311	−	171.354i	−0.0313816	−	0.0543545i
$216$	−1942.19	−	2679.13i	−0.611803	−	0.843943i
$217$	−96.2355	−	1849.99i	−0.0301055	−	0.578734i
$218$			19.2554i			0.00598228i
$219$	−1937.84	+	1743.61i	−0.597933	+	0.538001i
$220$	−191.496	−	110.560i	−0.0586848	−	0.0338817i
$221$	1777.26	+	1026.10i	0.540955	+	0.312321i
$222$	1400.74	−	1260.34i	0.423475	−	0.381029i
$223$			3040.54i			0.913047i	0.889711	+	0.456523i	$0.150905\pi$
$223$			3040.54i			0.913047i	−0.889711	+	0.456523i	$0.849095\pi$
$224$	−162.862	−	3130.78i	−0.0485788	−	0.933856i
$225$	−3045.79	+	1353.51i	−0.902455	+	0.401040i
$226$	843.984	+	1461.82i	0.248411	+	0.430261i
$227$	−2198.24	+	3807.46i	−0.642741	+	1.11326i	0.342078	+	0.939672i	$0.388869\pi$
$227$	−2198.24	+	3807.46i	−0.642741	+	1.11326i	−0.984818	+	0.173588i	$0.944464\pi$
$228$	870.821	+	283.285i	0.252945	+	0.0822851i
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	−0.726937	−	0.686704i	$-0.759057\pi$
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	0.231234	+	0.972898i	$0.425724\pi$
$230$	191.451			0.0548865
$231$	−3781.65	−	1016.28i	−1.07712	−	0.289466i
$232$	−4993.49			−1.41310
$233$	3787.78	−	2186.87i	1.06500	−	0.614879i	0.138191	−	0.990406i	$-0.455871\pi$
$233$	3787.78	−	2186.87i	1.06500	−	0.614879i	0.926812	+	0.375526i	$0.122538\pi$
$234$	106.281	−	1004.41i	0.0296914	−	0.280599i
$235$	−223.329	+	386.818i	−0.0619932	+	0.107375i
$236$	−1362.59	−	2360.07i	−0.375834	−	0.650964i
$237$	314.699	−	66.7758i	0.0862527	−	0.0183019i
$238$	3105.55	−	2015.06i	0.845810	−	0.548810i
$239$		−	3826.41i		−	1.03561i	−0.855500	−	0.517803i	$-0.826750\pi$
$239$		−	3826.41i		−	1.03561i	0.855500	−	0.517803i	$-0.173250\pi$
$240$	−44.0965	−	49.0087i	−0.0118601	−	0.0131813i
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	0.842158	−	0.539231i	$-0.181285\pi$
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	−0.0459083	+	0.998946i	$0.514618\pi$
$242$	536.813	+	309.929i	0.142594	+	0.0823264i
$243$	3787.99	+	6.65062i	0.999998	+	0.00175571i
$244$			3519.07i			0.923300i
$245$	425.553	−	44.3943i	0.110970	−	0.0115765i
$246$	−384.483	−	1811.98i	−0.0996493	−	0.469624i
$247$	396.398	+	686.582i	0.102114	+	0.176867i
$248$	1179.61	−	2043.14i	0.302036	−	0.523142i
$249$	117.532	−	361.296i	0.0299129	−	0.0919525i
$250$	−512.314	+	295.785i	−0.129606	+	0.0748282i
$251$	2046.61			0.514664			0.257332	−	0.966323i	$-0.417157\pi$
$251$	2046.61			0.514664			0.257332	+	0.966323i	$0.417157\pi$
$252$	1825.66	+	1188.42i	0.456371	+	0.297078i
$253$	3271.72			0.813008
$254$	−1388.82	+	801.835i	−0.343080	+	0.198077i
$255$	−209.974	+	645.463i	−0.0515651	+	0.158512i
$256$	2173.51	−	3764.63i	0.530642	−	0.919099i
$257$	3025.57	+	5240.44i	0.734357	+	1.27194i	0.955005	+	0.296590i	$0.0958496\pi$
$257$	3025.57	+	5240.44i	0.734357	+	1.27194i	−0.220648	+	0.975354i	$0.570817\pi$
$258$	−326.560	−	1539.00i	−0.0788014	−	0.371372i
$259$	−1598.53	+	3134.29i	−0.383505	+	0.751950i
$260$			106.495i			0.0254021i
$261$	3363.16	−	4622.16i	0.797603	−	1.09619i
$262$	856.143	+	494.294i	0.201880	+	0.116556i
$263$	−5433.69	−	3137.14i	−1.27398	−	0.735530i	−0.298242	−	0.954490i	$-0.596400\pi$
$263$	−5433.69	−	3137.14i	−1.27398	−	0.735530i	−0.975734	+	0.218960i	$0.929733\pi$
$264$	−3335.62	−	3707.20i	−0.777626	−	0.864251i
$265$		−	527.844i		−	0.122359i
$266$	1428.22	−	74.2951i	0.329209	−	0.0171253i
$267$	−583.245	+	123.758i	−0.133685	+	0.0283666i
$268$	−650.284	−	1126.32i	−0.148218	−	0.256721i
$269$	1668.18	−	2889.37i	0.378106	−	0.654899i	−0.612681	−	0.790331i	$-0.709909\pi$
$269$	1668.18	−	2889.37i	0.378106	−	0.654899i	0.990787	+	0.135432i	$0.0432421\pi$
$270$	332.265	−	34.5686i	0.0748927	−	0.00779178i
$271$	2462.26	−	1421.59i	0.551925	−	0.318654i	−0.197973	−	0.980207i	$-0.563436\pi$
$271$	2462.26	−	1421.59i	0.551925	−	0.318654i	0.749898	+	0.661553i	$0.230103\pi$
$272$	1065.11			0.237433
$273$	486.769	+	1822.03i	0.107914	+	0.403934i
$274$	−2096.03			−0.462138
$275$	−4350.06	+	2511.51i	−0.953886	+	0.550726i
$276$	−1730.79	−	563.038i	−0.377468	−	0.122793i
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	0.283809	+	0.958881i	$0.408402\pi$
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	−0.972320	+	0.233654i	$0.924932\pi$
$278$	790.512	+	1369.21i	0.170546	+	0.295394i
$279$	1096.73	+	2467.96i	0.235339	+	0.529580i
$280$	485.411	+	247.566i	0.103603	+	0.0528390i
$281$			3735.88i			0.793110i	0.918011	+	0.396555i	$0.129794\pi$
$281$			3735.88i			0.793110i	−0.918011	+	0.396555i	$0.870206\pi$
$282$	−2640.14	+	2375.51i	−0.557510	+	0.501630i
$283$	−4777.96	−	2758.56i	−1.00361	−	0.579432i	−0.0942927	−	0.995545i	$-0.530059\pi$
$283$	−4777.96	−	2758.56i	−1.00361	−	0.579432i	−0.909313	+	0.416112i	$0.863392\pi$
$284$	1718.05	+	991.914i	0.358969	+	0.207251i
$285$	−194.925	+	175.388i	−0.0405136	+	0.0364529i
$286$		−	1522.15i		−	0.314709i
$287$	1882.62	+	2901.44i	0.387205	+	0.596748i
$288$	1856.02	+	4176.59i	0.379747	+	0.854541i
$289$	−3026.48	−	5242.01i	−0.616014	−	1.06697i
$290$	252.054	−	436.570i	0.0510383	−	0.0884008i
$291$	−6999.37	−	2276.95i	−1.41000	−	0.458685i
$292$	1892.70	−	1092.75i	0.379321	−	0.219001i
$293$	−7574.50			−1.51026			−0.755131	−	0.655574i	$-0.772427\pi$
$293$	−7574.50			−1.51026			−0.755131	+	0.655574i	$0.772427\pi$
$294$	3326.93	+	711.075i	0.659968	+	0.141057i
$295$	780.333			0.154009
$296$	−3880.48	+	2240.40i	−0.761988	+	0.439934i
$297$	5678.10	−	590.745i	1.10935	−	0.115416i
$298$	−851.904	+	1475.54i	−0.165602	+	0.286831i
$299$	−787.855	−	1364.61i	−0.152384	−	0.263937i
$300$	2733.46	−	580.012i	0.526055	−	0.111623i
$301$	1599.01	+	2464.34i	0.306196	+	0.471901i
$302$			2720.15i			0.518302i
$303$	836.951	+	930.184i	0.158685	+	0.176362i
$304$	356.343	+	205.735i	0.0672291	+	0.0388148i
$305$	−872.657	−	503.829i	−0.163830	−	0.0945874i
$306$	−3175.36	+	4364.06i	−0.593213	+	0.815283i
$307$		−	10635.6i		−	1.97723i	−0.150480	−	0.988613i	$-0.548082\pi$
$307$		−	10635.6i		−	1.97723i	0.150480	−	0.988613i	$-0.451918\pi$
$308$	2924.57	+	1491.57i	0.541047	+	0.275941i
$309$	1196.16	+	5637.21i	0.220217	+	1.03783i
$310$	119.085	+	206.261i	0.0218179	+	0.0377897i
$311$	2885.59	−	4997.99i	0.526132	−	0.911287i	−0.473405	−	0.880845i	$-0.656975\pi$
$311$	2885.59	−	4997.99i	0.526132	−	0.911287i	0.999537	−	0.0304419i	$-0.00969146\pi$
$312$	−742.998	+	2283.98i	−0.134820	+	0.414439i
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	−0.672000	−	0.740551i	$-0.734565\pi$
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	0.305336	+	0.952245i	$0.401231\pi$
$314$	−539.730			−0.0970023
$315$	−556.086	+	282.577i	−0.0994664	+	0.0505442i
$316$	−269.712			−0.0480142
$317$	6852.10	−	3956.06i	1.21405	−	0.700929i	0.250407	−	0.968141i	$-0.419435\pi$
$317$	6852.10	−	3956.06i	1.21405	−	0.700929i	0.963638	+	0.267211i	$0.0861021\pi$
$318$	1298.37	−	3991.19i	0.228958	−	0.703820i
$319$	4307.36	−	7460.56i	0.756005	−	1.30944i
$320$	252.280	+	436.962i	0.0440715	+	0.0763341i
$321$	1151.56	+	5427.03i	0.200230	+	0.943637i
$322$	−2838.63	+	147.664i	−0.491275	+	0.0255559i
$323$		−	4236.32i		−	0.729769i
$324$	−3105.46	−	664.646i	−0.532486	−	0.113965i
$325$	2095.06	+	1209.58i	0.357579	+	0.206448i
$326$	−3828.79	−	2210.55i	−0.650482	−	0.375556i
$327$	35.0596	+	38.9652i	0.00592906	+	0.00658954i
$328$			4404.78i			0.741505i
$329$	3012.94	−	5907.57i	0.504889	−	0.989953i
$330$	492.482	−	104.500i	0.0821523	−	0.0174319i
$331$	2440.02	+	4226.23i	0.405182	+	0.701797i	0.994343	−	0.106220i	$-0.0338747\pi$
$331$	2440.02	+	4226.23i	0.405182	+	0.701797i	−0.589160	+	0.808016i	$0.700541\pi$
$332$	−159.264	+	275.854i	−0.0263276	+	0.0456007i
$333$	539.743	−	5100.85i	0.0888220	−	0.839414i
$334$	3876.02	−	2237.82i	0.634989	−	0.366611i
$335$	372.407			0.0607367
$336$	691.615	+	692.637i	0.112294	+	0.112460i
$337$	−4136.39			−0.668616			−0.334308	−	0.942464i	$-0.608503\pi$
$337$	−4136.39			−0.668616			−0.334308	+	0.942464i	$0.608503\pi$
$338$	2996.97	−	1730.30i	0.482290	−	0.278450i
$339$	4369.53	+	1421.44i	0.700061	+	0.227735i
$340$	284.529	−	492.819i	0.0453846	−	0.0786085i
$341$	2035.04	+	3524.80i	0.323178	+	0.559761i
$342$	−1905.30	+	846.691i	−0.301248	+	0.133871i
$343$	−6275.39	+	986.454i	−0.987869	+	0.155287i
$344$			3741.20i			0.586373i
$345$	387.421	−	348.589i	0.0604580	−	0.0543982i
$346$	−1708.97	−	986.676i	−0.265535	−	0.153306i
$347$	−2009.83	−	1160.38i	−0.310933	−	0.179517i	0.336411	−	0.941715i	$-0.390787\pi$
$347$	−2009.83	−	1160.38i	−0.310933	−	0.179517i	−0.647344	+	0.762198i	$0.724120\pi$
$348$	−3562.56	+	3205.48i	−0.548774	+	0.493770i
$349$		−	226.795i		−	0.0347853i	−0.999849	−	0.0173926i	$-0.994463\pi$
$349$		−	226.795i		−	0.0347853i	0.999849	−	0.0173926i	$-0.00553653\pi$
$350$	3660.88	−	2375.39i	0.559092	−	0.362771i
$351$	−1613.73	−	2226.03i	−0.245397	−	0.338509i
$352$	3443.95	+	5965.10i	0.521486	+	0.903241i
$353$	−742.854	+	1286.66i	−0.112006	+	0.194000i	−0.916579	−	0.399854i	$-0.869061\pi$
$353$	−742.854	+	1286.66i	−0.112006	+	0.194000i	0.804573	+	0.593854i	$0.202394\pi$
$354$	5900.33	+	1919.43i	0.885873	+	0.288182i
$355$	−491.949	+	284.027i	−0.0735491	+	0.0424636i
$356$	499.869			0.0744185
$357$	2615.43	−	9732.18i	0.387740	−	1.44280i
$358$	276.556			0.0408280
$359$	−9419.94	+	5438.60i	−1.38486	+	0.799550i	−0.992730	−	0.120359i	$-0.961595\pi$
$359$	−9419.94	+	5438.60i	−1.38486	+	0.799550i	−0.392131	+	0.919909i	$0.628262\pi$
$360$	−789.976	−	83.5907i	−0.115654	−	0.0122378i
$361$	−2611.22	+	4522.77i	−0.380700	+	0.659392i
$362$	−1963.39	−	3400.70i	−0.285066	−	0.493748i
$363$	1650.61	−	350.241i	0.238662	−	0.0506416i
$364$	−82.1386	−	1578.99i	−0.0118276	−	0.227367i
$365$			625.800i			0.0897421i
$366$	−5359.13	−	5956.12i	−0.765372	−	0.850633i
$367$	−3299.69	−	1905.08i	−0.469325	−	0.270965i	0.246632	−	0.969109i	$-0.420676\pi$
$367$	−3299.69	−	1905.08i	−0.469325	−	0.270965i	−0.715957	+	0.698144i	$0.754009\pi$
$368$	−708.243	−	408.904i	−0.100325	−	0.0579229i
$369$	−4077.24	−	2966.66i	−0.575210	−	0.418532i
$370$		−	452.349i		−	0.0635581i
$371$	407.121	+	7826.30i	0.0569721	+	1.09521i
$372$	−469.976	−	2214.89i	−0.0655030	−	0.308700i
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	0.976185	+	0.216938i	$0.0696070\pi$
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	−0.300219	+	0.953870i	$0.597060\pi$
$374$	−4066.83	+	7043.95i	−0.562274	+	0.973888i
$375$	−498.163	+	1531.36i	−0.0686001	+	0.210877i
$376$	7314.00	−	4222.74i	1.00317	−	0.579179i
$377$	−4148.98			−0.566800
$378$	−4899.80	+	768.819i	−0.666716	+	0.104613i
$379$	320.171			0.0433933			0.0216967	−	0.999765i	$-0.493093\pi$
$379$	320.171			0.0433933			0.0216967	+	0.999765i	$0.493093\pi$
$380$	190.384	−	109.918i	0.0257013	−	0.0148386i
$381$	−1350.46	+	4151.32i	−0.181591	+	0.558211i
$382$	2814.30	−	4874.51i	0.376943	−	0.652884i
$383$	2185.13	+	3784.75i	0.291527	+	0.504939i	0.974171	−	0.225812i	$-0.0725034\pi$
$383$	2185.13	+	3784.75i	0.291527	+	0.504939i	−0.682644	+	0.730751i	$0.739170\pi$
$384$	−627.829	−	2958.81i	−0.0834343	−	0.393206i
$385$	−788.592	+	511.683i	−0.104391	+	0.0677346i
$386$		−	4334.57i		−	0.571564i
$387$	−3463.00	−	2519.74i	−0.454869	−	0.330970i
$388$	5344.11	+	3085.42i	0.699242	+	0.403708i
$389$	11877.4	+	6857.42i	1.54809	+	0.893791i	0.998288	+	0.0584981i	$0.0186311\pi$
$389$	11877.4	+	6857.42i	1.54809	+	0.893791i	0.549805	+	0.835293i	$0.314702\pi$
$390$	−162.180	−	180.246i	−0.0210571	−	0.0234029i
$391$			8419.84i			1.08903i
$392$	−7388.10	−	3296.25i	−0.951927	−	0.424709i
$393$	2632.49	−	558.587i	0.337892	−	0.0716971i
$394$	473.246	+	819.687i	0.0605122	+	0.104810i
$395$	38.6150	−	66.8832i	0.00491882	−	0.00851964i
$396$	−4759.54	−	503.628i	−0.603980	−	0.0639097i
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	−0.631520	−	0.775360i	$-0.717568\pi$
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	0.355722	+	0.934592i	$0.384235\pi$
$398$	1602.86			0.201869
$399$	2754.86	−	2750.80i	0.345653	−	0.345143i
$400$	1255.57			0.156946
$401$	2268.96	−	1309.98i	0.282560	−	0.163136i	−0.352022	−	0.935992i	$-0.614506\pi$
$401$	2268.96	−	1309.98i	0.282560	−	0.163136i	0.634582	+	0.772856i	$0.281172\pi$
$402$	2815.89	+	916.030i	0.349362	+	0.113650i
$403$	980.109	−	1697.60i	0.121148	−	0.209835i
$404$	−524.530	−	908.513i	−0.0645950	−	0.111882i
$405$	609.431	−	674.933i	0.0747725	−	0.0828091i
$406$	−3400.45	+	6667.38i	−0.415669	+	0.815016i
$407$		−	7730.22i		−	0.941456i
$408$	9540.56	−	8584.30i	1.15767	−	1.04163i
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.458952	−	0.888461i	$-0.651775\pi$
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.998906	+	0.0467669i	$0.985108\pi$
$410$	−385.101	−	222.338i	−0.0463872	−	0.0267817i
$411$	−4241.53	+	3816.40i	−0.509049	+	0.458027i
$412$		−	4831.36i		−	0.577729i
$413$	−11569.9	+	601.863i	−1.37850	+	0.0717088i
$414$	3786.85	−	1682.83i	0.449549	−	0.199774i
$415$	−45.6041	−	78.9886i	−0.00539426	−	0.00934313i
$416$	1658.66	−	2872.89i	0.195487	−	0.338593i
$417$	4092.70	+	1331.39i	0.480624	+	0.156351i
$418$	−2721.19	+	1571.08i	−0.318416	+	0.183837i
$419$	15171.1			1.76887			0.884433	−	0.466666i	$-0.154545\pi$
$419$	15171.1			1.76887			0.884433	+	0.466666i	$0.154545\pi$
$420$	505.234	−	134.977i	0.0586973	−	0.0156815i
$421$	−1052.53			−0.121846			−0.0609228	−	0.998142i	$-0.519404\pi$
$421$	−1052.53			−0.121846			−0.0609228	+	0.998142i	$0.519404\pi$
$422$	6615.22	−	3819.30i	0.763090	−	0.440570i
$423$	−1017.32	+	9614.18i	−0.116935	+	1.10510i
$424$	−4990.27	+	8643.40i	−0.571578	+	0.990002i
$425$	−6463.43	−	11195.0i	−0.737700	−	1.27773i
$426$	−4418.41	+	937.541i	−0.502518	+	0.106629i
$427$	13327.4	+	6797.16i	1.51044	+	0.770345i
$428$		−	4651.23i		−	0.525294i
$429$	−2771.50	−	3080.23i	−0.311909	−	0.346655i
$430$	−327.085	−	188.843i	−0.0366824	−	0.0211786i
$431$	6923.58	+	3997.33i	0.773776	+	0.446740i	0.834220	−	0.551432i	$-0.185918\pi$
$431$	6923.58	+	3997.33i	0.773776	+	0.446740i	−0.0604442	+	0.998172i	$0.519252\pi$
$432$	−1303.00	−	581.777i	−0.145117	−	0.0647934i
$433$		−	12889.4i		−	1.43055i	−0.698845	−	0.715273i	$-0.746303\pi$
$433$		−	12889.4i		−	1.43055i	0.698845	−	0.715273i	$-0.253697\pi$
$434$	−1924.74	−	2966.36i	−0.212882	−	0.328087i
$435$	−284.838	−	1342.38i	−0.0313953	−	0.147959i
$436$	−21.9724	−	38.0574i	−0.00241351	−	0.00418032i
$437$	−1626.36	+	2816.94i	−0.178030	+	0.308358i
$438$	−1539.31	+	4731.86i	−0.167925	+	0.516204i
$439$	12456.7	−	7191.89i	1.35427	−	0.781891i	0.365430	−	0.930839i	$-0.380922\pi$
$439$	12456.7	−	7191.89i	1.35427	−	0.781891i	0.988845	+	0.148948i	$0.0475888\pi$
$440$	−1197.19			−0.129713
$441$	8027.09	−	4618.65i	0.866763	−	0.498721i
$442$	3917.30			0.421554
$443$	3432.16	−	1981.56i	0.368097	−	0.212521i	−0.304530	−	0.952503i	$-0.598499\pi$
$443$	3432.16	−	1981.56i	0.368097	−	0.212521i	0.672627	+	0.739982i	$0.265166\pi$
$444$	−1330.31	+	4089.40i	−0.142193	+	0.437104i
$445$	−71.5668	+	123.957i	−0.00762380	+	0.0132048i
$446$	2901.94	+	5026.30i	0.308096	+	0.533637i
$447$	962.710	+	4537.03i	0.101867	+	0.480076i
$448$	−4077.56	−	6284.22i	−0.430015	−	0.662726i
$449$			13479.1i			1.41675i	0.705838	+	0.708373i	$0.250570\pi$
$449$			13479.1i			1.41675i	−0.705838	+	0.708373i	$0.749430\pi$
$450$	−3743.17	+	5144.43i	−0.392121	+	0.538912i
$451$	−6581.00	−	3799.54i	−0.687112	−	0.396704i
$452$	−3336.19	−	1926.15i	−0.347171	−	0.200439i
$453$	4952.78	+	5504.51i	0.513691	+	0.570915i
$454$			8392.13i			0.867538i
$455$	403.318	+	205.698i	0.0415557	+	0.0211940i
$456$	4850.01	−	1029.12i	0.498076	−	0.105686i
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	0.746036	−	0.665905i	$-0.231955\pi$
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	−0.949709	+	0.313134i	$0.898621\pi$
$458$	−1893.14	+	3279.01i	−0.193145	+	0.334537i
$459$	1520.30	+	14612.7i	0.154600	+	1.48598i
$460$	−378.395	+	218.466i	−0.0383538	+	0.0221436i
$461$	−9053.72			−0.914694			−0.457347	−	0.889288i	$-0.651200\pi$
$461$	−9053.72			−0.914694			−0.457347	+	0.889288i	$0.651200\pi$
$462$	−7221.39	+	1929.25i	−0.727207	+	0.194279i
$463$	−5736.10			−0.575764			−0.287882	−	0.957666i	$-0.592951\pi$
$463$	−5736.10			−0.575764			−0.287882	+	0.957666i	$0.592951\pi$
$464$	−1864.87	+	1076.68i	−0.186582	+	0.107723i
$465$	616.534	+	200.563i	0.0614862	+	0.0200019i
$466$	4174.37	−	7230.23i	0.414966	−	0.718742i
$467$	−6196.30	−	10732.3i	−0.613984	−	1.06345i	−0.990562	−	0.137067i	$-0.956232\pi$
$467$	−6196.30	−	10732.3i	−0.613984	−	1.06345i	0.376578	−	0.926385i	$-0.377101\pi$
$468$	936.077	+	2106.44i	0.0924576	+	0.208056i
$469$	−5521.65	+	287.234i	−0.543638	+	0.0282798i
$470$			852.596i			0.0836752i
$471$	−1092.20	+	982.726i	−0.106849	+	0.0961393i
$472$	−12777.9	−	7377.32i	−1.24608	−	0.719425i
$473$	−5589.57	−	3227.14i	−0.543359	−	0.313709i
$474$	456.496	−	410.740i	0.0442353	−	0.0398015i
$475$		−	4993.85i		−	0.482387i
$476$	−3838.58	+	7526.44i	−0.369624	+	0.724735i
$477$	−4639.67	−	10440.6i	−0.445359	−	1.00219i
$478$	−3651.98	−	6325.42i	−0.349452	−	0.605268i
$479$	−4133.87	+	7160.07i	−0.394324	+	0.682989i	−0.993015	−	0.117991i	$-0.962355\pi$
$479$	−4133.87	+	7160.07i	−0.394324	+	0.682989i	0.598691	+	0.800980i	$0.295688\pi$
$480$	1043.37	+	339.418i	0.0992152	+	0.0322755i
$481$	−3224.21	+	1861.50i	−0.305637	+	0.176460i
$482$	6566.17			0.620499
$483$	−5475.39	+	5467.31i	−0.515815	+	0.515054i
$484$	−1414.65			−0.132856
$485$	−1530.24	+	883.487i	−0.143268	+	0.0827156i
$486$	6268.26	−	3604.32i	0.585049	−	0.336410i
$487$	−470.075	+	814.194i	−0.0437395	+	0.0757590i	−0.887066	−	0.461642i	$-0.847260\pi$
$487$	−470.075	+	814.194i	−0.0437395	+	0.0757590i	0.843327	+	0.537401i	$0.180594\pi$
$488$	9526.46	+	16500.3i	0.883694	+	1.53060i
$489$	−11772.9	+	2498.08i	−1.08873	+	0.231017i
$490$	661.109	−	479.542i	0.0609507	−	0.0442112i
$491$		−	1057.30i		−	0.0971801i	−0.998819	−	0.0485900i	$-0.984527\pi$
$491$		−	1057.30i		−	0.0971801i	0.998819	−	0.0485900i	$-0.0154728\pi$
$492$	2827.57	+	3142.56i	0.259099	+	0.287962i
$493$	19199.9	+	11085.1i	1.75400	+	1.01267i
$494$	1310.57	+	756.658i	0.119363	+	0.0689142i
$495$	806.318	−	1108.16i	0.0732148	−	0.100623i
$496$		−	1017.37i		−	0.0920995i
$497$	7075.02	−	4590.68i	0.638547	−	0.414326i
$498$	−150.534	−	709.431i	−0.0135454	−	0.0638361i
$499$	3086.65	+	5346.23i	0.276909	+	0.479620i	0.970615	−	0.240638i	$-0.0773568\pi$
$499$	3086.65	+	5346.23i	0.276909	+	0.479620i	−0.693706	+	0.720258i	$0.744023\pi$
$500$	675.044	−	1169.21i	0.0603778	−	0.104577i
$501$	3768.95	−	11585.8i	0.336097	−	1.03316i
$502$	3383.24	−	1953.31i	0.300800	−	0.173667i
$503$	4284.28			0.379775			0.189887	−	0.981806i	$-0.439188\pi$
$503$	4284.28			0.379775			0.189887	+	0.981806i	$0.439188\pi$
$504$	11777.4	+	630.093i	1.04088	+	0.0556876i
$505$	300.390			0.0264697
$506$	5408.46	−	3122.58i	0.475169	−	0.274339i
$507$	2914.19	−	8958.26i	0.255274	−	0.784714i
$508$	1829.96	−	3169.58i	0.159826	−	0.276826i
$509$	−7550.52	−	13077.9i	−0.657507	−	1.13884i	−0.981259	−	0.192693i	$-0.938278\pi$
$509$	−7550.52	−	13077.9i	−0.657507	−	1.13884i	0.323752	−	0.946142i	$-0.395056\pi$
$510$	268.932	+	1267.42i	0.0233500	+	0.110043i
$511$	−482.673	−	9278.68i	−0.0417851	−	0.803258i
$512$		−	3640.92i		−	0.314272i
$513$	−2313.93	+	5182.48i	−0.199148	+	0.446028i
$514$	10003.1	+	5775.30i	0.858401	+	0.495598i
$515$	1198.08	+	691.712i	0.102512	+	0.0591854i
$516$	2401.60	+	2669.13i	0.204893	+	0.227717i
$517$			14570.1i			1.23944i
$518$	348.892	+	6706.94i	0.0295935	+	0.568892i
$519$	−5254.79	+	1115.01i	−0.444431	+	0.0943037i
$520$	288.293	+	499.338i	0.0243125	+	0.0421104i
$521$	6894.00	−	11940.8i	0.579715	−	1.00410i	−0.415796	−	0.909458i	$-0.636497\pi$
$521$	6894.00	−	11940.8i	0.579715	−	1.00410i	0.995512	−	0.0946385i	$-0.0301695\pi$
$522$	1148.16	−	10850.7i	0.0962715	−	0.909816i
$523$	−832.513	+	480.652i	−0.0696047	+	0.0401863i	−0.534398	−	0.845233i	$-0.679462\pi$
$523$	−832.513	+	480.652i	−0.0696047	+	0.0401863i	0.464794	+	0.885419i	$0.346128\pi$
$524$	−2256.17			−0.188094
$525$	3083.12	−	11472.5i	0.256301	−	0.953713i
$526$	−11976.5			−0.992780
$527$	−9071.15	+	5237.23i	−0.749802	+	0.432898i
$528$	−2045.05	−	665.273i	−0.168560	−	0.0548339i
$529$	−2851.06	+	4938.17i	−0.234327	+	0.405866i
$530$	−503.783	−	872.577i	−0.0412885	−	0.0715138i
$531$	15434.8	−	6859.02i	1.26142	−	0.560557i
$532$	−2738.03	+	1776.59i	−0.223136	+	0.144784i
$533$			3659.84i			0.297421i
$534$	−846.042	+	761.242i	−0.0685615	+	0.0616895i
$535$	1153.41	+	665.922i	0.0932080	+	0.0538137i
$536$	−6098.14	−	3520.76i	−0.491417	−	0.283720i
$537$	559.639	−	503.545i	0.0449724	−	0.0404648i
$538$		−	6368.54i		−	0.510348i
$539$	11297.7	−	8194.92i	0.902834	−	0.654880i
$540$	−617.261	+	447.474i	−0.0491902	+	0.0356596i
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	0.888803	−	0.458290i	$-0.151538\pi$
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	−0.841292	+	0.540581i	$0.818204\pi$
$542$	2713.57	−	4700.04i	0.215051	−	0.372480i
$543$	−10165.0	−	3306.77i	−0.803358	−	0.261339i
$544$	−15351.3	+	8863.09i	−1.20989	+	0.698533i
$545$	12.5833			0.000989006
$546$	2543.65	+	2547.40i	0.199374	+	0.199668i
$547$	18601.8			1.45403			0.727014	−	0.686622i	$-0.240907\pi$
$547$	18601.8			1.45403			0.727014	+	0.686622i	$0.240907\pi$
$548$	4142.71	−	2391.80i	0.322934	−	0.186446i
$549$	−21689.5	−	2295.06i	−1.68613	−	0.178417i
$550$	−4794.05	+	8303.53i	−0.371671	+	0.643753i
$551$	4282.34	+	7417.24i	0.331096	+	0.573475i
$552$	−9639.56	+	2045.41i	−0.743274	+	0.157715i
$553$	−520.955	+	1021.45i	−0.0400601	+	0.0785473i
$554$			12117.9i			0.929315i
$555$	−823.625	−	915.375i	−0.0629927	−	0.0700099i
$556$	−3124.83	−	1804.12i	−0.238349	−	0.137611i
$557$	−5908.09	−	3411.04i	−0.449432	−	0.259480i	0.258158	−	0.966103i	$-0.416884\pi$
$557$	−5908.09	−	3411.04i	−0.449432	−	0.259480i	−0.707590	+	0.706623i	$0.750218\pi$
$558$	4168.46	+	3033.04i	0.316245	+	0.230105i
$559$			3108.49i			0.235197i
$560$	234.661	−	12.2070i	0.0177076	−	0.000921141i
$561$	4595.80	+	21658.9i	0.345873	+	1.63002i
$562$	3565.58	+	6175.77i	0.267624	+	0.463539i
$563$	5679.80	−	9837.71i	0.425178	−	0.736430i	−0.571259	−	0.820770i	$-0.693545\pi$
$563$	5679.80	−	9837.71i	0.425178	−	0.736430i	0.996437	+	0.0843399i	$0.0268782\pi$
$564$	2507.40	−	7707.78i	0.187200	−	0.575454i
$565$	955.293	−	551.539i	0.0711318	−	0.0410680i
$566$	−10531.2			−0.782087
$567$	−8515.41	+	10477.2i	−0.630712	+	0.776017i
$568$	10740.8			0.793443
$569$	−18467.2	+	10662.1i	−1.36061	+	0.785549i	−0.989705	−	0.143122i	$-0.954286\pi$
$569$	−18467.2	+	10662.1i	−1.36061	+	0.785549i	−0.370905	+	0.928671i	$0.620953\pi$
$570$	−154.838	+	475.972i	−0.0113779	+	0.0349759i
$571$	7384.00	−	12789.5i	0.541175	−	0.937343i	−0.457662	−	0.889126i	$-0.651313\pi$
$571$	7384.00	−	12789.5i	0.541175	−	0.937343i	0.998837	−	0.0482163i	$-0.0153537\pi$
$572$	1736.94	+	3008.47i	0.126967	+	0.219913i
$573$	−3180.36	−	14988.3i	−0.231870	−	1.09275i
$574$	5881.34	+	2999.56i	0.427670	+	0.218117i
$575$			9925.45i			0.719861i
$576$	8830.87	+	6425.48i	0.638807	+	0.464806i
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.961936	−	0.273275i	$-0.0881068\pi$
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.244305	+	0.969698i	$0.421440\pi$
$578$	−10006.1	−	5777.04i	−0.720069	−	0.415732i
$579$	−7892.27	−	8771.45i	−0.566479	−	0.629584i
$580$			1150.48i			0.0823640i
$581$	737.091	+	1135.98i	0.0526328	+	0.0811162i
$582$	−13743.8	+	2916.29i	−0.978863	+	0.207705i
$583$	−8609.17	−	14911.5i	−0.611587	−	1.05930i
$584$	5916.35	−	10247.4i	0.419213	−	0.726099i
$585$	−656.374	−	69.4538i	−0.0463893	−	0.00490865i
$586$	−12521.4	+	7229.22i	−0.882684	+	0.509618i
$587$	−4397.46			−0.309204			−0.154602	−	0.987977i	$-0.549410\pi$
$587$	−4397.46			−0.309204			−0.154602	+	0.987977i	$0.549410\pi$
$588$	−7386.95	+	2390.98i	−0.518083	+	0.167691i
$589$	−4046.45			−0.283075
$590$	1289.97	−	744.762i	0.0900119	−	0.0519684i
$591$	2450.13	+	797.045i	0.170532	+	0.0554756i
$592$	−966.135	+	1673.40i	−0.0670742	+	0.116176i
$593$	10970.1	+	19000.8i	0.759677	+	1.31580i	0.943015	+	0.332749i	$0.107976\pi$
$593$	10970.1	+	19000.8i	0.759677	+	1.31580i	−0.183339	+	0.983050i	$0.558691\pi$
$594$	8822.62	−	6395.82i	0.609422	−	0.441791i
$595$	−1316.83	−	2029.46i	−0.0907307	−	0.139832i
$596$		−	3888.46i		−	0.267244i
$597$	3243.54	−	2918.44i	0.222361	−	0.200073i
$598$	−2604.80	−	1503.88i	−0.178124	−	0.102840i
$599$	4765.07	+	2751.12i	0.325034	+	0.187659i	0.653634	−	0.756810i	$-0.273243\pi$
$599$	4765.07	+	2751.12i	0.325034	+	0.187659i	−0.328600	+	0.944469i	$0.606577\pi$
$600$	11246.6	−	10119.3i	0.765233	−	0.688533i
$601$		−	5814.58i		−	0.394645i	−0.980339	−	0.197322i	$-0.936775\pi$
$601$		−	5814.58i		−	0.394645i	0.980339	−	0.197322i	$-0.0632246\pi$
$602$	4995.31	+	2547.68i	0.338196	+	0.172484i
$603$	7366.11	−	3273.41i	0.497465	−	0.221067i
$604$	−3103.99	−	5376.27i	−0.209105	−	0.362181i
$605$	202.537	−	350.804i	0.0136104	−	0.0235739i
$606$	2271.34	+	738.886i	0.152256	+	0.0495300i
$607$	−11510.7	+	6645.69i	−0.769693	+	0.444382i	−0.832765	−	0.553627i	$-0.813244\pi$
$607$	−11510.7	+	6645.69i	−0.769693	+	0.444382i	0.0630721	+	0.998009i	$0.479910\pi$
$608$	−6847.90			−0.456775
$609$	5258.63	+	19683.6i	0.349902	+	1.30972i
$610$	−1923.45			−0.127669
$611$	6077.05	−	3508.59i	0.402375	−	0.232311i
$612$	1296.10	−	12248.8i	0.0856073	−	0.809033i
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	0.338661	+	0.940909i	$0.390026\pi$
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	−0.984181	+	0.177166i	$0.943307\pi$
$614$	−10150.8	−	17581.7i	−0.667189	−	1.15561i
$615$	−1184.12	+	251.257i	−0.0776394	+	0.0164743i
$616$	17750.6	−	923.379i	1.16103	−	0.0603961i
$617$		−	348.388i		−	0.0227319i	−0.999935	−	0.0113660i	$-0.996382\pi$
$617$		−	348.388i		−	0.0227319i	0.999935	−	0.0113660i	$-0.00361797\pi$
$618$	7357.60	+	8177.22i	0.478910	+	0.532259i
$619$	5867.68	+	3387.71i	0.381005	+	0.219973i	0.678255	−	0.734826i	$-0.262736\pi$
$619$	5867.68	+	3387.71i	0.381005	+	0.219973i	−0.297251	+	0.954799i	$0.596070\pi$
$620$	−470.731	−	271.777i	−0.0304920	−	0.0176045i
$621$	4599.02	−	10300.4i	0.297186	−	0.665602i
$622$		−	11016.2i		−	0.710145i
$623$	965.508	−	1893.10i	0.0620903	−	0.121742i
$624$	214.986	+	1013.18i	0.0137922	+	0.0649994i
$625$	−7521.95	−	13028.4i	−0.481405	−	0.833818i
$626$	−2237.65	+	3875.72i	−0.142866	+	0.247452i
$627$	−2646.03	+	8133.91i	−0.168536	+	0.518082i
$628$	1066.75	−	615.890i	0.0677836	−	0.0391349i
$629$	19893.9			1.26108
$630$	−649.568	+	997.865i	−0.0410784	+	0.0631046i
$631$	−7326.82			−0.462244			−0.231122	−	0.972925i	$-0.574240\pi$
$631$	−7326.82			−0.462244			−0.231122	+	0.972925i	$0.574240\pi$
$632$	−1264.64	+	730.138i	−0.0795957	+	0.0459546i
$633$	6432.49	−	19773.6i	0.403900	−	1.24159i
$634$	7551.46	−	13079.5i	0.473039	−	0.819327i
$635$	523.995	+	907.586i	0.0327466	+	0.0567188i
$636$	1988.21	+	9369.98i	0.123959	+	0.584189i
$637$	−6138.62	−	2738.79i	−0.381822	−	0.170353i
$638$		−	16444.0i		−	1.02042i
$639$	−7234.06	+	9942.13i	−0.447848	+	0.615500i
$640$	−628.838	−	363.060i	−0.0388391	−	0.0224238i
$641$	2433.38	+	1404.91i	0.149942	+	0.0865689i	0.573094	−	0.819490i	$-0.305743\pi$
$641$	2433.38	+	1404.91i	0.149942	+	0.0865689i	−0.423152	+	0.906059i	$0.639076\pi$
$642$	7083.28	+	7872.34i	0.435444	+	0.483951i
$643$			27485.5i			1.68573i	0.538128	+	0.842863i	$0.319132\pi$
$643$			27485.5i			1.68573i	−0.538128	+	0.842863i	$0.680868\pi$
$644$	5441.92	−	3531.03i	0.332984	−	0.216059i
$645$	−1005.73	+	213.405i	−0.0613962	+	0.0130276i
$646$	−4043.21	−	7003.05i	−0.246251	−	0.426519i
$647$	−14659.9	+	25391.7i	−0.890790	+	1.54289i	−0.0518595	+	0.998654i	$0.516515\pi$
$647$	−14659.9	+	25391.7i	−0.890790	+	1.54289i	−0.838930	+	0.544239i	$0.816819\pi$
$648$	−16360.2	+	5290.37i	−0.991807	+	0.320718i
$649$	22044.3	−	12727.3i	1.33330	−	0.769783i
$650$	4617.78			0.278653
$651$	−9295.98	−	2498.21i	−0.559659	−	0.150403i
$652$	10089.9			0.606061
$653$	14500.6	−	8371.91i	0.868992	−	0.501713i	0.00197863	−	0.999998i	$-0.499370\pi$
$653$	14500.6	−	8371.91i	0.868992	−	0.501713i	0.867013	+	0.498285i	$0.166037\pi$
$654$	95.1460	+	30.9517i	0.00568884	+	0.00185062i
$655$	323.019	−	559.485i	0.0192693	−	0.0333754i
$656$	949.747	+	1645.01i	0.0565265	+	0.0979068i
$657$	5500.69	+	12378.1i	0.326640	+	0.735034i
$658$	−657.599	−	12641.4i	−0.0389603	−	0.748954i
$659$		−	9520.47i		−	0.562769i	−0.959595	−	0.281385i	$-0.909206\pi$
$659$		−	9520.47i		−	0.562769i	0.959595	−	0.281385i	$-0.0907937\pi$
$660$	−854.125	+	768.515i	−0.0503739	+	0.0453248i
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.231434	−	0.972851i	$-0.574342\pi$
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.958230	+	0.285998i	$0.907675\pi$
$662$	8067.16	+	4657.58i	0.473624	+	0.273447i
$663$	7927.06	−	7132.51i	0.464346	−	0.417804i
$664$			1724.58i			0.100793i
$665$	−48.5515	−	933.331i	−0.00283120	−	0.0544256i
$666$	−3976.08	−	8947.34i	−0.231337	−	0.520574i
$667$	−8511.31	−	14742.0i	−0.494092	−	0.855792i
$668$	−5107.19	+	8845.91i	−0.295813	+	0.512363i
$669$	15024.1	+	4887.46i	0.868260	+	0.282452i
$670$	615.625	−	355.431i	0.0354980	−	0.0204948i
$671$	−32869.9			−1.89110
$672$	−15731.8	−	4227.78i	−0.903077	−	0.242693i
$673$	−12283.5			−0.703559			−0.351780	−	0.936083i	$-0.614423\pi$
$673$	−12283.5			−0.703559			−0.351780	+	0.936083i	$0.614423\pi$
$674$	−6837.85	+	3947.84i	−0.390778	+	0.225616i
$675$	1792.15	+	17225.7i	0.102193	+	0.982250i
$676$	−3948.93	+	6839.74i	−0.224677	+	0.389152i
$677$	6495.88	+	11251.2i	0.368769	+	0.638727i	0.989373	−	0.145397i	$-0.0464459\pi$
$677$	6495.88	+	11251.2i	0.368769	+	0.638727i	−0.620604	+	0.784124i	$0.713113\pi$
$678$	8579.91	−	1820.57i	0.486002	−	0.103125i
$679$	22007.4	−	14279.6i	1.24384	−	0.807072i
$680$		−	3081.00i		−	0.173751i
$681$	15280.2	+	16982.3i	0.859819	+	0.955601i
$682$	6728.24	+	3884.55i	0.377768	+	0.218104i
$683$	−7366.62	−	4253.12i	−0.412703	−	0.238274i	0.279248	−	0.960219i	$-0.409915\pi$
$683$	−7366.62	−	4253.12i	−0.412703	−	0.238274i	−0.691950	+	0.721945i	$0.743248\pi$
$684$	2799.57	−	3847.60i	0.156498	−	0.215083i
$685$			1369.74i			0.0764018i
$686$	−9432.34	+	7620.03i	−0.524968	+	0.424102i
$687$	2139.38	+	10082.4i	0.118810	+	0.559923i
$688$	806.667	+	1397.19i	0.0447004	+	0.0774234i
$689$	−4146.31	+	7181.62i	−0.229263	+	0.397095i
$690$	307.745	−	946.011i	0.0169792	−	0.0521942i
$691$	−22372.0	+	12916.5i	−1.23165	+	0.711093i	−0.967374	−	0.253354i	$-0.918466\pi$
$691$	−22372.0	+	12916.5i	−1.23165	+	0.711093i	−0.264276	+	0.964447i	$0.585133\pi$
$692$	4503.61			0.247401
$693$	−11100.5	+	17052.6i	−0.608475	+	0.934738i
$694$	−4429.93			−0.242303
$695$	894.770	−	516.595i	0.0488353	−	0.0281951i
$696$	−8026.70	+	24674.2i	−0.437143	+	1.34378i
$697$	9778.22	−	16936.4i	0.531387	−	0.920389i
$698$	−216.457	−	374.914i	−0.0117378	−	0.0203305i
$699$	−4717.33	−	22231.7i	−0.255259	−	1.20298i
$700$	−4524.99	+	8872.30i	−0.244327	+	0.479059i
$701$		−	22607.8i		−	1.21810i	−0.793134	−	0.609048i	$-0.791552\pi$
$701$		−	22607.8i		−	1.21810i	0.793134	−	0.609048i	$-0.208448\pi$
$702$	−4792.20	−	2139.68i	−0.257650	−	0.115038i
$703$	6655.69	+	3842.67i	0.357076	+	0.206158i
$704$	14253.8	+	8229.41i	0.763080	+	0.440565i
$705$	1552.38	+	1725.32i	0.0829308	+	0.0921690i
$706$			2835.96i			0.151180i
$707$	−4453.86	+	231.688i	−0.236923	+	0.0123246i
$708$	−13852.0	+	2939.26i	−0.735298	+	0.156023i
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	0.973779	−	0.227494i	$-0.0730532\pi$
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	−0.683905	+	0.729571i	$0.739720\pi$
$710$	−542.159	+	939.048i	−0.0286576	+	0.0496364i
$711$	175.900	−	1662.35i	0.00927818	−	0.0876835i
$712$	2343.80	−	1353.19i	0.123368	−	0.0712263i
$713$	8042.46			0.422430
$714$	−4964.98	−	18584.4i	−0.260238	−	0.974096i
$715$	−994.720			−0.0520285
$716$	−546.601	+	315.580i	−0.0285299	+	0.0164718i
$717$	−18907.3	−	6150.70i	−0.984808	−	0.320366i
$718$	−10381.4	+	17981.1i	−0.539595	+	0.934607i
$719$	−12885.3	−	22317.9i	−0.668344	−	1.15761i	−0.978367	−	0.206877i	$-0.933670\pi$
$719$	−12885.3	−	22317.9i	−0.668344	−	1.15761i	0.310023	−	0.950729i	$-0.399663\pi$
$720$	−313.048	+	139.114i	−0.0162036	+	0.00720068i
$721$	−18297.3	−	9331.88i	−0.945116	−	0.482021i
$722$			9968.76i			0.513849i
$723$	13287.3	−	11955.5i	0.683486	−	0.614979i
$724$	7761.13	+	4480.89i	0.398398	+	0.230015i
$725$	22633.2	+	13067.3i	1.15942	+	0.669389i
$726$	2394.34	−	2154.35i	0.122400	−	0.110131i
$727$			15593.1i			0.795485i	0.917497	+	0.397742i	$0.130206\pi$
$727$			15593.1i			0.795485i	−0.917497	+	0.397742i	$0.869794\pi$
$728$	−4659.63	−	7181.28i	−0.237221	−	0.365599i
$729$	6121.81	−	18706.8i	0.311020	−	0.950403i
$730$	597.273	+	1034.51i	0.0302823	+	0.0524505i
$731$	8305.13	−	14384.9i	0.420214	−	0.727832i
$732$	17388.7	+	5656.67i	0.878011	+	0.285624i
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	−0.482442	−	0.875928i	$-0.660250\pi$
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	0.517355	+	0.855771i	$0.326917\pi$
$734$	−7272.94			−0.365734
$735$	464.684	−	2174.13i	0.0233199	−	0.109108i
$736$	13610.4			0.681641
$737$	10520.5	−	6073.99i	0.525815	−	0.303580i
$738$	−9571.50	−	1012.80i	−0.477414	−	0.0505173i
$739$	454.445	−	787.122i	0.0226211	−	0.0391810i	−0.854493	−	0.519463i	$-0.826132\pi$
$739$	454.445	−	787.122i	0.0226211	−	0.0391810i	0.877114	+	0.480282i	$0.159466\pi$
$740$	516.179	+	894.048i	0.0256421	+	0.0444133i
$741$	4029.77	−	855.076i	0.199781	−	0.0423914i
$742$	8142.55	+	12549.1i	0.402860	+	0.620877i
$743$		−	8109.00i		−	0.400391i	−0.979756	−	0.200195i	$-0.935842\pi$
$743$		−	8109.00i		−	0.400391i	0.979756	−	0.200195i	$-0.0641577\pi$
$744$	−8199.55	−	9112.96i	−0.404046	−	0.449055i
$745$	964.258	+	556.715i	0.0474197	+	0.0273778i
$746$	16099.7	+	9295.14i	0.790148	+	0.456192i
$747$	−1596.33	−	1161.52i	−0.0781885	−	0.0568912i
$748$		−	18562.8i		−	0.907382i
$749$	−17615.1	−	8983.95i	−0.859337	−	0.438273i
$750$	638.041	+	3006.94i	0.0310639	+	0.146397i
$751$	10382.2	+	17982.5i	0.504463	+	0.873756i	0.999987	+	0.00516122i	$0.00164288\pi$
$751$	10382.2	+	17982.5i	0.504463	+	0.873756i	−0.495524	+	0.868594i	$0.665024\pi$
$752$	1820.99	−	3154.05i	0.0883041	−	0.152947i
$753$	3289.79	−	10112.8i	0.159212	−	0.489419i
$754$	−6858.67	+	3959.85i	−0.331271	+	0.191259i
$755$	1777.61			0.0856870
$756$	8806.95	−	7110.74i	0.423685	−	0.342084i
$757$	23295.6			1.11848			0.559242	−	0.829005i	$-0.311092\pi$
$757$	23295.6			1.11848			0.559242	+	0.829005i	$0.311092\pi$
$758$	529.273	−	305.576i	0.0253616	−	0.0146425i
$759$	5259.07	−	16166.4i	0.251505	−	0.773128i
$760$	595.119	−	1030.78i	0.0284042	−	0.0491976i
$761$	−5014.38	−	8685.16i	−0.238858	−	0.413715i	0.721529	−	0.692385i	$-0.243440\pi$
$761$	−5014.38	−	8685.16i	−0.238858	−	0.413715i	−0.960387	+	0.278670i	$0.910106\pi$
$762$	1729.65	+	8151.43i	0.0822290	+	0.387526i
$763$	−186.571	+	9.70535i	−0.00885233	+	0.000460494i
$764$			12845.7i			0.608299i
$765$	2851.89	+	2075.08i	0.134785	+	0.0980715i
$766$	7224.45	+	4171.04i	0.340770	+	0.196744i
$767$	−10616.9	−	6129.66i	−0.499809	−	0.288565i
$768$	−15108.3	−	16791.3i	−0.709861	−	0.788938i
$769$		−	13500.3i		−	0.633074i	−0.948580	−	0.316537i	$-0.897480\pi$
$769$		−	13500.3i		−	0.633074i	0.948580	−	0.316537i	$-0.102520\pi$
$770$	−815.259	+	1598.51i	−0.0381557	+	0.0748132i
$771$	30757.8	−	6526.49i	1.43673	−	0.304858i
$772$	4946.21	+	8567.09i	0.230593	+	0.399399i
$773$	−11644.9	+	20169.5i	−0.541833	+	0.938482i	0.456966	+	0.889484i	$0.348936\pi$
$773$	−11644.9	+	20169.5i	−0.541833	+	0.938482i	−0.998799	+	0.0489979i	$0.984397\pi$
$774$	−8129.55	−	860.223i	−0.377533	−	0.0399484i
$775$	−10693.2	+	6173.74i	−0.495629	+	0.286151i
$776$	33410.2			1.54556
$777$	12917.8	+	12936.9i	0.596428	+	0.597310i
$778$	26179.3			1.20639
$779$	6542.79	−	3777.48i	0.300924	−	0.173739i
$780$	526.221	+	171.184i	0.0241561	+	0.00785817i
$781$	−9264.99	+	16047.4i	−0.424491	+	0.735240i
$782$	8036.02	+	13918.8i	0.367478	+	0.636490i
$783$	−17433.3	−	24048.1i	−0.795677	−	1.09759i
$784$	−3469.88	+	361.983i	−0.158067	+	0.0164898i
$785$			352.711i			0.0160367i
$786$	3818.63	−	3435.89i	0.173290	−	0.155921i
$787$	−20635.4	−	11913.8i	−0.934653	−	0.539622i	−0.0463726	−	0.998924i	$-0.514766\pi$
$787$	−20635.4	−	11913.8i	−0.934653	−	0.539622i	−0.888280	+	0.459302i	$0.848099\pi$
$788$	−1870.70	−	1080.05i	−0.0845698	−	0.0488264i
$789$	−24235.8	+	21806.6i	−1.09356	+	0.983947i
$790$		−	147.419i		−	0.00663916i
$791$	−13738.7	+	8914.42i	−0.617560	+	0.400709i
$792$	−23680.1	+	10523.1i	−1.06242	+	0.472125i
$793$	7915.34	+	13709.8i	0.354454	+	0.613932i
$794$	−2404.27	+	4164.32i	−0.107461	+	0.186129i
$795$	−2608.22	−	848.475i	−0.116357	−	0.0378519i
$796$	−3167.98	+	1829.03i	−0.141063	+	0.0814426i
$797$	12609.3			0.560406			0.280203	−	0.959941i	$-0.409598\pi$
$797$	12609.3			0.560406			0.280203	+	0.959941i	$0.409598\pi$
$798$	1928.65	−	7176.62i	0.0855557	−	0.318358i
$799$	−37496.4			−1.66023
$800$	−18096.4	+	10448.0i	−0.799756	+	0.461739i
$801$	−326.004	+	3080.90i	−0.0143805	+	0.135903i
$802$	2500.54	−	4331.06i	0.110096	−	0.190692i
$803$	10206.8	+	17678.8i	0.448557	+	0.776924i
$804$	−6610.76	+	1402.74i	−0.289980	+	0.0615307i
$805$	96.4977	+	1855.03i	0.00422497	+	0.0812188i
$806$		−	3741.73i		−	0.163519i
$807$	−11595.7	−	12887.4i	−0.505807	−	0.562153i
$808$	−4918.87	−	2839.91i	−0.214165	−	0.123648i
$809$	−30281.4	−	17483.0i	−1.31599	−	0.759789i	−0.332912	−	0.942958i	$-0.608031\pi$
$809$	−30281.4	−	17483.0i	−1.31599	−	0.759789i	−0.983082	+	0.183169i	$0.941365\pi$
$810$	363.282	−	1697.38i	0.0157585	−	0.0736294i
$811$			5691.42i			0.246428i	0.992380	+	0.123214i	$0.0393201\pi$
$811$			5691.42i			0.246428i	−0.992380	+	0.123214i	$0.960680\pi$
$812$	−887.354	−	17058.1i	−0.0383498	−	0.737218i
$813$	−3066.52	−	14451.8i	−0.132285	−	0.623428i
$814$	−7377.84	−	12778.8i	−0.317682	−	0.550241i
$815$	−1444.59	+	2502.10i	−0.0620879	+	0.107539i
$816$	1712.10	−	5263.00i	0.0734502	−	0.225787i
$817$	5557.12	−	3208.40i	0.237967	−	0.137390i
$818$	−26578.9			−1.13607
$819$	9785.57	+	523.531i	0.417504	+	0.0223366i
$820$	1014.85			0.0432195
$821$	−10487.0	+	6054.70i	−0.445798	+	0.257382i	−0.706054	−	0.708158i	$-0.749526\pi$
$821$	−10487.0	+	6054.70i	−0.445798	+	0.257382i	0.260256	+	0.965540i	$0.416193\pi$
$822$	−3369.23	+	10357.1i	−0.142963	+	0.439469i
$823$	15861.0	−	27472.0i	0.671784	−	1.16356i	−0.305614	−	0.952155i	$-0.598862\pi$
$823$	15861.0	−	27472.0i	0.671784	−	1.16356i	0.977398	−	0.211408i	$-0.0678049\pi$
$824$	−13079.0	−	22653.5i	−0.552946	−	0.957731i
$825$	5417.61	+	25531.9i	0.228627	+	1.07746i
$826$	−18551.8	+	12037.5i	−0.781476	+	0.507066i
$827$			36401.9i			1.53061i	0.643666	+	0.765307i	$0.277413\pi$
$827$			36401.9i			1.53061i	−0.643666	+	0.765307i	$0.722587\pi$
$828$	−5564.25	+	7647.23i	−0.233540	+	0.320966i
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.947230	−	0.320554i	$-0.103869\pi$
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.196007	+	0.980602i	$0.437202\pi$
$830$	−150.776	−	87.0505i	−0.00630543	−	0.00364044i
$831$	22064.0	+	24521.8i	0.921047	+	1.02365i
$832$		−	7926.83i		−	0.330305i
$833$	21089.8	+	29075.0i	0.877214	+	1.20935i
$834$	8036.32	−	1705.22i	0.333663	−	0.0707998i
$835$	−1462.40	−	2532.96i	−0.0606090	−	0.104978i
$836$	3585.54	−	6210.34i	0.148336	−	0.256925i
$837$	13957.8	−	1452.16i	0.576406	−	0.0599688i
$838$	25079.2	−	14479.5i	1.03383	−	0.596881i
$839$	13781.4			0.567090			0.283545	−	0.958959i	$-0.408490\pi$
$839$	13781.4			0.567090			0.283545	+	0.958959i	$0.408490\pi$
$840$	2003.56	−	2000.60i	0.0822968	−	0.0821754i
$841$	−20433.0			−0.837796
$842$	−1739.93	+	1004.55i	−0.0712136	+	0.0411152i
$843$	18460.0	+	6005.18i	0.754206	+	0.245349i
$844$	−8716.46	+	15097.4i	−0.355489	+	0.615726i
$845$	−1130.74	−	1958.51i	−0.0460341	−	0.0797334i
$846$	7494.20	+	16864.1i	0.304558	+	0.685343i
$847$	−2732.43	+	5357.56i	−0.110847	+	0.217341i
$848$			4303.95i			0.174290i
$849$	−21311.0	+	19175.0i	−0.861476	+	0.775129i
$850$	−21369.3	−	12337.6i	−0.862309	−	0.497854i
$851$	−13228.4	−	7637.43i	−0.532860	−	0.307647i
$852$	7662.96	−	6894.89i	0.308132	−	0.277248i
$853$		−	11376.3i		−	0.456645i	−0.973586	−	0.228322i	$-0.926676\pi$
$853$		−	11376.3i		−	0.456645i	0.973586	−	0.228322i	$-0.0733240\pi$
$854$	28518.8	−	1483.54i	1.14273	−	0.0594444i
$855$	553.308	+	1245.10i	0.0221318	+	0.0498030i
$856$	−12591.3	−	21808.8i	−0.502761	−	0.870807i
$857$	21559.6	−	37342.3i	0.859349	−	1.48844i	−0.0132022	−	0.999913i	$-0.504203\pi$
$857$	21559.6	−	37342.3i	0.859349	−	1.48844i	0.872551	−	0.488523i	$-0.162464\pi$
$858$	−7521.37	−	2446.76i	−0.299272	−	0.0973556i
$859$	32325.9	−	18663.4i	1.28399	−	0.741311i	0.306413	−	0.951899i	$-0.400871\pi$
$859$	32325.9	−	18663.4i	1.28399	−	0.741311i	0.977575	+	0.210588i	$0.0675378\pi$
$860$	861.960			0.0341774
$861$	17363.0	−	4638.67i	0.687259	−	0.183607i
$862$	15260.5			0.602986
$863$	30262.7	−	17472.2i	1.19369	−	0.689176i	0.234547	−	0.972105i	$-0.424639\pi$
$863$	30262.7	−	17472.2i	1.19369	−	0.689176i	0.959141	+	0.282929i	$0.0913060\pi$
$864$	23621.1	−	2457.52i	0.930099	−	0.0967668i
$865$	−644.788	+	1116.80i	−0.0253450	+	0.0438988i
$866$	−12301.9	−	21307.5i	−0.482719	−	0.836093i
$867$	−30767.1	+	6528.45i	−1.20520	+	0.255730i
$868$	7189.11	+	3666.54i	0.281122	+	0.143376i
$869$		−	2519.25i		−	0.0983426i
$870$	−1752.05	−	1947.22i	−0.0682759	−	0.0758816i
$871$	−5066.82	−	2925.33i	−0.197110	−	0.113801i
$872$	−206.050	−	118.963i	−0.00800200	−	0.00461995i
$873$	−22502.1	+	30925.7i	−0.872370	+	1.19894i
$874$			6208.89i			0.240296i
$875$	−3124.17	−	4814.88i	−0.120704	−	0.186026i
$876$	−2357.18	−	11108.8i	−0.0909152	−	0.428462i
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	0.823757	−	0.566944i	$-0.191874\pi$
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	−0.902866	+	0.429922i	$0.858541\pi$
$878$	13728.1	−	23777.8i	0.527678	−	0.913964i
$879$	−12175.5	+	37427.6i	−0.467201	+	1.43618i
$880$	−447.102	+	258.134i	−0.0171271	+	0.00988831i
$881$	−15697.6			−0.600301			−0.300151	−	0.953892i	$-0.597037\pi$
$881$	−15697.6			−0.600301			−0.300151	+	0.953892i	$0.597037\pi$
$882$	8861.44	−	15296.3i	0.338299	−	0.583959i
$883$	−44102.6			−1.68083			−0.840413	−	0.541946i	$-0.817688\pi$
$883$	−44102.6			−1.68083			−0.840413	+	0.541946i	$0.817688\pi$
$884$	−7742.37	+	4470.06i	−0.294575	+	0.170073i
$885$	1254.33	−	3855.84i	0.0476429	−	0.146455i
$886$	3782.46	−	6551.42i	0.143425	−	0.248419i
$887$	14164.5	+	24533.5i	0.536185	+	0.928699i	0.999105	+	0.0422991i	$0.0134682\pi$
$887$	14164.5	+	24533.5i	0.536185	+	0.928699i	−0.462920	+	0.886400i	$0.653198\pi$
$888$	4832.79	+	22775.8i	0.182633	+	0.860704i
$889$	−8469.24	−	13052.5i	−0.319515	−	0.492428i
$890$			273.218i			0.0102902i
$891$	6208.14	−	29006.6i	0.233424	−	1.09064i
$892$	−11471.1	−	6622.84i	−0.430584	−	0.248598i
$893$	−12544.8	−	7242.73i	−0.470095	−	0.271409i
$894$	5921.66	+	6581.32i	0.221533	+	0.246211i
$895$		−	180.728i		−	0.00674979i
$896$	9603.75	+	4898.04i	0.358079	+	0.182625i
$897$	−8009.31	+	1699.49i	−0.298131	+	0.0632602i
$898$	12864.7	+	22282.3i	0.478062	+	0.828028i
$899$	10588.3	−	18339.4i	0.392812	−	0.680370i
$900$	1527.86	−	14439.1i	0.0565875	−	0.534781i
$901$	38375.1	−	22155.9i	1.41894	−	0.819223i
$902$	−14505.4			−0.535450
$903$	14747.3	−	3939.85i	0.543476	−	0.145194i
$904$	−20857.1			−0.767365
$905$	−2222.34	+	1283.07i	−0.0816277	+	0.0471278i
$906$	13441.0	+	4372.47i	0.492878	+	0.160337i
$907$	−7102.79	+	12302.4i	−0.260027	+	0.450380i	−0.966249	−	0.257611i	$-0.917065\pi$
$907$	−7102.79	+	12302.4i	−0.260027	+	0.450380i	0.706222	+	0.707991i	$0.250398\pi$
$908$	−9576.32	−	16586.7i	−0.350002	−	0.606220i
$909$	5941.64	−	2640.39i	0.216800	−	0.0963434i
$910$	863.045	−	44.8952i	0.0314392	−	0.00163545i
$911$			17955.9i			0.653025i	0.945193	+	0.326512i	$0.105873\pi$
$911$			17955.9i			0.653025i	−0.945193	+	0.326512i	$0.894127\pi$
$912$	1589.39	−	1430.08i	0.0577082	−	0.0519240i
$913$	−2576.62	−	1487.61i	−0.0933993	−	0.0539241i
$914$	−6578.63	−	3798.17i	−0.238076	−	0.137453i
$915$	−3892.30	+	3502.16i	−0.140629	+	0.126533i
$916$		−	8641.09i		−	0.311692i
$917$	−4357.84	+	8544.57i	−0.156934	+	0.307706i
$918$	16459.8	+	22705.2i	0.591781	+	0.816323i
$919$	21121.3	+	36583.1i	0.758135	+	1.31313i	0.943800	+	0.330516i	$0.107223\pi$
$919$	21121.3	+	36583.1i	0.758135	+	1.31313i	−0.185665	+	0.982613i	$0.559444\pi$
$920$	−1182.82	+	2048.70i	−0.0423874	+	0.0734171i
$921$	−52553.6	−	17096.1i	−1.88024	−	0.611657i
$922$	−14966.7	+	8641.01i	−0.534600	+	0.308651i
$923$	8924.34			0.318254
$924$	12071.3	−	12053.5i	0.429779	−	0.429145i
$925$	23451.3			0.833593
$926$	−9482.32	+	5474.62i	−0.336510	+	0.194284i
$927$	29777.7	+	3150.91i	1.05505	+	0.111639i
$928$	17918.7	−	31036.2i	0.633849	−	1.09786i
$929$	22338.1	+	38690.6i	0.788900	+	1.36641i	0.926642	+	0.375946i	$0.122682\pi$
$929$	22338.1	+	38690.6i	0.788900	+	1.36641i	−0.137742	+	0.990468i	$0.543984\pi$
$930$	1210.61	−	256.879i	0.0426854	−	0.00905741i
$931$	1439.74	+	13801.0i	0.0506826	+	0.485831i
$932$			19053.6i			0.669660i
$933$	−20058.0	−	22292.4i	−0.703827	−	0.782231i
$934$	−20486.2	−	11827.7i	−0.717696	−	0.414362i
$935$	4603.19	+	2657.65i	0.161006	+	0.0929566i
$936$	10091.5	+	7342.71i	0.352403	+	0.256414i
$937$		−	15309.3i		−	0.533761i	−0.963730	−	0.266880i	$-0.914007\pi$
$937$		−	15309.3i		−	0.533761i	0.963730	−	0.266880i	$-0.0859929\pi$
$938$	−8853.68	+	5744.78i	−0.308191	+	0.199972i
$939$	2528.70	+	11917.2i	0.0878817	+	0.414166i
$940$	−972.904	−	1685.12i	−0.0337581	−	0.0584708i
$941$	−21192.2	+	36706.0i	−0.734162	+	1.27161i	0.220928	+	0.975290i	$0.429091\pi$
$941$	−21192.2	+	36706.0i	−0.734162	+	1.27161i	−0.955090	+	0.296316i	$0.904242\pi$
$942$	−867.581	+	2666.95i	−0.0300078	+	0.0922442i
$943$	−13004.0	+	7507.87i	−0.449066	+	0.259268i
$944$	−6362.70			−0.219373
$945$	502.419	+	3202.00i	0.0172949	+	0.110223i
$946$	−12320.1			−0.423427
$947$	−10648.1	+	6147.69i	−0.365383	+	0.210954i	−0.671439	−	0.741060i	$-0.734324\pi$
$947$	−10648.1	+	6147.69i	−0.365383	+	0.210954i	0.306057	+	0.952013i	$0.400990\pi$
$948$	−433.545	+	1332.72i	−0.0148533	+	0.0456590i
$949$	4915.78	−	8514.37i	0.168148	−	0.291242i
$950$	−4766.21	−	8255.32i	−0.162775	−	0.281935i
$951$	−8533.67	−	40217.2i	−0.290981	−	1.37133i
$952$	2376.34	+	45681.6i	0.0809008	+	1.55520i
$953$		−	1322.78i		−	0.0449621i	−0.999747	−	0.0224811i	$-0.992843\pi$
$953$		−	1322.78i		−	0.0449621i	0.999747	−	0.0224811i	$-0.00715655\pi$
$954$	−17634.5	−	12831.1i	−0.598468	−	0.435455i
$955$	−3185.47	−	1839.13i	−0.107936	−	0.0623171i
$956$	14436.0	+	8334.62i	0.488382	+	0.281967i
$957$	−29940.8	−	33276.2i	−1.01134	−	1.12400i
$958$			15781.7i			0.532238i
$959$	−1056.47	−	20309.1i	−0.0355737	−	0.683852i
$960$	2564.67	−	544.197i	0.0862234	−	0.0182957i
$961$	−9893.00	−	17135.2i	−0.332080	−	0.575180i
$962$	−3553.29	+	6154.47i	−0.119088	+	0.206266i
$963$	28667.5	+	3033.43i	0.959291	+	0.101507i
$964$	−12977.7	+	7492.70i	−0.433594	+	0.250336i
$965$	−2832.62			−0.0944925
$966$	−3833.26	+	14263.8i	−0.127674	+	0.475082i
$967$	36887.2			1.22669			0.613346	−	0.789814i	$-0.289823\pi$
$967$	36887.2			1.22669			0.613346	+	0.789814i	$0.289823\pi$
$968$	−6633.06	+	3829.60i	−0.220242	+	0.127157i
$969$	−20932.8	−	6809.61i	−0.693972	−	0.225755i
$970$	−1686.43	+	2920.98i	−0.0558226	+	0.0966875i
$971$	−3409.79	−	5905.93i	−0.112693	−	0.195191i	0.804162	−	0.594410i	$-0.202614\pi$
$971$	−3409.79	−	5905.93i	−0.112693	−	0.195191i	−0.916855	+	0.399220i	$0.869281\pi$
$972$	−8276.02	+	14276.5i	−0.273100	+	0.471111i
$973$	−12868.2	+	8349.64i	−0.423984	+	0.275105i
$974$			1794.59i			0.0590373i
$975$	9344.55	−	8407.93i	0.306939	−	0.276174i
$976$	7115.50	+	4108.14i	0.233362	+	0.134732i
$977$	−42700.8	−	24653.3i	−1.39828	−	0.807298i	−0.404068	−	0.914729i	$-0.632404\pi$
$977$	−42700.8	−	24653.3i	−1.39828	−	0.807298i	−0.994213	+	0.107431i	$0.965738\pi$
$978$	−17077.5	+	15365.8i	−0.558362	+	0.502396i
$979$			4669.03i			0.152424i
$980$	−759.444	+	1702.19i	−0.0247546	+	0.0554842i
$981$	248.894	−	110.605i	0.00810047	−	0.00359975i
$982$	−1009.11	−	1747.82i	−0.0327921	−	0.0567977i
$983$	9765.55	−	16914.4i	0.316859	−	0.548816i	−0.662972	−	0.748644i	$-0.730705\pi$
$983$	9765.55	−	16914.4i	0.316859	−	0.548816i	0.979831	+	0.199828i	$0.0640384\pi$
$984$	21765.2	+	7080.40i	0.705132	+	0.229385i
$985$	535.661	−	309.264i	0.0173275	−	0.0100040i
$986$	42319.1			1.36685
$987$	−24347.8	−	24383.8i	−0.785206	−	0.786366i
$988$	−3453.71			−0.111212
$989$	−11045.0	+	6376.81i	−0.355116	+	0.205026i
$990$	275.272	−	2601.47i	0.00883710	−	0.0835151i
$991$	−9285.39	+	16082.8i	−0.297639	+	0.515526i	−0.975595	−	0.219576i	$-0.929533\pi$
$991$	−9285.39	+	16082.8i	−0.297639	+	0.515526i	0.677956	+	0.735102i	$0.262866\pi$
$992$	8465.85	+	14663.3i	0.270959	+	0.469314i
$993$	24805.1	−	5263.39i	0.792716	−	0.168206i
$994$	7314.27	−	14341.3i	0.233395	−	0.457625i
$995$		−	1047.46i		−	0.0333735i
$996$	1107.06	+	1230.38i	0.0352195	+	0.0391428i
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	0.775276	−	0.631622i	$-0.217611\pi$
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	−0.159363	+	0.987220i	$0.550944\pi$
$998$	10205.1	+	5891.89i	0.323683	+	0.186878i
$999$	−24337.1	−	10866.3i	−0.770762	−	0.344139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.4.g.a.17.4	yes	12
3.2	odd	2	inner	21.4.g.a.17.3	yes	12
4.3	odd	2		336.4.bc.d.17.3		12
7.2	even	3		147.4.g.d.68.3		12
7.3	odd	6		147.4.c.a.146.8		12
7.4	even	3		147.4.c.a.146.7		12
7.5	odd	6	inner	21.4.g.a.5.3	✓	12
7.6	odd	2		147.4.g.d.80.4		12
12.11	even	2		336.4.bc.d.17.5		12
21.2	odd	6		147.4.g.d.68.4		12
21.5	even	6	inner	21.4.g.a.5.4	yes	12
21.11	odd	6		147.4.c.a.146.6		12
21.17	even	6		147.4.c.a.146.5		12
21.20	even	2		147.4.g.d.80.3		12
28.19	even	6		336.4.bc.d.257.5		12
84.47	odd	6		336.4.bc.d.257.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.3	✓	12	7.5	odd	6	inner
21.4.g.a.5.4	yes	12	21.5	even	6	inner
21.4.g.a.17.3	yes	12	3.2	odd	2	inner
21.4.g.a.17.4	yes	12	1.1	even	1	trivial
147.4.c.a.146.5		12	21.17	even	6
147.4.c.a.146.6		12	21.11	odd	6
147.4.c.a.146.7		12	7.4	even	3
147.4.c.a.146.8		12	7.3	odd	6
147.4.g.d.68.3		12	7.2	even	3
147.4.g.d.68.4		12	21.2	odd	6
147.4.g.d.80.3		12	21.20	even	2
147.4.g.d.80.4		12	7.6	odd	2
336.4.bc.d.17.3		12	4.3	odd	2
336.4.bc.d.17.5		12	12.11	even	2
336.4.bc.d.257.3		12	84.47	odd	6
336.4.bc.d.257.5		12	28.19	even	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65310 - 0.954416i) q^{2} +(1.60743 - 4.94127i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(-0.623706 - 1.08029i) q^{5} +(-2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} +23.5862i q^{8} +(-21.8323 - 15.8855i) q^{9} +O(q^{10})\)	\(q+(1.65310 - 0.954416i) q^{2} +(1.60743 - 4.94127i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(-0.623706 - 1.08029i) q^{5} +(-2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} +23.5862i q^{8} +(-21.8323 - 15.8855i) q^{9} +(-2.06209 - 1.19055i) q^{10} +(-35.2392 - 20.3453i) q^{11} +(15.1408 + 16.8274i) q^{12} +19.5973i q^{13} +(31.4927 + 16.0617i) q^{14} +(-6.34057 + 1.34540i) q^{15} +(5.08559 + 8.80850i) q^{16} +(52.3592 - 90.6889i) q^{17} +(-51.2523 - 5.42323i) q^{18} +(35.0345 - 20.2272i) q^{19} +5.43418 q^{20} +(92.9734 - 24.8386i) q^{21} -77.6716 q^{22} +(-69.6324 + 40.2023i) q^{23} +(116.546 + 37.9133i) q^{24} +(61.7220 - 106.906i) q^{25} +(18.7040 + 32.3962i) q^{26} +(-113.589 + 82.3444i) q^{27} +(-80.5720 + 4.19132i) q^{28} +211.712i q^{29} +(-9.19750 + 8.27562i) q^{30} +(-86.6242 - 50.0125i) q^{31} +(-146.596 - 84.6373i) q^{32} +(-157.176 + 141.422i) q^{33} -199.890i q^{34} +(10.4962 - 20.5803i) q^{35} +(107.486 - 47.7656i) q^{36} +(94.9875 + 164.523i) q^{37} +(38.6103 - 66.8750i) q^{38} +(96.8355 + 31.5014i) q^{39} +(25.4799 - 14.7109i) q^{40} +186.753 q^{41} +(129.988 - 129.796i) q^{42} +158.618 q^{43} +(153.515 - 88.6317i) q^{44} +(-3.54405 + 33.4931i) q^{45} +(-76.7393 + 132.916i) q^{46} +(-179.034 - 310.097i) q^{47} +(51.6999 - 10.9702i) q^{48} +(-139.753 + 313.238i) q^{49} -235.634i q^{50} +(-363.954 - 404.498i) q^{51} +(-73.9351 - 42.6865i) q^{52} +(366.460 + 211.576i) q^{53} +(-109.182 + 244.534i) q^{54} +50.7580i q^{55} +(-366.442 + 237.769i) q^{56} +(-43.6323 - 205.629i) q^{57} +(202.061 + 349.980i) q^{58} +(-312.781 + 541.753i) q^{59} +(8.73508 - 26.8517i) q^{60} +(699.575 - 403.900i) q^{61} -190.931 q^{62} +(26.7144 - 499.333i) q^{63} -404.486 q^{64} +(21.1708 - 12.2229i) q^{65} +(-124.852 + 383.797i) q^{66} +(-149.272 + 258.547i) q^{67} +(228.096 + 395.074i) q^{68} +(86.7208 + 408.695i) q^{69} +(-2.29089 - 44.0390i) q^{70} -455.386i q^{71} +(374.680 - 514.941i) q^{72} +(-434.467 - 250.840i) q^{73} +(314.047 + 181.315i) q^{74} +(-429.035 - 476.829i) q^{75} +176.234i q^{76} +(-39.1491 - 752.584i) q^{77} +(190.144 - 40.3465i) q^{78} +(30.9561 + 53.6176i) q^{79} +(6.34382 - 10.9878i) q^{80} +(224.299 + 693.636i) q^{81} +(308.720 - 178.240i) q^{82} +73.1180 q^{83} +(-108.804 + 404.866i) q^{84} -130.627 q^{85} +(262.211 - 151.388i) q^{86} +(1046.13 + 340.313i) q^{87} +(479.870 - 831.158i) q^{88} +(-57.3723 - 99.3717i) q^{89} +(26.1077 + 58.7498i) q^{90} +(-304.469 + 197.557i) q^{91} -350.271i q^{92} +(-386.368 + 347.642i) q^{93} +(-591.922 - 341.746i) q^{94} +(-43.7025 - 25.2316i) q^{95} +(-653.860 + 588.322i) q^{96} -1416.51i q^{97} +(67.9336 + 651.195i) q^{98} +(446.156 + 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 1479 * q^93 - 1356 * q^94 - 4410 * q^96 - 3354 * q^99

Introduction

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