LMFDB - Embedded newform 21.4.g.a.5.4

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			5.4
Root			$2.85284 - 0.928053i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.4.g.a.17.4

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.762903	−	0.646513i	$-0.223773\pi$
$2$	1.65310	+	0.954416i	0.584458	+	0.337437i	−0.178445	+	0.983950i	$0.557107\pi$
$3$	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	−0.892570	−	0.450909i	$-0.851100\pi$
$5$	−0.623706	+	1.08029i	−0.0557859	+	0.0966240i	0.836784	+	0.547533i	$0.184433\pi$
$6$	−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	−0.897987	−	0.440022i	$-0.854971\pi$
$11$	−35.2392	+	20.3453i	−0.965910	+	0.557668i	−0.0679230	+	0.997691i	$0.521637\pi$
$12$	15.1408	−	16.8274i	0.364230	−	0.404804i
$13$		−	19.5973i		−	0.418101i	−0.977905	−	0.209050i	$-0.932963\pi$
$13$		−	19.5973i		−	0.418101i	0.977905	−	0.209050i	$-0.0670373\pi$
$14$	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	0.949255	+	0.314507i	$0.101839\pi$
$17$	52.3592	+	90.6889i	0.746999	+	1.29384i	−0.202256	+	0.979333i	$0.564827\pi$
$18$	−51.2523	+	5.42323i	−0.671127	+	0.0710148i
$19$	35.0345	+	20.2272i	0.423025	+	0.244234i	0.696371	−	0.717682i	$-0.254797\pi$
$19$	35.0345	+	20.2272i	0.423025	+	0.244234i	−0.273346	+	0.961916i	$0.588130\pi$
$20$	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	0.149970	−	0.988691i	$-0.452082\pi$
$23$	−69.6324	−	40.2023i	−0.631276	−	0.364467i	−0.781246	+	0.624223i	$0.785416\pi$
$24$	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	$-0.762922\pi$
$29$		−	211.712i		−	1.35565i	0.735222	−	0.677827i	$-0.237078\pi$
$30$	−9.19750	−	8.27562i	−0.0559742	−	0.0503638i
$31$	−86.6242	+	50.0125i	−0.501876	+	0.289758i	−0.729488	−	0.683994i	$-0.760242\pi$
$31$	−86.6242	+	50.0125i	−0.501876	+	0.289758i	0.227612	+	0.973752i	$0.426908\pi$
$32$	−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	−0.574090	−	0.818792i	$-0.694644\pi$
$37$	94.9875	−	164.523i	0.422050	−	0.731012i	0.996140	+	0.0877801i	$0.0279773\pi$
$38$	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	0.442219	+	0.896907i	$0.354191\pi$
$47$	−179.034	+	310.097i	−0.555635	+	0.962388i	−0.997854	+	0.0654808i	$0.979142\pi$
$48$	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	0.0567521	−	0.998388i	$-0.481926\pi$
$53$	366.460	−	211.576i	0.949758	−	0.548343i	0.893006	+	0.450045i	$0.148592\pi$
$54$	−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	−0.971779	−	0.235895i	$-0.924198\pi$
$59$	−312.781	−	541.753i	−0.690180	−	1.19543i	0.281599	−	0.959532i	$-0.409135\pi$
$60$	8.73508	+	26.8517i	0.0187949	+	0.0577757i
$61$	699.575	+	403.900i	1.46838	+	0.847772i	0.999372	−	0.0354209i	$-0.0112772\pi$
$61$	699.575	+	403.900i	1.46838	+	0.847772i	0.469011	+	0.883192i	$0.344611\pi$
$62$	−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	0.697235	−	0.716843i	$-0.254413\pi$
$67$	−149.272	−	258.547i	−0.272187	−	0.471441i	−0.969421	+	0.245402i	$0.921080\pi$
$68$	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	$0.124281\pi$
$71$			455.386i			0.761189i	−0.924742	+	0.380594i	$0.875719\pi$
$72$	374.680	+	514.941i	0.613284	+	0.842867i
$73$	−434.467	+	250.840i	−0.696582	+	0.402172i	−0.806073	−	0.591816i	$-0.798411\pi$
$73$	−434.467	+	250.840i	−0.696582	+	0.402172i	0.109491	+	0.993988i	$0.465078\pi$
$74$	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	−0.843140	−	0.537694i	$-0.819296\pi$
$79$	30.9561	−	53.6176i	0.0440865	−	0.0763601i	0.887227	+	0.461334i	$0.152629\pi$
$80$	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	−0.898167	−	0.439655i	$-0.855101\pi$
$89$	−57.3723	+	99.3717i	−0.0683309	+	0.118353i	0.829836	+	0.558008i	$0.188434\pi$
$90$	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	$0.265822\pi$
$97$			1416.51i			1.48273i	−0.671101	+	0.741366i	$0.734178\pi$
$98$	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	0.800600	−	0.599199i	$-0.204514\pi$
$101$	−120.406	−	208.549i	−0.118622	−	0.205459i	−0.919222	+	0.393740i	$0.871181\pi$
$102$	−987.710	+	321.310i	−0.958802	+	0.311906i
$103$	−960.453	−	554.518i	−0.918799	−	0.530469i	−0.0355471	−	0.999368i	$-0.511317\pi$
$103$	−960.453	−	554.518i	−0.918799	−	0.530469i	−0.883252	+	0.468899i	$0.844651\pi$
$104$	−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	0.0202926	−	0.999794i	$-0.493540\pi$
$107$	−924.644	−	533.843i	−0.835408	−	0.482323i	−0.855701	+	0.517471i	$0.826874\pi$
$108$	−63.2455	+	607.900i	−0.0563500	+	0.541622i
$109$	−5.04376	−	8.73604i	−0.00443215	−	0.00767671i	0.863801	−	0.503833i	$-0.168077\pi$
$109$	−5.04376	−	8.73604i	−0.00443215	−	0.00767671i	−0.868233	+	0.496157i	$0.834744\pi$
$110$	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	$-0.880013\pi$
$113$		−	884.294i		−	0.736171i	0.929792	−	0.368086i	$-0.119987\pi$
$114$	−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	−0.766658	−	0.642056i	$-0.778082\pi$
$131$	258.951	−	448.517i	0.172707	−	0.299138i	0.939366	+	0.342918i	$0.111415\pi$
$132$	−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	−0.766296	−	0.642487i	$-0.777903\pi$
$137$	−950.957	+	549.035i	−0.593034	+	0.342389i	0.173262	+	0.984876i	$0.444569\pi$
$138$	533.423	−	592.844i	0.329043	−	0.365697i
$139$		−	828.268i		−	0.505416i	−0.967543	−	0.252708i	$-0.918679\pi$
$139$		−	828.268i		−	0.505416i	0.967543	−	0.252708i	$-0.0813212\pi$
$140$	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	0.272206	−	0.962239i	$-0.412247\pi$
$149$	−773.007	−	446.296i	−0.425015	−	0.245382i	−0.697221	+	0.716857i	$0.745580\pi$
$150$	−1164.33	+	378.766i	−0.633781	+	0.206174i
$151$	−712.518	−	1234.12i	−0.383999	−	0.665106i	0.607630	−	0.794220i	$-0.292120\pi$
$151$	−712.518	−	1234.12i	−0.383999	−	0.665106i	−0.991630	+	0.129113i	$0.958787\pi$
$152$	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	−0.560946	−	0.827853i	$-0.689562\pi$
$157$	−244.872	+	141.377i	−0.124477	+	0.0718670i	0.436468	+	0.899720i	$0.356229\pi$
$158$	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	0.441303	+	0.897358i	$0.354516\pi$
$163$	−1158.07	+	2005.83i	−0.556484	+	0.963858i	−0.997786	+	0.0664997i	$0.978817\pi$
$164$	−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	−0.956966	−	0.290199i	$-0.906278\pi$
$173$	−516.901	+	895.298i	−0.227163	+	0.393458i	0.729803	+	0.683657i	$0.239612\pi$
$174$	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	−0.473575	−	0.880753i	$-0.657037\pi$
$179$	125.472	−	72.4412i	0.0523922	−	0.0302486i	0.525967	+	0.850505i	$0.323703\pi$
$180$	−118.641	+	86.3248i	−0.0491275	+	0.0357460i
$181$			2057.17i			0.844797i	0.906410	+	0.422398i	$0.138812\pi$
$181$			2057.17i			0.844797i	−0.906410	+	0.422398i	$0.861188\pi$
$182$	−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	0.898448	−	0.439080i	$-0.144696\pi$
$191$	2553.66	+	1474.36i	0.967417	+	0.558538i	0.0689690	+	0.997619i	$0.478029\pi$
$192$	−650.185	−	1998.68i	−0.244391	−	0.751260i
$193$	1135.40	+	1966.57i	0.423460	+	0.733455i	0.996275	−	0.0862300i	$-0.0274820\pi$
$193$	1135.40	+	1966.57i	0.423460	+	0.733455i	−0.572815	+	0.819685i	$0.694149\pi$
$194$	−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	$-0.971421\pi$
$197$		−	495.849i		−	0.179329i	0.995972	−	0.0896645i	$-0.0285795\pi$
$198$	1695.75	−	1233.86i	0.608645	−	0.442860i
$199$	727.207	−	419.853i	0.259047	−	0.149561i	−0.364853	−	0.931065i	$-0.618881\pi$
$199$	727.207	−	419.853i	0.259047	−	0.149561i	0.623900	+	0.781504i	$0.285547\pi$
$200$	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	$-0.849095\pi$
$223$		−	3040.54i		−	0.913047i	0.889711	−	0.456523i	$-0.150905\pi$
$224$	−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	−0.984818	−	0.173588i	$-0.944464\pi$
$227$	−2198.24	−	3807.46i	−0.642741	−	1.11326i	0.342078	−	0.939672i	$-0.388869\pi$
$228$	870.821	−	283.285i	0.252945	−	0.0822851i
$229$	−1717.81	−	991.778i	−0.495703	−	0.286194i	0.231234	−	0.972898i	$-0.425724\pi$
$229$	−1717.81	−	991.778i	−0.495703	−	0.286194i	−0.726937	+	0.686704i	$0.759057\pi$
$230$	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	0.926812	−	0.375526i	$-0.122538\pi$
$233$	3787.78	+	2186.87i	1.06500	+	0.614879i	0.138191	+	0.990406i	$0.455871\pi$
$234$	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	$0.173250\pi$
$239$			3826.41i			1.03561i	−0.855500	+	0.517803i	$0.826750\pi$
$240$	−44.0965	+	49.0087i	−0.0118601	+	0.0131813i
$241$	2979.03	−	1719.94i	0.796250	−	0.459715i	−0.0459083	−	0.998946i	$-0.514618\pi$
$241$	2979.03	−	1719.94i	0.796250	−	0.459715i	0.842158	+	0.539231i	$0.181285\pi$
$242$	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	−0.220648	−	0.975354i	$-0.570817\pi$
$257$	3025.57	−	5240.44i	0.734357	−	1.27194i	0.955005	−	0.296590i	$-0.0958496\pi$
$258$	−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	−0.975734	−	0.218960i	$-0.929733\pi$
$263$	−5433.69	+	3137.14i	−1.27398	+	0.735530i	−0.298242	+	0.954490i	$0.596400\pi$
$264$	−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	0.990787	−	0.135432i	$-0.0432421\pi$
$269$	1668.18	+	2889.37i	0.378106	+	0.654899i	−0.612681	+	0.790331i	$0.709909\pi$
$270$	332.265	+	34.5686i	0.0748927	+	0.00779178i
$271$	2462.26	+	1421.59i	0.551925	+	0.318654i	0.749898	−	0.661553i	$-0.230103\pi$
$271$	2462.26	+	1421.59i	0.551925	+	0.318654i	−0.197973	+	0.980207i	$0.563436\pi$
$272$	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	−0.972320	−	0.233654i	$-0.924932\pi$
$277$	−3174.17	−	5497.82i	−0.688510	−	1.19253i	0.283809	−	0.958881i	$-0.408402\pi$
$278$	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	$-0.870206\pi$
$281$		−	3735.88i		−	0.793110i	0.918011	−	0.396555i	$-0.129794\pi$
$282$	−2640.14	−	2375.51i	−0.557510	−	0.501630i
$283$	−4777.96	+	2758.56i	−1.00361	+	0.579432i	−0.909313	−	0.416112i	$-0.863392\pi$
$283$	−4777.96	+	2758.56i	−1.00361	+	0.579432i	−0.0942927	+	0.995545i	$0.530059\pi$
$284$	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	$0.451918\pi$
$307$			10635.6i			1.97723i	−0.150480	+	0.988613i	$0.548082\pi$
$308$	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	0.999537	+	0.0304419i	$0.00969146\pi$
$311$	2885.59	+	4997.99i	0.526132	+	0.911287i	−0.473405	+	0.880845i	$0.656975\pi$
$312$	−742.998	−	2283.98i	−0.134820	−	0.414439i
$313$	−2030.41	−	1172.26i	−0.366664	−	0.211694i	0.305336	−	0.952245i	$-0.401231\pi$
$313$	−2030.41	−	1172.26i	−0.366664	−	0.211694i	−0.672000	+	0.740551i	$0.734565\pi$
$314$	−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	0.963638	−	0.267211i	$-0.0861021\pi$
$317$	6852.10	+	3956.06i	1.21405	+	0.700929i	0.250407	+	0.968141i	$0.419435\pi$
$318$	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	−0.589160	−	0.808016i	$-0.700541\pi$
$331$	2440.02	−	4226.23i	0.405182	−	0.701797i	0.994343	+	0.106220i	$0.0338747\pi$
$332$	−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	−0.647344	−	0.762198i	$-0.724120\pi$
$347$	−2009.83	+	1160.38i	−0.310933	+	0.179517i	0.336411	+	0.941715i	$0.390787\pi$
$348$	−3562.56	−	3205.48i	−0.548774	−	0.493770i
$349$			226.795i			0.0347853i	0.999849	+	0.0173926i	$0.00553653\pi$
$349$			226.795i			0.0347853i	−0.999849	+	0.0173926i	$0.994463\pi$
$350$	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	0.804573	−	0.593854i	$-0.202394\pi$
$353$	−742.854	−	1286.66i	−0.112006	−	0.194000i	−0.916579	+	0.399854i	$0.869061\pi$
$354$	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	−0.392131	−	0.919909i	$-0.628262\pi$
$359$	−9419.94	−	5438.60i	−1.38486	−	0.799550i	−0.992730	+	0.120359i	$0.961595\pi$
$360$	−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	−0.715957	−	0.698144i	$-0.754009\pi$
$367$	−3299.69	+	1905.08i	−0.469325	+	0.270965i	0.246632	+	0.969109i	$0.420676\pi$
$368$	−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	−0.300219	−	0.953870i	$-0.597060\pi$
$373$	4869.55	−	8434.30i	0.675967	−	1.17081i	0.976185	−	0.216938i	$-0.0696070\pi$
$374$	−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	−0.682644	−	0.730751i	$-0.739170\pi$
$383$	2185.13	−	3784.75i	0.291527	−	0.504939i	0.974171	+	0.225812i	$0.0725034\pi$
$384$	−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	0.549805	−	0.835293i	$-0.314702\pi$
$389$	11877.4	−	6857.42i	1.54809	−	0.893791i	0.998288	−	0.0584981i	$-0.0186311\pi$
$390$	−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	0.355722	−	0.934592i	$-0.384235\pi$
$397$	−2181.61	−	1259.55i	−0.275798	−	0.159232i	−0.631520	+	0.775360i	$0.717568\pi$
$398$	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	0.634582	−	0.772856i	$-0.281172\pi$
$401$	2268.96	+	1309.98i	0.282560	+	0.163136i	−0.352022	+	0.935992i	$0.614506\pi$
$402$	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	−0.998906	−	0.0467669i	$-0.985108\pi$
$409$	−12058.7	+	6962.09i	−1.45786	+	0.841694i	−0.458952	+	0.888461i	$0.651775\pi$
$410$	−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	−0.0604442	−	0.998172i	$-0.519252\pi$
$431$	6923.58	−	3997.33i	0.773776	−	0.446740i	0.834220	+	0.551432i	$0.185918\pi$
$432$	−1303.00	+	581.777i	−0.145117	+	0.0647934i
$433$			12889.4i			1.43055i	0.698845	+	0.715273i	$0.253697\pi$
$433$			12889.4i			1.43055i	−0.698845	+	0.715273i	$0.746303\pi$
$434$	−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	0.988845	−	0.148948i	$-0.0475888\pi$
$439$	12456.7	+	7191.89i	1.35427	+	0.781891i	0.365430	+	0.930839i	$0.380922\pi$
$440$	−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	0.672627	−	0.739982i	$-0.265166\pi$
$443$	3432.16	+	1981.56i	0.368097	+	0.212521i	−0.304530	+	0.952503i	$0.598499\pi$
$444$	−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	$-0.749430\pi$
$449$		−	13479.1i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$450$	−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	−0.949709	−	0.313134i	$-0.898621\pi$
$457$	−1989.79	+	3446.42i	−0.203673	+	0.352772i	0.746036	+	0.665905i	$0.231955\pi$
$458$	−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	0.376578	+	0.926385i	$0.377101\pi$
$467$	−6196.30	+	10732.3i	−0.613984	+	1.06345i	−0.990562	+	0.137067i	$0.956232\pi$
$468$	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	0.598691	−	0.800980i	$-0.295688\pi$
$479$	−4133.87	−	7160.07i	−0.394324	−	0.682989i	−0.993015	+	0.117991i	$0.962355\pi$
$480$	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	0.843327	−	0.537401i	$-0.180594\pi$
$487$	−470.075	−	814.194i	−0.0437395	−	0.0757590i	−0.887066	+	0.461642i	$0.847260\pi$
$488$	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	$0.0154728\pi$
$491$			1057.30i			0.0971801i	−0.998819	+	0.0485900i	$0.984527\pi$
$492$	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	−0.693706	−	0.720258i	$-0.744023\pi$
$499$	3086.65	−	5346.23i	0.276909	−	0.479620i	0.970615	+	0.240638i	$0.0773568\pi$
$500$	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	0.323752	+	0.946142i	$0.395056\pi$
$509$	−7550.52	+	13077.9i	−0.657507	+	1.13884i	−0.981259	+	0.192693i	$0.938278\pi$
$510$	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	0.995512	+	0.0946385i	$0.0301695\pi$
$521$	6894.00	+	11940.8i	0.579715	+	1.00410i	−0.415796	+	0.909458i	$0.636497\pi$
$522$	1148.16	+	10850.7i	0.0962715	+	0.909816i
$523$	−832.513	−	480.652i	−0.0696047	−	0.0401863i	0.464794	−	0.885419i	$-0.346128\pi$
$523$	−832.513	−	480.652i	−0.0696047	−	0.0401863i	−0.534398	+	0.845233i	$0.679462\pi$
$524$	−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	−0.841292	−	0.540581i	$-0.818204\pi$
$541$	597.846	−	1035.50i	0.0475109	−	0.0822913i	0.888803	+	0.458290i	$0.151538\pi$
$542$	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	−0.707590	−	0.706623i	$-0.750218\pi$
$557$	−5908.09	+	3411.04i	−0.449432	+	0.259480i	0.258158	+	0.966103i	$0.416884\pi$
$558$	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	0.996437	−	0.0843399i	$-0.0268782\pi$
$563$	5679.80	+	9837.71i	0.425178	+	0.736430i	−0.571259	+	0.820770i	$0.693545\pi$
$564$	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	−0.370905	−	0.928671i	$-0.620953\pi$
$569$	−18467.2	−	10662.1i	−1.36061	−	0.785549i	−0.989705	+	0.143122i	$0.954286\pi$
$570$	−154.838	−	475.972i	−0.0113779	−	0.0349759i
$571$	7384.00	+	12789.5i	0.541175	+	0.937343i	0.998837	+	0.0482163i	$0.0153537\pi$
$571$	7384.00	+	12789.5i	0.541175	+	0.937343i	−0.457662	+	0.889126i	$0.651313\pi$
$572$	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	0.244305	−	0.969698i	$-0.421440\pi$
$577$	16718.5	−	9652.44i	1.20624	−	0.696424i	0.961936	+	0.273275i	$0.0881068\pi$
$578$	−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	−0.183339	−	0.983050i	$-0.558691\pi$
$593$	10970.1	−	19000.8i	0.759677	−	1.31580i	0.943015	−	0.332749i	$-0.107976\pi$
$594$	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	−0.328600	−	0.944469i	$-0.606577\pi$
$599$	4765.07	−	2751.12i	0.325034	−	0.187659i	0.653634	+	0.756810i	$0.273243\pi$
$600$	11246.6	+	10119.3i	0.765233	+	0.688533i
$601$			5814.58i			0.394645i	0.980339	+	0.197322i	$0.0632246\pi$
$601$			5814.58i			0.394645i	−0.980339	+	0.197322i	$0.936775\pi$
$602$	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	0.0630721	−	0.998009i	$-0.479910\pi$
$607$	−11510.7	−	6645.69i	−0.769693	−	0.444382i	−0.832765	+	0.553627i	$0.813244\pi$
$608$	−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	−0.984181	−	0.177166i	$-0.943307\pi$
$613$	−9797.17	−	16969.2i	−0.645520	−	1.11807i	0.338661	−	0.940909i	$-0.390026\pi$
$614$	−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	$0.00361797\pi$
$617$			348.388i			0.0227319i	−0.999935	+	0.0113660i	$0.996382\pi$
$618$	7357.60	−	8177.22i	0.478910	−	0.532259i
$619$	5867.68	−	3387.71i	0.381005	−	0.219973i	−0.297251	−	0.954799i	$-0.596070\pi$
$619$	5867.68	−	3387.71i	0.381005	−	0.219973i	0.678255	+	0.734826i	$0.262736\pi$
$620$	−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	−0.423152	−	0.906059i	$-0.639076\pi$
$641$	2433.38	−	1404.91i	0.149942	−	0.0865689i	0.573094	+	0.819490i	$0.305743\pi$
$642$	7083.28	−	7872.34i	0.435444	−	0.483951i
$643$		−	27485.5i		−	1.68573i	−0.538128	−	0.842863i	$-0.680868\pi$
$643$		−	27485.5i		−	1.68573i	0.538128	−	0.842863i	$-0.319132\pi$
$644$	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	−0.838930	−	0.544239i	$-0.816819\pi$
$647$	−14659.9	−	25391.7i	−0.890790	−	1.54289i	−0.0518595	−	0.998654i	$-0.516515\pi$
$648$	−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	0.867013	−	0.498285i	$-0.166037\pi$
$653$	14500.6	+	8371.91i	0.868992	+	0.501713i	0.00197863	+	0.999998i	$0.499370\pi$
$654$	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	$0.0907937\pi$
$659$			9520.47i			0.562769i	−0.959595	+	0.281385i	$0.909206\pi$
$660$	−854.125	−	768.515i	−0.0503739	−	0.0453248i
$661$	−20217.5	+	11672.6i	−1.18966	+	0.686853i	−0.958230	−	0.285998i	$-0.907675\pi$
$661$	−20217.5	+	11672.6i	−1.18966	+	0.686853i	−0.231434	+	0.972851i	$0.574342\pi$
$662$	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	−0.620604	−	0.784124i	$-0.713113\pi$
$677$	6495.88	−	11251.2i	0.368769	−	0.638727i	0.989373	+	0.145397i	$0.0464459\pi$
$678$	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	−0.691950	−	0.721945i	$-0.743248\pi$
$683$	−7366.62	+	4253.12i	−0.412703	+	0.238274i	0.279248	+	0.960219i	$0.409915\pi$
$684$	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	−0.264276	−	0.964447i	$-0.585133\pi$
$691$	−22372.0	−	12916.5i	−1.23165	−	0.711093i	−0.967374	+	0.253354i	$0.918466\pi$
$692$	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	$0.208448\pi$
$701$			22607.8i			1.21810i	−0.793134	+	0.609048i	$0.791552\pi$
$702$	−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	−0.683905	−	0.729571i	$-0.739720\pi$
$709$	5472.41	−	9478.50i	0.289874	−	0.502077i	0.973779	+	0.227494i	$0.0730532\pi$
$710$	−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	0.310023	+	0.950729i	$0.399663\pi$
$719$	−12885.3	+	22317.9i	−0.668344	+	1.15761i	−0.978367	+	0.206877i	$0.933670\pi$
$720$	−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	$-0.869794\pi$
$727$		−	15593.1i		−	0.795485i	0.917497	−	0.397742i	$-0.130206\pi$
$728$	−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	0.517355	−	0.855771i	$-0.326917\pi$
$733$	692.858	+	400.022i	0.0349131	+	0.0201571i	−0.482442	+	0.875928i	$0.660250\pi$
$734$	−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	0.877114	−	0.480282i	$-0.159466\pi$
$739$	454.445	+	787.122i	0.0226211	+	0.0391810i	−0.854493	+	0.519463i	$0.826132\pi$
$740$	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	$0.0641577\pi$
$743$			8109.00i			0.400391i	−0.979756	+	0.200195i	$0.935842\pi$
$744$	−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	−0.495524	−	0.868594i	$-0.665024\pi$
$751$	10382.2	−	17982.5i	0.504463	−	0.873756i	0.999987	−	0.00516122i	$-0.00164288\pi$
$752$	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	−0.960387	−	0.278670i	$-0.910106\pi$
$761$	−5014.38	+	8685.16i	−0.238858	+	0.413715i	0.721529	+	0.692385i	$0.243440\pi$
$762$	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	$0.102520\pi$
$769$			13500.3i			0.633074i	−0.948580	+	0.316537i	$0.897480\pi$
$770$	−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	−0.998799	−	0.0489979i	$-0.984397\pi$
$773$	−11644.9	−	20169.5i	−0.541833	−	0.938482i	0.456966	−	0.889484i	$-0.348936\pi$
$774$	−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	−0.888280	−	0.459302i	$-0.848099\pi$
$787$	−20635.4	+	11913.8i	−0.934653	+	0.539622i	−0.0463726	+	0.998924i	$0.514766\pi$
$788$	−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	−0.983082	−	0.183169i	$-0.941365\pi$
$809$	−30281.4	+	17483.0i	−1.31599	+	0.759789i	−0.332912	+	0.942958i	$0.608031\pi$
$810$	363.282	+	1697.38i	0.0157585	+	0.0736294i
$811$		−	5691.42i		−	0.246428i	−0.992380	−	0.123214i	$-0.960680\pi$
$811$		−	5691.42i		−	0.246428i	0.992380	−	0.123214i	$-0.0393201\pi$
$812$	−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	0.260256	−	0.965540i	$-0.416193\pi$
$821$	−10487.0	−	6054.70i	−0.445798	−	0.257382i	−0.706054	+	0.708158i	$0.749526\pi$
$822$	−3369.23	−	10357.1i	−0.142963	−	0.439469i
$823$	15861.0	+	27472.0i	0.671784	+	1.16356i	0.977398	+	0.211408i	$0.0678049\pi$
$823$	15861.0	+	27472.0i	0.671784	+	1.16356i	−0.305614	+	0.952155i	$0.598862\pi$
$824$	−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	$-0.722587\pi$
$827$		−	36401.9i		−	1.53061i	0.643666	−	0.765307i	$-0.277413\pi$
$828$	−5564.25	−	7647.23i	−0.233540	−	0.320966i
$829$	27287.8	−	15754.6i	1.14324	−	0.660049i	0.196007	−	0.980602i	$-0.437202\pi$
$829$	27287.8	−	15754.6i	1.14324	−	0.660049i	0.947230	+	0.320554i	$0.103869\pi$
$830$	−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	$0.0733240\pi$
$853$			11376.3i			0.456645i	−0.973586	+	0.228322i	$0.926676\pi$
$854$	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	0.872551	+	0.488523i	$0.162464\pi$
$857$	21559.6	+	37342.3i	0.859349	+	1.48844i	−0.0132022	+	0.999913i	$0.504203\pi$
$858$	−7521.37	+	2446.76i	−0.299272	+	0.0973556i
$859$	32325.9	+	18663.4i	1.28399	+	0.741311i	0.977575	−	0.210588i	$-0.0675378\pi$
$859$	32325.9	+	18663.4i	1.28399	+	0.741311i	0.306413	+	0.951899i	$0.400871\pi$
$860$	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	0.959141	−	0.282929i	$-0.0913060\pi$
$863$	30262.7	+	17472.2i	1.19369	+	0.689176i	0.234547	+	0.972105i	$0.424639\pi$
$864$	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	−0.902866	−	0.429922i	$-0.858541\pi$
$877$	−2054.59	+	3558.66i	−0.0791092	+	0.137021i	0.823757	+	0.566944i	$0.191874\pi$
$878$	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	−0.462920	−	0.886400i	$-0.653198\pi$
$887$	14164.5	−	24533.5i	0.536185	−	0.928699i	0.999105	−	0.0422991i	$-0.0134682\pi$
$888$	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	0.706222	−	0.707991i	$-0.250398\pi$
$907$	−7102.79	−	12302.4i	−0.260027	−	0.450380i	−0.966249	+	0.257611i	$0.917065\pi$
$908$	−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	$-0.894127\pi$
$911$		−	17955.9i		−	0.653025i	0.945193	−	0.326512i	$-0.105873\pi$
$912$	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	−0.185665	−	0.982613i	$-0.559444\pi$
$919$	21121.3	−	36583.1i	0.758135	−	1.31313i	0.943800	−	0.330516i	$-0.107223\pi$
$920$	−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	−0.137742	−	0.990468i	$-0.543984\pi$
$929$	22338.1	−	38690.6i	0.788900	−	1.36641i	0.926642	−	0.375946i	$-0.122682\pi$
$930$	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	$0.0859929\pi$
$937$			15309.3i			0.533761i	−0.963730	+	0.266880i	$0.914007\pi$
$938$	−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	−0.955090	−	0.296316i	$-0.904242\pi$
$941$	−21192.2	−	36706.0i	−0.734162	−	1.27161i	0.220928	−	0.975290i	$-0.429091\pi$
$942$	−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	0.306057	−	0.952013i	$-0.400990\pi$
$947$	−10648.1	−	6147.69i	−0.365383	−	0.210954i	−0.671439	+	0.741060i	$0.734324\pi$
$948$	−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	$0.00715655\pi$
$953$			1322.78i			0.0449621i	−0.999747	+	0.0224811i	$0.992843\pi$
$954$	−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	−0.916855	−	0.399220i	$-0.869281\pi$
$971$	−3409.79	+	5905.93i	−0.112693	+	0.195191i	0.804162	+	0.594410i	$0.202614\pi$
$972$	−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	−0.994213	−	0.107431i	$-0.965738\pi$
$977$	−42700.8	+	24653.3i	−1.39828	+	0.807298i	−0.404068	+	0.914729i	$0.632404\pi$
$978$	−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	0.979831	−	0.199828i	$-0.0640384\pi$
$983$	9765.55	+	16914.4i	0.316859	+	0.548816i	−0.662972	+	0.748644i	$0.730705\pi$
$984$	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	0.677956	−	0.735102i	$-0.262866\pi$
$991$	−9285.39	−	16082.8i	−0.297639	−	0.515526i	−0.975595	+	0.219576i	$0.929533\pi$
$992$	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	−0.159363	−	0.987220i	$-0.550944\pi$
$997$	19389.3	−	11194.4i	0.615913	−	0.355598i	0.775276	+	0.631622i	$0.217611\pi$
$998$	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.5.4	yes	12
3.2	odd	2	inner	21.4.g.a.5.3	✓	12
4.3	odd	2		336.4.bc.d.257.3		12
7.2	even	3		147.4.c.a.146.5		12
7.3	odd	6	inner	21.4.g.a.17.3	yes	12
7.4	even	3		147.4.g.d.80.3		12
7.5	odd	6		147.4.c.a.146.6		12
7.6	odd	2		147.4.g.d.68.4		12
12.11	even	2		336.4.bc.d.257.5		12
21.2	odd	6		147.4.c.a.146.8		12
21.5	even	6		147.4.c.a.146.7		12
21.11	odd	6		147.4.g.d.80.4		12
21.17	even	6	inner	21.4.g.a.17.4	yes	12
21.20	even	2		147.4.g.d.68.3		12
28.3	even	6		336.4.bc.d.17.5		12
84.59	odd	6		336.4.bc.d.17.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.3	✓	12	3.2	odd	2	inner
21.4.g.a.5.4	yes	12	1.1	even	1	trivial
21.4.g.a.17.3	yes	12	7.3	odd	6	inner
21.4.g.a.17.4	yes	12	21.17	even	6	inner
147.4.c.a.146.5		12	7.2	even	3
147.4.c.a.146.6		12	7.5	odd	6
147.4.c.a.146.7		12	21.5	even	6
147.4.c.a.146.8		12	21.2	odd	6
147.4.g.d.68.3		12	21.20	even	2
147.4.g.d.68.4		12	7.6	odd	2
147.4.g.d.80.3		12	7.4	even	3
147.4.g.d.80.4		12	21.11	odd	6
336.4.bc.d.17.3		12	84.59	odd	6
336.4.bc.d.17.5		12	28.3	even	6
336.4.bc.d.257.3		12	4.3	odd	2
336.4.bc.d.257.5		12	12.11	even	2

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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