LMFDB - Embedded newform 105.4.i.c.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.646154928.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} - 8x^{3} + 121x^{2} - 44x + 16 $ x^6 + 11x^4 - 8x^3 + 121x^2 - 44x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$-1.74267 + 3.01840i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.4.i.c.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24267 - 2.15238i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.911519 + 1.57880i) q^{4} +(-2.50000 + 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 + 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.24267 - 2.15238i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.911519 + 1.57880i) q^{4} +(-2.50000 + 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 + 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.21337 + 10.7619i) q^{10} +(13.0299 + 22.5684i) q^{11} +(-2.73456 + 4.73639i) q^{12} +3.20425 q^{13} +(23.9375 + 39.3153i) q^{14} -15.0000 q^{15} +(23.0461 - 39.9170i) q^{16} +(9.01624 + 15.6166i) q^{17} +(11.1841 + 19.3714i) q^{18} +(17.1199 - 29.6526i) q^{19} -9.11519 q^{20} +(-55.5457 + 1.29492i) q^{21} +64.7676 q^{22} +(49.5912 - 85.8945i) q^{23} +(36.6205 + 63.4286i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(3.98184 - 6.89675i) q^{26} -27.0000 q^{27} +(-33.7540 + 0.786896i) q^{28} +212.096 q^{29} +(-18.6401 + 32.2856i) q^{30} +(-146.585 - 253.893i) q^{31} +(40.3771 + 69.9352i) q^{32} +(-39.0896 + 67.7052i) q^{33} +44.8170 q^{34} +(-48.1571 - 79.0942i) q^{35} -16.4073 q^{36} +(-10.3520 + 17.9301i) q^{37} +(-42.5490 - 73.6971i) q^{38} +(4.80637 + 8.32488i) q^{39} +(-61.0342 + 105.714i) q^{40} -207.842 q^{41} +(-66.2381 + 121.164i) q^{42} +5.96397 q^{43} +(-23.7540 + 41.1431i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(-123.252 - 213.478i) q^{46} +(-200.949 + 348.055i) q^{47} +138.277 q^{48} +(-185.156 - 288.732i) q^{49} -62.1337 q^{50} +(-27.0487 + 46.8497i) q^{51} +(2.92073 + 5.05886i) q^{52} +(3.65770 + 6.33533i) q^{53} +(-33.5522 + 58.1141i) q^{54} -130.299 q^{55} +(-216.886 + 396.734i) q^{56} +102.720 q^{57} +(263.566 - 456.510i) q^{58} +(-20.2045 - 34.9952i) q^{59} +(-13.6728 - 23.6820i) q^{60} +(179.242 - 310.456i) q^{61} -728.631 q^{62} +(-86.6828 - 142.370i) q^{63} +569.440 q^{64} +(-8.01062 + 13.8748i) q^{65} +(97.1514 + 168.271i) q^{66} +(-293.731 - 508.757i) q^{67} +(-16.4369 + 28.4696i) q^{68} +297.547 q^{69} +(-230.084 + 5.36388i) q^{70} +803.405 q^{71} +(-109.862 + 190.286i) q^{72} +(328.025 + 568.157i) q^{73} +(25.7282 + 44.5626i) q^{74} +(37.5000 - 64.9519i) q^{75} +62.4206 q^{76} +(-482.502 + 11.2484i) q^{77} +23.8910 q^{78} +(637.780 - 1104.67i) q^{79} +(115.231 + 199.585i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-258.280 + 447.354i) q^{82} +244.647 q^{83} +(-52.6754 - 86.5150i) q^{84} -90.1624 q^{85} +(7.41127 - 12.8367i) q^{86} +(318.144 + 551.041i) q^{87} +(318.107 + 550.978i) q^{88} +(705.542 - 1222.03i) q^{89} -111.841 q^{90} +(-28.4659 + 52.0706i) q^{91} +180.813 q^{92} +(439.756 - 761.679i) q^{93} +(499.429 + 865.037i) q^{94} +(85.5997 + 148.263i) q^{95} +(-121.131 + 209.805i) q^{96} -952.212 q^{97} +(-851.549 + 39.7254i) q^{98} -234.538 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.24267	−	2.15238i	0.439352	−	0.760980i	−0.558288	−	0.829647i	$-0.688541\pi$
$2$	1.24267	−	2.15238i	0.439352	−	0.760980i	0.997640	+	0.0686676i	$0.0218748\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	0.911519	+	1.57880i	0.113940	+	0.197350i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	7.45605			0.507320
$7$	−8.88380	+	16.2505i	−0.479680	+	0.877443i
$7$	−8.88380	+	16.2505i	−0.479680	+	0.877443i
$8$	24.4137			1.07894
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	6.21337	+	10.7619i	0.196484	+	0.340320i
$11$	13.0299	+	22.5684i	0.357151	+	0.618603i	0.987484	−	0.157722i	$-0.0504150\pi$
$11$	13.0299	+	22.5684i	0.357151	+	0.618603i	−0.630333	+	0.776325i	$0.717082\pi$
$12$	−2.73456	+	4.73639i	−0.0657832	+	0.113940i
$13$	3.20425			0.0683614			0.0341807	−	0.999416i	$-0.489118\pi$
$13$	3.20425			0.0683614			0.0341807	+	0.999416i	$0.489118\pi$
$14$	23.9375	+	39.3153i	0.456968	+	0.750533i
$15$	−15.0000			−0.258199
$16$	23.0461	−	39.9170i	0.360096	−	0.623704i
$17$	9.01624	+	15.6166i	0.128633	+	0.222799i	0.923147	−	0.384447i	$-0.125608\pi$
$17$	9.01624	+	15.6166i	0.128633	+	0.222799i	−0.794514	+	0.607245i	$0.792274\pi$
$18$	11.1841	+	19.3714i	0.146451	+	0.253660i
$19$	17.1199	−	29.6526i	0.206715	−	0.358041i	−0.743963	−	0.668221i	$-0.767056\pi$
$19$	17.1199	−	29.6526i	0.206715	−	0.358041i	0.950678	+	0.310180i	$0.100389\pi$
$20$	−9.11519			−0.101911
$21$	−55.5457	+	1.29492i	−0.577193	+	0.0134559i
$22$	64.7676			0.627659
$23$	49.5912	−	85.8945i	0.449586	−	0.778706i	−0.548773	−	0.835972i	$-0.684905\pi$
$23$	49.5912	−	85.8945i	0.449586	−	0.778706i	0.998359	+	0.0572653i	$0.0182381\pi$
$24$	36.6205	+	63.4286i	0.311464	+	0.539471i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	3.98184	−	6.89675i	0.0300347	−	0.0520217i
$27$	−27.0000			−0.192450
$28$	−33.7540	+	0.786896i	−0.227818	+	0.00531105i
$29$	212.096			1.35811			0.679055	−	0.734088i	$-0.262390\pi$
$29$	212.096			1.35811			0.679055	+	0.734088i	$0.262390\pi$
$30$	−18.6401	+	32.2856i	−0.113440	+	0.196484i
$31$	−146.585	−	253.893i	−0.849274	−	1.47099i	−0.881857	−	0.471516i	$-0.843707\pi$
$31$	−146.585	−	253.893i	−0.849274	−	1.47099i	0.0325838	−	0.999469i	$-0.489626\pi$
$32$	40.3771	+	69.9352i	0.223054	+	0.386341i
$33$	−39.0896	+	67.7052i	−0.206201	+	0.357151i
$34$	44.8170			0.226060
$35$	−48.1571	−	79.0942i	−0.232573	−	0.381982i
$36$	−16.4073			−0.0759599
$37$	−10.3520	+	17.9301i	−0.0459960	+	0.0796674i	−0.888107	−	0.459637i	$-0.847979\pi$
$37$	−10.3520	+	17.9301i	−0.0459960	+	0.0796674i	0.842111	+	0.539304i	$0.181313\pi$
$38$	−42.5490	−	73.6971i	−0.181641	−	0.314612i
$39$	4.80637	+	8.32488i	0.0197342	+	0.0341807i
$40$	−61.0342	+	105.714i	−0.241259	+	0.417873i
$41$	−207.842			−0.791695			−0.395847	−	0.918316i	$-0.629549\pi$
$41$	−207.842			−0.791695			−0.395847	+	0.918316i	$0.629549\pi$
$42$	−66.2381	+	121.164i	−0.243351	+	0.445144i
$43$	5.96397			0.0211511			0.0105755	−	0.999944i	$-0.496634\pi$
$43$	5.96397			0.0211511			0.0105755	+	0.999944i	$0.496634\pi$
$44$	−23.7540	+	41.1431i	−0.0813874	+	0.140967i
$45$	−22.5000	−	38.9711i	−0.0745356	−	0.129099i
$46$	−123.252	−	213.478i	−0.395053	−	0.684252i
$47$	−200.949	+	348.055i	−0.623649	+	1.08019i	0.365152	+	0.930948i	$0.381017\pi$
$47$	−200.949	+	348.055i	−0.623649	+	1.08019i	−0.988801	+	0.149243i	$0.952316\pi$
$48$	138.277			0.415803
$49$	−185.156	−	288.732i	−0.539814	−	0.841785i
$50$	−62.1337			−0.175741
$51$	−27.0487	+	46.8497i	−0.0742662	+	0.128633i
$52$	2.92073	+	5.05886i	0.00778909	+	0.0134911i
$53$	3.65770	+	6.33533i	0.00947970	+	0.0164193i	0.870726	−	0.491768i	$-0.163649\pi$
$53$	3.65770	+	6.33533i	0.00947970	+	0.0164193i	−0.861247	+	0.508187i	$0.830316\pi$
$54$	−33.5522	+	58.1141i	−0.0845533	+	0.146451i
$55$	−130.299			−0.319445
$56$	−216.886	+	396.734i	−0.517547	+	0.946711i
$57$	102.720			0.238694
$58$	263.566	−	456.510i	0.596688	−	1.03349i
$59$	−20.2045	−	34.9952i	−0.0445830	−	0.0772200i	0.842873	−	0.538113i	$-0.180863\pi$
$59$	−20.2045	−	34.9952i	−0.0445830	−	0.0772200i	−0.887456	+	0.460893i	$0.847529\pi$
$60$	−13.6728	−	23.6820i	−0.0294191	−	0.0509555i
$61$	179.242	−	310.456i	0.376223	−	0.651637i	−0.614287	−	0.789083i	$-0.710556\pi$
$61$	179.242	−	310.456i	0.376223	−	0.651637i	0.990509	+	0.137446i	$0.0438895\pi$
$62$	−728.631			−1.49252
$63$	−86.6828	−	142.370i	−0.173349	−	0.284712i
$64$	569.440			1.11219
$65$	−8.01062	+	13.8748i	−0.0152861	+	0.0264763i
$66$	97.1514	+	168.271i	0.181190	+	0.313830i
$67$	−293.731	−	508.757i	−0.535597	−	0.927681i	−0.999134	−	0.0416035i	$-0.986753\pi$
$67$	−293.731	−	508.757i	−0.535597	−	0.927681i	0.463537	−	0.886077i	$-0.346580\pi$
$68$	−16.4369	+	28.4696i	−0.0293128	+	0.0507713i
$69$	297.547			0.519138
$70$	−230.084	+	5.36388i	−0.392862	+	0.00915866i
$71$	803.405			1.34291			0.671455	−	0.741045i	$-0.265670\pi$
$71$	803.405			1.34291			0.671455	+	0.741045i	$0.265670\pi$
$72$	−109.862	+	190.286i	−0.179824	+	0.311464i
$73$	328.025	+	568.157i	0.525924	+	0.910928i	0.999544	+	0.0301981i	$0.00961381\pi$
$73$	328.025	+	568.157i	0.525924	+	0.910928i	−0.473620	+	0.880729i	$0.657053\pi$
$74$	25.7282	+	44.5626i	0.0404168	+	0.0700040i
$75$	37.5000	−	64.9519i	0.0577350	−	0.100000i
$76$	62.4206			0.0942123
$77$	−482.502	+	11.2484i	−0.714107	+	0.0166478i
$78$	23.8910			0.0346811
$79$	637.780	−	1104.67i	0.908302	−	1.57323i	0.0918807	−	0.995770i	$-0.470712\pi$
$79$	637.780	−	1104.67i	0.908302	−	1.57323i	0.816422	−	0.577456i	$-0.195955\pi$
$80$	115.231	+	199.585i	0.161040	+	0.278929i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−258.280	+	447.354i	−0.347832	+	0.602464i
$83$	244.647			0.323537			0.161768	−	0.986829i	$-0.448280\pi$
$83$	244.647			0.323537			0.161768	+	0.986829i	$0.448280\pi$
$84$	−52.6754	−	86.5150i	−0.0684209	−	0.112376i
$85$	−90.1624			−0.115053
$86$	7.41127	−	12.8367i	0.00929277	−	0.0160955i
$87$	318.144	+	551.041i	0.392053	+	0.679055i
$88$	318.107	+	550.978i	0.385345	+	0.667437i
$89$	705.542	−	1222.03i	0.840307	−	1.45545i	−0.0493291	−	0.998783i	$-0.515708\pi$
$89$	705.542	−	1222.03i	0.840307	−	1.45545i	0.889636	−	0.456671i	$-0.150958\pi$
$90$	−111.841			−0.130989
$91$	−28.4659	+	52.0706i	−0.0327916	+	0.0599833i
$92$	180.813			0.204903
$93$	439.756	−	761.679i	0.490328	−	0.849274i
$94$	499.429	+	865.037i	0.548002	+	0.949168i
$95$	85.5997	+	148.263i	0.0924458	+	0.160121i
$96$	−121.131	+	209.805i	−0.128780	+	0.223054i
$97$	−952.212			−0.996727			−0.498363	−	0.866968i	$-0.666065\pi$
$97$	−952.212			−0.996727			−0.498363	+	0.866968i	$0.666065\pi$
$98$	−851.549	+	39.7254i	−0.877749	+	0.0409476i
$99$	−234.538			−0.238100
$100$	22.7880	−	39.4699i	0.0227880	−	0.0394699i
$101$	720.732	+	1248.35i	0.710055	+	1.22985i	0.964836	+	0.262852i	$0.0846633\pi$
$101$	720.732	+	1248.35i	0.710055	+	1.22985i	−0.254781	+	0.966999i	$0.582003\pi$
$102$	67.2255	+	116.438i	0.0652580	+	0.113030i
$103$	−569.993	+	987.257i	−0.545273	+	0.944440i	0.453317	+	0.891349i	$0.350241\pi$
$103$	−569.993	+	987.257i	−0.545273	+	0.944440i	−0.998590	+	0.0530906i	$0.983093\pi$
$104$	78.2275			0.0737581
$105$	133.257	−	243.757i	0.123853	−	0.226555i
$106$	18.1813			0.0166597
$107$	−346.702	+	600.505i	−0.313242	+	0.542552i	−0.979062	−	0.203561i	$-0.934749\pi$
$107$	−346.702	+	600.505i	−0.313242	+	0.542552i	0.665820	+	0.746113i	$0.268082\pi$
$108$	−24.6110	−	42.6275i	−0.0219277	−	0.0379800i
$109$	570.059	+	987.371i	0.500933	+	0.867642i	0.999999	+	0.00107792i	$0.000343113\pi$
$109$	570.059	+	987.371i	0.500933	+	0.867642i	−0.499066	+	0.866564i	$0.666324\pi$
$110$	−161.919	+	280.452i	−0.140349	+	0.243091i
$111$	−62.1117			−0.0531116
$112$	443.934	+	729.126i	0.374534	+	0.615142i
$113$	1154.64			0.961237			0.480618	−	0.876930i	$-0.340412\pi$
$113$	1154.64			0.961237			0.480618	+	0.876930i	$0.340412\pi$
$114$	127.647	−	221.091i	0.104871	−	0.181641i
$115$	247.956	+	429.473i	0.201061	+	0.348248i
$116$	193.329	+	334.856i	0.154743	+	0.268022i
$117$	−14.4191	+	24.9746i	−0.0113936	+	0.0197342i
$118$	−100.430			−0.0783505
$119$	−333.875	+	7.78353i	−0.257196	+	0.00599593i
$120$	−366.205			−0.278582
$121$	325.945	−	564.552i	0.244887	−	0.424157i
$122$	−445.479	−	771.592i	−0.330588	−	0.572595i
$123$	−311.763	−	539.990i	−0.228543	−	0.395847i
$124$	267.230	−	462.857i	0.193532	−	0.335208i
$125$	125.000			0.0894427
$126$	−414.151	+	9.65498i	−0.292822	+	0.00682646i
$127$	−1453.32			−1.01544			−0.507722	−	0.861521i	$-0.669512\pi$
$127$	−1453.32			−1.01544			−0.507722	+	0.861521i	$0.669512\pi$
$128$	384.612	−	666.168i	0.265588	−	0.460012i
$129$	8.94595	+	15.4948i	0.00610579	+	0.0105755i
$130$	19.9092	+	34.4837i	0.0134319	+	0.0232648i
$131$	769.788	−	1333.31i	0.513410	−	0.889252i	−0.486469	−	0.873698i	$-0.661715\pi$
$131$	769.788	−	1333.31i	0.513410	−	0.889252i	0.999879	−	0.0155543i	$-0.00495129\pi$
$132$	−142.524			−0.0939781
$133$	329.779	+	541.635i	0.215003	+	0.353126i
$134$	−1460.05			−0.941262
$135$	67.5000	−	116.913i	0.0430331	−	0.0745356i
$136$	220.120	+	381.258i	0.138787	+	0.240387i
$137$	−1457.77	−	2524.93i	−0.909093	−	1.57460i	−0.815327	−	0.579001i	$-0.803443\pi$
$137$	−1457.77	−	2524.93i	−0.909093	−	1.57460i	−0.0937658	−	0.995594i	$-0.529891\pi$
$138$	369.755	−	640.434i	0.228084	−	0.395053i
$139$	−2338.76			−1.42713			−0.713565	−	0.700589i	$-0.752920\pi$
$139$	−2338.76			−1.42713			−0.713565	+	0.700589i	$0.752920\pi$
$140$	80.9775	−	148.126i	0.0488847	−	0.0894211i
$141$	−1205.70			−0.720127
$142$	998.371	−	1729.23i	0.590010	−	1.02193i
$143$	41.7510	+	72.3148i	0.0244153	+	0.0422886i
$144$	207.415	+	359.253i	0.120032	+	0.207901i
$145$	−530.239	+	918.401i	−0.303683	+	0.525994i
$146$	1630.52			0.924263
$147$	472.414	−	914.148i	0.265061	−	0.512909i
$148$	−37.7440			−0.0209631
$149$	246.088	−	426.237i	0.135304	−	0.234354i	−0.790409	−	0.612579i	$-0.790132\pi$
$149$	246.088	−	426.237i	0.135304	−	0.234354i	0.925714	+	0.378225i	$0.123466\pi$
$150$	−93.2006	−	161.428i	−0.0507320	−	0.0878704i
$151$	−540.975	−	936.996i	−0.291549	−	0.504978i	0.682627	−	0.730767i	$-0.260837\pi$
$151$	−540.975	−	936.996i	−0.291549	−	0.504978i	−0.974176	+	0.225789i	$0.927504\pi$
$152$	417.961	−	723.930i	0.223034	−	0.386306i
$153$	−162.292			−0.0857552
$154$	−575.383	+	1052.50i	−0.301076	+	0.550735i
$155$	1465.85			0.759613
$156$	−8.76220	+	15.1766i	−0.00449703	+	0.00778909i
$157$	1445.65	+	2503.95i	0.734877	+	1.27284i	0.954777	+	0.297322i	$0.0960936\pi$
$157$	1445.65	+	2503.95i	0.734877	+	1.27284i	−0.219900	+	0.975522i	$0.570573\pi$
$158$	−1585.11	−	2745.49i	−0.798129	−	1.38240i
$159$	−10.9731	+	19.0060i	−0.00547311	+	0.00947970i
$160$	−403.771			−0.199506
$161$	955.268	+	1568.95i	0.467613	+	0.768017i
$162$	−201.313			−0.0976337
$163$	−1262.53	+	2186.76i	−0.606680	+	1.05080i	0.385104	+	0.922873i	$0.374166\pi$
$163$	−1262.53	+	2186.76i	−0.606680	+	1.05080i	−0.991784	+	0.127927i	$0.959168\pi$
$164$	−189.452	−	328.140i	−0.0902056	−	0.156241i
$165$	−195.448	−	338.526i	−0.0922159	−	0.159723i
$166$	304.017	−	526.573i	0.142146	−	0.246205i
$167$	−2891.98			−1.34005			−0.670025	−	0.742338i	$-0.733717\pi$
$167$	−2891.98			−1.34005			−0.670025	+	0.742338i	$0.733717\pi$
$168$	−1356.07	+	31.6138i	−0.622759	+	0.0145182i
$169$	−2186.73			−0.995327
$170$	−112.042	+	194.063i	−0.0505486	+	0.0875528i
$171$	154.080	+	266.874i	0.0689050	+	0.119347i
$172$	5.43627	+	9.41589i	0.00240995	+	0.00417416i
$173$	1452.47	−	2515.75i	0.638320	−	1.10560i	−0.347481	−	0.937687i	$-0.612963\pi$
$173$	1452.47	−	2515.75i	0.638320	−	1.10560i	0.985801	−	0.167916i	$-0.0537037\pi$
$174$	1581.40			0.688996
$175$	462.881	−	10.7910i	0.199946	−	0.00466127i
$176$	1201.15			0.514433
$177$	60.6134	−	104.985i	0.0257400	−	0.0445830i
$178$	−1753.52	−	3037.18i	−0.738380	−	1.27891i
$179$	−11.5520	−	20.0087i	−0.00482369	−	0.00835487i	0.863603	−	0.504172i	$-0.168202\pi$
$179$	−11.5520	−	20.0087i	−0.00482369	−	0.00835487i	−0.868427	+	0.495817i	$0.834869\pi$
$180$	41.0184	−	71.0459i	0.0169852	−	0.0294191i
$181$	−3024.01			−1.24184			−0.620919	−	0.783875i	$-0.713240\pi$
$181$	−3024.01			−1.24184			−0.620919	+	0.783875i	$0.713240\pi$
$182$	76.7016	+	125.976i	0.0312390	+	0.0513075i
$183$	1075.45			0.434424
$184$	1210.70	−	2097.00i	0.485078	−	0.840179i
$185$	−51.7598	−	89.6506i	−0.0205700	−	0.0356283i
$186$	−1092.95	−	1893.04i	−0.430853	−	0.746260i
$187$	−234.961	+	406.964i	−0.0918826	+	0.159145i
$188$	−732.677			−0.284234
$189$	239.863	−	438.763i	0.0923145	−	0.168864i
$190$	425.490			0.162465
$191$	−1948.45	+	3374.81i	−0.738140	+	1.27850i	0.215192	+	0.976572i	$0.430962\pi$
$191$	−1948.45	+	3374.81i	−0.738140	+	1.27850i	−0.953332	+	0.301924i	$0.902371\pi$
$192$	854.160	+	1479.45i	0.321061	+	0.556094i
$193$	2304.64	+	3991.76i	0.859543	+	1.48877i	0.872366	+	0.488854i	$0.162585\pi$
$193$	2304.64	+	3991.76i	0.859543	+	1.48877i	−0.0128229	+	0.999918i	$0.504082\pi$
$194$	−1183.29	+	2049.52i	−0.437914	+	0.758489i
$195$	−48.0637			−0.0176508
$196$	287.076	−	555.509i	0.104620	−	0.202445i
$197$	3119.11			1.12806			0.564029	−	0.825755i	$-0.309251\pi$
$197$	3119.11			1.12806			0.564029	+	0.825755i	$0.309251\pi$
$198$	−291.454	+	504.814i	−0.104610	+	0.181190i
$199$	2074.47	+	3593.08i	0.738970	+	1.27993i	0.952960	+	0.303098i	$0.0980208\pi$
$199$	2074.47	+	3593.08i	0.738970	+	1.27993i	−0.213990	+	0.976836i	$0.568646\pi$
$200$	−305.171	−	528.572i	−0.107894	−	0.186878i
$201$	881.194	−	1526.27i	0.309227	−	0.535597i
$202$	3582.54			1.24786
$203$	−1884.22	+	3446.66i	−0.651458	+	1.19166i
$204$	−98.6216			−0.0338475
$205$	519.605	−	899.983i	0.177028	−	0.306622i
$206$	1416.63	+	2453.68i	0.479133	+	0.829883i
$207$	446.321	+	773.051i	0.149862	+	0.259569i
$208$	73.8455	−	127.904i	0.0246166	−	0.0426373i
$209$	892.283			0.295314
$210$	−359.062	−	589.730i	−0.117989	−	0.193787i
$211$	−3835.74			−1.25148			−0.625742	−	0.780030i	$-0.715204\pi$
$211$	−3835.74			−1.25148			−0.625742	+	0.780030i	$0.715204\pi$
$212$	−6.66813	+	11.5495i	−0.00216023	+	0.00374163i
$213$	1205.11	+	2087.31i	0.387665	+	0.671455i
$214$	861.675	+	1492.47i	0.275247	+	0.476742i
$215$	−14.9099	+	25.8247i	−0.00472953	+	0.00819178i
$216$	−659.169			−0.207643
$217$	5428.12	−	126.544i	1.69809	−	0.0395870i
$218$	2833.59			0.880344
$219$	−984.076	+	1704.47i	−0.303643	+	0.525924i
$220$	−118.770	−	205.715i	−0.0363975	−	0.0630424i
$221$	28.8903	+	50.0394i	0.00879353	+	0.0152308i
$222$	−77.1847	+	133.688i	−0.0233347	+	0.0404168i
$223$	−750.330			−0.225318			−0.112659	−	0.993634i	$-0.535937\pi$
$223$	−750.330			−0.225318			−0.112659	+	0.993634i	$0.535937\pi$
$224$	−1495.18	+	34.8567i	−0.445987	+	0.0103972i
$225$	225.000			0.0666667
$226$	1434.85	−	2485.23i	0.422321	−	0.731482i
$227$	314.420	+	544.591i	0.0919329	+	0.159232i	0.908324	−	0.418266i	$-0.137362\pi$
$227$	314.420	+	544.591i	0.0919329	+	0.159232i	−0.816392	+	0.577499i	$0.804029\pi$
$228$	93.6309	+	162.174i	0.0271968	+	0.0471062i
$229$	1223.66	−	2119.45i	0.353109	−	0.611603i	−0.633683	−	0.773593i	$-0.718458\pi$
$229$	1223.66	−	2119.45i	0.353109	−	0.611603i	0.986792	+	0.161989i	$0.0517910\pi$
$230$	1232.52			0.353346
$231$	−752.978	−	1236.71i	−0.214469	−	0.352248i
$232$	5178.04			1.46532
$233$	−1580.58	+	2737.65i	−0.444409	+	0.769739i	−0.998011	−	0.0630423i	$-0.979920\pi$
$233$	−1580.58	+	2737.65i	−0.444409	+	0.769739i	0.553602	+	0.832782i	$0.313253\pi$
$234$	35.8365	+	62.0707i	0.0100116	+	0.0173406i
$235$	−1004.75	−	1740.27i	−0.278904	−	0.483076i
$236$	36.8335	−	63.7975i	0.0101596	−	0.0175969i
$237$	3826.68			1.04882
$238$	−398.145	+	728.298i	−0.108437	+	0.198355i
$239$	−6018.30			−1.62884			−0.814418	−	0.580279i	$-0.802944\pi$
$239$	−6018.30			−1.62884			−0.814418	+	0.580279i	$0.802944\pi$
$240$	−345.692	+	598.756i	−0.0929763	+	0.161040i
$241$	−2859.22	−	4952.31i	−0.764225	−	1.32368i	−0.940655	−	0.339364i	$-0.889788\pi$
$241$	−2859.22	−	4952.31i	−0.764225	−	1.32368i	0.176430	−	0.984313i	$-0.443545\pi$
$242$	−810.086	−	1403.11i	−0.215183	−	0.372708i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	653.530			0.171467
$245$	1713.14	−	79.9191i	0.446728	−	0.0208402i
$246$	−1549.68			−0.401642
$247$	54.8566	−	95.0143i	0.0141313	−	0.0244762i
$248$	−3578.69	−	6198.46i	−0.916317	−	1.58711i
$249$	366.971	+	635.612i	0.0933970	+	0.161768i
$250$	155.334	−	269.047i	0.0392968	−	0.0680641i
$251$	1236.06			0.310834			0.155417	−	0.987849i	$-0.450328\pi$
$251$	1236.06			0.310834			0.155417	+	0.987849i	$0.450328\pi$
$252$	145.760	−	266.627i	0.0364365	−	0.0666505i
$253$	2584.67			0.642280
$254$	−1806.01	+	3128.09i	−0.446137	+	0.772733i
$255$	−135.244	−	234.249i	−0.0332129	−	0.0575264i
$256$	1321.86	+	2289.54i	0.322721	+	0.558969i
$257$	549.467	−	951.705i	0.133365	−	0.230995i	−0.791607	−	0.611031i	$-0.790755\pi$
$257$	549.467	−	951.705i	0.133365	−	0.230995i	0.924972	+	0.380036i	$0.124088\pi$
$258$	44.4676			0.0107304
$259$	−199.408	−	327.512i	−0.0478402	−	0.0785737i
$260$	−29.2073			−0.00696678
$261$	−954.431	+	1653.12i	−0.226352	+	0.392053i
$262$	−1913.19	−	3313.75i	−0.451135	−	0.781389i
$263$	3361.74	+	5822.70i	0.788189	+	1.36518i	0.927075	+	0.374875i	$0.122314\pi$
$263$	3361.74	+	5822.70i	0.788189	+	1.36518i	−0.138886	+	0.990308i	$0.544352\pi$
$264$	−954.322	+	1652.93i	−0.222479	+	0.385345i
$265$	−36.5770			−0.00847891
$266$	1575.61	−	36.7317i	0.363184	−	0.00846679i
$267$	4233.25			0.970302
$268$	535.483	−	927.484i	0.122052	−	0.211400i
$269$	−2570.07	−	4451.49i	−0.582527	−	1.00897i	−0.995179	−	0.0980772i	$-0.968731\pi$
$269$	−2570.07	−	4451.49i	−0.582527	−	1.00897i	0.412652	−	0.910889i	$-0.364603\pi$
$270$	−167.761	−	290.571i	−0.0378134	−	0.0654947i
$271$	−1457.50	+	2524.47i	−0.326705	+	0.565870i	−0.981856	−	0.189628i	$-0.939272\pi$
$271$	−1457.50	+	2524.47i	−0.326705	+	0.565870i	0.655151	+	0.755498i	$0.272605\pi$
$272$	831.157			0.185280
$273$	−177.982	+	4.14924i	−0.0394578	+	0.000919867i
$274$	−7246.14			−1.59765
$275$	325.747	−	564.210i	0.0714301	−	0.123721i
$276$	271.220	+	469.767i	0.0591505	+	0.102452i
$277$	−892.967	−	1546.66i	−0.193694	−	0.335488i	0.752778	−	0.658275i	$-0.228714\pi$
$277$	−892.967	−	1546.66i	−0.193694	−	0.335488i	−0.946472	+	0.322787i	$0.895380\pi$
$278$	−2906.32	+	5033.89i	−0.627012	+	1.08602i
$279$	2638.53			0.566182
$280$	−1175.69	−	1930.98i	−0.250932	−	0.412136i
$281$	1264.76			0.268503			0.134252	−	0.990947i	$-0.457137\pi$
$281$	1264.76			0.268503			0.134252	+	0.990947i	$0.457137\pi$
$282$	−1498.29	+	2595.11i	−0.316389	+	0.548002i
$283$	−4183.20	−	7245.52i	−0.878677	−	1.52191i	−0.852794	−	0.522247i	$-0.825094\pi$
$283$	−4183.20	−	7245.52i	−0.878677	−	1.52191i	−0.0258826	−	0.999665i	$-0.508240\pi$
$284$	732.319	+	1268.41i	0.153011	+	0.265023i
$285$	−256.799	+	444.789i	−0.0533736	+	0.0924458i
$286$	207.532			0.0429077
$287$	1846.43	−	3377.53i	0.379760	−	0.694667i
$288$	−726.787			−0.148703
$289$	2293.91	−	3973.18i	0.466907	−	0.808707i
$290$	1317.83	+	2282.55i	0.266847	+	0.462193i
$291$	−1428.32	−	2473.92i	−0.287730	−	0.498363i
$292$	−598.003	+	1035.77i	−0.119847	+	0.207582i
$293$	−1552.76			−0.309602			−0.154801	−	0.987946i	$-0.549474\pi$
$293$	−1552.76			−0.309602			−0.154801	+	0.987946i	$0.549474\pi$
$294$	−1380.53	−	2152.80i	−0.273858	−	0.427054i
$295$	202.045			0.0398762
$296$	−252.729	+	437.740i	−0.0496270	+	0.0859565i
$297$	−351.807	−	609.347i	−0.0687337	−	0.119050i
$298$	−611.615	−	1059.35i	−0.118892	−	0.205927i
$299$	158.903	−	275.227i	0.0307344	−	0.0532335i
$300$	136.728			0.0263133
$301$	−52.9827	+	96.9173i	−0.0101458	+	0.0185589i
$302$	−2689.02			−0.512370
$303$	−2162.20	+	3745.04i	−0.409950	+	0.710055i
$304$	−789.096	−	1366.76i	−0.148874	−	0.257858i
$305$	896.210	+	1552.28i	0.168252	+	0.291421i
$306$	−201.676	+	349.314i	−0.0376767	+	0.0652580i
$307$	−6847.06			−1.27291			−0.636453	−	0.771315i	$-0.719599\pi$
$307$	−6847.06			−1.27291			−0.636453	+	0.771315i	$0.719599\pi$
$308$	−457.569	−	751.520i	−0.0846507	−	0.139032i
$309$	−3419.96			−0.629627
$310$	1821.58	−	3155.06i	0.333738	−	0.578050i
$311$	−1175.13	−	2035.38i	−0.214262	−	0.371113i	0.738782	−	0.673944i	$-0.235401\pi$
$311$	−1175.13	−	2035.38i	−0.214262	−	0.371113i	−0.953044	+	0.302832i	$0.902068\pi$
$312$	117.341	+	203.241i	0.0212921	+	0.0368790i
$313$	2045.92	−	3543.64i	0.369465	−	0.639931i	−0.620017	−	0.784588i	$-0.712874\pi$
$313$	2045.92	−	3543.64i	0.369465	−	0.639931i	0.989482	+	0.144657i	$0.0462078\pi$
$314$	7185.91			1.29148
$315$	833.185	−	19.4238i	0.149031	−	0.00347431i
$316$	2325.40			0.413967
$317$	496.845	−	860.562i	0.0880304	−	0.152473i	−0.818648	−	0.574295i	$-0.805276\pi$
$317$	496.845	−	860.562i	0.0880304	−	0.152473i	0.906678	+	0.421822i	$0.138609\pi$
$318$	27.2720	+	47.2365i	0.00480924	+	0.00832985i
$319$	2763.58	+	4786.66i	0.485050	+	0.840131i
$320$	−1423.60	+	2465.75i	−0.248693	+	0.430748i
$321$	−2080.21			−0.361701
$322$	4564.06	−	106.401i	0.789892	−	0.0184145i
$323$	617.430			0.106361
$324$	73.8330	−	127.883i	0.0126600	−	0.0219277i
$325$	−40.0531	−	69.3740i	−0.00683614	−	0.0118405i
$326$	3137.82	+	5434.87i	0.533092	+	0.923342i
$327$	−1710.18	+	2962.11i	−0.289214	+	0.500933i
$328$	−5074.19			−0.854193
$329$	−3870.86	−	6357.57i	−0.648654	−	1.06536i
$330$	−971.514			−0.162061
$331$	−1530.07	+	2650.16i	−0.254079	+	0.440078i	−0.964645	−	0.263553i	$-0.915106\pi$
$331$	−1530.07	+	2650.16i	−0.254079	+	0.440078i	0.710566	+	0.703631i	$0.248439\pi$
$332$	223.001	+	386.249i	0.0368637	+	0.0638498i
$333$	−93.1676	−	161.371i	−0.0153320	−	0.0265558i
$334$	−3593.80	+	6224.64i	−0.588754	+	1.01975i
$335$	2937.31			0.479052
$336$	−1228.42	+	2247.06i	−0.199452	+	0.364843i
$337$	−2761.72			−0.446411			−0.223205	−	0.974771i	$-0.571652\pi$
$337$	−2761.72			−0.446411			−0.223205	+	0.974771i	$0.571652\pi$
$338$	−2717.40	+	4706.67i	−0.437299	+	0.757423i
$339$	1731.97	+	2999.85i	0.277485	+	0.480618i
$340$	−82.1847	−	142.348i	−0.0131091	−	0.0227056i
$341$	3819.98	−	6616.39i	0.606637	−	1.05073i
$342$	765.883			0.121094
$343$	6336.92	−	443.836i	0.997556	−	0.0698684i
$344$	145.602			0.0228208
$345$	−743.868	+	1288.42i	−0.116083	+	0.201061i
$346$	−3609.90	−	6252.53i	−0.560894	−	0.971497i
$347$	−6265.03	−	10851.4i	−0.969235	−	1.67876i	−0.697779	−	0.716313i	$-0.745828\pi$
$347$	−6265.03	−	10851.4i	−0.969235	−	1.67876i	−0.271456	−	0.962451i	$-0.587505\pi$
$348$	−579.988	+	1004.57i	−0.0893408	+	0.154743i
$349$	3744.12			0.574263			0.287132	−	0.957891i	$-0.407298\pi$
$349$	3744.12			0.574263			0.287132	+	0.957891i	$0.407298\pi$
$350$	551.984	−	1009.70i	0.0842994	−	0.154203i
$351$	−86.5147			−0.0131562
$352$	−1052.22	+	1822.49i	−0.159328	+	0.275964i
$353$	1122.02	+	1943.39i	0.169175	+	0.293020i	0.938130	−	0.346283i	$-0.112556\pi$
$353$	1122.02	+	1943.39i	0.169175	+	0.293020i	−0.768955	+	0.639303i	$0.779223\pi$
$354$	−150.645	−	260.926i	−0.0226178	−	0.0391752i
$355$	−2008.51	+	3478.84i	−0.300284	+	0.520107i
$356$	2572.46			0.382978
$357$	−521.035	−	855.758i	−0.0772440	−	0.126867i
$358$	−57.4217			−0.00847718
$359$	470.588	−	815.083i	0.0691830	−	0.119828i	−0.829359	−	0.558716i	$-0.811294\pi$
$359$	470.588	−	815.083i	0.0691830	−	0.119828i	0.898542	+	0.438888i	$0.144627\pi$
$360$	−549.308	−	951.429i	−0.0804196	−	0.139291i
$361$	2843.31	+	4924.77i	0.414538	+	0.718001i
$362$	−3757.86	+	6508.80i	−0.545604	+	0.945013i
$363$	1955.67			0.282771
$364$	−108.156	+	2.52141i	−0.0155740	+	0.000363071i
$365$	−3280.25			−0.470401
$366$	1336.44	−	2314.78i	0.190865	−	0.330588i
$367$	−242.112	−	419.350i	−0.0344363	−	0.0596455i	0.848294	−	0.529526i	$-0.177630\pi$
$367$	−242.112	−	419.350i	−0.0344363	−	0.0596455i	−0.882730	+	0.469881i	$0.844297\pi$
$368$	−2285.77	−	3959.07i	−0.323788	−	0.560817i
$369$	935.289	−	1619.97i	0.131949	−	0.228543i
$370$	−257.282			−0.0361499
$371$	−135.446	+	3.15762i	−0.0189543	+	0.000441875i
$372$	1603.38			0.223472
$373$	5211.12	−	9025.93i	0.723383	−	1.25294i	−0.236253	−	0.971691i	$-0.575920\pi$
$373$	5211.12	−	9025.93i	0.723383	−	1.25294i	0.959636	−	0.281244i	$-0.0907471\pi$
$374$	583.960	+	1011.45i	0.0807376	+	0.139842i
$375$	187.500	+	324.760i	0.0258199	+	0.0447214i
$376$	−4905.91	+	8497.29i	−0.672881	+	1.16546i
$377$	679.607			0.0928423
$378$	−646.311	−	1061.51i	−0.0879436	−	0.144440i
$379$	−6388.05			−0.865784			−0.432892	−	0.901446i	$-0.642507\pi$
$379$	−6388.05			−0.865784			−0.432892	+	0.901446i	$0.642507\pi$
$380$	−156.052	+	270.289i	−0.0210665	+	0.0364883i
$381$	−2179.98	−	3775.84i	−0.293134	−	0.507722i
$382$	4842.57	+	8387.58i	0.648606	+	1.12342i
$383$	2491.40	−	4315.22i	0.332387	−	0.575712i	−0.650592	−	0.759427i	$-0.725479\pi$
$383$	2491.40	−	4315.22i	0.332387	−	0.575712i	0.982979	+	0.183716i	$0.0588125\pi$
$384$	2307.67			0.306674
$385$	1157.55	−	2117.42i	0.153232	−	0.280295i
$386$	11455.7			1.51057
$387$	−26.8379	+	46.4845i	−0.00352518	+	0.00610579i
$388$	−867.960	−	1503.35i	−0.113567	−	0.196704i
$389$	3374.32	+	5844.50i	0.439807	+	0.761769i	0.997674	−	0.0681618i	$-0.0217134\pi$
$389$	3374.32	+	5844.50i	0.439807	+	0.761769i	−0.557867	+	0.829930i	$0.688380\pi$
$390$	−59.7276	+	103.451i	−0.00775493	+	0.0134319i
$391$	1788.50			0.231326
$392$	−4520.34	−	7049.01i	−0.582428	−	0.908237i
$393$	4618.73			0.592835
$394$	3876.04	−	6713.49i	0.495614	−	0.858429i
$395$	3188.90	+	5523.34i	0.406205	+	0.703568i
$396$	−213.786	−	370.288i	−0.0271291	−	0.0469890i
$397$	−1991.14	+	3448.76i	−0.251720	+	0.435991i	−0.963999	−	0.265904i	$-0.914329\pi$
$397$	−1991.14	+	3448.76i	−0.251720	+	0.435991i	0.712280	+	0.701896i	$0.247663\pi$
$398$	10311.5			1.29867
$399$	−912.541	+	1669.24i	−0.114497	+	0.209440i
$400$	−1152.31			−0.144038
$401$	−3284.14	+	5688.29i	−0.408982	+	0.708378i	−0.994776	−	0.102082i	$-0.967450\pi$
$401$	−3284.14	+	5688.29i	−0.408982	+	0.708378i	0.585794	+	0.810460i	$0.300783\pi$
$402$	−2190.07	−	3793.32i	−0.271719	−	0.470631i
$403$	−469.695	−	813.536i	−0.0580576	−	0.100559i
$404$	−1313.92	+	2275.78i	−0.161807	+	0.280258i
$405$	405.000			0.0496904
$406$	5077.03	+	8338.61i	0.620613	+	1.01931i
$407$	−539.539			−0.0657100
$408$	−660.359	+	1143.77i	−0.0801290	+	0.138787i
$409$	2478.39	+	4292.69i	0.299629	+	0.518973i	0.976051	−	0.217541i	$-0.0698037\pi$
$409$	2478.39	+	4292.69i	0.299629	+	0.518973i	−0.676422	+	0.736514i	$0.736470\pi$
$410$	−1291.40	−	2236.77i	−0.155555	−	0.269430i
$411$	4373.31	−	7574.80i	0.524865	−	0.909093i
$412$	−2078.24			−0.248513
$413$	748.180	−	17.4421i	0.0891418	−	0.00207813i
$414$	2218.53			0.263369
$415$	−611.618	+	1059.35i	−0.0723450	+	0.125305i
$416$	129.378	+	224.090i	0.0152483	+	0.0264108i
$417$	−3508.14	−	6076.27i	−0.411977	−	0.713565i
$418$	1108.82	−	1920.53i	0.129747	−	0.224728i
$419$	5778.60			0.673754			0.336877	−	0.941549i	$-0.390629\pi$
$419$	5778.60			0.673754			0.336877	+	0.941549i	$0.390629\pi$
$420$	506.309	−	11.8034i	0.0588223	−	0.00137131i
$421$	7463.23			0.863980			0.431990	−	0.901878i	$-0.357812\pi$
$421$	7463.23			0.863980			0.431990	+	0.901878i	$0.357812\pi$
$422$	−4766.58	+	8255.96i	−0.549842	+	0.952355i
$423$	−1808.54	−	3132.49i	−0.207883	−	0.360064i
$424$	89.2980	+	154.669i	0.0102281	+	0.0177155i
$425$	225.406	−	390.414i	0.0257266	−	0.0445597i
$426$	5990.22			0.681285
$427$	3452.71	+	5670.80i	0.391308	+	0.642691i
$428$	−1264.10			−0.142763
$429$	−125.253	+	216.944i	−0.0140962	+	0.0244153i
$430$	37.0564	+	64.1835i	0.00415585	+	0.00719815i
$431$	−1520.79	−	2634.09i	−0.169963	−	0.294384i	0.768444	−	0.639917i	$-0.221031\pi$
$431$	−1520.79	−	2634.09i	−0.169963	−	0.294384i	−0.938406	+	0.345533i	$0.887698\pi$
$432$	−622.245	+	1077.76i	−0.0693004	+	0.120032i
$433$	4047.48			0.449214			0.224607	−	0.974449i	$-0.427890\pi$
$433$	4047.48			0.449214			0.224607	+	0.974449i	$0.427890\pi$
$434$	6473.01	−	11840.6i	0.715932	−	1.30960i
$435$	−3181.44			−0.350662
$436$	−1039.24	+	1800.01i	−0.114153	+	0.197718i
$437$	−1698.00	−	2941.02i	−0.185872	−	0.321941i
$438$	2445.77	+	4236.20i	0.266812	+	0.462132i
$439$	1366.46	−	2366.77i	0.148559	−	0.257312i	−0.782136	−	0.623108i	$-0.785870\pi$
$439$	1366.46	−	2366.77i	0.148559	−	0.257312i	0.930695	+	0.365796i	$0.119203\pi$
$440$	−3181.07			−0.344663
$441$	3083.65	−	143.854i	0.332971	−	0.0155334i
$442$	143.605			0.0154538
$443$	−3199.52	+	5541.73i	−0.343146	+	0.594347i	−0.985015	−	0.172468i	$-0.944826\pi$
$443$	−3199.52	+	5541.73i	−0.343146	+	0.594347i	0.641869	+	0.766814i	$0.278159\pi$
$444$	−56.6160	−	98.0618i	−0.00605153	−	0.0104816i
$445$	3527.71	+	6110.17i	0.375797	+	0.650899i
$446$	−932.416	+	1614.99i	−0.0989937	+	0.171462i
$447$	1476.53			0.156236
$448$	−5058.79	+	9253.67i	−0.533495	+	0.975882i
$449$	−16489.7			−1.73318			−0.866588	−	0.499024i	$-0.833692\pi$
$449$	−16489.7			−1.73318			−0.866588	+	0.499024i	$0.833692\pi$
$450$	279.602	−	484.285i	0.0292901	−	0.0507320i
$451$	−2708.16	−	4690.67i	−0.282754	−	0.489745i
$452$	1052.48	+	1822.95i	0.109523	+	0.189700i
$453$	1622.92	−	2810.99i	0.168326	−	0.291549i
$454$	1562.89			0.161564
$455$	−154.307	−	253.437i	−0.0158990	−	0.0261128i
$456$	2507.77			0.257537
$457$	−7187.97	+	12449.9i	−0.735753	+	1.27436i	0.218639	+	0.975806i	$0.429838\pi$
$457$	−7187.97	+	12449.9i	−0.735753	+	1.27436i	−0.954392	+	0.298556i	$0.903495\pi$
$458$	−3041.23	−	5267.57i	−0.310278	−	0.537418i
$459$	−243.438	−	421.648i	−0.0247554	−	0.0428776i
$460$	−452.033	+	782.945i	−0.0458178	+	0.0793587i
$461$	1000.39			0.101069			0.0505346	−	0.998722i	$-0.483907\pi$
$461$	1000.39			0.101069			0.0505346	+	0.998722i	$0.483907\pi$
$462$	−3597.56	+	83.8688i	−0.362281	+	0.00844574i
$463$	−626.125			−0.0628477			−0.0314239	−	0.999506i	$-0.510004\pi$
$463$	−626.125			−0.0628477			−0.0314239	+	0.999506i	$0.510004\pi$
$464$	4887.98	−	8466.23i	0.489049	−	0.847058i
$465$	2198.78	+	3808.40i	0.219282	+	0.379807i
$466$	3928.30	+	6804.01i	0.390504	+	0.676373i
$467$	−459.520	+	795.912i	−0.0455333	+	0.0788659i	−0.887894	−	0.460048i	$-0.847832\pi$
$467$	−459.520	+	795.912i	−0.0455333	+	0.0788659i	0.842361	+	0.538914i	$0.181165\pi$
$468$	−52.5732			−0.00519273
$469$	10877.0	−	253.572i	1.07090	−	0.0249656i
$470$	−4994.29			−0.490148
$471$	−4336.96	+	7511.84i	−0.424282	+	0.734877i
$472$	−493.265	−	854.361i	−0.0481025	−	0.0833160i
$473$	77.7098	+	134.597i	0.00755412	+	0.0130841i
$474$	4755.32	−	8236.46i	0.460800	−	0.798129i
$475$	−855.997			−0.0826860
$476$	−316.622	−	520.027i	−0.0304882	−	0.0500743i
$477$	−65.8387			−0.00631980
$478$	−7478.80	+	12953.7i	−0.715632	+	1.23951i
$479$	7831.84	+	13565.1i	0.747068	+	1.29396i	0.949222	+	0.314606i	$0.101873\pi$
$479$	7831.84	+	13565.1i	0.747068	+	1.29396i	−0.202154	+	0.979354i	$0.564794\pi$
$480$	−605.656	−	1049.03i	−0.0575923	−	0.0997528i
$481$	−33.1702	+	57.4525i	−0.00314435	+	0.00544618i
$482$	−14212.3			−1.34305
$483$	−2643.35	+	4835.29i	−0.249020	+	0.455514i
$484$	1188.42			0.111610
$485$	2380.53	−	4123.20i	0.222875	−	0.386031i
$486$	−301.970	−	523.027i	−0.0281844	−	0.0488169i
$487$	−7220.23	−	12505.8i	−0.671827	−	1.16364i	−0.977385	−	0.211466i	$-0.932176\pi$
$487$	−7220.23	−	12505.8i	−0.671827	−	1.16364i	0.305558	−	0.952173i	$-0.401157\pi$
$488$	4375.95	−	7579.38i	0.405922	−	0.703078i
$489$	−7575.16			−0.700533
$490$	1956.86	−	3786.63i	0.180412	−	0.349107i
$491$	−19320.8			−1.77584			−0.887918	−	0.460001i	$-0.847849\pi$
$491$	−19320.8			−1.77584			−0.887918	+	0.460001i	$0.847849\pi$
$492$	568.356	−	984.421i	0.0520802	−	0.0902056i
$493$	1912.30	+	3312.21i	0.174698	+	0.302585i
$494$	−136.338	−	236.144i	−0.0124173	−	0.0215073i
$495$	586.345	−	1015.58i	0.0532409	−	0.0922159i
$496$	−13512.9			−1.22328
$497$	−7137.29	+	13055.7i	−0.644167	+	1.17833i
$498$	1824.10			0.164137
$499$	2266.59	−	3925.86i	0.203340	−	0.352195i	−0.746263	−	0.665652i	$-0.768154\pi$
$499$	2266.59	−	3925.86i	0.203340	−	0.352195i	0.949603	+	0.313456i	$0.101487\pi$
$500$	113.940	+	197.350i	0.0101911	+	0.0176515i
$501$	−4337.98	−	7513.60i	−0.386839	−	0.670025i
$502$	1536.02	−	2660.47i	0.136566	−	0.236539i
$503$	1296.32			0.114911			0.0574554	−	0.998348i	$-0.481701\pi$
$503$	1296.32			0.114911			0.0574554	+	0.998348i	$0.481701\pi$
$504$	−2116.25	−	3475.76i	−0.187034	−	0.307188i
$505$	−7207.32			−0.635092
$506$	3211.90	−	5563.18i	0.282187	−	0.488762i
$507$	−3280.10	−	5681.30i	−0.287326	−	0.497663i
$508$	−1324.73	−	2294.50i	−0.115700	−	0.200398i
$509$	3266.81	−	5658.28i	0.284477	−	0.492728i	−0.688005	−	0.725706i	$-0.741513\pi$
$509$	3266.81	−	5658.28i	0.284477	−	0.492728i	0.972482	+	0.232977i	$0.0748468\pi$
$510$	−672.255			−0.0583685
$511$	−12146.9	+	283.178i	−1.05156	+	0.0245148i
$512$	12724.4			1.09833
$513$	−462.239	+	800.621i	−0.0397823	+	0.0689050i
$514$	−1365.62	−	2365.32i	−0.117188	−	0.202976i
$515$	−2849.97	−	4936.28i	−0.243853	−	0.422366i
$516$	−16.3088	+	28.2477i	−0.00139139	+	0.00240995i
$517$	−10473.4			−0.890946
$518$	−952.728	+	22.2107i	−0.0808117	+	0.00188394i
$519$	8714.83			0.737068
$520$	−195.569	+	338.735i	−0.0164928	+	0.0285664i
$521$	−411.791	−	713.244i	−0.0346275	−	0.0599765i	0.848192	−	0.529688i	$-0.177691\pi$
$521$	−411.791	−	713.244i	−0.0346275	−	0.0599765i	−0.882820	+	0.469712i	$0.844358\pi$
$522$	2372.09	+	4108.59i	0.198896	+	0.344498i
$523$	8626.23	−	14941.1i	0.721221	−	1.24919i	−0.239289	−	0.970948i	$-0.576914\pi$
$523$	8626.23	−	14941.1i	0.721221	−	1.24919i	0.960511	−	0.278243i	$-0.0897522\pi$
$524$	2806.71			0.233991
$525$	722.357	+	1186.41i	0.0600500	+	0.0986272i
$526$	16710.2			1.38517
$527$	2643.29	−	4578.32i	0.218489	−	0.378434i
$528$	1801.73	+	3120.69i	0.148504	+	0.257217i
$529$	1164.92	+	2017.70i	0.0957443	+	0.165834i
$530$	−45.4534	+	78.7275i	−0.00372522	+	0.00645228i
$531$	363.680			0.0297220
$532$	−554.532	+	1014.36i	−0.0451918	+	0.0826660i
$533$	−665.978			−0.0541214
$534$	5260.55	−	9111.55i	0.426304	−	0.738380i
$535$	−1733.51	−	3002.53i	−0.140086	−	0.242637i
$536$	−7171.06	−	12420.6i	−0.577878	−	1.00091i
$537$	34.6561	−	60.0261i	0.00278496	−	0.00482369i
$538$	−12775.0			−1.02374
$539$	4103.66	−	7940.82i	0.327936	−	0.634574i
$540$	246.110			0.0196128
$541$	8572.43	−	14847.9i	0.681252	−	1.17996i	−0.293347	−	0.956006i	$-0.594769\pi$
$541$	8572.43	−	14847.9i	0.681252	−	1.17996i	0.974599	−	0.223957i	$-0.0718976\pi$
$542$	3622.41	+	6274.19i	0.287077	+	0.497232i
$543$	−4536.01	−	7856.60i	−0.358488	−	0.620919i
$544$	−728.099	+	1261.10i	−0.0573841	+	0.0993922i
$545$	−5700.59			−0.448048
$546$	−212.243	+	388.241i	−0.0166358	+	0.0304307i
$547$	−14217.3			−1.11131			−0.555656	−	0.831412i	$-0.687533\pi$
$547$	−14217.3			−1.11131			−0.555656	+	0.831412i	$0.687533\pi$
$548$	2657.57	−	4603.05i	0.207164	−	0.358818i
$549$	1613.18	+	2794.10i	0.125408	+	0.217212i
$550$	−809.595	−	1402.26i	−0.0627659	−	0.108714i
$551$	3631.07	−	6289.19i	0.280742	−	0.486259i
$552$	7264.23			0.560120
$553$	12285.5	+	20177.9i	0.944722	+	1.55163i
$554$	−4438.67			−0.340399
$555$	155.279	−	268.952i	0.0118761	−	0.0205700i
$556$	−2131.82	−	3692.43i	−0.162607	−	0.281643i
$557$	9695.91	+	16793.8i	0.737575	+	1.27752i	0.953584	+	0.301126i	$0.0973623\pi$
$557$	9695.91	+	16793.8i	0.737575	+	1.27752i	−0.216010	+	0.976391i	$0.569304\pi$
$558$	3278.84	−	5679.12i	0.248753	−	0.430853i
$559$	19.1100			0.00144592
$560$	−4267.04	+	99.4762i	−0.321992	+	0.00750649i
$561$	−1409.77			−0.106097
$562$	1571.69	−	2722.24i	0.117967	−	0.204325i
$563$	2081.20	+	3604.75i	0.155794	+	0.269844i	0.933348	−	0.358973i	$-0.116873\pi$
$563$	2081.20	+	3604.75i	0.155794	+	0.269844i	−0.777554	+	0.628817i	$0.783540\pi$
$564$	−1099.02	−	1903.55i	−0.0820512	−	0.142117i
$565$	−2886.61	+	4999.76i	−0.214939	+	0.372285i
$566$	−20793.4			−1.54419
$567$	1499.73	−	34.9628i	0.111081	−	0.00258960i
$568$	19614.1			1.44892
$569$	5348.05	−	9263.10i	0.394028	−	0.682477i	−0.598948	−	0.800788i	$-0.704415\pi$
$569$	5348.05	−	9263.10i	0.394028	−	0.682477i	0.992977	+	0.118311i	$0.0377479\pi$
$570$	638.236	+	1105.46i	0.0468996	+	0.0812324i
$571$	−6235.48	−	10800.2i	−0.456999	−	0.791546i	0.541801	−	0.840506i	$-0.317742\pi$
$571$	−6235.48	−	10800.2i	−0.456999	−	0.791546i	−0.998801	+	0.0489606i	$0.984409\pi$
$572$	−76.1136	+	131.833i	−0.00556376	+	0.00963671i
$573$	−11690.7			−0.852331
$574$	−4975.21	−	8171.38i	−0.361779	−	0.594193i
$575$	−2479.56			−0.179835
$576$	−2562.48	+	4438.35i	−0.185365	+	0.321061i
$577$	7851.02	+	13598.4i	0.566451	+	0.981122i	0.996913	+	0.0785131i	$0.0250173\pi$
$577$	7851.02	+	13598.4i	0.566451	+	0.981122i	−0.430462	+	0.902609i	$0.641649\pi$
$578$	−5701.18	−	9874.73i	−0.410273	−	0.710614i
$579$	−6913.93	+	11975.3i	−0.496257	+	0.859543i
$580$	−1933.29			−0.138406
$581$	−2173.40	+	3975.64i	−0.155194	+	0.283885i
$582$	−7099.74			−0.505659
$583$	−95.3189	+	165.097i	−0.00677136	+	0.0117283i
$584$	8008.31	+	13870.8i	0.567442	+	0.982838i
$585$	−72.0956	−	124.873i	−0.00509536	−	0.00882542i
$586$	−1929.58	+	3342.13i	−0.136024	+	0.235601i
$587$	22423.3			1.57668			0.788339	−	0.615241i	$-0.210941\pi$
$587$	22423.3			1.57668			0.788339	+	0.615241i	$0.210941\pi$
$588$	1873.87	−	87.4173i	0.131423	−	0.00613100i
$589$	−10038.1			−0.702230
$590$	251.076	−	434.876i	0.0175197	−	0.0303450i
$591$	4678.66	+	8103.68i	0.325642	+	0.564029i
$592$	477.145	+	826.439i	0.0331259	+	0.0573757i
$593$	−266.968	+	462.403i	−0.0184875	+	0.0320213i	−0.875121	−	0.483904i	$-0.839218\pi$
$593$	−266.968	+	462.403i	−0.0184875	+	0.0320213i	0.856634	+	0.515925i	$0.172552\pi$
$594$	−1748.73			−0.120793
$595$	800.985	−	1465.18i	0.0551885	−	0.100952i
$596$	897.255			0.0616661
$597$	−6223.40	+	10779.2i	−0.426645	+	0.738970i
$598$	−394.929	−	684.036i	−0.0270064	−	0.0467765i
$599$	2813.30	+	4872.78i	0.191900	+	0.332381i	0.945880	−	0.324517i	$-0.105202\pi$
$599$	2813.30	+	4872.78i	0.191900	+	0.332381i	−0.753980	+	0.656898i	$0.771868\pi$
$600$	915.513	−	1585.72i	0.0622928	−	0.107894i
$601$	8563.09			0.581191			0.290596	−	0.956846i	$-0.406147\pi$
$601$	8563.09			0.581191			0.290596	+	0.956846i	$0.406147\pi$
$602$	142.762	+	234.475i	0.00966537	+	0.0158746i
$603$	5287.16			0.357065
$604$	986.217	−	1708.18i	0.0664381	−	0.115074i
$605$	1629.72	+	2822.76i	0.109517	+	0.189689i
$606$	5373.82	+	9307.72i	0.360225	+	0.623928i
$607$	10366.6	−	17955.5i	0.693194	−	1.20065i	−0.277592	−	0.960699i	$-0.589536\pi$
$607$	10366.6	−	17955.5i	0.693194	−	1.20065i	0.970786	−	0.239948i	$-0.0771304\pi$
$608$	2765.01			0.184434
$609$	−11781.0	+	274.647i	−0.783892	+	0.0182746i
$610$	4454.79			0.295687
$611$	−643.892	+	1115.25i	−0.0426335	+	0.0738434i
$612$	−147.932	−	256.227i	−0.00977094	−	0.0169238i
$613$	−6225.28	−	10782.5i	−0.410174	−	0.710443i	0.584734	−	0.811225i	$-0.301199\pi$
$613$	−6225.28	−	10782.5i	−0.410174	−	0.710443i	−0.994909	+	0.100782i	$0.967865\pi$
$614$	−8508.67	+	14737.4i	−0.559254	+	0.968656i
$615$	3117.63			0.204415
$616$	−11779.7	+	274.616i	−0.770481	+	0.0179620i
$617$	6173.86			0.402837			0.201418	−	0.979505i	$-0.435445\pi$
$617$	6173.86			0.402837			0.201418	+	0.979505i	$0.435445\pi$
$618$	−4249.90	+	7361.04i	−0.276628	+	0.479133i
$619$	13335.8	+	23098.3i	0.865930	+	1.49984i	0.866120	+	0.499835i	$0.166606\pi$
$619$	13335.8	+	23098.3i	0.865930	+	1.49984i	−0.000189984		1.00000i	$0.500060\pi$
$620$	1336.15	+	2314.28i	0.0865503	+	0.149909i
$621$	−1338.96	+	2319.15i	−0.0865229	+	0.149862i
$622$	−5841.22			−0.376546
$623$	13590.7	+	22321.7i	0.874000	+	1.43547i
$624$	443.073			0.0284249
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−5084.83	−	8807.19i	−0.324650	−	0.562310i
$627$	1338.42	+	2318.22i	0.0852497	+	0.147657i
$628$	−2635.48	+	4564.79i	−0.167464	+	0.290056i
$629$	−373.343			−0.0236664
$630$	993.571	−	1817.47i	0.0628330	−	0.114936i
$631$	25175.3			1.58829			0.794147	−	0.607726i	$-0.207918\pi$
$631$	25175.3			1.58829			0.794147	+	0.607726i	$0.207918\pi$
$632$	15570.6	−	26969.0i	0.980006	−	1.69742i
$633$	−5753.61	−	9965.55i	−0.361273	−	0.625742i
$634$	−1234.83	−	2138.80i	−0.0773526	−	0.133979i
$635$	3633.30	−	6293.07i	0.227060	−	0.393280i
$636$	−40.0088			−0.00249442
$637$	−593.286	−	925.169i	−0.0369024	−	0.0575456i
$638$	13736.9			0.852430
$639$	−3615.32	+	6261.92i	−0.223818	+	0.387665i
$640$	1923.06	+	3330.84i	0.118774	+	0.205723i
$641$	3951.07	+	6843.45i	0.243460	+	0.421685i	0.961697	−	0.274113i	$-0.0883842\pi$
$641$	3951.07	+	6843.45i	0.243460	+	0.421685i	−0.718238	+	0.695798i	$0.755051\pi$
$642$	−2585.03	+	4477.40i	−0.158914	+	0.275247i
$643$	−18223.2			−1.11766			−0.558828	−	0.829284i	$-0.688749\pi$
$643$	−18223.2			−1.11766			−0.558828	+	0.829284i	$0.688749\pi$
$644$	−1606.31	+	2938.30i	−0.0982880	+	0.179791i
$645$	−89.4595			−0.00546119
$646$	767.264	−	1328.94i	0.0467301	−	0.0809388i
$647$	11989.7	+	20766.8i	0.728539	+	1.26187i	0.957500	+	0.288432i	$0.0931338\pi$
$647$	11989.7	+	20766.8i	0.728539	+	1.26187i	−0.228961	+	0.973436i	$0.573533\pi$
$648$	−988.754	−	1712.57i	−0.0599413	−	0.103821i
$649$	526.523	−	911.965i	0.0318457	−	0.0551583i
$650$	−199.092			−0.0120139
$651$	8470.95	+	13912.8i	0.509989	+	0.837615i
$652$	−4603.27			−0.276500
$653$	−5459.18	+	9455.57i	−0.327158	+	0.566654i	−0.981947	−	0.189158i	$-0.939424\pi$
$653$	−5459.18	+	9455.57i	−0.327158	+	0.566654i	0.654789	+	0.755812i	$0.272758\pi$
$654$	4250.39	+	7361.88i	0.254133	+	0.440172i
$655$	3848.94	+	6666.56i	0.229604	+	0.397686i
$656$	−4789.95	+	8296.44i	−0.285086	+	0.493783i
$657$	−5904.46			−0.350616
$658$	−18494.1	+	431.147i	−1.09571	+	0.0255439i
$659$	−910.217			−0.0538043			−0.0269021	−	0.999638i	$-0.508564\pi$
$659$	−910.217			−0.0538043			−0.0269021	+	0.999638i	$0.508564\pi$
$660$	356.309	−	617.146i	0.0210141	−	0.0363975i
$661$	5321.44	+	9217.00i	0.313132	+	0.542360i	0.979039	−	0.203675i	$-0.0652886\pi$
$661$	5321.44	+	9217.00i	0.313132	+	0.542360i	−0.665907	+	0.746035i	$0.731955\pi$
$662$	3802.76	+	6586.57i	0.223260	+	0.386698i
$663$	−86.6708	+	150.118i	−0.00507694	+	0.00879353i
$664$	5972.74			0.349077
$665$	−3169.80	+	73.8965i	−0.184841	+	0.00430915i
$666$	−463.108			−0.0269446
$667$	10518.1	−	18217.9i	0.610588	−	1.05757i
$668$	−2636.10	−	4565.86i	−0.152685	−	0.264459i
$669$	−1125.49	−	1949.41i	−0.0650436	−	0.112659i
$670$	3650.12	−	6322.20i	0.210473	−	0.364549i
$671$	9342.00			0.537472
$672$	−2333.33	−	3832.31i	−0.133944	−	0.219992i
$673$	12314.8			0.705351			0.352676	−	0.935746i	$-0.385272\pi$
$673$	12314.8			0.705351			0.352676	+	0.935746i	$0.385272\pi$
$674$	−3431.92	+	5944.25i	−0.196131	+	0.339709i
$675$	337.500	+	584.567i	0.0192450	+	0.0333333i
$676$	−1993.25	−	3452.41i	−0.113407	−	0.196427i
$677$	−4907.95	+	8500.81i	−0.278623	+	0.482589i	−0.971043	−	0.238906i	$-0.923211\pi$
$677$	−4907.95	+	8500.81i	−0.278623	+	0.482589i	0.692420	+	0.721495i	$0.256545\pi$
$678$	8609.08			0.487655
$679$	8459.27	−	15473.9i	0.478110	−	0.874571i
$680$	−2201.20			−0.124135
$681$	−943.259	+	1633.77i	−0.0530775	+	0.0919329i
$682$	−9493.97	−	16444.0i	−0.533054	−	0.923277i
$683$	−2177.36	−	3771.29i	−0.121983	−	0.211281i	0.798567	−	0.601906i	$-0.205592\pi$
$683$	−2177.36	−	3771.29i	−0.121983	−	0.211281i	−0.920550	+	0.390626i	$0.872259\pi$
$684$	−280.893	+	486.521i	−0.0157021	+	0.0271968i
$685$	14577.7			0.813117
$686$	6919.44	−	14191.0i	0.385110	−	0.789817i
$687$	7341.99			0.407735
$688$	137.446	−	238.064i	0.00761641	−	0.0131920i
$689$	11.7202	+	20.3000i	0.000648046	+	0.00112245i
$690$	1848.77	+	3202.17i	0.102002	+	0.176673i
$691$	−6744.58	+	11682.0i	−0.371311	+	0.643130i	−0.989768	−	0.142689i	$-0.954425\pi$
$691$	−6744.58	+	11682.0i	−0.371311	+	0.643130i	0.618456	+	0.785819i	$0.287758\pi$
$692$	5295.82			0.290920
$693$	2083.59	−	3811.35i	0.114212	−	0.208920i
$694$	−31141.6			−1.70334
$695$	5846.90	−	10127.1i	0.319116	−	0.552725i
$696$	7767.06	+	13452.9i	0.423002	+	0.732661i
$697$	−1873.95	−	3245.78i	−0.101838	−	0.176388i
$698$	4652.72	−	8058.75i	0.252304	−	0.437003i
$699$	−9483.49			−0.513160
$700$	438.961	+	720.959i	0.0237017	+	0.0389281i
$701$	−17175.4			−0.925399			−0.462700	−	0.886515i	$-0.653119\pi$
$701$	−17175.4			−0.925399			−0.462700	+	0.886515i	$0.653119\pi$
$702$	−107.510	+	186.212i	−0.00578019	+	0.0100116i
$703$	354.450	+	613.925i	0.0190161	+	0.0329369i
$704$	7419.74	+	12851.4i	0.397219	+	0.688003i
$705$	3014.24	−	5220.82i	0.161025	−	0.278904i
$706$	5577.21			0.297310
$707$	−26689.0	+	622.194i	−1.41972	+	0.0330976i
$708$	221.001			0.0117313
$709$	−906.735	+	1570.51i	−0.0480298	+	0.0831901i	−0.889041	−	0.457828i	$-0.848628\pi$
$709$	−906.735	+	1570.51i	−0.0480298	+	0.0831901i	0.841011	+	0.541018i	$0.181961\pi$
$710$	4991.85	+	8646.14i	0.263860	+	0.457020i
$711$	5740.02	+	9942.01i	0.302767	+	0.524409i
$712$	17224.9	−	29834.4i	0.906642	−	1.57035i
$713$	−29077.4			−1.52729
$714$	−2489.39	+	58.0344i	−0.130481	+	0.00304185i
$715$	−417.510			−0.0218377
$716$	21.0598	−	36.4766i	0.00109922	−	0.00190391i
$717$	−9027.46	−	15636.0i	−0.470204	−	0.814418i
$718$	−1169.58	−	2025.77i	−0.0607914	−	0.105294i
$719$	−11350.9	+	19660.4i	−0.588760	+	1.01976i	0.405636	+	0.914035i	$0.367050\pi$
$719$	−11350.9	+	19660.4i	−0.588760	+	1.01976i	−0.994395	+	0.105727i	$0.966283\pi$
$720$	−2074.15			−0.107360
$721$	−10979.7	−	18033.3i	−0.567136	−	0.931475i
$722$	14133.3			0.728512
$723$	8577.65	−	14856.9i	0.441226	−	0.764225i
$724$	−2756.44	−	4774.29i	−0.141495	−	0.245076i
$725$	−2651.20	−	4592.01i	−0.135811	−	0.235232i
$726$	2430.26	−	4209.33i	0.124236	−	0.215183i
$727$	29667.1			1.51347			0.756734	−	0.653723i	$-0.226794\pi$
$727$	29667.1			1.51347			0.756734	+	0.653723i	$0.226794\pi$
$728$	−694.958	+	1271.23i	−0.0353803	+	0.0647185i
$729$	729.000			0.0370370
$730$	−4076.29	+	7060.34i	−0.206672	+	0.357966i
$731$	53.7725	+	93.1368i	0.00272072	+	0.00471243i
$732$	980.294	+	1697.92i	0.0494983	+	0.0857335i
$733$	−5287.33	+	9157.92i	−0.266428	+	0.461467i	−0.967937	−	0.251194i	$-0.919177\pi$
$733$	−5287.33	+	9157.92i	−0.266428	+	0.461467i	0.701509	+	0.712661i	$0.252510\pi$
$734$	−1203.46			−0.0605187
$735$	2777.34	+	4330.98i	0.139379	+	0.217348i
$736$	8009.39			0.401128
$737$	7654.57	−	13258.1i	0.382577	−	0.662643i
$738$	−2324.52	−	4026.19i	−0.115944	−	0.200821i
$739$	−15764.8	−	27305.4i	−0.784730	−	1.35919i	−0.929160	−	0.369678i	$-0.879468\pi$
$739$	−15764.8	−	27305.4i	−0.784730	−	1.35919i	0.144429	−	0.989515i	$-0.453865\pi$
$740$	94.3600	−	163.436i	0.00468749	−	0.00811897i
$741$	329.139			0.0163175
$742$	−161.520	+	295.456i	−0.00799133	+	0.0146179i
$743$	8886.27			0.438769			0.219385	−	0.975638i	$-0.429595\pi$
$743$	8886.27			0.438769			0.219385	+	0.975638i	$0.429595\pi$
$744$	10736.1	−	18595.4i	0.529036	−	0.916317i
$745$	1230.44	+	2131.18i	0.0605098	+	0.104806i
$746$	−12951.5	−	22432.6i	−0.635639	−	1.10096i
$747$	−1100.91	+	1906.84i	−0.0539228	+	0.0933970i
$748$	−856.685			−0.0418764
$749$	−6678.47	−	10968.8i	−0.325802	−	0.535104i
$750$	932.006			0.0453761
$751$	10241.2	−	17738.2i	0.497610	−	0.861886i	−0.502386	−	0.864644i	$-0.667544\pi$
$751$	10241.2	−	17738.2i	0.497610	−	0.861886i	0.999996	+	0.00275714i	$0.000877627\pi$
$752$	9262.21	+	16042.6i	0.449146	+	0.777944i
$753$	1854.09	+	3211.38i	0.0897301	+	0.155417i
$754$	844.531	−	1462.77i	0.0407905	−	0.0706511i
$755$	5409.75			0.260769
$756$	911.357	−	21.2462i	0.0438436	−	0.00102211i
$757$	−9959.68			−0.478191			−0.239096	−	0.970996i	$-0.576851\pi$
$757$	−9959.68			−0.478191			−0.239096	+	0.970996i	$0.576851\pi$
$758$	−7938.27	+	13749.5i	−0.380384	+	0.658844i
$759$	3877.01	+	6715.17i	0.185410	+	0.321140i
$760$	2089.80	+	3619.65i	0.0997437	+	0.172761i
$761$	2278.35	−	3946.21i	0.108528	−	0.187976i	−0.806646	−	0.591035i	$-0.798720\pi$
$761$	2278.35	−	3946.21i	0.108528	−	0.187976i	0.915174	+	0.403058i	$0.132053\pi$
$762$	−10836.0			−0.515155
$763$	−21109.5	+	492.120i	−1.00159	+	0.0233499i
$764$	−7104.19			−0.336414
$765$	405.731	−	702.746i	0.0191755	−	0.0332129i
$766$	−6191.99	−	10724.8i	−0.292070	−	0.505880i
$767$	−64.7401	−	112.133i	−0.00304776	−	0.00527887i
$768$	−3965.59	+	6868.61i	−0.186323	+	0.322721i
$769$	−23304.9			−1.09284			−0.546421	−	0.837511i	$-0.684010\pi$
$769$	−23304.9			−1.09284			−0.546421	+	0.837511i	$0.684010\pi$
$770$	−3119.02	−	5122.74i	−0.145976	−	0.239754i
$771$	3296.80			0.153997
$772$	−4201.45	+	7277.12i	−0.195872	+	0.339261i
$773$	−19795.7	−	34287.2i	−0.921090	−	1.59537i	−0.797732	−	0.603013i	$-0.793967\pi$
$773$	−19795.7	−	34287.2i	−0.921090	−	1.59537i	−0.123359	−	0.992362i	$-0.539367\pi$
$774$	66.7014	+	115.530i	0.00309759	+	0.00536518i
$775$	−3664.63	+	6347.33i	−0.169855	+	0.294197i
$776$	−23247.0			−1.07541
$777$	551.788	−	1009.35i	0.0254766	−	0.0466024i
$778$	16772.8			0.772921
$779$	−3558.24	+	6163.06i	−0.163655	+	0.283459i
$780$	−43.8110	−	75.8829i	−0.00201114	−	0.00348339i
$781$	10468.3	+	18131.6i	0.479621	+	0.830728i
$782$	2222.53	−	3849.53i	0.101634	−	0.176035i
$783$	−5726.58			−0.261368
$784$	−15792.5	+	736.730i	−0.719409	+	0.0335609i
$785$	−14456.5			−0.657294
$786$	5739.58	−	9941.24i	0.260463	−	0.451135i
$787$	−11195.6	−	19391.3i	−0.507089	−	0.878304i	−0.999966	−	0.00820496i	$-0.997388\pi$
$787$	−11195.6	−	19391.3i	−0.507089	−	0.878304i	0.492877	−	0.870099i	$-0.335945\pi$
$788$	2843.13	+	4924.44i	0.128531	+	0.222622i
$789$	−10085.2	+	17468.1i	−0.455061	+	0.788189i
$790$	15851.1			0.713868
$791$	−10257.6	+	18763.5i	−0.461086	+	0.843431i
$792$	−5725.93			−0.256897
$793$	574.336	−	994.778i	0.0257191	−	0.0445468i
$794$	4948.69	+	8571.38i	0.221187	+	0.383107i
$795$	−54.8656	−	95.0299i	−0.00244765	−	0.00423945i
$796$	−3781.83	+	6550.32i	−0.168396	+	0.291671i
$797$	−16409.1			−0.729285			−0.364642	−	0.931148i	$-0.618809\pi$
$797$	−16409.1			−0.729285			−0.364642	+	0.931148i	$0.618809\pi$
$798$	2458.85	+	4038.46i	0.109076	+	0.179148i
$799$	−7247.23			−0.320887
$800$	1009.43	−	1748.38i	0.0446108	−	0.0772682i
$801$	6349.88	+	10998.3i	0.280102	+	0.485151i
$802$	8162.22	+	14137.4i	0.359374	+	0.622454i
$803$	−8548.26	+	14806.0i	−0.375668	+	0.650677i
$804$	3212.90			0.140933
$805$	−9181.93	+	214.055i	−0.402013	+	0.00937200i
$806$	−2334.71			−0.102031
$807$	7710.20	−	13354.5i	0.336322	−	0.582527i
$808$	17595.7	+	30476.7i	0.766108	+	1.32694i
$809$	−21773.8	−	37713.3i	−0.946260	−	1.63897i	−0.753208	−	0.657782i	$-0.771495\pi$
$809$	−21773.8	−	37713.3i	−0.946260	−	1.63897i	−0.193052	−	0.981188i	$-0.561839\pi$
$810$	503.283	−	871.712i	0.0218316	−	0.0378134i
$811$	23780.0			1.02963			0.514814	−	0.857302i	$-0.327861\pi$
$811$	23780.0			1.02963			0.514814	+	0.857302i	$0.327861\pi$
$812$	−7159.07	+	166.897i	−0.309402	+	0.00721298i
$813$	−8745.02			−0.377246
$814$	−670.471	+	1161.29i	−0.0288698	+	0.0500039i
$815$	−6312.64	−	10933.8i	−0.271315	−	0.469932i
$816$	1246.74	+	2159.41i	0.0534859	+	0.0926402i
$817$	102.103	−	176.847i	0.00437225	−	0.00757295i
$818$	12319.3			0.526571
$819$	−277.753	−	456.187i	−0.0118504	−	0.0194633i
$820$	1894.52			0.0806823
$821$	−15615.7	+	27047.2i	−0.663814	+	1.14976i	0.315792	+	0.948829i	$0.397730\pi$
$821$	−15615.7	+	27047.2i	−0.663814	+	1.14976i	−0.979605	+	0.200931i	$0.935603\pi$
$822$	−10869.2	−	18826.0i	−0.461201	−	0.798823i
$823$	−1667.96	−	2889.00i	−0.0706458	−	0.122362i	0.828539	−	0.559932i	$-0.189173\pi$
$823$	−1667.96	−	2889.00i	−0.0706458	−	0.122362i	−0.899185	+	0.437570i	$0.855839\pi$
$824$	−13915.6	+	24102.6i	−0.588318	+	1.01900i
$825$	1954.48			0.0824804
$826$	892.203	−	1632.04i	0.0375832	−	0.0687481i
$827$	32281.3			1.35735			0.678677	−	0.734437i	$-0.262554\pi$
$827$	32281.3			1.35735			0.678677	+	0.734437i	$0.262554\pi$
$828$	−813.660	+	1409.30i	−0.0341505	+	0.0591505i
$829$	14756.4	+	25558.9i	0.618230	+	1.07081i	0.989809	+	0.142404i	$0.0454831\pi$
$829$	14756.4	+	25558.9i	0.618230	+	1.07081i	−0.371579	+	0.928401i	$0.621184\pi$
$830$	1520.09	+	2632.87i	0.0635698	+	0.110106i
$831$	2678.90	−	4639.99i	0.111829	−	0.193694i
$832$	1824.63			0.0760308
$833$	2839.60	−	5494.78i	0.118111	−	0.228551i
$834$	−17437.9			−0.724011
$835$	7229.96	−	12522.7i	0.299644	−	0.518999i
$836$	813.333	+	1408.73i	0.0336480	+	0.0582800i
$837$	3957.80	+	6855.11i	0.163443	+	0.283091i
$838$	7180.91	−	12437.7i	0.296015	−	0.512713i
$839$	17025.0			0.700558			0.350279	−	0.936645i	$-0.386087\pi$
$839$	17025.0			0.700558			0.350279	+	0.936645i	$0.386087\pi$
$840$	3253.30	−	5951.01i	0.133630	−	0.244440i
$841$	20595.6			0.844462
$842$	9274.37	−	16063.7i	0.379591	−	0.657471i
$843$	1897.14	+	3285.95i	0.0775102	+	0.134252i
$844$	−3496.35	−	6055.86i	−0.142594	−	0.246980i
$845$	5466.83	−	9468.83i	0.222562	−	0.385488i
$846$	−8989.73			−0.365335
$847$	6278.62	+	10312.1i	0.254706	+	0.418334i
$848$	337.184			0.0136544
$849$	12549.6	−	21736.5i	0.507304	−	0.878677i
$850$	−560.212	−	970.316i	−0.0226060	−	0.0391548i
$851$	1026.73	+	1778.35i	0.0413583	+	0.0716347i
$852$	−2196.96	+	3805.24i	−0.0883409	+	0.153011i
$853$	−19970.0			−0.801593			−0.400796	−	0.916167i	$-0.631267\pi$
$853$	−19970.0			−0.801593			−0.400796	+	0.916167i	$0.631267\pi$
$854$	16496.3	−	384.573i	0.660997	−	0.0154096i
$855$	−1540.80			−0.0616305
$856$	−8464.27	+	14660.5i	−0.337971	+	0.585382i
$857$	−2344.96	−	4061.60i	−0.0934685	−	0.161892i	0.815500	−	0.578757i	$-0.196462\pi$
$857$	−2344.96	−	4061.60i	−0.0934685	−	0.161892i	−0.908968	+	0.416865i	$0.863129\pi$
$858$	311.297	+	539.183i	0.0123864	+	0.0214538i
$859$	−17201.2	+	29793.4i	−0.683235	+	1.18340i	0.290753	+	0.956798i	$0.406094\pi$
$859$	−17201.2	+	29793.4i	−0.683235	+	1.18340i	−0.973988	+	0.226600i	$0.927239\pi$
$860$	−54.3627			−0.00215553
$861$	11544.7	−	269.139i	0.456961	−	0.0106530i
$862$	−7559.39			−0.298694
$863$	−1658.93	+	2873.35i	−0.0654351	+	0.113337i	−0.896887	−	0.442260i	$-0.854177\pi$
$863$	−1658.93	+	2873.35i	−0.0654351	+	0.113337i	0.831452	+	0.555597i	$0.187510\pi$
$864$	−1090.18	−	1888.25i	−0.0429268	−	0.0743513i
$865$	7262.36	+	12578.8i	0.285465	+	0.494441i
$866$	5029.71	−	8711.71i	0.197363	−	0.341843i
$867$	13763.5			0.539138
$868$	5147.62	+	8454.55i	0.201292	+	0.330606i
$869$	33240.8			1.29760
$870$	−3953.49	+	6847.64i	−0.154064	+	0.266847i
$871$	−941.188	−	1630.19i	−0.0366142	−	0.0634176i
$872$	13917.2	+	24105.4i	0.540478	+	0.936136i
$873$	4284.96	−	7421.76i	0.166121	−	0.287730i
$874$	−8440.24			−0.326654
$875$	−1110.48	+	2031.31i	−0.0429039	+	0.0784809i
$876$	−3588.02			−0.138388
$877$	−13434.1	+	23268.6i	−0.517261	+	0.895922i	0.482538	+	0.875875i	$0.339715\pi$
$877$	−13434.1	+	23268.6i	−0.517261	+	0.895922i	−0.999799	+	0.0200472i	$0.993618\pi$
$878$	−3396.12	−	5882.25i	−0.130539	−	0.226101i
$879$	−2329.15	−	4034.20i	−0.0893744	−	0.154801i
$880$	−3002.88	+	5201.14i	−0.115031	+	0.199239i
$881$	−12933.5			−0.494599			−0.247300	−	0.968939i	$-0.579543\pi$
$881$	−12933.5			−0.494599			−0.247300	+	0.968939i	$0.579543\pi$
$882$	3522.34	−	6815.93i	0.134471	−	0.260209i
$883$	−17537.5			−0.668386			−0.334193	−	0.942505i	$-0.608464\pi$
$883$	−17537.5			−0.668386			−0.334193	+	0.942505i	$0.608464\pi$
$884$	−52.6680	+	91.2237i	−0.00200387	+	0.00347080i
$885$	303.067	+	524.927i	0.0115113	+	0.0199381i
$886$	7951.93	+	13773.1i	0.301524	+	0.522255i
$887$	17647.2	−	30565.9i	0.668022	−	1.15705i	−0.310435	−	0.950595i	$-0.600475\pi$
$887$	17647.2	−	30565.9i	0.668022	−	1.15705i	0.978456	−	0.206453i	$-0.0661921\pi$
$888$	−1516.38			−0.0573043
$889$	12911.0	−	23617.2i	0.487089	−	0.890995i
$890$	17535.2			0.660428
$891$	1055.42	−	1828.04i	0.0396834	−	0.0687337i
$892$	−683.940	−	1184.62i	−0.0256726	−	0.0444663i
$893$	6880.49	+	11917.3i	0.257835	+	0.446583i
$894$	1834.84	−	3178.04i	0.0686425	−	0.118892i
$895$	115.520			0.00431444
$896$	7408.73	+	12168.2i	0.276237	+	0.453697i
$897$	953.416			0.0354890
$898$	−20491.3	+	35492.0i	−0.761474	+	1.31891i
$899$	−31090.1	−	53849.6i	−1.15341	−	1.99776i
$900$	205.092	+	355.229i	0.00759599	+	0.0131566i
$901$	−65.9575	+	114.242i	−0.00243880	+	0.00422413i
$902$	−13461.4			−0.496914
$903$	−331.273	+	7.72286i	−0.0122083	+	0.000284608i
$904$	28189.1			1.03712
$905$	7560.02	−	13094.3i	0.277683	−	0.480962i
$906$	−4033.53	−	6986.29i	−0.147909	−	0.256185i
$907$	−15307.9	−	26514.0i	−0.560408	−	0.970655i	−0.997461	−	0.0712189i	$-0.977311\pi$
$907$	−15307.9	−	26514.0i	−0.560408	−	0.970655i	0.437053	−	0.899436i	$-0.356022\pi$
$908$	−573.199	+	992.810i	−0.0209496	+	0.0362859i
$909$	−12973.2			−0.473370
$910$	−737.247	+	17.1872i	−0.0268566	+	0.000626099i
$911$	28971.0			1.05362			0.526812	−	0.849982i	$-0.323387\pi$
$911$	28971.0			1.05362			0.526812	+	0.849982i	$0.323387\pi$
$912$	2367.29	−	4100.27i	0.0859526	−	0.148874i
$913$	3187.73	+	5521.30i	0.115551	+	0.200141i
$914$	17864.6	+	30942.4i	0.646509	+	1.11979i
$915$	−2688.63	+	4656.84i	−0.0971402	+	0.168252i
$916$	4461.57			0.160933
$917$	14828.3	+	24354.3i	0.533996	+	0.877045i
$918$	−1210.06			−0.0435053
$919$	−13119.7	+	22724.0i	−0.470924	+	0.815664i	−0.999447	−	0.0332552i	$-0.989413\pi$
$919$	−13119.7	+	22724.0i	−0.470924	+	0.815664i	0.528523	+	0.848919i	$0.322746\pi$
$920$	6053.52	+	10485.0i	0.216933	+	0.375740i
$921$	−10270.6	−	17789.2i	−0.367456	−	0.636453i
$922$	1243.16	−	2153.22i	0.0444049	−	0.0769116i
$923$	2574.31			0.0918032
$924$	1266.15	−	2316.08i	0.0450794	−	0.0824604i
$925$	517.598			0.0183984
$926$	−778.070	+	1347.66i	−0.0276123	+	0.0478258i
$927$	−5129.94	−	8885.31i	−0.181758	−	0.314813i
$928$	8563.80	+	14832.9i	0.302932	+	0.524693i
$929$	8971.61	−	15539.3i	0.316845	−	0.548792i	−0.662983	−	0.748635i	$-0.730710\pi$
$929$	8971.61	−	15539.3i	0.316845	−	0.548792i	0.979828	+	0.199843i	$0.0640431\pi$
$930$	10929.5			0.385367
$931$	−11731.5	+	547.284i	−0.412981	+	0.0192659i
$932$	−5762.92			−0.202544
$933$	3525.39	−	6106.15i	0.123704	−	0.214262i
$934$	1142.07	+	1978.12i	0.0400103	+	0.0692998i
$935$	−1174.80	−	2034.82i	−0.0410911	−	0.0711719i
$936$	−352.024	+	609.723i	−0.0122930	+	0.0212921i
$937$	43418.1			1.51378			0.756888	−	0.653545i	$-0.226719\pi$
$937$	43418.1			1.51378			0.756888	+	0.653545i	$0.226719\pi$
$938$	12970.8	−	23726.5i	0.451505	−	0.825904i
$939$	12275.5			0.426621
$940$	1831.69	−	3172.58i	0.0635566	−	0.110083i
$941$	−15447.5	−	26755.8i	−0.535146	−	0.926901i	−0.999156	−	0.0410706i	$-0.986923\pi$
$941$	−15447.5	−	26755.8i	−0.535146	−	0.926901i	0.464010	−	0.885830i	$-0.346410\pi$
$942$	10778.9	+	18669.5i	0.372818	+	0.645739i
$943$	−10307.1	+	17852.5i	−0.355935	+	0.616498i
$944$	−1862.54			−0.0642166
$945$	1300.24	+	2135.54i	0.0447586	+	0.0735124i
$946$	386.272			0.0132757
$947$	−3876.31	+	6713.97i	−0.133013	+	0.230385i	−0.924837	−	0.380365i	$-0.875798\pi$
$947$	−3876.31	+	6713.97i	−0.133013	+	0.230385i	0.791824	+	0.610750i	$0.209132\pi$
$948$	3488.09	+	6041.55i	0.119502	+	0.206984i
$949$	1051.07	+	1820.52i	0.0359529	+	0.0622723i
$950$	−1063.73	+	1842.43i	−0.0363282	+	0.0629224i
$951$	2981.07			0.101649
$952$	−8151.13	+	190.025i	−0.277499	+	0.00646926i
$953$	21377.5			0.726638			0.363319	−	0.931665i	$-0.381644\pi$
$953$	21377.5			0.726638			0.363319	+	0.931665i	$0.381644\pi$
$954$	−81.8161	+	141.710i	−0.00277662	+	0.00480924i
$955$	−9742.24	−	16874.1i	−0.330106	−	0.571761i
$956$	−5485.80	−	9501.68i	−0.185589	−	0.321450i
$957$	−8290.74	+	14360.0i	−0.280044	+	0.485050i
$958$	38929.7			1.31290
$959$	53981.9	−	1258.46i	1.81769	−	0.0423753i
$960$	−8541.60			−0.287166
$961$	−28079.0	+	48634.2i	−0.942532	+	1.63251i
$962$	82.4396	+	142.790i	0.00276295	+	0.00478557i
$963$	−3120.32	−	5404.55i	−0.104414	−	0.180851i
$964$	5212.46	−	9028.24i	0.174151	−	0.301639i
$965$	−23046.4			−0.768798
$966$	7122.53	+	11698.2i	0.237229	+	0.389630i
$967$	−47707.3			−1.58652			−0.793259	−	0.608885i	$-0.791617\pi$
$967$	−47707.3			−1.58652			−0.793259	+	0.608885i	$0.791617\pi$
$968$	7957.51	−	13782.8i	0.264219	−	0.457641i
$969$	926.145	+	1604.13i	0.0307039	+	0.0531807i
$970$	−5916.45	−	10247.6i	−0.195841	−	0.339207i
$971$	21717.3	−	37615.4i	0.717756	−	1.24319i	−0.244131	−	0.969742i	$-0.578503\pi$
$971$	21717.3	−	37615.4i	0.717756	−	1.24319i	0.961887	−	0.273447i	$-0.0881640\pi$
$972$	442.998			0.0146185
$973$	20777.1	−	38006.0i	0.684566	−	1.25222i
$974$	−35889.6			−1.18067
$975$	120.159	−	208.122i	0.00394685	−	0.00683614i
$976$	−8261.66	−	14309.6i	−0.270952	−	0.469303i
$977$	16743.8	+	29001.1i	0.548292	+	0.949669i	0.998392	+	0.0566908i	$0.0180549\pi$
$977$	16743.8	+	29001.1i	0.548292	+	0.949669i	−0.450100	+	0.892978i	$0.648612\pi$
$978$	−9413.46	+	16304.6i	−0.307781	+	0.533092i
$979$	36772.5			1.20046
$980$	1687.73	+	2631.85i	0.0550129	+	0.0857870i
$981$	−10261.1			−0.333955
$982$	−24009.5	+	41585.6i	−0.780217	+	1.35138i
$983$	−7883.76	−	13655.1i	−0.255802	−	0.443061i	0.709311	−	0.704895i	$-0.249006\pi$
$983$	−7883.76	−	13655.1i	−0.255802	−	0.443061i	−0.965113	+	0.261834i	$0.915673\pi$
$984$	−7611.29	−	13183.1i	−0.246584	−	0.427096i
$985$	−7797.77	+	13506.1i	−0.252241	+	0.436895i
$986$	9505.49			0.307015
$987$	10711.2	−	19593.1i	0.345431	−	0.631871i
$988$	200.011			0.00644049
$989$	295.760	−	512.272i	0.00950924	−	0.0164705i
$990$	−1457.27	−	2524.07i	−0.0467829	−	0.0810304i
$991$	1792.30	+	3104.35i	0.0574512	+	0.0995084i	0.893321	−	0.449420i	$-0.148369\pi$
$991$	1792.30	+	3104.35i	0.0574512	+	0.0995084i	−0.835869	+	0.548928i	$0.815036\pi$
$992$	11837.4	−	20502.9i	0.378868	−	0.656218i
$993$	−9180.42			−0.293386
$994$	19231.5	+	31586.1i	0.613667	+	1.00790i
$995$	−20744.7			−0.660955
$996$	−669.002	+	1158.75i	−0.0212833	+	0.0368637i
$997$	18006.7	+	31188.6i	0.571995	+	0.990724i	0.996361	+	0.0852334i	$0.0271636\pi$
$997$	18006.7	+	31188.6i	0.571995	+	0.990724i	−0.424366	+	0.905491i	$0.639503\pi$
$998$	−5633.28	−	9757.13i	−0.178676	−	0.309475i
$999$	279.503	−	484.113i	0.00885193	−	0.0153320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.c.16.3	✓	6
3.2	odd	2		315.4.j.e.226.1		6
7.2	even	3		735.4.a.r.1.1		3
7.4	even	3	inner	105.4.i.c.46.3	yes	6
7.5	odd	6		735.4.a.s.1.1		3
21.2	odd	6		2205.4.a.bi.1.3		3
21.5	even	6		2205.4.a.bj.1.3		3
21.11	odd	6		315.4.j.e.46.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.c.16.3	✓	6	1.1	even	1	trivial
105.4.i.c.46.3	yes	6	7.4	even	3	inner
315.4.j.e.46.1		6	21.11	odd	6
315.4.j.e.226.1		6	3.2	odd	2
735.4.a.r.1.1		3	7.2	even	3
735.4.a.s.1.1		3	7.5	odd	6
2205.4.a.bi.1.3		3	21.2	odd	6
2205.4.a.bj.1.3		3	21.5	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24267 - 2.15238i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.911519 + 1.57880i) q^{4} +(-2.50000 + 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 + 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.24267 - 2.15238i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.911519 + 1.57880i) q^{4} +(-2.50000 + 4.33013i) q^{5} +7.45605 q^{6} +(-8.88380 + 16.2505i) q^{7} +24.4137 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.21337 + 10.7619i) q^{10} +(13.0299 + 22.5684i) q^{11} +(-2.73456 + 4.73639i) q^{12} +3.20425 q^{13} +(23.9375 + 39.3153i) q^{14} -15.0000 q^{15} +(23.0461 - 39.9170i) q^{16} +(9.01624 + 15.6166i) q^{17} +(11.1841 + 19.3714i) q^{18} +(17.1199 - 29.6526i) q^{19} -9.11519 q^{20} +(-55.5457 + 1.29492i) q^{21} +64.7676 q^{22} +(49.5912 - 85.8945i) q^{23} +(36.6205 + 63.4286i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(3.98184 - 6.89675i) q^{26} -27.0000 q^{27} +(-33.7540 + 0.786896i) q^{28} +212.096 q^{29} +(-18.6401 + 32.2856i) q^{30} +(-146.585 - 253.893i) q^{31} +(40.3771 + 69.9352i) q^{32} +(-39.0896 + 67.7052i) q^{33} +44.8170 q^{34} +(-48.1571 - 79.0942i) q^{35} -16.4073 q^{36} +(-10.3520 + 17.9301i) q^{37} +(-42.5490 - 73.6971i) q^{38} +(4.80637 + 8.32488i) q^{39} +(-61.0342 + 105.714i) q^{40} -207.842 q^{41} +(-66.2381 + 121.164i) q^{42} +5.96397 q^{43} +(-23.7540 + 41.1431i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(-123.252 - 213.478i) q^{46} +(-200.949 + 348.055i) q^{47} +138.277 q^{48} +(-185.156 - 288.732i) q^{49} -62.1337 q^{50} +(-27.0487 + 46.8497i) q^{51} +(2.92073 + 5.05886i) q^{52} +(3.65770 + 6.33533i) q^{53} +(-33.5522 + 58.1141i) q^{54} -130.299 q^{55} +(-216.886 + 396.734i) q^{56} +102.720 q^{57} +(263.566 - 456.510i) q^{58} +(-20.2045 - 34.9952i) q^{59} +(-13.6728 - 23.6820i) q^{60} +(179.242 - 310.456i) q^{61} -728.631 q^{62} +(-86.6828 - 142.370i) q^{63} +569.440 q^{64} +(-8.01062 + 13.8748i) q^{65} +(97.1514 + 168.271i) q^{66} +(-293.731 - 508.757i) q^{67} +(-16.4369 + 28.4696i) q^{68} +297.547 q^{69} +(-230.084 + 5.36388i) q^{70} +803.405 q^{71} +(-109.862 + 190.286i) q^{72} +(328.025 + 568.157i) q^{73} +(25.7282 + 44.5626i) q^{74} +(37.5000 - 64.9519i) q^{75} +62.4206 q^{76} +(-482.502 + 11.2484i) q^{77} +23.8910 q^{78} +(637.780 - 1104.67i) q^{79} +(115.231 + 199.585i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-258.280 + 447.354i) q^{82} +244.647 q^{83} +(-52.6754 - 86.5150i) q^{84} -90.1624 q^{85} +(7.41127 - 12.8367i) q^{86} +(318.144 + 551.041i) q^{87} +(318.107 + 550.978i) q^{88} +(705.542 - 1222.03i) q^{89} -111.841 q^{90} +(-28.4659 + 52.0706i) q^{91} +180.813 q^{92} +(439.756 - 761.679i) q^{93} +(499.429 + 865.037i) q^{94} +(85.5997 + 148.263i) q^{95} +(-121.131 + 209.805i) q^{96} -952.212 q^{97} +(-851.549 + 39.7254i) q^{98} -234.538 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

Introduction

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